diff --git a/-EgKluVR2Ug.txt b/-EgKluVR2Ug.txt
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+++ b/-EgKluVR2Ug.txt
@@ -0,0 +1,16621 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a creative commons license your support
+
+ align:start position:0%
+a creative commons license your support
+ 
+
+ align:start position:0%
+a creative commons license your support
+will help mit opencourseware continue to
+
+ align:start position:0%
+will help mit opencourseware continue to
+ 
+
+ align:start position:0%
+will help mit opencourseware continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of mit courses
+
+ align:start position:0%
+materials from hundreds of mit courses
+ 
+
+ align:start position:0%
+materials from hundreds of mit courses
+visit mit opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good morning everyone
+
+ align:start position:0%
+good morning everyone
+ 
+
+ align:start position:0%
+good morning everyone
+good evening in singapore
+
+ align:start position:0%
+good evening in singapore
+ 
+
+ align:start position:0%
+good evening in singapore
+where is everyone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think they're on the way we'll be here
+
+ align:start position:0%
+i think they're on the way we'll be here
+ 
+
+ align:start position:0%
+i think they're on the way we'll be here
+in a minute okay
+
+ align:start position:0%
+in a minute okay
+ 
+
+ align:start position:0%
+in a minute okay
+i'm gonna
+
+ align:start position:0%
+i'm gonna
+ 
+
+ align:start position:0%
+i'm gonna
+go ahead and
+
+ align:start position:0%
+go ahead and
+ 
+
+ align:start position:0%
+go ahead and
+uh start what i wanted to do is uh i
+
+ align:start position:0%
+uh start what i wanted to do is uh i
+ 
+
+ align:start position:0%
+uh start what i wanted to do is uh i
+sent a message around about these team
+
+ align:start position:0%
+sent a message around about these team
+ 
+
+ align:start position:0%
+sent a message around about these team
+guidelines so
+
+ align:start position:0%
+guidelines so
+ 
+
+ align:start position:0%
+guidelines so
+our team project guidelines so i'm not
+
+ align:start position:0%
+our team project guidelines so i'm not
+ 
+
+ align:start position:0%
+our team project guidelines so i'm not
+going to go in great detail through
+
+ align:start position:0%
+going to go in great detail through
+ 
+
+ align:start position:0%
+going to go in great detail through
+these slides hopefully everybody is well
+
+ align:start position:0%
+these slides hopefully everybody is well
+ 
+
+ align:start position:0%
+these slides hopefully everybody is well
+on the way towards identifying a team
+
+ align:start position:0%
+on the way towards identifying a team
+ 
+
+ align:start position:0%
+on the way towards identifying a team
+but i wanted to go quickly through this
+
+ align:start position:0%
+but i wanted to go quickly through this
+ 
+
+ align:start position:0%
+but i wanted to go quickly through this
+and then answer any questions you may
+
+ align:start position:0%
+and then answer any questions you may
+ 
+
+ align:start position:0%
+and then answer any questions you may
+have on the on the team projects
+
+ align:start position:0%
+have on the on the team projects
+ 
+
+ align:start position:0%
+have on the on the team projects
+a quick reminder that the team projects
+
+ align:start position:0%
+a quick reminder that the team projects
+ 
+
+ align:start position:0%
+a quick reminder that the team projects
+are about 20
+
+ align:start position:0%
+are about 20
+ 
+
+ align:start position:0%
+are about 20
+uh of the grade so they are an important
+
+ align:start position:0%
+uh of the grade so they are an important
+ 
+
+ align:start position:0%
+uh of the grade so they are an important
+part of this
+
+ align:start position:0%
+part of this
+ 
+
+ align:start position:0%
+part of this
+and the basic expectation is this is
+
+ align:start position:0%
+and the basic expectation is this is
+ 
+
+ align:start position:0%
+and the basic expectation is this is
+where you get a chance to dive deep into
+
+ align:start position:0%
+where you get a chance to dive deep into
+ 
+
+ align:start position:0%
+where you get a chance to dive deep into
+the analysis
+
+ align:start position:0%
+the analysis
+ 
+
+ align:start position:0%
+the analysis
+and exercising and some of the kinds of
+
+ align:start position:0%
+and exercising and some of the kinds of
+ 
+
+ align:start position:0%
+and exercising and some of the kinds of
+tools and approaches we've been talking
+
+ align:start position:0%
+tools and approaches we've been talking
+ 
+
+ align:start position:0%
+tools and approaches we've been talking
+about with a set of data
+
+ align:start position:0%
+about with a set of data
+ 
+
+ align:start position:0%
+about with a set of data
+our hope is that you can find data
+
+ align:start position:0%
+our hope is that you can find data
+ 
+
+ align:start position:0%
+our hope is that you can find data
+yourself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through the various members of the class
+
+ align:start position:0%
+through the various members of the class
+ 
+
+ align:start position:0%
+through the various members of the class
+i think
+
+ align:start position:0%
+i think
+ 
+
+ align:start position:0%
+i think
+in one of the earlier problem sets we
+
+ align:start position:0%
+in one of the earlier problem sets we
+ 
+
+ align:start position:0%
+in one of the earlier problem sets we
+asked for
+
+ align:start position:0%
+asked for
+ 
+
+ align:start position:0%
+asked for
+your experiences perhaps with some past
+
+ align:start position:0%
+your experiences perhaps with some past
+ 
+
+ align:start position:0%
+your experiences perhaps with some past
+data i think there's plenty of data
+
+ align:start position:0%
+data i think there's plenty of data
+ 
+
+ align:start position:0%
+data i think there's plenty of data
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+if you are not able to tap into some
+
+ align:start position:0%
+if you are not able to tap into some
+ 
+
+ align:start position:0%
+if you are not able to tap into some
+past data you you or colleagues have
+
+ align:start position:0%
+past data you you or colleagues have
+ 
+
+ align:start position:0%
+past data you you or colleagues have
+generated in the lab in a previous job
+
+ align:start position:0%
+generated in the lab in a previous job
+ 
+
+ align:start position:0%
+generated in the lab in a previous job
+that you can share
+
+ align:start position:0%
+that you can share
+ 
+
+ align:start position:0%
+that you can share
+or whatever you can also tap into the
+
+ align:start position:0%
+or whatever you can also tap into the
+ 
+
+ align:start position:0%
+or whatever you can also tap into the
+literature
+
+ align:start position:0%
+literature
+ 
+
+ align:start position:0%
+literature
+so if you find data in the literature
+
+ align:start position:0%
+so if you find data in the literature
+ 
+
+ align:start position:0%
+so if you find data in the literature
+that is perfectly fine as well
+
+ align:start position:0%
+that is perfectly fine as well
+ 
+
+ align:start position:0%
+that is perfectly fine as well
+um and then in a few cases we actually
+
+ align:start position:0%
+um and then in a few cases we actually
+ 
+
+ align:start position:0%
+um and then in a few cases we actually
+have some data from our own
+
+ align:start position:0%
+have some data from our own
+ 
+
+ align:start position:0%
+have some data from our own
+experimentation
+
+ align:start position:0%
+experimentation
+ 
+
+ align:start position:0%
+experimentation
+and research so if you're really stuck
+
+ align:start position:0%
+and research so if you're really stuck
+ 
+
+ align:start position:0%
+and research so if you're really stuck
+uh let me know or let hayden know and we
+
+ align:start position:0%
+uh let me know or let hayden know and we
+ 
+
+ align:start position:0%
+uh let me know or let hayden know and we
+can try to connect you up to something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i've listed a few topic areas i don't
+
+ align:start position:0%
+i've listed a few topic areas i don't
+ 
+
+ align:start position:0%
+i've listed a few topic areas i don't
+want these to be
+
+ align:start position:0%
+want these to be
+ 
+
+ align:start position:0%
+want these to be
+limiting but i mean these are the main
+
+ align:start position:0%
+limiting but i mean these are the main
+ 
+
+ align:start position:0%
+limiting but i mean these are the main
+main kinds of topics we've been dealing
+
+ align:start position:0%
+main kinds of topics we've been dealing
+ 
+
+ align:start position:0%
+main kinds of topics we've been dealing
+with in the class things like process
+
+ align:start position:0%
+with in the class things like process
+ 
+
+ align:start position:0%
+with in the class things like process
+diagnosis looking at the data to detect
+
+ align:start position:0%
+diagnosis looking at the data to detect
+ 
+
+ align:start position:0%
+diagnosis looking at the data to detect
+uh problems
+
+ align:start position:0%
+uh problems
+ 
+
+ align:start position:0%
+uh problems
+ways of optimizing or improving the
+
+ align:start position:0%
+ways of optimizing or improving the
+ 
+
+ align:start position:0%
+ways of optimizing or improving the
+process through
+
+ align:start position:0%
+process through
+ 
+
+ align:start position:0%
+process through
+design of experiments optimization and
+
+ align:start position:0%
+design of experiments optimization and
+ 
+
+ align:start position:0%
+design of experiments optimization and
+so on and then some other sort of
+
+ align:start position:0%
+so on and then some other sort of
+ 
+
+ align:start position:0%
+so on and then some other sort of
+advanced applications things like
+
+ align:start position:0%
+advanced applications things like
+ 
+
+ align:start position:0%
+advanced applications things like
+nested variants
+
+ align:start position:0%
+nested variants
+ 
+
+ align:start position:0%
+nested variants
+some of the spatial yield modeling
+
+ align:start position:0%
+some of the spatial yield modeling
+ 
+
+ align:start position:0%
+some of the spatial yield modeling
+that sort of thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i think it works well to have three
+
+ align:start position:0%
+so i think it works well to have three
+ 
+
+ align:start position:0%
+so i think it works well to have three
+or even four members in the team so the
+
+ align:start position:0%
+or even four members in the team so the
+ 
+
+ align:start position:0%
+or even four members in the team so the
+goal is
+
+ align:start position:0%
+goal is
+ 
+
+ align:start position:0%
+goal is
+have a fairly rich data set and have
+
+ align:start position:0%
+have a fairly rich data set and have
+ 
+
+ align:start position:0%
+have a fairly rich data set and have
+multiple members of the team applying
+
+ align:start position:0%
+multiple members of the team applying
+ 
+
+ align:start position:0%
+multiple members of the team applying
+different kinds of analyses to the
+
+ align:start position:0%
+different kinds of analyses to the
+ 
+
+ align:start position:0%
+different kinds of analyses to the
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+i think it does work where
+
+ align:start position:0%
+i think it does work where
+ 
+
+ align:start position:0%
+i think it does work where
+you're able to identify contributions
+
+ align:start position:0%
+you're able to identify contributions
+ 
+
+ align:start position:0%
+you're able to identify contributions
+from each of the
+
+ align:start position:0%
+from each of the
+ 
+
+ align:start position:0%
+from each of the
+each of the team members but the whole
+
+ align:start position:0%
+each of the team members but the whole
+ 
+
+ align:start position:0%
+each of the team members but the whole
+point of this is is actually
+
+ align:start position:0%
+point of this is is actually
+ 
+
+ align:start position:0%
+point of this is is actually
+you know to be able to
+
+ align:start position:0%
+you know to be able to
+ 
+
+ align:start position:0%
+you know to be able to
+pick over the data
+
+ align:start position:0%
+pick over the data
+ 
+
+ align:start position:0%
+pick over the data
+talk about the data
+
+ align:start position:0%
+talk about the data
+ 
+
+ align:start position:0%
+talk about the data
+talk about your approach to
+
+ align:start position:0%
+talk about your approach to
+ 
+
+ align:start position:0%
+talk about your approach to
+analysis
+
+ align:start position:0%
+analysis
+ 
+
+ align:start position:0%
+analysis
+and looking at the problem with your
+
+ align:start position:0%
+and looking at the problem with your
+ 
+
+ align:start position:0%
+and looking at the problem with your
+teammates
+
+ align:start position:0%
+teammates
+ 
+
+ align:start position:0%
+teammates
+thursday the project proposal is due
+
+ align:start position:0%
+thursday the project proposal is due
+ 
+
+ align:start position:0%
+thursday the project proposal is due
+this is just one or two pages describing
+
+ align:start position:0%
+this is just one or two pages describing
+ 
+
+ align:start position:0%
+this is just one or two pages describing
+the basic data the basic
+
+ align:start position:0%
+the basic data the basic
+ 
+
+ align:start position:0%
+the basic data the basic
+problem in your plan for attack what
+
+ align:start position:0%
+problem in your plan for attack what
+ 
+
+ align:start position:0%
+problem in your plan for attack what
+kinds of analyses you hope to do and of
+
+ align:start position:0%
+kinds of analyses you hope to do and of
+ 
+
+ align:start position:0%
+kinds of analyses you hope to do and of
+course list who your team members are
+
+ align:start position:0%
+course list who your team members are
+ 
+
+ align:start position:0%
+course list who your team members are
+and what their roles are
+
+ align:start position:0%
+and what their roles are
+ 
+
+ align:start position:0%
+and what their roles are
+the goal then is over the coming week
+
+ align:start position:0%
+the goal then is over the coming week
+ 
+
+ align:start position:0%
+the goal then is over the coming week
+and maybe even starting
+
+ align:start position:0%
+and maybe even starting
+ 
+
+ align:start position:0%
+and maybe even starting
+perhaps even after class for for folks
+
+ align:start position:0%
+perhaps even after class for for folks
+ 
+
+ align:start position:0%
+perhaps even after class for for folks
+in singapore
+
+ align:start position:0%
+in singapore
+ 
+
+ align:start position:0%
+in singapore
+on thursday certainly on tuesday
+
+ align:start position:0%
+on thursday certainly on tuesday
+ 
+
+ align:start position:0%
+on thursday certainly on tuesday
+to have a
+
+ align:start position:0%
+to have a
+ 
+
+ align:start position:0%
+to have a
+a chance to meet with me
+
+ align:start position:0%
+a chance to meet with me
+ 
+
+ align:start position:0%
+a chance to meet with me
+or dave if he's available
+
+ align:start position:0%
+or dave if he's available
+ 
+
+ align:start position:0%
+or dave if he's available
+to basically go over your plan
+
+ align:start position:0%
+to basically go over your plan
+ 
+
+ align:start position:0%
+to basically go over your plan
+and your analysis so far if you're if
+
+ align:start position:0%
+and your analysis so far if you're if
+ 
+
+ align:start position:0%
+and your analysis so far if you're if
+you're part way through it so we'll need
+
+ align:start position:0%
+you're part way through it so we'll need
+ 
+
+ align:start position:0%
+you're part way through it so we'll need
+to do that by video conference with uh
+
+ align:start position:0%
+to do that by video conference with uh
+ 
+
+ align:start position:0%
+to do that by video conference with uh
+with folks in singapore if we do it
+
+ align:start position:0%
+with folks in singapore if we do it
+ 
+
+ align:start position:0%
+with folks in singapore if we do it
+right after class we can probably
+
+ align:start position:0%
+right after class we can probably
+ 
+
+ align:start position:0%
+right after class we can probably
+try to arrange
+
+ align:start position:0%
+try to arrange
+ 
+
+ align:start position:0%
+try to arrange
+this facility otherwise we'll use the
+
+ align:start position:0%
+this facility otherwise we'll use the
+ 
+
+ align:start position:0%
+this facility otherwise we'll use the
+conference room
+
+ align:start position:0%
+conference room
+ 
+
+ align:start position:0%
+conference room
+near the
+
+ align:start position:0%
+near the
+ 
+
+ align:start position:0%
+near the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+sma
+
+ align:start position:0%
+sma
+ 
+
+ align:start position:0%
+sma
+your sma offices
+
+ align:start position:0%
+your sma offices
+ 
+
+ align:start position:0%
+your sma offices
+then the expectations are two parts
+
+ align:start position:0%
+then the expectations are two parts
+ 
+
+ align:start position:0%
+then the expectations are two parts
+there'll be a group presentation
+
+ align:start position:0%
+there'll be a group presentation
+ 
+
+ align:start position:0%
+there'll be a group presentation
+by the way not necessarily every single
+
+ align:start position:0%
+by the way not necessarily every single
+ 
+
+ align:start position:0%
+by the way not necessarily every single
+member of your team needs to
+
+ align:start position:0%
+member of your team needs to
+ 
+
+ align:start position:0%
+member of your team needs to
+present part of the presentation trying
+
+ align:start position:0%
+present part of the presentation trying
+ 
+
+ align:start position:0%
+present part of the presentation trying
+to have four team members in a 15-minute
+
+ align:start position:0%
+to have four team members in a 15-minute
+ 
+
+ align:start position:0%
+to have four team members in a 15-minute
+chunk
+
+ align:start position:0%
+chunk
+ 
+
+ align:start position:0%
+chunk
+often can be kind of a kind of a
+
+ align:start position:0%
+often can be kind of a kind of a
+ 
+
+ align:start position:0%
+often can be kind of a kind of a
+coordination mess so as a team you need
+
+ align:start position:0%
+coordination mess so as a team you need
+ 
+
+ align:start position:0%
+coordination mess so as a team you need
+to put together a presentation
+
+ align:start position:0%
+to put together a presentation
+ 
+
+ align:start position:0%
+to put together a presentation
+and have one or maybe two people uh most
+
+ align:start position:0%
+and have one or maybe two people uh most
+ 
+
+ align:start position:0%
+and have one or maybe two people uh most
+likely presenting uh some of those
+
+ align:start position:0%
+likely presenting uh some of those
+ 
+
+ align:start position:0%
+likely presenting uh some of those
+results and then at the end of that week
+
+ align:start position:0%
+results and then at the end of that week
+ 
+
+ align:start position:0%
+results and then at the end of that week
+on friday uh may 16th which is the
+
+ align:start position:0%
+on friday uh may 16th which is the
+ 
+
+ align:start position:0%
+on friday uh may 16th which is the
+the end of the term given that we do not
+
+ align:start position:0%
+the end of the term given that we do not
+ 
+
+ align:start position:0%
+the end of the term given that we do not
+have a final exam
+
+ align:start position:0%
+have a final exam
+ 
+
+ align:start position:0%
+have a final exam
+a single shared group report
+
+ align:start position:0%
+a single shared group report
+ 
+
+ align:start position:0%
+a single shared group report
+needs to be submitted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are just some example example
+
+ align:start position:0%
+these are just some example example
+ 
+
+ align:start position:0%
+these are just some example example
+topics i'm not sure if those have been
+
+ align:start position:0%
+topics i'm not sure if those have been
+ 
+
+ align:start position:0%
+topics i'm not sure if those have been
+drawn from
+
+ align:start position:0%
+drawn from
+ 
+
+ align:start position:0%
+drawn from
+past semesters or not
+
+ align:start position:0%
+past semesters or not
+ 
+
+ align:start position:0%
+past semesters or not
+uh here's some additional kinds of
+
+ align:start position:0%
+uh here's some additional kinds of
+ 
+
+ align:start position:0%
+uh here's some additional kinds of
+suggestions that
+
+ align:start position:0%
+suggestions that
+ 
+
+ align:start position:0%
+suggestions that
+that that i mentioned kinds of analyses
+
+ align:start position:0%
+that that i mentioned kinds of analyses
+ 
+
+ align:start position:0%
+that that i mentioned kinds of analyses
+that might be of interest
+
+ align:start position:0%
+that might be of interest
+ 
+
+ align:start position:0%
+that might be of interest
+uh in the report these are some
+
+ align:start position:0%
+uh in the report these are some
+ 
+
+ align:start position:0%
+uh in the report these are some
+guidelines on what we'd like to see in
+
+ align:start position:0%
+guidelines on what we'd like to see in
+ 
+
+ align:start position:0%
+guidelines on what we'd like to see in
+the report one note here and i haven't
+
+ align:start position:0%
+the report one note here and i haven't
+ 
+
+ align:start position:0%
+the report one note here and i haven't
+posted it yet
+
+ align:start position:0%
+posted it yet
+ 
+
+ align:start position:0%
+posted it yet
+is whoops is we'd like to
+
+ align:start position:0%
+is whoops is we'd like to
+ 
+
+ align:start position:0%
+is whoops is we'd like to
+use a common
+
+ align:start position:0%
+use a common
+ 
+
+ align:start position:0%
+use a common
+template just for the formatting and
+
+ align:start position:0%
+template just for the formatting and
+ 
+
+ align:start position:0%
+template just for the formatting and
+guidelines and basically the ieee
+
+ align:start position:0%
+guidelines and basically the ieee
+ 
+
+ align:start position:0%
+guidelines and basically the ieee
+two-column format has worked really
+
+ align:start position:0%
+two-column format has worked really
+ 
+
+ align:start position:0%
+two-column format has worked really
+nicely we have word templates i think we
+
+ align:start position:0%
+nicely we have word templates i think we
+ 
+
+ align:start position:0%
+nicely we have word templates i think we
+even have latex templates if there's
+
+ align:start position:0%
+even have latex templates if there's
+ 
+
+ align:start position:0%
+even have latex templates if there's
+anybody who still uses latex
+
+ align:start position:0%
+anybody who still uses latex
+ 
+
+ align:start position:0%
+anybody who still uses latex
+i will post that
+
+ align:start position:0%
+i will post that
+ 
+
+ align:start position:0%
+i will post that
+that template
+
+ align:start position:0%
+that template
+ 
+
+ align:start position:0%
+that template
+on the web what's nice about that
+
+ align:start position:0%
+on the web what's nice about that
+ 
+
+ align:start position:0%
+on the web what's nice about that
+is we can actually then put together all
+
+ align:start position:0%
+is we can actually then put together all
+ 
+
+ align:start position:0%
+is we can actually then put together all
+of the written reports from the class
+
+ align:start position:0%
+of the written reports from the class
+ 
+
+ align:start position:0%
+of the written reports from the class
+into almost a little booklet and it's a
+
+ align:start position:0%
+into almost a little booklet and it's a
+ 
+
+ align:start position:0%
+into almost a little booklet and it's a
+it almost looks like a little a little
+
+ align:start position:0%
+it almost looks like a little a little
+ 
+
+ align:start position:0%
+it almost looks like a little a little
+mini
+
+ align:start position:0%
+mini
+ 
+
+ align:start position:0%
+mini
+uh journal or a little mini conference
+
+ align:start position:0%
+uh journal or a little mini conference
+ 
+
+ align:start position:0%
+uh journal or a little mini conference
+proceeding if you will
+
+ align:start position:0%
+proceeding if you will
+ 
+
+ align:start position:0%
+proceeding if you will
+with these
+
+ align:start position:0%
+with these
+ 
+
+ align:start position:0%
+with these
+these reports it also is a nice
+
+ align:start position:0%
+these reports it also is a nice
+ 
+
+ align:start position:0%
+these reports it also is a nice
+professional looking
+
+ align:start position:0%
+professional looking
+ 
+
+ align:start position:0%
+professional looking
+report so we'll distribute
+
+ align:start position:0%
+report so we'll distribute
+ 
+
+ align:start position:0%
+report so we'll distribute
+that as well
+
+ align:start position:0%
+that as well
+ 
+
+ align:start position:0%
+that as well
+so finally i just uh
+
+ align:start position:0%
+so finally i just uh
+ 
+
+ align:start position:0%
+so finally i just uh
+grabbed from the past two or three years
+
+ align:start position:0%
+grabbed from the past two or three years
+ 
+
+ align:start position:0%
+grabbed from the past two or three years
+some of the titles from some of the
+
+ align:start position:0%
+some of the titles from some of the
+ 
+
+ align:start position:0%
+some of the titles from some of the
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+uh or team report uh
+
+ align:start position:0%
+uh or team report uh
+ 
+
+ align:start position:0%
+uh or team report uh
+and presentations
+
+ align:start position:0%
+and presentations
+ 
+
+ align:start position:0%
+and presentations
+just to give you a little bit of a sense
+
+ align:start position:0%
+just to give you a little bit of a sense
+ 
+
+ align:start position:0%
+just to give you a little bit of a sense
+of the variety of of kinds of things
+
+ align:start position:0%
+of the variety of of kinds of things
+ 
+
+ align:start position:0%
+of the variety of of kinds of things
+that we saw
+
+ align:start position:0%
+that we saw
+ 
+
+ align:start position:0%
+that we saw
+so those might give you some idea by the
+
+ align:start position:0%
+so those might give you some idea by the
+ 
+
+ align:start position:0%
+so those might give you some idea by the
+way back in 2005 we we were more focused
+
+ align:start position:0%
+way back in 2005 we we were more focused
+ 
+
+ align:start position:0%
+way back in 2005 we we were more focused
+on like two-person projects or
+
+ align:start position:0%
+on like two-person projects or
+ 
+
+ align:start position:0%
+on like two-person projects or
+one-person projects
+
+ align:start position:0%
+one-person projects
+ 
+
+ align:start position:0%
+one-person projects
+uh and these were great reports but we
+
+ align:start position:0%
+uh and these were great reports but we
+ 
+
+ align:start position:0%
+uh and these were great reports but we
+did decide that uh
+
+ align:start position:0%
+did decide that uh
+ 
+
+ align:start position:0%
+did decide that uh
+sharing and interacting uh made made
+
+ align:start position:0%
+sharing and interacting uh made made
+ 
+
+ align:start position:0%
+sharing and interacting uh made made
+things uh
+
+ align:start position:0%
+things uh
+ 
+
+ align:start position:0%
+things uh
+a better learning experience for all so
+
+ align:start position:0%
+a better learning experience for all so
+ 
+
+ align:start position:0%
+a better learning experience for all so
+so with that let me open it up anybody
+
+ align:start position:0%
+so with that let me open it up anybody
+ 
+
+ align:start position:0%
+so with that let me open it up anybody
+have questions on how the team reports
+
+ align:start position:0%
+have questions on how the team reports
+ 
+
+ align:start position:0%
+have questions on how the team reports
+team projects team presentations need to
+
+ align:start position:0%
+team projects team presentations need to
+ 
+
+ align:start position:0%
+team projects team presentations need to
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+i'll try to break
+
+ align:start position:0%
+i'll try to break
+ 
+
+ align:start position:0%
+i'll try to break
+does pretty much everybody have a team
+
+ align:start position:0%
+does pretty much everybody have a team
+ 
+
+ align:start position:0%
+does pretty much everybody have a team
+in formation
+
+ align:start position:0%
+in formation
+ 
+
+ align:start position:0%
+in formation
+are there people who kind of are still
+
+ align:start position:0%
+are there people who kind of are still
+ 
+
+ align:start position:0%
+are there people who kind of are still
+looking for possible partners
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay one or two okay i'll try to break
+
+ align:start position:0%
+okay one or two okay i'll try to break
+ 
+
+ align:start position:0%
+okay one or two okay i'll try to break
+you know maybe five minutes earlier
+
+ align:start position:0%
+you know maybe five minutes earlier
+ 
+
+ align:start position:0%
+you know maybe five minutes earlier
+which may mean actually break on time um
+
+ align:start position:0%
+which may mean actually break on time um
+ 
+
+ align:start position:0%
+which may mean actually break on time um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+at the end of class so
+
+ align:start position:0%
+at the end of class so
+ 
+
+ align:start position:0%
+at the end of class so
+uh could be a little bit of a discussion
+
+ align:start position:0%
+uh could be a little bit of a discussion
+ 
+
+ align:start position:0%
+uh could be a little bit of a discussion
+while people are still face to face uh
+
+ align:start position:0%
+while people are still face to face uh
+ 
+
+ align:start position:0%
+while people are still face to face uh
+on that
+
+ align:start position:0%
+on that
+ 
+
+ align:start position:0%
+on that
+any other questions on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+professor yes
+
+ align:start position:0%
+professor yes
+ 
+
+ align:start position:0%
+professor yes
+um just now you mentioned um
+
+ align:start position:0%
+um just now you mentioned um
+ 
+
+ align:start position:0%
+um just now you mentioned um
+having a rich set of data
+
+ align:start position:0%
+having a rich set of data
+ 
+
+ align:start position:0%
+having a rich set of data
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+from my understanding we are supposed to
+
+ align:start position:0%
+from my understanding we are supposed to
+ 
+
+ align:start position:0%
+from my understanding we are supposed to
+do the experiments ourselves so i would
+
+ align:start position:0%
+do the experiments ourselves so i would
+ 
+
+ align:start position:0%
+do the experiments ourselves so i would
+like to know how
+
+ align:start position:0%
+like to know how
+ 
+
+ align:start position:0%
+like to know how
+big a set of data are you expecting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+my expectation or
+
+ align:start position:0%
+my expectation or
+ 
+
+ align:start position:0%
+my expectation or
+minimal expectation i would say is more
+
+ align:start position:0%
+minimal expectation i would say is more
+ 
+
+ align:start position:0%
+minimal expectation i would say is more
+that you might be able to tap into data
+
+ align:start position:0%
+that you might be able to tap into data
+ 
+
+ align:start position:0%
+that you might be able to tap into data
+that has already previously been
+
+ align:start position:0%
+that has already previously been
+ 
+
+ align:start position:0%
+that has already previously been
+generated
+
+ align:start position:0%
+generated
+ 
+
+ align:start position:0%
+generated
+it's ambitious and i would applaud
+
+ align:start position:0%
+it's ambitious and i would applaud
+ 
+
+ align:start position:0%
+it's ambitious and i would applaud
+uh people wanting to go and generate
+
+ align:start position:0%
+uh people wanting to go and generate
+ 
+
+ align:start position:0%
+uh people wanting to go and generate
+additional data
+
+ align:start position:0%
+additional data
+ 
+
+ align:start position:0%
+additional data
+so we could certainly talk and depending
+
+ align:start position:0%
+so we could certainly talk and depending
+ 
+
+ align:start position:0%
+so we could certainly talk and depending
+on the data you have in mind but but
+
+ align:start position:0%
+on the data you have in mind but but
+ 
+
+ align:start position:0%
+on the data you have in mind but but
+what i mean by a rich set of data is
+
+ align:start position:0%
+what i mean by a rich set of data is
+ 
+
+ align:start position:0%
+what i mean by a rich set of data is
+something that will support
+
+ align:start position:0%
+something that will support
+ 
+
+ align:start position:0%
+something that will support
+enough of the kinds of analyses that
+
+ align:start position:0%
+enough of the kinds of analyses that
+ 
+
+ align:start position:0%
+enough of the kinds of analyses that
+we've been been talking about through
+
+ align:start position:0%
+we've been been talking about through
+ 
+
+ align:start position:0%
+we've been been talking about through
+through the term
+
+ align:start position:0%
+through the term
+ 
+
+ align:start position:0%
+through the term
+so if it's a doe it needs to be
+
+ align:start position:0%
+so if it's a doe it needs to be
+ 
+
+ align:start position:0%
+so if it's a doe it needs to be
+you know probably several parameters of
+
+ align:start position:0%
+you know probably several parameters of
+ 
+
+ align:start position:0%
+you know probably several parameters of
+input several parameters of output
+
+ align:start position:0%
+input several parameters of output
+ 
+
+ align:start position:0%
+input several parameters of output
+maybe you have some
+
+ align:start position:0%
+maybe you have some
+ 
+
+ align:start position:0%
+maybe you have some
+additional twist to it that's kind of
+
+ align:start position:0%
+additional twist to it that's kind of
+ 
+
+ align:start position:0%
+additional twist to it that's kind of
+interesting or or non-standard
+
+ align:start position:0%
+interesting or or non-standard
+ 
+
+ align:start position:0%
+interesting or or non-standard
+that included some
+
+ align:start position:0%
+that included some
+ 
+
+ align:start position:0%
+that included some
+some thorny issues in the data maybe
+
+ align:start position:0%
+some thorny issues in the data maybe
+ 
+
+ align:start position:0%
+some thorny issues in the data maybe
+it's an unbalanced design or an
+
+ align:start position:0%
+it's an unbalanced design or an
+ 
+
+ align:start position:0%
+it's an unbalanced design or an
+imperfect design and you have to try to
+
+ align:start position:0%
+imperfect design and you have to try to
+ 
+
+ align:start position:0%
+imperfect design and you have to try to
+try to accommodate that i'm i'm all i
+
+ align:start position:0%
+try to accommodate that i'm i'm all i
+ 
+
+ align:start position:0%
+try to accommodate that i'm i'm all i
+mean is is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+enough data to do what you would like to
+
+ align:start position:0%
+enough data to do what you would like to
+ 
+
+ align:start position:0%
+enough data to do what you would like to
+propose
+
+ align:start position:0%
+propose
+ 
+
+ align:start position:0%
+propose
+to do and that that that we can talk
+
+ align:start position:0%
+to do and that that that we can talk
+ 
+
+ align:start position:0%
+to do and that that that we can talk
+about uh
+
+ align:start position:0%
+about uh
+ 
+
+ align:start position:0%
+about uh
+about finding acceptable
+
+ align:start position:0%
+about finding acceptable
+ 
+
+ align:start position:0%
+about finding acceptable
+so were you actually looking at going in
+
+ align:start position:0%
+so were you actually looking at going in
+ 
+
+ align:start position:0%
+so were you actually looking at going in
+and generating some data on a one of the
+
+ align:start position:0%
+and generating some data on a one of the
+ 
+
+ align:start position:0%
+and generating some data on a one of the
+processes or tools or equipment there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh my girl haven't had a discussion yet
+
+ align:start position:0%
+uh my girl haven't had a discussion yet
+ 
+
+ align:start position:0%
+uh my girl haven't had a discussion yet
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it's a requirement oh okay yeah so we
+
+ align:start position:0%
+it's a requirement oh okay yeah so we
+ 
+
+ align:start position:0%
+it's a requirement oh okay yeah so we
+can follow up with hayden
+
+ align:start position:0%
+can follow up with hayden
+ 
+
+ align:start position:0%
+can follow up with hayden
+on that i think you know bonding and
+
+ align:start position:0%
+on that i think you know bonding and
+ 
+
+ align:start position:0%
+on that i think you know bonding and
+that sort of thing would be great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we won't be too ambitious it'll be
+
+ align:start position:0%
+so we won't be too ambitious it'll be
+ 
+
+ align:start position:0%
+so we won't be too ambitious it'll be
+doable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all kind of manufacturing processes
+
+ align:start position:0%
+all kind of manufacturing processes
+ 
+
+ align:start position:0%
+all kind of manufacturing processes
+but i have a
+
+ align:start position:0%
+but i have a
+ 
+
+ align:start position:0%
+but i have a
+past lab data
+
+ align:start position:0%
+past lab data
+ 
+
+ align:start position:0%
+past lab data
+from kind of material engineering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure so the question was you know is is
+
+ align:start position:0%
+sure so the question was you know is is
+ 
+
+ align:start position:0%
+sure so the question was you know is is
+material engineering data
+
+ align:start position:0%
+material engineering data
+ 
+
+ align:start position:0%
+material engineering data
+mechanical pro processes mechanical
+
+ align:start position:0%
+mechanical pro processes mechanical
+ 
+
+ align:start position:0%
+mechanical pro processes mechanical
+properties
+
+ align:start position:0%
+properties
+ 
+
+ align:start position:0%
+properties
+is that okay and the answer is
+
+ align:start position:0%
+is that okay and the answer is
+ 
+
+ align:start position:0%
+is that okay and the answer is
+absolutely i mean if you look at some of
+
+ align:start position:0%
+absolutely i mean if you look at some of
+ 
+
+ align:start position:0%
+absolutely i mean if you look at some of
+these past
+
+ align:start position:0%
+these past
+ 
+
+ align:start position:0%
+these past
+projects you've got everything from you
+
+ align:start position:0%
+projects you've got everything from you
+ 
+
+ align:start position:0%
+projects you've got everything from you
+know some things that look kind of like
+
+ align:start position:0%
+know some things that look kind of like
+ 
+
+ align:start position:0%
+know some things that look kind of like
+semiconductor stuff laser diode it's not
+
+ align:start position:0%
+semiconductor stuff laser diode it's not
+ 
+
+ align:start position:0%
+semiconductor stuff laser diode it's not
+transistors but you have other things of
+
+ align:start position:0%
+transistors but you have other things of
+ 
+
+ align:start position:0%
+transistors but you have other things of
+of bending printed circuit boards sheet
+
+ align:start position:0%
+of bending printed circuit boards sheet
+ 
+
+ align:start position:0%
+of bending printed circuit boards sheet
+metal blanket surface quality and
+
+ align:start position:0%
+metal blanket surface quality and
+ 
+
+ align:start position:0%
+metal blanket surface quality and
+milling
+
+ align:start position:0%
+milling
+ 
+
+ align:start position:0%
+milling
+all kinds this is sort of general
+
+ align:start position:0%
+all kinds this is sort of general
+ 
+
+ align:start position:0%
+all kinds this is sort of general
+general manufacturing
+
+ align:start position:0%
+general manufacturing
+ 
+
+ align:start position:0%
+general manufacturing
+and general processes
+
+ align:start position:0%
+and general processes
+ 
+
+ align:start position:0%
+and general processes
+so that would be no problem at all yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+can you post like one of the reports on
+
+ align:start position:0%
+can you post like one of the reports on
+ 
+
+ align:start position:0%
+can you post like one of the reports on
+stanley so you can take a look
+
+ align:start position:0%
+stanley so you can take a look
+ 
+
+ align:start position:0%
+stanley so you can take a look
+uh yeah well i think what we've done in
+
+ align:start position:0%
+uh yeah well i think what we've done in
+ 
+
+ align:start position:0%
+uh yeah well i think what we've done in
+the past is put up some example some of
+
+ align:start position:0%
+the past is put up some example some of
+ 
+
+ align:start position:0%
+the past is put up some example some of
+the prior year reports we haven't posted
+
+ align:start position:0%
+the prior year reports we haven't posted
+ 
+
+ align:start position:0%
+the prior year reports we haven't posted
+those yet but i'll try to do that today
+
+ align:start position:0%
+those yet but i'll try to do that today
+ 
+
+ align:start position:0%
+those yet but i'll try to do that today
+great thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any other questions
+
+ align:start position:0%
+okay any other questions
+ 
+
+ align:start position:0%
+okay any other questions
+all right let me switch here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+again what we're doing now is sort of
+
+ align:start position:0%
+again what we're doing now is sort of
+ 
+
+ align:start position:0%
+again what we're doing now is sort of
+switching to some case studies there's
+
+ align:start position:0%
+switching to some case studies there's
+ 
+
+ align:start position:0%
+switching to some case studies there's
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+perhaps uh in a few of the lectures some
+
+ align:start position:0%
+perhaps uh in a few of the lectures some
+ 
+
+ align:start position:0%
+perhaps uh in a few of the lectures some
+new material if you will coming along
+
+ align:start position:0%
+new material if you will coming along
+ 
+
+ align:start position:0%
+new material if you will coming along
+in in this case study the first case
+
+ align:start position:0%
+in in this case study the first case
+ 
+
+ align:start position:0%
+in in this case study the first case
+study
+
+ align:start position:0%
+study
+ 
+
+ align:start position:0%
+study
+uh i don't think there's actually that
+
+ align:start position:0%
+uh i don't think there's actually that
+ 
+
+ align:start position:0%
+uh i don't think there's actually that
+much new in terms of uh
+
+ align:start position:0%
+much new in terms of uh
+ 
+
+ align:start position:0%
+much new in terms of uh
+methodologies and so on i just think
+
+ align:start position:0%
+methodologies and so on i just think
+ 
+
+ align:start position:0%
+methodologies and so on i just think
+this is a nice example though a little
+
+ align:start position:0%
+this is a nice example though a little
+ 
+
+ align:start position:0%
+this is a nice example though a little
+dated now of a fairly
+
+ align:start position:0%
+dated now of a fairly
+ 
+
+ align:start position:0%
+dated now of a fairly
+straightforward but thorough application
+
+ align:start position:0%
+straightforward but thorough application
+ 
+
+ align:start position:0%
+straightforward but thorough application
+of design of experiments and response
+
+ align:start position:0%
+of design of experiments and response
+ 
+
+ align:start position:0%
+of design of experiments and response
+surface modeling
+
+ align:start position:0%
+surface modeling
+ 
+
+ align:start position:0%
+surface modeling
+so i also by the way posted
+
+ align:start position:0%
+so i also by the way posted
+ 
+
+ align:start position:0%
+so i also by the way posted
+the paper
+
+ align:start position:0%
+the paper
+ 
+
+ align:start position:0%
+the paper
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+this case study on the site as well it's
+
+ align:start position:0%
+this case study on the site as well it's
+ 
+
+ align:start position:0%
+this case study on the site as well it's
+down in the reading section that goes
+
+ align:start position:0%
+down in the reading section that goes
+ 
+
+ align:start position:0%
+down in the reading section that goes
+readings that goes with the lecture
+
+ align:start position:0%
+readings that goes with the lecture
+ 
+
+ align:start position:0%
+readings that goes with the lecture
+so you know you'll have to go and pop
+
+ align:start position:0%
+so you know you'll have to go and pop
+ 
+
+ align:start position:0%
+so you know you'll have to go and pop
+off this
+
+ align:start position:0%
+off this
+ 
+
+ align:start position:0%
+off this
+what is it eight or nine page
+
+ align:start position:0%
+what is it eight or nine page
+ 
+
+ align:start position:0%
+what is it eight or nine page
+paper
+
+ align:start position:0%
+paper
+ 
+
+ align:start position:0%
+paper
+as well i should mention some of the
+
+ align:start position:0%
+as well i should mention some of the
+ 
+
+ align:start position:0%
+as well i should mention some of the
+other case studies will also have papers
+
+ align:start position:0%
+other case studies will also have papers
+ 
+
+ align:start position:0%
+other case studies will also have papers
+from the literature
+
+ align:start position:0%
+from the literature
+ 
+
+ align:start position:0%
+from the literature
+for you to grab
+
+ align:start position:0%
+for you to grab
+ 
+
+ align:start position:0%
+for you to grab
+and read
+
+ align:start position:0%
+and read
+ 
+
+ align:start position:0%
+and read
+so this case study comes from
+
+ align:start position:0%
+so this case study comes from
+ 
+
+ align:start position:0%
+so this case study comes from
+semiconductor manufacturing
+
+ align:start position:0%
+semiconductor manufacturing
+ 
+
+ align:start position:0%
+semiconductor manufacturing
+it's a little dated now it goes back to
+
+ align:start position:0%
+it's a little dated now it goes back to
+ 
+
+ align:start position:0%
+it's a little dated now it goes back to
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+but this was actually kind of just the
+
+ align:start position:0%
+but this was actually kind of just the
+ 
+
+ align:start position:0%
+but this was actually kind of just the
+time when things like
+
+ align:start position:0%
+time when things like
+ 
+
+ align:start position:0%
+time when things like
+statistical process control more
+
+ align:start position:0%
+statistical process control more
+ 
+
+ align:start position:0%
+statistical process control more
+thorough design of experiments response
+
+ align:start position:0%
+thorough design of experiments response
+ 
+
+ align:start position:0%
+thorough design of experiments response
+service modeling was really finally
+
+ align:start position:0%
+service modeling was really finally
+ 
+
+ align:start position:0%
+service modeling was really finally
+hitting the semiconductor
+
+ align:start position:0%
+hitting the semiconductor
+ 
+
+ align:start position:0%
+hitting the semiconductor
+industry
+
+ align:start position:0%
+industry
+ 
+
+ align:start position:0%
+industry
+and really
+
+ align:start position:0%
+and really
+ 
+
+ align:start position:0%
+and really
+starting to be more
+
+ align:start position:0%
+starting to be more
+ 
+
+ align:start position:0%
+starting to be more
+widespread in
+
+ align:start position:0%
+widespread in
+ 
+
+ align:start position:0%
+widespread in
+adoption
+
+ align:start position:0%
+adoption
+ 
+
+ align:start position:0%
+adoption
+so i think this is a nice case it's a
+
+ align:start position:0%
+so i think this is a nice case it's a
+ 
+
+ align:start position:0%
+so i think this is a nice case it's a
+nice case study because they actually
+
+ align:start position:0%
+nice case study because they actually
+ 
+
+ align:start position:0%
+nice case study because they actually
+show us the
+
+ align:start position:0%
+show us the
+ 
+
+ align:start position:0%
+show us the
+experimental conditions the actual data
+
+ align:start position:0%
+experimental conditions the actual data
+ 
+
+ align:start position:0%
+experimental conditions the actual data
+and the actual models that they
+
+ align:start position:0%
+and the actual models that they
+ 
+
+ align:start position:0%
+and the actual models that they
+generated
+
+ align:start position:0%
+generated
+ 
+
+ align:start position:0%
+generated
+some of the things are a little dated
+
+ align:start position:0%
+some of the things are a little dated
+ 
+
+ align:start position:0%
+some of the things are a little dated
+for example they talk about
+
+ align:start position:0%
+for example they talk about
+ 
+
+ align:start position:0%
+for example they talk about
+millimeter wafers
+
+ align:start position:0%
+millimeter wafers
+ 
+
+ align:start position:0%
+millimeter wafers
+so this is five inch wafer processing
+
+ align:start position:0%
+so this is five inch wafer processing
+ 
+
+ align:start position:0%
+so this is five inch wafer processing
+which is kind of a weird size but it
+
+ align:start position:0%
+which is kind of a weird size but it
+ 
+
+ align:start position:0%
+which is kind of a weird size but it
+also you know we're up to 300 millimeter
+
+ align:start position:0%
+also you know we're up to 300 millimeter
+ 
+
+ align:start position:0%
+also you know we're up to 300 millimeter
+12 inch wafers so it shows the march of
+
+ align:start position:0%
+12 inch wafers so it shows the march of
+ 
+
+ align:start position:0%
+12 inch wafers so it shows the march of
+progress of of technology however
+
+ align:start position:0%
+progress of of technology however
+ 
+
+ align:start position:0%
+progress of of technology however
+cbd and cvd of blanket tungsten is is
+
+ align:start position:0%
+cbd and cvd of blanket tungsten is is
+ 
+
+ align:start position:0%
+cbd and cvd of blanket tungsten is is
+still heavily used very integral so it's
+
+ align:start position:0%
+still heavily used very integral so it's
+ 
+
+ align:start position:0%
+still heavily used very integral so it's
+still a relevant process
+
+ align:start position:0%
+still a relevant process
+ 
+
+ align:start position:0%
+still a relevant process
+so what i want to do
+
+ align:start position:0%
+so what i want to do
+ 
+
+ align:start position:0%
+so what i want to do
+in looking at this case is go through
+
+ align:start position:0%
+in looking at this case is go through
+ 
+
+ align:start position:0%
+in looking at this case is go through
+talk a little bit about the bank
+
+ align:start position:0%
+talk a little bit about the bank
+ 
+
+ align:start position:0%
+talk a little bit about the bank
+background of tungsten cbd things that
+
+ align:start position:0%
+background of tungsten cbd things that
+ 
+
+ align:start position:0%
+background of tungsten cbd things that
+aren't in the paper but may give you a
+
+ align:start position:0%
+aren't in the paper but may give you a
+ 
+
+ align:start position:0%
+aren't in the paper but may give you a
+little bit of a
+
+ align:start position:0%
+little bit of a
+ 
+
+ align:start position:0%
+little bit of a
+a feel on the more of a feel on the
+
+ align:start position:0%
+a feel on the more of a feel on the
+ 
+
+ align:start position:0%
+a feel on the more of a feel on the
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+talk a little bit about the preliminary
+
+ align:start position:0%
+talk a little bit about the preliminary
+ 
+
+ align:start position:0%
+talk a little bit about the preliminary
+work that
+
+ align:start position:0%
+work that
+ 
+
+ align:start position:0%
+work that
+they did
+
+ align:start position:0%
+they did
+ 
+
+ align:start position:0%
+they did
+looking back at the prior paper that
+
+ align:start position:0%
+looking back at the prior paper that
+ 
+
+ align:start position:0%
+looking back at the prior paper that
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+that they cite
+
+ align:start position:0%
+that they cite
+ 
+
+ align:start position:0%
+that they cite
+and then we'll go through the
+
+ align:start position:0%
+and then we'll go through the
+ 
+
+ align:start position:0%
+and then we'll go through the
+experimental design that they performed
+
+ align:start position:0%
+experimental design that they performed
+ 
+
+ align:start position:0%
+experimental design that they performed
+to try to optimize
+
+ align:start position:0%
+to try to optimize
+ 
+
+ align:start position:0%
+to try to optimize
+this tungsten cbd process to understand
+
+ align:start position:0%
+this tungsten cbd process to understand
+ 
+
+ align:start position:0%
+this tungsten cbd process to understand
+it model it and then optimize it so
+
+ align:start position:0%
+it model it and then optimize it so
+ 
+
+ align:start position:0%
+it model it and then optimize it so
+we'll look at the data we'll do some rsm
+
+ align:start position:0%
+we'll look at the data we'll do some rsm
+ 
+
+ align:start position:0%
+we'll look at the data we'll do some rsm
+analysis or
+
+ align:start position:0%
+analysis or
+ 
+
+ align:start position:0%
+analysis or
+mostly looking at
+
+ align:start position:0%
+mostly looking at
+ 
+
+ align:start position:0%
+mostly looking at
+their analysis in the paper
+
+ align:start position:0%
+their analysis in the paper
+ 
+
+ align:start position:0%
+their analysis in the paper
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+assuming i have time at the end and i
+
+ align:start position:0%
+assuming i have time at the end and i
+ 
+
+ align:start position:0%
+assuming i have time at the end and i
+think i will
+
+ align:start position:0%
+think i will
+ 
+
+ align:start position:0%
+think i will
+i'll switch over and we'll we'll use
+
+ align:start position:0%
+i'll switch over and we'll we'll use
+ 
+
+ align:start position:0%
+i'll switch over and we'll we'll use
+play around with jump a little bit with
+
+ align:start position:0%
+play around with jump a little bit with
+ 
+
+ align:start position:0%
+play around with jump a little bit with
+that same data set and
+
+ align:start position:0%
+that same data set and
+ 
+
+ align:start position:0%
+that same data set and
+show you a few of the kinds of analyses
+
+ align:start position:0%
+show you a few of the kinds of analyses
+ 
+
+ align:start position:0%
+show you a few of the kinds of analyses
+that are possible
+
+ align:start position:0%
+that are possible
+ 
+
+ align:start position:0%
+that are possible
+with that tool
+
+ align:start position:0%
+with that tool
+ 
+
+ align:start position:0%
+with that tool
+both for
+
+ align:start position:0%
+both for
+ 
+
+ align:start position:0%
+both for
+regression some of the stepwise
+
+ align:start position:0%
+regression some of the stepwise
+ 
+
+ align:start position:0%
+regression some of the stepwise
+regression that's referred to
+
+ align:start position:0%
+regression that's referred to
+ 
+
+ align:start position:0%
+regression that's referred to
+in the paper and then some of the neat
+
+ align:start position:0%
+in the paper and then some of the neat
+ 
+
+ align:start position:0%
+in the paper and then some of the neat
+tools actually in the interactive
+
+ align:start position:0%
+tools actually in the interactive
+ 
+
+ align:start position:0%
+tools actually in the interactive
+capabilities of jump for for
+
+ align:start position:0%
+capabilities of jump for for
+ 
+
+ align:start position:0%
+capabilities of jump for for
+optimization
+
+ align:start position:0%
+optimization
+ 
+
+ align:start position:0%
+optimization
+now throughout this
+
+ align:start position:0%
+now throughout this
+ 
+
+ align:start position:0%
+now throughout this
+think a little bit about where you see
+
+ align:start position:0%
+think a little bit about where you see
+ 
+
+ align:start position:0%
+think a little bit about where you see
+weaknesses or alternative ideas or
+
+ align:start position:0%
+weaknesses or alternative ideas or
+ 
+
+ align:start position:0%
+weaknesses or alternative ideas or
+things like that because at the end i
+
+ align:start position:0%
+things like that because at the end i
+ 
+
+ align:start position:0%
+things like that because at the end i
+might ask what are some of your ideas of
+
+ align:start position:0%
+might ask what are some of your ideas of
+ 
+
+ align:start position:0%
+might ask what are some of your ideas of
+things you think might have been
+
+ align:start position:0%
+things you think might have been
+ 
+
+ align:start position:0%
+things you think might have been
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+uh or important to try or to improve on
+
+ align:start position:0%
+uh or important to try or to improve on
+ 
+
+ align:start position:0%
+uh or important to try or to improve on
+this so have that in mind what what
+
+ align:start position:0%
+this so have that in mind what what
+ 
+
+ align:start position:0%
+this so have that in mind what what
+where where do you think they did a good
+
+ align:start position:0%
+where where do you think they did a good
+ 
+
+ align:start position:0%
+where where do you think they did a good
+job what do you think they did a a
+
+ align:start position:0%
+job what do you think they did a a
+ 
+
+ align:start position:0%
+job what do you think they did a a
+weaker job what might you suggest and
+
+ align:start position:0%
+weaker job what might you suggest and
+ 
+
+ align:start position:0%
+weaker job what might you suggest and
+i'll ask you that question at the at the
+
+ align:start position:0%
+i'll ask you that question at the at the
+ 
+
+ align:start position:0%
+i'll ask you that question at the at the
+end okay
+
+ align:start position:0%
+end okay
+ 
+
+ align:start position:0%
+end okay
+so let me talk a little bit about
+
+ align:start position:0%
+so let me talk a little bit about
+ 
+
+ align:start position:0%
+so let me talk a little bit about
+tungsten and in particular tungsten
+
+ align:start position:0%
+tungsten and in particular tungsten
+ 
+
+ align:start position:0%
+tungsten and in particular tungsten
+plugs
+
+ align:start position:0%
+plugs
+ 
+
+ align:start position:0%
+plugs
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+tungsten
+
+ align:start position:0%
+tungsten
+ 
+
+ align:start position:0%
+tungsten
+here is generally used as a conductor in
+
+ align:start position:0%
+here is generally used as a conductor in
+ 
+
+ align:start position:0%
+here is generally used as a conductor in
+semiconductor fabrication it's not a
+
+ align:start position:0%
+semiconductor fabrication it's not a
+ 
+
+ align:start position:0%
+semiconductor fabrication it's not a
+great conductor meaning it it's
+
+ align:start position:0%
+great conductor meaning it it's
+ 
+
+ align:start position:0%
+great conductor meaning it it's
+often a little bit higher resistivity
+
+ align:start position:0%
+often a little bit higher resistivity
+ 
+
+ align:start position:0%
+often a little bit higher resistivity
+than other metals like aluminum
+
+ align:start position:0%
+than other metals like aluminum
+ 
+
+ align:start position:0%
+than other metals like aluminum
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+or now copper
+
+ align:start position:0%
+or now copper
+ 
+
+ align:start position:0%
+or now copper
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+continues to be heavily used for
+
+ align:start position:0%
+continues to be heavily used for
+ 
+
+ align:start position:0%
+continues to be heavily used for
+contacts and plugs
+
+ align:start position:0%
+contacts and plugs
+ 
+
+ align:start position:0%
+contacts and plugs
+so contacts are the holes that are
+
+ align:start position:0%
+so contacts are the holes that are
+ 
+
+ align:start position:0%
+so contacts are the holes that are
+drilled between or into
+
+ align:start position:0%
+drilled between or into
+ 
+
+ align:start position:0%
+drilled between or into
+an insulating layer from the first level
+
+ align:start position:0%
+an insulating layer from the first level
+ 
+
+ align:start position:0%
+an insulating layer from the first level
+of metal down to the underlying silicon
+
+ align:start position:0%
+of metal down to the underlying silicon
+ 
+
+ align:start position:0%
+of metal down to the underlying silicon
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+plugs are the same idea but at other
+
+ align:start position:0%
+plugs are the same idea but at other
+ 
+
+ align:start position:0%
+plugs are the same idea but at other
+levels of interconnect so you would have
+
+ align:start position:0%
+levels of interconnect so you would have
+ 
+
+ align:start position:0%
+levels of interconnect so you would have
+a a plug
+
+ align:start position:0%
+a a plug
+ 
+
+ align:start position:0%
+a a plug
+from metal one to metal two or metal two
+
+ align:start position:0%
+from metal one to metal two or metal two
+ 
+
+ align:start position:0%
+from metal one to metal two or metal two
+to metal 3 and so on
+
+ align:start position:0%
+to metal 3 and so on
+ 
+
+ align:start position:0%
+to metal 3 and so on
+terminology is not completely uniform
+
+ align:start position:0%
+terminology is not completely uniform
+ 
+
+ align:start position:0%
+terminology is not completely uniform
+but that's that's
+
+ align:start position:0%
+but that's that's
+ 
+
+ align:start position:0%
+but that's that's
+that's the typical terminology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the examples drawn from from this paper
+
+ align:start position:0%
+the examples drawn from from this paper
+ 
+
+ align:start position:0%
+the examples drawn from from this paper
+they talk about tungsten plugs in
+
+ align:start position:0%
+they talk about tungsten plugs in
+ 
+
+ align:start position:0%
+they talk about tungsten plugs in
+conjunction with aluminum interconnect
+
+ align:start position:0%
+conjunction with aluminum interconnect
+ 
+
+ align:start position:0%
+conjunction with aluminum interconnect
+and they're actually mostly focused i
+
+ align:start position:0%
+and they're actually mostly focused i
+ 
+
+ align:start position:0%
+and they're actually mostly focused i
+think on tungsten between
+
+ align:start position:0%
+think on tungsten between
+ 
+
+ align:start position:0%
+think on tungsten between
+or tungsten contacts
+
+ align:start position:0%
+or tungsten contacts
+ 
+
+ align:start position:0%
+or tungsten contacts
+with the idea that in older technology
+
+ align:start position:0%
+with the idea that in older technology
+ 
+
+ align:start position:0%
+with the idea that in older technology
+in fact you didn't need to drill and
+
+ align:start position:0%
+in fact you didn't need to drill and
+ 
+
+ align:start position:0%
+in fact you didn't need to drill and
+form separate
+
+ align:start position:0%
+form separate
+ 
+
+ align:start position:0%
+form separate
+plugs between layers you could just
+
+ align:start position:0%
+plugs between layers you could just
+ 
+
+ align:start position:0%
+plugs between layers you could just
+allow say an aluminum deposition to go
+
+ align:start position:0%
+allow say an aluminum deposition to go
+ 
+
+ align:start position:0%
+allow say an aluminum deposition to go
+in and fill
+
+ align:start position:0%
+in and fill
+ 
+
+ align:start position:0%
+in and fill
+that layer and then
+
+ align:start position:0%
+that layer and then
+ 
+
+ align:start position:0%
+that layer and then
+etch off where you where you didn't want
+
+ align:start position:0%
+etch off where you where you didn't want
+ 
+
+ align:start position:0%
+etch off where you where you didn't want
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+with scaling it became pretty much
+
+ align:start position:0%
+with scaling it became pretty much
+ 
+
+ align:start position:0%
+with scaling it became pretty much
+essential to be able to form the plugs
+
+ align:start position:0%
+essential to be able to form the plugs
+ 
+
+ align:start position:0%
+essential to be able to form the plugs
+separately from the interconnect
+
+ align:start position:0%
+separately from the interconnect
+ 
+
+ align:start position:0%
+separately from the interconnect
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+then tungsten was used to fill fill
+
+ align:start position:0%
+then tungsten was used to fill fill
+ 
+
+ align:start position:0%
+then tungsten was used to fill fill
+those plugs between metal layers as well
+
+ align:start position:0%
+those plugs between metal layers as well
+ 
+
+ align:start position:0%
+those plugs between metal layers as well
+as we've gone to copper interconnect
+
+ align:start position:0%
+as we've gone to copper interconnect
+ 
+
+ align:start position:0%
+as we've gone to copper interconnect
+tungsten still appears
+
+ align:start position:0%
+tungsten still appears
+ 
+
+ align:start position:0%
+tungsten still appears
+in most uh advanced technologies now
+
+ align:start position:0%
+in most uh advanced technologies now
+ 
+
+ align:start position:0%
+in most uh advanced technologies now
+primarily just as the first level of of
+
+ align:start position:0%
+primarily just as the first level of of
+ 
+
+ align:start position:0%
+primarily just as the first level of of
+contact
+
+ align:start position:0%
+contact
+ 
+
+ align:start position:0%
+contact
+from a copper interconnect down to the
+
+ align:start position:0%
+from a copper interconnect down to the
+ 
+
+ align:start position:0%
+from a copper interconnect down to the
+silicon so it is still used
+
+ align:start position:0%
+silicon so it is still used
+ 
+
+ align:start position:0%
+silicon so it is still used
+and extensions where it may not purely
+
+ align:start position:0%
+and extensions where it may not purely
+ 
+
+ align:start position:0%
+and extensions where it may not purely
+be be tungsten plugs but it may also be
+
+ align:start position:0%
+be be tungsten plugs but it may also be
+ 
+
+ align:start position:0%
+be be tungsten plugs but it may also be
+in some cases
+
+ align:start position:0%
+in some cases
+ 
+
+ align:start position:0%
+in some cases
+some local
+
+ align:start position:0%
+some local
+ 
+
+ align:start position:0%
+some local
+some local interconnect
+
+ align:start position:0%
+some local interconnect
+ 
+
+ align:start position:0%
+some local interconnect
+so you can down very close to the
+
+ align:start position:0%
+so you can down very close to the
+ 
+
+ align:start position:0%
+so you can down very close to the
+silicon form little straps or other
+
+ align:start position:0%
+silicon form little straps or other
+ 
+
+ align:start position:0%
+silicon form little straps or other
+sorts of local tungsten based uh
+
+ align:start position:0%
+sorts of local tungsten based uh
+ 
+
+ align:start position:0%
+sorts of local tungsten based uh
+short very short run
+
+ align:start position:0%
+short very short run
+ 
+
+ align:start position:0%
+short very short run
+interconnect
+
+ align:start position:0%
+interconnect
+ 
+
+ align:start position:0%
+interconnect
+to form electrical connections
+
+ align:start position:0%
+to form electrical connections
+ 
+
+ align:start position:0%
+to form electrical connections
+now the important part of tungsten why
+
+ align:start position:0%
+now the important part of tungsten why
+ 
+
+ align:start position:0%
+now the important part of tungsten why
+it's used is that it's also
+
+ align:start position:0%
+it's used is that it's also
+ 
+
+ align:start position:0%
+it's used is that it's also
+can be
+
+ align:start position:0%
+can be
+ 
+
+ align:start position:0%
+can be
+conformally
+
+ align:start position:0%
+conformally
+ 
+
+ align:start position:0%
+conformally
+filled
+
+ align:start position:0%
+filled
+ 
+
+ align:start position:0%
+filled
+and can
+
+ align:start position:0%
+and can
+ 
+
+ align:start position:0%
+and can
+especially with uh chemical vapor
+
+ align:start position:0%
+especially with uh chemical vapor
+ 
+
+ align:start position:0%
+especially with uh chemical vapor
+deposition or plasma processing uh can
+
+ align:start position:0%
+deposition or plasma processing uh can
+ 
+
+ align:start position:0%
+deposition or plasma processing uh can
+fill fairly small holes
+
+ align:start position:0%
+fill fairly small holes
+ 
+
+ align:start position:0%
+fill fairly small holes
+so the basic idea
+
+ align:start position:0%
+so the basic idea
+ 
+
+ align:start position:0%
+so the basic idea
+or progression
+
+ align:start position:0%
+or progression
+ 
+
+ align:start position:0%
+or progression
+in a tungsten deposition
+
+ align:start position:0%
+in a tungsten deposition
+ 
+
+ align:start position:0%
+in a tungsten deposition
+is you primarily get
+
+ align:start position:0%
+is you primarily get
+ 
+
+ align:start position:0%
+is you primarily get
+conformal deposition so in time
+
+ align:start position:0%
+conformal deposition so in time
+ 
+
+ align:start position:0%
+conformal deposition so in time
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+gases
+
+ align:start position:0%
+gases
+ 
+
+ align:start position:0%
+gases
+that are that are present in the plasma
+
+ align:start position:0%
+that are that are present in the plasma
+ 
+
+ align:start position:0%
+that are that are present in the plasma
+chamber and reactor
+
+ align:start position:0%
+chamber and reactor
+ 
+
+ align:start position:0%
+chamber and reactor
+interface with the surface form
+
+ align:start position:0%
+interface with the surface form
+ 
+
+ align:start position:0%
+interface with the surface form
+reactions
+
+ align:start position:0%
+reactions
+ 
+
+ align:start position:0%
+reactions
+and basically build up in a conformal
+
+ align:start position:0%
+and basically build up in a conformal
+ 
+
+ align:start position:0%
+and basically build up in a conformal
+way to fill
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fill the plug
+
+ align:start position:0%
+fill the plug
+ 
+
+ align:start position:0%
+fill the plug
+now you want to do this in a way that
+
+ align:start position:0%
+now you want to do this in a way that
+ 
+
+ align:start position:0%
+now you want to do this in a way that
+does not result in seams or
+
+ align:start position:0%
+does not result in seams or
+ 
+
+ align:start position:0%
+does not result in seams or
+or voids in the middle so that can be a
+
+ align:start position:0%
+or voids in the middle so that can be a
+ 
+
+ align:start position:0%
+or voids in the middle so that can be a
+little bit tricky but but that can be
+
+ align:start position:0%
+little bit tricky but but that can be
+ 
+
+ align:start position:0%
+little bit tricky but but that can be
+done in in such a way that one
+
+ align:start position:0%
+done in in such a way that one
+ 
+
+ align:start position:0%
+done in in such a way that one
+avoids those those plugs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the way this paper uses tungsten
+
+ align:start position:0%
+now the way this paper uses tungsten
+ 
+
+ align:start position:0%
+now the way this paper uses tungsten
+plugs is with a process they refer to as
+
+ align:start position:0%
+plugs is with a process they refer to as
+ 
+
+ align:start position:0%
+plugs is with a process they refer to as
+plasma etchback so if i do that
+
+ align:start position:0%
+plasma etchback so if i do that
+ 
+
+ align:start position:0%
+plasma etchback so if i do that
+conformal deposition
+
+ align:start position:0%
+conformal deposition
+ 
+
+ align:start position:0%
+conformal deposition
+finally to this this surface
+
+ align:start position:0%
+finally to this this surface
+ 
+
+ align:start position:0%
+finally to this this surface
+uh now i've got
+
+ align:start position:0%
+uh now i've got
+ 
+
+ align:start position:0%
+uh now i've got
+you know the
+
+ align:start position:0%
+you know the
+ 
+
+ align:start position:0%
+you know the
+tungsten not only in the plug but i've
+
+ align:start position:0%
+tungsten not only in the plug but i've
+ 
+
+ align:start position:0%
+tungsten not only in the plug but i've
+also got all this excess tungsten out
+
+ align:start position:0%
+also got all this excess tungsten out
+ 
+
+ align:start position:0%
+also got all this excess tungsten out
+here in the
+
+ align:start position:0%
+here in the
+ 
+
+ align:start position:0%
+here in the
+neighboring regions that i want to
+
+ align:start position:0%
+neighboring regions that i want to
+ 
+
+ align:start position:0%
+neighboring regions that i want to
+remove
+
+ align:start position:0%
+remove
+ 
+
+ align:start position:0%
+remove
+and the idea of of etchback was that
+
+ align:start position:0%
+and the idea of of etchback was that
+ 
+
+ align:start position:0%
+and the idea of of etchback was that
+through the deposition process i fill
+
+ align:start position:0%
+through the deposition process i fill
+ 
+
+ align:start position:0%
+through the deposition process i fill
+the surface
+
+ align:start position:0%
+the surface
+ 
+
+ align:start position:0%
+the surface
+but i leave essentially a nearly planar
+
+ align:start position:0%
+but i leave essentially a nearly planar
+ 
+
+ align:start position:0%
+but i leave essentially a nearly planar
+surface that now if i just etch
+
+ align:start position:0%
+surface that now if i just etch
+ 
+
+ align:start position:0%
+surface that now if i just etch
+uniformly
+
+ align:start position:0%
+uniformly
+ 
+
+ align:start position:0%
+uniformly
+back that whole surface
+
+ align:start position:0%
+back that whole surface
+ 
+
+ align:start position:0%
+back that whole surface
+i can remove down to the underlying
+
+ align:start position:0%
+i can remove down to the underlying
+ 
+
+ align:start position:0%
+i can remove down to the underlying
+interface metal or interface layer or
+
+ align:start position:0%
+interface metal or interface layer or
+ 
+
+ align:start position:0%
+interface metal or interface layer or
+the oxide
+
+ align:start position:0%
+the oxide
+ 
+
+ align:start position:0%
+the oxide
+and leave the metal just in the in the
+
+ align:start position:0%
+and leave the metal just in the in the
+ 
+
+ align:start position:0%
+and leave the metal just in the in the
+plug where i wanted it
+
+ align:start position:0%
+plug where i wanted it
+ 
+
+ align:start position:0%
+plug where i wanted it
+in the paper they refer to using this as
+
+ align:start position:0%
+in the paper they refer to using this as
+ 
+
+ align:start position:0%
+in the paper they refer to using this as
+are using plasma etchback to do this
+
+ align:start position:0%
+are using plasma etchback to do this
+ 
+
+ align:start position:0%
+are using plasma etchback to do this
+uniform etchback
+
+ align:start position:0%
+uniform etchback
+ 
+
+ align:start position:0%
+uniform etchback
+in modern processing this step has
+
+ align:start position:0%
+in modern processing this step has
+ 
+
+ align:start position:0%
+in modern processing this step has
+pretty much been replaced with cmp
+
+ align:start position:0%
+pretty much been replaced with cmp
+ 
+
+ align:start position:0%
+pretty much been replaced with cmp
+because that has a much higher
+
+ align:start position:0%
+because that has a much higher
+ 
+
+ align:start position:0%
+because that has a much higher
+controllability and
+
+ align:start position:0%
+controllability and
+ 
+
+ align:start position:0%
+controllability and
+gets around an important limitation
+
+ align:start position:0%
+gets around an important limitation
+ 
+
+ align:start position:0%
+gets around an important limitation
+that's kind of pictured here in this in
+
+ align:start position:0%
+that's kind of pictured here in this in
+ 
+
+ align:start position:0%
+that's kind of pictured here in this in
+this in this diagram
+
+ align:start position:0%
+this in this diagram
+ 
+
+ align:start position:0%
+this in this diagram
+having to do with
+
+ align:start position:0%
+having to do with
+ 
+
+ align:start position:0%
+having to do with
+very tight constraints on uniformity
+
+ align:start position:0%
+very tight constraints on uniformity
+ 
+
+ align:start position:0%
+very tight constraints on uniformity
+with a plasma etchback
+
+ align:start position:0%
+with a plasma etchback
+ 
+
+ align:start position:0%
+with a plasma etchback
+the basic issue with uniformity is if i
+
+ align:start position:0%
+the basic issue with uniformity is if i
+ 
+
+ align:start position:0%
+the basic issue with uniformity is if i
+in fact have deposition
+
+ align:start position:0%
+in fact have deposition
+ 
+
+ align:start position:0%
+in fact have deposition
+that results in different thicknesses
+
+ align:start position:0%
+that results in different thicknesses
+ 
+
+ align:start position:0%
+that results in different thicknesses
+either in different locations within the
+
+ align:start position:0%
+either in different locations within the
+ 
+
+ align:start position:0%
+either in different locations within the
+chip
+
+ align:start position:0%
+chip
+ 
+
+ align:start position:0%
+chip
+or in different chips across the wafer
+
+ align:start position:0%
+or in different chips across the wafer
+ 
+
+ align:start position:0%
+or in different chips across the wafer
+and i uniformly etch back
+
+ align:start position:0%
+and i uniformly etch back
+ 
+
+ align:start position:0%
+and i uniformly etch back
+first off if i only etch back this
+
+ align:start position:0%
+first off if i only etch back this
+ 
+
+ align:start position:0%
+first off if i only etch back this
+amount
+
+ align:start position:0%
+amount
+ 
+
+ align:start position:0%
+amount
+in both regions then i have not
+
+ align:start position:0%
+in both regions then i have not
+ 
+
+ align:start position:0%
+in both regions then i have not
+completely removed what i needed to in
+
+ align:start position:0%
+completely removed what i needed to in
+ 
+
+ align:start position:0%
+completely removed what i needed to in
+the other regions so i have to make sure
+
+ align:start position:0%
+the other regions so i have to make sure
+ 
+
+ align:start position:0%
+the other regions so i have to make sure
+i do enough overarch
+
+ align:start position:0%
+i do enough overarch
+ 
+
+ align:start position:0%
+i do enough overarch
+to at least clear off and make sure i
+
+ align:start position:0%
+to at least clear off and make sure i
+ 
+
+ align:start position:0%
+to at least clear off and make sure i
+don't have any shorts
+
+ align:start position:0%
+don't have any shorts
+ 
+
+ align:start position:0%
+don't have any shorts
+anywhere on the wafer and when you do
+
+ align:start position:0%
+anywhere on the wafer and when you do
+ 
+
+ align:start position:0%
+anywhere on the wafer and when you do
+that to make sure that i'm down to the
+
+ align:start position:0%
+that to make sure that i'm down to the
+ 
+
+ align:start position:0%
+that to make sure that i'm down to the
+surface
+
+ align:start position:0%
+surface
+ 
+
+ align:start position:0%
+surface
+in the thickest area you get over etch
+
+ align:start position:0%
+in the thickest area you get over etch
+ 
+
+ align:start position:0%
+in the thickest area you get over etch
+lossage
+
+ align:start position:0%
+lossage
+ 
+
+ align:start position:0%
+lossage
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+the thinnest regions so you have a
+
+ align:start position:0%
+the thinnest regions so you have a
+ 
+
+ align:start position:0%
+the thinnest regions so you have a
+fairly tight constraint then on what the
+
+ align:start position:0%
+fairly tight constraint then on what the
+ 
+
+ align:start position:0%
+fairly tight constraint then on what the
+thickness uniformity is
+
+ align:start position:0%
+thickness uniformity is
+ 
+
+ align:start position:0%
+thickness uniformity is
+as well as the etch uniformity in order
+
+ align:start position:0%
+as well as the etch uniformity in order
+ 
+
+ align:start position:0%
+as well as the etch uniformity in order
+to achieve that
+
+ align:start position:0%
+to achieve that
+ 
+
+ align:start position:0%
+to achieve that
+okay so the paper does talk a bit and in
+
+ align:start position:0%
+okay so the paper does talk a bit and in
+ 
+
+ align:start position:0%
+okay so the paper does talk a bit and in
+fact we'll see later explicitly models
+
+ align:start position:0%
+fact we'll see later explicitly models
+ 
+
+ align:start position:0%
+fact we'll see later explicitly models
+the wafer uniformity as one of the
+
+ align:start position:0%
+the wafer uniformity as one of the
+ 
+
+ align:start position:0%
+the wafer uniformity as one of the
+outputs
+
+ align:start position:0%
+outputs
+ 
+
+ align:start position:0%
+outputs
+in order to try to understand as they
+
+ align:start position:0%
+in order to try to understand as they
+ 
+
+ align:start position:0%
+in order to try to understand as they
+play with some of the process conditions
+
+ align:start position:0%
+play with some of the process conditions
+ 
+
+ align:start position:0%
+play with some of the process conditions
+how uniformity is going to be affected
+
+ align:start position:0%
+how uniformity is going to be affected
+ 
+
+ align:start position:0%
+how uniformity is going to be affected
+by their choice of these conditions
+
+ align:start position:0%
+by their choice of these conditions
+ 
+
+ align:start position:0%
+by their choice of these conditions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh there's a couple of other interesting
+
+ align:start position:0%
+uh there's a couple of other interesting
+ 
+
+ align:start position:0%
+uh there's a couple of other interesting
+aspects of plasma etchback that are
+
+ align:start position:0%
+aspects of plasma etchback that are
+ 
+
+ align:start position:0%
+aspects of plasma etchback that are
+that are important uh
+
+ align:start position:0%
+that are important uh
+ 
+
+ align:start position:0%
+that are important uh
+as well in particular help
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inform the modeling that this paper uh
+
+ align:start position:0%
+inform the modeling that this paper uh
+ 
+
+ align:start position:0%
+inform the modeling that this paper uh
+undertakes and that has to do with
+
+ align:start position:0%
+undertakes and that has to do with
+ 
+
+ align:start position:0%
+undertakes and that has to do with
+surface roughness so not only if will
+
+ align:start position:0%
+surface roughness so not only if will
+ 
+
+ align:start position:0%
+surface roughness so not only if will
+these sorts of features this topography
+
+ align:start position:0%
+these sorts of features this topography
+ 
+
+ align:start position:0%
+these sorts of features this topography
+like that little dimple there
+
+ align:start position:0%
+like that little dimple there
+ 
+
+ align:start position:0%
+like that little dimple there
+but also
+
+ align:start position:0%
+but also
+ 
+
+ align:start position:0%
+but also
+if the surface of the film the deposited
+
+ align:start position:0%
+if the surface of the film the deposited
+ 
+
+ align:start position:0%
+if the surface of the film the deposited
+film is rough
+
+ align:start position:0%
+film is rough
+ 
+
+ align:start position:0%
+film is rough
+and i do a uniform plasma etch back
+
+ align:start position:0%
+and i do a uniform plasma etch back
+ 
+
+ align:start position:0%
+and i do a uniform plasma etch back
+sort of a vertical plasma etch back
+
+ align:start position:0%
+sort of a vertical plasma etch back
+ 
+
+ align:start position:0%
+sort of a vertical plasma etch back
+that surface roughness can in fact then
+
+ align:start position:0%
+that surface roughness can in fact then
+ 
+
+ align:start position:0%
+that surface roughness can in fact then
+this is rough
+
+ align:start position:0%
+this is rough
+ 
+
+ align:start position:0%
+this is rough
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+in truth may be transmitted to the final
+
+ align:start position:0%
+in truth may be transmitted to the final
+ 
+
+ align:start position:0%
+in truth may be transmitted to the final
+surface of the of the plug
+
+ align:start position:0%
+surface of the of the plug
+ 
+
+ align:start position:0%
+surface of the of the plug
+so another important parameter that they
+
+ align:start position:0%
+so another important parameter that they
+ 
+
+ align:start position:0%
+so another important parameter that they
+will be explicitly modeling is
+
+ align:start position:0%
+will be explicitly modeling is
+ 
+
+ align:start position:0%
+will be explicitly modeling is
+tungsten the deposited tungsten
+
+ align:start position:0%
+tungsten the deposited tungsten
+ 
+
+ align:start position:0%
+tungsten the deposited tungsten
+roughness
+
+ align:start position:0%
+roughness
+ 
+
+ align:start position:0%
+roughness
+okay and generally less rough is better
+
+ align:start position:0%
+okay and generally less rough is better
+ 
+
+ align:start position:0%
+okay and generally less rough is better
+it's going to give a high better surface
+
+ align:start position:0%
+it's going to give a high better surface
+ 
+
+ align:start position:0%
+it's going to give a high better surface
+quality less prone to defects more
+
+ align:start position:0%
+quality less prone to defects more
+ 
+
+ align:start position:0%
+quality less prone to defects more
+uniform in resistance and so on
+
+ align:start position:0%
+uniform in resistance and so on
+ 
+
+ align:start position:0%
+uniform in resistance and so on
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that by the way is another reason for
+
+ align:start position:0%
+that by the way is another reason for
+ 
+
+ align:start position:0%
+that by the way is another reason for
+switching to cmp
+
+ align:start position:0%
+switching to cmp
+ 
+
+ align:start position:0%
+switching to cmp
+cmp
+
+ align:start position:0%
+cmp
+ 
+
+ align:start position:0%
+cmp
+planarizes
+
+ align:start position:0%
+planarizes
+ 
+
+ align:start position:0%
+planarizes
+can deal with not only this kind of
+
+ align:start position:0%
+can deal with not only this kind of
+ 
+
+ align:start position:0%
+can deal with not only this kind of
+surface topography
+
+ align:start position:0%
+surface topography
+ 
+
+ align:start position:0%
+surface topography
+on a large scale
+
+ align:start position:0%
+on a large scale
+ 
+
+ align:start position:0%
+on a large scale
+but it also smooths the surface on sort
+
+ align:start position:0%
+but it also smooths the surface on sort
+ 
+
+ align:start position:0%
+but it also smooths the surface on sort
+of the atomic scale and so you tend to
+
+ align:start position:0%
+of the atomic scale and so you tend to
+ 
+
+ align:start position:0%
+of the atomic scale and so you tend to
+get much
+
+ align:start position:0%
+get much
+ 
+
+ align:start position:0%
+get much
+much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+higher quality final
+
+ align:start position:0%
+higher quality final
+ 
+
+ align:start position:0%
+higher quality final
+final plugs
+
+ align:start position:0%
+final plugs
+ 
+
+ align:start position:0%
+final plugs
+okay any questions on basic tungsten
+
+ align:start position:0%
+okay any questions on basic tungsten
+ 
+
+ align:start position:0%
+okay any questions on basic tungsten
+little lesson on tungsten plugs so let's
+
+ align:start position:0%
+little lesson on tungsten plugs so let's
+ 
+
+ align:start position:0%
+little lesson on tungsten plugs so let's
+talk a little bit about the process
+
+ align:start position:0%
+talk a little bit about the process
+ 
+
+ align:start position:0%
+talk a little bit about the process
+equipment and the process parameters
+
+ align:start position:0%
+equipment and the process parameters
+ 
+
+ align:start position:0%
+equipment and the process parameters
+that are going to be in in this case
+
+ align:start position:0%
+that are going to be in in this case
+ 
+
+ align:start position:0%
+that are going to be in in this case
+study
+
+ align:start position:0%
+study
+ 
+
+ align:start position:0%
+study
+this is a schematic crocs section of an
+
+ align:start position:0%
+this is a schematic crocs section of an
+ 
+
+ align:start position:0%
+this is a schematic crocs section of an
+applied materials precision 5000 reactor
+
+ align:start position:0%
+applied materials precision 5000 reactor
+ 
+
+ align:start position:0%
+applied materials precision 5000 reactor
+configured for tungsten cbd
+
+ align:start position:0%
+configured for tungsten cbd
+ 
+
+ align:start position:0%
+configured for tungsten cbd
+by the way this is a classic tool
+
+ align:start position:0%
+by the way this is a classic tool
+ 
+
+ align:start position:0%
+by the way this is a classic tool
+the eight uh
+
+ align:start position:0%
+the eight uh
+ 
+
+ align:start position:0%
+the eight uh
+p5000
+
+ align:start position:0%
+p5000
+ 
+
+ align:start position:0%
+p5000
+a map p5000 there's one of these in the
+
+ align:start position:0%
+a map p5000 there's one of these in the
+ 
+
+ align:start position:0%
+a map p5000 there's one of these in the
+smithsonian institute
+
+ align:start position:0%
+smithsonian institute
+ 
+
+ align:start position:0%
+smithsonian institute
+it was the tool that made applied
+
+ align:start position:0%
+it was the tool that made applied
+ 
+
+ align:start position:0%
+it was the tool that made applied
+materials what it is today
+
+ align:start position:0%
+materials what it is today
+ 
+
+ align:start position:0%
+materials what it is today
+it was one of the first single wafer
+
+ align:start position:0%
+it was one of the first single wafer
+ 
+
+ align:start position:0%
+it was one of the first single wafer
+processing tools that really gave
+
+ align:start position:0%
+processing tools that really gave
+ 
+
+ align:start position:0%
+processing tools that really gave
+good control over the atmospheric
+
+ align:start position:0%
+good control over the atmospheric
+ 
+
+ align:start position:0%
+good control over the atmospheric
+conditions for deposition for etching
+
+ align:start position:0%
+conditions for deposition for etching
+ 
+
+ align:start position:0%
+conditions for deposition for etching
+these sorts of things so so
+
+ align:start position:0%
+these sorts of things so so
+ 
+
+ align:start position:0%
+these sorts of things so so
+we're seeing a glimpse back into history
+
+ align:start position:0%
+we're seeing a glimpse back into history
+ 
+
+ align:start position:0%
+we're seeing a glimpse back into history
+here even looking at this cross-section
+
+ align:start position:0%
+here even looking at this cross-section
+ 
+
+ align:start position:0%
+here even looking at this cross-section
+by the way p5000s are still in use all
+
+ align:start position:0%
+by the way p5000s are still in use all
+ 
+
+ align:start position:0%
+by the way p5000s are still in use all
+over the place
+
+ align:start position:0%
+over the place
+ 
+
+ align:start position:0%
+over the place
+we have some
+
+ align:start position:0%
+we have some
+ 
+
+ align:start position:0%
+we have some
+i guess just one in mtl
+
+ align:start position:0%
+i guess just one in mtl
+ 
+
+ align:start position:0%
+i guess just one in mtl
+i think mostly for etching
+
+ align:start position:0%
+i think mostly for etching
+ 
+
+ align:start position:0%
+i think mostly for etching
+but uh even in some fabs i i still run
+
+ align:start position:0%
+but uh even in some fabs i i still run
+ 
+
+ align:start position:0%
+but uh even in some fabs i i still run
+into them
+
+ align:start position:0%
+into them
+ 
+
+ align:start position:0%
+into them
+they've been scaled up and improved and
+
+ align:start position:0%
+they've been scaled up and improved and
+ 
+
+ align:start position:0%
+they've been scaled up and improved and
+configured you know changed in
+
+ align:start position:0%
+configured you know changed in
+ 
+
+ align:start position:0%
+configured you know changed in
+configuration uh but but they are still
+
+ align:start position:0%
+configuration uh but but they are still
+ 
+
+ align:start position:0%
+configuration uh but but they are still
+around so the basic idea here is that
+
+ align:start position:0%
+around so the basic idea here is that
+ 
+
+ align:start position:0%
+around so the basic idea here is that
+the wafer
+
+ align:start position:0%
+the wafer
+ 
+
+ align:start position:0%
+the wafer
+will sit
+
+ align:start position:0%
+will sit
+ 
+
+ align:start position:0%
+will sit
+here on a susceptor
+
+ align:start position:0%
+here on a susceptor
+ 
+
+ align:start position:0%
+here on a susceptor
+in this plasma reactor
+
+ align:start position:0%
+in this plasma reactor
+ 
+
+ align:start position:0%
+in this plasma reactor
+this low low pressure uh
+
+ align:start position:0%
+this low low pressure uh
+ 
+
+ align:start position:0%
+this low low pressure uh
+plasma reactor in fact there are usually
+
+ align:start position:0%
+plasma reactor in fact there are usually
+ 
+
+ align:start position:0%
+plasma reactor in fact there are usually
+pins uh i think three or four pins that
+
+ align:start position:0%
+pins uh i think three or four pins that
+ 
+
+ align:start position:0%
+pins uh i think three or four pins that
+hold the wafer the robot loads the wafer
+
+ align:start position:0%
+hold the wafer the robot loads the wafer
+ 
+
+ align:start position:0%
+hold the wafer the robot loads the wafer
+in onto these pins and then the pins uh
+
+ align:start position:0%
+in onto these pins and then the pins uh
+ 
+
+ align:start position:0%
+in onto these pins and then the pins uh
+these lift fingers here i guess
+
+ align:start position:0%
+these lift fingers here i guess
+ 
+
+ align:start position:0%
+these lift fingers here i guess
+recede and the wafer then sits on this
+
+ align:start position:0%
+recede and the wafer then sits on this
+ 
+
+ align:start position:0%
+recede and the wafer then sits on this
+on this susceptor the susceptor
+
+ align:start position:0%
+on this susceptor the susceptor
+ 
+
+ align:start position:0%
+on this susceptor the susceptor
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+optically heated so there are these heat
+
+ align:start position:0%
+optically heated so there are these heat
+ 
+
+ align:start position:0%
+optically heated so there are these heat
+lamps i think there's something like
+
+ align:start position:0%
+lamps i think there's something like
+ 
+
+ align:start position:0%
+lamps i think there's something like
+thousand watt
+
+ align:start position:0%
+thousand watt
+ 
+
+ align:start position:0%
+thousand watt
+heat lamps in this configuration that
+
+ align:start position:0%
+heat lamps in this configuration that
+ 
+
+ align:start position:0%
+heat lamps in this configuration that
+heat up
+
+ align:start position:0%
+heat up
+ 
+
+ align:start position:0%
+heat up
+and hold the temperature
+
+ align:start position:0%
+and hold the temperature
+ 
+
+ align:start position:0%
+and hold the temperature
+of the whole platen the whole susceptor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's then gas flow coming in from a a
+
+ align:start position:0%
+there's then gas flow coming in from a a
+ 
+
+ align:start position:0%
+there's then gas flow coming in from a a
+gas feed there's a little mixing chamber
+
+ align:start position:0%
+gas feed there's a little mixing chamber
+ 
+
+ align:start position:0%
+gas feed there's a little mixing chamber
+in here so that you can mix different
+
+ align:start position:0%
+in here so that you can mix different
+ 
+
+ align:start position:0%
+in here so that you can mix different
+combinations of different gas flows and
+
+ align:start position:0%
+combinations of different gas flows and
+ 
+
+ align:start position:0%
+combinations of different gas flows and
+then it goes through a shower head
+
+ align:start position:0%
+then it goes through a shower head
+ 
+
+ align:start position:0%
+then it goes through a shower head
+this thing right here is typically
+
+ align:start position:0%
+this thing right here is typically
+ 
+
+ align:start position:0%
+this thing right here is typically
+referred to as a shower head
+
+ align:start position:0%
+referred to as a shower head
+ 
+
+ align:start position:0%
+referred to as a shower head
+and you can imagine it's basically you
+
+ align:start position:0%
+and you can imagine it's basically you
+ 
+
+ align:start position:0%
+and you can imagine it's basically you
+know like a shower head in your shower
+
+ align:start position:0%
+know like a shower head in your shower
+ 
+
+ align:start position:0%
+know like a shower head in your shower
+it's got holes in it that basically
+
+ align:start position:0%
+it's got holes in it that basically
+ 
+
+ align:start position:0%
+it's got holes in it that basically
+allow the gases to flow through
+
+ align:start position:0%
+allow the gases to flow through
+ 
+
+ align:start position:0%
+allow the gases to flow through
+hopefully in a fairly uniform
+
+ align:start position:0%
+hopefully in a fairly uniform
+ 
+
+ align:start position:0%
+hopefully in a fairly uniform
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+across the surface of the wafer
+
+ align:start position:0%
+across the surface of the wafer
+ 
+
+ align:start position:0%
+across the surface of the wafer
+and then there's a vacuum control and a
+
+ align:start position:0%
+and then there's a vacuum control and a
+ 
+
+ align:start position:0%
+and then there's a vacuum control and a
+number of different vacuum outlets
+
+ align:start position:0%
+number of different vacuum outlets
+ 
+
+ align:start position:0%
+number of different vacuum outlets
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+for the for the gases to flow
+
+ align:start position:0%
+for the for the gases to flow
+ 
+
+ align:start position:0%
+for the for the gases to flow
+so some of the key inputs there's lots
+
+ align:start position:0%
+so some of the key inputs there's lots
+ 
+
+ align:start position:0%
+so some of the key inputs there's lots
+and lots of knobs to control on these
+
+ align:start position:0%
+and lots of knobs to control on these
+ 
+
+ align:start position:0%
+and lots of knobs to control on these
+equipment
+
+ align:start position:0%
+equipment
+ 
+
+ align:start position:0%
+equipment
+some of the key inputs that are used in
+
+ align:start position:0%
+some of the key inputs that are used in
+ 
+
+ align:start position:0%
+some of the key inputs that are used in
+this study
+
+ align:start position:0%
+this study
+ 
+
+ align:start position:0%
+this study
+in the paper that we're looking at are
+
+ align:start position:0%
+in the paper that we're looking at are
+ 
+
+ align:start position:0%
+in the paper that we're looking at are
+gap space temperature h2 pressure and
+
+ align:start position:0%
+gap space temperature h2 pressure and
+ 
+
+ align:start position:0%
+gap space temperature h2 pressure and
+wf6
+
+ align:start position:0%
+wf6
+ 
+
+ align:start position:0%
+wf6
+pressure so the gap space refers to
+
+ align:start position:0%
+pressure so the gap space refers to
+ 
+
+ align:start position:0%
+pressure so the gap space refers to
+i believe essentially the height of this
+
+ align:start position:0%
+i believe essentially the height of this
+ 
+
+ align:start position:0%
+i believe essentially the height of this
+deceptor one can play with the distance
+
+ align:start position:0%
+deceptor one can play with the distance
+ 
+
+ align:start position:0%
+deceptor one can play with the distance
+between the gas inflow and the wafer
+
+ align:start position:0%
+between the gas inflow and the wafer
+ 
+
+ align:start position:0%
+between the gas inflow and the wafer
+moving it between say two to four or
+
+ align:start position:0%
+moving it between say two to four or
+ 
+
+ align:start position:0%
+moving it between say two to four or
+five inches
+
+ align:start position:0%
+five inches
+ 
+
+ align:start position:0%
+five inches
+and that changes a number of the plasma
+
+ align:start position:0%
+and that changes a number of the plasma
+ 
+
+ align:start position:0%
+and that changes a number of the plasma
+characteristics it changes perhaps some
+
+ align:start position:0%
+characteristics it changes perhaps some
+ 
+
+ align:start position:0%
+characteristics it changes perhaps some
+of the gas flow characteristics may also
+
+ align:start position:0%
+of the gas flow characteristics may also
+ 
+
+ align:start position:0%
+of the gas flow characteristics may also
+change some of the thermal
+
+ align:start position:0%
+change some of the thermal
+ 
+
+ align:start position:0%
+change some of the thermal
+characteristics so it is a control
+
+ align:start position:0%
+characteristics so it is a control
+ 
+
+ align:start position:0%
+characteristics so it is a control
+parameter that is not entirely obvious
+
+ align:start position:0%
+parameter that is not entirely obvious
+ 
+
+ align:start position:0%
+parameter that is not entirely obvious
+up front how it affects the growth of or
+
+ align:start position:0%
+up front how it affects the growth of or
+ 
+
+ align:start position:0%
+up front how it affects the growth of or
+deposition of this this tungsten so
+
+ align:start position:0%
+deposition of this this tungsten so
+ 
+
+ align:start position:0%
+deposition of this this tungsten so
+that's going to be one of the parameters
+
+ align:start position:0%
+that's going to be one of the parameters
+ 
+
+ align:start position:0%
+that's going to be one of the parameters
+that needs to be empirically
+
+ align:start position:0%
+that needs to be empirically
+ 
+
+ align:start position:0%
+that needs to be empirically
+studied
+
+ align:start position:0%
+studied
+ 
+
+ align:start position:0%
+studied
+certainly temperature is going to have a
+
+ align:start position:0%
+certainly temperature is going to have a
+ 
+
+ align:start position:0%
+certainly temperature is going to have a
+very strong effect
+
+ align:start position:0%
+very strong effect
+ 
+
+ align:start position:0%
+very strong effect
+in this process on things like uh growth
+
+ align:start position:0%
+in this process on things like uh growth
+ 
+
+ align:start position:0%
+in this process on things like uh growth
+rate perhaps also
+
+ align:start position:0%
+rate perhaps also
+ 
+
+ align:start position:0%
+rate perhaps also
+the surface morphology or the roughness
+
+ align:start position:0%
+the surface morphology or the roughness
+ 
+
+ align:start position:0%
+the surface morphology or the roughness
+of the film the amount of incorporation
+
+ align:start position:0%
+of the film the amount of incorporation
+ 
+
+ align:start position:0%
+of the film the amount of incorporation
+of tungsten and the ultimate resistivity
+
+ align:start position:0%
+of tungsten and the ultimate resistivity
+ 
+
+ align:start position:0%
+of tungsten and the ultimate resistivity
+of the film those sorts of parameters
+
+ align:start position:0%
+of the film those sorts of parameters
+ 
+
+ align:start position:0%
+of the film those sorts of parameters
+and then both hydrogen and tungsten
+
+ align:start position:0%
+and then both hydrogen and tungsten
+ 
+
+ align:start position:0%
+and then both hydrogen and tungsten
+hexafluoride
+
+ align:start position:0%
+hexafluoride
+ 
+
+ align:start position:0%
+hexafluoride
+gas flow pressures will also be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clearly
+
+ align:start position:0%
+clearly
+ 
+
+ align:start position:0%
+clearly
+of influence in
+
+ align:start position:0%
+of influence in
+ 
+
+ align:start position:0%
+of influence in
+rate resistivity and so on
+
+ align:start position:0%
+rate resistivity and so on
+ 
+
+ align:start position:0%
+rate resistivity and so on
+so this is kind of a neat paper because
+
+ align:start position:0%
+so this is kind of a neat paper because
+ 
+
+ align:start position:0%
+so this is kind of a neat paper because
+they actually are measuring about eight
+
+ align:start position:0%
+they actually are measuring about eight
+ 
+
+ align:start position:0%
+they actually are measuring about eight
+different parameters
+
+ align:start position:0%
+different parameters
+ 
+
+ align:start position:0%
+different parameters
+and modeling each of them
+
+ align:start position:0%
+and modeling each of them
+ 
+
+ align:start position:0%
+and modeling each of them
+so it's kind of a four input eight
+
+ align:start position:0%
+so it's kind of a four input eight
+ 
+
+ align:start position:0%
+so it's kind of a four input eight
+output uh kind of doe so just to go
+
+ align:start position:0%
+output uh kind of doe so just to go
+ 
+
+ align:start position:0%
+output uh kind of doe so just to go
+through some of these parameters many of
+
+ align:start position:0%
+through some of these parameters many of
+ 
+
+ align:start position:0%
+through some of these parameters many of
+them are pretty obvious but a couple of
+
+ align:start position:0%
+them are pretty obvious but a couple of
+ 
+
+ align:start position:0%
+them are pretty obvious but a couple of
+them i want to explain a little bit more
+
+ align:start position:0%
+them i want to explain a little bit more
+ 
+
+ align:start position:0%
+them i want to explain a little bit more
+so that you
+
+ align:start position:0%
+so that you
+ 
+
+ align:start position:0%
+so that you
+have have a good feel for what they are
+
+ align:start position:0%
+have have a good feel for what they are
+ 
+
+ align:start position:0%
+have have a good feel for what they are
+deposition rate i think that's pretty
+
+ align:start position:0%
+deposition rate i think that's pretty
+ 
+
+ align:start position:0%
+deposition rate i think that's pretty
+obvious
+
+ align:start position:0%
+obvious
+ 
+
+ align:start position:0%
+obvious
+generally you would like to have a
+
+ align:start position:0%
+generally you would like to have a
+ 
+
+ align:start position:0%
+generally you would like to have a
+fairly high rate
+
+ align:start position:0%
+fairly high rate
+ 
+
+ align:start position:0%
+fairly high rate
+it's going to you know make the process
+
+ align:start position:0%
+it's going to you know make the process
+ 
+
+ align:start position:0%
+it's going to you know make the process
+time as short as possible
+
+ align:start position:0%
+time as short as possible
+ 
+
+ align:start position:0%
+time as short as possible
+efficiency in the tool use and so on
+
+ align:start position:0%
+efficiency in the tool use and so on
+ 
+
+ align:start position:0%
+efficiency in the tool use and so on
+the paper mentions wanting to have about
+
+ align:start position:0%
+the paper mentions wanting to have about
+ 
+
+ align:start position:0%
+the paper mentions wanting to have about
+500 nanometers and minute
+
+ align:start position:0%
+500 nanometers and minute
+ 
+
+ align:start position:0%
+500 nanometers and minute
+type type rates
+
+ align:start position:0%
+type type rates
+ 
+
+ align:start position:0%
+type type rates
+with these processes
+
+ align:start position:0%
+with these processes
+ 
+
+ align:start position:0%
+with these processes
+the resistivity value
+
+ align:start position:0%
+the resistivity value
+ 
+
+ align:start position:0%
+the resistivity value
+or row here
+
+ align:start position:0%
+or row here
+ 
+
+ align:start position:0%
+or row here
+generally you kind of want a low
+
+ align:start position:0%
+generally you kind of want a low
+ 
+
+ align:start position:0%
+generally you kind of want a low
+resistance or a low resistivity film
+
+ align:start position:0%
+resistance or a low resistivity film
+ 
+
+ align:start position:0%
+resistance or a low resistivity film
+an interesting twist here is depending
+
+ align:start position:0%
+an interesting twist here is depending
+ 
+
+ align:start position:0%
+an interesting twist here is depending
+on the application
+
+ align:start position:0%
+on the application
+ 
+
+ align:start position:0%
+on the application
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+the actual resistivity you want and
+
+ align:start position:0%
+the actual resistivity you want and
+ 
+
+ align:start position:0%
+the actual resistivity you want and
+whether it's all that low
+
+ align:start position:0%
+whether it's all that low
+ 
+
+ align:start position:0%
+whether it's all that low
+actually changes
+
+ align:start position:0%
+actually changes
+ 
+
+ align:start position:0%
+actually changes
+so for example if you're using it as a
+
+ align:start position:0%
+so for example if you're using it as a
+ 
+
+ align:start position:0%
+so for example if you're using it as a
+short run metal wire
+
+ align:start position:0%
+short run metal wire
+ 
+
+ align:start position:0%
+short run metal wire
+pretty much all the time low resistance
+
+ align:start position:0%
+pretty much all the time low resistance
+ 
+
+ align:start position:0%
+pretty much all the time low resistance
+is important
+
+ align:start position:0%
+is important
+ 
+
+ align:start position:0%
+is important
+but it turns out interestingly when you
+
+ align:start position:0%
+but it turns out interestingly when you
+ 
+
+ align:start position:0%
+but it turns out interestingly when you
+use tungsten plugs in conjunction with
+
+ align:start position:0%
+use tungsten plugs in conjunction with
+ 
+
+ align:start position:0%
+use tungsten plugs in conjunction with
+aluminum layers you may actually want
+
+ align:start position:0%
+aluminum layers you may actually want
+ 
+
+ align:start position:0%
+aluminum layers you may actually want
+the tungsten plug to be a little bit
+
+ align:start position:0%
+the tungsten plug to be a little bit
+ 
+
+ align:start position:0%
+the tungsten plug to be a little bit
+higher resistance than the aluminum
+
+ align:start position:0%
+higher resistance than the aluminum
+ 
+
+ align:start position:0%
+higher resistance than the aluminum
+itself so that because it's a very small
+
+ align:start position:0%
+itself so that because it's a very small
+ 
+
+ align:start position:0%
+itself so that because it's a very small
+constrained
+
+ align:start position:0%
+constrained
+ 
+
+ align:start position:0%
+constrained
+spatial area
+
+ align:start position:0%
+spatial area
+ 
+
+ align:start position:0%
+spatial area
+the higher resistance
+
+ align:start position:0%
+the higher resistance
+ 
+
+ align:start position:0%
+the higher resistance
+causes the current flow to spread out a
+
+ align:start position:0%
+causes the current flow to spread out a
+ 
+
+ align:start position:0%
+causes the current flow to spread out a
+little bit more uniformly and actually
+
+ align:start position:0%
+little bit more uniformly and actually
+ 
+
+ align:start position:0%
+little bit more uniformly and actually
+improves the reliability of these
+
+ align:start position:0%
+improves the reliability of these
+ 
+
+ align:start position:0%
+improves the reliability of these
+tungsten plugs
+
+ align:start position:0%
+tungsten plugs
+ 
+
+ align:start position:0%
+tungsten plugs
+so you'd actually like to understand
+
+ align:start position:0%
+so you'd actually like to understand
+ 
+
+ align:start position:0%
+so you'd actually like to understand
+what the resistance is and be able to
+
+ align:start position:0%
+what the resistance is and be able to
+ 
+
+ align:start position:0%
+what the resistance is and be able to
+tune that in so that's going to motivate
+
+ align:start position:0%
+tune that in so that's going to motivate
+ 
+
+ align:start position:0%
+tune that in so that's going to motivate
+some of some of the modeling that that's
+
+ align:start position:0%
+some of some of the modeling that that's
+ 
+
+ align:start position:0%
+some of some of the modeling that that's
+done here it's not always purely a lower
+
+ align:start position:0%
+done here it's not always purely a lower
+ 
+
+ align:start position:0%
+done here it's not always purely a lower
+resistance is better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rs uniformity refers to sheet resistance
+
+ align:start position:0%
+rs uniformity refers to sheet resistance
+ 
+
+ align:start position:0%
+rs uniformity refers to sheet resistance
+uniformity this is the
+
+ align:start position:0%
+uniformity this is the
+ 
+
+ align:start position:0%
+uniformity this is the
+ohms per square
+
+ align:start position:0%
+ohms per square
+ 
+
+ align:start position:0%
+ohms per square
+of of sheet resistance or
+
+ align:start position:0%
+of of sheet resistance or
+ 
+
+ align:start position:0%
+of of sheet resistance or
+but then a uniformity number calculated
+
+ align:start position:0%
+but then a uniformity number calculated
+ 
+
+ align:start position:0%
+but then a uniformity number calculated
+for that measured sheet resistance
+
+ align:start position:0%
+for that measured sheet resistance
+ 
+
+ align:start position:0%
+for that measured sheet resistance
+across the entire wafer and so you want
+
+ align:start position:0%
+across the entire wafer and so you want
+ 
+
+ align:start position:0%
+across the entire wafer and so you want
+a very good uniformity the three percent
+
+ align:start position:0%
+a very good uniformity the three percent
+ 
+
+ align:start position:0%
+a very good uniformity the three percent
+non-uniformity number is the deviation
+
+ align:start position:0%
+non-uniformity number is the deviation
+ 
+
+ align:start position:0%
+non-uniformity number is the deviation
+percentage deviation of the thickness
+
+ align:start position:0%
+percentage deviation of the thickness
+ 
+
+ align:start position:0%
+percentage deviation of the thickness
+sort of one standard deviation over mean
+
+ align:start position:0%
+sort of one standard deviation over mean
+ 
+
+ align:start position:0%
+sort of one standard deviation over mean
+is what they're referring to in here i
+
+ align:start position:0%
+is what they're referring to in here i
+ 
+
+ align:start position:0%
+is what they're referring to in here i
+believe for this uniformity
+
+ align:start position:0%
+believe for this uniformity
+ 
+
+ align:start position:0%
+believe for this uniformity
+and again one of the motivations there
+
+ align:start position:0%
+and again one of the motivations there
+ 
+
+ align:start position:0%
+and again one of the motivations there
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+uniformity in
+
+ align:start position:0%
+uniformity in
+ 
+
+ align:start position:0%
+uniformity in
+the plasma etch back you want to avoid
+
+ align:start position:0%
+the plasma etch back you want to avoid
+ 
+
+ align:start position:0%
+the plasma etch back you want to avoid
+recess of these plugs in some region
+
+ align:start position:0%
+recess of these plugs in some region
+ 
+
+ align:start position:0%
+recess of these plugs in some region
+which can make it difficult for the
+
+ align:start position:0%
+which can make it difficult for the
+ 
+
+ align:start position:0%
+which can make it difficult for the
+subsequent aluminum to reach down in and
+
+ align:start position:0%
+subsequent aluminum to reach down in and
+ 
+
+ align:start position:0%
+subsequent aluminum to reach down in and
+actually contact
+
+ align:start position:0%
+actually contact
+ 
+
+ align:start position:0%
+actually contact
+those recessed plugs
+
+ align:start position:0%
+those recessed plugs
+ 
+
+ align:start position:0%
+those recessed plugs
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh film stress is another important uh
+
+ align:start position:0%
+uh film stress is another important uh
+ 
+
+ align:start position:0%
+uh film stress is another important uh
+parameter
+
+ align:start position:0%
+parameter
+ 
+
+ align:start position:0%
+parameter
+let me see if i've got other slides on
+
+ align:start position:0%
+let me see if i've got other slides on
+ 
+
+ align:start position:0%
+let me see if i've got other slides on
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+nope not much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+essentially the uh
+
+ align:start position:0%
+essentially the uh
+ 
+
+ align:start position:0%
+essentially the uh
+there is a volumetric mismatch to the
+
+ align:start position:0%
+there is a volumetric mismatch to the
+ 
+
+ align:start position:0%
+there is a volumetric mismatch to the
+deposited tungsten compared to the
+
+ align:start position:0%
+deposited tungsten compared to the
+ 
+
+ align:start position:0%
+deposited tungsten compared to the
+underlying silicon substrate uh wafer
+
+ align:start position:0%
+underlying silicon substrate uh wafer
+ 
+
+ align:start position:0%
+underlying silicon substrate uh wafer
+and in fact what you typically find is
+
+ align:start position:0%
+and in fact what you typically find is
+ 
+
+ align:start position:0%
+and in fact what you typically find is
+that the wafer will undergo
+
+ align:start position:0%
+that the wafer will undergo
+ 
+
+ align:start position:0%
+that the wafer will undergo
+or be in tensile stress so basically
+
+ align:start position:0%
+or be in tensile stress so basically
+ 
+
+ align:start position:0%
+or be in tensile stress so basically
+there's more volume in the deposited
+
+ align:start position:0%
+there's more volume in the deposited
+ 
+
+ align:start position:0%
+there's more volume in the deposited
+film
+
+ align:start position:0%
+film
+ 
+
+ align:start position:0%
+film
+and it's
+
+ align:start position:0%
+and it's
+ 
+
+ align:start position:0%
+and it's
+causing
+
+ align:start position:0%
+causing
+ 
+
+ align:start position:0%
+causing
+a thick a you know a a
+
+ align:start position:0%
+a thick a you know a a
+ 
+
+ align:start position:0%
+a thick a you know a a
+layer depending on the thickness of of
+
+ align:start position:0%
+layer depending on the thickness of of
+ 
+
+ align:start position:0%
+layer depending on the thickness of of
+the layer in fact in the in the design
+
+ align:start position:0%
+the layer in fact in the in the design
+ 
+
+ align:start position:0%
+the layer in fact in the in the design
+they're talking about two different
+
+ align:start position:0%
+they're talking about two different
+ 
+
+ align:start position:0%
+they're talking about two different
+thicknesses that they explore that
+
+ align:start position:0%
+thicknesses that they explore that
+ 
+
+ align:start position:0%
+thicknesses that they explore that
+causes the wafer to bow
+
+ align:start position:0%
+causes the wafer to bow
+ 
+
+ align:start position:0%
+causes the wafer to bow
+so i've got a
+
+ align:start position:0%
+so i've got a
+ 
+
+ align:start position:0%
+so i've got a
+film that wants to spread out a little
+
+ align:start position:0%
+film that wants to spread out a little
+ 
+
+ align:start position:0%
+film that wants to spread out a little
+bit more
+
+ align:start position:0%
+bit more
+ 
+
+ align:start position:0%
+bit more
+especially at lower temperature compared
+
+ align:start position:0%
+especially at lower temperature compared
+ 
+
+ align:start position:0%
+especially at lower temperature compared
+to the temperature of processing
+
+ align:start position:0%
+to the temperature of processing
+ 
+
+ align:start position:0%
+to the temperature of processing
+and that wafer bow is a nice indicator
+
+ align:start position:0%
+and that wafer bow is a nice indicator
+ 
+
+ align:start position:0%
+and that wafer bow is a nice indicator
+of intrinsic internal stress in those
+
+ align:start position:0%
+of intrinsic internal stress in those
+ 
+
+ align:start position:0%
+of intrinsic internal stress in those
+films
+
+ align:start position:0%
+films
+ 
+
+ align:start position:0%
+films
+in general you don't want stress
+
+ align:start position:0%
+in general you don't want stress
+ 
+
+ align:start position:0%
+in general you don't want stress
+mismatches between different layers on
+
+ align:start position:0%
+mismatches between different layers on
+ 
+
+ align:start position:0%
+mismatches between different layers on
+your wafer
+
+ align:start position:0%
+your wafer
+ 
+
+ align:start position:0%
+your wafer
+because that means there's sort of this
+
+ align:start position:0%
+because that means there's sort of this
+ 
+
+ align:start position:0%
+because that means there's sort of this
+excess energy around that would like to
+
+ align:start position:0%
+excess energy around that would like to
+ 
+
+ align:start position:0%
+excess energy around that would like to
+release itself and one way it releases
+
+ align:start position:0%
+release itself and one way it releases
+ 
+
+ align:start position:0%
+release itself and one way it releases
+itself is by having those layers
+
+ align:start position:0%
+itself is by having those layers
+ 
+
+ align:start position:0%
+itself is by having those layers
+delaminate
+
+ align:start position:0%
+delaminate
+ 
+
+ align:start position:0%
+delaminate
+okay so a reliability concern
+
+ align:start position:0%
+okay so a reliability concern
+ 
+
+ align:start position:0%
+okay so a reliability concern
+is to try to avoid very high stresses
+
+ align:start position:0%
+is to try to avoid very high stresses
+ 
+
+ align:start position:0%
+is to try to avoid very high stresses
+in order to support subsequent
+
+ align:start position:0%
+in order to support subsequent
+ 
+
+ align:start position:0%
+in order to support subsequent
+processing and long-term reliability
+
+ align:start position:0%
+processing and long-term reliability
+ 
+
+ align:start position:0%
+processing and long-term reliability
+of the material on the wafer
+
+ align:start position:0%
+of the material on the wafer
+ 
+
+ align:start position:0%
+of the material on the wafer
+okay so they're making some measurements
+
+ align:start position:0%
+okay so they're making some measurements
+ 
+
+ align:start position:0%
+okay so they're making some measurements
+of film stress in fact the way they make
+
+ align:start position:0%
+of film stress in fact the way they make
+ 
+
+ align:start position:0%
+of film stress in fact the way they make
+this measurement i believe if i remember
+
+ align:start position:0%
+this measurement i believe if i remember
+ 
+
+ align:start position:0%
+this measurement i believe if i remember
+right is they measure the wafer bow
+
+ align:start position:0%
+right is they measure the wafer bow
+ 
+
+ align:start position:0%
+right is they measure the wafer bow
+and then based on
+
+ align:start position:0%
+and then based on
+ 
+
+ align:start position:0%
+and then based on
+assumed numbers for the modulus
+
+ align:start position:0%
+assumed numbers for the modulus
+ 
+
+ align:start position:0%
+assumed numbers for the modulus
+the young's modulus
+
+ align:start position:0%
+the young's modulus
+ 
+
+ align:start position:0%
+the young's modulus
+and perhaps the thickness they may
+
+ align:start position:0%
+and perhaps the thickness they may
+ 
+
+ align:start position:0%
+and perhaps the thickness they may
+measure the thickness separately
+
+ align:start position:0%
+measure the thickness separately
+ 
+
+ align:start position:0%
+measure the thickness separately
+they basically calculate or or estimate
+
+ align:start position:0%
+they basically calculate or or estimate
+ 
+
+ align:start position:0%
+they basically calculate or or estimate
+what the film stress stress
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in some sense at whatever temperature
+
+ align:start position:0%
+in some sense at whatever temperature
+ 
+
+ align:start position:0%
+in some sense at whatever temperature
+you're you're doing if you could deposit
+
+ align:start position:0%
+you're you're doing if you could deposit
+ 
+
+ align:start position:0%
+you're you're doing if you could deposit
+the film and keep the wafer at 300
+
+ align:start position:0%
+the film and keep the wafer at 300
+ 
+
+ align:start position:0%
+the film and keep the wafer at 300
+degrees or 100 whatever it is
+
+ align:start position:0%
+degrees or 100 whatever it is
+ 
+
+ align:start position:0%
+degrees or 100 whatever it is
+at that point in time i don't believe
+
+ align:start position:0%
+at that point in time i don't believe
+ 
+
+ align:start position:0%
+at that point in time i don't believe
+the wafer undergoes or experiences much
+
+ align:start position:0%
+the wafer undergoes or experiences much
+ 
+
+ align:start position:0%
+the wafer undergoes or experiences much
+stress during this deposition but then
+
+ align:start position:0%
+stress during this deposition but then
+ 
+
+ align:start position:0%
+stress during this deposition but then
+it's a
+
+ align:start position:0%
+it's a
+ 
+
+ align:start position:0%
+it's a
+temperature expansion difference
+
+ align:start position:0%
+temperature expansion difference
+ 
+
+ align:start position:0%
+temperature expansion difference
+i'm not entirely sure of that it's
+
+ align:start position:0%
+i'm not entirely sure of that it's
+ 
+
+ align:start position:0%
+i'm not entirely sure of that it's
+possible that the simple incorporation
+
+ align:start position:0%
+possible that the simple incorporation
+ 
+
+ align:start position:0%
+possible that the simple incorporation
+at the time
+
+ align:start position:0%
+at the time
+ 
+
+ align:start position:0%
+at the time
+of deposition
+
+ align:start position:0%
+of deposition
+ 
+
+ align:start position:0%
+of deposition
+also has some stress but really we're
+
+ align:start position:0%
+also has some stress but really we're
+ 
+
+ align:start position:0%
+also has some stress but really we're
+talking about intrinsic stress that our
+
+ align:start position:0%
+talking about intrinsic stress that our
+ 
+
+ align:start position:0%
+talking about intrinsic stress that our
+extrinsic stress that
+
+ align:start position:0%
+extrinsic stress that
+ 
+
+ align:start position:0%
+extrinsic stress that
+remains at the end of into processing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know any more on that hayden
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean there are there are situations
+
+ align:start position:0%
+i mean there are there are situations
+ 
+
+ align:start position:0%
+i mean there are there are situations
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+you're depositing
+
+ align:start position:0%
+you're depositing
+ 
+
+ align:start position:0%
+you're depositing
+you know an epitaxial layer of say a
+
+ align:start position:0%
+you know an epitaxial layer of say a
+ 
+
+ align:start position:0%
+you know an epitaxial layer of say a
+semiconductor
+
+ align:start position:0%
+semiconductor
+ 
+
+ align:start position:0%
+semiconductor
+where that has a very clearly defined
+
+ align:start position:0%
+where that has a very clearly defined
+ 
+
+ align:start position:0%
+where that has a very clearly defined
+lattice whose pitch is mismatched with
+
+ align:start position:0%
+lattice whose pitch is mismatched with
+ 
+
+ align:start position:0%
+lattice whose pitch is mismatched with
+the substrate underneath in that case
+
+ align:start position:0%
+the substrate underneath in that case
+ 
+
+ align:start position:0%
+the substrate underneath in that case
+you know there's i guess a definite
+
+ align:start position:0%
+you know there's i guess a definite
+ 
+
+ align:start position:0%
+you know there's i guess a definite
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+definite built-in stress that's going to
+
+ align:start position:0%
+definite built-in stress that's going to
+ 
+
+ align:start position:0%
+definite built-in stress that's going to
+result in that deposition that isn't
+
+ align:start position:0%
+result in that deposition that isn't
+ 
+
+ align:start position:0%
+result in that deposition that isn't
+connected with thermal contraction but i
+
+ align:start position:0%
+connected with thermal contraction but i
+ 
+
+ align:start position:0%
+connected with thermal contraction but i
+would have thought
+
+ align:start position:0%
+would have thought
+ 
+
+ align:start position:0%
+would have thought
+in this situation
+
+ align:start position:0%
+in this situation
+ 
+
+ align:start position:0%
+in this situation
+it's mostly
+
+ align:start position:0%
+it's mostly
+ 
+
+ align:start position:0%
+it's mostly
+it's mostly to do with
+
+ align:start position:0%
+it's mostly to do with
+ 
+
+ align:start position:0%
+it's mostly to do with
+you know the presence of impurities
+
+ align:start position:0%
+you know the presence of impurities
+ 
+
+ align:start position:0%
+you know the presence of impurities
+changing the cte of the deposited life
+
+ align:start position:0%
+changing the cte of the deposited life
+ 
+
+ align:start position:0%
+changing the cte of the deposited life
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+stretch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the fifth parameter that they measure
+
+ align:start position:0%
+the fifth parameter that they measure
+ 
+
+ align:start position:0%
+the fifth parameter that they measure
+and model is step coverage and so here
+
+ align:start position:0%
+and model is step coverage and so here
+ 
+
+ align:start position:0%
+and model is step coverage and so here
+that refers to
+
+ align:start position:0%
+that refers to
+ 
+
+ align:start position:0%
+that refers to
+essentially how good the deposition
+
+ align:start position:0%
+essentially how good the deposition
+ 
+
+ align:start position:0%
+essentially how good the deposition
+process is
+
+ align:start position:0%
+process is
+ 
+
+ align:start position:0%
+process is
+right here
+
+ align:start position:0%
+right here
+ 
+
+ align:start position:0%
+right here
+in filling
+
+ align:start position:0%
+in filling
+ 
+
+ align:start position:0%
+in filling
+filling these features now if all of
+
+ align:start position:0%
+filling these features now if all of
+ 
+
+ align:start position:0%
+filling these features now if all of
+your features are exactly the same size
+
+ align:start position:0%
+your features are exactly the same size
+ 
+
+ align:start position:0%
+your features are exactly the same size
+then that's that's a little bit easier
+
+ align:start position:0%
+then that's that's a little bit easier
+ 
+
+ align:start position:0%
+then that's that's a little bit easier
+so if all you're doing is filling
+
+ align:start position:0%
+so if all you're doing is filling
+ 
+
+ align:start position:0%
+so if all you're doing is filling
+contacts of exactly the same size
+
+ align:start position:0%
+contacts of exactly the same size
+ 
+
+ align:start position:0%
+contacts of exactly the same size
+then you've got a nice well-defined
+
+ align:start position:0%
+then you've got a nice well-defined
+ 
+
+ align:start position:0%
+then you've got a nice well-defined
+number for step coverage and that's
+
+ align:start position:0%
+number for step coverage and that's
+ 
+
+ align:start position:0%
+number for step coverage and that's
+really what they're doing in this
+
+ align:start position:0%
+really what they're doing in this
+ 
+
+ align:start position:0%
+really what they're doing in this
+application but i should mention that
+
+ align:start position:0%
+application but i should mention that
+ 
+
+ align:start position:0%
+application but i should mention that
+these kind of conformal depositions can
+
+ align:start position:0%
+these kind of conformal depositions can
+ 
+
+ align:start position:0%
+these kind of conformal depositions can
+actually be a very strong challenge for
+
+ align:start position:0%
+actually be a very strong challenge for
+ 
+
+ align:start position:0%
+actually be a very strong challenge for
+dealing with patterns or features of
+
+ align:start position:0%
+dealing with patterns or features of
+ 
+
+ align:start position:0%
+dealing with patterns or features of
+different sizes so you can imagine for
+
+ align:start position:0%
+different sizes so you can imagine for
+ 
+
+ align:start position:0%
+different sizes so you can imagine for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+having some contacts here
+
+ align:start position:0%
+having some contacts here
+ 
+
+ align:start position:0%
+having some contacts here
+having some structures that might in
+
+ align:start position:0%
+having some structures that might in
+ 
+
+ align:start position:0%
+having some structures that might in
+fact be lines then having some other
+
+ align:start position:0%
+fact be lines then having some other
+ 
+
+ align:start position:0%
+fact be lines then having some other
+structures that are in fact very wide
+
+ align:start position:0%
+structures that are in fact very wide
+ 
+
+ align:start position:0%
+structures that are in fact very wide
+lines
+
+ align:start position:0%
+lines
+ 
+
+ align:start position:0%
+lines
+and now if i can formally fill i might
+
+ align:start position:0%
+and now if i can formally fill i might
+ 
+
+ align:start position:0%
+and now if i can formally fill i might
+be able to fill the narrow structures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the wider ones will not necessarily
+
+ align:start position:0%
+but the wider ones will not necessarily
+ 
+
+ align:start position:0%
+but the wider ones will not necessarily
+fill completely i won't have excellent
+
+ align:start position:0%
+fill completely i won't have excellent
+ 
+
+ align:start position:0%
+fill completely i won't have excellent
+excellent step coverage now i believe
+
+ align:start position:0%
+excellent step coverage now i believe
+ 
+
+ align:start position:0%
+excellent step coverage now i believe
+what they're doing in this
+
+ align:start position:0%
+what they're doing in this
+ 
+
+ align:start position:0%
+what they're doing in this
+in this
+
+ align:start position:0%
+in this
+ 
+
+ align:start position:0%
+in this
+paper
+
+ align:start position:0%
+paper
+ 
+
+ align:start position:0%
+paper
+is really just looking locally
+
+ align:start position:0%
+is really just looking locally
+ 
+
+ align:start position:0%
+is really just looking locally
+after the deposition and looking to see
+
+ align:start position:0%
+after the deposition and looking to see
+ 
+
+ align:start position:0%
+after the deposition and looking to see
+sort of what percentage of volume
+
+ align:start position:0%
+sort of what percentage of volume
+ 
+
+ align:start position:0%
+sort of what percentage of volume
+is missing in that little in that little
+
+ align:start position:0%
+is missing in that little in that little
+ 
+
+ align:start position:0%
+is missing in that little in that little
+uh indentation resulting from the
+
+ align:start position:0%
+uh indentation resulting from the
+ 
+
+ align:start position:0%
+uh indentation resulting from the
+conformal deposition and looking for
+
+ align:start position:0%
+conformal deposition and looking for
+ 
+
+ align:start position:0%
+conformal deposition and looking for
+fairly high near 100
+
+ align:start position:0%
+fairly high near 100
+ 
+
+ align:start position:0%
+fairly high near 100
+step coverage so that there's not a
+
+ align:start position:0%
+step coverage so that there's not a
+ 
+
+ align:start position:0%
+step coverage so that there's not a
+missing percentage
+
+ align:start position:0%
+missing percentage
+ 
+
+ align:start position:0%
+missing percentage
+of the feature
+
+ align:start position:0%
+of the feature
+ 
+
+ align:start position:0%
+of the feature
+compared to say
+
+ align:start position:0%
+compared to say
+ 
+
+ align:start position:0%
+compared to say
+one of these large structures that might
+
+ align:start position:0%
+one of these large structures that might
+ 
+
+ align:start position:0%
+one of these large structures that might
+have a very high missing missing volume
+
+ align:start position:0%
+have a very high missing missing volume
+ 
+
+ align:start position:0%
+have a very high missing missing volume
+generally they're able to achieve fairly
+
+ align:start position:0%
+generally they're able to achieve fairly
+ 
+
+ align:start position:0%
+generally they're able to achieve fairly
+high
+
+ align:start position:0%
+high
+ 
+
+ align:start position:0%
+high
+step coverages so that's not one of the
+
+ align:start position:0%
+step coverages so that's not one of the
+ 
+
+ align:start position:0%
+step coverages so that's not one of the
+critical critical output parameters in
+
+ align:start position:0%
+critical critical output parameters in
+ 
+
+ align:start position:0%
+critical critical output parameters in
+this process
+
+ align:start position:0%
+this process
+ 
+
+ align:start position:0%
+this process
+now also shown on this this picture and
+
+ align:start position:0%
+now also shown on this this picture and
+ 
+
+ align:start position:0%
+now also shown on this this picture and
+maybe a little bit hard for you to see
+
+ align:start position:0%
+maybe a little bit hard for you to see
+ 
+
+ align:start position:0%
+maybe a little bit hard for you to see
+it's also in the paper but on the right
+
+ align:start position:0%
+it's also in the paper but on the right
+ 
+
+ align:start position:0%
+it's also in the paper but on the right
+you see a
+
+ align:start position:0%
+you see a
+ 
+
+ align:start position:0%
+you see a
+top-down photograph or or sem micrograph
+
+ align:start position:0%
+top-down photograph or or sem micrograph
+ 
+
+ align:start position:0%
+top-down photograph or or sem micrograph
+of the surface structure and it gives
+
+ align:start position:0%
+of the surface structure and it gives
+ 
+
+ align:start position:0%
+of the surface structure and it gives
+you a sense a little bit of two things
+
+ align:start position:0%
+you a sense a little bit of two things
+ 
+
+ align:start position:0%
+you a sense a little bit of two things
+one is there's a lot of surface
+
+ align:start position:0%
+one is there's a lot of surface
+ 
+
+ align:start position:0%
+one is there's a lot of surface
+morphology going on
+
+ align:start position:0%
+morphology going on
+ 
+
+ align:start position:0%
+morphology going on
+surface roughness but the other basic
+
+ align:start position:0%
+surface roughness but the other basic
+ 
+
+ align:start position:0%
+surface roughness but the other basic
+thing that happens is as you're
+
+ align:start position:0%
+thing that happens is as you're
+ 
+
+ align:start position:0%
+thing that happens is as you're
+depositing these uh
+
+ align:start position:0%
+depositing these uh
+ 
+
+ align:start position:0%
+depositing these uh
+these materials they are lining up in
+
+ align:start position:0%
+these materials they are lining up in
+ 
+
+ align:start position:0%
+these materials they are lining up in
+sort of a polycrystalline kind of kind
+
+ align:start position:0%
+sort of a polycrystalline kind of kind
+ 
+
+ align:start position:0%
+sort of a polycrystalline kind of kind
+of way you do get some local
+
+ align:start position:0%
+of way you do get some local
+ 
+
+ align:start position:0%
+of way you do get some local
+self-organization you can see that also
+
+ align:start position:0%
+self-organization you can see that also
+ 
+
+ align:start position:0%
+self-organization you can see that also
+over here on the on the left side if you
+
+ align:start position:0%
+over here on the on the left side if you
+ 
+
+ align:start position:0%
+over here on the on the left side if you
+kind of see there's little crystals or
+
+ align:start position:0%
+kind of see there's little crystals or
+ 
+
+ align:start position:0%
+kind of see there's little crystals or
+little threads or
+
+ align:start position:0%
+little threads or
+ 
+
+ align:start position:0%
+little threads or
+and in here you can see
+
+ align:start position:0%
+and in here you can see
+ 
+
+ align:start position:0%
+and in here you can see
+see a little bit of the polycrystalline
+
+ align:start position:0%
+see a little bit of the polycrystalline
+ 
+
+ align:start position:0%
+see a little bit of the polycrystalline
+structure and that's actually one of the
+
+ align:start position:0%
+structure and that's actually one of the
+ 
+
+ align:start position:0%
+structure and that's actually one of the
+things that gives that surface roughness
+
+ align:start position:0%
+things that gives that surface roughness
+ 
+
+ align:start position:0%
+things that gives that surface roughness
+it's not surface roughness on the atom
+
+ align:start position:0%
+it's not surface roughness on the atom
+ 
+
+ align:start position:0%
+it's not surface roughness on the atom
+by atom level it's really these
+
+ align:start position:0%
+by atom level it's really these
+ 
+
+ align:start position:0%
+by atom level it's really these
+preferential growth directions in some
+
+ align:start position:0%
+preferential growth directions in some
+ 
+
+ align:start position:0%
+preferential growth directions in some
+of these some of these grains if you
+
+ align:start position:0%
+of these some of these grains if you
+ 
+
+ align:start position:0%
+of these some of these grains if you
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+as as they're growing
+
+ align:start position:0%
+as as they're growing
+ 
+
+ align:start position:0%
+as as they're growing
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+only two or three more parameters here
+
+ align:start position:0%
+only two or three more parameters here
+ 
+
+ align:start position:0%
+only two or three more parameters here
+another one and this is kind of neat i
+
+ align:start position:0%
+another one and this is kind of neat i
+ 
+
+ align:start position:0%
+another one and this is kind of neat i
+think because it's a
+
+ align:start position:0%
+think because it's a
+ 
+
+ align:start position:0%
+think because it's a
+nice parameter that contrasts with the
+
+ align:start position:0%
+nice parameter that contrasts with the
+ 
+
+ align:start position:0%
+nice parameter that contrasts with the
+other ones the other ones are let's see
+
+ align:start position:0%
+other ones the other ones are let's see
+ 
+
+ align:start position:0%
+other ones the other ones are let's see
+most of these things like step coverage
+
+ align:start position:0%
+most of these things like step coverage
+ 
+
+ align:start position:0%
+most of these things like step coverage
+film stress uniformity resistance
+
+ align:start position:0%
+film stress uniformity resistance
+ 
+
+ align:start position:0%
+film stress uniformity resistance
+uniformity those are parameters of the
+
+ align:start position:0%
+uniformity those are parameters of the
+ 
+
+ align:start position:0%
+uniformity those are parameters of the
+final wafer or the intermediate wafer
+
+ align:start position:0%
+final wafer or the intermediate wafer
+ 
+
+ align:start position:0%
+final wafer or the intermediate wafer
+state that you want to achieve
+
+ align:start position:0%
+state that you want to achieve
+ 
+
+ align:start position:0%
+state that you want to achieve
+deposition rate and wf6 conversion are
+
+ align:start position:0%
+deposition rate and wf6 conversion are
+ 
+
+ align:start position:0%
+deposition rate and wf6 conversion are
+both more manufacturing parameters
+
+ align:start position:0%
+both more manufacturing parameters
+ 
+
+ align:start position:0%
+both more manufacturing parameters
+in some sense they don't really matter
+
+ align:start position:0%
+in some sense they don't really matter
+ 
+
+ align:start position:0%
+in some sense they don't really matter
+to the final wafer product but they can
+
+ align:start position:0%
+to the final wafer product but they can
+ 
+
+ align:start position:0%
+to the final wafer product but they can
+matter a great deal for the cost
+
+ align:start position:0%
+matter a great deal for the cost
+ 
+
+ align:start position:0%
+matter a great deal for the cost
+efficiency or the time efficiency of the
+
+ align:start position:0%
+efficiency or the time efficiency of the
+ 
+
+ align:start position:0%
+efficiency or the time efficiency of the
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+so wf6 conversion is what percentage of
+
+ align:start position:0%
+so wf6 conversion is what percentage of
+ 
+
+ align:start position:0%
+so wf6 conversion is what percentage of
+the incoming
+
+ align:start position:0%
+the incoming
+ 
+
+ align:start position:0%
+the incoming
+gas is actually resulting in
+
+ align:start position:0%
+gas is actually resulting in
+ 
+
+ align:start position:0%
+gas is actually resulting in
+the deposited film so you might have
+
+ align:start position:0%
+the deposited film so you might have
+ 
+
+ align:start position:0%
+the deposited film so you might have
+uh only you know one percent of the
+
+ align:start position:0%
+uh only you know one percent of the
+ 
+
+ align:start position:0%
+uh only you know one percent of the
+tungsten
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going on to the wafer and 99 percent
+
+ align:start position:0%
+going on to the wafer and 99 percent
+ 
+
+ align:start position:0%
+going on to the wafer and 99 percent
+going out the exhaust pipe
+
+ align:start position:0%
+going out the exhaust pipe
+ 
+
+ align:start position:0%
+going out the exhaust pipe
+that's terrible waste they have some
+
+ align:start position:0%
+that's terrible waste they have some
+ 
+
+ align:start position:0%
+that's terrible waste they have some
+environmental implications
+
+ align:start position:0%
+environmental implications
+ 
+
+ align:start position:0%
+environmental implications
+but it also uh has a lot of cost
+
+ align:start position:0%
+but it also uh has a lot of cost
+ 
+
+ align:start position:0%
+but it also uh has a lot of cost
+implications because tungsten
+
+ align:start position:0%
+implications because tungsten
+ 
+
+ align:start position:0%
+implications because tungsten
+hexafluoride is not a cheap gas
+
+ align:start position:0%
+hexafluoride is not a cheap gas
+ 
+
+ align:start position:0%
+hexafluoride is not a cheap gas
+you know very very highly purified so i
+
+ align:start position:0%
+you know very very highly purified so i
+ 
+
+ align:start position:0%
+you know very very highly purified so i
+like this paper in terms of they're
+
+ align:start position:0%
+like this paper in terms of they're
+ 
+
+ align:start position:0%
+like this paper in terms of they're
+actually trying to track and keep track
+
+ align:start position:0%
+actually trying to track and keep track
+ 
+
+ align:start position:0%
+actually trying to track and keep track
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+and model
+
+ align:start position:0%
+and model
+ 
+
+ align:start position:0%
+and model
+the ws6 conversion rate and try to
+
+ align:start position:0%
+the ws6 conversion rate and try to
+ 
+
+ align:start position:0%
+the ws6 conversion rate and try to
+optimize that
+
+ align:start position:0%
+optimize that
+ 
+
+ align:start position:0%
+optimize that
+parameter also
+
+ align:start position:0%
+parameter also
+ 
+
+ align:start position:0%
+parameter also
+then finally a couple more
+
+ align:start position:0%
+then finally a couple more
+ 
+
+ align:start position:0%
+then finally a couple more
+parameters here reflectance is basically
+
+ align:start position:0%
+parameters here reflectance is basically
+ 
+
+ align:start position:0%
+parameters here reflectance is basically
+an optical reflectance uh percentage
+
+ align:start position:0%
+an optical reflectance uh percentage
+ 
+
+ align:start position:0%
+an optical reflectance uh percentage
+light reflected uh kind of measurement
+
+ align:start position:0%
+light reflected uh kind of measurement
+ 
+
+ align:start position:0%
+light reflected uh kind of measurement
+uh of the surface
+
+ align:start position:0%
+uh of the surface
+ 
+
+ align:start position:0%
+uh of the surface
+topography so that's how they're trying
+
+ align:start position:0%
+topography so that's how they're trying
+ 
+
+ align:start position:0%
+topography so that's how they're trying
+to estimate or correlate to the
+
+ align:start position:0%
+to estimate or correlate to the
+ 
+
+ align:start position:0%
+to estimate or correlate to the
+roughness of the surface film
+
+ align:start position:0%
+roughness of the surface film
+ 
+
+ align:start position:0%
+roughness of the surface film
+and then finally another manufacturing
+
+ align:start position:0%
+and then finally another manufacturing
+ 
+
+ align:start position:0%
+and then finally another manufacturing
+parameter is
+
+ align:start position:0%
+parameter is
+ 
+
+ align:start position:0%
+parameter is
+reproducibility not just wafer
+
+ align:start position:0%
+reproducibility not just wafer
+ 
+
+ align:start position:0%
+reproducibility not just wafer
+uniformity
+
+ align:start position:0%
+uniformity
+ 
+
+ align:start position:0%
+uniformity
+you know wait for one one wafer at a
+
+ align:start position:0%
+you know wait for one one wafer at a
+ 
+
+ align:start position:0%
+you know wait for one one wafer at a
+time but wait for it to wait for
+
+ align:start position:0%
+time but wait for it to wait for
+ 
+
+ align:start position:0%
+time but wait for it to wait for
+repeatability or reproducibility of the
+
+ align:start position:0%
+repeatability or reproducibility of the
+ 
+
+ align:start position:0%
+repeatability or reproducibility of the
+process so they are actually making in
+
+ align:start position:0%
+process so they are actually making in
+ 
+
+ align:start position:0%
+process so they are actually making in
+this case i think the assumption
+
+ align:start position:0%
+this case i think the assumption
+ 
+
+ align:start position:0%
+this case i think the assumption
+that pretty much all of these processes
+
+ align:start position:0%
+that pretty much all of these processes
+ 
+
+ align:start position:0%
+that pretty much all of these processes
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more or less similarly repeatable but
+
+ align:start position:0%
+more or less similarly repeatable but
+ 
+
+ align:start position:0%
+more or less similarly repeatable but
+they want to estimate how
+
+ align:start position:0%
+they want to estimate how
+ 
+
+ align:start position:0%
+they want to estimate how
+repeatable the process is and we'll see
+
+ align:start position:0%
+repeatable the process is and we'll see
+ 
+
+ align:start position:0%
+repeatable the process is and we'll see
+that in their doe they're going to
+
+ align:start position:0%
+that in their doe they're going to
+ 
+
+ align:start position:0%
+that in their doe they're going to
+basically do some replicates
+
+ align:start position:0%
+basically do some replicates
+ 
+
+ align:start position:0%
+basically do some replicates
+at one of the design points and use that
+
+ align:start position:0%
+at one of the design points and use that
+ 
+
+ align:start position:0%
+at one of the design points and use that
+to estimate reproducibility
+
+ align:start position:0%
+to estimate reproducibility
+ 
+
+ align:start position:0%
+to estimate reproducibility
+so they're not going in and trying to
+
+ align:start position:0%
+so they're not going in and trying to
+ 
+
+ align:start position:0%
+so they're not going in and trying to
+estimate where
+
+ align:start position:0%
+estimate where
+ 
+
+ align:start position:0%
+estimate where
+the noise or the variance is minimum
+
+ align:start position:0%
+the noise or the variance is minimum
+ 
+
+ align:start position:0%
+the noise or the variance is minimum
+across their operating space they're
+
+ align:start position:0%
+across their operating space they're
+ 
+
+ align:start position:0%
+across their operating space they're
+actually assuming that that's
+
+ align:start position:0%
+actually assuming that that's
+ 
+
+ align:start position:0%
+actually assuming that that's
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+similar okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+here's what they do in the paper their
+
+ align:start position:0%
+here's what they do in the paper their
+ 
+
+ align:start position:0%
+here's what they do in the paper their
+goals are to build response service
+
+ align:start position:0%
+goals are to build response service
+ 
+
+ align:start position:0%
+goals are to build response service
+models just classic response surface
+
+ align:start position:0%
+models just classic response surface
+ 
+
+ align:start position:0%
+models just classic response surface
+models
+
+ align:start position:0%
+models
+ 
+
+ align:start position:0%
+models
+and then i as i said the reproducibility
+
+ align:start position:0%
+and then i as i said the reproducibility
+ 
+
+ align:start position:0%
+and then i as i said the reproducibility
+is really focused just on the center
+
+ align:start position:0%
+is really focused just on the center
+ 
+
+ align:start position:0%
+is really focused just on the center
+point designs
+
+ align:start position:0%
+point designs
+ 
+
+ align:start position:0%
+point designs
+and applying that throughout the entire
+
+ align:start position:0%
+and applying that throughout the entire
+ 
+
+ align:start position:0%
+and applying that throughout the entire
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+and then they want to use these response
+
+ align:start position:0%
+and then they want to use these response
+ 
+
+ align:start position:0%
+and then they want to use these response
+surface models
+
+ align:start position:0%
+surface models
+ 
+
+ align:start position:0%
+surface models
+they want to qualitatively understand
+
+ align:start position:0%
+they want to qualitatively understand
+ 
+
+ align:start position:0%
+they want to qualitatively understand
+some of the trends
+
+ align:start position:0%
+some of the trends
+ 
+
+ align:start position:0%
+some of the trends
+very good engineering use you know
+
+ align:start position:0%
+very good engineering use you know
+ 
+
+ align:start position:0%
+very good engineering use you know
+trying to understand from an engineering
+
+ align:start position:0%
+trying to understand from an engineering
+ 
+
+ align:start position:0%
+trying to understand from an engineering
+point and then they also want to use
+
+ align:start position:0%
+point and then they also want to use
+ 
+
+ align:start position:0%
+point and then they also want to use
+these models in an optimization
+
+ align:start position:0%
+these models in an optimization
+ 
+
+ align:start position:0%
+these models in an optimization
+kind of loop to try to drive towards
+
+ align:start position:0%
+kind of loop to try to drive towards
+ 
+
+ align:start position:0%
+kind of loop to try to drive towards
+satisfaction of multiple
+
+ align:start position:0%
+satisfaction of multiple
+ 
+
+ align:start position:0%
+satisfaction of multiple
+limits or goals on those
+
+ align:start position:0%
+limits or goals on those
+ 
+
+ align:start position:0%
+limits or goals on those
+what was it seven or eight uh output
+
+ align:start position:0%
+what was it seven or eight uh output
+ 
+
+ align:start position:0%
+what was it seven or eight uh output
+parameters
+
+ align:start position:0%
+parameters
+ 
+
+ align:start position:0%
+parameters
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now the paper does refer to some prior
+
+ align:start position:0%
+now the paper does refer to some prior
+ 
+
+ align:start position:0%
+now the paper does refer to some prior
+work on screening experiments in fact
+
+ align:start position:0%
+work on screening experiments in fact
+ 
+
+ align:start position:0%
+work on screening experiments in fact
+uh these uh
+
+ align:start position:0%
+uh these uh
+ 
+
+ align:start position:0%
+uh these uh
+precision 5000 tools and most fab tools
+
+ align:start position:0%
+precision 5000 tools and most fab tools
+ 
+
+ align:start position:0%
+precision 5000 tools and most fab tools
+probably have
+
+ align:start position:0%
+probably have
+ 
+
+ align:start position:0%
+probably have
+literally in some cases dozens of
+
+ align:start position:0%
+literally in some cases dozens of
+ 
+
+ align:start position:0%
+literally in some cases dozens of
+control settings some
+
+ align:start position:0%
+control settings some
+ 
+
+ align:start position:0%
+control settings some
+subset of which maybe only
+
+ align:start position:0%
+subset of which maybe only
+ 
+
+ align:start position:0%
+subset of which maybe only
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+are easily settable electronically and
+
+ align:start position:0%
+are easily settable electronically and
+ 
+
+ align:start position:0%
+are easily settable electronically and
+another 15 might be more mechanical or
+
+ align:start position:0%
+another 15 might be more mechanical or
+ 
+
+ align:start position:0%
+another 15 might be more mechanical or
+other you know more permanent
+
+ align:start position:0%
+other you know more permanent
+ 
+
+ align:start position:0%
+other you know more permanent
+adjustments but there's a huge space of
+
+ align:start position:0%
+adjustments but there's a huge space of
+ 
+
+ align:start position:0%
+adjustments but there's a huge space of
+possible parameters the paper just
+
+ align:start position:0%
+possible parameters the paper just
+ 
+
+ align:start position:0%
+possible parameters the paper just
+refers to prior screening experiments to
+
+ align:start position:0%
+refers to prior screening experiments to
+ 
+
+ align:start position:0%
+refers to prior screening experiments to
+narrow down to these four parameters so
+
+ align:start position:0%
+narrow down to these four parameters so
+ 
+
+ align:start position:0%
+narrow down to these four parameters so
+i don't want you to think that they knew
+
+ align:start position:0%
+i don't want you to think that they knew
+ 
+
+ align:start position:0%
+i don't want you to think that they knew
+automatically up front what four
+
+ align:start position:0%
+automatically up front what four
+ 
+
+ align:start position:0%
+automatically up front what four
+parameters they wanted to play with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there is a reference if you want to go
+
+ align:start position:0%
+there is a reference if you want to go
+ 
+
+ align:start position:0%
+there is a reference if you want to go
+try to track it down further for their
+
+ align:start position:0%
+try to track it down further for their
+ 
+
+ align:start position:0%
+try to track it down further for their
+prior work it's actually in some obscure
+
+ align:start position:0%
+prior work it's actually in some obscure
+ 
+
+ align:start position:0%
+prior work it's actually in some obscure
+conference thing so it's hard to hard to
+
+ align:start position:0%
+conference thing so it's hard to hard to
+ 
+
+ align:start position:0%
+conference thing so it's hard to hard to
+find um
+
+ align:start position:0%
+find um
+ 
+
+ align:start position:0%
+find um
+so the details exactly of what they did
+
+ align:start position:0%
+so the details exactly of what they did
+ 
+
+ align:start position:0%
+so the details exactly of what they did
+in their in their screening are not
+
+ align:start position:0%
+in their in their screening are not
+ 
+
+ align:start position:0%
+in their in their screening are not
+entirely clear but the point is they
+
+ align:start position:0%
+entirely clear but the point is they
+ 
+
+ align:start position:0%
+entirely clear but the point is they
+probably did something like
+
+ align:start position:0%
+probably did something like
+ 
+
+ align:start position:0%
+probably did something like
+a fractional factorial
+
+ align:start position:0%
+a fractional factorial
+ 
+
+ align:start position:0%
+a fractional factorial
+highly fractionalized factorial kind of
+
+ align:start position:0%
+highly fractionalized factorial kind of
+ 
+
+ align:start position:0%
+highly fractionalized factorial kind of
+design
+
+ align:start position:0%
+design
+ 
+
+ align:start position:0%
+design
+to explore the space of just trying to
+
+ align:start position:0%
+to explore the space of just trying to
+ 
+
+ align:start position:0%
+to explore the space of just trying to
+see what parameters are significant what
+
+ align:start position:0%
+see what parameters are significant what
+ 
+
+ align:start position:0%
+see what parameters are significant what
+influence what input parameters
+
+ align:start position:0%
+influence what input parameters
+ 
+
+ align:start position:0%
+influence what input parameters
+influence the outputs that they were
+
+ align:start position:0%
+influence the outputs that they were
+ 
+
+ align:start position:0%
+influence the outputs that they were
+of concern and then narrow that down to
+
+ align:start position:0%
+of concern and then narrow that down to
+ 
+
+ align:start position:0%
+of concern and then narrow that down to
+just these four parameters that they
+
+ align:start position:0%
+just these four parameters that they
+ 
+
+ align:start position:0%
+just these four parameters that they
+wanted to do
+
+ align:start position:0%
+wanted to do
+ 
+
+ align:start position:0%
+wanted to do
+a second set of experiments which is
+
+ align:start position:0%
+a second set of experiments which is
+ 
+
+ align:start position:0%
+a second set of experiments which is
+what's in this in this paper that are
+
+ align:start position:0%
+what's in this in this paper that are
+ 
+
+ align:start position:0%
+what's in this in this paper that are
+focused on response surface modeling
+
+ align:start position:0%
+focused on response surface modeling
+ 
+
+ align:start position:0%
+focused on response surface modeling
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+there's another
+
+ align:start position:0%
+there's another
+ 
+
+ align:start position:0%
+there's another
+interesting subtle point that
+
+ align:start position:0%
+interesting subtle point that
+ 
+
+ align:start position:0%
+interesting subtle point that
+pops up in the in the description of the
+
+ align:start position:0%
+pops up in the in the description of the
+ 
+
+ align:start position:0%
+pops up in the in the description of the
+paper
+
+ align:start position:0%
+paper
+ 
+
+ align:start position:0%
+paper
+some of these parameters things like
+
+ align:start position:0%
+some of these parameters things like
+ 
+
+ align:start position:0%
+some of these parameters things like
+sheet resistance sheet resistance is
+
+ align:start position:0%
+sheet resistance sheet resistance is
+ 
+
+ align:start position:0%
+sheet resistance sheet resistance is
+resistivity
+
+ align:start position:0%
+resistivity
+ 
+
+ align:start position:0%
+resistivity
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is it divided by
+
+ align:start position:0%
+is it divided by
+ 
+
+ align:start position:0%
+is it divided by
+per square resistivity the the pure
+
+ align:start position:0%
+per square resistivity the the pure
+ 
+
+ align:start position:0%
+per square resistivity the the pure
+resistivity divided by the thickness
+
+ align:start position:0%
+resistivity divided by the thickness
+ 
+
+ align:start position:0%
+resistivity divided by the thickness
+uh of the film
+
+ align:start position:0%
+uh of the film
+ 
+
+ align:start position:0%
+uh of the film
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that the thickness of the deposited
+
+ align:start position:0%
+so that the thickness of the deposited
+ 
+
+ align:start position:0%
+so that the thickness of the deposited
+film will change the rs measure
+
+ align:start position:0%
+film will change the rs measure
+ 
+
+ align:start position:0%
+film will change the rs measure
+on the wafer okay
+
+ align:start position:0%
+on the wafer okay
+ 
+
+ align:start position:0%
+on the wafer okay
+what that means is to do a fair
+
+ align:start position:0%
+what that means is to do a fair
+ 
+
+ align:start position:0%
+what that means is to do a fair
+comparison just of truly the resistivity
+
+ align:start position:0%
+comparison just of truly the resistivity
+ 
+
+ align:start position:0%
+comparison just of truly the resistivity
+of the film
+
+ align:start position:0%
+of the film
+ 
+
+ align:start position:0%
+of the film
+and uh or to estimate that you actually
+
+ align:start position:0%
+and uh or to estimate that you actually
+ 
+
+ align:start position:0%
+and uh or to estimate that you actually
+want to grow
+
+ align:start position:0%
+want to grow
+ 
+
+ align:start position:0%
+want to grow
+all of your films to about the same
+
+ align:start position:0%
+all of your films to about the same
+ 
+
+ align:start position:0%
+all of your films to about the same
+thickness
+
+ align:start position:0%
+thickness
+ 
+
+ align:start position:0%
+thickness
+well if the deposition rate is a
+
+ align:start position:0%
+well if the deposition rate is a
+ 
+
+ align:start position:0%
+well if the deposition rate is a
+parameter that you don't necessarily
+
+ align:start position:0%
+parameter that you don't necessarily
+ 
+
+ align:start position:0%
+parameter that you don't necessarily
+know and you're trying to model how do
+
+ align:start position:0%
+know and you're trying to model how do
+ 
+
+ align:start position:0%
+know and you're trying to model how do
+you do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in other words if i run for a fixed
+
+ align:start position:0%
+so in other words if i run for a fixed
+ 
+
+ align:start position:0%
+so in other words if i run for a fixed
+period of time maybe i run for 60
+
+ align:start position:0%
+period of time maybe i run for 60
+ 
+
+ align:start position:0%
+period of time maybe i run for 60
+seconds on each of these design points
+
+ align:start position:0%
+seconds on each of these design points
+ 
+
+ align:start position:0%
+seconds on each of these design points
+but i have deposition rates that are
+
+ align:start position:0%
+but i have deposition rates that are
+ 
+
+ align:start position:0%
+but i have deposition rates that are
+different by a factor of 2 5 10 i'm
+
+ align:start position:0%
+different by a factor of 2 5 10 i'm
+ 
+
+ align:start position:0%
+different by a factor of 2 5 10 i'm
+going to get widely varying thicknesses
+
+ align:start position:0%
+going to get widely varying thicknesses
+ 
+
+ align:start position:0%
+going to get widely varying thicknesses
+and therefore when i make some of these
+
+ align:start position:0%
+and therefore when i make some of these
+ 
+
+ align:start position:0%
+and therefore when i make some of these
+simple sheet resistance measurements
+
+ align:start position:0%
+simple sheet resistance measurements
+ 
+
+ align:start position:0%
+simple sheet resistance measurements
+that's that's going to be very very
+
+ align:start position:0%
+that's that's going to be very very
+ 
+
+ align:start position:0%
+that's that's going to be very very
+tricky
+
+ align:start position:0%
+tricky
+ 
+
+ align:start position:0%
+tricky
+furthermore if if my thickness is
+
+ align:start position:0%
+furthermore if if my thickness is
+ 
+
+ align:start position:0%
+furthermore if if my thickness is
+varying
+
+ align:start position:0%
+varying
+ 
+
+ align:start position:0%
+varying
+that makes it basis for comparison of
+
+ align:start position:0%
+that makes it basis for comparison of
+ 
+
+ align:start position:0%
+that makes it basis for comparison of
+many of these other parameters really
+
+ align:start position:0%
+many of these other parameters really
+ 
+
+ align:start position:0%
+many of these other parameters really
+hard
+
+ align:start position:0%
+hard
+ 
+
+ align:start position:0%
+hard
+how about film stress
+
+ align:start position:0%
+how about film stress
+ 
+
+ align:start position:0%
+how about film stress
+well is it a film stress that i'm seeing
+
+ align:start position:0%
+well is it a film stress that i'm seeing
+ 
+
+ align:start position:0%
+well is it a film stress that i'm seeing
+because of the thickness difference or
+
+ align:start position:0%
+because of the thickness difference or
+ 
+
+ align:start position:0%
+because of the thickness difference or
+is it truly intrinsic film stress in the
+
+ align:start position:0%
+is it truly intrinsic film stress in the
+ 
+
+ align:start position:0%
+is it truly intrinsic film stress in the
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+the layer
+
+ align:start position:0%
+the layer
+ 
+
+ align:start position:0%
+the layer
+so what they've done is been and i think
+
+ align:start position:0%
+so what they've done is been and i think
+ 
+
+ align:start position:0%
+so what they've done is been and i think
+this is very cool they were very careful
+
+ align:start position:0%
+this is very cool they were very careful
+ 
+
+ align:start position:0%
+this is very cool they were very careful
+and they
+
+ align:start position:0%
+and they
+ 
+
+ align:start position:0%
+and they
+say that they are doing this to where
+
+ align:start position:0%
+say that they are doing this to where
+ 
+
+ align:start position:0%
+say that they are doing this to where
+all films are grown to about one micron
+
+ align:start position:0%
+all films are grown to about one micron
+ 
+
+ align:start position:0%
+all films are grown to about one micron
+thickness in this
+
+ align:start position:0%
+thickness in this
+ 
+
+ align:start position:0%
+thickness in this
+doe what's sneaky is i think to actually
+
+ align:start position:0%
+doe what's sneaky is i think to actually
+ 
+
+ align:start position:0%
+doe what's sneaky is i think to actually
+do this
+
+ align:start position:0%
+do this
+ 
+
+ align:start position:0%
+do this
+which is also good because that
+
+ align:start position:0%
+which is also good because that
+ 
+
+ align:start position:0%
+which is also good because that
+is really the the thickness that's close
+
+ align:start position:0%
+is really the the thickness that's close
+ 
+
+ align:start position:0%
+is really the the thickness that's close
+to their target application
+
+ align:start position:0%
+to their target application
+ 
+
+ align:start position:0%
+to their target application
+what's what's a little bit sneaky is to
+
+ align:start position:0%
+what's what's a little bit sneaky is to
+ 
+
+ align:start position:0%
+what's what's a little bit sneaky is to
+do that i think they basically had to do
+
+ align:start position:0%
+do that i think they basically had to do
+ 
+
+ align:start position:0%
+do that i think they basically had to do
+prior runs maybe at each individual voe
+
+ align:start position:0%
+prior runs maybe at each individual voe
+ 
+
+ align:start position:0%
+prior runs maybe at each individual voe
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+do the run
+
+ align:start position:0%
+do the run
+ 
+
+ align:start position:0%
+do the run
+measure the thickness
+
+ align:start position:0%
+measure the thickness
+ 
+
+ align:start position:0%
+measure the thickness
+estimate the growth rate
+
+ align:start position:0%
+estimate the growth rate
+ 
+
+ align:start position:0%
+estimate the growth rate
+and then adjust the time for the real
+
+ align:start position:0%
+and then adjust the time for the real
+ 
+
+ align:start position:0%
+and then adjust the time for the real
+doe run
+
+ align:start position:0%
+doe run
+ 
+
+ align:start position:0%
+doe run
+on each of the design points so i think
+
+ align:start position:0%
+on each of the design points so i think
+ 
+
+ align:start position:0%
+on each of the design points so i think
+that there's a whole extra duplicate set
+
+ align:start position:0%
+that there's a whole extra duplicate set
+ 
+
+ align:start position:0%
+that there's a whole extra duplicate set
+of experiments that they're not talking
+
+ align:start position:0%
+of experiments that they're not talking
+ 
+
+ align:start position:0%
+of experiments that they're not talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+that that that were done in order to be
+
+ align:start position:0%
+that that that were done in order to be
+ 
+
+ align:start position:0%
+that that that were done in order to be
+able to normalize
+
+ align:start position:0%
+able to normalize
+ 
+
+ align:start position:0%
+able to normalize
+and get a very nice
+
+ align:start position:0%
+and get a very nice
+ 
+
+ align:start position:0%
+and get a very nice
+set of experiments in here
+
+ align:start position:0%
+set of experiments in here
+ 
+
+ align:start position:0%
+set of experiments in here
+that they could talk about and be able
+
+ align:start position:0%
+that they could talk about and be able
+ 
+
+ align:start position:0%
+that they could talk about and be able
+to use to use
+
+ align:start position:0%
+to use to use
+ 
+
+ align:start position:0%
+to use to use
+to make the right kinds of optimization
+
+ align:start position:0%
+to make the right kinds of optimization
+ 
+
+ align:start position:0%
+to make the right kinds of optimization
+and judgment
+
+ align:start position:0%
+and judgment
+ 
+
+ align:start position:0%
+and judgment
+so it's kind of an interesting lesson i
+
+ align:start position:0%
+so it's kind of an interesting lesson i
+ 
+
+ align:start position:0%
+so it's kind of an interesting lesson i
+think there may often be additional
+
+ align:start position:0%
+think there may often be additional
+ 
+
+ align:start position:0%
+think there may often be additional
+experimentation around
+
+ align:start position:0%
+experimentation around
+ 
+
+ align:start position:0%
+experimentation around
+your main doe that you have to do in
+
+ align:start position:0%
+your main doe that you have to do in
+ 
+
+ align:start position:0%
+your main doe that you have to do in
+order for your main doe to really be a
+
+ align:start position:0%
+order for your main doe to really be a
+ 
+
+ align:start position:0%
+order for your main doe to really be a
+good clean
+
+ align:start position:0%
+good clean
+ 
+
+ align:start position:0%
+good clean
+doe
+
+ align:start position:0%
+doe
+ 
+
+ align:start position:0%
+doe
+now it's possible that maybe
+
+ align:start position:0%
+now it's possible that maybe
+ 
+
+ align:start position:0%
+now it's possible that maybe
+their screening experiment gave them
+
+ align:start position:0%
+their screening experiment gave them
+ 
+
+ align:start position:0%
+their screening experiment gave them
+some information to be able to do a
+
+ align:start position:0%
+some information to be able to do a
+ 
+
+ align:start position:0%
+some information to be able to do a
+rough estimate a good enough estimate of
+
+ align:start position:0%
+rough estimate a good enough estimate of
+ 
+
+ align:start position:0%
+rough estimate a good enough estimate of
+deposition rate so it's possible they
+
+ align:start position:0%
+deposition rate so it's possible they
+ 
+
+ align:start position:0%
+deposition rate so it's possible they
+were able to get that benefit from from
+
+ align:start position:0%
+were able to get that benefit from from
+ 
+
+ align:start position:0%
+were able to get that benefit from from
+their prior screening doe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay here's their experimental design
+
+ align:start position:0%
+okay here's their experimental design
+ 
+
+ align:start position:0%
+okay here's their experimental design
+what they're going to do is a central
+
+ align:start position:0%
+what they're going to do is a central
+ 
+
+ align:start position:0%
+what they're going to do is a central
+composite with five levels
+
+ align:start position:0%
+composite with five levels
+ 
+
+ align:start position:0%
+composite with five levels
+at each
+
+ align:start position:0%
+at each
+ 
+
+ align:start position:0%
+at each
+design point which is pretty cool i
+
+ align:start position:0%
+design point which is pretty cool i
+ 
+
+ align:start position:0%
+design point which is pretty cool i
+think that's better than the three
+
+ align:start position:0%
+think that's better than the three
+ 
+
+ align:start position:0%
+think that's better than the three
+levels
+
+ align:start position:0%
+levels
+ 
+
+ align:start position:0%
+levels
+what's one reason that you might like
+
+ align:start position:0%
+what's one reason that you might like
+ 
+
+ align:start position:0%
+what's one reason that you might like
+five levels
+
+ align:start position:0%
+five levels
+ 
+
+ align:start position:0%
+five levels
+rather than three especially if you want
+
+ align:start position:0%
+rather than three especially if you want
+ 
+
+ align:start position:0%
+rather than three especially if you want
+to build say quadratic response surface
+
+ align:start position:0%
+to build say quadratic response surface
+ 
+
+ align:start position:0%
+to build say quadratic response surface
+models
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we haven't explicitly done this before
+
+ align:start position:0%
+we haven't explicitly done this before
+ 
+
+ align:start position:0%
+we haven't explicitly done this before
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+for example on on on quiz 2
+
+ align:start position:0%
+for example on on on quiz 2
+ 
+
+ align:start position:0%
+for example on on on quiz 2
+you're going from a linear model to a
+
+ align:start position:0%
+you're going from a linear model to a
+ 
+
+ align:start position:0%
+you're going from a linear model to a
+quadratic model and asking questions
+
+ align:start position:0%
+quadratic model and asking questions
+ 
+
+ align:start position:0%
+quadratic model and asking questions
+about lack of fit
+
+ align:start position:0%
+about lack of fit
+ 
+
+ align:start position:0%
+about lack of fit
+in order to say whether a linear model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+had lack of fit i needed a third design
+
+ align:start position:0%
+had lack of fit i needed a third design
+ 
+
+ align:start position:0%
+had lack of fit i needed a third design
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+right so that i could say well
+
+ align:start position:0%
+right so that i could say well
+ 
+
+ align:start position:0%
+right so that i could say well
+does that third design point give me
+
+ align:start position:0%
+does that third design point give me
+ 
+
+ align:start position:0%
+does that third design point give me
+indication that the linear model was not
+
+ align:start position:0%
+indication that the linear model was not
+ 
+
+ align:start position:0%
+indication that the linear model was not
+sufficient if i do three levels
+
+ align:start position:0%
+sufficient if i do three levels
+ 
+
+ align:start position:0%
+sufficient if i do three levels
+and build a quadratic model
+
+ align:start position:0%
+and build a quadratic model
+ 
+
+ align:start position:0%
+and build a quadratic model
+and i want to ask the question is a
+
+ align:start position:0%
+and i want to ask the question is a
+ 
+
+ align:start position:0%
+and i want to ask the question is a
+quadratic model sufficient
+
+ align:start position:0%
+quadratic model sufficient
+ 
+
+ align:start position:0%
+quadratic model sufficient
+or is there lack of fit in the quadratic
+
+ align:start position:0%
+or is there lack of fit in the quadratic
+ 
+
+ align:start position:0%
+or is there lack of fit in the quadratic
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+can i do that
+
+ align:start position:0%
+can i do that
+ 
+
+ align:start position:0%
+can i do that
+with just three
+
+ align:start position:0%
+with just three
+ 
+
+ align:start position:0%
+with just three
+data points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no right you can fit a quadratic two to
+
+ align:start position:0%
+no right you can fit a quadratic two to
+ 
+
+ align:start position:0%
+no right you can fit a quadratic two to
+three data points so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you won't detect if there's some other
+
+ align:start position:0%
+you won't detect if there's some other
+ 
+
+ align:start position:0%
+you won't detect if there's some other
+structure going on so in order to be
+
+ align:start position:0%
+structure going on so in order to be
+ 
+
+ align:start position:0%
+structure going on so in order to be
+able to do a lack of fit analysis up to
+
+ align:start position:0%
+able to do a lack of fit analysis up to
+ 
+
+ align:start position:0%
+able to do a lack of fit analysis up to
+seeing if a quadratic model exhibits
+
+ align:start position:0%
+seeing if a quadratic model exhibits
+ 
+
+ align:start position:0%
+seeing if a quadratic model exhibits
+then you need at least additional levels
+
+ align:start position:0%
+then you need at least additional levels
+ 
+
+ align:start position:0%
+then you need at least additional levels
+implicitly somewhere in the design so
+
+ align:start position:0%
+implicitly somewhere in the design so
+ 
+
+ align:start position:0%
+implicitly somewhere in the design so
+that's kind of a neat a neat thing that
+
+ align:start position:0%
+that's kind of a neat a neat thing that
+ 
+
+ align:start position:0%
+that's kind of a neat a neat thing that
+they do here
+
+ align:start position:0%
+they do here
+ 
+
+ align:start position:0%
+they do here
+so what they've done is normalized all
+
+ align:start position:0%
+so what they've done is normalized all
+ 
+
+ align:start position:0%
+so what they've done is normalized all
+of their factors their five five four
+
+ align:start position:0%
+of their factors their five five four
+ 
+
+ align:start position:0%
+of their factors their five five four
+factors here space temperature and so on
+
+ align:start position:0%
+factors here space temperature and so on
+ 
+
+ align:start position:0%
+factors here space temperature and so on
+again not just two in our in their case
+
+ align:start position:0%
+again not just two in our in their case
+ 
+
+ align:start position:0%
+again not just two in our in their case
+not just to a minus one plus one but uh
+
+ align:start position:0%
+not just to a minus one plus one but uh
+ 
+
+ align:start position:0%
+not just to a minus one plus one but uh
+they use with their five levels a minus
+
+ align:start position:0%
+they use with their five levels a minus
+ 
+
+ align:start position:0%
+they use with their five levels a minus
+two to plus two normalization but
+
+ align:start position:0%
+two to plus two normalization but
+ 
+
+ align:start position:0%
+two to plus two normalization but
+essentially they're doing five up to
+
+ align:start position:0%
+essentially they're doing five up to
+ 
+
+ align:start position:0%
+essentially they're doing five up to
+five levels
+
+ align:start position:0%
+five levels
+ 
+
+ align:start position:0%
+five levels
+on each of their parameters and so
+
+ align:start position:0%
+on each of their parameters and so
+ 
+
+ align:start position:0%
+on each of their parameters and so
+they're using coded variables that we'll
+
+ align:start position:0%
+they're using coded variables that we'll
+ 
+
+ align:start position:0%
+they're using coded variables that we'll
+see in the later
+
+ align:start position:0%
+see in the later
+ 
+
+ align:start position:0%
+see in the later
+tables just like
+
+ align:start position:0%
+tables just like
+ 
+
+ align:start position:0%
+tables just like
+we're used to
+
+ align:start position:0%
+we're used to
+ 
+
+ align:start position:0%
+we're used to
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+of course the other benefit of doing a
+
+ align:start position:0%
+of course the other benefit of doing a
+ 
+
+ align:start position:0%
+of course the other benefit of doing a
+screening experiment
+
+ align:start position:0%
+screening experiment
+ 
+
+ align:start position:0%
+screening experiment
+is that also helps give you some
+
+ align:start position:0%
+is that also helps give you some
+ 
+
+ align:start position:0%
+is that also helps give you some
+information about reasonable design
+
+ align:start position:0%
+information about reasonable design
+ 
+
+ align:start position:0%
+information about reasonable design
+space for picking the range that you
+
+ align:start position:0%
+space for picking the range that you
+ 
+
+ align:start position:0%
+space for picking the range that you
+want to explore these parameters in
+
+ align:start position:0%
+want to explore these parameters in
+ 
+
+ align:start position:0%
+want to explore these parameters in
+otherwise they probably would have had
+
+ align:start position:0%
+otherwise they probably would have had
+ 
+
+ align:start position:0%
+otherwise they probably would have had
+to just go by by
+
+ align:start position:0%
+to just go by by
+ 
+
+ align:start position:0%
+to just go by by
+prior experience
+
+ align:start position:0%
+prior experience
+ 
+
+ align:start position:0%
+prior experience
+that's another advantage of doing sort
+
+ align:start position:0%
+that's another advantage of doing sort
+ 
+
+ align:start position:0%
+that's another advantage of doing sort
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+two-stage experimentation with screening
+
+ align:start position:0%
+two-stage experimentation with screening
+ 
+
+ align:start position:0%
+two-stage experimentation with screening
+followed by a more extensive
+
+ align:start position:0%
+followed by a more extensive
+ 
+
+ align:start position:0%
+followed by a more extensive
+either a new doe or adding to the
+
+ align:start position:0%
+either a new doe or adding to the
+ 
+
+ align:start position:0%
+either a new doe or adding to the
+screening doe
+
+ align:start position:0%
+screening doe
+ 
+
+ align:start position:0%
+screening doe
+so they're going to be building second
+
+ align:start position:0%
+so they're going to be building second
+ 
+
+ align:start position:0%
+so they're going to be building second
+order polynomial models that is to say
+
+ align:start position:0%
+order polynomial models that is to say
+ 
+
+ align:start position:0%
+order polynomial models that is to say
+quadratic models with both
+
+ align:start position:0%
+quadratic models with both
+ 
+
+ align:start position:0%
+quadratic models with both
+interactions and then square terms
+
+ align:start position:0%
+interactions and then square terms
+ 
+
+ align:start position:0%
+interactions and then square terms
+just square terms
+
+ align:start position:0%
+just square terms
+ 
+
+ align:start position:0%
+just square terms
+in individual parameters
+
+ align:start position:0%
+in individual parameters
+ 
+
+ align:start position:0%
+in individual parameters
+they also mentioned that they're not
+
+ align:start position:0%
+they also mentioned that they're not
+ 
+
+ align:start position:0%
+they also mentioned that they're not
+going to do any transformations of the
+
+ align:start position:0%
+going to do any transformations of the
+ 
+
+ align:start position:0%
+going to do any transformations of the
+output
+
+ align:start position:0%
+output
+ 
+
+ align:start position:0%
+output
+variables such as a log or an inverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we've already talked i think
+
+ align:start position:0%
+okay so we've already talked i think
+ 
+
+ align:start position:0%
+okay so we've already talked i think
+about those two those two points so in
+
+ align:start position:0%
+about those two those two points so in
+ 
+
+ align:start position:0%
+about those two those two points so in
+the in the paper they show the the
+
+ align:start position:0%
+the in the paper they show the the
+ 
+
+ align:start position:0%
+the in the paper they show the the
+variable uh test levels coded here's
+
+ align:start position:0%
+variable uh test levels coded here's
+ 
+
+ align:start position:0%
+variable uh test levels coded here's
+again our four inputs and the trials
+
+ align:start position:0%
+again our four inputs and the trials
+ 
+
+ align:start position:0%
+again our four inputs and the trials
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+if you look you can start to get a very
+
+ align:start position:0%
+if you look you can start to get a very
+ 
+
+ align:start position:0%
+if you look you can start to get a very
+nice sense of what this central
+
+ align:start position:0%
+nice sense of what this central
+ 
+
+ align:start position:0%
+nice sense of what this central
+composite looks like
+
+ align:start position:0%
+composite looks like
+ 
+
+ align:start position:0%
+composite looks like
+what they're essentially doing here
+
+ align:start position:0%
+what they're essentially doing here
+ 
+
+ align:start position:0%
+what they're essentially doing here
+breaking it up into let's call it three
+
+ align:start position:0%
+breaking it up into let's call it three
+ 
+
+ align:start position:0%
+breaking it up into let's call it three
+different segments
+
+ align:start position:0%
+different segments
+ 
+
+ align:start position:0%
+different segments
+of of design points
+
+ align:start position:0%
+of of design points
+ 
+
+ align:start position:0%
+of of design points
+what are these design points what do
+
+ align:start position:0%
+what are these design points what do
+ 
+
+ align:start position:0%
+what are these design points what do
+those correspond to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a term we refer to those kind of
+
+ align:start position:0%
+there's a term we refer to those kind of
+ 
+
+ align:start position:0%
+there's a term we refer to those kind of
+design points as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where does one of those design points
+
+ align:start position:0%
+where does one of those design points
+ 
+
+ align:start position:0%
+where does one of those design points
+lie
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take trial number one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right it's way out minus two on the
+
+ align:start position:0%
+right it's way out minus two on the
+ 
+
+ align:start position:0%
+right it's way out minus two on the
+space axis
+
+ align:start position:0%
+space axis
+ 
+
+ align:start position:0%
+space axis
+and holding the others at their median
+
+ align:start position:0%
+and holding the others at their median
+ 
+
+ align:start position:0%
+and holding the others at their median
+or their their nominal value right
+
+ align:start position:0%
+or their their nominal value right
+ 
+
+ align:start position:0%
+or their their nominal value right
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+out on the end of one of the axes
+
+ align:start position:0%
+out on the end of one of the axes
+ 
+
+ align:start position:0%
+out on the end of one of the axes
+then the plus two minus two that's the
+
+ align:start position:0%
+then the plus two minus two that's the
+ 
+
+ align:start position:0%
+then the plus two minus two that's the
+other end of this so those are our axial
+
+ align:start position:0%
+other end of this so those are our axial
+ 
+
+ align:start position:0%
+other end of this so those are our axial
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+in a central composite design
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're sort of the classic hold
+
+ align:start position:0%
+they're sort of the classic hold
+ 
+
+ align:start position:0%
+they're sort of the classic hold
+everything else constant vary one
+
+ align:start position:0%
+everything else constant vary one
+ 
+
+ align:start position:0%
+everything else constant vary one
+parameter at a time so they are giving
+
+ align:start position:0%
+parameter at a time so they are giving
+ 
+
+ align:start position:0%
+parameter at a time so they are giving
+you unambiguous sense of what that one
+
+ align:start position:0%
+you unambiguous sense of what that one
+ 
+
+ align:start position:0%
+you unambiguous sense of what that one
+parameter is doing but not able to
+
+ align:start position:0%
+parameter is doing but not able to
+ 
+
+ align:start position:0%
+parameter is doing but not able to
+capture interactions and so on they're
+
+ align:start position:0%
+capture interactions and so on they're
+ 
+
+ align:start position:0%
+capture interactions and so on they're
+also exploring sort of the outer limits
+
+ align:start position:0%
+also exploring sort of the outer limits
+ 
+
+ align:start position:0%
+also exploring sort of the outer limits
+of the design
+
+ align:start position:0%
+of the design
+ 
+
+ align:start position:0%
+of the design
+how about these points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many of them are there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+looks like there's 16 of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+corner points exactly
+
+ align:start position:0%
+corner points exactly
+ 
+
+ align:start position:0%
+corner points exactly
+so those are all corner combinations of
+
+ align:start position:0%
+so those are all corner combinations of
+ 
+
+ align:start position:0%
+so those are all corner combinations of
+four parameters
+
+ align:start position:0%
+four parameters
+ 
+
+ align:start position:0%
+four parameters
+four squared 16 different corners
+
+ align:start position:0%
+four squared 16 different corners
+ 
+
+ align:start position:0%
+four squared 16 different corners
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then finally these
+
+ align:start position:0%
+and then finally these
+ 
+
+ align:start position:0%
+and then finally these
+these are easy what are these
+
+ align:start position:0%
+these are easy what are these
+ 
+
+ align:start position:0%
+these are easy what are these
+center points right
+
+ align:start position:0%
+center points right
+ 
+
+ align:start position:0%
+center points right
+and so i don't know whether they have
+
+ align:start position:0%
+and so i don't know whether they have
+ 
+
+ align:start position:0%
+and so i don't know whether they have
+seven seven replicates
+
+ align:start position:0%
+seven seven replicates
+ 
+
+ align:start position:0%
+seven seven replicates
+so the other points are unreplicated
+
+ align:start position:0%
+so the other points are unreplicated
+ 
+
+ align:start position:0%
+so the other points are unreplicated
+by the way so you might be a little bit
+
+ align:start position:0%
+by the way so you might be a little bit
+ 
+
+ align:start position:0%
+by the way so you might be a little bit
+susceptible to to outliers in some of
+
+ align:start position:0%
+susceptible to to outliers in some of
+ 
+
+ align:start position:0%
+susceptible to to outliers in some of
+the other points but they have a fairly
+
+ align:start position:0%
+the other points but they have a fairly
+ 
+
+ align:start position:0%
+the other points but they have a fairly
+reasonable number seven replicates at
+
+ align:start position:0%
+reasonable number seven replicates at
+ 
+
+ align:start position:0%
+reasonable number seven replicates at
+the center so that'll allow some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more or less reasonable estimate of some
+
+ align:start position:0%
+more or less reasonable estimate of some
+ 
+
+ align:start position:0%
+more or less reasonable estimate of some
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+reproducibility some of the inherent
+
+ align:start position:0%
+reproducibility some of the inherent
+ 
+
+ align:start position:0%
+reproducibility some of the inherent
+variances in the process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+they say by the way that
+
+ align:start position:0%
+they say by the way that
+ 
+
+ align:start position:0%
+they say by the way that
+those replicates generally result in
+
+ align:start position:0%
+those replicates generally result in
+ 
+
+ align:start position:0%
+those replicates generally result in
+about one and a half to five percent one
+
+ align:start position:0%
+about one and a half to five percent one
+ 
+
+ align:start position:0%
+about one and a half to five percent one
+sigma
+
+ align:start position:0%
+sigma
+ 
+
+ align:start position:0%
+sigma
+range in the output
+
+ align:start position:0%
+range in the output
+ 
+
+ align:start position:0%
+range in the output
+parameters the paper says they did a
+
+ align:start position:0%
+parameters the paper says they did a
+ 
+
+ align:start position:0%
+parameters the paper says they did a
+randomized run order
+
+ align:start position:0%
+randomized run order
+ 
+
+ align:start position:0%
+randomized run order
+why would you do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why not just run you got trial one
+
+ align:start position:0%
+why not just run you got trial one
+ 
+
+ align:start position:0%
+why not just run you got trial one
+et cetera why not just run all the way
+
+ align:start position:0%
+et cetera why not just run all the way
+ 
+
+ align:start position:0%
+et cetera why not just run all the way
+down to
+
+ align:start position:0%
+down to
+ 
+
+ align:start position:0%
+down to
+run trial number 31 in this order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to be independent
+
+ align:start position:0%
+to be independent
+ 
+
+ align:start position:0%
+to be independent
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+independent of what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressure different appreciation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i think you're right but but as you
+
+ align:start position:0%
+i think you're right but but as you
+ 
+
+ align:start position:0%
+i think you're right but but as you
+change these parameters that we're only
+
+ align:start position:0%
+change these parameters that we're only
+ 
+
+ align:start position:0%
+change these parameters that we're only
+playing with these these four parameters
+
+ align:start position:0%
+playing with these these four parameters
+ 
+
+ align:start position:0%
+playing with these these four parameters
+but there might still be noise other
+
+ align:start position:0%
+but there might still be noise other
+ 
+
+ align:start position:0%
+but there might still be noise other
+noise in the process or drifts like we
+
+ align:start position:0%
+noise in the process or drifts like we
+ 
+
+ align:start position:0%
+noise in the process or drifts like we
+talked about and it turns out in many of
+
+ align:start position:0%
+talked about and it turns out in many of
+ 
+
+ align:start position:0%
+talked about and it turns out in many of
+these deposition processes you actually
+
+ align:start position:0%
+these deposition processes you actually
+ 
+
+ align:start position:0%
+these deposition processes you actually
+have to worry about possible drifts
+
+ align:start position:0%
+have to worry about possible drifts
+ 
+
+ align:start position:0%
+have to worry about possible drifts
+in that you may get film build up on the
+
+ align:start position:0%
+in that you may get film build up on the
+ 
+
+ align:start position:0%
+in that you may get film build up on the
+inside of the reactor
+
+ align:start position:0%
+inside of the reactor
+ 
+
+ align:start position:0%
+inside of the reactor
+that over time might change a little bit
+
+ align:start position:0%
+that over time might change a little bit
+ 
+
+ align:start position:0%
+that over time might change a little bit
+the deposition process so by randomizing
+
+ align:start position:0%
+the deposition process so by randomizing
+ 
+
+ align:start position:0%
+the deposition process so by randomizing
+the run order you're randomizing the
+
+ align:start position:0%
+the run order you're randomizing the
+ 
+
+ align:start position:0%
+the run order you're randomizing the
+outputs and converting if there is a
+
+ align:start position:0%
+outputs and converting if there is a
+ 
+
+ align:start position:0%
+outputs and converting if there is a
+trend you basically convert that
+
+ align:start position:0%
+trend you basically convert that
+ 
+
+ align:start position:0%
+trend you basically convert that
+systematic trend into
+
+ align:start position:0%
+systematic trend into
+ 
+
+ align:start position:0%
+systematic trend into
+noise
+
+ align:start position:0%
+noise
+ 
+
+ align:start position:0%
+noise
+it may still perturb your values but now
+
+ align:start position:0%
+it may still perturb your values but now
+ 
+
+ align:start position:0%
+it may still perturb your values but now
+it does it kind of distributed in a
+
+ align:start position:0%
+it does it kind of distributed in a
+ 
+
+ align:start position:0%
+it does it kind of distributed in a
+random fashion across all of your
+
+ align:start position:0%
+random fashion across all of your
+ 
+
+ align:start position:0%
+random fashion across all of your
+outputs and it will add to the noise the
+
+ align:start position:0%
+outputs and it will add to the noise the
+ 
+
+ align:start position:0%
+outputs and it will add to the noise the
+change the reproducibility values
+
+ align:start position:0%
+change the reproducibility values
+ 
+
+ align:start position:0%
+change the reproducibility values
+but at least then it's not
+
+ align:start position:0%
+but at least then it's not
+ 
+
+ align:start position:0%
+but at least then it's not
+fooling you in a systematic way about
+
+ align:start position:0%
+fooling you in a systematic way about
+ 
+
+ align:start position:0%
+fooling you in a systematic way about
+confusing if there is that kind of other
+
+ align:start position:0%
+confusing if there is that kind of other
+ 
+
+ align:start position:0%
+confusing if there is that kind of other
+drift it will not confuse you or alias
+
+ align:start position:0%
+drift it will not confuse you or alias
+ 
+
+ align:start position:0%
+drift it will not confuse you or alias
+with some other parameter
+
+ align:start position:0%
+with some other parameter
+ 
+
+ align:start position:0%
+with some other parameter
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i have one minor annoyance in the paper
+
+ align:start position:0%
+i have one minor annoyance in the paper
+ 
+
+ align:start position:0%
+i have one minor annoyance in the paper
+and so if you're writing papers and
+
+ align:start position:0%
+and so if you're writing papers and
+ 
+
+ align:start position:0%
+and so if you're writing papers and
+you're you do a randomized run
+
+ align:start position:0%
+you're you do a randomized run
+ 
+
+ align:start position:0%
+you're you do a randomized run
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+tell me what the run order actually was
+
+ align:start position:0%
+tell me what the run order actually was
+ 
+
+ align:start position:0%
+tell me what the run order actually was
+if you're telling me the data i would
+
+ align:start position:0%
+if you're telling me the data i would
+ 
+
+ align:start position:0%
+if you're telling me the data i would
+love to actually know the run order
+
+ align:start position:0%
+love to actually know the run order
+ 
+
+ align:start position:0%
+love to actually know the run order
+because then when i do residual analysis
+
+ align:start position:0%
+because then when i do residual analysis
+ 
+
+ align:start position:0%
+because then when i do residual analysis
+and look at the residuals as a function
+
+ align:start position:0%
+and look at the residuals as a function
+ 
+
+ align:start position:0%
+and look at the residuals as a function
+of time
+
+ align:start position:0%
+of time
+ 
+
+ align:start position:0%
+of time
+i can actually
+
+ align:start position:0%
+i can actually
+ 
+
+ align:start position:0%
+i can actually
+go in and see if there was perhaps a
+
+ align:start position:0%
+go in and see if there was perhaps a
+ 
+
+ align:start position:0%
+go in and see if there was perhaps a
+systematic time drift
+
+ align:start position:0%
+systematic time drift
+ 
+
+ align:start position:0%
+systematic time drift
+and it really doesn't cost much
+
+ align:start position:0%
+and it really doesn't cost much
+ 
+
+ align:start position:0%
+and it really doesn't cost much
+to do that in
+
+ align:start position:0%
+to do that in
+ 
+
+ align:start position:0%
+to do that in
+ink space in the paper
+
+ align:start position:0%
+ink space in the paper
+ 
+
+ align:start position:0%
+ink space in the paper
+so for example here they had trial some
+
+ align:start position:0%
+so for example here they had trial some
+ 
+
+ align:start position:0%
+so for example here they had trial some
+papers you will actually see they go in
+
+ align:start position:0%
+papers you will actually see they go in
+ 
+
+ align:start position:0%
+papers you will actually see they go in
+and might put
+
+ align:start position:0%
+and might put
+ 
+
+ align:start position:0%
+and might put
+a number sort of right beside it
+
+ align:start position:0%
+a number sort of right beside it
+ 
+
+ align:start position:0%
+a number sort of right beside it
+in parentheses or something like that or
+
+ align:start position:0%
+in parentheses or something like that or
+ 
+
+ align:start position:0%
+in parentheses or something like that or
+actual another
+
+ align:start position:0%
+actual another
+ 
+
+ align:start position:0%
+actual another
+column in the table or whatever that
+
+ align:start position:0%
+column in the table or whatever that
+ 
+
+ align:start position:0%
+column in the table or whatever that
+tells me run order not just trial number
+
+ align:start position:0%
+tells me run order not just trial number
+ 
+
+ align:start position:0%
+tells me run order not just trial number
+okay so do that
+
+ align:start position:0%
+okay so do that
+ 
+
+ align:start position:0%
+okay so do that
+if you write write papers with data in
+
+ align:start position:0%
+if you write write papers with data in
+ 
+
+ align:start position:0%
+if you write write papers with data in
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+they also say they do did some outlier
+
+ align:start position:0%
+they also say they do did some outlier
+ 
+
+ align:start position:0%
+they also say they do did some outlier
+analysis they don't really uh
+
+ align:start position:0%
+analysis they don't really uh
+ 
+
+ align:start position:0%
+analysis they don't really uh
+say what that was but they know they do
+
+ align:start position:0%
+say what that was but they know they do
+ 
+
+ align:start position:0%
+say what that was but they know they do
+note it in the data
+
+ align:start position:0%
+note it in the data
+ 
+
+ align:start position:0%
+note it in the data
+and by the way
+
+ align:start position:0%
+and by the way
+ 
+
+ align:start position:0%
+and by the way
+oh i may not have put this on the
+
+ align:start position:0%
+oh i may not have put this on the
+ 
+
+ align:start position:0%
+oh i may not have put this on the
+site yet i will also add the spreadsheet
+
+ align:start position:0%
+site yet i will also add the spreadsheet
+ 
+
+ align:start position:0%
+site yet i will also add the spreadsheet
+with this basic data so if you want to
+
+ align:start position:0%
+with this basic data so if you want to
+ 
+
+ align:start position:0%
+with this basic data so if you want to
+grab this later and play with the data
+
+ align:start position:0%
+grab this later and play with the data
+ 
+
+ align:start position:0%
+grab this later and play with the data
+and do some of your own response surface
+
+ align:start position:0%
+and do some of your own response surface
+ 
+
+ align:start position:0%
+and do some of your own response surface
+model fits with
+
+ align:start position:0%
+model fits with
+ 
+
+ align:start position:0%
+model fits with
+jump or some of the other tools you can
+
+ align:start position:0%
+jump or some of the other tools you can
+ 
+
+ align:start position:0%
+jump or some of the other tools you can
+do that
+
+ align:start position:0%
+do that
+ 
+
+ align:start position:0%
+do that
+here's the output
+
+ align:start position:0%
+here's the output
+ 
+
+ align:start position:0%
+here's the output
+trial number and then each of the seven
+
+ align:start position:0%
+trial number and then each of the seven
+ 
+
+ align:start position:0%
+trial number and then each of the seven
+different outputs so these are the seven
+
+ align:start position:0%
+different outputs so these are the seven
+ 
+
+ align:start position:0%
+different outputs so these are the seven
+different outputs and basically just the
+
+ align:start position:0%
+different outputs and basically just the
+ 
+
+ align:start position:0%
+different outputs and basically just the
+raw the raw measured data
+
+ align:start position:0%
+raw the raw measured data
+ 
+
+ align:start position:0%
+raw the raw measured data
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+also may have asterisked or footnoted a
+
+ align:start position:0%
+also may have asterisked or footnoted a
+ 
+
+ align:start position:0%
+also may have asterisked or footnoted a
+few of these which is a good practice
+
+ align:start position:0%
+few of these which is a good practice
+ 
+
+ align:start position:0%
+few of these which is a good practice
+they said you know
+
+ align:start position:0%
+they said you know
+ 
+
+ align:start position:0%
+they said you know
+weird things like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+indicates entries determined to be
+
+ align:start position:0%
+indicates entries determined to be
+ 
+
+ align:start position:0%
+indicates entries determined to be
+outliers
+
+ align:start position:0%
+outliers
+ 
+
+ align:start position:0%
+outliers
+or if they knew something weird happened
+
+ align:start position:0%
+or if they knew something weird happened
+ 
+
+ align:start position:0%
+or if they knew something weird happened
+with the measurement of that particular
+
+ align:start position:0%
+with the measurement of that particular
+ 
+
+ align:start position:0%
+with the measurement of that particular
+data point or that entire row
+
+ align:start position:0%
+data point or that entire row
+ 
+
+ align:start position:0%
+data point or that entire row
+they would note that that can be really
+
+ align:start position:0%
+they would note that that can be really
+ 
+
+ align:start position:0%
+they would note that that can be really
+critical when you're interpreting the
+
+ align:start position:0%
+critical when you're interpreting the
+ 
+
+ align:start position:0%
+critical when you're interpreting the
+data
+
+ align:start position:0%
+data
+ 
+
+ align:start position:0%
+data
+then what they've done down here at the
+
+ align:start position:0%
+then what they've done down here at the
+ 
+
+ align:start position:0%
+then what they've done down here at the
+bottom is simply calculated
+
+ align:start position:0%
+bottom is simply calculated
+ 
+
+ align:start position:0%
+bottom is simply calculated
+things like
+
+ align:start position:0%
+things like
+ 
+
+ align:start position:0%
+things like
+the standard deviation
+
+ align:start position:0%
+the standard deviation
+ 
+
+ align:start position:0%
+the standard deviation
+across
+
+ align:start position:0%
+across
+ 
+
+ align:start position:0%
+across
+across all of those
+
+ align:start position:0%
+across all of those
+ 
+
+ align:start position:0%
+across all of those
+i think that's across
+
+ align:start position:0%
+i think that's across
+ 
+
+ align:start position:0%
+i think that's across
+just the replicate runs you can see that
+
+ align:start position:0%
+just the replicate runs you can see that
+ 
+
+ align:start position:0%
+just the replicate runs you can see that
+underneath here
+
+ align:start position:0%
+underneath here
+ 
+
+ align:start position:0%
+underneath here
+yeah okay
+
+ align:start position:0%
+yeah okay
+ 
+
+ align:start position:0%
+yeah okay
+so it gives you a sense of the
+
+ align:start position:0%
+so it gives you a sense of the
+ 
+
+ align:start position:0%
+so it gives you a sense of the
+percentage variance one sigma percentage
+
+ align:start position:0%
+percentage variance one sigma percentage
+ 
+
+ align:start position:0%
+percentage variance one sigma percentage
+variance in each of the output
+
+ align:start position:0%
+variance in each of the output
+ 
+
+ align:start position:0%
+variance in each of the output
+parameters
+
+ align:start position:0%
+parameters
+ 
+
+ align:start position:0%
+parameters
+yes question
+
+ align:start position:0%
+yes question
+ 
+
+ align:start position:0%
+yes question
+if one of the entries was
+
+ align:start position:0%
+if one of the entries was
+ 
+
+ align:start position:0%
+if one of the entries was
+as an issue doesn't that mean
+
+ align:start position:0%
+as an issue doesn't that mean
+ 
+
+ align:start position:0%
+as an issue doesn't that mean
+the whole row
+
+ align:start position:0%
+the whole row
+ 
+
+ align:start position:0%
+the whole row
+as an issue
+
+ align:start position:0%
+as an issue
+ 
+
+ align:start position:0%
+as an issue
+so shouldn't that whole row be discarded
+
+ align:start position:0%
+so shouldn't that whole row be discarded
+ 
+
+ align:start position:0%
+so shouldn't that whole row be discarded
+how can you for example you know in run
+
+ align:start position:0%
+how can you for example you know in run
+ 
+
+ align:start position:0%
+how can you for example you know in run
+six have an issue with let's say 8.1 and
+
+ align:start position:0%
+six have an issue with let's say 8.1 and
+ 
+
+ align:start position:0%
+six have an issue with let's say 8.1 and
+say you know this looks weird
+
+ align:start position:0%
+say you know this looks weird
+ 
+
+ align:start position:0%
+say you know this looks weird
+and you're not going to
+
+ align:start position:0%
+and you're not going to
+ 
+
+ align:start position:0%
+and you're not going to
+um use it in the row uh
+
+ align:start position:0%
+um use it in the row uh
+ 
+
+ align:start position:0%
+um use it in the row uh
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how can you have just an issue with one
+
+ align:start position:0%
+how can you have just an issue with one
+ 
+
+ align:start position:0%
+how can you have just an issue with one
+element and not an issue with the whole
+
+ align:start position:0%
+element and not an issue with the whole
+ 
+
+ align:start position:0%
+element and not an issue with the whole
+row
+
+ align:start position:0%
+row
+ 
+
+ align:start position:0%
+row
+basically i think it comes down to some
+
+ align:start position:0%
+basically i think it comes down to some
+ 
+
+ align:start position:0%
+basically i think it comes down to some
+engineering knowledge on what the issue
+
+ align:start position:0%
+engineering knowledge on what the issue
+ 
+
+ align:start position:0%
+engineering knowledge on what the issue
+may actually be so in particular if
+
+ align:start position:0%
+may actually be so in particular if
+ 
+
+ align:start position:0%
+may actually be so in particular if
+you're worried that
+
+ align:start position:0%
+you're worried that
+ 
+
+ align:start position:0%
+you're worried that
+there's something wrong with the
+
+ align:start position:0%
+there's something wrong with the
+ 
+
+ align:start position:0%
+there's something wrong with the
+measurement
+
+ align:start position:0%
+measurement
+ 
+
+ align:start position:0%
+measurement
+then that does not necessarily
+
+ align:start position:0%
+then that does not necessarily
+ 
+
+ align:start position:0%
+then that does not necessarily
+contaminate your measurements of other
+
+ align:start position:0%
+contaminate your measurements of other
+ 
+
+ align:start position:0%
+contaminate your measurements of other
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+other columns
+
+ align:start position:0%
+other columns
+ 
+
+ align:start position:0%
+other columns
+if you think it's really an indicator
+
+ align:start position:0%
+if you think it's really an indicator
+ 
+
+ align:start position:0%
+if you think it's really an indicator
+that the whole run
+
+ align:start position:0%
+that the whole run
+ 
+
+ align:start position:0%
+that the whole run
+or the whole trial was
+
+ align:start position:0%
+or the whole trial was
+ 
+
+ align:start position:0%
+or the whole trial was
+was messed up somehow
+
+ align:start position:0%
+was messed up somehow
+ 
+
+ align:start position:0%
+was messed up somehow
+then i agree you would probably want to
+
+ align:start position:0%
+then i agree you would probably want to
+ 
+
+ align:start position:0%
+then i agree you would probably want to
+to omit that entire run from your whole
+
+ align:start position:0%
+to omit that entire run from your whole
+ 
+
+ align:start position:0%
+to omit that entire run from your whole
+table or maybe repeat that run
+
+ align:start position:0%
+table or maybe repeat that run
+ 
+
+ align:start position:0%
+table or maybe repeat that run
+in this case with single wafer
+
+ align:start position:0%
+in this case with single wafer
+ 
+
+ align:start position:0%
+in this case with single wafer
+processing is probably an easy thing to
+
+ align:start position:0%
+processing is probably an easy thing to
+ 
+
+ align:start position:0%
+processing is probably an easy thing to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+i guess the second question if you're
+
+ align:start position:0%
+i guess the second question if you're
+ 
+
+ align:start position:0%
+i guess the second question if you're
+doing experiments
+
+ align:start position:0%
+doing experiments
+ 
+
+ align:start position:0%
+doing experiments
+that's an issue
+
+ align:start position:0%
+that's an issue
+ 
+
+ align:start position:0%
+that's an issue
+one of the numbers looks
+
+ align:start position:0%
+one of the numbers looks
+ 
+
+ align:start position:0%
+one of the numbers looks
+funky yeah um
+
+ align:start position:0%
+funky yeah um
+ 
+
+ align:start position:0%
+funky yeah um
+the fact and we want to eliminate that
+
+ align:start position:0%
+the fact and we want to eliminate that
+ 
+
+ align:start position:0%
+the fact and we want to eliminate that
+whole row what does that mean for
+
+ align:start position:0%
+whole row what does that mean for
+ 
+
+ align:start position:0%
+whole row what does that mean for
+our experiment if it's for example like
+
+ align:start position:0%
+our experiment if it's for example like
+ 
+
+ align:start position:0%
+our experiment if it's for example like
+the only we didn't do replicas is the
+
+ align:start position:0%
+the only we didn't do replicas is the
+ 
+
+ align:start position:0%
+the only we didn't do replicas is the
+center point and now we don't have a
+
+ align:start position:0%
+center point and now we don't have a
+ 
+
+ align:start position:0%
+center point and now we don't have a
+center point yeah so the other question
+
+ align:start position:0%
+center point yeah so the other question
+ 
+
+ align:start position:0%
+center point yeah so the other question
+is if you do have a bad data row how
+
+ align:start position:0%
+is if you do have a bad data row how
+ 
+
+ align:start position:0%
+is if you do have a bad data row how
+does that mess up your data analysis
+
+ align:start position:0%
+does that mess up your data analysis
+ 
+
+ align:start position:0%
+does that mess up your data analysis
+and and
+
+ align:start position:0%
+and and
+ 
+
+ align:start position:0%
+and and
+the answer is depending on the kind of
+
+ align:start position:0%
+the answer is depending on the kind of
+ 
+
+ align:start position:0%
+the answer is depending on the kind of
+doe that you have and the kinds of
+
+ align:start position:0%
+doe that you have and the kinds of
+ 
+
+ align:start position:0%
+doe that you have and the kinds of
+analysis that you apply
+
+ align:start position:0%
+analysis that you apply
+ 
+
+ align:start position:0%
+analysis that you apply
+you can be more or less robust to those
+
+ align:start position:0%
+you can be more or less robust to those
+ 
+
+ align:start position:0%
+you can be more or less robust to those
+kinds of missing data points
+
+ align:start position:0%
+kinds of missing data points
+ 
+
+ align:start position:0%
+kinds of missing data points
+one of the nice things about a central
+
+ align:start position:0%
+one of the nice things about a central
+ 
+
+ align:start position:0%
+one of the nice things about a central
+composite design
+
+ align:start position:0%
+composite design
+ 
+
+ align:start position:0%
+composite design
+and especially one where they've got you
+
+ align:start position:0%
+and especially one where they've got you
+ 
+
+ align:start position:0%
+and especially one where they've got you
+know kind of this these five levels is
+
+ align:start position:0%
+know kind of this these five levels is
+ 
+
+ align:start position:0%
+know kind of this these five levels is
+if you do that in conjunction with
+
+ align:start position:0%
+if you do that in conjunction with
+ 
+
+ align:start position:0%
+if you do that in conjunction with
+response surface modeling regression
+
+ align:start position:0%
+response surface modeling regression
+ 
+
+ align:start position:0%
+response surface modeling regression
+modeling in particular the numerical
+
+ align:start position:0%
+modeling in particular the numerical
+ 
+
+ align:start position:0%
+modeling in particular the numerical
+regression modeling you're fairly well
+
+ align:start position:0%
+regression modeling you're fairly well
+ 
+
+ align:start position:0%
+regression modeling you're fairly well
+off if you have a few missing data
+
+ align:start position:0%
+off if you have a few missing data
+ 
+
+ align:start position:0%
+off if you have a few missing data
+points it would throw you for a loop in
+
+ align:start position:0%
+points it would throw you for a loop in
+ 
+
+ align:start position:0%
+points it would throw you for a loop in
+some of the shorthand formation of
+
+ align:start position:0%
+some of the shorthand formation of
+ 
+
+ align:start position:0%
+some of the shorthand formation of
+contrast that we talked about because
+
+ align:start position:0%
+contrast that we talked about because
+ 
+
+ align:start position:0%
+contrast that we talked about because
+then you know your typical averaging
+
+ align:start position:0%
+then you know your typical averaging
+ 
+
+ align:start position:0%
+then you know your typical averaging
+that's implicit and some of those are
+
+ align:start position:0%
+that's implicit and some of those are
+ 
+
+ align:start position:0%
+that's implicit and some of those are
+wrong
+
+ align:start position:0%
+wrong
+ 
+
+ align:start position:0%
+wrong
+so you've got to be able but but if you
+
+ align:start position:0%
+so you've got to be able but but if you
+ 
+
+ align:start position:0%
+so you've got to be able but but if you
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+regression modeling in conjunction with
+
+ align:start position:0%
+regression modeling in conjunction with
+ 
+
+ align:start position:0%
+regression modeling in conjunction with
+a fairly rich
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+extra data points are lurking in there
+
+ align:start position:0%
+extra data points are lurking in there
+ 
+
+ align:start position:0%
+extra data points are lurking in there
+extra degrees of freedom are lurking in
+
+ align:start position:0%
+extra degrees of freedom are lurking in
+ 
+
+ align:start position:0%
+extra degrees of freedom are lurking in
+there that still allow you to reliably
+
+ align:start position:0%
+there that still allow you to reliably
+ 
+
+ align:start position:0%
+there that still allow you to reliably
+fit models
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the paper says the anova is performed
+
+ align:start position:0%
+so the paper says the anova is performed
+ 
+
+ align:start position:0%
+so the paper says the anova is performed
+but it is not shown
+
+ align:start position:0%
+but it is not shown
+ 
+
+ align:start position:0%
+but it is not shown
+i want to see the anova table so well we
+
+ align:start position:0%
+i want to see the anova table so well we
+ 
+
+ align:start position:0%
+i want to see the anova table so well we
+can basically generate those on our own
+
+ align:start position:0%
+can basically generate those on our own
+ 
+
+ align:start position:0%
+can basically generate those on our own
+and so in this case
+
+ align:start position:0%
+and so in this case
+ 
+
+ align:start position:0%
+and so in this case
+if the paper has the raw data in it i
+
+ align:start position:0%
+if the paper has the raw data in it i
+ 
+
+ align:start position:0%
+if the paper has the raw data in it i
+think it's okay that they didn't show
+
+ align:start position:0%
+think it's okay that they didn't show
+ 
+
+ align:start position:0%
+think it's okay that they didn't show
+the anova because i can regenerate that
+
+ align:start position:0%
+the anova because i can regenerate that
+ 
+
+ align:start position:0%
+the anova because i can regenerate that
+papers i hate are they don't show you
+
+ align:start position:0%
+papers i hate are they don't show you
+ 
+
+ align:start position:0%
+papers i hate are they don't show you
+the data and they don't show you the
+
+ align:start position:0%
+the data and they don't show you the
+ 
+
+ align:start position:0%
+the data and they don't show you the
+anova and so you don't know really what
+
+ align:start position:0%
+anova and so you don't know really what
+ 
+
+ align:start position:0%
+anova and so you don't know really what
+the noise was you don't know
+
+ align:start position:0%
+the noise was you don't know
+ 
+
+ align:start position:0%
+the noise was you don't know
+significances of parameters you don't
+
+ align:start position:0%
+significances of parameters you don't
+ 
+
+ align:start position:0%
+significances of parameters you don't
+know which parameters often they won't
+
+ align:start position:0%
+know which parameters often they won't
+ 
+
+ align:start position:0%
+know which parameters often they won't
+tell you really the significance level
+
+ align:start position:0%
+tell you really the significance level
+ 
+
+ align:start position:0%
+tell you really the significance level
+that was used to accept a model all of
+
+ align:start position:0%
+that was used to accept a model all of
+ 
+
+ align:start position:0%
+that was used to accept a model all of
+those sorts of things so in this case
+
+ align:start position:0%
+those sorts of things so in this case
+ 
+
+ align:start position:0%
+those sorts of things so in this case
+i'm i'm happy with the paper because
+
+ align:start position:0%
+i'm i'm happy with the paper because
+ 
+
+ align:start position:0%
+i'm i'm happy with the paper because
+i've got the raw data
+
+ align:start position:0%
+i've got the raw data
+ 
+
+ align:start position:0%
+i've got the raw data
+they claim that each of the model is
+
+ align:start position:0%
+they claim that each of the model is
+ 
+
+ align:start position:0%
+they claim that each of the model is
+significant at 99.9 percent uh
+
+ align:start position:0%
+significant at 99.9 percent uh
+ 
+
+ align:start position:0%
+significant at 99.9 percent uh
+significance level that's just
+
+ align:start position:0%
+significance level that's just
+ 
+
+ align:start position:0%
+significance level that's just
+their their p-value on the f-test for
+
+ align:start position:0%
+their their p-value on the f-test for
+ 
+
+ align:start position:0%
+their their p-value on the f-test for
+the whole model
+
+ align:start position:0%
+the whole model
+ 
+
+ align:start position:0%
+the whole model
+so these are very
+
+ align:start position:0%
+so these are very
+ 
+
+ align:start position:0%
+so these are very
+uh at least there is some parameter that
+
+ align:start position:0%
+uh at least there is some parameter that
+ 
+
+ align:start position:0%
+uh at least there is some parameter that
+is significant in influencing the output
+
+ align:start position:0%
+is significant in influencing the output
+ 
+
+ align:start position:0%
+is significant in influencing the output
+they report also r squareds which are is
+
+ align:start position:0%
+they report also r squareds which are is
+ 
+
+ align:start position:0%
+they report also r squareds which are is
+nice and for most of the models they are
+
+ align:start position:0%
+nice and for most of the models they are
+ 
+
+ align:start position:0%
+nice and for most of the models they are
+really quite high in the 0.88 to 0.97
+
+ align:start position:0%
+really quite high in the 0.88 to 0.97
+ 
+
+ align:start position:0%
+really quite high in the 0.88 to 0.97
+range
+
+ align:start position:0%
+range
+ 
+
+ align:start position:0%
+range
+the lowest one was
+
+ align:start position:0%
+the lowest one was
+ 
+
+ align:start position:0%
+the lowest one was
+resistivity at about 0.79
+
+ align:start position:0%
+resistivity at about 0.79
+ 
+
+ align:start position:0%
+resistivity at about 0.79
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they also report some lack of fit
+
+ align:start position:0%
+they also report some lack of fit
+ 
+
+ align:start position:0%
+they also report some lack of fit
+mention a little bit of evidence of lack
+
+ align:start position:0%
+mention a little bit of evidence of lack
+ 
+
+ align:start position:0%
+mention a little bit of evidence of lack
+of fit for uniformity and reflectance
+
+ align:start position:0%
+of fit for uniformity and reflectance
+ 
+
+ align:start position:0%
+of fit for uniformity and reflectance
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+lack of fit for sheet resistance
+
+ align:start position:0%
+lack of fit for sheet resistance
+ 
+
+ align:start position:0%
+lack of fit for sheet resistance
+uniformity
+
+ align:start position:0%
+uniformity
+ 
+
+ align:start position:0%
+uniformity
+is really interesting
+
+ align:start position:0%
+is really interesting
+ 
+
+ align:start position:0%
+is really interesting
+and in fact so interesting
+
+ align:start position:0%
+and in fact so interesting
+ 
+
+ align:start position:0%
+and in fact so interesting
+that i think a week from today if dave
+
+ align:start position:0%
+that i think a week from today if dave
+ 
+
+ align:start position:0%
+that i think a week from today if dave
+is talking on thursday
+
+ align:start position:0%
+is talking on thursday
+ 
+
+ align:start position:0%
+is talking on thursday
+i will spend a whole lecture
+
+ align:start position:0%
+i will spend a whole lecture
+ 
+
+ align:start position:0%
+i will spend a whole lecture
+on modeling of uniformity
+
+ align:start position:0%
+on modeling of uniformity
+ 
+
+ align:start position:0%
+on modeling of uniformity
+response surface modeling approaches
+
+ align:start position:0%
+response surface modeling approaches
+ 
+
+ align:start position:0%
+response surface modeling approaches
+spatial modeling approaches appropriate
+
+ align:start position:0%
+spatial modeling approaches appropriate
+ 
+
+ align:start position:0%
+spatial modeling approaches appropriate
+for uniformity
+
+ align:start position:0%
+for uniformity
+ 
+
+ align:start position:0%
+for uniformity
+the preview is
+
+ align:start position:0%
+the preview is
+ 
+
+ align:start position:0%
+the preview is
+think of the calculations that go into a
+
+ align:start position:0%
+think of the calculations that go into a
+ 
+
+ align:start position:0%
+think of the calculations that go into a
+wafer level uniformity calcu
+
+ align:start position:0%
+wafer level uniformity calcu
+ 
+
+ align:start position:0%
+wafer level uniformity calcu
+you know the calculation of that
+
+ align:start position:0%
+you know the calculation of that
+ 
+
+ align:start position:0%
+you know the calculation of that
+you might measure i think they're
+
+ align:start position:0%
+you might measure i think they're
+ 
+
+ align:start position:0%
+you might measure i think they're
+measuring 49 points across the wafer
+
+ align:start position:0%
+measuring 49 points across the wafer
+ 
+
+ align:start position:0%
+measuring 49 points across the wafer
+they're do it forming sums of squared
+
+ align:start position:0%
+they're do it forming sums of squared
+ 
+
+ align:start position:0%
+they're do it forming sums of squared
+deviations and then taking a square root
+
+ align:start position:0%
+deviations and then taking a square root
+ 
+
+ align:start position:0%
+deviations and then taking a square root
+and then perhaps normalizing by some
+
+ align:start position:0%
+and then perhaps normalizing by some
+ 
+
+ align:start position:0%
+and then perhaps normalizing by some
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+does that sound like a set of linear
+
+ align:start position:0%
+does that sound like a set of linear
+ 
+
+ align:start position:0%
+does that sound like a set of linear
+operations
+
+ align:start position:0%
+operations
+ 
+
+ align:start position:0%
+operations
+no that there's a lot of implicit
+
+ align:start position:0%
+no that there's a lot of implicit
+ 
+
+ align:start position:0%
+no that there's a lot of implicit
+non-linearity
+
+ align:start position:0%
+non-linearity
+ 
+
+ align:start position:0%
+non-linearity
+lurking just in the calculation of that
+
+ align:start position:0%
+lurking just in the calculation of that
+ 
+
+ align:start position:0%
+lurking just in the calculation of that
+of that metric
+
+ align:start position:0%
+of that metric
+ 
+
+ align:start position:0%
+of that metric
+and so it's not surprising that there's
+
+ align:start position:0%
+and so it's not surprising that there's
+ 
+
+ align:start position:0%
+and so it's not surprising that there's
+quadratic lack of fit or inability of a
+
+ align:start position:0%
+quadratic lack of fit or inability of a
+ 
+
+ align:start position:0%
+quadratic lack of fit or inability of a
+quadratic model to deal with a
+
+ align:start position:0%
+quadratic model to deal with a
+ 
+
+ align:start position:0%
+quadratic model to deal with a
+uniformity metric
+
+ align:start position:0%
+uniformity metric
+ 
+
+ align:start position:0%
+uniformity metric
+a spatial uniformity metric and we'll
+
+ align:start position:0%
+a spatial uniformity metric and we'll
+ 
+
+ align:start position:0%
+a spatial uniformity metric and we'll
+talk more about that next week but
+
+ align:start position:0%
+talk more about that next week but
+ 
+
+ align:start position:0%
+talk more about that next week but
+but um
+
+ align:start position:0%
+but um
+ 
+
+ align:start position:0%
+but um
+so they they do mention this uh at least
+
+ align:start position:0%
+so they they do mention this uh at least
+ 
+
+ align:start position:0%
+so they they do mention this uh at least
+they also mentioned some some potential
+
+ align:start position:0%
+they also mentioned some some potential
+ 
+
+ align:start position:0%
+they also mentioned some some potential
+lack of fit and reflectance i don't have
+
+ align:start position:0%
+lack of fit and reflectance i don't have
+ 
+
+ align:start position:0%
+lack of fit and reflectance i don't have
+an explanation for that they conjecture
+
+ align:start position:0%
+an explanation for that they conjecture
+ 
+
+ align:start position:0%
+an explanation for that they conjecture
+it's due to a very small pure error term
+
+ align:start position:0%
+it's due to a very small pure error term
+ 
+
+ align:start position:0%
+it's due to a very small pure error term
+so that you're able to detect
+
+ align:start position:0%
+so that you're able to detect
+ 
+
+ align:start position:0%
+so that you're able to detect
+with pretty fine resolution if there's
+
+ align:start position:0%
+with pretty fine resolution if there's
+ 
+
+ align:start position:0%
+with pretty fine resolution if there's
+any subtle non-quadratic
+
+ align:start position:0%
+any subtle non-quadratic
+ 
+
+ align:start position:0%
+any subtle non-quadratic
+uh trends but they're not concerned with
+
+ align:start position:0%
+uh trends but they're not concerned with
+ 
+
+ align:start position:0%
+uh trends but they're not concerned with
+it it's
+
+ align:start position:0%
+it it's
+ 
+
+ align:start position:0%
+it it's
+they still feel that they have very good
+
+ align:start position:0%
+they still feel that they have very good
+ 
+
+ align:start position:0%
+they still feel that they have very good
+good models
+
+ align:start position:0%
+good models
+ 
+
+ align:start position:0%
+good models
+it's also the case
+
+ align:start position:0%
+it's also the case
+ 
+
+ align:start position:0%
+it's also the case
+that there may be transformations
+
+ align:start position:0%
+that there may be transformations
+ 
+
+ align:start position:0%
+that there may be transformations
+that could be applied to improve these
+
+ align:start position:0%
+that could be applied to improve these
+ 
+
+ align:start position:0%
+that could be applied to improve these
+models
+
+ align:start position:0%
+models
+ 
+
+ align:start position:0%
+models
+and that also for the sheet resistivity
+
+ align:start position:0%
+and that also for the sheet resistivity
+ 
+
+ align:start position:0%
+and that also for the sheet resistivity
+or sheet resistance measurement
+
+ align:start position:0%
+or sheet resistance measurement
+ 
+
+ align:start position:0%
+or sheet resistance measurement
+there might be natural transformations
+
+ align:start position:0%
+there might be natural transformations
+ 
+
+ align:start position:0%
+there might be natural transformations
+that you might think that apply
+
+ align:start position:0%
+that you might think that apply
+ 
+
+ align:start position:0%
+that you might think that apply
+in fact if this is related to things
+
+ align:start position:0%
+in fact if this is related to things
+ 
+
+ align:start position:0%
+in fact if this is related to things
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+resistance divided by a thickness
+
+ align:start position:0%
+resistance divided by a thickness
+ 
+
+ align:start position:0%
+resistance divided by a thickness
+and the thickness
+
+ align:start position:0%
+and the thickness
+ 
+
+ align:start position:0%
+and the thickness
+grows linearly
+
+ align:start position:0%
+grows linearly
+ 
+
+ align:start position:0%
+grows linearly
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+you know maybe you have a linear
+
+ align:start position:0%
+you know maybe you have a linear
+ 
+
+ align:start position:0%
+you know maybe you have a linear
+dependence on on
+
+ align:start position:0%
+dependence on on
+ 
+
+ align:start position:0%
+dependence on on
+uh growth rate or something like that
+
+ align:start position:0%
+uh growth rate or something like that
+ 
+
+ align:start position:0%
+uh growth rate or something like that
+there may be inherent in there some one
+
+ align:start position:0%
+there may be inherent in there some one
+ 
+
+ align:start position:0%
+there may be inherent in there some one
+over kinds of transformations that might
+
+ align:start position:0%
+over kinds of transformations that might
+ 
+
+ align:start position:0%
+over kinds of transformations that might
+actually be a better thing to do to take
+
+ align:start position:0%
+actually be a better thing to do to take
+ 
+
+ align:start position:0%
+actually be a better thing to do to take
+that sheet resistance invert it and
+
+ align:start position:0%
+that sheet resistance invert it and
+ 
+
+ align:start position:0%
+that sheet resistance invert it and
+model the inverse of sheet resistance as
+
+ align:start position:0%
+model the inverse of sheet resistance as
+ 
+
+ align:start position:0%
+model the inverse of sheet resistance as
+a function of the input parameters
+
+ align:start position:0%
+a function of the input parameters
+ 
+
+ align:start position:0%
+a function of the input parameters
+so you can play around with that and
+
+ align:start position:0%
+so you can play around with that and
+ 
+
+ align:start position:0%
+so you can play around with that and
+actually that's a neat fun thing to play
+
+ align:start position:0%
+actually that's a neat fun thing to play
+ 
+
+ align:start position:0%
+actually that's a neat fun thing to play
+around with with some of these models
+
+ align:start position:0%
+around with with some of these models
+ 
+
+ align:start position:0%
+around with with some of these models
+they didn't do that
+
+ align:start position:0%
+they didn't do that
+ 
+
+ align:start position:0%
+they didn't do that
+but you could
+
+ align:start position:0%
+but you could
+ 
+
+ align:start position:0%
+but you could
+and then they do show the regression
+
+ align:start position:0%
+and then they do show the regression
+ 
+
+ align:start position:0%
+and then they do show the regression
+models here's the output these are the
+
+ align:start position:0%
+models here's the output these are the
+ 
+
+ align:start position:0%
+models here's the output these are the
+regression coefficients all of the
+
+ align:start position:0%
+regression coefficients all of the
+ 
+
+ align:start position:0%
+regression coefficients all of the
+linear terms and the cross terms and the
+
+ align:start position:0%
+linear terms and the cross terms and the
+ 
+
+ align:start position:0%
+linear terms and the cross terms and the
+square terms and what they've done in
+
+ align:start position:0%
+square terms and what they've done in
+ 
+
+ align:start position:0%
+square terms and what they've done in
+this table is report the
+
+ align:start position:0%
+this table is report the
+ 
+
+ align:start position:0%
+this table is report the
+the fit for just the significant terms
+
+ align:start position:0%
+the fit for just the significant terms
+ 
+
+ align:start position:0%
+the fit for just the significant terms
+if the coefficient was
+
+ align:start position:0%
+if the coefficient was
+ 
+
+ align:start position:0%
+if the coefficient was
+determined in their stepwise regression
+
+ align:start position:0%
+determined in their stepwise regression
+ 
+
+ align:start position:0%
+determined in their stepwise regression
+to be insignificant they've left it off
+
+ align:start position:0%
+to be insignificant they've left it off
+ 
+
+ align:start position:0%
+to be insignificant they've left it off
+i don't think they actually told us
+
+ align:start position:0%
+i don't think they actually told us
+ 
+
+ align:start position:0%
+i don't think they actually told us
+what their criteria for inclusion what
+
+ align:start position:0%
+what their criteria for inclusion what
+ 
+
+ align:start position:0%
+what their criteria for inclusion what
+their significance level cut off
+
+ align:start position:0%
+their significance level cut off
+ 
+
+ align:start position:0%
+their significance level cut off
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+in here so that would be a good thing to
+
+ align:start position:0%
+in here so that would be a good thing to
+ 
+
+ align:start position:0%
+in here so that would be a good thing to
+do as well but you can see lots of lots
+
+ align:start position:0%
+do as well but you can see lots of lots
+ 
+
+ align:start position:0%
+do as well but you can see lots of lots
+of models lots of
+
+ align:start position:0%
+of models lots of
+ 
+
+ align:start position:0%
+of models lots of
+uh second order terms these are you know
+
+ align:start position:0%
+uh second order terms these are you know
+ 
+
+ align:start position:0%
+uh second order terms these are you know
+interactions
+
+ align:start position:0%
+interactions
+ 
+
+ align:start position:0%
+interactions
+b 1 1 b 2 2 b 3 3 b
+
+ align:start position:0%
+b 1 1 b 2 2 b 3 3 b
+ 
+
+ align:start position:0%
+b 1 1 b 2 2 b 3 3 b
+those are pure square terms and then
+
+ align:start position:0%
+those are pure square terms and then
+ 
+
+ align:start position:0%
+those are pure square terms and then
+these are interactions so there's a fair
+
+ align:start position:0%
+these are interactions so there's a fair
+ 
+
+ align:start position:0%
+these are interactions so there's a fair
+amount of square activity going on
+
+ align:start position:0%
+amount of square activity going on
+ 
+
+ align:start position:0%
+amount of square activity going on
+as well as interactions
+
+ align:start position:0%
+as well as interactions
+ 
+
+ align:start position:0%
+as well as interactions
+they also then use those fit models to
+
+ align:start position:0%
+they also then use those fit models to
+ 
+
+ align:start position:0%
+they also then use those fit models to
+start to form
+
+ align:start position:0%
+start to form
+ 
+
+ align:start position:0%
+start to form
+contour plots and this is how they start
+
+ align:start position:0%
+contour plots and this is how they start
+ 
+
+ align:start position:0%
+contour plots and this is how they start
+to make then some engineering judgment
+
+ align:start position:0%
+to make then some engineering judgment
+ 
+
+ align:start position:0%
+to make then some engineering judgment
+about different trends so they would
+
+ align:start position:0%
+about different trends so they would
+ 
+
+ align:start position:0%
+about different trends so they would
+plot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+realize they've got four inputs and
+
+ align:start position:0%
+realize they've got four inputs and
+ 
+
+ align:start position:0%
+realize they've got four inputs and
+seven outputs you possibly can't
+
+ align:start position:0%
+seven outputs you possibly can't
+ 
+
+ align:start position:0%
+seven outputs you possibly can't
+possibly have a
+
+ align:start position:0%
+possibly have a
+ 
+
+ align:start position:0%
+possibly have a
+whatever you know four-dimensional input
+
+ align:start position:0%
+whatever you know four-dimensional input
+ 
+
+ align:start position:0%
+whatever you know four-dimensional input
+space is very hard to visualize so what
+
+ align:start position:0%
+space is very hard to visualize so what
+ 
+
+ align:start position:0%
+space is very hard to visualize so what
+you resort to are typically either two
+
+ align:start position:0%
+you resort to are typically either two
+ 
+
+ align:start position:0%
+you resort to are typically either two
+typically sort of two dimensional plots
+
+ align:start position:0%
+typically sort of two dimensional plots
+ 
+
+ align:start position:0%
+typically sort of two dimensional plots
+where you might plot one output or two
+
+ align:start position:0%
+where you might plot one output or two
+ 
+
+ align:start position:0%
+where you might plot one output or two
+outputs as a contour so in this
+
+ align:start position:0%
+outputs as a contour so in this
+ 
+
+ align:start position:0%
+outputs as a contour so in this
+particular plot the solid line i believe
+
+ align:start position:0%
+particular plot the solid line i believe
+ 
+
+ align:start position:0%
+particular plot the solid line i believe
+is growth rate
+
+ align:start position:0%
+is growth rate
+ 
+
+ align:start position:0%
+is growth rate
+and the dashed line here is wf6
+
+ align:start position:0%
+and the dashed line here is wf6
+ 
+
+ align:start position:0%
+and the dashed line here is wf6
+conversion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can start to feel get a feel for
+
+ align:start position:0%
+and you can start to feel get a feel for
+ 
+
+ align:start position:0%
+and you can start to feel get a feel for
+as for example
+
+ align:start position:0%
+as for example
+ 
+
+ align:start position:0%
+as for example
+the wf-6 pressure and the temperature
+
+ align:start position:0%
+the wf-6 pressure and the temperature
+ 
+
+ align:start position:0%
+the wf-6 pressure and the temperature
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+what trends you get in those two
+
+ align:start position:0%
+what trends you get in those two
+ 
+
+ align:start position:0%
+what trends you get in those two
+parameters and what trade-offs you get
+
+ align:start position:0%
+parameters and what trade-offs you get
+ 
+
+ align:start position:0%
+parameters and what trade-offs you get
+in those two parameters so things like
+
+ align:start position:0%
+in those two parameters so things like
+ 
+
+ align:start position:0%
+in those two parameters so things like
+as the temperature increases
+
+ align:start position:0%
+as the temperature increases
+ 
+
+ align:start position:0%
+as the temperature increases
+so temperature increasing this way the
+
+ align:start position:0%
+so temperature increasing this way the
+ 
+
+ align:start position:0%
+so temperature increasing this way the
+growth rate
+
+ align:start position:0%
+growth rate
+ 
+
+ align:start position:0%
+growth rate
+kind of increases
+
+ align:start position:0%
+kind of increases
+ 
+
+ align:start position:0%
+kind of increases
+right so the growth rate is the solid
+
+ align:start position:0%
+right so the growth rate is the solid
+ 
+
+ align:start position:0%
+right so the growth rate is the solid
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+so pretty directly
+
+ align:start position:0%
+so pretty directly
+ 
+
+ align:start position:0%
+so pretty directly
+with temperature that looks like a
+
+ align:start position:0%
+with temperature that looks like a
+ 
+
+ align:start position:0%
+with temperature that looks like a
+fairly strong direct impact as you might
+
+ align:start position:0%
+fairly strong direct impact as you might
+ 
+
+ align:start position:0%
+fairly strong direct impact as you might
+expect with a chemically
+
+ align:start position:0%
+expect with a chemically
+ 
+
+ align:start position:0%
+expect with a chemically
+dependent kind of process
+
+ align:start position:0%
+dependent kind of process
+ 
+
+ align:start position:0%
+dependent kind of process
+so they can start to get a feel for what
+
+ align:start position:0%
+so they can start to get a feel for what
+ 
+
+ align:start position:0%
+so they can start to get a feel for what
+some of these trends are and look at
+
+ align:start position:0%
+some of these trends are and look at
+ 
+
+ align:start position:0%
+some of these trends are and look at
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+for example has the biggest impact on
+
+ align:start position:0%
+for example has the biggest impact on
+ 
+
+ align:start position:0%
+for example has the biggest impact on
+growth rate of these of these parameters
+
+ align:start position:0%
+growth rate of these of these parameters
+ 
+
+ align:start position:0%
+growth rate of these of these parameters
+and which have
+
+ align:start position:0%
+and which have
+ 
+
+ align:start position:0%
+and which have
+either insignificant or small in
+
+ align:start position:0%
+either insignificant or small in
+ 
+
+ align:start position:0%
+either insignificant or small in
+magnitude
+
+ align:start position:0%
+magnitude
+ 
+
+ align:start position:0%
+magnitude
+kinds of effects
+
+ align:start position:0%
+kinds of effects
+ 
+
+ align:start position:0%
+kinds of effects
+now they can also start to do things
+
+ align:start position:0%
+now they can also start to do things
+ 
+
+ align:start position:0%
+now they can also start to do things
+like overlay requirements or conditions
+
+ align:start position:0%
+like overlay requirements or conditions
+ 
+
+ align:start position:0%
+like overlay requirements or conditions
+on these to start to understand the
+
+ align:start position:0%
+on these to start to understand the
+ 
+
+ align:start position:0%
+on these to start to understand the
+feasible operating space for process
+
+ align:start position:0%
+feasible operating space for process
+ 
+
+ align:start position:0%
+feasible operating space for process
+design and optimization so for example
+
+ align:start position:0%
+design and optimization so for example
+ 
+
+ align:start position:0%
+design and optimization so for example
+if your growth rate had to be 500
+
+ align:start position:0%
+if your growth rate had to be 500
+ 
+
+ align:start position:0%
+if your growth rate had to be 500
+nanometers per minute or higher
+
+ align:start position:0%
+nanometers per minute or higher
+ 
+
+ align:start position:0%
+nanometers per minute or higher
+you might then have whoops
+
+ align:start position:0%
+you might then have whoops
+ 
+
+ align:start position:0%
+you might then have whoops
+you know kind of shading on this plot
+
+ align:start position:0%
+you know kind of shading on this plot
+ 
+
+ align:start position:0%
+you know kind of shading on this plot
+you would say okay i really need to be
+
+ align:start position:0%
+you would say okay i really need to be
+ 
+
+ align:start position:0%
+you would say okay i really need to be
+above that 500 nanometer per minute
+
+ align:start position:0%
+above that 500 nanometer per minute
+ 
+
+ align:start position:0%
+above that 500 nanometer per minute
+contour and that tells me
+
+ align:start position:0%
+contour and that tells me
+ 
+
+ align:start position:0%
+contour and that tells me
+where i need to be at least with respect
+
+ align:start position:0%
+where i need to be at least with respect
+ 
+
+ align:start position:0%
+where i need to be at least with respect
+to those two parameters in terms of
+
+ align:start position:0%
+to those two parameters in terms of
+ 
+
+ align:start position:0%
+to those two parameters in terms of
+feasible operating space
+
+ align:start position:0%
+feasible operating space
+ 
+
+ align:start position:0%
+feasible operating space
+so already it tells you a lot just
+
+ align:start position:0%
+so already it tells you a lot just
+ 
+
+ align:start position:0%
+so already it tells you a lot just
+looking at these plots of where you
+
+ align:start position:0%
+looking at these plots of where you
+ 
+
+ align:start position:0%
+looking at these plots of where you
+might need to be in order to to achieve
+
+ align:start position:0%
+might need to be in order to to achieve
+ 
+
+ align:start position:0%
+might need to be in order to to achieve
+your multiple goals it may not give you
+
+ align:start position:0%
+your multiple goals it may not give you
+ 
+
+ align:start position:0%
+your multiple goals it may not give you
+a numerical optimum point
+
+ align:start position:0%
+a numerical optimum point
+ 
+
+ align:start position:0%
+a numerical optimum point
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+all by itself lots of looking at the
+
+ align:start position:0%
+all by itself lots of looking at the
+ 
+
+ align:start position:0%
+all by itself lots of looking at the
+data and plotting of the data is really
+
+ align:start position:0%
+data and plotting of the data is really
+ 
+
+ align:start position:0%
+data and plotting of the data is really
+valuable
+
+ align:start position:0%
+valuable
+ 
+
+ align:start position:0%
+valuable
+they do that for not only growth rate
+
+ align:start position:0%
+they do that for not only growth rate
+ 
+
+ align:start position:0%
+they do that for not only growth rate
+and wf6 but things like resistivity
+
+ align:start position:0%
+and wf6 but things like resistivity
+ 
+
+ align:start position:0%
+and wf6 but things like resistivity
+reflectance
+
+ align:start position:0%
+reflectance
+ 
+
+ align:start position:0%
+reflectance
+they start to look and see you know is
+
+ align:start position:0%
+they start to look and see you know is
+ 
+
+ align:start position:0%
+they start to look and see you know is
+the overall design going to be feasible
+
+ align:start position:0%
+the overall design going to be feasible
+ 
+
+ align:start position:0%
+the overall design going to be feasible
+what has the biggest effect on
+
+ align:start position:0%
+what has the biggest effect on
+ 
+
+ align:start position:0%
+what has the biggest effect on
+morphology
+
+ align:start position:0%
+morphology
+ 
+
+ align:start position:0%
+morphology
+those sorts of things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we found uh
+
+ align:start position:0%
+we found uh
+ 
+
+ align:start position:0%
+we found uh
+if you look at their contour plots most
+
+ align:start position:0%
+if you look at their contour plots most
+ 
+
+ align:start position:0%
+if you look at their contour plots most
+of these contour plots are are
+
+ align:start position:0%
+of these contour plots are are
+ 
+
+ align:start position:0%
+of these contour plots are are
+reasonably
+
+ align:start position:0%
+reasonably
+ 
+
+ align:start position:0%
+reasonably
+you know these are nice
+
+ align:start position:0%
+you know these are nice
+ 
+
+ align:start position:0%
+you know these are nice
+semi-linear kinds of plots
+
+ align:start position:0%
+semi-linear kinds of plots
+ 
+
+ align:start position:0%
+semi-linear kinds of plots
+their uniformity plot these look bizarre
+
+ align:start position:0%
+their uniformity plot these look bizarre
+ 
+
+ align:start position:0%
+their uniformity plot these look bizarre
+right very complex surfaces
+
+ align:start position:0%
+right very complex surfaces
+ 
+
+ align:start position:0%
+right very complex surfaces
+and again that's a reflection that this
+
+ align:start position:0%
+and again that's a reflection that this
+ 
+
+ align:start position:0%
+and again that's a reflection that this
+uniformity metric the spatial uniform
+
+ align:start position:0%
+uniformity metric the spatial uniform
+ 
+
+ align:start position:0%
+uniformity metric the spatial uniform
+internet is a very complex function of
+
+ align:start position:0%
+internet is a very complex function of
+ 
+
+ align:start position:0%
+internet is a very complex function of
+the input parameters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what they then do finally to round out
+
+ align:start position:0%
+what they then do finally to round out
+ 
+
+ align:start position:0%
+what they then do finally to round out
+the paper is talk a little bit about
+
+ align:start position:0%
+the paper is talk a little bit about
+ 
+
+ align:start position:0%
+the paper is talk a little bit about
+optimization so what they will have is
+
+ align:start position:0%
+optimization so what they will have is
+ 
+
+ align:start position:0%
+optimization so what they will have is
+some of those limits like i i said for
+
+ align:start position:0%
+some of those limits like i i said for
+ 
+
+ align:start position:0%
+some of those limits like i i said for
+example on the growth rate i guess i
+
+ align:start position:0%
+example on the growth rate i guess i
+ 
+
+ align:start position:0%
+example on the growth rate i guess i
+guess it wasn't a 500 nanometer cut off
+
+ align:start position:0%
+guess it wasn't a 500 nanometer cut off
+ 
+
+ align:start position:0%
+guess it wasn't a 500 nanometer cut off
+they needed at least 300 nanometer but
+
+ align:start position:0%
+they needed at least 300 nanometer but
+ 
+
+ align:start position:0%
+they needed at least 300 nanometer but
+they would like to get that
+
+ align:start position:0%
+they would like to get that
+ 
+
+ align:start position:0%
+they would like to get that
+higher is better and they would
+
+ align:start position:0%
+higher is better and they would
+ 
+
+ align:start position:0%
+higher is better and they would
+basically have different
+
+ align:start position:0%
+basically have different
+ 
+
+ align:start position:0%
+basically have different
+lower or upper bounds on each of the
+
+ align:start position:0%
+lower or upper bounds on each of the
+ 
+
+ align:start position:0%
+lower or upper bounds on each of the
+other parameters as well as
+
+ align:start position:0%
+other parameters as well as
+ 
+
+ align:start position:0%
+other parameters as well as
+desires to sort of hit either targets or
+
+ align:start position:0%
+desires to sort of hit either targets or
+ 
+
+ align:start position:0%
+desires to sort of hit either targets or
+make those bigger or smaller
+
+ align:start position:0%
+make those bigger or smaller
+ 
+
+ align:start position:0%
+make those bigger or smaller
+now they don't really describe very much
+
+ align:start position:0%
+now they don't really describe very much
+ 
+
+ align:start position:0%
+now they don't really describe very much
+what their
+
+ align:start position:0%
+what their
+ 
+
+ align:start position:0%
+what their
+what their
+
+ align:start position:0%
+what their
+ 
+
+ align:start position:0%
+what their
+optimization procedure is
+
+ align:start position:0%
+optimization procedure is
+ 
+
+ align:start position:0%
+optimization procedure is
+all they do is report that using the
+
+ align:start position:0%
+all they do is report that using the
+ 
+
+ align:start position:0%
+all they do is report that using the
+model they were able to achieve the
+
+ align:start position:0%
+model they were able to achieve the
+ 
+
+ align:start position:0%
+model they were able to achieve the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+best
+
+ align:start position:0%
+best
+ 
+
+ align:start position:0%
+best
+condition which they report and are very
+
+ align:start position:0%
+condition which they report and are very
+ 
+
+ align:start position:0%
+condition which they report and are very
+satisfied with so things like you know
+
+ align:start position:0%
+satisfied with so things like you know
+ 
+
+ align:start position:0%
+satisfied with so things like you know
+very high 99 step coverage
+
+ align:start position:0%
+very high 99 step coverage
+ 
+
+ align:start position:0%
+very high 99 step coverage
+improved or fairly good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conversion rate and so on so that's
+
+ align:start position:0%
+conversion rate and so on so that's
+ 
+
+ align:start position:0%
+conversion rate and so on so that's
+actually one of the fun things one could
+
+ align:start position:0%
+actually one of the fun things one could
+ 
+
+ align:start position:0%
+actually one of the fun things one could
+play with i think with the actual data
+
+ align:start position:0%
+play with i think with the actual data
+ 
+
+ align:start position:0%
+play with i think with the actual data
+is apply some of the hill climbing or
+
+ align:start position:0%
+is apply some of the hill climbing or
+ 
+
+ align:start position:0%
+is apply some of the hill climbing or
+other kinds of optimization algorithms
+
+ align:start position:0%
+other kinds of optimization algorithms
+ 
+
+ align:start position:0%
+other kinds of optimization algorithms
+to this data
+
+ align:start position:0%
+to this data
+ 
+
+ align:start position:0%
+to this data
+they do note in the paper that some of
+
+ align:start position:0%
+they do note in the paper that some of
+ 
+
+ align:start position:0%
+they do note in the paper that some of
+these constraints or limits
+
+ align:start position:0%
+these constraints or limits
+ 
+
+ align:start position:0%
+these constraints or limits
+do not greatly reduce their factor space
+
+ align:start position:0%
+do not greatly reduce their factor space
+ 
+
+ align:start position:0%
+do not greatly reduce their factor space
+they do not constrain
+
+ align:start position:0%
+they do not constrain
+ 
+
+ align:start position:0%
+they do not constrain
+where they need to operate and that
+
+ align:start position:0%
+where they need to operate and that
+ 
+
+ align:start position:0%
+where they need to operate and that
+gives them lots of latitude to be able
+
+ align:start position:0%
+gives them lots of latitude to be able
+ 
+
+ align:start position:0%
+gives them lots of latitude to be able
+to that's a good thing that gives them
+
+ align:start position:0%
+to that's a good thing that gives them
+ 
+
+ align:start position:0%
+to that's a good thing that gives them
+latitude to play with those parameters
+
+ align:start position:0%
+latitude to play with those parameters
+ 
+
+ align:start position:0%
+latitude to play with those parameters
+to achieve perhaps some other uh
+
+ align:start position:0%
+to achieve perhaps some other uh
+ 
+
+ align:start position:0%
+to achieve perhaps some other uh
+some other goals
+
+ align:start position:0%
+some other goals
+ 
+
+ align:start position:0%
+some other goals
+okay so what i want to do in the last
+
+ align:start position:0%
+okay so what i want to do in the last
+ 
+
+ align:start position:0%
+okay so what i want to do in the last
+six minutes is switch over here
+
+ align:start position:0%
+six minutes is switch over here
+ 
+
+ align:start position:0%
+six minutes is switch over here
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so are we ready to do a switch because
+
+ align:start position:0%
+so are we ready to do a switch because
+ 
+
+ align:start position:0%
+so are we ready to do a switch because
+what i want to do is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what i'm going to be doing here is
+
+ align:start position:0%
+so what i'm going to be doing here is
+ 
+
+ align:start position:0%
+so what i'm going to be doing here is
+basically showing you some jump
+
+ align:start position:0%
+basically showing you some jump
+ 
+
+ align:start position:0%
+basically showing you some jump
+analysis
+
+ align:start position:0%
+analysis
+ 
+
+ align:start position:0%
+analysis
+of this data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh dear
+
+ align:start position:0%
+oh dear
+ 
+
+ align:start position:0%
+oh dear
+maybe i'm not online
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what i've basically done is just
+
+ align:start position:0%
+so what i've basically done is just
+ 
+
+ align:start position:0%
+so what i've basically done is just
+sucked in the raw data and their their
+
+ align:start position:0%
+sucked in the raw data and their their
+ 
+
+ align:start position:0%
+sucked in the raw data and their their
+input conditions and their output
+
+ align:start position:0%
+input conditions and their output
+ 
+
+ align:start position:0%
+input conditions and their output
+conditions and we'll play with two
+
+ align:start position:0%
+conditions and we'll play with two
+ 
+
+ align:start position:0%
+conditions and we'll play with two
+things i just want to give you a little
+
+ align:start position:0%
+things i just want to give you a little
+ 
+
+ align:start position:0%
+things i just want to give you a little
+bit of a glimpse here
+
+ align:start position:0%
+bit of a glimpse here
+ 
+
+ align:start position:0%
+bit of a glimpse here
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+excellent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay can you see that in singapore
+
+ align:start position:0%
+okay can you see that in singapore
+ 
+
+ align:start position:0%
+okay can you see that in singapore
+excellent all right i'm psyched
+
+ align:start position:0%
+excellent all right i'm psyched
+ 
+
+ align:start position:0%
+excellent all right i'm psyched
+okay so what i've done here is use jump
+
+ align:start position:0%
+okay so what i've done here is use jump
+ 
+
+ align:start position:0%
+okay so what i've done here is use jump
+jump seven in fact which is a more
+
+ align:start position:0%
+jump seven in fact which is a more
+ 
+
+ align:start position:0%
+jump seven in fact which is a more
+recent version that i'm used to so some
+
+ align:start position:0%
+recent version that i'm used to so some
+ 
+
+ align:start position:0%
+recent version that i'm used to so some
+of the controls are a little bit
+
+ align:start position:0%
+of the controls are a little bit
+ 
+
+ align:start position:0%
+of the controls are a little bit
+different uh by the way i don't know if
+
+ align:start position:0%
+different uh by the way i don't know if
+ 
+
+ align:start position:0%
+different uh by the way i don't know if
+you've played with jump before
+
+ align:start position:0%
+you've played with jump before
+ 
+
+ align:start position:0%
+you've played with jump before
+as you're looking at
+
+ align:start position:0%
+as you're looking at
+ 
+
+ align:start position:0%
+as you're looking at
+your projects
+
+ align:start position:0%
+your projects
+ 
+
+ align:start position:0%
+your projects
+uh there is a 30-day free trial license
+
+ align:start position:0%
+uh there is a 30-day free trial license
+ 
+
+ align:start position:0%
+uh there is a 30-day free trial license
+of the full version of jump so you can
+
+ align:start position:0%
+of the full version of jump so you can
+ 
+
+ align:start position:0%
+of the full version of jump so you can
+download
+
+ align:start position:0%
+download
+ 
+
+ align:start position:0%
+download
+uh the trial version if you want if you
+
+ align:start position:0%
+uh the trial version if you want if you
+ 
+
+ align:start position:0%
+uh the trial version if you want if you
+want to grab it and and play with it uh
+
+ align:start position:0%
+want to grab it and and play with it uh
+ 
+
+ align:start position:0%
+want to grab it and and play with it uh
+especially for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the project i believe there's also
+
+ align:start position:0%
+for the project i believe there's also
+ 
+
+ align:start position:0%
+for the project i believe there's also
+an academic version it's like fifty
+
+ align:start position:0%
+an academic version it's like fifty
+ 
+
+ align:start position:0%
+an academic version it's like fifty
+dollars for a year license or something
+
+ align:start position:0%
+dollars for a year license or something
+ 
+
+ align:start position:0%
+dollars for a year license or something
+which is pretty nice because the
+
+ align:start position:0%
+which is pretty nice because the
+ 
+
+ align:start position:0%
+which is pretty nice because the
+commercial version is
+
+ align:start position:0%
+commercial version is
+ 
+
+ align:start position:0%
+commercial version is
+hundreds of dollars so so it's a nice
+
+ align:start position:0%
+hundreds of dollars so so it's a nice
+ 
+
+ align:start position:0%
+hundreds of dollars so so it's a nice
+package so all i did is i sucked in the
+
+ align:start position:0%
+package so all i did is i sucked in the
+ 
+
+ align:start position:0%
+package so all i did is i sucked in the
+the inputs these are our four input
+
+ align:start position:0%
+the inputs these are our four input
+ 
+
+ align:start position:0%
+the inputs these are our four input
+conditions here and then our growth rate
+
+ align:start position:0%
+conditions here and then our growth rate
+ 
+
+ align:start position:0%
+conditions here and then our growth rate
+and output conditions and i would always
+
+ align:start position:0%
+and output conditions and i would always
+ 
+
+ align:start position:0%
+and output conditions and i would always
+encourage you as a first step to explore
+
+ align:start position:0%
+encourage you as a first step to explore
+ 
+
+ align:start position:0%
+encourage you as a first step to explore
+your data just look at it see if it
+
+ align:start position:0%
+your data just look at it see if it
+ 
+
+ align:start position:0%
+your data just look at it see if it
+makes sense do univariate plots of
+
+ align:start position:0%
+makes sense do univariate plots of
+ 
+
+ align:start position:0%
+makes sense do univariate plots of
+outputs as a function of inputs and by
+
+ align:start position:0%
+outputs as a function of inputs and by
+ 
+
+ align:start position:0%
+outputs as a function of inputs and by
+the way there's some very cool things
+
+ align:start position:0%
+the way there's some very cool things
+ 
+
+ align:start position:0%
+the way there's some very cool things
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+scatter plot 3d where you might take
+
+ align:start position:0%
+scatter plot 3d where you might take
+ 
+
+ align:start position:0%
+scatter plot 3d where you might take
+three of these parameters
+
+ align:start position:0%
+three of these parameters
+ 
+
+ align:start position:0%
+three of these parameters
+and plot them against each other
+
+ align:start position:0%
+and plot them against each other
+ 
+
+ align:start position:0%
+and plot them against each other
+and so you get
+
+ align:start position:0%
+and so you get
+ 
+
+ align:start position:0%
+and so you get
+cool things like this that give you
+
+ align:start position:0%
+cool things like this that give you
+ 
+
+ align:start position:0%
+cool things like this that give you
+a picture of the scatter plot
+
+ align:start position:0%
+a picture of the scatter plot
+ 
+
+ align:start position:0%
+a picture of the scatter plot
+as a function
+
+ align:start position:0%
+as a function
+ 
+
+ align:start position:0%
+as a function
+you know of those three inputs or
+
+ align:start position:0%
+you know of those three inputs or
+ 
+
+ align:start position:0%
+you know of those three inputs or
+i guess this is a scatter plot of three
+
+ align:start position:0%
+i guess this is a scatter plot of three
+ 
+
+ align:start position:0%
+i guess this is a scatter plot of three
+outputs versus each other see if there's
+
+ align:start position:0%
+outputs versus each other see if there's
+ 
+
+ align:start position:0%
+outputs versus each other see if there's
+some correlation between these outputs
+
+ align:start position:0%
+some correlation between these outputs
+ 
+
+ align:start position:0%
+some correlation between these outputs
+you can do it one output as a function
+
+ align:start position:0%
+you can do it one output as a function
+ 
+
+ align:start position:0%
+you can do it one output as a function
+of two others um and so on so one of the
+
+ align:start position:0%
+of two others um and so on so one of the
+ 
+
+ align:start position:0%
+of two others um and so on so one of the
+nice things i like about
+
+ align:start position:0%
+nice things i like about
+ 
+
+ align:start position:0%
+nice things i like about
+jump and you should look for in a good
+
+ align:start position:0%
+jump and you should look for in a good
+ 
+
+ align:start position:0%
+jump and you should look for in a good
+interactive package is that interaction
+
+ align:start position:0%
+interactive package is that interaction
+ 
+
+ align:start position:0%
+interactive package is that interaction
+you can actually interact with the data
+
+ align:start position:0%
+you can actually interact with the data
+ 
+
+ align:start position:0%
+you can actually interact with the data
+and one of the things that excel is not
+
+ align:start position:0%
+and one of the things that excel is not
+ 
+
+ align:start position:0%
+and one of the things that excel is not
+good at so
+
+ align:start position:0%
+good at so
+ 
+
+ align:start position:0%
+good at so
+other tools like matlab are good at this
+
+ align:start position:0%
+other tools like matlab are good at this
+ 
+
+ align:start position:0%
+other tools like matlab are good at this
+as well
+
+ align:start position:0%
+as well
+ 
+
+ align:start position:0%
+as well
+okay so having done that
+
+ align:start position:0%
+okay so having done that
+ 
+
+ align:start position:0%
+okay so having done that
+another thing i like about jump is it
+
+ align:start position:0%
+another thing i like about jump is it
+ 
+
+ align:start position:0%
+another thing i like about jump is it
+allows you to
+
+ align:start position:0%
+allows you to
+ 
+
+ align:start position:0%
+allows you to
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+highlight what are bad data points so i
+
+ align:start position:0%
+highlight what are bad data points so i
+ 
+
+ align:start position:0%
+highlight what are bad data points so i
+don't i can deal with missing data
+
+ align:start position:0%
+don't i can deal with missing data
+ 
+
+ align:start position:0%
+don't i can deal with missing data
+points and jump so i've pulled those
+
+ align:start position:0%
+points and jump so i've pulled those
+ 
+
+ align:start position:0%
+points and jump so i've pulled those
+from the uh from the paper as well
+
+ align:start position:0%
+from the uh from the paper as well
+ 
+
+ align:start position:0%
+from the uh from the paper as well
+and then i can start to do things like
+
+ align:start position:0%
+and then i can start to do things like
+ 
+
+ align:start position:0%
+and then i can start to do things like
+build regression models so there are
+
+ align:start position:0%
+build regression models so there are
+ 
+
+ align:start position:0%
+build regression models so there are
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+oops
+
+ align:start position:0%
+oops
+ 
+
+ align:start position:0%
+oops
+i'm sorry
+
+ align:start position:0%
+i'm sorry
+ 
+
+ align:start position:0%
+i'm sorry
+a analyze
+
+ align:start position:0%
+a analyze
+ 
+
+ align:start position:0%
+a analyze
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+so here i might say okay i want to build
+
+ align:start position:0%
+so here i might say okay i want to build
+ 
+
+ align:start position:0%
+so here i might say okay i want to build
+a model for
+
+ align:start position:0%
+a model for
+ 
+
+ align:start position:0%
+a model for
+i'll just pick one for the moment growth
+
+ align:start position:0%
+i'll just pick one for the moment growth
+ 
+
+ align:start position:0%
+i'll just pick one for the moment growth
+rate as a function of these four input
+
+ align:start position:0%
+rate as a function of these four input
+ 
+
+ align:start position:0%
+rate as a function of these four input
+parameters and i can do things like say
+
+ align:start position:0%
+parameters and i can do things like say
+ 
+
+ align:start position:0%
+parameters and i can do things like say
+i really am doing a response surface
+
+ align:start position:0%
+i really am doing a response surface
+ 
+
+ align:start position:0%
+i really am doing a response surface
+model up to polynomial degree 2
+
+ align:start position:0%
+model up to polynomial degree 2
+ 
+
+ align:start position:0%
+model up to polynomial degree 2
+and it builds for me
+
+ align:start position:0%
+and it builds for me
+ 
+
+ align:start position:0%
+and it builds for me
+the template if you will for all of the
+
+ align:start position:0%
+the template if you will for all of the
+ 
+
+ align:start position:0%
+the template if you will for all of the
+interaction terms the square terms all
+
+ align:start position:0%
+interaction terms the square terms all
+ 
+
+ align:start position:0%
+interaction terms the square terms all
+of those things that if you were doing
+
+ align:start position:0%
+of those things that if you were doing
+ 
+
+ align:start position:0%
+of those things that if you were doing
+this in excel you would have to you know
+
+ align:start position:0%
+this in excel you would have to you know
+ 
+
+ align:start position:0%
+this in excel you would have to you know
+yourself build those fictional
+
+ align:start position:0%
+yourself build those fictional
+ 
+
+ align:start position:0%
+yourself build those fictional
+input parameters but here i'm basically
+
+ align:start position:0%
+input parameters but here i'm basically
+ 
+
+ align:start position:0%
+input parameters but here i'm basically
+telling it directly what the structure
+
+ align:start position:0%
+telling it directly what the structure
+ 
+
+ align:start position:0%
+telling it directly what the structure
+of the model i want to fit is
+
+ align:start position:0%
+of the model i want to fit is
+ 
+
+ align:start position:0%
+of the model i want to fit is
+now one thing that we haven't talked a
+
+ align:start position:0%
+now one thing that we haven't talked a
+ 
+
+ align:start position:0%
+now one thing that we haven't talked a
+lot about that i wanted to to highlight
+
+ align:start position:0%
+lot about that i wanted to to highlight
+ 
+
+ align:start position:0%
+lot about that i wanted to to highlight
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+how to go about building the model i
+
+ align:start position:0%
+how to go about building the model i
+ 
+
+ align:start position:0%
+how to go about building the model i
+could go ahead and do a full anova a
+
+ align:start position:0%
+could go ahead and do a full anova a
+ 
+
+ align:start position:0%
+could go ahead and do a full anova a
+full regression and a nova and look at
+
+ align:start position:0%
+full regression and a nova and look at
+ 
+
+ align:start position:0%
+full regression and a nova and look at
+each of the terms and decide what's
+
+ align:start position:0%
+each of the terms and decide what's
+ 
+
+ align:start position:0%
+each of the terms and decide what's
+significant and what's not
+
+ align:start position:0%
+significant and what's not
+ 
+
+ align:start position:0%
+significant and what's not
+there is a
+
+ align:start position:0%
+there is a
+ 
+
+ align:start position:0%
+there is a
+stepwise
+
+ align:start position:0%
+stepwise
+ 
+
+ align:start position:0%
+stepwise
+version of that same process
+
+ align:start position:0%
+version of that same process
+ 
+
+ align:start position:0%
+version of that same process
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+what we do is one parameter at a time
+
+ align:start position:0%
+what we do is one parameter at a time
+ 
+
+ align:start position:0%
+what we do is one parameter at a time
+add
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i wonder if i lost my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay can you see can you see it uh just
+
+ align:start position:0%
+okay can you see can you see it uh just
+ 
+
+ align:start position:0%
+okay can you see can you see it uh just
+uh maybe we'll just transmit i'm i'll
+
+ align:start position:0%
+uh maybe we'll just transmit i'm i'll
+ 
+
+ align:start position:0%
+uh maybe we'll just transmit i'm i'll
+i'll try
+
+ align:start position:0%
+i'll try
+ 
+
+ align:start position:0%
+i'll try
+it's not accepting the net meeting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it won't look as good but let's
+
+ align:start position:0%
+yeah it won't look as good but let's
+ 
+
+ align:start position:0%
+yeah it won't look as good but let's
+let's at least do that since we only
+
+ align:start position:0%
+let's at least do that since we only
+ 
+
+ align:start position:0%
+let's at least do that since we only
+have a couple more minutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah that's fine
+
+ align:start position:0%
+yeah that's fine
+ 
+
+ align:start position:0%
+yeah that's fine
+so we're just going to project so you
+
+ align:start position:0%
+so we're just going to project so you
+ 
+
+ align:start position:0%
+so we're just going to project so you
+can see see kind of crudely on the
+
+ align:start position:0%
+can see see kind of crudely on the
+ 
+
+ align:start position:0%
+can see see kind of crudely on the
+screen but the basic idea of this
+
+ align:start position:0%
+screen but the basic idea of this
+ 
+
+ align:start position:0%
+screen but the basic idea of this
+stepwise regression is that you can
+
+ align:start position:0%
+stepwise regression is that you can
+ 
+
+ align:start position:0%
+stepwise regression is that you can
+set the significance level for accepting
+
+ align:start position:0%
+set the significance level for accepting
+ 
+
+ align:start position:0%
+set the significance level for accepting
+a model parameter
+
+ align:start position:0%
+a model parameter
+ 
+
+ align:start position:0%
+a model parameter
+and then one step at a time so for
+
+ align:start position:0%
+and then one step at a time so for
+ 
+
+ align:start position:0%
+and then one step at a time so for
+example if i do this step
+
+ align:start position:0%
+example if i do this step
+ 
+
+ align:start position:0%
+example if i do this step
+it's it's pulling in
+
+ align:start position:0%
+it's it's pulling in
+ 
+
+ align:start position:0%
+it's it's pulling in
+additional coefficients that are of
+
+ align:start position:0%
+additional coefficients that are of
+ 
+
+ align:start position:0%
+additional coefficients that are of
+acceptable significance and in fact i
+
+ align:start position:0%
+acceptable significance and in fact i
+ 
+
+ align:start position:0%
+acceptable significance and in fact i
+think the probability to enter it needs
+
+ align:start position:0%
+think the probability to enter it needs
+ 
+
+ align:start position:0%
+think the probability to enter it needs
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+it's set to 0.25 this is 75 confidence
+
+ align:start position:0%
+it's set to 0.25 this is 75 confidence
+ 
+
+ align:start position:0%
+it's set to 0.25 this is 75 confidence
+level needs to be achieved in order to
+
+ align:start position:0%
+level needs to be achieved in order to
+ 
+
+ align:start position:0%
+level needs to be achieved in order to
+accept
+
+ align:start position:0%
+accept
+ 
+
+ align:start position:0%
+accept
+the model and i can keep stepping
+
+ align:start position:0%
+the model and i can keep stepping
+ 
+
+ align:start position:0%
+the model and i can keep stepping
+through and it iteratively is basically
+
+ align:start position:0%
+through and it iteratively is basically
+ 
+
+ align:start position:0%
+through and it iteratively is basically
+making determinations based on
+
+ align:start position:0%
+making determinations based on
+ 
+
+ align:start position:0%
+making determinations based on
+my setting of significance values to
+
+ align:start position:0%
+my setting of significance values to
+ 
+
+ align:start position:0%
+my setting of significance values to
+pull in or discard model terms
+
+ align:start position:0%
+pull in or discard model terms
+ 
+
+ align:start position:0%
+pull in or discard model terms
+and if it discards a model term then it
+
+ align:start position:0%
+and if it discards a model term then it
+ 
+
+ align:start position:0%
+and if it discards a model term then it
+takes those degrees of freedom throws
+
+ align:start position:0%
+takes those degrees of freedom throws
+ 
+
+ align:start position:0%
+takes those degrees of freedom throws
+them back into the error term
+
+ align:start position:0%
+them back into the error term
+ 
+
+ align:start position:0%
+them back into the error term
+not purely as a function of you know the
+
+ align:start position:0%
+not purely as a function of you know the
+ 
+
+ align:start position:0%
+not purely as a function of you know the
+replicate error but it gives it it does
+
+ align:start position:0%
+replicate error but it gives it it does
+ 
+
+ align:start position:0%
+replicate error but it gives it it does
+this kind of stepwise
+
+ align:start position:0%
+this kind of stepwise
+ 
+
+ align:start position:0%
+this kind of stepwise
+multiple regression in order to build
+
+ align:start position:0%
+multiple regression in order to build
+ 
+
+ align:start position:0%
+multiple regression in order to build
+the overall model
+
+ align:start position:0%
+the overall model
+ 
+
+ align:start position:0%
+the overall model
+so here you can see for example for the
+
+ align:start position:0%
+so here you can see for example for the
+ 
+
+ align:start position:0%
+so here you can see for example for the
+this particular output of growth rate
+
+ align:start position:0%
+this particular output of growth rate
+ 
+
+ align:start position:0%
+this particular output of growth rate
+you can see which terms end up being
+
+ align:start position:0%
+you can see which terms end up being
+ 
+
+ align:start position:0%
+you can see which terms end up being
+significant you've got things like
+
+ align:start position:0%
+significant you've got things like
+ 
+
+ align:start position:0%
+significant you've got things like
+temperature squared
+
+ align:start position:0%
+temperature squared
+ 
+
+ align:start position:0%
+temperature squared
+and temperature h2 pressure interactions
+
+ align:start position:0%
+and temperature h2 pressure interactions
+ 
+
+ align:start position:0%
+and temperature h2 pressure interactions
+okay doing that you can then accept one
+
+ align:start position:0%
+okay doing that you can then accept one
+ 
+
+ align:start position:0%
+okay doing that you can then accept one
+of these models and build another column
+
+ align:start position:0%
+of these models and build another column
+ 
+
+ align:start position:0%
+of these models and build another column
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in jump that is in fact the prediction
+
+ align:start position:0%
+in jump that is in fact the prediction
+ 
+
+ align:start position:0%
+in jump that is in fact the prediction
+formula for one of these parameters so
+
+ align:start position:0%
+formula for one of these parameters so
+ 
+
+ align:start position:0%
+formula for one of these parameters so
+for example this might be the prediction
+
+ align:start position:0%
+for example this might be the prediction
+ 
+
+ align:start position:0%
+for example this might be the prediction
+formula for growth rate it now has that
+
+ align:start position:0%
+formula for growth rate it now has that
+ 
+
+ align:start position:0%
+formula for growth rate it now has that
+polynomial model in it and one of the
+
+ align:start position:0%
+polynomial model in it and one of the
+ 
+
+ align:start position:0%
+polynomial model in it and one of the
+cool things about jump just so that you
+
+ align:start position:0%
+cool things about jump just so that you
+ 
+
+ align:start position:0%
+cool things about jump just so that you
+know it's there and then you can play
+
+ align:start position:0%
+know it's there and then you can play
+ 
+
+ align:start position:0%
+know it's there and then you can play
+with it
+
+ align:start position:0%
+with it
+ 
+
+ align:start position:0%
+with it
+or you can also now start to go in and
+
+ align:start position:0%
+or you can also now start to go in and
+ 
+
+ align:start position:0%
+or you can also now start to go in and
+do things like
+
+ align:start position:0%
+do things like
+ 
+
+ align:start position:0%
+do things like
+profiler or contour profiler for
+
+ align:start position:0%
+profiler or contour profiler for
+ 
+
+ align:start position:0%
+profiler or contour profiler for
+optimization and exploration of that
+
+ align:start position:0%
+optimization and exploration of that
+ 
+
+ align:start position:0%
+optimization and exploration of that
+design space
+
+ align:start position:0%
+design space
+ 
+
+ align:start position:0%
+design space
+so doing a a simple
+
+ align:start position:0%
+so doing a a simple
+ 
+
+ align:start position:0%
+so doing a a simple
+one parameter profiler i might say okay
+
+ align:start position:0%
+one parameter profiler i might say okay
+ 
+
+ align:start position:0%
+one parameter profiler i might say okay
+i want to profile growth rate and row
+
+ align:start position:0%
+i want to profile growth rate and row
+ 
+
+ align:start position:0%
+i want to profile growth rate and row
+i'll just do those two
+
+ align:start position:0%
+i'll just do those two
+ 
+
+ align:start position:0%
+i'll just do those two
+parameters
+
+ align:start position:0%
+parameters
+ 
+
+ align:start position:0%
+parameters
+and what i've got is this prediction
+
+ align:start position:0%
+and what i've got is this prediction
+ 
+
+ align:start position:0%
+and what i've got is this prediction
+profiler that has
+
+ align:start position:0%
+profiler that has
+ 
+
+ align:start position:0%
+profiler that has
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the two outputs growth rate is the first
+
+ align:start position:0%
+the two outputs growth rate is the first
+ 
+
+ align:start position:0%
+the two outputs growth rate is the first
+row and
+
+ align:start position:0%
+row and
+ 
+
+ align:start position:0%
+row and
+whatever it was
+
+ align:start position:0%
+whatever it was
+ 
+
+ align:start position:0%
+whatever it was
+is it i can't remember what the second
+
+ align:start position:0%
+is it i can't remember what the second
+ 
+
+ align:start position:0%
+is it i can't remember what the second
+one was it's a little hard to see there
+
+ align:start position:0%
+one was it's a little hard to see there
+ 
+
+ align:start position:0%
+one was it's a little hard to see there
+formula row okay so the resistance and
+
+ align:start position:0%
+formula row okay so the resistance and
+ 
+
+ align:start position:0%
+formula row okay so the resistance and
+the growth rate as a function of each of
+
+ align:start position:0%
+the growth rate as a function of each of
+ 
+
+ align:start position:0%
+the growth rate as a function of each of
+the individual parameters so this is the
+
+ align:start position:0%
+the individual parameters so this is the
+ 
+
+ align:start position:0%
+the individual parameters so this is the
+univariate dependence depending on my
+
+ align:start position:0%
+univariate dependence depending on my
+ 
+
+ align:start position:0%
+univariate dependence depending on my
+current operating point
+
+ align:start position:0%
+current operating point
+ 
+
+ align:start position:0%
+current operating point
+and then i can move that operating point
+
+ align:start position:0%
+and then i can move that operating point
+ 
+
+ align:start position:0%
+and then i can move that operating point
+and see how the other parameters
+
+ align:start position:0%
+and see how the other parameters
+ 
+
+ align:start position:0%
+and see how the other parameters
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+so as i change temperature
+
+ align:start position:0%
+so as i change temperature
+ 
+
+ align:start position:0%
+so as i change temperature
+how does that affect my my outputs
+
+ align:start position:0%
+how does that affect my my outputs
+ 
+
+ align:start position:0%
+how does that affect my my outputs
+okay so it's kind of fun you can play
+
+ align:start position:0%
+okay so it's kind of fun you can play
+ 
+
+ align:start position:0%
+okay so it's kind of fun you can play
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+and see how
+
+ align:start position:0%
+and see how
+ 
+
+ align:start position:0%
+and see how
+how those things happen you can also do
+
+ align:start position:0%
+how those things happen you can also do
+ 
+
+ align:start position:0%
+how those things happen you can also do
+essentially close to what they did in
+
+ align:start position:0%
+essentially close to what they did in
+ 
+
+ align:start position:0%
+essentially close to what they did in
+the paper and do contour plot
+
+ align:start position:0%
+the paper and do contour plot
+ 
+
+ align:start position:0%
+the paper and do contour plot
+explorations so i might for example do
+
+ align:start position:0%
+explorations so i might for example do
+ 
+
+ align:start position:0%
+explorations so i might for example do
+those same parameters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's fine
+
+ align:start position:0%
+yeah that's fine
+ 
+
+ align:start position:0%
+yeah that's fine
+and actually now plot the current
+
+ align:start position:0%
+and actually now plot the current
+ 
+
+ align:start position:0%
+and actually now plot the current
+operating point the response
+
+ align:start position:0%
+operating point the response
+ 
+
+ align:start position:0%
+operating point the response
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+growth rate row
+
+ align:start position:0%
+growth rate row
+ 
+
+ align:start position:0%
+growth rate row
+resistance uniformity
+
+ align:start position:0%
+resistance uniformity
+ 
+
+ align:start position:0%
+resistance uniformity
+in the design space so that i can see
+
+ align:start position:0%
+in the design space so that i can see
+ 
+
+ align:start position:0%
+in the design space so that i can see
+how those things change as i change my
+
+ align:start position:0%
+how those things change as i change my
+ 
+
+ align:start position:0%
+how those things change as i change my
+gap spacing or my temperature and i can
+
+ align:start position:0%
+gap spacing or my temperature and i can
+ 
+
+ align:start position:0%
+gap spacing or my temperature and i can
+also apply things like the limits maybe
+
+ align:start position:0%
+also apply things like the limits maybe
+ 
+
+ align:start position:0%
+also apply things like the limits maybe
+i have a low limit of 500 for the growth
+
+ align:start position:0%
+i have a low limit of 500 for the growth
+ 
+
+ align:start position:0%
+i have a low limit of 500 for the growth
+rate i need again 500 nanometers and
+
+ align:start position:0%
+rate i need again 500 nanometers and
+ 
+
+ align:start position:0%
+rate i need again 500 nanometers and
+what it does is it'll start to shade out
+
+ align:start position:0%
+what it does is it'll start to shade out
+ 
+
+ align:start position:0%
+what it does is it'll start to shade out
+unallowable regions to achieve those
+
+ align:start position:0%
+unallowable regions to achieve those
+ 
+
+ align:start position:0%
+unallowable regions to achieve those
+kinds of goals
+
+ align:start position:0%
+kinds of goals
+ 
+
+ align:start position:0%
+kinds of goals
+so this is just a nice interactive tool
+
+ align:start position:0%
+so this is just a nice interactive tool
+ 
+
+ align:start position:0%
+so this is just a nice interactive tool
+that lets you do that kind of
+
+ align:start position:0%
+that lets you do that kind of
+ 
+
+ align:start position:0%
+that lets you do that kind of
+uh dynamic exploration of the optimism
+
+ align:start position:0%
+uh dynamic exploration of the optimism
+ 
+
+ align:start position:0%
+uh dynamic exploration of the optimism
+of the optimal space
+
+ align:start position:0%
+of the optimal space
+ 
+
+ align:start position:0%
+of the optimal space
+so i'll put the uh put that data uh up
+
+ align:start position:0%
+so i'll put the uh put that data uh up
+ 
+
+ align:start position:0%
+so i'll put the uh put that data uh up
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+the web as well and you can play around
+
+ align:start position:0%
+the web as well and you can play around
+ 
+
+ align:start position:0%
+the web as well and you can play around
+with it but this is uh uh kind of where
+
+ align:start position:0%
+with it but this is uh uh kind of where
+ 
+
+ align:start position:0%
+with it but this is uh uh kind of where
+i'll i'll leave it for you to explore
+
+ align:start position:0%
+i'll i'll leave it for you to explore
+ 
+
+ align:start position:0%
+i'll i'll leave it for you to explore
+more if you want to with jump either on
+
+ align:start position:0%
+more if you want to with jump either on
+ 
+
+ align:start position:0%
+more if you want to with jump either on
+this data or
+
+ align:start position:0%
+this data or
+ 
+
+ align:start position:0%
+this data or
+perhaps more efficiently on your team
+
+ align:start position:0%
+perhaps more efficiently on your team
+ 
+
+ align:start position:0%
+perhaps more efficiently on your team
+project data
+
+ align:start position:0%
+project data
+ 
+
+ align:start position:0%
+project data
+but wanted to get get this case study so
+
+ align:start position:0%
+but wanted to get get this case study so
+ 
+
+ align:start position:0%
+but wanted to get get this case study so
+you know some of the capabilities so i
+
+ align:start position:0%
+you know some of the capabilities so i
+ 
+
+ align:start position:0%
+you know some of the capabilities so i
+think with that i'm going to break
+
+ align:start position:0%
+think with that i'm going to break
+ 
+
+ align:start position:0%
+think with that i'm going to break
+and we can chat a little bit if people
+
+ align:start position:0%
+and we can chat a little bit if people
+ 
+
+ align:start position:0%
+and we can chat a little bit if people
+have questions about team projects and
+
+ align:start position:0%
+have questions about team projects and
+ 
+
+ align:start position:0%
+have questions about team projects and
+and whatnot
\ No newline at end of file
diff --git a/02wEjlKtxKw.txt b/02wEjlKtxKw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..79c16bd2d386308a460b3fa20c33dec87c492438
--- /dev/null
+++ b/02wEjlKtxKw.txt
@@ -0,0 +1,14955 @@
+align:start position:0%
+ 
+it's very simple but doesn't completely
+
+ align:start position:0%
+it's very simple but doesn't completely
+ 
+
+ align:start position:0%
+it's very simple but doesn't completely
+capture all of the the reality uh the
+
+ align:start position:0%
+capture all of the the reality uh the
+ 
+
+ align:start position:0%
+capture all of the the reality uh the
+simp the simplest analytic expression
+
+ align:start position:0%
+simp the simplest analytic expression
+ 
+
+ align:start position:0%
+simp the simplest analytic expression
+that captures profiles reasonably well
+
+ align:start position:0%
+that captures profiles reasonably well
+ 
+
+ align:start position:0%
+that captures profiles reasonably well
+is the Pearson four which has four
+
+ align:start position:0%
+is the Pearson four which has four
+ 
+
+ align:start position:0%
+is the Pearson four which has four
+moments uh and those moments are
+
+ align:start position:0%
+moments uh and those moments are
+ 
+
+ align:start position:0%
+moments uh and those moments are
+generally tabulated in
+
+ align:start position:0%
+generally tabulated in
+ 
+
+ align:start position:0%
+generally tabulated in
+tables we also uh presented the idea of
+
+ align:start position:0%
+tables we also uh presented the idea of
+ 
+
+ align:start position:0%
+tables we also uh presented the idea of
+Monte Carlo uh or numerical solutions
+
+ align:start position:0%
+Monte Carlo uh or numerical solutions
+ 
+
+ align:start position:0%
+Monte Carlo uh or numerical solutions
+for example Monte Carlo
+
+ align:start position:0%
+for example Monte Carlo
+ 
+
+ align:start position:0%
+for example Monte Carlo
+simulation uh which is uh very quite
+
+ align:start position:0%
+simulation uh which is uh very quite
+ 
+
+ align:start position:0%
+simulation uh which is uh very quite
+accurate and another thing called the
+
+ align:start position:0%
+accurate and another thing called the
+ 
+
+ align:start position:0%
+accurate and another thing called the
+bolman transport equation
+
+ align:start position:0%
+bolman transport equation
+ 
+
+ align:start position:0%
+bolman transport equation
+solution um the other thing we um
+
+ align:start position:0%
+solution um the other thing we um
+ 
+
+ align:start position:0%
+solution um the other thing we um
+mentioned is that there's this process
+
+ align:start position:0%
+mentioned is that there's this process
+ 
+
+ align:start position:0%
+mentioned is that there's this process
+called ion channeling ion channeling
+
+ align:start position:0%
+called ion channeling ion channeling
+ 
+
+ align:start position:0%
+called ion channeling ion channeling
+itself is a quite a challenge in
+
+ align:start position:0%
+itself is a quite a challenge in
+ 
+
+ align:start position:0%
+itself is a quite a challenge in
+calculating profiles calculating the
+
+ align:start position:0%
+calculating profiles calculating the
+ 
+
+ align:start position:0%
+calculating profiles calculating the
+profiles pretty accurately into
+
+ align:start position:0%
+profiles pretty accurately into
+ 
+
+ align:start position:0%
+profiles pretty accurately into
+amorphous solids uh or amorphous
+
+ align:start position:0%
+amorphous solids uh or amorphous
+ 
+
+ align:start position:0%
+amorphous solids uh or amorphous
+material is quite is reasonably routine
+
+ align:start position:0%
+material is quite is reasonably routine
+ 
+
+ align:start position:0%
+material is quite is reasonably routine
+but once you have to model ion
+
+ align:start position:0%
+but once you have to model ion
+ 
+
+ align:start position:0%
+but once you have to model ion
+channeling it gets a little
+
+ align:start position:0%
+channeling it gets a little
+ 
+
+ align:start position:0%
+channeling it gets a little
+tricky today I want to cover things that
+
+ align:start position:0%
+tricky today I want to cover things that
+ 
+
+ align:start position:0%
+tricky today I want to cover things that
+we didn't get a chance to talk about we
+
+ align:start position:0%
+we didn't get a chance to talk about we
+ 
+
+ align:start position:0%
+we didn't get a chance to talk about we
+never even talked about last time the
+
+ align:start position:0%
+never even talked about last time the
+ 
+
+ align:start position:0%
+never even talked about last time the
+physics of the modeling of the ion
+
+ align:start position:0%
+physics of the modeling of the ion
+ 
+
+ align:start position:0%
+physics of the modeling of the ion
+implantation process that is the
+
+ align:start position:0%
+implantation process that is the
+ 
+
+ align:start position:0%
+implantation process that is the
+physical energy loss mechanisms of the
+
+ align:start position:0%
+physical energy loss mechanisms of the
+ 
+
+ align:start position:0%
+physical energy loss mechanisms of the
+ions as they Traverse we want to talk
+
+ align:start position:0%
+ions as they Traverse we want to talk
+ 
+
+ align:start position:0%
+ions as they Traverse we want to talk
+about that once we've covered that uh we
+
+ align:start position:0%
+about that once we've covered that uh we
+ 
+
+ align:start position:0%
+about that once we've covered that uh we
+want to talk about damage how do we
+
+ align:start position:0%
+want to talk about damage how do we
+ 
+
+ align:start position:0%
+want to talk about damage how do we
+model the damage that takes place in the
+
+ align:start position:0%
+model the damage that takes place in the
+ 
+
+ align:start position:0%
+model the damage that takes place in the
+Silicon substrate um and how do we knal
+
+ align:start position:0%
+Silicon substrate um and how do we knal
+ 
+
+ align:start position:0%
+Silicon substrate um and how do we knal
+it and then I'll give a very brief
+
+ align:start position:0%
+it and then I'll give a very brief
+ 
+
+ align:start position:0%
+it and then I'll give a very brief
+introduction to Transit enhanced
+
+ align:start position:0%
+introduction to Transit enhanced
+ 
+
+ align:start position:0%
+introduction to Transit enhanced
+diffusion the next lecture on next
+
+ align:start position:0%
+diffusion the next lecture on next
+ 
+
+ align:start position:0%
+diffusion the next lecture on next
+Tuesday is going to be dedicated to
+
+ align:start position:0%
+Tuesday is going to be dedicated to
+ 
+
+ align:start position:0%
+Tuesday is going to be dedicated to
+talking about teed but I'll I'll at
+
+ align:start position:0%
+talking about teed but I'll I'll at
+ 
+
+ align:start position:0%
+talking about teed but I'll I'll at
+least uh briefly introduce uh the topic
+
+ align:start position:0%
+least uh briefly introduce uh the topic
+ 
+
+ align:start position:0%
+least uh briefly introduce uh the topic
+okay let's go on to slide number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two on the right hand SL uh side of this
+
+ align:start position:0%
+two on the right hand SL uh side of this
+ 
+
+ align:start position:0%
+two on the right hand SL uh side of this
+uh slide is it's just a schematic
+
+ align:start position:0%
+uh slide is it's just a schematic
+ 
+
+ align:start position:0%
+uh slide is it's just a schematic
+picture um of a cartoon where you're um
+
+ align:start position:0%
+picture um of a cartoon where you're um
+ 
+
+ align:start position:0%
+picture um of a cartoon where you're um
+shooting an ion into a um a silicon
+
+ align:start position:0%
+shooting an ion into a um a silicon
+ 
+
+ align:start position:0%
+shooting an ion into a um a silicon
+surface and all these little um open
+
+ align:start position:0%
+surface and all these little um open
+ 
+
+ align:start position:0%
+surface and all these little um open
+symbols here represent silicon atoms on
+
+ align:start position:0%
+symbols here represent silicon atoms on
+ 
+
+ align:start position:0%
+symbols here represent silicon atoms on
+some kind of a lattice you see an ion
+
+ align:start position:0%
+some kind of a lattice you see an ion
+ 
+
+ align:start position:0%
+some kind of a lattice you see an ion
+which is this dark uh dark uh bullet
+
+ align:start position:0%
+which is this dark uh dark uh bullet
+ 
+
+ align:start position:0%
+which is this dark uh dark uh bullet
+that here it comes in and it hits the
+
+ align:start position:0%
+that here it comes in and it hits the
+ 
+
+ align:start position:0%
+that here it comes in and it hits the
+target and what it does it may have have
+
+ align:start position:0%
+target and what it does it may have have
+ 
+
+ align:start position:0%
+target and what it does it may have have
+some kind of a nuclear Collision here it
+
+ align:start position:0%
+some kind of a nuclear Collision here it
+ 
+
+ align:start position:0%
+some kind of a nuclear Collision here it
+may Collide uh with the target atom and
+
+ align:start position:0%
+may Collide uh with the target atom and
+ 
+
+ align:start position:0%
+may Collide uh with the target atom and
+be deflected uh there'll be some energy
+
+ align:start position:0%
+be deflected uh there'll be some energy
+ 
+
+ align:start position:0%
+be deflected uh there'll be some energy
+loss there then the target atom itself
+
+ align:start position:0%
+loss there then the target atom itself
+ 
+
+ align:start position:0%
+loss there then the target atom itself
+is going to be um recoiled uh in and and
+
+ align:start position:0%
+is going to be um recoiled uh in and and
+ 
+
+ align:start position:0%
+is going to be um recoiled uh in and and
+and will have some energy imparted to it
+
+ align:start position:0%
+and will have some energy imparted to it
+ 
+
+ align:start position:0%
+and will have some energy imparted to it
+but that deflection is going to then
+
+ align:start position:0%
+but that deflection is going to then
+ 
+
+ align:start position:0%
+but that deflection is going to then
+knock the uh ion a little bit uh into a
+
+ align:start position:0%
+knock the uh ion a little bit uh into a
+ 
+
+ align:start position:0%
+knock the uh ion a little bit uh into a
+different direction change its direction
+
+ align:start position:0%
+different direction change its direction
+ 
+
+ align:start position:0%
+different direction change its direction
+and interestingly you see it going down
+
+ align:start position:0%
+and interestingly you see it going down
+ 
+
+ align:start position:0%
+and interestingly you see it going down
+a path and right here after this
+
+ align:start position:0%
+a path and right here after this
+ 
+
+ align:start position:0%
+a path and right here after this
+Collision right here interestingly the
+
+ align:start position:0%
+Collision right here interestingly the
+ 
+
+ align:start position:0%
+Collision right here interestingly the
+ion got knocked into a channel is what
+
+ align:start position:0%
+ion got knocked into a channel is what
+ 
+
+ align:start position:0%
+ion got knocked into a channel is what
+we're supposed to to represent you see
+
+ align:start position:0%
+we're supposed to to represent you see
+ 
+
+ align:start position:0%
+we're supposed to to represent you see
+the ion got its direction got changed by
+
+ align:start position:0%
+the ion got its direction got changed by
+ 
+
+ align:start position:0%
+the ion got its direction got changed by
+this nuclear collision and now it's it's
+
+ align:start position:0%
+this nuclear collision and now it's it's
+ 
+
+ align:start position:0%
+this nuclear collision and now it's it's
+work it's working its way down a little
+
+ align:start position:0%
+work it's working its way down a little
+ 
+
+ align:start position:0%
+work it's working its way down a little
+bit of a channel still losing energy
+
+ align:start position:0%
+bit of a channel still losing energy
+ 
+
+ align:start position:0%
+bit of a channel still losing energy
+perhaps at a slightly different rate and
+
+ align:start position:0%
+perhaps at a slightly different rate and
+ 
+
+ align:start position:0%
+perhaps at a slightly different rate and
+still with each Collision creating a
+
+ align:start position:0%
+still with each Collision creating a
+ 
+
+ align:start position:0%
+still with each Collision creating a
+silicon uh recoil that that's been
+
+ align:start position:0%
+silicon uh recoil that that's been
+ 
+
+ align:start position:0%
+silicon uh recoil that that's been
+knocked off its
+
+ align:start position:0%
+knocked off its
+ 
+
+ align:start position:0%
+knocked off its
+lattice so just a very schematic picture
+
+ align:start position:0%
+lattice so just a very schematic picture
+ 
+
+ align:start position:0%
+lattice so just a very schematic picture
+so we're again we're bombarding the
+
+ align:start position:0%
+so we're again we're bombarding the
+ 
+
+ align:start position:0%
+so we're again we're bombarding the
+wafer the energy of this incoming uh
+
+ align:start position:0%
+wafer the energy of this incoming uh
+ 
+
+ align:start position:0%
+wafer the energy of this incoming uh
+dark colored ion is typically anywhere
+
+ align:start position:0%
+dark colored ion is typically anywhere
+ 
+
+ align:start position:0%
+dark colored ion is typically anywhere
+well some of the lowest energy implants
+
+ align:start position:0%
+well some of the lowest energy implants
+ 
+
+ align:start position:0%
+well some of the lowest energy implants
+being being done today are 1 kilovolt or
+
+ align:start position:0%
+being being done today are 1 kilovolt or
+ 
+
+ align:start position:0%
+being being done today are 1 kilovolt or
+maybe slightly less that's very low but
+
+ align:start position:0%
+maybe slightly less that's very low but
+ 
+
+ align:start position:0%
+maybe slightly less that's very low but
+that's that is being done and some of
+
+ align:start position:0%
+that's that is being done and some of
+ 
+
+ align:start position:0%
+that's that is being done and some of
+the highest energy implants for making
+
+ align:start position:0%
+the highest energy implants for making
+ 
+
+ align:start position:0%
+the highest energy implants for making
+oh in bipolar they make um selectively
+
+ align:start position:0%
+oh in bipolar they make um selectively
+ 
+
+ align:start position:0%
+oh in bipolar they make um selectively
+implanted collector regions that are
+
+ align:start position:0%
+implanted collector regions that are
+ 
+
+ align:start position:0%
+implanted collector regions that are
+quite deep um they they can work in the
+
+ align:start position:0%
+quite deep um they they can work in the
+ 
+
+ align:start position:0%
+quite deep um they they can work in the
+one MV range so there's a very wide
+
+ align:start position:0%
+one MV range so there's a very wide
+ 
+
+ align:start position:0%
+one MV range so there's a very wide
+range of that people are on imp planting
+
+ align:start position:0%
+range of that people are on imp planting
+ 
+
+ align:start position:0%
+range of that people are on imp planting
+typically implants are between you know
+
+ align:start position:0%
+typically implants are between you know
+ 
+
+ align:start position:0%
+typically implants are between you know
+something like 10 to 100 K but there
+
+ align:start position:0%
+something like 10 to 100 K but there
+ 
+
+ align:start position:0%
+something like 10 to 100 K but there
+people to use the full range now look at
+
+ align:start position:0%
+people to use the full range now look at
+ 
+
+ align:start position:0%
+people to use the full range now look at
+The Binding energy of a silicon atom on
+
+ align:start position:0%
+The Binding energy of a silicon atom on
+ 
+
+ align:start position:0%
+The Binding energy of a silicon atom on
+the lattice that's only 15 electron
+
+ align:start position:0%
+the lattice that's only 15 electron
+ 
+
+ align:start position:0%
+the lattice that's only 15 electron
+volts so you can imagine that we're
+
+ align:start position:0%
+volts so you can imagine that we're
+ 
+
+ align:start position:0%
+volts so you can imagine that we're
+coming in with a species that has
+
+ align:start position:0%
+coming in with a species that has
+ 
+
+ align:start position:0%
+coming in with a species that has
+thousands of times more energy than the
+
+ align:start position:0%
+thousands of times more energy than the
+ 
+
+ align:start position:0%
+thousands of times more energy than the
+binding energy so obviously if um it's
+
+ align:start position:0%
+binding energy so obviously if um it's
+ 
+
+ align:start position:0%
+binding energy so obviously if um it's
+quite possible to have you know bilar
+
+ align:start position:0%
+quite possible to have you know bilar
+ 
+
+ align:start position:0%
+quite possible to have you know bilar
+ball like collisions where you knock
+
+ align:start position:0%
+ball like collisions where you knock
+ 
+
+ align:start position:0%
+ball like collisions where you knock
+these silicon atoms off of their ltic
+
+ align:start position:0%
+these silicon atoms off of their ltic
+ 
+
+ align:start position:0%
+these silicon atoms off of their ltic
+sites so the ions Collide um and they
+
+ align:start position:0%
+sites so the ions Collide um and they
+ 
+
+ align:start position:0%
+sites so the ions Collide um and they
+Collide elastically uh and they have uh
+
+ align:start position:0%
+Collide elastically uh and they have uh
+ 
+
+ align:start position:0%
+Collide elastically uh and they have uh
+uh as a result we have ion deflections
+
+ align:start position:0%
+uh as a result we have ion deflections
+ 
+
+ align:start position:0%
+uh as a result we have ion deflections
+which I just showed you here where the
+
+ align:start position:0%
+which I just showed you here where the
+ 
+
+ align:start position:0%
+which I just showed you here where the
+ions change their Direction and when you
+
+ align:start position:0%
+ions change their Direction and when you
+ 
+
+ align:start position:0%
+ions change their Direction and when you
+Collide of course you lose a certain
+
+ align:start position:0%
+Collide of course you lose a certain
+ 
+
+ align:start position:0%
+Collide of course you lose a certain
+amount of energy uh the ion loses some
+
+ align:start position:0%
+amount of energy uh the ion loses some
+ 
+
+ align:start position:0%
+amount of energy uh the ion loses some
+energy and it displaces silicon atoms
+
+ align:start position:0%
+energy and it displaces silicon atoms
+ 
+
+ align:start position:0%
+energy and it displaces silicon atoms
+which we end up calling
+
+ align:start position:0%
+which we end up calling
+ 
+
+ align:start position:0%
+which we end up calling
+recoils in addition to this Collision
+
+ align:start position:0%
+recoils in addition to this Collision
+ 
+
+ align:start position:0%
+recoils in addition to this Collision
+this this sort of pool table type of
+
+ align:start position:0%
+this this sort of pool table type of
+ 
+
+ align:start position:0%
+this this sort of pool table type of
+collision uh of bilar balls the ions can
+
+ align:start position:0%
+collision uh of bilar balls the ions can
+ 
+
+ align:start position:0%
+collision uh of bilar balls the ions can
+also uh suffer sort of an inelastic drag
+
+ align:start position:0%
+also uh suffer sort of an inelastic drag
+ 
+
+ align:start position:0%
+also uh suffer sort of an inelastic drag
+Force um from the target electrons and
+
+ align:start position:0%
+Force um from the target electrons and
+ 
+
+ align:start position:0%
+Force um from the target electrons and
+so this leads to an electronic stopping
+
+ align:start position:0%
+so this leads to an electronic stopping
+ 
+
+ align:start position:0%
+so this leads to an electronic stopping
+where the where you lose ion energy and
+
+ align:start position:0%
+where the where you lose ion energy and
+ 
+
+ align:start position:0%
+where the where you lose ion energy and
+it actually hats the lattice to a
+
+ align:start position:0%
+it actually hats the lattice to a
+ 
+
+ align:start position:0%
+it actually hats the lattice to a
+certain extent uh because they're this
+
+ align:start position:0%
+certain extent uh because they're this
+ 
+
+ align:start position:0%
+certain extent uh because they're this
+this medium that has electrons in it um
+
+ align:start position:0%
+this medium that has electrons in it um
+ 
+
+ align:start position:0%
+this medium that has electrons in it um
+eventually this ion and all the ions
+
+ align:start position:0%
+eventually this ion and all the ions
+ 
+
+ align:start position:0%
+eventually this ion and all the ions
+come to rest after they've lost all of
+
+ align:start position:0%
+come to rest after they've lost all of
+ 
+
+ align:start position:0%
+come to rest after they've lost all of
+their energy in both collisional
+
+ align:start position:0%
+their energy in both collisional
+ 
+
+ align:start position:0%
+their energy in both collisional
+processes and in this drag force uh and
+
+ align:start position:0%
+processes and in this drag force uh and
+ 
+
+ align:start position:0%
+processes and in this drag force uh and
+channeling as I I mentioned we talked
+
+ align:start position:0%
+channeling as I I mentioned we talked
+ 
+
+ align:start position:0%
+channeling as I I mentioned we talked
+about last time along certain directions
+
+ align:start position:0%
+about last time along certain directions
+ 
+
+ align:start position:0%
+about last time along certain directions
+ions can travel in the crystal uh with
+
+ align:start position:0%
+ions can travel in the crystal uh with
+ 
+
+ align:start position:0%
+ions can travel in the crystal uh with
+very few collisions and little drag so
+
+ align:start position:0%
+very few collisions and little drag so
+ 
+
+ align:start position:0%
+very few collisions and little drag so
+they can go uh deeper than they would
+
+ align:start position:0%
+they can go uh deeper than they would
+ 
+
+ align:start position:0%
+they can go uh deeper than they would
+otherwise and that's and that's tough to
+
+ align:start position:0%
+otherwise and that's and that's tough to
+ 
+
+ align:start position:0%
+otherwise and that's and that's tough to
+model so if we go to page uh three uh or
+
+ align:start position:0%
+model so if we go to page uh three uh or
+ 
+
+ align:start position:0%
+model so if we go to page uh three uh or
+slide three uh how do we model these
+
+ align:start position:0%
+slide three uh how do we model these
+ 
+
+ align:start position:0%
+slide three uh how do we model these
+range statistics well uh what we do is
+
+ align:start position:0%
+range statistics well uh what we do is
+ 
+
+ align:start position:0%
+range statistics well uh what we do is
+we write down the total energy loss
+
+ align:start position:0%
+we write down the total energy loss
+ 
+
+ align:start position:0%
+we write down the total energy loss
+during an ion trajectory trajectory and
+
+ align:start position:0%
+during an ion trajectory trajectory and
+ 
+
+ align:start position:0%
+during an ion trajectory trajectory and
+we write it as a linear sum so we treat
+
+ align:start position:0%
+we write it as a linear sum so we treat
+ 
+
+ align:start position:0%
+we write it as a linear sum so we treat
+these two processes independently
+
+ align:start position:0%
+these two processes independently
+ 
+
+ align:start position:0%
+these two processes independently
+nuclear um losses and electronic losses
+
+ align:start position:0%
+nuclear um losses and electronic losses
+ 
+
+ align:start position:0%
+nuclear um losses and electronic losses
+so we write uh the rate of energy loss
+
+ align:start position:0%
+so we write uh the rate of energy loss
+ 
+
+ align:start position:0%
+so we write uh the rate of energy loss
+as a function of distance as this
+
+ align:start position:0%
+as a function of distance as this
+ 
+
+ align:start position:0%
+as a function of distance as this
+equation d by
+
+ align:start position:0%
+equation d by
+ 
+
+ align:start position:0%
+equation d by
+DX um uh is given by uh it's a negative
+
+ align:start position:0%
+DX um uh is given by uh it's a negative
+ 
+
+ align:start position:0%
+DX um uh is given by uh it's a negative
+number because it's you're losing energy
+
+ align:start position:0%
+number because it's you're losing energy
+ 
+
+ align:start position:0%
+number because it's you're losing energy
+n where n is the target atom density
+
+ align:start position:0%
+n where n is the target atom density
+ 
+
+ align:start position:0%
+n where n is the target atom density
+atoms per cubic centimeter times the Su
+
+ align:start position:0%
+atoms per cubic centimeter times the Su
+ 
+
+ align:start position:0%
+atoms per cubic centimeter times the Su
+of these two um quantities S subn Plus
+
+ align:start position:0%
+of these two um quantities S subn Plus
+ 
+
+ align:start position:0%
+of these two um quantities S subn Plus
+sub
+
+ align:start position:0%
+sub
+ 
+
+ align:start position:0%
+sub
+subb again n is the target atom density
+
+ align:start position:0%
+subb again n is the target atom density
+ 
+
+ align:start position:0%
+subb again n is the target atom density
+s subn is a function of energy it's the
+
+ align:start position:0%
+s subn is a function of energy it's the
+ 
+
+ align:start position:0%
+s subn is a function of energy it's the
+nuclear stopping power uh it's uh and it
+
+ align:start position:0%
+nuclear stopping power uh it's uh and it
+ 
+
+ align:start position:0%
+nuclear stopping power uh it's uh and it
+has units of energy uh times area so
+
+ align:start position:0%
+has units of energy uh times area so
+ 
+
+ align:start position:0%
+has units of energy uh times area so
+it's EV sl- cenim squ is a typical unit
+
+ align:start position:0%
+it's EV sl- cenim squ is a typical unit
+ 
+
+ align:start position:0%
+it's EV sl- cenim squ is a typical unit
+and s to b is the electronic stopping
+
+ align:start position:0%
+and s to b is the electronic stopping
+ 
+
+ align:start position:0%
+and s to b is the electronic stopping
+power again EV cim squ and you can see
+
+ align:start position:0%
+power again EV cim squ and you can see
+ 
+
+ align:start position:0%
+power again EV cim squ and you can see
+the units work out if s has units of EV
+
+ align:start position:0%
+the units work out if s has units of EV
+ 
+
+ align:start position:0%
+the units work out if s has units of EV
+centimet squared you multiply it by
+
+ align:start position:0%
+centimet squared you multiply it by
+ 
+
+ align:start position:0%
+centimet squared you multiply it by
+atoms per cubic centimeter you get a
+
+ align:start position:0%
+atoms per cubic centimeter you get a
+ 
+
+ align:start position:0%
+atoms per cubic centimeter you get a
+certain amount of EV per centimeter or
+
+ align:start position:0%
+certain amount of EV per centimeter or
+ 
+
+ align:start position:0%
+certain amount of EV per centimeter or
+energy loss per unit length uh in in
+
+ align:start position:0%
+energy loss per unit length uh in in
+ 
+
+ align:start position:0%
+energy loss per unit length uh in in
+going into the
+
+ align:start position:0%
+going into the
+ 
+
+ align:start position:0%
+going into the
+crystal the thing to remember is that
+
+ align:start position:0%
+crystal the thing to remember is that
+ 
+
+ align:start position:0%
+crystal the thing to remember is that
+these functions these are in general the
+
+ align:start position:0%
+these functions these are in general the
+ 
+
+ align:start position:0%
+these functions these are in general the
+stopping powers are going to be a
+
+ align:start position:0%
+stopping powers are going to be a
+ 
+
+ align:start position:0%
+stopping powers are going to be a
+function of the energy um that is the
+
+ align:start position:0%
+function of the energy um that is the
+ 
+
+ align:start position:0%
+function of the energy um that is the
+rate at which you lose energy is a
+
+ align:start position:0%
+rate at which you lose energy is a
+ 
+
+ align:start position:0%
+rate at which you lose energy is a
+function of how fast you're going of how
+
+ align:start position:0%
+function of how fast you're going of how
+ 
+
+ align:start position:0%
+function of how fast you're going of how
+much energy you actually have um if we
+
+ align:start position:0%
+much energy you actually have um if we
+ 
+
+ align:start position:0%
+much energy you actually have um if we
+know s subn of e as a function and we
+
+ align:start position:0%
+know s subn of e as a function and we
+ 
+
+ align:start position:0%
+know s subn of e as a function and we
+know SB the electronic stopping as a
+
+ align:start position:0%
+know SB the electronic stopping as a
+ 
+
+ align:start position:0%
+know SB the electronic stopping as a
+function of energy then you can simply
+
+ align:start position:0%
+function of energy then you can simply
+ 
+
+ align:start position:0%
+function of energy then you can simply
+compute the range by doing this integral
+
+ align:start position:0%
+compute the range by doing this integral
+ 
+
+ align:start position:0%
+compute the range by doing this integral
+so you integrate the range would just be
+
+ align:start position:0%
+so you integrate the range would just be
+ 
+
+ align:start position:0%
+so you integrate the range would just be
+the integral from zero to e uh e uh
+
+ align:start position:0%
+the integral from zero to e uh e uh
+ 
+
+ align:start position:0%
+the integral from zero to e uh e uh
+whatever your incoming energy is your
+
+ align:start position:0%
+whatever your incoming energy is your
+ 
+
+ align:start position:0%
+whatever your incoming energy is your
+inip plet energy say 100 kilovolts of De
+
+ align:start position:0%
+inip plet energy say 100 kilovolts of De
+ 
+
+ align:start position:0%
+inip plet energy say 100 kilovolts of De
+divided by um the sum of the two um uh
+
+ align:start position:0%
+divided by um the sum of the two um uh
+ 
+
+ align:start position:0%
+divided by um the sum of the two um uh
+stopping powers and the here again the
+
+ align:start position:0%
+stopping powers and the here again the
+ 
+
+ align:start position:0%
+stopping powers and the here again the
+density is a constant number it's just
+
+ align:start position:0%
+density is a constant number it's just
+ 
+
+ align:start position:0%
+density is a constant number it's just
+been pulled out so you can find the
+
+ align:start position:0%
+been pulled out so you can find the
+ 
+
+ align:start position:0%
+been pulled out so you can find the
+range uh mathematically if you know the
+
+ align:start position:0%
+range uh mathematically if you know the
+ 
+
+ align:start position:0%
+range uh mathematically if you know the
+physics of these two stopping
+
+ align:start position:0%
+physics of these two stopping
+ 
+
+ align:start position:0%
+physics of these two stopping
+Powers so that's where a lot of the
+
+ align:start position:0%
+Powers so that's where a lot of the
+ 
+
+ align:start position:0%
+Powers so that's where a lot of the
+modeling uh has been done in
+
+ align:start position:0%
+modeling uh has been done in
+ 
+
+ align:start position:0%
+modeling uh has been done in
+understanding the physics of s suben s
+
+ align:start position:0%
+understanding the physics of s suben s
+ 
+
+ align:start position:0%
+understanding the physics of s suben s
+and and we'll first talk about um on
+
+ align:start position:0%
+and and we'll first talk about um on
+ 
+
+ align:start position:0%
+and and we'll first talk about um on
+slide four talk about nucleus stopping
+
+ align:start position:0%
+slide four talk about nucleus stopping
+ 
+
+ align:start position:0%
+slide four talk about nucleus stopping
+uh it it above a certain energy so it's
+
+ align:start position:0%
+uh it it above a certain energy so it's
+ 
+
+ align:start position:0%
+uh it it above a certain energy so it's
+about half a half a kilovolt or five EV
+
+ align:start position:0%
+about half a half a kilovolt or five EV
+ 
+
+ align:start position:0%
+about half a half a kilovolt or five EV
+now be careful because we're approaching
+
+ align:start position:0%
+now be careful because we're approaching
+ 
+
+ align:start position:0%
+now be careful because we're approaching
+this range for some of our very lowest
+
+ align:start position:0%
+this range for some of our very lowest
+ 
+
+ align:start position:0%
+this range for some of our very lowest
+energy implants making very shallow sore
+
+ align:start position:0%
+energy implants making very shallow sore
+ 
+
+ align:start position:0%
+energy implants making very shallow sore
+strain extensions people are using quite
+
+ align:start position:0%
+strain extensions people are using quite
+ 
+
+ align:start position:0%
+strain extensions people are using quite
+low energies but if you're above this
+
+ align:start position:0%
+low energies but if you're above this
+ 
+
+ align:start position:0%
+low energies but if you're above this
+it's it's reasonably valid to model
+
+ align:start position:0%
+it's it's reasonably valid to model
+ 
+
+ align:start position:0%
+it's it's reasonably valid to model
+nuclear stopping uh as a classical two
+
+ align:start position:0%
+nuclear stopping uh as a classical two
+ 
+
+ align:start position:0%
+nuclear stopping uh as a classical two
+body collision between um a um a silicon
+
+ align:start position:0%
+body collision between um a um a silicon
+ 
+
+ align:start position:0%
+body collision between um a um a silicon
+atom that's sitting still and an instant
+
+ align:start position:0%
+atom that's sitting still and an instant
+ 
+
+ align:start position:0%
+atom that's sitting still and an instant
+ion that's coming in with some uh some
+
+ align:start position:0%
+ion that's coming in with some uh some
+ 
+
+ align:start position:0%
+ion that's coming in with some uh some
+velocity so it can be bottled as a uh
+
+ align:start position:0%
+velocity so it can be bottled as a uh
+ 
+
+ align:start position:0%
+velocity so it can be bottled as a uh
+just like on a pool table two balls
+
+ align:start position:0%
+just like on a pool table two balls
+ 
+
+ align:start position:0%
+just like on a pool table two balls
+colliding uh using the conservation of
+
+ align:start position:0%
+colliding uh using the conservation of
+ 
+
+ align:start position:0%
+colliding uh using the conservation of
+energy and the conservation of momentum
+
+ align:start position:0%
+energy and the conservation of momentum
+ 
+
+ align:start position:0%
+energy and the conservation of momentum
+principles that you learned in your
+
+ align:start position:0%
+principles that you learned in your
+ 
+
+ align:start position:0%
+principles that you learned in your
+basic physics class um now why does this
+
+ align:start position:0%
+basic physics class um now why does this
+ 
+
+ align:start position:0%
+basic physics class um now why does this
+have to be above a certain energy why is
+
+ align:start position:0%
+have to be above a certain energy why is
+ 
+
+ align:start position:0%
+have to be above a certain energy why is
+that the case well it turns out if the
+
+ align:start position:0%
+that the case well it turns out if the
+ 
+
+ align:start position:0%
+that the case well it turns out if the
+energy is is lower than this or
+
+ align:start position:0%
+energy is is lower than this or
+ 
+
+ align:start position:0%
+energy is is lower than this or
+significantly lower then what happens is
+
+ align:start position:0%
+significantly lower then what happens is
+ 
+
+ align:start position:0%
+significantly lower then what happens is
+as this incident ion comes in instead of
+
+ align:start position:0%
+as this incident ion comes in instead of
+ 
+
+ align:start position:0%
+as this incident ion comes in instead of
+sort of looking like a billiard ball um
+
+ align:start position:0%
+sort of looking like a billiard ball um
+ 
+
+ align:start position:0%
+sort of looking like a billiard ball um
+a hard sphere model this ion has time to
+
+ align:start position:0%
+a hard sphere model this ion has time to
+ 
+
+ align:start position:0%
+a hard sphere model this ion has time to
+sort of hang around the target atom and
+
+ align:start position:0%
+sort of hang around the target atom and
+ 
+
+ align:start position:0%
+sort of hang around the target atom and
+the interaction is not just like a um a
+
+ align:start position:0%
+the interaction is not just like a um a
+ 
+
+ align:start position:0%
+the interaction is not just like a um a
+hard SPI Collision you have other types
+
+ align:start position:0%
+hard SPI Collision you have other types
+ 
+
+ align:start position:0%
+hard SPI Collision you have other types
+of of interactions you could have
+
+ align:start position:0%
+of of interactions you could have
+ 
+
+ align:start position:0%
+of of interactions you could have
+multiple uh interacts with a lattice
+
+ align:start position:0%
+multiple uh interacts with a lattice
+ 
+
+ align:start position:0%
+multiple uh interacts with a lattice
+maybe in in the sense of it's going slow
+
+ align:start position:0%
+maybe in in the sense of it's going slow
+ 
+
+ align:start position:0%
+maybe in in the sense of it's going slow
+enough that as it passes by the nucleus
+
+ align:start position:0%
+enough that as it passes by the nucleus
+ 
+
+ align:start position:0%
+enough that as it passes by the nucleus
+it has different types of interaction so
+
+ align:start position:0%
+it has different types of interaction so
+ 
+
+ align:start position:0%
+it has different types of interaction so
+um if you your energy is low enough
+
+ align:start position:0%
+um if you your energy is low enough
+ 
+
+ align:start position:0%
+um if you your energy is low enough
+these these models break down but the
+
+ align:start position:0%
+these these models break down but the
+ 
+
+ align:start position:0%
+these these models break down but the
+good thing about ion implantation most
+
+ align:start position:0%
+good thing about ion implantation most
+ 
+
+ align:start position:0%
+good thing about ion implantation most
+of the time you're you're well above
+
+ align:start position:0%
+of the time you're you're well above
+ 
+
+ align:start position:0%
+of the time you're you're well above
+that U that
+
+ align:start position:0%
+that U that
+ 
+
+ align:start position:0%
+that U that
+threshold so uh as you remember from
+
+ align:start position:0%
+threshold so uh as you remember from
+ 
+
+ align:start position:0%
+threshold so uh as you remember from
+your basic physics class we have an
+
+ align:start position:0%
+your basic physics class we have an
+ 
+
+ align:start position:0%
+your basic physics class we have an
+incident ball coming in hitting another
+
+ align:start position:0%
+incident ball coming in hitting another
+ 
+
+ align:start position:0%
+incident ball coming in hitting another
+ball that was originally at rest this
+
+ align:start position:0%
+ball that was originally at rest this
+ 
+
+ align:start position:0%
+ball that was originally at rest this
+incident ion is is going to be scattered
+
+ align:start position:0%
+incident ion is is going to be scattered
+ 
+
+ align:start position:0%
+incident ion is is going to be scattered
+at some angle uh and you can figure that
+
+ align:start position:0%
+at some angle uh and you can figure that
+ 
+
+ align:start position:0%
+at some angle uh and you can figure that
+out once you know the interaction
+
+ align:start position:0%
+out once you know the interaction
+ 
+
+ align:start position:0%
+out once you know the interaction
+potential v as a function of r r being
+
+ align:start position:0%
+potential v as a function of r r being
+ 
+
+ align:start position:0%
+potential v as a function of r r being
+the distance between the two bodies uh
+
+ align:start position:0%
+the distance between the two bodies uh
+ 
+
+ align:start position:0%
+the distance between the two bodies uh
+once that's known um then you integrate
+
+ align:start position:0%
+once that's known um then you integrate
+ 
+
+ align:start position:0%
+once that's known um then you integrate
+that uh along the path of the iron you
+
+ align:start position:0%
+that uh along the path of the iron you
+ 
+
+ align:start position:0%
+that uh along the path of the iron you
+can calculate the scattering angle for
+
+ align:start position:0%
+can calculate the scattering angle for
+ 
+
+ align:start position:0%
+can calculate the scattering angle for
+the Collision uh and uh you can you can
+
+ align:start position:0%
+the Collision uh and uh you can you can
+ 
+
+ align:start position:0%
+the Collision uh and uh you can you can
+do it once and then do it look look in a
+
+ align:start position:0%
+do it once and then do it look look in a
+ 
+
+ align:start position:0%
+do it once and then do it look look in a
+lookup
+
+ align:start position:0%
+lookup
+ 
+
+ align:start position:0%
+lookup
+table um so you apply basic physics of
+
+ align:start position:0%
+table um so you apply basic physics of
+ 
+
+ align:start position:0%
+table um so you apply basic physics of
+uh conservation of energy momentum you
+
+ align:start position:0%
+uh conservation of energy momentum you
+ 
+
+ align:start position:0%
+uh conservation of energy momentum you
+can get these numbers again the inter
+
+ align:start position:0%
+can get these numbers again the inter
+ 
+
+ align:start position:0%
+can get these numbers again the inter
+thing about I implantation of all the
+
+ align:start position:0%
+thing about I implantation of all the
+ 
+
+ align:start position:0%
+thing about I implantation of all the
+processes we talk about in this class or
+
+ align:start position:0%
+processes we talk about in this class or
+ 
+
+ align:start position:0%
+processes we talk about in this class or
+anyone does in ic faab it's the only one
+
+ align:start position:0%
+anyone does in ic faab it's the only one
+ 
+
+ align:start position:0%
+anyone does in ic faab it's the only one
+where from first principles physics you
+
+ align:start position:0%
+where from first principles physics you
+ 
+
+ align:start position:0%
+where from first principles physics you
+can actually predict something you don't
+
+ align:start position:0%
+can actually predict something you don't
+ 
+
+ align:start position:0%
+can actually predict something you don't
+have too many uh free variables the way
+
+ align:start position:0%
+have too many uh free variables the way
+ 
+
+ align:start position:0%
+have too many uh free variables the way
+you do in some of these chemical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+processes so the what it boils down to
+
+ align:start position:0%
+processes so the what it boils down to
+ 
+
+ align:start position:0%
+processes so the what it boils down to
+as far as nuclear scattering goes is
+
+ align:start position:0%
+as far as nuclear scattering goes is
+ 
+
+ align:start position:0%
+as far as nuclear scattering goes is
+figuring out what are the what is the
+
+ align:start position:0%
+figuring out what are the what is the
+ 
+
+ align:start position:0%
+figuring out what are the what is the
+appropriate interaction potential the
+
+ align:start position:0%
+appropriate interaction potential the
+ 
+
+ align:start position:0%
+appropriate interaction potential the
+nuclear scattering potential well if you
+
+ align:start position:0%
+nuclear scattering potential well if you
+ 
+
+ align:start position:0%
+nuclear scattering potential well if you
+think about these two um
+
+ align:start position:0%
+think about these two um
+ 
+
+ align:start position:0%
+think about these two um
+bodies these two an ion and a silicon
+
+ align:start position:0%
+bodies these two an ion and a silicon
+ 
+
+ align:start position:0%
+bodies these two an ion and a silicon
+atom with the ion approaching it the um
+
+ align:start position:0%
+atom with the ion approaching it the um
+ 
+
+ align:start position:0%
+atom with the ion approaching it the um
+the first thing you might think about is
+
+ align:start position:0%
+the first thing you might think about is
+ 
+
+ align:start position:0%
+the first thing you might think about is
+because you know the nucleus is charged
+
+ align:start position:0%
+because you know the nucleus is charged
+ 
+
+ align:start position:0%
+because you know the nucleus is charged
+right it has a certain charge uh which
+
+ align:start position:0%
+right it has a certain charge uh which
+ 
+
+ align:start position:0%
+right it has a certain charge uh which
+is the um charge on the electron Q times
+
+ align:start position:0%
+is the um charge on the electron Q times
+ 
+
+ align:start position:0%
+is the um charge on the electron Q times
+it's the Z
+
+ align:start position:0%
+it's the Z
+ 
+
+ align:start position:0%
+it's the Z
+number okay so you might imagine that
+
+ align:start position:0%
+number okay so you might imagine that
+ 
+
+ align:start position:0%
+number okay so you might imagine that
+the the simplest type of potential
+
+ align:start position:0%
+the the simplest type of potential
+ 
+
+ align:start position:0%
+the the simplest type of potential
+interaction between these two charged
+
+ align:start position:0%
+interaction between these two charged
+ 
+
+ align:start position:0%
+interaction between these two charged
+nuclei um is just the kulic potential
+
+ align:start position:0%
+nuclei um is just the kulic potential
+ 
+
+ align:start position:0%
+nuclei um is just the kulic potential
+which is just given by uh the Z numbers
+
+ align:start position:0%
+which is just given by uh the Z numbers
+ 
+
+ align:start position:0%
+which is just given by uh the Z numbers
+multiplied together divided by R so it's
+
+ align:start position:0%
+multiplied together divided by R so it's
+ 
+
+ align:start position:0%
+multiplied together divided by R so it's
+a one over R type of uh good
+
+ align:start position:0%
+a one over R type of uh good
+ 
+
+ align:start position:0%
+a one over R type of uh good
+oldfashioned coolon
+
+ align:start position:0%
+oldfashioned coolon
+ 
+
+ align:start position:0%
+oldfashioned coolon
+potential that's a little bit too simple
+
+ align:start position:0%
+potential that's a little bit too simple
+ 
+
+ align:start position:0%
+potential that's a little bit too simple
+though because the an atom is just not a
+
+ align:start position:0%
+though because the an atom is just not a
+ 
+
+ align:start position:0%
+though because the an atom is just not a
+nucleus an atom has an electron cloud
+
+ align:start position:0%
+nucleus an atom has an electron cloud
+ 
+
+ align:start position:0%
+nucleus an atom has an electron cloud
+around it so the electrons around the
+
+ align:start position:0%
+around it so the electrons around the
+ 
+
+ align:start position:0%
+around it so the electrons around the
+target atom uh nucleus actually ends up
+
+ align:start position:0%
+target atom uh nucleus actually ends up
+ 
+
+ align:start position:0%
+target atom uh nucleus actually ends up
+screening the core potential of of the
+
+ align:start position:0%
+screening the core potential of of the
+ 
+
+ align:start position:0%
+screening the core potential of of the
+of the nucleus to a certain extent uh
+
+ align:start position:0%
+of the nucleus to a certain extent uh
+ 
+
+ align:start position:0%
+of the nucleus to a certain extent uh
+from the incoming ion so it's it's not
+
+ align:start position:0%
+from the incoming ion so it's it's not
+ 
+
+ align:start position:0%
+from the incoming ion so it's it's not
+this is a little bit oversimplified so
+
+ align:start position:0%
+this is a little bit oversimplified so
+ 
+
+ align:start position:0%
+this is a little bit oversimplified so
+what people do is they put in a
+
+ align:start position:0%
+what people do is they put in a
+ 
+
+ align:start position:0%
+what people do is they put in a
+generalized function f which they
+
+ align:start position:0%
+generalized function f which they
+ 
+
+ align:start position:0%
+generalized function f which they
+multiply by the classical aulum unscreen
+
+ align:start position:0%
+multiply by the classical aulum unscreen
+ 
+
+ align:start position:0%
+multiply by the classical aulum unscreen
+potential and then this becomes the
+
+ align:start position:0%
+potential and then this becomes the
+ 
+
+ align:start position:0%
+potential and then this becomes the
+screened potential V is a function of r
+
+ align:start position:0%
+screened potential V is a function of r
+ 
+
+ align:start position:0%
+screened potential V is a function of r
+f is some generalized function of um f
+
+ align:start position:0%
+f is some generalized function of um f
+ 
+
+ align:start position:0%
+f is some generalized function of um f
+over a r over a again R is the distance
+
+ align:start position:0%
+over a r over a again R is the distance
+ 
+
+ align:start position:0%
+over a r over a again R is the distance
+between the nucleus uh the two
+
+ align:start position:0%
+between the nucleus uh the two
+ 
+
+ align:start position:0%
+between the nucleus uh the two
+nuclei and um a is a Thomas FY parameter
+
+ align:start position:0%
+nuclei and um a is a Thomas FY parameter
+ 
+
+ align:start position:0%
+nuclei and um a is a Thomas FY parameter
+which is related to the bore radius it's
+
+ align:start position:0%
+which is related to the bore radius it's
+ 
+
+ align:start position:0%
+which is related to the bore radius it's
+some some function of the bore radius uh
+
+ align:start position:0%
+some some function of the bore radius uh
+ 
+
+ align:start position:0%
+some some function of the bore radius uh
+times a function of the Z numbers uh so
+
+ align:start position:0%
+times a function of the Z numbers uh so
+ 
+
+ align:start position:0%
+times a function of the Z numbers uh so
+it gives you a is some measure of the
+
+ align:start position:0%
+it gives you a is some measure of the
+ 
+
+ align:start position:0%
+it gives you a is some measure of the
+if you want to call it the the you know
+
+ align:start position:0%
+if you want to call it the the you know
+ 
+
+ align:start position:0%
+if you want to call it the the you know
+the size of the atom in some way um and
+
+ align:start position:0%
+the size of the atom in some way um and
+ 
+
+ align:start position:0%
+the size of the atom in some way um and
+R is of course the distance between the
+
+ align:start position:0%
+R is of course the distance between the
+ 
+
+ align:start position:0%
+R is of course the distance between the
+the two the the colliding ion and the
+
+ align:start position:0%
+the two the the colliding ion and the
+ 
+
+ align:start position:0%
+the two the the colliding ion and the
+Silicon uh atom so a very common uh
+
+ align:start position:0%
+Silicon uh atom so a very common uh
+ 
+
+ align:start position:0%
+Silicon uh atom so a very common uh
+potential that's often used is an
+
+ align:start position:0%
+potential that's often used is an
+ 
+
+ align:start position:0%
+potential that's often used is an
+exponential function you assume that the
+
+ align:start position:0%
+exponential function you assume that the
+ 
+
+ align:start position:0%
+exponential function you assume that the
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+exponentially um uh dampen out the
+
+ align:start position:0%
+exponentially um uh dampen out the
+ 
+
+ align:start position:0%
+exponentially um uh dampen out the
+coolum uh potential and people use
+
+ align:start position:0%
+coolum uh potential and people use
+ 
+
+ align:start position:0%
+coolum uh potential and people use
+what's called a Thomas fmy potential so
+
+ align:start position:0%
+what's called a Thomas fmy potential so
+ 
+
+ align:start position:0%
+what's called a Thomas fmy potential so
+this this function here shown on the
+
+ align:start position:0%
+this this function here shown on the
+ 
+
+ align:start position:0%
+this this function here shown on the
+third equation on Slide Five is the
+
+ align:start position:0%
+third equation on Slide Five is the
+ 
+
+ align:start position:0%
+third equation on Slide Five is the
+Thomas Fair meat potential for ION
+
+ align:start position:0%
+Thomas Fair meat potential for ION
+ 
+
+ align:start position:0%
+Thomas Fair meat potential for ION
+implantation so it's got a A 1 / R
+
+ align:start position:0%
+implantation so it's got a A 1 / R
+ 
+
+ align:start position:0%
+implantation so it's got a A 1 / R
+dependence times an exponential uh e the
+
+ align:start position:0%
+dependence times an exponential uh e the
+ 
+
+ align:start position:0%
+dependence times an exponential uh e the
+minus r over a where again again a is
+
+ align:start position:0%
+minus r over a where again again a is
+ 
+
+ align:start position:0%
+minus r over a where again again a is
+this Thomas fmy um screening
+
+ align:start position:0%
+this Thomas fmy um screening
+ 
+
+ align:start position:0%
+this Thomas fmy um screening
+parameter that's potential that's one
+
+ align:start position:0%
+parameter that's potential that's one
+ 
+
+ align:start position:0%
+parameter that's potential that's one
+that was often used in modeling of O
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implantation so it turns
+
+ align:start position:0%
+implantation so it turns
+ 
+
+ align:start position:0%
+implantation so it turns
+out that when the screening function is
+
+ align:start position:0%
+out that when the screening function is
+ 
+
+ align:start position:0%
+out that when the screening function is
+instead um uh of using exponential if
+
+ align:start position:0%
+instead um uh of using exponential if
+ 
+
+ align:start position:0%
+instead um uh of using exponential if
+you use the screening function F just to
+
+ align:start position:0%
+you use the screening function F just to
+ 
+
+ align:start position:0%
+you use the screening function F just to
+be a over R um then it's it's um it
+
+ align:start position:0%
+be a over R um then it's it's um it
+ 
+
+ align:start position:0%
+be a over R um then it's it's um it
+turns out that if this F is just a over
+
+ align:start position:0%
+turns out that if this F is just a over
+ 
+
+ align:start position:0%
+turns out that if this F is just a over
+R then this just the potential just goes
+
+ align:start position:0%
+R then this just the potential just goes
+ 
+
+ align:start position:0%
+R then this just the potential just goes
+like one over R squ that's another way
+
+ align:start position:0%
+like one over R squ that's another way
+ 
+
+ align:start position:0%
+like one over R squ that's another way
+of doing the screening function uh in
+
+ align:start position:0%
+of doing the screening function uh in
+ 
+
+ align:start position:0%
+of doing the screening function uh in
+that case the nuclear stopping power can
+
+ align:start position:0%
+that case the nuclear stopping power can
+ 
+
+ align:start position:0%
+that case the nuclear stopping power can
+be approximated by a
+
+ align:start position:0%
+be approximated by a
+ 
+
+ align:start position:0%
+be approximated by a
+constant um so it turns out that this
+
+ align:start position:0%
+constant um so it turns out that this
+ 
+
+ align:start position:0%
+constant um so it turns out that this
+this number if you and if if you want to
+
+ align:start position:0%
+this number if you and if if you want to
+ 
+
+ align:start position:0%
+this number if you and if if you want to
+see that derivation you can go to this
+
+ align:start position:0%
+see that derivation you can go to this
+ 
+
+ align:start position:0%
+see that derivation you can go to this
+article by Gibbons back from the
+
+ align:start position:0%
+article by Gibbons back from the
+ 
+
+ align:start position:0%
+article by Gibbons back from the
+proceedings of the i e uh oh um back in
+
+ align:start position:0%
+proceedings of the i e uh oh um back in
+ 
+
+ align:start position:0%
+proceedings of the i e uh oh um back in
+1968 and in fact they deriv that it can
+
+ align:start position:0%
+1968 and in fact they deriv that it can
+ 
+
+ align:start position:0%
+1968 and in fact they deriv that it can
+be a constant number um that depends
+
+ align:start position:0%
+be a constant number um that depends
+ 
+
+ align:start position:0%
+be a constant number um that depends
+just on the Z number uh of the ion uh
+
+ align:start position:0%
+just on the Z number uh of the ion uh
+ 
+
+ align:start position:0%
+just on the Z number uh of the ion uh
+and it's and the mass of the ion and the
+
+ align:start position:0%
+and it's and the mass of the ion and the
+ 
+
+ align:start position:0%
+and it's and the mass of the ion and the
+Z number in the mass of the
+
+ align:start position:0%
+Z number in the mass of the
+ 
+
+ align:start position:0%
+Z number in the mass of the
+substrate so this is a simple equation
+
+ align:start position:0%
+substrate so this is a simple equation
+ 
+
+ align:start position:0%
+substrate so this is a simple equation
+you can use if you're stuck on a desert
+
+ align:start position:0%
+you can use if you're stuck on a desert
+ 
+
+ align:start position:0%
+you can use if you're stuck on a desert
+island you need to know stopping nuclear
+
+ align:start position:0%
+island you need to know stopping nuclear
+ 
+
+ align:start position:0%
+island you need to know stopping nuclear
+stopping power you can just program this
+
+ align:start position:0%
+stopping power you can just program this
+ 
+
+ align:start position:0%
+stopping power you can just program this
+into your calculator and and I just did
+
+ align:start position:0%
+into your calculator and and I just did
+ 
+
+ align:start position:0%
+into your calculator and and I just did
+a simple calculation for phosphorus
+
+ align:start position:0%
+a simple calculation for phosphorus
+ 
+
+ align:start position:0%
+a simple calculation for phosphorus
+which has a z number of 15 and an atomic
+
+ align:start position:0%
+which has a z number of 15 and an atomic
+ 
+
+ align:start position:0%
+which has a z number of 15 and an atomic
+mass of twice that or roughly of 31
+
+ align:start position:0%
+mass of twice that or roughly of 31
+ 
+
+ align:start position:0%
+mass of twice that or roughly of 31
+silicon has a z number of 14 a mass of
+
+ align:start position:0%
+silicon has a z number of 14 a mass of
+ 
+
+ align:start position:0%
+silicon has a z number of 14 a mass of
+28 AMU you plug these numbers in and you
+
+ align:start position:0%
+28 AMU you plug these numbers in and you
+ 
+
+ align:start position:0%
+28 AMU you plug these numbers in and you
+do the calculation I get an s subn
+
+ align:start position:0%
+do the calculation I get an s subn
+ 
+
+ align:start position:0%
+do the calculation I get an s subn
+number of about
+
+ align:start position:0%
+number of about
+ 
+
+ align:start position:0%
+number of about
+550 Kil electron volts per
+
+ align:start position:0%
+550 Kil electron volts per
+ 
+
+ align:start position:0%
+550 Kil electron volts per
+Micron so that's how much energy I
+
+ align:start position:0%
+Micron so that's how much energy I
+ 
+
+ align:start position:0%
+Micron so that's how much energy I
+phosphorus going in you know assuming
+
+ align:start position:0%
+phosphorus going in you know assuming
+ 
+
+ align:start position:0%
+phosphorus going in you know assuming
+it's a constant linear number 550 K per
+
+ align:start position:0%
+it's a constant linear number 550 K per
+ 
+
+ align:start position:0%
+it's a constant linear number 550 K per
+Micron just gives you a rough idea uh if
+
+ align:start position:0%
+Micron just gives you a rough idea uh if
+ 
+
+ align:start position:0%
+Micron just gives you a rough idea uh if
+you that's again assuming uh a screening
+
+ align:start position:0%
+you that's again assuming uh a screening
+ 
+
+ align:start position:0%
+you that's again assuming uh a screening
+function is just a 1 over R type of
+
+ align:start position:0%
+function is just a 1 over R type of
+ 
+
+ align:start position:0%
+function is just a 1 over R type of
+screening due to the electrons around
+
+ align:start position:0%
+screening due to the electrons around
+ 
+
+ align:start position:0%
+screening due to the electrons around
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+nucleus and in fact if you go on slide
+
+ align:start position:0%
+nucleus and in fact if you go on slide
+ 
+
+ align:start position:0%
+nucleus and in fact if you go on slide
+seven uh of your handout this I took
+
+ align:start position:0%
+seven uh of your handout this I took
+ 
+
+ align:start position:0%
+seven uh of your handout this I took
+this plot from mayor and La book I
+
+ align:start position:0%
+this plot from mayor and La book I
+ 
+
+ align:start position:0%
+this plot from mayor and La book I
+referred to Mayor and Lao um uh earlier
+
+ align:start position:0%
+referred to Mayor and Lao um uh earlier
+ 
+
+ align:start position:0%
+referred to Mayor and Lao um uh earlier
+in the in the course in fact handout one
+
+ align:start position:0%
+in the in the course in fact handout one
+ 
+
+ align:start position:0%
+in the in the course in fact handout one
+has the um has the full reference for
+
+ align:start position:0%
+has the um has the full reference for
+ 
+
+ align:start position:0%
+has the um has the full reference for
+his his textbook and what he's plotting
+
+ align:start position:0%
+his his textbook and what he's plotting
+ 
+
+ align:start position:0%
+his his textbook and what he's plotting
+here is De by DX so again that's a Kev
+
+ align:start position:0%
+here is De by DX so again that's a Kev
+ 
+
+ align:start position:0%
+here is De by DX so again that's a Kev
+per Micron uh so it's a stopping power
+
+ align:start position:0%
+per Micron uh so it's a stopping power
+ 
+
+ align:start position:0%
+per Micron uh so it's a stopping power
+um or if you want uh you can change both
+
+ align:start position:0%
+um or if you want uh you can change both
+ 
+
+ align:start position:0%
+um or if you want uh you can change both
+the energy unit and the length unit it's
+
+ align:start position:0%
+the energy unit and the length unit it's
+ 
+
+ align:start position:0%
+the energy unit and the length unit it's
+equivalent to E
+
+ align:start position:0%
+equivalent to E
+ 
+
+ align:start position:0%
+equivalent to E
+per nanometer I I I prefer to think of K
+
+ align:start position:0%
+per nanometer I I I prefer to think of K
+ 
+
+ align:start position:0%
+per nanometer I I I prefer to think of K
+per Micron but it's just uh either way
+
+ align:start position:0%
+per Micron but it's just uh either way
+ 
+
+ align:start position:0%
+per Micron but it's just uh either way
+uh and it's on a log log plot and the
+
+ align:start position:0%
+uh and it's on a log log plot and the
+ 
+
+ align:start position:0%
+uh and it's on a log log plot and the
+x-axis is the energy of the
+
+ align:start position:0%
+x-axis is the energy of the
+ 
+
+ align:start position:0%
+x-axis is the energy of the
+ion so and there are two um two
+
+ align:start position:0%
+ion so and there are two um two
+ 
+
+ align:start position:0%
+ion so and there are two um two
+different types of stopping Powers shown
+
+ align:start position:0%
+different types of stopping Powers shown
+ 
+
+ align:start position:0%
+different types of stopping Powers shown
+here right now all we've talked about is
+
+ align:start position:0%
+here right now all we've talked about is
+ 
+
+ align:start position:0%
+here right now all we've talked about is
+nuclear but let's let's focus on this
+
+ align:start position:0%
+nuclear but let's let's focus on this
+ 
+
+ align:start position:0%
+nuclear but let's let's focus on this
+dash line here for phosphorus that
+
+ align:start position:0%
+dash line here for phosphorus that
+ 
+
+ align:start position:0%
+dash line here for phosphorus that
+starts up at 10 Kev and it's about uh
+
+ align:start position:0%
+starts up at 10 Kev and it's about uh
+ 
+
+ align:start position:0%
+starts up at 10 Kev and it's about uh
+it's about 500 or so little over 500 Kev
+
+ align:start position:0%
+it's about 500 or so little over 500 Kev
+ 
+
+ align:start position:0%
+it's about 500 or so little over 500 Kev
+per Micron and then as you can see in
+
+ align:start position:0%
+per Micron and then as you can see in
+ 
+
+ align:start position:0%
+per Micron and then as you can see in
+reality the nuclear stopping power given
+
+ align:start position:0%
+reality the nuclear stopping power given
+ 
+
+ align:start position:0%
+reality the nuclear stopping power given
+by this dash line is actually going down
+
+ align:start position:0%
+by this dash line is actually going down
+ 
+
+ align:start position:0%
+by this dash line is actually going down
+as you go to higher energies but lo and
+
+ align:start position:0%
+as you go to higher energies but lo and
+ 
+
+ align:start position:0%
+as you go to higher energies but lo and
+behold the number we just calculated in
+
+ align:start position:0%
+behold the number we just calculated in
+ 
+
+ align:start position:0%
+behold the number we just calculated in
+our simple calculator uh again assuming
+
+ align:start position:0%
+our simple calculator uh again assuming
+ 
+
+ align:start position:0%
+our simple calculator uh again assuming
+atomas fmy screening uh function of one
+
+ align:start position:0%
+atomas fmy screening uh function of one
+ 
+
+ align:start position:0%
+atomas fmy screening uh function of one
+over R comes out at low energies to give
+
+ align:start position:0%
+over R comes out at low energies to give
+ 
+
+ align:start position:0%
+over R comes out at low energies to give
+you pretty close ASM totically to what
+
+ align:start position:0%
+you pretty close ASM totically to what
+ 
+
+ align:start position:0%
+you pretty close ASM totically to what
+people calculate with more sophisticated
+
+ align:start position:0%
+people calculate with more sophisticated
+ 
+
+ align:start position:0%
+people calculate with more sophisticated
+uh screening functions uh indeed my
+
+ align:start position:0%
+uh screening functions uh indeed my
+ 
+
+ align:start position:0%
+uh screening functions uh indeed my
+calculation here of 550 KB for micron at
+
+ align:start position:0%
+calculation here of 550 KB for micron at
+ 
+
+ align:start position:0%
+calculation here of 550 KB for micron at
+10 kilovolts it's pretty darn close to
+
+ align:start position:0%
+10 kilovolts it's pretty darn close to
+ 
+
+ align:start position:0%
+10 kilovolts it's pretty darn close to
+that dash line for phosphorus so it's
+
+ align:start position:0%
+that dash line for phosphorus so it's
+ 
+
+ align:start position:0%
+that dash line for phosphorus so it's
+interesting you can check it out
+
+ align:start position:0%
+interesting you can check it out
+ 
+
+ align:start position:0%
+interesting you can check it out
+yourself for arsenic again you know the
+
+ align:start position:0%
+yourself for arsenic again you know the
+ 
+
+ align:start position:0%
+yourself for arsenic again you know the
+Z number in the mass you can check it
+
+ align:start position:0%
+Z number in the mass you can check it
+ 
+
+ align:start position:0%
+Z number in the mass you can check it
+out to see how accurate uh at low
+
+ align:start position:0%
+out to see how accurate uh at low
+ 
+
+ align:start position:0%
+out to see how accurate uh at low
+energies it ASM totically approaches um
+
+ align:start position:0%
+energies it ASM totically approaches um
+ 
+
+ align:start position:0%
+energies it ASM totically approaches um
+so uh what do we notice well obvious
+
+ align:start position:0%
+so uh what do we notice well obvious
+ 
+
+ align:start position:0%
+so uh what do we notice well obvious
+arsenic is a very high uh Z number a
+
+ align:start position:0%
+arsenic is a very high uh Z number a
+ 
+
+ align:start position:0%
+arsenic is a very high uh Z number a
+high mass element and it's nuclear
+
+ align:start position:0%
+high mass element and it's nuclear
+ 
+
+ align:start position:0%
+high mass element and it's nuclear
+stopping power is quite large it's on
+
+ align:start position:0%
+stopping power is quite large it's on
+ 
+
+ align:start position:0%
+stopping power is quite large it's on
+the order of uh a thousand KV per Micron
+
+ align:start position:0%
+the order of uh a thousand KV per Micron
+ 
+
+ align:start position:0%
+the order of uh a thousand KV per Micron
+something like that uh phosphorus is
+
+ align:start position:0%
+something like that uh phosphorus is
+ 
+
+ align:start position:0%
+something like that uh phosphorus is
+being less and Boron nuclear stopping uh
+
+ align:start position:0%
+being less and Boron nuclear stopping uh
+ 
+
+ align:start position:0%
+being less and Boron nuclear stopping uh
+even lower an order of magnitude lower
+
+ align:start position:0%
+even lower an order of magnitude lower
+ 
+
+ align:start position:0%
+even lower an order of magnitude lower
+uh than for arsenic
+
+ align:start position:0%
+uh than for arsenic
+ 
+
+ align:start position:0%
+uh than for arsenic
+uh the other thing on this plot um are
+
+ align:start position:0%
+uh the other thing on this plot um are
+ 
+
+ align:start position:0%
+uh the other thing on this plot um are
+these so besides these nuclear stopping
+
+ align:start position:0%
+these so besides these nuclear stopping
+ 
+
+ align:start position:0%
+these so besides these nuclear stopping
+Powers all the ones subn are nuclear
+
+ align:start position:0%
+Powers all the ones subn are nuclear
+ 
+
+ align:start position:0%
+Powers all the ones subn are nuclear
+these straight lines that increase with
+
+ align:start position:0%
+these straight lines that increase with
+ 
+
+ align:start position:0%
+these straight lines that increase with
+energy these are the electronic stopping
+
+ align:start position:0%
+energy these are the electronic stopping
+ 
+
+ align:start position:0%
+energy these are the electronic stopping
+powers and we'll talk about that next
+
+ align:start position:0%
+powers and we'll talk about that next
+ 
+
+ align:start position:0%
+powers and we'll talk about that next
+this is due this is uh the type of
+
+ align:start position:0%
+this is due this is uh the type of
+ 
+
+ align:start position:0%
+this is due this is uh the type of
+stopping that's due to the drag force of
+
+ align:start position:0%
+stopping that's due to the drag force of
+ 
+
+ align:start position:0%
+stopping that's due to the drag force of
+the electrons in the
+
+ align:start position:0%
+the electrons in the
+ 
+
+ align:start position:0%
+the electrons in the
+substrate so let's go
+
+ align:start position:0%
+substrate so let's go
+ 
+
+ align:start position:0%
+substrate so let's go
+on to uh slide 8 and talk exactly about
+
+ align:start position:0%
+on to uh slide 8 and talk exactly about
+ 
+
+ align:start position:0%
+on to uh slide 8 and talk exactly about
+that this this sort of non-local uh why
+
+ align:start position:0%
+that this this sort of non-local uh why
+ 
+
+ align:start position:0%
+that this this sort of non-local uh why
+is it non-local well the nuclear
+
+ align:start position:0%
+is it non-local well the nuclear
+ 
+
+ align:start position:0%
+is it non-local well the nuclear
+stopping power is local in the sense of
+
+ align:start position:0%
+stopping power is local in the sense of
+ 
+
+ align:start position:0%
+stopping power is local in the sense of
+you're having a collision the uh ion is
+
+ align:start position:0%
+you're having a collision the uh ion is
+ 
+
+ align:start position:0%
+you're having a collision the uh ion is
+coming very close to the to the uh atom
+
+ align:start position:0%
+coming very close to the to the uh atom
+ 
+
+ align:start position:0%
+coming very close to the to the uh atom
+and the substrate you're having a
+
+ align:start position:0%
+and the substrate you're having a
+ 
+
+ align:start position:0%
+and the substrate you're having a
+deflection so it's it's an actual um
+
+ align:start position:0%
+deflection so it's it's an actual um
+ 
+
+ align:start position:0%
+deflection so it's it's an actual um
+physical uh uh collision and they
+
+ align:start position:0%
+physical uh uh collision and they
+ 
+
+ align:start position:0%
+physical uh uh collision and they
+interact by this kulic
+
+ align:start position:0%
+interact by this kulic
+ 
+
+ align:start position:0%
+interact by this kulic
+Force this is a non-local uh phenomenon
+
+ align:start position:0%
+Force this is a non-local uh phenomenon
+ 
+
+ align:start position:0%
+Force this is a non-local uh phenomenon
+uh called uh uh non-local or local
+
+ align:start position:0%
+uh called uh uh non-local or local
+ 
+
+ align:start position:0%
+uh called uh uh non-local or local
+electronic stopping and there are two
+
+ align:start position:0%
+electronic stopping and there are two
+ 
+
+ align:start position:0%
+electronic stopping and there are two
+ways of viewing it uh you can imagine uh
+
+ align:start position:0%
+ways of viewing it uh you can imagine uh
+ 
+
+ align:start position:0%
+ways of viewing it uh you can imagine uh
+some kind of drag Force caused by the
+
+ align:start position:0%
+some kind of drag Force caused by the
+ 
+
+ align:start position:0%
+some kind of drag Force caused by the
+fact that I have a charged ion coming in
+
+ align:start position:0%
+fact that I have a charged ion coming in
+ 
+
+ align:start position:0%
+fact that I have a charged ion coming in
+going at some velocity so it's as plus
+
+ align:start position:0%
+going at some velocity so it's as plus
+ 
+
+ align:start position:0%
+going at some velocity so it's as plus
+arsenic Plus or Boron plus Boron uh uh
+
+ align:start position:0%
+arsenic Plus or Boron plus Boron uh uh
+ 
+
+ align:start position:0%
+arsenic Plus or Boron plus Boron uh uh
+minus is is in this sea of electrons
+
+ align:start position:0%
+minus is is in this sea of electrons
+ 
+
+ align:start position:0%
+minus is is in this sea of electrons
+this sea of electrons where where do
+
+ align:start position:0%
+this sea of electrons where where do
+ 
+
+ align:start position:0%
+this sea of electrons where where do
+they come from well every atom um in the
+
+ align:start position:0%
+they come from well every atom um in the
+ 
+
+ align:start position:0%
+they come from well every atom um in the
+in in the crystal um has electrons
+
+ align:start position:0%
+in in the crystal um has electrons
+ 
+
+ align:start position:0%
+in in the crystal um has electrons
+associated with it in fact they're
+
+ align:start position:0%
+associated with it in fact they're
+ 
+
+ align:start position:0%
+associated with it in fact they're
+calent
+
+ align:start position:0%
+calent
+ 
+
+ align:start position:0%
+calent
+bonds uh there are four calent bonds uh
+
+ align:start position:0%
+bonds uh there are four calent bonds uh
+ 
+
+ align:start position:0%
+bonds uh there are four calent bonds uh
+for every silicon atom with eight
+
+ align:start position:0%
+for every silicon atom with eight
+ 
+
+ align:start position:0%
+for every silicon atom with eight
+electrons participating you know uh per
+
+ align:start position:0%
+electrons participating you know uh per
+ 
+
+ align:start position:0%
+electrons participating you know uh per
+Bond I mean per per atom uh uh and these
+
+ align:start position:0%
+Bond I mean per per atom uh uh and these
+ 
+
+ align:start position:0%
+Bond I mean per per atom uh uh and these
+coal these calent electrons are are
+
+ align:start position:0%
+coal these calent electrons are are
+ 
+
+ align:start position:0%
+coal these calent electrons are are
+essentially can produce um a retarding
+
+ align:start position:0%
+essentially can produce um a retarding
+ 
+
+ align:start position:0%
+essentially can produce um a retarding
+effect uh on the on the ion going
+
+ align:start position:0%
+effect uh on the on the ion going
+ 
+
+ align:start position:0%
+effect uh on the on the ion going
+through it so you can think of it as
+
+ align:start position:0%
+through it so you can think of it as
+ 
+
+ align:start position:0%
+through it so you can think of it as
+sort of a retarding field uh imagine the
+
+ align:start position:0%
+sort of a retarding field uh imagine the
+ 
+
+ align:start position:0%
+sort of a retarding field uh imagine the
+Silicon or the substrate as sort of a
+
+ align:start position:0%
+Silicon or the substrate as sort of a
+ 
+
+ align:start position:0%
+Silicon or the substrate as sort of a
+some kind of dialectric medium you have
+
+ align:start position:0%
+some kind of dialectric medium you have
+ 
+
+ align:start position:0%
+some kind of dialectric medium you have
+an ion coming through it at some
+
+ align:start position:0%
+an ion coming through it at some
+ 
+
+ align:start position:0%
+an ion coming through it at some
+velocity this this is a blue uh circle
+
+ align:start position:0%
+velocity this this is a blue uh circle
+ 
+
+ align:start position:0%
+velocity this this is a blue uh circle
+is meant to represent say the Boron or
+
+ align:start position:0%
+is meant to represent say the Boron or
+ 
+
+ align:start position:0%
+is meant to represent say the Boron or
+the Arsenic ion and there's this
+
+ align:start position:0%
+the Arsenic ion and there's this
+ 
+
+ align:start position:0%
+the Arsenic ion and there's this
+retarding uh electric
+
+ align:start position:0%
+retarding uh electric
+ 
+
+ align:start position:0%
+retarding uh electric
+field uh so the interesting thing the
+
+ align:start position:0%
+field uh so the interesting thing the
+ 
+
+ align:start position:0%
+field uh so the interesting thing the
+thing you need to know the main point is
+
+ align:start position:0%
+thing you need to know the main point is
+ 
+
+ align:start position:0%
+thing you need to know the main point is
+this this is a dissipative loss
+
+ align:start position:0%
+this this is a dissipative loss
+ 
+
+ align:start position:0%
+this this is a dissipative loss
+mechanism but it doesn't change the
+
+ align:start position:0%
+mechanism but it doesn't change the
+ 
+
+ align:start position:0%
+mechanism but it doesn't change the
+direction the electrons are way too
+
+ align:start position:0%
+direction the electrons are way too
+ 
+
+ align:start position:0%
+direction the electrons are way too
+light uh they're they're very very light
+
+ align:start position:0%
+light uh they're they're very very light
+ 
+
+ align:start position:0%
+light uh they're they're very very light
+they can or slow down the ion but
+
+ align:start position:0%
+they can or slow down the ion but
+ 
+
+ align:start position:0%
+they can or slow down the ion but
+they're not going to change its
+
+ align:start position:0%
+they're not going to change its
+ 
+
+ align:start position:0%
+they're not going to change its
+direction there's no deflection as a
+
+ align:start position:0%
+direction there's no deflection as a
+ 
+
+ align:start position:0%
+direction there's no deflection as a
+result of this uh so unlike nuclear
+
+ align:start position:0%
+result of this uh so unlike nuclear
+ 
+
+ align:start position:0%
+result of this uh so unlike nuclear
+scattering so that's one way of thinking
+
+ align:start position:0%
+scattering so that's one way of thinking
+ 
+
+ align:start position:0%
+scattering so that's one way of thinking
+of as a drag force in a dialectric
+
+ align:start position:0%
+of as a drag force in a dialectric
+ 
+
+ align:start position:0%
+of as a drag force in a dialectric
+medium the other way is you can imagine
+
+ align:start position:0%
+medium the other way is you can imagine
+ 
+
+ align:start position:0%
+medium the other way is you can imagine
+a quote unquote Collision now just be
+
+ align:start position:0%
+a quote unquote Collision now just be
+ 
+
+ align:start position:0%
+a quote unquote Collision now just be
+careful in the word Collision the use of
+
+ align:start position:0%
+careful in the word Collision the use of
+ 
+
+ align:start position:0%
+careful in the word Collision the use of
+it with electrons around the atoms
+
+ align:start position:0%
+it with electrons around the atoms
+ 
+
+ align:start position:0%
+it with electrons around the atoms
+transferring some momentum to those
+
+ align:start position:0%
+transferring some momentum to those
+ 
+
+ align:start position:0%
+transferring some momentum to those
+electrons uh from the electrons uh in
+
+ align:start position:0%
+electrons uh from the electrons uh in
+ 
+
+ align:start position:0%
+electrons uh from the electrons uh in
+the uh uh from from the the ion itself
+
+ align:start position:0%
+the uh uh from from the the ion itself
+ 
+
+ align:start position:0%
+the uh uh from from the the ion itself
+so you can imagine here's this target
+
+ align:start position:0%
+so you can imagine here's this target
+ 
+
+ align:start position:0%
+so you can imagine here's this target
+atom it's got these electron cloud
+
+ align:start position:0%
+atom it's got these electron cloud
+ 
+
+ align:start position:0%
+atom it's got these electron cloud
+around it and it uh it transfers
+
+ align:start position:0%
+around it and it uh it transfers
+ 
+
+ align:start position:0%
+around it and it uh it transfers
+momentum um and actually results in
+
+ align:start position:0%
+momentum um and actually results in
+ 
+
+ align:start position:0%
+momentum um and actually results in
+locally slowing down um this uh um this
+
+ align:start position:0%
+locally slowing down um this uh um this
+ 
+
+ align:start position:0%
+locally slowing down um this uh um this
+ion basically reducing its
+
+ align:start position:0%
+ion basically reducing its
+ 
+
+ align:start position:0%
+ion basically reducing its
+velocity uh again there's no change in
+
+ align:start position:0%
+velocity uh again there's no change in
+ 
+
+ align:start position:0%
+velocity uh again there's no change in
+this mechanism no change in the
+
+ align:start position:0%
+this mechanism no change in the
+ 
+
+ align:start position:0%
+this mechanism no change in the
+direction of of the of the incoming onon
+
+ align:start position:0%
+direction of of the of the incoming onon
+ 
+
+ align:start position:0%
+direction of of the of the incoming onon
+when it when this this process happens
+
+ align:start position:0%
+when it when this this process happens
+ 
+
+ align:start position:0%
+when it when this this process happens
+uh so both of these uh don't change
+
+ align:start position:0%
+uh so both of these uh don't change
+ 
+
+ align:start position:0%
+uh so both of these uh don't change
+direction and both mechanisms uh are
+
+ align:start position:0%
+direction and both mechanisms uh are
+ 
+
+ align:start position:0%
+direction and both mechanisms uh are
+related to or involve the speed or the
+
+ align:start position:0%
+related to or involve the speed or the
+ 
+
+ align:start position:0%
+related to or involve the speed or the
+velocity of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ion okay so if we go to the
+
+ align:start position:0%
+ion okay so if we go to the
+ 
+
+ align:start position:0%
+ion okay so if we go to the
+um next slide on slide nine to first
+
+ align:start position:0%
+um next slide on slide nine to first
+ 
+
+ align:start position:0%
+um next slide on slide nine to first
+order people have found they can write
+
+ align:start position:0%
+order people have found they can write
+ 
+
+ align:start position:0%
+order people have found they can write
+the electronic stopping power as some
+
+ align:start position:0%
+the electronic stopping power as some
+ 
+
+ align:start position:0%
+the electronic stopping power as some
+constant times the velocity so the this
+
+ align:start position:0%
+constant times the velocity so the this
+ 
+
+ align:start position:0%
+constant times the velocity so the this
+drag mechanism the Kev loss per Micron
+
+ align:start position:0%
+drag mechanism the Kev loss per Micron
+ 
+
+ align:start position:0%
+drag mechanism the Kev loss per Micron
+due to electronic stopping increases
+
+ align:start position:0%
+due to electronic stopping increases
+ 
+
+ align:start position:0%
+due to electronic stopping increases
+directly proportional uh proportionally
+
+ align:start position:0%
+directly proportional uh proportionally
+ 
+
+ align:start position:0%
+directly proportional uh proportionally
+uh to the velocity of the
+
+ align:start position:0%
+uh to the velocity of the
+ 
+
+ align:start position:0%
+uh to the velocity of the
+electron and what is the velocity well
+
+ align:start position:0%
+electron and what is the velocity well
+ 
+
+ align:start position:0%
+electron and what is the velocity well
+the velocity just goes like the square
+
+ align:start position:0%
+the velocity just goes like the square
+ 
+
+ align:start position:0%
+the velocity just goes like the square
+root of energy right um so you can write
+
+ align:start position:0%
+root of energy right um so you can write
+ 
+
+ align:start position:0%
+root of energy right um so you can write
+electronic stopping as some constant K
+
+ align:start position:0%
+electronic stopping as some constant K
+ 
+
+ align:start position:0%
+electronic stopping as some constant K
+times the square root of e and in fact K
+
+ align:start position:0%
+times the square root of e and in fact K
+ 
+
+ align:start position:0%
+times the square root of e and in fact K
+has this very roughly you can
+
+ align:start position:0%
+has this very roughly you can
+ 
+
+ align:start position:0%
+has this very roughly you can
+approximate K by about uh 2 * 10 Theus
+
+ align:start position:0%
+approximate K by about uh 2 * 10 Theus
+ 
+
+ align:start position:0%
+approximate K by about uh 2 * 10 Theus
+14th square or EV cenim squar as shown
+
+ align:start position:0%
+14th square or EV cenim squar as shown
+ 
+
+ align:start position:0%
+14th square or EV cenim squar as shown
+up on the top of that slide so this is
+
+ align:start position:0%
+up on the top of that slide so this is
+ 
+
+ align:start position:0%
+up on the top of that slide so this is
+an approximation but to first order it
+
+ align:start position:0%
+an approximation but to first order it
+ 
+
+ align:start position:0%
+an approximation but to first order it
+seems to work um I should note here I'm
+
+ align:start position:0%
+seems to work um I should note here I'm
+ 
+
+ align:start position:0%
+seems to work um I should note here I'm
+noting in the upper right corner that a
+
+ align:start position:0%
+noting in the upper right corner that a
+ 
+
+ align:start position:0%
+noting in the upper right corner that a
+lot of the improvements in ion implant
+
+ align:start position:0%
+lot of the improvements in ion implant
+ 
+
+ align:start position:0%
+lot of the improvements in ion implant
+modeling over the last five 10 years or
+
+ align:start position:0%
+modeling over the last five 10 years or
+ 
+
+ align:start position:0%
+modeling over the last five 10 years or
+however long have actually come from a
+
+ align:start position:0%
+however long have actually come from a
+ 
+
+ align:start position:0%
+however long have actually come from a
+better a more accurate treatment of
+
+ align:start position:0%
+better a more accurate treatment of
+ 
+
+ align:start position:0%
+better a more accurate treatment of
+electronic stopping nuclear stopping is
+
+ align:start position:0%
+electronic stopping nuclear stopping is
+ 
+
+ align:start position:0%
+electronic stopping nuclear stopping is
+very much nuclear physics and that's
+
+ align:start position:0%
+very much nuclear physics and that's
+ 
+
+ align:start position:0%
+very much nuclear physics and that's
+been known for a long time now uh but
+
+ align:start position:0%
+been known for a long time now uh but
+ 
+
+ align:start position:0%
+been known for a long time now uh but
+this electronic drag force is a little
+
+ align:start position:0%
+this electronic drag force is a little
+ 
+
+ align:start position:0%
+this electronic drag force is a little
+bit more mysterious a little bit more
+
+ align:start position:0%
+bit more mysterious a little bit more
+ 
+
+ align:start position:0%
+bit more mysterious a little bit more
+difficult to model and and this is where
+
+ align:start position:0%
+difficult to model and and this is where
+ 
+
+ align:start position:0%
+difficult to model and and this is where
+a lot of the improvements have come uh
+
+ align:start position:0%
+a lot of the improvements have come uh
+ 
+
+ align:start position:0%
+a lot of the improvements have come uh
+in in the literature and particularly
+
+ align:start position:0%
+in in the literature and particularly
+ 
+
+ align:start position:0%
+in in the literature and particularly
+this affects light ions like Boron which
+
+ align:start position:0%
+this affects light ions like Boron which
+ 
+
+ align:start position:0%
+this affects light ions like Boron which
+for which most of this stopping is
+
+ align:start position:0%
+for which most of this stopping is
+ 
+
+ align:start position:0%
+for which most of this stopping is
+actually electronic Boron isn't very
+
+ align:start position:0%
+actually electronic Boron isn't very
+ 
+
+ align:start position:0%
+actually electronic Boron isn't very
+heavy it doesn't experience that much
+
+ align:start position:0%
+heavy it doesn't experience that much
+ 
+
+ align:start position:0%
+heavy it doesn't experience that much
+nuclear stopping most of what slows down
+
+ align:start position:0%
+nuclear stopping most of what slows down
+ 
+
+ align:start position:0%
+nuclear stopping most of what slows down
+at Boron ion implanted into silicon is
+
+ align:start position:0%
+at Boron ion implanted into silicon is
+ 
+
+ align:start position:0%
+at Boron ion implanted into silicon is
+electronic stopping so Boron profiles
+
+ align:start position:0%
+electronic stopping so Boron profiles
+ 
+
+ align:start position:0%
+electronic stopping so Boron profiles
+have become more accurate more
+
+ align:start position:0%
+have become more accurate more
+ 
+
+ align:start position:0%
+have become more accurate more
+accurately modeled over the last X
+
+ align:start position:0%
+accurately modeled over the last X
+ 
+
+ align:start position:0%
+accurately modeled over the last X
+number of years because people have a
+
+ align:start position:0%
+number of years because people have a
+ 
+
+ align:start position:0%
+number of years because people have a
+little better models for electronic
+
+ align:start position:0%
+little better models for electronic
+ 
+
+ align:start position:0%
+little better models for electronic
+stopping so if we look at this plot on
+
+ align:start position:0%
+stopping so if we look at this plot on
+ 
+
+ align:start position:0%
+stopping so if we look at this plot on
+on slide nine this is the total stopping
+
+ align:start position:0%
+on slide nine this is the total stopping
+ 
+
+ align:start position:0%
+on slide nine this is the total stopping
+power it plots both the nuclear
+
+ align:start position:0%
+power it plots both the nuclear
+ 
+
+ align:start position:0%
+power it plots both the nuclear
+electronic so again the units are Kev
+
+ align:start position:0%
+electronic so again the units are Kev
+ 
+
+ align:start position:0%
+electronic so again the units are Kev
+per Micron in the vertical axis and Kev
+
+ align:start position:0%
+per Micron in the vertical axis and Kev
+ 
+
+ align:start position:0%
+per Micron in the vertical axis and Kev
+on the y- axis and these are the same
+
+ align:start position:0%
+on the y- axis and these are the same
+ 
+
+ align:start position:0%
+on the y- axis and these are the same
+plots I just showed you they're just
+
+ align:start position:0%
+plots I just showed you they're just
+ 
+
+ align:start position:0%
+plots I just showed you they're just
+different color here's arsenic nuclear
+
+ align:start position:0%
+different color here's arsenic nuclear
+ 
+
+ align:start position:0%
+different color here's arsenic nuclear
+stopping phosphorus nuclear Boron
+
+ align:start position:0%
+stopping phosphorus nuclear Boron
+ 
+
+ align:start position:0%
+stopping phosphorus nuclear Boron
+nuclear stopping and here's the
+
+ align:start position:0%
+nuclear stopping and here's the
+ 
+
+ align:start position:0%
+nuclear stopping and here's the
+electronic
+
+ align:start position:0%
+electronic
+ 
+
+ align:start position:0%
+electronic
+stopping um and again it's uh just
+
+ align:start position:0%
+stopping um and again it's uh just
+ 
+
+ align:start position:0%
+stopping um and again it's uh just
+basically proportional to the velocity
+
+ align:start position:0%
+basically proportional to the velocity
+ 
+
+ align:start position:0%
+basically proportional to the velocity
+there's only a small dependence and we
+
+ align:start position:0%
+there's only a small dependence and we
+ 
+
+ align:start position:0%
+there's only a small dependence and we
+don't even show it here on the type of
+
+ align:start position:0%
+don't even show it here on the type of
+ 
+
+ align:start position:0%
+don't even show it here on the type of
+ion so we're just writing this as this
+
+ align:start position:0%
+ion so we're just writing this as this
+ 
+
+ align:start position:0%
+ion so we're just writing this as this
+uh this black line so interestingly uh
+
+ align:start position:0%
+uh this black line so interestingly uh
+ 
+
+ align:start position:0%
+uh this black line so interestingly uh
+what you see an interesting energy to
+
+ align:start position:0%
+what you see an interesting energy to
+ 
+
+ align:start position:0%
+what you see an interesting energy to
+point out is the energy at which these
+
+ align:start position:0%
+point out is the energy at which these
+ 
+
+ align:start position:0%
+point out is the energy at which these
+lines cross and that's called the
+
+ align:start position:0%
+lines cross and that's called the
+ 
+
+ align:start position:0%
+lines cross and that's called the
+critical energy e subc and at that point
+
+ align:start position:0%
+critical energy e subc and at that point
+ 
+
+ align:start position:0%
+critical energy e subc and at that point
+the nuclear electronic stopping are
+
+ align:start position:0%
+the nuclear electronic stopping are
+ 
+
+ align:start position:0%
+the nuclear electronic stopping are
+equal uh beyond that the electronic
+
+ align:start position:0%
+equal uh beyond that the electronic
+ 
+
+ align:start position:0%
+equal uh beyond that the electronic
+stopping is actually taken over it's
+
+ align:start position:0%
+stopping is actually taken over it's
+ 
+
+ align:start position:0%
+stopping is actually taken over it's
+much larger because again the nuclear
+
+ align:start position:0%
+much larger because again the nuclear
+ 
+
+ align:start position:0%
+much larger because again the nuclear
+stopping power is going down as you go
+
+ align:start position:0%
+stopping power is going down as you go
+ 
+
+ align:start position:0%
+stopping power is going down as you go
+go faster uh but uh or increases as you
+
+ align:start position:0%
+go faster uh but uh or increases as you
+ 
+
+ align:start position:0%
+go faster uh but uh or increases as you
+go go slower but the electronic is going
+
+ align:start position:0%
+go go slower but the electronic is going
+ 
+
+ align:start position:0%
+go go slower but the electronic is going
+the opposite direction so Boron at 17
+
+ align:start position:0%
+the opposite direction so Boron at 17
+ 
+
+ align:start position:0%
+the opposite direction so Boron at 17
+Kev above that uh or below that energy
+
+ align:start position:0%
+Kev above that uh or below that energy
+ 
+
+ align:start position:0%
+Kev above that uh or below that energy
+uh basically nuclear stopping will be
+
+ align:start position:0%
+uh basically nuclear stopping will be
+ 
+
+ align:start position:0%
+uh basically nuclear stopping will be
+important above that energy which is a
+
+ align:start position:0%
+important above that energy which is a
+ 
+
+ align:start position:0%
+important above that energy which is a
+lot of our implants um born is pretty
+
+ align:start position:0%
+lot of our implants um born is pretty
+ 
+
+ align:start position:0%
+lot of our implants um born is pretty
+much being stopped by electronic
+
+ align:start position:0%
+much being stopped by electronic
+ 
+
+ align:start position:0%
+much being stopped by electronic
+stopping uh phosphorus it's about 150 so
+
+ align:start position:0%
+stopping uh phosphorus it's about 150 so
+ 
+
+ align:start position:0%
+stopping uh phosphorus it's about 150 so
+any energy um less than 150 you're going
+
+ align:start position:0%
+any energy um less than 150 you're going
+ 
+
+ align:start position:0%
+any energy um less than 150 you're going
+to be dominated by um nuclear stopping
+
+ align:start position:0%
+to be dominated by um nuclear stopping
+ 
+
+ align:start position:0%
+to be dominated by um nuclear stopping
+above that will be um electronic and
+
+ align:start position:0%
+above that will be um electronic and
+ 
+
+ align:start position:0%
+above that will be um electronic and
+arsenic is almost always dominant
+
+ align:start position:0%
+arsenic is almost always dominant
+ 
+
+ align:start position:0%
+arsenic is almost always dominant
+uh at least in the beginning of its path
+
+ align:start position:0%
+uh at least in the beginning of its path
+ 
+
+ align:start position:0%
+uh at least in the beginning of its path
+uh by nuclear stopping the interesting
+
+ align:start position:0%
+uh by nuclear stopping the interesting
+ 
+
+ align:start position:0%
+uh by nuclear stopping the interesting
+thing about this though think about an
+
+ align:start position:0%
+thing about this though think about an
+ 
+
+ align:start position:0%
+thing about this though think about an
+individual ion as an ion comes in of
+
+ align:start position:0%
+individual ion as an ion comes in of
+ 
+
+ align:start position:0%
+individual ion as an ion comes in of
+course it comes in with a lot of energy
+
+ align:start position:0%
+course it comes in with a lot of energy
+ 
+
+ align:start position:0%
+course it comes in with a lot of energy
+right 10 KV 100 but by the time it stops
+
+ align:start position:0%
+right 10 KV 100 but by the time it stops
+ 
+
+ align:start position:0%
+right 10 KV 100 but by the time it stops
+it's got zero so every ion has to
+
+ align:start position:0%
+it's got zero so every ion has to
+ 
+
+ align:start position:0%
+it's got zero so every ion has to
+Traverse as I first come in let's say I
+
+ align:start position:0%
+Traverse as I first come in let's say I
+ 
+
+ align:start position:0%
+Traverse as I first come in let's say I
+start coming in at 10 Kev and I'm uh uh
+
+ align:start position:0%
+start coming in at 10 Kev and I'm uh uh
+ 
+
+ align:start position:0%
+start coming in at 10 Kev and I'm uh uh
+or rather 100 Kev and I'm right here um
+
+ align:start position:0%
+or rather 100 Kev and I'm right here um
+ 
+
+ align:start position:0%
+or rather 100 Kev and I'm right here um
+so as I'm coming in um here uh for for
+
+ align:start position:0%
+so as I'm coming in um here uh for for
+ 
+
+ align:start position:0%
+so as I'm coming in um here uh for for
+Boron you'd say 100 KV well um
+
+ align:start position:0%
+Boron you'd say 100 KV well um
+ 
+
+ align:start position:0%
+Boron you'd say 100 KV well um
+electronic stopping is dominant that's
+
+ align:start position:0%
+electronic stopping is dominant that's
+ 
+
+ align:start position:0%
+electronic stopping is dominant that's
+true but as the Boron ion slows down it
+
+ align:start position:0%
+true but as the Boron ion slows down it
+ 
+
+ align:start position:0%
+true but as the Boron ion slows down it
+walks down this curve and walks up this
+
+ align:start position:0%
+walks down this curve and walks up this
+ 
+
+ align:start position:0%
+walks down this curve and walks up this
+point and when it gets to very low
+
+ align:start position:0%
+point and when it gets to very low
+ 
+
+ align:start position:0%
+point and when it gets to very low
+energies just before it stops in fact
+
+ align:start position:0%
+energies just before it stops in fact
+ 
+
+ align:start position:0%
+energies just before it stops in fact
+nuclear stopping always takes over uh
+
+ align:start position:0%
+nuclear stopping always takes over uh
+ 
+
+ align:start position:0%
+nuclear stopping always takes over uh
+because at low energies you really can
+
+ align:start position:0%
+because at low energies you really can
+ 
+
+ align:start position:0%
+because at low energies you really can
+have a lot of bil ball like collisions
+
+ align:start position:0%
+have a lot of bil ball like collisions
+ 
+
+ align:start position:0%
+have a lot of bil ball like collisions
+so that's why at the end of the
+
+ align:start position:0%
+so that's why at the end of the
+ 
+
+ align:start position:0%
+so that's why at the end of the
+range uh back at the you know at the
+
+ align:start position:0%
+range uh back at the you know at the
+ 
+
+ align:start position:0%
+range uh back at the you know at the
+depths of the implant that's near the
+
+ align:start position:0%
+depths of the implant that's near the
+ 
+
+ align:start position:0%
+depths of the implant that's near the
+end of range there's a lot of nuclear
+
+ align:start position:0%
+end of range there's a lot of nuclear
+ 
+
+ align:start position:0%
+end of range there's a lot of nuclear
+stopping that goes on and and we'll talk
+
+ align:start position:0%
+stopping that goes on and and we'll talk
+ 
+
+ align:start position:0%
+stopping that goes on and and we'll talk
+about what impact that has for for
+
+ align:start position:0%
+about what impact that has for for
+ 
+
+ align:start position:0%
+about what impact that has for for
+damage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+profiles here's just an example on page
+
+ align:start position:0%
+profiles here's just an example on page
+ 
+
+ align:start position:0%
+profiles here's just an example on page
+10 a different type of plot that was a
+
+ align:start position:0%
+10 a different type of plot that was a
+ 
+
+ align:start position:0%
+10 a different type of plot that was a
+log log plot I've plotted these nuclear
+
+ align:start position:0%
+log log plot I've plotted these nuclear
+ 
+
+ align:start position:0%
+log log plot I've plotted these nuclear
+and electronic now on um linear axes
+
+ align:start position:0%
+and electronic now on um linear axes
+ 
+
+ align:start position:0%
+and electronic now on um linear axes
+just so you get a feel for what they
+
+ align:start position:0%
+just so you get a feel for what they
+ 
+
+ align:start position:0%
+just so you get a feel for what they
+look like on linear so this is De by DX
+
+ align:start position:0%
+look like on linear so this is De by DX
+ 
+
+ align:start position:0%
+look like on linear so this is De by DX
+and uh this is well it's actually it's a
+
+ align:start position:0%
+and uh this is well it's actually it's a
+ 
+
+ align:start position:0%
+and uh this is well it's actually it's a
+square root of energy that helps
+
+ align:start position:0%
+square root of energy that helps
+ 
+
+ align:start position:0%
+square root of energy that helps
+linearize the uh this straight line of
+
+ align:start position:0%
+linearize the uh this straight line of
+ 
+
+ align:start position:0%
+linearize the uh this straight line of
+course then is the electronic
+
+ align:start position:0%
+course then is the electronic
+ 
+
+ align:start position:0%
+course then is the electronic
+stopping um and this um other line here
+
+ align:start position:0%
+stopping um and this um other line here
+ 
+
+ align:start position:0%
+stopping um and this um other line here
+that it Peaks at some energy E1 and then
+
+ align:start position:0%
+that it Peaks at some energy E1 and then
+ 
+
+ align:start position:0%
+that it Peaks at some energy E1 and then
+starts to decrease down that's the
+
+ align:start position:0%
+starts to decrease down that's the
+ 
+
+ align:start position:0%
+starts to decrease down that's the
+nuclear stopping so on a linear scale
+
+ align:start position:0%
+nuclear stopping so on a linear scale
+ 
+
+ align:start position:0%
+nuclear stopping so on a linear scale
+you can actually see what it looks like
+
+ align:start position:0%
+you can actually see what it looks like
+ 
+
+ align:start position:0%
+you can actually see what it looks like
+and again I took this from mayor and
+
+ align:start position:0%
+and again I took this from mayor and
+ 
+
+ align:start position:0%
+and again I took this from mayor and
+LA's textbook in general the nuclear
+
+ align:start position:0%
+LA's textbook in general the nuclear
+ 
+
+ align:start position:0%
+LA's textbook in general the nuclear
+stopping dominates as we said at low
+
+ align:start position:0%
+stopping dominates as we said at low
+ 
+
+ align:start position:0%
+stopping dominates as we said at low
+energy towards the end of the range um
+
+ align:start position:0%
+energy towards the end of the range um
+ 
+
+ align:start position:0%
+energy towards the end of the range um
+and that's the the location of of the uh
+
+ align:start position:0%
+and that's the the location of of the uh
+ 
+
+ align:start position:0%
+and that's the the location of of the uh
+in this in the in the substrate where
+
+ align:start position:0%
+in this in the in the substrate where
+ 
+
+ align:start position:0%
+in this in the in the substrate where
+the nuclear collisions are going to
+
+ align:start position:0%
+the nuclear collisions are going to
+ 
+
+ align:start position:0%
+the nuclear collisions are going to
+produce most of the damage so we call
+
+ align:start position:0%
+produce most of the damage so we call
+ 
+
+ align:start position:0%
+produce most of the damage so we call
+that end of range
+
+ align:start position:0%
+that end of range
+ 
+
+ align:start position:0%
+that end of range
+damage at very high energies up here
+
+ align:start position:0%
+damage at very high energies up here
+ 
+
+ align:start position:0%
+damage at very high energies up here
+where I'm up up here particles travel
+
+ align:start position:0%
+where I'm up up here particles travel
+ 
+
+ align:start position:0%
+where I'm up up here particles travel
+very quickly they have less time to
+
+ align:start position:0%
+very quickly they have less time to
+ 
+
+ align:start position:0%
+very quickly they have less time to
+interact with a nucleus so nuclear
+
+ align:start position:0%
+interact with a nucleus so nuclear
+ 
+
+ align:start position:0%
+interact with a nucleus so nuclear
+stopping is not very is not as important
+
+ align:start position:0%
+stopping is not very is not as important
+ 
+
+ align:start position:0%
+stopping is not very is not as important
+um they have less interaction time and
+
+ align:start position:0%
+um they have less interaction time and
+ 
+
+ align:start position:0%
+um they have less interaction time and
+so you tend to they tend to be dragged
+
+ align:start position:0%
+so you tend to they tend to be dragged
+ 
+
+ align:start position:0%
+so you tend to they tend to be dragged
+down nuclear stopping is going down with
+
+ align:start position:0%
+down nuclear stopping is going down with
+ 
+
+ align:start position:0%
+down nuclear stopping is going down with
+energy where electronic is is
+
+ align:start position:0%
+energy where electronic is is
+ 
+
+ align:start position:0%
+energy where electronic is is
+increasing okay so that gives you an
+
+ align:start position:0%
+increasing okay so that gives you an
+ 
+
+ align:start position:0%
+increasing okay so that gives you an
+idea of some of the um physics of a loss
+
+ align:start position:0%
+idea of some of the um physics of a loss
+ 
+
+ align:start position:0%
+idea of some of the um physics of a loss
+mechanisms so let's go on to slide 11 so
+
+ align:start position:0%
+mechanisms so let's go on to slide 11 so
+ 
+
+ align:start position:0%
+mechanisms so let's go on to slide 11 so
+I have these let's say I have these
+
+ align:start position:0%
+I have these let's say I have these
+ 
+
+ align:start position:0%
+I have these let's say I have these
+nuclear stopping Powers as a function of
+
+ align:start position:0%
+nuclear stopping Powers as a function of
+ 
+
+ align:start position:0%
+nuclear stopping Powers as a function of
+energy and I have the electronic how do
+
+ align:start position:0%
+energy and I have the electronic how do
+ 
+
+ align:start position:0%
+energy and I have the electronic how do
+I get from that to a calculated profile
+
+ align:start position:0%
+I get from that to a calculated profile
+ 
+
+ align:start position:0%
+I get from that to a calculated profile
+well we know we just simply need to do
+
+ align:start position:0%
+well we know we just simply need to do
+ 
+
+ align:start position:0%
+well we know we just simply need to do
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+integral um if if you want to compute
+
+ align:start position:0%
+integral um if if you want to compute
+ 
+
+ align:start position:0%
+integral um if if you want to compute
+the range uh or um you can directly from
+
+ align:start position:0%
+the range uh or um you can directly from
+ 
+
+ align:start position:0%
+the range uh or um you can directly from
+Monte caros simulations you can actually
+
+ align:start position:0%
+Monte caros simulations you can actually
+ 
+
+ align:start position:0%
+Monte caros simulations you can actually
+simulate those that billiard ball and
+
+ align:start position:0%
+simulate those that billiard ball and
+ 
+
+ align:start position:0%
+simulate those that billiard ball and
+those electronic stopping
+
+ align:start position:0%
+those electronic stopping
+ 
+
+ align:start position:0%
+those electronic stopping
+processes um many years ago um three
+
+ align:start position:0%
+processes um many years ago um three
+ 
+
+ align:start position:0%
+processes um many years ago um three
+folks lindhard sharf and shiat actually
+
+ align:start position:0%
+folks lindhard sharf and shiat actually
+ 
+
+ align:start position:0%
+folks lindhard sharf and shiat actually
+uh took these equations put in uh
+
+ align:start position:0%
+uh took these equations put in uh
+ 
+
+ align:start position:0%
+uh took these equations put in uh
+nuclear and electronic stopping powers
+
+ align:start position:0%
+nuclear and electronic stopping powers
+ 
+
+ align:start position:0%
+nuclear and electronic stopping powers
+and computed uh the moments of
+
+ align:start position:0%
+and computed uh the moments of
+ 
+
+ align:start position:0%
+and computed uh the moments of
+distributions given
+
+ align:start position:0%
+distributions given
+ 
+
+ align:start position:0%
+distributions given
+uh S suban and S subb and in fact that
+
+ align:start position:0%
+uh S suban and S subb and in fact that
+ 
+
+ align:start position:0%
+uh S suban and S subb and in fact that
+so-called LSS Theory generated these
+
+ align:start position:0%
+so-called LSS Theory generated these
+ 
+
+ align:start position:0%
+so-called LSS Theory generated these
+tables I think we showed these tables
+
+ align:start position:0%
+tables I think we showed these tables
+ 
+
+ align:start position:0%
+tables I think we showed these tables
+last time for uh common dopant in
+
+ align:start position:0%
+last time for uh common dopant in
+ 
+
+ align:start position:0%
+last time for uh common dopant in
+Silicon generated tables of the first
+
+ align:start position:0%
+Silicon generated tables of the first
+ 
+
+ align:start position:0%
+Silicon generated tables of the first
+few moments maybe the the first three
+
+ align:start position:0%
+few moments maybe the the first three
+ 
+
+ align:start position:0%
+few moments maybe the the first three
+moments that generate RP this Delta RP
+
+ align:start position:0%
+moments that generate RP this Delta RP
+ 
+
+ align:start position:0%
+moments that generate RP this Delta RP
+or the standard deviation Sigma and the
+
+ align:start position:0%
+or the standard deviation Sigma and the
+ 
+
+ align:start position:0%
+or the standard deviation Sigma and the
+skis gamma they are tabulated and they
+
+ align:start position:0%
+skis gamma they are tabulated and they
+ 
+
+ align:start position:0%
+skis gamma they are tabulated and they
+were calculated originally by
+
+ align:start position:0%
+were calculated originally by
+ 
+
+ align:start position:0%
+were calculated originally by
+LSS um and or they've been fit to
+
+ align:start position:0%
+LSS um and or they've been fit to
+ 
+
+ align:start position:0%
+LSS um and or they've been fit to
+experimental data but you can calculate
+
+ align:start position:0%
+experimental data but you can calculate
+ 
+
+ align:start position:0%
+experimental data but you can calculate
+these moments
+
+ align:start position:0%
+these moments
+ 
+
+ align:start position:0%
+these moments
+um from first principles physics uh
+
+ align:start position:0%
+um from first principles physics uh
+ 
+
+ align:start position:0%
+um from first principles physics uh
+estimates of San as a function of energy
+
+ align:start position:0%
+estimates of San as a function of energy
+ 
+
+ align:start position:0%
+estimates of San as a function of energy
+and S as a function of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy okay so that's basically how how
+
+ align:start position:0%
+energy okay so that's basically how how
+ 
+
+ align:start position:0%
+energy okay so that's basically how how
+people do the calculations uh they what
+
+ align:start position:0%
+people do the calculations uh they what
+ 
+
+ align:start position:0%
+people do the calculations uh they what
+it boils down to the calculations boils
+
+ align:start position:0%
+it boils down to the calculations boils
+ 
+
+ align:start position:0%
+it boils down to the calculations boils
+down to boil down to how accurately do I
+
+ align:start position:0%
+down to boil down to how accurately do I
+ 
+
+ align:start position:0%
+down to boil down to how accurately do I
+know the nuclear stopping power as a
+
+ align:start position:0%
+know the nuclear stopping power as a
+ 
+
+ align:start position:0%
+know the nuclear stopping power as a
+function of energy and electronic
+
+ align:start position:0%
+function of energy and electronic
+ 
+
+ align:start position:0%
+function of energy and electronic
+stopping if I know that I can use a
+
+ align:start position:0%
+stopping if I know that I can use a
+ 
+
+ align:start position:0%
+stopping if I know that I can use a
+computer you can regenerate the old LSS
+
+ align:start position:0%
+computer you can regenerate the old LSS
+ 
+
+ align:start position:0%
+computer you can regenerate the old LSS
+statistics or you can actually use a
+
+ align:start position:0%
+statistics or you can actually use a
+ 
+
+ align:start position:0%
+statistics or you can actually use a
+computer to do Monte car
+
+ align:start position:0%
+computer to do Monte car
+ 
+
+ align:start position:0%
+computer to do Monte car
+um simulation uh because once once you
+
+ align:start position:0%
+um simulation uh because once once you
+ 
+
+ align:start position:0%
+um simulation uh because once once you
+know those stopping Powers uh given that
+
+ align:start position:0%
+know those stopping Powers uh given that
+ 
+
+ align:start position:0%
+know those stopping Powers uh given that
+okay so we we we we can figure out where
+
+ align:start position:0%
+okay so we we we we can figure out where
+ 
+
+ align:start position:0%
+okay so we we we we can figure out where
+the ions end up in the lattice now we
+
+ align:start position:0%
+the ions end up in the lattice now we
+ 
+
+ align:start position:0%
+the ions end up in the lattice now we
+want to know about what kind of damage
+
+ align:start position:0%
+want to know about what kind of damage
+ 
+
+ align:start position:0%
+want to know about what kind of damage
+does this incoming ion come uh coming in
+
+ align:start position:0%
+does this incoming ion come uh coming in
+ 
+
+ align:start position:0%
+does this incoming ion come uh coming in
+at a certain energy due to the lattice
+
+ align:start position:0%
+at a certain energy due to the lattice
+ 
+
+ align:start position:0%
+at a certain energy due to the lattice
+so imagine I have 30 K electron volts
+
+ align:start position:0%
+so imagine I have 30 K electron volts
+ 
+
+ align:start position:0%
+so imagine I have 30 K electron volts
+arsenic um which is coming into the
+
+ align:start position:0%
+arsenic um which is coming into the
+ 
+
+ align:start position:0%
+arsenic um which is coming into the
+Silicon lattice and if you look that up
+
+ align:start position:0%
+Silicon lattice and if you look that up
+ 
+
+ align:start position:0%
+Silicon lattice and if you look that up
+uh in your table in your textbook you'll
+
+ align:start position:0%
+uh in your table in your textbook you'll
+ 
+
+ align:start position:0%
+uh in your table in your textbook you'll
+find it has a range of 25 nanometers
+
+ align:start position:0%
+find it has a range of 25 nanometers
+ 
+
+ align:start position:0%
+find it has a range of 25 nanometers
+um so or about 250
+
+ align:start position:0%
+um so or about 250
+ 
+
+ align:start position:0%
+um so or about 250
+angstroms um so in 250 angstroms
+
+ align:start position:0%
+angstroms um so in 250 angstroms
+ 
+
+ align:start position:0%
+angstroms um so in 250 angstroms
+actually you can figure that out that is
+
+ align:start position:0%
+actually you can figure that out that is
+ 
+
+ align:start position:0%
+actually you can figure that out that is
+equivalent to roughly um 100 Atomic
+
+ align:start position:0%
+equivalent to roughly um 100 Atomic
+ 
+
+ align:start position:0%
+equivalent to roughly um 100 Atomic
+planes is about 0.25 or two and a half
+
+ align:start position:0%
+planes is about 0.25 or two and a half
+ 
+
+ align:start position:0%
+planes is about 0.25 or two and a half
+angstroms per uh per plane interplaner
+
+ align:start position:0%
+angstroms per uh per plane interplaner
+ 
+
+ align:start position:0%
+angstroms per uh per plane interplaner
+spacing um so you can imagine this
+
+ align:start position:0%
+spacing um so you can imagine this
+ 
+
+ align:start position:0%
+spacing um so you can imagine this
+arsenic ion is coming in it goes through
+
+ align:start position:0%
+arsenic ion is coming in it goes through
+ 
+
+ align:start position:0%
+arsenic ion is coming in it goes through
+about 100 Atomic PLS uh and how many so
+
+ align:start position:0%
+about 100 Atomic PLS uh and how many so
+ 
+
+ align:start position:0%
+about 100 Atomic PLS uh and how many so
+in fact you can think of this 30kv
+
+ align:start position:0%
+in fact you can think of this 30kv
+ 
+
+ align:start position:0%
+in fact you can think of this 30kv
+arsenic is coming in like this this is
+
+ align:start position:0%
+arsenic is coming in like this this is
+ 
+
+ align:start position:0%
+arsenic is coming in like this this is
+this squiggly line as meant to represent
+
+ align:start position:0%
+this squiggly line as meant to represent
+ 
+
+ align:start position:0%
+this squiggly line as meant to represent
+its path here's where it ends up and you
+
+ align:start position:0%
+its path here's where it ends up and you
+ 
+
+ align:start position:0%
+its path here's where it ends up and you
+can think of the cylinder around that um
+
+ align:start position:0%
+can think of the cylinder around that um
+ 
+
+ align:start position:0%
+can think of the cylinder around that um
+uh the sort of a cylinder that
+
+ align:start position:0%
+uh the sort of a cylinder that
+ 
+
+ align:start position:0%
+uh the sort of a cylinder that
+represents the region which is uh which
+
+ align:start position:0%
+represents the region which is uh which
+ 
+
+ align:start position:0%
+represents the region which is uh which
+is damaged because it does a lot of
+
+ align:start position:0%
+is damaged because it does a lot of
+ 
+
+ align:start position:0%
+is damaged because it does a lot of
+nuclear stopping and you have a lot of
+
+ align:start position:0%
+nuclear stopping and you have a lot of
+ 
+
+ align:start position:0%
+nuclear stopping and you have a lot of
+recoils generated uh until it comes to
+
+ align:start position:0%
+recoils generated uh until it comes to
+ 
+
+ align:start position:0%
+recoils generated uh until it comes to
+stop uh and in fact there's a simplified
+
+ align:start position:0%
+stop uh and in fact there's a simplified
+ 
+
+ align:start position:0%
+stop uh and in fact there's a simplified
+formula the KP formula that people use
+
+ align:start position:0%
+formula the KP formula that people use
+ 
+
+ align:start position:0%
+formula the KP formula that people use
+to figure out roughly uh the number of
+
+ align:start position:0%
+to figure out roughly uh the number of
+ 
+
+ align:start position:0%
+to figure out roughly uh the number of
+displaced particles so that' be the
+
+ align:start position:0%
+displaced particles so that' be the
+ 
+
+ align:start position:0%
+displaced particles so that' be the
+number of displaced silicon atoms
+
+ align:start position:0%
+number of displaced silicon atoms
+ 
+
+ align:start position:0%
+number of displaced silicon atoms
+created by an incoming ion and basically
+
+ align:start position:0%
+created by an incoming ion and basically
+ 
+
+ align:start position:0%
+created by an incoming ion and basically
+in in simple you can imagine it might be
+
+ align:start position:0%
+in in simple you can imagine it might be
+ 
+
+ align:start position:0%
+in in simple you can imagine it might be
+related to the energy of that ion which
+
+ align:start position:0%
+related to the energy of that ion which
+ 
+
+ align:start position:0%
+related to the energy of that ion which
+is 300 Kil electron volts so that's
+
+ align:start position:0%
+is 300 Kil electron volts so that's
+ 
+
+ align:start position:0%
+is 300 Kil electron volts so that's
+30,000 volts electron volts and divided
+
+ align:start position:0%
+30,000 volts electron volts and divided
+ 
+
+ align:start position:0%
+30,000 volts electron volts and divided
+by the displacement energy um well we
+
+ align:start position:0%
+by the displacement energy um well we
+ 
+
+ align:start position:0%
+by the displacement energy um well we
+use a factor of 1/2 in front of that but
+
+ align:start position:0%
+use a factor of 1/2 in front of that but
+ 
+
+ align:start position:0%
+use a factor of 1/2 in front of that but
+the displacement energy we said was 15
+
+ align:start position:0%
+the displacement energy we said was 15
+ 
+
+ align:start position:0%
+the displacement energy we said was 15
+electron volts so just order of
+
+ align:start position:0%
+electron volts so just order of
+ 
+
+ align:start position:0%
+electron volts so just order of
+magnitude estimate um by comparing the
+
+ align:start position:0%
+magnitude estimate um by comparing the
+ 
+
+ align:start position:0%
+magnitude estimate um by comparing the
+incoming energy to the energy it takes
+
+ align:start position:0%
+incoming energy to the energy it takes
+ 
+
+ align:start position:0%
+incoming energy to the energy it takes
+to displace an atom
+
+ align:start position:0%
+to displace an atom
+ 
+
+ align:start position:0%
+to displace an atom
+um from the lattice we're talking about
+
+ align:start position:0%
+um from the lattice we're talking about
+ 
+
+ align:start position:0%
+um from the lattice we're talking about
+maybe a thousand recoils of silicon are
+
+ align:start position:0%
+maybe a thousand recoils of silicon are
+ 
+
+ align:start position:0%
+maybe a thousand recoils of silicon are
+created by this one Arsenic atom that's
+
+ align:start position:0%
+created by this one Arsenic atom that's
+ 
+
+ align:start position:0%
+created by this one Arsenic atom that's
+that's quite a bit so you're essentially
+
+ align:start position:0%
+that's quite a bit so you're essentially
+ 
+
+ align:start position:0%
+that's quite a bit so you're essentially
+doing little ion implants inside um
+
+ align:start position:0%
+doing little ion implants inside um
+ 
+
+ align:start position:0%
+doing little ion implants inside um
+inside the substrate every time an
+
+ align:start position:0%
+inside the substrate every time an
+ 
+
+ align:start position:0%
+inside the substrate every time an
+Arsenic atom deflects silicon it creates
+
+ align:start position:0%
+Arsenic atom deflects silicon it creates
+ 
+
+ align:start position:0%
+Arsenic atom deflects silicon it creates
+what they call silicon knock on uh the
+
+ align:start position:0%
+what they call silicon knock on uh the
+ 
+
+ align:start position:0%
+what they call silicon knock on uh the
+silicons are knocked on and they
+
+ align:start position:0%
+silicons are knocked on and they
+ 
+
+ align:start position:0%
+silicons are knocked on and they
+themselves have a certain energy and
+
+ align:start position:0%
+themselves have a certain energy and
+ 
+
+ align:start position:0%
+themselves have a certain energy and
+they can do more damage so you it
+
+ align:start position:0%
+they can do more damage so you it
+ 
+
+ align:start position:0%
+they can do more damage so you it
+creates this sort of cylinder uh like
+
+ align:start position:0%
+creates this sort of cylinder uh like
+ 
+
+ align:start position:0%
+creates this sort of cylinder uh like
+region of damage just du to one
+
+ align:start position:0%
+region of damage just du to one
+ 
+
+ align:start position:0%
+region of damage just du to one
+ion and in fact here's a that was a very
+
+ align:start position:0%
+ion and in fact here's a that was a very
+ 
+
+ align:start position:0%
+ion and in fact here's a that was a very
+schematic uh Cartoon that we just drew
+
+ align:start position:0%
+schematic uh Cartoon that we just drew
+ 
+
+ align:start position:0%
+schematic uh Cartoon that we just drew
+with the computer this is a little more
+
+ align:start position:0%
+with the computer this is a little more
+ 
+
+ align:start position:0%
+with the computer this is a little more
+sophisticated on slide 13 these are
+
+ align:start position:0%
+sophisticated on slide 13 these are
+ 
+
+ align:start position:0%
+sophisticated on slide 13 these are
+actually what's called molecular Dynamic
+
+ align:start position:0%
+actually what's called molecular Dynamic
+ 
+
+ align:start position:0%
+actually what's called molecular Dynamic
+simulations where people build in the
+
+ align:start position:0%
+simulations where people build in the
+ 
+
+ align:start position:0%
+simulations where people build in the
+computer and of course this is done at
+
+ align:start position:0%
+computer and of course this is done at
+ 
+
+ align:start position:0%
+computer and of course this is done at
+Lawrence Livermore National Lab would
+
+ align:start position:0%
+Lawrence Livermore National Lab would
+ 
+
+ align:start position:0%
+Lawrence Livermore National Lab would
+have huge supercomputing capability they
+
+ align:start position:0%
+have huge supercomputing capability they
+ 
+
+ align:start position:0%
+have huge supercomputing capability they
+uh they build up a model of the silic
+
+ align:start position:0%
+uh they build up a model of the silic
+ 
+
+ align:start position:0%
+uh they build up a model of the silic
+and lattice and they actually model the
+
+ align:start position:0%
+and lattice and they actually model the
+ 
+
+ align:start position:0%
+and lattice and they actually model the
+physics of an incoming atom or ion
+
+ align:start position:0%
+physics of an incoming atom or ion
+ 
+
+ align:start position:0%
+physics of an incoming atom or ion
+here's a 5k EV born ion coming in that's
+
+ align:start position:0%
+here's a 5k EV born ion coming in that's
+ 
+
+ align:start position:0%
+here's a 5k EV born ion coming in that's
+ion implanted into the substrate and
+
+ align:start position:0%
+ion implanted into the substrate and
+ 
+
+ align:start position:0%
+ion implanted into the substrate and
+they actually follow a whole bunch of
+
+ align:start position:0%
+they actually follow a whole bunch of
+ 
+
+ align:start position:0%
+they actually follow a whole bunch of
+ions and actually look at what happens
+
+ align:start position:0%
+ions and actually look at what happens
+ 
+
+ align:start position:0%
+ions and actually look at what happens
+uh to these displaced recoils and each
+
+ align:start position:0%
+uh to these displaced recoils and each
+ 
+
+ align:start position:0%
+uh to these displaced recoils and each
+little snapshot picture here I apologize
+
+ align:start position:0%
+little snapshot picture here I apologize
+ 
+
+ align:start position:0%
+little snapshot picture here I apologize
+it didn't come out very well when we
+
+ align:start position:0%
+it didn't come out very well when we
+ 
+
+ align:start position:0%
+it didn't come out very well when we
+copied it um is a snapshot in time so
+
+ align:start position:0%
+copied it um is a snapshot in time so
+ 
+
+ align:start position:0%
+copied it um is a snapshot in time so
+the first little um cube is supposed to
+
+ align:start position:0%
+the first little um cube is supposed to
+ 
+
+ align:start position:0%
+the first little um cube is supposed to
+represent a region of the Silicon where
+
+ align:start position:0%
+represent a region of the Silicon where
+ 
+
+ align:start position:0%
+represent a region of the Silicon where
+uh after 0.1 P seconds so this ion has
+
+ align:start position:0%
+uh after 0.1 P seconds so this ion has
+ 
+
+ align:start position:0%
+uh after 0.1 P seconds so this ion has
+come in and just at the time of 0.1 SEC
+
+ align:start position:0%
+come in and just at the time of 0.1 SEC
+ 
+
+ align:start position:0%
+come in and just at the time of 0.1 SEC
+second there's this little Cloud here
+
+ align:start position:0%
+second there's this little Cloud here
+ 
+
+ align:start position:0%
+second there's this little Cloud here
+you can see this little Cloud that cloud
+
+ align:start position:0%
+you can see this little Cloud that cloud
+ 
+
+ align:start position:0%
+you can see this little Cloud that cloud
+represents all the displaced silicon
+
+ align:start position:0%
+represents all the displaced silicon
+ 
+
+ align:start position:0%
+represents all the displaced silicon
+atoms so they're actually following all
+
+ align:start position:0%
+atoms so they're actually following all
+ 
+
+ align:start position:0%
+atoms so they're actually following all
+all these atoms displaced from their
+
+ align:start position:0%
+all these atoms displaced from their
+ 
+
+ align:start position:0%
+all these atoms displaced from their
+their lattice sites and then at five
+
+ align:start position:0%
+their lattice sites and then at five
+ 
+
+ align:start position:0%
+their lattice sites and then at five
+times that time so at half a peak a
+
+ align:start position:0%
+times that time so at half a peak a
+ 
+
+ align:start position:0%
+times that time so at half a peak a
+second look how that cloud has grown
+
+ align:start position:0%
+second look how that cloud has grown
+ 
+
+ align:start position:0%
+second look how that cloud has grown
+it's gone in deeper and it's expanded
+
+ align:start position:0%
+it's gone in deeper and it's expanded
+ 
+
+ align:start position:0%
+it's gone in deeper and it's expanded
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+laterally um and then interestingly uh
+
+ align:start position:0%
+laterally um and then interestingly uh
+ 
+
+ align:start position:0%
+laterally um and then interestingly uh
+10 times that again roughly at six Peak
+
+ align:start position:0%
+10 times that again roughly at six Peak
+ 
+
+ align:start position:0%
+10 times that again roughly at six Peak
+a seconds the cloud looks a little bit
+
+ align:start position:0%
+a seconds the cloud looks a little bit
+ 
+
+ align:start position:0%
+a seconds the cloud looks a little bit
+smaller it's reached some size not that
+
+ align:start position:0%
+smaller it's reached some size not that
+ 
+
+ align:start position:0%
+smaller it's reached some size not that
+much different from its first size but
+
+ align:start position:0%
+much different from its first size but
+ 
+
+ align:start position:0%
+much different from its first size but
+because why well what's happened is that
+
+ align:start position:0%
+because why well what's happened is that
+ 
+
+ align:start position:0%
+because why well what's happened is that
+some of these silicon atoms um that were
+
+ align:start position:0%
+some of these silicon atoms um that were
+ 
+
+ align:start position:0%
+some of these silicon atoms um that were
+knocked off have found vacant Lattis
+
+ align:start position:0%
+knocked off have found vacant Lattis
+ 
+
+ align:start position:0%
+knocked off have found vacant Lattis
+sites right so you're creating ions of
+
+ align:start position:0%
+sites right so you're creating ions of
+ 
+
+ align:start position:0%
+sites right so you're creating ions of
+silicon atoms that are displaced but
+
+ align:start position:0%
+silicon atoms that are displaced but
+ 
+
+ align:start position:0%
+silicon atoms that are displaced but
+you're also they find holes in the lce
+
+ align:start position:0%
+you're also they find holes in the lce
+ 
+
+ align:start position:0%
+you're also they find holes in the lce
+where they can sit uh and so this this
+
+ align:start position:0%
+where they can sit uh and so this this
+ 
+
+ align:start position:0%
+where they can sit uh and so this this
+becomes sort of what the offsite silicon
+
+ align:start position:0%
+becomes sort of what the offsite silicon
+ 
+
+ align:start position:0%
+becomes sort of what the offsite silicon
+atoms look like after about six PCS so
+
+ align:start position:0%
+atoms look like after about six PCS so
+ 
+
+ align:start position:0%
+atoms look like after about six PCS so
+people actually do try to simulate this
+
+ align:start position:0%
+people actually do try to simulate this
+ 
+
+ align:start position:0%
+people actually do try to simulate this
+from first principles uh physics as
+
+ align:start position:0%
+from first principles uh physics as
+ 
+
+ align:start position:0%
+from first principles uh physics as
+well so that's a more modern uh kind of
+
+ align:start position:0%
+well so that's a more modern uh kind of
+ 
+
+ align:start position:0%
+well so that's a more modern uh kind of
+calculation on uh slide 14 I'm showing
+
+ align:start position:0%
+calculation on uh slide 14 I'm showing
+ 
+
+ align:start position:0%
+calculation on uh slide 14 I'm showing
+you maybe a little bit more traditional
+
+ align:start position:0%
+you maybe a little bit more traditional
+ 
+
+ align:start position:0%
+you maybe a little bit more traditional
+or oldfashioned calculation what people
+
+ align:start position:0%
+or oldfashioned calculation what people
+ 
+
+ align:start position:0%
+or oldfashioned calculation what people
+used to do in the 1980s in fact this was
+
+ align:start position:0%
+used to do in the 1980s in fact this was
+ 
+
+ align:start position:0%
+used to do in the 1980s in fact this was
+taken from uh a book called the handbook
+
+ align:start position:0%
+taken from uh a book called the handbook
+ 
+
+ align:start position:0%
+taken from uh a book called the handbook
+on semiconductors on iron implantation
+
+ align:start position:0%
+on semiconductors on iron implantation
+ 
+
+ align:start position:0%
+on semiconductors on iron implantation
+published back in 1980 but what it is um
+
+ align:start position:0%
+published back in 1980 but what it is um
+ 
+
+ align:start position:0%
+published back in 1980 but what it is um
+rather than that that uh following every
+
+ align:start position:0%
+rather than that that uh following every
+ 
+
+ align:start position:0%
+rather than that that uh following every
+atom and figuring out what people do is
+
+ align:start position:0%
+atom and figuring out what people do is
+ 
+
+ align:start position:0%
+atom and figuring out what people do is
+they found a way to calculate the energy
+
+ align:start position:0%
+they found a way to calculate the energy
+ 
+
+ align:start position:0%
+they found a way to calculate the energy
+deposited into nuclear processes again
+
+ align:start position:0%
+deposited into nuclear processes again
+ 
+
+ align:start position:0%
+deposited into nuclear processes again
+we know the nuclear stopping power as a
+
+ align:start position:0%
+we know the nuclear stopping power as a
+ 
+
+ align:start position:0%
+we know the nuclear stopping power as a
+function of energy so so as we integrate
+
+ align:start position:0%
+function of energy so so as we integrate
+ 
+
+ align:start position:0%
+function of energy so so as we integrate
+those equations in depth we can figure
+
+ align:start position:0%
+those equations in depth we can figure
+ 
+
+ align:start position:0%
+those equations in depth we can figure
+out at any given depth we know the
+
+ align:start position:0%
+out at any given depth we know the
+ 
+
+ align:start position:0%
+out at any given depth we know the
+energy of the atom of the ion we can we
+
+ align:start position:0%
+energy of the atom of the ion we can we
+ 
+
+ align:start position:0%
+energy of the atom of the ion we can we
+can kind of integrate that up and figure
+
+ align:start position:0%
+can kind of integrate that up and figure
+ 
+
+ align:start position:0%
+can kind of integrate that up and figure
+out um how much nuclear stopping is
+
+ align:start position:0%
+out um how much nuclear stopping is
+ 
+
+ align:start position:0%
+out um how much nuclear stopping is
+taking place at that depth and therefore
+
+ align:start position:0%
+taking place at that depth and therefore
+ 
+
+ align:start position:0%
+taking place at that depth and therefore
+how much you can think of how much of
+
+ align:start position:0%
+how much you can think of how much of
+ 
+
+ align:start position:0%
+how much you can think of how much of
+the energy loss um in in uh Kev per
+
+ align:start position:0%
+the energy loss um in in uh Kev per
+ 
+
+ align:start position:0%
+the energy loss um in in uh Kev per
+Micron or EV per angstrom is there at a
+
+ align:start position:0%
+Micron or EV per angstrom is there at a
+ 
+
+ align:start position:0%
+Micron or EV per angstrom is there at a
+given depth uh and here's a picture of
+
+ align:start position:0%
+given depth uh and here's a picture of
+ 
+
+ align:start position:0%
+given depth uh and here's a picture of
+that calculation or a plot it's
+
+ align:start position:0%
+that calculation or a plot it's
+ 
+
+ align:start position:0%
+that calculation or a plot it's
+so-called damage density so uh it's the
+
+ align:start position:0%
+so-called damage density so uh it's the
+ 
+
+ align:start position:0%
+so-called damage density so uh it's the
+amount of energy that is lost at a given
+
+ align:start position:0%
+amount of energy that is lost at a given
+ 
+
+ align:start position:0%
+amount of energy that is lost at a given
+depth due to nuclear processes and it
+
+ align:start position:0%
+depth due to nuclear processes and it
+ 
+
+ align:start position:0%
+depth due to nuclear processes and it
+has the units of EV for Ev per angstrom
+
+ align:start position:0%
+has the units of EV for Ev per angstrom
+ 
+
+ align:start position:0%
+has the units of EV for Ev per angstrom
+uh as a function of
+
+ align:start position:0%
+uh as a function of
+ 
+
+ align:start position:0%
+uh as a function of
+depth and um this is for a particular I
+
+ align:start position:0%
+depth and um this is for a particular I
+ 
+
+ align:start position:0%
+depth and um this is for a particular I
+imp plant this is boron 11 being
+
+ align:start position:0%
+imp plant this is boron 11 being
+ 
+
+ align:start position:0%
+imp plant this is boron 11 being
+implanted into silicon at 100 Kil
+
+ align:start position:0%
+implanted into silicon at 100 Kil
+ 
+
+ align:start position:0%
+implanted into silicon at 100 Kil
+electron volts and you can see the
+
+ align:start position:0%
+electron volts and you can see the
+ 
+
+ align:start position:0%
+electron volts and you can see the
+damage energy the damage energy density
+
+ align:start position:0%
+damage energy the damage energy density
+ 
+
+ align:start position:0%
+damage energy the damage energy density
+has a certain profile um and the solid
+
+ align:start position:0%
+has a certain profile um and the solid
+ 
+
+ align:start position:0%
+has a certain profile um and the solid
+line represents a calculation where it
+
+ align:start position:0%
+line represents a calculation where it
+ 
+
+ align:start position:0%
+line represents a calculation where it
+includes the Silicon recoils uh that is
+
+ align:start position:0%
+includes the Silicon recoils uh that is
+ 
+
+ align:start position:0%
+includes the Silicon recoils uh that is
+the Silicon ions that are generated and
+
+ align:start position:0%
+the Silicon ions that are generated and
+ 
+
+ align:start position:0%
+the Silicon ions that are generated and
+the dash line is when we have only the
+
+ align:start position:0%
+the dash line is when we have only the
+ 
+
+ align:start position:0%
+the dash line is when we have only the
+primary ion so there's not much
+
+ align:start position:0%
+primary ion so there's not much
+ 
+
+ align:start position:0%
+primary ion so there's not much
+difference in this case uh but here's an
+
+ align:start position:0%
+difference in this case uh but here's an
+ 
+
+ align:start position:0%
+difference in this case uh but here's an
+example of blond so it's a relatively
+
+ align:start position:0%
+example of blond so it's a relatively
+ 
+
+ align:start position:0%
+example of blond so it's a relatively
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+ion um and and the interesting thing
+
+ align:start position:0%
+ion um and and the interesting thing
+ 
+
+ align:start position:0%
+ion um and and the interesting thing
+that it's plotted here is it's a
+
+ align:start position:0%
+that it's plotted here is it's a
+ 
+
+ align:start position:0%
+that it's plotted here is it's a
+function of X over RP so remember RP is
+
+ align:start position:0%
+function of X over RP so remember RP is
+ 
+
+ align:start position:0%
+function of X over RP so remember RP is
+going to be roughly close to where the
+
+ align:start position:0%
+going to be roughly close to where the
+ 
+
+ align:start position:0%
+going to be roughly close to where the
+peak of the Boron so the Boron would
+
+ align:start position:0%
+peak of the Boron so the Boron would
+ 
+
+ align:start position:0%
+peak of the Boron so the Boron would
+Peak here at
+
+ align:start position:0%
+Peak here at
+ 
+
+ align:start position:0%
+Peak here at
+one um but so the range of the Boron
+
+ align:start position:0%
+one um but so the range of the Boron
+ 
+
+ align:start position:0%
+one um but so the range of the Boron
+atom is actually much greater than the
+
+ align:start position:0%
+atom is actually much greater than the
+ 
+
+ align:start position:0%
+atom is actually much greater than the
+range of the average silicon recoil as
+
+ align:start position:0%
+range of the average silicon recoil as
+ 
+
+ align:start position:0%
+range of the average silicon recoil as
+big as the Boron is light so it can't
+
+ align:start position:0%
+big as the Boron is light so it can't
+ 
+
+ align:start position:0%
+big as the Boron is light so it can't
+push the Silicon that much deeper in so
+
+ align:start position:0%
+push the Silicon that much deeper in so
+ 
+
+ align:start position:0%
+push the Silicon that much deeper in so
+actually the damage density for silicon
+
+ align:start position:0%
+actually the damage density for silicon
+ 
+
+ align:start position:0%
+actually the damage density for silicon
+recoils doesn't contribute that much you
+
+ align:start position:0%
+recoils doesn't contribute that much you
+ 
+
+ align:start position:0%
+recoils doesn't contribute that much you
+can see that these two dash and the
+
+ align:start position:0%
+can see that these two dash and the
+ 
+
+ align:start position:0%
+can see that these two dash and the
+solid look pretty much the same but
+
+ align:start position:0%
+solid look pretty much the same but
+ 
+
+ align:start position:0%
+solid look pretty much the same but
+interestingly where does the the the
+
+ align:start position:0%
+interestingly where does the the the
+ 
+
+ align:start position:0%
+interestingly where does the the the
+damage Peak pretty close to RP in fact
+
+ align:start position:0%
+damage Peak pretty close to RP in fact
+ 
+
+ align:start position:0%
+damage Peak pretty close to RP in fact
+it's just at maybe 80% of RP and that's
+
+ align:start position:0%
+it's just at maybe 80% of RP and that's
+ 
+
+ align:start position:0%
+it's just at maybe 80% of RP and that's
+a good rule of thumb you can use if you
+
+ align:start position:0%
+a good rule of thumb you can use if you
+ 
+
+ align:start position:0%
+a good rule of thumb you can use if you
+want to know all right I'm going to ion
+
+ align:start position:0%
+want to know all right I'm going to ion
+ 
+
+ align:start position:0%
+want to know all right I'm going to ion
+implant something into a silicon
+
+ align:start position:0%
+implant something into a silicon
+ 
+
+ align:start position:0%
+implant something into a silicon
+substrate um maybe I don't know how to
+
+ align:start position:0%
+substrate um maybe I don't know how to
+ 
+
+ align:start position:0%
+substrate um maybe I don't know how to
+calculate the damage energy density but
+
+ align:start position:0%
+calculate the damage energy density but
+ 
+
+ align:start position:0%
+calculate the damage energy density but
+I can know how to calculate the profile
+
+ align:start position:0%
+I can know how to calculate the profile
+ 
+
+ align:start position:0%
+I can know how to calculate the profile
+of that ion
+
+ align:start position:0%
+of that ion
+ 
+
+ align:start position:0%
+of that ion
+where is the maximum damage well it's
+
+ align:start position:0%
+where is the maximum damage well it's
+ 
+
+ align:start position:0%
+where is the maximum damage well it's
+close to RP but in fact it's Just sh shy
+
+ align:start position:0%
+close to RP but in fact it's Just sh shy
+ 
+
+ align:start position:0%
+close to RP but in fact it's Just sh shy
+of RP uh so if you want to do a lot of
+
+ align:start position:0%
+of RP uh so if you want to do a lot of
+ 
+
+ align:start position:0%
+of RP uh so if you want to do a lot of
+damage or usually you don't but uh or
+
+ align:start position:0%
+damage or usually you don't but uh or
+ 
+
+ align:start position:0%
+damage or usually you don't but uh or
+you want to minimize you can figure out
+
+ align:start position:0%
+you want to minimize you can figure out
+ 
+
+ align:start position:0%
+you want to minimize you can figure out
+just just below RP is where you're going
+
+ align:start position:0%
+just just below RP is where you're going
+ 
+
+ align:start position:0%
+just just below RP is where you're going
+to Peak uh in terms of doing the most
+
+ align:start position:0%
+to Peak uh in terms of doing the most
+ 
+
+ align:start position:0%
+to Peak uh in terms of doing the most
+damage to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+substrate uh here's an example on slide
+
+ align:start position:0%
+substrate uh here's an example on slide
+ 
+
+ align:start position:0%
+substrate uh here's an example on slide
+15 a different
+
+ align:start position:0%
+15 a different
+ 
+
+ align:start position:0%
+15 a different
+situation um Navas is a heavy Lon the
+
+ align:start position:0%
+situation um Navas is a heavy Lon the
+ 
+
+ align:start position:0%
+situation um Navas is a heavy Lon the
+same kind of calculations published in
+
+ align:start position:0%
+same kind of calculations published in
+ 
+
+ align:start position:0%
+same kind of calculations published in
+in gib's book handbook on semiconductors
+
+ align:start position:0%
+in gib's book handbook on semiconductors
+ 
+
+ align:start position:0%
+in gib's book handbook on semiconductors
+uh ion implantation
+
+ align:start position:0%
+uh ion implantation
+ 
+
+ align:start position:0%
+uh ion implantation
+volume uh again damage energy density in
+
+ align:start position:0%
+volume uh again damage energy density in
+ 
+
+ align:start position:0%
+volume uh again damage energy density in
+EV per angstrom again versus X over RP
+
+ align:start position:0%
+EV per angstrom again versus X over RP
+ 
+
+ align:start position:0%
+EV per angstrom again versus X over RP
+but look at this this time the solid
+
+ align:start position:0%
+but look at this this time the solid
+ 
+
+ align:start position:0%
+but look at this this time the solid
+line now again includes
+
+ align:start position:0%
+line now again includes
+ 
+
+ align:start position:0%
+line now again includes
+recoils um and you get this sort of uh
+
+ align:start position:0%
+recoils um and you get this sort of uh
+ 
+
+ align:start position:0%
+recoils um and you get this sort of uh
+distribution the dash line um is for the
+
+ align:start position:0%
+distribution the dash line um is for the
+ 
+
+ align:start position:0%
+distribution the dash line um is for the
+Damage Done just by the animony itself
+
+ align:start position:0%
+Damage Done just by the animony itself
+ 
+
+ align:start position:0%
+Damage Done just by the animony itself
+uh and you we get a very different
+
+ align:start position:0%
+uh and you we get a very different
+ 
+
+ align:start position:0%
+uh and you we get a very different
+damage distribution so what this says is
+
+ align:start position:0%
+damage distribution so what this says is
+ 
+
+ align:start position:0%
+damage distribution so what this says is
+for a heavy ion like animony um animony
+
+ align:start position:0%
+for a heavy ion like animony um animony
+ 
+
+ align:start position:0%
+for a heavy ion like animony um animony
+is big enough that it can impart a lot
+
+ align:start position:0%
+is big enough that it can impart a lot
+ 
+
+ align:start position:0%
+is big enough that it can impart a lot
+of energy to Silicon ions or the silicon
+
+ align:start position:0%
+of energy to Silicon ions or the silicon
+ 
+
+ align:start position:0%
+of energy to Silicon ions or the silicon
+recoils and uh the Silicon recoil
+
+ align:start position:0%
+recoils and uh the Silicon recoil
+ 
+
+ align:start position:0%
+recoils and uh the Silicon recoil
+recoils transport a lot of that damage
+
+ align:start position:0%
+recoils transport a lot of that damage
+ 
+
+ align:start position:0%
+recoils transport a lot of that damage
+energy deeper into the substrate so if
+
+ align:start position:0%
+energy deeper into the substrate so if
+ 
+
+ align:start position:0%
+energy deeper into the substrate so if
+you don't take it when you calculate
+
+ align:start position:0%
+you don't take it when you calculate
+ 
+
+ align:start position:0%
+you don't take it when you calculate
+damage and you have a heavy iron coming
+
+ align:start position:0%
+damage and you have a heavy iron coming
+ 
+
+ align:start position:0%
+damage and you have a heavy iron coming
+in if you don't take into account the
+
+ align:start position:0%
+in if you don't take into account the
+ 
+
+ align:start position:0%
+in if you don't take into account the
+Silicon recoils you're going to get
+
+ align:start position:0%
+Silicon recoils you're going to get
+ 
+
+ align:start position:0%
+Silicon recoils you're going to get
+pretty somewhat inaccurate distribution
+
+ align:start position:0%
+pretty somewhat inaccurate distribution
+ 
+
+ align:start position:0%
+pretty somewhat inaccurate distribution
+of where the where most of the damage is
+
+ align:start position:0%
+of where the where most of the damage is
+ 
+
+ align:start position:0%
+of where the where most of the damage is
+done so you really need to use the solid
+
+ align:start position:0%
+done so you really need to use the solid
+ 
+
+ align:start position:0%
+done so you really need to use the solid
+line and include the Silicon recoils in
+
+ align:start position:0%
+line and include the Silicon recoils in
+ 
+
+ align:start position:0%
+line and include the Silicon recoils in
+your damag because the Silicon atoms
+
+ align:start position:0%
+your damag because the Silicon atoms
+ 
+
+ align:start position:0%
+your damag because the Silicon atoms
+then go on and and damage further the
+
+ align:start position:0%
+then go on and and damage further the
+ 
+
+ align:start position:0%
+then go on and and damage further the
+lattice they they they um impart energy
+
+ align:start position:0%
+lattice they they they um impart energy
+ 
+
+ align:start position:0%
+lattice they they they um impart energy
+to other silicon atoms this is for 100
+
+ align:start position:0%
+to other silicon atoms this is for 100
+ 
+
+ align:start position:0%
+to other silicon atoms this is for 100
+Kilt uh animon but again look where the
+
+ align:start position:0%
+Kilt uh animon but again look where the
+ 
+
+ align:start position:0%
+Kilt uh animon but again look where the
+peak is the peak and the Damage still
+
+ align:start position:0%
+peak is the peak and the Damage still
+ 
+
+ align:start position:0%
+peak is the peak and the Damage still
+occurs at about close to 80% or so of
+
+ align:start position:0%
+occurs at about close to 80% or so of
+ 
+
+ align:start position:0%
+occurs at about close to 80% or so of
+the projected range of the animony uh
+
+ align:start position:0%
+the projected range of the animony uh
+ 
+
+ align:start position:0%
+the projected range of the animony uh
+ion so that's a handy rule of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thumb now what can we do with a damage
+
+ align:start position:0%
+thumb now what can we do with a damage
+ 
+
+ align:start position:0%
+thumb now what can we do with a damage
+energy profile like this or a damage uh
+
+ align:start position:0%
+energy profile like this or a damage uh
+ 
+
+ align:start position:0%
+energy profile like this or a damage uh
+density versus uh X or X over RP well if
+
+ align:start position:0%
+density versus uh X or X over RP well if
+ 
+
+ align:start position:0%
+density versus uh X or X over RP well if
+you know how much damage in a given
+
+ align:start position:0%
+you know how much damage in a given
+ 
+
+ align:start position:0%
+you know how much damage in a given
+angstrom how much energy in a given
+
+ align:start position:0%
+angstrom how much energy in a given
+ 
+
+ align:start position:0%
+angstrom how much energy in a given
+angstrom will uh tend to produce
+
+ align:start position:0%
+angstrom will uh tend to produce
+ 
+
+ align:start position:0%
+angstrom will uh tend to produce
+amorphization you could actually use
+
+ align:start position:0%
+amorphization you could actually use
+ 
+
+ align:start position:0%
+amorphization you could actually use
+this plot to figure out what how which
+
+ align:start position:0%
+this plot to figure out what how which
+ 
+
+ align:start position:0%
+this plot to figure out what how which
+part of the lattice is um which depths
+
+ align:start position:0%
+part of the lattice is um which depths
+ 
+
+ align:start position:0%
+part of the lattice is um which depths
+are amorphized and so here's an example
+
+ align:start position:0%
+are amorphized and so here's an example
+ 
+
+ align:start position:0%
+are amorphized and so here's an example
+what I'm doing here I'm taking this
+
+ align:start position:0%
+what I'm doing here I'm taking this
+ 
+
+ align:start position:0%
+what I'm doing here I'm taking this
+calculation which we showed for Boron a
+
+ align:start position:0%
+calculation which we showed for Boron a
+ 
+
+ align:start position:0%
+calculation which we showed for Boron a
+couple of slides ago and I'm assuming
+
+ align:start position:0%
+couple of slides ago and I'm assuming
+ 
+
+ align:start position:0%
+couple of slides ago and I'm assuming
+that there's a threshold for
+
+ align:start position:0%
+that there's a threshold for
+ 
+
+ align:start position:0%
+that there's a threshold for
+amorphization now this has been both
+
+ align:start position:0%
+amorphization now this has been both
+ 
+
+ align:start position:0%
+amorphization now this has been both
+calculated and people have tried to
+
+ align:start position:0%
+calculated and people have tried to
+ 
+
+ align:start position:0%
+calculated and people have tried to
+measure it I'm assuming the threshold
+
+ align:start position:0%
+measure it I'm assuming the threshold
+ 
+
+ align:start position:0%
+measure it I'm assuming the threshold
+for amorphization at room temperature is
+
+ align:start position:0%
+for amorphization at room temperature is
+ 
+
+ align:start position:0%
+for amorphization at room temperature is
+six electron volts per angstrom so
+
+ align:start position:0%
+six electron volts per angstrom so
+ 
+
+ align:start position:0%
+six electron volts per angstrom so
+people have kind of looked at this
+
+ align:start position:0%
+people have kind of looked at this
+ 
+
+ align:start position:0%
+people have kind of looked at this
+either theoretically or from um by
+
+ align:start position:0%
+either theoretically or from um by
+ 
+
+ align:start position:0%
+either theoretically or from um by
+looking at actual uh amorphization zones
+
+ align:start position:0%
+looking at actual uh amorphization zones
+ 
+
+ align:start position:0%
+looking at actual uh amorphization zones
+amorphous zones and said that when you
+
+ align:start position:0%
+amorphous zones and said that when you
+ 
+
+ align:start position:0%
+amorphous zones and said that when you
+get above about six electron volts
+
+ align:start position:0%
+get above about six electron volts
+ 
+
+ align:start position:0%
+get above about six electron volts
+deposited into nuclear processes per
+
+ align:start position:0%
+deposited into nuclear processes per
+ 
+
+ align:start position:0%
+deposited into nuclear processes per
+anstrom of depth the Silicon has so much
+
+ align:start position:0%
+anstrom of depth the Silicon has so much
+ 
+
+ align:start position:0%
+anstrom of depth the Silicon has so much
+damage that it goes Amorphis so it's
+
+ align:start position:0%
+damage that it goes Amorphis so it's
+ 
+
+ align:start position:0%
+damage that it goes Amorphis so it's
+lost its crystal structure in fact if I
+
+ align:start position:0%
+lost its crystal structure in fact if I
+ 
+
+ align:start position:0%
+lost its crystal structure in fact if I
+draw a line here at six and I see where
+
+ align:start position:0%
+draw a line here at six and I see where
+ 
+
+ align:start position:0%
+draw a line here at six and I see where
+it cuts this profile that would say that
+
+ align:start position:0%
+it cuts this profile that would say that
+ 
+
+ align:start position:0%
+it cuts this profile that would say that
+this substrate uh if you're imp planting
+
+ align:start position:0%
+this substrate uh if you're imp planting
+ 
+
+ align:start position:0%
+this substrate uh if you're imp planting
+waron at 100 Kilts um I don't know what
+
+ align:start position:0%
+waron at 100 Kilts um I don't know what
+ 
+
+ align:start position:0%
+waron at 100 Kilts um I don't know what
+the uh uh what the dose was in this
+
+ align:start position:0%
+the uh uh what the dose was in this
+ 
+
+ align:start position:0%
+the uh uh what the dose was in this
+particular case but it was it would be a
+
+ align:start position:0%
+particular case but it was it would be a
+ 
+
+ align:start position:0%
+particular case but it was it would be a
+morphed uh between about half of RP and
+
+ align:start position:0%
+morphed uh between about half of RP and
+ 
+
+ align:start position:0%
+morphed uh between about half of RP and
+up to about RP so in that region between
+
+ align:start position:0%
+up to about RP so in that region between
+ 
+
+ align:start position:0%
+up to about RP so in that region between
+half RP and and RP the uh between these
+
+ align:start position:0%
+half RP and and RP the uh between these
+ 
+
+ align:start position:0%
+half RP and and RP the uh between these
+two lines it's it's predicted according
+
+ align:start position:0%
+two lines it's it's predicted according
+ 
+
+ align:start position:0%
+two lines it's it's predicted according
+to this model again you're it's going to
+
+ align:start position:0%
+to this model again you're it's going to
+ 
+
+ align:start position:0%
+to this model again you're it's going to
+be very sensitive to your amorphization
+
+ align:start position:0%
+be very sensitive to your amorphization
+ 
+
+ align:start position:0%
+be very sensitive to your amorphization
+threshold this region in here will be
+
+ align:start position:0%
+threshold this region in here will be
+ 
+
+ align:start position:0%
+threshold this region in here will be
+amorphized everything else will be
+
+ align:start position:0%
+amorphized everything else will be
+ 
+
+ align:start position:0%
+amorphized everything else will be
+heavily damaged uh so you can see what
+
+ align:start position:0%
+heavily damaged uh so you can see what
+ 
+
+ align:start position:0%
+heavily damaged uh so you can see what
+Boron tends to do
+
+ align:start position:0%
+Boron tends to do
+ 
+
+ align:start position:0%
+Boron tends to do
+uh because of its distribution um it
+
+ align:start position:0%
+uh because of its distribution um it
+ 
+
+ align:start position:0%
+uh because of its distribution um it
+tends to create a buried amorphous layer
+
+ align:start position:0%
+tends to create a buried amorphous layer
+ 
+
+ align:start position:0%
+tends to create a buried amorphous layer
+with heavily damaged single Crystal
+
+ align:start position:0%
+with heavily damaged single Crystal
+ 
+
+ align:start position:0%
+with heavily damaged single Crystal
+silicon on either
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side and I just want to say a little
+
+ align:start position:0%
+side and I just want to say a little
+ 
+
+ align:start position:0%
+side and I just want to say a little
+more uh about amorphization shown here
+
+ align:start position:0%
+more uh about amorphization shown here
+ 
+
+ align:start position:0%
+more uh about amorphization shown here
+on slide um
+
+ align:start position:0%
+on slide um
+ 
+
+ align:start position:0%
+on slide um
+17 uh as as we've talked about before if
+
+ align:start position:0%
+17 uh as as we've talked about before if
+ 
+
+ align:start position:0%
+17 uh as as we've talked about before if
+you give it a high enough dose you have
+
+ align:start position:0%
+you give it a high enough dose you have
+ 
+
+ align:start position:0%
+you give it a high enough dose you have
+enough of the dis crystal is displaced
+
+ align:start position:0%
+enough of the dis crystal is displaced
+ 
+
+ align:start position:0%
+enough of the dis crystal is displaced
+it becomes completely amorphous it loses
+
+ align:start position:0%
+it becomes completely amorphous it loses
+ 
+
+ align:start position:0%
+it becomes completely amorphous it loses
+all of its crystal structure there's no
+
+ align:start position:0%
+all of its crystal structure there's no
+ 
+
+ align:start position:0%
+all of its crystal structure there's no
+more long range order
+
+ align:start position:0%
+more long range order
+ 
+
+ align:start position:0%
+more long range order
+at this point we have a random uh
+
+ align:start position:0%
+at this point we have a random uh
+ 
+
+ align:start position:0%
+at this point we have a random uh
+Arrangement and the Damage accumulation
+
+ align:start position:0%
+Arrangement and the Damage accumulation
+ 
+
+ align:start position:0%
+Arrangement and the Damage accumulation
+is saturated you really can't talk about
+
+ align:start position:0%
+is saturated you really can't talk about
+ 
+
+ align:start position:0%
+is saturated you really can't talk about
+damage anymore once you a moriz there
+
+ align:start position:0%
+damage anymore once you a moriz there
+ 
+
+ align:start position:0%
+damage anymore once you a moriz there
+are no lattice sites so you can't really
+
+ align:start position:0%
+are no lattice sites so you can't really
+ 
+
+ align:start position:0%
+are no lattice sites so you can't really
+knock somebody off a lattice site
+
+ align:start position:0%
+knock somebody off a lattice site
+ 
+
+ align:start position:0%
+knock somebody off a lattice site
+because there is no lce site uh it's
+
+ align:start position:0%
+because there is no lce site uh it's
+ 
+
+ align:start position:0%
+because there is no lce site uh it's
+it's no longer a lattice uh but just
+
+ align:start position:0%
+it's no longer a lattice uh but just
+ 
+
+ align:start position:0%
+it's no longer a lattice uh but just
+gives you an idea this is um uh taken
+
+ align:start position:0%
+gives you an idea this is um uh taken
+ 
+
+ align:start position:0%
+gives you an idea this is um uh taken
+from your textbook this is a
+
+ align:start position:0%
+from your textbook this is a
+ 
+
+ align:start position:0%
+from your textbook this is a
+cross-sectional temm so this is
+
+ align:start position:0%
+cross-sectional temm so this is
+ 
+
+ align:start position:0%
+cross-sectional temm so this is
+transmission electron micro micrograph
+
+ align:start position:0%
+transmission electron micro micrograph
+ 
+
+ align:start position:0%
+transmission electron micro micrograph
+pictures of an amorphous layer formation
+
+ align:start position:0%
+pictures of an amorphous layer formation
+ 
+
+ align:start position:0%
+pictures of an amorphous layer formation
+with increasing implant dose from left
+
+ align:start position:0%
+with increasing implant dose from left
+ 
+
+ align:start position:0%
+with increasing implant dose from left
+to right so this is a very high energy
+
+ align:start position:0%
+to right so this is a very high energy
+ 
+
+ align:start position:0%
+to right so this is a very high energy
+it's 300 Kilts silicon being implanted
+
+ align:start position:0%
+it's 300 Kilts silicon being implanted
+ 
+
+ align:start position:0%
+it's 300 Kilts silicon being implanted
+into a silicon substrate uh so the
+
+ align:start position:0%
+into a silicon substrate uh so the
+ 
+
+ align:start position:0%
+into a silicon substrate uh so the
+interesting thing is the ion now is
+
+ align:start position:0%
+interesting thing is the ion now is
+ 
+
+ align:start position:0%
+interesting thing is the ion now is
+silicon it has the same mass as a
+
+ align:start position:0%
+silicon it has the same mass as a
+ 
+
+ align:start position:0%
+silicon it has the same mass as a
+substrate it's relatively light though
+
+ align:start position:0%
+substrate it's relatively light though
+ 
+
+ align:start position:0%
+substrate it's relatively light though
+so here at at5 what do I see well here's
+
+ align:start position:0%
+so here at at5 what do I see well here's
+ 
+
+ align:start position:0%
+so here at at5 what do I see well here's
+the surface of the Silicon substrate and
+
+ align:start position:0%
+the surface of the Silicon substrate and
+ 
+
+ align:start position:0%
+the surface of the Silicon substrate and
+you see there's this band this region
+
+ align:start position:0%
+you see there's this band this region
+ 
+
+ align:start position:0%
+you see there's this band this region
+where there appears to be Darkness there
+
+ align:start position:0%
+where there appears to be Darkness there
+ 
+
+ align:start position:0%
+where there appears to be Darkness there
+seems to be a lot of damage uh a lot of
+
+ align:start position:0%
+seems to be a lot of damage uh a lot of
+ 
+
+ align:start position:0%
+seems to be a lot of damage uh a lot of
+stuff going on here dark contrast you
+
+ align:start position:0%
+stuff going on here dark contrast you
+ 
+
+ align:start position:0%
+stuff going on here dark contrast you
+can imagine um be associated with some
+
+ align:start position:0%
+can imagine um be associated with some
+ 
+
+ align:start position:0%
+can imagine um be associated with some
+kind of U dislocation Loops or some kind
+
+ align:start position:0%
+kind of U dislocation Loops or some kind
+ 
+
+ align:start position:0%
+kind of U dislocation Loops or some kind
+of uh damage in the substrate here
+
+ align:start position:0%
+of uh damage in the substrate here
+ 
+
+ align:start position:0%
+of uh damage in the substrate here
+here's a band here now at one and a half
+
+ align:start position:0%
+here's a band here now at one and a half
+ 
+
+ align:start position:0%
+here's a band here now at one and a half
+times 10 the 15th there's a band which
+
+ align:start position:0%
+times 10 the 15th there's a band which
+ 
+
+ align:start position:0%
+times 10 the 15th there's a band which
+really has um it's buried and it's lost
+
+ align:start position:0%
+really has um it's buried and it's lost
+ 
+
+ align:start position:0%
+really has um it's buried and it's lost
+its its crystalline uh structure if we
+
+ align:start position:0%
+its its crystalline uh structure if we
+ 
+
+ align:start position:0%
+its its crystalline uh structure if we
+were to zoom in here and do a selected
+
+ align:start position:0%
+were to zoom in here and do a selected
+ 
+
+ align:start position:0%
+were to zoom in here and do a selected
+area defraction on this region we find
+
+ align:start position:0%
+area defraction on this region we find
+ 
+
+ align:start position:0%
+area defraction on this region we find
+it's not a crystal there will be no
+
+ align:start position:0%
+it's not a crystal there will be no
+ 
+
+ align:start position:0%
+it's not a crystal there will be no
+defraction lowiy spots whereas if you go
+
+ align:start position:0%
+defraction lowiy spots whereas if you go
+ 
+
+ align:start position:0%
+defraction lowiy spots whereas if you go
+down here you would see crystalling um
+
+ align:start position:0%
+down here you would see crystalling um
+ 
+
+ align:start position:0%
+down here you would see crystalling um
+here's that amorphous layer at 2 * 10
+
+ align:start position:0%
+here's that amorphous layer at 2 * 10
+ 
+
+ align:start position:0%
+here's that amorphous layer at 2 * 10
+15th it's increased in its width it
+
+ align:start position:0%
+15th it's increased in its width it
+ 
+
+ align:start position:0%
+15th it's increased in its width it
+still hasn't reached the surface though
+
+ align:start position:0%
+still hasn't reached the surface though
+ 
+
+ align:start position:0%
+still hasn't reached the surface though
+and at 41 the 15th it's it's increased
+
+ align:start position:0%
+and at 41 the 15th it's it's increased
+ 
+
+ align:start position:0%
+and at 41 the 15th it's it's increased
+in depth but again hasn't quite reached
+
+ align:start position:0%
+in depth but again hasn't quite reached
+ 
+
+ align:start position:0%
+in depth but again hasn't quite reached
+the surface 5 10 the 15th almost and
+
+ align:start position:0%
+the surface 5 10 the 15th almost and
+ 
+
+ align:start position:0%
+the surface 5 10 the 15th almost and
+finally uh at 10 to the 16th that's a
+
+ align:start position:0%
+finally uh at 10 to the 16th that's a
+ 
+
+ align:start position:0%
+finally uh at 10 to the 16th that's a
+very large dose you've created an
+
+ align:start position:0%
+very large dose you've created an
+ 
+
+ align:start position:0%
+very large dose you've created an
+amorphous layer all the way from the
+
+ align:start position:0%
+amorphous layer all the way from the
+ 
+
+ align:start position:0%
+amorphous layer all the way from the
+surface down to some depth I don't know
+
+ align:start position:0%
+surface down to some depth I don't know
+ 
+
+ align:start position:0%
+surface down to some depth I don't know
+what this is half Micron or whatever um
+
+ align:start position:0%
+what this is half Micron or whatever um
+ 
+
+ align:start position:0%
+what this is half Micron or whatever um
+and completely am morphies from the
+
+ align:start position:0%
+and completely am morphies from the
+ 
+
+ align:start position:0%
+and completely am morphies from the
+surface um
+
+ align:start position:0%
+surface um
+ 
+
+ align:start position:0%
+surface um
+down uh and this is all um at room
+
+ align:start position:0%
+down uh and this is all um at room
+ 
+
+ align:start position:0%
+down uh and this is all um at room
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+uh it turns out it's much easier to form
+
+ align:start position:0%
+uh it turns out it's much easier to form
+ 
+
+ align:start position:0%
+uh it turns out it's much easier to form
+an amorphous layer at low temperatures
+
+ align:start position:0%
+an amorphous layer at low temperatures
+ 
+
+ align:start position:0%
+an amorphous layer at low temperatures
+77 Kelvin so you will sometimes see
+
+ align:start position:0%
+77 Kelvin so you will sometimes see
+ 
+
+ align:start position:0%
+77 Kelvin so you will sometimes see
+people specifying their implant energy
+
+ align:start position:0%
+people specifying their implant energy
+ 
+
+ align:start position:0%
+people specifying their implant energy
+they want to use a special item planner
+
+ align:start position:0%
+they want to use a special item planner
+ 
+
+ align:start position:0%
+they want to use a special item planner
+that does if you're doing uh some of
+
+ align:start position:0%
+that does if you're doing uh some of
+ 
+
+ align:start position:0%
+that does if you're doing uh some of
+these materials experiments that can
+
+ align:start position:0%
+these materials experiments that can
+ 
+
+ align:start position:0%
+these materials experiments that can
+that can hold the Waf for at 77 Kelvin
+
+ align:start position:0%
+that can hold the Waf for at 77 Kelvin
+ 
+
+ align:start position:0%
+that can hold the Waf for at 77 Kelvin
+that means the damage is much more
+
+ align:start position:0%
+that means the damage is much more
+ 
+
+ align:start position:0%
+that means the damage is much more
+stable remember we were talking about
+
+ align:start position:0%
+stable remember we were talking about
+ 
+
+ align:start position:0%
+stable remember we were talking about
+that that simulation from uh Lawrence
+
+ align:start position:0%
+that that simulation from uh Lawrence
+ 
+
+ align:start position:0%
+that that simulation from uh Lawrence
+Livermore Labs you saw that damag cloud
+
+ align:start position:0%
+Livermore Labs you saw that damag cloud
+ 
+
+ align:start position:0%
+Livermore Labs you saw that damag cloud
+and then a lot of recombination by
+
+ align:start position:0%
+and then a lot of recombination by
+ 
+
+ align:start position:0%
+and then a lot of recombination by
+diffusion and things well if you're at
+
+ align:start position:0%
+diffusion and things well if you're at
+ 
+
+ align:start position:0%
+diffusion and things well if you're at
+low temperatures you have a lot less
+
+ align:start position:0%
+low temperatures you have a lot less
+ 
+
+ align:start position:0%
+low temperatures you have a lot less
+recombination so the damage tend to be
+
+ align:start position:0%
+recombination so the damage tend to be
+ 
+
+ align:start position:0%
+recombination so the damage tend to be
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+stable especially with the light ion so
+
+ align:start position:0%
+stable especially with the light ion so
+ 
+
+ align:start position:0%
+stable especially with the light ion so
+if you want to am morfy silicon with a
+
+ align:start position:0%
+if you want to am morfy silicon with a
+ 
+
+ align:start position:0%
+if you want to am morfy silicon with a
+light iron like Boron or silicon you
+
+ align:start position:0%
+light iron like Boron or silicon you
+ 
+
+ align:start position:0%
+light iron like Boron or silicon you
+pretty much to do it reliably you pretty
+
+ align:start position:0%
+pretty much to do it reliably you pretty
+ 
+
+ align:start position:0%
+pretty much to do it reliably you pretty
+much have to hold the wafer at low
+
+ align:start position:0%
+much have to hold the wafer at low
+ 
+
+ align:start position:0%
+much have to hold the wafer at low
+temperatures like 77 Kelvin if you have
+
+ align:start position:0%
+temperatures like 77 Kelvin if you have
+ 
+
+ align:start position:0%
+temperatures like 77 Kelvin if you have
+a a heavy ion that does a lot of damage
+
+ align:start position:0%
+a a heavy ion that does a lot of damage
+ 
+
+ align:start position:0%
+a a heavy ion that does a lot of damage
+like arnik or animon you can easily
+
+ align:start position:0%
+like arnik or animon you can easily
+ 
+
+ align:start position:0%
+like arnik or animon you can easily
+amorphize a layer from the surface down
+
+ align:start position:0%
+amorphize a layer from the surface down
+ 
+
+ align:start position:0%
+amorphize a layer from the surface down
+at room
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temperature okay so let's go on to slide
+
+ align:start position:0%
+temperature okay so let's go on to slide
+ 
+
+ align:start position:0%
+temperature okay so let's go on to slide
+that's a picture of of damage let's go
+
+ align:start position:0%
+that's a picture of of damage let's go
+ 
+
+ align:start position:0%
+that's a picture of of damage let's go
+on to slide 18 and talk about um damage
+
+ align:start position:0%
+on to slide 18 and talk about um damage
+ 
+
+ align:start position:0%
+on to slide 18 and talk about um damage
+and kneeling so uh we have to do uh an
+
+ align:start position:0%
+and kneeling so uh we have to do uh an
+ 
+
+ align:start position:0%
+and kneeling so uh we have to do uh an
+kneeling after we do an ion implant
+
+ align:start position:0%
+kneeling after we do an ion implant
+ 
+
+ align:start position:0%
+kneeling after we do an ion implant
+because we bashed up the crystal so what
+
+ align:start position:0%
+because we bashed up the crystal so what
+ 
+
+ align:start position:0%
+because we bashed up the crystal so what
+do we want to do when we we want to
+
+ align:start position:0%
+do we want to do when we we want to
+ 
+
+ align:start position:0%
+do we want to do when we we want to
+remove the primary damage caused by the
+
+ align:start position:0%
+remove the primary damage caused by the
+ 
+
+ align:start position:0%
+remove the primary damage caused by the
+implant you want to put all the dopin
+
+ align:start position:0%
+implant you want to put all the dopin
+ 
+
+ align:start position:0%
+implant you want to put all the dopin
+onto um substitutional sites that way
+
+ align:start position:0%
+onto um substitutional sites that way
+ 
+
+ align:start position:0%
+onto um substitutional sites that way
+they can they can be donors or acceptors
+
+ align:start position:0%
+they can they can be donors or acceptors
+ 
+
+ align:start position:0%
+they can they can be donors or acceptors
+uh we try to make the crystallin uh the
+
+ align:start position:0%
+uh we try to make the crystallin uh the
+ 
+
+ align:start position:0%
+uh we try to make the crystallin uh the
+crystal as perfect as it was when you
+
+ align:start position:0%
+crystal as perfect as it was when you
+ 
+
+ align:start position:0%
+crystal as perfect as it was when you
+first started you never really get it
+
+ align:start position:0%
+first started you never really get it
+ 
+
+ align:start position:0%
+first started you never really get it
+quite as
+
+ align:start position:0%
+quite as
+ 
+
+ align:start position:0%
+quite as
+perfect um we'd also so in doing that we
+
+ align:start position:0%
+perfect um we'd also so in doing that we
+ 
+
+ align:start position:0%
+perfect um we'd also so in doing that we
+want to restore the electron and whole
+
+ align:start position:0%
+want to restore the electron and whole
+ 
+
+ align:start position:0%
+want to restore the electron and whole
+mobilities and the carrier lifetime
+
+ align:start position:0%
+mobilities and the carrier lifetime
+ 
+
+ align:start position:0%
+mobilities and the carrier lifetime
+hopefully to what it was and you want to
+
+ align:start position:0%
+hopefully to what it was and you want to
+ 
+
+ align:start position:0%
+hopefully to what it was and you want to
+do all these things without really
+
+ align:start position:0%
+do all these things without really
+ 
+
+ align:start position:0%
+do all these things without really
+having much dope and diffusion so it's a
+
+ align:start position:0%
+having much dope and diffusion so it's a
+ 
+
+ align:start position:0%
+having much dope and diffusion so it's a
+tough job it's a tough job um and this
+
+ align:start position:0%
+tough job it's a tough job um and this
+ 
+
+ align:start position:0%
+tough job it's a tough job um and this
+is a model for damage and kneeling uh
+
+ align:start position:0%
+is a model for damage and kneeling uh
+ 
+
+ align:start position:0%
+is a model for damage and kneeling uh
+relatively simple but that was published
+
+ align:start position:0%
+relatively simple but that was published
+ 
+
+ align:start position:0%
+relatively simple but that was published
+back in 1991 that that is is very famous
+
+ align:start position:0%
+back in 1991 that that is is very famous
+ 
+
+ align:start position:0%
+back in 1991 that that is is very famous
+now uh by Martin Giles uh which is
+
+ align:start position:0%
+now uh by Martin Giles uh which is
+ 
+
+ align:start position:0%
+now uh by Martin Giles uh which is
+called the plus one model for residual
+
+ align:start position:0%
+called the plus one model for residual
+ 
+
+ align:start position:0%
+called the plus one model for residual
+damage kind of a name but what Martin
+
+ align:start position:0%
+damage kind of a name but what Martin
+ 
+
+ align:start position:0%
+damage kind of a name but what Martin
+did was he he said the following things
+
+ align:start position:0%
+did was he he said the following things
+ 
+
+ align:start position:0%
+did was he he said the following things
+he said that most recoiled silicon
+
+ align:start position:0%
+he said that most recoiled silicon
+ 
+
+ align:start position:0%
+he said that most recoiled silicon
+interstitials so again we're going to
+
+ align:start position:0%
+interstitials so again we're going to
+ 
+
+ align:start position:0%
+interstitials so again we're going to
+call this guy who's recoiled who ends up
+
+ align:start position:0%
+call this guy who's recoiled who ends up
+ 
+
+ align:start position:0%
+call this guy who's recoiled who ends up
+in an interstitial space um an i or a
+
+ align:start position:0%
+in an interstitial space um an i or a
+ 
+
+ align:start position:0%
+in an interstitial space um an i or a
+silicon interstitial most of them will
+
+ align:start position:0%
+silicon interstitial most of them will
+ 
+
+ align:start position:0%
+silicon interstitial most of them will
+find a vacancy and they'll recombine
+
+ align:start position:0%
+find a vacancy and they'll recombine
+ 
+
+ align:start position:0%
+find a vacancy and they'll recombine
+very very
+
+ align:start position:0%
+very very
+ 
+
+ align:start position:0%
+very very
+rapidly either during the implantation
+
+ align:start position:0%
+rapidly either during the implantation
+ 
+
+ align:start position:0%
+rapidly either during the implantation
+process or in the first few seconds of
+
+ align:start position:0%
+process or in the first few seconds of
+ 
+
+ align:start position:0%
+process or in the first few seconds of
+analing a lot of recombination takes
+
+ align:start position:0%
+analing a lot of recombination takes
+ 
+
+ align:start position:0%
+analing a lot of recombination takes
+place um in fact he calculated the
+
+ align:start position:0%
+place um in fact he calculated the
+ 
+
+ align:start position:0%
+place um in fact he calculated the
+distribution of remaining recoils
+
+ align:start position:0%
+distribution of remaining recoils
+ 
+
+ align:start position:0%
+distribution of remaining recoils
+um after iron implantation without even
+
+ align:start position:0%
+um after iron implantation without even
+ 
+
+ align:start position:0%
+um after iron implantation without even
+any kneeling and what he found there's a
+
+ align:start position:0%
+any kneeling and what he found there's a
+ 
+
+ align:start position:0%
+any kneeling and what he found there's a
+net excess of vacancies near the surface
+
+ align:start position:0%
+net excess of vacancies near the surface
+ 
+
+ align:start position:0%
+net excess of vacancies near the surface
+and a net excess of interstitials
+
+ align:start position:0%
+and a net excess of interstitials
+ 
+
+ align:start position:0%
+and a net excess of interstitials
+towards the bulk but there's still a lot
+
+ align:start position:0%
+towards the bulk but there's still a lot
+ 
+
+ align:start position:0%
+towards the bulk but there's still a lot
+of them recombined so this is a
+
+ align:start position:0%
+of them recombined so this is a
+ 
+
+ align:start position:0%
+of them recombined so this is a
+calculation from Giles and he's got
+
+ align:start position:0%
+calculation from Giles and he's got
+ 
+
+ align:start position:0%
+calculation from Giles and he's got
+concentration of interstitials and
+
+ align:start position:0%
+concentration of interstitials and
+ 
+
+ align:start position:0%
+concentration of interstitials and
+vacancies as a function of depth this
+
+ align:start position:0%
+vacancies as a function of depth this
+ 
+
+ align:start position:0%
+vacancies as a function of depth this
+solid line or this this line on top here
+
+ align:start position:0%
+solid line or this this line on top here
+ 
+
+ align:start position:0%
+solid line or this this line on top here
+that starts at around 10 of the 20 or or
+
+ align:start position:0%
+that starts at around 10 of the 20 or or
+ 
+
+ align:start position:0%
+that starts at around 10 of the 20 or or
+mid 10 of the 20 and then goes
+
+ align:start position:0%
+mid 10 of the 20 and then goes
+ 
+
+ align:start position:0%
+mid 10 of the 20 and then goes
+down um he these are these are the total
+
+ align:start position:0%
+down um he these are these are the total
+ 
+
+ align:start position:0%
+down um he these are these are the total
+interstitials and vacancy concentrations
+
+ align:start position:0%
+interstitials and vacancy concentrations
+ 
+
+ align:start position:0%
+interstitials and vacancy concentrations
+he calculated they're almost on top of
+
+ align:start position:0%
+he calculated they're almost on top of
+ 
+
+ align:start position:0%
+he calculated they're almost on top of
+each other you know on this log scale
+
+ align:start position:0%
+each other you know on this log scale
+ 
+
+ align:start position:0%
+each other you know on this log scale
+you can't tell the difference so you
+
+ align:start position:0%
+you can't tell the difference so you
+ 
+
+ align:start position:0%
+you can't tell the difference so you
+create a tremendous number of
+
+ align:start position:0%
+create a tremendous number of
+ 
+
+ align:start position:0%
+create a tremendous number of
+interstitials tremendous number of
+
+ align:start position:0%
+interstitials tremendous number of
+ 
+
+ align:start position:0%
+interstitials tremendous number of
+vacancies but but most of them all
+
+ align:start position:0%
+vacancies but but most of them all
+ 
+
+ align:start position:0%
+vacancies but but most of them all
+recombined and in fact what he's plotted
+
+ align:start position:0%
+recombined and in fact what he's plotted
+ 
+
+ align:start position:0%
+recombined and in fact what he's plotted
+here is the net interstitials so that's
+
+ align:start position:0%
+here is the net interstitials so that's
+ 
+
+ align:start position:0%
+here is the net interstitials so that's
+the number of interstitials minus the
+
+ align:start position:0%
+the number of interstitials minus the
+ 
+
+ align:start position:0%
+the number of interstitials minus the
+number of vacancies at a given point so
+
+ align:start position:0%
+number of vacancies at a given point so
+ 
+
+ align:start position:0%
+number of vacancies at a given point so
+that's how many are left over so the net
+
+ align:start position:0%
+that's how many are left over so the net
+ 
+
+ align:start position:0%
+that's how many are left over so the net
+interstitials um look like this in fact
+
+ align:start position:0%
+interstitials um look like this in fact
+ 
+
+ align:start position:0%
+interstitials um look like this in fact
+if you plot the net profiles here in in
+
+ align:start position:0%
+if you plot the net profiles here in in
+ 
+
+ align:start position:0%
+if you plot the net profiles here in in
+the near surface region you have net
+
+ align:start position:0%
+the near surface region you have net
+ 
+
+ align:start position:0%
+the near surface region you have net
+vacancies so there's there's extra
+
+ align:start position:0%
+vacancies so there's there's extra
+ 
+
+ align:start position:0%
+vacancies so there's there's extra
+vacancies down in deep you have net
+
+ align:start position:0%
+vacancies down in deep you have net
+ 
+
+ align:start position:0%
+vacancies down in deep you have net
+interstitials um but the total numbers
+
+ align:start position:0%
+interstitials um but the total numbers
+ 
+
+ align:start position:0%
+interstitials um but the total numbers
+of these net are much much uh less than
+
+ align:start position:0%
+of these net are much much uh less than
+ 
+
+ align:start position:0%
+of these net are much much uh less than
+you know when you do the subtraction of
+
+ align:start position:0%
+you know when you do the subtraction of
+ 
+
+ align:start position:0%
+you know when you do the subtraction of
+the interstitials from the vacancies
+
+ align:start position:0%
+the interstitials from the vacancies
+ 
+
+ align:start position:0%
+the interstitials from the vacancies
+than the total interstitial or vacancies
+
+ align:start position:0%
+than the total interstitial or vacancies
+ 
+
+ align:start position:0%
+than the total interstitial or vacancies
+that were actually created so that's his
+
+ align:start position:0%
+that were actually created so that's his
+ 
+
+ align:start position:0%
+that were actually created so that's his
+point to you know within three orders of
+
+ align:start position:0%
+point to you know within three orders of
+ 
+
+ align:start position:0%
+point to you know within three orders of
+magnitude a lot most of these guys Rec
+
+ align:start position:0%
+magnitude a lot most of these guys Rec
+ 
+
+ align:start position:0%
+magnitude a lot most of these guys Rec
+combine uh so to first order what he
+
+ align:start position:0%
+combine uh so to first order what he
+ 
+
+ align:start position:0%
+combine uh so to first order what he
+said is that you can imagine that all of
+
+ align:start position:0%
+said is that you can imagine that all of
+ 
+
+ align:start position:0%
+said is that you can imagine that all of
+the original damage recombines and
+
+ align:start position:0%
+the original damage recombines and
+ 
+
+ align:start position:0%
+the original damage recombines and
+leaves behind only one
+
+ align:start position:0%
+leaves behind only one
+ 
+
+ align:start position:0%
+leaves behind only one
+interstitial created for every
+
+ align:start position:0%
+interstitial created for every
+ 
+
+ align:start position:0%
+interstitial created for every
+phosphorus atom or every ion implanted
+
+ align:start position:0%
+phosphorus atom or every ion implanted
+ 
+
+ align:start position:0%
+phosphorus atom or every ion implanted
+ion uh that that is Ion implanted so you
+
+ align:start position:0%
+ion uh that that is Ion implanted so you
+ 
+
+ align:start position:0%
+ion uh that that is Ion implanted so you
+can imag let's say you are implanting a
+
+ align:start position:0%
+can imag let's say you are implanting a
+ 
+
+ align:start position:0%
+can imag let's say you are implanting a
+dose of phosphorus and this particular
+
+ align:start position:0%
+dose of phosphorus and this particular
+ 
+
+ align:start position:0%
+dose of phosphorus and this particular
+example I guess is 80 K 10 13th he was
+
+ align:start position:0%
+example I guess is 80 K 10 13th he was
+ 
+
+ align:start position:0%
+example I guess is 80 K 10 13th he was
+saying that there's what one
+
+ align:start position:0%
+saying that there's what one
+ 
+
+ align:start position:0%
+saying that there's what one
+interstitial created for every Frost
+
+ align:start position:0%
+interstitial created for every Frost
+ 
+
+ align:start position:0%
+interstitial created for every Frost
+phosphorus incoming so he would say
+
+ align:start position:0%
+phosphorus incoming so he would say
+ 
+
+ align:start position:0%
+phosphorus incoming so he would say
+there's 10 13th per square centimeter
+
+ align:start position:0%
+there's 10 13th per square centimeter
+ 
+
+ align:start position:0%
+there's 10 13th per square centimeter
+silicon interstitials created so I mean
+
+ align:start position:0%
+silicon interstitials created so I mean
+ 
+
+ align:start position:0%
+silicon interstitials created so I mean
+it's incredibly simple you just take the
+
+ align:start position:0%
+it's incredibly simple you just take the
+ 
+
+ align:start position:0%
+it's incredibly simple you just take the
+dose of the atoms that are implanted of
+
+ align:start position:0%
+dose of the atoms that are implanted of
+ 
+
+ align:start position:0%
+dose of the atoms that are implanted of
+the ions that are implanted say that's
+
+ align:start position:0%
+the ions that are implanted say that's
+ 
+
+ align:start position:0%
+the ions that are implanted say that's
+the number of interstitials per square
+
+ align:start position:0%
+the number of interstitials per square
+ 
+
+ align:start position:0%
+the number of interstitials per square
+centimeter that I create 10 13th uh it's
+
+ align:start position:0%
+centimeter that I create 10 13th uh it's
+ 
+
+ align:start position:0%
+centimeter that I create 10 13th uh it's
+called plus one because you know and
+
+ align:start position:0%
+called plus one because you know and
+ 
+
+ align:start position:0%
+called plus one because you know and
+intuitively what he's saying is if your
+
+ align:start position:0%
+intuitively what he's saying is if your
+ 
+
+ align:start position:0%
+intuitively what he's saying is if your
+implant is totally activated so every
+
+ align:start position:0%
+implant is totally activated so every
+ 
+
+ align:start position:0%
+implant is totally activated so every
+implanted phosphorus ion finds a
+
+ align:start position:0%
+implanted phosphorus ion finds a
+ 
+
+ align:start position:0%
+implanted phosphorus ion finds a
+substitutional site well where did that
+
+ align:start position:0%
+substitutional site well where did that
+ 
+
+ align:start position:0%
+substitutional site well where did that
+silicon go it had to knock that silicon
+
+ align:start position:0%
+silicon go it had to knock that silicon
+ 
+
+ align:start position:0%
+silicon go it had to knock that silicon
+is somewhere as an interstitial okay and
+
+ align:start position:0%
+is somewhere as an interstitial okay and
+ 
+
+ align:start position:0%
+is somewhere as an interstitial okay and
+that's all he said he said assuming your
+
+ align:start position:0%
+that's all he said he said assuming your
+ 
+
+ align:start position:0%
+that's all he said he said assuming your
+analing is good you know what you're
+
+ align:start position:0%
+analing is good you know what you're
+ 
+
+ align:start position:0%
+analing is good you know what you're
+doing to to first order so this is get
+
+ align:start position:0%
+doing to to first order so this is get
+ 
+
+ align:start position:0%
+doing to to first order so this is get
+an order of magnitude estimate the
+
+ align:start position:0%
+an order of magnitude estimate the
+ 
+
+ align:start position:0%
+an order of magnitude estimate the
+number of interstitials I create is
+
+ align:start position:0%
+number of interstitials I create is
+ 
+
+ align:start position:0%
+number of interstitials I create is
+equal to the dose of what I implanted so
+
+ align:start position:0%
+equal to the dose of what I implanted so
+ 
+
+ align:start position:0%
+equal to the dose of what I implanted so
+that's pretty simple I implant 10 the
+
+ align:start position:0%
+that's pretty simple I implant 10 the
+ 
+
+ align:start position:0%
+that's pretty simple I implant 10 the
+15th I have 10 the 15th excess
+
+ align:start position:0%
+15th I have 10 the 15th excess
+ 
+
+ align:start position:0%
+15th I have 10 the 15th excess
+interstitials now in my crystal and
+
+ align:start position:0%
+interstitials now in my crystal and
+ 
+
+ align:start position:0%
+interstitials now in my crystal and
+that's with the so-called plus one
+
+ align:start position:0%
+that's with the so-called plus one
+ 
+
+ align:start position:0%
+that's with the so-called plus one
+model um this is tells you a little bit
+
+ align:start position:0%
+model um this is tells you a little bit
+ 
+
+ align:start position:0%
+model um this is tells you a little bit
+more about how accurate that assumption
+
+ align:start position:0%
+more about how accurate that assumption
+ 
+
+ align:start position:0%
+more about how accurate that assumption
+might be this is on slide number 19 uh I
+
+ align:start position:0%
+might be this is on slide number 19 uh I
+ 
+
+ align:start position:0%
+might be this is on slide number 19 uh I
+took this from your
+
+ align:start position:0%
+took this from your
+ 
+
+ align:start position:0%
+took this from your
+textbook it's a little bit about damage
+
+ align:start position:0%
+textbook it's a little bit about damage
+ 
+
+ align:start position:0%
+textbook it's a little bit about damage
+evolution in time so uh what it's a plot
+
+ align:start position:0%
+evolution in time so uh what it's a plot
+ 
+
+ align:start position:0%
+evolution in time so uh what it's a plot
+of is the um annihilated uh
+
+ align:start position:0%
+of is the um annihilated uh
+ 
+
+ align:start position:0%
+of is the um annihilated uh
+interstitials so the recombined ones and
+
+ align:start position:0%
+interstitials so the recombined ones and
+ 
+
+ align:start position:0%
+interstitials so the recombined ones and
+vacancies per implanted
+
+ align:start position:0%
+vacancies per implanted
+ 
+
+ align:start position:0%
+vacancies per implanted
+ion okay um so if we and and it's kind
+
+ align:start position:0%
+ion okay um so if we and and it's kind
+ 
+
+ align:start position:0%
+ion okay um so if we and and it's kind
+of as here as a function of of time um
+
+ align:start position:0%
+of as here as a function of of time um
+ 
+
+ align:start position:0%
+of as here as a function of of time um
+so if you look at uh these are Monte
+
+ align:start position:0%
+so if you look at uh these are Monte
+ 
+
+ align:start position:0%
+so if you look at uh these are Monte
+caros simulations basically of
+
+ align:start position:0%
+caros simulations basically of
+ 
+
+ align:start position:0%
+caros simulations basically of
+interstitial and vacancy
+
+ align:start position:0%
+interstitial and vacancy
+ 
+
+ align:start position:0%
+interstitial and vacancy
+recombination and if you go after a
+
+ align:start position:0%
+recombination and if you go after a
+ 
+
+ align:start position:0%
+recombination and if you go after a
+short time uh really um only excess uh
+
+ align:start position:0%
+short time uh really um only excess uh
+ 
+
+ align:start position:0%
+short time uh really um only excess uh
+interstitials remain and uh these can
+
+ align:start position:0%
+interstitials remain and uh these can
+ 
+
+ align:start position:0%
+interstitials remain and uh these can
+end up forming clusters but basically um
+
+ align:start position:0%
+end up forming clusters but basically um
+ 
+
+ align:start position:0%
+end up forming clusters but basically um
+this bulk and surface recombination take
+
+ align:start position:0%
+this bulk and surface recombination take
+ 
+
+ align:start position:0%
+this bulk and surface recombination take
+place on a very short time scale so look
+
+ align:start position:0%
+place on a very short time scale so look
+ 
+
+ align:start position:0%
+place on a very short time scale so look
+at the bulk re combination uh very
+
+ align:start position:0%
+at the bulk re combination uh very
+ 
+
+ align:start position:0%
+at the bulk re combination uh very
+quickly after uh here um after only well
+
+ align:start position:0%
+quickly after uh here um after only well
+ 
+
+ align:start position:0%
+quickly after uh here um after only well
+I don't know 10 to the minus 6 seconds
+
+ align:start position:0%
+I don't know 10 to the minus 6 seconds
+ 
+
+ align:start position:0%
+I don't know 10 to the minus 6 seconds
+with that a microc um there's a lot of
+
+ align:start position:0%
+with that a microc um there's a lot of
+ 
+
+ align:start position:0%
+with that a microc um there's a lot of
+bulk recombination that's taken place
+
+ align:start position:0%
+bulk recombination that's taken place
+ 
+
+ align:start position:0%
+bulk recombination that's taken place
+surf service recombination maybe takes
+
+ align:start position:0%
+surf service recombination maybe takes
+ 
+
+ align:start position:0%
+surf service recombination maybe takes
+uh for vacancies takes a shorter time
+
+ align:start position:0%
+uh for vacancies takes a shorter time
+ 
+
+ align:start position:0%
+uh for vacancies takes a shorter time
+and then finally surface interstitial uh
+
+ align:start position:0%
+and then finally surface interstitial uh
+ 
+
+ align:start position:0%
+and then finally surface interstitial uh
+recombination can take place within uh
+
+ align:start position:0%
+recombination can take place within uh
+ 
+
+ align:start position:0%
+recombination can take place within uh
+100 to 1
+
+ align:start position:0%
+100 to 1
+ 
+
+ align:start position:0%
+100 to 1
+second so you have a lot of um uh
+
+ align:start position:0%
+second so you have a lot of um uh
+ 
+
+ align:start position:0%
+second so you have a lot of um uh
+interstitial uh and and vacancy
+
+ align:start position:0%
+interstitial uh and and vacancy
+ 
+
+ align:start position:0%
+interstitial uh and and vacancy
+recombination that was the point of what
+
+ align:start position:0%
+recombination that was the point of what
+ 
+
+ align:start position:0%
+recombination that was the point of what
+Giles was saying so that only plus one
+
+ align:start position:0%
+Giles was saying so that only plus one
+ 
+
+ align:start position:0%
+Giles was saying so that only plus one
+interstitial uh excess interstitial
+
+ align:start position:0%
+interstitial uh excess interstitial
+ 
+
+ align:start position:0%
+interstitial uh excess interstitial
+remains now what happens to those 10 to
+
+ align:start position:0%
+remains now what happens to those 10 to
+ 
+
+ align:start position:0%
+remains now what happens to those 10 to
+the 15th if I un implant 10 to the 15th
+
+ align:start position:0%
+the 15th if I un implant 10 to the 15th
+ 
+
+ align:start position:0%
+the 15th if I un implant 10 to the 15th
+phosphorus atoms I have 10 to the 15th
+
+ align:start position:0%
+phosphorus atoms I have 10 to the 15th
+ 
+
+ align:start position:0%
+phosphorus atoms I have 10 to the 15th
+excess
+
+ align:start position:0%
+excess
+ 
+
+ align:start position:0%
+excess
+interstitials the name of the game is
+
+ align:start position:0%
+interstitials the name of the game is
+ 
+
+ align:start position:0%
+interstitials the name of the game is
+what happens to all these interstitials
+
+ align:start position:0%
+what happens to all these interstitials
+ 
+
+ align:start position:0%
+what happens to all these interstitials
+well it turns out they coales they get
+
+ align:start position:0%
+well it turns out they coales they get
+ 
+
+ align:start position:0%
+well it turns out they coales they get
+together into little defects these
+
+ align:start position:0%
+together into little defects these
+ 
+
+ align:start position:0%
+together into little defects these
+little defects are called in in curly
+
+ align:start position:0%
+little defects are called in in curly
+ 
+
+ align:start position:0%
+little defects are called in in curly
+brackets called 311 defects and we'll
+
+ align:start position:0%
+brackets called 311 defects and we'll
+ 
+
+ align:start position:0%
+brackets called 311 defects and we'll
+talk about in detail next time about
+
+ align:start position:0%
+talk about in detail next time about
+ 
+
+ align:start position:0%
+talk about in detail next time about
+311's uh but the interesting thing about
+
+ align:start position:0%
+311's uh but the interesting thing about
+ 
+
+ align:start position:0%
+311's uh but the interesting thing about
+these little clusters these 31 ons they
+
+ align:start position:0%
+these little clusters these 31 ons they
+ 
+
+ align:start position:0%
+these little clusters these 31 ons they
+are defects end up being stable for very
+
+ align:start position:0%
+are defects end up being stable for very
+ 
+
+ align:start position:0%
+are defects end up being stable for very
+long periods so the interstitials come
+
+ align:start position:0%
+long periods so the interstitials come
+ 
+
+ align:start position:0%
+long periods so the interstitials come
+we have all these excess interstitials
+
+ align:start position:0%
+we have all these excess interstitials
+ 
+
+ align:start position:0%
+we have all these excess interstitials
+they end up getting together and forming
+
+ align:start position:0%
+they end up getting together and forming
+ 
+
+ align:start position:0%
+they end up getting together and forming
+little defects which then can stay
+
+ align:start position:0%
+little defects which then can stay
+ 
+
+ align:start position:0%
+little defects which then can stay
+around for 10 seconds 100 seconds maybe
+
+ align:start position:0%
+around for 10 seconds 100 seconds maybe
+ 
+
+ align:start position:0%
+around for 10 seconds 100 seconds maybe
+even minutes and and hours depending on
+
+ align:start position:0%
+even minutes and and hours depending on
+ 
+
+ align:start position:0%
+even minutes and and hours depending on
+the temperature and it's these little
+
+ align:start position:0%
+the temperature and it's these little
+ 
+
+ align:start position:0%
+the temperature and it's these little
+defects these 311's then that end up
+
+ align:start position:0%
+defects these 311's then that end up
+ 
+
+ align:start position:0%
+defects these 311's then that end up
+being responsible for the process of
+
+ align:start position:0%
+being responsible for the process of
+ 
+
+ align:start position:0%
+being responsible for the process of
+trans enhanced Fusion that we're going
+
+ align:start position:0%
+trans enhanced Fusion that we're going
+ 
+
+ align:start position:0%
+trans enhanced Fusion that we're going
+to model uh in the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lecture in fact uh on slide 20 just by
+
+ align:start position:0%
+lecture in fact uh on slide 20 just by
+ 
+
+ align:start position:0%
+lecture in fact uh on slide 20 just by
+way of introduction these are uh this
+
+ align:start position:0%
+way of introduction these are uh this
+ 
+
+ align:start position:0%
+way of introduction these are uh this
+these are pictures of 311 defects um uh
+
+ align:start position:0%
+these are pictures of 311 defects um uh
+ 
+
+ align:start position:0%
+these are pictures of 311 defects um uh
+the right hand side is an actual uh high
+
+ align:start position:0%
+the right hand side is an actual uh high
+ 
+
+ align:start position:0%
+the right hand side is an actual uh high
+resolution cross-section transmission
+
+ align:start position:0%
+resolution cross-section transmission
+ 
+
+ align:start position:0%
+resolution cross-section transmission
+electron micrograph and I can tell it's
+
+ align:start position:0%
+electron micrograph and I can tell it's
+ 
+
+ align:start position:0%
+electron micrograph and I can tell it's
+high resolution because you can see
+
+ align:start position:0%
+high resolution because you can see
+ 
+
+ align:start position:0%
+high resolution because you can see
+little these little dots and they they
+
+ align:start position:0%
+little these little dots and they they
+ 
+
+ align:start position:0%
+little these little dots and they they
+form in Planes well these little dots
+
+ align:start position:0%
+form in Planes well these little dots
+ 
+
+ align:start position:0%
+form in Planes well these little dots
+each Dot represents two silicon atoms so
+
+ align:start position:0%
+each Dot represents two silicon atoms so
+ 
+
+ align:start position:0%
+each Dot represents two silicon atoms so
+you're actually and they're all lined up
+
+ align:start position:0%
+you're actually and they're all lined up
+ 
+
+ align:start position:0%
+you're actually and they're all lined up
+in in sort of planes because you're
+
+ align:start position:0%
+in in sort of planes because you're
+ 
+
+ align:start position:0%
+in in sort of planes because you're
+looking at the Crystal planes uh of of
+
+ align:start position:0%
+looking at the Crystal planes uh of of
+ 
+
+ align:start position:0%
+looking at the Crystal planes uh of of
+um uh in the Silicon lattice and you see
+
+ align:start position:0%
+um uh in the Silicon lattice and you see
+ 
+
+ align:start position:0%
+um uh in the Silicon lattice and you see
+this little funny looking thing right
+
+ align:start position:0%
+this little funny looking thing right
+ 
+
+ align:start position:0%
+this little funny looking thing right
+here that's tilted at an angle goes from
+
+ align:start position:0%
+here that's tilted at an angle goes from
+ 
+
+ align:start position:0%
+here that's tilted at an angle goes from
+this point here this dark band of
+
+ align:start position:0%
+this point here this dark band of
+ 
+
+ align:start position:0%
+this point here this dark band of
+contrast to this point here that is a a
+
+ align:start position:0%
+contrast to this point here that is a a
+ 
+
+ align:start position:0%
+contrast to this point here that is a a
+ribbon-like region that is identified
+
+ align:start position:0%
+ribbon-like region that is identified
+ 
+
+ align:start position:0%
+ribbon-like region that is identified
+that is the 311
+
+ align:start position:0%
+that is the 311
+ 
+
+ align:start position:0%
+that is the 311
+defect and that's an actual
+
+ align:start position:0%
+defect and that's an actual
+ 
+
+ align:start position:0%
+defect and that's an actual
+cross-section te micrograph on the left
+
+ align:start position:0%
+cross-section te micrograph on the left
+ 
+
+ align:start position:0%
+cross-section te micrograph on the left
+is meant to represent uh a color cartoon
+
+ align:start position:0%
+is meant to represent uh a color cartoon
+ 
+
+ align:start position:0%
+is meant to represent uh a color cartoon
+of what this thing actually looks like
+
+ align:start position:0%
+of what this thing actually looks like
+ 
+
+ align:start position:0%
+of what this thing actually looks like
+um the axis here along with the effect
+
+ align:start position:0%
+um the axis here along with the effect
+ 
+
+ align:start position:0%
+um the axis here along with the effect
+it is represented by this Vector here
+
+ align:start position:0%
+it is represented by this Vector here
+ 
+
+ align:start position:0%
+it is represented by this Vector here
+that it turns out to be this Vector um
+
+ align:start position:0%
+that it turns out to be this Vector um
+ 
+
+ align:start position:0%
+that it turns out to be this Vector um
+turns out to be in the 311 Direction
+
+ align:start position:0%
+turns out to be in the 311 Direction
+ 
+
+ align:start position:0%
+turns out to be in the 311 Direction
+that's how these things got their name
+
+ align:start position:0%
+that's how these things got their name
+ 
+
+ align:start position:0%
+that's how these things got their name
+they were tilted in the 311 Direction um
+
+ align:start position:0%
+they were tilted in the 311 Direction um
+ 
+
+ align:start position:0%
+they were tilted in the 311 Direction um
+the long axis of the ribbon this is a
+
+ align:start position:0%
+the long axis of the ribbon this is a
+ 
+
+ align:start position:0%
+the long axis of the ribbon this is a
+ribbonlike defect the long axis points
+
+ align:start position:0%
+ribbonlike defect the long axis points
+ 
+
+ align:start position:0%
+ribbonlike defect the long axis points
+along one One Direction in the crystal
+
+ align:start position:0%
+along one One Direction in the crystal
+ 
+
+ align:start position:0%
+along one One Direction in the crystal
+that's so the long axis here you can't
+
+ align:start position:0%
+that's so the long axis here you can't
+ 
+
+ align:start position:0%
+that's so the long axis here you can't
+really see it would be into the board or
+
+ align:start position:0%
+really see it would be into the board or
+ 
+
+ align:start position:0%
+really see it would be into the board or
+or into the uh uh into the into the
+
+ align:start position:0%
+or into the uh uh into the into the
+ 
+
+ align:start position:0%
+or into the uh uh into the into the
+slide these little round things here
+
+ align:start position:0%
+slide these little round things here
+ 
+
+ align:start position:0%
+slide these little round things here
+these um circles represent interstitials
+
+ align:start position:0%
+these um circles represent interstitials
+ 
+
+ align:start position:0%
+these um circles represent interstitials
+and they're they're little diers they're
+
+ align:start position:0%
+and they're they're little diers they're
+ 
+
+ align:start position:0%
+and they're they're little diers they're
+coming Pairs and they line up along this
+
+ align:start position:0%
+coming Pairs and they line up along this
+ 
+
+ align:start position:0%
+coming Pairs and they line up along this
+direction could be 100 angstroms long uh
+
+ align:start position:0%
+direction could be 100 angstroms long uh
+ 
+
+ align:start position:0%
+direction could be 100 angstroms long uh
+and uh it's got some sort of width to it
+
+ align:start position:0%
+and uh it's got some sort of width to it
+ 
+
+ align:start position:0%
+and uh it's got some sort of width to it
+uh which you can see here and it has a
+
+ align:start position:0%
+uh which you can see here and it has a
+ 
+
+ align:start position:0%
+uh which you can see here and it has a
+certain capture radius within a certain
+
+ align:start position:0%
+certain capture radius within a certain
+ 
+
+ align:start position:0%
+certain capture radius within a certain
+region it'll capture these interstitials
+
+ align:start position:0%
+region it'll capture these interstitials
+ 
+
+ align:start position:0%
+region it'll capture these interstitials
+and form this little
+
+ align:start position:0%
+and form this little
+ 
+
+ align:start position:0%
+and form this little
+cluster um these 311 defects once
+
+ align:start position:0%
+cluster um these 311 defects once
+ 
+
+ align:start position:0%
+cluster um these 311 defects once
+they're they FL pretty quickly in a
+
+ align:start position:0%
+they're they FL pretty quickly in a
+ 
+
+ align:start position:0%
+they're they FL pretty quickly in a
+matter of a second or less but they anal
+
+ align:start position:0%
+matter of a second or less but they anal
+ 
+
+ align:start position:0%
+matter of a second or less but they anal
+out in time scale of minutes at moderate
+
+ align:start position:0%
+out in time scale of minutes at moderate
+ 
+
+ align:start position:0%
+out in time scale of minutes at moderate
+temperatures and as they kneel out as
+
+ align:start position:0%
+temperatures and as they kneel out as
+ 
+
+ align:start position:0%
+temperatures and as they kneel out as
+this this ribbon heels it spits out
+
+ align:start position:0%
+this this ribbon heels it spits out
+ 
+
+ align:start position:0%
+this this ribbon heels it spits out
+silicon interstitials and it's these um
+
+ align:start position:0%
+silicon interstitials and it's these um
+ 
+
+ align:start position:0%
+silicon interstitials and it's these um
+silicon interstitials that are coming
+
+ align:start position:0%
+silicon interstitials that are coming
+ 
+
+ align:start position:0%
+silicon interstitials that are coming
+out of this 311 ribbon uh that lead to
+
+ align:start position:0%
+out of this 311 ribbon uh that lead to
+ 
+
+ align:start position:0%
+out of this 311 ribbon uh that lead to
+the transit enhanced diffusion effect
+
+ align:start position:0%
+the transit enhanced diffusion effect
+ 
+
+ align:start position:0%
+the transit enhanced diffusion effect
+these excess silicon
+
+ align:start position:0%
+these excess silicon
+ 
+
+ align:start position:0%
+these excess silicon
+interstitials um it turns out that below
+
+ align:start position:0%
+interstitials um it turns out that below
+ 
+
+ align:start position:0%
+interstitials um it turns out that below
+a certain dose or below a certain damage
+
+ align:start position:0%
+a certain dose or below a certain damage
+ 
+
+ align:start position:0%
+a certain dose or below a certain damage
+uh value these 311 defects can dissolve
+
+ align:start position:0%
+uh value these 311 defects can dissolve
+ 
+
+ align:start position:0%
+uh value these 311 defects can dissolve
+completely so you can dissolve them you
+
+ align:start position:0%
+completely so you can dissolve them you
+ 
+
+ align:start position:0%
+completely so you can dissolve them you
+can completely get rid of them and at
+
+ align:start position:0%
+can completely get rid of them and at
+ 
+
+ align:start position:0%
+can completely get rid of them and at
+that point when they're completely gone
+
+ align:start position:0%
+that point when they're completely gone
+ 
+
+ align:start position:0%
+that point when they're completely gone
+you have no more teed after that amount
+
+ align:start position:0%
+you have no more teed after that amount
+ 
+
+ align:start position:0%
+you have no more teed after that amount
+of time you go back to normal diffusion
+
+ align:start position:0%
+of time you go back to normal diffusion
+ 
+
+ align:start position:0%
+of time you go back to normal diffusion
+uh above a certain damage level actually
+
+ align:start position:0%
+uh above a certain damage level actually
+ 
+
+ align:start position:0%
+uh above a certain damage level actually
+it's a little more complicated they turn
+
+ align:start position:0%
+it's a little more complicated they turn
+ 
+
+ align:start position:0%
+it's a little more complicated they turn
+into the they uh they actually get
+
+ align:start position:0%
+into the they uh they actually get
+ 
+
+ align:start position:0%
+into the they uh they actually get
+together they turn into stable
+
+ align:start position:0%
+together they turn into stable
+ 
+
+ align:start position:0%
+together they turn into stable
+dislocation Loops which are more
+
+ align:start position:0%
+dislocation Loops which are more
+ 
+
+ align:start position:0%
+dislocation Loops which are more
+difficult or sometimes impossible to
+
+ align:start position:0%
+difficult or sometimes impossible to
+ 
+
+ align:start position:0%
+difficult or sometimes impossible to
+remove that like like end of range
+
+ align:start position:0%
+remove that like like end of range
+ 
+
+ align:start position:0%
+remove that like like end of range
+damage but there's a certain region in
+
+ align:start position:0%
+damage but there's a certain region in
+ 
+
+ align:start position:0%
+damage but there's a certain region in
+which you can remove all the 31 ones
+
+ align:start position:0%
+which you can remove all the 31 ones
+ 
+
+ align:start position:0%
+which you can remove all the 31 ones
+certain amount of damage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so when we're going to talk about
+
+ align:start position:0%
+okay so when we're going to talk about
+ 
+
+ align:start position:0%
+okay so when we're going to talk about
+311's and their analing kinetics in
+
+ align:start position:0%
+311's and their analing kinetics in
+ 
+
+ align:start position:0%
+311's and their analing kinetics in
+great detail next lecture when we go
+
+ align:start position:0%
+great detail next lecture when we go
+ 
+
+ align:start position:0%
+great detail next lecture when we go
+through the whole kinetics of uh Transit
+
+ align:start position:0%
+through the whole kinetics of uh Transit
+ 
+
+ align:start position:0%
+through the whole kinetics of uh Transit
+enhanced diffusion the meantime I want
+
+ align:start position:0%
+enhanced diffusion the meantime I want
+ 
+
+ align:start position:0%
+enhanced diffusion the meantime I want
+to go on and continue to talk about
+
+ align:start position:0%
+to go on and continue to talk about
+ 
+
+ align:start position:0%
+to go on and continue to talk about
+other aspects of analing so we know we
+
+ align:start position:0%
+other aspects of analing so we know we
+ 
+
+ align:start position:0%
+other aspects of analing so we know we
+create all these interstitials they get
+
+ align:start position:0%
+create all these interstitials they get
+ 
+
+ align:start position:0%
+create all these interstitials they get
+together in
+
+ align:start position:0%
+together in
+ 
+
+ align:start position:0%
+together in
+311's um we know if we go to high enough
+
+ align:start position:0%
+311's um we know if we go to high enough
+ 
+
+ align:start position:0%
+311's um we know if we go to high enough
+dose remember I showed you a picture
+
+ align:start position:0%
+dose remember I showed you a picture
+ 
+
+ align:start position:0%
+dose remember I showed you a picture
+that we can amorphize the crystal well
+
+ align:start position:0%
+that we can amorphize the crystal well
+ 
+
+ align:start position:0%
+that we can amorphize the crystal well
+let's say I do create an amorphous layer
+
+ align:start position:0%
+let's say I do create an amorphous layer
+ 
+
+ align:start position:0%
+let's say I do create an amorphous layer
+at the surface how can I get rid of that
+
+ align:start position:0%
+at the surface how can I get rid of that
+ 
+
+ align:start position:0%
+at the surface how can I get rid of that
+amorphous layer and restore the crystal
+
+ align:start position:0%
+amorphous layer and restore the crystal
+ 
+
+ align:start position:0%
+amorphous layer and restore the crystal
+to perfect or to some kind of crystallin
+
+ align:start position:0%
+to perfect or to some kind of crystallin
+ 
+
+ align:start position:0%
+to perfect or to some kind of crystallin
+well this is exactly what happens I'm
+
+ align:start position:0%
+well this is exactly what happens I'm
+ 
+
+ align:start position:0%
+well this is exactly what happens I'm
+showing here um crosssection temm images
+
+ align:start position:0%
+showing here um crosssection temm images
+ 
+
+ align:start position:0%
+showing here um crosssection temm images
+this layer is originally amorphus from
+
+ align:start position:0%
+this layer is originally amorphus from
+ 
+
+ align:start position:0%
+this layer is originally amorphus from
+the surface of the wafer down to some
+
+ align:start position:0%
+the surface of the wafer down to some
+ 
+
+ align:start position:0%
+the surface of the wafer down to some
+depth and we're regrowing it so we're
+
+ align:start position:0%
+depth and we're regrowing it so we're
+ 
+
+ align:start position:0%
+depth and we're regrowing it so we're
+annealing the wafer at
+
+ align:start position:0%
+annealing the wafer at
+ 
+
+ align:start position:0%
+annealing the wafer at
+525 uh the initial implant was quite
+
+ align:start position:0%
+525 uh the initial implant was quite
+ 
+
+ align:start position:0%
+525 uh the initial implant was quite
+high it's 200 kilovolts 6 * 10 the 15th
+
+ align:start position:0%
+high it's 200 kilovolts 6 * 10 the 15th
+ 
+
+ align:start position:0%
+high it's 200 kilovolts 6 * 10 the 15th
+of antimony again it's it's antimony is
+
+ align:start position:0%
+of antimony again it's it's antimony is
+ 
+
+ align:start position:0%
+of antimony again it's it's antimony is
+a very heavy atom so it am morphies from
+
+ align:start position:0%
+a very heavy atom so it am morphies from
+ 
+
+ align:start position:0%
+a very heavy atom so it am morphies from
+the surface down um and we're looking
+
+ align:start position:0%
+the surface down um and we're looking
+ 
+
+ align:start position:0%
+the surface down um and we're looking
+here initially at zero minutes so I
+
+ align:start position:0%
+here initially at zero minutes so I
+ 
+
+ align:start position:0%
+here initially at zero minutes so I
+guess that kind of got cut off of the
+
+ align:start position:0%
+guess that kind of got cut off of the
+ 
+
+ align:start position:0%
+guess that kind of got cut off of the
+slide but this should be uh at here at
+
+ align:start position:0%
+slide but this should be uh at here at
+ 
+
+ align:start position:0%
+slide but this should be uh at here at
+zero minutes so just when you first
+
+ align:start position:0%
+zero minutes so just when you first
+ 
+
+ align:start position:0%
+zero minutes so just when you first
+start after 10 minutes of analing at 525
+
+ align:start position:0%
+start after 10 minutes of analing at 525
+ 
+
+ align:start position:0%
+start after 10 minutes of analing at 525
+look at this the interface between the
+
+ align:start position:0%
+look at this the interface between the
+ 
+
+ align:start position:0%
+look at this the interface between the
+Amorphis and the Crystal substrate has
+
+ align:start position:0%
+Amorphis and the Crystal substrate has
+ 
+
+ align:start position:0%
+Amorphis and the Crystal substrate has
+moved up so the amorphous layer is
+
+ align:start position:0%
+moved up so the amorphous layer is
+ 
+
+ align:start position:0%
+moved up so the amorphous layer is
+actually grown uh or regrown by a
+
+ align:start position:0%
+actually grown uh or regrown by a
+ 
+
+ align:start position:0%
+actually grown uh or regrown by a
+process called solid phase epex so
+
+ align:start position:0%
+process called solid phase epex so
+ 
+
+ align:start position:0%
+process called solid phase epex so
+there's no melting going on but in a
+
+ align:start position:0%
+there's no melting going on but in a
+ 
+
+ align:start position:0%
+there's no melting going on but in a
+layer by layer method the atoms in each
+
+ align:start position:0%
+layer by layer method the atoms in each
+ 
+
+ align:start position:0%
+layer by layer method the atoms in each
+layer
+
+ align:start position:0%
+layer
+ 
+
+ align:start position:0%
+layer
+are taking the template from the
+
+ align:start position:0%
+are taking the template from the
+ 
+
+ align:start position:0%
+are taking the template from the
+substrate and rearranging themselves
+
+ align:start position:0%
+substrate and rearranging themselves
+ 
+
+ align:start position:0%
+substrate and rearranging themselves
+back into single Crystal form and this
+
+ align:start position:0%
+back into single Crystal form and this
+ 
+
+ align:start position:0%
+back into single Crystal form and this
+amorphous layer is progressing up from
+
+ align:start position:0%
+amorphous layer is progressing up from
+ 
+
+ align:start position:0%
+amorphous layer is progressing up from
+the depth towards the surface you can
+
+ align:start position:0%
+the depth towards the surface you can
+ 
+
+ align:start position:0%
+the depth towards the surface you can
+see it as time goes on in kind of a
+
+ align:start position:0%
+see it as time goes on in kind of a
+ 
+
+ align:start position:0%
+see it as time goes on in kind of a
+linear fashion uh in an epitaxial growth
+
+ align:start position:0%
+linear fashion uh in an epitaxial growth
+ 
+
+ align:start position:0%
+linear fashion uh in an epitaxial growth
+so we call it solidphase Epi as opposed
+
+ align:start position:0%
+so we call it solidphase Epi as opposed
+ 
+
+ align:start position:0%
+so we call it solidphase Epi as opposed
+to Vapor phase Vapor phase would be if I
+
+ align:start position:0%
+to Vapor phase Vapor phase would be if I
+ 
+
+ align:start position:0%
+to Vapor phase Vapor phase would be if I
+had I have injecting silene or something
+
+ align:start position:0%
+had I have injecting silene or something
+ 
+
+ align:start position:0%
+had I have injecting silene or something
+and growing Epi here I just have a solid
+
+ align:start position:0%
+and growing Epi here I just have a solid
+ 
+
+ align:start position:0%
+and growing Epi here I just have a solid
+solution that's R growing at
+
+ align:start position:0%
+solution that's R growing at
+ 
+
+ align:start position:0%
+solution that's R growing at
+525 when you're done or and well this
+
+ align:start position:0%
+525 when you're done or and well this
+ 
+
+ align:start position:0%
+525 when you're done or and well this
+isn't quite done at 20 minutes it's
+
+ align:start position:0%
+isn't quite done at 20 minutes it's
+ 
+
+ align:start position:0%
+isn't quite done at 20 minutes it's
+almost done maybe half an hour you would
+
+ align:start position:0%
+almost done maybe half an hour you would
+ 
+
+ align:start position:0%
+almost done maybe half an hour you would
+see this the entire region amorphous
+
+ align:start position:0%
+see this the entire region amorphous
+ 
+
+ align:start position:0%
+see this the entire region amorphous
+region will have been regrown it'll be
+
+ align:start position:0%
+region will have been regrown it'll be
+ 
+
+ align:start position:0%
+region will have been regrown it'll be
+all be single Crystal and you'll be left
+
+ align:start position:0%
+all be single Crystal and you'll be left
+ 
+
+ align:start position:0%
+all be single Crystal and you'll be left
+with something though there's a band of
+
+ align:start position:0%
+with something though there's a band of
+ 
+
+ align:start position:0%
+with something though there's a band of
+residual
+
+ align:start position:0%
+residual
+ 
+
+ align:start position:0%
+residual
+damage that occurs called end of range
+
+ align:start position:0%
+damage that occurs called end of range
+ 
+
+ align:start position:0%
+damage that occurs called end of range
+damage or E and these are defects that
+
+ align:start position:0%
+damage or E and these are defects that
+ 
+
+ align:start position:0%
+damage or E and these are defects that
+are just below the amorphous crystallin
+
+ align:start position:0%
+are just below the amorphous crystallin
+ 
+
+ align:start position:0%
+are just below the amorphous crystallin
+interface so you get an idea of where
+
+ align:start position:0%
+interface so you get an idea of where
+ 
+
+ align:start position:0%
+interface so you get an idea of where
+they are they they're always just below
+
+ align:start position:0%
+they are they they're always just below
+ 
+
+ align:start position:0%
+they are they they're always just below
+that and those are pretty pretty hard to
+
+ align:start position:0%
+that and those are pretty pretty hard to
+ 
+
+ align:start position:0%
+that and those are pretty pretty hard to
+get out those generally don't ever go
+
+ align:start position:0%
+get out those generally don't ever go
+ 
+
+ align:start position:0%
+get out those generally don't ever go
+away you have a C amount of that for
+
+ align:start position:0%
+away you have a C amount of that for
+ 
+
+ align:start position:0%
+away you have a C amount of that for
+such a high dose that you have to live
+
+ align:start position:0%
+such a high dose that you have to live
+ 
+
+ align:start position:0%
+such a high dose that you have to live
+with you have to find a way to deal with
+
+ align:start position:0%
+with you have to find a way to deal with
+ 
+
+ align:start position:0%
+with you have to find a way to deal with
+it um this slide on page 22 actually
+
+ align:start position:0%
+it um this slide on page 22 actually
+ 
+
+ align:start position:0%
+it um this slide on page 22 actually
+shows you from some data from a book uh
+
+ align:start position:0%
+shows you from some data from a book uh
+ 
+
+ align:start position:0%
+shows you from some data from a book uh
+a book by Gibbons and Sigman called
+
+ align:start position:0%
+a book by Gibbons and Sigman called
+ 
+
+ align:start position:0%
+a book by Gibbons and Sigman called
+laser raling of semiconductors so it's
+
+ align:start position:0%
+laser raling of semiconductors so it's
+ 
+
+ align:start position:0%
+laser raling of semiconductors so it's
+about laser raling uh the book is but
+
+ align:start position:0%
+about laser raling uh the book is but
+ 
+
+ align:start position:0%
+about laser raling uh the book is but
+this particular chapter is about solid
+
+ align:start position:0%
+this particular chapter is about solid
+ 
+
+ align:start position:0%
+this particular chapter is about solid
+phase Epi or solid phase regrowth just
+
+ align:start position:0%
+phase Epi or solid phase regrowth just
+ 
+
+ align:start position:0%
+phase Epi or solid phase regrowth just
+in a furnace um and what they're
+
+ align:start position:0%
+in a furnace um and what they're
+ 
+
+ align:start position:0%
+in a furnace um and what they're
+plotting here is the regrowth rate so so
+
+ align:start position:0%
+plotting here is the regrowth rate so so
+ 
+
+ align:start position:0%
+plotting here is the regrowth rate so so
+this gives you the number of angstroms
+
+ align:start position:0%
+this gives you the number of angstroms
+ 
+
+ align:start position:0%
+this gives you the number of angstroms
+per minute as that amorphous layer
+
+ align:start position:0%
+per minute as that amorphous layer
+ 
+
+ align:start position:0%
+per minute as that amorphous layer
+traverses from down below up the number
+
+ align:start position:0%
+traverses from down below up the number
+ 
+
+ align:start position:0%
+traverses from down below up the number
+of angrum per minute that it goes as a
+
+ align:start position:0%
+of angrum per minute that it goes as a
+ 
+
+ align:start position:0%
+of angrum per minute that it goes as a
+function of inverse temperature uh for
+
+ align:start position:0%
+function of inverse temperature uh for
+ 
+
+ align:start position:0%
+function of inverse temperature uh for
+silicon and under different conditions
+
+ align:start position:0%
+silicon and under different conditions
+ 
+
+ align:start position:0%
+silicon and under different conditions
+so let's take a curve here let's take
+
+ align:start position:0%
+so let's take a curve here let's take
+ 
+
+ align:start position:0%
+so let's take a curve here let's take
+this one curve right here that is called
+
+ align:start position:0%
+this one curve right here that is called
+ 
+
+ align:start position:0%
+this one curve right here that is called
+10 silicon
+
+ align:start position:0%
+10 silicon
+ 
+
+ align:start position:0%
+10 silicon
+undoped as a function of temperature and
+
+ align:start position:0%
+undoped as a function of temperature and
+ 
+
+ align:start position:0%
+undoped as a function of temperature and
+you can see for undoped silicon say at
+
+ align:start position:0%
+you can see for undoped silicon say at
+ 
+
+ align:start position:0%
+you can see for undoped silicon say at
+525 the regrowth rate is about 20 or 30
+
+ align:start position:0%
+525 the regrowth rate is about 20 or 30
+ 
+
+ align:start position:0%
+525 the regrowth rate is about 20 or 30
+angstroms per minute
+
+ align:start position:0%
+angstroms per minute
+ 
+
+ align:start position:0%
+angstroms per minute
+so is is a constant rate these people
+
+ align:start position:0%
+so is is a constant rate these people
+ 
+
+ align:start position:0%
+so is is a constant rate these people
+have measured this there's there's a
+
+ align:start position:0%
+have measured this there's there's a
+ 
+
+ align:start position:0%
+have measured this there's there's a
+technique called Rutherford back
+
+ align:start position:0%
+technique called Rutherford back
+ 
+
+ align:start position:0%
+technique called Rutherford back
+scattering ion channeling you can
+
+ align:start position:0%
+scattering ion channeling you can
+ 
+
+ align:start position:0%
+scattering ion channeling you can
+actually measure this rate going up and
+
+ align:start position:0%
+actually measure this rate going up and
+ 
+
+ align:start position:0%
+actually measure this rate going up and
+you can you can see how fast it goes um
+
+ align:start position:0%
+you can you can see how fast it goes um
+ 
+
+ align:start position:0%
+you can you can see how fast it goes um
+gives you an idea of how that amorphous
+
+ align:start position:0%
+gives you an idea of how that amorphous
+ 
+
+ align:start position:0%
+gives you an idea of how that amorphous
+layer regrows and um that's at 525 so
+
+ align:start position:0%
+layer regrows and um that's at 525 so
+ 
+
+ align:start position:0%
+layer regrows and um that's at 525 so
+you can see a morphous layer regrowth
+
+ align:start position:0%
+you can see a morphous layer regrowth
+ 
+
+ align:start position:0%
+you can see a morphous layer regrowth
+can happen at reasonably low
+
+ align:start position:0%
+can happen at reasonably low
+ 
+
+ align:start position:0%
+can happen at reasonably low
+temperatures you don't have to go too
+
+ align:start position:0%
+temperatures you don't have to go too
+ 
+
+ align:start position:0%
+temperatures you don't have to go too
+hot interestingly though there are lots
+
+ align:start position:0%
+hot interestingly though there are lots
+ 
+
+ align:start position:0%
+hot interestingly though there are lots
+of different curves here if you go to
+
+ align:start position:0%
+of different curves here if you go to
+ 
+
+ align:start position:0%
+of different curves here if you go to
+the 11 silicon so if you buy a wafer
+
+ align:start position:0%
+the 11 silicon so if you buy a wafer
+ 
+
+ align:start position:0%
+the 11 silicon so if you buy a wafer
+that is 110 surface instead uh you got a
+
+ align:start position:0%
+that is 110 surface instead uh you got a
+ 
+
+ align:start position:0%
+that is 110 surface instead uh you got a
+different Atomic density on that 11
+
+ align:start position:0%
+different Atomic density on that 11
+ 
+
+ align:start position:0%
+different Atomic density on that 11
+plane and in fact it regrows slower the
+
+ align:start position:0%
+plane and in fact it regrows slower the
+ 
+
+ align:start position:0%
+plane and in fact it regrows slower the
+same activation energy EA of 2.3
+
+ align:start position:0%
+same activation energy EA of 2.3
+ 
+
+ align:start position:0%
+same activation energy EA of 2.3
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+volts uh interestingly that that number
+
+ align:start position:0%
+volts uh interestingly that that number
+ 
+
+ align:start position:0%
+volts uh interestingly that that number
+is kind of intriguing that's also what
+
+ align:start position:0%
+is kind of intriguing that's also what
+ 
+
+ align:start position:0%
+is kind of intriguing that's also what
+people believe 2.2 is roughly the bond
+
+ align:start position:0%
+people believe 2.2 is roughly the bond
+ 
+
+ align:start position:0%
+people believe 2.2 is roughly the bond
+breaking energy uh and so you know
+
+ align:start position:0%
+breaking energy uh and so you know
+ 
+
+ align:start position:0%
+breaking energy uh and so you know
+imagine if that interface between the
+
+ align:start position:0%
+imagine if that interface between the
+ 
+
+ align:start position:0%
+imagine if that interface between the
+amorphism of a single Crystal you
+
+ align:start position:0%
+amorphism of a single Crystal you
+ 
+
+ align:start position:0%
+amorphism of a single Crystal you
+probably have to break some bonds there
+
+ align:start position:0%
+probably have to break some bonds there
+ 
+
+ align:start position:0%
+probably have to break some bonds there
+initially uh at in order to realign the
+
+ align:start position:0%
+initially uh at in order to realign the
+ 
+
+ align:start position:0%
+initially uh at in order to realign the
+atoms um so SP is pretty fast it depends
+
+ align:start position:0%
+atoms um so SP is pretty fast it depends
+ 
+
+ align:start position:0%
+atoms um so SP is pretty fast it depends
+on orientation and it depends what's
+
+ align:start position:0%
+on orientation and it depends what's
+ 
+
+ align:start position:0%
+on orientation and it depends what's
+really interesting it depends uh very
+
+ align:start position:0%
+really interesting it depends uh very
+ 
+
+ align:start position:0%
+really interesting it depends uh very
+much so on
+
+ align:start position:0%
+much so on
+ 
+
+ align:start position:0%
+much so on
+doping uh so for example here's silicon
+
+ align:start position:0%
+doping uh so for example here's silicon
+ 
+
+ align:start position:0%
+doping uh so for example here's silicon
+that's doped with arsenic you can be um
+
+ align:start position:0%
+that's doped with arsenic you can be um
+ 
+
+ align:start position:0%
+that's doped with arsenic you can be um
+quite a bit faster three five times
+
+ align:start position:0%
+quite a bit faster three five times
+ 
+
+ align:start position:0%
+quite a bit faster three five times
+faster or even or phosphorus or Boron
+
+ align:start position:0%
+faster or even or phosphorus or Boron
+ 
+
+ align:start position:0%
+faster or even or phosphorus or Boron
+here Boron is the fastest it looks like
+
+ align:start position:0%
+here Boron is the fastest it looks like
+ 
+
+ align:start position:0%
+here Boron is the fastest it looks like
+um if you accidentally put oxygen or
+
+ align:start position:0%
+um if you accidentally put oxygen or
+ 
+
+ align:start position:0%
+um if you accidentally put oxygen or
+nitrogen into your sample look what
+
+ align:start position:0%
+nitrogen into your sample look what
+ 
+
+ align:start position:0%
+nitrogen into your sample look what
+happens to the regrowth rate you can go
+
+ align:start position:0%
+happens to the regrowth rate you can go
+ 
+
+ align:start position:0%
+happens to the regrowth rate you can go
+down by almost in order of magnitude so
+
+ align:start position:0%
+down by almost in order of magnitude so
+ 
+
+ align:start position:0%
+down by almost in order of magnitude so
+impurities have a big effect um and uh
+
+ align:start position:0%
+impurities have a big effect um and uh
+ 
+
+ align:start position:0%
+impurities have a big effect um and uh
+which is which argant would even really
+
+ align:start position:0%
+which is which argant would even really
+ 
+
+ align:start position:0%
+which is which argant would even really
+do it really frustrates the regrowth and
+
+ align:start position:0%
+do it really frustrates the regrowth and
+ 
+
+ align:start position:0%
+do it really frustrates the regrowth and
+and so it's important to know what's in
+
+ align:start position:0%
+and so it's important to know what's in
+ 
+
+ align:start position:0%
+and so it's important to know what's in
+your Crystal what your eyon and planning
+
+ align:start position:0%
+your Crystal what your eyon and planning
+ 
+
+ align:start position:0%
+your Crystal what your eyon and planning
+will have a big effect on the regrowth
+
+ align:start position:0%
+will have a big effect on the regrowth
+ 
+
+ align:start position:0%
+will have a big effect on the regrowth
+rate um interestingly when you do this
+
+ align:start position:0%
+rate um interestingly when you do this
+ 
+
+ align:start position:0%
+rate um interestingly when you do this
+most of the dopen atoms like arsenic
+
+ align:start position:0%
+most of the dopen atoms like arsenic
+ 
+
+ align:start position:0%
+most of the dopen atoms like arsenic
+phosphorus Boron are incorporated as
+
+ align:start position:0%
+phosphorus Boron are incorporated as
+ 
+
+ align:start position:0%
+phosphorus Boron are incorporated as
+that amorphous layer moves up they're
+
+ align:start position:0%
+that amorphous layer moves up they're
+ 
+
+ align:start position:0%
+that amorphous layer moves up they're
+actually mostly Incorporated on
+
+ align:start position:0%
+actually mostly Incorporated on
+ 
+
+ align:start position:0%
+actually mostly Incorporated on
+substitutional sites even at low
+
+ align:start position:0%
+substitutional sites even at low
+ 
+
+ align:start position:0%
+substitutional sites even at low
+temperatures so um it it turns out if
+
+ align:start position:0%
+temperatures so um it it turns out if
+ 
+
+ align:start position:0%
+temperatures so um it it turns out if
+you can create an amorphous layer this
+
+ align:start position:0%
+you can create an amorphous layer this
+ 
+
+ align:start position:0%
+you can create an amorphous layer this
+is one of the best ways of activating uh
+
+ align:start position:0%
+is one of the best ways of activating uh
+ 
+
+ align:start position:0%
+is one of the best ways of activating uh
+a dopet um is to create an amorphous
+
+ align:start position:0%
+a dopet um is to create an amorphous
+ 
+
+ align:start position:0%
+a dopet um is to create an amorphous
+layer in Silicon now this is the way
+
+ align:start position:0%
+layer in Silicon now this is the way
+ 
+
+ align:start position:0%
+layer in Silicon now this is the way
+silicon inals other semiconductors
+
+ align:start position:0%
+silicon inals other semiconductors
+ 
+
+ align:start position:0%
+silicon inals other semiconductors
+Gallum arsenide for example is just the
+
+ align:start position:0%
+Gallum arsenide for example is just the
+ 
+
+ align:start position:0%
+Gallum arsenide for example is just the
+opposite if you amorphize it God help
+
+ align:start position:0%
+opposite if you amorphize it God help
+ 
+
+ align:start position:0%
+opposite if you amorphize it God help
+you trying to trying to get the dopin to
+
+ align:start position:0%
+you trying to trying to get the dopin to
+ 
+
+ align:start position:0%
+you trying to trying to get the dopin to
+uh get reg um to get to activate it it's
+
+ align:start position:0%
+uh get reg um to get to activate it it's
+ 
+
+ align:start position:0%
+uh get reg um to get to activate it it's
+not so easy but silicon has this
+
+ align:start position:0%
+not so easy but silicon has this
+ 
+
+ align:start position:0%
+not so easy but silicon has this
+beautiful property that as that layer
+
+ align:start position:0%
+beautiful property that as that layer
+ 
+
+ align:start position:0%
+beautiful property that as that layer
+moves up a lot of the dopen atoms get
+
+ align:start position:0%
+moves up a lot of the dopen atoms get
+ 
+
+ align:start position:0%
+moves up a lot of the dopen atoms get
+forced onto substitutional sites and
+
+ align:start position:0%
+forced onto substitutional sites and
+ 
+
+ align:start position:0%
+forced onto substitutional sites and
+then the donors and the acceptors are
+
+ align:start position:0%
+then the donors and the acceptors are
+ 
+
+ align:start position:0%
+then the donors and the acceptors are
+already activated at low temperature to
+
+ align:start position:0%
+already activated at low temperature to
+ 
+
+ align:start position:0%
+already activated at low temperature to
+to a great degree so that's a nice a
+
+ align:start position:0%
+to a great degree so that's a nice a
+ 
+
+ align:start position:0%
+to a great degree so that's a nice a
+nice property
+
+ align:start position:0%
+nice property
+ 
+
+ align:start position:0%
+nice property
+assuming you fully amorphize the
+
+ align:start position:0%
+assuming you fully amorphize the
+ 
+
+ align:start position:0%
+assuming you fully amorphize the
+crystal okay let's go to slide 23 I
+
+ align:start position:0%
+crystal okay let's go to slide 23 I
+ 
+
+ align:start position:0%
+crystal okay let's go to slide 23 I
+mentioned the life is not perfect even
+
+ align:start position:0%
+mentioned the life is not perfect even
+ 
+
+ align:start position:0%
+mentioned the life is not perfect even
+if you amorphize um you always end up
+
+ align:start position:0%
+if you amorphize um you always end up
+ 
+
+ align:start position:0%
+if you amorphize um you always end up
+with this end of range damage um and
+
+ align:start position:0%
+with this end of range damage um and
+ 
+
+ align:start position:0%
+with this end of range damage um and
+here's a here's a a plot on the left of
+
+ align:start position:0%
+here's a here's a a plot on the left of
+ 
+
+ align:start position:0%
+here's a here's a a plot on the left of
+uh this let's say this is the surface of
+
+ align:start position:0%
+uh this let's say this is the surface of
+ 
+
+ align:start position:0%
+uh this let's say this is the surface of
+a silicon wafer here going down in depth
+
+ align:start position:0%
+a silicon wafer here going down in depth
+ 
+
+ align:start position:0%
+a silicon wafer here going down in depth
+and here's my concentration and let's
+
+ align:start position:0%
+and here's my concentration and let's
+ 
+
+ align:start position:0%
+and here's my concentration and let's
+say I've implanted something maybe it's
+
+ align:start position:0%
+say I've implanted something maybe it's
+ 
+
+ align:start position:0%
+say I've implanted something maybe it's
+arsenic I don't know what and it has
+
+ align:start position:0%
+arsenic I don't know what and it has
+ 
+
+ align:start position:0%
+arsenic I don't know what and it has
+this ion implanted profile it looks like
+
+ align:start position:0%
+this ion implanted profile it looks like
+ 
+
+ align:start position:0%
+this ion implanted profile it looks like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so it it's and there is um there's uh
+
+ align:start position:0%
+so it it's and there is um there's uh
+ 
+
+ align:start position:0%
+so it it's and there is um there's uh
+the maximum damage for this particular
+
+ align:start position:0%
+the maximum damage for this particular
+ 
+
+ align:start position:0%
+the maximum damage for this particular
+profile is just below um the
+
+ align:start position:0%
+profile is just below um the
+ 
+
+ align:start position:0%
+profile is just below um the
+amorphization threshold so this region
+
+ align:start position:0%
+amorphization threshold so this region
+ 
+
+ align:start position:0%
+amorphization threshold so this region
+from here to here from the surface down
+
+ align:start position:0%
+from here to here from the surface down
+ 
+
+ align:start position:0%
+from here to here from the surface down
+to the what what's this dash line is
+
+ align:start position:0%
+to the what what's this dash line is
+ 
+
+ align:start position:0%
+to the what what's this dash line is
+called the amorphous Crystal interface
+
+ align:start position:0%
+called the amorphous Crystal interface
+ 
+
+ align:start position:0%
+called the amorphous Crystal interface
+that's all amorphized so that's going to
+
+ align:start position:0%
+that's all amorphized so that's going to
+ 
+
+ align:start position:0%
+that's all amorphized so that's going to
+regrow layer by layer and give you very
+
+ align:start position:0%
+regrow layer by layer and give you very
+ 
+
+ align:start position:0%
+regrow layer by layer and give you very
+good Crystal quality if I just go back a
+
+ align:start position:0%
+good Crystal quality if I just go back a
+ 
+
+ align:start position:0%
+good Crystal quality if I just go back a
+couple slides here again um the uh
+
+ align:start position:0%
+couple slides here again um the uh
+ 
+
+ align:start position:0%
+couple slides here again um the uh
+amorph it was aor I to this depth if you
+
+ align:start position:0%
+amorph it was aor I to this depth if you
+ 
+
+ align:start position:0%
+amorph it was aor I to this depth if you
+look at this depth when you're done
+
+ align:start position:0%
+look at this depth when you're done
+ 
+
+ align:start position:0%
+look at this depth when you're done
+there are no there is no residual damage
+
+ align:start position:0%
+there are no there is no residual damage
+ 
+
+ align:start position:0%
+there are no there is no residual damage
+it's below the initial amorphous Crystal
+
+ align:start position:0%
+it's below the initial amorphous Crystal
+ 
+
+ align:start position:0%
+it's below the initial amorphous Crystal
+interface by some distance that you end
+
+ align:start position:0%
+interface by some distance that you end
+ 
+
+ align:start position:0%
+interface by some distance that you end
+up with this end of range where and it
+
+ align:start position:0%
+up with this end of range where and it
+ 
+
+ align:start position:0%
+up with this end of range where and it
+kind of makes sense because uh at this
+
+ align:start position:0%
+kind of makes sense because uh at this
+ 
+
+ align:start position:0%
+kind of makes sense because uh at this
+point you have deposited adver at this
+
+ align:start position:0%
+point you have deposited adver at this
+ 
+
+ align:start position:0%
+point you have deposited adver at this
+depth enough energy to amorphize the
+
+ align:start position:0%
+depth enough energy to amorphize the
+ 
+
+ align:start position:0%
+depth enough energy to amorphize the
+crystal below that you've deposited a
+
+ align:start position:0%
+crystal below that you've deposited a
+ 
+
+ align:start position:0%
+crystal below that you've deposited a
+huge amount of energy but not enough to
+
+ align:start position:0%
+huge amount of energy but not enough to
+ 
+
+ align:start position:0%
+huge amount of energy but not enough to
+amorphize so you've really bashed it up
+
+ align:start position:0%
+amorphize so you've really bashed it up
+ 
+
+ align:start position:0%
+amorphize so you've really bashed it up
+but it's not amorphous so it can't
+
+ align:start position:0%
+but it's not amorphous so it can't
+ 
+
+ align:start position:0%
+but it's not amorphous so it can't
+regrow by solid phase eping instead it
+
+ align:start position:0%
+regrow by solid phase eping instead it
+ 
+
+ align:start position:0%
+regrow by solid phase eping instead it
+creates dislocation loops and that's
+
+ align:start position:0%
+creates dislocation loops and that's
+ 
+
+ align:start position:0%
+creates dislocation loops and that's
+what we call the end of range so if I go
+
+ align:start position:0%
+what we call the end of range so if I go
+ 
+
+ align:start position:0%
+what we call the end of range so if I go
+back to the slide number
+
+ align:start position:0%
+back to the slide number
+ 
+
+ align:start position:0%
+back to the slide number
+23 just below the amorphous region of
+
+ align:start position:0%
+23 just below the amorphous region of
+ 
+
+ align:start position:0%
+23 just below the amorphous region of
+this end of range damage and here is my
+
+ align:start position:0%
+this end of range damage and here is my
+ 
+
+ align:start position:0%
+this end of range damage and here is my
+uh I implanted arsenic okay so now let's
+
+ align:start position:0%
+uh I implanted arsenic okay so now let's
+ 
+
+ align:start position:0%
+uh I implanted arsenic okay so now let's
+see I'm using this to make an NP
+
+ align:start position:0%
+see I'm using this to make an NP
+ 
+
+ align:start position:0%
+see I'm using this to make an NP
+Junction um so uh what I need to do if
+
+ align:start position:0%
+Junction um so uh what I need to do if
+ 
+
+ align:start position:0%
+Junction um so uh what I need to do if
+I'm going to make an NP Junction what I
+
+ align:start position:0%
+I'm going to make an NP Junction what I
+ 
+
+ align:start position:0%
+I'm going to make an NP Junction what I
+typically want to do is just to diffuse
+
+ align:start position:0%
+typically want to do is just to diffuse
+ 
+
+ align:start position:0%
+typically want to do is just to diffuse
+the end type dopen a little bit deeper
+
+ align:start position:0%
+the end type dopen a little bit deeper
+ 
+
+ align:start position:0%
+the end type dopen a little bit deeper
+than the end of range damage so we we
+
+ align:start position:0%
+than the end of range damage so we we
+ 
+
+ align:start position:0%
+than the end of range damage so we we
+tend to try to try to get a little a
+
+ align:start position:0%
+tend to try to try to get a little a
+ 
+
+ align:start position:0%
+tend to try to try to get a little a
+little bit of diffusion after we've done
+
+ align:start position:0%
+little bit of diffusion after we've done
+ 
+
+ align:start position:0%
+little bit of diffusion after we've done
+an ion implant sometimes that can be
+
+ align:start position:0%
+an ion implant sometimes that can be
+ 
+
+ align:start position:0%
+an ion implant sometimes that can be
+helpful because why would that matter
+
+ align:start position:0%
+helpful because why would that matter
+ 
+
+ align:start position:0%
+helpful because why would that matter
+well here's my end of i' I've done an
+
+ align:start position:0%
+well here's my end of i' I've done an
+ 
+
+ align:start position:0%
+well here's my end of i' I've done an
+overlay this is a cross-section temm
+
+ align:start position:0%
+overlay this is a cross-section temm
+ 
+
+ align:start position:0%
+overlay this is a cross-section temm
+microgr and here's my end of range
+
+ align:start position:0%
+microgr and here's my end of range
+ 
+
+ align:start position:0%
+microgr and here's my end of range
+damage this little black dislocation bar
+
+ align:start position:0%
+damage this little black dislocation bar
+ 
+
+ align:start position:0%
+damage this little black dislocation bar
+and imagine I I I diffuse this arsenic
+
+ align:start position:0%
+and imagine I I I diffuse this arsenic
+ 
+
+ align:start position:0%
+and imagine I I I diffuse this arsenic
+just a little deeper so now I have an
+
+ align:start position:0%
+just a little deeper so now I have an
+ 
+
+ align:start position:0%
+just a little deeper so now I have an
+npl region that goes just below the end
+
+ align:start position:0%
+npl region that goes just below the end
+ 
+
+ align:start position:0%
+npl region that goes just below the end
+of range damage and then below that I
+
+ align:start position:0%
+of range damage and then below that I
+ 
+
+ align:start position:0%
+of range damage and then below that I
+have P well this is n plus this is p the
+
+ align:start position:0%
+have P well this is n plus this is p the
+ 
+
+ align:start position:0%
+have P well this is n plus this is p the
+depletion region again always tends to
+
+ align:start position:0%
+depletion region again always tends to
+ 
+
+ align:start position:0%
+depletion region again always tends to
+extend if you remember your NP or p and
+
+ align:start position:0%
+extend if you remember your NP or p and
+ 
+
+ align:start position:0%
+extend if you remember your NP or p and
+Junction physics the depl region is
+
+ align:start position:0%
+Junction physics the depl region is
+ 
+
+ align:start position:0%
+Junction physics the depl region is
+going to be in the lightly dope side
+
+ align:start position:0%
+going to be in the lightly dope side
+ 
+
+ align:start position:0%
+going to be in the lightly dope side
+where the yellow is so the yellow is
+
+ align:start position:0%
+where the yellow is so the yellow is
+ 
+
+ align:start position:0%
+where the yellow is so the yellow is
+depleted to free carriers and you know
+
+ align:start position:0%
+depleted to free carriers and you know
+ 
+
+ align:start position:0%
+depleted to free carriers and you know
+in the depletion region that's where you
+
+ align:start position:0%
+in the depletion region that's where you
+ 
+
+ align:start position:0%
+in the depletion region that's where you
+get the most amount of recombination of
+
+ align:start position:0%
+get the most amount of recombination of
+ 
+
+ align:start position:0%
+get the most amount of recombination of
+electrons and holes to create leakage in
+
+ align:start position:0%
+electrons and holes to create leakage in
+ 
+
+ align:start position:0%
+electrons and holes to create leakage in
+a p in Junction so depletion region is
+
+ align:start position:0%
+a p in Junction so depletion region is
+ 
+
+ align:start position:0%
+a p in Junction so depletion region is
+the last place you want damage or
+
+ align:start position:0%
+the last place you want damage or
+ 
+
+ align:start position:0%
+the last place you want damage or
+defects because in a dep region electron
+
+ align:start position:0%
+defects because in a dep region electron
+ 
+
+ align:start position:0%
+defects because in a dep region electron
+hole recombination is very efficient so
+
+ align:start position:0%
+hole recombination is very efficient so
+ 
+
+ align:start position:0%
+hole recombination is very efficient so
+what we do what people do this is kind
+
+ align:start position:0%
+what we do what people do this is kind
+ 
+
+ align:start position:0%
+what we do what people do this is kind
+of cheating but they cover up the end of
+
+ align:start position:0%
+of cheating but they cover up the end of
+ 
+
+ align:start position:0%
+of cheating but they cover up the end of
+range damage with a heavily doped region
+
+ align:start position:0%
+range damage with a heavily doped region
+ 
+
+ align:start position:0%
+range damage with a heavily doped region
+so if you see people making Source drain
+
+ align:start position:0%
+so if you see people making Source drain
+ 
+
+ align:start position:0%
+so if you see people making Source drain
+Junctions they often diffuse it just a
+
+ align:start position:0%
+Junctions they often diffuse it just a
+ 
+
+ align:start position:0%
+Junctions they often diffuse it just a
+little ways beyond the E and then they
+
+ align:start position:0%
+little ways beyond the E and then they
+ 
+
+ align:start position:0%
+little ways beyond the E and then they
+get diodes that are pretty good
+
+ align:start position:0%
+get diodes that are pretty good
+ 
+
+ align:start position:0%
+get diodes that are pretty good
+reasonably good if they don't diffuse it
+
+ align:start position:0%
+reasonably good if they don't diffuse it
+ 
+
+ align:start position:0%
+reasonably good if they don't diffuse it
+at all they say I'm going to have a
+
+ align:start position:0%
+at all they say I'm going to have a
+ 
+
+ align:start position:0%
+at all they say I'm going to have a
+perfect anal no diffusion um in fact
+
+ align:start position:0%
+perfect anal no diffusion um in fact
+ 
+
+ align:start position:0%
+perfect anal no diffusion um in fact
+then the the N plus Junction might have
+
+ align:start position:0%
+then the the N plus Junction might have
+ 
+
+ align:start position:0%
+then the the N plus Junction might have
+been back here and then the E might have
+
+ align:start position:0%
+been back here and then the E might have
+ 
+
+ align:start position:0%
+been back here and then the E might have
+been in the yellow region in the
+
+ align:start position:0%
+been in the yellow region in the
+ 
+
+ align:start position:0%
+been in the yellow region in the
+depletion region the end of range damage
+
+ align:start position:0%
+depletion region the end of range damage
+ 
+
+ align:start position:0%
+depletion region the end of range damage
+and you could get a lot leak or
+
+ align:start position:0%
+and you could get a lot leak or
+ 
+
+ align:start position:0%
+and you could get a lot leak or
+diode so this is there's a lot of
+
+ align:start position:0%
+diode so this is there's a lot of
+ 
+
+ align:start position:0%
+diode so this is there's a lot of
+optimization when people activate sore
+
+ align:start position:0%
+optimization when people activate sore
+ 
+
+ align:start position:0%
+optimization when people activate sore
+strains or something uh where they care
+
+ align:start position:0%
+strains or something uh where they care
+ 
+
+ align:start position:0%
+strains or something uh where they care
+about leakage they um there's a lot of
+
+ align:start position:0%
+about leakage they um there's a lot of
+ 
+
+ align:start position:0%
+about leakage they um there's a lot of
+optimization in just exactly how much
+
+ align:start position:0%
+optimization in just exactly how much
+ 
+
+ align:start position:0%
+optimization in just exactly how much
+damage or dop and to Fusion do I allow
+
+ align:start position:0%
+damage or dop and to Fusion do I allow
+ 
+
+ align:start position:0%
+damage or dop and to Fusion do I allow
+and how much time do I allow to to um to
+
+ align:start position:0%
+and how much time do I allow to to um to
+ 
+
+ align:start position:0%
+and how much time do I allow to to um to
+try to to um get rid of these
+
+ align:start position:0%
+try to to um get rid of these
+ 
+
+ align:start position:0%
+try to to um get rid of these
+Loops um and and it's so it's kind of an
+
+ align:start position:0%
+Loops um and and it's so it's kind of an
+ 
+
+ align:start position:0%
+Loops um and and it's so it's kind of an
+interesting damage and kneeling is an
+
+ align:start position:0%
+interesting damage and kneeling is an
+ 
+
+ align:start position:0%
+interesting damage and kneeling is an
+interesting combination between
+
+ align:start position:0%
+interesting combination between
+ 
+
+ align:start position:0%
+interesting combination between
+knowledge of uh P injunction physics and
+
+ align:start position:0%
+knowledge of uh P injunction physics and
+ 
+
+ align:start position:0%
+knowledge of uh P injunction physics and
+and electronic Rec combination
+
+ align:start position:0%
+and electronic Rec combination
+ 
+
+ align:start position:0%
+and electronic Rec combination
+mechanisms and knowledge of the crystal
+
+ align:start position:0%
+mechanisms and knowledge of the crystal
+ 
+
+ align:start position:0%
+mechanisms and knowledge of the crystal
+structure and what kind of damage you've
+
+ align:start position:0%
+structure and what kind of damage you've
+ 
+
+ align:start position:0%
+structure and what kind of damage you've
+created and you need to optimize that
+
+ align:start position:0%
+created and you need to optimize that
+ 
+
+ align:start position:0%
+created and you need to optimize that
+because you'll never get rid of all
+
+ align:start position:0%
+because you'll never get rid of all
+ 
+
+ align:start position:0%
+because you'll never get rid of all
+damage to a certain extent for every
+
+ align:start position:0%
+damage to a certain extent for every
+ 
+
+ align:start position:0%
+damage to a certain extent for every
+single implant some implants are easier
+
+ align:start position:0%
+single implant some implants are easier
+ 
+
+ align:start position:0%
+single implant some implants are easier
+to kneel than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+others okay so that was in terms of I I
+
+ align:start position:0%
+others okay so that was in terms of I I
+ 
+
+ align:start position:0%
+others okay so that was in terms of I I
+I spoke there quite a while about trying
+
+ align:start position:0%
+I spoke there quite a while about trying
+ 
+
+ align:start position:0%
+I spoke there quite a while about trying
+to get rid of damage because I wanted to
+
+ align:start position:0%
+to get rid of damage because I wanted to
+ 
+
+ align:start position:0%
+to get rid of damage because I wanted to
+get good P injunctions I want to get low
+
+ align:start position:0%
+get good P injunctions I want to get low
+ 
+
+ align:start position:0%
+get good P injunctions I want to get low
+leakage okay that's only one requirement
+
+ align:start position:0%
+leakage okay that's only one requirement
+ 
+
+ align:start position:0%
+leakage okay that's only one requirement
+is it is low leakage uh in the crystal I
+
+ align:start position:0%
+is it is low leakage uh in the crystal I
+ 
+
+ align:start position:0%
+is it is low leakage uh in the crystal I
+also want to activate the dopin you know
+
+ align:start position:0%
+also want to activate the dopin you know
+ 
+
+ align:start position:0%
+also want to activate the dopin you know
+you want to ion implant 10 15th arsenic
+
+ align:start position:0%
+you want to ion implant 10 15th arsenic
+ 
+
+ align:start position:0%
+you want to ion implant 10 15th arsenic
+atoms per square cenm you'd like to get
+
+ align:start position:0%
+atoms per square cenm you'd like to get
+ 
+
+ align:start position:0%
+atoms per square cenm you'd like to get
+10 the 15th electrons per square cenm
+
+ align:start position:0%
+10 the 15th electrons per square cenm
+ 
+
+ align:start position:0%
+10 the 15th electrons per square cenm
+you'd like to have all of that activated
+
+ align:start position:0%
+you'd like to have all of that activated
+ 
+
+ align:start position:0%
+you'd like to have all of that activated
+or Boron that's the whole reason you're
+
+ align:start position:0%
+or Boron that's the whole reason you're
+ 
+
+ align:start position:0%
+or Boron that's the whole reason you're
+putting it in you don't care about Bor
+
+ align:start position:0%
+putting it in you don't care about Bor
+ 
+
+ align:start position:0%
+putting it in you don't care about Bor
+in a lattice it's the holes that it
+
+ align:start position:0%
+in a lattice it's the holes that it
+ 
+
+ align:start position:0%
+in a lattice it's the holes that it
+produces or the electrons that that Arc
+
+ align:start position:0%
+produces or the electrons that that Arc
+ 
+
+ align:start position:0%
+produces or the electrons that that Arc
+produce well it turns out uh if you
+
+ align:start position:0%
+produce well it turns out uh if you
+ 
+
+ align:start position:0%
+produce well it turns out uh if you
+amorphize the substrate again this only
+
+ align:start position:0%
+amorphize the substrate again this only
+ 
+
+ align:start position:0%
+amorphize the substrate again this only
+applies to Silicon dely moride is just
+
+ align:start position:0%
+applies to Silicon dely moride is just
+ 
+
+ align:start position:0%
+applies to Silicon dely moride is just
+the opposite but if you morphies the
+
+ align:start position:0%
+the opposite but if you morphies the
+ 
+
+ align:start position:0%
+the opposite but if you morphies the
+Silicon that we we mentioned that solid
+
+ align:start position:0%
+Silicon that we we mentioned that solid
+ 
+
+ align:start position:0%
+Silicon that we we mentioned that solid
+phas Epi is an ideal way of repairing
+
+ align:start position:0%
+phas Epi is an ideal way of repairing
+ 
+
+ align:start position:0%
+phas Epi is an ideal way of repairing
+the damage and also getting the dopin
+
+ align:start position:0%
+the damage and also getting the dopin
+ 
+
+ align:start position:0%
+the damage and also getting the dopin
+onto substitutional
+
+ align:start position:0%
+onto substitutional
+ 
+
+ align:start position:0%
+onto substitutional
+sites if you don't amorphize so you do a
+
+ align:start position:0%
+sites if you don't amorphize so you do a
+ 
+
+ align:start position:0%
+sites if you don't amorphize so you do a
+lower dose that does a lot of damage but
+
+ align:start position:0%
+lower dose that does a lot of damage but
+ 
+
+ align:start position:0%
+lower dose that does a lot of damage but
+doesn't create an an amorphous layer so
+
+ align:start position:0%
+doesn't create an an amorphous layer so
+ 
+
+ align:start position:0%
+doesn't create an an amorphous layer so
+you can't have SP it turns out that
+
+ align:start position:0%
+you can't have SP it turns out that
+ 
+
+ align:start position:0%
+you can't have SP it turns out that
+activation is a lot more complex because
+
+ align:start position:0%
+activation is a lot more complex because
+ 
+
+ align:start position:0%
+activation is a lot more complex because
+you create defects that are somewhat
+
+ align:start position:0%
+you create defects that are somewhat
+ 
+
+ align:start position:0%
+you create defects that are somewhat
+stable over time and temperature so
+
+ align:start position:0%
+stable over time and temperature so
+ 
+
+ align:start position:0%
+stable over time and temperature so
+here's just an example of a plot of the
+
+ align:start position:0%
+here's just an example of a plot of the
+ 
+
+ align:start position:0%
+here's just an example of a plot of the
+analing characteristics of Arsenic and
+
+ align:start position:0%
+analing characteristics of Arsenic and
+ 
+
+ align:start position:0%
+analing characteristics of Arsenic and
+silicon I took out of your
+
+ align:start position:0%
+silicon I took out of your
+ 
+
+ align:start position:0%
+silicon I took out of your
+textbook and the y- axis here is the
+
+ align:start position:0%
+textbook and the y- axis here is the
+ 
+
+ align:start position:0%
+textbook and the y- axis here is the
+fraction active so if I if I want to be
+
+ align:start position:0%
+fraction active so if I if I want to be
+ 
+
+ align:start position:0%
+fraction active so if I if I want to be
+up to if I'm at one that means every
+
+ align:start position:0%
+up to if I'm at one that means every
+ 
+
+ align:start position:0%
+up to if I'm at one that means every
+single aric atom that I planted
+
+ align:start position:0%
+single aric atom that I planted
+ 
+
+ align:start position:0%
+single aric atom that I planted
+contributes electron and they're all
+
+ align:start position:0%
+contributes electron and they're all
+ 
+
+ align:start position:0%
+contributes electron and they're all
+electrically active and this is as a
+
+ align:start position:0%
+electrically active and this is as a
+ 
+
+ align:start position:0%
+electrically active and this is as a
+function of of of temp a kneeling
+
+ align:start position:0%
+function of of of temp a kneeling
+ 
+
+ align:start position:0%
+function of of of temp a kneeling
+temperature uh and there are different
+
+ align:start position:0%
+temperature uh and there are different
+ 
+
+ align:start position:0%
+temperature uh and there are different
+doses shown here so the red curve
+
+ align:start position:0%
+doses shown here so the red curve
+ 
+
+ align:start position:0%
+doses shown here so the red curve
+assumes I have amorphized the silicon
+
+ align:start position:0%
+assumes I have amorphized the silicon
+ 
+
+ align:start position:0%
+assumes I have amorphized the silicon
+and look at this very interesting at 550
+
+ align:start position:0%
+and look at this very interesting at 550
+ 
+
+ align:start position:0%
+and look at this very interesting at 550
+525 I can activate for a 1 E15 implant I
+
+ align:start position:0%
+525 I can activate for a 1 E15 implant I
+ 
+
+ align:start position:0%
+525 I can activate for a 1 E15 implant I
+can activate almost 80% that's pretty
+
+ align:start position:0%
+can activate almost 80% that's pretty
+ 
+
+ align:start position:0%
+can activate almost 80% that's pretty
+good and if I increase the temperature
+
+ align:start position:0%
+good and if I increase the temperature
+ 
+
+ align:start position:0%
+good and if I increase the temperature
+up to 800 it doesn't actually activate
+
+ align:start position:0%
+up to 800 it doesn't actually activate
+ 
+
+ align:start position:0%
+up to 800 it doesn't actually activate
+much more so if I want to do a really
+
+ align:start position:0%
+much more so if I want to do a really
+ 
+
+ align:start position:0%
+much more so if I want to do a really
+low temperature anal and silicon I can
+
+ align:start position:0%
+low temperature anal and silicon I can
+ 
+
+ align:start position:0%
+low temperature anal and silicon I can
+do that with a one5 implant I get you
+
+ align:start position:0%
+do that with a one5 implant I get you
+ 
+
+ align:start position:0%
+do that with a one5 implant I get you
+know except for 20% of my atoms I get
+
+ align:start position:0%
+know except for 20% of my atoms I get
+ 
+
+ align:start position:0%
+know except for 20% of my atoms I get
+them active but let's say I only
+
+ align:start position:0%
+them active but let's say I only
+ 
+
+ align:start position:0%
+them active but let's say I only
+implanted 1 E4 Instead at that same
+
+ align:start position:0%
+implanted 1 E4 Instead at that same
+ 
+
+ align:start position:0%
+implanted 1 E4 Instead at that same
+temperature only 10% are active very few
+
+ align:start position:0%
+temperature only 10% are active very few
+ 
+
+ align:start position:0%
+temperature only 10% are active very few
+so if I have a intermediate dose uh
+
+ align:start position:0%
+so if I have a intermediate dose uh
+ 
+
+ align:start position:0%
+so if I have a intermediate dose uh
+one14 might be more typical dose say for
+
+ align:start position:0%
+one14 might be more typical dose say for
+ 
+
+ align:start position:0%
+one14 might be more typical dose say for
+the source strain extensions might be
+
+ align:start position:0%
+the source strain extensions might be
+ 
+
+ align:start position:0%
+the source strain extensions might be
+one14 that's a miserable dose because
+
+ align:start position:0%
+one14 that's a miserable dose because
+ 
+
+ align:start position:0%
+one14 that's a miserable dose because
+it's it's low it's it's pretty high do
+
+ align:start position:0%
+it's it's low it's it's pretty high do
+ 
+
+ align:start position:0%
+it's it's low it's it's pretty high do
+with some damage but it's low enough it
+
+ align:start position:0%
+with some damage but it's low enough it
+ 
+
+ align:start position:0%
+with some damage but it's low enough it
+doesn't am morphies and so to activate
+
+ align:start position:0%
+doesn't am morphies and so to activate
+ 
+
+ align:start position:0%
+doesn't am morphies and so to activate
+the extensions here this one14 dose you
+
+ align:start position:0%
+the extensions here this one14 dose you
+ 
+
+ align:start position:0%
+the extensions here this one14 dose you
+really need to get up to 750 800 or
+
+ align:start position:0%
+really need to get up to 750 800 or
+ 
+
+ align:start position:0%
+really need to get up to 750 800 or
+whatever uh to get 80% activation uh so
+
+ align:start position:0%
+whatever uh to get 80% activation uh so
+ 
+
+ align:start position:0%
+whatever uh to get 80% activation uh so
+don't we don't just think oh for any
+
+ align:start position:0%
+don't we don't just think oh for any
+ 
+
+ align:start position:0%
+don't we don't just think oh for any
+implant I want I just do a certain uh
+
+ align:start position:0%
+implant I want I just do a certain uh
+ 
+
+ align:start position:0%
+implant I want I just do a certain uh
+anneal and I'll get the same results it
+
+ align:start position:0%
+anneal and I'll get the same results it
+ 
+
+ align:start position:0%
+anneal and I'll get the same results it
+really depends on the the amount of
+
+ align:start position:0%
+really depends on the the amount of
+ 
+
+ align:start position:0%
+really depends on the the amount of
+damage I did um and whether I was below
+
+ align:start position:0%
+damage I did um and whether I was below
+ 
+
+ align:start position:0%
+damage I did um and whether I was below
+or above the amorphization threshold
+
+ align:start position:0%
+or above the amorphization threshold
+ 
+
+ align:start position:0%
+or above the amorphization threshold
+here if you go to really low doses it's
+
+ align:start position:0%
+here if you go to really low doses it's
+ 
+
+ align:start position:0%
+here if you go to really low doses it's
+a piece of cake again here at at 10 to
+
+ align:start position:0%
+a piece of cake again here at at 10 to
+ 
+
+ align:start position:0%
+a piece of cake again here at at 10 to
+the 12 it's not bad because you did so
+
+ align:start position:0%
+the 12 it's not bad because you did so
+ 
+
+ align:start position:0%
+the 12 it's not bad because you did so
+little damage even at 600 700 you can
+
+ align:start position:0%
+little damage even at 600 700 you can
+ 
+
+ align:start position:0%
+little damage even at 600 700 you can
+get pretty close to 80 to 100%
+
+ align:start position:0%
+get pretty close to 80 to 100%
+ 
+
+ align:start position:0%
+get pretty close to 80 to 100%
+Activation so the tough spot is this
+
+ align:start position:0%
+Activation so the tough spot is this
+ 
+
+ align:start position:0%
+Activation so the tough spot is this
+intermediate dose regime which is
+
+ align:start position:0%
+intermediate dose regime which is
+ 
+
+ align:start position:0%
+intermediate dose regime which is
+exactly the dose regime where we're I
+
+ align:start position:0%
+exactly the dose regime where we're I
+ 
+
+ align:start position:0%
+exactly the dose regime where we're I
+implanting Source Trin tips or Source
+
+ align:start position:0%
+implanting Source Trin tips or Source
+ 
+
+ align:start position:0%
+implanting Source Trin tips or Source
+drain extensions and those need to be
+
+ align:start position:0%
+drain extensions and those need to be
+ 
+
+ align:start position:0%
+drain extensions and those need to be
+active as full as possible so uh you
+
+ align:start position:0%
+active as full as possible so uh you
+ 
+
+ align:start position:0%
+active as full as possible so uh you
+know unfortunately it does make our life
+
+ align:start position:0%
+know unfortunately it does make our life
+ 
+
+ align:start position:0%
+know unfortunately it does make our life
+a little more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+challenging that was arsenic that
+
+ align:start position:0%
+challenging that was arsenic that
+ 
+
+ align:start position:0%
+challenging that was arsenic that
+actually isn't that bad even more
+
+ align:start position:0%
+actually isn't that bad even more
+ 
+
+ align:start position:0%
+actually isn't that bad even more
+complicated is boron um and again I took
+
+ align:start position:0%
+complicated is boron um and again I took
+ 
+
+ align:start position:0%
+complicated is boron um and again I took
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+uh plot from your textbook uh it's the
+
+ align:start position:0%
+uh plot from your textbook uh it's the
+ 
+
+ align:start position:0%
+uh plot from your textbook uh it's the
+same kind of plot now I'm on a um a semi
+
+ align:start position:0%
+same kind of plot now I'm on a um a semi
+ 
+
+ align:start position:0%
+same kind of plot now I'm on a um a semi
+log plot so I've got a log scale on the
+
+ align:start position:0%
+log plot so I've got a log scale on the
+ 
+
+ align:start position:0%
+log plot so I've got a log scale on the
+y- axis and temperature of a kneeling on
+
+ align:start position:0%
+y- axis and temperature of a kneeling on
+ 
+
+ align:start position:0%
+y- axis and temperature of a kneeling on
+the x-axis and different doses again um
+
+ align:start position:0%
+the x-axis and different doses again um
+ 
+
+ align:start position:0%
+the x-axis and different doses again um
+so for Boron if you have a low dose up
+
+ align:start position:0%
+so for Boron if you have a low dose up
+ 
+
+ align:start position:0%
+so for Boron if you have a low dose up
+here 8 * 10 of 12 again at 550 600 I can
+
+ align:start position:0%
+here 8 * 10 of 12 again at 550 600 I can
+ 
+
+ align:start position:0%
+here 8 * 10 of 12 again at 550 600 I can
+get oh maybe 70 or 50 to 60% active you
+
+ align:start position:0%
+get oh maybe 70 or 50 to 60% active you
+ 
+
+ align:start position:0%
+get oh maybe 70 or 50 to 60% active you
+know not not that great but but not
+
+ align:start position:0%
+know not not that great but but not
+ 
+
+ align:start position:0%
+know not not that great but but not
+terrible uh interestingly at the very
+
+ align:start position:0%
+terrible uh interestingly at the very
+ 
+
+ align:start position:0%
+terrible uh interestingly at the very
+high do regime 2 * 10 15th if I kneel at
+
+ align:start position:0%
+high do regime 2 * 10 15th if I kneel at
+ 
+
+ align:start position:0%
+high do regime 2 * 10 15th if I kneel at
+very low temperatures say 500 um I get a
+
+ align:start position:0%
+very low temperatures say 500 um I get a
+ 
+
+ align:start position:0%
+very low temperatures say 500 um I get a
+reasonable active well it's not very
+
+ align:start position:0%
+reasonable active well it's not very
+ 
+
+ align:start position:0%
+reasonable active well it's not very
+good it's only 1 and 10 but it actually
+
+ align:start position:0%
+good it's only 1 and 10 but it actually
+ 
+
+ align:start position:0%
+good it's only 1 and 10 but it actually
+goes down it actually goes down in a
+
+ align:start position:0%
+goes down it actually goes down in a
+ 
+
+ align:start position:0%
+goes down it actually goes down in a
+certain temperature range between 550
+
+ align:start position:0%
+certain temperature range between 550
+ 
+
+ align:start position:0%
+certain temperature range between 550
+and 700 so you're actually reverse
+
+ align:start position:0%
+and 700 so you're actually reverse
+ 
+
+ align:start position:0%
+and 700 so you're actually reverse
+analing you're taking the dopen atoms
+
+ align:start position:0%
+analing you're taking the dopen atoms
+ 
+
+ align:start position:0%
+analing you're taking the dopen atoms
+offsite and then finally it takes up
+
+ align:start position:0%
+offsite and then finally it takes up
+ 
+
+ align:start position:0%
+offsite and then finally it takes up
+again when you it takes off again when
+
+ align:start position:0%
+again when you it takes off again when
+ 
+
+ align:start position:0%
+again when you it takes off again when
+you get up above about um 750 or 800 so
+
+ align:start position:0%
+you get up above about um 750 or 800 so
+ 
+
+ align:start position:0%
+you get up above about um 750 or 800 so
+to get full activation of boron you
+
+ align:start position:0%
+to get full activation of boron you
+ 
+
+ align:start position:0%
+to get full activation of boron you
+really need to be in Silicon at um at
+
+ align:start position:0%
+really need to be in Silicon at um at
+ 
+
+ align:start position:0%
+really need to be in Silicon at um at
+almost any dose you need to be in the
+
+ align:start position:0%
+almost any dose you need to be in the
+ 
+
+ align:start position:0%
+almost any dose you need to be in the
+high temperature regime 900 or above and
+
+ align:start position:0%
+high temperature regime 900 or above and
+ 
+
+ align:start position:0%
+high temperature regime 900 or above and
+and that's a real problem that's why you
+
+ align:start position:0%
+and that's a real problem that's why you
+ 
+
+ align:start position:0%
+and that's a real problem that's why you
+will see hear people say oh Boron is
+
+ align:start position:0%
+will see hear people say oh Boron is
+ 
+
+ align:start position:0%
+will see hear people say oh Boron is
+hard to activate in general it requires
+
+ align:start position:0%
+hard to activate in general it requires
+ 
+
+ align:start position:0%
+hard to activate in general it requires
+higher temperatures or some kind of more
+
+ align:start position:0%
+higher temperatures or some kind of more
+ 
+
+ align:start position:0%
+higher temperatures or some kind of more
+sophisticated analing technique than
+
+ align:start position:0%
+sophisticated analing technique than
+ 
+
+ align:start position:0%
+sophisticated analing technique than
+Arsenic and that's because of the type
+
+ align:start position:0%
+Arsenic and that's because of the type
+ 
+
+ align:start position:0%
+Arsenic and that's because of the type
+of damage it does it does not tend to
+
+ align:start position:0%
+of damage it does it does not tend to
+ 
+
+ align:start position:0%
+of damage it does it does not tend to
+amorphize unless you go to really high
+
+ align:start position:0%
+amorphize unless you go to really high
+ 
+
+ align:start position:0%
+amorphize unless you go to really high
+doses it's very hard to get an amorphus
+
+ align:start position:0%
+doses it's very hard to get an amorphus
+ 
+
+ align:start position:0%
+doses it's very hard to get an amorphus
+and so you cannot take advantage as
+
+ align:start position:0%
+and so you cannot take advantage as
+ 
+
+ align:start position:0%
+and so you cannot take advantage as
+easily of this solid phase Epi
+
+ align:start position:0%
+easily of this solid phase Epi
+ 
+
+ align:start position:0%
+easily of this solid phase Epi
+regro um now one thing you can do you
+
+ align:start position:0%
+regro um now one thing you can do you
+ 
+
+ align:start position:0%
+regro um now one thing you can do you
+say Okay Boron doesn't amorphize what
+
+ align:start position:0%
+say Okay Boron doesn't amorphize what
+ 
+
+ align:start position:0%
+say Okay Boron doesn't amorphize what
+could I do people do something called
+
+ align:start position:0%
+could I do people do something called
+ 
+
+ align:start position:0%
+could I do people do something called
+pre amorphization so before they implant
+
+ align:start position:0%
+pre amorphization so before they implant
+ 
+
+ align:start position:0%
+pre amorphization so before they implant
+a boron profile they might implant a
+
+ align:start position:0%
+a boron profile they might implant a
+ 
+
+ align:start position:0%
+a boron profile they might implant a
+high dose of silicon or morphies the
+
+ align:start position:0%
+high dose of silicon or morphies the
+ 
+
+ align:start position:0%
+high dose of silicon or morphies the
+crystal to a certain depth then to put
+
+ align:start position:0%
+crystal to a certain depth then to put
+ 
+
+ align:start position:0%
+crystal to a certain depth then to put
+the boron in by implant and then regrow
+
+ align:start position:0%
+the boron in by implant and then regrow
+ 
+
+ align:start position:0%
+the boron in by implant and then regrow
+the whole thing by SP and you can cheat
+
+ align:start position:0%
+the whole thing by SP and you can cheat
+ 
+
+ align:start position:0%
+the whole thing by SP and you can cheat
+that way in some sense or or it's an
+
+ align:start position:0%
+that way in some sense or or it's an
+ 
+
+ align:start position:0%
+that way in some sense or or it's an
+extra step but then you can get a little
+
+ align:start position:0%
+extra step but then you can get a little
+ 
+
+ align:start position:0%
+extra step but then you can get a little
+better analing characteristics but this
+
+ align:start position:0%
+better analing characteristics but this
+ 
+
+ align:start position:0%
+better analing characteristics but this
+is assuming you didn't do any
+
+ align:start position:0%
+is assuming you didn't do any
+ 
+
+ align:start position:0%
+is assuming you didn't do any
+priorization this is just implant the
+
+ align:start position:0%
+priorization this is just implant the
+ 
+
+ align:start position:0%
+priorization this is just implant the
+Bor at this dose and try to anal it um
+
+ align:start position:0%
+Bor at this dose and try to anal it um
+ 
+
+ align:start position:0%
+Bor at this dose and try to anal it um
+so what is this reverse analing behavior
+
+ align:start position:0%
+so what is this reverse analing behavior
+ 
+
+ align:start position:0%
+so what is this reverse analing behavior
+um well uh it's probably oh there's a
+
+ align:start position:0%
+um well uh it's probably oh there's a
+ 
+
+ align:start position:0%
+um well uh it's probably oh there's a
+typo here it's thought there's a t
+
+ align:start position:0%
+typo here it's thought there's a t
+ 
+
+ align:start position:0%
+typo here it's thought there's a t
+missing it's thought to occur because
+
+ align:start position:0%
+missing it's thought to occur because
+ 
+
+ align:start position:0%
+missing it's thought to occur because
+there's some kind of competition here
+
+ align:start position:0%
+there's some kind of competition here
+ 
+
+ align:start position:0%
+there's some kind of competition here
+between the the native interstitial
+
+ align:start position:0%
+between the the native interstitial
+ 
+
+ align:start position:0%
+between the the native interstitial
+Point defects um uh you know that the
+
+ align:start position:0%
+Point defects um uh you know that the
+ 
+
+ align:start position:0%
+Point defects um uh you know that the
+things that you're creating remember you
+
+ align:start position:0%
+things that you're creating remember you
+ 
+
+ align:start position:0%
+things that you're creating remember you
+create more Point defects as you raise
+
+ align:start position:0%
+create more Point defects as you raise
+ 
+
+ align:start position:0%
+create more Point defects as you raise
+the temperature and the Boron atoms
+
+ align:start position:0%
+the temperature and the Boron atoms
+ 
+
+ align:start position:0%
+the temperature and the Boron atoms
+themselves for the latti sites because
+
+ align:start position:0%
+themselves for the latti sites because
+ 
+
+ align:start position:0%
+themselves for the latti sites because
+again we did not amorphize the crystal
+
+ align:start position:0%
+again we did not amorphize the crystal
+ 
+
+ align:start position:0%
+again we did not amorphize the crystal
+which just created a lot of damage um so
+
+ align:start position:0%
+which just created a lot of damage um so
+ 
+
+ align:start position:0%
+which just created a lot of damage um so
+there's a sort of range where you just
+
+ align:start position:0%
+there's a sort of range where you just
+ 
+
+ align:start position:0%
+there's a sort of range where you just
+don't want to be in healing here at this
+
+ align:start position:0%
+don't want to be in healing here at this
+ 
+
+ align:start position:0%
+don't want to be in healing here at this
+dose of 210 10 the 14th uh you want to
+
+ align:start position:0%
+dose of 210 10 the 14th uh you want to
+ 
+
+ align:start position:0%
+dose of 210 10 the 14th uh you want to
+take the BW up
+
+ align:start position:0%
+take the BW up
+ 
+
+ align:start position:0%
+take the BW up
+higher the problem with going to higher
+
+ align:start position:0%
+higher the problem with going to higher
+ 
+
+ align:start position:0%
+higher the problem with going to higher
+temperatures of course is you get more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diffusion so let me go on to slide 26
+
+ align:start position:0%
+diffusion so let me go on to slide 26
+ 
+
+ align:start position:0%
+diffusion so let me go on to slide 26
+and just say a few words we're going to
+
+ align:start position:0%
+and just say a few words we're going to
+ 
+
+ align:start position:0%
+and just say a few words we're going to
+spend the entire next lecture on this
+
+ align:start position:0%
+spend the entire next lecture on this
+ 
+
+ align:start position:0%
+spend the entire next lecture on this
+but on something called Transit enhanced
+
+ align:start position:0%
+but on something called Transit enhanced
+ 
+
+ align:start position:0%
+but on something called Transit enhanced
+diffusion and and this is sort of um
+
+ align:start position:0%
+diffusion and and this is sort of um
+ 
+
+ align:start position:0%
+diffusion and and this is sort of um
+exemplified here here is a um uh an
+
+ align:start position:0%
+exemplified here here is a um uh an
+ 
+
+ align:start position:0%
+exemplified here here is a um uh an
+implant that was done uh say uh of it
+
+ align:start position:0%
+implant that was done uh say uh of it
+ 
+
+ align:start position:0%
+implant that was done uh say uh of it
+could be Boron or think it doesn't
+
+ align:start position:0%
+could be Boron or think it doesn't
+ 
+
+ align:start position:0%
+could be Boron or think it doesn't
+really matter at this point but uh let's
+
+ align:start position:0%
+really matter at this point but uh let's
+ 
+
+ align:start position:0%
+really matter at this point but uh let's
+say it's Boron and what we we see two
+
+ align:start position:0%
+say it's Boron and what we we see two
+ 
+
+ align:start position:0%
+say it's Boron and what we we see two
+different anals the blue curve I did um
+
+ align:start position:0%
+different anals the blue curve I did um
+ 
+
+ align:start position:0%
+different anals the blue curve I did um
+a th000 degre c for 10
+
+ align:start position:0%
+a th000 degre c for 10
+ 
+
+ align:start position:0%
+a th000 degre c for 10
+seconds and I got that diffusion profile
+
+ align:start position:0%
+seconds and I got that diffusion profile
+ 
+
+ align:start position:0%
+seconds and I got that diffusion profile
+uh after I implanted the Boron um and
+
+ align:start position:0%
+uh after I implanted the Boron um and
+ 
+
+ align:start position:0%
+uh after I implanted the Boron um and
+now the red curve is 2 minutes at
+
+ align:start position:0%
+now the red curve is 2 minutes at
+ 
+
+ align:start position:0%
+now the red curve is 2 minutes at
+800 um and so uh interestingly you would
+
+ align:start position:0%
+800 um and so uh interestingly you would
+ 
+
+ align:start position:0%
+800 um and so uh interestingly you would
+think well I'm go I'm knealing it at 800
+
+ align:start position:0%
+think well I'm go I'm knealing it at 800
+ 
+
+ align:start position:0%
+think well I'm go I'm knealing it at 800
+that's a much lower temperature the
+
+ align:start position:0%
+that's a much lower temperature the
+ 
+
+ align:start position:0%
+that's a much lower temperature the
+Boron diffusion coefficient is down by
+
+ align:start position:0%
+Boron diffusion coefficient is down by
+ 
+
+ align:start position:0%
+Boron diffusion coefficient is down by
+two waters of magnitude at 800 so even
+
+ align:start position:0%
+two waters of magnitude at 800 so even
+ 
+
+ align:start position:0%
+two waters of magnitude at 800 so even
+though I'm anealing it for a slightly
+
+ align:start position:0%
+though I'm anealing it for a slightly
+ 
+
+ align:start position:0%
+though I'm anealing it for a slightly
+longer time it's certainly not 100 times
+
+ align:start position:0%
+longer time it's certainly not 100 times
+ 
+
+ align:start position:0%
+longer time it's certainly not 100 times
+longer or 200 times longer so you would
+
+ align:start position:0%
+longer or 200 times longer so you would
+ 
+
+ align:start position:0%
+longer or 200 times longer so you would
+think that the 800 VC profile should be
+
+ align:start position:0%
+think that the 800 VC profile should be
+ 
+
+ align:start position:0%
+think that the 800 VC profile should be
+shallower than the a thousand so D teed
+
+ align:start position:0%
+shallower than the a thousand so D teed
+ 
+
+ align:start position:0%
+shallower than the a thousand so D teed
+unfortunately is this strange effect and
+
+ align:start position:0%
+unfortunately is this strange effect and
+ 
+
+ align:start position:0%
+unfortunately is this strange effect and
+we'll talk about how this can happen um
+
+ align:start position:0%
+we'll talk about how this can happen um
+ 
+
+ align:start position:0%
+we'll talk about how this can happen um
+is that even at lower temperatures you
+
+ align:start position:0%
+is that even at lower temperatures you
+ 
+
+ align:start position:0%
+is that even at lower temperatures you
+can even get deeper Junctions then you
+
+ align:start position:0%
+can even get deeper Junctions then you
+ 
+
+ align:start position:0%
+can even get deeper Junctions then you
+can get at higher temperatures so RIS
+
+ align:start position:0%
+can get at higher temperatures so RIS
+ 
+
+ align:start position:0%
+can get at higher temperatures so RIS
+really annoyed people and was quite
+
+ align:start position:0%
+really annoyed people and was quite
+ 
+
+ align:start position:0%
+really annoyed people and was quite
+confusing and it needs to be explained
+
+ align:start position:0%
+confusing and it needs to be explained
+ 
+
+ align:start position:0%
+confusing and it needs to be explained
+uh by this the implant damage and its
+
+ align:start position:0%
+uh by this the implant damage and its
+ 
+
+ align:start position:0%
+uh by this the implant damage and its
+effect on how the bwn diffuses and in
+
+ align:start position:0%
+effect on how the bwn diffuses and in
+ 
+
+ align:start position:0%
+effect on how the bwn diffuses and in
+fact Ted today is pretty much the
+
+ align:start position:0%
+fact Ted today is pretty much the
+ 
+
+ align:start position:0%
+fact Ted today is pretty much the
+dominant effect that determines Junction
+
+ align:start position:0%
+dominant effect that determines Junction
+ 
+
+ align:start position:0%
+dominant effect that determines Junction
+depths and shallow profiles it's not so
+
+ align:start position:0%
+depths and shallow profiles it's not so
+ 
+
+ align:start position:0%
+depths and shallow profiles it's not so
+much ordinary diffusion or concentration
+
+ align:start position:0%
+much ordinary diffusion or concentration
+ 
+
+ align:start position:0%
+much ordinary diffusion or concentration
+dependent diffusion well for arsenic
+
+ align:start position:0%
+dependent diffusion well for arsenic
+ 
+
+ align:start position:0%
+dependent diffusion well for arsenic
+maybe but for Boron everything is you
+
+ align:start position:0%
+maybe but for Boron everything is you
+ 
+
+ align:start position:0%
+maybe but for Boron everything is you
+cannot possibly model a shallow Junction
+
+ align:start position:0%
+cannot possibly model a shallow Junction
+ 
+
+ align:start position:0%
+cannot possibly model a shallow Junction
+unless you know how to model
+
+ align:start position:0%
+unless you know how to model
+ 
+
+ align:start position:0%
+unless you know how to model
+teed um and if I just go on to the next
+
+ align:start position:0%
+teed um and if I just go on to the next
+ 
+
+ align:start position:0%
+teed um and if I just go on to the next
+slide just to show you if you if I had
+
+ align:start position:0%
+slide just to show you if you if I had
+ 
+
+ align:start position:0%
+slide just to show you if you if I had
+given you that problem and told you
+
+ align:start position:0%
+given you that problem and told you
+ 
+
+ align:start position:0%
+given you that problem and told you
+nothing about teed and and you would
+
+ align:start position:0%
+nothing about teed and and you would
+ 
+
+ align:start position:0%
+nothing about teed and and you would
+have looked up in your book say uh at
+
+ align:start position:0%
+have looked up in your book say uh at
+ 
+
+ align:start position:0%
+have looked up in your book say uh at
+800° um which is somewhere right around
+
+ align:start position:0%
+800° um which is somewhere right around
+ 
+
+ align:start position:0%
+800° um which is somewhere right around
+here here's the Boron diffusion
+
+ align:start position:0%
+here here's the Boron diffusion
+ 
+
+ align:start position:0%
+here here's the Boron diffusion
+coefficient right at this point and that
+
+ align:start position:0%
+coefficient right at this point and that
+ 
+
+ align:start position:0%
+coefficient right at this point and that
+at a th000 degrees it's up here and the
+
+ align:start position:0%
+at a th000 degrees it's up here and the
+ 
+
+ align:start position:0%
+at a th000 degrees it's up here and the
+difference between the two is more than
+
+ align:start position:0%
+difference between the two is more than
+ 
+
+ align:start position:0%
+difference between the two is more than
+two orders of magnitude so it's it's
+
+ align:start position:0%
+two orders of magnitude so it's it's
+ 
+
+ align:start position:0%
+two orders of magnitude so it's it's
+almost a factor of a thousand so clearly
+
+ align:start position:0%
+almost a factor of a thousand so clearly
+ 
+
+ align:start position:0%
+almost a factor of a thousand so clearly
+if you're diffusing at 800 it should be
+
+ align:start position:0%
+if you're diffusing at 800 it should be
+ 
+
+ align:start position:0%
+if you're diffusing at 800 it should be
+a lot less uh a lot shallower Junction
+
+ align:start position:0%
+a lot less uh a lot shallower Junction
+ 
+
+ align:start position:0%
+a lot less uh a lot shallower Junction
+um even if you're doing it for two
+
+ align:start position:0%
+um even if you're doing it for two
+ 
+
+ align:start position:0%
+um even if you're doing it for two
+minutes versus 10 seconds I mean two
+
+ align:start position:0%
+minutes versus 10 seconds I mean two
+ 
+
+ align:start position:0%
+minutes versus 10 seconds I mean two
+minutes is 120 seconds right so 10 into
+
+ align:start position:0%
+minutes is 120 seconds right so 10 into
+ 
+
+ align:start position:0%
+minutes is 120 seconds right so 10 into
+that so I'm doing it 12 times longer
+
+ align:start position:0%
+that so I'm doing it 12 times longer
+ 
+
+ align:start position:0%
+that so I'm doing it 12 times longer
+fine but the diffus diffusion
+
+ align:start position:0%
+fine but the diffus diffusion
+ 
+
+ align:start position:0%
+fine but the diffus diffusion
+coefficient is a thousand times should
+
+ align:start position:0%
+coefficient is a thousand times should
+ 
+
+ align:start position:0%
+coefficient is a thousand times should
+be a thousand times slower at 800 but
+
+ align:start position:0%
+be a thousand times slower at 800 but
+ 
+
+ align:start position:0%
+be a thousand times slower at 800 but
+it's not in fact it's thousand times
+
+ align:start position:0%
+it's not in fact it's thousand times
+ 
+
+ align:start position:0%
+it's not in fact it's thousand times
+faster it's a lot faster and that whole
+
+ align:start position:0%
+faster it's a lot faster and that whole
+ 
+
+ align:start position:0%
+faster it's a lot faster and that whole
+effect is called trans enhanced
+
+ align:start position:0%
+effect is called trans enhanced
+ 
+
+ align:start position:0%
+effect is called trans enhanced
+diffusion it results from all the
+
+ align:start position:0%
+diffusion it results from all the
+ 
+
+ align:start position:0%
+diffusion it results from all the
+interstitials that were implanted that
+
+ align:start position:0%
+interstitials that were implanted that
+ 
+
+ align:start position:0%
+interstitials that were implanted that
+plus one interstitials giving rise to
+
+ align:start position:0%
+plus one interstitials giving rise to
+ 
+
+ align:start position:0%
+plus one interstitials giving rise to
+311's and all that and so the next
+
+ align:start position:0%
+311's and all that and so the next
+ 
+
+ align:start position:0%
+311's and all that and so the next
+lecture we're going to spend trying to
+
+ align:start position:0%
+lecture we're going to spend trying to
+ 
+
+ align:start position:0%
+lecture we're going to spend trying to
+understand these profiles and their um
+
+ align:start position:0%
+understand these profiles and their um
+ 
+
+ align:start position:0%
+understand these profiles and their um
+in their time depend
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dependence so let me summarize slide 28
+
+ align:start position:0%
+dependence so let me summarize slide 28
+ 
+
+ align:start position:0%
+dependence so let me summarize slide 28
+basically so far uh in this lecture we
+
+ align:start position:0%
+basically so far uh in this lecture we
+ 
+
+ align:start position:0%
+basically so far uh in this lecture we
+said that that we can separate the
+
+ align:start position:0%
+said that that we can separate the
+ 
+
+ align:start position:0%
+said that that we can separate the
+energy loss processes completely
+
+ align:start position:0%
+energy loss processes completely
+ 
+
+ align:start position:0%
+energy loss processes completely
+independent of each other to first order
+
+ align:start position:0%
+independent of each other to first order
+ 
+
+ align:start position:0%
+independent of each other to first order
+we have nuclear processes which are
+
+ align:start position:0%
+we have nuclear processes which are
+ 
+
+ align:start position:0%
+we have nuclear processes which are
+these uh bilard ball collisions and we
+
+ align:start position:0%
+these uh bilard ball collisions and we
+ 
+
+ align:start position:0%
+these uh bilard ball collisions and we
+have electronic drag Force the nuclear
+
+ align:start position:0%
+have electronic drag Force the nuclear
+ 
+
+ align:start position:0%
+have electronic drag Force the nuclear
+stopping dominates when we have a heavy
+
+ align:start position:0%
+stopping dominates when we have a heavy
+ 
+
+ align:start position:0%
+stopping dominates when we have a heavy
+ion uh over most of its path for a light
+
+ align:start position:0%
+ion uh over most of its path for a light
+ 
+
+ align:start position:0%
+ion uh over most of its path for a light
+ion nuclear stopping dominates only at
+
+ align:start position:0%
+ion nuclear stopping dominates only at
+ 
+
+ align:start position:0%
+ion nuclear stopping dominates only at
+the end of um of range at at very at low
+
+ align:start position:0%
+the end of um of range at at very at low
+ 
+
+ align:start position:0%
+the end of um of range at at very at low
+energies um it's the nuclear stopping
+
+ align:start position:0%
+energies um it's the nuclear stopping
+ 
+
+ align:start position:0%
+energies um it's the nuclear stopping
+that damages the crystal uh by the
+
+ align:start position:0%
+that damages the crystal uh by the
+ 
+
+ align:start position:0%
+that damages the crystal uh by the
+creation of silicon recoil so it knocks
+
+ align:start position:0%
+creation of silicon recoil so it knocks
+ 
+
+ align:start position:0%
+creation of silicon recoil so it knocks
+silicons off of their lyes and they
+
+ align:start position:0%
+silicons off of their lyes and they
+ 
+
+ align:start position:0%
+silicons off of their lyes and they
+knock other people other atoms off and
+
+ align:start position:0%
+knock other people other atoms off and
+ 
+
+ align:start position:0%
+knock other people other atoms off and
+that creates what's called a collision
+
+ align:start position:0%
+that creates what's called a collision
+ 
+
+ align:start position:0%
+that creates what's called a collision
+Cascade the damage profile Peaks right
+
+ align:start position:0%
+Cascade the damage profile Peaks right
+ 
+
+ align:start position:0%
+Cascade the damage profile Peaks right
+near
+
+ align:start position:0%
+near
+ 
+
+ align:start position:0%
+near
+RP um if you want to calculate that you
+
+ align:start position:0%
+RP um if you want to calculate that you
+ 
+
+ align:start position:0%
+RP um if you want to calculate that you
+can just maybe 80% of RP gives you a
+
+ align:start position:0%
+can just maybe 80% of RP gives you a
+ 
+
+ align:start position:0%
+can just maybe 80% of RP gives you a
+rough idea of the depth of
+
+ align:start position:0%
+rough idea of the depth of
+ 
+
+ align:start position:0%
+rough idea of the depth of
+damage for heavy ions the damage is more
+
+ align:start position:0%
+damage for heavy ions the damage is more
+ 
+
+ align:start position:0%
+damage for heavy ions the damage is more
+stable that is it doesn't tend to anal
+
+ align:start position:0%
+stable that is it doesn't tend to anal
+ 
+
+ align:start position:0%
+stable that is it doesn't tend to anal
+out in the ion implanter uh at room
+
+ align:start position:0%
+out in the ion implanter uh at room
+ 
+
+ align:start position:0%
+out in the ion implanter uh at room
+temperature and there's a tendency for a
+
+ align:start position:0%
+temperature and there's a tendency for a
+ 
+
+ align:start position:0%
+temperature and there's a tendency for a
+heavy ion to form an amorphous layer
+
+ align:start position:0%
+heavy ion to form an amorphous layer
+ 
+
+ align:start position:0%
+heavy ion to form an amorphous layer
+from the surface all the way down to
+
+ align:start position:0%
+from the surface all the way down to
+ 
+
+ align:start position:0%
+from the surface all the way down to
+some depth that amorphous layer can be
+
+ align:start position:0%
+some depth that amorphous layer can be
+ 
+
+ align:start position:0%
+some depth that amorphous layer can be
+regrown relatively easily in Silicon not
+
+ align:start position:0%
+regrown relatively easily in Silicon not
+ 
+
+ align:start position:0%
+regrown relatively easily in Silicon not
+true in other semiconductors however uh
+
+ align:start position:0%
+true in other semiconductors however uh
+ 
+
+ align:start position:0%
+true in other semiconductors however uh
+it results in uh relatively efficient
+
+ align:start position:0%
+it results in uh relatively efficient
+ 
+
+ align:start position:0%
+it results in uh relatively efficient
+dopen
+
+ align:start position:0%
+dopen
+ 
+
+ align:start position:0%
+dopen
+activation for light ions like B and
+
+ align:start position:0%
+activation for light ions like B and
+ 
+
+ align:start position:0%
+activation for light ions like B and
+phosphorus below a certain dose is
+
+ align:start position:0%
+phosphorus below a certain dose is
+ 
+
+ align:start position:0%
+phosphorus below a certain dose is
+difficult to produce an amorphous layer
+
+ align:start position:0%
+difficult to produce an amorphous layer
+ 
+
+ align:start position:0%
+difficult to produce an amorphous layer
+at room temperature and as a result the
+
+ align:start position:0%
+at room temperature and as a result the
+ 
+
+ align:start position:0%
+at room temperature and as a result the
+activation of dop is a lot more complex
+
+ align:start position:0%
+activation of dop is a lot more complex
+ 
+
+ align:start position:0%
+activation of dop is a lot more complex
+it's very dose dependent and it can be
+
+ align:start position:0%
+it's very dose dependent and it can be
+ 
+
+ align:start position:0%
+it's very dose dependent and it can be
+be temperature dependent in an odd
+
+ align:start position:0%
+be temperature dependent in an odd
+ 
+
+ align:start position:0%
+be temperature dependent in an odd
+fashion um there is this plus one model
+
+ align:start position:0%
+fashion um there is this plus one model
+ 
+
+ align:start position:0%
+fashion um there is this plus one model
+for residual damage that says that
+
+ align:start position:0%
+for residual damage that says that
+ 
+
+ align:start position:0%
+for residual damage that says that
+there's roughly one excess interstitial
+
+ align:start position:0%
+there's roughly one excess interstitial
+ 
+
+ align:start position:0%
+there's roughly one excess interstitial
+for every primary ion that ion implanted
+
+ align:start position:0%
+for every primary ion that ion implanted
+ 
+
+ align:start position:0%
+for every primary ion that ion implanted
+so it's relatively um easy order of
+
+ align:start position:0%
+so it's relatively um easy order of
+ 
+
+ align:start position:0%
+so it's relatively um easy order of
+magnitude estimate and this is after the
+
+ align:start position:0%
+magnitude estimate and this is after the
+ 
+
+ align:start position:0%
+magnitude estimate and this is after the
+initial vacancy and interstitial
+
+ align:start position:0%
+initial vacancy and interstitial
+ 
+
+ align:start position:0%
+initial vacancy and interstitial
+recombination is taking place which only
+
+ align:start position:0%
+recombination is taking place which only
+ 
+
+ align:start position:0%
+recombination is taking place which only
+takes a few fractions of a second these
+
+ align:start position:0%
+takes a few fractions of a second these
+ 
+
+ align:start position:0%
+takes a few fractions of a second these
+excess interstitials however they
+
+ align:start position:0%
+excess interstitials however they
+ 
+
+ align:start position:0%
+excess interstitials however they
+cluster into little 311 defix
+
+ align:start position:0%
+cluster into little 311 defix
+ 
+
+ align:start position:0%
+cluster into little 311 defix
+those defects dissolve at a relatively
+
+ align:start position:0%
+those defects dissolve at a relatively
+ 
+
+ align:start position:0%
+those defects dissolve at a relatively
+slow rate on the order of 10 seconds to
+
+ align:start position:0%
+slow rate on the order of 10 seconds to
+ 
+
+ align:start position:0%
+slow rate on the order of 10 seconds to
+minutes and it's those little that's
+
+ align:start position:0%
+minutes and it's those little that's
+ 
+
+ align:start position:0%
+minutes and it's those little that's
+that 311 um evaporation or dissolution
+
+ align:start position:0%
+that 311 um evaporation or dissolution
+ 
+
+ align:start position:0%
+that 311 um evaporation or dissolution
+that gives rise to the time dependence
+
+ align:start position:0%
+that gives rise to the time dependence
+ 
+
+ align:start position:0%
+that gives rise to the time dependence
+of teed so by understanding 311 defects
+
+ align:start position:0%
+of teed so by understanding 311 defects
+ 
+
+ align:start position:0%
+of teed so by understanding 311 defects
+to a certain extent we can understand
+
+ align:start position:0%
+to a certain extent we can understand
+ 
+
+ align:start position:0%
+to a certain extent we can understand
+that the time dependence of Ted and in
+
+ align:start position:0%
+that the time dependence of Ted and in
+ 
+
+ align:start position:0%
+that the time dependence of Ted and in
+fact by understanding 311 defects we'll
+
+ align:start position:0%
+fact by understanding 311 defects we'll
+ 
+
+ align:start position:0%
+fact by understanding 311 defects we'll
+be able to come up with a model that
+
+ align:start position:0%
+be able to come up with a model that
+ 
+
+ align:start position:0%
+be able to come up with a model that
+could predict this um kind of strange
+
+ align:start position:0%
+could predict this um kind of strange
+ 
+
+ align:start position:0%
+could predict this um kind of strange
+looking uh
+
+ align:start position:0%
+looking uh
+ 
+
+ align:start position:0%
+looking uh
+Behavior okay so that's that's what I
+
+ align:start position:0%
+Behavior okay so that's that's what I
+ 
+
+ align:start position:0%
+Behavior okay so that's that's what I
+wanted to go through today um there were
+
+ align:start position:0%
+wanted to go through today um there were
+ 
+
+ align:start position:0%
+wanted to go through today um there were
+three handouts make sure you got them
+
+ align:start position:0%
+three handouts make sure you got them
+ 
+
+ align:start position:0%
+three handouts make sure you got them
+today's lecture notes homework number
+
+ align:start position:0%
+today's lecture notes homework number
+ 
+
+ align:start position:0%
+today's lecture notes homework number
+four which is due on November 2nd and
+
+ align:start position:0%
+four which is due on November 2nd and
+ 
+
+ align:start position:0%
+four which is due on November 2nd and
+the solutions to homework number two the
+
+ align:start position:0%
+the solutions to homework number two the
+ 
+
+ align:start position:0%
+the solutions to homework number two the
+solutions have been on the web for a
+
+ align:start position:0%
+solutions have been on the web for a
+ 
+
+ align:start position:0%
+solutions have been on the web for a
+while I just forgot to hand out the
+
+ align:start position:0%
+while I just forgot to hand out the
+ 
+
+ align:start position:0%
+while I just forgot to hand out the
+paper
+
+ align:start position:0%
+paper
+ 
+
+ align:start position:0%
+paper
+copy okay so we'll see you uh next
+
+ align:start position:0%
+copy okay so we'll see you uh next
+ 
+
+ align:start position:0%
+copy okay so we'll see you uh next
+Tuesday hopefully we get to watch the
+
+ align:start position:0%
+Tuesday hopefully we get to watch the
+ 
+
+ align:start position:0%
+Tuesday hopefully we get to watch the
+World
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Series
\ No newline at end of file
diff --git a/09vU-wVwW3U.txt b/09vU-wVwW3U.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0de4a648157ef1f290f00009ecc4d6b6db3c405b
--- /dev/null
+++ b/09vU-wVwW3U.txt
@@ -0,0 +1,7456 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right welcome everyone
+
+ align:start position:0%
+ocw.mit.edu all right welcome everyone
+ 
+
+ align:start position:0%
+ocw.mit.edu all right welcome everyone
+uh this is 6046
+
+ align:start position:0%
+uh this is 6046
+ 
+
+ align:start position:0%
+uh this is 6046
+recitation just make sure you're in the
+
+ align:start position:0%
+recitation just make sure you're in the
+ 
+
+ align:start position:0%
+recitation just make sure you're in the
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+place uh my name is Ling Ren I'm one of
+
+ align:start position:0%
+place uh my name is Ling Ren I'm one of
+ 
+
+ align:start position:0%
+place uh my name is Ling Ren I'm one of
+the 10 t for this
+
+ align:start position:0%
+the 10 t for this
+ 
+
+ align:start position:0%
+the 10 t for this
+class and we do have a second ta for
+
+ align:start position:0%
+class and we do have a second ta for
+ 
+
+ align:start position:0%
+class and we do have a second ta for
+this section I think uh he's not here
+
+ align:start position:0%
+this section I think uh he's not here
+ 
+
+ align:start position:0%
+this section I think uh he's not here
+right now but uh basically shanen and I
+
+ align:start position:0%
+right now but uh basically shanen and I
+ 
+
+ align:start position:0%
+right now but uh basically shanen and I
+will be switching every other
+
+ align:start position:0%
+will be switching every other
+ 
+
+ align:start position:0%
+will be switching every other
+week I want to remind you uh just a
+
+ align:start position:0%
+week I want to remind you uh just a
+ 
+
+ align:start position:0%
+week I want to remind you uh just a
+heads up uh this section is recorded for
+
+ align:start position:0%
+heads up uh this section is recorded for
+ 
+
+ align:start position:0%
+heads up uh this section is recorded for
+ocw purpose but uh I think he's Al he's
+
+ align:start position:0%
+ocw purpose but uh I think he's Al he's
+ 
+
+ align:start position:0%
+ocw purpose but uh I think he's Al he's
+only recording uh us the TS he won't
+
+ align:start position:0%
+only recording uh us the TS he won't
+ 
+
+ align:start position:0%
+only recording uh us the TS he won't
+yeah not you're not in the camera
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right so the only purpose uh we
+
+ align:start position:0%
+okay all right so the only purpose uh we
+ 
+
+ align:start position:0%
+okay all right so the only purpose uh we
+are here is to help you learn this very
+
+ align:start position:0%
+are here is to help you learn this very
+ 
+
+ align:start position:0%
+are here is to help you learn this very
+interesting and also very useful class
+
+ align:start position:0%
+interesting and also very useful class
+ 
+
+ align:start position:0%
+interesting and also very useful class
+so don't hesitate to ask any questions
+
+ align:start position:0%
+so don't hesitate to ask any questions
+ 
+
+ align:start position:0%
+so don't hesitate to ask any questions
+or give us any feedback like whether I'm
+
+ align:start position:0%
+or give us any feedback like whether I'm
+ 
+
+ align:start position:0%
+or give us any feedback like whether I'm
+going too fast or too slow whether you
+
+ align:start position:0%
+going too fast or too slow whether you
+ 
+
+ align:start position:0%
+going too fast or too slow whether you
+want us to cover something that's not in
+
+ align:start position:0%
+want us to cover something that's not in
+ 
+
+ align:start position:0%
+want us to cover something that's not in
+the posted
+
+ align:start position:0%
+the posted
+ 
+
+ align:start position:0%
+the posted
+schedule or yeah just any anything
+
+ align:start position:0%
+schedule or yeah just any anything
+ 
+
+ align:start position:0%
+schedule or yeah just any anything
+anything we can help all right so let's
+
+ align:start position:0%
+anything we can help all right so let's
+ 
+
+ align:start position:0%
+anything we can help all right so let's
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+started the two lectures in this week in
+
+ align:start position:0%
+started the two lectures in this week in
+ 
+
+ align:start position:0%
+started the two lectures in this week in
+the first week focus on divide and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conquer it is a class of algorithm that
+
+ align:start position:0%
+conquer it is a class of algorithm that
+ 
+
+ align:start position:0%
+conquer it is a class of algorithm that
+usually involves recursion uh in the
+
+ align:start position:0%
+usually involves recursion uh in the
+ 
+
+ align:start position:0%
+usually involves recursion uh in the
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+description and Professor davidas work
+
+ align:start position:0%
+description and Professor davidas work
+ 
+
+ align:start position:0%
+description and Professor davidas work
+uh gone through
+
+ align:start position:0%
+uh gone through
+ 
+
+ align:start position:0%
+uh gone through
+several algorithms including weighted
+
+ align:start position:0%
+several algorithms including weighted
+ 
+
+ align:start position:0%
+several algorithms including weighted
+interval scheduling and some a bunch of
+
+ align:start position:0%
+interval scheduling and some a bunch of
+ 
+
+ align:start position:0%
+interval scheduling and some a bunch of
+others and he left several open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems so we will answer those open
+
+ align:start position:0%
+problems so we will answer those open
+ 
+
+ align:start position:0%
+problems so we will answer those open
+questions in this section and we'll also
+
+ align:start position:0%
+questions in this section and we'll also
+ 
+
+ align:start position:0%
+questions in this section and we'll also
+uh show you a new algorithm and analyze
+
+ align:start position:0%
+uh show you a new algorithm and analyze
+ 
+
+ align:start position:0%
+uh show you a new algorithm and analyze
+a bunch of other
+
+ align:start position:0%
+a bunch of other
+ 
+
+ align:start position:0%
+a bunch of other
+Ms so just to remind everyone what weed
+
+ align:start position:0%
+Ms so just to remind everyone what weed
+ 
+
+ align:start position:0%
+Ms so just to remind everyone what weed
+interval scheduling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is uh in this problem we are given a
+
+ align:start position:0%
+is uh in this problem we are given a
+ 
+
+ align:start position:0%
+is uh in this problem we are given a
+bunch of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+requests each with a start time and the
+
+ align:start position:0%
+requests each with a start time and the
+ 
+
+ align:start position:0%
+requests each with a start time and the
+finish time and our goal is to find a
+
+ align:start position:0%
+finish time and our goal is to find a
+ 
+
+ align:start position:0%
+finish time and our goal is to find a
+subset of them that are compatible
+
+ align:start position:0%
+subset of them that are compatible
+ 
+
+ align:start position:0%
+subset of them that are compatible
+meaning they do not overlap and uh that
+
+ align:start position:0%
+meaning they do not overlap and uh that
+ 
+
+ align:start position:0%
+meaning they do not overlap and uh that
+have a largest combined weight okay
+
+ align:start position:0%
+have a largest combined weight okay
+ 
+
+ align:start position:0%
+have a largest combined weight okay
+every you clear everyone clear about
+
+ align:start position:0%
+every you clear everyone clear about
+ 
+
+ align:start position:0%
+every you clear everyone clear about
+that so uh a easier case is when the
+
+ align:start position:0%
+that so uh a easier case is when the
+ 
+
+ align:start position:0%
+that so uh a easier case is when the
+problem is unweighted meaning that all
+
+ align:start position:0%
+problem is unweighted meaning that all
+ 
+
+ align:start position:0%
+problem is unweighted meaning that all
+you can think of every task has the same
+
+ align:start position:0%
+you can think of every task has the same
+ 
+
+ align:start position:0%
+you can think of every task has the same
+weight in that case we can just solve it
+
+ align:start position:0%
+weight in that case we can just solve it
+ 
+
+ align:start position:0%
+weight in that case we can just solve it
+using a gry
+
+ align:start position:0%
+using a gry
+ 
+
+ align:start position:0%
+using a gry
+algorithm but when the problem becomes
+
+ align:start position:0%
+algorithm but when the problem becomes
+ 
+
+ align:start position:0%
+algorithm but when the problem becomes
+weighted uh we have to use dynamic
+
+ align:start position:0%
+weighted uh we have to use dynamic
+ 
+
+ align:start position:0%
+weighted uh we have to use dynamic
+programming or recursion and S uh
+
+ align:start position:0%
+programming or recursion and S uh
+ 
+
+ align:start position:0%
+programming or recursion and S uh
+introduced a simple one a basic version
+
+ align:start position:0%
+introduced a simple one a basic version
+ 
+
+ align:start position:0%
+introduced a simple one a basic version
+in a class can someone remind us how
+
+ align:start position:0%
+in a class can someone remind us how
+ 
+
+ align:start position:0%
+in a class can someone remind us how
+that algorithm
+
+ align:start position:0%
+that algorithm
+ 
+
+ align:start position:0%
+that algorithm
+Works any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volunteers you Pi the
+
+ align:start position:0%
+volunteers you Pi the
+ 
+
+ align:start position:0%
+volunteers you Pi the
+mhm can speak louder take the earliest
+
+ align:start position:0%
+mhm can speak louder take the earliest
+ 
+
+ align:start position:0%
+mhm can speak louder take the earliest
+finish time for the next info so we find
+
+ align:start position:0%
+finish time for the next info so we find
+ 
+
+ align:start position:0%
+finish time for the next info so we find
+the next non conflicting info the
+
+ align:start position:0%
+the next non conflicting info the
+ 
+
+ align:start position:0%
+the next non conflicting info the
+earliest finish time and I think
+
+ align:start position:0%
+earliest finish time and I think
+ 
+
+ align:start position:0%
+earliest finish time and I think
+that uh so what's your name
+
+ align:start position:0%
+that uh so what's your name
+ 
+
+ align:start position:0%
+that uh so what's your name
+uh uhhuh then again is
+
+ align:start position:0%
+uh uhhuh then again is
+ 
+
+ align:start position:0%
+uh uhhuh then again is
+that uh yeah I think uh the version you
+
+ align:start position:0%
+that uh yeah I think uh the version you
+ 
+
+ align:start position:0%
+that uh yeah I think uh the version you
+described is for the unweighted case in
+
+ align:start position:0%
+described is for the unweighted case in
+ 
+
+ align:start position:0%
+described is for the unweighted case in
+unweighted case we just scheduled the
+
+ align:start position:0%
+unweighted case we just scheduled the
+ 
+
+ align:start position:0%
+unweighted case we just scheduled the
+earliest uh the one with the earliest
+
+ align:start position:0%
+earliest uh the one with the earliest
+ 
+
+ align:start position:0%
+earliest uh the one with the earliest
+finish time and then we remove all the
+
+ align:start position:0%
+finish time and then we remove all the
+ 
+
+ align:start position:0%
+finish time and then we remove all the
+incompatible ones and we keep going
+
+ align:start position:0%
+incompatible ones and we keep going
+ 
+
+ align:start position:0%
+incompatible ones and we keep going
+right that solve the unweighted version
+
+ align:start position:0%
+right that solve the unweighted version
+ 
+
+ align:start position:0%
+right that solve the unweighted version
+if it's the weighted version we need to
+
+ align:start position:0%
+if it's the weighted version we need to
+ 
+
+ align:start position:0%
+if it's the weighted version we need to
+use recursion and remember uh we break
+
+ align:start position:0%
+use recursion and remember uh we break
+ 
+
+ align:start position:0%
+use recursion and remember uh we break
+the problem into many sub problems and
+
+ align:start position:0%
+the problem into many sub problems and
+ 
+
+ align:start position:0%
+the problem into many sub problems and
+each one can potentially be a optimal
+
+ align:start position:0%
+each one can potentially be a optimal
+ 
+
+ align:start position:0%
+each one can potentially be a optimal
+solution does anyone remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that can you give it a try sure um so we
+
+ align:start position:0%
+that can you give it a try sure um so we
+ 
+
+ align:start position:0%
+that can you give it a try sure um so we
+break into some problem which is the
+
+ align:start position:0%
+break into some problem which is the
+ 
+
+ align:start position:0%
+break into some problem which is the
+best solution from a certain point mhm
+
+ align:start position:0%
+best solution from a certain point mhm
+ 
+
+ align:start position:0%
+best solution from a certain point mhm
+um and then we come Cate that's a
+
+ align:start position:0%
+um and then we come Cate that's a
+ 
+
+ align:start position:0%
+um and then we come Cate that's a
+problem starting at all the different
+
+ align:start position:0%
+problem starting at all the different
+ 
+
+ align:start position:0%
+problem starting at all the different
+finish times we find the maximum of that
+
+ align:start position:0%
+finish times we find the maximum of that
+ 
+
+ align:start position:0%
+finish times we find the maximum of that
+great uh what is the name I mean what is
+
+ align:start position:0%
+great uh what is the name I mean what is
+ 
+
+ align:start position:0%
+great uh what is the name I mean what is
+your Amy am me am me okay that means
+
+ align:start position:0%
+your Amy am me am me okay that means
+ 
+
+ align:start position:0%
+your Amy am me am me okay that means
+that uh let's just try everyone as our
+
+ align:start position:0%
+that uh let's just try everyone as our
+ 
+
+ align:start position:0%
+that uh let's just try everyone as our
+potential first request
+
+ align:start position:0%
+potential first request
+ 
+
+ align:start position:0%
+potential first request
+okay so if I set if I if we choose
+
+ align:start position:0%
+okay so if I set if I if we choose
+ 
+
+ align:start position:0%
+okay so if I set if I if we choose
+request J as our first we get this
+
+ align:start position:0%
+request J as our first we get this
+ 
+
+ align:start position:0%
+request J as our first we get this
+weight right and then we're going to
+
+ align:start position:0%
+weight right and then we're going to
+ 
+
+ align:start position:0%
+weight right and then we're going to
+solve a sub problem so let me equ call
+
+ align:start position:0%
+solve a sub problem so let me equ call
+ 
+
+ align:start position:0%
+solve a sub problem so let me equ call
+the original problem we did interal
+
+ align:start position:0%
+the original problem we did interal
+ 
+
+ align:start position:0%
+the original problem we did interal
+scheduling
+
+ align:start position:0%
+scheduling
+ 
+
+ align:start position:0%
+scheduling
+with all the incoming
+
+ align:start position:0%
+with all the incoming
+ 
+
+ align:start position:0%
+with all the incoming
+requests now we choose J request as our
+
+ align:start position:0%
+requests now we choose J request as our
+ 
+
+ align:start position:0%
+requests now we choose J request as our
+first now we are left with the sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem uh that starts after request J
+
+ align:start position:0%
+problem uh that starts after request J
+ 
+
+ align:start position:0%
+problem uh that starts after request J
+finishes so I'll write that as
+
+ align:start position:0%
+finishes so I'll write that as
+ 
+
+ align:start position:0%
+finishes so I'll write that as
+RJ where I def find
+
+ align:start position:0%
+RJ where I def find
+ 
+
+ align:start position:0%
+RJ where I def find
+RJ to be the set of
+
+ align:start position:0%
+RJ to be the set of
+ 
+
+ align:start position:0%
+RJ to be the set of
+request where their start
+
+ align:start position:0%
+request where their start
+ 
+
+ align:start position:0%
+request where their start
+time is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+later than the finish time of the J
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+request okay to re uh just to
+
+ align:start position:0%
+request okay to re uh just to
+ 
+
+ align:start position:0%
+request okay to re uh just to
+repeat we choose a request as the
+
+ align:start position:0%
+repeat we choose a request as the
+ 
+
+ align:start position:0%
+repeat we choose a request as the
+potential potentially the first request
+
+ align:start position:0%
+potential potentially the first request
+ 
+
+ align:start position:0%
+potential potentially the first request
+and then we look at all the request that
+
+ align:start position:0%
+and then we look at all the request that
+ 
+
+ align:start position:0%
+and then we look at all the request that
+start after it and solve a sub
+
+ align:start position:0%
+start after it and solve a sub
+ 
+
+ align:start position:0%
+start after it and solve a sub
+problem of uh of that case then we take
+
+ align:start position:0%
+problem of uh of that case then we take
+ 
+
+ align:start position:0%
+problem of uh of that case then we take
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Max of all the candidate we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have and that's going to give us the
+
+ align:start position:0%
+have and that's going to give us the
+ 
+
+ align:start position:0%
+have and that's going to give us the
+optimal
+
+ align:start position:0%
+optimal
+ 
+
+ align:start position:0%
+optimal
+solution any question about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm okay so this algorithm runs in
+
+ align:start position:0%
+algorithm okay so this algorithm runs in
+ 
+
+ align:start position:0%
+algorithm okay so this algorithm runs in
+n s
+
+ align:start position:0%
+n s
+ 
+
+ align:start position:0%
+n s
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we're going to try to optimize that
+
+ align:start position:0%
+now we're going to try to optimize that
+ 
+
+ align:start position:0%
+now we're going to try to optimize that
+and come up with a better
+
+ align:start position:0%
+and come up with a better
+ 
+
+ align:start position:0%
+and come up with a better
+algorithm so uh in order to improve
+
+ align:start position:0%
+algorithm so uh in order to improve
+ 
+
+ align:start position:0%
+algorithm so uh in order to improve
+anything we first want to identify the
+
+ align:start position:0%
+anything we first want to identify the
+ 
+
+ align:start position:0%
+anything we first want to identify the
+inefficiency in this algorithm right so
+
+ align:start position:0%
+inefficiency in this algorithm right so
+ 
+
+ align:start position:0%
+inefficiency in this algorithm right so
+which part in the algorithm do you think
+
+ align:start position:0%
+which part in the algorithm do you think
+ 
+
+ align:start position:0%
+which part in the algorithm do you think
+is inefficient or silly unnecessary go
+
+ align:start position:0%
+is inefficient or silly unnecessary go
+ 
+
+ align:start position:0%
+is inefficient or silly unnecessary go
+ahead so it's inefficient to to look
+
+ align:start position:0%
+ahead so it's inefficient to to look
+ 
+
+ align:start position:0%
+ahead so it's inefficient to to look
+through every previous sub
+
+ align:start position:0%
+through every previous sub
+ 
+
+ align:start position:0%
+through every previous sub
+problem uh when trying to
+
+ align:start position:0%
+problem uh when trying to
+ 
+
+ align:start position:0%
+problem uh when trying to
+find so you find
+
+ align:start position:0%
+find so you find
+ 
+
+ align:start position:0%
+find so you find
+Max I was saying that we don't need to
+
+ align:start position:0%
+Max I was saying that we don't need to
+ 
+
+ align:start position:0%
+Max I was saying that we don't need to
+go through every of this
+
+ align:start position:0%
+go through every of this
+ 
+
+ align:start position:0%
+go through every of this
+case yeah yeah we
+
+ align:start position:0%
+case yeah yeah we
+ 
+
+ align:start position:0%
+case yeah yeah we
+should well we should be able to
+
+ align:start position:0%
+should well we should be able to
+ 
+
+ align:start position:0%
+should well we should be able to
+efficiently query
+
+ align:start position:0%
+efficiently query
+ 
+
+ align:start position:0%
+efficiently query
+for uh the right one mhm okay uh I think
+
+ align:start position:0%
+for uh the right one mhm okay uh I think
+ 
+
+ align:start position:0%
+for uh the right one mhm okay uh I think
+you are definitely correct so let me
+
+ align:start position:0%
+you are definitely correct so let me
+ 
+
+ align:start position:0%
+you are definitely correct so let me
+just go through uh what this algorithm
+
+ align:start position:0%
+just go through uh what this algorithm
+ 
+
+ align:start position:0%
+just go through uh what this algorithm
+does and it will be more clear so what
+
+ align:start position:0%
+does and it will be more clear so what
+ 
+
+ align:start position:0%
+does and it will be more clear so what
+this means is I'll choose my I'll choose
+
+ align:start position:0%
+this means is I'll choose my I'll choose
+ 
+
+ align:start position:0%
+this means is I'll choose my I'll choose
+the first request I request one as my
+
+ align:start position:0%
+the first request I request one as my
+ 
+
+ align:start position:0%
+the first request I request one as my
+first request then I'm going to consider
+
+ align:start position:0%
+first request then I'm going to consider
+ 
+
+ align:start position:0%
+first request then I'm going to consider
+only the request that start after one
+
+ align:start position:0%
+only the request that start after one
+ 
+
+ align:start position:0%
+only the request that start after one
+finishes right that only leaves request
+
+ align:start position:0%
+finishes right that only leaves request
+ 
+
+ align:start position:0%
+finishes right that only leaves request
+five potentially some others I didn't
+
+ align:start position:0%
+five potentially some others I didn't
+ 
+
+ align:start position:0%
+five potentially some others I didn't
+draw there okay that's my first
+
+ align:start position:0%
+draw there okay that's my first
+ 
+
+ align:start position:0%
+draw there okay that's my first
+candidate in that Max my second
+
+ align:start position:0%
+candidate in that Max my second
+ 
+
+ align:start position:0%
+candidate in that Max my second
+candidate is I choose request two as my
+
+ align:start position:0%
+candidate is I choose request two as my
+ 
+
+ align:start position:0%
+candidate is I choose request two as my
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+request then I have to remove request
+
+ align:start position:0%
+request then I have to remove request
+ 
+
+ align:start position:0%
+request then I have to remove request
+one because it starts too early and then
+
+ align:start position:0%
+one because it starts too early and then
+ 
+
+ align:start position:0%
+one because it starts too early and then
+I'm left with all the remaining request
+
+ align:start position:0%
+I'm left with all the remaining request
+ 
+
+ align:start position:0%
+I'm left with all the remaining request
+I'll solve that sub problem that's
+
+ align:start position:0%
+I'll solve that sub problem that's
+ 
+
+ align:start position:0%
+I'll solve that sub problem that's
+candidate two candidate
+
+ align:start position:0%
+candidate two candidate
+ 
+
+ align:start position:0%
+candidate two candidate
+three I choose request three as my first
+
+ align:start position:0%
+three I choose request three as my first
+ 
+
+ align:start position:0%
+three I choose request three as my first
+request and then I have to remove one
+
+ align:start position:0%
+request and then I have to remove one
+ 
+
+ align:start position:0%
+request and then I have to remove one
+and two because they start too early oh
+
+ align:start position:0%
+and two because they start too early oh
+ 
+
+ align:start position:0%
+and two because they start too early oh
+four as well it also starts too early
+
+ align:start position:0%
+four as well it also starts too early
+ 
+
+ align:start position:0%
+four as well it also starts too early
+right before three finishes everyone
+
+ align:start position:0%
+right before three finishes everyone
+ 
+
+ align:start position:0%
+right before three finishes everyone
+follow following that so we're left with
+
+ align:start position:0%
+follow following that so we're left with
+ 
+
+ align:start position:0%
+follow following that so we're left with
+the remaining
+
+ align:start position:0%
+the remaining
+ 
+
+ align:start position:0%
+the remaining
+request okay is it more clear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now go ahead so candidate I mean if you
+
+ align:start position:0%
+now go ahead so candidate I mean if you
+ 
+
+ align:start position:0%
+now go ahead so candidate I mean if you
+start with three that's actually a sub
+
+ align:start position:0%
+start with three that's actually a sub
+ 
+
+ align:start position:0%
+start with three that's actually a sub
+problem of two so you see that like
+
+ align:start position:0%
+problem of two so you see that like
+ 
+
+ align:start position:0%
+problem of two so you see that like
+you're doing a lot of extra work great
+
+ align:start position:0%
+you're doing a lot of extra work great
+ 
+
+ align:start position:0%
+you're doing a lot of extra work great
+Point uh so what's your name Andrew
+
+ align:start position:0%
+Point uh so what's your name Andrew
+ 
+
+ align:start position:0%
+Point uh so what's your name Andrew
+Andrew Andrew said um we can potentially
+
+ align:start position:0%
+Andrew Andrew said um we can potentially
+ 
+
+ align:start position:0%
+Andrew Andrew said um we can potentially
+be solving many repeated
+
+ align:start position:0%
+be solving many repeated
+ 
+
+ align:start position:0%
+be solving many repeated
+sub problems right because yeah we
+
+ align:start position:0%
+sub problems right because yeah we
+ 
+
+ align:start position:0%
+sub problems right because yeah we
+definitely don't want to do that and
+
+ align:start position:0%
+definitely don't want to do that and
+ 
+
+ align:start position:0%
+definitely don't want to do that and
+that's actually the core idea the one
+
+ align:start position:0%
+that's actually the core idea the one
+ 
+
+ align:start position:0%
+that's actually the core idea the one
+crisp idea of dynamic programming uh
+
+ align:start position:0%
+crisp idea of dynamic programming uh
+ 
+
+ align:start position:0%
+crisp idea of dynamic programming uh
+Andrew can you tell me what's the
+
+ align:start position:0%
+Andrew can you tell me what's the
+ 
+
+ align:start position:0%
+Andrew can you tell me what's the
+definition of dynamic programming don't
+
+ align:start position:0%
+definition of dynamic programming don't
+ 
+
+ align:start position:0%
+definition of dynamic programming don't
+remember anyone remember
+
+ align:start position:0%
+remember anyone remember
+ 
+
+ align:start position:0%
+remember anyone remember
+that go ahead you can just memorize some
+
+ align:start position:0%
+that go ahead you can just memorize some
+ 
+
+ align:start position:0%
+that go ahead you can just memorize some
+problems and look them up exactly so
+
+ align:start position:0%
+problems and look them up exactly so
+ 
+
+ align:start position:0%
+problems and look them up exactly so
+dynamic programming uh says we will
+
+ align:start position:0%
+dynamic programming uh says we will
+ 
+
+ align:start position:0%
+dynamic programming uh says we will
+break a problem a problem into sub
+
+ align:start position:0%
+break a problem a problem into sub
+ 
+
+ align:start position:0%
+break a problem a problem into sub
+problems and sub problem into even more
+
+ align:start position:0%
+problems and sub problem into even more
+ 
+
+ align:start position:0%
+problems and sub problem into even more
+sub problems but whenever we solve one
+
+ align:start position:0%
+sub problems but whenever we solve one
+ 
+
+ align:start position:0%
+sub problems but whenever we solve one
+we should memorize or just remember its
+
+ align:start position:0%
+we should memorize or just remember its
+ 
+
+ align:start position:0%
+we should memorize or just remember its
+result and store it somewhere and if you
+
+ align:start position:0%
+result and store it somewhere and if you
+ 
+
+ align:start position:0%
+result and store it somewhere and if you
+need it again we'll just retrieve it
+
+ align:start position:0%
+need it again we'll just retrieve it
+ 
+
+ align:start position:0%
+need it again we'll just retrieve it
+right without resolving the
+
+ align:start position:0%
+right without resolving the
+ 
+
+ align:start position:0%
+right without resolving the
+problem that's definitely a great Point
+
+ align:start position:0%
+problem that's definitely a great Point
+ 
+
+ align:start position:0%
+problem that's definitely a great Point
+uh so we we can analyze this the
+
+ align:start position:0%
+uh so we we can analyze this the
+ 
+
+ align:start position:0%
+uh so we we can analyze this the
+complexity of this algorithm uh later
+
+ align:start position:0%
+complexity of this algorithm uh later
+ 
+
+ align:start position:0%
+complexity of this algorithm uh later
+because I want to touch on this more
+
+ align:start position:0%
+because I want to touch on this more
+ 
+
+ align:start position:0%
+because I want to touch on this more
+efficient algorithm first and we will
+
+ align:start position:0%
+efficient algorithm first and we will
+ 
+
+ align:start position:0%
+efficient algorithm first and we will
+see that even after Andrew's
+
+ align:start position:0%
+see that even after Andrew's
+ 
+
+ align:start position:0%
+see that even after Andrew's
+optimization it runtime is n Square so
+
+ align:start position:0%
+optimization it runtime is n Square so
+ 
+
+ align:start position:0%
+optimization it runtime is n Square so
+without that observation if we are
+
+ align:start position:0%
+without that observation if we are
+ 
+
+ align:start position:0%
+without that observation if we are
+solving repeated sub problems it will be
+
+ align:start position:0%
+solving repeated sub problems it will be
+ 
+
+ align:start position:0%
+solving repeated sub problems it will be
+a lot worse than
+
+ align:start position:0%
+a lot worse than
+ 
+
+ align:start position:0%
+a lot worse than
+that anything to yeah go ahead you can
+
+ align:start position:0%
+that anything to yeah go ahead you can
+ 
+
+ align:start position:0%
+that anything to yeah go ahead you can
+also trim ones that like get to the same
+
+ align:start position:0%
+also trim ones that like get to the same
+ 
+
+ align:start position:0%
+also trim ones that like get to the same
+place so you don't need to explore two
+
+ align:start position:0%
+place so you don't need to explore two
+ 
+
+ align:start position:0%
+place so you don't need to explore two
+pths sorry SP again you don't need to
+
+ align:start position:0%
+pths sorry SP again you don't need to
+ 
+
+ align:start position:0%
+pths sorry SP again you don't need to
+explore two paths I get to like both
+
+ align:start position:0%
+explore two paths I get to like both
+ 
+
+ align:start position:0%
+explore two paths I get to like both
+explore and three once you're once
+
+ align:start position:0%
+explore and three once you're once
+ 
+
+ align:start position:0%
+explore and three once you're once
+they're both looking at three then you
+
+ align:start position:0%
+they're both looking at three then you
+ 
+
+ align:start position:0%
+they're both looking at three then you
+only to do the one that's more addition
+
+ align:start position:0%
+only to do the one that's more addition
+ 
+
+ align:start position:0%
+only to do the one that's more addition
+to that point mhm okay cool M go
+
+ align:start position:0%
+to that point mhm okay cool M go
+ 
+
+ align:start position:0%
+to that point mhm okay cool M go
+ahead oh you same thing well I have
+
+ align:start position:0%
+ahead oh you same thing well I have
+ 
+
+ align:start position:0%
+ahead oh you same thing well I have
+another another one as well so I think
+
+ align:start position:0%
+another another one as well so I think
+ 
+
+ align:start position:0%
+another another one as well so I think
+to get better than x square I think we
+
+ align:start position:0%
+to get better than x square I think we
+ 
+
+ align:start position:0%
+to get better than x square I think we
+need to make the observation that it's
+
+ align:start position:0%
+need to make the observation that it's
+ 
+
+ align:start position:0%
+need to make the observation that it's
+um always fine
+
+ align:start position:0%
+um always fine
+ 
+
+ align:start position:0%
+um always fine
+to start a sub problem
+
+ align:start position:0%
+to start a sub problem
+ 
+
+ align:start position:0%
+to start a sub problem
+later so if you if you decided you're
+
+ align:start position:0%
+later so if you if you decided you're
+ 
+
+ align:start position:0%
+later so if you if you decided you're
+taking a certain sequence of intervals
+
+ align:start position:0%
+taking a certain sequence of intervals
+ 
+
+ align:start position:0%
+taking a certain sequence of intervals
+with your first interval and then you
+
+ align:start position:0%
+with your first interval and then you
+ 
+
+ align:start position:0%
+with your first interval and then you
+want to see how to continue from there
+
+ align:start position:0%
+want to see how to continue from there
+ 
+
+ align:start position:0%
+want to see how to continue from there
+um it it's always valid to start later
+
+ align:start position:0%
+um it it's always valid to start later
+ 
+
+ align:start position:0%
+um it it's always valid to start later
+mhm um then um then maybe you had to so
+
+ align:start position:0%
+mhm um then um then maybe you had to so
+ 
+
+ align:start position:0%
+mhm um then um then maybe you had to so
+so that means that we can if we can
+
+ align:start position:0%
+so that means that we can if we can
+ 
+
+ align:start position:0%
+so that means that we can if we can
+efficiently starting at any particular
+
+ align:start position:0%
+efficiently starting at any particular
+ 
+
+ align:start position:0%
+efficiently starting at any particular
+Point query for the
+
+ align:start position:0%
+Point query for the
+ 
+
+ align:start position:0%
+Point query for the
+maximum um of any of the sub problems
+
+ align:start position:0%
+maximum um of any of the sub problems
+ 
+
+ align:start position:0%
+maximum um of any of the sub problems
+starting after that point then we can
+
+ align:start position:0%
+starting after that point then we can
+ 
+
+ align:start position:0%
+starting after that point then we can
+okay great yeah I think uh we are on the
+
+ align:start position:0%
+okay great yeah I think uh we are on the
+ 
+
+ align:start position:0%
+okay great yeah I think uh we are on the
+same page
+
+ align:start position:0%
+same page
+ 
+
+ align:start position:0%
+same page
+so um when I describe the steps of this
+
+ align:start position:0%
+so um when I describe the steps of this
+ 
+
+ align:start position:0%
+so um when I describe the steps of this
+algorithm remember the first uh the
+
+ align:start position:0%
+algorithm remember the first uh the
+ 
+
+ align:start position:0%
+algorithm remember the first uh the
+third candidate I choose this as my
+
+ align:start position:0%
+third candidate I choose this as my
+ 
+
+ align:start position:0%
+third candidate I choose this as my
+first right it makes zero sense because
+
+ align:start position:0%
+first right it makes zero sense because
+ 
+
+ align:start position:0%
+first right it makes zero sense because
+if I do that I might as well put in two
+
+ align:start position:0%
+if I do that I might as well put in two
+ 
+
+ align:start position:0%
+if I do that I might as well put in two
+as well doesn't hurt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right everyone get
+
+ align:start position:0%
+right everyone get
+ 
+
+ align:start position:0%
+right everyone get
+that so yeah the idea is that we
+
+ align:start position:0%
+that so yeah the idea is that we
+ 
+
+ align:start position:0%
+that so yeah the idea is that we
+shouldn't try every
+
+ align:start position:0%
+shouldn't try every
+ 
+
+ align:start position:0%
+shouldn't try every
+possible uh W uh request as my first
+
+ align:start position:0%
+possible uh W uh request as my first
+ 
+
+ align:start position:0%
+possible uh W uh request as my first
+some requests are just better as more
+
+ align:start position:0%
+some requests are just better as more
+ 
+
+ align:start position:0%
+some requests are just better as more
+suited to be the first request
+
+ align:start position:0%
+suited to be the first request
+ 
+
+ align:start position:0%
+suited to be the first request
+and how we're going to do that so
+
+ align:start position:0%
+and how we're going to do that so
+ 
+
+ align:start position:0%
+and how we're going to do that so
+apparently one can potentially be the
+
+ align:start position:0%
+apparently one can potentially be the
+ 
+
+ align:start position:0%
+apparently one can potentially be the
+first request two can also be but it
+
+ align:start position:0%
+first request two can also be but it
+ 
+
+ align:start position:0%
+first request two can also be but it
+make it doesn't make any sense for any
+
+ align:start position:0%
+make it doesn't make any sense for any
+ 
+
+ align:start position:0%
+make it doesn't make any sense for any
+request come after that yeah because
+
+ align:start position:0%
+request come after that yeah because
+ 
+
+ align:start position:0%
+request come after that yeah because
+there's an earlier request right so the
+
+ align:start position:0%
+there's an earlier request right so the
+ 
+
+ align:start position:0%
+there's an earlier request right so the
+efficient algorithm uh let's first sort
+
+ align:start position:0%
+efficient algorithm uh let's first sort
+ 
+
+ align:start position:0%
+efficient algorithm uh let's first sort
+them by their start time we're going to
+
+ align:start position:0%
+them by their start time we're going to
+ 
+
+ align:start position:0%
+them by their start time we're going to
+consider the request that comes early
+
+ align:start position:0%
+consider the request that comes early
+ 
+
+ align:start position:0%
+consider the request that comes early
+first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I have my entire problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here now I'm going to ask a question
+
+ align:start position:0%
+here now I'm going to ask a question
+ 
+
+ align:start position:0%
+here now I'm going to ask a question
+should I include request one in my
+
+ align:start position:0%
+should I include request one in my
+ 
+
+ align:start position:0%
+should I include request one in my
+solution or not that's only two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cases so if I do not uh select one in my
+
+ align:start position:0%
+cases so if I do not uh select one in my
+ 
+
+ align:start position:0%
+cases so if I do not uh select one in my
+solution what sub problem am I left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with any
+
+ align:start position:0%
+with any
+ 
+
+ align:start position:0%
+with any
+ideas if I decide I will not include one
+
+ align:start position:0%
+ideas if I decide I will not include one
+ 
+
+ align:start position:0%
+ideas if I decide I will not include one
+in my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution yeah
+
+ align:start position:0%
+solution yeah
+ 
+
+ align:start position:0%
+solution yeah
+exactly cuz it does uh there's no
+
+ align:start position:0%
+exactly cuz it does uh there's no
+ 
+
+ align:start position:0%
+exactly cuz it does uh there's no
+conflicts anywhere I'll solve a sub
+
+ align:start position:0%
+conflicts anywhere I'll solve a sub
+ 
+
+ align:start position:0%
+conflicts anywhere I'll solve a sub
+problem from 2 to n if I do decide to
+
+ align:start position:0%
+problem from 2 to n if I do decide to
+ 
+
+ align:start position:0%
+problem from 2 to n if I do decide to
+put my request one in the solution I get
+
+ align:start position:0%
+put my request one in the solution I get
+ 
+
+ align:start position:0%
+put my request one in the solution I get
+this weight so what's the sub problem
+
+ align:start position:0%
+this weight so what's the sub problem
+ 
+
+ align:start position:0%
+this weight so what's the sub problem
+I'm left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+mhm yeah in this example is five correct
+
+ align:start position:0%
+mhm yeah in this example is five correct
+ 
+
+ align:start position:0%
+mhm yeah in this example is five correct
+but more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generally you find RJ so like every
+
+ align:start position:0%
+generally you find RJ so like every
+ 
+
+ align:start position:0%
+generally you find RJ so like every
+request that starts after fines exactly
+
+ align:start position:0%
+request that starts after fines exactly
+ 
+
+ align:start position:0%
+request that starts after fines exactly
+every request that starts after one
+
+ align:start position:0%
+every request that starts after one
+ 
+
+ align:start position:0%
+every request that starts after one
+finishes okay now suddenly we are not
+
+ align:start position:0%
+finishes okay now suddenly we are not
+ 
+
+ align:start position:0%
+finishes okay now suddenly we are not
+breaking the original problem into N Sub
+
+ align:start position:0%
+breaking the original problem into N Sub
+ 
+
+ align:start position:0%
+breaking the original problem into N Sub
+problems we only have two sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem so let me do a recursion tree
+
+ align:start position:0%
+problem so let me do a recursion tree
+ 
+
+ align:start position:0%
+problem so let me do a recursion tree
+which is uh a powerful tool in analyzing
+
+ align:start position:0%
+which is uh a powerful tool in analyzing
+ 
+
+ align:start position:0%
+which is uh a powerful tool in analyzing
+this sort of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things so we start with our original
+
+ align:start position:0%
+things so we start with our original
+ 
+
+ align:start position:0%
+things so we start with our original
+problem from one to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n and we have two sub problems two 2 N
+
+ align:start position:0%
+n and we have two sub problems two 2 N
+ 
+
+ align:start position:0%
+n and we have two sub problems two 2 N
+and R1 2
+
+ align:start position:0%
+and R1 2
+ 
+
+ align:start position:0%
+and R1 2
+N this one will also break them into sub
+
+ align:start position:0%
+N this one will also break them into sub
+ 
+
+ align:start position:0%
+N this one will also break them into sub
+problems so what is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay um I have my sub problem 2 to n
+
+ align:start position:0%
+one okay um I have my sub problem 2 to n
+ 
+
+ align:start position:0%
+one okay um I have my sub problem 2 to n
+and I need to further reply the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mhm
+
+ align:start position:0%
+mhm
+ 
+
+ align:start position:0%
+mhm
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+w the max of w oh sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry sorry these are these are the two
+
+ align:start position:0%
+sorry sorry these are these are the two
+ 
+
+ align:start position:0%
+sorry sorry these are these are the two
+cases right either I
+
+ align:start position:0%
+cases right either I
+ 
+
+ align:start position:0%
+cases right either I
+schedule uh either I do not schedule my
+
+ align:start position:0%
+schedule uh either I do not schedule my
+ 
+
+ align:start position:0%
+schedule uh either I do not schedule my
+first or I schedule it and this my first
+
+ align:start position:0%
+first or I schedule it and this my first
+ 
+
+ align:start position:0%
+first or I schedule it and this my first
+request right now here I'm left with
+
+ align:start position:0%
+request right now here I'm left with
+ 
+
+ align:start position:0%
+request right now here I'm left with
+this problem either I do not schedule it
+
+ align:start position:0%
+this problem either I do not schedule it
+ 
+
+ align:start position:0%
+this problem either I do not schedule it
+or I schedule it as my first request so
+
+ align:start position:0%
+or I schedule it as my first request so
+ 
+
+ align:start position:0%
+or I schedule it as my first request so
+so what is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one 3 to n right cuz now I'm asking the
+
+ align:start position:0%
+one 3 to n right cuz now I'm asking the
+ 
+
+ align:start position:0%
+one 3 to n right cuz now I'm asking the
+same question for two and here I'll have
+
+ align:start position:0%
+same question for two and here I'll have
+ 
+
+ align:start position:0%
+same question for two and here I'll have
+R2 2 N so on and so
+
+ align:start position:0%
+R2 2 N so on and so
+ 
+
+ align:start position:0%
+R2 2 N so on and so
+forth now uh let me point out the uh big
+
+ align:start position:0%
+forth now uh let me point out the uh big
+ 
+
+ align:start position:0%
+forth now uh let me point out the uh big
+difference for this version and for the
+
+ align:start position:0%
+difference for this version and for the
+ 
+
+ align:start position:0%
+difference for this version and for the
+basic version
+
+ align:start position:0%
+basic version
+ 
+
+ align:start position:0%
+basic version
+so I'm starting with the request that
+
+ align:start position:0%
+so I'm starting with the request that
+ 
+
+ align:start position:0%
+so I'm starting with the request that
+starts first if I do not do that say if
+
+ align:start position:0%
+starts first if I do not do that say if
+ 
+
+ align:start position:0%
+starts first if I do not do that say if
+here I I'm asking the question for five
+
+ align:start position:0%
+here I I'm asking the question for five
+ 
+
+ align:start position:0%
+here I I'm asking the question for five
+do I schedule five as my first or not
+
+ align:start position:0%
+do I schedule five as my first or not
+ 
+
+ align:start position:0%
+do I schedule five as my first or not
+then what
+
+ align:start position:0%
+then what
+ 
+
+ align:start position:0%
+then what
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+then these two branches do not cover all
+
+ align:start position:0%
+then these two branches do not cover all
+ 
+
+ align:start position:0%
+then these two branches do not cover all
+the cases right cuz I can potentially
+
+ align:start position:0%
+the cases right cuz I can potentially
+ 
+
+ align:start position:0%
+the cases right cuz I can potentially
+schedule it but not as my first in
+
+ align:start position:0%
+schedule it but not as my first in
+ 
+
+ align:start position:0%
+schedule it but not as my first in
+optimal solution
+
+ align:start position:0%
+optimal solution
+ 
+
+ align:start position:0%
+optimal solution
+if I'm asking a question for a random
+
+ align:start position:0%
+if I'm asking a question for a random
+ 
+
+ align:start position:0%
+if I'm asking a question for a random
+request however if I start with the
+
+ align:start position:0%
+request however if I start with the
+ 
+
+ align:start position:0%
+request however if I start with the
+first request uh first meaning it starts
+
+ align:start position:0%
+first request uh first meaning it starts
+ 
+
+ align:start position:0%
+first request uh first meaning it starts
+earliest it will either be not scheduled
+
+ align:start position:0%
+earliest it will either be not scheduled
+ 
+
+ align:start position:0%
+earliest it will either be not scheduled
+or it will be scheduled and as the first
+
+ align:start position:0%
+or it will be scheduled and as the first
+ 
+
+ align:start position:0%
+or it will be scheduled and as the first
+because it cannot be the second request
+
+ align:start position:0%
+because it cannot be the second request
+ 
+
+ align:start position:0%
+because it cannot be the second request
+in my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution any questions about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now this is algorithm uh let's
+
+ align:start position:0%
+okay now this is algorithm uh let's
+ 
+
+ align:start position:0%
+okay now this is algorithm uh let's
+analyze its
+
+ align:start position:0%
+analyze its
+ 
+
+ align:start position:0%
+analyze its
+complexity so what's the overall
+
+ align:start position:0%
+complexity so what's the overall
+ 
+
+ align:start position:0%
+complexity so what's the overall
+complexity um when we go all the way
+
+ align:start position:0%
+complexity um when we go all the way
+ 
+
+ align:start position:0%
+complexity um when we go all the way
+down solve the entire original
+
+ align:start position:0%
+down solve the entire original
+ 
+
+ align:start position:0%
+down solve the entire original
+problem any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guesses what do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think what do you
+
+ align:start position:0%
+think what do you
+ 
+
+ align:start position:0%
+think what do you
+think go ahead
+
+ align:start position:0%
+think go ahead
+ 
+
+ align:start position:0%
+think go ahead
+uh it should be L because need to sort
+
+ align:start position:0%
+uh it should be L because need to sort
+ 
+
+ align:start position:0%
+uh it should be L because need to sort
+the intervals and we're going to need to
+
+ align:start position:0%
+the intervals and we're going to need to
+ 
+
+ align:start position:0%
+the intervals and we're going to need to
+for every
+
+ align:start position:0%
+for every
+ 
+
+ align:start position:0%
+for every
+interval find the um next interval
+
+ align:start position:0%
+interval find the um next interval
+ 
+
+ align:start position:0%
+interval find the um next interval
+starts that starts after it finishes
+
+ align:start position:0%
+starts that starts after it finishes
+ 
+
+ align:start position:0%
+starts that starts after it finishes
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and cool so cuz the first step is
+
+ align:start position:0%
+and cool so cuz the first step is
+ 
+
+ align:start position:0%
+and cool so cuz the first step is
+sorting which is n log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in now after I sort everything
+
+ align:start position:0%
+in now after I sort everything
+ 
+
+ align:start position:0%
+in now after I sort everything
+uh the question I need to answer is how
+
+ align:start position:0%
+uh the question I need to answer is how
+ 
+
+ align:start position:0%
+uh the question I need to answer is how
+many unique sub problems are there right
+
+ align:start position:0%
+many unique sub problems are there right
+ 
+
+ align:start position:0%
+many unique sub problems are there right
+in this entire recursion tree so I'm not
+
+ align:start position:0%
+in this entire recursion tree so I'm not
+ 
+
+ align:start position:0%
+in this entire recursion tree so I'm not
+going to solve the same problem
+
+ align:start position:0%
+going to solve the same problem
+ 
+
+ align:start position:0%
+going to solve the same problem
+twice how many unique problems exist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here n of them right just this left
+
+ align:start position:0%
+here n of them right just this left
+ 
+
+ align:start position:0%
+here n of them right just this left
+Branch okay all the others will be one
+
+ align:start position:0%
+Branch okay all the others will be one
+ 
+
+ align:start position:0%
+Branch okay all the others will be one
+of this right so I can start from bottom
+
+ align:start position:0%
+of this right so I can start from bottom
+ 
+
+ align:start position:0%
+of this right so I can start from bottom
+the bottom of the tree and work my my
+
+ align:start position:0%
+the bottom of the tree and work my my
+ 
+
+ align:start position:0%
+the bottom of the tree and work my my
+way up and uh when I say when I want to
+
+ align:start position:0%
+way up and uh when I say when I want to
+ 
+
+ align:start position:0%
+way up and uh when I say when I want to
+go this take this step uh I'll look up
+
+ align:start position:0%
+go this take this step uh I'll look up
+ 
+
+ align:start position:0%
+go this take this step uh I'll look up
+the result of this in one of one of the
+
+ align:start position:0%
+the result of this in one of one of the
+ 
+
+ align:start position:0%
+the result of this in one of one of the
+sub problems I've already solved okay so
+
+ align:start position:0%
+sub problems I've already solved okay so
+ 
+
+ align:start position:0%
+sub problems I've already solved okay so
+actually the recursion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+itself is only o of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n what what is the story referring
+
+ align:start position:0%
+n what what is the story referring
+ 
+
+ align:start position:0%
+n what what is the story referring
+to okay so we need to uh start with the
+
+ align:start position:0%
+to okay so we need to uh start with the
+ 
+
+ align:start position:0%
+to okay so we need to uh start with the
+request that starts first right we need
+
+ align:start position:0%
+request that starts first right we need
+ 
+
+ align:start position:0%
+request that starts first right we need
+to decide whether we schedule it or
+
+ align:start position:0%
+to decide whether we schedule it or
+ 
+
+ align:start position:0%
+to decide whether we schedule it or
+not and then we need to uh do the same
+
+ align:start position:0%
+not and then we need to uh do the same
+ 
+
+ align:start position:0%
+not and then we need to uh do the same
+thing for this request to is the start
+
+ align:start position:0%
+thing for this request to is the start
+ 
+
+ align:start position:0%
+thing for this request to is the start
+earliest request in this subset we
+
+ align:start position:0%
+earliest request in this subset we
+ 
+
+ align:start position:0%
+earliest request in this subset we
+always need to do that for all the sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems so the overall complexity
+
+ align:start position:0%
+problems so the overall complexity
+ 
+
+ align:start position:0%
+problems so the overall complexity
+is unlog
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in but if we only focus on this cursion
+
+ align:start position:0%
+in but if we only focus on this cursion
+ 
+
+ align:start position:0%
+in but if we only focus on this cursion
+step our Improvement is actually larger
+
+ align:start position:0%
+step our Improvement is actually larger
+ 
+
+ align:start position:0%
+step our Improvement is actually larger
+than that cuz it went from n
+
+ align:start position:0%
+than that cuz it went from n
+ 
+
+ align:start position:0%
+than that cuz it went from n
+Square to um all of n so why is the
+
+ align:start position:0%
+Square to um all of n so why is the
+ 
+
+ align:start position:0%
+Square to um all of n so why is the
+original algorithm n
+
+ align:start position:0%
+original algorithm n
+ 
+
+ align:start position:0%
+original algorithm n
+s I think it also has only n unique sub
+
+ align:start position:0%
+s I think it also has only n unique sub
+ 
+
+ align:start position:0%
+s I think it also has only n unique sub
+problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so do you agree that the original
+
+ align:start position:0%
+right so do you agree that the original
+ 
+
+ align:start position:0%
+right so do you agree that the original
+algorithm is n squ or do you think it's
+
+ align:start position:0%
+algorithm is n squ or do you think it's
+ 
+
+ align:start position:0%
+algorithm is n squ or do you think it's
+also all of n just focus on the cursion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+step in the original algorithm you solve
+
+ align:start position:0%
+step in the original algorithm you solve
+ 
+
+ align:start position:0%
+step in the original algorithm you solve
+some soling problems up to n times so
+
+ align:start position:0%
+some soling problems up to n times so
+ 
+
+ align:start position:0%
+some soling problems up to n times so
+that's why it's still s you solve the
+
+ align:start position:0%
+that's why it's still s you solve the
+ 
+
+ align:start position:0%
+that's why it's still s you solve the
+same thing time um but assuming I do not
+
+ align:start position:0%
+same thing time um but assuming I do not
+ 
+
+ align:start position:0%
+same thing time um but assuming I do not
+do that assuming whenever solve it once
+
+ align:start position:0%
+do that assuming whenever solve it once
+ 
+
+ align:start position:0%
+do that assuming whenever solve it once
+I store the result somewhere and I
+
+ align:start position:0%
+I store the result somewhere and I
+ 
+
+ align:start position:0%
+I store the result somewhere and I
+directly get it okay assuming I do that
+
+ align:start position:0%
+directly get it okay assuming I do that
+ 
+
+ align:start position:0%
+directly get it okay assuming I do that
+what's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complexity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go ahead uhhuh you think it's all
+
+ align:start position:0%
+go ahead uhhuh you think it's all
+ 
+
+ align:start position:0%
+go ahead uhhuh you think it's all
+event so anyone think this uh n Square
+
+ align:start position:0%
+event so anyone think this uh n Square
+ 
+
+ align:start position:0%
+event so anyone think this uh n Square
+cuz I think three said is n Square go
+
+ align:start position:0%
+cuz I think three said is n Square go
+ 
+
+ align:start position:0%
+cuz I think three said is n Square go
+ahead yeah like I think the original
+
+ align:start position:0%
+ahead yeah like I think the original
+ 
+
+ align:start position:0%
+ahead yeah like I think the original
+origal is
+
+ align:start position:0%
+origal is
+ 
+
+ align:start position:0%
+origal is
+weing for every sub problem exactly
+
+ align:start position:0%
+weing for every sub problem exactly
+ 
+
+ align:start position:0%
+weing for every sub problem exactly
+right yeah so here whenever we go up one
+
+ align:start position:0%
+right yeah so here whenever we go up one
+ 
+
+ align:start position:0%
+right yeah so here whenever we go up one
+step I'm doing constant number of work
+
+ align:start position:0%
+step I'm doing constant number of work
+ 
+
+ align:start position:0%
+step I'm doing constant number of work
+right I'm just comparing two numbers and
+
+ align:start position:0%
+right I'm just comparing two numbers and
+ 
+
+ align:start position:0%
+right I'm just comparing two numbers and
+taking a Max however in the original
+
+ align:start position:0%
+taking a Max however in the original
+ 
+
+ align:start position:0%
+taking a Max however in the original
+algorithm which is here whenever I want
+
+ align:start position:0%
+algorithm which is here whenever I want
+ 
+
+ align:start position:0%
+algorithm which is here whenever I want
+to go one step up there are n branches
+
+ align:start position:0%
+to go one step up there are n branches
+ 
+
+ align:start position:0%
+to go one step up there are n branches
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+tree so my total amount of work is like
+
+ align:start position:0%
+tree so my total amount of work is like
+ 
+
+ align:start position:0%
+tree so my total amount of work is like
+1 + 2 + 3 plus n right every step
+
+ align:start position:0%
+1 + 2 + 3 plus n right every step
+ 
+
+ align:start position:0%
+1 + 2 + 3 plus n right every step
+becomes harder when I go up and this is
+
+ align:start position:0%
+becomes harder when I go up and this is
+ 
+
+ align:start position:0%
+becomes harder when I go up and this is
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay uh this is so much for our
+
+ align:start position:0%
+that okay uh this is so much for our
+ 
+
+ align:start position:0%
+that okay uh this is so much for our
+weighted interval scheduling now I'm
+
+ align:start position:0%
+weighted interval scheduling now I'm
+ 
+
+ align:start position:0%
+weighted interval scheduling now I'm
+going to transition into the next topic
+
+ align:start position:0%
+going to transition into the next topic
+ 
+
+ align:start position:0%
+going to transition into the next topic
+so any question uh on this side in
+
+ align:start position:0%
+so any question uh on this side in
+ 
+
+ align:start position:0%
+so any question uh on this side in
+general for the scheduling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem do you have a question no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah uh now let's turn to a a
+
+ align:start position:0%
+okay yeah uh now let's turn to a a
+ 
+
+ align:start position:0%
+okay yeah uh now let's turn to a a
+second topic of this section which is
+
+ align:start position:0%
+second topic of this section which is
+ 
+
+ align:start position:0%
+second topic of this section which is
+Sten
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm ston algorithm is a effent
+
+ align:start position:0%
+algorithm ston algorithm is a effent
+ 
+
+ align:start position:0%
+algorithm ston algorithm is a effent
+algorithm for matrix
+
+ align:start position:0%
+algorithm for matrix
+ 
+
+ align:start position:0%
+algorithm for matrix
+multiplication and matrix multiplication
+
+ align:start position:0%
+multiplication and matrix multiplication
+ 
+
+ align:start position:0%
+multiplication and matrix multiplication
+is a really useful primitive or it has
+
+ align:start position:0%
+is a really useful primitive or it has
+ 
+
+ align:start position:0%
+is a really useful primitive or it has
+applications in almost every area like I
+
+ align:start position:0%
+applications in almost every area like I
+ 
+
+ align:start position:0%
+applications in almost every area like I
+can think of circuit Sim simulation
+
+ align:start position:0%
+can think of circuit Sim simulation
+ 
+
+ align:start position:0%
+can think of circuit Sim simulation
+climate simulation and physics basically
+
+ align:start position:0%
+climate simulation and physics basically
+ 
+
+ align:start position:0%
+climate simulation and physics basically
+everything now I actually had some
+
+ align:start position:0%
+everything now I actually had some
+ 
+
+ align:start position:0%
+everything now I actually had some
+experience with Matrix multipication
+
+ align:start position:0%
+experience with Matrix multipication
+ 
+
+ align:start position:0%
+experience with Matrix multipication
+because my undergrad research uh was
+
+ align:start position:0%
+because my undergrad research uh was
+ 
+
+ align:start position:0%
+because my undergrad research uh was
+improving Matrix algorithms and actually
+
+ align:start position:0%
+improving Matrix algorithms and actually
+ 
+
+ align:start position:0%
+improving Matrix algorithms and actually
+many Matrix algorithms including like
+
+ align:start position:0%
+many Matrix algorithms including like
+ 
+
+ align:start position:0%
+many Matrix algorithms including like
+inversion solving equations they all use
+
+ align:start position:0%
+inversion solving equations they all use
+ 
+
+ align:start position:0%
+inversion solving equations they all use
+multiplication as a primitive so it
+
+ align:start position:0%
+multiplication as a primitive so it
+ 
+
+ align:start position:0%
+multiplication as a primitive so it
+actually comes down to improving matrix
+
+ align:start position:0%
+actually comes down to improving matrix
+ 
+
+ align:start position:0%
+actually comes down to improving matrix
+multiplication and I tried very
+
+ align:start position:0%
+multiplication and I tried very
+ 
+
+ align:start position:0%
+multiplication and I tried very
+hard to just optimize this basic matrix
+
+ align:start position:0%
+hard to just optimize this basic matrix
+ 
+
+ align:start position:0%
+hard to just optimize this basic matrix
+multiplication we take a row uh you take
+
+ align:start position:0%
+multiplication we take a row uh you take
+ 
+
+ align:start position:0%
+multiplication we take a row uh you take
+a column and then you get your answer
+
+ align:start position:0%
+a column and then you get your answer
+ 
+
+ align:start position:0%
+a column and then you get your answer
+for this spot everyone's familiar with
+
+ align:start position:0%
+for this spot everyone's familiar with
+ 
+
+ align:start position:0%
+for this spot everyone's familiar with
+that right I tried very hard but it's
+
+ align:start position:0%
+that right I tried very hard but it's
+ 
+
+ align:start position:0%
+that right I tried very hard but it's
+still 100x slower than the best
+
+ align:start position:0%
+still 100x slower than the best
+ 
+
+ align:start position:0%
+still 100x slower than the best
+algorithm out there so I finally look it
+
+ align:start position:0%
+algorithm out there so I finally look it
+ 
+
+ align:start position:0%
+algorithm out there so I finally look it
+up and I was completely mind blown when
+
+ align:start position:0%
+up and I was completely mind blown when
+ 
+
+ align:start position:0%
+up and I was completely mind blown when
+I know that Matrix algorithm complexity
+
+ align:start position:0%
+I know that Matrix algorithm complexity
+ 
+
+ align:start position:0%
+I know that Matrix algorithm complexity
+is not n cubic it's it's actually
+
+ align:start position:0%
+is not n cubic it's it's actually
+ 
+
+ align:start position:0%
+is not n cubic it's it's actually
+smaller than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is this a surprise too anyone
+
+ align:start position:0%
+that is this a surprise too anyone
+ 
+
+ align:start position:0%
+that is this a surprise too anyone
+expect that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before and uh the technique the more
+
+ align:start position:0%
+before and uh the technique the more
+ 
+
+ align:start position:0%
+before and uh the technique the more
+efficient algorithm uses is exactly Sten
+
+ align:start position:0%
+efficient algorithm uses is exactly Sten
+ 
+
+ align:start position:0%
+efficient algorithm uses is exactly Sten
+algorithm now that we're talking about
+
+ align:start position:0%
+algorithm now that we're talking about
+ 
+
+ align:start position:0%
+algorithm now that we're talking about
+divide and conquer uh you can guess it
+
+ align:start position:0%
+divide and conquer uh you can guess it
+ 
+
+ align:start position:0%
+divide and conquer uh you can guess it
+must be a divide and conquer algorithm
+
+ align:start position:0%
+must be a divide and conquer algorithm
+ 
+
+ align:start position:0%
+must be a divide and conquer algorithm
+and so does anyone have an idea how to
+
+ align:start position:0%
+and so does anyone have an idea how to
+ 
+
+ align:start position:0%
+and so does anyone have an idea how to
+divide the original
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem you want to give it give it a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+try so are you familiar with tiled
+
+ align:start position:0%
+try so are you familiar with tiled
+ 
+
+ align:start position:0%
+try so are you familiar with tiled
+matrix multiplication or blocked matrix
+
+ align:start position:0%
+matrix multiplication or blocked matrix
+ 
+
+ align:start position:0%
+matrix multiplication or blocked matrix
+multiplication okay uh can you tell us
+
+ align:start position:0%
+multiplication okay uh can you tell us
+ 
+
+ align:start position:0%
+multiplication okay uh can you tell us
+what that is uh yeah you can break it
+
+ align:start position:0%
+what that is uh yeah you can break it
+ 
+
+ align:start position:0%
+what that is uh yeah you can break it
+into like quadrants
+
+ align:start position:0%
+into like quadrants
+ 
+
+ align:start position:0%
+into like quadrants
+ESS there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay cool so say this is our A and B and
+
+ align:start position:0%
+Okay cool so say this is our A and B and
+ 
+
+ align:start position:0%
+Okay cool so say this is our A and B and
+we want C we can break each Matrix into
+
+ align:start position:0%
+we want C we can break each Matrix into
+ 
+
+ align:start position:0%
+we want C we can break each Matrix into
+four parts I'll call this a11 a12 a21
+
+ align:start position:0%
+four parts I'll call this a11 a12 a21
+ 
+
+ align:start position:0%
+four parts I'll call this a11 a12 a21
+a22 b11 B12 B21
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B22 same thing for
+
+ align:start position:0%
+B22 same thing for
+ 
+
+ align:start position:0%
+B22 same thing for
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I would like someone to tell me what
+
+ align:start position:0%
+uh I would like someone to tell me what
+ 
+
+ align:start position:0%
+uh I would like someone to tell me what
+is C11 in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead A1 2 B2 1 yeah and
+
+ align:start position:0%
+ahead A1 2 B2 1 yeah and
+ 
+
+ align:start position:0%
+ahead A1 2 B2 1 yeah and
+C12
+
+ align:start position:0%
+C12
+ 
+
+ align:start position:0%
+C12
+is just Pi up
+
+ align:start position:0%
+is just Pi up
+ 
+
+ align:start position:0%
+is just Pi up
+don't be
+
+ align:start position:0%
+don't be
+ 
+
+ align:start position:0%
+don't be
+shy okay this is also my first section
+
+ align:start position:0%
+shy okay this is also my first section
+ 
+
+ align:start position:0%
+shy okay this is also my first section
+ever in my life teaching a recitation
+
+ align:start position:0%
+ever in my life teaching a recitation
+ 
+
+ align:start position:0%
+ever in my life teaching a recitation
+I'm more nervous than you
+
+ align:start position:0%
+I'm more nervous than you
+ 
+
+ align:start position:0%
+I'm more nervous than you
+guys mhm what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C12
+
+ align:start position:0%
+C12
+ 
+
+ align:start position:0%
+C12
+a112
+
+ align:start position:0%
+a112
+ 
+
+ align:start position:0%
+a112
+a one one
+
+ align:start position:0%
+a one one
+ 
+
+ align:start position:0%
+a one one
+B12 a12 B22 right so the rule is the
+
+ align:start position:0%
+B12 a12 B22 right so the rule is the
+ 
+
+ align:start position:0%
+B12 a12 B22 right so the rule is the
+same as before Matrix modifcation
+
+ align:start position:0%
+same as before Matrix modifcation
+ 
+
+ align:start position:0%
+same as before Matrix modifcation
+compute this we take this row this
+
+ align:start position:0%
+compute this we take this row this
+ 
+
+ align:start position:0%
+compute this we take this row this
+column and it gives us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this right Thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You a12 B2 1 right
+
+ align:start position:0%
+You a12 B2 1 right
+ 
+
+ align:start position:0%
+You a12 B2 1 right
+a11 okay and same thing c21 we're going
+
+ align:start position:0%
+a11 okay and same thing c21 we're going
+ 
+
+ align:start position:0%
+a11 okay and same thing c21 we're going
+to take this row and this column a21 B1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 plus a 22 B 21
+
+ align:start position:0%
+1 plus a 22 B 21
+ 
+
+ align:start position:0%
+1 plus a 22 B 21
+c22 is a 21
+
+ align:start position:0%
+c22 is a 21
+ 
+
+ align:start position:0%
+c22 is a 21
+B12 plus
+
+ align:start position:0%
+B12 plus
+ 
+
+ align:start position:0%
+B12 plus
+a22 B22
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any everyone understands this okay
+
+ align:start position:0%
+okay any everyone understands this okay
+ 
+
+ align:start position:0%
+okay any everyone understands this okay
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+so now we've broken up the original
+
+ align:start position:0%
+so now we've broken up the original
+ 
+
+ align:start position:0%
+so now we've broken up the original
+problem into several sub problems we
+
+ align:start position:0%
+problem into several sub problems we
+ 
+
+ align:start position:0%
+problem into several sub problems we
+only need to do matrix multiplication
+
+ align:start position:0%
+only need to do matrix multiplication
+ 
+
+ align:start position:0%
+only need to do matrix multiplication
+here eight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times and each of this Matrix is uh half
+
+ align:start position:0%
+times and each of this Matrix is uh half
+ 
+
+ align:start position:0%
+times and each of this Matrix is uh half
+in size right if the original algorithm
+
+ align:start position:0%
+in size right if the original algorithm
+ 
+
+ align:start position:0%
+in size right if the original algorithm
+is in cubic now each sub problem is half
+
+ align:start position:0%
+is in cubic now each sub problem is half
+ 
+
+ align:start position:0%
+is in cubic now each sub problem is half
+in cubic then we have eight of them so
+
+ align:start position:0%
+in cubic then we have eight of them so
+ 
+
+ align:start position:0%
+in cubic then we have eight of them so
+the complexity is still in cubic no
+
+ align:start position:0%
+the complexity is still in cubic no
+ 
+
+ align:start position:0%
+the complexity is still in cubic no
+improve Improvement at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all so actually to be more precise uh we
+
+ align:start position:0%
+all so actually to be more precise uh we
+ 
+
+ align:start position:0%
+all so actually to be more precise uh we
+should so to know because we can further
+
+ align:start position:0%
+should so to know because we can further
+ 
+
+ align:start position:0%
+should so to know because we can further
+break up these matrices into smaller
+
+ align:start position:0%
+break up these matrices into smaller
+ 
+
+ align:start position:0%
+break up these matrices into smaller
+blocks so to be precise it's uh
+
+ align:start position:0%
+blocks so to be precise it's uh
+ 
+
+ align:start position:0%
+blocks so to be precise it's uh
+complexity should be given by a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recursion eight sub problems each one
+
+ align:start position:0%
+recursion eight sub problems each one
+ 
+
+ align:start position:0%
+recursion eight sub problems each one
+half the size
+
+ align:start position:0%
+half the size
+ 
+
+ align:start position:0%
+half the size
+plus can anyone anyone tell me was the
+
+ align:start position:0%
+plus can anyone anyone tell me was the
+ 
+
+ align:start position:0%
+plus can anyone anyone tell me was the
+merging
+
+ align:start position:0%
+merging
+ 
+
+ align:start position:0%
+merging
+complexity once I get uh all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the go ahead is it just constant because
+
+ align:start position:0%
+the go ahead is it just constant because
+ 
+
+ align:start position:0%
+the go ahead is it just constant because
+you're adding
+
+ align:start position:0%
+you're adding
+ 
+
+ align:start position:0%
+you're adding
+or uh yeah because I'm adding but is it
+
+ align:start position:0%
+or uh yeah because I'm adding but is it
+ 
+
+ align:start position:0%
+or uh yeah because I'm adding but is it
+constant I'm adding this two
+
+ align:start position:0%
+constant I'm adding this two
+ 
+
+ align:start position:0%
+constant I'm adding this two
+matrices Bas for each level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for each level base case uh yeah for
+
+ align:start position:0%
+for each level base case uh yeah for
+ 
+
+ align:start position:0%
+for each level base case uh yeah for
+base case is of course constant so okay
+
+ align:start position:0%
+base case is of course constant so okay
+ 
+
+ align:start position:0%
+base case is of course constant so okay
+so maybe I'm not clear about this what's
+
+ align:start position:0%
+so maybe I'm not clear about this what's
+ 
+
+ align:start position:0%
+so maybe I'm not clear about this what's
+what's the sub problem in this case is
+
+ align:start position:0%
+what's the sub problem in this case is
+ 
+
+ align:start position:0%
+what's the sub problem in this case is
+this multiplication operation okay and
+
+ align:start position:0%
+this multiplication operation okay and
+ 
+
+ align:start position:0%
+this multiplication operation okay and
+so these are the eight sub problems I
+
+ align:start position:0%
+so these are the eight sub problems I
+ 
+
+ align:start position:0%
+so these are the eight sub problems I
+will solve after solving them I need to
+
+ align:start position:0%
+will solve after solving them I need to
+ 
+
+ align:start position:0%
+will solve after solving them I need to
+add them together and adding two
+
+ align:start position:0%
+add them together and adding two
+ 
+
+ align:start position:0%
+add them together and adding two
+matrices and each is size half of n the
+
+ align:start position:0%
+matrices and each is size half of n the
+ 
+
+ align:start position:0%
+matrices and each is size half of n the
+complexity
+
+ align:start position:0%
+complexity
+ 
+
+ align:start position:0%
+complexity
+is yeah it's n
+
+ align:start position:0%
+is yeah it's n
+ 
+
+ align:start position:0%
+is yeah it's n
+Square basically n Square so to get a
+
+ align:start position:0%
+Square basically n Square so to get a
+ 
+
+ align:start position:0%
+Square basically n Square so to get a
+precise uh complexity we should solve
+
+ align:start position:0%
+precise uh complexity we should solve
+ 
+
+ align:start position:0%
+precise uh complexity we should solve
+this recursion but it will end up being
+
+ align:start position:0%
+this recursion but it will end up being
+ 
+
+ align:start position:0%
+this recursion but it will end up being
+the same thing as uh this intuition and
+
+ align:start position:0%
+the same thing as uh this intuition and
+ 
+
+ align:start position:0%
+the same thing as uh this intuition and
+cubic okay so now this is the magic so
+
+ align:start position:0%
+cubic okay so now this is the magic so
+ 
+
+ align:start position:0%
+cubic okay so now this is the magic so
+Sten in
+
+ align:start position:0%
+Sten in
+ 
+
+ align:start position:0%
+Sten in
+1969 came up with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm and squ from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh each of these is a two n half n by
+
+ align:start position:0%
+uh each of these is a two n half n by
+ 
+
+ align:start position:0%
+uh each of these is a two n half n by
+half n matress Okay
+
+ align:start position:0%
+half n matress Okay
+ 
+
+ align:start position:0%
+half n matress Okay
+Okay Okay cool so ston came up with this
+
+ align:start position:0%
+Okay Okay cool so ston came up with this
+ 
+
+ align:start position:0%
+Okay Okay cool so ston came up with this
+algorithm he somehow defined M1 through
+
+ align:start position:0%
+algorithm he somehow defined M1 through
+ 
+
+ align:start position:0%
+algorithm he somehow defined M1 through
+M7 seven
+
+ align:start position:0%
+M7 seven
+ 
+
+ align:start position:0%
+M7 seven
+matrices in this way that I can't
+
+ align:start position:0%
+matrices in this way that I can't
+ 
+
+ align:start position:0%
+matrices in this way that I can't
+provide any intuition because I didn't
+
+ align:start position:0%
+provide any intuition because I didn't
+ 
+
+ align:start position:0%
+provide any intuition because I didn't
+came up with this and somehow
+
+ align:start position:0%
+came up with this and somehow
+ 
+
+ align:start position:0%
+came up with this and somehow
+with those seven
+
+ align:start position:0%
+with those seven
+ 
+
+ align:start position:0%
+with those seven
+matrices he can reconstruct he can
+
+ align:start position:0%
+matrices he can reconstruct he can
+ 
+
+ align:start position:0%
+matrices he can reconstruct he can
+compute all the four uh sub matrices in
+
+ align:start position:0%
+compute all the four uh sub matrices in
+ 
+
+ align:start position:0%
+compute all the four uh sub matrices in
+C and it's not very interesting to check
+
+ align:start position:0%
+C and it's not very interesting to check
+ 
+
+ align:start position:0%
+C and it's not very interesting to check
+it because the algorithm is definitely
+
+ align:start position:0%
+it because the algorithm is definitely
+ 
+
+ align:start position:0%
+it because the algorithm is definitely
+correct um but let's just do one of them
+
+ align:start position:0%
+correct um but let's just do one of them
+ 
+
+ align:start position:0%
+correct um but let's just do one of them
+okay how about this one so c21 is M2 +
+
+ align:start position:0%
+okay how about this one so c21 is M2 +
+ 
+
+ align:start position:0%
+okay how about this one so c21 is M2 +
+M4 it's m2+ M4 so M2 have uh a12
+
+ align:start position:0%
+M4 it's m2+ M4 so M2 have uh a12
+ 
+
+ align:start position:0%
+M4 it's m2+ M4 so M2 have uh a12
+b11 a22 B b11 so there's M4 there's a22
+
+ align:start position:0%
+b11 a22 B b11 so there's M4 there's a22
+ 
+
+ align:start position:0%
+b11 a22 B b11 so there's M4 there's a22
+minus b11 so that cancels out right so
+
+ align:start position:0%
+minus b11 so that cancels out right so
+ 
+
+ align:start position:0%
+minus b11 so that cancels out right so
+we are left with a21 b11 plus a22
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B21 that's the correct
+
+ align:start position:0%
+B21 that's the correct
+ 
+
+ align:start position:0%
+B21 that's the correct
+answer so this is a I guess it's a very
+
+ align:start position:0%
+answer so this is a I guess it's a very
+ 
+
+ align:start position:0%
+answer so this is a I guess it's a very
+clever algorithm you have to work in
+
+ align:start position:0%
+clever algorithm you have to work in
+ 
+
+ align:start position:0%
+clever algorithm you have to work in
+that area for 10 years to come up with
+
+ align:start position:0%
+that area for 10 years to come up with
+ 
+
+ align:start position:0%
+that area for 10 years to come up with
+this so that's not our concern our goal
+
+ align:start position:0%
+this so that's not our concern our goal
+ 
+
+ align:start position:0%
+this so that's not our concern our goal
+is to analyze this algorithm what's the
+
+ align:start position:0%
+is to analyze this algorithm what's the
+ 
+
+ align:start position:0%
+is to analyze this algorithm what's the
+complexity of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so does anyone understand this
+
+ align:start position:0%
+it so does anyone understand this
+ 
+
+ align:start position:0%
+it so does anyone understand this
+recursion can someone tell me what's the
+
+ align:start position:0%
+recursion can someone tell me what's the
+ 
+
+ align:start position:0%
+recursion can someone tell me what's the
+recursion for this part for this ston
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithm we have the original
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem and we have some go ahead
+
+ align:start position:0%
+problem and we have some go ahead
+ 
+
+ align:start position:0%
+problem and we have some go ahead
+so since each of the like1 only require
+
+ align:start position:0%
+so since each of the like1 only require
+ 
+
+ align:start position:0%
+so since each of the like1 only require
+one multiplication M we only need to
+
+ align:start position:0%
+one multiplication M we only need to
+ 
+
+ align:start position:0%
+one multiplication M we only need to
+solve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s yeah that's absolutely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correct everyone guess
+
+ align:start position:0%
+correct everyone guess
+ 
+
+ align:start position:0%
+correct everyone guess
+this so what ston did is it he came up
+
+ align:start position:0%
+this so what ston did is it he came up
+ 
+
+ align:start position:0%
+this so what ston did is it he came up
+with seven matrices each one requires
+
+ align:start position:0%
+with seven matrices each one requires
+ 
+
+ align:start position:0%
+with seven matrices each one requires
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+one multiplication so we have seven sub
+
+ align:start position:0%
+one multiplication so we have seven sub
+ 
+
+ align:start position:0%
+one multiplication so we have seven sub
+problems instead of eight and that's
+
+ align:start position:0%
+problems instead of eight and that's
+ 
+
+ align:start position:0%
+problems instead of eight and that's
+going to give us a benefit an improve an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+improvement now so the question now
+
+ align:start position:0%
+improvement now so the question now
+ 
+
+ align:start position:0%
+improvement now so the question now
+becomes how do I solve this recursion
+
+ align:start position:0%
+becomes how do I solve this recursion
+ 
+
+ align:start position:0%
+becomes how do I solve this recursion
+right given this recursion how do I know
+
+ align:start position:0%
+right given this recursion how do I know
+ 
+
+ align:start position:0%
+right given this recursion how do I know
+it's complexity and same question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there anyone want to give it a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+try so that's going to uh
+
+ align:start position:0%
+try so that's going to uh
+ 
+
+ align:start position:0%
+try so that's going to uh
+be covered in the third
+
+ align:start position:0%
+be covered in the third
+ 
+
+ align:start position:0%
+be covered in the third
+topic what can I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+erase which is Master
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem so Master theorem does exactly
+
+ align:start position:0%
+theorem so Master theorem does exactly
+ 
+
+ align:start position:0%
+theorem so Master theorem does exactly
+that all it does is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given the
+
+ align:start position:0%
+given the
+ 
+
+ align:start position:0%
+given the
+recursion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a and t of m / B
+
+ align:start position:0%
+a and t of m / B
+ 
+
+ align:start position:0%
+a and t of m / B
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+some work for
+
+ align:start position:0%
+some work for
+ 
+
+ align:start position:0%
+some work for
+merging where A and B are constants it
+
+ align:start position:0%
+merging where A and B are constants it
+ 
+
+ align:start position:0%
+merging where A and B are constants it
+directly tells you what TN is in some
+
+ align:start position:0%
+directly tells you what TN is in some
+ 
+
+ align:start position:0%
+directly tells you what TN is in some
+cases so I'll first write the
+
+ align:start position:0%
+cases so I'll first write the
+ 
+
+ align:start position:0%
+cases so I'll first write the
+formula uh Master theorem has actually
+
+ align:start position:0%
+formula uh Master theorem has actually
+ 
+
+ align:start position:0%
+formula uh Master theorem has actually
+has three cases the first case is
+
+ align:start position:0%
+has three cases the first case is
+ 
+
+ align:start position:0%
+has three cases the first case is
+FN is
+
+ align:start position:0%
+FN is
+ 
+
+ align:start position:0%
+FN is
+order n raised to C where C is less than
+
+ align:start position:0%
+order n raised to C where C is less than
+ 
+
+ align:start position:0%
+order n raised to C where C is less than
+log P of a then Master theorem says it's
+
+ align:start position:0%
+log P of a then Master theorem says it's
+ 
+
+ align:start position:0%
+log P of a then Master theorem says it's
+complexity is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta log B of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A second case
+
+ align:start position:0%
+A second case
+ 
+
+ align:start position:0%
+A second case
+FN is
+
+ align:start position:0%
+FN is
+ 
+
+ align:start position:0%
+FN is
+Theta then C log
+
+ align:start position:0%
+Theta then C log
+ 
+
+ align:start position:0%
+Theta then C log
+K where C
+
+ align:start position:0%
+K where C
+ 
+
+ align:start position:0%
+K where C
+is l b equal
+
+ align:start position:0%
+is l b equal
+ 
+
+ align:start position:0%
+is l b equal
+to B of A then it's comp complexity is n
+
+ align:start position:0%
+to B of A then it's comp complexity is n
+ 
+
+ align:start position:0%
+to B of A then it's comp complexity is n
+raised to C log k + 1
+
+ align:start position:0%
+raised to C log k + 1
+ 
+
+ align:start position:0%
+raised to C log k + 1
+n you don't necessarily have to copy
+
+ align:start position:0%
+n you don't necessarily have to copy
+ 
+
+ align:start position:0%
+n you don't necessarily have to copy
+them Cu uh you can just find them find
+
+ align:start position:0%
+them Cu uh you can just find them find
+ 
+
+ align:start position:0%
+them Cu uh you can just find them find
+it anywhere and the third case you can
+
+ align:start position:0%
+it anywhere and the third case you can
+ 
+
+ align:start position:0%
+it anywhere and the third case you can
+imagine it's the other uh the only
+
+ align:start position:0%
+imagine it's the other uh the only
+ 
+
+ align:start position:0%
+imagine it's the other uh the only
+remaining case which is FN is large is
+
+ align:start position:0%
+remaining case which is FN is large is
+ 
+
+ align:start position:0%
+remaining case which is FN is large is
+Omega n ra to C where C is greater than
+
+ align:start position:0%
+Omega n ra to C where C is greater than
+ 
+
+ align:start position:0%
+Omega n ra to C where C is greater than
+log B of
+
+ align:start position:0%
+log B of
+ 
+
+ align:start position:0%
+log B of
+A then Master theorem says is complexity
+
+ align:start position:0%
+A then Master theorem says is complexity
+ 
+
+ align:start position:0%
+A then Master theorem says is complexity
+of the complexity of TN is
+
+ align:start position:0%
+of the complexity of TN is
+ 
+
+ align:start position:0%
+of the complexity of TN is
+Theta
+
+ align:start position:0%
+Theta
+ 
+
+ align:start position:0%
+Theta
+FN so intuitively if FN is not too much
+
+ align:start position:0%
+FN so intuitively if FN is not too much
+ 
+
+ align:start position:0%
+FN so intuitively if FN is not too much
+work then it's basically this recursion
+
+ align:start position:0%
+work then it's basically this recursion
+ 
+
+ align:start position:0%
+work then it's basically this recursion
+what recursion gives you if FN dominates
+
+ align:start position:0%
+what recursion gives you if FN dominates
+ 
+
+ align:start position:0%
+what recursion gives you if FN dominates
+FN is the uh biggest component then TN
+
+ align:start position:0%
+FN is the uh biggest component then TN
+ 
+
+ align:start position:0%
+FN is the uh biggest component then TN
+is roughly on the order of FN and
+
+ align:start position:0%
+is roughly on the order of FN and
+ 
+
+ align:start position:0%
+is roughly on the order of FN and
+there's a case in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+middle now let's uh see why that is case
+
+ align:start position:0%
+middle now let's uh see why that is case
+ 
+
+ align:start position:0%
+middle now let's uh see why that is case
+uh I'll only cover one case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again we are going to draw a
+
+ align:start position:0%
+so again we are going to draw a
+ 
+
+ align:start position:0%
+so again we are going to draw a
+recursion tree because that is very
+
+ align:start position:0%
+recursion tree because that is very
+ 
+
+ align:start position:0%
+recursion tree because that is very
+useful in all the recursion
+
+ align:start position:0%
+useful in all the recursion
+ 
+
+ align:start position:0%
+useful in all the recursion
+problems so we start with the problem of
+
+ align:start position:0%
+problems so we start with the problem of
+ 
+
+ align:start position:0%
+problems so we start with the problem of
+size
+
+ align:start position:0%
+size
+ 
+
+ align:start position:0%
+size
+n and we break them into problem size n/
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B so on and so forth and what's the size
+
+ align:start position:0%
+B so on and so forth and what's the size
+ 
+
+ align:start position:0%
+B so on and so forth and what's the size
+of this this sub problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that recursion represents a
+
+ align:start position:0%
+okay so that recursion represents a
+ 
+
+ align:start position:0%
+okay so that recursion represents a
+class of recursive
+
+ align:start position:0%
+class of recursive
+ 
+
+ align:start position:0%
+class of recursive
+algorithm every time it breaks the
+
+ align:start position:0%
+algorithm every time it breaks the
+ 
+
+ align:start position:0%
+algorithm every time it breaks the
+problem uh it reduce the problem size by
+
+ align:start position:0%
+problem uh it reduce the problem size by
+ 
+
+ align:start position:0%
+problem uh it reduce the problem size by
+effect of B so what do I have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here go
+
+ align:start position:0%
+here go
+ 
+
+ align:start position:0%
+here go
+ahead n/ B
+
+ align:start position:0%
+ahead n/ B
+ 
+
+ align:start position:0%
+ahead n/ B
+squ so on and so forth so what is a in
+
+ align:start position:0%
+squ so on and so forth so what is a in
+ 
+
+ align:start position:0%
+squ so on and so forth so what is a in
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graph go ahead three I think so three
+
+ align:start position:0%
+graph go ahead three I think so three
+ 
+
+ align:start position:0%
+graph go ahead three I think so three
+right a is just a branching factor of
+
+ align:start position:0%
+right a is just a branching factor of
+ 
+
+ align:start position:0%
+right a is just a branching factor of
+this tree right I keep going finally I
+
+ align:start position:0%
+this tree right I keep going finally I
+ 
+
+ align:start position:0%
+this tree right I keep going finally I
+will reach my base
+
+ align:start position:0%
+will reach my base
+ 
+
+ align:start position:0%
+will reach my base
+case so my next question is after how
+
+ align:start position:0%
+case so my next question is after how
+ 
+
+ align:start position:0%
+case so my next question is after how
+many levels of recursion will I reach a
+
+ align:start position:0%
+many levels of recursion will I reach a
+ 
+
+ align:start position:0%
+many levels of recursion will I reach a
+base case of size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead log B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of log B
+
+ align:start position:0%
+of log B
+ 
+
+ align:start position:0%
+of log B
+of okay so cuz here is n / B N / B
+
+ align:start position:0%
+of okay so cuz here is n / B N / B
+ 
+
+ align:start position:0%
+of okay so cuz here is n / B N / B
+Square next one n b cubic so on and so
+
+ align:start position:0%
+Square next one n b cubic so on and so
+ 
+
+ align:start position:0%
+Square next one n b cubic so on and so
+forth so for the say this last level is
+
+ align:start position:0%
+forth so for the say this last level is
+ 
+
+ align:start position:0%
+forth so for the say this last level is
+teeth level then the problem size is n
+
+ align:start position:0%
+teeth level then the problem size is n
+ 
+
+ align:start position:0%
+teeth level then the problem size is n
+over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B to
+
+ align:start position:0%
+B to
+ 
+
+ align:start position:0%
+B to
+T and we want that to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be a constant so what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t log
+
+ align:start position:0%
+t log
+ 
+
+ align:start position:0%
+t log
+B of
+
+ align:start position:0%
+B of
+ 
+
+ align:start position:0%
+B of
+n this is the recursion tree and we have
+
+ align:start position:0%
+n this is the recursion tree and we have
+ 
+
+ align:start position:0%
+n this is the recursion tree and we have
+that FN amount of merging work to do so
+
+ align:start position:0%
+that FN amount of merging work to do so
+ 
+
+ align:start position:0%
+that FN amount of merging work to do so
+here we have to do FN work right to
+
+ align:start position:0%
+here we have to do FN work right to
+ 
+
+ align:start position:0%
+here we have to do FN work right to
+merge this a results
+
+ align:start position:0%
+merge this a results
+ 
+
+ align:start position:0%
+merge this a results
+to uh the the solution of our problem n
+
+ align:start position:0%
+to uh the the solution of our problem n
+ 
+
+ align:start position:0%
+to uh the the solution of our problem n
+and we have
+
+ align:start position:0%
+and we have
+ 
+
+ align:start position:0%
+and we have
+F what's the merging work for this level
+
+ align:start position:0%
+F what's the merging work for this level
+ 
+
+ align:start position:0%
+F what's the merging work for this level
+for this part of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tree this is my Pro problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size n/ B right and we have a of them
+
+ align:start position:0%
+size n/ B right and we have a of them
+ 
+
+ align:start position:0%
+size n/ B right and we have a of them
+okay so so on and so forth so then we
+
+ align:start position:0%
+okay so so on and so forth so then we
+ 
+
+ align:start position:0%
+okay so so on and so forth so then we
+can we know what is TN let's just
+
+ align:start position:0%
+can we know what is TN let's just
+ 
+
+ align:start position:0%
+can we know what is TN let's just
+enumerate all the work we have to do so
+
+ align:start position:0%
+enumerate all the work we have to do so
+ 
+
+ align:start position:0%
+enumerate all the work we have to do so
+on the first level we have to do
+
+ align:start position:0%
+on the first level we have to do
+ 
+
+ align:start position:0%
+on the first level we have to do
+FN okay on second level
+
+ align:start position:0%
+FN okay on second level
+ 
+
+ align:start position:0%
+FN okay on second level
+a f n of B sorry n/ B and what's the
+
+ align:start position:0%
+a f n of B sorry n/ B and what's the
+ 
+
+ align:start position:0%
+a f n of B sorry n/ B and what's the
+next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level we have how many sub
+
+ align:start position:0%
+level we have how many sub
+ 
+
+ align:start position:0%
+level we have how many sub
+problems speak
+
+ align:start position:0%
+problems speak
+ 
+
+ align:start position:0%
+problems speak
+louder a square sub problems and each of
+
+ align:start position:0%
+louder a square sub problems and each of
+ 
+
+ align:start position:0%
+louder a square sub problems and each of
+them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is n / B
+
+ align:start position:0%
+is n / B
+ 
+
+ align:start position:0%
+is n / B
+S and finally I reach
+
+ align:start position:0%
+S and finally I reach
+ 
+
+ align:start position:0%
+S and finally I reach
+my last
+
+ align:start position:0%
+my last
+ 
+
+ align:start position:0%
+my last
+level they are all base cases so I have
+
+ align:start position:0%
+level they are all base cases so I have
+ 
+
+ align:start position:0%
+level they are all base cases so I have
+a raised to T of them right cuz I Define
+
+ align:start position:0%
+a raised to T of them right cuz I Define
+ 
+
+ align:start position:0%
+a raised to T of them right cuz I Define
+t to be my depth of the tree
+
+ align:start position:0%
+t to be my depth of the tree
+ 
+
+ align:start position:0%
+t to be my depth of the tree
+and each of them is T of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay so that's TN I'm not entirely
+
+ align:start position:0%
+one okay so that's TN I'm not entirely
+ 
+
+ align:start position:0%
+one okay so that's TN I'm not entirely
+happy with this formula because I have
+
+ align:start position:0%
+happy with this formula because I have
+ 
+
+ align:start position:0%
+happy with this formula because I have
+this beautiful pattern here right except
+
+ align:start position:0%
+this beautiful pattern here right except
+ 
+
+ align:start position:0%
+this beautiful pattern here right except
+for the last
+
+ align:start position:0%
+for the last
+ 
+
+ align:start position:0%
+for the last
+guy it's a uh add one a and divide 1 B
+
+ align:start position:0%
+guy it's a uh add one a and divide 1 B
+ 
+
+ align:start position:0%
+guy it's a uh add one a and divide 1 B
+blah blah
+
+ align:start position:0%
+blah blah
+ 
+
+ align:start position:0%
+blah blah
+blah so I'm going to change this T into
+
+ align:start position:0%
+blah so I'm going to change this T into
+ 
+
+ align:start position:0%
+blah so I'm going to change this T into
+F can I do that because the SYM
+
+ align:start position:0%
+F can I do that because the SYM
+ 
+
+ align:start position:0%
+F can I do that because the SYM
+totically it's the same right T1 is a
+
+ align:start position:0%
+totically it's the same right T1 is a
+ 
+
+ align:start position:0%
+totically it's the same right T1 is a
+constant F1 is also a constant then I
+
+ align:start position:0%
+constant F1 is also a constant then I
+ 
+
+ align:start position:0%
+constant F1 is also a constant then I
+get my beautiful form
+
+ align:start position:0%
+get my beautiful form
+ 
+
+ align:start position:0%
+get my beautiful form
+where it's a
+
+ align:start position:0%
+where it's a
+ 
+
+ align:start position:0%
+where it's a
+sum from I equal Z to T what's the
+
+ align:start position:0%
+sum from I equal Z to T what's the
+ 
+
+ align:start position:0%
+sum from I equal Z to T what's the
+what's in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead a raed to I f n / d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i everyone guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that now uh you can roughly see why we
+
+ align:start position:0%
+that now uh you can roughly see why we
+ 
+
+ align:start position:0%
+that now uh you can roughly see why we
+have three
+
+ align:start position:0%
+have three
+ 
+
+ align:start position:0%
+have three
+cases so uh let me deal with the first
+
+ align:start position:0%
+cases so uh let me deal with the first
+ 
+
+ align:start position:0%
+cases so uh let me deal with the first
+case the first case says FN is all
+
+ align:start position:0%
+case the first case says FN is all
+ 
+
+ align:start position:0%
+case the first case says FN is all
+the N rais to
+
+ align:start position:0%
+the N rais to
+ 
+
+ align:start position:0%
+the N rais to
+C right what does that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean it means this guy
+
+ align:start position:0%
+mean it means this guy
+ 
+
+ align:start position:0%
+mean it means this guy
+here is Sigma a ra to n
+
+ align:start position:0%
+here is Sigma a ra to n
+ 
+
+ align:start position:0%
+here is Sigma a ra to n
+then this is what's in my
+
+ align:start position:0%
+then this is what's in my
+ 
+
+ align:start position:0%
+then this is what's in my
+f raised to C okay there should be a
+
+ align:start position:0%
+f raised to C okay there should be a
+ 
+
+ align:start position:0%
+f raised to C okay there should be a
+order here but everything has a order
+
+ align:start position:0%
+order here but everything has a order
+ 
+
+ align:start position:0%
+order here but everything has a order
+before it right so I just admit that so
+
+ align:start position:0%
+before it right so I just admit that so
+ 
+
+ align:start position:0%
+before it right so I just admit that so
+it actually should be this
+
+ align:start position:0%
+it actually should be this
+ 
+
+ align:start position:0%
+it actually should be this
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+this cuz nised to C is actually
+
+ align:start position:0%
+this cuz nised to C is actually
+ 
+
+ align:start position:0%
+this cuz nised to C is actually
+independent of this sum I can put it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what am I left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with is that
+
+ align:start position:0%
+with is that
+ 
+
+ align:start position:0%
+with is that
+correct now this is a sum of geometric
+
+ align:start position:0%
+correct now this is a sum of geometric
+ 
+
+ align:start position:0%
+correct now this is a sum of geometric
+sequence right we know how to solve that
+
+ align:start position:0%
+sequence right we know how to solve that
+ 
+
+ align:start position:0%
+sequence right we know how to solve that
+right uh but we need to check whether
+
+ align:start position:0%
+right uh but we need to check whether
+ 
+
+ align:start position:0%
+right uh but we need to check whether
+this ratio is greater or larger than one
+
+ align:start position:0%
+this ratio is greater or larger than one
+ 
+
+ align:start position:0%
+this ratio is greater or larger than one
+or if it's equal to one and what is this
+
+ align:start position:0%
+or if it's equal to one and what is this
+ 
+
+ align:start position:0%
+or if it's equal to one and what is this
+ratio the case tells us right so C is
+
+ align:start position:0%
+ratio the case tells us right so C is
+ 
+
+ align:start position:0%
+ratio the case tells us right so C is
+less than log B of A that means if I B
+
+ align:start position:0%
+less than log B of A that means if I B
+ 
+
+ align:start position:0%
+less than log B of A that means if I B
+raised to C is less than b raised to
+
+ align:start position:0%
+raised to C is less than b raised to
+ 
+
+ align:start position:0%
+raised to C is less than b raised to
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guy which
+
+ align:start position:0%
+guy which
+ 
+
+ align:start position:0%
+guy which
+is a right so we know our denominator is
+
+ align:start position:0%
+is a right so we know our denominator is
+ 
+
+ align:start position:0%
+is a right so we know our denominator is
+greater than
+
+ align:start position:0%
+greater than
+ 
+
+ align:start position:0%
+greater than
+our is smaller than our numerator so
+
+ align:start position:0%
+our is smaller than our numerator so
+ 
+
+ align:start position:0%
+our is smaller than our numerator so
+this is a a increasing sequence right so
+
+ align:start position:0%
+this is a a increasing sequence right so
+ 
+
+ align:start position:0%
+this is a a increasing sequence right so
+what we have is n rais to C then
+
+ align:start position:0%
+what we have is n rais to C then
+ 
+
+ align:start position:0%
+what we have is n rais to C then
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+thing ra to T minus one divided by this
+
+ align:start position:0%
+thing ra to T minus one divided by this
+ 
+
+ align:start position:0%
+thing ra to T minus one divided by this
+this thing minus one but they are all
+
+ align:start position:0%
+this thing minus one but they are all
+ 
+
+ align:start position:0%
+this thing minus one but they are all
+constants right everyone familiar with
+
+ align:start position:0%
+constants right everyone familiar with
+ 
+
+ align:start position:0%
+constants right everyone familiar with
+the this formula of GE geometric
+
+ align:start position:0%
+the this formula of GE geometric
+ 
+
+ align:start position:0%
+the this formula of GE geometric
+sequence okay so that's what we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have next we have t equals log B of
+
+ align:start position:0%
+have next we have t equals log B of
+ 
+
+ align:start position:0%
+have next we have t equals log B of
+n that
+
+ align:start position:0%
+n that
+ 
+
+ align:start position:0%
+n that
+means V raised to
+
+ align:start position:0%
+means V raised to
+ 
+
+ align:start position:0%
+means V raised to
+T is n
+
+ align:start position:0%
+T is n
+ 
+
+ align:start position:0%
+T is n
+correct so then B raised to T is n then
+
+ align:start position:0%
+correct so then B raised to T is n then
+ 
+
+ align:start position:0%
+correct so then B raised to T is n then
+we have raised to C cancel them can they
+
+ align:start position:0%
+we have raised to C cancel them can they
+ 
+
+ align:start position:0%
+we have raised to C cancel them can they
+cancel out what do we
+
+ align:start position:0%
+cancel out what do we
+ 
+
+ align:start position:0%
+cancel out what do we
+have and make sure everyone is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+mhm a ra to T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no questions you do that St okay let me
+
+ align:start position:0%
+no questions you do that St okay let me
+ 
+
+ align:start position:0%
+no questions you do that St okay let me
+do that again uh okay it's actually a ra
+
+ align:start position:0%
+do that again uh okay it's actually a ra
+ 
+
+ align:start position:0%
+do that again uh okay it's actually a ra
+to T and then n/ BT raised to C right I
+
+ align:start position:0%
+to T and then n/ BT raised to C right I
+ 
+
+ align:start position:0%
+to T and then n/ BT raised to C right I
+mean how did you get from the line above
+
+ align:start position:0%
+mean how did you get from the line above
+ 
+
+ align:start position:0%
+mean how did you get from the line above
+this one to here yeah oh it's the uh sum
+
+ align:start position:0%
+this one to here yeah oh it's the uh sum
+ 
+
+ align:start position:0%
+this one to here yeah oh it's the uh sum
+of geometric sequence so if I have 1 + Q
+
+ align:start position:0%
+of geometric sequence so if I have 1 + Q
+ 
+
+ align:start position:0%
+of geometric sequence so if I have 1 + Q
++ Q ² Plus all the way to QT is
+
+ align:start position:0%
++ Q ² Plus all the way to QT is
+ 
+
+ align:start position:0%
++ Q ² Plus all the way to QT is
+q t + 1 I guess or T I don't remember
+
+ align:start position:0%
+q t + 1 I guess or T I don't remember
+ 
+
+ align:start position:0%
+q t + 1 I guess or T I don't remember
+very well minus one then Q -
+
+ align:start position:0%
+very well minus one then Q -
+ 
+
+ align:start position:0%
+very well minus one then Q -
+one okay I guess this should be t+ one
+
+ align:start position:0%
+one okay I guess this should be t+ one
+ 
+
+ align:start position:0%
+one okay I guess this should be t+ one
+right okay so this what we were doing so
+
+ align:start position:0%
+right okay so this what we were doing so
+ 
+
+ align:start position:0%
+right okay so this what we were doing so
+this is our Q minus one and divided by Q
+
+ align:start position:0%
+this is our Q minus one and divided by Q
+ 
+
+ align:start position:0%
+this is our Q minus one and divided by Q
+-1 they are all constants so I don't
+
+ align:start position:0%
+-1 they are all constants so I don't
+ 
+
+ align:start position:0%
+-1 they are all constants so I don't
+care about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them so a to a ra to t plus this thing
+
+ align:start position:0%
+them so a to a ra to t plus this thing
+ 
+
+ align:start position:0%
+them so a to a ra to t plus this thing
+raised to C but we said that b ra B raed
+
+ align:start position:0%
+raised to C but we said that b ra B raed
+ 
+
+ align:start position:0%
+raised to C but we said that b ra B raed
+to T is equal to n so we're just left
+
+ align:start position:0%
+to T is equal to n so we're just left
+ 
+
+ align:start position:0%
+to T is equal to n so we're just left
+with a ra to
+
+ align:start position:0%
+with a ra to
+ 
+
+ align:start position:0%
+with a ra to
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+and what is
+
+ align:start position:0%
+and what is
+ 
+
+ align:start position:0%
+and what is
+t t is log B of
+
+ align:start position:0%
+t t is log B of
+ 
+
+ align:start position:0%
+t t is log B of
+N I can write it as log a of n over log
+
+ align:start position:0%
+N I can write it as log a of n over log
+ 
+
+ align:start position:0%
+N I can write it as log a of n over log
+a of
+
+ align:start position:0%
+a of
+ 
+
+ align:start position:0%
+a of
+B everyone familiar with
+
+ align:start position:0%
+B everyone familiar with
+ 
+
+ align:start position:0%
+B everyone familiar with
+that that means log a of n log B of A
+
+ align:start position:0%
+that that means log a of n log B of A
+ 
+
+ align:start position:0%
+that that means log a of n log B of A
+okay this one I flipped them so it
+
+ align:start position:0%
+okay this one I flipped them so it
+ 
+
+ align:start position:0%
+okay this one I flipped them so it
+uh so this what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n okay we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh not exactly CU I have an order here
+
+ align:start position:0%
+uh not exactly CU I have an order here
+ 
+
+ align:start position:0%
+uh not exactly CU I have an order here
+right so everything is
+
+ align:start position:0%
+right so everything is
+ 
+
+ align:start position:0%
+right so everything is
+order if you only care about order a big
+
+ align:start position:0%
+order if you only care about order a big
+ 
+
+ align:start position:0%
+order if you only care about order a big
+O then it's fine but that theorem says
+
+ align:start position:0%
+O then it's fine but that theorem says
+ 
+
+ align:start position:0%
+O then it's fine but that theorem says
+Theta so you have to prove it the other
+
+ align:start position:0%
+Theta so you have to prove it the other
+ 
+
+ align:start position:0%
+Theta so you have to prove it the other
+way that it's no less than that okay but
+
+ align:start position:0%
+way that it's no less than that okay but
+ 
+
+ align:start position:0%
+way that it's no less than that okay but
+I'm not going to do that it's not it's
+
+ align:start position:0%
+I'm not going to do that it's not it's
+ 
+
+ align:start position:0%
+I'm not going to do that it's not it's
+not very hard uh next I'm going to apply
+
+ align:start position:0%
+not very hard uh next I'm going to apply
+ 
+
+ align:start position:0%
+not very hard uh next I'm going to apply
+this theorem to the two um problems we
+
+ align:start position:0%
+this theorem to the two um problems we
+ 
+
+ align:start position:0%
+this theorem to the two um problems we
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so let's apply Master theorem to this
+
+ align:start position:0%
+so let's apply Master theorem to this
+ 
+
+ align:start position:0%
+so let's apply Master theorem to this
+recurrence I think you're still looking
+
+ align:start position:0%
+recurrence I think you're still looking
+ 
+
+ align:start position:0%
+recurrence I think you're still looking
+at that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side so what is the a b c for for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this a is 8 B is two right and C
+
+ align:start position:0%
+this a is 8 B is two right and C
+ 
+
+ align:start position:0%
+this a is 8 B is two right and C
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+two log B of A is three
+
+ align:start position:0%
+two log B of A is three
+ 
+
+ align:start position:0%
+two log B of A is three
+so that's the which case of the master
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem okay so the theorem says it
+
+ align:start position:0%
+theorem okay so the theorem says it
+ 
+
+ align:start position:0%
+theorem okay so the theorem says it
+should be n rais to log B of A which is
+
+ align:start position:0%
+should be n rais to log B of A which is
+ 
+
+ align:start position:0%
+should be n rais to log B of A which is
+three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now what we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here can I invite someone to do that for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+want to give it a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+try go
+
+ align:start position:0%
+try go
+ 
+
+ align:start position:0%
+try go
+ahead okay so we
+
+ align:start position:0%
+ahead okay so we
+ 
+
+ align:start position:0%
+ahead okay so we
+have a =
+
+ align:start position:0%
+have a =
+ 
+
+ align:start position:0%
+have a =
+7 b =
+
+ align:start position:0%
+7 b =
+ 
+
+ align:start position:0%
+7 b =
+2 and C = 2 like
+
+ align:start position:0%
+2 and C = 2 like
+ 
+
+ align:start position:0%
+2 and C = 2 like
+before um and now we want to see
+
+ align:start position:0%
+before um and now we want to see
+ 
+
+ align:start position:0%
+before um and now we want to see
+whether uh c = 2 is is less than
+
+ align:start position:0%
+whether uh c = 2 is is less than
+ 
+
+ align:start position:0%
+whether uh c = 2 is is less than
+uh log B
+
+ align:start position:0%
+uh log B
+ 
+
+ align:start position:0%
+uh log B
+of A which is log 2 of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+7 uh
+
+ align:start position:0%
+7 uh
+ 
+
+ align:start position:0%
+7 uh
+and pretty sure that's still the case so
+
+ align:start position:0%
+and pretty sure that's still the case so
+ 
+
+ align:start position:0%
+and pretty sure that's still the case so
+we should just get into
+
+ align:start position:0%
+we should just get into
+ 
+
+ align:start position:0%
+we should just get into
+the log 207 yeah exactly so yeah log 20
+
+ align:start position:0%
+the log 207 yeah exactly so yeah log 20
+ 
+
+ align:start position:0%
+the log 207 yeah exactly so yeah log 20
+yeah thank you let's give him a round of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+applause so log two of seven uh is
+
+ align:start position:0%
+applause so log two of seven uh is
+ 
+
+ align:start position:0%
+applause so log two of seven uh is
+definitely greater than two why because
+
+ align:start position:0%
+definitely greater than two why because
+ 
+
+ align:start position:0%
+definitely greater than two why because
+log two of four is two right so this
+
+ align:start position:0%
+log two of four is two right so this
+ 
+
+ align:start position:0%
+log two of four is two right so this
+happens to be n raised to
+
+ align:start position:0%
+happens to be n raised to
+ 
+
+ align:start position:0%
+happens to be n raised to
+2.80 and many other digits but it's less
+
+ align:start position:0%
+2.80 and many other digits but it's less
+ 
+
+ align:start position:0%
+2.80 and many other digits but it's less
+than in
+
+ align:start position:0%
+than in
+ 
+
+ align:start position:0%
+than in
+cubic and uh just for knowledge purpose
+
+ align:start position:0%
+cubic and uh just for knowledge purpose
+ 
+
+ align:start position:0%
+cubic and uh just for knowledge purpose
+this is no longer the best it it was the
+
+ align:start position:0%
+this is no longer the best it it was the
+ 
+
+ align:start position:0%
+this is no longer the best it it was the
+best when it was proposed and well
+
+ align:start position:0%
+best when it was proposed and well
+ 
+
+ align:start position:0%
+best when it was proposed and well
+researchers in that area has got get it
+
+ align:start position:0%
+researchers in that area has got get it
+ 
+
+ align:start position:0%
+researchers in that area has got get it
+down to n raised to 2.3 5 I think 2.37
+
+ align:start position:0%
+down to n raised to 2.3 5 I think 2.37
+ 
+
+ align:start position:0%
+down to n raised to 2.3 5 I think 2.37
+first then
+
+ align:start position:0%
+first then
+ 
+
+ align:start position:0%
+first then
+2.35 I'm not following the literature
+
+ align:start position:0%
+2.35 I'm not following the literature
+ 
+
+ align:start position:0%
+2.35 I'm not following the literature
+very closely so maybe it's 2.34
+
+ align:start position:0%
+very closely so maybe it's 2.34
+ 
+
+ align:start position:0%
+very closely so maybe it's 2.34
+now okay so I should have one more thing
+
+ align:start position:0%
+now okay so I should have one more thing
+ 
+
+ align:start position:0%
+now okay so I should have one more thing
+to uh cover but I think we are running
+
+ align:start position:0%
+to uh cover but I think we are running
+ 
+
+ align:start position:0%
+to uh cover but I think we are running
+of time sorry about that uh I can post
+
+ align:start position:0%
+of time sorry about that uh I can post
+ 
+
+ align:start position:0%
+of time sorry about that uh I can post
+uh so the last thing we we should do is
+
+ align:start position:0%
+uh so the last thing we we should do is
+ 
+
+ align:start position:0%
+uh so the last thing we we should do is
+remember we have this median finding
+
+ align:start position:0%
+remember we have this median finding
+ 
+
+ align:start position:0%
+remember we have this median finding
+algorithm where we have a recurrence uh
+
+ align:start position:0%
+algorithm where we have a recurrence uh
+ 
+
+ align:start position:0%
+algorithm where we have a recurrence uh
+which is I think n over 5 some C and
+
+ align:start position:0%
+which is I think n over 5 some C and
+ 
+
+ align:start position:0%
+which is I think n over 5 some C and
+then plus uh this right and plus some
+
+ align:start position:0%
+then plus uh this right and plus some
+ 
+
+ align:start position:0%
+then plus uh this right and plus some
+Theta n and uh we want to solve this
+
+ align:start position:0%
+Theta n and uh we want to solve this
+ 
+
+ align:start position:0%
+Theta n and uh we want to solve this
+recursion but we cannot apply Master
+
+ align:start position:0%
+recursion but we cannot apply Master
+ 
+
+ align:start position:0%
+recursion but we cannot apply Master
+theorem right apparently it's not right
+
+ align:start position:0%
+theorem right apparently it's not right
+ 
+
+ align:start position:0%
+theorem right apparently it's not right
+form so we have so when Master theorem
+
+ align:start position:0%
+form so we have so when Master theorem
+ 
+
+ align:start position:0%
+form so we have so when Master theorem
+doesn't apply we have to study it Case
+
+ align:start position:0%
+doesn't apply we have to study it Case
+ 
+
+ align:start position:0%
+doesn't apply we have to study it Case
+by case let me see if I have time to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay I think I probably probably
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do so uh to solve that case first can
+
+ align:start position:0%
+do so uh to solve that case first can
+ 
+
+ align:start position:0%
+do so uh to solve that case first can
+someone tell me what's the definition of
+
+ align:start position:0%
+someone tell me what's the definition of
+ 
+
+ align:start position:0%
+someone tell me what's the definition of
+theta we have to go back to the
+
+ align:start position:0%
+theta we have to go back to the
+ 
+
+ align:start position:0%
+theta we have to go back to the
+definition to solve
+
+ align:start position:0%
+definition to solve
+ 
+
+ align:start position:0%
+definition to solve
+that what does Theta mean even mean so
+
+ align:start position:0%
+that what does Theta mean even mean so
+ 
+
+ align:start position:0%
+that what does Theta mean even mean so
+if I say FN is Theta n what do I really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean go ahead uh it's tightly bounded so
+
+ align:start position:0%
+mean go ahead uh it's tightly bounded so
+ 
+
+ align:start position:0%
+mean go ahead uh it's tightly bounded so
+both our the big go either side great so
+
+ align:start position:0%
+both our the big go either side great so
+ 
+
+ align:start position:0%
+both our the big go either side great so
+it means I can find some K1 and
+
+ align:start position:0%
+it means I can find some K1 and
+ 
+
+ align:start position:0%
+it means I can find some K1 and
+K2 such that this holds when n gets uh
+
+ align:start position:0%
+K2 such that this holds when n gets uh
+ 
+
+ align:start position:0%
+K2 such that this holds when n gets uh
+sufficiently large okay so now we're
+
+ align:start position:0%
+sufficiently large okay so now we're
+ 
+
+ align:start position:0%
+sufficiently large okay so now we're
+going to do an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+induction assuming for all the small n
+
+ align:start position:0%
+induction assuming for all the small n
+ 
+
+ align:start position:0%
+induction assuming for all the small n
+less than capital N uh my TN is bounded
+
+ align:start position:0%
+less than capital N uh my TN is bounded
+ 
+
+ align:start position:0%
+less than capital N uh my TN is bounded
+by this K2 and K1
+
+ align:start position:0%
+by this K2 and K1
+ 
+
+ align:start position:0%
+by this K2 and K1
+thing okay
+
+ align:start position:0%
+thing okay
+ 
+
+ align:start position:0%
+thing okay
+then uh my next step is T of this
+
+ align:start position:0%
+then uh my next step is T of this
+ 
+
+ align:start position:0%
+then uh my next step is T of this
+capital N would be bounded uh I'll do
+
+ align:start position:0%
+capital N would be bounded uh I'll do
+ 
+
+ align:start position:0%
+capital N would be bounded uh I'll do
+the left right side first will be
+
+ align:start position:0%
+the left right side first will be
+ 
+
+ align:start position:0%
+the left right side first will be
+bounded by
+
+ align:start position:0%
+bounded by
+ 
+
+ align:start position:0%
+bounded by
+K2 and 5
+
+ align:start position:0%
+K2 and 5
+ 
+
+ align:start position:0%
+K2 and 5
+cing
+
+ align:start position:0%
+cing
+ 
+
+ align:start position:0%
+cing
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+K2 like things in that uh in the second
+
+ align:start position:0%
+K2 like things in that uh in the second
+ 
+
+ align:start position:0%
+K2 like things in that uh in the second
+term and plus another Theta n so we know
+
+ align:start position:0%
+term and plus another Theta n so we know
+ 
+
+ align:start position:0%
+term and plus another Theta n so we know
+that means it's bounded by some other
+
+ align:start position:0%
+that means it's bounded by some other
+ 
+
+ align:start position:0%
+that means it's bounded by some other
+number I'll say A2 n okay that's the
+
+ align:start position:0%
+number I'll say A2 n okay that's the
+ 
+
+ align:start position:0%
+number I'll say A2 n okay that's the
+definition of theeta
+
+ align:start position:0%
+definition of theeta
+ 
+
+ align:start position:0%
+definition of theeta
+n then can I find I want this to be
+
+ align:start position:0%
+n then can I find I want this to be
+ 
+
+ align:start position:0%
+n then can I find I want this to be
+sorry all of them should be capital n
+
+ align:start position:0%
+sorry all of them should be capital n
+ 
+
+ align:start position:0%
+sorry all of them should be capital n
+capital n capital N I want this to be
+
+ align:start position:0%
+capital n capital N I want this to be
+ 
+
+ align:start position:0%
+capital n capital N I want this to be
+smaller than K2 capital n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right cuz this uh so let me redo this
+
+ align:start position:0%
+right cuz this uh so let me redo this
+ 
+
+ align:start position:0%
+right cuz this uh so let me redo this
+first step this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+roughly 5 of K2
+
+ align:start position:0%
+roughly 5 of K2
+ 
+
+ align:start position:0%
+roughly 5 of K2
+plus 7 / 10 K2 and plus A2 of n plus a
+
+ align:start position:0%
+plus 7 / 10 K2 and plus A2 of n plus a
+ 
+
+ align:start position:0%
+plus 7 / 10 K2 and plus A2 of n plus a
+bunch of constants that I don't care I
+
+ align:start position:0%
+bunch of constants that I don't care I
+ 
+
+ align:start position:0%
+bunch of constants that I don't care I
+want it to be smaller than K2 of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n can I reach that of course I can right
+
+ align:start position:0%
+n can I reach that of course I can right
+ 
+
+ align:start position:0%
+n can I reach that of course I can right
+if I select K2 to be greater then all we
+
+ align:start position:0%
+if I select K2 to be greater then all we
+ 
+
+ align:start position:0%
+if I select K2 to be greater then all we
+have here right what is this this is 9/
+
+ align:start position:0%
+have here right what is this this is 9/
+ 
+
+ align:start position:0%
+have here right what is this this is 9/
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+n 9/ 10 K2 plus A2
+
+ align:start position:0%
+n 9/ 10 K2 plus A2
+ 
+
+ align:start position:0%
+n 9/ 10 K2 plus A2
+right so if I select K2 to be greater
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+than 10 *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A2 is everyone following that when n is
+
+ align:start position:0%
+A2 is everyone following that when n is
+ 
+
+ align:start position:0%
+A2 is everyone following that when n is
+sufficiently large TN should be bounded
+
+ align:start position:0%
+sufficiently large TN should be bounded
+ 
+
+ align:start position:0%
+sufficiently large TN should be bounded
+by k2n right that's my uh that's the
+
+ align:start position:0%
+by k2n right that's my uh that's the
+ 
+
+ align:start position:0%
+by k2n right that's my uh that's the
+induction I'm assuming when n is smaller
+
+ align:start position:0%
+induction I'm assuming when n is smaller
+ 
+
+ align:start position:0%
+induction I'm assuming when n is smaller
+than capital N I have solved them so I
+
+ align:start position:0%
+than capital N I have solved them so I
+ 
+
+ align:start position:0%
+than capital N I have solved them so I
+can use these two and I still The Next
+
+ align:start position:0%
+can use these two and I still The Next
+ 
+
+ align:start position:0%
+can use these two and I still The Next
+Step so there's the other side which is
+
+ align:start position:0%
+Step so there's the other side which is
+ 
+
+ align:start position:0%
+Step so there's the other side which is
+very similar I'm not going to go through
+
+ align:start position:0%
+very similar I'm not going to go through
+ 
+
+ align:start position:0%
+very similar I'm not going to go through
+that all right so uh that's all for
+
+ align:start position:0%
+that all right so uh that's all for
+ 
+
+ align:start position:0%
+that all right so uh that's all for
+today and just to quickly recap we went
+
+ align:start position:0%
+today and just to quickly recap we went
+ 
+
+ align:start position:0%
+today and just to quickly recap we went
+through uh the weighted in scheduling
+
+ align:start position:0%
+through uh the weighted in scheduling
+ 
+
+ align:start position:0%
+through uh the weighted in scheduling
+weighted interval scheduling and string
+
+ align:start position:0%
+weighted interval scheduling and string
+ 
+
+ align:start position:0%
+weighted interval scheduling and string
+algorithm Master theorem and applying
+
+ align:start position:0%
+algorithm Master theorem and applying
+ 
+
+ align:start position:0%
+algorithm Master theorem and applying
+Master theorem and that a case study of
+
+ align:start position:0%
+Master theorem and that a case study of
+ 
+
+ align:start position:0%
+Master theorem and that a case study of
+a new
+
+ align:start position:0%
+a new
+ 
+
+ align:start position:0%
+a new
+recursion okay then thanks everyone for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coming
\ No newline at end of file
diff --git a/0CIdzHHvUjQ.txt b/0CIdzHHvUjQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..011c138d2b991a6394af5fcec3dca41051624c66
--- /dev/null
+++ b/0CIdzHHvUjQ.txt
@@ -0,0 +1,1955 @@
+align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so what are the conditions for a value
+
+ align:start position:0%
+so what are the conditions for a value
+ 
+
+ align:start position:0%
+so what are the conditions for a value
+function that is
+
+ align:start position:0%
+function that is
+ 
+
+ align:start position:0%
+function that is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that the construct of a value function
+
+ align:start position:0%
+that the construct of a value function
+ 
+
+ align:start position:0%
+that the construct of a value function
+that one that is legitimate and size
+
+ align:start position:0%
+that one that is legitimate and size
+ 
+
+ align:start position:0%
+that one that is legitimate and size
+meaningful and unambiguous
+
+ align:start position:0%
+meaningful and unambiguous
+ 
+
+ align:start position:0%
+meaningful and unambiguous
+uh depends upon three
+
+ align:start position:0%
+uh depends upon three
+ 
+
+ align:start position:0%
+uh depends upon three
+actions three assumptions if you wishes
+
+ align:start position:0%
+actions three assumptions if you wishes
+ 
+
+ align:start position:0%
+actions three assumptions if you wishes
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+you might have and i'm going to go
+
+ align:start position:0%
+you might have and i'm going to go
+ 
+
+ align:start position:0%
+you might have and i'm going to go
+through them but by going through them
+
+ align:start position:0%
+through them but by going through them
+ 
+
+ align:start position:0%
+through them but by going through them
+we also recognize when it is not
+
+ align:start position:0%
+we also recognize when it is not
+ 
+
+ align:start position:0%
+we also recognize when it is not
+possible to have a value function and i
+
+ align:start position:0%
+possible to have a value function and i
+ 
+
+ align:start position:0%
+possible to have a value function and i
+want to emphasize that and this
+
+ align:start position:0%
+want to emphasize that and this
+ 
+
+ align:start position:0%
+want to emphasize that and this
+addresses a very important aspect in
+
+ align:start position:0%
+addresses a very important aspect in
+ 
+
+ align:start position:0%
+addresses a very important aspect in
+terms of
+
+ align:start position:0%
+terms of
+ 
+
+ align:start position:0%
+terms of
+optimization in particular but in terms
+
+ align:start position:0%
+optimization in particular but in terms
+ 
+
+ align:start position:0%
+optimization in particular but in terms
+of valuation there's a large branch of
+
+ align:start position:0%
+of valuation there's a large branch of
+ 
+
+ align:start position:0%
+of valuation there's a large branch of
+literature which simply does not
+
+ align:start position:0%
+literature which simply does not
+ 
+
+ align:start position:0%
+literature which simply does not
+recognize this reality and i want to
+
+ align:start position:0%
+recognize this reality and i want to
+ 
+
+ align:start position:0%
+recognize this reality and i want to
+draw your attention to it
+
+ align:start position:0%
+draw your attention to it
+ 
+
+ align:start position:0%
+draw your attention to it
+so there are three actions the first one
+
+ align:start position:0%
+so there are three actions the first one
+ 
+
+ align:start position:0%
+so there are three actions the first one
+is known as completeness or complete
+
+ align:start position:0%
+is known as completeness or complete
+ 
+
+ align:start position:0%
+is known as completeness or complete
+pre-order
+
+ align:start position:0%
+pre-order
+ 
+
+ align:start position:0%
+pre-order
+and it basically says that people in
+
+ align:start position:0%
+and it basically says that people in
+ 
+
+ align:start position:0%
+and it basically says that people in
+fact have preferences overall choices
+
+ align:start position:0%
+fact have preferences overall choices
+ 
+
+ align:start position:0%
+fact have preferences overall choices
+that doesn't in no way means you've
+
+ align:start position:0%
+that doesn't in no way means you've
+ 
+
+ align:start position:0%
+that doesn't in no way means you've
+thought about all the possible choices
+
+ align:start position:0%
+thought about all the possible choices
+ 
+
+ align:start position:0%
+thought about all the possible choices
+but you are capable of making a
+
+ align:start position:0%
+but you are capable of making a
+ 
+
+ align:start position:0%
+but you are capable of making a
+preference there isn't something which
+
+ align:start position:0%
+preference there isn't something which
+ 
+
+ align:start position:0%
+preference there isn't something which
+you could not decide about
+
+ align:start position:0%
+you could not decide about
+ 
+
+ align:start position:0%
+you could not decide about
+and deciding about it permits to say
+
+ align:start position:0%
+and deciding about it permits to say
+ 
+
+ align:start position:0%
+and deciding about it permits to say
+that i'm equally attractive to
+
+ align:start position:0%
+that i'm equally attractive to
+ 
+
+ align:start position:0%
+that i'm equally attractive to
+having chocolate or strawberry ice cream
+
+ align:start position:0%
+having chocolate or strawberry ice cream
+ 
+
+ align:start position:0%
+having chocolate or strawberry ice cream
+that you don't have to necessarily
+
+ align:start position:0%
+that you don't have to necessarily
+ 
+
+ align:start position:0%
+that you don't have to necessarily
+prefer one to the other but you could
+
+ align:start position:0%
+prefer one to the other but you could
+ 
+
+ align:start position:0%
+prefer one to the other but you could
+have a valuation and it's okay to say
+
+ align:start position:0%
+have a valuation and it's okay to say
+ 
+
+ align:start position:0%
+have a valuation and it's okay to say
+a dish of strawberry or chocolate ice
+
+ align:start position:0%
+a dish of strawberry or chocolate ice
+ 
+
+ align:start position:0%
+a dish of strawberry or chocolate ice
+cream has the same value for me it
+
+ align:start position:0%
+cream has the same value for me it
+ 
+
+ align:start position:0%
+cream has the same value for me it
+doesn't mean you have to prefer one to
+
+ align:start position:0%
+doesn't mean you have to prefer one to
+ 
+
+ align:start position:0%
+doesn't mean you have to prefer one to
+the other but you can make choices
+
+ align:start position:0%
+the other but you can make choices
+ 
+
+ align:start position:0%
+the other but you can make choices
+um that is for a
+
+ align:start position:0%
+um that is for a
+ 
+
+ align:start position:0%
+um that is for a
+logical one a lot that's a necessary
+
+ align:start position:0%
+logical one a lot that's a necessary
+ 
+
+ align:start position:0%
+logical one a lot that's a necessary
+assumption
+
+ align:start position:0%
+assumption
+ 
+
+ align:start position:0%
+assumption
+otherwise it doesn't mean if you can't
+
+ align:start position:0%
+otherwise it doesn't mean if you can't
+ 
+
+ align:start position:0%
+otherwise it doesn't mean if you can't
+make preferences you can't have a
+
+ align:start position:0%
+make preferences you can't have a
+ 
+
+ align:start position:0%
+make preferences you can't have a
+function over what happens
+
+ align:start position:0%
+function over what happens
+ 
+
+ align:start position:0%
+function over what happens
+the second one is transitivity
+
+ align:start position:0%
+the second one is transitivity
+ 
+
+ align:start position:0%
+the second one is transitivity
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that is if thing x1 is preferred to
+
+ align:start position:0%
+that is if thing x1 is preferred to
+ 
+
+ align:start position:0%
+that is if thing x1 is preferred to
+thing x2
+
+ align:start position:0%
+thing x2
+ 
+
+ align:start position:0%
+thing x2
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and thing x2 is preferred to thing x3
+
+ align:start position:0%
+and thing x2 is preferred to thing x3
+ 
+
+ align:start position:0%
+and thing x2 is preferred to thing x3
+then it's the preference is transitive
+
+ align:start position:0%
+then it's the preference is transitive
+ 
+
+ align:start position:0%
+then it's the preference is transitive
+that the x1 is better than x2 which is
+
+ align:start position:0%
+that the x1 is better than x2 which is
+ 
+
+ align:start position:0%
+that the x1 is better than x2 which is
+better than x3 therefore x1 is preferred
+
+ align:start position:0%
+better than x3 therefore x1 is preferred
+ 
+
+ align:start position:0%
+better than x3 therefore x1 is preferred
+to x3
+
+ align:start position:0%
+to x3
+ 
+
+ align:start position:0%
+to x3
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um it's assumed true for individuals
+
+ align:start position:0%
+um it's assumed true for individuals
+ 
+
+ align:start position:0%
+um it's assumed true for individuals
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it is true that depending on how you
+
+ align:start position:0%
+it is true that depending on how you
+ 
+
+ align:start position:0%
+it is true that depending on how you
+phrase it there are various
+
+ align:start position:0%
+phrase it there are various
+ 
+
+ align:start position:0%
+phrase it there are various
+ways you can trick people into thinking
+
+ align:start position:0%
+ways you can trick people into thinking
+ 
+
+ align:start position:0%
+ways you can trick people into thinking
+differently about it depending on what
+
+ align:start position:0%
+differently about it depending on what
+ 
+
+ align:start position:0%
+differently about it depending on what
+else the context you put in their known
+
+ align:start position:0%
+else the context you put in their known
+ 
+
+ align:start position:0%
+else the context you put in their known
+examples of it but this is a fairly
+
+ align:start position:0%
+examples of it but this is a fairly
+ 
+
+ align:start position:0%
+examples of it but this is a fairly
+standard one if if you're a strawberry
+
+ align:start position:0%
+standard one if if you're a strawberry
+ 
+
+ align:start position:0%
+standard one if if you're a strawberry
+ice cream fan
+
+ align:start position:0%
+ice cream fan
+ 
+
+ align:start position:0%
+ice cream fan
+and you prefer to chocolate and you
+
+ align:start position:0%
+and you prefer to chocolate and you
+ 
+
+ align:start position:0%
+and you prefer to chocolate and you
+really hate um i don't know
+
+ align:start position:0%
+really hate um i don't know
+ 
+
+ align:start position:0%
+really hate um i don't know
+marshmallow ice cream
+
+ align:start position:0%
+marshmallow ice cream
+ 
+
+ align:start position:0%
+marshmallow ice cream
+then it's presumed that you are
+
+ align:start position:0%
+then it's presumed that you are
+ 
+
+ align:start position:0%
+then it's presumed that you are
+preferring strawberry to marshmallow
+
+ align:start position:0%
+preferring strawberry to marshmallow
+ 
+
+ align:start position:0%
+preferring strawberry to marshmallow
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this is a normal thing the trick here
+
+ align:start position:0%
+this is a normal thing the trick here
+ 
+
+ align:start position:0%
+this is a normal thing the trick here
+that i want to bring to your mind we'll
+
+ align:start position:0%
+that i want to bring to your mind we'll
+ 
+
+ align:start position:0%
+that i want to bring to your mind we'll
+explore it in a moment
+
+ align:start position:0%
+explore it in a moment
+ 
+
+ align:start position:0%
+explore it in a moment
+is that this
+
+ align:start position:0%
+is that this
+ 
+
+ align:start position:0%
+is that this
+fairly obvious
+
+ align:start position:0%
+fairly obvious
+ 
+
+ align:start position:0%
+fairly obvious
+choice
+
+ align:start position:0%
+choice
+ 
+
+ align:start position:0%
+choice
+of a being preferred to be being
+
+ align:start position:0%
+of a being preferred to be being
+ 
+
+ align:start position:0%
+of a being preferred to be being
+preferred to c therefore a is preferred
+
+ align:start position:0%
+preferred to c therefore a is preferred
+ 
+
+ align:start position:0%
+preferred to c therefore a is preferred
+to c
+
+ align:start position:0%
+to c
+ 
+
+ align:start position:0%
+to c
+that is not necessarily true for groups
+
+ align:start position:0%
+that is not necessarily true for groups
+ 
+
+ align:start position:0%
+that is not necessarily true for groups
+so whereas we can have a meaningful
+
+ align:start position:0%
+so whereas we can have a meaningful
+ 
+
+ align:start position:0%
+so whereas we can have a meaningful
+value function for individuals having it
+
+ align:start position:0%
+value function for individuals having it
+ 
+
+ align:start position:0%
+value function for individuals having it
+for groups
+
+ align:start position:0%
+for groups
+ 
+
+ align:start position:0%
+for groups
+is not very plausible
+
+ align:start position:0%
+is not very plausible
+ 
+
+ align:start position:0%
+is not very plausible
+that is i mean i mean when i talk about
+
+ align:start position:0%
+that is i mean i mean when i talk about
+ 
+
+ align:start position:0%
+that is i mean i mean when i talk about
+groups i mean we're talking about a
+
+ align:start position:0%
+groups i mean we're talking about a
+ 
+
+ align:start position:0%
+groups i mean we're talking about a
+board of directors we're talking about a
+
+ align:start position:0%
+board of directors we're talking about a
+ 
+
+ align:start position:0%
+board of directors we're talking about a
+design team we're talking about
+
+ align:start position:0%
+design team we're talking about
+ 
+
+ align:start position:0%
+design team we're talking about
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+a city council we're talking about
+
+ align:start position:0%
+a city council we're talking about
+ 
+
+ align:start position:0%
+a city council we're talking about
+almost anything that you can imagine
+
+ align:start position:0%
+almost anything that you can imagine
+ 
+
+ align:start position:0%
+almost anything that you can imagine
+where you have individuals or factions
+
+ align:start position:0%
+where you have individuals or factions
+ 
+
+ align:start position:0%
+where you have individuals or factions
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+business groups uh talking about things
+
+ align:start position:0%
+business groups uh talking about things
+ 
+
+ align:start position:0%
+business groups uh talking about things
+right now i'm dealing with a company uh
+
+ align:start position:0%
+right now i'm dealing with a company uh
+ 
+
+ align:start position:0%
+right now i'm dealing with a company uh
+in morocco and as with others
+
+ align:start position:0%
+in morocco and as with others
+ 
+
+ align:start position:0%
+in morocco and as with others
+getting decisions made is a tug of war
+
+ align:start position:0%
+getting decisions made is a tug of war
+ 
+
+ align:start position:0%
+getting decisions made is a tug of war
+between the finance people
+
+ align:start position:0%
+between the finance people
+ 
+
+ align:start position:0%
+between the finance people
+the marketing people the industrial
+
+ align:start position:0%
+the marketing people the industrial
+ 
+
+ align:start position:0%
+the marketing people the industrial
+people each have a different set of
+
+ align:start position:0%
+people each have a different set of
+ 
+
+ align:start position:0%
+people each have a different set of
+values as what makes sense from their
+
+ align:start position:0%
+values as what makes sense from their
+ 
+
+ align:start position:0%
+values as what makes sense from their
+point of view and
+
+ align:start position:0%
+point of view and
+ 
+
+ align:start position:0%
+point of view and
+they are
+
+ align:start position:0%
+they are
+ 
+
+ align:start position:0%
+they are
+do not have a consistent uh value
+
+ align:start position:0%
+do not have a consistent uh value
+ 
+
+ align:start position:0%
+do not have a consistent uh value
+function for
+
+ align:start position:0%
+function for
+ 
+
+ align:start position:0%
+function for
+decisions about what to spend money on
+
+ align:start position:0%
+decisions about what to spend money on
+ 
+
+ align:start position:0%
+decisions about what to spend money on
+or how to run the company
+
+ align:start position:0%
+or how to run the company
+ 
+
+ align:start position:0%
+or how to run the company
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+but that's the transitivity one yes
+
+ align:start position:0%
+but that's the transitivity one yes
+ 
+
+ align:start position:0%
+but that's the transitivity one yes
+yeah so i just had a comment on
+
+ align:start position:0%
+yeah so i just had a comment on
+ 
+
+ align:start position:0%
+yeah so i just had a comment on
+transitivity so
+
+ align:start position:0%
+transitivity so
+ 
+
+ align:start position:0%
+transitivity so
+um these are um some of the some of
+
+ align:start position:0%
+um these are um some of the some of
+ 
+
+ align:start position:0%
+um these are um some of the some of
+savage's axioms i'm assuming for um
+
+ align:start position:0%
+savage's axioms i'm assuming for um
+ 
+
+ align:start position:0%
+savage's axioms i'm assuming for um
+subjective expected utility but um the
+
+ align:start position:0%
+subjective expected utility but um the
+ 
+
+ align:start position:0%
+subjective expected utility but um the
+transitivity one
+
+ align:start position:0%
+transitivity one
+ 
+
+ align:start position:0%
+transitivity one
+there was this experiment that was done
+
+ align:start position:0%
+there was this experiment that was done
+ 
+
+ align:start position:0%
+there was this experiment that was done
+and it's called the ellsberg paradox
+
+ align:start position:0%
+and it's called the ellsberg paradox
+ 
+
+ align:start position:0%
+and it's called the ellsberg paradox
+that's that shows that under ambiguity
+
+ align:start position:0%
+that's that shows that under ambiguity
+ 
+
+ align:start position:0%
+that's that shows that under ambiguity
+transitivity doesn't always hold because
+
+ align:start position:0%
+transitivity doesn't always hold because
+ 
+
+ align:start position:0%
+transitivity doesn't always hold because
+people will
+
+ align:start position:0%
+people will
+ 
+
+ align:start position:0%
+people will
+want to choose the
+
+ align:start position:0%
+want to choose the
+ 
+
+ align:start position:0%
+want to choose the
+non-ambiguous option
+
+ align:start position:0%
+non-ambiguous option
+ 
+
+ align:start position:0%
+non-ambiguous option
+usually there's there's a
+
+ align:start position:0%
+usually there's there's a
+ 
+
+ align:start position:0%
+usually there's there's a
+yes well point well taken um and
+
+ align:start position:0%
+yes well point well taken um and
+ 
+
+ align:start position:0%
+yes well point well taken um and
+um there are various ways that as you
+
+ align:start position:0%
+um there are various ways that as you
+ 
+
+ align:start position:0%
+um there are various ways that as you
+say under various ambiguous situations
+
+ align:start position:0%
+say under various ambiguous situations
+ 
+
+ align:start position:0%
+say under various ambiguous situations
+and there's also the alley paradox and
+
+ align:start position:0%
+and there's also the alley paradox and
+ 
+
+ align:start position:0%
+and there's also the alley paradox and
+there's a a cluster of psychological
+
+ align:start position:0%
+there's a a cluster of psychological
+ 
+
+ align:start position:0%
+there's a a cluster of psychological
+experiments where you by
+
+ align:start position:0%
+experiments where you by
+ 
+
+ align:start position:0%
+experiments where you by
+asking a question in the context of
+
+ align:start position:0%
+asking a question in the context of
+ 
+
+ align:start position:0%
+asking a question in the context of
+something else you can sort of get
+
+ align:start position:0%
+something else you can sort of get
+ 
+
+ align:start position:0%
+something else you can sort of get
+people to focus on different aspects so
+
+ align:start position:0%
+people to focus on different aspects so
+ 
+
+ align:start position:0%
+people to focus on different aspects so
+you can there
+
+ align:start position:0%
+you can there
+ 
+
+ align:start position:0%
+you can there
+there's a range of exceptions but in
+
+ align:start position:0%
+there's a range of exceptions but in
+ 
+
+ align:start position:0%
+there's a range of exceptions but in
+general um
+
+ align:start position:0%
+general um
+ 
+
+ align:start position:0%
+general um
+uh this is an acceptable one and my
+
+ align:start position:0%
+uh this is an acceptable one and my
+ 
+
+ align:start position:0%
+uh this is an acceptable one and my
+point here is not so much to say that it
+
+ align:start position:0%
+point here is not so much to say that it
+ 
+
+ align:start position:0%
+point here is not so much to say that it
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+there aren't exceptions it is that in
+
+ align:start position:0%
+there aren't exceptions it is that in
+ 
+
+ align:start position:0%
+there aren't exceptions it is that in
+this case it's relatively okay if you
+
+ align:start position:0%
+this case it's relatively okay if you
+ 
+
+ align:start position:0%
+this case it's relatively okay if you
+had to think about your own decisions um
+
+ align:start position:0%
+had to think about your own decisions um
+ 
+
+ align:start position:0%
+had to think about your own decisions um
+but when we get to groups it is
+
+ align:start position:0%
+but when we get to groups it is
+ 
+
+ align:start position:0%
+but when we get to groups it is
+definitely not okay that's that's the
+
+ align:start position:0%
+definitely not okay that's that's the
+ 
+
+ align:start position:0%
+definitely not okay that's that's the
+point i want to uh emphasize in this
+
+ align:start position:0%
+point i want to uh emphasize in this
+ 
+
+ align:start position:0%
+point i want to uh emphasize in this
+context so
+
+ align:start position:0%
+context so
+ 
+
+ align:start position:0%
+context so
+well done from a um
+
+ align:start position:0%
+well done from a um
+ 
+
+ align:start position:0%
+well done from a um
+an advanced doctoral student who studied
+
+ align:start position:0%
+an advanced doctoral student who studied
+ 
+
+ align:start position:0%
+an advanced doctoral student who studied
+this and you're absolutely correct but
+
+ align:start position:0%
+this and you're absolutely correct but
+ 
+
+ align:start position:0%
+this and you're absolutely correct but
+for the that's yeah let me just leave it
+
+ align:start position:0%
+for the that's yeah let me just leave it
+ 
+
+ align:start position:0%
+for the that's yeah let me just leave it
+at that well said i appreciate your
+
+ align:start position:0%
+at that well said i appreciate your
+ 
+
+ align:start position:0%
+at that well said i appreciate your
+comment it's excellent
+
+ align:start position:0%
+comment it's excellent
+ 
+
+ align:start position:0%
+comment it's excellent
+um good going
+
+ align:start position:0%
+um good going
+ 
+
+ align:start position:0%
+um good going
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so the third one is the sometimes called
+
+ align:start position:0%
+so the third one is the sometimes called
+ 
+
+ align:start position:0%
+so the third one is the sometimes called
+the our comedian principle the
+
+ align:start position:0%
+the our comedian principle the
+ 
+
+ align:start position:0%
+the our comedian principle the
+multnicity
+
+ align:start position:0%
+multnicity
+ 
+
+ align:start position:0%
+multnicity
+but it basically says that if we
+
+ align:start position:0%
+but it basically says that if we
+ 
+
+ align:start position:0%
+but it basically says that if we
+are looking between a range
+
+ align:start position:0%
+are looking between a range
+ 
+
+ align:start position:0%
+are looking between a range
+um which is the thing at the top between
+
+ align:start position:0%
+um which is the thing at the top between
+ 
+
+ align:start position:0%
+um which is the thing at the top between
+the best of something or the most of
+
+ align:start position:0%
+the best of something or the most of
+ 
+
+ align:start position:0%
+the best of something or the most of
+something and the worst of something
+
+ align:start position:0%
+something and the worst of something
+ 
+
+ align:start position:0%
+something and the worst of something
+for anything in between
+
+ align:start position:0%
+for anything in between
+ 
+
+ align:start position:0%
+for anything in between
+that the value the thing in between is a
+
+ align:start position:0%
+that the value the thing in between is a
+ 
+
+ align:start position:0%
+that the value the thing in between is a
+waiting function
+
+ align:start position:0%
+waiting function
+ 
+
+ align:start position:0%
+waiting function
+that is a sum proportion such that the
+
+ align:start position:0%
+that is a sum proportion such that the
+ 
+
+ align:start position:0%
+that is a sum proportion such that the
+value of the thing in between is a
+
+ align:start position:0%
+value of the thing in between is a
+ 
+
+ align:start position:0%
+value of the thing in between is a
+certain proportion of the best and the
+
+ align:start position:0%
+certain proportion of the best and the
+ 
+
+ align:start position:0%
+certain proportion of the best and the
+complementary proportion of the worst it
+
+ align:start position:0%
+complementary proportion of the worst it
+ 
+
+ align:start position:0%
+complementary proportion of the worst it
+basically says that the valuation may be
+
+ align:start position:0%
+basically says that the valuation may be
+ 
+
+ align:start position:0%
+basically says that the valuation may be
+going up all the time or maybe going
+
+ align:start position:0%
+going up all the time or maybe going
+ 
+
+ align:start position:0%
+going up all the time or maybe going
+down all the time but it's not going up
+
+ align:start position:0%
+down all the time but it's not going up
+ 
+
+ align:start position:0%
+down all the time but it's not going up
+and then down or up and and down and up
+
+ align:start position:0%
+and then down or up and and down and up
+ 
+
+ align:start position:0%
+and then down or up and and down and up
+that is it is basically monotonic so
+
+ align:start position:0%
+that is it is basically monotonic so
+ 
+
+ align:start position:0%
+that is it is basically monotonic so
+that you can think about something being
+
+ align:start position:0%
+that you can think about something being
+ 
+
+ align:start position:0%
+that you can think about something being
+better than something and some others
+
+ align:start position:0%
+better than something and some others
+ 
+
+ align:start position:0%
+better than something and some others
+thing being better if you uh don't have
+
+ align:start position:0%
+thing being better if you uh don't have
+ 
+
+ align:start position:0%
+thing being better if you uh don't have
+that you can't have be transitive
+
+ align:start position:0%
+that you can't have be transitive
+ 
+
+ align:start position:0%
+that you can't have be transitive
+so um the question is then
+
+ align:start position:0%
+so um the question is then
+ 
+
+ align:start position:0%
+so um the question is then
+well okay is this a reasonable thing
+
+ align:start position:0%
+well okay is this a reasonable thing
+ 
+
+ align:start position:0%
+well okay is this a reasonable thing
+because if you want a consistent way to
+
+ align:start position:0%
+because if you want a consistent way to
+ 
+
+ align:start position:0%
+because if you want a consistent way to
+value something so if you're saying i'm
+
+ align:start position:0%
+value something so if you're saying i'm
+ 
+
+ align:start position:0%
+value something so if you're saying i'm
+saving lives or making money that more
+
+ align:start position:0%
+saving lives or making money that more
+ 
+
+ align:start position:0%
+saving lives or making money that more
+more is always better or less less less
+
+ align:start position:0%
+more is always better or less less less
+ 
+
+ align:start position:0%
+more is always better or less less less
+is always better that there isn't a
+
+ align:start position:0%
+is always better that there isn't a
+ 
+
+ align:start position:0%
+is always better that there isn't a
+point where you say well it's good to
+
+ align:start position:0%
+point where you say well it's good to
+ 
+
+ align:start position:0%
+point where you say well it's good to
+have so much but then i've had more
+
+ align:start position:0%
+have so much but then i've had more
+ 
+
+ align:start position:0%
+have so much but then i've had more
+money that's really bad or i've saved
+
+ align:start position:0%
+money that's really bad or i've saved
+ 
+
+ align:start position:0%
+money that's really bad or i've saved
+lives but if i save more it's really bad
+
+ align:start position:0%
+lives but if i save more it's really bad
+ 
+
+ align:start position:0%
+lives but if i save more it's really bad
+or worse so it's is it a reasonable
+
+ align:start position:0%
+or worse so it's is it a reasonable
+ 
+
+ align:start position:0%
+or worse so it's is it a reasonable
+assumption i mean it's a necessary
+
+ align:start position:0%
+assumption i mean it's a necessary
+ 
+
+ align:start position:0%
+assumption i mean it's a necessary
+assumption for a consistent value
+
+ align:start position:0%
+assumption for a consistent value
+ 
+
+ align:start position:0%
+assumption for a consistent value
+function but it is reasonable
+
+ align:start position:0%
+function but it is reasonable
+ 
+
+ align:start position:0%
+function but it is reasonable
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+no it's not always true and the reason i
+
+ align:start position:0%
+no it's not always true and the reason i
+ 
+
+ align:start position:0%
+no it's not always true and the reason i
+bring it up and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's continue on here
+
+ align:start position:0%
+let's continue on here
+ 
+
+ align:start position:0%
+let's continue on here
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's look at some examples cases um
+
+ align:start position:0%
+let's look at some examples cases um
+ 
+
+ align:start position:0%
+let's look at some examples cases um
+if i have sound from a speaker
+
+ align:start position:0%
+if i have sound from a speaker
+ 
+
+ align:start position:0%
+if i have sound from a speaker
+uh i want loud enough so i can hear it
+
+ align:start position:0%
+uh i want loud enough so i can hear it
+ 
+
+ align:start position:0%
+uh i want loud enough so i can hear it
+but at some point if the sound got too
+
+ align:start position:0%
+but at some point if the sound got too
+ 
+
+ align:start position:0%
+but at some point if the sound got too
+loud
+
+ align:start position:0%
+loud
+ 
+
+ align:start position:0%
+loud
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+maybe it's just because i'm older than
+
+ align:start position:0%
+maybe it's just because i'm older than
+ 
+
+ align:start position:0%
+maybe it's just because i'm older than
+the youngest people who might like it
+
+ align:start position:0%
+the youngest people who might like it
+ 
+
+ align:start position:0%
+the youngest people who might like it
+really booming but at some point it's
+
+ align:start position:0%
+really booming but at some point it's
+ 
+
+ align:start position:0%
+really booming but at some point it's
+just too loud for me i can't do it
+
+ align:start position:0%
+just too loud for me i can't do it
+ 
+
+ align:start position:0%
+just too loud for me i can't do it
+do i like salt in my food or sugar in my
+
+ align:start position:0%
+do i like salt in my food or sugar in my
+ 
+
+ align:start position:0%
+do i like salt in my food or sugar in my
+coffee or whatever well
+
+ align:start position:0%
+coffee or whatever well
+ 
+
+ align:start position:0%
+coffee or whatever well
+more is better up to a point until more
+
+ align:start position:0%
+more is better up to a point until more
+ 
+
+ align:start position:0%
+more is better up to a point until more
+is worse
+
+ align:start position:0%
+is worse
+ 
+
+ align:start position:0%
+is worse
+so the point being this valuation can be
+
+ align:start position:0%
+so the point being this valuation can be
+ 
+
+ align:start position:0%
+so the point being this valuation can be
+very complicated
+
+ align:start position:0%
+very complicated
+ 
+
+ align:start position:0%
+very complicated
+now we get around this in many cases by
+
+ align:start position:0%
+now we get around this in many cases by
+ 
+
+ align:start position:0%
+now we get around this in many cases by
+saying
+
+ align:start position:0%
+saying
+ 
+
+ align:start position:0%
+saying
+say the salt on the food we can say all
+
+ align:start position:0%
+say the salt on the food we can say all
+ 
+
+ align:start position:0%
+say the salt on the food we can say all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+um i don't mind having more salt it's
+
+ align:start position:0%
+um i don't mind having more salt it's
+ 
+
+ align:start position:0%
+um i don't mind having more salt it's
+always better to have more salt on the
+
+ align:start position:0%
+always better to have more salt on the
+ 
+
+ align:start position:0%
+always better to have more salt on the
+table i suppose but i don't have to use
+
+ align:start position:0%
+table i suppose but i don't have to use
+ 
+
+ align:start position:0%
+table i suppose but i don't have to use
+it so having it available is not the
+
+ align:start position:0%
+it so having it available is not the
+ 
+
+ align:start position:0%
+it so having it available is not the
+same thing as having to use it
+
+ align:start position:0%
+same thing as having to use it
+ 
+
+ align:start position:0%
+same thing as having to use it
+so in that case you can just assume you
+
+ align:start position:0%
+so in that case you can just assume you
+ 
+
+ align:start position:0%
+so in that case you can just assume you
+can think through the problem of saying
+
+ align:start position:0%
+can think through the problem of saying
+ 
+
+ align:start position:0%
+can think through the problem of saying
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+at a certain point i don't benefit any
+
+ align:start position:0%
+at a certain point i don't benefit any
+ 
+
+ align:start position:0%
+at a certain point i don't benefit any
+more from it so it levels off but it's
+
+ align:start position:0%
+more from it so it levels off but it's
+ 
+
+ align:start position:0%
+more from it so it levels off but it's
+not worse to have it available so there
+
+ align:start position:0%
+not worse to have it available so there
+ 
+
+ align:start position:0%
+not worse to have it available so there
+are ways around this particular thing
+
+ align:start position:0%
+are ways around this particular thing
+ 
+
+ align:start position:0%
+are ways around this particular thing
+but what i want to
+
+ align:start position:0%
+but what i want to
+ 
+
+ align:start position:0%
+but what i want to
+emphasize here that
+
+ align:start position:0%
+emphasize here that
+ 
+
+ align:start position:0%
+emphasize here that
+uh there is this
+
+ align:start position:0%
+uh there is this
+ 
+
+ align:start position:0%
+uh there is this
+monotonic this monotonicity assumption
+
+ align:start position:0%
+monotonic this monotonicity assumption
+ 
+
+ align:start position:0%
+monotonic this monotonicity assumption
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it doesn't always uh apply unless you
+
+ align:start position:0%
+it doesn't always uh apply unless you
+ 
+
+ align:start position:0%
+it doesn't always uh apply unless you
+work your way around it and in some way
\ No newline at end of file
diff --git a/0oqHExM3_Ko.txt b/0oqHExM3_Ko.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bbeaa957c6152da1fdadb2b728aee522c5fbc1cb
--- /dev/null
+++ b/0oqHExM3_Ko.txt
@@ -0,0 +1,619 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK, welcome back.
+
+We're going to be looking at
+problem number 11 in the fall
+
+2009 final exam.
+
+This is one of those problems on
+the exam that kind of tests
+
+a whole bunch of other
+stuff we couldn't get
+
+into one big question.
+
+So it's looking at a bunch
+of different areas.
+
+But the main themes are going
+to be bonding and reaction
+
+rates and half lives.
+
+So the things I think you need
+to know, the W I N list as I
+
+usually call it, you
+need to understand
+
+reaction rate orders.
+
+What they mean, how they
+apply to reactions.
+
+What a half life is and
+how you use that.
+
+And the third thing is melting
+points and how they are
+
+related to intermolecular forces
+and how intermolecular
+
+forces affect melting points.
+
+So review these three things and
+once you've got them under
+
+your belt then let's attempt
+the problem.
+
+So let's start the problem.
+
+The first part is asking us to
+determine the half life for a
+
+particular reaction.
+
+So there's two places
+you could start.
+
+We saw both answers.
+
+You could start with the
+definition of half life.
+
+If you've got it down on your
+equation sheet, you could just
+
+say, well I know this is the
+equation which is the natural
+
+log of the starting
+concentration--
+
+c naught--
+
+divided by the current
+concentration that you're
+
+looking at-- c--
+
+equals kt, where t is time and
+k is your constant for k.
+
+Or your reaction
+rate constant.
+
+Or-- and this is the place
+that I would recommend
+
+starting because it's
+universally useful to use for
+
+doing kinetics problems
+and also for
+
+doing half life decays--
+
+you start with your
+rate equation.
+
+This is a very general rate
+equation, which I'm going to
+
+show you how it can be
+transformed to solve this very
+
+simple problem.
+
+We're told here that we're
+looking at the half life of a
+
+particular reagent,
+it's not listed.
+
+And we're also told
+that it falls by
+
+factor of 11 in 11 minutes.
+
+Because we're looking at one
+material, we don't need two
+
+different items. So we're
+just going to look at a.
+
+Let's forget about b.
+
+There's no b.
+
+OK, we're just looking at
+how a changes over time.
+
+We're also told that
+it's first order.
+
+So we're given this information
+in the problem.
+
+First order means that you
+have an n equal to 1.
+
+So n equals 1, which turns this
+equation into k times the
+
+concentration of species a.
+
+We also know that rate is
+nothing more than the changing
+
+concentration with respect
+to the change in time.
+
+So in calculus that
+would be da / dt.
+
+So looking at this now, we've
+already got a differential
+
+equation, which we can solve
+and given certain boundary
+
+conditions we can apply as
+a naught as our starting
+
+concentration, we can create
+a new equation.
+
+So the way we're going to do
+this is we're going to do the
+
+calculus-- which I'm not going
+to do for you here--
+
+it's very simply you're going
+to find this equation.
+
+This is all coming from the
+very general rate equation
+
+that we started with.
+
+So there we are.
+
+That's where we're at and you'll
+notice if I bring this
+
+a to the other side, I take
+the natural log, I put a
+
+negative sign in there, I return
+back to my original
+
+equation that I sort
+of luckily--
+
+or didn't luckily-- have
+on my equation sheet.
+
+So now we've got
+this equation.
+
+And now we can actually go ahead
+and solve the first part
+
+of the problem very easily.
+
+So I'm going to move
+over here.
+
+We're going to start off.
+
+We're going to say we're told
+that in 11 minutes we have now
+
+1/11 of the concentration
+we originally had.
+
+So let me write that
+mathematically for you.
+
+I'm going to write a naught
+as my starting
+
+concentration of a.
+
+So in 11 minutes we're going to
+have 1/11 a naught a naught
+
+e to the negative k.
+
+And that occurs in 11 minutes.
+
+Just express the statement
+mathematically.
+
+We've can cancel out these a
+naughts so they don't matter.
+
+Which is good because we
+don't know what it is
+
+in the first place.
+
+And now we can rearrange this
+equation pretty simply.
+
+We can just do it as,
+solve for k, our
+
+reaction rate constant.
+
+That's going to be negative
+1/11, natural log of 1/11.
+
+That's k.
+
+And now we have a value for k.
+
+Now that we know the value
+for k we can go back and
+
+find the half life.
+
+And half life is simply defined
+very, very similar to
+
+how we approached the problem
+to begin with.
+
+Half life is how long it takes
+for the concentration to drop
+
+from its original value to half
+of that original value.
+
+So let me write that now
+in mathematical terms.
+
+In this problem we know
+k now but we don't
+
+know the half life.
+
+We don't know t 1/2.
+
+I'm going to call it t 1/2 to
+designate it and to mark it
+
+differently than before.
+
+Again we can cancel these off.
+
+And now we can solve.
+
+Because we know k.
+
+So let's plug in everything.
+
+We can reverse everything.
+
+So let me do that for you.
+
+We're going to have this.
+
+Natural log of 1/2 being equal
+to negative k, t to the 1/2.
+
+And now we can solve for our t
+1/2 because we know that k--
+
+let's bring k to the
+other side, and the
+
+negative sign as well--
+
+k is going to be negative
+1/11 natural log 1/11.
+
+We can then change natural log
+1/2 into natural log 2.
+
+That actually looks like our
+original half life equation if
+
+you had that on your
+equation sheet.
+
+So when you solve this out,
+you're solving for t 1/2, t
+
+1/2 the long and the short
+of it is 3.18 minutes.
+
+The main takeaway from this
+problem is that you don't need
+
+to have memorized any number
+of equations to do it.
+
+You can start from a very
+general equation, which is the
+
+rate equation, which we showed
+in the beginning, and go from
+
+there using logic and then just
+mathematically represent
+
+what the problem is telling you
+to do in the first place.
+
+So that's part A and that's the
+majority of the points on
+
+this problem.
+
+Moving over, part B and C are
+very quick, very short.
+
+Just to check if you
+know the facts.
+
+Let's do them right now.
+
+We're asking you--
+
+we're going to do B 1
+and B 2 together--
+
+to tell us which one of
+the compounds has a
+
+higher boiling point.
+
+And we give you two
+different cases.
+
+In each case there's
+two compounds.
+
+So number 1, you're given
+silene and phosphene.
+
+So the first thing you should
+do is actually draw those
+
+molecules out.
+
+So that's what I did.
+
+Silene looks like this.
+
+And then phosphene--
+
+put the bonds in there--
+
+phosphene looks something
+like this.
+
+So now we have to sort of
+identify which one of these
+
+has a higher melting point.
+
+Now in order to do that you need
+to have reviewed and know
+
+that melting point is related
+to the intermolecular forces
+
+between the between
+the molecules.
+
+The forces between the molecules
+are dependent on
+
+both their geometry and
+their chemistry.
+
+So knowing that, if something
+has stronger intermolecular
+
+bonds, it'll have a higher
+melting point.
+
+So let's take a look at
+these two molecules.
+
+Which one has stronger
+intermolecular bonds?
+
+We have in silene case, we have
+van der Waals forces,
+
+they're generally very weak.
+
+We've got those tpo
+for the phosphene.
+
+But in phosphene we additionally
+have a dipole.
+
+We have partial--
+
+we put maybe delta minus here
+and delta plus here and here
+
+on this side.
+
+So our molecule is actually
+polarized.
+
+There's a plus region
+and a minus region.
+
+And because of that you have
+much stronger intermolecular
+
+forces between the phosphenes
+then you do the silenes.
+
+And because these have stronger
+intermolecular
+
+forces, this one has a
+higher melting point.
+
+The last part of the
+problem, part 2.
+
+We try to throw a little trick
+in there with you.
+
+We look at ammonia
+and phosphene.
+
+So now we're doing
+NH3 and PH3.
+
+And they actually both
+look identical in
+
+terms of their geometry.
+
+So let me do that now.
+
+It actually looks tetragonal
+if you were to draw the
+
+structure out.
+
+There's ammonia and here's
+our phosphene again.
+
+You can tell they
+look the same.
+
+So I think you have to sort of
+reason out which one has the
+
+higher melting point, which is
+the same thing as saying which
+
+one has stronger intermolecular
+forces.
+
+A very common answer we got
+was that the nitrogen is a
+
+smaller atom, therefore
+everything is held more
+
+closely, therefore the
+forces are stronger.
+
+That's not really the answer
+that is most dominant and it's
+
+also not the answer we
+were looking for.
+
+The correct answer here is that
+even though both of these
+
+have the same--
+
+probably very similar-- van der
+Waals forces, they're both
+
+polarized molecules, nitrogen
+has hydrogen bonding.
+
+So remember the hydrogen bonding
+elements you should
+
+probably know are fluorine,
+oxygen, chlorine, nitrogen,
+
+four of them.
+
+So nitrogen will hydrogen bond,
+which means that this
+
+nitrogen will have a hydrogen
+bond with some other ammonia
+
+molecule over here.
+
+This H might be bonded to
+an N somewhere else.
+
+And because there are additional
+hydrogen bonding
+
+force in the system, the
+intermolecular forces are
+
+stronger and more prevalent in
+ammonia, which means that
+
+ammonia will have a higher
+boiling point, which is true.
+
+The answer here is ammonia.
+
+So all you have to take way
+from this is that the
+
+mechanical properties as well
+as the melting and boiling
+
+properties of a material are
+very much governed by the
+
+intermolecular forces that
+exist in that particular
+
+material, that the liquid
+or the solid state.
+
+And so in this case we're
+looking at these compounds and
+
+we've identified this one as
+being a higher melting point
+
+because it has a polarity
+whereas this one doesn't.
+
+And in this case where we try to
+trick you up, we identified
+
+that nitrogen has
+this additional
+
+hydrogen bonding force.
+
+And that's all there is to it.
\ No newline at end of file
diff --git a/1cEXNLP5uE0.txt b/1cEXNLP5uE0.txt
new file mode 100644
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--- /dev/null
+++ b/1cEXNLP5uE0.txt
@@ -0,0 +1,5571 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ocw.mit.edu
+ 
+
+ align:start position:0%
+ocw.mit.edu
+I'm sure you'll agree with me when I say
+
+ align:start position:0%
+I'm sure you'll agree with me when I say
+ 
+
+ align:start position:0%
+I'm sure you'll agree with me when I say
+that lasers are fantastic
+
+ align:start position:0%
+that lasers are fantastic
+ 
+
+ align:start position:0%
+that lasers are fantastic
+devices in fact every day we hear of
+
+ align:start position:0%
+devices in fact every day we hear of
+ 
+
+ align:start position:0%
+devices in fact every day we hear of
+more and more
+
+ align:start position:0%
+more and more
+ 
+
+ align:start position:0%
+more and more
+applications I don't think there's a
+
+ align:start position:0%
+applications I don't think there's a
+ 
+
+ align:start position:0%
+applications I don't think there's a
+field that has not been touched by the
+
+ align:start position:0%
+field that has not been touched by the
+ 
+
+ align:start position:0%
+field that has not been touched by the
+laser course most of us are familiar
+
+ align:start position:0%
+laser course most of us are familiar
+ 
+
+ align:start position:0%
+laser course most of us are familiar
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+supermarket checkout counters with the
+
+ align:start position:0%
+supermarket checkout counters with the
+ 
+
+ align:start position:0%
+supermarket checkout counters with the
+laser uh barcode readers as well as
+
+ align:start position:0%
+laser uh barcode readers as well as
+ 
+
+ align:start position:0%
+laser uh barcode readers as well as
+laser discs and uh laser printers and
+
+ align:start position:0%
+laser discs and uh laser printers and
+ 
+
+ align:start position:0%
+laser discs and uh laser printers and
+now we having uh laser fiber optic
+
+ align:start position:0%
+now we having uh laser fiber optic
+ 
+
+ align:start position:0%
+now we having uh laser fiber optic
+communication systems but there are all
+
+ align:start position:0%
+communication systems but there are all
+ 
+
+ align:start position:0%
+communication systems but there are all
+sorts of other applications that some of
+
+ align:start position:0%
+sorts of other applications that some of
+ 
+
+ align:start position:0%
+sorts of other applications that some of
+us uh don't know too much about for
+
+ align:start position:0%
+us uh don't know too much about for
+ 
+
+ align:start position:0%
+us uh don't know too much about for
+example uh laser surgery is now becoming
+
+ align:start position:0%
+example uh laser surgery is now becoming
+ 
+
+ align:start position:0%
+example uh laser surgery is now becoming
+very important as well as retinal uh
+
+ align:start position:0%
+very important as well as retinal uh
+ 
+
+ align:start position:0%
+very important as well as retinal uh
+welding and so on materials processing
+
+ align:start position:0%
+welding and so on materials processing
+ 
+
+ align:start position:0%
+welding and so on materials processing
+when it comes to sensors or laser
+
+ align:start position:0%
+when it comes to sensors or laser
+ 
+
+ align:start position:0%
+when it comes to sensors or laser
+sensors lasers can measure almost
+
+ align:start position:0%
+sensors lasers can measure almost
+ 
+
+ align:start position:0%
+sensors lasers can measure almost
+anything and sometime they do it very
+
+ align:start position:0%
+anything and sometime they do it very
+ 
+
+ align:start position:0%
+anything and sometime they do it very
+well for example in uh for navigation
+
+ align:start position:0%
+well for example in uh for navigation
+ 
+
+ align:start position:0%
+well for example in uh for navigation
+systems the laser gyroscopes uh that are
+
+ align:start position:0%
+systems the laser gyroscopes uh that are
+ 
+
+ align:start position:0%
+systems the laser gyroscopes uh that are
+used uh right now in lots of
+
+ align:start position:0%
+used uh right now in lots of
+ 
+
+ align:start position:0%
+used uh right now in lots of
+airplanes um also we have things like 3D
+
+ align:start position:0%
+airplanes um also we have things like 3D
+ 
+
+ align:start position:0%
+airplanes um also we have things like 3D
+imaging using holography which we've
+
+ align:start position:0%
+imaging using holography which we've
+ 
+
+ align:start position:0%
+imaging using holography which we've
+never uh had
+
+ align:start position:0%
+never uh had
+ 
+
+ align:start position:0%
+never uh had
+before the uh even Optical
+
+ align:start position:0%
+before the uh even Optical
+ 
+
+ align:start position:0%
+before the uh even Optical
+computers are now being taken a little
+
+ align:start position:0%
+computers are now being taken a little
+ 
+
+ align:start position:0%
+computers are now being taken a little
+bit more
+
+ align:start position:0%
+bit more
+ 
+
+ align:start position:0%
+bit more
+seriously as well as the numerous
+
+ align:start position:0%
+seriously as well as the numerous
+ 
+
+ align:start position:0%
+seriously as well as the numerous
+applications in fundamental physics
+
+ align:start position:0%
+applications in fundamental physics
+ 
+
+ align:start position:0%
+applications in fundamental physics
+chemistry history and so on so you can
+
+ align:start position:0%
+chemistry history and so on so you can
+ 
+
+ align:start position:0%
+chemistry history and so on so you can
+see there are lots of applications for
+
+ align:start position:0%
+see there are lots of applications for
+ 
+
+ align:start position:0%
+see there are lots of applications for
+lasers now to learn about lasers and the
+
+ align:start position:0%
+lasers now to learn about lasers and the
+ 
+
+ align:start position:0%
+lasers now to learn about lasers and the
+associated
+
+ align:start position:0%
+associated
+ 
+
+ align:start position:0%
+associated
+Optics one normally takes a course
+
+ align:start position:0%
+Optics one normally takes a course
+ 
+
+ align:start position:0%
+Optics one normally takes a course
+or gets the information from books and
+
+ align:start position:0%
+or gets the information from books and
+ 
+
+ align:start position:0%
+or gets the information from books and
+papers but there's always something
+
+ align:start position:0%
+papers but there's always something
+ 
+
+ align:start position:0%
+papers but there's always something
+that's missing in in this kind of
+
+ align:start position:0%
+that's missing in in this kind of
+ 
+
+ align:start position:0%
+that's missing in in this kind of
+learning and that is the actual seeing
+
+ align:start position:0%
+learning and that is the actual seeing
+ 
+
+ align:start position:0%
+learning and that is the actual seeing
+of the optical phenomena associated with
+
+ align:start position:0%
+of the optical phenomena associated with
+ 
+
+ align:start position:0%
+of the optical phenomena associated with
+lasers and also that relate to physical
+
+ align:start position:0%
+lasers and also that relate to physical
+ 
+
+ align:start position:0%
+lasers and also that relate to physical
+Optics so we have tried to fill this
+
+ align:start position:0%
+Optics so we have tried to fill this
+ 
+
+ align:start position:0%
+Optics so we have tried to fill this
+need by creating these videotaped
+
+ align:start position:0%
+need by creating these videotaped
+ 
+
+ align:start position:0%
+need by creating these videotaped
+demonstrations in fact we have about
+
+ align:start position:0%
+demonstrations in fact we have about
+ 
+
+ align:start position:0%
+demonstrations in fact we have about
+eight hours of them five
+
+ align:start position:0%
+eight hours of them five
+ 
+
+ align:start position:0%
+eight hours of them five
+hours in Optics and about 3 hours in
+
+ align:start position:0%
+hours in Optics and about 3 hours in
+ 
+
+ align:start position:0%
+hours in Optics and about 3 hours in
+laser
+
+ align:start position:0%
+laser
+ 
+
+ align:start position:0%
+laser
+fundamentals
+
+ align:start position:0%
+fundamentals
+ 
+
+ align:start position:0%
+fundamentals
+the these tape demonstrations are
+
+ align:start position:0%
+the these tape demonstrations are
+ 
+
+ align:start position:0%
+the these tape demonstrations are
+intended for the individual learner
+
+ align:start position:0%
+intended for the individual learner
+ 
+
+ align:start position:0%
+intended for the individual learner
+Studies by himself or herself or in
+
+ align:start position:0%
+Studies by himself or herself or in
+ 
+
+ align:start position:0%
+Studies by himself or herself or in
+small groups and also it's intended for
+
+ align:start position:0%
+small groups and also it's intended for
+ 
+
+ align:start position:0%
+small groups and also it's intended for
+the instructor people who teach lasers
+
+ align:start position:0%
+the instructor people who teach lasers
+ 
+
+ align:start position:0%
+the instructor people who teach lasers
+and Optics and and related uh related
+
+ align:start position:0%
+and Optics and and related uh related
+ 
+
+ align:start position:0%
+and Optics and and related uh related
+areas so we have both of these people uh
+
+ align:start position:0%
+areas so we have both of these people uh
+ 
+
+ align:start position:0%
+areas so we have both of these people uh
+in mind when developing these tape
+
+ align:start position:0%
+in mind when developing these tape
+ 
+
+ align:start position:0%
+in mind when developing these tape
+demonstrations now what I'd like to do
+
+ align:start position:0%
+demonstrations now what I'd like to do
+ 
+
+ align:start position:0%
+demonstrations now what I'd like to do
+is tell you a little bit more about uh
+
+ align:start position:0%
+is tell you a little bit more about uh
+ 
+
+ align:start position:0%
+is tell you a little bit more about uh
+these uh these
+
+ align:start position:0%
+these uh these
+ 
+
+ align:start position:0%
+these uh these
+demonstrations first let me start with
+
+ align:start position:0%
+demonstrations first let me start with
+ 
+
+ align:start position:0%
+demonstrations first let me start with
+those demonstrations relating to
+
+ align:start position:0%
+those demonstrations relating to
+ 
+
+ align:start position:0%
+those demonstrations relating to
+physical
+
+ align:start position:0%
+physical
+ 
+
+ align:start position:0%
+physical
+Optics first set is related to
+
+ align:start position:0%
+Optics first set is related to
+ 
+
+ align:start position:0%
+Optics first set is related to
+polarization the first one in the area
+
+ align:start position:0%
+polarization the first one in the area
+ 
+
+ align:start position:0%
+polarization the first one in the area
+of polarization is associated with a
+
+ align:start position:0%
+of polarization is associated with a
+ 
+
+ align:start position:0%
+of polarization is associated with a
+linear polarizer and here all we do is
+
+ align:start position:0%
+linear polarizer and here all we do is
+ 
+
+ align:start position:0%
+linear polarizer and here all we do is
+show the use of a linear polarizer in
+
+ align:start position:0%
+show the use of a linear polarizer in
+ 
+
+ align:start position:0%
+show the use of a linear polarizer in
+determining the state of polarization of
+
+ align:start position:0%
+determining the state of polarization of
+ 
+
+ align:start position:0%
+determining the state of polarization of
+a laser the next one we look at the
+
+ align:start position:0%
+a laser the next one we look at the
+ 
+
+ align:start position:0%
+a laser the next one we look at the
+rotation of the uh plane of polarization
+
+ align:start position:0%
+rotation of the uh plane of polarization
+ 
+
+ align:start position:0%
+rotation of the uh plane of polarization
+using uh pair of
+
+ align:start position:0%
+using uh pair of
+ 
+
+ align:start position:0%
+using uh pair of
+polarizers and then we go on and
+
+ align:start position:0%
+polarizers and then we go on and
+ 
+
+ align:start position:0%
+polarizers and then we go on and
+illustrate the uses of a quarter wave
+
+ align:start position:0%
+illustrate the uses of a quarter wave
+ 
+
+ align:start position:0%
+illustrate the uses of a quarter wave
+plate and a half wve plate and then in
+
+ align:start position:0%
+plate and a half wve plate and then in
+ 
+
+ align:start position:0%
+plate and a half wve plate and then in
+number five we actually take advantage
+
+ align:start position:0%
+number five we actually take advantage
+ 
+
+ align:start position:0%
+number five we actually take advantage
+of what we learned about polarization
+
+ align:start position:0%
+of what we learned about polarization
+ 
+
+ align:start position:0%
+of what we learned about polarization
+components to uh to demonstrate an
+
+ align:start position:0%
+components to uh to demonstrate an
+ 
+
+ align:start position:0%
+components to uh to demonstrate an
+optical isolator or an optical diode
+
+ align:start position:0%
+optical isolator or an optical diode
+ 
+
+ align:start position:0%
+optical isolator or an optical diode
+where light can only go in One Direction
+
+ align:start position:0%
+where light can only go in One Direction
+ 
+
+ align:start position:0%
+where light can only go in One Direction
+and not in the other and then finally
+
+ align:start position:0%
+and not in the other and then finally
+ 
+
+ align:start position:0%
+and not in the other and then finally
+under the area polarization we look at
+
+ align:start position:0%
+under the area polarization we look at
+ 
+
+ align:start position:0%
+under the area polarization we look at
+the scattered light in a dialectric and
+
+ align:start position:0%
+the scattered light in a dialectric and
+ 
+
+ align:start position:0%
+the scattered light in a dialectric and
+we look at the its polarization uh as a
+
+ align:start position:0%
+we look at the its polarization uh as a
+ 
+
+ align:start position:0%
+we look at the its polarization uh as a
+function of the input polarization of
+
+ align:start position:0%
+function of the input polarization of
+ 
+
+ align:start position:0%
+function of the input polarization of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+light then we go on and look at the
+
+ align:start position:0%
+light then we go on and look at the
+ 
+
+ align:start position:0%
+light then we go on and look at the
+behavior of light at dialectric
+
+ align:start position:0%
+behavior of light at dialectric
+ 
+
+ align:start position:0%
+behavior of light at dialectric
+boundaries for example a piece of
+
+ align:start position:0%
+boundaries for example a piece of
+ 
+
+ align:start position:0%
+boundaries for example a piece of
+glass the uh here we look at an air
+
+ align:start position:0%
+glass the uh here we look at an air
+ 
+
+ align:start position:0%
+glass the uh here we look at an air
+glass boundary first where we
+
+ align:start position:0%
+glass boundary first where we
+ 
+
+ align:start position:0%
+glass boundary first where we
+demonstrate the Brewster angle wherefore
+
+ align:start position:0%
+demonstrate the Brewster angle wherefore
+ 
+
+ align:start position:0%
+demonstrate the Brewster angle wherefore
+certain polar ization there's no
+
+ align:start position:0%
+certain polar ization there's no
+ 
+
+ align:start position:0%
+certain polar ization there's no
+reflection at the boundary H in the next
+
+ align:start position:0%
+reflection at the boundary H in the next
+ 
+
+ align:start position:0%
+reflection at the boundary H in the next
+one which is even more fascinating which
+
+ align:start position:0%
+one which is even more fascinating which
+ 
+
+ align:start position:0%
+one which is even more fascinating which
+is the glass air boundary where we can
+
+ align:start position:0%
+is the glass air boundary where we can
+ 
+
+ align:start position:0%
+is the glass air boundary where we can
+also look at uh the total internal
+
+ align:start position:0%
+also look at uh the total internal
+ 
+
+ align:start position:0%
+also look at uh the total internal
+reflection and as well as the Brewster
+
+ align:start position:0%
+reflection and as well as the Brewster
+ 
+
+ align:start position:0%
+reflection and as well as the Brewster
+condition and finally here we look at
+
+ align:start position:0%
+condition and finally here we look at
+ 
+
+ align:start position:0%
+condition and finally here we look at
+the facee
+
+ align:start position:0%
+the facee
+ 
+
+ align:start position:0%
+the facee
+shift for different polarizations in
+
+ align:start position:0%
+shift for different polarizations in
+ 
+
+ align:start position:0%
+shift for different polarizations in
+total internal
+
+ align:start position:0%
+total internal
+ 
+
+ align:start position:0%
+total internal
+reflection then we we look at two beam
+
+ align:start position:0%
+reflection then we we look at two beam
+ 
+
+ align:start position:0%
+reflection then we we look at two beam
+interference where the phenomena are
+
+ align:start position:0%
+interference where the phenomena are
+ 
+
+ align:start position:0%
+interference where the phenomena are
+much more Dynamic to uh to
+
+ align:start position:0%
+much more Dynamic to uh to
+ 
+
+ align:start position:0%
+much more Dynamic to uh to
+see in uh two beam interference we have
+
+ align:start position:0%
+see in uh two beam interference we have
+ 
+
+ align:start position:0%
+see in uh two beam interference we have
+we start first with a simple Michaelson
+
+ align:start position:0%
+we start first with a simple Michaelson
+ 
+
+ align:start position:0%
+we start first with a simple Michaelson
+interferometer using cated beams and
+
+ align:start position:0%
+interferometer using cated beams and
+ 
+
+ align:start position:0%
+interferometer using cated beams and
+show what fringes look like and then we
+
+ align:start position:0%
+show what fringes look like and then we
+ 
+
+ align:start position:0%
+show what fringes look like and then we
+switch to diverging beams or spherical
+
+ align:start position:0%
+switch to diverging beams or spherical
+ 
+
+ align:start position:0%
+switch to diverging beams or spherical
+beams and we see Rings instead of line
+
+ align:start position:0%
+beams and we see Rings instead of line
+ 
+
+ align:start position:0%
+beams and we see Rings instead of line
+fringes and we look at both the light
+
+ align:start position:0%
+fringes and we look at both the light
+ 
+
+ align:start position:0%
+fringes and we look at both the light
+that's transmitted through the
+
+ align:start position:0%
+that's transmitted through the
+ 
+
+ align:start position:0%
+that's transmitted through the
+interferometer as well as the light
+
+ align:start position:0%
+interferometer as well as the light
+ 
+
+ align:start position:0%
+interferometer as well as the light
+reflected through inter the
+
+ align:start position:0%
+reflected through inter the
+ 
+
+ align:start position:0%
+reflected through inter the
+interferometer then we get to a fun one
+
+ align:start position:0%
+interferometer then we get to a fun one
+ 
+
+ align:start position:0%
+interferometer then we get to a fun one
+here uh and that is what happens to the
+
+ align:start position:0%
+here uh and that is what happens to the
+ 
+
+ align:start position:0%
+here uh and that is what happens to the
+light or where does the light go when we
+
+ align:start position:0%
+light or where does the light go when we
+ 
+
+ align:start position:0%
+light or where does the light go when we
+have uh destructive interference when we
+
+ align:start position:0%
+have uh destructive interference when we
+ 
+
+ align:start position:0%
+have uh destructive interference when we
+have actually no light coming out of the
+
+ align:start position:0%
+have actually no light coming out of the
+ 
+
+ align:start position:0%
+have actually no light coming out of the
+Michaels inter interferometer where does
+
+ align:start position:0%
+Michaels inter interferometer where does
+ 
+
+ align:start position:0%
+Michaels inter interferometer where does
+the light go and in fact I would like to
+
+ align:start position:0%
+the light go and in fact I would like to
+ 
+
+ align:start position:0%
+the light go and in fact I would like to
+to uh give you a little preview of this
+
+ align:start position:0%
+to uh give you a little preview of this
+ 
+
+ align:start position:0%
+to uh give you a little preview of this
+uh of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+demonstration so let's go to the monitor
+
+ align:start position:0%
+demonstration so let's go to the monitor
+ 
+
+ align:start position:0%
+demonstration so let's go to the monitor
+and see this uh
+
+ align:start position:0%
+and see this uh
+ 
+
+ align:start position:0%
+and see this uh
+demonstration now as we see in in the uh
+
+ align:start position:0%
+demonstration now as we see in in the uh
+ 
+
+ align:start position:0%
+demonstration now as we see in in the uh
+on the monitor we see the Michael Teter
+
+ align:start position:0%
+on the monitor we see the Michael Teter
+ 
+
+ align:start position:0%
+on the monitor we see the Michael Teter
+on the right and the output of the
+
+ align:start position:0%
+on the right and the output of the
+ 
+
+ align:start position:0%
+on the right and the output of the
+Michael andrometer in the inset above
+
+ align:start position:0%
+Michael andrometer in the inset above
+ 
+
+ align:start position:0%
+Michael andrometer in the inset above
+and as I lean on the table we see that
+
+ align:start position:0%
+and as I lean on the table we see that
+ 
+
+ align:start position:0%
+and as I lean on the table we see that
+the light goes all the way from very
+
+ align:start position:0%
+the light goes all the way from very
+ 
+
+ align:start position:0%
+the light goes all the way from very
+bright to completely dark or no light at
+
+ align:start position:0%
+bright to completely dark or no light at
+ 
+
+ align:start position:0%
+bright to completely dark or no light at
+all now just to show that indeed there
+
+ align:start position:0%
+all now just to show that indeed there
+ 
+
+ align:start position:0%
+all now just to show that indeed there
+is light inside the interferometer what
+
+ align:start position:0%
+is light inside the interferometer what
+ 
+
+ align:start position:0%
+is light inside the interferometer what
+I'm going to do is block one arm with a
+
+ align:start position:0%
+I'm going to do is block one arm with a
+ 
+
+ align:start position:0%
+I'm going to do is block one arm with a
+card
+
+ align:start position:0%
+card
+ 
+
+ align:start position:0%
+card
+and then if we look in the closeup we
+
+ align:start position:0%
+and then if we look in the closeup we
+ 
+
+ align:start position:0%
+and then if we look in the closeup we
+see that indeed there is light in the
+
+ align:start position:0%
+see that indeed there is light in the
+ 
+
+ align:start position:0%
+see that indeed there is light in the
+interferometer when that arm is blocked
+
+ align:start position:0%
+interferometer when that arm is blocked
+ 
+
+ align:start position:0%
+interferometer when that arm is blocked
+now when I block the other arm again we
+
+ align:start position:0%
+now when I block the other arm again we
+ 
+
+ align:start position:0%
+now when I block the other arm again we
+see that indeed there's light being
+
+ align:start position:0%
+see that indeed there's light being
+ 
+
+ align:start position:0%
+see that indeed there's light being
+reflected from each arm into front of
+
+ align:start position:0%
+reflected from each arm into front of
+ 
+
+ align:start position:0%
+reflected from each arm into front of
+but when I take the card
+
+ align:start position:0%
+but when I take the card
+ 
+
+ align:start position:0%
+but when I take the card
+off I
+
+ align:start position:0%
+off I
+ 
+
+ align:start position:0%
+off I
+can make the light Disappear Completely
+
+ align:start position:0%
+can make the light Disappear Completely
+ 
+
+ align:start position:0%
+can make the light Disappear Completely
+which means I have complete destructive
+
+ align:start position:0%
+which means I have complete destructive
+ 
+
+ align:start position:0%
+which means I have complete destructive
+interference so the whole question is is
+
+ align:start position:0%
+interference so the whole question is is
+ 
+
+ align:start position:0%
+interference so the whole question is is
+that where does the light go when I have
+
+ align:start position:0%
+that where does the light go when I have
+ 
+
+ align:start position:0%
+that where does the light go when I have
+complete destruction destructive
+
+ align:start position:0%
+complete destruction destructive
+ 
+
+ align:start position:0%
+complete destruction destructive
+interference the next demonstration in
+
+ align:start position:0%
+interference the next demonstration in
+ 
+
+ align:start position:0%
+interference the next demonstration in
+the in the area of uh uh Tu beam
+
+ align:start position:0%
+the in the area of uh uh Tu beam
+ 
+
+ align:start position:0%
+the in the area of uh uh Tu beam
+interferometry relates to Fringe
+
+ align:start position:0%
+interferometry relates to Fringe
+ 
+
+ align:start position:0%
+interferometry relates to Fringe
+contrast as we see we have a number of
+
+ align:start position:0%
+contrast as we see we have a number of
+ 
+
+ align:start position:0%
+contrast as we see we have a number of
+them one we look at the effect of
+
+ align:start position:0%
+them one we look at the effect of
+ 
+
+ align:start position:0%
+them one we look at the effect of
+vibrations on Fringe contrast then we
+
+ align:start position:0%
+vibrations on Fringe contrast then we
+ 
+
+ align:start position:0%
+vibrations on Fringe contrast then we
+look at the effect of different
+
+ align:start position:0%
+look at the effect of different
+ 
+
+ align:start position:0%
+look at the effect of different
+intensities in the two arms of the
+
+ align:start position:0%
+intensities in the two arms of the
+ 
+
+ align:start position:0%
+intensities in the two arms of the
+interferometer and how it relates to
+
+ align:start position:0%
+interferometer and how it relates to
+ 
+
+ align:start position:0%
+interferometer and how it relates to
+Fringe contrast then we look at an
+
+ align:start position:0%
+Fringe contrast then we look at an
+ 
+
+ align:start position:0%
+Fringe contrast then we look at an
+interesting one the effect of different
+
+ align:start position:0%
+interesting one the effect of different
+ 
+
+ align:start position:0%
+interesting one the effect of different
+polarizations uh in the two arms of the
+
+ align:start position:0%
+polarizations uh in the two arms of the
+ 
+
+ align:start position:0%
+polarizations uh in the two arms of the
+interferometer and finally here we look
+
+ align:start position:0%
+interferometer and finally here we look
+ 
+
+ align:start position:0%
+interferometer and finally here we look
+at The Fringe contrast as a function of
+
+ align:start position:0%
+at The Fringe contrast as a function of
+ 
+
+ align:start position:0%
+at The Fringe contrast as a function of
+path length difference between the two
+
+ align:start position:0%
+path length difference between the two
+ 
+
+ align:start position:0%
+path length difference between the two
+arms of the interferometer and as we
+
+ align:start position:0%
+arms of the interferometer and as we
+ 
+
+ align:start position:0%
+arms of the interferometer and as we
+know the if indeed the laser is not
+
+ align:start position:0%
+know the if indeed the laser is not
+ 
+
+ align:start position:0%
+know the if indeed the laser is not
+single frequency then The Fringe
+
+ align:start position:0%
+single frequency then The Fringe
+ 
+
+ align:start position:0%
+single frequency then The Fringe
+contrast will uh be very poor in uh for
+
+ align:start position:0%
+contrast will uh be very poor in uh for
+ 
+
+ align:start position:0%
+contrast will uh be very poor in uh for
+for certain path length differences now
+
+ align:start position:0%
+for certain path length differences now
+ 
+
+ align:start position:0%
+for certain path length differences now
+in in demonstration number 17 we do
+
+ align:start position:0%
+in in demonstration number 17 we do
+ 
+
+ align:start position:0%
+in in demonstration number 17 we do
+quite a comprehensive study of Fringe
+
+ align:start position:0%
+quite a comprehensive study of Fringe
+ 
+
+ align:start position:0%
+quite a comprehensive study of Fringe
+contrast or coherence length and its
+
+ align:start position:0%
+contrast or coherence length and its
+ 
+
+ align:start position:0%
+contrast or coherence length and its
+relationship to the spectrum of the of
+
+ align:start position:0%
+relationship to the spectrum of the of
+ 
+
+ align:start position:0%
+relationship to the spectrum of the of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+laser now I'd like to show you a little
+
+ align:start position:0%
+laser now I'd like to show you a little
+ 
+
+ align:start position:0%
+laser now I'd like to show you a little
+bit from this
+
+ align:start position:0%
+bit from this
+ 
+
+ align:start position:0%
+bit from this
+demonstration as you see on the scope we
+
+ align:start position:0%
+demonstration as you see on the scope we
+ 
+
+ align:start position:0%
+demonstration as you see on the scope we
+show we show the spectrum of the laser
+
+ align:start position:0%
+show we show the spectrum of the laser
+ 
+
+ align:start position:0%
+show we show the spectrum of the laser
+and this indicates that the laser is
+
+ align:start position:0%
+and this indicates that the laser is
+ 
+
+ align:start position:0%
+and this indicates that the laser is
+oscillating at three frequencies below
+
+ align:start position:0%
+oscillating at three frequencies below
+ 
+
+ align:start position:0%
+oscillating at three frequencies below
+is the Michaelson interferometer setup
+
+ align:start position:0%
+is the Michaelson interferometer setup
+ 
+
+ align:start position:0%
+is the Michaelson interferometer setup
+and at first I'll start with equal path
+
+ align:start position:0%
+and at first I'll start with equal path
+ 
+
+ align:start position:0%
+and at first I'll start with equal path
+lens in the two arms of the
+
+ align:start position:0%
+lens in the two arms of the
+ 
+
+ align:start position:0%
+lens in the two arms of the
+interferometer and then we can look at
+
+ align:start position:0%
+interferometer and then we can look at
+ 
+
+ align:start position:0%
+interferometer and then we can look at
+the at the FR Fringe contrast here is a
+
+ align:start position:0%
+the at the FR Fringe contrast here is a
+ 
+
+ align:start position:0%
+the at the FR Fringe contrast here is a
+fringe contrast for equal path length
+
+ align:start position:0%
+fringe contrast for equal path length
+ 
+
+ align:start position:0%
+fringe contrast for equal path length
+looks very very good now what I do I
+
+ align:start position:0%
+looks very very good now what I do I
+ 
+
+ align:start position:0%
+looks very very good now what I do I
+start to change the length of one of the
+
+ align:start position:0%
+start to change the length of one of the
+ 
+
+ align:start position:0%
+start to change the length of one of the
+arms here I am around 5 cm path length
+
+ align:start position:0%
+arms here I am around 5 cm path length
+ 
+
+ align:start position:0%
+arms here I am around 5 cm path length
+difference and The Fringe contrast looks
+
+ align:start position:0%
+difference and The Fringe contrast looks
+ 
+
+ align:start position:0%
+difference and The Fringe contrast looks
+looks pretty bad here 10 close to 10 cm
+
+ align:start position:0%
+looks pretty bad here 10 close to 10 cm
+ 
+
+ align:start position:0%
+looks pretty bad here 10 close to 10 cm
+path difference you can hardly see the
+
+ align:start position:0%
+path difference you can hardly see the
+ 
+
+ align:start position:0%
+path difference you can hardly see the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+fringes again here's around 12 is still
+
+ align:start position:0%
+fringes again here's around 12 is still
+ 
+
+ align:start position:0%
+fringes again here's around 12 is still
+pretty bad then as I go further this is
+
+ align:start position:0%
+pretty bad then as I go further this is
+ 
+
+ align:start position:0%
+pretty bad then as I go further this is
+about 15 cm or so I see that The Fringe
+
+ align:start position:0%
+about 15 cm or so I see that The Fringe
+ 
+
+ align:start position:0%
+about 15 cm or so I see that The Fringe
+contrast comes
+
+ align:start position:0%
+contrast comes
+ 
+
+ align:start position:0%
+contrast comes
+back here I am it's getting better and
+
+ align:start position:0%
+back here I am it's getting better and
+ 
+
+ align:start position:0%
+back here I am it's getting better and
+better here around about 20 cm path
+
+ align:start position:0%
+better here around about 20 cm path
+ 
+
+ align:start position:0%
+better here around about 20 cm path
+difference or
+
+ align:start position:0%
+difference or
+ 
+
+ align:start position:0%
+difference or
+so the quality of the fringes look as
+
+ align:start position:0%
+so the quality of the fringes look as
+ 
+
+ align:start position:0%
+so the quality of the fringes look as
+good as they were
+
+ align:start position:0%
+good as they were
+ 
+
+ align:start position:0%
+good as they were
+before now I'd like to to show you other
+
+ align:start position:0%
+before now I'd like to to show you other
+ 
+
+ align:start position:0%
+before now I'd like to to show you other
+demonstrations that relate to something
+
+ align:start position:0%
+demonstrations that relate to something
+ 
+
+ align:start position:0%
+demonstrations that relate to something
+even more exciting than two beam
+
+ align:start position:0%
+even more exciting than two beam
+ 
+
+ align:start position:0%
+even more exciting than two beam
+interferometry which is the effect of
+
+ align:start position:0%
+interferometry which is the effect of
+ 
+
+ align:start position:0%
+interferometry which is the effect of
+multiple beam
+
+ align:start position:0%
+multiple beam
+ 
+
+ align:start position:0%
+multiple beam
+interference and under multiple beam
+
+ align:start position:0%
+interference and under multiple beam
+ 
+
+ align:start position:0%
+interference and under multiple beam
+interference we have plain mirror cavity
+
+ align:start position:0%
+interference we have plain mirror cavity
+ 
+
+ align:start position:0%
+interference we have plain mirror cavity
+we start with a plain mirror cavity
+
+ align:start position:0%
+we start with a plain mirror cavity
+ 
+
+ align:start position:0%
+we start with a plain mirror cavity
+using columnated beams and again I would
+
+ align:start position:0%
+using columnated beams and again I would
+ 
+
+ align:start position:0%
+using columnated beams and again I would
+like to show you a little bit from uh
+
+ align:start position:0%
+like to show you a little bit from uh
+ 
+
+ align:start position:0%
+like to show you a little bit from uh
+from this fascinating uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+demonstration on your screen you see the
+
+ align:start position:0%
+demonstration on your screen you see the
+ 
+
+ align:start position:0%
+demonstration on your screen you see the
+plain parallel fabri pero cavity below
+
+ align:start position:0%
+plain parallel fabri pero cavity below
+ 
+
+ align:start position:0%
+plain parallel fabri pero cavity below
+with a spacing a few millimeters and
+
+ align:start position:0%
+with a spacing a few millimeters and
+ 
+
+ align:start position:0%
+with a spacing a few millimeters and
+right above it you see the individual
+
+ align:start position:0%
+right above it you see the individual
+ 
+
+ align:start position:0%
+right above it you see the individual
+beams when the cavity is misalign now as
+
+ align:start position:0%
+beams when the cavity is misalign now as
+ 
+
+ align:start position:0%
+beams when the cavity is misalign now as
+I start to align the cavity the beam
+
+ align:start position:0%
+I start to align the cavity the beam
+ 
+
+ align:start position:0%
+I start to align the cavity the beam
+start to superimpose until I reach the
+
+ align:start position:0%
+start to superimpose until I reach the
+ 
+
+ align:start position:0%
+start to superimpose until I reach the
+condition when they're all overlapping
+
+ align:start position:0%
+condition when they're all overlapping
+ 
+
+ align:start position:0%
+condition when they're all overlapping
+and we see the
+
+ align:start position:0%
+and we see the
+ 
+
+ align:start position:0%
+and we see the
+interference and here we are in fact
+
+ align:start position:0%
+interference and here we are in fact
+ 
+
+ align:start position:0%
+interference and here we are in fact
+there's no practically no light coming
+
+ align:start position:0%
+there's no practically no light coming
+ 
+
+ align:start position:0%
+there's no practically no light coming
+out of the interferometer and as I lean
+
+ align:start position:0%
+out of the interferometer and as I lean
+ 
+
+ align:start position:0%
+out of the interferometer and as I lean
+on one of the mirrors I can uh bring the
+
+ align:start position:0%
+on one of the mirrors I can uh bring the
+ 
+
+ align:start position:0%
+on one of the mirrors I can uh bring the
+transmitted light into maximum and then
+
+ align:start position:0%
+transmitted light into maximum and then
+ 
+
+ align:start position:0%
+transmitted light into maximum and then
+into into a uh minimum it's a very very
+
+ align:start position:0%
+into into a uh minimum it's a very very
+ 
+
+ align:start position:0%
+into into a uh minimum it's a very very
+dramatic demonstration of multiple beam
+
+ align:start position:0%
+dramatic demonstration of multiple beam
+ 
+
+ align:start position:0%
+dramatic demonstration of multiple beam
+interference now the the uh next one in
+
+ align:start position:0%
+interference now the the uh next one in
+ 
+
+ align:start position:0%
+interference now the the uh next one in
+the area of multiple beam interference
+
+ align:start position:0%
+the area of multiple beam interference
+ 
+
+ align:start position:0%
+the area of multiple beam interference
+we look at again a plain mirror cavity
+
+ align:start position:0%
+we look at again a plain mirror cavity
+ 
+
+ align:start position:0%
+we look at again a plain mirror cavity
+with diverging beams this time instead
+
+ align:start position:0%
+with diverging beams this time instead
+ 
+
+ align:start position:0%
+with diverging beams this time instead
+of cated beams and here we see the Rings
+
+ align:start position:0%
+of cated beams and here we see the Rings
+ 
+
+ align:start position:0%
+of cated beams and here we see the Rings
+and the bullseye and so on and also we
+
+ align:start position:0%
+and the bullseye and so on and also we
+ 
+
+ align:start position:0%
+and the bullseye and so on and also we
+look at the not just the transmitted
+
+ align:start position:0%
+look at the not just the transmitted
+ 
+
+ align:start position:0%
+look at the not just the transmitted
+beam but we also look at the reflected
+
+ align:start position:0%
+beam but we also look at the reflected
+ 
+
+ align:start position:0%
+beam but we also look at the reflected
+beam from this cavity to see what that
+
+ align:start position:0%
+beam from this cavity to see what that
+ 
+
+ align:start position:0%
+beam from this cavity to see what that
+looks like and then we switch from plain
+
+ align:start position:0%
+looks like and then we switch from plain
+ 
+
+ align:start position:0%
+looks like and then we switch from plain
+mirror cavities to curved mirror
+
+ align:start position:0%
+mirror cavities to curved mirror
+ 
+
+ align:start position:0%
+mirror cavities to curved mirror
+cavities and here we excite lots of
+
+ align:start position:0%
+cavities and here we excite lots of
+ 
+
+ align:start position:0%
+cavities and here we excite lots of
+transverse modes or radial modes uh in
+
+ align:start position:0%
+transverse modes or radial modes uh in
+ 
+
+ align:start position:0%
+transverse modes or radial modes uh in
+the cavity so I'd like again to show you
+
+ align:start position:0%
+the cavity so I'd like again to show you
+ 
+
+ align:start position:0%
+the cavity so I'd like again to show you
+just briefly a few of these uh beautiful
+
+ align:start position:0%
+just briefly a few of these uh beautiful
+ 
+
+ align:start position:0%
+just briefly a few of these uh beautiful
+transverse
+
+ align:start position:0%
+transverse
+ 
+
+ align:start position:0%
+transverse
+modes on the screen you see one of the
+
+ align:start position:0%
+modes on the screen you see one of the
+ 
+
+ align:start position:0%
+modes on the screen you see one of the
+higher transverse
+
+ align:start position:0%
+higher transverse
+ 
+
+ align:start position:0%
+higher transverse
+modes as the cavity is uh is being tuned
+
+ align:start position:0%
+modes as the cavity is uh is being tuned
+ 
+
+ align:start position:0%
+modes as the cavity is uh is being tuned
+here we are we have
+
+ align:start position:0%
+here we are we have
+ 
+
+ align:start position:0%
+here we are we have
+a much larger mode and here's a another
+
+ align:start position:0%
+a much larger mode and here's a another
+ 
+
+ align:start position:0%
+a much larger mode and here's a another
+one they're very very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pretty and in addition to just looking
+
+ align:start position:0%
+pretty and in addition to just looking
+ 
+
+ align:start position:0%
+pretty and in addition to just looking
+at the transverse modes we also this
+
+ align:start position:0%
+at the transverse modes we also this
+ 
+
+ align:start position:0%
+at the transverse modes we also this
+demonstration we're going to look at
+
+ align:start position:0%
+demonstration we're going to look at
+ 
+
+ align:start position:0%
+demonstration we're going to look at
+their frequencies and again there's a
+
+ align:start position:0%
+their frequencies and again there's a
+ 
+
+ align:start position:0%
+their frequencies and again there's a
+lot to be learned from
+
+ align:start position:0%
+lot to be learned from
+ 
+
+ align:start position:0%
+lot to be learned from
+there the final one under multiple beam
+
+ align:start position:0%
+there the final one under multiple beam
+ 
+
+ align:start position:0%
+there the final one under multiple beam
+interference it relates to uh the use of
+
+ align:start position:0%
+interference it relates to uh the use of
+ 
+
+ align:start position:0%
+interference it relates to uh the use of
+a curved mirror cavity as an optical
+
+ align:start position:0%
+a curved mirror cavity as an optical
+ 
+
+ align:start position:0%
+a curved mirror cavity as an optical
+Spectrum analyzer the so-called con
+
+ align:start position:0%
+Spectrum analyzer the so-called con
+ 
+
+ align:start position:0%
+Spectrum analyzer the so-called con
+focal resonator so we show you what
+
+ align:start position:0%
+focal resonator so we show you what
+ 
+
+ align:start position:0%
+focal resonator so we show you what
+happens at con focal and what happens
+
+ align:start position:0%
+happens at con focal and what happens
+ 
+
+ align:start position:0%
+happens at con focal and what happens
+when you are below above uh con focal
+
+ align:start position:0%
+when you are below above uh con focal
+ 
+
+ align:start position:0%
+when you are below above uh con focal
+condition the uh and this sort of
+
+ align:start position:0%
+condition the uh and this sort of
+ 
+
+ align:start position:0%
+condition the uh and this sort of
+summarizes the interference uh
+
+ align:start position:0%
+summarizes the interference uh
+ 
+
+ align:start position:0%
+summarizes the interference uh
+demonstrations now we want to turn to
+
+ align:start position:0%
+demonstrations now we want to turn to
+ 
+
+ align:start position:0%
+demonstrations now we want to turn to
+defraction and we'll start with Fran
+
+ align:start position:0%
+defraction and we'll start with Fran
+ 
+
+ align:start position:0%
+defraction and we'll start with Fran
+Hofer defraction now when I demonstrate
+
+ align:start position:0%
+Hofer defraction now when I demonstrate
+ 
+
+ align:start position:0%
+Hofer defraction now when I demonstrate
+defraction I like to be able to change
+
+ align:start position:0%
+defraction I like to be able to change
+ 
+
+ align:start position:0%
+defraction I like to be able to change
+things while uh while I demonstrate I
+
+ align:start position:0%
+things while uh while I demonstrate I
+ 
+
+ align:start position:0%
+things while uh while I demonstrate I
+don't like these Statics static
+
+ align:start position:0%
+don't like these Statics static
+ 
+
+ align:start position:0%
+don't like these Statics static
+demonstrations so what we have here we
+
+ align:start position:0%
+demonstrations so what we have here we
+ 
+
+ align:start position:0%
+demonstrations so what we have here we
+have an adjustable slit slit we'll start
+
+ align:start position:0%
+have an adjustable slit slit we'll start
+ 
+
+ align:start position:0%
+have an adjustable slit slit we'll start
+with an adjustable slit defraction and
+
+ align:start position:0%
+with an adjustable slit defraction and
+ 
+
+ align:start position:0%
+with an adjustable slit defraction and
+we'll show what happens as a function of
+
+ align:start position:0%
+we'll show what happens as a function of
+ 
+
+ align:start position:0%
+we'll show what happens as a function of
+slit width then we go and look at what
+
+ align:start position:0%
+slit width then we go and look at what
+ 
+
+ align:start position:0%
+slit width then we go and look at what
+happens when we have two slits and then
+
+ align:start position:0%
+happens when we have two slits and then
+ 
+
+ align:start position:0%
+happens when we have two slits and then
+when it comes to multiple multiple slits
+
+ align:start position:0%
+when it comes to multiple multiple slits
+ 
+
+ align:start position:0%
+when it comes to multiple multiple slits
+instead of just showing you just the
+
+ align:start position:0%
+instead of just showing you just the
+ 
+
+ align:start position:0%
+instead of just showing you just the
+defraction pattern of lots of slits what
+
+ align:start position:0%
+defraction pattern of lots of slits what
+ 
+
+ align:start position:0%
+defraction pattern of lots of slits what
+what we do here we
+
+ align:start position:0%
+what we do here we
+ 
+
+ align:start position:0%
+what we do here we
+introduce each slit at a one slit at a
+
+ align:start position:0%
+introduce each slit at a one slit at a
+ 
+
+ align:start position:0%
+introduce each slit at a one slit at a
+time so we start with 1 2 3 4 5 6 7 and
+
+ align:start position:0%
+time so we start with 1 2 3 4 5 6 7 and
+ 
+
+ align:start position:0%
+time so we start with 1 2 3 4 5 6 7 and
+so on and you'll see how the patent
+
+ align:start position:0%
+so on and you'll see how the patent
+ 
+
+ align:start position:0%
+so on and you'll see how the patent
+changes as a function of the number of
+
+ align:start position:0%
+changes as a function of the number of
+ 
+
+ align:start position:0%
+changes as a function of the number of
+slits then we quickly look at the
+
+ align:start position:0%
+slits then we quickly look at the
+ 
+
+ align:start position:0%
+slits then we quickly look at the
+defraction patterns of uh thin wires and
+
+ align:start position:0%
+defraction patterns of uh thin wires and
+ 
+
+ align:start position:0%
+defraction patterns of uh thin wires and
+and try to relate them to uh to those of
+
+ align:start position:0%
+and try to relate them to uh to those of
+ 
+
+ align:start position:0%
+and try to relate them to uh to those of
+uh of narrow
+
+ align:start position:0%
+uh of narrow
+ 
+
+ align:start position:0%
+uh of narrow
+slits then we go into two dimensional
+
+ align:start position:0%
+slits then we go into two dimensional
+ 
+
+ align:start position:0%
+slits then we go into two dimensional
+front half of defraction patterns and uh
+
+ align:start position:0%
+front half of defraction patterns and uh
+ 
+
+ align:start position:0%
+front half of defraction patterns and uh
+we have a variable rectangular aperture
+
+ align:start position:0%
+we have a variable rectangular aperture
+ 
+
+ align:start position:0%
+we have a variable rectangular aperture
+and here is very pretty you look at the
+
+ align:start position:0%
+and here is very pretty you look at the
+ 
+
+ align:start position:0%
+and here is very pretty you look at the
+uh defraction pattern from that and then
+
+ align:start position:0%
+uh defraction pattern from that and then
+ 
+
+ align:start position:0%
+uh defraction pattern from that and then
+we look at uh circular apertures and
+
+ align:start position:0%
+we look at uh circular apertures and
+ 
+
+ align:start position:0%
+we look at uh circular apertures and
+finally we look at uh the the defraction
+
+ align:start position:0%
+finally we look at uh the the defraction
+ 
+
+ align:start position:0%
+finally we look at uh the the defraction
+pattern associated with AC crossed
+
+ align:start position:0%
+pattern associated with AC crossed
+ 
+
+ align:start position:0%
+pattern associated with AC crossed
+multiple slits essentially we have here
+
+ align:start position:0%
+multiple slits essentially we have here
+ 
+
+ align:start position:0%
+multiple slits essentially we have here
+is two rcky rulings that we cross and
+
+ align:start position:0%
+is two rcky rulings that we cross and
+ 
+
+ align:start position:0%
+is two rcky rulings that we cross and
+then we vary the angle between them and
+
+ align:start position:0%
+then we vary the angle between them and
+ 
+
+ align:start position:0%
+then we vary the angle between them and
+look at the uh look at the
+
+ align:start position:0%
+look at the uh look at the
+ 
+
+ align:start position:0%
+look at the uh look at the
+pattern and uh so after Fran hofa
+
+ align:start position:0%
+pattern and uh so after Fran hofa
+ 
+
+ align:start position:0%
+pattern and uh so after Fran hofa
+defraction then we show you a little bit
+
+ align:start position:0%
+defraction then we show you a little bit
+ 
+
+ align:start position:0%
+defraction then we show you a little bit
+of fernel defraction now on the fernel
+
+ align:start position:0%
+of fernel defraction now on the fernel
+ 
+
+ align:start position:0%
+of fernel defraction now on the fernel
+defraction again we go back to the
+
+ align:start position:0%
+defraction again we go back to the
+ 
+
+ align:start position:0%
+defraction again we go back to the
+adjustable slit but here what's
+
+ align:start position:0%
+adjustable slit but here what's
+ 
+
+ align:start position:0%
+adjustable slit but here what's
+interesting about this demonstration
+
+ align:start position:0%
+interesting about this demonstration
+ 
+
+ align:start position:0%
+interesting about this demonstration
+that we show you the transition from the
+
+ align:start position:0%
+that we show you the transition from the
+ 
+
+ align:start position:0%
+that we show you the transition from the
+Fran haer condition to the fernel using
+
+ align:start position:0%
+Fran haer condition to the fernel using
+ 
+
+ align:start position:0%
+Fran haer condition to the fernel using
+just that adjustable pair of slits and
+
+ align:start position:0%
+just that adjustable pair of slits and
+ 
+
+ align:start position:0%
+just that adjustable pair of slits and
+it's it's a fascinating experiment to
+
+ align:start position:0%
+it's it's a fascinating experiment to
+ 
+
+ align:start position:0%
+it's it's a fascinating experiment to
+see how the Maxwell's equations are
+
+ align:start position:0%
+see how the Maxwell's equations are
+ 
+
+ align:start position:0%
+see how the Maxwell's equations are
+solved by uh by this uh uh by this uh
+
+ align:start position:0%
+solved by uh by this uh uh by this uh
+ 
+
+ align:start position:0%
+solved by uh by this uh uh by this uh
+slit and then we end for nail defraction
+
+ align:start position:0%
+slit and then we end for nail defraction
+ 
+
+ align:start position:0%
+slit and then we end for nail defraction
+by showing you the uh pattern that
+
+ align:start position:0%
+by showing you the uh pattern that
+ 
+
+ align:start position:0%
+by showing you the uh pattern that
+relates to uh the Fel pattern that that
+
+ align:start position:0%
+relates to uh the Fel pattern that that
+ 
+
+ align:start position:0%
+relates to uh the Fel pattern that that
+relates to a number of circular
+
+ align:start position:0%
+relates to a number of circular
+ 
+
+ align:start position:0%
+relates to a number of circular
+apertures and again as a function of the
+
+ align:start position:0%
+apertures and again as a function of the
+ 
+
+ align:start position:0%
+apertures and again as a function of the
+curvature uh of the uh of the field
+
+ align:start position:0%
+curvature uh of the uh of the field
+ 
+
+ align:start position:0%
+curvature uh of the uh of the field
+incident on on the on the aperture and
+
+ align:start position:0%
+incident on on the on the aperture and
+ 
+
+ align:start position:0%
+incident on on the on the aperture and
+we close our uh demonstrations in
+
+ align:start position:0%
+we close our uh demonstrations in
+ 
+
+ align:start position:0%
+we close our uh demonstrations in
+physical Optics by looking at the
+
+ align:start position:0%
+physical Optics by looking at the
+ 
+
+ align:start position:0%
+physical Optics by looking at the
+propagation of light in fibers and as we
+
+ align:start position:0%
+propagation of light in fibers and as we
+ 
+
+ align:start position:0%
+propagation of light in fibers and as we
+know today fibers are very very
+
+ align:start position:0%
+know today fibers are very very
+ 
+
+ align:start position:0%
+know today fibers are very very
+important and so what we do here we show
+
+ align:start position:0%
+important and so what we do here we show
+ 
+
+ align:start position:0%
+important and so what we do here we show
+you the behavior of a single mode
+
+ align:start position:0%
+you the behavior of a single mode
+ 
+
+ align:start position:0%
+you the behavior of a single mode
+fiber first and uh and what happens to
+
+ align:start position:0%
+fiber first and uh and what happens to
+ 
+
+ align:start position:0%
+fiber first and uh and what happens to
+the uh to the light coming out of the
+
+ align:start position:0%
+the uh to the light coming out of the
+ 
+
+ align:start position:0%
+the uh to the light coming out of the
+fiber as a function of bending and so on
+
+ align:start position:0%
+fiber as a function of bending and so on
+ 
+
+ align:start position:0%
+fiber as a function of bending and so on
+and then we'll switch to a multimode
+
+ align:start position:0%
+and then we'll switch to a multimode
+ 
+
+ align:start position:0%
+and then we'll switch to a multimode
+fiber where the output is no longer a
+
+ align:start position:0%
+fiber where the output is no longer a
+ 
+
+ align:start position:0%
+fiber where the output is no longer a
+single spot but is consist of of of
+
+ align:start position:0%
+single spot but is consist of of of
+ 
+
+ align:start position:0%
+single spot but is consist of of of
+different spot just like in the
+
+ align:start position:0%
+different spot just like in the
+ 
+
+ align:start position:0%
+different spot just like in the
+resonators and
+
+ align:start position:0%
+resonators and
+ 
+
+ align:start position:0%
+resonators and
+finally uh here we look at the
+
+ align:start position:0%
+finally uh here we look at the
+ 
+
+ align:start position:0%
+finally uh here we look at the
+polarization the polarization issue in a
+
+ align:start position:0%
+polarization the polarization issue in a
+ 
+
+ align:start position:0%
+polarization the polarization issue in a
+in a single mode fiber and show how how
+
+ align:start position:0%
+in a single mode fiber and show how how
+ 
+
+ align:start position:0%
+in a single mode fiber and show how how
+touchy it is and how you can change the
+
+ align:start position:0%
+touchy it is and how you can change the
+ 
+
+ align:start position:0%
+touchy it is and how you can change the
+state of polarization coming out of the
+
+ align:start position:0%
+state of polarization coming out of the
+ 
+
+ align:start position:0%
+state of polarization coming out of the
+fiber by simply just just stressing it
+
+ align:start position:0%
+fiber by simply just just stressing it
+ 
+
+ align:start position:0%
+fiber by simply just just stressing it
+or just even breathing on
+
+ align:start position:0%
+or just even breathing on
+ 
+
+ align:start position:0%
+or just even breathing on
+it and this concludes about 5 hours or
+
+ align:start position:0%
+it and this concludes about 5 hours or
+ 
+
+ align:start position:0%
+it and this concludes about 5 hours or
+so as I said before of demonstrations in
+
+ align:start position:0%
+so as I said before of demonstrations in
+ 
+
+ align:start position:0%
+so as I said before of demonstrations in
+physical Optics now let's look at our
+
+ align:start position:0%
+physical Optics now let's look at our
+ 
+
+ align:start position:0%
+physical Optics now let's look at our
+demonstrations in uh laser
+
+ align:start position:0%
+demonstrations in uh laser
+ 
+
+ align:start position:0%
+demonstrations in uh laser
+fundamentals the the first one in uh in
+
+ align:start position:0%
+fundamentals the the first one in uh in
+ 
+
+ align:start position:0%
+fundamentals the the first one in uh in
+laser fundamentals is just a simple
+
+ align:start position:0%
+laser fundamentals is just a simple
+ 
+
+ align:start position:0%
+laser fundamentals is just a simple
+laser so we start with a simple laser we
+
+ align:start position:0%
+laser so we start with a simple laser we
+ 
+
+ align:start position:0%
+laser so we start with a simple laser we
+show you what a simple laser looks like
+
+ align:start position:0%
+show you what a simple laser looks like
+ 
+
+ align:start position:0%
+show you what a simple laser looks like
+and then we look at the uh very
+
+ align:start position:0%
+and then we look at the uh very
+ 
+
+ align:start position:0%
+and then we look at the uh very
+important obviously important thing in
+
+ align:start position:0%
+important obviously important thing in
+ 
+
+ align:start position:0%
+important obviously important thing in
+lasers and that is the the amp the
+
+ align:start position:0%
+lasers and that is the the amp the
+ 
+
+ align:start position:0%
+lasers and that is the the amp the
+amplifier the light amplifier which is
+
+ align:start position:0%
+amplifier the light amplifier which is
+ 
+
+ align:start position:0%
+amplifier the light amplifier which is
+the heart of the of the laser so what
+
+ align:start position:0%
+the heart of the of the laser so what
+ 
+
+ align:start position:0%
+the heart of the of the laser so what
+I'd like to do is show you a little bit
+
+ align:start position:0%
+I'd like to do is show you a little bit
+ 
+
+ align:start position:0%
+I'd like to do is show you a little bit
+from uh this demonstration on your
+
+ align:start position:0%
+from uh this demonstration on your
+ 
+
+ align:start position:0%
+from uh this demonstration on your
+screen we now see the amplifier down
+
+ align:start position:0%
+screen we now see the amplifier down
+ 
+
+ align:start position:0%
+screen we now see the amplifier down
+below and we have a laser beam that
+
+ align:start position:0%
+below and we have a laser beam that
+ 
+
+ align:start position:0%
+below and we have a laser beam that
+enters the amplifier from the right and
+
+ align:start position:0%
+enters the amplifier from the right and
+ 
+
+ align:start position:0%
+enters the amplifier from the right and
+exits on the left and then goes to a
+
+ align:start position:0%
+exits on the left and then goes to a
+ 
+
+ align:start position:0%
+exits on the left and then goes to a
+detector and above we have a scope that
+
+ align:start position:0%
+detector and above we have a scope that
+ 
+
+ align:start position:0%
+detector and above we have a scope that
+we monitor the laser intensity on and
+
+ align:start position:0%
+we monitor the laser intensity on and
+ 
+
+ align:start position:0%
+we monitor the laser intensity on and
+also a digital voltmeter that again
+
+ align:start position:0%
+also a digital voltmeter that again
+ 
+
+ align:start position:0%
+also a digital voltmeter that again
+monitors the uh laser
+
+ align:start position:0%
+monitors the uh laser
+ 
+
+ align:start position:0%
+monitors the uh laser
+intensity now when we turn on the the
+
+ align:start position:0%
+intensity now when we turn on the the
+ 
+
+ align:start position:0%
+intensity now when we turn on the the
+amplifier and you can see it nice and
+
+ align:start position:0%
+amplifier and you can see it nice and
+ 
+
+ align:start position:0%
+amplifier and you can see it nice and
+bright when we turn on the amplifier you
+
+ align:start position:0%
+bright when we turn on the amplifier you
+ 
+
+ align:start position:0%
+bright when we turn on the amplifier you
+see that indeed we get a 5% increase in
+
+ align:start position:0%
+see that indeed we get a 5% increase in
+ 
+
+ align:start position:0%
+see that indeed we get a 5% increase in
+the light going through the amplifier
+
+ align:start position:0%
+the light going through the amplifier
+ 
+
+ align:start position:0%
+the light going through the amplifier
+and we do that a few times to convince
+
+ align:start position:0%
+and we do that a few times to convince
+ 
+
+ align:start position:0%
+and we do that a few times to convince
+you that indeed that we are uh observing
+
+ align:start position:0%
+you that indeed that we are uh observing
+ 
+
+ align:start position:0%
+you that indeed that we are uh observing
+gain and we also check on initial
+
+ align:start position:0%
+gain and we also check on initial
+ 
+
+ align:start position:0%
+gain and we also check on initial
+conditions and so on but but this is
+
+ align:start position:0%
+conditions and so on but but this is
+ 
+
+ align:start position:0%
+conditions and so on but but this is
+just as a say a glimpse of this
+
+ align:start position:0%
+just as a say a glimpse of this
+ 
+
+ align:start position:0%
+just as a say a glimpse of this
+experiment now in the in the next uh
+
+ align:start position:0%
+experiment now in the in the next uh
+ 
+
+ align:start position:0%
+experiment now in the in the next uh
+demonstration we're going to look at the
+
+ align:start position:0%
+demonstration we're going to look at the
+ 
+
+ align:start position:0%
+demonstration we're going to look at the
+polarization of uh of laser light we
+
+ align:start position:0%
+polarization of uh of laser light we
+ 
+
+ align:start position:0%
+polarization of uh of laser light we
+have two kinds of lasers one with
+
+ align:start position:0%
+have two kinds of lasers one with
+ 
+
+ align:start position:0%
+have two kinds of lasers one with
+internal mirrors and one with uh
+
+ align:start position:0%
+internal mirrors and one with uh
+ 
+
+ align:start position:0%
+internal mirrors and one with uh
+external
+
+ align:start position:0%
+external
+ 
+
+ align:start position:0%
+external
+mirrors and then after that we look at
+
+ align:start position:0%
+mirrors and then after that we look at
+ 
+
+ align:start position:0%
+mirrors and then after that we look at
+uh the spectrum of the of the laser
+
+ align:start position:0%
+uh the spectrum of the of the laser
+ 
+
+ align:start position:0%
+uh the spectrum of the of the laser
+light you see whether it's indeed
+
+ align:start position:0%
+light you see whether it's indeed
+ 
+
+ align:start position:0%
+light you see whether it's indeed
+oscillating single frequency multip
+
+ align:start position:0%
+oscillating single frequency multip
+ 
+
+ align:start position:0%
+oscillating single frequency multip
+multiple frequency and so on and also
+
+ align:start position:0%
+multiple frequency and so on and also
+ 
+
+ align:start position:0%
+multiple frequency and so on and also
+the polarization of each each of these
+
+ align:start position:0%
+the polarization of each each of these
+ 
+
+ align:start position:0%
+the polarization of each each of these
+uh frequencies that that comes out from
+
+ align:start position:0%
+uh frequencies that that comes out from
+ 
+
+ align:start position:0%
+uh frequencies that that comes out from
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+laser then we have a we included a an
+
+ align:start position:0%
+laser then we have a we included a an
+ 
+
+ align:start position:0%
+laser then we have a we included a an
+interesting little demonstration here
+
+ align:start position:0%
+interesting little demonstration here
+ 
+
+ align:start position:0%
+interesting little demonstration here
+that shows that the light inside a laser
+
+ align:start position:0%
+that shows that the light inside a laser
+ 
+
+ align:start position:0%
+that shows that the light inside a laser
+cavity is much brighter than the light
+
+ align:start position:0%
+cavity is much brighter than the light
+ 
+
+ align:start position:0%
+cavity is much brighter than the light
+outside most of us who understand the
+
+ align:start position:0%
+outside most of us who understand the
+ 
+
+ align:start position:0%
+outside most of us who understand the
+theory of lasers uh believe this but
+
+ align:start position:0%
+theory of lasers uh believe this but
+ 
+
+ align:start position:0%
+theory of lasers uh believe this but
+it's nothing like uh uh demonstrating it
+
+ align:start position:0%
+it's nothing like uh uh demonstrating it
+ 
+
+ align:start position:0%
+it's nothing like uh uh demonstrating it
+and observing it then uh we show a
+
+ align:start position:0%
+and observing it then uh we show a
+ 
+
+ align:start position:0%
+and observing it then uh we show a
+little bit about the Optics of laser
+
+ align:start position:0%
+little bit about the Optics of laser
+ 
+
+ align:start position:0%
+little bit about the Optics of laser
+beams we look at the beam straight
+
+ align:start position:0%
+beams we look at the beam straight
+ 
+
+ align:start position:0%
+beams we look at the beam straight
+coming out straight from the laser then
+
+ align:start position:0%
+coming out straight from the laser then
+ 
+
+ align:start position:0%
+coming out straight from the laser then
+we spatially filter it clean it up and
+
+ align:start position:0%
+we spatially filter it clean it up and
+ 
+
+ align:start position:0%
+we spatially filter it clean it up and
+looks looks fascinating that Gan
+
+ align:start position:0%
+looks looks fascinating that Gan
+ 
+
+ align:start position:0%
+looks looks fascinating that Gan
+distribution and then we focus it and
+
+ align:start position:0%
+distribution and then we focus it and
+ 
+
+ align:start position:0%
+distribution and then we focus it and
+observe it by looking at the scattered
+
+ align:start position:0%
+observe it by looking at the scattered
+ 
+
+ align:start position:0%
+observe it by looking at the scattered
+light in uh in water we change the focal
+
+ align:start position:0%
+light in uh in water we change the focal
+ 
+
+ align:start position:0%
+light in uh in water we change the focal
+length of lenses and show you a little
+
+ align:start position:0%
+length of lenses and show you a little
+ 
+
+ align:start position:0%
+length of lenses and show you a little
+bit about the uh how the shape of the
+
+ align:start position:0%
+bit about the uh how the shape of the
+ 
+
+ align:start position:0%
+bit about the uh how the shape of the
+Gan spherical
+
+ align:start position:0%
+Gan spherical
+ 
+
+ align:start position:0%
+Gan spherical
+beam and then then the next one in the
+
+ align:start position:0%
+beam and then then the next one in the
+ 
+
+ align:start position:0%
+beam and then then the next one in the
+seventh experiment demonstration on the
+
+ align:start position:0%
+seventh experiment demonstration on the
+ 
+
+ align:start position:0%
+seventh experiment demonstration on the
+lasers we look at the transverse modes
+
+ align:start position:0%
+lasers we look at the transverse modes
+ 
+
+ align:start position:0%
+lasers we look at the transverse modes
+of a laser now these are not normally
+
+ align:start position:0%
+of a laser now these are not normally
+ 
+
+ align:start position:0%
+of a laser now these are not normally
+observed in commercial lasers because
+
+ align:start position:0%
+observed in commercial lasers because
+ 
+
+ align:start position:0%
+observed in commercial lasers because
+commercial lasers are not supposed to uh
+
+ align:start position:0%
+commercial lasers are not supposed to uh
+ 
+
+ align:start position:0%
+commercial lasers are not supposed to uh
+have transverse modes but in this case
+
+ align:start position:0%
+have transverse modes but in this case
+ 
+
+ align:start position:0%
+have transverse modes but in this case
+we got a laser that by adjusting the
+
+ align:start position:0%
+we got a laser that by adjusting the
+ 
+
+ align:start position:0%
+we got a laser that by adjusting the
+mirrors and what have you we can
+
+ align:start position:0%
+mirrors and what have you we can
+ 
+
+ align:start position:0%
+mirrors and what have you we can
+illustrate these transverse modes and
+
+ align:start position:0%
+illustrate these transverse modes and
+ 
+
+ align:start position:0%
+illustrate these transverse modes and
+then I'd like to show you a little bit
+
+ align:start position:0%
+then I'd like to show you a little bit
+ 
+
+ align:start position:0%
+then I'd like to show you a little bit
+from from this
+
+ align:start position:0%
+from from this
+ 
+
+ align:start position:0%
+from from this
+demonstration on your scope now you see
+
+ align:start position:0%
+demonstration on your scope now you see
+ 
+
+ align:start position:0%
+demonstration on your scope now you see
+on the left we see a donut mode and this
+
+ align:start position:0%
+on the left we see a donut mode and this
+ 
+
+ align:start position:0%
+on the left we see a donut mode and this
+is different quite a bit different from
+
+ align:start position:0%
+is different quite a bit different from
+ 
+
+ align:start position:0%
+is different quite a bit different from
+the normal uh single spot that we get
+
+ align:start position:0%
+the normal uh single spot that we get
+ 
+
+ align:start position:0%
+the normal uh single spot that we get
+from uh commercial lasers and uh in the
+
+ align:start position:0%
+from uh commercial lasers and uh in the
+ 
+
+ align:start position:0%
+from uh commercial lasers and uh in the
+the bottom right hand corner I'm
+
+ align:start position:0%
+the bottom right hand corner I'm
+ 
+
+ align:start position:0%
+the bottom right hand corner I'm
+adjusting the the uh the alignment of
+
+ align:start position:0%
+adjusting the the uh the alignment of
+ 
+
+ align:start position:0%
+adjusting the the uh the alignment of
+the of this laser to bring in a variety
+
+ align:start position:0%
+the of this laser to bring in a variety
+ 
+
+ align:start position:0%
+the of this laser to bring in a variety
+of these very very pretty uh transverse
+
+ align:start position:0%
+of these very very pretty uh transverse
+ 
+
+ align:start position:0%
+of these very very pretty uh transverse
+transverse modes now in the in the
+
+ align:start position:0%
+transverse modes now in the in the
+ 
+
+ align:start position:0%
+transverse modes now in the in the
+demonstration we
+
+ align:start position:0%
+demonstration we
+ 
+
+ align:start position:0%
+demonstration we
+also look at the the spectrum of these
+
+ align:start position:0%
+also look at the the spectrum of these
+ 
+
+ align:start position:0%
+also look at the the spectrum of these
+uh of these modes not just the shape of
+
+ align:start position:0%
+uh of these modes not just the shape of
+ 
+
+ align:start position:0%
+uh of these modes not just the shape of
+them we also look at the at the Spectrum
+
+ align:start position:0%
+them we also look at the at the Spectrum
+ 
+
+ align:start position:0%
+them we also look at the at the Spectrum
+and we add uh few little more
+
+ align:start position:0%
+and we add uh few little more
+ 
+
+ align:start position:0%
+and we add uh few little more
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+uh things about uh about such
+
+ align:start position:0%
+uh things about uh about such
+ 
+
+ align:start position:0%
+uh things about uh about such
+behavior number eight on the lasers is
+
+ align:start position:0%
+behavior number eight on the lasers is
+ 
+
+ align:start position:0%
+behavior number eight on the lasers is
+associated with the laser spectral width
+
+ align:start position:0%
+associated with the laser spectral width
+ 
+
+ align:start position:0%
+associated with the laser spectral width
+now the laser spectral width the
+
+ align:start position:0%
+now the laser spectral width the
+ 
+
+ align:start position:0%
+now the laser spectral width the
+intrinsic laser spectral width is
+
+ align:start position:0%
+intrinsic laser spectral width is
+ 
+
+ align:start position:0%
+intrinsic laser spectral width is
+normally not observed because it's very
+
+ align:start position:0%
+normally not observed because it's very
+ 
+
+ align:start position:0%
+normally not observed because it's very
+very narrow and it's usually corrupted
+
+ align:start position:0%
+very narrow and it's usually corrupted
+ 
+
+ align:start position:0%
+very narrow and it's usually corrupted
+by vibrations or what have you of the
+
+ align:start position:0%
+by vibrations or what have you of the
+ 
+
+ align:start position:0%
+by vibrations or what have you of the
+and shaking of the of the cavity but
+
+ align:start position:0%
+and shaking of the of the cavity but
+ 
+
+ align:start position:0%
+and shaking of the of the cavity but
+here we uh we do some clever little
+
+ align:start position:0%
+here we uh we do some clever little
+ 
+
+ align:start position:0%
+here we uh we do some clever little
+tricks to to give you a feel for the
+
+ align:start position:0%
+tricks to to give you a feel for the
+ 
+
+ align:start position:0%
+tricks to to give you a feel for the
+indeed the very extremely narrow line
+
+ align:start position:0%
+indeed the very extremely narrow line
+ 
+
+ align:start position:0%
+indeed the very extremely narrow line
+width uh that comes out from a uh from a
+
+ align:start position:0%
+width uh that comes out from a uh from a
+ 
+
+ align:start position:0%
+width uh that comes out from a uh from a
+laser uh without the effect of this
+
+ align:start position:0%
+laser uh without the effect of this
+ 
+
+ align:start position:0%
+laser uh without the effect of this
+cavity uh
+
+ align:start position:0%
+cavity uh
+ 
+
+ align:start position:0%
+cavity uh
+shaking the next one the next
+
+ align:start position:0%
+shaking the next one the next
+ 
+
+ align:start position:0%
+shaking the next one the next
+demonstration on the reflection back
+
+ align:start position:0%
+demonstration on the reflection back
+ 
+
+ align:start position:0%
+demonstration on the reflection back
+into the laser this gives us a feel of
+
+ align:start position:0%
+into the laser this gives us a feel of
+ 
+
+ align:start position:0%
+into the laser this gives us a feel of
+how lasers misbehave when we reflect the
+
+ align:start position:0%
+how lasers misbehave when we reflect the
+ 
+
+ align:start position:0%
+how lasers misbehave when we reflect the
+uh the light back into into the laser
+
+ align:start position:0%
+uh the light back into into the laser
+ 
+
+ align:start position:0%
+uh the light back into into the laser
+cavity we we we we show here that the uh
+
+ align:start position:0%
+cavity we we we we show here that the uh
+ 
+
+ align:start position:0%
+cavity we we we we show here that the uh
+that the you get a of frequency
+
+ align:start position:0%
+that the you get a of frequency
+ 
+
+ align:start position:0%
+that the you get a of frequency
+instability as well as amplitude
+
+ align:start position:0%
+instability as well as amplitude
+ 
+
+ align:start position:0%
+instability as well as amplitude
+instability when uh the laser light is
+
+ align:start position:0%
+instability when uh the laser light is
+ 
+
+ align:start position:0%
+instability when uh the laser light is
+reflected back into into the cavity then
+
+ align:start position:0%
+reflected back into into the cavity then
+ 
+
+ align:start position:0%
+reflected back into into the cavity then
+the next demonstrations we we then
+
+ align:start position:0%
+the next demonstrations we we then
+ 
+
+ align:start position:0%
+the next demonstrations we we then
+change from Helium neon laser to an
+
+ align:start position:0%
+change from Helium neon laser to an
+ 
+
+ align:start position:0%
+change from Helium neon laser to an
+argon laser and in this one number 10 we
+
+ align:start position:0%
+argon laser and in this one number 10 we
+ 
+
+ align:start position:0%
+argon laser and in this one number 10 we
+show you how powerful even an unfocused
+
+ align:start position:0%
+show you how powerful even an unfocused
+ 
+
+ align:start position:0%
+show you how powerful even an unfocused
+beam from an argon laser is just by
+
+ align:start position:0%
+beam from an argon laser is just by
+ 
+
+ align:start position:0%
+beam from an argon laser is just by
+simply uh letting it fall on a piece of
+
+ align:start position:0%
+simply uh letting it fall on a piece of
+ 
+
+ align:start position:0%
+simply uh letting it fall on a piece of
+cardboard and uh setting it on fire the
+
+ align:start position:0%
+cardboard and uh setting it on fire the
+ 
+
+ align:start position:0%
+cardboard and uh setting it on fire the
+uh next one we show that an AR laser can
+
+ align:start position:0%
+uh next one we show that an AR laser can
+ 
+
+ align:start position:0%
+uh next one we show that an AR laser can
+uh lay in several wavelengths and we can
+
+ align:start position:0%
+uh lay in several wavelengths and we can
+ 
+
+ align:start position:0%
+uh lay in several wavelengths and we can
+using using a grating we can uh we can
+
+ align:start position:0%
+using using a grating we can uh we can
+ 
+
+ align:start position:0%
+using using a grating we can uh we can
+show that indeed a laser can oscillate
+
+ align:start position:0%
+show that indeed a laser can oscillate
+ 
+
+ align:start position:0%
+show that indeed a laser can oscillate
+simultaneously at several
+
+ align:start position:0%
+simultaneously at several
+ 
+
+ align:start position:0%
+simultaneously at several
+wavelengths and here we look at a a
+
+ align:start position:0%
+wavelengths and here we look at a a
+ 
+
+ align:start position:0%
+wavelengths and here we look at a a
+method of uh of achieving single
+
+ align:start position:0%
+method of uh of achieving single
+ 
+
+ align:start position:0%
+method of uh of achieving single
+frequency behavior in a uh long uh argon
+
+ align:start position:0%
+frequency behavior in a uh long uh argon
+ 
+
+ align:start position:0%
+frequency behavior in a uh long uh argon
+laser by the use of an intra cavity
+
+ align:start position:0%
+laser by the use of an intra cavity
+ 
+
+ align:start position:0%
+laser by the use of an intra cavity
+atlon and then we show what happens if
+
+ align:start position:0%
+atlon and then we show what happens if
+ 
+
+ align:start position:0%
+atlon and then we show what happens if
+the atlon is is adjusted right and also
+
+ align:start position:0%
+the atlon is is adjusted right and also
+ 
+
+ align:start position:0%
+the atlon is is adjusted right and also
+what happens when it's not adjusted
+
+ align:start position:0%
+what happens when it's not adjusted
+ 
+
+ align:start position:0%
+what happens when it's not adjusted
+right then we go to to the very colorful
+
+ align:start position:0%
+right then we go to to the very colorful
+ 
+
+ align:start position:0%
+right then we go to to the very colorful
+uh laser which is the tunable uh D laser
+
+ align:start position:0%
+uh laser which is the tunable uh D laser
+ 
+
+ align:start position:0%
+uh laser which is the tunable uh D laser
+where we can tune the wavelength
+
+ align:start position:0%
+where we can tune the wavelength
+ 
+
+ align:start position:0%
+where we can tune the wavelength
+anywhere from Green uh to red and I
+
+ align:start position:0%
+anywhere from Green uh to red and I
+ 
+
+ align:start position:0%
+anywhere from Green uh to red and I
+would like to just take a few moments to
+
+ align:start position:0%
+would like to just take a few moments to
+ 
+
+ align:start position:0%
+would like to just take a few moments to
+show you the change in color from coming
+
+ align:start position:0%
+show you the change in color from coming
+ 
+
+ align:start position:0%
+show you the change in color from coming
+out from this uh di laser so on your on
+
+ align:start position:0%
+out from this uh di laser so on your on
+ 
+
+ align:start position:0%
+out from this uh di laser so on your on
+your screen now
+
+ align:start position:0%
+your screen now
+ 
+
+ align:start position:0%
+your screen now
+we see that the output from uh from the
+
+ align:start position:0%
+we see that the output from uh from the
+ 
+
+ align:start position:0%
+we see that the output from uh from the
+Dil laser now we we just diffuse it and
+
+ align:start position:0%
+Dil laser now we we just diffuse it and
+ 
+
+ align:start position:0%
+Dil laser now we we just diffuse it and
+let it fall on the screen you can see
+
+ align:start position:0%
+let it fall on the screen you can see
+ 
+
+ align:start position:0%
+let it fall on the screen you can see
+it's going from green to sort of uh
+
+ align:start position:0%
+it's going from green to sort of uh
+ 
+
+ align:start position:0%
+it's going from green to sort of uh
+orange and if your screen is set right
+
+ align:start position:0%
+orange and if your screen is set right
+ 
+
+ align:start position:0%
+orange and if your screen is set right
+now it's going to red and even deep red
+
+ align:start position:0%
+now it's going to red and even deep red
+ 
+
+ align:start position:0%
+now it's going to red and even deep red
+by simply uh tuning the uh uh the D
+
+ align:start position:0%
+by simply uh tuning the uh uh the D
+ 
+
+ align:start position:0%
+by simply uh tuning the uh uh the D
+laser and in the last two
+
+ align:start position:0%
+laser and in the last two
+ 
+
+ align:start position:0%
+laser and in the last two
+demonstrations we use the dilay
+
+ align:start position:0%
+demonstrations we use the dilay
+ 
+
+ align:start position:0%
+demonstrations we use the dilay
+to to
+
+ align:start position:0%
+to to
+ 
+
+ align:start position:0%
+to to
+excite uh Atomic sodium we look at the
+
+ align:start position:0%
+excite uh Atomic sodium we look at the
+ 
+
+ align:start position:0%
+excite uh Atomic sodium we look at the
+the strong fluoresence resin fluoresence
+
+ align:start position:0%
+the strong fluoresence resin fluoresence
+ 
+
+ align:start position:0%
+the strong fluoresence resin fluoresence
+from Atomic sodium when the D laser is
+
+ align:start position:0%
+from Atomic sodium when the D laser is
+ 
+
+ align:start position:0%
+from Atomic sodium when the D laser is
+tuned to it and in the final one we look
+
+ align:start position:0%
+tuned to it and in the final one we look
+ 
+
+ align:start position:0%
+tuned to it and in the final one we look
+at fluorescence from molecular iodine
+
+ align:start position:0%
+at fluorescence from molecular iodine
+ 
+
+ align:start position:0%
+at fluorescence from molecular iodine
+now in this in this
+
+ align:start position:0%
+now in this in this
+ 
+
+ align:start position:0%
+now in this in this
+demonstration we we actually show the
+
+ align:start position:0%
+demonstration we we actually show the
+ 
+
+ align:start position:0%
+demonstration we we actually show the
+the incident laser light the color of
+
+ align:start position:0%
+the incident laser light the color of
+ 
+
+ align:start position:0%
+the incident laser light the color of
+the incident laser light and
+
+ align:start position:0%
+the incident laser light and
+ 
+
+ align:start position:0%
+the incident laser light and
+simultaneously we show the color of the
+
+ align:start position:0%
+simultaneously we show the color of the
+ 
+
+ align:start position:0%
+simultaneously we show the color of the
+iodine fluoresence induced by the laser
+
+ align:start position:0%
+iodine fluoresence induced by the laser
+ 
+
+ align:start position:0%
+iodine fluoresence induced by the laser
+in some cases the colors are identical
+
+ align:start position:0%
+in some cases the colors are identical
+ 
+
+ align:start position:0%
+in some cases the colors are identical
+in some cases they're not identical at
+
+ align:start position:0%
+in some cases they're not identical at
+ 
+
+ align:start position:0%
+in some cases they're not identical at
+all and that's makes a very very nice uh
+
+ align:start position:0%
+all and that's makes a very very nice uh
+ 
+
+ align:start position:0%
+all and that's makes a very very nice uh
+demonstration now the in in uh in
+
+ align:start position:0%
+demonstration now the in in uh in
+ 
+
+ align:start position:0%
+demonstration now the in in uh in
+viewing these
+
+ align:start position:0%
+viewing these
+ 
+
+ align:start position:0%
+viewing these
+demonstrations uh you may want to use uh
+
+ align:start position:0%
+demonstrations uh you may want to use uh
+ 
+
+ align:start position:0%
+demonstrations uh you may want to use uh
+black and white instead of color because
+
+ align:start position:0%
+black and white instead of color because
+ 
+
+ align:start position:0%
+black and white instead of color because
+of the limitations in uh in video
+
+ align:start position:0%
+of the limitations in uh in video
+ 
+
+ align:start position:0%
+of the limitations in uh in video
+recording especially VHS you may want to
+
+ align:start position:0%
+recording especially VHS you may want to
+ 
+
+ align:start position:0%
+recording especially VHS you may want to
+use uh black and white in certain cases
+
+ align:start position:0%
+use uh black and white in certain cases
+ 
+
+ align:start position:0%
+use uh black and white in certain cases
+so what I'd like to do now is illustrate
+
+ align:start position:0%
+so what I'd like to do now is illustrate
+ 
+
+ align:start position:0%
+so what I'd like to do now is illustrate
+in uh in one of the defraction
+
+ align:start position:0%
+in uh in one of the defraction
+ 
+
+ align:start position:0%
+in uh in one of the defraction
+experiments in the Cross Beam defra
+
+ align:start position:0%
+experiments in the Cross Beam defra
+ 
+
+ align:start position:0%
+experiments in the Cross Beam defra
+cross multiple slit defraction
+
+ align:start position:0%
+cross multiple slit defraction
+ 
+
+ align:start position:0%
+cross multiple slit defraction
+experiment I'd like to show you how
+
+ align:start position:0%
+experiment I'd like to show you how
+ 
+
+ align:start position:0%
+experiment I'd like to show you how
+things improve the viewing improves if
+
+ align:start position:0%
+things improve the viewing improves if
+ 
+
+ align:start position:0%
+things improve the viewing improves if
+we switch to black and white
+
+ align:start position:0%
+we switch to black and white
+ 
+
+ align:start position:0%
+we switch to black and white
+one now on your screen you see the Fran
+
+ align:start position:0%
+one now on your screen you see the Fran
+ 
+
+ align:start position:0%
+one now on your screen you see the Fran
+Hofer defraction pattern of cross
+
+ align:start position:0%
+Hofer defraction pattern of cross
+ 
+
+ align:start position:0%
+Hofer defraction pattern of cross
+multiple slits or Rony
+
+ align:start position:0%
+multiple slits or Rony
+ 
+
+ align:start position:0%
+multiple slits or Rony
+rulings in the left bottom corner you
+
+ align:start position:0%
+rulings in the left bottom corner you
+ 
+
+ align:start position:0%
+rulings in the left bottom corner you
+see me uh adjusting the orientation of
+
+ align:start position:0%
+see me uh adjusting the orientation of
+ 
+
+ align:start position:0%
+see me uh adjusting the orientation of
+one of the Rony rulings with respect to
+
+ align:start position:0%
+one of the Rony rulings with respect to
+ 
+
+ align:start position:0%
+one of the Rony rulings with respect to
+the other one you can see the pattern
+
+ align:start position:0%
+the other one you can see the pattern
+ 
+
+ align:start position:0%
+the other one you can see the pattern
+which constitutes many many dots you see
+
+ align:start position:0%
+which constitutes many many dots you see
+ 
+
+ align:start position:0%
+which constitutes many many dots you see
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+rotates uh as I rotate uh one of the
+
+ align:start position:0%
+rotates uh as I rotate uh one of the
+ 
+
+ align:start position:0%
+rotates uh as I rotate uh one of the
+Rony
+
+ align:start position:0%
+Rony
+ 
+
+ align:start position:0%
+Rony
+rulings so now let's turn off the color
+
+ align:start position:0%
+rulings so now let's turn off the color
+ 
+
+ align:start position:0%
+rulings so now let's turn off the color
+and go to black and white and inde you
+
+ align:start position:0%
+and go to black and white and inde you
+ 
+
+ align:start position:0%
+and go to black and white and inde you
+can see the resolution now is higher
+
+ align:start position:0%
+can see the resolution now is higher
+ 
+
+ align:start position:0%
+can see the resolution now is higher
+because the the red doesn't uh now
+
+ align:start position:0%
+because the the red doesn't uh now
+ 
+
+ align:start position:0%
+because the the red doesn't uh now
+doesn't show the bleeding and uh and
+
+ align:start position:0%
+doesn't show the bleeding and uh and
+ 
+
+ align:start position:0%
+doesn't show the bleeding and uh and
+then you can see some of the finer spots
+
+ align:start position:0%
+then you can see some of the finer spots
+ 
+
+ align:start position:0%
+then you can see some of the finer spots
+again let's go back to full
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+color here we are back in full color and
+
+ align:start position:0%
+color here we are back in full color and
+ 
+
+ align:start position:0%
+color here we are back in full color and
+then let's switch back to black and
+
+ align:start position:0%
+then let's switch back to black and
+ 
+
+ align:start position:0%
+then let's switch back to black and
+white to show the the higher resolution
+
+ align:start position:0%
+white to show the the higher resolution
+ 
+
+ align:start position:0%
+white to show the the higher resolution
+now you may want to do that wherever you
+
+ align:start position:0%
+now you may want to do that wherever you
+ 
+
+ align:start position:0%
+now you may want to do that wherever you
+think you need uh more uh more more
+
+ align:start position:0%
+think you need uh more uh more more
+ 
+
+ align:start position:0%
+think you need uh more uh more more
+resolution to help you observe the
+
+ align:start position:0%
+resolution to help you observe the
+ 
+
+ align:start position:0%
+resolution to help you observe the
+effect now in other cases for example in
+
+ align:start position:0%
+effect now in other cases for example in
+ 
+
+ align:start position:0%
+effect now in other cases for example in
+the case of where does the light go in
+
+ align:start position:0%
+the case of where does the light go in
+ 
+
+ align:start position:0%
+the case of where does the light go in
+destructive interference in a two- beam
+
+ align:start position:0%
+destructive interference in a two- beam
+ 
+
+ align:start position:0%
+destructive interference in a two- beam
+interferometer You may wish to use
+
+ align:start position:0%
+interferometer You may wish to use
+ 
+
+ align:start position:0%
+interferometer You may wish to use
+Freeze Frame if you have that Freeze
+
+ align:start position:0%
+Freeze Frame if you have that Freeze
+ 
+
+ align:start position:0%
+Freeze Frame if you have that Freeze
+Frame
+
+ align:start position:0%
+Frame
+ 
+
+ align:start position:0%
+Frame
+capability and then you can admire the
+
+ align:start position:0%
+capability and then you can admire the
+ 
+
+ align:start position:0%
+capability and then you can admire the
+complete darkness uh the output in the
+
+ align:start position:0%
+complete darkness uh the output in the
+ 
+
+ align:start position:0%
+complete darkness uh the output in the
+output of the Michaelson
+
+ align:start position:0%
+output of the Michaelson
+ 
+
+ align:start position:0%
+output of the Michaelson
+interferometer
+
+ align:start position:0%
+interferometer
+ 
+
+ align:start position:0%
+interferometer
+now the uh most of the demonstrations
+
+ align:start position:0%
+now the uh most of the demonstrations
+ 
+
+ align:start position:0%
+now the uh most of the demonstrations
+were actually uh recorded in in here in
+
+ align:start position:0%
+were actually uh recorded in in here in
+ 
+
+ align:start position:0%
+were actually uh recorded in in here in
+the studio uh on this table uh using uh
+
+ align:start position:0%
+the studio uh on this table uh using uh
+ 
+
+ align:start position:0%
+the studio uh on this table uh using uh
+a laser like this and in fact this laser
+
+ align:start position:0%
+a laser like this and in fact this laser
+ 
+
+ align:start position:0%
+a laser like this and in fact this laser
+in most cases and some of the optical
+
+ align:start position:0%
+in most cases and some of the optical
+ 
+
+ align:start position:0%
+in most cases and some of the optical
+components few of the other
+
+ align:start position:0%
+components few of the other
+ 
+
+ align:start position:0%
+components few of the other
+demonstrations for example one with the
+
+ align:start position:0%
+demonstrations for example one with the
+ 
+
+ align:start position:0%
+demonstrations for example one with the
+Argon laser and the D laser were done in
+
+ align:start position:0%
+Argon laser and the D laser were done in
+ 
+
+ align:start position:0%
+Argon laser and the D laser were done in
+uh my laboratory at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+MIT let me remind you of one important
+
+ align:start position:0%
+MIT let me remind you of one important
+ 
+
+ align:start position:0%
+MIT let me remind you of one important
+thing that in all these
+
+ align:start position:0%
+thing that in all these
+ 
+
+ align:start position:0%
+thing that in all these
+demonstrations I do not present any
+
+ align:start position:0%
+demonstrations I do not present any
+ 
+
+ align:start position:0%
+demonstrations I do not present any
+Theory nor
+
+ align:start position:0%
+Theory nor
+ 
+
+ align:start position:0%
+Theory nor
+equations nor a
+
+ align:start position:0%
+equations nor a
+ 
+
+ align:start position:0%
+equations nor a
+diagram I think the the setup that I
+
+ align:start position:0%
+diagram I think the the setup that I
+ 
+
+ align:start position:0%
+diagram I think the the setup that I
+will use in a lot of the demonstration
+
+ align:start position:0%
+will use in a lot of the demonstration
+ 
+
+ align:start position:0%
+will use in a lot of the demonstration
+is is quite simple to follow and I
+
+ align:start position:0%
+is is quite simple to follow and I
+ 
+
+ align:start position:0%
+is is quite simple to follow and I
+describe it very very
+
+ align:start position:0%
+describe it very very
+ 
+
+ align:start position:0%
+describe it very very
+slowly but I do give some references for
+
+ align:start position:0%
+slowly but I do give some references for
+ 
+
+ align:start position:0%
+slowly but I do give some references for
+background reading in fact uh I have
+
+ align:start position:0%
+background reading in fact uh I have
+ 
+
+ align:start position:0%
+background reading in fact uh I have
+listed over here uh some of them uh in
+
+ align:start position:0%
+listed over here uh some of them uh in
+ 
+
+ align:start position:0%
+listed over here uh some of them uh in
+the area of
+
+ align:start position:0%
+the area of
+ 
+
+ align:start position:0%
+the area of
+Optics uh one recommended text is
+
+ align:start position:0%
+Optics uh one recommended text is
+ 
+
+ align:start position:0%
+Optics uh one recommended text is
+Introduction to Modern Optics by fouls
+
+ align:start position:0%
+Introduction to Modern Optics by fouls
+ 
+
+ align:start position:0%
+Introduction to Modern Optics by fouls
+and another one Optics by by hect and
+
+ align:start position:0%
+and another one Optics by by hect and
+ 
+
+ align:start position:0%
+and another one Optics by by hect and
+there of course other ones and you may
+
+ align:start position:0%
+there of course other ones and you may
+ 
+
+ align:start position:0%
+there of course other ones and you may
+have your uh your favorite uh uh Book on
+
+ align:start position:0%
+have your uh your favorite uh uh Book on
+ 
+
+ align:start position:0%
+have your uh your favorite uh uh Book on
+an Optics and you can certainly uh use
+
+ align:start position:0%
+an Optics and you can certainly uh use
+ 
+
+ align:start position:0%
+an Optics and you can certainly uh use
+that to review background material in
+
+ align:start position:0%
+that to review background material in
+ 
+
+ align:start position:0%
+that to review background material in
+the area of lasers I've selected
+
+ align:start position:0%
+the area of lasers I've selected
+ 
+
+ align:start position:0%
+the area of lasers I've selected
+introduction to Optical Electronics by
+
+ align:start position:0%
+introduction to Optical Electronics by
+ 
+
+ align:start position:0%
+introduction to Optical Electronics by
+yariv another one lasers by
+
+ align:start position:0%
+yariv another one lasers by
+ 
+
+ align:start position:0%
+yariv another one lasers by
+Sigman and Laser Electronics by
+
+ align:start position:0%
+Sigman and Laser Electronics by
+ 
+
+ align:start position:0%
+Sigman and Laser Electronics by
+Verdan and finally a very readable uh
+
+ align:start position:0%
+Verdan and finally a very readable uh
+ 
+
+ align:start position:0%
+Verdan and finally a very readable uh
+simplified treatment uh of lasers uh
+
+ align:start position:0%
+simplified treatment uh of lasers uh
+ 
+
+ align:start position:0%
+simplified treatment uh of lasers uh
+with a title introduction to lasers and
+
+ align:start position:0%
+with a title introduction to lasers and
+ 
+
+ align:start position:0%
+with a title introduction to lasers and
+their applications by OA Ken and uh and
+
+ align:start position:0%
+their applications by OA Ken and uh and
+ 
+
+ align:start position:0%
+their applications by OA Ken and uh and
+Roads and as I mentioned before uh I'll
+
+ align:start position:0%
+Roads and as I mentioned before uh I'll
+ 
+
+ align:start position:0%
+Roads and as I mentioned before uh I'll
+uh mention some background reading if if
+
+ align:start position:0%
+uh mention some background reading if if
+ 
+
+ align:start position:0%
+uh mention some background reading if if
+you need to connect the the background
+
+ align:start position:0%
+you need to connect the the background
+ 
+
+ align:start position:0%
+you need to connect the the background
+reading with the with the
+
+ align:start position:0%
+reading with the with the
+ 
+
+ align:start position:0%
+reading with the with the
+demonstrations now I'd like to turn to
+
+ align:start position:0%
+demonstrations now I'd like to turn to
+ 
+
+ align:start position:0%
+demonstrations now I'd like to turn to
+some hints for people who who are going
+
+ align:start position:0%
+some hints for people who who are going
+ 
+
+ align:start position:0%
+some hints for people who who are going
+to be using or viewing these tapes now
+
+ align:start position:0%
+to be using or viewing these tapes now
+ 
+
+ align:start position:0%
+to be using or viewing these tapes now
+for the individual or people or maybe in
+
+ align:start position:0%
+for the individual or people or maybe in
+ 
+
+ align:start position:0%
+for the individual or people or maybe in
+small groups I think what you want to do
+
+ align:start position:0%
+small groups I think what you want to do
+ 
+
+ align:start position:0%
+small groups I think what you want to do
+first is to review the material so that
+
+ align:start position:0%
+first is to review the material so that
+ 
+
+ align:start position:0%
+first is to review the material so that
+it's uh you appreciate the
+
+ align:start position:0%
+it's uh you appreciate the
+ 
+
+ align:start position:0%
+it's uh you appreciate the
+demonstrations uh a little bit more and
+
+ align:start position:0%
+demonstrations uh a little bit more and
+ 
+
+ align:start position:0%
+demonstrations uh a little bit more and
+then I'd like you to answer some of the
+
+ align:start position:0%
+then I'd like you to answer some of the
+ 
+
+ align:start position:0%
+then I'd like you to answer some of the
+questions that I leave unanswered or the
+
+ align:start position:0%
+questions that I leave unanswered or the
+ 
+
+ align:start position:0%
+questions that I leave unanswered or the
+question that I pose in the
+
+ align:start position:0%
+question that I pose in the
+ 
+
+ align:start position:0%
+question that I pose in the
+demonstrations and finally I'd like you
+
+ align:start position:0%
+demonstrations and finally I'd like you
+ 
+
+ align:start position:0%
+demonstrations and finally I'd like you
+to go back and reexamine the the
+
+ align:start position:0%
+to go back and reexamine the the
+ 
+
+ align:start position:0%
+to go back and reexamine the the
+background material and hopefully that
+
+ align:start position:0%
+background material and hopefully that
+ 
+
+ align:start position:0%
+background material and hopefully that
+you'll get uh more out of these
+
+ align:start position:0%
+you'll get uh more out of these
+ 
+
+ align:start position:0%
+you'll get uh more out of these
+demonstration this
+
+ align:start position:0%
+demonstration this
+ 
+
+ align:start position:0%
+demonstration this
+way now for the
+
+ align:start position:0%
+way now for the
+ 
+
+ align:start position:0%
+way now for the
+instructor of
+
+ align:start position:0%
+instructor of
+ 
+
+ align:start position:0%
+instructor of
+course we all know that instructors
+
+ align:start position:0%
+course we all know that instructors
+ 
+
+ align:start position:0%
+course we all know that instructors
+already know their background material
+
+ align:start position:0%
+already know their background material
+ 
+
+ align:start position:0%
+already know their background material
+so you don't need to review that but I
+
+ align:start position:0%
+so you don't need to review that but I
+ 
+
+ align:start position:0%
+so you don't need to review that but I
+would like you to do before showing
+
+ align:start position:0%
+would like you to do before showing
+ 
+
+ align:start position:0%
+would like you to do before showing
+these demonstrations in class is is look
+
+ align:start position:0%
+these demonstrations in class is is look
+ 
+
+ align:start position:0%
+these demonstrations in class is is look
+at these
+
+ align:start position:0%
+at these
+ 
+
+ align:start position:0%
+at these
+demonstrations select appropriate
+
+ align:start position:0%
+demonstrations select appropriate
+ 
+
+ align:start position:0%
+demonstrations select appropriate
+sections and then only show these
+
+ align:start position:0%
+sections and then only show these
+ 
+
+ align:start position:0%
+sections and then only show these
+appropriate sections in class as you as
+
+ align:start position:0%
+appropriate sections in class as you as
+ 
+
+ align:start position:0%
+appropriate sections in class as you as
+you uh discuss the the theory or
+
+ align:start position:0%
+you uh discuss the the theory or
+ 
+
+ align:start position:0%
+you uh discuss the the theory or
+whatever the background that that that
+
+ align:start position:0%
+whatever the background that that that
+ 
+
+ align:start position:0%
+whatever the background that that that
+you give the the students and I think in
+
+ align:start position:0%
+you give the the students and I think in
+ 
+
+ align:start position:0%
+you give the the students and I think in
+this way uh uh it it will come at a very
+
+ align:start position:0%
+this way uh uh it it will come at a very
+ 
+
+ align:start position:0%
+this way uh uh it it will come at a very
+opportune
+
+ align:start position:0%
+opportune
+ 
+
+ align:start position:0%
+opportune
+moment
+
+ align:start position:0%
+moment
+ 
+
+ align:start position:0%
+moment
+finally I think in some
+
+ align:start position:0%
+finally I think in some
+ 
+
+ align:start position:0%
+finally I think in some
+cases you may want to turn off the audio
+
+ align:start position:0%
+cases you may want to turn off the audio
+ 
+
+ align:start position:0%
+cases you may want to turn off the audio
+and substitute your own voice describing
+
+ align:start position:0%
+and substitute your own voice describing
+ 
+
+ align:start position:0%
+and substitute your own voice describing
+describing the the effects because in in
+
+ align:start position:0%
+describing the the effects because in in
+ 
+
+ align:start position:0%
+describing the the effects because in in
+some of the cases uh the uh the
+
+ align:start position:0%
+some of the cases uh the uh the
+ 
+
+ align:start position:0%
+some of the cases uh the uh the
+demonstrations are elaborate and and
+
+ align:start position:0%
+demonstrations are elaborate and and
+ 
+
+ align:start position:0%
+demonstrations are elaborate and and
+take a while and if you don't have that
+
+ align:start position:0%
+take a while and if you don't have that
+ 
+
+ align:start position:0%
+take a while and if you don't have that
+much time in class then there's no
+
+ align:start position:0%
+much time in class then there's no
+ 
+
+ align:start position:0%
+much time in class then there's no
+reason why you can turn off the audio
+
+ align:start position:0%
+reason why you can turn off the audio
+ 
+
+ align:start position:0%
+reason why you can turn off the audio
+and uh and describe it yourself and then
+
+ align:start position:0%
+and uh and describe it yourself and then
+ 
+
+ align:start position:0%
+and uh and describe it yourself and then
+you can make the experiment the
+
+ align:start position:0%
+you can make the experiment the
+ 
+
+ align:start position:0%
+you can make the experiment the
+demonstration uh um seem much shorter as
+
+ align:start position:0%
+demonstration uh um seem much shorter as
+ 
+
+ align:start position:0%
+demonstration uh um seem much shorter as
+I mentioned earlier we have 8 hours of
+
+ align:start position:0%
+I mentioned earlier we have 8 hours of
+ 
+
+ align:start position:0%
+I mentioned earlier we have 8 hours of
+videotape
+
+ align:start position:0%
+videotape
+ 
+
+ align:start position:0%
+videotape
+demonstrations they certainly wouldn't
+
+ align:start position:0%
+demonstrations they certainly wouldn't
+ 
+
+ align:start position:0%
+demonstrations they certainly wouldn't
+have been possible
+
+ align:start position:0%
+have been possible
+ 
+
+ align:start position:0%
+have been possible
+if it wasn't for the able contributions
+
+ align:start position:0%
+if it wasn't for the able contributions
+ 
+
+ align:start position:0%
+if it wasn't for the able contributions
+of two of my graduate students Steven
+
+ align:start position:0%
+of two of my graduate students Steven
+ 
+
+ align:start position:0%
+of two of my graduate students Steven
+Smith and farad Zarin
+
+ align:start position:0%
+Smith and farad Zarin
+ 
+
+ align:start position:0%
+Smith and farad Zarin
+nich in addition I'd like to give credit
+
+ align:start position:0%
+nich in addition I'd like to give credit
+ 
+
+ align:start position:0%
+nich in addition I'd like to give credit
+to the very able CES video staff for
+
+ align:start position:0%
+to the very able CES video staff for
+ 
+
+ align:start position:0%
+to the very able CES video staff for
+developing these demonstrations with us
+
+ align:start position:0%
+developing these demonstrations with us
+ 
+
+ align:start position:0%
+developing these demonstrations with us
+as you can imagine it's not like your
+
+ align:start position:0%
+as you can imagine it's not like your
+ 
+
+ align:start position:0%
+as you can imagine it's not like your
+normal uh uh video program where you're
+
+ align:start position:0%
+normal uh uh video program where you're
+ 
+
+ align:start position:0%
+normal uh uh video program where you're
+only recording people
+
+ align:start position:0%
+only recording people
+ 
+
+ align:start position:0%
+only recording people
+talking and finally I'd like to thank
+
+ align:start position:0%
+talking and finally I'd like to thank
+ 
+
+ align:start position:0%
+talking and finally I'd like to thank
+all my students over the years both in
+
+ align:start position:0%
+all my students over the years both in
+ 
+
+ align:start position:0%
+all my students over the years both in
+regular MIT classes as well in the as in
+
+ align:start position:0%
+regular MIT classes as well in the as in
+ 
+
+ align:start position:0%
+regular MIT classes as well in the as in
+the summer session all those students
+
+ align:start position:0%
+the summer session all those students
+ 
+
+ align:start position:0%
+the summer session all those students
+who asked good questions because it's
+
+ align:start position:0%
+who asked good questions because it's
+ 
+
+ align:start position:0%
+who asked good questions because it's
+these questions that that really
+
+ align:start position:0%
+these questions that that really
+ 
+
+ align:start position:0%
+these questions that that really
+encouraged us to develop these video
+
+ align:start position:0%
+encouraged us to develop these video
+ 
+
+ align:start position:0%
+encouraged us to develop these video
+demonstrations and in closing
+
+ align:start position:0%
+demonstrations and in closing
+ 
+
+ align:start position:0%
+demonstrations and in closing
+before I let you go and view these
+
+ align:start position:0%
+before I let you go and view these
+ 
+
+ align:start position:0%
+before I let you go and view these
+demonstrations I'd like to say that I
+
+ align:start position:0%
+demonstrations I'd like to say that I
+ 
+
+ align:start position:0%
+demonstrations I'd like to say that I
+hope you'll enjoy
+
+ align:start position:0%
+hope you'll enjoy
+ 
+
+ align:start position:0%
+hope you'll enjoy
+looking at them and learn from
+
+ align:start position:0%
+looking at them and learn from
+ 
+
+ align:start position:0%
+looking at them and learn from
+them and more important I hope that they
+
+ align:start position:0%
+them and more important I hope that they
+ 
+
+ align:start position:0%
+them and more important I hope that they
+will increase your excitement and
+
+ align:start position:0%
+will increase your excitement and
+ 
+
+ align:start position:0%
+will increase your excitement and
+enthusiasm for the laser and Optics feel
+
+ align:start position:0%
+enthusiasm for the laser and Optics feel
+ 
+
+ align:start position:0%
+enthusiasm for the laser and Optics feel
+now these demonstrations are by no means
+
+ align:start position:0%
+now these demonstrations are by no means
+ 
+
+ align:start position:0%
+now these demonstrations are by no means
+perfect I'm sure there are lots of
+
+ align:start position:0%
+perfect I'm sure there are lots of
+ 
+
+ align:start position:0%
+perfect I'm sure there are lots of
+improvements that can be made but I
+
+ align:start position:0%
+improvements that can be made but I
+ 
+
+ align:start position:0%
+improvements that can be made but I
+think that they illustrate what they're
+
+ align:start position:0%
+think that they illustrate what they're
+ 
+
+ align:start position:0%
+think that they illustrate what they're
+supposed to illustrate quite clearly
+
+ align:start position:0%
+supposed to illustrate quite clearly
+ 
+
+ align:start position:0%
+supposed to illustrate quite clearly
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+finally after viewing these
+
+ align:start position:0%
+finally after viewing these
+ 
+
+ align:start position:0%
+finally after viewing these
+demonstrations if you have any comments
+
+ align:start position:0%
+demonstrations if you have any comments
+ 
+
+ align:start position:0%
+demonstrations if you have any comments
+or some suggestions for other
+
+ align:start position:0%
+or some suggestions for other
+ 
+
+ align:start position:0%
+or some suggestions for other
+demonstrations that we may have left out
+
+ align:start position:0%
+demonstrations that we may have left out
+ 
+
+ align:start position:0%
+demonstrations that we may have left out
+we certainly would be
+
+ align:start position:0%
+we certainly would be
+ 
+
+ align:start position:0%
+we certainly would be
+grateful if you would contact us and let
+
+ align:start position:0%
+grateful if you would contact us and let
+ 
+
+ align:start position:0%
+grateful if you would contact us and let
+us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know
\ No newline at end of file
diff --git a/1i5TDkri78Y.txt b/1i5TDkri78Y.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ebe58107e93c5dc73080f8d0fe56b17ccc82bf45
--- /dev/null
+++ b/1i5TDkri78Y.txt
@@ -0,0 +1,1251 @@
+align:start position:0%
+ 
+in this video we're going to explore our
+
+ align:start position:0%
+in this video we're going to explore our
+ 
+
+ align:start position:0%
+in this video we're going to explore our
+linear optimization model further we're
+
+ align:start position:0%
+linear optimization model further we're
+ 
+
+ align:start position:0%
+linear optimization model further we're
+going to use it to answer some what-if
+
+ align:start position:0%
+going to use it to answer some what-if
+ 
+
+ align:start position:0%
+going to use it to answer some what-if
+questions and to conduct some
+
+ align:start position:0%
+questions and to conduct some
+ 
+
+ align:start position:0%
+questions and to conduct some
+sensitivity analysis so here we have a
+
+ align:start position:0%
+sensitivity analysis so here we have a
+ 
+
+ align:start position:0%
+sensitivity analysis so here we have a
+spreadsheet that's formatted very
+
+ align:start position:0%
+spreadsheet that's formatted very
+ 
+
+ align:start position:0%
+spreadsheet that's formatted very
+similar to the spreadsheets that we've
+
+ align:start position:0%
+similar to the spreadsheets that we've
+ 
+
+ align:start position:0%
+similar to the spreadsheets that we've
+used in video 5 and video 6 so we have
+
+ align:start position:0%
+used in video 5 and video 6 so we have
+ 
+
+ align:start position:0%
+used in video 5 and video 6 so we have
+the data up here we have the price per
+
+ align:start position:0%
+the data up here we have the price per
+ 
+
+ align:start position:0%
+the data up here we have the price per
+click the click-through rate the average
+
+ align:start position:0%
+click the click-through rate the average
+ 
+
+ align:start position:0%
+click the click-through rate the average
+price per display the budgets the query
+
+ align:start position:0%
+price per display the budgets the query
+ 
+
+ align:start position:0%
+price per display the budgets the query
+estimates below those we have the
+
+ align:start position:0%
+estimates below those we have the
+ 
+
+ align:start position:0%
+estimates below those we have the
+variables so we have the cells
+
+ align:start position:0%
+variables so we have the cells
+ 
+
+ align:start position:0%
+variables so we have the cells
+corresponding to the decision variables
+
+ align:start position:0%
+corresponding to the decision variables
+ 
+
+ align:start position:0%
+corresponding to the decision variables
+we have the cell corresponding to the
+
+ align:start position:0%
+we have the cell corresponding to the
+ 
+
+ align:start position:0%
+we have the cell corresponding to the
+objective and to the right of these we
+
+ align:start position:0%
+objective and to the right of these we
+ 
+
+ align:start position:0%
+objective and to the right of these we
+have cells that are containing the
+
+ align:start position:0%
+have cells that are containing the
+ 
+
+ align:start position:0%
+have cells that are containing the
+values of the decision variables and a
+
+ align:start position:0%
+values of the decision variables and a
+ 
+
+ align:start position:0%
+values of the decision variables and a
+cell that contains the value of the
+
+ align:start position:0%
+cell that contains the value of the
+ 
+
+ align:start position:0%
+cell that contains the value of the
+revenue from our original solution from
+
+ align:start position:0%
+revenue from our original solution from
+ 
+
+ align:start position:0%
+revenue from our original solution from
+video 5 and so what we're going to do is
+
+ align:start position:0%
+video 5 and so what we're going to do is
+ 
+
+ align:start position:0%
+video 5 and so what we're going to do is
+we're going to change our data that
+
+ align:start position:0%
+we're going to change our data that
+ 
+
+ align:start position:0%
+we're going to change our data that
+we're going to see how the solution
+
+ align:start position:0%
+we're going to see how the solution
+ 
+
+ align:start position:0%
+we're going to see how the solution
+changes and how the objective value
+
+ align:start position:0%
+changes and how the objective value
+ 
+
+ align:start position:0%
+changes and how the objective value
+changes and compare it to original
+
+ align:start position:0%
+changes and compare it to original
+ 
+
+ align:start position:0%
+changes and compare it to original
+solution so as one of the questions that
+
+ align:start position:0%
+solution so as one of the questions that
+ 
+
+ align:start position:0%
+solution so as one of the questions that
+we might consider let's consider the
+
+ align:start position:0%
+we might consider let's consider the
+ 
+
+ align:start position:0%
+we might consider let's consider the
+following question what would happen if
+
+ align:start position:0%
+following question what would happen if
+ 
+
+ align:start position:0%
+following question what would happen if
+the click-through rate of AT&T with
+
+ align:start position:0%
+the click-through rate of AT&T with
+ 
+
+ align:start position:0%
+the click-through rate of AT&T with
+query 1 increased from 0.1 to 0.5 so to
+
+ align:start position:0%
+query 1 increased from 0.1 to 0.5 so to
+ 
+
+ align:start position:0%
+query 1 increased from 0.1 to 0.5 so to
+answer this question let's curl up in
+
+ align:start position:0%
+answer this question let's curl up in
+ 
+
+ align:start position:0%
+answer this question let's curl up in
+the spreadsheet until we hit the
+
+ align:start position:0%
+the spreadsheet until we hit the
+ 
+
+ align:start position:0%
+the spreadsheet until we hit the
+click-through rate and let's change the
+
+ align:start position:0%
+click-through rate and let's change the
+ 
+
+ align:start position:0%
+click-through rate and let's change the
+click-through rates from 0.1 to 0.5 now
+
+ align:start position:0%
+click-through rates from 0.1 to 0.5 now
+ 
+
+ align:start position:0%
+click-through rates from 0.1 to 0.5 now
+if we do this you may have noticed that
+
+ align:start position:0%
+if we do this you may have noticed that
+ 
+
+ align:start position:0%
+if we do this you may have noticed that
+the average price per display 480 and
+
+ align:start position:0%
+the average price per display 480 and
+ 
+
+ align:start position:0%
+the average price per display 480 and
+query 1 also changed so of course this
+
+ align:start position:0%
+query 1 also changed so of course this
+ 
+
+ align:start position:0%
+query 1 also changed so of course this
+makes sense because the average price
+
+ align:start position:0%
+makes sense because the average price
+ 
+
+ align:start position:0%
+makes sense because the average price
+per display is just a click through rate
+
+ align:start position:0%
+per display is just a click through rate
+ 
+
+ align:start position:0%
+per display is just a click through rate
+multiply it by the price per click and
+
+ align:start position:0%
+multiply it by the price per click and
+ 
+
+ align:start position:0%
+multiply it by the price per click and
+here the way we spread up we've set up
+
+ align:start position:0%
+here the way we spread up we've set up
+ 
+
+ align:start position:0%
+here the way we spread up we've set up
+the spreadsheet is so that these cells
+
+ align:start position:0%
+the spreadsheet is so that these cells
+ 
+
+ align:start position:0%
+the spreadsheet is so that these cells
+are exactly the product of the
+
+ align:start position:0%
+are exactly the product of the
+ 
+
+ align:start position:0%
+are exactly the product of the
+corresponding cells so the cells that
+
+ align:start position:0%
+corresponding cells so the cells that
+ 
+
+ align:start position:0%
+corresponding cells so the cells that
+corresponds to the click-through rate
+
+ align:start position:0%
+corresponds to the click-through rate
+ 
+
+ align:start position:0%
+corresponds to the click-through rate
+and the price per click for that
+
+ align:start position:0%
+and the price per click for that
+ 
+
+ align:start position:0%
+and the price per click for that
+respective query and advertiser
+
+ align:start position:0%
+respective query and advertiser
+ 
+
+ align:start position:0%
+respective query and advertiser
+combination so so our average price per
+
+ align:start position:0%
+combination so so our average price per
+ 
+
+ align:start position:0%
+combination so so our average price per
+display has changed appropriately and so
+
+ align:start position:0%
+display has changed appropriately and so
+ 
+
+ align:start position:0%
+display has changed appropriately and so
+now we just scroll down until we see our
+
+ align:start position:0%
+now we just scroll down until we see our
+ 
+
+ align:start position:0%
+now we just scroll down until we see our
+variables and we see our objective and
+
+ align:start position:0%
+variables and we see our objective and
+ 
+
+ align:start position:0%
+variables and we see our objective and
+let's click on tools' let's open up the
+
+ align:start position:0%
+let's click on tools' let's open up the
+ 
+
+ align:start position:0%
+let's click on tools' let's open up the
+solver and we have the solver configured
+
+ align:start position:0%
+solver and we have the solver configured
+ 
+
+ align:start position:0%
+solver and we have the solver configured
+the exact same way from last time so we
+
+ align:start position:0%
+the exact same way from last time so we
+ 
+
+ align:start position:0%
+the exact same way from last time so we
+don't need to do anything here and so
+
+ align:start position:0%
+don't need to do anything here and so
+ 
+
+ align:start position:0%
+don't need to do anything here and so
+now all we have to do is just hit solve
+
+ align:start position:0%
+now all we have to do is just hit solve
+ 
+
+ align:start position:0%
+now all we have to do is just hit solve
+and click on keep result and voila we
+
+ align:start position:0%
+and click on keep result and voila we
+ 
+
+ align:start position:0%
+and click on keep result and voila we
+have a new solution so now several
+
+ align:start position:0%
+have a new solution so now several
+ 
+
+ align:start position:0%
+have a new solution so now several
+things have changed with this
+
+ align:start position:0%
+things have changed with this
+ 
+
+ align:start position:0%
+things have changed with this
+solution if you if you can see so the
+
+ align:start position:0%
+solution if you if you can see so the
+ 
+
+ align:start position:0%
+solution if you if you can see so the
+first thing is that the allocations have
+
+ align:start position:0%
+first thing is that the allocations have
+ 
+
+ align:start position:0%
+first thing is that the allocations have
+changed so for instance we allocate
+
+ align:start position:0%
+changed so for instance we allocate
+ 
+
+ align:start position:0%
+changed so for instance we allocate
+query one and eighty sixty eight times
+
+ align:start position:0%
+query one and eighty sixty eight times
+ 
+
+ align:start position:0%
+query one and eighty sixty eight times
+so we decide to show eighteen t sad with
+
+ align:start position:0%
+so we decide to show eighteen t sad with
+ 
+
+ align:start position:0%
+so we decide to show eighteen t sad with
+query 168 times as opposed to the
+
+ align:start position:0%
+query 168 times as opposed to the
+ 
+
+ align:start position:0%
+query 168 times as opposed to the
+original solution where we did it forty
+
+ align:start position:0%
+original solution where we did it forty
+ 
+
+ align:start position:0%
+original solution where we did it forty
+times and we can also see that eighty is
+
+ align:start position:0%
+times and we can also see that eighty is
+ 
+
+ align:start position:0%
+times and we can also see that eighty is
+never shown with query two or query
+
+ align:start position:0%
+never shown with query two or query
+ 
+
+ align:start position:0%
+never shown with query two or query
+three in her new solution whereas before
+
+ align:start position:0%
+three in her new solution whereas before
+ 
+
+ align:start position:0%
+three in her new solution whereas before
+it was shown 40 times the query two and
+
+ align:start position:0%
+it was shown 40 times the query two and
+ 
+
+ align:start position:0%
+it was shown 40 times the query two and
+eighty times with curry three similarly
+
+ align:start position:0%
+eighty times with curry three similarly
+ 
+
+ align:start position:0%
+eighty times with curry three similarly
+we show t-mobile 72 times with Clary one
+
+ align:start position:0%
+we show t-mobile 72 times with Clary one
+ 
+
+ align:start position:0%
+we show t-mobile 72 times with Clary one
+whereas before we only showed it hundred
+
+ align:start position:0%
+whereas before we only showed it hundred
+ 
+
+ align:start position:0%
+whereas before we only showed it hundred
+times and we also show T Mobile with
+
+ align:start position:0%
+times and we also show T Mobile with
+ 
+
+ align:start position:0%
+times and we also show T Mobile with
+query three fourteen times whereas
+
+ align:start position:0%
+query three fourteen times whereas
+ 
+
+ align:start position:0%
+query three fourteen times whereas
+before we didn't show it at all with
+
+ align:start position:0%
+before we didn't show it at all with
+ 
+
+ align:start position:0%
+before we didn't show it at all with
+query three and Verizon's allocations
+
+ align:start position:0%
+query three and Verizon's allocations
+ 
+
+ align:start position:0%
+query three and Verizon's allocations
+say the same as before
+
+ align:start position:0%
+say the same as before
+ 
+
+ align:start position:0%
+say the same as before
+in terms of the revenue our revenue has
+
+ align:start position:0%
+in terms of the revenue our revenue has
+ 
+
+ align:start position:0%
+in terms of the revenue our revenue has
+gone up slightly from four hundred
+
+ align:start position:0%
+gone up slightly from four hundred
+ 
+
+ align:start position:0%
+gone up slightly from four hundred
+twenty eight dollars in the original
+
+ align:start position:0%
+twenty eight dollars in the original
+ 
+
+ align:start position:0%
+twenty eight dollars in the original
+solution to four hundred and thirty
+
+ align:start position:0%
+solution to four hundred and thirty
+ 
+
+ align:start position:0%
+solution to four hundred and thirty
+dollars in the new solution now this may
+
+ align:start position:0%
+dollars in the new solution now this may
+ 
+
+ align:start position:0%
+dollars in the new solution now this may
+seem by it like a small amount but
+
+ align:start position:0%
+seem by it like a small amount but
+ 
+
+ align:start position:0%
+seem by it like a small amount but
+actually this is the most that we can
+
+ align:start position:0%
+actually this is the most that we can
+ 
+
+ align:start position:0%
+actually this is the most that we can
+hope to achieve and the reason for this
+
+ align:start position:0%
+hope to achieve and the reason for this
+ 
+
+ align:start position:0%
+hope to achieve and the reason for this
+is if we scroll down if we look at our
+
+ align:start position:0%
+is if we scroll down if we look at our
+ 
+
+ align:start position:0%
+is if we scroll down if we look at our
+budgets so the budget for AT&T is 170
+
+ align:start position:0%
+budgets so the budget for AT&T is 170
+ 
+
+ align:start position:0%
+budgets so the budget for AT&T is 170
+for t-mobile hundred and four isin is
+
+ align:start position:0%
+for t-mobile hundred and four isin is
+ 
+
+ align:start position:0%
+for t-mobile hundred and four isin is
+160 if we add up these values you can
+
+ align:start position:0%
+160 if we add up these values you can
+ 
+
+ align:start position:0%
+160 if we add up these values you can
+see that actually the sum of these
+
+ align:start position:0%
+see that actually the sum of these
+ 
+
+ align:start position:0%
+see that actually the sum of these
+values is 430 now this isn't a
+
+ align:start position:0%
+values is 430 now this isn't a
+ 
+
+ align:start position:0%
+values is 430 now this isn't a
+coincidence
+
+ align:start position:0%
+coincidence
+ 
+
+ align:start position:0%
+coincidence
+in fact if you think about it this makes
+
+ align:start position:0%
+in fact if you think about it this makes
+ 
+
+ align:start position:0%
+in fact if you think about it this makes
+sense because what Google earns from
+
+ align:start position:0%
+sense because what Google earns from
+ 
+
+ align:start position:0%
+sense because what Google earns from
+each advertiser is exactly how much that
+
+ align:start position:0%
+each advertiser is exactly how much that
+ 
+
+ align:start position:0%
+each advertiser is exactly how much that
+advertiser spends and if the most that
+
+ align:start position:0%
+advertiser spends and if the most that
+ 
+
+ align:start position:0%
+advertiser spends and if the most that
+each advertiser spends is that
+
+ align:start position:0%
+each advertiser spends is that
+ 
+
+ align:start position:0%
+each advertiser spends is that
+advertisers budget then the most the
+
+ align:start position:0%
+advertisers budget then the most the
+ 
+
+ align:start position:0%
+advertisers budget then the most the
+Google could hope to earn is in fact the
+
+ align:start position:0%
+Google could hope to earn is in fact the
+ 
+
+ align:start position:0%
+Google could hope to earn is in fact the
+sum of these budgets so in fact we're
+
+ align:start position:0%
+sum of these budgets so in fact we're
+ 
+
+ align:start position:0%
+sum of these budgets so in fact we're
+attaining the highest possible revenue
+
+ align:start position:0%
+attaining the highest possible revenue
+ 
+
+ align:start position:0%
+attaining the highest possible revenue
+that we can hope to a team in this case
+
+ align:start position:0%
+that we can hope to a team in this case
+ 
+
+ align:start position:0%
+that we can hope to a team in this case
+so that was rather interesting and now
+
+ align:start position:0%
+so that was rather interesting and now
+ 
+
+ align:start position:0%
+so that was rather interesting and now
+let's change back the click-through rate
+
+ align:start position:0%
+let's change back the click-through rate
+ 
+
+ align:start position:0%
+let's change back the click-through rate
+from 0.5 back to the original value of
+
+ align:start position:0%
+from 0.5 back to the original value of
+ 
+
+ align:start position:0%
+from 0.5 back to the original value of
+0.1 and let's answer another question so
+
+ align:start position:0%
+0.1 and let's answer another question so
+ 
+
+ align:start position:0%
+0.1 and let's answer another question so
+the question that we deny a lot that we
+
+ align:start position:0%
+the question that we deny a lot that we
+ 
+
+ align:start position:0%
+the question that we deny a lot that we
+now like to answer is what would happen
+
+ align:start position:0%
+now like to answer is what would happen
+ 
+
+ align:start position:0%
+now like to answer is what would happen
+if 18 T's budget increased from 170 to
+
+ align:start position:0%
+if 18 T's budget increased from 170 to
+ 
+
+ align:start position:0%
+if 18 T's budget increased from 170 to
+200 so for example 18 T calls us and
+
+ align:start position:0%
+200 so for example 18 T calls us and
+ 
+
+ align:start position:0%
+200 so for example 18 T calls us and
+tells us that actually you know they can
+
+ align:start position:0%
+tells us that actually you know they can
+ 
+
+ align:start position:0%
+tells us that actually you know they can
+afford more advertisements so how would
+
+ align:start position:0%
+afford more advertisements so how would
+ 
+
+ align:start position:0%
+afford more advertisements so how would
+that change your solution well in this
+
+ align:start position:0%
+that change your solution well in this
+ 
+
+ align:start position:0%
+that change your solution well in this
+case let's just find eight
+
+ align:start position:0%
+case let's just find eight
+ 
+
+ align:start position:0%
+case let's just find eight
+tee's budget data so in this case it is
+
+ align:start position:0%
+tee's budget data so in this case it is
+ 
+
+ align:start position:0%
+tee's budget data so in this case it is
+the cell here and let's change it from
+
+ align:start position:0%
+the cell here and let's change it from
+ 
+
+ align:start position:0%
+the cell here and let's change it from
+170 to 200 now let's scroll down to our
+
+ align:start position:0%
+170 to 200 now let's scroll down to our
+ 
+
+ align:start position:0%
+170 to 200 now let's scroll down to our
+variables and our objective and let's
+
+ align:start position:0%
+variables and our objective and let's
+ 
+
+ align:start position:0%
+variables and our objective and let's
+just set them back to 0 and now let's go
+
+ align:start position:0%
+just set them back to 0 and now let's go
+ 
+
+ align:start position:0%
+just set them back to 0 and now let's go
+to tools again let's open up the solver
+
+ align:start position:0%
+to tools again let's open up the solver
+ 
+
+ align:start position:0%
+to tools again let's open up the solver
+and let's get solve we get 428 which is
+
+ align:start position:0%
+and let's get solve we get 428 which is
+ 
+
+ align:start position:0%
+and let's get solve we get 428 which is
+actually the same objective that we got
+
+ align:start position:0%
+actually the same objective that we got
+ 
+
+ align:start position:0%
+actually the same objective that we got
+from before and let's just click on keep
+
+ align:start position:0%
+from before and let's just click on keep
+ 
+
+ align:start position:0%
+from before and let's just click on keep
+result and take a look at the solution
+
+ align:start position:0%
+result and take a look at the solution
+ 
+
+ align:start position:0%
+result and take a look at the solution
+now interestingly this new solution is
+
+ align:start position:0%
+now interestingly this new solution is
+ 
+
+ align:start position:0%
+now interestingly this new solution is
+actually exactly the same as the old
+
+ align:start position:0%
+actually exactly the same as the old
+ 
+
+ align:start position:0%
+actually exactly the same as the old
+solution so what happened here
+
+ align:start position:0%
+solution so what happened here
+ 
+
+ align:start position:0%
+solution so what happened here
+why didn't why didn't this change
+
+ align:start position:0%
+why didn't why didn't this change
+ 
+
+ align:start position:0%
+why didn't why didn't this change
+anything well actually if you recall
+
+ align:start position:0%
+anything well actually if you recall
+ 
+
+ align:start position:0%
+anything well actually if you recall
+from the previous solution in the
+
+ align:start position:0%
+from the previous solution in the
+ 
+
+ align:start position:0%
+from the previous solution in the
+previous solution we actually only used
+
+ align:start position:0%
+previous solution we actually only used
+ 
+
+ align:start position:0%
+previous solution we actually only used
+168 dollars of 18 T's budget and in the
+
+ align:start position:0%
+168 dollars of 18 T's budget and in the
+ 
+
+ align:start position:0%
+168 dollars of 18 T's budget and in the
+previous solution 18 T's budget was 170
+
+ align:start position:0%
+previous solution 18 T's budget was 170
+ 
+
+ align:start position:0%
+previous solution 18 T's budget was 170
+dollars so in the previous solution we
+
+ align:start position:0%
+dollars so in the previous solution we
+ 
+
+ align:start position:0%
+dollars so in the previous solution we
+didn't actually use up all of ATT's
+
+ align:start position:0%
+didn't actually use up all of ATT's
+ 
+
+ align:start position:0%
+didn't actually use up all of ATT's
+budget and since this constraint was not
+
+ align:start position:0%
+budget and since this constraint was not
+ 
+
+ align:start position:0%
+budget and since this constraint was not
+binding then increasing this constraint
+
+ align:start position:0%
+binding then increasing this constraint
+ 
+
+ align:start position:0%
+binding then increasing this constraint
+beyond 117 so increasing the budget from
+
+ align:start position:0%
+beyond 117 so increasing the budget from
+ 
+
+ align:start position:0%
+beyond 117 so increasing the budget from
+170 to 200 will actually have an effect
+
+ align:start position:0%
+170 to 200 will actually have an effect
+ 
+
+ align:start position:0%
+170 to 200 will actually have an effect
+on the solution so this is why the
+
+ align:start position:0%
+on the solution so this is why the
+ 
+
+ align:start position:0%
+on the solution so this is why the
+solution didn't change and in fact in
+
+ align:start position:0%
+solution didn't change and in fact in
+ 
+
+ align:start position:0%
+solution didn't change and in fact in
+this case we didn't really need to
+
+ align:start position:0%
+this case we didn't really need to
+ 
+
+ align:start position:0%
+this case we didn't really need to
+change data and to solve a problem again
+
+ align:start position:0%
+change data and to solve a problem again
+ 
+
+ align:start position:0%
+change data and to solve a problem again
+we could have deduced this from actually
+
+ align:start position:0%
+we could have deduced this from actually
+ 
+
+ align:start position:0%
+we could have deduced this from actually
+looking at the budget values so these
+
+ align:start position:0%
+looking at the budget values so these
+ 
+
+ align:start position:0%
+looking at the budget values so these
+are examples of two questions that we
+
+ align:start position:0%
+are examples of two questions that we
+ 
+
+ align:start position:0%
+are examples of two questions that we
+might consider in the setting and so
+
+ align:start position:0%
+might consider in the setting and so
+ 
+
+ align:start position:0%
+might consider in the setting and so
+this concludes our exploration of this
+
+ align:start position:0%
+this concludes our exploration of this
+ 
+
+ align:start position:0%
+this concludes our exploration of this
+problem in libreoffice in the next video
+
+ align:start position:0%
+problem in libreoffice in the next video
+ 
+
+ align:start position:0%
+problem in libreoffice in the next video
+we will return to the slides and we will
+
+ align:start position:0%
+we will return to the slides and we will
+ 
+
+ align:start position:0%
+we will return to the slides and we will
+discuss some ways that we can extend the
+
+ align:start position:0%
+discuss some ways that we can extend the
+ 
+
+ align:start position:0%
+discuss some ways that we can extend the
+problem beyond sort of the formulation
+
+ align:start position:0%
+problem beyond sort of the formulation
+ 
+
+ align:start position:0%
+problem beyond sort of the formulation
+that we've been thinking about here and
+
+ align:start position:0%
+that we've been thinking about here and
+ 
+
+ align:start position:0%
+that we've been thinking about here and
+we will also summarize what we have
+
+ align:start position:0%
+we will also summarize what we have
+ 
+
+ align:start position:0%
+we will also summarize what we have
+discussed so far so see you in
+
+ align:start position:0%
+discussed so far so see you in
+ 
+
+ align:start position:0%
+discussed so far so see you in
+PowerPoint
\ No newline at end of file
diff --git a/2cPGZ4H67Ek.txt b/2cPGZ4H67Ek.txt
new file mode 100644
index 0000000000000000000000000000000000000000..68f2a7fdfe42d5ca9d9e2cf5d07e51be4cdec26f
--- /dev/null
+++ b/2cPGZ4H67Ek.txt
@@ -0,0 +1,3043 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is a mangrove
+
+ align:start position:0%
+what is a mangrove
+ 
+
+ align:start position:0%
+what is a mangrove
+forest Mangrove are the only Forest
+
+ align:start position:0%
+forest Mangrove are the only Forest
+ 
+
+ align:start position:0%
+forest Mangrove are the only Forest
+found on the edge of the sea in warm
+
+ align:start position:0%
+found on the edge of the sea in warm
+ 
+
+ align:start position:0%
+found on the edge of the sea in warm
+subtropical and tropical environments
+
+ align:start position:0%
+subtropical and tropical environments
+ 
+
+ align:start position:0%
+subtropical and tropical environments
+they can be easily recognized by the
+
+ align:start position:0%
+they can be easily recognized by the
+ 
+
+ align:start position:0%
+they can be easily recognized by the
+dense tangle of prop roots that make the
+
+ align:start position:0%
+dense tangle of prop roots that make the
+ 
+
+ align:start position:0%
+dense tangle of prop roots that make the
+trees appear to be standing on SS above
+
+ align:start position:0%
+trees appear to be standing on SS above
+ 
+
+ align:start position:0%
+trees appear to be standing on SS above
+the water Mangrove are a valuable
+
+ align:start position:0%
+the water Mangrove are a valuable
+ 
+
+ align:start position:0%
+the water Mangrove are a valuable
+resource they are estimated to provide
+
+ align:start position:0%
+resource they are estimated to provide
+ 
+
+ align:start position:0%
+resource they are estimated to provide
+at least 1.6 billion dollars annually in
+
+ align:start position:0%
+at least 1.6 billion dollars annually in
+ 
+
+ align:start position:0%
+at least 1.6 billion dollars annually in
+arous Services the multiple benefits
+
+ align:start position:0%
+arous Services the multiple benefits
+ 
+
+ align:start position:0%
+arous Services the multiple benefits
+that humankind enjoys from ecosystems
+
+ align:start position:0%
+that humankind enjoys from ecosystems
+ 
+
+ align:start position:0%
+that humankind enjoys from ecosystems
+this value is in the real of national
+
+ align:start position:0%
+this value is in the real of national
+ 
+
+ align:start position:0%
+this value is in the real of national
+gdps such as that of the Virgin Islands
+
+ align:start position:0%
+gdps such as that of the Virgin Islands
+ 
+
+ align:start position:0%
+gdps such as that of the Virgin Islands
+in recognitions of the significance of
+
+ align:start position:0%
+in recognitions of the significance of
+ 
+
+ align:start position:0%
+in recognitions of the significance of
+mro the ramsa convention for
+
+ align:start position:0%
+mro the ramsa convention for
+ 
+
+ align:start position:0%
+mro the ramsa convention for
+conservation and sustainable utiliz I
+
+ align:start position:0%
+conservation and sustainable utiliz I
+ 
+
+ align:start position:0%
+conservation and sustainable utiliz I
+ations of Mangrove was signed on the
+
+ align:start position:0%
+ations of Mangrove was signed on the
+ 
+
+ align:start position:0%
+ations of Mangrove was signed on the
+February 2nd
+
+ align:start position:0%
+February 2nd
+ 
+
+ align:start position:0%
+February 2nd
+1971 February 2nd has been declared
+
+ align:start position:0%
+1971 February 2nd has been declared
+ 
+
+ align:start position:0%
+1971 February 2nd has been declared
+World Wetlands day a unique mix of
+
+ align:start position:0%
+World Wetlands day a unique mix of
+ 
+
+ align:start position:0%
+World Wetlands day a unique mix of
+marine and teral species live in mangr
+
+ align:start position:0%
+marine and teral species live in mangr
+ 
+
+ align:start position:0%
+marine and teral species live in mangr
+ecosystems especially in Asian region
+
+ align:start position:0%
+ecosystems especially in Asian region
+ 
+
+ align:start position:0%
+ecosystems especially in Asian region
+the calm sheltered Waters Among The
+
+ align:start position:0%
+the calm sheltered Waters Among The
+ 
+
+ align:start position:0%
+the calm sheltered Waters Among The
+Mangrove Roots provide breeding feeding
+
+ align:start position:0%
+Mangrove Roots provide breeding feeding
+ 
+
+ align:start position:0%
+Mangrove Roots provide breeding feeding
+and nursary grounds for fish and
+
+ align:start position:0%
+and nursary grounds for fish and
+ 
+
+ align:start position:0%
+and nursary grounds for fish and
+anthropods herons Spa bills and even
+
+ align:start position:0%
+anthropods herons Spa bills and even
+ 
+
+ align:start position:0%
+anthropods herons Spa bills and even
+eagles make their nest in the upper
+
+ align:start position:0%
+eagles make their nest in the upper
+ 
+
+ align:start position:0%
+eagles make their nest in the upper
+branches of mangrove
+
+ align:start position:0%
+branches of mangrove
+ 
+
+ align:start position:0%
+branches of mangrove
+trees reptiles are
+
+ align:start position:0%
+trees reptiles are
+ 
+
+ align:start position:0%
+trees reptiles are
+plenty Mangrove play a very important
+
+ align:start position:0%
+plenty Mangrove play a very important
+ 
+
+ align:start position:0%
+plenty Mangrove play a very important
+role in soil formation and shorelines
+
+ align:start position:0%
+role in soil formation and shorelines
+ 
+
+ align:start position:0%
+role in soil formation and shorelines
+protection their unique Above Ground
+
+ align:start position:0%
+protection their unique Above Ground
+ 
+
+ align:start position:0%
+protection their unique Above Ground
+Road structures dampen water
+
+ align:start position:0%
+Road structures dampen water
+ 
+
+ align:start position:0%
+Road structures dampen water
+currents they also reduce the impact of
+
+ align:start position:0%
+currents they also reduce the impact of
+ 
+
+ align:start position:0%
+currents they also reduce the impact of
+strong winds and TI the wave that
+
+ align:start position:0%
+strong winds and TI the wave that
+ 
+
+ align:start position:0%
+strong winds and TI the wave that
+accompany tropical
+
+ align:start position:0%
+accompany tropical
+ 
+
+ align:start position:0%
+accompany tropical
+storms
+
+ align:start position:0%
+storms
+ 
+
+ align:start position:0%
+storms
+Mangrove are among the most carbon Rich
+
+ align:start position:0%
+Mangrove are among the most carbon Rich
+ 
+
+ align:start position:0%
+Mangrove are among the most carbon Rich
+forest in the tropics containing on
+
+ align:start position:0%
+forest in the tropics containing on
+ 
+
+ align:start position:0%
+forest in the tropics containing on
+average 1,23 m carbon per Hector at
+
+ align:start position:0%
+average 1,23 m carbon per Hector at
+ 
+
+ align:start position:0%
+average 1,23 m carbon per Hector at
+least three times that of the upper
+
+ align:start position:0%
+least three times that of the upper
+ 
+
+ align:start position:0%
+least three times that of the upper
+tropical
+
+ align:start position:0%
+tropical
+ 
+
+ align:start position:0%
+tropical
+forest mangr wood is most commonly used
+
+ align:start position:0%
+forest mangr wood is most commonly used
+ 
+
+ align:start position:0%
+forest mangr wood is most commonly used
+as a source of Fu for local communities
+
+ align:start position:0%
+as a source of Fu for local communities
+ 
+
+ align:start position:0%
+as a source of Fu for local communities
+and as the primary construction material
+
+ align:start position:0%
+and as the primary construction material
+ 
+
+ align:start position:0%
+and as the primary construction material
+for boats houses and
+
+ align:start position:0%
+for boats houses and
+ 
+
+ align:start position:0%
+for boats houses and
+furniture
+
+ align:start position:0%
+furniture
+ 
+
+ align:start position:0%
+furniture
+in addition Mangrove maintain commercial
+
+ align:start position:0%
+in addition Mangrove maintain commercial
+ 
+
+ align:start position:0%
+in addition Mangrove maintain commercial
+Fisheries the main source of livelihood
+
+ align:start position:0%
+Fisheries the main source of livelihood
+ 
+
+ align:start position:0%
+Fisheries the main source of livelihood
+for many local
+
+ align:start position:0%
+for many local
+ 
+
+ align:start position:0%
+for many local
+communities mro also contain great
+
+ align:start position:0%
+communities mro also contain great
+ 
+
+ align:start position:0%
+communities mro also contain great
+medicinal value in treating toets
+
+ align:start position:0%
+medicinal value in treating toets
+ 
+
+ align:start position:0%
+medicinal value in treating toets
+bleeding and malaria to name a few
+
+ align:start position:0%
+bleeding and malaria to name a few
+ 
+
+ align:start position:0%
+bleeding and malaria to name a few
+canable Mangrove fruit for instance is
+
+ align:start position:0%
+canable Mangrove fruit for instance is
+ 
+
+ align:start position:0%
+canable Mangrove fruit for instance is
+used to treat diarrhea in many parts of
+
+ align:start position:0%
+used to treat diarrhea in many parts of
+ 
+
+ align:start position:0%
+used to treat diarrhea in many parts of
+the world Mangrove also bear great
+
+ align:start position:0%
+the world Mangrove also bear great
+ 
+
+ align:start position:0%
+the world Mangrove also bear great
+cultural significance for local
+
+ align:start position:0%
+cultural significance for local
+ 
+
+ align:start position:0%
+cultural significance for local
+communities such as the indigenous
+
+ align:start position:0%
+communities such as the indigenous
+ 
+
+ align:start position:0%
+communities such as the indigenous
+peoples of the Taurus STS Islands who
+
+ align:start position:0%
+peoples of the Taurus STS Islands who
+ 
+
+ align:start position:0%
+peoples of the Taurus STS Islands who
+have used Australia's Mangrove for more
+
+ align:start position:0%
+have used Australia's Mangrove for more
+ 
+
+ align:start position:0%
+have used Australia's Mangrove for more
+than 40,000 years despite its importance
+
+ align:start position:0%
+than 40,000 years despite its importance
+ 
+
+ align:start position:0%
+than 40,000 years despite its importance
+the rate of Mangrove deforestation is
+
+ align:start position:0%
+the rate of Mangrove deforestation is
+ 
+
+ align:start position:0%
+the rate of Mangrove deforestation is
+among the highest of any Forest type and
+
+ align:start position:0%
+among the highest of any Forest type and
+ 
+
+ align:start position:0%
+among the highest of any Forest type and
+urbanization has been identified as a
+
+ align:start position:0%
+urbanization has been identified as a
+ 
+
+ align:start position:0%
+urbanization has been identified as a
+significant track to the survival of
+
+ align:start position:0%
+significant track to the survival of
+ 
+
+ align:start position:0%
+significant track to the survival of
+these Coastal Flagship natural
+
+ align:start position:0%
+these Coastal Flagship natural
+ 
+
+ align:start position:0%
+these Coastal Flagship natural
+resources urbanizations refer to the
+
+ align:start position:0%
+resources urbanizations refer to the
+ 
+
+ align:start position:0%
+resources urbanizations refer to the
+concentrations of human population into
+
+ align:start position:0%
+concentrations of human population into
+ 
+
+ align:start position:0%
+concentrations of human population into
+discrete areas cities leading to the
+
+ align:start position:0%
+discrete areas cities leading to the
+ 
+
+ align:start position:0%
+discrete areas cities leading to the
+transformations of land
+
+ align:start position:0%
+transformations of land
+ 
+
+ align:start position:0%
+transformations of land
+it is a global phenomenon that is
+
+ align:start position:0%
+it is a global phenomenon that is
+ 
+
+ align:start position:0%
+it is a global phenomenon that is
+intensifying especially in low and
+
+ align:start position:0%
+intensifying especially in low and
+ 
+
+ align:start position:0%
+intensifying especially in low and
+median inome countries today half of the
+
+ align:start position:0%
+median inome countries today half of the
+ 
+
+ align:start position:0%
+median inome countries today half of the
+world's populations live within 60
+
+ align:start position:0%
+world's populations live within 60
+ 
+
+ align:start position:0%
+world's populations live within 60
+kilometers of the sea and 3/4s of all
+
+ align:start position:0%
+kilometers of the sea and 3/4s of all
+ 
+
+ align:start position:0%
+kilometers of the sea and 3/4s of all
+the largest cities are located on the
+
+ align:start position:0%
+the largest cities are located on the
+ 
+
+ align:start position:0%
+the largest cities are located on the
+cast while cities Foster economic growth
+
+ align:start position:0%
+cast while cities Foster economic growth
+ 
+
+ align:start position:0%
+cast while cities Foster economic growth
+and offer the vast majority of
+
+ align:start position:0%
+and offer the vast majority of
+ 
+
+ align:start position:0%
+and offer the vast majority of
+employment opportunities urbanization
+
+ align:start position:0%
+employment opportunities urbanization
+ 
+
+ align:start position:0%
+employment opportunities urbanization
+also brings congestion and pollution it
+
+ align:start position:0%
+also brings congestion and pollution it
+ 
+
+ align:start position:0%
+also brings congestion and pollution it
+also escalates social RIS such as
+
+ align:start position:0%
+also escalates social RIS such as
+ 
+
+ align:start position:0%
+also escalates social RIS such as
+displacements of native peopers and
+
+ align:start position:0%
+displacements of native peopers and
+ 
+
+ align:start position:0%
+displacements of native peopers and
+urban poverty the fundamental change it
+
+ align:start position:0%
+urban poverty the fundamental change it
+ 
+
+ align:start position:0%
+urban poverty the fundamental change it
+causes however is the transformation of
+
+ align:start position:0%
+causes however is the transformation of
+ 
+
+ align:start position:0%
+causes however is the transformation of
+nature globally Urban Development is the
+
+ align:start position:0%
+nature globally Urban Development is the
+ 
+
+ align:start position:0%
+nature globally Urban Development is the
+major driver of climate change producing
+
+ align:start position:0%
+major driver of climate change producing
+ 
+
+ align:start position:0%
+major driver of climate change producing
+half of all greenhouse gas emissions
+
+ align:start position:0%
+half of all greenhouse gas emissions
+ 
+
+ align:start position:0%
+half of all greenhouse gas emissions
+locally land in coastal area is
+
+ align:start position:0%
+locally land in coastal area is
+ 
+
+ align:start position:0%
+locally land in coastal area is
+reclaimed for property development and
+
+ align:start position:0%
+reclaimed for property development and
+ 
+
+ align:start position:0%
+reclaimed for property development and
+Mangrove forests are transformed into
+
+ align:start position:0%
+Mangrove forests are transformed into
+ 
+
+ align:start position:0%
+Mangrove forests are transformed into
+urban waterfronts Malaysia is a mediate
+
+ align:start position:0%
+urban waterfronts Malaysia is a mediate
+ 
+
+ align:start position:0%
+urban waterfronts Malaysia is a mediate
+income country located in Southeast Asia
+
+ align:start position:0%
+income country located in Southeast Asia
+ 
+
+ align:start position:0%
+income country located in Southeast Asia
+with a total Coastline of
+
+ align:start position:0%
+with a total Coastline of
+ 
+
+ align:start position:0%
+with a total Coastline of
+4,675 km in these coastal areas mangr
+
+ align:start position:0%
+4,675 km in these coastal areas mangr
+ 
+
+ align:start position:0%
+4,675 km in these coastal areas mangr
+Forest are found which at the end of
+
+ align:start position:0%
+Forest are found which at the end of
+ 
+
+ align:start position:0%
+Forest are found which at the end of
+2006 were estimated at
+
+ align:start position:0%
+2006 were estimated at
+ 
+
+ align:start position:0%
+2006 were estimated at
+107,2 hectares in Peninsula Malaysia
+
+ align:start position:0%
+107,2 hectares in Peninsula Malaysia
+ 
+
+ align:start position:0%
+107,2 hectares in Peninsula Malaysia
+alone today very few mang grth remain
+
+ align:start position:0%
+alone today very few mang grth remain
+ 
+
+ align:start position:0%
+alone today very few mang grth remain
+over 18% of the mang grth were lost
+
+ align:start position:0%
+over 18% of the mang grth were lost
+ 
+
+ align:start position:0%
+over 18% of the mang grth were lost
+between 1975 and 2005 primarily due to
+
+ align:start position:0%
+between 1975 and 2005 primarily due to
+ 
+
+ align:start position:0%
+between 1975 and 2005 primarily due to
+conversions of land for agriculture
+
+ align:start position:0%
+conversions of land for agriculture
+ 
+
+ align:start position:0%
+conversions of land for agriculture
+stream ponds or Urban Development Johor
+
+ align:start position:0%
+stream ponds or Urban Development Johor
+ 
+
+ align:start position:0%
+stream ponds or Urban Development Johor
+Malaysia's southern most state is home
+
+ align:start position:0%
+Malaysia's southern most state is home
+ 
+
+ align:start position:0%
+Malaysia's southern most state is home
+to more than a quarter of the total
+
+ align:start position:0%
+to more than a quarter of the total
+ 
+
+ align:start position:0%
+to more than a quarter of the total
+remaining Mangrove in panicula
+
+ align:start position:0%
+remaining Mangrove in panicula
+ 
+
+ align:start position:0%
+remaining Mangrove in panicula
+Malaysia it is also home to three ramsa
+
+ align:start position:0%
+Malaysia it is also home to three ramsa
+ 
+
+ align:start position:0%
+Malaysia it is also home to three ramsa
+sites areas of international importance
+
+ align:start position:0%
+sites areas of international importance
+ 
+
+ align:start position:0%
+sites areas of international importance
+for conserving
+
+ align:start position:0%
+for conserving
+ 
+
+ align:start position:0%
+for conserving
+biodiversity all three of these ramsa
+
+ align:start position:0%
+biodiversity all three of these ramsa
+ 
+
+ align:start position:0%
+biodiversity all three of these ramsa
+sites are located within iscandar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Malaysia established in 2006 iscandar
+
+ align:start position:0%
+Malaysia established in 2006 iscandar
+ 
+
+ align:start position:0%
+Malaysia established in 2006 iscandar
+Malaysia is a national special economic
+
+ align:start position:0%
+Malaysia is a national special economic
+ 
+
+ align:start position:0%
+Malaysia is a national special economic
+region located in southern joho just
+
+ align:start position:0%
+region located in southern joho just
+ 
+
+ align:start position:0%
+region located in southern joho just
+across the streets from
+
+ align:start position:0%
+across the streets from
+ 
+
+ align:start position:0%
+across the streets from
+Singapore it is model after the PE River
+
+ align:start position:0%
+Singapore it is model after the PE River
+ 
+
+ align:start position:0%
+Singapore it is model after the PE River
+delta economic zone of China with the
+
+ align:start position:0%
+delta economic zone of China with the
+ 
+
+ align:start position:0%
+delta economic zone of China with the
+purpose to capitalize on its existing
+
+ align:start position:0%
+purpose to capitalize on its existing
+ 
+
+ align:start position:0%
+purpose to capitalize on its existing
+synergies with
+
+ align:start position:0%
+synergies with
+ 
+
+ align:start position:0%
+synergies with
+Singapore the region has a land size
+
+ align:start position:0%
+Singapore the region has a land size
+ 
+
+ align:start position:0%
+Singapore the region has a land size
+that is three times that of Singapore
+
+ align:start position:0%
+that is three times that of Singapore
+ 
+
+ align:start position:0%
+that is three times that of Singapore
+and is administrated by the iscandar
+
+ align:start position:0%
+and is administrated by the iscandar
+ 
+
+ align:start position:0%
+and is administrated by the iscandar
+regional Development Authority or either
+
+ align:start position:0%
+regional Development Authority or either
+ 
+
+ align:start position:0%
+regional Development Authority or either
+in short the indigenous group oreta once
+
+ align:start position:0%
+in short the indigenous group oreta once
+ 
+
+ align:start position:0%
+in short the indigenous group oreta once
+practicing a nomadic lifestyle have
+
+ align:start position:0%
+practicing a nomadic lifestyle have
+ 
+
+ align:start position:0%
+practicing a nomadic lifestyle have
+settled out along the southern coast of
+
+ align:start position:0%
+settled out along the southern coast of
+ 
+
+ align:start position:0%
+settled out along the southern coast of
+Johor they live in Casta areas and river
+
+ align:start position:0%
+Johor they live in Casta areas and river
+ 
+
+ align:start position:0%
+Johor they live in Casta areas and river
+estares and like many other local people
+
+ align:start position:0%
+estares and like many other local people
+ 
+
+ align:start position:0%
+estares and like many other local people
+are dependent on Mangrove for their
+
+ align:start position:0%
+are dependent on Mangrove for their
+ 
+
+ align:start position:0%
+are dependent on Mangrove for their
+livelihood today Mangrove conservation
+
+ align:start position:0%
+livelihood today Mangrove conservation
+ 
+
+ align:start position:0%
+livelihood today Mangrove conservation
+in joho is becoming Critical with fast-
+
+ align:start position:0%
+in joho is becoming Critical with fast-
+ 
+
+ align:start position:0%
+in joho is becoming Critical with fast-
+face urbanization taking place in
+
+ align:start position:0%
+face urbanization taking place in
+ 
+
+ align:start position:0%
+face urbanization taking place in
+iscandar Malaysia local and Indigenous
+
+ align:start position:0%
+iscandar Malaysia local and Indigenous
+ 
+
+ align:start position:0%
+iscandar Malaysia local and Indigenous
+groups dependent on mro Face the threat
+
+ align:start position:0%
+groups dependent on mro Face the threat
+ 
+
+ align:start position:0%
+groups dependent on mro Face the threat
+of losing their homes and source of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+livelihood iscandar Malaysia aims to be
+
+ align:start position:0%
+livelihood iscandar Malaysia aims to be
+ 
+
+ align:start position:0%
+livelihood iscandar Malaysia aims to be
+a strong and sustainable Metropolis of
+
+ align:start position:0%
+a strong and sustainable Metropolis of
+ 
+
+ align:start position:0%
+a strong and sustainable Metropolis of
+international standing to support this
+
+ align:start position:0%
+international standing to support this
+ 
+
+ align:start position:0%
+international standing to support this
+Vision three mang grth management
+
+ align:start position:0%
+Vision three mang grth management
+ 
+
+ align:start position:0%
+Vision three mang grth management
+strategies can and should be pursued
+
+ align:start position:0%
+strategies can and should be pursued
+ 
+
+ align:start position:0%
+strategies can and should be pursued
+strategy one ecotourism as a man growth
+
+ align:start position:0%
+strategy one ecotourism as a man growth
+ 
+
+ align:start position:0%
+strategy one ecotourism as a man growth
+environmental
+
+ align:start position:0%
+environmental
+ 
+
+ align:start position:0%
+environmental
+service an ecotourism project in isanda
+
+ align:start position:0%
+service an ecotourism project in isanda
+ 
+
+ align:start position:0%
+service an ecotourism project in isanda
+Malaysia has been launched in
+
+ align:start position:0%
+Malaysia has been launched in
+ 
+
+ align:start position:0%
+Malaysia has been launched in
+2013 however it was limited to a single
+
+ align:start position:0%
+2013 however it was limited to a single
+ 
+
+ align:start position:0%
+2013 however it was limited to a single
+Village kongu at the malayu river
+
+ align:start position:0%
+Village kongu at the malayu river
+ 
+
+ align:start position:0%
+Village kongu at the malayu river
+meanwhile a study on tourism potential
+
+ align:start position:0%
+meanwhile a study on tourism potential
+ 
+
+ align:start position:0%
+meanwhile a study on tourism potential
+of the pulai river region was conducted
+
+ align:start position:0%
+of the pulai river region was conducted
+ 
+
+ align:start position:0%
+of the pulai river region was conducted
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+2010 but the actual implementation have
+
+ align:start position:0%
+2010 but the actual implementation have
+ 
+
+ align:start position:0%
+2010 but the actual implementation have
+not taken place it is promising that
+
+ align:start position:0%
+not taken place it is promising that
+ 
+
+ align:start position:0%
+not taken place it is promising that
+tourism with education at its core can
+
+ align:start position:0%
+tourism with education at its core can
+ 
+
+ align:start position:0%
+tourism with education at its core can
+be ecologically and economically
+
+ align:start position:0%
+be ecologically and economically
+ 
+
+ align:start position:0%
+be ecologically and economically
+beneficial to local villages
+
+ align:start position:0%
+beneficial to local villages
+ 
+
+ align:start position:0%
+beneficial to local villages
+however this strategy and its benefits
+
+ align:start position:0%
+however this strategy and its benefits
+ 
+
+ align:start position:0%
+however this strategy and its benefits
+must be shared by more communities to
+
+ align:start position:0%
+must be shared by more communities to
+ 
+
+ align:start position:0%
+must be shared by more communities to
+include both the local and Indigenous
+
+ align:start position:0%
+include both the local and Indigenous
+ 
+
+ align:start position:0%
+include both the local and Indigenous
+people in the tanun Kang subdistrict
+
+ align:start position:0%
+people in the tanun Kang subdistrict
+ 
+
+ align:start position:0%
+people in the tanun Kang subdistrict
+along pulai river as well in addition
+
+ align:start position:0%
+along pulai river as well in addition
+ 
+
+ align:start position:0%
+along pulai river as well in addition
+capacity building for tourism operations
+
+ align:start position:0%
+capacity building for tourism operations
+ 
+
+ align:start position:0%
+capacity building for tourism operations
+and the linkage between local businesses
+
+ align:start position:0%
+and the linkage between local businesses
+ 
+
+ align:start position:0%
+and the linkage between local businesses
+and tourism networks at the state level
+
+ align:start position:0%
+and tourism networks at the state level
+ 
+
+ align:start position:0%
+and tourism networks at the state level
+must be established for this the
+
+ align:start position:0%
+must be established for this the
+ 
+
+ align:start position:0%
+must be established for this the
+ministry of Tourism and culture must
+
+ align:start position:0%
+ministry of Tourism and culture must
+ 
+
+ align:start position:0%
+ministry of Tourism and culture must
+take the lead in working with all
+
+ align:start position:0%
+take the lead in working with all
+ 
+
+ align:start position:0%
+take the lead in working with all
+relevance
+
+ align:start position:0%
+relevance
+ 
+
+ align:start position:0%
+relevance
+stakeholders strategy two technology for
+
+ align:start position:0%
+stakeholders strategy two technology for
+ 
+
+ align:start position:0%
+stakeholders strategy two technology for
+M grth monitoring the applications of
+
+ align:start position:0%
+M grth monitoring the applications of
+ 
+
+ align:start position:0%
+M grth monitoring the applications of
+GIS and remote sensing in Mangrove
+
+ align:start position:0%
+GIS and remote sensing in Mangrove
+ 
+
+ align:start position:0%
+GIS and remote sensing in Mangrove
+management must be incorporated in the
+
+ align:start position:0%
+management must be incorporated in the
+ 
+
+ align:start position:0%
+management must be incorporated in the
+existing manual monitoring practices by
+
+ align:start position:0%
+existing manual monitoring practices by
+ 
+
+ align:start position:0%
+existing manual monitoring practices by
+the Joo Forestry Department these
+
+ align:start position:0%
+the Joo Forestry Department these
+ 
+
+ align:start position:0%
+the Joo Forestry Department these
+Technologies are powerful at
+
+ align:start position:0%
+Technologies are powerful at
+ 
+
+ align:start position:0%
+Technologies are powerful at
+systematically and periodically
+
+ align:start position:0%
+systematically and periodically
+ 
+
+ align:start position:0%
+systematically and periodically
+measuring the effectiveness of ongoing
+
+ align:start position:0%
+measuring the effectiveness of ongoing
+ 
+
+ align:start position:0%
+measuring the effectiveness of ongoing
+management practices subsequently this
+
+ align:start position:0%
+management practices subsequently this
+ 
+
+ align:start position:0%
+management practices subsequently this
+provides a more defense sensible basis
+
+ align:start position:0%
+provides a more defense sensible basis
+ 
+
+ align:start position:0%
+provides a more defense sensible basis
+for management actions towards
+
+ align:start position:0%
+for management actions towards
+ 
+
+ align:start position:0%
+for management actions towards
+conservation remote sensing um is one of
+
+ align:start position:0%
+conservation remote sensing um is one of
+ 
+
+ align:start position:0%
+conservation remote sensing um is one of
+the um latest um technology I wouldn't
+
+ align:start position:0%
+the um latest um technology I wouldn't
+ 
+
+ align:start position:0%
+the um latest um technology I wouldn't
+say latest because it is there um in the
+
+ align:start position:0%
+say latest because it is there um in the
+ 
+
+ align:start position:0%
+say latest because it is there um in the
+market since
+
+ align:start position:0%
+market since
+ 
+
+ align:start position:0%
+market since
+1970s um is the um only practical way to
+
+ align:start position:0%
+1970s um is the um only practical way to
+ 
+
+ align:start position:0%
+1970s um is the um only practical way to
+get uh rapid information about mangr
+
+ align:start position:0%
+get uh rapid information about mangr
+ 
+
+ align:start position:0%
+get uh rapid information about mangr
+changes strategy three call management
+
+ align:start position:0%
+changes strategy three call management
+ 
+
+ align:start position:0%
+changes strategy three call management
+for mang grth governance the
+
+ align:start position:0%
+for mang grth governance the
+ 
+
+ align:start position:0%
+for mang grth governance the
+institutional structure for managing
+
+ align:start position:0%
+institutional structure for managing
+ 
+
+ align:start position:0%
+institutional structure for managing
+natural resources in most develop ing
+
+ align:start position:0%
+natural resources in most develop ing
+ 
+
+ align:start position:0%
+natural resources in most develop ing
+countries including Malaysia is based on
+
+ align:start position:0%
+countries including Malaysia is based on
+ 
+
+ align:start position:0%
+countries including Malaysia is based on
+a top- down approach and is very much
+
+ align:start position:0%
+a top- down approach and is very much
+ 
+
+ align:start position:0%
+a top- down approach and is very much
+development
+
+ align:start position:0%
+development
+ 
+
+ align:start position:0%
+development
+driven in light of sustainable Ci's
+
+ align:start position:0%
+driven in light of sustainable Ci's
+ 
+
+ align:start position:0%
+driven in light of sustainable Ci's
+development objectives and the current
+
+ align:start position:0%
+development objectives and the current
+ 
+
+ align:start position:0%
+development objectives and the current
+state of Mangrove destruction
+
+ align:start position:0%
+state of Mangrove destruction
+ 
+
+ align:start position:0%
+state of Mangrove destruction
+coordination amongst interdependence
+
+ align:start position:0%
+coordination amongst interdependence
+ 
+
+ align:start position:0%
+coordination amongst interdependence
+governance structures is the core of
+
+ align:start position:0%
+governance structures is the core of
+ 
+
+ align:start position:0%
+governance structures is the core of
+effective mang grth management as land
+
+ align:start position:0%
+effective mang grth management as land
+ 
+
+ align:start position:0%
+effective mang grth management as land
+is prescribed as state matter under the
+
+ align:start position:0%
+is prescribed as state matter under the
+ 
+
+ align:start position:0%
+is prescribed as state matter under the
+Federal
+
+ align:start position:0%
+Federal
+ 
+
+ align:start position:0%
+Federal
+Constitution the agency is dealing with
+
+ align:start position:0%
+Constitution the agency is dealing with
+ 
+
+ align:start position:0%
+Constitution the agency is dealing with
+M grth such as the department of
+
+ align:start position:0%
+M grth such as the department of
+ 
+
+ align:start position:0%
+M grth such as the department of
+environment enement are merely technical
+
+ align:start position:0%
+environment enement are merely technical
+ 
+
+ align:start position:0%
+environment enement are merely technical
+advisers revie Land Development
+
+ align:start position:0%
+advisers revie Land Development
+ 
+
+ align:start position:0%
+advisers revie Land Development
+proposals they have L power when it
+
+ align:start position:0%
+proposals they have L power when it
+ 
+
+ align:start position:0%
+proposals they have L power when it
+comes to Land Development decision
+
+ align:start position:0%
+comes to Land Development decision
+ 
+
+ align:start position:0%
+comes to Land Development decision
+making it is recommended that these
+
+ align:start position:0%
+making it is recommended that these
+ 
+
+ align:start position:0%
+making it is recommended that these
+agencies be given more poers and be
+
+ align:start position:0%
+agencies be given more poers and be
+ 
+
+ align:start position:0%
+agencies be given more poers and be
+directly involved in the decision making
+
+ align:start position:0%
+directly involved in the decision making
+ 
+
+ align:start position:0%
+directly involved in the decision making
+process moreover the environmental
+
+ align:start position:0%
+process moreover the environmental
+ 
+
+ align:start position:0%
+process moreover the environmental
+impact assessment requirement must be
+
+ align:start position:0%
+impact assessment requirement must be
+ 
+
+ align:start position:0%
+impact assessment requirement must be
+strictly
+
+ align:start position:0%
+strictly
+ 
+
+ align:start position:0%
+strictly
+enforced at the local level the iscandar
+
+ align:start position:0%
+enforced at the local level the iscandar
+ 
+
+ align:start position:0%
+enforced at the local level the iscandar
+regional Development Authority has initi
+
+ align:start position:0%
+regional Development Authority has initi
+ 
+
+ align:start position:0%
+regional Development Authority has initi
+efforts to include local communities in
+
+ align:start position:0%
+efforts to include local communities in
+ 
+
+ align:start position:0%
+efforts to include local communities in
+mangr conservation
+
+ align:start position:0%
+mangr conservation
+ 
+
+ align:start position:0%
+mangr conservation
+projects however the scope of
+
+ align:start position:0%
+projects however the scope of
+ 
+
+ align:start position:0%
+projects however the scope of
+participation is confined to public
+
+ align:start position:0%
+participation is confined to public
+ 
+
+ align:start position:0%
+participation is confined to public
+aarness and the capacity building
+
+ align:start position:0%
+aarness and the capacity building
+ 
+
+ align:start position:0%
+aarness and the capacity building
+related to Resource
+
+ align:start position:0%
+related to Resource
+ 
+
+ align:start position:0%
+related to Resource
+consumption uh within era we've got a
+
+ align:start position:0%
+consumption uh within era we've got a
+ 
+
+ align:start position:0%
+consumption uh within era we've got a
+Social Development Division that works
+
+ align:start position:0%
+Social Development Division that works
+ 
+
+ align:start position:0%
+Social Development Division that works
+closely with the communities to ensure
+
+ align:start position:0%
+closely with the communities to ensure
+ 
+
+ align:start position:0%
+closely with the communities to ensure
+that whatever economic development that
+
+ align:start position:0%
+that whatever economic development that
+ 
+
+ align:start position:0%
+that whatever economic development that
+we bring uh to the region it needs to
+
+ align:start position:0%
+we bring uh to the region it needs to
+ 
+
+ align:start position:0%
+we bring uh to the region it needs to
+have the inclusion of the people uh for
+
+ align:start position:0%
+have the inclusion of the people uh for
+ 
+
+ align:start position:0%
+have the inclusion of the people uh for
+example closely to uh Mangrove uh
+
+ align:start position:0%
+example closely to uh Mangrove uh
+ 
+
+ align:start position:0%
+example closely to uh Mangrove uh
+communities is the kampu so we have been
+
+ align:start position:0%
+communities is the kampu so we have been
+ 
+
+ align:start position:0%
+communities is the kampu so we have been
+working closely with them for the last
+
+ align:start position:0%
+working closely with them for the last
+ 
+
+ align:start position:0%
+working closely with them for the last
+few years to build uh the capacity of
+
+ align:start position:0%
+few years to build uh the capacity of
+ 
+
+ align:start position:0%
+few years to build uh the capacity of
+the community in um arranging uh visits
+
+ align:start position:0%
+the community in um arranging uh visits
+ 
+
+ align:start position:0%
+the community in um arranging uh visits
+by tourists to the surrounding Mangrove
+
+ align:start position:0%
+by tourists to the surrounding Mangrove
+ 
+
+ align:start position:0%
+by tourists to the surrounding Mangrove
+so boat visits uh to the mangr forest
+
+ align:start position:0%
+so boat visits uh to the mangr forest
+ 
+
+ align:start position:0%
+so boat visits uh to the mangr forest
+and also to the um Kong where the uh
+
+ align:start position:0%
+and also to the um Kong where the uh
+ 
+
+ align:start position:0%
+and also to the um Kong where the uh
+Community is rearing muscles green
+
+ align:start position:0%
+Community is rearing muscles green
+ 
+
+ align:start position:0%
+Community is rearing muscles green
+muscles and also some fishes um so I
+
+ align:start position:0%
+muscles and also some fishes um so I
+ 
+
+ align:start position:0%
+muscles and also some fishes um so I
+think the Cass and all that we working
+
+ align:start position:0%
+think the Cass and all that we working
+ 
+
+ align:start position:0%
+think the Cass and all that we working
+with the people um because there's a
+
+ align:start position:0%
+with the people um because there's a
+ 
+
+ align:start position:0%
+with the people um because there's a
+flat platform that was created a friends
+
+ align:start position:0%
+flat platform that was created a friends
+ 
+
+ align:start position:0%
+flat platform that was created a friends
+of isanda ramza to work with them in
+
+ align:start position:0%
+of isanda ramza to work with them in
+ 
+
+ align:start position:0%
+of isanda ramza to work with them in
+carrying out um educational research uh
+
+ align:start position:0%
+carrying out um educational research uh
+ 
+
+ align:start position:0%
+carrying out um educational research uh
+programs it is whiter that the level of
+
+ align:start position:0%
+programs it is whiter that the level of
+ 
+
+ align:start position:0%
+programs it is whiter that the level of
+participations amongst local and
+
+ align:start position:0%
+participations amongst local and
+ 
+
+ align:start position:0%
+participations amongst local and
+Indigenous communities be extended and
+
+ align:start position:0%
+Indigenous communities be extended and
+ 
+
+ align:start position:0%
+Indigenous communities be extended and
+that they are not only given the rights
+
+ align:start position:0%
+that they are not only given the rights
+ 
+
+ align:start position:0%
+that they are not only given the rights
+to use mangr resources as granted by the
+
+ align:start position:0%
+to use mangr resources as granted by the
+ 
+
+ align:start position:0%
+to use mangr resources as granted by the
+authorities but also the right to take
+
+ align:start position:0%
+authorities but also the right to take
+ 
+
+ align:start position:0%
+authorities but also the right to take
+part in managing those resources
+
+ align:start position:0%
+part in managing those resources
+ 
+
+ align:start position:0%
+part in managing those resources
+together with government agencies for
+
+ align:start position:0%
+together with government agencies for
+ 
+
+ align:start position:0%
+together with government agencies for
+that Co management becomes a viable
+
+ align:start position:0%
+that Co management becomes a viable
+ 
+
+ align:start position:0%
+that Co management becomes a viable
+means to bring all stakeholders together
+
+ align:start position:0%
+means to bring all stakeholders together
+ 
+
+ align:start position:0%
+means to bring all stakeholders together
+despite their different
+
+ align:start position:0%
+despite their different
+ 
+
+ align:start position:0%
+despite their different
+interests here finding the right mix of
+
+ align:start position:0%
+interests here finding the right mix of
+ 
+
+ align:start position:0%
+interests here finding the right mix of
+stakeholders to govern the resources
+
+ align:start position:0%
+stakeholders to govern the resources
+ 
+
+ align:start position:0%
+stakeholders to govern the resources
+becomes the key the suai pulai Forest
+
+ align:start position:0%
+becomes the key the suai pulai Forest
+ 
+
+ align:start position:0%
+becomes the key the suai pulai Forest
+Reserve an area in urgent need for
+
+ align:start position:0%
+Reserve an area in urgent need for
+ 
+
+ align:start position:0%
+Reserve an area in urgent need for
+protected area status provides an
+
+ align:start position:0%
+protected area status provides an
+ 
+
+ align:start position:0%
+protected area status provides an
+example of the need for a Coe management
+
+ align:start position:0%
+example of the need for a Coe management
+ 
+
+ align:start position:0%
+example of the need for a Coe management
+strategy at present harvesting based on
+
+ align:start position:0%
+strategy at present harvesting based on
+ 
+
+ align:start position:0%
+strategy at present harvesting based on
+on a 20 years rotation schedule is the
+
+ align:start position:0%
+on a 20 years rotation schedule is the
+ 
+
+ align:start position:0%
+on a 20 years rotation schedule is the
+major economic activities here the
+
+ align:start position:0%
+major economic activities here the
+ 
+
+ align:start position:0%
+major economic activities here the
+manang gr management plan is outlined in
+
+ align:start position:0%
+manang gr management plan is outlined in
+ 
+
+ align:start position:0%
+manang gr management plan is outlined in
+the overall forry management plan but
+
+ align:start position:0%
+the overall forry management plan but
+ 
+
+ align:start position:0%
+the overall forry management plan but
+this will expire in 2015 if it is
+
+ align:start position:0%
+this will expire in 2015 if it is
+ 
+
+ align:start position:0%
+this will expire in 2015 if it is
+talking about the rle of the forestry I
+
+ align:start position:0%
+talking about the rle of the forestry I
+ 
+
+ align:start position:0%
+talking about the rle of the forestry I
+think they're doing a very good job
+
+ align:start position:0%
+think they're doing a very good job
+ 
+
+ align:start position:0%
+think they're doing a very good job
+although you see Mangrove being cut but
+
+ align:start position:0%
+although you see Mangrove being cut but
+ 
+
+ align:start position:0%
+although you see Mangrove being cut but
+uh this is on rotational basis small
+
+ align:start position:0%
+uh this is on rotational basis small
+ 
+
+ align:start position:0%
+uh this is on rotational basis small
+areas where the concessionary will
+
+ align:start position:0%
+areas where the concessionary will
+ 
+
+ align:start position:0%
+areas where the concessionary will
+replan so the only fa is uh the original
+
+ align:start position:0%
+replan so the only fa is uh the original
+ 
+
+ align:start position:0%
+replan so the only fa is uh the original
+species may be WIP out because they
+
+ align:start position:0%
+species may be WIP out because they
+ 
+
+ align:start position:0%
+species may be WIP out because they
+going to monocropping therefore the
+
+ align:start position:0%
+going to monocropping therefore the
+ 
+
+ align:start position:0%
+going to monocropping therefore the
+preparations of a comprehensive
+
+ align:start position:0%
+preparations of a comprehensive
+ 
+
+ align:start position:0%
+preparations of a comprehensive
+management plan specifically for mangr
+
+ align:start position:0%
+management plan specifically for mangr
+ 
+
+ align:start position:0%
+management plan specifically for mangr
+Forest is urgently needed to indicate
+
+ align:start position:0%
+Forest is urgently needed to indicate
+ 
+
+ align:start position:0%
+Forest is urgently needed to indicate
+the permitted land users the carring
+
+ align:start position:0%
+the permitted land users the carring
+ 
+
+ align:start position:0%
+the permitted land users the carring
+capacity of those users and the
+
+ align:start position:0%
+capacity of those users and the
+ 
+
+ align:start position:0%
+capacity of those users and the
+stakeholders that need to be involved in
+
+ align:start position:0%
+stakeholders that need to be involved in
+ 
+
+ align:start position:0%
+stakeholders that need to be involved in
+the management process apart from the
+
+ align:start position:0%
+the management process apart from the
+ 
+
+ align:start position:0%
+the management process apart from the
+three strategies just describe the
+
+ align:start position:0%
+three strategies just describe the
+ 
+
+ align:start position:0%
+three strategies just describe the
+potential for moral considerations and
+
+ align:start position:0%
+potential for moral considerations and
+ 
+
+ align:start position:0%
+potential for moral considerations and
+religious values to play a unifying and
+
+ align:start position:0%
+religious values to play a unifying and
+ 
+
+ align:start position:0%
+religious values to play a unifying and
+revitalizing role in mang grth
+
+ align:start position:0%
+revitalizing role in mang grth
+ 
+
+ align:start position:0%
+revitalizing role in mang grth
+conservation and nature conservation in
+
+ align:start position:0%
+conservation and nature conservation in
+ 
+
+ align:start position:0%
+conservation and nature conservation in
+general must be further explore in
+
+ align:start position:0%
+general must be further explore in
+ 
+
+ align:start position:0%
+general must be further explore in
+development planning and at the societal
+
+ align:start position:0%
+development planning and at the societal
+ 
+
+ align:start position:0%
+development planning and at the societal
+level in fact a holistic approach to
+
+ align:start position:0%
+level in fact a holistic approach to
+ 
+
+ align:start position:0%
+level in fact a holistic approach to
+land use development planning known as
+
+ align:start position:0%
+land use development planning known as
+ 
+
+ align:start position:0%
+land use development planning known as
+the tal planning Doctrine was introduced
+
+ align:start position:0%
+the tal planning Doctrine was introduced
+ 
+
+ align:start position:0%
+the tal planning Doctrine was introduced
+in the mid 1990s by the federal
+
+ align:start position:0%
+in the mid 1990s by the federal
+ 
+
+ align:start position:0%
+in the mid 1990s by the federal
+government of Malaysia it aims to
+
+ align:start position:0%
+government of Malaysia it aims to
+ 
+
+ align:start position:0%
+government of Malaysia it aims to
+integrate physical and social planning
+
+ align:start position:0%
+integrate physical and social planning
+ 
+
+ align:start position:0%
+integrate physical and social planning
+with moral and spirit spiritual values
+
+ align:start position:0%
+with moral and spirit spiritual values
+ 
+
+ align:start position:0%
+with moral and spirit spiritual values
+however little evidence shows the
+
+ align:start position:0%
+however little evidence shows the
+ 
+
+ align:start position:0%
+however little evidence shows the
+implementations of the approach in
+
+ align:start position:0%
+implementations of the approach in
+ 
+
+ align:start position:0%
+implementations of the approach in
+reality at the societal level the
+
+ align:start position:0%
+reality at the societal level the
+ 
+
+ align:start position:0%
+reality at the societal level the
+dominant religious Customs have been
+
+ align:start position:0%
+dominant religious Customs have been
+ 
+
+ align:start position:0%
+dominant religious Customs have been
+still mainly confined to discret
+
+ align:start position:0%
+still mainly confined to discret
+ 
+
+ align:start position:0%
+still mainly confined to discret
+practices rather than a way of life
+
+ align:start position:0%
+practices rather than a way of life
+ 
+
+ align:start position:0%
+practices rather than a way of life
+which has the potential to cultivate a
+
+ align:start position:0%
+which has the potential to cultivate a
+ 
+
+ align:start position:0%
+which has the potential to cultivate a
+direct connection between humans and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+environment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+urbanization is one of the most complex
+
+ align:start position:0%
+urbanization is one of the most complex
+ 
+
+ align:start position:0%
+urbanization is one of the most complex
+and important social economic phenomena
+
+ align:start position:0%
+and important social economic phenomena
+ 
+
+ align:start position:0%
+and important social economic phenomena
+of the 21st
+
+ align:start position:0%
+of the 21st
+ 
+
+ align:start position:0%
+of the 21st
+century it is forceful irreversible and
+
+ align:start position:0%
+century it is forceful irreversible and
+ 
+
+ align:start position:0%
+century it is forceful irreversible and
+constantly
+
+ align:start position:0%
+constantly
+ 
+
+ align:start position:0%
+constantly
+evolving it also represents a major
+
+ align:start position:0%
+evolving it also represents a major
+ 
+
+ align:start position:0%
+evolving it also represents a major
+change in the extraction and
+
+ align:start position:0%
+change in the extraction and
+ 
+
+ align:start position:0%
+change in the extraction and
+consumptions of natural resources and
+
+ align:start position:0%
+consumptions of natural resources and
+ 
+
+ align:start position:0%
+consumptions of natural resources and
+the way that Society interacts with
+
+ align:start position:0%
+the way that Society interacts with
+ 
+
+ align:start position:0%
+the way that Society interacts with
+nature
+
+ align:start position:0%
+nature
+ 
+
+ align:start position:0%
+nature
+nature yet if we only see cities as a
+
+ align:start position:0%
+nature yet if we only see cities as a
+ 
+
+ align:start position:0%
+nature yet if we only see cities as a
+problem we fail to recognize how cities
+
+ align:start position:0%
+problem we fail to recognize how cities
+ 
+
+ align:start position:0%
+problem we fail to recognize how cities
+offer improved quality of life and serve
+
+ align:start position:0%
+offer improved quality of life and serve
+ 
+
+ align:start position:0%
+offer improved quality of life and serve
+as the centers for
+
+ align:start position:0%
+as the centers for
+ 
+
+ align:start position:0%
+as the centers for
+culture the strategies recommended in
+
+ align:start position:0%
+culture the strategies recommended in
+ 
+
+ align:start position:0%
+culture the strategies recommended in
+this video for mang grth government in
+
+ align:start position:0%
+this video for mang grth government in
+ 
+
+ align:start position:0%
+this video for mang grth government in
+iscandar Malaysia incorporates a wide
+
+ align:start position:0%
+iscandar Malaysia incorporates a wide
+ 
+
+ align:start position:0%
+iscandar Malaysia incorporates a wide
+range of appreciations for mang
+
+ align:start position:0%
+range of appreciations for mang
+ 
+
+ align:start position:0%
+range of appreciations for mang
+grth this Deens the Quest for a
+
+ align:start position:0%
+grth this Deens the Quest for a
+ 
+
+ align:start position:0%
+grth this Deens the Quest for a
+meaningful practice of sustainable Urban
+
+ align:start position:0%
+meaningful practice of sustainable Urban
+ 
+
+ align:start position:0%
+meaningful practice of sustainable Urban
+Development at the regional level the
+
+ align:start position:0%
+Development at the regional level the
+ 
+
+ align:start position:0%
+Development at the regional level the
+strong presence of mang grth and
+
+ align:start position:0%
+strong presence of mang grth and
+ 
+
+ align:start position:0%
+strong presence of mang grth and
+Indigenous people presents an
+
+ align:start position:0%
+Indigenous people presents an
+ 
+
+ align:start position:0%
+Indigenous people presents an
+opportunity for incand Malaysia to be a
+
+ align:start position:0%
+opportunity for incand Malaysia to be a
+ 
+
+ align:start position:0%
+opportunity for incand Malaysia to be a
+unique living model of a developing
+
+ align:start position:0%
+unique living model of a developing
+ 
+
+ align:start position:0%
+unique living model of a developing
+countries that sustainably improve the
+
+ align:start position:0%
+countries that sustainably improve the
+ 
+
+ align:start position:0%
+countries that sustainably improve the
+Metropolis by making the relationship
+
+ align:start position:0%
+Metropolis by making the relationship
+ 
+
+ align:start position:0%
+Metropolis by making the relationship
+between nature culture and build
+
+ align:start position:0%
+between nature culture and build
+ 
+
+ align:start position:0%
+between nature culture and build
+environment a synergized and symbiotic
+
+ align:start position:0%
+environment a synergized and symbiotic
+ 
+
+ align:start position:0%
+environment a synergized and symbiotic
+one at the national level mangr
+
+ align:start position:0%
+one at the national level mangr
+ 
+
+ align:start position:0%
+one at the national level mangr
+conservation directly supports
+
+ align:start position:0%
+conservation directly supports
+ 
+
+ align:start position:0%
+conservation directly supports
+Malaysians efforts to reduce carbon
+
+ align:start position:0%
+Malaysians efforts to reduce carbon
+ 
+
+ align:start position:0%
+Malaysians efforts to reduce carbon
+emission in light of the global climate
+
+ align:start position:0%
+emission in light of the global climate
+ 
+
+ align:start position:0%
+emission in light of the global climate
+change agenda so are these strategies
+
+ align:start position:0%
+change agenda so are these strategies
+ 
+
+ align:start position:0%
+change agenda so are these strategies
+likely to be useful for other cities
+
+ align:start position:0%
+likely to be useful for other cities
+ 
+
+ align:start position:0%
+likely to be useful for other cities
+facing similar development driven
+
+ align:start position:0%
+facing similar development driven
+ 
+
+ align:start position:0%
+facing similar development driven
+challenges yes they are this studies is
+
+ align:start position:0%
+challenges yes they are this studies is
+ 
+
+ align:start position:0%
+challenges yes they are this studies is
+an example of north south South learning
+
+ align:start position:0%
+an example of north south South learning
+ 
+
+ align:start position:0%
+an example of north south South learning
+by sharing lessons and ideas through
+
+ align:start position:0%
+by sharing lessons and ideas through
+ 
+
+ align:start position:0%
+by sharing lessons and ideas through
+digital
+
+ align:start position:0%
+digital
+ 
+
+ align:start position:0%
+digital
+communication similar to the case of
+
+ align:start position:0%
+communication similar to the case of
+ 
+
+ align:start position:0%
+communication similar to the case of
+iscandar Malaysia many emerging cities
+
+ align:start position:0%
+iscandar Malaysia many emerging cities
+ 
+
+ align:start position:0%
+iscandar Malaysia many emerging cities
+in developing countries are rich in
+
+ align:start position:0%
+in developing countries are rich in
+ 
+
+ align:start position:0%
+in developing countries are rich in
+natural resources and culture
+
+ align:start position:0%
+natural resources and culture
+ 
+
+ align:start position:0%
+natural resources and culture
+and striving for economic development
+
+ align:start position:0%
+and striving for economic development
+ 
+
+ align:start position:0%
+and striving for economic development
+has put tremendous pressure on these
+
+ align:start position:0%
+has put tremendous pressure on these
+ 
+
+ align:start position:0%
+has put tremendous pressure on these
+precious assets meanwhile transparency
+
+ align:start position:0%
+precious assets meanwhile transparency
+ 
+
+ align:start position:0%
+precious assets meanwhile transparency
+has been a key concern in developing
+
+ align:start position:0%
+has been a key concern in developing
+ 
+
+ align:start position:0%
+has been a key concern in developing
+countries yet L evidence reveals that
+
+ align:start position:0%
+countries yet L evidence reveals that
+ 
+
+ align:start position:0%
+countries yet L evidence reveals that
+transparency alone can make a
+
+ align:start position:0%
+transparency alone can make a
+ 
+
+ align:start position:0%
+transparency alone can make a
+significant contribution toward
+
+ align:start position:0%
+significant contribution toward
+ 
+
+ align:start position:0%
+significant contribution toward
+sustainability's goals benefit sharing
+
+ align:start position:0%
+sustainability's goals benefit sharing
+ 
+
+ align:start position:0%
+sustainability's goals benefit sharing
+and capacity building as highlighted in
+
+ align:start position:0%
+and capacity building as highlighted in
+ 
+
+ align:start position:0%
+and capacity building as highlighted in
+the mang gr management strategies in
+
+ align:start position:0%
+the mang gr management strategies in
+ 
+
+ align:start position:0%
+the mang gr management strategies in
+this video are believed to be the
+
+ align:start position:0%
+this video are believed to be the
+ 
+
+ align:start position:0%
+this video are believed to be the
+enabling factors for transparency to
+
+ align:start position:0%
+enabling factors for transparency to
+ 
+
+ align:start position:0%
+enabling factors for transparency to
+achieve its
+
+ align:start position:0%
+achieve its
+ 
+
+ align:start position:0%
+achieve its
+effect however the prioritizations of
+
+ align:start position:0%
+effect however the prioritizations of
+ 
+
+ align:start position:0%
+effect however the prioritizations of
+these strategies require careful
+
+ align:start position:0%
+these strategies require careful
+ 
+
+ align:start position:0%
+these strategies require careful
+considerations of the past and present
+
+ align:start position:0%
+considerations of the past and present
+ 
+
+ align:start position:0%
+considerations of the past and present
+political and social cultural context of
+
+ align:start position:0%
+political and social cultural context of
+ 
+
+ align:start position:0%
+political and social cultural context of
+the city as well as the state and the
+
+ align:start position:0%
+the city as well as the state and the
+ 
+
+ align:start position:0%
+the city as well as the state and the
+ideologies behind the Region's Economic
+
+ align:start position:0%
+ideologies behind the Region's Economic
+ 
+
+ align:start position:0%
+ideologies behind the Region's Economic
+Development
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+activity
+
+ align:start position:0%
+activity
+ 
+
+ align:start position:0%
+activity
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+bye-bye
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/33w-baH49rA.txt b/33w-baH49rA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..09bf1ea8c0db1ee7a7bba3beec5df1cfff77de29
--- /dev/null
+++ b/33w-baH49rA.txt
@@ -0,0 +1,15386 @@
+align:start position:0%
+ 
+okay last time
+
+ align:start position:0%
+okay last time
+ 
+
+ align:start position:0%
+okay last time
+we discussed oxidative phosphorylation
+
+ align:start position:0%
+we discussed oxidative phosphorylation
+ 
+
+ align:start position:0%
+we discussed oxidative phosphorylation
+which is how to couple the nadh
+
+ align:start position:0%
+which is how to couple the nadh
+ 
+
+ align:start position:0%
+which is how to couple the nadh
+generated from sugar fatty acids etc
+
+ align:start position:0%
+generated from sugar fatty acids etc
+ 
+
+ align:start position:0%
+generated from sugar fatty acids etc
+the oxidation of carbon as a way to
+
+ align:start position:0%
+the oxidation of carbon as a way to
+ 
+
+ align:start position:0%
+the oxidation of carbon as a way to
+carry out favorable electron transfer to
+
+ align:start position:0%
+carry out favorable electron transfer to
+ 
+
+ align:start position:0%
+carry out favorable electron transfer to
+oxygen
+
+ align:start position:0%
+oxygen
+ 
+
+ align:start position:0%
+oxygen
+and use that energy release to charge a
+
+ align:start position:0%
+and use that energy release to charge a
+ 
+
+ align:start position:0%
+and use that energy release to charge a
+battery that is
+
+ align:start position:0%
+battery that is
+ 
+
+ align:start position:0%
+battery that is
+create this delta psi delta ph
+
+ align:start position:0%
+create this delta psi delta ph
+ 
+
+ align:start position:0%
+create this delta psi delta ph
+that can subsequently be used by the
+
+ align:start position:0%
+that can subsequently be used by the
+ 
+
+ align:start position:0%
+that can subsequently be used by the
+battery to
+
+ align:start position:0%
+battery to
+ 
+
+ align:start position:0%
+battery to
+do work including the synthesis of atp
+
+ align:start position:0%
+do work including the synthesis of atp
+ 
+
+ align:start position:0%
+do work including the synthesis of atp
+and of course this can occur at a
+
+ align:start position:0%
+and of course this can occur at a
+ 
+
+ align:start position:0%
+and of course this can occur at a
+physiological atp adp ratio
+
+ align:start position:0%
+physiological atp adp ratio
+ 
+
+ align:start position:0%
+physiological atp adp ratio
+and therefore allow the cell to couple
+
+ align:start position:0%
+and therefore allow the cell to couple
+ 
+
+ align:start position:0%
+and therefore allow the cell to couple
+atp to adp conversion to other
+
+ align:start position:0%
+atp to adp conversion to other
+ 
+
+ align:start position:0%
+atp to adp conversion to other
+unfavorable processes in the cell
+
+ align:start position:0%
+unfavorable processes in the cell
+ 
+
+ align:start position:0%
+unfavorable processes in the cell
+now all of these reactions occur at the
+
+ align:start position:0%
+now all of these reactions occur at the
+ 
+
+ align:start position:0%
+now all of these reactions occur at the
+mitochondria and i
+
+ align:start position:0%
+mitochondria and i
+ 
+
+ align:start position:0%
+mitochondria and i
+drew here a schematic mitochondria for
+
+ align:start position:0%
+drew here a schematic mitochondria for
+ 
+
+ align:start position:0%
+drew here a schematic mitochondria for
+us just to start
+
+ align:start position:0%
+us just to start
+ 
+
+ align:start position:0%
+us just to start
+remember the mitochondria has its own
+
+ align:start position:0%
+remember the mitochondria has its own
+ 
+
+ align:start position:0%
+remember the mitochondria has its own
+genome this is a vestige of its
+
+ align:start position:0%
+genome this is a vestige of its
+ 
+
+ align:start position:0%
+genome this is a vestige of its
+this symbiotic relationship that
+
+ align:start position:0%
+this symbiotic relationship that
+ 
+
+ align:start position:0%
+this symbiotic relationship that
+developed you know
+
+ align:start position:0%
+developed you know
+ 
+
+ align:start position:0%
+developed you know
+long long ago where two prokaryotes came
+
+ align:start position:0%
+long long ago where two prokaryotes came
+ 
+
+ align:start position:0%
+long long ago where two prokaryotes came
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+leading to this um this
+
+ align:start position:0%
+leading to this um this
+ 
+
+ align:start position:0%
+leading to this um this
+symbiotic relationship but of course the
+
+ align:start position:0%
+symbiotic relationship but of course the
+ 
+
+ align:start position:0%
+symbiotic relationship but of course the
+mitochondrial dna
+
+ align:start position:0%
+mitochondrial dna
+ 
+
+ align:start position:0%
+mitochondrial dna
+encoding many of the key components of
+
+ align:start position:0%
+encoding many of the key components of
+ 
+
+ align:start position:0%
+encoding many of the key components of
+this electron transport chain
+
+ align:start position:0%
+this electron transport chain
+ 
+
+ align:start position:0%
+this electron transport chain
+and atp synthesis machinery that remains
+
+ align:start position:0%
+and atp synthesis machinery that remains
+ 
+
+ align:start position:0%
+and atp synthesis machinery that remains
+in the mitochondria
+
+ align:start position:0%
+in the mitochondria
+ 
+
+ align:start position:0%
+in the mitochondria
+today now ultimately this process
+
+ align:start position:0%
+today now ultimately this process
+ 
+
+ align:start position:0%
+today now ultimately this process
+involves the re-oxidation
+
+ align:start position:0%
+involves the re-oxidation
+ 
+
+ align:start position:0%
+involves the re-oxidation
+of nadh back to nad
+
+ align:start position:0%
+of nadh back to nad
+ 
+
+ align:start position:0%
+of nadh back to nad
+that occurs at complex 1 of the electron
+
+ align:start position:0%
+that occurs at complex 1 of the electron
+ 
+
+ align:start position:0%
+that occurs at complex 1 of the electron
+transport chain
+
+ align:start position:0%
+transport chain
+ 
+
+ align:start position:0%
+transport chain
+those electrons are transferred into the
+
+ align:start position:0%
+those electrons are transferred into the
+ 
+
+ align:start position:0%
+those electrons are transferred into the
+q pool which then go into complex 3
+
+ align:start position:0%
+q pool which then go into complex 3
+ 
+
+ align:start position:0%
+q pool which then go into complex 3
+to cytochrome c to complex 4 ultimately
+
+ align:start position:0%
+to cytochrome c to complex 4 ultimately
+ 
+
+ align:start position:0%
+to cytochrome c to complex 4 ultimately
+being transferred to oxygen as the
+
+ align:start position:0%
+being transferred to oxygen as the
+ 
+
+ align:start position:0%
+being transferred to oxygen as the
+final electron acceptor and it's this
+
+ align:start position:0%
+final electron acceptor and it's this
+ 
+
+ align:start position:0%
+final electron acceptor and it's this
+process of favorable electron transport
+
+ align:start position:0%
+process of favorable electron transport
+ 
+
+ align:start position:0%
+process of favorable electron transport
+that is electrons moving from a lower to
+
+ align:start position:0%
+that is electrons moving from a lower to
+ 
+
+ align:start position:0%
+that is electrons moving from a lower to
+a higher standard reduction potential
+
+ align:start position:0%
+a higher standard reduction potential
+ 
+
+ align:start position:0%
+a higher standard reduction potential
+that is coupled to the pumping of
+
+ align:start position:0%
+that is coupled to the pumping of
+ 
+
+ align:start position:0%
+that is coupled to the pumping of
+protons and the generation of this delta
+
+ align:start position:0%
+protons and the generation of this delta
+ 
+
+ align:start position:0%
+protons and the generation of this delta
+psi delta ph
+
+ align:start position:0%
+psi delta ph
+ 
+
+ align:start position:0%
+psi delta ph
+now we also discussed complex two of the
+
+ align:start position:0%
+now we also discussed complex two of the
+ 
+
+ align:start position:0%
+now we also discussed complex two of the
+electron transport chain which is
+
+ align:start position:0%
+electron transport chain which is
+ 
+
+ align:start position:0%
+electron transport chain which is
+identical to
+
+ align:start position:0%
+identical to
+ 
+
+ align:start position:0%
+identical to
+succinate dehydrogenase in the tca cycle
+
+ align:start position:0%
+succinate dehydrogenase in the tca cycle
+ 
+
+ align:start position:0%
+succinate dehydrogenase in the tca cycle
+this is involving that fad fadh2
+
+ align:start position:0%
+this is involving that fad fadh2
+ 
+
+ align:start position:0%
+this is involving that fad fadh2
+which can itself also transfer electrons
+
+ align:start position:0%
+which can itself also transfer electrons
+ 
+
+ align:start position:0%
+which can itself also transfer electrons
+to the q pool
+
+ align:start position:0%
+to the q pool
+ 
+
+ align:start position:0%
+to the q pool
+ultimately passing those to complex 3 to
+
+ align:start position:0%
+ultimately passing those to complex 3 to
+ 
+
+ align:start position:0%
+ultimately passing those to complex 3 to
+cytochrome c to complex 4.
+
+ align:start position:0%
+cytochrome c to complex 4.
+ 
+
+ align:start position:0%
+cytochrome c to complex 4.
+again with oxygen as electron acceptor
+
+ align:start position:0%
+again with oxygen as electron acceptor
+ 
+
+ align:start position:0%
+again with oxygen as electron acceptor
+ultimately forming what is essentially
+
+ align:start position:0%
+ultimately forming what is essentially
+ 
+
+ align:start position:0%
+ultimately forming what is essentially
+two different
+
+ align:start position:0%
+two different
+ 
+
+ align:start position:0%
+two different
+variations on the electron transport
+
+ align:start position:0%
+variations on the electron transport
+ 
+
+ align:start position:0%
+variations on the electron transport
+chain
+
+ align:start position:0%
+chain
+ 
+
+ align:start position:0%
+chain
+as a way to generate delta psi delta ph
+
+ align:start position:0%
+as a way to generate delta psi delta ph
+ 
+
+ align:start position:0%
+as a way to generate delta psi delta ph
+now i show here on the slide
+
+ align:start position:0%
+now i show here on the slide
+ 
+
+ align:start position:0%
+now i show here on the slide
+that there's really many versions of
+
+ align:start position:0%
+that there's really many versions of
+ 
+
+ align:start position:0%
+that there's really many versions of
+this electron transport chain
+
+ align:start position:0%
+this electron transport chain
+ 
+
+ align:start position:0%
+this electron transport chain
+and another one we discussed is shown
+
+ align:start position:0%
+and another one we discussed is shown
+ 
+
+ align:start position:0%
+and another one we discussed is shown
+down here so up here is the
+
+ align:start position:0%
+down here so up here is the
+ 
+
+ align:start position:0%
+down here so up here is the
+typical one to regenerate nad plus using
+
+ align:start position:0%
+typical one to regenerate nad plus using
+ 
+
+ align:start position:0%
+typical one to regenerate nad plus using
+complex one
+
+ align:start position:0%
+complex one
+ 
+
+ align:start position:0%
+complex one
+to the q pool to three to c to four
+
+ align:start position:0%
+to the q pool to three to c to four
+ 
+
+ align:start position:0%
+to the q pool to three to c to four
+here's the one
+
+ align:start position:0%
+here's the one
+ 
+
+ align:start position:0%
+here's the one
+involving um complex two so succinate
+
+ align:start position:0%
+involving um complex two so succinate
+ 
+
+ align:start position:0%
+involving um complex two so succinate
+dehydrogenase reaction
+
+ align:start position:0%
+dehydrogenase reaction
+ 
+
+ align:start position:0%
+dehydrogenase reaction
+via complex two to the q pool complex
+
+ align:start position:0%
+via complex two to the q pool complex
+ 
+
+ align:start position:0%
+via complex two to the q pool complex
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+c four and then there's yet a third one
+
+ align:start position:0%
+c four and then there's yet a third one
+ 
+
+ align:start position:0%
+c four and then there's yet a third one
+here from fatty acid oxidation so this
+
+ align:start position:0%
+here from fatty acid oxidation so this
+ 
+
+ align:start position:0%
+here from fatty acid oxidation so this
+is acyl coa dehydrogenase again light
+
+ align:start position:0%
+is acyl coa dehydrogenase again light
+ 
+
+ align:start position:0%
+is acyl coa dehydrogenase again light
+complex
+
+ align:start position:0%
+complex
+ 
+
+ align:start position:0%
+complex
+ii involves fad fadh2 this occurs at the
+
+ align:start position:0%
+ii involves fad fadh2 this occurs at the
+ 
+
+ align:start position:0%
+ii involves fad fadh2 this occurs at the
+membrane
+
+ align:start position:0%
+membrane
+ 
+
+ align:start position:0%
+membrane
+transfers electrons to the q pool to
+
+ align:start position:0%
+transfers electrons to the q pool to
+ 
+
+ align:start position:0%
+transfers electrons to the q pool to
+three to c to four 4
+
+ align:start position:0%
+three to c to four 4
+ 
+
+ align:start position:0%
+three to c to four 4
+ultimately reducing oxygen to water
+
+ align:start position:0%
+ultimately reducing oxygen to water
+ 
+
+ align:start position:0%
+ultimately reducing oxygen to water
+and so the net effect of these various
+
+ align:start position:0%
+and so the net effect of these various
+ 
+
+ align:start position:0%
+and so the net effect of these various
+electron transport chains
+
+ align:start position:0%
+electron transport chains
+ 
+
+ align:start position:0%
+electron transport chains
+or shown up here is generating this
+
+ align:start position:0%
+or shown up here is generating this
+ 
+
+ align:start position:0%
+or shown up here is generating this
+delta psi delta ph which can then be
+
+ align:start position:0%
+delta psi delta ph which can then be
+ 
+
+ align:start position:0%
+delta psi delta ph which can then be
+used to do work
+
+ align:start position:0%
+used to do work
+ 
+
+ align:start position:0%
+used to do work
+now the cool thing is is that this is
+
+ align:start position:0%
+now the cool thing is is that this is
+ 
+
+ align:start position:0%
+now the cool thing is is that this is
+occurring in this case at the inner
+
+ align:start position:0%
+occurring in this case at the inner
+ 
+
+ align:start position:0%
+occurring in this case at the inner
+mitochondrial membrane
+
+ align:start position:0%
+mitochondrial membrane
+ 
+
+ align:start position:0%
+mitochondrial membrane
+and so you can do work in lots of
+
+ align:start position:0%
+and so you can do work in lots of
+ 
+
+ align:start position:0%
+and so you can do work in lots of
+different ways it doesn't have to be
+
+ align:start position:0%
+different ways it doesn't have to be
+ 
+
+ align:start position:0%
+different ways it doesn't have to be
+next to the complex you have a charge
+
+ align:start position:0%
+next to the complex you have a charge
+ 
+
+ align:start position:0%
+next to the complex you have a charge
+across the membrane
+
+ align:start position:0%
+across the membrane
+ 
+
+ align:start position:0%
+across the membrane
+that can be used different places in
+
+ align:start position:0%
+that can be used different places in
+ 
+
+ align:start position:0%
+that can be used different places in
+space such as
+
+ align:start position:0%
+space such as
+ 
+
+ align:start position:0%
+space such as
+so-called complex 5 or the f1 f0 atpase
+
+ align:start position:0%
+so-called complex 5 or the f1 f0 atpase
+ 
+
+ align:start position:0%
+so-called complex 5 or the f1 f0 atpase
+which can use dissipation of that proton
+
+ align:start position:0%
+which can use dissipation of that proton
+ 
+
+ align:start position:0%
+which can use dissipation of that proton
+gradient
+
+ align:start position:0%
+gradient
+ 
+
+ align:start position:0%
+gradient
+to drive that rotational catalysis
+
+ align:start position:0%
+to drive that rotational catalysis
+ 
+
+ align:start position:0%
+to drive that rotational catalysis
+machine we described last time
+
+ align:start position:0%
+machine we described last time
+ 
+
+ align:start position:0%
+machine we described last time
+and ultimately take adp plus phosphate
+
+ align:start position:0%
+and ultimately take adp plus phosphate
+ 
+
+ align:start position:0%
+and ultimately take adp plus phosphate
+and synthesize
+
+ align:start position:0%
+and synthesize
+ 
+
+ align:start position:0%
+and synthesize
+atp but that's not the only work it can
+
+ align:start position:0%
+atp but that's not the only work it can
+ 
+
+ align:start position:0%
+atp but that's not the only work it can
+do you can
+
+ align:start position:0%
+do you can
+ 
+
+ align:start position:0%
+do you can
+uncouple the whole thing we discussed
+
+ align:start position:0%
+uncouple the whole thing we discussed
+ 
+
+ align:start position:0%
+uncouple the whole thing we discussed
+these uncoupling proteins which
+
+ align:start position:0%
+these uncoupling proteins which
+ 
+
+ align:start position:0%
+these uncoupling proteins which
+effectively just let protons
+
+ align:start position:0%
+effectively just let protons
+ 
+
+ align:start position:0%
+effectively just let protons
+leak back across into the membranes
+
+ align:start position:0%
+leak back across into the membranes
+ 
+
+ align:start position:0%
+leak back across into the membranes
+that's short-circuiting
+
+ align:start position:0%
+that's short-circuiting
+ 
+
+ align:start position:0%
+that's short-circuiting
+this potential and that's a way to
+
+ align:start position:0%
+this potential and that's a way to
+ 
+
+ align:start position:0%
+this potential and that's a way to
+generate heat
+
+ align:start position:0%
+generate heat
+ 
+
+ align:start position:0%
+generate heat
+other type of work we can do is we can
+
+ align:start position:0%
+other type of work we can do is we can
+ 
+
+ align:start position:0%
+other type of work we can do is we can
+use this
+
+ align:start position:0%
+use this
+ 
+
+ align:start position:0%
+use this
+proton gradient to power the transport
+
+ align:start position:0%
+proton gradient to power the transport
+ 
+
+ align:start position:0%
+proton gradient to power the transport
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+other ions we discussed this happening
+
+ align:start position:0%
+other ions we discussed this happening
+ 
+
+ align:start position:0%
+other ions we discussed this happening
+with atp
+
+ align:start position:0%
+with atp
+ 
+
+ align:start position:0%
+with atp
+adp exchange because of course atp and
+
+ align:start position:0%
+adp exchange because of course atp and
+ 
+
+ align:start position:0%
+adp exchange because of course atp and
+adp conversion
+
+ align:start position:0%
+adp conversion
+ 
+
+ align:start position:0%
+adp conversion
+needed in the cytosol the favor
+
+ align:start position:0%
+needed in the cytosol the favor
+ 
+
+ align:start position:0%
+needed in the cytosol the favor
+unfavorable processes there
+
+ align:start position:0%
+unfavorable processes there
+ 
+
+ align:start position:0%
+unfavorable processes there
+need to exchange those in and out of the
+
+ align:start position:0%
+need to exchange those in and out of the
+ 
+
+ align:start position:0%
+need to exchange those in and out of the
+mitochondria so you can regenerate
+
+ align:start position:0%
+mitochondria so you can regenerate
+ 
+
+ align:start position:0%
+mitochondria so you can regenerate
+atp with the atp synthase machinery and
+
+ align:start position:0%
+atp with the atp synthase machinery and
+ 
+
+ align:start position:0%
+atp with the atp synthase machinery and
+yet another thing we talked about is you
+
+ align:start position:0%
+yet another thing we talked about is you
+ 
+
+ align:start position:0%
+yet another thing we talked about is you
+can use this as a way to concentrate
+
+ align:start position:0%
+can use this as a way to concentrate
+ 
+
+ align:start position:0%
+can use this as a way to concentrate
+ions such as
+
+ align:start position:0%
+ions such as
+ 
+
+ align:start position:0%
+ions such as
+calcium and the mitochondria ends up
+
+ align:start position:0%
+calcium and the mitochondria ends up
+ 
+
+ align:start position:0%
+calcium and the mitochondria ends up
+being a major calcium store
+
+ align:start position:0%
+being a major calcium store
+ 
+
+ align:start position:0%
+being a major calcium store
+for cells now
+
+ align:start position:0%
+for cells now
+ 
+
+ align:start position:0%
+for cells now
+we discussed last time
+
+ align:start position:0%
+we discussed last time
+ 
+
+ align:start position:0%
+we discussed last time
+that this is great having all of these
+
+ align:start position:0%
+that this is great having all of these
+ 
+
+ align:start position:0%
+that this is great having all of these
+oxidation processes the tca cycle fatty
+
+ align:start position:0%
+oxidation processes the tca cycle fatty
+ 
+
+ align:start position:0%
+oxidation processes the tca cycle fatty
+acid oxidation
+
+ align:start position:0%
+acid oxidation
+ 
+
+ align:start position:0%
+acid oxidation
+all occurring in the matrix because it
+
+ align:start position:0%
+all occurring in the matrix because it
+ 
+
+ align:start position:0%
+all occurring in the matrix because it
+gives a location for
+
+ align:start position:0%
+gives a location for
+ 
+
+ align:start position:0%
+gives a location for
+nadnadh to happen where it has easy
+
+ align:start position:0%
+nadnadh to happen where it has easy
+ 
+
+ align:start position:0%
+nadnadh to happen where it has easy
+access to
+
+ align:start position:0%
+access to
+ 
+
+ align:start position:0%
+access to
+this electron transport machinery and
+
+ align:start position:0%
+this electron transport machinery and
+ 
+
+ align:start position:0%
+this electron transport machinery and
+the ability to regenerate the nad
+
+ align:start position:0%
+the ability to regenerate the nad
+ 
+
+ align:start position:0%
+the ability to regenerate the nad
+necessary to keep these processes going
+
+ align:start position:0%
+necessary to keep these processes going
+ 
+
+ align:start position:0%
+necessary to keep these processes going
+but of course the very first process we
+
+ align:start position:0%
+but of course the very first process we
+ 
+
+ align:start position:0%
+but of course the very first process we
+talked about happens in the cytosol and
+
+ align:start position:0%
+talked about happens in the cytosol and
+ 
+
+ align:start position:0%
+talked about happens in the cytosol and
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+glycolysis and we discussed how you can
+
+ align:start position:0%
+glycolysis and we discussed how you can
+ 
+
+ align:start position:0%
+glycolysis and we discussed how you can
+bring
+
+ align:start position:0%
+bring
+ 
+
+ align:start position:0%
+bring
+pyruvate into the mitochondria through
+
+ align:start position:0%
+pyruvate into the mitochondria through
+ 
+
+ align:start position:0%
+pyruvate into the mitochondria through
+this mitochondrial pyruvate carrier
+
+ align:start position:0%
+this mitochondrial pyruvate carrier
+ 
+
+ align:start position:0%
+this mitochondrial pyruvate carrier
+then it has access to the pyruvate
+
+ align:start position:0%
+then it has access to the pyruvate
+ 
+
+ align:start position:0%
+then it has access to the pyruvate
+dehydrogenase reaction which of course
+
+ align:start position:0%
+dehydrogenase reaction which of course
+ 
+
+ align:start position:0%
+dehydrogenase reaction which of course
+generates acetyl coa and nadh in the
+
+ align:start position:0%
+generates acetyl coa and nadh in the
+ 
+
+ align:start position:0%
+generates acetyl coa and nadh in the
+right place
+
+ align:start position:0%
+right place
+ 
+
+ align:start position:0%
+right place
+however if you go way back to when we
+
+ align:start position:0%
+however if you go way back to when we
+ 
+
+ align:start position:0%
+however if you go way back to when we
+discuss fermentation remember the reason
+
+ align:start position:0%
+discuss fermentation remember the reason
+ 
+
+ align:start position:0%
+discuss fermentation remember the reason
+we had to send pyruvate to fermentation
+
+ align:start position:0%
+we had to send pyruvate to fermentation
+ 
+
+ align:start position:0%
+we had to send pyruvate to fermentation
+was to
+
+ align:start position:0%
+was to
+ 
+
+ align:start position:0%
+was to
+regenerate that nad in the cytosol
+
+ align:start position:0%
+regenerate that nad in the cytosol
+ 
+
+ align:start position:0%
+regenerate that nad in the cytosol
+that's necessary to keep glycolysis
+
+ align:start position:0%
+that's necessary to keep glycolysis
+ 
+
+ align:start position:0%
+that's necessary to keep glycolysis
+going now of course if we're going to
+
+ align:start position:0%
+going now of course if we're going to
+ 
+
+ align:start position:0%
+going now of course if we're going to
+fully oxidize pyruvate carbon in the
+
+ align:start position:0%
+fully oxidize pyruvate carbon in the
+ 
+
+ align:start position:0%
+fully oxidize pyruvate carbon in the
+mitochondria
+
+ align:start position:0%
+mitochondria
+ 
+
+ align:start position:0%
+mitochondria
+we still have to solve this electron
+
+ align:start position:0%
+we still have to solve this electron
+ 
+
+ align:start position:0%
+we still have to solve this electron
+balance problem for
+
+ align:start position:0%
+balance problem for
+ 
+
+ align:start position:0%
+balance problem for
+glycolysis and as we discussed we can
+
+ align:start position:0%
+glycolysis and as we discussed we can
+ 
+
+ align:start position:0%
+glycolysis and as we discussed we can
+solve that by giving those electrons to
+
+ align:start position:0%
+solve that by giving those electrons to
+ 
+
+ align:start position:0%
+solve that by giving those electrons to
+oxygen
+
+ align:start position:0%
+oxygen
+ 
+
+ align:start position:0%
+oxygen
+but now you see that there's this
+
+ align:start position:0%
+but now you see that there's this
+ 
+
+ align:start position:0%
+but now you see that there's this
+additional complication
+
+ align:start position:0%
+additional complication
+ 
+
+ align:start position:0%
+additional complication
+is that these electrons in the form of
+
+ align:start position:0%
+is that these electrons in the form of
+ 
+
+ align:start position:0%
+is that these electrons in the form of
+nadh
+
+ align:start position:0%
+nadh
+ 
+
+ align:start position:0%
+nadh
+need to get inside the mitochondrial
+
+ align:start position:0%
+need to get inside the mitochondrial
+ 
+
+ align:start position:0%
+need to get inside the mitochondrial
+matrix or get to the electron transport
+
+ align:start position:0%
+matrix or get to the electron transport
+ 
+
+ align:start position:0%
+matrix or get to the electron transport
+chain
+
+ align:start position:0%
+chain
+ 
+
+ align:start position:0%
+chain
+as a way to use oxygen
+
+ align:start position:0%
+as a way to use oxygen
+ 
+
+ align:start position:0%
+as a way to use oxygen
+to ultimately dispose of those electrons
+
+ align:start position:0%
+to ultimately dispose of those electrons
+ 
+
+ align:start position:0%
+to ultimately dispose of those electrons
+and so effectively
+
+ align:start position:0%
+and so effectively
+ 
+
+ align:start position:0%
+and so effectively
+that nadh needs to be gotten to
+
+ align:start position:0%
+that nadh needs to be gotten to
+ 
+
+ align:start position:0%
+that nadh needs to be gotten to
+complex one which would be the matrix um
+
+ align:start position:0%
+complex one which would be the matrix um
+ 
+
+ align:start position:0%
+complex one which would be the matrix um
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+way we've drawn it here now
+
+ align:start position:0%
+way we've drawn it here now
+ 
+
+ align:start position:0%
+way we've drawn it here now
+really the way that this happens is not
+
+ align:start position:0%
+really the way that this happens is not
+ 
+
+ align:start position:0%
+really the way that this happens is not
+direct so you don't transport nadh
+
+ align:start position:0%
+direct so you don't transport nadh
+ 
+
+ align:start position:0%
+direct so you don't transport nadh
+from the cytosol into the mitochondria
+
+ align:start position:0%
+from the cytosol into the mitochondria
+ 
+
+ align:start position:0%
+from the cytosol into the mitochondria
+and that's partially because one of the
+
+ align:start position:0%
+and that's partially because one of the
+ 
+
+ align:start position:0%
+and that's partially because one of the
+benefits remember of having
+
+ align:start position:0%
+benefits remember of having
+ 
+
+ align:start position:0%
+benefits remember of having
+compartmentalized metabolism
+
+ align:start position:0%
+compartmentalized metabolism
+ 
+
+ align:start position:0%
+compartmentalized metabolism
+is your ability to have different
+
+ align:start position:0%
+is your ability to have different
+ 
+
+ align:start position:0%
+is your ability to have different
+conditions different atp adp ratios nad
+
+ align:start position:0%
+conditions different atp adp ratios nad
+ 
+
+ align:start position:0%
+conditions different atp adp ratios nad
+nadh ratios
+
+ align:start position:0%
+nadh ratios
+ 
+
+ align:start position:0%
+nadh ratios
+in different compartments because that
+
+ align:start position:0%
+in different compartments because that
+ 
+
+ align:start position:0%
+in different compartments because that
+can favor different chemistry
+
+ align:start position:0%
+can favor different chemistry
+ 
+
+ align:start position:0%
+can favor different chemistry
+and so the way that you get electrons
+
+ align:start position:0%
+and so the way that you get electrons
+ 
+
+ align:start position:0%
+and so the way that you get electrons
+into the matrix or get electrons to the
+
+ align:start position:0%
+into the matrix or get electrons to the
+ 
+
+ align:start position:0%
+into the matrix or get electrons to the
+electron transport chains
+
+ align:start position:0%
+electron transport chains
+ 
+
+ align:start position:0%
+electron transport chains
+doesn't occur directly you do not
+
+ align:start position:0%
+doesn't occur directly you do not
+ 
+
+ align:start position:0%
+doesn't occur directly you do not
+transport nad
+
+ align:start position:0%
+transport nad
+ 
+
+ align:start position:0%
+transport nad
+or nadh directly instead you use
+
+ align:start position:0%
+or nadh directly instead you use
+ 
+
+ align:start position:0%
+or nadh directly instead you use
+so-called
+
+ align:start position:0%
+so-called
+ 
+
+ align:start position:0%
+so-called
+shuttles which are
+
+ align:start position:0%
+shuttles which are
+ 
+
+ align:start position:0%
+shuttles which are
+analogous to some of the other shuttles
+
+ align:start position:0%
+analogous to some of the other shuttles
+ 
+
+ align:start position:0%
+analogous to some of the other shuttles
+we've talked about
+
+ align:start position:0%
+we've talked about
+ 
+
+ align:start position:0%
+we've talked about
+in order to get materials across
+
+ align:start position:0%
+in order to get materials across
+ 
+
+ align:start position:0%
+in order to get materials across
+membranes in this case this is a way to
+
+ align:start position:0%
+membranes in this case this is a way to
+ 
+
+ align:start position:0%
+membranes in this case this is a way to
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+electrons generated from oxidation
+
+ align:start position:0%
+electrons generated from oxidation
+ 
+
+ align:start position:0%
+electrons generated from oxidation
+reactions in the cytosol
+
+ align:start position:0%
+reactions in the cytosol
+ 
+
+ align:start position:0%
+reactions in the cytosol
+production of nadh in the cytosol things
+
+ align:start position:0%
+production of nadh in the cytosol things
+ 
+
+ align:start position:0%
+production of nadh in the cytosol things
+like glycolysis
+
+ align:start position:0%
+like glycolysis
+ 
+
+ align:start position:0%
+like glycolysis
+into to the electron transport chain
+
+ align:start position:0%
+into to the electron transport chain
+ 
+
+ align:start position:0%
+into to the electron transport chain
+so that they can ultimately be
+
+ align:start position:0%
+so that they can ultimately be
+ 
+
+ align:start position:0%
+so that they can ultimately be
+transferred
+
+ align:start position:0%
+transferred
+ 
+
+ align:start position:0%
+transferred
+to oxygen and so these
+
+ align:start position:0%
+to oxygen and so these
+ 
+
+ align:start position:0%
+to oxygen and so these
+shuttles or redox shuttles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually come in several different ways
+
+ align:start position:0%
+actually come in several different ways
+ 
+
+ align:start position:0%
+actually come in several different ways
+that cells can deal with cytosolic
+
+ align:start position:0%
+that cells can deal with cytosolic
+ 
+
+ align:start position:0%
+that cells can deal with cytosolic
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+and so these shuttles
+
+ align:start position:0%
+and so these shuttles
+ 
+
+ align:start position:0%
+and so these shuttles
+also in in essence help cells
+
+ align:start position:0%
+also in in essence help cells
+ 
+
+ align:start position:0%
+also in in essence help cells
+also establish these different
+
+ align:start position:0%
+also establish these different
+ 
+
+ align:start position:0%
+also establish these different
+conditions these different nad nadh
+
+ align:start position:0%
+conditions these different nad nadh
+ 
+
+ align:start position:0%
+conditions these different nad nadh
+ratios in different compartments
+
+ align:start position:0%
+ratios in different compartments
+ 
+
+ align:start position:0%
+ratios in different compartments
+and so you can imagine that the shuttles
+
+ align:start position:0%
+and so you can imagine that the shuttles
+ 
+
+ align:start position:0%
+and so you can imagine that the shuttles
+themselves can be regulated as a way
+
+ align:start position:0%
+themselves can be regulated as a way
+ 
+
+ align:start position:0%
+themselves can be regulated as a way
+to do this now there's two major
+
+ align:start position:0%
+to do this now there's two major
+ 
+
+ align:start position:0%
+to do this now there's two major
+redox shuttles that allow you to move
+
+ align:start position:0%
+redox shuttles that allow you to move
+ 
+
+ align:start position:0%
+redox shuttles that allow you to move
+electrons from the cytosol
+
+ align:start position:0%
+electrons from the cytosol
+ 
+
+ align:start position:0%
+electrons from the cytosol
+into the mitochondria um and
+
+ align:start position:0%
+into the mitochondria um and
+ 
+
+ align:start position:0%
+into the mitochondria um and
+we'll discuss those two here next
+
+ align:start position:0%
+we'll discuss those two here next
+ 
+
+ align:start position:0%
+we'll discuss those two here next
+um these are the two that probably are
+
+ align:start position:0%
+um these are the two that probably are
+ 
+
+ align:start position:0%
+um these are the two that probably are
+being looked for
+
+ align:start position:0%
+being looked for
+ 
+
+ align:start position:0%
+being looked for
+if you get this question um
+
+ align:start position:0%
+if you get this question um
+ 
+
+ align:start position:0%
+if you get this question um
+on an mcat exam or something like that
+
+ align:start position:0%
+on an mcat exam or something like that
+ 
+
+ align:start position:0%
+on an mcat exam or something like that
+they're the ones that are described in
+
+ align:start position:0%
+they're the ones that are described in
+ 
+
+ align:start position:0%
+they're the ones that are described in
+the text as the way to get electrons um
+
+ align:start position:0%
+the text as the way to get electrons um
+ 
+
+ align:start position:0%
+the text as the way to get electrons um
+to the electron transport chain
+
+ align:start position:0%
+to the electron transport chain
+ 
+
+ align:start position:0%
+to the electron transport chain
+but however as we go through them you
+
+ align:start position:0%
+but however as we go through them you
+ 
+
+ align:start position:0%
+but however as we go through them you
+will see that
+
+ align:start position:0%
+will see that
+ 
+
+ align:start position:0%
+will see that
+there's a couple different ways one can
+
+ align:start position:0%
+there's a couple different ways one can
+ 
+
+ align:start position:0%
+there's a couple different ways one can
+do this they basically involve
+
+ align:start position:0%
+do this they basically involve
+ 
+
+ align:start position:0%
+do this they basically involve
+oxidation and reduction of a pair of
+
+ align:start position:0%
+oxidation and reduction of a pair of
+ 
+
+ align:start position:0%
+oxidation and reduction of a pair of
+molecules on either side of the membrane
+
+ align:start position:0%
+molecules on either side of the membrane
+ 
+
+ align:start position:0%
+molecules on either side of the membrane
+and there's lots of ways you can do that
+
+ align:start position:0%
+and there's lots of ways you can do that
+ 
+
+ align:start position:0%
+and there's lots of ways you can do that
+in addition to these
+
+ align:start position:0%
+in addition to these
+ 
+
+ align:start position:0%
+in addition to these
+other shuttles it'll become more clear
+
+ align:start position:0%
+other shuttles it'll become more clear
+ 
+
+ align:start position:0%
+other shuttles it'll become more clear
+what i mean by this but i guess i just
+
+ align:start position:0%
+what i mean by this but i guess i just
+ 
+
+ align:start position:0%
+what i mean by this but i guess i just
+want you to know
+
+ align:start position:0%
+want you to know
+ 
+
+ align:start position:0%
+want you to know
+that these are not the only ways one
+
+ align:start position:0%
+that these are not the only ways one
+ 
+
+ align:start position:0%
+that these are not the only ways one
+could shuttle electrons into the
+
+ align:start position:0%
+could shuttle electrons into the
+ 
+
+ align:start position:0%
+could shuttle electrons into the
+mitochondria
+
+ align:start position:0%
+mitochondria
+ 
+
+ align:start position:0%
+mitochondria
+these are just the major ways that um
+
+ align:start position:0%
+these are just the major ways that um
+ 
+
+ align:start position:0%
+these are just the major ways that um
+have been discussed and are usually
+
+ align:start position:0%
+have been discussed and are usually
+ 
+
+ align:start position:0%
+have been discussed and are usually
+derived
+
+ align:start position:0%
+derived
+ 
+
+ align:start position:0%
+derived
+discussed in textbooks okay so the first
+
+ align:start position:0%
+discussed in textbooks okay so the first
+ 
+
+ align:start position:0%
+discussed in textbooks okay so the first
+shuttle system is something called the
+
+ align:start position:0%
+shuttle system is something called the
+ 
+
+ align:start position:0%
+shuttle system is something called the
+glycerol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phosphate shuttle
+
+ align:start position:0%
+phosphate shuttle
+ 
+
+ align:start position:0%
+phosphate shuttle
+and so the glycerol phosphate shuttle
+
+ align:start position:0%
+and so the glycerol phosphate shuttle
+ 
+
+ align:start position:0%
+and so the glycerol phosphate shuttle
+involves a reaction that we've already
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discussed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's our old friend
+
+ align:start position:0%
+so here's our old friend
+ 
+
+ align:start position:0%
+so here's our old friend
+dihydroxyacetone phosphate from
+
+ align:start position:0%
+dihydroxyacetone phosphate from
+ 
+
+ align:start position:0%
+dihydroxyacetone phosphate from
+glycolysis remember when we talked about
+
+ align:start position:0%
+glycolysis remember when we talked about
+ 
+
+ align:start position:0%
+glycolysis remember when we talked about
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+generation of and metabolism of glycerol
+
+ align:start position:0%
+generation of and metabolism of glycerol
+ 
+
+ align:start position:0%
+generation of and metabolism of glycerol
+in order to make
+
+ align:start position:0%
+in order to make
+ 
+
+ align:start position:0%
+in order to make
+triacylglycerides phospholipids remember
+
+ align:start position:0%
+triacylglycerides phospholipids remember
+ 
+
+ align:start position:0%
+triacylglycerides phospholipids remember
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+described that you can take
+
+ align:start position:0%
+described that you can take
+ 
+
+ align:start position:0%
+described that you can take
+dihydroxyacetone phosphate
+
+ align:start position:0%
+dihydroxyacetone phosphate
+ 
+
+ align:start position:0%
+dihydroxyacetone phosphate
+if you use nadh to reduce
+
+ align:start position:0%
+if you use nadh to reduce
+ 
+
+ align:start position:0%
+if you use nadh to reduce
+that ketone to the alcohol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that generates this molecule glycerol
+
+ align:start position:0%
+that generates this molecule glycerol
+ 
+
+ align:start position:0%
+that generates this molecule glycerol
+phosphate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and of course because you're reducing
+
+ align:start position:0%
+and of course because you're reducing
+ 
+
+ align:start position:0%
+and of course because you're reducing
+the ketone to the alcohol something else
+
+ align:start position:0%
+the ketone to the alcohol something else
+ 
+
+ align:start position:0%
+the ketone to the alcohol something else
+has to be oxidized
+
+ align:start position:0%
+has to be oxidized
+ 
+
+ align:start position:0%
+has to be oxidized
+you re-oxidized nadh back to nad plus
+
+ align:start position:0%
+you re-oxidized nadh back to nad plus
+ 
+
+ align:start position:0%
+you re-oxidized nadh back to nad plus
+effectively disposing of those electrons
+
+ align:start position:0%
+effectively disposing of those electrons
+ 
+
+ align:start position:0%
+effectively disposing of those electrons
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+say glycolysis that generated nadh
+
+ align:start position:0%
+say glycolysis that generated nadh
+ 
+
+ align:start position:0%
+say glycolysis that generated nadh
+to regenerate nad plus okay
+
+ align:start position:0%
+to regenerate nad plus okay
+ 
+
+ align:start position:0%
+to regenerate nad plus okay
+now rather than use this glycerol
+
+ align:start position:0%
+now rather than use this glycerol
+ 
+
+ align:start position:0%
+now rather than use this glycerol
+phosphate and lipid synthesis
+
+ align:start position:0%
+phosphate and lipid synthesis
+ 
+
+ align:start position:0%
+phosphate and lipid synthesis
+turns out there's a complex that can
+
+ align:start position:0%
+turns out there's a complex that can
+ 
+
+ align:start position:0%
+turns out there's a complex that can
+directly
+
+ align:start position:0%
+directly
+ 
+
+ align:start position:0%
+directly
+transfer those electrons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to fad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to generate fad
+
+ align:start position:0%
+to generate fad
+ 
+
+ align:start position:0%
+to generate fad
+h2 and this complex sits
+
+ align:start position:0%
+h2 and this complex sits
+ 
+
+ align:start position:0%
+h2 and this complex sits
+within the inner mitochondrial membrane
+
+ align:start position:0%
+within the inner mitochondrial membrane
+ 
+
+ align:start position:0%
+within the inner mitochondrial membrane
+facing the cytosolic
+
+ align:start position:0%
+facing the cytosolic
+ 
+
+ align:start position:0%
+facing the cytosolic
+side of the membrane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's the inner mitochondrial membrane
+
+ align:start position:0%
+there's the inner mitochondrial membrane
+ 
+
+ align:start position:0%
+there's the inner mitochondrial membrane
+this would be the matrix
+
+ align:start position:0%
+this would be the matrix
+ 
+
+ align:start position:0%
+this would be the matrix
+and so transferring those electrons to
+
+ align:start position:0%
+and so transferring those electrons to
+ 
+
+ align:start position:0%
+and so transferring those electrons to
+fad to reduced fadh2
+
+ align:start position:0%
+fad to reduced fadh2
+ 
+
+ align:start position:0%
+fad to reduced fadh2
+reoxidizes the glycerol phosphate back
+
+ align:start position:0%
+reoxidizes the glycerol phosphate back
+ 
+
+ align:start position:0%
+reoxidizes the glycerol phosphate back
+to dihydroxyacetone phosphate
+
+ align:start position:0%
+to dihydroxyacetone phosphate
+ 
+
+ align:start position:0%
+to dihydroxyacetone phosphate
+and of course in this membrane you can
+
+ align:start position:0%
+and of course in this membrane you can
+ 
+
+ align:start position:0%
+and of course in this membrane you can
+in this complex
+
+ align:start position:0%
+in this complex
+ 
+
+ align:start position:0%
+in this complex
+transfer those electrons by re-oxidizing
+
+ align:start position:0%
+transfer those electrons by re-oxidizing
+ 
+
+ align:start position:0%
+transfer those electrons by re-oxidizing
+the fad
+
+ align:start position:0%
+the fad
+ 
+
+ align:start position:0%
+the fad
+and sending them to uh the coenzyme q
+
+ align:start position:0%
+and sending them to uh the coenzyme q
+ 
+
+ align:start position:0%
+and sending them to uh the coenzyme q
+pool that can take the ubiquinone makes
+
+ align:start position:0%
+pool that can take the ubiquinone makes
+ 
+
+ align:start position:0%
+pool that can take the ubiquinone makes
+ubiquinol
+
+ align:start position:0%
+ubiquinol
+ 
+
+ align:start position:0%
+ubiquinol
+those electrons can go to complex three
+
+ align:start position:0%
+those electrons can go to complex three
+ 
+
+ align:start position:0%
+those electrons can go to complex three
+that can go to cytochrome c
+
+ align:start position:0%
+that can go to cytochrome c
+ 
+
+ align:start position:0%
+that can go to cytochrome c
+they can go to complex four ultimately
+
+ align:start position:0%
+they can go to complex four ultimately
+ 
+
+ align:start position:0%
+they can go to complex four ultimately
+ending up reducing oxygen to water
+
+ align:start position:0%
+ending up reducing oxygen to water
+ 
+
+ align:start position:0%
+ending up reducing oxygen to water
+using oxygen as a final electron
+
+ align:start position:0%
+using oxygen as a final electron
+ 
+
+ align:start position:0%
+using oxygen as a final electron
+acceptor
+
+ align:start position:0%
+acceptor
+ 
+
+ align:start position:0%
+acceptor
+again this is effectively another
+
+ align:start position:0%
+again this is effectively another
+ 
+
+ align:start position:0%
+again this is effectively another
+alternative to the electron transport
+
+ align:start position:0%
+alternative to the electron transport
+ 
+
+ align:start position:0%
+alternative to the electron transport
+chain
+
+ align:start position:0%
+chain
+ 
+
+ align:start position:0%
+chain
+and so i show that here on the slide and
+
+ align:start position:0%
+and so i show that here on the slide and
+ 
+
+ align:start position:0%
+and so i show that here on the slide and
+so we've discussed here's
+
+ align:start position:0%
+so we've discussed here's
+ 
+
+ align:start position:0%
+so we've discussed here's
+complex 3 the fad fadh2 containing
+
+ align:start position:0%
+complex 3 the fad fadh2 containing
+ 
+
+ align:start position:0%
+complex 3 the fad fadh2 containing
+enzyme sorry
+
+ align:start position:0%
+enzyme sorry
+ 
+
+ align:start position:0%
+enzyme sorry
+the complex 2 this is the fad fadh2
+
+ align:start position:0%
+the complex 2 this is the fad fadh2
+ 
+
+ align:start position:0%
+the complex 2 this is the fad fadh2
+containing
+
+ align:start position:0%
+containing
+ 
+
+ align:start position:0%
+containing
+enzyme is complex 2 succinate
+
+ align:start position:0%
+enzyme is complex 2 succinate
+ 
+
+ align:start position:0%
+enzyme is complex 2 succinate
+dehydrogenase sits
+
+ align:start position:0%
+dehydrogenase sits
+ 
+
+ align:start position:0%
+dehydrogenase sits
+in the inner mitochondrial membrane
+
+ align:start position:0%
+in the inner mitochondrial membrane
+ 
+
+ align:start position:0%
+in the inner mitochondrial membrane
+converts succinate to fumarate those
+
+ align:start position:0%
+converts succinate to fumarate those
+ 
+
+ align:start position:0%
+converts succinate to fumarate those
+enzymes those electrons end up on fadh2
+
+ align:start position:0%
+enzymes those electrons end up on fadh2
+ 
+
+ align:start position:0%
+enzymes those electrons end up on fadh2
+can get transferred to the cube pool
+
+ align:start position:0%
+can get transferred to the cube pool
+ 
+
+ align:start position:0%
+can get transferred to the cube pool
+re-oxidizing fad
+
+ align:start position:0%
+re-oxidizing fad
+ 
+
+ align:start position:0%
+re-oxidizing fad
+to complex three to cytochrome c to
+
+ align:start position:0%
+to complex three to cytochrome c to
+ 
+
+ align:start position:0%
+to complex three to cytochrome c to
+complex forward water
+
+ align:start position:0%
+complex forward water
+ 
+
+ align:start position:0%
+complex forward water
+uh i started to oxygen to water um
+
+ align:start position:0%
+uh i started to oxygen to water um
+ 
+
+ align:start position:0%
+uh i started to oxygen to water um
+we already discussed acell koa
+
+ align:start position:0%
+we already discussed acell koa
+ 
+
+ align:start position:0%
+we already discussed acell koa
+dehydrogenase same thing
+
+ align:start position:0%
+dehydrogenase same thing
+ 
+
+ align:start position:0%
+dehydrogenase same thing
+fad containing reaction in there is also
+
+ align:start position:0%
+fad containing reaction in there is also
+ 
+
+ align:start position:0%
+fad containing reaction in there is also
+in the membrane
+
+ align:start position:0%
+in the membrane
+ 
+
+ align:start position:0%
+in the membrane
+ultimately allows another version
+
+ align:start position:0%
+ultimately allows another version
+ 
+
+ align:start position:0%
+ultimately allows another version
+electron transport chain
+
+ align:start position:0%
+electron transport chain
+ 
+
+ align:start position:0%
+electron transport chain
+and here's yet a third one involving an
+
+ align:start position:0%
+and here's yet a third one involving an
+ 
+
+ align:start position:0%
+and here's yet a third one involving an
+fad using enzyme
+
+ align:start position:0%
+fad using enzyme
+ 
+
+ align:start position:0%
+fad using enzyme
+the difference is is that these have the
+
+ align:start position:0%
+the difference is is that these have the
+ 
+
+ align:start position:0%
+the difference is is that these have the
+oxidation reduction reaction occurring
+
+ align:start position:0%
+oxidation reduction reaction occurring
+ 
+
+ align:start position:0%
+oxidation reduction reaction occurring
+on the matrix side
+
+ align:start position:0%
+on the matrix side
+ 
+
+ align:start position:0%
+on the matrix side
+succinate to fumarate in the matrix size
+
+ align:start position:0%
+succinate to fumarate in the matrix size
+ 
+
+ align:start position:0%
+succinate to fumarate in the matrix size
+the introduction of a
+
+ align:start position:0%
+the introduction of a
+ 
+
+ align:start position:0%
+the introduction of a
+double bond for fatty acid oxidation on
+
+ align:start position:0%
+double bond for fatty acid oxidation on
+ 
+
+ align:start position:0%
+double bond for fatty acid oxidation on
+the matrix side
+
+ align:start position:0%
+the matrix side
+ 
+
+ align:start position:0%
+the matrix side
+this one here instead faces the
+
+ align:start position:0%
+this one here instead faces the
+ 
+
+ align:start position:0%
+this one here instead faces the
+cytosolic side
+
+ align:start position:0%
+cytosolic side
+ 
+
+ align:start position:0%
+cytosolic side
+so glycerol 3-phosphate
+
+ align:start position:0%
+so glycerol 3-phosphate
+ 
+
+ align:start position:0%
+so glycerol 3-phosphate
+can be re-oxidized to dihydroxyacetone
+
+ align:start position:0%
+can be re-oxidized to dihydroxyacetone
+ 
+
+ align:start position:0%
+can be re-oxidized to dihydroxyacetone
+phosphate looks like i have those arrows
+
+ align:start position:0%
+phosphate looks like i have those arrows
+ 
+
+ align:start position:0%
+phosphate looks like i have those arrows
+drawn backwards sorry
+
+ align:start position:0%
+drawn backwards sorry
+ 
+
+ align:start position:0%
+drawn backwards sorry
+ultimately sending electrons
+
+ align:start position:0%
+ultimately sending electrons
+ 
+
+ align:start position:0%
+ultimately sending electrons
+into this glycerol phosphate shuttle
+
+ align:start position:0%
+into this glycerol phosphate shuttle
+ 
+
+ align:start position:0%
+into this glycerol phosphate shuttle
+reducing fadh2 which can be re-oxidized
+
+ align:start position:0%
+reducing fadh2 which can be re-oxidized
+ 
+
+ align:start position:0%
+reducing fadh2 which can be re-oxidized
+by giving those electrons to the q pool
+
+ align:start position:0%
+by giving those electrons to the q pool
+ 
+
+ align:start position:0%
+by giving those electrons to the q pool
+to complex 3 to cytochrome c to complex
+
+ align:start position:0%
+to complex 3 to cytochrome c to complex
+ 
+
+ align:start position:0%
+to complex 3 to cytochrome c to complex
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ultimately with water serving as the
+
+ align:start position:0%
+ultimately with water serving as the
+ 
+
+ align:start position:0%
+ultimately with water serving as the
+final
+
+ align:start position:0%
+final
+ 
+
+ align:start position:0%
+final
+electron acceptor as i've drawn here
+
+ align:start position:0%
+electron acceptor as i've drawn here
+ 
+
+ align:start position:0%
+electron acceptor as i've drawn here
+now if you notice if we use
+
+ align:start position:0%
+now if you notice if we use
+ 
+
+ align:start position:0%
+now if you notice if we use
+this system or any of these
+
+ align:start position:0%
+this system or any of these
+ 
+
+ align:start position:0%
+this system or any of these
+systems these alternative fad fadh2
+
+ align:start position:0%
+systems these alternative fad fadh2
+ 
+
+ align:start position:0%
+systems these alternative fad fadh2
+using electron transport chains you
+
+ align:start position:0%
+using electron transport chains you
+ 
+
+ align:start position:0%
+using electron transport chains you
+don't use
+
+ align:start position:0%
+don't use
+ 
+
+ align:start position:0%
+don't use
+complex one remember complex one
+
+ align:start position:0%
+complex one remember complex one
+ 
+
+ align:start position:0%
+complex one remember complex one
+will pump a proton complex two will not
+
+ align:start position:0%
+will pump a proton complex two will not
+ 
+
+ align:start position:0%
+will pump a proton complex two will not
+and that means that if you use any of
+
+ align:start position:0%
+and that means that if you use any of
+ 
+
+ align:start position:0%
+and that means that if you use any of
+these fad fadh2
+
+ align:start position:0%
+these fad fadh2
+ 
+
+ align:start position:0%
+these fad fadh2
+using alternative electron transport
+
+ align:start position:0%
+using alternative electron transport
+ 
+
+ align:start position:0%
+using alternative electron transport
+chains you
+
+ align:start position:0%
+chains you
+ 
+
+ align:start position:0%
+chains you
+pump fewer protons into the cytosol and
+
+ align:start position:0%
+pump fewer protons into the cytosol and
+ 
+
+ align:start position:0%
+pump fewer protons into the cytosol and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if you donate the electrons to complex
+
+ align:start position:0%
+if you donate the electrons to complex
+ 
+
+ align:start position:0%
+if you donate the electrons to complex
+one from the matrix
+
+ align:start position:0%
+one from the matrix
+ 
+
+ align:start position:0%
+one from the matrix
+you pump a proton as you go through
+
+ align:start position:0%
+you pump a proton as you go through
+ 
+
+ align:start position:0%
+you pump a proton as you go through
+complex one to the q pool
+
+ align:start position:0%
+complex one to the q pool
+ 
+
+ align:start position:0%
+complex one to the q pool
+if you go through the glycerol phosphate
+
+ align:start position:0%
+if you go through the glycerol phosphate
+ 
+
+ align:start position:0%
+if you go through the glycerol phosphate
+shuttle you avoid complex one because
+
+ align:start position:0%
+shuttle you avoid complex one because
+ 
+
+ align:start position:0%
+shuttle you avoid complex one because
+you give those electrons directly
+
+ align:start position:0%
+you give those electrons directly
+ 
+
+ align:start position:0%
+you give those electrons directly
+to the glycerol phosphate shuttle an
+
+ align:start position:0%
+to the glycerol phosphate shuttle an
+ 
+
+ align:start position:0%
+to the glycerol phosphate shuttle an
+fadfh2 enzyme
+
+ align:start position:0%
+fadfh2 enzyme
+ 
+
+ align:start position:0%
+fadfh2 enzyme
+those end up in the q pool less protons
+
+ align:start position:0%
+those end up in the q pool less protons
+ 
+
+ align:start position:0%
+those end up in the q pool less protons
+are pumped
+
+ align:start position:0%
+are pumped
+ 
+
+ align:start position:0%
+are pumped
+and this is why sometimes in textbooks
+
+ align:start position:0%
+and this is why sometimes in textbooks
+ 
+
+ align:start position:0%
+and this is why sometimes in textbooks
+you'll see that you get less atp
+
+ align:start position:0%
+you'll see that you get less atp
+ 
+
+ align:start position:0%
+you'll see that you get less atp
+per nadh produced in the cytosol than
+
+ align:start position:0%
+per nadh produced in the cytosol than
+ 
+
+ align:start position:0%
+per nadh produced in the cytosol than
+you get
+
+ align:start position:0%
+you get
+ 
+
+ align:start position:0%
+you get
+for nadh produced in the mitochondria
+
+ align:start position:0%
+for nadh produced in the mitochondria
+ 
+
+ align:start position:0%
+for nadh produced in the mitochondria
+and this helps in some of this is one of
+
+ align:start position:0%
+and this helps in some of this is one of
+ 
+
+ align:start position:0%
+and this helps in some of this is one of
+the ways that you end up with these
+
+ align:start position:0%
+the ways that you end up with these
+ 
+
+ align:start position:0%
+the ways that you end up with these
+accounting yields
+
+ align:start position:0%
+accounting yields
+ 
+
+ align:start position:0%
+accounting yields
+for glucose oxidation something we'll
+
+ align:start position:0%
+for glucose oxidation something we'll
+ 
+
+ align:start position:0%
+for glucose oxidation something we'll
+talk about
+
+ align:start position:0%
+talk about
+ 
+
+ align:start position:0%
+talk about
+in a minute but the deeper reason for
+
+ align:start position:0%
+in a minute but the deeper reason for
+ 
+
+ align:start position:0%
+in a minute but the deeper reason for
+this which i want you to appreciate
+
+ align:start position:0%
+this which i want you to appreciate
+ 
+
+ align:start position:0%
+this which i want you to appreciate
+is because fadh2
+
+ align:start position:0%
+is because fadh2
+ 
+
+ align:start position:0%
+is because fadh2
+has a higher standard reduction
+
+ align:start position:0%
+has a higher standard reduction
+ 
+
+ align:start position:0%
+has a higher standard reduction
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+so the standard reduction potential
+
+ align:start position:0%
+so the standard reduction potential
+ 
+
+ align:start position:0%
+so the standard reduction potential
+of fad fadh2
+
+ align:start position:0%
+of fad fadh2
+ 
+
+ align:start position:0%
+of fad fadh2
+is greater than it is
+
+ align:start position:0%
+is greater than it is
+ 
+
+ align:start position:0%
+is greater than it is
+for nad nadh
+
+ align:start position:0%
+for nad nadh
+ 
+
+ align:start position:0%
+for nad nadh
+in essence that means that there's less
+
+ align:start position:0%
+in essence that means that there's less
+ 
+
+ align:start position:0%
+in essence that means that there's less
+change in standard reduction potential
+
+ align:start position:0%
+change in standard reduction potential
+ 
+
+ align:start position:0%
+change in standard reduction potential
+for transferring
+
+ align:start position:0%
+for transferring
+ 
+
+ align:start position:0%
+for transferring
+fadh2 electrons to oxygen
+
+ align:start position:0%
+fadh2 electrons to oxygen
+ 
+
+ align:start position:0%
+fadh2 electrons to oxygen
+is there is for transferring nadh
+
+ align:start position:0%
+is there is for transferring nadh
+ 
+
+ align:start position:0%
+is there is for transferring nadh
+electrons to oxygen
+
+ align:start position:0%
+electrons to oxygen
+ 
+
+ align:start position:0%
+electrons to oxygen
+and so less energy released less protons
+
+ align:start position:0%
+and so less energy released less protons
+ 
+
+ align:start position:0%
+and so less energy released less protons
+pumped
+
+ align:start position:0%
+pumped
+ 
+
+ align:start position:0%
+pumped
+and so that's why you get less atp
+
+ align:start position:0%
+and so that's why you get less atp
+ 
+
+ align:start position:0%
+and so that's why you get less atp
+if you will produced going through the
+
+ align:start position:0%
+if you will produced going through the
+ 
+
+ align:start position:0%
+if you will produced going through the
+glycerol phosphate
+
+ align:start position:0%
+glycerol phosphate
+ 
+
+ align:start position:0%
+glycerol phosphate
+shuttle all right
+
+ align:start position:0%
+shuttle all right
+ 
+
+ align:start position:0%
+shuttle all right
+next i want to discuss another
+
+ align:start position:0%
+next i want to discuss another
+ 
+
+ align:start position:0%
+next i want to discuss another
+alternative
+
+ align:start position:0%
+alternative
+ 
+
+ align:start position:0%
+alternative
+shuttle to get electrons into the
+
+ align:start position:0%
+shuttle to get electrons into the
+ 
+
+ align:start position:0%
+shuttle to get electrons into the
+mitochondria and
+
+ align:start position:0%
+mitochondria and
+ 
+
+ align:start position:0%
+mitochondria and
+this involves much more what i was
+
+ align:start position:0%
+this involves much more what i was
+ 
+
+ align:start position:0%
+this involves much more what i was
+alluding to earlier and that's
+
+ align:start position:0%
+alluding to earlier and that's
+ 
+
+ align:start position:0%
+alluding to earlier and that's
+oxidation and reduction of a pair of
+
+ align:start position:0%
+oxidation and reduction of a pair of
+ 
+
+ align:start position:0%
+oxidation and reduction of a pair of
+metabolites
+
+ align:start position:0%
+metabolites
+ 
+
+ align:start position:0%
+metabolites
+that are transported across the membrane
+
+ align:start position:0%
+that are transported across the membrane
+ 
+
+ align:start position:0%
+that are transported across the membrane
+on either side of the membrane
+
+ align:start position:0%
+on either side of the membrane
+ 
+
+ align:start position:0%
+on either side of the membrane
+effectively moving
+
+ align:start position:0%
+effectively moving
+ 
+
+ align:start position:0%
+effectively moving
+electrons from one compartment
+
+ align:start position:0%
+electrons from one compartment
+ 
+
+ align:start position:0%
+electrons from one compartment
+in the cell to another now to understand
+
+ align:start position:0%
+in the cell to another now to understand
+ 
+
+ align:start position:0%
+in the cell to another now to understand
+how this shuttle works i have to
+
+ align:start position:0%
+how this shuttle works i have to
+ 
+
+ align:start position:0%
+how this shuttle works i have to
+um it was because it's a little more
+
+ align:start position:0%
+um it was because it's a little more
+ 
+
+ align:start position:0%
+um it was because it's a little more
+complicated i have to
+
+ align:start position:0%
+complicated i have to
+ 
+
+ align:start position:0%
+complicated i have to
+first describe that there's a
+
+ align:start position:0%
+first describe that there's a
+ 
+
+ align:start position:0%
+first describe that there's a
+relationship between amino
+
+ align:start position:0%
+relationship between amino
+ 
+
+ align:start position:0%
+relationship between amino
+acids and alpha keto acids and so what
+
+ align:start position:0%
+acids and alpha keto acids and so what
+ 
+
+ align:start position:0%
+acids and alpha keto acids and so what
+do i mean by that well
+
+ align:start position:0%
+do i mean by that well
+ 
+
+ align:start position:0%
+do i mean by that well
+here's a alpha keto acid
+
+ align:start position:0%
+here's a alpha keto acid
+ 
+
+ align:start position:0%
+here's a alpha keto acid
+that we've talked about a lot so this
+
+ align:start position:0%
+that we've talked about a lot so this
+ 
+
+ align:start position:0%
+that we've talked about a lot so this
+is oxaloacetate remember it's an alpha
+
+ align:start position:0%
+is oxaloacetate remember it's an alpha
+ 
+
+ align:start position:0%
+is oxaloacetate remember it's an alpha
+keto acid because
+
+ align:start position:0%
+keto acid because
+ 
+
+ align:start position:0%
+keto acid because
+this ketone is alpha to this
+
+ align:start position:0%
+this ketone is alpha to this
+ 
+
+ align:start position:0%
+this ketone is alpha to this
+carboxylic acid okay so an alpha
+
+ align:start position:0%
+carboxylic acid okay so an alpha
+ 
+
+ align:start position:0%
+carboxylic acid okay so an alpha
+keto acid turns out that alpha keto
+
+ align:start position:0%
+keto acid turns out that alpha keto
+ 
+
+ align:start position:0%
+keto acid turns out that alpha keto
+acids
+
+ align:start position:0%
+acids
+ 
+
+ align:start position:0%
+acids
+are related to amino acids
+
+ align:start position:0%
+are related to amino acids
+ 
+
+ align:start position:0%
+are related to amino acids
+in the following way and so
+
+ align:start position:0%
+in the following way and so
+ 
+
+ align:start position:0%
+in the following way and so
+if i take that alpha keto group and
+
+ align:start position:0%
+if i take that alpha keto group and
+ 
+
+ align:start position:0%
+if i take that alpha keto group and
+instead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make it an amino group this here
+
+ align:start position:0%
+make it an amino group this here
+ 
+
+ align:start position:0%
+make it an amino group this here
+is the amino acid aspartate
+
+ align:start position:0%
+is the amino acid aspartate
+ 
+
+ align:start position:0%
+is the amino acid aspartate
+now we'll discuss later in the course
+
+ align:start position:0%
+now we'll discuss later in the course
+ 
+
+ align:start position:0%
+now we'll discuss later in the course
+the chemistry that allows you to
+
+ align:start position:0%
+the chemistry that allows you to
+ 
+
+ align:start position:0%
+the chemistry that allows you to
+interconvert this alpha keto group
+
+ align:start position:0%
+interconvert this alpha keto group
+ 
+
+ align:start position:0%
+interconvert this alpha keto group
+with this amino group but that's
+
+ align:start position:0%
+with this amino group but that's
+ 
+
+ align:start position:0%
+with this amino group but that's
+effectively where your
+
+ align:start position:0%
+effectively where your
+ 
+
+ align:start position:0%
+effectively where your
+amino acids come from how your amino
+
+ align:start position:0%
+amino acids come from how your amino
+ 
+
+ align:start position:0%
+amino acids come from how your amino
+acids are related to
+
+ align:start position:0%
+acids are related to
+ 
+
+ align:start position:0%
+acids are related to
+other um aspects of carbon metabolism
+
+ align:start position:0%
+other um aspects of carbon metabolism
+ 
+
+ align:start position:0%
+other um aspects of carbon metabolism
+alpha keto acids
+
+ align:start position:0%
+alpha keto acids
+ 
+
+ align:start position:0%
+alpha keto acids
+that are generated in metabolism and so
+
+ align:start position:0%
+that are generated in metabolism and so
+ 
+
+ align:start position:0%
+that are generated in metabolism and so
+there's one example
+
+ align:start position:0%
+there's one example
+ 
+
+ align:start position:0%
+there's one example
+um oxaloacetate and aspartate
+
+ align:start position:0%
+um oxaloacetate and aspartate
+ 
+
+ align:start position:0%
+um oxaloacetate and aspartate
+an alpha keto acid an amino acid
+
+ align:start position:0%
+an alpha keto acid an amino acid
+ 
+
+ align:start position:0%
+an alpha keto acid an amino acid
+here's another one so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is alpha keto
+
+ align:start position:0%
+so this is alpha keto
+ 
+
+ align:start position:0%
+so this is alpha keto
+glutarate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on alpha keto acid and
+
+ align:start position:0%
+on alpha keto acid and
+ 
+
+ align:start position:0%
+on alpha keto acid and
+if we change that alpha keto group
+
+ align:start position:0%
+if we change that alpha keto group
+ 
+
+ align:start position:0%
+if we change that alpha keto group
+to an amino group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we get the amino acid
+
+ align:start position:0%
+now we get the amino acid
+ 
+
+ align:start position:0%
+now we get the amino acid
+glutamate okay let's remind you the
+
+ align:start position:0%
+glutamate okay let's remind you the
+ 
+
+ align:start position:0%
+glutamate okay let's remind you the
+three-letter
+
+ align:start position:0%
+three-letter
+ 
+
+ align:start position:0%
+three-letter
+abbreviation for aspartate is asp the
+
+ align:start position:0%
+abbreviation for aspartate is asp the
+ 
+
+ align:start position:0%
+abbreviation for aspartate is asp the
+one letter is d
+
+ align:start position:0%
+one letter is d
+ 
+
+ align:start position:0%
+one letter is d
+the three-letter abbreviation for
+
+ align:start position:0%
+the three-letter abbreviation for
+ 
+
+ align:start position:0%
+the three-letter abbreviation for
+glutamate
+
+ align:start position:0%
+glutamate
+ 
+
+ align:start position:0%
+glutamate
+is glu and the one letter abbreviation
+
+ align:start position:0%
+is glu and the one letter abbreviation
+ 
+
+ align:start position:0%
+is glu and the one letter abbreviation
+is e and i just remind you of that in
+
+ align:start position:0%
+is e and i just remind you of that in
+ 
+
+ align:start position:0%
+is e and i just remind you of that in
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+i use those abbreviations but
+
+ align:start position:0%
+i use those abbreviations but
+ 
+
+ align:start position:0%
+i use those abbreviations but
+effectively
+
+ align:start position:0%
+effectively
+ 
+
+ align:start position:0%
+effectively
+you can note that if you couple
+
+ align:start position:0%
+you can note that if you couple
+ 
+
+ align:start position:0%
+you can note that if you couple
+these swaps to each other that is if i
+
+ align:start position:0%
+these swaps to each other that is if i
+ 
+
+ align:start position:0%
+these swaps to each other that is if i
+take
+
+ align:start position:0%
+take
+ 
+
+ align:start position:0%
+take
+oxaloacetate and turn it into
+
+ align:start position:0%
+oxaloacetate and turn it into
+ 
+
+ align:start position:0%
+oxaloacetate and turn it into
+aspartate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+while at the same time taking glutamate
+
+ align:start position:0%
+while at the same time taking glutamate
+ 
+
+ align:start position:0%
+while at the same time taking glutamate
+and turning it into alpha ketoglutarate
+
+ align:start position:0%
+and turning it into alpha ketoglutarate
+ 
+
+ align:start position:0%
+and turning it into alpha ketoglutarate
+you can see that that is a reaction
+
+ align:start position:0%
+you can see that that is a reaction
+ 
+
+ align:start position:0%
+you can see that that is a reaction
+where all atoms are conserved that is if
+
+ align:start position:0%
+where all atoms are conserved that is if
+ 
+
+ align:start position:0%
+where all atoms are conserved that is if
+i turn this alpha keto acid
+
+ align:start position:0%
+i turn this alpha keto acid
+ 
+
+ align:start position:0%
+i turn this alpha keto acid
+i'm sorry this amino acid into this
+
+ align:start position:0%
+i'm sorry this amino acid into this
+ 
+
+ align:start position:0%
+i'm sorry this amino acid into this
+alpha-keto acid
+
+ align:start position:0%
+alpha-keto acid
+ 
+
+ align:start position:0%
+alpha-keto acid
+while at the same time turning that
+
+ align:start position:0%
+while at the same time turning that
+ 
+
+ align:start position:0%
+while at the same time turning that
+alpha-keto acid into this amino acid
+
+ align:start position:0%
+alpha-keto acid into this amino acid
+ 
+
+ align:start position:0%
+alpha-keto acid into this amino acid
+i've not gained or lost any
+
+ align:start position:0%
+i've not gained or lost any
+ 
+
+ align:start position:0%
+i've not gained or lost any
+atoms or molecules in the process
+
+ align:start position:0%
+atoms or molecules in the process
+ 
+
+ align:start position:0%
+atoms or molecules in the process
+and we will see later in the course that
+
+ align:start position:0%
+and we will see later in the course that
+ 
+
+ align:start position:0%
+and we will see later in the course that
+these types of inner conversions
+
+ align:start position:0%
+these types of inner conversions
+ 
+
+ align:start position:0%
+these types of inner conversions
+is exactly how you um run
+
+ align:start position:0%
+is exactly how you um run
+ 
+
+ align:start position:0%
+is exactly how you um run
+these um these reactions to do these
+
+ align:start position:0%
+these um these reactions to do these
+ 
+
+ align:start position:0%
+these um these reactions to do these
+inner conversions between alpha keto
+
+ align:start position:0%
+inner conversions between alpha keto
+ 
+
+ align:start position:0%
+inner conversions between alpha keto
+acids
+
+ align:start position:0%
+acids
+ 
+
+ align:start position:0%
+acids
+and amino acids okay
+
+ align:start position:0%
+and amino acids okay
+ 
+
+ align:start position:0%
+and amino acids okay
+why am i telling you this now because it
+
+ align:start position:0%
+why am i telling you this now because it
+ 
+
+ align:start position:0%
+why am i telling you this now because it
+turns out this is central to understand
+
+ align:start position:0%
+turns out this is central to understand
+ 
+
+ align:start position:0%
+turns out this is central to understand
+the other major way the other major
+
+ align:start position:0%
+the other major way the other major
+ 
+
+ align:start position:0%
+the other major way the other major
+shuttle
+
+ align:start position:0%
+shuttle
+ 
+
+ align:start position:0%
+shuttle
+which is referred to as the malate
+
+ align:start position:0%
+which is referred to as the malate
+ 
+
+ align:start position:0%
+which is referred to as the malate
+aspartate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shuttle as another way to get electrons
+
+ align:start position:0%
+shuttle as another way to get electrons
+ 
+
+ align:start position:0%
+shuttle as another way to get electrons
+on nadh from the cytosol
+
+ align:start position:0%
+on nadh from the cytosol
+ 
+
+ align:start position:0%
+on nadh from the cytosol
+into the mitochondria all right so
+
+ align:start position:0%
+into the mitochondria all right so
+ 
+
+ align:start position:0%
+into the mitochondria all right so
+how does this happen so here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's oxaloacetate this is
+
+ align:start position:0%
+here's oxaloacetate this is
+ 
+
+ align:start position:0%
+here's oxaloacetate this is
+occurring up here in the cytosol
+
+ align:start position:0%
+occurring up here in the cytosol
+ 
+
+ align:start position:0%
+occurring up here in the cytosol
+okay and if we take oxaloacetate
+
+ align:start position:0%
+okay and if we take oxaloacetate
+ 
+
+ align:start position:0%
+okay and if we take oxaloacetate
+in the cytosol and we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+utilize
+
+ align:start position:0%
+utilize
+ 
+
+ align:start position:0%
+utilize
+the malate dehydrogenase reaction
+
+ align:start position:0%
+the malate dehydrogenase reaction
+ 
+
+ align:start position:0%
+the malate dehydrogenase reaction
+that we heard about from the tca cycle
+
+ align:start position:0%
+that we heard about from the tca cycle
+ 
+
+ align:start position:0%
+that we heard about from the tca cycle
+so basically this is the reverse of the
+
+ align:start position:0%
+so basically this is the reverse of the
+ 
+
+ align:start position:0%
+so basically this is the reverse of the
+malate dehydrogenase reaction we
+
+ align:start position:0%
+malate dehydrogenase reaction we
+ 
+
+ align:start position:0%
+malate dehydrogenase reaction we
+discussed in the tca cycle
+
+ align:start position:0%
+discussed in the tca cycle
+ 
+
+ align:start position:0%
+discussed in the tca cycle
+we're going to reduce this ketone to the
+
+ align:start position:0%
+we're going to reduce this ketone to the
+ 
+
+ align:start position:0%
+we're going to reduce this ketone to the
+alcohol
+
+ align:start position:0%
+alcohol
+ 
+
+ align:start position:0%
+alcohol
+nadh is re-oxidized to nad plus
+
+ align:start position:0%
+nadh is re-oxidized to nad plus
+ 
+
+ align:start position:0%
+nadh is re-oxidized to nad plus
+that will generate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+malate and now
+
+ align:start position:0%
+malate and now
+ 
+
+ align:start position:0%
+malate and now
+we've regenerated nad plus
+
+ align:start position:0%
+we've regenerated nad plus
+ 
+
+ align:start position:0%
+we've regenerated nad plus
+in the cytosol by putting those
+
+ align:start position:0%
+in the cytosol by putting those
+ 
+
+ align:start position:0%
+in the cytosol by putting those
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+onto oxaloacetate to make malate
+
+ align:start position:0%
+onto oxaloacetate to make malate
+ 
+
+ align:start position:0%
+onto oxaloacetate to make malate
+all right now we can take
+
+ align:start position:0%
+all right now we can take
+ 
+
+ align:start position:0%
+all right now we can take
+that malate send it across
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the mitochondrial membranes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by a transporter to
+
+ align:start position:0%
+by a transporter to
+ 
+
+ align:start position:0%
+by a transporter to
+generate on the matrix side of the
+
+ align:start position:0%
+generate on the matrix side of the
+ 
+
+ align:start position:0%
+generate on the matrix side of the
+membrane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+malate
+
+ align:start position:0%
+malate
+ 
+
+ align:start position:0%
+malate
+whereas you know from the tca cycle we
+
+ align:start position:0%
+whereas you know from the tca cycle we
+ 
+
+ align:start position:0%
+whereas you know from the tca cycle we
+also have
+
+ align:start position:0%
+also have
+ 
+
+ align:start position:0%
+also have
+malate dehydrogenase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now re-oxidize that
+
+ align:start position:0%
+now re-oxidize that
+ 
+
+ align:start position:0%
+now re-oxidize that
+carbon from the alcohol to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ketone and regenerate oxaloacetate
+
+ align:start position:0%
+ketone and regenerate oxaloacetate
+ 
+
+ align:start position:0%
+ketone and regenerate oxaloacetate
+effectively by carrying out the same
+
+ align:start position:0%
+effectively by carrying out the same
+ 
+
+ align:start position:0%
+effectively by carrying out the same
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+through a redox pair on two sides of the
+
+ align:start position:0%
+through a redox pair on two sides of the
+ 
+
+ align:start position:0%
+through a redox pair on two sides of the
+membrane effectively what i've done
+
+ align:start position:0%
+membrane effectively what i've done
+ 
+
+ align:start position:0%
+membrane effectively what i've done
+is i've moved the electrons from nadh in
+
+ align:start position:0%
+is i've moved the electrons from nadh in
+ 
+
+ align:start position:0%
+is i've moved the electrons from nadh in
+the cytosol
+
+ align:start position:0%
+the cytosol
+ 
+
+ align:start position:0%
+the cytosol
+to now being nadh in the mitochondrial
+
+ align:start position:0%
+to now being nadh in the mitochondrial
+ 
+
+ align:start position:0%
+to now being nadh in the mitochondrial
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+where this can now donate the electrons
+
+ align:start position:0%
+where this can now donate the electrons
+ 
+
+ align:start position:0%
+where this can now donate the electrons
+to complex one to the q pool
+
+ align:start position:0%
+to complex one to the q pool
+ 
+
+ align:start position:0%
+to complex one to the q pool
+to complex 3 to cytochrome c to complex
+
+ align:start position:0%
+to complex 3 to cytochrome c to complex
+ 
+
+ align:start position:0%
+to complex 3 to cytochrome c to complex
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and ultimately to oxygen just like
+
+ align:start position:0%
+and ultimately to oxygen just like
+ 
+
+ align:start position:0%
+and ultimately to oxygen just like
+it would for the tca cycle
+
+ align:start position:0%
+it would for the tca cycle
+ 
+
+ align:start position:0%
+it would for the tca cycle
+all right now the simplest thing of
+
+ align:start position:0%
+all right now the simplest thing of
+ 
+
+ align:start position:0%
+all right now the simplest thing of
+course would just be to send the
+
+ align:start position:0%
+course would just be to send the
+ 
+
+ align:start position:0%
+course would just be to send the
+oxaloacetate back out
+
+ align:start position:0%
+oxaloacetate back out
+ 
+
+ align:start position:0%
+oxaloacetate back out
+to the cytosol but that's not what
+
+ align:start position:0%
+to the cytosol but that's not what
+ 
+
+ align:start position:0%
+to the cytosol but that's not what
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+instead what happens is you turn that
+
+ align:start position:0%
+instead what happens is you turn that
+ 
+
+ align:start position:0%
+instead what happens is you turn that
+oxaloacetate
+
+ align:start position:0%
+oxaloacetate
+ 
+
+ align:start position:0%
+oxaloacetate
+into aspartate this is an alpha
+
+ align:start position:0%
+into aspartate this is an alpha
+ 
+
+ align:start position:0%
+into aspartate this is an alpha
+keto acid turn it into the amino acid
+
+ align:start position:0%
+keto acid turn it into the amino acid
+ 
+
+ align:start position:0%
+keto acid turn it into the amino acid
+if you do that you basically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at the same time turn glutamate into
+
+ align:start position:0%
+at the same time turn glutamate into
+ 
+
+ align:start position:0%
+at the same time turn glutamate into
+alpha-ketoglutarate all right
+
+ align:start position:0%
+alpha-ketoglutarate all right
+ 
+
+ align:start position:0%
+alpha-ketoglutarate all right
+turns out it's that alpha-ketoglutarate
+
+ align:start position:0%
+turns out it's that alpha-ketoglutarate
+ 
+
+ align:start position:0%
+turns out it's that alpha-ketoglutarate
+that is exchanged
+
+ align:start position:0%
+that is exchanged
+ 
+
+ align:start position:0%
+that is exchanged
+when you bring malate into the cell so
+
+ align:start position:0%
+when you bring malate into the cell so
+ 
+
+ align:start position:0%
+when you bring malate into the cell so
+malate
+
+ align:start position:0%
+malate
+ 
+
+ align:start position:0%
+malate
+is exchanged for alpha-ketoglutarate
+
+ align:start position:0%
+is exchanged for alpha-ketoglutarate
+ 
+
+ align:start position:0%
+is exchanged for alpha-ketoglutarate
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at the same time you exchange
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aspartate for
+
+ align:start position:0%
+aspartate for
+ 
+
+ align:start position:0%
+aspartate for
+a glutamate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so now you can
+
+ align:start position:0%
+all right so now you can
+ 
+
+ align:start position:0%
+all right so now you can
+take that aspartate turn it back into
+
+ align:start position:0%
+take that aspartate turn it back into
+ 
+
+ align:start position:0%
+take that aspartate turn it back into
+oxaloacetate to do so
+
+ align:start position:0%
+oxaloacetate to do so
+ 
+
+ align:start position:0%
+oxaloacetate to do so
+you need to balance this so you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+return your alpha-ketoglutarate back
+
+ align:start position:0%
+return your alpha-ketoglutarate back
+ 
+
+ align:start position:0%
+return your alpha-ketoglutarate back
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+glutamate and effectively this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the malate aspartate shuttle
+
+ align:start position:0%
+the malate aspartate shuttle
+ 
+
+ align:start position:0%
+the malate aspartate shuttle
+okay so electrons
+
+ align:start position:0%
+okay so electrons
+ 
+
+ align:start position:0%
+okay so electrons
+from oxaloacetate to malate and then
+
+ align:start position:0%
+from oxaloacetate to malate and then
+ 
+
+ align:start position:0%
+from oxaloacetate to malate and then
+malate back to oxaloacetate moves the
+
+ align:start position:0%
+malate back to oxaloacetate moves the
+ 
+
+ align:start position:0%
+malate back to oxaloacetate moves the
+electrons on nadh from the cytosol
+
+ align:start position:0%
+electrons on nadh from the cytosol
+ 
+
+ align:start position:0%
+electrons on nadh from the cytosol
+into the mitochondria to get that malate
+
+ align:start position:0%
+into the mitochondria to get that malate
+ 
+
+ align:start position:0%
+into the mitochondria to get that malate
+across the membrane you exchange it for
+
+ align:start position:0%
+across the membrane you exchange it for
+ 
+
+ align:start position:0%
+across the membrane you exchange it for
+alpha-ketoglutarate
+
+ align:start position:0%
+alpha-ketoglutarate
+ 
+
+ align:start position:0%
+alpha-ketoglutarate
+and to maintain carbon balance across
+
+ align:start position:0%
+and to maintain carbon balance across
+ 
+
+ align:start position:0%
+and to maintain carbon balance across
+the whole
+
+ align:start position:0%
+the whole
+ 
+
+ align:start position:0%
+the whole
+nitrogen balance across the whole thing
+
+ align:start position:0%
+nitrogen balance across the whole thing
+ 
+
+ align:start position:0%
+nitrogen balance across the whole thing
+at the same time you also exchange
+
+ align:start position:0%
+at the same time you also exchange
+ 
+
+ align:start position:0%
+at the same time you also exchange
+an aspartate for a glutamate
+
+ align:start position:0%
+an aspartate for a glutamate
+ 
+
+ align:start position:0%
+an aspartate for a glutamate
+which allows you to um
+
+ align:start position:0%
+which allows you to um
+ 
+
+ align:start position:0%
+which allows you to um
+basically interconvert the oxaloacetate
+
+ align:start position:0%
+basically interconvert the oxaloacetate
+ 
+
+ align:start position:0%
+basically interconvert the oxaloacetate
+and the aspartate on either side of the
+
+ align:start position:0%
+and the aspartate on either side of the
+ 
+
+ align:start position:0%
+and the aspartate on either side of the
+membrane via inner converting
+
+ align:start position:0%
+membrane via inner converting
+ 
+
+ align:start position:0%
+membrane via inner converting
+glutamate and alpha-ketoglutarate so
+
+ align:start position:0%
+glutamate and alpha-ketoglutarate so
+ 
+
+ align:start position:0%
+glutamate and alpha-ketoglutarate so
+somewhat confusing systems
+
+ align:start position:0%
+somewhat confusing systems
+ 
+
+ align:start position:0%
+somewhat confusing systems
+but recognize that the net effect is
+
+ align:start position:0%
+but recognize that the net effect is
+ 
+
+ align:start position:0%
+but recognize that the net effect is
+moving nadh from one side of the
+
+ align:start position:0%
+moving nadh from one side of the
+ 
+
+ align:start position:0%
+moving nadh from one side of the
+membrane
+
+ align:start position:0%
+membrane
+ 
+
+ align:start position:0%
+membrane
+to the other and that occurs because
+
+ align:start position:0%
+to the other and that occurs because
+ 
+
+ align:start position:0%
+to the other and that occurs because
+you're interconverting
+
+ align:start position:0%
+you're interconverting
+ 
+
+ align:start position:0%
+you're interconverting
+two redox pairs in opposite directions
+
+ align:start position:0%
+two redox pairs in opposite directions
+ 
+
+ align:start position:0%
+two redox pairs in opposite directions
+in this case oxaloacetate and malate
+
+ align:start position:0%
+in this case oxaloacetate and malate
+ 
+
+ align:start position:0%
+in this case oxaloacetate and malate
+on either side of the membrane and
+
+ align:start position:0%
+on either side of the membrane and
+ 
+
+ align:start position:0%
+on either side of the membrane and
+that's why
+
+ align:start position:0%
+that's why
+ 
+
+ align:start position:0%
+that's why
+what i alluded to earlier you can
+
+ align:start position:0%
+what i alluded to earlier you can
+ 
+
+ align:start position:0%
+what i alluded to earlier you can
+imagine
+
+ align:start position:0%
+imagine
+ 
+
+ align:start position:0%
+imagine
+that you could easily come up with other
+
+ align:start position:0%
+that you could easily come up with other
+ 
+
+ align:start position:0%
+that you could easily come up with other
+shuttle systems
+
+ align:start position:0%
+shuttle systems
+ 
+
+ align:start position:0%
+shuttle systems
+where you have a redox reaction on one
+
+ align:start position:0%
+where you have a redox reaction on one
+ 
+
+ align:start position:0%
+where you have a redox reaction on one
+side of the membrane
+
+ align:start position:0%
+side of the membrane
+ 
+
+ align:start position:0%
+side of the membrane
+and the reverse of that redox reaction
+
+ align:start position:0%
+and the reverse of that redox reaction
+ 
+
+ align:start position:0%
+and the reverse of that redox reaction
+on the other side of the membrane
+
+ align:start position:0%
+on the other side of the membrane
+ 
+
+ align:start position:0%
+on the other side of the membrane
+and as long as you can maintain carbon
+
+ align:start position:0%
+and as long as you can maintain carbon
+ 
+
+ align:start position:0%
+and as long as you can maintain carbon
+balance the net effect is
+
+ align:start position:0%
+balance the net effect is
+ 
+
+ align:start position:0%
+balance the net effect is
+moving electrons across the membranes
+
+ align:start position:0%
+moving electrons across the membranes
+ 
+
+ align:start position:0%
+moving electrons across the membranes
+from one compartment
+
+ align:start position:0%
+from one compartment
+ 
+
+ align:start position:0%
+from one compartment
+to another and that is a way to allow
+
+ align:start position:0%
+to another and that is a way to allow
+ 
+
+ align:start position:0%
+to another and that is a way to allow
+you to
+
+ align:start position:0%
+you to
+ 
+
+ align:start position:0%
+you to
+generate an adh that's now in the matrix
+
+ align:start position:0%
+generate an adh that's now in the matrix
+ 
+
+ align:start position:0%
+generate an adh that's now in the matrix
+which has access
+
+ align:start position:0%
+which has access
+ 
+
+ align:start position:0%
+which has access
+to complex one of the electron transport
+
+ align:start position:0%
+to complex one of the electron transport
+ 
+
+ align:start position:0%
+to complex one of the electron transport
+chain
+
+ align:start position:0%
+chain
+ 
+
+ align:start position:0%
+chain
+as we discussed now
+
+ align:start position:0%
+as we discussed now
+ 
+
+ align:start position:0%
+as we discussed now
+several times all right now we're ready
+
+ align:start position:0%
+several times all right now we're ready
+ 
+
+ align:start position:0%
+several times all right now we're ready
+to go through and discuss the
+
+ align:start position:0%
+to go through and discuss the
+ 
+
+ align:start position:0%
+to go through and discuss the
+accounting that you
+
+ align:start position:0%
+accounting that you
+ 
+
+ align:start position:0%
+accounting that you
+see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the accounting that comes up all the
+
+ align:start position:0%
+the accounting that comes up all the
+ 
+
+ align:start position:0%
+the accounting that comes up all the
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+that is in textbooks and perhaps you
+
+ align:start position:0%
+that is in textbooks and perhaps you
+ 
+
+ align:start position:0%
+that is in textbooks and perhaps you
+memorized from previous classes
+
+ align:start position:0%
+memorized from previous classes
+ 
+
+ align:start position:0%
+memorized from previous classes
+about how the atp yield works for
+
+ align:start position:0%
+about how the atp yield works for
+ 
+
+ align:start position:0%
+about how the atp yield works for
+different pathways so hopefully it's
+
+ align:start position:0%
+different pathways so hopefully it's
+ 
+
+ align:start position:0%
+different pathways so hopefully it's
+clear to you by now that these numbers
+
+ align:start position:0%
+clear to you by now that these numbers
+ 
+
+ align:start position:0%
+clear to you by now that these numbers
+that you get
+
+ align:start position:0%
+that you get
+ 
+
+ align:start position:0%
+that you get
+are estimates and that's because there
+
+ align:start position:0%
+are estimates and that's because there
+ 
+
+ align:start position:0%
+are estimates and that's because there
+is no direct relationship
+
+ align:start position:0%
+is no direct relationship
+ 
+
+ align:start position:0%
+is no direct relationship
+between nadh or fadh2
+
+ align:start position:0%
+between nadh or fadh2
+ 
+
+ align:start position:0%
+between nadh or fadh2
+and atp these interconversions occur via
+
+ align:start position:0%
+and atp these interconversions occur via
+ 
+
+ align:start position:0%
+and atp these interconversions occur via
+oxidative phosphorylation these electron
+
+ align:start position:0%
+oxidative phosphorylation these electron
+ 
+
+ align:start position:0%
+oxidative phosphorylation these electron
+transport chain delta psi delta ph
+
+ align:start position:0%
+transport chain delta psi delta ph
+ 
+
+ align:start position:0%
+transport chain delta psi delta ph
+and so all of these estimates take into
+
+ align:start position:0%
+and so all of these estimates take into
+ 
+
+ align:start position:0%
+and so all of these estimates take into
+account
+
+ align:start position:0%
+account
+ 
+
+ align:start position:0%
+account
+various assumptions about how efficient
+
+ align:start position:0%
+various assumptions about how efficient
+ 
+
+ align:start position:0%
+various assumptions about how efficient
+the electron transport chain is
+
+ align:start position:0%
+the electron transport chain is
+ 
+
+ align:start position:0%
+the electron transport chain is
+oxidative phosphorylation works
+
+ align:start position:0%
+oxidative phosphorylation works
+ 
+
+ align:start position:0%
+oxidative phosphorylation works
+bounded of course by the change in
+
+ align:start position:0%
+bounded of course by the change in
+ 
+
+ align:start position:0%
+bounded of course by the change in
+standard reduction potential
+
+ align:start position:0%
+standard reduction potential
+ 
+
+ align:start position:0%
+standard reduction potential
+how much what's the free energy released
+
+ align:start position:0%
+how much what's the free energy released
+ 
+
+ align:start position:0%
+how much what's the free energy released
+from that
+
+ align:start position:0%
+from that
+ 
+
+ align:start position:0%
+from that
+what's the free energy to synthesize adp
+
+ align:start position:0%
+what's the free energy to synthesize adp
+ 
+
+ align:start position:0%
+what's the free energy to synthesize adp
+to atp of course that those require
+
+ align:start position:0%
+to atp of course that those require
+ 
+
+ align:start position:0%
+to atp of course that those require
+assumptions
+
+ align:start position:0%
+assumptions
+ 
+
+ align:start position:0%
+assumptions
+and it's in the end why if you read
+
+ align:start position:0%
+and it's in the end why if you read
+ 
+
+ align:start position:0%
+and it's in the end why if you read
+different textbooks and different
+
+ align:start position:0%
+different textbooks and different
+ 
+
+ align:start position:0%
+different textbooks and different
+sources
+
+ align:start position:0%
+sources
+ 
+
+ align:start position:0%
+sources
+you will find numbers that are actually
+
+ align:start position:0%
+you will find numbers that are actually
+ 
+
+ align:start position:0%
+you will find numbers that are actually
+a range there is no
+
+ align:start position:0%
+a range there is no
+ 
+
+ align:start position:0%
+a range there is no
+fixed number for what the equivalent is
+
+ align:start position:0%
+fixed number for what the equivalent is
+ 
+
+ align:start position:0%
+fixed number for what the equivalent is
+of an atp for an nadh
+
+ align:start position:0%
+of an atp for an nadh
+ 
+
+ align:start position:0%
+of an atp for an nadh
+and that's because it really depends on
+
+ align:start position:0%
+and that's because it really depends on
+ 
+
+ align:start position:0%
+and that's because it really depends on
+several variables so
+
+ align:start position:0%
+several variables so
+ 
+
+ align:start position:0%
+several variables so
+let's go through what those variables
+
+ align:start position:0%
+let's go through what those variables
+ 
+
+ align:start position:0%
+let's go through what those variables
+are because if we can understand that
+
+ align:start position:0%
+are because if we can understand that
+ 
+
+ align:start position:0%
+are because if we can understand that
+you really understand how this system
+
+ align:start position:0%
+you really understand how this system
+ 
+
+ align:start position:0%
+you really understand how this system
+works so the first variable
+
+ align:start position:0%
+works so the first variable
+ 
+
+ align:start position:0%
+works so the first variable
+at least if we're talking about
+
+ align:start position:0%
+at least if we're talking about
+ 
+
+ align:start position:0%
+at least if we're talking about
+something like glucose where
+
+ align:start position:0%
+something like glucose where
+ 
+
+ align:start position:0%
+something like glucose where
+we generate nadh in the cytosol
+
+ align:start position:0%
+we generate nadh in the cytosol
+ 
+
+ align:start position:0%
+we generate nadh in the cytosol
+we have to consider the redox
+
+ align:start position:0%
+we have to consider the redox
+ 
+
+ align:start position:0%
+we have to consider the redox
+shuttles and hopefully you appreciate
+
+ align:start position:0%
+shuttles and hopefully you appreciate
+ 
+
+ align:start position:0%
+shuttles and hopefully you appreciate
+now that you have this need to
+
+ align:start position:0%
+now that you have this need to
+ 
+
+ align:start position:0%
+now that you have this need to
+regenerate nad and the cytosol to keep
+
+ align:start position:0%
+regenerate nad and the cytosol to keep
+ 
+
+ align:start position:0%
+regenerate nad and the cytosol to keep
+glycolysis going
+
+ align:start position:0%
+glycolysis going
+ 
+
+ align:start position:0%
+glycolysis going
+you got to get those electrons somehow
+
+ align:start position:0%
+you got to get those electrons somehow
+ 
+
+ align:start position:0%
+you got to get those electrons somehow
+to the electron transport chain
+
+ align:start position:0%
+to the electron transport chain
+ 
+
+ align:start position:0%
+to the electron transport chain
+and i just described for you two
+
+ align:start position:0%
+and i just described for you two
+ 
+
+ align:start position:0%
+and i just described for you two
+different ways you can do that
+
+ align:start position:0%
+different ways you can do that
+ 
+
+ align:start position:0%
+different ways you can do that
+now if i use the glycerol phosphate
+
+ align:start position:0%
+now if i use the glycerol phosphate
+ 
+
+ align:start position:0%
+now if i use the glycerol phosphate
+shuttle i'm skipping complex one
+
+ align:start position:0%
+shuttle i'm skipping complex one
+ 
+
+ align:start position:0%
+shuttle i'm skipping complex one
+altogether
+
+ align:start position:0%
+altogether
+ 
+
+ align:start position:0%
+altogether
+and so that's not pumping any protons if
+
+ align:start position:0%
+and so that's not pumping any protons if
+ 
+
+ align:start position:0%
+and so that's not pumping any protons if
+i'm using the mallite aspartate shuttle
+
+ align:start position:0%
+i'm using the mallite aspartate shuttle
+ 
+
+ align:start position:0%
+i'm using the mallite aspartate shuttle
+well i have all the energetics of doing
+
+ align:start position:0%
+well i have all the energetics of doing
+ 
+
+ align:start position:0%
+well i have all the energetics of doing
+this gymnastics but in the end now i can
+
+ align:start position:0%
+this gymnastics but in the end now i can
+ 
+
+ align:start position:0%
+this gymnastics but in the end now i can
+use complex one and pump protons and so
+
+ align:start position:0%
+use complex one and pump protons and so
+ 
+
+ align:start position:0%
+use complex one and pump protons and so
+the yield of atp if you will how many
+
+ align:start position:0%
+the yield of atp if you will how many
+ 
+
+ align:start position:0%
+the yield of atp if you will how many
+protons i can pump
+
+ align:start position:0%
+protons i can pump
+ 
+
+ align:start position:0%
+protons i can pump
+to generate delta psi delta ph will be
+
+ align:start position:0%
+to generate delta psi delta ph will be
+ 
+
+ align:start position:0%
+to generate delta psi delta ph will be
+different if i use the glycerol
+
+ align:start position:0%
+different if i use the glycerol
+ 
+
+ align:start position:0%
+different if i use the glycerol
+phosphate shuttle
+
+ align:start position:0%
+phosphate shuttle
+ 
+
+ align:start position:0%
+phosphate shuttle
+or a shuttle like the malate aspartate
+
+ align:start position:0%
+or a shuttle like the malate aspartate
+ 
+
+ align:start position:0%
+or a shuttle like the malate aspartate
+shuttle
+
+ align:start position:0%
+shuttle
+ 
+
+ align:start position:0%
+shuttle
+the second variable in consideration
+
+ align:start position:0%
+the second variable in consideration
+ 
+
+ align:start position:0%
+the second variable in consideration
+is what is the efficiency
+
+ align:start position:0%
+is what is the efficiency
+ 
+
+ align:start position:0%
+is what is the efficiency
+of proton pumping
+
+ align:start position:0%
+of proton pumping
+ 
+
+ align:start position:0%
+of proton pumping
+by the various electron transport chain
+
+ align:start position:0%
+by the various electron transport chain
+ 
+
+ align:start position:0%
+by the various electron transport chain
+etc complexes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's not so straightforward and of
+
+ align:start position:0%
+that's not so straightforward and of
+ 
+
+ align:start position:0%
+that's not so straightforward and of
+course is going to depend
+
+ align:start position:0%
+course is going to depend
+ 
+
+ align:start position:0%
+course is going to depend
+on a couple things remember we spent a
+
+ align:start position:0%
+on a couple things remember we spent a
+ 
+
+ align:start position:0%
+on a couple things remember we spent a
+long time talking about
+
+ align:start position:0%
+long time talking about
+ 
+
+ align:start position:0%
+long time talking about
+atp adp and how it's the ratio of atp
+
+ align:start position:0%
+atp adp and how it's the ratio of atp
+ 
+
+ align:start position:0%
+atp adp and how it's the ratio of atp
+adp
+
+ align:start position:0%
+adp
+ 
+
+ align:start position:0%
+adp
+that was really the energy there because
+
+ align:start position:0%
+that was really the energy there because
+ 
+
+ align:start position:0%
+that was really the energy there because
+remember thermodynamics is dependent on
+
+ align:start position:0%
+remember thermodynamics is dependent on
+ 
+
+ align:start position:0%
+remember thermodynamics is dependent on
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+you know log of the reactants over the
+
+ align:start position:0%
+you know log of the reactants over the
+ 
+
+ align:start position:0%
+you know log of the reactants over the
+products term
+
+ align:start position:0%
+products term
+ 
+
+ align:start position:0%
+products term
+um in the delta g equation well the
+
+ align:start position:0%
+um in the delta g equation well the
+ 
+
+ align:start position:0%
+um in the delta g equation well the
+any that's true also for the nadnadh
+
+ align:start position:0%
+any that's true also for the nadnadh
+ 
+
+ align:start position:0%
+any that's true also for the nadnadh
+ratio
+
+ align:start position:0%
+ratio
+ 
+
+ align:start position:0%
+ratio
+and it's also true for how high the
+
+ align:start position:0%
+and it's also true for how high the
+ 
+
+ align:start position:0%
+and it's also true for how high the
+membrane potential is
+
+ align:start position:0%
+membrane potential is
+ 
+
+ align:start position:0%
+membrane potential is
+and so how efficient this pumping is
+
+ align:start position:0%
+and so how efficient this pumping is
+ 
+
+ align:start position:0%
+and so how efficient this pumping is
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+is going to be depending on what is the
+
+ align:start position:0%
+is going to be depending on what is the
+ 
+
+ align:start position:0%
+is going to be depending on what is the
+delta side to begin with and what is the
+
+ align:start position:0%
+delta side to begin with and what is the
+ 
+
+ align:start position:0%
+delta side to begin with and what is the
+nadnadh ratio or the fad h2 fad ratio
+
+ align:start position:0%
+nadnadh ratio or the fad h2 fad ratio
+ 
+
+ align:start position:0%
+nadnadh ratio or the fad h2 fad ratio
+because all of those things will affect
+
+ align:start position:0%
+because all of those things will affect
+ 
+
+ align:start position:0%
+because all of those things will affect
+how much free energy there is to be able
+
+ align:start position:0%
+how much free energy there is to be able
+ 
+
+ align:start position:0%
+how much free energy there is to be able
+to move protons from one side
+
+ align:start position:0%
+to move protons from one side
+ 
+
+ align:start position:0%
+to move protons from one side
+of the membrane to the other
+
+ align:start position:0%
+of the membrane to the other
+ 
+
+ align:start position:0%
+of the membrane to the other
+once i get those protons across the
+
+ align:start position:0%
+once i get those protons across the
+ 
+
+ align:start position:0%
+once i get those protons across the
+membrane then there's a question
+
+ align:start position:0%
+membrane then there's a question
+ 
+
+ align:start position:0%
+membrane then there's a question
+of how and for lack of a better word i'm
+
+ align:start position:0%
+of how and for lack of a better word i'm
+ 
+
+ align:start position:0%
+of how and for lack of a better word i'm
+going to say
+
+ align:start position:0%
+going to say
+ 
+
+ align:start position:0%
+going to say
+tight the membrane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is to proton
+
+ align:start position:0%
+is to proton
+ 
+
+ align:start position:0%
+is to proton
+leak that is you can imagine that
+
+ align:start position:0%
+leak that is you can imagine that
+ 
+
+ align:start position:0%
+leak that is you can imagine that
+to make atp i have to send those protons
+
+ align:start position:0%
+to make atp i have to send those protons
+ 
+
+ align:start position:0%
+to make atp i have to send those protons
+back through the atp synthase complex 5
+
+ align:start position:0%
+back through the atp synthase complex 5
+ 
+
+ align:start position:0%
+back through the atp synthase complex 5
+f1 f080p whatever you want to call it
+
+ align:start position:0%
+f1 f080p whatever you want to call it
+ 
+
+ align:start position:0%
+f1 f080p whatever you want to call it
+and if some of those protons just leak
+
+ align:start position:0%
+and if some of those protons just leak
+ 
+
+ align:start position:0%
+and if some of those protons just leak
+back across the membrane
+
+ align:start position:0%
+back across the membrane
+ 
+
+ align:start position:0%
+back across the membrane
+well that's how we generate heat and so
+
+ align:start position:0%
+well that's how we generate heat and so
+ 
+
+ align:start position:0%
+well that's how we generate heat and so
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+tight that membrane is that is how
+
+ align:start position:0%
+tight that membrane is that is how
+ 
+
+ align:start position:0%
+tight that membrane is that is how
+coupled respiration
+
+ align:start position:0%
+coupled respiration
+ 
+
+ align:start position:0%
+coupled respiration
+is to uh how
+
+ align:start position:0%
+is to uh how
+ 
+
+ align:start position:0%
+is to uh how
+coupled delta psi size delta ph's to to
+
+ align:start position:0%
+coupled delta psi size delta ph's to to
+ 
+
+ align:start position:0%
+coupled delta psi size delta ph's to to
+um atp synthesis is another variable
+
+ align:start position:0%
+um atp synthesis is another variable
+ 
+
+ align:start position:0%
+um atp synthesis is another variable
+and of course the last one is is the
+
+ align:start position:0%
+and of course the last one is is the
+ 
+
+ align:start position:0%
+and of course the last one is is the
+efficiency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of h plus
+
+ align:start position:0%
+of h plus
+ 
+
+ align:start position:0%
+of h plus
+turning the f zero f1 atp ace
+
+ align:start position:0%
+turning the f zero f1 atp ace
+ 
+
+ align:start position:0%
+turning the f zero f1 atp ace
+which is the same considerations we
+
+ align:start position:0%
+which is the same considerations we
+ 
+
+ align:start position:0%
+which is the same considerations we
+already talked about for number two that
+
+ align:start position:0%
+already talked about for number two that
+ 
+
+ align:start position:0%
+already talked about for number two that
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the higher delta side delta ph the more
+
+ align:start position:0%
+the higher delta side delta ph the more
+ 
+
+ align:start position:0%
+the higher delta side delta ph the more
+free energy that's stored there
+
+ align:start position:0%
+free energy that's stored there
+ 
+
+ align:start position:0%
+free energy that's stored there
+and the higher lower the atp adp ratio
+
+ align:start position:0%
+and the higher lower the atp adp ratio
+ 
+
+ align:start position:0%
+and the higher lower the atp adp ratio
+is the easier
+
+ align:start position:0%
+is the easier
+ 
+
+ align:start position:0%
+is the easier
+harder it is to synthesize
+
+ align:start position:0%
+harder it is to synthesize
+ 
+
+ align:start position:0%
+harder it is to synthesize
+adp and so basically
+
+ align:start position:0%
+adp and so basically
+ 
+
+ align:start position:0%
+adp and so basically
+these different things two through four
+
+ align:start position:0%
+these different things two through four
+ 
+
+ align:start position:0%
+these different things two through four
+in general is takes into account a term
+
+ align:start position:0%
+in general is takes into account a term
+ 
+
+ align:start position:0%
+in general is takes into account a term
+called coupled respiration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by coupled respiration is really how
+
+ align:start position:0%
+by coupled respiration is really how
+ 
+
+ align:start position:0%
+by coupled respiration is really how
+tightly
+
+ align:start position:0%
+tightly
+ 
+
+ align:start position:0%
+tightly
+is oxidation moving electrons on the
+
+ align:start position:0%
+is oxidation moving electrons on the
+ 
+
+ align:start position:0%
+is oxidation moving electrons on the
+electron transport chain to oxygen
+
+ align:start position:0%
+electron transport chain to oxygen
+ 
+
+ align:start position:0%
+electron transport chain to oxygen
+to phosphorylation synthesizing atp from
+
+ align:start position:0%
+to phosphorylation synthesizing atp from
+ 
+
+ align:start position:0%
+to phosphorylation synthesizing atp from
+adp
+
+ align:start position:0%
+adp
+ 
+
+ align:start position:0%
+adp
+and so how tight or how well coupled
+
+ align:start position:0%
+and so how tight or how well coupled
+ 
+
+ align:start position:0%
+and so how tight or how well coupled
+is respiration to phosphorylation
+
+ align:start position:0%
+is respiration to phosphorylation
+ 
+
+ align:start position:0%
+is respiration to phosphorylation
+really is a variable that is going to
+
+ align:start position:0%
+really is a variable that is going to
+ 
+
+ align:start position:0%
+really is a variable that is going to
+very much
+
+ align:start position:0%
+very much
+ 
+
+ align:start position:0%
+very much
+depend on conditions and so
+
+ align:start position:0%
+depend on conditions and so
+ 
+
+ align:start position:0%
+depend on conditions and so
+ultimately to give numbers for what
+
+ align:start position:0%
+ultimately to give numbers for what
+ 
+
+ align:start position:0%
+ultimately to give numbers for what
+is the atp produced from various
+
+ align:start position:0%
+is the atp produced from various
+ 
+
+ align:start position:0%
+is the atp produced from various
+oxidation processes
+
+ align:start position:0%
+oxidation processes
+ 
+
+ align:start position:0%
+oxidation processes
+one has to make assumptions about all of
+
+ align:start position:0%
+one has to make assumptions about all of
+ 
+
+ align:start position:0%
+one has to make assumptions about all of
+these things how coupled respiration is
+
+ align:start position:0%
+these things how coupled respiration is
+ 
+
+ align:start position:0%
+these things how coupled respiration is
+in which redox shuttles are used if it's
+
+ align:start position:0%
+in which redox shuttles are used if it's
+ 
+
+ align:start position:0%
+in which redox shuttles are used if it's
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+like glycolysis that involves the the
+
+ align:start position:0%
+like glycolysis that involves the the
+ 
+
+ align:start position:0%
+like glycolysis that involves the the
+cytosol
+
+ align:start position:0%
+cytosol
+ 
+
+ align:start position:0%
+cytosol
+and this is why these numbers are made
+
+ align:start position:0%
+and this is why these numbers are made
+ 
+
+ align:start position:0%
+and this is why these numbers are made
+up and it's makes no sense in my view
+
+ align:start position:0%
+up and it's makes no sense in my view
+ 
+
+ align:start position:0%
+up and it's makes no sense in my view
+to memorize these numbers but i think it
+
+ align:start position:0%
+to memorize these numbers but i think it
+ 
+
+ align:start position:0%
+to memorize these numbers but i think it
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+important to understand where those
+
+ align:start position:0%
+important to understand where those
+ 
+
+ align:start position:0%
+important to understand where those
+numbers come from
+
+ align:start position:0%
+numbers come from
+ 
+
+ align:start position:0%
+numbers come from
+because if you understand that that
+
+ align:start position:0%
+because if you understand that that
+ 
+
+ align:start position:0%
+because if you understand that that
+means you understand all the assumptions
+
+ align:start position:0%
+means you understand all the assumptions
+ 
+
+ align:start position:0%
+means you understand all the assumptions
+and why the numbers are variable you
+
+ align:start position:0%
+and why the numbers are variable you
+ 
+
+ align:start position:0%
+and why the numbers are variable you
+really understand
+
+ align:start position:0%
+really understand
+ 
+
+ align:start position:0%
+really understand
+the bioenergetics of what's going on in
+
+ align:start position:0%
+the bioenergetics of what's going on in
+ 
+
+ align:start position:0%
+the bioenergetics of what's going on in
+metabolism
+
+ align:start position:0%
+metabolism
+ 
+
+ align:start position:0%
+metabolism
+all right so now let's go through one of
+
+ align:start position:0%
+all right so now let's go through one of
+ 
+
+ align:start position:0%
+all right so now let's go through one of
+these calculations
+
+ align:start position:0%
+these calculations
+ 
+
+ align:start position:0%
+these calculations
+just to fully illustrate what i'm
+
+ align:start position:0%
+just to fully illustrate what i'm
+ 
+
+ align:start position:0%
+just to fully illustrate what i'm
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+so let's go through the calculation for
+
+ align:start position:0%
+so let's go through the calculation for
+ 
+
+ align:start position:0%
+so let's go through the calculation for
+glycolysis so if i
+
+ align:start position:0%
+glycolysis so if i
+ 
+
+ align:start position:0%
+glycolysis so if i
+run glycolysis and turn glucose into
+
+ align:start position:0%
+run glycolysis and turn glucose into
+ 
+
+ align:start position:0%
+run glycolysis and turn glucose into
+two pyruvate so
+
+ align:start position:0%
+two pyruvate so
+ 
+
+ align:start position:0%
+two pyruvate so
+what do we get from that of course we
+
+ align:start position:0%
+what do we get from that of course we
+ 
+
+ align:start position:0%
+what do we get from that of course we
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+two atps produced and we get
+
+ align:start position:0%
+two atps produced and we get
+ 
+
+ align:start position:0%
+two atps produced and we get
+two nadh is produced
+
+ align:start position:0%
+two nadh is produced
+ 
+
+ align:start position:0%
+two nadh is produced
+in the cytosol okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the cytosol
+
+ align:start position:0%
+so this is the cytosol
+ 
+
+ align:start position:0%
+so this is the cytosol
+this is the mitochondria all right we're
+
+ align:start position:0%
+this is the mitochondria all right we're
+ 
+
+ align:start position:0%
+this is the mitochondria all right we're
+going to completely oxidize that
+
+ align:start position:0%
+going to completely oxidize that
+ 
+
+ align:start position:0%
+going to completely oxidize that
+pyruvate
+
+ align:start position:0%
+pyruvate
+ 
+
+ align:start position:0%
+pyruvate
+we send that pyruvate into the
+
+ align:start position:0%
+we send that pyruvate into the
+ 
+
+ align:start position:0%
+we send that pyruvate into the
+mitochondria
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we run the pdh reaction that gives us
+
+ align:start position:0%
+we run the pdh reaction that gives us
+ 
+
+ align:start position:0%
+we run the pdh reaction that gives us
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+acetyl coa which is a yield of
+
+ align:start position:0%
+acetyl coa which is a yield of
+ 
+
+ align:start position:0%
+acetyl coa which is a yield of
+two more nadhs
+
+ align:start position:0%
+two more nadhs
+ 
+
+ align:start position:0%
+two more nadhs
+all right if we now take those acetyl
+
+ align:start position:0%
+all right if we now take those acetyl
+ 
+
+ align:start position:0%
+all right if we now take those acetyl
+coas
+
+ align:start position:0%
+coas
+ 
+
+ align:start position:0%
+coas
+and we burn them completely two cycles
+
+ align:start position:0%
+and we burn them completely two cycles
+ 
+
+ align:start position:0%
+and we burn them completely two cycles
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+the tca cycle okay now we get
+
+ align:start position:0%
+the tca cycle okay now we get
+ 
+
+ align:start position:0%
+the tca cycle okay now we get
+two more fadh2s
+
+ align:start position:0%
+two more fadh2s
+ 
+
+ align:start position:0%
+two more fadh2s
+and six
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nadhs one fadh2 three nadhs from each
+
+ align:start position:0%
+nadhs one fadh2 three nadhs from each
+ 
+
+ align:start position:0%
+nadhs one fadh2 three nadhs from each
+turn
+
+ align:start position:0%
+turn
+ 
+
+ align:start position:0%
+turn
+as well as a gtp and so that's a total
+
+ align:start position:0%
+as well as a gtp and so that's a total
+ 
+
+ align:start position:0%
+as well as a gtp and so that's a total
+of two fadh2s six nadhs
+
+ align:start position:0%
+of two fadh2s six nadhs
+ 
+
+ align:start position:0%
+of two fadh2s six nadhs
+and two gtps and so
+
+ align:start position:0%
+and two gtps and so
+ 
+
+ align:start position:0%
+and two gtps and so
+now if i come together what is our yield
+
+ align:start position:0%
+now if i come together what is our yield
+ 
+
+ align:start position:0%
+now if i come together what is our yield
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+from the mitochondria i've generated a
+
+ align:start position:0%
+from the mitochondria i've generated a
+ 
+
+ align:start position:0%
+from the mitochondria i've generated a
+total of
+
+ align:start position:0%
+total of
+ 
+
+ align:start position:0%
+total of
+two fadh2s and
+
+ align:start position:0%
+two fadh2s and
+ 
+
+ align:start position:0%
+two fadh2s and
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+nadhs and then up here
+
+ align:start position:0%
+nadhs and then up here
+ 
+
+ align:start position:0%
+nadhs and then up here
+there's an additional two nadhs
+
+ align:start position:0%
+there's an additional two nadhs
+ 
+
+ align:start position:0%
+there's an additional two nadhs
+that are made in the cytosol and so have
+
+ align:start position:0%
+that are made in the cytosol and so have
+ 
+
+ align:start position:0%
+that are made in the cytosol and so have
+to access the electron transport chain
+
+ align:start position:0%
+to access the electron transport chain
+ 
+
+ align:start position:0%
+to access the electron transport chain
+via a shuttle a typical number that's
+
+ align:start position:0%
+via a shuttle a typical number that's
+ 
+
+ align:start position:0%
+via a shuttle a typical number that's
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+is you get 1.5 atp
+
+ align:start position:0%
+is you get 1.5 atp
+ 
+
+ align:start position:0%
+is you get 1.5 atp
+for something that has to access via a
+
+ align:start position:0%
+for something that has to access via a
+ 
+
+ align:start position:0%
+for something that has to access via a
+shuttle
+
+ align:start position:0%
+shuttle
+ 
+
+ align:start position:0%
+shuttle
+or an fadh2
+
+ align:start position:0%
+or an fadh2
+ 
+
+ align:start position:0%
+or an fadh2
+that would make sense because fadh2 is
+
+ align:start position:0%
+that would make sense because fadh2 is
+ 
+
+ align:start position:0%
+that would make sense because fadh2 is
+really the same as a glycerol phosphate
+
+ align:start position:0%
+really the same as a glycerol phosphate
+ 
+
+ align:start position:0%
+really the same as a glycerol phosphate
+shuttle
+
+ align:start position:0%
+shuttle
+ 
+
+ align:start position:0%
+shuttle
+and so if i do that that would be 3 atp
+
+ align:start position:0%
+and so if i do that that would be 3 atp
+ 
+
+ align:start position:0%
+and so if i do that that would be 3 atp
+from the two glycolysis nadhs
+
+ align:start position:0%
+from the two glycolysis nadhs
+ 
+
+ align:start position:0%
+from the two glycolysis nadhs
+and three atp
+
+ align:start position:0%
+and three atp
+ 
+
+ align:start position:0%
+and three atp
+from the two tca cycle fadh2s
+
+ align:start position:0%
+from the two tca cycle fadh2s
+ 
+
+ align:start position:0%
+from the two tca cycle fadh2s
+because the nadh is produced in the
+
+ align:start position:0%
+because the nadh is produced in the
+ 
+
+ align:start position:0%
+because the nadh is produced in the
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+can generate pump protons by a complex
+
+ align:start position:0%
+can generate pump protons by a complex
+ 
+
+ align:start position:0%
+can generate pump protons by a complex
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+oftentimes that's said to be oh that's
+
+ align:start position:0%
+oftentimes that's said to be oh that's
+ 
+
+ align:start position:0%
+oftentimes that's said to be oh that's
+about two and a half atp
+
+ align:start position:0%
+about two and a half atp
+ 
+
+ align:start position:0%
+about two and a half atp
+so eight times two and a half is 20 atp
+
+ align:start position:0%
+so eight times two and a half is 20 atp
+ 
+
+ align:start position:0%
+so eight times two and a half is 20 atp
+and if we add all these numbers together
+
+ align:start position:0%
+and if we add all these numbers together
+ 
+
+ align:start position:0%
+and if we add all these numbers together
+20 plus 3
+
+ align:start position:0%
+20 plus 3
+ 
+
+ align:start position:0%
+20 plus 3
+plus 3 plus 2 plus 2
+
+ align:start position:0%
+plus 3 plus 2 plus 2
+ 
+
+ align:start position:0%
+plus 3 plus 2 plus 2
+that is a total of 30
+
+ align:start position:0%
+that is a total of 30
+ 
+
+ align:start position:0%
+that is a total of 30
+atp per
+
+ align:start position:0%
+atp per
+ 
+
+ align:start position:0%
+atp per
+glucose that's completely oxidized to
+
+ align:start position:0%
+glucose that's completely oxidized to
+ 
+
+ align:start position:0%
+glucose that's completely oxidized to
+co2 okay so 26 atp
+
+ align:start position:0%
+co2 okay so 26 atp
+ 
+
+ align:start position:0%
+co2 okay so 26 atp
+over here plus another
+
+ align:start position:0%
+over here plus another
+ 
+
+ align:start position:0%
+over here plus another
+two from gtp plus another two from
+
+ align:start position:0%
+two from gtp plus another two from
+ 
+
+ align:start position:0%
+two from gtp plus another two from
+glycolysis is a total of
+
+ align:start position:0%
+glycolysis is a total of
+ 
+
+ align:start position:0%
+glycolysis is a total of
+30 atp per glucose that is a number
+
+ align:start position:0%
+30 atp per glucose that is a number
+ 
+
+ align:start position:0%
+30 atp per glucose that is a number
+it made certain assumptions obviously if
+
+ align:start position:0%
+it made certain assumptions obviously if
+ 
+
+ align:start position:0%
+it made certain assumptions obviously if
+i assume
+
+ align:start position:0%
+i assume
+ 
+
+ align:start position:0%
+i assume
+that this is not the uh glycerol
+
+ align:start position:0%
+that this is not the uh glycerol
+ 
+
+ align:start position:0%
+that this is not the uh glycerol
+phosphate shuttle but instead the mallet
+
+ align:start position:0%
+phosphate shuttle but instead the mallet
+ 
+
+ align:start position:0%
+phosphate shuttle but instead the mallet
+aspartate
+
+ align:start position:0%
+aspartate
+ 
+
+ align:start position:0%
+aspartate
+shuttle maybe i bump this number up by
+
+ align:start position:0%
+shuttle maybe i bump this number up by
+ 
+
+ align:start position:0%
+shuttle maybe i bump this number up by
+multiplying that by two and a half maybe
+
+ align:start position:0%
+multiplying that by two and a half maybe
+ 
+
+ align:start position:0%
+multiplying that by two and a half maybe
+i use
+
+ align:start position:0%
+i use
+ 
+
+ align:start position:0%
+i use
+different conversion factors and if you
+
+ align:start position:0%
+different conversion factors and if you
+ 
+
+ align:start position:0%
+different conversion factors and if you
+read in textbooks
+
+ align:start position:0%
+read in textbooks
+ 
+
+ align:start position:0%
+read in textbooks
+you get numbers that range from 30 to 36
+
+ align:start position:0%
+you get numbers that range from 30 to 36
+ 
+
+ align:start position:0%
+you get numbers that range from 30 to 36
+i think the highest i've ever seen is 38
+
+ align:start position:0%
+i think the highest i've ever seen is 38
+ 
+
+ align:start position:0%
+i think the highest i've ever seen is 38
+atp per glucose and the fact that you
+
+ align:start position:0%
+atp per glucose and the fact that you
+ 
+
+ align:start position:0%
+atp per glucose and the fact that you
+actually see this range
+
+ align:start position:0%
+actually see this range
+ 
+
+ align:start position:0%
+actually see this range
+really reflects that different authors
+
+ align:start position:0%
+really reflects that different authors
+ 
+
+ align:start position:0%
+really reflects that different authors
+of textbooks
+
+ align:start position:0%
+of textbooks
+ 
+
+ align:start position:0%
+of textbooks
+or whoever writes these things makes
+
+ align:start position:0%
+or whoever writes these things makes
+ 
+
+ align:start position:0%
+or whoever writes these things makes
+different assumptions
+
+ align:start position:0%
+different assumptions
+ 
+
+ align:start position:0%
+different assumptions
+about all of these things over here
+
+ align:start position:0%
+about all of these things over here
+ 
+
+ align:start position:0%
+about all of these things over here
+to understand how to make these
+
+ align:start position:0%
+to understand how to make these
+ 
+
+ align:start position:0%
+to understand how to make these
+conversions but the important thing is
+
+ align:start position:0%
+conversions but the important thing is
+ 
+
+ align:start position:0%
+conversions but the important thing is
+realizing that these are not
+
+ align:start position:0%
+realizing that these are not
+ 
+
+ align:start position:0%
+realizing that these are not
+real numbers all right let's quickly go
+
+ align:start position:0%
+real numbers all right let's quickly go
+ 
+
+ align:start position:0%
+real numbers all right let's quickly go
+through and just do
+
+ align:start position:0%
+through and just do
+ 
+
+ align:start position:0%
+through and just do
+the similar exercise one last time just
+
+ align:start position:0%
+the similar exercise one last time just
+ 
+
+ align:start position:0%
+the similar exercise one last time just
+to come back to i'm not going to go
+
+ align:start position:0%
+to come back to i'm not going to go
+ 
+
+ align:start position:0%
+to come back to i'm not going to go
+through as much detail but we talked
+
+ align:start position:0%
+through as much detail but we talked
+ 
+
+ align:start position:0%
+through as much detail but we talked
+about that 6-0 fatty acid that we did
+
+ align:start position:0%
+about that 6-0 fatty acid that we did
+ 
+
+ align:start position:0%
+about that 6-0 fatty acid that we did
+accounting for earlier
+
+ align:start position:0%
+accounting for earlier
+ 
+
+ align:start position:0%
+accounting for earlier
+if you look back in your notes what we
+
+ align:start position:0%
+if you look back in your notes what we
+ 
+
+ align:start position:0%
+if you look back in your notes what we
+wrote down is that
+
+ align:start position:0%
+wrote down is that
+ 
+
+ align:start position:0%
+wrote down is that
+from completely oxidizing that fully
+
+ align:start position:0%
+from completely oxidizing that fully
+ 
+
+ align:start position:0%
+from completely oxidizing that fully
+saturated six carbon fatty acid we got
+
+ align:start position:0%
+saturated six carbon fatty acid we got
+ 
+
+ align:start position:0%
+saturated six carbon fatty acid we got
+11 atp
+
+ align:start position:0%
+11 atp
+ 
+
+ align:start position:0%
+11 atp
+11 nad we got one sorry one atp
+
+ align:start position:0%
+11 nad we got one sorry one atp
+ 
+
+ align:start position:0%
+11 nad we got one sorry one atp
+11 nadhs and five
+
+ align:start position:0%
+11 nadhs and five
+ 
+
+ align:start position:0%
+11 nadhs and five
+fad h2s if we make
+
+ align:start position:0%
+fad h2s if we make
+ 
+
+ align:start position:0%
+fad h2s if we make
+remember all these are being generated
+
+ align:start position:0%
+remember all these are being generated
+ 
+
+ align:start position:0%
+remember all these are being generated
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+all these nadhs and fadh2s are already
+
+ align:start position:0%
+all these nadhs and fadh2s are already
+ 
+
+ align:start position:0%
+all these nadhs and fadh2s are already
+in the mitochondria
+
+ align:start position:0%
+in the mitochondria
+ 
+
+ align:start position:0%
+in the mitochondria
+and so if we just use the same
+
+ align:start position:0%
+and so if we just use the same
+ 
+
+ align:start position:0%
+and so if we just use the same
+conversion factors
+
+ align:start position:0%
+conversion factors
+ 
+
+ align:start position:0%
+conversion factors
+that we used for um over there in our
+
+ align:start position:0%
+that we used for um over there in our
+ 
+
+ align:start position:0%
+that we used for um over there in our
+calculation for glycolysis
+
+ align:start position:0%
+calculation for glycolysis
+ 
+
+ align:start position:0%
+calculation for glycolysis
+what we get is 27 and a half
+
+ align:start position:0%
+what we get is 27 and a half
+ 
+
+ align:start position:0%
+what we get is 27 and a half
+atp for the nadhs
+
+ align:start position:0%
+atp for the nadhs
+ 
+
+ align:start position:0%
+atp for the nadhs
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seven and a half atp for the fadh2s
+
+ align:start position:0%
+seven and a half atp for the fadh2s
+ 
+
+ align:start position:0%
+seven and a half atp for the fadh2s
+which is a total of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+35 atp
+
+ align:start position:0%
+35 atp
+ 
+
+ align:start position:0%
+35 atp
+for these 28
+
+ align:start position:0%
+for these 28
+ 
+
+ align:start position:0%
+for these 28
+35 plus the one so a total of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+36 atp
+
+ align:start position:0%
+36 atp
+ 
+
+ align:start position:0%
+36 atp
+from complete oxidation of our six
+
+ align:start position:0%
+from complete oxidation of our six
+ 
+
+ align:start position:0%
+from complete oxidation of our six
+carbon fatty acid
+
+ align:start position:0%
+carbon fatty acid
+ 
+
+ align:start position:0%
+carbon fatty acid
+which is certainly greater than the 30
+
+ align:start position:0%
+which is certainly greater than the 30
+ 
+
+ align:start position:0%
+which is certainly greater than the 30
+atp we got from complete
+
+ align:start position:0%
+atp we got from complete
+ 
+
+ align:start position:0%
+atp we got from complete
+oxidation of glucose that makes sense
+
+ align:start position:0%
+oxidation of glucose that makes sense
+ 
+
+ align:start position:0%
+oxidation of glucose that makes sense
+fatty acids are more reduced than
+
+ align:start position:0%
+fatty acids are more reduced than
+ 
+
+ align:start position:0%
+fatty acids are more reduced than
+glucose more calories
+
+ align:start position:0%
+glucose more calories
+ 
+
+ align:start position:0%
+glucose more calories
+should be able to get more atp from it
+
+ align:start position:0%
+should be able to get more atp from it
+ 
+
+ align:start position:0%
+should be able to get more atp from it
+and this calculation illustrates
+
+ align:start position:0%
+and this calculation illustrates
+ 
+
+ align:start position:0%
+and this calculation illustrates
+that we get that the typical calculation
+
+ align:start position:0%
+that we get that the typical calculation
+ 
+
+ align:start position:0%
+that we get that the typical calculation
+in textbook usually describes
+
+ align:start position:0%
+in textbook usually describes
+ 
+
+ align:start position:0%
+in textbook usually describes
+complete oxidation of a 16 0
+
+ align:start position:0%
+complete oxidation of a 16 0
+ 
+
+ align:start position:0%
+complete oxidation of a 16 0
+a fully saturated 16 carbon fatty acid
+
+ align:start position:0%
+a fully saturated 16 carbon fatty acid
+ 
+
+ align:start position:0%
+a fully saturated 16 carbon fatty acid
+that's palmitate that's the one of the
+
+ align:start position:0%
+that's palmitate that's the one of the
+ 
+
+ align:start position:0%
+that's palmitate that's the one of the
+most abundant fatty acids in the cell
+
+ align:start position:0%
+most abundant fatty acids in the cell
+ 
+
+ align:start position:0%
+most abundant fatty acids in the cell
+this if you completely oxidize it the
+
+ align:start position:0%
+this if you completely oxidize it the
+ 
+
+ align:start position:0%
+this if you completely oxidize it the
+number in a lot of textbooks
+
+ align:start position:0%
+number in a lot of textbooks
+ 
+
+ align:start position:0%
+number in a lot of textbooks
+is 106 atp
+
+ align:start position:0%
+is 106 atp
+ 
+
+ align:start position:0%
+is 106 atp
+per palmitate completely oxidized to co2
+
+ align:start position:0%
+per palmitate completely oxidized to co2
+ 
+
+ align:start position:0%
+per palmitate completely oxidized to co2
+if you're so inclined you can go through
+
+ align:start position:0%
+if you're so inclined you can go through
+ 
+
+ align:start position:0%
+if you're so inclined you can go through
+and do the calculations yourself and see
+
+ align:start position:0%
+and do the calculations yourself and see
+ 
+
+ align:start position:0%
+and do the calculations yourself and see
+if you agree with that but the key point
+
+ align:start position:0%
+if you agree with that but the key point
+ 
+
+ align:start position:0%
+if you agree with that but the key point
+of all of this
+
+ align:start position:0%
+of all of this
+ 
+
+ align:start position:0%
+of all of this
+accounting is that none of this are real
+
+ align:start position:0%
+accounting is that none of this are real
+ 
+
+ align:start position:0%
+accounting is that none of this are real
+numbers
+
+ align:start position:0%
+numbers
+ 
+
+ align:start position:0%
+numbers
+and i hope you now better appreciate
+
+ align:start position:0%
+and i hope you now better appreciate
+ 
+
+ align:start position:0%
+and i hope you now better appreciate
+what energy really means that is
+
+ align:start position:0%
+what energy really means that is
+ 
+
+ align:start position:0%
+what energy really means that is
+how oxidation of carbon by being
+
+ align:start position:0%
+how oxidation of carbon by being
+ 
+
+ align:start position:0%
+how oxidation of carbon by being
+favorable
+
+ align:start position:0%
+favorable
+ 
+
+ align:start position:0%
+favorable
+can be coupled either to
+
+ align:start position:0%
+can be coupled either to
+ 
+
+ align:start position:0%
+can be coupled either to
+direct charging of an atp adp ratio
+
+ align:start position:0%
+direct charging of an atp adp ratio
+ 
+
+ align:start position:0%
+direct charging of an atp adp ratio
+as occurs in the gap dh step of
+
+ align:start position:0%
+as occurs in the gap dh step of
+ 
+
+ align:start position:0%
+as occurs in the gap dh step of
+glycolysis
+
+ align:start position:0%
+glycolysis
+ 
+
+ align:start position:0%
+glycolysis
+as well as the succinic thiokinase step
+
+ align:start position:0%
+as well as the succinic thiokinase step
+ 
+
+ align:start position:0%
+as well as the succinic thiokinase step
+of the tca cycle
+
+ align:start position:0%
+of the tca cycle
+ 
+
+ align:start position:0%
+of the tca cycle
+but most energy transduction involves
+
+ align:start position:0%
+but most energy transduction involves
+ 
+
+ align:start position:0%
+but most energy transduction involves
+this charging up nad nadh ratios
+
+ align:start position:0%
+this charging up nad nadh ratios
+ 
+
+ align:start position:0%
+this charging up nad nadh ratios
+or reactions that are coupled to
+
+ align:start position:0%
+or reactions that are coupled to
+ 
+
+ align:start position:0%
+or reactions that are coupled to
+fadfadh2
+
+ align:start position:0%
+fadfadh2
+ 
+
+ align:start position:0%
+fadfadh2
+via these membrane complexes that
+
+ align:start position:0%
+via these membrane complexes that
+ 
+
+ align:start position:0%
+via these membrane complexes that
+ultimately lead to this favorable
+
+ align:start position:0%
+ultimately lead to this favorable
+ 
+
+ align:start position:0%
+ultimately lead to this favorable
+electron transport
+
+ align:start position:0%
+electron transport
+ 
+
+ align:start position:0%
+electron transport
+from lower to higher standard reduction
+
+ align:start position:0%
+from lower to higher standard reduction
+ 
+
+ align:start position:0%
+from lower to higher standard reduction
+potentials
+
+ align:start position:0%
+potentials
+ 
+
+ align:start position:0%
+potentials
+that favorable electron transport can be
+
+ align:start position:0%
+that favorable electron transport can be
+ 
+
+ align:start position:0%
+that favorable electron transport can be
+used to create
+
+ align:start position:0%
+used to create
+ 
+
+ align:start position:0%
+used to create
+a battery delta side delta ph what can
+
+ align:start position:0%
+a battery delta side delta ph what can
+ 
+
+ align:start position:0%
+a battery delta side delta ph what can
+then be coupled to do other work
+
+ align:start position:0%
+then be coupled to do other work
+ 
+
+ align:start position:0%
+then be coupled to do other work
+including synthesizing atp at the high
+
+ align:start position:0%
+including synthesizing atp at the high
+ 
+
+ align:start position:0%
+including synthesizing atp at the high
+atp adp
+
+ align:start position:0%
+atp adp
+ 
+
+ align:start position:0%
+atp adp
+ratio that can then be used by other
+
+ align:start position:0%
+ratio that can then be used by other
+ 
+
+ align:start position:0%
+ratio that can then be used by other
+reactions in the cell that would
+
+ align:start position:0%
+reactions in the cell that would
+ 
+
+ align:start position:0%
+reactions in the cell that would
+otherwise be unfavorable and allow cells
+
+ align:start position:0%
+otherwise be unfavorable and allow cells
+ 
+
+ align:start position:0%
+otherwise be unfavorable and allow cells
+to basically extract energy
+
+ align:start position:0%
+to basically extract energy
+ 
+
+ align:start position:0%
+to basically extract energy
+from its environment in order to fuel
+
+ align:start position:0%
+from its environment in order to fuel
+ 
+
+ align:start position:0%
+from its environment in order to fuel
+the processes
+
+ align:start position:0%
+the processes
+ 
+
+ align:start position:0%
+the processes
+that are unfavorable and are necessary
+
+ align:start position:0%
+that are unfavorable and are necessary
+ 
+
+ align:start position:0%
+that are unfavorable and are necessary
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+sustain life all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+so thus far we have focused
+
+ align:start position:0%
+so thus far we have focused
+ 
+
+ align:start position:0%
+so thus far we have focused
+almost entirely on how you oxidize
+
+ align:start position:0%
+almost entirely on how you oxidize
+ 
+
+ align:start position:0%
+almost entirely on how you oxidize
+carbon
+
+ align:start position:0%
+carbon
+ 
+
+ align:start position:0%
+carbon
+as a way to release energy
+
+ align:start position:0%
+as a way to release energy
+ 
+
+ align:start position:0%
+as a way to release energy
+and that's great but of course that
+
+ align:start position:0%
+and that's great but of course that
+ 
+
+ align:start position:0%
+and that's great but of course that
+reduced carbon
+
+ align:start position:0%
+reduced carbon
+ 
+
+ align:start position:0%
+reduced carbon
+has to come from somewhere to begin with
+
+ align:start position:0%
+has to come from somewhere to begin with
+ 
+
+ align:start position:0%
+has to come from somewhere to begin with
+and every one of us learned in grade
+
+ align:start position:0%
+and every one of us learned in grade
+ 
+
+ align:start position:0%
+and every one of us learned in grade
+school
+
+ align:start position:0%
+school
+ 
+
+ align:start position:0%
+school
+that the energy for all life ultimately
+
+ align:start position:0%
+that the energy for all life ultimately
+ 
+
+ align:start position:0%
+that the energy for all life ultimately
+comes from the sun and that's of course
+
+ align:start position:0%
+comes from the sun and that's of course
+ 
+
+ align:start position:0%
+comes from the sun and that's of course
+photosynthesis
+
+ align:start position:0%
+photosynthesis
+ 
+
+ align:start position:0%
+photosynthesis
+and now i want to turn to beginning to
+
+ align:start position:0%
+and now i want to turn to beginning to
+ 
+
+ align:start position:0%
+and now i want to turn to beginning to
+discuss
+
+ align:start position:0%
+discuss
+ 
+
+ align:start position:0%
+discuss
+photosynthesis and how it works
+
+ align:start position:0%
+photosynthesis and how it works
+ 
+
+ align:start position:0%
+photosynthesis and how it works
+in other words how does life harvest
+
+ align:start position:0%
+in other words how does life harvest
+ 
+
+ align:start position:0%
+in other words how does life harvest
+solar energy in a usable form
+
+ align:start position:0%
+solar energy in a usable form
+ 
+
+ align:start position:0%
+solar energy in a usable form
+that ultimately involves
+
+ align:start position:0%
+that ultimately involves
+ 
+
+ align:start position:0%
+that ultimately involves
+using atmospheric co2
+
+ align:start position:0%
+using atmospheric co2
+ 
+
+ align:start position:0%
+using atmospheric co2
+which gets reduced to generate
+
+ align:start position:0%
+which gets reduced to generate
+ 
+
+ align:start position:0%
+which gets reduced to generate
+reduce carbon that of course originally
+
+ align:start position:0%
+reduce carbon that of course originally
+ 
+
+ align:start position:0%
+reduce carbon that of course originally
+occurred
+
+ align:start position:0%
+occurred
+ 
+
+ align:start position:0%
+occurred
+because plants or for any photosynthetic
+
+ align:start position:0%
+because plants or for any photosynthetic
+ 
+
+ align:start position:0%
+because plants or for any photosynthetic
+organism has the same issues as us
+
+ align:start position:0%
+organism has the same issues as us
+ 
+
+ align:start position:0%
+organism has the same issues as us
+that is to fight thermodynamics maintain
+
+ align:start position:0%
+that is to fight thermodynamics maintain
+ 
+
+ align:start position:0%
+that is to fight thermodynamics maintain
+and survive it constantly has to be
+
+ align:start position:0%
+and survive it constantly has to be
+ 
+
+ align:start position:0%
+and survive it constantly has to be
+charging an atp
+
+ align:start position:0%
+charging an atp
+ 
+
+ align:start position:0%
+charging an atp
+adp ratio in order to fuel the
+
+ align:start position:0%
+adp ratio in order to fuel the
+ 
+
+ align:start position:0%
+adp ratio in order to fuel the
+otherwise unfavorable processes that are
+
+ align:start position:0%
+otherwise unfavorable processes that are
+ 
+
+ align:start position:0%
+otherwise unfavorable processes that are
+required
+
+ align:start position:0%
+required
+ 
+
+ align:start position:0%
+required
+to maintain order in the cell
+
+ align:start position:0%
+to maintain order in the cell
+ 
+
+ align:start position:0%
+to maintain order in the cell
+this has to occur during the day when
+
+ align:start position:0%
+this has to occur during the day when
+ 
+
+ align:start position:0%
+this has to occur during the day when
+the sun is out and there's
+
+ align:start position:0%
+the sun is out and there's
+ 
+
+ align:start position:0%
+the sun is out and there's
+light energy photosynthesis but also has
+
+ align:start position:0%
+light energy photosynthesis but also has
+ 
+
+ align:start position:0%
+light energy photosynthesis but also has
+to occur
+
+ align:start position:0%
+to occur
+ 
+
+ align:start position:0%
+to occur
+at night or at times when there is no
+
+ align:start position:0%
+at night or at times when there is no
+ 
+
+ align:start position:0%
+at night or at times when there is no
+sun and so
+
+ align:start position:0%
+sun and so
+ 
+
+ align:start position:0%
+sun and so
+thus plants basically stored
+
+ align:start position:0%
+thus plants basically stored
+ 
+
+ align:start position:0%
+thus plants basically stored
+energy as reduced carbon so that they
+
+ align:start position:0%
+energy as reduced carbon so that they
+ 
+
+ align:start position:0%
+energy as reduced carbon so that they
+had something to eat at night that is to
+
+ align:start position:0%
+had something to eat at night that is to
+ 
+
+ align:start position:0%
+had something to eat at night that is to
+keep their atp adp ratios
+
+ align:start position:0%
+keep their atp adp ratios
+ 
+
+ align:start position:0%
+keep their atp adp ratios
+high at night so they can do all these
+
+ align:start position:0%
+high at night so they can do all these
+ 
+
+ align:start position:0%
+high at night so they can do all these
+catabolic processes
+
+ align:start position:0%
+catabolic processes
+ 
+
+ align:start position:0%
+catabolic processes
+at night now fortunately
+
+ align:start position:0%
+at night now fortunately
+ 
+
+ align:start position:0%
+at night now fortunately
+for us the fact that photosynthetic
+
+ align:start position:0%
+for us the fact that photosynthetic
+ 
+
+ align:start position:0%
+for us the fact that photosynthetic
+organisms stored all this reduced carbon
+
+ align:start position:0%
+organisms stored all this reduced carbon
+ 
+
+ align:start position:0%
+organisms stored all this reduced carbon
+allowed other life like us to evolve
+
+ align:start position:0%
+allowed other life like us to evolve
+ 
+
+ align:start position:0%
+allowed other life like us to evolve
+that is entirely dependent on
+
+ align:start position:0%
+that is entirely dependent on
+ 
+
+ align:start position:0%
+that is entirely dependent on
+photosynthetic organisms
+
+ align:start position:0%
+photosynthetic organisms
+ 
+
+ align:start position:0%
+photosynthetic organisms
+either directly or indirectly for food
+
+ align:start position:0%
+either directly or indirectly for food
+ 
+
+ align:start position:0%
+either directly or indirectly for food
+and so photosynthesis also is the
+
+ align:start position:0%
+and so photosynthesis also is the
+ 
+
+ align:start position:0%
+and so photosynthesis also is the
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+that ultimately oxygenated our
+
+ align:start position:0%
+that ultimately oxygenated our
+ 
+
+ align:start position:0%
+that ultimately oxygenated our
+atmosphere aerobic life also something
+
+ align:start position:0%
+atmosphere aerobic life also something
+ 
+
+ align:start position:0%
+atmosphere aerobic life also something
+that was necessary for
+
+ align:start position:0%
+that was necessary for
+ 
+
+ align:start position:0%
+that was necessary for
+us to survive because oxygen is such a
+
+ align:start position:0%
+us to survive because oxygen is such a
+ 
+
+ align:start position:0%
+us to survive because oxygen is such a
+key electron
+
+ align:start position:0%
+key electron
+ 
+
+ align:start position:0%
+key electron
+acceptor really key to our bioenergetics
+
+ align:start position:0%
+acceptor really key to our bioenergetics
+ 
+
+ align:start position:0%
+acceptor really key to our bioenergetics
+well the fact that photosynthetic
+
+ align:start position:0%
+well the fact that photosynthetic
+ 
+
+ align:start position:0%
+well the fact that photosynthetic
+organisms put oxygen
+
+ align:start position:0%
+organisms put oxygen
+ 
+
+ align:start position:0%
+organisms put oxygen
+in our atmosphere also was really
+
+ align:start position:0%
+in our atmosphere also was really
+ 
+
+ align:start position:0%
+in our atmosphere also was really
+essential for
+
+ align:start position:0%
+essential for
+ 
+
+ align:start position:0%
+essential for
+aerobic life us to
+
+ align:start position:0%
+aerobic life us to
+ 
+
+ align:start position:0%
+aerobic life us to
+ultimately evolve and so
+
+ align:start position:0%
+ultimately evolve and so
+ 
+
+ align:start position:0%
+ultimately evolve and so
+photosynthesis is often in biochemistry
+
+ align:start position:0%
+photosynthesis is often in biochemistry
+ 
+
+ align:start position:0%
+photosynthesis is often in biochemistry
+courses
+
+ align:start position:0%
+courses
+ 
+
+ align:start position:0%
+courses
+almost a side light and forgotten
+
+ align:start position:0%
+almost a side light and forgotten
+ 
+
+ align:start position:0%
+almost a side light and forgotten
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+but of course it is really really
+
+ align:start position:0%
+but of course it is really really
+ 
+
+ align:start position:0%
+but of course it is really really
+central to how life works because
+
+ align:start position:0%
+central to how life works because
+ 
+
+ align:start position:0%
+central to how life works because
+no life could exist without
+
+ align:start position:0%
+no life could exist without
+ 
+
+ align:start position:0%
+no life could exist without
+photosynthesis and the conditions that
+
+ align:start position:0%
+photosynthesis and the conditions that
+ 
+
+ align:start position:0%
+photosynthesis and the conditions that
+allowed
+
+ align:start position:0%
+allowed
+ 
+
+ align:start position:0%
+allowed
+aerobic most multicellular life that we
+
+ align:start position:0%
+aerobic most multicellular life that we
+ 
+
+ align:start position:0%
+aerobic most multicellular life that we
+know of that's not photosynthetic
+
+ align:start position:0%
+know of that's not photosynthetic
+ 
+
+ align:start position:0%
+know of that's not photosynthetic
+including ourselves could not have
+
+ align:start position:0%
+including ourselves could not have
+ 
+
+ align:start position:0%
+including ourselves could not have
+evolved without
+
+ align:start position:0%
+evolved without
+ 
+
+ align:start position:0%
+evolved without
+photosynthesis oxygenating the
+
+ align:start position:0%
+photosynthesis oxygenating the
+ 
+
+ align:start position:0%
+photosynthesis oxygenating the
+atmosphere
+
+ align:start position:0%
+atmosphere
+ 
+
+ align:start position:0%
+atmosphere
+and generating all this reduced carbon
+
+ align:start position:0%
+and generating all this reduced carbon
+ 
+
+ align:start position:0%
+and generating all this reduced carbon
+that really is where we get
+
+ align:start position:0%
+that really is where we get
+ 
+
+ align:start position:0%
+that really is where we get
+our energy from as food
+
+ align:start position:0%
+our energy from as food
+ 
+
+ align:start position:0%
+our energy from as food
+now you also learned in grade school
+
+ align:start position:0%
+now you also learned in grade school
+ 
+
+ align:start position:0%
+now you also learned in grade school
+when you learned that life depends on
+
+ align:start position:0%
+when you learned that life depends on
+ 
+
+ align:start position:0%
+when you learned that life depends on
+energy of the sun
+
+ align:start position:0%
+energy of the sun
+ 
+
+ align:start position:0%
+energy of the sun
+that the process that life uses is
+
+ align:start position:0%
+that the process that life uses is
+ 
+
+ align:start position:0%
+that the process that life uses is
+this materials photosynthesis
+
+ align:start position:0%
+this materials photosynthesis
+ 
+
+ align:start position:0%
+this materials photosynthesis
+as we go through this over the rest of
+
+ align:start position:0%
+as we go through this over the rest of
+ 
+
+ align:start position:0%
+as we go through this over the rest of
+today and in the next lecture i want you
+
+ align:start position:0%
+today and in the next lecture i want you
+ 
+
+ align:start position:0%
+today and in the next lecture i want you
+to appreciate
+
+ align:start position:0%
+to appreciate
+ 
+
+ align:start position:0%
+to appreciate
+what photosynthesis is and that is
+
+ align:start position:0%
+what photosynthesis is and that is
+ 
+
+ align:start position:0%
+what photosynthesis is and that is
+how life really takes solar energy
+
+ align:start position:0%
+how life really takes solar energy
+ 
+
+ align:start position:0%
+how life really takes solar energy
+and harvests that energy in a
+
+ align:start position:0%
+and harvests that energy in a
+ 
+
+ align:start position:0%
+and harvests that energy in a
+biologically
+
+ align:start position:0%
+biologically
+ 
+
+ align:start position:0%
+biologically
+useful form bearing in mind
+
+ align:start position:0%
+useful form bearing in mind
+ 
+
+ align:start position:0%
+useful form bearing in mind
+all of the concepts that we've already
+
+ align:start position:0%
+all of the concepts that we've already
+ 
+
+ align:start position:0%
+all of the concepts that we've already
+talked about
+
+ align:start position:0%
+talked about
+ 
+
+ align:start position:0%
+talked about
+because that will ultimately help you
+
+ align:start position:0%
+because that will ultimately help you
+ 
+
+ align:start position:0%
+because that will ultimately help you
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+how that energy from the sun is used
+
+ align:start position:0%
+how that energy from the sun is used
+ 
+
+ align:start position:0%
+how that energy from the sun is used
+to make all this reduced carbon this
+
+ align:start position:0%
+to make all this reduced carbon this
+ 
+
+ align:start position:0%
+to make all this reduced carbon this
+carbohydrate and fat
+
+ align:start position:0%
+carbohydrate and fat
+ 
+
+ align:start position:0%
+carbohydrate and fat
+that is energy that we can use for later
+
+ align:start position:0%
+that is energy that we can use for later
+ 
+
+ align:start position:0%
+that is energy that we can use for later
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+also of course allows how photosynthetic
+
+ align:start position:0%
+also of course allows how photosynthetic
+ 
+
+ align:start position:0%
+also of course allows how photosynthetic
+organisms can
+
+ align:start position:0%
+organisms can
+ 
+
+ align:start position:0%
+organisms can
+use light from the sun to just power
+
+ align:start position:0%
+use light from the sun to just power
+ 
+
+ align:start position:0%
+use light from the sun to just power
+things directly
+
+ align:start position:0%
+things directly
+ 
+
+ align:start position:0%
+things directly
+from that solar battery and ultimately
+
+ align:start position:0%
+from that solar battery and ultimately
+ 
+
+ align:start position:0%
+from that solar battery and ultimately
+of course
+
+ align:start position:0%
+of course
+ 
+
+ align:start position:0%
+of course
+you should appreciate that these things
+
+ align:start position:0%
+you should appreciate that these things
+ 
+
+ align:start position:0%
+you should appreciate that these things
+all came first photosynthesis obviously
+
+ align:start position:0%
+all came first photosynthesis obviously
+ 
+
+ align:start position:0%
+all came first photosynthesis obviously
+existed first
+
+ align:start position:0%
+existed first
+ 
+
+ align:start position:0%
+existed first
+and so most of what we already talked
+
+ align:start position:0%
+and so most of what we already talked
+ 
+
+ align:start position:0%
+and so most of what we already talked
+about well
+
+ align:start position:0%
+about well
+ 
+
+ align:start position:0%
+about well
+we'll draw parallels when we talk about
+
+ align:start position:0%
+we'll draw parallels when we talk about
+ 
+
+ align:start position:0%
+we'll draw parallels when we talk about
+photosynthesis of the stuff we already
+
+ align:start position:0%
+photosynthesis of the stuff we already
+ 
+
+ align:start position:0%
+photosynthesis of the stuff we already
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+of course photosynthesis came first and
+
+ align:start position:0%
+of course photosynthesis came first and
+ 
+
+ align:start position:0%
+of course photosynthesis came first and
+the stuff you've already learned about
+
+ align:start position:0%
+the stuff you've already learned about
+ 
+
+ align:start position:0%
+the stuff you've already learned about
+evolved from photosynthesis
+
+ align:start position:0%
+evolved from photosynthesis
+ 
+
+ align:start position:0%
+evolved from photosynthesis
+all right now like all pathways
+
+ align:start position:0%
+all right now like all pathways
+ 
+
+ align:start position:0%
+all right now like all pathways
+photosynthesis also has to follow the
+
+ align:start position:0%
+photosynthesis also has to follow the
+ 
+
+ align:start position:0%
+photosynthesis also has to follow the
+same rules
+
+ align:start position:0%
+same rules
+ 
+
+ align:start position:0%
+same rules
+and laws of thermodynamics that were
+
+ align:start position:0%
+and laws of thermodynamics that were
+ 
+
+ align:start position:0%
+and laws of thermodynamics that were
+true for
+
+ align:start position:0%
+true for
+ 
+
+ align:start position:0%
+true for
+all pathways so plants and animals have
+
+ align:start position:0%
+all pathways so plants and animals have
+ 
+
+ align:start position:0%
+all pathways so plants and animals have
+to follow
+
+ align:start position:0%
+to follow
+ 
+
+ align:start position:0%
+to follow
+the same rules and so what is
+
+ align:start position:0%
+the same rules and so what is
+ 
+
+ align:start position:0%
+the same rules and so what is
+photosynthesis well it's ultimately
+
+ align:start position:0%
+photosynthesis well it's ultimately
+ 
+
+ align:start position:0%
+photosynthesis well it's ultimately
+co2 in the atmosphere that gets reduced
+
+ align:start position:0%
+co2 in the atmosphere that gets reduced
+ 
+
+ align:start position:0%
+co2 in the atmosphere that gets reduced
+to carbohydrate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's classically photosynthesis but of
+
+ align:start position:0%
+that's classically photosynthesis but of
+ 
+
+ align:start position:0%
+that's classically photosynthesis but of
+course plants also make
+
+ align:start position:0%
+course plants also make
+ 
+
+ align:start position:0%
+course plants also make
+fatty acids okay
+
+ align:start position:0%
+fatty acids okay
+ 
+
+ align:start position:0%
+fatty acids okay
+this is carbon reduction
+
+ align:start position:0%
+this is carbon reduction
+ 
+
+ align:start position:0%
+this is carbon reduction
+remember carbon oxidation generally is
+
+ align:start position:0%
+remember carbon oxidation generally is
+ 
+
+ align:start position:0%
+remember carbon oxidation generally is
+favorable
+
+ align:start position:0%
+favorable
+ 
+
+ align:start position:0%
+favorable
+carbon reduction is not delta g
+
+ align:start position:0%
+carbon reduction is not delta g
+ 
+
+ align:start position:0%
+carbon reduction is not delta g
+not prime for this is greater than zero
+
+ align:start position:0%
+not prime for this is greater than zero
+ 
+
+ align:start position:0%
+not prime for this is greater than zero
+right this direction is favored that
+
+ align:start position:0%
+right this direction is favored that
+ 
+
+ align:start position:0%
+right this direction is favored that
+direction is not
+
+ align:start position:0%
+direction is not
+ 
+
+ align:start position:0%
+direction is not
+which means you need energy input to
+
+ align:start position:0%
+which means you need energy input to
+ 
+
+ align:start position:0%
+which means you need energy input to
+reduce that co2 to carbohydrate or fatty
+
+ align:start position:0%
+reduce that co2 to carbohydrate or fatty
+ 
+
+ align:start position:0%
+reduce that co2 to carbohydrate or fatty
+acid
+
+ align:start position:0%
+acid
+ 
+
+ align:start position:0%
+acid
+and of course it's the sun's energy the
+
+ align:start position:0%
+and of course it's the sun's energy the
+ 
+
+ align:start position:0%
+and of course it's the sun's energy the
+solar
+
+ align:start position:0%
+solar
+ 
+
+ align:start position:0%
+solar
+energy that ultimately must be done
+
+ align:start position:0%
+energy that ultimately must be done
+ 
+
+ align:start position:0%
+energy that ultimately must be done
+to make this favorable now we're
+
+ align:start position:0%
+to make this favorable now we're
+ 
+
+ align:start position:0%
+to make this favorable now we're
+reducing
+
+ align:start position:0%
+reducing
+ 
+
+ align:start position:0%
+reducing
+carbon that means we need to add
+
+ align:start position:0%
+carbon that means we need to add
+ 
+
+ align:start position:0%
+carbon that means we need to add
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+those electrons have to come from
+
+ align:start position:0%
+those electrons have to come from
+ 
+
+ align:start position:0%
+those electrons have to come from
+somewhere and so we're
+
+ align:start position:0%
+somewhere and so we're
+ 
+
+ align:start position:0%
+somewhere and so we're
+reducing the carbon that means something
+
+ align:start position:0%
+reducing the carbon that means something
+ 
+
+ align:start position:0%
+reducing the carbon that means something
+else has to be oxidized
+
+ align:start position:0%
+else has to be oxidized
+ 
+
+ align:start position:0%
+else has to be oxidized
+just like when we oxidized carbon those
+
+ align:start position:0%
+just like when we oxidized carbon those
+ 
+
+ align:start position:0%
+just like when we oxidized carbon those
+electrons had to go somewhere
+
+ align:start position:0%
+electrons had to go somewhere
+ 
+
+ align:start position:0%
+electrons had to go somewhere
+something else had to be reduced that
+
+ align:start position:0%
+something else had to be reduced that
+ 
+
+ align:start position:0%
+something else had to be reduced that
+was pyruvate to lactate in fermentation
+
+ align:start position:0%
+was pyruvate to lactate in fermentation
+ 
+
+ align:start position:0%
+was pyruvate to lactate in fermentation
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+oxygen to water via all of the
+
+ align:start position:0%
+oxygen to water via all of the
+ 
+
+ align:start position:0%
+oxygen to water via all of the
+oxidative phosphorylation things we just
+
+ align:start position:0%
+oxidative phosphorylation things we just
+ 
+
+ align:start position:0%
+oxidative phosphorylation things we just
+talked about
+
+ align:start position:0%
+talked about
+ 
+
+ align:start position:0%
+talked about
+and so in this case those electrons have
+
+ align:start position:0%
+and so in this case those electrons have
+ 
+
+ align:start position:0%
+and so in this case those electrons have
+to come from somewhere and those
+
+ align:start position:0%
+to come from somewhere and those
+ 
+
+ align:start position:0%
+to come from somewhere and those
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+ultimately for photosynthesis
+
+ align:start position:0%
+ultimately for photosynthesis
+ 
+
+ align:start position:0%
+ultimately for photosynthesis
+this reduction the electrons come from
+
+ align:start position:0%
+this reduction the electrons come from
+ 
+
+ align:start position:0%
+this reduction the electrons come from
+oxidation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ultimately of water which will generate
+
+ align:start position:0%
+ultimately of water which will generate
+ 
+
+ align:start position:0%
+ultimately of water which will generate
+oxygen and
+
+ align:start position:0%
+oxygen and
+ 
+
+ align:start position:0%
+oxygen and
+this is effectively then the reverse
+
+ align:start position:0%
+this is effectively then the reverse
+ 
+
+ align:start position:0%
+this is effectively then the reverse
+of what you learned about for the
+
+ align:start position:0%
+of what you learned about for the
+ 
+
+ align:start position:0%
+of what you learned about for the
+mitochondrial electron transport
+
+ align:start position:0%
+mitochondrial electron transport
+ 
+
+ align:start position:0%
+mitochondrial electron transport
+why this well water is
+
+ align:start position:0%
+why this well water is
+ 
+
+ align:start position:0%
+why this well water is
+very abundant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has been for all of life on earth at
+
+ align:start position:0%
+has been for all of life on earth at
+ 
+
+ align:start position:0%
+has been for all of life on earth at
+water sent
+
+ align:start position:0%
+water sent
+ 
+
+ align:start position:0%
+water sent
+is obviously life depends on
+
+ align:start position:0%
+is obviously life depends on
+ 
+
+ align:start position:0%
+is obviously life depends on
+water and so you can
+
+ align:start position:0%
+water and so you can
+ 
+
+ align:start position:0%
+water and so you can
+oxidize the water
+
+ align:start position:0%
+oxidize the water
+ 
+
+ align:start position:0%
+oxidize the water
+to generate um oxygen
+
+ align:start position:0%
+to generate um oxygen
+ 
+
+ align:start position:0%
+to generate um oxygen
+this will obviously generate electrons
+
+ align:start position:0%
+this will obviously generate electrons
+ 
+
+ align:start position:0%
+this will obviously generate electrons
+that can be used
+
+ align:start position:0%
+that can be used
+ 
+
+ align:start position:0%
+that can be used
+to reduce carbon and it's
+
+ align:start position:0%
+to reduce carbon and it's
+ 
+
+ align:start position:0%
+to reduce carbon and it's
+effectively the photosynthetic oxidation
+
+ align:start position:0%
+effectively the photosynthetic oxidation
+ 
+
+ align:start position:0%
+effectively the photosynthetic oxidation
+of water
+
+ align:start position:0%
+of water
+ 
+
+ align:start position:0%
+of water
+to make oxygen that was the source of
+
+ align:start position:0%
+to make oxygen that was the source of
+ 
+
+ align:start position:0%
+to make oxygen that was the source of
+oxygen in the atmosphere
+
+ align:start position:0%
+oxygen in the atmosphere
+ 
+
+ align:start position:0%
+oxygen in the atmosphere
+that really today makes aerobic lyse
+
+ align:start position:0%
+that really today makes aerobic lyse
+ 
+
+ align:start position:0%
+that really today makes aerobic lyse
+possible now of course the fact that
+
+ align:start position:0%
+possible now of course the fact that
+ 
+
+ align:start position:0%
+possible now of course the fact that
+oxygen is a good electron acceptor we've
+
+ align:start position:0%
+oxygen is a good electron acceptor we've
+ 
+
+ align:start position:0%
+oxygen is a good electron acceptor we've
+been talking about this forever
+
+ align:start position:0%
+been talking about this forever
+ 
+
+ align:start position:0%
+been talking about this forever
+this means that of course you might
+
+ align:start position:0%
+this means that of course you might
+ 
+
+ align:start position:0%
+this means that of course you might
+guess that
+
+ align:start position:0%
+guess that
+ 
+
+ align:start position:0%
+guess that
+delta g not prime for this process
+
+ align:start position:0%
+delta g not prime for this process
+ 
+
+ align:start position:0%
+delta g not prime for this process
+is not going to be favorable
+
+ align:start position:0%
+is not going to be favorable
+ 
+
+ align:start position:0%
+is not going to be favorable
+just put it another way oxygen's a great
+
+ align:start position:0%
+just put it another way oxygen's a great
+ 
+
+ align:start position:0%
+just put it another way oxygen's a great
+electron acceptor and water is a poor
+
+ align:start position:0%
+electron acceptor and water is a poor
+ 
+
+ align:start position:0%
+electron acceptor and water is a poor
+electron donor and so really the way
+
+ align:start position:0%
+electron donor and so really the way
+ 
+
+ align:start position:0%
+electron donor and so really the way
+photosynthesis the magic of
+
+ align:start position:0%
+photosynthesis the magic of
+ 
+
+ align:start position:0%
+photosynthesis the magic of
+photosynthesis if you will
+
+ align:start position:0%
+photosynthesis if you will
+ 
+
+ align:start position:0%
+photosynthesis if you will
+is making water a
+
+ align:start position:0%
+is making water a
+ 
+
+ align:start position:0%
+is making water a
+good electron donor
+
+ align:start position:0%
+good electron donor
+ 
+
+ align:start position:0%
+good electron donor
+because ultimately that is what is going
+
+ align:start position:0%
+because ultimately that is what is going
+ 
+
+ align:start position:0%
+because ultimately that is what is going
+to make
+
+ align:start position:0%
+to make
+ 
+
+ align:start position:0%
+to make
+this whole thing work energetically
+
+ align:start position:0%
+this whole thing work energetically
+ 
+
+ align:start position:0%
+this whole thing work energetically
+and so you probably
+
+ align:start position:0%
+and so you probably
+ 
+
+ align:start position:0%
+and so you probably
+could guess that if these processes are
+
+ align:start position:0%
+could guess that if these processes are
+ 
+
+ align:start position:0%
+could guess that if these processes are
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+are really about these electron
+
+ align:start position:0%
+are really about these electron
+ 
+
+ align:start position:0%
+are really about these electron
+transfers we need electron carriers
+
+ align:start position:0%
+transfers we need electron carriers
+ 
+
+ align:start position:0%
+transfers we need electron carriers
+this is true for photosynthesis just as
+
+ align:start position:0%
+this is true for photosynthesis just as
+ 
+
+ align:start position:0%
+this is true for photosynthesis just as
+it was true
+
+ align:start position:0%
+it was true
+ 
+
+ align:start position:0%
+it was true
+for oxidative phosphorylation
+
+ align:start position:0%
+for oxidative phosphorylation
+ 
+
+ align:start position:0%
+for oxidative phosphorylation
+um but remember we'll describe a lot of
+
+ align:start position:0%
+um but remember we'll describe a lot of
+ 
+
+ align:start position:0%
+um but remember we'll describe a lot of
+the same electron carriers are used
+
+ align:start position:0%
+the same electron carriers are used
+ 
+
+ align:start position:0%
+the same electron carriers are used
+but as we would describe them remember
+
+ align:start position:0%
+but as we would describe them remember
+ 
+
+ align:start position:0%
+but as we would describe them remember
+that the photosynthesis came first and
+
+ align:start position:0%
+that the photosynthesis came first and
+ 
+
+ align:start position:0%
+that the photosynthesis came first and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the other processes like oxfos that use
+
+ align:start position:0%
+the other processes like oxfos that use
+ 
+
+ align:start position:0%
+the other processes like oxfos that use
+these electron carriers use them because
+
+ align:start position:0%
+these electron carriers use them because
+ 
+
+ align:start position:0%
+these electron carriers use them because
+they were first used in photosynthesis
+
+ align:start position:0%
+they were first used in photosynthesis
+ 
+
+ align:start position:0%
+they were first used in photosynthesis
+and then they were repurposed for
+
+ align:start position:0%
+and then they were repurposed for
+ 
+
+ align:start position:0%
+and then they were repurposed for
+oxidative
+
+ align:start position:0%
+oxidative
+ 
+
+ align:start position:0%
+oxidative
+phosphorylation now to discuss this
+
+ align:start position:0%
+phosphorylation now to discuss this
+ 
+
+ align:start position:0%
+phosphorylation now to discuss this
+i want to first start by introducing an
+
+ align:start position:0%
+i want to first start by introducing an
+ 
+
+ align:start position:0%
+i want to first start by introducing an
+electron carrier
+
+ align:start position:0%
+electron carrier
+ 
+
+ align:start position:0%
+electron carrier
+that's important for this that's really
+
+ align:start position:0%
+that's important for this that's really
+ 
+
+ align:start position:0%
+that's important for this that's really
+a variation
+
+ align:start position:0%
+a variation
+ 
+
+ align:start position:0%
+a variation
+on nadh and it's an electron carrier
+
+ align:start position:0%
+on nadh and it's an electron carrier
+ 
+
+ align:start position:0%
+on nadh and it's an electron carrier
+that's found in
+
+ align:start position:0%
+that's found in
+ 
+
+ align:start position:0%
+that's found in
+excuse me all plants all animals all
+
+ align:start position:0%
+excuse me all plants all animals all
+ 
+
+ align:start position:0%
+excuse me all plants all animals all
+life
+
+ align:start position:0%
+life
+ 
+
+ align:start position:0%
+life
+and is very important in anabolic
+
+ align:start position:0%
+and is very important in anabolic
+ 
+
+ align:start position:0%
+and is very important in anabolic
+pathways
+
+ align:start position:0%
+pathways
+ 
+
+ align:start position:0%
+pathways
+like photosynthesis remember
+
+ align:start position:0%
+like photosynthesis remember
+ 
+
+ align:start position:0%
+like photosynthesis remember
+that anabolism building stuff has to be
+
+ align:start position:0%
+that anabolism building stuff has to be
+ 
+
+ align:start position:0%
+that anabolism building stuff has to be
+distinct from
+
+ align:start position:0%
+distinct from
+ 
+
+ align:start position:0%
+distinct from
+catabolism breaking stuff down for a
+
+ align:start position:0%
+catabolism breaking stuff down for a
+ 
+
+ align:start position:0%
+catabolism breaking stuff down for a
+number of reasons we saw this in
+
+ align:start position:0%
+number of reasons we saw this in
+ 
+
+ align:start position:0%
+number of reasons we saw this in
+glycolysis and gluconeogenesis
+
+ align:start position:0%
+glycolysis and gluconeogenesis
+ 
+
+ align:start position:0%
+glycolysis and gluconeogenesis
+glycogen synthesis glycogen breakdown
+
+ align:start position:0%
+glycogen synthesis glycogen breakdown
+ 
+
+ align:start position:0%
+glycogen synthesis glycogen breakdown
+remember delta g not prime can only
+
+ align:start position:0%
+remember delta g not prime can only
+ 
+
+ align:start position:0%
+remember delta g not prime can only
+favor one direction
+
+ align:start position:0%
+favor one direction
+ 
+
+ align:start position:0%
+favor one direction
+and so in the direction that's favorable
+
+ align:start position:0%
+and so in the direction that's favorable
+ 
+
+ align:start position:0%
+and so in the direction that's favorable
+it works and the other direction to
+
+ align:start position:0%
+it works and the other direction to
+ 
+
+ align:start position:0%
+it works and the other direction to
+actually make it happen we have to make
+
+ align:start position:0%
+actually make it happen we have to make
+ 
+
+ align:start position:0%
+actually make it happen we have to make
+delta g less than zero
+
+ align:start position:0%
+delta g less than zero
+ 
+
+ align:start position:0%
+delta g less than zero
+that has to happen by energy addition
+
+ align:start position:0%
+that has to happen by energy addition
+ 
+
+ align:start position:0%
+that has to happen by energy addition
+and so now we had to have these separate
+
+ align:start position:0%
+and so now we had to have these separate
+ 
+
+ align:start position:0%
+and so now we had to have these separate
+pathways you also need separate pathways
+
+ align:start position:0%
+pathways you also need separate pathways
+ 
+
+ align:start position:0%
+pathways you also need separate pathways
+because that allows separate regulation
+
+ align:start position:0%
+because that allows separate regulation
+ 
+
+ align:start position:0%
+because that allows separate regulation
+a voice
+
+ align:start position:0%
+a voice
+ 
+
+ align:start position:0%
+a voice
+futile cycle and enable cells to match
+
+ align:start position:0%
+futile cycle and enable cells to match
+ 
+
+ align:start position:0%
+futile cycle and enable cells to match
+needs with processes and as we already
+
+ align:start position:0%
+needs with processes and as we already
+ 
+
+ align:start position:0%
+needs with processes and as we already
+discussed one way to keep these anabolic
+
+ align:start position:0%
+discussed one way to keep these anabolic
+ 
+
+ align:start position:0%
+discussed one way to keep these anabolic
+and catabolic processes distinct is by
+
+ align:start position:0%
+and catabolic processes distinct is by
+ 
+
+ align:start position:0%
+and catabolic processes distinct is by
+building separate
+
+ align:start position:0%
+building separate
+ 
+
+ align:start position:0%
+building separate
+compartments right it's useful to have
+
+ align:start position:0%
+compartments right it's useful to have
+ 
+
+ align:start position:0%
+compartments right it's useful to have
+separate compartments
+
+ align:start position:0%
+separate compartments
+ 
+
+ align:start position:0%
+separate compartments
+different conditions in different
+
+ align:start position:0%
+different conditions in different
+ 
+
+ align:start position:0%
+different conditions in different
+compartments that can favor different
+
+ align:start position:0%
+compartments that can favor different
+ 
+
+ align:start position:0%
+compartments that can favor different
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+happening however not all cells have
+
+ align:start position:0%
+happening however not all cells have
+ 
+
+ align:start position:0%
+happening however not all cells have
+separate compartments prokaryotes don't
+
+ align:start position:0%
+separate compartments prokaryotes don't
+ 
+
+ align:start position:0%
+separate compartments prokaryotes don't
+and you might think of situations where
+
+ align:start position:0%
+and you might think of situations where
+ 
+
+ align:start position:0%
+and you might think of situations where
+you clearly want to have
+
+ align:start position:0%
+you clearly want to have
+ 
+
+ align:start position:0%
+you clearly want to have
+two different types of reactions
+
+ align:start position:0%
+two different types of reactions
+ 
+
+ align:start position:0%
+two different types of reactions
+happening in the same compartment
+
+ align:start position:0%
+happening in the same compartment
+ 
+
+ align:start position:0%
+happening in the same compartment
+and so what if you want to both do
+
+ align:start position:0%
+and so what if you want to both do
+ 
+
+ align:start position:0%
+and so what if you want to both do
+oxidation and reduction in different
+
+ align:start position:0%
+oxidation and reduction in different
+ 
+
+ align:start position:0%
+oxidation and reduction in different
+reactions
+
+ align:start position:0%
+reactions
+ 
+
+ align:start position:0%
+reactions
+in the same compartment well clearly
+
+ align:start position:0%
+in the same compartment well clearly
+ 
+
+ align:start position:0%
+in the same compartment well clearly
+you need some way that will favor some
+
+ align:start position:0%
+you need some way that will favor some
+ 
+
+ align:start position:0%
+you need some way that will favor some
+reactions being oxidation
+
+ align:start position:0%
+reactions being oxidation
+ 
+
+ align:start position:0%
+reactions being oxidation
+and other reactions being reductions and
+
+ align:start position:0%
+and other reactions being reductions and
+ 
+
+ align:start position:0%
+and other reactions being reductions and
+if you simply rely
+
+ align:start position:0%
+if you simply rely
+ 
+
+ align:start position:0%
+if you simply rely
+on nadh
+
+ align:start position:0%
+on nadh
+ 
+
+ align:start position:0%
+on nadh
+nad plus as your oxidant or your
+
+ align:start position:0%
+nad plus as your oxidant or your
+ 
+
+ align:start position:0%
+nad plus as your oxidant or your
+reductant
+
+ align:start position:0%
+reductant
+ 
+
+ align:start position:0%
+reductant
+this now becomes a problem
+
+ align:start position:0%
+this now becomes a problem
+ 
+
+ align:start position:0%
+this now becomes a problem
+all right so a solution is
+
+ align:start position:0%
+all right so a solution is
+ 
+
+ align:start position:0%
+all right so a solution is
+well let's make a distinct electron
+
+ align:start position:0%
+well let's make a distinct electron
+ 
+
+ align:start position:0%
+well let's make a distinct electron
+carrier
+
+ align:start position:0%
+carrier
+ 
+
+ align:start position:0%
+carrier
+for the oxidation reactions in the cells
+
+ align:start position:0%
+for the oxidation reactions in the cells
+ 
+
+ align:start position:0%
+for the oxidation reactions in the cells
+so that's what
+
+ align:start position:0%
+so that's what
+ 
+
+ align:start position:0%
+so that's what
+this is turns out you keep your nadn adh
+
+ align:start position:0%
+this is turns out you keep your nadn adh
+ 
+
+ align:start position:0%
+this is turns out you keep your nadn adh
+ratio to largely favor
+
+ align:start position:0%
+ratio to largely favor
+ 
+
+ align:start position:0%
+ratio to largely favor
+the oxidation reactions you want to do
+
+ align:start position:0%
+the oxidation reactions you want to do
+ 
+
+ align:start position:0%
+the oxidation reactions you want to do
+and let's create a different currency
+
+ align:start position:0%
+and let's create a different currency
+ 
+
+ align:start position:0%
+and let's create a different currency
+for reduction and this currency
+
+ align:start position:0%
+for reduction and this currency
+ 
+
+ align:start position:0%
+for reduction and this currency
+ends up being a different molecule nadph
+
+ align:start position:0%
+ends up being a different molecule nadph
+ 
+
+ align:start position:0%
+ends up being a different molecule nadph
+nad p plus and you use
+
+ align:start position:0%
+nad p plus and you use
+ 
+
+ align:start position:0%
+nad p plus and you use
+this as a cofactor pair for
+
+ align:start position:0%
+this as a cofactor pair for
+ 
+
+ align:start position:0%
+this as a cofactor pair for
+reduction well what is nadph
+
+ align:start position:0%
+reduction well what is nadph
+ 
+
+ align:start position:0%
+reduction well what is nadph
+well it's effectively the same thing as
+
+ align:start position:0%
+well it's effectively the same thing as
+ 
+
+ align:start position:0%
+well it's effectively the same thing as
+nadh but now you mark it as a separate
+
+ align:start position:0%
+nadh but now you mark it as a separate
+ 
+
+ align:start position:0%
+nadh but now you mark it as a separate
+pool
+
+ align:start position:0%
+pool
+ 
+
+ align:start position:0%
+pool
+with a two prime phosphate
+
+ align:start position:0%
+with a two prime phosphate
+ 
+
+ align:start position:0%
+with a two prime phosphate
+on the adp portion of the molecule
+
+ align:start position:0%
+on the adp portion of the molecule
+ 
+
+ align:start position:0%
+on the adp portion of the molecule
+let me draw it out for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this here is
+
+ align:start position:0%
+okay so this here is
+ 
+
+ align:start position:0%
+okay so this here is
+any so i took this phosphate off this
+
+ align:start position:0%
+any so i took this phosphate off this
+ 
+
+ align:start position:0%
+any so i took this phosphate off this
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+nadh put a two fine prime phosphate on
+
+ align:start position:0%
+nadh put a two fine prime phosphate on
+ 
+
+ align:start position:0%
+nadh put a two fine prime phosphate on
+now i mark this as a separate molecule
+
+ align:start position:0%
+now i mark this as a separate molecule
+ 
+
+ align:start position:0%
+now i mark this as a separate molecule
+pool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nad
+
+ align:start position:0%
+nad
+ 
+
+ align:start position:0%
+nad
+ph um
+
+ align:start position:0%
+ph um
+ 
+
+ align:start position:0%
+ph um
+a is an adenine remember it's a
+
+ align:start position:0%
+a is an adenine remember it's a
+ 
+
+ align:start position:0%
+a is an adenine remember it's a
+nicotinamide adenine
+
+ align:start position:0%
+nicotinamide adenine
+ 
+
+ align:start position:0%
+nicotinamide adenine
+dinucleoside okay so here's a
+
+ align:start position:0%
+dinucleoside okay so here's a
+ 
+
+ align:start position:0%
+dinucleoside okay so here's a
+adenine phosphate phosphate other
+
+ align:start position:0%
+adenine phosphate phosphate other
+ 
+
+ align:start position:0%
+adenine phosphate phosphate other
+nucleoside with the nicotinamide group
+
+ align:start position:0%
+nucleoside with the nicotinamide group
+ 
+
+ align:start position:0%
+nucleoside with the nicotinamide group
+this here is in the reduced form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seen this now a million times but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can oxidize it as possible
+
+ align:start position:0%
+we can oxidize it as possible
+ 
+
+ align:start position:0%
+we can oxidize it as possible
+that generates this two electron hydride
+
+ align:start position:0%
+that generates this two electron hydride
+ 
+
+ align:start position:0%
+that generates this two electron hydride
+ion so remove two electrons and now this
+
+ align:start position:0%
+ion so remove two electrons and now this
+ 
+
+ align:start position:0%
+ion so remove two electrons and now this
+nicotinamide form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is here in the nadp
+
+ align:start position:0%
+is here in the nadp
+ 
+
+ align:start position:0%
+is here in the nadp
+plus or oxidized
+
+ align:start position:0%
+plus or oxidized
+ 
+
+ align:start position:0%
+plus or oxidized
+form of the molecule and so effectively
+
+ align:start position:0%
+form of the molecule and so effectively
+ 
+
+ align:start position:0%
+form of the molecule and so effectively
+by marking this
+
+ align:start position:0%
+by marking this
+ 
+
+ align:start position:0%
+by marking this
+as a separate pool with that two prime
+
+ align:start position:0%
+as a separate pool with that two prime
+ 
+
+ align:start position:0%
+as a separate pool with that two prime
+phosphate
+
+ align:start position:0%
+phosphate
+ 
+
+ align:start position:0%
+phosphate
+you can have a different nadh
+
+ align:start position:0%
+you can have a different nadh
+ 
+
+ align:start position:0%
+you can have a different nadh
+and adplus ratio in cells then you have
+
+ align:start position:0%
+and adplus ratio in cells then you have
+ 
+
+ align:start position:0%
+and adplus ratio in cells then you have
+nadph and adp plus ratio
+
+ align:start position:0%
+nadph and adp plus ratio
+ 
+
+ align:start position:0%
+nadph and adp plus ratio
+in cells use one cofactor pair to favor
+
+ align:start position:0%
+in cells use one cofactor pair to favor
+ 
+
+ align:start position:0%
+in cells use one cofactor pair to favor
+oxidation
+
+ align:start position:0%
+oxidation
+ 
+
+ align:start position:0%
+oxidation
+and the other cofactor pair to favor
+
+ align:start position:0%
+and the other cofactor pair to favor
+ 
+
+ align:start position:0%
+and the other cofactor pair to favor
+reduction and so i want to give
+
+ align:start position:0%
+reduction and so i want to give
+ 
+
+ align:start position:0%
+reduction and so i want to give
+a quick aside on nadph because it's
+
+ align:start position:0%
+a quick aside on nadph because it's
+ 
+
+ align:start position:0%
+a quick aside on nadph because it's
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+also nadph that can be very important in
+
+ align:start position:0%
+also nadph that can be very important in
+ 
+
+ align:start position:0%
+also nadph that can be very important in
+keeping
+
+ align:start position:0%
+keeping
+ 
+
+ align:start position:0%
+keeping
+the cytosol of cells reduced
+
+ align:start position:0%
+the cytosol of cells reduced
+ 
+
+ align:start position:0%
+the cytosol of cells reduced
+so what do i mean by that well remember
+
+ align:start position:0%
+so what do i mean by that well remember
+ 
+
+ align:start position:0%
+so what do i mean by that well remember
+you learned from professor yaffi
+
+ align:start position:0%
+you learned from professor yaffi
+ 
+
+ align:start position:0%
+you learned from professor yaffi
+we talked about proteins that you can
+
+ align:start position:0%
+we talked about proteins that you can
+ 
+
+ align:start position:0%
+we talked about proteins that you can
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+these inside the cytosol you'd have your
+
+ align:start position:0%
+these inside the cytosol you'd have your
+ 
+
+ align:start position:0%
+these inside the cytosol you'd have your
+cysteine residues on proteins
+
+ align:start position:0%
+cysteine residues on proteins
+ 
+
+ align:start position:0%
+cysteine residues on proteins
+be in this reduced form and outside the
+
+ align:start position:0%
+be in this reduced form and outside the
+ 
+
+ align:start position:0%
+be in this reduced form and outside the
+cell
+
+ align:start position:0%
+cell
+ 
+
+ align:start position:0%
+cell
+you'd form these disulfide bonds which
+
+ align:start position:0%
+you'd form these disulfide bonds which
+ 
+
+ align:start position:0%
+you'd form these disulfide bonds which
+is basically
+
+ align:start position:0%
+is basically
+ 
+
+ align:start position:0%
+is basically
+oxidized cysteine and so in the cytosol
+
+ align:start position:0%
+oxidized cysteine and so in the cytosol
+ 
+
+ align:start position:0%
+oxidized cysteine and so in the cytosol
+you want your cysteine is reduced and
+
+ align:start position:0%
+you want your cysteine is reduced and
+ 
+
+ align:start position:0%
+you want your cysteine is reduced and
+outside the cell
+
+ align:start position:0%
+outside the cell
+ 
+
+ align:start position:0%
+outside the cell
+you end up with these disulfide bonds on
+
+ align:start position:0%
+you end up with these disulfide bonds on
+ 
+
+ align:start position:0%
+you end up with these disulfide bonds on
+proteins why does
+
+ align:start position:0%
+proteins why does
+ 
+
+ align:start position:0%
+proteins why does
+cysteine tend to get oxidized outside
+
+ align:start position:0%
+cysteine tend to get oxidized outside
+ 
+
+ align:start position:0%
+cysteine tend to get oxidized outside
+the cell
+
+ align:start position:0%
+the cell
+ 
+
+ align:start position:0%
+the cell
+well there's lots of oxygen in our
+
+ align:start position:0%
+well there's lots of oxygen in our
+ 
+
+ align:start position:0%
+well there's lots of oxygen in our
+atmosphere
+
+ align:start position:0%
+atmosphere
+ 
+
+ align:start position:0%
+atmosphere
+oxygen's a good electron acceptor it's
+
+ align:start position:0%
+oxygen's a good electron acceptor it's
+ 
+
+ align:start position:0%
+oxygen's a good electron acceptor it's
+very good at oxidation
+
+ align:start position:0%
+very good at oxidation
+ 
+
+ align:start position:0%
+very good at oxidation
+in fact that's what gives it this
+
+ align:start position:0%
+in fact that's what gives it this
+ 
+
+ align:start position:0%
+in fact that's what gives it this
+property that makes oxidative
+
+ align:start position:0%
+property that makes oxidative
+ 
+
+ align:start position:0%
+property that makes oxidative
+phosphorylation work
+
+ align:start position:0%
+phosphorylation work
+ 
+
+ align:start position:0%
+phosphorylation work
+and so it turns out that these cysteines
+
+ align:start position:0%
+and so it turns out that these cysteines
+ 
+
+ align:start position:0%
+and so it turns out that these cysteines
+these sulfhydryl groups
+
+ align:start position:0%
+these sulfhydryl groups
+ 
+
+ align:start position:0%
+these sulfhydryl groups
+like to give their electrons to oxygen
+
+ align:start position:0%
+like to give their electrons to oxygen
+ 
+
+ align:start position:0%
+like to give their electrons to oxygen
+and that leads to these
+
+ align:start position:0%
+and that leads to these
+ 
+
+ align:start position:0%
+and that leads to these
+more oxidized things outside the cell
+
+ align:start position:0%
+more oxidized things outside the cell
+ 
+
+ align:start position:0%
+more oxidized things outside the cell
+in fact oxygen is very good at accepting
+
+ align:start position:0%
+in fact oxygen is very good at accepting
+ 
+
+ align:start position:0%
+in fact oxygen is very good at accepting
+electrons from lots of donors
+
+ align:start position:0%
+electrons from lots of donors
+ 
+
+ align:start position:0%
+electrons from lots of donors
+okay so if you have iron two plus
+
+ align:start position:0%
+okay so if you have iron two plus
+ 
+
+ align:start position:0%
+okay so if you have iron two plus
+sitting around outside the cell oxygen
+
+ align:start position:0%
+sitting around outside the cell oxygen
+ 
+
+ align:start position:0%
+sitting around outside the cell oxygen
+is very good at oxidizing that iron two
+
+ align:start position:0%
+is very good at oxidizing that iron two
+ 
+
+ align:start position:0%
+is very good at oxidizing that iron two
+plus to iron three plus that's rust
+
+ align:start position:0%
+plus to iron three plus that's rust
+ 
+
+ align:start position:0%
+plus to iron three plus that's rust
+okay and this process in the end
+
+ align:start position:0%
+okay and this process in the end
+ 
+
+ align:start position:0%
+okay and this process in the end
+ends up transferring electrons to oxygen
+
+ align:start position:0%
+ends up transferring electrons to oxygen
+ 
+
+ align:start position:0%
+ends up transferring electrons to oxygen
+and can generate lots of oxygen species
+
+ align:start position:0%
+and can generate lots of oxygen species
+ 
+
+ align:start position:0%
+and can generate lots of oxygen species
+including oxygen radicals
+
+ align:start position:0%
+including oxygen radicals
+ 
+
+ align:start position:0%
+including oxygen radicals
+so you can get things like this o2 minus
+
+ align:start position:0%
+so you can get things like this o2 minus
+ 
+
+ align:start position:0%
+so you can get things like this o2 minus
+superoxide
+
+ align:start position:0%
+superoxide
+ 
+
+ align:start position:0%
+superoxide
+ultimately hydrogen peroxide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comes from oxygen picking up electrons
+
+ align:start position:0%
+comes from oxygen picking up electrons
+ 
+
+ align:start position:0%
+comes from oxygen picking up electrons
+and as you know very reactive molecules
+
+ align:start position:0%
+and as you know very reactive molecules
+ 
+
+ align:start position:0%
+and as you know very reactive molecules
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+can damage membranes damage proteins
+
+ align:start position:0%
+can damage membranes damage proteins
+ 
+
+ align:start position:0%
+can damage membranes damage proteins
+kill cells
+
+ align:start position:0%
+kill cells
+ 
+
+ align:start position:0%
+kill cells
+what do we use hydrogen peroxide for in
+
+ align:start position:0%
+what do we use hydrogen peroxide for in
+ 
+
+ align:start position:0%
+what do we use hydrogen peroxide for in
+daily life use it to clean wounds kills
+
+ align:start position:0%
+daily life use it to clean wounds kills
+ 
+
+ align:start position:0%
+daily life use it to clean wounds kills
+a bunch of bacteria
+
+ align:start position:0%
+a bunch of bacteria
+ 
+
+ align:start position:0%
+a bunch of bacteria
+and ultimately production of these
+
+ align:start position:0%
+and ultimately production of these
+ 
+
+ align:start position:0%
+and ultimately production of these
+so-called ros or reactive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oxygen species in excess
+
+ align:start position:0%
+oxygen species in excess
+ 
+
+ align:start position:0%
+oxygen species in excess
+can be very bad for biological systems
+
+ align:start position:0%
+can be very bad for biological systems
+ 
+
+ align:start position:0%
+can be very bad for biological systems
+and this is one of the arguments for why
+
+ align:start position:0%
+and this is one of the arguments for why
+ 
+
+ align:start position:0%
+and this is one of the arguments for why
+antioxidants are good for us they
+
+ align:start position:0%
+antioxidants are good for us they
+ 
+
+ align:start position:0%
+antioxidants are good for us they
+protect our us and ourselves from these
+
+ align:start position:0%
+protect our us and ourselves from these
+ 
+
+ align:start position:0%
+protect our us and ourselves from these
+reactive oxygen species okay
+
+ align:start position:0%
+reactive oxygen species okay
+ 
+
+ align:start position:0%
+reactive oxygen species okay
+now cells of course have endogenous ways
+
+ align:start position:0%
+now cells of course have endogenous ways
+ 
+
+ align:start position:0%
+now cells of course have endogenous ways
+to deal with this to keep
+
+ align:start position:0%
+to deal with this to keep
+ 
+
+ align:start position:0%
+to deal with this to keep
+cysteines in our cytosol reduced to keep
+
+ align:start position:0%
+cysteines in our cytosol reduced to keep
+ 
+
+ align:start position:0%
+cysteines in our cytosol reduced to keep
+our cytosol in this reducing environment
+
+ align:start position:0%
+our cytosol in this reducing environment
+ 
+
+ align:start position:0%
+our cytosol in this reducing environment
+prevent this
+
+ align:start position:0%
+prevent this
+ 
+
+ align:start position:0%
+prevent this
+ros damage and really if you're going to
+
+ align:start position:0%
+ros damage and really if you're going to
+ 
+
+ align:start position:0%
+ros damage and really if you're going to
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+things to deal with these reactive
+
+ align:start position:0%
+things to deal with these reactive
+ 
+
+ align:start position:0%
+things to deal with these reactive
+molecules what do you want well you want
+
+ align:start position:0%
+molecules what do you want well you want
+ 
+
+ align:start position:0%
+molecules what do you want well you want
+something that's going to
+
+ align:start position:0%
+something that's going to
+ 
+
+ align:start position:0%
+something that's going to
+buffer the damage that these things can
+
+ align:start position:0%
+buffer the damage that these things can
+ 
+
+ align:start position:0%
+buffer the damage that these things can
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+cause that is if these things are going
+
+ align:start position:0%
+cause that is if these things are going
+ 
+
+ align:start position:0%
+cause that is if these things are going
+to react with lipids and proteins and
+
+ align:start position:0%
+to react with lipids and proteins and
+ 
+
+ align:start position:0%
+to react with lipids and proteins and
+cause damage
+
+ align:start position:0%
+cause damage
+ 
+
+ align:start position:0%
+cause damage
+and you want to keep the cytosol reduced
+
+ align:start position:0%
+and you want to keep the cytosol reduced
+ 
+
+ align:start position:0%
+and you want to keep the cytosol reduced
+you really want to have a series of
+
+ align:start position:0%
+you really want to have a series of
+ 
+
+ align:start position:0%
+you really want to have a series of
+molecules that will actually
+
+ align:start position:0%
+molecules that will actually
+ 
+
+ align:start position:0%
+molecules that will actually
+instead undergo this process before it
+
+ align:start position:0%
+instead undergo this process before it
+ 
+
+ align:start position:0%
+instead undergo this process before it
+can damage critical structures
+
+ align:start position:0%
+can damage critical structures
+ 
+
+ align:start position:0%
+can damage critical structures
+in the cell and a key system cells used
+
+ align:start position:0%
+in the cell and a key system cells used
+ 
+
+ align:start position:0%
+in the cell and a key system cells used
+to do this
+
+ align:start position:0%
+to do this
+ 
+
+ align:start position:0%
+to do this
+is something called glutathione
+
+ align:start position:0%
+is something called glutathione
+ 
+
+ align:start position:0%
+is something called glutathione
+so what is glutathione well glutathione
+
+ align:start position:0%
+so what is glutathione well glutathione
+ 
+
+ align:start position:0%
+so what is glutathione well glutathione
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+small molecule tripeptide all right and
+
+ align:start position:0%
+small molecule tripeptide all right and
+ 
+
+ align:start position:0%
+small molecule tripeptide all right and
+it's among the most
+
+ align:start position:0%
+it's among the most
+ 
+
+ align:start position:0%
+it's among the most
+abundant small molecules found in
+
+ align:start position:0%
+abundant small molecules found in
+ 
+
+ align:start position:0%
+abundant small molecules found in
+cells and effectively what glutathione
+
+ align:start position:0%
+cells and effectively what glutathione
+ 
+
+ align:start position:0%
+cells and effectively what glutathione
+does is it serves this purpose of
+
+ align:start position:0%
+does is it serves this purpose of
+ 
+
+ align:start position:0%
+does is it serves this purpose of
+reacting with
+
+ align:start position:0%
+reacting with
+ 
+
+ align:start position:0%
+reacting with
+nasty stuff before it can damage other
+
+ align:start position:0%
+nasty stuff before it can damage other
+ 
+
+ align:start position:0%
+nasty stuff before it can damage other
+biomolecules and hurt the cell
+
+ align:start position:0%
+biomolecules and hurt the cell
+ 
+
+ align:start position:0%
+biomolecules and hurt the cell
+and so by tripeptide what it is is it's
+
+ align:start position:0%
+and so by tripeptide what it is is it's
+ 
+
+ align:start position:0%
+and so by tripeptide what it is is it's
+a tripeptide of
+
+ align:start position:0%
+a tripeptide of
+ 
+
+ align:start position:0%
+a tripeptide of
+glutamate with a gamma peptide bond
+
+ align:start position:0%
+glutamate with a gamma peptide bond
+ 
+
+ align:start position:0%
+glutamate with a gamma peptide bond
+to glycine and then cysteine so
+
+ align:start position:0%
+to glycine and then cysteine so
+ 
+
+ align:start position:0%
+to glycine and then cysteine so
+glutamate glycine cysteine
+
+ align:start position:0%
+glutamate glycine cysteine
+ 
+
+ align:start position:0%
+glutamate glycine cysteine
+tripeptide that looks like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this here is the amino acid
+
+ align:start position:0%
+okay so this here is the amino acid
+ 
+
+ align:start position:0%
+okay so this here is the amino acid
+glutamate
+
+ align:start position:0%
+glutamate
+ 
+
+ align:start position:0%
+glutamate
+here's the um the alpha carbon
+
+ align:start position:0%
+here's the um the alpha carbon
+ 
+
+ align:start position:0%
+here's the um the alpha carbon
+with the carboxylic acid and the amine
+
+ align:start position:0%
+with the carboxylic acid and the amine
+ 
+
+ align:start position:0%
+with the carboxylic acid and the amine
+group so you would typically think of
+
+ align:start position:0%
+group so you would typically think of
+ 
+
+ align:start position:0%
+group so you would typically think of
+the peptide
+
+ align:start position:0%
+the peptide
+ 
+
+ align:start position:0%
+the peptide
+bond if glutamate was in a chain as
+
+ align:start position:0%
+bond if glutamate was in a chain as
+ 
+
+ align:start position:0%
+bond if glutamate was in a chain as
+being from this nitrogen to the next
+
+ align:start position:0%
+being from this nitrogen to the next
+ 
+
+ align:start position:0%
+being from this nitrogen to the next
+amino acid and that carbon
+
+ align:start position:0%
+amino acid and that carbon
+ 
+
+ align:start position:0%
+amino acid and that carbon
+to the next amino acid but in this case
+
+ align:start position:0%
+to the next amino acid but in this case
+ 
+
+ align:start position:0%
+to the next amino acid but in this case
+it uses the nitrogen on the side chain
+
+ align:start position:0%
+it uses the nitrogen on the side chain
+ 
+
+ align:start position:0%
+it uses the nitrogen on the side chain
+the so-called
+
+ align:start position:0%
+the so-called
+ 
+
+ align:start position:0%
+the so-called
+gamma linkage here to form a peptide
+
+ align:start position:0%
+gamma linkage here to form a peptide
+ 
+
+ align:start position:0%
+gamma linkage here to form a peptide
+bond
+
+ align:start position:0%
+bond
+ 
+
+ align:start position:0%
+bond
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whoops sorry
+
+ align:start position:0%
+whoops sorry
+ 
+
+ align:start position:0%
+whoops sorry
+this would be glutamic acid it uses this
+
+ align:start position:0%
+this would be glutamic acid it uses this
+ 
+
+ align:start position:0%
+this would be glutamic acid it uses this
+gamma carboxylic acid on the side chain
+
+ align:start position:0%
+gamma carboxylic acid on the side chain
+ 
+
+ align:start position:0%
+gamma carboxylic acid on the side chain
+of glutamate
+
+ align:start position:0%
+of glutamate
+ 
+
+ align:start position:0%
+of glutamate
+to form a peptide bond
+
+ align:start position:0%
+to form a peptide bond
+ 
+
+ align:start position:0%
+to form a peptide bond
+with glycine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is
+
+ align:start position:0%
+okay so this is
+ 
+
+ align:start position:0%
+okay so this is
+glutamate this is
+
+ align:start position:0%
+glutamate this is
+ 
+
+ align:start position:0%
+glutamate this is
+glycine and then this has a peptide bond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+too
+
+ align:start position:0%
+too
+ 
+
+ align:start position:0%
+too
+cysteine which contributes that
+
+ align:start position:0%
+cysteine which contributes that
+ 
+
+ align:start position:0%
+cysteine which contributes that
+sulfhydryl group that can either exist
+
+ align:start position:0%
+sulfhydryl group that can either exist
+ 
+
+ align:start position:0%
+sulfhydryl group that can either exist
+in this reduced form or if there's
+
+ align:start position:0%
+in this reduced form or if there's
+ 
+
+ align:start position:0%
+in this reduced form or if there's
+two of them together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can go into this oxidized form
+
+ align:start position:0%
+can go into this oxidized form
+ 
+
+ align:start position:0%
+can go into this oxidized form
+and so often this is drawn as
+
+ align:start position:0%
+and so often this is drawn as
+ 
+
+ align:start position:0%
+and so often this is drawn as
+glutathione gsh in the reduced form
+
+ align:start position:0%
+glutathione gsh in the reduced form
+ 
+
+ align:start position:0%
+glutathione gsh in the reduced form
+and if you have two glutathione
+
+ align:start position:0%
+and if you have two glutathione
+ 
+
+ align:start position:0%
+and if you have two glutathione
+molecules
+
+ align:start position:0%
+molecules
+ 
+
+ align:start position:0%
+molecules
+that then basically form a disulfide
+
+ align:start position:0%
+that then basically form a disulfide
+ 
+
+ align:start position:0%
+that then basically form a disulfide
+bond
+
+ align:start position:0%
+bond
+ 
+
+ align:start position:0%
+bond
+to give you this gssg oxidized
+
+ align:start position:0%
+to give you this gssg oxidized
+ 
+
+ align:start position:0%
+to give you this gssg oxidized
+form of the molecule and
+
+ align:start position:0%
+form of the molecule and
+ 
+
+ align:start position:0%
+form of the molecule and
+nadph plays a key role in the cell
+
+ align:start position:0%
+nadph plays a key role in the cell
+ 
+
+ align:start position:0%
+nadph plays a key role in the cell
+because that's an oxidation reduction
+
+ align:start position:0%
+because that's an oxidation reduction
+ 
+
+ align:start position:0%
+because that's an oxidation reduction
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+in keeping glutathione in the reduced
+
+ align:start position:0%
+in keeping glutathione in the reduced
+ 
+
+ align:start position:0%
+in keeping glutathione in the reduced
+form so if you have two
+
+ align:start position:0%
+form so if you have two
+ 
+
+ align:start position:0%
+form so if you have two
+gsh molecules that can cycle to a
+
+ align:start position:0%
+gsh molecules that can cycle to a
+ 
+
+ align:start position:0%
+gsh molecules that can cycle to a
+oxidized gssg so
+
+ align:start position:0%
+oxidized gssg so
+ 
+
+ align:start position:0%
+oxidized gssg so
+this is reduced this is
+
+ align:start position:0%
+this is reduced this is
+ 
+
+ align:start position:0%
+this is reduced this is
+oxidized on the other side you can
+
+ align:start position:0%
+oxidized on the other side you can
+ 
+
+ align:start position:0%
+oxidized on the other side you can
+cycle those electrons if something gets
+
+ align:start position:0%
+cycle those electrons if something gets
+ 
+
+ align:start position:0%
+cycle those electrons if something gets
+oxidized something else has to be
+
+ align:start position:0%
+oxidized something else has to be
+ 
+
+ align:start position:0%
+oxidized something else has to be
+reduced
+
+ align:start position:0%
+reduced
+ 
+
+ align:start position:0%
+reduced
+so you can have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nadp plus and nadph
+
+ align:start position:0%
+nadp plus and nadph
+ 
+
+ align:start position:0%
+nadp plus and nadph
+this is reduced this is
+
+ align:start position:0%
+this is reduced this is
+ 
+
+ align:start position:0%
+this is reduced this is
+oxidized and so by maintaining
+
+ align:start position:0%
+oxidized and so by maintaining
+ 
+
+ align:start position:0%
+oxidized and so by maintaining
+a high ratio of nadph to nadp
+
+ align:start position:0%
+a high ratio of nadph to nadp
+ 
+
+ align:start position:0%
+a high ratio of nadph to nadp
+plus you can keep a high ratio
+
+ align:start position:0%
+plus you can keep a high ratio
+ 
+
+ align:start position:0%
+plus you can keep a high ratio
+of reduced to oxidized glutathione in
+
+ align:start position:0%
+of reduced to oxidized glutathione in
+ 
+
+ align:start position:0%
+of reduced to oxidized glutathione in
+the cell
+
+ align:start position:0%
+the cell
+ 
+
+ align:start position:0%
+the cell
+and keep the cell in a protected
+
+ align:start position:0%
+and keep the cell in a protected
+ 
+
+ align:start position:0%
+and keep the cell in a protected
+reducing environment
+
+ align:start position:0%
+reducing environment
+ 
+
+ align:start position:0%
+reducing environment
+where you have these glutathione
+
+ align:start position:0%
+where you have these glutathione
+ 
+
+ align:start position:0%
+where you have these glutathione
+molecules to
+
+ align:start position:0%
+molecules to
+ 
+
+ align:start position:0%
+molecules to
+react with other things before it causes
+
+ align:start position:0%
+react with other things before it causes
+ 
+
+ align:start position:0%
+react with other things before it causes
+damage
+
+ align:start position:0%
+damage
+ 
+
+ align:start position:0%
+damage
+to the cell all right a little bit of a
+
+ align:start position:0%
+to the cell all right a little bit of a
+ 
+
+ align:start position:0%
+to the cell all right a little bit of a
+diversion
+
+ align:start position:0%
+diversion
+ 
+
+ align:start position:0%
+diversion
+but a very important system that cells
+
+ align:start position:0%
+but a very important system that cells
+ 
+
+ align:start position:0%
+but a very important system that cells
+use related to oxidation reduction and
+
+ align:start position:0%
+use related to oxidation reduction and
+ 
+
+ align:start position:0%
+use related to oxidation reduction and
+nadph
+
+ align:start position:0%
+nadph
+ 
+
+ align:start position:0%
+nadph
+and needed a place to talk about it
+
+ align:start position:0%
+and needed a place to talk about it
+ 
+
+ align:start position:0%
+and needed a place to talk about it
+somewhere in the course
+
+ align:start position:0%
+somewhere in the course
+ 
+
+ align:start position:0%
+somewhere in the course
+all right now back to photosynthesis
+
+ align:start position:0%
+all right now back to photosynthesis
+ 
+
+ align:start position:0%
+all right now back to photosynthesis
+now for photosynthesis this reduced
+
+ align:start position:0%
+now for photosynthesis this reduced
+ 
+
+ align:start position:0%
+now for photosynthesis this reduced
+nadph molecule is of course useful
+
+ align:start position:0%
+nadph molecule is of course useful
+ 
+
+ align:start position:0%
+nadph molecule is of course useful
+because it can serve
+
+ align:start position:0%
+because it can serve
+ 
+
+ align:start position:0%
+because it can serve
+as a source of electrons to donate
+
+ align:start position:0%
+as a source of electrons to donate
+ 
+
+ align:start position:0%
+as a source of electrons to donate
+carbons
+
+ align:start position:0%
+carbons
+ 
+
+ align:start position:0%
+carbons
+to reduce co2 so if you're going to
+
+ align:start position:0%
+to reduce co2 so if you're going to
+ 
+
+ align:start position:0%
+to reduce co2 so if you're going to
+reduce co2
+
+ align:start position:0%
+reduce co2
+ 
+
+ align:start position:0%
+reduce co2
+to make carbohydrate or fat
+
+ align:start position:0%
+to make carbohydrate or fat
+ 
+
+ align:start position:0%
+to make carbohydrate or fat
+you need those source of electrons those
+
+ align:start position:0%
+you need those source of electrons those
+ 
+
+ align:start position:0%
+you need those source of electrons those
+can come from nadph which can be
+
+ align:start position:0%
+can come from nadph which can be
+ 
+
+ align:start position:0%
+can come from nadph which can be
+oxidized
+
+ align:start position:0%
+oxidized
+ 
+
+ align:start position:0%
+oxidized
+to nadp plus
+
+ align:start position:0%
+to nadp plus
+ 
+
+ align:start position:0%
+to nadp plus
+and so perhaps at this point you've
+
+ align:start position:0%
+and so perhaps at this point you've
+ 
+
+ align:start position:0%
+and so perhaps at this point you've
+already guessed or maybe already know
+
+ align:start position:0%
+already guessed or maybe already know
+ 
+
+ align:start position:0%
+already guessed or maybe already know
+that photosynthesis uses the favorable
+
+ align:start position:0%
+that photosynthesis uses the favorable
+ 
+
+ align:start position:0%
+that photosynthesis uses the favorable
+electron transfer from water
+
+ align:start position:0%
+electron transfer from water
+ 
+
+ align:start position:0%
+electron transfer from water
+to generate nadph
+
+ align:start position:0%
+to generate nadph
+ 
+
+ align:start position:0%
+to generate nadph
+and to do that you use the energy of the
+
+ align:start position:0%
+and to do that you use the energy of the
+ 
+
+ align:start position:0%
+and to do that you use the energy of the
+sun
+
+ align:start position:0%
+sun
+ 
+
+ align:start position:0%
+sun
+now of course if you're going to do a
+
+ align:start position:0%
+now of course if you're going to do a
+ 
+
+ align:start position:0%
+now of course if you're going to do a
+favorable electron
+
+ align:start position:0%
+favorable electron
+ 
+
+ align:start position:0%
+favorable electron
+transfer that can be
+
+ align:start position:0%
+transfer that can be
+ 
+
+ align:start position:0%
+transfer that can be
+coupled just like we talked about for
+
+ align:start position:0%
+coupled just like we talked about for
+ 
+
+ align:start position:0%
+coupled just like we talked about for
+oxidative phosphorylation
+
+ align:start position:0%
+oxidative phosphorylation
+ 
+
+ align:start position:0%
+oxidative phosphorylation
+to make delta psi delta ph
+
+ align:start position:0%
+to make delta psi delta ph
+ 
+
+ align:start position:0%
+to make delta psi delta ph
+and if we can use that favorable
+
+ align:start position:0%
+and if we can use that favorable
+ 
+
+ align:start position:0%
+and if we can use that favorable
+electron transfer to make delta psi
+
+ align:start position:0%
+electron transfer to make delta psi
+ 
+
+ align:start position:0%
+electron transfer to make delta psi
+delta ph we can also use it to do other
+
+ align:start position:0%
+delta ph we can also use it to do other
+ 
+
+ align:start position:0%
+delta ph we can also use it to do other
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+including making atp exactly
+
+ align:start position:0%
+including making atp exactly
+ 
+
+ align:start position:0%
+including making atp exactly
+as we described for oxidative
+
+ align:start position:0%
+as we described for oxidative
+ 
+
+ align:start position:0%
+as we described for oxidative
+phosphorylation
+
+ align:start position:0%
+phosphorylation
+ 
+
+ align:start position:0%
+phosphorylation
+and at the highest level this is exactly
+
+ align:start position:0%
+and at the highest level this is exactly
+ 
+
+ align:start position:0%
+and at the highest level this is exactly
+how photosynthesis traps solar energy
+
+ align:start position:0%
+how photosynthesis traps solar energy
+ 
+
+ align:start position:0%
+how photosynthesis traps solar energy
+and uses that energy to both remake
+
+ align:start position:0%
+and uses that energy to both remake
+ 
+
+ align:start position:0%
+and uses that energy to both remake
+reduced carbon
+
+ align:start position:0%
+reduced carbon
+ 
+
+ align:start position:0%
+reduced carbon
+and generates a battery
+
+ align:start position:0%
+and generates a battery
+ 
+
+ align:start position:0%
+and generates a battery
+for the photosynthetic organism they can
+
+ align:start position:0%
+for the photosynthetic organism they can
+ 
+
+ align:start position:0%
+for the photosynthetic organism they can
+be used to make atp
+
+ align:start position:0%
+be used to make atp
+ 
+
+ align:start position:0%
+be used to make atp
+or do other work provided that
+
+ align:start position:0%
+or do other work provided that
+ 
+
+ align:start position:0%
+or do other work provided that
+sun is available and so
+
+ align:start position:0%
+sun is available and so
+ 
+
+ align:start position:0%
+sun is available and so
+classically photosynthesis can really be
+
+ align:start position:0%
+classically photosynthesis can really be
+ 
+
+ align:start position:0%
+classically photosynthesis can really be
+separated into i guess two distinct
+
+ align:start position:0%
+separated into i guess two distinct
+ 
+
+ align:start position:0%
+separated into i guess two distinct
+processes
+
+ align:start position:0%
+processes
+ 
+
+ align:start position:0%
+processes
+all right so you have this process
+
+ align:start position:0%
+all right so you have this process
+ 
+
+ align:start position:0%
+all right so you have this process
+of taking solar energy
+
+ align:start position:0%
+of taking solar energy
+ 
+
+ align:start position:0%
+of taking solar energy
+okay using that solar energy
+
+ align:start position:0%
+okay using that solar energy
+ 
+
+ align:start position:0%
+okay using that solar energy
+to charge up a battery delta psi delta
+
+ align:start position:0%
+to charge up a battery delta psi delta
+ 
+
+ align:start position:0%
+to charge up a battery delta psi delta
+ph
+
+ align:start position:0%
+ph
+ 
+
+ align:start position:0%
+ph
+which of course can be used to generate
+
+ align:start position:0%
+which of course can be used to generate
+ 
+
+ align:start position:0%
+which of course can be used to generate
+atp or do other work
+
+ align:start position:0%
+atp or do other work
+ 
+
+ align:start position:0%
+atp or do other work
+and at the same time gives you
+
+ align:start position:0%
+and at the same time gives you
+ 
+
+ align:start position:0%
+and at the same time gives you
+an electron donor nadph
+
+ align:start position:0%
+an electron donor nadph
+ 
+
+ align:start position:0%
+an electron donor nadph
+that is useful to generate reduced
+
+ align:start position:0%
+that is useful to generate reduced
+ 
+
+ align:start position:0%
+that is useful to generate reduced
+carbon
+
+ align:start position:0%
+carbon
+ 
+
+ align:start position:0%
+carbon
+once you generate high atp adp ratio
+
+ align:start position:0%
+once you generate high atp adp ratio
+ 
+
+ align:start position:0%
+once you generate high atp adp ratio
+high nadph and adp ratio
+
+ align:start position:0%
+high nadph and adp ratio
+ 
+
+ align:start position:0%
+high nadph and adp ratio
+now we can use that to be coupled to do
+
+ align:start position:0%
+now we can use that to be coupled to do
+ 
+
+ align:start position:0%
+now we can use that to be coupled to do
+something else unfavorable and that
+
+ align:start position:0%
+something else unfavorable and that
+ 
+
+ align:start position:0%
+something else unfavorable and that
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+something like reduced co2
+
+ align:start position:0%
+something like reduced co2
+ 
+
+ align:start position:0%
+something like reduced co2
+to generate a carbohydrate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and typically when we talk about
+
+ align:start position:0%
+and typically when we talk about
+ 
+
+ align:start position:0%
+and typically when we talk about
+photosynthesis
+
+ align:start position:0%
+photosynthesis
+ 
+
+ align:start position:0%
+photosynthesis
+the way it's often described is how you
+
+ align:start position:0%
+the way it's often described is how you
+ 
+
+ align:start position:0%
+the way it's often described is how you
+reduce co2 to carbohydrate and we'll do
+
+ align:start position:0%
+reduce co2 to carbohydrate and we'll do
+ 
+
+ align:start position:0%
+reduce co2 to carbohydrate and we'll do
+that too
+
+ align:start position:0%
+that too
+ 
+
+ align:start position:0%
+that too
+but of course we'll then see once you
+
+ align:start position:0%
+but of course we'll then see once you
+ 
+
+ align:start position:0%
+but of course we'll then see once you
+have carbohydrates
+
+ align:start position:0%
+have carbohydrates
+ 
+
+ align:start position:0%
+have carbohydrates
+obviously it's just further reduction of
+
+ align:start position:0%
+obviously it's just further reduction of
+ 
+
+ align:start position:0%
+obviously it's just further reduction of
+carbon to make
+
+ align:start position:0%
+carbon to make
+ 
+
+ align:start position:0%
+carbon to make
+fatty acids and lipids
+
+ align:start position:0%
+fatty acids and lipids
+ 
+
+ align:start position:0%
+fatty acids and lipids
+we'll discuss later how we can use those
+
+ align:start position:0%
+we'll discuss later how we can use those
+ 
+
+ align:start position:0%
+we'll discuss later how we can use those
+to make amino acids which
+
+ align:start position:0%
+to make amino acids which
+ 
+
+ align:start position:0%
+to make amino acids which
+allow you to make proteins and of course
+
+ align:start position:0%
+allow you to make proteins and of course
+ 
+
+ align:start position:0%
+allow you to make proteins and of course
+we can also
+
+ align:start position:0%
+we can also
+ 
+
+ align:start position:0%
+we can also
+store
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those carbohydrates as disaccharides or
+
+ align:start position:0%
+those carbohydrates as disaccharides or
+ 
+
+ align:start position:0%
+those carbohydrates as disaccharides or
+polysaccharides storage sugars
+
+ align:start position:0%
+polysaccharides storage sugars
+ 
+
+ align:start position:0%
+polysaccharides storage sugars
+which is what plants do they make starch
+
+ align:start position:0%
+which is what plants do they make starch
+ 
+
+ align:start position:0%
+which is what plants do they make starch
+they make sucrose etc
+
+ align:start position:0%
+they make sucrose etc
+ 
+
+ align:start position:0%
+they make sucrose etc
+as a way to store that reduced carbon
+
+ align:start position:0%
+as a way to store that reduced carbon
+ 
+
+ align:start position:0%
+as a way to store that reduced carbon
+so that they can have a source of energy
+
+ align:start position:0%
+so that they can have a source of energy
+ 
+
+ align:start position:0%
+so that they can have a source of energy
+do the oxidation reactions
+
+ align:start position:0%
+do the oxidation reactions
+ 
+
+ align:start position:0%
+do the oxidation reactions
+to deal with their energetic needs when
+
+ align:start position:0%
+to deal with their energetic needs when
+ 
+
+ align:start position:0%
+to deal with their energetic needs when
+the sun is not shining
+
+ align:start position:0%
+the sun is not shining
+ 
+
+ align:start position:0%
+the sun is not shining
+all right so let's
+
+ align:start position:0%
+all right so let's
+ 
+
+ align:start position:0%
+all right so let's
+break down these two processes
+
+ align:start position:0%
+break down these two processes
+ 
+
+ align:start position:0%
+break down these two processes
+and so to just be very explicit the
+
+ align:start position:0%
+and so to just be very explicit the
+ 
+
+ align:start position:0%
+and so to just be very explicit the
+first part is basically
+
+ align:start position:0%
+first part is basically
+ 
+
+ align:start position:0%
+first part is basically
+trapping energy to make a battery
+
+ align:start position:0%
+trapping energy to make a battery
+ 
+
+ align:start position:0%
+trapping energy to make a battery
+all right and so this means that we need
+
+ align:start position:0%
+all right and so this means that we need
+ 
+
+ align:start position:0%
+all right and so this means that we need
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+generate delta psi delta ph
+
+ align:start position:0%
+generate delta psi delta ph
+ 
+
+ align:start position:0%
+generate delta psi delta ph
+via favorable electron transport exactly
+
+ align:start position:0%
+via favorable electron transport exactly
+ 
+
+ align:start position:0%
+via favorable electron transport exactly
+what we described for oxfos but of
+
+ align:start position:0%
+what we described for oxfos but of
+ 
+
+ align:start position:0%
+what we described for oxfos but of
+course photosynthesis was first
+
+ align:start position:0%
+course photosynthesis was first
+ 
+
+ align:start position:0%
+course photosynthesis was first
+this would then allow us to use atp to
+
+ align:start position:0%
+this would then allow us to use atp to
+ 
+
+ align:start position:0%
+this would then allow us to use atp to
+fill our energy needs
+
+ align:start position:0%
+fill our energy needs
+ 
+
+ align:start position:0%
+fill our energy needs
+and we get nadph if we set it up in the
+
+ align:start position:0%
+and we get nadph if we set it up in the
+ 
+
+ align:start position:0%
+and we get nadph if we set it up in the
+right way
+
+ align:start position:0%
+right way
+ 
+
+ align:start position:0%
+right way
+which is important for carbon reduction
+
+ align:start position:0%
+which is important for carbon reduction
+ 
+
+ align:start position:0%
+which is important for carbon reduction
+then we need to use nadph and atp via
+
+ align:start position:0%
+then we need to use nadph and atp via
+ 
+
+ align:start position:0%
+then we need to use nadph and atp via
+pathways to describe how we can use
+
+ align:start position:0%
+pathways to describe how we can use
+ 
+
+ align:start position:0%
+pathways to describe how we can use
+that to reduce co2 and ultimately
+
+ align:start position:0%
+that to reduce co2 and ultimately
+ 
+
+ align:start position:0%
+that to reduce co2 and ultimately
+produce
+
+ align:start position:0%
+produce
+ 
+
+ align:start position:0%
+produce
+glucose which allows us to store energy
+
+ align:start position:0%
+glucose which allows us to store energy
+ 
+
+ align:start position:0%
+glucose which allows us to store energy
+for later
+
+ align:start position:0%
+for later
+ 
+
+ align:start position:0%
+for later
+all right so that is at a very high
+
+ align:start position:0%
+all right so that is at a very high
+ 
+
+ align:start position:0%
+all right so that is at a very high
+level what photosynthesis is
+
+ align:start position:0%
+level what photosynthesis is
+ 
+
+ align:start position:0%
+level what photosynthesis is
+and of course this occurs in plants
+
+ align:start position:0%
+and of course this occurs in plants
+ 
+
+ align:start position:0%
+and of course this occurs in plants
+all right but perhaps more importantly
+
+ align:start position:0%
+all right but perhaps more importantly
+ 
+
+ align:start position:0%
+all right but perhaps more importantly
+it also occurs
+
+ align:start position:0%
+it also occurs
+ 
+
+ align:start position:0%
+it also occurs
+in algae and other
+
+ align:start position:0%
+in algae and other
+ 
+
+ align:start position:0%
+in algae and other
+unicellular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eukaryotes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as well as in prokaryotes photosynthetic
+
+ align:start position:0%
+as well as in prokaryotes photosynthetic
+ 
+
+ align:start position:0%
+as well as in prokaryotes photosynthetic
+prokaryotes bacteria
+
+ align:start position:0%
+prokaryotes bacteria
+ 
+
+ align:start position:0%
+prokaryotes bacteria
+and of course photosynthetic bacteria
+
+ align:start position:0%
+and of course photosynthetic bacteria
+ 
+
+ align:start position:0%
+and of course photosynthetic bacteria
+unicellular eukaryotes algae
+
+ align:start position:0%
+unicellular eukaryotes algae
+ 
+
+ align:start position:0%
+unicellular eukaryotes algae
+these really are the heroes of life
+
+ align:start position:0%
+these really are the heroes of life
+ 
+
+ align:start position:0%
+these really are the heroes of life
+these are the things that
+
+ align:start position:0%
+these are the things that
+ 
+
+ align:start position:0%
+these are the things that
+life started from and generated the
+
+ align:start position:0%
+life started from and generated the
+ 
+
+ align:start position:0%
+life started from and generated the
+oxygenated atmosphere and ultimately led
+
+ align:start position:0%
+oxygenated atmosphere and ultimately led
+ 
+
+ align:start position:0%
+oxygenated atmosphere and ultimately led
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+evolution of higher plants but also
+
+ align:start position:0%
+evolution of higher plants but also
+ 
+
+ align:start position:0%
+evolution of higher plants but also
+enabled
+
+ align:start position:0%
+enabled
+ 
+
+ align:start position:0%
+enabled
+the formation of animal life and really
+
+ align:start position:0%
+the formation of animal life and really
+ 
+
+ align:start position:0%
+the formation of animal life and really
+anything that lives off of
+
+ align:start position:0%
+anything that lives off of
+ 
+
+ align:start position:0%
+anything that lives off of
+eating other organisms
+
+ align:start position:0%
+eating other organisms
+ 
+
+ align:start position:0%
+eating other organisms
+just a few facts about photosynthesis
+
+ align:start position:0%
+just a few facts about photosynthesis
+ 
+
+ align:start position:0%
+just a few facts about photosynthesis
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+it's really quite an amazing process and
+
+ align:start position:0%
+it's really quite an amazing process and
+ 
+
+ align:start position:0%
+it's really quite an amazing process and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+about 10 to the 17th kilojoules
+
+ align:start position:0%
+about 10 to the 17th kilojoules
+ 
+
+ align:start position:0%
+about 10 to the 17th kilojoules
+at least by some estimate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of energy is harvested
+
+ align:start position:0%
+of energy is harvested
+ 
+
+ align:start position:0%
+of energy is harvested
+on our planet from photosynthesis every
+
+ align:start position:0%
+on our planet from photosynthesis every
+ 
+
+ align:start position:0%
+on our planet from photosynthesis every
+year
+
+ align:start position:0%
+year
+ 
+
+ align:start position:0%
+year
+just to give you a perspective of what
+
+ align:start position:0%
+just to give you a perspective of what
+ 
+
+ align:start position:0%
+just to give you a perspective of what
+that number means that is
+
+ align:start position:0%
+that number means that is
+ 
+
+ align:start position:0%
+that number means that is
+10 times the worldwide energy use by all
+
+ align:start position:0%
+10 times the worldwide energy use by all
+ 
+
+ align:start position:0%
+10 times the worldwide energy use by all
+people on earth so if you add up all the
+
+ align:start position:0%
+people on earth so if you add up all the
+ 
+
+ align:start position:0%
+people on earth so if you add up all the
+energy that we as humans use in the
+
+ align:start position:0%
+energy that we as humans use in the
+ 
+
+ align:start position:0%
+energy that we as humans use in the
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+it is tenfold less than the amount of
+
+ align:start position:0%
+it is tenfold less than the amount of
+ 
+
+ align:start position:0%
+it is tenfold less than the amount of
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+that is harvested by photosynthesis
+
+ align:start position:0%
+that is harvested by photosynthesis
+ 
+
+ align:start position:0%
+that is harvested by photosynthesis
+by photosynthetic organisms around the
+
+ align:start position:0%
+by photosynthetic organisms around the
+ 
+
+ align:start position:0%
+by photosynthetic organisms around the
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+photosynthetic organisms when they do
+
+ align:start position:0%
+photosynthetic organisms when they do
+ 
+
+ align:start position:0%
+photosynthetic organisms when they do
+this consume
+
+ align:start position:0%
+this consume
+ 
+
+ align:start position:0%
+this consume
+co2 all right so that is removing
+
+ align:start position:0%
+co2 all right so that is removing
+ 
+
+ align:start position:0%
+co2 all right so that is removing
+co2 the greenhouse gas from
+
+ align:start position:0%
+co2 the greenhouse gas from
+ 
+
+ align:start position:0%
+co2 the greenhouse gas from
+our atmosphere and this occurs
+
+ align:start position:0%
+our atmosphere and this occurs
+ 
+
+ align:start position:0%
+our atmosphere and this occurs
+on a massive scale so this is better
+
+ align:start position:0%
+on a massive scale so this is better
+ 
+
+ align:start position:0%
+on a massive scale so this is better
+than any
+
+ align:start position:0%
+than any
+ 
+
+ align:start position:0%
+than any
+man-made engineering solution that we
+
+ align:start position:0%
+man-made engineering solution that we
+ 
+
+ align:start position:0%
+man-made engineering solution that we
+have come up with
+
+ align:start position:0%
+have come up with
+ 
+
+ align:start position:0%
+have come up with
+by far and i think this really
+
+ align:start position:0%
+by far and i think this really
+ 
+
+ align:start position:0%
+by far and i think this really
+illustrates the awesome power of biology
+
+ align:start position:0%
+illustrates the awesome power of biology
+ 
+
+ align:start position:0%
+illustrates the awesome power of biology
+to solve some of the biggest problems
+
+ align:start position:0%
+to solve some of the biggest problems
+ 
+
+ align:start position:0%
+to solve some of the biggest problems
+that face our society
+
+ align:start position:0%
+that face our society
+ 
+
+ align:start position:0%
+that face our society
+today so world energy problems
+
+ align:start position:0%
+today so world energy problems
+ 
+
+ align:start position:0%
+today so world energy problems
+photosynthesis generates a ton
+
+ align:start position:0%
+photosynthesis generates a ton
+ 
+
+ align:start position:0%
+photosynthesis generates a ton
+of or harnesses a ton of energy
+
+ align:start position:0%
+of or harnesses a ton of energy
+ 
+
+ align:start position:0%
+of or harnesses a ton of energy
+global warming greenhouse gases
+
+ align:start position:0%
+global warming greenhouse gases
+ 
+
+ align:start position:0%
+global warming greenhouse gases
+photosynthesis
+
+ align:start position:0%
+photosynthesis
+ 
+
+ align:start position:0%
+photosynthesis
+better than almost anything at dealing
+
+ align:start position:0%
+better than almost anything at dealing
+ 
+
+ align:start position:0%
+better than almost anything at dealing
+with these
+
+ align:start position:0%
+with these
+ 
+
+ align:start position:0%
+with these
+co2 that is produced however
+
+ align:start position:0%
+co2 that is produced however
+ 
+
+ align:start position:0%
+co2 that is produced however
+this also illustrates what some of the
+
+ align:start position:0%
+this also illustrates what some of the
+ 
+
+ align:start position:0%
+this also illustrates what some of the
+problems are and what some of the issues
+
+ align:start position:0%
+problems are and what some of the issues
+ 
+
+ align:start position:0%
+problems are and what some of the issues
+are with fossil fuels because
+
+ align:start position:0%
+are with fossil fuels because
+ 
+
+ align:start position:0%
+are with fossil fuels because
+what are fossil fuels well they're
+
+ align:start position:0%
+what are fossil fuels well they're
+ 
+
+ align:start position:0%
+what are fossil fuels well they're
+effectively reduced carbon
+
+ align:start position:0%
+effectively reduced carbon
+ 
+
+ align:start position:0%
+effectively reduced carbon
+that is trapped in the ground somewhere
+
+ align:start position:0%
+that is trapped in the ground somewhere
+ 
+
+ align:start position:0%
+that is trapped in the ground somewhere
+that is effectively
+
+ align:start position:0%
+that is effectively
+ 
+
+ align:start position:0%
+that is effectively
+old photosynthesis so these are
+
+ align:start position:0%
+old photosynthesis so these are
+ 
+
+ align:start position:0%
+old photosynthesis so these are
+organisms in
+
+ align:start position:0%
+organisms in
+ 
+
+ align:start position:0%
+organisms in
+you know many many many many years ago
+
+ align:start position:0%
+you know many many many many years ago
+ 
+
+ align:start position:0%
+you know many many many many years ago
+that did photosynthesis made reduced
+
+ align:start position:0%
+that did photosynthesis made reduced
+ 
+
+ align:start position:0%
+that did photosynthesis made reduced
+carbon
+
+ align:start position:0%
+carbon
+ 
+
+ align:start position:0%
+carbon
+that was effectively trapped in the
+
+ align:start position:0%
+that was effectively trapped in the
+ 
+
+ align:start position:0%
+that was effectively trapped in the
+ground and so
+
+ align:start position:0%
+ground and so
+ 
+
+ align:start position:0%
+ground and so
+the fact that we're you know
+
+ align:start position:0%
+the fact that we're you know
+ 
+
+ align:start position:0%
+the fact that we're you know
+photosynthesis
+
+ align:start position:0%
+photosynthesis
+ 
+
+ align:start position:0%
+photosynthesis
+transduces 10 to the 17th kilojoules of
+
+ align:start position:0%
+transduces 10 to the 17th kilojoules of
+ 
+
+ align:start position:0%
+transduces 10 to the 17th kilojoules of
+energy per year
+
+ align:start position:0%
+energy per year
+ 
+
+ align:start position:0%
+energy per year
+and we're using one tenth of that amount
+
+ align:start position:0%
+and we're using one tenth of that amount
+ 
+
+ align:start position:0%
+and we're using one tenth of that amount
+of energy
+
+ align:start position:0%
+of energy
+ 
+
+ align:start position:0%
+of energy
+if that's all coming from fossil fuels
+
+ align:start position:0%
+if that's all coming from fossil fuels
+ 
+
+ align:start position:0%
+if that's all coming from fossil fuels
+that means we're using
+
+ align:start position:0%
+that means we're using
+ 
+
+ align:start position:0%
+that means we're using
+one-tenths of a year's worth of
+
+ align:start position:0%
+one-tenths of a year's worth of
+ 
+
+ align:start position:0%
+one-tenths of a year's worth of
+photosynthesis and of course not a year
+
+ align:start position:0%
+photosynthesis and of course not a year
+ 
+
+ align:start position:0%
+photosynthesis and of course not a year
+is not entirely stored in the ground
+
+ align:start position:0%
+is not entirely stored in the ground
+ 
+
+ align:start position:0%
+is not entirely stored in the ground
+per year so that's a lot of energy and
+
+ align:start position:0%
+per year so that's a lot of energy and
+ 
+
+ align:start position:0%
+per year so that's a lot of energy and
+it really comes down to
+
+ align:start position:0%
+it really comes down to
+ 
+
+ align:start position:0%
+it really comes down to
+why people say fossil fuels can't last
+
+ align:start position:0%
+why people say fossil fuels can't last
+ 
+
+ align:start position:0%
+why people say fossil fuels can't last
+forever
+
+ align:start position:0%
+forever
+ 
+
+ align:start position:0%
+forever
+and also why the net release of these
+
+ align:start position:0%
+and also why the net release of these
+ 
+
+ align:start position:0%
+and also why the net release of these
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+can change our atmosphere because of
+
+ align:start position:0%
+can change our atmosphere because of
+ 
+
+ align:start position:0%
+can change our atmosphere because of
+course once upon a time there is much
+
+ align:start position:0%
+course once upon a time there is much
+ 
+
+ align:start position:0%
+course once upon a time there is much
+more co2 in the atmosphere
+
+ align:start position:0%
+more co2 in the atmosphere
+ 
+
+ align:start position:0%
+more co2 in the atmosphere
+and photosynthesis over millennia
+
+ align:start position:0%
+and photosynthesis over millennia
+ 
+
+ align:start position:0%
+and photosynthesis over millennia
+trapping these things as fossil fuels
+
+ align:start position:0%
+trapping these things as fossil fuels
+ 
+
+ align:start position:0%
+trapping these things as fossil fuels
+really has what has lowered co2 in our
+
+ align:start position:0%
+really has what has lowered co2 in our
+ 
+
+ align:start position:0%
+really has what has lowered co2 in our
+atmosphere to the levels that they
+
+ align:start position:0%
+atmosphere to the levels that they
+ 
+
+ align:start position:0%
+atmosphere to the levels that they
+exist today and how basically
+
+ align:start position:0%
+exist today and how basically
+ 
+
+ align:start position:0%
+exist today and how basically
+burning fossil fuels on the scale that
+
+ align:start position:0%
+burning fossil fuels on the scale that
+ 
+
+ align:start position:0%
+burning fossil fuels on the scale that
+we are
+
+ align:start position:0%
+we are
+ 
+
+ align:start position:0%
+we are
+is able to change our
+
+ align:start position:0%
+is able to change our
+ 
+
+ align:start position:0%
+is able to change our
+atmosphere so you can view this both as
+
+ align:start position:0%
+atmosphere so you can view this both as
+ 
+
+ align:start position:0%
+atmosphere so you can view this both as
+glass half full and glass half empty
+
+ align:start position:0%
+glass half full and glass half empty
+ 
+
+ align:start position:0%
+glass half full and glass half empty
+it really says understanding
+
+ align:start position:0%
+it really says understanding
+ 
+
+ align:start position:0%
+it really says understanding
+photosynthesis could be a key
+
+ align:start position:0%
+photosynthesis could be a key
+ 
+
+ align:start position:0%
+photosynthesis could be a key
+to solving some of these problems but it
+
+ align:start position:0%
+to solving some of these problems but it
+ 
+
+ align:start position:0%
+to solving some of these problems but it
+also points out
+
+ align:start position:0%
+also points out
+ 
+
+ align:start position:0%
+also points out
+why some of these things might be
+
+ align:start position:0%
+why some of these things might be
+ 
+
+ align:start position:0%
+why some of these things might be
+problems to begin with
+
+ align:start position:0%
+problems to begin with
+ 
+
+ align:start position:0%
+problems to begin with
+all right now we want to discuss first
+
+ align:start position:0%
+all right now we want to discuss first
+ 
+
+ align:start position:0%
+all right now we want to discuss first
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+photosynthesis traps and energy and
+
+ align:start position:0%
+photosynthesis traps and energy and
+ 
+
+ align:start position:0%
+photosynthesis traps and energy and
+you'll see that
+
+ align:start position:0%
+you'll see that
+ 
+
+ align:start position:0%
+you'll see that
+it is similar to oxidative
+
+ align:start position:0%
+it is similar to oxidative
+ 
+
+ align:start position:0%
+it is similar to oxidative
+phosphorylation
+
+ align:start position:0%
+phosphorylation
+ 
+
+ align:start position:0%
+phosphorylation
+in many many ways okay so it's going to
+
+ align:start position:0%
+in many many ways okay so it's going to
+ 
+
+ align:start position:0%
+in many many ways okay so it's going to
+occur
+
+ align:start position:0%
+occur
+ 
+
+ align:start position:0%
+occur
+at a membrane
+
+ align:start position:0%
+at a membrane
+ 
+
+ align:start position:0%
+at a membrane
+all right it's going to
+
+ align:start position:0%
+all right it's going to
+ 
+
+ align:start position:0%
+all right it's going to
+involve a series of
+
+ align:start position:0%
+involve a series of
+ 
+
+ align:start position:0%
+involve a series of
+protein complexes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where we're going to favor we're going
+
+ align:start position:0%
+where we're going to favor we're going
+ 
+
+ align:start position:0%
+where we're going to favor we're going
+to couple
+
+ align:start position:0%
+to couple
+ 
+
+ align:start position:0%
+to couple
+favorable electron transport to
+
+ align:start position:0%
+favorable electron transport to
+ 
+
+ align:start position:0%
+favorable electron transport to
+along a electron transport chain to
+
+ align:start position:0%
+along a electron transport chain to
+ 
+
+ align:start position:0%
+along a electron transport chain to
+favor
+
+ align:start position:0%
+favor
+ 
+
+ align:start position:0%
+favor
+proton pumping that is going to generate
+
+ align:start position:0%
+proton pumping that is going to generate
+ 
+
+ align:start position:0%
+proton pumping that is going to generate
+a membrane potential delta psi
+
+ align:start position:0%
+a membrane potential delta psi
+ 
+
+ align:start position:0%
+a membrane potential delta psi
+delta ph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in order to do that of course we need
+
+ align:start position:0%
+in order to do that of course we need
+ 
+
+ align:start position:0%
+in order to do that of course we need
+favorable electron transport from
+
+ align:start position:0%
+favorable electron transport from
+ 
+
+ align:start position:0%
+favorable electron transport from
+something that is lower standard
+
+ align:start position:0%
+something that is lower standard
+ 
+
+ align:start position:0%
+something that is lower standard
+reduction potential to something that is
+
+ align:start position:0%
+reduction potential to something that is
+ 
+
+ align:start position:0%
+reduction potential to something that is
+higher standard reduction potential that
+
+ align:start position:0%
+higher standard reduction potential that
+ 
+
+ align:start position:0%
+higher standard reduction potential that
+is what is going to make it favorable
+
+ align:start position:0%
+is what is going to make it favorable
+ 
+
+ align:start position:0%
+is what is going to make it favorable
+allow proton pumping um that when it
+
+ align:start position:0%
+allow proton pumping um that when it
+ 
+
+ align:start position:0%
+allow proton pumping um that when it
+generates delta psi
+
+ align:start position:0%
+generates delta psi
+ 
+
+ align:start position:0%
+generates delta psi
+delta ph right we can now harness that
+
+ align:start position:0%
+delta ph right we can now harness that
+ 
+
+ align:start position:0%
+delta ph right we can now harness that
+as a way to
+
+ align:start position:0%
+as a way to
+ 
+
+ align:start position:0%
+as a way to
+synthesize atp
+
+ align:start position:0%
+synthesize atp
+ 
+
+ align:start position:0%
+synthesize atp
+or do other work as we've now talked
+
+ align:start position:0%
+or do other work as we've now talked
+ 
+
+ align:start position:0%
+or do other work as we've now talked
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+a lot looks a lot like oxidative
+
+ align:start position:0%
+a lot looks a lot like oxidative
+ 
+
+ align:start position:0%
+a lot looks a lot like oxidative
+phosphorylation and it makes sense
+
+ align:start position:0%
+phosphorylation and it makes sense
+ 
+
+ align:start position:0%
+phosphorylation and it makes sense
+oxidative phosphorylation came from
+
+ align:start position:0%
+oxidative phosphorylation came from
+ 
+
+ align:start position:0%
+oxidative phosphorylation came from
+photosynthesis however there's some
+
+ align:start position:0%
+photosynthesis however there's some
+ 
+
+ align:start position:0%
+photosynthesis however there's some
+really big differences
+
+ align:start position:0%
+really big differences
+ 
+
+ align:start position:0%
+really big differences
+between the two and that is in
+
+ align:start position:0%
+between the two and that is in
+ 
+
+ align:start position:0%
+between the two and that is in
+photosynthesis
+
+ align:start position:0%
+photosynthesis
+ 
+
+ align:start position:0%
+photosynthesis
+as i've already alluded to the electron
+
+ align:start position:0%
+as i've already alluded to the electron
+ 
+
+ align:start position:0%
+as i've already alluded to the electron
+donor
+
+ align:start position:0%
+donor
+ 
+
+ align:start position:0%
+donor
+is going to be water which will generate
+
+ align:start position:0%
+is going to be water which will generate
+ 
+
+ align:start position:0%
+is going to be water which will generate
+oxygen and the electron acceptor
+
+ align:start position:0%
+oxygen and the electron acceptor
+ 
+
+ align:start position:0%
+oxygen and the electron acceptor
+is nadp plus which will generate
+
+ align:start position:0%
+is nadp plus which will generate
+ 
+
+ align:start position:0%
+is nadp plus which will generate
+nad ph um
+
+ align:start position:0%
+nad ph um
+ 
+
+ align:start position:0%
+nad ph um
+and you might now be asking well how on
+
+ align:start position:0%
+and you might now be asking well how on
+ 
+
+ align:start position:0%
+and you might now be asking well how on
+earth can this be possible
+
+ align:start position:0%
+earth can this be possible
+ 
+
+ align:start position:0%
+earth can this be possible
+because remember the standard reduction
+
+ align:start position:0%
+because remember the standard reduction
+ 
+
+ align:start position:0%
+because remember the standard reduction
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+of nadh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is less than the standard reduction
+
+ align:start position:0%
+is less than the standard reduction
+ 
+
+ align:start position:0%
+is less than the standard reduction
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+of our oxygen water pair
+
+ align:start position:0%
+of our oxygen water pair
+ 
+
+ align:start position:0%
+of our oxygen water pair
+and it's really this that makes
+
+ align:start position:0%
+and it's really this that makes
+ 
+
+ align:start position:0%
+and it's really this that makes
+the change in standard reduction
+
+ align:start position:0%
+the change in standard reduction
+ 
+
+ align:start position:0%
+the change in standard reduction
+potential positive
+
+ align:start position:0%
+potential positive
+ 
+
+ align:start position:0%
+potential positive
+which means that delta g is going to be
+
+ align:start position:0%
+which means that delta g is going to be
+ 
+
+ align:start position:0%
+which means that delta g is going to be
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+which is why electron transport and
+
+ align:start position:0%
+which is why electron transport and
+ 
+
+ align:start position:0%
+which is why electron transport and
+oxidative phosphorylation is favorable
+
+ align:start position:0%
+oxidative phosphorylation is favorable
+ 
+
+ align:start position:0%
+oxidative phosphorylation is favorable
+and can be coupled to make
+
+ align:start position:0%
+and can be coupled to make
+ 
+
+ align:start position:0%
+and can be coupled to make
+delta psi delta ph
+
+ align:start position:0%
+delta psi delta ph
+ 
+
+ align:start position:0%
+delta psi delta ph
+now adding a phosphate to nadnadh
+
+ align:start position:0%
+now adding a phosphate to nadnadh
+ 
+
+ align:start position:0%
+now adding a phosphate to nadnadh
+does not change its standard reduction
+
+ align:start position:0%
+does not change its standard reduction
+ 
+
+ align:start position:0%
+does not change its standard reduction
+potential in a way that is at all
+
+ align:start position:0%
+potential in a way that is at all
+ 
+
+ align:start position:0%
+potential in a way that is at all
+meaningful
+
+ align:start position:0%
+meaningful
+ 
+
+ align:start position:0%
+meaningful
+to impact what goes on and so this is
+
+ align:start position:0%
+to impact what goes on and so this is
+ 
+
+ align:start position:0%
+to impact what goes on and so this is
+really where
+
+ align:start position:0%
+really where
+ 
+
+ align:start position:0%
+really where
+energy input from the sun becomes
+
+ align:start position:0%
+energy input from the sun becomes
+ 
+
+ align:start position:0%
+energy input from the sun becomes
+critical
+
+ align:start position:0%
+critical
+ 
+
+ align:start position:0%
+critical
+and that is it is
+
+ align:start position:0%
+and that is it is
+ 
+
+ align:start position:0%
+and that is it is
+this light energy from a photon
+
+ align:start position:0%
+this light energy from a photon
+ 
+
+ align:start position:0%
+this light energy from a photon
+that in the end makes water a good
+
+ align:start position:0%
+that in the end makes water a good
+ 
+
+ align:start position:0%
+that in the end makes water a good
+electron donor
+
+ align:start position:0%
+electron donor
+ 
+
+ align:start position:0%
+electron donor
+such that all of these other things are
+
+ align:start position:0%
+such that all of these other things are
+ 
+
+ align:start position:0%
+such that all of these other things are
+satisfied
+
+ align:start position:0%
+satisfied
+ 
+
+ align:start position:0%
+satisfied
+that electron transport is favorable
+
+ align:start position:0%
+that electron transport is favorable
+ 
+
+ align:start position:0%
+that electron transport is favorable
+going from lower to higher standard
+
+ align:start position:0%
+going from lower to higher standard
+ 
+
+ align:start position:0%
+going from lower to higher standard
+reduction potential
+
+ align:start position:0%
+reduction potential
+ 
+
+ align:start position:0%
+reduction potential
+with nadp plus ultimately being
+
+ align:start position:0%
+with nadp plus ultimately being
+ 
+
+ align:start position:0%
+with nadp plus ultimately being
+the final electron acceptor such that
+
+ align:start position:0%
+the final electron acceptor such that
+ 
+
+ align:start position:0%
+the final electron acceptor such that
+the change in standard reduction
+
+ align:start position:0%
+the change in standard reduction
+ 
+
+ align:start position:0%
+the change in standard reduction
+potential is
+
+ align:start position:0%
+potential is
+ 
+
+ align:start position:0%
+potential is
+positive and that really is
+
+ align:start position:0%
+positive and that really is
+ 
+
+ align:start position:0%
+positive and that really is
+the magic of photosynthesis and of
+
+ align:start position:0%
+the magic of photosynthesis and of
+ 
+
+ align:start position:0%
+the magic of photosynthesis and of
+course once you do that now you have
+
+ align:start position:0%
+course once you do that now you have
+ 
+
+ align:start position:0%
+course once you do that now you have
+delta psi delta ph
+
+ align:start position:0%
+delta psi delta ph
+ 
+
+ align:start position:0%
+delta psi delta ph
+you can use that to make atp do other
+
+ align:start position:0%
+you can use that to make atp do other
+ 
+
+ align:start position:0%
+you can use that to make atp do other
+work for the photosynthetic organism and
+
+ align:start position:0%
+work for the photosynthetic organism and
+ 
+
+ align:start position:0%
+work for the photosynthetic organism and
+you also get nadph which is an electron
+
+ align:start position:0%
+you also get nadph which is an electron
+ 
+
+ align:start position:0%
+you also get nadph which is an electron
+donor
+
+ align:start position:0%
+donor
+ 
+
+ align:start position:0%
+donor
+for carbon reduction and the net
+
+ align:start position:0%
+for carbon reduction and the net
+ 
+
+ align:start position:0%
+for carbon reduction and the net
+result is is that you get this familiar
+
+ align:start position:0%
+result is is that you get this familiar
+ 
+
+ align:start position:0%
+result is is that you get this familiar
+formula
+
+ align:start position:0%
+formula
+ 
+
+ align:start position:0%
+formula
+that you learned in grade school for
+
+ align:start position:0%
+that you learned in grade school for
+ 
+
+ align:start position:0%
+that you learned in grade school for
+photosynthesis
+
+ align:start position:0%
+photosynthesis
+ 
+
+ align:start position:0%
+photosynthesis
+co2 plus water with light
+
+ align:start position:0%
+co2 plus water with light
+ 
+
+ align:start position:0%
+co2 plus water with light
+goes to oxygen plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+carbohydrate which is of course
+
+ align:start position:0%
+carbohydrate which is of course
+ 
+
+ align:start position:0%
+carbohydrate which is of course
+the exact opposite of combustion
+
+ align:start position:0%
+the exact opposite of combustion
+ 
+
+ align:start position:0%
+the exact opposite of combustion
+right we talked a lot about how burning
+
+ align:start position:0%
+right we talked a lot about how burning
+ 
+
+ align:start position:0%
+right we talked a lot about how burning
+wood combustion is the opposite reaction
+
+ align:start position:0%
+wood combustion is the opposite reaction
+ 
+
+ align:start position:0%
+wood combustion is the opposite reaction
+that's favorable
+
+ align:start position:0%
+that's favorable
+ 
+
+ align:start position:0%
+that's favorable
+lots of energy released and
+
+ align:start position:0%
+lots of energy released and
+ 
+
+ align:start position:0%
+lots of energy released and
+so the energy input here is
+
+ align:start position:0%
+so the energy input here is
+ 
+
+ align:start position:0%
+so the energy input here is
+obviously the opposite of that to do
+
+ align:start position:0%
+obviously the opposite of that to do
+ 
+
+ align:start position:0%
+obviously the opposite of that to do
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+opposite of combustion and stores lots
+
+ align:start position:0%
+opposite of combustion and stores lots
+ 
+
+ align:start position:0%
+opposite of combustion and stores lots
+of energy
+
+ align:start position:0%
+of energy
+ 
+
+ align:start position:0%
+of energy
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+again i want to say why use water as an
+
+ align:start position:0%
+again i want to say why use water as an
+ 
+
+ align:start position:0%
+again i want to say why use water as an
+electron donor
+
+ align:start position:0%
+electron donor
+ 
+
+ align:start position:0%
+electron donor
+well because it's abundant there's
+
+ align:start position:0%
+well because it's abundant there's
+ 
+
+ align:start position:0%
+well because it's abundant there's
+nothing particularly special about water
+
+ align:start position:0%
+nothing particularly special about water
+ 
+
+ align:start position:0%
+nothing particularly special about water
+other than its abundance
+
+ align:start position:0%
+other than its abundance
+ 
+
+ align:start position:0%
+other than its abundance
+just like we talked about in oxygen is
+
+ align:start position:0%
+just like we talked about in oxygen is
+ 
+
+ align:start position:0%
+just like we talked about in oxygen is
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+really being special other than that
+
+ align:start position:0%
+really being special other than that
+ 
+
+ align:start position:0%
+really being special other than that
+it's a good electron acceptor and
+
+ align:start position:0%
+it's a good electron acceptor and
+ 
+
+ align:start position:0%
+it's a good electron acceptor and
+abundant
+
+ align:start position:0%
+abundant
+ 
+
+ align:start position:0%
+abundant
+um you could obviously build systems
+
+ align:start position:0%
+um you could obviously build systems
+ 
+
+ align:start position:0%
+um you could obviously build systems
+that do something other than
+
+ align:start position:0%
+that do something other than
+ 
+
+ align:start position:0%
+that do something other than
+oxygen and water and so there are
+
+ align:start position:0%
+oxygen and water and so there are
+ 
+
+ align:start position:0%
+oxygen and water and so there are
+extremophiles out there that instead
+
+ align:start position:0%
+extremophiles out there that instead
+ 
+
+ align:start position:0%
+extremophiles out there that instead
+do hydrogen sulfide
+
+ align:start position:0%
+do hydrogen sulfide
+ 
+
+ align:start position:0%
+do hydrogen sulfide
+to make reduced sulfur as
+
+ align:start position:0%
+to make reduced sulfur as
+ 
+
+ align:start position:0%
+to make reduced sulfur as
+a another um
+
+ align:start position:0%
+a another um
+ 
+
+ align:start position:0%
+a another um
+sorry oxidized sulfur as a way of
+
+ align:start position:0%
+sorry oxidized sulfur as a way of
+ 
+
+ align:start position:0%
+sorry oxidized sulfur as a way of
+doing um photosynthesis exact same
+
+ align:start position:0%
+doing um photosynthesis exact same
+ 
+
+ align:start position:0%
+doing um photosynthesis exact same
+concepts
+
+ align:start position:0%
+concepts
+ 
+
+ align:start position:0%
+concepts
+would apply is what we're going to talk
+
+ align:start position:0%
+would apply is what we're going to talk
+ 
+
+ align:start position:0%
+would apply is what we're going to talk
+about here
+
+ align:start position:0%
+about here
+ 
+
+ align:start position:0%
+about here
+all right now the parts of
+
+ align:start position:0%
+all right now the parts of
+ 
+
+ align:start position:0%
+all right now the parts of
+photosynthesis
+
+ align:start position:0%
+photosynthesis
+ 
+
+ align:start position:0%
+photosynthesis
+as you might guess are spatially
+
+ align:start position:0%
+as you might guess are spatially
+ 
+
+ align:start position:0%
+as you might guess are spatially
+distinct
+
+ align:start position:0%
+distinct
+ 
+
+ align:start position:0%
+distinct
+that is we're going to generate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delta psi delta ph and nadph
+
+ align:start position:0%
+delta psi delta ph and nadph
+ 
+
+ align:start position:0%
+delta psi delta ph and nadph
+those are basically this electron
+
+ align:start position:0%
+those are basically this electron
+ 
+
+ align:start position:0%
+those are basically this electron
+transport chain reactions
+
+ align:start position:0%
+transport chain reactions
+ 
+
+ align:start position:0%
+transport chain reactions
+charge the battery etc and then
+
+ align:start position:0%
+charge the battery etc and then
+ 
+
+ align:start position:0%
+charge the battery etc and then
+imagine if we're going to fix co2
+
+ align:start position:0%
+imagine if we're going to fix co2
+ 
+
+ align:start position:0%
+imagine if we're going to fix co2
+as carbohydrate
+
+ align:start position:0%
+as carbohydrate
+ 
+
+ align:start position:0%
+as carbohydrate
+well effectively that's come more like
+
+ align:start position:0%
+well effectively that's come more like
+ 
+
+ align:start position:0%
+well effectively that's come more like
+what we talked about with
+
+ align:start position:0%
+what we talked about with
+ 
+
+ align:start position:0%
+what we talked about with
+gluconeogenesis
+
+ align:start position:0%
+gluconeogenesis
+ 
+
+ align:start position:0%
+gluconeogenesis
+that's the you know chemical reactions
+
+ align:start position:0%
+that's the you know chemical reactions
+ 
+
+ align:start position:0%
+that's the you know chemical reactions
+that we just have to build a pathway for
+
+ align:start position:0%
+that we just have to build a pathway for
+ 
+
+ align:start position:0%
+that we just have to build a pathway for
+like gluconeogenesis
+
+ align:start position:0%
+like gluconeogenesis
+ 
+
+ align:start position:0%
+like gluconeogenesis
+now these two things are often referred
+
+ align:start position:0%
+now these two things are often referred
+ 
+
+ align:start position:0%
+now these two things are often referred
+to as the
+
+ align:start position:0%
+to as the
+ 
+
+ align:start position:0%
+to as the
+light and
+
+ align:start position:0%
+light and
+ 
+
+ align:start position:0%
+light and
+dark reactions
+
+ align:start position:0%
+dark reactions
+ 
+
+ align:start position:0%
+dark reactions
+of photosynthesis and that's because
+
+ align:start position:0%
+of photosynthesis and that's because
+ 
+
+ align:start position:0%
+of photosynthesis and that's because
+the first set of reactions generating
+
+ align:start position:0%
+the first set of reactions generating
+ 
+
+ align:start position:0%
+the first set of reactions generating
+the membrane potential and making nadph
+
+ align:start position:0%
+the membrane potential and making nadph
+ 
+
+ align:start position:0%
+the membrane potential and making nadph
+requires solar energy inputs it requires
+
+ align:start position:0%
+requires solar energy inputs it requires
+ 
+
+ align:start position:0%
+requires solar energy inputs it requires
+light from the sun
+
+ align:start position:0%
+light from the sun
+ 
+
+ align:start position:0%
+light from the sun
+this fixing of co2 which will just use
+
+ align:start position:0%
+this fixing of co2 which will just use
+ 
+
+ align:start position:0%
+this fixing of co2 which will just use
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+from nadph to reduce co2
+
+ align:start position:0%
+from nadph to reduce co2
+ 
+
+ align:start position:0%
+from nadph to reduce co2
+can occur of course it can occur in the
+
+ align:start position:0%
+can occur of course it can occur in the
+ 
+
+ align:start position:0%
+can occur of course it can occur in the
+light but it doesn't need light so it
+
+ align:start position:0%
+light but it doesn't need light so it
+ 
+
+ align:start position:0%
+light but it doesn't need light so it
+can occur in the light or the dark
+
+ align:start position:0%
+can occur in the light or the dark
+ 
+
+ align:start position:0%
+can occur in the light or the dark
+hence called the dark reactions and so
+
+ align:start position:0%
+hence called the dark reactions and so
+ 
+
+ align:start position:0%
+hence called the dark reactions and so
+these light reactions can really be
+
+ align:start position:0%
+these light reactions can really be
+ 
+
+ align:start position:0%
+these light reactions can really be
+broken up into
+
+ align:start position:0%
+broken up into
+ 
+
+ align:start position:0%
+broken up into
+water plus nadp plus
+
+ align:start position:0%
+water plus nadp plus
+ 
+
+ align:start position:0%
+water plus nadp plus
+goes to nad ph
+
+ align:start position:0%
+goes to nad ph
+ 
+
+ align:start position:0%
+goes to nad ph
+plus oxygen and the dark reactions
+
+ align:start position:0%
+plus oxygen and the dark reactions
+ 
+
+ align:start position:0%
+plus oxygen and the dark reactions
+are nadph
+
+ align:start position:0%
+are nadph
+ 
+
+ align:start position:0%
+are nadph
+plus co2 goes to
+
+ align:start position:0%
+plus co2 goes to
+ 
+
+ align:start position:0%
+plus co2 goes to
+carbohydrate plus
+
+ align:start position:0%
+carbohydrate plus
+ 
+
+ align:start position:0%
+carbohydrate plus
+nadp plus which of course
+
+ align:start position:0%
+nadp plus which of course
+ 
+
+ align:start position:0%
+nadp plus which of course
+gives us our net water plus
+
+ align:start position:0%
+gives us our net water plus
+ 
+
+ align:start position:0%
+gives us our net water plus
+co2 goes to carbohydrate
+
+ align:start position:0%
+co2 goes to carbohydrate
+ 
+
+ align:start position:0%
+co2 goes to carbohydrate
+plus oxygen and in the next lecture
+
+ align:start position:0%
+plus oxygen and in the next lecture
+ 
+
+ align:start position:0%
+plus oxygen and in the next lecture
+what we'll talk about is we'll go
+
+ align:start position:0%
+what we'll talk about is we'll go
+ 
+
+ align:start position:0%
+what we'll talk about is we'll go
+through the details
+
+ align:start position:0%
+through the details
+ 
+
+ align:start position:0%
+through the details
+of how these light and dark reactions
+
+ align:start position:0%
+of how these light and dark reactions
+ 
+
+ align:start position:0%
+of how these light and dark reactions
+work but when we do so bear in mind that
+
+ align:start position:0%
+work but when we do so bear in mind that
+ 
+
+ align:start position:0%
+work but when we do so bear in mind that
+we're really going to
+
+ align:start position:0%
+we're really going to
+ 
+
+ align:start position:0%
+we're really going to
+follow all of the concepts and rules
+
+ align:start position:0%
+follow all of the concepts and rules
+ 
+
+ align:start position:0%
+follow all of the concepts and rules
+that we talked about
+
+ align:start position:0%
+that we talked about
+ 
+
+ align:start position:0%
+that we talked about
+for past thermodynamic considerations of
+
+ align:start position:0%
+for past thermodynamic considerations of
+ 
+
+ align:start position:0%
+for past thermodynamic considerations of
+pathways
+
+ align:start position:0%
+pathways
+ 
+
+ align:start position:0%
+pathways
+as well as what we've been discussing
+
+ align:start position:0%
+as well as what we've been discussing
+ 
+
+ align:start position:0%
+as well as what we've been discussing
+about how oxidative phosphorylation
+
+ align:start position:0%
+about how oxidative phosphorylation
+ 
+
+ align:start position:0%
+about how oxidative phosphorylation
+works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thanks
\ No newline at end of file
diff --git a/4Ywsdc6pCOk.txt b/4Ywsdc6pCOk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d93f5bf2607c4b7f9708f4ba064c0f3d0d61db68
--- /dev/null
+++ b/4Ywsdc6pCOk.txt
@@ -0,0 +1,1758 @@
+ANNOUNCER: The following content
+is provided under a
+
+Creative Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or to view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+HERBERT GROSS: Hi, today
+we start a new
+
+segment of our course.
+
+It could be entitled 'Techniques
+of Integration'.
+
+And a subtitle could be the
+difference between 'knowing
+
+what to do and knowing
+how to do it'.
+
+You see, essentially in this
+chapter, it shall be our aim
+
+to develop various recipes
+to evaluate the inverse
+
+derivative.
+
+So in fact, let's
+call it that.
+
+Some basic recipes.
+
+The idea is something
+like this.
+
+Let's start with an
+easier problem.
+
+Let's suppose we start with a
+differentiable function 'G'.
+
+Suppose, for example, that 'G'
+prime is equal to 'f'.
+
+Then in terms of the language of
+the indefinite integral, or
+
+the inverse derivative, what we
+have is that the indefinite
+
+integral of 'f of x' with
+respect to 'x' is then 'G of
+
+x' plus 'c'.
+
+Now, you see, the harder
+problem is
+
+the inverse of this.
+
+What we're going to be talking
+about is not do you find 'f'
+
+once 'G' is given, but
+techniques for finding 'G'
+
+once 'f' is given.
+
+And as we've seen on several
+occasions already, that given
+
+'f', it is not that easy, in
+general, to find a function
+
+whose derivative is 'f'.
+
+In fact, in many cases, we can't
+do it as explicitly as
+
+we would like to no matter
+how sharp we are.
+
+For example, oh, I've just
+reviewed this so that you can
+
+think of this in one block.
+
+Given 'f' to require 'G' may
+not exist in familiar form.
+
+I don't want to pin down what
+familiar means any more than
+
+that right now.
+
+For example, the illustration
+that we've used several times
+
+already in the course, suppose
+'f of x' is 'e to
+
+the minus 'x squared''.
+
+And we want a function whose
+derivative is 'e to the minus
+
+'x squared''.
+
+In terms of areas, the second
+fundamental theorem of
+
+integral calculus, we can
+construct such a function in a
+
+rather straightforward way,
+even though it may be
+
+difficult to name it in terms
+of familiar functions.
+
+Namely, what we do is we take
+the curve 'y' equals 'e to the
+
+minus 't squared''
+in the yt-plane.
+
+Compute the area bounded above
+by that curve, below by the
+
+t-axis, on the left by the
+y-axis, and on the right by
+
+the line 't' equals 'x'.
+
+And the area under the curve
+is a function of 'x'.
+
+And what we've already seen is
+that in this particular case,
+
+'A prime of x' is precisely 'e
+to the minus 'x squared''.
+
+In other words, this area
+function, which is a function
+
+of 'x', does turn out to be the
+function whose derivative
+
+with respect to 'x' is 'e to
+the minus 'x squared''.
+
+Now you see, that will not
+be primarily what we're
+
+interested in, in
+this particular
+
+phase of our course.
+
+What we're interested in this
+phase of the course is given
+
+various classifications for
+the function 'f', to find
+
+recipes that will give us 'G' in
+familiar form, where 'G' is
+
+the function whose derivative
+is 'f'.
+
+Summarize for you
+to look at here.
+
+The objective of this block of
+material is to find recipes
+
+for finding 'G of x' for various
+types of 'f of x'.
+
+Now the best way to illustrate
+what that means is to actually
+
+pick a few examples.
+
+And by the way, what you'll
+notice in today's lecture is,
+
+roughly speaking, we do nothing
+at all that's new.
+
+The new stuff will begin with
+out next lecture essentially.
+
+But for now what we'll really
+be doing is giving us an
+
+excuse to pull together all
+of the recipes that we've
+
+developed so far.
+
+All of the recipes either called
+indefinite integrals or
+
+inverse derivatives.
+
+For example, the first class
+of functions which we could
+
+handle were things of the form
+integral ''u to the n' du'.
+
+Recall that very early in our
+course, we found out that the
+
+integral of ''u to the n' du'
+was ''u to the 'n + 1'' over
+
+'n plus 1' plus a constant if
+'n' was unequal to minus 1.
+
+And then, in our last block of
+material we learned to handle
+
+the case where 'n' was
+equal to minus 1.
+
+Namely, when 'n' is minus
+1, integral ''u to
+
+the minus 1' du'.
+
+Namely, integral 'du' over 'u'
+is natural log absolute value
+
+of 'u' plus a constant.
+
+Now this then, is one of our
+basic building blocks.
+
+What we're saying is, if an
+indefinite integral can be
+
+written in this form, we already
+have a recipe that
+
+allows us to evaluate
+the integral.
+
+By the way, let us also point
+out as was mentioned again,
+
+several times in the past, that
+'u' is the generic name
+
+for a variable over here.
+
+It is not important in this
+recipe that we use 'u'.
+
+What is important is that
+whatever is being raised to
+
+the n-th power inside the
+integrand must be precisely
+
+the thing that's following
+the 'd' over here.
+
+For example, instead of
+'u', suppose I used
+
+'sine x' over here.
+
+In other words, suppose I
+had 'sine x' to the n-th
+
+power 'd sine x'.
+
+See, what's being raised to
+the n-th power is the same
+
+thing as what's following
+the 'd'.
+
+That's all I really
+care about.
+
+In other words, if this had been
+the integrand, the recipe
+
+would have said, this is 1 over
+'n + 1' times 'sine x' to
+
+the 'n + 1' power.
+
+Plus a constant if 'n' is
+not equal to minus 1.
+
+And it's natural log absolute
+value of 'sine x' plus a
+
+constant if 'n' is
+equal to minus 1.
+
+Again, the important thing is
+not the 'u', but the fact that
+
+what's being raised to the
+n-th power is the same as
+
+what's following the
+'d' over here.
+
+By the way, we can write this
+in more familiar form.
+
+You see, namely, notice that the
+differential of 'sine x'
+
+is 'cosine x dx'.
+
+And consequently, in this form
+what our recipe says is that
+
+integral 'sine x' to the n-th
+power times 'cosine x dx' is
+
+given by this.
+
+In other words, it's sine to the
+'n + 1' power 'x over 'n +
+
+1'' plus a constant if 'n'
+is unequal to minus 1.
+
+And it's the natural log
+absolute value of 'sine x'
+
+plus 'c' if 'n' is
+equal to minus 1.
+
+Again, notice this looks more
+complicated than this.
+
+But to get our problem, to get
+into the form ''u to the n'
+
+du', notice that the natural
+substitution here is to let
+
+'u' equal 'sine x'.
+
+In which case, 'du' would
+be 'cosine x dx'.
+
+In other words, the extra factor
+of 'cosine x' here
+
+actually is to our advantage
+over here.
+
+That when we make the
+substitution, it gives us the
+
+form that we want.
+
+With the factor missing, we're
+in a little bit of trouble.
+
+By the way, this is what makes
+this a rather exciting topic.
+
+That there seems to be no really
+canned ways of finding
+
+indefinite integrals.
+
+That we have recipes.
+
+Frequently, the recipe that
+we have doesn't cover the
+
+situation that we have.
+
+In fact, I know a lot of times
+in teaching a course like this
+
+students say, why do we have
+to learn these recipes and
+
+techniques?
+
+Why can't we just look them
+up in the tables?
+
+And the answer quite simply, is
+that in many applications,
+
+the integral that we have
+doesn't appear in
+
+that form in the table.
+
+That frequently what we must do
+is a tremendous amount of
+
+algebraic manipulation and the
+like to even get the given
+
+integral to resemble one that
+we can find in the table.
+
+Oh, we're starting
+off on a fairly
+
+straightforward level here.
+
+Nothing really too tricky.
+
+But at least enough so that we
+get an idea of what kind of
+
+gimmicks are involved.
+
+For example, suppose we had
+'cosine x' to the seventh
+
+power 'dx'.
+
+You see the idea here is that
+when you have cosine raised to
+
+a power, it would have been nice
+if a 'sine x' factor had
+
+been in here.
+
+Because the differential
+of 'cosine x' is
+
+minus 'sine x dx'.
+
+And what I'm driving at here is
+that we often have to have
+
+a certain kind of ingenuity that
+allows us to reduce a new
+
+integrand to a more
+familiar one.
+
+And, as I say, there are many
+
+techniques done in the textbook.
+
+There'll be plenty of exercises
+again, that will
+
+allow you to experiment
+on this.
+
+All I want to do is hit a few
+highlights and create the mood
+
+as to what's going on.
+
+For example, you see frequently
+what happens is, if
+
+we have 'cosine x' raised
+to an odd power, a very
+
+convenient way of handling this
+is to split off one of
+
+the factors of 'cosine
+x' separately.
+
+In other words, write this as
+'cosine x' to the sixth power
+
+times 'cosine x dx'.
+
+The idea being that cosine
+squared can be written as '1
+
+minus 'sine squared''.
+
+In other words, 'cosine x' to
+the sixth power is really
+
+'cosine squared x' cubed.
+
+But 'cosine squared x' is '1
+minus 'sine squared x''.
+
+In other words, notice again the
+role of the trigonometric
+
+identities.
+
+I take this integrand, write it
+this way, and now you see
+
+if I use the binomial theorem
+and expand this, notice that
+
+my typical term will have 'sine
+x' to a power multiplied
+
+by a 'cosine x'.
+
+And that's precisely the kind
+of a term that I handled in
+
+the previous case.
+
+And again, I'm not
+going to bore you
+
+with the details here.
+
+That is the easiest part
+of the problem.
+
+The hard part is getting to
+understand why one would want
+
+to use this particular
+kind of form.
+
+Another variation is, what
+happens if the cosine is
+
+raised to an even power rather
+than to an odd power?
+
+How do we handle that?
+
+Again, the same kind of use of
+trigonometric identities.
+
+For example, it would not be to
+our advantage in this case,
+
+to replace cosine squared
+by 1 minus sine squared.
+
+Because then we would wind
+up with the same kind of
+
+integrands that we started with,
+only using powers of
+
+sine instead of powers
+of cosine.
+
+You see, the idea is that if
+we have a power of sine, we
+
+want a cosine factor
+to accompany it.
+
+And inversely, if we have a
+power of cosine, we'd like a
+
+factor of sine to
+accompany it.
+
+Why?
+
+So that we can get the integral
+into the form ''u to
+
+the n' du'.
+
+In this particular case, a
+very common device is to
+
+invoke the identity that cosine
+squared of an angle is
+
+1 plus cosine twice
+the angle over 2.
+
+You see again, this is where
+all of these particular
+
+identities come into play.
+
+It's not a case of saying, let's
+learn these identities
+
+so that we can recite them.
+
+It's a case of getting into a
+situation where you want a
+
+certain answer, can't handle
+it conveniently in the form
+
+that you're in, and hope that
+you can pick off a synonym
+
+that allows you to tackle the
+problem more successfully.
+
+That's where this becomes a
+matter of insight, lucky
+
+guessing, skill, whatever
+you want to call it.
+
+It's one thing to transform an
+integral into an equivalent
+
+one, and another thing to have
+that equivalent integral be
+
+something that you can handle.
+
+Well, at any rate, for example
+in a problem of this type, a
+
+tendency is to write cosine
+sixth theta as
+
+cosine squared cubed.
+
+Cosine squared theta is 1 plus
+cosine 2 theta over 2.
+
+To cube this we can take
+out the factor of 1/8.
+
+You see, we use the binomial
+theorem to expand 1 plus
+
+cosine 2 theta cubed.
+
+And notice that of the
+terms that we get,
+
+this term we can handle.
+
+This term we can handle,
+it's just cosine
+
+to the first power.
+
+Which involves a sine term
+when we integrate.
+
+And here's a cosine cubed.
+
+But we've just seen how you can
+handle something to an odd
+
+power, so that reduces
+this term to a
+
+type that we can handle.
+
+And then we see what?
+
+That we have another term
+in here, which is
+
+cosine squared 2 theta.
+
+That's an even power
+of cosine.
+
+Again, we do what?
+
+We write cosine squared 2 theta
+as 1 plus cosine of
+
+twice this angle.
+
+That's 1 plus cosine
+4 theta over 2.
+
+In other words, we keep reducing
+these things, always
+
+hoping to break them down into
+collections of problems that
+
+we solved before.
+
+As I said, these are things
+that we'll drill on in the
+
+exercises and I think it will
+become more meaningful there.
+
+Here, as I say, the main aim
+is to create the mood that
+
+what we're trying to do is to
+reduce unfamiliar problems to
+
+equivalent familiar
+ones to which we
+
+already know the answer.
+
+Now again, in the way of review,
+sometimes an integrand
+
+occurs in the form of the sum or
+difference of two squares.
+
+We've already handled this in
+terms of the inverse circular
+
+functions and the inverse
+hyperbolic functions.
+
+It's covered for the first time
+in our textbook at this
+
+particular stage
+of the course.
+
+And I think it's a tough enough
+concept so that it's
+
+worth emphasizing
+at this stage.
+
+So I just separate this
+particular type out.
+
+How do we handle sums and
+differences of squares?
+
+And what I intend to show is,
+is that by a suitable
+
+trigonometric function, either
+circular trigonometric or
+
+hyperbolic trigonometric, we can
+always reduce that kind of
+
+a problem to the type
+that we can handle.
+
+Again, to keep computation at a
+minimum, I have not tried to
+
+pick a rather complicated
+situation.
+
+In fact, I've picked ones where
+you can very easily look
+
+them up in the table
+if that was the
+
+main aim of the exercise.
+
+You see here, it's not so much
+that I want to get this
+
+answer, as much as it is that
+I want to emphasize the
+
+technique that one uses.
+
+The idea is something
+like this.
+
+Here we see the difference
+of two squares.
+
+That's the square root of a
+squared minus x squared.
+
+What this should do for us is
+to suggest a right triangle
+
+whose hypotenuse is a and one
+of whose sides is 'x'.
+
+That's the diagram I've
+drawn over here.
+
+This is my reference triangle.
+
+As I say, we've done this
+before, but I would like to
+
+reinforce this at this
+particular stage.
+
+Especially now that we're more
+familiar with both the inverse
+
+circular and inverse hyperbolic
+functions.
+
+At any rate, we use this
+reference triangle.
+
+From this triangle, the easiest
+relationship to pick
+
+off involving 'x' is that sine
+theta is 'x over a', or 'a
+
+'sine theta'' equals 'x'.
+
+From which it follows that
+''a' cosine theta
+
+'d theta'' is 'dx'.
+
+The square root of ''a squared'
+minus 'x squared''
+
+over 'a' is cosine theta.
+
+Therefore, the square root
+of ''a squared' minus 'x
+
+squared'' is 'a cosine theta'.
+
+If we now make this substitution
+in this
+
+particular integral, we wind up
+with integral 'dx' over the
+
+square root of ''a squared'
+minus 'x squared'' is equal to
+
+integral 'd theta'.
+
+Which is theta plus 'c'.
+
+And since theta is the number
+whose sine is 'x over a', we
+
+have that the answer to this
+problem is inverse 'sine 'x
+
+over a'' plus a constant.
+
+Again, just a straightforward
+review, but a
+
+rather important technique.
+
+In our textbook, this is put in
+a separate section, and the
+
+technique is called
+trigonometric substitution.
+
+And I just wanted to show
+you what motivates the
+
+trigonometric substitution.
+
+The harder part as I mentioned
+in our previous lecture, is
+
+how you motivate trigonometric
+substitutions when it's the
+
+hyperbolic functions
+that are involved.
+
+You see, what I'd like to do now
+is instead of dealing with
+
+the square root of ''a squared'
+minus 'x squared'',
+
+let me just reverse the
+order of the terms.
+
+And now let me take integral
+'dx' over the 'square root of
+
+''x squared' minus
+'a squared'''.
+
+Notice that the difference
+between ''x squared' minus 'a
+
+squared'' and ''a squared' minus
+'x squared'' is just a
+
+factor of minus 1.
+
+And the fact that that minus 1
+is under the square root sign,
+
+really means in a certain manner
+of speaking that you've
+
+multiplied by i, the square root
+of minus 1, to transform
+
+the integral that we
+just had into this
+
+particular form here.
+
+And in terms of our lecture on
+the hyperbolic functions that
+
+should, in some way, give us a
+preview of things to come in
+
+the sense that the hyperbolic
+functions are very strongly
+
+related to the circular
+functions.
+
+My technique for doing this--
+
+and again, this is highly
+subjective.
+
+It's very simple.
+
+I learnt the circular functions
+long before I learnt
+
+the hyperbolic functions.
+
+Consequently, I feel very
+much at home with
+
+the circular functions.
+
+As a result, whenever I see the
+sum or difference of two
+
+squares, I always think in
+terms of a triangle.
+
+I make a circular trigonometric
+substitution.
+
+If that works for me, fine.
+
+I haven't lost anything.
+
+If it doesn't work for me, it
+gives me the hint that I can't
+
+seem to get in my own mind
+without this hint as to which
+
+hyperbolic function
+I should use.
+
+Let me show you this in terms
+of this particular example.
+
+If I saw this problem from
+scratch and didn't have any
+
+previous knowledge of how to
+handle this I'd say, this
+
+seems like I should think of
+a right triangle whose
+
+hypotenuse is 'x' and one
+of whose sides is 'a'.
+
+So I think of this particular
+reference triangle.
+
+Now, thinking of this triangle,
+and in fact, even
+
+look at this triangle, I very
+easily pick off that 'x' is
+
+equal to 'a cosecant theta'.
+
+See, 'x over a' is 1
+over sine theta.
+
+That's cosecant theta.
+
+Therefore and remembering how to
+differentiate the cosecant,
+
+I take the differential of both
+sides and I find that
+
+minus 'a cosecant theta
+cotangent theta
+
+'d theta'' is 'dx'.
+
+Again, from this diagram I see
+that the square root of ''x
+
+squared' minus 'a
+squared'' is--
+
+well, let's see.
+
+The square root of ''x squared'
+minus 'a squared''
+
+over 'a' would be
+cotangent theta.
+
+So the square root of ''x
+squared' minus 'a squared''
+
+itself is 'a cotangent theta'.
+
+Making the substitution in the
+integral 'dx' over the square
+
+root of ''x squared' minus 'a
+squared'', notice that the
+
+'a's cancel, the cotangent's
+cancel, and I'm left with
+
+'cosecant theta 'd theta''
+and a minus
+
+sign inside my integral.
+
+In other words, somehow or
+other, this circular
+
+trigonometric function replaces
+the integral 'dx'
+
+over the 'square root of ''x
+squared' minus 'a squared'''
+
+by integral minus 'cosecant
+theta 'd theta''.
+
+And the point I'd like to
+emphasize at this particular
+
+stage is that we don't
+say that the
+
+substitution has failed.
+
+The substitution
+has been made.
+
+We have replaced an integral
+involving 'x' by
+
+one involving theta.
+
+It's just that in the same way
+that it's difficult to
+
+integrate secant theta--
+
+in fact, that will be later
+in this block of
+
+material we'll do that.
+
+But the point is that secant
+and cosecant are rather
+
+difficult functions
+to integrate.
+
+In fact, at this stage of our
+development, we do not know a
+
+function whose derivative
+is cosecant theta.
+
+Consequently, we don't know one
+whose derivative is minus
+
+cosecant theta.
+
+We seemed to have arrived
+at an impasse here.
+
+We have successfully made the
+substitution, but the key
+
+point is that the new integral
+is no easier for us to handle
+
+than the old integral.
+
+Now, here's how I visualize the
+hyperbolic substitutions.
+
+We did this in the
+last lecture.
+
+I think it's tough enough, so
+I'd like to do it a second
+
+time and give you a chance of
+seeing how easy this is once
+
+you see the structural form.
+
+Notice that the substitution I
+made here was 'x' equals 'a
+
+cosecant theta'.
+
+The cosecant was the
+key step here.
+
+The reference triangle, knowing
+how to draw this
+
+geometrically, allowed me not
+to consciously have to think
+
+of the trigonometric
+identities.
+
+But what I really did in
+evaluating this problem, if I
+
+left the diagram out and wanted
+to do it analytically,
+
+the identity that I made use
+of was the one that said
+
+cosecant squared theta minus
+cotangent squared theta is
+
+identically 1.
+
+In other words, I would like an
+identity for the hyperbolic
+
+functions that has the structure
+that the difference
+
+of two squares is
+identically 1.
+
+The easiest one I can think of
+is the one that says cosh
+
+squared theta minus sinh
+squared theta is 1.
+
+You see, structurally, these
+two are equivalent.
+
+In other words, sinh and cosh
+are related hyperbolically,
+
+the same way that cotangent and
+cosecant are in terms of
+
+circular functions.
+
+The identification is this.
+
+Since in the original problem I
+tried 'x' equals 'a cosecant
+
+theta', and since the
+identification here is that
+
+cosecant and cosh are matched
+up, what I try next-- see once
+
+this has failed, I very quickly
+now say, OK, what I'll
+
+do is instead of 'x' equals 'a
+cosecant theta', I'll try 'x'
+
+equals 'a cosh theta'.
+
+That's exactly what
+I did over here.
+
+'a cosh theta' equals 'x'.
+
+From which it follows
+that 'dx' is 'a
+
+sinh theta 'd theta''.
+
+The square root of ''x squared'
+minus 'a squared'' is
+
+just ''a squared' cosh
+squared theta'.
+
+That's 'x squared'.
+
+Minus 'a squared'.
+
+That can be written as the
+square root of 'a squared'
+
+times the quantity 'cosh
+squared theta minus 1'.
+
+Now, the interesting point is
+the 'cosh squared theta minus
+
+1' turns out to be sinh
+squared theta.
+
+In fact, if we want to just look
+back here for a moment,
+
+recall that's exactly what
+we have over here.
+
+That cosh squared theta is 1.
+
+Well, cosh squared theta is
+1 plus sinh squared theta.
+
+cosh squared theta minus 1
+is sinh squared theta.
+
+And you might, say wasn't
+that terrific?
+
+What a lucky break it was that
+this complicated expression
+
+just happened to be sinh
+squared theta.
+
+And now taking the square
+root I get a sinh theta.
+
+The thing I'd like to point
+out is that the element of
+
+luck was removed from this at
+the instant that I recognized
+
+the fact that cosh and sinh
+were related by the same
+
+identity that cosecant
+and cotangent were.
+
+In other words, I rigged this
+thing so that when I finally
+
+had to take this particular
+difference, I had to wind up
+
+with an easy square
+root to extract.
+
+You see, I had the right
+structure to begin with.
+
+At any rate, to make a long
+story short here, 'dx' is 'a
+
+sinh theta 'd theta''.
+
+The square root of ''x squared'
+minus 'a squared'' is
+
+'a sinh theta'.
+
+Therefore, 'dx' over the square
+root of ''x squared'
+
+minus 'a squared''.
+
+Well, look how nicely
+this works out.
+
+The a sinh theta cancels from
+both the numerator and the
+
+denominator.
+
+And it turns out that the
+integral that I'm looking for,
+
+'dx' over the square root
+of ''x squared' minus 'a
+
+squared'' is just theta
+plus a constant.
+
+But now, recalling that a
+cosh theta equals 'x'.
+
+In other words, cosh theta
+is 'x over a'.
+
+And therefore, theta is 'inverse
+cosh 'x over a'', I
+
+arrive at the result that this
+integral is 'inverse cosh 'x
+
+over a'' plus a constant.
+
+In other words, what I hope that
+these two little examples
+
+show is that when I have the
+sum or difference of two
+
+squares, the trigonometric
+substitutions will usually
+
+give me a crack at getting an
+equivalent integral that will
+
+be easier to handle.
+
+What may happen is that the
+circular functions won't help
+
+me, but the hyperbolic
+ones will.
+
+Or vice versa, and I hope that
+you see how these are so
+
+delicately connected.
+
+Well, there is one final type of
+technique that I would like
+
+to show for today's lesson
+that's related to what we've
+
+already done.
+
+And with that, we'll conclude
+today's lesson and go into
+
+some more elaborate
+recipes next time.
+
+But this is a take-off on our
+old high school construction
+
+of completing a square.
+
+In other words, let's suppose
+we have an expression of the
+
+form 'ax squared' plus
+'bx' plus 'c'.
+
+And this may sound
+old hat to you.
+
+You may remember this as looking
+pretty much like the
+
+development of the quadratic
+equation.
+
+The idea works something
+like this.
+
+First of all, I can factor
+an a out of here.
+
+I'm assuming that a is not 0.
+
+In fact, if a were 0, I
+really wouldn't have a
+
+square term in here.
+
+I factor out an 'a' and I'm
+left with 'a' times 'x
+
+squared' plus ''b over
+a'x' plus 'c over a'.
+
+Now it turns out that whenever
+you have something of the form
+
+'x squared' plus something times
+'x', to convert that
+
+into a perfect square.
+
+And again, we'll have ample
+opportunity to practice this
+
+in the exercises.
+
+You take half the coefficient
+of 'x' and square it.
+
+Half the coefficient of 'x'
+here is 'b over 2a'.
+
+If I square that it's 'b
+squared' over ''4a' squared'.
+
+Now to keep the identity intact
+here, if I add in 'b
+
+squared' over ''4a' squared',
+I must subtract that.
+
+In other words, I just add and
+subtract this term that will
+
+make this a perfect square.
+
+In fact, what is 'x squared'
+plus ''b over a'x' plus ''b
+
+squared' over '4a' squared''?
+
+You'll notice that
+this is just ''x'
+
+plus 'b over 2a' squared'.
+
+'x squared'.
+
+Just multiply this thing out.
+
+You see how this particular
+thing works.
+
+In other words, what I've done
+is I can write this as 'a'
+
+times a perfect square.
+
+And by the way, what's left over
+here if I multiply these
+
+two terms through by 'a'?
+
+This is 'c' minus 'b
+squared over 4a'.
+
+In other words, recognizing that
+this is ''x' plus 'b over
+
+2a' squared'.
+
+And multiplying these two terms
+through by 'a', I wind
+
+up with the fact that ''ax'
+squared' plus 'bx' plus 'c'
+
+can always be written in
+this particular form.
+
+This is called completing
+the square.
+
+And notice that this is now a
+perfect square and this is
+
+some constant.
+
+And the question that comes up
+is, what does this have to do
+
+with integral calculus?
+
+In other words, with finding
+antiderivatives.
+
+And again, as is so often
+the case, and granted
+
+that as this course--
+
+especially this chapter gets
+more complicated, the degree
+
+of sophistication will
+become much greater.
+
+But the basic idea will always
+remain the same.
+
+Somehow or other, we will always
+try to reduce a new
+
+situation to a more
+familiar one.
+
+In other words, let's suppose
+now we don't have an integrand
+
+that's the sum and difference of
+two squares, but we have an
+
+integrand that involves a
+quadratic expression.
+
+Say, for example, we have
+'dx' over ''ax' squared'
+
+plus 'bx' plus 'c'.
+
+Well, you see, using hindsight
+rather than foresight, I
+
+already took care of this
+problem before we started.
+
+Namely, we just finished
+completing
+
+the square over here.
+
+Namely, what is ''ax' squared'
+plus 'bx' plus 'c'?
+
+Notice it can be written
+in what form?
+
+Let's come back here
+and take a look.
+
+It's 'a' times ''x'
+plus 'b over 2a'
+
+squared' plus some constant.
+
+I don't care what it
+happens to be here.
+
+I'll just call that constant
+'c sub 1'.
+
+And by the way, notice depending
+upon the relative
+
+sizes of 'a', 'b', and 'c', this
+constant can be either
+
+positive or negative.
+
+Or in fact, even 0.
+
+So to handle that what I'll say
+is I can always write this
+
+denominator in the form 'a'
+times ''x' plus 'b over 2a'
+
+squared' plus or minus
+some constant.
+
+Where I'm assuming now that
+the constant is positive.
+
+That's why I put the plus
+or minus sign in.
+
+It's plus some positive constant
+or else it's minus
+
+some positive constant.
+
+Now what I can do is factor out
+an a from the denominator.
+
+If I factor out an a from the
+denominator here, I have 1
+
+over 'a' times a certain
+integral.
+
+What integral?
+
+'dx' over 'x plus 'b over 2a'
+squared' plus or minus still
+
+some constant.
+
+In other words, I
+had 'c1' here.
+
+I factored out on 'a'. 'c2'
+was actually 'c1 over a'.
+
+I just factored out an 'a'
+from this thing here.
+
+But it doesn't make
+any difference.
+
+The important point is I now
+have this written in this
+
+particular form.
+
+Now if I assume that 'c2' is a
+positive constant, notice that
+
+any positive number is
+a perfect square.
+
+Namely, it's the square
+of its square root.
+
+And again, as I say with the
+exercises, this will become
+
+clearer when we work with
+specific numbers.
+
+But the idea here is what?
+
+This is some perfect square,
+which I'll call 'k'.
+
+And in other words, this
+integrand can now be written
+
+in the form '1 over a', 'dx'
+over 'x plus 'b over 2a'
+
+squared' plus or minus
+'k squared'.
+
+Well, again, what am
+I leading up to?
+
+If I now make the substitution
+that 'u' equals 'x plus 'b
+
+over 2a'', notice that my
+denominator simply becomes 'u
+
+squared' plus or minus
+'k squared'.
+
+In other words, my denominator
+now has the form of either the
+
+sum or difference
+of two squares.
+
+On the other hand, if 'u'
+is 'x plus 'b over
+
+2a'', what is 'du'?
+
+Remember, 'b' and 'a'
+are constants.
+
+'b over 2a' is a constant.
+
+The derivative of
+a constant is 0.
+
+So 'du' is equal to 'dx'.
+
+In other words, notice that if
+I now make this substitution
+
+in here, outside I have a '1
+over a', inside I have 'du'
+
+over ''u squared' plus or
+minus 'k squared''.
+
+In other words, when I have a
+quadratic I can write that in
+
+the form the sum and/or
+difference of two squares,
+
+simply by completing
+the square.
+
+Simply by completing square.
+
+In other words, I can solve the
+problem of the quadratic
+
+by converting it back into an
+integral, the type of which
+
+I've solved before.
+
+And this, by and large, becomes
+the technique that we
+
+will use throughout
+this chapter.
+
+Well, at any rate, I won't
+go into that in any more
+
+detail right now.
+
+We will pick up additional
+
+techniques in our next lecture.
+
+And until the next
+lecture, goodbye.
+
+ANNOUNCER: Funding for the
+publication of this video was
+
+provided by the Gabriella and
+Paul Rosenbaum Foundation.
+
+Help OCW continue to provide
+free and open access to MIT
+
+courses by making a donation
+at ocw.mit.edu/donate.
\ No newline at end of file
diff --git a/4dj1ogUwTEM.txt b/4dj1ogUwTEM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fd5588610bee2610a74f46d8e1cf4afdf2027c6b
--- /dev/null
+++ b/4dj1ogUwTEM.txt
@@ -0,0 +1,3779 @@
+align:start position:0%
+ 
+so it's time to examine uncountable sets
+
+ align:start position:0%
+so it's time to examine uncountable sets
+ 
+
+ align:start position:0%
+so it's time to examine uncountable sets
+and that's what we're going to do in
+
+ align:start position:0%
+and that's what we're going to do in
+ 
+
+ align:start position:0%
+and that's what we're going to do in
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+segment so Canter's question was are all
+
+ align:start position:0%
+segment so Canter's question was are all
+ 
+
+ align:start position:0%
+segment so Canter's question was are all
+sets the same size and he gives a
+
+ align:start position:0%
+sets the same size and he gives a
+ 
+
+ align:start position:0%
+sets the same size and he gives a
+definitive answer of
+
+ align:start position:0%
+definitive answer of
+ 
+
+ align:start position:0%
+definitive answer of
+no uh Canter's theorem which we're about
+
+ align:start position:0%
+no uh Canter's theorem which we're about
+ 
+
+ align:start position:0%
+no uh Canter's theorem which we're about
+to present will show that in fact there
+
+ align:start position:0%
+to present will show that in fact there
+ 
+
+ align:start position:0%
+to present will show that in fact there
+isn't any biggest Infinity for any given
+
+ align:start position:0%
+isn't any biggest Infinity for any given
+ 
+
+ align:start position:0%
+isn't any biggest Infinity for any given
+Infinity you can find a bigger one in a
+
+ align:start position:0%
+Infinity you can find a bigger one in a
+ 
+
+ align:start position:0%
+Infinity you can find a bigger one in a
+very simple way
+
+ align:start position:0%
+very simple way
+ 
+
+ align:start position:0%
+very simple way
+um but let's begin by coming up with a
+
+ align:start position:0%
+um but let's begin by coming up with a
+ 
+
+ align:start position:0%
+um but let's begin by coming up with a
+the simplest form of Cancer's diagonal
+
+ align:start position:0%
+the simplest form of Cancer's diagonal
+ 
+
+ align:start position:0%
+the simplest form of Cancer's diagonal
+argument uh of how do you prove that a
+
+ align:start position:0%
+argument uh of how do you prove that a
+ 
+
+ align:start position:0%
+argument uh of how do you prove that a
+set is not countable well remember a set
+
+ align:start position:0%
+set is not countable well remember a set
+ 
+
+ align:start position:0%
+set is not countable well remember a set
+is countable if you can list it possibly
+
+ align:start position:0%
+is countable if you can list it possibly
+ 
+
+ align:start position:0%
+is countable if you can list it possibly
+with repeats so a is countable if
+
+ align:start position:0%
+with repeats so a is countable if
+ 
+
+ align:start position:0%
+with repeats so a is countable if
+there's a sequence a z A1 A2 such that
+
+ align:start position:0%
+there's a sequence a z A1 A2 such that
+ 
+
+ align:start position:0%
+there's a sequence a z A1 A2 such that
+every element in the set a shows up at
+
+ align:start position:0%
+every element in the set a shows up at
+ 
+
+ align:start position:0%
+every element in the set a shows up at
+some time or other in the list possibly
+
+ align:start position:0%
+some time or other in the list possibly
+ 
+
+ align:start position:0%
+some time or other in the list possibly
+more than once uh and the only things in
+
+ align:start position:0%
+more than once uh and the only things in
+ 
+
+ align:start position:0%
+more than once uh and the only things in
+the list are elements of a
+
+ align:start position:0%
+the list are elements of a
+ 
+
+ align:start position:0%
+the list are elements of a
+uh and we saw as an example that the
+
+ align:start position:0%
+uh and we saw as an example that the
+ 
+
+ align:start position:0%
+uh and we saw as an example that the
+finite bit strings the finite strings of
+
+ align:start position:0%
+finite bit strings the finite strings of
+ 
+
+ align:start position:0%
+finite bit strings the finite strings of
+zeros and ones uh or the finite binary
+
+ align:start position:0%
+zeros and ones uh or the finite binary
+ 
+
+ align:start position:0%
+zeros and ones uh or the finite binary
+words are a an example of accountable
+
+ align:start position:0%
+words are a an example of accountable
+ 
+
+ align:start position:0%
+words are a an example of accountable
+set and like we claimed last time and
+
+ align:start position:0%
+set and like we claimed last time and
+ 
+
+ align:start position:0%
+set and like we claimed last time and
+now we're about to prove that the
+
+ align:start position:0%
+now we're about to prove that the
+ 
+
+ align:start position:0%
+now we're about to prove that the
+difference is that if you look at the
+
+ align:start position:0%
+difference is that if you look at the
+ 
+
+ align:start position:0%
+difference is that if you look at the
+infinite bit strings the oneway infinite
+
+ align:start position:0%
+infinite bit strings the oneway infinite
+ 
+
+ align:start position:0%
+infinite bit strings the oneway infinite
+they have a beginning and they go on
+
+ align:start position:0%
+they have a beginning and they go on
+ 
+
+ align:start position:0%
+they have a beginning and they go on
+infinitely to the right the notation
+
+ align:start position:0%
+infinitely to the right the notation
+ 
+
+ align:start position:0%
+infinitely to the right the notation
+being 0 one to the Omega where Omega is
+
+ align:start position:0%
+being 0 one to the Omega where Omega is
+ 
+
+ align:start position:0%
+being 0 one to the Omega where Omega is
+an indication of one of the symbols for
+
+ align:start position:0%
+an indication of one of the symbols for
+ 
+
+ align:start position:0%
+an indication of one of the symbols for
+kind of Infinity uh and this is going to
+
+ align:start position:0%
+kind of Infinity uh and this is going to
+ 
+
+ align:start position:0%
+kind of Infinity uh and this is going to
+be an example of an uncountable set how
+
+ align:start position:0%
+be an example of an uncountable set how
+ 
+
+ align:start position:0%
+be an example of an uncountable set how
+are we going to prove that well uh the
+
+ align:start position:0%
+are we going to prove that well uh the
+ 
+
+ align:start position:0%
+are we going to prove that well uh the
+setup for uh using a diagonal argument
+
+ align:start position:0%
+setup for uh using a diagonal argument
+ 
+
+ align:start position:0%
+setup for uh using a diagonal argument
+is to think about drawing a matrix
+
+ align:start position:0%
+is to think about drawing a matrix
+ 
+
+ align:start position:0%
+is to think about drawing a matrix
+suppose that I have some way of
+
+ align:start position:0%
+suppose that I have some way of
+ 
+
+ align:start position:0%
+suppose that I have some way of
+enumerating the infinite binary
+
+ align:start position:0%
+enumerating the infinite binary
+ 
+
+ align:start position:0%
+enumerating the infinite binary
+sequences the in 0 one to the Omega so
+
+ align:start position:0%
+sequences the in 0 one to the Omega so
+ 
+
+ align:start position:0%
+sequences the in 0 one to the Omega so
+there's a sequence s0 there's a sequence
+
+ align:start position:0%
+there's a sequence s0 there's a sequence
+ 
+
+ align:start position:0%
+there's a sequence s0 there's a sequence
+S1 there's a sequence S2 let's lay them
+
+ align:start position:0%
+S1 there's a sequence S2 let's lay them
+ 
+
+ align:start position:0%
+S1 there's a sequence S2 let's lay them
+out as though they were the rows of a
+
+ align:start position:0%
+out as though they were the rows of a
+ 
+
+ align:start position:0%
+out as though they were the rows of a
+matrix so s0 is this infinite binary
+
+ align:start position:0%
+matrix so s0 is this infinite binary
+ 
+
+ align:start position:0%
+matrix so s0 is this infinite binary
+sequence 0 0 one zero so on um and uh
+
+ align:start position:0%
+sequence 0 0 one zero so on um and uh
+ 
+
+ align:start position:0%
+sequence 0 0 one zero so on um and uh
+the column labels are simply the
+
+ align:start position:0%
+the column labels are simply the
+ 
+
+ align:start position:0%
+the column labels are simply the
+coordinate labels for s0 so this is s0 0
+
+ align:start position:0%
+coordinate labels for s0 so this is s0 0
+ 
+
+ align:start position:0%
+coordinate labels for s0 so this is s0 0
+S01 and so on um S1 is the next um uh
+
+ align:start position:0%
+S01 and so on um S1 is the next um uh
+ 
+
+ align:start position:0%
+S01 and so on um S1 is the next um uh
+infinite binary sequence in this
+
+ align:start position:0%
+infinite binary sequence in this
+ 
+
+ align:start position:0%
+infinite binary sequence in this
+hypothetical list uh and it starts 0 one
+
+ align:start position:0%
+hypothetical list uh and it starts 0 one
+ 
+
+ align:start position:0%
+hypothetical list uh and it starts 0 one
+one zero and goes on and so on down the
+
+ align:start position:0%
+one zero and goes on and so on down the
+ 
+
+ align:start position:0%
+one zero and goes on and so on down the
+line so the row labels are this
+
+ align:start position:0%
+line so the row labels are this
+ 
+
+ align:start position:0%
+line so the row labels are this
+enumeration of binary sequences uh and
+
+ align:start position:0%
+enumeration of binary sequences uh and
+ 
+
+ align:start position:0%
+enumeration of binary sequences uh and
+the column labels are coordinate labels
+
+ align:start position:0%
+the column labels are coordinate labels
+ 
+
+ align:start position:0%
+the column labels are coordinate labels
+and this is a matrix that's infinite to
+
+ align:start position:0%
+and this is a matrix that's infinite to
+ 
+
+ align:start position:0%
+and this is a matrix that's infinite to
+the right and infinite down but it
+
+ align:start position:0%
+the right and infinite down but it
+ 
+
+ align:start position:0%
+the right and infinite down but it
+definitely has an upper left
+
+ align:start position:0%
+definitely has an upper left
+ 
+
+ align:start position:0%
+definitely has an upper left
+corner so the trick is to try to find an
+
+ align:start position:0%
+corner so the trick is to try to find an
+ 
+
+ align:start position:0%
+corner so the trick is to try to find an
+infinite binary sequence that is not in
+
+ align:start position:0%
+infinite binary sequence that is not in
+ 
+
+ align:start position:0%
+infinite binary sequence that is not in
+this list that it differs from every row
+
+ align:start position:0%
+this list that it differs from every row
+ 
+
+ align:start position:0%
+this list that it differs from every row
+if I can do that then I've shown that
+
+ align:start position:0%
+if I can do that then I've shown that
+ 
+
+ align:start position:0%
+if I can do that then I've shown that
+any attempt to enumerate all of the
+
+ align:start position:0%
+any attempt to enumerate all of the
+ 
+
+ align:start position:0%
+any attempt to enumerate all of the
+binary sequences in 01 to the Omega any
+
+ align:start position:0%
+binary sequences in 01 to the Omega any
+ 
+
+ align:start position:0%
+binary sequences in 01 to the Omega any
+sequence like s0 S1 and S2 of binary
+
+ align:start position:0%
+sequence like s0 S1 and S2 of binary
+ 
+
+ align:start position:0%
+sequence like s0 S1 and S2 of binary
+sequences is missing something which
+
+ align:start position:0%
+sequences is missing something which
+ 
+
+ align:start position:0%
+sequences is missing something which
+means you can't really list it well how
+
+ align:start position:0%
+means you can't really list it well how
+ 
+
+ align:start position:0%
+means you can't really list it well how
+do you find something that's missing
+
+ align:start position:0%
+do you find something that's missing
+ 
+
+ align:start position:0%
+do you find something that's missing
+some how do you find a sequence that's
+
+ align:start position:0%
+some how do you find a sequence that's
+ 
+
+ align:start position:0%
+some how do you find a sequence that's
+not here well it's pretty easy um you
+
+ align:start position:0%
+not here well it's pretty easy um you
+ 
+
+ align:start position:0%
+not here well it's pretty easy um you
+look at the first digit and that was a
+
+ align:start position:0%
+look at the first digit and that was a
+ 
+
+ align:start position:0%
+look at the first digit and that was a
+zero so you choose the first digit of
+
+ align:start position:0%
+zero so you choose the first digit of
+ 
+
+ align:start position:0%
+zero so you choose the first digit of
+the new sequence to be one the opposite
+
+ align:start position:0%
+the new sequence to be one the opposite
+ 
+
+ align:start position:0%
+the new sequence to be one the opposite
+of zero you choose the second digit to
+
+ align:start position:0%
+of zero you choose the second digit to
+ 
+
+ align:start position:0%
+of zero you choose the second digit to
+be the opposite of the coordinate of s
+
+ align:start position:0%
+be the opposite of the coordinate of s
+ 
+
+ align:start position:0%
+be the opposite of the coordinate of s
+the F of uh a digit one of S1 and
+
+ align:start position:0%
+the F of uh a digit one of S1 and
+ 
+
+ align:start position:0%
+the F of uh a digit one of S1 and
+complement that now here the digit two
+
+ align:start position:0%
+complement that now here the digit two
+ 
+
+ align:start position:0%
+complement that now here the digit two
+of S2 is a zero so let's make that a one
+
+ align:start position:0%
+of S2 is a zero so let's make that a one
+ 
+
+ align:start position:0%
+of S2 is a zero so let's make that a one
+and the next one on the diagonal is a
+
+ align:start position:0%
+and the next one on the diagonal is a
+ 
+
+ align:start position:0%
+and the next one on the diagonal is a
+zero and so on we're going to complement
+
+ align:start position:0%
+zero and so on we're going to complement
+ 
+
+ align:start position:0%
+zero and so on we're going to complement
+all of the bits along this diagonal so I
+
+ align:start position:0%
+all of the bits along this diagonal so I
+ 
+
+ align:start position:0%
+all of the bits along this diagonal so I
+get a diagonal sequence that's why this
+
+ align:start position:0%
+get a diagonal sequence that's why this
+ 
+
+ align:start position:0%
+get a diagonal sequence that's why this
+argument is called a diagonal argument
+
+ align:start position:0%
+argument is called a diagonal argument
+ 
+
+ align:start position:0%
+argument is called a diagonal argument
+well let's think about this diagonal
+
+ align:start position:0%
+well let's think about this diagonal
+ 
+
+ align:start position:0%
+well let's think about this diagonal
+sequence it just goes on right down the
+
+ align:start position:0%
+sequence it just goes on right down the
+ 
+
+ align:start position:0%
+sequence it just goes on right down the
+diagonal of this two-dimensional
+
+ align:start position:0%
+diagonal of this two-dimensional
+ 
+
+ align:start position:0%
+diagonal of this two-dimensional
+infinite Matrix what we can say about it
+
+ align:start position:0%
+infinite Matrix what we can say about it
+ 
+
+ align:start position:0%
+infinite Matrix what we can say about it
+is that it differs from every row why is
+
+ align:start position:0%
+is that it differs from every row why is
+ 
+
+ align:start position:0%
+is that it differs from every row why is
+that well it differs from the 15th row
+
+ align:start position:0%
+that well it differs from the 15th row
+ 
+
+ align:start position:0%
+that well it differs from the 15th row
+at the position or coordinate 15 it
+
+ align:start position:0%
+at the position or coordinate 15 it
+ 
+
+ align:start position:0%
+at the position or coordinate 15 it
+differs from the 99th row at coordinate
+
+ align:start position:0%
+differs from the 99th row at coordinate
+ 
+
+ align:start position:0%
+differs from the 99th row at coordinate
+99 it's not in the matrix it's not a row
+
+ align:start position:0%
+99 it's not in the matrix it's not a row
+ 
+
+ align:start position:0%
+99 it's not in the matrix it's not a row
+of any Matrix and that immediately tells
+
+ align:start position:0%
+of any Matrix and that immediately tells
+ 
+
+ align:start position:0%
+of any Matrix and that immediately tells
+you it's over uh any attempt to list all
+
+ align:start position:0%
+you it's over uh any attempt to list all
+ 
+
+ align:start position:0%
+you it's over uh any attempt to list all
+of the elements in 0 one to the Omega is
+
+ align:start position:0%
+of the elements in 0 one to the Omega is
+ 
+
+ align:start position:0%
+of the elements in 0 one to the Omega is
+going to Omit a diagonal element it's
+
+ align:start position:0%
+going to Omit a diagonal element it's
+ 
+
+ align:start position:0%
+going to Omit a diagonal element it's
+not possible to list all of them in
+
+ align:start position:0%
+not possible to list all of them in
+ 
+
+ align:start position:0%
+not possible to list all of them in
+other words um uh there isn't any
+
+ align:start position:0%
+other words um uh there isn't any
+ 
+
+ align:start position:0%
+other words um uh there isn't any
+surjection from the non- negative
+
+ align:start position:0%
+surjection from the non- negative
+ 
+
+ align:start position:0%
+surjection from the non- negative
+integers to 01 to the Omega because I've
+
+ align:start position:0%
+integers to 01 to the Omega because I've
+ 
+
+ align:start position:0%
+integers to 01 to the Omega because I've
+just shown you how if you give me a
+
+ align:start position:0%
+just shown you how if you give me a
+ 
+
+ align:start position:0%
+just shown you how if you give me a
+surjection of uh anti binary sequences
+
+ align:start position:0%
+surjection of uh anti binary sequences
+ 
+
+ align:start position:0%
+surjection of uh anti binary sequences
+um in effect I'm giving you with n a
+
+ align:start position:0%
+um in effect I'm giving you with n a
+ 
+
+ align:start position:0%
+um in effect I'm giving you with n a
+zero sequence a first sequence a third a
+
+ align:start position:0%
+zero sequence a first sequence a third a
+ 
+
+ align:start position:0%
+zero sequence a first sequence a third a
+second sequence and so on then I know
+
+ align:start position:0%
+second sequence and so on then I know
+ 
+
+ align:start position:0%
+second sequence and so on then I know
+exactly how to find something that's not
+
+ align:start position:0%
+exactly how to find something that's not
+ 
+
+ align:start position:0%
+exactly how to find something that's not
+there there can't be a surjection from n
+
+ align:start position:0%
+there there can't be a surjection from n
+ 
+
+ align:start position:0%
+there there can't be a surjection from n
+to 01 to the Omega it's just not true um
+
+ align:start position:0%
+to 01 to the Omega it's just not true um
+ 
+
+ align:start position:0%
+to 01 to the Omega it's just not true um
+and that's why we can say that 0 one to
+
+ align:start position:0%
+and that's why we can say that 0 one to
+ 
+
+ align:start position:0%
+and that's why we can say that 0 one to
+the Omega is uncountable definition of
+
+ align:start position:0%
+the Omega is uncountable definition of
+ 
+
+ align:start position:0%
+the Omega is uncountable definition of
+countable or an equivalent formulation
+
+ align:start position:0%
+countable or an equivalent formulation
+ 
+
+ align:start position:0%
+countable or an equivalent formulation
+of countable remember is that there's a
+
+ align:start position:0%
+of countable remember is that there's a
+ 
+
+ align:start position:0%
+of countable remember is that there's a
+surjection from the non- negative
+
+ align:start position:0%
+surjection from the non- negative
+ 
+
+ align:start position:0%
+surjection from the non- negative
+integers to the set well there isn't any
+
+ align:start position:0%
+integers to the set well there isn't any
+ 
+
+ align:start position:0%
+integers to the set well there isn't any
+we just proved it okay so uh n is not
+
+ align:start position:0%
+we just proved it okay so uh n is not
+ 
+
+ align:start position:0%
+we just proved it okay so uh n is not
+surge Z1 by the way it's also quite easy
+
+ align:start position:0%
+surge Z1 by the way it's also quite easy
+ 
+
+ align:start position:0%
+surge Z1 by the way it's also quite easy
+to see that there is a subjection from
+
+ align:start position:0%
+to see that there is a subjection from
+ 
+
+ align:start position:0%
+to see that there is a subjection from
+the infinite binary sequence to the non-
+
+ align:start position:0%
+the infinite binary sequence to the non-
+ 
+
+ align:start position:0%
+the infinite binary sequence to the non-
+negative integers um you could map a
+
+ align:start position:0%
+negative integers um you could map a
+ 
+
+ align:start position:0%
+negative integers um you could map a
+binary sequence to uh the coordinate of
+
+ align:start position:0%
+binary sequence to uh the coordinate of
+ 
+
+ align:start position:0%
+binary sequence to uh the coordinate of
+the first one in it um and that Maps
+
+ align:start position:0%
+the first one in it um and that Maps
+ 
+
+ align:start position:0%
+the first one in it um and that Maps
+every infinite binary sequence to a non-
+
+ align:start position:0%
+every infinite binary sequence to a non-
+ 
+
+ align:start position:0%
+every infinite binary sequence to a non-
+negative integer and hits every non-
+
+ align:start position:0%
+negative integer and hits every non-
+ 
+
+ align:start position:0%
+negative integer and hits every non-
+integer negative integer lots of times
+
+ align:start position:0%
+integer negative integer lots of times
+ 
+
+ align:start position:0%
+integer negative integer lots of times
+uh I hit you know five with a sequence
+
+ align:start position:0%
+uh I hit you know five with a sequence
+ 
+
+ align:start position:0%
+uh I hit you know five with a sequence
+that starts with four zeros and a one
+
+ align:start position:0%
+that starts with four zeros and a one
+ 
+
+ align:start position:0%
+that starts with four zeros and a one
+the only sequence that doesn't go
+
+ align:start position:0%
+the only sequence that doesn't go
+ 
+
+ align:start position:0%
+the only sequence that doesn't go
+anywhere is the all zero sequence but by
+
+ align:start position:0%
+anywhere is the all zero sequence but by
+ 
+
+ align:start position:0%
+anywhere is the all zero sequence but by
+the way if you check the definition of
+
+ align:start position:0%
+the way if you check the definition of
+ 
+
+ align:start position:0%
+the way if you check the definition of
+surge it doesn't require that the
+
+ align:start position:0%
+surge it doesn't require that the
+ 
+
+ align:start position:0%
+surge it doesn't require that the
+function be total surge means that there
+
+ align:start position:0%
+function be total surge means that there
+ 
+
+ align:start position:0%
+function be total surge means that there
+is a uh a function that is a subjection
+
+ align:start position:0%
+is a uh a function that is a subjection
+ 
+
+ align:start position:0%
+is a uh a function that is a subjection
+to n uh but there doesn't have to be
+
+ align:start position:0%
+to n uh but there doesn't have to be
+ 
+
+ align:start position:0%
+to n uh but there doesn't have to be
+greater than or equal one Arrow out
+
+ align:start position:0%
+greater than or equal one Arrow out
+ 
+
+ align:start position:0%
+greater than or equal one Arrow out
+there just has to be less than or equal
+
+ align:start position:0%
+there just has to be less than or equal
+ 
+
+ align:start position:0%
+there just has to be less than or equal
+to one Arrow so it's a function but of
+
+ align:start position:0%
+to one Arrow so it's a function but of
+ 
+
+ align:start position:0%
+to one Arrow so it's a function but of
+course it's easy enough to make it total
+
+ align:start position:0%
+course it's easy enough to make it total
+ 
+
+ align:start position:0%
+course it's easy enough to make it total
+the all zero sequence just map it to
+
+ align:start position:0%
+the all zero sequence just map it to
+ 
+
+ align:start position:0%
+the all zero sequence just map it to
+zero um so now you have uh both zero and
+
+ align:start position:0%
+zero um so now you have uh both zero and
+ 
+
+ align:start position:0%
+zero um so now you have uh both zero and
+uh the sequence that starts with the
+
+ align:start position:0%
+uh the sequence that starts with the
+ 
+
+ align:start position:0%
+uh the sequence that starts with the
+sequence that any sequence that starts
+
+ align:start position:0%
+sequence that any sequence that starts
+ 
+
+ align:start position:0%
+sequence that any sequence that starts
+with one will all map to zero okay so uh
+
+ align:start position:0%
+with one will all map to zero okay so uh
+ 
+
+ align:start position:0%
+with one will all map to zero okay so uh
+if we remember our intuition surge is
+
+ align:start position:0%
+if we remember our intuition surge is
+ 
+
+ align:start position:0%
+if we remember our intuition surge is
+read as greater than or equal to so this
+
+ align:start position:0%
+read as greater than or equal to so this
+ 
+
+ align:start position:0%
+read as greater than or equal to so this
+tells us that the infinite binary
+
+ align:start position:0%
+tells us that the infinite binary
+ 
+
+ align:start position:0%
+tells us that the infinite binary
+sequences are a larger set at least as
+
+ align:start position:0%
+sequences are a larger set at least as
+ 
+
+ align:start position:0%
+sequences are a larger set at least as
+larg as set as the non- negative
+
+ align:start position:0%
+larg as set as the non- negative
+ 
+
+ align:start position:0%
+larg as set as the non- negative
+integers and the converse is true the
+
+ align:start position:0%
+integers and the converse is true the
+ 
+
+ align:start position:0%
+integers and the converse is true the
+non- negative integers are not as least
+
+ align:start position:0%
+non- negative integers are not as least
+ 
+
+ align:start position:0%
+non- negative integers are not as least
+at least as large as the infinite binary
+
+ align:start position:0%
+at least as large as the infinite binary
+ 
+
+ align:start position:0%
+at least as large as the infinite binary
+sequences so we can really say that the
+
+ align:start position:0%
+sequences so we can really say that the
+ 
+
+ align:start position:0%
+sequences so we can really say that the
+non- negative integers are strictly
+
+ align:start position:0%
+non- negative integers are strictly
+ 
+
+ align:start position:0%
+non- negative integers are strictly
+smaller than the set of infinite binary
+
+ align:start position:0%
+smaller than the set of infinite binary
+ 
+
+ align:start position:0%
+smaller than the set of infinite binary
+sequences now strictly smaller is in
+
+ align:start position:0%
+sequences now strictly smaller is in
+ 
+
+ align:start position:0%
+sequences now strictly smaller is in
+quotes because again we don't know
+
+ align:start position:0%
+quotes because again we don't know
+ 
+
+ align:start position:0%
+quotes because again we don't know
+exactly what the size of infinite sets
+
+ align:start position:0%
+exactly what the size of infinite sets
+ 
+
+ align:start position:0%
+exactly what the size of infinite sets
+is all we're doing really are talking
+
+ align:start position:0%
+is all we're doing really are talking
+ 
+
+ align:start position:0%
+is all we're doing really are talking
+about properties
+
+ align:start position:0%
+about properties
+ 
+
+ align:start position:0%
+about properties
+objections bje surjections
+
+ align:start position:0%
+objections bje surjections
+ 
+
+ align:start position:0%
+objections bje surjections
+injections okay so let's make an
+
+ align:start position:0%
+injections okay so let's make an
+ 
+
+ align:start position:0%
+injections okay so let's make an
+explicit definition I'm going to say
+
+ align:start position:0%
+explicit definition I'm going to say
+ 
+
+ align:start position:0%
+explicit definition I'm going to say
+that a strict B means that there is no
+
+ align:start position:0%
+that a strict B means that there is no
+ 
+
+ align:start position:0%
+that a strict B means that there is no
+surjection from A to B so if we read a
+
+ align:start position:0%
+surjection from A to B so if we read a
+ 
+
+ align:start position:0%
+surjection from A to B so if we read a
+surjection b intuitively as a greater
+
+ align:start position:0%
+surjection b intuitively as a greater
+ 
+
+ align:start position:0%
+surjection b intuitively as a greater
+than equal to B this is saying it's not
+
+ align:start position:0%
+than equal to B this is saying it's not
+ 
+
+ align:start position:0%
+than equal to B this is saying it's not
+true that a is greater than equal to b
+
+ align:start position:0%
+true that a is greater than equal to b
+ 
+
+ align:start position:0%
+true that a is greater than equal to b
+or in ordinary language and thinking
+
+ align:start position:0%
+or in ordinary language and thinking
+ 
+
+ align:start position:0%
+or in ordinary language and thinking
+about sets if it's not true that you're
+
+ align:start position:0%
+about sets if it's not true that you're
+ 
+
+ align:start position:0%
+about sets if it's not true that you're
+greater than or equal to B you must be
+
+ align:start position:0%
+greater than or equal to B you must be
+ 
+
+ align:start position:0%
+greater than or equal to B you must be
+strictly less than b so that's the
+
+ align:start position:0%
+strictly less than b so that's the
+ 
+
+ align:start position:0%
+strictly less than b so that's the
+motivation for the word strict but
+
+ align:start position:0%
+motivation for the word strict but
+ 
+
+ align:start position:0%
+motivation for the word strict but
+remember we're talking about infinite
+
+ align:start position:0%
+remember we're talking about infinite
+ 
+
+ align:start position:0%
+remember we're talking about infinite
+sets and we can't go around assuming too
+
+ align:start position:0%
+sets and we can't go around assuming too
+ 
+
+ align:start position:0%
+sets and we can't go around assuming too
+many properties of strict until we've
+
+ align:start position:0%
+many properties of strict until we've
+ 
+
+ align:start position:0%
+many properties of strict until we've
+prove them one non-trivial property by
+
+ align:start position:0%
+prove them one non-trivial property by
+ 
+
+ align:start position:0%
+prove them one non-trivial property by
+the way is I've defined strict that it's
+
+ align:start position:0%
+the way is I've defined strict that it's
+ 
+
+ align:start position:0%
+the way is I've defined strict that it's
+not true that there's a subjection from
+
+ align:start position:0%
+not true that there's a subjection from
+ 
+
+ align:start position:0%
+not true that there's a subjection from
+A to B uh B but I'm not insisting that
+
+ align:start position:0%
+A to B uh B but I'm not insisting that
+ 
+
+ align:start position:0%
+A to B uh B but I'm not insisting that
+there must be a surjection from B to a
+
+ align:start position:0%
+there must be a surjection from B to a
+ 
+
+ align:start position:0%
+there must be a surjection from B to a
+um which would be the second companion
+
+ align:start position:0%
+um which would be the second companion
+ 
+
+ align:start position:0%
+um which would be the second companion
+part that is a is not greater than equal
+
+ align:start position:0%
+part that is a is not greater than equal
+ 
+
+ align:start position:0%
+part that is a is not greater than equal
+to B and B is greater than equal to a
+
+ align:start position:0%
+to B and B is greater than equal to a
+ 
+
+ align:start position:0%
+to B and B is greater than equal to a
+turns out technically you can prove that
+
+ align:start position:0%
+turns out technically you can prove that
+ 
+
+ align:start position:0%
+turns out technically you can prove that
+if there isn't any surjection from A to
+
+ align:start position:0%
+if there isn't any surjection from A to
+ 
+
+ align:start position:0%
+if there isn't any surjection from A to
+B there will be a surjection from B to a
+
+ align:start position:0%
+B there will be a surjection from B to a
+ 
+
+ align:start position:0%
+B there will be a surjection from B to a
+but that's using a set theoretic
+
+ align:start position:0%
+but that's using a set theoretic
+ 
+
+ align:start position:0%
+but that's using a set theoretic
+argument that's not so obvious and we
+
+ align:start position:0%
+argument that's not so obvious and we
+ 
+
+ align:start position:0%
+argument that's not so obvious and we
+don't need it so this is the definition
+
+ align:start position:0%
+don't need it so this is the definition
+ 
+
+ align:start position:0%
+don't need it so this is the definition
+of strict a strict b means you cannot
+
+ align:start position:0%
+of strict a strict b means you cannot
+ 
+
+ align:start position:0%
+of strict a strict b means you cannot
+get a surjection from A to B and we're
+
+ align:start position:0%
+get a surjection from A to B and we're
+ 
+
+ align:start position:0%
+get a surjection from A to B and we're
+intuitively reading it as a is strictly
+
+ align:start position:0%
+intuitively reading it as a is strictly
+ 
+
+ align:start position:0%
+intuitively reading it as a is strictly
+smaller than b and we what we've just
+
+ align:start position:0%
+smaller than b and we what we've just
+ 
+
+ align:start position:0%
+smaller than b and we what we've just
+shown then is that the non- negative
+
+ align:start position:0%
+shown then is that the non- negative
+ 
+
+ align:start position:0%
+shown then is that the non- negative
+integers strict uh 0 one to the Omega
+
+ align:start position:0%
+integers strict uh 0 one to the Omega
+ 
+
+ align:start position:0%
+integers strict uh 0 one to the Omega
+the infinite binary sequences okay now
+
+ align:start position:0%
+the infinite binary sequences okay now
+ 
+
+ align:start position:0%
+the infinite binary sequences okay now
+cantis theorem is a wonderful uh
+
+ align:start position:0%
+cantis theorem is a wonderful uh
+ 
+
+ align:start position:0%
+cantis theorem is a wonderful uh
+generalization of this it's a powerful
+
+ align:start position:0%
+generalization of this it's a powerful
+ 
+
+ align:start position:0%
+generalization of this it's a powerful
+generalization but the proof is pretty
+
+ align:start position:0%
+generalization but the proof is pretty
+ 
+
+ align:start position:0%
+generalization but the proof is pretty
+much the same although it sometimes
+
+ align:start position:0%
+much the same although it sometimes
+ 
+
+ align:start position:0%
+much the same although it sometimes
+looks a little different as it's written
+
+ align:start position:0%
+looks a little different as it's written
+ 
+
+ align:start position:0%
+looks a little different as it's written
+up and what cantis theorem says is just
+
+ align:start position:0%
+up and what cantis theorem says is just
+ 
+
+ align:start position:0%
+up and what cantis theorem says is just
+it's it's just beautifully elegant and
+
+ align:start position:0%
+it's it's just beautifully elegant and
+ 
+
+ align:start position:0%
+it's it's just beautifully elegant and
+simple it simp it says simply that the
+
+ align:start position:0%
+simple it simp it says simply that the
+ 
+
+ align:start position:0%
+simple it simp it says simply that the
+power set is strictly bigger than the
+
+ align:start position:0%
+power set is strictly bigger than the
+ 
+
+ align:start position:0%
+power set is strictly bigger than the
+set a strict power set of a for every
+
+ align:start position:0%
+set a strict power set of a for every
+ 
+
+ align:start position:0%
+set a strict power set of a for every
+set a even if a is finite because
+
+ align:start position:0%
+set a even if a is finite because
+ 
+
+ align:start position:0%
+set a even if a is finite because
+remember if a is finite say a has n
+
+ align:start position:0%
+remember if a is finite say a has n
+ 
+
+ align:start position:0%
+remember if a is finite say a has n
+elements then the power set of a has two
+
+ align:start position:0%
+elements then the power set of a has two
+ 
+
+ align:start position:0%
+elements then the power set of a has two
+to the N elements and you can check that
+
+ align:start position:0%
+to the N elements and you can check that
+ 
+
+ align:start position:0%
+to the N elements and you can check that
+even for n equal zero n is less than or
+
+ align:start position:0%
+even for n equal zero n is less than or
+ 
+
+ align:start position:0%
+even for n equal zero n is less than or
+equal to 2 to the N is less than 2 to
+
+ align:start position:0%
+equal to 2 to the N is less than 2 to
+ 
+
+ align:start position:0%
+equal to 2 to the N is less than 2 to
+the n uh 0 is less than two to the 0
+
+ align:start position:0%
+the n uh 0 is less than two to the 0
+ 
+
+ align:start position:0%
+the n uh 0 is less than two to the 0
+which is one um uh two is less than 2^
+
+ align:start position:0%
+which is one um uh two is less than 2^
+ 
+
+ align:start position:0%
+which is one um uh two is less than 2^
+2ar which is four and so on so even for
+
+ align:start position:0%
+2ar which is four and so on so even for
+ 
+
+ align:start position:0%
+2ar which is four and so on so even for
+finite sets we have a strict power set
+
+ align:start position:0%
+finite sets we have a strict power set
+ 
+
+ align:start position:0%
+finite sets we have a strict power set
+of a but the cool thing is that it works
+
+ align:start position:0%
+of a but the cool thing is that it works
+ 
+
+ align:start position:0%
+of a but the cool thing is that it works
+even for infinite sets let's take a look
+
+ align:start position:0%
+even for infinite sets let's take a look
+ 
+
+ align:start position:0%
+even for infinite sets let's take a look
+it's a diagonal argument again but now I
+
+ align:start position:0%
+it's a diagonal argument again but now I
+ 
+
+ align:start position:0%
+it's a diagonal argument again but now I
+mustn't assume that a is countable I'm
+
+ align:start position:0%
+mustn't assume that a is countable I'm
+ 
+
+ align:start position:0%
+mustn't assume that a is countable I'm
+not going to assume that I can really
+
+ align:start position:0%
+not going to assume that I can really
+ 
+
+ align:start position:0%
+not going to assume that I can really
+list the elements of a but we'll think
+
+ align:start position:0%
+list the elements of a but we'll think
+ 
+
+ align:start position:0%
+list the elements of a but we'll think
+about it as though we could let's think
+
+ align:start position:0%
+about it as though we could let's think
+ 
+
+ align:start position:0%
+about it as though we could let's think
+about this Matrix again so suppose a is
+
+ align:start position:0%
+about this Matrix again so suppose a is
+ 
+
+ align:start position:0%
+about this Matrix again so suppose a is
+this set of elements a b s TDE e I'm
+
+ align:start position:0%
+this set of elements a b s TDE e I'm
+ 
+
+ align:start position:0%
+this set of elements a b s TDE e I'm
+scrambling up the alphabet on purpose
+
+ align:start position:0%
+scrambling up the alphabet on purpose
+ 
+
+ align:start position:0%
+scrambling up the alphabet on purpose
+because I don't want you to get the idea
+
+ align:start position:0%
+because I don't want you to get the idea
+ 
+
+ align:start position:0%
+because I don't want you to get the idea
+that we're assuming that a is countable
+
+ align:start position:0%
+that we're assuming that a is countable
+ 
+
+ align:start position:0%
+that we're assuming that a is countable
+that you can list all the elements of a
+
+ align:start position:0%
+that you can list all the elements of a
+ 
+
+ align:start position:0%
+that you can list all the elements of a
+I'm not assuming that but I'm just
+
+ align:start position:0%
+I'm not assuming that but I'm just
+ 
+
+ align:start position:0%
+I'm not assuming that but I'm just
+writing out a sample of elements of a
+
+ align:start position:0%
+writing out a sample of elements of a
+ 
+
+ align:start position:0%
+writing out a sample of elements of a
+and let's suppose that I was trying to
+
+ align:start position:0%
+and let's suppose that I was trying to
+ 
+
+ align:start position:0%
+and let's suppose that I was trying to
+get a surjection from a to the power set
+
+ align:start position:0%
+get a surjection from a to the power set
+ 
+
+ align:start position:0%
+get a surjection from a to the power set
+of a so suppose I have a function f that
+
+ align:start position:0%
+of a so suppose I have a function f that
+ 
+
+ align:start position:0%
+of a so suppose I have a function f that
+Maps each of the successive elements of
+
+ align:start position:0%
+Maps each of the successive elements of
+ 
+
+ align:start position:0%
+Maps each of the successive elements of
+a to some subset of a so F of a is
+
+ align:start position:0%
+a to some subset of a so F of a is
+ 
+
+ align:start position:0%
+a to some subset of a so F of a is
+is part of the power set it's a subset
+
+ align:start position:0%
+is part of the power set it's a subset
+ 
+
+ align:start position:0%
+is part of the power set it's a subset
+of capital A F of B is a subset of
+
+ align:start position:0%
+of capital A F of B is a subset of
+ 
+
+ align:start position:0%
+of capital A F of B is a subset of
+capital A and so on and suppose I had a
+
+ align:start position:0%
+capital A and so on and suppose I had a
+ 
+
+ align:start position:0%
+capital A and so on and suppose I had a
+set up like this I'm going to draw a
+
+ align:start position:0%
+set up like this I'm going to draw a
+ 
+
+ align:start position:0%
+set up like this I'm going to draw a
+matrix that looks like the diagonal
+
+ align:start position:0%
+matrix that looks like the diagonal
+ 
+
+ align:start position:0%
+matrix that looks like the diagonal
+matrix and we're going to extract the
+
+ align:start position:0%
+matrix and we're going to extract the
+ 
+
+ align:start position:0%
+matrix and we're going to extract the
+diagonal set and discover that that
+
+ align:start position:0%
+diagonal set and discover that that
+ 
+
+ align:start position:0%
+diagonal set and discover that that
+diagonal set is not one of the fs it's
+
+ align:start position:0%
+diagonal set is not one of the fs it's
+ 
+
+ align:start position:0%
+diagonal set is not one of the fs it's
+not F of anything which means that f is
+
+ align:start position:0%
+not F of anything which means that f is
+ 
+
+ align:start position:0%
+not F of anything which means that f is
+not going to be a surjection so let's
+
+ align:start position:0%
+not going to be a surjection so let's
+ 
+
+ align:start position:0%
+not going to be a surjection so let's
+look at it again so here's this Matrix
+
+ align:start position:0%
+look at it again so here's this Matrix
+ 
+
+ align:start position:0%
+look at it again so here's this Matrix
+where I'm labeling The Columns of the
+
+ align:start position:0%
+where I'm labeling The Columns of the
+ 
+
+ align:start position:0%
+where I'm labeling The Columns of the
+matrix by the elements of a uh no
+
+ align:start position:0%
+matrix by the elements of a uh no
+ 
+
+ align:start position:0%
+matrix by the elements of a uh no
+particular order here but I in order to
+
+ align:start position:0%
+particular order here but I in order to
+ 
+
+ align:start position:0%
+particular order here but I in order to
+draw Matrix I have to write them down in
+
+ align:start position:0%
+draw Matrix I have to write them down in
+ 
+
+ align:start position:0%
+draw Matrix I have to write them down in
+some order and likewise the first row is
+
+ align:start position:0%
+some order and likewise the first row is
+ 
+
+ align:start position:0%
+some order and likewise the first row is
+going to be F of this element a well
+
+ align:start position:0%
+going to be F of this element a well
+ 
+
+ align:start position:0%
+going to be F of this element a well
+what is an F of a f of a is going to be
+
+ align:start position:0%
+what is an F of a f of a is going to be
+ 
+
+ align:start position:0%
+what is an F of a f of a is going to be
+a set of elements so let's just write
+
+ align:start position:0%
+a set of elements so let's just write
+ 
+
+ align:start position:0%
+a set of elements so let's just write
+the elements in F of a Down Under the
+
+ align:start position:0%
+the elements in F of a Down Under the
+ 
+
+ align:start position:0%
+the elements in F of a Down Under the
+corresponding column label so here's an
+
+ align:start position:0%
+corresponding column label so here's an
+ 
+
+ align:start position:0%
+corresponding column label so here's an
+example where F of a it has an A in it
+
+ align:start position:0%
+example where F of a it has an A in it
+ 
+
+ align:start position:0%
+example where F of a it has an A in it
+and no B but it has an s in it and a t
+
+ align:start position:0%
+and no B but it has an s in it and a t
+ 
+
+ align:start position:0%
+and no B but it has an s in it and a t
+in it no C uh no D it has an e like F of
+
+ align:start position:0%
+in it no C uh no D it has an e like F of
+ 
+
+ align:start position:0%
+in it no C uh no D it has an e like F of
+B has an A and A B and no s or t but
+
+ align:start position:0%
+B has an A and A B and no s or t but
+ 
+
+ align:start position:0%
+B has an A and A B and no s or t but
+it's got a C and so so I filled in this
+
+ align:start position:0%
+it's got a C and so so I filled in this
+ 
+
+ align:start position:0%
+it's got a C and so so I filled in this
+matrix by taking F of an element in a
+
+ align:start position:0%
+matrix by taking F of an element in a
+ 
+
+ align:start position:0%
+matrix by taking F of an element in a
+which is supposed to be a subset of a
+
+ align:start position:0%
+which is supposed to be a subset of a
+ 
+
+ align:start position:0%
+which is supposed to be a subset of a
+and writing out all of the elements in
+
+ align:start position:0%
+and writing out all of the elements in
+ 
+
+ align:start position:0%
+and writing out all of the elements in
+that subset um uh under the
+
+ align:start position:0%
+that subset um uh under the
+ 
+
+ align:start position:0%
+that subset um uh under the
+corresponding uh letter
+
+ align:start position:0%
+corresponding uh letter
+ 
+
+ align:start position:0%
+corresponding uh letter
+or corresponding element that of the
+
+ align:start position:0%
+or corresponding element that of the
+ 
+
+ align:start position:0%
+or corresponding element that of the
+subset so a b goes under a b if it's in
+
+ align:start position:0%
+subset so a b goes under a b if it's in
+ 
+
+ align:start position:0%
+subset so a b goes under a b if it's in
+F of C and S goes under an s if it's in
+
+ align:start position:0%
+F of C and S goes under an s if it's in
+ 
+
+ align:start position:0%
+F of C and S goes under an s if it's in
+F of C nothing goes under a t if T is
+
+ align:start position:0%
+F of C nothing goes under a t if T is
+ 
+
+ align:start position:0%
+F of C nothing goes under a t if T is
+not an F of C that's what we're seeing
+
+ align:start position:0%
+not an F of C that's what we're seeing
+ 
+
+ align:start position:0%
+not an F of C that's what we're seeing
+here so I'm laying out as though I was
+
+ align:start position:0%
+here so I'm laying out as though I was
+ 
+
+ align:start position:0%
+here so I'm laying out as though I was
+using zeros and ones for an infinite
+
+ align:start position:0%
+using zeros and ones for an infinite
+ 
+
+ align:start position:0%
+using zeros and ones for an infinite
+binary sequence I'm laying out each of
+
+ align:start position:0%
+binary sequence I'm laying out each of
+ 
+
+ align:start position:0%
+binary sequence I'm laying out each of
+the sets that uh that are in the range
+
+ align:start position:0%
+the sets that uh that are in the range
+ 
+
+ align:start position:0%
+the sets that uh that are in the range
+of f um along this row and now with this
+
+ align:start position:0%
+of f um along this row and now with this
+ 
+
+ align:start position:0%
+of f um along this row and now with this
+set up I can define a new set which is
+
+ align:start position:0%
+set up I can define a new set which is
+ 
+
+ align:start position:0%
+set up I can define a new set which is
+not going to be an F how do I get that
+
+ align:start position:0%
+not going to be an F how do I get that
+ 
+
+ align:start position:0%
+not going to be an F how do I get that
+well um what I'm going to do is not in
+
+ align:start position:0%
+well um what I'm going to do is not in
+ 
+
+ align:start position:0%
+well um what I'm going to do is not in
+my new set I'm not going to have any of
+
+ align:start position:0%
+my new set I'm not going to have any of
+ 
+
+ align:start position:0%
+my new set I'm not going to have any of
+the elements that appear on the diagonal
+
+ align:start position:0%
+the elements that appear on the diagonal
+ 
+
+ align:start position:0%
+the elements that appear on the diagonal
+so if a is a member of f of a that means
+
+ align:start position:0%
+so if a is a member of f of a that means
+ 
+
+ align:start position:0%
+so if a is a member of f of a that means
+that a appears in this coordinate it's
+
+ align:start position:0%
+that a appears in this coordinate it's
+ 
+
+ align:start position:0%
+that a appears in this coordinate it's
+not going to be in my set if B is in F
+
+ align:start position:0%
+not going to be in my set if B is in F
+ 
+
+ align:start position:0%
+not going to be in my set if B is in F
+of B meaning that b appears in uh that b
+
+ align:start position:0%
+of B meaning that b appears in uh that b
+ 
+
+ align:start position:0%
+of B meaning that b appears in uh that b
+appears in the F ofb row under the
+
+ align:start position:0%
+appears in the F ofb row under the
+ 
+
+ align:start position:0%
+appears in the F ofb row under the
+column B it's not going to be in my Set
+
+ align:start position:0%
+column B it's not going to be in my Set
+ 
+
+ align:start position:0%
+column B it's not going to be in my Set
+uh on the other hand uh s is not an F of
+
+ align:start position:0%
+uh on the other hand uh s is not an F of
+ 
+
+ align:start position:0%
+uh on the other hand uh s is not an F of
+s because there's no s there so I'm G to
+
+ align:start position:0%
+s because there's no s there so I'm G to
+ 
+
+ align:start position:0%
+s because there's no s there so I'm G to
+put an S there in in mag magenta and
+
+ align:start position:0%
+put an S there in in mag magenta and
+ 
+
+ align:start position:0%
+put an S there in in mag magenta and
+likewise I'm going to stick elements in
+
+ align:start position:0%
+likewise I'm going to stick elements in
+ 
+
+ align:start position:0%
+likewise I'm going to stick elements in
+or out the opposite of whether they
+
+ align:start position:0%
+or out the opposite of whether they
+ 
+
+ align:start position:0%
+or out the opposite of whether they
+appear on the diagonal and this is going
+
+ align:start position:0%
+appear on the diagonal and this is going
+ 
+
+ align:start position:0%
+appear on the diagonal and this is going
+to give me a set D um which is going to
+
+ align:start position:0%
+to give me a set D um which is going to
+ 
+
+ align:start position:0%
+to give me a set D um which is going to
+be my diagonal set okay um so if we
+
+ align:start position:0%
+be my diagonal set okay um so if we
+ 
+
+ align:start position:0%
+be my diagonal set okay um so if we
+write this out so what we're saying is
+
+ align:start position:0%
+write this out so what we're saying is
+ 
+
+ align:start position:0%
+write this out so what we're saying is
+suppose that I have a function f from a
+
+ align:start position:0%
+suppose that I have a function f from a
+ 
+
+ align:start position:0%
+suppose that I have a function f from a
+to the power set of a uh then what I'm
+
+ align:start position:0%
+to the power set of a uh then what I'm
+ 
+
+ align:start position:0%
+to the power set of a uh then what I'm
+going to do is Define a subset of a
+
+ align:start position:0%
+going to do is Define a subset of a
+ 
+
+ align:start position:0%
+going to do is Define a subset of a
+that's not in the range of f namely set
+
+ align:start position:0%
+that's not in the range of f namely set
+ 
+
+ align:start position:0%
+that's not in the range of f namely set
+B um which is the set of those elements
+
+ align:start position:0%
+B um which is the set of those elements
+ 
+
+ align:start position:0%
+B um which is the set of those elements
+in a such that little a is not in F of a
+
+ align:start position:0%
+in a such that little a is not in F of a
+ 
+
+ align:start position:0%
+in a such that little a is not in F of a
+namely if uh if an element appeared on
+
+ align:start position:0%
+namely if uh if an element appeared on
+ 
+
+ align:start position:0%
+namely if uh if an element appeared on
+the diagonal because an element um uh uh
+
+ align:start position:0%
+the diagonal because an element um uh uh
+ 
+
+ align:start position:0%
+the diagonal because an element um uh uh
+with column label a was in the row F of
+
+ align:start position:0%
+with column label a was in the row F of
+ 
+
+ align:start position:0%
+with column label a was in the row F of
+a then I left it out of my set and if it
+
+ align:start position:0%
+a then I left it out of my set and if it
+ 
+
+ align:start position:0%
+a then I left it out of my set and if it
+was not in uh in that location in The
+
+ align:start position:0%
+was not in uh in that location in The
+ 
+
+ align:start position:0%
+was not in uh in that location in The
+Matrix I put it in my set so I'm keeping
+
+ align:start position:0%
+Matrix I put it in my set so I'm keeping
+ 
+
+ align:start position:0%
+Matrix I put it in my set so I'm keeping
+all the elements that aren't in on the
+
+ align:start position:0%
+all the elements that aren't in on the
+ 
+
+ align:start position:0%
+all the elements that aren't in on the
+diagonal that's my diagonal set D and
+
+ align:start position:0%
+diagonal that's my diagonal set D and
+ 
+
+ align:start position:0%
+diagonal that's my diagonal set D and
+what I know about it is that D is not in
+
+ align:start position:0%
+what I know about it is that D is not in
+ 
+
+ align:start position:0%
+what I know about it is that D is not in
+the range of f because it differs from
+
+ align:start position:0%
+the range of f because it differs from
+ 
+
+ align:start position:0%
+the range of f because it differs from
+every possible row of the Matrix um if
+
+ align:start position:0%
+every possible row of the Matrix um if
+ 
+
+ align:start position:0%
+every possible row of the Matrix um if
+the row was labeled with uh with f of a
+
+ align:start position:0%
+the row was labeled with uh with f of a
+ 
+
+ align:start position:0%
+the row was labeled with uh with f of a
+as F of a then it differs in the column
+
+ align:start position:0%
+as F of a then it differs in the column
+ 
+
+ align:start position:0%
+as F of a then it differs in the column
+A F of a from that row and therefore my
+
+ align:start position:0%
+A F of a from that row and therefore my
+ 
+
+ align:start position:0%
+A F of a from that row and therefore my
+set D is not uh a row of this Matrix and
+
+ align:start position:0%
+set D is not uh a row of this Matrix and
+ 
+
+ align:start position:0%
+set D is not uh a row of this Matrix and
+that means that it's not equal to F of
+
+ align:start position:0%
+that means that it's not equal to F of
+ 
+
+ align:start position:0%
+that means that it's not equal to F of
+anything so I've just found that there's
+
+ align:start position:0%
+anything so I've just found that there's
+ 
+
+ align:start position:0%
+anything so I've just found that there's
+no F Arrow into d d is not in the range
+
+ align:start position:0%
+no F Arrow into d d is not in the range
+ 
+
+ align:start position:0%
+no F Arrow into d d is not in the range
+of F that means that if I had such an F
+
+ align:start position:0%
+of F that means that if I had such an F
+ 
+
+ align:start position:0%
+of F that means that if I had such an F
+from a to the power set of a it's not a
+
+ align:start position:0%
+from a to the power set of a it's not a
+ 
+
+ align:start position:0%
+from a to the power set of a it's not a
+subjection because D is always left out
+
+ align:start position:0%
+subjection because D is always left out
+ 
+
+ align:start position:0%
+subjection because D is always left out
+so f is not a subjection and since you
+
+ align:start position:0%
+so f is not a subjection and since you
+ 
+
+ align:start position:0%
+so f is not a subjection and since you
+know f is any function from a to the
+
+ align:start position:0%
+know f is any function from a to the
+ 
+
+ align:start position:0%
+know f is any function from a to the
+power set of a none of them are
+
+ align:start position:0%
+power set of a none of them are
+ 
+
+ align:start position:0%
+power set of a none of them are
+subjections and that means there's no
+
+ align:start position:0%
+subjections and that means there's no
+ 
+
+ align:start position:0%
+subjections and that means there's no
+subjection from a to the power set of a
+
+ align:start position:0%
+subjection from a to the power set of a
+ 
+
+ align:start position:0%
+subjection from a to the power set of a
+in other words a strict power set of a
+
+ align:start position:0%
+in other words a strict power set of a
+ 
+
+ align:start position:0%
+in other words a strict power set of a
+there's no Sur
+
+ align:start position:0%
+there's no Sur
+ 
+
+ align:start position:0%
+there's no Sur
+now uh a special case of this of course
+
+ align:start position:0%
+now uh a special case of this of course
+ 
+
+ align:start position:0%
+now uh a special case of this of course
+is that the non- negative integers are
+
+ align:start position:0%
+is that the non- negative integers are
+ 
+
+ align:start position:0%
+is that the non- negative integers are
+uh a strictly smaller than the power set
+
+ align:start position:0%
+uh a strictly smaller than the power set
+ 
+
+ align:start position:0%
+uh a strictly smaller than the power set
+of n because that's just an instance of
+
+ align:start position:0%
+of n because that's just an instance of
+ 
+
+ align:start position:0%
+of n because that's just an instance of
+of canas theorem where we're applying uh
+
+ align:start position:0%
+of canas theorem where we're applying uh
+ 
+
+ align:start position:0%
+of canas theorem where we're applying uh
+uh a being the set of non- negative
+
+ align:start position:0%
+uh a being the set of non- negative
+ 
+
+ align:start position:0%
+uh a being the set of non- negative
+integers so there's no subjection from
+
+ align:start position:0%
+integers so there's no subjection from
+ 
+
+ align:start position:0%
+integers so there's no subjection from
+the non- negative integers to the
+
+ align:start position:0%
+the non- negative integers to the
+ 
+
+ align:start position:0%
+the non- negative integers to the
+subsets of non- negative integers uh
+
+ align:start position:0%
+subsets of non- negative integers uh
+ 
+
+ align:start position:0%
+subsets of non- negative integers uh
+again that means that the power set of n
+
+ align:start position:0%
+again that means that the power set of n
+ 
+
+ align:start position:0%
+again that means that the power set of n
+is an example of an uncountable set
+
+ align:start position:0%
+is an example of an uncountable set
+ 
+
+ align:start position:0%
+is an example of an uncountable set
+because um the definition of countable
+
+ align:start position:0%
+because um the definition of countable
+ 
+
+ align:start position:0%
+because um the definition of countable
+is that there would be a surjection from
+
+ align:start position:0%
+is that there would be a surjection from
+ 
+
+ align:start position:0%
+is that there would be a surjection from
+n to power set of n we're saying there
+
+ align:start position:0%
+n to power set of n we're saying there
+ 
+
+ align:start position:0%
+n to power set of n we're saying there
+isn't any so it's not countable or not
+
+ align:start position:0%
+isn't any so it's not countable or not
+ 
+
+ align:start position:0%
+isn't any so it's not countable or not
+countable is is usually phrased as
+
+ align:start position:0%
+countable is is usually phrased as
+ 
+
+ align:start position:0%
+countable is is usually phrased as
+uncountable so the power set of n is
+
+ align:start position:0%
+uncountable so the power set of n is
+ 
+
+ align:start position:0%
+uncountable so the power set of n is
+maybe our uh second example of an
+
+ align:start position:0%
+maybe our uh second example of an
+ 
+
+ align:start position:0%
+maybe our uh second example of an
+uncountable set the first one being the
+
+ align:start position:0%
+uncountable set the first one being the
+ 
+
+ align:start position:0%
+uncountable set the first one being the
+infinite sequences of binary numbers now
+
+ align:start position:0%
+infinite sequences of binary numbers now
+ 
+
+ align:start position:0%
+infinite sequences of binary numbers now
+as a matter of fact um there's a just as
+
+ align:start position:0%
+as a matter of fact um there's a just as
+ 
+
+ align:start position:0%
+as a matter of fact um there's a just as
+we had a general way to prove
+
+ align:start position:0%
+we had a general way to prove
+ 
+
+ align:start position:0%
+we had a general way to prove
+countability um you can show that a set
+
+ align:start position:0%
+countability um you can show that a set
+ 
+
+ align:start position:0%
+countability um you can show that a set
+is countable if there's a surjection
+
+ align:start position:0%
+is countable if there's a surjection
+ 
+
+ align:start position:0%
+is countable if there's a surjection
+from a set you know is countable onto
+
+ align:start position:0%
+from a set you know is countable onto
+ 
+
+ align:start position:0%
+from a set you know is countable onto
+the target then the target's countable
+
+ align:start position:0%
+the target then the target's countable
+ 
+
+ align:start position:0%
+the target then the target's countable
+take the contrapositive of that Lemma
+
+ align:start position:0%
+take the contrapositive of that Lemma
+ 
+
+ align:start position:0%
+take the contrapositive of that Lemma
+and you can say that if a set uh a is
+
+ align:start position:0%
+and you can say that if a set uh a is
+ 
+
+ align:start position:0%
+and you can say that if a set uh a is
+uncountable and there's a surjection
+
+ align:start position:0%
+uncountable and there's a surjection
+ 
+
+ align:start position:0%
+uncountable and there's a surjection
+from C to a then C has to be uncountable
+
+ align:start position:0%
+from C to a then C has to be uncountable
+ 
+
+ align:start position:0%
+from C to a then C has to be uncountable
+that's just a contrapositive of the
+
+ align:start position:0%
+that's just a contrapositive of the
+ 
+
+ align:start position:0%
+that's just a contrapositive of the
+previous one if C was countable then a
+
+ align:start position:0%
+previous one if C was countable then a
+ 
+
+ align:start position:0%
+previous one if C was countable then a
+would be countable so if a is
+
+ align:start position:0%
+would be countable so if a is
+ 
+
+ align:start position:0%
+would be countable so if a is
+uncountable C must be uncountable so
+
+ align:start position:0%
+uncountable C must be uncountable so
+ 
+
+ align:start position:0%
+uncountable C must be uncountable so
+this gives us again a nice General way
+
+ align:start position:0%
+this gives us again a nice General way
+ 
+
+ align:start position:0%
+this gives us again a nice General way
+to prove uncountability of sets once I
+
+ align:start position:0%
+to prove uncountability of sets once I
+ 
+
+ align:start position:0%
+to prove uncountability of sets once I
+have a couple in my repertoire um well
+
+ align:start position:0%
+have a couple in my repertoire um well
+ 
+
+ align:start position:0%
+have a couple in my repertoire um well
+uh means that we could have deduced that
+
+ align:start position:0%
+uh means that we could have deduced that
+ 
+
+ align:start position:0%
+uh means that we could have deduced that
+01 to the Omega that the infinite binary
+
+ align:start position:0%
+01 to the Omega that the infinite binary
+ 
+
+ align:start position:0%
+01 to the Omega that the infinite binary
+sequences were uncountable because we
+
+ align:start position:0%
+sequences were uncountable because we
+ 
+
+ align:start position:0%
+sequences were uncountable because we
+know that there's a bje between uh the
+
+ align:start position:0%
+know that there's a bje between uh the
+ 
+
+ align:start position:0%
+know that there's a bje between uh the
+infinite binary sequences and the power
+
+ align:start position:0%
+infinite binary sequences and the power
+ 
+
+ align:start position:0%
+infinite binary sequences and the power
+set of n we we describe that bje without
+
+ align:start position:0%
+set of n we we describe that bje without
+ 
+
+ align:start position:0%
+set of n we we describe that bje without
+knowing anything about any other
+
+ align:start position:0%
+knowing anything about any other
+ 
+
+ align:start position:0%
+knowing anything about any other
+properties of the infinite binary
+
+ align:start position:0%
+properties of the infinite binary
+ 
+
+ align:start position:0%
+properties of the infinite binary
+sequences in the power set of n whether
+
+ align:start position:0%
+sequences in the power set of n whether
+ 
+
+ align:start position:0%
+sequences in the power set of n whether
+they were countable or not but now that
+
+ align:start position:0%
+they were countable or not but now that
+ 
+
+ align:start position:0%
+they were countable or not but now that
+caner theorem tells us that the power
+
+ align:start position:0%
+caner theorem tells us that the power
+ 
+
+ align:start position:0%
+caner theorem tells us that the power
+set of n is uncountable and there's a
+
+ align:start position:0%
+set of n is uncountable and there's a
+ 
+
+ align:start position:0%
+set of n is uncountable and there's a
+bje the previous Lemma says in
+
+ align:start position:0%
+bje the previous Lemma says in
+ 
+
+ align:start position:0%
+bje the previous Lemma says in
+particular there's a surjection from 01
+
+ align:start position:0%
+particular there's a surjection from 01
+ 
+
+ align:start position:0%
+particular there's a surjection from 01
+to the Omega uh to the power set of n
+
+ align:start position:0%
+to the Omega uh to the power set of n
+ 
+
+ align:start position:0%
+to the Omega uh to the power set of n
+which means 01 to the Omega is
+
+ align:start position:0%
+which means 01 to the Omega is
+ 
+
+ align:start position:0%
+which means 01 to the Omega is
+uncountable so and what I'm illustrating
+
+ align:start position:0%
+uncountable so and what I'm illustrating
+ 
+
+ align:start position:0%
+uncountable so and what I'm illustrating
+then is that the proof that we used
+
+ align:start position:0%
+then is that the proof that we used
+ 
+
+ align:start position:0%
+then is that the proof that we used
+directly on by a diagonal argument to
+
+ align:start position:0%
+directly on by a diagonal argument to
+ 
+
+ align:start position:0%
+directly on by a diagonal argument to
+figure out that 01 to the Omega um was
+
+ align:start position:0%
+figure out that 01 to the Omega um was
+ 
+
+ align:start position:0%
+figure out that 01 to the Omega um was
+uncountable it's really a special case
+
+ align:start position:0%
+uncountable it's really a special case
+ 
+
+ align:start position:0%
+uncountable it's really a special case
+of the more General diagonal argument
+
+ align:start position:0%
+of the more General diagonal argument
+ 
+
+ align:start position:0%
+of the more General diagonal argument
+that we use to prove Canter's theorem
+
+ align:start position:0%
+that we use to prove Canter's theorem
+ 
+
+ align:start position:0%
+that we use to prove Canter's theorem
+and we get that 01 to the Omega is
+
+ align:start position:0%
+and we get that 01 to the Omega is
+ 
+
+ align:start position:0%
+and we get that 01 to the Omega is
+uncountable as a consequence of Canter's
+
+ align:start position:0%
+uncountable as a consequence of Canter's
+ 
+
+ align:start position:0%
+uncountable as a consequence of Canter's
+theorem about the power set of n um and
+
+ align:start position:0%
+theorem about the power set of n um and
+ 
+
+ align:start position:0%
+theorem about the power set of n um and
+uh so we've got two different ways then
+
+ align:start position:0%
+uh so we've got two different ways then
+ 
+
+ align:start position:0%
+uh so we've got two different ways then
+to prove that the infinite binary
+
+ align:start position:0%
+to prove that the infinite binary
+ 
+
+ align:start position:0%
+to prove that the infinite binary
+sequences are
+
+ align:start position:0%
+sequences are
+ 
+
+ align:start position:0%
+sequences are
+uncountable another example of an
+
+ align:start position:0%
+uncountable another example of an
+ 
+
+ align:start position:0%
+uncountable another example of an
+uncountable set it's the real numbers uh
+
+ align:start position:0%
+uncountable set it's the real numbers uh
+ 
+
+ align:start position:0%
+uncountable set it's the real numbers uh
+and they're a cute example remember we
+
+ align:start position:0%
+and they're a cute example remember we
+ 
+
+ align:start position:0%
+and they're a cute example remember we
+saw that the rational numbers were
+
+ align:start position:0%
+saw that the rational numbers were
+ 
+
+ align:start position:0%
+saw that the rational numbers were
+countable the real numbers are
+
+ align:start position:0%
+countable the real numbers are
+ 
+
+ align:start position:0%
+countable the real numbers are
+uncountable well how do I prove that I'm
+
+ align:start position:0%
+uncountable well how do I prove that I'm
+ 
+
+ align:start position:0%
+uncountable well how do I prove that I'm
+just going to show you a surjection from
+
+ align:start position:0%
+just going to show you a surjection from
+ 
+
+ align:start position:0%
+just going to show you a surjection from
+the real numbers onto the infinite
+
+ align:start position:0%
+the real numbers onto the infinite
+ 
+
+ align:start position:0%
+the real numbers onto the infinite
+binary sequences um how am I going to do
+
+ align:start position:0%
+binary sequences um how am I going to do
+ 
+
+ align:start position:0%
+binary sequences um how am I going to do
+that well it's a kind of stupid trick
+
+ align:start position:0%
+that well it's a kind of stupid trick
+ 
+
+ align:start position:0%
+that well it's a kind of stupid trick
+but it works um uh I'm using both
+
+ align:start position:0%
+but it works um uh I'm using both
+ 
+
+ align:start position:0%
+but it works um uh I'm using both
+positive and negative reals so let's
+
+ align:start position:0%
+positive and negative reals so let's
+ 
+
+ align:start position:0%
+positive and negative reals so let's
+look at some uh real number and look at
+
+ align:start position:0%
+look at some uh real number and look at
+ 
+
+ align:start position:0%
+look at some uh real number and look at
+its binary representation assume for the
+
+ align:start position:0%
+its binary representation assume for the
+ 
+
+ align:start position:0%
+its binary representation assume for the
+moment that it's um uh positive so let's
+
+ align:start position:0%
+moment that it's um uh positive so let's
+ 
+
+ align:start position:0%
+moment that it's um uh positive so let's
+look at say the binary representation of
+
+ align:start position:0%
+look at say the binary representation of
+ 
+
+ align:start position:0%
+look at say the binary representation of
+some number like three and a thir so
+
+ align:start position:0%
+some number like three and a thir so
+ 
+
+ align:start position:0%
+some number like three and a thir so
+that means that if we're thinking of
+
+ align:start position:0%
+that means that if we're thinking of
+ 
+
+ align:start position:0%
+that means that if we're thinking of
+these as the as binary places this is
+
+ align:start position:0%
+these as the as binary places this is
+ 
+
+ align:start position:0%
+these as the as binary places this is
+the zeroth place the two's place the
+
+ align:start position:0%
+the zeroth place the two's place the
+ 
+
+ align:start position:0%
+the zeroth place the two's place the
+fourth place this is the half's place
+
+ align:start position:0%
+fourth place this is the half's place
+ 
+
+ align:start position:0%
+fourth place this is the half's place
+the quarter's place the eighth's place
+
+ align:start position:0%
+the quarter's place the eighth's place
+ 
+
+ align:start position:0%
+the quarter's place the eighth's place
+then the uh binary representation of 3
+
+ align:start position:0%
+then the uh binary representation of 3
+ 
+
+ align:start position:0%
+then the uh binary representation of 3
+and A3 would be three and then this
+
+ align:start position:0%
+and A3 would be three and then this
+ 
+
+ align:start position:0%
+and A3 would be three and then this
+infinite uh repeating not decimal but B
+
+ align:start position:0%
+infinite uh repeating not decimal but B
+ 
+
+ align:start position:0%
+infinite uh repeating not decimal but B
+but bple or binary expansion 01 0 one 01
+
+ align:start position:0%
+but bple or binary expansion 01 0 one 01
+ 
+
+ align:start position:0%
+but bple or binary expansion 01 0 one 01
+and we will examine how I know that
+
+ align:start position:0%
+and we will examine how I know that
+ 
+
+ align:start position:0%
+and we will examine how I know that
+that's a third but take it for granted
+
+ align:start position:0%
+that's a third but take it for granted
+ 
+
+ align:start position:0%
+that's a third but take it for granted
+that that's what you get is the repeated
+
+ align:start position:0%
+that that's what you get is the repeated
+ 
+
+ align:start position:0%
+that that's what you get is the repeated
+fraction you could figure that out by
+
+ align:start position:0%
+fraction you could figure that out by
+ 
+
+ align:start position:0%
+fraction you could figure that out by
+just doing a division of one by three in
+
+ align:start position:0%
+just doing a division of one by three in
+ 
+
+ align:start position:0%
+just doing a division of one by three in
+binary anyway um there is just as
+
+ align:start position:0%
+binary anyway um there is just as
+ 
+
+ align:start position:0%
+binary anyway um there is just as
+there's a decimal expansion of every uh
+
+ align:start position:0%
+there's a decimal expansion of every uh
+ 
+
+ align:start position:0%
+there's a decimal expansion of every uh
+real number there's a binary expansion
+
+ align:start position:0%
+real number there's a binary expansion
+ 
+
+ align:start position:0%
+real number there's a binary expansion
+just using base 2 so here's the binary
+
+ align:start position:0%
+just using base 2 so here's the binary
+ 
+
+ align:start position:0%
+just using base 2 so here's the binary
+expansion of 3 and A3 so what I'm going
+
+ align:start position:0%
+expansion of 3 and A3 so what I'm going
+ 
+
+ align:start position:0%
+expansion of 3 and A3 so what I'm going
+to do is I'm going to map 3 and A3 to
+
+ align:start position:0%
+to do is I'm going to map 3 and A3 to
+ 
+
+ align:start position:0%
+to do is I'm going to map 3 and A3 to
+this binary sequence I'm going to ignore
+
+ align:start position:0%
+this binary sequence I'm going to ignore
+ 
+
+ align:start position:0%
+this binary sequence I'm going to ignore
+the decimal place a binary it's not a
+
+ align:start position:0%
+the decimal place a binary it's not a
+ 
+
+ align:start position:0%
+the decimal place a binary it's not a
+decimal place it's a Bimal place or
+
+ align:start position:0%
+decimal place it's a Bimal place or
+ 
+
+ align:start position:0%
+decimal place it's a Bimal place or
+binary uh position and I'm just going to
+
+ align:start position:0%
+binary uh position and I'm just going to
+ 
+
+ align:start position:0%
+binary uh position and I'm just going to
+take this to the mapping the sequence
+
+ align:start position:0%
+take this to the mapping the sequence
+ 
+
+ align:start position:0%
+take this to the mapping the sequence
+one one Z1 01 01
+
+ align:start position:0%
+one one Z1 01 01
+ 
+
+ align:start position:0%
+one one Z1 01 01
+okay um and I claim that this is a
+
+ align:start position:0%
+okay um and I claim that this is a
+ 
+
+ align:start position:0%
+okay um and I claim that this is a
+surjection because you're going to hit
+
+ align:start position:0%
+surjection because you're going to hit
+ 
+
+ align:start position:0%
+surjection because you're going to hit
+um every possible binary sequence in
+
+ align:start position:0%
+um every possible binary sequence in
+ 
+
+ align:start position:0%
+um every possible binary sequence in
+this way well almost let's take a close
+
+ align:start position:0%
+this way well almost let's take a close
+ 
+
+ align:start position:0%
+this way well almost let's take a close
+look um uh there's a problem with
+
+ align:start position:0%
+look um uh there's a problem with
+ 
+
+ align:start position:0%
+look um uh there's a problem with
+mapping
+
+ align:start position:0%
+mapping
+ 
+
+ align:start position:0%
+mapping
+um to things that start with zero
+
+ align:start position:0%
+um to things that start with zero
+ 
+
+ align:start position:0%
+um to things that start with zero
+because let's examine that a half is
+
+ align:start position:0%
+because let's examine that a half is
+ 
+
+ align:start position:0%
+because let's examine that a half is
+.100 so I would map it to that and uh
+
+ align:start position:0%
+.100 so I would map it to that and uh
+ 
+
+ align:start position:0%
+.100 so I would map it to that and uh
+and it will and but there's an ambiguity
+
+ align:start position:0%
+and it will and but there's an ambiguity
+ 
+
+ align:start position:0%
+and it will and but there's an ambiguity
+because a half is also equal to 0.011
+
+ align:start position:0%
+because a half is also equal to 0.011
+ 
+
+ align:start position:0%
+because a half is also equal to 0.011
+one11 just as um 999999 9 is equal to
+
+ align:start position:0%
+one11 just as um 999999 9 is equal to
+ 
+
+ align:start position:0%
+one11 just as um 999999 9 is equal to
+1.0 in decimal you get the same infinite
+
+ align:start position:0%
+1.0 in decimal you get the same infinite
+ 
+
+ align:start position:0%
+1.0 in decimal you get the same infinite
+carry issue here in binary so uh numbers
+
+ align:start position:0%
+carry issue here in binary so uh numbers
+ 
+
+ align:start position:0%
+carry issue here in binary so uh numbers
+that end in all ones have another way to
+
+ align:start position:0%
+that end in all ones have another way to
+ 
+
+ align:start position:0%
+that end in all ones have another way to
+represent the very same number by a
+
+ align:start position:0%
+represent the very same number by a
+ 
+
+ align:start position:0%
+represent the very same number by a
+sequence that ends in all zeros so how
+
+ align:start position:0%
+sequence that ends in all zeros so how
+ 
+
+ align:start position:0%
+sequence that ends in all zeros so how
+am I going to hit if I'm using up a half
+
+ align:start position:0%
+am I going to hit if I'm using up a half
+ 
+
+ align:start position:0%
+am I going to hit if I'm using up a half
+to hit this one what's left to hit that
+
+ align:start position:0%
+to hit this one what's left to hit that
+ 
+
+ align:start position:0%
+to hit this one what's left to hit that
+one well how about using minus a half
+
+ align:start position:0%
+one well how about using minus a half
+ 
+
+ align:start position:0%
+one well how about using minus a half
+it's there and that's part of R so I'm
+
+ align:start position:0%
+it's there and that's part of R so I'm
+ 
+
+ align:start position:0%
+it's there and that's part of R so I'm
+just going to map the negative numbers
+
+ align:start position:0%
+just going to map the negative numbers
+ 
+
+ align:start position:0%
+just going to map the negative numbers
+to the version of the expansion that uh
+
+ align:start position:0%
+to the version of the expansion that uh
+ 
+
+ align:start position:0%
+to the version of the expansion that uh
+starts with zero and has an infinite
+
+ align:start position:0%
+starts with zero and has an infinite
+ 
+
+ align:start position:0%
+starts with zero and has an infinite
+number of ones and the positive one that
+
+ align:start position:0%
+number of ones and the positive one that
+ 
+
+ align:start position:0%
+number of ones and the positive one that
+that ends with an infinite number of
+
+ align:start position:0%
+that ends with an infinite number of
+ 
+
+ align:start position:0%
+that ends with an infinite number of
+zeros and otherwise I'm going to map
+
+ align:start position:0%
+zeros and otherwise I'm going to map
+ 
+
+ align:start position:0%
+zeros and otherwise I'm going to map
+plus and minus numbers to the same place
+
+ align:start position:0%
+plus and minus numbers to the same place
+ 
+
+ align:start position:0%
+plus and minus numbers to the same place
+so this is going to give me the needed
+
+ align:start position:0%
+so this is going to give me the needed
+ 
+
+ align:start position:0%
+so this is going to give me the needed
+surjection from R to the infinite binary
+
+ align:start position:0%
+surjection from R to the infinite binary
+ 
+
+ align:start position:0%
+surjection from R to the infinite binary
+sequences and by our previous Lemma that
+
+ align:start position:0%
+sequences and by our previous Lemma that
+ 
+
+ align:start position:0%
+sequences and by our previous Lemma that
+implies sure enough that the real
+
+ align:start position:0%
+implies sure enough that the real
+ 
+
+ align:start position:0%
+implies sure enough that the real
+numbers are uncountable
\ No newline at end of file
diff --git a/56QUjMD3xoI.txt b/56QUjMD3xoI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1342d07729c8895f803017fac226f5fa7ed271fe
--- /dev/null
+++ b/56QUjMD3xoI.txt
@@ -0,0 +1,222 @@
+Okay, now let's apply all this analysis to
+improving the performance of our circuits.
+
+The latency of a combinational logic circuit
+is simply its propagation delay t_PD.
+
+And the throughput is just 1/t_PD since we
+start processing the next input only after
+
+finishing the computation on the current input.
+
+Consider a combinational system with three
+components: F, G, and H, where F and G work
+
+in parallel to produce the inputs to H.
+Using this timing diagram we can follow the
+
+processing of a particular input value X.
+Sometime after X is valid and stable, the
+
+F and G modules produce their outputs F(X)
+and G(X).
+
+Now that the inputs to H are valid and stable,
+the H module will produce the system output
+
+P(X) after a delay set by the propagation
+delay of H.
+
+The total elapsed time from valid input to
+valid output is determined by the propagation
+
+delays of the component modules.
+
+Assuming we use those modules as-is, we can't
+make any improvements on this latency.
+
+But what about the system's throughput?
+
+Observe that after producing their outputs,
+the F and G modules are sitting sitting idle,
+
+just holding their outputs stable while H
+performs its computation.
+
+Can we figure out a way for F and G to get
+started processing the next input while still
+
+letting H do its job on the first input?
+
+In other words, can we divide the processing
+of the combinational circuit into two stages
+
+where the first stage computes F(X) and G(X),
+and the second stage computes H(X)?
+
+If we can, then we can increase the throughput
+of the system.
+
+Mr. Blue's inspiration is to use registers
+to hold the values F(X) and G(X) for use by
+
+H, while the F and G modules start working
+on the next input value.
+
+To make our timing analysis a little easier,
+we'll assume that our pipelining registers
+
+have a zero propagation delay and setup time.
+
+The appropriate clock period for this sequential
+circuit is determined by the propagation delay
+
+of the slowest processing stage.
+
+In this example, the stage with F and G needs
+a clock period of at least 20 ns to work correctly.
+
+And the stage with H needs a clock period
+of 25 ns to work correctly.
+
+So the second stage is the slowest and sets
+the system clock period at 25 ns.
+
+This will be our general plan for increasing
+the throughput of combinational logic:
+
+we'll use registers to divide the processing
+into a sequence of stages, where the registers
+
+capture the outputs from one processing stage
+and hold them as inputs for the next processing
+
+stage.
+
+A particular input will progress through the
+system at the rate of one stage per clock
+
+cycle.
+
+In this example, there are two stages in the
+processing pipeline and the clock period is
+
+25 ns, so the latency of the pipelined system
+is 50 ns, i.e., the number of stages times
+
+the system's clock period.
+
+The latency of the pipeline system is a little
+longer than the latency of the unpipelined
+
+system.
+
+However, the pipeline system produces 1 output
+every clock period, or 25 ns.
+
+The pipeline system has considerably better
+throughput at the cost of a small increase
+
+in latency.
+
+Pipeline diagrams help us visualize the operation
+of a pipelined system.
+
+The rows of the pipeline diagram represent
+the pipeline stages and the columns are successive
+
+clock cycles.
+
+At the beginning of clock cycle i the input
+X_i becomes stable and valid.
+
+Then during clock cycle i the F and G modules
+process that input and at the end of the cycle
+
+the results F(X_i) and G(X_i) are captured
+by the pipeline registers between the first
+
+and second stages.
+
+Then in cycle i+1, H uses the captured values
+do its share of the processing of X_i.
+
+And, meanwhile, the F and G modules are working
+on X_i+1.
+
+You can see that the processing for a particular
+input value moves diagonally through the diagram,
+
+one pipeline stage per clock cycle.
+
+At the end of cycle i+1, the output of H is
+captured by the final pipeline register and
+
+is available for use during cycle i+2.
+
+The total time elapsed between the arrival
+of an input and the availability of the output
+
+is two cycles.
+
+The processing continues cycle after cycle,
+producing a new output every clock cycle.
+
+Using the pipeline diagram we can track how
+a particular input progresses through the
+
+system or see what all the stages are doing
+in any particular cycle.
+
+We'll define a K-stage pipeline (or K-pipeline
+for short) as an acyclic circuit having exactly
+
+K registers on every path from input to output.
+
+An unpipelined combinational circuit is thus
+a 0-stage pipeline.
+
+To make it easy to build larger pipelined
+systems out of pipelined components, we'll
+
+adopt the convention that every pipeline stage,
+and hence every K-stage pipeline, has a register
+
+on its output.
+
+We'll use the techniques we learned for analyzing
+the timing of sequential circuits to ensure
+
+the clock signal common to all the pipeline
+registers has a period sufficient to ensure
+
+correct operation of each stage.
+
+So for every register-to-register and input-to-register
+path, we need to compute the sum of the propagation
+
+delay of the input register, plus the propagation
+delay of the combinational logic, plus the
+
+setup time of the output register.
+
+Then we'll choose the system's clock period
+to be greater than or equal to the largest
+
+such sum.
+
+With the correct clock period and exactly
+K-registers along each path from system input
+
+to system output, we are guaranteed that the
+K-pipeline will compute the same outputs as
+
+the original unpipelined combinational circuit.
+
+The latency of a K-pipeline is K times the
+period of the system's clock.
+
+And the throughput of a K-pipeline is the
+frequency of the system's clock, i.e., 1 over
+
+the clock period.
\ No newline at end of file
diff --git a/57o2JJSLNxI.txt b/57o2JJSLNxI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4ea845af0878cab36285a7973484f13d6915754f
--- /dev/null
+++ b/57o2JJSLNxI.txt
@@ -0,0 +1,4403 @@
+align:start position:0%
+ 
+it's an exciting time the last few
+
+ align:start position:0%
+it's an exciting time the last few
+ 
+
+ align:start position:0%
+it's an exciting time the last few
+minutes before launch
+
+ align:start position:0%
+minutes before launch
+ 
+
+ align:start position:0%
+minutes before launch
+you as the the shuttle really comes
+
+ align:start position:0%
+you as the the shuttle really comes
+ 
+
+ align:start position:0%
+you as the the shuttle really comes
+alive
+
+ align:start position:0%
+alive
+ 
+
+ align:start position:0%
+alive
+and then all of a sudden you get this
+
+ align:start position:0%
+and then all of a sudden you get this
+ 
+
+ align:start position:0%
+and then all of a sudden you get this
+big kick in the pants and
+
+ align:start position:0%
+big kick in the pants and
+ 
+
+ align:start position:0%
+big kick in the pants and
+you look out the window and there's the
+
+ align:start position:0%
+you look out the window and there's the
+ 
+
+ align:start position:0%
+you look out the window and there's the
+ground falling away and everything is
+
+ align:start position:0%
+ground falling away and everything is
+ 
+
+ align:start position:0%
+ground falling away and everything is
+shaking
+
+ align:start position:0%
+shaking
+ 
+
+ align:start position:0%
+shaking
+today on shock radio we're heading back
+
+ align:start position:0%
+today on shock radio we're heading back
+ 
+
+ align:start position:0%
+today on shock radio we're heading back
+into space
+
+ align:start position:0%
+into space
+ 
+
+ align:start position:0%
+into space
+my best friend from the second grade
+
+ align:start position:0%
+my best friend from the second grade
+ 
+
+ align:start position:0%
+my best friend from the second grade
+after i became an astronaut
+
+ align:start position:0%
+after i became an astronaut
+ 
+
+ align:start position:0%
+after i became an astronaut
+he said to me you know jeff this is
+
+ align:start position:0%
+he said to me you know jeff this is
+ 
+
+ align:start position:0%
+he said to me you know jeff this is
+incredible you know i used to play
+
+ align:start position:0%
+incredible you know i used to play
+ 
+
+ align:start position:0%
+incredible you know i used to play
+space man with you and now you're
+
+ align:start position:0%
+space man with you and now you're
+ 
+
+ align:start position:0%
+space man with you and now you're
+actually going up into space
+
+ align:start position:0%
+actually going up into space
+ 
+
+ align:start position:0%
+ 
+i'm your host sarah hansen and with us
+
+ align:start position:0%
+i'm your host sarah hansen and with us
+ 
+
+ align:start position:0%
+i'm your host sarah hansen and with us
+this week is professor jeff hoffman
+
+ align:start position:0%
+this week is professor jeff hoffman
+ 
+
+ align:start position:0%
+this week is professor jeff hoffman
+a former nasa astronaut over the course
+
+ align:start position:0%
+a former nasa astronaut over the course
+ 
+
+ align:start position:0%
+a former nasa astronaut over the course
+of five
+
+ align:start position:0%
+of five
+ 
+
+ align:start position:0%
+of five
+missions he's logged over 1 000 hours in
+
+ align:start position:0%
+missions he's logged over 1 000 hours in
+ 
+
+ align:start position:0%
+missions he's logged over 1 000 hours in
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+and yep some of those do include space
+
+ align:start position:0%
+and yep some of those do include space
+ 
+
+ align:start position:0%
+and yep some of those do include space
+walks
+
+ align:start position:0%
+walks
+ 
+
+ align:start position:0%
+walks
+professor hoffman teaches aeronautics
+
+ align:start position:0%
+professor hoffman teaches aeronautics
+ 
+
+ align:start position:0%
+professor hoffman teaches aeronautics
+and astronautics at mit
+
+ align:start position:0%
+and astronautics at mit
+ 
+
+ align:start position:0%
+and astronautics at mit
+but he's also committed to unlocking
+
+ align:start position:0%
+but he's also committed to unlocking
+ 
+
+ align:start position:0%
+but he's also committed to unlocking
+this knowledge for the world
+
+ align:start position:0%
+this knowledge for the world
+ 
+
+ align:start position:0%
+this knowledge for the world
+he's shared course 1600 introduction to
+
+ align:start position:0%
+he's shared course 1600 introduction to
+ 
+
+ align:start position:0%
+he's shared course 1600 introduction to
+aerospace engineering on mitx
+
+ align:start position:0%
+aerospace engineering on mitx
+ 
+
+ align:start position:0%
+aerospace engineering on mitx
+and 16885 engineering the space shuttle
+
+ align:start position:0%
+and 16885 engineering the space shuttle
+ 
+
+ align:start position:0%
+and 16885 engineering the space shuttle
+which can be found on mitx and ocw
+
+ align:start position:0%
+which can be found on mitx and ocw
+ 
+
+ align:start position:0%
+which can be found on mitx and ocw
+one of the things i loved about my
+
+ align:start position:0%
+one of the things i loved about my
+ 
+
+ align:start position:0%
+one of the things i loved about my
+conversation with professor hoffman was
+
+ align:start position:0%
+conversation with professor hoffman was
+ 
+
+ align:start position:0%
+conversation with professor hoffman was
+his take on perspective
+
+ align:start position:0%
+his take on perspective
+ 
+
+ align:start position:0%
+his take on perspective
+and how a grander scale view like say
+
+ align:start position:0%
+and how a grander scale view like say
+ 
+
+ align:start position:0%
+and how a grander scale view like say
+from outer space
+
+ align:start position:0%
+from outer space
+ 
+
+ align:start position:0%
+from outer space
+can dramatically shift the way we live
+
+ align:start position:0%
+can dramatically shift the way we live
+ 
+
+ align:start position:0%
+can dramatically shift the way we live
+here on earth
+
+ align:start position:0%
+here on earth
+ 
+
+ align:start position:0%
+here on earth
+we fly so much in airplanes and probably
+
+ align:start position:0%
+we fly so much in airplanes and probably
+ 
+
+ align:start position:0%
+we fly so much in airplanes and probably
+most people don't remember the first
+
+ align:start position:0%
+most people don't remember the first
+ 
+
+ align:start position:0%
+most people don't remember the first
+time they look out of an airplane
+
+ align:start position:0%
+time they look out of an airplane
+ 
+
+ align:start position:0%
+time they look out of an airplane
+window and see the earth i mean it's a
+
+ align:start position:0%
+window and see the earth i mean it's a
+ 
+
+ align:start position:0%
+window and see the earth i mean it's a
+completely different perspective
+
+ align:start position:0%
+completely different perspective
+ 
+
+ align:start position:0%
+completely different perspective
+that you get and and now rockets and
+
+ align:start position:0%
+that you get and and now rockets and
+ 
+
+ align:start position:0%
+that you get and and now rockets and
+space travel which allow us to go
+
+ align:start position:0%
+space travel which allow us to go
+ 
+
+ align:start position:0%
+space travel which allow us to go
+even farther and to try to give
+
+ align:start position:0%
+even farther and to try to give
+ 
+
+ align:start position:0%
+even farther and to try to give
+people the perspective of looking at the
+
+ align:start position:0%
+people the perspective of looking at the
+ 
+
+ align:start position:0%
+people the perspective of looking at the
+earth from
+
+ align:start position:0%
+earth from
+ 
+
+ align:start position:0%
+earth from
+space is very important i mean
+
+ align:start position:0%
+space is very important i mean
+ 
+
+ align:start position:0%
+space is very important i mean
+you know i was an astronomer i i know
+
+ align:start position:0%
+you know i was an astronomer i i know
+ 
+
+ align:start position:0%
+you know i was an astronomer i i know
+the earth as a planet i mean
+
+ align:start position:0%
+the earth as a planet i mean
+ 
+
+ align:start position:0%
+the earth as a planet i mean
+you know give me a break but
+
+ align:start position:0%
+you know give me a break but
+ 
+
+ align:start position:0%
+you know give me a break but
+nevertheless when you actually
+
+ align:start position:0%
+nevertheless when you actually
+ 
+
+ align:start position:0%
+nevertheless when you actually
+see it from the perspective of being in
+
+ align:start position:0%
+see it from the perspective of being in
+ 
+
+ align:start position:0%
+see it from the perspective of being in
+space i mean imagine
+
+ align:start position:0%
+space i mean imagine
+ 
+
+ align:start position:0%
+space i mean imagine
+you know you go up into space and you
+
+ align:start position:0%
+you know you go up into space and you
+ 
+
+ align:start position:0%
+you know you go up into space and you
+look at this
+
+ align:start position:0%
+look at this
+ 
+
+ align:start position:0%
+look at this
+thin blue line on the horizon which is
+
+ align:start position:0%
+thin blue line on the horizon which is
+ 
+
+ align:start position:0%
+thin blue line on the horizon which is
+the earth's atmosphere i mean you go out
+
+ align:start position:0%
+the earth's atmosphere i mean you go out
+ 
+
+ align:start position:0%
+the earth's atmosphere i mean you go out
+here from the surface of the earth on
+
+ align:start position:0%
+here from the surface of the earth on
+ 
+
+ align:start position:0%
+here from the surface of the earth on
+a clear day and there's a big blue sky
+
+ align:start position:0%
+a clear day and there's a big blue sky
+ 
+
+ align:start position:0%
+a clear day and there's a big blue sky
+and it looks like it goes on forever
+
+ align:start position:0%
+and it looks like it goes on forever
+ 
+
+ align:start position:0%
+and it looks like it goes on forever
+and unfortunately that gives many people
+
+ align:start position:0%
+and unfortunately that gives many people
+ 
+
+ align:start position:0%
+and unfortunately that gives many people
+the idea that
+
+ align:start position:0%
+the idea that
+ 
+
+ align:start position:0%
+the idea that
+you know it doesn't matter what you put
+
+ align:start position:0%
+you know it doesn't matter what you put
+ 
+
+ align:start position:0%
+you know it doesn't matter what you put
+into the atmosphere because it's so big
+
+ align:start position:0%
+into the atmosphere because it's so big
+ 
+
+ align:start position:0%
+into the atmosphere because it's so big
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+it can absorb it and it's the same thing
+
+ align:start position:0%
+it can absorb it and it's the same thing
+ 
+
+ align:start position:0%
+it can absorb it and it's the same thing
+with the oceans and
+
+ align:start position:0%
+with the oceans and
+ 
+
+ align:start position:0%
+with the oceans and
+when you finally get that gut feeling
+
+ align:start position:0%
+when you finally get that gut feeling
+ 
+
+ align:start position:0%
+when you finally get that gut feeling
+of the finiteness of the earth you know
+
+ align:start position:0%
+of the finiteness of the earth you know
+ 
+
+ align:start position:0%
+of the finiteness of the earth you know
+the oceans
+
+ align:start position:0%
+the oceans
+ 
+
+ align:start position:0%
+the oceans
+the atmosphere and you realize we live
+
+ align:start position:0%
+the atmosphere and you realize we live
+ 
+
+ align:start position:0%
+the atmosphere and you realize we live
+in a closed system
+
+ align:start position:0%
+in a closed system
+ 
+
+ align:start position:0%
+in a closed system
+that the earth is a finite system um
+
+ align:start position:0%
+that the earth is a finite system um
+ 
+
+ align:start position:0%
+that the earth is a finite system um
+that makes a difference because
+
+ align:start position:0%
+that makes a difference because
+ 
+
+ align:start position:0%
+that makes a difference because
+exponential growth
+
+ align:start position:0%
+exponential growth
+ 
+
+ align:start position:0%
+exponential growth
+cannot continue forever in a closed
+
+ align:start position:0%
+cannot continue forever in a closed
+ 
+
+ align:start position:0%
+cannot continue forever in a closed
+system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+professor hoffman's first expedition
+
+ align:start position:0%
+professor hoffman's first expedition
+ 
+
+ align:start position:0%
+professor hoffman's first expedition
+into space
+
+ align:start position:0%
+into space
+ 
+
+ align:start position:0%
+into space
+was in 1985. before that
+
+ align:start position:0%
+was in 1985. before that
+ 
+
+ align:start position:0%
+was in 1985. before that
+he was actually doing work here at mit
+
+ align:start position:0%
+he was actually doing work here at mit
+ 
+
+ align:start position:0%
+he was actually doing work here at mit
+launching telescopes into space
+
+ align:start position:0%
+launching telescopes into space
+ 
+
+ align:start position:0%
+launching telescopes into space
+long before that though like many kids
+
+ align:start position:0%
+long before that though like many kids
+ 
+
+ align:start position:0%
+long before that though like many kids
+since the second half of the 20th
+
+ align:start position:0%
+since the second half of the 20th
+ 
+
+ align:start position:0%
+since the second half of the 20th
+century
+
+ align:start position:0%
+century
+ 
+
+ align:start position:0%
+century
+he wanted to go to space himself
+
+ align:start position:0%
+he wanted to go to space himself
+ 
+
+ align:start position:0%
+he wanted to go to space himself
+when i was a little kid i used to love
+
+ align:start position:0%
+when i was a little kid i used to love
+ 
+
+ align:start position:0%
+when i was a little kid i used to love
+looking up
+
+ align:start position:0%
+looking up
+ 
+
+ align:start position:0%
+looking up
+at the stars of course early part of my
+
+ align:start position:0%
+at the stars of course early part of my
+ 
+
+ align:start position:0%
+at the stars of course early part of my
+life we lived in new york city
+
+ align:start position:0%
+life we lived in new york city
+ 
+
+ align:start position:0%
+life we lived in new york city
+and more often it would be looking up at
+
+ align:start position:0%
+and more often it would be looking up at
+ 
+
+ align:start position:0%
+and more often it would be looking up at
+the stars in the planetarium
+
+ align:start position:0%
+the stars in the planetarium
+ 
+
+ align:start position:0%
+the stars in the planetarium
+but i was fascinated with that and
+
+ align:start position:0%
+but i was fascinated with that and
+ 
+
+ align:start position:0%
+but i was fascinated with that and
+it was the dawn of the space age and
+
+ align:start position:0%
+it was the dawn of the space age and
+ 
+
+ align:start position:0%
+it was the dawn of the space age and
+there were lots of
+
+ align:start position:0%
+there were lots of
+ 
+
+ align:start position:0%
+there were lots of
+articles in newspapers magazines
+
+ align:start position:0%
+articles in newspapers magazines
+ 
+
+ align:start position:0%
+articles in newspapers magazines
+television shows about the coming of the
+
+ align:start position:0%
+television shows about the coming of the
+ 
+
+ align:start position:0%
+television shows about the coming of the
+space age and i
+
+ align:start position:0%
+space age and i
+ 
+
+ align:start position:0%
+space age and i
+i ate it up um in fact
+
+ align:start position:0%
+i ate it up um in fact
+ 
+
+ align:start position:0%
+i ate it up um in fact
+my best friend from the second grade
+
+ align:start position:0%
+my best friend from the second grade
+ 
+
+ align:start position:0%
+my best friend from the second grade
+after i became an astronaut
+
+ align:start position:0%
+after i became an astronaut
+ 
+
+ align:start position:0%
+after i became an astronaut
+you know he he said to me uh you know
+
+ align:start position:0%
+you know he he said to me uh you know
+ 
+
+ align:start position:0%
+you know he he said to me uh you know
+jeff this is incredible you know i used
+
+ align:start position:0%
+jeff this is incredible you know i used
+ 
+
+ align:start position:0%
+jeff this is incredible you know i used
+to play
+
+ align:start position:0%
+to play
+ 
+
+ align:start position:0%
+to play
+space man with you and now you're
+
+ align:start position:0%
+space man with you and now you're
+ 
+
+ align:start position:0%
+space man with you and now you're
+actually going up into space
+
+ align:start position:0%
+actually going up into space
+ 
+
+ align:start position:0%
+actually going up into space
+it was a combination of the fascination
+
+ align:start position:0%
+it was a combination of the fascination
+ 
+
+ align:start position:0%
+it was a combination of the fascination
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+how far away things were and and the
+
+ align:start position:0%
+how far away things were and and the
+ 
+
+ align:start position:0%
+how far away things were and and the
+fact that
+
+ align:start position:0%
+fact that
+ 
+
+ align:start position:0%
+fact that
+by going up you got a completely new
+
+ align:start position:0%
+by going up you got a completely new
+ 
+
+ align:start position:0%
+by going up you got a completely new
+view of things and
+
+ align:start position:0%
+view of things and
+ 
+
+ align:start position:0%
+view of things and
+and also that space travel represented
+
+ align:start position:0%
+and also that space travel represented
+ 
+
+ align:start position:0%
+and also that space travel represented
+the future
+
+ align:start position:0%
+the future
+ 
+
+ align:start position:0%
+the future
+and and i found that really exciting so
+
+ align:start position:0%
+and and i found that really exciting so
+ 
+
+ align:start position:0%
+and and i found that really exciting so
+then when the first astronauts started
+
+ align:start position:0%
+then when the first astronauts started
+ 
+
+ align:start position:0%
+then when the first astronauts started
+to fly
+
+ align:start position:0%
+to fly
+ 
+
+ align:start position:0%
+to fly
+uh you know they were our heroes and
+
+ align:start position:0%
+uh you know they were our heroes and
+ 
+
+ align:start position:0%
+uh you know they were our heroes and
+i just wanted to go up there and look
+
+ align:start position:0%
+i just wanted to go up there and look
+ 
+
+ align:start position:0%
+i just wanted to go up there and look
+down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unfortunately i soon realized that all
+
+ align:start position:0%
+unfortunately i soon realized that all
+ 
+
+ align:start position:0%
+unfortunately i soon realized that all
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+astronauts were military pilots and that
+
+ align:start position:0%
+astronauts were military pilots and that
+ 
+
+ align:start position:0%
+astronauts were military pilots and that
+was not really a
+
+ align:start position:0%
+was not really a
+ 
+
+ align:start position:0%
+was not really a
+career for me but that that desire to
+
+ align:start position:0%
+career for me but that that desire to
+ 
+
+ align:start position:0%
+career for me but that that desire to
+you know look further out
+
+ align:start position:0%
+you know look further out
+ 
+
+ align:start position:0%
+you know look further out
+to understand what's what's above what's
+
+ align:start position:0%
+to understand what's what's above what's
+ 
+
+ align:start position:0%
+to understand what's what's above what's
+out there
+
+ align:start position:0%
+out there
+ 
+
+ align:start position:0%
+out there
+uh that remained with me and and so i
+
+ align:start position:0%
+uh that remained with me and and so i
+ 
+
+ align:start position:0%
+uh that remained with me and and so i
+ended up with a
+
+ align:start position:0%
+ended up with a
+ 
+
+ align:start position:0%
+ended up with a
+degree advanced degrees in astrophysics
+
+ align:start position:0%
+degree advanced degrees in astrophysics
+ 
+
+ align:start position:0%
+degree advanced degrees in astrophysics
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i was launching telescopes to look at
+
+ align:start position:0%
+i was launching telescopes to look at
+ 
+
+ align:start position:0%
+i was launching telescopes to look at
+x-rays
+
+ align:start position:0%
+x-rays
+ 
+
+ align:start position:0%
+x-rays
+and you have to go above the atmosphere
+
+ align:start position:0%
+and you have to go above the atmosphere
+ 
+
+ align:start position:0%
+and you have to go above the atmosphere
+to look at x-rays that's what i was
+
+ align:start position:0%
+to look at x-rays that's what i was
+ 
+
+ align:start position:0%
+to look at x-rays that's what i was
+doing here at mit
+
+ align:start position:0%
+doing here at mit
+ 
+
+ align:start position:0%
+doing here at mit
+then nasa started to develop what was
+
+ align:start position:0%
+then nasa started to develop what was
+ 
+
+ align:start position:0%
+then nasa started to develop what was
+then the brand new space shuttle and now
+
+ align:start position:0%
+then the brand new space shuttle and now
+ 
+
+ align:start position:0%
+then the brand new space shuttle and now
+we're up to the the late 70s
+
+ align:start position:0%
+we're up to the the late 70s
+ 
+
+ align:start position:0%
+we're up to the the late 70s
+and the thing about the shuttle was
+
+ align:start position:0%
+and the thing about the shuttle was
+ 
+
+ align:start position:0%
+and the thing about the shuttle was
+they had a crew of seven and they only
+
+ align:start position:0%
+they had a crew of seven and they only
+ 
+
+ align:start position:0%
+they had a crew of seven and they only
+needed two pilots so that was great
+
+ align:start position:0%
+needed two pilots so that was great
+ 
+
+ align:start position:0%
+needed two pilots so that was great
+because that
+
+ align:start position:0%
+because that
+ 
+
+ align:start position:0%
+because that
+that's what really opened things up for
+
+ align:start position:0%
+that's what really opened things up for
+ 
+
+ align:start position:0%
+that's what really opened things up for
+scientists engineers medical doctors and
+
+ align:start position:0%
+scientists engineers medical doctors and
+ 
+
+ align:start position:0%
+scientists engineers medical doctors and
+that's what gave me my chance and i
+
+ align:start position:0%
+that's what gave me my chance and i
+ 
+
+ align:start position:0%
+that's what gave me my chance and i
+applied for it and was lucky enough to
+
+ align:start position:0%
+applied for it and was lucky enough to
+ 
+
+ align:start position:0%
+applied for it and was lucky enough to
+get selected and
+
+ align:start position:0%
+get selected and
+ 
+
+ align:start position:0%
+get selected and
+so then i could get the real overview
+
+ align:start position:0%
+so then i could get the real overview
+ 
+
+ align:start position:0%
+so then i could get the real overview
+from space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+five missions later and professor
+
+ align:start position:0%
+five missions later and professor
+ 
+
+ align:start position:0%
+five missions later and professor
+hoffman is back on earth
+
+ align:start position:0%
+hoffman is back on earth
+ 
+
+ align:start position:0%
+hoffman is back on earth
+and since 2001 he's been teaching a
+
+ align:start position:0%
+and since 2001 he's been teaching a
+ 
+
+ align:start position:0%
+and since 2001 he's been teaching a
+series of courses on aeronautics and
+
+ align:start position:0%
+series of courses on aeronautics and
+ 
+
+ align:start position:0%
+series of courses on aeronautics and
+engineering here at mit
+
+ align:start position:0%
+engineering here at mit
+ 
+
+ align:start position:0%
+engineering here at mit
+luckily for us professor hoffman infuses
+
+ align:start position:0%
+luckily for us professor hoffman infuses
+ 
+
+ align:start position:0%
+luckily for us professor hoffman infuses
+much of his nasa experiences and
+
+ align:start position:0%
+much of his nasa experiences and
+ 
+
+ align:start position:0%
+much of his nasa experiences and
+learnings into his courses
+
+ align:start position:0%
+learnings into his courses
+ 
+
+ align:start position:0%
+learnings into his courses
+to help his students really understand
+
+ align:start position:0%
+to help his students really understand
+ 
+
+ align:start position:0%
+to help his students really understand
+the big picture
+
+ align:start position:0%
+the big picture
+ 
+
+ align:start position:0%
+the big picture
+like he had to at nasa he emphasizes the
+
+ align:start position:0%
+like he had to at nasa he emphasizes the
+ 
+
+ align:start position:0%
+like he had to at nasa he emphasizes the
+concept of
+
+ align:start position:0%
+concept of
+ 
+
+ align:start position:0%
+concept of
+systems engineering understanding
+
+ align:start position:0%
+systems engineering understanding
+ 
+
+ align:start position:0%
+systems engineering understanding
+systems engineering helps students and
+
+ align:start position:0%
+systems engineering helps students and
+ 
+
+ align:start position:0%
+systems engineering helps students and
+astronauts alike
+
+ align:start position:0%
+astronauts alike
+ 
+
+ align:start position:0%
+astronauts alike
+to tackle complex problems and it all
+
+ align:start position:0%
+to tackle complex problems and it all
+ 
+
+ align:start position:0%
+to tackle complex problems and it all
+starts
+
+ align:start position:0%
+starts
+ 
+
+ align:start position:0%
+starts
+by looking at the bigger picture
+
+ align:start position:0%
+by looking at the bigger picture
+ 
+
+ align:start position:0%
+by looking at the bigger picture
+particularly
+
+ align:start position:0%
+particularly
+ 
+
+ align:start position:0%
+particularly
+anything having to do with with space
+
+ align:start position:0%
+anything having to do with with space
+ 
+
+ align:start position:0%
+anything having to do with with space
+with all
+
+ align:start position:0%
+with all
+ 
+
+ align:start position:0%
+with all
+complex systems in general you know we
+
+ align:start position:0%
+complex systems in general you know we
+ 
+
+ align:start position:0%
+complex systems in general you know we
+try to teach systems engineering
+
+ align:start position:0%
+try to teach systems engineering
+ 
+
+ align:start position:0%
+try to teach systems engineering
+here you have to have the big picture if
+
+ align:start position:0%
+here you have to have the big picture if
+ 
+
+ align:start position:0%
+here you have to have the big picture if
+you're going to be able to manage a
+
+ align:start position:0%
+you're going to be able to manage a
+ 
+
+ align:start position:0%
+you're going to be able to manage a
+complex
+
+ align:start position:0%
+complex
+ 
+
+ align:start position:0%
+complex
+engineering or scientific project
+
+ align:start position:0%
+engineering or scientific project
+ 
+
+ align:start position:0%
+engineering or scientific project
+in in the aero astra department at mit
+
+ align:start position:0%
+in in the aero astra department at mit
+ 
+
+ align:start position:0%
+in in the aero astra department at mit
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+we don't really teach systems
+
+ align:start position:0%
+we don't really teach systems
+ 
+
+ align:start position:0%
+we don't really teach systems
+engineering as a specific
+
+ align:start position:0%
+engineering as a specific
+ 
+
+ align:start position:0%
+engineering as a specific
+subject until the graduate level because
+
+ align:start position:0%
+subject until the graduate level because
+ 
+
+ align:start position:0%
+subject until the graduate level because
+really if you're going to be a
+
+ align:start position:0%
+really if you're going to be a
+ 
+
+ align:start position:0%
+really if you're going to be a
+professional systems engineer and be
+
+ align:start position:0%
+professional systems engineer and be
+ 
+
+ align:start position:0%
+professional systems engineer and be
+good at it
+
+ align:start position:0%
+good at it
+ 
+
+ align:start position:0%
+good at it
+you really need a background in some of
+
+ align:start position:0%
+you really need a background in some of
+ 
+
+ align:start position:0%
+you really need a background in some of
+the basics
+
+ align:start position:0%
+the basics
+ 
+
+ align:start position:0%
+the basics
+of engineering so it's like at nasa and
+
+ align:start position:0%
+of engineering so it's like at nasa and
+ 
+
+ align:start position:0%
+of engineering so it's like at nasa and
+mission control you don't start out
+
+ align:start position:0%
+mission control you don't start out
+ 
+
+ align:start position:0%
+mission control you don't start out
+being a flight director you start out
+
+ align:start position:0%
+being a flight director you start out
+ 
+
+ align:start position:0%
+being a flight director you start out
+working in one of the
+
+ align:start position:0%
+working in one of the
+ 
+
+ align:start position:0%
+working in one of the
+individual disciplines and usually the
+
+ align:start position:0%
+individual disciplines and usually the
+ 
+
+ align:start position:0%
+individual disciplines and usually the
+most successful flight directors have
+
+ align:start position:0%
+most successful flight directors have
+ 
+
+ align:start position:0%
+most successful flight directors have
+worked in at least two disciplines and
+
+ align:start position:0%
+worked in at least two disciplines and
+ 
+
+ align:start position:0%
+worked in at least two disciplines and
+then you understand how a discipline
+
+ align:start position:0%
+then you understand how a discipline
+ 
+
+ align:start position:0%
+then you understand how a discipline
+engineer
+
+ align:start position:0%
+engineer
+ 
+
+ align:start position:0%
+engineer
+approaches a problem and then you can be
+
+ align:start position:0%
+approaches a problem and then you can be
+ 
+
+ align:start position:0%
+approaches a problem and then you can be
+more useful trying to get the the big
+
+ align:start position:0%
+more useful trying to get the the big
+ 
+
+ align:start position:0%
+more useful trying to get the the big
+view of things
+
+ align:start position:0%
+view of things
+ 
+
+ align:start position:0%
+view of things
+another really wonderful part of
+
+ align:start position:0%
+another really wonderful part of
+ 
+
+ align:start position:0%
+another really wonderful part of
+professor hoffman's courses
+
+ align:start position:0%
+professor hoffman's courses
+ 
+
+ align:start position:0%
+professor hoffman's courses
+is how they combine theory with real
+
+ align:start position:0%
+is how they combine theory with real
+ 
+
+ align:start position:0%
+is how they combine theory with real
+hands-on experience
+
+ align:start position:0%
+hands-on experience
+ 
+
+ align:start position:0%
+hands-on experience
+the majority of our students they they
+
+ align:start position:0%
+the majority of our students they they
+ 
+
+ align:start position:0%
+the majority of our students they they
+are going to be working engineers
+
+ align:start position:0%
+are going to be working engineers
+ 
+
+ align:start position:0%
+are going to be working engineers
+they're going to go out into the world
+
+ align:start position:0%
+they're going to go out into the world
+ 
+
+ align:start position:0%
+they're going to go out into the world
+many of them get jobs in aerospace
+
+ align:start position:0%
+many of them get jobs in aerospace
+ 
+
+ align:start position:0%
+many of them get jobs in aerospace
+companies and
+
+ align:start position:0%
+companies and
+ 
+
+ align:start position:0%
+companies and
+they're going to build the next
+
+ align:start position:0%
+they're going to build the next
+ 
+
+ align:start position:0%
+they're going to build the next
+generation of space vehicles
+
+ align:start position:0%
+generation of space vehicles
+ 
+
+ align:start position:0%
+generation of space vehicles
+and we want them to have had some
+
+ align:start position:0%
+and we want them to have had some
+ 
+
+ align:start position:0%
+and we want them to have had some
+experience actually
+
+ align:start position:0%
+experience actually
+ 
+
+ align:start position:0%
+experience actually
+building something for instance here i
+
+ align:start position:0%
+building something for instance here i
+ 
+
+ align:start position:0%
+building something for instance here i
+teach the freshman course
+
+ align:start position:0%
+teach the freshman course
+ 
+
+ align:start position:0%
+teach the freshman course
+in introduction to aerospace engineering
+
+ align:start position:0%
+in introduction to aerospace engineering
+ 
+
+ align:start position:0%
+in introduction to aerospace engineering
+and human space flight
+
+ align:start position:0%
+and human space flight
+ 
+
+ align:start position:0%
+and human space flight
+and we have the students build a project
+
+ align:start position:0%
+and we have the students build a project
+ 
+
+ align:start position:0%
+and we have the students build a project
+a lighter than air vehicle we you know
+
+ align:start position:0%
+a lighter than air vehicle we you know
+ 
+
+ align:start position:0%
+a lighter than air vehicle we you know
+we give them the material
+
+ align:start position:0%
+we give them the material
+ 
+
+ align:start position:0%
+we give them the material
+we give them some radio control
+
+ align:start position:0%
+we give them some radio control
+ 
+
+ align:start position:0%
+we give them some radio control
+equipment
+
+ align:start position:0%
+equipment
+ 
+
+ align:start position:0%
+equipment
+motors servos propellers and
+
+ align:start position:0%
+motors servos propellers and
+ 
+
+ align:start position:0%
+motors servos propellers and
+kind of lead them through in in
+
+ align:start position:0%
+kind of lead them through in in
+ 
+
+ align:start position:0%
+kind of lead them through in in
+a systems engineering way of going about
+
+ align:start position:0%
+a systems engineering way of going about
+ 
+
+ align:start position:0%
+a systems engineering way of going about
+the project without formally telling
+
+ align:start position:0%
+the project without formally telling
+ 
+
+ align:start position:0%
+the project without formally telling
+them that they're
+
+ align:start position:0%
+them that they're
+ 
+
+ align:start position:0%
+them that they're
+practicing systems engineering i mean
+
+ align:start position:0%
+practicing systems engineering i mean
+ 
+
+ align:start position:0%
+practicing systems engineering i mean
+even if you're going to be
+
+ align:start position:0%
+even if you're going to be
+ 
+
+ align:start position:0%
+even if you're going to be
+a discipline engineer and just
+
+ align:start position:0%
+a discipline engineer and just
+ 
+
+ align:start position:0%
+a discipline engineer and just
+concentrate on one aspect of a system
+
+ align:start position:0%
+concentrate on one aspect of a system
+ 
+
+ align:start position:0%
+concentrate on one aspect of a system
+it still helps to have the concept
+
+ align:start position:0%
+it still helps to have the concept
+ 
+
+ align:start position:0%
+it still helps to have the concept
+that you know somehow all these systems
+
+ align:start position:0%
+that you know somehow all these systems
+ 
+
+ align:start position:0%
+that you know somehow all these systems
+have to play together
+
+ align:start position:0%
+have to play together
+ 
+
+ align:start position:0%
+have to play together
+another way professor hoffman ensures
+
+ align:start position:0%
+another way professor hoffman ensures
+ 
+
+ align:start position:0%
+another way professor hoffman ensures
+that these ideas really sink
+
+ align:start position:0%
+that these ideas really sink
+ 
+
+ align:start position:0%
+that these ideas really sink
+in is with something called c d i
+
+ align:start position:0%
+in is with something called c d i
+ 
+
+ align:start position:0%
+in is with something called c d i
+o cdio stands for conceive
+
+ align:start position:0%
+o cdio stands for conceive
+ 
+
+ align:start position:0%
+o cdio stands for conceive
+design implement and operate and it's a
+
+ align:start position:0%
+design implement and operate and it's a
+ 
+
+ align:start position:0%
+design implement and operate and it's a
+learning tool that helps students to
+
+ align:start position:0%
+learning tool that helps students to
+ 
+
+ align:start position:0%
+learning tool that helps students to
+think through a problem
+
+ align:start position:0%
+think through a problem
+ 
+
+ align:start position:0%
+think through a problem
+from to nuts as he puts it what's
+
+ align:start position:0%
+from to nuts as he puts it what's
+ 
+
+ align:start position:0%
+from to nuts as he puts it what's
+wonderful about it
+
+ align:start position:0%
+wonderful about it
+ 
+
+ align:start position:0%
+wonderful about it
+beyond the fact that it's helped us put
+
+ align:start position:0%
+beyond the fact that it's helped us put
+ 
+
+ align:start position:0%
+beyond the fact that it's helped us put
+humans into space and on the moon
+
+ align:start position:0%
+humans into space and on the moon
+ 
+
+ align:start position:0%
+humans into space and on the moon
+is that it can be useful in tons of
+
+ align:start position:0%
+is that it can be useful in tons of
+ 
+
+ align:start position:0%
+is that it can be useful in tons of
+different contexts even beyond
+
+ align:start position:0%
+different contexts even beyond
+ 
+
+ align:start position:0%
+different contexts even beyond
+engineering
+
+ align:start position:0%
+engineering
+ 
+
+ align:start position:0%
+engineering
+the bottom line and the moral of all of
+
+ align:start position:0%
+the bottom line and the moral of all of
+ 
+
+ align:start position:0%
+the bottom line and the moral of all of
+this is you really
+
+ align:start position:0%
+this is you really
+ 
+
+ align:start position:0%
+this is you really
+need from the very beginning when you're
+
+ align:start position:0%
+need from the very beginning when you're
+ 
+
+ align:start position:0%
+need from the very beginning when you're
+designing a system
+
+ align:start position:0%
+designing a system
+ 
+
+ align:start position:0%
+designing a system
+to think about the end user you know
+
+ align:start position:0%
+to think about the end user you know
+ 
+
+ align:start position:0%
+to think about the end user you know
+very often the people who design it
+
+ align:start position:0%
+very often the people who design it
+ 
+
+ align:start position:0%
+very often the people who design it
+never have to use the system they they
+
+ align:start position:0%
+never have to use the system they they
+ 
+
+ align:start position:0%
+never have to use the system they they
+come up with a design then they throw it
+
+ align:start position:0%
+come up with a design then they throw it
+ 
+
+ align:start position:0%
+come up with a design then they throw it
+over the fence and
+
+ align:start position:0%
+over the fence and
+ 
+
+ align:start position:0%
+over the fence and
+somebody else builds it and they don't
+
+ align:start position:0%
+somebody else builds it and they don't
+ 
+
+ align:start position:0%
+somebody else builds it and they don't
+have to use it they throw it over the
+
+ align:start position:0%
+have to use it they throw it over the
+ 
+
+ align:start position:0%
+have to use it they throw it over the
+fence and then the end user takes over
+
+ align:start position:0%
+fence and then the end user takes over
+ 
+
+ align:start position:0%
+fence and then the end user takes over
+and so it's it's really critical so the
+
+ align:start position:0%
+and so it's it's really critical so the
+ 
+
+ align:start position:0%
+and so it's it's really critical so the
+cdio
+
+ align:start position:0%
+cdio
+ 
+
+ align:start position:0%
+cdio
+it's a way of approaching engineering
+
+ align:start position:0%
+it's a way of approaching engineering
+ 
+
+ align:start position:0%
+it's a way of approaching engineering
+particularly complex systems that from
+
+ align:start position:0%
+particularly complex systems that from
+ 
+
+ align:start position:0%
+particularly complex systems that from
+the very beginning
+
+ align:start position:0%
+the very beginning
+ 
+
+ align:start position:0%
+the very beginning
+you take into account all of those
+
+ align:start position:0%
+you take into account all of those
+ 
+
+ align:start position:0%
+you take into account all of those
+phases of
+
+ align:start position:0%
+phases of
+ 
+
+ align:start position:0%
+phases of
+an engineering system i mean it's not
+
+ align:start position:0%
+an engineering system i mean it's not
+ 
+
+ align:start position:0%
+an engineering system i mean it's not
+not just
+
+ align:start position:0%
+not just
+ 
+
+ align:start position:0%
+not just
+engineering systems when you're you
+
+ align:start position:0%
+engineering systems when you're you
+ 
+
+ align:start position:0%
+engineering systems when you're you
+build a house
+
+ align:start position:0%
+build a house
+ 
+
+ align:start position:0%
+build a house
+i mean you know you better figure out
+
+ align:start position:0%
+i mean you know you better figure out
+ 
+
+ align:start position:0%
+i mean you know you better figure out
+what it's going to be
+
+ align:start position:0%
+what it's going to be
+ 
+
+ align:start position:0%
+what it's going to be
+to live in this house before it gets
+
+ align:start position:0%
+to live in this house before it gets
+ 
+
+ align:start position:0%
+to live in this house before it gets
+built otherwise you're going to have a
+
+ align:start position:0%
+built otherwise you're going to have a
+ 
+
+ align:start position:0%
+built otherwise you're going to have a
+lot of
+
+ align:start position:0%
+lot of
+ 
+
+ align:start position:0%
+lot of
+you know bills with a contractor to make
+
+ align:start position:0%
+you know bills with a contractor to make
+ 
+
+ align:start position:0%
+you know bills with a contractor to make
+changes at the last minute and that's
+
+ align:start position:0%
+changes at the last minute and that's
+ 
+
+ align:start position:0%
+changes at the last minute and that's
+one of the other things you learn
+
+ align:start position:0%
+one of the other things you learn
+ 
+
+ align:start position:0%
+one of the other things you learn
+in one of the basic principles of
+
+ align:start position:0%
+in one of the basic principles of
+ 
+
+ align:start position:0%
+in one of the basic principles of
+systems engineering
+
+ align:start position:0%
+systems engineering
+ 
+
+ align:start position:0%
+systems engineering
+and particularly in the space business
+
+ align:start position:0%
+and particularly in the space business
+ 
+
+ align:start position:0%
+and particularly in the space business
+is that the further you get into
+
+ align:start position:0%
+is that the further you get into
+ 
+
+ align:start position:0%
+is that the further you get into
+the implementation of the system the
+
+ align:start position:0%
+the implementation of the system the
+ 
+
+ align:start position:0%
+the implementation of the system the
+more expensive it it
+
+ align:start position:0%
+more expensive it it
+ 
+
+ align:start position:0%
+more expensive it it
+is to make any changes i feel like
+
+ align:start position:0%
+is to make any changes i feel like
+ 
+
+ align:start position:0%
+is to make any changes i feel like
+that's one of the beauties of this
+
+ align:start position:0%
+that's one of the beauties of this
+ 
+
+ align:start position:0%
+that's one of the beauties of this
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+you might be working in a completely
+
+ align:start position:0%
+you might be working in a completely
+ 
+
+ align:start position:0%
+you might be working in a completely
+different discipline but you can find
+
+ align:start position:0%
+different discipline but you can find
+ 
+
+ align:start position:0%
+different discipline but you can find
+something useful
+
+ align:start position:0%
+something useful
+ 
+
+ align:start position:0%
+something useful
+that is kind of the subtext of the
+
+ align:start position:0%
+that is kind of the subtext of the
+ 
+
+ align:start position:0%
+that is kind of the subtext of the
+course is
+
+ align:start position:0%
+course is
+ 
+
+ align:start position:0%
+course is
+it's not just about the space shuttle
+
+ align:start position:0%
+it's not just about the space shuttle
+ 
+
+ align:start position:0%
+it's not just about the space shuttle
+it's learning
+
+ align:start position:0%
+it's learning
+ 
+
+ align:start position:0%
+it's learning
+how a very very complex system
+
+ align:start position:0%
+how a very very complex system
+ 
+
+ align:start position:0%
+how a very very complex system
+was initially conceived designed
+
+ align:start position:0%
+was initially conceived designed
+ 
+
+ align:start position:0%
+was initially conceived designed
+implemented and operated and that's why
+
+ align:start position:0%
+implemented and operated and that's why
+ 
+
+ align:start position:0%
+implemented and operated and that's why
+after the central part of the course
+
+ align:start position:0%
+after the central part of the course
+ 
+
+ align:start position:0%
+after the central part of the course
+where we talk about the design and the
+
+ align:start position:0%
+where we talk about the design and the
+ 
+
+ align:start position:0%
+where we talk about the design and the
+building of all these complex subsystems
+
+ align:start position:0%
+building of all these complex subsystems
+ 
+
+ align:start position:0%
+building of all these complex subsystems
+then we brought in people who actually
+
+ align:start position:0%
+then we brought in people who actually
+ 
+
+ align:start position:0%
+then we brought in people who actually
+operated the shuttle the
+
+ align:start position:0%
+operated the shuttle the
+ 
+
+ align:start position:0%
+operated the shuttle the
+the launch director the flight director
+
+ align:start position:0%
+the launch director the flight director
+ 
+
+ align:start position:0%
+the launch director the flight director
+the payload operator
+
+ align:start position:0%
+the payload operator
+ 
+
+ align:start position:0%
+the payload operator
+an astronaut pilot who flew the shuttle
+
+ align:start position:0%
+an astronaut pilot who flew the shuttle
+ 
+
+ align:start position:0%
+an astronaut pilot who flew the shuttle
+and and so on because
+
+ align:start position:0%
+and and so on because
+ 
+
+ align:start position:0%
+and and so on because
+that's the final phase of the whole cdio
+
+ align:start position:0%
+that's the final phase of the whole cdio
+ 
+
+ align:start position:0%
+that's the final phase of the whole cdio
+is from as i say from soup to nuts this
+
+ align:start position:0%
+is from as i say from soup to nuts this
+ 
+
+ align:start position:0%
+is from as i say from soup to nuts this
+is what the shuttle was all about
+
+ align:start position:0%
+is what the shuttle was all about
+ 
+
+ align:start position:0%
+is what the shuttle was all about
+to really understand the development of
+
+ align:start position:0%
+to really understand the development of
+ 
+
+ align:start position:0%
+to really understand the development of
+the space program here in the us
+
+ align:start position:0%
+the space program here in the us
+ 
+
+ align:start position:0%
+the space program here in the us
+it helps to look at the interconnected
+
+ align:start position:0%
+it helps to look at the interconnected
+ 
+
+ align:start position:0%
+it helps to look at the interconnected
+series of systems that built it
+
+ align:start position:0%
+series of systems that built it
+ 
+
+ align:start position:0%
+series of systems that built it
+and they go well beyond engineering and
+
+ align:start position:0%
+and they go well beyond engineering and
+ 
+
+ align:start position:0%
+and they go well beyond engineering and
+mathematics
+
+ align:start position:0%
+mathematics
+ 
+
+ align:start position:0%
+mathematics
+for example politics played a huge role
+
+ align:start position:0%
+for example politics played a huge role
+ 
+
+ align:start position:0%
+for example politics played a huge role
+in aerospace engineering
+
+ align:start position:0%
+in aerospace engineering
+ 
+
+ align:start position:0%
+in aerospace engineering
+we really thought it was important to
+
+ align:start position:0%
+we really thought it was important to
+ 
+
+ align:start position:0%
+we really thought it was important to
+devote the beginning
+
+ align:start position:0%
+devote the beginning
+ 
+
+ align:start position:0%
+devote the beginning
+lectures of the course to
+
+ align:start position:0%
+lectures of the course to
+ 
+
+ align:start position:0%
+lectures of the course to
+you know what what were all these uh
+
+ align:start position:0%
+you know what what were all these uh
+ 
+
+ align:start position:0%
+you know what what were all these uh
+influences which
+
+ align:start position:0%
+influences which
+ 
+
+ align:start position:0%
+influences which
+had such an important impact on the
+
+ align:start position:0%
+had such an important impact on the
+ 
+
+ align:start position:0%
+had such an important impact on the
+design
+
+ align:start position:0%
+design
+ 
+
+ align:start position:0%
+design
+economically it was no longer possible
+
+ align:start position:0%
+economically it was no longer possible
+ 
+
+ align:start position:0%
+economically it was no longer possible
+to treat nasa
+
+ align:start position:0%
+to treat nasa
+ 
+
+ align:start position:0%
+to treat nasa
+uh in such a special way as had been
+
+ align:start position:0%
+uh in such a special way as had been
+ 
+
+ align:start position:0%
+uh in such a special way as had been
+done by
+
+ align:start position:0%
+done by
+ 
+
+ align:start position:0%
+done by
+apollo i mean 400 000 people working on
+
+ align:start position:0%
+apollo i mean 400 000 people working on
+ 
+
+ align:start position:0%
+apollo i mean 400 000 people working on
+apollo with the
+
+ align:start position:0%
+apollo with the
+ 
+
+ align:start position:0%
+apollo with the
+at the height of it four percent of the
+
+ align:start position:0%
+at the height of it four percent of the
+ 
+
+ align:start position:0%
+at the height of it four percent of the
+federal budget going to space
+
+ align:start position:0%
+federal budget going to space
+ 
+
+ align:start position:0%
+federal budget going to space
+exploration
+
+ align:start position:0%
+exploration
+ 
+
+ align:start position:0%
+exploration
+this is not normal for space activities
+
+ align:start position:0%
+this is not normal for space activities
+ 
+
+ align:start position:0%
+this is not normal for space activities
+it was a very special time in our
+
+ align:start position:0%
+it was a very special time in our
+ 
+
+ align:start position:0%
+it was a very special time in our
+history
+
+ align:start position:0%
+history
+ 
+
+ align:start position:0%
+history
+then you get to the late 60s i mean even
+
+ align:start position:0%
+then you get to the late 60s i mean even
+ 
+
+ align:start position:0%
+then you get to the late 60s i mean even
+even john kennedy
+
+ align:start position:0%
+even john kennedy
+ 
+
+ align:start position:0%
+even john kennedy
+after having made this commitment to go
+
+ align:start position:0%
+after having made this commitment to go
+ 
+
+ align:start position:0%
+after having made this commitment to go
+to the moon started to have second
+
+ align:start position:0%
+to the moon started to have second
+ 
+
+ align:start position:0%
+to the moon started to have second
+thoughts about how much it was going to
+
+ align:start position:0%
+thoughts about how much it was going to
+ 
+
+ align:start position:0%
+thoughts about how much it was going to
+cost
+
+ align:start position:0%
+cost
+ 
+
+ align:start position:0%
+cost
+then of course he was assassinated and
+
+ align:start position:0%
+then of course he was assassinated and
+ 
+
+ align:start position:0%
+then of course he was assassinated and
+and getting to the moon
+
+ align:start position:0%
+and getting to the moon
+ 
+
+ align:start position:0%
+and getting to the moon
+by the end of the decade be sort of
+
+ align:start position:0%
+by the end of the decade be sort of
+ 
+
+ align:start position:0%
+by the end of the decade be sort of
+became our way of honoring kennedy's
+
+ align:start position:0%
+became our way of honoring kennedy's
+ 
+
+ align:start position:0%
+became our way of honoring kennedy's
+legacy so so it wasn't question we did
+
+ align:start position:0%
+legacy so so it wasn't question we did
+ 
+
+ align:start position:0%
+legacy so so it wasn't question we did
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+but you know along came the nixon
+
+ align:start position:0%
+but you know along came the nixon
+ 
+
+ align:start position:0%
+but you know along came the nixon
+administration
+
+ align:start position:0%
+administration
+ 
+
+ align:start position:0%
+administration
+following president johnson's great
+
+ align:start position:0%
+following president johnson's great
+ 
+
+ align:start position:0%
+following president johnson's great
+society program
+
+ align:start position:0%
+society program
+ 
+
+ align:start position:0%
+society program
+huge increase in social spending and
+
+ align:start position:0%
+huge increase in social spending and
+ 
+
+ align:start position:0%
+huge increase in social spending and
+then the vietnam war
+
+ align:start position:0%
+then the vietnam war
+ 
+
+ align:start position:0%
+then the vietnam war
+and uh you know space it was clear and
+
+ align:start position:0%
+and uh you know space it was clear and
+ 
+
+ align:start position:0%
+and uh you know space it was clear and
+nixon was explicit about this you know
+
+ align:start position:0%
+nixon was explicit about this you know
+ 
+
+ align:start position:0%
+nixon was explicit about this you know
+the space program has to take
+
+ align:start position:0%
+the space program has to take
+ 
+
+ align:start position:0%
+the space program has to take
+its proper role among all
+
+ align:start position:0%
+its proper role among all
+ 
+
+ align:start position:0%
+its proper role among all
+other national priorities and and that
+
+ align:start position:0%
+other national priorities and and that
+ 
+
+ align:start position:0%
+other national priorities and and that
+really involved a huge decrease
+
+ align:start position:0%
+really involved a huge decrease
+ 
+
+ align:start position:0%
+really involved a huge decrease
+in nasa's budget and and the people
+
+ align:start position:0%
+in nasa's budget and and the people
+ 
+
+ align:start position:0%
+in nasa's budget and and the people
+running nasa saw that coming and
+
+ align:start position:0%
+running nasa saw that coming and
+ 
+
+ align:start position:0%
+running nasa saw that coming and
+and so how do you continue to explore
+
+ align:start position:0%
+and so how do you continue to explore
+ 
+
+ align:start position:0%
+and so how do you continue to explore
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+they were faced with the real
+
+ align:start position:0%
+they were faced with the real
+ 
+
+ align:start position:0%
+they were faced with the real
+possibility that that human space flight
+
+ align:start position:0%
+possibility that that human space flight
+ 
+
+ align:start position:0%
+possibility that that human space flight
+in this country might come to an end
+
+ align:start position:0%
+in this country might come to an end
+ 
+
+ align:start position:0%
+in this country might come to an end
+and and nasa realized quite correctly
+
+ align:start position:0%
+and and nasa realized quite correctly
+ 
+
+ align:start position:0%
+and and nasa realized quite correctly
+that reusability was a key
+
+ align:start position:0%
+that reusability was a key
+ 
+
+ align:start position:0%
+that reusability was a key
+but then you get into all of the social
+
+ align:start position:0%
+but then you get into all of the social
+ 
+
+ align:start position:0%
+but then you get into all of the social
+economic political influences
+
+ align:start position:0%
+economic political influences
+ 
+
+ align:start position:0%
+economic political influences
+that put a lot of very very
+
+ align:start position:0%
+that put a lot of very very
+ 
+
+ align:start position:0%
+that put a lot of very very
+tight requirements on the shuttle
+
+ align:start position:0%
+tight requirements on the shuttle
+ 
+
+ align:start position:0%
+tight requirements on the shuttle
+particularly
+
+ align:start position:0%
+particularly
+ 
+
+ align:start position:0%
+particularly
+since in order to justify the expense
+
+ align:start position:0%
+since in order to justify the expense
+ 
+
+ align:start position:0%
+since in order to justify the expense
+nasa basically sold the shuttle as
+
+ align:start position:0%
+nasa basically sold the shuttle as
+ 
+
+ align:start position:0%
+nasa basically sold the shuttle as
+capable of doing anything we needed to
+
+ align:start position:0%
+capable of doing anything we needed to
+ 
+
+ align:start position:0%
+capable of doing anything we needed to
+do in space we could do with a shuttle
+
+ align:start position:0%
+do in space we could do with a shuttle
+ 
+
+ align:start position:0%
+do in space we could do with a shuttle
+we used it for scientific experiments we
+
+ align:start position:0%
+we used it for scientific experiments we
+ 
+
+ align:start position:0%
+we used it for scientific experiments we
+used it to launch satellites we used it
+
+ align:start position:0%
+used it to launch satellites we used it
+ 
+
+ align:start position:0%
+used it to launch satellites we used it
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+test out new engineering system we used
+
+ align:start position:0%
+test out new engineering system we used
+ 
+
+ align:start position:0%
+test out new engineering system we used
+it to repair
+
+ align:start position:0%
+it to repair
+ 
+
+ align:start position:0%
+it to repair
+satellites like the hubble space
+
+ align:start position:0%
+satellites like the hubble space
+ 
+
+ align:start position:0%
+satellites like the hubble space
+telescope we used it to build the
+
+ align:start position:0%
+telescope we used it to build the
+ 
+
+ align:start position:0%
+telescope we used it to build the
+international space station
+
+ align:start position:0%
+international space station
+ 
+
+ align:start position:0%
+international space station
+for me all my flights were in the space
+
+ align:start position:0%
+for me all my flights were in the space
+ 
+
+ align:start position:0%
+for me all my flights were in the space
+shuttle so
+
+ align:start position:0%
+shuttle so
+ 
+
+ align:start position:0%
+shuttle so
+you know i look on it with a great
+
+ align:start position:0%
+you know i look on it with a great
+ 
+
+ align:start position:0%
+you know i look on it with a great
+fondness
+
+ align:start position:0%
+fondness
+ 
+
+ align:start position:0%
+fondness
+recognizing its limitations but also
+
+ align:start position:0%
+recognizing its limitations but also
+ 
+
+ align:start position:0%
+recognizing its limitations but also
+understanding the incredible things that
+
+ align:start position:0%
+understanding the incredible things that
+ 
+
+ align:start position:0%
+understanding the incredible things that
+it allowed us to accomplish
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+while professor hoffman's classes offer
+
+ align:start position:0%
+while professor hoffman's classes offer
+ 
+
+ align:start position:0%
+while professor hoffman's classes offer
+incredible insights into what he's
+
+ align:start position:0%
+incredible insights into what he's
+ 
+
+ align:start position:0%
+incredible insights into what he's
+learned at nasa
+
+ align:start position:0%
+learned at nasa
+ 
+
+ align:start position:0%
+learned at nasa
+not to mention some deeply important
+
+ align:start position:0%
+not to mention some deeply important
+ 
+
+ align:start position:0%
+not to mention some deeply important
+skills for any student or intrigued ocw
+
+ align:start position:0%
+skills for any student or intrigued ocw
+ 
+
+ align:start position:0%
+skills for any student or intrigued ocw
+user
+
+ align:start position:0%
+user
+ 
+
+ align:start position:0%
+user
+it's not every day that i get to sit
+
+ align:start position:0%
+it's not every day that i get to sit
+ 
+
+ align:start position:0%
+it's not every day that i get to sit
+down with a real astronaut
+
+ align:start position:0%
+down with a real astronaut
+ 
+
+ align:start position:0%
+down with a real astronaut
+so of course i had to ask him what it
+
+ align:start position:0%
+so of course i had to ask him what it
+ 
+
+ align:start position:0%
+so of course i had to ask him what it
+was all like
+
+ align:start position:0%
+was all like
+ 
+
+ align:start position:0%
+was all like
+being launched into space being in orbit
+
+ align:start position:0%
+being launched into space being in orbit
+ 
+
+ align:start position:0%
+being launched into space being in orbit
+doing a spacewalk
+
+ align:start position:0%
+doing a spacewalk
+ 
+
+ align:start position:0%
+doing a spacewalk
+before my first launch i i asked many of
+
+ align:start position:0%
+before my first launch i i asked many of
+ 
+
+ align:start position:0%
+before my first launch i i asked many of
+the astronauts who had already flown
+
+ align:start position:0%
+the astronauts who had already flown
+ 
+
+ align:start position:0%
+the astronauts who had already flown
+what's it going to be like they put us
+
+ align:start position:0%
+what's it going to be like they put us
+ 
+
+ align:start position:0%
+what's it going to be like they put us
+in simulators and they shake the
+
+ align:start position:0%
+in simulators and they shake the
+ 
+
+ align:start position:0%
+in simulators and they shake the
+simulator a little bit but they said you
+
+ align:start position:0%
+simulator a little bit but they said you
+ 
+
+ align:start position:0%
+simulator a little bit but they said you
+know forget it that's nothing like the
+
+ align:start position:0%
+know forget it that's nothing like the
+ 
+
+ align:start position:0%
+know forget it that's nothing like the
+real thing
+
+ align:start position:0%
+real thing
+ 
+
+ align:start position:0%
+real thing
+it's hard to prepare yourself it's an
+
+ align:start position:0%
+it's hard to prepare yourself it's an
+ 
+
+ align:start position:0%
+it's hard to prepare yourself it's an
+exciting time the last few minutes
+
+ align:start position:0%
+exciting time the last few minutes
+ 
+
+ align:start position:0%
+exciting time the last few minutes
+before launch
+
+ align:start position:0%
+before launch
+ 
+
+ align:start position:0%
+before launch
+you as the the shuttle really comes
+
+ align:start position:0%
+you as the the shuttle really comes
+ 
+
+ align:start position:0%
+you as the the shuttle really comes
+alive
+
+ align:start position:0%
+alive
+ 
+
+ align:start position:0%
+alive
+and then all of a sudden you get this
+
+ align:start position:0%
+and then all of a sudden you get this
+ 
+
+ align:start position:0%
+and then all of a sudden you get this
+big kick in the pants and
+
+ align:start position:0%
+big kick in the pants and
+ 
+
+ align:start position:0%
+big kick in the pants and
+you look out the window and there's the
+
+ align:start position:0%
+you look out the window and there's the
+ 
+
+ align:start position:0%
+you look out the window and there's the
+ground falling away and everything is
+
+ align:start position:0%
+ground falling away and everything is
+ 
+
+ align:start position:0%
+ground falling away and everything is
+shaking
+
+ align:start position:0%
+shaking
+ 
+
+ align:start position:0%
+shaking
+and and tremendous noise people told me
+
+ align:start position:0%
+and and tremendous noise people told me
+ 
+
+ align:start position:0%
+and and tremendous noise people told me
+that there was going to be more
+
+ align:start position:0%
+that there was going to be more
+ 
+
+ align:start position:0%
+that there was going to be more
+vibration than i could ever imagine
+
+ align:start position:0%
+vibration than i could ever imagine
+ 
+
+ align:start position:0%
+vibration than i could ever imagine
+and and they were right because i
+
+ align:start position:0%
+and and they were right because i
+ 
+
+ align:start position:0%
+and and they were right because i
+couldn't imagine it
+
+ align:start position:0%
+couldn't imagine it
+ 
+
+ align:start position:0%
+couldn't imagine it
+45 seconds later you're going straight
+
+ align:start position:0%
+45 seconds later you're going straight
+ 
+
+ align:start position:0%
+45 seconds later you're going straight
+up and you break the sound barrier
+
+ align:start position:0%
+up and you break the sound barrier
+ 
+
+ align:start position:0%
+up and you break the sound barrier
+and and that gives you even more
+
+ align:start position:0%
+and and that gives you even more
+ 
+
+ align:start position:0%
+and and that gives you even more
+vibration because you get all these
+
+ align:start position:0%
+vibration because you get all these
+ 
+
+ align:start position:0%
+vibration because you get all these
+shock waves and
+
+ align:start position:0%
+shock waves and
+ 
+
+ align:start position:0%
+shock waves and
+i remember thinking to myself now this
+
+ align:start position:0%
+i remember thinking to myself now this
+ 
+
+ align:start position:0%
+i remember thinking to myself now this
+can't be normal something
+
+ align:start position:0%
+can't be normal something
+ 
+
+ align:start position:0%
+can't be normal something
+that the wings are going to fall off you
+
+ align:start position:0%
+that the wings are going to fall off you
+ 
+
+ align:start position:0%
+that the wings are going to fall off you
+know this something's wrong
+
+ align:start position:0%
+know this something's wrong
+ 
+
+ align:start position:0%
+know this something's wrong
+but i mean the structural engineers knew
+
+ align:start position:0%
+but i mean the structural engineers knew
+ 
+
+ align:start position:0%
+but i mean the structural engineers knew
+what they were doing and the wings did
+
+ align:start position:0%
+what they were doing and the wings did
+ 
+
+ align:start position:0%
+what they were doing and the wings did
+not fall off or else i would be
+
+ align:start position:0%
+not fall off or else i would be
+ 
+
+ align:start position:0%
+not fall off or else i would be
+here talking with you with the shuttle
+
+ align:start position:0%
+here talking with you with the shuttle
+ 
+
+ align:start position:0%
+here talking with you with the shuttle
+it was those two big solid rocket
+
+ align:start position:0%
+it was those two big solid rocket
+ 
+
+ align:start position:0%
+it was those two big solid rocket
+boosters that caused all of the
+
+ align:start position:0%
+boosters that caused all of the
+ 
+
+ align:start position:0%
+boosters that caused all of the
+vibration and they
+
+ align:start position:0%
+vibration and they
+ 
+
+ align:start position:0%
+vibration and they
+they burn for the first two minutes once
+
+ align:start position:0%
+they burn for the first two minutes once
+ 
+
+ align:start position:0%
+they burn for the first two minutes once
+they fall off
+
+ align:start position:0%
+they fall off
+ 
+
+ align:start position:0%
+they fall off
+it's a really smooth ride i mean
+
+ align:start position:0%
+it's a really smooth ride i mean
+ 
+
+ align:start position:0%
+it's a really smooth ride i mean
+everybody then talks about you know
+
+ align:start position:0%
+everybody then talks about you know
+ 
+
+ align:start position:0%
+everybody then talks about you know
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+electric ride all the way up into orbit
+
+ align:start position:0%
+electric ride all the way up into orbit
+ 
+
+ align:start position:0%
+electric ride all the way up into orbit
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+yeah that that contrast between the
+
+ align:start position:0%
+yeah that that contrast between the
+ 
+
+ align:start position:0%
+yeah that that contrast between the
+extreme vibration of riding on the side
+
+ align:start position:0%
+extreme vibration of riding on the side
+ 
+
+ align:start position:0%
+extreme vibration of riding on the side
+of a solid rocket
+
+ align:start position:0%
+of a solid rocket
+ 
+
+ align:start position:0%
+of a solid rocket
+booster and then just the burning of the
+
+ align:start position:0%
+booster and then just the burning of the
+ 
+
+ align:start position:0%
+booster and then just the burning of the
+the hydrogen oxygen engines was was
+
+ align:start position:0%
+the hydrogen oxygen engines was was
+ 
+
+ align:start position:0%
+the hydrogen oxygen engines was was
+really quite extraordinary
+
+ align:start position:0%
+really quite extraordinary
+ 
+
+ align:start position:0%
+really quite extraordinary
+did anyone ever just get really scared
+
+ align:start position:0%
+did anyone ever just get really scared
+ 
+
+ align:start position:0%
+did anyone ever just get really scared
+right before liftoff
+
+ align:start position:0%
+right before liftoff
+ 
+
+ align:start position:0%
+right before liftoff
+there are some astronauts who will tell
+
+ align:start position:0%
+there are some astronauts who will tell
+ 
+
+ align:start position:0%
+there are some astronauts who will tell
+you they don't like launches because of
+
+ align:start position:0%
+you they don't like launches because of
+ 
+
+ align:start position:0%
+you they don't like launches because of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the risk involved for me i mean i
+
+ align:start position:0%
+the risk involved for me i mean i
+ 
+
+ align:start position:0%
+the risk involved for me i mean i
+remember before the first flight
+
+ align:start position:0%
+remember before the first flight
+ 
+
+ align:start position:0%
+remember before the first flight
+riding out to the launch pad and looking
+
+ align:start position:0%
+riding out to the launch pad and looking
+ 
+
+ align:start position:0%
+riding out to the launch pad and looking
+up at this incredible vehicle that i'm
+
+ align:start position:0%
+up at this incredible vehicle that i'm
+ 
+
+ align:start position:0%
+up at this incredible vehicle that i'm
+going to get in
+
+ align:start position:0%
+going to get in
+ 
+
+ align:start position:0%
+going to get in
+and thinking to myself first of all you
+
+ align:start position:0%
+and thinking to myself first of all you
+ 
+
+ align:start position:0%
+and thinking to myself first of all you
+know this is not the time to be asking
+
+ align:start position:0%
+know this is not the time to be asking
+ 
+
+ align:start position:0%
+know this is not the time to be asking
+yourself if you really want to do this
+
+ align:start position:0%
+yourself if you really want to do this
+ 
+
+ align:start position:0%
+yourself if you really want to do this
+okay but then what was really going
+
+ align:start position:0%
+okay but then what was really going
+ 
+
+ align:start position:0%
+okay but then what was really going
+through in my mind is
+
+ align:start position:0%
+through in my mind is
+ 
+
+ align:start position:0%
+through in my mind is
+you know ever since i was six years old
+
+ align:start position:0%
+you know ever since i was six years old
+ 
+
+ align:start position:0%
+you know ever since i was six years old
+and i saw flash gordon take off in his
+
+ align:start position:0%
+and i saw flash gordon take off in his
+ 
+
+ align:start position:0%
+and i saw flash gordon take off in his
+rocket ship
+
+ align:start position:0%
+rocket ship
+ 
+
+ align:start position:0%
+rocket ship
+in science fiction and i always dreamed
+
+ align:start position:0%
+in science fiction and i always dreamed
+ 
+
+ align:start position:0%
+in science fiction and i always dreamed
+of doing it and i'm about to
+
+ align:start position:0%
+of doing it and i'm about to
+ 
+
+ align:start position:0%
+of doing it and i'm about to
+uh you know leave the planet it was it's
+
+ align:start position:0%
+uh you know leave the planet it was it's
+ 
+
+ align:start position:0%
+uh you know leave the planet it was it's
+exciting i mean so
+
+ align:start position:0%
+exciting i mean so
+ 
+
+ align:start position:0%
+exciting i mean so
+my idea was you know sit back and enjoy
+
+ align:start position:0%
+my idea was you know sit back and enjoy
+ 
+
+ align:start position:0%
+my idea was you know sit back and enjoy
+the ride
+
+ align:start position:0%
+the ride
+ 
+
+ align:start position:0%
+the ride
+i'm not a pilot so i didn't have to even
+
+ align:start position:0%
+i'm not a pilot so i didn't have to even
+ 
+
+ align:start position:0%
+i'm not a pilot so i didn't have to even
+worry about flying the shuttle i could
+
+ align:start position:0%
+worry about flying the shuttle i could
+ 
+
+ align:start position:0%
+worry about flying the shuttle i could
+just look out the window and
+
+ align:start position:0%
+just look out the window and
+ 
+
+ align:start position:0%
+just look out the window and
+enjoy this incredible experience which
+
+ align:start position:0%
+enjoy this incredible experience which
+ 
+
+ align:start position:0%
+enjoy this incredible experience which
+it certainly was then all of a sudden
+
+ align:start position:0%
+it certainly was then all of a sudden
+ 
+
+ align:start position:0%
+it certainly was then all of a sudden
+you feel yourself sort of floating up in
+
+ align:start position:0%
+you feel yourself sort of floating up in
+ 
+
+ align:start position:0%
+you feel yourself sort of floating up in
+your seat
+
+ align:start position:0%
+your seat
+ 
+
+ align:start position:0%
+your seat
+you're weightless i remember unstrapping
+
+ align:start position:0%
+you're weightless i remember unstrapping
+ 
+
+ align:start position:0%
+you're weightless i remember unstrapping
+and floating over the window and there
+
+ align:start position:0%
+and floating over the window and there
+ 
+
+ align:start position:0%
+and floating over the window and there
+was the coast of africa coming over the
+
+ align:start position:0%
+was the coast of africa coming over the
+ 
+
+ align:start position:0%
+was the coast of africa coming over the
+horizon
+
+ align:start position:0%
+horizon
+ 
+
+ align:start position:0%
+horizon
+and that's when it really hit me oh my
+
+ align:start position:0%
+and that's when it really hit me oh my
+ 
+
+ align:start position:0%
+and that's when it really hit me oh my
+god i'm in space
+
+ align:start position:0%
+god i'm in space
+ 
+
+ align:start position:0%
+god i'm in space
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+while launching into space is certainly
+
+ align:start position:0%
+while launching into space is certainly
+ 
+
+ align:start position:0%
+while launching into space is certainly
+an incredible ride
+
+ align:start position:0%
+an incredible ride
+ 
+
+ align:start position:0%
+an incredible ride
+professor hoffman also did a number of
+
+ align:start position:0%
+professor hoffman also did a number of
+ 
+
+ align:start position:0%
+professor hoffman also did a number of
+space walks during his career
+
+ align:start position:0%
+space walks during his career
+ 
+
+ align:start position:0%
+space walks during his career
+he shared with us the story of one of
+
+ align:start position:0%
+he shared with us the story of one of
+ 
+
+ align:start position:0%
+he shared with us the story of one of
+them i remember my very first base walk
+
+ align:start position:0%
+them i remember my very first base walk
+ 
+
+ align:start position:0%
+them i remember my very first base walk
+on my first space flight
+
+ align:start position:0%
+on my first space flight
+ 
+
+ align:start position:0%
+on my first space flight
+i went out we had to attach some special
+
+ align:start position:0%
+i went out we had to attach some special
+ 
+
+ align:start position:0%
+i went out we had to attach some special
+tools to the end of the robotic arm
+
+ align:start position:0%
+tools to the end of the robotic arm
+ 
+
+ align:start position:0%
+tools to the end of the robotic arm
+as part of an attempt to rescue a
+
+ align:start position:0%
+as part of an attempt to rescue a
+ 
+
+ align:start position:0%
+as part of an attempt to rescue a
+satellite which had been deployed but
+
+ align:start position:0%
+satellite which had been deployed but
+ 
+
+ align:start position:0%
+satellite which had been deployed but
+didn't turn on
+
+ align:start position:0%
+didn't turn on
+ 
+
+ align:start position:0%
+didn't turn on
+and then we had been out for about two
+
+ align:start position:0%
+and then we had been out for about two
+ 
+
+ align:start position:0%
+and then we had been out for about two
+hours or so
+
+ align:start position:0%
+hours or so
+ 
+
+ align:start position:0%
+hours or so
+and the sun set and then they didn't
+
+ align:start position:0%
+and the sun set and then they didn't
+ 
+
+ align:start position:0%
+and the sun set and then they didn't
+have the right lighting conditions and
+
+ align:start position:0%
+have the right lighting conditions and
+ 
+
+ align:start position:0%
+have the right lighting conditions and
+i'll never forget the call that came up
+
+ align:start position:0%
+i'll never forget the call that came up
+ 
+
+ align:start position:0%
+i'll never forget the call that came up
+from the ground
+
+ align:start position:0%
+from the ground
+ 
+
+ align:start position:0%
+from the ground
+hey jeff and dave would you mind staying
+
+ align:start position:0%
+hey jeff and dave would you mind staying
+ 
+
+ align:start position:0%
+hey jeff and dave would you mind staying
+outside for another 45 minutes while we
+
+ align:start position:0%
+outside for another 45 minutes while we
+ 
+
+ align:start position:0%
+outside for another 45 minutes while we
+wait for the sun to come
+
+ align:start position:0%
+wait for the sun to come
+ 
+
+ align:start position:0%
+wait for the sun to come
+oh my gosh and i had nothing to do i was
+
+ align:start position:0%
+oh my gosh and i had nothing to do i was
+ 
+
+ align:start position:0%
+oh my gosh and i had nothing to do i was
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+i mean i was a tourist out in a
+
+ align:start position:0%
+i mean i was a tourist out in a
+ 
+
+ align:start position:0%
+i mean i was a tourist out in a
+spacesuit holding on
+
+ align:start position:0%
+spacesuit holding on
+ 
+
+ align:start position:0%
+spacesuit holding on
+i thought to myself i'm just gonna have
+
+ align:start position:0%
+i thought to myself i'm just gonna have
+ 
+
+ align:start position:0%
+i thought to myself i'm just gonna have
+some fun
+
+ align:start position:0%
+some fun
+ 
+
+ align:start position:0%
+some fun
+so i actually i was sort of crawling all
+
+ align:start position:0%
+so i actually i was sort of crawling all
+ 
+
+ align:start position:0%
+so i actually i was sort of crawling all
+over the shuttle
+
+ align:start position:0%
+over the shuttle
+ 
+
+ align:start position:0%
+over the shuttle
+thinking back how i crawled halfway
+
+ align:start position:0%
+thinking back how i crawled halfway
+ 
+
+ align:start position:0%
+thinking back how i crawled halfway
+up the tail and and the commander told
+
+ align:start position:0%
+up the tail and and the commander told
+ 
+
+ align:start position:0%
+up the tail and and the commander told
+me he was doing his best to keep the tv
+
+ align:start position:0%
+me he was doing his best to keep the tv
+ 
+
+ align:start position:0%
+me he was doing his best to keep the tv
+cameras off me i mean i just i was so
+
+ align:start position:0%
+cameras off me i mean i just i was so
+ 
+
+ align:start position:0%
+cameras off me i mean i just i was so
+ecstatic i wasn't
+
+ align:start position:0%
+ecstatic i wasn't
+ 
+
+ align:start position:0%
+ecstatic i wasn't
+thinking about the fact that you know
+
+ align:start position:0%
+thinking about the fact that you know
+ 
+
+ align:start position:0%
+thinking about the fact that you know
+maybe some people on the ground wouldn't
+
+ align:start position:0%
+maybe some people on the ground wouldn't
+ 
+
+ align:start position:0%
+maybe some people on the ground wouldn't
+want to see an astronaut hanging from
+
+ align:start position:0%
+want to see an astronaut hanging from
+ 
+
+ align:start position:0%
+want to see an astronaut hanging from
+the tail of the shuttle but i did it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's all a matter of perspective to
+
+ align:start position:0%
+it's all a matter of perspective to
+ 
+
+ align:start position:0%
+it's all a matter of perspective to
+broaden your own horizons from the
+
+ align:start position:0%
+broaden your own horizons from the
+ 
+
+ align:start position:0%
+broaden your own horizons from the
+safety of your own home
+
+ align:start position:0%
+safety of your own home
+ 
+
+ align:start position:0%
+safety of your own home
+be sure to check out professor hoffman's
+
+ align:start position:0%
+be sure to check out professor hoffman's
+ 
+
+ align:start position:0%
+be sure to check out professor hoffman's
+course materials on mit open courseware
+
+ align:start position:0%
+course materials on mit open courseware
+ 
+
+ align:start position:0%
+course materials on mit open courseware
+or on the mit open learning library
+
+ align:start position:0%
+or on the mit open learning library
+ 
+
+ align:start position:0%
+or on the mit open learning library
+thanks so much for listening your
+
+ align:start position:0%
+thanks so much for listening your
+ 
+
+ align:start position:0%
+thanks so much for listening your
+comments have inspired me to keep
+
+ align:start position:0%
+comments have inspired me to keep
+ 
+
+ align:start position:0%
+comments have inspired me to keep
+learning
+
+ align:start position:0%
+learning
+ 
+
+ align:start position:0%
+learning
+until next time signing off from
+
+ align:start position:0%
+until next time signing off from
+ 
+
+ align:start position:0%
+until next time signing off from
+cambridge massachusetts
+
+ align:start position:0%
+cambridge massachusetts
+ 
+
+ align:start position:0%
+cambridge massachusetts
+i'm sarah hansen from mit open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+courseware
+
+ align:start position:0%
+courseware
+ 
+
+ align:start position:0%
+courseware
+mom passed the car
\ No newline at end of file
diff --git a/5QUe51d_22w.txt b/5QUe51d_22w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f61b28ae4d4651e9dc3639290ac67da9f6cf1076
--- /dev/null
+++ b/5QUe51d_22w.txt
@@ -0,0 +1,2219 @@
+align:start position:0%
+ 
+welcome back to age2 in this section we
+
+ align:start position:0%
+welcome back to age2 in this section we
+ 
+
+ align:start position:0%
+welcome back to age2 in this section we
+want to talk about time time keeping and
+
+ align:start position:0%
+want to talk about time time keeping and
+ 
+
+ align:start position:0%
+want to talk about time time keeping and
+how to relate time between two different
+
+ align:start position:0%
+how to relate time between two different
+ 
+
+ align:start position:0%
+how to relate time between two different
+reference now let me start start with a
+
+ align:start position:0%
+reference now let me start start with a
+ 
+
+ align:start position:0%
+reference now let me start start with a
+quote by Albert Einstein everything
+
+ align:start position:0%
+quote by Albert Einstein everything
+ 
+
+ align:start position:0%
+quote by Albert Einstein everything
+should be as simple as possible but not
+
+ align:start position:0%
+should be as simple as possible but not
+ 
+
+ align:start position:0%
+should be as simple as possible but not
+simpler so let's start with this in mind
+
+ align:start position:0%
+simpler so let's start with this in mind
+ 
+
+ align:start position:0%
+simpler so let's start with this in mind
+and recall that we ended the last
+
+ align:start position:0%
+and recall that we ended the last
+ 
+
+ align:start position:0%
+and recall that we ended the last
+section by finding that you know the
+
+ align:start position:0%
+section by finding that you know the
+ 
+
+ align:start position:0%
+section by finding that you know the
+wave Isa model doesn't really describe
+
+ align:start position:0%
+wave Isa model doesn't really describe
+ 
+
+ align:start position:0%
+wave Isa model doesn't really describe
+electromagnetic waves uh very well we
+
+ align:start position:0%
+electromagnetic waves uh very well we
+ 
+
+ align:start position:0%
+electromagnetic waves uh very well we
+see that there is a uh problem between
+
+ align:start position:0%
+see that there is a uh problem between
+ 
+
+ align:start position:0%
+see that there is a uh problem between
+the experiments specifically the one by
+
+ align:start position:0%
+the experiments specifically the one by
+ 
+
+ align:start position:0%
+the experiments specifically the one by
+Michaels and moley um and the
+
+ align:start position:0%
+Michaels and moley um and the
+ 
+
+ align:start position:0%
+Michaels and moley um and the
+theoretical picture people had in mind
+
+ align:start position:0%
+theoretical picture people had in mind
+ 
+
+ align:start position:0%
+theoretical picture people had in mind
+so Einstein approached this um in
+
+ align:start position:0%
+so Einstein approached this um in
+ 
+
+ align:start position:0%
+so Einstein approached this um in
+a interesting way he simply postulated
+
+ align:start position:0%
+a interesting way he simply postulated
+ 
+
+ align:start position:0%
+a interesting way he simply postulated
+the things he thought need to be true he
+
+ align:start position:0%
+the things he thought need to be true he
+ 
+
+ align:start position:0%
+the things he thought need to be true he
+said the same law of electrodynamics
+
+ align:start position:0%
+said the same law of electrodynamics
+ 
+
+ align:start position:0%
+said the same law of electrodynamics
+will be valid for all reference frames
+
+ align:start position:0%
+will be valid for all reference frames
+ 
+
+ align:start position:0%
+will be valid for all reference frames
+where all laws of mechanics hold good
+
+ align:start position:0%
+where all laws of mechanics hold good
+ 
+
+ align:start position:0%
+where all laws of mechanics hold good
+this is the principle of
+
+ align:start position:0%
+this is the principle of
+ 
+
+ align:start position:0%
+this is the principle of
+Relativity the second postulate is that
+
+ align:start position:0%
+Relativity the second postulate is that
+ 
+
+ align:start position:0%
+Relativity the second postulate is that
+light is always propagated in empty
+
+ align:start position:0%
+light is always propagated in empty
+ 
+
+ align:start position:0%
+light is always propagated in empty
+space at a velocity see independent of
+
+ align:start position:0%
+space at a velocity see independent of
+ 
+
+ align:start position:0%
+space at a velocity see independent of
+the state of motion of the emitting body
+
+ align:start position:0%
+the state of motion of the emitting body
+ 
+
+ align:start position:0%
+the state of motion of the emitting body
+so with this two postulates we will now
+
+ align:start position:0%
+so with this two postulates we will now
+ 
+
+ align:start position:0%
+so with this two postulates we will now
+derive the theory of special relativity
+
+ align:start position:0%
+derive the theory of special relativity
+ 
+
+ align:start position:0%
+derive the theory of special relativity
+and again we'll start by talking about
+
+ align:start position:0%
+and again we'll start by talking about
+ 
+
+ align:start position:0%
+and again we'll start by talking about
+time so time is suspect and I alluded to
+
+ align:start position:0%
+time so time is suspect and I alluded to
+ 
+
+ align:start position:0%
+time so time is suspect and I alluded to
+this already when we looked at Galilean
+
+ align:start position:0%
+this already when we looked at Galilean
+ 
+
+ align:start position:0%
+this already when we looked at Galilean
+transformation where we simply out of
+
+ align:start position:0%
+transformation where we simply out of
+ 
+
+ align:start position:0%
+transformation where we simply out of
+our intuition assumed that time is
+
+ align:start position:0%
+our intuition assumed that time is
+ 
+
+ align:start position:0%
+our intuition assumed that time is
+invariant
+
+ align:start position:0%
+invariant
+ 
+
+ align:start position:0%
+invariant
+now when we now talk about time the the
+
+ align:start position:0%
+now when we now talk about time the the
+ 
+
+ align:start position:0%
+now when we now talk about time the the
+the Viewpoint I would like you to have
+
+ align:start position:0%
+the Viewpoint I would like you to have
+ 
+
+ align:start position:0%
+the Viewpoint I would like you to have
+is that we want to look at clocks from
+
+ align:start position:0%
+is that we want to look at clocks from
+ 
+
+ align:start position:0%
+is that we want to look at clocks from
+different reference frames and we want
+
+ align:start position:0%
+different reference frames and we want
+ 
+
+ align:start position:0%
+different reference frames and we want
+to investigate whether or not events
+
+ align:start position:0%
+to investigate whether or not events
+ 
+
+ align:start position:0%
+to investigate whether or not events
+happened simultaneously or not what does
+
+ align:start position:0%
+happened simultaneously or not what does
+ 
+
+ align:start position:0%
+happened simultaneously or not what does
+it mean when we make a statement like a
+
+ align:start position:0%
+it mean when we make a statement like a
+ 
+
+ align:start position:0%
+it mean when we make a statement like a
+train arrives at 7:00 what we mean is
+
+ align:start position:0%
+train arrives at 7:00 what we mean is
+ 
+
+ align:start position:0%
+train arrives at 7:00 what we mean is
+that there is a simultaneous two
+
+ align:start position:0%
+that there is a simultaneous two
+ 
+
+ align:start position:0%
+that there is a simultaneous two
+simultaneous event happen one is that
+
+ align:start position:0%
+simultaneous event happen one is that
+ 
+
+ align:start position:0%
+simultaneous event happen one is that
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+little um clock here
+
+ align:start position:0%
+little um clock here
+ 
+
+ align:start position:0%
+little um clock here
+shows uh to point at 7 and 12 meaning
+
+ align:start position:0%
+shows uh to point at 7 and 12 meaning
+ 
+
+ align:start position:0%
+shows uh to point at 7 and 12 meaning
+that it indicates to us that this event
+
+ align:start position:0%
+that it indicates to us that this event
+ 
+
+ align:start position:0%
+that it indicates to us that this event
+indicates to us that it's 7:00 and the
+
+ align:start position:0%
+indicates to us that it's 7:00 and the
+ 
+
+ align:start position:0%
+indicates to us that it's 7:00 and the
+second event is that the train actually
+
+ align:start position:0%
+second event is that the train actually
+ 
+
+ align:start position:0%
+second event is that the train actually
+arrived at the station so those two
+
+ align:start position:0%
+arrived at the station so those two
+ 
+
+ align:start position:0%
+arrived at the station so those two
+events happen
+
+ align:start position:0%
+events happen
+ 
+
+ align:start position:0%
+events happen
+simultaneously the question now is
+
+ align:start position:0%
+simultaneously the question now is
+ 
+
+ align:start position:0%
+simultaneously the question now is
+whether or not two observers one
+
+ align:start position:0%
+whether or not two observers one
+ 
+
+ align:start position:0%
+whether or not two observers one
+stationary and one moving agree with
+
+ align:start position:0%
+stationary and one moving agree with
+ 
+
+ align:start position:0%
+stationary and one moving agree with
+this observation and I'll take it away
+
+ align:start position:0%
+this observation and I'll take it away
+ 
+
+ align:start position:0%
+this observation and I'll take it away
+the answer is no there is a relativity
+
+ align:start position:0%
+the answer is no there is a relativity
+ 
+
+ align:start position:0%
+the answer is no there is a relativity
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+simultaneity um meaning that two
+
+ align:start position:0%
+simultaneity um meaning that two
+ 
+
+ align:start position:0%
+simultaneity um meaning that two
+observers can very much agree on the
+
+ align:start position:0%
+observers can very much agree on the
+ 
+
+ align:start position:0%
+observers can very much agree on the
+description of two events but not
+
+ align:start position:0%
+description of two events but not
+ 
+
+ align:start position:0%
+description of two events but not
+necessarily that those two events happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simultaneously so let's investigate and
+
+ align:start position:0%
+simultaneously so let's investigate and
+ 
+
+ align:start position:0%
+simultaneously so let's investigate and
+we use our two friends Ellis and Bob in
+
+ align:start position:0%
+we use our two friends Ellis and Bob in
+ 
+
+ align:start position:0%
+we use our two friends Ellis and Bob in
+order to have this
+
+ align:start position:0%
+order to have this
+ 
+
+ align:start position:0%
+order to have this
+discussion all right so we start from a
+
+ align:start position:0%
+discussion all right so we start from a
+ 
+
+ align:start position:0%
+discussion all right so we start from a
+situation where Ellis and Bob are both
+
+ align:start position:0%
+situation where Ellis and Bob are both
+ 
+
+ align:start position:0%
+situation where Ellis and Bob are both
+stationary Ellis is on her spacecraft
+
+ align:start position:0%
+stationary Ellis is on her spacecraft
+ 
+
+ align:start position:0%
+stationary Ellis is on her spacecraft
+and she has a device on her spacecraft
+
+ align:start position:0%
+and she has a device on her spacecraft
+ 
+
+ align:start position:0%
+and she has a device on her spacecraft
+which shoots light or paintballs towards
+
+ align:start position:0%
+which shoots light or paintballs towards
+ 
+
+ align:start position:0%
+which shoots light or paintballs towards
+two clocks and each time this happens
+
+ align:start position:0%
+two clocks and each time this happens
+ 
+
+ align:start position:0%
+two clocks and each time this happens
+the clock
+
+ align:start position:0%
+the clock
+ 
+
+ align:start position:0%
+the clock
+ticks right and we just look at one
+
+ align:start position:0%
+ticks right and we just look at one
+ 
+
+ align:start position:0%
+ticks right and we just look at one
+situation so she has a clock on the left
+
+ align:start position:0%
+situation so she has a clock on the left
+ 
+
+ align:start position:0%
+situation so she has a clock on the left
+and the clock on the right Bob observes
+
+ align:start position:0%
+and the clock on the right Bob observes
+ 
+
+ align:start position:0%
+and the clock on the right Bob observes
+Ellis's clock and you can compare
+
+ align:start position:0%
+Ellis's clock and you can compare
+ 
+
+ align:start position:0%
+Ellis's clock and you can compare
+Ellis's this observation of Ellis's
+
+ align:start position:0%
+Ellis's this observation of Ellis's
+ 
+
+ align:start position:0%
+Ellis's this observation of Ellis's
+clock with um his own so in this
+
+ align:start position:0%
+clock with um his own so in this
+ 
+
+ align:start position:0%
+clock with um his own so in this
+stational situation there's a TA and a
+
+ align:start position:0%
+stational situation there's a TA and a
+ 
+
+ align:start position:0%
+stational situation there's a TA and a
+TB those are the times of Ellis and Bob
+
+ align:start position:0%
+TB those are the times of Ellis and Bob
+ 
+
+ align:start position:0%
+TB those are the times of Ellis and Bob
+both are zero this is when the situation
+
+ align:start position:0%
+both are zero this is when the situation
+ 
+
+ align:start position:0%
+both are zero this is when the situation
+starts and the capital T indicates for
+
+ align:start position:0%
+starts and the capital T indicates for
+ 
+
+ align:start position:0%
+starts and the capital T indicates for
+Ellis and for Bob when they observe that
+
+ align:start position:0%
+Ellis and for Bob when they observe that
+ 
+
+ align:start position:0%
+Ellis and for Bob when they observe that
+the clock has been
+
+ align:start position:0%
+the clock has been
+ 
+
+ align:start position:0%
+the clock has been
+hit um I should add here that when we
+
+ align:start position:0%
+hit um I should add here that when we
+ 
+
+ align:start position:0%
+hit um I should add here that when we
+talk about observation in this entire
+
+ align:start position:0%
+talk about observation in this entire
+ 
+
+ align:start position:0%
+talk about observation in this entire
+class unless I make a very explicit
+
+ align:start position:0%
+class unless I make a very explicit
+ 
+
+ align:start position:0%
+class unless I make a very explicit
+exception to this we don't consider the
+
+ align:start position:0%
+exception to this we don't consider the
+ 
+
+ align:start position:0%
+exception to this we don't consider the
+fact that observing actually means that
+
+ align:start position:0%
+fact that observing actually means that
+ 
+
+ align:start position:0%
+fact that observing actually means that
+light has to be emitted from the clock
+
+ align:start position:0%
+light has to be emitted from the clock
+ 
+
+ align:start position:0%
+light has to be emitted from the clock
+and enters Bob's eye in order to for him
+
+ align:start position:0%
+and enters Bob's eye in order to for him
+ 
+
+ align:start position:0%
+and enters Bob's eye in order to for him
+to conclude that there was something
+
+ align:start position:0%
+to conclude that there was something
+ 
+
+ align:start position:0%
+to conclude that there was something
+happen happening uh the observation is
+
+ align:start position:0%
+happen happening uh the observation is
+ 
+
+ align:start position:0%
+happen happening uh the observation is
+like taking a an instantaneous
+
+ align:start position:0%
+like taking a an instantaneous
+ 
+
+ align:start position:0%
+like taking a an instantaneous
+picture okay so we have to keep this in
+
+ align:start position:0%
+picture okay so we have to keep this in
+ 
+
+ align:start position:0%
+picture okay so we have to keep this in
+mind but in this simple situation
+
+ align:start position:0%
+mind but in this simple situation
+ 
+
+ align:start position:0%
+mind but in this simple situation
+nothing is moving um you can hopefully
+
+ align:start position:0%
+nothing is moving um you can hopefully
+ 
+
+ align:start position:0%
+nothing is moving um you can hopefully
+agree that the um the times being read
+
+ align:start position:0%
+agree that the um the times being read
+ 
+
+ align:start position:0%
+agree that the um the times being read
+uh for Ellis and Bob on the left and the
+
+ align:start position:0%
+uh for Ellis and Bob on the left and the
+ 
+
+ align:start position:0%
+uh for Ellis and Bob on the left and the
+right clock are all the
+
+ align:start position:0%
+right clock are all the
+ 
+
+ align:start position:0%
+right clock are all the
+same now we go in the second situation
+
+ align:start position:0%
+same now we go in the second situation
+ 
+
+ align:start position:0%
+same now we go in the second situation
+where we use the same device but with a
+
+ align:start position:0%
+where we use the same device but with a
+ 
+
+ align:start position:0%
+where we use the same device but with a
+paintball so now Alis moves and Bob is
+
+ align:start position:0%
+paintball so now Alis moves and Bob is
+ 
+
+ align:start position:0%
+paintball so now Alis moves and Bob is
+observing her she moves with a relative
+
+ align:start position:0%
+observing her she moves with a relative
+ 
+
+ align:start position:0%
+observing her she moves with a relative
+velocity V and shoots off the pain balls
+
+ align:start position:0%
+velocity V and shoots off the pain balls
+ 
+
+ align:start position:0%
+velocity V and shoots off the pain balls
+with the velocity U the velocities will
+
+ align:start position:0%
+with the velocity U the velocities will
+ 
+
+ align:start position:0%
+with the velocity U the velocities will
+add meaning that you know they and those
+
+ align:start position:0%
+add meaning that you know they and those
+ 
+
+ align:start position:0%
+add meaning that you know they and those
+two clocks are initially synchronized so
+
+ align:start position:0%
+two clocks are initially synchronized so
+ 
+
+ align:start position:0%
+two clocks are initially synchronized so
+there is an small t a equal small TB
+
+ align:start position:0%
+there is an small t a equal small TB
+ 
+
+ align:start position:0%
+there is an small t a equal small TB
+equal zero once the clock hit you can
+
+ align:start position:0%
+equal zero once the clock hit you can
+ 
+
+ align:start position:0%
+equal zero once the clock hit you can
+hopefully agree that uh Ellis and Bob
+
+ align:start position:0%
+hopefully agree that uh Ellis and Bob
+ 
+
+ align:start position:0%
+hopefully agree that uh Ellis and Bob
+will agree that
+
+ align:start position:0%
+will agree that
+ 
+
+ align:start position:0%
+will agree that
+the times when the left clock and the
+
+ align:start position:0%
+the times when the left clock and the
+ 
+
+ align:start position:0%
+the times when the left clock and the
+right clock hit are the same right but
+
+ align:start position:0%
+right clock hit are the same right but
+ 
+
+ align:start position:0%
+right clock hit are the same right but
+now we want to enter the situation where
+
+ align:start position:0%
+now we want to enter the situation where
+ 
+
+ align:start position:0%
+now we want to enter the situation where
+we use light so we use a phaser in order
+
+ align:start position:0%
+we use light so we use a phaser in order
+ 
+
+ align:start position:0%
+we use light so we use a phaser in order
+to do the very thing so Einstein just
+
+ align:start position:0%
+to do the very thing so Einstein just
+ 
+
+ align:start position:0%
+to do the very thing so Einstein just
+postulated that the speed of light is
+
+ align:start position:0%
+postulated that the speed of light is
+ 
+
+ align:start position:0%
+postulated that the speed of light is
+constant is C and it's the same in all
+
+ align:start position:0%
+constant is C and it's the same in all
+ 
+
+ align:start position:0%
+constant is C and it's the same in all
+reference frames and it's independent of
+
+ align:start position:0%
+reference frames and it's independent of
+ 
+
+ align:start position:0%
+reference frames and it's independent of
+theid which means that we cannot add at
+
+ align:start position:0%
+theid which means that we cannot add at
+ 
+
+ align:start position:0%
+theid which means that we cannot add at
+the velocities anymore so the velocity
+
+ align:start position:0%
+the velocities anymore so the velocity
+ 
+
+ align:start position:0%
+the velocities anymore so the velocity
+um as seen by Alice of light is C the
+
+ align:start position:0%
+um as seen by Alice of light is C the
+ 
+
+ align:start position:0%
+um as seen by Alice of light is C the
+veloc vity of light of the same light by
+
+ align:start position:0%
+veloc vity of light of the same light by
+ 
+
+ align:start position:0%
+veloc vity of light of the same light by
+the moving Observer Bob is also C so
+
+ align:start position:0%
+the moving Observer Bob is also C so
+ 
+
+ align:start position:0%
+the moving Observer Bob is also C so
+here we can conclude that the times for
+
+ align:start position:0%
+here we can conclude that the times for
+ 
+
+ align:start position:0%
+here we can conclude that the times for
+Ellis for where the situation is
+
+ align:start position:0%
+Ellis for where the situation is
+ 
+
+ align:start position:0%
+Ellis for where the situation is
+stationary both clocks will hit at the
+
+ align:start position:0%
+stationary both clocks will hit at the
+ 
+
+ align:start position:0%
+stationary both clocks will hit at the
+very same time those two events clock
+
+ align:start position:0%
+very same time those two events clock
+ 
+
+ align:start position:0%
+very same time those two events clock
+one and clock two hit are hit are
+
+ align:start position:0%
+one and clock two hit are hit are
+ 
+
+ align:start position:0%
+one and clock two hit are hit are
+simultaneous why for Bobs this is
+
+ align:start position:0%
+simultaneous why for Bobs this is
+ 
+
+ align:start position:0%
+simultaneous why for Bobs this is
+clearly not the
+
+ align:start position:0%
+clearly not the
+ 
+
+ align:start position:0%
+clearly not the
+case you can see
+
+ align:start position:0%
+case you can see
+ 
+
+ align:start position:0%
+case you can see
+here you can see here that this
+
+ align:start position:0%
+here you can see here that this
+ 
+
+ align:start position:0%
+here you can see here that this
+this lagging clock is being hit first
+
+ align:start position:0%
+this lagging clock is being hit first
+ 
+
+ align:start position:0%
+this lagging clock is being hit first
+while the leading clock is hit a little
+
+ align:start position:0%
+while the leading clock is hit a little
+ 
+
+ align:start position:0%
+while the leading clock is hit a little
+a little while after so if Bob and Alice
+
+ align:start position:0%
+a little while after so if Bob and Alice
+ 
+
+ align:start position:0%
+a little while after so if Bob and Alice
+know meet and they discuss whether or
+
+ align:start position:0%
+know meet and they discuss whether or
+ 
+
+ align:start position:0%
+know meet and they discuss whether or
+not those two events happen
+
+ align:start position:0%
+not those two events happen
+ 
+
+ align:start position:0%
+not those two events happen
+simultaneously they will disagree for
+
+ align:start position:0%
+simultaneously they will disagree for
+ 
+
+ align:start position:0%
+simultaneously they will disagree for
+Alice those two clocks were hit
+
+ align:start position:0%
+Alice those two clocks were hit
+ 
+
+ align:start position:0%
+Alice those two clocks were hit
+simultaneously at the same time for her
+
+ align:start position:0%
+simultaneously at the same time for her
+ 
+
+ align:start position:0%
+simultaneously at the same time for her
+but for Bob um the first clock was hit
+
+ align:start position:0%
+but for Bob um the first clock was hit
+ 
+
+ align:start position:0%
+but for Bob um the first clock was hit
+first and the second the leading clock
+
+ align:start position:0%
+first and the second the leading clock
+ 
+
+ align:start position:0%
+first and the second the leading clock
+was hit second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right we can
+
+ align:start position:0%
+all right we can
+ 
+
+ align:start position:0%
+all right we can
+conclude that two events can be
+
+ align:start position:0%
+conclude that two events can be
+ 
+
+ align:start position:0%
+conclude that two events can be
+simultaneously to one Observer but not
+
+ align:start position:0%
+simultaneously to one Observer but not
+ 
+
+ align:start position:0%
+simultaneously to one Observer but not
+to another one this is rather confusing
+
+ align:start position:0%
+to another one this is rather confusing
+ 
+
+ align:start position:0%
+to another one this is rather confusing
+and we will see and use this fact a few
+
+ align:start position:0%
+and we will see and use this fact a few
+ 
+
+ align:start position:0%
+and we will see and use this fact a few
+times later on when we discuss uh the
+
+ align:start position:0%
+times later on when we discuss uh the
+ 
+
+ align:start position:0%
+times later on when we discuss uh the
+famous paradoxes of special
+
+ align:start position:0%
+famous paradoxes of special
+ 
+
+ align:start position:0%
+famous paradoxes of special
+relativity so let's look at this uh in a
+
+ align:start position:0%
+relativity so let's look at this uh in a
+ 
+
+ align:start position:0%
+relativity so let's look at this uh in a
+concept question to just make sure that
+
+ align:start position:0%
+concept question to just make sure that
+ 
+
+ align:start position:0%
+concept question to just make sure that
+we're all on the same page again we
+
+ align:start position:0%
+we're all on the same page again we
+ 
+
+ align:start position:0%
+we're all on the same page again we
+discussed here diagram three Alis moves
+
+ align:start position:0%
+discussed here diagram three Alis moves
+ 
+
+ align:start position:0%
+discussed here diagram three Alis moves
+to the right Bob is the Observer Alis
+
+ align:start position:0%
+to the right Bob is the Observer Alis
+ 
+
+ align:start position:0%
+to the right Bob is the Observer Alis
+fire surfacer at times equal zero um
+
+ align:start position:0%
+fire surfacer at times equal zero um
+ 
+
+ align:start position:0%
+fire surfacer at times equal zero um
+then the situation unfolds at time ta
+
+ align:start position:0%
+then the situation unfolds at time ta
+ 
+
+ align:start position:0%
+then the situation unfolds at time ta
+Capital ta Alice observes that both
+
+ align:start position:0%
+Capital ta Alice observes that both
+ 
+
+ align:start position:0%
+Capital ta Alice observes that both
+clocks are hit at time tb1 Bob observes
+
+ align:start position:0%
+clocks are hit at time tb1 Bob observes
+ 
+
+ align:start position:0%
+clocks are hit at time tb1 Bob observes
+that the left clock is hit at time tb2
+
+ align:start position:0%
+that the left clock is hit at time tb2
+ 
+
+ align:start position:0%
+that the left clock is hit at time tb2
+it's the right clock which of the
+
+ align:start position:0%
+it's the right clock which of the
+ 
+
+ align:start position:0%
+it's the right clock which of the
+following answers is correctly so here
+
+ align:start position:0%
+following answers is correctly so here
+ 
+
+ align:start position:0%
+following answers is correctly so here
+you want to stop the video and think
+
+ align:start position:0%
+you want to stop the video and think
+ 
+
+ align:start position:0%
+you want to stop the video and think
+about which of the ANS this is correct
+
+ align:start position:0%
+about which of the ANS this is correct
+ 
+
+ align:start position:0%
+about which of the ANS this is correct
+so moving forward the correct answer is
+
+ align:start position:0%
+so moving forward the correct answer is
+ 
+
+ align:start position:0%
+so moving forward the correct answer is
+number three where tb1 is smaller than
+
+ align:start position:0%
+number three where tb1 is smaller than
+ 
+
+ align:start position:0%
+number three where tb1 is smaller than
+ta is smaller than TV2 so again the
+
+ align:start position:0%
+ta is smaller than TV2 so again the
+ 
+
+ align:start position:0%
+ta is smaller than TV2 so again the
+leading clock lags the leading clock has
+
+ align:start position:0%
+leading clock lags the leading clock has
+ 
+
+ align:start position:0%
+leading clock lags the leading clock has
+a larger TB which means for that clock
+
+ align:start position:0%
+a larger TB which means for that clock
+ 
+
+ align:start position:0%
+a larger TB which means for that clock
+ticks a little
+
+ align:start position:0%
+ticks a little
+ 
+
+ align:start position:0%
+ticks a little
+slower and again the two events that can
+
+ align:start position:0%
+slower and again the two events that can
+ 
+
+ align:start position:0%
+slower and again the two events that can
+be simultaneously to one Observer Alis
+
+ align:start position:0%
+be simultaneously to one Observer Alis
+ 
+
+ align:start position:0%
+be simultaneously to one Observer Alis
+in this case but not to another Bob
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right let's look at clocks a little
+
+ align:start position:0%
+all right let's look at clocks a little
+ 
+
+ align:start position:0%
+all right let's look at clocks a little
+bit more and design an optical clock so
+
+ align:start position:0%
+bit more and design an optical clock so
+ 
+
+ align:start position:0%
+bit more and design an optical clock so
+here's the situation is as follows we
+
+ align:start position:0%
+here's the situation is as follows we
+ 
+
+ align:start position:0%
+here's the situation is as follows we
+have two mirrors in which we inject
+
+ align:start position:0%
+have two mirrors in which we inject
+ 
+
+ align:start position:0%
+have two mirrors in which we inject
+light the light travels up and travels
+
+ align:start position:0%
+light the light travels up and travels
+ 
+
+ align:start position:0%
+light the light travels up and travels
+down and that's what we call one clock
+
+ align:start position:0%
+down and that's what we call one clock
+ 
+
+ align:start position:0%
+down and that's what we call one clock
+tick of this Optical clock the length
+
+ align:start position:0%
+tick of this Optical clock the length
+ 
+
+ align:start position:0%
+tick of this Optical clock the length
+between the two mirrors is L so for Alis
+
+ align:start position:0%
+between the two mirrors is L so for Alis
+ 
+
+ align:start position:0%
+between the two mirrors is L so for Alis
+she has this clock in her hand and she
+
+ align:start position:0%
+she has this clock in her hand and she
+ 
+
+ align:start position:0%
+she has this clock in her hand and she
+can happily observe you know the ticking
+
+ align:start position:0%
+can happily observe you know the ticking
+ 
+
+ align:start position:0%
+can happily observe you know the ticking
+of her clock
+
+ align:start position:0%
+of her clock
+ 
+
+ align:start position:0%
+of her clock
+okay Bob observes Ellis clock and
+
+ align:start position:0%
+okay Bob observes Ellis clock and
+ 
+
+ align:start position:0%
+okay Bob observes Ellis clock and
+Compares it with his own identical clock
+
+ align:start position:0%
+Compares it with his own identical clock
+ 
+
+ align:start position:0%
+Compares it with his own identical clock
+um there's a relative speed between
+
+ align:start position:0%
+um there's a relative speed between
+ 
+
+ align:start position:0%
+um there's a relative speed between
+Ellis and Bob and that that's V in X
+
+ align:start position:0%
+Ellis and Bob and that that's V in X
+ 
+
+ align:start position:0%
+Ellis and Bob and that that's V in X
+Direction now the task for you is to
+
+ align:start position:0%
+Direction now the task for you is to
+ 
+
+ align:start position:0%
+Direction now the task for you is to
+relate the clock ticks which are
+
+ align:start position:0%
+relate the clock ticks which are
+ 
+
+ align:start position:0%
+relate the clock ticks which are
+observed by Bob and the ones which are
+
+ align:start position:0%
+observed by Bob and the ones which are
+ 
+
+ align:start position:0%
+observed by Bob and the ones which are
+observed by Ellis in Ellis's
+
+ align:start position:0%
+observed by Ellis in Ellis's
+ 
+
+ align:start position:0%
+observed by Ellis in Ellis's
+clock so again stop the video and work
+
+ align:start position:0%
+clock so again stop the video and work
+ 
+
+ align:start position:0%
+clock so again stop the video and work
+out the algebra the answer is going to
+
+ align:start position:0%
+out the algebra the answer is going to
+ 
+
+ align:start position:0%
+out the algebra the answer is going to
+be again surprising
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we do this
+
+ align:start position:0%
+so if we do this
+ 
+
+ align:start position:0%
+so if we do this
+now we um find this picture so we
+
+ align:start position:0%
+now we um find this picture so we
+ 
+
+ align:start position:0%
+now we um find this picture so we
+calculate how long does the clock tick
+
+ align:start position:0%
+calculate how long does the clock tick
+ 
+
+ align:start position:0%
+calculate how long does the clock tick
+take the light has to travel 2 L with a
+
+ align:start position:0%
+take the light has to travel 2 L with a
+ 
+
+ align:start position:0%
+take the light has to travel 2 L with a
+velocity C so the clock tick is 2 L over
+
+ align:start position:0%
+velocity C so the clock tick is 2 L over
+ 
+
+ align:start position:0%
+velocity C so the clock tick is 2 L over
+C the length can be expressed as C * T
+
+ align:start position:0%
+C the length can be expressed as C * T
+ 
+
+ align:start position:0%
+C the length can be expressed as C * T
+Delta ta/ 2 for Bobs the situation is a
+
+ align:start position:0%
+Delta ta/ 2 for Bobs the situation is a
+ 
+
+ align:start position:0%
+Delta ta/ 2 for Bobs the situation is a
+little bit more complicated and we have
+
+ align:start position:0%
+little bit more complicated and we have
+ 
+
+ align:start position:0%
+little bit more complicated and we have
+to use Pythagoras in order to calculate
+
+ align:start position:0%
+to use Pythagoras in order to calculate
+ 
+
+ align:start position:0%
+to use Pythagoras in order to calculate
+calculate the length so we Define that
+
+ align:start position:0%
+calculate the length so we Define that
+ 
+
+ align:start position:0%
+calculate the length so we Define that
+the length the light has to travel D
+
+ align:start position:0%
+the length the light has to travel D
+ 
+
+ align:start position:0%
+the length the light has to travel D
+then the Delta TB as Bob observes this
+
+ align:start position:0%
+then the Delta TB as Bob observes this
+ 
+
+ align:start position:0%
+then the Delta TB as Bob observes this
+is 2 * D over C again for Bob the light
+
+ align:start position:0%
+is 2 * D over C again for Bob the light
+ 
+
+ align:start position:0%
+is 2 * D over C again for Bob the light
+travels with the speed of light Einstein
+
+ align:start position:0%
+travels with the speed of light Einstein
+ 
+
+ align:start position:0%
+travels with the speed of light Einstein
+just postulated as and then we find the
+
+ align:start position:0%
+just postulated as and then we find the
+ 
+
+ align:start position:0%
+just postulated as and then we find the
+length expressed to the the time as C *
+
+ align:start position:0%
+length expressed to the the time as C *
+ 
+
+ align:start position:0%
+length expressed to the the time as C *
+Delta TB over
+
+ align:start position:0%
+Delta TB over
+ 
+
+ align:start position:0%
+Delta TB over
+2 the length in X is simply given by the
+
+ align:start position:0%
+2 the length in X is simply given by the
+ 
+
+ align:start position:0%
+2 the length in X is simply given by the
+relative velocity V times the time it
+
+ align:start position:0%
+relative velocity V times the time it
+ 
+
+ align:start position:0%
+relative velocity V times the time it
+takes for the clock to tick V times
+
+ align:start position:0%
+takes for the clock to tick V times
+ 
+
+ align:start position:0%
+takes for the clock to tick V times
+Delta TB so then we can express d sare d
+
+ align:start position:0%
+Delta TB so then we can express d sare d
+ 
+
+ align:start position:0%
+Delta TB so then we can express d sare d
+sare we l s + x² over 4 and use those
+
+ align:start position:0%
+sare we l s + x² over 4 and use those
+ 
+
+ align:start position:0%
+sare we l s + x² over 4 and use those
+expressions here so we just use this for
+
+ align:start position:0%
+expressions here so we just use this for
+ 
+
+ align:start position:0%
+expressions here so we just use this for
+L this for D and this for x and we find
+
+ align:start position:0%
+L this for D and this for x and we find
+ 
+
+ align:start position:0%
+L this for D and this for x and we find
+this expression here all right and then
+
+ align:start position:0%
+this expression here all right and then
+ 
+
+ align:start position:0%
+this expression here all right and then
+we solve this for Delta
+
+ align:start position:0%
+we solve this for Delta
+ 
+
+ align:start position:0%
+we solve this for Delta
+TB and we find the relation between
+
+ align:start position:0%
+TB and we find the relation between
+ 
+
+ align:start position:0%
+TB and we find the relation between
+Delta TB and Delta ta and can find that
+
+ align:start position:0%
+Delta TB and Delta ta and can find that
+ 
+
+ align:start position:0%
+Delta TB and Delta ta and can find that
+it's one over < TK 1 minus V s/ c² which
+
+ align:start position:0%
+it's one over < TK 1 minus V s/ c² which
+ 
+
+ align:start position:0%
+it's one over < TK 1 minus V s/ c² which
+is the low Factor so we just with a
+
+ align:start position:0%
+is the low Factor so we just with a
+ 
+
+ align:start position:0%
+is the low Factor so we just with a
+simple clock and Einstein's postulate
+
+ align:start position:0%
+simple clock and Einstein's postulate
+ 
+
+ align:start position:0%
+simple clock and Einstein's postulate
+derived um time dilation you find that
+
+ align:start position:0%
+derived um time dilation you find that
+ 
+
+ align:start position:0%
+derived um time dilation you find that
+for uh Bob Ellis's moving clock moves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slower great so again gamma is one over
+
+ align:start position:0%
+slower great so again gamma is one over
+ 
+
+ align:start position:0%
+slower great so again gamma is one over
+um square root 1 minus v s over C sare
+
+ align:start position:0%
+um square root 1 minus v s over C sare
+ 
+
+ align:start position:0%
+um square root 1 minus v s over C sare
+we often use in short beta as a
+
+ align:start position:0%
+we often use in short beta as a
+ 
+
+ align:start position:0%
+we often use in short beta as a
+relativistic velocity it's unitless and
+
+ align:start position:0%
+relativistic velocity it's unitless and
+ 
+
+ align:start position:0%
+relativistic velocity it's unitless and
+defined as v/ C
+
+ align:start position:0%
+defined as v/ C
+ 
+
+ align:start position:0%
+defined as v/ C
+gamma is always greater or equal one and
+
+ align:start position:0%
+gamma is always greater or equal one and
+ 
+
+ align:start position:0%
+gamma is always greater or equal one and
+it's mostly one for everything we
+
+ align:start position:0%
+it's mostly one for everything we
+ 
+
+ align:start position:0%
+it's mostly one for everything we
+observe in nature so in in one of the p
+
+ align:start position:0%
+observe in nature so in in one of the p
+ 
+
+ align:start position:0%
+observe in nature so in in one of the p
+sets and also here I invite you to
+
+ align:start position:0%
+sets and also here I invite you to
+ 
+
+ align:start position:0%
+sets and also here I invite you to
+Simply calculate values for for gamma
+
+ align:start position:0%
+Simply calculate values for for gamma
+ 
+
+ align:start position:0%
+Simply calculate values for for gamma
+for things you might think are fast
+
+ align:start position:0%
+for things you might think are fast
+ 
+
+ align:start position:0%
+for things you might think are fast
+moving objects so we start with the
+
+ align:start position:0%
+moving objects so we start with the
+ 
+
+ align:start position:0%
+moving objects so we start with the
+fighter jet we look at the International
+
+ align:start position:0%
+fighter jet we look at the International
+ 
+
+ align:start position:0%
+fighter jet we look at the International
+Space Station the Earth around the Sun
+
+ align:start position:0%
+Space Station the Earth around the Sun
+ 
+
+ align:start position:0%
+Space Station the Earth around the Sun
+the particle which almost moves with the
+
+ align:start position:0%
+the particle which almost moves with the
+ 
+
+ align:start position:0%
+the particle which almost moves with the
+speed of light and the proton at the
+
+ align:start position:0%
+speed of light and the proton at the
+ 
+
+ align:start position:0%
+speed of light and the proton at the
+large hatron collider which is only
+
+ align:start position:0%
+large hatron collider which is only
+ 
+
+ align:start position:0%
+large hatron collider which is only
+three 3 m/ second slower than the speed
+
+ align:start position:0%
+three 3 m/ second slower than the speed
+ 
+
+ align:start position:0%
+three 3 m/ second slower than the speed
+of so again stop the video and work out
+
+ align:start position:0%
+of so again stop the video and work out
+ 
+
+ align:start position:0%
+of so again stop the video and work out
+work out those numbers you will need a
+
+ align:start position:0%
+work out those numbers you will need a
+ 
+
+ align:start position:0%
+work out those numbers you will need a
+calculator for
+
+ align:start position:0%
+calculator for
+ 
+
+ align:start position:0%
+calculator for
+that so if I do this I find for this
+
+ align:start position:0%
+that so if I do this I find for this
+ 
+
+ align:start position:0%
+that so if I do this I find for this
+very very fast F15 fighter jet which
+
+ align:start position:0%
+very very fast F15 fighter jet which
+ 
+
+ align:start position:0%
+very very fast F15 fighter jet which
+moves with 3 2,680 kilom per hour that
+
+ align:start position:0%
+moves with 3 2,680 kilom per hour that
+ 
+
+ align:start position:0%
+moves with 3 2,680 kilom per hour that
+the number for gamma is
+
+ align:start position:0%
+the number for gamma is
+ 
+
+ align:start position:0%
+the number for gamma is
+1.0
+
+ align:start position:0%
+1.0
+ 
+
+ align:start position:0%
+1.0
+z0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z0 which is 11 Z three so we find this
+
+ align:start position:0%
+z0 which is 11 Z three so we find this
+ 
+
+ align:start position:0%
+z0 which is 11 Z three so we find this
+very very uh small number or number
+
+ align:start position:0%
+very very uh small number or number
+ 
+
+ align:start position:0%
+very very uh small number or number
+which is very very close to one
+
+ align:start position:0%
+which is very very close to one
+ 
+
+ align:start position:0%
+which is very very close to one
+situation for the International Space
+
+ align:start position:0%
+situation for the International Space
+ 
+
+ align:start position:0%
+situation for the International Space
+Station changes a bit only 9 zeros for
+
+ align:start position:0%
+Station changes a bit only 9 zeros for
+ 
+
+ align:start position:0%
+Station changes a bit only 9 zeros for
+the Earth around the Sun the Earth is
+
+ align:start position:0%
+the Earth around the Sun the Earth is
+ 
+
+ align:start position:0%
+the Earth around the Sun the Earth is
+really really fast travels a long
+
+ align:start position:0%
+really really fast travels a long
+ 
+
+ align:start position:0%
+really really fast travels a long
+distance every year you travel Once
+
+ align:start position:0%
+distance every year you travel Once
+ 
+
+ align:start position:0%
+distance every year you travel Once
+Around the Sun and you know every year
+
+ align:start position:0%
+Around the Sun and you know every year
+ 
+
+ align:start position:0%
+Around the Sun and you know every year
+you get older you have a lot of mileage
+
+ align:start position:0%
+you get older you have a lot of mileage
+ 
+
+ align:start position:0%
+you get older you have a lot of mileage
+on your back here you have eight Zer
+
+ align:start position:0%
+on your back here you have eight Zer
+ 
+
+ align:start position:0%
+on your back here you have eight Zer
+particle which moves with 0.9 times the
+
+ align:start position:0%
+particle which moves with 0.9 times the
+ 
+
+ align:start position:0%
+particle which moves with 0.9 times the
+speed of light here here the gamma
+
+ align:start position:0%
+speed of light here here the gamma
+ 
+
+ align:start position:0%
+speed of light here here the gamma
+factor is very different from one it's
+
+ align:start position:0%
+factor is very different from one it's
+ 
+
+ align:start position:0%
+factor is very different from one it's
+2.3 and the protons we have at the LHC
+
+ align:start position:0%
+2.3 and the protons we have at the LHC
+ 
+
+ align:start position:0%
+2.3 and the protons we have at the LHC
+they have a gamma factor of 7,000 so you
+
+ align:start position:0%
+they have a gamma factor of 7,000 so you
+ 
+
+ align:start position:0%
+they have a gamma factor of 7,000 so you
+see once you get close to the speed of
+
+ align:start position:0%
+see once you get close to the speed of
+ 
+
+ align:start position:0%
+see once you get close to the speed of
+light the gamma Factor approaches large
+
+ align:start position:0%
+light the gamma Factor approaches large
+ 
+
+ align:start position:0%
+light the gamma Factor approaches large
+numbers and that's where our relistic
+
+ align:start position:0%
+numbers and that's where our relistic
+ 
+
+ align:start position:0%
+numbers and that's where our relistic
+effects really are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+visible e
\ No newline at end of file
diff --git a/5eKqzY-dyxQ.txt b/5eKqzY-dyxQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4534dfdfdc2d5768a80b47b41ce2aa3b16c172ab
--- /dev/null
+++ b/5eKqzY-dyxQ.txt
@@ -0,0 +1,1371 @@
+align:start position:0%
+ 
+welcome to our week six it's time to
+
+ align:start position:0%
+welcome to our week six it's time to
+ 
+
+ align:start position:0%
+welcome to our week six it's time to
+negotiate the next generation social
+
+ align:start position:0%
+negotiate the next generation social
+ 
+
+ align:start position:0%
+negotiate the next generation social
+contract so I'm looking forward to
+
+ align:start position:0%
+contract so I'm looking forward to
+ 
+
+ align:start position:0%
+contract so I'm looking forward to
+really exciting and fruitful week all
+
+ align:start position:0%
+really exciting and fruitful week all
+ 
+
+ align:start position:0%
+really exciting and fruitful week all
+the instructions are now on the platform
+
+ align:start position:0%
+the instructions are now on the platform
+ 
+
+ align:start position:0%
+the instructions are now on the platform
+on week six so all you need to do is to
+
+ align:start position:0%
+on week six so all you need to do is to
+ 
+
+ align:start position:0%
+on week six so all you need to do is to
+go to it you'll see instructions for how
+
+ align:start position:0%
+go to it you'll see instructions for how
+ 
+
+ align:start position:0%
+go to it you'll see instructions for how
+to find your team your role assignments
+
+ align:start position:0%
+to find your team your role assignments
+ 
+
+ align:start position:0%
+to find your team your role assignments
+then you go through and you'll complete
+
+ align:start position:0%
+then you go through and you'll complete
+ 
+
+ align:start position:0%
+then you go through and you'll complete
+the preparation survey you'll negotiate
+
+ align:start position:0%
+the preparation survey you'll negotiate
+ 
+
+ align:start position:0%
+the preparation survey you'll negotiate
+online with your counterparts hopefully
+
+ align:start position:0%
+online with your counterparts hopefully
+ 
+
+ align:start position:0%
+online with your counterparts hopefully
+in the same time zone where you are
+
+ align:start position:0%
+in the same time zone where you are
+ 
+
+ align:start position:0%
+in the same time zone where you are
+located and then as you complete the
+
+ align:start position:0%
+located and then as you complete the
+ 
+
+ align:start position:0%
+located and then as you complete the
+survey form at the end to record your
+
+ align:start position:0%
+survey form at the end to record your
+ 
+
+ align:start position:0%
+survey form at the end to record your
+settlements those of you who are taking
+
+ align:start position:0%
+settlements those of you who are taking
+ 
+
+ align:start position:0%
+settlements those of you who are taking
+the course for certification and for
+
+ align:start position:0%
+the course for certification and for
+ 
+
+ align:start position:0%
+the course for certification and for
+grade will get some extra credit as
+
+ align:start position:0%
+grade will get some extra credit as
+ 
+
+ align:start position:0%
+grade will get some extra credit as
+described on the platform so we're
+
+ align:start position:0%
+described on the platform so we're
+ 
+
+ align:start position:0%
+described on the platform so we're
+excited about it we're looking forward
+
+ align:start position:0%
+excited about it we're looking forward
+ 
+
+ align:start position:0%
+excited about it we're looking forward
+to hearing what you have in mind for
+
+ align:start position:0%
+to hearing what you have in mind for
+ 
+
+ align:start position:0%
+to hearing what you have in mind for
+shaping the future of work as a bonus we
+
+ align:start position:0%
+shaping the future of work as a bonus we
+ 
+
+ align:start position:0%
+shaping the future of work as a bonus we
+will provide a facilitator one of our
+
+ align:start position:0%
+will provide a facilitator one of our
+ 
+
+ align:start position:0%
+will provide a facilitator one of our
+MBA students what we call our community
+
+ align:start position:0%
+MBA students what we call our community
+ 
+
+ align:start position:0%
+MBA students what we call our community
+TAS will be assigned to your group what
+
+ align:start position:0%
+TAS will be assigned to your group what
+ 
+
+ align:start position:0%
+TAS will be assigned to your group what
+is a facilitator a facilitator is just
+
+ align:start position:0%
+is a facilitator a facilitator is just
+ 
+
+ align:start position:0%
+is a facilitator a facilitator is just
+what that term sounds like it's a
+
+ align:start position:0%
+what that term sounds like it's a
+ 
+
+ align:start position:0%
+what that term sounds like it's a
+neutral person it's a person who helps
+
+ align:start position:0%
+neutral person it's a person who helps
+ 
+
+ align:start position:0%
+neutral person it's a person who helps
+move you through the process without
+
+ align:start position:0%
+move you through the process without
+ 
+
+ align:start position:0%
+move you through the process without
+influencing your proposals or the
+
+ align:start position:0%
+influencing your proposals or the
+ 
+
+ align:start position:0%
+influencing your proposals or the
+particular terms of the agreement that
+
+ align:start position:0%
+particular terms of the agreement that
+ 
+
+ align:start position:0%
+particular terms of the agreement that
+you reach so this individual will help
+
+ align:start position:0%
+you reach so this individual will help
+ 
+
+ align:start position:0%
+you reach so this individual will help
+you in scheduling times or answering
+
+ align:start position:0%
+you in scheduling times or answering
+ 
+
+ align:start position:0%
+you in scheduling times or answering
+questions and be a liaison back to the
+
+ align:start position:0%
+questions and be a liaison back to the
+ 
+
+ align:start position:0%
+questions and be a liaison back to the
+rest of us as needed so use the
+
+ align:start position:0%
+rest of us as needed so use the
+ 
+
+ align:start position:0%
+rest of us as needed so use the
+facilitator at your choice and we'll see
+
+ align:start position:0%
+facilitator at your choice and we'll see
+ 
+
+ align:start position:0%
+facilitator at your choice and we'll see
+how all of this works the deadline is
+
+ align:start position:0%
+how all of this works the deadline is
+ 
+
+ align:start position:0%
+how all of this works the deadline is
+Thursday at the end of the day UTC time
+
+ align:start position:0%
+Thursday at the end of the day UTC time
+ 
+
+ align:start position:0%
+Thursday at the end of the day UTC time
+1159 p.m. so it's important that you and
+
+ align:start position:0%
+1159 p.m. so it's important that you and
+ 
+
+ align:start position:0%
+1159 p.m. so it's important that you and
+your teammates work on an agreement when
+
+ align:start position:0%
+your teammates work on an agreement when
+ 
+
+ align:start position:0%
+your teammates work on an agreement when
+to negotiate engage in the course
+
+ align:start position:0%
+to negotiate engage in the course
+ 
+
+ align:start position:0%
+to negotiate engage in the course
+discussion has instructed and we'll see
+
+ align:start position:0%
+discussion has instructed and we'll see
+ 
+
+ align:start position:0%
+discussion has instructed and we'll see
+what we learn from this experience next
+
+ align:start position:0%
+what we learn from this experience next
+ 
+
+ align:start position:0%
+what we learn from this experience next
+week is the grand finale of this course
+
+ align:start position:0%
+week is the grand finale of this course
+ 
+
+ align:start position:0%
+week is the grand finale of this course
+and we have a special event it's called
+
+ align:start position:0%
+and we have a special event it's called
+ 
+
+ align:start position:0%
+and we have a special event it's called
+a live video event or video chat
+
+ align:start position:0%
+a live video event or video chat
+ 
+
+ align:start position:0%
+a live video event or video chat
+whatever one wants to call it on Tuesday
+
+ align:start position:0%
+whatever one wants to call it on Tuesday
+ 
+
+ align:start position:0%
+whatever one wants to call it on Tuesday
+May tenth
+
+ align:start position:0%
+May tenth
+ 
+
+ align:start position:0%
+May tenth
+at UTC time 8pm we will have an hour and
+
+ align:start position:0%
+at UTC time 8pm we will have an hour and
+ 
+
+ align:start position:0%
+at UTC time 8pm we will have an hour and
+a half live interaction with all of you
+
+ align:start position:0%
+a half live interaction with all of you
+ 
+
+ align:start position:0%
+a half live interaction with all of you
+where we will summarize what we have
+
+ align:start position:0%
+where we will summarize what we have
+ 
+
+ align:start position:0%
+where we will summarize what we have
+taken away as the key lessons from this
+
+ align:start position:0%
+taken away as the key lessons from this
+ 
+
+ align:start position:0%
+taken away as the key lessons from this
+course and we will incorporate the
+
+ align:start position:0%
+course and we will incorporate the
+ 
+
+ align:start position:0%
+course and we will incorporate the
+materials not only from the course but
+
+ align:start position:0%
+materials not only from the course but
+ 
+
+ align:start position:0%
+materials not only from the course but
+also your materials from the polls that
+
+ align:start position:0%
+also your materials from the polls that
+ 
+
+ align:start position:0%
+also your materials from the polls that
+you completed surveys the assignments
+
+ align:start position:0%
+you completed surveys the assignments
+ 
+
+ align:start position:0%
+you completed surveys the assignments
+that you did the discussions that you've
+
+ align:start position:0%
+that you did the discussions that you've
+ 
+
+ align:start position:0%
+that you did the discussions that you've
+had on the forum all of this will come
+
+ align:start position:0%
+had on the forum all of this will come
+ 
+
+ align:start position:0%
+had on the forum all of this will come
+together and with your engagement
+
+ align:start position:0%
+together and with your engagement
+ 
+
+ align:start position:0%
+together and with your engagement
+directly by passing on questions to us
+
+ align:start position:0%
+directly by passing on questions to us
+ 
+
+ align:start position:0%
+directly by passing on questions to us
+or comments as we go along for an hour
+
+ align:start position:0%
+or comments as we go along for an hour
+ 
+
+ align:start position:0%
+or comments as we go along for an hour
+and a half we will see what did we learn
+
+ align:start position:0%
+and a half we will see what did we learn
+ 
+
+ align:start position:0%
+and a half we will see what did we learn
+from this where are we going and how can
+
+ align:start position:0%
+from this where are we going and how can
+ 
+
+ align:start position:0%
+from this where are we going and how can
+we use all of this material effectively
+
+ align:start position:0%
+we use all of this material effectively
+ 
+
+ align:start position:0%
+we use all of this material effectively
+not only for yourselves but for external
+
+ align:start position:0%
+not only for yourselves but for external
+ 
+
+ align:start position:0%
+not only for yourselves but for external
+audiences who are also interested in
+
+ align:start position:0%
+audiences who are also interested in
+ 
+
+ align:start position:0%
+audiences who are also interested in
+shaping the future of work so please put
+
+ align:start position:0%
+shaping the future of work so please put
+ 
+
+ align:start position:0%
+shaping the future of work so please put
+this on your calendar be ready with
+
+ align:start position:0%
+this on your calendar be ready with
+ 
+
+ align:start position:0%
+this on your calendar be ready with
+questions or comments will send you
+
+ align:start position:0%
+questions or comments will send you
+ 
+
+ align:start position:0%
+questions or comments will send you
+information next Monday the day before
+
+ align:start position:0%
+information next Monday the day before
+ 
+
+ align:start position:0%
+information next Monday the day before
+this event on how to tune in how to wear
+
+ align:start position:0%
+this event on how to tune in how to wear
+ 
+
+ align:start position:0%
+this event on how to tune in how to wear
+to link in for this interesting I hope
+
+ align:start position:0%
+to link in for this interesting I hope
+ 
+
+ align:start position:0%
+to link in for this interesting I hope
+interesting and informative wrap up for
+
+ align:start position:0%
+interesting and informative wrap up for
+ 
+
+ align:start position:0%
+interesting and informative wrap up for
+the course let me make a special request
+
+ align:start position:0%
+the course let me make a special request
+ 
+
+ align:start position:0%
+the course let me make a special request
+of you to make sure that we bring your
+
+ align:start position:0%
+of you to make sure that we bring your
+ 
+
+ align:start position:0%
+of you to make sure that we bring your
+voices into this process one segment of
+
+ align:start position:0%
+voices into this process one segment of
+ 
+
+ align:start position:0%
+voices into this process one segment of
+the summary will ask the question what
+
+ align:start position:0%
+the summary will ask the question what
+ 
+
+ align:start position:0%
+the summary will ask the question what
+is our key message to the future leaders
+
+ align:start position:0%
+is our key message to the future leaders
+ 
+
+ align:start position:0%
+is our key message to the future leaders
+who will shape the future of work
+
+ align:start position:0%
+who will shape the future of work
+ 
+
+ align:start position:0%
+who will shape the future of work
+business leaders and HR professionals
+
+ align:start position:0%
+business leaders and HR professionals
+ 
+
+ align:start position:0%
+business leaders and HR professionals
+labor leaders and their advocates
+
+ align:start position:0%
+labor leaders and their advocates
+ 
+
+ align:start position:0%
+labor leaders and their advocates
+government policymakers and those of us
+
+ align:start position:0%
+government policymakers and those of us
+ 
+
+ align:start position:0%
+government policymakers and those of us
+in the education field so make sure that
+
+ align:start position:0%
+in the education field so make sure that
+ 
+
+ align:start position:0%
+in the education field so make sure that
+on the discussion board this week where
+
+ align:start position:0%
+on the discussion board this week where
+ 
+
+ align:start position:0%
+on the discussion board this week where
+we will post questions or a place where
+
+ align:start position:0%
+we will post questions or a place where
+ 
+
+ align:start position:0%
+we will post questions or a place where
+you can add your thoughts to each of
+
+ align:start position:0%
+you can add your thoughts to each of
+ 
+
+ align:start position:0%
+you can add your thoughts to each of
+these stakeholders that you bring your
+
+ align:start position:0%
+these stakeholders that you bring your
+ 
+
+ align:start position:0%
+these stakeholders that you bring your
+voice into this process and will
+
+ align:start position:0%
+voice into this process and will
+ 
+
+ align:start position:0%
+voice into this process and will
+incorporate that into the discussion
+
+ align:start position:0%
+incorporate that into the discussion
+ 
+
+ align:start position:0%
+incorporate that into the discussion
+next week tuesday so i look forward to
+
+ align:start position:0%
+next week tuesday so i look forward to
+ 
+
+ align:start position:0%
+next week tuesday so i look forward to
+seeing what you have on your mind and
+
+ align:start position:0%
+seeing what you have on your mind and
+ 
+
+ align:start position:0%
+seeing what you have on your mind and
+what message you want to deliver to
+
+ align:start position:0%
+what message you want to deliver to
+ 
+
+ align:start position:0%
+what message you want to deliver to
+these groups who will help to shape the
+
+ align:start position:0%
+these groups who will help to shape the
+ 
+
+ align:start position:0%
+these groups who will help to shape the
+future of work last week we had a very
+
+ align:start position:0%
+future of work last week we had a very
+ 
+
+ align:start position:0%
+future of work last week we had a very
+very rich and engaging discussion and in
+
+ align:start position:0%
+very rich and engaging discussion and in
+ 
+
+ align:start position:0%
+very rich and engaging discussion and in
+fact throughout this course many of you
+
+ align:start position:0%
+fact throughout this course many of you
+ 
+
+ align:start position:0%
+fact throughout this course many of you
+commented on the subject for last week
+
+ align:start position:0%
+commented on the subject for last week
+ 
+
+ align:start position:0%
+commented on the subject for last week
+and that is what's the future of labor
+
+ align:start position:0%
+and that is what's the future of labor
+ 
+
+ align:start position:0%
+and that is what's the future of labor
+is there still a need for labor
+
+ align:start position:0%
+is there still a need for labor
+ 
+
+ align:start position:0%
+is there still a need for labor
+organizations for unions as we've called
+
+ align:start position:0%
+organizations for unions as we've called
+ 
+
+ align:start position:0%
+organizations for unions as we've called
+them over many years and in fact over
+
+ align:start position:0%
+them over many years and in fact over
+ 
+
+ align:start position:0%
+them over many years and in fact over
+several centuries is a new form of
+
+ align:start position:0%
+several centuries is a new form of
+ 
+
+ align:start position:0%
+several centuries is a new form of
+representation are there new ways and
+
+ align:start position:0%
+representation are there new ways and
+ 
+
+ align:start position:0%
+representation are there new ways and
+which workers can get a voice at work
+
+ align:start position:0%
+which workers can get a voice at work
+ 
+
+ align:start position:0%
+which workers can get a voice at work
+and assert their interests and work with
+
+ align:start position:0%
+and assert their interests and work with
+ 
+
+ align:start position:0%
+and assert their interests and work with
+their employers to shape the future of
+
+ align:start position:0%
+their employers to shape the future of
+ 
+
+ align:start position:0%
+their employers to shape the future of
+work most of you do see the need for
+
+ align:start position:0%
+work most of you do see the need for
+ 
+
+ align:start position:0%
+work most of you do see the need for
+some form of labor representation maybe
+
+ align:start position:0%
+some form of labor representation maybe
+ 
+
+ align:start position:0%
+some form of labor representation maybe
+not for everyone but for the people who
+
+ align:start position:0%
+not for everyone but for the people who
+ 
+
+ align:start position:0%
+not for everyone but for the people who
+really want to have a collective voice
+
+ align:start position:0%
+really want to have a collective voice
+ 
+
+ align:start position:0%
+really want to have a collective voice
+at the workplace but you also see the
+
+ align:start position:0%
+at the workplace but you also see the
+ 
+
+ align:start position:0%
+at the workplace but you also see the
+need for change and for innovation to
+
+ align:start position:0%
+need for change and for innovation to
+ 
+
+ align:start position:0%
+need for change and for innovation to
+build on the strengths of what unions
+
+ align:start position:0%
+build on the strengths of what unions
+ 
+
+ align:start position:0%
+build on the strengths of what unions
+have done historically for so many
+
+ align:start position:0%
+have done historically for so many
+ 
+
+ align:start position:0%
+have done historically for so many
+workers around the world you talked
+
+ align:start position:0%
+workers around the world you talked
+ 
+
+ align:start position:0%
+workers around the world you talked
+about the need to expand more
+
+ align:start position:0%
+about the need to expand more
+ 
+
+ align:start position:0%
+about the need to expand more
+labor-management partnerships like the
+
+ align:start position:0%
+labor-management partnerships like the
+ 
+
+ align:start position:0%
+labor-management partnerships like the
+one out at Kaiser Permanente that we
+
+ align:start position:0%
+one out at Kaiser Permanente that we
+ 
+
+ align:start position:0%
+one out at Kaiser Permanente that we
+discussed many of you are focused in a
+
+ align:start position:0%
+discussed many of you are focused in a
+ 
+
+ align:start position:0%
+discussed many of you are focused in a
+very rich dialogue over the need for
+
+ align:start position:0%
+very rich dialogue over the need for
+ 
+
+ align:start position:0%
+very rich dialogue over the need for
+what you call digital unions that is
+
+ align:start position:0%
+what you call digital unions that is
+ 
+
+ align:start position:0%
+what you call digital unions that is
+using information technology social
+
+ align:start position:0%
+using information technology social
+ 
+
+ align:start position:0%
+using information technology social
+media and related mechanisms to convey
+
+ align:start position:0%
+media and related mechanisms to convey
+ 
+
+ align:start position:0%
+media and related mechanisms to convey
+your ideas and to communicate with each
+
+ align:start position:0%
+your ideas and to communicate with each
+ 
+
+ align:start position:0%
+your ideas and to communicate with each
+other across the world and indeed you
+
+ align:start position:0%
+other across the world and indeed you
+ 
+
+ align:start position:0%
+other across the world and indeed you
+talked about the need for global unions
+
+ align:start position:0%
+talked about the need for global unions
+ 
+
+ align:start position:0%
+talked about the need for global unions
+because obviously today where people
+
+ align:start position:0%
+because obviously today where people
+ 
+
+ align:start position:0%
+because obviously today where people
+work how people are affected by jobs
+
+ align:start position:0%
+work how people are affected by jobs
+ 
+
+ align:start position:0%
+work how people are affected by jobs
+that are created by companies around the
+
+ align:start position:0%
+that are created by companies around the
+ 
+
+ align:start position:0%
+that are created by companies around the
+world is not simply a national issue
+
+ align:start position:0%
+world is not simply a national issue
+ 
+
+ align:start position:0%
+world is not simply a national issue
+some of you talked about the need to
+
+ align:start position:0%
+some of you talked about the need to
+ 
+
+ align:start position:0%
+some of you talked about the need to
+return to these interesting
+
+ align:start position:0%
+return to these interesting
+ 
+
+ align:start position:0%
+return to these interesting
+organizations called guilds where
+
+ align:start position:0%
+organizations called guilds where
+ 
+
+ align:start position:0%
+organizations called guilds where
+workers came together cooperatively to
+
+ align:start position:0%
+workers came together cooperatively to
+ 
+
+ align:start position:0%
+workers came together cooperatively to
+enhance their profession or their
+
+ align:start position:0%
+enhance their profession or their
+ 
+
+ align:start position:0%
+enhance their profession or their
+particular occupation and to work to
+
+ align:start position:0%
+particular occupation and to work to
+ 
+
+ align:start position:0%
+particular occupation and to work to
+enhance their professionalism you talked
+
+ align:start position:0%
+enhance their professionalism you talked
+ 
+
+ align:start position:0%
+enhance their professionalism you talked
+about the need for apps to share
+
+ align:start position:0%
+about the need for apps to share
+ 
+
+ align:start position:0%
+about the need for apps to share
+information on where good jobs are in
+
+ align:start position:0%
+information on where good jobs are in
+ 
+
+ align:start position:0%
+information on where good jobs are in
+good employers are along the lines that
+
+ align:start position:0%
+good employers are along the lines that
+ 
+
+ align:start position:0%
+good employers are along the lines that
+we used in the good job survey that some
+
+ align:start position:0%
+we used in the good job survey that some
+ 
+
+ align:start position:0%
+we used in the good job survey that some
+of you have done and then many of you
+
+ align:start position:0%
+of you have done and then many of you
+ 
+
+ align:start position:0%
+of you have done and then many of you
+talked about the need for new forms of
+
+ align:start position:0%
+talked about the need for new forms of
+ 
+
+ align:start position:0%
+talked about the need for new forms of
+advocates for low-wage workers in the
+
+ align:start position:0%
+advocates for low-wage workers in the
+ 
+
+ align:start position:0%
+advocates for low-wage workers in the
+United States in Europe in developing
+
+ align:start position:0%
+United States in Europe in developing
+ 
+
+ align:start position:0%
+United States in Europe in developing
+countries all around the world
+
+ align:start position:0%
+countries all around the world
+ 
+
+ align:start position:0%
+countries all around the world
+particularly focusing on the role that
+
+ align:start position:0%
+particularly focusing on the role that
+ 
+
+ align:start position:0%
+particularly focusing on the role that
+NGOs are now playing so I think the
+
+ align:start position:0%
+NGOs are now playing so I think the
+ 
+
+ align:start position:0%
+NGOs are now playing so I think the
+bottom line of all of this don't just
+
+ align:start position:0%
+bottom line of all of this don't just
+ 
+
+ align:start position:0%
+bottom line of all of this don't just
+observe these trends get involved
+
+ align:start position:0%
+observe these trends get involved
+ 
+
+ align:start position:0%
+observe these trends get involved
+whether it's working
+
+ align:start position:0%
+whether it's working
+ 
+
+ align:start position:0%
+whether it's working
+on the side of advocates for labor
+
+ align:start position:0%
+on the side of advocates for labor
+ 
+
+ align:start position:0%
+on the side of advocates for labor
+whether it's enriching and strengthening
+
+ align:start position:0%
+whether it's enriching and strengthening
+ 
+
+ align:start position:0%
+whether it's enriching and strengthening
+the role that HR plays in our
+
+ align:start position:0%
+the role that HR plays in our
+ 
+
+ align:start position:0%
+the role that HR plays in our
+organizations whether it's thinking
+
+ align:start position:0%
+organizations whether it's thinking
+ 
+
+ align:start position:0%
+organizations whether it's thinking
+about the future of labor policy in our
+
+ align:start position:0%
+about the future of labor policy in our
+ 
+
+ align:start position:0%
+about the future of labor policy in our
+countries or whether you're like me
+
+ align:start position:0%
+countries or whether you're like me
+ 
+
+ align:start position:0%
+countries or whether you're like me
+working in the education sphere either
+
+ align:start position:0%
+working in the education sphere either
+ 
+
+ align:start position:0%
+working in the education sphere either
+on the university level with outside
+
+ align:start position:0%
+on the university level with outside
+ 
+
+ align:start position:0%
+on the university level with outside
+world all of you in this global based
+
+ align:start position:0%
+world all of you in this global based
+ 
+
+ align:start position:0%
+world all of you in this global based
+online course or our students in high
+
+ align:start position:0%
+online course or our students in high
+ 
+
+ align:start position:0%
+online course or our students in high
+schools and community colleges we all
+
+ align:start position:0%
+schools and community colleges we all
+ 
+
+ align:start position:0%
+schools and community colleges we all
+have a role to play we've emphasized
+
+ align:start position:0%
+have a role to play we've emphasized
+ 
+
+ align:start position:0%
+have a role to play we've emphasized
+that throughout this course now it's
+
+ align:start position:0%
+that throughout this course now it's
+ 
+
+ align:start position:0%
+that throughout this course now it's
+time for us to put our ideas to work so
+
+ align:start position:0%
+time for us to put our ideas to work so
+ 
+
+ align:start position:0%
+time for us to put our ideas to work so
+I look forward to a very invigorating
+
+ align:start position:0%
+I look forward to a very invigorating
+ 
+
+ align:start position:0%
+I look forward to a very invigorating
+week of negotiations will summarize the
+
+ align:start position:0%
+week of negotiations will summarize the
+ 
+
+ align:start position:0%
+week of negotiations will summarize the
+settlements that were that are achieved
+
+ align:start position:0%
+settlements that were that are achieved
+ 
+
+ align:start position:0%
+settlements that were that are achieved
+next week when we come together and
+
+ align:start position:0%
+next week when we come together and
+ 
+
+ align:start position:0%
+next week when we come together and
+we'll see if we can't really summarize
+
+ align:start position:0%
+we'll see if we can't really summarize
+ 
+
+ align:start position:0%
+we'll see if we can't really summarize
+and bring together what did we learn
+
+ align:start position:0%
+and bring together what did we learn
+ 
+
+ align:start position:0%
+and bring together what did we learn
+what are the key takeaways from our
+
+ align:start position:0%
+what are the key takeaways from our
+ 
+
+ align:start position:0%
+what are the key takeaways from our
+efforts to shape the future of work
\ No newline at end of file
diff --git a/5mJd--JCwBI.txt b/5mJd--JCwBI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..da190cd47bd429bb09835828fe5ab21650a732d6
--- /dev/null
+++ b/5mJd--JCwBI.txt
@@ -0,0 +1,1131 @@
+align:start position:0%
+ 
+in the last chapter we developed
+
+ align:start position:0%
+in the last chapter we developed
+ 
+
+ align:start position:0%
+in the last chapter we developed
+sequential logic which contains both
+
+ align:start position:0%
+sequential logic which contains both
+ 
+
+ align:start position:0%
+sequential logic which contains both
+combinational logic and memory
+
+ align:start position:0%
+combinational logic and memory
+ 
+
+ align:start position:0%
+combinational logic and memory
+components the combinational logic cloud
+
+ align:start position:0%
+components the combinational logic cloud
+ 
+
+ align:start position:0%
+components the combinational logic cloud
+is an acyclic graph of components that
+
+ align:start position:0%
+is an acyclic graph of components that
+ 
+
+ align:start position:0%
+is an acyclic graph of components that
+obey the static discipline the static
+
+ align:start position:0%
+obey the static discipline the static
+ 
+
+ align:start position:0%
+obey the static discipline the static
+discipline guarantees if we supply valid
+
+ align:start position:0%
+discipline guarantees if we supply valid
+ 
+
+ align:start position:0%
+discipline guarantees if we supply valid
+and stable inputs then we will get valid
+
+ align:start position:0%
+and stable inputs then we will get valid
+ 
+
+ align:start position:0%
+and stable inputs then we will get valid
+and stable digital outputs by some
+
+ align:start position:0%
+and stable digital outputs by some
+ 
+
+ align:start position:0%
+and stable digital outputs by some
+specified interval after the last input
+
+ align:start position:0%
+specified interval after the last input
+ 
+
+ align:start position:0%
+specified interval after the last input
+transition there's also a functional
+
+ align:start position:0%
+transition there's also a functional
+ 
+
+ align:start position:0%
+transition there's also a functional
+specification that tells us the output
+
+ align:start position:0%
+specification that tells us the output
+ 
+
+ align:start position:0%
+specification that tells us the output
+values for every possible combination of
+
+ align:start position:0%
+values for every possible combination of
+ 
+
+ align:start position:0%
+values for every possible combination of
+input values in this diagram there are K
+
+ align:start position:0%
+input values in this diagram there are K
+ 
+
+ align:start position:0%
+input values in this diagram there are K
+plus M inputs and k plus n outputs so
+
+ align:start position:0%
+plus M inputs and k plus n outputs so
+ 
+
+ align:start position:0%
+plus M inputs and k plus n outputs so
+the truth table for the combinational
+
+ align:start position:0%
+the truth table for the combinational
+ 
+
+ align:start position:0%
+the truth table for the combinational
+logic will have 2 to the k plus m rows
+
+ align:start position:0%
+logic will have 2 to the k plus m rows
+ 
+
+ align:start position:0%
+logic will have 2 to the k plus m rows
+and K plus n output columns the job of
+
+ align:start position:0%
+and K plus n output columns the job of
+ 
+
+ align:start position:0%
+and K plus n output columns the job of
+the state registers is to remember the
+
+ align:start position:0%
+the state registers is to remember the
+ 
+
+ align:start position:0%
+the state registers is to remember the
+current state of the sequential logic
+
+ align:start position:0%
+current state of the sequential logic
+ 
+
+ align:start position:0%
+current state of the sequential logic
+the state is encoded as some number K of
+
+ align:start position:0%
+the state is encoded as some number K of
+ 
+
+ align:start position:0%
+the state is encoded as some number K of
+bits which will allow us to represent
+
+ align:start position:0%
+bits which will allow us to represent
+ 
+
+ align:start position:0%
+bits which will allow us to represent
+two to the K unique States recall that
+
+ align:start position:0%
+two to the K unique States recall that
+ 
+
+ align:start position:0%
+two to the K unique States recall that
+the state is used to capture in some
+
+ align:start position:0%
+the state is used to capture in some
+ 
+
+ align:start position:0%
+the state is used to capture in some
+appropriate way the relevant history of
+
+ align:start position:0%
+appropriate way the relevant history of
+ 
+
+ align:start position:0%
+appropriate way the relevant history of
+the input sequence to the extent that
+
+ align:start position:0%
+the input sequence to the extent that
+ 
+
+ align:start position:0%
+the input sequence to the extent that
+previous input values influence the
+
+ align:start position:0%
+previous input values influence the
+ 
+
+ align:start position:0%
+previous input values influence the
+operation of the sequential logic that
+
+ align:start position:0%
+operation of the sequential logic that
+ 
+
+ align:start position:0%
+operation of the sequential logic that
+happens through the storage state bits
+
+ align:start position:0%
+happens through the storage state bits
+ 
+
+ align:start position:0%
+happens through the storage state bits
+typically the load input of the state
+
+ align:start position:0%
+typically the load input of the state
+ 
+
+ align:start position:0%
+typically the load input of the state
+registers is triggered by the rising
+
+ align:start position:0%
+registers is triggered by the rising
+ 
+
+ align:start position:0%
+registers is triggered by the rising
+edge of a periodic signal which updates
+
+ align:start position:0%
+edge of a periodic signal which updates
+ 
+
+ align:start position:0%
+edge of a periodic signal which updates
+the storage state with a new state
+
+ align:start position:0%
+the storage state with a new state
+ 
+
+ align:start position:0%
+the storage state with a new state
+calculated by the combinational logic as
+
+ align:start position:0%
+calculated by the combinational logic as
+ 
+
+ align:start position:0%
+calculated by the combinational logic as
+designers we have several tasks first we
+
+ align:start position:0%
+designers we have several tasks first we
+ 
+
+ align:start position:0%
+designers we have several tasks first we
+must decide on what output sequences
+
+ align:start position:0%
+must decide on what output sequences
+ 
+
+ align:start position:0%
+must decide on what output sequences
+need to be generated in response to the
+
+ align:start position:0%
+need to be generated in response to the
+ 
+
+ align:start position:0%
+need to be generated in response to the
+expected input sequences a particular
+
+ align:start position:0%
+expected input sequences a particular
+ 
+
+ align:start position:0%
+expected input sequences a particular
+input may in fact generate a long
+
+ align:start position:0%
+input may in fact generate a long
+ 
+
+ align:start position:0%
+input may in fact generate a long
+sequence of output values where the
+
+ align:start position:0%
+sequence of output values where the
+ 
+
+ align:start position:0%
+sequence of output values where the
+output may remain unchanged while the
+
+ align:start position:0%
+output may remain unchanged while the
+ 
+
+ align:start position:0%
+output may remain unchanged while the
+input sequences process step by step
+
+ align:start position:0%
+input sequences process step by step
+ 
+
+ align:start position:0%
+input sequences process step by step
+where the FSM is remembering the
+
+ align:start position:0%
+where the FSM is remembering the
+ 
+
+ align:start position:0%
+where the FSM is remembering the
+relevant information by updating its
+
+ align:start position:0%
+relevant information by updating its
+ 
+
+ align:start position:0%
+relevant information by updating its
+internal state then we have to develop
+
+ align:start position:0%
+internal state then we have to develop
+ 
+
+ align:start position:0%
+internal state then we have to develop
+the functional specification for the
+
+ align:start position:0%
+the functional specification for the
+ 
+
+ align:start position:0%
+the functional specification for the
+logic so it calculates the correct
+
+ align:start position:0%
+logic so it calculates the correct
+ 
+
+ align:start position:0%
+logic so it calculates the correct
+output and next state values finally we
+
+ align:start position:0%
+output and next state values finally we
+ 
+
+ align:start position:0%
+output and next state values finally we
+need to come up with an actual circuit
+
+ align:start position:0%
+need to come up with an actual circuit
+ 
+
+ align:start position:0%
+need to come up with an actual circuit
+diagram for the sequential logic system
+
+ align:start position:0%
+diagram for the sequential logic system
+ 
+
+ align:start position:0%
+diagram for the sequential logic system
+all the tasks are pretty interesting so
+
+ align:start position:0%
+all the tasks are pretty interesting so
+ 
+
+ align:start position:0%
+all the tasks are pretty interesting so
+let's get started as an example
+
+ align:start position:0%
+let's get started as an example
+ 
+
+ align:start position:0%
+let's get started as an example
+sequential system
+
+ align:start position:0%
+sequential system
+ 
+
+ align:start position:0%
+sequential system
+let's make
+
+ align:start position:0%
+let's make
+ 
+
+ align:start position:0%
+let's make
+combination lock the lock has a 1-bit
+
+ align:start position:0%
+combination lock the lock has a 1-bit
+ 
+
+ align:start position:0%
+combination lock the lock has a 1-bit
+input signal where the user enters the
+
+ align:start position:0%
+input signal where the user enters the
+ 
+
+ align:start position:0%
+input signal where the user enters the
+combination as a sequence of bits
+
+ align:start position:0%
+combination as a sequence of bits
+ 
+
+ align:start position:0%
+combination as a sequence of bits
+there's one output signal unlock which
+
+ align:start position:0%
+there's one output signal unlock which
+ 
+
+ align:start position:0%
+there's one output signal unlock which
+is one if and only if the correct
+
+ align:start position:0%
+is one if and only if the correct
+ 
+
+ align:start position:0%
+is one if and only if the correct
+combination has been entered in this
+
+ align:start position:0%
+combination has been entered in this
+ 
+
+ align:start position:0%
+combination has been entered in this
+example we want to assert unlock in
+
+ align:start position:0%
+example we want to assert unlock in
+ 
+
+ align:start position:0%
+example we want to assert unlock in
+other words set unlock to 1 when the
+
+ align:start position:0%
+other words set unlock to 1 when the
+ 
+
+ align:start position:0%
+other words set unlock to 1 when the
+last 4 input values are the sequence 0 1
+
+ align:start position:0%
+last 4 input values are the sequence 0 1
+ 
+
+ align:start position:0%
+last 4 input values are the sequence 0 1
+1 0 mr. blue is asking a good question
+
+ align:start position:0%
+1 0 mr. blue is asking a good question
+ 
+
+ align:start position:0%
+1 0 mr. blue is asking a good question
+how many state bits do we need do we
+
+ align:start position:0%
+how many state bits do we need do we
+ 
+
+ align:start position:0%
+how many state bits do we need do we
+have to remember the last 4 input bits
+
+ align:start position:0%
+have to remember the last 4 input bits
+ 
+
+ align:start position:0%
+have to remember the last 4 input bits
+in which case we need for state bits or
+
+ align:start position:0%
+in which case we need for state bits or
+ 
+
+ align:start position:0%
+in which case we need for state bits or
+can we remember less information and
+
+ align:start position:0%
+can we remember less information and
+ 
+
+ align:start position:0%
+can we remember less information and
+still do our job ah-ha we don't need the
+
+ align:start position:0%
+still do our job ah-ha we don't need the
+ 
+
+ align:start position:0%
+still do our job ah-ha we don't need the
+complete history of the last 4 inputs we
+
+ align:start position:0%
+complete history of the last 4 inputs we
+ 
+
+ align:start position:0%
+complete history of the last 4 inputs we
+only need to know if the most recent
+
+ align:start position:0%
+only need to know if the most recent
+ 
+
+ align:start position:0%
+only need to know if the most recent
+entries represent some part of a
+
+ align:start position:0%
+entries represent some part of a
+ 
+
+ align:start position:0%
+entries represent some part of a
+partially entered correct combination in
+
+ align:start position:0%
+partially entered correct combination in
+ 
+
+ align:start position:0%
+partially entered correct combination in
+other words if the input sequence
+
+ align:start position:0%
+other words if the input sequence
+ 
+
+ align:start position:0%
+other words if the input sequence
+doesn't represent a correct combination
+
+ align:start position:0%
+doesn't represent a correct combination
+ 
+
+ align:start position:0%
+doesn't represent a correct combination
+we don't need to keep track of exactly
+
+ align:start position:0%
+we don't need to keep track of exactly
+ 
+
+ align:start position:0%
+we don't need to keep track of exactly
+how its incorrect we only need to know
+
+ align:start position:0%
+how its incorrect we only need to know
+ 
+
+ align:start position:0%
+how its incorrect we only need to know
+that it is incorrect with that
+
+ align:start position:0%
+that it is incorrect with that
+ 
+
+ align:start position:0%
+that it is incorrect with that
+observation in mind let's figure out how
+
+ align:start position:0%
+observation in mind let's figure out how
+ 
+
+ align:start position:0%
+observation in mind let's figure out how
+to represent the desired behavior of our
+
+ align:start position:0%
+to represent the desired behavior of our
+ 
+
+ align:start position:0%
+to represent the desired behavior of our
+digital system we can characterize the
+
+ align:start position:0%
+digital system we can characterize the
+ 
+
+ align:start position:0%
+digital system we can characterize the
+behavior of a sequential system using a
+
+ align:start position:0%
+behavior of a sequential system using a
+ 
+
+ align:start position:0%
+behavior of a sequential system using a
+new abstraction called a finite state
+
+ align:start position:0%
+new abstraction called a finite state
+ 
+
+ align:start position:0%
+new abstraction called a finite state
+machine or FSM for short the goal of the
+
+ align:start position:0%
+machine or FSM for short the goal of the
+ 
+
+ align:start position:0%
+machine or FSM for short the goal of the
+FSM abstraction is to describe the
+
+ align:start position:0%
+FSM abstraction is to describe the
+ 
+
+ align:start position:0%
+FSM abstraction is to describe the
+input-output behavior of the sequential
+
+ align:start position:0%
+input-output behavior of the sequential
+ 
+
+ align:start position:0%
+input-output behavior of the sequential
+logic independent of its actual
+
+ align:start position:0%
+logic independent of its actual
+ 
+
+ align:start position:0%
+logic independent of its actual
+implementation a finite state machine
+
+ align:start position:0%
+implementation a finite state machine
+ 
+
+ align:start position:0%
+implementation a finite state machine
+has a periodic clock input a rising
+
+ align:start position:0%
+has a periodic clock input a rising
+ 
+
+ align:start position:0%
+has a periodic clock input a rising
+clock edge will trigger the transition
+
+ align:start position:0%
+clock edge will trigger the transition
+ 
+
+ align:start position:0%
+clock edge will trigger the transition
+from the current state to the next state
+
+ align:start position:0%
+from the current state to the next state
+ 
+
+ align:start position:0%
+from the current state to the next state
+the FSM has some fixed number of states
+
+ align:start position:0%
+the FSM has some fixed number of states
+ 
+
+ align:start position:0%
+the FSM has some fixed number of states
+with a particular state designated is
+
+ align:start position:0%
+with a particular state designated is
+ 
+
+ align:start position:0%
+with a particular state designated is
+the initial or starting state when the
+
+ align:start position:0%
+the initial or starting state when the
+ 
+
+ align:start position:0%
+the initial or starting state when the
+FSM is first turned on one of the
+
+ align:start position:0%
+FSM is first turned on one of the
+ 
+
+ align:start position:0%
+FSM is first turned on one of the
+interesting challenges in designing an
+
+ align:start position:0%
+interesting challenges in designing an
+ 
+
+ align:start position:0%
+interesting challenges in designing an
+FSM is to determine the required number
+
+ align:start position:0%
+FSM is to determine the required number
+ 
+
+ align:start position:0%
+FSM is to determine the required number
+of states since there's often a
+
+ align:start position:0%
+of states since there's often a
+ 
+
+ align:start position:0%
+of states since there's often a
+trade-off between the number of state
+
+ align:start position:0%
+trade-off between the number of state
+ 
+
+ align:start position:0%
+trade-off between the number of state
+bits and the complexity of the internal
+
+ align:start position:0%
+bits and the complexity of the internal
+ 
+
+ align:start position:0%
+bits and the complexity of the internal
+combinational logic required to compute
+
+ align:start position:0%
+combinational logic required to compute
+ 
+
+ align:start position:0%
+combinational logic required to compute
+the next state and outputs there are
+
+ align:start position:0%
+the next state and outputs there are
+ 
+
+ align:start position:0%
+the next state and outputs there are
+some number of inputs used to convey all
+
+ align:start position:0%
+some number of inputs used to convey all
+ 
+
+ align:start position:0%
+some number of inputs used to convey all
+the external information necessary for
+
+ align:start position:0%
+the external information necessary for
+ 
+
+ align:start position:0%
+the external information necessary for
+the FSM to do its job again there are
+
+ align:start position:0%
+the FSM to do its job again there are
+ 
+
+ align:start position:0%
+the FSM to do its job again there are
+interesting design trade-offs suppose
+
+ align:start position:0%
+interesting design trade-offs suppose
+ 
+
+ align:start position:0%
+interesting design trade-offs suppose
+the FSM required 100 bits of input
+
+ align:start position:0%
+the FSM required 100 bits of input
+ 
+
+ align:start position:0%
+the FSM required 100 bits of input
+should we have 100 inputs and deliver
+
+ align:start position:0%
+should we have 100 inputs and deliver
+ 
+
+ align:start position:0%
+should we have 100 inputs and deliver
+all the information at once or should we
+
+ align:start position:0%
+all the information at once or should we
+ 
+
+ align:start position:0%
+all the information at once or should we
+have a single input and deliver the
+
+ align:start position:0%
+have a single input and deliver the
+ 
+
+ align:start position:0%
+have a single input and deliver the
+information as a hundred cycle sequence
+
+ align:start position:0%
+information as a hundred cycle sequence
+ 
+
+ align:start position:0%
+information as a hundred cycle sequence
+in many real-world situations where the
+
+ align:start position:0%
+in many real-world situations where the
+ 
+
+ align:start position:0%
+in many real-world situations where the
+sequential logic is much faster than
+
+ align:start position:0%
+sequential logic is much faster than
+ 
+
+ align:start position:0%
+sequential logic is much faster than
+whatever physical process we're trying
+
+ align:start position:0%
+whatever physical process we're trying
+ 
+
+ align:start position:0%
+whatever physical process we're trying
+to control will often see the use of bit
+
+ align:start position:0%
+to control will often see the use of bit
+ 
+
+ align:start position:0%
+to control will often see the use of bit
+serial inputs where the information
+
+ align:start position:0%
+serial inputs where the information
+ 
+
+ align:start position:0%
+serial inputs where the information
+arrives as a sequence one bit at a time
+
+ align:start position:0%
+arrives as a sequence one bit at a time
+ 
+
+ align:start position:0%
+arrives as a sequence one bit at a time
+that will allow us to use much less
+
+ align:start position:0%
+that will allow us to use much less
+ 
+
+ align:start position:0%
+that will allow us to use much less
+signaling hardware that the cost of the
+
+ align:start position:0%
+signaling hardware that the cost of the
+ 
+
+ align:start position:0%
+signaling hardware that the cost of the
+time required to transmit the
+
+ align:start position:0%
+time required to transmit the
+ 
+
+ align:start position:0%
+time required to transmit the
+information sequentially the FSM has
+
+ align:start position:0%
+information sequentially the FSM has
+ 
+
+ align:start position:0%
+information sequentially the FSM has
+some number of outputs to convey the
+
+ align:start position:0%
+some number of outputs to convey the
+ 
+
+ align:start position:0%
+some number of outputs to convey the
+results of the sequential logics
+
+ align:start position:0%
+results of the sequential logics
+ 
+
+ align:start position:0%
+results of the sequential logics
+computations the comments before about
+
+ align:start position:0%
+computations the comments before about
+ 
+
+ align:start position:0%
+computations the comments before about
+serial versus parallel inputs applies
+
+ align:start position:0%
+serial versus parallel inputs applies
+ 
+
+ align:start position:0%
+serial versus parallel inputs applies
+equally to choosing how information
+
+ align:start position:0%
+equally to choosing how information
+ 
+
+ align:start position:0%
+equally to choosing how information
+should be encoded on the outputs there
+
+ align:start position:0%
+should be encoded on the outputs there
+ 
+
+ align:start position:0%
+should be encoded on the outputs there
+are a set of transition rules specifying
+
+ align:start position:0%
+are a set of transition rules specifying
+ 
+
+ align:start position:0%
+are a set of transition rules specifying
+how the next state s prime is determined
+
+ align:start position:0%
+how the next state s prime is determined
+ 
+
+ align:start position:0%
+how the next state s prime is determined
+from the current state s in the inputs I
+
+ align:start position:0%
+from the current state s in the inputs I
+ 
+
+ align:start position:0%
+from the current state s in the inputs I
+the specification must be complete in
+
+ align:start position:0%
+the specification must be complete in
+ 
+
+ align:start position:0%
+the specification must be complete in
+numerating s prime for every possible
+
+ align:start position:0%
+numerating s prime for every possible
+ 
+
+ align:start position:0%
+numerating s prime for every possible
+combination of s and I and finally
+
+ align:start position:0%
+combination of s and I and finally
+ 
+
+ align:start position:0%
+combination of s and I and finally
+there's a specification for how the
+
+ align:start position:0%
+there's a specification for how the
+ 
+
+ align:start position:0%
+there's a specification for how the
+output values should be determined the
+
+ align:start position:0%
+output values should be determined the
+ 
+
+ align:start position:0%
+output values should be determined the
+FSM design is often a bit simpler if the
+
+ align:start position:0%
+FSM design is often a bit simpler if the
+ 
+
+ align:start position:0%
+FSM design is often a bit simpler if the
+outputs are strictly a function of the
+
+ align:start position:0%
+outputs are strictly a function of the
+ 
+
+ align:start position:0%
+outputs are strictly a function of the
+current state s but in general the
+
+ align:start position:0%
+current state s but in general the
+ 
+
+ align:start position:0%
+current state s but in general the
+outputs can be a function of both s and
+
+ align:start position:0%
+outputs can be a function of both s and
+ 
+
+ align:start position:0%
+outputs can be a function of both s and
+the current inputs now that we have our
+
+ align:start position:0%
+the current inputs now that we have our
+ 
+
+ align:start position:0%
+the current inputs now that we have our
+abstraction in place let's see how to
+
+ align:start position:0%
+abstraction in place let's see how to
+ 
+
+ align:start position:0%
+abstraction in place let's see how to
+use it to design our combinational lock
\ No newline at end of file
diff --git a/6-7BOpZ2k04.txt b/6-7BOpZ2k04.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9df1b6219d9a1fdca83c4ebae8654717dbc3d050
--- /dev/null
+++ b/6-7BOpZ2k04.txt
@@ -0,0 +1,1435 @@
+align:start position:0%
+ 
+let's look at some examples of
+
+ align:start position:0%
+let's look at some examples of
+ 
+
+ align:start position:0%
+let's look at some examples of
+one-dimensional elastic collisions with
+
+ align:start position:0%
+one-dimensional elastic collisions with
+ 
+
+ align:start position:0%
+one-dimensional elastic collisions with
+no external forces with between two
+
+ align:start position:0%
+no external forces with between two
+ 
+
+ align:start position:0%
+no external forces with between two
+particles so suppose I have particle 1
+
+ align:start position:0%
+particles so suppose I have particle 1
+ 
+
+ align:start position:0%
+particles so suppose I have particle 1
+and particle 2 and we have them moving
+
+ align:start position:0%
+and particle 2 and we have them moving
+ 
+
+ align:start position:0%
+and particle 2 and we have them moving
+on a frictionless surface and let's
+
+ align:start position:0%
+on a frictionless surface and let's
+ 
+
+ align:start position:0%
+on a frictionless surface and let's
+choose a reference frame in which we'll
+
+ align:start position:0%
+choose a reference frame in which we'll
+ 
+
+ align:start position:0%
+choose a reference frame in which we'll
+call the laboratory frame in which the
+
+ align:start position:0%
+call the laboratory frame in which the
+ 
+
+ align:start position:0%
+call the laboratory frame in which the
+initial velocity of particle 2 is 0 so
+
+ align:start position:0%
+initial velocity of particle 2 is 0 so
+ 
+
+ align:start position:0%
+initial velocity of particle 2 is 0 so
+our frame is called the laboratory frame
+
+ align:start position:0%
+our frame is called the laboratory frame
+ 
+
+ align:start position:0%
+our frame is called the laboratory frame
+and in this frame we're thinking of
+
+ align:start position:0%
+and in this frame we're thinking of
+ 
+
+ align:start position:0%
+and in this frame we're thinking of
+Parga particle 2 as our target and the
+
+ align:start position:0%
+Parga particle 2 as our target and the
+ 
+
+ align:start position:0%
+Parga particle 2 as our target and the
+target is at rest and particle 1 is
+
+ align:start position:0%
+target is at rest and particle 1 is
+ 
+
+ align:start position:0%
+target is at rest and particle 1 is
+moving in with some initial velocity and
+
+ align:start position:0%
+moving in with some initial velocity and
+ 
+
+ align:start position:0%
+moving in with some initial velocity and
+so here is our initial picture and then
+
+ align:start position:0%
+so here is our initial picture and then
+ 
+
+ align:start position:0%
+so here is our initial picture and then
+our final state both the target and the
+
+ align:start position:0%
+our final state both the target and the
+ 
+
+ align:start position:0%
+our final state both the target and the
+particles can be moving so we'll just
+
+ align:start position:0%
+particles can be moving so we'll just
+ 
+
+ align:start position:0%
+particles can be moving so we'll just
+indicate the 1 final and we'll have at
+
+ align:start position:0%
+indicate the 1 final and we'll have at
+ 
+
+ align:start position:0%
+indicate the 1 final and we'll have at
+our target is also moving with V 2 final
+
+ align:start position:0%
+our target is also moving with V 2 final
+ 
+
+ align:start position:0%
+our target is also moving with V 2 final
+and we have I hat so let's now look at
+
+ align:start position:0%
+and we have I hat so let's now look at
+ 
+
+ align:start position:0%
+and we have I hat so let's now look at
+some examples where we're analyzing this
+
+ align:start position:0%
+some examples where we're analyzing this
+ 
+
+ align:start position:0%
+some examples where we're analyzing this
+type of collision in which both energy
+
+ align:start position:0%
+type of collision in which both energy
+ 
+
+ align:start position:0%
+type of collision in which both energy
+and momentum are constant and for a
+
+ align:start position:0%
+and momentum are constant and for a
+ 
+
+ align:start position:0%
+and momentum are constant and for a
+particular example that we want to look
+
+ align:start position:0%
+particular example that we want to look
+ 
+
+ align:start position:0%
+particular example that we want to look
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+we'll have m2 m2 is twice m1 now for our
+
+ align:start position:0%
+we'll have m2 m2 is twice m1 now for our
+ 
+
+ align:start position:0%
+we'll have m2 m2 is twice m1 now for our
+two equations that we're going to write
+
+ align:start position:0%
+two equations that we're going to write
+ 
+
+ align:start position:0%
+two equations that we're going to write
+about we'll choose components and we'll
+
+ align:start position:0%
+about we'll choose components and we'll
+ 
+
+ align:start position:0%
+about we'll choose components and we'll
+write our energy equation as one-half m1
+
+ align:start position:0%
+write our energy equation as one-half m1
+ 
+
+ align:start position:0%
+write our energy equation as one-half m1
+v1 X initial squared plus one-half m2 so
+
+ align:start position:0%
+v1 X initial squared plus one-half m2 so
+ 
+
+ align:start position:0%
+v1 X initial squared plus one-half m2 so
+now we're going to write 2 m1 but the
+
+ align:start position:0%
+now we're going to write 2 m1 but the
+ 
+
+ align:start position:0%
+now we're going to write 2 m1 but the
+object 2 is at rest so we don't have to
+
+ align:start position:0%
+object 2 is at rest so we don't have to
+ 
+
+ align:start position:0%
+object 2 is at rest so we don't have to
+worry about that one yet and so our
+
+ align:start position:0%
+worry about that one yet and so our
+ 
+
+ align:start position:0%
+worry about that one yet and so our
+initial kinetic energy is just equal to
+
+ align:start position:0%
+initial kinetic energy is just equal to
+ 
+
+ align:start position:0%
+initial kinetic energy is just equal to
+the final kinetic energy one-half m1 v1
+
+ align:start position:0%
+the final kinetic energy one-half m1 v1
+ 
+
+ align:start position:0%
+the final kinetic energy one-half m1 v1
+X final squared and now I'm going to
+
+ align:start position:0%
+X final squared and now I'm going to
+ 
+
+ align:start position:0%
+X final squared and now I'm going to
+substitute in to m1 for the mass of m2
+
+ align:start position:0%
+substitute in to m1 for the mass of m2
+ 
+
+ align:start position:0%
+substitute in to m1 for the mass of m2
+be 2x final squared and that's our
+
+ align:start position:0%
+be 2x final squared and that's our
+ 
+
+ align:start position:0%
+be 2x final squared and that's our
+energy condition and then our momentum
+
+ align:start position:0%
+energy condition and then our momentum
+ 
+
+ align:start position:0%
+energy condition and then our momentum
+condition is that the incoming momentum
+
+ align:start position:0%
+condition is that the incoming momentum
+ 
+
+ align:start position:0%
+condition is that the incoming momentum
+one-half X and
+
+ align:start position:0%
+one-half X and
+ 
+
+ align:start position:0%
+one-half X and
+is equal to the outgoing momentum m1v1
+
+ align:start position:0%
+is equal to the outgoing momentum m1v1
+ 
+
+ align:start position:0%
+is equal to the outgoing momentum m1v1
+x-final
+
+ align:start position:0%
+x-final
+ 
+
+ align:start position:0%
+x-final
+and again I'm going to substitute for m2
+
+ align:start position:0%
+and again I'm going to substitute for m2
+ 
+
+ align:start position:0%
+and again I'm going to substitute for m2
+that's to m1 the 2x final and these two
+
+ align:start position:0%
+that's to m1 the 2x final and these two
+ 
+
+ align:start position:0%
+that's to m1 the 2x final and these two
+equations represent a system a linear as
+
+ align:start position:0%
+equations represent a system a linear as
+ 
+
+ align:start position:0%
+equations represent a system a linear as
+a system of two equations with two
+
+ align:start position:0%
+a system of two equations with two
+ 
+
+ align:start position:0%
+a system of two equations with two
+unknowns
+
+ align:start position:0%
+unknowns
+ 
+
+ align:start position:0%
+unknowns
+we'll treat these this is Givens along
+
+ align:start position:0%
+we'll treat these this is Givens along
+ 
+
+ align:start position:0%
+we'll treat these this is Givens along
+with the initial velocity of particle
+
+ align:start position:0%
+with the initial velocity of particle
+ 
+
+ align:start position:0%
+with the initial velocity of particle
+one and our target here is to solve for
+
+ align:start position:0%
+one and our target here is to solve for
+ 
+
+ align:start position:0%
+one and our target here is to solve for
+the what 1x final and B 2x final so we
+
+ align:start position:0%
+the what 1x final and B 2x final so we
+ 
+
+ align:start position:0%
+the what 1x final and B 2x final so we
+have two equations and two unknowns now
+
+ align:start position:0%
+have two equations and two unknowns now
+ 
+
+ align:start position:0%
+have two equations and two unknowns now
+it's a quadratic equation so we have to
+
+ align:start position:0%
+it's a quadratic equation so we have to
+ 
+
+ align:start position:0%
+it's a quadratic equation so we have to
+identify from problem solving strategy
+
+ align:start position:0%
+identify from problem solving strategy
+ 
+
+ align:start position:0%
+identify from problem solving strategy
+we have to identify which quantity we're
+
+ align:start position:0%
+we have to identify which quantity we're
+ 
+
+ align:start position:0%
+we have to identify which quantity we're
+going to solve first and so let's solve
+
+ align:start position:0%
+going to solve first and so let's solve
+ 
+
+ align:start position:0%
+going to solve first and so let's solve
+for V 1 X final which means we need to
+
+ align:start position:0%
+for V 1 X final which means we need to
+ 
+
+ align:start position:0%
+for V 1 X final which means we need to
+eliminate V 2 X final and the way I'll
+
+ align:start position:0%
+eliminate V 2 X final and the way I'll
+ 
+
+ align:start position:0%
+eliminate V 2 X final and the way I'll
+eliminate V 2 X final is I'll use the
+
+ align:start position:0%
+eliminate V 2 X final is I'll use the
+ 
+
+ align:start position:0%
+eliminate V 2 X final is I'll use the
+momentum equation and notice that the MS
+
+ align:start position:0%
+momentum equation and notice that the MS
+ 
+
+ align:start position:0%
+momentum equation and notice that the MS
+will cancel in the momentum equation and
+
+ align:start position:0%
+will cancel in the momentum equation and
+ 
+
+ align:start position:0%
+will cancel in the momentum equation and
+so if I divide through by 2m in the
+
+ align:start position:0%
+so if I divide through by 2m in the
+ 
+
+ align:start position:0%
+so if I divide through by 2m in the
+momentum equation and bring this term
+
+ align:start position:0%
+momentum equation and bring this term
+ 
+
+ align:start position:0%
+momentum equation and bring this term
+over to the other side equation 2 a
+
+ align:start position:0%
+over to the other side equation 2 a
+ 
+
+ align:start position:0%
+over to the other side equation 2 a
+becomes V 2 X final equals I'm dividing
+
+ align:start position:0%
+becomes V 2 X final equals I'm dividing
+ 
+
+ align:start position:0%
+becomes V 2 X final equals I'm dividing
+through by 2 one-half V 1 X initial
+
+ align:start position:0%
+through by 2 one-half V 1 X initial
+ 
+
+ align:start position:0%
+through by 2 one-half V 1 X initial
+minus 1/2 B 1x final so this gives me a
+
+ align:start position:0%
+minus 1/2 B 1x final so this gives me a
+ 
+
+ align:start position:0%
+minus 1/2 B 1x final so this gives me a
+target v 2x final I can substitute into
+
+ align:start position:0%
+target v 2x final I can substitute into
+ 
+
+ align:start position:0%
+target v 2x final I can substitute into
+there this equation again can be cleaned
+
+ align:start position:0%
+there this equation again can be cleaned
+ 
+
+ align:start position:0%
+there this equation again can be cleaned
+up let's clean it up before we can get
+
+ align:start position:0%
+up let's clean it up before we can get
+ 
+
+ align:start position:0%
+up let's clean it up before we can get
+rid of the house we can get rid of the M
+
+ align:start position:0%
+rid of the house we can get rid of the M
+ 
+
+ align:start position:0%
+rid of the house we can get rid of the M
+ones and so the quadratic equation that
+
+ align:start position:0%
+ones and so the quadratic equation that
+ 
+
+ align:start position:0%
+ones and so the quadratic equation that
+we're going to be working with is V 1 X
+
+ align:start position:0%
+we're going to be working with is V 1 X
+ 
+
+ align:start position:0%
+we're going to be working with is V 1 X
+initial squared equals V 1 X final
+
+ align:start position:0%
+initial squared equals V 1 X final
+ 
+
+ align:start position:0%
+initial squared equals V 1 X final
+squared and I'm dividing through by 2 so
+
+ align:start position:0%
+squared and I'm dividing through by 2 so
+ 
+
+ align:start position:0%
+squared and I'm dividing through by 2 so
+I have the factor 2 plus to be 2x final
+
+ align:start position:0%
+I have the factor 2 plus to be 2x final
+ 
+
+ align:start position:0%
+I have the factor 2 plus to be 2x final
+squared now that's our energy equation
+
+ align:start position:0%
+squared now that's our energy equation
+ 
+
+ align:start position:0%
+squared now that's our energy equation
+and here's our momentum equation so if
+
+ align:start position:0%
+and here's our momentum equation so if
+ 
+
+ align:start position:0%
+and here's our momentum equation so if
+we substitute
+
+ align:start position:0%
+we substitute
+ 
+
+ align:start position:0%
+we substitute
+this in and square it we can now
+
+ align:start position:0%
+this in and square it we can now
+ 
+
+ align:start position:0%
+this in and square it we can now
+substitute and we get B 1 X initial
+
+ align:start position:0%
+substitute and we get B 1 X initial
+ 
+
+ align:start position:0%
+substitute and we get B 1 X initial
+squared equals V 1 X final squared plus
+
+ align:start position:0%
+squared equals V 1 X final squared plus
+ 
+
+ align:start position:0%
+squared equals V 1 X final squared plus
+2 now we make our substitution so that's
+
+ align:start position:0%
+2 now we make our substitution so that's
+ 
+
+ align:start position:0%
+2 now we make our substitution so that's
+1/2 V 1 X initial minus 1/2 V 1 X final
+
+ align:start position:0%
+1/2 V 1 X initial minus 1/2 V 1 X final
+ 
+
+ align:start position:0%
+1/2 V 1 X initial minus 1/2 V 1 X final
+quantity squared so let's now expand
+
+ align:start position:0%
+quantity squared so let's now expand
+ 
+
+ align:start position:0%
+quantity squared so let's now expand
+this and we have to be careful not to
+
+ align:start position:0%
+this and we have to be careful not to
+ 
+
+ align:start position:0%
+this and we have to be careful not to
+make any mistakes V 1 X initial squared
+
+ align:start position:0%
+make any mistakes V 1 X initial squared
+ 
+
+ align:start position:0%
+make any mistakes V 1 X initial squared
+equals V 1 X final squared now if I pull
+
+ align:start position:0%
+equals V 1 X final squared now if I pull
+ 
+
+ align:start position:0%
+equals V 1 X final squared now if I pull
+the 2 out I get a quarter in front and
+
+ align:start position:0%
+the 2 out I get a quarter in front and
+ 
+
+ align:start position:0%
+the 2 out I get a quarter in front and
+divide that by a half so I get one-half
+
+ align:start position:0%
+divide that by a half so I get one-half
+ 
+
+ align:start position:0%
+divide that by a half so I get one-half
+V 1 X initial squared plus another one
+
+ align:start position:0%
+V 1 X initial squared plus another one
+ 
+
+ align:start position:0%
+V 1 X initial squared plus another one
+plus a 1/2 V 1 X final squared those
+
+ align:start position:0%
+plus a 1/2 V 1 X final squared those
+ 
+
+ align:start position:0%
+plus a 1/2 V 1 X final squared those
+represent the squaring out those two
+
+ align:start position:0%
+represent the squaring out those two
+ 
+
+ align:start position:0%
+represent the squaring out those two
+terms now the cross term will have a
+
+ align:start position:0%
+terms now the cross term will have a
+ 
+
+ align:start position:0%
+terms now the cross term will have a
+factor of 1/2 in the front but a factor
+
+ align:start position:0%
+factor of 1/2 in the front but a factor
+ 
+
+ align:start position:0%
+factor of 1/2 in the front but a factor
+of 2 so we have a simple cross term of V
+
+ align:start position:0%
+of 2 so we have a simple cross term of V
+ 
+
+ align:start position:0%
+of 2 so we have a simple cross term of V
+1 X initial B 1 X final
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now when we let's collect terms let's
+
+ align:start position:0%
+now when we let's collect terms let's
+ 
+
+ align:start position:0%
+now when we let's collect terms let's
+bring everything over to this side so we
+
+ align:start position:0%
+bring everything over to this side so we
+ 
+
+ align:start position:0%
+bring everything over to this side so we
+have a zero equals three-halves b 1x
+
+ align:start position:0%
+have a zero equals three-halves b 1x
+ 
+
+ align:start position:0%
+have a zero equals three-halves b 1x
+final squared minus 1/2 B 1 X initial
+
+ align:start position:0%
+final squared minus 1/2 B 1 X initial
+ 
+
+ align:start position:0%
+final squared minus 1/2 B 1 X initial
+squared and minus B 1 X initial B 1 X
+
+ align:start position:0%
+squared and minus B 1 X initial B 1 X
+ 
+
+ align:start position:0%
+squared and minus B 1 X initial B 1 X
+final now I always like to just write
+
+ align:start position:0%
+final now I always like to just write
+ 
+
+ align:start position:0%
+final now I always like to just write
+this up in a simple way to use the
+
+ align:start position:0%
+this up in a simple way to use the
+ 
+
+ align:start position:0%
+this up in a simple way to use the
+quadratic formula so I'm going to divide
+
+ align:start position:0%
+quadratic formula so I'm going to divide
+ 
+
+ align:start position:0%
+quadratic formula so I'm going to divide
+through by two-thirds and I get minus
+
+ align:start position:0%
+through by two-thirds and I get minus
+ 
+
+ align:start position:0%
+through by two-thirds and I get minus
+one-third v1x
+
+ align:start position:0%
+one-third v1x
+ 
+
+ align:start position:0%
+one-third v1x
+initial squared minus 2/3 V 1 X initial
+
+ align:start position:0%
+initial squared minus 2/3 V 1 X initial
+ 
+
+ align:start position:0%
+initial squared minus 2/3 V 1 X initial
+v 1x final and this is now a simple
+
+ align:start position:0%
+v 1x final and this is now a simple
+ 
+
+ align:start position:0%
+v 1x final and this is now a simple
+application of the quadratic formula
+
+ align:start position:0%
+application of the quadratic formula
+ 
+
+ align:start position:0%
+application of the quadratic formula
+negative B is plus two-thirds v1 X
+
+ align:start position:0%
+negative B is plus two-thirds v1 X
+ 
+
+ align:start position:0%
+negative B is plus two-thirds v1 X
+initial plus or minus and we're going to
+
+ align:start position:0%
+initial plus or minus and we're going to
+ 
+
+ align:start position:0%
+initial plus or minus and we're going to
+interpret those two roots in a moment we
+
+ align:start position:0%
+interpret those two roots in a moment we
+ 
+
+ align:start position:0%
+interpret those two roots in a moment we
+have the factor two-thirds v1 X initial
+
+ align:start position:0%
+have the factor two-thirds v1 X initial
+ 
+
+ align:start position:0%
+have the factor two-thirds v1 X initial
+squared minus 4 ay C so that's another
+
+ align:start position:0%
+squared minus 4 ay C so that's another
+ 
+
+ align:start position:0%
+squared minus 4 ay C so that's another
+minus sign with the plus so that's plus
+
+ align:start position:0%
+minus sign with the plus so that's plus
+ 
+
+ align:start position:0%
+minus sign with the plus so that's plus
+4/3 B 1 X initial squared all to the
+
+ align:start position:0%
+4/3 B 1 X initial squared all to the
+ 
+
+ align:start position:0%
+4/3 B 1 X initial squared all to the
+square root and everything divided by 2
+
+ align:start position:0%
+square root and everything divided by 2
+ 
+
+ align:start position:0%
+square root and everything divided by 2
+now here let's just look at this factor
+
+ align:start position:0%
+now here let's just look at this factor
+ 
+
+ align:start position:0%
+now here let's just look at this factor
+this is 4/9 plus 4/3 4/3 is 12 9 so
+
+ align:start position:0%
+this is 4/9 plus 4/3 4/3 is 12 9 so
+ 
+
+ align:start position:0%
+this is 4/9 plus 4/3 4/3 is 12 9 so
+that's 16 ninths which is very
+
+ align:start position:0%
+that's 16 ninths which is very
+ 
+
+ align:start position:0%
+that's 16 ninths which is very
+convenient because when you take the
+
+ align:start position:0%
+convenient because when you take the
+ 
+
+ align:start position:0%
+convenient because when you take the
+square root that's 4/3 so we get equal
+
+ align:start position:0%
+square root that's 4/3 so we get equal
+ 
+
+ align:start position:0%
+square root that's 4/3 so we get equal
+to 2/3 V 1 X initial plus or minus 4/3 V
+
+ align:start position:0%
+to 2/3 V 1 X initial plus or minus 4/3 V
+ 
+
+ align:start position:0%
+to 2/3 V 1 X initial plus or minus 4/3 V
+1 X initial divided by 2 now we see that
+
+ align:start position:0%
+1 X initial divided by 2 now we see that
+ 
+
+ align:start position:0%
+1 X initial divided by 2 now we see that
+there is two different roots so when you
+
+ align:start position:0%
+there is two different roots so when you
+ 
+
+ align:start position:0%
+there is two different roots so when you
+add them you get 6 32 32 V 1 X initial
+
+ align:start position:0%
+add them you get 6 32 32 V 1 X initial
+ 
+
+ align:start position:0%
+add them you get 6 32 32 V 1 X initial
+divided by 2 so there's one solution and
+
+ align:start position:0%
+divided by 2 so there's one solution and
+ 
+
+ align:start position:0%
+divided by 2 so there's one solution and
+when you subtract them you're getting
+
+ align:start position:0%
+when you subtract them you're getting
+ 
+
+ align:start position:0%
+when you subtract them you're getting
+2/3 minus 4/3 that's negative 2/3
+
+ align:start position:0%
+2/3 minus 4/3 that's negative 2/3
+ 
+
+ align:start position:0%
+2/3 minus 4/3 that's negative 2/3
+divided by 2 so that is another solution
+
+ align:start position:0%
+divided by 2 so that is another solution
+ 
+
+ align:start position:0%
+divided by 2 so that is another solution
+v 1x final
+
+ align:start position:0%
+v 1x final
+ 
+
+ align:start position:0%
+v 1x final
+equals negative one-third b1x initial
+
+ align:start position:0%
+equals negative one-third b1x initial
+ 
+
+ align:start position:0%
+equals negative one-third b1x initial
+now let's think about the meaning of
+
+ align:start position:0%
+now let's think about the meaning of
+ 
+
+ align:start position:0%
+now let's think about the meaning of
+these two possible solutions this
+
+ align:start position:0%
+these two possible solutions this
+ 
+
+ align:start position:0%
+these two possible solutions this
+solution has v 1x final equals V 1 X
+
+ align:start position:0%
+solution has v 1x final equals V 1 X
+ 
+
+ align:start position:0%
+solution has v 1x final equals V 1 X
+initial so that's the initial conditions
+
+ align:start position:0%
+initial so that's the initial conditions
+ 
+
+ align:start position:0%
+initial so that's the initial conditions
+just repeat it and that will always be
+
+ align:start position:0%
+just repeat it and that will always be
+ 
+
+ align:start position:0%
+just repeat it and that will always be
+the case
+
+ align:start position:0%
+the case
+ 
+
+ align:start position:0%
+the case
+one solution will describe the initial
+
+ align:start position:0%
+one solution will describe the initial
+ 
+
+ align:start position:0%
+one solution will describe the initial
+state and the other solution will define
+
+ align:start position:0%
+state and the other solution will define
+ 
+
+ align:start position:0%
+state and the other solution will define
+the final state you can check for
+
+ align:start position:0%
+the final state you can check for
+ 
+
+ align:start position:0%
+the final state you can check for
+yourself that if you just put VX one
+
+ align:start position:0%
+yourself that if you just put VX one
+ 
+
+ align:start position:0%
+yourself that if you just put VX one
+final into this equal to VX one and an
+
+ align:start position:0%
+final into this equal to VX one and an
+ 
+
+ align:start position:0%
+final into this equal to VX one and an
+initial into this momentum equation then
+
+ align:start position:0%
+initial into this momentum equation then
+ 
+
+ align:start position:0%
+initial into this momentum equation then
+V 2 X final is 0 which just repeats the
+
+ align:start position:0%
+V 2 X final is 0 which just repeats the
+ 
+
+ align:start position:0%
+V 2 X final is 0 which just repeats the
+initial conditions so this solution is
+
+ align:start position:0%
+initial conditions so this solution is
+ 
+
+ align:start position:0%
+initial conditions so this solution is
+the initial state and this solution here
+
+ align:start position:0%
+the initial state and this solution here
+ 
+
+ align:start position:0%
+the initial state and this solution here
+is the final state now just to complete
+
+ align:start position:0%
+is the final state now just to complete
+ 
+
+ align:start position:0%
+is the final state now just to complete
+the picture B 2x final well that's equal
+
+ align:start position:0%
+the picture B 2x final well that's equal
+ 
+
+ align:start position:0%
+the picture B 2x final well that's equal
+to 1/2 V 1 X initial minus 1/2 times V 1
+
+ align:start position:0%
+to 1/2 V 1 X initial minus 1/2 times V 1
+ 
+
+ align:start position:0%
+to 1/2 V 1 X initial minus 1/2 times V 1
+X final but V 1 X final is negative 1/3
+
+ align:start position:0%
+X final but V 1 X final is negative 1/3
+ 
+
+ align:start position:0%
+X final but V 1 X final is negative 1/3
+so we have 1/2 minus 1/2 times minus 1/3
+
+ align:start position:0%
+so we have 1/2 minus 1/2 times minus 1/3
+ 
+
+ align:start position:0%
+so we have 1/2 minus 1/2 times minus 1/3
+so that's 1/2 plus 1/6 which is 4 sixths
+
+ align:start position:0%
+so that's 1/2 plus 1/6 which is 4 sixths
+ 
+
+ align:start position:0%
+so that's 1/2 plus 1/6 which is 4 sixths
+or 2/3 DX initial so that's 2/3 the 1 X
+
+ align:start position:0%
+or 2/3 DX initial so that's 2/3 the 1 X
+ 
+
+ align:start position:0%
+or 2/3 DX initial so that's 2/3 the 1 X
+initial and that represents the solution
+
+ align:start position:0%
+initial and that represents the solution
+ 
+
+ align:start position:0%
+initial and that represents the solution
+to this particular problem now of course
+
+ align:start position:0%
+to this particular problem now of course
+ 
+
+ align:start position:0%
+to this particular problem now of course
+what the what you want to do is you want
+
+ align:start position:0%
+what the what you want to do is you want
+ 
+
+ align:start position:0%
+what the what you want to do is you want
+to check we know the momentum condition
+
+ align:start position:0%
+to check we know the momentum condition
+ 
+
+ align:start position:0%
+to check we know the momentum condition
+is already satisfied but just as a check
+
+ align:start position:0%
+is already satisfied but just as a check
+ 
+
+ align:start position:0%
+is already satisfied but just as a check
+you would like to put it into the energy
+
+ align:start position:0%
+you would like to put it into the energy
+ 
+
+ align:start position:0%
+you would like to put it into the energy
+condition just to make sure that when
+
+ align:start position:0%
+condition just to make sure that when
+ 
+
+ align:start position:0%
+condition just to make sure that when
+you square these things out you get the
+
+ align:start position:0%
+you square these things out you get the
+ 
+
+ align:start position:0%
+you square these things out you get the
+right terms however we're very confident
+
+ align:start position:0%
+right terms however we're very confident
+ 
+
+ align:start position:0%
+right terms however we're very confident
+of our result because we've already
+
+ align:start position:0%
+of our result because we've already
+ 
+
+ align:start position:0%
+of our result because we've already
+reproduced the initial conditions and
+
+ align:start position:0%
+reproduced the initial conditions and
+ 
+
+ align:start position:0%
+reproduced the initial conditions and
+that wouldn't happen if we made some
+
+ align:start position:0%
+that wouldn't happen if we made some
+ 
+
+ align:start position:0%
+that wouldn't happen if we made some
+algebraic mistake so that by itself is
+
+ align:start position:0%
+algebraic mistake so that by itself is
+ 
+
+ align:start position:0%
+algebraic mistake so that by itself is
+the sufficient check that this is a
+
+ align:start position:0%
+the sufficient check that this is a
+ 
+
+ align:start position:0%
+the sufficient check that this is a
+correct solution one thing we should sit
+
+ align:start position:0%
+correct solution one thing we should sit
+ 
+
+ align:start position:0%
+correct solution one thing we should sit
+back and think about is that when we use
+
+ align:start position:0%
+back and think about is that when we use
+ 
+
+ align:start position:0%
+back and think about is that when we use
+the energy and momentum that we're
+
+ align:start position:0%
+the energy and momentum that we're
+ 
+
+ align:start position:0%
+the energy and momentum that we're
+inevitably dealing with quadratics and
+
+ align:start position:0%
+inevitably dealing with quadratics and
+ 
+
+ align:start position:0%
+inevitably dealing with quadratics and
+so we expect to use a
+
+ align:start position:0%
+so we expect to use a
+ 
+
+ align:start position:0%
+so we expect to use a
+to solve a quadratic equation at one
+
+ align:start position:0%
+to solve a quadratic equation at one
+ 
+
+ align:start position:0%
+to solve a quadratic equation at one
+point and here was right here now we're
+
+ align:start position:0%
+point and here was right here now we're
+ 
+
+ align:start position:0%
+point and here was right here now we're
+going to find another way to do this
+
+ align:start position:0%
+going to find another way to do this
+ 
+
+ align:start position:0%
+going to find another way to do this
+by linearizing the system which will be
+
+ align:start position:0%
+by linearizing the system which will be
+ 
+
+ align:start position:0%
+by linearizing the system which will be
+a lot easier
\ No newline at end of file
diff --git a/6dQQAn4L24s.txt b/6dQQAn4L24s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e7c04b2618752428d39bd13a408a4ed7be4aafb8
--- /dev/null
+++ b/6dQQAn4L24s.txt
@@ -0,0 +1,12568 @@
+align:start position:0%
+ 
+good morning good afternoon welcome to
+
+ align:start position:0%
+good morning good afternoon welcome to
+ 
+
+ align:start position:0%
+good morning good afternoon welcome to
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+six um today we will be um finishing up
+
+ align:start position:0%
+six um today we will be um finishing up
+ 
+
+ align:start position:0%
+six um today we will be um finishing up
+our discussion of summations that
+
+ align:start position:0%
+our discussion of summations that
+ 
+
+ align:start position:0%
+our discussion of summations that
+binmore started for us last time and
+
+ align:start position:0%
+binmore started for us last time and
+ 
+
+ align:start position:0%
+binmore started for us last time and
+then moving on to uh asymptotic notation
+
+ align:start position:0%
+then moving on to uh asymptotic notation
+ 
+
+ align:start position:0%
+then moving on to uh asymptotic notation
+which is one of the bread and butter
+
+ align:start position:0%
+which is one of the bread and butter
+ 
+
+ align:start position:0%
+which is one of the bread and butter
+topics of algorithm analysis it's a
+
+ align:start position:0%
+topics of algorithm analysis it's a
+ 
+
+ align:start position:0%
+topics of algorithm analysis it's a
+really useful uh language and
+
+ align:start position:0%
+really useful uh language and
+ 
+
+ align:start position:0%
+really useful uh language and
+terminology that we can use to talk
+
+ align:start position:0%
+terminology that we can use to talk
+ 
+
+ align:start position:0%
+terminology that we can use to talk
+about algorithms and compare algorithms
+
+ align:start position:0%
+about algorithms and compare algorithms
+ 
+
+ align:start position:0%
+about algorithms and compare algorithms
+without getting bogged down in all the
+
+ align:start position:0%
+without getting bogged down in all the
+ 
+
+ align:start position:0%
+without getting bogged down in all the
+details but before we do that let's talk
+
+ align:start position:0%
+details but before we do that let's talk
+ 
+
+ align:start position:0%
+details but before we do that let's talk
+about sums and before we do that let's
+
+ align:start position:0%
+about sums and before we do that let's
+ 
+
+ align:start position:0%
+about sums and before we do that let's
+play with
+
+ align:start position:0%
+play with
+ 
+
+ align:start position:0%
+play with
+blocks um so here is a very cool
+
+ align:start position:0%
+blocks um so here is a very cool
+ 
+
+ align:start position:0%
+blocks um so here is a very cool
+question I have a stack of blocks you
+
+ align:start position:0%
+question I have a stack of blocks you
+ 
+
+ align:start position:0%
+question I have a stack of blocks you
+could imagine it's even taller than this
+
+ align:start position:0%
+could imagine it's even taller than this
+ 
+
+ align:start position:0%
+could imagine it's even taller than this
+I just grabbed six for now um and what I
+
+ align:start position:0%
+I just grabbed six for now um and what I
+ 
+
+ align:start position:0%
+I just grabbed six for now um and what I
+want to do is sort of lean them out over
+
+ align:start position:0%
+want to do is sort of lean them out over
+ 
+
+ align:start position:0%
+want to do is sort of lean them out over
+the table and well okay don't want them
+
+ align:start position:0%
+the table and well okay don't want them
+ 
+
+ align:start position:0%
+the table and well okay don't want them
+to fall that's that's Criterion one what
+
+ align:start position:0%
+to fall that's that's Criterion one what
+ 
+
+ align:start position:0%
+to fall that's that's Criterion one what
+I'm hoping for is to get this top block
+
+ align:start position:0%
+I'm hoping for is to get this top block
+ 
+
+ align:start position:0%
+I'm hoping for is to get this top block
+all the way off of this table um so none
+
+ align:start position:0%
+all the way off of this table um so none
+ 
+
+ align:start position:0%
+all the way off of this table um so none
+of the block is over the table so
+
+ align:start position:0%
+of the block is over the table so
+ 
+
+ align:start position:0%
+of the block is over the table so
+currently I'm not quite there we can see
+
+ align:start position:0%
+currently I'm not quite there we can see
+ 
+
+ align:start position:0%
+currently I'm not quite there we can see
+there's like an inch half an inch left
+
+ align:start position:0%
+there's like an inch half an inch left
+ 
+
+ align:start position:0%
+there's like an inch half an inch left
+um so seems possible maybe um so the
+
+ align:start position:0%
+um so seems possible maybe um so the
+ 
+
+ align:start position:0%
+um so seems possible maybe um so the
+rules are we can only have one block per
+
+ align:start position:0%
+rules are we can only have one block per
+ 
+
+ align:start position:0%
+rules are we can only have one block per
+layer we can't double up we can't do
+
+ align:start position:0%
+layer we can't double up we can't do
+ 
+
+ align:start position:0%
+layer we can't double up we can't do
+weird angles and whatnot it's just slide
+
+ align:start position:0%
+weird angles and whatnot it's just slide
+ 
+
+ align:start position:0%
+weird angles and whatnot it's just slide
+these left and right until you're happy
+
+ align:start position:0%
+these left and right until you're happy
+ 
+
+ align:start position:0%
+these left and right until you're happy
+and hopefully it doesn't fall um are we
+
+ align:start position:0%
+and hopefully it doesn't fall um are we
+ 
+
+ align:start position:0%
+and hopefully it doesn't fall um are we
+clear on the game nice who thinks it's
+
+ align:start position:0%
+clear on the game nice who thinks it's
+ 
+
+ align:start position:0%
+clear on the game nice who thinks it's
+possible raise your hand who thinks it's
+
+ align:start position:0%
+possible raise your hand who thinks it's
+ 
+
+ align:start position:0%
+possible raise your hand who thinks it's
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+possible all right well let's try
+
+ align:start position:0%
+possible all right well let's try
+ 
+
+ align:start position:0%
+possible all right well let's try
+hopefully I don't hurt myself um all
+
+ align:start position:0%
+hopefully I don't hurt myself um all
+ 
+
+ align:start position:0%
+hopefully I don't hurt myself um all
+right so I'm going to follow a nice
+
+ align:start position:0%
+right so I'm going to follow a nice
+ 
+
+ align:start position:0%
+right so I'm going to follow a nice
+greedy strategy so I'm going to start
+
+ align:start position:0%
+greedy strategy so I'm going to start
+ 
+
+ align:start position:0%
+greedy strategy so I'm going to start
+from the top and then I'm just going to
+
+ align:start position:0%
+from the top and then I'm just going to
+ 
+
+ align:start position:0%
+from the top and then I'm just going to
+keep sliding left as much as I can until
+
+ align:start position:0%
+keep sliding left as much as I can until
+ 
+
+ align:start position:0%
+keep sliding left as much as I can until
+it's about to fall over so if I go past
+
+ align:start position:0%
+it's about to fall over so if I go past
+ 
+
+ align:start position:0%
+it's about to fall over so if I go past
+the center of mass it's going to fall
+
+ align:start position:0%
+the center of mass it's going to fall
+ 
+
+ align:start position:0%
+the center of mass it's going to fall
+over so I'm going to go right up until
+
+ align:start position:0%
+over so I'm going to go right up until
+ 
+
+ align:start position:0%
+over so I'm going to go right up until
+that edge and stop and don't worry about
+
+ align:start position:0%
+that edge and stop and don't worry about
+ 
+
+ align:start position:0%
+that edge and stop and don't worry about
+the physics we're not here to talk about
+
+ align:start position:0%
+the physics we're not here to talk about
+ 
+
+ align:start position:0%
+the physics we're not here to talk about
+physics um but I'm going to do the same
+
+ align:start position:0%
+physics um but I'm going to do the same
+ 
+
+ align:start position:0%
+physics um but I'm going to do the same
+so let's freeze the top two layers and
+
+ align:start position:0%
+so let's freeze the top two layers and
+ 
+
+ align:start position:0%
+so let's freeze the top two layers and
+try again let's slide this over until
+
+ align:start position:0%
+try again let's slide this over until
+ 
+
+ align:start position:0%
+try again let's slide this over until
+it's just about to fall it feels right
+
+ align:start position:0%
+it's just about to fall it feels right
+ 
+
+ align:start position:0%
+it's just about to fall it feels right
+around there all right let's keep
+
+ align:start position:0%
+around there all right let's keep
+ 
+
+ align:start position:0%
+around there all right let's keep
+going all
+
+ align:start position:0%
+going all
+ 
+
+ align:start position:0%
+going all
+right yep okay it leaned a little bit
+
+ align:start position:0%
+right yep okay it leaned a little bit
+ 
+
+ align:start position:0%
+right yep okay it leaned a little bit
+I'm getting worried but we'll make it
+
+ align:start position:0%
+I'm getting worried but we'll make it
+ 
+
+ align:start position:0%
+I'm getting worried but we'll make it
+work let's see uh
+
+ align:start position:0%
+work let's see uh
+ 
+
+ align:start position:0%
+work let's see uh
+yeah okay and I think I might already be
+
+ align:start position:0%
+yeah okay and I think I might already be
+ 
+
+ align:start position:0%
+yeah okay and I think I might already be
+off the table which was my goal but
+
+ align:start position:0%
+off the table which was my goal but
+ 
+
+ align:start position:0%
+off the table which was my goal but
+let's let's go a little further why not
+
+ align:start position:0%
+let's let's go a little further why not
+ 
+
+ align:start position:0%
+let's let's go a little further why not
+uh yes okay and
+
+ align:start position:0%
+uh yes okay and
+ 
+
+ align:start position:0%
+uh yes okay and
+finally right around okay that's as far
+
+ align:start position:0%
+finally right around okay that's as far
+ 
+
+ align:start position:0%
+finally right around okay that's as far
+as I'm willing to go I
+
+ align:start position:0%
+as I'm willing to go I
+ 
+
+ align:start position:0%
+as I'm willing to go I
+think that is off the
+
+ align:start position:0%
+think that is off the
+ 
+
+ align:start position:0%
+think that is off the
+table it's possible yes thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I cheated I put little marks on the back
+
+ align:start position:0%
+I cheated I put little marks on the back
+ 
+
+ align:start position:0%
+I cheated I put little marks on the back
+so I knew how far to
+
+ align:start position:0%
+so I knew how far to
+ 
+
+ align:start position:0%
+so I knew how far to
+go um but it is possible and now we can
+
+ align:start position:0%
+go um but it is possible and now we can
+ 
+
+ align:start position:0%
+go um but it is possible and now we can
+raise the question how far can we go can
+
+ align:start position:0%
+raise the question how far can we go can
+ 
+
+ align:start position:0%
+raise the question how far can we go can
+we get two lengths out here's what that
+
+ align:start position:0%
+we get two lengths out here's what that
+ 
+
+ align:start position:0%
+we get two lengths out here's what that
+would look like two lengths out can we
+
+ align:start position:0%
+would look like two lengths out can we
+ 
+
+ align:start position:0%
+would look like two lengths out can we
+get five lengths out 10 lengths out
+
+ align:start position:0%
+get five lengths out 10 lengths out
+ 
+
+ align:start position:0%
+get five lengths out 10 lengths out
+let's stop at 10 who thinks we can get
+
+ align:start position:0%
+let's stop at 10 who thinks we can get
+ 
+
+ align:start position:0%
+let's stop at 10 who thinks we can get
+10 lengths out over the table who thinks
+
+ align:start position:0%
+10 lengths out over the table who thinks
+ 
+
+ align:start position:0%
+10 lengths out over the table who thinks
+10 is possible who thinks 10 is not
+
+ align:start position:0%
+10 is possible who thinks 10 is not
+ 
+
+ align:start position:0%
+10 is possible who thinks 10 is not
+possible all right you're both right
+
+ align:start position:0%
+possible all right you're both right
+ 
+
+ align:start position:0%
+possible all right you're both right
+um I'll explain why in a second uh let's
+
+ align:start position:0%
+um I'll explain why in a second uh let's
+ 
+
+ align:start position:0%
+um I'll explain why in a second uh let's
+not have an accident during lecture
+
+ align:start position:0%
+not have an accident during lecture
+ 
+
+ align:start position:0%
+not have an accident during lecture
+there we go so turns out I'm not going
+
+ align:start position:0%
+there we go so turns out I'm not going
+ 
+
+ align:start position:0%
+there we go so turns out I'm not going
+to prove this now but turns out that
+
+ align:start position:0%
+to prove this now but turns out that
+ 
+
+ align:start position:0%
+to prove this now but turns out that
+greedy strategy I just used is the best
+
+ align:start position:0%
+greedy strategy I just used is the best
+ 
+
+ align:start position:0%
+greedy strategy I just used is the best
+you can do uh it's not too hard to prove
+
+ align:start position:0%
+you can do uh it's not too hard to prove
+ 
+
+ align:start position:0%
+you can do uh it's not too hard to prove
+it's in the textbook if you're curious
+
+ align:start position:0%
+it's in the textbook if you're curious
+ 
+
+ align:start position:0%
+it's in the textbook if you're curious
+um but let me tell you what that greedy
+
+ align:start position:0%
+um but let me tell you what that greedy
+ 
+
+ align:start position:0%
+um but let me tell you what that greedy
+strategy ends up looking like um if I
+
+ align:start position:0%
+strategy ends up looking like um if I
+ 
+
+ align:start position:0%
+strategy ends up looking like um if I
+have some chalk here we
+
+ align:start position:0%
+have some chalk here we
+ 
+
+ align:start position:0%
+have some chalk here we
+go so as you might imagine this first
+
+ align:start position:0%
+go so as you might imagine this first
+ 
+
+ align:start position:0%
+go so as you might imagine this first
+block sticks out half a unit over the
+
+ align:start position:0%
+block sticks out half a unit over the
+ 
+
+ align:start position:0%
+block sticks out half a unit over the
+next block so its Center of mass is
+
+ align:start position:0%
+next block so its Center of mass is
+ 
+
+ align:start position:0%
+next block so its Center of mass is
+right here on the edge um by the way I'm
+
+ align:start position:0%
+right here on the edge um by the way I'm
+ 
+
+ align:start position:0%
+right here on the edge um by the way I'm
+I'm imagining these blocks are one unit
+
+ align:start position:0%
+I'm imagining these blocks are one unit
+ 
+
+ align:start position:0%
+I'm imagining these blocks are one unit
+wide um the next one right here that's a
+
+ align:start position:0%
+wide um the next one right here that's a
+ 
+
+ align:start position:0%
+wide um the next one right here that's a
+quarter unit because that's what it
+
+ align:start position:0%
+quarter unit because that's what it
+ 
+
+ align:start position:0%
+quarter unit because that's what it
+takes to put the center of mass of these
+
+ align:start position:0%
+takes to put the center of mass of these
+ 
+
+ align:start position:0%
+takes to put the center of mass of these
+two blocks combined right over the edge
+
+ align:start position:0%
+two blocks combined right over the edge
+ 
+
+ align:start position:0%
+two blocks combined right over the edge
+of the third block turns out this right
+
+ align:start position:0%
+of the third block turns out this right
+ 
+
+ align:start position:0%
+of the third block turns out this right
+here is a sixth this right here is an
+
+ align:start position:0%
+here is a sixth this right here is an
+ 
+
+ align:start position:0%
+here is a sixth this right here is an
+eighth and all the way down until the
+
+ align:start position:0%
+eighth and all the way down until the
+ 
+
+ align:start position:0%
+eighth and all the way down until the
+very n until the the it is the the very
+
+ align:start position:0%
+very n until the the it is the the very
+ 
+
+ align:start position:0%
+very n until the the it is the the very
+n the nth
+
+ align:start position:0%
+n the nth
+ 
+
+ align:start position:0%
+n the nth
+block has a gap of 1 over 2 N so this is
+
+ align:start position:0%
+block has a gap of 1 over 2 N so this is
+ 
+
+ align:start position:0%
+block has a gap of 1 over 2 N so this is
+block 1 2 3 four five all the way to n
+
+ align:start position:0%
+block 1 2 3 four five all the way to n
+ 
+
+ align:start position:0%
+block 1 2 3 four five all the way to n
+turns out this is the best you can do
+
+ align:start position:0%
+turns out this is the best you can do
+ 
+
+ align:start position:0%
+turns out this is the best you can do
+which means the distance you can get
+
+ align:start position:0%
+which means the distance you can get
+ 
+
+ align:start position:0%
+which means the distance you can get
+with n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+blocks is 12 plus a 4 plus a 6 up to 1
+
+ align:start position:0%
+blocks is 12 plus a 4 plus a 6 up to 1
+ 
+
+ align:start position:0%
+blocks is 12 plus a 4 plus a 6 up to 1
+over 2
+
+ align:start position:0%
+over 2
+ 
+
+ align:start position:0%
+over 2
+N which let's factor out the 1/2 just
+
+ align:start position:0%
+N which let's factor out the 1/2 just
+ 
+
+ align:start position:0%
+N which let's factor out the 1/2 just
+because that's cleaner that's the sum K
+
+ align:start position:0%
+because that's cleaner that's the sum K
+ 
+
+ align:start position:0%
+because that's cleaner that's the sum K
+= 1 to n of 1 over
+
+ align:start position:0%
+= 1 to n of 1 over
+ 
+
+ align:start position:0%
+= 1 to n of 1 over
+K this is also known as 1 12
+
+ align:start position:0%
+K this is also known as 1 12
+ 
+
+ align:start position:0%
+K this is also known as 1 12
+time the N harmonic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+harmonic
+
+ align:start position:0%
+harmonic
+ 
+
+ align:start position:0%
+harmonic
+number this is a standard name for this
+
+ align:start position:0%
+number this is a standard name for this
+ 
+
+ align:start position:0%
+number this is a standard name for this
+sum 1 plus a half plus a thir plus a 4th
+
+ align:start position:0%
+sum 1 plus a half plus a thir plus a 4th
+ 
+
+ align:start position:0%
+sum 1 plus a half plus a thir plus a 4th
+up to 1/
+
+ align:start position:0%
+up to 1/
+ 
+
+ align:start position:0%
+up to 1/
+n um and half of that is exactly as far
+
+ align:start position:0%
+n um and half of that is exactly as far
+ 
+
+ align:start position:0%
+n um and half of that is exactly as far
+as we can get with n
+
+ align:start position:0%
+as we can get with n
+ 
+
+ align:start position:0%
+as we can get with n
+blocks right so now the question is how
+
+ align:start position:0%
+blocks right so now the question is how
+ 
+
+ align:start position:0%
+blocks right so now the question is how
+how big does this get if I have a
+
+ align:start position:0%
+how big does this get if I have a
+ 
+
+ align:start position:0%
+how big does this get if I have a
+thousand blocks how far can I get if I
+
+ align:start position:0%
+thousand blocks how far can I get if I
+ 
+
+ align:start position:0%
+thousand blocks how far can I get if I
+have a million blocks if I have an
+
+ align:start position:0%
+have a million blocks if I have an
+ 
+
+ align:start position:0%
+have a million blocks if I have an
+unlimited number of blocks how far can I
+
+ align:start position:0%
+unlimited number of blocks how far can I
+ 
+
+ align:start position:0%
+unlimited number of blocks how far can I
+get which means we're asking about this
+
+ align:start position:0%
+get which means we're asking about this
+ 
+
+ align:start position:0%
+get which means we're asking about this
+sum this harmonic number I want to know
+
+ align:start position:0%
+sum this harmonic number I want to know
+ 
+
+ align:start position:0%
+sum this harmonic number I want to know
+about that sum do we have a closed form
+
+ align:start position:0%
+about that sum do we have a closed form
+ 
+
+ align:start position:0%
+about that sum do we have a closed form
+for it no not
+
+ align:start position:0%
+for it no not
+ 
+
+ align:start position:0%
+for it no not
+really but as we saw last time we don't
+
+ align:start position:0%
+really but as we saw last time we don't
+ 
+
+ align:start position:0%
+really but as we saw last time we don't
+especially need a closed form if all we
+
+ align:start position:0%
+especially need a closed form if all we
+ 
+
+ align:start position:0%
+especially need a closed form if all we
+care about is approximation so let's
+
+ align:start position:0%
+care about is approximation so let's
+ 
+
+ align:start position:0%
+care about is approximation so let's
+approximate that sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have our sum hn which is defined
+
+ align:start position:0%
+so we have our sum hn which is defined
+ 
+
+ align:start position:0%
+so we have our sum hn which is defined
+as the sum of the first n
+
+ align:start position:0%
+as the sum of the first n
+ 
+
+ align:start position:0%
+as the sum of the first n
+reciprocals and we want to approximate
+
+ align:start position:0%
+reciprocals and we want to approximate
+ 
+
+ align:start position:0%
+reciprocals and we want to approximate
+it and can someone remind me what tool
+
+ align:start position:0%
+it and can someone remind me what tool
+ 
+
+ align:start position:0%
+it and can someone remind me what tool
+we have to approximate sums like
+
+ align:start position:0%
+we have to approximate sums like
+ 
+
+ align:start position:0%
+we have to approximate sums like
+this yes the integral method absolutely
+
+ align:start position:0%
+this yes the integral method absolutely
+ 
+
+ align:start position:0%
+this yes the integral method absolutely
+so this function 1/x is a decreasing
+
+ align:start position:0%
+so this function 1/x is a decreasing
+ 
+
+ align:start position:0%
+so this function 1/x is a decreasing
+function and so we have our integral
+
+ align:start position:0%
+function and so we have our integral
+ 
+
+ align:start position:0%
+function and so we have our integral
+method our integral bound that says that
+
+ align:start position:0%
+method our integral bound that says that
+ 
+
+ align:start position:0%
+method our integral bound that says that
+sum
+
+ align:start position:0%
+sum
+ 
+
+ align:start position:0%
+sum
+hn is between the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral plus the last term in this case
+
+ align:start position:0%
+integral plus the last term in this case
+ 
+
+ align:start position:0%
+integral plus the last term in this case
+the last term is sorry plus the first
+
+ align:start position:0%
+the last term is sorry plus the first
+ 
+
+ align:start position:0%
+the last term is sorry plus the first
+term
+
+ align:start position:0%
+term
+ 
+
+ align:start position:0%
+term
+one and the integral 1 to n of 1x DX
+
+ align:start position:0%
+one and the integral 1 to n of 1x DX
+ 
+
+ align:start position:0%
+one and the integral 1 to n of 1x DX
+plus the last term which is 1
+
+ align:start position:0%
+plus the last term which is 1
+ 
+
+ align:start position:0%
+plus the last term which is 1
+n so this bound is integral plus F of n
+
+ align:start position:0%
+n so this bound is integral plus F of n
+ 
+
+ align:start position:0%
+n so this bound is integral plus F of n
+less equal to the sum is less equal to
+
+ align:start position:0%
+less equal to the sum is less equal to
+ 
+
+ align:start position:0%
+less equal to the sum is less equal to
+the integral plus F of
+
+ align:start position:0%
+the integral plus F of
+ 
+
+ align:start position:0%
+the integral plus F of
+one and I claim this bound is really
+
+ align:start position:0%
+one and I claim this bound is really
+ 
+
+ align:start position:0%
+one and I claim this bound is really
+easy to remember um like I plus FN I
+
+ align:start position:0%
+easy to remember um like I plus FN I
+ 
+
+ align:start position:0%
+easy to remember um like I plus FN I
+plus F1 are pretty simple things and
+
+ align:start position:0%
+plus F1 are pretty simple things and
+ 
+
+ align:start position:0%
+plus F1 are pretty simple things and
+also if you if if you're dealing with an
+
+ align:start position:0%
+also if you if if you're dealing with an
+ 
+
+ align:start position:0%
+also if you if if you're dealing with an
+increasing function instead of a
+
+ align:start position:0%
+increasing function instead of a
+ 
+
+ align:start position:0%
+increasing function instead of a
+decreasing function it's the same two
+
+ align:start position:0%
+decreasing function it's the same two
+ 
+
+ align:start position:0%
+decreasing function it's the same two
+bounds but they're on the other side
+
+ align:start position:0%
+bounds but they're on the other side
+ 
+
+ align:start position:0%
+bounds but they're on the other side
+just because if it's increasing then FN
+
+ align:start position:0%
+just because if it's increasing then FN
+ 
+
+ align:start position:0%
+just because if it's increasing then FN
+is going to be bigger than F1 so
+
+ align:start position:0%
+is going to be bigger than F1 so
+ 
+
+ align:start position:0%
+is going to be bigger than F1 so
+certainly FN should be on the bigger
+
+ align:start position:0%
+certainly FN should be on the bigger
+ 
+
+ align:start position:0%
+certainly FN should be on the bigger
+side but this is a really clean bound um
+
+ align:start position:0%
+side but this is a really clean bound um
+ 
+
+ align:start position:0%
+side but this is a really clean bound um
+and and we can write out what this what
+
+ align:start position:0%
+and and we can write out what this what
+ 
+
+ align:start position:0%
+and and we can write out what this what
+this says integral from one of 1 /x DX
+
+ align:start position:0%
+this says integral from one of 1 /x DX
+ 
+
+ align:start position:0%
+this says integral from one of 1 /x DX
+from 1 to n that's Ln of n let's assume
+
+ align:start position:0%
+from 1 to n that's Ln of n let's assume
+ 
+
+ align:start position:0%
+from 1 to n that's Ln of n let's assume
+we can do that um without writing it
+
+ align:start position:0%
+we can do that um without writing it
+ 
+
+ align:start position:0%
+we can do that um without writing it
+down I you don't want to see me
+
+ align:start position:0%
+down I you don't want to see me
+ 
+
+ align:start position:0%
+down I you don't want to see me
+integrate live that will go
+
+ align:start position:0%
+integrate live that will go
+ 
+
+ align:start position:0%
+integrate live that will go
+poorly um but what this says is that um
+
+ align:start position:0%
+poorly um but what this says is that um
+ 
+
+ align:start position:0%
+poorly um but what this says is that um
+Ln of n + 1 n is less equal to hn is
+
+ align:start position:0%
+Ln of n + 1 n is less equal to hn is
+ 
+
+ align:start position:0%
+Ln of n + 1 n is less equal to hn is
+less equal to Ln of
+
+ align:start position:0%
+less equal to Ln of
+ 
+
+ align:start position:0%
+less equal to Ln of
+n + one
+
+ align:start position:0%
+n + one
+ 
+
+ align:start position:0%
+n + one
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right which is a pretty nice
+
+ align:start position:0%
+right which is a pretty nice
+ 
+
+ align:start position:0%
+right which is a pretty nice
+bound um but we're really interested
+
+ align:start position:0%
+bound um but we're really interested
+ 
+
+ align:start position:0%
+bound um but we're really interested
+in well first let's answer our question
+
+ align:start position:0%
+in well first let's answer our question
+ 
+
+ align:start position:0%
+in well first let's answer our question
+um if we want to get 10 blocks out then
+
+ align:start position:0%
+um if we want to get 10 blocks out then
+ 
+
+ align:start position:0%
+um if we want to get 10 blocks out then
+we're asking for hn to be about
+
+ align:start position:0%
+we're asking for hn to be about
+ 
+
+ align:start position:0%
+we're asking for hn to be about
+20 which means we're asking for these
+
+ align:start position:0%
+20 which means we're asking for these
+ 
+
+ align:start position:0%
+20 which means we're asking for these
+bounds these bounds are kind of
+
+ align:start position:0%
+bounds these bounds are kind of
+ 
+
+ align:start position:0%
+bounds these bounds are kind of
+basically Ln of n right the one over n
+
+ align:start position:0%
+basically Ln of n right the one over n
+ 
+
+ align:start position:0%
+basically Ln of n right the one over n
+and and the one don't affect things all
+
+ align:start position:0%
+and and the one don't affect things all
+ 
+
+ align:start position:0%
+and and the one don't affect things all
+that much so really hn is basically Ln
+
+ align:start position:0%
+that much so really hn is basically Ln
+ 
+
+ align:start position:0%
+that much so really hn is basically Ln
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+n yeah this is I'm being imprecise here
+
+ align:start position:0%
+n yeah this is I'm being imprecise here
+ 
+
+ align:start position:0%
+n yeah this is I'm being imprecise here
+but we'll be more precise about it in a
+
+ align:start position:0%
+but we'll be more precise about it in a
+ 
+
+ align:start position:0%
+but we'll be more precise about it in a
+bit but for now it's about Ln of n which
+
+ align:start position:0%
+bit but for now it's about Ln of n which
+ 
+
+ align:start position:0%
+bit but for now it's about Ln of n which
+means to get 10 blocks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out we need hn equals 20 because the
+
+ align:start position:0%
+out we need hn equals 20 because the
+ 
+
+ align:start position:0%
+out we need hn equals 20 because the
+distance was half hn uh which means we
+
+ align:start position:0%
+distance was half hn uh which means we
+ 
+
+ align:start position:0%
+distance was half hn uh which means we
+need n is approximately e to the
+
+ align:start position:0%
+need n is approximately e to the
+ 
+
+ align:start position:0%
+need n is approximately e to the
+20 we need that many
+
+ align:start position:0%
+20 we need that many
+ 
+
+ align:start position:0%
+20 we need that many
+blocks uh we need about four 400 billion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+blocks to get 10 blocks away from the
+
+ align:start position:0%
+blocks to get 10 blocks away from the
+ 
+
+ align:start position:0%
+blocks to get 10 blocks away from the
+table um each one is about an inch and a
+
+ align:start position:0%
+table um each one is about an inch and a
+ 
+
+ align:start position:0%
+table um each one is about an inch and a
+half thick so that gets us to carry the
+
+ align:start position:0%
+half thick so that gets us to carry the
+ 
+
+ align:start position:0%
+half thick so that gets us to carry the
+one 40 times the distance to the
+
+ align:start position:0%
+one 40 times the distance to the
+ 
+
+ align:start position:0%
+one 40 times the distance to the
+Moon um probably going to run into some
+
+ align:start position:0%
+Moon um probably going to run into some
+ 
+
+ align:start position:0%
+Moon um probably going to run into some
+other issues before you're able to stack
+
+ align:start position:0%
+other issues before you're able to stack
+ 
+
+ align:start position:0%
+other issues before you're able to stack
+something that tall um so mathematically
+
+ align:start position:0%
+something that tall um so mathematically
+ 
+
+ align:start position:0%
+something that tall um so mathematically
+yes we can get 10 blocks over the table
+
+ align:start position:0%
+yes we can get 10 blocks over the table
+ 
+
+ align:start position:0%
+yes we can get 10 blocks over the table
+physically not so much that's why you're
+
+ align:start position:0%
+physically not so much that's why you're
+ 
+
+ align:start position:0%
+physically not so much that's why you're
+both right
+
+ align:start position:0%
+both right
+ 
+
+ align:start position:0%
+both right
+um but all of this was really an excuse
+
+ align:start position:0%
+um but all of this was really an excuse
+ 
+
+ align:start position:0%
+um but all of this was really an excuse
+to get us here hn is approximately Ln of
+
+ align:start position:0%
+to get us here hn is approximately Ln of
+ 
+
+ align:start position:0%
+to get us here hn is approximately Ln of
+n plus some smaller
+
+ align:start position:0%
+n plus some smaller
+ 
+
+ align:start position:0%
+n plus some smaller
+terms um and let's try to make that a
+
+ align:start position:0%
+terms um and let's try to make that a
+ 
+
+ align:start position:0%
+terms um and let's try to make that a
+little more precise what do we mean by
+
+ align:start position:0%
+little more precise what do we mean by
+ 
+
+ align:start position:0%
+little more precise what do we mean by
+that what do we mean by hn is
+
+ align:start position:0%
+that what do we mean by hn is
+ 
+
+ align:start position:0%
+that what do we mean by hn is
+approximately Ln of n well let me give
+
+ align:start position:0%
+approximately Ln of n well let me give
+ 
+
+ align:start position:0%
+approximately Ln of n well let me give
+us a definition
+
+ align:start position:0%
+us a definition
+ 
+
+ align:start position:0%
+us a definition
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's write that F of n that's a Tilda F
+
+ align:start position:0%
+let's write that F of n that's a Tilda F
+ 
+
+ align:start position:0%
+let's write that F of n that's a Tilda F
+of n is Tia of G of n so this
+
+ align:start position:0%
+of n is Tia of G of n so this
+ 
+
+ align:start position:0%
+of n is Tia of G of n so this
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+asymptotically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equivalent so f and g are ASM totically
+
+ align:start position:0%
+equivalent so f and g are ASM totically
+ 
+
+ align:start position:0%
+equivalent so f and g are ASM totically
+equivalent if and only if the
+
+ align:start position:0%
+equivalent if and only if the
+ 
+
+ align:start position:0%
+equivalent if and only if the
+limit of FN over G of n as n goes to
+
+ align:start position:0%
+limit of FN over G of n as n goes to
+ 
+
+ align:start position:0%
+limit of FN over G of n as n goes to
+Infinity
+
+ align:start position:0%
+Infinity
+ 
+
+ align:start position:0%
+Infinity
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+one if you divide them and get a limit
+
+ align:start position:0%
+one if you divide them and get a limit
+ 
+
+ align:start position:0%
+one if you divide them and get a limit
+of one then these functions are ASM
+
+ align:start position:0%
+of one then these functions are ASM
+ 
+
+ align:start position:0%
+of one then these functions are ASM
+totically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equivalent and in this case well we have
+
+ align:start position:0%
+equivalent and in this case well we have
+ 
+
+ align:start position:0%
+equivalent and in this case well we have
+these nice bounds on
+
+ align:start position:0%
+these nice bounds on
+ 
+
+ align:start position:0%
+these nice bounds on
+hn well let's take that inequality let's
+
+ align:start position:0%
+hn well let's take that inequality let's
+ 
+
+ align:start position:0%
+hn well let's take that inequality let's
+divide all three sides U by Ln of n what
+
+ align:start position:0%
+divide all three sides U by Ln of n what
+ 
+
+ align:start position:0%
+divide all three sides U by Ln of n what
+are we going to get we're going to get 1
+
+ align:start position:0%
+are we going to get we're going to get 1
+ 
+
+ align:start position:0%
+are we going to get we're going to get 1
++ 1 over n Ln of n is less equal to hn
+
+ align:start position:0%
++ 1 over n Ln of n is less equal to hn
+ 
+
+ align:start position:0%
++ 1 over n Ln of n is less equal to hn
+over Ln of n is less equal to 1 + 1 / Ln
+
+ align:start position:0%
+over Ln of n is less equal to 1 + 1 / Ln
+ 
+
+ align:start position:0%
+over Ln of n is less equal to 1 + 1 / Ln
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+N and as we take the limit as n goes to
+
+ align:start position:0%
+N and as we take the limit as n goes to
+ 
+
+ align:start position:0%
+N and as we take the limit as n goes to
+Infinity the left side looks like one
+
+ align:start position:0%
+Infinity the left side looks like one
+ 
+
+ align:start position:0%
+Infinity the left side looks like one
+this thing in the denominator gets big
+
+ align:start position:0%
+this thing in the denominator gets big
+ 
+
+ align:start position:0%
+this thing in the denominator gets big
+so one over that gets small the left
+
+ align:start position:0%
+so one over that gets small the left
+ 
+
+ align:start position:0%
+so one over that gets small the left
+side goes to
+
+ align:start position:0%
+side goes to
+ 
+
+ align:start position:0%
+side goes to
+one limb n goes to Infinity of hn over
+
+ align:start position:0%
+one limb n goes to Infinity of hn over
+ 
+
+ align:start position:0%
+one limb n goes to Infinity of hn over
+Ln of N and on the right side we have
+
+ align:start position:0%
+Ln of N and on the right side we have
+ 
+
+ align:start position:0%
+Ln of N and on the right side we have
+one plus something that goes to zero cuz
+
+ align:start position:0%
+one plus something that goes to zero cuz
+ 
+
+ align:start position:0%
+one plus something that goes to zero cuz
+that denominator gets arbitrarily
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+big so the limit equals
+
+ align:start position:0%
+big so the limit equals
+ 
+
+ align:start position:0%
+big so the limit equals
+one I learned this in high school as the
+
+ align:start position:0%
+one I learned this in high school as the
+ 
+
+ align:start position:0%
+one I learned this in high school as the
+squeeze theorem if you can bound your
+
+ align:start position:0%
+squeeze theorem if you can bound your
+ 
+
+ align:start position:0%
+squeeze theorem if you can bound your
+limit between two things that are the
+
+ align:start position:0%
+limit between two things that are the
+ 
+
+ align:start position:0%
+limit between two things that are the
+same then the limit is that thing um but
+
+ align:start position:0%
+same then the limit is that thing um but
+ 
+
+ align:start position:0%
+same then the limit is that thing um but
+what we've concluded here is that hn
+
+ align:start position:0%
+what we've concluded here is that hn
+ 
+
+ align:start position:0%
+what we've concluded here is that hn
+ided Ln of n limits to one as n goes to
+
+ align:start position:0%
+ided Ln of n limits to one as n goes to
+ 
+
+ align:start position:0%
+ided Ln of n limits to one as n goes to
+infinity and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+therefore uh sorry hn over Ln of n
+
+ align:start position:0%
+therefore uh sorry hn over Ln of n
+ 
+
+ align:start position:0%
+therefore uh sorry hn over Ln of n
+equals 1 which implies that hn is ASM
+
+ align:start position:0%
+equals 1 which implies that hn is ASM
+ 
+
+ align:start position:0%
+equals 1 which implies that hn is ASM
+totically
+
+ align:start position:0%
+totically
+ 
+
+ align:start position:0%
+totically
+equivalent to Ln of
+
+ align:start position:0%
+equivalent to Ln of
+ 
+
+ align:start position:0%
+equivalent to Ln of
+n so when I wrote approximately Ln of n
+
+ align:start position:0%
+n so when I wrote approximately Ln of n
+ 
+
+ align:start position:0%
+n so when I wrote approximately Ln of n
+up there probably what I meant was this
+
+ align:start position:0%
+up there probably what I meant was this
+ 
+
+ align:start position:0%
+up there probably what I meant was this
+much more precise thing that these are
+
+ align:start position:0%
+much more precise thing that these are
+ 
+
+ align:start position:0%
+much more precise thing that these are
+approximately equal in the sense that
+
+ align:start position:0%
+approximately equal in the sense that
+ 
+
+ align:start position:0%
+approximately equal in the sense that
+their ratio limits to one does that make
+
+ align:start position:0%
+their ratio limits to one does that make
+ 
+
+ align:start position:0%
+their ratio limits to one does that make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+nice all
+
+ align:start position:0%
+nice all
+ 
+
+ align:start position:0%
+nice all
+right um
+
+ align:start position:0%
+right um
+ 
+
+ align:start position:0%
+right um
+now before moving on to ASM totic fully
+
+ align:start position:0%
+now before moving on to ASM totic fully
+ 
+
+ align:start position:0%
+now before moving on to ASM totic fully
+uh there's one other topic in summations
+
+ align:start position:0%
+uh there's one other topic in summations
+ 
+
+ align:start position:0%
+uh there's one other topic in summations
+that I want to talk about which is not
+
+ align:start position:0%
+that I want to talk about which is not
+ 
+
+ align:start position:0%
+that I want to talk about which is not
+summations at all but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+products um and really what I want to
+
+ align:start position:0%
+products um and really what I want to
+ 
+
+ align:start position:0%
+products um and really what I want to
+say about products is that often you can
+
+ align:start position:0%
+say about products is that often you can
+ 
+
+ align:start position:0%
+say about products is that often you can
+analyze products as if they were
+
+ align:start position:0%
+analyze products as if they were
+ 
+
+ align:start position:0%
+analyze products as if they were
+sums turn into
+
+ align:start position:0%
+sums turn into
+ 
+
+ align:start position:0%
+sums turn into
+sums for example if we care about n
+
+ align:start position:0%
+sums for example if we care about n
+ 
+
+ align:start position:0%
+sums for example if we care about n
+factorial
+
+ align:start position:0%
+factorial
+ 
+
+ align:start position:0%
+factorial
+which is uh here 1 * 2 * 3 all the way
+
+ align:start position:0%
+which is uh here 1 * 2 * 3 all the way
+ 
+
+ align:start position:0%
+which is uh here 1 * 2 * 3 all the way
+up to
+
+ align:start position:0%
+up to
+ 
+
+ align:start position:0%
+up to
+n who can tell me how to turn this into
+
+ align:start position:0%
+n who can tell me how to turn this into
+ 
+
+ align:start position:0%
+n who can tell me how to turn this into
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum it's something written on this
+
+ align:start position:0%
+sum it's something written on this
+ 
+
+ align:start position:0%
+sum it's something written on this
+board
+
+ align:start position:0%
+board
+ 
+
+ align:start position:0%
+board
+yes yeah take logs perfect what happens
+
+ align:start position:0%
+yes yeah take logs perfect what happens
+ 
+
+ align:start position:0%
+yes yeah take logs perfect what happens
+if we take the log of both
+
+ align:start position:0%
+if we take the log of both
+ 
+
+ align:start position:0%
+if we take the log of both
+sides so log of n factorial uh here
+
+ align:start position:0%
+sides so log of n factorial uh here
+ 
+
+ align:start position:0%
+sides so log of n factorial uh here
+let's let's be precise we'll call it Ln
+
+ align:start position:0%
+let's let's be precise we'll call it Ln
+ 
+
+ align:start position:0%
+let's let's be precise we'll call it Ln
+of n factorial the natural log so log
+
+ align:start position:0%
+of n factorial the natural log so log
+ 
+
+ align:start position:0%
+of n factorial the natural log so log
+base
+
+ align:start position:0%
+base
+ 
+
+ align:start position:0%
+base
+e well remember when you take logs
+
+ align:start position:0%
+e well remember when you take logs
+ 
+
+ align:start position:0%
+e well remember when you take logs
+products turn to sums in this sense this
+
+ align:start position:0%
+products turn to sums in this sense this
+ 
+
+ align:start position:0%
+products turn to sums in this sense this
+becomes Ln of one plus Ln of 2 plus Ln
+
+ align:start position:0%
+becomes Ln of one plus Ln of 2 plus Ln
+ 
+
+ align:start position:0%
+becomes Ln of one plus Ln of 2 plus Ln
+of 3 plus Ln of
+
+ align:start position:0%
+of 3 plus Ln of
+ 
+
+ align:start position:0%
+of 3 plus Ln of
+n so if we want to understand n
+
+ align:start position:0%
+n so if we want to understand n
+ 
+
+ align:start position:0%
+n so if we want to understand n
+factorial we could just as well
+
+ align:start position:0%
+factorial we could just as well
+ 
+
+ align:start position:0%
+factorial we could just as well
+understand its log and its log is the
+
+ align:start position:0%
+understand its log and its log is the
+ 
+
+ align:start position:0%
+understand its log and its log is the
+sum of a bunch of other logs and now we
+
+ align:start position:0%
+sum of a bunch of other logs and now we
+ 
+
+ align:start position:0%
+sum of a bunch of other logs and now we
+have a sum and we can use all of our
+
+ align:start position:0%
+have a sum and we can use all of our
+ 
+
+ align:start position:0%
+have a sum and we can use all of our
+summation uh tools on this sum to get
+
+ align:start position:0%
+summation uh tools on this sum to get
+ 
+
+ align:start position:0%
+summation uh tools on this sum to get
+information about n
+
+ align:start position:0%
+information about n
+ 
+
+ align:start position:0%
+information about n
+factorial for example we could use the
+
+ align:start position:0%
+factorial for example we could use the
+ 
+
+ align:start position:0%
+factorial for example we could use the
+integral bound Ln of X is an increasing
+
+ align:start position:0%
+integral bound Ln of X is an increasing
+ 
+
+ align:start position:0%
+integral bound Ln of X is an increasing
+function this time so we use the
+
+ align:start position:0%
+function this time so we use the
+ 
+
+ align:start position:0%
+function this time so we use the
+increasing version of the
+
+ align:start position:0%
+increasing version of the
+ 
+
+ align:start position:0%
+increasing version of the
+bound uh which says
+
+ align:start position:0%
+bound uh which says
+ 
+
+ align:start position:0%
+bound uh which says
+that uh here we go so Ln of one plus the
+
+ align:start position:0%
+that uh here we go so Ln of one plus the
+ 
+
+ align:start position:0%
+that uh here we go so Ln of one plus the
+integral from 1 to n of Ln of X DX is
+
+ align:start position:0%
+integral from 1 to n of Ln of X DX is
+ 
+
+ align:start position:0%
+integral from 1 to n of Ln of X DX is
+less equal to the sum of Ln of K
+
+ align:start position:0%
+less equal to the sum of Ln of K
+ 
+
+ align:start position:0%
+less equal to the sum of Ln of K
+K = 1 to n Which is less equal to Ln of
+
+ align:start position:0%
+K = 1 to n Which is less equal to Ln of
+ 
+
+ align:start position:0%
+K = 1 to n Which is less equal to Ln of
+n plus the same
+
+ align:start position:0%
+n plus the same
+ 
+
+ align:start position:0%
+n plus the same
+integral and if we do out that integral
+
+ align:start position:0%
+integral and if we do out that integral
+ 
+
+ align:start position:0%
+integral and if we do out that integral
+like I said you don't want to see me
+
+ align:start position:0%
+like I said you don't want to see me
+ 
+
+ align:start position:0%
+like I said you don't want to see me
+integrate live I will get it wrong um
+
+ align:start position:0%
+integrate live I will get it wrong um
+ 
+
+ align:start position:0%
+integrate live I will get it wrong um
+but if we trust my notes this integral
+
+ align:start position:0%
+but if we trust my notes this integral
+ 
+
+ align:start position:0%
+but if we trust my notes this integral
+comes out to um n Ln of
+
+ align:start position:0%
+comes out to um n Ln of
+ 
+
+ align:start position:0%
+comes out to um n Ln of
+n um minus n +
+
+ align:start position:0%
+n um minus n +
+ 
+
+ align:start position:0%
+n um minus n +
+1 Ln of one is zero thankfully keeps
+
+ align:start position:0%
+1 Ln of one is zero thankfully keeps
+ 
+
+ align:start position:0%
+1 Ln of one is zero thankfully keeps
+things simple and so what we end up
+
+ align:start position:0%
+things simple and so what we end up
+ 
+
+ align:start position:0%
+things simple and so what we end up
+finding is that n Ln of nus n + 1 is
+
+ align:start position:0%
+finding is that n Ln of nus n + 1 is
+ 
+
+ align:start position:0%
+finding is that n Ln of nus n + 1 is
+less equal to this sum which as we know
+
+ align:start position:0%
+less equal to this sum which as we know
+ 
+
+ align:start position:0%
+less equal to this sum which as we know
+is Ln of n factorial Which is less equal
+
+ align:start position:0%
+is Ln of n factorial Which is less equal
+ 
+
+ align:start position:0%
+is Ln of n factorial Which is less equal
+to this same integral plus another Ln of
+
+ align:start position:0%
+to this same integral plus another Ln of
+ 
+
+ align:start position:0%
+to this same integral plus another Ln of
+n n + one Ln of nus n +
+
+ align:start position:0%
+n n + one Ln of nus n +
+ 
+
+ align:start position:0%
+n n + one Ln of nus n +
+1 so we were able to translate this
+
+ align:start position:0%
+1 so we were able to translate this
+ 
+
+ align:start position:0%
+1 so we were able to translate this
+product into a sum and then use our
+
+ align:start position:0%
+product into a sum and then use our
+ 
+
+ align:start position:0%
+product into a sum and then use our
+summation tool um to get get us a bound
+
+ align:start position:0%
+summation tool um to get get us a bound
+ 
+
+ align:start position:0%
+summation tool um to get get us a bound
+on Ln of N and if we want to bound on N
+
+ align:start position:0%
+on Ln of N and if we want to bound on N
+ 
+
+ align:start position:0%
+on Ln of N and if we want to bound on N
+factor sorry Ln of n factorial I
+
+ align:start position:0%
+factor sorry Ln of n factorial I
+ 
+
+ align:start position:0%
+factor sorry Ln of n factorial I
+misspoke if we want to bound on Ln I
+
+ align:start position:0%
+misspoke if we want to bound on Ln I
+ 
+
+ align:start position:0%
+misspoke if we want to bound on Ln I
+misspoke again apologies if we want to
+
+ align:start position:0%
+misspoke again apologies if we want to
+ 
+
+ align:start position:0%
+misspoke again apologies if we want to
+bound on N factorial itself we can just
+
+ align:start position:0%
+bound on N factorial itself we can just
+ 
+
+ align:start position:0%
+bound on N factorial itself we can just
+undo the log by exponentiating all three
+
+ align:start position:0%
+undo the log by exponentiating all three
+ 
+
+ align:start position:0%
+undo the log by exponentiating all three
+of these take e to this e to this e to
+
+ align:start position:0%
+of these take e to this e to this e to
+ 
+
+ align:start position:0%
+of these take e to this e to this e to
+this that preserves our
+
+ align:start position:0%
+this that preserves our
+ 
+
+ align:start position:0%
+this that preserves our
+inequalities and what we'll end up
+
+ align:start position:0%
+inequalities and what we'll end up
+ 
+
+ align:start position:0%
+inequalities and what we'll end up
+getting after we simplify it a bit is
+
+ align:start position:0%
+getting after we simplify it a bit is
+ 
+
+ align:start position:0%
+getting after we simplify it a bit is
+that n the N over e to the N minus1 is
+
+ align:start position:0%
+that n the N over e to the N minus1 is
+ 
+
+ align:start position:0%
+that n the N over e to the N minus1 is
+less equ to n factorial is less equal to
+
+ align:start position:0%
+less equ to n factorial is less equal to
+ 
+
+ align:start position:0%
+less equ to n factorial is less equal to
+n n
+
+ align:start position:0%
+n n
+ 
+
+ align:start position:0%
+n n
++1 over e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nus1 so same denominator on both sides
+
+ align:start position:0%
+nus1 so same denominator on both sides
+ 
+
+ align:start position:0%
+nus1 so same denominator on both sides
+we have n the N versus n the N plus one
+
+ align:start position:0%
+we have n the N versus n the N plus one
+ 
+
+ align:start position:0%
+we have n the N versus n the N plus one
+on the two sides so the two bounds are
+
+ align:start position:0%
+on the two sides so the two bounds are
+ 
+
+ align:start position:0%
+on the two sides so the two bounds are
+off by a factor of n not as good as we
+
+ align:start position:0%
+off by a factor of n not as good as we
+ 
+
+ align:start position:0%
+off by a factor of n not as good as we
+had last time we are off by an additive
+
+ align:start position:0%
+had last time we are off by an additive
+ 
+
+ align:start position:0%
+had last time we are off by an additive
+one less than that even but a factor of
+
+ align:start position:0%
+one less than that even but a factor of
+ 
+
+ align:start position:0%
+one less than that even but a factor of
+n isn't bad for a number as big as n
+
+ align:start position:0%
+n isn't bad for a number as big as n
+ 
+
+ align:start position:0%
+n isn't bad for a number as big as n
+factorial this isn't a bad
+
+ align:start position:0%
+factorial this isn't a bad
+ 
+
+ align:start position:0%
+factorial this isn't a bad
+bound um is everyone clear on how we got
+
+ align:start position:0%
+bound um is everyone clear on how we got
+ 
+
+ align:start position:0%
+bound um is everyone clear on how we got
+to this
+
+ align:start position:0%
+to this
+ 
+
+ align:start position:0%
+to this
+bound wonderful it's not the best bound
+
+ align:start position:0%
+bound wonderful it's not the best bound
+ 
+
+ align:start position:0%
+bound wonderful it's not the best bound
+we have
+
+ align:start position:0%
+we have
+ 
+
+ align:start position:0%
+we have
+ow um let me tell you uh two better ones
+
+ align:start position:0%
+ow um let me tell you uh two better ones
+ 
+
+ align:start position:0%
+ow um let me tell you uh two better ones
+oh sorry before that is this bound
+
+ align:start position:0%
+oh sorry before that is this bound
+ 
+
+ align:start position:0%
+oh sorry before that is this bound
+enough to say that n factorial is ASM
+
+ align:start position:0%
+enough to say that n factorial is ASM
+ 
+
+ align:start position:0%
+enough to say that n factorial is ASM
+totically equivalent to one side or the
+
+ align:start position:0%
+totically equivalent to one side or the
+ 
+
+ align:start position:0%
+totically equivalent to one side or the
+other I see some head shakes can someone
+
+ align:start position:0%
+other I see some head shakes can someone
+ 
+
+ align:start position:0%
+other I see some head shakes can someone
+tell me why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's all right I'm tired
+
+ align:start position:0%
+that's all right I'm tired
+ 
+
+ align:start position:0%
+that's all right I'm tired
+too um these two bounds are too far
+
+ align:start position:0%
+too um these two bounds are too far
+ 
+
+ align:start position:0%
+too um these two bounds are too far
+apart from each other they're a factor
+
+ align:start position:0%
+apart from each other they're a factor
+ 
+
+ align:start position:0%
+apart from each other they're a factor
+of n apart and so we can't say that this
+
+ align:start position:0%
+of n apart and so we can't say that this
+ 
+
+ align:start position:0%
+of n apart and so we can't say that this
+divided by this limits to one or this
+
+ align:start position:0%
+divided by this limits to one or this
+ 
+
+ align:start position:0%
+divided by this limits to one or this
+divided by this limits to one because we
+
+ align:start position:0%
+divided by this limits to one because we
+ 
+
+ align:start position:0%
+divided by this limits to one because we
+have an N range in there to account for
+
+ align:start position:0%
+have an N range in there to account for
+ 
+
+ align:start position:0%
+have an N range in there to account for
+and N grows to Infinity so we don't know
+
+ align:start position:0%
+and N grows to Infinity so we don't know
+ 
+
+ align:start position:0%
+and N grows to Infinity so we don't know
+where in this range and factorial lies
+
+ align:start position:0%
+where in this range and factorial lies
+ 
+
+ align:start position:0%
+where in this range and factorial lies
+and so we can't pin down that limit
+
+ align:start position:0%
+and so we can't pin down that limit
+ 
+
+ align:start position:0%
+and so we can't pin down that limit
+going to a specific value so this isn't
+
+ align:start position:0%
+going to a specific value so this isn't
+ 
+
+ align:start position:0%
+going to a specific value so this isn't
+tight enough to say that n factorial is
+
+ align:start position:0%
+tight enough to say that n factorial is
+ 
+
+ align:start position:0%
+tight enough to say that n factorial is
+ASM totically equivalent to
+
+ align:start position:0%
+ASM totically equivalent to
+ 
+
+ align:start position:0%
+ASM totically equivalent to
+something um but that's where Sterling's
+
+ align:start position:0%
+something um but that's where Sterling's
+ 
+
+ align:start position:0%
+something um but that's where Sterling's
+approximation comes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in um Sterling's approximation says that
+
+ align:start position:0%
+in um Sterling's approximation says that
+ 
+
+ align:start position:0%
+in um Sterling's approximation says that
+n factorial is ASM totically equivalent
+
+ align:start position:0%
+n factorial is ASM totically equivalent
+ 
+
+ align:start position:0%
+n factorial is ASM totically equivalent
+to theun of 2 piun n * n e to the
+
+ align:start position:0%
+to theun of 2 piun n * n e to the
+ 
+
+ align:start position:0%
+to theun of 2 piun n * n e to the
+end we're not going to prove that but
+
+ align:start position:0%
+end we're not going to prove that but
+ 
+
+ align:start position:0%
+end we're not going to prove that but
+it's really useful you should write it
+
+ align:start position:0%
+it's really useful you should write it
+ 
+
+ align:start position:0%
+it's really useful you should write it
+down you might end up using it in the
+
+ align:start position:0%
+down you might end up using it in the
+ 
+
+ align:start position:0%
+down you might end up using it in the
+problem set hint
+
+ align:start position:0%
+problem set hint
+ 
+
+ align:start position:0%
+problem set hint
+hint um extremely
+
+ align:start position:0%
+hint um extremely
+ 
+
+ align:start position:0%
+hint um extremely
+useful um but remember this is this is
+
+ align:start position:0%
+useful um but remember this is this is
+ 
+
+ align:start position:0%
+useful um but remember this is this is
+just saying that n factorial divided by
+
+ align:start position:0%
+just saying that n factorial divided by
+ 
+
+ align:start position:0%
+just saying that n factorial divided by
+this limits to one so when n is really
+
+ align:start position:0%
+this limits to one so when n is really
+ 
+
+ align:start position:0%
+this limits to one so when n is really
+really big the quotient of these two
+
+ align:start position:0%
+really big the quotient of these two
+ 
+
+ align:start position:0%
+really big the quotient of these two
+things is close to one
+
+ align:start position:0%
+things is close to one
+ 
+
+ align:start position:0%
+things is close to one
+what it doesn't tell us is what happens
+
+ align:start position:0%
+what it doesn't tell us is what happens
+ 
+
+ align:start position:0%
+what it doesn't tell us is what happens
+for smaller values of n what if n is
+
+ align:start position:0%
+for smaller values of n what if n is
+ 
+
+ align:start position:0%
+for smaller values of n what if n is
+just 10 can we use this to approximate
+
+ align:start position:0%
+just 10 can we use this to approximate
+ 
+
+ align:start position:0%
+just 10 can we use this to approximate
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+factorial how about 100 how about a
+
+ align:start position:0%
+factorial how about 100 how about a
+ 
+
+ align:start position:0%
+factorial how about 100 how about a
+thousand I don't know this doesn't
+
+ align:start position:0%
+thousand I don't know this doesn't
+ 
+
+ align:start position:0%
+thousand I don't know this doesn't
+really tell us it doesn't tell us how
+
+ align:start position:0%
+really tell us it doesn't tell us how
+ 
+
+ align:start position:0%
+really tell us it doesn't tell us how
+good an approximation this is all it
+
+ align:start position:0%
+good an approximation this is all it
+ 
+
+ align:start position:0%
+good an approximation this is all it
+says is that it's good in the
+
+ align:start position:0%
+says is that it's good in the
+ 
+
+ align:start position:0%
+says is that it's good in the
+limit um so let me tell you an even
+
+ align:start position:0%
+limit um so let me tell you an even
+ 
+
+ align:start position:0%
+limit um so let me tell you an even
+stronger
+
+ align:start position:0%
+stronger
+ 
+
+ align:start position:0%
+stronger
+bound uh I don't know who to credit this
+
+ align:start position:0%
+bound uh I don't know who to credit this
+ 
+
+ align:start position:0%
+bound uh I don't know who to credit this
+bound to but it's even more precise than
+
+ align:start position:0%
+bound to but it's even more precise than
+ 
+
+ align:start position:0%
+bound to but it's even more precise than
+this one
+
+ align:start position:0%
+this one
+ 
+
+ align:start position:0%
+this one
+uh it says that n factorial divided by
+
+ align:start position:0%
+uh it says that n factorial divided by
+ 
+
+ align:start position:0%
+uh it says that n factorial divided by
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+Thing 2 pi n n / e to the N so this is a
+
+ align:start position:0%
+Thing 2 pi n n / e to the N so this is a
+ 
+
+ align:start position:0%
+Thing 2 pi n n / e to the N so this is a
+thing that Sterling tells us limits to
+
+ align:start position:0%
+thing that Sterling tells us limits to
+ 
+
+ align:start position:0%
+thing that Sterling tells us limits to
+one and now we have some bounds on how
+
+ align:start position:0%
+one and now we have some bounds on how
+ 
+
+ align:start position:0%
+one and now we have some bounds on how
+quickly it does that e to 1 over
+
+ align:start position:0%
+quickly it does that e to 1 over
+ 
+
+ align:start position:0%
+quickly it does that e to 1 over
+12n e to 1 over 12n +
+
+ align:start position:0%
+12n e to 1 over 12n +
+ 
+
+ align:start position:0%
+12n e to 1 over 12n +
+1 so not only does this limit to one it
+
+ align:start position:0%
+1 so not only does this limit to one it
+ 
+
+ align:start position:0%
+1 so not only does this limit to one it
+does so very very fast exponentially
+
+ align:start position:0%
+does so very very fast exponentially
+ 
+
+ align:start position:0%
+does so very very fast exponentially
+fast
+
+ align:start position:0%
+fast
+ 
+
+ align:start position:0%
+fast
+and this we can plug in specific values
+
+ align:start position:0%
+and this we can plug in specific values
+ 
+
+ align:start position:0%
+and this we can plug in specific values
+of N and see okay how close is this
+
+ align:start position:0%
+of N and see okay how close is this
+ 
+
+ align:start position:0%
+of N and see okay how close is this
+approximation to n factorial this is an
+
+ align:start position:0%
+approximation to n factorial this is an
+ 
+
+ align:start position:0%
+approximation to n factorial this is an
+effective bound one we can get actual
+
+ align:start position:0%
+effective bound one we can get actual
+ 
+
+ align:start position:0%
+effective bound one we can get actual
+approximations out of this is just a
+
+ align:start position:0%
+approximations out of this is just a
+ 
+
+ align:start position:0%
+approximations out of this is just a
+limiting bound but of course this is a
+
+ align:start position:0%
+limiting bound but of course this is a
+ 
+
+ align:start position:0%
+limiting bound but of course this is a
+lot more complicated sometimes we don't
+
+ align:start position:0%
+lot more complicated sometimes we don't
+ 
+
+ align:start position:0%
+lot more complicated sometimes we don't
+want to deal with all these details and
+
+ align:start position:0%
+want to deal with all these details and
+ 
+
+ align:start position:0%
+want to deal with all these details and
+this is enough sometimes even that's too
+
+ align:start position:0%
+this is enough sometimes even that's too
+ 
+
+ align:start position:0%
+this is enough sometimes even that's too
+much and that's enough so pick your
+
+ align:start position:0%
+much and that's enough so pick your
+ 
+
+ align:start position:0%
+much and that's enough so pick your
+level of granularity as you need
+
+ align:start position:0%
+level of granularity as you need
+ 
+
+ align:start position:0%
+level of granularity as you need
+it we're also not going to prove this
+
+ align:start position:0%
+it we're also not going to prove this
+ 
+
+ align:start position:0%
+it we're also not going to prove this
+bound um that's even harder than
+
+ align:start position:0%
+bound um that's even harder than
+ 
+
+ align:start position:0%
+bound um that's even harder than
+Sterling um but it's true and useful
+
+ align:start position:0%
+Sterling um but it's true and useful
+ 
+
+ align:start position:0%
+Sterling um but it's true and useful
+questions on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that all right so that's everything I
+
+ align:start position:0%
+that all right so that's everything I
+ 
+
+ align:start position:0%
+that all right so that's everything I
+wanted to say about summations and now
+
+ align:start position:0%
+wanted to say about summations and now
+ 
+
+ align:start position:0%
+wanted to say about summations and now
+let's jump back to astics we already
+
+ align:start position:0%
+let's jump back to astics we already
+ 
+
+ align:start position:0%
+let's jump back to astics we already
+started talking about astics with um ASM
+
+ align:start position:0%
+started talking about astics with um ASM
+ 
+
+ align:start position:0%
+started talking about astics with um ASM
+totic
+
+ align:start position:0%
+totic
+ 
+
+ align:start position:0%
+totic
+equivalents um and let's do an
+
+ align:start position:0%
+equivalents um and let's do an
+ 
+
+ align:start position:0%
+equivalents um and let's do an
+experiment uh let's do an exercise um
+
+ align:start position:0%
+experiment uh let's do an exercise um
+ 
+
+ align:start position:0%
+experiment uh let's do an exercise um
+we've already seen a sorting algorithm
+
+ align:start position:0%
+we've already seen a sorting algorithm
+ 
+
+ align:start position:0%
+we've already seen a sorting algorithm
+we saw swap sort um in lecture four
+
+ align:start position:0%
+we saw swap sort um in lecture four
+ 
+
+ align:start position:0%
+we saw swap sort um in lecture four
+where you you have a you want to put it
+
+ align:start position:0%
+where you you have a you want to put it
+ 
+
+ align:start position:0%
+where you you have a you want to put it
+in sorted order and you do that by
+
+ align:start position:0%
+in sorted order and you do that by
+ 
+
+ align:start position:0%
+in sorted order and you do that by
+finding a pair that's out of order and
+
+ align:start position:0%
+finding a pair that's out of order and
+ 
+
+ align:start position:0%
+finding a pair that's out of order and
+next to each other and changing their
+
+ align:start position:0%
+next to each other and changing their
+ 
+
+ align:start position:0%
+next to each other and changing their
+order and you keep doing that keep
+
+ align:start position:0%
+order and you keep doing that keep
+ 
+
+ align:start position:0%
+order and you keep doing that keep
+finding pairs that are next to each
+
+ align:start position:0%
+finding pairs that are next to each
+ 
+
+ align:start position:0%
+finding pairs that are next to each
+other and out of order until the whole
+
+ align:start position:0%
+other and out of order until the whole
+ 
+
+ align:start position:0%
+other and out of order until the whole
+thing is
+
+ align:start position:0%
+thing is
+ 
+
+ align:start position:0%
+thing is
+sorted uh and we saw so I'm going to
+
+ align:start position:0%
+sorted uh and we saw so I'm going to
+ 
+
+ align:start position:0%
+sorted uh and we saw so I'm going to
+call that swap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sort we saw that the the number of swaps
+
+ align:start position:0%
+sort we saw that the the number of swaps
+ 
+
+ align:start position:0%
+sort we saw that the the number of swaps
+that you'll need to make is exactly
+
+ align:start position:0%
+that you'll need to make is exactly
+ 
+
+ align:start position:0%
+that you'll need to make is exactly
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+to number of
+
+ align:start position:0%
+to number of
+ 
+
+ align:start position:0%
+to number of
+swaps is exactly equal to the number of
+
+ align:start position:0%
+swaps is exactly equal to the number of
+ 
+
+ align:start position:0%
+swaps is exactly equal to the number of
+inverted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pairs so the number of pairs of two
+
+ align:start position:0%
+pairs so the number of pairs of two
+ 
+
+ align:start position:0%
+pairs so the number of pairs of two
+numbers in our list where the big one is
+
+ align:start position:0%
+numbers in our list where the big one is
+ 
+
+ align:start position:0%
+numbers in our list where the big one is
+somewhere to the left of the small one
+
+ align:start position:0%
+somewhere to the left of the small one
+ 
+
+ align:start position:0%
+somewhere to the left of the small one
+so they're in the wrong order and we'll
+
+ align:start position:0%
+so they're in the wrong order and we'll
+ 
+
+ align:start position:0%
+so they're in the wrong order and we'll
+eventually need to change
+
+ align:start position:0%
+eventually need to change
+ 
+
+ align:start position:0%
+eventually need to change
+order um and well how many inverted
+
+ align:start position:0%
+order um and well how many inverted
+ 
+
+ align:start position:0%
+order um and well how many inverted
+pairs could there be in the worst case
+
+ align:start position:0%
+pairs could there be in the worst case
+ 
+
+ align:start position:0%
+pairs could there be in the worst case
+well in the worst case every pair is
+
+ align:start position:0%
+well in the worst case every pair is
+ 
+
+ align:start position:0%
+well in the worst case every pair is
+inverted one the number one is is
+
+ align:start position:0%
+inverted one the number one is is
+ 
+
+ align:start position:0%
+inverted one the number one is is
+inverted with 2 through n
+
+ align:start position:0%
+inverted with 2 through n
+ 
+
+ align:start position:0%
+inverted with 2 through n
+and two is inverted well it's already
+
+ align:start position:0%
+and two is inverted well it's already
+ 
+
+ align:start position:0%
+and two is inverted well it's already
+inverted through one we already counted
+
+ align:start position:0%
+inverted through one we already counted
+ 
+
+ align:start position:0%
+inverted through one we already counted
+that but two would be inverted with
+
+ align:start position:0%
+that but two would be inverted with
+ 
+
+ align:start position:0%
+that but two would be inverted with
+three through
+
+ align:start position:0%
+three through
+ 
+
+ align:start position:0%
+three through
+n those are new in inversions that we
+
+ align:start position:0%
+n those are new in inversions that we
+ 
+
+ align:start position:0%
+n those are new in inversions that we
+haven't counted yet uh three is inverted
+
+ align:start position:0%
+haven't counted yet uh three is inverted
+ 
+
+ align:start position:0%
+haven't counted yet uh three is inverted
+with everything after
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it plus one so this is the worst case
+
+ align:start position:0%
+it plus one so this is the worst case
+ 
+
+ align:start position:0%
+it plus one so this is the worst case
+number of swaps we'll have to make um
+
+ align:start position:0%
+number of swaps we'll have to make um
+ 
+
+ align:start position:0%
+number of swaps we'll have to make um
+and as we as we've seen we know how to
+
+ align:start position:0%
+and as we as we've seen we know how to
+ 
+
+ align:start position:0%
+and as we as we've seen we know how to
+compute this sum this is n minus one * n
+
+ align:start position:0%
+compute this sum this is n minus one * n
+ 
+
+ align:start position:0%
+compute this sum this is n minus one * n
+/ two also known as n ^2 over 2us n
+
+ align:start position:0%
+/ two also known as n ^2 over 2us n
+ 
+
+ align:start position:0%
+/ two also known as n ^2 over 2us n
+/2 and this I'm going to
+
+ align:start position:0%
+/2 and this I'm going to
+ 
+
+ align:start position:0%
+/2 and this I'm going to
+call S of n we have our function s of n
+
+ align:start position:0%
+call S of n we have our function s of n
+ 
+
+ align:start position:0%
+call S of n we have our function s of n
+s being reminiscent of swap sort it's a
+
+ align:start position:0%
+s being reminiscent of swap sort it's a
+ 
+
+ align:start position:0%
+s being reminiscent of swap sort it's a
+function describing the worst case
+
+ align:start position:0%
+function describing the worst case
+ 
+
+ align:start position:0%
+function describing the worst case
+number of swaps we'll need to make in
+
+ align:start position:0%
+number of swaps we'll need to make in
+ 
+
+ align:start position:0%
+number of swaps we'll need to make in
+swap
+
+ align:start position:0%
+swap
+ 
+
+ align:start position:0%
+swap
+sort on Thursday we're going to see
+
+ align:start position:0%
+sort on Thursday we're going to see
+ 
+
+ align:start position:0%
+sort on Thursday we're going to see
+another sorting algorithm called merge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sort uh I'll describe it then I'm not
+
+ align:start position:0%
+sort uh I'll describe it then I'm not
+ 
+
+ align:start position:0%
+sort uh I'll describe it then I'm not
+not going to describe it now that's we
+
+ align:start position:0%
+not going to describe it now that's we
+ 
+
+ align:start position:0%
+not going to describe it now that's we
+don't need to know what it does or how
+
+ align:start position:0%
+don't need to know what it does or how
+ 
+
+ align:start position:0%
+don't need to know what it does or how
+uh we just need to know how fast it runs
+
+ align:start position:0%
+uh we just need to know how fast it runs
+ 
+
+ align:start position:0%
+uh we just need to know how fast it runs
+how many comparisons does it have to
+
+ align:start position:0%
+how many comparisons does it have to
+ 
+
+ align:start position:0%
+how many comparisons does it have to
+make um so let's
+
+ align:start position:0%
+make um so let's
+ 
+
+ align:start position:0%
+make um so let's
+define M of n this is going to be n log
+
+ align:start position:0%
+define M of n this is going to be n log
+ 
+
+ align:start position:0%
+define M of n this is going to be n log
+2 of n minus n + one uh and on Thursday
+
+ align:start position:0%
+2 of n minus n + one uh and on Thursday
+ 
+
+ align:start position:0%
+2 of n minus n + one uh and on Thursday
+we'll see that uh that merge sort takes
+
+ align:start position:0%
+we'll see that uh that merge sort takes
+ 
+
+ align:start position:0%
+we'll see that uh that merge sort takes
+at most this many steps to
+
+ align:start position:0%
+at most this many steps to
+ 
+
+ align:start position:0%
+at most this many steps to
+complete and now I want to know between
+
+ align:start position:0%
+complete and now I want to know between
+ 
+
+ align:start position:0%
+complete and now I want to know between
+these two function
+
+ align:start position:0%
+these two function
+ 
+
+ align:start position:0%
+these two function
+between these two algorithms which one
+
+ align:start position:0%
+between these two algorithms which one
+ 
+
+ align:start position:0%
+between these two algorithms which one
+is a better choice for sorting lots of
+
+ align:start position:0%
+is a better choice for sorting lots of
+ 
+
+ align:start position:0%
+is a better choice for sorting lots of
+numbers if these are the two algorithms
+
+ align:start position:0%
+numbers if these are the two algorithms
+ 
+
+ align:start position:0%
+numbers if these are the two algorithms
+I have to pick from and I know their run
+
+ align:start position:0%
+I have to pick from and I know their run
+ 
+
+ align:start position:0%
+I have to pick from and I know their run
+times they're n^2 / 2 - n / 2 versus n
+
+ align:start position:0%
+times they're n^2 / 2 - n / 2 versus n
+ 
+
+ align:start position:0%
+times they're n^2 / 2 - n / 2 versus n
+log 2 N - n +
+
+ align:start position:0%
+log 2 N - n +
+ 
+
+ align:start position:0%
+log 2 N - n +
+1 this is s this is
+
+ align:start position:0%
+1 this is s this is
+ 
+
+ align:start position:0%
+1 this is s this is
+M which one's the better
+
+ align:start position:0%
+M which one's the better
+ 
+
+ align:start position:0%
+M which one's the better
+choice um and sorry that was rhetorical
+
+ align:start position:0%
+choice um and sorry that was rhetorical
+ 
+
+ align:start position:0%
+choice um and sorry that was rhetorical
+um let's talk through it um let's do
+
+ align:start position:0%
+um let's talk through it um let's do
+ 
+
+ align:start position:0%
+um let's talk through it um let's do
+sort of an eye tracker to see which
+
+ align:start position:0%
+sort of an eye tracker to see which
+ 
+
+ align:start position:0%
+sort of an eye tracker to see which
+parts of the various formulas we look at
+
+ align:start position:0%
+parts of the various formulas we look at
+ 
+
+ align:start position:0%
+parts of the various formulas we look at
+when making this comparison uh and just
+
+ align:start position:0%
+when making this comparison uh and just
+ 
+
+ align:start position:0%
+when making this comparison uh and just
+to emphasize I'm I'm most worried about
+
+ align:start position:0%
+to emphasize I'm I'm most worried about
+ 
+
+ align:start position:0%
+to emphasize I'm I'm most worried about
+what happens with lots and lots and lots
+
+ align:start position:0%
+what happens with lots and lots and lots
+ 
+
+ align:start position:0%
+what happens with lots and lots and lots
+of numbers I'm trying to sort a million
+
+ align:start position:0%
+of numbers I'm trying to sort a million
+ 
+
+ align:start position:0%
+of numbers I'm trying to sort a million
+a billion a trillion numbers um so I'm
+
+ align:start position:0%
+a billion a trillion numbers um so I'm
+ 
+
+ align:start position:0%
+a billion a trillion numbers um so I'm
+interested in what happens in the limit
+
+ align:start position:0%
+interested in what happens in the limit
+ 
+
+ align:start position:0%
+interested in what happens in the limit
+as n gets really really big if we're
+
+ align:start position:0%
+as n gets really really big if we're
+ 
+
+ align:start position:0%
+as n gets really really big if we're
+trying to sort 10 numbers well I don't
+
+ align:start position:0%
+trying to sort 10 numbers well I don't
+ 
+
+ align:start position:0%
+trying to sort 10 numbers well I don't
+care that's what however you want to do
+
+ align:start position:0%
+care that's what however you want to do
+ 
+
+ align:start position:0%
+care that's what however you want to do
+it is fine 10 is small um but with big
+
+ align:start position:0%
+it is fine 10 is small um but with big
+ 
+
+ align:start position:0%
+it is fine 10 is small um but with big
+data no one uses that term anymore I
+
+ align:start position:0%
+data no one uses that term anymore I
+ 
+
+ align:start position:0%
+data no one uses that term anymore I
+don't know why um with lots and lots of
+
+ align:start position:0%
+don't know why um with lots and lots of
+ 
+
+ align:start position:0%
+don't know why um with lots and lots of
+data these these differences matter so
+
+ align:start position:0%
+data these these differences matter so
+ 
+
+ align:start position:0%
+data these these differences matter so
+let's see how we make this comparison
+
+ align:start position:0%
+let's see how we make this comparison
+ 
+
+ align:start position:0%
+let's see how we make this comparison
+what are we going to look at well the
+
+ align:start position:0%
+what are we going to look at well the
+ 
+
+ align:start position:0%
+what are we going to look at well the
+first thing my eye goes
+
+ align:start position:0%
+first thing my eye goes
+ 
+
+ align:start position:0%
+first thing my eye goes
+to is this right here which is to say
+
+ align:start position:0%
+to is this right here which is to say
+ 
+
+ align:start position:0%
+to is this right here which is to say
+that's the last place my eye goes I
+
+ align:start position:0%
+that's the last place my eye goes I
+ 
+
+ align:start position:0%
+that's the last place my eye goes I
+don't care about that term the n^2 over
+
+ align:start position:0%
+don't care about that term the n^2 over
+ 
+
+ align:start position:0%
+don't care about that term the n^2 over
+two is much more important
+
+ align:start position:0%
+two is much more important
+ 
+
+ align:start position:0%
+two is much more important
+um by the time we're up into the N squar
+
+ align:start position:0%
+um by the time we're up into the N squar
+ 
+
+ align:start position:0%
+um by the time we're up into the N squar
+it's an a little measly n / two doesn't
+
+ align:start position:0%
+it's an a little measly n / two doesn't
+ 
+
+ align:start position:0%
+it's an a little measly n / two doesn't
+really make much of a difference right
+
+ align:start position:0%
+really make much of a difference right
+ 
+
+ align:start position:0%
+really make much of a difference right
+intuitively anyway I haven't made this
+
+ align:start position:0%
+intuitively anyway I haven't made this
+ 
+
+ align:start position:0%
+intuitively anyway I haven't made this
+precise but the first thing that I do
+
+ align:start position:0%
+precise but the first thing that I do
+ 
+
+ align:start position:0%
+precise but the first thing that I do
+when looking at this is I just
+
+ align:start position:0%
+when looking at this is I just
+ 
+
+ align:start position:0%
+when looking at this is I just
+completely ignore that N /2 I don't care
+
+ align:start position:0%
+completely ignore that N /2 I don't care
+ 
+
+ align:start position:0%
+completely ignore that N /2 I don't care
+likewise I don't care about this n minus
+
+ align:start position:0%
+likewise I don't care about this n minus
+ 
+
+ align:start position:0%
+likewise I don't care about this n minus
+one that we're subtracting the N log n
+
+ align:start position:0%
+one that we're subtracting the N log n
+ 
+
+ align:start position:0%
+one that we're subtracting the N log n
+grows faster than that uh so with big n
+
+ align:start position:0%
+grows faster than that uh so with big n
+ 
+
+ align:start position:0%
+grows faster than that uh so with big n
+this is going to dominate and this is
+
+ align:start position:0%
+this is going to dominate and this is
+ 
+
+ align:start position:0%
+this is going to dominate and this is
+just going to be a rounding eror
+
+ align:start position:0%
+just going to be a rounding eror
+ 
+
+ align:start position:0%
+just going to be a rounding eror
+so that's the first thing I do ignore
+
+ align:start position:0%
+so that's the first thing I do ignore
+ 
+
+ align:start position:0%
+so that's the first thing I do ignore
+the lower
+
+ align:start position:0%
+the lower
+ 
+
+ align:start position:0%
+the lower
+terms now I'm just comparing n^2 2
+
+ align:start position:0%
+terms now I'm just comparing n^2 2
+ 
+
+ align:start position:0%
+terms now I'm just comparing n^2 2
+versus n log
+
+ align:start position:0%
+versus n log
+ 
+
+ align:start position:0%
+versus n log
+n the next thing I
+
+ align:start position:0%
+n the next thing I
+ 
+
+ align:start position:0%
+n the next thing I
+ignore is this over
+
+ align:start position:0%
+ignore is this over
+ 
+
+ align:start position:0%
+ignore is this over
+two I don't really
+
+ align:start position:0%
+two I don't really
+ 
+
+ align:start position:0%
+two I don't really
+care I don't care that we're dividing by
+
+ align:start position:0%
+care I don't care that we're dividing by
+ 
+
+ align:start position:0%
+care I don't care that we're dividing by
+two if this had been n^2 divided a th if
+
+ align:start position:0%
+two if this had been n^2 divided a th if
+ 
+
+ align:start position:0%
+two if this had been n^2 divided a th if
+this had been a million time n log n is
+
+ align:start position:0%
+this had been a million time n log n is
+ 
+
+ align:start position:0%
+this had been a million time n log n is
+that really going to change my
+
+ align:start position:0%
+that really going to change my
+ 
+
+ align:start position:0%
+that really going to change my
+determination
+
+ align:start position:0%
+determination
+ 
+
+ align:start position:0%
+determination
+for small n values yeah those constants
+
+ align:start position:0%
+for small n values yeah those constants
+ 
+
+ align:start position:0%
+for small n values yeah those constants
+matter those lower terms matter for that
+
+ align:start position:0%
+matter those lower terms matter for that
+ 
+
+ align:start position:0%
+matter those lower terms matter for that
+matter when n is small but in the limit
+
+ align:start position:0%
+matter when n is small but in the limit
+ 
+
+ align:start position:0%
+matter when n is small but in the limit
+as n gets bigger and
+
+ align:start position:0%
+as n gets bigger and
+ 
+
+ align:start position:0%
+as n gets bigger and
+bigger that that extra factor of n is
+
+ align:start position:0%
+bigger that that extra factor of n is
+ 
+
+ align:start position:0%
+bigger that that extra factor of n is
+going to overtake that extra factor of
+
+ align:start position:0%
+going to overtake that extra factor of
+ 
+
+ align:start position:0%
+going to overtake that extra factor of
+log n no matter what constants we throw
+
+ align:start position:0%
+log n no matter what constants we throw
+ 
+
+ align:start position:0%
+log n no matter what constants we throw
+in there
+
+ align:start position:0%
+in there
+ 
+
+ align:start position:0%
+in there
+right so I don't really care about those
+
+ align:start position:0%
+right so I don't really care about those
+ 
+
+ align:start position:0%
+right so I don't really care about those
+as well really all I'm focusing on is
+
+ align:start position:0%
+as well really all I'm focusing on is
+ 
+
+ align:start position:0%
+as well really all I'm focusing on is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+N2 versus the N log n does that make
+
+ align:start position:0%
+N2 versus the N log n does that make
+ 
+
+ align:start position:0%
+N2 versus the N log n does that make
+sense um every everything I just did was
+
+ align:start position:0%
+sense um every everything I just did was
+ 
+
+ align:start position:0%
+sense um every everything I just did was
+completely informal I haven't Justified
+
+ align:start position:0%
+completely informal I haven't Justified
+ 
+
+ align:start position:0%
+completely informal I haven't Justified
+any of that but we will um but first we
+
+ align:start position:0%
+any of that but we will um but first we
+ 
+
+ align:start position:0%
+any of that but we will um but first we
+need to motivate it and there's one
+
+ align:start position:0%
+need to motivate it and there's one
+ 
+
+ align:start position:0%
+need to motivate it and there's one
+other reason uh one other motivation for
+
+ align:start position:0%
+other reason uh one other motivation for
+ 
+
+ align:start position:0%
+other reason uh one other motivation for
+not really caring about this constant
+
+ align:start position:0%
+not really caring about this constant
+ 
+
+ align:start position:0%
+not really caring about this constant
+Factor uh with swap sort we were
+
+ align:start position:0%
+Factor uh with swap sort we were
+ 
+
+ align:start position:0%
+Factor uh with swap sort we were
+counting what were we counting the
+
+ align:start position:0%
+counting what were we counting the
+ 
+
+ align:start position:0%
+counting what were we counting the
+number of actual swaps we
+
+ align:start position:0%
+number of actual swaps we
+ 
+
+ align:start position:0%
+number of actual swaps we
+make um we didn't say how you're finding
+
+ align:start position:0%
+make um we didn't say how you're finding
+ 
+
+ align:start position:0%
+make um we didn't say how you're finding
+those swaps but there are there are
+
+ align:start position:0%
+those swaps but there are there are
+ 
+
+ align:start position:0%
+those swaps but there are there are
+clean ways to do it so that the number
+
+ align:start position:0%
+clean ways to do it so that the number
+ 
+
+ align:start position:0%
+clean ways to do it so that the number
+of steps you take um in the whole
+
+ align:start position:0%
+of steps you take um in the whole
+ 
+
+ align:start position:0%
+of steps you take um in the whole
+algorithm is about n^2 over
+
+ align:start position:0%
+algorithm is about n^2 over
+ 
+
+ align:start position:0%
+algorithm is about n^2 over
+two um but wait we have to do more steps
+
+ align:start position:0%
+two um but wait we have to do more steps
+ 
+
+ align:start position:0%
+two um but wait we have to do more steps
+than just the swaps right we have to
+
+ align:start position:0%
+than just the swaps right we have to
+ 
+
+ align:start position:0%
+than just the swaps right we have to
+like read numbers from memory we have to
+
+ align:start position:0%
+like read numbers from memory we have to
+ 
+
+ align:start position:0%
+like read numbers from memory we have to
+um compare them we have to write numbers
+
+ align:start position:0%
+um compare them we have to write numbers
+ 
+
+ align:start position:0%
+um compare them we have to write numbers
+to memory we have to increment our index
+
+ align:start position:0%
+to memory we have to increment our index
+ 
+
+ align:start position:0%
+to memory we have to increment our index
+we have lots and lots of instructions
+
+ align:start position:0%
+we have lots and lots of instructions
+ 
+
+ align:start position:0%
+we have lots and lots of instructions
+that we have to do during this algorithm
+
+ align:start position:0%
+that we have to do during this algorithm
+ 
+
+ align:start position:0%
+that we have to do during this algorithm
+so maybe it's just those four
+
+ align:start position:0%
+so maybe it's just those four
+ 
+
+ align:start position:0%
+so maybe it's just those four
+instructions every time we make a swap
+
+ align:start position:0%
+instructions every time we make a swap
+ 
+
+ align:start position:0%
+instructions every time we make a swap
+so it's really four times n^2 over two
+
+ align:start position:0%
+so it's really four times n^2 over two
+ 
+
+ align:start position:0%
+so it's really four times n^2 over two
+instructions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right instead of counting swaps we're
+
+ align:start position:0%
+right instead of counting swaps we're
+ 
+
+ align:start position:0%
+right instead of counting swaps we're
+now counting instructions and I'm being
+
+ align:start position:0%
+now counting instructions and I'm being
+ 
+
+ align:start position:0%
+now counting instructions and I'm being
+very loose about that but doesn't matter
+
+ align:start position:0%
+very loose about that but doesn't matter
+ 
+
+ align:start position:0%
+very loose about that but doesn't matter
+um okay well not all instructions are
+
+ align:start position:0%
+um okay well not all instructions are
+ 
+
+ align:start position:0%
+um okay well not all instructions are
+are created equal um every instruction
+
+ align:start position:0%
+are created equal um every instruction
+ 
+
+ align:start position:0%
+are created equal um every instruction
+on your CPU happens on a a fixed regular
+
+ align:start position:0%
+on your CPU happens on a a fixed regular
+ 
+
+ align:start position:0%
+on your CPU happens on a a fixed regular
+clock um and maybe ads
+
+ align:start position:0%
+clock um and maybe ads
+ 
+
+ align:start position:0%
+clock um and maybe ads
+take when we have to increment our index
+
+ align:start position:0%
+take when we have to increment our index
+ 
+
+ align:start position:0%
+take when we have to increment our index
+maybe that takes I don't know five
+
+ align:start position:0%
+maybe that takes I don't know five
+ 
+
+ align:start position:0%
+maybe that takes I don't know five
+Cycles uh and
+
+ align:start position:0%
+Cycles uh and
+ 
+
+ align:start position:0%
+Cycles uh and
+comparisons take 15 cycles and
+
+ align:start position:0%
+comparisons take 15 cycles and
+ 
+
+ align:start position:0%
+comparisons take 15 cycles and
+read and write to memory take I don't
+
+ align:start position:0%
+read and write to memory take I don't
+ 
+
+ align:start position:0%
+read and write to memory take I don't
+know 200 Cycles because memory is a lot
+
+ align:start position:0%
+know 200 Cycles because memory is a lot
+ 
+
+ align:start position:0%
+know 200 Cycles because memory is a lot
+slower than arithmetic I made up these
+
+ align:start position:0%
+slower than arithmetic I made up these
+ 
+
+ align:start position:0%
+slower than arithmetic I made up these
+numbers by the way these aren't real
+
+ align:start position:0%
+numbers by the way these aren't real
+ 
+
+ align:start position:0%
+numbers by the way these aren't real
+don't trust me on that um but in this
+
+ align:start position:0%
+don't trust me on that um but in this
+ 
+
+ align:start position:0%
+don't trust me on that um but in this
+fiction if we're counting Cycles instead
+
+ align:start position:0%
+fiction if we're counting Cycles instead
+ 
+
+ align:start position:0%
+fiction if we're counting Cycles instead
+of instructions we're doing like one of
+
+ align:start position:0%
+of instructions we're doing like one of
+ 
+
+ align:start position:0%
+of instructions we're doing like one of
+each of these per per round or something
+
+ align:start position:0%
+each of these per per round or something
+ 
+
+ align:start position:0%
+each of these per per round or something
+um so really we're doing if I did my
+
+ align:start position:0%
+um so really we're doing if I did my
+ 
+
+ align:start position:0%
+um so really we're doing if I did my
+math right about 210 *
+
+ align:start position:0%
+math right about 210 *
+ 
+
+ align:start position:0%
+math right about 210 *
+n^2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cycles okay so we're changing our unit
+
+ align:start position:0%
+Cycles okay so we're changing our unit
+ 
+
+ align:start position:0%
+Cycles okay so we're changing our unit
+we're measuring different things um
+
+ align:start position:0%
+we're measuring different things um
+ 
+
+ align:start position:0%
+we're measuring different things um
+let's measure something else say we're
+
+ align:start position:0%
+let's measure something else say we're
+ 
+
+ align:start position:0%
+let's measure something else say we're
+on a 2.4 gigahertz processor 2.4
+
+ align:start position:0%
+on a 2.4 gigahertz processor 2.4
+ 
+
+ align:start position:0%
+on a 2.4 gigahertz processor 2.4
+gigahertz processor how long does this
+
+ align:start position:0%
+gigahertz processor how long does this
+ 
+
+ align:start position:0%
+gigahertz processor how long does this
+take in in real life time well it takes
+
+ align:start position:0%
+take in in real life time well it takes
+ 
+
+ align:start position:0%
+take in in real life time well it takes
+about 210 divided 2.4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+billion seconds uh sorry times n^ 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds right so if we change what we're
+
+ align:start position:0%
+seconds right so if we change what we're
+ 
+
+ align:start position:0%
+seconds right so if we change what we're
+measuring if we change our units
+
+ align:start position:0%
+measuring if we change our units
+ 
+
+ align:start position:0%
+measuring if we change our units
+instructions Cycles
+
+ align:start position:0%
+instructions Cycles
+ 
+
+ align:start position:0%
+instructions Cycles
+seconds the thing that stays is the N
+
+ align:start position:0%
+seconds the thing that stays is the N
+ 
+
+ align:start position:0%
+seconds the thing that stays is the N
+squared the constant
+
+ align:start position:0%
+squared the constant
+ 
+
+ align:start position:0%
+squared the constant
+changes but it's always proportional to
+
+ align:start position:0%
+changes but it's always proportional to
+ 
+
+ align:start position:0%
+changes but it's always proportional to
+n^2 get a better um CPU um higher
+
+ align:start position:0%
+n^2 get a better um CPU um higher
+ 
+
+ align:start position:0%
+n^2 get a better um CPU um higher
+throughput your time decreases but only
+
+ align:start position:0%
+throughput your time decreases but only
+ 
+
+ align:start position:0%
+throughput your time decreases but only
+by a constant factor it's still
+
+ align:start position:0%
+by a constant factor it's still
+ 
+
+ align:start position:0%
+by a constant factor it's still
+proportional to
+
+ align:start position:0%
+proportional to
+ 
+
+ align:start position:0%
+proportional to
+n^2 this is another reason that it's
+
+ align:start position:0%
+n^2 this is another reason that it's
+ 
+
+ align:start position:0%
+n^2 this is another reason that it's
+useful to be able to just ignore that
+
+ align:start position:0%
+useful to be able to just ignore that
+ 
+
+ align:start position:0%
+useful to be able to just ignore that
+constant I don't care what it is because
+
+ align:start position:0%
+constant I don't care what it is because
+ 
+
+ align:start position:0%
+constant I don't care what it is because
+I don't really care specifically what
+
+ align:start position:0%
+I don't really care specifically what
+ 
+
+ align:start position:0%
+I don't really care specifically what
+units we're
+
+ align:start position:0%
+units we're
+ 
+
+ align:start position:0%
+units we're
+measuring um I just care that it's
+
+ align:start position:0%
+measuring um I just care that it's
+ 
+
+ align:start position:0%
+measuring um I just care that it's
+proportional to the right
+
+ align:start position:0%
+proportional to the right
+ 
+
+ align:start position:0%
+proportional to the right
+answer does that kind of make sense why
+
+ align:start position:0%
+answer does that kind of make sense why
+ 
+
+ align:start position:0%
+answer does that kind of make sense why
+we might want to throw away information
+
+ align:start position:0%
+we might want to throw away information
+ 
+
+ align:start position:0%
+we might want to throw away information
+like this because it's easier to think
+
+ align:start position:0%
+like this because it's easier to think
+ 
+
+ align:start position:0%
+like this because it's easier to think
+about n squ is easier to think about
+
+ align:start position:0%
+about n squ is easier to think about
+ 
+
+ align:start position:0%
+about n squ is easier to think about
+than all this other junk cluttering it
+
+ align:start position:0%
+than all this other junk cluttering it
+ 
+
+ align:start position:0%
+than all this other junk cluttering it
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+um one more one more motivating example
+
+ align:start position:0%
+um one more one more motivating example
+ 
+
+ align:start position:0%
+um one more one more motivating example
+what's the population of the
+
+ align:start position:0%
+what's the population of the
+ 
+
+ align:start position:0%
+what's the population of the
+US does anyone know just off the top
+
+ align:start position:0%
+US does anyone know just off the top
+ 
+
+ align:start position:0%
+US does anyone know just off the top
+yes about 330 million
+
+ align:start position:0%
+yes about 330 million
+ 
+
+ align:start position:0%
+yes about 330 million
+absolutely about
+
+ align:start position:0%
+absolutely about
+ 
+
+ align:start position:0%
+absolutely about
+335 um what is it um I wrote it down
+
+ align:start position:0%
+335 um what is it um I wrote it down
+ 
+
+ align:start position:0%
+335 um what is it um I wrote it down
+893,00
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that more useful than what your
+
+ align:start position:0%
+is that more useful than what your
+ 
+
+ align:start position:0%
+is that more useful than what your
+colleague said 330
+
+ align:start position:0%
+colleague said 330
+ 
+
+ align:start position:0%
+colleague said 330
+million I don't get any more information
+
+ align:start position:0%
+million I don't get any more information
+ 
+
+ align:start position:0%
+million I don't get any more information
+out of that in in my measly little brain
+
+ align:start position:0%
+out of that in in my measly little brain
+ 
+
+ align:start position:0%
+out of that in in my measly little brain
+330 is I already have trouble conceiving
+
+ align:start position:0%
+330 is I already have trouble conceiving
+ 
+
+ align:start position:0%
+330 is I already have trouble conceiving
+of a number that large I don't need all
+
+ align:start position:0%
+of a number that large I don't need all
+ 
+
+ align:start position:0%
+of a number that large I don't need all
+the extra detail
+
+ align:start position:0%
+the extra detail
+ 
+
+ align:start position:0%
+the extra detail
+right same for algorithm analysis I want
+
+ align:start position:0%
+right same for algorithm analysis I want
+ 
+
+ align:start position:0%
+right same for algorithm analysis I want
+to be able to just focus in on the parts
+
+ align:start position:0%
+to be able to just focus in on the parts
+ 
+
+ align:start position:0%
+to be able to just focus in on the parts
+that matter and have the option to strip
+
+ align:start position:0%
+that matter and have the option to strip
+ 
+
+ align:start position:0%
+that matter and have the option to strip
+off the parts that don't so that's our
+
+ align:start position:0%
+off the parts that don't so that's our
+ 
+
+ align:start position:0%
+off the parts that don't so that's our
+motivation we want to be able to to
+
+ align:start position:0%
+motivation we want to be able to to
+ 
+
+ align:start position:0%
+motivation we want to be able to to
+communicate less information about the
+
+ align:start position:0%
+communicate less information about the
+ 
+
+ align:start position:0%
+communicate less information about the
+run times of our algorithms or about
+
+ align:start position:0%
+run times of our algorithms or about
+ 
+
+ align:start position:0%
+run times of our algorithms or about
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+functions while still being
+
+ align:start position:0%
+functions while still being
+ 
+
+ align:start position:0%
+functions while still being
+mathematically precise about it and
+
+ align:start position:0%
+mathematically precise about it and
+ 
+
+ align:start position:0%
+mathematically precise about it and
+making sure we know what what was lost
+
+ align:start position:0%
+making sure we know what what was lost
+ 
+
+ align:start position:0%
+making sure we know what what was lost
+what information are we retaining and
+
+ align:start position:0%
+what information are we retaining and
+ 
+
+ align:start position:0%
+what information are we retaining and
+what information are we losing never to
+
+ align:start position:0%
+what information are we losing never to
+ 
+
+ align:start position:0%
+what information are we losing never to
+to get again because
+
+ align:start position:0%
+to get again because
+ 
+
+ align:start position:0%
+to get again because
+sometimes you need that extra
+
+ align:start position:0%
+sometimes you need that extra
+ 
+
+ align:start position:0%
+sometimes you need that extra
+information throwing away all this stuff
+
+ align:start position:0%
+information throwing away all this stuff
+ 
+
+ align:start position:0%
+information throwing away all this stuff
+is a great like broad Strokes way to
+
+ align:start position:0%
+is a great like broad Strokes way to
+ 
+
+ align:start position:0%
+is a great like broad Strokes way to
+compare um certain algorithms but if we
+
+ align:start position:0%
+compare um certain algorithms but if we
+ 
+
+ align:start position:0%
+compare um certain algorithms but if we
+have two algorithms that are both
+
+ align:start position:0%
+have two algorithms that are both
+ 
+
+ align:start position:0%
+have two algorithms that are both
+proportional to n log n oh well now that
+
+ align:start position:0%
+proportional to n log n oh well now that
+ 
+
+ align:start position:0%
+proportional to n log n oh well now that
+constant Factor really matters and we
+
+ align:start position:0%
+constant Factor really matters and we
+ 
+
+ align:start position:0%
+constant Factor really matters and we
+better go and figure out what it is
+
+ align:start position:0%
+better go and figure out what it is
+ 
+
+ align:start position:0%
+better go and figure out what it is
+likewise if we're comparing the US
+
+ align:start position:0%
+likewise if we're comparing the US
+ 
+
+ align:start position:0%
+likewise if we're comparing the US
+population between this year and last
+
+ align:start position:0%
+population between this year and last
+ 
+
+ align:start position:0%
+population between this year and last
+year well last year it was also about
+
+ align:start position:0%
+year well last year it was also about
+ 
+
+ align:start position:0%
+year well last year it was also about
+330 million in change so if all we know
+
+ align:start position:0%
+330 million in change so if all we know
+ 
+
+ align:start position:0%
+330 million in change so if all we know
+is 330 330 we can't compare them we
+
+ align:start position:0%
+is 330 330 we can't compare them we
+ 
+
+ align:start position:0%
+is 330 330 we can't compare them we
+don't know if it went up or down or by
+
+ align:start position:0%
+don't know if it went up or down or by
+ 
+
+ align:start position:0%
+don't know if it went up or down or by
+how much um turns out last year it was
+
+ align:start position:0%
+how much um turns out last year it was
+ 
+
+ align:start position:0%
+how much um turns out last year it was
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+334 um2 million
+
+ align:start position:0%
+334 um2 million
+ 
+
+ align:start position:0%
+334 um2 million
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+million so now we had a reason that we
+
+ align:start position:0%
+million so now we had a reason that we
+ 
+
+ align:start position:0%
+million so now we had a reason that we
+wanted more information wanted more
+
+ align:start position:0%
+wanted more information wanted more
+ 
+
+ align:start position:0%
+wanted more information wanted more
+precise measurements of the population
+
+ align:start position:0%
+precise measurements of the population
+ 
+
+ align:start position:0%
+precise measurements of the population
+than just 330
+
+ align:start position:0%
+than just 330
+ 
+
+ align:start position:0%
+than just 330
+million um but wait until you have that
+
+ align:start position:0%
+million um but wait until you have that
+ 
+
+ align:start position:0%
+million um but wait until you have that
+reason let's let's do the broad stroke
+
+ align:start position:0%
+reason let's let's do the broad stroke
+ 
+
+ align:start position:0%
+reason let's let's do the broad stroke
+stuff first and often that'll be
+
+ align:start position:0%
+stuff first and often that'll be
+ 
+
+ align:start position:0%
+stuff first and often that'll be
+enough does that make sense as a
+
+ align:start position:0%
+enough does that make sense as a
+ 
+
+ align:start position:0%
+enough does that make sense as a
+motivation for why we want to throw away
+
+ align:start position:0%
+motivation for why we want to throw away
+ 
+
+ align:start position:0%
+motivation for why we want to throw away
+information about our functions
+
+ align:start position:0%
+information about our functions
+ 
+
+ align:start position:0%
+information about our functions
+nice so
+
+ align:start position:0%
+nice so
+ 
+
+ align:start position:0%
+nice so
+let's talk about how to do
+
+ align:start position:0%
+let's talk about how to do
+ 
+
+ align:start position:0%
+let's talk about how to do
+that uh and the the main one we're going
+
+ align:start position:0%
+that uh and the the main one we're going
+ 
+
+ align:start position:0%
+that uh and the the main one we're going
+to talk about is called Big O
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation the idea this is not yet a
+
+ align:start position:0%
+notation the idea this is not yet a
+ 
+
+ align:start position:0%
+notation the idea this is not yet a
+definition still an idea uh we're going
+
+ align:start position:0%
+definition still an idea uh we're going
+ 
+
+ align:start position:0%
+definition still an idea uh we're going
+to say that F of n belongs to Big O of G
+
+ align:start position:0%
+to say that F of n belongs to Big O of G
+ 
+
+ align:start position:0%
+to say that F of n belongs to Big O of G
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+n weird notation but you'll get used to
+
+ align:start position:0%
+n weird notation but you'll get used to
+ 
+
+ align:start position:0%
+n weird notation but you'll get used to
+it um
+
+ align:start position:0%
+it um
+ 
+
+ align:start position:0%
+it um
+when well roughly
+
+ align:start position:0%
+when well roughly
+ 
+
+ align:start position:0%
+when well roughly
+F of n is less equal to G of
+
+ align:start position:0%
+F of n is less equal to G of
+ 
+
+ align:start position:0%
+F of n is less equal to G of
+n roughly if we say f is Big O of G what
+
+ align:start position:0%
+n roughly if we say f is Big O of G what
+ 
+
+ align:start position:0%
+n roughly if we say f is Big O of G what
+we're saying is that an algorithm with
+
+ align:start position:0%
+we're saying is that an algorithm with
+ 
+
+ align:start position:0%
+we're saying is that an algorithm with
+runtime f ofn is at least as fast maybe
+
+ align:start position:0%
+runtime f ofn is at least as fast maybe
+ 
+
+ align:start position:0%
+runtime f ofn is at least as fast maybe
+maybe much faster than an algorithm with
+
+ align:start position:0%
+maybe much faster than an algorithm with
+ 
+
+ align:start position:0%
+maybe much faster than an algorithm with
+runtime G of
+
+ align:start position:0%
+runtime G of
+ 
+
+ align:start position:0%
+runtime G of
+n with some
+
+ align:start position:0%
+n with some
+ 
+
+ align:start position:0%
+n with some
+caveats with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+caveats first of all let's throw away
+
+ align:start position:0%
+caveats first of all let's throw away
+ 
+
+ align:start position:0%
+caveats first of all let's throw away
+constant factors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we have to scale G up by 10 and now G
+
+ align:start position:0%
+if we have to scale G up by 10 and now G
+ 
+
+ align:start position:0%
+if we have to scale G up by 10 and now G
+is bigger that's fine that's still Big O
+
+ align:start position:0%
+is bigger that's fine that's still Big O
+ 
+
+ align:start position:0%
+is bigger that's fine that's still Big O
+uh and likewise we're going to ignore I
+
+ align:start position:0%
+uh and likewise we're going to ignore I
+ 
+
+ align:start position:0%
+uh and likewise we're going to ignore I
+don't care what happens for small
+
+ align:start position:0%
+don't care what happens for small
+ 
+
+ align:start position:0%
+don't care what happens for small
+numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ignoring small n don't need them I care
+
+ align:start position:0%
+ignoring small n don't need them I care
+ 
+
+ align:start position:0%
+ignoring small n don't need them I care
+about what happens in the limit what are
+
+ align:start position:0%
+about what happens in the limit what are
+ 
+
+ align:start position:0%
+about what happens in the limit what are
+the trends when n gets bigger and bigger
+
+ align:start position:0%
+the trends when n gets bigger and bigger
+ 
+
+ align:start position:0%
+the trends when n gets bigger and bigger
+so these are my intuitions um
+
+ align:start position:0%
+so these are my intuitions um
+ 
+
+ align:start position:0%
+so these are my intuitions um
+also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ignoring lower order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terms I still haven't defined that
+
+ align:start position:0%
+terms I still haven't defined that
+ 
+
+ align:start position:0%
+terms I still haven't defined that
+either by the way but we talked about
+
+ align:start position:0%
+either by the way but we talked about
+ 
+
+ align:start position:0%
+either by the way but we talked about
+them over here like the N /2 was a lower
+
+ align:start position:0%
+them over here like the N /2 was a lower
+ 
+
+ align:start position:0%
+them over here like the N /2 was a lower
+order term compared to n^2 over two I
+
+ align:start position:0%
+order term compared to n^2 over two I
+ 
+
+ align:start position:0%
+order term compared to n^2 over two I
+want to be able to ignore things like
+
+ align:start position:0%
+want to be able to ignore things like
+ 
+
+ align:start position:0%
+want to be able to ignore things like
+that so this is still not precise let's
+
+ align:start position:0%
+that so this is still not precise let's
+ 
+
+ align:start position:0%
+that so this is still not precise let's
+finally finally make it precise after
+
+ align:start position:0%
+finally finally make it precise after
+ 
+
+ align:start position:0%
+finally finally make it precise after
+this question
+
+ align:start position:0%
+this question
+ 
+
+ align:start position:0%
+this question
+yes oh no I want to give the definition
+
+ align:start position:0%
+yes oh no I want to give the definition
+ 
+
+ align:start position:0%
+yes oh no I want to give the definition
+thank
+
+ align:start position:0%
+thank
+ 
+
+ align:start position:0%
+thank
+you uh okay so our definition our actual
+
+ align:start position:0%
+you uh okay so our definition our actual
+ 
+
+ align:start position:0%
+you uh okay so our definition our actual
+final definition of Big O is the
+
+ align:start position:0%
+final definition of Big O is the
+ 
+
+ align:start position:0%
+final definition of Big O is the
+following um f of n is in Big O of G of
+
+ align:start position:0%
+following um f of n is in Big O of G of
+ 
+
+ align:start position:0%
+following um f of n is in Big O of G of
+N
+
+ align:start position:0%
+N
+ 
+
+ align:start position:0%
+N
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+okay there exists a number greater than
+
+ align:start position:0%
+okay there exists a number greater than
+ 
+
+ align:start position:0%
+okay there exists a number greater than
+zero and there exists a natural number
+
+ align:start position:0%
+zero and there exists a natural number
+ 
+
+ align:start position:0%
+zero and there exists a natural number
+and not
+
+ align:start position:0%
+and not
+ 
+
+ align:start position:0%
+and not
+such that for all n greater or equal to
+
+ align:start position:0%
+such that for all n greater or equal to
+ 
+
+ align:start position:0%
+such that for all n greater or equal to
+n f of n is less equal to C
+
+ align:start position:0%
+n f of n is less equal to C
+ 
+
+ align:start position:0%
+n f of n is less equal to C
+* G of
+
+ align:start position:0%
+* G of
+ 
+
+ align:start position:0%
+* G of
+n um and if we're not being if we're not
+
+ align:start position:0%
+n um and if we're not being if we're not
+ 
+
+ align:start position:0%
+n um and if we're not being if we're not
+restricting to positive functions
+
+ align:start position:0%
+restricting to positive functions
+ 
+
+ align:start position:0%
+restricting to positive functions
+sometimes we put an absolute value in
+
+ align:start position:0%
+sometimes we put an absolute value in
+ 
+
+ align:start position:0%
+sometimes we put an absolute value in
+there that's less important the other
+
+ align:start position:0%
+there that's less important the other
+ 
+
+ align:start position:0%
+there that's less important the other
+parts of the formula are the more
+
+ align:start position:0%
+parts of the formula are the more
+ 
+
+ align:start position:0%
+parts of the formula are the more
+important parts there exists a constant
+
+ align:start position:0%
+important parts there exists a constant
+ 
+
+ align:start position:0%
+important parts there exists a constant
+factor C so that f is less equal to C *
+
+ align:start position:0%
+factor C so that f is less equal to C *
+ 
+
+ align:start position:0%
+factor C so that f is less equal to C *
+G that's this ignoring constant
+
+ align:start position:0%
+G that's this ignoring constant
+ 
+
+ align:start position:0%
+G that's this ignoring constant
+factors um there exists an N so that all
+
+ align:start position:0%
+factors um there exists an N so that all
+ 
+
+ align:start position:0%
+factors um there exists an N so that all
+n greater than n greater than or equal
+
+ align:start position:0%
+n greater than n greater than or equal
+ 
+
+ align:start position:0%
+n greater than n greater than or equal
+to n so there's some starting point so
+
+ align:start position:0%
+to n so there's some starting point so
+ 
+
+ align:start position:0%
+to n so there's some starting point so
+that after that starting point this this
+
+ align:start position:0%
+that after that starting point this this
+ 
+
+ align:start position:0%
+that after that starting point this this
+inequality is always true and I don't
+
+ align:start position:0%
+inequality is always true and I don't
+ 
+
+ align:start position:0%
+inequality is always true and I don't
+care what happens before n
+
+ align:start position:0%
+care what happens before n
+ 
+
+ align:start position:0%
+care what happens before n
+knot
+
+ align:start position:0%
+knot
+ 
+
+ align:start position:0%
+knot
+um so that's this point here ignoring
+
+ align:start position:0%
+um so that's this point here ignoring
+ 
+
+ align:start position:0%
+um so that's this point here ignoring
+small n small n are the ones smaller
+
+ align:start position:0%
+small n small n are the ones smaller
+ 
+
+ align:start position:0%
+small n small n are the ones smaller
+than n then n not um n Subzero is
+
+ align:start position:0%
+than n then n not um n Subzero is
+ 
+
+ align:start position:0%
+than n then n not um n Subzero is
+sometimes pronounced n not n a u g
+
+ align:start position:0%
+sometimes pronounced n not n a u g
+ 
+
+ align:start position:0%
+sometimes pronounced n not n a u g
+HT uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question oh gosh yes thank
+
+ align:start position:0%
+question oh gosh yes thank
+ 
+
+ align:start position:0%
+question oh gosh yes thank
+you uh G of
+
+ align:start position:0%
+you uh G of
+ 
+
+ align:start position:0%
+you uh G of
+n not the line I wanted to mess up today
+
+ align:start position:0%
+n not the line I wanted to mess up today
+ 
+
+ align:start position:0%
+n not the line I wanted to mess up today
+thank you so much yes F of n is in bigo
+
+ align:start position:0%
+thank you so much yes F of n is in bigo
+ 
+
+ align:start position:0%
+thank you so much yes F of n is in bigo
+of G of N means roughly that g is bigger
+
+ align:start position:0%
+of G of N means roughly that g is bigger
+ 
+
+ align:start position:0%
+of G of N means roughly that g is bigger
+if you're allowed to scale it by a
+
+ align:start position:0%
+if you're allowed to scale it by a
+ 
+
+ align:start position:0%
+if you're allowed to scale it by a
+constant and throw away small
+
+ align:start position:0%
+constant and throw away small
+ 
+
+ align:start position:0%
+constant and throw away small
+values all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yeah um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um FN is in bigo of g ofn means that
+
+ align:start position:0%
+um FN is in bigo of g ofn means that
+ 
+
+ align:start position:0%
+um FN is in bigo of g ofn means that
+there's some positive value C and some
+
+ align:start position:0%
+there's some positive value C and some
+ 
+
+ align:start position:0%
+there's some positive value C and some
+starting point n KN so that for all
+
+ align:start position:0%
+starting point n KN so that for all
+ 
+
+ align:start position:0%
+starting point n KN so that for all
+input values that are bigger than n not
+
+ align:start position:0%
+input values that are bigger than n not
+ 
+
+ align:start position:0%
+input values that are bigger than n not
+or equal FN is less or equal to C * G of
+
+ align:start position:0%
+or equal FN is less or equal to C * G of
+ 
+
+ align:start position:0%
+or equal FN is less or equal to C * G of
+n uh so this is extending our intuition
+
+ align:start position:0%
+n uh so this is extending our intuition
+ 
+
+ align:start position:0%
+n uh so this is extending our intuition
+that FN is small that f is smaller than
+
+ align:start position:0%
+that FN is small that f is smaller than
+ 
+
+ align:start position:0%
+that FN is small that f is smaller than
+G but you're allowed to put in a
+
+ align:start position:0%
+G but you're allowed to put in a
+ 
+
+ align:start position:0%
+G but you're allowed to put in a
+constant Factor if you need to before
+
+ align:start position:0%
+constant Factor if you need to before
+ 
+
+ align:start position:0%
+constant Factor if you need to before
+that's true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes um yeah so why are the question was
+
+ align:start position:0%
+yes um yeah so why are the question was
+ 
+
+ align:start position:0%
+yes um yeah so why are the question was
+why are we putting in a constant Factor
+
+ align:start position:0%
+why are we putting in a constant Factor
+ 
+
+ align:start position:0%
+why are we putting in a constant Factor
+when the whole point was to ignore the
+
+ align:start position:0%
+when the whole point was to ignore the
+ 
+
+ align:start position:0%
+when the whole point was to ignore the
+constant Factor we ignore it by saying
+
+ align:start position:0%
+constant Factor we ignore it by saying
+ 
+
+ align:start position:0%
+constant Factor we ignore it by saying
+that there exists a constant factor and
+
+ align:start position:0%
+that there exists a constant factor and
+ 
+
+ align:start position:0%
+that there exists a constant factor and
+I don't care what it is as long as some
+
+ align:start position:0%
+I don't care what it is as long as some
+ 
+
+ align:start position:0%
+I don't care what it is as long as some
+constant exists that makes this formula
+
+ align:start position:0%
+constant exists that makes this formula
+ 
+
+ align:start position:0%
+constant exists that makes this formula
+true then f is Big O of
+
+ align:start position:0%
+true then f is Big O of
+ 
+
+ align:start position:0%
+true then f is Big O of
+G um so we put it in so that we can not
+
+ align:start position:0%
+G um so we put it in so that we can not
+ 
+
+ align:start position:0%
+G um so we put it in so that we can not
+care what its value is um yes can the
+
+ align:start position:0%
+care what its value is um yes can the
+ 
+
+ align:start position:0%
+care what its value is um yes can the
+Conant between Z and one can the
+
+ align:start position:0%
+Conant between Z and one can the
+ 
+
+ align:start position:0%
+Conant between Z and one can the
+constant be between zero and one good
+
+ align:start position:0%
+constant be between zero and one good
+ 
+
+ align:start position:0%
+constant be between zero and one good
+question sure why not um if you want to
+
+ align:start position:0%
+question sure why not um if you want to
+ 
+
+ align:start position:0%
+question sure why not um if you want to
+make G smaller and it's still bigger
+
+ align:start position:0%
+make G smaller and it's still bigger
+ 
+
+ align:start position:0%
+make G smaller and it's still bigger
+than F go for
+
+ align:start position:0%
+than F go for
+ 
+
+ align:start position:0%
+than F go for
+it no problems there all right let's do
+
+ align:start position:0%
+it no problems there all right let's do
+ 
+
+ align:start position:0%
+it no problems there all right let's do
+some examples hopefully some concrete
+
+ align:start position:0%
+some examples hopefully some concrete
+ 
+
+ align:start position:0%
+some examples hopefully some concrete
+examples will make this a bit
+
+ align:start position:0%
+examples will make this a bit
+ 
+
+ align:start position:0%
+examples will make this a bit
+clearer um let's
+
+ align:start position:0%
+clearer um let's
+ 
+
+ align:start position:0%
+clearer um let's
+say F of n is n g of n is n
+
+ align:start position:0%
+say F of n is n g of n is n
+ 
+
+ align:start position:0%
+say F of n is n g of n is n
+2 is f of n in Big O of G of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n so is n in Big O of n
+
+ align:start position:0%
+n so is n in Big O of n
+ 
+
+ align:start position:0%
+n so is n in Big O of n
+squ well if this is supposed to say that
+
+ align:start position:0%
+squ well if this is supposed to say that
+ 
+
+ align:start position:0%
+squ well if this is supposed to say that
+the thing on the right is bigger then
+
+ align:start position:0%
+the thing on the right is bigger then
+ 
+
+ align:start position:0%
+the thing on the right is bigger then
+hopefully we would want n squ to be
+
+ align:start position:0%
+hopefully we would want n squ to be
+ 
+
+ align:start position:0%
+hopefully we would want n squ to be
+bigger than n and thankfully it is um in
+
+ align:start position:0%
+bigger than n and thankfully it is um in
+ 
+
+ align:start position:0%
+bigger than n and thankfully it is um in
+this case we don't need the C to help us
+
+ align:start position:0%
+this case we don't need the C to help us
+ 
+
+ align:start position:0%
+this case we don't need the C to help us
+f is already smaller than g n is already
+
+ align:start position:0%
+f is already smaller than g n is already
+ 
+
+ align:start position:0%
+f is already smaller than g n is already
+smaller than
+
+ align:start position:0%
+smaller than
+ 
+
+ align:start position:0%
+smaller than
+n^2 n is less equal to 1 * n^
+
+ align:start position:0%
+n^2 n is less equal to 1 * n^
+ 
+
+ align:start position:0%
+n^2 n is less equal to 1 * n^
+2 for all n for all natural numbers n so
+
+ align:start position:0%
+2 for all n for all natural numbers n so
+ 
+
+ align:start position:0%
+2 for all n for all natural numbers n so
+this would be our n value of zero and
+
+ align:start position:0%
+this would be our n value of zero and
+ 
+
+ align:start position:0%
+this would be our n value of zero and
+this would be our C value of one all we
+
+ align:start position:0%
+this would be our C value of one all we
+ 
+
+ align:start position:0%
+this would be our C value of one all we
+have to do is show that some not exists
+
+ align:start position:0%
+have to do is show that some not exists
+ 
+
+ align:start position:0%
+have to do is show that some not exists
+and some C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exists to make this statement true and
+
+ align:start position:0%
+exists to make this statement true and
+ 
+
+ align:start position:0%
+exists to make this statement true and
+then we're able to conclude that n is
+
+ align:start position:0%
+then we're able to conclude that n is
+ 
+
+ align:start position:0%
+then we're able to conclude that n is
+Big O of n^ s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question um ah good question um don't we
+
+ align:start position:0%
+question um ah good question um don't we
+ 
+
+ align:start position:0%
+question um ah good question um don't we
+need n not to be one because this
+
+ align:start position:0%
+need n not to be one because this
+ 
+
+ align:start position:0%
+need n not to be one because this
+inequality is false when n is between
+
+ align:start position:0%
+inequality is false when n is between
+ 
+
+ align:start position:0%
+inequality is false when n is between
+zero and one um excellent point um
+
+ align:start position:0%
+zero and one um excellent point um
+ 
+
+ align:start position:0%
+zero and one um excellent point um
+I'm going to give two fixes for that
+
+ align:start position:0%
+I'm going to give two fixes for that
+ 
+
+ align:start position:0%
+I'm going to give two fixes for that
+first of all we could change this to one
+
+ align:start position:0%
+first of all we could change this to one
+ 
+
+ align:start position:0%
+first of all we could change this to one
+absolutely that's fine um the other
+
+ align:start position:0%
+absolutely that's fine um the other
+ 
+
+ align:start position:0%
+absolutely that's fine um the other
+change is that let's go ahead and assume
+
+ align:start position:0%
+change is that let's go ahead and assume
+ 
+
+ align:start position:0%
+change is that let's go ahead and assume
+that f and g are mapping the natural
+
+ align:start position:0%
+that f and g are mapping the natural
+ 
+
+ align:start position:0%
+that f and g are mapping the natural
+numbers to the real
+
+ align:start position:0%
+numbers to the real
+ 
+
+ align:start position:0%
+numbers to the real
+numbers so the inputs are just 0 1 2 3
+
+ align:start position:0%
+numbers so the inputs are just 0 1 2 3
+ 
+
+ align:start position:0%
+numbers so the inputs are just 0 1 2 3
+and not all the real numbers in between
+
+ align:start position:0%
+and not all the real numbers in between
+ 
+
+ align:start position:0%
+and not all the real numbers in between
+often that's what we use when we're
+
+ align:start position:0%
+often that's what we use when we're
+ 
+
+ align:start position:0%
+often that's what we use when we're
+analyzing algorithms because we don't
+
+ align:start position:0%
+analyzing algorithms because we don't
+ 
+
+ align:start position:0%
+analyzing algorithms because we don't
+have fractional inputs to to algorithms
+
+ align:start position:0%
+have fractional inputs to to algorithms
+ 
+
+ align:start position:0%
+have fractional inputs to to algorithms
+um you could absolutely do all of this
+
+ align:start position:0%
+um you could absolutely do all of this
+ 
+
+ align:start position:0%
+um you could absolutely do all of this
+analysis and all these definitions if
+
+ align:start position:0%
+analysis and all these definitions if
+ 
+
+ align:start position:0%
+analysis and all these definitions if
+your domain was the reals
+
+ align:start position:0%
+your domain was the reals
+ 
+
+ align:start position:0%
+your domain was the reals
+instead um but let's let's deal with
+
+ align:start position:0%
+instead um but let's let's deal with
+ 
+
+ align:start position:0%
+instead um but let's let's deal with
+Naturals great uh great point also in
+
+ align:start position:0%
+Naturals great uh great point also in
+ 
+
+ align:start position:0%
+Naturals great uh great point also in
+fact why don't we go ahead and assume
+
+ align:start position:0%
+fact why don't we go ahead and assume
+ 
+
+ align:start position:0%
+fact why don't we go ahead and assume
+that all our functions are positive
+
+ align:start position:0%
+that all our functions are positive
+ 
+
+ align:start position:0%
+that all our functions are positive
+valued um then we won't need that weird
+
+ align:start position:0%
+valued um then we won't need that weird
+ 
+
+ align:start position:0%
+valued um then we won't need that weird
+absolute value you can still do a lot of
+
+ align:start position:0%
+absolute value you can still do a lot of
+ 
+
+ align:start position:0%
+absolute value you can still do a lot of
+this um if you allow some of your
+
+ align:start position:0%
+this um if you allow some of your
+ 
+
+ align:start position:0%
+this um if you allow some of your
+functions to be zero or negative but but
+
+ align:start position:0%
+functions to be zero or negative but but
+ 
+
+ align:start position:0%
+functions to be zero or negative but but
+let's not clutter our minds with that
+
+ align:start position:0%
+let's not clutter our minds with that
+ 
+
+ align:start position:0%
+let's not clutter our minds with that
+today let's go ahead and assume that all
+
+ align:start position:0%
+today let's go ahead and assume that all
+ 
+
+ align:start position:0%
+today let's go ahead and assume that all
+of our functions map the natural numbers
+
+ align:start position:0%
+of our functions map the natural numbers
+ 
+
+ align:start position:0%
+of our functions map the natural numbers
+to positive real values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes um the question was is this
+
+ align:start position:0%
+yes um the question was is this
+ 
+
+ align:start position:0%
+yes um the question was is this
+statement equivalent to saying that f is
+
+ align:start position:0%
+statement equivalent to saying that f is
+ 
+
+ align:start position:0%
+statement equivalent to saying that f is
+ASM totically equivalent to some
+
+ align:start position:0%
+ASM totically equivalent to some
+ 
+
+ align:start position:0%
+ASM totically equivalent to some
+constant multiple of G that's a great
+
+ align:start position:0%
+constant multiple of G that's a great
+ 
+
+ align:start position:0%
+constant multiple of G that's a great
+question the answer is no uh and I'll
+
+ align:start position:0%
+question the answer is no uh and I'll
+ 
+
+ align:start position:0%
+question the answer is no uh and I'll
+challenge you to think about why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let's do a few more examples uh
+
+ align:start position:0%
+um let's do a few more examples uh
+ 
+
+ align:start position:0%
+um let's do a few more examples uh
+actually I want to come back over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here all right F of n is n
+
+ align:start position:0%
+here all right F of n is n
+ 
+
+ align:start position:0%
+here all right F of n is n
+s g of n is n F of n in Big O of G of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n is n s smaller than n if you're
+
+ align:start position:0%
+n is n s smaller than n if you're
+ 
+
+ align:start position:0%
+n is n s smaller than n if you're
+allowed to scale by a
+
+ align:start position:0%
+allowed to scale by a
+ 
+
+ align:start position:0%
+allowed to scale by a
+constant and this time the answer is
+
+ align:start position:0%
+constant and this time the answer is
+ 
+
+ align:start position:0%
+constant and this time the answer is
+no um an algorithm that takes n s time
+
+ align:start position:0%
+no um an algorithm that takes n s time
+ 
+
+ align:start position:0%
+no um an algorithm that takes n s time
+certainly wants to look slower take
+
+ align:start position:0%
+certainly wants to look slower take
+ 
+
+ align:start position:0%
+certainly wants to look slower take
+longer than an algorithm that takes n
+
+ align:start position:0%
+longer than an algorithm that takes n
+ 
+
+ align:start position:0%
+longer than an algorithm that takes n
+time so if Big O is going to be useful
+
+ align:start position:0%
+time so if Big O is going to be useful
+ 
+
+ align:start position:0%
+time so if Big O is going to be useful
+for algorithm
+
+ align:start position:0%
+for algorithm
+ 
+
+ align:start position:0%
+for algorithm
+comparison we hope that this would be f
+
+ align:start position:0%
+comparison we hope that this would be f
+ 
+
+ align:start position:0%
+comparison we hope that this would be f
+and thankfully it is and let's talk
+
+ align:start position:0%
+and thankfully it is and let's talk
+ 
+
+ align:start position:0%
+and thankfully it is and let's talk
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+why um so if n s were in Big O of n we
+
+ align:start position:0%
+why um so if n s were in Big O of n we
+ 
+
+ align:start position:0%
+why um so if n s were in Big O of n we
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+need there exists a c and there exists
+
+ align:start position:0%
+need there exists a c and there exists
+ 
+
+ align:start position:0%
+need there exists a c and there exists
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+N so that for all n greater equal to n
+
+ align:start position:0%
+N so that for all n greater equal to n
+ 
+
+ align:start position:0%
+N so that for all n greater equal to n
+KN uh let's see n^2 is less equal to C *
+
+ align:start position:0%
+KN uh let's see n^2 is less equal to C *
+ 
+
+ align:start position:0%
+KN uh let's see n^2 is less equal to C *
+n right I just wrote out the
+
+ align:start position:0%
+n right I just wrote out the
+ 
+
+ align:start position:0%
+n right I just wrote out the
+definition so we would need to be able
+
+ align:start position:0%
+definition so we would need to be able
+ 
+
+ align:start position:0%
+definition so we would need to be able
+to pick some constant and some starting
+
+ align:start position:0%
+to pick some constant and some starting
+ 
+
+ align:start position:0%
+to pick some constant and some starting
+point so that after that starting point
+
+ align:start position:0%
+point so that after that starting point
+ 
+
+ align:start position:0%
+point so that after that starting point
+n^2 is always less equal to that fixed
+
+ align:start position:0%
+n^2 is always less equal to that fixed
+ 
+
+ align:start position:0%
+n^2 is always less equal to that fixed
+constant times n but no matter what
+
+ align:start position:0%
+constant times n but no matter what
+ 
+
+ align:start position:0%
+constant times n but no matter what
+constant we
+
+ align:start position:0%
+constant we
+ 
+
+ align:start position:0%
+constant we
+pick when n gets big enough this
+
+ align:start position:0%
+pick when n gets big enough this
+ 
+
+ align:start position:0%
+pick when n gets big enough this
+inequality is always
+
+ align:start position:0%
+inequality is always
+ 
+
+ align:start position:0%
+inequality is always
+false we can't pick a constant big
+
+ align:start position:0%
+false we can't pick a constant big
+ 
+
+ align:start position:0%
+false we can't pick a constant big
+enough so that this remains true for all
+
+ align:start position:0%
+enough so that this remains true for all
+ 
+
+ align:start position:0%
+enough so that this remains true for all
+n for all big n if we pick C is a th
+
+ align:start position:0%
+n for all big n if we pick C is a th
+ 
+
+ align:start position:0%
+n for all big n if we pick C is a th
+then from a th and one on this
+
+ align:start position:0%
+then from a th and one on this
+ 
+
+ align:start position:0%
+then from a th and one on this
+inequality is going to be be false if C
+
+ align:start position:0%
+inequality is going to be be false if C
+ 
+
+ align:start position:0%
+inequality is going to be be false if C
+is a million then from a million and one
+
+ align:start position:0%
+is a million then from a million and one
+ 
+
+ align:start position:0%
+is a million then from a million and one
+on this inequality is false no matter
+
+ align:start position:0%
+on this inequality is false no matter
+ 
+
+ align:start position:0%
+on this inequality is false no matter
+what C we pick the left side will
+
+ align:start position:0%
+what C we pick the left side will
+ 
+
+ align:start position:0%
+what C we pick the left side will
+overtake the right
+
+ align:start position:0%
+overtake the right
+ 
+
+ align:start position:0%
+overtake the right
+side right and increasing n not doesn't
+
+ align:start position:0%
+side right and increasing n not doesn't
+ 
+
+ align:start position:0%
+side right and increasing n not doesn't
+help with
+
+ align:start position:0%
+help with
+ 
+
+ align:start position:0%
+help with
+that even if we ignore more small values
+
+ align:start position:0%
+that even if we ignore more small values
+ 
+
+ align:start position:0%
+that even if we ignore more small values
+all the big values fail you can't ignore
+
+ align:start position:0%
+all the big values fail you can't ignore
+ 
+
+ align:start position:0%
+all the big values fail you can't ignore
+all the values
+
+ align:start position:0%
+all the values
+ 
+
+ align:start position:0%
+all the values
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um can't
+
+ align:start position:0%
+um can't
+ 
+
+ align:start position:0%
+um can't
+choose c big enough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so thankfully n^2 is not Big O
+
+ align:start position:0%
+all right so thankfully n^2 is not Big O
+ 
+
+ align:start position:0%
+all right so thankfully n^2 is not Big O
+of n uh let's do another example uh is
+
+ align:start position:0%
+of n uh let's do another example uh is
+ 
+
+ align:start position:0%
+of n uh let's do another example uh is
+n^2 + 3 n + 7 is that Big O of
+
+ align:start position:0%
+n^2 + 3 n + 7 is that Big O of
+ 
+
+ align:start position:0%
+n^2 + 3 n + 7 is that Big O of
+n^2 we said we wanted to be able to
+
+ align:start position:0%
+n^2 we said we wanted to be able to
+ 
+
+ align:start position:0%
+n^2 we said we wanted to be able to
+ignore lower order terms ignore things
+
+ align:start position:0%
+ignore lower order terms ignore things
+ 
+
+ align:start position:0%
+ignore lower order terms ignore things
+that look
+
+ align:start position:0%
+that look
+ 
+
+ align:start position:0%
+that look
+smaller um
+
+ align:start position:0%
+smaller um
+ 
+
+ align:start position:0%
+smaller um
+well this one ends up being true and
+
+ align:start position:0%
+well this one ends up being true and
+ 
+
+ align:start position:0%
+well this one ends up being true and
+let's see why well we can write right
+
+ align:start position:0%
+let's see why well we can write right
+ 
+
+ align:start position:0%
+let's see why well we can write right
+there are lots of ways to prove this um
+
+ align:start position:0%
+there are lots of ways to prove this um
+ 
+
+ align:start position:0%
+there are lots of ways to prove this um
+I'm going to be extremely wasteful and
+
+ align:start position:0%
+I'm going to be extremely wasteful and
+ 
+
+ align:start position:0%
+I'm going to be extremely wasteful and
+do the following n^2 + 3 n + 7 is less
+
+ align:start position:0%
+do the following n^2 + 3 n + 7 is less
+ 
+
+ align:start position:0%
+do the following n^2 + 3 n + 7 is less
+equal to n^2 + 3 n^ 2 + 7 n^
+
+ align:start position:0%
+equal to n^2 + 3 n^ 2 + 7 n^
+ 
+
+ align:start position:0%
+equal to n^2 + 3 n^ 2 + 7 n^
+2 all I'm doing is saying this n is less
+
+ align:start position:0%
+2 all I'm doing is saying this n is less
+ 
+
+ align:start position:0%
+2 all I'm doing is saying this n is less
+equal to n s this
+
+ align:start position:0%
+equal to n s this
+ 
+
+ align:start position:0%
+equal to n s this
+seven uh this seven is less equal to 7 n
+
+ align:start position:0%
+seven uh this seven is less equal to 7 n
+ 
+
+ align:start position:0%
+seven uh this seven is less equal to 7 n
+2 right and this
+
+ align:start position:0%
+2 right and this
+ 
+
+ align:start position:0%
+2 right and this
+equals 11 N2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so we've we were able to show that
+
+ align:start position:0%
+and so we've we were able to show that
+ 
+
+ align:start position:0%
+and so we've we were able to show that
+this function is less equal to 11 * this
+
+ align:start position:0%
+this function is less equal to 11 * this
+ 
+
+ align:start position:0%
+this function is less equal to 11 * this
+function for all
+
+ align:start position:0%
+function for all
+ 
+
+ align:start position:0%
+function for all
+n so we can take n equals z and C is 11
+
+ align:start position:0%
+n so we can take n equals z and C is 11
+ 
+
+ align:start position:0%
+n so we can take n equals z and C is 11
+and we're
+
+ align:start position:0%
+and we're
+ 
+
+ align:start position:0%
+and we're
+done so lower order terms like this at
+
+ align:start position:0%
+done so lower order terms like this at
+ 
+
+ align:start position:0%
+done so lower order terms like this at
+most Force us to pick a bigger C if we
+
+ align:start position:0%
+most Force us to pick a bigger C if we
+ 
+
+ align:start position:0%
+most Force us to pick a bigger C if we
+want but again we don't care about the
+
+ align:start position:0%
+want but again we don't care about the
+ 
+
+ align:start position:0%
+want but again we don't care about the
+specific value of C as long as such a
+
+ align:start position:0%
+specific value of C as long as such a
+ 
+
+ align:start position:0%
+specific value of C as long as such a
+value exists so we can always swallow up
+
+ align:start position:0%
+value exists so we can always swallow up
+ 
+
+ align:start position:0%
+value exists so we can always swallow up
+these these smaller terms just absorb
+
+ align:start position:0%
+these these smaller terms just absorb
+ 
+
+ align:start position:0%
+these these smaller terms just absorb
+them into that c constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes good question what if we didn't know
+
+ align:start position:0%
+yes good question what if we didn't know
+ 
+
+ align:start position:0%
+yes good question what if we didn't know
+whether one function is bigger than
+
+ align:start position:0%
+whether one function is bigger than
+ 
+
+ align:start position:0%
+whether one function is bigger than
+another function just by looking at it
+
+ align:start position:0%
+another function just by looking at it
+ 
+
+ align:start position:0%
+another function just by looking at it
+um well that is that is our task um
+
+ align:start position:0%
+um well that is that is our task um
+ 
+
+ align:start position:0%
+um well that is that is our task um
+we're trying to compare these functions
+
+ align:start position:0%
+we're trying to compare these functions
+ 
+
+ align:start position:0%
+we're trying to compare these functions
+and if we don't know which one's bigger
+
+ align:start position:0%
+and if we don't know which one's bigger
+ 
+
+ align:start position:0%
+and if we don't know which one's bigger
+then we better figure figure that out
+
+ align:start position:0%
+then we better figure figure that out
+ 
+
+ align:start position:0%
+then we better figure figure that out
+before we get our
+
+ align:start position:0%
+before we get our
+ 
+
+ align:start position:0%
+before we get our
+answer so I don't have a general way to
+
+ align:start position:0%
+answer so I don't have a general way to
+ 
+
+ align:start position:0%
+answer so I don't have a general way to
+do that um I'm I can just say that it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+necessary um let's do another example 3
+
+ align:start position:0%
+necessary um let's do another example 3
+ 
+
+ align:start position:0%
+necessary um let's do another example 3
+n is that Big O of n minus 4 we were
+
+ align:start position:0%
+n is that Big O of n minus 4 we were
+ 
+
+ align:start position:0%
+n is that Big O of n minus 4 we were
+also saying we'd like to be able to
+
+ align:start position:0%
+also saying we'd like to be able to
+ 
+
+ align:start position:0%
+also saying we'd like to be able to
+ignore lower order terms on the right
+
+ align:start position:0%
+ignore lower order terms on the right
+ 
+
+ align:start position:0%
+ignore lower order terms on the right
+hand side and intuitively that n minus 4
+
+ align:start position:0%
+hand side and intuitively that n minus 4
+ 
+
+ align:start position:0%
+hand side and intuitively that n minus 4
+that minus 4 term doesn't really change
+
+ align:start position:0%
+that minus 4 term doesn't really change
+ 
+
+ align:start position:0%
+that minus 4 term doesn't really change
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+this should still look like Big O of
+
+ align:start position:0%
+this should still look like Big O of
+ 
+
+ align:start position:0%
+this should still look like Big O of
+n right and we can make that precise um
+
+ align:start position:0%
+n right and we can make that precise um
+ 
+
+ align:start position:0%
+n right and we can make that precise um
+nus 4 is greater than or equal to n
+
+ align:start position:0%
+nus 4 is greater than or equal to n
+ 
+
+ align:start position:0%
+nus 4 is greater than or equal to n
+minus well n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+/2 when n is at least
+
+ align:start position:0%
+/2 when n is at least
+ 
+
+ align:start position:0%
+/2 when n is at least
+eight all we're saying is that the N
+
+ align:start position:0%
+eight all we're saying is that the N
+ 
+
+ align:start position:0%
+eight all we're saying is that the N
+function overtakes the four
+
+ align:start position:0%
+function overtakes the four
+ 
+
+ align:start position:0%
+function overtakes the four
+function excuse me so this four we can
+
+ align:start position:0%
+function excuse me so this four we can
+ 
+
+ align:start position:0%
+function excuse me so this four we can
+pretend it's a
+
+ align:start position:0%
+pretend it's a
+ 
+
+ align:start position:0%
+pretend it's a
+n/2 we've lost a lot but it doesn't
+
+ align:start position:0%
+n/2 we've lost a lot but it doesn't
+ 
+
+ align:start position:0%
+n/2 we've lost a lot but it doesn't
+matter because this is still a
+
+ align:start position:0%
+matter because this is still a
+ 
+
+ align:start position:0%
+matter because this is still a
+constant time
+
+ align:start position:0%
+constant time
+ 
+
+ align:start position:0%
+constant time
+n so this
+
+ align:start position:0%
+n so this
+ 
+
+ align:start position:0%
+n so this
+function is bigger than a constant time
+
+ align:start position:0%
+function is bigger than a constant time
+ 
+
+ align:start position:0%
+function is bigger than a constant time
+n and we can use that to do our proof um
+
+ align:start position:0%
+n and we can use that to do our proof um
+ 
+
+ align:start position:0%
+n and we can use that to do our proof um
+3n let's see 3 n is less equal to 6 * 12
+
+ align:start position:0%
+3n let's see 3 n is less equal to 6 * 12
+ 
+
+ align:start position:0%
+3n let's see 3 n is less equal to 6 * 12
+n Which is less equal to 6
+
+ align:start position:0%
+n Which is less equal to 6
+ 
+
+ align:start position:0%
+n Which is less equal to 6
+* um that's that so nus 4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when n is at least
+
+ align:start position:0%
+when n is at least
+ 
+
+ align:start position:0%
+when n is at least
+eight and so now we have our
+
+ align:start position:0%
+eight and so now we have our
+ 
+
+ align:start position:0%
+eight and so now we have our
+C and we have our
+
+ align:start position:0%
+C and we have our
+ 
+
+ align:start position:0%
+C and we have our
+n 3n is less equal to a constant times n
+
+ align:start position:0%
+n 3n is less equal to a constant times n
+ 
+
+ align:start position:0%
+n 3n is less equal to a constant times n
+minus 4 which is the function we care
+
+ align:start position:0%
+minus 4 which is the function we care
+ 
+
+ align:start position:0%
+minus 4 which is the function we care
+about so in the same way we can ignore
+
+ align:start position:0%
+about so in the same way we can ignore
+ 
+
+ align:start position:0%
+about so in the same way we can ignore
+lower order terms on the right again by
+
+ align:start position:0%
+lower order terms on the right again by
+ 
+
+ align:start position:0%
+lower order terms on the right again by
+just swallowing them into the constant C
+
+ align:start position:0%
+just swallowing them into the constant C
+ 
+
+ align:start position:0%
+just swallowing them into the constant C
+at the cost of a slightly higher
+
+ align:start position:0%
+at the cost of a slightly higher
+ 
+
+ align:start position:0%
+at the cost of a slightly higher
+constant C does that make
+
+ align:start position:0%
+constant C does that make
+ 
+
+ align:start position:0%
+constant C does that make
+sense nice now some of you might
+
+ align:start position:0%
+sense nice now some of you might
+ 
+
+ align:start position:0%
+sense nice now some of you might
+recognize the definition of Big O is
+
+ align:start position:0%
+recognize the definition of Big O is
+ 
+
+ align:start position:0%
+recognize the definition of Big O is
+looking a lot like Epsilon Delta
+
+ align:start position:0%
+looking a lot like Epsilon Delta
+ 
+
+ align:start position:0%
+looking a lot like Epsilon Delta
+definitions of limits and you if you
+
+ align:start position:0%
+definitions of limits and you if you
+ 
+
+ align:start position:0%
+definitions of limits and you if you
+haven't seen those that's fine don't
+
+ align:start position:0%
+haven't seen those that's fine don't
+ 
+
+ align:start position:0%
+haven't seen those that's fine don't
+worry it doesn't matter but um they are
+
+ align:start position:0%
+worry it doesn't matter but um they are
+ 
+
+ align:start position:0%
+worry it doesn't matter but um they are
+similar Concepts and we have a useful
+
+ align:start position:0%
+similar Concepts and we have a useful
+ 
+
+ align:start position:0%
+similar Concepts and we have a useful
+fact that um compares the two that I
+
+ align:start position:0%
+fact that um compares the two that I
+ 
+
+ align:start position:0%
+fact that um compares the two that I
+will write down now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem so we're assuming that f and g
+
+ align:start position:0%
+theorem so we're assuming that f and g
+ 
+
+ align:start position:0%
+theorem so we're assuming that f and g
+are functions from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n to r+ to the positive
+
+ align:start position:0%
+n to r+ to the positive
+ 
+
+ align:start position:0%
+n to r+ to the positive
+reals
+
+ align:start position:0%
+reals
+ 
+
+ align:start position:0%
+reals
+if the limit of f of n over G of n as n
+
+ align:start position:0%
+if the limit of f of n over G of n as n
+ 
+
+ align:start position:0%
+if the limit of f of n over G of n as n
+goes to
+
+ align:start position:0%
+goes to
+ 
+
+ align:start position:0%
+goes to
+Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exists and equals
+
+ align:start position:0%
+exists and equals
+ 
+
+ align:start position:0%
+exists and equals
+infinity so if F over G gets arbitrarily
+
+ align:start position:0%
+infinity so if F over G gets arbitrarily
+ 
+
+ align:start position:0%
+infinity so if F over G gets arbitrarily
+big then there's no constant you can
+
+ align:start position:0%
+big then there's no constant you can
+ 
+
+ align:start position:0%
+big then there's no constant you can
+choose to bring G back up to F because F
+
+ align:start position:0%
+choose to bring G back up to F because F
+ 
+
+ align:start position:0%
+choose to bring G back up to F because F
+gets um bigger and bigger compared to
+
+ align:start position:0%
+gets um bigger and bigger compared to
+ 
+
+ align:start position:0%
+gets um bigger and bigger compared to
+G then f is not
+
+ align:start position:0%
+G then f is not
+ 
+
+ align:start position:0%
+G then f is not
+in Big O of
+
+ align:start position:0%
+in Big O of
+ 
+
+ align:start position:0%
+in Big O of
+G
+
+ align:start position:0%
+G
+ 
+
+ align:start position:0%
+G
+likewise if the limit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exists and is less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinity then f is
+
+ align:start position:0%
+infinity then f is
+ 
+
+ align:start position:0%
+infinity then f is
+in Big O of
+
+ align:start position:0%
+in Big O of
+ 
+
+ align:start position:0%
+in Big O of
+G and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finally if the limit does not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exist inconclusive F might be Big O of g
+
+ align:start position:0%
+exist inconclusive F might be Big O of g
+ 
+
+ align:start position:0%
+exist inconclusive F might be Big O of g
+f might not be Big O of G if the limit
+
+ align:start position:0%
+f might not be Big O of G if the limit
+ 
+
+ align:start position:0%
+f might not be Big O of G if the limit
+doesn't exist the limit doesn't help us
+
+ align:start position:0%
+doesn't exist the limit doesn't help us
+ 
+
+ align:start position:0%
+doesn't exist the limit doesn't help us
+get an
+
+ align:start position:0%
+get an
+ 
+
+ align:start position:0%
+get an
+answer but if the limit does exist it
+
+ align:start position:0%
+answer but if the limit does exist it
+ 
+
+ align:start position:0%
+answer but if the limit does exist it
+tells us the answer if the limit exists
+
+ align:start position:0%
+tells us the answer if the limit exists
+ 
+
+ align:start position:0%
+tells us the answer if the limit exists
+it tells us yes in this case no in that
+
+ align:start position:0%
+it tells us yes in this case no in that
+ 
+
+ align:start position:0%
+it tells us yes in this case no in that
+case so this is a one-sided test if the
+
+ align:start position:0%
+case so this is a one-sided test if the
+ 
+
+ align:start position:0%
+case so this is a one-sided test if the
+limit exists you're golden if the limit
+
+ align:start position:0%
+limit exists you're golden if the limit
+ 
+
+ align:start position:0%
+limit exists you're golden if the limit
+doesn't exist you have to fall back to
+
+ align:start position:0%
+doesn't exist you have to fall back to
+ 
+
+ align:start position:0%
+doesn't exist you have to fall back to
+the more complicated
+
+ align:start position:0%
+the more complicated
+ 
+
+ align:start position:0%
+the more complicated
+definition all right uh I'm not going to
+
+ align:start position:0%
+definition all right uh I'm not going to
+ 
+
+ align:start position:0%
+definition all right uh I'm not going to
+prove that it's uh not difficult to
+
+ align:start position:0%
+prove that it's uh not difficult to
+ 
+
+ align:start position:0%
+prove that it's uh not difficult to
+prove it's in the notes if you want to
+
+ align:start position:0%
+prove it's in the notes if you want to
+ 
+
+ align:start position:0%
+prove it's in the notes if you want to
+read about it but let's use it uh let's
+
+ align:start position:0%
+read about it but let's use it uh let's
+ 
+
+ align:start position:0%
+read about it but let's use it uh let's
+see is n^2 in Big O of a million
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n well how do we test that let let's use
+
+ align:start position:0%
+n well how do we test that let let's use
+ 
+
+ align:start position:0%
+n well how do we test that let let's use
+this limit test we can look at the limit
+
+ align:start position:0%
+this limit test we can look at the limit
+ 
+
+ align:start position:0%
+this limit test we can look at the limit
+of f over G of n^2 over a million n as n
+
+ align:start position:0%
+of f over G of n^2 over a million n as n
+ 
+
+ align:start position:0%
+of f over G of n^2 over a million n as n
+goes to Infinity n^2 over a constant
+
+ align:start position:0%
+goes to Infinity n^2 over a constant
+ 
+
+ align:start position:0%
+goes to Infinity n^2 over a constant
+time n that's
+
+ align:start position:0%
+time n that's
+ 
+
+ align:start position:0%
+time n that's
+infinity and so the limit exists it
+
+ align:start position:0%
+infinity and so the limit exists it
+ 
+
+ align:start position:0%
+infinity and so the limit exists it
+equals infinity and that tells us that f
+
+ align:start position:0%
+equals infinity and that tells us that f
+ 
+
+ align:start position:0%
+equals infinity and that tells us that f
+is not Big O of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so very often if you're working with
+
+ align:start position:0%
+so very often if you're working with
+ 
+
+ align:start position:0%
+so very often if you're working with
+actual functions and you can actually
+
+ align:start position:0%
+actual functions and you can actually
+ 
+
+ align:start position:0%
+actual functions and you can actually
+take the limit and the limit actually
+
+ align:start position:0%
+take the limit and the limit actually
+ 
+
+ align:start position:0%
+take the limit and the limit actually
+exists you get your answer much faster
+
+ align:start position:0%
+exists you get your answer much faster
+ 
+
+ align:start position:0%
+exists you get your answer much faster
+than if you were trying to think through
+
+ align:start position:0%
+than if you were trying to think through
+ 
+
+ align:start position:0%
+than if you were trying to think through
+the C's and the nend knots and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whatnot um another example is a thousand
+
+ align:start position:0%
+whatnot um another example is a thousand
+ 
+
+ align:start position:0%
+whatnot um another example is a thousand
+in Big O of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n^2 what the heck do I even mean by that
+
+ align:start position:0%
+n^2 what the heck do I even mean by that
+ 
+
+ align:start position:0%
+n^2 what the heck do I even mean by that
+a thousand isn't a function of N I
+
+ align:start position:0%
+a thousand isn't a function of N I
+ 
+
+ align:start position:0%
+a thousand isn't a function of N I
+thought we were talking about functions
+
+ align:start position:0%
+thought we were talking about functions
+ 
+
+ align:start position:0%
+thought we were talking about functions
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+right well it is a function of n if you
+
+ align:start position:0%
+right well it is a function of n if you
+ 
+
+ align:start position:0%
+right well it is a function of n if you
+want to think of it that way let me plot
+
+ align:start position:0%
+want to think of it that way let me plot
+ 
+
+ align:start position:0%
+want to think of it that way let me plot
+it for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you let let me plot the N
+
+ align:start position:0%
+you let let me plot the N
+ 
+
+ align:start position:0%
+you let let me plot the N
+SAR this is uh n s and let me plot the
+
+ align:start position:0%
+SAR this is uh n s and let me plot the
+ 
+
+ align:start position:0%
+SAR this is uh n s and let me plot the
+function that takes every n and sends it
+
+ align:start position:0%
+function that takes every n and sends it
+ 
+
+ align:start position:0%
+function that takes every n and sends it
+to the value a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+th right right so this is f of n which
+
+ align:start position:0%
+th right right so this is f of n which
+ 
+
+ align:start position:0%
+th right right so this is f of n which
+is defined as no matter what your input
+
+ align:start position:0%
+is defined as no matter what your input
+ 
+
+ align:start position:0%
+is defined as no matter what your input
+is ignore it and spit out a thousand
+
+ align:start position:0%
+is ignore it and spit out a thousand
+ 
+
+ align:start position:0%
+is ignore it and spit out a thousand
+it's the constant function that spits
+
+ align:start position:0%
+it's the constant function that spits
+ 
+
+ align:start position:0%
+it's the constant function that spits
+out a thousand so when you see something
+
+ align:start position:0%
+out a thousand so when you see something
+ 
+
+ align:start position:0%
+out a thousand so when you see something
+like this when you see a constant in one
+
+ align:start position:0%
+like this when you see a constant in one
+ 
+
+ align:start position:0%
+like this when you see a constant in one
+of these ASM totic uh notations it's
+
+ align:start position:0%
+of these ASM totic uh notations it's
+ 
+
+ align:start position:0%
+of these ASM totic uh notations it's
+really talking about the constant
+
+ align:start position:0%
+really talking about the constant
+ 
+
+ align:start position:0%
+really talking about the constant
+function that sends every n to that
+
+ align:start position:0%
+function that sends every n to that
+ 
+
+ align:start position:0%
+function that sends every n to that
+value and in that
+
+ align:start position:0%
+value and in that
+ 
+
+ align:start position:0%
+value and in that
+sense now we can ask is this constant
+
+ align:start position:0%
+sense now we can ask is this constant
+ 
+
+ align:start position:0%
+sense now we can ask is this constant
+function Big O of
+
+ align:start position:0%
+function Big O of
+ 
+
+ align:start position:0%
+function Big O of
+n^2 and we can answer it the same way as
+
+ align:start position:0%
+n^2 and we can answer it the same way as
+ 
+
+ align:start position:0%
+n^2 and we can answer it the same way as
+before by looking at the limmit of f
+
+ align:start position:0%
+before by looking at the limmit of f
+ 
+
+ align:start position:0%
+before by looking at the limmit of f
+over G the limit of f which is a th over
+
+ align:start position:0%
+over G the limit of f which is a th over
+ 
+
+ align:start position:0%
+over G the limit of f which is a th over
+G which is N2 2 as n goes to
+
+ align:start position:0%
+G which is N2 2 as n goes to
+ 
+
+ align:start position:0%
+G which is N2 2 as n goes to
+Infinity that limit is zero so
+
+ align:start position:0%
+Infinity that limit is zero so
+ 
+
+ align:start position:0%
+Infinity that limit is zero so
+yes yes a th is Big O of n^2 when the
+
+ align:start position:0%
+yes yes a th is Big O of n^2 when the
+ 
+
+ align:start position:0%
+yes yes a th is Big O of n^2 when the
+limit exists it's great we're very
+
+ align:start position:0%
+limit exists it's great we're very
+ 
+
+ align:start position:0%
+limit exists it's great we're very
+happy more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+examples we're trying to be permissive
+
+ align:start position:0%
+examples we're trying to be permissive
+ 
+
+ align:start position:0%
+examples we're trying to be permissive
+with constant factors right
+
+ align:start position:0%
+with constant factors right
+ 
+
+ align:start position:0%
+with constant factors right
+so is it true that 3 to the N is Big O
+
+ align:start position:0%
+so is it true that 3 to the N is Big O
+ 
+
+ align:start position:0%
+so is it true that 3 to the N is Big O
+of 2 to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+N if constant factors don't matter then
+
+ align:start position:0%
+N if constant factors don't matter then
+ 
+
+ align:start position:0%
+N if constant factors don't matter then
+maybe I maybe I should be able to change
+
+ align:start position:0%
+maybe I maybe I should be able to change
+ 
+
+ align:start position:0%
+maybe I maybe I should be able to change
+this constant to a different constant
+
+ align:start position:0%
+this constant to a different constant
+ 
+
+ align:start position:0%
+this constant to a different constant
+and it won't really change according to
+
+ align:start position:0%
+and it won't really change according to
+ 
+
+ align:start position:0%
+and it won't really change according to
+Big O is this
+
+ align:start position:0%
+Big O is this
+ 
+
+ align:start position:0%
+Big O is this
+true and this time it's not because we
+
+ align:start position:0%
+true and this time it's not because we
+ 
+
+ align:start position:0%
+true and this time it's not because we
+can try our limit test the limit of f
+
+ align:start position:0%
+can try our limit test the limit of f
+ 
+
+ align:start position:0%
+can try our limit test the limit of f
+over G that's 3 the N over 2 the
+
+ align:start position:0%
+over G that's 3 the N over 2 the
+ 
+
+ align:start position:0%
+over G that's 3 the N over 2 the
+N that's the limit of 1.5 to the
+
+ align:start position:0%
+N that's the limit of 1.5 to the
+ 
+
+ align:start position:0%
+N that's the limit of 1.5 to the
+N which is
+
+ align:start position:0%
+N which is
+ 
+
+ align:start position:0%
+N which is
+infinity so the answer is no changing
+
+ align:start position:0%
+infinity so the answer is no changing
+ 
+
+ align:start position:0%
+infinity so the answer is no changing
+this two to a three isn't changing by a
+
+ align:start position:0%
+this two to a three isn't changing by a
+ 
+
+ align:start position:0%
+this two to a three isn't changing by a
+constant factor it's changing by a
+
+ align:start position:0%
+constant factor it's changing by a
+ 
+
+ align:start position:0%
+constant factor it's changing by a
+constant Factor n
+
+ align:start position:0%
+constant Factor n
+ 
+
+ align:start position:0%
+constant Factor n
+times and that n um gets bigger and
+
+ align:start position:0%
+times and that n um gets bigger and
+ 
+
+ align:start position:0%
+times and that n um gets bigger and
+bigger so the difference between the two
+
+ align:start position:0%
+bigger so the difference between the two
+ 
+
+ align:start position:0%
+bigger so the difference between the two
+sides gets bigger and bigger so this is
+
+ align:start position:0%
+sides gets bigger and bigger so this is
+ 
+
+ align:start position:0%
+sides gets bigger and bigger so this is
+uh this is a no
+
+ align:start position:0%
+uh this is a no
+ 
+
+ align:start position:0%
+uh this is a no
+all right um some quick
+
+ align:start position:0%
+all right um some quick
+ 
+
+ align:start position:0%
+all right um some quick
+notation I've been
+
+ align:start position:0%
+notation I've been
+ 
+
+ align:start position:0%
+notation I've been
+writing F of n is in Big O of G of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n um and this is my preferred notation
+
+ align:start position:0%
+n um and this is my preferred notation
+ 
+
+ align:start position:0%
+n um and this is my preferred notation
+this is set notation f ofn is an element
+
+ align:start position:0%
+this is set notation f ofn is an element
+ 
+
+ align:start position:0%
+this is set notation f ofn is an element
+of this set so big O of G of n is really
+
+ align:start position:0%
+of this set so big O of G of n is really
+ 
+
+ align:start position:0%
+of this set so big O of G of n is really
+a set of all the functions that have the
+
+ align:start position:0%
+a set of all the functions that have the
+ 
+
+ align:start position:0%
+a set of all the functions that have the
+relationship we
+
+ align:start position:0%
+relationship we
+ 
+
+ align:start position:0%
+relationship we
+described this I think is the clearest
+
+ align:start position:0%
+described this I think is the clearest
+ 
+
+ align:start position:0%
+described this I think is the clearest
+notation it's what I it's what I
+
+ align:start position:0%
+notation it's what I it's what I
+ 
+
+ align:start position:0%
+notation it's what I it's what I
+encourage you to use but you're going to
+
+ align:start position:0%
+encourage you to use but you're going to
+ 
+
+ align:start position:0%
+encourage you to use but you're going to
+see some other not ations for example
+
+ align:start position:0%
+see some other not ations for example
+ 
+
+ align:start position:0%
+see some other not ations for example
+you're going to see F of n equals Big O
+
+ align:start position:0%
+you're going to see F of n equals Big O
+ 
+
+ align:start position:0%
+you're going to see F of n equals Big O
+of G of n which is just super confusing
+
+ align:start position:0%
+of G of n which is just super confusing
+ 
+
+ align:start position:0%
+of G of n which is just super confusing
+I don't like it I don't recommend using
+
+ align:start position:0%
+I don't like it I don't recommend using
+ 
+
+ align:start position:0%
+I don't like it I don't recommend using
+it but it is pretty standard in the math
+
+ align:start position:0%
+it but it is pretty standard in the math
+ 
+
+ align:start position:0%
+it but it is pretty standard in the math
+community so you are going to see it so
+
+ align:start position:0%
+community so you are going to see it so
+ 
+
+ align:start position:0%
+community so you are going to see it so
+I have to warn you
+
+ align:start position:0%
+I have to warn you
+ 
+
+ align:start position:0%
+I have to warn you
+um you're also going to see f ofn is
+
+ align:start position:0%
+um you're also going to see f ofn is
+ 
+
+ align:start position:0%
+um you're also going to see f ofn is
+less equal to Big O of G of
+
+ align:start position:0%
+less equal to Big O of G of
+ 
+
+ align:start position:0%
+less equal to Big O of G of
+n this is again an an abuse of notation
+
+ align:start position:0%
+n this is again an an abuse of notation
+ 
+
+ align:start position:0%
+n this is again an an abuse of notation
+FN is a function this thing on the right
+
+ align:start position:0%
+FN is a function this thing on the right
+ 
+
+ align:start position:0%
+FN is a function this thing on the right
+is a set but it's communicating the same
+
+ align:start position:0%
+is a set but it's communicating the same
+ 
+
+ align:start position:0%
+is a set but it's communicating the same
+idea in fact it's emphasizing that same
+
+ align:start position:0%
+idea in fact it's emphasizing that same
+ 
+
+ align:start position:0%
+idea in fact it's emphasizing that same
+idea Big O means that g is bigger than F
+
+ align:start position:0%
+idea Big O means that g is bigger than F
+ 
+
+ align:start position:0%
+idea Big O means that g is bigger than F
+roughly and so this less equal sign is
+
+ align:start position:0%
+roughly and so this less equal sign is
+ 
+
+ align:start position:0%
+roughly and so this less equal sign is
+just a reminder of that so this is also
+
+ align:start position:0%
+just a reminder of that so this is also
+ 
+
+ align:start position:0%
+just a reminder of that so this is also
+good notation I recommend it if you want
+
+ align:start position:0%
+good notation I recommend it if you want
+ 
+
+ align:start position:0%
+good notation I recommend it if you want
+to use
+
+ align:start position:0%
+to use
+ 
+
+ align:start position:0%
+to use
+it um you're also going to see f ofn is
+
+ align:start position:0%
+it um you're also going to see f ofn is
+ 
+
+ align:start position:0%
+it um you're also going to see f ofn is
+Big O G of n instead of is an element of
+
+ align:start position:0%
+Big O G of n instead of is an element of
+ 
+
+ align:start position:0%
+Big O G of n instead of is an element of
+Big O of G of n that's also fine um
+
+ align:start position:0%
+Big O of G of n that's also fine um
+ 
+
+ align:start position:0%
+Big O of G of n that's also fine um
+pretty clear unambiguous
+
+ align:start position:0%
+pretty clear unambiguous
+ 
+
+ align:start position:0%
+pretty clear unambiguous
+all of these mean exactly the same
+
+ align:start position:0%
+all of these mean exactly the same
+ 
+
+ align:start position:0%
+all of these mean exactly the same
+thing sound
+
+ align:start position:0%
+thing sound
+ 
+
+ align:start position:0%
+thing sound
+good all right what you should not write
+
+ align:start position:0%
+good all right what you should not write
+ 
+
+ align:start position:0%
+good all right what you should not write
+ever um so we were
+
+ align:start position:0%
+ever um so we were
+ 
+
+ align:start position:0%
+ever um so we were
+saying uh for example we know that merge
+
+ align:start position:0%
+saying uh for example we know that merge
+ 
+
+ align:start position:0%
+saying uh for example we know that merge
+merge sort MN is less equal to Big O of
+
+ align:start position:0%
+merge sort MN is less equal to Big O of
+ 
+
+ align:start position:0%
+merge sort MN is less equal to Big O of
+uh swap swort of n those two functions
+
+ align:start position:0%
+uh swap swort of n those two functions
+ 
+
+ align:start position:0%
+uh swap swort of n those two functions
+we looked at earlier the n s one and the
+
+ align:start position:0%
+we looked at earlier the n s one and the
+ 
+
+ align:start position:0%
+we looked at earlier the n s one and the
+N log N1 so this is a true statement
+
+ align:start position:0%
+N log N1 so this is a true statement
+ 
+
+ align:start position:0%
+N log N1 so this is a true statement
+right the one was smaller if we want to
+
+ align:start position:0%
+right the one was smaller if we want to
+ 
+
+ align:start position:0%
+right the one was smaller if we want to
+say that the S is
+
+ align:start position:0%
+say that the S is
+ 
+
+ align:start position:0%
+say that the S is
+bigger should we say that SN is greater
+
+ align:start position:0%
+bigger should we say that SN is greater
+ 
+
+ align:start position:0%
+bigger should we say that SN is greater
+or equal to Big O of M of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+N and from the way I'm phrasing the
+
+ align:start position:0%
+N and from the way I'm phrasing the
+ 
+
+ align:start position:0%
+N and from the way I'm phrasing the
+question the answer is probably no um no
+
+ align:start position:0%
+question the answer is probably no um no
+ 
+
+ align:start position:0%
+question the answer is probably no um no
+we should not write this that's like
+
+ align:start position:0%
+we should not write this that's like
+ 
+
+ align:start position:0%
+we should not write this that's like
+saying you must be at least 60 in or
+
+ align:start position:0%
+saying you must be at least 60 in or
+ 
+
+ align:start position:0%
+saying you must be at least 60 in or
+less to ride this
+
+ align:start position:0%
+less to ride this
+ 
+
+ align:start position:0%
+less to ride this
+ride how tall do I need to be
+
+ align:start position:0%
+ride how tall do I need to be
+ 
+
+ align:start position:0%
+ride how tall do I need to be
+6 it's not correct um Big O is functions
+
+ align:start position:0%
+6 it's not correct um Big O is functions
+ 
+
+ align:start position:0%
+6 it's not correct um Big O is functions
+that are smaller than M of N and if
+
+ align:start position:0%
+that are smaller than M of N and if
+ 
+
+ align:start position:0%
+that are smaller than M of N and if
+we're supposed to be bigger than some
+
+ align:start position:0%
+we're supposed to be bigger than some
+ 
+
+ align:start position:0%
+we're supposed to be bigger than some
+functions that are smaller than M of n
+
+ align:start position:0%
+functions that are smaller than M of n
+ 
+
+ align:start position:0%
+functions that are smaller than M of n
+it doesn't make sense don't write that
+
+ align:start position:0%
+it doesn't make sense don't write that
+ 
+
+ align:start position:0%
+it doesn't make sense don't write that
+however this is still an idea that we
+
+ align:start position:0%
+however this is still an idea that we
+ 
+
+ align:start position:0%
+however this is still an idea that we
+often want to communicate s is bigger
+
+ align:start position:0%
+often want to communicate s is bigger
+ 
+
+ align:start position:0%
+often want to communicate s is bigger
+than M we want to emphasize that s is
+
+ align:start position:0%
+than M we want to emphasize that s is
+ 
+
+ align:start position:0%
+than M we want to emphasize that s is
+bigger than M instead of emphasizing
+
+ align:start position:0%
+bigger than M instead of emphasizing
+ 
+
+ align:start position:0%
+bigger than M instead of emphasizing
+that m is smaller than S and we have
+
+ align:start position:0%
+that m is smaller than S and we have
+ 
+
+ align:start position:0%
+that m is smaller than S and we have
+different notation for that instead of a
+
+ align:start position:0%
+different notation for that instead of a
+ 
+
+ align:start position:0%
+different notation for that instead of a
+big O we use S is
+
+ align:start position:0%
+big O we use S is
+ 
+
+ align:start position:0%
+big O we use S is
+big
+
+ align:start position:0%
+big
+ 
+
+ align:start position:0%
+big
+Omega of M of M of
+
+ align:start position:0%
+Omega of M of M of
+ 
+
+ align:start position:0%
+Omega of M of M of
+n so big Omega is just the the reverse
+
+ align:start position:0%
+n so big Omega is just the the reverse
+ 
+
+ align:start position:0%
+n so big Omega is just the the reverse
+of Big O U we have our
+
+ align:start position:0%
+of Big O U we have our
+ 
+
+ align:start position:0%
+of Big O U we have our
+definition f is in big Omega of g
+
+ align:start position:0%
+definition f is in big Omega of g
+ 
+
+ align:start position:0%
+definition f is in big Omega of g
+means that g is in Big O of f let's take
+
+ align:start position:0%
+means that g is in Big O of f let's take
+ 
+
+ align:start position:0%
+means that g is in Big O of f let's take
+that as our
+
+ align:start position:0%
+that as our
+ 
+
+ align:start position:0%
+that as our
+definition and we're getting lots of
+
+ align:start position:0%
+definition and we're getting lots of
+ 
+
+ align:start position:0%
+definition and we're getting lots of
+symbols around here so let's see if we
+
+ align:start position:0%
+symbols around here so let's see if we
+ 
+
+ align:start position:0%
+symbols around here so let's see if we
+can compile them into a table
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we started with f is ASM totically
+
+ align:start position:0%
+so we started with f is ASM totically
+ 
+
+ align:start position:0%
+so we started with f is ASM totically
+equivalent to
+
+ align:start position:0%
+equivalent to
+ 
+
+ align:start position:0%
+equivalent to
+G um the definition is that the limit as
+
+ align:start position:0%
+G um the definition is that the limit as
+ 
+
+ align:start position:0%
+G um the definition is that the limit as
+n goes to Infinity of f of n over G of n
+
+ align:start position:0%
+n goes to Infinity of f of n over G of n
+ 
+
+ align:start position:0%
+n goes to Infinity of f of n over G of n
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+1 the idea the intuition is that f is
+
+ align:start position:0%
+1 the idea the intuition is that f is
+ 
+
+ align:start position:0%
+1 the idea the intuition is that f is
+equivalent to
+
+ align:start position:0%
+equivalent to
+ 
+
+ align:start position:0%
+equivalent to
+G um up to lower order terms lower order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terms that was our
+
+ align:start position:0%
+terms that was our
+ 
+
+ align:start position:0%
+terms that was our
+intuition then we had Big O F is in Big
+
+ align:start position:0%
+intuition then we had Big O F is in Big
+ 
+
+ align:start position:0%
+intuition then we had Big O F is in Big
+O of
+
+ align:start position:0%
+O of
+ 
+
+ align:start position:0%
+O of
+G the definition this time was there
+
+ align:start position:0%
+G the definition this time was there
+ 
+
+ align:start position:0%
+G the definition this time was there
+exists C greater Z there exists uh n KN
+
+ align:start position:0%
+exists C greater Z there exists uh n KN
+ 
+
+ align:start position:0%
+exists C greater Z there exists uh n KN
+greater equal zero so that for all n
+
+ align:start position:0%
+greater equal zero so that for all n
+ 
+
+ align:start position:0%
+greater equal zero so that for all n
+greater equal to
+
+ align:start position:0%
+greater equal to
+ 
+
+ align:start position:0%
+greater equal to
+n uh F of n is less equal to C * G of
+
+ align:start position:0%
+n uh F of n is less equal to C * G of
+ 
+
+ align:start position:0%
+n uh F of n is less equal to C * G of
+n so that's our definition
+
+ align:start position:0%
+n so that's our definition
+ 
+
+ align:start position:0%
+n so that's our definition
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+intuition is that f is less equal to
+
+ align:start position:0%
+intuition is that f is less equal to
+ 
+
+ align:start position:0%
+intuition is that f is less equal to
+G up to constant values up to constant
+
+ align:start position:0%
+G up to constant values up to constant
+ 
+
+ align:start position:0%
+G up to constant values up to constant
+factors and I'll say lower order
+
+ align:start position:0%
+factors and I'll say lower order
+ 
+
+ align:start position:0%
+factors and I'll say lower order
+terms and ignoring small numbers but
+
+ align:start position:0%
+terms and ignoring small numbers but
+ 
+
+ align:start position:0%
+terms and ignoring small numbers but
+that one does that
+
+ align:start position:0%
+that one does that
+ 
+
+ align:start position:0%
+that one does that
+too please don't confuse the intuition
+
+ align:start position:0%
+too please don't confuse the intuition
+ 
+
+ align:start position:0%
+too please don't confuse the intuition
+with the
+
+ align:start position:0%
+with the
+ 
+
+ align:start position:0%
+with the
+definition and please don't use the
+
+ align:start position:0%
+definition and please don't use the
+ 
+
+ align:start position:0%
+definition and please don't use the
+intuition language in your proofs use
+
+ align:start position:0%
+intuition language in your proofs use
+ 
+
+ align:start position:0%
+intuition language in your proofs use
+the the definition language in your
+
+ align:start position:0%
+the the definition language in your
+ 
+
+ align:start position:0%
+the the definition language in your
+proofs so think about it this way but
+
+ align:start position:0%
+proofs so think about it this way but
+ 
+
+ align:start position:0%
+proofs so think about it this way but
+write it this
+
+ align:start position:0%
+write it this
+ 
+
+ align:start position:0%
+write it this
+way and we Justus
+
+ align:start position:0%
+way and we Justus
+ 
+
+ align:start position:0%
+way and we Justus
+defined f is in big Omega of
+
+ align:start position:0%
+defined f is in big Omega of
+ 
+
+ align:start position:0%
+defined f is in big Omega of
+g means the definition is that
+
+ align:start position:0%
+g means the definition is that
+ 
+
+ align:start position:0%
+g means the definition is that
+g uh is in Big O of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F and the idea is that uh G is greater
+
+ align:start position:0%
+F and the idea is that uh G is greater
+ 
+
+ align:start position:0%
+F and the idea is that uh G is greater
+sorry is
+
+ align:start position:0%
+sorry is
+ 
+
+ align:start position:0%
+sorry is
+that f is greater equal to
+
+ align:start position:0%
+that f is greater equal to
+ 
+
+ align:start position:0%
+that f is greater equal to
+G up two
+
+ align:start position:0%
+G up two
+ 
+
+ align:start position:0%
+G up two
+constants and lower order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+terms right so we have a a more
+
+ align:start position:0%
+terms right so we have a a more
+ 
+
+ align:start position:0%
+terms right so we have a a more
+permissive version of less equal that's
+
+ align:start position:0%
+permissive version of less equal that's
+ 
+
+ align:start position:0%
+permissive version of less equal that's
+Big O A more permissive version of
+
+ align:start position:0%
+Big O A more permissive version of
+ 
+
+ align:start position:0%
+Big O A more permissive version of
+greater equal that's big
+
+ align:start position:0%
+greater equal that's big
+ 
+
+ align:start position:0%
+greater equal that's big
+Omega questions about
+
+ align:start position:0%
+Omega questions about
+ 
+
+ align:start position:0%
+Omega questions about
+that all
+
+ align:start position:0%
+that all
+ 
+
+ align:start position:0%
+that all
+right um what did I want to say about
+
+ align:start position:0%
+right um what did I want to say about
+ 
+
+ align:start position:0%
+right um what did I want to say about
+that let me Define one more while I'm
+
+ align:start position:0%
+that let me Define one more while I'm
+ 
+
+ align:start position:0%
+that let me Define one more while I'm
+over here f is in Theta
+
+ align:start position:0%
+over here f is in Theta
+ 
+
+ align:start position:0%
+over here f is in Theta
+of G that's a capital Greek
+
+ align:start position:0%
+of G that's a capital Greek
+ 
+
+ align:start position:0%
+of G that's a capital Greek
+Theta um and this is going to mean
+
+ align:start position:0%
+Theta um and this is going to mean
+ 
+
+ align:start position:0%
+Theta um and this is going to mean
+roughly uh f equals
+
+ align:start position:0%
+roughly uh f equals
+ 
+
+ align:start position:0%
+roughly uh f equals
+g sorry f is approximately equal to
+
+ align:start position:0%
+g sorry f is approximately equal to
+ 
+
+ align:start position:0%
+g sorry f is approximately equal to
+G up to
+
+ align:start position:0%
+G up to
+ 
+
+ align:start position:0%
+G up to
+constants and lower order
+
+ align:start position:0%
+constants and lower order
+ 
+
+ align:start position:0%
+constants and lower order
+terms and the definition is just
+
+ align:start position:0%
+terms and the definition is just
+ 
+
+ align:start position:0%
+terms and the definition is just
+f is in Big O of
+
+ align:start position:0%
+f is in Big O of
+ 
+
+ align:start position:0%
+f is in Big O of
+G and G is in in Big O of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f so f and g are roughly within constant
+
+ align:start position:0%
+f so f and g are roughly within constant
+ 
+
+ align:start position:0%
+f so f and g are roughly within constant
+factors of each other in both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+directions uh and I want to call
+
+ align:start position:0%
+directions uh and I want to call
+ 
+
+ align:start position:0%
+directions uh and I want to call
+attention to this first one versus this
+
+ align:start position:0%
+attention to this first one versus this
+ 
+
+ align:start position:0%
+attention to this first one versus this
+last
+
+ align:start position:0%
+last
+ 
+
+ align:start position:0%
+last
+one ASM totic equivalence said that f
+
+ align:start position:0%
+one ASM totic equivalence said that f
+ 
+
+ align:start position:0%
+one ASM totic equivalence said that f
+and g were roughly equal up to lower
+
+ align:start position:0%
+and g were roughly equal up to lower
+ 
+
+ align:start position:0%
+and g were roughly equal up to lower
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+terms Theta says that f and g are
+
+ align:start position:0%
+terms Theta says that f and g are
+ 
+
+ align:start position:0%
+terms Theta says that f and g are
+approximately equal up to con constant
+
+ align:start position:0%
+approximately equal up to con constant
+ 
+
+ align:start position:0%
+approximately equal up to con constant
+factors and lower order
+
+ align:start position:0%
+factors and lower order
+ 
+
+ align:start position:0%
+factors and lower order
+terms Theta is more permissive than
+
+ align:start position:0%
+terms Theta is more permissive than
+ 
+
+ align:start position:0%
+terms Theta is more permissive than
+Tilda um where did I leave off on the
+
+ align:start position:0%
+Tilda um where did I leave off on the
+ 
+
+ align:start position:0%
+Tilda um where did I leave off on the
+boards over here yeah over
+
+ align:start position:0%
+boards over here yeah over
+ 
+
+ align:start position:0%
+boards over here yeah over
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B so we can say that our our s of n
+
+ align:start position:0%
+B so we can say that our our s of n
+ 
+
+ align:start position:0%
+B so we can say that our our s of n
+function our our swap sort our simple
+
+ align:start position:0%
+function our our swap sort our simple
+ 
+
+ align:start position:0%
+function our our swap sort our simple
+sort function n^2 over two and junk
+
+ align:start position:0%
+sort function n^2 over two and junk
+ 
+
+ align:start position:0%
+sort function n^2 over two and junk
+uh is in Theta of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n^2 it's both greater than um n^2 and
+
+ align:start position:0%
+n^2 it's both greater than um n^2 and
+ 
+
+ align:start position:0%
+n^2 it's both greater than um n^2 and
+less than n^2 if you're allowed to put
+
+ align:start position:0%
+less than n^2 if you're allowed to put
+ 
+
+ align:start position:0%
+less than n^2 if you're allowed to put
+constants in
+
+ align:start position:0%
+constants in
+ 
+
+ align:start position:0%
+constants in
+there all
+
+ align:start position:0%
+there all
+ 
+
+ align:start position:0%
+there all
+right um what's not
+
+ align:start position:0%
+right um what's not
+ 
+
+ align:start position:0%
+right um what's not
+true is SN is ASM totically equivalent
+
+ align:start position:0%
+true is SN is ASM totically equivalent
+ 
+
+ align:start position:0%
+true is SN is ASM totically equivalent
+to N2 this is
+
+ align:start position:0%
+to N2 this is
+ 
+
+ align:start position:0%
+to N2 this is
+false um because if you if you take this
+
+ align:start position:0%
+false um because if you if you take this
+ 
+
+ align:start position:0%
+false um because if you if you take this
+and divide by that and take the limit
+
+ align:start position:0%
+and divide by that and take the limit
+ 
+
+ align:start position:0%
+and divide by that and take the limit
+you get two not one that n^2 over two
+
+ align:start position:0%
+you get two not one that n^2 over two
+ 
+
+ align:start position:0%
+you get two not one that n^2 over two
+matters um so this cares what that
+
+ align:start position:0%
+matters um so this cares what that
+ 
+
+ align:start position:0%
+matters um so this cares what that
+constant factor is this doesn't um this
+
+ align:start position:0%
+constant factor is this doesn't um this
+ 
+
+ align:start position:0%
+constant factor is this doesn't um this
+would be a true statement if you put the
+
+ align:start position:0%
+would be a true statement if you put the
+ 
+
+ align:start position:0%
+would be a true statement if you put the
+one/ half in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there so the ASM totic equivalence does
+
+ align:start position:0%
+there so the ASM totic equivalence does
+ 
+
+ align:start position:0%
+there so the ASM totic equivalence does
+single out that constant Factor whereas
+
+ align:start position:0%
+single out that constant Factor whereas
+ 
+
+ align:start position:0%
+single out that constant Factor whereas
+Theta ignores that constant
+
+ align:start position:0%
+Theta ignores that constant
+ 
+
+ align:start position:0%
+Theta ignores that constant
+Factor was there a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay so the question was um similar
+
+ align:start position:0%
+um okay so the question was um similar
+ 
+
+ align:start position:0%
+um okay so the question was um similar
+to your previous question um does f in
+
+ align:start position:0%
+to your previous question um does f in
+ 
+
+ align:start position:0%
+to your previous question um does f in
+Theta of g
+
+ align:start position:0%
+Theta of g
+ 
+
+ align:start position:0%
+Theta of g
+mean that there exists a
+
+ align:start position:0%
+mean that there exists a
+ 
+
+ align:start position:0%
+mean that there exists a
+constant such that f is Tilda of C time
+
+ align:start position:0%
+constant such that f is Tilda of C time
+ 
+
+ align:start position:0%
+constant such that f is Tilda of C time
+G that's a really good
+
+ align:start position:0%
+G that's a really good
+ 
+
+ align:start position:0%
+G that's a really good
+question um
+
+ align:start position:0%
+question um
+ 
+
+ align:start position:0%
+question um
+and the answer I will tell you um is
+
+ align:start position:0%
+and the answer I will tell you um is
+ 
+
+ align:start position:0%
+and the answer I will tell you um is
+actually the other
+
+ align:start position:0%
+actually the other
+ 
+
+ align:start position:0%
+actually the other
+way if there's a constant factor between
+
+ align:start position:0%
+way if there's a constant factor between
+ 
+
+ align:start position:0%
+way if there's a constant factor between
+them and then the limit goes to one uh
+
+ align:start position:0%
+them and then the limit goes to one uh
+ 
+
+ align:start position:0%
+them and then the limit goes to one uh
+then absolutely they are Theta of each
+
+ align:start position:0%
+then absolutely they are Theta of each
+ 
+
+ align:start position:0%
+then absolutely they are Theta of each
+other but there doesn't have to be that
+
+ align:start position:0%
+other but there doesn't have to be that
+ 
+
+ align:start position:0%
+other but there doesn't have to be that
+constant factor and let's look at an
+
+ align:start position:0%
+constant factor and let's look at an
+ 
+
+ align:start position:0%
+constant factor and let's look at an
+example of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see 3 + sin of
+
+ align:start position:0%
+let's see 3 + sin of
+ 
+
+ align:start position:0%
+let's see 3 + sin of
+n is that
+
+ align:start position:0%
+n is that
+ 
+
+ align:start position:0%
+n is that
+Theta of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one 3 + S of n we want to know is it
+
+ align:start position:0%
+one 3 + S of n we want to know is it
+ 
+
+ align:start position:0%
+one 3 + S of n we want to know is it
+Theta of
+
+ align:start position:0%
+Theta of
+ 
+
+ align:start position:0%
+Theta of
+one so is it bounded below and bounded
+
+ align:start position:0%
+one so is it bounded below and bounded
+ 
+
+ align:start position:0%
+one so is it bounded below and bounded
+above by some constant times
+
+ align:start position:0%
+above by some constant times
+ 
+
+ align:start position:0%
+above by some constant times
+one and in this case yes it is because 2
+
+ align:start position:0%
+one and in this case yes it is because 2
+ 
+
+ align:start position:0%
+one and in this case yes it is because 2
+is less equal to 3 + s of n Which is
+
+ align:start position:0%
+is less equal to 3 + s of n Which is
+ 
+
+ align:start position:0%
+is less equal to 3 + s of n Which is
+less equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four so there's we can scale this by a
+
+ align:start position:0%
+four so there's we can scale this by a
+ 
+
+ align:start position:0%
+four so there's we can scale this by a
+constant and it's always smaller than
+
+ align:start position:0%
+constant and it's always smaller than
+ 
+
+ align:start position:0%
+constant and it's always smaller than
+our function we can scale this by a
+
+ align:start position:0%
+our function we can scale this by a
+ 
+
+ align:start position:0%
+our function we can scale this by a
+different constant and it's always
+
+ align:start position:0%
+different constant and it's always
+ 
+
+ align:start position:0%
+different constant and it's always
+bigger than our function and that's the
+
+ align:start position:0%
+bigger than our function and that's the
+ 
+
+ align:start position:0%
+bigger than our function and that's the
+condition we needed for Big O on both
+
+ align:start position:0%
+condition we needed for Big O on both
+ 
+
+ align:start position:0%
+condition we needed for Big O on both
+sides so yes this is
+
+ align:start position:0%
+sides so yes this is
+ 
+
+ align:start position:0%
+sides so yes this is
+true however you're never going to find
+
+ align:start position:0%
+true however you're never going to find
+ 
+
+ align:start position:0%
+true however you're never going to find
+a constant where 3 + sin of
+
+ align:start position:0%
+a constant where 3 + sin of
+ 
+
+ align:start position:0%
+a constant where 3 + sin of
+n is ASM totically equivalent to that
+
+ align:start position:0%
+n is ASM totically equivalent to that
+ 
+
+ align:start position:0%
+n is ASM totically equivalent to that
+constant * 1
+
+ align:start position:0%
+constant * 1
+ 
+
+ align:start position:0%
+constant * 1
+because that ratio isn't going to have a
+
+ align:start position:0%
+because that ratio isn't going to have a
+ 
+
+ align:start position:0%
+because that ratio isn't going to have a
+limit this is an example where the
+
+ align:start position:0%
+limit this is an example where the
+ 
+
+ align:start position:0%
+limit this is an example where the
+limit of 3 + sin of n over
+
+ align:start position:0%
+limit of 3 + sin of n over
+ 
+
+ align:start position:0%
+limit of 3 + sin of n over
+one does not
+
+ align:start position:0%
+one does not
+ 
+
+ align:start position:0%
+one does not
+exist the function just keeps doing this
+
+ align:start position:0%
+exist the function just keeps doing this
+ 
+
+ align:start position:0%
+exist the function just keeps doing this
+forever and never settles down and picks
+
+ align:start position:0%
+forever and never settles down and picks
+ 
+
+ align:start position:0%
+forever and never settles down and picks
+a single
+
+ align:start position:0%
+a single
+ 
+
+ align:start position:0%
+a single
+value so this is an example where the
+
+ align:start position:0%
+value so this is an example where the
+ 
+
+ align:start position:0%
+value so this is an example where the
+limit between them does not
+
+ align:start position:0%
+limit between them does not
+ 
+
+ align:start position:0%
+limit between them does not
+exist but still they are Big O of each
+
+ align:start position:0%
+exist but still they are Big O of each
+ 
+
+ align:start position:0%
+exist but still they are Big O of each
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right um in fact in both directions we
+
+ align:start position:0%
+right um in fact in both directions we
+ 
+
+ align:start position:0%
+right um in fact in both directions we
+mentioned earlier that if the limit
+
+ align:start position:0%
+mentioned earlier that if the limit
+ 
+
+ align:start position:0%
+mentioned earlier that if the limit
+doesn't exist sometimes um they are not
+
+ align:start position:0%
+doesn't exist sometimes um they are not
+ 
+
+ align:start position:0%
+doesn't exist sometimes um they are not
+Big O of each other can anyone think of
+
+ align:start position:0%
+Big O of each other can anyone think of
+ 
+
+ align:start position:0%
+Big O of each other can anyone think of
+an example of that two functions uh
+
+ align:start position:0%
+an example of that two functions uh
+ 
+
+ align:start position:0%
+an example of that two functions uh
+whose ratio does not have a limit where
+
+ align:start position:0%
+whose ratio does not have a limit where
+ 
+
+ align:start position:0%
+whose ratio does not have a limit where
+f is not Big O of G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+tricky uh let me give Let me Give an
+
+ align:start position:0%
+tricky uh let me give Let me Give an
+ 
+
+ align:start position:0%
+tricky uh let me give Let me Give an
+example uh let's say that F of
+
+ align:start position:0%
+example uh let's say that F of
+ 
+
+ align:start position:0%
+example uh let's say that F of
+n is
+
+ align:start position:0%
+n is
+ 
+
+ align:start position:0%
+n is
+n and G of n is one when n is
+
+ align:start position:0%
+n and G of n is one when n is
+ 
+
+ align:start position:0%
+n and G of n is one when n is
+odd and n^ S when n is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+even so if we plot
+
+ align:start position:0%
+even so if we plot
+ 
+
+ align:start position:0%
+even so if we plot
+F of n is just n g of n um is following
+
+ align:start position:0%
+F of n is just n g of n um is following
+ 
+
+ align:start position:0%
+F of n is just n g of n um is following
+one or n s depending where you are and
+
+ align:start position:0%
+one or n s depending where you are and
+ 
+
+ align:start position:0%
+one or n s depending where you are and
+it's sort of zigzagging between the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two if you scale G by a constant you'll
+
+ align:start position:0%
+two if you scale G by a constant you'll
+ 
+
+ align:start position:0%
+two if you scale G by a constant you'll
+never be able to make it bigger or
+
+ align:start position:0%
+never be able to make it bigger or
+ 
+
+ align:start position:0%
+never be able to make it bigger or
+smaller than
+
+ align:start position:0%
+smaller than
+ 
+
+ align:start position:0%
+smaller than
+n um because the the ratio is is too
+
+ align:start position:0%
+n um because the the ratio is is too
+ 
+
+ align:start position:0%
+n um because the the ratio is is too
+much depending whether you're looking at
+
+ align:start position:0%
+much depending whether you're looking at
+ 
+
+ align:start position:0%
+much depending whether you're looking at
+the odds or the evens
+
+ align:start position:0%
+the odds or the evens
+ 
+
+ align:start position:0%
+the odds or the evens
+um you can't scale it in either
+
+ align:start position:0%
+um you can't scale it in either
+ 
+
+ align:start position:0%
+um you can't scale it in either
+direction so F in Big O of G is
+
+ align:start position:0%
+direction so F in Big O of G is
+ 
+
+ align:start position:0%
+direction so F in Big O of G is
+false and G in Big O of f is also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+false um and it was specially
+
+ align:start position:0%
+false um and it was specially
+ 
+
+ align:start position:0%
+false um and it was specially
+constructed so that
+
+ align:start position:0%
+constructed so that
+ 
+
+ align:start position:0%
+constructed so that
+limit of f over G as n goes to
+
+ align:start position:0%
+limit of f over G as n goes to
+ 
+
+ align:start position:0%
+limit of f over G as n goes to
+Infinity um does not
+
+ align:start position:0%
+Infinity um does not
+ 
+
+ align:start position:0%
+Infinity um does not
+exist because on the odds F overg grows
+
+ align:start position:0%
+exist because on the odds F overg grows
+ 
+
+ align:start position:0%
+exist because on the odds F overg grows
+really big and on the evens f over G is
+
+ align:start position:0%
+really big and on the evens f over G is
+ 
+
+ align:start position:0%
+really big and on the evens f over G is
+really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+small sound good
+
+ align:start position:0%
+small sound good
+ 
+
+ align:start position:0%
+small sound good
+nice all
+
+ align:start position:0%
+nice all
+ 
+
+ align:start position:0%
+nice all
+right speaking of getting really big and
+
+ align:start position:0%
+right speaking of getting really big and
+ 
+
+ align:start position:0%
+right speaking of getting really big and
+really small um there are two more ASM
+
+ align:start position:0%
+really small um there are two more ASM
+ 
+
+ align:start position:0%
+really small um there are two more ASM
+totic symbols that we need to add to our
+
+ align:start position:0%
+totic symbols that we need to add to our
+ 
+
+ align:start position:0%
+totic symbols that we need to add to our
+table uh and those are the last two I
+
+ align:start position:0%
+table uh and those are the last two I
+ 
+
+ align:start position:0%
+table uh and those are the last two I
+promise um the first one I want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Define is
+
+ align:start position:0%
+Define is
+ 
+
+ align:start position:0%
+Define is
+called little o
+
+ align:start position:0%
+called little o
+ 
+
+ align:start position:0%
+called little o
+so f is in little o of
+
+ align:start position:0%
+so f is in little o of
+ 
+
+ align:start position:0%
+so f is in little o of
+G the definition is going to be that the
+
+ align:start position:0%
+G the definition is going to be that the
+ 
+
+ align:start position:0%
+G the definition is going to be that the
+limit as n goes to
+
+ align:start position:0%
+limit as n goes to
+ 
+
+ align:start position:0%
+limit as n goes to
+Infinity of f of n over G of
+
+ align:start position:0%
+Infinity of f of n over G of
+ 
+
+ align:start position:0%
+Infinity of f of n over G of
+n equals z and the
+
+ align:start position:0%
+n equals z and the
+ 
+
+ align:start position:0%
+n equals z and the
+intuition is that f is much much much
+
+ align:start position:0%
+intuition is that f is much much much
+ 
+
+ align:start position:0%
+intuition is that f is much much much
+smaller than
+
+ align:start position:0%
+smaller than
+ 
+
+ align:start position:0%
+smaller than
+G if we want to say that f is
+
+ align:start position:0%
+G if we want to say that f is
+ 
+
+ align:start position:0%
+G if we want to say that f is
+insignificant compared to G
+
+ align:start position:0%
+insignificant compared to G
+ 
+
+ align:start position:0%
+insignificant compared to G
+that's just saying that the limit
+
+ align:start position:0%
+that's just saying that the limit
+ 
+
+ align:start position:0%
+that's just saying that the limit
+between them goes to
+
+ align:start position:0%
+between them goes to
+ 
+
+ align:start position:0%
+between them goes to
+zero right so that's our that's going to
+
+ align:start position:0%
+zero right so that's our that's going to
+ 
+
+ align:start position:0%
+zero right so that's our that's going to
+be our definition of little O notation
+
+ align:start position:0%
+be our definition of little O notation
+ 
+
+ align:start position:0%
+be our definition of little O notation
+wise little o and Big O look
+
+ align:start position:0%
+wise little o and Big O look
+ 
+
+ align:start position:0%
+wise little o and Big O look
+similar um so when you're writing those
+
+ align:start position:0%
+similar um so when you're writing those
+ 
+
+ align:start position:0%
+similar um so when you're writing those
+by hand please try to exaggerate uh I I
+
+ align:start position:0%
+by hand please try to exaggerate uh I I
+ 
+
+ align:start position:0%
+by hand please try to exaggerate uh I I
+like to write My Little O's really
+
+ align:start position:0%
+like to write My Little O's really
+ 
+
+ align:start position:0%
+like to write My Little O's really
+really small um like even smaller than
+
+ align:start position:0%
+really small um like even smaller than
+ 
+
+ align:start position:0%
+really small um like even smaller than
+other lowercase letters and I like to
+
+ align:start position:0%
+other lowercase letters and I like to
+ 
+
+ align:start position:0%
+other lowercase letters and I like to
+write my Big O really really big not
+
+ align:start position:0%
+write my Big O really really big not
+ 
+
+ align:start position:0%
+write my Big O really really big not
+like hilariously big but noticeably big
+
+ align:start position:0%
+like hilariously big but noticeably big
+ 
+
+ align:start position:0%
+like hilariously big but noticeably big
+so no one's going to confuse it for a
+
+ align:start position:0%
+so no one's going to confuse it for a
+ 
+
+ align:start position:0%
+so no one's going to confuse it for a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+o
+
+ align:start position:0%
+o
+ 
+
+ align:start position:0%
+o
+um annoying notation that those look
+
+ align:start position:0%
+um annoying notation that those look
+ 
+
+ align:start position:0%
+um annoying notation that those look
+similar so just be aware and uh try to
+
+ align:start position:0%
+similar so just be aware and uh try to
+ 
+
+ align:start position:0%
+similar so just be aware and uh try to
+correct for it um and there's the
+
+ align:start position:0%
+correct for it um and there's the
+ 
+
+ align:start position:0%
+correct for it um and there's the
+reverse f is in little Omega of G that's
+
+ align:start position:0%
+reverse f is in little Omega of G that's
+ 
+
+ align:start position:0%
+reverse f is in little Omega of G that's
+the lowercase Omega compared to the
+
+ align:start position:0%
+the lowercase Omega compared to the
+ 
+
+ align:start position:0%
+the lowercase Omega compared to the
+capital Omega up there means the
+
+ align:start position:0%
+capital Omega up there means the
+ 
+
+ align:start position:0%
+capital Omega up there means the
+opposite that the limit as n goes to
+
+ align:start position:0%
+opposite that the limit as n goes to
+ 
+
+ align:start position:0%
+opposite that the limit as n goes to
+Infinity of f of n over G of n equals
+
+ align:start position:0%
+Infinity of f of n over G of n equals
+ 
+
+ align:start position:0%
+Infinity of f of n over G of n equals
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+AKA G is in little o of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f so if we want to stress that f is much
+
+ align:start position:0%
+f so if we want to stress that f is much
+ 
+
+ align:start position:0%
+f so if we want to stress that f is much
+much bigger than G we can use the little
+
+ align:start position:0%
+much bigger than G we can use the little
+ 
+
+ align:start position:0%
+much bigger than G we can use the little
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+notation that f is much much bigger than
+
+ align:start position:0%
+notation that f is much much bigger than
+ 
+
+ align:start position:0%
+notation that f is much much bigger than
+G all
+
+ align:start position:0%
+G all
+ 
+
+ align:start position:0%
+G all
+right and these are
+
+ align:start position:0%
+right and these are
+ 
+
+ align:start position:0%
+right and these are
+useful I mean for the same reasons the
+
+ align:start position:0%
+useful I mean for the same reasons the
+ 
+
+ align:start position:0%
+useful I mean for the same reasons the
+other things are useful they're giving
+
+ align:start position:0%
+other things are useful they're giving
+ 
+
+ align:start position:0%
+other things are useful they're giving
+us more vocabulary to compare functions
+
+ align:start position:0%
+us more vocabulary to compare functions
+ 
+
+ align:start position:0%
+us more vocabulary to compare functions
+um in ways that let us think about only
+
+ align:start position:0%
+um in ways that let us think about only
+ 
+
+ align:start position:0%
+um in ways that let us think about only
+a small amount of information about each
+
+ align:start position:0%
+a small amount of information about each
+ 
+
+ align:start position:0%
+a small amount of information about each
+function um but little o is sort of
+
+ align:start position:0%
+function um but little o is sort of
+ 
+
+ align:start position:0%
+function um but little o is sort of
+exactly what we meant by lower order
+
+ align:start position:0%
+exactly what we meant by lower order
+ 
+
+ align:start position:0%
+exactly what we meant by lower order
+term uh
+
+ align:start position:0%
+term uh
+ 
+
+ align:start position:0%
+term uh
+claim uh that f is going to be ASM
+
+ align:start position:0%
+claim uh that f is going to be ASM
+ 
+
+ align:start position:0%
+claim uh that f is going to be ASM
+totically equivalent to f plus
+
+ align:start position:0%
+totically equivalent to f plus
+ 
+
+ align:start position:0%
+totically equivalent to f plus
+h if and only if
+
+ align:start position:0%
+h if and only if
+ 
+
+ align:start position:0%
+h if and only if
+H is in little o of
+
+ align:start position:0%
+H is in little o of
+ 
+
+ align:start position:0%
+H is in little o of
+f if and only
+
+ align:start position:0%
+f if and only
+ 
+
+ align:start position:0%
+f if and only
+if the limit of H over f is
+
+ align:start position:0%
+if the limit of H over f is
+ 
+
+ align:start position:0%
+if the limit of H over f is
+zero h of n over F of n as n goes to
+
+ align:start position:0%
+zero h of n over F of n as n goes to
+ 
+
+ align:start position:0%
+zero h of n over F of n as n goes to
+Infinity so lower order term just means
+
+ align:start position:0%
+Infinity so lower order term just means
+ 
+
+ align:start position:0%
+Infinity so lower order term just means
+the ratio goes to zero in the
+
+ align:start position:0%
+the ratio goes to zero in the
+ 
+
+ align:start position:0%
+the ratio goes to zero in the
+limit uh and that's consistent with what
+
+ align:start position:0%
+limit uh and that's consistent with what
+ 
+
+ align:start position:0%
+limit uh and that's consistent with what
+we've been saying with lower order terms
+
+ align:start position:0%
+we've been saying with lower order terms
+ 
+
+ align:start position:0%
+we've been saying with lower order terms
+all throughout today lower order term
+
+ align:start position:0%
+all throughout today lower order term
+ 
+
+ align:start position:0%
+all throughout today lower order term
+just means limit goes to zero and we
+
+ align:start position:0%
+just means limit goes to zero and we
+ 
+
+ align:start position:0%
+just means limit goes to zero and we
+have a special notation for that
+
+ align:start position:0%
+have a special notation for that
+ 
+
+ align:start position:0%
+have a special notation for that
+o um f is ASM totically equivalent to f
+
+ align:start position:0%
+o um f is ASM totically equivalent to f
+ 
+
+ align:start position:0%
+o um f is ASM totically equivalent to f
+plus h means that according to ASM totic
+
+ align:start position:0%
+plus h means that according to ASM totic
+ 
+
+ align:start position:0%
+plus h means that according to ASM totic
+equivalence the H didn't change
+
+ align:start position:0%
+equivalence the H didn't change
+ 
+
+ align:start position:0%
+equivalence the H didn't change
+anything the H was insignificant so
+
+ align:start position:0%
+anything the H was insignificant so
+ 
+
+ align:start position:0%
+anything the H was insignificant so
+that's another way to think about what
+
+ align:start position:0%
+that's another way to think about what
+ 
+
+ align:start position:0%
+that's another way to think about what
+we mean by lower order
+
+ align:start position:0%
+we mean by lower order
+ 
+
+ align:start position:0%
+we mean by lower order
+term make
+
+ align:start position:0%
+term make
+ 
+
+ align:start position:0%
+term make
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+nice um cool last thing I want to do
+
+ align:start position:0%
+nice um cool last thing I want to do
+ 
+
+ align:start position:0%
+nice um cool last thing I want to do
+today is a big old warning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Asim totic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notation and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+induction don't mix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+easily if you're ever doing astics and
+
+ align:start position:0%
+easily if you're ever doing astics and
+ 
+
+ align:start position:0%
+easily if you're ever doing astics and
+induction in the same same
+
+ align:start position:0%
+induction in the same same
+ 
+
+ align:start position:0%
+induction in the same same
+breadth step back take care let's see
+
+ align:start position:0%
+breadth step back take care let's see
+ 
+
+ align:start position:0%
+breadth step back take care let's see
+what can go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wrong all right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theorem question
+
+ align:start position:0%
+theorem question
+ 
+
+ align:start position:0%
+theorem question
+mark 2 to the N is Big O of
+
+ align:start position:0%
+mark 2 to the N is Big O of
+ 
+
+ align:start position:0%
+mark 2 to the N is Big O of
+one now we really really hope this isn't
+
+ align:start position:0%
+one now we really really hope this isn't
+ 
+
+ align:start position:0%
+one now we really really hope this isn't
+true in algorithm terms this is an
+
+ align:start position:0%
+true in algorithm terms this is an
+ 
+
+ align:start position:0%
+true in algorithm terms this is an
+algorithm that takes exponential time
+
+ align:start position:0%
+algorithm that takes exponential time
+ 
+
+ align:start position:0%
+algorithm that takes exponential time
+this is an algorithm that takes constant
+
+ align:start position:0%
+this is an algorithm that takes constant
+ 
+
+ align:start position:0%
+this is an algorithm that takes constant
+time certainly this one's supposed to be
+
+ align:start position:0%
+time certainly this one's supposed to be
+ 
+
+ align:start position:0%
+time certainly this one's supposed to be
+the smaller one so 2 to the N should
+
+ align:start position:0%
+the smaller one so 2 to the N should
+ 
+
+ align:start position:0%
+the smaller one so 2 to the N should
+absolutely not be in Big O of one but
+
+ align:start position:0%
+absolutely not be in Big O of one but
+ 
+
+ align:start position:0%
+absolutely not be in Big O of one but
+let's prove it anyway proof by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+induction let's do our base
+
+ align:start position:0%
+induction let's do our base
+ 
+
+ align:start position:0%
+induction let's do our base
+case n equals z so 2 to the 0o is in Big
+
+ align:start position:0%
+case n equals z so 2 to the 0o is in Big
+ 
+
+ align:start position:0%
+case n equals z so 2 to the 0o is in Big
+O of one
+
+ align:start position:0%
+O of one
+ 
+
+ align:start position:0%
+O of one
+that's just that's saying that one is
+
+ align:start position:0%
+that's just that's saying that one is
+ 
+
+ align:start position:0%
+that's just that's saying that one is
+Big O of one which it certainly
+
+ align:start position:0%
+Big O of one which it certainly
+ 
+
+ align:start position:0%
+Big O of one which it certainly
+is all right inductive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+step uh assume n is at least
+
+ align:start position:0%
+step uh assume n is at least
+ 
+
+ align:start position:0%
+step uh assume n is at least
+zero and that 2 to the N is in Big O of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one want to show 2 the n + 1 is in Big O
+
+ align:start position:0%
+one want to show 2 the n + 1 is in Big O
+ 
+
+ align:start position:0%
+one want to show 2 the n + 1 is in Big O
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+one but
+
+ align:start position:0%
+one but
+ 
+
+ align:start position:0%
+one but
+but well 2 the n + 1 that's 2 the n + 2
+
+ align:start position:0%
+but well 2 the n + 1 that's 2 the n + 2
+ 
+
+ align:start position:0%
+but well 2 the n + 1 that's 2 the n + 2
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+N which is Big O of one plus Big O of
+
+ align:start position:0%
+N which is Big O of one plus Big O of
+ 
+
+ align:start position:0%
+N which is Big O of one plus Big O of
+one by our inductive
+
+ align:start position:0%
+one by our inductive
+ 
+
+ align:start position:0%
+one by our inductive
+assumption and that is Big O of
+
+ align:start position:0%
+assumption and that is Big O of
+ 
+
+ align:start position:0%
+assumption and that is Big O of
+one so 2 the N plus one is Big O of one
+
+ align:start position:0%
+one so 2 the N plus one is Big O of one
+ 
+
+ align:start position:0%
+one so 2 the N plus one is Big O of one
+and we're
+
+ align:start position:0%
+and we're
+ 
+
+ align:start position:0%
+and we're
+done we proved our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+induction what the heck went wrong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes 2 the N plus 1 is not equal to 2 the
+
+ align:start position:0%
+yes 2 the N plus 1 is not equal to 2 the
+ 
+
+ align:start position:0%
+yes 2 the N plus 1 is not equal to 2 the
+N plus 2 the N um it is 2 the N plus 1
+
+ align:start position:0%
+N plus 2 the N um it is 2 the N plus 1
+ 
+
+ align:start position:0%
+N plus 2 the N um it is 2 the N plus 1
+is just 2 * 2 the N um which I can write
+
+ align:start position:0%
+is just 2 * 2 the N um which I can write
+ 
+
+ align:start position:0%
+is just 2 * 2 the N um which I can write
+as two copies of two to the UN added
+
+ align:start position:0%
+as two copies of two to the UN added
+ 
+
+ align:start position:0%
+as two copies of two to the UN added
+together um I will tell you the mistake
+
+ align:start position:0%
+together um I will tell you the mistake
+ 
+
+ align:start position:0%
+together um I will tell you the mistake
+isn't in this line at all I know I did
+
+ align:start position:0%
+isn't in this line at all I know I did
+ 
+
+ align:start position:0%
+isn't in this line at all I know I did
+something really sketchy right here what
+
+ align:start position:0%
+something really sketchy right here what
+ 
+
+ align:start position:0%
+something really sketchy right here what
+do I mean by o of one plus o of one
+
+ align:start position:0%
+do I mean by o of one plus o of one
+ 
+
+ align:start position:0%
+do I mean by o of one plus o of one
+that's a set and that's a set why am I
+
+ align:start position:0%
+that's a set and that's a set why am I
+ 
+
+ align:start position:0%
+that's a set and that's a set why am I
+able to add them also I accidentally Ed
+
+ align:start position:0%
+able to add them also I accidentally Ed
+ 
+
+ align:start position:0%
+able to add them also I accidentally Ed
+that when I meant set membership instead
+
+ align:start position:0%
+that when I meant set membership instead
+ 
+
+ align:start position:0%
+that when I meant set membership instead
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+equality but actually this is kind of
+
+ align:start position:0%
+equality but actually this is kind of
+ 
+
+ align:start position:0%
+equality but actually this is kind of
+fine this is an abusive notation we
+
+ align:start position:0%
+fine this is an abusive notation we
+ 
+
+ align:start position:0%
+fine this is an abusive notation we
+didn't really Define what this
+
+ align:start position:0%
+didn't really Define what this
+ 
+
+ align:start position:0%
+didn't really Define what this
+means but all we mean by it um o of f
+
+ align:start position:0%
+means but all we mean by it um o of f
+ 
+
+ align:start position:0%
+means but all we mean by it um o of f
+plus o of G this is just the set of
+
+ align:start position:0%
+plus o of G this is just the set of
+ 
+
+ align:start position:0%
+plus o of G this is just the set of
+functions um a plus
+
+ align:start position:0%
+functions um a plus
+ 
+
+ align:start position:0%
+functions um a plus
+b where a is in o of F and B is in O of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G this just means the set of things you
+
+ align:start position:0%
+G this just means the set of things you
+ 
+
+ align:start position:0%
+G this just means the set of things you
+can form by taking a one function from
+
+ align:start position:0%
+can form by taking a one function from
+ 
+
+ align:start position:0%
+can form by taking a one function from
+this side and one function from that
+
+ align:start position:0%
+this side and one function from that
+ 
+
+ align:start position:0%
+this side and one function from that
+side and adding them
+
+ align:start position:0%
+side and adding them
+ 
+
+ align:start position:0%
+side and adding them
+together um and it is true that in this
+
+ align:start position:0%
+together um and it is true that in this
+ 
+
+ align:start position:0%
+together um and it is true that in this
+case o of one plus o of one equals o of
+
+ align:start position:0%
+case o of one plus o of one equals o of
+ 
+
+ align:start position:0%
+case o of one plus o of one equals o of
+one as sets so that's fine that's not
+
+ align:start position:0%
+one as sets so that's fine that's not
+ 
+
+ align:start position:0%
+one as sets so that's fine that's not
+the mistake yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right um so let me reiterate um I
+
+ align:start position:0%
+all right um so let me reiterate um I
+ 
+
+ align:start position:0%
+all right um so let me reiterate um I
+proved that every number two to the N is
+
+ align:start position:0%
+proved that every number two to the N is
+ 
+
+ align:start position:0%
+proved that every number two to the N is
+Big O of one itself but I didn't prove
+
+ align:start position:0%
+Big O of one itself but I didn't prove
+ 
+
+ align:start position:0%
+Big O of one itself but I didn't prove
+the function 2 to the N is Big O of one
+
+ align:start position:0%
+the function 2 to the N is Big O of one
+ 
+
+ align:start position:0%
+the function 2 to the N is Big O of one
+that's exactly the idea so let's see
+
+ align:start position:0%
+that's exactly the idea so let's see
+ 
+
+ align:start position:0%
+that's exactly the idea so let's see
+what we actually proved here this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here is a correct proof by
+
+ align:start position:0%
+here is a correct proof by
+ 
+
+ align:start position:0%
+here is a correct proof by
+induction but what is it proving it it's
+
+ align:start position:0%
+induction but what is it proving it it's
+ 
+
+ align:start position:0%
+induction but what is it proving it it's
+a proof of what we what we really proved
+
+ align:start position:0%
+a proof of what we what we really proved
+ 
+
+ align:start position:0%
+a proof of what we what we really proved
+is that two to the is is that one is in
+
+ align:start position:0%
+is that two to the is is that one is in
+ 
+
+ align:start position:0%
+is that two to the is is that one is in
+Big O of one that was our base case we
+
+ align:start position:0%
+Big O of one that was our base case we
+ 
+
+ align:start position:0%
+Big O of one that was our base case we
+proved that two is in Big O of one four
+
+ align:start position:0%
+proved that two is in Big O of one four
+ 
+
+ align:start position:0%
+proved that two is in Big O of one four
+is in Big O of one eight is in Big O of
+
+ align:start position:0%
+is in Big O of one eight is in Big O of
+ 
+
+ align:start position:0%
+is in Big O of one eight is in Big O of
+one 16 is in Big O of
+
+ align:start position:0%
+one 16 is in Big O of
+ 
+
+ align:start position:0%
+one 16 is in Big O of
+one we proved that each individual power
+
+ align:start position:0%
+one we proved that each individual power
+ 
+
+ align:start position:0%
+one we proved that each individual power
+of two when considered as a constant
+
+ align:start position:0%
+of two when considered as a constant
+ 
+
+ align:start position:0%
+of two when considered as a constant
+function is Big O of one so every
+
+ align:start position:0%
+function is Big O of one so every
+ 
+
+ align:start position:0%
+function is Big O of one so every
+constant function is Big O of one yeah
+
+ align:start position:0%
+constant function is Big O of one yeah
+ 
+
+ align:start position:0%
+constant function is Big O of one yeah
+that's true we proved it by induction
+
+ align:start position:0%
+that's true we proved it by induction
+ 
+
+ align:start position:0%
+that's true we proved it by induction
+that has absolutely nothing to do with
+
+ align:start position:0%
+that has absolutely nothing to do with
+ 
+
+ align:start position:0%
+that has absolutely nothing to do with
+the two to the N function has absolutely
+
+ align:start position:0%
+the two to the N function has absolutely
+ 
+
+ align:start position:0%
+the two to the N function has absolutely
+nothing to do with the definition of 2
+
+ align:start position:0%
+nothing to do with the definition of 2
+ 
+
+ align:start position:0%
+nothing to do with the definition of 2
+to the N being in Big O of
+
+ align:start position:0%
+to the N being in Big O of
+ 
+
+ align:start position:0%
+to the N being in Big O of
+one so we didn't prove the right theorem
+
+ align:start position:0%
+one so we didn't prove the right theorem
+ 
+
+ align:start position:0%
+one so we didn't prove the right theorem
+we proved something completely
+
+ align:start position:0%
+we proved something completely
+ 
+
+ align:start position:0%
+we proved something completely
+irrelevant does that make
+
+ align:start position:0%
+irrelevant does that make
+ 
+
+ align:start position:0%
+irrelevant does that make
+sense so this is why induction and
+
+ align:start position:0%
+sense so this is why induction and
+ 
+
+ align:start position:0%
+sense so this is why induction and
+astics don't mix when you see a function
+
+ align:start position:0%
+astics don't mix when you see a function
+ 
+
+ align:start position:0%
+astics don't mix when you see a function
+of n you can't break that function
+
+ align:start position:0%
+of n you can't break that function
+ 
+
+ align:start position:0%
+of n you can't break that function
+into individual constant functions one
+
+ align:start position:0%
+into individual constant functions one
+ 
+
+ align:start position:0%
+into individual constant functions one
+for each n value you can't induct on N
+
+ align:start position:0%
+for each n value you can't induct on N
+ 
+
+ align:start position:0%
+for each n value you can't induct on N
+you have to treat that function
+
+ align:start position:0%
+you have to treat that function
+ 
+
+ align:start position:0%
+you have to treat that function
+holistically as a single
+
+ align:start position:0%
+holistically as a single
+ 
+
+ align:start position:0%
+holistically as a single
+function sound
+
+ align:start position:0%
+function sound
+ 
+
+ align:start position:0%
+function sound
+good all right um does anyone have any
+
+ align:start position:0%
+good all right um does anyone have any
+ 
+
+ align:start position:0%
+good all right um does anyone have any
+questions about anything we talked about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes excellent question does little o
+
+ align:start position:0%
+yes excellent question does little o
+ 
+
+ align:start position:0%
+yes excellent question does little o
+imply Big O uh so if we know that f o
+
+ align:start position:0%
+imply Big O uh so if we know that f o
+ 
+
+ align:start position:0%
+imply Big O uh so if we know that f o
+sorry if we know that f is in little o
+
+ align:start position:0%
+sorry if we know that f is in little o
+ 
+
+ align:start position:0%
+sorry if we know that f is in little o
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+G does that imply that f is in Big O of
+
+ align:start position:0%
+G does that imply that f is in Big O of
+ 
+
+ align:start position:0%
+G does that imply that f is in Big O of
+G yeah yeah absolutely um and let's
+
+ align:start position:0%
+G yeah yeah absolutely um and let's
+ 
+
+ align:start position:0%
+G yeah yeah absolutely um and let's
+let's think about why this so little o
+
+ align:start position:0%
+let's think about why this so little o
+ 
+
+ align:start position:0%
+let's think about why this so little o
+is defined by uh let's see f um sorry F
+
+ align:start position:0%
+is defined by uh let's see f um sorry F
+ 
+
+ align:start position:0%
+is defined by uh let's see f um sorry F
+over G that limit equals zero
+
+ align:start position:0%
+over G that limit equals zero
+ 
+
+ align:start position:0%
+over G that limit equals zero
+but remember we already said early on
+
+ align:start position:0%
+but remember we already said early on
+ 
+
+ align:start position:0%
+but remember we already said early on
+that if the limit
+
+ align:start position:0%
+that if the limit
+ 
+
+ align:start position:0%
+that if the limit
+exists then it tells you whether or not
+
+ align:start position:0%
+exists then it tells you whether or not
+ 
+
+ align:start position:0%
+exists then it tells you whether or not
+it's Big O and in this case the limit is
+
+ align:start position:0%
+it's Big O and in this case the limit is
+ 
+
+ align:start position:0%
+it's Big O and in this case the limit is
+zero so it tells us yes we are Big
+
+ align:start position:0%
+zero so it tells us yes we are Big
+ 
+
+ align:start position:0%
+zero so it tells us yes we are Big
+O yep so little o is absolutely stronger
+
+ align:start position:0%
+O yep so little o is absolutely stronger
+ 
+
+ align:start position:0%
+O yep so little o is absolutely stronger
+than Big O it implies Big O um we we
+
+ align:start position:0%
+than Big O it implies Big O um we we
+ 
+
+ align:start position:0%
+than Big O it implies Big O um we we
+certainly don't go the other
+
+ align:start position:0%
+certainly don't go the other
+ 
+
+ align:start position:0%
+certainly don't go the other
+way um likewise
+
+ align:start position:0%
+way um likewise
+ 
+
+ align:start position:0%
+way um likewise
+um uh let's see there are lots of other
+
+ align:start position:0%
+um uh let's see there are lots of other
+ 
+
+ align:start position:0%
+um uh let's see there are lots of other
+implications between this between these
+
+ align:start position:0%
+implications between this between these
+ 
+
+ align:start position:0%
+implications between this between these
+so um Theta if f is a Theta of G well
+
+ align:start position:0%
+so um Theta if f is a Theta of G well
+ 
+
+ align:start position:0%
+so um Theta if f is a Theta of G well
+that certainly implies Big O and big
+
+ align:start position:0%
+that certainly implies Big O and big
+ 
+
+ align:start position:0%
+that certainly implies Big O and big
+Omega because that's how we Define Theta
+
+ align:start position:0%
+Omega because that's how we Define Theta
+ 
+
+ align:start position:0%
+Omega because that's how we Define Theta
+and in turn these also imply little o
+
+ align:start position:0%
+and in turn these also imply little o
+ 
+
+ align:start position:0%
+and in turn these also imply little o
+and little
+
+ align:start position:0%
+and little
+ 
+
+ align:start position:0%
+and little
+Omega um because Big O implies little o
+
+ align:start position:0%
+Omega um because Big O implies little o
+ 
+
+ align:start position:0%
+Omega um because Big O implies little o
+as we just saw which means big Omega
+
+ align:start position:0%
+as we just saw which means big Omega
+ 
+
+ align:start position:0%
+as we just saw which means big Omega
+implies little Omega because we're just
+
+ align:start position:0%
+implies little Omega because we're just
+ 
+
+ align:start position:0%
+implies little Omega because we're just
+swapping the
+
+ align:start position:0%
+swapping the
+ 
+
+ align:start position:0%
+swapping the
+order uh so yeah so we have lots of
+
+ align:start position:0%
+order uh so yeah so we have lots of
+ 
+
+ align:start position:0%
+order uh so yeah so we have lots of
+implications like this um let me write
+
+ align:start position:0%
+implications like this um let me write
+ 
+
+ align:start position:0%
+implications like this um let me write
+it this
+
+ align:start position:0%
+it this
+ 
+
+ align:start position:0%
+it this
+way this implies little o and this
+
+ align:start position:0%
+way this implies little o and this
+ 
+
+ align:start position:0%
+way this implies little o and this
+implies little
+
+ align:start position:0%
+implies little
+ 
+
+ align:start position:0%
+implies little
+Omega uh and as we already saw ASM totic
+
+ align:start position:0%
+Omega uh and as we already saw ASM totic
+ 
+
+ align:start position:0%
+Omega uh and as we already saw ASM totic
+equivalence implies
+
+ align:start position:0%
+equivalence implies
+ 
+
+ align:start position:0%
+equivalence implies
+Theta which in turn implies all the
+
+ align:start position:0%
+Theta which in turn implies all the
+ 
+
+ align:start position:0%
+Theta which in turn implies all the
+others
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes I got these arrows wrong thank you
+
+ align:start position:0%
+yes I got these arrows wrong thank you
+ 
+
+ align:start position:0%
+yes I got these arrows wrong thank you
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+I'm see I I shouldn't add live at the
+
+ align:start position:0%
+I'm see I I shouldn't add live at the
+ 
+
+ align:start position:0%
+I'm see I I shouldn't add live at the
+board I'm always going to get it wrong
+
+ align:start position:0%
+board I'm always going to get it wrong
+ 
+
+ align:start position:0%
+board I'm always going to get it wrong
+um yeah I apologize Theta implies the
+
+ align:start position:0%
+um yeah I apologize Theta implies the
+ 
+
+ align:start position:0%
+um yeah I apologize Theta implies the
+big ones not the little ones um the
+
+ align:start position:0%
+big ones not the little ones um the
+ 
+
+ align:start position:0%
+big ones not the little ones um the
+little one implies the big one not the
+
+ align:start position:0%
+little one implies the big one not the
+ 
+
+ align:start position:0%
+little one implies the big one not the
+not the other way around sorry for the
+
+ align:start position:0%
+not the other way around sorry for the
+ 
+
+ align:start position:0%
+not the other way around sorry for the
+confusion um one more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question all right thanks everyone we'll
+
+ align:start position:0%
+question all right thanks everyone we'll
+ 
+
+ align:start position:0%
+question all right thanks everyone we'll
+see you tomorrow at recitation
\ No newline at end of file
diff --git a/6h3T3qIkxqw.txt b/6h3T3qIkxqw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fffa44c1ab64580ce6f33f41684337642ef8f256
--- /dev/null
+++ b/6h3T3qIkxqw.txt
@@ -0,0 +1,355 @@
+align:start position:0%
+ 
+we recently introduced a vector quantity
+
+ align:start position:0%
+we recently introduced a vector quantity
+ 
+
+ align:start position:0%
+we recently introduced a vector quantity
+called torque a sort of rotational
+
+ align:start position:0%
+called torque a sort of rotational
+ 
+
+ align:start position:0%
+called torque a sort of rotational
+analog to force and we saw that an
+
+ align:start position:0%
+analog to force and we saw that an
+ 
+
+ align:start position:0%
+analog to force and we saw that an
+applied torque changes the angular
+
+ align:start position:0%
+applied torque changes the angular
+ 
+
+ align:start position:0%
+applied torque changes the angular
+motion of a rotating body in just the
+
+ align:start position:0%
+motion of a rotating body in just the
+ 
+
+ align:start position:0%
+motion of a rotating body in just the
+same way that an applied force changes
+
+ align:start position:0%
+same way that an applied force changes
+ 
+
+ align:start position:0%
+same way that an applied force changes
+the linear motion of a translating body
+
+ align:start position:0%
+the linear motion of a translating body
+ 
+
+ align:start position:0%
+the linear motion of a translating body
+this week we're going to introduce the
+
+ align:start position:0%
+this week we're going to introduce the
+ 
+
+ align:start position:0%
+this week we're going to introduce the
+concept of angular momentum which
+
+ align:start position:0%
+concept of angular momentum which
+ 
+
+ align:start position:0%
+concept of angular momentum which
+relates to torque and rotational motion
+
+ align:start position:0%
+relates to torque and rotational motion
+ 
+
+ align:start position:0%
+relates to torque and rotational motion
+in the same way that ordinary momentum
+
+ align:start position:0%
+in the same way that ordinary momentum
+ 
+
+ align:start position:0%
+in the same way that ordinary momentum
+relates to force and translational
+
+ align:start position:0%
+relates to force and translational
+ 
+
+ align:start position:0%
+relates to force and translational
+motion like torque angular momentum is
+
+ align:start position:0%
+motion like torque angular momentum is
+ 
+
+ align:start position:0%
+motion like torque angular momentum is
+defined in terms of a cross product or a
+
+ align:start position:0%
+defined in terms of a cross product or a
+ 
+
+ align:start position:0%
+defined in terms of a cross product or a
+vector product specifically the angular
+
+ align:start position:0%
+vector product specifically the angular
+ 
+
+ align:start position:0%
+vector product specifically the angular
+momentum vector L for a point mass is
+
+ align:start position:0%
+momentum vector L for a point mass is
+ 
+
+ align:start position:0%
+momentum vector L for a point mass is
+equal to the cross product R cross P
+
+ align:start position:0%
+equal to the cross product R cross P
+ 
+
+ align:start position:0%
+equal to the cross product R cross P
+where R is the position vector measured
+
+ align:start position:0%
+where R is the position vector measured
+ 
+
+ align:start position:0%
+where R is the position vector measured
+from a chosen reference point and P is
+
+ align:start position:0%
+from a chosen reference point and P is
+ 
+
+ align:start position:0%
+from a chosen reference point and P is
+the ordinary momentum vector we will
+
+ align:start position:0%
+the ordinary momentum vector we will
+ 
+
+ align:start position:0%
+the ordinary momentum vector we will
+also encounter where third conservation
+
+ align:start position:0%
+also encounter where third conservation
+ 
+
+ align:start position:0%
+also encounter where third conservation
+principle this time for angular momentum
+
+ align:start position:0%
+principle this time for angular momentum
+ 
+
+ align:start position:0%
+principle this time for angular momentum
+an applied torque causes the angular
+
+ align:start position:0%
+an applied torque causes the angular
+ 
+
+ align:start position:0%
+an applied torque causes the angular
+momentum to change however if there are
+
+ align:start position:0%
+momentum to change however if there are
+ 
+
+ align:start position:0%
+momentum to change however if there are
+no external torques on a system then the
+
+ align:start position:0%
+no external torques on a system then the
+ 
+
+ align:start position:0%
+no external torques on a system then the
+angular momentum of the system is
+
+ align:start position:0%
+angular momentum of the system is
+ 
+
+ align:start position:0%
+angular momentum of the system is
+conserved or remains constant this is a
+
+ align:start position:0%
+conserved or remains constant this is a
+ 
+
+ align:start position:0%
+conserved or remains constant this is a
+powerful tool for solving many problems
+
+ align:start position:0%
+powerful tool for solving many problems
+ 
+
+ align:start position:0%
+powerful tool for solving many problems
+one subtlety is that angular momentum
+
+ align:start position:0%
+one subtlety is that angular momentum
+ 
+
+ align:start position:0%
+one subtlety is that angular momentum
+like torque is defined relative to a
+
+ align:start position:0%
+like torque is defined relative to a
+ 
+
+ align:start position:0%
+like torque is defined relative to a
+specified point so for a given system
+
+ align:start position:0%
+specified point so for a given system
+ 
+
+ align:start position:0%
+specified point so for a given system
+the angular momentum with respect to one
+
+ align:start position:0%
+the angular momentum with respect to one
+ 
+
+ align:start position:0%
+the angular momentum with respect to one
+point might be conserved
+
+ align:start position:0%
+point might be conserved
+ 
+
+ align:start position:0%
+point might be conserved
+while the angular momentum with respect
+
+ align:start position:0%
+while the angular momentum with respect
+ 
+
+ align:start position:0%
+while the angular momentum with respect
+to a different point might be changing
+
+ align:start position:0%
+to a different point might be changing
+ 
+
+ align:start position:0%
+to a different point might be changing
+often in analyzing a system we must be
+
+ align:start position:0%
+often in analyzing a system we must be
+ 
+
+ align:start position:0%
+often in analyzing a system we must be
+careful about our choice of reference
+
+ align:start position:0%
+careful about our choice of reference
+ 
+
+ align:start position:0%
+careful about our choice of reference
+point for torques and angular momentum
+
+ align:start position:0%
+point for torques and angular momentum
+ 
+
+ align:start position:0%
+point for torques and angular momentum
+in order to take full advantage of the
+
+ align:start position:0%
+in order to take full advantage of the
+ 
+
+ align:start position:0%
+in order to take full advantage of the
+conservation principle angular momentum
+
+ align:start position:0%
+conservation principle angular momentum
+ 
+
+ align:start position:0%
+conservation principle angular momentum
+is a particularly subtle and
+
+ align:start position:0%
+is a particularly subtle and
+ 
+
+ align:start position:0%
+is a particularly subtle and
+non-intuitive concept in comparison to
+
+ align:start position:0%
+non-intuitive concept in comparison to
+ 
+
+ align:start position:0%
+non-intuitive concept in comparison to
+momentum and energy and the resulting
+
+ align:start position:0%
+momentum and energy and the resulting
+ 
+
+ align:start position:0%
+momentum and energy and the resulting
+motion is often surprising it is worthy
+
+ align:start position:0%
+motion is often surprising it is worthy
+ 
+
+ align:start position:0%
+motion is often surprising it is worthy
+of particularly careful study
\ No newline at end of file
diff --git a/6wTuOMgTrU4.txt b/6wTuOMgTrU4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0920f203dcf8554b9ede2fde00664e0f1d515c38
--- /dev/null
+++ b/6wTuOMgTrU4.txt
@@ -0,0 +1,1719 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR JOHN GUTTAG: In the
+example we looked at, we had a
+
+list of ints.
+
+That's actually quite easy
+to do in constant time.
+
+If you think about it, an int is
+always going to occupy the
+
+same amount of space, roughly
+speaking, either 32 or 64
+
+bits, depending upon
+how big an int the
+
+language wants to support.
+
+So let's just, for the sake
+of argument, assume an int
+
+occupies four units of memory.
+
+And I don't care
+what a unit is.
+
+Is a unit 8 bits, 16 bits?
+
+It doesn't matter.
+
+4 units.
+
+How would we get to the i-th
+element of the list?
+
+What is the location in
+memory of L-th of i?
+
+Well, if we know the location
+of the start of the list--
+
+and certainly we can know that
+because our identifier, say L
+
+in this case, will point to
+the start of the list--
+
+then it's simply going to be
+the start plus 4 times i.
+
+My list looks like this.
+
+I point to the start.
+
+The first element is here.
+
+So, that's start
+plus 4 times 0.
+
+Makes perfect sense.
+
+The second element is here.
+
+So, that's going to be
+start plus 4 times 1.
+
+Sure enough, this would be
+location 4, relative to the
+
+start of the list, et cetera.
+
+This is a very conventional
+way to implement lists.
+
+But what does its correctness
+depend upon?
+
+It depends upon the fact that
+each element of the list is of
+
+the same size.
+
+In this case, it's 4.
+
+But I don't care if it's 4.
+
+If it's 2, it's 2 times i.
+
+If it's 58, it's 58 times i.
+
+It doesn't matter.
+
+But what matters is that each
+element is the same size.
+
+So this trick would work for
+accessing elements of lists of
+
+floats, lists of ints, anything
+that's of fixed size.
+
+But that's not the way
+lists are in Python.
+
+In Python, I can have a list
+that contains ints, and
+
+floats, and strings, and
+other lists, and
+
+dicts, almost anything.
+
+So, in Python, it's not this
+nice picture where the lists
+
+are all homogeneous.
+
+In many languages they
+are, by the way.
+
+And those languages would
+implement it exactly as I've
+
+outlined it on the board here.
+
+But what about languages where
+they're not, like Python?
+
+One possibility--
+
+and this is probably the oldest
+way that people used to
+
+implement lists--
+
+is the notion of
+a linked list.
+
+These were used way back
+in the 1960s, when
+
+Lisp was first invented.
+
+And, effectively, there,
+what you do is a list.
+
+Every element of the list is a
+pointer to the next element.
+
+And then the value.
+
+So what it looks like in memory
+is we have the list.
+
+And this points to the next
+element, which maybe has a
+
+much bigger value field.
+
+But that's OK.
+
+This points to the
+next element.
+
+Let's say this one, maybe,
+is a tiny value field.
+
+And then at the end of the
+list, I might write none,
+
+saying there is no
+next element.
+
+Or nil, in Lisp speak.
+
+But what's the cost here of
+accessing the nth element of
+
+the list, of the i-th
+element of the list?
+
+Somebody?
+
+How many steps does it take
+to find element i?
+
+AUDIENCE: i.
+
+AUDIENCE: i?
+
+PROFESSOR JOHN GUTTAG:
+i steps, exactly.
+
+So for a linked list, finding
+the i-th element is order i.
+
+That's not very good.
+
+That won't help me with
+binary search.
+
+Because if this were the case
+for finding an element of a
+
+list in Python, binary search
+would not be log length of the
+
+list, but it would be order
+length of the list.
+
+Because the worst case is I'd
+have to visit every element of
+
+the list, say, to discover
+something isn't in it.
+
+So, this is not what
+you want to do.
+
+Instead, Python uses
+something like the
+
+picture in your handout.
+
+And the key idea here is
+one of indirection.
+
+So in Python, what a list looks
+like is it is a list, a
+
+section of memory, a list of
+objects each of the same size.
+
+Because now what each
+object is a pointer.
+
+So we've now separated in
+space the values of the
+
+members of the list and the
+pointers to, if you
+
+will, the next one.
+
+So now, it can be very simple.
+
+This first element
+could be big.
+
+Second element could be small.
+
+We don't care.
+
+Now I'm back to exactly the
+model we looked at here.
+
+If, say, a pointer to someplace
+in memory is 4 units
+
+long, then to find l-th of i, I
+use that trick to find, say,
+
+the i-th pointer.
+
+And then it takes me only one
+step to follow it to get to
+
+the object.
+
+So, I can now, in constant time,
+access any object into a
+
+list, even though the
+objects in the list
+
+are of varying size.
+
+This is the way it's done
+in all object-oriented
+
+programming languages.
+
+Does that makes sense
+to everybody?
+
+This concept of indirection is
+one of the most powerful
+
+programming techniques
+we have.
+
+It gets used a lot.
+
+My dictionary defines
+indirection as a lack of
+
+straightforwardness and openness
+and as a synonym uses
+
+deceitfulness.
+
+And it had this pejorative term
+until about 1950 when
+
+computer scientists discovered
+it and decided it was a
+
+wonderful thing.
+
+There's something that's often
+quoted at people who do
+
+algorithms.
+
+They say quote, "all problems
+in computer science can be
+
+solved by another level of
+indirection." So, it's sort
+
+of, whenever you're stuck,
+you add another level of
+
+indirection.
+
+The caveat to this is the one
+problem that can't be solved
+
+by adding another level of
+indirection is too many levels
+
+of indirection, which
+can be a problem.
+
+As you look at certain kinds of
+memory structures, the fact
+
+that you've separated the
+pointers from the value fields
+
+can lead to them being in very
+far apart in memory, which can
+
+disturb behaviors of caches
+and things like that.
+
+So in some models of memory this
+can lead to surprising
+
+inefficiency.
+
+But most of the time
+it's really a great
+
+implementation technique.
+
+And I highly recommend it.
+
+So that's how we do the trick.
+
+Now we can convince ourselves
+that binary search is indeed
+
+order log n.
+
+And as we saw Tuesday,
+logarithmic
+
+growth is very slow.
+
+So it means we can use binary
+search to search enormous
+
+lists and get the answer
+very quickly.
+
+All right.
+
+There's still one catch.
+
+And what's the catch?
+
+There's an assumption
+to binary search.
+
+Binary search works only when
+what assumption is true?
+
+AUDIENCE: It's sorted.
+
+PROFESSOR JOHN GUTTAG: The
+list is sorted because it
+
+depends on that piece
+of knowledge.
+
+So, that raises the question,
+how did it get sorted?
+
+Or the other question it raises,
+if I ask you to search
+
+for something, does it make
+sense to follow the algorithm
+
+of (1) sort L, (2) use
+binary search?
+
+Does that make sense?
+
+Well, what does it depend upon,
+whether this makes sense
+
+from an efficiency
+point of view?
+
+We know that that's order log
+length of L. We also know if
+
+the list isn't sorted, we can
+do it in order L. We can
+
+always use linear search.
+
+So, whether or not this makes
+a good idea depends upon
+
+whether we can do this
+fast enough.
+
+It has the question is order
+question mark plus order log
+
+len of L less than order L?
+
+If it's not, it doesn't make
+sense to sort it first in
+
+sums, right?
+
+So what's the answer
+to this question?
+
+Do we think we can sort
+a list fast enough?
+
+And what would fast
+enough mean?
+
+What would it have to be?
+
+For this to be better than this,
+we know that we have to
+
+be able to sort a list
+in sublinear time.
+
+Can we do that?
+
+Alas, the answer
+is provably no.
+
+No matter how clever we are,
+there is no algorithm that
+
+will sort a list in
+sublinear time.
+
+And if you think of it, that
+makes a lot of sense.
+
+Because, how can you get
+a list in ascending or
+
+descending order without looking
+at every element in
+
+the list at least once?
+
+Logic says you just
+can't do it.
+
+If you're going to put something
+in order, you're
+
+going to have to look at it.
+
+So we know that we have a lower
+bound on sorting, which
+
+is order L. And we know that
+order L plus order log length
+
+L is the same as order L, which
+is not better than that.
+
+So why do we care?
+
+If this is true, why are we
+interested in things like
+
+binary search at all?
+
+And the reason is we're often
+interested in something called
+
+amortized complexity.
+
+I know that there are some
+course 15 students in the
+
+class who will know what
+amortization means.
+
+But maybe not everybody does.
+
+The idea here is that if we can
+sort the list once and end
+
+up searching it many times, the
+cost of the sort can be
+
+allocated, a little bit of it,
+to each of the searches.
+
+And if we do enough searches,
+then in fact it doesn't really
+
+matter how long the
+sort takes.
+
+So if we were going to search
+this list a million times,
+
+maybe we don't care
+about the one-time
+
+overhead of sorting it.
+
+And this kind of amortized
+analysis is quite common and
+
+is what we really end up doing
+most of the time in practice.
+
+So the real question we want
+to ask is, if we plan on
+
+performing k searches--
+
+who knows how long it will
+take to sort it--
+
+what we'll take is order of
+whatever sort of the list is,
+
+plus k times log length of
+L. Is that less than k
+
+times len of L?
+
+If I don't sort it, to do
+k sort searches will
+
+take this much time.
+
+If I do sort it, it will
+take this much time.
+
+The answer to this question, of
+course, depends upon what's
+
+the complexity of that
+and how big is k.
+
+Does that make sense?
+
+In practice, k is
+often very big.
+
+The number of times we access,
+say, a student record is quite
+
+large compared to the
+number of times
+
+students enroll in MIT.
+
+So if at the start of each
+semester we produce a sorted
+
+list, it pays off to
+do the searches.
+
+In fact, we don't do
+a sorted list.
+
+We do something more complex.
+
+But you understand the
+concept I hope.
+
+Now we have to say, how
+well can we do that?
+
+That's what I want to spend most
+of the rest of today on
+
+now is talking about how do we
+do sorting because it is a
+
+very common operation.
+
+First of all, let's look at
+a way we don't do sorting.
+
+There was a famous computer
+scientist who
+
+opined on this topic.
+
+We can look for him this way.
+
+A well-known technique
+is bubble sort.
+
+Actually, stop.
+
+We're going to need
+sound for this.
+
+Do we have sound in the booth?
+
+Do we have somebody
+in the booth?
+
+Well, we either have
+sound or we don't.
+
+We'll find out shortly.
+
+Other way.
+
+Come on.
+
+You should know.
+
+Oh there.
+
+Thank you.
+
+[VIDEO PLAYBACK]
+
+-Now, it's hard to get
+a job as President.
+
+And you're going through
+the rigors now.
+
+It's also hard to get
+a job at Google.
+
+We have questions, and we ask
+our candidates questions.
+
+And this one is from
+Larry Schwimmer.
+
+[LAUGHTER]
+
+-You guys think I'm kidding?
+
+It's right here.
+
+What is the most efficient
+way to sort a
+
+million 32-bit integers?
+
+[LAUGHTER]
+
+-Well, uh.
+
+-I'm Sorry, maybe
+that's not a--
+
+-I think the bubble sort would
+be the wrong way to go.
+
+[LAUGHTER]
+
+-Come on, who told him this?
+
+I didn't see computer science
+in your background.
+
+-We've got our spies in there.
+
+-OK, let's ask a different
+interval--
+
+[END VIDEO PLAYBACK]
+
+PROFESSOR JOHN GUTTAG: All
+right, so as he sometimes is,
+
+the President was correct.
+
+Bubble sort, though often
+discussed, is almost always
+
+the wrong answer.
+
+So we're not going to talk
+about bubble sort.
+
+I, by the way, know Larry
+Schwimmer and can believe he
+
+did ask that question.
+
+But yes, I'm surprised.
+
+Someone had obviously warned
+the President, actually the
+
+then future president I think.
+
+Let's look at a different one
+that's often used, and that's
+
+called selection sort.
+
+This is about as simple
+as it gets.
+
+The basic idea of
+selection sort--
+
+and it's not a very good way
+to sort, but it is a useful
+
+kind of thing to look
+at because it
+
+introduces some ideas.
+
+Like many algorithms, it depends
+upon establishing and
+
+maintaining an invariant.
+
+An invariant is something
+that's invariantly true.
+
+The invariant we're going to
+maintain here is we're going
+
+to have a pointer
+into the list.
+
+And that pointer is going to
+divide the list into a prefix
+
+and a suffix.
+
+And the invariant that we're
+going to maintain is that the
+
+prefix is always sorted.
+
+We'll start where the
+prefix is empty.
+
+It contains none of the list.
+
+And then each step through the
+algorithm, we'll decrease the
+
+size of the suffix by one
+element and increase the size
+
+of the prefix by one
+element while
+
+maintaining the invariant.
+
+And we'll be done when the size
+of the suffix is 0, and
+
+therefore the prefix contains
+all the elements.
+
+And because we've been
+maintaining this invariant, we
+
+know that we have now
+sorted the list.
+
+So, you can think about it.
+
+For example, if I have a list
+that looks like 4, 2, 3, I'll
+
+start pointing here.
+
+And the prefix, which contains
+nothing, obeys the invariant.
+
+I'll then go through the list
+and find the smallest element
+
+in the list and swap it with
+the first element.
+
+My next step, the list will
+look like 2, 4, 3.
+
+I'll now point here.
+
+My invariant is true.
+
+The prefix contains only
+one element, so it is
+
+in ascending order.
+
+And I've increased
+its size by 1.
+
+I don't have to look at this
+element again because I know
+
+by construction that's
+the smallest.
+
+Now I move here, and I look for
+the smallest element in
+
+the suffix, which will be 3.
+
+I swapped 3 and 4.
+
+And then I'm going to be done.
+
+Does that make sense?
+
+It's very straightforward.
+
+It's, in some sense, the most
+obvious way to sort a list.
+
+And if you look at the code,
+that's exactly what it does.
+
+I've stated the invariant
+here.
+
+And I just go through
+and I sort it.
+
+So we can run it.
+
+Let's do that.
+
+I'm going to sort the list 3,
+4, 5, et cetera, 35, 45.
+
+I'm going to call
+selection sort.
+
+And I don't think this is in
+your handout, but just to make
+
+it obvious what's going on, each
+iteration of the loop I'm
+
+going to print the partially
+sorted list so we can see
+
+what's happening.
+
+The first step, it finds 4 and
+puts that in the beginning.
+
+It actually finds 0, puts it in
+the beginning, et cetera.
+
+All right?
+
+So, people see what's
+going on here?
+
+It's essentially doing
+exactly what I did on
+
+the board over there.
+
+And when we're done, we have
+the list completely sorted.
+
+What's the complexity of this?
+
+What's the complexity
+of selection sort?
+
+There are two things going on.
+
+I'm doing a bunch
+of comparisons.
+
+And I'm doing a bunch
+of swaps.
+
+Since I do, at most, the same
+number of comparisons as I do
+
+swap or swaps as I
+do comparisons--
+
+I never swap without doing
+a comparison--
+
+we can calculate complexity by
+looking at the number of
+
+comparisons I'm doing.
+
+You can see that in
+the code as well.
+
+So how many comparisons might
+I have to do here?
+
+The key thing to notice is each
+time I look at it, each
+
+iteration, I'm looking at
+every element in what?
+
+In the list?
+
+No, every element
+in the suffix.
+
+The first time through,
+I'm going to look at--
+
+let's just say n equals the
+length of the list.
+
+So the first time through, I'm
+going to look at n elements.
+
+Then I'm going to look
+at n minus 1.
+
+Then I'm going to look
+at n minus 2.
+
+Until I'm done, right?
+
+So that's how many operations
+I'm doing.
+
+And what is the order of n plus
+n minus 1 plus n minus 2?
+
+Exactly.
+
+Order n.
+
+So, selection sort is order n.
+
+Is that right?
+
+Somebody said order n.
+
+Do you believe it's n?
+
+Is this really n?
+
+It's not n.
+
+What is it?
+
+Somebody raise your hand, so
+I can throw the candy out.
+
+Yeah.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR JOHN GUTTAG:
+It's not n factorial.
+
+AUDIENCE: n-squared?
+
+PROFESSOR JOHN GUTTAG: You said
+that with a question mark
+
+at the end of your voice.
+
+AUDIENCE: No, it's like the sum
+of the numbers is, like, n
+
+times n minus 1 over 2 or
+something like that.
+
+PROFESSOR JOHN GUTTAG: It's
+really exactly right.
+
+It's a little smaller
+than n-squared,
+
+but it's order n-squared.
+
+I'm doing a lot of
+these additions.
+
+So I can't ignore all of
+these extra terms and
+
+say they don't matter.
+
+It's almost as bad as comparing
+every element to
+
+every other element.
+
+So, selection sort is
+order n-squared.
+
+And you can do it by
+understanding that sum or you
+
+can look at the code here.
+
+And that sort of will
+also tip you off.
+
+Ok. so now, can we do better?
+
+There was a while where people
+were pretty unsure whether you
+
+could do better.
+
+But we can.
+
+If we think about it now, it was
+a method invented by John
+
+von Neumann, a very
+famous guy.
+
+And he, back in the '40s
+amazingly enough, viewed this
+
+as a kind of divide and
+conquer algorithm.
+
+And we've looked at divide
+and conquer before.
+
+What is the general form
+of divide and conquer?
+
+A phrase you've heard me use
+many times, popularized, by
+
+the way, I think, by Machiavelli
+in The Prince, in
+
+a not very nice context.
+
+So, what we do-- and they're
+all of a kind, the same--
+
+we start with 1.
+
+Let me get over here and get
+a full board for this.
+
+First, we have to choose
+a threshold size.
+
+Let's call it n0.
+
+And that will be, essentially,
+the smallest problem.
+
+So, we can keep dividing, making
+our problem smaller--
+
+this is what we saw with binary
+search, for example--
+
+until it's small enough that we
+say, oh the heck with it.
+
+We'll stop dividing it.
+
+Now we'll just solve
+it directly.
+
+So, that's how small we need to
+do it, the smallest thing
+
+we'll divide things into.
+
+The next thing we have to ask
+ourselves is, how many
+
+instances at each division?
+
+We have a big problem.
+
+We divide it into smaller
+problems.
+
+How many are we going
+to divide it into?
+
+We divide it into smaller
+problems until we reach the
+
+threshold where we can
+solve it directly.
+
+And then the third and most
+important part is we need some
+
+algorithm to combine
+the sub-solutions.
+
+It's no good solving the small
+problem if we don't have some
+
+way to combine them to solve
+the larger problem.
+
+We saw that before, and now
+we're going to see it again.
+
+And we're going to see it, in
+particular, in the context of
+
+merge sort.
+
+If I use this board, can people
+see it or is the screen
+
+going to occlude it?
+
+Is there anyone who cannot see
+this board if I write on it?
+
+All right then, I will
+write on it.
+
+Let's first look at
+this problem.
+
+What von Neumann observed
+in 1945 is
+
+given two sorted lists--
+
+and amazingly enough, this is
+still the most popular sorting
+
+algorithm or one of the two most
+popular I should say--
+
+you can merge them quickly.
+
+Let's look at an example.
+
+I'll take the lists 1, 5,
+12, 18, 19, and 20.
+
+That's list one.
+
+And I'll try and merge it with
+the list 2, 3, 4, and 17.
+
+The way you do the merge is
+you start by comparing the
+
+first element to the
+first element.
+
+And then you choose and
+say all right, 1 is
+
+smaller than 2.
+
+So that will be the first
+element of the merge list.
+
+I'm now done with 1,
+and I never have
+
+to look at it again.
+
+The next thing I do is I compare
+5 and 2, the head of
+
+the two remaining lists.
+
+And I say, well, 2 is
+smaller than 5.
+
+I never have to look
+at 2 again.
+
+And then compare 5 and 3.
+
+I say 3 is smaller.
+
+I never have to look
+at 3 again.
+
+I then compare 4 and 5.
+
+4 is smaller.
+
+I then compare 5 and 17.
+
+5 is smaller.
+
+Et cetera.
+
+Now, how many comparisons am
+I going to do this time?
+
+Well, let's first ask the
+question, how many elements am
+
+I going to copy from one of
+these lists to this list?
+
+Copy each element once, right?
+
+So, the number of copies is
+order len of the list.
+
+That's pretty good.
+
+That's linear.
+
+That's sort of at
+the lower bound.
+
+But how many comparisons?
+
+That's a little trickier
+to think about.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR JOHN GUTTAG: Pardon?
+
+AUDIENCE: At most, the length
+of the longer list.
+
+PROFESSOR JOHN GUTTAG: At most,
+the length of the longer
+
+list, which would also
+be, we could claim to
+
+be, order len of--
+
+I sort of cheated using L
+when we have two lists.
+
+But just think of it
+as the longer list.
+
+So, you'd think that
+many comparisons.
+
+You think we can do this whole
+thing in linear time?
+
+And the answer is yes.
+
+That's our merge.
+
+That's a good thing.
+
+Now, that takes care
+of this step.
+
+But now we have to ask,
+how many times are we
+
+going to do a merge?
+
+Because remember, this
+worked because
+
+these lists were sorted.
+
+And so I only had to compare
+the front of each list.
+
+When I think about how I'm going
+to do the binary or the
+
+merge sort, what I'm going to do
+is take the original list,
+
+break it up, break it up, break
+it up, break it up,
+
+until I have a list
+of length 1.
+
+Well, those are all sorted,
+trivially sorted.
+
+And then I'll have, at
+the end, a bunch of
+
+lists of length 1.
+
+I'll merge pairs of those.
+
+Now I'll have sorted
+lists of length 2.
+
+Then I'll merge those, getting
+sorted lists of length 4.
+
+Until at the end, I'll be
+merging two lists, each half
+
+the length of the
+original list.
+
+Right.
+
+Does that make sense
+to everybody?
+
+Now I have to ask the question,
+how many times am I
+
+going to call merge?
+
+Yeah.
+
+AUDIENCE: Base 2 log of
+one of the lists.
+
+PROFESSOR JOHN GUTTAG: Yes, I'm
+going to call merge log
+
+length of the list times.
+
+So, if each merge is order n
+where n is length of the list,
+
+and I call merge log n times,
+what's the total complexity of
+
+the merge sort?
+
+AUDIENCE: nlog(n).
+
+PROFESSOR JOHN GUTTAG:
+nlog(n).
+
+Thank you.
+
+Let's see, I have to choose
+a heavy candy
+
+because they carry better.
+
+Not well enough though.
+
+All right, you can
+relay it back.
+
+Now let's look at an
+implementation.
+
+Here's the implementation
+of sort.
+
+And I don't think you need
+to look at it in detail.
+
+It's doing exactly what
+I did on the board.
+
+Actually, you do need to
+look at in detail,
+
+but not in real time.
+
+And then sort.
+
+Now, there's a little
+complication here because I
+
+wanted to show another
+feature to you.
+
+For the moment, we'll ignore the
+complication, which is--
+
+it's, in principle, working,
+but it's not very bright.
+
+I'll use the mouse.
+
+What we see here is, whenever
+you do a sort, you're sorting
+
+by some ordering metric.
+
+It could be less than.
+
+It could be greater than.
+
+It could be anything you want.
+
+If you're sorting people, you
+could sort them by weight or
+
+you could sort them by height.
+
+You could sort them by,
+God forbid, GPA,
+
+whatever you want.
+
+So, I've written sort to take
+as an argument the ordering.
+
+I've used this funny thing
+called lambda, which you don't
+
+actually have to be
+responsible for.
+
+You're never going to, probably,
+need to use it in
+
+this course.
+
+But it's a way to dynamically
+build a function on the fly.
+
+The function I've built is I've
+said the default value of
+
+LT is x less than y.
+
+Lambda x, lambda xy says
+x and y are the
+
+parameters to a function.
+
+And the body of the function is
+simply return the value x
+
+less than y.
+
+All right?
+
+Nothing very exciting there.
+
+What is exciting is having a
+function as an argument.
+
+And that is something that
+you'll be doing in future
+
+problem sets.
+
+Because it's one of the very
+powerful and most useful
+
+features in Python, is using
+functional arguments.
+
+Right.
+
+Having got past that, what we
+see is we first say if the
+
+length of L is less than 2--
+
+that's my threshold--
+
+then I'm just going to return
+L, actually a copy of L.
+
+Otherwise, I'm going to find
+roughly the middle of L.
+
+Then I'm going to call sort
+recursively with the part to
+
+the left of the middle and the
+part to the right of the
+
+middle, and then merge them.
+
+So I'm going to go all the way
+down until I get to list of
+
+length 1, and then bubble
+all the way back up,
+
+merging as I go.
+
+So, we can see that the depth
+of the recursion will be
+
+log(n), as observed before.
+
+This is exactly what we
+looked at when we
+
+looked at binary search.
+
+How many times can you divide
+something in half --
+
+log(n) times?
+
+And each recursion we're
+going to call merge.
+
+So, this is consistent with the
+notion that the complexity
+
+of the overall algorithm
+is nlog(n).
+
+Let's run it.
+
+And I'm going to print as we
+go what's getting merged.
+
+Get rid of this one.
+
+This was our selection sort.
+
+We already looked at that.
+
+Yeah.
+
+So what we'll see here is the
+first example, I was just
+
+sorting a list of integers.
+
+Maybe we'll look at that
+all by itself.
+
+I didn't pass it in the second
+argument, so it used the
+
+default less than.
+
+It was first merge 4 and 5.
+
+Then it had to merge 35
+with 4 and 5, then 29
+
+with 17, 58 and 0.
+
+And then the longer list, 1729
+with 058, 04535 with 0172958.
+
+And then we were done.
+
+So, indeed it did a logarithmic
+number of merges.
+
+The next piece of code, I'm
+taking advantage of the fact
+
+that this function can sort
+lists of different kinds.
+
+And I'm calling it now with
+the list of floats.
+
+And I am passing in the
+second argument,
+
+which is going to be--
+
+well, let's for fun, I wonder
+what happens if I make this
+
+greater than.
+
+Let's see what we get.
+
+Now you note, it's sorted
+it in the other order.
+
+Because I passed in the ordering
+that said I want to
+
+use a different comparison then
+less than, I want to use
+
+greater than.
+
+So the same code did the
+sort the other way.
+
+I can do more interesting
+things.
+
+So, here I'm assuming I
+have a list of names.
+
+And I've written two ordering
+functions myself, one that
+
+first compares the last names
+and then the first names.
+
+And a different one that
+compares the first names and
+
+then the last names.
+
+And we can look at those.
+
+Just to avoid cluttering
+up the screen, let
+
+me get rid of this.
+
+What we can see is we got--
+
+we did the same way of dividing
+things initially, but
+
+now we got different
+orderings.
+
+So, if we look at the first
+ordering I used, we start with
+
+Giselle Brady and then Tom
+Brady and then Chancellor
+
+Grimson, et cetera.
+
+And if we do the second
+ordering, we see, among other
+
+things, you have me between
+Giselle and Tom.
+
+Not a bad outcome from
+my perspective.
+
+But again, a lot
+of flexibility.
+
+By using this functional
+argument, I can define
+
+whatever functions I want, and
+using the same sort, get lots
+
+of different code.
+
+And you will discover that in
+fact the built in sort of
+
+Python has this kind
+of flexibility.
+
+You will also find, as you
+write your own programs,
+
+increasingly you'll want to use
+functions as arguments.
+
+Because it allows you to write
+a lot less code to accomplish
+
+the same tasks.
\ No newline at end of file
diff --git a/7FzD5EH7_q8.txt b/7FzD5EH7_q8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a02a37e39649b669f7e931d3b68c22a12f0d0400
--- /dev/null
+++ b/7FzD5EH7_q8.txt
@@ -0,0 +1,23368 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay so uh to begin so in
+
+ align:start position:0%
+ocw.mit.edu okay so uh to begin so in
+ 
+
+ align:start position:0%
+ocw.mit.edu okay so uh to begin so in
+the last class uh we talked them about
+
+ align:start position:0%
+the last class uh we talked them about
+ 
+
+ align:start position:0%
+the last class uh we talked them about
+some of the early uh documentary films
+
+ align:start position:0%
+some of the early uh documentary films
+ 
+
+ align:start position:0%
+some of the early uh documentary films
+um the films by uh n the north by FL and
+
+ align:start position:0%
+um the films by uh n the north by FL and
+ 
+
+ align:start position:0%
+um the films by uh n the north by FL and
+man with a movie camera by by ziga verto
+
+ align:start position:0%
+man with a movie camera by by ziga verto
+ 
+
+ align:start position:0%
+man with a movie camera by by ziga verto
+and in today's class we're going to be
+
+ align:start position:0%
+and in today's class we're going to be
+ 
+
+ align:start position:0%
+and in today's class we're going to be
+shifting a bit and thinking a bit more
+
+ align:start position:0%
+shifting a bit and thinking a bit more
+ 
+
+ align:start position:0%
+shifting a bit and thinking a bit more
+about the question of the relationship
+
+ align:start position:0%
+about the question of the relationship
+ 
+
+ align:start position:0%
+about the question of the relationship
+between documentary film and science um
+
+ align:start position:0%
+between documentary film and science um
+ 
+
+ align:start position:0%
+between documentary film and science um
+and one of the things that many
+
+ align:start position:0%
+and one of the things that many
+ 
+
+ align:start position:0%
+and one of the things that many
+commentators um argue often links um
+
+ align:start position:0%
+commentators um argue often links um
+ 
+
+ align:start position:0%
+commentators um argue often links um
+science and documentary in terms of
+
+ align:start position:0%
+science and documentary in terms of
+ 
+
+ align:start position:0%
+science and documentary in terms of
+people's common perception of it is that
+
+ align:start position:0%
+people's common perception of it is that
+ 
+
+ align:start position:0%
+people's common perception of it is that
+there's often a tendency to think of
+
+ align:start position:0%
+there's often a tendency to think of
+ 
+
+ align:start position:0%
+there's often a tendency to think of
+both of them is sort of offering
+
+ align:start position:0%
+both of them is sort of offering
+ 
+
+ align:start position:0%
+both of them is sort of offering
+unmediated access um onto the world out
+
+ align:start position:0%
+unmediated access um onto the world out
+ 
+
+ align:start position:0%
+unmediated access um onto the world out
+there um right so there's often the
+
+ align:start position:0%
+there um right so there's often the
+ 
+
+ align:start position:0%
+there um right so there's often the
+strong tendency for people to see
+
+ align:start position:0%
+strong tendency for people to see
+ 
+
+ align:start position:0%
+strong tendency for people to see
+documentary as simply a window onto
+
+ align:start position:0%
+documentary as simply a window onto
+ 
+
+ align:start position:0%
+documentary as simply a window onto
+reality rather than being an
+
+ align:start position:0%
+reality rather than being an
+ 
+
+ align:start position:0%
+reality rather than being an
+interpretation of the reality that's out
+
+ align:start position:0%
+interpretation of the reality that's out
+ 
+
+ align:start position:0%
+interpretation of the reality that's out
+there and certainly that's the case for
+
+ align:start position:0%
+there and certainly that's the case for
+ 
+
+ align:start position:0%
+there and certainly that's the case for
+for for science in an even stronger
+
+ align:start position:0%
+for for science in an even stronger
+ 
+
+ align:start position:0%
+for for science in an even stronger
+sense that for many people the idea is
+
+ align:start position:0%
+sense that for many people the idea is
+ 
+
+ align:start position:0%
+sense that for many people the idea is
+that um uh they like to think of science
+
+ align:start position:0%
+that um uh they like to think of science
+ 
+
+ align:start position:0%
+that um uh they like to think of science
+as allowing um completely direct access
+
+ align:start position:0%
+as allowing um completely direct access
+ 
+
+ align:start position:0%
+as allowing um completely direct access
+um to the outer physical world but many
+
+ align:start position:0%
+um to the outer physical world but many
+ 
+
+ align:start position:0%
+um to the outer physical world but many
+science study Scholars would argue that
+
+ align:start position:0%
+science study Scholars would argue that
+ 
+
+ align:start position:0%
+science study Scholars would argue that
+science doesn't just simply offer
+
+ align:start position:0%
+science doesn't just simply offer
+ 
+
+ align:start position:0%
+science doesn't just simply offer
+unmediated unmediated access onto the
+
+ align:start position:0%
+unmediated unmediated access onto the
+ 
+
+ align:start position:0%
+unmediated unmediated access onto the
+world um how do scientists measure or
+
+ align:start position:0%
+world um how do scientists measure or
+ 
+
+ align:start position:0%
+world um how do scientists measure or
+monitor or present the natural world um
+
+ align:start position:0%
+monitor or present the natural world um
+ 
+
+ align:start position:0%
+monitor or present the natural world um
+often they have to do so through
+
+ align:start position:0%
+often they have to do so through
+ 
+
+ align:start position:0%
+often they have to do so through
+technical instruments um right for
+
+ align:start position:0%
+technical instruments um right for
+ 
+
+ align:start position:0%
+technical instruments um right for
+example and those instruments serve as a
+
+ align:start position:0%
+example and those instruments serve as a
+ 
+
+ align:start position:0%
+example and those instruments serve as a
+form of mediation um and when scientists
+
+ align:start position:0%
+form of mediation um and when scientists
+ 
+
+ align:start position:0%
+form of mediation um and when scientists
+use those instruments for example or
+
+ align:start position:0%
+use those instruments for example or
+ 
+
+ align:start position:0%
+use those instruments for example or
+they might use um visual pictures or
+
+ align:start position:0%
+they might use um visual pictures or
+ 
+
+ align:start position:0%
+they might use um visual pictures or
+diagrams based on what those instruments
+
+ align:start position:0%
+diagrams based on what those instruments
+ 
+
+ align:start position:0%
+diagrams based on what those instruments
+might say those visual images also have
+
+ align:start position:0%
+might say those visual images also have
+ 
+
+ align:start position:0%
+might say those visual images also have
+to be perceived or interpreted right and
+
+ align:start position:0%
+to be perceived or interpreted right and
+ 
+
+ align:start position:0%
+to be perceived or interpreted right and
+this is increasingly the case given
+
+ align:start position:0%
+this is increasingly the case given
+ 
+
+ align:start position:0%
+this is increasingly the case given
+computer Sim simulations so for example
+
+ align:start position:0%
+computer Sim simulations so for example
+ 
+
+ align:start position:0%
+computer Sim simulations so for example
+I have a student who's working on the
+
+ align:start position:0%
+I have a student who's working on the
+ 
+
+ align:start position:0%
+I have a student who's working on the
+issue of uranium mining um and it used
+
+ align:start position:0%
+issue of uranium mining um and it used
+ 
+
+ align:start position:0%
+issue of uranium mining um and it used
+to be the case that when people when
+
+ align:start position:0%
+to be the case that when people when
+ 
+
+ align:start position:0%
+to be the case that when people when
+geologists went off to do work on
+
+ align:start position:0%
+geologists went off to do work on
+ 
+
+ align:start position:0%
+geologists went off to do work on
+uranium mining they would they would go
+
+ align:start position:0%
+uranium mining they would they would go
+ 
+
+ align:start position:0%
+uranium mining they would they would go
+off and do actual um field field work at
+
+ align:start position:0%
+off and do actual um field field work at
+ 
+
+ align:start position:0%
+off and do actual um field field work at
+geological sites um and that would be
+
+ align:start position:0%
+geological sites um and that would be
+ 
+
+ align:start position:0%
+geological sites um and that would be
+the basis um of of their be the basis of
+
+ align:start position:0%
+the basis um of of their be the basis of
+ 
+
+ align:start position:0%
+the basis um of of their be the basis of
+their work but now increasingly
+
+ align:start position:0%
+their work but now increasingly
+ 
+
+ align:start position:0%
+their work but now increasingly
+geologists are relying on statistical
+
+ align:start position:0%
+geologists are relying on statistical
+ 
+
+ align:start position:0%
+geologists are relying on statistical
+modeling to find out where they think
+
+ align:start position:0%
+modeling to find out where they think
+ 
+
+ align:start position:0%
+modeling to find out where they think
+that uranium deposits might be for
+
+ align:start position:0%
+that uranium deposits might be for
+ 
+
+ align:start position:0%
+that uranium deposits might be for
+example so there's there so there's an
+
+ align:start position:0%
+example so there's there so there's an
+ 
+
+ align:start position:0%
+example so there's there so there's an
+increasing way with the use of computers
+
+ align:start position:0%
+increasing way with the use of computers
+ 
+
+ align:start position:0%
+increasing way with the use of computers
+in visual modeling that visual images
+
+ align:start position:0%
+in visual modeling that visual images
+ 
+
+ align:start position:0%
+in visual modeling that visual images
+and diagrams and pictures become
+
+ align:start position:0%
+and diagrams and pictures become
+ 
+
+ align:start position:0%
+and diagrams and pictures become
+increasingly Central to how um science
+
+ align:start position:0%
+increasingly Central to how um science
+ 
+
+ align:start position:0%
+increasingly Central to how um science
+gets conveyed or talked about or thought
+
+ align:start position:0%
+gets conveyed or talked about or thought
+ 
+
+ align:start position:0%
+gets conveyed or talked about or thought
+through so if you think about those
+
+ align:start position:0%
+through so if you think about those
+ 
+
+ align:start position:0%
+through so if you think about those
+visual images you always have to you
+
+ align:start position:0%
+visual images you always have to you
+ 
+
+ align:start position:0%
+visual images you always have to you
+know how are the visual images
+
+ align:start position:0%
+know how are the visual images
+ 
+
+ align:start position:0%
+know how are the visual images
+constructed how do people interpret
+
+ align:start position:0%
+constructed how do people interpret
+ 
+
+ align:start position:0%
+constructed how do people interpret
+those images how do they think through
+
+ align:start position:0%
+those images how do they think through
+ 
+
+ align:start position:0%
+those images how do they think through
+them so there's all these kinds of
+
+ align:start position:0%
+them so there's all these kinds of
+ 
+
+ align:start position:0%
+them so there's all these kinds of
+layers of interpretation and mediation
+
+ align:start position:0%
+layers of interpretation and mediation
+ 
+
+ align:start position:0%
+layers of interpretation and mediation
+that happen through those kinds of um
+
+ align:start position:0%
+that happen through those kinds of um
+ 
+
+ align:start position:0%
+that happen through those kinds of um
+visual images and and then for
+
+ align:start position:0%
+visual images and and then for
+ 
+
+ align:start position:0%
+visual images and and then for
+scientists when they want to talk or
+
+ align:start position:0%
+scientists when they want to talk or
+ 
+
+ align:start position:0%
+scientists when they want to talk or
+write about their work or they want to
+
+ align:start position:0%
+write about their work or they want to
+ 
+
+ align:start position:0%
+write about their work or they want to
+convey it to others we have to do it
+
+ align:start position:0%
+convey it to others we have to do it
+ 
+
+ align:start position:0%
+convey it to others we have to do it
+through speaking right we rely upon the
+
+ align:start position:0%
+through speaking right we rely upon the
+ 
+
+ align:start position:0%
+through speaking right we rely upon the
+language that we use and there's certain
+
+ align:start position:0%
+language that we use and there's certain
+ 
+
+ align:start position:0%
+language that we use and there's certain
+conventions then about well how do you
+
+ align:start position:0%
+conventions then about well how do you
+ 
+
+ align:start position:0%
+conventions then about well how do you
+write up the science that you're engaged
+
+ align:start position:0%
+write up the science that you're engaged
+ 
+
+ align:start position:0%
+write up the science that you're engaged
+in doing how do you
+
+ align:start position:0%
+in doing how do you
+ 
+
+ align:start position:0%
+in doing how do you
+persuade fellow scientists that this is
+
+ align:start position:0%
+persuade fellow scientists that this is
+ 
+
+ align:start position:0%
+persuade fellow scientists that this is
+a good argument what are the conventions
+
+ align:start position:0%
+a good argument what are the conventions
+ 
+
+ align:start position:0%
+a good argument what are the conventions
+within your discipline about what makes
+
+ align:start position:0%
+within your discipline about what makes
+ 
+
+ align:start position:0%
+within your discipline about what makes
+a um a good or convincing argument
+
+ align:start position:0%
+a um a good or convincing argument
+ 
+
+ align:start position:0%
+a um a good or convincing argument
+um so all of these different kinds of
+
+ align:start position:0%
+um so all of these different kinds of
+ 
+
+ align:start position:0%
+um so all of these different kinds of
+representation and language help to
+
+ align:start position:0%
+representation and language help to
+ 
+
+ align:start position:0%
+representation and language help to
+mediate how we perceive and understand
+
+ align:start position:0%
+mediate how we perceive and understand
+ 
+
+ align:start position:0%
+mediate how we perceive and understand
+the world that we're part of um in
+
+ align:start position:0%
+the world that we're part of um in
+ 
+
+ align:start position:0%
+the world that we're part of um in
+addition to whatever our own personal
+
+ align:start position:0%
+addition to whatever our own personal
+ 
+
+ align:start position:0%
+addition to whatever our own personal
+kind of social positioning or
+
+ align:start position:0%
+kind of social positioning or
+ 
+
+ align:start position:0%
+kind of social positioning or
+institutional positioning might be and
+
+ align:start position:0%
+institutional positioning might be and
+ 
+
+ align:start position:0%
+institutional positioning might be and
+similarly documentary film theorists
+
+ align:start position:0%
+similarly documentary film theorists
+ 
+
+ align:start position:0%
+similarly documentary film theorists
+would argue that documentary film also
+
+ align:start position:0%
+would argue that documentary film also
+ 
+
+ align:start position:0%
+would argue that documentary film also
+doesn't offer just simply unmediated
+
+ align:start position:0%
+doesn't offer just simply unmediated
+ 
+
+ align:start position:0%
+doesn't offer just simply unmediated
+access onto the world I mean documentary
+
+ align:start position:0%
+access onto the world I mean documentary
+ 
+
+ align:start position:0%
+access onto the world I mean documentary
+films are about the real world but
+
+ align:start position:0%
+films are about the real world but
+ 
+
+ align:start position:0%
+films are about the real world but
+they're also interpretations of of what
+
+ align:start position:0%
+they're also interpretations of of what
+ 
+
+ align:start position:0%
+they're also interpretations of of what
+that real world is right so um and and
+
+ align:start position:0%
+that real world is right so um and and
+ 
+
+ align:start position:0%
+that real world is right so um and and
+again it's not to say that some
+
+ align:start position:0%
+again it's not to say that some
+ 
+
+ align:start position:0%
+again it's not to say that some
+interpretations aren't better than
+
+ align:start position:0%
+interpretations aren't better than
+ 
+
+ align:start position:0%
+interpretations aren't better than
+others because some interpretations are
+
+ align:start position:0%
+others because some interpretations are
+ 
+
+ align:start position:0%
+others because some interpretations are
+better than others um but filmmakers do
+
+ align:start position:0%
+better than others um but filmmakers do
+ 
+
+ align:start position:0%
+better than others um but filmmakers do
+I mean obviously filmmakers choose their
+
+ align:start position:0%
+I mean obviously filmmakers choose their
+ 
+
+ align:start position:0%
+I mean obviously filmmakers choose their
+subjects uh they choose what to shoot
+
+ align:start position:0%
+subjects uh they choose what to shoot
+ 
+
+ align:start position:0%
+subjects uh they choose what to shoot
+they shoot they choose what to exclude
+
+ align:start position:0%
+they shoot they choose what to exclude
+ 
+
+ align:start position:0%
+they shoot they choose what to exclude
+from the frame they choose how to create
+
+ align:start position:0%
+from the frame they choose how to create
+ 
+
+ align:start position:0%
+from the frame they choose how to create
+a narrative out of those images through
+
+ align:start position:0%
+a narrative out of those images through
+ 
+
+ align:start position:0%
+a narrative out of those images through
+the process of editing and then you also
+
+ align:start position:0%
+the process of editing and then you also
+ 
+
+ align:start position:0%
+the process of editing and then you also
+have the issue of you know the subjects
+
+ align:start position:0%
+have the issue of you know the subjects
+ 
+
+ align:start position:0%
+have the issue of you know the subjects
+the documentary
+
+ align:start position:0%
+the documentary
+ 
+
+ align:start position:0%
+the documentary
+filmmakers are filming what are those
+
+ align:start position:0%
+filmmakers are filming what are those
+ 
+
+ align:start position:0%
+filmmakers are filming what are those
+subjects interpretations of the world
+
+ align:start position:0%
+subjects interpretations of the world
+ 
+
+ align:start position:0%
+subjects interpretations of the world
+and then you have the people who at the
+
+ align:start position:0%
+and then you have the people who at the
+ 
+
+ align:start position:0%
+and then you have the people who at the
+end view the film who have their
+
+ align:start position:0%
+end view the film who have their
+ 
+
+ align:start position:0%
+end view the film who have their
+interpretations of what they think's
+
+ align:start position:0%
+interpretations of what they think's
+ 
+
+ align:start position:0%
+interpretations of what they think's
+going on so you have the subjects who
+
+ align:start position:0%
+going on so you have the subjects who
+ 
+
+ align:start position:0%
+going on so you have the subjects who
+are being filmed their interpretations
+
+ align:start position:0%
+are being filmed their interpretations
+ 
+
+ align:start position:0%
+are being filmed their interpretations
+and Medi of the world you have the
+
+ align:start position:0%
+and Medi of the world you have the
+ 
+
+ align:start position:0%
+and Medi of the world you have the
+filmmaker creating mediations of what's
+
+ align:start position:0%
+filmmaker creating mediations of what's
+ 
+
+ align:start position:0%
+filmmaker creating mediations of what's
+going on through what the filmmaker is
+
+ align:start position:0%
+going on through what the filmmaker is
+ 
+
+ align:start position:0%
+going on through what the filmmaker is
+doing and then you have the people who
+
+ align:start position:0%
+doing and then you have the people who
+ 
+
+ align:start position:0%
+doing and then you have the people who
+watch it at the end who who are
+
+ align:start position:0%
+watch it at the end who who are
+ 
+
+ align:start position:0%
+watch it at the end who who are
+interpreting and mediating it at the
+
+ align:start position:0%
+interpreting and mediating it at the
+ 
+
+ align:start position:0%
+interpreting and mediating it at the
+same end so you have these all these
+
+ align:start position:0%
+same end so you have these all these
+ 
+
+ align:start position:0%
+same end so you have these all these
+kinds of different layers of
+
+ align:start position:0%
+kinds of different layers of
+ 
+
+ align:start position:0%
+kinds of different layers of
+interpretation that all go on um as
+
+ align:start position:0%
+interpretation that all go on um as
+ 
+
+ align:start position:0%
+interpretation that all go on um as
+people uh make and view documentary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+films um and so in this class I just
+
+ align:start position:0%
+films um and so in this class I just
+ 
+
+ align:start position:0%
+films um and so in this class I just
+want to briefly just very briefly talk
+
+ align:start position:0%
+want to briefly just very briefly talk
+ 
+
+ align:start position:0%
+want to briefly just very briefly talk
+about um some social science
+
+ align:start position:0%
+about um some social science
+ 
+
+ align:start position:0%
+about um some social science
+perspectives on thinking about science I
+
+ align:start position:0%
+perspectives on thinking about science I
+ 
+
+ align:start position:0%
+perspectives on thinking about science I
+and that got referred to in your a bit
+
+ align:start position:0%
+and that got referred to in your a bit
+ 
+
+ align:start position:0%
+and that got referred to in your a bit
+as STS studies and I know that article
+
+ align:start position:0%
+as STS studies and I know that article
+ 
+
+ align:start position:0%
+as STS studies and I know that article
+um there was a kind of an overview
+
+ align:start position:0%
+um there was a kind of an overview
+ 
+
+ align:start position:0%
+um there was a kind of an overview
+article that I gave you by Susan silby
+
+ align:start position:0%
+article that I gave you by Susan silby
+ 
+
+ align:start position:0%
+article that I gave you by Susan silby
+who's who's the chair of the department
+
+ align:start position:0%
+who's who's the chair of the department
+ 
+
+ align:start position:0%
+who's who's the chair of the department
+here actually um and Sophia Roose I know
+
+ align:start position:0%
+here actually um and Sophia Roose I know
+ 
+
+ align:start position:0%
+here actually um and Sophia Roose I know
+it's a difficult article you're not
+
+ align:start position:0%
+it's a difficult article you're not
+ 
+
+ align:start position:0%
+it's a difficult article you're not
+really expected to most of you are
+
+ align:start position:0%
+really expected to most of you are
+ 
+
+ align:start position:0%
+really expected to most of you are
+undergraduate up Karina um Kina has to
+
+ align:start position:0%
+undergraduate up Karina um Kina has to
+ 
+
+ align:start position:0%
+undergraduate up Karina um Kina has to
+understand everything in it
+
+ align:start position:0%
+understand everything in it
+ 
+
+ align:start position:0%
+understand everything in it
+um but for the rest of you the point is
+
+ align:start position:0%
+um but for the rest of you the point is
+ 
+
+ align:start position:0%
+um but for the rest of you the point is
+just to give you some sense of sort of
+
+ align:start position:0%
+just to give you some sense of sort of
+ 
+
+ align:start position:0%
+just to give you some sense of sort of
+the train of the arguments and you're
+
+ align:start position:0%
+the train of the arguments and you're
+ 
+
+ align:start position:0%
+the train of the arguments and you're
+not really expected to to sort of know
+
+ align:start position:0%
+not really expected to to sort of know
+ 
+
+ align:start position:0%
+not really expected to to sort of know
+all the the ins and outs and details of
+
+ align:start position:0%
+all the the ins and outs and details of
+ 
+
+ align:start position:0%
+all the the ins and outs and details of
+all that um um literature but just just
+
+ align:start position:0%
+all that um um literature but just just
+ 
+
+ align:start position:0%
+all that um um literature but just just
+suffice to say that um social studies of
+
+ align:start position:0%
+suffice to say that um social studies of
+ 
+
+ align:start position:0%
+suffice to say that um social studies of
+science it gets called by different
+
+ align:start position:0%
+science it gets called by different
+ 
+
+ align:start position:0%
+science it gets called by different
+names science studies social studies of
+
+ align:start position:0%
+names science studies social studies of
+ 
+
+ align:start position:0%
+names science studies social studies of
+science STS lots of other different
+
+ align:start position:0%
+science STS lots of other different
+ 
+
+ align:start position:0%
+science STS lots of other different
+names we won't go into um has been an
+
+ align:start position:0%
+names we won't go into um has been an
+ 
+
+ align:start position:0%
+names we won't go into um has been an
+interdisciplinary Venture by historians
+
+ align:start position:0%
+interdisciplinary Venture by historians
+ 
+
+ align:start position:0%
+interdisciplinary Venture by historians
+philosophers anthropologists
+
+ align:start position:0%
+philosophers anthropologists
+ 
+
+ align:start position:0%
+philosophers anthropologists
+sociologists um and others that gained
+
+ align:start position:0%
+sociologists um and others that gained
+ 
+
+ align:start position:0%
+sociologists um and others that gained
+um considerable M momentum during the
+
+ align:start position:0%
+um considerable M momentum during the
+ 
+
+ align:start position:0%
+um considerable M momentum during the
+1960s and 70s and it's offered a way to
+
+ align:start position:0%
+1960s and 70s and it's offered a way to
+ 
+
+ align:start position:0%
+1960s and 70s and it's offered a way to
+think about science and social terms and
+
+ align:start position:0%
+think about science and social terms and
+ 
+
+ align:start position:0%
+think about science and social terms and
+right to to to stand back a bit from the
+
+ align:start position:0%
+right to to to stand back a bit from the
+ 
+
+ align:start position:0%
+right to to to stand back a bit from the
+science and think about what it is um
+
+ align:start position:0%
+science and think about what it is um
+ 
+
+ align:start position:0%
+science and think about what it is um
+and in terms of the ideas at work not
+
+ align:start position:0%
+and in terms of the ideas at work not
+ 
+
+ align:start position:0%
+and in terms of the ideas at work not
+only the ideas at work but also in terms
+
+ align:start position:0%
+only the ideas at work but also in terms
+ 
+
+ align:start position:0%
+only the ideas at work but also in terms
+of the people who practice science uh
+
+ align:start position:0%
+of the people who practice science uh
+ 
+
+ align:start position:0%
+of the people who practice science uh
+the communities and institutions that
+
+ align:start position:0%
+the communities and institutions that
+ 
+
+ align:start position:0%
+the communities and institutions that
+they're part of um and these are
+
+ align:start position:0%
+they're part of um and these are
+ 
+
+ align:start position:0%
+they're part of um and these are
+important social questions for us to be
+
+ align:start position:0%
+important social questions for us to be
+ 
+
+ align:start position:0%
+important social questions for us to be
+thinking about right because um you know
+
+ align:start position:0%
+thinking about right because um you know
+ 
+
+ align:start position:0%
+thinking about right because um you know
+science and modern Technologies are so
+
+ align:start position:0%
+science and modern Technologies are so
+ 
+
+ align:start position:0%
+science and modern Technologies are so
+incredibly crucial to our contemporary
+
+ align:start position:0%
+incredibly crucial to our contemporary
+ 
+
+ align:start position:0%
+incredibly crucial to our contemporary
+lives they shape how we live how we
+
+ align:start position:0%
+lives they shape how we live how we
+ 
+
+ align:start position:0%
+lives they shape how we live how we
+think in the world and the kinds of
+
+ align:start position:0%
+think in the world and the kinds of
+ 
+
+ align:start position:0%
+think in the world and the kinds of
+policy DEC decisions that get made the
+
+ align:start position:0%
+policy DEC decisions that get made the
+ 
+
+ align:start position:0%
+policy DEC decisions that get made the
+health of our bodies the kinds of
+
+ align:start position:0%
+health of our bodies the kinds of
+ 
+
+ align:start position:0%
+health of our bodies the kinds of
+knowledge we consider valid I mean so
+
+ align:start position:0%
+knowledge we consider valid I mean so
+ 
+
+ align:start position:0%
+knowledge we consider valid I mean so
+these are all completely Central Social
+
+ align:start position:0%
+these are all completely Central Social
+ 
+
+ align:start position:0%
+these are all completely Central Social
+questions so for social scientists um
+
+ align:start position:0%
+questions so for social scientists um
+ 
+
+ align:start position:0%
+questions so for social scientists um
+and philosophers these kinds of
+
+ align:start position:0%
+and philosophers these kinds of
+ 
+
+ align:start position:0%
+and philosophers these kinds of
+questions around science are also
+
+ align:start position:0%
+questions around science are also
+ 
+
+ align:start position:0%
+questions around science are also
+extremely important so it's not only
+
+ align:start position:0%
+extremely important so it's not only
+ 
+
+ align:start position:0%
+extremely important so it's not only
+important for for Science and Engineers
+
+ align:start position:0%
+important for for Science and Engineers
+ 
+
+ align:start position:0%
+important for for Science and Engineers
+but it's also important for for people
+
+ align:start position:0%
+but it's also important for for people
+ 
+
+ align:start position:0%
+but it's also important for for people
+in other disciplines to be thinking
+
+ align:start position:0%
+in other disciplines to be thinking
+ 
+
+ align:start position:0%
+in other disciplines to be thinking
+about these kinds of questions and I
+
+ align:start position:0%
+about these kinds of questions and I
+ 
+
+ align:start position:0%
+about these kinds of questions and I
+just want to throw out a couple
+
+ align:start position:0%
+just want to throw out a couple
+ 
+
+ align:start position:0%
+just want to throw out a couple
+important points that science studies
+
+ align:start position:0%
+important points that science studies
+ 
+
+ align:start position:0%
+important points that science studies
+has made that I think it might be useful
+
+ align:start position:0%
+has made that I think it might be useful
+ 
+
+ align:start position:0%
+has made that I think it might be useful
+for all of us in thinking about this
+
+ align:start position:0%
+for all of us in thinking about this
+ 
+
+ align:start position:0%
+for all of us in thinking about this
+class and as you think about your final
+
+ align:start position:0%
+class and as you think about your final
+ 
+
+ align:start position:0%
+class and as you think about your final
+projects um and you think about sort of
+
+ align:start position:0%
+projects um and you think about sort of
+ 
+
+ align:start position:0%
+projects um and you think about sort of
+what kind of project you want to do it
+
+ align:start position:0%
+what kind of project you want to do it
+ 
+
+ align:start position:0%
+what kind of project you want to do it
+might sort of help a bit in thinking
+
+ align:start position:0%
+might sort of help a bit in thinking
+ 
+
+ align:start position:0%
+might sort of help a bit in thinking
+about it um so one important Insight
+
+ align:start position:0%
+about it um so one important Insight
+ 
+
+ align:start position:0%
+about it um so one important Insight
+from science studies is that instead of
+
+ align:start position:0%
+from science studies is that instead of
+ 
+
+ align:start position:0%
+from science studies is that instead of
+seeing sort of well here's Society over
+
+ align:start position:0%
+seeing sort of well here's Society over
+ 
+
+ align:start position:0%
+seeing sort of well here's Society over
+here and here's science over here and
+
+ align:start position:0%
+here and here's science over here and
+ 
+
+ align:start position:0%
+here and here's science over here and
+they're somehow separate and in
+
+ align:start position:0%
+they're somehow separate and in
+ 
+
+ align:start position:0%
+they're somehow separate and in
+opposition to each other that one of the
+
+ align:start position:0%
+opposition to each other that one of the
+ 
+
+ align:start position:0%
+opposition to each other that one of the
+the major points of science studies is
+
+ align:start position:0%
+the major points of science studies is
+ 
+
+ align:start position:0%
+the major points of science studies is
+that you always have to see science and
+
+ align:start position:0%
+that you always have to see science and
+ 
+
+ align:start position:0%
+that you always have to see science and
+society as being co-produced or in
+
+ align:start position:0%
+society as being co-produced or in
+ 
+
+ align:start position:0%
+society as being co-produced or in
+relationship to each other um and maybe
+
+ align:start position:0%
+relationship to each other um and maybe
+ 
+
+ align:start position:0%
+relationship to each other um and maybe
+some of this sounds a bit obvious I'm
+
+ align:start position:0%
+some of this sounds a bit obvious I'm
+ 
+
+ align:start position:0%
+some of this sounds a bit obvious I'm
+not sure but but but obviously science
+
+ align:start position:0%
+not sure but but but obviously science
+ 
+
+ align:start position:0%
+not sure but but but obviously science
+comes out of our social world it's part
+
+ align:start position:0%
+comes out of our social world it's part
+ 
+
+ align:start position:0%
+comes out of our social world it's part
+of the the social worlds in which we um
+
+ align:start position:0%
+of the the social worlds in which we um
+ 
+
+ align:start position:0%
+of the the social worlds in which we um
+exist science gets produced by people in
+
+ align:start position:0%
+exist science gets produced by people in
+ 
+
+ align:start position:0%
+exist science gets produced by people in
+particular historical times and places
+
+ align:start position:0%
+particular historical times and places
+ 
+
+ align:start position:0%
+particular historical times and places
+and because of the times and places in
+
+ align:start position:0%
+and because of the times and places in
+ 
+
+ align:start position:0%
+and because of the times and places in
+which in which we all exist we ask
+
+ align:start position:0%
+which in which we all exist we ask
+ 
+
+ align:start position:0%
+which in which we all exist we ask
+certain kinds of questions and we don't
+
+ align:start position:0%
+certain kinds of questions and we don't
+ 
+
+ align:start position:0%
+certain kinds of questions and we don't
+ask other kinds of questions um the the
+
+ align:start position:0%
+ask other kinds of questions um the the
+ 
+
+ align:start position:0%
+ask other kinds of questions um the the
+time periods in which we're operating um
+
+ align:start position:0%
+time periods in which we're operating um
+ 
+
+ align:start position:0%
+time periods in which we're operating um
+shapes what we consider to be important
+
+ align:start position:0%
+shapes what we consider to be important
+ 
+
+ align:start position:0%
+shapes what we consider to be important
+or not it shapes what gets funded or not
+
+ align:start position:0%
+or not it shapes what gets funded or not
+ 
+
+ align:start position:0%
+or not it shapes what gets funded or not
+um and and science as Susan syby argued
+
+ align:start position:0%
+um and and science as Susan syby argued
+ 
+
+ align:start position:0%
+um and and science as Susan syby argued
+science is a communal process right for
+
+ align:start position:0%
+science is a communal process right for
+ 
+
+ align:start position:0%
+science is a communal process right for
+the most part it happens through
+
+ align:start position:0%
+the most part it happens through
+ 
+
+ align:start position:0%
+the most part it happens through
+institutions it's a collective
+
+ align:start position:0%
+institutions it's a collective
+ 
+
+ align:start position:0%
+institutions it's a collective
+Enterprise that happens at places like
+
+ align:start position:0%
+Enterprise that happens at places like
+ 
+
+ align:start position:0%
+Enterprise that happens at places like
+MIT and in through other kinds of
+
+ align:start position:0%
+MIT and in through other kinds of
+ 
+
+ align:start position:0%
+MIT and in through other kinds of
+Institutions students get trained in
+
+ align:start position:0%
+Institutions students get trained in
+ 
+
+ align:start position:0%
+Institutions students get trained in
+particular kinds of ways um again
+
+ align:start position:0%
+particular kinds of ways um again
+ 
+
+ align:start position:0%
+particular kinds of ways um again
+there's there's whole funding bodies
+
+ align:start position:0%
+there's there's whole funding bodies
+ 
+
+ align:start position:0%
+there's there's whole funding bodies
+that off that operate in certain certain
+
+ align:start position:0%
+that off that operate in certain certain
+ 
+
+ align:start position:0%
+that off that operate in certain certain
+kinds of ways and they fund certain
+
+ align:start position:0%
+kinds of ways and they fund certain
+ 
+
+ align:start position:0%
+kinds of ways and they fund certain
+kinds of issues and not others and so so
+
+ align:start position:0%
+kinds of issues and not others and so so
+ 
+
+ align:start position:0%
+kinds of issues and not others and so so
+we have to think of science as being
+
+ align:start position:0%
+we have to think of science as being
+ 
+
+ align:start position:0%
+we have to think of science as being
+fundamentally a social or Collective
+
+ align:start position:0%
+fundamentally a social or Collective
+ 
+
+ align:start position:0%
+fundamentally a social or Collective
+kind of activity okay and I just want to
+
+ align:start position:0%
+kind of activity okay and I just want to
+ 
+
+ align:start position:0%
+kind of activity okay and I just want to
+make very clear though that that this
+
+ align:start position:0%
+make very clear though that that this
+ 
+
+ align:start position:0%
+make very clear though that that this
+does not in any way undermine the the
+
+ align:start position:0%
+does not in any way undermine the the
+ 
+
+ align:start position:0%
+does not in any way undermine the the
+the the validity or the importance of
+
+ align:start position:0%
+the the validity or the importance of
+ 
+
+ align:start position:0%
+the the validity or the importance of
+the knowledge that comes out of um that
+
+ align:start position:0%
+the knowledge that comes out of um that
+ 
+
+ align:start position:0%
+the knowledge that comes out of um that
+comes out of science um and if anything
+
+ align:start position:0%
+comes out of science um and if anything
+ 
+
+ align:start position:0%
+comes out of science um and if anything
+I would I would argue that it adds a
+
+ align:start position:0%
+I would I would argue that it adds a
+ 
+
+ align:start position:0%
+I would I would argue that it adds a
+certain richness and appreciation to
+
+ align:start position:0%
+certain richness and appreciation to
+ 
+
+ align:start position:0%
+certain richness and appreciation to
+understanding it because there's also
+
+ align:start position:0%
+understanding it because there's also
+ 
+
+ align:start position:0%
+understanding it because there's also
+these these whole layers of social
+
+ align:start position:0%
+these these whole layers of social
+ 
+
+ align:start position:0%
+these these whole layers of social
+complexity that are also part of it as
+
+ align:start position:0%
+complexity that are also part of it as
+ 
+
+ align:start position:0%
+complexity that are also part of it as
+well um so that's
+
+ align:start position:0%
+well um so that's
+ 
+
+ align:start position:0%
+well um so that's
+one crucial Point secondly uh another
+
+ align:start position:0%
+one crucial Point secondly uh another
+ 
+
+ align:start position:0%
+one crucial Point secondly uh another
+crucial point is that science studies um
+
+ align:start position:0%
+crucial point is that science studies um
+ 
+
+ align:start position:0%
+crucial point is that science studies um
+has has shifted in it even in its own
+
+ align:start position:0%
+has has shifted in it even in its own
+ 
+
+ align:start position:0%
+has has shifted in it even in its own
+thinking from not only thinking about
+
+ align:start position:0%
+thinking from not only thinking about
+ 
+
+ align:start position:0%
+thinking from not only thinking about
+the content of scientific knowledge but
+
+ align:start position:0%
+the content of scientific knowledge but
+ 
+
+ align:start position:0%
+the content of scientific knowledge but
+also to thinking about science as
+
+ align:start position:0%
+also to thinking about science as
+ 
+
+ align:start position:0%
+also to thinking about science as
+something that people do right and so
+
+ align:start position:0%
+something that people do right and so
+ 
+
+ align:start position:0%
+something that people do right and so
+you have a number of science study
+
+ align:start position:0%
+you have a number of science study
+ 
+
+ align:start position:0%
+you have a number of science study
+Scholars that engage that have been
+
+ align:start position:0%
+Scholars that engage that have been
+ 
+
+ align:start position:0%
+Scholars that engage that have been
+engaged in laborator studies
+
+ align:start position:0%
+engaged in laborator studies
+ 
+
+ align:start position:0%
+engaged in laborator studies
+well so they go and they spend time in
+
+ align:start position:0%
+well so they go and they spend time in
+ 
+
+ align:start position:0%
+well so they go and they spend time in
+lab Laboratories because they want to
+
+ align:start position:0%
+lab Laboratories because they want to
+ 
+
+ align:start position:0%
+lab Laboratories because they want to
+pay attention to science as a process
+
+ align:start position:0%
+pay attention to science as a process
+ 
+
+ align:start position:0%
+pay attention to science as a process
+what do scientists actually do how do
+
+ align:start position:0%
+what do scientists actually do how do
+ 
+
+ align:start position:0%
+what do scientists actually do how do
+they know what they know how do they
+
+ align:start position:0%
+they know what they know how do they
+ 
+
+ align:start position:0%
+they know what they know how do they
+think about it how do they learn it how
+
+ align:start position:0%
+think about it how do they learn it how
+ 
+
+ align:start position:0%
+think about it how do they learn it how
+do they train their students um how does
+
+ align:start position:0%
+do they train their students um how does
+ 
+
+ align:start position:0%
+do they train their students um how does
+this this fact affect the ways that
+
+ align:start position:0%
+this this fact affect the ways that
+ 
+
+ align:start position:0%
+this this fact affect the ways that
+knowledge um ends up being produced okay
+
+ align:start position:0%
+knowledge um ends up being produced okay
+ 
+
+ align:start position:0%
+knowledge um ends up being produced okay
+and so you have social scientist
+
+ align:start position:0%
+and so you have social scientist
+ 
+
+ align:start position:0%
+and so you have social scientist
+Scholars who who do work in Laboratories
+
+ align:start position:0%
+Scholars who who do work in Laboratories
+ 
+
+ align:start position:0%
+Scholars who who do work in Laboratories
+one of the articles that you read for
+
+ align:start position:0%
+one of the articles that you read for
+ 
+
+ align:start position:0%
+one of the articles that you read for
+today by Sharon Trawick she's done a
+
+ align:start position:0%
+today by Sharon Trawick she's done a
+ 
+
+ align:start position:0%
+today by Sharon Trawick she's done a
+very famous ethnography called beam
+
+ align:start position:0%
+very famous ethnography called beam
+ 
+
+ align:start position:0%
+very famous ethnography called beam
+times and lifetimes where she did
+
+ align:start position:0%
+times and lifetimes where she did
+ 
+
+ align:start position:0%
+times and lifetimes where she did
+research in Laboratories with physicists
+
+ align:start position:0%
+research in Laboratories with physicists
+ 
+
+ align:start position:0%
+research in Laboratories with physicists
+both in the US and in Japan um which is
+
+ align:start position:0%
+both in the US and in Japan um which is
+ 
+
+ align:start position:0%
+both in the US and in Japan um which is
+quite an interesting study I sometimes
+
+ align:start position:0%
+quite an interesting study I sometimes
+ 
+
+ align:start position:0%
+quite an interesting study I sometimes
+use it in in anthro it's good read if
+
+ align:start position:0%
+use it in in anthro it's good read if
+ 
+
+ align:start position:0%
+use it in in anthro it's good read if
+anybody's interested um and then you
+
+ align:start position:0%
+anybody's interested um and then you
+ 
+
+ align:start position:0%
+anybody's interested um and then you
+have other social um um science study
+
+ align:start position:0%
+have other social um um science study
+ 
+
+ align:start position:0%
+have other social um um science study
+Scholars that also look at scientists
+
+ align:start position:0%
+Scholars that also look at scientists
+ 
+
+ align:start position:0%
+Scholars that also look at scientists
+beyond the laboratory so you have uh
+
+ align:start position:0%
+beyond the laboratory so you have uh
+ 
+
+ align:start position:0%
+beyond the laboratory so you have uh
+Hugh gusterson um somebody else who used
+
+ align:start position:0%
+Hugh gusterson um somebody else who used
+ 
+
+ align:start position:0%
+Hugh gusterson um somebody else who used
+to te Teach here at MIT who no longer
+
+ align:start position:0%
+to te Teach here at MIT who no longer
+ 
+
+ align:start position:0%
+to te Teach here at MIT who no longer
+does um he said George Mason now um but
+
+ align:start position:0%
+does um he said George Mason now um but
+ 
+
+ align:start position:0%
+does um he said George Mason now um but
+he did work with nuclear weapons design
+
+ align:start position:0%
+he did work with nuclear weapons design
+ 
+
+ align:start position:0%
+he did work with nuclear weapons design
+ERS at Livermore lab and because it was
+
+ align:start position:0%
+ERS at Livermore lab and because it was
+ 
+
+ align:start position:0%
+ERS at Livermore lab and because it was
+classified he couldn't get access to
+
+ align:start position:0%
+classified he couldn't get access to
+ 
+
+ align:start position:0%
+classified he couldn't get access to
+where they were actually doing the work
+
+ align:start position:0%
+where they were actually doing the work
+ 
+
+ align:start position:0%
+where they were actually doing the work
+and so he ended up you know kind of
+
+ align:start position:0%
+and so he ended up you know kind of
+ 
+
+ align:start position:0%
+and so he ended up you know kind of
+lurking around Livermore lab uh
+
+ align:start position:0%
+lurking around Livermore lab uh
+ 
+
+ align:start position:0%
+lurking around Livermore lab uh
+basically on the outside and so he would
+
+ align:start position:0%
+basically on the outside and so he would
+ 
+
+ align:start position:0%
+basically on the outside and so he would
+he would go to coffee shops with people
+
+ align:start position:0%
+he would go to coffee shops with people
+ 
+
+ align:start position:0%
+he would go to coffee shops with people
+go to their houses he would go to church
+
+ align:start position:0%
+go to their houses he would go to church
+ 
+
+ align:start position:0%
+go to their houses he would go to church
+he would go shopping and so and he would
+
+ align:start position:0%
+he would go shopping and so and he would
+ 
+
+ align:start position:0%
+he would go shopping and so and he would
+do these really in-depth interviews with
+
+ align:start position:0%
+do these really in-depth interviews with
+ 
+
+ align:start position:0%
+do these really in-depth interviews with
+people and so he spent a lot of time
+
+ align:start position:0%
+people and so he spent a lot of time
+ 
+
+ align:start position:0%
+people and so he spent a lot of time
+sort of hanging out in the areas where
+
+ align:start position:0%
+sort of hanging out in the areas where
+ 
+
+ align:start position:0%
+sort of hanging out in the areas where
+uh nuclear weapons designers were
+
+ align:start position:0%
+uh nuclear weapons designers were
+ 
+
+ align:start position:0%
+uh nuclear weapons designers were
+spending time talking to them um and he
+
+ align:start position:0%
+spending time talking to them um and he
+ 
+
+ align:start position:0%
+spending time talking to them um and he
+became uh it was
+
+ align:start position:0%
+became uh it was
+ 
+
+ align:start position:0%
+became uh it was
+very interesting in um in his work from
+
+ align:start position:0%
+very interesting in um in his work from
+ 
+
+ align:start position:0%
+very interesting in um in his work from
+the beginning it was kind of like well
+
+ align:start position:0%
+the beginning it was kind of like well
+ 
+
+ align:start position:0%
+the beginning it was kind of like well
+who are you and then afterwards I think
+
+ align:start position:0%
+who are you and then afterwards I think
+ 
+
+ align:start position:0%
+who are you and then afterwards I think
+um people came to so sort of enjoy
+
+ align:start position:0%
+um people came to so sort of enjoy
+ 
+
+ align:start position:0%
+um people came to so sort of enjoy
+telling their story to him because a lot
+
+ align:start position:0%
+telling their story to him because a lot
+ 
+
+ align:start position:0%
+telling their story to him because a lot
+of people hadn't had a chance to tell
+
+ align:start position:0%
+of people hadn't had a chance to tell
+ 
+
+ align:start position:0%
+of people hadn't had a chance to tell
+their story about what they did and why
+
+ align:start position:0%
+their story about what they did and why
+ 
+
+ align:start position:0%
+their story about what they did and why
+they did and how they thought about it
+
+ align:start position:0%
+they did and how they thought about it
+ 
+
+ align:start position:0%
+they did and how they thought about it
+and moral and other kinds of terms that
+
+ align:start position:0%
+and moral and other kinds of terms that
+ 
+
+ align:start position:0%
+and moral and other kinds of terms that
+it sort of became um the thing to do
+
+ align:start position:0%
+it sort of became um the thing to do
+ 
+
+ align:start position:0%
+it sort of became um the thing to do
+that everybody wanted to be interviewed
+
+ align:start position:0%
+that everybody wanted to be interviewed
+ 
+
+ align:start position:0%
+that everybody wanted to be interviewed
+by Hugh and so and so everybody's like
+
+ align:start position:0%
+by Hugh and so and so everybody's like
+ 
+
+ align:start position:0%
+by Hugh and so and so everybody's like
+well you interviewed everybody else how
+
+ align:start position:0%
+well you interviewed everybody else how
+ 
+
+ align:start position:0%
+well you interviewed everybody else how
+you haven't interviewed me yet so he
+
+ align:start position:0%
+you haven't interviewed me yet so he
+ 
+
+ align:start position:0%
+you haven't interviewed me yet so he
+kind of became the the the resident
+
+ align:start position:0%
+kind of became the the the resident
+ 
+
+ align:start position:0%
+kind of became the the the resident
+Anthropologist of all the the nuclear
+
+ align:start position:0%
+Anthropologist of all the the nuclear
+ 
+
+ align:start position:0%
+Anthropologist of all the the nuclear
+weapons Folks at Livermore lab um and
+
+ align:start position:0%
+weapons Folks at Livermore lab um and
+ 
+
+ align:start position:0%
+weapons Folks at Livermore lab um and
+then you have Stephan helch who's
+
+ align:start position:0%
+then you have Stephan helch who's
+ 
+
+ align:start position:0%
+then you have Stephan helch who's
+Another Science Study scholar here um at
+
+ align:start position:0%
+Another Science Study scholar here um at
+ 
+
+ align:start position:0%
+Another Science Study scholar here um at
+MIT who also he did work with um um
+
+ align:start position:0%
+MIT who also he did work with um um
+ 
+
+ align:start position:0%
+MIT who also he did work with um um
+marine
+
+ align:start position:0%
+marine
+ 
+
+ align:start position:0%
+marine
+microbiologists and following them
+
+ align:start position:0%
+microbiologists and following them
+ 
+
+ align:start position:0%
+microbiologists and following them
+around not only um in Laboratories but
+
+ align:start position:0%
+around not only um in Laboratories but
+ 
+
+ align:start position:0%
+around not only um in Laboratories but
+sort of taking a trip down in Alvin
+
+ align:start position:0%
+sort of taking a trip down in Alvin
+ 
+
+ align:start position:0%
+sort of taking a trip down in Alvin
+under the water um going to conferences
+
+ align:start position:0%
+under the water um going to conferences
+ 
+
+ align:start position:0%
+under the water um going to conferences
+other places where scientists might go
+
+ align:start position:0%
+other places where scientists might go
+ 
+
+ align:start position:0%
+other places where scientists might go
+so you have a number of science study
+
+ align:start position:0%
+so you have a number of science study
+ 
+
+ align:start position:0%
+so you have a number of science study
+Scholars doing work sort of on what is
+
+ align:start position:0%
+Scholars doing work sort of on what is
+ 
+
+ align:start position:0%
+Scholars doing work sort of on what is
+it that scientists are doing and sort of
+
+ align:start position:0%
+it that scientists are doing and sort of
+ 
+
+ align:start position:0%
+it that scientists are doing and sort of
+following scientists around where they
+
+ align:start position:0%
+following scientists around where they
+ 
+
+ align:start position:0%
+following scientists around where they
+um where they go and so the big question
+
+ align:start position:0%
+um where they go and so the big question
+ 
+
+ align:start position:0%
+um where they go and so the big question
+from this is how does science
+
+ align:start position:0%
+from this is how does science
+ 
+
+ align:start position:0%
+from this is how does science
+potentially look different when we think
+
+ align:start position:0%
+potentially look different when we think
+ 
+
+ align:start position:0%
+potentially look different when we think
+about it as something that people do do
+
+ align:start position:0%
+about it as something that people do do
+ 
+
+ align:start position:0%
+about it as something that people do do
+we think about science differently when
+
+ align:start position:0%
+we think about science differently when
+ 
+
+ align:start position:0%
+we think about science differently when
+you think about it as a process as an
+
+ align:start position:0%
+you think about it as a process as an
+ 
+
+ align:start position:0%
+you think about it as a process as an
+activity rather than simply you know
+
+ align:start position:0%
+activity rather than simply you know
+ 
+
+ align:start position:0%
+activity rather than simply you know
+some data that you could get in a
+
+ align:start position:0%
+some data that you could get in a
+ 
+
+ align:start position:0%
+some data that you could get in a
+textbook if you think about it as an
+
+ align:start position:0%
+textbook if you think about it as an
+ 
+
+ align:start position:0%
+textbook if you think about it as an
+activity um I think a lot of Scholars
+
+ align:start position:0%
+activity um I think a lot of Scholars
+ 
+
+ align:start position:0%
+activity um I think a lot of Scholars
+who do this kind of work would argue it
+
+ align:start position:0%
+who do this kind of work would argue it
+ 
+
+ align:start position:0%
+who do this kind of work would argue it
+actually kind of opens up and frees up a
+
+ align:start position:0%
+actually kind of opens up and frees up a
+ 
+
+ align:start position:0%
+actually kind of opens up and frees up a
+lot of ways of thinking about science
+
+ align:start position:0%
+lot of ways of thinking about science
+ 
+
+ align:start position:0%
+lot of ways of thinking about science
+and that's particularly going to be
+
+ align:start position:0%
+and that's particularly going to be
+ 
+
+ align:start position:0%
+and that's particularly going to be
+relevant for us since since film is a
+
+ align:start position:0%
+relevant for us since since film is a
+ 
+
+ align:start position:0%
+relevant for us since since film is a
+medium that focuses on activity
+
+ align:start position:0%
+medium that focuses on activity
+ 
+
+ align:start position:0%
+medium that focuses on activity
+um so the third issue I wanted to throw
+
+ align:start position:0%
+um so the third issue I wanted to throw
+ 
+
+ align:start position:0%
+um so the third issue I wanted to throw
+out um is that science study scholarship
+
+ align:start position:0%
+out um is that science study scholarship
+ 
+
+ align:start position:0%
+out um is that science study scholarship
+has also been helpful in thinking about
+
+ align:start position:0%
+has also been helpful in thinking about
+ 
+
+ align:start position:0%
+has also been helpful in thinking about
+questions of Science and Technology as
+
+ align:start position:0%
+questions of Science and Technology as
+ 
+
+ align:start position:0%
+questions of Science and Technology as
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+travel throughout our social world even
+
+ align:start position:0%
+travel throughout our social world even
+ 
+
+ align:start position:0%
+travel throughout our social world even
+apart from scientists and other kinds of
+
+ align:start position:0%
+apart from scientists and other kinds of
+ 
+
+ align:start position:0%
+apart from scientists and other kinds of
+folks so the question of how do debates
+
+ align:start position:0%
+folks so the question of how do debates
+ 
+
+ align:start position:0%
+folks so the question of how do debates
+about science spread through other
+
+ align:start position:0%
+about science spread through other
+ 
+
+ align:start position:0%
+about science spread through other
+aspects of not only us Society but but
+
+ align:start position:0%
+aspects of not only us Society but but
+ 
+
+ align:start position:0%
+aspects of not only us Society but but
+other regions of the world so you can
+
+ align:start position:0%
+other regions of the world so you can
+ 
+
+ align:start position:0%
+other regions of the world so you can
+think about this question uh say I mean
+
+ align:start position:0%
+think about this question uh say I mean
+ 
+
+ align:start position:0%
+think about this question uh say I mean
+lots of different ways to think about it
+
+ align:start position:0%
+lots of different ways to think about it
+ 
+
+ align:start position:0%
+lots of different ways to think about it
+but um in relation to environmental
+
+ align:start position:0%
+but um in relation to environmental
+ 
+
+ align:start position:0%
+but um in relation to environmental
+pollution is one example right so if
+
+ align:start position:0%
+pollution is one example right so if
+ 
+
+ align:start position:0%
+pollution is one example right so if
+people live in a community that they
+
+ align:start position:0%
+people live in a community that they
+ 
+
+ align:start position:0%
+people live in a community that they
+they have concerns about environmental
+
+ align:start position:0%
+they have concerns about environmental
+ 
+
+ align:start position:0%
+they have concerns about environmental
+pollution science becomes really crucial
+
+ align:start position:0%
+pollution science becomes really crucial
+ 
+
+ align:start position:0%
+pollution science becomes really crucial
+in terms of trying to figure out well
+
+ align:start position:0%
+in terms of trying to figure out well
+ 
+
+ align:start position:0%
+in terms of trying to figure out well
+what what is the nature of the pollution
+
+ align:start position:0%
+what what is the nature of the pollution
+ 
+
+ align:start position:0%
+what what is the nature of the pollution
+what is the extent of it there might be
+
+ align:start position:0%
+what is the extent of it there might be
+ 
+
+ align:start position:0%
+what is the extent of it there might be
+debates about what kinds of knowledge
+
+ align:start position:0%
+debates about what kinds of knowledge
+ 
+
+ align:start position:0%
+debates about what kinds of knowledge
+gets gets counted or doesn't get counted
+
+ align:start position:0%
+gets gets counted or doesn't get counted
+ 
+
+ align:start position:0%
+gets gets counted or doesn't get counted
+but for a lot of people in their
+
+ align:start position:0%
+but for a lot of people in their
+ 
+
+ align:start position:0%
+but for a lot of people in their
+day-to-day lives I mean science is
+
+ align:start position:0%
+day-to-day lives I mean science is
+ 
+
+ align:start position:0%
+day-to-day lives I mean science is
+obviously something that's a crucial
+
+ align:start position:0%
+obviously something that's a crucial
+ 
+
+ align:start position:0%
+obviously something that's a crucial
+part just for for average people um in
+
+ align:start position:0%
+part just for for average people um in
+ 
+
+ align:start position:0%
+part just for for average people um in
+terms of of living in the Contemporary
+
+ align:start position:0%
+terms of of living in the Contemporary
+ 
+
+ align:start position:0%
+terms of of living in the Contemporary
+world and in ter you think about
+
+ align:start position:0%
+world and in ter you think about
+ 
+
+ align:start position:0%
+world and in ter you think about
+International Development a lot of the
+
+ align:start position:0%
+International Development a lot of the
+ 
+
+ align:start position:0%
+International Development a lot of the
+language of International Development
+
+ align:start position:0%
+language of International Development
+ 
+
+ align:start position:0%
+language of International Development
+projects uses um managerial language but
+
+ align:start position:0%
+projects uses um managerial language but
+ 
+
+ align:start position:0%
+projects uses um managerial language but
+also language of science science and
+
+ align:start position:0%
+also language of science science and
+ 
+
+ align:start position:0%
+also language of science science and
+technology is part of it right so so
+
+ align:start position:0%
+technology is part of it right so so
+ 
+
+ align:start position:0%
+technology is part of it right so so
+there's all these questions about well
+
+ align:start position:0%
+there's all these questions about well
+ 
+
+ align:start position:0%
+there's all these questions about well
+what are the discussions about science
+
+ align:start position:0%
+what are the discussions about science
+ 
+
+ align:start position:0%
+what are the discussions about science
+and technology and all these spaces
+
+ align:start position:0%
+and technology and all these spaces
+ 
+
+ align:start position:0%
+and technology and all these spaces
+apart from Laboratories and scientists
+
+ align:start position:0%
+apart from Laboratories and scientists
+ 
+
+ align:start position:0%
+apart from Laboratories and scientists
+and places like MIT how does it work
+
+ align:start position:0%
+and places like MIT how does it work
+ 
+
+ align:start position:0%
+and places like MIT how does it work
+sort of out there in the world okay and
+
+ align:start position:0%
+sort of out there in the world okay and
+ 
+
+ align:start position:0%
+sort of out there in the world okay and
+part of the reason I think that's
+
+ align:start position:0%
+part of the reason I think that's
+ 
+
+ align:start position:0%
+part of the reason I think that's
+important for this class is again as you
+
+ align:start position:0%
+important for this class is again as you
+ 
+
+ align:start position:0%
+important for this class is again as you
+think about your final projects we're
+
+ align:start position:0%
+think about your final projects we're
+ 
+
+ align:start position:0%
+think about your final projects we're
+we're encouraging people to do final
+
+ align:start position:0%
+we're encouraging people to do final
+ 
+
+ align:start position:0%
+we're encouraging people to do final
+projects around Science and Technology
+
+ align:start position:0%
+projects around Science and Technology
+ 
+
+ align:start position:0%
+projects around Science and Technology
+but we also want you to think broadly
+
+ align:start position:0%
+but we also want you to think broadly
+ 
+
+ align:start position:0%
+but we also want you to think broadly
+about that you don't have to just think
+
+ align:start position:0%
+about that you don't have to just think
+ 
+
+ align:start position:0%
+about that you don't have to just think
+sort of doing science in a lab although
+
+ align:start position:0%
+sort of doing science in a lab although
+ 
+
+ align:start position:0%
+sort of doing science in a lab although
+that can be really fascinating you know
+
+ align:start position:0%
+that can be really fascinating you know
+ 
+
+ align:start position:0%
+that can be really fascinating you know
+so if you can think of a good project
+
+ align:start position:0%
+so if you can think of a good project
+ 
+
+ align:start position:0%
+so if you can think of a good project
+you want to do based on that that could
+
+ align:start position:0%
+you want to do based on that that could
+ 
+
+ align:start position:0%
+you want to do based on that that could
+be fantastic but if you also sort of
+
+ align:start position:0%
+be fantastic but if you also sort of
+ 
+
+ align:start position:0%
+be fantastic but if you also sort of
+want to follow things outside MIT or
+
+ align:start position:0%
+want to follow things outside MIT or
+ 
+
+ align:start position:0%
+want to follow things outside MIT or
+take an unconventional angle on this
+
+ align:start position:0%
+take an unconventional angle on this
+ 
+
+ align:start position:0%
+take an unconventional angle on this
+um do it you be creative with this think
+
+ align:start position:0%
+um do it you be creative with this think
+ 
+
+ align:start position:0%
+um do it you be creative with this think
+about how this stuff moves how it goes
+
+ align:start position:0%
+about how this stuff moves how it goes
+ 
+
+ align:start position:0%
+about how this stuff moves how it goes
+to different kinds of places what do
+
+ align:start position:0%
+to different kinds of places what do
+ 
+
+ align:start position:0%
+to different kinds of places what do
+people do with it um so anyway so we
+
+ align:start position:0%
+people do with it um so anyway so we
+ 
+
+ align:start position:0%
+people do with it um so anyway so we
+want you to be thinking in those
+
+ align:start position:0%
+want you to be thinking in those
+ 
+
+ align:start position:0%
+want you to be thinking in those
+terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay so and just once again to
+
+ align:start position:0%
+um okay so and just once again to
+ 
+
+ align:start position:0%
+um okay so and just once again to
+emphasize this point that for us in
+
+ align:start position:0%
+emphasize this point that for us in
+ 
+
+ align:start position:0%
+emphasize this point that for us in
+thinking of this class we really want to
+
+ align:start position:0%
+thinking of this class we really want to
+ 
+
+ align:start position:0%
+thinking of this class we really want to
+be thinking about science as a process
+
+ align:start position:0%
+be thinking about science as a process
+ 
+
+ align:start position:0%
+be thinking about science as a process
+um not only questions about um knowledge
+
+ align:start position:0%
+um not only questions about um knowledge
+ 
+
+ align:start position:0%
+um not only questions about um knowledge
+as an end product but a process of um
+
+ align:start position:0%
+as an end product but a process of um
+ 
+
+ align:start position:0%
+as an end product but a process of um
+what do scientists do how do they come
+
+ align:start position:0%
+what do scientists do how do they come
+ 
+
+ align:start position:0%
+what do scientists do how do they come
+to know what are the relationships that
+
+ align:start position:0%
+to know what are the relationships that
+ 
+
+ align:start position:0%
+to know what are the relationships that
+scientists are part of how does Science
+
+ align:start position:0%
+scientists are part of how does Science
+ 
+
+ align:start position:0%
+scientists are part of how does Science
+and Technology circulate out there what
+
+ align:start position:0%
+and Technology circulate out there what
+ 
+
+ align:start position:0%
+and Technology circulate out there what
+kinds of debates are they part of what
+
+ align:start position:0%
+kinds of debates are they part of what
+ 
+
+ align:start position:0%
+kinds of debates are they part of what
+are the implications of the debates now
+
+ align:start position:0%
+are the implications of the debates now
+ 
+
+ align:start position:0%
+are the implications of the debates now
+I lost my my next page sorry anyway
+
+ align:start position:0%
+I lost my my next page sorry anyway
+ 
+
+ align:start position:0%
+I lost my my next page sorry anyway
+um sorry I had I had file I had file
+
+ align:start position:0%
+um sorry I had I had file I had file
+ 
+
+ align:start position:0%
+um sorry I had I had file I had file
+conversion problems so I'm I got a bit
+
+ align:start position:0%
+conversion problems so I'm I got a bit
+ 
+
+ align:start position:0%
+conversion problems so I'm I got a bit
+stuck here um anyway okay um and I think
+
+ align:start position:0%
+stuck here um anyway okay um and I think
+ 
+
+ align:start position:0%
+stuck here um anyway okay um and I think
+this focus on practices again is useful
+
+ align:start position:0%
+this focus on practices again is useful
+ 
+
+ align:start position:0%
+this focus on practices again is useful
+for for many different
+
+ align:start position:0%
+for for many different
+ 
+
+ align:start position:0%
+for for many different
+reasons you know in addition to thinking
+
+ align:start position:0%
+reasons you know in addition to thinking
+ 
+
+ align:start position:0%
+reasons you know in addition to thinking
+about the film angle but but but also
+
+ align:start position:0%
+about the film angle but but but also
+ 
+
+ align:start position:0%
+about the film angle but but but also
+thinking um of science as as a kind of
+
+ align:start position:0%
+thinking um of science as as a kind of
+ 
+
+ align:start position:0%
+thinking um of science as as a kind of
+practice or as a process I think also
+
+ align:start position:0%
+practice or as a process I think also
+ 
+
+ align:start position:0%
+practice or as a process I think also
+helps to make science human right it
+
+ align:start position:0%
+helps to make science human right it
+ 
+
+ align:start position:0%
+helps to make science human right it
+helps to bring sort of the human element
+
+ align:start position:0%
+helps to bring sort of the human element
+ 
+
+ align:start position:0%
+helps to bring sort of the human element
+back in and make science more
+
+ align:start position:0%
+back in and make science more
+ 
+
+ align:start position:0%
+back in and make science more
+approachable and again this is also
+
+ align:start position:0%
+approachable and again this is also
+ 
+
+ align:start position:0%
+approachable and again this is also
+relevant for thinking about doing
+
+ align:start position:0%
+relevant for thinking about doing
+ 
+
+ align:start position:0%
+relevant for thinking about doing
+documentary films about this
+
+ align:start position:0%
+documentary films about this
+ 
+
+ align:start position:0%
+documentary films about this
+um and it's also focusing on how people
+
+ align:start position:0%
+um and it's also focusing on how people
+ 
+
+ align:start position:0%
+um and it's also focusing on how people
+come to have also by focusing on how
+
+ align:start position:0%
+come to have also by focusing on how
+ 
+
+ align:start position:0%
+come to have also by focusing on how
+people come to have knowledge that you
+
+ align:start position:0%
+people come to have knowledge that you
+ 
+
+ align:start position:0%
+people come to have knowledge that you
+gain appreciation for that kind of
+
+ align:start position:0%
+gain appreciation for that kind of
+ 
+
+ align:start position:0%
+gain appreciation for that kind of
+knowledge as well as you see the
+
+ align:start position:0%
+knowledge as well as you see the
+ 
+
+ align:start position:0%
+knowledge as well as you see the
+limitations of that knowledge um right
+
+ align:start position:0%
+limitations of that knowledge um right
+ 
+
+ align:start position:0%
+limitations of that knowledge um right
+when you when you focus on well how are
+
+ align:start position:0%
+when you when you focus on well how are
+ 
+
+ align:start position:0%
+when you when you focus on well how are
+we about getting knowledge what are we
+
+ align:start position:0%
+we about getting knowledge what are we
+ 
+
+ align:start position:0%
+we about getting knowledge what are we
+able to get access to or what not what's
+
+ align:start position:0%
+able to get access to or what not what's
+ 
+
+ align:start position:0%
+able to get access to or what not what's
+the potential constraints what's the
+
+ align:start position:0%
+the potential constraints what's the
+ 
+
+ align:start position:0%
+the potential constraints what's the
+things that we're really good at like
+
+ align:start position:0%
+things that we're really good at like
+ 
+
+ align:start position:0%
+things that we're really good at like
+isn't it amazing that people were able
+
+ align:start position:0%
+isn't it amazing that people were able
+ 
+
+ align:start position:0%
+isn't it amazing that people were able
+to figure this kind of thing out but
+
+ align:start position:0%
+to figure this kind of thing out but
+ 
+
+ align:start position:0%
+to figure this kind of thing out but
+what's the kind of stuff that's
+
+ align:start position:0%
+what's the kind of stuff that's
+ 
+
+ align:start position:0%
+what's the kind of stuff that's
+difficult to think about that it's
+
+ align:start position:0%
+difficult to think about that it's
+ 
+
+ align:start position:0%
+difficult to think about that it's
+actually by sort of following these
+
+ align:start position:0%
+actually by sort of following these
+ 
+
+ align:start position:0%
+actually by sort of following these
+activities of science that we sort of
+
+ align:start position:0%
+activities of science that we sort of
+ 
+
+ align:start position:0%
+activities of science that we sort of
+get a stronger sense and again I think a
+
+ align:start position:0%
+get a stronger sense and again I think a
+ 
+
+ align:start position:0%
+get a stronger sense and again I think a
+richer sense of of what do we know well
+
+ align:start position:0%
+richer sense of of what do we know well
+ 
+
+ align:start position:0%
+richer sense of of what do we know well
+and what do we what do we know uh what
+
+ align:start position:0%
+and what do we what do we know uh what
+ 
+
+ align:start position:0%
+and what do we what do we know uh what
+do we know less
+
+ align:start position:0%
+do we know less
+ 
+
+ align:start position:0%
+do we know less
+well um and as we've talked about
+
+ align:start position:0%
+well um and as we've talked about
+ 
+
+ align:start position:0%
+well um and as we've talked about
+earlier in class part of the goal of
+
+ align:start position:0%
+earlier in class part of the goal of
+ 
+
+ align:start position:0%
+earlier in class part of the goal of
+this class is also thinking about
+
+ align:start position:0%
+this class is also thinking about
+ 
+
+ align:start position:0%
+this class is also thinking about
+doumentary film as a as um as a process
+
+ align:start position:0%
+doumentary film as a as um as a process
+ 
+
+ align:start position:0%
+doumentary film as a as um as a process
+itself so again we're not just looking
+
+ align:start position:0%
+itself so again we're not just looking
+ 
+
+ align:start position:0%
+itself so again we're not just looking
+at documentary films as a product right
+
+ align:start position:0%
+at documentary films as a product right
+ 
+
+ align:start position:0%
+at documentary films as a product right
+we're not just looking at the final
+
+ align:start position:0%
+we're not just looking at the final
+ 
+
+ align:start position:0%
+we're not just looking at the final
+product we're also trying to think about
+
+ align:start position:0%
+product we're also trying to think about
+ 
+
+ align:start position:0%
+product we're also trying to think about
+what were the contexts in which the
+
+ align:start position:0%
+what were the contexts in which the
+ 
+
+ align:start position:0%
+what were the contexts in which the
+films got made what were the social
+
+ align:start position:0%
+films got made what were the social
+ 
+
+ align:start position:0%
+films got made what were the social
+relationships like that were part of the
+
+ align:start position:0%
+relationships like that were part of the
+ 
+
+ align:start position:0%
+relationships like that were part of the
+documentary film making what kinds of
+
+ align:start position:0%
+documentary film making what kinds of
+ 
+
+ align:start position:0%
+documentary film making what kinds of
+choices got made both aesthetic choices
+
+ align:start position:0%
+choices got made both aesthetic choices
+ 
+
+ align:start position:0%
+choices got made both aesthetic choices
+but also choices between relationships
+
+ align:start position:0%
+but also choices between relationships
+ 
+
+ align:start position:0%
+but also choices between relationships
+between subjects and audiences um what
+
+ align:start position:0%
+between subjects and audiences um what
+ 
+
+ align:start position:0%
+between subjects and audiences um what
+got included in the films what got left
+
+ align:start position:0%
+got included in the films what got left
+ 
+
+ align:start position:0%
+got included in the films what got left
+out of the films right so with thinking
+
+ align:start position:0%
+out of the films right so with thinking
+ 
+
+ align:start position:0%
+out of the films right so with thinking
+back to the discussion we had about
+
+ align:start position:0%
+back to the discussion we had about
+ 
+
+ align:start position:0%
+back to the discussion we had about
+verto and flare so all those questions
+
+ align:start position:0%
+verto and flare so all those questions
+ 
+
+ align:start position:0%
+verto and flare so all those questions
+were become important right I mean what
+
+ align:start position:0%
+were become important right I mean what
+ 
+
+ align:start position:0%
+were become important right I mean what
+were the social contexts in which those
+
+ align:start position:0%
+were the social contexts in which those
+ 
+
+ align:start position:0%
+were the social contexts in which those
+films were made who were they made for
+
+ align:start position:0%
+films were made who were they made for
+ 
+
+ align:start position:0%
+films were made who were they made for
+how were how were choices made what were
+
+ align:start position:0%
+how were how were choices made what were
+ 
+
+ align:start position:0%
+how were how were choices made what were
+the relationships that got set up
+
+ align:start position:0%
+the relationships that got set up
+ 
+
+ align:start position:0%
+the relationships that got set up
+through through the making of
+
+ align:start position:0%
+through through the making of
+ 
+
+ align:start position:0%
+through through the making of
+documentary film so we're thinking about
+
+ align:start position:0%
+documentary film so we're thinking about
+ 
+
+ align:start position:0%
+documentary film so we're thinking about
+both science as a process and we're
+
+ align:start position:0%
+both science as a process and we're
+ 
+
+ align:start position:0%
+both science as a process and we're
+thinking about documentary film making
+
+ align:start position:0%
+thinking about documentary film making
+ 
+
+ align:start position:0%
+thinking about documentary film making
+as a process and so the idea of this
+
+ align:start position:0%
+as a process and so the idea of this
+ 
+
+ align:start position:0%
+as a process and so the idea of this
+class is to put the two of them together
+
+ align:start position:0%
+class is to put the two of them together
+ 
+
+ align:start position:0%
+class is to put the two of them together
+right so thinking about the process of
+
+ align:start position:0%
+right so thinking about the process of
+ 
+
+ align:start position:0%
+right so thinking about the process of
+documentary film Mak thinking about
+
+ align:start position:0%
+documentary film Mak thinking about
+ 
+
+ align:start position:0%
+documentary film Mak thinking about
+science as a process and hopefully
+
+ align:start position:0%
+science as a process and hopefully
+ 
+
+ align:start position:0%
+science as a process and hopefully
+trying to make videos and films about
+
+ align:start position:0%
+trying to make videos and films about
+ 
+
+ align:start position:0%
+trying to make videos and films about
+that okay the conjuncture where they
+
+ align:start position:0%
+that okay the conjuncture where they
+ 
+
+ align:start position:0%
+that okay the conjuncture where they
+where they both come together okay and
+
+ align:start position:0%
+where they both come together okay and
+ 
+
+ align:start position:0%
+where they both come together okay and
+again we're going to go back to this at
+
+ align:start position:0%
+again we're going to go back to this at
+ 
+
+ align:start position:0%
+again we're going to go back to this at
+the end of the class where we talk more
+
+ align:start position:0%
+the end of the class where we talk more
+ 
+
+ align:start position:0%
+the end of the class where we talk more
+about your final projects but first we
+
+ align:start position:0%
+about your final projects but first we
+ 
+
+ align:start position:0%
+about your final projects but first we
+want to show you some um um um some uh
+
+ align:start position:0%
+want to show you some um um um some uh
+ 
+
+ align:start position:0%
+want to show you some um um um some uh
+documentary films that have been made
+
+ align:start position:0%
+documentary films that have been made
+ 
+
+ align:start position:0%
+documentary films that have been made
+about science and I just wanted to throw
+
+ align:start position:0%
+about science and I just wanted to throw
+ 
+
+ align:start position:0%
+about science and I just wanted to throw
+I'm going to be tethered so this can be
+
+ align:start position:0%
+I'm going to be tethered so this can be
+ 
+
+ align:start position:0%
+I'm going to be tethered so this can be
+a little bit difficult um okay but as we
+
+ align:start position:0%
+a little bit difficult um okay but as we
+ 
+
+ align:start position:0%
+a little bit difficult um okay but as we
+talked about in the very first class
+
+ align:start position:0%
+talked about in the very first class
+ 
+
+ align:start position:0%
+talked about in the very first class
+science films have always been there
+
+ align:start position:0%
+science films have always been there
+ 
+
+ align:start position:0%
+science films have always been there
+from the very beginning of film making
+
+ align:start position:0%
+from the very beginning of film making
+ 
+
+ align:start position:0%
+from the very beginning of film making
+as we saw um we saw early on from those
+
+ align:start position:0%
+as we saw um we saw early on from those
+ 
+
+ align:start position:0%
+as we saw um we saw early on from those
+1905 films by Charles Urban um uh that
+
+ align:start position:0%
+1905 films by Charles Urban um uh that
+ 
+
+ align:start position:0%
+1905 films by Charles Urban um uh that
+we discussed so so very very long
+
+ align:start position:0%
+we discussed so so very very long
+ 
+
+ align:start position:0%
+we discussed so so very very long
+history but we want to list some of the
+
+ align:start position:0%
+history but we want to list some of the
+ 
+
+ align:start position:0%
+history but we want to list some of the
+ways in which um film making and science
+
+ align:start position:0%
+ways in which um film making and science
+ 
+
+ align:start position:0%
+ways in which um film making and science
+have come together and I just want to
+
+ align:start position:0%
+have come together and I just want to
+ 
+
+ align:start position:0%
+have come together and I just want to
+list four and maybe you all can help me
+
+ align:start position:0%
+list four and maybe you all can help me
+ 
+
+ align:start position:0%
+list four and maybe you all can help me
+think of others
+
+ align:start position:0%
+think of others
+ 
+
+ align:start position:0%
+think of others
+um but one major way has been for some
+
+ align:start position:0%
+um but one major way has been for some
+ 
+
+ align:start position:0%
+um but one major way has been for some
+people anyway to think of uh film or
+
+ align:start position:0%
+people anyway to think of uh film or
+ 
+
+ align:start position:0%
+people anyway to think of uh film or
+video as a means of collecting data
+
+ align:start position:0%
+video as a means of collecting data
+ 
+
+ align:start position:0%
+video as a means of collecting data
+right how can how can we use film or
+
+ align:start position:0%
+right how can how can we use film or
+ 
+
+ align:start position:0%
+right how can how can we use film or
+video as a way to collect data to
+
+ align:start position:0%
+video as a way to collect data to
+ 
+
+ align:start position:0%
+video as a way to collect data to
+collect information about the world so
+
+ align:start position:0%
+collect information about the world so
+ 
+
+ align:start position:0%
+collect information about the world so
+whether it's about using film or video
+
+ align:start position:0%
+whether it's about using film or video
+ 
+
+ align:start position:0%
+whether it's about using film or video
+to slow things down do things in slow
+
+ align:start position:0%
+to slow things down do things in slow
+ 
+
+ align:start position:0%
+to slow things down do things in slow
+motion that we wouldn't be able to see
+
+ align:start position:0%
+motion that we wouldn't be able to see
+ 
+
+ align:start position:0%
+motion that we wouldn't be able to see
+otherwise potentially speed things up um
+
+ align:start position:0%
+otherwise potentially speed things up um
+ 
+
+ align:start position:0%
+otherwise potentially speed things up um
+you know so a whole range of of of what
+
+ align:start position:0%
+you know so a whole range of of of what
+ 
+
+ align:start position:0%
+you know so a whole range of of of what
+can you do with these kinds of
+
+ align:start position:0%
+can you do with these kinds of
+ 
+
+ align:start position:0%
+can you do with these kinds of
+technologies that allows you to see uh
+
+ align:start position:0%
+technologies that allows you to see uh
+ 
+
+ align:start position:0%
+technologies that allows you to see uh
+um not only allows you to see things in
+
+ align:start position:0%
+um not only allows you to see things in
+ 
+
+ align:start position:0%
+um not only allows you to see things in
+different kinds of ways but that you can
+
+ align:start position:0%
+different kinds of ways but that you can
+ 
+
+ align:start position:0%
+different kinds of ways but that you can
+actually use as data um and then there's
+
+ align:start position:0%
+actually use as data um and then there's
+ 
+
+ align:start position:0%
+actually use as data um and then there's
+the whole range of other things that
+
+ align:start position:0%
+the whole range of other things that
+ 
+
+ align:start position:0%
+the whole range of other things that
+this can lead off into in The Sciences
+
+ align:start position:0%
+this can lead off into in The Sciences
+ 
+
+ align:start position:0%
+this can lead off into in The Sciences
+where you have all kinds of Imaging
+
+ align:start position:0%
+where you have all kinds of Imaging
+ 
+
+ align:start position:0%
+where you have all kinds of Imaging
+techniques where you know you could be
+
+ align:start position:0%
+techniques where you know you could be
+ 
+
+ align:start position:0%
+techniques where you know you could be
+brain scans or other kinds of scin so
+
+ align:start position:0%
+brain scans or other kinds of scin so
+ 
+
+ align:start position:0%
+brain scans or other kinds of scin so
+that's that's a whole other kind of
+
+ align:start position:0%
+that's that's a whole other kind of
+ 
+
+ align:start position:0%
+that's that's a whole other kind of
+using visual images as data collection
+
+ align:start position:0%
+using visual images as data collection
+ 
+
+ align:start position:0%
+using visual images as data collection
+but here we're we're focusing on
+
+ align:start position:0%
+but here we're we're focusing on
+ 
+
+ align:start position:0%
+but here we're we're focusing on
+particular kinds of um uh uses of film
+
+ align:start position:0%
+particular kinds of um uh uses of film
+ 
+
+ align:start position:0%
+particular kinds of um uh uses of film
+and video as data
+
+ align:start position:0%
+and video as data
+ 
+
+ align:start position:0%
+and video as data
+collecting another way the two have been
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linked is this question of how can we
+
+ align:start position:0%
+linked is this question of how can we
+ 
+
+ align:start position:0%
+linked is this question of how can we
+use film or uh video as a way to go out
+
+ align:start position:0%
+use film or uh video as a way to go out
+ 
+
+ align:start position:0%
+use film or uh video as a way to go out
+and explore the
+
+ align:start position:0%
+and explore the
+ 
+
+ align:start position:0%
+and explore the
+world how can we use these instruments
+
+ align:start position:0%
+world how can we use these instruments
+ 
+
+ align:start position:0%
+world how can we use these instruments
+these Technologies to explore these
+
+ align:start position:0%
+these Technologies to explore these
+ 
+
+ align:start position:0%
+these Technologies to explore these
+worlds the these these social worlds
+
+ align:start position:0%
+worlds the these these social worlds
+ 
+
+ align:start position:0%
+worlds the these these social worlds
+around science or questions that science
+
+ align:start position:0%
+around science or questions that science
+ 
+
+ align:start position:0%
+around science or questions that science
+might might raise for us how how do we
+
+ align:start position:0%
+might might raise for us how how do we
+ 
+
+ align:start position:0%
+might might raise for us how how do we
+use them can we use them as tools of
+
+ align:start position:0%
+use them can we use them as tools of
+ 
+
+ align:start position:0%
+use them can we use them as tools of
+exploration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay a third way in which which they
+
+ align:start position:0%
+okay a third way in which which they
+ 
+
+ align:start position:0%
+okay a third way in which which they
+have been linked is an obvious one
+
+ align:start position:0%
+have been linked is an obvious one
+ 
+
+ align:start position:0%
+have been linked is an obvious one
+that's probably familiar to all of us is
+
+ align:start position:0%
+that's probably familiar to all of us is
+ 
+
+ align:start position:0%
+that's probably familiar to all of us is
+is education right and there's two
+
+ align:start position:0%
+is education right and there's two
+ 
+
+ align:start position:0%
+is education right and there's two
+aspects of this one coming from the end
+
+ align:start position:0%
+aspects of this one coming from the end
+ 
+
+ align:start position:0%
+aspects of this one coming from the end
+of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scientists and one coming from the end
+
+ align:start position:0%
+scientists and one coming from the end
+ 
+
+ align:start position:0%
+scientists and one coming from the end
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+filmmakers okay um so a question is
+
+ align:start position:0%
+filmmakers okay um so a question is
+ 
+
+ align:start position:0%
+filmmakers okay um so a question is
+then for scientists you know the
+
+ align:start position:0%
+then for scientists you know the
+ 
+
+ align:start position:0%
+then for scientists you know the
+question one of the main questions about
+
+ align:start position:0%
+question one of the main questions about
+ 
+
+ align:start position:0%
+question one of the main questions about
+film and and video could be how can we
+
+ align:start position:0%
+film and and video could be how can we
+ 
+
+ align:start position:0%
+film and and video could be how can we
+use these kinds of Technologies in order
+
+ align:start position:0%
+use these kinds of Technologies in order
+ 
+
+ align:start position:0%
+use these kinds of Technologies in order
+to educate people about about the
+
+ align:start position:0%
+to educate people about about the
+ 
+
+ align:start position:0%
+to educate people about about the
+Sciences okay and then one of the
+
+ align:start position:0%
+Sciences okay and then one of the
+ 
+
+ align:start position:0%
+Sciences okay and then one of the
+primary questions for the science
+
+ align:start position:0%
+primary questions for the science
+ 
+
+ align:start position:0%
+primary questions for the science
+scientists become how do we take the
+
+ align:start position:0%
+scientists become how do we take the
+ 
+
+ align:start position:0%
+scientists become how do we take the
+work that we've done and convey that in
+
+ align:start position:0%
+work that we've done and convey that in
+ 
+
+ align:start position:0%
+work that we've done and convey that in
+visual terms what what are the means we
+
+ align:start position:0%
+visual terms what what are the means we
+ 
+
+ align:start position:0%
+visual terms what what are the means we
+can use to convey this and these are
+
+ align:start position:0%
+can use to convey this and these are
+ 
+
+ align:start position:0%
+can use to convey this and these are
+difficult questions right and these are
+
+ align:start position:0%
+difficult questions right and these are
+ 
+
+ align:start position:0%
+difficult questions right and these are
+also difficult questions for um
+
+ align:start position:0%
+also difficult questions for um
+ 
+
+ align:start position:0%
+also difficult questions for um
+scientists when they when they when they
+
+ align:start position:0%
+scientists when they when they when they
+ 
+
+ align:start position:0%
+scientists when they when they when they
+write right because how do you explain
+
+ align:start position:0%
+write right because how do you explain
+ 
+
+ align:start position:0%
+write right because how do you explain
+to other people what it is that you're
+
+ align:start position:0%
+to other people what it is that you're
+ 
+
+ align:start position:0%
+to other people what it is that you're
+working on and often scientists have to
+
+ align:start position:0%
+working on and often scientists have to
+ 
+
+ align:start position:0%
+working on and often scientists have to
+rely about rely upon certain kinds of um
+
+ align:start position:0%
+rely about rely upon certain kinds of um
+ 
+
+ align:start position:0%
+rely about rely upon certain kinds of um
+written metaphors to try to explain what
+
+ align:start position:0%
+written metaphors to try to explain what
+ 
+
+ align:start position:0%
+written metaphors to try to explain what
+they're getting at are those metaphors I
+
+ align:start position:0%
+they're getting at are those metaphors I
+ 
+
+ align:start position:0%
+they're getting at are those metaphors I
+mean and do the metaphors I mean they
+
+ align:start position:0%
+mean and do the metaphors I mean they
+ 
+
+ align:start position:0%
+mean and do the metaphors I mean they
+never quite exactly work right I mean
+
+ align:start position:0%
+never quite exactly work right I mean
+ 
+
+ align:start position:0%
+never quite exactly work right I mean
+and so one of the questions that
+
+ align:start position:0%
+and so one of the questions that
+ 
+
+ align:start position:0%
+and so one of the questions that
+scientists always have to have to think
+
+ align:start position:0%
+scientists always have to have to think
+ 
+
+ align:start position:0%
+scientists always have to have to think
+about then is is the metaphor that I'm
+
+ align:start position:0%
+about then is is the metaphor that I'm
+ 
+
+ align:start position:0%
+about then is is the metaphor that I'm
+using is it is it hell floors is are
+
+ align:start position:0%
+using is it is it hell floors is are
+ 
+
+ align:start position:0%
+using is it is it hell floors is are
+potentially leading things astray okay
+
+ align:start position:0%
+potentially leading things astray okay
+ 
+
+ align:start position:0%
+potentially leading things astray okay
+and the same kinds of questions then
+
+ align:start position:0%
+and the same kinds of questions then
+ 
+
+ align:start position:0%
+and the same kinds of questions then
+when scientists want to use visual
+
+ align:start position:0%
+when scientists want to use visual
+ 
+
+ align:start position:0%
+when scientists want to use visual
+Technologies when you're using uh film
+
+ align:start position:0%
+Technologies when you're using uh film
+ 
+
+ align:start position:0%
+Technologies when you're using uh film
+and video to try to educate people about
+
+ align:start position:0%
+and video to try to educate people about
+ 
+
+ align:start position:0%
+and video to try to educate people about
+the Sciences what kinds of um visual
+
+ align:start position:0%
+the Sciences what kinds of um visual
+ 
+
+ align:start position:0%
+the Sciences what kinds of um visual
+images or narratives are you going to
+
+ align:start position:0%
+images or narratives are you going to
+ 
+
+ align:start position:0%
+images or narratives are you going to
+use to try to convey that that
+
+ align:start position:0%
+use to try to convey that that
+ 
+
+ align:start position:0%
+use to try to convey that that
+information and what's the potential you
+
+ align:start position:0%
+information and what's the potential you
+ 
+
+ align:start position:0%
+information and what's the potential you
+know benefits or of constraints about
+
+ align:start position:0%
+know benefits or of constraints about
+ 
+
+ align:start position:0%
+know benefits or of constraints about
+about the way that you choose to do it
+
+ align:start position:0%
+about the way that you choose to do it
+ 
+
+ align:start position:0%
+about the way that you choose to do it
+so that becomes a major question for
+
+ align:start position:0%
+so that becomes a major question for
+ 
+
+ align:start position:0%
+so that becomes a major question for
+scientists for filmmakers one of the
+
+ align:start position:0%
+scientists for filmmakers one of the
+ 
+
+ align:start position:0%
+scientists for filmmakers one of the
+major questions becomes well what kinds
+
+ align:start position:0%
+major questions becomes well what kinds
+ 
+
+ align:start position:0%
+major questions becomes well what kinds
+of narratives can you use to talk about
+
+ align:start position:0%
+of narratives can you use to talk about
+ 
+
+ align:start position:0%
+of narratives can you use to talk about
+the science that are going to keep
+
+ align:start position:0%
+the science that are going to keep
+ 
+
+ align:start position:0%
+the science that are going to keep
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+interested right I mean so so their goal
+
+ align:start position:0%
+interested right I mean so so their goal
+ 
+
+ align:start position:0%
+interested right I mean so so their goal
+also has to be how do you make something
+
+ align:start position:0%
+also has to be how do you make something
+ 
+
+ align:start position:0%
+also has to be how do you make something
+interesting that people want to see so
+
+ align:start position:0%
+interesting that people want to see so
+ 
+
+ align:start position:0%
+interesting that people want to see so
+it BEC it becomes this well what
+
+ align:start position:0%
+it BEC it becomes this well what
+ 
+
+ align:start position:0%
+it BEC it becomes this well what
+interests people about science how do I
+
+ align:start position:0%
+interests people about science how do I
+ 
+
+ align:start position:0%
+interests people about science how do I
+convey something in a visually
+
+ align:start position:0%
+convey something in a visually
+ 
+
+ align:start position:0%
+convey something in a visually
+interesting way
+
+ align:start position:0%
+interesting way
+ 
+
+ align:start position:0%
+interesting way
+that tells a story in a way that will
+
+ align:start position:0%
+that tells a story in a way that will
+ 
+
+ align:start position:0%
+that tells a story in a way that will
+bring people in will they'll want to
+
+ align:start position:0%
+bring people in will they'll want to
+ 
+
+ align:start position:0%
+bring people in will they'll want to
+learn more about the science okay so
+
+ align:start position:0%
+learn more about the science okay so
+ 
+
+ align:start position:0%
+learn more about the science okay so
+these kinds of questions about how we
+
+ align:start position:0%
+these kinds of questions about how we
+ 
+
+ align:start position:0%
+these kinds of questions about how we
+use film and video um as means of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Education
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then also there's you know
+
+ align:start position:0%
+okay and then also there's you know
+ 
+
+ align:start position:0%
+okay and then also there's you know
+certainly within popular culture there's
+
+ align:start position:0%
+certainly within popular culture there's
+ 
+
+ align:start position:0%
+certainly within popular culture there's
+also just a lot of uh fascination with
+
+ align:start position:0%
+also just a lot of uh fascination with
+ 
+
+ align:start position:0%
+also just a lot of uh fascination with
+science right so then there's also using
+
+ align:start position:0%
+science right so then there's also using
+ 
+
+ align:start position:0%
+science right so then there's also using
+film and video Technologies as a way to
+
+ align:start position:0%
+film and video Technologies as a way to
+ 
+
+ align:start position:0%
+film and video Technologies as a way to
+satisfy um popular curiosity about about
+
+ align:start position:0%
+satisfy um popular curiosity about about
+ 
+
+ align:start position:0%
+satisfy um popular curiosity about about
+science and a way that might not quite
+
+ align:start position:0%
+science and a way that might not quite
+ 
+
+ align:start position:0%
+science and a way that might not quite
+be strictly educational so again we
+
+ align:start position:0%
+be strictly educational so again we
+ 
+
+ align:start position:0%
+be strictly educational so again we
+talked to them about you know sort of
+
+ align:start position:0%
+talked to them about you know sort of
+ 
+
+ align:start position:0%
+talked to them about you know sort of
+the IMX films and they might be somewhat
+
+ align:start position:0%
+the IMX films and they might be somewhat
+ 
+
+ align:start position:0%
+the IMX films and they might be somewhat
+educational somewhat entertainment um
+
+ align:start position:0%
+educational somewhat entertainment um
+ 
+
+ align:start position:0%
+educational somewhat entertainment um
+but in a way that satisfies sort of
+
+ align:start position:0%
+but in a way that satisfies sort of
+ 
+
+ align:start position:0%
+but in a way that satisfies sort of
+public curiosity about um about the
+
+ align:start position:0%
+public curiosity about um about the
+ 
+
+ align:start position:0%
+public curiosity about um about the
+Sciences okay and so first we're going
+
+ align:start position:0%
+Sciences okay and so first we're going
+ 
+
+ align:start position:0%
+Sciences okay and so first we're going
+to think about all of these a bit um as
+
+ align:start position:0%
+to think about all of these a bit um as
+ 
+
+ align:start position:0%
+to think about all of these a bit um as
+we watch uh various Clips tonight um and
+
+ align:start position:0%
+we watch uh various Clips tonight um and
+ 
+
+ align:start position:0%
+we watch uh various Clips tonight um and
+the first one we're going to think about
+
+ align:start position:0%
+the first one we're going to think about
+ 
+
+ align:start position:0%
+the first one we're going to think about
+is using film film and video as a
+
+ align:start position:0%
+is using film film and video as a
+ 
+
+ align:start position:0%
+is using film film and video as a
+technique for generating data and we're
+
+ align:start position:0%
+technique for generating data and we're
+ 
+
+ align:start position:0%
+technique for generating data and we're
+going to be doing this through the
+
+ align:start position:0%
+going to be doing this through the
+ 
+
+ align:start position:0%
+going to be doing this through the
+figure of D doc ederton any of you know
+
+ align:start position:0%
+figure of D doc ederton any of you know
+ 
+
+ align:start position:0%
+figure of D doc ederton any of you know
+who doc Edon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wasita sorry he has a c here right
+
+ align:start position:0%
+wasita sorry he has a c here right
+ 
+
+ align:start position:0%
+wasita sorry he has a c here right
+the yeah so doc Edon was he he he
+
+ align:start position:0%
+the yeah so doc Edon was he he he
+ 
+
+ align:start position:0%
+the yeah so doc Edon was he he he
+trained here um he was born in 1903 he
+
+ align:start position:0%
+trained here um he was born in 1903 he
+ 
+
+ align:start position:0%
+trained here um he was born in 1903 he
+died in
+
+ align:start position:0%
+died in
+ 
+
+ align:start position:0%
+died in
+1990 um heend MIT Faculty Club did he
+
+ align:start position:0%
+1990 um heend MIT Faculty Club did he
+ 
+
+ align:start position:0%
+1990 um heend MIT Faculty Club did he
+really collapsed and died yes really
+
+ align:start position:0%
+really collapsed and died yes really
+ 
+
+ align:start position:0%
+really collapsed and died yes really
+yes anyway wow uh he had been a faculty
+
+ align:start position:0%
+yes anyway wow uh he had been a faculty
+ 
+
+ align:start position:0%
+yes anyway wow uh he had been a faculty
+member here at MIT for 40 years he had
+
+ align:start position:0%
+member here at MIT for 40 years he had
+ 
+
+ align:start position:0%
+member here at MIT for 40 years he had
+been here as an undergraduate he went
+
+ align:start position:0%
+been here as an undergraduate he went
+ 
+
+ align:start position:0%
+been here as an undergraduate he went
+off and did research uh at GE I believe
+
+ align:start position:0%
+off and did research uh at GE I believe
+ 
+
+ align:start position:0%
+off and did research uh at GE I believe
+it was for a few years and then he came
+
+ align:start position:0%
+it was for a few years and then he came
+ 
+
+ align:start position:0%
+it was for a few years and then he came
+back to do his PhD um here at MIT and he
+
+ align:start position:0%
+back to do his PhD um here at MIT and he
+ 
+
+ align:start position:0%
+back to do his PhD um here at MIT and he
+became interested um he was working with
+
+ align:start position:0%
+became interested um he was working with
+ 
+
+ align:start position:0%
+became interested um he was working with
+motors um and one of the things that he
+
+ align:start position:0%
+motors um and one of the things that he
+ 
+
+ align:start position:0%
+motors um and one of the things that he
+noticed when he was doing his work that
+
+ align:start position:0%
+noticed when he was doing his work that
+ 
+
+ align:start position:0%
+noticed when he was doing his work that
+when there were problems with electrical
+
+ align:start position:0%
+when there were problems with electrical
+ 
+
+ align:start position:0%
+when there were problems with electrical
+transmission lines and the lights would
+
+ align:start position:0%
+transmission lines and the lights would
+ 
+
+ align:start position:0%
+transmission lines and the lights would
+flicker that he could observe changes in
+
+ align:start position:0%
+flicker that he could observe changes in
+ 
+
+ align:start position:0%
+flicker that he could observe changes in
+the motion of the motor
+
+ align:start position:0%
+the motion of the motor
+ 
+
+ align:start position:0%
+the motion of the motor
+that he couldn't otherwise and so what
+
+ align:start position:0%
+that he couldn't otherwise and so what
+ 
+
+ align:start position:0%
+that he couldn't otherwise and so what
+he ended up doing during the 1930s was
+
+ align:start position:0%
+he ended up doing during the 1930s was
+ 
+
+ align:start position:0%
+he ended up doing during the 1930s was
+he developed a repeatable short duration
+
+ align:start position:0%
+he developed a repeatable short duration
+ 
+
+ align:start position:0%
+he developed a repeatable short duration
+electronic flash or a St stroboscopic
+
+ align:start position:0%
+electronic flash or a St stroboscopic
+ 
+
+ align:start position:0%
+electronic flash or a St stroboscopic
+light that could reveal Motion in
+
+ align:start position:0%
+light that could reveal Motion in
+ 
+
+ align:start position:0%
+light that could reveal Motion in
+segments so you could capture fast
+
+ align:start position:0%
+segments so you could capture fast
+ 
+
+ align:start position:0%
+segments so you could capture fast
+motion in a way that was not accessible
+
+ align:start position:0%
+motion in a way that was not accessible
+ 
+
+ align:start position:0%
+motion in a way that was not accessible
+to our normal
+
+ align:start position:0%
+to our normal
+ 
+
+ align:start position:0%
+to our normal
+perception okay so he did I mean I I
+
+ align:start position:0%
+perception okay so he did I mean I I
+ 
+
+ align:start position:0%
+perception okay so he did I mean I I
+didn't write it down but well I think
+
+ align:start position:0%
+didn't write it down but well I think
+ 
+
+ align:start position:0%
+didn't write it down but well I think
+it's in here exactly how it worked um so
+
+ align:start position:0%
+it's in here exactly how it worked um so
+ 
+
+ align:start position:0%
+it's in here exactly how it worked um so
+ederton called his unit a stroboscope it
+
+ align:start position:0%
+ederton called his unit a stroboscope it
+ 
+
+ align:start position:0%
+ederton called his unit a stroboscope it
+could emit 6010 micro second flashes per
+
+ align:start position:0%
+could emit 6010 micro second flashes per
+ 
+
+ align:start position:0%
+could emit 6010 micro second flashes per
+second a hither to unimaginable speed
+
+ align:start position:0%
+second a hither to unimaginable speed
+ 
+
+ align:start position:0%
+second a hither to unimaginable speed
+okay so so through his invention um uh
+
+ align:start position:0%
+okay so so through his invention um uh
+ 
+
+ align:start position:0%
+okay so so through his invention um uh
+doc ederton was able to capture things
+
+ align:start position:0%
+doc ederton was able to capture things
+ 
+
+ align:start position:0%
+doc ederton was able to capture things
+uh using photography so it's he did both
+
+ align:start position:0%
+uh using photography so it's he did both
+ 
+
+ align:start position:0%
+uh using photography so it's he did both
+still photography but also obviously if
+
+ align:start position:0%
+still photography but also obviously if
+ 
+
+ align:start position:0%
+still photography but also obviously if
+you do still photography that quickly
+
+ align:start position:0%
+you do still photography that quickly
+ 
+
+ align:start position:0%
+you do still photography that quickly
+and you run it together you have moving
+
+ align:start position:0%
+and you run it together you have moving
+ 
+
+ align:start position:0%
+and you run it together you have moving
+images um right so this is also sort of
+
+ align:start position:0%
+images um right so this is also sort of
+ 
+
+ align:start position:0%
+images um right so this is also sort of
+the the intersection of Photography and
+
+ align:start position:0%
+the the intersection of Photography and
+ 
+
+ align:start position:0%
+the the intersection of Photography and
+um and moving pictures um so he did
+
+ align:start position:0%
+um and moving pictures um so he did
+ 
+
+ align:start position:0%
+um and moving pictures um so he did
+uh um so he did this fascinating work
+
+ align:start position:0%
+uh um so he did this fascinating work
+ 
+
+ align:start position:0%
+uh um so he did this fascinating work
+where he did extraordinarily famous work
+
+ align:start position:0%
+where he did extraordinarily famous work
+ 
+
+ align:start position:0%
+where he did extraordinarily famous work
+again both in in in still photography
+
+ align:start position:0%
+again both in in in still photography
+ 
+
+ align:start position:0%
+again both in in in still photography
+and in um um and in moving images um I'm
+
+ align:start position:0%
+and in um um and in moving images um I'm
+ 
+
+ align:start position:0%
+and in um um and in moving images um I'm
+sure many of you have seen his even if
+
+ align:start position:0%
+sure many of you have seen his even if
+ 
+
+ align:start position:0%
+sure many of you have seen his even if
+you're not aware that they were NE
+
+ align:start position:0%
+you're not aware that they were NE
+ 
+
+ align:start position:0%
+you're not aware that they were NE
+necessarily uh doc edgerton's work uh
+
+ align:start position:0%
+necessarily uh doc edgerton's work uh
+ 
+
+ align:start position:0%
+necessarily uh doc edgerton's work uh
+his his work became extremely famous um
+
+ align:start position:0%
+his his work became extremely famous um
+ 
+
+ align:start position:0%
+his his work became extremely famous um
+he actually there was um a
+
+ align:start position:0%
+he actually there was um a
+ 
+
+ align:start position:0%
+he actually there was um a
+short um there was a short film that was
+
+ align:start position:0%
+short um there was a short film that was
+ 
+
+ align:start position:0%
+short um there was a short film that was
+made about his work I think it was in
+
+ align:start position:0%
+made about his work I think it was in
+ 
+
+ align:start position:0%
+made about his work I think it was in
+the 1940s that won an acad award um his
+
+ align:start position:0%
+the 1940s that won an acad award um his
+ 
+
+ align:start position:0%
+the 1940s that won an acad award um his
+work was shown all over and it also
+
+ align:start position:0%
+work was shown all over and it also
+ 
+
+ align:start position:0%
+work was shown all over and it also
+crossed the boundary between science and
+
+ align:start position:0%
+crossed the boundary between science and
+ 
+
+ align:start position:0%
+crossed the boundary between science and
+art where some of his work was just seen
+
+ align:start position:0%
+art where some of his work was just seen
+ 
+
+ align:start position:0%
+art where some of his work was just seen
+as so gorgeous um that it was shown in
+
+ align:start position:0%
+as so gorgeous um that it was shown in
+ 
+
+ align:start position:0%
+as so gorgeous um that it was shown in
+museums as artwork so he was kind of
+
+ align:start position:0%
+museums as artwork so he was kind of
+ 
+
+ align:start position:0%
+museums as artwork so he was kind of
+working on that boundary then between
+
+ align:start position:0%
+working on that boundary then between
+ 
+
+ align:start position:0%
+working on that boundary then between
+the world of science and the world of
+
+ align:start position:0%
+the world of science and the world of
+ 
+
+ align:start position:0%
+the world of science and the world of
+art he also uh did other things as well
+
+ align:start position:0%
+art he also uh did other things as well
+ 
+
+ align:start position:0%
+art he also uh did other things as well
+with a couple students from here at MIT
+
+ align:start position:0%
+with a couple students from here at MIT
+ 
+
+ align:start position:0%
+with a couple students from here at MIT
+he became involved during the second
+
+ align:start position:0%
+he became involved during the second
+ 
+
+ align:start position:0%
+he became involved during the second
+world war in um classified military work
+
+ align:start position:0%
+world war in um classified military work
+ 
+
+ align:start position:0%
+world war in um classified military work
+so they did work on um inventions for
+
+ align:start position:0%
+so they did work on um inventions for
+ 
+
+ align:start position:0%
+so they did work on um inventions for
+aerial um reconnaissance aerial
+
+ align:start position:0%
+aerial um reconnaissance aerial
+ 
+
+ align:start position:0%
+aerial um reconnaissance aerial
+photography and then also later they did
+
+ align:start position:0%
+photography and then also later they did
+ 
+
+ align:start position:0%
+photography and then also later they did
+um uh photographic images of nuclear
+
+ align:start position:0%
+um uh photographic images of nuclear
+ 
+
+ align:start position:0%
+um uh photographic images of nuclear
+weapons blasts um and there's actually
+
+ align:start position:0%
+weapons blasts um and there's actually
+ 
+
+ align:start position:0%
+weapons blasts um and there's actually
+some online you can actually see them if
+
+ align:start position:0%
+some online you can actually see them if
+ 
+
+ align:start position:0%
+some online you can actually see them if
+you're interested um in that he worked
+
+ align:start position:0%
+you're interested um in that he worked
+ 
+
+ align:start position:0%
+you're interested um in that he worked
+with Shak custo helping Jac kusto
+
+ align:start position:0%
+with Shak custo helping Jac kusto
+ 
+
+ align:start position:0%
+with Shak custo helping Jac kusto
+develop underwater um camera equipment
+
+ align:start position:0%
+develop underwater um camera equipment
+ 
+
+ align:start position:0%
+develop underwater um camera equipment
+so he was an inventor uh he was a
+
+ align:start position:0%
+so he was an inventor uh he was a
+ 
+
+ align:start position:0%
+so he was an inventor uh he was a
+scientist he was some people would call
+
+ align:start position:0%
+scientist he was some people would call
+ 
+
+ align:start position:0%
+scientist he was some people would call
+him an artist he he said uh don't make
+
+ align:start position:0%
+him an artist he he said uh don't make
+ 
+
+ align:start position:0%
+him an artist he he said uh don't make
+me out to be an artist I'm an engineer I
+
+ align:start position:0%
+me out to be an artist I'm an engineer I
+ 
+
+ align:start position:0%
+me out to be an artist I'm an engineer I
+am uh after the facts only the facts but
+
+ align:start position:0%
+am uh after the facts only the facts but
+ 
+
+ align:start position:0%
+am uh after the facts only the facts but
+what his work I think suggests for a lot
+
+ align:start position:0%
+what his work I think suggests for a lot
+ 
+
+ align:start position:0%
+what his work I think suggests for a lot
+of people is sort is
+
+ align:start position:0%
+of people is sort is
+ 
+
+ align:start position:0%
+of people is sort is
+can can work that is science also be art
+
+ align:start position:0%
+can can work that is science also be art
+ 
+
+ align:start position:0%
+can can work that is science also be art
+at the same time um so anyway so let's
+
+ align:start position:0%
+at the same time um so anyway so let's
+ 
+
+ align:start position:0%
+at the same time um so anyway so let's
+watch a few so yeah I don't know which
+
+ align:start position:0%
+watch a few so yeah I don't know which
+ 
+
+ align:start position:0%
+watch a few so yeah I don't know which
+on you want to watch you should uh you
+
+ align:start position:0%
+on you want to watch you should uh you
+ 
+
+ align:start position:0%
+on you want to watch you should uh you
+should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that was a bit of an introductory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's another one of his famous milk
+
+ align:start position:0%
+so here's another one of his famous milk
+ 
+
+ align:start position:0%
+so here's another one of his famous milk
+drop pieces but this is later uh later
+
+ align:start position:0%
+drop pieces but this is later uh later
+ 
+
+ align:start position:0%
+drop pieces but this is later uh later
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+color
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I'm sure you've seen some of his uh
+
+ align:start position:0%
+okay I'm sure you've seen some of his uh
+ 
+
+ align:start position:0%
+okay I'm sure you've seen some of his uh
+famous Stills have you seen the one with
+
+ align:start position:0%
+famous Stills have you seen the one with
+ 
+
+ align:start position:0%
+famous Stills have you seen the one with
+the still photograph with the apple with
+
+ align:start position:0%
+the still photograph with the apple with
+ 
+
+ align:start position:0%
+the still photograph with the apple with
+a bullet going through it have you ever
+
+ align:start position:0%
+a bullet going through it have you ever
+ 
+
+ align:start position:0%
+a bullet going through it have you ever
+seen that an image seen the photograph
+
+ align:start position:0%
+seen that an image seen the photograph
+ 
+
+ align:start position:0%
+seen that an image seen the photograph
+you've seen the photograph yeah um which
+
+ align:start position:0%
+you've seen the photograph yeah um which
+ 
+
+ align:start position:0%
+you've seen the photograph yeah um which
+which he famously titled making
+
+ align:start position:0%
+which he famously titled making
+ 
+
+ align:start position:0%
+which he famously titled making
+applesauce at
+
+ align:start position:0%
+applesauce at
+ 
+
+ align:start position:0%
+applesauce at
+MIT and you might have seen this famous
+
+ align:start position:0%
+MIT and you might have seen this famous
+ 
+
+ align:start position:0%
+MIT and you might have seen this famous
+one of a card with a bullet going
+
+ align:start position:0%
+one of a card with a bullet going
+ 
+
+ align:start position:0%
+one of a card with a bullet going
+through a card like still images that
+
+ align:start position:0%
+through a card like still images that
+ 
+
+ align:start position:0%
+through a card like still images that
+they were they were shown them in um
+
+ align:start position:0%
+they were they were shown them in um
+ 
+
+ align:start position:0%
+they were they were shown them in um
+Publications like life during their time
+
+ align:start position:0%
+Publications like life during their time
+ 
+
+ align:start position:0%
+Publications like life during their time
+I mean they they really circulated
+
+ align:start position:0%
+I mean they they really circulated
+ 
+
+ align:start position:0%
+I mean they they really circulated
+widely um let me show you a few
+
+ align:start position:0%
+widely um let me show you a few
+ 
+
+ align:start position:0%
+widely um let me show you a few
+more I think a couple ofay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+build yeah I wouldn't be surprised
+
+ align:start position:0%
+build yeah I wouldn't be surprised
+ 
+
+ align:start position:0%
+build yeah I wouldn't be surprised
+because the 150th anniversary there's
+
+ align:start position:0%
+because the 150th anniversary there's
+ 
+
+ align:start position:0%
+because the 150th anniversary there's
+there's a lot of interest in um and I
+
+ align:start position:0%
+there's a lot of interest in um and I
+ 
+
+ align:start position:0%
+there's a lot of interest in um and I
+think the MIT Museum is doing is doing a
+
+ align:start position:0%
+think the MIT Museum is doing is doing a
+ 
+
+ align:start position:0%
+think the MIT Museum is doing is doing a
+doc ederton display right now because of
+
+ align:start position:0%
+doc ederton display right now because of
+ 
+
+ align:start position:0%
+doc ederton display right now because of
+the 150th anniversary so there's
+
+ align:start position:0%
+the 150th anniversary so there's
+ 
+
+ align:start position:0%
+the 150th anniversary so there's
+probably a um a fair amount of stuff
+
+ align:start position:0%
+probably a um a fair amount of stuff
+ 
+
+ align:start position:0%
+probably a um a fair amount of stuff
+around right now um hummingbird this is
+
+ align:start position:0%
+around right now um hummingbird this is
+ 
+
+ align:start position:0%
+around right now um hummingbird this is
+really pretty
+
+ align:start position:0%
+really pretty
+ 
+
+ align:start position:0%
+really pretty
+too there's a
+
+ align:start position:0%
+too there's a
+ 
+
+ align:start position:0%
+too there's a
+milk milk milk drop poster in lobby 7
+
+ align:start position:0%
+milk milk milk drop poster in lobby 7
+ 
+
+ align:start position:0%
+milk milk milk drop poster in lobby 7
+yeah that's right that's right yeah and
+
+ align:start position:0%
+yeah that's right that's right yeah and
+ 
+
+ align:start position:0%
+yeah that's right that's right yeah and
+if anybody you know has any doubt about
+
+ align:start position:0%
+if anybody you know has any doubt about
+ 
+
+ align:start position:0%
+if anybody you know has any doubt about
+whether or not he actually had artistic
+
+ align:start position:0%
+whether or not he actually had artistic
+ 
+
+ align:start position:0%
+whether or not he actually had artistic
+sensibilities or intentions I mean look
+
+ align:start position:0%
+sensibilities or intentions I mean look
+ 
+
+ align:start position:0%
+sensibilities or intentions I mean look
+at the way he set that up with the red
+
+ align:start position:0%
+at the way he set that up with the red
+ 
+
+ align:start position:0%
+at the way he set that up with the red
+red cup and you know
+
+ align:start position:0%
+red cup and you know
+ 
+
+ align:start position:0%
+red cup and you know
+it's even the shape of the plates yeah I
+
+ align:start position:0%
+it's even the shape of the plates yeah I
+ 
+
+ align:start position:0%
+it's even the shape of the plates yeah I
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+exactly yeah oops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry so this is back to one of the
+
+ align:start position:0%
+sorry so this is back to one of the
+ 
+
+ align:start position:0%
+sorry so this is back to one of the
+older Black and Whites
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there there's there's tons of stuff
+
+ align:start position:0%
+so there there's there's tons of stuff
+ 
+
+ align:start position:0%
+so there there's there's tons of stuff
+on here we could see a range of
+
+ align:start position:0%
+on here we could see a range of
+ 
+
+ align:start position:0%
+on here we could see a range of
+different things depending on what
+
+ align:start position:0%
+different things depending on what
+ 
+
+ align:start position:0%
+different things depending on what
+you're do you want to see a nuclear
+
+ align:start position:0%
+you're do you want to see a nuclear
+ 
+
+ align:start position:0%
+you're do you want to see a nuclear
+blast do you want to see some of them
+
+ align:start position:0%
+blast do you want to see some of them
+ 
+
+ align:start position:0%
+blast do you want to see some of them
+some of them it's very interesting it
+
+ align:start position:0%
+some of them it's very interesting it
+ 
+
+ align:start position:0%
+some of them it's very interesting it
+goes back to the very first stuff that
+
+ align:start position:0%
+goes back to the very first stuff that
+ 
+
+ align:start position:0%
+goes back to the very first stuff that
+we saw from 1905 there's also time lapse
+
+ align:start position:0%
+we saw from 1905 there's also time lapse
+ 
+
+ align:start position:0%
+we saw from 1905 there's also time lapse
+of um of um uh
+
+ align:start position:0%
+of um of um uh
+ 
+
+ align:start position:0%
+of um of um uh
+plants unfolding the same way we saw in
+
+ align:start position:0%
+plants unfolding the same way we saw in
+ 
+
+ align:start position:0%
+plants unfolding the same way we saw in
+the very early pieces so again a similar
+
+ align:start position:0%
+the very early pieces so again a similar
+ 
+
+ align:start position:0%
+the very early pieces so again a similar
+kind of you you know you remember back
+
+ align:start position:0%
+kind of you you know you remember back
+ 
+
+ align:start position:0%
+kind of you you know you remember back
+to those very early pieces where they
+
+ align:start position:0%
+to those very early pieces where they
+ 
+
+ align:start position:0%
+to those very early pieces where they
+were in they were of interest to
+
+ align:start position:0%
+were in they were of interest to
+ 
+
+ align:start position:0%
+were in they were of interest to
+scientists but they were also shown in
+
+ align:start position:0%
+scientists but they were also shown in
+ 
+
+ align:start position:0%
+scientists but they were also shown in
+public theaters with kind of Vaudeville
+
+ align:start position:0%
+public theaters with kind of Vaudeville
+ 
+
+ align:start position:0%
+public theaters with kind of Vaudeville
+music in the background um so they were
+
+ align:start position:0%
+music in the background um so they were
+ 
+
+ align:start position:0%
+music in the background um so they were
+meant to be both popular entertainment
+
+ align:start position:0%
+meant to be both popular entertainment
+ 
+
+ align:start position:0%
+meant to be both popular entertainment
+and so I mean he's different position
+
+ align:start position:0%
+and so I mean he's different position
+ 
+
+ align:start position:0%
+and so I mean he's different position
+differently positioned with a scientific
+
+ align:start position:0%
+differently positioned with a scientific
+ 
+
+ align:start position:0%
+differently positioned with a scientific
+institution but but still an interest in
+
+ align:start position:0%
+institution but but still an interest in
+ 
+
+ align:start position:0%
+institution but but still an interest in
+sort of engaging a broader audience and
+
+ align:start position:0%
+sort of engaging a broader audience and
+ 
+
+ align:start position:0%
+sort of engaging a broader audience and
+again kinds of images that people um um
+
+ align:start position:0%
+again kinds of images that people um um
+ 
+
+ align:start position:0%
+again kinds of images that people um um
+that many people found very fascinating
+
+ align:start position:0%
+that many people found very fascinating
+ 
+
+ align:start position:0%
+that many people found very fascinating
+but there's nuclear
+
+ align:start position:0%
+but there's nuclear
+ 
+
+ align:start position:0%
+but there's nuclear
+nuclear um explosions you could see him
+
+ align:start position:0%
+nuclear um explosions you could see him
+ 
+
+ align:start position:0%
+nuclear um explosions you could see him
+hanging out with Jac
+
+ align:start position:0%
+hanging out with Jac
+ 
+
+ align:start position:0%
+hanging out with Jac
+custo there's a a whole range of
+
+ align:start position:0%
+custo there's a a whole range of
+ 
+
+ align:start position:0%
+custo there's a a whole range of
+different things we can look at oh the
+
+ align:start position:0%
+different things we can look at oh the
+ 
+
+ align:start position:0%
+different things we can look at oh the
+pigeon is cool I'll do this pigeon one
+
+ align:start position:0%
+pigeon is cool I'll do this pigeon one
+ 
+
+ align:start position:0%
+pigeon is cool I'll do this pigeon one
+before we do the science
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recorder
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay just watch a few minutes this
+
+ align:start position:0%
+okay okay just watch a few minutes this
+ 
+
+ align:start position:0%
+okay okay just watch a few minutes this
+one we'll just watch it's this is a half
+
+ align:start position:0%
+one we'll just watch it's this is a half
+ 
+
+ align:start position:0%
+one we'll just watch it's this is a half
+hour episode about him that gives a
+
+ align:start position:0%
+hour episode about him that gives a
+ 
+
+ align:start position:0%
+hour episode about him that gives a
+little context but we'll just watch a
+
+ align:start position:0%
+little context but we'll just watch a
+ 
+
+ align:start position:0%
+little context but we'll just watch a
+few minutes minutes of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you are watching a swimmer taking
+
+ align:start position:0%
+you are watching a swimmer taking
+ 
+
+ align:start position:0%
+you are watching a swimmer taking
+pictures with an underwater camera but
+
+ align:start position:0%
+pictures with an underwater camera but
+ 
+
+ align:start position:0%
+pictures with an underwater camera but
+below a few hundred ft as the light
+
+ align:start position:0%
+below a few hundred ft as the light
+ 
+
+ align:start position:0%
+below a few hundred ft as the light
+disappears and the pressures become too
+
+ align:start position:0%
+disappears and the pressures become too
+ 
+
+ align:start position:0%
+disappears and the pressures become too
+great for human endurance other
+
+ align:start position:0%
+great for human endurance other
+ 
+
+ align:start position:0%
+great for human endurance other
+techniques for photographing the silent
+
+ align:start position:0%
+techniques for photographing the silent
+ 
+
+ align:start position:0%
+techniques for photographing the silent
+world of the deep oceans have to be used
+
+ align:start position:0%
+world of the deep oceans have to be used
+ 
+
+ align:start position:0%
+world of the deep oceans have to be used
+these techniques for deep sea
+
+ align:start position:0%
+these techniques for deep sea
+ 
+
+ align:start position:0%
+these techniques for deep sea
+photography are our story today on
+
+ align:start position:0%
+photography are our story today on
+ 
+
+ align:start position:0%
+photography are our story today on
+science
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+report
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+hello I'm John Fitch MIT science
+
+ align:start position:0%
+hello I'm John Fitch MIT science
+ 
+
+ align:start position:0%
+hello I'm John Fitch MIT science
+reporter we're at the MIT swimming pool
+
+ align:start position:0%
+reporter we're at the MIT swimming pool
+ 
+
+ align:start position:0%
+reporter we're at the MIT swimming pool
+today to talk to a man who has made
+
+ align:start position:0%
+today to talk to a man who has made
+ 
+
+ align:start position:0%
+today to talk to a man who has made
+major contributions to the science of
+
+ align:start position:0%
+major contributions to the science of
+ 
+
+ align:start position:0%
+major contributions to the science of
+Photography he is Dr Harold ederton a
+
+ align:start position:0%
+Photography he is Dr Harold ederton a
+ 
+
+ align:start position:0%
+Photography he is Dr Harold ederton a
+professor of electrical measurements in
+
+ align:start position:0%
+professor of electrical measurements in
+ 
+
+ align:start position:0%
+professor of electrical measurements in
+the department of electrical engineering
+
+ align:start position:0%
+the department of electrical engineering
+ 
+
+ align:start position:0%
+the department of electrical engineering
+at MIT a man who was both an inventor
+
+ align:start position:0%
+at MIT a man who was both an inventor
+ 
+
+ align:start position:0%
+at MIT a man who was both an inventor
+and a teacher and internationally famous
+
+ align:start position:0%
+and a teacher and internationally famous
+ 
+
+ align:start position:0%
+and a teacher and internationally famous
+as the father of modern high-speed
+
+ align:start position:0%
+as the father of modern high-speed
+ 
+
+ align:start position:0%
+as the father of modern high-speed
+photography at the age of 28 Dr ederton
+
+ align:start position:0%
+photography at the age of 28 Dr ederton
+ 
+
+ align:start position:0%
+photography at the age of 28 Dr ederton
+invented an electronic device which
+
+ align:start position:0%
+invented an electronic device which
+ 
+
+ align:start position:0%
+invented an electronic device which
+allowed invisible motion much too fast
+
+ align:start position:0%
+allowed invisible motion much too fast
+ 
+
+ align:start position:0%
+allowed invisible motion much too fast
+for the human eye to see such as the
+
+ align:start position:0%
+for the human eye to see such as the
+ 
+
+ align:start position:0%
+for the human eye to see such as the
+swing of a golf club or the path of a
+
+ align:start position:0%
+swing of a golf club or the path of a
+ 
+
+ align:start position:0%
+swing of a golf club or the path of a
+bullettin flight to be frozen onto a
+
+ align:start position:0%
+bullettin flight to be frozen onto a
+ 
+
+ align:start position:0%
+bullettin flight to be frozen onto a
+single photographic plate more recently
+
+ align:start position:0%
+single photographic plate more recently
+ 
+
+ align:start position:0%
+single photographic plate more recently
+Dr Edon has been adap adapting his
+
+ align:start position:0%
+Dr Edon has been adap adapting his
+ 
+
+ align:start position:0%
+Dr Edon has been adap adapting his
+electronic flashlamps to photograph
+
+ align:start position:0%
+electronic flashlamps to photograph
+ 
+
+ align:start position:0%
+electronic flashlamps to photograph
+another world which is invisible to the
+
+ align:start position:0%
+another world which is invisible to the
+ 
+
+ align:start position:0%
+another world which is invisible to the
+naked eye the world of the ocean depths
+
+ align:start position:0%
+naked eye the world of the ocean depths
+ 
+
+ align:start position:0%
+naked eye the world of the ocean depths
+some of the equipment designed by Dr
+
+ align:start position:0%
+some of the equipment designed by Dr
+ 
+
+ align:start position:0%
+some of the equipment designed by Dr
+ederon for deep sea photography is set
+
+ align:start position:0%
+ederon for deep sea photography is set
+ 
+
+ align:start position:0%
+ederon for deep sea photography is set
+up here at the swimming pool and we're
+
+ align:start position:0%
+up here at the swimming pool and we're
+ 
+
+ align:start position:0%
+up here at the swimming pool and we're
+going to meet Dr ederton and learn more
+
+ align:start position:0%
+going to meet Dr ederton and learn more
+ 
+
+ align:start position:0%
+going to meet Dr ederton and learn more
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+it everything work all
+
+ align:start position:0%
+it everything work all
+ 
+
+ align:start position:0%
+it everything work all
+right fine then we'll have it covered
+
+ align:start position:0%
+right fine then we'll have it covered
+ 
+
+ align:start position:0%
+right fine then we'll have it covered
+from several angles Dr Edon that looks
+
+ align:start position:0%
+from several angles Dr Edon that looks
+ 
+
+ align:start position:0%
+from several angles Dr Edon that looks
+very much like an ordinary camera what
+
+ align:start position:0%
+very much like an ordinary camera what
+ 
+
+ align:start position:0%
+very much like an ordinary camera what
+keeps the water out from ruing the film
+
+ align:start position:0%
+keeps the water out from ruing the film
+ 
+
+ align:start position:0%
+keeps the water out from ruing the film
+well this camera is uh like an ordinary
+
+ align:start position:0%
+well this camera is uh like an ordinary
+ 
+
+ align:start position:0%
+well this camera is uh like an ordinary
+camera except the case a of waterpr case
+
+ align:start position:0%
+camera except the case a of waterpr case
+ 
+
+ align:start position:0%
+camera except the case a of waterpr case
+it was developed in France by Captain
+
+ align:start position:0%
+it was developed in France by Captain
+ 
+
+ align:start position:0%
+it was developed in France by Captain
+jaim custo whom I've been many times
+
+ align:start position:0%
+jaim custo whom I've been many times
+ 
+
+ align:start position:0%
+jaim custo whom I've been many times
+it's now made in Japan this uh the lens
+
+ align:start position:0%
+it's now made in Japan this uh the lens
+ 
+
+ align:start position:0%
+it's now made in Japan this uh the lens
+for example comes out and the lens is
+
+ align:start position:0%
+for example comes out and the lens is
+ 
+
+ align:start position:0%
+for example comes out and the lens is
+protected uh by rubber rings called o
+
+ align:start position:0%
+protected uh by rubber rings called o
+ 
+
+ align:start position:0%
+protected uh by rubber rings called o
+rings which seal against a
+
+ align:start position:0%
+rings which seal against a
+ 
+
+ align:start position:0%
+rings which seal against a
+surface nice now how do you focus and
+
+ align:start position:0%
+surface nice now how do you focus and
+ 
+
+ align:start position:0%
+surface nice now how do you focus and
+set the distance and the aperture and
+
+ align:start position:0%
+set the distance and the aperture and
+ 
+
+ align:start position:0%
+set the distance and the aperture and
+all those things well you turn those
+
+ align:start position:0%
+all those things well you turn those
+ 
+
+ align:start position:0%
+all those things well you turn those
+knobs and you see one of them changes
+
+ align:start position:0%
+knobs and you see one of them changes
+ 
+
+ align:start position:0%
+knobs and you see one of them changes
+Focus the other one changes the
+
+ align:start position:0%
+Focus the other one changes the
+ 
+
+ align:start position:0%
+Focus the other one changes the
+aperture very C and this uh fits in
+
+ align:start position:0%
+aperture very C and this uh fits in
+ 
+
+ align:start position:0%
+aperture very C and this uh fits in
+through through the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+O-ring and that seals now the I'm not
+
+ align:start position:0%
+O-ring and that seals now the I'm not
+ 
+
+ align:start position:0%
+O-ring and that seals now the I'm not
+going to take this part because it has
+
+ align:start position:0%
+going to take this part because it has
+ 
+
+ align:start position:0%
+going to take this part because it has
+this film in here right but if you pull
+
+ align:start position:0%
+this film in here right but if you pull
+ 
+
+ align:start position:0%
+this film in here right but if you pull
+these two levers the entire mechanism
+
+ align:start position:0%
+these two levers the entire mechanism
+ 
+
+ align:start position:0%
+these two levers the entire mechanism
+camera mechanism comes out and you can
+
+ align:start position:0%
+camera mechanism comes out and you can
+ 
+
+ align:start position:0%
+camera mechanism comes out and you can
+get at at the film it's also seal SE in
+
+ align:start position:0%
+get at at the film it's also seal SE in
+ 
+
+ align:start position:0%
+get at at the film it's also seal SE in
+it's also sealed in and you trigger The
+
+ align:start position:0%
+it's also sealed in and you trigger The
+ 
+
+ align:start position:0%
+it's also sealed in and you trigger The
+Thing by means of a a pusher at this
+
+ align:start position:0%
+Thing by means of a a pusher at this
+ 
+
+ align:start position:0%
+Thing by means of a a pusher at this
+point release I know he also had to took
+
+ align:start position:0%
+point release I know he also had to took
+ 
+
+ align:start position:0%
+point release I know he also had to took
+his own light along with him yes of
+
+ align:start position:0%
+his own light along with him yes of
+ 
+
+ align:start position:0%
+his own light along with him yes of
+course uh every picture must have light
+
+ align:start position:0%
+course uh every picture must have light
+ 
+
+ align:start position:0%
+course uh every picture must have light
+and in underwater it's particularly
+
+ align:start position:0%
+and in underwater it's particularly
+ 
+
+ align:start position:0%
+and in underwater it's particularly
+important because the sunlight does not
+
+ align:start position:0%
+important because the sunlight does not
+ 
+
+ align:start position:0%
+important because the sunlight does not
+penetrate too well and you always want
+
+ align:start position:0%
+penetrate too well and you always want
+ 
+
+ align:start position:0%
+penetrate too well and you always want
+to fill in
+
+ align:start position:0%
+to fill in
+ 
+
+ align:start position:0%
+to fill in
+Shadows of course in this
+
+ align:start position:0%
+Shadows of course in this
+ 
+
+ align:start position:0%
+Shadows of course in this
+dayo's equipment was developed with Doc
+
+ align:start position:0%
+dayo's equipment was developed with Doc
+ 
+
+ align:start position:0%
+dayo's equipment was developed with Doc
+ederton in in the alumni pool right over
+
+ align:start position:0%
+ederton in in the alumni pool right over
+ 
+
+ align:start position:0%
+ederton in in the alumni pool right over
+there which is uh where is shot so it's
+
+ align:start position:0%
+there which is uh where is shot so it's
+ 
+
+ align:start position:0%
+there which is uh where is shot so it's
+one of those kind of amazing things
+
+ align:start position:0%
+one of those kind of amazing things
+ 
+
+ align:start position:0%
+one of those kind of amazing things
+about walking around MIT campus when you
+
+ align:start position:0%
+about walking around MIT campus when you
+ 
+
+ align:start position:0%
+about walking around MIT campus when you
+start to learn more about the history
+
+ align:start position:0%
+start to learn more about the history
+ 
+
+ align:start position:0%
+start to learn more about the history
+and sort of everything was going on
+
+ align:start position:0%
+and sort of everything was going on
+ 
+
+ align:start position:0%
+and sort of everything was going on
+these these spaces that we don't really
+
+ align:start position:0%
+these these spaces that we don't really
+ 
+
+ align:start position:0%
+these these spaces that we don't really
+pay that much attention to as we just
+
+ align:start position:0%
+pay that much attention to as we just
+ 
+
+ align:start position:0%
+pay that much attention to as we just
+walk around um but we can have you had
+
+ align:start position:0%
+walk around um but we can have you had
+ 
+
+ align:start position:0%
+walk around um but we can have you had
+enough of Doc or or do you want to see a
+
+ align:start position:0%
+enough of Doc or or do you want to see a
+ 
+
+ align:start position:0%
+enough of Doc or or do you want to see a
+nuclear explosion or or something or a
+
+ align:start position:0%
+nuclear explosion or or something or a
+ 
+
+ align:start position:0%
+nuclear explosion or or something or a
+plant unfolding
+
+ align:start position:0%
+plant unfolding
+ 
+
+ align:start position:0%
+plant unfolding
+or flowers or nuclear exposion the
+
+ align:start position:0%
+or flowers or nuclear exposion the
+ 
+
+ align:start position:0%
+or flowers or nuclear exposion the
+nuclear explosions they're yeah let's
+
+ align:start position:0%
+nuclear explosions they're yeah let's
+ 
+
+ align:start position:0%
+nuclear explosions they're yeah let's
+we'll take a quick look okay
+
+ align:start position:0%
+we'll take a quick look okay
+ 
+
+ align:start position:0%
+we'll take a quick look okay
+um here we go
+
+ align:start position:0%
+um here we go
+ 
+
+ align:start position:0%
+um here we go
+he actually did some really
+
+ align:start position:0%
+he actually did some really
+ 
+
+ align:start position:0%
+he actually did some really
+extraordinary still photos um of I mean
+
+ align:start position:0%
+extraordinary still photos um of I mean
+ 
+
+ align:start position:0%
+extraordinary still photos um of I mean
+just images you've never seen before of
+
+ align:start position:0%
+just images you've never seen before of
+ 
+
+ align:start position:0%
+just images you've never seen before of
+the first few micros seconds of a
+
+ align:start position:0%
+the first few micros seconds of a
+ 
+
+ align:start position:0%
+the first few micros seconds of a
+nuclear explosion when it's still this
+
+ align:start position:0%
+nuclear explosion when it's still this
+ 
+
+ align:start position:0%
+nuclear explosion when it's still this
+tiny tightly packed ball of energy and
+
+ align:start position:0%
+tiny tightly packed ball of energy and
+ 
+
+ align:start position:0%
+tiny tightly packed ball of energy and
+it doesn't look like a nuclear explo
+
+ align:start position:0%
+it doesn't look like a nuclear explo
+ 
+
+ align:start position:0%
+it doesn't look like a nuclear explo
+explosion it's really amazing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be the Swift turning of the motor could
+
+ align:start position:0%
+be the Swift turning of the motor could
+ 
+
+ align:start position:0%
+be the Swift turning of the motor could
+be studied in slow motion so again sort
+
+ align:start position:0%
+be studied in slow motion so again sort
+ 
+
+ align:start position:0%
+be studied in slow motion so again sort
+of how exactly
+
+ align:start position:0%
+of how exactly
+ 
+
+ align:start position:0%
+of how exactly
+um how exactly it all works other
+
+ align:start position:0%
+um how exactly it all works other
+ 
+
+ align:start position:0%
+um how exactly it all works other
+reactions thoughts how
+
+ align:start position:0%
+reactions thoughts how
+ 
+
+ align:start position:0%
+reactions thoughts how
+aesthetically appealing it is I mean
+
+ align:start position:0%
+aesthetically appealing it is I mean
+ 
+
+ align:start position:0%
+aesthetically appealing it is I mean
+it's very interesting to see the
+
+ align:start position:0%
+it's very interesting to see the
+ 
+
+ align:start position:0%
+it's very interesting to see the
+movement of the wings of the bird but
+
+ align:start position:0%
+movement of the wings of the bird but
+ 
+
+ align:start position:0%
+movement of the wings of the bird but
+most of all it's just
+
+ align:start position:0%
+most of all it's just
+ 
+
+ align:start position:0%
+most of all it's just
+beautiful can science be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+art well it's a really interesting
+
+ align:start position:0%
+art well it's a really interesting
+ 
+
+ align:start position:0%
+art well it's a really interesting
+relationship between data and art and
+
+ align:start position:0%
+relationship between data and art and
+ 
+
+ align:start position:0%
+relationship between data and art and
+it's something that you see continuing
+
+ align:start position:0%
+it's something that you see continuing
+ 
+
+ align:start position:0%
+it's something that you see continuing
+if for those of you who saw Tom
+
+ align:start position:0%
+if for those of you who saw Tom
+ 
+
+ align:start position:0%
+if for those of you who saw Tom
+Schilling's piece uh that that he made
+
+ align:start position:0%
+Schilling's piece uh that that he made
+ 
+
+ align:start position:0%
+Schilling's piece uh that that he made
+for our last class that was shown at
+
+ align:start position:0%
+for our last class that was shown at
+ 
+
+ align:start position:0%
+for our last class that was shown at
+last week at the Museum one of the
+
+ align:start position:0%
+last week at the Museum one of the
+ 
+
+ align:start position:0%
+last week at the Museum one of the
+things among others that strikes me
+
+ align:start position:0%
+things among others that strikes me
+ 
+
+ align:start position:0%
+things among others that strikes me
+about some of the uh AFM Nano Nano
+
+ align:start position:0%
+about some of the uh AFM Nano Nano
+ 
+
+ align:start position:0%
+about some of the uh AFM Nano Nano
+images that are in that piece is how
+
+ align:start position:0%
+images that are in that piece is how
+ 
+
+ align:start position:0%
+images that are in that piece is how
+beautiful they are and so if you watch
+
+ align:start position:0%
+beautiful they are and so if you watch
+ 
+
+ align:start position:0%
+beautiful they are and so if you watch
+the piece you start to wonder are they
+
+ align:start position:0%
+the piece you start to wonder are they
+ 
+
+ align:start position:0%
+the piece you start to wonder are they
+beautiful because they just happen to be
+
+ align:start position:0%
+beautiful because they just happen to be
+ 
+
+ align:start position:0%
+beautiful because they just happen to be
+beautiful or are they beautiful because
+
+ align:start position:0%
+beautiful or are they beautiful because
+ 
+
+ align:start position:0%
+beautiful or are they beautiful because
+the people making them and designing the
+
+ align:start position:0%
+the people making them and designing the
+ 
+
+ align:start position:0%
+the people making them and designing the
+machines that create them that are you
+
+ align:start position:0%
+machines that create them that are you
+ 
+
+ align:start position:0%
+machines that create them that are you
+know these analogs to something that's
+
+ align:start position:0%
+know these analogs to something that's
+ 
+
+ align:start position:0%
+know these analogs to something that's
+real have a bias towards making them
+
+ align:start position:0%
+real have a bias towards making them
+ 
+
+ align:start position:0%
+real have a bias towards making them
+beautiful this reminds me there's a a
+
+ align:start position:0%
+beautiful this reminds me there's a a
+ 
+
+ align:start position:0%
+beautiful this reminds me there's a a
+museum in London there a welcome
+
+ align:start position:0%
+museum in London there a welcome
+ 
+
+ align:start position:0%
+museum in London there a welcome
+collection and there was an exhibition
+
+ align:start position:0%
+collection and there was an exhibition
+ 
+
+ align:start position:0%
+collection and there was an exhibition
+well there was a competition on
+
+ align:start position:0%
+well there was a competition on
+ 
+
+ align:start position:0%
+well there was a competition on
+um kind of Imaging of of bodily tissues
+
+ align:start position:0%
+um kind of Imaging of of bodily tissues
+ 
+
+ align:start position:0%
+um kind of Imaging of of bodily tissues
+and kind of uh kind of Medical Imaging
+
+ align:start position:0%
+and kind of uh kind of Medical Imaging
+ 
+
+ align:start position:0%
+and kind of uh kind of Medical Imaging
+and the the competition and there was an
+
+ align:start position:0%
+and the the competition and there was an
+ 
+
+ align:start position:0%
+and the the competition and there was an
+exhibition of of the best 15 Works
+
+ align:start position:0%
+exhibition of of the best 15 Works
+ 
+
+ align:start position:0%
+exhibition of of the best 15 Works
+selected and they were showing you know
+
+ align:start position:0%
+selected and they were showing you know
+ 
+
+ align:start position:0%
+selected and they were showing you know
+tissues with cancer and all sort of very
+
+ align:start position:0%
+tissues with cancer and all sort of very
+ 
+
+ align:start position:0%
+tissues with cancer and all sort of very
+intimate kind of horrible details of of
+
+ align:start position:0%
+intimate kind of horrible details of of
+ 
+
+ align:start position:0%
+intimate kind of horrible details of of
+disease but it was like an aesthetic
+
+ align:start position:0%
+disease but it was like an aesthetic
+ 
+
+ align:start position:0%
+disease but it was like an aesthetic
+competition these were selected for
+
+ align:start position:0%
+competition these were selected for
+ 
+
+ align:start position:0%
+competition these were selected for
+their aesthetic qualities it's kind of
+
+ align:start position:0%
+their aesthetic qualities it's kind of
+ 
+
+ align:start position:0%
+their aesthetic qualities it's kind of
+incredible so you were walking through
+
+ align:start position:0%
+incredible so you were walking through
+ 
+
+ align:start position:0%
+incredible so you were walking through
+the collection and you didn't know what
+
+ align:start position:0%
+the collection and you didn't know what
+ 
+
+ align:start position:0%
+the collection and you didn't know what
+you were looking at and how you you were
+
+ align:start position:0%
+you were looking at and how you you were
+ 
+
+ align:start position:0%
+you were looking at and how you you were
+supposed to relate to it I think the C
+
+ align:start position:0%
+supposed to relate to it I think the C
+ 
+
+ align:start position:0%
+supposed to relate to it I think the C
+Institute is doing something similar
+
+ align:start position:0%
+Institute is doing something similar
+ 
+
+ align:start position:0%
+Institute is doing something similar
+with their Lobby uh display area they're
+
+ align:start position:0%
+with their Lobby uh display area they're
+ 
+
+ align:start position:0%
+with their Lobby uh display area they're
+uh they've had a competition of Bio
+
+ align:start position:0%
+uh they've had a competition of Bio
+ 
+
+ align:start position:0%
+uh they've had a competition of Bio
+Imaging and it's being judged on
+
+ align:start position:0%
+Imaging and it's being judged on
+ 
+
+ align:start position:0%
+Imaging and it's being judged on
+certainly not just scientific uh Merit
+
+ align:start position:0%
+certainly not just scientific uh Merit
+ 
+
+ align:start position:0%
+certainly not just scientific uh Merit
+but but Beauty and Aesthetics and I
+
+ align:start position:0%
+but but Beauty and Aesthetics and I
+ 
+
+ align:start position:0%
+but but Beauty and Aesthetics and I
+wonder if it is a shift that's happening
+
+ align:start position:0%
+wonder if it is a shift that's happening
+ 
+
+ align:start position:0%
+wonder if it is a shift that's happening
+more broadly where whereas I I
+
+ align:start position:0%
+more broadly where whereas I I
+ 
+
+ align:start position:0%
+more broadly where whereas I I
+think you know a few years back as
+
+ align:start position:0%
+think you know a few years back as
+ 
+
+ align:start position:0%
+think you know a few years back as
+people when people were trained I think
+
+ align:start position:0%
+people when people were trained I think
+ 
+
+ align:start position:0%
+people when people were trained I think
+there were there was sort of a a strong
+
+ align:start position:0%
+there were there was sort of a a strong
+ 
+
+ align:start position:0%
+there were there was sort of a a strong
+bias that sort of if you had Tendencies
+
+ align:start position:0%
+bias that sort of if you had Tendencies
+ 
+
+ align:start position:0%
+bias that sort of if you had Tendencies
+towards those artistic directions that
+
+ align:start position:0%
+towards those artistic directions that
+ 
+
+ align:start position:0%
+towards those artistic directions that
+that somehow undermined your science and
+
+ align:start position:0%
+that somehow undermined your science and
+ 
+
+ align:start position:0%
+that somehow undermined your science and
+you come someh you kind of had to choose
+
+ align:start position:0%
+you come someh you kind of had to choose
+ 
+
+ align:start position:0%
+you come someh you kind of had to choose
+you couldn't be one or the other or you
+
+ align:start position:0%
+you couldn't be one or the other or you
+ 
+
+ align:start position:0%
+you couldn't be one or the other or you
+weren't seen as being credible in one
+
+ align:start position:0%
+weren't seen as being credible in one
+ 
+
+ align:start position:0%
+weren't seen as being credible in one
+realm if you were seen as being you know
+
+ align:start position:0%
+realm if you were seen as being you know
+ 
+
+ align:start position:0%
+realm if you were seen as being you know
+credible in the other realm but I wonder
+
+ align:start position:0%
+credible in the other realm but I wonder
+ 
+
+ align:start position:0%
+credible in the other realm but I wonder
+if that is breaking down a bit with the
+
+ align:start position:0%
+if that is breaking down a bit with the
+ 
+
+ align:start position:0%
+if that is breaking down a bit with the
+kinds of new Imaging Technologies that
+
+ align:start position:0%
+kinds of new Imaging Technologies that
+ 
+
+ align:start position:0%
+kinds of new Imaging Technologies that
+you have which are incredibly
+
+ align:start position:0%
+you have which are incredibly
+ 
+
+ align:start position:0%
+you have which are incredibly
+aesthetically pleasing at the same time
+
+ align:start position:0%
+aesthetically pleasing at the same time
+ 
+
+ align:start position:0%
+aesthetically pleasing at the same time
+and I wonder if it's sort of a similar
+
+ align:start position:0%
+and I wonder if it's sort of a similar
+ 
+
+ align:start position:0%
+and I wonder if it's sort of a similar
+kind of moment where maybe sort of the
+
+ align:start position:0%
+kind of moment where maybe sort of the
+ 
+
+ align:start position:0%
+kind of moment where maybe sort of the
+art and the science are kind of coming
+
+ align:start position:0%
+art and the science are kind of coming
+ 
+
+ align:start position:0%
+art and the science are kind of coming
+together in a way that um maybe hasn't
+
+ align:start position:0%
+together in a way that um maybe hasn't
+ 
+
+ align:start position:0%
+together in a way that um maybe hasn't
+been true that in more recent years well
+
+ align:start position:0%
+been true that in more recent years well
+ 
+
+ align:start position:0%
+been true that in more recent years well
+besides it also come outly refers to how
+
+ align:start position:0%
+besides it also come outly refers to how
+ 
+
+ align:start position:0%
+besides it also come outly refers to how
+this specific technology is used the
+
+ align:start position:0%
+this specific technology is used the
+ 
+
+ align:start position:0%
+this specific technology is used the
+relationship between sence and violence
+
+ align:start position:0%
+relationship between sence and violence
+ 
+
+ align:start position:0%
+relationship between sence and violence
+we watching a weapon of mass destruction
+
+ align:start position:0%
+we watching a weapon of mass destruction
+ 
+
+ align:start position:0%
+we watching a weapon of mass destruction
+and how exactly it works it's beautiful
+
+ align:start position:0%
+and how exactly it works it's beautiful
+ 
+
+ align:start position:0%
+and how exactly it works it's beautiful
+but essentially it's history science and
+
+ align:start position:0%
+but essentially it's history science and
+ 
+
+ align:start position:0%
+but essentially it's history science and
+technology developed to serve the
+
+ align:start position:0%
+technology developed to serve the
+ 
+
+ align:start position:0%
+technology developed to serve the
+military purposes and the violence so I
+
+ align:start position:0%
+military purposes and the violence so I
+ 
+
+ align:start position:0%
+military purposes and the violence so I
+don't know just it was look disturb Yeah
+
+ align:start position:0%
+don't know just it was look disturb Yeah
+ 
+
+ align:start position:0%
+don't know just it was look disturb Yeah
+well yeah I mean that's I mean so
+
+ align:start position:0%
+well yeah I mean that's I mean so
+ 
+
+ align:start position:0%
+well yeah I mean that's I mean so
+there's both flowers unfolding and hum
+
+ align:start position:0%
+there's both flowers unfolding and hum
+ 
+
+ align:start position:0%
+there's both flowers unfolding and hum
+hummingbirds in flight and there's also
+
+ align:start position:0%
+hummingbirds in flight and there's also
+ 
+
+ align:start position:0%
+hummingbirds in flight and there's also
+nuclear
+
+ align:start position:0%
+nuclear
+ 
+
+ align:start position:0%
+nuclear
+detonations right so so there are so
+
+ align:start position:0%
+detonations right so so there are so
+ 
+
+ align:start position:0%
+detonations right so so there are so
+there's both ends of this and then
+
+ align:start position:0%
+there's both ends of this and then
+ 
+
+ align:start position:0%
+there's both ends of this and then
+there's the questions of you know as
+
+ align:start position:0%
+there's the questions of you know as
+ 
+
+ align:start position:0%
+there's the questions of you know as
+this stuff gets turned into art do are
+
+ align:start position:0%
+this stuff gets turned into art do are
+ 
+
+ align:start position:0%
+this stuff gets turned into art do are
+you aestheticizing things like violence
+
+ align:start position:0%
+you aestheticizing things like violence
+ 
+
+ align:start position:0%
+you aestheticizing things like violence
+and that's partly the the question you
+
+ align:start position:0%
+and that's partly the the question you
+ 
+
+ align:start position:0%
+and that's partly the the question you
+raising there too and it's things like
+
+ align:start position:0%
+raising there too and it's things like
+ 
+
+ align:start position:0%
+raising there too and it's things like
+sort of cancers on people's bodies right
+
+ align:start position:0%
+sort of cancers on people's bodies right
+ 
+
+ align:start position:0%
+sort of cancers on people's bodies right
+I mean what's the is that something
+
+ align:start position:0%
+I mean what's the is that something
+ 
+
+ align:start position:0%
+I mean what's the is that something
+that's properly aestheticized or not how
+
+ align:start position:0%
+that's properly aestheticized or not how
+ 
+
+ align:start position:0%
+that's properly aestheticized or not how
+are you supposed to relate to those
+
+ align:start position:0%
+are you supposed to relate to those
+ 
+
+ align:start position:0%
+are you supposed to relate to those
+kinds of images um is it appropriate to
+
+ align:start position:0%
+kinds of images um is it appropriate to
+ 
+
+ align:start position:0%
+kinds of images um is it appropriate to
+look for beauty in certain kinds of
+
+ align:start position:0%
+look for beauty in certain kinds of
+ 
+
+ align:start position:0%
+look for beauty in certain kinds of
+images when they're images of violence
+
+ align:start position:0%
+images when they're images of violence
+ 
+
+ align:start position:0%
+images when they're images of violence
+for example um so that raises a whole
+
+ align:start position:0%
+for example um so that raises a whole
+ 
+
+ align:start position:0%
+for example um so that raises a whole
+range of other kinds of questions which
+
+ align:start position:0%
+range of other kinds of questions which
+ 
+
+ align:start position:0%
+range of other kinds of questions which
+are very present in film as well I mean
+
+ align:start position:0%
+are very present in film as well I mean
+ 
+
+ align:start position:0%
+are very present in film as well I mean
+if you think about the way violence is
+
+ align:start position:0%
+if you think about the way violence is
+ 
+
+ align:start position:0%
+if you think about the way violence is
+handled in mainstream films uh that's
+
+ align:start position:0%
+handled in mainstream films uh that's
+ 
+
+ align:start position:0%
+handled in mainstream films uh that's
+clearly an issue that you may or may not
+
+ align:start position:0%
+clearly an issue that you may or may not
+ 
+
+ align:start position:0%
+clearly an issue that you may or may not
+be concerned about the aestheticization
+
+ align:start position:0%
+be concerned about the aestheticization
+ 
+
+ align:start position:0%
+be concerned about the aestheticization
+of violence uh and it's something that
+
+ align:start position:0%
+of violence uh and it's something that
+ 
+
+ align:start position:0%
+of violence uh and it's something that
+comes up in documentaries as
+
+ align:start position:0%
+comes up in documentaries as
+ 
+
+ align:start position:0%
+comes up in documentaries as
+well so any further thoughts on all
+
+ align:start position:0%
+well so any further thoughts on all
+ 
+
+ align:start position:0%
+well so any further thoughts on all
+this okay so let's move on so the second
+
+ align:start position:0%
+this okay so let's move on so the second
+ 
+
+ align:start position:0%
+this okay so let's move on so the second
+major use of Science and documentary
+
+ align:start position:0%
+major use of Science and documentary
+ 
+
+ align:start position:0%
+major use of Science and documentary
+images that we're going to talk about
+
+ align:start position:0%
+images that we're going to talk about
+ 
+
+ align:start position:0%
+images that we're going to talk about
+today is educational which we've already
+
+ align:start position:0%
+today is educational which we've already
+ 
+
+ align:start position:0%
+today is educational which we've already
+mentioned and there's obviously long but
+
+ align:start position:0%
+mentioned and there's obviously long but
+ 
+
+ align:start position:0%
+mentioned and there's obviously long but
+a an interest in using film um and
+
+ align:start position:0%
+a an interest in using film um and
+ 
+
+ align:start position:0%
+a an interest in using film um and
+documentary as a mean to means to
+
+ align:start position:0%
+documentary as a mean to means to
+ 
+
+ align:start position:0%
+documentary as a mean to means to
+educate uh the public about science and
+
+ align:start position:0%
+educate uh the public about science and
+ 
+
+ align:start position:0%
+educate uh the public about science and
+as I mentioned before one of the the
+
+ align:start position:0%
+as I mentioned before one of the the
+ 
+
+ align:start position:0%
+as I mentioned before one of the the
+questions that immediately comes up from
+
+ align:start position:0%
+questions that immediately comes up from
+ 
+
+ align:start position:0%
+questions that immediately comes up from
+the end of the end of the scientist is
+
+ align:start position:0%
+the end of the end of the scientist is
+ 
+
+ align:start position:0%
+the end of the end of the scientist is
+how do you visually convey to audiences
+
+ align:start position:0%
+how do you visually convey to audiences
+ 
+
+ align:start position:0%
+how do you visually convey to audiences
+what it is that you want them to get if
+
+ align:start position:0%
+what it is that you want them to get if
+ 
+
+ align:start position:0%
+what it is that you want them to get if
+you want visual media to serve as a form
+
+ align:start position:0%
+you want visual media to serve as a form
+ 
+
+ align:start position:0%
+you want visual media to serve as a form
+of Education how do you translate things
+
+ align:start position:0%
+of Education how do you translate things
+ 
+
+ align:start position:0%
+of Education how do you translate things
+visually in a way that actually um will
+
+ align:start position:0%
+visually in a way that actually um will
+ 
+
+ align:start position:0%
+visually in a way that actually um will
+educate your audience and get them
+
+ align:start position:0%
+educate your audience and get them
+ 
+
+ align:start position:0%
+educate your audience and get them
+engaged with the topic and so then the
+
+ align:start position:0%
+engaged with the topic and so then the
+ 
+
+ align:start position:0%
+engaged with the topic and so then the
+next piece that we're going to see is a
+
+ align:start position:0%
+next piece that we're going to see is a
+ 
+
+ align:start position:0%
+next piece that we're going to see is a
+a film that was made in 1960 uh called
+
+ align:start position:0%
+a film that was made in 1960 uh called
+ 
+
+ align:start position:0%
+a film that was made in 1960 uh called
+frames of reference um that that tries
+
+ align:start position:0%
+frames of reference um that that tries
+ 
+
+ align:start position:0%
+frames of reference um that that tries
+to do this in an interesting way I'd be
+
+ align:start position:0%
+to do this in an interesting way I'd be
+ 
+
+ align:start position:0%
+to do this in an interesting way I'd be
+curious to see what your reactions are
+
+ align:start position:0%
+curious to see what your reactions are
+ 
+
+ align:start position:0%
+curious to see what your reactions are
+it was made by Ricky lecock Ricky Leck
+
+ align:start position:0%
+it was made by Ricky lecock Ricky Leck
+ 
+
+ align:start position:0%
+it was made by Ricky lecock Ricky Leck
+had studied physics at Harvard um and he
+
+ align:start position:0%
+had studied physics at Harvard um and he
+ 
+
+ align:start position:0%
+had studied physics at Harvard um and he
+later became a documentary filmmaker an
+
+ align:start position:0%
+later became a documentary filmmaker an
+ 
+
+ align:start position:0%
+later became a documentary filmmaker an
+extremely famous documentary filmmaker
+
+ align:start position:0%
+extremely famous documentary filmmaker
+ 
+
+ align:start position:0%
+extremely famous documentary filmmaker
+in the direct Cinema tradition actually
+
+ align:start position:0%
+in the direct Cinema tradition actually
+ 
+
+ align:start position:0%
+in the direct Cinema tradition actually
+if you think back in that first class
+
+ align:start position:0%
+if you think back in that first class
+ 
+
+ align:start position:0%
+if you think back in that first class
+the images of um uh primary with the JFK
+
+ align:start position:0%
+the images of um uh primary with the JFK
+ 
+
+ align:start position:0%
+the images of um uh primary with the JFK
+election he was uh camer person for that
+
+ align:start position:0%
+election he was uh camer person for that
+ 
+
+ align:start position:0%
+election he was uh camer person for that
+extrem did a number of very famous films
+
+ align:start position:0%
+extrem did a number of very famous films
+ 
+
+ align:start position:0%
+extrem did a number of very famous films
+some of which you you might have seen
+
+ align:start position:0%
+some of which you you might have seen
+ 
+
+ align:start position:0%
+some of which you you might have seen
+pieces of he taught here at MIT uh for
+
+ align:start position:0%
+pieces of he taught here at MIT uh for
+ 
+
+ align:start position:0%
+pieces of he taught here at MIT uh for
+many years there was a film program at
+
+ align:start position:0%
+many years there was a film program at
+ 
+
+ align:start position:0%
+many years there was a film program at
+at MIT that was extremely influential um
+
+ align:start position:0%
+at MIT that was extremely influential um
+ 
+
+ align:start position:0%
+at MIT that was extremely influential um
+it sort of got phased out when the media
+
+ align:start position:0%
+it sort of got phased out when the media
+ 
+
+ align:start position:0%
+it sort of got phased out when the media
+lab came in um but he was a had been a
+
+ align:start position:0%
+lab came in um but he was a had been a
+ 
+
+ align:start position:0%
+lab came in um but he was a had been a
+very central figure here at MIT um but
+
+ align:start position:0%
+very central figure here at MIT um but
+ 
+
+ align:start position:0%
+very central figure here at MIT um but
+this was a film that he made very early
+
+ align:start position:0%
+this was a film that he made very early
+ 
+
+ align:start position:0%
+this was a film that he made very early
+on with two other physicists and this is
+
+ align:start position:0%
+on with two other physicists and this is
+ 
+
+ align:start position:0%
+on with two other physicists and this is
+before he became um a a um you know he
+
+ align:start position:0%
+before he became um a a um you know he
+ 
+
+ align:start position:0%
+before he became um a a um you know he
+was obviously making films at this point
+
+ align:start position:0%
+was obviously making films at this point
+ 
+
+ align:start position:0%
+was obviously making films at this point
+but it was before he he sort of went off
+
+ align:start position:0%
+but it was before he he sort of went off
+ 
+
+ align:start position:0%
+but it was before he he sort of went off
+and became a direct uh direct Cinema
+
+ align:start position:0%
+and became a direct uh direct Cinema
+ 
+
+ align:start position:0%
+and became a direct uh direct Cinema
+filmmaker um so I think early years
+
+ align:start position:0%
+filmmaker um so I think early years
+ 
+
+ align:start position:0%
+filmmaker um so I think early years
+right before 22 something when he made
+
+ align:start position:0%
+right before 22 something when he made
+ 
+
+ align:start position:0%
+right before 22 something when he made
+this 23 years old okay so again called
+
+ align:start position:0%
+this 23 years old okay so again called
+ 
+
+ align:start position:0%
+this 23 years old okay so again called
+frames of reference from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1960 oh and he also worked with flare on
+
+ align:start position:0%
+1960 oh and he also worked with flare on
+ 
+
+ align:start position:0%
+1960 oh and he also worked with flare on
+something he was like a camera person
+
+ align:start position:0%
+something he was like a camera person
+ 
+
+ align:start position:0%
+something he was like a camera person
+for uh flare on flarey ended up doing a
+
+ align:start position:0%
+for uh flare on flarey ended up doing a
+ 
+
+ align:start position:0%
+for uh flare on flarey ended up doing a
+film about um uh rural Louisiana and he
+
+ align:start position:0%
+film about um uh rural Louisiana and he
+ 
+
+ align:start position:0%
+film about um uh rural Louisiana and he
+ended up being the camera person for
+
+ align:start position:0%
+ended up being the camera person for
+ 
+
+ align:start position:0%
+ended up being the camera person for
+that as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're used to seeing things from a
+
+ align:start position:0%
+you're used to seeing things from a
+ 
+
+ align:start position:0%
+you're used to seeing things from a
+particular point of view that is from a
+
+ align:start position:0%
+particular point of view that is from a
+ 
+
+ align:start position:0%
+particular point of view that is from a
+particular frame of reference and things
+
+ align:start position:0%
+particular frame of reference and things
+ 
+
+ align:start position:0%
+particular frame of reference and things
+look different to us under different
+
+ align:start position:0%
+look different to us under different
+ 
+
+ align:start position:0%
+look different to us under different
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+circumstances at the moment things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+look you look
+
+ align:start position:0%
+look you look
+ 
+
+ align:start position:0%
+look you look
+peculiar you're upside down no you're
+
+ align:start position:0%
+peculiar you're upside down no you're
+ 
+
+ align:start position:0%
+peculiar you're upside down no you're
+the one that's upside down no you're
+
+ align:start position:0%
+the one that's upside down no you're
+ 
+
+ align:start position:0%
+the one that's upside down no you're
+upside down no I'm
+
+ align:start position:0%
+upside down no I'm
+ 
+
+ align:start position:0%
+upside down no I'm
+not he's the one that's upside down
+
+ align:start position:0%
+not he's the one that's upside down
+ 
+
+ align:start position:0%
+not he's the one that's upside down
+isn't he well that stops for us all
+
+ align:start position:0%
+isn't he well that stops for us all
+ 
+
+ align:start position:0%
+isn't he well that stops for us all
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you lose he's the one that's really
+
+ align:start position:0%
+okay you lose he's the one that's really
+ 
+
+ align:start position:0%
+okay you lose he's the one that's really
+upside down you better come into my
+
+ align:start position:0%
+upside down you better come into my
+ 
+
+ align:start position:0%
+upside down you better come into my
+frame of reference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+now my frame of reference was inverted
+
+ align:start position:0%
+now my frame of reference was inverted
+ 
+
+ align:start position:0%
+now my frame of reference was inverted
+from what it usually
+
+ align:start position:0%
+from what it usually
+ 
+
+ align:start position:0%
+from what it usually
+is that few of things would be normal
+
+ align:start position:0%
+is that few of things would be normal
+ 
+
+ align:start position:0%
+is that few of things would be normal
+for me if I normally walked on my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hands this represents a frame of
+
+ align:start position:0%
+hands this represents a frame of
+ 
+
+ align:start position:0%
+hands this represents a frame of
+reference just three rods stuck together
+
+ align:start position:0%
+reference just three rods stuck together
+ 
+
+ align:start position:0%
+reference just three rods stuck together
+so that each is at right angles to the
+
+ align:start position:0%
+so that each is at right angles to the
+ 
+
+ align:start position:0%
+so that each is at right angles to the
+other two now I'm going to move in this
+
+ align:start position:0%
+other two now I'm going to move in this
+ 
+
+ align:start position:0%
+other two now I'm going to move in this
+direction you see the frame at the same
+
+ align:start position:0%
+direction you see the frame at the same
+ 
+
+ align:start position:0%
+direction you see the frame at the same
+spot on your screen but you know I'm
+
+ align:start position:0%
+spot on your screen but you know I'm
+ 
+
+ align:start position:0%
+spot on your screen but you know I'm
+moving this way because you see the wall
+
+ align:start position:0%
+moving this way because you see the wall
+ 
+
+ align:start position:0%
+moving this way because you see the wall
+moving this way behind me but how do you
+
+ align:start position:0%
+moving this way behind me but how do you
+ 
+
+ align:start position:0%
+moving this way behind me but how do you
+know that I'm not standing standing
+
+ align:start position:0%
+know that I'm not standing standing
+ 
+
+ align:start position:0%
+know that I'm not standing standing
+still and the wall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moving it was the wall that was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moving now the wall has disappeared and
+
+ align:start position:0%
+moving now the wall has disappeared and
+ 
+
+ align:start position:0%
+moving now the wall has disappeared and
+you have no way of telling whether I am
+
+ align:start position:0%
+you have no way of telling whether I am
+ 
+
+ align:start position:0%
+you have no way of telling whether I am
+moving or not but now you know that I'm
+
+ align:start position:0%
+moving or not but now you know that I'm
+ 
+
+ align:start position:0%
+moving or not but now you know that I'm
+moving the point of this is that all
+
+ align:start position:0%
+moving the point of this is that all
+ 
+
+ align:start position:0%
+moving the point of this is that all
+motion is relative in both cases I was
+
+ align:start position:0%
+motion is relative in both cases I was
+ 
+
+ align:start position:0%
+motion is relative in both cases I was
+moving relative to the wall and the wall
+
+ align:start position:0%
+moving relative to the wall and the wall
+ 
+
+ align:start position:0%
+moving relative to the wall and the wall
+was moving relative to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me all motion is relative but we tend to
+
+ align:start position:0%
+me all motion is relative but we tend to
+ 
+
+ align:start position:0%
+me all motion is relative but we tend to
+think of one thing as being fixed and
+
+ align:start position:0%
+think of one thing as being fixed and
+ 
+
+ align:start position:0%
+think of one thing as being fixed and
+the other thing as being moving we
+
+ align:start position:0%
+the other thing as being moving we
+ 
+
+ align:start position:0%
+the other thing as being moving we
+usually think of the earth as fixed and
+
+ align:start position:0%
+usually think of the earth as fixed and
+ 
+
+ align:start position:0%
+usually think of the earth as fixed and
+walls are usually fixed to the Earth so
+
+ align:start position:0%
+walls are usually fixed to the Earth so
+ 
+
+ align:start position:0%
+walls are usually fixed to the Earth so
+perhaps you were surprised the first
+
+ align:start position:0%
+perhaps you were surprised the first
+ 
+
+ align:start position:0%
+perhaps you were surprised the first
+time when it was the wall that was
+
+ align:start position:0%
+time when it was the wall that was
+ 
+
+ align:start position:0%
+time when it was the wall that was
+moving and not Dr hum a frame of
+
+ align:start position:0%
+moving and not Dr hum a frame of
+ 
+
+ align:start position:0%
+moving and not Dr hum a frame of
+reference fixed to the Earth is the most
+
+ align:start position:0%
+reference fixed to the Earth is the most
+ 
+
+ align:start position:0%
+reference fixed to the Earth is the most
+common frame of reference in which to
+
+ align:start position:0%
+common frame of reference in which to
+ 
+
+ align:start position:0%
+common frame of reference in which to
+observe the motion of other things
+
+ align:start position:0%
+observe the motion of other things
+ 
+
+ align:start position:0%
+observe the motion of other things
+this is the frame of reference that
+
+ align:start position:0%
+this is the frame of reference that
+ 
+
+ align:start position:0%
+this is the frame of reference that
+you're used to the frame is fastened to
+
+ align:start position:0%
+you're used to the frame is fastened to
+ 
+
+ align:start position:0%
+you're used to the frame is fastened to
+the table the table is boled to the
+
+ align:start position:0%
+the table the table is boled to the
+ 
+
+ align:start position:0%
+the table the table is boled to the
+floor the floor is anchored in the
+
+ align:start position:0%
+floor the floor is anchored in the
+ 
+
+ align:start position:0%
+floor the floor is anchored in the
+building and the building is firmly
+
+ align:start position:0%
+building and the building is firmly
+ 
+
+ align:start position:0%
+building and the building is firmly
+attached to the Earth of course the
+
+ align:start position:0%
+attached to the Earth of course the
+ 
+
+ align:start position:0%
+attached to the Earth of course the
+reason for having three rods is the
+
+ align:start position:0%
+reason for having three rods is the
+ 
+
+ align:start position:0%
+reason for having three rods is the
+position of any object such as this ball
+
+ align:start position:0%
+position of any object such as this ball
+ 
+
+ align:start position:0%
+position of any object such as this ball
+can be specified using these three
+
+ align:start position:0%
+can be specified using these three
+ 
+
+ align:start position:0%
+can be specified using these three
+reference lines this reference line
+
+ align:start position:0%
+reference lines this reference line
+ 
+
+ align:start position:0%
+reference lines this reference line
+points in the direction which we call up
+
+ align:start position:0%
+points in the direction which we call up
+ 
+
+ align:start position:0%
+points in the direction which we call up
+which is a different Direction here than
+
+ align:start position:0%
+which is a different Direction here than
+ 
+
+ align:start position:0%
+which is a different Direction here than
+it is in the other side of the earth and
+
+ align:start position:0%
+it is in the other side of the earth and
+ 
+
+ align:start position:0%
+it is in the other side of the earth and
+these two reference lines specify a
+
+ align:start position:0%
+these two reference lines specify a
+ 
+
+ align:start position:0%
+these two reference lines specify a
+plane which we call horizontal or level
+
+ align:start position:0%
+plane which we call horizontal or level
+ 
+
+ align:start position:0%
+plane which we call horizontal or level
+in this film we're going to look at the
+
+ align:start position:0%
+in this film we're going to look at the
+ 
+
+ align:start position:0%
+in this film we're going to look at the
+motion of objects in this earth frame of
+
+ align:start position:0%
+motion of objects in this earth frame of
+ 
+
+ align:start position:0%
+motion of objects in this earth frame of
+reference and in other frames of
+
+ align:start position:0%
+reference and in other frames of
+ 
+
+ align:start position:0%
+reference and in other frames of
+reference moving in different ways
+
+ align:start position:0%
+reference moving in different ways
+ 
+
+ align:start position:0%
+reference moving in different ways
+relative to the Earth frame well let's
+
+ align:start position:0%
+relative to the Earth frame well let's
+ 
+
+ align:start position:0%
+relative to the Earth frame well let's
+look at a
+
+ align:start position:0%
+look at a
+ 
+
+ align:start position:0%
+look at a
+motion this steel ball can be held up by
+
+ align:start position:0%
+motion this steel ball can be held up by
+ 
+
+ align:start position:0%
+motion this steel ball can be held up by
+the electrom
+
+ align:start position:0%
+the electrom
+ 
+
+ align:start position:0%
+the electrom
+now I'm going to open the switch and you
+
+ align:start position:0%
+now I'm going to open the switch and you
+ 
+
+ align:start position:0%
+now I'm going to open the switch and you
+watch the motion of the
+
+ align:start position:0%
+watch the motion of the
+ 
+
+ align:start position:0%
+watch the motion of the
+ball the ball is accelerated straight
+
+ align:start position:0%
+ball the ball is accelerated straight
+ 
+
+ align:start position:0%
+ball the ball is accelerated straight
+down by gravity along a line parallel to
+
+ align:start position:0%
+down by gravity along a line parallel to
+ 
+
+ align:start position:0%
+down by gravity along a line parallel to
+this vertical reference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line as you can see the electromagnet is
+
+ align:start position:0%
+line as you can see the electromagnet is
+ 
+
+ align:start position:0%
+line as you can see the electromagnet is
+mounted on a cart that can move and I'm
+
+ align:start position:0%
+mounted on a cart that can move and I'm
+ 
+
+ align:start position:0%
+mounted on a cart that can move and I'm
+going to do exactly the same experiment
+
+ align:start position:0%
+going to do exactly the same experiment
+ 
+
+ align:start position:0%
+going to do exactly the same experiment
+that Dr Hume did but this time while the
+
+ align:start position:0%
+that Dr Hume did but this time while the
+ 
+
+ align:start position:0%
+that Dr Hume did but this time while the
+car is moving at a constant velocity the
+
+ align:start position:0%
+car is moving at a constant velocity the
+ 
+
+ align:start position:0%
+car is moving at a constant velocity the
+car
+
+ align:start position:0%
+car
+ 
+
+ align:start position:0%
+car
+is pulled Along by a string which is
+
+ align:start position:0%
+is pulled Along by a string which is
+ 
+
+ align:start position:0%
+is pulled Along by a string which is
+wound around this phonograph turntable
+
+ align:start position:0%
+wound around this phonograph turntable
+ 
+
+ align:start position:0%
+wound around this phonograph turntable
+and that pulls it with a constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+velocity when the cart passes this
+
+ align:start position:0%
+velocity when the cart passes this
+ 
+
+ align:start position:0%
+velocity when the cart passes this
+line the
+
+ align:start position:0%
+line the
+ 
+
+ align:start position:0%
+line the
+ball is released as you can
+
+ align:start position:0%
+ball is released as you can
+ 
+
+ align:start position:0%
+ball is released as you can
+see I'm going to start the C down at the
+
+ align:start position:0%
+see I'm going to start the C down at the
+ 
+
+ align:start position:0%
+see I'm going to start the C down at the
+end of the table so that by the time it
+
+ align:start position:0%
+end of the table so that by the time it
+ 
+
+ align:start position:0%
+end of the table so that by the time it
+gets to this point I can be sure it's
+
+ align:start position:0%
+gets to this point I can be sure it's
+ 
+
+ align:start position:0%
+gets to this point I can be sure it's
+moving with a constant velocity now I
+
+ align:start position:0%
+moving with a constant velocity now I
+ 
+
+ align:start position:0%
+moving with a constant velocity now I
+want you to watch right right here so
+
+ align:start position:0%
+want you to watch right right here so
+ 
+
+ align:start position:0%
+want you to watch right right here so
+that you will see the ball
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+falling I think you can see that the
+
+ align:start position:0%
+falling I think you can see that the
+ 
+
+ align:start position:0%
+falling I think you can see that the
+ball landed in exactly the same position
+
+ align:start position:0%
+ball landed in exactly the same position
+ 
+
+ align:start position:0%
+ball landed in exactly the same position
+that it did before when Dr hum did the
+
+ align:start position:0%
+that it did before when Dr hum did the
+ 
+
+ align:start position:0%
+that it did before when Dr hum did the
+experiment with the c fixed but this
+
+ align:start position:0%
+experiment with the c fixed but this
+ 
+
+ align:start position:0%
+experiment with the c fixed but this
+time the ball could not have fallen
+
+ align:start position:0%
+time the ball could not have fallen
+ 
+
+ align:start position:0%
+time the ball could not have fallen
+straight down let me show you
+
+ align:start position:0%
+straight down let me show you
+ 
+
+ align:start position:0%
+straight down let me show you
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+the ball was
+
+ align:start position:0%
+the ball was
+ 
+
+ align:start position:0%
+the ball was
+released at that point if it had fallen
+
+ align:start position:0%
+released at that point if it had fallen
+ 
+
+ align:start position:0%
+released at that point if it had fallen
+straight down because the cart moves on
+
+ align:start position:0%
+straight down because the cart moves on
+ 
+
+ align:start position:0%
+straight down because the cart moves on
+and the time that it takes to fall would
+
+ align:start position:0%
+and the time that it takes to fall would
+ 
+
+ align:start position:0%
+and the time that it takes to fall would
+have landed back here somewhere but it
+
+ align:start position:0%
+have landed back here somewhere but it
+ 
+
+ align:start position:0%
+have landed back here somewhere but it
+didn't so I'm going to do the experiment
+
+ align:start position:0%
+didn't so I'm going to do the experiment
+ 
+
+ align:start position:0%
+didn't so I'm going to do the experiment
+again this time I'm going to let you
+
+ align:start position:0%
+again this time I'm going to let you
+ 
+
+ align:start position:0%
+again this time I'm going to let you
+watch the motion through a slow motion
+
+ align:start position:0%
+watch the motion through a slow motion
+ 
+
+ align:start position:0%
+watch the motion through a slow motion
+camera which is
+
+ align:start position:0%
+camera which is
+ 
+
+ align:start position:0%
+camera which is
+fixed here is the cart moves by the ball
+
+ align:start position:0%
+fixed here is the cart moves by the ball
+ 
+
+ align:start position:0%
+fixed here is the cart moves by the ball
+will fall and you can watch in the slow
+
+ align:start position:0%
+will fall and you can watch in the slow
+ 
+
+ align:start position:0%
+will fall and you can watch in the slow
+motion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+camera I'll show you this again this
+
+ align:start position:0%
+camera I'll show you this again this
+ 
+
+ align:start position:0%
+camera I'll show you this again this
+time there will be a line on the film so
+
+ align:start position:0%
+time there will be a line on the film so
+ 
+
+ align:start position:0%
+time there will be a line on the film so
+that you can see the
+
+ align:start position:0%
+that you can see the
+ 
+
+ align:start position:0%
+that you can see the
+path I think that you can see that the
+
+ align:start position:0%
+path I think that you can see that the
+ 
+
+ align:start position:0%
+path I think that you can see that the
+path of the ball is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parabola but all of this has been in a
+
+ align:start position:0%
+parabola but all of this has been in a
+ 
+
+ align:start position:0%
+parabola but all of this has been in a
+frame of reference fixed to the Earth
+
+ align:start position:0%
+frame of reference fixed to the Earth
+ 
+
+ align:start position:0%
+frame of reference fixed to the Earth
+how would this motion look in in a frame
+
+ align:start position:0%
+how would this motion look in in a frame
+ 
+
+ align:start position:0%
+how would this motion look in in a frame
+of reference which was moving along with
+
+ align:start position:0%
+of reference which was moving along with
+ 
+
+ align:start position:0%
+of reference which was moving along with
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cart frame of reference like that well
+
+ align:start position:0%
+cart frame of reference like that well
+ 
+
+ align:start position:0%
+cart frame of reference like that well
+so that you can see what it looks like
+
+ align:start position:0%
+so that you can see what it looks like
+ 
+
+ align:start position:0%
+so that you can see what it looks like
+I'm going to fix this slow motion
+
+ align:start position:0%
+I'm going to fix this slow motion
+ 
+
+ align:start position:0%
+I'm going to fix this slow motion
+camera so that it moves with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+car like this I'm going to do the
+
+ align:start position:0%
+car like this I'm going to do the
+ 
+
+ align:start position:0%
+car like this I'm going to do the
+experiment again and incidentally I'll
+
+ align:start position:0%
+experiment again and incidentally I'll
+ 
+
+ align:start position:0%
+experiment again and incidentally I'll
+start it and then I'm going to stand
+
+ align:start position:0%
+start it and then I'm going to stand
+ 
+
+ align:start position:0%
+start it and then I'm going to stand
+here so that when the ball Falls you
+
+ align:start position:0%
+here so that when the ball Falls you
+ 
+
+ align:start position:0%
+here so that when the ball Falls you
+will have something which is fixed as a
+
+ align:start position:0%
+will have something which is fixed as a
+ 
+
+ align:start position:0%
+will have something which is fixed as a
+reference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point in the moving frame of reference I
+
+ align:start position:0%
+point in the moving frame of reference I
+ 
+
+ align:start position:0%
+point in the moving frame of reference I
+think you could see that the path of the
+
+ align:start position:0%
+think you could see that the path of the
+ 
+
+ align:start position:0%
+think you could see that the path of the
+ball is a vertical straight line it
+
+ align:start position:0%
+ball is a vertical straight line it
+ 
+
+ align:start position:0%
+ball is a vertical straight line it
+looks exactly the same as it did before
+
+ align:start position:0%
+looks exactly the same as it did before
+ 
+
+ align:start position:0%
+looks exactly the same as it did before
+when Dr hum did the experiment with the
+
+ align:start position:0%
+when Dr hum did the experiment with the
+ 
+
+ align:start position:0%
+when Dr hum did the experiment with the
+Cart
+
+ align:start position:0%
+Cart
+ 
+
+ align:start position:0%
+Cart
+fixed if we were moving along in this
+
+ align:start position:0%
+fixed if we were moving along in this
+ 
+
+ align:start position:0%
+fixed if we were moving along in this
+frame of reference and we couldn't see
+
+ align:start position:0%
+frame of reference and we couldn't see
+ 
+
+ align:start position:0%
+frame of reference and we couldn't see
+the surroundings then we wouldn't be
+
+ align:start position:0%
+the surroundings then we wouldn't be
+ 
+
+ align:start position:0%
+the surroundings then we wouldn't be
+able to tell by this experiment that we
+
+ align:start position:0%
+able to tell by this experiment that we
+ 
+
+ align:start position:0%
+able to tell by this experiment that we
+were moving at a constant velocity as a
+
+ align:start position:0%
+were moving at a constant velocity as a
+ 
+
+ align:start position:0%
+were moving at a constant velocity as a
+matter of fact we wouldn't be able to
+
+ align:start position:0%
+matter of fact we wouldn't be able to
+ 
+
+ align:start position:0%
+matter of fact we wouldn't be able to
+tell by any experiment that we were
+
+ align:start position:0%
+tell by any experiment that we were
+ 
+
+ align:start position:0%
+tell by any experiment that we were
+moving at a constant velocity I'm going
+
+ align:start position:0%
+moving at a constant velocity I'm going
+ 
+
+ align:start position:0%
+moving at a constant velocity I'm going
+to do the experiment once more and this
+
+ align:start position:0%
+to do the experiment once more and this
+ 
+
+ align:start position:0%
+to do the experiment once more and this
+time I'm not going to stand here behind
+
+ align:start position:0%
+time I'm not going to stand here behind
+ 
+
+ align:start position:0%
+time I'm not going to stand here behind
+the ball as it falls so that you won't
+
+ align:start position:0%
+the ball as it falls so that you won't
+ 
+
+ align:start position:0%
+the ball as it falls so that you won't
+have any fixed reference
+
+ align:start position:0%
+have any fixed reference
+ 
+
+ align:start position:0%
+have any fixed reference
+frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+as far as you're concern that time the
+
+ align:start position:0%
+as far as you're concern that time the
+ 
+
+ align:start position:0%
+as far as you're concern that time the
+cart wasn't necessarily moving at all
+
+ align:start position:0%
+cart wasn't necessarily moving at all
+ 
+
+ align:start position:0%
+cart wasn't necessarily moving at all
+that time when you couldn't see the
+
+ align:start position:0%
+that time when you couldn't see the
+ 
+
+ align:start position:0%
+that time when you couldn't see the
+background then I think perhaps it was
+
+ align:start position:0%
+background then I think perhaps it was
+ 
+
+ align:start position:0%
+background then I think perhaps it was
+harder for you to realize that you were
+
+ align:start position:0%
+harder for you to realize that you were
+ 
+
+ align:start position:0%
+harder for you to realize that you were
+in a moving frame of
+
+ align:start position:0%
+in a moving frame of
+ 
+
+ align:start position:0%
+in a moving frame of
+reference so if anybody's interested
+
+ align:start position:0%
+reference so if anybody's interested
+ 
+
+ align:start position:0%
+reference so if anybody's interested
+this is uh available online and it's
+
+ align:start position:0%
+this is uh available online and it's
+ 
+
+ align:start position:0%
+this is uh available online and it's
+goes on uh quite interesting lots of
+
+ align:start position:0%
+goes on uh quite interesting lots of
+ 
+
+ align:start position:0%
+goes on uh quite interesting lots of
+great little toys and uh
+
+ align:start position:0%
+great little toys and uh
+ 
+
+ align:start position:0%
+great little toys and uh
+experiments so uh reactions
+
+ align:start position:0%
+experiments so uh reactions
+ 
+
+ align:start position:0%
+experiments so uh reactions
+comments this is a slightly random
+
+ align:start position:0%
+comments this is a slightly random
+ 
+
+ align:start position:0%
+comments this is a slightly random
+comment but there was a speck of pain on
+
+ align:start position:0%
+comment but there was a speck of pain on
+ 
+
+ align:start position:0%
+comment but there was a speck of pain on
+the wall
+
+ align:start position:0%
+the wall
+ 
+
+ align:start position:0%
+the wall
+yeah so you could see that yeah moving
+
+ align:start position:0%
+yeah so you could see that yeah moving
+ 
+
+ align:start position:0%
+yeah so you could see that yeah moving
+yeah I just thought i' thr that out yeah
+
+ align:start position:0%
+yeah I just thought i' thr that out yeah
+ 
+
+ align:start position:0%
+yeah I just thought i' thr that out yeah
+no and it's I noticed that too it's it's
+
+ align:start position:0%
+no and it's I noticed that too it's it's
+ 
+
+ align:start position:0%
+no and it's I noticed that too it's it's
+funny because one of the things I love
+
+ align:start position:0%
+funny because one of the things I love
+ 
+
+ align:start position:0%
+funny because one of the things I love
+about this film is that they have such
+
+ align:start position:0%
+about this film is that they have such
+ 
+
+ align:start position:0%
+about this film is that they have such
+great Rigs and toys and they've set it
+
+ align:start position:0%
+great Rigs and toys and they've set it
+ 
+
+ align:start position:0%
+great Rigs and toys and they've set it
+all up and they make it really really
+
+ align:start position:0%
+all up and they make it really really
+ 
+
+ align:start position:0%
+all up and they make it really really
+easy seeming so well put the little
+
+ align:start position:0%
+easy seeming so well put the little
+ 
+
+ align:start position:0%
+easy seeming so well put the little
+screw in here and now the camera is
+
+ align:start position:0%
+screw in here and now the camera is
+ 
+
+ align:start position:0%
+screw in here and now the camera is
+attached to the cart and the photograph
+
+ align:start position:0%
+attached to the cart and the photograph
+ 
+
+ align:start position:0%
+attached to the cart and the photograph
+turntable will turn it at a constant
+
+ align:start position:0%
+turntable will turn it at a constant
+ 
+
+ align:start position:0%
+turntable will turn it at a constant
+speed so it it all seems really
+
+ align:start position:0%
+speed so it it all seems really
+ 
+
+ align:start position:0%
+speed so it it all seems really
+effortless and the whole rig of the guy
+
+ align:start position:0%
+effortless and the whole rig of the guy
+ 
+
+ align:start position:0%
+effortless and the whole rig of the guy
+upside down and the camera spinning
+
+ align:start position:0%
+upside down and the camera spinning
+ 
+
+ align:start position:0%
+upside down and the camera spinning
+around but yeah the the speck of pain is
+
+ align:start position:0%
+around but yeah the the speck of pain is
+ 
+
+ align:start position:0%
+around but yeah the the speck of pain is
+just a little detail they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+missed kind of looks like a um
+
+ align:start position:0%
+missed kind of looks like a um
+ 
+
+ align:start position:0%
+missed kind of looks like a um
+like when this kind of TV Chef's program
+
+ align:start position:0%
+like when this kind of TV Chef's program
+ 
+
+ align:start position:0%
+like when this kind of TV Chef's program
+they they have all their equipment it
+
+ align:start position:0%
+they they have all their equipment it
+ 
+
+ align:start position:0%
+they they have all their equipment it
+looks really easy so who who is this
+
+ align:start position:0%
+looks really easy so who who is this
+ 
+
+ align:start position:0%
+looks really easy so who who is this
+made for it was it's an educational film
+
+ align:start position:0%
+made for it was it's an educational film
+ 
+
+ align:start position:0%
+made for it was it's an educational film
+uh it was made with uh grants grant
+
+ align:start position:0%
+uh it was made with uh grants grant
+ 
+
+ align:start position:0%
+uh it was made with uh grants grant
+funding in do you know the year the 1960
+
+ align:start position:0%
+funding in do you know the year the 1960
+ 
+
+ align:start position:0%
+funding in do you know the year the 1960
+1960 yeah and for for schools yeah for
+
+ align:start position:0%
+1960 yeah and for for schools yeah for
+ 
+
+ align:start position:0%
+1960 yeah and for for schools yeah for
+schools to educate people about physics
+
+ align:start position:0%
+schools to educate people about physics
+ 
+
+ align:start position:0%
+schools to educate people about physics
+yeah I think it's the whole sort of uh
+
+ align:start position:0%
+yeah I think it's the whole sort of uh
+ 
+
+ align:start position:0%
+yeah I think it's the whole sort of uh
+idea of laying the foundation for
+
+ align:start position:0%
+idea of laying the foundation for
+ 
+
+ align:start position:0%
+idea of laying the foundation for
+relativity and just understanding
+
+ align:start position:0%
+relativity and just understanding
+ 
+
+ align:start position:0%
+relativity and just understanding
+how how how speeds are you know objects
+
+ align:start position:0%
+how how how speeds are you know objects
+ 
+
+ align:start position:0%
+how how how speeds are you know objects
+are um either fixed or not fixed
+
+ align:start position:0%
+are um either fixed or not fixed
+ 
+
+ align:start position:0%
+are um either fixed or not fixed
+depending on where the Observer is but
+
+ align:start position:0%
+depending on where the Observer is but
+ 
+
+ align:start position:0%
+depending on where the Observer is but
+what it's very famous for is that that
+
+ align:start position:0%
+what it's very famous for is that that
+ 
+
+ align:start position:0%
+what it's very famous for is that that
+the beginning yeah the opening with the
+
+ align:start position:0%
+the beginning yeah the opening with the
+ 
+
+ align:start position:0%
+the beginning yeah the opening with the
+the as you can imagine
+
+ align:start position:0%
+the as you can imagine
+ 
+
+ align:start position:0%
+the as you can imagine
+um which is quite a I mean so that's
+
+ align:start position:0%
+um which is quite a I mean so that's
+ 
+
+ align:start position:0%
+um which is quite a I mean so that's
+something to think about too then as you
+
+ align:start position:0%
+something to think about too then as you
+ 
+
+ align:start position:0%
+something to think about too then as you
+go to think about making films not not
+
+ align:start position:0%
+go to think about making films not not
+ 
+
+ align:start position:0%
+go to think about making films not not
+that you're
+
+ align:start position:0%
+that you're
+ 
+
+ align:start position:0%
+that you're
+expected to put that much effort in you
+
+ align:start position:0%
+expected to put that much effort in you
+ 
+
+ align:start position:0%
+expected to put that much effort in you
+know but but you know they were trying
+
+ align:start position:0%
+know but but you know they were trying
+ 
+
+ align:start position:0%
+know but but you know they were trying
+to think about well how would you convey
+
+ align:start position:0%
+to think about well how would you convey
+ 
+
+ align:start position:0%
+to think about well how would you convey
+something in a visually arresting way to
+
+ align:start position:0%
+something in a visually arresting way to
+ 
+
+ align:start position:0%
+something in a visually arresting way to
+an a general audience that would sort of
+
+ align:start position:0%
+an a general audience that would sort of
+ 
+
+ align:start position:0%
+an a general audience that would sort of
+really make the point that they're
+
+ align:start position:0%
+really make the point that they're
+ 
+
+ align:start position:0%
+really make the point that they're
+talking about you know in terms of
+
+ align:start position:0%
+talking about you know in terms of
+ 
+
+ align:start position:0%
+talking about you know in terms of
+frames of reference and I mean it is
+
+ align:start position:0%
+frames of reference and I mean it is
+ 
+
+ align:start position:0%
+frames of reference and I mean it is
+kind of a brilliant way to get into it
+
+ align:start position:0%
+kind of a brilliant way to get into it
+ 
+
+ align:start position:0%
+kind of a brilliant way to get into it
+and it takes an incredible amount of
+
+ align:start position:0%
+and it takes an incredible amount of
+ 
+
+ align:start position:0%
+and it takes an incredible amount of
+work I mean you think about how much
+
+ align:start position:0%
+work I mean you think about how much
+ 
+
+ align:start position:0%
+work I mean you think about how much
+work they put into as Chris said setting
+
+ align:start position:0%
+work they put into as Chris said setting
+ 
+
+ align:start position:0%
+work they put into as Chris said setting
+up all of these rigs to actually convey
+
+ align:start position:0%
+up all of these rigs to actually convey
+ 
+
+ align:start position:0%
+up all of these rigs to actually convey
+that but you know the kind of
+
+ align:start position:0%
+that but you know the kind of
+ 
+
+ align:start position:0%
+that but you know the kind of
+forethought that goes into well how do
+
+ align:start position:0%
+forethought that goes into well how do
+ 
+
+ align:start position:0%
+forethought that goes into well how do
+you convey what you want to convey
+
+ align:start position:0%
+you convey what you want to convey
+ 
+
+ align:start position:0%
+you convey what you want to convey
+um if you want to educate someone about
+
+ align:start position:0%
+um if you want to educate someone about
+ 
+
+ align:start position:0%
+um if you want to educate someone about
+these kinds of Concepts how would you
+
+ align:start position:0%
+these kinds of Concepts how would you
+ 
+
+ align:start position:0%
+these kinds of Concepts how would you
+translate that into visual
+
+ align:start position:0%
+translate that into visual
+ 
+
+ align:start position:0%
+translate that into visual
+terms and the sort of way certain visual
+
+ align:start position:0%
+terms and the sort of way certain visual
+ 
+
+ align:start position:0%
+terms and the sort of way certain visual
+images persist uh everybody who sees
+
+ align:start position:0%
+images persist uh everybody who sees
+ 
+
+ align:start position:0%
+images persist uh everybody who sees
+this film remembers that beginning you
+
+ align:start position:0%
+this film remembers that beginning you
+ 
+
+ align:start position:0%
+this film remembers that beginning you
+may not remember anything else but
+
+ align:start position:0%
+may not remember anything else but
+ 
+
+ align:start position:0%
+may not remember anything else but
+everybody remembers that that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+opening very effective because um it
+
+ align:start position:0%
+opening very effective because um it
+ 
+
+ align:start position:0%
+opening very effective because um it
+it's effective because the first thing
+
+ align:start position:0%
+it's effective because the first thing
+ 
+
+ align:start position:0%
+it's effective because the first thing
+because you I mean if now we see
+
+ align:start position:0%
+because you I mean if now we see
+ 
+
+ align:start position:0%
+because you I mean if now we see
+something like that we wouldn't think
+
+ align:start position:0%
+something like that we wouldn't think
+ 
+
+ align:start position:0%
+something like that we wouldn't think
+that that's actual if that's real we
+
+ align:start position:0%
+that that's actual if that's real we
+ 
+
+ align:start position:0%
+that that's actual if that's real we
+think that's just a trick but I could I
+
+ align:start position:0%
+think that's just a trick but I could I
+ 
+
+ align:start position:0%
+think that's just a trick but I could I
+was I was confused I was like um but it
+
+ align:start position:0%
+was I was confused I was like um but it
+ 
+
+ align:start position:0%
+was I was confused I was like um but it
+doesn't it's say old it can't be
+
+ align:start position:0%
+doesn't it's say old it can't be
+ 
+
+ align:start position:0%
+doesn't it's say old it can't be
+trick what are they doing right exactly
+
+ align:start position:0%
+trick what are they doing right exactly
+ 
+
+ align:start position:0%
+trick what are they doing right exactly
+yeah I think that's because this is old
+
+ align:start position:0%
+yeah I think that's because this is old
+ 
+
+ align:start position:0%
+yeah I think that's because this is old
+so you wouldn't expect it but like right
+
+ align:start position:0%
+so you wouldn't expect it but like right
+ 
+
+ align:start position:0%
+so you wouldn't expect it but like right
+now you're somebody something so okay
+
+ align:start position:0%
+now you're somebody something so okay
+ 
+
+ align:start position:0%
+now you're somebody something so okay
+whatever right true enough it wouldn't
+
+ align:start position:0%
+whatever right true enough it wouldn't
+ 
+
+ align:start position:0%
+whatever right true enough it wouldn't
+carry quite the same cache today it's
+
+ align:start position:0%
+carry quite the same cache today it's
+ 
+
+ align:start position:0%
+carry quite the same cache today it's
+true well that's why even then I mean
+
+ align:start position:0%
+true well that's why even then I mean
+ 
+
+ align:start position:0%
+true well that's why even then I mean
+they they had sort of
+
+ align:start position:0%
+they they had sort of
+ 
+
+ align:start position:0%
+they they had sort of
+some ability to manipulate space and do
+
+ align:start position:0%
+some ability to manipulate space and do
+ 
+
+ align:start position:0%
+some ability to manipulate space and do
+do composits and so on but that's why
+
+ align:start position:0%
+do composits and so on but that's why
+ 
+
+ align:start position:0%
+do composits and so on but that's why
+you have to pull out and see the quarter
+
+ align:start position:0%
+you have to pull out and see the quarter
+ 
+
+ align:start position:0%
+you have to pull out and see the quarter
+fall and see them flip around it it's
+
+ align:start position:0%
+fall and see them flip around it it's
+ 
+
+ align:start position:0%
+fall and see them flip around it it's
+it's very much uh a magician showing you
+
+ align:start position:0%
+it's very much uh a magician showing you
+ 
+
+ align:start position:0%
+it's very much uh a magician showing you
+how it's done rather than just having it
+
+ align:start position:0%
+how it's done rather than just having it
+ 
+
+ align:start position:0%
+how it's done rather than just having it
+stay magic I me this um very simple
+
+ align:start position:0%
+stay magic I me this um very simple
+ 
+
+ align:start position:0%
+stay magic I me this um very simple
+comment the fact that they're talken to
+
+ align:start position:0%
+comment the fact that they're talken to
+ 
+
+ align:start position:0%
+comment the fact that they're talken to
+you and that you are at the same time
+
+ align:start position:0%
+you and that you are at the same time
+ 
+
+ align:start position:0%
+you and that you are at the same time
+encouraged to watch the the film but
+
+ align:start position:0%
+encouraged to watch the the film but
+ 
+
+ align:start position:0%
+encouraged to watch the the film but
+also watching what's happening in the
+
+ align:start position:0%
+also watching what's happening in the
+ 
+
+ align:start position:0%
+also watching what's happening in the
+film and I think these are two different
+
+ align:start position:0%
+film and I think these are two different
+ 
+
+ align:start position:0%
+film and I think these are two different
+things and it's it's um definitely an
+
+ align:start position:0%
+things and it's it's um definitely an
+ 
+
+ align:start position:0%
+things and it's it's um definitely an
+effective uh educational strategy it's
+
+ align:start position:0%
+effective uh educational strategy it's
+ 
+
+ align:start position:0%
+effective uh educational strategy it's
+it's also kind of it's obvious but it's
+
+ align:start position:0%
+it's also kind of it's obvious but it's
+ 
+
+ align:start position:0%
+it's also kind of it's obvious but it's
+sort of worth saying that it's an
+
+ align:start position:0%
+sort of worth saying that it's an
+ 
+
+ align:start position:0%
+sort of worth saying that it's an
+interesting example of the camera is you
+
+ align:start position:0%
+interesting example of the camera is you
+ 
+
+ align:start position:0%
+interesting example of the camera is you
+it's I mean of course they're talking to
+
+ align:start position:0%
+it's I mean of course they're talking to
+ 
+
+ align:start position:0%
+it's I mean of course they're talking to
+the camera but it's also right along on
+
+ align:start position:0%
+the camera but it's also right along on
+ 
+
+ align:start position:0%
+the camera but it's also right along on
+the cart and the camera goes on the cart
+
+ align:start position:0%
+the cart and the camera goes on the cart
+ 
+
+ align:start position:0%
+the cart and the camera goes on the cart
+and then you're on the cart you are the
+
+ align:start position:0%
+and then you're on the cart you are the
+ 
+
+ align:start position:0%
+and then you're on the cart you are the
+camera you're the audience but not
+
+ align:start position:0%
+camera you're the audience but not
+ 
+
+ align:start position:0%
+camera you're the audience but not
+always because you are a different
+
+ align:start position:0%
+always because you are a different
+ 
+
+ align:start position:0%
+always because you are a different
+camera sometimes so you see the camera
+
+ align:start position:0%
+camera sometimes so you see the camera
+ 
+
+ align:start position:0%
+camera sometimes so you see the camera
+and then you enter and then you become
+
+ align:start position:0%
+and then you enter and then you become
+ 
+
+ align:start position:0%
+and then you enter and then you become
+that camera yes you do switch sometimes
+
+ align:start position:0%
+that camera yes you do switch sometimes
+ 
+
+ align:start position:0%
+that camera yes you do switch sometimes
+you're in a different camera yeah that's
+
+ align:start position:0%
+you're in a different camera yeah that's
+ 
+
+ align:start position:0%
+you're in a different camera yeah that's
+true oh so I was going to say it also on
+
+ align:start position:0%
+true oh so I was going to say it also on
+ 
+
+ align:start position:0%
+true oh so I was going to say it also on
+that point it's also interesting that um
+
+ align:start position:0%
+that point it's also interesting that um
+ 
+
+ align:start position:0%
+that point it's also interesting that um
+like throughout the whole piece you like
+
+ align:start position:0%
+like throughout the whole piece you like
+ 
+
+ align:start position:0%
+like throughout the whole piece you like
+from the very after the first scene then
+
+ align:start position:0%
+from the very after the first scene then
+ 
+
+ align:start position:0%
+from the very after the first scene then
+you start thinking oh I'm going to be
+
+ align:start position:0%
+you start thinking oh I'm going to be
+ 
+
+ align:start position:0%
+you start thinking oh I'm going to be
+tricked I need to like pay attention you
+
+ align:start position:0%
+tricked I need to like pay attention you
+ 
+
+ align:start position:0%
+tricked I need to like pay attention you
+know think about like what's what's
+
+ align:start position:0%
+know think about like what's what's
+ 
+
+ align:start position:0%
+know think about like what's what's
+happening and I think that's also really
+
+ align:start position:0%
+happening and I think that's also really
+ 
+
+ align:start position:0%
+happening and I think that's also really
+effective in engaging the audience and
+
+ align:start position:0%
+effective in engaging the audience and
+ 
+
+ align:start position:0%
+effective in engaging the audience and
+then it also just makes it really
+
+ align:start position:0%
+then it also just makes it really
+ 
+
+ align:start position:0%
+then it also just makes it really
+interesting I think because you're like
+
+ align:start position:0%
+interesting I think because you're like
+ 
+
+ align:start position:0%
+interesting I think because you're like
+it's kind of like a puzzle you have to
+
+ align:start position:0%
+it's kind of like a puzzle you have to
+ 
+
+ align:start position:0%
+it's kind of like a puzzle you have to
+try to figure out okay what are they
+
+ align:start position:0%
+try to figure out okay what are they
+ 
+
+ align:start position:0%
+try to figure out okay what are they
+going to do next like I can't be tripped
+
+ align:start position:0%
+going to do next like I can't be tripped
+ 
+
+ align:start position:0%
+going to do next like I can't be tripped
+yeah well and you think think back to to
+
+ align:start position:0%
+yeah well and you think think back to to
+ 
+
+ align:start position:0%
+yeah well and you think think back to to
+flarity again when he was a doing the
+
+ align:start position:0%
+flarity again when he was a doing the
+ 
+
+ align:start position:0%
+flarity again when he was a doing the
+igloo and and when nanuk does the window
+
+ align:start position:0%
+igloo and and when nanuk does the window
+ 
+
+ align:start position:0%
+igloo and and when nanuk does the window
+and he doesn't tell you immediately
+
+ align:start position:0%
+and he doesn't tell you immediately
+ 
+
+ align:start position:0%
+and he doesn't tell you immediately
+what's going on you're supposed to watch
+
+ align:start position:0%
+what's going on you're supposed to watch
+ 
+
+ align:start position:0%
+what's going on you're supposed to watch
+and figure it out so that's one of the
+
+ align:start position:0%
+and figure it out so that's one of the
+ 
+
+ align:start position:0%
+and figure it out so that's one of the
+things that filmmakers do use very
+
+ align:start position:0%
+things that filmmakers do use very
+ 
+
+ align:start position:0%
+things that filmmakers do use very
+effectively to pull audiences in is to
+
+ align:start position:0%
+effectively to pull audiences in is to
+ 
+
+ align:start position:0%
+effectively to pull audiences in is to
+allow allow the audience to be able to
+
+ align:start position:0%
+allow allow the audience to be able to
+ 
+
+ align:start position:0%
+allow allow the audience to be able to
+discover things through the process of
+
+ align:start position:0%
+discover things through the process of
+ 
+
+ align:start position:0%
+discover things through the process of
+film making without just telling them
+
+ align:start position:0%
+film making without just telling them
+ 
+
+ align:start position:0%
+film making without just telling them
+everything or the idea here that you
+
+ align:start position:0%
+everything or the idea here that you
+ 
+
+ align:start position:0%
+everything or the idea here that you
+better pay attention because there's
+
+ align:start position:0%
+better pay attention because there's
+ 
+
+ align:start position:0%
+better pay attention because there's
+going to be something G to be going on
+
+ align:start position:0%
+going to be something G to be going on
+ 
+
+ align:start position:0%
+going to be something G to be going on
+there's going to be some kind of trick
+
+ align:start position:0%
+there's going to be some kind of trick
+ 
+
+ align:start position:0%
+there's going to be some kind of trick
+involved or you know as again a how do
+
+ align:start position:0%
+involved or you know as again a how do
+ 
+
+ align:start position:0%
+involved or you know as again a how do
+you engage your your audience and get
+
+ align:start position:0%
+you engage your your audience and get
+ 
+
+ align:start position:0%
+you engage your your audience and get
+them and get them emotionally involved
+
+ align:start position:0%
+them and get them emotionally involved
+ 
+
+ align:start position:0%
+them and get them emotionally involved
+in what's going on and sometimes
+
+ align:start position:0%
+in what's going on and sometimes
+ 
+
+ align:start position:0%
+in what's going on and sometimes
+revealing is the way to do it and
+
+ align:start position:0%
+revealing is the way to do it and
+ 
+
+ align:start position:0%
+revealing is the way to do it and
+sometimes not revealing certain things
+
+ align:start position:0%
+sometimes not revealing certain things
+ 
+
+ align:start position:0%
+sometimes not revealing certain things
+can be the way to do it making it like a
+
+ align:start position:0%
+can be the way to do it making it like a
+ 
+
+ align:start position:0%
+can be the way to do it making it like a
+puzzle as you said as you said yeah
+
+ align:start position:0%
+puzzle as you said as you said yeah
+ 
+
+ align:start position:0%
+puzzle as you said as you said yeah
+exactly making it like a puzzle
+
+ align:start position:0%
+exactly making it like a puzzle
+ 
+
+ align:start position:0%
+exactly making it like a puzzle
+um and then just one one last thing that
+
+ align:start position:0%
+um and then just one one last thing that
+ 
+
+ align:start position:0%
+um and then just one one last thing that
+I uh another very small thing that I
+
+ align:start position:0%
+I uh another very small thing that I
+ 
+
+ align:start position:0%
+I uh another very small thing that I
+think is cool um we talked in the first
+
+ align:start position:0%
+think is cool um we talked in the first
+ 
+
+ align:start position:0%
+think is cool um we talked in the first
+class about the plastic elements of film
+
+ align:start position:0%
+class about the plastic elements of film
+ 
+
+ align:start position:0%
+class about the plastic elements of film
+and all of the different things you can
+
+ align:start position:0%
+and all of the different things you can
+ 
+
+ align:start position:0%
+and all of the different things you can
+change and techniques you can use and
+
+ align:start position:0%
+change and techniques you can use and
+ 
+
+ align:start position:0%
+change and techniques you can use and
+obviously there's a lot of interesting
+
+ align:start position:0%
+obviously there's a lot of interesting
+ 
+
+ align:start position:0%
+obviously there's a lot of interesting
+rigging going on here and and camera
+
+ align:start position:0%
+rigging going on here and and camera
+ 
+
+ align:start position:0%
+rigging going on here and and camera
+techniques um but one very simple thing
+
+ align:start position:0%
+techniques um but one very simple thing
+ 
+
+ align:start position:0%
+techniques um but one very simple thing
+that I think is is kind of effective in
+
+ align:start position:0%
+that I think is is kind of effective in
+ 
+
+ align:start position:0%
+that I think is is kind of effective in
+a in a good way is this prop that they
+
+ align:start position:0%
+a in a good way is this prop that they
+ 
+
+ align:start position:0%
+a in a good way is this prop that they
+have with the X Y and Z axis and so to
+
+ align:start position:0%
+have with the X Y and Z axis and so to
+ 
+
+ align:start position:0%
+have with the X Y and Z axis and so to
+show you what frame of reference you're
+
+ align:start position:0%
+show you what frame of reference you're
+ 
+
+ align:start position:0%
+show you what frame of reference you're
+going to be in next they put it on the
+
+ align:start position:0%
+going to be in next they put it on the
+ 
+
+ align:start position:0%
+going to be in next they put it on the
+cart they put it on the table and it's
+
+ align:start position:0%
+cart they put it on the table and it's
+ 
+
+ align:start position:0%
+cart they put it on the table and it's
+just a very very simple prop it's a very
+
+ align:start position:0%
+just a very very simple prop it's a very
+ 
+
+ align:start position:0%
+just a very very simple prop it's a very
+simple idea but it really works because
+
+ align:start position:0%
+simple idea but it really works because
+ 
+
+ align:start position:0%
+simple idea but it really works because
+it kind of prepares you for the next
+
+ align:start position:0%
+it kind of prepares you for the next
+ 
+
+ align:start position:0%
+it kind of prepares you for the next
+sort of world you're going to enter with
+
+ align:start position:0%
+sort of world you're going to enter with
+ 
+
+ align:start position:0%
+sort of world you're going to enter with
+as the camera um and it's just a nice
+
+ align:start position:0%
+as the camera um and it's just a nice
+ 
+
+ align:start position:0%
+as the camera um and it's just a nice
+use of of a prop as a plastic element
+
+ align:start position:0%
+use of of a prop as a plastic element
+ 
+
+ align:start position:0%
+use of of a prop as a plastic element
+you could have made the film without it
+
+ align:start position:0%
+you could have made the film without it
+ 
+
+ align:start position:0%
+you could have made the film without it
+but it would have just been that much
+
+ align:start position:0%
+but it would have just been that much
+ 
+
+ align:start position:0%
+but it would have just been that much
+more slightly confusing as to what frame
+
+ align:start position:0%
+more slightly confusing as to what frame
+ 
+
+ align:start position:0%
+more slightly confusing as to what frame
+of reference you were actually in and so
+
+ align:start position:0%
+of reference you were actually in and so
+ 
+
+ align:start position:0%
+of reference you were actually in and so
+if you you end up for your final
+
+ align:start position:0%
+if you you end up for your final
+ 
+
+ align:start position:0%
+if you you end up for your final
+projects end up doing a film on a
+
+ align:start position:0%
+projects end up doing a film on a
+ 
+
+ align:start position:0%
+projects end up doing a film on a
+project where you want to
+
+ align:start position:0%
+project where you want to
+ 
+
+ align:start position:0%
+project where you want to
+convey um you know some of the the ideas
+
+ align:start position:0%
+convey um you know some of the the ideas
+ 
+
+ align:start position:0%
+convey um you know some of the the ideas
+behind um the science or whatever it is
+
+ align:start position:0%
+behind um the science or whatever it is
+ 
+
+ align:start position:0%
+behind um the science or whatever it is
+that that you're going to be doing your
+
+ align:start position:0%
+that that you're going to be doing your
+ 
+
+ align:start position:0%
+that that you're going to be doing your
+work on um if it ends up being a a topic
+
+ align:start position:0%
+work on um if it ends up being a a topic
+ 
+
+ align:start position:0%
+work on um if it ends up being a a topic
+some kind of topic like this it becomes
+
+ align:start position:0%
+some kind of topic like this it becomes
+ 
+
+ align:start position:0%
+some kind of topic like this it becomes
+one of the questions becomes how do you
+
+ align:start position:0%
+one of the questions becomes how do you
+ 
+
+ align:start position:0%
+one of the questions becomes how do you
+convey things in a way that's both
+
+ align:start position:0%
+convey things in a way that's both
+ 
+
+ align:start position:0%
+convey things in a way that's both
+accurate and insightful and compelling
+
+ align:start position:0%
+accurate and insightful and compelling
+ 
+
+ align:start position:0%
+accurate and insightful and compelling
+to the viewer right so how do you be
+
+ align:start position:0%
+to the viewer right so how do you be
+ 
+
+ align:start position:0%
+to the viewer right so how do you be
+accurate to the science of what you're
+
+ align:start position:0%
+accurate to the science of what you're
+ 
+
+ align:start position:0%
+accurate to the science of what you're
+trying to convey how do you do it in a
+
+ align:start position:0%
+trying to convey how do you do it in a
+ 
+
+ align:start position:0%
+trying to convey how do you do it in a
+way that's insightful that allows the
+
+ align:start position:0%
+way that's insightful that allows the
+ 
+
+ align:start position:0%
+way that's insightful that allows the
+audience to go ah aha I got I got that
+
+ align:start position:0%
+audience to go ah aha I got I got that
+ 
+
+ align:start position:0%
+audience to go ah aha I got I got that
+and that and that pulls them in and that
+
+ align:start position:0%
+and that and that pulls them in and that
+ 
+
+ align:start position:0%
+and that and that pulls them in and that
+and that's tricky that's not that's not
+
+ align:start position:0%
+and that's tricky that's not that's not
+ 
+
+ align:start position:0%
+and that's tricky that's not that's not
+an easy thing to do and it it requires a
+
+ align:start position:0%
+an easy thing to do and it it requires a
+ 
+
+ align:start position:0%
+an easy thing to do and it it requires a
+you know fair amount of thinking about
+
+ align:start position:0%
+you know fair amount of thinking about
+ 
+
+ align:start position:0%
+you know fair amount of thinking about
+how you want to go about doing
+
+ align:start position:0%
+how you want to go about doing
+ 
+
+ align:start position:0%
+how you want to go about doing
+it um and so okay so this kind of
+
+ align:start position:0%
+it um and so okay so this kind of
+ 
+
+ align:start position:0%
+it um and so okay so this kind of
+educational video obviously is from the
+
+ align:start position:0%
+educational video obviously is from the
+ 
+
+ align:start position:0%
+educational video obviously is from the
+point of view of the scientist wanting
+
+ align:start position:0%
+point of view of the scientist wanting
+ 
+
+ align:start position:0%
+point of view of the scientist wanting
+to convey and to educate and I mentioned
+
+ align:start position:0%
+to convey and to educate and I mentioned
+ 
+
+ align:start position:0%
+to convey and to educate and I mentioned
+also uh you have to think about these
+
+ align:start position:0%
+also uh you have to think about these
+ 
+
+ align:start position:0%
+also uh you have to think about these
+questions also from the point of view of
+
+ align:start position:0%
+questions also from the point of view of
+ 
+
+ align:start position:0%
+questions also from the point of view of
+the filmmaker so again from the
+
+ align:start position:0%
+the filmmaker so again from the
+ 
+
+ align:start position:0%
+the filmmaker so again from the
+filmmaker how do you convey things in a
+
+ align:start position:0%
+filmmaker how do you convey things in a
+ 
+
+ align:start position:0%
+filmmaker how do you convey things in a
+way that's and obviously well we're
+
+ align:start position:0%
+way that's and obviously well we're
+ 
+
+ align:start position:0%
+way that's and obviously well we're
+talking about that here too with Ricky
+
+ align:start position:0%
+talking about that here too with Ricky
+ 
+
+ align:start position:0%
+talking about that here too with Ricky
+Leck how did he you know you know
+
+ align:start position:0%
+Leck how did he you know you know
+ 
+
+ align:start position:0%
+Leck how did he you know you know
+presumably He was discussing with the
+
+ align:start position:0%
+presumably He was discussing with the
+ 
+
+ align:start position:0%
+presumably He was discussing with the
+scientists about the physicists about
+
+ align:start position:0%
+scientists about the physicists about
+ 
+
+ align:start position:0%
+scientists about the physicists about
+how do exactly do we want to convey this
+
+ align:start position:0%
+how do exactly do we want to convey this
+ 
+
+ align:start position:0%
+how do exactly do we want to convey this
+in a way that's compelling um but we're
+
+ align:start position:0%
+in a way that's compelling um but we're
+ 
+
+ align:start position:0%
+in a way that's compelling um but we're
+going to be talking later in class uh
+
+ align:start position:0%
+going to be talking later in class uh
+ 
+
+ align:start position:0%
+going to be talking later in class uh
+when we get to Errol Morris and some of
+
+ align:start position:0%
+when we get to Errol Morris and some of
+ 
+
+ align:start position:0%
+when we get to Errol Morris and some of
+the other things about four filmmakers
+
+ align:start position:0%
+the other things about four filmmakers
+ 
+
+ align:start position:0%
+the other things about four filmmakers
+making films about science and
+
+ align:start position:0%
+making films about science and
+ 
+
+ align:start position:0%
+making films about science and
+scientists what kinds of narratives do
+
+ align:start position:0%
+scientists what kinds of narratives do
+ 
+
+ align:start position:0%
+scientists what kinds of narratives do
+they want to draw on again as a way to
+
+ align:start position:0%
+they want to draw on again as a way to
+ 
+
+ align:start position:0%
+they want to draw on again as a way to
+pull people in so we're going to come
+
+ align:start position:0%
+pull people in so we're going to come
+ 
+
+ align:start position:0%
+pull people in so we're going to come
+back to those kinds of of questions a
+
+ align:start position:0%
+back to those kinds of of questions a
+ 
+
+ align:start position:0%
+back to those kinds of of questions a
+little bit later in the class um but the
+
+ align:start position:0%
+little bit later in the class um but the
+ 
+
+ align:start position:0%
+little bit later in the class um but the
+third thing that we want to uh talk
+
+ align:start position:0%
+third thing that we want to uh talk
+ 
+
+ align:start position:0%
+third thing that we want to uh talk
+about in today's class a third major use
+
+ align:start position:0%
+about in today's class a third major use
+ 
+
+ align:start position:0%
+about in today's class a third major use
+of Science and documentary um is to
+
+ align:start position:0%
+of Science and documentary um is to
+ 
+
+ align:start position:0%
+of Science and documentary um is to
+satisfy partly po popular fascination
+
+ align:start position:0%
+satisfy partly po popular fascination
+ 
+
+ align:start position:0%
+satisfy partly po popular fascination
+with science I and again you know all
+
+ align:start position:0%
+with science I and again you know all
+ 
+
+ align:start position:0%
+with science I and again you know all
+these things can over can overlap too so
+
+ align:start position:0%
+these things can over can overlap too so
+ 
+
+ align:start position:0%
+these things can over can overlap too so
+the educational aspect can overlap with
+
+ align:start position:0%
+the educational aspect can overlap with
+ 
+
+ align:start position:0%
+the educational aspect can overlap with
+sort of the the popular interest um with
+
+ align:start position:0%
+sort of the the popular interest um with
+ 
+
+ align:start position:0%
+sort of the the popular interest um with
+popular interest in science
+
+ align:start position:0%
+popular interest in science
+ 
+
+ align:start position:0%
+popular interest in science
+um and again around this question sum
+
+ align:start position:0%
+um and again around this question sum
+ 
+
+ align:start position:0%
+um and again around this question sum
+what are the what are some of the
+
+ align:start position:0%
+what are the what are some of the
+ 
+
+ align:start position:0%
+what are the what are some of the
+stories that audiences find fascinating
+
+ align:start position:0%
+stories that audiences find fascinating
+ 
+
+ align:start position:0%
+stories that audiences find fascinating
+and want to hear about science and and
+
+ align:start position:0%
+and want to hear about science and and
+ 
+
+ align:start position:0%
+and want to hear about science and and
+uh Chris and I had spent some time sort
+
+ align:start position:0%
+uh Chris and I had spent some time sort
+ 
+
+ align:start position:0%
+uh Chris and I had spent some time sort
+of trying to think through what are some
+
+ align:start position:0%
+of trying to think through what are some
+ 
+
+ align:start position:0%
+of trying to think through what are some
+of the various
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ways can I have a chalk
+
+ align:start position:0%
+ways can I have a chalk
+ 
+
+ align:start position:0%
+ways can I have a chalk
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way think it's supposed to go that way
+
+ align:start position:0%
+way think it's supposed to go that way
+ 
+
+ align:start position:0%
+way think it's supposed to go that way
+the other board down
+
+ align:start position:0%
+the other board down
+ 
+
+ align:start position:0%
+the other board down
+anyway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so again this question of what are
+
+ align:start position:0%
+um so again this question of what are
+ 
+
+ align:start position:0%
+um so again this question of what are
+some of the stories um that audiences
+
+ align:start position:0%
+some of the stories um that audiences
+ 
+
+ align:start position:0%
+some of the stories um that audiences
+find fascinating want to hear and hear
+
+ align:start position:0%
+find fascinating want to hear and hear
+ 
+
+ align:start position:0%
+find fascinating want to hear and hear
+about science we've talked about some of
+
+ align:start position:0%
+about science we've talked about some of
+ 
+
+ align:start position:0%
+about science we've talked about some of
+these before there's the element of
+
+ align:start position:0%
+these before there's the element of
+ 
+
+ align:start position:0%
+these before there's the element of
+spectacle um and again think about IMAX
+
+ align:start position:0%
+spectacle um and again think about IMAX
+ 
+
+ align:start position:0%
+spectacle um and again think about IMAX
+movies where sort of again the science
+
+ align:start position:0%
+movies where sort of again the science
+ 
+
+ align:start position:0%
+movies where sort of again the science
+is a way to see things about the world
+
+ align:start position:0%
+is a way to see things about the world
+ 
+
+ align:start position:0%
+is a way to see things about the world
+in the way we wouldn't do it before in
+
+ align:start position:0%
+in the way we wouldn't do it before in
+ 
+
+ align:start position:0%
+in the way we wouldn't do it before in
+particularly in ways that are sort of uh
+
+ align:start position:0%
+particularly in ways that are sort of uh
+ 
+
+ align:start position:0%
+particularly in ways that are sort of uh
+very much visually arresting and sort of
+
+ align:start position:0%
+very much visually arresting and sort of
+ 
+
+ align:start position:0%
+very much visually arresting and sort of
+you know influencing people on a kind of
+
+ align:start position:0%
+you know influencing people on a kind of
+ 
+
+ align:start position:0%
+you know influencing people on a kind of
+physical level so so spectacle like IMAX
+
+ align:start position:0%
+physical level so so spectacle like IMAX
+ 
+
+ align:start position:0%
+physical level so so spectacle like IMAX
+movies or flies juggling balls flies
+
+ align:start position:0%
+movies or flies juggling balls flies
+ 
+
+ align:start position:0%
+movies or flies juggling balls flies
+juggling balls as we as we saw earlier
+
+ align:start position:0%
+juggling balls as we as we saw earlier
+ 
+
+ align:start position:0%
+juggling balls as we as we saw earlier
+um another narrative that audiences are
+
+ align:start position:0%
+um another narrative that audiences are
+ 
+
+ align:start position:0%
+um another narrative that audiences are
+often interested in is science is hero
+
+ align:start position:0%
+often interested in is science is hero
+ 
+
+ align:start position:0%
+often interested in is science is hero
+scientist is hero
+
+ align:start position:0%
+scientist is hero
+ 
+
+ align:start position:0%
+scientist is hero
+so um so there's often a fascination
+
+ align:start position:0%
+so um so there's often a fascination
+ 
+
+ align:start position:0%
+so um so there's often a fascination
+with um scientists and thinking about
+
+ align:start position:0%
+with um scientists and thinking about
+ 
+
+ align:start position:0%
+with um scientists and thinking about
+well how did a scientist sort of
+
+ align:start position:0%
+well how did a scientist sort of
+ 
+
+ align:start position:0%
+well how did a scientist sort of
+heroically go off and discover something
+
+ align:start position:0%
+heroically go off and discover something
+ 
+
+ align:start position:0%
+heroically go off and discover something
+for example that had had a strong impact
+
+ align:start position:0%
+for example that had had a strong impact
+ 
+
+ align:start position:0%
+for example that had had a strong impact
+upon the world so that's a a a common
+
+ align:start position:0%
+upon the world so that's a a a common
+ 
+
+ align:start position:0%
+upon the world so that's a a a common
+kind of narrative that audiences are
+
+ align:start position:0%
+kind of narrative that audiences are
+ 
+
+ align:start position:0%
+kind of narrative that audiences are
+interested in another one is science's
+
+ align:start position:0%
+interested in another one is science's
+ 
+
+ align:start position:0%
+interested in another one is science's
+detective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+story right where audiences are often
+
+ align:start position:0%
+story right where audiences are often
+ 
+
+ align:start position:0%
+story right where audiences are often
+fascinated with how do things get
+
+ align:start position:0%
+fascinated with how do things get
+ 
+
+ align:start position:0%
+fascinated with how do things get
+figured out thinking of it like a
+
+ align:start position:0%
+figured out thinking of it like a
+ 
+
+ align:start position:0%
+figured out thinking of it like a
+detective story some people are
+
+ align:start position:0%
+detective story some people are
+ 
+
+ align:start position:0%
+detective story some people are
+interested in thinking about science in
+
+ align:start position:0%
+interested in thinking about science in
+ 
+
+ align:start position:0%
+interested in thinking about science in
+terms of
+
+ align:start position:0%
+terms of
+ 
+
+ align:start position:0%
+terms of
+um what's the relationship between
+
+ align:start position:0%
+um what's the relationship between
+ 
+
+ align:start position:0%
+um what's the relationship between
+reason and and emotion um with science
+
+ align:start position:0%
+reason and and emotion um with science
+ 
+
+ align:start position:0%
+reason and and emotion um with science
+often you know sort of stereotyped as
+
+ align:start position:0%
+often you know sort of stereotyped as
+ 
+
+ align:start position:0%
+often you know sort of stereotyped as
+sort of you know this being solely about
+
+ align:start position:0%
+sort of you know this being solely about
+ 
+
+ align:start position:0%
+sort of you know this being solely about
+reason and and what are the kind of
+
+ align:start position:0%
+reason and and what are the kind of
+ 
+
+ align:start position:0%
+reason and and what are the kind of
+quandaries when it comes up against
+
+ align:start position:0%
+quandaries when it comes up against
+ 
+
+ align:start position:0%
+quandaries when it comes up against
+emotion and obviously the quintessential
+
+ align:start position:0%
+emotion and obviously the quintessential
+ 
+
+ align:start position:0%
+emotion and obviously the quintessential
+example of this is the early Star Trek
+
+ align:start position:0%
+example of this is the early Star Trek
+ 
+
+ align:start position:0%
+example of this is the early Star Trek
+movies where you have Spock right I mean
+
+ align:start position:0%
+movies where you have Spock right I mean
+ 
+
+ align:start position:0%
+movies where you have Spock right I mean
+so Spock is all about the tension
+
+ align:start position:0%
+so Spock is all about the tension
+ 
+
+ align:start position:0%
+so Spock is all about the tension
+between you know trying to be solely
+
+ align:start position:0%
+between you know trying to be solely
+ 
+
+ align:start position:0%
+between you know trying to be solely
+about reason but you know having
+
+ align:start position:0%
+about reason but you know having
+ 
+
+ align:start position:0%
+about reason but you know having
+emotional feelings at the same time and
+
+ align:start position:0%
+emotional feelings at the same time and
+ 
+
+ align:start position:0%
+emotional feelings at the same time and
+how does he deal with that kind of
+
+ align:start position:0%
+how does he deal with that kind of
+ 
+
+ align:start position:0%
+how does he deal with that kind of
+relationship and and often those kinds
+
+ align:start position:0%
+relationship and and often those kinds
+ 
+
+ align:start position:0%
+relationship and and often those kinds
+of uh quandaries uh get talked about in
+
+ align:start position:0%
+of uh quandaries uh get talked about in
+ 
+
+ align:start position:0%
+of uh quandaries uh get talked about in
+popular culture through a science figure
+
+ align:start position:0%
+popular culture through a science figure
+ 
+
+ align:start position:0%
+popular culture through a science figure
+in there somewhere um man there too many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cords
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then there's also an in an
+
+ align:start position:0%
+okay and then there's also an in an
+ 
+
+ align:start position:0%
+okay and then there's also an in an
+interest in sort of science almost for
+
+ align:start position:0%
+interest in sort of science almost for
+ 
+
+ align:start position:0%
+interest in sort of science almost for
+the bizarre where science itself becomes
+
+ align:start position:0%
+the bizarre where science itself becomes
+ 
+
+ align:start position:0%
+the bizarre where science itself becomes
+kind of a science fiction about like wow
+
+ align:start position:0%
+kind of a science fiction about like wow
+ 
+
+ align:start position:0%
+kind of a science fiction about like wow
+look at this crazy stuff that science is
+
+ align:start position:0%
+look at this crazy stuff that science is
+ 
+
+ align:start position:0%
+look at this crazy stuff that science is
+up to it's it's even crazier than than
+
+ align:start position:0%
+up to it's it's even crazier than than
+ 
+
+ align:start position:0%
+up to it's it's even crazier than than
+actual Science Fiction it's it's so
+
+ align:start position:0%
+actual Science Fiction it's it's so
+ 
+
+ align:start position:0%
+actual Science Fiction it's it's so
+crazy you couldn't even make it up I
+
+ align:start position:0%
+crazy you couldn't even make it up I
+ 
+
+ align:start position:0%
+crazy you couldn't even make it up I
+mean you've heard that kind of line
+
+ align:start position:0%
+mean you've heard that kind of line
+ 
+
+ align:start position:0%
+mean you've heard that kind of line
+often I think in popular discussions
+
+ align:start position:0%
+often I think in popular discussions
+ 
+
+ align:start position:0%
+often I think in popular discussions
+about science so a kind of fascination
+
+ align:start position:0%
+about science so a kind of fascination
+ 
+
+ align:start position:0%
+about science so a kind of fascination
+with science about you know how um
+
+ align:start position:0%
+with science about you know how um
+ 
+
+ align:start position:0%
+with science about you know how um
+strange and odd it can be even Stranger
+
+ align:start position:0%
+strange and odd it can be even Stranger
+ 
+
+ align:start position:0%
+strange and odd it can be even Stranger
+Than things that could be made up so
+
+ align:start position:0%
+Than things that could be made up so
+ 
+
+ align:start position:0%
+Than things that could be made up so
+this is kind of the list that we had
+
+ align:start position:0%
+this is kind of the list that we had
+ 
+
+ align:start position:0%
+this is kind of the list that we had
+come up with can you guys think of
+
+ align:start position:0%
+come up with can you guys think of
+ 
+
+ align:start position:0%
+come up with can you guys think of
+others um sort of
+
+ align:start position:0%
+others um sort of
+ 
+
+ align:start position:0%
+others um sort of
+popular
+
+ align:start position:0%
+popular
+ 
+
+ align:start position:0%
+popular
+um popular ways that people relate to to
+
+ align:start position:0%
+um popular ways that people relate to to
+ 
+
+ align:start position:0%
+um popular ways that people relate to to
+two science or stories that they're
+
+ align:start position:0%
+two science or stories that they're
+ 
+
+ align:start position:0%
+two science or stories that they're
+interested in hearing about science or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scientists um I guess maybe stories that
+
+ align:start position:0%
+scientists um I guess maybe stories that
+ 
+
+ align:start position:0%
+scientists um I guess maybe stories that
+have kind of like a moral value that
+
+ align:start position:0%
+have kind of like a moral value that
+ 
+
+ align:start position:0%
+have kind of like a moral value that
+maybe science discovering something
+
+ align:start position:0%
+maybe science discovering something
+ 
+
+ align:start position:0%
+maybe science discovering something
+causes you to question the morality of
+
+ align:start position:0%
+causes you to question the morality of
+ 
+
+ align:start position:0%
+causes you to question the morality of
+it or whether it's right or yeah do you
+
+ align:start position:0%
+it or whether it's right or yeah do you
+ 
+
+ align:start position:0%
+it or whether it's right or yeah do you
+have any specific example you're
+
+ align:start position:0%
+have any specific example you're
+ 
+
+ align:start position:0%
+have any specific example you're
+thinking of um I was thinking Jurassic
+
+ align:start position:0%
+thinking of um I was thinking Jurassic
+ 
+
+ align:start position:0%
+thinking of um I was thinking Jurassic
+Park uh you know like they learn to you
+
+ align:start position:0%
+Park uh you know like they learn to you
+ 
+
+ align:start position:0%
+Park uh you know like they learn to you
+know bring back this ancient animal but
+
+ align:start position:0%
+know bring back this ancient animal but
+ 
+
+ align:start position:0%
+know bring back this ancient animal but
+is that right and you know right so the
+
+ align:start position:0%
+is that right and you know right so the
+ 
+
+ align:start position:0%
+is that right and you know right so the
+kind of ethical issues and the kind of
+
+ align:start position:0%
+kind of ethical issues and the kind of
+ 
+
+ align:start position:0%
+kind of ethical issues and the kind of
+ethical issues then you know that issue
+
+ align:start position:0%
+ethical issues then you know that issue
+ 
+
+ align:start position:0%
+ethical issues then you know that issue
+issues around cloning about sort of oh
+
+ align:start position:0%
+issues around cloning about sort of oh
+ 
+
+ align:start position:0%
+issues around cloning about sort of oh
+and actually I think we had had it on
+
+ align:start position:0%
+and actually I think we had had it on
+ 
+
+ align:start position:0%
+and actually I think we had had it on
+this list and I forgot to put it up but
+
+ align:start position:0%
+this list and I forgot to put it up but
+ 
+
+ align:start position:0%
+this list and I forgot to put it up but
+that the kind of moral quandries around
+
+ align:start position:0%
+that the kind of moral quandries around
+ 
+
+ align:start position:0%
+that the kind of moral quandries around
+sort of scientist playing God like when
+
+ align:start position:0%
+sort of scientist playing God like when
+ 
+
+ align:start position:0%
+sort of scientist playing God like when
+is it
+
+ align:start position:0%
+is it
+ 
+
+ align:start position:0%
+is it
+okay when do to push when is it okay to
+
+ align:start position:0%
+okay when do to push when is it okay to
+ 
+
+ align:start position:0%
+okay when do to push when is it okay to
+push sort of human knowledge and what
+
+ align:start position:0%
+push sort of human knowledge and what
+ 
+
+ align:start position:0%
+push sort of human knowledge and what
+people can do and when does it sort of
+
+ align:start position:0%
+people can do and when does it sort of
+ 
+
+ align:start position:0%
+people can do and when does it sort of
+cross a line into something that is is
+
+ align:start position:0%
+cross a line into something that is is
+ 
+
+ align:start position:0%
+cross a line into something that is is
+potentially morally suspect um yeah
+
+ align:start position:0%
+potentially morally suspect um yeah
+ 
+
+ align:start position:0%
+potentially morally suspect um yeah
+exactly where where is the line that we
+
+ align:start position:0%
+exactly where where is the line that we
+ 
+
+ align:start position:0%
+exactly where where is the line that we
+want to draw here or not so that kind of
+
+ align:start position:0%
+want to draw here or not so that kind of
+ 
+
+ align:start position:0%
+want to draw here or not so that kind of
+fascination with those kinds of stories
+
+ align:start position:0%
+fascination with those kinds of stories
+ 
+
+ align:start position:0%
+fascination with those kinds of stories
+how do we how do we think about that
+
+ align:start position:0%
+how do we how do we think about that
+ 
+
+ align:start position:0%
+how do we how do we think about that
+relationship Sabrina kind of like a
+
+ align:start position:0%
+relationship Sabrina kind of like a
+ 
+
+ align:start position:0%
+relationship Sabrina kind of like a
+coolness factor of Personality like if
+
+ align:start position:0%
+coolness factor of Personality like if
+ 
+
+ align:start position:0%
+coolness factor of Personality like if
+like someone like Brian Green the McD
+
+ align:start position:0%
+like someone like Brian Green the McD
+ 
+
+ align:start position:0%
+like someone like Brian Green the McD
+universe is very entertaining like the
+
+ align:start position:0%
+universe is very entertaining like the
+ 
+
+ align:start position:0%
+universe is very entertaining like the
+person presenting it is trying to
+
+ align:start position:0%
+person presenting it is trying to
+ 
+
+ align:start position:0%
+person presenting it is trying to
+like turn people yeah that's kind of a
+
+ align:start position:0%
+like turn people yeah that's kind of a
+ 
+
+ align:start position:0%
+like turn people yeah that's kind of a
+subset of scientist is hero scientist is
+
+ align:start position:0%
+subset of scientist is hero scientist is
+ 
+
+ align:start position:0%
+subset of scientist is hero scientist is
+cool science that science is cool
+
+ align:start position:0%
+cool science that science is cool
+ 
+
+ align:start position:0%
+cool science that science is cool
+yeah science is
+
+ align:start position:0%
+yeah science is
+ 
+
+ align:start position:0%
+yeah science is
+cool right and a focus on that's
+
+ align:start position:0%
+cool right and a focus on that's
+ 
+
+ align:start position:0%
+cool right and a focus on that's
+supposed to be as cool if you can read
+
+ align:start position:0%
+supposed to be as cool if you can read
+ 
+
+ align:start position:0%
+supposed to be as cool if you can read
+that um and and then also the focus on
+
+ align:start position:0%
+that um and and then also the focus on
+ 
+
+ align:start position:0%
+that um and and then also the focus on
+particular kinds of charismatic
+
+ align:start position:0%
+particular kinds of charismatic
+ 
+
+ align:start position:0%
+particular kinds of charismatic
+individuals who are seen as conveying a
+
+ align:start position:0%
+individuals who are seen as conveying a
+ 
+
+ align:start position:0%
+individuals who are seen as conveying a
+certain kind of image of of science that
+
+ align:start position:0%
+certain kind of image of of science that
+ 
+
+ align:start position:0%
+certain kind of image of of science that
+people want to respond to anahita um
+
+ align:start position:0%
+people want to respond to anahita um
+ 
+
+ align:start position:0%
+people want to respond to anahita um
+also I can think about some examples of
+
+ align:start position:0%
+also I can think about some examples of
+ 
+
+ align:start position:0%
+also I can think about some examples of
+science as the superior to human being
+
+ align:start position:0%
+science as the superior to human being
+ 
+
+ align:start position:0%
+science as the superior to human being
+or the villain like in the movie say
+
+ align:start position:0%
+or the villain like in the movie say
+ 
+
+ align:start position:0%
+or the villain like in the movie say
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+uh when when the robot so the science
+
+ align:start position:0%
+uh when when the robot so the science
+ 
+
+ align:start position:0%
+uh when when the robot so the science
+act against humans and so when when does
+
+ align:start position:0%
+act against humans and so when when does
+ 
+
+ align:start position:0%
+act against humans and so when when does
+science become the villain you're right
+
+ align:start position:0%
+science become the villain you're right
+ 
+
+ align:start position:0%
+science become the villain you're right
+when the science becomes smarter than
+
+ align:start position:0%
+when the science becomes smarter than
+ 
+
+ align:start position:0%
+when the science becomes smarter than
+humans or overcomes the int human
+
+ align:start position:0%
+humans or overcomes the int human
+ 
+
+ align:start position:0%
+humans or overcomes the int human
+intelligence so and again that kind of
+
+ align:start position:0%
+intelligence so and again that kind of
+ 
+
+ align:start position:0%
+intelligence so and again that kind of
+uh question of sort of when does science
+
+ align:start position:0%
+uh question of sort of when does science
+ 
+
+ align:start position:0%
+uh question of sort of when does science
+become about human hubris where it
+
+ align:start position:0%
+become about human hubris where it
+ 
+
+ align:start position:0%
+become about human hubris where it
+surpasses itself and then the technology
+
+ align:start position:0%
+surpasses itself and then the technology
+ 
+
+ align:start position:0%
+surpasses itself and then the technology
+or the science becomes a danger back to
+
+ align:start position:0%
+or the science becomes a danger back to
+ 
+
+ align:start position:0%
+or the science becomes a danger back to
+humans themselves and so you know and
+
+ align:start position:0%
+humans themselves and so you know and
+ 
+
+ align:start position:0%
+humans themselves and so you know and
+you would see that around um um you know
+
+ align:start position:0%
+you would see that around um um you know
+ 
+
+ align:start position:0%
+you would see that around um um you know
+in the 1950s when you think about sort
+
+ align:start position:0%
+in the 1950s when you think about sort
+ 
+
+ align:start position:0%
+in the 1950s when you think about sort
+of all you know all the pop culture
+
+ align:start position:0%
+of all you know all the pop culture
+ 
+
+ align:start position:0%
+of all you know all the pop culture
+movies you know that were you know kind
+
+ align:start position:0%
+movies you know that were you know kind
+ 
+
+ align:start position:0%
+movies you know that were you know kind
+of veiled or overt references to to
+
+ align:start position:0%
+of veiled or overt references to to
+ 
+
+ align:start position:0%
+of veiled or overt references to to
+nuclear technologies or other kinds of
+
+ align:start position:0%
+nuclear technologies or other kinds of
+ 
+
+ align:start position:0%
+nuclear technologies or other kinds of
+things that sort of want you know with
+
+ align:start position:0%
+things that sort of want you know with
+ 
+
+ align:start position:0%
+things that sort of want you know with
+people struggling with the question of
+
+ align:start position:0%
+people struggling with the question of
+ 
+
+ align:start position:0%
+people struggling with the question of
+when to things sort of go beyond a
+
+ align:start position:0%
+when to things sort of go beyond a
+ 
+
+ align:start position:0%
+when to things sort of go beyond a
+certain point where the worry becomes
+
+ align:start position:0%
+certain point where the worry becomes
+ 
+
+ align:start position:0%
+certain point where the worry becomes
+about the science itself coming back on
+
+ align:start position:0%
+about the science itself coming back on
+ 
+
+ align:start position:0%
+about the science itself coming back on
+its impact on people and more recently
+
+ align:start position:0%
+its impact on people and more recently
+ 
+
+ align:start position:0%
+its impact on people and more recently
+you have the whole sort of you know the
+
+ align:start position:0%
+you have the whole sort of you know the
+ 
+
+ align:start position:0%
+you have the whole sort of you know the
+Matrix franchise the Terminator
+
+ align:start position:0%
+Matrix franchise the Terminator
+ 
+
+ align:start position:0%
+Matrix franchise the Terminator
+franchise which are about Ai and and
+
+ align:start position:0%
+franchise which are about Ai and and
+ 
+
+ align:start position:0%
+franchise which are about Ai and and
+technologies that become their own
+
+ align:start position:0%
+technologies that become their own
+ 
+
+ align:start position:0%
+technologies that become their own
+creators and and then reject the the
+
+ align:start position:0%
+creators and and then reject the the
+ 
+
+ align:start position:0%
+creators and and then reject the the
+human beings that created them and and
+
+ align:start position:0%
+human beings that created them and and
+ 
+
+ align:start position:0%
+human beings that created them and and
+attempt to destroy them Sabrina science
+
+ align:start position:0%
+attempt to destroy them Sabrina science
+ 
+
+ align:start position:0%
+attempt to destroy them Sabrina science
+is like a competition when you have like
+
+ align:start position:0%
+is like a competition when you have like
+ 
+
+ align:start position:0%
+is like a competition when you have like
+different people trying to do the same
+
+ align:start position:0%
+different people trying to do the same
+ 
+
+ align:start position:0%
+different people trying to do the same
+thing and like kind of making it seem
+
+ align:start position:0%
+thing and like kind of making it seem
+ 
+
+ align:start position:0%
+thing and like kind of making it seem
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah a fascination with right science is
+
+ align:start position:0%
+yeah a fascination with right science is
+ 
+
+ align:start position:0%
+yeah a fascination with right science is
+competition about which becomes part of
+
+ align:start position:0%
+competition about which becomes part of
+ 
+
+ align:start position:0%
+competition about which becomes part of
+the the discovery process in a way
+
+ align:start position:0%
+the the discovery process in a way
+ 
+
+ align:start position:0%
+the the discovery process in a way
+except you've got the added element of
+
+ align:start position:0%
+except you've got the added element of
+ 
+
+ align:start position:0%
+except you've got the added element of
+drama with competition about you know
+
+ align:start position:0%
+drama with competition about you know
+ 
+
+ align:start position:0%
+drama with competition about you know
+sort of who's going to you know crack
+
+ align:start position:0%
+sort of who's going to you know crack
+ 
+
+ align:start position:0%
+sort of who's going to you know crack
+the DNA code or you know what were these
+
+ align:start position:0%
+the DNA code or you know what were these
+ 
+
+ align:start position:0%
+the DNA code or you know what were these
+kinds of scientific competitions about
+
+ align:start position:0%
+kinds of scientific competitions about
+ 
+
+ align:start position:0%
+kinds of scientific competitions about
+how did people discover things and that
+
+ align:start position:0%
+how did people discover things and that
+ 
+
+ align:start position:0%
+how did people discover things and that
+added element of drama I think Le to
+
+ align:start position:0%
+added element of drama I think Le to
+ 
+
+ align:start position:0%
+added element of drama I think Le to
+that is kind of science has Crea the
+
+ align:start position:0%
+that is kind of science has Crea the
+ 
+
+ align:start position:0%
+that is kind of science has Crea the
+history and creating the future so a
+
+ align:start position:0%
+history and creating the future so a
+ 
+
+ align:start position:0%
+history and creating the future so a
+certain like a lot of representations of
+
+ align:start position:0%
+certain like a lot of representations of
+ 
+
+ align:start position:0%
+certain like a lot of representations of
+kind of new things they is if the future
+
+ align:start position:0%
+kind of new things they is if the future
+ 
+
+ align:start position:0%
+kind of new things they is if the future
+has been brought to the
+
+ align:start position:0%
+has been brought to the
+ 
+
+ align:start position:0%
+has been brought to the
+present yeah I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+so science almost as a way to
+
+ align:start position:0%
+so science almost as a way to
+ 
+
+ align:start position:0%
+so science almost as a way to
+um for people to to think about the
+
+ align:start position:0%
+um for people to to think about the
+ 
+
+ align:start position:0%
+um for people to to think about the
+future and the possibilities that the
+
+ align:start position:0%
+future and the possibilities that the
+ 
+
+ align:start position:0%
+future and the possibilities that the
+future might bring or to
+
+ align:start position:0%
+future might bring or to
+ 
+
+ align:start position:0%
+future might bring or to
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um yeah I think that I think that
+
+ align:start position:0%
+um yeah I think that I think that
+ 
+
+ align:start position:0%
+um yeah I think that I think that
+happens a lot when when you know sort in
+
+ align:start position:0%
+happens a lot when when you know sort in
+ 
+
+ align:start position:0%
+happens a lot when when you know sort in
+popular cultural representations when
+
+ align:start position:0%
+popular cultural representations when
+ 
+
+ align:start position:0%
+popular cultural representations when
+people think about you know sort of
+
+ align:start position:0%
+people think about you know sort of
+ 
+
+ align:start position:0%
+people think about you know sort of
+their nervousness or concerns or worries
+
+ align:start position:0%
+their nervousness or concerns or worries
+ 
+
+ align:start position:0%
+their nervousness or concerns or worries
+about what the future or or their hopes
+
+ align:start position:0%
+about what the future or or their hopes
+ 
+
+ align:start position:0%
+about what the future or or their hopes
+for that matter too about what the
+
+ align:start position:0%
+for that matter too about what the
+ 
+
+ align:start position:0%
+for that matter too about what the
+future might bring
+
+ align:start position:0%
+future might bring
+ 
+
+ align:start position:0%
+future might bring
+often that future is expressed through a
+
+ align:start position:0%
+often that future is expressed through a
+ 
+
+ align:start position:0%
+often that future is expressed through a
+reference to Science and Technology and
+
+ align:start position:0%
+reference to Science and Technology and
+ 
+
+ align:start position:0%
+reference to Science and Technology and
+what it might do rather than sort of
+
+ align:start position:0%
+what it might do rather than sort of
+ 
+
+ align:start position:0%
+what it might do rather than sort of
+other kinds of social issues per se
+
+ align:start position:0%
+other kinds of social issues per se
+ 
+
+ align:start position:0%
+other kinds of social issues per se
+because I mean again I mean how do we
+
+ align:start position:0%
+because I mean again I mean how do we
+ 
+
+ align:start position:0%
+because I mean again I mean how do we
+know necessarily what the future is
+
+ align:start position:0%
+know necessarily what the future is
+ 
+
+ align:start position:0%
+know necessarily what the future is
+going to be about but science and
+
+ align:start position:0%
+going to be about but science and
+ 
+
+ align:start position:0%
+going to be about but science and
+technology is often used to represent
+
+ align:start position:0%
+technology is often used to represent
+ 
+
+ align:start position:0%
+technology is often used to represent
+what we think the future is going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be so it's so yeah so the the way it's
+
+ align:start position:0%
+be so it's so yeah so the the way it's
+ 
+
+ align:start position:0%
+be so it's so yeah so the the way it's
+the symbolic uh connotations the
+
+ align:start position:0%
+the symbolic uh connotations the
+ 
+
+ align:start position:0%
+the symbolic uh connotations the
+symbolic relationship that it has to
+
+ align:start position:0%
+symbolic relationship that it has to
+ 
+
+ align:start position:0%
+symbolic relationship that it has to
+certain kinds of ideas about time and
+
+ align:start position:0%
+certain kinds of ideas about time and
+ 
+
+ align:start position:0%
+certain kinds of ideas about time and
+and seen as being representative of the
+
+ align:start position:0%
+and seen as being representative of the
+ 
+
+ align:start position:0%
+and seen as being representative of the
+future Anita
+
+ align:start position:0%
+future Anita
+ 
+
+ align:start position:0%
+future Anita
+I mean it might go a little bit with the
+
+ align:start position:0%
+I mean it might go a little bit with the
+ 
+
+ align:start position:0%
+I mean it might go a little bit with the
+idea of Science and competition but also
+
+ align:start position:0%
+idea of Science and competition but also
+ 
+
+ align:start position:0%
+idea of Science and competition but also
+I think creates that kind of hierarchy
+
+ align:start position:0%
+I think creates that kind of hierarchy
+ 
+
+ align:start position:0%
+I think creates that kind of hierarchy
+or power relation you see the science
+
+ align:start position:0%
+or power relation you see the science
+ 
+
+ align:start position:0%
+or power relation you see the science
+fiction movie and especially I think
+
+ align:start position:0%
+fiction movie and especially I think
+ 
+
+ align:start position:0%
+fiction movie and especially I think
+it's more relevant to the younger people
+
+ align:start position:0%
+it's more relevant to the younger people
+ 
+
+ align:start position:0%
+it's more relevant to the younger people
+like feeling that oh this is this
+
+ align:start position:0%
+like feeling that oh this is this
+ 
+
+ align:start position:0%
+like feeling that oh this is this
+scientist uh C hierarchy that oh they
+
+ align:start position:0%
+scientist uh C hierarchy that oh they
+ 
+
+ align:start position:0%
+scientist uh C hierarchy that oh they
+have all these resources and this
+
+ align:start position:0%
+have all these resources and this
+ 
+
+ align:start position:0%
+have all these resources and this
+position to like be so cool be heroes be
+
+ align:start position:0%
+position to like be so cool be heroes be
+ 
+
+ align:start position:0%
+position to like be so cool be heroes be
+the future or do all the cool things but
+
+ align:start position:0%
+the future or do all the cool things but
+ 
+
+ align:start position:0%
+the future or do all the cool things but
+here I am looking at it so it's like a
+
+ align:start position:0%
+here I am looking at it so it's like a
+ 
+
+ align:start position:0%
+here I am looking at it so it's like a
+higher between you and whatever's going
+
+ align:start position:0%
+higher between you and whatever's going
+ 
+
+ align:start position:0%
+higher between you and whatever's going
+on so so um a kind of concern with okay
+
+ align:start position:0%
+on so so um a kind of concern with okay
+ 
+
+ align:start position:0%
+on so so um a kind of concern with okay
+sort of who are these people who have
+
+ align:start position:0%
+sort of who are these people who have
+ 
+
+ align:start position:0%
+sort of who are these people who have
+this Authority who are making these
+
+ align:start position:0%
+this Authority who are making these
+ 
+
+ align:start position:0%
+this Authority who are making these
+kinds of decisions that I don't
+
+ align:start position:0%
+kinds of decisions that I don't
+ 
+
+ align:start position:0%
+kinds of decisions that I don't
+necessarily have input into and sort of
+
+ align:start position:0%
+necessarily have input into and sort of
+ 
+
+ align:start position:0%
+necessarily have input into and sort of
+are they people doing this sort of for
+
+ align:start position:0%
+are they people doing this sort of for
+ 
+
+ align:start position:0%
+are they people doing this sort of for
+the greater good in a way that's going
+
+ align:start position:0%
+the greater good in a way that's going
+ 
+
+ align:start position:0%
+the greater good in a way that's going
+to help me or is this potentially very
+
+ align:start position:0%
+to help me or is this potentially very
+ 
+
+ align:start position:0%
+to help me or is this potentially very
+you know um the decisions that they're
+
+ align:start position:0%
+you know um the decisions that they're
+ 
+
+ align:start position:0%
+you know um the decisions that they're
+going to make are going to be extremely
+
+ align:start position:0%
+going to make are going to be extremely
+ 
+
+ align:start position:0%
+going to make are going to be extremely
+problematic and science is power so
+
+ align:start position:0%
+problematic and science is power so
+ 
+
+ align:start position:0%
+problematic and science is power so
+people who have the science are the
+
+ align:start position:0%
+people who have the science are the
+ 
+
+ align:start position:0%
+people who have the science are the
+powerful people and I if I want to be
+
+ align:start position:0%
+powerful people and I if I want to be
+ 
+
+ align:start position:0%
+powerful people and I if I want to be
+powerful have to have the science and
+
+ align:start position:0%
+powerful have to have the science and
+ 
+
+ align:start position:0%
+powerful have to have the science and
+kind of The Narrative of the
+
+ align:start position:0%
+kind of The Narrative of the
+ 
+
+ align:start position:0%
+kind of The Narrative of the
+disconnected scientist the scientist who
+
+ align:start position:0%
+disconnected scientist the scientist who
+ 
+
+ align:start position:0%
+disconnected scientist the scientist who
+which is again a little like science
+
+ align:start position:0%
+which is again a little like science
+ 
+
+ align:start position:0%
+which is again a little like science
+versus emotion the scientist who stands
+
+ align:start position:0%
+versus emotion the scientist who stands
+ 
+
+ align:start position:0%
+versus emotion the scientist who stands
+apart who has this power but who doesn't
+
+ align:start position:0%
+apart who has this power but who doesn't
+ 
+
+ align:start position:0%
+apart who has this power but who doesn't
+understand what the power can do or
+
+ align:start position:0%
+understand what the power can do or
+ 
+
+ align:start position:0%
+understand what the power can do or
+doesn't have a relationship to people
+
+ align:start position:0%
+doesn't have a relationship to people
+ 
+
+ align:start position:0%
+doesn't have a relationship to people
+average people who are going to be
+
+ align:start position:0%
+average people who are going to be
+ 
+
+ align:start position:0%
+average people who are going to be
+affected by
+
+ align:start position:0%
+affected by
+ 
+
+ align:start position:0%
+affected by
+something yeah I mean I think all this
+
+ align:start position:0%
+something yeah I mean I think all this
+ 
+
+ align:start position:0%
+something yeah I mean I think all this
+is really important to get out because
+
+ align:start position:0%
+is really important to get out because
+ 
+
+ align:start position:0%
+is really important to get out because
+there's both again what people on the
+
+ align:start position:0%
+there's both again what people on the
+ 
+
+ align:start position:0%
+there's both again what people on the
+science end might want to convey to the
+
+ align:start position:0%
+science end might want to convey to the
+ 
+
+ align:start position:0%
+science end might want to convey to the
+public and then there's also sort of
+
+ align:start position:0%
+public and then there's also sort of
+ 
+
+ align:start position:0%
+public and then there's also sort of
+sort of on the the the public end sort
+
+ align:start position:0%
+sort of on the the the public end sort
+ 
+
+ align:start position:0%
+sort of on the the the public end sort
+of what is the
+
+ align:start position:0%
+of what is the
+ 
+
+ align:start position:0%
+of what is the
+fascination with the scientists and what
+
+ align:start position:0%
+fascination with the scientists and what
+ 
+
+ align:start position:0%
+fascination with the scientists and what
+are the sort of the concerns and
+
+ align:start position:0%
+are the sort of the concerns and
+ 
+
+ align:start position:0%
+are the sort of the concerns and
+quandaries and things that people are
+
+ align:start position:0%
+quandaries and things that people are
+ 
+
+ align:start position:0%
+quandaries and things that people are
+interested in in thinking about in
+
+ align:start position:0%
+interested in in thinking about in
+ 
+
+ align:start position:0%
+interested in in thinking about in
+relation to science and obviously it's
+
+ align:start position:0%
+relation to science and obviously it's
+ 
+
+ align:start position:0%
+relation to science and obviously it's
+not just you know the separate thing we
+
+ align:start position:0%
+not just you know the separate thing we
+ 
+
+ align:start position:0%
+not just you know the separate thing we
+have the scientists over here and pop
+
+ align:start position:0%
+have the scientists over here and pop
+ 
+
+ align:start position:0%
+have the scientists over here and pop
+culture over here I mean one of the
+
+ align:start position:0%
+culture over here I mean one of the
+ 
+
+ align:start position:0%
+culture over here I mean one of the
+things that's really fascinating we're
+
+ align:start position:0%
+things that's really fascinating we're
+ 
+
+ align:start position:0%
+things that's really fascinating we're
+going to talk about this later in class
+
+ align:start position:0%
+going to talk about this later in class
+ 
+
+ align:start position:0%
+going to talk about this later in class
+is you know if you talk to um many
+
+ align:start position:0%
+is you know if you talk to um many
+ 
+
+ align:start position:0%
+is you know if you talk to um many
+people at MIT and actually this is going
+
+ align:start position:0%
+people at MIT and actually this is going
+ 
+
+ align:start position:0%
+people at MIT and actually this is going
+to come up in relation to the next film
+
+ align:start position:0%
+to come up in relation to the next film
+ 
+
+ align:start position:0%
+to come up in relation to the next film
+we're going to see um but if you talk to
+
+ align:start position:0%
+we're going to see um but if you talk to
+ 
+
+ align:start position:0%
+we're going to see um but if you talk to
+many people um around MIT of a certain
+
+ align:start position:0%
+many people um around MIT of a certain
+ 
+
+ align:start position:0%
+many people um around MIT of a certain
+generation
+
+ align:start position:0%
+generation
+ 
+
+ align:start position:0%
+generation
+you know they might have gotten
+
+ align:start position:0%
+you know they might have gotten
+ 
+
+ align:start position:0%
+you know they might have gotten
+interested in you know doing what they
+
+ align:start position:0%
+interested in you know doing what they
+ 
+
+ align:start position:0%
+interested in you know doing what they
+do because maybe they were really
+
+ align:start position:0%
+do because maybe they were really
+ 
+
+ align:start position:0%
+do because maybe they were really
+fascinated with st Trek when they were
+
+ align:start position:0%
+fascinated with st Trek when they were
+ 
+
+ align:start position:0%
+fascinated with st Trek when they were
+kids and they decided you know a Astro I
+
+ align:start position:0%
+kids and they decided you know a Astro I
+ 
+
+ align:start position:0%
+kids and they decided you know a Astro I
+mean that's that's where I want to go
+
+ align:start position:0%
+mean that's that's where I want to go
+ 
+
+ align:start position:0%
+mean that's that's where I want to go
+and and so a lot of times if you go back
+
+ align:start position:0%
+and and so a lot of times if you go back
+ 
+
+ align:start position:0%
+and and so a lot of times if you go back
+and you talk to people well what
+
+ align:start position:0%
+and you talk to people well what
+ 
+
+ align:start position:0%
+and you talk to people well what
+originally got you interested um and
+
+ align:start position:0%
+originally got you interested um and
+ 
+
+ align:start position:0%
+originally got you interested um and
+thinking about this often people will
+
+ align:start position:0%
+thinking about this often people will
+ 
+
+ align:start position:0%
+thinking about this often people will
+refer back to sort of Pop cult cultural
+
+ align:start position:0%
+refer back to sort of Pop cult cultural
+ 
+
+ align:start position:0%
+refer back to sort of Pop cult cultural
+images from when they were a kid about
+
+ align:start position:0%
+images from when they were a kid about
+ 
+
+ align:start position:0%
+images from when they were a kid about
+whether it's you know again Star Trek or
+
+ align:start position:0%
+whether it's you know again Star Trek or
+ 
+
+ align:start position:0%
+whether it's you know again Star Trek or
+actually this next uh this is actually a
+
+ align:start position:0%
+actually this next uh this is actually a
+ 
+
+ align:start position:0%
+actually this next uh this is actually a
+good segue into this next video that
+
+ align:start position:0%
+good segue into this next video that
+ 
+
+ align:start position:0%
+good segue into this next video that
+we're going to see because um you know
+
+ align:start position:0%
+we're going to see because um you know
+ 
+
+ align:start position:0%
+we're going to see because um you know
+according to Chris a number of people
+
+ align:start position:0%
+according to Chris a number of people
+ 
+
+ align:start position:0%
+according to Chris a number of people
+that he's talked to around MIT mentioned
+
+ align:start position:0%
+that he's talked to around MIT mentioned
+ 
+
+ align:start position:0%
+that he's talked to around MIT mentioned
+this um this series um connections um
+
+ align:start position:0%
+this um this series um connections um
+ 
+
+ align:start position:0%
+this um this series um connections um
+that um that had had been on the BBC as
+
+ align:start position:0%
+that um that had had been on the BBC as
+ 
+
+ align:start position:0%
+that um that had had been on the BBC as
+something that very much influenced them
+
+ align:start position:0%
+something that very much influenced them
+ 
+
+ align:start position:0%
+something that very much influenced them
+when they were younger um when uh they
+
+ align:start position:0%
+when they were younger um when uh they
+ 
+
+ align:start position:0%
+when they were younger um when uh they
+decided that they wanted to become um
+
+ align:start position:0%
+decided that they wanted to become um
+ 
+
+ align:start position:0%
+decided that they wanted to become um
+scientists so so okay so I'll use
+
+ align:start position:0%
+scientists so so okay so I'll use
+ 
+
+ align:start position:0%
+scientists so so okay so I'll use
+that uh as a segue into this and so this
+
+ align:start position:0%
+that uh as a segue into this and so this
+ 
+
+ align:start position:0%
+that uh as a segue into this and so this
+this series connections that I just uh
+
+ align:start position:0%
+this series connections that I just uh
+ 
+
+ align:start position:0%
+this series connections that I just uh
+mentioned um it's mostly in that kind of
+
+ align:start position:0%
+mentioned um it's mostly in that kind of
+ 
+
+ align:start position:0%
+mentioned um it's mostly in that kind of
+genre of science as detective story
+
+ align:start position:0%
+genre of science as detective story
+ 
+
+ align:start position:0%
+genre of science as detective story
+Story I mean obviously it's also meant
+
+ align:start position:0%
+Story I mean obviously it's also meant
+ 
+
+ align:start position:0%
+Story I mean obviously it's also meant
+to be partly educational but also
+
+ align:start position:0%
+to be partly educational but also
+ 
+
+ align:start position:0%
+to be partly educational but also
+science's detective story it's a series
+
+ align:start position:0%
+science's detective story it's a series
+ 
+
+ align:start position:0%
+science's detective story it's a series
+that came out in the late 1970s and the
+
+ align:start position:0%
+that came out in the late 1970s and the
+ 
+
+ align:start position:0%
+that came out in the late 1970s and the
+narrator is this guy um James Burke um
+
+ align:start position:0%
+narrator is this guy um James Burke um
+ 
+
+ align:start position:0%
+narrator is this guy um James Burke um
+he was an Irishman who was trained at
+
+ align:start position:0%
+he was an Irishman who was trained at
+ 
+
+ align:start position:0%
+he was an Irishman who was trained at
+Oxford and he became a science
+
+ align:start position:0%
+Oxford and he became a science
+ 
+
+ align:start position:0%
+Oxford and he became a science
+journalist at the BBC and so this ended
+
+ align:start position:0%
+journalist at the BBC and so this ended
+ 
+
+ align:start position:0%
+journalist at the BBC and so this ended
+up becoming a very famous series on um
+
+ align:start position:0%
+up becoming a very famous series on um
+ 
+
+ align:start position:0%
+up becoming a very famous series on um
+science and technology and so we're
+
+ align:start position:0%
+science and technology and so we're
+ 
+
+ align:start position:0%
+science and technology and so we're
+going to watch part of the uh the first
+
+ align:start position:0%
+going to watch part of the uh the first
+ 
+
+ align:start position:0%
+going to watch part of the uh the first
+episode of this um he was often
+
+ align:start position:0%
+episode of this um he was often
+ 
+
+ align:start position:0%
+episode of this um he was often
+described as being kind of the Sherlock
+
+ align:start position:0%
+described as being kind of the Sherlock
+ 
+
+ align:start position:0%
+described as being kind of the Sherlock
+Holmes of science um
+
+ align:start position:0%
+Holmes of science um
+ 
+
+ align:start position:0%
+Holmes of science um
+uh okay I'm not gonna say any more than
+
+ align:start position:0%
+uh okay I'm not gonna say any more than
+ 
+
+ align:start position:0%
+uh okay I'm not gonna say any more than
+that I'll just let you respond and see
+
+ align:start position:0%
+that I'll just let you respond and see
+ 
+
+ align:start position:0%
+that I'll just let you respond and see
+and see what you all and I'll just say
+
+ align:start position:0%
+and see what you all and I'll just say
+ 
+
+ align:start position:0%
+and see what you all and I'll just say
+uh try to think about this this film and
+
+ align:start position:0%
+uh try to think about this this film and
+ 
+
+ align:start position:0%
+uh try to think about this this film and
+I mean all the other films that we've
+
+ align:start position:0%
+I mean all the other films that we've
+ 
+
+ align:start position:0%
+I mean all the other films that we've
+been seeing as well but this one in
+
+ align:start position:0%
+been seeing as well but this one in
+ 
+
+ align:start position:0%
+been seeing as well but this one in
+particular from the point of view of
+
+ align:start position:0%
+particular from the point of view of
+ 
+
+ align:start position:0%
+particular from the point of view of
+narrative strategies keeping the
+
+ align:start position:0%
+narrative strategies keeping the
+ 
+
+ align:start position:0%
+narrative strategies keeping the
+audience engaged and how that relates to
+
+ align:start position:0%
+audience engaged and how that relates to
+ 
+
+ align:start position:0%
+audience engaged and how that relates to
+the information that's being
+
+ align:start position:0%
+the information that's being
+ 
+
+ align:start position:0%
+the information that's being
+imparted and again this series this
+
+ align:start position:0%
+imparted and again this series this
+ 
+
+ align:start position:0%
+imparted and again this series this
+series was an extremely popular series
+
+ align:start position:0%
+series was an extremely popular series
+ 
+
+ align:start position:0%
+series was an extremely popular series
+um and they had a lot of funing to do it
+
+ align:start position:0%
+um and they had a lot of funing to do it
+ 
+
+ align:start position:0%
+um and they had a lot of funing to do it
+um but extremely popular series that was
+
+ align:start position:0%
+um but extremely popular series that was
+ 
+
+ align:start position:0%
+um but extremely popular series that was
+um um that was quite influential um yeah
+
+ align:start position:0%
+um um that was quite influential um yeah
+ 
+
+ align:start position:0%
+um um that was quite influential um yeah
+as I as Chris mentioned if you talk to a
+
+ align:start position:0%
+as I as Chris mentioned if you talk to a
+ 
+
+ align:start position:0%
+as I as Chris mentioned if you talk to a
+lot of professors in their 40s um who
+
+ align:start position:0%
+lot of professors in their 40s um who
+ 
+
+ align:start position:0%
+lot of professors in their 40s um who
+were you know who were teenagers when
+
+ align:start position:0%
+were you know who were teenagers when
+ 
+
+ align:start position:0%
+were you know who were teenagers when
+this came out a lot of them will say oh
+
+ align:start position:0%
+this came out a lot of them will say oh
+ 
+
+ align:start position:0%
+this came out a lot of them will say oh
+I saw connections on PBS when I was a
+
+ align:start position:0%
+I saw connections on PBS when I was a
+ 
+
+ align:start position:0%
+I saw connections on PBS when I was a
+kid and that was it I wanted to be an
+
+ align:start position:0%
+kid and that was it I wanted to be an
+ 
+
+ align:start position:0%
+kid and that was it I wanted to be an
+engineer or a scientist and again this
+
+ align:start position:0%
+engineer or a scientist and again this
+ 
+
+ align:start position:0%
+engineer or a scientist and again this
+tendency we often have a tendency to
+
+ align:start position:0%
+tendency we often have a tendency to
+ 
+
+ align:start position:0%
+tendency we often have a tendency to
+think of like well science is the
+
+ align:start position:0%
+think of like well science is the
+ 
+
+ align:start position:0%
+think of like well science is the
+serious stuff over here and like the pop
+
+ align:start position:0%
+serious stuff over here and like the pop
+ 
+
+ align:start position:0%
+serious stuff over here and like the pop
+culture stuff is the not serious stuff
+
+ align:start position:0%
+culture stuff is the not serious stuff
+ 
+
+ align:start position:0%
+culture stuff is the not serious stuff
+over here but again as human beings we
+
+ align:start position:0%
+over here but again as human beings we
+ 
+
+ align:start position:0%
+over here but again as human beings we
+get influenced by all of this stuff
+
+ align:start position:0%
+get influenced by all of this stuff
+ 
+
+ align:start position:0%
+get influenced by all of this stuff
+right and and so the pop cultural
+
+ align:start position:0%
+right and and so the pop cultural
+ 
+
+ align:start position:0%
+right and and so the pop cultural
+representations become part of who we
+
+ align:start position:0%
+representations become part of who we
+ 
+
+ align:start position:0%
+representations become part of who we
+are and why we're interested in these
+
+ align:start position:0%
+are and why we're interested in these
+ 
+
+ align:start position:0%
+are and why we're interested in these
+questions to begin with and they might
+
+ align:start position:0%
+questions to begin with and they might
+ 
+
+ align:start position:0%
+questions to begin with and they might
+be what pushes people into a certain
+
+ align:start position:0%
+be what pushes people into a certain
+ 
+
+ align:start position:0%
+be what pushes people into a certain
+direction to ask certain kinds of
+
+ align:start position:0%
+direction to ask certain kinds of
+ 
+
+ align:start position:0%
+direction to ask certain kinds of
+questions so it's in a way it's kind of
+
+ align:start position:0%
+questions so it's in a way it's kind of
+ 
+
+ align:start position:0%
+questions so it's in a way it's kind of
+um um well we want to be thinking on
+
+ align:start position:0%
+um um well we want to be thinking on
+ 
+
+ align:start position:0%
+um um well we want to be thinking on
+about both ends and the potential
+
+ align:start position:0%
+about both ends and the potential
+ 
+
+ align:start position:0%
+about both ends and the potential
+relationship that there that's out there
+
+ align:start position:0%
+relationship that there that's out there
+ 
+
+ align:start position:0%
+relationship that there that's out there
+as well and we actually have a class
+
+ align:start position:0%
+as well and we actually have a class
+ 
+
+ align:start position:0%
+as well and we actually have a class
+later on in the semester that's
+
+ align:start position:0%
+later on in the semester that's
+ 
+
+ align:start position:0%
+later on in the semester that's
+specifically on science fiction um
+
+ align:start position:0%
+specifically on science fiction um
+ 
+
+ align:start position:0%
+specifically on science fiction um
+that's partly around these kind of VAR
+
+ align:start position:0%
+that's partly around these kind of VAR
+ 
+
+ align:start position:0%
+that's partly around these kind of VAR
+kinds of questions about sort of how
+
+ align:start position:0%
+kinds of questions about sort of how
+ 
+
+ align:start position:0%
+kinds of questions about sort of how
+science moves over into the pop culture
+
+ align:start position:0%
+science moves over into the pop culture
+ 
+
+ align:start position:0%
+science moves over into the pop culture
+realm and the influence sort of back and
+
+ align:start position:0%
+realm and the influence sort of back and
+ 
+
+ align:start position:0%
+realm and the influence sort of back and
+forth between science and and the the
+
+ align:start position:0%
+forth between science and and the the
+ 
+
+ align:start position:0%
+forth between science and and the the
+the world of fiction but here you're
+
+ align:start position:0%
+the world of fiction but here you're
+ 
+
+ align:start position:0%
+the world of fiction but here you're
+going to see a science documentary that
+
+ align:start position:0%
+going to see a science documentary that
+ 
+
+ align:start position:0%
+going to see a science documentary that
+among other things is very heavily
+
+ align:start position:0%
+among other things is very heavily
+ 
+
+ align:start position:0%
+among other things is very heavily
+influenced by the world of fiction film
+
+ align:start position:0%
+influenced by the world of fiction film
+ 
+
+ align:start position:0%
+influenced by the world of fiction film
+making
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+would you do me a favor I'd like to stop
+
+ align:start position:0%
+would you do me a favor I'd like to stop
+ 
+
+ align:start position:0%
+would you do me a favor I'd like to stop
+talking for a minute and when I do take
+
+ align:start position:0%
+talking for a minute and when I do take
+ 
+
+ align:start position:0%
+talking for a minute and when I do take
+a look at the room you're in and above
+
+ align:start position:0%
+a look at the room you're in and above
+ 
+
+ align:start position:0%
+a look at the room you're in and above
+all at the man-made objects in that room
+
+ align:start position:0%
+all at the man-made objects in that room
+ 
+
+ align:start position:0%
+all at the man-made objects in that room
+that surround you the television set the
+
+ align:start position:0%
+that surround you the television set the
+ 
+
+ align:start position:0%
+that surround you the television set the
+lights the phone and so on and ask
+
+ align:start position:0%
+lights the phone and so on and ask
+ 
+
+ align:start position:0%
+lights the phone and so on and ask
+yourself what those objects do to your
+
+ align:start position:0%
+yourself what those objects do to your
+ 
+
+ align:start position:0%
+yourself what those objects do to your
+life just because they're
+
+ align:start position:0%
+life just because they're
+ 
+
+ align:start position:0%
+life just because they're
+there go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ahead well that is what this series is
+
+ align:start position:0%
+ahead well that is what this series is
+ 
+
+ align:start position:0%
+ahead well that is what this series is
+going to be all
+
+ align:start position:0%
+going to be all
+ 
+
+ align:start position:0%
+going to be all
+about it's about the things that
+
+ align:start position:0%
+about it's about the things that
+ 
+
+ align:start position:0%
+about it's about the things that
+surround you in the modern world and
+
+ align:start position:0%
+surround you in the modern world and
+ 
+
+ align:start position:0%
+surround you in the modern world and
+just because they're there shape the way
+
+ align:start position:0%
+just because they're there shape the way
+ 
+
+ align:start position:0%
+just because they're there shape the way
+you think and behave and why they exist
+
+ align:start position:0%
+you think and behave and why they exist
+ 
+
+ align:start position:0%
+you think and behave and why they exist
+in the form they do and who or what was
+
+ align:start position:0%
+in the form they do and who or what was
+ 
+
+ align:start position:0%
+in the form they do and who or what was
+responsible for them existing at
+
+ align:start position:0%
+responsible for them existing at
+ 
+
+ align:start position:0%
+responsible for them existing at
+all the search for those Clues will take
+
+ align:start position:0%
+all the search for those Clues will take
+ 
+
+ align:start position:0%
+all the search for those Clues will take
+us all over the world and 12,000 years
+
+ align:start position:0%
+us all over the world and 12,000 years
+ 
+
+ align:start position:0%
+us all over the world and 12,000 years
+into the past because it's in those
+
+ align:start position:0%
+into the past because it's in those
+ 
+
+ align:start position:0%
+into the past because it's in those
+strange places and in those long gone
+
+ align:start position:0%
+strange places and in those long gone
+ 
+
+ align:start position:0%
+strange places and in those long gone
+centuries that the secret of the modern
+
+ align:start position:0%
+centuries that the secret of the modern
+ 
+
+ align:start position:0%
+centuries that the secret of the modern
+world lies and you never believe the
+
+ align:start position:0%
+world lies and you never believe the
+ 
+
+ align:start position:0%
+world lies and you never believe the
+extraordinary things that led to us
+
+ align:start position:0%
+extraordinary things that led to us
+ 
+
+ align:start position:0%
+extraordinary things that led to us
+being the way we are
+
+ align:start position:0%
+being the way we are
+ 
+
+ align:start position:0%
+being the way we are
+today things like for instance why a
+
+ align:start position:0%
+today things like for instance why a
+ 
+
+ align:start position:0%
+today things like for instance why a
+16th century do at the court of Queen
+
+ align:start position:0%
+16th century do at the court of Queen
+ 
+
+ align:start position:0%
+16th century do at the court of Queen
+Elizabeth did something that made it
+
+ align:start position:0%
+Elizabeth did something that made it
+ 
+
+ align:start position:0%
+Elizabeth did something that made it
+possible for you to watch this screen
+
+ align:start position:0%
+possible for you to watch this screen
+ 
+
+ align:start position:0%
+possible for you to watch this screen
+now or the fact that because 18th
+
+ align:start position:0%
+now or the fact that because 18th
+ 
+
+ align:start position:0%
+now or the fact that because 18th
+century Merchants were worried about
+
+ align:start position:0%
+century Merchants were worried about
+ 
+
+ align:start position:0%
+century Merchants were worried about
+ships bottoms you have nylon to
+
+ align:start position:0%
+ships bottoms you have nylon to
+ 
+
+ align:start position:0%
+ships bottoms you have nylon to
+wear or why a group of French monks and
+
+ align:start position:0%
+wear or why a group of French monks and
+ 
+
+ align:start position:0%
+wear or why a group of French monks and
+their involvement with sheep rearing
+
+ align:start position:0%
+their involvement with sheep rearing
+ 
+
+ align:start position:0%
+their involvement with sheep rearing
+helped to give the modern world the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+computer or what medieval Europeans did
+
+ align:start position:0%
+computer or what medieval Europeans did
+ 
+
+ align:start position:0%
+computer or what medieval Europeans did
+with their fire in Winter that led to
+
+ align:start position:0%
+with their fire in Winter that led to
+ 
+
+ align:start position:0%
+with their fire in Winter that led to
+Motorcar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+manufacturer
+
+ align:start position:0%
+manufacturer
+ 
+
+ align:start position:0%
+manufacturer
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the story of the events and the people
+
+ align:start position:0%
+the story of the events and the people
+ 
+
+ align:start position:0%
+the story of the events and the people
+who over centuries came together to
+
+ align:start position:0%
+who over centuries came together to
+ 
+
+ align:start position:0%
+who over centuries came together to
+bring us in from the cold and to wrap us
+
+ align:start position:0%
+bring us in from the cold and to wrap us
+ 
+
+ align:start position:0%
+bring us in from the cold and to wrap us
+in a warm blanket of technology is a
+
+ align:start position:0%
+in a warm blanket of technology is a
+ 
+
+ align:start position:0%
+in a warm blanket of technology is a
+matter of vital importance since more
+
+ align:start position:0%
+matter of vital importance since more
+ 
+
+ align:start position:0%
+matter of vital importance since more
+and more of that technology infiltrates
+
+ align:start position:0%
+and more of that technology infiltrates
+ 
+
+ align:start position:0%
+and more of that technology infiltrates
+every aspect of Our Lives it's become a
+
+ align:start position:0%
+every aspect of Our Lives it's become a
+ 
+
+ align:start position:0%
+every aspect of Our Lives it's become a
+life support system without which we
+
+ align:start position:0%
+life support system without which we
+ 
+
+ align:start position:0%
+life support system without which we
+can't survive and yet how much of it do
+
+ align:start position:0%
+can't survive and yet how much of it do
+ 
+
+ align:start position:0%
+can't survive and yet how much of it do
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+understand do I bother myself with the
+
+ align:start position:0%
+understand do I bother myself with the
+ 
+
+ align:start position:0%
+understand do I bother myself with the
+reality of what happens when I get into
+
+ align:start position:0%
+reality of what happens when I get into
+ 
+
+ align:start position:0%
+reality of what happens when I get into
+a big steel box press a button and Rise
+
+ align:start position:0%
+a big steel box press a button and Rise
+ 
+
+ align:start position:0%
+a big steel box press a button and Rise
+into the sky of course I
+
+ align:start position:0%
+into the sky of course I
+ 
+
+ align:start position:0%
+into the sky of course I
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+don't okay reactions
+
+ align:start position:0%
+don't okay reactions
+ 
+
+ align:start position:0%
+don't okay reactions
+comments H it's nice how it's like a
+
+ align:start position:0%
+comments H it's nice how it's like a
+ 
+
+ align:start position:0%
+comments H it's nice how it's like a
+reenactment but it's like so like
+
+ align:start position:0%
+reenactment but it's like so like
+ 
+
+ align:start position:0%
+reenactment but it's like so like
+theatrical that it's really interesting
+
+ align:start position:0%
+theatrical that it's really interesting
+ 
+
+ align:start position:0%
+theatrical that it's really interesting
+even
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+though it's interesting like the the
+
+ align:start position:0%
+though it's interesting like the the
+ 
+
+ align:start position:0%
+though it's interesting like the the
+pace at which it's narrated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah kind of exoticized them and
+
+ align:start position:0%
+um yeah kind of exoticized them and
+ 
+
+ align:start position:0%
+um yeah kind of exoticized them and
+shows them in in their capacity of of
+
+ align:start position:0%
+shows them in in their capacity of of
+ 
+
+ align:start position:0%
+shows them in in their capacity of of
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+
+ align:start position:0%
+breaking down so any this kind of
+ 
+
+ align:start position:0%
+breaking down so any this kind of
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+
+ align:start position:0%
+romantic notion of you know in the end
+ 
+
+ align:start position:0%
+romantic notion of you know in the end
+everything this one tiny little bit can
+
+ align:start position:0%
+everything this one tiny little bit can
+ 
+
+ align:start position:0%
+everything this one tiny little bit can
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+
+ align:start position:0%
+make everything else fall apart and it's
+ 
+
+ align:start position:0%
+make everything else fall apart and it's
+um I mean it just looks like a a fiction
+
+ align:start position:0%
+um I mean it just looks like a a fiction
+ 
+
+ align:start position:0%
+um I mean it just looks like a a fiction
+movie yeah so stylistically right so
+
+ align:start position:0%
+movie yeah so stylistically right so
+ 
+
+ align:start position:0%
+movie yeah so stylistically right so
+it's filmed as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a well you also have to see the
+
+ align:start position:0%
+a well you also have to see the
+ 
+
+ align:start position:0%
+a well you also have to see the
+relationship between this one this is
+
+ align:start position:0%
+relationship between this one this is
+ 
+
+ align:start position:0%
+relationship between this one this is
+the first episode and some of the other
+
+ align:start position:0%
+the first episode and some of the other
+ 
+
+ align:start position:0%
+the first episode and some of the other
+episodes in the series so this one
+
+ align:start position:0%
+episodes in the series so this one
+ 
+
+ align:start position:0%
+episodes in the series so this one
+focuses on New York City as the
+
+ align:start position:0%
+focuses on New York City as the
+ 
+
+ align:start position:0%
+focuses on New York City as the
+modern technological Metropolis um a lot
+
+ align:start position:0%
+modern technological Metropolis um a lot
+ 
+
+ align:start position:0%
+modern technological Metropolis um a lot
+of the other episodes in the series um
+
+ align:start position:0%
+of the other episodes in the series um
+ 
+
+ align:start position:0%
+of the other episodes in the series um
+travel to different parts of the world
+
+ align:start position:0%
+travel to different parts of the world
+ 
+
+ align:start position:0%
+travel to different parts of the world
+and different historical time periods so
+
+ align:start position:0%
+and different historical time periods so
+ 
+
+ align:start position:0%
+and different historical time periods so
+it might start off you know in you know
+
+ align:start position:0%
+it might start off you know in you know
+ 
+
+ align:start position:0%
+it might start off you know in you know
+it might be about the development of the
+
+ align:start position:0%
+it might be about the development of the
+ 
+
+ align:start position:0%
+it might be about the development of the
+the printing press and it might go back
+
+ align:start position:0%
+the printing press and it might go back
+ 
+
+ align:start position:0%
+the printing press and it might go back
+to the Middle Ages and then but it's
+
+ align:start position:0%
+to the Middle Ages and then but it's
+ 
+
+ align:start position:0%
+to the Middle Ages and then but it's
+following some technology historically
+
+ align:start position:0%
+following some technology historically
+ 
+
+ align:start position:0%
+following some technology historically
+through time and how this technology
+
+ align:start position:0%
+through time and how this technology
+ 
+
+ align:start position:0%
+through time and how this technology
+triggered all these kinds of impacts and
+
+ align:start position:0%
+triggered all these kinds of impacts and
+ 
+
+ align:start position:0%
+triggered all these kinds of impacts and
+so the idea is to take things that you
+
+ align:start position:0%
+so the idea is to take things that you
+ 
+
+ align:start position:0%
+so the idea is to take things that you
+would never expect and Trace back its
+
+ align:start position:0%
+would never expect and Trace back its
+ 
+
+ align:start position:0%
+would never expect and Trace back its
+genealogy and to argue that well it was
+
+ align:start position:0%
+genealogy and to argue that well it was
+ 
+
+ align:start position:0%
+genealogy and to argue that well it was
+linked to this kind of technological
+
+ align:start position:0%
+linked to this kind of technological
+ 
+
+ align:start position:0%
+linked to this kind of technological
+trans transformation that happened in
+
+ align:start position:0%
+trans transformation that happened in
+ 
+
+ align:start position:0%
+trans transformation that happened in
+this part of the world in this time that
+
+ align:start position:0%
+this part of the world in this time that
+ 
+
+ align:start position:0%
+this part of the world in this time that
+you never would have suspected basically
+
+ align:start position:0%
+you never would have suspected basically
+ 
+
+ align:start position:0%
+you never would have suspected basically
+yeah I mean the the thesis is just as an
+
+ align:start position:0%
+yeah I mean the the thesis is just as an
+ 
+
+ align:start position:0%
+yeah I mean the the thesis is just as an
+example the second episode uh begins
+
+ align:start position:0%
+example the second episode uh begins
+ 
+
+ align:start position:0%
+example the second episode uh begins
+with uh the coining of money the first
+
+ align:start position:0%
+with uh the coining of money the first
+ 
+
+ align:start position:0%
+with uh the coining of money the first
+money uh several th you know over 2,000
+
+ align:start position:0%
+money uh several th you know over 2,000
+ 
+
+ align:start position:0%
+money uh several th you know over 2,000
+years ago and traces this argument that
+
+ align:start position:0%
+years ago and traces this argument that
+ 
+
+ align:start position:0%
+years ago and traces this argument that
+the direct result of that was the
+
+ align:start position:0%
+the direct result of that was the
+ 
+
+ align:start position:0%
+the direct result of that was the
+development of the atomic
+
+ align:start position:0%
+development of the atomic
+ 
+
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+development of the atomic
+bomb and traces sort of a technological
+
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+bomb and traces sort of a technological
+ 
+
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+bomb and traces sort of a technological
+evolutionary
+
+ align:start position:0%
+evolutionary
+ 
+
+ align:start position:0%
+evolutionary
+connection argument from one to the
+
+ align:start position:0%
+connection argument from one to the
+ 
+
+ align:start position:0%
+connection argument from one to the
+other with multiple steps in between so
+
+ align:start position:0%
+other with multiple steps in between so
+ 
+
+ align:start position:0%
+other with multiple steps in between so
+the and you know the connection in that
+
+ align:start position:0%
+the and you know the connection in that
+ 
+
+ align:start position:0%
+the and you know the connection in that
+instance is the connection between this
+
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+instance is the connection between this
+ 
+
+ align:start position:0%
+instance is the connection between this
+one tiny accident of technology in one
+
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+one tiny accident of technology in one
+ 
+
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+one tiny accident of technology in one
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+
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+part of the world with the next one with
+ 
+
+ align:start position:0%
+part of the world with the next one with
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+
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+the next one with the next one so this
+ 
+
+ align:start position:0%
+the next one with the next one so this
+is kind of Interest an interesting
+
+ align:start position:0%
+is kind of Interest an interesting
+ 
+
+ align:start position:0%
+is kind of Interest an interesting
+thematic way of getting into it because
+
+ align:start position:0%
+thematic way of getting into it because
+ 
+
+ align:start position:0%
+thematic way of getting into it because
+uh he's looking at a network and how one
+
+ align:start position:0%
+uh he's looking at a network and how one
+ 
+
+ align:start position:0%
+uh he's looking at a network and how one
+tiny piece of a of a network can have
+
+ align:start position:0%
+tiny piece of a of a network can have
+ 
+
+ align:start position:0%
+tiny piece of a of a network can have
+these massive repercussions across the
+
+ align:start position:0%
+these massive repercussions across the
+ 
+
+ align:start position:0%
+these massive repercussions across the
+network which is exactly what he then
+
+ align:start position:0%
+network which is exactly what he then
+ 
+
+ align:start position:0%
+network which is exactly what he then
+says about technology throughout the
+
+ align:start position:0%
+says about technology throughout the
+ 
+
+ align:start position:0%
+says about technology throughout the
+rest of the series so there's there's
+
+ align:start position:0%
+rest of the series so there's there's
+ 
+
+ align:start position:0%
+rest of the series so there's there's
+two questions to be asked then I mean
+
+ align:start position:0%
+two questions to be asked then I mean
+ 
+
+ align:start position:0%
+two questions to be asked then I mean
+one so once you know where the rest of
+
+ align:start position:0%
+one so once you know where the rest of
+ 
+
+ align:start position:0%
+one so once you know where the rest of
+the series is going and then it's set up
+
+ align:start position:0%
+the series is going and then it's set up
+ 
+
+ align:start position:0%
+the series is going and then it's set up
+sort of as this detective series through
+
+ align:start position:0%
+sort of as this detective series through
+ 
+
+ align:start position:0%
+sort of as this detective series through
+time and across space how do they convey
+
+ align:start position:0%
+time and across space how do they convey
+ 
+
+ align:start position:0%
+time and across space how do they convey
+aesthetically the sense that this is
+
+ align:start position:0%
+aesthetically the sense that this is
+ 
+
+ align:start position:0%
+aesthetically the sense that this is
+sort of a detective story and if you
+
+ align:start position:0%
+sort of a detective story and if you
+ 
+
+ align:start position:0%
+sort of a detective story and if you
+think back I mean how many of you have
+
+ align:start position:0%
+think back I mean how many of you have
+ 
+
+ align:start position:0%
+think back I mean how many of you have
+watched old film Noir
+
+ align:start position:0%
+watched old film Noir
+ 
+
+ align:start position:0%
+watched old film Noir
+movies you know the film Noir genre the
+
+ align:start position:0%
+movies you know the film Noir genre the
+ 
+
+ align:start position:0%
+movies you know the film Noir genre the
+the old black and white where you know
+
+ align:start position:0%
+the old black and white where you know
+ 
+
+ align:start position:0%
+the old black and white where you know
+so so the shots of him with half his
+
+ align:start position:0%
+so so the shots of him with half his
+ 
+
+ align:start position:0%
+so so the shots of him with half his
+face and Shadow you know wearing the
+
+ align:start position:0%
+face and Shadow you know wearing the
+ 
+
+ align:start position:0%
+face and Shadow you know wearing the
+Overcoat you don't you there's a lot of
+
+ align:start position:0%
+Overcoat you don't you there's a lot of
+ 
+
+ align:start position:0%
+Overcoat you don't you there's a lot of
+darkness in here right that's that's the
+
+ align:start position:0%
+darkness in here right that's that's the
+ 
+
+ align:start position:0%
+darkness in here right that's that's the
+old film Noir style so it's deliberately
+
+ align:start position:0%
+old film Noir style so it's deliberately
+ 
+
+ align:start position:0%
+old film Noir style so it's deliberately
+drawing on the earlier film Noir Style
+
+ align:start position:0%
+drawing on the earlier film Noir Style
+ 
+
+ align:start position:0%
+drawing on the earlier film Noir Style
+of you know the late 40s you know or
+
+ align:start position:0%
+of you know the late 40s you know or
+ 
+
+ align:start position:0%
+of you know the late 40s you know or
+early 50s if that's that's right
+
+ align:start position:0%
+early 50s if that's that's right
+ 
+
+ align:start position:0%
+early 50s if that's that's right
+chronologically um you know darkness in
+
+ align:start position:0%
+chronologically um you know darkness in
+ 
+
+ align:start position:0%
+chronologically um you know darkness in
+Shadow to convey that sense to audiences
+
+ align:start position:0%
+Shadow to convey that sense to audiences
+ 
+
+ align:start position:0%
+Shadow to convey that sense to audiences
+would have that would have been very
+
+ align:start position:0%
+would have that would have been very
+ 
+
+ align:start position:0%
+would have that would have been very
+familiar with that genre the sense that
+
+ align:start position:0%
+familiar with that genre the sense that
+ 
+
+ align:start position:0%
+familiar with that genre the sense that
+ah this is some dark mysterious
+
+ align:start position:0%
+ah this is some dark mysterious
+ 
+
+ align:start position:0%
+ah this is some dark mysterious
+detective story that we're going to be
+
+ align:start position:0%
+detective story that we're going to be
+ 
+
+ align:start position:0%
+detective story that we're going to be
+you know taking you on so one question
+
+ align:start position:0%
+you know taking you on so one question
+ 
+
+ align:start position:0%
+you know taking you on so one question
+is about the kinds of aesthetic choices
+
+ align:start position:0%
+is about the kinds of aesthetic choices
+ 
+
+ align:start position:0%
+is about the kinds of aesthetic choices
+that they made to convey the kind of
+
+ align:start position:0%
+that they made to convey the kind of
+ 
+
+ align:start position:0%
+that they made to convey the kind of
+narrative that they wanted to convey
+
+ align:start position:0%
+narrative that they wanted to convey
+ 
+
+ align:start position:0%
+narrative that they wanted to convey
+about science that this is a detective
+
+ align:start position:0%
+about science that this is a detective
+ 
+
+ align:start position:0%
+about science that this is a detective
+story so that's one question and then
+
+ align:start position:0%
+story so that's one question and then
+ 
+
+ align:start position:0%
+story so that's one question and then
+the other thing um as Chris was just
+
+ align:start position:0%
+the other thing um as Chris was just
+ 
+
+ align:start position:0%
+the other thing um as Chris was just
+describing sort of the relationship
+
+ align:start position:0%
+describing sort of the relationship
+ 
+
+ align:start position:0%
+describing sort of the relationship
+between the different episodes it gets
+
+ align:start position:0%
+between the different episodes it gets
+ 
+
+ align:start position:0%
+between the different episodes it gets
+to this question about um accuracy I
+
+ align:start position:0%
+to this question about um accuracy I
+ 
+
+ align:start position:0%
+to this question about um accuracy I
+mean so this so the way they have of
+
+ align:start position:0%
+mean so this so the way they have of
+ 
+
+ align:start position:0%
+mean so this so the way they have of
+doing this well uh well so you start out
+
+ align:start position:0%
+doing this well uh well so you start out
+ 
+
+ align:start position:0%
+doing this well uh well so you start out
+with this uh transformation here and it
+
+ align:start position:0%
+with this uh transformation here and it
+ 
+
+ align:start position:0%
+with this uh transformation here and it
+has these incredible repercussions way
+
+ align:start position:0%
+has these incredible repercussions way
+ 
+
+ align:start position:0%
+has these incredible repercussions way
+over here and
+
+ align:start position:0%
+over here and
+ 
+
+ align:start position:0%
+over here and
+then one of the questions that we kind
+
+ align:start position:0%
+then one of the questions that we kind
+ 
+
+ align:start position:0%
+then one of the questions that we kind
+of always have about the series is like
+
+ align:start position:0%
+of always have about the series is like
+ 
+
+ align:start position:0%
+of always have about the series is like
+how much does sort of it ended up being
+
+ align:start position:0%
+how much does sort of it ended up being
+ 
+
+ align:start position:0%
+how much does sort of it ended up being
+sort of Just So Stories and I mean can
+
+ align:start position:0%
+sort of Just So Stories and I mean can
+ 
+
+ align:start position:0%
+sort of Just So Stories and I mean can
+you really kind of do that kind of um
+
+ align:start position:0%
+you really kind of do that kind of um
+ 
+
+ align:start position:0%
+you really kind of do that kind of um
+you know that kind of linking in quite
+
+ align:start position:0%
+you know that kind of linking in quite
+ 
+
+ align:start position:0%
+you know that kind of linking in quite
+the way that it does they're all very
+
+ align:start position:0%
+the way that it does they're all very
+ 
+
+ align:start position:0%
+the way that it does they're all very
+cool and interesting connections but the
+
+ align:start position:0%
+cool and interesting connections but the
+ 
+
+ align:start position:0%
+cool and interesting connections but the
+question is at what point are they
+
+ align:start position:0%
+question is at what point are they
+ 
+
+ align:start position:0%
+question is at what point are they
+serving a narrative and at what point
+
+ align:start position:0%
+serving a narrative and at what point
+ 
+
+ align:start position:0%
+serving a narrative and at what point
+are they
+
+ align:start position:0%
+are they
+ 
+
+ align:start position:0%
+are they
+um really interesting making any kind of
+
+ align:start position:0%
+um really interesting making any kind of
+ 
+
+ align:start position:0%
+um really interesting making any kind of
+logical connection but they're just sort
+
+ align:start position:0%
+logical connection but they're just sort
+ 
+
+ align:start position:0%
+logical connection but they're just sort
+of asserting a connection because it's
+
+ align:start position:0%
+of asserting a connection because it's
+ 
+
+ align:start position:0%
+of asserting a connection because it's
+good thematically or narratively
+
+ align:start position:0%
+good thematically or narratively
+ 
+
+ align:start position:0%
+good thematically or narratively
+speaking let's let's take a a quick
+
+ align:start position:0%
+speaking let's let's take a a quick
+ 
+
+ align:start position:0%
+speaking let's let's take a a quick
+break so we have the entire series of
+
+ align:start position:0%
+break so we have the entire series of
+ 
+
+ align:start position:0%
+break so we have the entire series of
+this in the DV lab if anybody's
+
+ align:start position:0%
+this in the DV lab if anybody's
+ 
+
+ align:start position:0%
+this in the DV lab if anybody's
+interested I mean they do make these
+
+ align:start position:0%
+interested I mean they do make these
+ 
+
+ align:start position:0%
+interested I mean they do make these
+very compelling telling stories and
+
+ align:start position:0%
+very compelling telling stories and
+ 
+
+ align:start position:0%
+very compelling telling stories and
+whether they're Just So Stories as Chris
+
+ align:start position:0%
+whether they're Just So Stories as Chris
+ 
+
+ align:start position:0%
+whether they're Just So Stories as Chris
+said or whether they actually
+
+ align:start position:0%
+said or whether they actually
+ 
+
+ align:start position:0%
+said or whether they actually
+have uh something legit to say about how
+
+ align:start position:0%
+have uh something legit to say about how
+ 
+
+ align:start position:0%
+have uh something legit to say about how
+one one technology uh feeds another is
+
+ align:start position:0%
+one one technology uh feeds another is
+ 
+
+ align:start position:0%
+one one technology uh feeds another is
+probably a bit of both it's probably
+
+ align:start position:0%
+probably a bit of both it's probably
+ 
+
+ align:start position:0%
+probably a bit of both it's probably
+kind of a mix of narrative flourish and
+
+ align:start position:0%
+kind of a mix of narrative flourish and
+ 
+
+ align:start position:0%
+kind of a mix of narrative flourish and
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+substance but certainly they're they're
+
+ align:start position:0%
+substance but certainly they're they're
+ 
+
+ align:start position:0%
+substance but certainly they're they're
+fun to watch and they were as we
+
+ align:start position:0%
+fun to watch and they were as we
+ 
+
+ align:start position:0%
+fun to watch and they were as we
+mentioned very influential in um getting
+
+ align:start position:0%
+mentioned very influential in um getting
+ 
+
+ align:start position:0%
+mentioned very influential in um getting
+certain people to be interested in these
+
+ align:start position:0%
+certain people to be interested in these
+ 
+
+ align:start position:0%
+certain people to be interested in these
+kinds of questions and want to explore
+
+ align:start position:0%
+kinds of questions and want to explore
+ 
+
+ align:start position:0%
+kinds of questions and want to explore
+them well and I think in and how people
+
+ align:start position:0%
+them well and I think in and how people
+ 
+
+ align:start position:0%
+them well and I think in and how people
+think about yeah science and technology
+
+ align:start position:0%
+think about yeah science and technology
+ 
+
+ align:start position:0%
+think about yeah science and technology
+and in a in a kind of an evolutionary
+
+ align:start position:0%
+and in a in a kind of an evolutionary
+ 
+
+ align:start position:0%
+and in a in a kind of an evolutionary
+way um so at this point any any final
+
+ align:start position:0%
+way um so at this point any any final
+ 
+
+ align:start position:0%
+way um so at this point any any final
+comments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on any final comments on on uh
+
+ align:start position:0%
+on any final comments on on uh
+ 
+
+ align:start position:0%
+on any final comments on on uh
+connections I think it's just funny how
+
+ align:start position:0%
+connections I think it's just funny how
+ 
+
+ align:start position:0%
+connections I think it's just funny how
+like whenever there's a mystery movie
+
+ align:start position:0%
+like whenever there's a mystery movie
+ 
+
+ align:start position:0%
+like whenever there's a mystery movie
+it's they always like it has to be like
+
+ align:start position:0%
+it's they always like it has to be like
+ 
+
+ align:start position:0%
+it's they always like it has to be like
+someone British or with an accent right
+
+ align:start position:0%
+someone British or with an accent right
+ 
+
+ align:start position:0%
+someone British or with an accent right
+exactly and it kind of like dark maybe
+
+ align:start position:0%
+exactly and it kind of like dark maybe
+ 
+
+ align:start position:0%
+exactly and it kind of like dark maybe
+like damp sort of environments yeah
+
+ align:start position:0%
+like damp sort of environments yeah
+ 
+
+ align:start position:0%
+like damp sort of environments yeah
+exactly and what's funny one of the
+
+ align:start position:0%
+exactly and what's funny one of the
+ 
+
+ align:start position:0%
+exactly and what's funny one of the
+things that I think is absolutely
+
+ align:start position:0%
+things that I think is absolutely
+ 
+
+ align:start position:0%
+things that I think is absolutely
+hysterical um well he has an Overcoat on
+
+ align:start position:0%
+hysterical um well he has an Overcoat on
+ 
+
+ align:start position:0%
+hysterical um well he has an Overcoat on
+this so you don't see it a lot but he
+
+ align:start position:0%
+this so you don't see it a lot but he
+ 
+
+ align:start position:0%
+this so you don't see it a lot but he
+always wears this this tan leisure suit
+
+ align:start position:0%
+always wears this this tan leisure suit
+ 
+
+ align:start position:0%
+always wears this this tan leisure suit
+and so you go through all the episodes
+
+ align:start position:0%
+and so you go through all the episodes
+ 
+
+ align:start position:0%
+and so you go through all the episodes
+he's always got the tan leisure suit on
+
+ align:start position:0%
+he's always got the tan leisure suit on
+ 
+
+ align:start position:0%
+he's always got the tan leisure suit on
+so it's like that's one of the things
+
+ align:start position:0%
+so it's like that's one of the things
+ 
+
+ align:start position:0%
+so it's like that's one of the things
+that they that they use as element of
+
+ align:start position:0%
+that they that they use as element of
+ 
+
+ align:start position:0%
+that they that they use as element of
+continuity through throughout a lot of
+
+ align:start position:0%
+continuity through throughout a lot of
+ 
+
+ align:start position:0%
+continuity through throughout a lot of
+the throughout a lot of the videos but
+
+ align:start position:0%
+the throughout a lot of the videos but
+ 
+
+ align:start position:0%
+the throughout a lot of the videos but
+the but as you say the you know the
+
+ align:start position:0%
+the but as you say the you know the
+ 
+
+ align:start position:0%
+the but as you say the you know the
+British accent the kind of collar turned
+
+ align:start position:0%
+British accent the kind of collar turned
+ 
+
+ align:start position:0%
+British accent the kind of collar turned
+up the you know the film Noir lighting
+
+ align:start position:0%
+up the you know the film Noir lighting
+ 
+
+ align:start position:0%
+up the you know the film Noir lighting
+so again through various kinds of
+
+ align:start position:0%
+so again through various kinds of
+ 
+
+ align:start position:0%
+so again through various kinds of
+aesthetic choices um and how people are
+
+ align:start position:0%
+aesthetic choices um and how people are
+ 
+
+ align:start position:0%
+aesthetic choices um and how people are
+addressed what kinds of things get
+
+ align:start position:0%
+addressed what kinds of things get
+ 
+
+ align:start position:0%
+addressed what kinds of things get
+conveyed when you go to make your final
+
+ align:start position:0%
+conveyed when you go to make your final
+ 
+
+ align:start position:0%
+conveyed when you go to make your final
+projects um how do those kinds of
+
+ align:start position:0%
+projects um how do those kinds of
+ 
+
+ align:start position:0%
+projects um how do those kinds of
+aesthetic um elements um affect the kind
+
+ align:start position:0%
+aesthetic um elements um affect the kind
+ 
+
+ align:start position:0%
+aesthetic um elements um affect the kind
+of narrative that's going to end up
+
+ align:start position:0%
+of narrative that's going to end up
+ 
+
+ align:start position:0%
+of narrative that's going to end up
+being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+told okay so just just to sort of
+
+ align:start position:0%
+told okay so just just to sort of
+ 
+
+ align:start position:0%
+told okay so just just to sort of
+summarize some of this up so one of the
+
+ align:start position:0%
+summarize some of this up so one of the
+ 
+
+ align:start position:0%
+summarize some of this up so one of the
+things we've been we've uh uh been
+
+ align:start position:0%
+things we've been we've uh uh been
+ 
+
+ align:start position:0%
+things we've been we've uh uh been
+wanting to think about
+
+ align:start position:0%
+wanting to think about
+ 
+
+ align:start position:0%
+wanting to think about
+here is the question or at least get out
+
+ align:start position:0%
+here is the question or at least get out
+ 
+
+ align:start position:0%
+here is the question or at least get out
+on the table what kinds of narratives
+
+ align:start position:0%
+on the table what kinds of narratives
+ 
+
+ align:start position:0%
+on the table what kinds of narratives
+have commonly been told about science
+
+ align:start position:0%
+have commonly been told about science
+ 
+
+ align:start position:0%
+have commonly been told about science
+through documentary film and there's
+
+ align:start position:0%
+through documentary film and there's
+ 
+
+ align:start position:0%
+through documentary film and there's
+been certain genres of documentary film
+
+ align:start position:0%
+been certain genres of documentary film
+ 
+
+ align:start position:0%
+been certain genres of documentary film
+Mak about science that have been more
+
+ align:start position:0%
+Mak about science that have been more
+ 
+
+ align:start position:0%
+Mak about science that have been more
+common than others for example this kind
+
+ align:start position:0%
+common than others for example this kind
+ 
+
+ align:start position:0%
+common than others for example this kind
+of detective version or the educational
+
+ align:start position:0%
+of detective version or the educational
+ 
+
+ align:start position:0%
+of detective version or the educational
+film or whatever it is but one of the
+
+ align:start position:0%
+film or whatever it is but one of the
+ 
+
+ align:start position:0%
+film or whatever it is but one of the
+other questions that we want to throw
+
+ align:start position:0%
+other questions that we want to throw
+ 
+
+ align:start position:0%
+other questions that we want to throw
+out is what kinds of narratives about
+
+ align:start position:0%
+out is what kinds of narratives about
+ 
+
+ align:start position:0%
+out is what kinds of narratives about
+science have not been commonly told
+
+ align:start position:0%
+science have not been commonly told
+ 
+
+ align:start position:0%
+science have not been commonly told
+right and I think there's a lot of other
+
+ align:start position:0%
+right and I think there's a lot of other
+ 
+
+ align:start position:0%
+right and I think there's a lot of other
+narratives out there about science and
+
+ align:start position:0%
+narratives out there about science and
+ 
+
+ align:start position:0%
+narratives out there about science and
+technology that haven't necessarily been
+
+ align:start position:0%
+technology that haven't necessarily been
+ 
+
+ align:start position:0%
+technology that haven't necessarily been
+told a whole lot
+
+ align:start position:0%
+told a whole lot
+ 
+
+ align:start position:0%
+told a whole lot
+and uh one of the so Chris Chris and I
+
+ align:start position:0%
+and uh one of the so Chris Chris and I
+ 
+
+ align:start position:0%
+and uh one of the so Chris Chris and I
+when we were thinking about setting up
+
+ align:start position:0%
+when we were thinking about setting up
+ 
+
+ align:start position:0%
+when we were thinking about setting up
+this class I mean one of the things that
+
+ align:start position:0%
+this class I mean one of the things that
+ 
+
+ align:start position:0%
+this class I mean one of the things that
+we tried to think about was sort of the
+
+ align:start position:0%
+we tried to think about was sort of the
+ 
+
+ align:start position:0%
+we tried to think about was sort of the
+direct Cinema style which we're going to
+
+ align:start position:0%
+direct Cinema style which we're going to
+ 
+
+ align:start position:0%
+direct Cinema style which we're going to
+talk about in a couple weeks but if you
+
+ align:start position:0%
+talk about in a couple weeks but if you
+ 
+
+ align:start position:0%
+talk about in a couple weeks but if you
+think again back to that film primary
+
+ align:start position:0%
+think again back to that film primary
+ 
+
+ align:start position:0%
+think again back to that film primary
+where it's sort of like handheld cameras
+
+ align:start position:0%
+where it's sort of like handheld cameras
+ 
+
+ align:start position:0%
+where it's sort of like handheld cameras
+focusing on the action moving around you
+
+ align:start position:0%
+focusing on the action moving around you
+ 
+
+ align:start position:0%
+focusing on the action moving around you
+it's much rarer for example to see films
+
+ align:start position:0%
+it's much rarer for example to see films
+ 
+
+ align:start position:0%
+it's much rarer for example to see films
+made about sort of science and
+
+ align:start position:0%
+made about sort of science and
+ 
+
+ align:start position:0%
+made about sort of science and
+technology that that draw upon those
+
+ align:start position:0%
+technology that that draw upon those
+ 
+
+ align:start position:0%
+technology that that draw upon those
+kinds of techniques um compared to some
+
+ align:start position:0%
+kinds of techniques um compared to some
+ 
+
+ align:start position:0%
+kinds of techniques um compared to some
+others or certain kinds of narratives
+
+ align:start position:0%
+others or certain kinds of narratives
+ 
+
+ align:start position:0%
+others or certain kinds of narratives
+that would come out of that kind of
+
+ align:start position:0%
+that would come out of that kind of
+ 
+
+ align:start position:0%
+that would come out of that kind of
+style of film making um so one of the
+
+ align:start position:0%
+style of film making um so one of the
+ 
+
+ align:start position:0%
+style of film making um so one of the
+things that we want you to be thinking
+
+ align:start position:0%
+things that we want you to be thinking
+ 
+
+ align:start position:0%
+things that we want you to be thinking
+about through the course of this class
+
+ align:start position:0%
+about through the course of this class
+ 
+
+ align:start position:0%
+about through the course of this class
+is okay so there's the there's the the
+
+ align:start position:0%
+is okay so there's the there's the the
+ 
+
+ align:start position:0%
+is okay so there's the there's the the
+the more common narratives that could
+
+ align:start position:0%
+the more common narratives that could
+ 
+
+ align:start position:0%
+the more common narratives that could
+told about science and those might be
+
+ align:start position:0%
+told about science and those might be
+ 
+
+ align:start position:0%
+told about science and those might be
+very compelling and you might very well
+
+ align:start position:0%
+very compelling and you might very well
+ 
+
+ align:start position:0%
+very compelling and you might very well
+want to draw on a fi final project that
+
+ align:start position:0%
+want to draw on a fi final project that
+ 
+
+ align:start position:0%
+want to draw on a fi final project that
+draws on some of those kinds of genres
+
+ align:start position:0%
+draws on some of those kinds of genres
+ 
+
+ align:start position:0%
+draws on some of those kinds of genres
+or you might also want to be thinking
+
+ align:start position:0%
+or you might also want to be thinking
+ 
+
+ align:start position:0%
+or you might also want to be thinking
+about what kinds of stories about
+
+ align:start position:0%
+about what kinds of stories about
+ 
+
+ align:start position:0%
+about what kinds of stories about
+science haven't been told as much that
+
+ align:start position:0%
+science haven't been told as much that
+ 
+
+ align:start position:0%
+science haven't been told as much that
+maybe I want to tell okay so we want to
+
+ align:start position:0%
+maybe I want to tell okay so we want to
+ 
+
+ align:start position:0%
+maybe I want to tell okay so we want to
+kind of keep it all open to you and get
+
+ align:start position:0%
+kind of keep it all open to you and get
+ 
+
+ align:start position:0%
+kind of keep it all open to you and get
+you thinking about all of those and the
+
+ align:start position:0%
+you thinking about all of those and the
+ 
+
+ align:start position:0%
+you thinking about all of those and the
+way we tried to set up the class is that
+
+ align:start position:0%
+way we tried to set up the class is that
+ 
+
+ align:start position:0%
+way we tried to set up the class is that
+throughout the course you're going to be
+
+ align:start position:0%
+throughout the course you're going to be
+ 
+
+ align:start position:0%
+throughout the course you're going to be
+exposed to lots of different kinds of
+
+ align:start position:0%
+exposed to lots of different kinds of
+ 
+
+ align:start position:0%
+exposed to lots of different kinds of
+documentary film making techniques um um
+
+ align:start position:0%
+documentary film making techniques um um
+ 
+
+ align:start position:0%
+documentary film making techniques um um
+as well as a whole range of different
+
+ align:start position:0%
+as well as a whole range of different
+ 
+
+ align:start position:0%
+as well as a whole range of different
+kinds of narrative styles for talking
+
+ align:start position:0%
+kinds of narrative styles for talking
+ 
+
+ align:start position:0%
+kinds of narrative styles for talking
+about science and documentary so the
+
+ align:start position:0%
+about science and documentary so the
+ 
+
+ align:start position:0%
+about science and documentary so the
+idea is to kind of give you a broad
+
+ align:start position:0%
+idea is to kind of give you a broad
+ 
+
+ align:start position:0%
+idea is to kind of give you a broad
+toolkit okay both in terms of the kinds
+
+ align:start position:0%
+toolkit okay both in terms of the kinds
+ 
+
+ align:start position:0%
+toolkit okay both in terms of the kinds
+of narratives you might want to use or
+
+ align:start position:0%
+of narratives you might want to use or
+ 
+
+ align:start position:0%
+of narratives you might want to use or
+or you might want to be telling um but
+
+ align:start position:0%
+or you might want to be telling um but
+ 
+
+ align:start position:0%
+or you might want to be telling um but
+also in terms of the kinds of techniques
+
+ align:start position:0%
+also in terms of the kinds of techniques
+ 
+
+ align:start position:0%
+also in terms of the kinds of techniques
+or styles of shooting that you might
+
+ align:start position:0%
+or styles of shooting that you might
+ 
+
+ align:start position:0%
+or styles of shooting that you might
+want to engage in so the idea is to give
+
+ align:start position:0%
+want to engage in so the idea is to give
+ 
+
+ align:start position:0%
+want to engage in so the idea is to give
+you this you know present this kind of
+
+ align:start position:0%
+you this you know present this kind of
+ 
+
+ align:start position:0%
+you this you know present this kind of
+whole range of things um and then this
+
+ align:start position:0%
+whole range of things um and then this
+ 
+
+ align:start position:0%
+whole range of things um and then this
+is your toolbox and you get to decide
+
+ align:start position:0%
+is your toolbox and you get to decide
+ 
+
+ align:start position:0%
+is your toolbox and you get to decide
+what what kind of story do you want to
+
+ align:start position:0%
+what what kind of story do you want to
+ 
+
+ align:start position:0%
+what what kind of story do you want to
+tell and in order to tell that story
+
+ align:start position:0%
+tell and in order to tell that story
+ 
+
+ align:start position:0%
+tell and in order to tell that story
+what kinds of tools do you want to use
+
+ align:start position:0%
+what kinds of tools do you want to use
+ 
+
+ align:start position:0%
+what kinds of tools do you want to use
+what kind of narrative do you want to
+
+ align:start position:0%
+what kind of narrative do you want to
+ 
+
+ align:start position:0%
+what kind of narrative do you want to
+convey what kind of narrative best gets
+
+ align:start position:0%
+convey what kind of narrative best gets
+ 
+
+ align:start position:0%
+convey what kind of narrative best gets
+at what you want to what you want to get
+
+ align:start position:0%
+at what you want to what you want to get
+ 
+
+ align:start position:0%
+at what you want to what you want to get
+across okay so that um is the idea for
+
+ align:start position:0%
+across okay so that um is the idea for
+ 
+
+ align:start position:0%
+across okay so that um is the idea for
+that anything to add onto that or no I
+
+ align:start position:0%
+that anything to add onto that or no I
+ 
+
+ align:start position:0%
+that anything to add onto that or no I
+think that's good summary okay so then
+
+ align:start position:0%
+think that's good summary okay so then
+ 
+
+ align:start position:0%
+think that's good summary okay so then
+uh before we end then the last little
+
+ align:start position:0%
+uh before we end then the last little
+ 
+
+ align:start position:0%
+uh before we end then the last little
+thing that we want to do is just talk a
+
+ align:start position:0%
+thing that we want to do is just talk a
+ 
+
+ align:start position:0%
+thing that we want to do is just talk a
+bit more about your final projects so
+
+ align:start position:0%
+bit more about your final projects so
+ 
+
+ align:start position:0%
+bit more about your final projects so
+that you're thinking thinking more about
+
+ align:start position:0%
+that you're thinking thinking more about
+ 
+
+ align:start position:0%
+that you're thinking thinking more about
+that again I know so Sabrina and Jessica
+
+ align:start position:0%
+that again I know so Sabrina and Jessica
+ 
+
+ align:start position:0%
+that again I know so Sabrina and Jessica
+and Karina and both of you you were also
+
+ align:start position:0%
+and Karina and both of you you were also
+ 
+
+ align:start position:0%
+and Karina and both of you you were also
+at the DV lab screening right at the
+
+ align:start position:0%
+at the DV lab screening right at the
+ 
+
+ align:start position:0%
+at the DV lab screening right at the
+Museum so um I don't know if there was
+
+ align:start position:0%
+Museum so um I don't know if there was
+ 
+
+ align:start position:0%
+Museum so um I don't know if there was
+sort
+
+ align:start position:0%
+sort
+ 
+
+ align:start position:0%
+sort
+of any reaction to those things that you
+
+ align:start position:0%
+of any reaction to those things that you
+ 
+
+ align:start position:0%
+of any reaction to those things that you
+thought were interesting as topics or
+
+ align:start position:0%
+thought were interesting as topics or
+ 
+
+ align:start position:0%
+thought were interesting as topics or
+narratives or things to potentially
+
+ align:start position:0%
+narratives or things to potentially
+ 
+
+ align:start position:0%
+narratives or things to potentially
+explore or things that you might have
+
+ align:start position:0%
+explore or things that you might have
+ 
+
+ align:start position:0%
+explore or things that you might have
+thought would have been interesting
+
+ align:start position:0%
+thought would have been interesting
+ 
+
+ align:start position:0%
+thought would have been interesting
+kinds of projects that weren't
+
+ align:start position:0%
+kinds of projects that weren't
+ 
+
+ align:start position:0%
+kinds of projects that weren't
+necessarily you didn't necessarily be
+
+ align:start position:0%
+necessarily you didn't necessarily be
+ 
+
+ align:start position:0%
+necessarily you didn't necessarily be
+made
+
+ align:start position:0%
+made
+ 
+
+ align:start position:0%
+made
+um anyway any kind of responses to the
+
+ align:start position:0%
+um anyway any kind of responses to the
+ 
+
+ align:start position:0%
+um anyway any kind of responses to the
+ones that you saw or if you just want to
+
+ align:start position:0%
+ones that you saw or if you just want to
+ 
+
+ align:start position:0%
+ones that you saw or if you just want to
+sort of skip to what you're potentially
+
+ align:start position:0%
+sort of skip to what you're potentially
+ 
+
+ align:start position:0%
+sort of skip to what you're potentially
+interested in doing I don't know how
+
+ align:start position:0%
+interested in doing I don't know how
+ 
+
+ align:start position:0%
+interested in doing I don't know how
+much thought you've put into what you EV
+
+ align:start position:0%
+much thought you've put into what you EV
+ 
+
+ align:start position:0%
+much thought you've put into what you EV
+obviously this is very casual at this
+
+ align:start position:0%
+obviously this is very casual at this
+ 
+
+ align:start position:0%
+obviously this is very casual at this
+point there is kind of a formal process
+
+ align:start position:0%
+point there is kind of a formal process
+ 
+
+ align:start position:0%
+point there is kind of a formal process
+later in the class of people presenting
+
+ align:start position:0%
+later in the class of people presenting
+ 
+
+ align:start position:0%
+later in the class of people presenting
+ideas and being able to sort of pick
+
+ align:start position:0%
+ideas and being able to sort of pick
+ 
+
+ align:start position:0%
+ideas and being able to sort of pick
+between several ideas hopefully so that
+
+ align:start position:0%
+between several ideas hopefully so that
+ 
+
+ align:start position:0%
+between several ideas hopefully so that
+you don't have to sort of settle very
+
+ align:start position:0%
+you don't have to sort of settle very
+ 
+
+ align:start position:0%
+you don't have to sort of settle very
+very quickly on something right so right
+
+ align:start position:0%
+very quickly on something right so right
+ 
+
+ align:start position:0%
+very quickly on something right so right
+at this stage now we just want sort of
+
+ align:start position:0%
+at this stage now we just want sort of
+ 
+
+ align:start position:0%
+at this stage now we just want sort of
+preliminary just to get you starting to
+
+ align:start position:0%
+preliminary just to get you starting to
+ 
+
+ align:start position:0%
+preliminary just to get you starting to
+think about stuff and you and you know
+
+ align:start position:0%
+think about stuff and you and you know
+ 
+
+ align:start position:0%
+think about stuff and you and you know
+even if you have the vaguest idea or
+
+ align:start position:0%
+even if you have the vaguest idea or
+ 
+
+ align:start position:0%
+even if you have the vaguest idea or
+maybe you don't even have any idea I
+
+ align:start position:0%
+maybe you don't even have any idea I
+ 
+
+ align:start position:0%
+maybe you don't even have any idea I
+mean any of that's okay but I'm just
+
+ align:start position:0%
+mean any of that's okay but I'm just
+ 
+
+ align:start position:0%
+mean any of that's okay but I'm just
+wondering what you're potentially
+
+ align:start position:0%
+wondering what you're potentially
+ 
+
+ align:start position:0%
+wondering what you're potentially
+thinking about doing and and something
+
+ align:start position:0%
+thinking about doing and and something
+ 
+
+ align:start position:0%
+thinking about doing and and something
+else to think about is again this is a
+
+ align:start position:0%
+else to think about is again this is a
+ 
+
+ align:start position:0%
+else to think about is again this is a
+class you know it's not film school
+
+ align:start position:0%
+class you know it's not film school
+ 
+
+ align:start position:0%
+class you know it's not film school
+right you don't have massive amounts of
+
+ align:start position:0%
+right you don't have massive amounts of
+ 
+
+ align:start position:0%
+right you don't have massive amounts of
+time also you have to be thinking about
+
+ align:start position:0%
+time also you have to be thinking about
+ 
+
+ align:start position:0%
+time also you have to be thinking about
+if you want to tell a particular story
+
+ align:start position:0%
+if you want to tell a particular story
+ 
+
+ align:start position:0%
+if you want to tell a particular story
+do you have enough time to be able to
+
+ align:start position:0%
+do you have enough time to be able to
+ 
+
+ align:start position:0%
+do you have enough time to be able to
+tell that story right so we we're not
+
+ align:start position:0%
+tell that story right so we we're not
+ 
+
+ align:start position:0%
+tell that story right so we we're not
+asking you to do these massive projects
+
+ align:start position:0%
+asking you to do these massive projects
+ 
+
+ align:start position:0%
+asking you to do these massive projects
+and keep in mind again that the DV Lab
+
+ align:start position:0%
+and keep in mind again that the DV Lab
+ 
+
+ align:start position:0%
+and keep in mind again that the DV Lab
+videos that you saw students worked on
+
+ align:start position:0%
+videos that you saw students worked on
+ 
+
+ align:start position:0%
+videos that you saw students worked on
+it one semester but then they also had a
+
+ align:start position:0%
+it one semester but then they also had a
+ 
+
+ align:start position:0%
+it one semester but then they also had a
+half class followup where they just
+
+ align:start position:0%
+half class followup where they just
+ 
+
+ align:start position:0%
+half class followup where they just
+worked on whatever project that they
+
+ align:start position:0%
+worked on whatever project that they
+ 
+
+ align:start position:0%
+worked on whatever project that they
+were doing most of them came out of that
+
+ align:start position:0%
+were doing most of them came out of that
+ 
+
+ align:start position:0%
+were doing most of them came out of that
+there were a couple few a few of them
+
+ align:start position:0%
+there were a couple few a few of them
+ 
+
+ align:start position:0%
+there were a couple few a few of them
+were just from the from few were just
+
+ align:start position:0%
+were just from the from few were just
+ 
+
+ align:start position:0%
+were just from the from few were just
+from the first
+
+ align:start position:0%
+from the first
+ 
+
+ align:start position:0%
+from the first
+semester but for your final project so
+
+ align:start position:0%
+semester but for your final project so
+ 
+
+ align:start position:0%
+semester but for your final project so
+we're not expecting some half hour piece
+
+ align:start position:0%
+we're not expecting some half hour piece
+ 
+
+ align:start position:0%
+we're not expecting some half hour piece
+in fact we would encourage people to
+
+ align:start position:0%
+in fact we would encourage people to
+ 
+
+ align:start position:0%
+in fact we would encourage people to
+keep it small how would you well
+
+ align:start position:0%
+keep it small how would you well
+ 
+
+ align:start position:0%
+keep it small how would you well
+TimeWise certainly you know probably
+
+ align:start position:0%
+TimeWise certainly you know probably
+ 
+
+ align:start position:0%
+TimeWise certainly you know probably
+under 10 minutes realistically um
+
+ align:start position:0%
+under 10 minutes realistically um
+ 
+
+ align:start position:0%
+under 10 minutes realistically um
+somewhere between two and 10 minutes
+
+ align:start position:0%
+somewhere between two and 10 minutes
+ 
+
+ align:start position:0%
+somewhere between two and 10 minutes
+some of the ones we saw on Friday were
+
+ align:start position:0%
+some of the ones we saw on Friday were
+ 
+
+ align:start position:0%
+some of the ones we saw on Friday were
+longer but again they had longer to work
+
+ align:start position:0%
+longer but again they had longer to work
+ 
+
+ align:start position:0%
+longer but again they had longer to work
+on them
+
+ align:start position:0%
+on them
+ 
+
+ align:start position:0%
+on them
+MH I think it was interesting to see I
+
+ align:start position:0%
+MH I think it was interesting to see I
+ 
+
+ align:start position:0%
+MH I think it was interesting to see I
+mean the the contast between Tom's piece
+
+ align:start position:0%
+mean the the contast between Tom's piece
+ 
+
+ align:start position:0%
+mean the the contast between Tom's piece
+and Emily's piece and I was trying to
+
+ align:start position:0%
+and Emily's piece and I was trying to
+ 
+
+ align:start position:0%
+and Emily's piece and I was trying to
+think where I want to situate myself
+
+ align:start position:0%
+think where I want to situate myself
+ 
+
+ align:start position:0%
+think where I want to situate myself
+along this continence just go somewhere
+
+ align:start position:0%
+along this continence just go somewhere
+ 
+
+ align:start position:0%
+along this continence just go somewhere
+and and you know shoot everything and
+
+ align:start position:0%
+and and you know shoot everything and
+ 
+
+ align:start position:0%
+and and you know shoot everything and
+and trying to get to shoot interesting
+
+ align:start position:0%
+and trying to get to shoot interesting
+ 
+
+ align:start position:0%
+and trying to get to shoot interesting
+things and people saying things that
+
+ align:start position:0%
+things and people saying things that
+ 
+
+ align:start position:0%
+things and people saying things that
+have some kind of you know powerful um
+
+ align:start position:0%
+have some kind of you know powerful um
+ 
+
+ align:start position:0%
+have some kind of you know powerful um
+narrative input in in in themselves and
+
+ align:start position:0%
+narrative input in in in themselves and
+ 
+
+ align:start position:0%
+narrative input in in in themselves and
+and then getting a lot of material is
+
+ align:start position:0%
+and then getting a lot of material is
+ 
+
+ align:start position:0%
+and then getting a lot of material is
+also kind of uh of the point and then
+
+ align:start position:0%
+also kind of uh of the point and then
+ 
+
+ align:start position:0%
+also kind of uh of the point and then
+you have this incredible editing problem
+
+ align:start position:0%
+you have this incredible editing problem
+ 
+
+ align:start position:0%
+you have this incredible editing problem
+and I think Tom went through completely
+
+ align:start position:0%
+and I think Tom went through completely
+ 
+
+ align:start position:0%
+and I think Tom went through completely
+different process also for the nature of
+
+ align:start position:0%
+different process also for the nature of
+ 
+
+ align:start position:0%
+different process also for the nature of
+the questions he was asking the story
+
+ align:start position:0%
+the questions he was asking the story
+ 
+
+ align:start position:0%
+the questions he was asking the story
+went to tell he had to completely
+
+ align:start position:0%
+went to tell he had to completely
+ 
+
+ align:start position:0%
+went to tell he had to completely
+construct everything and basically have
+
+ align:start position:0%
+construct everything and basically have
+ 
+
+ align:start position:0%
+construct everything and basically have
+actors and which one Tom was about the
+
+ align:start position:0%
+actors and which one Tom was about the
+ 
+
+ align:start position:0%
+actors and which one Tom was about the
+controversy so you had the guy on Skype
+
+ align:start position:0%
+controversy so you had the guy on Skype
+ 
+
+ align:start position:0%
+controversy so you had the guy on Skype
+and the other PhD student talking about
+
+ align:start position:0%
+and the other PhD student talking about
+ 
+
+ align:start position:0%
+and the other PhD student talking about
+the lab and the electron Force
+
+ align:start position:0%
+the lab and the electron Force
+ 
+
+ align:start position:0%
+the lab and the electron Force
+microscopy lab with the conflict within
+
+ align:start position:0%
+microscopy lab with the conflict within
+ 
+
+ align:start position:0%
+microscopy lab with the conflict within
+and Emily's piece at the end hers was
+
+ align:start position:0%
+and Emily's piece at the end hers was
+ 
+
+ align:start position:0%
+and Emily's piece at the end hers was
+one about sort
+
+ align:start position:0%
+one about sort
+ 
+
+ align:start position:0%
+one about sort
+of yeah the cows the Agricultural Fair
+
+ align:start position:0%
+of yeah the cows the Agricultural Fair
+ 
+
+ align:start position:0%
+of yeah the cows the Agricultural Fair
+so so and and Ty you weren't there but
+
+ align:start position:0%
+so so and and Ty you weren't there but
+ 
+
+ align:start position:0%
+so so and and Ty you weren't there but
+so the first piece is more much more
+
+ align:start position:0%
+so the first piece is more much more
+ 
+
+ align:start position:0%
+so the first piece is more much more
+interview based talking about this
+
+ align:start position:0%
+interview based talking about this
+ 
+
+ align:start position:0%
+interview based talking about this
+controversy within the lab and we could
+
+ align:start position:0%
+controversy within the lab and we could
+ 
+
+ align:start position:0%
+controversy within the lab and we could
+raise there certain you know the kind of
+
+ align:start position:0%
+raise there certain you know the kind of
+ 
+
+ align:start position:0%
+raise there certain you know the kind of
+question too about what kinds of things
+
+ align:start position:0%
+question too about what kinds of things
+ 
+
+ align:start position:0%
+question too about what kinds of things
+can you get access to or not and he
+
+ align:start position:0%
+can you get access to or not and he
+ 
+
+ align:start position:0%
+can you get access to or not and he
+ended up having reenactments because he
+
+ align:start position:0%
+ended up having reenactments because he
+ 
+
+ align:start position:0%
+ended up having reenactments because he
+couldn't get access to shooting certain
+
+ align:start position:0%
+couldn't get access to shooting certain
+ 
+
+ align:start position:0%
+couldn't get access to shooting certain
+kinds of things which we should talk
+
+ align:start position:0%
+kinds of things which we should talk
+ 
+
+ align:start position:0%
+kinds of things which we should talk
+about um and then Emily's piece much
+
+ align:start position:0%
+about um and then Emily's piece much
+ 
+
+ align:start position:0%
+about um and then Emily's piece much
+more sort of um observational style
+
+ align:start position:0%
+more sort of um observational style
+ 
+
+ align:start position:0%
+more sort of um observational style
+where it's more sort of kind of quietly
+
+ align:start position:0%
+where it's more sort of kind of quietly
+ 
+
+ align:start position:0%
+where it's more sort of kind of quietly
+going around with the camera and just
+
+ align:start position:0%
+going around with the camera and just
+ 
+
+ align:start position:0%
+going around with the camera and just
+watching what people are
+
+ align:start position:0%
+watching what people are
+ 
+
+ align:start position:0%
+watching what people are
+doing um there was a big actually a a
+
+ align:start position:0%
+doing um there was a big actually a a
+ 
+
+ align:start position:0%
+doing um there was a big actually a a
+strong similarity to the two pieces in
+
+ align:start position:0%
+strong similarity to the two pieces in
+ 
+
+ align:start position:0%
+strong similarity to the two pieces in
+the origination however because both of
+
+ align:start position:0%
+the origination however because both of
+ 
+
+ align:start position:0%
+the origination however because both of
+them started out with an idea with an
+
+ align:start position:0%
+them started out with an idea with an
+ 
+
+ align:start position:0%
+them started out with an idea with an
+abstract idea not a story or a profile
+
+ align:start position:0%
+abstract idea not a story or a profile
+ 
+
+ align:start position:0%
+abstract idea not a story or a profile
+of a person uh Tom wanted to talk talk
+
+ align:start position:0%
+of a person uh Tom wanted to talk talk
+ 
+
+ align:start position:0%
+of a person uh Tom wanted to talk talk
+about some fairly abstract things about
+
+ align:start position:0%
+about some fairly abstract things about
+ 
+
+ align:start position:0%
+about some fairly abstract things about
+Imaging and what images mean and what
+
+ align:start position:0%
+Imaging and what images mean and what
+ 
+
+ align:start position:0%
+Imaging and what images mean and what
+and the relationship between something
+
+ align:start position:0%
+and the relationship between something
+ 
+
+ align:start position:0%
+and the relationship between something
+you see and evidence uh and also to
+
+ align:start position:0%
+you see and evidence uh and also to
+ 
+
+ align:start position:0%
+you see and evidence uh and also to
+start to take a look at this controversy
+
+ align:start position:0%
+start to take a look at this controversy
+ 
+
+ align:start position:0%
+start to take a look at this controversy
+which had happened in the past the
+
+ align:start position:0%
+which had happened in the past the
+ 
+
+ align:start position:0%
+which had happened in the past the
+people had left MIT except for one
+
+ align:start position:0%
+people had left MIT except for one
+ 
+
+ align:start position:0%
+people had left MIT except for one
+person he had no material on it no
+
+ align:start position:0%
+person he had no material on it no
+ 
+
+ align:start position:0%
+person he had no material on it no
+footage or anything so he had to find a
+
+ align:start position:0%
+footage or anything so he had to find a
+ 
+
+ align:start position:0%
+footage or anything so he had to find a
+story to put all that stuff on and
+
+ align:start position:0%
+story to put all that stuff on and
+ 
+
+ align:start position:0%
+story to put all that stuff on and
+create it uh as he went along and and
+
+ align:start position:0%
+create it uh as he went along and and
+ 
+
+ align:start position:0%
+create it uh as he went along and and
+and Emily basically went to the fair
+
+ align:start position:0%
+and Emily basically went to the fair
+ 
+
+ align:start position:0%
+and Emily basically went to the fair
+with this idea that she wanted to shoot
+
+ align:start position:0%
+with this idea that she wanted to shoot
+ 
+
+ align:start position:0%
+with this idea that she wanted to shoot
+things that involved animal human
+
+ align:start position:0%
+things that involved animal human
+ 
+
+ align:start position:0%
+things that involved animal human
+interactions and she had to find a story
+
+ align:start position:0%
+interactions and she had to find a story
+ 
+
+ align:start position:0%
+interactions and she had to find a story
+in the edit room uh she just shot for
+
+ align:start position:0%
+in the edit room uh she just shot for
+ 
+
+ align:start position:0%
+in the edit room uh she just shot for
+three or four days shot a lot of
+
+ align:start position:0%
+three or four days shot a lot of
+ 
+
+ align:start position:0%
+three or four days shot a lot of
+material and found a really nice
+
+ align:start position:0%
+material and found a really nice
+ 
+
+ align:start position:0%
+material and found a really nice
+interesting narrative with all these
+
+ align:start position:0%
+interesting narrative with all these
+ 
+
+ align:start position:0%
+interesting narrative with all these
+kind of connections that that get made
+
+ align:start position:0%
+kind of connections that that get made
+ 
+
+ align:start position:0%
+kind of connections that that get made
+through the film um so so again the idea
+
+ align:start position:0%
+through the film um so so again the idea
+ 
+
+ align:start position:0%
+through the film um so so again the idea
+in both situations was that they didn't
+
+ align:start position:0%
+in both situations was that they didn't
+ 
+
+ align:start position:0%
+in both situations was that they didn't
+have a strong narrative like a process
+
+ align:start position:0%
+have a strong narrative like a process
+ 
+
+ align:start position:0%
+have a strong narrative like a process
+or a profile of a person or a
+
+ align:start position:0%
+or a profile of a person or a
+ 
+
+ align:start position:0%
+or a profile of a person or a
+competition you you know a lot of the
+
+ align:start position:0%
+competition you you know a lot of the
+ 
+
+ align:start position:0%
+competition you you know a lot of the
+things that we were just talking about
+
+ align:start position:0%
+things that we were just talking about
+ 
+
+ align:start position:0%
+things that we were just talking about
+uh they had to find those things as they
+
+ align:start position:0%
+uh they had to find those things as they
+ 
+
+ align:start position:0%
+uh they had to find those things as they
+went
+
+ align:start position:0%
+went
+ 
+
+ align:start position:0%
+went
+along what what Chris means is that you
+
+ align:start position:0%
+along what what Chris means is that you
+ 
+
+ align:start position:0%
+along what what Chris means is that you
+know some of this like you know
+
+ align:start position:0%
+know some of this like you know
+ 
+
+ align:start position:0%
+know some of this like you know
+detective story it it it has intrinsic
+
+ align:start position:0%
+detective story it it it has intrinsic
+ 
+
+ align:start position:0%
+detective story it it it has intrinsic
+to it a certain kind of narrative Arc
+
+ align:start position:0%
+to it a certain kind of narrative Arc
+ 
+
+ align:start position:0%
+to it a certain kind of narrative Arc
+but if you don't int or of a competition
+
+ align:start position:0%
+but if you don't int or of a competition
+ 
+
+ align:start position:0%
+but if you don't int or of a competition
+if you film a competition that has its
+
+ align:start position:0%
+if you film a competition that has its
+ 
+
+ align:start position:0%
+if you film a competition that has its
+own kind of narrative Arc built into it
+
+ align:start position:0%
+own kind of narrative Arc built into it
+ 
+
+ align:start position:0%
+own kind of narrative Arc built into it
+but if you if you're filming a topic
+
+ align:start position:0%
+but if you if you're filming a topic
+ 
+
+ align:start position:0%
+but if you if you're filming a topic
+that doesn't have a kind of drama that's
+
+ align:start position:0%
+that doesn't have a kind of drama that's
+ 
+
+ align:start position:0%
+that doesn't have a kind of drama that's
+automatically built into the topic then
+
+ align:start position:0%
+automatically built into the topic then
+ 
+
+ align:start position:0%
+automatically built into the topic then
+you have to create the The Narrative
+
+ align:start position:0%
+you have to create the The Narrative
+ 
+
+ align:start position:0%
+you have to create the The Narrative
+thread and so you do it through editing
+
+ align:start position:0%
+thread and so you do it through editing
+ 
+
+ align:start position:0%
+thread and so you do it through editing
+or through through other kinds of means
+
+ align:start position:0%
+or through through other kinds of means
+ 
+
+ align:start position:0%
+or through through other kinds of means
+an example of something that has a a
+
+ align:start position:0%
+an example of something that has a a
+ 
+
+ align:start position:0%
+an example of something that has a a
+built-in narrative Arc uh last year one
+
+ align:start position:0%
+built-in narrative Arc uh last year one
+ 
+
+ align:start position:0%
+built-in narrative Arc uh last year one
+of the students for an earlier project
+
+ align:start position:0%
+of the students for an earlier project
+ 
+
+ align:start position:0%
+of the students for an earlier project
+shot a very interesting fun little film
+
+ align:start position:0%
+shot a very interesting fun little film
+ 
+
+ align:start position:0%
+shot a very interesting fun little film
+uh about the uh pie eating contest at Pi
+
+ align:start position:0%
+uh about the uh pie eating contest at Pi
+ 
+
+ align:start position:0%
+uh about the uh pie eating contest at Pi
+Day and it was great people sit down
+
+ align:start position:0%
+Day and it was great people sit down
+ 
+
+ align:start position:0%
+Day and it was great people sit down
+who's going to win pies it's fun there's
+
+ align:start position:0%
+who's going to win pies it's fun there's
+ 
+
+ align:start position:0%
+who's going to win pies it's fun there's
+all sorts of interesting
+
+ align:start position:0%
+all sorts of interesting
+ 
+
+ align:start position:0%
+all sorts of interesting
+um oh no not not the pting contest the
+
+ align:start position:0%
+um oh no not not the pting contest the
+ 
+
+ align:start position:0%
+um oh no not not the pting contest the
+the naming the the the the the numbers
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+ align:start position:0%
+the naming the the the the the numbers
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+ align:start position:0%
+the naming the the the the the numbers
+of pi how many how many places of Pi can
+
+ align:start position:0%
+of pi how many how many places of Pi can
+ 
+
+ align:start position:0%
+of pi how many how many places of Pi can
+you can you name and uh there's Pi at
+
+ align:start position:0%
+you can you name and uh there's Pi at
+ 
+
+ align:start position:0%
+you can you name and uh there's Pi at
+the end of it um so so but it's a
+
+ align:start position:0%
+the end of it um so so but it's a
+ 
+
+ align:start position:0%
+the end of it um so so but it's a
+competition there are interesting quirky
+
+ align:start position:0%
+competition there are interesting quirky
+ 
+
+ align:start position:0%
+competition there are interesting quirky
+characters and moments you get kind of
+
+ align:start position:0%
+characters and moments you get kind of
+ 
+
+ align:start position:0%
+characters and moments you get kind of
+involved in who's going to win somebody
+
+ align:start position:0%
+involved in who's going to win somebody
+ 
+
+ align:start position:0%
+involved in who's going to win somebody
+wins and there's a danong uh so there's
+
+ align:start position:0%
+wins and there's a danong uh so there's
+ 
+
+ align:start position:0%
+wins and there's a danong uh so there's
+a narrative built into the story and she
+
+ align:start position:0%
+a narrative built into the story and she
+ 
+
+ align:start position:0%
+a narrative built into the story and she
+went in knowing what the the narrative
+
+ align:start position:0%
+went in knowing what the the narrative
+ 
+
+ align:start position:0%
+went in knowing what the the narrative
+was going to be the election right and
+
+ align:start position:0%
+was going to be the election right and
+ 
+
+ align:start position:0%
+was going to be the election right and
+somebody also did a very fun piece on
+
+ align:start position:0%
+somebody also did a very fun piece on
+ 
+
+ align:start position:0%
+somebody also did a very fun piece on
+student elections uh people running for
+
+ align:start position:0%
+student elections uh people running for
+ 
+
+ align:start position:0%
+student elections uh people running for
+office so and then somebody wins right
+
+ align:start position:0%
+office so and then somebody wins right
+ 
+
+ align:start position:0%
+office so and then somebody wins right
+so again there's closure to it so
+
+ align:start position:0%
+so again there's closure to it so
+ 
+
+ align:start position:0%
+so again there's closure to it so
+there's certain kinds of topics you can
+
+ align:start position:0%
+there's certain kinds of topics you can
+ 
+
+ align:start position:0%
+there's certain kinds of topics you can
+pick that are easier in some sense
+
+ align:start position:0%
+pick that are easier in some sense
+ 
+
+ align:start position:0%
+pick that are easier in some sense
+because they have built into them again
+
+ align:start position:0%
+because they have built into them again
+ 
+
+ align:start position:0%
+because they have built into them again
+a certain kind of drama and if you
+
+ align:start position:0%
+a certain kind of drama and if you
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+
+ align:start position:0%
+a certain kind of drama and if you
+decide you want to do a topic that might
+
+ align:start position:0%
+decide you want to do a topic that might
+ 
+
+ align:start position:0%
+decide you want to do a topic that might
+be incredibly fascinating and wonderful
+
+ align:start position:0%
+be incredibly fascinating and wonderful
+ 
+
+ align:start position:0%
+be incredibly fascinating and wonderful
+to do that doesn't have that again it
+
+ align:start position:0%
+to do that doesn't have that again it
+ 
+
+ align:start position:0%
+to do that doesn't have that again it
+just means you just have to do some
+
+ align:start position:0%
+just means you just have to do some
+ 
+
+ align:start position:0%
+just means you just have to do some
+additional kind of work in terms of
+
+ align:start position:0%
+additional kind of work in terms of
+ 
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+ align:start position:0%
+additional kind of work in terms of
+thinking about how you're going to draw
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+ align:start position:0%
+thinking about how you're going to draw
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+
+ align:start position:0%
+thinking about how you're going to draw
+it or create some kind of story because
+
+ align:start position:0%
+it or create some kind of story because
+ 
+
+ align:start position:0%
+it or create some kind of story because
+because Ely in order for anybody to want
+
+ align:start position:0%
+because Ely in order for anybody to want
+ 
+
+ align:start position:0%
+because Ely in order for anybody to want
+to watch something you have to have some
+
+ align:start position:0%
+to watch something you have to have some
+ 
+
+ align:start position:0%
+to watch something you have to have some
+kind of story be there you have to be
+
+ align:start position:0%
+kind of story be there you have to be
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+
+ align:start position:0%
+kind of story be there you have to be
+saying something with what it is that
+
+ align:start position:0%
+saying something with what it is that
+ 
+
+ align:start position:0%
+saying something with what it is that
+you shoot okay and maybe not at the
+
+ align:start position:0%
+you shoot okay and maybe not at the
+ 
+
+ align:start position:0%
+you shoot okay and maybe not at the
+beginning maybe not when you start the
+
+ align:start position:0%
+beginning maybe not when you start the
+ 
+
+ align:start position:0%
+beginning maybe not when you start the
+shooting process I mean again people
+
+ align:start position:0%
+shooting process I mean again people
+ 
+
+ align:start position:0%
+shooting process I mean again people
+come to these things in very different
+
+ align:start position:0%
+come to these things in very different
+ 
+
+ align:start position:0%
+come to these things in very different
+kinds of ways you know a kind of a very
+
+ align:start position:0%
+kinds of ways you know a kind of a very
+ 
+
+ align:start position:0%
+kinds of ways you know a kind of a very
+anthropological approach to shooting
+
+ align:start position:0%
+anthropological approach to shooting
+ 
+
+ align:start position:0%
+anthropological approach to shooting
+would be okay well I'm interested in
+
+ align:start position:0%
+would be okay well I'm interested in
+ 
+
+ align:start position:0%
+would be okay well I'm interested in
+this topic kind of like Emily with with
+
+ align:start position:0%
+this topic kind of like Emily with with
+ 
+
+ align:start position:0%
+this topic kind of like Emily with with
+the the the Agricultural Fair I'm
+
+ align:start position:0%
+the the the Agricultural Fair I'm
+ 
+
+ align:start position:0%
+the the the Agricultural Fair I'm
+interested in animal human interactions
+
+ align:start position:0%
+interested in animal human interactions
+ 
+
+ align:start position:0%
+interested in animal human interactions
+but I'm not going to assume I'm not
+
+ align:start position:0%
+but I'm not going to assume I'm not
+ 
+
+ align:start position:0%
+but I'm not going to assume I'm not
+going to assume anything about what I'm
+
+ align:start position:0%
+going to assume anything about what I'm
+ 
+
+ align:start position:0%
+going to assume anything about what I'm
+going to find I'm just going to go and
+
+ align:start position:0%
+going to find I'm just going to go and
+ 
+
+ align:start position:0%
+going to find I'm just going to go and
+shoot and I'm going to see and I'm going
+
+ align:start position:0%
+shoot and I'm going to see and I'm going
+ 
+
+ align:start position:0%
+shoot and I'm going to see and I'm going
+to think think about it and then I've
+
+ align:start position:0%
+to think think about it and then I've
+ 
+
+ align:start position:0%
+to think think about it and then I've
+got all this footage and I'm going to
+
+ align:start position:0%
+got all this footage and I'm going to
+ 
+
+ align:start position:0%
+got all this footage and I'm going to
+sort of ponder that well what was that
+
+ align:start position:0%
+sort of ponder that well what was that
+ 
+
+ align:start position:0%
+sort of ponder that well what was that
+about and then through the process of
+
+ align:start position:0%
+about and then through the process of
+ 
+
+ align:start position:0%
+about and then through the process of
+kind of pondering that you decide like
+
+ align:start position:0%
+kind of pondering that you decide like
+ 
+
+ align:start position:0%
+kind of pondering that you decide like
+oh kind of this is this is kind of what
+
+ align:start position:0%
+oh kind of this is this is kind of what
+ 
+
+ align:start position:0%
+oh kind of this is this is kind of what
+this is about and you you start to put
+
+ align:start position:0%
+this is about and you you start to put
+ 
+
+ align:start position:0%
+this is about and you you start to put
+together the visual images in a way that
+
+ align:start position:0%
+together the visual images in a way that
+ 
+
+ align:start position:0%
+together the visual images in a way that
+that kind of tell that story so some
+
+ align:start position:0%
+that kind of tell that story so some
+ 
+
+ align:start position:0%
+that kind of tell that story so some
+people have it more kind of as a process
+
+ align:start position:0%
+people have it more kind of as a process
+ 
+
+ align:start position:0%
+people have it more kind of as a process
+of exploration in the world and you pull
+
+ align:start position:0%
+of exploration in the world and you pull
+ 
+
+ align:start position:0%
+of exploration in the world and you pull
+it out and others kind of have something
+
+ align:start position:0%
+it out and others kind of have something
+ 
+
+ align:start position:0%
+it out and others kind of have something
+either more built into the event itself
+
+ align:start position:0%
+either more built into the event itself
+ 
+
+ align:start position:0%
+either more built into the event itself
+or people have some kind of story that
+
+ align:start position:0%
+or people have some kind of story that
+ 
+
+ align:start position:0%
+or people have some kind of story that
+they want to tell more clearly and
+
+ align:start position:0%
+they want to tell more clearly and
+ 
+
+ align:start position:0%
+they want to tell more clearly and
+they're looking to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Illustrated and then the other thing I
+
+ align:start position:0%
+Illustrated and then the other thing I
+ 
+
+ align:start position:0%
+Illustrated and then the other thing I
+think we'd both encourage you to think
+
+ align:start position:0%
+think we'd both encourage you to think
+ 
+
+ align:start position:0%
+think we'd both encourage you to think
+about our stories of Science and
+
+ align:start position:0%
+about our stories of Science and
+ 
+
+ align:start position:0%
+about our stories of Science and
+Technology uh that are non-traditional I
+
+ align:start position:0%
+Technology uh that are non-traditional I
+ 
+
+ align:start position:0%
+Technology uh that are non-traditional I
+mean there there are the lab stories uh
+
+ align:start position:0%
+mean there there are the lab stories uh
+ 
+
+ align:start position:0%
+mean there there are the lab stories uh
+but we Define Science and Technology
+
+ align:start position:0%
+but we Define Science and Technology
+ 
+
+ align:start position:0%
+but we Define Science and Technology
+pretty broadly uh in fact really broadly
+
+ align:start position:0%
+pretty broadly uh in fact really broadly
+ 
+
+ align:start position:0%
+pretty broadly uh in fact really broadly
+you know the Puppet Theater is not
+
+ align:start position:0%
+you know the Puppet Theater is not
+ 
+
+ align:start position:0%
+you know the Puppet Theater is not
+exactly I mean there's again a craft a a
+
+ align:start position:0%
+exactly I mean there's again a craft a a
+ 
+
+ align:start position:0%
+exactly I mean there's again a craft a a
+craft portion to to what they're doing
+
+ align:start position:0%
+craft portion to to what they're doing
+ 
+
+ align:start position:0%
+craft portion to to what they're doing
+craft technology but but it's a pretty
+
+ align:start position:0%
+craft technology but but it's a pretty
+ 
+
+ align:start position:0%
+craft technology but but it's a pretty
+broad interpretation of what a what a
+
+ align:start position:0%
+broad interpretation of what a what a
+ 
+
+ align:start position:0%
+broad interpretation of what a what a
+science or technology related film would
+
+ align:start position:0%
+science or technology related film would
+ 
+
+ align:start position:0%
+science or technology related film would
+be and there are a lot of really
+
+ align:start position:0%
+be and there are a lot of really
+ 
+
+ align:start position:0%
+be and there are a lot of really
+interesting things going on at MIT right
+
+ align:start position:0%
+interesting things going on at MIT right
+ 
+
+ align:start position:0%
+interesting things going on at MIT right
+now that I we would both encourage you
+
+ align:start position:0%
+now that I we would both encourage you
+ 
+
+ align:start position:0%
+now that I we would both encourage you
+to think about there's the Festival of
+
+ align:start position:0%
+to think about there's the Festival of
+ 
+
+ align:start position:0%
+to think about there's the Festival of
+art science and technology which is just
+
+ align:start position:0%
+art science and technology which is just
+ 
+
+ align:start position:0%
+art science and technology which is just
+filled with uh really interesting events
+
+ align:start position:0%
+filled with uh really interesting events
+ 
+
+ align:start position:0%
+filled with uh really interesting events
+and projects and happenings between now
+
+ align:start position:0%
+and projects and happenings between now
+ 
+
+ align:start position:0%
+and projects and happenings between now
+and the end of the semester um there are
+
+ align:start position:0%
+and the end of the semester um there are
+ 
+
+ align:start position:0%
+and the end of the semester um there are
+multiple possibilities there for for a
+
+ align:start position:0%
+multiple possibilities there for for a
+ 
+
+ align:start position:0%
+multiple possibilities there for for a
+film
+
+ align:start position:0%
+film
+ 
+
+ align:start position:0%
+film
+uh which isn't to say that that a
+
+ align:start position:0%
+uh which isn't to say that that a
+ 
+
+ align:start position:0%
+uh which isn't to say that that a
+fantastic film about lab research is is
+
+ align:start position:0%
+fantastic film about lab research is is
+ 
+
+ align:start position:0%
+fantastic film about lab research is is
+not a a great way to go too which could
+
+ align:start position:0%
+not a a great way to go too which could
+ 
+
+ align:start position:0%
+not a a great way to go too which could
+be really which could be really trific
+
+ align:start position:0%
+be really which could be really trific
+ 
+
+ align:start position:0%
+be really which could be really trific
+there's also the 150th is going on now
+
+ align:start position:0%
+there's also the 150th is going on now
+ 
+
+ align:start position:0%
+there's also the 150th is going on now
+too so you could do a film about MIT
+
+ align:start position:0%
+too so you could do a film about MIT
+ 
+
+ align:start position:0%
+too so you could do a film about MIT
+reflecting on itself at 150th you know
+
+ align:start position:0%
+reflecting on itself at 150th you know
+ 
+
+ align:start position:0%
+reflecting on itself at 150th you know
+so it doesn't have to be mit's narrative
+
+ align:start position:0%
+so it doesn't have to be mit's narrative
+ 
+
+ align:start position:0%
+so it doesn't have to be mit's narrative
+about itself but it could be sort of
+
+ align:start position:0%
+about itself but it could be sort of
+ 
+
+ align:start position:0%
+about itself but it could be sort of
+your take on what they're presenting as
+
+ align:start position:0%
+your take on what they're presenting as
+ 
+
+ align:start position:0%
+your take on what they're presenting as
+that I'm just trying to throw out other
+
+ align:start position:0%
+that I'm just trying to throw out other
+ 
+
+ align:start position:0%
+that I'm just trying to throw out other
+things that are sort of out there going
+
+ align:start position:0%
+things that are sort of out there going
+ 
+
+ align:start position:0%
+things that are sort of out there going
+around that are happen right
+
+ align:start position:0%
+around that are happen right
+ 
+
+ align:start position:0%
+around that are happen right
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um things that are happening right now
+
+ align:start position:0%
+um things that are happening right now
+ 
+
+ align:start position:0%
+um things that are happening right now
+are obviously easier to shoot I mean we
+
+ align:start position:0%
+are obviously easier to shoot I mean we
+ 
+
+ align:start position:0%
+are obviously easier to shoot I mean we
+did the the the a film that Chris did
+
+ align:start position:0%
+did the the the a film that Chris did
+ 
+
+ align:start position:0%
+did the the the a film that Chris did
+that I helped out on um Chris I think I
+
+ align:start position:0%
+that I helped out on um Chris I think I
+ 
+
+ align:start position:0%
+that I helped out on um Chris I think I
+mentioned this a first class he did a
+
+ align:start position:0%
+mentioned this a first class he did a
+ 
+
+ align:start position:0%
+mentioned this a first class he did a
+film about the 19 a documentary about
+
+ align:start position:0%
+film about the 19 a documentary about
+ 
+
+ align:start position:0%
+film about the 19 a documentary about
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+1979 nuclear AC accident at Three Mile
+
+ align:start position:0%
+1979 nuclear AC accident at Three Mile
+ 
+
+ align:start position:0%
+1979 nuclear AC accident at Three Mile
+Island so we're we were making the film
+
+ align:start position:0%
+Island so we're we were making the film
+ 
+
+ align:start position:0%
+Island so we're we were making the film
+much after the accident so there's
+
+ align:start position:0%
+much after the accident so there's
+ 
+
+ align:start position:0%
+much after the accident so there's
+interviews with all the people in the
+
+ align:start position:0%
+interviews with all the people in the
+ 
+
+ align:start position:0%
+interviews with all the people in the
+area but there's also a strong Reliance
+
+ align:start position:0%
+area but there's also a strong Reliance
+ 
+
+ align:start position:0%
+area but there's also a strong Reliance
+on archival footage and getting people
+
+ align:start position:0%
+on archival footage and getting people
+ 
+
+ align:start position:0%
+on archival footage and getting people
+to talk about the past and so the film
+
+ align:start position:0%
+to talk about the past and so the film
+ 
+
+ align:start position:0%
+to talk about the past and so the film
+becomes very much about memory as well
+
+ align:start position:0%
+becomes very much about memory as well
+ 
+
+ align:start position:0%
+becomes very much about memory as well
+so if you want to get at a historical
+
+ align:start position:0%
+so if you want to get at a historical
+ 
+
+ align:start position:0%
+so if you want to get at a historical
+topic there's a whole other range of
+
+ align:start position:0%
+topic there's a whole other range of
+ 
+
+ align:start position:0%
+topic there's a whole other range of
+issues that you kind of have to deal
+
+ align:start position:0%
+issues that you kind of have to deal
+ 
+
+ align:start position:0%
+issues that you kind of have to deal
+with if it's stuff that's not happening
+
+ align:start position:0%
+with if it's stuff that's not happening
+ 
+
+ align:start position:0%
+with if it's stuff that's not happening
+in the current moment how do you tell
+
+ align:start position:0%
+in the current moment how do you tell
+ 
+
+ align:start position:0%
+in the current moment how do you tell
+that story if it's something that's
+
+ align:start position:0%
+that story if it's something that's
+ 
+
+ align:start position:0%
+that story if it's something that's
+happening right
+
+ align:start position:0%
+happening right
+ 
+
+ align:start position:0%
+happening right
+now right I mean you know that's
+
+ align:start position:0%
+now right I mean you know that's
+ 
+
+ align:start position:0%
+now right I mean you know that's
+something that's really well suited to
+
+ align:start position:0%
+something that's really well suited to
+ 
+
+ align:start position:0%
+something that's really well suited to
+say the direct Cinema style which is a
+
+ align:start position:0%
+say the direct Cinema style which is a
+ 
+
+ align:start position:0%
+say the direct Cinema style which is a
+very kind of observational style where
+
+ align:start position:0%
+very kind of observational style where
+ 
+
+ align:start position:0%
+very kind of observational style where
+you style where you just go out and sort
+
+ align:start position:0%
+you style where you just go out and sort
+ 
+
+ align:start position:0%
+you style where you just go out and sort
+of explore that thing that's going on
+
+ align:start position:0%
+of explore that thing that's going on
+ 
+
+ align:start position:0%
+of explore that thing that's going on
+but if you want to do something about
+
+ align:start position:0%
+but if you want to do something about
+ 
+
+ align:start position:0%
+but if you want to do something about
+the past you could do something about
+
+ align:start position:0%
+the past you could do something about
+ 
+
+ align:start position:0%
+the past you could do something about
+doc Edon you could do something
+
+ align:start position:0%
+doc Edon you could do something
+ 
+
+ align:start position:0%
+doc Edon you could do something
+something about I mean God knows what I
+
+ align:start position:0%
+something about I mean God knows what I
+ 
+
+ align:start position:0%
+something about I mean God knows what I
+mean there's there Z topics and just I
+
+ align:start position:0%
+mean there's there Z topics and just I
+ 
+
+ align:start position:0%
+mean there's there Z topics and just I
+think as we've sort of mentioned before
+
+ align:start position:0%
+think as we've sort of mentioned before
+ 
+
+ align:start position:0%
+think as we've sort of mentioned before
+film tends to love action it loves
+
+ align:start position:0%
+film tends to love action it loves
+ 
+
+ align:start position:0%
+film tends to love action it loves
+movement it loves activity uh action
+
+ align:start position:0%
+movement it loves activity uh action
+ 
+
+ align:start position:0%
+movement it loves activity uh action
+films is not just uh what we think of as
+
+ align:start position:0%
+films is not just uh what we think of as
+ 
+
+ align:start position:0%
+films is not just uh what we think of as
+as action films I mean films are about
+
+ align:start position:0%
+as action films I mean films are about
+ 
+
+ align:start position:0%
+as action films I mean films are about
+actions and that isn't to say that you
+
+ align:start position:0%
+actions and that isn't to say that you
+ 
+
+ align:start position:0%
+actions and that isn't to say that you
+can't start with a very very abstract
+
+ align:start position:0%
+can't start with a very very abstract
+ 
+
+ align:start position:0%
+can't start with a very very abstract
+idea but you just need to kind of come
+
+ align:start position:0%
+idea but you just need to kind of come
+ 
+
+ align:start position:0%
+idea but you just need to kind of come
+up with a strategy for turning that
+
+ align:start position:0%
+up with a strategy for turning that
+ 
+
+ align:start position:0%
+up with a strategy for turning that
+abstract idea into actions and if you
+
+ align:start position:0%
+abstract idea into actions and if you
+ 
+
+ align:start position:0%
+abstract idea into actions and if you
+think about the the clip of fast cheap
+
+ align:start position:0%
+think about the the clip of fast cheap
+ 
+
+ align:start position:0%
+think about the the clip of fast cheap
+and out of control that we saw that has
+
+ align:start position:0%
+and out of control that we saw that has
+ 
+
+ align:start position:0%
+and out of control that we saw that has
+this um very very uh abstract idea about
+
+ align:start position:0%
+this um very very uh abstract idea about
+ 
+
+ align:start position:0%
+this um very very uh abstract idea about
+uh uh groups and networks and and um and
+
+ align:start position:0%
+uh uh groups and networks and and um and
+ 
+
+ align:start position:0%
+uh uh groups and networks and and um and
+controlling uh
+
+ align:start position:0%
+controlling uh
+ 
+
+ align:start position:0%
+controlling uh
+nature uh and Rodney Brooks it's brought
+
+ align:start position:0%
+nature uh and Rodney Brooks it's brought
+ 
+
+ align:start position:0%
+nature uh and Rodney Brooks it's brought
+alive with all this found footage arival
+
+ align:start position:0%
+alive with all this found footage arival
+ 
+
+ align:start position:0%
+alive with all this found footage arival
+footage cartoons all of this stuff sort
+
+ align:start position:0%
+footage cartoons all of this stuff sort
+ 
+
+ align:start position:0%
+footage cartoons all of this stuff sort
+of montaged together edited together in
+
+ align:start position:0%
+of montaged together edited together in
+ 
+
+ align:start position:0%
+of montaged together edited together in
+a very sort of interesting way um Emily
+
+ align:start position:0%
+a very sort of interesting way um Emily
+ 
+
+ align:start position:0%
+a very sort of interesting way um Emily
+had a very abstract idea but what was
+
+ align:start position:0%
+had a very abstract idea but what was
+ 
+
+ align:start position:0%
+had a very abstract idea but what was
+great was that she had people doing
+
+ align:start position:0%
+great was that she had people doing
+ 
+
+ align:start position:0%
+great was that she had people doing
+stuff competing in a in various
+
+ align:start position:0%
+stuff competing in a in various
+ 
+
+ align:start position:0%
+stuff competing in a in various
+competitions this fair with it was
+
+ align:start position:0%
+competitions this fair with it was
+ 
+
+ align:start position:0%
+competitions this fair with it was
+incredibly visual movement lots of
+
+ align:start position:0%
+incredibly visual movement lots of
+ 
+
+ align:start position:0%
+incredibly visual movement lots of
+animals running around um so it became
+
+ align:start position:0%
+animals running around um so it became
+ 
+
+ align:start position:0%
+animals running around um so it became
+very easy for her to turn that abstract
+
+ align:start position:0%
+very easy for her to turn that abstract
+ 
+
+ align:start position:0%
+very easy for her to turn that abstract
+idea into something that was film
+
+ align:start position:0%
+idea into something that was film
+ 
+
+ align:start position:0%
+idea into something that was film
+friendly Tom of course had to use actors
+
+ align:start position:0%
+friendly Tom of course had to use actors
+ 
+
+ align:start position:0%
+friendly Tom of course had to use actors
+that was his choice to to to make his
+
+ align:start position:0%
+that was his choice to to to make his
+ 
+
+ align:start position:0%
+that was his choice to to to make his
+turn his abstract idea and his thing
+
+ align:start position:0%
+turn his abstract idea and his thing
+ 
+
+ align:start position:0%
+turn his abstract idea and his thing
+that happened in the past into actions
+
+ align:start position:0%
+that happened in the past into actions
+ 
+
+ align:start position:0%
+that happened in the past into actions
+well and there was the related issue
+
+ align:start position:0%
+well and there was the related issue
+ 
+
+ align:start position:0%
+well and there was the related issue
+which we should just at least mention to
+
+ align:start position:0%
+which we should just at least mention to
+ 
+
+ align:start position:0%
+which we should just at least mention to
+that there's issue of access and what
+
+ align:start position:0%
+that there's issue of access and what
+ 
+
+ align:start position:0%
+that there's issue of access and what
+you can get permission for and again you
+
+ align:start position:0%
+you can get permission for and again you
+ 
+
+ align:start position:0%
+you can get permission for and again you
+you all there's permission forms that
+
+ align:start position:0%
+you all there's permission forms that
+ 
+
+ align:start position:0%
+you all there's permission forms that
+when you go to do interviews you have to
+
+ align:start position:0%
+when you go to do interviews you have to
+ 
+
+ align:start position:0%
+when you go to do interviews you have to
+get permission from people when you do
+
+ align:start position:0%
+get permission from people when you do
+ 
+
+ align:start position:0%
+get permission from people when you do
+this and one of the the the issues about
+
+ align:start position:0%
+this and one of the the the issues about
+ 
+
+ align:start position:0%
+this and one of the the the issues about
+I mean we were sort of strongly
+
+ align:start position:0%
+I mean we were sort of strongly
+ 
+
+ align:start position:0%
+I mean we were sort of strongly
+encouraging people last semester again
+
+ align:start position:0%
+encouraging people last semester again
+ 
+
+ align:start position:0%
+encouraging people last semester again
+to kind of go out and try to explore new
+
+ align:start position:0%
+to kind of go out and try to explore new
+ 
+
+ align:start position:0%
+to kind of go out and try to explore new
+narratives about science and you know
+
+ align:start position:0%
+narratives about science and you know
+ 
+
+ align:start position:0%
+narratives about science and you know
+the idea sort of doing a more kind of
+
+ align:start position:0%
+the idea sort of doing a more kind of
+ 
+
+ align:start position:0%
+the idea sort of doing a more kind of
+focus ing on science's
+
+ align:start position:0%
+focus ing on science's
+ 
+
+ align:start position:0%
+focus ing on science's
+process and getting some of the
+
+ align:start position:0%
+process and getting some of the
+ 
+
+ align:start position:0%
+process and getting some of the
+day-to-day of how science and
+
+ align:start position:0%
+day-to-day of how science and
+ 
+
+ align:start position:0%
+day-to-day of how science and
+engineering actually plays out in a
+
+ align:start position:0%
+engineering actually plays out in a
+ 
+
+ align:start position:0%
+engineering actually plays out in a
+day-to-day way is really fascinating
+
+ align:start position:0%
+day-to-day way is really fascinating
+ 
+
+ align:start position:0%
+day-to-day way is really fascinating
+something that hasn't been done that
+
+ align:start position:0%
+something that hasn't been done that
+ 
+
+ align:start position:0%
+something that hasn't been done that
+much but there's also if you choose to
+
+ align:start position:0%
+much but there's also if you choose to
+ 
+
+ align:start position:0%
+much but there's also if you choose to
+go that route which which I think is a
+
+ align:start position:0%
+go that route which which I think is a
+ 
+
+ align:start position:0%
+go that route which which I think is a
+really fabulous route to go and I'd
+
+ align:start position:0%
+really fabulous route to go and I'd
+ 
+
+ align:start position:0%
+really fabulous route to go and I'd
+encourage you I mean that's one one
+
+ align:start position:0%
+encourage you I mean that's one one
+ 
+
+ align:start position:0%
+encourage you I mean that's one one
+route that could be really cool to do um
+
+ align:start position:0%
+route that could be really cool to do um
+ 
+
+ align:start position:0%
+route that could be really cool to do um
+but one of the difficulties with that
+
+ align:start position:0%
+but one of the difficulties with that
+ 
+
+ align:start position:0%
+but one of the difficulties with that
+that students last semester found out
+
+ align:start position:0%
+that students last semester found out
+ 
+
+ align:start position:0%
+that students last semester found out
+was that you have to think about um
+
+ align:start position:0%
+was that you have to think about um
+ 
+
+ align:start position:0%
+was that you have to think about um
+there might be a lot of issues around
+
+ align:start position:0%
+there might be a lot of issues around
+ 
+
+ align:start position:0%
+there might be a lot of issues around
+permissions for example right so what
+
+ align:start position:0%
+permissions for example right so what
+ 
+
+ align:start position:0%
+permissions for example right so what
+would happen was that a number of the
+
+ align:start position:0%
+would happen was that a number of the
+ 
+
+ align:start position:0%
+would happen was that a number of the
+students last semester they they found
+
+ align:start position:0%
+students last semester they they found
+ 
+
+ align:start position:0%
+students last semester they they found
+some totally cool thing that was
+
+ align:start position:0%
+some totally cool thing that was
+ 
+
+ align:start position:0%
+some totally cool thing that was
+happening in some lab on campus and they
+
+ align:start position:0%
+happening in some lab on campus and they
+ 
+
+ align:start position:0%
+happening in some lab on campus and they
+had friends who were graduate students
+
+ align:start position:0%
+had friends who were graduate students
+ 
+
+ align:start position:0%
+had friends who were graduate students
+The Graduate stud like yeah this is
+
+ align:start position:0%
+The Graduate stud like yeah this is
+ 
+
+ align:start position:0%
+The Graduate stud like yeah this is
+great and maybe they did preliminary
+
+ align:start position:0%
+great and maybe they did preliminary
+ 
+
+ align:start position:0%
+great and maybe they did preliminary
+interviews with that grad student and
+
+ align:start position:0%
+interviews with that grad student and
+ 
+
+ align:start position:0%
+interviews with that grad student and
+there fantastic stuff but then they had
+
+ align:start position:0%
+there fantastic stuff but then they had
+ 
+
+ align:start position:0%
+there fantastic stuff but then they had
+to ask the pi of that graduate student
+
+ align:start position:0%
+to ask the pi of that graduate student
+ 
+
+ align:start position:0%
+to ask the pi of that graduate student
+in the pi said
+
+ align:start position:0%
+in the pi said
+ 
+
+ align:start position:0%
+in the pi said
+no um
+
+ align:start position:0%
+no um
+ 
+
+ align:start position:0%
+no um
+because you know there's there's worry
+
+ align:start position:0%
+because you know there's there's worry
+ 
+
+ align:start position:0%
+because you know there's there's worry
+some you know in certain Labs
+
+ align:start position:0%
+some you know in certain Labs
+ 
+
+ align:start position:0%
+some you know in certain Labs
+understandably that if stuff gets out um
+
+ align:start position:0%
+understandably that if stuff gets out um
+ 
+
+ align:start position:0%
+understandably that if stuff gets out um
+before it's been published it's kind of
+
+ align:start position:0%
+before it's been published it's kind of
+ 
+
+ align:start position:0%
+before it's been published it's kind of
+kind of a it's kind of a um a
+
+ align:start position:0%
+kind of a it's kind of a um a
+ 
+
+ align:start position:0%
+kind of a it's kind of a um a
+pre-publication kind of you know what's
+
+ align:start position:0%
+pre-publication kind of you know what's
+ 
+
+ align:start position:0%
+pre-publication kind of you know what's
+going on inside the lab is going to be
+
+ align:start position:0%
+going on inside the lab is going to be
+ 
+
+ align:start position:0%
+going on inside the lab is going to be
+disseminate in a way that they NE don't
+
+ align:start position:0%
+disseminate in a way that they NE don't
+ 
+
+ align:start position:0%
+disseminate in a way that they NE don't
+necessarily want if it hasn't
+
+ align:start position:0%
+necessarily want if it hasn't
+ 
+
+ align:start position:0%
+necessarily want if it hasn't
+necessarily been published yet and then
+
+ align:start position:0%
+necessarily been published yet and then
+ 
+
+ align:start position:0%
+necessarily been published yet and then
+there's also I mean for obvious reasons
+
+ align:start position:0%
+there's also I mean for obvious reasons
+ 
+
+ align:start position:0%
+there's also I mean for obvious reasons
+people like to control the images of
+
+ align:start position:0%
+people like to control the images of
+ 
+
+ align:start position:0%
+people like to control the images of
+themselves right so if you're the head
+
+ align:start position:0%
+themselves right so if you're the head
+ 
+
+ align:start position:0%
+themselves right so if you're the head
+of a lab and you've got funding sources
+
+ align:start position:0%
+of a lab and you've got funding sources
+ 
+
+ align:start position:0%
+of a lab and you've got funding sources
+you know it's not surprising that people
+
+ align:start position:0%
+you know it's not surprising that people
+ 
+
+ align:start position:0%
+you know it's not surprising that people
+sort of want to control the image that's
+
+ align:start position:0%
+sort of want to control the image that's
+ 
+
+ align:start position:0%
+sort of want to control the image that's
+going to come out of their laboratory
+
+ align:start position:0%
+going to come out of their laboratory
+ 
+
+ align:start position:0%
+going to come out of their laboratory
+the same way that you know
+
+ align:start position:0%
+the same way that you know
+ 
+
+ align:start position:0%
+the same way that you know
+at MIT in general there's sometimes a
+
+ align:start position:0%
+at MIT in general there's sometimes a
+ 
+
+ align:start position:0%
+at MIT in general there's sometimes a
+desire to control what's the image of
+
+ align:start position:0%
+desire to control what's the image of
+ 
+
+ align:start position:0%
+desire to control what's the image of
+MIT that that's gonna that's going to
+
+ align:start position:0%
+MIT that that's gonna that's going to
+ 
+
+ align:start position:0%
+MIT that that's gonna that's going to
+come out so that doesn't mean you can't
+
+ align:start position:0%
+come out so that doesn't mean you can't
+ 
+
+ align:start position:0%
+come out so that doesn't mean you can't
+get permission to do those kinds of
+
+ align:start position:0%
+get permission to do those kinds of
+ 
+
+ align:start position:0%
+get permission to do those kinds of
+things but it it might take longer than
+
+ align:start position:0%
+things but it it might take longer than
+ 
+
+ align:start position:0%
+things but it it might take longer than
+you think so that was one of the things
+
+ align:start position:0%
+you think so that was one of the things
+ 
+
+ align:start position:0%
+you think so that was one of the things
+that sort of stuck some of the students
+
+ align:start position:0%
+that sort of stuck some of the students
+ 
+
+ align:start position:0%
+that sort of stuck some of the students
+um don't assume slow them down a bit
+
+ align:start position:0%
+um don't assume slow them down a bit
+ 
+
+ align:start position:0%
+um don't assume slow them down a bit
+think think about who you need to give
+
+ align:start position:0%
+think think about who you need to give
+ 
+
+ align:start position:0%
+think think about who you need to give
+you the final say that you can do a
+
+ align:start position:0%
+you the final say that you can do a
+ 
+
+ align:start position:0%
+you the final say that you can do a
+project if there if it involves things
+
+ align:start position:0%
+project if there if it involves things
+ 
+
+ align:start position:0%
+project if there if it involves things
+like that and really explain to them
+
+ align:start position:0%
+like that and really explain to them
+ 
+
+ align:start position:0%
+like that and really explain to them
+what you're planning on doing what
+
+ align:start position:0%
+what you're planning on doing what
+ 
+
+ align:start position:0%
+what you're planning on doing what
+you're not planning on doing um you know
+
+ align:start position:0%
+you're not planning on doing um you know
+ 
+
+ align:start position:0%
+you're not planning on doing um you know
+we we've been putting the ones that the
+
+ align:start position:0%
+we we've been putting the ones that the
+ 
+
+ align:start position:0%
+we we've been putting the ones that the
+class videos that we've had permissions
+
+ align:start position:0%
+class videos that we've had permissions
+ 
+
+ align:start position:0%
+class videos that we've had permissions
+for we've put them up online but you
+
+ align:start position:0%
+for we've put them up online but you
+ 
+
+ align:start position:0%
+for we've put them up online but you
+don't necessarily have to do that if you
+
+ align:start position:0%
+don't necessarily have to do that if you
+ 
+
+ align:start position:0%
+don't necessarily have to do that if you
+want to just shoot it as an exercise for
+
+ align:start position:0%
+want to just shoot it as an exercise for
+ 
+
+ align:start position:0%
+want to just shoot it as an exercise for
+yourself you can tell them that it's not
+
+ align:start position:0%
+yourself you can tell them that it's not
+ 
+
+ align:start position:0%
+yourself you can tell them that it's not
+going to go up anywhere beyond that and
+
+ align:start position:0%
+going to go up anywhere beyond that and
+ 
+
+ align:start position:0%
+going to go up anywhere beyond that and
+and you know and and then we abide by
+
+ align:start position:0%
+and you know and and then we abide by
+ 
+
+ align:start position:0%
+and you know and and then we abide by
+that although we would for your final
+
+ align:start position:0%
+that although we would for your final
+ 
+
+ align:start position:0%
+that although we would for your final
+projects we would strongly encourage you
+
+ align:start position:0%
+projects we would strongly encourage you
+ 
+
+ align:start position:0%
+projects we would strongly encourage you
+to try to get the necessary permissions
+
+ align:start position:0%
+to try to get the necessary permissions
+ 
+
+ align:start position:0%
+to try to get the necessary permissions
+so that it can be published online you
+
+ align:start position:0%
+so that it can be published online you
+ 
+
+ align:start position:0%
+so that it can be published online you
+know it's just better for you and yeah
+
+ align:start position:0%
+know it's just better for you and yeah
+ 
+
+ align:start position:0%
+know it's just better for you and yeah
+if you do a final project and you put a
+
+ align:start position:0%
+if you do a final project and you put a
+ 
+
+ align:start position:0%
+if you do a final project and you put a
+ton of work into it you want to be able
+
+ align:start position:0%
+ton of work into it you want to be able
+ 
+
+ align:start position:0%
+ton of work into it you want to be able
+to share it yeah you're going to be sad
+
+ align:start position:0%
+to share it yeah you're going to be sad
+ 
+
+ align:start position:0%
+to share it yeah you're going to be sad
+then at the end if you can't show it to
+
+ align:start position:0%
+then at the end if you can't show it to
+ 
+
+ align:start position:0%
+then at the end if you can't show it to
+anybody other than the class is but
+
+ align:start position:0%
+anybody other than the class is but
+ 
+
+ align:start position:0%
+anybody other than the class is but
+there are there are also creative
+
+ align:start position:0%
+there are there are also creative
+ 
+
+ align:start position:0%
+there are there are also creative
+workarounds I mean for those of you who
+
+ align:start position:0%
+workarounds I mean for those of you who
+ 
+
+ align:start position:0%
+workarounds I mean for those of you who
+were there Friday night uh Max dunnet
+
+ align:start position:0%
+were there Friday night uh Max dunnet
+ 
+
+ align:start position:0%
+were there Friday night uh Max dunnet
+did the film about the uh the researcher
+
+ align:start position:0%
+did the film about the uh the researcher
+ 
+
+ align:start position:0%
+did the film about the uh the researcher
+standup comic and basically he was not
+
+ align:start position:0%
+standup comic and basically he was not
+ 
+
+ align:start position:0%
+standup comic and basically he was not
+allowed to say where the what lab he
+
+ align:start position:0%
+allowed to say where the what lab he
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+
+ align:start position:0%
+allowed to say where the what lab he
+worked in what exactly he did and
+
+ align:start position:0%
+worked in what exactly he did and
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+
+ align:start position:0%
+worked in what exactly he did and
+because he was feeding cocaine to rats
+
+ align:start position:0%
+because he was feeding cocaine to rats
+ 
+
+ align:start position:0%
+because he was feeding cocaine to rats
+and so they didn't want the the the the
+
+ align:start position:0%
+and so they didn't want the the the the
+ 
+
+ align:start position:0%
+and so they didn't want the the the the
+the lab didn't want that discussed
+
+ align:start position:0%
+the lab didn't want that discussed
+ 
+
+ align:start position:0%
+the lab didn't want that discussed
+although he had all this YouTube right
+
+ align:start position:0%
+although he had all this YouTube right
+ 
+
+ align:start position:0%
+although he had all this YouTube right
+so he discussed it without talking about
+
+ align:start position:0%
+so he discussed it without talking about
+ 
+
+ align:start position:0%
+so he discussed it without talking about
+exactly what school he went to which was
+
+ align:start position:0%
+exactly what school he went to which was
+ 
+
+ align:start position:0%
+exactly what school he went to which was
+an MIT uh what lab he worked in uh any
+
+ align:start position:0%
+an MIT uh what lab he worked in uh any
+ 
+
+ align:start position:0%
+an MIT uh what lab he worked in uh any
+of his co-workers any of that all that
+
+ align:start position:0%
+of his co-workers any of that all that
+ 
+
+ align:start position:0%
+of his co-workers any of that all that
+was out of the so it was made a joke out
+
+ align:start position:0%
+was out of the so it was made a joke out
+ 
+
+ align:start position:0%
+was out of the so it was made a joke out
+of which in a way that worked so this is
+
+ align:start position:0%
+of which in a way that worked so this is
+ 
+
+ align:start position:0%
+of which in a way that worked so this is
+something that's different for those of
+
+ align:start position:0%
+something that's different for those of
+ 
+
+ align:start position:0%
+something that's different for those of
+us who are used to doing you C I mean
+
+ align:start position:0%
+us who are used to doing you C I mean
+ 
+
+ align:start position:0%
+us who are used to doing you C I mean
+those of
+
+ align:start position:0%
+those of
+ 
+
+ align:start position:0%
+those of
+us who who sort of work in the social
+
+ align:start position:0%
+us who who sort of work in the social
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+
+ align:start position:0%
+us who who sort of work in the social
+sciences the way we usually handle this
+
+ align:start position:0%
+sciences the way we usually handle this
+ 
+
+ align:start position:0%
+sciences the way we usually handle this
+in our written work is that we use
+
+ align:start position:0%
+in our written work is that we use
+ 
+
+ align:start position:0%
+in our written work is that we use
+pseudonyms that's how we give protection
+
+ align:start position:0%
+pseudonyms that's how we give protection
+ 
+
+ align:start position:0%
+pseudonyms that's how we give protection
+to the people that we do our research on
+
+ align:start position:0%
+to the people that we do our research on
+ 
+
+ align:start position:0%
+to the people that we do our research on
+as we use pseudonyms so you know so that
+
+ align:start position:0%
+as we use pseudonyms so you know so that
+ 
+
+ align:start position:0%
+as we use pseudonyms so you know so that
+people have privacy and there's not you
+
+ align:start position:0%
+people have privacy and there's not you
+ 
+
+ align:start position:0%
+people have privacy and there's not you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+you know harmful outcomes to them in the
+
+ align:start position:0%
+you know harmful outcomes to them in the
+ 
+
+ align:start position:0%
+you know harmful outcomes to them in the
+end but when you're doing video work you
+
+ align:start position:0%
+end but when you're doing video work you
+ 
+
+ align:start position:0%
+end but when you're doing video work you
+can't do that so that imposes certain
+
+ align:start position:0%
+can't do that so that imposes certain
+ 
+
+ align:start position:0%
+can't do that so that imposes certain
+kinds of constraints in terms of what
+
+ align:start position:0%
+kinds of constraints in terms of what
+ 
+
+ align:start position:0%
+kinds of constraints in terms of what
+stories you you can tell or how you
+
+ align:start position:0%
+stories you you can tell or how you
+ 
+
+ align:start position:0%
+stories you you can tell or how you
+would do it and the way that Tom dealt
+
+ align:start position:0%
+would do it and the way that Tom dealt
+ 
+
+ align:start position:0%
+would do it and the way that Tom dealt
+with that because he was dealing with
+
+ align:start position:0%
+with that because he was dealing with
+ 
+
+ align:start position:0%
+with that because he was dealing with
+controversies within a lab right that
+
+ align:start position:0%
+controversies within a lab right that
+ 
+
+ align:start position:0%
+controversies within a lab right that
+were very um you know they were they
+
+ align:start position:0%
+were very um you know they were they
+ 
+
+ align:start position:0%
+were very um you know they were they
+were you know passions were strong
+
+ align:start position:0%
+were you know passions were strong
+ 
+
+ align:start position:0%
+were you know passions were strong
+around those controversies and it stood
+
+ align:start position:0%
+around those controversies and it stood
+ 
+
+ align:start position:0%
+around those controversies and it stood
+to affect people's reputations and it
+
+ align:start position:0%
+to affect people's reputations and it
+ 
+
+ align:start position:0%
+to affect people's reputations and it
+could have you know some of the graduate
+
+ align:start position:0%
+could have you know some of the graduate
+ 
+
+ align:start position:0%
+could have you know some of the graduate
+students felt like well it could have
+
+ align:start position:0%
+students felt like well it could have
+ 
+
+ align:start position:0%
+students felt like well it could have
+affected their reputation it would make
+
+ align:start position:0%
+affected their reputation it would make
+ 
+
+ align:start position:0%
+affected their reputation it would make
+it difficult for them to get work after
+
+ align:start position:0%
+it difficult for them to get work after
+ 
+
+ align:start position:0%
+it difficult for them to get work after
+afterwards so the way that he dealt with
+
+ align:start position:0%
+afterwards so the way that he dealt with
+ 
+
+ align:start position:0%
+afterwards so the way that he dealt with
+that is that he had his friends reenact
+
+ align:start position:0%
+that is that he had his friends reenact
+ 
+
+ align:start position:0%
+that is that he had his friends reenact
+those scenes and it was you know and all
+
+ align:start position:0%
+those scenes and it was you know and all
+ 
+
+ align:start position:0%
+those scenes and it was you know and all
+of his friends were you know students
+
+ align:start position:0%
+of his friends were you know students
+ 
+
+ align:start position:0%
+of his friends were you know students
+who had worked in labs and experienced
+
+ align:start position:0%
+who had worked in labs and experienced
+ 
+
+ align:start position:0%
+who had worked in labs and experienced
+something different so it was actually
+
+ align:start position:0%
+something different so it was actually
+ 
+
+ align:start position:0%
+something different so it was actually
+kind of this this fun thing where they
+
+ align:start position:0%
+kind of this this fun thing where they
+ 
+
+ align:start position:0%
+kind of this this fun thing where they
+got to sort of act out like the drama
+
+ align:start position:0%
+got to sort of act out like the drama
+ 
+
+ align:start position:0%
+got to sort of act out like the drama
+within their their own lab groups so it
+
+ align:start position:0%
+within their their own lab groups so it
+ 
+
+ align:start position:0%
+within their their own lab groups so it
+ended up being a really fun kind of
+
+ align:start position:0%
+ended up being a really fun kind of
+ 
+
+ align:start position:0%
+ended up being a really fun kind of
+reflection on what they actually do but
+
+ align:start position:0%
+reflection on what they actually do but
+ 
+
+ align:start position:0%
+reflection on what they actually do but
+that was a really creative way he got
+
+ align:start position:0%
+that was a really creative way he got
+ 
+
+ align:start position:0%
+that was a really creative way he got
+around that issue and the other thing is
+
+ align:start position:0%
+around that issue and the other thing is
+ 
+
+ align:start position:0%
+around that issue and the other thing is
+uh he embargoed the film all of last
+
+ align:start position:0%
+uh he embargoed the film all of last
+ 
+
+ align:start position:0%
+uh he embargoed the film all of last
+year and until the last person left MIT
+
+ align:start position:0%
+year and until the last person left MIT
+ 
+
+ align:start position:0%
+year and until the last person left MIT
+who had been inv and now it's on the
+
+ align:start position:0%
+who had been inv and now it's on the
+ 
+
+ align:start position:0%
+who had been inv and now it's on the
+front page of tech TV as of today
+
+ align:start position:0%
+front page of tech TV as of today
+ 
+
+ align:start position:0%
+front page of tech TV as of today
+because we can finally show it show it
+
+ align:start position:0%
+because we can finally show it show it
+ 
+
+ align:start position:0%
+because we can finally show it show it
+because everybody's left MIT so yeah
+
+ align:start position:0%
+because everybody's left MIT so yeah
+ 
+
+ align:start position:0%
+because everybody's left MIT so yeah
+anyway so we've done a lot of talking
+
+ align:start position:0%
+anyway so we've done a lot of talking
+ 
+
+ align:start position:0%
+anyway so we've done a lot of talking
+now but does do any of you have any
+
+ align:start position:0%
+now but does do any of you have any
+ 
+
+ align:start position:0%
+now but does do any of you have any
+ideas yet on what potentially you might
+
+ align:start position:0%
+ideas yet on what potentially you might
+ 
+
+ align:start position:0%
+ideas yet on what potentially you might
+want to do or whether something might be
+
+ align:start position:0%
+want to do or whether something might be
+ 
+
+ align:start position:0%
+want to do or whether something might be
+feasible um after seeing the videos um I
+
+ align:start position:0%
+feasible um after seeing the videos um I
+ 
+
+ align:start position:0%
+feasible um after seeing the videos um I
+realized like it would have been really
+
+ align:start position:0%
+realized like it would have been really
+ 
+
+ align:start position:0%
+realized like it would have been really
+helpful according to a lot of to work
+
+ align:start position:0%
+helpful according to a lot of to work
+ 
+
+ align:start position:0%
+helpful according to a lot of to work
+with another person and partner so Ty
+
+ align:start position:0%
+with another person and partner so Ty
+ 
+
+ align:start position:0%
+with another person and partner so Ty
+and I were thinking of doing a film
+
+ align:start position:0%
+and I were thinking of doing a film
+ 
+
+ align:start position:0%
+and I were thinking of doing a film
+about RC and like my
+
+ align:start position:0%
+about RC and like my
+ 
+
+ align:start position:0%
+about RC and like my
+Roy is the the um Reserve officer
+
+ align:start position:0%
+Roy is the the um Reserve officer
+ 
+
+ align:start position:0%
+Roy is the the um Reserve officer
+attaining cor yeah um and so like it
+
+ align:start position:0%
+attaining cor yeah um and so like it
+ 
+
+ align:start position:0%
+attaining cor yeah um and so like it
+would show how their students are not
+
+ align:start position:0%
+would show how their students are not
+ 
+
+ align:start position:0%
+would show how their students are not
+only like preparing to be soldiers but
+
+ align:start position:0%
+only like preparing to be soldiers but
+ 
+
+ align:start position:0%
+only like preparing to be soldiers but
+also like their engineering and like
+
+ align:start position:0%
+also like their engineering and like
+ 
+
+ align:start position:0%
+also like their engineering and like
+science like educational background and
+
+ align:start position:0%
+science like educational background and
+ 
+
+ align:start position:0%
+science like educational background and
+then how they balance the two part yeah
+
+ align:start position:0%
+then how they balance the two part yeah
+ 
+
+ align:start position:0%
+then how they balance the two part yeah
+that's a fascinating topic just to
+
+ align:start position:0%
+that's a fascinating topic just to
+ 
+
+ align:start position:0%
+that's a fascinating topic just to
+clarify one thing everybody does have to
+
+ align:start position:0%
+clarify one thing everybody does have to
+ 
+
+ align:start position:0%
+clarify one thing everybody does have to
+do their own film project at the end but
+
+ align:start position:0%
+do their own film project at the end but
+ 
+
+ align:start position:0%
+do their own film project at the end but
+but you but you can still work together
+
+ align:start position:0%
+but you but you can still work together
+ 
+
+ align:start position:0%
+but you but you can still work together
+I mean what Tom was talking about was
+
+ align:start position:0%
+I mean what Tom was talking about was
+ 
+
+ align:start position:0%
+I mean what Tom was talking about was
+when the idea is and this is the way
+
+ align:start position:0%
+when the idea is and this is the way
+ 
+
+ align:start position:0%
+when the idea is and this is the way
+sort of it commonly Works in film school
+
+ align:start position:0%
+sort of it commonly Works in film school
+ 
+
+ align:start position:0%
+sort of it commonly Works in film school
+is that when people are working on their
+
+ align:start position:0%
+is that when people are working on their
+ 
+
+ align:start position:0%
+is that when people are working on their
+projects you draw on your classmates to
+
+ align:start position:0%
+projects you draw on your classmates to
+ 
+
+ align:start position:0%
+projects you draw on your classmates to
+help you to do sound or to help while
+
+ align:start position:0%
+help you to do sound or to help while
+ 
+
+ align:start position:0%
+help you to do sound or to help while
+you're interviewing maybe somebody does
+
+ align:start position:0%
+you're interviewing maybe somebody does
+ 
+
+ align:start position:0%
+you're interviewing maybe somebody does
+the camera because you need to be able
+
+ align:start position:0%
+the camera because you need to be able
+ 
+
+ align:start position:0%
+the camera because you need to be able
+to talk and interact so part of the idea
+
+ align:start position:0%
+to talk and interact so part of the idea
+ 
+
+ align:start position:0%
+to talk and interact so part of the idea
+is that you you kind of build a cohort
+
+ align:start position:0%
+is that you you kind of build a cohort
+ 
+
+ align:start position:0%
+is that you you kind of build a cohort
+as time goes on and other people help
+
+ align:start position:0%
+as time goes on and other people help
+ 
+
+ align:start position:0%
+as time goes on and other people help
+you and then you help them in turn and
+
+ align:start position:0%
+you and then you help them in turn and
+ 
+
+ align:start position:0%
+you and then you help them in turn and
+it really does help the whole quality of
+
+ align:start position:0%
+it really does help the whole quality of
+ 
+
+ align:start position:0%
+it really does help the whole quality of
+of the film making process so there is
+
+ align:start position:0%
+of the film making process so there is
+ 
+
+ align:start position:0%
+of the film making process so there is
+this kind of collaborative Collective
+
+ align:start position:0%
+this kind of collaborative Collective
+ 
+
+ align:start position:0%
+this kind of collaborative Collective
+aspect to making this stuff that we
+
+ align:start position:0%
+aspect to making this stuff that we
+ 
+
+ align:start position:0%
+aspect to making this stuff that we
+would really encourage so we would
+
+ align:start position:0%
+would really encourage so we would
+ 
+
+ align:start position:0%
+would really encourage so we would
+encourage you to work in in teams but to
+
+ align:start position:0%
+encourage you to work in in teams but to
+ 
+
+ align:start position:0%
+encourage you to work in in teams but to
+do to so the outcome would have to be
+
+ align:start position:0%
+do to so the outcome would have to be
+ 
+
+ align:start position:0%
+do to so the outcome would have to be
+separate to be to be graded we have to
+
+ align:start position:0%
+separate to be to be graded we have to
+ 
+
+ align:start position:0%
+separate to be to be graded we have to
+be graded separately but you can even do
+
+ align:start position:0%
+be graded separately but you can even do
+ 
+
+ align:start position:0%
+be graded separately but you can even do
+I mean even do two related projects yeah
+
+ align:start position:0%
+I mean even do two related projects yeah
+ 
+
+ align:start position:0%
+I mean even do two related projects yeah
+exactly I mean so you could do the same
+
+ align:start position:0%
+exactly I mean so you could do the same
+ 
+
+ align:start position:0%
+exactly I mean so you could do the same
+topic if you want it and have two
+
+ align:start position:0%
+topic if you want it and have two
+ 
+
+ align:start position:0%
+topic if you want it and have two
+different different takes on it or two
+
+ align:start position:0%
+different different takes on it or two
+ 
+
+ align:start position:0%
+different different takes on it or two
+but but two different visual prod U
+
+ align:start position:0%
+but but two different visual prod U
+ 
+
+ align:start position:0%
+but but two different visual prod U
+products at the end so so if if you did
+
+ align:start position:0%
+products at the end so so if if you did
+ 
+
+ align:start position:0%
+products at the end so so if if you did
+both did films on Roc and and shared a
+
+ align:start position:0%
+both did films on Roc and and shared a
+ 
+
+ align:start position:0%
+both did films on Roc and and shared a
+lot of the camera duties you would still
+
+ align:start position:0%
+lot of the camera duties you would still
+ 
+
+ align:start position:0%
+lot of the camera duties you would still
+need to edit your own own projects
+
+ align:start position:0%
+need to edit your own own projects
+ 
+
+ align:start position:0%
+need to edit your own own projects
+because part of it in terms of grading
+
+ align:start position:0%
+because part of it in terms of grading
+ 
+
+ align:start position:0%
+because part of it in terms of grading
+to be able to sort of you know that
+
+ align:start position:0%
+to be able to sort of you know that
+ 
+
+ align:start position:0%
+to be able to sort of you know that
+people you know sort of got the basics
+
+ align:start position:0%
+people you know sort of got the basics
+ 
+
+ align:start position:0%
+people you know sort of got the basics
+of sort of how to shoot how to edit um
+
+ align:start position:0%
+of sort of how to shoot how to edit um
+ 
+
+ align:start position:0%
+of sort of how to shoot how to edit um
+because again we don't want to as we
+
+ align:start position:0%
+because again we don't want to as we
+ 
+
+ align:start position:0%
+because again we don't want to as we
+said in the very first class we don't
+
+ align:start position:0%
+said in the very first class we don't
+ 
+
+ align:start position:0%
+said in the very first class we don't
+want to have to grade people on just the
+
+ align:start position:0%
+want to have to grade people on just the
+ 
+
+ align:start position:0%
+want to have to grade people on just the
+final product and how
+
+ align:start position:0%
+final product and how
+ 
+
+ align:start position:0%
+final product and how
+aesthetically you know good it is
+
+ align:start position:0%
+aesthetically you know good it is
+ 
+
+ align:start position:0%
+aesthetically you know good it is
+because people might be coming from very
+
+ align:start position:0%
+because people might be coming from very
+ 
+
+ align:start position:0%
+because people might be coming from very
+different backgrounds but so we also
+
+ align:start position:0%
+different backgrounds but so we also
+ 
+
+ align:start position:0%
+different backgrounds but so we also
+want to do a fair amount of the grading
+
+ align:start position:0%
+want to do a fair amount of the grading
+ 
+
+ align:start position:0%
+want to do a fair amount of the grading
+in terms of amount of effort that people
+
+ align:start position:0%
+in terms of amount of effort that people
+ 
+
+ align:start position:0%
+in terms of amount of effort that people
+put into and if it's done
+
+ align:start position:0%
+put into and if it's done
+ 
+
+ align:start position:0%
+put into and if it's done
+collaboratively we can't tell you know
+
+ align:start position:0%
+collaboratively we can't tell you know
+ 
+
+ align:start position:0%
+collaboratively we can't tell you know
+if one person did 3/4 of the work and
+
+ align:start position:0%
+if one person did 3/4 of the work and
+ 
+
+ align:start position:0%
+if one person did 3/4 of the work and
+one person did a quarter it's harder for
+
+ align:start position:0%
+one person did a quarter it's harder for
+ 
+
+ align:start position:0%
+one person did a quarter it's harder for
+us to judge in certainly shoot
+
+ align:start position:0%
+us to judge in certainly shoot
+ 
+
+ align:start position:0%
+us to judge in certainly shoot
+collaboratively and we would strongly
+
+ align:start position:0%
+collaboratively and we would strongly
+ 
+
+ align:start position:0%
+collaboratively and we would strongly
+encourage everybody to do that yeah do
+
+ align:start position:0%
+encourage everybody to do that yeah do
+ 
+
+ align:start position:0%
+encourage everybody to do that yeah do
+that does that make sense or is that
+
+ align:start position:0%
+that does that make sense or is that
+ 
+
+ align:start position:0%
+that does that make sense or is that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+how let's say we we we we have a topic
+
+ align:start position:0%
+how let's say we we we we have a topic
+ 
+
+ align:start position:0%
+how let's say we we we we have a topic
+in mind we don't know we don't know much
+
+ align:start position:0%
+in mind we don't know we don't know much
+ 
+
+ align:start position:0%
+in mind we don't know we don't know much
+about it so we don't know what kind of
+
+ align:start position:0%
+about it so we don't know what kind of
+ 
+
+ align:start position:0%
+about it so we don't know what kind of
+stories there are there so what's the
+
+ align:start position:0%
+stories there are there so what's the
+ 
+
+ align:start position:0%
+stories there are there so what's the
+best way is
+
+ align:start position:0%
+best way is
+ 
+
+ align:start position:0%
+best way is
+it would you just go and start filming
+
+ align:start position:0%
+it would you just go and start filming
+ 
+
+ align:start position:0%
+it would you just go and start filming
+and like I realized the other day when
+
+ align:start position:0%
+and like I realized the other day when
+ 
+
+ align:start position:0%
+and like I realized the other day when
+we were filming just the very basic kind
+
+ align:start position:0%
+we were filming just the very basic kind
+ 
+
+ align:start position:0%
+we were filming just the very basic kind
+of scene of like somebody chopping
+
+ align:start position:0%
+of scene of like somebody chopping
+ 
+
+ align:start position:0%
+of scene of like somebody chopping
+things then then there was a story to it
+
+ align:start position:0%
+things then then there was a story to it
+ 
+
+ align:start position:0%
+things then then there was a story to it
+I mean there was kind of relationship
+
+ align:start position:0%
+I mean there was kind of relationship
+ 
+
+ align:start position:0%
+I mean there was kind of relationship
+very essential relationship with
+
+ align:start position:0%
+very essential relationship with
+ 
+
+ align:start position:0%
+very essential relationship with
+vegetables which I wouldn't have thought
+
+ align:start position:0%
+vegetables which I wouldn't have thought
+ 
+
+ align:start position:0%
+vegetables which I wouldn't have thought
+about until when I I could hear the
+
+ align:start position:0%
+about until when I I could hear the
+ 
+
+ align:start position:0%
+about until when I I could hear the
+sounds and you know the vegetables being
+
+ align:start position:0%
+sounds and you know the vegetables being
+ 
+
+ align:start position:0%
+sounds and you know the vegetables being
+eaten and like seen like the beauty of
+
+ align:start position:0%
+eaten and like seen like the beauty of
+ 
+
+ align:start position:0%
+eaten and like seen like the beauty of
+and it really came out only when I was
+
+ align:start position:0%
+and it really came out only when I was
+ 
+
+ align:start position:0%
+and it really came out only when I was
+looking is with the camera so or or or
+
+ align:start position:0%
+looking is with the camera so or or or
+ 
+
+ align:start position:0%
+looking is with the camera so or or or
+or or should you kind of think about it
+
+ align:start position:0%
+or or should you kind of think about it
+ 
+
+ align:start position:0%
+or or should you kind of think about it
+more before starting to well this
+
+ align:start position:0%
+more before starting to well this
+ 
+
+ align:start position:0%
+more before starting to well this
+there's sort of an interesting answer
+
+ align:start position:0%
+there's sort of an interesting answer
+ 
+
+ align:start position:0%
+there's sort of an interesting answer
+which comes out of the technology that
+
+ align:start position:0%
+which comes out of the technology that
+ 
+
+ align:start position:0%
+which comes out of the technology that
+we're using um the the way to begin a
+
+ align:start position:0%
+we're using um the the way to begin a
+ 
+
+ align:start position:0%
+we're using um the the way to begin a
+project like some of these projects are
+
+ align:start position:0%
+project like some of these projects are
+ 
+
+ align:start position:0%
+project like some of these projects are
+uh traditionally would have been to go
+
+ align:start position:0%
+uh traditionally would have been to go
+ 
+
+ align:start position:0%
+uh traditionally would have been to go
+uh do some pre-interviews to do a site
+
+ align:start position:0%
+uh do some pre-interviews to do a site
+ 
+
+ align:start position:0%
+uh do some pre-interviews to do a site
+visit if you're say you're doing doing
+
+ align:start position:0%
+visit if you're say you're doing doing
+ 
+
+ align:start position:0%
+visit if you're say you're doing doing
+something on a lab you go visit the lab
+
+ align:start position:0%
+something on a lab you go visit the lab
+ 
+
+ align:start position:0%
+something on a lab you go visit the lab
+without a camera you interview the the
+
+ align:start position:0%
+without a camera you interview the the
+ 
+
+ align:start position:0%
+without a camera you interview the the
+researchers you sort of just get the lay
+
+ align:start position:0%
+researchers you sort of just get the lay
+ 
+
+ align:start position:0%
+researchers you sort of just get the lay
+of the land you start you look for
+
+ align:start position:0%
+of the land you start you look for
+ 
+
+ align:start position:0%
+of the land you start you look for
+stories and the advantage of that is
+
+ align:start position:0%
+stories and the advantage of that is
+ 
+
+ align:start position:0%
+stories and the advantage of that is
+that they see you as a human being
+
+ align:start position:0%
+that they see you as a human being
+ 
+
+ align:start position:0%
+that they see you as a human being
+before they see you as a camera and
+
+ align:start position:0%
+before they see you as a camera and
+ 
+
+ align:start position:0%
+before they see you as a camera and
+that's really really important because
+
+ align:start position:0%
+that's really really important because
+ 
+
+ align:start position:0%
+that's really really important because
+you make a human connection before you
+
+ align:start position:0%
+you make a human connection before you
+ 
+
+ align:start position:0%
+you make a human connection before you
+jump jump up and take out the camera
+
+ align:start position:0%
+jump jump up and take out the camera
+ 
+
+ align:start position:0%
+jump jump up and take out the camera
+stick it in their face and say be in my
+
+ align:start position:0%
+stick it in their face and say be in my
+ 
+
+ align:start position:0%
+stick it in their face and say be in my
+movie um but on the other hand the the
+
+ align:start position:0%
+movie um but on the other hand the the
+ 
+
+ align:start position:0%
+movie um but on the other hand the the
+great thing about these cameras is that
+
+ align:start position:0%
+great thing about these cameras is that
+ 
+
+ align:start position:0%
+great thing about these cameras is that
+they're so small that you can just throw
+
+ align:start position:0%
+they're so small that you can just throw
+ 
+
+ align:start position:0%
+they're so small that you can just throw
+them in bag and bring them and so what I
+
+ align:start position:0%
+them in bag and bring them and so what I
+ 
+
+ align:start position:0%
+them in bag and bring them and so what I
+often do and what I would think that you
+
+ align:start position:0%
+often do and what I would think that you
+ 
+
+ align:start position:0%
+often do and what I would think that you
+might want to consider is do exactly
+
+ align:start position:0%
+might want to consider is do exactly
+ 
+
+ align:start position:0%
+might want to consider is do exactly
+what I just said set up a site visit uh
+
+ align:start position:0%
+what I just said set up a site visit uh
+ 
+
+ align:start position:0%
+what I just said set up a site visit uh
+with no camera uh go in and meet the
+
+ align:start position:0%
+with no camera uh go in and meet the
+ 
+
+ align:start position:0%
+with no camera uh go in and meet the
+people but if you have the camera in
+
+ align:start position:0%
+people but if you have the camera in
+ 
+
+ align:start position:0%
+people but if you have the camera in
+your bag and you're sensitive enough and
+
+ align:start position:0%
+your bag and you're sensitive enough and
+ 
+
+ align:start position:0%
+your bag and you're sensitive enough and
+have your sort of antenna out enough
+
+ align:start position:0%
+have your sort of antenna out enough
+ 
+
+ align:start position:0%
+have your sort of antenna out enough
+about what's going on at some point it
+
+ align:start position:0%
+about what's going on at some point it
+ 
+
+ align:start position:0%
+about what's going on at some point it
+may be okay and just completely natural
+
+ align:start position:0%
+may be okay and just completely natural
+ 
+
+ align:start position:0%
+may be okay and just completely natural
+for you to take out the
+
+ align:start position:0%
+for you to take out the
+ 
+
+ align:start position:0%
+for you to take out the
+camera and you obviously need to ask
+
+ align:start position:0%
+camera and you obviously need to ask
+ 
+
+ align:start position:0%
+camera and you obviously need to ask
+before do it you need to make sure that
+
+ align:start position:0%
+before do it you need to make sure that
+ 
+
+ align:start position:0%
+before do it you need to make sure that
+you've kind of established a rapport and
+
+ align:start position:0%
+you've kind of established a rapport and
+ 
+
+ align:start position:0%
+you've kind of established a rapport and
+that everything is good and they're
+
+ align:start position:0%
+that everything is good and they're
+ 
+
+ align:start position:0%
+that everything is good and they're
+enthusiastic and interested and you'll
+
+ align:start position:0%
+enthusiastic and interested and you'll
+ 
+
+ align:start position:0%
+enthusiastic and interested and you'll
+want to listen to yourself and your own
+
+ align:start position:0%
+want to listen to yourself and your own
+ 
+
+ align:start position:0%
+want to listen to yourself and your own
+instincts about whether or not you want
+
+ align:start position:0%
+instincts about whether or not you want
+ 
+
+ align:start position:0%
+instincts about whether or not you want
+to shoot because as you said you started
+
+ align:start position:0%
+to shoot because as you said you started
+ 
+
+ align:start position:0%
+to shoot because as you said you started
+seeing things really differently through
+
+ align:start position:0%
+seeing things really differently through
+ 
+
+ align:start position:0%
+seeing things really differently through
+the camera and you have ideas that you
+
+ align:start position:0%
+the camera and you have ideas that you
+ 
+
+ align:start position:0%
+the camera and you have ideas that you
+wouldn't have necessarily had if you're
+
+ align:start position:0%
+wouldn't have necessarily had if you're
+ 
+
+ align:start position:0%
+wouldn't have necessarily had if you're
+just talking to the people and I've been
+
+ align:start position:0%
+just talking to the people and I've been
+ 
+
+ align:start position:0%
+just talking to the people and I've been
+on the other side of that coin where I'm
+
+ align:start position:0%
+on the other side of that coin where I'm
+ 
+
+ align:start position:0%
+on the other side of that coin where I'm
+on a site visit or some kind of
+
+ align:start position:0%
+on a site visit or some kind of
+ 
+
+ align:start position:0%
+on a site visit or some kind of
+pre-production thing and I realized oh
+
+ align:start position:0%
+pre-production thing and I realized oh
+ 
+
+ align:start position:0%
+pre-production thing and I realized oh
+my God why didn't I bring the camera
+
+ align:start position:0%
+my God why didn't I bring the camera
+ 
+
+ align:start position:0%
+my God why didn't I bring the camera
+there's some amazing stuff happening
+
+ align:start position:0%
+there's some amazing stuff happening
+ 
+
+ align:start position:0%
+there's some amazing stuff happening
+here why why why can't I shoot it but
+
+ align:start position:0%
+here why why why can't I shoot it but
+ 
+
+ align:start position:0%
+here why why why can't I shoot it but
+you just have to be aware that if you
+
+ align:start position:0%
+you just have to be aware that if you
+ 
+
+ align:start position:0%
+you just have to be aware that if you
+walk in with a camera right off the bat
+
+ align:start position:0%
+walk in with a camera right off the bat
+ 
+
+ align:start position:0%
+walk in with a camera right off the bat
+on your shoulder ready to go you may
+
+ align:start position:0%
+on your shoulder ready to go you may
+ 
+
+ align:start position:0%
+on your shoulder ready to go you may
+alienate the people and it's not it's
+
+ align:start position:0%
+alienate the people and it's not it's
+ 
+
+ align:start position:0%
+alienate the people and it's not it's
+it's it's kind of a rude way of
+
+ align:start position:0%
+it's it's kind of a rude way of
+ 
+
+ align:start position:0%
+it's it's kind of a rude way of
+introducing yourself y so so this gives
+
+ align:start position:0%
+introducing yourself y so so this gives
+ 
+
+ align:start position:0%
+introducing yourself y so so this gives
+you the The Best of Both Worlds go make
+
+ align:start position:0%
+you the The Best of Both Worlds go make
+ 
+
+ align:start position:0%
+you the The Best of Both Worlds go make
+a site visit don't plan to film but have
+
+ align:start position:0%
+a site visit don't plan to film but have
+ 
+
+ align:start position:0%
+a site visit don't plan to film but have
+the camera in your bag and if if the
+
+ align:start position:0%
+the camera in your bag and if if the
+ 
+
+ align:start position:0%
+the camera in your bag and if if the
+moment is right and the Rapport is good
+
+ align:start position:0%
+moment is right and the Rapport is good
+ 
+
+ align:start position:0%
+moment is right and the Rapport is good
+and something really fascinating is
+
+ align:start position:0%
+and something really fascinating is
+ 
+
+ align:start position:0%
+and something really fascinating is
+happening you can ask and and film and
+
+ align:start position:0%
+happening you can ask and and film and
+ 
+
+ align:start position:0%
+happening you can ask and and film and
+and you know kind of on the the even
+
+ align:start position:0%
+and you know kind of on the the even
+ 
+
+ align:start position:0%
+and you know kind of on the the even
+more um extreme end from that um say
+
+ align:start position:0%
+more um extreme end from that um say
+ 
+
+ align:start position:0%
+more um extreme end from that um say
+people with anthropological training who
+
+ align:start position:0%
+people with anthropological training who
+ 
+
+ align:start position:0%
+people with anthropological training who
+go to make documentary films sometimes
+
+ align:start position:0%
+go to make documentary films sometimes
+ 
+
+ align:start position:0%
+go to make documentary films sometimes
+they'll spend a year before they even
+
+ align:start position:0%
+they'll spend a year before they even
+ 
+
+ align:start position:0%
+they'll spend a year before they even
+take out a camera and depending on where
+
+ align:start position:0%
+take out a camera and depending on where
+ 
+
+ align:start position:0%
+take out a camera and depending on where
+you are and if what's going on is is
+
+ align:start position:0%
+you are and if what's going on is is
+ 
+
+ align:start position:0%
+you are and if what's going on is is
+really socially sensitive that people
+
+ align:start position:0%
+really socially sensitive that people
+ 
+
+ align:start position:0%
+really socially sensitive that people
+will spend that time just building
+
+ align:start position:0%
+will spend that time just building
+ 
+
+ align:start position:0%
+will spend that time just building
+relationships knowing what's going on
+
+ align:start position:0%
+relationships knowing what's going on
+ 
+
+ align:start position:0%
+relationships knowing what's going on
+developing that sense of um of
+
+ align:start position:0%
+developing that sense of um of
+ 
+
+ align:start position:0%
+developing that sense of um of
+relationship and trust with people so
+
+ align:start position:0%
+relationship and trust with people so
+ 
+
+ align:start position:0%
+relationship and trust with people so
+that when they actually go and pull out
+
+ align:start position:0%
+that when they actually go and pull out
+ 
+
+ align:start position:0%
+that when they actually go and pull out
+the camera it's a completely different
+
+ align:start position:0%
+the camera it's a completely different
+ 
+
+ align:start position:0%
+the camera it's a completely different
+product in the end because you can feel
+
+ align:start position:0%
+product in the end because you can feel
+ 
+
+ align:start position:0%
+product in the end because you can feel
+the kind of interaction between between
+
+ align:start position:0%
+the kind of interaction between between
+ 
+
+ align:start position:0%
+the kind of interaction between between
+the people who are being filmed in the
+
+ align:start position:0%
+the people who are being filmed in the
+ 
+
+ align:start position:0%
+the people who are being filmed in the
+filmaker and it's completely different
+
+ align:start position:0%
+filmaker and it's completely different
+ 
+
+ align:start position:0%
+filmaker and it's completely different
+than somebody who sort of just came in
+
+ align:start position:0%
+than somebody who sort of just came in
+ 
+
+ align:start position:0%
+than somebody who sort of just came in
+for you know you know a couple days to
+
+ align:start position:0%
+for you know you know a couple days to
+ 
+
+ align:start position:0%
+for you know you know a couple days to
+shoot something it's a totally different
+
+ align:start position:0%
+shoot something it's a totally different
+ 
+
+ align:start position:0%
+shoot something it's a totally different
+product and so I I'm trying to remember
+
+ align:start position:0%
+product and so I I'm trying to remember
+ 
+
+ align:start position:0%
+product and so I I'm trying to remember
+now what films were were showing you for
+
+ align:start position:0%
+now what films were were showing you for
+ 
+
+ align:start position:0%
+now what films were were showing you for
+the ethnographic film section but I
+
+ align:start position:0%
+the ethnographic film section but I
+ 
+
+ align:start position:0%
+the ethnographic film section but I
+maybe maybe I'll switch it a bit and try
+
+ align:start position:0%
+maybe maybe I'll switch it a bit and try
+ 
+
+ align:start position:0%
+maybe maybe I'll switch it a bit and try
+to pull out some that sort of convey
+
+ align:start position:0%
+to pull out some that sort of convey
+ 
+
+ align:start position:0%
+to pull out some that sort of convey
+that kind of long-term relationship so
+
+ align:start position:0%
+that kind of long-term relationship so
+ 
+
+ align:start position:0%
+that kind of long-term relationship so
+in some cases when people have the time
+
+ align:start position:0%
+in some cases when people have the time
+ 
+
+ align:start position:0%
+in some cases when people have the time
+and the money and the ability to do it
+
+ align:start position:0%
+and the money and the ability to do it
+ 
+
+ align:start position:0%
+and the money and the ability to do it
+people will
+
+ align:start position:0%
+people will
+ 
+
+ align:start position:0%
+people will
+spend a year or so in advance just
+
+ align:start position:0%
+spend a year or so in advance just
+ 
+
+ align:start position:0%
+spend a year or so in advance just
+building building relationships before
+
+ align:start position:0%
+building building relationships before
+ 
+
+ align:start position:0%
+building building relationships before
+they ever start filming so obviously you
+
+ align:start position:0%
+they ever start filming so obviously you
+ 
+
+ align:start position:0%
+they ever start filming so obviously you
+can't do
+
+ align:start position:0%
+can't do
+ 
+
+ align:start position:0%
+can't do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+but the I mean the other thing is is too
+
+ align:start position:0%
+but the I mean the other thing is is too
+ 
+
+ align:start position:0%
+but the I mean the other thing is is too
+that but just to emphasize the the
+
+ align:start position:0%
+that but just to emphasize the the
+ 
+
+ align:start position:0%
+that but just to emphasize the the
+importance of the social relationships
+
+ align:start position:0%
+importance of the social relationships
+ 
+
+ align:start position:0%
+importance of the social relationships
+and the and establishing the Comfort
+
+ align:start position:0%
+and the and establishing the Comfort
+ 
+
+ align:start position:0%
+and the and establishing the Comfort
+level of the people that you're working
+
+ align:start position:0%
+level of the people that you're working
+ 
+
+ align:start position:0%
+level of the people that you're working
+with is really crucial that's the key um
+
+ align:start position:0%
+with is really crucial that's the key um
+ 
+
+ align:start position:0%
+with is really crucial that's the key um
+but I was going to say even there is has
+
+ align:start position:0%
+but I was going to say even there is has
+ 
+
+ align:start position:0%
+but I was going to say even there is has
+been a shift I think with that with
+
+ align:start position:0%
+been a shift I think with that with
+ 
+
+ align:start position:0%
+been a shift I think with that with
+video because video is so cheap and the
+
+ align:start position:0%
+video because video is so cheap and the
+ 
+
+ align:start position:0%
+video because video is so cheap and the
+cameras are so small and so ubiquitous
+
+ align:start position:0%
+cameras are so small and so ubiquitous
+ 
+
+ align:start position:0%
+cameras are so small and so ubiquitous
+that you still spend the year or more
+
+ align:start position:0%
+that you still spend the year or more
+ 
+
+ align:start position:0%
+that you still spend the year or more
+building the relationships but you can
+
+ align:start position:0%
+building the relationships but you can
+ 
+
+ align:start position:0%
+building the relationships but you can
+introduce the camera soon
+
+ align:start position:0%
+introduce the camera soon
+ 
+
+ align:start position:0%
+introduce the camera soon
+and then the camera just kind of
+
+ align:start position:0%
+and then the camera just kind of
+ 
+
+ align:start position:0%
+and then the camera just kind of
+disappears
+
+ align:start position:0%
+disappears
+ 
+
+ align:start position:0%
+disappears
+eventually so um it's but it's the same
+
+ align:start position:0%
+eventually so um it's but it's the same
+ 
+
+ align:start position:0%
+eventually so um it's but it's the same
+principle you've got to you've got to be
+
+ align:start position:0%
+principle you've got to you've got to be
+ 
+
+ align:start position:0%
+principle you've got to you've got to be
+seen as a human being and have that
+
+ align:start position:0%
+seen as a human being and have that
+ 
+
+ align:start position:0%
+seen as a human being and have that
+human relationship before you become a
+
+ align:start position:0%
+human relationship before you become a
+ 
+
+ align:start position:0%
+human relationship before you become a
+camera and if you do it at the right
+
+ align:start position:0%
+camera and if you do it at the right
+ 
+
+ align:start position:0%
+camera and if you do it at the right
+pace or the best Pace you possibly can
+
+ align:start position:0%
+pace or the best Pace you possibly can
+ 
+
+ align:start position:0%
+pace or the best Pace you possibly can
+given your time and your budget and your
+
+ align:start position:0%
+given your time and your budget and your
+ 
+
+ align:start position:0%
+given your time and your budget and your
+schedule um the camera will be more
+
+ align:start position:0%
+schedule um the camera will be more
+ 
+
+ align:start position:0%
+schedule um the camera will be more
+likely to disappear and this is why it's
+
+ align:start position:0%
+likely to disappear and this is why it's
+ 
+
+ align:start position:0%
+likely to disappear and this is why it's
+better often to have two people if you
+
+ align:start position:0%
+better often to have two people if you
+ 
+
+ align:start position:0%
+better often to have two people if you
+do have I mean some of you might be
+
+ align:start position:0%
+do have I mean some of you might be
+ 
+
+ align:start position:0%
+do have I mean some of you might be
+doing sit down interviews and some of
+
+ align:start position:0%
+doing sit down interviews and some of
+ 
+
+ align:start position:0%
+doing sit down interviews and some of
+you might be doing handheld where you
+
+ align:start position:0%
+you might be doing handheld where you
+ 
+
+ align:start position:0%
+you might be doing handheld where you
+want it to be about action about
+
+ align:start position:0%
+want it to be about action about
+ 
+
+ align:start position:0%
+want it to be about action about
+movement and you don't want to do sit
+
+ align:start position:0%
+movement and you don't want to do sit
+ 
+
+ align:start position:0%
+movement and you don't want to do sit
+down interviews but if you do decide you
+
+ align:start position:0%
+down interviews but if you do decide you
+ 
+
+ align:start position:0%
+down interviews but if you do decide you
+want to do well either way either way
+
+ align:start position:0%
+want to do well either way either way
+ 
+
+ align:start position:0%
+want to do well either way either way
+you do it if you're going to be talking
+
+ align:start position:0%
+you do it if you're going to be talking
+ 
+
+ align:start position:0%
+you do it if you're going to be talking
+to people and have them and have them
+
+ align:start position:0%
+to people and have them and have them
+ 
+
+ align:start position:0%
+to people and have them and have them
+talking back directly to the camera with
+
+ align:start position:0%
+talking back directly to the camera with
+ 
+
+ align:start position:0%
+talking back directly to the camera with
+Comfort level people are often much more
+
+ align:start position:0%
+Comfort level people are often much more
+ 
+
+ align:start position:0%
+Comfort level people are often much more
+comfortable talking again to I'd be much
+
+ align:start position:0%
+comfortable talking again to I'd be much
+ 
+
+ align:start position:0%
+comfortable talking again to I'd be much
+more comfortable talking to you if you
+
+ align:start position:0%
+more comfortable talking to you if you
+ 
+
+ align:start position:0%
+more comfortable talking to you if you
+didn't have a camera in in my face so so
+
+ align:start position:0%
+didn't have a camera in in my face so so
+ 
+
+ align:start position:0%
+didn't have a camera in in my face so so
+this is again where it's really helpful
+
+ align:start position:0%
+this is again where it's really helpful
+ 
+
+ align:start position:0%
+this is again where it's really helpful
+to team up that if you have somebody
+
+ align:start position:0%
+to team up that if you have somebody
+ 
+
+ align:start position:0%
+to team up that if you have somebody
+else going with you you know maybe
+
+ align:start position:0%
+else going with you you know maybe
+ 
+
+ align:start position:0%
+else going with you you know maybe
+somebody else could help do the camera
+
+ align:start position:0%
+somebody else could help do the camera
+ 
+
+ align:start position:0%
+somebody else could help do the camera
+work and maybe Katarina is filming me
+
+ align:start position:0%
+work and maybe Katarina is filming me
+ 
+
+ align:start position:0%
+work and maybe Katarina is filming me
+but I'm talking to you you know and and
+
+ align:start position:0%
+but I'm talking to you you know and and
+ 
+
+ align:start position:0%
+but I'm talking to you you know and and
+and you know and you're really paying
+
+ align:start position:0%
+and you know and you're really paying
+ 
+
+ align:start position:0%
+and you know and you're really paying
+attention to me because you're not
+
+ align:start position:0%
+attention to me because you're not
+ 
+
+ align:start position:0%
+attention to me because you're not
+worrying about the camera and whether
+
+ align:start position:0%
+worrying about the camera and whether
+ 
+
+ align:start position:0%
+worrying about the camera and whether
+it's exposed right and you know you know
+
+ align:start position:0%
+it's exposed right and you know you know
+ 
+
+ align:start position:0%
+it's exposed right and you know you know
+and all these other kinds of questions
+
+ align:start position:0%
+and all these other kinds of questions
+ 
+
+ align:start position:0%
+and all these other kinds of questions
+and we can establish a certain kind of
+
+ align:start position:0%
+and we can establish a certain kind of
+ 
+
+ align:start position:0%
+and we can establish a certain kind of
+relationship that somebody else could
+
+ align:start position:0%
+relationship that somebody else could
+ 
+
+ align:start position:0%
+relationship that somebody else could
+film and it makes it a more intimate
+
+ align:start position:0%
+film and it makes it a more intimate
+ 
+
+ align:start position:0%
+film and it makes it a more intimate
+interaction so this is again where it's
+
+ align:start position:0%
+interaction so this is again where it's
+ 
+
+ align:start position:0%
+interaction so this is again where it's
+helpful to have some potentially to have
+
+ align:start position:0%
+helpful to have some potentially to have
+ 
+
+ align:start position:0%
+helpful to have some potentially to have
+somebody else go with
+
+ align:start position:0%
+somebody else go with
+ 
+
+ align:start position:0%
+somebody else go with
+you you know so you as a filmmaker you
+
+ align:start position:0%
+you you know so you as a filmmaker you
+ 
+
+ align:start position:0%
+you you know so you as a filmmaker you
+might either choose that you would
+
+ align:start position:0%
+might either choose that you would
+ 
+
+ align:start position:0%
+might either choose that you would
+rather do the filming and have the other
+
+ align:start position:0%
+rather do the filming and have the other
+ 
+
+ align:start position:0%
+rather do the filming and have the other
+person do the interviewing or or vice
+
+ align:start position:0%
+person do the interviewing or or vice
+ 
+
+ align:start position:0%
+person do the interviewing or or vice
+versa but it's often helpful to have
+
+ align:start position:0%
+versa but it's often helpful to have
+ 
+
+ align:start position:0%
+versa but it's often helpful to have
+somebody just kind of do be about the
+
+ align:start position:0%
+somebody just kind of do be about the
+ 
+
+ align:start position:0%
+somebody just kind of do be about the
+social relationship part and somebody
+
+ align:start position:0%
+social relationship part and somebody
+ 
+
+ align:start position:0%
+social relationship part and somebody
+else focusing on the technical ends like
+
+ align:start position:0%
+else focusing on the technical ends like
+ 
+
+ align:start position:0%
+else focusing on the technical ends like
+you know are you know you know do we
+
+ align:start position:0%
+you know are you know you know do we
+ 
+
+ align:start position:0%
+you know are you know you know do we
+have again the exposure right and the
+
+ align:start position:0%
+have again the exposure right and the
+ 
+
+ align:start position:0%
+have again the exposure right and the
+Focus right and you know our our wires
+
+ align:start position:0%
+Focus right and you know our our wires
+ 
+
+ align:start position:0%
+Focus right and you know our our wires
+all tangled up in a mess and batteries
+
+ align:start position:0%
+all tangled up in a mess and batteries
+ 
+
+ align:start position:0%
+all tangled up in a mess and batteries
+or have someone focusing on that one
+
+ align:start position:0%
+or have someone focusing on that one
+ 
+
+ align:start position:0%
+or have someone focusing on that one
+just one last thing on this topic uh a
+
+ align:start position:0%
+just one last thing on this topic uh a
+ 
+
+ align:start position:0%
+just one last thing on this topic uh a
+lot of really interesting work has come
+
+ align:start position:0%
+lot of really interesting work has come
+ 
+
+ align:start position:0%
+lot of really interesting work has come
+out of this class when people have
+
+ align:start position:0%
+out of this class when people have
+ 
+
+ align:start position:0%
+out of this class when people have
+filmed their friends and the reason for
+
+ align:start position:0%
+filmed their friends and the reason for
+ 
+
+ align:start position:0%
+filmed their friends and the reason for
+that is that people are obviously very
+
+ align:start position:0%
+that is that people are obviously very
+ 
+
+ align:start position:0%
+that is that people are obviously very
+comfortable with each other uh they try
+
+ align:start position:0%
+comfortable with each other uh they try
+ 
+
+ align:start position:0%
+comfortable with each other uh they try
+there's a lot of trust if you're filming
+
+ align:start position:0%
+there's a lot of trust if you're filming
+ 
+
+ align:start position:0%
+there's a lot of trust if you're filming
+your friends so some great work has has
+
+ align:start position:0%
+your friends so some great work has has
+ 
+
+ align:start position:0%
+your friends so some great work has has
+happened the downside of that is that
+
+ align:start position:0%
+happened the downside of that is that
+ 
+
+ align:start position:0%
+happened the downside of that is that
+you're not taking yourself out of a
+
+ align:start position:0%
+you're not taking yourself out of a
+ 
+
+ align:start position:0%
+you're not taking yourself out of a
+comfort zone as a filmmaker you're doing
+
+ align:start position:0%
+comfort zone as a filmmaker you're doing
+ 
+
+ align:start position:0%
+comfort zone as a filmmaker you're doing
+you're sort of shooting fish in a barrel
+
+ align:start position:0%
+you're sort of shooting fish in a barrel
+ 
+
+ align:start position:0%
+you're sort of shooting fish in a barrel
+um so I have I have kind of mixed
+
+ align:start position:0%
+um so I have I have kind of mixed
+ 
+
+ align:start position:0%
+um so I have I have kind of mixed
+feelings about that and I would say
+
+ align:start position:0%
+feelings about that and I would say
+ 
+
+ align:start position:0%
+feelings about that and I would say
+about that that there are a number of
+
+ align:start position:0%
+about that that there are a number of
+ 
+
+ align:start position:0%
+about that that there are a number of
+intermediary steps before you do your
+
+ align:start position:0%
+intermediary steps before you do your
+ 
+
+ align:start position:0%
+intermediary steps before you do your
+final project there a lot of small
+
+ align:start position:0%
+final project there a lot of small
+ 
+
+ align:start position:0%
+final project there a lot of small
+things along the way and you might
+
+ align:start position:0%
+things along the way and you might
+ 
+
+ align:start position:0%
+things along the way and you might
+experiment with kind of both both both
+
+ align:start position:0%
+experiment with kind of both both both
+ 
+
+ align:start position:0%
+experiment with kind of both both both
+sides of that coin doing a topic and and
+
+ align:start position:0%
+sides of that coin doing a topic and and
+ 
+
+ align:start position:0%
+sides of that coin doing a topic and and
+filming people that you know very well
+
+ align:start position:0%
+filming people that you know very well
+ 
+
+ align:start position:0%
+filming people that you know very well
+and um then kind of taking yourself out
+
+ align:start position:0%
+and um then kind of taking yourself out
+ 
+
+ align:start position:0%
+and um then kind of taking yourself out
+of that comfort
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zone
\ No newline at end of file
diff --git a/7GZTjIxm32I.txt b/7GZTjIxm32I.txt
new file mode 100644
index 0000000000000000000000000000000000000000..82d2a6d2de5fd1b5d91e58db0ebe0198014f6514
--- /dev/null
+++ b/7GZTjIxm32I.txt
@@ -0,0 +1,2168 @@
+FEMALE ANNOUNCER: The following
+content is provided
+
+under a Creative Commons
+license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or to view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+HERBERT GROSS: Hi.
+
+In our last few lectures we were
+trying to establish the
+
+identity of integral calculus
+and differential calculus in
+
+their own right, independently
+of one another, and then by
+
+the fundamental theorems of
+integral calculus to show the
+
+amazing relationship between
+these two subjects.
+
+Now what we would like to do
+today is to emphasize this
+
+topic in terms of an application
+unlike what we've
+
+been doing before.
+
+In particular, what we will do
+today is discuss the question
+
+of finding volumes.
+
+And in doing this, several
+interesting things should
+
+happen, not the least of which
+is that we will rederive
+
+certain results that we've been
+taking for granted about
+
+solid regions--
+
+volumes of regions--
+for quite awhile.
+
+And also, it will give us an
+excellent chance to understand
+
+what we really mean by a
+mathematical structure.
+
+Well, at any rate, to emphasize
+the structure part,
+
+I've called today's lesson,
+'3-dimensional Area'.
+
+See, instead of calling
+it volume, I call it
+
+3-dimensional area, and the
+reason for this is I'd like to
+
+show you how one can study
+volumes in a completely
+
+analogous way to how
+we studied areas.
+
+Remember, we had three basic
+assumptions for area.
+
+I'm now going to assume three
+similar assumptions for volume
+
+except where I have to amend
+them by necessity.
+
+And the only place this
+amendment has to take place is
+
+whereas the rectangle was the
+basic building block of areas,
+
+the so-called cylinder
+will be the basic
+
+building block of volumes.
+
+Let me take a moment to digress
+here and explain to
+
+you mathematically what the
+
+mathematician calls a cylinder.
+
+We start with any closed curve,
+say, in a plane, and we
+
+then take a line perpendicular
+to that plane.
+
+And with that line we trace
+along the curve.
+
+And we then take another plane
+parallel to the plane that the
+
+curve is in and slice this
+thing off someplace.
+
+In other words, by definition, a
+cylinder has congruent cross
+
+sections all the way through.
+
+And what we're saying is that--
+in fact, the familiar
+
+form of a cylinder is the
+one where the cross
+
+section is a circle.
+
+That's called the right
+circular cylinder.
+
+Remember, the volume of a right
+circular cylinder is 'pi
+
+r squared h', the area
+of the cross
+
+section times the height.
+
+Well, that's the generalization
+that we make.
+
+In other words, our first
+assumption is that for any
+
+cylinder the volume of
+the cylinder is the
+
+cross-sectional area
+times the height.
+
+Or you could call it the area of
+the base times the height,
+
+since the cross-sectional area
+is the same for all slices.
+
+OK?
+
+The next assumption says, if we
+think of volume as meaning
+
+the amount of space only in
+three dimensions, whereas area
+
+means the amount of space in
+two dimensions, our next
+
+assumption is that if the three
+dimensional region 'R'
+
+is contained in the three
+dimensional region 'S', then
+
+the volume of 'R' is less than
+or equal to the volume of 'S'.
+
+And finally, we assume an
+analogous result about the
+
+area of the whole equals the sum
+of the areas of the parts.
+
+We assume that if a region is
+made up of the union of 'n'
+
+regions which do not overlap--
+
+notice the union
+notation here.
+
+The union of 'R sub 1' up to 'R
+sub n' and if the 'R's do
+
+not overlap, then the volume of
+the region 'R' is the sum
+
+of the volumes of the
+constituent parts.
+
+In other words, notice that
+except for the fact that
+
+cylinder replaces rectangle, the
+basic axioms for studying
+
+volume are precisely the
+same as the axioms
+
+for studying area.
+
+In particular, then, what this
+means is that structurally the
+
+same results that we were able
+to show for area should follow
+
+word for word, essentially,
+for volumes.
+
+And I thought what we would
+do is start with a rather
+
+familiar example.
+
+You may recall--
+
+of course, we've used this
+result many times--
+
+that the volume of a cylinder
+is given by 1/3--
+
+that the volume of a cone is
+'1/3 pi r squared h' where 'r'
+
+is the radius of the base
+and 'h' is the height.
+
+And you may remember that
+in solid geometry as a
+
+traditional high school
+curriculum went, these results
+
+were given but seldom
+if ever proved.
+
+So what I thought we would do
+now is see how we can use
+
+these axioms to arrive at these
+results, and to get the
+
+spirit of what we've been trying
+to do, I will do this
+
+by integral calculus at least
+first and then by differential
+
+calculus later.
+
+But the idea is something
+like this.
+
+To visualize the cone, the
+radius of whose base is 'r'
+
+and whose height is 'h', we can
+think of the straight line
+
+that joins the origin to the
+point (r, h), this region
+
+here, this right triangle.
+
+And we can think of that as
+being revolved about the
+
+x-axis to give the cone.
+
+Now when we were dealing with
+areas, you may recall that we
+
+broke things down into
+rectangles that were too big,
+
+rectangles that were too small,
+and we computed, say,
+
+'U sub n' and 'L sub
+n', et cetera.
+
+We can do the same thing now.
+
+What we do is we again
+circumscribe rectangles.
+
+Now the idea is whatever volume
+is traced out by this
+
+piece here, whatever volume is
+traced out when we rotate this
+
+triangle about the x-axis, that
+volume will be less than
+
+the volume generated by this
+particular rectangle, because,
+
+you see, the volume that we're
+looking for is contained
+
+inside the rectangle when we
+revolve this particular thing.
+
+Now notice that this particular
+rectangle when
+
+revolved gives me a right
+circular cylinder, and we're
+
+assuming that we know how to
+find the volume of a cylinder.
+
+It's the cross sectional
+area times the height.
+
+Let's focus our attention on
+what I call the k-th region
+
+here and see what this
+thing looks like.
+
+First of all, notice that if
+we've divided this length,
+
+which is 'h' units long into 'n'
+equal parts, each of these
+
+pieces is 'h' over 'n'.
+
+Secondly, notice that the radius
+of the base of the
+
+cylinder that we're going to
+get-- well, let's see.
+
+It's going to be this
+y-coordinate.
+
+Given the x-coordinate, 'y' is
+determined by multiplying the
+
+x-coordinate by 'r/h'.
+
+The x-coordinate is
+'kh' over 'n'.
+
+I multiply that by 'r/h'.
+
+That gives me 'kr' over 'n'.
+
+That's the height of this--
+
+the radius of the base
+of the cylinder that
+
+we're going to revolve.
+
+Now what is the volume
+of this cylinder?
+
+The area of the base is 'pi y
+squared', and I'm now going to
+
+multiply that by the height,
+which is 'h/n'.
+
+And if I do that,
+I obtain what?
+
+The volume of this particular
+cylinder is 'pi r squared h'
+
+times 'k squared'
+over 'n cubed'.
+
+And now, if I add up all of
+these volumes as 'k' goes from
+
+1 to 'n', that will give me a
+bunch of stacked cylinders
+
+which enclose my cone.
+
+In other words, an answer
+that will be too
+
+large will be what?
+
+This sum as 'k' goes from 1 to
+'n', notice that this is the
+
+only portion that depends
+on 'k', so the upper
+
+approximation--
+
+in other words, the volume
+that's too large to be the
+
+right answer--
+
+is 'pi r squared h' over 'n
+cubed' times the sum as 'k'
+
+goes from 1 to 'n',
+'k squared''.
+
+Now you notice I always stick
+to problems where we have
+
+something fairly simple like
+this, because this limit
+
+process, as we've mentioned in
+the previous lectures, becomes
+
+very, very difficult to do in
+general, the beauty or one of
+
+the beauties of our fundamental
+theorem.
+
+But the idea is I do know that
+this sum is 'n' times 'n + 1'
+
+times '2n + 1' over 6.
+
+Now distributing the 'n cubed'
+one factor at a time, the way
+
+we have before, I can now write
+that this is '1/6 pi r
+
+squared h'.
+
+'n + 1' over 'n'
+is '1 + '1/n''.
+
+'2n + 1' over 'n'
+is '2 + '1/n''.
+
+And I find that my upper
+approximation is given by this
+
+expression.
+
+And if I now take the limit of
+'U sub n' as 'n' goes to
+
+infinity, this factor
+approaches 1.
+
+This factor approaches 2.
+
+Therefore, our entire product
+approaches in the limit '1/3
+
+pi r squared h', which
+is the familiar
+
+result of solid geometry.
+
+Of course, we've taken a lot
+for granted over here.
+
+What we've really proven here
+is not that the volume of a
+
+cone is '1/3 pi r squared h'.
+
+What we have proven is at the
+limit of 'U sub n' as 'n'
+
+approaches infinity, it's
+'1/3 pi r squared h'.
+
+The question that comes up is
+how do you know that as these
+
+divisions get small
+that the volume--
+
+the upper approximation gets
+arbitrarily close to the
+
+correct answer.
+
+And again, notice how we can
+reason analogously to what we
+
+did in the case of area.
+
+Namely, what we could do next,
+you see, is take the smallest
+
+cylinder that can be
+inscribed here.
+
+In other words, this would give
+us an approximation which
+
+is too small.
+
+The total error is no more than
+the solid generated by
+
+this hatch region revolving
+about the x-axis.
+
+Notice, however, that each of
+these pieces fits very nicely
+
+in here, so that the total error
+between an approximation
+
+which is too big and an
+approximation which is too
+
+small is this height,
+which is 'r'.
+
+OK?
+
+Let's see, the cross-sectional
+area-- this is 'r'.
+
+So 'pi r squared' is the
+area of the base.
+
+The height is 'h/n'.
+
+Notice that 'r' and 'h' are
+given constants, therefore, as
+
+'n' goes to infinity, the
+numerator stays constant.
+
+The denominator goes
+to infinity.
+
+The difference goes to 0.
+
+In other words, again, we can
+show that 'U sub n' and 'L sub
+
+n' have a common limit.
+
+In fact, we can generalize this
+result rather nicely.
+
+Take this drawing to be whatever
+you'd like it to be.
+
+I've simply tried to visualize
+here a solid region.
+
+This is a 3-dimensional
+region.
+
+It has various cross sections.
+
+And I know that as I look at it
+in the 'x' direction, the
+
+region begins at 'x' equals
+'a' and terminates at 'x'
+
+equals 'b'.
+
+And the question is how can
+I find the volume of this
+
+particular region, assuming I
+know the cross-sectional area
+
+for any slice?
+
+And the idea, again, is what?
+
+We can slice this solid up into
+'n' parts, which I call
+
+'delta V1' up to 'delta Vn'.
+
+The sum of these would be
+the true volume that
+
+we're looking for.
+
+Now, I focus my attention on
+the k-th piece here, and
+
+again, what I do is I inscribe
+and circumscribe cylinders,
+
+one of which is contained
+entirely within 'delta V sub
+
+k', and the other of which
+surrounds 'delta V sub k'.
+
+In other words, what I do is is
+I find the biggest possible
+
+cross-sectional area I have in
+this interval, and I denote
+
+the 'x' value at which that
+occurs by 'M sub k'.
+
+I find the value of 'x', which
+I call 'm sub k', at which I
+
+get the smallest cross-sectional
+area.
+
+And therefore, the inscribed
+cylinder has
+
+volume given by this.
+
+The circumscribed cylinder has
+volume given by this, and the
+
+piece that I'm looking for,
+the true volume, is caught
+
+between these two.
+
+Therefore, if I add these up
+as 'k' goes from 1 to 'n',
+
+I've caught 'V' between 'U
+sub n' and 'L sub n'.
+
+Assuming only that the area is
+a continuous function, the
+
+difference between the largest
+cross section and the smallest
+
+cross section approaches 0 as
+'delta x sub k' approaches 0.
+
+In essence then, the same as
+we did before, what we can
+
+show is that as 'n' goes to
+infinity, both 'U sub n' and
+
+'L sub n' approach a common
+limit, and therefore, the 'V'
+
+being caught between these two
+is equal to the common limit.
+
+Now here's the interesting
+point.
+
+When we talked about the
+definite integral, no one
+
+asked physically what the
+function 'f' was or what the
+
+'c sub k's that we're using here
+were, only that they be
+
+in the proper interval and 'f'
+be a continuous function.
+
+Notice that we're assuming
+that 'A' is continuous.
+
+In essence then, by the
+definition of the definite
+
+integral, that volume
+is just what?
+
+The definite integral from 'a'
+to 'b', 'f of x' 'dx'.
+
+In other words, it's this sum
+taken in the limit as 'n'
+
+approaches infinity, or another
+way of saying that, as
+
+the maximum 'delta X sub
+k' approaches 0.
+
+That, by the way, is the
+integral calculus approach.
+
+If we want the differential
+calculus approach, remember
+
+what we do, we say look it.
+
+The change in volume is less
+than or equal to the maximum
+
+cross-sectional area times
+'delta X' and greater than or
+
+equal to the minimum
+cross-sectional area
+
+times 'delta X'.
+
+Same as we did for area,
+you see, we divide
+
+through by 'delta X'.
+
+We have that 'delta V' divided
+by 'delta X' is caught between
+
+'A of M', 'A of m', where 'm'
+and 'M' are in this interval.
+
+And now you see as 'delta X'
+approaches 0, 'm' and 'M' both
+
+approach 'x'.
+
+You see the same procedure
+as we had before.
+
+You see what we're saying going
+back to this diagram is,
+
+for example, here is a 'delta
+X', and 'm' and 'M' are points
+
+in here, and as 'delta X' goes
+to 0, 'm' and 'M' both
+
+approach the end point 'x'.
+
+And since 'A' is assumed to be
+continuous, if 'M' and 'm'
+
+approach 'x', 'A of M', 'A of
+m' approach 'A of x', and we
+
+arrive at, by differential
+calculus, that 'dV dx' is 'A
+
+of x', and therefore, 'V' is
+again equal to integral ''A of
+
+x' 'dx'' as 'x' goes
+from 'a' to 'b'.
+
+Where now by differential
+calculus, this means what?
+
+It simply means 'G of b' minus
+'G of a', where 'G' is any
+
+function whose derivative
+is 'f'.
+
+Now again, I have to go through
+this thing rather
+
+hurriedly because I want to
+get some examples done.
+
+But what I hope is that we went
+slowly enough so that you
+
+can again sense how we're
+using integral calculus,
+
+differential calculus, and the
+relationship between them.
+
+Let's, at any rate, illustrate
+some of these results more
+
+concretely in terms of--
+
+well, first of all, let's talk
+about one particular type of
+
+solid, what's called a
+solid of revolution.
+
+That's the particular type of
+solid where you have a region
+
+in the 'xy' plane, and you take
+that region and rotate it
+
+either around the x-axis or the
+y-axis, thus generating a
+
+3-dimensional region.
+
+See, in other words, a plane
+area is rotated through 360
+
+degrees either with respect to
+the x-axis or the y-axis.
+
+I'll consider the x-axis here.
+
+Notice that this is a special
+case of what we've just
+
+studied, namely, in this
+particular case, if 'y' equals
+
+'f of x' is a continuous
+function, notice that every
+
+cross section here, every cross
+
+section will be a circle.
+
+The area of the circle
+is 'pi y squared'.
+
+That's 'pi 'f of x' squared'.
+
+And therefore, according to our
+fundamental theorem, since
+
+the area is continuous--
+
+and why is the area
+continuous?
+
+Well, if 'f' is continuous,
+remember the product of
+
+continuous functions
+is continuous.
+
+If 'f' is continuous, 'f
+squared' is continuous.
+
+So according to our result, the
+volume of the region 'R'
+
+is just the integral from
+'a' to 'b', 'pi 'f
+
+of x' squared' 'dx'.
+
+And you see, using differential
+calculus, all we
+
+need now is a function whose
+derivative is 'pi 'f of x'
+
+squared', and we call
+that function 'G'.
+
+We compute 'G of b' minus 'G
+of a' and that gives us the
+
+volume that we're looking for.
+
+Remember, when we talked about
+areas, we mentioned this was
+
+highly specialized.
+
+What if you had a region
+like this?
+
+And again, sparing the details,
+observe that if we
+
+have a region like this, we can
+draw in the lines where
+
+the curve doubles back.
+
+We can now visualize this
+as the volume--
+
+the difference of two volumes.
+
+Namely, we can find this volume
+and subtract from that
+
+volume this volume.
+
+See, in other words, both of
+these have the right form.
+
+And by this difference,
+what's left?
+
+The difference of the big volume
+minus the small volume
+
+is the volume generated
+by 'R'.
+
+And as I say, these are rather
+simple details that we can
+
+check out computationally in
+terms of exercises, but the
+
+reason I wanted to mention the
+solid of revolution is that
+
+not only is this a rather common
+and important category,
+
+but it also happens to be the
+type of solid that we opened
+
+our program with.
+
+Remember, the cone may
+be viewed as what?
+
+The solid generated by a
+particular right triangle
+
+being revolved about
+the x-axis.
+
+In fact, I thought we could
+try that same problem now
+
+doing it by the antiderivative
+method.
+
+Namely, we take this particular
+region 'R' and
+
+notice now, if we revolve
+this about the x-axis--
+
+let's see, the cross-sectional
+area will be what?
+
+Well, it's a circle
+of radius 'y'.
+
+For a given value of 'x',
+'y' is equal to 'r'
+
+times 'x' over 'h'.
+
+See the slope of this
+line is 'r/h'.
+
+It passes through
+the origin here.
+
+So the cross-sectional area
+is 'y squared' times pi.
+
+That's 'pi 'r squared h'
+squared' over 'h squared'
+
+times 'x squared'.
+
+And to find that volume,
+I simply integrate this
+
+between 0 and 'h'.
+
+Recalling that pi, 'r', and 'h'
+are constants, I can take
+
+the constants outside of
+the integral sign.
+
+The integral of 'x squared',
+meaning what?
+
+The inverse derivative
+is '1/3 x cubed'.
+
+If I evaluate that between 0 and
+'h', I get '1/3 h cubed'.
+
+The 'h cubed' in the numerator
+cancels the 'h squared' in the
+
+denominator, leaving a factor of
+'h' in the numerator, and I
+
+wind up, as I saw before, that
+the volume of this cone is
+
+'1/3 pi r squared h'.
+
+And this is nice that I get
+the same answer as by the
+
+limit method, because according
+to the fundamental
+
+theorem, the first fundamental
+theorem, this is precisely
+
+what was supposed to happen.
+
+In other words, I can do these
+either by limits or by
+
+derivatives.
+
+I want you to see these things
+side by side, because in
+
+certain cases, as I've
+emphasized in the previous
+
+lectures, there will be times
+when we cannot, by
+
+differential calculus, find a
+function 'G' whose derivative
+
+is equal to a given
+function 'f of x'.
+
+But enough about that
+for the time being.
+
+The next question that comes up
+gives us a review of what
+
+happens with inverse
+functions.
+
+It's a rather interesting
+type of situation.
+
+It's called the method of
+cylindrical shells and it's
+
+motivated by the following.
+
+Let's suppose again we're given
+a very nice region 'R'.
+
+What do I mean by very nice?
+
+Well, to simplify the
+computation, even though it
+
+doesn't change the theory at
+all, I'm assuming that 'y'
+
+equals 'f of x' is an
+increasing curve.
+
+In other words, I'm even
+assuming that we have a
+
+one-to-one function here.
+
+Now the idea is here's this
+nice region and instead of
+
+revolving this about the
+x-axis, I would like to
+
+revolve it about the y-axis.
+
+Now you see, to use the method
+of revolution here, to revolve
+
+this about the y-axis,
+essentially what I do is I
+
+pick a washer-shaped
+region, you see?
+
+I have to compute the volume
+generated by the 'y' part.
+
+See, in other words, I do this
+as two separate parts.
+
+I find the volume of the big
+piece minus the volume of the
+
+small piece, and what's
+left is the volume
+
+generated by 'R'.
+
+But notice a rather difficult
+computational
+
+thing occurs here.
+
+Namely, notice that this
+length here has to be
+
+expressed as 'x' goes from one
+value to another value.
+
+Now, you see, if this is 'b',
+and this is 'a', you see,
+
+notice what's happening
+here, how our
+
+strips are being chosen.
+
+You see, for a given strip, the
+final 'x' value is 'b',
+
+but what is the initial
+'x' value?
+
+See, down here the 'x'
+value is 'a', but
+
+what happens up here?
+
+In other words, how do you find
+what the 'x' value is for
+
+a given value of 'y' here?
+
+Well, you see what you must do
+is invert the relationship.
+
+Now even though I've
+picked a case
+
+where the inverse exists--
+
+see, this is a one-to-one
+function--
+
+we've already had ample examples
+in which we've shown
+
+that computationally it's
+extremely difficult if it's
+
+even possible to explicitly
+perform the inversion.
+
+And this is where the method
+of cylindrical
+
+shells comes from.
+
+Essentially what the method of
+cylindrical shells says is
+
+wouldn't it have been nice if
+we chose our generating
+
+element to be this way?
+
+In other words, what we say
+is look at this piece
+
+of area over here.
+
+One way of visualizing this
+solid being rotated is to
+
+think of this particular region
+being rotated about the
+
+x-axis, and it generates
+a certain volume.
+
+By the way, what volume
+will it generate?
+
+The volume that it will generate
+will be less than the
+
+volume that this rectangle
+generates but greater than the
+
+volume that this rectangle
+here generates.
+
+Now what is the volume
+generated
+
+by the large rectangle?
+
+And, by the way, notice that I
+mean by the volume generated
+
+by the rectangle think of this
+as being a slab of a certain
+
+amount of material and I
+rotate that slab around
+
+through 360 degrees.
+
+The volume I'm thinking of is
+the volume of the material in
+
+that slab, not the material
+that's enclosed.
+
+It would be like, if
+you're thinking in
+
+terms of a tin can.
+
+I'm not thinking of the volume
+enclosed by the tin can.
+
+I'm thinking of the volume
+of the tin itself that
+
+makes up the can.
+
+Well, you see again, to go
+through this thing as rapidly
+
+as possible but still hitting
+the main points, you see,
+
+notice that the volume that I'm
+looking for, what is the
+
+volume that's cut out by
+this big rectangle?
+
+Well, notice that the area of
+the base from-- if I look at
+
+this as being this cylinder
+minus this cylinder, the
+
+volume of the big cylinder is
+pi times ''x + delta X'
+
+squared' times the height
+here, which is 'f
+
+of 'x + delta X'.
+
+And the volume of the
+hollow part from
+
+here to here is what?
+
+It's 'pi x squared'--
+
+that's the radius
+of the base--
+
+times the height, which is still
+'f of 'x + delta X''.
+
+In other words, 'delta V' is
+bounded above by this volume.
+
+In other words, as messy as this
+looks, that's only what?
+
+That's the volume of the region
+
+generated by this big rectangle.
+
+If we take the smallest
+rectangle, namely the one
+
+that's inscribed inside this
+region, we get the same
+
+results, except that the height
+is now replaced by 'f
+
+of x' rather than by 'f
+of 'x + delta X''.
+
+In other words, we catch
+'delta V' between two
+
+expressions involving 'x'.
+
+By the way, notice how the
+bracketed expression
+
+simplifies the 'pi x squared'
+here cancels with the 'pi x
+
+squared' here leaving inside the
+parentheses just '2x delta
+
+X' plus 'delta X squared'.
+
+In other words, simplifying
+this thing, I can now show
+
+that 'delta V' is caught between
+these two expressions
+
+now, this expression here, which
+is too big, and this
+
+expression here, which
+is too small.
+
+Now I divide by 'delta X'.
+
+The usual procedure to find
+'dV dx', it's 'delta V'
+
+divided by 'delta X'.
+
+Then I will take the limit as
+'delta X' approaches 0.
+
+You see, so I divide through
+by 'delta X'.
+
+We're assuming, of course,
+that 'delta X' is not 0.
+
+That's what the limit means
+as 'delta X' approaches 0.
+
+You see, it's not zero, but it
+gets arbitrarily close to 0.
+
+Notice then that my 'delta V'
+divided by 'delta X' is caught
+
+between pi times '2x + delta X'
+times 'f of 'x + delta X'',
+
+and pi times '2x + delta
+X' times 'f of x'.
+
+And I now let 'delta
+X' approach 0.
+
+And here's the key point.
+
+As 'delta X' approaches 0,
+notice that the left hand side
+
+becomes '2 pi x'
+times 'f of x'.
+
+Notice also what happens
+to the right hand side.
+
+This factor, as 'delta X'
+approaches 0, becomes '2x'.
+
+And because 'f' is continuous,
+as 'delta X' approaches 0, 'f
+
+of 'x + delta X'' approaches
+'f of x'.
+
+In other words, then, in the
+limit, as 'delta X' approaches
+
+0, I have that 'dV dx' on the
+one hand can't be any greater
+
+than '2 pi x' times 'f of x'.
+
+On the other hand, it can't
+be any less than '2 pi
+
+x' times 'f of x'.
+
+Consequently, it must equal
+'2 pi x' times 'f of x'.
+
+Therefore, if this is 'dV dx',
+then 'V' itself is the
+
+integral of this thing evaluated
+between 'a' and 'b',
+
+because that's where we're
+adding these things up from.
+
+In other words, if we're using
+differential calculus, this is
+
+'G of b' minus 'G of a' where
+'G prime' equals 'f'.
+
+If we're using integral
+calculus, we've found the 'U
+
+sub n' and 'L sub n' and we've
+caught 'V' between 'U sub n'
+
+and 'L sub n'.
+
+But, in any event, what we've
+shown rigorously now is that
+
+by the cylindrical shell
+method-- and we'll illustrate
+
+these with examples to finish
+off today's lesson--
+
+that the volume is given
+by integral from 'a'
+
+to 'b' '2 pi x'--
+
+and let me just replace
+'f of x' by 'y' to
+
+make my diagram simpler--
+
+times 'dx'.
+
+And if you want to think of
+this in what I call the
+
+traditional engineering point
+of view where you think of a
+
+thin rectangle generating a
+volume, what we're saying is
+
+if you think of a little thin
+piece like this being revolved
+
+to generate, say, some material
+in a tin can, notice
+
+that the amount of material
+in here will be what?
+
+Well, when you unroll
+this thing--
+
+see, this thing sort
+of like this.
+
+When you unroll this thing,
+the radius is 'x', so the
+
+circumference when you unroll
+it will be '2 pi x'.
+
+The height is 'y'.
+
+So the cross-sectional area
+is '2 pi x y' and the
+
+thickness is 'dx'.
+
+So if I multiply that by dx,
+that gives me the volume
+
+generated by this piece.
+
+And then in the proud tradition
+of the sigma
+
+notation, which I'll come back
+to in the next lecture to show
+
+how dangerous this really
+is, but the
+
+shortcut method is what?
+
+Add up all of these
+contributions as 'x' goes from
+
+'a' to 'b'.
+
+At any rate, that's called the
+method of cylindrical shells.
+
+Essentially, one uses
+cylindrical shells when we
+
+think of a generating element
+being parallel
+
+to the axis of rotation.
+
+We use revolution, when
+it's perpendicular
+
+to the axis of rotation.
+
+Which of the two is easier
+depends on the particular
+
+computational technique
+necessitated by the
+
+relationship between the
+variables in the problem.
+
+Well, at any rate, let's do
+a couple of examples.
+
+The first example I'd like to do
+is to take that same region
+
+'R', namely, the right
+triangle whose
+
+legs are 'r' and 'h'.
+
+We've already solved this
+problem of finding the volume
+
+when we rotate this
+about the x-axis.
+
+What I'd now like to do is see
+what volume is generated by
+
+this as I rotate it
+about the y-axis.
+
+And again, I find that I can
+do this problem in several
+
+ways, but I thought it was an
+easy enough problem to do by
+
+cylindrical shells, because, as
+we so often do, I thought
+
+the first problem that we do by
+cylindrical shells should
+
+be one that we can check
+by another method.
+
+But at any rate, using
+cylindrical shells, let's see
+
+what happens over here.
+
+The volume is what?
+
+It's the integral from 0 to
+'h', '2 pi x' times this
+
+height, which is 'rx'
+over 'h' integrated
+
+with respect to 'x'.
+
+That's just '2 pi r' over
+'h'-- we can take that
+
+outside, because that's
+a constant factor--
+
+integral 'x squared dx'.
+
+The integral of 'x squared'
+is '1/3 x cubed'.
+
+We evaluate that between
+0 and 'h'.
+
+That gives us '1/3 h cubed'.
+
+We cancel the 'h' in the
+denominator with one of the
+
+'h's in the numerator, and we
+find that the volume that's
+
+generated is '2/3 pi r h
+squared', not 'r squared h',
+
+'r h squared', not 1/3, 2/3.
+
+Remember, by the way, what
+this thing looks like.
+
+I think you can visualize
+this.
+
+This is a cylinder with
+a cone cut out of it.
+
+See, in other words, if this
+thing had been solid, we'd
+
+have called it a right circular
+cylinder, and then
+
+what's missing is the cone
+shaped region over here.
+
+In fact, that's how
+we can check this.
+
+See, what would the
+volume be that's
+
+generated by this rectangle?
+
+This would be a cylinder the
+radius of whose base is 'h',
+
+whose height is 'r', and the
+volume of that cylinder is 'pi
+
+h squared r'.
+
+The cone that's missing, the
+cone that was cut out of this
+
+thing, has the radius of a space
+equal to 'h' and its
+
+height equal to 'r', so
+its volume is '1/3
+
+pi h squared r'.
+
+And, therefore, the volume
+that's left when we subtract
+
+this off is '2/3 pi h
+squared r', which
+
+does check with this.
+
+By the way, just as an aside,
+notice that the region 'R'
+
+generates a different volume
+if we rotate it about the
+
+y-axis than it did if we rotate
+it about the x-axis.
+
+Numerically, what we're saying
+is that we just found that the
+
+volume when rotated around
+the y-axis is '2/3
+
+pi h squared r'.
+
+We know that when we revolve
+that about the x-axis, it's
+
+'1/3 pi r squared h',
+and these two
+
+expressions are not identical.
+
+In fact, if we divide both sides
+by 'pi r h' over 3, we
+
+find that equality holds only
+if we have that highly
+
+specialized case that '2h'
+equals 'r', which is not
+
+really important.
+
+I just threw that
+in as an aside.
+
+But I do want you to notice that
+the same area, of course,
+
+generates different volumes
+depending on what you rotate
+
+it with respect to.
+
+Well, at any rate, at least
+this was a problem that we
+
+could check by another method.
+
+Let me just use cylindrical
+shells for a problem which is
+
+slightly tougher but one that
+can still be checked by
+
+another method.
+
+Let's take the following
+region.
+
+Let's take the curve 'y'
+equals '2x - x squared'
+
+between 'x' equals 0
+and 'x' equals 2.
+
+Leaving the details as a rather
+trivial exercise, it is
+
+not difficult to see that this
+is the parabola that peaks at
+
+1, 1 and crosses the x-axis at
+'x' equals 0 and 'x' equals 2.
+
+If I now want to compute this
+volume as I rotate the region
+
+'R' about the y-axis--
+
+see, I'm going to rotate
+this about the y-axis.
+
+I want to find out what volume
+is generated by this region
+
+'R' in this case.
+
+Remember I can use either
+cylindrical shells or I can
+
+use revolution here.
+
+Notice the problem I'm
+going to be in.
+
+Notice that this particular
+function is single valued but
+
+not one-to-one.
+
+When I try to find these two
+'x' values I'm going to run
+
+into multi-values.
+
+I'm going to have to invert.
+
+All sorts of computational
+skills are going to
+
+come into play here.
+
+On the other hand, if I take my
+generating element parallel
+
+to the y-axis, I have a very
+simple expression for this,
+
+and now that indicates what?
+
+By the method of cylindrical
+shells, this will be the
+
+integral from 0 to 2.
+
+The generating arm is 'x', so
+that cuts out '2 pi x'.
+
+The height is 'y', which
+is '2x - x squared'.
+
+The thickness is 'dx'.
+
+In other words, mechanically
+I must evaluate
+
+this particular integral.
+
+OK?
+
+At any rate, it's factoring
+out the 2 pi and just
+
+observing that the
+integral of '2 x
+
+squared' is '2/3 x cubed'.
+
+The integral of 'x'
+to the fourth is
+
+'1/4 'x to the 4th''.
+
+Evaluating that between
+0 and 2, I get 2 pi
+
+times 16/3 minus 4.
+
+The lower limit is 0 here.
+
+This just comes out to be 16
+minus 12, 4/3 times 2 pi.
+
+That's 8 pi over 3.
+
+By the way, before I go any
+further with this, let's make
+
+the interesting observation.
+
+See, 8 pi over 3 is the volume
+generated by this whole thing
+
+being revolved about
+the y-axis.
+
+If I'd drawn in this line, which
+is a line of symmetry,
+
+notice that these two
+areas are congruent.
+
+These two regions
+are congruent.
+
+However, it's also interesting
+to observe that the volume
+
+generated by this piece as you
+revolve it about the y-axis is
+
+not twice the volume generated
+by this piece.
+
+See, notice that the integral
+from 0 to 1-- in other words,
+
+if we just took this region
+here, integrated this from 0
+
+to 1, we would get 5/6, 2/3
+minus 1/4 times 2 pi, 5/6.
+
+And if we double that,
+we would get 5/3.
+
+In other words, this
+area is 5/6.
+
+Double it would be
+5 pi over 6.
+
+Double it would be 5 pi over 3,
+and 5 pi over 3 is not the
+
+same as 8 pi over 3.
+
+The thing to keep in mind here
+is notice how the distance
+
+comes in again.
+
+You see, for example, these two
+lines here are symmetric
+
+with respect to the
+line 'x' equals 1.
+
+But notice that this generates a
+much larger volume than this
+
+because its generating
+arm is longer.
+
+It's further away.
+
+But at any rate, that's
+just an aside.
+
+Notice how by the method of
+cylindrical shells, we
+
+determine the volume
+is 8 pi over 3.
+
+Suppose we'd wanted to do this
+by the solid method-- the
+
+solid revolution method.
+
+Notice that we would first
+have to invert this
+
+relationship.
+
+We would first have to solve
+for 'x' in terms of 'y'.
+
+Notice that 'y' equals '2x - x
+squared' is the same as saying
+
+that ''x squared'
+- 2x + y' is 0.
+
+Using the quadratic formula, we
+can solve for 'x', and we
+
+now find that 'x' is 1 plus the
+square root of '1 - y' or
+
+1 minus the square
+root of '1 - y'.
+
+What that means, by the way,
+geometrically, is simply this.
+
+For a given value of 'y', there
+are two values of 'x'
+
+located symmetrically with
+respect to 'x' equals 1.
+
+See, they're on symmetrical
+portions.
+
+Well, this doesn't make
+that much difference.
+
+The thing now is what?
+
+What is my cross-sectional
+area?
+
+My cross-sectional area is pi
+times this length squared
+
+minus pi times this
+length squared.
+
+That's pi times 1 plus the
+square root of ''1 - y'
+
+squared' minus pi times the
+square root of 1 minus the
+
+square root of ''1
+- y' squared'.
+
+When I square this and subtract,
+all but the middle
+
+term drops out.
+
+In other words, I have twice
+the square root of '1 - y'
+
+here minus twice the square
+root of '1 - y' here.
+
+When I subtract, I get 4 times
+the square root of '1 - y'.
+
+I multiply that by pi.
+
+That's my cross-sectional
+area.
+
+And now to find the volume, I
+just integrate that as 'y'
+
+goes from 0 to 1.
+
+You see, and if I carry out
+this integration, noticing
+
+that the integral of ''1 - y'
+to the 1/2' is minus 2/3.
+
+Remember, the derivative of
+'1 - y' with respect to
+
+'y' is minus 1.
+
+''1 - y' to the 3/2'.
+
+Evaluate that between 0 and 1.
+
+The upper limit gives me 0.
+
+The lower limit is minus 2/3.
+
+I subtract the lower limit.
+
+It gives me 2/3.
+
+4 pi times 2/3 is 8 pi
+over 3, the same
+
+answer as I got before.
+
+Notice, by the way, that
+this was messy, but we
+
+could handle it.
+
+If this had been
+much tougher--
+
+say a 6 over here or something
+like that instead of a 2--
+
+how would we have solved for
+'x' in terms of 'y'?
+
+You see, in other words, this
+would have been a case where
+
+the shell method would have been
+necessitated because of
+
+the impossibility
+of the algebra.
+
+But at any rate, we have plenty
+of opportunity to
+
+illustrate that in terms of
+exercises and supplementary
+
+notes and reading material
+and what have you.
+
+That is actually the
+easiest part.
+
+The hard part is to understand
+the significance of what's
+
+going on, so I thought that to
+summarize today's lecture,
+
+let's keep in mind that whether
+you call it area or
+
+whether you call it volume or
+whether you call it distance
+
+traveled in velocity, the fact
+remains that if 'f' is a
+
+function continuous on the
+closed interval from 'a' to
+
+'b', and we partition that
+interval into 'n' parts, and
+
+we form the sum as 'k' goes from
+1 to 'n', 'f of 'c sub
+
+k'' times 'delta x sub k', where
+'c sub k' is in the k-th
+
+interval, and 'delta x sub
+k' is just 'x sub k'
+
+minus 'x sub 'k - 1''.
+
+If we take that limit as the
+largest 'delta x' approaches 0
+
+and call that 'Q', that
+limit 'Q' exists.
+
+Symbolically, it's written by
+the definite integral from 'a'
+
+to 'b', ''f of x' dx', and,
+more to the point, if you
+
+happen to know differential
+calculus, you can compute 'Q'
+
+just by computing 'G of b'
+minus 'G of a', where 'G
+
+prime' is any function whose
+derivative is 'f'.
+
+OK?
+
+Now again, this is why I'm
+calling it a summary.
+
+If you separate this out from
+all of the computational stuff
+
+that we did in today's lecture,
+this is the part
+
+that's left.
+
+OK?
+
+And what I want to do next
+time is to show you that
+
+things are not quite this
+straightforward all the time,
+
+that certain nice things have
+been happening here that allow
+
+us, essentially, to get
+away with murder.
+
+And what I mean by that will
+become clearer next time, but
+
+until next time then goodbye.
+
+MALE ANNOUNCER: Funding for the
+publication of this video
+
+was provided by the Gabriella
+and Paul Rosenbaum Foundation.
+
+Help OCW continue to provide
+free and open access to MIT
+
+courses by making a donation
+at ocw.mit.edu/donate.
\ No newline at end of file
diff --git a/7nu97OYx4X4.txt b/7nu97OYx4X4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..16ac9b2c8cdf8e1a94c44719054d371c09eda211
--- /dev/null
+++ b/7nu97OYx4X4.txt
@@ -0,0 +1,1603 @@
+align:start position:0%
+ 
+by this point we have discussed pretty
+
+ align:start position:0%
+by this point we have discussed pretty
+ 
+
+ align:start position:0%
+by this point we have discussed pretty
+much everything that is to be said about
+
+ align:start position:0%
+much everything that is to be said about
+ 
+
+ align:start position:0%
+much everything that is to be said about
+individual discrete random variables now
+
+ align:start position:0%
+individual discrete random variables now
+ 
+
+ align:start position:0%
+individual discrete random variables now
+let us move to the case where we're
+
+ align:start position:0%
+let us move to the case where we're
+ 
+
+ align:start position:0%
+let us move to the case where we're
+dealing with multiple discrete random
+
+ align:start position:0%
+dealing with multiple discrete random
+ 
+
+ align:start position:0%
+dealing with multiple discrete random
+variables simultaneously and talk about
+
+ align:start position:0%
+variables simultaneously and talk about
+ 
+
+ align:start position:0%
+variables simultaneously and talk about
+their distribution as we will see their
+
+ align:start position:0%
+their distribution as we will see their
+ 
+
+ align:start position:0%
+their distribution as we will see their
+distribution is characterized by a so
+
+ align:start position:0%
+distribution is characterized by a so
+ 
+
+ align:start position:0%
+distribution is characterized by a so
+called joint PMF so suppose that we have
+
+ align:start position:0%
+called joint PMF so suppose that we have
+ 
+
+ align:start position:0%
+called joint PMF so suppose that we have
+a probabilistic model and on that model
+
+ align:start position:0%
+a probabilistic model and on that model
+ 
+
+ align:start position:0%
+a probabilistic model and on that model
+we have defined two random variables x
+
+ align:start position:0%
+we have defined two random variables x
+ 
+
+ align:start position:0%
+we have defined two random variables x
+and y and that we have available their
+
+ align:start position:0%
+and y and that we have available their
+ 
+
+ align:start position:0%
+and y and that we have available their
+individual pmf's these pmf's tell us
+
+ align:start position:0%
+individual pmf's these pmf's tell us
+ 
+
+ align:start position:0%
+individual pmf's these pmf's tell us
+about one random variable at a time this
+
+ align:start position:0%
+about one random variable at a time this
+ 
+
+ align:start position:0%
+about one random variable at a time this
+tells us about X this tells us about Y
+
+ align:start position:0%
+tells us about X this tells us about Y
+ 
+
+ align:start position:0%
+tells us about X this tells us about Y
+but they do not give us any information
+
+ align:start position:0%
+but they do not give us any information
+ 
+
+ align:start position:0%
+but they do not give us any information
+about how the two random variables are
+
+ align:start position:0%
+about how the two random variables are
+ 
+
+ align:start position:0%
+about how the two random variables are
+related to each other for example if you
+
+ align:start position:0%
+related to each other for example if you
+ 
+
+ align:start position:0%
+related to each other for example if you
+wish to answer this question whether the
+
+ align:start position:0%
+wish to answer this question whether the
+ 
+
+ align:start position:0%
+wish to answer this question whether the
+numerical values that the two random
+
+ align:start position:0%
+numerical values that the two random
+ 
+
+ align:start position:0%
+numerical values that the two random
+variables happen to be equal and what is
+
+ align:start position:0%
+variables happen to be equal and what is
+ 
+
+ align:start position:0%
+variables happen to be equal and what is
+the probability of that event you will
+
+ align:start position:0%
+the probability of that event you will
+ 
+
+ align:start position:0%
+the probability of that event you will
+not be able to answer this question if
+
+ align:start position:0%
+not be able to answer this question if
+ 
+
+ align:start position:0%
+not be able to answer this question if
+you only know the two individual pmf's
+
+ align:start position:0%
+you only know the two individual pmf's
+ 
+
+ align:start position:0%
+you only know the two individual pmf's
+in order to be able to answer a question
+
+ align:start position:0%
+in order to be able to answer a question
+ 
+
+ align:start position:0%
+in order to be able to answer a question
+of this type we will need information
+
+ align:start position:0%
+of this type we will need information
+ 
+
+ align:start position:0%
+of this type we will need information
+that tells us what values of X tend to
+
+ align:start position:0%
+that tells us what values of X tend to
+ 
+
+ align:start position:0%
+that tells us what values of X tend to
+occur together with what values of Y and
+
+ align:start position:0%
+occur together with what values of Y and
+ 
+
+ align:start position:0%
+occur together with what values of Y and
+this information is captured in the so
+
+ align:start position:0%
+this information is captured in the so
+ 
+
+ align:start position:0%
+this information is captured in the so
+called joint PMF so the joint PMF is
+
+ align:start position:0%
+called joint PMF so the joint PMF is
+ 
+
+ align:start position:0%
+called joint PMF so the joint PMF is
+nothing but a piece of notation for an
+
+ align:start position:0%
+nothing but a piece of notation for an
+ 
+
+ align:start position:0%
+nothing but a piece of notation for an
+object that's familiar this is the
+
+ align:start position:0%
+object that's familiar this is the
+ 
+
+ align:start position:0%
+object that's familiar this is the
+probability that when we carry out the
+
+ align:start position:0%
+probability that when we carry out the
+ 
+
+ align:start position:0%
+probability that when we carry out the
+experiment we happen to see random
+
+ align:start position:0%
+experiment we happen to see random
+ 
+
+ align:start position:0%
+experiment we happen to see random
+variable X take on value little X and
+
+ align:start position:0%
+variable X take on value little X and
+ 
+
+ align:start position:0%
+variable X take on value little X and
+simultaneously see that random variable
+
+ align:start position:0%
+simultaneously see that random variable
+ 
+
+ align:start position:0%
+simultaneously see that random variable
+Y takes on a value little Y this
+
+ align:start position:0%
+Y takes on a value little Y this
+ 
+
+ align:start position:0%
+Y takes on a value little Y this
+quantity we indicated with this notation
+
+ align:start position:0%
+quantity we indicated with this notation
+ 
+
+ align:start position:0%
+quantity we indicated with this notation
+the letter little P stands for a PMF the
+
+ align:start position:0%
+the letter little P stands for a PMF the
+ 
+
+ align:start position:0%
+the letter little P stands for a PMF the
+subscripts tell us which random
+
+ align:start position:0%
+subscripts tell us which random
+ 
+
+ align:start position:0%
+subscripts tell us which random
+variables were talking about and finally
+
+ align:start position:0%
+variables were talking about and finally
+ 
+
+ align:start position:0%
+variables were talking about and finally
+this is a function of two arguments
+
+ align:start position:0%
+this is a function of two arguments
+ 
+
+ align:start position:0%
+this is a function of two arguments
+depending on what pair X Y were
+
+ align:start position:0%
+depending on what pair X Y were
+ 
+
+ align:start position:0%
+depending on what pair X Y were
+interested in we are going to get a
+
+ align:start position:0%
+interested in we are going to get a
+ 
+
+ align:start position:0%
+interested in we are going to get a
+different numerical value for this
+
+ align:start position:0%
+different numerical value for this
+ 
+
+ align:start position:0%
+different numerical value for this
+probability as an example of a joint PMF
+
+ align:start position:0%
+probability as an example of a joint PMF
+ 
+
+ align:start position:0%
+probability as an example of a joint PMF
+in which the two random variables take
+
+ align:start position:0%
+in which the two random variables take
+ 
+
+ align:start position:0%
+in which the two random variables take
+values in a finite set
+
+ align:start position:0%
+values in a finite set
+ 
+
+ align:start position:0%
+values in a finite set
+we might be given a table
+
+ align:start position:0%
+we might be given a table
+ 
+
+ align:start position:0%
+we might be given a table
+of this forum using this table we can
+
+ align:start position:0%
+of this forum using this table we can
+ 
+
+ align:start position:0%
+of this forum using this table we can
+answer questions such as the following
+
+ align:start position:0%
+answer questions such as the following
+ 
+
+ align:start position:0%
+answer questions such as the following
+what is the probability that the random
+
+ align:start position:0%
+what is the probability that the random
+ 
+
+ align:start position:0%
+what is the probability that the random
+variables x and y simultaneously take
+
+ align:start position:0%
+variables x and y simultaneously take
+ 
+
+ align:start position:0%
+variables x and y simultaneously take
+the values let us say 1 & 3 then we look
+
+ align:start position:0%
+the values let us say 1 & 3 then we look
+ 
+
+ align:start position:0%
+the values let us say 1 & 3 then we look
+up in this table and we identify that
+
+ align:start position:0%
+up in this table and we identify that
+ 
+
+ align:start position:0%
+up in this table and we identify that
+it's this probability X takes the value
+
+ align:start position:0%
+it's this probability X takes the value
+ 
+
+ align:start position:0%
+it's this probability X takes the value
+of 1 and Y takes the value of 3 and
+
+ align:start position:0%
+of 1 and Y takes the value of 3 and
+ 
+
+ align:start position:0%
+of 1 and Y takes the value of 3 and
+according to this table the answer would
+
+ align:start position:0%
+according to this table the answer would
+ 
+
+ align:start position:0%
+according to this table the answer would
+be 2 over 20 now something to notice
+
+ align:start position:0%
+be 2 over 20 now something to notice
+ 
+
+ align:start position:0%
+be 2 over 20 now something to notice
+about joint pmfs when you add over all
+
+ align:start position:0%
+about joint pmfs when you add over all
+ 
+
+ align:start position:0%
+about joint pmfs when you add over all
+possible pairs x and y this exhausts all
+
+ align:start position:0%
+possible pairs x and y this exhausts all
+ 
+
+ align:start position:0%
+possible pairs x and y this exhausts all
+the possibilities and therefore these
+
+ align:start position:0%
+the possibilities and therefore these
+ 
+
+ align:start position:0%
+the possibilities and therefore these
+probabilities should add to 1 in terms
+
+ align:start position:0%
+probabilities should add to 1 in terms
+ 
+
+ align:start position:0%
+probabilities should add to 1 in terms
+of this table all the entries that we
+
+ align:start position:0%
+of this table all the entries that we
+ 
+
+ align:start position:0%
+of this table all the entries that we
+have here should add to 1 now once we
+
+ align:start position:0%
+have here should add to 1 now once we
+ 
+
+ align:start position:0%
+have here should add to 1 now once we
+have in our hands the joint PMF we can
+
+ align:start position:0%
+have in our hands the joint PMF we can
+ 
+
+ align:start position:0%
+have in our hands the joint PMF we can
+use it to find the individual PMF of the
+
+ align:start position:0%
+use it to find the individual PMF of the
+ 
+
+ align:start position:0%
+use it to find the individual PMF of the
+random variables x and y and these
+
+ align:start position:0%
+random variables x and y and these
+ 
+
+ align:start position:0%
+random variables x and y and these
+individual pmfs are called the marginal
+
+ align:start position:0%
+individual pmfs are called the marginal
+ 
+
+ align:start position:0%
+individual pmfs are called the marginal
+pmfs how do we find them well the joint
+
+ align:start position:0%
+pmfs how do we find them well the joint
+ 
+
+ align:start position:0%
+pmfs how do we find them well the joint
+PMF tells us everything there is to be
+
+ align:start position:0%
+PMF tells us everything there is to be
+ 
+
+ align:start position:0%
+PMF tells us everything there is to be
+known about the two random variables so
+
+ align:start position:0%
+known about the two random variables so
+ 
+
+ align:start position:0%
+known about the two random variables so
+it should contain enough information for
+
+ align:start position:0%
+it should contain enough information for
+ 
+
+ align:start position:0%
+it should contain enough information for
+us to answer any kind of question so for
+
+ align:start position:0%
+us to answer any kind of question so for
+ 
+
+ align:start position:0%
+us to answer any kind of question so for
+example if we wish to find the
+
+ align:start position:0%
+example if we wish to find the
+ 
+
+ align:start position:0%
+example if we wish to find the
+probability that the random variable X
+
+ align:start position:0%
+probability that the random variable X
+ 
+
+ align:start position:0%
+probability that the random variable X
+takes the value of 4 we look at all
+
+ align:start position:0%
+takes the value of 4 we look at all
+ 
+
+ align:start position:0%
+takes the value of 4 we look at all
+possible outcomes in which X is equal to
+
+ align:start position:0%
+possible outcomes in which X is equal to
+ 
+
+ align:start position:0%
+possible outcomes in which X is equal to
+4 and add the probabilities of these
+
+ align:start position:0%
+4 and add the probabilities of these
+ 
+
+ align:start position:0%
+4 and add the probabilities of these
+outcomes so in this case it would be 1
+
+ align:start position:0%
+outcomes so in this case it would be 1
+ 
+
+ align:start position:0%
+outcomes so in this case it would be 1
+over 20 plus 2 over 20 so what we're
+
+ align:start position:0%
+over 20 plus 2 over 20 so what we're
+ 
+
+ align:start position:0%
+over 20 plus 2 over 20 so what we're
+doing is that if we're interested in a
+
+ align:start position:0%
+doing is that if we're interested in a
+ 
+
+ align:start position:0%
+doing is that if we're interested in a
+specific value of x the probability that
+
+ align:start position:0%
+specific value of x the probability that
+ 
+
+ align:start position:0%
+specific value of x the probability that
+X takes on a specific value we consider
+
+ align:start position:0%
+X takes on a specific value we consider
+ 
+
+ align:start position:0%
+X takes on a specific value we consider
+all possible pairs associated with that
+
+ align:start position:0%
+all possible pairs associated with that
+ 
+
+ align:start position:0%
+all possible pairs associated with that
+fixed X that is we are considering one
+
+ align:start position:0%
+fixed X that is we are considering one
+ 
+
+ align:start position:0%
+fixed X that is we are considering one
+column of the PMF and we're adding the
+
+ align:start position:0%
+column of the PMF and we're adding the
+ 
+
+ align:start position:0%
+column of the PMF and we're adding the
+corresponding probabilities so to find
+
+ align:start position:0%
+corresponding probabilities so to find
+ 
+
+ align:start position:0%
+corresponding probabilities so to find
+this entry here
+
+ align:start position:0%
+this entry here
+ 
+
+ align:start position:0%
+this entry here
+say px of three what we need is to add
+
+ align:start position:0%
+say px of three what we need is to add
+ 
+
+ align:start position:0%
+say px of three what we need is to add
+these terms on that column similarly we
+
+ align:start position:0%
+these terms on that column similarly we
+ 
+
+ align:start position:0%
+these terms on that column similarly we
+can find the PMF of the random variable
+
+ align:start position:0%
+can find the PMF of the random variable
+ 
+
+ align:start position:0%
+can find the PMF of the random variable
+Y so for example the probability that
+
+ align:start position:0%
+Y so for example the probability that
+ 
+
+ align:start position:0%
+Y so for example the probability that
+the random variable Y takes on a value
+
+ align:start position:0%
+the random variable Y takes on a value
+ 
+
+ align:start position:0%
+the random variable Y takes on a value
+of let's say 2 can be found as follows
+
+ align:start position:0%
+of let's say 2 can be found as follows
+ 
+
+ align:start position:0%
+of let's say 2 can be found as follows
+you look at the probabilities of all
+
+ align:start position:0%
+you look at the probabilities of all
+ 
+
+ align:start position:0%
+you look at the probabilities of all
+pairs associated with this specific Y
+
+ align:start position:0%
+pairs associated with this specific Y
+ 
+
+ align:start position:0%
+pairs associated with this specific Y
+and you add over the XS so we fix y to
+
+ align:start position:0%
+and you add over the XS so we fix y to
+ 
+
+ align:start position:0%
+and you add over the XS so we fix y to
+have a value of 2 and we add over all
+
+ align:start position:0%
+have a value of 2 and we add over all
+ 
+
+ align:start position:0%
+have a value of 2 and we add over all
+pairs in this row so in this example it
+
+ align:start position:0%
+pairs in this row so in this example it
+ 
+
+ align:start position:0%
+pairs in this row so in this example it
+would be 1 over 20 plus 3 over 20 plus 1
+
+ align:start position:0%
+would be 1 over 20 plus 3 over 20 plus 1
+ 
+
+ align:start position:0%
+would be 1 over 20 plus 3 over 20 plus 1
+over 20 finally notice that we are able
+
+ align:start position:0%
+over 20 finally notice that we are able
+ 
+
+ align:start position:0%
+over 20 finally notice that we are able
+to answer the question that got us
+
+ align:start position:0%
+to answer the question that got us
+ 
+
+ align:start position:0%
+to answer the question that got us
+motivated in the first place to find the
+
+ align:start position:0%
+motivated in the first place to find the
+ 
+
+ align:start position:0%
+motivated in the first place to find the
+probability that the two random
+
+ align:start position:0%
+probability that the two random
+ 
+
+ align:start position:0%
+probability that the two random
+variables take equal values we look at
+
+ align:start position:0%
+variables take equal values we look at
+ 
+
+ align:start position:0%
+variables take equal values we look at
+all the outcomes for which the two
+
+ align:start position:0%
+all the outcomes for which the two
+ 
+
+ align:start position:0%
+all the outcomes for which the two
+random variables indeed take the same
+
+ align:start position:0%
+random variables indeed take the same
+ 
+
+ align:start position:0%
+random variables indeed take the same
+numerical values and we see that it is
+
+ align:start position:0%
+numerical values and we see that it is
+ 
+
+ align:start position:0%
+numerical values and we see that it is
+this event in this diagram and the
+
+ align:start position:0%
+this event in this diagram and the
+ 
+
+ align:start position:0%
+this event in this diagram and the
+probability of that event is going to be
+
+ align:start position:0%
+probability of that event is going to be
+ 
+
+ align:start position:0%
+probability of that event is going to be
+2 over 20 so in general once we have
+
+ align:start position:0%
+2 over 20 so in general once we have
+ 
+
+ align:start position:0%
+2 over 20 so in general once we have
+available the joint PMF of two random
+
+ align:start position:0%
+available the joint PMF of two random
+ 
+
+ align:start position:0%
+available the joint PMF of two random
+variables we will be able to answer any
+
+ align:start position:0%
+variables we will be able to answer any
+ 
+
+ align:start position:0%
+variables we will be able to answer any
+questions regarding probabilities of
+
+ align:start position:0%
+questions regarding probabilities of
+ 
+
+ align:start position:0%
+questions regarding probabilities of
+events that have to do with these two
+
+ align:start position:0%
+events that have to do with these two
+ 
+
+ align:start position:0%
+events that have to do with these two
+random variables how about more than two
+
+ align:start position:0%
+random variables how about more than two
+ 
+
+ align:start position:0%
+random variables how about more than two
+random variables it's just a matter of
+
+ align:start position:0%
+random variables it's just a matter of
+ 
+
+ align:start position:0%
+random variables it's just a matter of
+notation for example we can define the
+
+ align:start position:0%
+notation for example we can define the
+ 
+
+ align:start position:0%
+notation for example we can define the
+joint PMF of three random variables and
+
+ align:start position:0%
+joint PMF of three random variables and
+ 
+
+ align:start position:0%
+joint PMF of three random variables and
+you can use the same idea for the joint
+
+ align:start position:0%
+you can use the same idea for the joint
+ 
+
+ align:start position:0%
+you can use the same idea for the joint
+PMF let's say of five or ten or n random
+
+ align:start position:0%
+PMF let's say of five or ten or n random
+ 
+
+ align:start position:0%
+PMF let's say of five or ten or n random
+variables let's just look at the
+
+ align:start position:0%
+variables let's just look at the
+ 
+
+ align:start position:0%
+variables let's just look at the
+notation for three there is a
+
+ align:start position:0%
+notation for three there is a
+ 
+
+ align:start position:0%
+notation for three there is a
+well-defined probability that when we
+
+ align:start position:0%
+well-defined probability that when we
+ 
+
+ align:start position:0%
+well-defined probability that when we
+carry out the experiment XY and Z as
+
+ align:start position:0%
+carry out the experiment XY and Z as
+ 
+
+ align:start position:0%
+carry out the experiment XY and Z as
+random variables take on certain
+
+ align:start position:0%
+random variables take on certain
+ 
+
+ align:start position:0%
+random variables take on certain
+specific values so we look at the
+
+ align:start position:0%
+specific values so we look at the
+ 
+
+ align:start position:0%
+specific values so we look at the
+probability of that particular triple
+
+ align:start position:0%
+probability of that particular triple
+ 
+
+ align:start position:0%
+probability of that particular triple
+and we indicate that probability with
+
+ align:start position:0%
+and we indicate that probability with
+ 
+
+ align:start position:0%
+and we indicate that probability with
+this notation once more the subscripts
+
+ align:start position:0%
+this notation once more the subscripts
+ 
+
+ align:start position:0%
+this notation once more the subscripts
+tell us which random variables were
+
+ align:start position:0%
+tell us which random variables were
+ 
+
+ align:start position:0%
+tell us which random variables were
+talking about and the PMF of course
+
+ align:start position:0%
+talking about and the PMF of course
+ 
+
+ align:start position:0%
+talking about and the PMF of course
+is going to be a function of this triple
+
+ align:start position:0%
+is going to be a function of this triple
+ 
+
+ align:start position:0%
+is going to be a function of this triple
+little X little Y little Z because each
+
+ align:start position:0%
+little X little Y little Z because each
+ 
+
+ align:start position:0%
+little X little Y little Z because each
+triple in general should have a
+
+ align:start position:0%
+triple in general should have a
+ 
+
+ align:start position:0%
+triple in general should have a
+different probability of course
+
+ align:start position:0%
+different probability of course
+ 
+
+ align:start position:0%
+different probability of course
+probabilities must always add to one so
+
+ align:start position:0%
+probabilities must always add to one so
+ 
+
+ align:start position:0%
+probabilities must always add to one so
+when we consider all triples and we add
+
+ align:start position:0%
+when we consider all triples and we add
+ 
+
+ align:start position:0%
+when we consider all triples and we add
+their corresponding probabilities we
+
+ align:start position:0%
+their corresponding probabilities we
+ 
+
+ align:start position:0%
+their corresponding probabilities we
+should get one and finally once we have
+
+ align:start position:0%
+should get one and finally once we have
+ 
+
+ align:start position:0%
+should get one and finally once we have
+the joint PMF we can again recover the
+
+ align:start position:0%
+the joint PMF we can again recover the
+ 
+
+ align:start position:0%
+the joint PMF we can again recover the
+marginal PMF for example to find the
+
+ align:start position:0%
+marginal PMF for example to find the
+ 
+
+ align:start position:0%
+marginal PMF for example to find the
+probability that the random variable
+
+ align:start position:0%
+probability that the random variable
+ 
+
+ align:start position:0%
+probability that the random variable
+takes on a specific value little X we
+
+ align:start position:0%
+takes on a specific value little X we
+ 
+
+ align:start position:0%
+takes on a specific value little X we
+consider all possible triples in which
+
+ align:start position:0%
+consider all possible triples in which
+ 
+
+ align:start position:0%
+consider all possible triples in which
+the random variable indeed takes that
+
+ align:start position:0%
+the random variable indeed takes that
+ 
+
+ align:start position:0%
+the random variable indeed takes that
+value little X and then we sum over all
+
+ align:start position:0%
+value little X and then we sum over all
+ 
+
+ align:start position:0%
+value little X and then we sum over all
+the possible Y's and Z's that could go
+
+ align:start position:0%
+the possible Y's and Z's that could go
+ 
+
+ align:start position:0%
+the possible Y's and Z's that could go
+together with this particular X in the
+
+ align:start position:0%
+together with this particular X in the
+ 
+
+ align:start position:0%
+together with this particular X in the
+same spirit the to find the probability
+
+ align:start position:0%
+same spirit the to find the probability
+ 
+
+ align:start position:0%
+same spirit the to find the probability
+that these two random variables take on
+
+ align:start position:0%
+that these two random variables take on
+ 
+
+ align:start position:0%
+that these two random variables take on
+two specific values we consider all the
+
+ align:start position:0%
+two specific values we consider all the
+ 
+
+ align:start position:0%
+two specific values we consider all the
+possible Z's that could go together with
+
+ align:start position:0%
+possible Z's that could go together with
+ 
+
+ align:start position:0%
+possible Z's that could go together with
+this XY pair so this way we're ranging
+
+ align:start position:0%
+this XY pair so this way we're ranging
+ 
+
+ align:start position:0%
+this XY pair so this way we're ranging
+over all outcomes in which X and y take
+
+ align:start position:0%
+over all outcomes in which X and y take
+ 
+
+ align:start position:0%
+over all outcomes in which X and y take
+on these specific values but Z is free
+
+ align:start position:0%
+on these specific values but Z is free
+ 
+
+ align:start position:0%
+on these specific values but Z is free
+to take any value and so we consider all
+
+ align:start position:0%
+to take any value and so we consider all
+ 
+
+ align:start position:0%
+to take any value and so we consider all
+those possible values of Z and sum the
+
+ align:start position:0%
+those possible values of Z and sum the
+ 
+
+ align:start position:0%
+those possible values of Z and sum the
+corresponding probabilities finally we
+
+ align:start position:0%
+corresponding probabilities finally we
+ 
+
+ align:start position:0%
+corresponding probabilities finally we
+can talk about functions of multiple
+
+ align:start position:0%
+can talk about functions of multiple
+ 
+
+ align:start position:0%
+can talk about functions of multiple
+random variables suppose that we have
+
+ align:start position:0%
+random variables suppose that we have
+ 
+
+ align:start position:0%
+random variables suppose that we have
+two random variables x and y and that we
+
+ align:start position:0%
+two random variables x and y and that we
+ 
+
+ align:start position:0%
+two random variables x and y and that we
+define a function of them so this
+
+ align:start position:0%
+define a function of them so this
+ 
+
+ align:start position:0%
+define a function of them so this
+function is of course a random variable
+
+ align:start position:0%
+function is of course a random variable
+ 
+
+ align:start position:0%
+function is of course a random variable
+and we can find the PMF of this random
+
+ align:start position:0%
+and we can find the PMF of this random
+ 
+
+ align:start position:0%
+and we can find the PMF of this random
+variable if we know the joint PMF of X
+
+ align:start position:0%
+variable if we know the joint PMF of X
+ 
+
+ align:start position:0%
+variable if we know the joint PMF of X
+and Y so the PMF which is the
+
+ align:start position:0%
+and Y so the PMF which is the
+ 
+
+ align:start position:0%
+and Y so the PMF which is the
+probability that the random variable
+
+ align:start position:0%
+probability that the random variable
+ 
+
+ align:start position:0%
+probability that the random variable
+takes on a specific numerical value
+
+ align:start position:0%
+takes on a specific numerical value
+ 
+
+ align:start position:0%
+takes on a specific numerical value
+that's the probability that the function
+
+ align:start position:0%
+that's the probability that the function
+ 
+
+ align:start position:0%
+that's the probability that the function
+of x and y takes on a specific numerical
+
+ align:start position:0%
+of x and y takes on a specific numerical
+ 
+
+ align:start position:0%
+of x and y takes on a specific numerical
+value and we can find this probability
+
+ align:start position:0%
+value and we can find this probability
+ 
+
+ align:start position:0%
+value and we can find this probability
+by adding the probabilities of all XY
+
+ align:start position:0%
+by adding the probabilities of all XY
+ 
+
+ align:start position:0%
+by adding the probabilities of all XY
+pairs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which XY pairs those XY pairs for which
+
+ align:start position:0%
+which XY pairs those XY pairs for which
+ 
+
+ align:start position:0%
+which XY pairs those XY pairs for which
+the value of Z would be equal to this
+
+ align:start position:0%
+the value of Z would be equal to this
+ 
+
+ align:start position:0%
+the value of Z would be equal to this
+particular number little Z that we care
+
+ align:start position:0%
+particular number little Z that we care
+ 
+
+ align:start position:0%
+particular number little Z that we care
+about so we collect essentially all
+
+ align:start position:0%
+about so we collect essentially all
+ 
+
+ align:start position:0%
+about so we collect essentially all
+possible outcomes that make this event
+
+ align:start position:0%
+possible outcomes that make this event
+ 
+
+ align:start position:0%
+possible outcomes that make this event
+to happen and we add the probabilities
+
+ align:start position:0%
+to happen and we add the probabilities
+ 
+
+ align:start position:0%
+to happen and we add the probabilities
+of all those outcomes
+
+ align:start position:0%
+of all those outcomes
+ 
+
+ align:start position:0%
+of all those outcomes
+finally similarly to the case where we
+
+ align:start position:0%
+finally similarly to the case where we
+ 
+
+ align:start position:0%
+finally similarly to the case where we
+have a single random variable and the
+
+ align:start position:0%
+have a single random variable and the
+ 
+
+ align:start position:0%
+have a single random variable and the
+function of it we now can talk about
+
+ align:start position:0%
+function of it we now can talk about
+ 
+
+ align:start position:0%
+function of it we now can talk about
+expected values of functions of two
+
+ align:start position:0%
+expected values of functions of two
+ 
+
+ align:start position:0%
+expected values of functions of two
+random variables and there is an
+
+ align:start position:0%
+random variables and there is an
+ 
+
+ align:start position:0%
+random variables and there is an
+expected value rule that parallels the
+
+ align:start position:0%
+expected value rule that parallels the
+ 
+
+ align:start position:0%
+expected value rule that parallels the
+expected value rule that we had
+
+ align:start position:0%
+expected value rule that we had
+ 
+
+ align:start position:0%
+expected value rule that we had
+developed for the case of a function of
+
+ align:start position:0%
+developed for the case of a function of
+ 
+
+ align:start position:0%
+developed for the case of a function of
+this form the form that the expected
+
+ align:start position:0%
+this form the form that the expected
+ 
+
+ align:start position:0%
+this form the form that the expected
+value rule takes is similar and it's
+
+ align:start position:0%
+value rule takes is similar and it's
+ 
+
+ align:start position:0%
+value rule takes is similar and it's
+quite natural the interpretation is as
+
+ align:start position:0%
+quite natural the interpretation is as
+ 
+
+ align:start position:0%
+quite natural the interpretation is as
+follows with this probability a specific
+
+ align:start position:0%
+follows with this probability a specific
+ 
+
+ align:start position:0%
+follows with this probability a specific
+XY pair will occur and when that occurs
+
+ align:start position:0%
+XY pair will occur and when that occurs
+ 
+
+ align:start position:0%
+XY pair will occur and when that occurs
+the value of our random variable is a
+
+ align:start position:0%
+the value of our random variable is a
+ 
+
+ align:start position:0%
+the value of our random variable is a
+certain number and the combination of
+
+ align:start position:0%
+certain number and the combination of
+ 
+
+ align:start position:0%
+certain number and the combination of
+these two terms gives us a contribution
+
+ align:start position:0%
+these two terms gives us a contribution
+ 
+
+ align:start position:0%
+these two terms gives us a contribution
+to the expected value now we consider
+
+ align:start position:0%
+to the expected value now we consider
+ 
+
+ align:start position:0%
+to the expected value now we consider
+all possible XY pairs that may occur and
+
+ align:start position:0%
+all possible XY pairs that may occur and
+ 
+
+ align:start position:0%
+all possible XY pairs that may occur and
+we sum over all these XY pairs
\ No newline at end of file
diff --git a/7pxSbSmPv2g.txt b/7pxSbSmPv2g.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e9b8982b4ca33cada7a215e9fbcf53c812c25943
--- /dev/null
+++ b/7pxSbSmPv2g.txt
@@ -0,0 +1,10522 @@
+align:start position:0%
+ 
+so let me write and in two Dimensions so
+
+ align:start position:0%
+so let me write and in two Dimensions so
+ 
+
+ align:start position:0%
+so let me write and in two Dimensions so
+let me write down that
+
+ align:start position:0%
+let me write down that
+ 
+
+ align:start position:0%
+let me write down that
+equation which must be the most studied
+
+ align:start position:0%
+equation which must be the most studied
+ 
+
+ align:start position:0%
+equation which must be the most studied
+uh partial differential
+
+ align:start position:0%
+uh partial differential
+ 
+
+ align:start position:0%
+uh partial differential
+equation uh so second derivative with
+
+ align:start position:0%
+equation uh so second derivative with
+ 
+
+ align:start position:0%
+equation uh so second derivative with
+respect to X Plus second derivative with
+
+ align:start position:0%
+respect to X Plus second derivative with
+ 
+
+ align:start position:0%
+respect to X Plus second derivative with
+respect to Y and we're just in two
+
+ align:start position:0%
+respect to Y and we're just in two
+ 
+
+ align:start position:0%
+respect to Y and we're just in two
+Dimensions equals say
+
+ align:start position:0%
+Dimensions equals say
+ 
+
+ align:start position:0%
+Dimensions equals say
+zero okay it's so so much studied for
+
+ align:start position:0%
+zero okay it's so so much studied for
+ 
+
+ align:start position:0%
+zero okay it's so so much studied for
+several reasons uh one is that it comes
+
+ align:start position:0%
+several reasons uh one is that it comes
+ 
+
+ align:start position:0%
+several reasons uh one is that it comes
+up all the time in
+
+ align:start position:0%
+up all the time in
+ 
+
+ align:start position:0%
+up all the time in
+applications I'm speaking about
+
+ align:start position:0%
+applications I'm speaking about
+ 
+
+ align:start position:0%
+applications I'm speaking about
+equilibrium steady state applications
+
+ align:start position:0%
+equilibrium steady state applications
+ 
+
+ align:start position:0%
+equilibrium steady state applications
+you see there's no time in this equation
+
+ align:start position:0%
+you see there's no time in this equation
+ 
+
+ align:start position:0%
+you see there's no time in this equation
+so it's a steady state problem it's an
+
+ align:start position:0%
+so it's a steady state problem it's an
+ 
+
+ align:start position:0%
+so it's a steady state problem it's an
+elliptic so so some of these words would
+
+ align:start position:0%
+elliptic so so some of these words would
+ 
+
+ align:start position:0%
+elliptic so so some of these words would
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+or uh steady state or eliptic type
+
+ align:start position:0%
+or uh steady state or eliptic type
+ 
+
+ align:start position:0%
+or uh steady state or eliptic type
+equation if we were
+
+ align:start position:0%
+equation if we were
+ 
+
+ align:start position:0%
+equation if we were
+classifying equations
+
+ align:start position:0%
+classifying equations
+ 
+
+ align:start position:0%
+classifying equations
+so it comes up in many many applications
+
+ align:start position:0%
+so it comes up in many many applications
+ 
+
+ align:start position:0%
+so it comes up in many many applications
+it's typical of more
+
+ align:start position:0%
+it's typical of more
+ 
+
+ align:start position:0%
+it's typical of more
+complicated equations so you you look
+
+ align:start position:0%
+complicated equations so you you look
+ 
+
+ align:start position:0%
+complicated equations so you you look
+here first for to to try to understand
+
+ align:start position:0%
+here first for to to try to understand
+ 
+
+ align:start position:0%
+here first for to to try to understand
+what's going on and
+
+ align:start position:0%
+what's going on and
+ 
+
+ align:start position:0%
+what's going on and
+then what's it has special it's quite
+
+ align:start position:0%
+then what's it has special it's quite
+ 
+
+ align:start position:0%
+then what's it has special it's quite
+special also special methods work for
+
+ align:start position:0%
+special also special methods work for
+ 
+
+ align:start position:0%
+special also special methods work for
+this equation that don't work for other
+
+ align:start position:0%
+this equation that don't work for other
+ 
+
+ align:start position:0%
+this equation that don't work for other
+equations and they're quite fun and just
+
+ align:start position:0%
+equations and they're quite fun and just
+ 
+
+ align:start position:0%
+equations and they're quite fun and just
+to say in a word what they
+
+ align:start position:0%
+to say in a word what they
+ 
+
+ align:start position:0%
+to say in a word what they
+are they
+
+ align:start position:0%
+are they
+ 
+
+ align:start position:0%
+are they
+involve the imaginary number
+
+ align:start position:0%
+involve the imaginary number
+ 
+
+ align:start position:0%
+involve the imaginary number
+I functions of X Plus i y complex
+
+ align:start position:0%
+I functions of X Plus i y complex
+ 
+
+ align:start position:0%
+I functions of X Plus i y complex
+variables come in for I mean it's a
+
+ align:start position:0%
+variables come in for I mean it's a
+ 
+
+ align:start position:0%
+variables come in for I mean it's a
+completely real equation and innocent
+
+ align:start position:0%
+completely real equation and innocent
+ 
+
+ align:start position:0%
+completely real equation and innocent
+but uh the the key trick in
+
+ align:start position:0%
+but uh the the key trick in
+ 
+
+ align:start position:0%
+but uh the the key trick in
+understanding it is connecting it to
+
+ align:start position:0%
+understanding it is connecting it to
+ 
+
+ align:start position:0%
+understanding it is connecting it to
+complex variables so I'll get to that
+
+ align:start position:0%
+complex variables so I'll get to that
+ 
+
+ align:start position:0%
+complex variables so I'll get to that
+let me start
+
+ align:start position:0%
+let me start
+ 
+
+ align:start position:0%
+let me start
+by just figuring out just let's make a
+
+ align:start position:0%
+by just figuring out just let's make a
+ 
+
+ align:start position:0%
+by just figuring out just let's make a
+list of some solutions that we can
+
+ align:start position:0%
+list of some solutions that we can
+ 
+
+ align:start position:0%
+list of some solutions that we can
+identify so so a list of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solutions I'm open to and the simpler
+
+ align:start position:0%
+solutions I'm open to and the simpler
+ 
+
+ align:start position:0%
+solutions I'm open to and the simpler
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+better so what's the very simplest
+
+ align:start position:0%
+better so what's the very simplest
+ 
+
+ align:start position:0%
+better so what's the very simplest
+solution to that
+
+ align:start position:0%
+solution to that
+ 
+
+ align:start position:0%
+solution to that
+equation a constant okay so I'll just
+
+ align:start position:0%
+equation a constant okay so I'll just
+ 
+
+ align:start position:0%
+equation a constant okay so I'll just
+put one on the list well you could say
+
+ align:start position:0%
+put one on the list well you could say
+ 
+
+ align:start position:0%
+put one on the list well you could say
+zero is even simpler but that's
+
+ align:start position:0%
+zero is even simpler but that's
+ 
+
+ align:start position:0%
+zero is even simpler but that's
+debatable okay uh Now give me one step
+
+ align:start position:0%
+debatable okay uh Now give me one step
+ 
+
+ align:start position:0%
+debatable okay uh Now give me one step
+more still very very simple but one step
+
+ align:start position:0%
+more still very very simple but one step
+ 
+
+ align:start position:0%
+more still very very simple but one step
+further what's another solution to that
+
+ align:start position:0%
+further what's another solution to that
+ 
+
+ align:start position:0%
+further what's another solution to that
+equation U equal linear equation a
+
+ align:start position:0%
+equation U equal linear equation a
+ 
+
+ align:start position:0%
+equation U equal linear equation a
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+equation x u equal x because the second
+
+ align:start position:0%
+equation x u equal x because the second
+ 
+
+ align:start position:0%
+equation x u equal x because the second
+derivative is certainly zero and the Y
+
+ align:start position:0%
+derivative is certainly zero and the Y
+ 
+
+ align:start position:0%
+derivative is certainly zero and the Y
+derivative is certainly zero and then or
+
+ align:start position:0%
+derivative is certainly zero and then or
+ 
+
+ align:start position:0%
+derivative is certainly zero and then or
+Y now you can already see I'm I'm making
+
+ align:start position:0%
+Y now you can already see I'm I'm making
+ 
+
+ align:start position:0%
+Y now you can already see I'm I'm making
+this I'm making two
+
+ align:start position:0%
+this I'm making two
+ 
+
+ align:start position:0%
+this I'm making two
+lists for a reason so now let's move up
+
+ align:start position:0%
+lists for a reason so now let's move up
+ 
+
+ align:start position:0%
+lists for a reason so now let's move up
+to the next one so if this pattern which
+
+ align:start position:0%
+to the next one so if this pattern which
+ 
+
+ align:start position:0%
+to the next one so if this pattern which
+is just sort of starting holds the next
+
+ align:start position:0%
+is just sort of starting holds the next
+ 
+
+ align:start position:0%
+is just sort of starting holds the next
+one I would look for would be what XY
+
+ align:start position:0%
+one I would look for would be what XY
+ 
+
+ align:start position:0%
+one I would look for would be what XY
+yeah quadratic second degree thing so an
+
+ align:start position:0%
+yeah quadratic second degree thing so an
+ 
+
+ align:start position:0%
+yeah quadratic second degree thing so an
+X what x x y does that work x x y works
+
+ align:start position:0%
+X what x x y does that work x x y works
+ 
+
+ align:start position:0%
+X what x x y does that work x x y works
+I'm going to put it in that
+
+ align:start position:0%
+I'm going to put it in that
+ 
+
+ align:start position:0%
+I'm going to put it in that
+list okay and I'm going to ask for
+
+ align:start position:0%
+list okay and I'm going to ask for
+ 
+
+ align:start position:0%
+list okay and I'm going to ask for
+somebody else in this list
+
+ align:start position:0%
+somebody else in this list
+ 
+
+ align:start position:0%
+somebody else in this list
+x + y I'm
+
+ align:start position:0%
+x + y I'm
+ 
+
+ align:start position:0%
+x + y I'm
+not g to go for because X Plus y so to
+
+ align:start position:0%
+not g to go for because X Plus y so to
+ 
+
+ align:start position:0%
+not g to go for because X Plus y so to
+speak I've already got uh good good
+
+ align:start position:0%
+speak I've already got uh good good
+ 
+
+ align:start position:0%
+speak I've already got uh good good
+point that that once we get this
+
+ align:start position:0%
+point that that once we get this
+ 
+
+ align:start position:0%
+point that that once we get this
+list any combination of these functions
+
+ align:start position:0%
+list any combination of these functions
+ 
+
+ align:start position:0%
+list any combination of these functions
+will also be a
+
+ align:start position:0%
+will also be a
+ 
+
+ align:start position:0%
+will also be a
+solution so these are this family of
+
+ align:start position:0%
+solution so these are this family of
+ 
+
+ align:start position:0%
+solution so these are this family of
+solutions may look kind of sparse just a
+
+ align:start position:0%
+solutions may look kind of sparse just a
+ 
+
+ align:start position:0%
+solutions may look kind of sparse just a
+few like a little list but
+
+ align:start position:0%
+few like a little list but
+ 
+
+ align:start position:0%
+few like a little list but
+since any combination gives a solution
+
+ align:start position:0%
+since any combination gives a solution
+ 
+
+ align:start position:0%
+since any combination gives a solution
+we get a whole wide family of solutions
+
+ align:start position:0%
+we get a whole wide family of solutions
+ 
+
+ align:start position:0%
+we get a whole wide family of solutions
+and in fact we'll get all we
+
+ align:start position:0%
+and in fact we'll get all we
+ 
+
+ align:start position:0%
+and in fact we'll get all we
+need okay so x + y we already have as a
+
+ align:start position:0%
+need okay so x + y we already have as a
+ 
+
+ align:start position:0%
+need okay so x + y we already have as a
+combination but what
+
+ align:start position:0%
+combination but what
+ 
+
+ align:start position:0%
+combination but what
+else X X2 Min - y I don't know how you
+
+ align:start position:0%
+else X X2 Min - y I don't know how you
+ 
+
+ align:start position:0%
+else X X2 Min - y I don't know how you
+spotted that one but it works right x^2
+
+ align:start position:0%
+spotted that one but it works right x^2
+ 
+
+ align:start position:0%
+spotted that one but it works right x^2
+-
+
+ align:start position:0%
+-
+ 
+
+ align:start position:0%
+-
+y^2 x^2 - y s cu the second X der now
+
+ align:start position:0%
+y^2 x^2 - y s cu the second X der now
+ 
+
+ align:start position:0%
+y^2 x^2 - y s cu the second X der now
+you see it's getting more subtle the
+
+ align:start position:0%
+you see it's getting more subtle the
+ 
+
+ align:start position:0%
+you see it's getting more subtle the
+second X derivative is one and the
+
+ align:start position:0%
+second X derivative is one and the
+ 
+
+ align:start position:0%
+second X derivative is one and the
+second y y derivative is minus one and
+
+ align:start position:0%
+second y y derivative is minus one and
+ 
+
+ align:start position:0%
+second y y derivative is minus one and
+and we get we're okay and then we and XY
+
+ align:start position:0%
+and we get we're okay and then we and XY
+ 
+
+ align:start position:0%
+and we get we're okay and then we and XY
+was okay because both derivatives were
+
+ align:start position:0%
+was okay because both derivatives were
+ 
+
+ align:start position:0%
+was okay because both derivatives were
+zero that was easier okay
+
+ align:start position:0%
+zero that was easier okay
+ 
+
+ align:start position:0%
+zero that was easier okay
+now now where can we get to the next guy
+
+ align:start position:0%
+now now where can we get to the next guy
+ 
+
+ align:start position:0%
+now now where can we get to the next guy
+which will
+
+ align:start position:0%
+which will
+ 
+
+ align:start position:0%
+which will
+be Oh e to the X that's out of my league
+
+ align:start position:0%
+be Oh e to the X that's out of my league
+ 
+
+ align:start position:0%
+be Oh e to the X that's out of my league
+here I'm just uh uh hoping for a cubic I
+
+ align:start position:0%
+here I'm just uh uh hoping for a cubic I
+ 
+
+ align:start position:0%
+here I'm just uh uh hoping for a cubic I
+guess if I if if I'm seeing this pattern
+
+ align:start position:0%
+guess if I if if I'm seeing this pattern
+ 
+
+ align:start position:0%
+guess if I if if I'm seeing this pattern
+either the I mean I shouldn't either x
+
+ align:start position:0%
+either the I mean I shouldn't either x
+ 
+
+ align:start position:0%
+either the I mean I shouldn't either x
+minus E to the Y I never thought of
+
+ align:start position:0%
+minus E to the Y I never thought of
+ 
+
+ align:start position:0%
+minus E to the Y I never thought of
+that I don't know if that
+
+ align:start position:0%
+that I don't know if that
+ 
+
+ align:start position:0%
+that I don't know if that
+works does it yeah does
+
+ align:start position:0%
+works does it yeah does
+ 
+
+ align:start position:0%
+works does it yeah does
+it do you want to try it I mean I never
+
+ align:start position:0%
+it do you want to try it I mean I never
+ 
+
+ align:start position:0%
+it do you want to try it I mean I never
+thought of it so so and most of these
+
+ align:start position:0%
+thought of it so so and most of these
+ 
+
+ align:start position:0%
+thought of it so so and most of these
+guys so if I take the second no it
+
+ align:start position:0%
+guys so if I take the second no it
+ 
+
+ align:start position:0%
+guys so if I take the second no it
+doesn't work does it the second X
+
+ align:start position:0%
+doesn't work does it the second X
+ 
+
+ align:start position:0%
+doesn't work does it the second X
+derivative would be
+
+ align:start position:0%
+derivative would be
+ 
+
+ align:start position:0%
+derivative would be
+what either the X and the second y
+
+ align:start position:0%
+what either the X and the second y
+ 
+
+ align:start position:0%
+what either the X and the second y
+derivative would be something else yeah
+
+ align:start position:0%
+derivative would be something else yeah
+ 
+
+ align:start position:0%
+derivative would be something else yeah
+wouldn't work but something some things
+
+ align:start position:0%
+wouldn't work but something some things
+ 
+
+ align:start position:0%
+wouldn't work but something some things
+like it some some things we will
+
+ align:start position:0%
+like it some some things we will
+ 
+
+ align:start position:0%
+like it some some things we will
+certainly want okay
+
+ align:start position:0%
+certainly want okay
+ 
+
+ align:start position:0%
+certainly want okay
+anyway oh boy you you guys are in the in
+
+ align:start position:0%
+anyway oh boy you you guys are in the in
+ 
+
+ align:start position:0%
+anyway oh boy you you guys are in the in
+these transcendental functions I'm just
+
+ align:start position:0%
+these transcendental functions I'm just
+ 
+
+ align:start position:0%
+these transcendental functions I'm just
+looking for pols here just just just uh
+
+ align:start position:0%
+looking for pols here just just just uh
+ 
+
+ align:start position:0%
+looking for pols here just just just uh
+slowly gradually this lecture it'll be
+
+ align:start position:0%
+slowly gradually this lecture it'll be
+ 
+
+ align:start position:0%
+slowly gradually this lecture it'll be
+over before it starts if you put in the
+
+ align:start position:0%
+over before it starts if you put in the
+ 
+
+ align:start position:0%
+over before it starts if you put in the
+okay give me a now X Cub you're going to
+
+ align:start position:0%
+okay give me a now X Cub you're going to
+ 
+
+ align:start position:0%
+okay give me a now X Cub you're going to
+object to right right you're not happy
+
+ align:start position:0%
+object to right right you're not happy
+ 
+
+ align:start position:0%
+object to right right you're not happy
+with xq but then I think maybe we could
+
+ align:start position:0%
+with xq but then I think maybe we could
+ 
+
+ align:start position:0%
+with xq but then I think maybe we could
+fix it
+
+ align:start position:0%
+fix it
+ 
+
+ align:start position:0%
+fix it
+up so what do we get out of X CU well
+
+ align:start position:0%
+up so what do we get out of X CU well
+ 
+
+ align:start position:0%
+up so what do we get out of X CU well
+the the second X derivative is
+
+ align:start position:0%
+the the second X derivative is
+ 
+
+ align:start position:0%
+the the second X derivative is
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+6X so what can we put over what can we
+
+ align:start position:0%
+6X so what can we put over what can we
+ 
+
+ align:start position:0%
+6X so what can we put over what can we
+subtract
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+away three 3 Y 2 3x y 3x y^2 good 3x y^
+
+ align:start position:0%
+away three 3 Y 2 3x y 3x y^2 good 3x y^
+ 
+
+ align:start position:0%
+away three 3 Y 2 3x y 3x y^2 good 3x y^
+2 because now the second y derivative of
+
+ align:start position:0%
+2 because now the second y derivative of
+ 
+
+ align:start position:0%
+2 because now the second y derivative of
+that is - 6 Min - 6X and cancels the 6X
+
+ align:start position:0%
+that is - 6 Min - 6X and cancels the 6X
+ 
+
+ align:start position:0%
+that is - 6 Min - 6X and cancels the 6X
+good okay now that ought to have uh
+
+ align:start position:0%
+good okay now that ought to have uh
+ 
+
+ align:start position:0%
+good okay now that ought to have uh
+somebody to go with y
+
+ align:start position:0%
+somebody to go with y
+ 
+
+ align:start position:0%
+somebody to go with y
+y y yeah y or Y
+
+ align:start position:0%
+y y yeah y or Y
+ 
+
+ align:start position:0%
+y y yeah y or Y
+Cub yeah y Cub
+
+ align:start position:0%
+Cub yeah y Cub
+ 
+
+ align:start position:0%
+Cub yeah y Cub
+minus 3 X2 y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that would work right the second y
+
+ align:start position:0%
+right that would work right the second y
+ 
+
+ align:start position:0%
+right that would work right the second y
+derivative would be 6 Y and the second X
+
+ align:start position:0%
+derivative would be 6 Y and the second X
+ 
+
+ align:start position:0%
+derivative would be 6 Y and the second X
+derivative would be Min - 6X and they
+
+ align:start position:0%
+derivative would be Min - 6X and they
+ 
+
+ align:start position:0%
+derivative would be Min - 6X and they
+would it would be minus 6 y second X
+
+ align:start position:0%
+would it would be minus 6 y second X
+ 
+
+ align:start position:0%
+would it would be minus 6 y second X
+derivative would be 2x derivatives would
+
+ align:start position:0%
+derivative would be 2x derivatives would
+ 
+
+ align:start position:0%
+derivative would be 2x derivatives would
+leave us with Min - 6 Y and 2 y
+
+ align:start position:0%
+leave us with Min - 6 Y and 2 y
+ 
+
+ align:start position:0%
+leave us with Min - 6 Y and 2 y
+derivatives would leave us with plus 6 Y
+
+ align:start position:0%
+derivatives would leave us with plus 6 Y
+ 
+
+ align:start position:0%
+derivatives would leave us with plus 6 Y
+and that would work okay
+
+ align:start position:0%
+and that would work okay
+ 
+
+ align:start position:0%
+and that would work okay
+now let's
+
+ align:start position:0%
+now let's
+ 
+
+ align:start position:0%
+now let's
+jump uh if possible
+
+ align:start position:0%
+jump uh if possible
+ 
+
+ align:start position:0%
+jump uh if possible
+to the general picture so what are we
+
+ align:start position:0%
+to the general picture so what are we
+ 
+
+ align:start position:0%
+to the general picture so what are we
+seeing here and it's a pattern that that
+
+ align:start position:0%
+seeing here and it's a pattern that that
+ 
+
+ align:start position:0%
+seeing here and it's a pattern that that
+I want to stay with I'm seeing like
+
+ align:start position:0%
+I want to stay with I'm seeing like
+ 
+
+ align:start position:0%
+I want to stay with I'm seeing like
+Solutions coming in pairs Solutions will
+
+ align:start position:0%
+Solutions coming in pairs Solutions will
+ 
+
+ align:start position:0%
+Solutions coming in pairs Solutions will
+come in pairs and and and those will
+
+ align:start position:0%
+come in pairs and and and those will
+ 
+
+ align:start position:0%
+come in pairs and and and those will
+represent in in the fluids application a
+
+ align:start position:0%
+represent in in the fluids application a
+ 
+
+ align:start position:0%
+represent in in the fluids application a
+possible equipotent possible potential
+
+ align:start position:0%
+possible equipotent possible potential
+ 
+
+ align:start position:0%
+possible equipotent possible potential
+and a possible stream function that' be
+
+ align:start position:0%
+and a possible stream function that' be
+ 
+
+ align:start position:0%
+and a possible stream function that' be
+called U and S so I'll write those down
+
+ align:start position:0%
+called U and S so I'll write those down
+ 
+
+ align:start position:0%
+called U and S so I'll write those down
+again anyway they come in
+
+ align:start position:0%
+again anyway they come in
+ 
+
+ align:start position:0%
+again anyway they come in
+pairs and uh well here they're coming in
+
+ align:start position:0%
+pairs and uh well here they're coming in
+ 
+
+ align:start position:0%
+pairs and uh well here they're coming in
+pairs of the same degree so I'm looking
+
+ align:start position:0%
+pairs of the same degree so I'm looking
+ 
+
+ align:start position:0%
+pairs of the same degree so I'm looking
+for the general pattern now the next I'm
+
+ align:start position:0%
+for the general pattern now the next I'm
+ 
+
+ align:start position:0%
+for the general pattern now the next I'm
+I'm ready to jump to not to exponentials
+
+ align:start position:0%
+I'm ready to jump to not to exponentials
+ 
+
+ align:start position:0%
+I'm ready to jump to not to exponentials
+yet but to degree n a pair of degree n
+
+ align:start position:0%
+yet but to degree n a pair of degree n
+ 
+
+ align:start position:0%
+yet but to degree n a pair of degree n
+polinomial okay now the clue that you
+
+ align:start position:0%
+polinomial okay now the clue that you
+ 
+
+ align:start position:0%
+polinomial okay now the clue that you
+might spot is in these numbers one and
+
+ align:start position:0%
+might spot is in these numbers one and
+ 
+
+ align:start position:0%
+might spot is in these numbers one and
+Min -3 and Min - 3 and one does that so
+
+ align:start position:0%
+Min -3 and Min - 3 and one does that so
+ 
+
+ align:start position:0%
+Min -3 and Min - 3 and one does that so
+I'm looking for The Clue here that that
+
+ align:start position:0%
+I'm looking for The Clue here that that
+ 
+
+ align:start position:0%
+I'm looking for The Clue here that that
+that that this um that this list is
+
+ align:start position:0%
+that that this um that this list is
+ 
+
+ align:start position:0%
+that that this um that this list is
+uh is um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+revealing well what are those numbers 13
+
+ align:start position:0%
+revealing well what are those numbers 13
+ 
+
+ align:start position:0%
+revealing well what are those numbers 13
+3 1 that that bom they're binomial
+
+ align:start position:0%
+3 1 that that bom they're binomial
+ 
+
+ align:start position:0%
+3 1 that that bom they're binomial
+numbers it suggests that we're maybe
+
+ align:start position:0%
+numbers it suggests that we're maybe
+ 
+
+ align:start position:0%
+numbers it suggests that we're maybe
+taking power so here here's the clue if
+
+ align:start position:0%
+taking power so here here's the clue if
+ 
+
+ align:start position:0%
+taking power so here here's the clue if
+I take if I take X oh no
+
+ align:start position:0%
+I take if I take X oh no
+ 
+
+ align:start position:0%
+I take if I take X oh no
+oh clue but magic now in comes this
+
+ align:start position:0%
+oh clue but magic now in comes this
+ 
+
+ align:start position:0%
+oh clue but magic now in comes this
+ridiculous imaginary number
+
+ align:start position:0%
+ridiculous imaginary number
+ 
+
+ align:start position:0%
+ridiculous imaginary number
+Y and I'll take its real part and it's
+
+ align:start position:0%
+Y and I'll take its real part and it's
+ 
+
+ align:start position:0%
+Y and I'll take its real part and it's
+imaginary part of this of this thing
+
+ align:start position:0%
+imaginary part of this of this thing
+ 
+
+ align:start position:0%
+imaginary part of this of this thing
+well actually what are the what's the
+
+ align:start position:0%
+well actually what are the what's the
+ 
+
+ align:start position:0%
+well actually what are the what's the
+real this is just
+
+ align:start position:0%
+real this is just
+ 
+
+ align:start position:0%
+real this is just
+a the function X Plus i y so its real
+
+ align:start position:0%
+a the function X Plus i y so its real
+ 
+
+ align:start position:0%
+a the function X Plus i y so its real
+part is X our guy and it's imaginary
+
+ align:start position:0%
+part is X our guy and it's imaginary
+ 
+
+ align:start position:0%
+part is X our guy and it's imaginary
+part is y okay now if I Square it if I
+
+ align:start position:0%
+part is y okay now if I Square it if I
+ 
+
+ align:start position:0%
+part is y okay now if I Square it if I
+take x + I y^ 2ar I'm I'm going to take
+
+ align:start position:0%
+take x + I y^ 2ar I'm I'm going to take
+ 
+
+ align:start position:0%
+take x + I y^ 2ar I'm I'm going to take
+Powers that's where these binomial
+
+ align:start position:0%
+Powers that's where these binomial
+ 
+
+ align:start position:0%
+Powers that's where these binomial
+numbers are going to come in let's do
+
+ align:start position:0%
+numbers are going to come in let's do
+ 
+
+ align:start position:0%
+numbers are going to come in let's do
+this one so this is what's X plus I so I
+
+ align:start position:0%
+this one so this is what's X plus I so I
+ 
+
+ align:start position:0%
+this one so this is what's X plus I so I
+want the real and the imaginary SE part
+
+ align:start position:0%
+want the real and the imaginary SE part
+ 
+
+ align:start position:0%
+want the real and the imaginary SE part
+separately can you I guess I better
+
+ align:start position:0%
+separately can you I guess I better
+ 
+
+ align:start position:0%
+separately can you I guess I better
+square that out right to see what it is
+
+ align:start position:0%
+square that out right to see what it is
+ 
+
+ align:start position:0%
+square that out right to see what it is
+so if I Square it out I get X squar and
+
+ align:start position:0%
+so if I Square it out I get X squar and
+ 
+
+ align:start position:0%
+so if I Square it out I get X squar and
+then I get an i y 2qu which is is what
+
+ align:start position:0%
+then I get an i y 2qu which is is what
+ 
+
+ align:start position:0%
+then I get an i y 2qu which is is what
+is minus y^2 CU all I'm using is that
+
+ align:start position:0%
+is minus y^2 CU all I'm using is that
+ 
+
+ align:start position:0%
+is minus y^2 CU all I'm using is that
+i^2 is minus one and then there's the
+
+ align:start position:0%
+i^2 is minus one and then there's the
+ 
+
+ align:start position:0%
+i^2 is minus one and then there's the
+cross term which is 2
+
+ align:start position:0%
+cross term which is 2
+ 
+
+ align:start position:0%
+cross term which is 2
+ixy and sure enough its real part is
+
+ align:start position:0%
+ixy and sure enough its real part is
+ 
+
+ align:start position:0%
+ixy and sure enough its real part is
+here and it's imaginary part well
+
+ align:start position:0%
+here and it's imaginary part well
+ 
+
+ align:start position:0%
+here and it's imaginary part well
+actually we're seeing that to keep
+
+ align:start position:0%
+actually we're seeing that to keep
+ 
+
+ align:start position:0%
+actually we're seeing that to keep
+everything beautiful and you you
+
+ align:start position:0%
+everything beautiful and you you
+ 
+
+ align:start position:0%
+everything beautiful and you you
+couldn't object to it right to if I call
+
+ align:start position:0%
+couldn't object to it right to if I call
+ 
+
+ align:start position:0%
+couldn't object to it right to if I call
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+2xy that then then we're really so this
+
+ align:start position:0%
+2xy that then then we're really so this
+ 
+
+ align:start position:0%
+2xy that then then we're really so this
+this list is real parts of x + i y to
+
+ align:start position:0%
+this list is real parts of x + i y to
+ 
+
+ align:start position:0%
+this list is real parts of x + i y to
+the nth power and this list just as good
+
+ align:start position:0%
+the nth power and this list just as good
+ 
+
+ align:start position:0%
+the nth power and this list just as good
+is is imaginary parts of the same thing
+
+ align:start position:0%
+is is imaginary parts of the same thing
+ 
+
+ align:start position:0%
+is is imaginary parts of the same thing
+the real and imaginary
+
+ align:start position:0%
+the real and imaginary
+ 
+
+ align:start position:0%
+the real and imaginary
+Parts all satisfy llosa's equation
+
+ align:start position:0%
+Parts all satisfy llosa's equation
+ 
+
+ align:start position:0%
+Parts all satisfy llosa's equation
+that's the
+
+ align:start position:0%
+that's the
+ 
+
+ align:start position:0%
+that's the
+magic we could do cubes if we liked and
+
+ align:start position:0%
+magic we could do cubes if we liked and
+ 
+
+ align:start position:0%
+magic we could do cubes if we liked and
+just and should we do cubes and fix up
+
+ align:start position:0%
+just and should we do cubes and fix up
+ 
+
+ align:start position:0%
+just and should we do cubes and fix up
+the fix up the
+
+ align:start position:0%
+the fix up the
+ 
+
+ align:start position:0%
+the fix up the
+uh the third one in our
+
+ align:start position:0%
+uh the third one in our
+ 
+
+ align:start position:0%
+uh the third one in our
+list just to see it all working so it'll
+
+ align:start position:0%
+list just to see it all working so it'll
+ 
+
+ align:start position:0%
+list just to see it all working so it'll
+be X Cub right well so I do binomial
+
+ align:start position:0%
+be X Cub right well so I do binomial
+ 
+
+ align:start position:0%
+be X Cub right well so I do binomial
+write out X cub and then 3 X2 i y and
+
+ align:start position:0%
+write out X cub and then 3 X2 i y and
+ 
+
+ align:start position:0%
+write out X cub and then 3 X2 i y and
+then 3 x i y^ 2ar and 1 i y Cub that's
+
+ align:start position:0%
+then 3 x i y^ 2ar and 1 i y Cub that's
+ 
+
+ align:start position:0%
+then 3 x i y^ 2ar and 1 i y Cub that's
+that's really seeing those
+
+ align:start position:0%
+that's really seeing those
+ 
+
+ align:start position:0%
+that's really seeing those
+1331 when you cube a thing you that's
+
+ align:start position:0%
+1331 when you cube a thing you that's
+ 
+
+ align:start position:0%
+1331 when you cube a thing you that's
+well all gamblers know these uh numbers
+
+ align:start position:0%
+well all gamblers know these uh numbers
+ 
+
+ align:start position:0%
+well all gamblers know these uh numbers
+anyway okay so what's the real part of
+
+ align:start position:0%
+anyway okay so what's the real part of
+ 
+
+ align:start position:0%
+anyway okay so what's the real part of
+that what's the real part of this X Plus
+
+ align:start position:0%
+that what's the real part of this X Plus
+ 
+
+ align:start position:0%
+that what's the real part of this X Plus
+i y cubed this is certainly
+
+ align:start position:0%
+i y cubed this is certainly
+ 
+
+ align:start position:0%
+i y cubed this is certainly
+real and what else is
+
+ align:start position:0%
+real and what else is
+ 
+
+ align:start position:0%
+real and what else is
+real this guy so that's our X oh that's
+
+ align:start position:0%
+real this guy so that's our X oh that's
+ 
+
+ align:start position:0%
+real this guy so that's our X oh that's
+it right we had it that's X cub and the
+
+ align:start position:0%
+it right we had it that's X cub and the
+ 
+
+ align:start position:0%
+it right we had it that's X cub and the
+i^2 is minus one so that's X Cub - 3x y^
+
+ align:start position:0%
+i^2 is minus one so that's X Cub - 3x y^
+ 
+
+ align:start position:0%
+i^2 is minus one so that's X Cub - 3x y^
+2 good and the imaginary part is
+
+ align:start position:0%
+2 good and the imaginary part is
+ 
+
+ align:start position:0%
+2 good and the imaginary part is
+what 3x^2
+
+ align:start position:0%
+what 3x^2
+ 
+
+ align:start position:0%
+what 3x^2
+y from the IM from I multiplying that
+
+ align:start position:0%
+y from the IM from I multiplying that
+ 
+
+ align:start position:0%
+y from the IM from I multiplying that
+and I Y cubed is what is minus I so
+
+ align:start position:0%
+and I Y cubed is what is minus I so
+ 
+
+ align:start position:0%
+and I Y cubed is what is minus I so
+there's so there a minus y cubed and
+
+ align:start position:0%
+there's so there a minus y cubed and
+ 
+
+ align:start position:0%
+there's so there a minus y cubed and
+that's that's our one except we didn't
+
+ align:start position:0%
+that's that's our one except we didn't
+ 
+
+ align:start position:0%
+that's that's our one except we didn't
+have the sign right it to to Really pair
+
+ align:start position:0%
+have the sign right it to to Really pair
+ 
+
+ align:start position:0%
+have the sign right it to to Really pair
+off I should reverse all the signs
+
+ align:start position:0%
+off I should reverse all the signs
+ 
+
+ align:start position:0%
+off I should reverse all the signs
+reverse the signs in that one which
+
+ align:start position:0%
+reverse the signs in that one which
+ 
+
+ align:start position:0%
+reverse the signs in that one which
+again is no problem our our the ples
+
+ align:start position:0%
+again is no problem our our the ples
+ 
+
+ align:start position:0%
+again is no problem our our the ples
+equation won't know the difference if we
+
+ align:start position:0%
+equation won't know the difference if we
+ 
+
+ align:start position:0%
+equation won't know the difference if we
+change U to minus U okay so now that's
+
+ align:start position:0%
+change U to minus U okay so now that's
+ 
+
+ align:start position:0%
+change U to minus U okay so now that's
+indicated at least that our pattern is
+
+ align:start position:0%
+indicated at least that our pattern is
+ 
+
+ align:start position:0%
+indicated at least that our pattern is
+working uh but why how do we see that it
+
+ align:start position:0%
+working uh but why how do we see that it
+ 
+
+ align:start position:0%
+working uh but why how do we see that it
+always works in fact I guess I really
+
+ align:start position:0%
+always works in fact I guess I really
+ 
+
+ align:start position:0%
+always works in fact I guess I really
+want to claim that I could take the real
+
+ align:start position:0%
+want to claim that I could take the real
+ 
+
+ align:start position:0%
+want to claim that I could take the real
+part and the imaginary part of any
+
+ align:start position:0%
+part and the imaginary part of any
+ 
+
+ align:start position:0%
+part and the imaginary part of any
+function of x + i y and those would both
+
+ align:start position:0%
+function of x + i y and those would both
+ 
+
+ align:start position:0%
+function of x + i y and those would both
+be good those would give me two
+
+ align:start position:0%
+be good those would give me two
+ 
+
+ align:start position:0%
+be good those would give me two
+Solutions and if I want this list of
+
+ align:start position:0%
+Solutions and if I want this list of
+ 
+
+ align:start position:0%
+Solutions and if I want this list of
+pols then I take these Powers but if I
+
+ align:start position:0%
+pols then I take these Powers but if I
+ 
+
+ align:start position:0%
+pols then I take these Powers but if I
+if I wanted to get an expon oh yeah I'm
+
+ align:start position:0%
+if I wanted to get an expon oh yeah I'm
+ 
+
+ align:start position:0%
+if I wanted to get an expon oh yeah I'm
+ready to get an exponential in here do
+
+ align:start position:0%
+ready to get an exponential in here do
+ 
+
+ align:start position:0%
+ready to get an exponential in here do
+you want to take do you want this try
+
+ align:start position:0%
+you want to take do you want this try
+ 
+
+ align:start position:0%
+you want to take do you want this try
+this function to
+
+ align:start position:0%
+this function to
+ 
+
+ align:start position:0%
+this function to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+exponential sure take the real and
+
+ align:start position:0%
+exponential sure take the real and
+ 
+
+ align:start position:0%
+exponential sure take the real and
+imaginary
+
+ align:start position:0%
+imaginary
+ 
+
+ align:start position:0%
+imaginary
+part of so so for example this is now an
+
+ align:start position:0%
+part of so so for example this is now an
+ 
+
+ align:start position:0%
+part of so so for example this is now an
+example the real Ander part of e to the
+
+ align:start position:0%
+example the real Ander part of e to the
+ 
+
+ align:start position:0%
+example the real Ander part of e to the
+x + i y okay so that this is like a
+
+ align:start position:0%
+x + i y okay so that this is like a
+ 
+
+ align:start position:0%
+x + i y okay so that this is like a
+little bit of practice with the with
+
+ align:start position:0%
+little bit of practice with the with
+ 
+
+ align:start position:0%
+little bit of practice with the with
+that imaginary number I now popping up
+
+ align:start position:0%
+that imaginary number I now popping up
+ 
+
+ align:start position:0%
+that imaginary number I now popping up
+into the exponent where here it was just
+
+ align:start position:0%
+into the exponent where here it was just
+ 
+
+ align:start position:0%
+into the exponent where here it was just
+down in the we just squared I cubed it
+
+ align:start position:0%
+down in the we just squared I cubed it
+ 
+
+ align:start position:0%
+down in the we just squared I cubed it
+no problem but now how do I what's the
+
+ align:start position:0%
+no problem but now how do I what's the
+ 
+
+ align:start position:0%
+no problem but now how do I what's the
+what's the real part of that
+
+ align:start position:0%
+what's the real part of that
+ 
+
+ align:start position:0%
+what's the real part of that
+thing yeah let's see what do we do how
+
+ align:start position:0%
+thing yeah let's see what do we do how
+ 
+
+ align:start position:0%
+thing yeah let's see what do we do how
+do we how do we deal with an e to the X
+
+ align:start position:0%
+do we how do we deal with an e to the X
+ 
+
+ align:start position:0%
+do we how do we deal with an e to the X
+Plus i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y times yeah the beauty of exponentials
+
+ align:start position:0%
+y times yeah the beauty of exponentials
+ 
+
+ align:start position:0%
+y times yeah the beauty of exponentials
+is this is the same
+
+ align:start position:0%
+is this is the same
+ 
+
+ align:start position:0%
+is this is the same
+as as e to the x times e to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+iy so this actually this e to the X we
+
+ align:start position:0%
+iy so this actually this e to the X we
+ 
+
+ align:start position:0%
+iy so this actually this e to the X we
+see is coming out as a as a just a a
+
+ align:start position:0%
+see is coming out as a as a just a a
+ 
+
+ align:start position:0%
+see is coming out as a as a just a a
+real Factor but e to the iy has got
+
+ align:start position:0%
+real Factor but e to the iy has got
+ 
+
+ align:start position:0%
+real Factor but e to the iy has got
+what's e to the i y that's that's the
+
+ align:start position:0%
+what's e to the i y that's that's the
+ 
+
+ align:start position:0%
+what's e to the i y that's that's the
+key now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is is yeah by the most fantastic Formula
+
+ align:start position:0%
+is is yeah by the most fantastic Formula
+ 
+
+ align:start position:0%
+is is yeah by the most fantastic Formula
+E to the i y is the same as the cosine
+
+ align:start position:0%
+E to the i y is the same as the cosine
+ 
+
+ align:start position:0%
+E to the i y is the same as the cosine
+of Y plus I * the S of y y is a real
+
+ align:start position:0%
+of Y plus I * the S of y y is a real
+ 
+
+ align:start position:0%
+of Y plus I * the S of y y is a real
+number so now I see the real part of
+
+ align:start position:0%
+number so now I see the real part of
+ 
+
+ align:start position:0%
+number so now I see the real part of
+this is that e to the X cos Y and the
+
+ align:start position:0%
+this is that e to the X cos Y and the
+ 
+
+ align:start position:0%
+this is that e to the X cos Y and the
+imaginary part is e to the X sin y so
+
+ align:start position:0%
+imaginary part is e to the X sin y so
+ 
+
+ align:start position:0%
+imaginary part is e to the X sin y so
+there's a pair quite a interesting pair
+
+ align:start position:0%
+there's a pair quite a interesting pair
+ 
+
+ align:start position:0%
+there's a pair quite a interesting pair
+that we could add to our list e to the x
+
+ align:start position:0%
+that we could add to our list e to the x
+ 
+
+ align:start position:0%
+that we could add to our list e to the x
+X cos y and e to X sin
+
+ align:start position:0%
+X cos y and e to X sin
+ 
+
+ align:start position:0%
+X cos y and e to X sin
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+okay e to the that that e to the that X
+
+ align:start position:0%
+okay e to the that that e to the that X
+ 
+
+ align:start position:0%
+okay e to the that that e to the that X
+is in the exponent up there and times
+
+ align:start position:0%
+is in the exponent up there and times
+ 
+
+ align:start position:0%
+is in the exponent up there and times
+cos y well right I mean we and and just
+
+ align:start position:0%
+cos y well right I mean we and and just
+ 
+
+ align:start position:0%
+cos y well right I mean we and and just
+better to check it maybe what's the
+
+ align:start position:0%
+better to check it maybe what's the
+ 
+
+ align:start position:0%
+better to check it maybe what's the
+second D the second X derivative of this
+
+ align:start position:0%
+second D the second X derivative of this
+ 
+
+ align:start position:0%
+second D the second X derivative of this
+thing just I I just want to see that
+
+ align:start position:0%
+thing just I I just want to see that
+ 
+
+ align:start position:0%
+thing just I I just want to see that
+this really is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+winner this if I take the second X
+
+ align:start position:0%
+winner this if I take the second X
+ 
+
+ align:start position:0%
+winner this if I take the second X
+derivative then as we were thinking it
+
+ align:start position:0%
+derivative then as we were thinking it
+ 
+
+ align:start position:0%
+derivative then as we were thinking it
+doesn't change right and if I take the
+
+ align:start position:0%
+doesn't change right and if I take the
+ 
+
+ align:start position:0%
+doesn't change right and if I take the
+second y derivative what
+
+ align:start position:0%
+second y derivative what
+ 
+
+ align:start position:0%
+second y derivative what
+happens it it goes negative because
+
+ align:start position:0%
+happens it it goes negative because
+ 
+
+ align:start position:0%
+happens it it goes negative because
+cosine becomes minus s becomes minus
+
+ align:start position:0%
+cosine becomes minus s becomes minus
+ 
+
+ align:start position:0%
+cosine becomes minus s becomes minus
+cosine so so sure enough the two the two
+
+ align:start position:0%
+cosine so so sure enough the two the two
+ 
+
+ align:start position:0%
+cosine so so sure enough the two the two
+pieces uh cancel each other and it
+
+ align:start position:0%
+pieces uh cancel each other and it
+ 
+
+ align:start position:0%
+pieces uh cancel each other and it
+solves theosis equation these are called
+
+ align:start position:0%
+solves theosis equation these are called
+ 
+
+ align:start position:0%
+solves theosis equation these are called
+This is called and if I use the word
+
+ align:start position:0%
+This is called and if I use the word
+ 
+
+ align:start position:0%
+This is called and if I use the word
+this is called an analytic
+
+ align:start position:0%
+this is called an analytic
+ 
+
+ align:start position:0%
+this is called an analytic
+function who knows
+
+ align:start position:0%
+function who knows
+ 
+
+ align:start position:0%
+function who knows
+why analytic function if it's if it's uh
+
+ align:start position:0%
+why analytic function if it's if it's uh
+ 
+
+ align:start position:0%
+why analytic function if it's if it's uh
+uh re smooth has derivatives and so
+
+ align:start position:0%
+uh re smooth has derivatives and so
+ 
+
+ align:start position:0%
+uh re smooth has derivatives and so
+forth any of the functions that we would
+
+ align:start position:0%
+forth any of the functions that we would
+ 
+
+ align:start position:0%
+forth any of the functions that we would
+sort of first think of and these pieces
+
+ align:start position:0%
+sort of first think of and these pieces
+ 
+
+ align:start position:0%
+sort of first think of and these pieces
+these pieces are called harmonic
+
+ align:start position:0%
+these pieces are called harmonic
+ 
+
+ align:start position:0%
+these pieces are called harmonic
+functions so so this says that U is a
+
+ align:start position:0%
+functions so so this says that U is a
+ 
+
+ align:start position:0%
+functions so so this says that U is a
+this is a harmonic function that's a I
+
+ align:start position:0%
+this is a harmonic function that's a I
+ 
+
+ align:start position:0%
+this is a harmonic function that's a I
+mean the pl equation is so important
+
+ align:start position:0%
+mean the pl equation is so important
+ 
+
+ align:start position:0%
+mean the pl equation is so important
+that it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cles
+
+ align:start position:0%
+cles
+ 
+
+ align:start position:0%
+cles
+equation well let's see we don't know
+
+ align:start position:0%
+equation well let's see we don't know
+ 
+
+ align:start position:0%
+equation well let's see we don't know
+what the function is so how do we do
+
+ align:start position:0%
+what the function is so how do we do
+ 
+
+ align:start position:0%
+what the function is so how do we do
+that what happens if I take the
+
+ align:start position:0%
+that what happens if I take the
+ 
+
+ align:start position:0%
+that what happens if I take the
+derivative of a function of X Plus i y
+
+ align:start position:0%
+derivative of a function of X Plus i y
+ 
+
+ align:start position:0%
+derivative of a function of X Plus i y
+do you remember that well I'll just get
+
+ align:start position:0%
+do you remember that well I'll just get
+ 
+
+ align:start position:0%
+do you remember that well I'll just get
+the D I'll just get so the derivative
+
+ align:start position:0%
+the D I'll just get so the derivative
+ 
+
+ align:start position:0%
+the D I'll just get so the derivative
+will be F
+
+ align:start position:0%
+will be F
+ 
+
+ align:start position:0%
+will be F
+Prime of the X derivative ah but what's
+
+ align:start position:0%
+Prime of the X derivative ah but what's
+ 
+
+ align:start position:0%
+Prime of the X derivative ah but what's
+the Y derivative of that that's the X
+
+ align:start position:0%
+the Y derivative of that that's the X
+ 
+
+ align:start position:0%
+the Y derivative of that that's the X
+derivative so this is the X
+
+ align:start position:0%
+derivative so this is the X
+ 
+
+ align:start position:0%
+derivative so this is the X
+derivative and what's the y
+
+ align:start position:0%
+derivative and what's the y
+ 
+
+ align:start position:0%
+derivative and what's the y
+derivative of this thing so I'm not yet
+
+ align:start position:0%
+derivative of this thing so I'm not yet
+ 
+
+ align:start position:0%
+derivative of this thing so I'm not yet
+on the second derivatives I'm just doing
+
+ align:start position:0%
+on the second derivatives I'm just doing
+ 
+
+ align:start position:0%
+on the second derivatives I'm just doing
+first derivatives do you remember how to
+
+ align:start position:0%
+first derivatives do you remember how to
+ 
+
+ align:start position:0%
+first derivatives do you remember how to
+take the derivative of a function of
+
+ align:start position:0%
+take the derivative of a function of
+ 
+
+ align:start position:0%
+take the derivative of a function of
+another function chain rule is the thing
+
+ align:start position:0%
+another function chain rule is the thing
+ 
+
+ align:start position:0%
+another function chain rule is the thing
+yeah yeah so the derivative of this with
+
+ align:start position:0%
+yeah yeah so the derivative of this with
+ 
+
+ align:start position:0%
+yeah yeah so the derivative of this with
+respect to the Y derivative of this you
+
+ align:start position:0%
+respect to the Y derivative of this you
+ 
+
+ align:start position:0%
+respect to the Y derivative of this you
+remember you you take the derivative of
+
+ align:start position:0%
+remember you you take the derivative of
+ 
+
+ align:start position:0%
+remember you you take the derivative of
+F and then you have to take the
+
+ align:start position:0%
+F and then you have to take the
+ 
+
+ align:start position:0%
+F and then you have to take the
+derivative of what's ins side the
+
+ align:start position:0%
+derivative of what's ins side the
+ 
+
+ align:start position:0%
+derivative of what's ins side the
+argument which is the Y derivative of
+
+ align:start position:0%
+argument which is the Y derivative of
+ 
+
+ align:start position:0%
+argument which is the Y derivative of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I okay where the X derivative was if we
+
+ align:start position:0%
+I okay where the X derivative was if we
+ 
+
+ align:start position:0%
+I okay where the X derivative was if we
+really used the chain rule was the
+
+ align:start position:0%
+really used the chain rule was the
+ 
+
+ align:start position:0%
+really used the chain rule was the
+derivative of the function times the
+
+ align:start position:0%
+derivative of the function times the
+ 
+
+ align:start position:0%
+derivative of the function times the
+derivative of what's inside the X
+
+ align:start position:0%
+derivative of what's inside the X
+ 
+
+ align:start position:0%
+derivative of what's inside the X
+derivative of what's inside was just a
+
+ align:start position:0%
+derivative of what's inside was just a
+ 
+
+ align:start position:0%
+derivative of what's inside was just a
+one okay so that's the X
+
+ align:start position:0%
+one okay so that's the X
+ 
+
+ align:start position:0%
+one okay so that's the X
+derivative now let me do the XX
+
+ align:start position:0%
+derivative now let me do the XX
+ 
+
+ align:start position:0%
+derivative now let me do the XX
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+okay this one should be easy because
+
+ align:start position:0%
+okay this one should be easy because
+ 
+
+ align:start position:0%
+okay this one should be easy because
+it'll just be two derivatives F Prime of
+
+ align:start position:0%
+it'll just be two derivatives F Prime of
+ 
+
+ align:start position:0%
+it'll just be two derivatives F Prime of
+x + i y * 1 * 1 but what's the the y y
+
+ align:start position:0%
+x + i y * 1 * 1 but what's the the y y
+ 
+
+ align:start position:0%
+x + i y * 1 * 1 but what's the the y y
+derivative and then we're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through of this thing yeah you see
+
+ align:start position:0%
+through of this thing yeah you see
+ 
+
+ align:start position:0%
+through of this thing yeah you see
+what's happening it's got a factor I
+
+ align:start position:0%
+what's happening it's got a factor I
+ 
+
+ align:start position:0%
+what's happening it's got a factor I
+that's a constant and now when I take
+
+ align:start position:0%
+that's a constant and now when I take
+ 
+
+ align:start position:0%
+that's a constant and now when I take
+another derivative I get F Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I had the old I from the first
+
+ align:start position:0%
+and I had the old I from the first
+ 
+
+ align:start position:0%
+and I had the old I from the first
+derivative but now the chain rule for
+
+ align:start position:0%
+derivative but now the chain rule for
+ 
+
+ align:start position:0%
+derivative but now the chain rule for
+the next derivative is also producing an
+
+ align:start position:0%
+the next derivative is also producing an
+ 
+
+ align:start position:0%
+the next derivative is also producing an
+I so there's an i squar and which is the
+
+ align:start position:0%
+I so there's an i squar and which is the
+ 
+
+ align:start position:0%
+I so there's an i squar and which is the
+the exactly the minus one we're hoping
+
+ align:start position:0%
+the exactly the minus one we're hoping
+ 
+
+ align:start position:0%
+the exactly the minus one we're hoping
+for so it all really fell fell apart
+
+ align:start position:0%
+for so it all really fell fell apart
+ 
+
+ align:start position:0%
+for so it all really fell fell apart
+when we used i^2 equal minus1 okay so I
+
+ align:start position:0%
+when we used i^2 equal minus1 okay so I
+ 
+
+ align:start position:0%
+when we used i^2 equal minus1 okay so I
+I'm
+
+ align:start position:0%
+I'm
+ 
+
+ align:start position:0%
+I'm
+uh I'm happy in two or three ways here
+
+ align:start position:0%
+uh I'm happy in two or three ways here
+ 
+
+ align:start position:0%
+uh I'm happy in two or three ways here
+one way is that we've got this good list
+
+ align:start position:0%
+one way is that we've got this good list
+ 
+
+ align:start position:0%
+one way is that we've got this good list
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+solutions except that they're getting
+
+ align:start position:0%
+solutions except that they're getting
+ 
+
+ align:start position:0%
+solutions except that they're getting
+somewhat Messier to describe so we would
+
+ align:start position:0%
+somewhat Messier to describe so we would
+ 
+
+ align:start position:0%
+somewhat Messier to describe so we would
+really like to have a better description
+
+ align:start position:0%
+really like to have a better description
+ 
+
+ align:start position:0%
+really like to have a better description
+of of this special list where the the
+
+ align:start position:0%
+of of this special list where the the
+ 
+
+ align:start position:0%
+of of this special list where the the
+function is just the the powers and not
+
+ align:start position:0%
+function is just the the powers and not
+ 
+
+ align:start position:0%
+function is just the the powers and not
+and then the second thing I'm happy
+
+ align:start position:0%
+and then the second thing I'm happy
+ 
+
+ align:start position:0%
+and then the second thing I'm happy
+about is to have
+
+ align:start position:0%
+about is to have
+ 
+
+ align:start position:0%
+about is to have
+uh begun to see the magic of uh these of
+
+ align:start position:0%
+uh begun to see the magic of uh these of
+ 
+
+ align:start position:0%
+uh begun to see the magic of uh these of
+letting of take of having this perfectly
+
+ align:start position:0%
+letting of take of having this perfectly
+ 
+
+ align:start position:0%
+letting of take of having this perfectly
+real equation but solving it by means of
+
+ align:start position:0%
+real equation but solving it by means of
+ 
+
+ align:start position:0%
+real equation but solving it by means of
+complex variables which is just like
+
+ align:start position:0%
+complex variables which is just like
+ 
+
+ align:start position:0%
+complex variables which is just like
+which by the way everybody might say
+
+ align:start position:0%
+which by the way everybody might say
+ 
+
+ align:start position:0%
+which by the way everybody might say
+okay what about the three-dimensional
+
+ align:start position:0%
+okay what about the three-dimensional
+ 
+
+ align:start position:0%
+okay what about the three-dimensional
+case uxx plus u y y plus u ZZ equals z
+
+ align:start position:0%
+case uxx plus u y y plus u ZZ equals z
+ 
+
+ align:start position:0%
+case uxx plus u y y plus u ZZ equals z
+well the things don't happen don't work
+
+ align:start position:0%
+well the things don't happen don't work
+ 
+
+ align:start position:0%
+well the things don't happen don't work
+so it's really quite special to two
+
+ align:start position:0%
+so it's really quite special to two
+ 
+
+ align:start position:0%
+so it's really quite special to two
+Dimensions unfortunately but everybody
+
+ align:start position:0%
+Dimensions unfortunately but everybody
+ 
+
+ align:start position:0%
+Dimensions unfortunately but everybody
+has tried but nobody's G anywhere okay
+
+ align:start position:0%
+has tried but nobody's G anywhere okay
+ 
+
+ align:start position:0%
+has tried but nobody's G anywhere okay
+now I so I come back to this list for a
+
+ align:start position:0%
+now I so I come back to this list for a
+ 
+
+ align:start position:0%
+now I so I come back to this list for a
+minute just to make it just to improve
+
+ align:start position:0%
+minute just to make it just to improve
+ 
+
+ align:start position:0%
+minute just to make it just to improve
+the uh the looks of
+
+ align:start position:0%
+the uh the looks of
+ 
+
+ align:start position:0%
+the uh the looks of
+it and how to do that go to Polar
+
+ align:start position:0%
+it and how to do that go to Polar
+ 
+
+ align:start position:0%
+it and how to do that go to Polar
+coordinates go from X and Y to R and
+
+ align:start position:0%
+coordinates go from X and Y to R and
+ 
+
+ align:start position:0%
+coordinates go from X and Y to R and
+Theta so because we're in the plane so
+
+ align:start position:0%
+Theta so because we're in the plane so
+ 
+
+ align:start position:0%
+Theta so because we're in the plane so
+we have a choice and XY is rectangular
+
+ align:start position:0%
+we have a choice and XY is rectangular
+ 
+
+ align:start position:0%
+we have a choice and XY is rectangular
+coordinates R and Theta you know of
+
+ align:start position:0%
+coordinates R and Theta you know of
+ 
+
+ align:start position:0%
+coordinates R and Theta you know of
+course is polar so let's write in what
+
+ align:start position:0%
+course is polar so let's write in what
+ 
+
+ align:start position:0%
+course is polar so let's write in what
+is x in terms of r
+
+ align:start position:0%
+is x in terms of r
+ 
+
+ align:start position:0%
+is x in terms of r
+Theta just uh do you remember you
+
+ align:start position:0%
+Theta just uh do you remember you
+ 
+
+ align:start position:0%
+Theta just uh do you remember you
+remember this picture of polar
+
+ align:start position:0%
+remember this picture of polar
+ 
+
+ align:start position:0%
+remember this picture of polar
+coordinates here here's we go out
+
+ align:start position:0%
+coordinates here here's we go out
+ 
+
+ align:start position:0%
+coordinates here here's we go out
+X right we go up Y and that distance is
+
+ align:start position:0%
+X right we go up Y and that distance is
+ 
+
+ align:start position:0%
+X right we go up Y and that distance is
+r and the angle is Theta so that point
+
+ align:start position:0%
+r and the angle is Theta so that point
+ 
+
+ align:start position:0%
+r and the angle is Theta so that point
+is is just is given by the Numbers R and
+
+ align:start position:0%
+is is just is given by the Numbers R and
+ 
+
+ align:start position:0%
+is is just is given by the Numbers R and
+Theta as well as by the Numbers X and Y
+
+ align:start position:0%
+Theta as well as by the Numbers X and Y
+ 
+
+ align:start position:0%
+Theta as well as by the Numbers X and Y
+and then X in this triangle is you were
+
+ align:start position:0%
+and then X in this triangle is you were
+ 
+
+ align:start position:0%
+and then X in this triangle is you were
+saying
+
+ align:start position:0%
+saying
+ 
+
+ align:start position:0%
+saying
+is R * cosine Theta and Y is R * sin
+
+ align:start position:0%
+is R * cosine Theta and Y is R * sin
+ 
+
+ align:start position:0%
+is R * cosine Theta and Y is R * sin
+Theta in other words I can
+
+ align:start position:0%
+Theta in other words I can
+ 
+
+ align:start position:0%
+Theta in other words I can
+now replace every X by R cos Theta and
+
+ align:start position:0%
+now replace every X by R cos Theta and
+ 
+
+ align:start position:0%
+now replace every X by R cos Theta and
+every y by R sin
+
+ align:start position:0%
+every y by R sin
+ 
+
+ align:start position:0%
+every y by R sin
+Theta and what I want to say is it'll
+
+ align:start position:0%
+Theta and what I want to say is it'll
+ 
+
+ align:start position:0%
+Theta and what I want to say is it'll
+all come out quite beautifully I mean
+
+ align:start position:0%
+all come out quite beautifully I mean
+ 
+
+ align:start position:0%
+all come out quite beautifully I mean
+that this will be R cos Theta and this
+
+ align:start position:0%
+that this will be R cos Theta and this
+ 
+
+ align:start position:0%
+that this will be R cos Theta and this
+is R sin Theta this one will turn out to
+
+ align:start position:0%
+is R sin Theta this one will turn out to
+ 
+
+ align:start position:0%
+is R sin Theta this one will turn out to
+be r^ 2 cos 2 Theta so let me put the
+
+ align:start position:0%
+be r^ 2 cos 2 Theta so let me put the
+ 
+
+ align:start position:0%
+be r^ 2 cos 2 Theta so let me put the
+erase one and zero because we this is a
+
+ align:start position:0%
+erase one and zero because we this is a
+ 
+
+ align:start position:0%
+erase one and zero because we this is a
+list of R to the N cos n Theta and this
+
+ align:start position:0%
+list of R to the N cos n Theta and this
+ 
+
+ align:start position:0%
+list of R to the N cos n Theta and this
+is a list of R to the N uh yes s n Theta
+
+ align:start position:0%
+is a list of R to the N uh yes s n Theta
+ 
+
+ align:start position:0%
+is a list of R to the N uh yes s n Theta
+so you see the the the ones on this list
+
+ align:start position:0%
+so you see the the the ones on this list
+ 
+
+ align:start position:0%
+so you see the the the ones on this list
+which look like they're getting Messier
+
+ align:start position:0%
+which look like they're getting Messier
+ 
+
+ align:start position:0%
+which look like they're getting Messier
+are really not in in polar coordinates
+
+ align:start position:0%
+are really not in in polar coordinates
+ 
+
+ align:start position:0%
+are really not in in polar coordinates
+those are the those are
+
+ align:start position:0%
+those are the those are
+ 
+
+ align:start position:0%
+those are the those are
+quite
+
+ align:start position:0%
+quite
+ 
+
+ align:start position:0%
+quite
+attractive uh now why did why is that
+
+ align:start position:0%
+attractive uh now why did why is that
+ 
+
+ align:start position:0%
+attractive uh now why did why is that
+true how do I see that that oh okay let
+
+ align:start position:0%
+true how do I see that that oh okay let
+ 
+
+ align:start position:0%
+true how do I see that that oh okay let
+me let me so I should just do this X
+
+ align:start position:0%
+me let me so I should just do this X
+ 
+
+ align:start position:0%
+me let me so I should just do this X
+Plus i y to the N yeah let me just do do
+
+ align:start position:0%
+Plus i y to the N yeah let me just do do
+ 
+
+ align:start position:0%
+Plus i y to the N yeah let me just do do
+I'm I'm taking the real I got that list
+
+ align:start position:0%
+I'm I'm taking the real I got that list
+ 
+
+ align:start position:0%
+I'm I'm taking the real I got that list
+by taking the real and imaginary parts
+
+ align:start position:0%
+by taking the real and imaginary parts
+ 
+
+ align:start position:0%
+by taking the real and imaginary parts
+of X Plus i y to the
+
+ align:start position:0%
+of X Plus i y to the
+ 
+
+ align:start position:0%
+of X Plus i y to the
+N but now what's X Plus i y if I go into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Polar yeah that's the key what is X Plus
+
+ align:start position:0%
+Polar yeah that's the key what is X Plus
+ 
+
+ align:start position:0%
+Polar yeah that's the key what is X Plus
+i y in polar coordinates that's that's
+
+ align:start position:0%
+i y in polar coordinates that's that's
+ 
+
+ align:start position:0%
+i y in polar coordinates that's that's
+the beautiful see a few things in math
+
+ align:start position:0%
+the beautiful see a few things in math
+ 
+
+ align:start position:0%
+the beautiful see a few things in math
+come out well okay and and what does it
+
+ align:start position:0%
+come out well okay and and what does it
+ 
+
+ align:start position:0%
+come out well okay and and what does it
+come out to be it's R * e to the I
+
+ align:start position:0%
+come out to be it's R * e to the I
+ 
+
+ align:start position:0%
+come out to be it's R * e to the I
+Theta you see that that's right because
+
+ align:start position:0%
+Theta you see that that's right because
+ 
+
+ align:start position:0%
+Theta you see that that's right because
+this e the I Theta
+
+ align:start position:0%
+this e the I Theta
+ 
+
+ align:start position:0%
+this e the I Theta
+is this is this is R and E to the I
+
+ align:start position:0%
+is this is this is R and E to the I
+ 
+
+ align:start position:0%
+is this is this is R and E to the I
+Theta as we said about e to the i y is
+
+ align:start position:0%
+Theta as we said about e to the i y is
+ 
+
+ align:start position:0%
+Theta as we said about e to the i y is
+cos theta plus I sin
+
+ align:start position:0%
+cos theta plus I sin
+ 
+
+ align:start position:0%
+cos theta plus I sin
+thet and sure enough R cos Theta agrees
+
+ align:start position:0%
+thet and sure enough R cos Theta agrees
+ 
+
+ align:start position:0%
+thet and sure enough R cos Theta agrees
+with X and R sin Theta agrees with Y so
+
+ align:start position:0%
+with X and R sin Theta agrees with Y so
+ 
+
+ align:start position:0%
+with X and R sin Theta agrees with Y so
+we have that beautiful formula so it's
+
+ align:start position:0%
+we have that beautiful formula so it's
+ 
+
+ align:start position:0%
+we have that beautiful formula so it's
+really just real and imaginary parts of
+
+ align:start position:0%
+really just real and imaginary parts of
+ 
+
+ align:start position:0%
+really just real and imaginary parts of
+r e to the I Theta to the N
+
+ align:start position:0%
+r e to the I Theta to the N
+ 
+
+ align:start position:0%
+r e to the I Theta to the N
+power so you see how tidy it is and when
+
+ align:start position:0%
+power so you see how tidy it is and when
+ 
+
+ align:start position:0%
+power so you see how tidy it is and when
+the thing is I guess the the the rule is
+
+ align:start position:0%
+the thing is I guess the the the rule is
+ 
+
+ align:start position:0%
+the thing is I guess the the the rule is
+when you're like multiplying or taking
+
+ align:start position:0%
+when you're like multiplying or taking
+ 
+
+ align:start position:0%
+when you're like multiplying or taking
+Powers polar is really nice because when
+
+ align:start position:0%
+Powers polar is really nice because when
+ 
+
+ align:start position:0%
+Powers polar is really nice because when
+you're multiplying complex numbers you
+
+ align:start position:0%
+you're multiplying complex numbers you
+ 
+
+ align:start position:0%
+you're multiplying complex numbers you
+just multiply the RS and add the angles
+
+ align:start position:0%
+just multiply the RS and add the angles
+ 
+
+ align:start position:0%
+just multiply the RS and add the angles
+you just that that's going to happen if
+
+ align:start position:0%
+you just that that's going to happen if
+ 
+
+ align:start position:0%
+you just that that's going to happen if
+I multiply re e to the I Theta times t e
+
+ align:start position:0%
+I multiply re e to the I Theta times t e
+ 
+
+ align:start position:0%
+I multiply re e to the I Theta times t e
+to the I Alpha then I'll multiply R and
+
+ align:start position:0%
+to the I Alpha then I'll multiply R and
+ 
+
+ align:start position:0%
+to the I Alpha then I'll multiply R and
+T and I'll in the exponent I'll add
+
+ align:start position:0%
+T and I'll in the exponent I'll add
+ 
+
+ align:start position:0%
+T and I'll in the exponent I'll add
+Theta and Alpha so in this
+
+ align:start position:0%
+Theta and Alpha so in this
+ 
+
+ align:start position:0%
+Theta and Alpha so in this
+whereas adding complex numbers is better
+
+ align:start position:0%
+whereas adding complex numbers is better
+ 
+
+ align:start position:0%
+whereas adding complex numbers is better
+over in this in the XY system but
+
+ align:start position:0%
+over in this in the XY system but
+ 
+
+ align:start position:0%
+over in this in the XY system but
+multiplying is much better here and
+
+ align:start position:0%
+multiplying is much better here and
+ 
+
+ align:start position:0%
+multiplying is much better here and
+taking Powers is even better still
+
+ align:start position:0%
+taking Powers is even better still
+ 
+
+ align:start position:0%
+taking Powers is even better still
+because we have R to the nth power e to
+
+ align:start position:0%
+because we have R to the nth power e to
+ 
+
+ align:start position:0%
+because we have R to the nth power e to
+the i n
+
+ align:start position:0%
+the i n
+ 
+
+ align:start position:0%
+the i n
+Theta and we can sure take the real part
+
+ align:start position:0%
+Theta and we can sure take the real part
+ 
+
+ align:start position:0%
+Theta and we can sure take the real part
+of that because that'll split
+
+ align:start position:0%
+of that because that'll split
+ 
+
+ align:start position:0%
+of that because that'll split
+into just like this now I have n Theta
+
+ align:start position:0%
+into just like this now I have n Theta
+ 
+
+ align:start position:0%
+into just like this now I have n Theta
+so it'll split into cosine n Theta and
+
+ align:start position:0%
+so it'll split into cosine n Theta and
+ 
+
+ align:start position:0%
+so it'll split into cosine n Theta and
+sin I sin n Theta and then the real part
+
+ align:start position:0%
+sin I sin n Theta and then the real part
+ 
+
+ align:start position:0%
+sin I sin n Theta and then the real part
+will be the cosine part so these sorry
+
+ align:start position:0%
+will be the cosine part so these sorry
+ 
+
+ align:start position:0%
+will be the cosine part so these sorry
+that these two steps are so widely
+
+ align:start position:0%
+that these two steps are so widely
+ 
+
+ align:start position:0%
+that these two steps are so widely
+separated on the board that these this
+
+ align:start position:0%
+separated on the board that these this
+ 
+
+ align:start position:0%
+separated on the board that these this
+pair in polar coordinates is exactly the
+
+ align:start position:0%
+pair in polar coordinates is exactly the
+ 
+
+ align:start position:0%
+pair in polar coordinates is exactly the
+far end of the board the real and
+
+ align:start position:0%
+far end of the board the real and
+ 
+
+ align:start position:0%
+far end of the board the real and
+imaginary parts of R to the N sin n
+
+ align:start position:0%
+imaginary parts of R to the N sin n
+ 
+
+ align:start position:0%
+imaginary parts of R to the N sin n
+Theta and R the COS n Theta so that's
+
+ align:start position:0%
+Theta and R the COS n Theta so that's
+ 
+
+ align:start position:0%
+Theta and R the COS n Theta so that's
+we're there
+
+ align:start position:0%
+we're there
+ 
+
+ align:start position:0%
+we're there
+that's a a lot of what I wanted to to
+
+ align:start position:0%
+that's a a lot of what I wanted to to
+ 
+
+ align:start position:0%
+that's a a lot of what I wanted to to
+mention uh about explicit
+
+ align:start position:0%
+mention uh about explicit
+ 
+
+ align:start position:0%
+mention uh about explicit
+solutions that we have this terrific
+
+ align:start position:0%
+solutions that we have this terrific
+ 
+
+ align:start position:0%
+solutions that we have this terrific
+list here which is pretty nearly pretty
+
+ align:start position:0%
+list here which is pretty nearly pretty
+ 
+
+ align:start position:0%
+list here which is pretty nearly pretty
+much of a complete list with its
+
+ align:start position:0%
+much of a complete list with its
+ 
+
+ align:start position:0%
+much of a complete list with its
+combinations or we can jump in and take
+
+ align:start position:0%
+combinations or we can jump in and take
+ 
+
+ align:start position:0%
+combinations or we can jump in and take
+something like this
+
+ align:start position:0%
+something like this
+ 
+
+ align:start position:0%
+something like this
+example which might be appropriate for a
+
+ align:start position:0%
+example which might be appropriate for a
+ 
+
+ align:start position:0%
+example which might be appropriate for a
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+geometry uh the the what do I mean by a
+
+ align:start position:0%
+geometry uh the the what do I mean by a
+ 
+
+ align:start position:0%
+geometry uh the the what do I mean by a
+particular geometry or what the the the
+
+ align:start position:0%
+particular geometry or what the the the
+ 
+
+ align:start position:0%
+particular geometry or what the the the
+um so one solution or another solution
+
+ align:start position:0%
+um so one solution or another solution
+ 
+
+ align:start position:0%
+um so one solution or another solution
+comes in depending well it'll depend on
+
+ align:start position:0%
+comes in depending well it'll depend on
+ 
+
+ align:start position:0%
+comes in depending well it'll depend on
+the boundary conditions the shape of the
+
+ align:start position:0%
+the boundary conditions the shape of the
+ 
+
+ align:start position:0%
+the boundary conditions the shape of the
+boundary and what's happening at the
+
+ align:start position:0%
+boundary and what's happening at the
+ 
+
+ align:start position:0%
+boundary and what's happening at the
+boundary and uh because I'm keeping zero
+
+ align:start position:0%
+boundary and uh because I'm keeping zero
+ 
+
+ align:start position:0%
+boundary and uh because I'm keeping zero
+inside and uh you know this might have
+
+ align:start position:0%
+inside and uh you know this might have
+ 
+
+ align:start position:0%
+inside and uh you know this might have
+PE people became very expert uh uh maybe
+
+ align:start position:0%
+PE people became very expert uh uh maybe
+ 
+
+ align:start position:0%
+PE people became very expert uh uh maybe
+some of you and I uh certainly never did
+
+ align:start position:0%
+some of you and I uh certainly never did
+ 
+
+ align:start position:0%
+some of you and I uh certainly never did
+um in choosing the function to match the
+
+ align:start position:0%
+um in choosing the function to match the
+ 
+
+ align:start position:0%
+um in choosing the function to match the
+geometry you might have flow in a slit
+
+ align:start position:0%
+geometry you might have flow in a slit
+ 
+
+ align:start position:0%
+geometry you might have flow in a slit
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+something or flow in a circle in a
+
+ align:start position:0%
+something or flow in a circle in a
+ 
+
+ align:start position:0%
+something or flow in a circle in a
+circle these would be good flow in some
+
+ align:start position:0%
+circle these would be good flow in some
+ 
+
+ align:start position:0%
+circle these would be good flow in some
+kind of a a slit being a long horizontal
+
+ align:start position:0%
+kind of a a slit being a long horizontal
+ 
+
+ align:start position:0%
+kind of a a slit being a long horizontal
+slit might have something to do with
+
+ align:start position:0%
+slit might have something to do with
+ 
+
+ align:start position:0%
+slit might have something to do with
+this with this with that choice flow in
+
+ align:start position:0%
+this with this with that choice flow in
+ 
+
+ align:start position:0%
+this with this with that choice flow in
+a half of us slit oh all sorts of flow
+
+ align:start position:0%
+a half of us slit oh all sorts of flow
+ 
+
+ align:start position:0%
+a half of us slit oh all sorts of flow
+in ellipses flow in in in strange shapes
+
+ align:start position:0%
+in ellipses flow in in in strange shapes
+ 
+
+ align:start position:0%
+in ellipses flow in in in strange shapes
+and uh so these all have to do with
+
+ align:start position:0%
+and uh so these all have to do with
+ 
+
+ align:start position:0%
+and uh so these all have to do with
+choosing the complex function the
+
+ align:start position:0%
+choosing the complex function the
+ 
+
+ align:start position:0%
+choosing the complex function the
+analytic function
+
+ align:start position:0%
+analytic function
+ 
+
+ align:start position:0%
+analytic function
+appropriately okay now uh what else can
+
+ align:start position:0%
+appropriately okay now uh what else can
+ 
+
+ align:start position:0%
+appropriately okay now uh what else can
+I say about these so this is this is
+
+ align:start position:0%
+I say about these so this is this is
+ 
+
+ align:start position:0%
+I say about these so this is this is
+going to be my list of functions U of X
+
+ align:start position:0%
+going to be my list of functions U of X
+ 
+
+ align:start position:0%
+going to be my list of functions U of X
+and Y y I'm going to call that the real
+
+ align:start position:0%
+and Y y I'm going to call that the real
+ 
+
+ align:start position:0%
+and Y y I'm going to call that the real
+part so this is the list of U's
+
+ align:start position:0%
+part so this is the list of U's
+ 
+
+ align:start position:0%
+part so this is the list of U's
+including that typical case and these
+
+ align:start position:0%
+including that typical case and these
+ 
+
+ align:start position:0%
+including that typical case and these
+guys I'm going to I'll the letter s is
+
+ align:start position:0%
+guys I'm going to I'll the letter s is
+ 
+
+ align:start position:0%
+guys I'm going to I'll the letter s is
+suggestive also of streamline and stream
+
+ align:start position:0%
+suggestive also of streamline and stream
+ 
+
+ align:start position:0%
+suggestive also of streamline and stream
+function so I'll break convention by
+
+ align:start position:0%
+function so I'll break convention by
+ 
+
+ align:start position:0%
+function so I'll break convention by
+calling these the imaginary Parts s of X
+
+ align:start position:0%
+calling these the imaginary Parts s of X
+ 
+
+ align:start position:0%
+calling these the imaginary Parts s of X
+and Y
+
+ align:start position:0%
+and Y
+ 
+
+ align:start position:0%
+and Y
+okay and now I just would like to draw
+
+ align:start position:0%
+okay and now I just would like to draw
+ 
+
+ align:start position:0%
+okay and now I just would like to draw
+some kind of pictures I feel I ought to
+
+ align:start position:0%
+some kind of pictures I feel I ought to
+ 
+
+ align:start position:0%
+some kind of pictures I feel I ought to
+draw some sort of picture maybe maybe a
+
+ align:start position:0%
+draw some sort of picture maybe maybe a
+ 
+
+ align:start position:0%
+draw some sort of picture maybe maybe a
+picture in that case could I draw the
+
+ align:start position:0%
+picture in that case could I draw the
+ 
+
+ align:start position:0%
+picture in that case could I draw the
+picture in that case where U is this and
+
+ align:start position:0%
+picture in that case where U is this and
+ 
+
+ align:start position:0%
+picture in that case where U is this and
+S is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this yeah let let's let's draw that
+
+ align:start position:0%
+this yeah let let's let's draw that
+ 
+
+ align:start position:0%
+this yeah let let's let's draw that
+picture are we I'm going to erase this
+
+ align:start position:0%
+picture are we I'm going to erase this
+ 
+
+ align:start position:0%
+picture are we I'm going to erase this
+part because we got our list set here so
+
+ align:start position:0%
+part because we got our list set here so
+ 
+
+ align:start position:0%
+part because we got our list set here so
+uh so I'll take off this this
+
+ align:start position:0%
+uh so I'll take off this this
+ 
+
+ align:start position:0%
+uh so I'll take off this this
+these particular guys who were in our
+
+ align:start position:0%
+these particular guys who were in our
+ 
+
+ align:start position:0%
+these particular guys who were in our
+list and the reason they were in their
+
+ align:start position:0%
+list and the reason they were in their
+ 
+
+ align:start position:0%
+list and the reason they were in their
+list was this little chain
+
+ align:start position:0%
+list was this little chain
+ 
+
+ align:start position:0%
+list was this little chain
+rule um for uh F ofx + I
+
+ align:start position:0%
+rule um for uh F ofx + I
+ 
+
+ align:start position:0%
+rule um for uh F ofx + I
+Y X Plus i y often being called
+
+ align:start position:0%
+Y X Plus i y often being called
+ 
+
+ align:start position:0%
+Y X Plus i y often being called
+Z and uh so so we're in the Z plane the
+
+ align:start position:0%
+Z and uh so so we're in the Z plane the
+ 
+
+ align:start position:0%
+Z and uh so so we're in the Z plane the
+XY speak about the complex plane is the
+
+ align:start position:0%
+XY speak about the complex plane is the
+ 
+
+ align:start position:0%
+XY speak about the complex plane is the
+real part going one way and the
+
+ align:start position:0%
+real part going one way and the
+ 
+
+ align:start position:0%
+real part going one way and the
+imaginary part the other okay so I want
+
+ align:start position:0%
+imaginary part the other okay so I want
+ 
+
+ align:start position:0%
+imaginary part the other okay so I want
+to take this particular pair and draw
+
+ align:start position:0%
+to take this particular pair and draw
+ 
+
+ align:start position:0%
+to take this particular pair and draw
+the equip
+
+ align:start position:0%
+the equip
+ 
+
+ align:start position:0%
+the equip
+potentials so I want to
+
+ align:start position:0%
+potentials so I want to
+ 
+
+ align:start position:0%
+potentials so I want to
+draw the the the lines U that's x^2 -
+
+ align:start position:0%
+draw the the the lines U that's x^2 -
+ 
+
+ align:start position:0%
+draw the the the lines U that's x^2 -
+y^2 equal a
+
+ align:start position:0%
+y^2 equal a
+ 
+
+ align:start position:0%
+y^2 equal a
+constant in the plane I want to see what
+
+ align:start position:0%
+constant in the plane I want to see what
+ 
+
+ align:start position:0%
+constant in the plane I want to see what
+kind of a flow is is associated with
+
+ align:start position:0%
+kind of a flow is is associated with
+ 
+
+ align:start position:0%
+kind of a flow is is associated with
+this with this uh potential and this
+
+ align:start position:0%
+this with this uh potential and this
+ 
+
+ align:start position:0%
+this with this uh potential and this
+streamline
+
+ align:start position:0%
+streamline
+ 
+
+ align:start position:0%
+streamline
+okay now what so
+
+ align:start position:0%
+okay now what so
+ 
+
+ align:start position:0%
+okay now what so
+for so I have a whole family of Curves
+
+ align:start position:0%
+for so I have a whole family of Curves
+ 
+
+ align:start position:0%
+for so I have a whole family of Curves
+here whole family of Curves and what's a
+
+ align:start position:0%
+here whole family of Curves and what's a
+ 
+
+ align:start position:0%
+here whole family of Curves and what's a
+typical one like x^2 - y^2 equal 1 what
+
+ align:start position:0%
+typical one like x^2 - y^2 equal 1 what
+ 
+
+ align:start position:0%
+typical one like x^2 - y^2 equal 1 what
+kind of a curve would that
+
+ align:start position:0%
+kind of a curve would that
+ 
+
+ align:start position:0%
+kind of a curve would that
+be anybody recognize that x^2 minus y^2
+
+ align:start position:0%
+be anybody recognize that x^2 minus y^2
+ 
+
+ align:start position:0%
+be anybody recognize that x^2 minus y^2
+let me take the constant to be one what
+
+ align:start position:0%
+let me take the constant to be one what
+ 
+
+ align:start position:0%
+let me take the constant to be one what
+what does that curve x^2 - y^2 equal 1
+
+ align:start position:0%
+what does that curve x^2 - y^2 equal 1
+ 
+
+ align:start position:0%
+what does that curve x^2 - y^2 equal 1
+look like if I plot all the points I'm
+
+ align:start position:0%
+look like if I plot all the points I'm
+ 
+
+ align:start position:0%
+look like if I plot all the points I'm
+trying to think
+
+ align:start position:0%
+trying to think
+ 
+
+ align:start position:0%
+trying to think
+myself it's a hyperbola for sure cuz
+
+ align:start position:0%
+myself it's a hyperbola for sure cuz
+ 
+
+ align:start position:0%
+myself it's a hyperbola for sure cuz
+these these being second degree is of
+
+ align:start position:0%
+these these being second degree is of
+ 
+
+ align:start position:0%
+these these being second degree is of
+course highly famous all those the
+
+ align:start position:0%
+course highly famous all those the
+ 
+
+ align:start position:0%
+course highly famous all those the
+Greeks caught on to all those cases and
+
+ align:start position:0%
+Greeks caught on to all those cases and
+ 
+
+ align:start position:0%
+Greeks caught on to all those cases and
+this case gives a hyperbola and what
+
+ align:start position:0%
+this case gives a hyperbola and what
+ 
+
+ align:start position:0%
+this case gives a hyperbola and what
+kind of a let's
+
+ align:start position:0%
+kind of a let's
+ 
+
+ align:start position:0%
+kind of a let's
+see I know it's a hyperbola but where
+
+ align:start position:0%
+see I know it's a hyperbola but where
+ 
+
+ align:start position:0%
+see I know it's a hyperbola but where
+does it GOC it's symmetric about
+
+ align:start position:0%
+does it GOC it's symmetric about
+ 
+
+ align:start position:0%
+does it GOC it's symmetric about
+something is it symmetric about
+
+ align:start position:0%
+something is it symmetric about
+ 
+
+ align:start position:0%
+something is it symmetric about
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+or the Y AIS you sure if I start drawing
+
+ align:start position:0%
+or the Y AIS you sure if I start drawing
+ 
+
+ align:start position:0%
+or the Y AIS you sure if I start drawing
+well I got an eraser so okay okay yeah
+
+ align:start position:0%
+well I got an eraser so okay okay yeah
+ 
+
+ align:start position:0%
+well I got an eraser so okay okay yeah
+put in some points is a good idea put in
+
+ align:start position:0%
+put in some points is a good idea put in
+ 
+
+ align:start position:0%
+put in some points is a good idea put in
+some points okay I'm taking this
+
+ align:start position:0%
+some points okay I'm taking this
+ 
+
+ align:start position:0%
+some points okay I'm taking this
+particular constant one and so this is
+
+ align:start position:0%
+particular constant one and so this is
+ 
+
+ align:start position:0%
+particular constant one and so this is
+an equip potential Line This is the
+
+ align:start position:0%
+an equip potential Line This is the
+ 
+
+ align:start position:0%
+an equip potential Line This is the
+potential function and all along the
+
+ align:start position:0%
+potential function and all along the
+ 
+
+ align:start position:0%
+potential function and all along the
+line it equals one okay so I put in some
+
+ align:start position:0%
+line it equals one okay so I put in some
+ 
+
+ align:start position:0%
+line it equals one okay so I put in some
+points xal 1 and y equal 0 that's a
+
+ align:start position:0%
+points xal 1 and y equal 0 that's a
+ 
+
+ align:start position:0%
+points xal 1 and y equal 0 that's a
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+and X = minus1 and Y equals 0 but
+
+ align:start position:0%
+and X = minus1 and Y equals 0 but
+ 
+
+ align:start position:0%
+and X = minus1 and Y equals 0 but
+there's no there will not be any points
+
+ align:start position:0%
+there's no there will not be any points
+ 
+
+ align:start position:0%
+there's no there will not be any points
+let's see what is that
+
+ align:start position:0%
+let's see what is that
+ 
+
+ align:start position:0%
+let's see what is that
+right when x equals z we're in trouble
+
+ align:start position:0%
+right when x equals z we're in trouble
+ 
+
+ align:start position:0%
+right when x equals z we're in trouble
+so we don't get a point this is just the
+
+ align:start position:0%
+so we don't get a point this is just the
+ 
+
+ align:start position:0%
+so we don't get a point this is just the
+regular XY
+
+ align:start position:0%
+regular XY
+ 
+
+ align:start position:0%
+regular XY
+plane so what do we do X could be bigger
+
+ align:start position:0%
+plane so what do we do X could be bigger
+ 
+
+ align:start position:0%
+plane so what do we do X could be bigger
+like two then I'd have 4 - y^2 and y^2 Y
+
+ align:start position:0%
+like two then I'd have 4 - y^2 and y^2 Y
+ 
+
+ align:start position:0%
+like two then I'd have 4 - y^2 and y^2 Y
+would be something like > 3 I think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+am I right that that somehow we get
+
+ align:start position:0%
+am I right that that somehow we get
+ 
+
+ align:start position:0%
+am I right that that somehow we get
+a if x is really giant what's
+
+ align:start position:0%
+a if x is really giant what's
+ 
+
+ align:start position:0%
+a if x is really giant what's
+y also also giant right almost the same
+
+ align:start position:0%
+y also also giant right almost the same
+ 
+
+ align:start position:0%
+y also also giant right almost the same
+as X right but not but slightly less
+
+ align:start position:0%
+as X right but not but slightly less
+ 
+
+ align:start position:0%
+as X right but not but slightly less
+because the square is supposed to leave
+
+ align:start position:0%
+because the square is supposed to leave
+ 
+
+ align:start position:0%
+because the square is supposed to leave
+a one so see yeah so does that no I
+
+ align:start position:0%
+a one so see yeah so does that no I
+ 
+
+ align:start position:0%
+a one so see yeah so does that no I
+think I draw the asmp tootes like this
+
+ align:start position:0%
+think I draw the asmp tootes like this
+ 
+
+ align:start position:0%
+think I draw the asmp tootes like this
+the 45 degree lines yeah and the minus
+
+ align:start position:0%
+the 45 degree lines yeah and the minus
+ 
+
+ align:start position:0%
+the 45 degree lines yeah and the minus
+45 I think and I think I think this
+
+ align:start position:0%
+45 I think and I think I think this
+ 
+
+ align:start position:0%
+45 I think and I think I think this
+curve is something like yeah does that
+
+ align:start position:0%
+curve is something like yeah does that
+ 
+
+ align:start position:0%
+curve is something like yeah does that
+look not
+
+ align:start position:0%
+look not
+ 
+
+ align:start position:0%
+look not
+bad it's not a parabola looks like one
+
+ align:start position:0%
+bad it's not a parabola looks like one
+ 
+
+ align:start position:0%
+bad it's not a parabola looks like one
+but it's a
+
+ align:start position:0%
+but it's a
+ 
+
+ align:start position:0%
+but it's a
+hyperbola okay and now if I change this
+
+ align:start position:0%
+hyperbola okay and now if I change this
+ 
+
+ align:start position:0%
+hyperbola okay and now if I change this
+to a
+
+ align:start position:0%
+to a
+ 
+
+ align:start position:0%
+to a
+two then it'll start at Square Ro TK of
+
+ align:start position:0%
+two then it'll start at Square Ro TK of
+ 
+
+ align:start position:0%
+two then it'll start at Square Ro TK of
+two and I'll get another
+
+ align:start position:0%
+two and I'll get another
+ 
+
+ align:start position:0%
+two and I'll get another
+hyperbola that also whoops I don't want
+
+ align:start position:0%
+hyperbola that also whoops I don't want
+ 
+
+ align:start position:0%
+hyperbola that also whoops I don't want
+it to it'll it'll get out near that guy
+
+ align:start position:0%
+it to it'll it'll get out near that guy
+ 
+
+ align:start position:0%
+it to it'll it'll get out near that guy
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+it'll something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay this is all they're all approaching
+
+ align:start position:0%
+okay this is all they're all approaching
+ 
+
+ align:start position:0%
+okay this is all they're all approaching
+that 45 degree ASM toote okay and and of
+
+ align:start position:0%
+that 45 degree ASM toote okay and and of
+ 
+
+ align:start position:0%
+that 45 degree ASM toote okay and and of
+course could be smaller one half then
+
+ align:start position:0%
+course could be smaller one half then
+ 
+
+ align:start position:0%
+course could be smaller one half then
+I'd get somebody in here so I've got a
+
+ align:start position:0%
+I'd get somebody in here so I've got a
+ 
+
+ align:start position:0%
+I'd get somebody in here so I've got a
+whole family of
+
+ align:start position:0%
+whole family of
+ 
+
+ align:start position:0%
+whole family of
+Curves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so it looks to me like this this oh
+
+ align:start position:0%
+okay so it looks to me like this this oh
+ 
+
+ align:start position:0%
+okay so it looks to me like this this oh
+now what so those were the equip
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potentials now what's the other curve
+
+ align:start position:0%
+potentials now what's the other curve
+ 
+
+ align:start position:0%
+potentials now what's the other curve
+that I other family of curves that I
+
+ align:start position:0%
+that I other family of curves that I
+ 
+
+ align:start position:0%
+that I other family of curves that I
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+draw the stream lines the stream lines
+
+ align:start position:0%
+draw the stream lines the stream lines
+ 
+
+ align:start position:0%
+draw the stream lines the stream lines
+come from the stream function so I want
+
+ align:start position:0%
+come from the stream function so I want
+ 
+
+ align:start position:0%
+come from the stream function so I want
+to D draw those now s equals
+
+ align:start position:0%
+to D draw those now s equals
+ 
+
+ align:start position:0%
+to D draw those now s equals
+2xy equals
+
+ align:start position:0%
+2xy equals
+ 
+
+ align:start position:0%
+2xy equals
+constant okay I I meant
+
+ align:start position:0%
+constant okay I I meant
+ 
+
+ align:start position:0%
+constant okay I I meant
+to make a little note as I usually do of
+
+ align:start position:0%
+to make a little note as I usually do of
+ 
+
+ align:start position:0%
+to make a little note as I usually do of
+which sections of
+
+ align:start position:0%
+which sections of
+ 
+
+ align:start position:0%
+which sections of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+text this lecture connects to section 33
+
+ align:start position:0%
+text this lecture connects to section 33
+ 
+
+ align:start position:0%
+text this lecture connects to section 33
+is specifically about ll's
+
+ align:start position:0%
+is specifically about ll's
+ 
+
+ align:start position:0%
+is specifically about ll's
+equation section
+
+ align:start position:0%
+equation section
+ 
+
+ align:start position:0%
+equation section
+4.4 is about the complex variable stuff
+
+ align:start position:0%
+4.4 is about the complex variable stuff
+ 
+
+ align:start position:0%
+4.4 is about the complex variable stuff
+and then there's one
+
+ align:start position:0%
+and then there's one
+ 
+
+ align:start position:0%
+and then there's one
+page um let's see I have a note here of
+
+ align:start position:0%
+page um let's see I have a note here of
+ 
+
+ align:start position:0%
+page um let's see I have a note here of
+the one page 277 I think that has a
+
+ align:start position:0%
+the one page 277 I think that has a
+ 
+
+ align:start position:0%
+the one page 277 I think that has a
+formula that we'll touch okay right let
+
+ align:start position:0%
+formula that we'll touch okay right let
+ 
+
+ align:start position:0%
+formula that we'll touch okay right let
+me okay I'm going to draw in the the the
+
+ align:start position:0%
+me okay I'm going to draw in the the the
+ 
+
+ align:start position:0%
+me okay I'm going to draw in the the the
+equip the streamlines and just complete
+
+ align:start position:0%
+equip the streamlines and just complete
+ 
+
+ align:start position:0%
+equip the streamlines and just complete
+that point so this what kind of a curve
+
+ align:start position:0%
+that point so this what kind of a curve
+ 
+
+ align:start position:0%
+that point so this what kind of a curve
+is 2x y equal constant equal one let's
+
+ align:start position:0%
+is 2x y equal constant equal one let's
+ 
+
+ align:start position:0%
+is 2x y equal constant equal one let's
+say so let the constant be one anybody
+
+ align:start position:0%
+say so let the constant be one anybody
+ 
+
+ align:start position:0%
+say so let the constant be one anybody
+recognize that kind of a curve 2x yal 1
+
+ align:start position:0%
+recognize that kind of a curve 2x yal 1
+ 
+
+ align:start position:0%
+recognize that kind of a curve 2x yal 1
+it's also a hyperbola so by a
+
+ align:start position:0%
+it's also a hyperbola so by a
+ 
+
+ align:start position:0%
+it's also a hyperbola so by a
+total like chance here we've got two
+
+ align:start position:0%
+total like chance here we've got two
+ 
+
+ align:start position:0%
+total like chance here we've got two
+hyperbolas and if I draw 2x yal 1 those
+
+ align:start position:0%
+hyperbolas and if I draw 2x yal 1 those
+ 
+
+ align:start position:0%
+hyperbolas and if I draw 2x yal 1 those
+are the those hyperbolas are swung
+
+ align:start position:0%
+are the those hyperbolas are swung
+ 
+
+ align:start position:0%
+are the those hyperbolas are swung
+around by 90° or something they these
+
+ align:start position:0%
+around by 90° or something they these
+ 
+
+ align:start position:0%
+around by 90° or something they these
+hyperbolas go right
+
+ align:start position:0%
+hyperbolas go right
+ 
+
+ align:start position:0%
+hyperbolas go right
+through perpendicular they hit they they
+
+ align:start position:0%
+through perpendicular they hit they they
+ 
+
+ align:start position:0%
+through perpendicular they hit they they
+they're like x y equal one oh yeah like
+
+ align:start position:0%
+they're like x y equal one oh yeah like
+ 
+
+ align:start position:0%
+they're like x y equal one oh yeah like
+x x y equal one is if x is Big Y is
+
+ align:start position:0%
+x x y equal one is if x is Big Y is
+ 
+
+ align:start position:0%
+x x y equal one is if x is Big Y is
+small if x is small Y is big in between
+
+ align:start position:0%
+small if x is small Y is big in between
+ 
+
+ align:start position:0%
+small if x is small Y is big in between
+they cross where x equals y so they yeah
+
+ align:start position:0%
+they cross where x equals y so they yeah
+ 
+
+ align:start position:0%
+they cross where x equals y so they yeah
+do you see how those things are going
+
+ align:start position:0%
+do you see how those things are going
+ 
+
+ align:start position:0%
+do you see how those things are going
+the the next one in will be steeper but
+
+ align:start position:0%
+the the next one in will be steeper but
+ 
+
+ align:start position:0%
+the the next one in will be steeper but
+it'll never touch the axis so they're
+
+ align:start position:0%
+it'll never touch the axis so they're
+ 
+
+ align:start position:0%
+it'll never touch the axis so they're
+asmic to the axes where the first guys
+
+ align:start position:0%
+asmic to the axes where the first guys
+ 
+
+ align:start position:0%
+asmic to the axes where the first guys
+were ASM totic to the 45 degree lines
+
+ align:start position:0%
+were ASM totic to the 45 degree lines
+ 
+
+ align:start position:0%
+were ASM totic to the 45 degree lines
+okay and the beauty of the whole thing
+
+ align:start position:0%
+okay and the beauty of the whole thing
+ 
+
+ align:start position:0%
+okay and the beauty of the whole thing
+is that this is these are all right
+
+ align:start position:0%
+is that this is these are all right
+ 
+
+ align:start position:0%
+is that this is these are all right
+angles every where they meet is a right
+
+ align:start position:0%
+angles every where they meet is a right
+ 
+
+ align:start position:0%
+angles every where they meet is a right
+angle and that comes from uh these
+
+ align:start position:0%
+angle and that comes from uh these
+ 
+
+ align:start position:0%
+angle and that comes from uh these
+crucial equations which I better write
+
+ align:start position:0%
+crucial equations which I better write
+ 
+
+ align:start position:0%
+crucial equations which I better write
+down the Koshi named after Koshi who was
+
+ align:start position:0%
+down the Koshi named after Koshi who was
+ 
+
+ align:start position:0%
+down the Koshi named after Koshi who was
+a great French mathematician and reman
+
+ align:start position:0%
+a great French mathematician and reman
+ 
+
+ align:start position:0%
+a great French mathematician and reman
+who was
+
+ align:start position:0%
+who was
+ 
+
+ align:start position:0%
+who was
+greater uh uh one of he was one of the
+
+ align:start position:0%
+greater uh uh one of he was one of the
+ 
+
+ align:start position:0%
+greater uh uh one of he was one of the
+great mathematicians of all time uh and
+
+ align:start position:0%
+great mathematicians of all time uh and
+ 
+
+ align:start position:0%
+great mathematicians of all time uh and
+the two equations connect the real part
+
+ align:start position:0%
+the two equations connect the real part
+ 
+
+ align:start position:0%
+the two equations connect the real part
+U with the imaginary part s and it's the
+
+ align:start position:0%
+U with the imaginary part s and it's the
+ 
+
+ align:start position:0%
+U with the imaginary part s and it's the
+X derivative of U agrees with the Y
+
+ align:start position:0%
+X derivative of U agrees with the Y
+ 
+
+ align:start position:0%
+X derivative of U agrees with the Y
+derivative of s and that actually comes
+
+ align:start position:0%
+derivative of s and that actually comes
+ 
+
+ align:start position:0%
+derivative of s and that actually comes
+from our now erased first derivative
+
+ align:start position:0%
+from our now erased first derivative
+ 
+
+ align:start position:0%
+from our now erased first derivative
+this because this is like first
+
+ align:start position:0%
+this because this is like first
+ 
+
+ align:start position:0%
+this because this is like first
+derivatives and the and the other one is
+
+ align:start position:0%
+derivatives and the and the other one is
+ 
+
+ align:start position:0%
+derivatives and the and the other one is
+duy comes out as minus DS
+
+ align:start position:0%
+duy comes out as minus DS
+ 
+
+ align:start position:0%
+duy comes out as minus DS
+DX those are great equations okay okay
+
+ align:start position:0%
+DX those are great equations okay okay
+ 
+
+ align:start position:0%
+DX those are great equations okay okay
+okay and uh they come directly for any
+
+ align:start position:0%
+okay and uh they come directly for any
+ 
+
+ align:start position:0%
+okay and uh they come directly for any
+as the real and imaginary Parts just
+
+ align:start position:0%
+as the real and imaginary Parts just
+ 
+
+ align:start position:0%
+as the real and imaginary Parts just
+from our first
+
+ align:start position:0%
+from our first
+ 
+
+ align:start position:0%
+from our first
+derivatives and they tell us that
+
+ align:start position:0%
+derivatives and they tell us that
+ 
+
+ align:start position:0%
+derivatives and they tell us that
+these curves these are the curves squal
+
+ align:start position:0%
+these curves these are the curves squal
+ 
+
+ align:start position:0%
+these curves these are the curves squal
+constant these are the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+streamlines and these were the equ
+
+ align:start position:0%
+streamlines and these were the equ
+ 
+
+ align:start position:0%
+streamlines and these were the equ
+potentials and those equations would
+
+ align:start position:0%
+potentials and those equations would
+ 
+
+ align:start position:0%
+potentials and those equations would
+tell us that they meet at right angles
+
+ align:start position:0%
+tell us that they meet at right angles
+ 
+
+ align:start position:0%
+tell us that they meet at right angles
+so it's the the geometry is
+
+ align:start position:0%
+so it's the the geometry is
+ 
+
+ align:start position:0%
+so it's the the geometry is
+fantastic and that will still be true
+
+ align:start position:0%
+fantastic and that will still be true
+ 
+
+ align:start position:0%
+fantastic and that will still be true
+even for these curves which uh would not
+
+ align:start position:0%
+even for these curves which uh would not
+ 
+
+ align:start position:0%
+even for these curves which uh would not
+be so easy to draw well I could draw the
+
+ align:start position:0%
+be so easy to draw well I could draw the
+ 
+
+ align:start position:0%
+be so easy to draw well I could draw the
+the easiest one would be what if the
+
+ align:start position:0%
+the easiest one would be what if the
+ 
+
+ align:start position:0%
+the easiest one would be what if the
+streamlines if the if the potential
+
+ align:start position:0%
+streamlines if the if the potential
+ 
+
+ align:start position:0%
+streamlines if the if the potential
+function is X let's I should have looked
+
+ align:start position:0%
+function is X let's I should have looked
+ 
+
+ align:start position:0%
+function is X let's I should have looked
+at that real easy case if the potential
+
+ align:start position:0%
+at that real easy case if the potential
+ 
+
+ align:start position:0%
+at that real easy case if the potential
+function U of XY is just x what are the
+
+ align:start position:0%
+function U of XY is just x what are the
+ 
+
+ align:start position:0%
+function U of XY is just x what are the
+equip
+
+ align:start position:0%
+equip
+ 
+
+ align:start position:0%
+equip
+potentials just x equal constants vertic
+
+ align:start position:0%
+potentials just x equal constants vertic
+ 
+
+ align:start position:0%
+potentials just x equal constants vertic
+lines and if the stream function is y
+
+ align:start position:0%
+lines and if the stream function is y
+ 
+
+ align:start position:0%
+lines and if the stream function is y
+what are the stream lines where is y
+
+ align:start position:0%
+what are the stream lines where is y
+ 
+
+ align:start position:0%
+what are the stream lines where is y
+constant they're the horizontal lines
+
+ align:start position:0%
+constant they're the horizontal lines
+ 
+
+ align:start position:0%
+constant they're the horizontal lines
+and of course those meet at right angles
+
+ align:start position:0%
+and of course those meet at right angles
+ 
+
+ align:start position:0%
+and of course those meet at right angles
+yeah so the X and the Y gives us the the
+
+ align:start position:0%
+yeah so the X and the Y gives us the the
+ 
+
+ align:start position:0%
+yeah so the X and the Y gives us the the
+case when the flow it's just like like
+
+ align:start position:0%
+case when the flow it's just like like
+ 
+
+ align:start position:0%
+case when the flow it's just like like
+on the Mississippi or something the flow
+
+ align:start position:0%
+on the Mississippi or something the flow
+ 
+
+ align:start position:0%
+on the Mississippi or something the flow
+is just following that streamline going
+
+ align:start position:0%
+is just following that streamline going
+ 
+
+ align:start position:0%
+is just following that streamline going
+straight well maybe the
+
+ align:start position:0%
+straight well maybe the
+ 
+
+ align:start position:0%
+straight well maybe the
+Mississippi doesn't go that straight but
+
+ align:start position:0%
+Mississippi doesn't go that straight but
+ 
+
+ align:start position:0%
+Mississippi doesn't go that straight but
+out in the middle of it looks pretty
+
+ align:start position:0%
+out in the middle of it looks pretty
+ 
+
+ align:start position:0%
+out in the middle of it looks pretty
+straight probably
+
+ align:start position:0%
+straight probably
+ 
+
+ align:start position:0%
+straight probably
+okay now now I'm ready for the final um
+
+ align:start position:0%
+okay now now I'm ready for the final um
+ 
+
+ align:start position:0%
+okay now now I'm ready for the final um
+thoughts here which are to solve the
+
+ align:start position:0%
+thoughts here which are to solve the
+ 
+
+ align:start position:0%
+thoughts here which are to solve the
+lasses equation Now with uh now so this
+
+ align:start position:0%
+lasses equation Now with uh now so this
+ 
+
+ align:start position:0%
+lasses equation Now with uh now so this
+is this is like the the key a key we got
+
+ align:start position:0%
+is this is like the the key a key we got
+ 
+
+ align:start position:0%
+is this is like the the key a key we got
+a lot of solutions but can we solve it
+
+ align:start position:0%
+a lot of solutions but can we solve it
+ 
+
+ align:start position:0%
+a lot of solutions but can we solve it
+with a Delta function can I can I solve
+
+ align:start position:0%
+with a Delta function can I can I solve
+ 
+
+ align:start position:0%
+with a Delta function can I can I solve
+uxx this will be now a two-dimensional
+
+ align:start position:0%
+uxx this will be now a two-dimensional
+ 
+
+ align:start position:0%
+uxx this will be now a two-dimensional
+Delta Del function uy y equals a Delta
+
+ align:start position:0%
+Delta Del function uy y equals a Delta
+ 
+
+ align:start position:0%
+Delta Del function uy y equals a Delta
+function at 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+or later I would like to solve it with a
+
+ align:start position:0%
+or later I would like to solve it with a
+ 
+
+ align:start position:0%
+or later I would like to solve it with a
+Delta function at some other
+
+ align:start position:0%
+Delta function at some other
+ 
+
+ align:start position:0%
+Delta function at some other
+point uh X notot Y KN move move so this
+
+ align:start position:0%
+point uh X notot Y KN move move so this
+ 
+
+ align:start position:0%
+point uh X notot Y KN move move so this
+is a point source so what what a
+
+ align:start position:0%
+is a point source so what what a
+ 
+
+ align:start position:0%
+is a point source so what what a
+equation am I solving physically with
+
+ align:start position:0%
+equation am I solving physically with
+ 
+
+ align:start position:0%
+equation am I solving physically with
+this with this case I'm it's like
+
+ align:start position:0%
+this with this case I'm it's like
+ 
+
+ align:start position:0%
+this with this case I'm it's like
+fluid is going away and it's there's a
+
+ align:start position:0%
+fluid is going away and it's there's a
+ 
+
+ align:start position:0%
+fluid is going away and it's there's a
+pipe at the origin feeding fluid in do
+
+ align:start position:0%
+pipe at the origin feeding fluid in do
+ 
+
+ align:start position:0%
+pipe at the origin feeding fluid in do
+you see what that picture would be like
+
+ align:start position:0%
+you see what that picture would be like
+ 
+
+ align:start position:0%
+you see what that picture would be like
+there's a source a point source at at
+
+ align:start position:0%
+there's a source a point source at at
+ 
+
+ align:start position:0%
+there's a source a point source at at
+the origin or at some other point and
+
+ align:start position:0%
+the origin or at some other point and
+ 
+
+ align:start position:0%
+the origin or at some other point and
+it's it's providing fluid which is then
+
+ align:start position:0%
+it's it's providing fluid which is then
+ 
+
+ align:start position:0%
+it's it's providing fluid which is then
+traveling away no other
+
+ align:start position:0%
+traveling away no other
+ 
+
+ align:start position:0%
+traveling away no other
+sources everywhere else the Delta
+
+ align:start position:0%
+sources everywhere else the Delta
+ 
+
+ align:start position:0%
+sources everywhere else the Delta
+function is zero but at that one point
+
+ align:start position:0%
+function is zero but at that one point
+ 
+
+ align:start position:0%
+function is zero but at that one point
+we have a true point source so this is
+
+ align:start position:0%
+we have a true point source so this is
+ 
+
+ align:start position:0%
+we have a true point source so this is
+the kind of problem you would solve in
+
+ align:start position:0%
+the kind of problem you would solve in
+ 
+
+ align:start position:0%
+the kind of problem you would solve in
+say analyzing the Boston Harbor or
+
+ align:start position:0%
+say analyzing the Boston Harbor or
+ 
+
+ align:start position:0%
+say analyzing the Boston Harbor or
+something you know it's got certain
+
+ align:start position:0%
+something you know it's got certain
+ 
+
+ align:start position:0%
+something you know it's got certain
+sources and what's what travels around
+
+ align:start position:0%
+sources and what's what travels around
+ 
+
+ align:start position:0%
+sources and what's what travels around
+and and then I'm I would also if if if
+
+ align:start position:0%
+and and then I'm I would also if if if
+ 
+
+ align:start position:0%
+and and then I'm I would also if if if
+just to say what I want to get in I
+
+ align:start position:0%
+just to say what I want to get in I
+ 
+
+ align:start position:0%
+just to say what I want to get in I
+would also like to solve the problem
+
+ align:start position:0%
+would also like to solve the problem
+ 
+
+ align:start position:0%
+would also like to solve the problem
+with with a source on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boundary on the in the boundary value
+
+ align:start position:0%
+boundary on the in the boundary value
+ 
+
+ align:start position:0%
+boundary on the in the boundary value
+instead of in the right hand side but so
+
+ align:start position:0%
+instead of in the right hand side but so
+ 
+
+ align:start position:0%
+instead of in the right hand side but so
+I'll come to that one okay let me tackle
+
+ align:start position:0%
+I'll come to that one okay let me tackle
+ 
+
+ align:start position:0%
+I'll come to that one okay let me tackle
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+guu well you can imagine what we need is
+
+ align:start position:0%
+guu well you can imagine what we need is
+ 
+
+ align:start position:0%
+guu well you can imagine what we need is
+like a good
+
+ align:start position:0%
+like a good
+ 
+
+ align:start position:0%
+like a good
+guess and
+
+ align:start position:0%
+guess and
+ 
+
+ align:start position:0%
+guess and
+uh here's a good guess I
+
+ align:start position:0%
+uh here's a good guess I
+ 
+
+ align:start position:0%
+uh here's a good guess I
+think uh
+
+ align:start position:0%
+think uh
+ 
+
+ align:start position:0%
+think uh
+you uh well I'm going to get a pair
+
+ align:start position:0%
+you uh well I'm going to get a pair
+ 
+
+ align:start position:0%
+you uh well I'm going to get a pair
+again so I'm going to think of my
+
+ align:start position:0%
+again so I'm going to think of my
+ 
+
+ align:start position:0%
+again so I'm going to think of my
+function as
+
+ align:start position:0%
+function as
+ 
+
+ align:start position:0%
+function as
+give the real part will be the U and
+
+ align:start position:0%
+give the real part will be the U and
+ 
+
+ align:start position:0%
+give the real part will be the U and
+then oh what will so actually you could
+
+ align:start position:0%
+then oh what will so actually you could
+ 
+
+ align:start position:0%
+then oh what will so actually you could
+predict here what will be my my geometry
+
+ align:start position:0%
+predict here what will be my my geometry
+ 
+
+ align:start position:0%
+predict here what will be my my geometry
+picture if I have yeah you can guess
+
+ align:start position:0%
+picture if I have yeah you can guess
+ 
+
+ align:start position:0%
+picture if I have yeah you can guess
+what what what's the flow going to do it
+
+ align:start position:0%
+what what what's the flow going to do it
+ 
+
+ align:start position:0%
+what what what's the flow going to do it
+it shows up at this Center and and it
+
+ align:start position:0%
+it shows up at this Center and and it
+ 
+
+ align:start position:0%
+it shows up at this Center and and it
+it's got no other reason to to choose
+
+ align:start position:0%
+it's got no other reason to to choose
+ 
+
+ align:start position:0%
+it's got no other reason to to choose
+any particular direction so where will
+
+ align:start position:0%
+any particular direction so where will
+ 
+
+ align:start position:0%
+any particular direction so where will
+it do it'll go out radially so the the
+
+ align:start position:0%
+it do it'll go out radially so the the
+ 
+
+ align:start position:0%
+it do it'll go out radially so the the
+it'll go out radially the Stream lines
+
+ align:start position:0%
+it'll go out radially the Stream lines
+ 
+
+ align:start position:0%
+it'll go out radially the Stream lines
+streamlines will be
+
+ align:start position:0%
+streamlines will be
+ 
+
+ align:start position:0%
+streamlines will be
+radial these will be the lines s equal
+
+ align:start position:0%
+radial these will be the lines s equal
+ 
+
+ align:start position:0%
+radial these will be the lines s equal
+constant and if this and and then now
+
+ align:start position:0%
+constant and if this and and then now
+ 
+
+ align:start position:0%
+constant and if this and and then now
+what curves are perpendicular to those
+
+ align:start position:0%
+what curves are perpendicular to those
+ 
+
+ align:start position:0%
+what curves are perpendicular to those
+Rays out from the origin circles around
+
+ align:start position:0%
+Rays out from the origin circles around
+ 
+
+ align:start position:0%
+Rays out from the origin circles around
+the origin so those will
+
+ align:start position:0%
+the origin so those will
+ 
+
+ align:start position:0%
+the origin so those will
+be what those will be
+
+ align:start position:0%
+be what those will be
+ 
+
+ align:start position:0%
+be what those will be
+the potential the equip potentials U
+
+ align:start position:0%
+the potential the equip potentials U
+ 
+
+ align:start position:0%
+the potential the equip potentials U
+equal constant okay let's see if we can
+
+ align:start position:0%
+equal constant okay let's see if we can
+ 
+
+ align:start position:0%
+equal constant okay let's see if we can
+make that happen so U equal constant
+
+ align:start position:0%
+make that happen so U equal constant
+ 
+
+ align:start position:0%
+make that happen so U equal constant
+will be a circle
+
+ align:start position:0%
+will be a circle
+ 
+
+ align:start position:0%
+will be a circle
+and S equal constant will be
+
+ align:start position:0%
+and S equal constant will be
+ 
+
+ align:start position:0%
+and S equal constant will be
+array okay well here's a here's a
+
+ align:start position:0%
+array okay well here's a here's a
+ 
+
+ align:start position:0%
+array okay well here's a here's a
+function look at the
+
+ align:start position:0%
+function look at the
+ 
+
+ align:start position:0%
+function look at the
+logarithm of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Z that's an interesting
+
+ align:start position:0%
+Z that's an interesting
+ 
+
+ align:start position:0%
+Z that's an interesting
+function all right let's figure out what
+
+ align:start position:0%
+function all right let's figure out what
+ 
+
+ align:start position:0%
+function all right let's figure out what
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+is okay so shall we use X Plus i y or re
+
+ align:start position:0%
+is okay so shall we use X Plus i y or re
+ 
+
+ align:start position:0%
+is okay so shall we use X Plus i y or re
+e to the I
+
+ align:start position:0%
+e to the I
+ 
+
+ align:start position:0%
+e to the I
+Theta re e to I Theta better
+
+ align:start position:0%
+Theta re e to I Theta better
+ 
+
+ align:start position:0%
+Theta re e to I Theta better
+right because the logarithm of a sum is
+
+ align:start position:0%
+right because the logarithm of a sum is
+ 
+
+ align:start position:0%
+right because the logarithm of a sum is
+who knows but the log of a product
+
+ align:start position:0%
+who knows but the log of a product
+ 
+
+ align:start position:0%
+who knows but the log of a product
+is convenient because the log of the
+
+ align:start position:0%
+is convenient because the log of the
+ 
+
+ align:start position:0%
+is convenient because the log of the
+product is the logarithm of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term plus the logarithm of the other
+
+ align:start position:0%
+term plus the logarithm of the other
+ 
+
+ align:start position:0%
+term plus the logarithm of the other
+term and what's the log of the other
+
+ align:start position:0%
+term and what's the log of the other
+ 
+
+ align:start position:0%
+term and what's the log of the other
+term what's the logarithm of e to the I
+
+ align:start position:0%
+term what's the logarithm of e to the I
+ 
+
+ align:start position:0%
+term what's the logarithm of e to the I
+Theta it's just I Theta right it's just
+
+ align:start position:0%
+Theta it's just I Theta right it's just
+ 
+
+ align:start position:0%
+Theta it's just I Theta right it's just
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+Theta
+
+ align:start position:0%
+Theta
+ 
+
+ align:start position:0%
+Theta
+so what do we what do we got here now we
+
+ align:start position:0%
+so what do we what do we got here now we
+ 
+
+ align:start position:0%
+so what do we what do we got here now we
+take the real part this is like a picnic
+
+ align:start position:0%
+take the real part this is like a picnic
+ 
+
+ align:start position:0%
+take the real part this is like a picnic
+here take the real part this is our
+
+ align:start position:0%
+here take the real part this is our
+ 
+
+ align:start position:0%
+here take the real part this is our
+U and our take the imaginary part and
+
+ align:start position:0%
+U and our take the imaginary part and
+ 
+
+ align:start position:0%
+U and our take the imaginary part and
+this is our
+
+ align:start position:0%
+this is our
+ 
+
+ align:start position:0%
+this is our
+s so it was really easy to split into
+
+ align:start position:0%
+s so it was really easy to split into
+ 
+
+ align:start position:0%
+s so it was really easy to split into
+the U and the S and now does that match
+
+ align:start position:0%
+the U and the S and now does that match
+ 
+
+ align:start position:0%
+the U and the S and now does that match
+so so far I just suggested this function
+
+ align:start position:0%
+so so far I just suggested this function
+ 
+
+ align:start position:0%
+so so far I just suggested this function
+but now notice how it does match the
+
+ align:start position:0%
+but now notice how it does match the
+ 
+
+ align:start position:0%
+but now notice how it does match the
+picture because the lines s equal
+
+ align:start position:0%
+picture because the lines s equal
+ 
+
+ align:start position:0%
+picture because the lines s equal
+constant are Theta equal constant those
+
+ align:start position:0%
+constant are Theta equal constant those
+ 
+
+ align:start position:0%
+constant are Theta equal constant those
+are rays and the lines log r equal
+
+ align:start position:0%
+are rays and the lines log r equal
+ 
+
+ align:start position:0%
+are rays and the lines log r equal
+constant are circles right if log R is
+
+ align:start position:0%
+constant are circles right if log R is
+ 
+
+ align:start position:0%
+constant are circles right if log R is
+six then R is some constant the e to the
+
+ align:start position:0%
+six then R is some constant the e to the
+ 
+
+ align:start position:0%
+six then R is some constant the e to the
+6 or something like that and e to the 6
+
+ align:start position:0%
+6 or something like that and e to the 6
+ 
+
+ align:start position:0%
+6 or something like that and e to the 6
+r equal constant is a circle so that
+
+ align:start position:0%
+r equal constant is a circle so that
+ 
+
+ align:start position:0%
+r equal constant is a circle so that
+this is the guy this is the good
+
+ align:start position:0%
+this is the guy this is the good
+ 
+
+ align:start position:0%
+this is the guy this is the good
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+then uh if we Pinn down more details we
+
+ align:start position:0%
+then uh if we Pinn down more details we
+ 
+
+ align:start position:0%
+then uh if we Pinn down more details we
+could show that it
+
+ align:start position:0%
+could show that it
+ 
+
+ align:start position:0%
+could show that it
+actually uh is like that uh well I think
+
+ align:start position:0%
+actually uh is like that uh well I think
+ 
+
+ align:start position:0%
+actually uh is like that uh well I think
+we maybe there's a two Pi comes into it
+
+ align:start position:0%
+we maybe there's a two Pi comes into it
+ 
+
+ align:start position:0%
+we maybe there's a two Pi comes into it
+there's a two Pi comes into it maybe if
+
+ align:start position:0%
+there's a two Pi comes into it maybe if
+ 
+
+ align:start position:0%
+there's a two Pi comes into it maybe if
+we maybe if we would have to be a little
+
+ align:start position:0%
+we maybe if we would have to be a little
+ 
+
+ align:start position:0%
+we maybe if we would have to be a little
+careful we' have to do that that greens
+
+ align:start position:0%
+careful we' have to do that that greens
+ 
+
+ align:start position:0%
+careful we' have to do that that greens
+function stuff to to see I mean what's
+
+ align:start position:0%
+function stuff to to see I mean what's
+ 
+
+ align:start position:0%
+function stuff to to see I mean what's
+the what's the idea of this Delta
+
+ align:start position:0%
+the what's the idea of this Delta
+ 
+
+ align:start position:0%
+the what's the idea of this Delta
+function what will be the
+
+ align:start position:0%
+function what will be the
+ 
+
+ align:start position:0%
+function what will be the
+yeah here we go if this right side is a
+
+ align:start position:0%
+yeah here we go if this right side is a
+ 
+
+ align:start position:0%
+yeah here we go if this right side is a
+Delta function at the origin that means
+
+ align:start position:0%
+Delta function at the origin that means
+ 
+
+ align:start position:0%
+Delta function at the origin that means
+that pipe is sending up it's a it's a
+
+ align:start position:0%
+that pipe is sending up it's a it's a
+ 
+
+ align:start position:0%
+that pipe is sending up it's a it's a
+it's a small pipe but it's sending up
+
+ align:start position:0%
+it's a small pipe but it's sending up
+ 
+
+ align:start position:0%
+it's a small pipe but it's sending up
+one unit of
+
+ align:start position:0%
+one unit of
+ 
+
+ align:start position:0%
+one unit of
+source one unit and where does that
+
+ align:start position:0%
+source one unit and where does that
+ 
+
+ align:start position:0%
+source one unit and where does that
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+go flows out right so the having that
+
+ align:start position:0%
+go flows out right so the having that
+ 
+
+ align:start position:0%
+go flows out right so the having that
+Delta function there we can check that
+
+ align:start position:0%
+Delta function there we can check that
+ 
+
+ align:start position:0%
+Delta function there we can check that
+we've got it right if the what should
+
+ align:start position:0%
+we've got it right if the what should
+ 
+
+ align:start position:0%
+we've got it right if the what should
+the flow out through
+
+ align:start position:0%
+the flow out through
+ 
+
+ align:start position:0%
+the flow out through
+on the flow out through this C out
+
+ align:start position:0%
+on the flow out through this C out
+ 
+
+ align:start position:0%
+on the flow out through this C out
+through every Circle actually like that
+
+ align:start position:0%
+through every Circle actually like that
+ 
+
+ align:start position:0%
+through every Circle actually like that
+one should be should be equal to the
+
+ align:start position:0%
+one should be should be equal to the
+ 
+
+ align:start position:0%
+one should be should be equal to the
+source right right maybe there's a two
+
+ align:start position:0%
+source right right maybe there's a two
+ 
+
+ align:start position:0%
+source right right maybe there's a two
+Pi I I won't I think somewhere in here
+
+ align:start position:0%
+Pi I I won't I think somewhere in here
+ 
+
+ align:start position:0%
+Pi I I won't I think somewhere in here
+it comes a two PI right so we would to
+
+ align:start position:0%
+it comes a two PI right so we would to
+ 
+
+ align:start position:0%
+it comes a two PI right so we would to
+to see that we really have got a Delta
+
+ align:start position:0%
+to see that we really have got a Delta
+ 
+
+ align:start position:0%
+to see that we really have got a Delta
+function I should integrate I should
+
+ align:start position:0%
+function I should integrate I should
+ 
+
+ align:start position:0%
+function I should integrate I should
+figure out what is the flow through it
+
+ align:start position:0%
+figure out what is the flow through it
+ 
+
+ align:start position:0%
+figure out what is the flow through it
+and it would come out right a constant
+
+ align:start position:0%
+and it would come out right a constant
+ 
+
+ align:start position:0%
+and it would come out right a constant
+and that constant might be at two pi
+
+ align:start position:0%
+and that constant might be at two pi
+ 
+
+ align:start position:0%
+and that constant might be at two pi
+like probably would be a two Pi yeah so
+
+ align:start position:0%
+like probably would be a two Pi yeah so
+ 
+
+ align:start position:0%
+like probably would be a two Pi yeah so
+okay so that that's uh that says yes
+
+ align:start position:0%
+okay so that that's uh that says yes
+ 
+
+ align:start position:0%
+okay so that that's uh that says yes
+we've got it okay
+
+ align:start position:0%
+we've got it okay
+ 
+
+ align:start position:0%
+we've got it okay
+now are you happy with that Solution
+
+ align:start position:0%
+now are you happy with that Solution
+ 
+
+ align:start position:0%
+now are you happy with that Solution
+that's quite remarkable then this is our
+
+ align:start position:0%
+that's quite remarkable then this is our
+ 
+
+ align:start position:0%
+that's quite remarkable then this is our
+U of X you if you might like it in polar
+
+ align:start position:0%
+U of X you if you might like it in polar
+ 
+
+ align:start position:0%
+U of X you if you might like it in polar
+coordinates in rectangular U of X and Y
+
+ align:start position:0%
+coordinates in rectangular U of X and Y
+ 
+
+ align:start position:0%
+coordinates in rectangular U of X and Y
+will be the logarithm of the square of
+
+ align:start position:0%
+will be the logarithm of the square of
+ 
+
+ align:start position:0%
+will be the logarithm of the square of
+X2 + y^ 2 that's that's
+
+ align:start position:0%
+X2 + y^ 2 that's that's
+ 
+
+ align:start position:0%
+X2 + y^ 2 that's that's
+R and S of X and Y y will be the Theta
+
+ align:start position:0%
+R and S of X and Y y will be the Theta
+ 
+
+ align:start position:0%
+R and S of X and Y y will be the Theta
+is the Theta which is oh what's that in
+
+ align:start position:0%
+is the Theta which is oh what's that in
+ 
+
+ align:start position:0%
+is the Theta which is oh what's that in
+X and Y nothing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nice I mean we could plug that in and
+
+ align:start position:0%
+nice I mean we could plug that in and
+ 
+
+ align:start position:0%
+nice I mean we could plug that in and
+say yeah that satisfies Theus equation
+
+ align:start position:0%
+say yeah that satisfies Theus equation
+ 
+
+ align:start position:0%
+say yeah that satisfies Theus equation
+even so you know take two derives of
+
+ align:start position:0%
+even so you know take two derives of
+ 
+
+ align:start position:0%
+even so you know take two derives of
+that would take a little while but it
+
+ align:start position:0%
+that would take a little while but it
+ 
+
+ align:start position:0%
+that would take a little while but it
+would work now what about this one so
+
+ align:start position:0%
+would work now what about this one so
+ 
+
+ align:start position:0%
+would work now what about this one so
+what's Theta it's the arc
+
+ align:start position:0%
+what's Theta it's the arc
+ 
+
+ align:start position:0%
+what's Theta it's the arc
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+of Y overx is
+
+ align:start position:0%
+of Y overx is
+ 
+
+ align:start position:0%
+of Y overx is
+it yeah Theta is the Theta is the angle
+
+ align:start position:0%
+it yeah Theta is the Theta is the angle
+ 
+
+ align:start position:0%
+it yeah Theta is the Theta is the angle
+whose tangent is
+
+ align:start position:0%
+whose tangent is
+ 
+
+ align:start position:0%
+whose tangent is
+YX well plug that in yeah you have to
+
+ align:start position:0%
+YX well plug that in yeah you have to
+ 
+
+ align:start position:0%
+YX well plug that in yeah you have to
+know the formula for derivatives of AR
+
+ align:start position:0%
+know the formula for derivatives of AR
+ 
+
+ align:start position:0%
+know the formula for derivatives of AR
+10 but plug it in and it will work
+
+ align:start position:0%
+10 but plug it in and it will work
+ 
+
+ align:start position:0%
+10 but plug it in and it will work
+except of course at one point at one
+
+ align:start position:0%
+except of course at one point at one
+ 
+
+ align:start position:0%
+except of course at one point at one
+point there's one point X and Y where
+
+ align:start position:0%
+point there's one point X and Y where
+ 
+
+ align:start position:0%
+point there's one point X and Y where
+the derivative blows up everything blows
+
+ align:start position:0%
+the derivative blows up everything blows
+ 
+
+ align:start position:0%
+the derivative blows up everything blows
+up and that which which is that point
+
+ align:start position:0%
+up and that which which is that point
+ 
+
+ align:start position:0%
+up and that which which is that point
+that's z0 right right it we can already
+
+ align:start position:0%
+that's z0 right right it we can already
+ 
+
+ align:start position:0%
+that's z0 right right it we can already
+see a little trouble at zero or we would
+
+ align:start position:0%
+see a little trouble at zero or we would
+ 
+
+ align:start position:0%
+see a little trouble at zero or we would
+be taking the log of zero we things
+
+ align:start position:0%
+be taking the log of zero we things
+ 
+
+ align:start position:0%
+be taking the log of zero we things
+won't be good at Z 0 and of course we
+
+ align:start position:0%
+won't be good at Z 0 and of course we
+ 
+
+ align:start position:0%
+won't be good at Z 0 and of course we
+don't expect them because our right side
+
+ align:start position:0%
+don't expect them because our right side
+ 
+
+ align:start position:0%
+don't expect them because our right side
+has a spike there okay
+
+ align:start position:0%
+has a spike there okay
+ 
+
+ align:start position:0%
+has a spike there okay
+now now I just would like to say a
+
+ align:start position:0%
+now now I just would like to say a
+ 
+
+ align:start position:0%
+now now I just would like to say a
+little about very little about suppose
+
+ align:start position:0%
+little about very little about suppose
+ 
+
+ align:start position:0%
+little about very little about suppose
+the suppose the
+
+ align:start position:0%
+the suppose the
+ 
+
+ align:start position:0%
+the suppose the
+um Delta function is somewhere else oh
+
+ align:start position:0%
+um Delta function is somewhere else oh
+ 
+
+ align:start position:0%
+um Delta function is somewhere else oh
+well yeah we could just take the logs we
+
+ align:start position:0%
+well yeah we could just take the logs we
+ 
+
+ align:start position:0%
+well yeah we could just take the logs we
+could just reenter we could just shift
+
+ align:start position:0%
+could just reenter we could just shift
+ 
+
+ align:start position:0%
+could just reenter we could just shift
+it over to that point so that would be a
+
+ align:start position:0%
+it over to that point so that would be a
+ 
+
+ align:start position:0%
+it over to that point so that would be a
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+huh now what I so I'm going to ask for
+
+ align:start position:0%
+huh now what I so I'm going to ask for
+ 
+
+ align:start position:0%
+huh now what I so I'm going to ask for
+something more I'm gonna so this would
+
+ align:start position:0%
+something more I'm gonna so this would
+ 
+
+ align:start position:0%
+something more I'm gonna so this would
+be like say that's the Boston Harbor or
+
+ align:start position:0%
+be like say that's the Boston Harbor or
+ 
+
+ align:start position:0%
+be like say that's the Boston Harbor or
+or or or or the Atlantic Ocean or
+
+ align:start position:0%
+or or or or the Atlantic Ocean or
+ 
+
+ align:start position:0%
+or or or or the Atlantic Ocean or
+something well Boston Harbor maybe with
+
+ align:start position:0%
+something well Boston Harbor maybe with
+ 
+
+ align:start position:0%
+something well Boston Harbor maybe with
+a point source in the middle okay now so
+
+ align:start position:0%
+a point source in the middle okay now so
+ 
+
+ align:start position:0%
+a point source in the middle okay now so
+that's that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really suppose yeah let me say this
+
+ align:start position:0%
+really suppose yeah let me say this
+ 
+
+ align:start position:0%
+really suppose yeah let me say this
+again suppose we were given lass's
+
+ align:start position:0%
+again suppose we were given lass's
+ 
+
+ align:start position:0%
+again suppose we were given lass's
+equation well we should be given
+
+ align:start position:0%
+equation well we should be given
+ 
+
+ align:start position:0%
+equation well we should be given
+boundary conditions
+
+ align:start position:0%
+boundary conditions
+ 
+
+ align:start position:0%
+boundary conditions
+right so and let this be the circle of
+
+ align:start position:0%
+right so and let this be the circle of
+ 
+
+ align:start position:0%
+right so and let this be the circle of
+radius one let let and say my boundary
+
+ align:start position:0%
+radius one let let and say my boundary
+ 
+
+ align:start position:0%
+radius one let let and say my boundary
+condition is U equals zero on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+circle now now I've stated a whole
+
+ align:start position:0%
+circle now now I've stated a whole
+ 
+
+ align:start position:0%
+circle now now I've stated a whole
+problem I've given the equation and I've
+
+ align:start position:0%
+problem I've given the equation and I've
+ 
+
+ align:start position:0%
+problem I've given the equation and I've
+given the boundary conditions on this
+
+ align:start position:0%
+given the boundary conditions on this
+ 
+
+ align:start position:0%
+given the boundary conditions on this
+unit circle okay and my my point is that
+
+ align:start position:0%
+unit circle okay and my my point is that
+ 
+
+ align:start position:0%
+unit circle okay and my my point is that
+we found the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer this is this is this is perfect U
+
+ align:start position:0%
+answer this is this is this is perfect U
+ 
+
+ align:start position:0%
+answer this is this is this is perfect U
+is log R the answer the answer is U is
+
+ align:start position:0%
+is log R the answer the answer is U is
+ 
+
+ align:start position:0%
+is log R the answer the answer is U is
+log
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R because log of on the circle where R
+
+ align:start position:0%
+R because log of on the circle where R
+ 
+
+ align:start position:0%
+R because log of on the circle where R
+is one the log of one is zero so it we
+
+ align:start position:0%
+is one the log of one is zero so it we
+ 
+
+ align:start position:0%
+is one the log of one is zero so it we
+we captured the boundary condition
+
+ align:start position:0%
+we captured the boundary condition
+ 
+
+ align:start position:0%
+we captured the boundary condition
+condition as well as the equation
+
+ align:start position:0%
+condition as well as the equation
+ 
+
+ align:start position:0%
+condition as well as the equation
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now you see what I want to do next I
+
+ align:start position:0%
+now you see what I want to do next I
+ 
+
+ align:start position:0%
+now you see what I want to do next I
+would like to be able to I would like to
+
+ align:start position:0%
+would like to be able to I would like to
+ 
+
+ align:start position:0%
+would like to be able to I would like to
+be able to solve this
+
+ align:start position:0%
+be able to solve this
+ 
+
+ align:start position:0%
+be able to solve this
+problem with the same
+
+ align:start position:0%
+problem with the same
+ 
+
+ align:start position:0%
+problem with the same
+Circle and the
+
+ align:start position:0%
+Circle and the
+ 
+
+ align:start position:0%
+Circle and the
+same boundary condition but the point
+
+ align:start position:0%
+same boundary condition but the point
+ 
+
+ align:start position:0%
+same boundary condition but the point
+load is somewhere the point source is
+
+ align:start position:0%
+load is somewhere the point source is
+ 
+
+ align:start position:0%
+load is somewhere the point source is
+somewhere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else and that's maybe not so
+
+ align:start position:0%
+else and that's maybe not so
+ 
+
+ align:start position:0%
+else and that's maybe not so
+clear and then this last guy that I
+
+ align:start position:0%
+clear and then this last guy that I
+ 
+
+ align:start position:0%
+clear and then this last guy that I
+would like to
+
+ align:start position:0%
+would like to
+ 
+
+ align:start position:0%
+would like to
+solve would have the same
+
+ align:start position:0%
+solve would have the same
+ 
+
+ align:start position:0%
+solve would have the same
+Circle but now oops now it
+
+ align:start position:0%
+Circle but now oops now it
+ 
+
+ align:start position:0%
+Circle but now oops now it
+now the source is on the boundary like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there that would that's a circle despite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+its and inside no source so the source
+
+ align:start position:0%
+its and inside no source so the source
+ 
+
+ align:start position:0%
+its and inside no source so the source
+is on the boundary so on this in this
+
+ align:start position:0%
+is on the boundary so on this in this
+ 
+
+ align:start position:0%
+is on the boundary so on this in this
+case I'm solving u l PL again uxx plus u
+
+ align:start position:0%
+case I'm solving u l PL again uxx plus u
+ 
+
+ align:start position:0%
+case I'm solving u l PL again uxx plus u
+y yal 0 inside but now on the boundary U
+
+ align:start position:0%
+y yal 0 inside but now on the boundary U
+ 
+
+ align:start position:0%
+y yal 0 inside but now on the boundary U
+is the the Delta function is at the
+
+ align:start position:0%
+is the the Delta function is at the
+ 
+
+ align:start position:0%
+is the the Delta function is at the
+boundary U here U on the boundary is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta so you see that I'm I'm I'm
+
+ align:start position:0%
+Delta so you see that I'm I'm I'm
+ 
+
+ align:start position:0%
+Delta so you see that I'm I'm I'm
+creating sort of very special problems
+
+ align:start position:0%
+creating sort of very special problems
+ 
+
+ align:start position:0%
+creating sort of very special problems
+and the reason is as as I'll show in the
+
+ align:start position:0%
+and the reason is as as I'll show in the
+ 
+
+ align:start position:0%
+and the reason is as as I'll show in the
+next lecture that if uh if I can solve
+
+ align:start position:0%
+next lecture that if uh if I can solve
+ 
+
+ align:start position:0%
+next lecture that if uh if I can solve
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+with with Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+functions either inside or on the
+
+ align:start position:0%
+functions either inside or on the
+ 
+
+ align:start position:0%
+functions either inside or on the
+boundary then I could solve them with
+
+ align:start position:0%
+boundary then I could solve them with
+ 
+
+ align:start position:0%
+boundary then I could solve them with
+other things I could combine the answers
+
+ align:start position:0%
+other things I could combine the answers
+ 
+
+ align:start position:0%
+other things I could combine the answers
+called they're called the greens
+
+ align:start position:0%
+called they're called the greens
+ 
+
+ align:start position:0%
+called they're called the greens
+function so this is the greens function
+
+ align:start position:0%
+function so this is the greens function
+ 
+
+ align:start position:0%
+function so this is the greens function
+for the source at the origin the answer
+
+ align:start position:0%
+for the source at the origin the answer
+ 
+
+ align:start position:0%
+for the source at the origin the answer
+here U will be the green function on a
+
+ align:start position:0%
+here U will be the green function on a
+ 
+
+ align:start position:0%
+here U will be the green function on a
+circle for the source at some inside
+
+ align:start position:0%
+circle for the source at some inside
+ 
+
+ align:start position:0%
+circle for the source at some inside
+point the solution U here once I find it
+
+ align:start position:0%
+point the solution U here once I find it
+ 
+
+ align:start position:0%
+point the solution U here once I find it
+is going to be the greens function for
+
+ align:start position:0%
+is going to be the greens function for
+ 
+
+ align:start position:0%
+is going to be the greens function for
+this problem on a circle with a Delta
+
+ align:start position:0%
+this problem on a circle with a Delta
+ 
+
+ align:start position:0%
+this problem on a circle with a Delta
+function at that boundary point so those
+
+ align:start position:0%
+function at that boundary point so those
+ 
+
+ align:start position:0%
+function at that boundary point so those
+are special problems but if we solve
+
+ align:start position:0%
+are special problems but if we solve
+ 
+
+ align:start position:0%
+are special problems but if we solve
+those we can use them to solve much more
+
+ align:start position:0%
+those we can use them to solve much more
+ 
+
+ align:start position:0%
+those we can use them to solve much more
+General problems because I can take a
+
+ align:start position:0%
+General problems because I can take a
+ 
+
+ align:start position:0%
+General problems because I can take a
+any source as like some combination of
+
+ align:start position:0%
+any source as like some combination of
+ 
+
+ align:start position:0%
+any source as like some combination of
+sources at different points or any bound
+
+ align:start position:0%
+sources at different points or any bound
+ 
+
+ align:start position:0%
+sources at different points or any bound
+condition would be like some combination
+
+ align:start position:0%
+condition would be like some combination
+ 
+
+ align:start position:0%
+condition would be like some combination
+of Deltas at different boundary points
+
+ align:start position:0%
+of Deltas at different boundary points
+ 
+
+ align:start position:0%
+of Deltas at different boundary points
+so those are the three problems and the
+
+ align:start position:0%
+so those are the three problems and the
+ 
+
+ align:start position:0%
+so those are the three problems and the
+first one is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solved that's where we stand now and now
+
+ align:start position:0%
+solved that's where we stand now and now
+ 
+
+ align:start position:0%
+solved that's where we stand now and now
+I I I would like to be able to solve the
+
+ align:start position:0%
+I I I would like to be able to solve the
+ 
+
+ align:start position:0%
+I I I would like to be able to solve the
+other two and then and then that you
+
+ align:start position:0%
+other two and then and then that you
+ 
+
+ align:start position:0%
+other two and then and then that you
+would see sort of some of the key points
+
+ align:start position:0%
+would see sort of some of the key points
+ 
+
+ align:start position:0%
+would see sort of some of the key points
+of how to deal with lass's equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay more much more could be said but I
+
+ align:start position:0%
+okay more much more could be said but I
+ 
+
+ align:start position:0%
+okay more much more could be said but I
+think uh this would give you the main
+
+ align:start position:0%
+think uh this would give you the main
+ 
+
+ align:start position:0%
+think uh this would give you the main
+points so let me erase this
+
+ align:start position:0%
+points so let me erase this
+ 
+
+ align:start position:0%
+points so let me erase this
+curve and and just write down some of
+
+ align:start position:0%
+curve and and just write down some of
+ 
+
+ align:start position:0%
+curve and and just write down some of
+the write down the answers for those
+
+ align:start position:0%
+the write down the answers for those
+ 
+
+ align:start position:0%
+the write down the answers for those
+last two problems
+
+ align:start position:0%
+last two problems
+ 
+
+ align:start position:0%
+last two problems
+okay okay and and and then try to
+
+ align:start position:0%
+okay okay and and and then try to
+ 
+
+ align:start position:0%
+okay okay and and and then try to
+understand them let me take the last
+
+ align:start position:0%
+understand them let me take the last
+ 
+
+ align:start position:0%
+understand them let me take the last
+problem boundary
+
+ align:start position:0%
+problem boundary
+ 
+
+ align:start position:0%
+problem boundary
+Source U equal Delta on the
+
+ align:start position:0%
+Source U equal Delta on the
+ 
+
+ align:start position:0%
+Source U equal Delta on the
+boundary with the ples equation inside I
+
+ align:start position:0%
+boundary with the ples equation inside I
+ 
+
+ align:start position:0%
+boundary with the ples equation inside I
+think the solution to that one is the
+
+ align:start position:0%
+think the solution to that one is the
+ 
+
+ align:start position:0%
+think the solution to that one is the
+solution and let's consider if it's
+
+ align:start position:0%
+solution and let's consider if it's
+ 
+
+ align:start position:0%
+solution and let's consider if it's
+right I think it's one minus or in poar
+
+ align:start position:0%
+right I think it's one minus or in poar
+ 
+
+ align:start position:0%
+right I think it's one minus or in poar
+it's it's natural we're we're dealing
+
+ align:start position:0%
+it's it's natural we're we're dealing
+ 
+
+ align:start position:0%
+it's it's natural we're we're dealing
+with circles so we better stay with
+
+ align:start position:0%
+with circles so we better stay with
+ 
+
+ align:start position:0%
+with circles so we better stay with
+polar coordinates over 1 + r 2 - 2 R cos
+
+ align:start position:0%
+polar coordinates over 1 + r 2 - 2 R cos
+ 
+
+ align:start position:0%
+polar coordinates over 1 + r 2 - 2 R cos
+Theta yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think that's the the right guy oh I
+
+ align:start position:0%
+I think that's the the right guy oh I
+ 
+
+ align:start position:0%
+I think that's the the right guy oh I
+need to divide by a two Pi always these
+
+ align:start position:0%
+need to divide by a two Pi always these
+ 
+
+ align:start position:0%
+need to divide by a two Pi always these
+numbers come
+
+ align:start position:0%
+numbers come
+ 
+
+ align:start position:0%
+numbers come
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+okay so how would
+
+ align:start position:0%
+okay so how would
+ 
+
+ align:start position:0%
+okay so how would
+we have and I I actually we'll arrive at
+
+ align:start position:0%
+we have and I I actually we'll arrive at
+ 
+
+ align:start position:0%
+we have and I I actually we'll arrive at
+this answer using forier Series so let
+
+ align:start position:0%
+this answer using forier Series so let
+ 
+
+ align:start position:0%
+this answer using forier Series so let
+me not try to anticipate the step of
+
+ align:start position:0%
+me not try to anticipate the step of
+ 
+
+ align:start position:0%
+me not try to anticipate the step of
+getting to this answer but just look at
+
+ align:start position:0%
+getting to this answer but just look at
+ 
+
+ align:start position:0%
+getting to this answer but just look at
+the answer after we've got it can you
+
+ align:start position:0%
+the answer after we've got it can you
+ 
+
+ align:start position:0%
+the answer after we've got it can you
+see that it satisfies the boundary
+
+ align:start position:0%
+see that it satisfies the boundary
+ 
+
+ align:start position:0%
+see that it satisfies the boundary
+condition I mean reasonably
+
+ align:start position:0%
+condition I mean reasonably
+ 
+
+ align:start position:0%
+condition I mean reasonably
+so what's so the boundary so we're on
+
+ align:start position:0%
+so what's so the boundary so we're on
+ 
+
+ align:start position:0%
+so what's so the boundary so we're on
+this unit
+
+ align:start position:0%
+this unit
+ 
+
+ align:start position:0%
+this unit
+circle and why does U come out zero at
+
+ align:start position:0%
+circle and why does U come out zero at
+ 
+
+ align:start position:0%
+circle and why does U come out zero at
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+point as it's supposed to because the
+
+ align:start position:0%
+point as it's supposed to because the
+ 
+
+ align:start position:0%
+point as it's supposed to because the
+source is like this the Delta function
+
+ align:start position:0%
+source is like this the Delta function
+ 
+
+ align:start position:0%
+source is like this the Delta function
+is there because R is one right no
+
+ align:start position:0%
+is there because R is one right no
+ 
+
+ align:start position:0%
+is there because R is one right no
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+um so all at all these other points are
+
+ align:start position:0%
+um so all at all these other points are
+ 
+
+ align:start position:0%
+um so all at all these other points are
+is one well why don't we get zero at
+
+ align:start position:0%
+is one well why don't we get zero at
+ 
+
+ align:start position:0%
+is one well why don't we get zero at
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point what's happening at that special
+
+ align:start position:0%
+point what's happening at that special
+ 
+
+ align:start position:0%
+point what's happening at that special
+point when R is one but Theta
+
+ align:start position:0%
+point when R is one but Theta
+ 
+
+ align:start position:0%
+point when R is one but Theta
+is zero at that point the denominator
+
+ align:start position:0%
+is zero at that point the denominator
+ 
+
+ align:start position:0%
+is zero at that point the denominator
+must be doing something too at this
+
+ align:start position:0%
+must be doing something too at this
+ 
+
+ align:start position:0%
+must be doing something too at this
+point at that point I'm I'm this is
+
+ align:start position:0%
+point at that point I'm I'm this is
+ 
+
+ align:start position:0%
+point at that point I'm I'm this is
+theta equals z of course because it's on
+
+ align:start position:0%
+theta equals z of course because it's on
+ 
+
+ align:start position:0%
+theta equals z of course because it's on
+this Ray yeah if I if I just look on
+
+ align:start position:0%
+this Ray yeah if I if I just look on
+ 
+
+ align:start position:0%
+this Ray yeah if I if I just look on
+this Ray theta equals 0 I kind of
+
+ align:start position:0%
+this Ray theta equals 0 I kind of
+ 
+
+ align:start position:0%
+this Ray theta equals 0 I kind of
+learned some stuff at this theta equals
+
+ align:start position:0%
+learned some stuff at this theta equals
+ 
+
+ align:start position:0%
+learned some stuff at this theta equals
+0 I have the 1 over 2 pi 1 - r^ 2 /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what let's see if Theta is zero what's
+
+ align:start position:0%
+what let's see if Theta is zero what's
+ 
+
+ align:start position:0%
+what let's see if Theta is zero what's
+that 1 + r 2 - 2
+
+ align:start position:0%
+that 1 + r 2 - 2
+ 
+
+ align:start position:0%
+that 1 + r 2 - 2
+R can we just offline look at 1 + 1 - 2
+
+ align:start position:0%
+R can we just offline look at 1 + 1 - 2
+ 
+
+ align:start position:0%
+R can we just offline look at 1 + 1 - 2
+R plus the r squar and say what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that it's 1 - R * 1 - R isn't it so I
+
+ align:start position:0%
+that it's 1 - R * 1 - R isn't it so I
+ 
+
+ align:start position:0%
+that it's 1 - R * 1 - R isn't it so I
+have a 1 - R * a 1 -
+
+ align:start position:0%
+have a 1 - R * a 1 -
+ 
+
+ align:start position:0%
+have a 1 - R * a 1 -
+R and one of those will cancel out of
+
+ align:start position:0%
+R and one of those will cancel out of
+ 
+
+ align:start position:0%
+R and one of those will cancel out of
+here and give
+
+ align:start position:0%
+here and give
+ 
+
+ align:start position:0%
+here and give
+what one plus r yeah so it comes out
+
+ align:start position:0%
+what one plus r yeah so it comes out
+ 
+
+ align:start position:0%
+what one plus r yeah so it comes out
+quite nicely if I divide that into that
+
+ align:start position:0%
+quite nicely if I divide that into that
+ 
+
+ align:start position:0%
+quite nicely if I divide that into that
+I'm left with a 1 plus
+
+ align:start position:0%
+I'm left with a 1 plus
+ 
+
+ align:start position:0%
+I'm left with a 1 plus
+r so I I still have one of these guys
+
+ align:start position:0%
+r so I I still have one of these guys
+ 
+
+ align:start position:0%
+r so I I still have one of these guys
+below and now it's a 1 plus r above oh
+
+ align:start position:0%
+below and now it's a 1 plus r above oh
+ 
+
+ align:start position:0%
+below and now it's a 1 plus r above oh
+isn't
+
+ align:start position:0%
+isn't
+ 
+
+ align:start position:0%
+isn't
+that that tells you what's going on all
+
+ align:start position:0%
+that that tells you what's going on all
+ 
+
+ align:start position:0%
+that that tells you what's going on all
+along this line so as R equals 1 we
+
+ align:start position:0%
+along this line so as R equals 1 we
+ 
+
+ align:start position:0%
+along this line so as R equals 1 we
+get oh along this line anyway out this
+
+ align:start position:0%
+get oh along this line anyway out this
+ 
+
+ align:start position:0%
+get oh along this line anyway out this
+Ray Thea equals z
+
+ align:start position:0%
+Ray Thea equals z
+ 
+
+ align:start position:0%
+Ray Thea equals z
+Ray yeah you see what's happening as R
+
+ align:start position:0%
+Ray yeah you see what's happening as R
+ 
+
+ align:start position:0%
+Ray yeah you see what's happening as R
+goes to one well it's true that this
+
+ align:start position:0%
+goes to one well it's true that this
+ 
+
+ align:start position:0%
+goes to one well it's true that this
+went to zero but this also went to zero
+
+ align:start position:0%
+went to zero but this also went to zero
+ 
+
+ align:start position:0%
+went to zero but this also went to zero
+and in fact faster because uh the thing
+
+ align:start position:0%
+and in fact faster because uh the thing
+ 
+
+ align:start position:0%
+and in fact faster because uh the thing
+is blowing up H now just one more key
+
+ align:start position:0%
+is blowing up H now just one more key
+ 
+
+ align:start position:0%
+is blowing up H now just one more key
+the place here in the circle is the
+
+ align:start position:0%
+the place here in the circle is the
+ 
+
+ align:start position:0%
+the place here in the circle is the
+center what's the what's the value of U
+
+ align:start position:0%
+center what's the what's the value of U
+ 
+
+ align:start position:0%
+center what's the what's the value of U
+at the center of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+circle yeah what what do I get for you
+
+ align:start position:0%
+circle yeah what what do I get for you
+ 
+
+ align:start position:0%
+circle yeah what what do I get for you
+at the right here at the center the
+
+ align:start position:0%
+at the right here at the center the
+ 
+
+ align:start position:0%
+at the right here at the center the
+where R is zero yeah so all this stuff
+
+ align:start position:0%
+where R is zero yeah so all this stuff
+ 
+
+ align:start position:0%
+where R is zero yeah so all this stuff
+is gone and I only get 1 over 2 pi and
+
+ align:start position:0%
+is gone and I only get 1 over 2 pi and
+ 
+
+ align:start position:0%
+is gone and I only get 1 over 2 pi and
+what's interesting about the Answer 1
+
+ align:start position:0%
+what's interesting about the Answer 1
+ 
+
+ align:start position:0%
+what's interesting about the Answer 1
+over 2 pi Pi U is one over so U at the
+
+ align:start position:0%
+over 2 pi Pi U is one over so U at the
+ 
+
+ align:start position:0%
+over 2 pi Pi U is one over so U at the
+center 0 0 is 1 over 2 pi and and what
+
+ align:start position:0%
+center 0 0 is 1 over 2 pi and and what
+ 
+
+ align:start position:0%
+center 0 0 is 1 over 2 pi and and what
+is that what's the message
+
+ align:start position:0%
+is that what's the message
+ 
+
+ align:start position:0%
+is that what's the message
+there it's the average of U around the
+
+ align:start position:0%
+there it's the average of U around the
+ 
+
+ align:start position:0%
+there it's the average of U around the
+boundary
+
+ align:start position:0%
+boundary
+ 
+
+ align:start position:0%
+boundary
+ah and this is like always true that the
+
+ align:start position:0%
+ah and this is like always true that the
+ 
+
+ align:start position:0%
+ah and this is like always true that the
+solution to lasses equation at any point
+
+ align:start position:0%
+solution to lasses equation at any point
+ 
+
+ align:start position:0%
+solution to lasses equation at any point
+is the average of
+
+ align:start position:0%
+is the average of
+ 
+
+ align:start position:0%
+is the average of
+the of around any Circle centered at
+
+ align:start position:0%
+the of around any Circle centered at
+ 
+
+ align:start position:0%
+the of around any Circle centered at
+that that point take any Circle I could
+
+ align:start position:0%
+that that point take any Circle I could
+ 
+
+ align:start position:0%
+that that point take any Circle I could
+actually take other
+
+ align:start position:0%
+actually take other
+ 
+
+ align:start position:0%
+actually take other
+circles there's the center well do am I
+
+ align:start position:0%
+circles there's the center well do am I
+ 
+
+ align:start position:0%
+circles there's the center well do am I
+okay in saying that 1 over 2 pi is the
+
+ align:start position:0%
+okay in saying that 1 over 2 pi is the
+ 
+
+ align:start position:0%
+okay in saying that 1 over 2 pi is the
+average of the Delta function that that
+
+ align:start position:0%
+average of the Delta function that that
+ 
+
+ align:start position:0%
+average of the Delta function that that
+asks you to to
+
+ align:start position:0%
+asks you to to
+ 
+
+ align:start position:0%
+asks you to to
+to distrib over Circle yeah distribute
+
+ align:start position:0%
+to distrib over Circle yeah distribute
+ 
+
+ align:start position:0%
+to distrib over Circle yeah distribute
+it over the circle
+
+ align:start position:0%
+it over the circle
+ 
+
+ align:start position:0%
+it over the circle
+right what would be the solution suppose
+
+ align:start position:0%
+right what would be the solution suppose
+ 
+
+ align:start position:0%
+right what would be the solution suppose
+it was a constant all the way around
+
+ align:start position:0%
+it was a constant all the way around
+ 
+
+ align:start position:0%
+it was a constant all the way around
+suppose suppose in can I switch you to a
+
+ align:start position:0%
+suppose suppose in can I switch you to a
+ 
+
+ align:start position:0%
+suppose suppose in can I switch you to a
+different boundary condition suppose the
+
+ align:start position:0%
+different boundary condition suppose the
+ 
+
+ align:start position:0%
+different boundary condition suppose the
+boundary condition was U equal 1 all the
+
+ align:start position:0%
+boundary condition was U equal 1 all the
+ 
+
+ align:start position:0%
+boundary condition was U equal 1 all the
+way round what would be the solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I'm looking for something that
+
+ align:start position:0%
+then I'm looking for something that
+ 
+
+ align:start position:0%
+then I'm looking for something that
+solves Theos equation and equals U
+
+ align:start position:0%
+solves Theos equation and equals U
+ 
+
+ align:start position:0%
+solves Theos equation and equals U
+equals one on the whole boundary well
+
+ align:start position:0%
+equals one on the whole boundary well
+ 
+
+ align:start position:0%
+equals one on the whole boundary well
+you can tell me that right away it's
+
+ align:start position:0%
+you can tell me that right away it's
+ 
+
+ align:start position:0%
+you can tell me that right away it's
+going to be one the constant one all
+
+ align:start position:0%
+going to be one the constant one all
+ 
+
+ align:start position:0%
+going to be one the constant one all
+right tell me so suppose you is one on
+
+ align:start position:0%
+right tell me so suppose you is one on
+ 
+
+ align:start position:0%
+right tell me so suppose you is one on
+the top half and zero on the bottom half
+
+ align:start position:0%
+the top half and zero on the bottom half
+ 
+
+ align:start position:0%
+the top half and zero on the bottom half
+okay what would be the temperature what
+
+ align:start position:0%
+okay what would be the temperature what
+ 
+
+ align:start position:0%
+okay what would be the temperature what
+would be the temperature if I have a
+
+ align:start position:0%
+would be the temperature if I have a
+ 
+
+ align:start position:0%
+would be the temperature if I have a
+circular block here and I heat the
+
+ align:start position:0%
+circular block here and I heat the
+ 
+
+ align:start position:0%
+circular block here and I heat the
+top semicircle to one and hold the
+
+ align:start position:0%
+top semicircle to one and hold the
+ 
+
+ align:start position:0%
+top semicircle to one and hold the
+bottom semicircle at zero what will be
+
+ align:start position:0%
+bottom semicircle at zero what will be
+ 
+
+ align:start position:0%
+bottom semicircle at zero what will be
+the temperature say at the center it'll
+
+ align:start position:0%
+the temperature say at the center it'll
+ 
+
+ align:start position:0%
+the temperature say at the center it'll
+be a half a half and a half will be
+
+ align:start position:0%
+be a half a half and a half will be
+ 
+
+ align:start position:0%
+be a half a half and a half will be
+exactly be the average value of one and
+
+ align:start position:0%
+exactly be the average value of one and
+ 
+
+ align:start position:0%
+exactly be the average value of one and
+zero around the circle actually it'll be
+
+ align:start position:0%
+zero around the circle actually it'll be
+ 
+
+ align:start position:0%
+zero around the circle actually it'll be
+a half all the way along here what it
+
+ align:start position:0%
+a half all the way along here what it
+ 
+
+ align:start position:0%
+a half all the way along here what it
+will be the rest
+
+ align:start position:0%
+will be the rest
+ 
+
+ align:start position:0%
+will be the rest
+ho not we could figure out some formula
+
+ align:start position:0%
+ho not we could figure out some formula
+ 
+
+ align:start position:0%
+ho not we could figure out some formula
+but it won't be totally simple I think
+
+ align:start position:0%
+but it won't be totally simple I think
+ 
+
+ align:start position:0%
+but it won't be totally simple I think
+yeah won't be completely simple anyway
+
+ align:start position:0%
+yeah won't be completely simple anyway
+ 
+
+ align:start position:0%
+yeah won't be completely simple anyway
+we're in a position to solve L pla's
+
+ align:start position:0%
+we're in a position to solve L pla's
+ 
+
+ align:start position:0%
+we're in a position to solve L pla's
+equation in a
+
+ align:start position:0%
+equation in a
+ 
+
+ align:start position:0%
+equation in a
+circle by this um by by knowing this
+
+ align:start position:0%
+circle by this um by by knowing this
+ 
+
+ align:start position:0%
+circle by this um by by knowing this
+answer for the Delta function okay I
+
+ align:start position:0%
+answer for the Delta function okay I
+ 
+
+ align:start position:0%
+answer for the Delta function okay I
+could and and the so the the key point
+
+ align:start position:0%
+could and and the so the the key point
+ 
+
+ align:start position:0%
+could and and the so the the key point
+to may be mention are
+
+ align:start position:0%
+to may be mention are
+ 
+
+ align:start position:0%
+to may be mention are
+that are first that at the value at
+
+ align:start position:0%
+that are first that at the value at
+ 
+
+ align:start position:0%
+that are first that at the value at
+every
+
+ align:start position:0%
+every
+ 
+
+ align:start position:0%
+every
+point will be the average of the values
+
+ align:start position:0%
+point will be the average of the values
+ 
+
+ align:start position:0%
+point will be the average of the values
+on any circle around that point so the
+
+ align:start position:0%
+on any circle around that point so the
+ 
+
+ align:start position:0%
+on any circle around that point so the
+solution inside
+
+ align:start position:0%
+solution inside
+ 
+
+ align:start position:0%
+solution inside
+is there's a maximum principle yeah
+
+ align:start position:0%
+is there's a maximum principle yeah
+ 
+
+ align:start position:0%
+is there's a maximum principle yeah
+that's worth mentioning there's a
+
+ align:start position:0%
+that's worth mentioning there's a
+ 
+
+ align:start position:0%
+that's worth mentioning there's a
+maximum where will the maximum value of
+
+ align:start position:0%
+maximum where will the maximum value of
+ 
+
+ align:start position:0%
+maximum where will the maximum value of
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+occur if if if my statement is true
+
+ align:start position:0%
+occur if if if my statement is true
+ 
+
+ align:start position:0%
+occur if if if my statement is true
+which it is that for Lassa equation the
+
+ align:start position:0%
+which it is that for Lassa equation the
+ 
+
+ align:start position:0%
+which it is that for Lassa equation the
+value at the center of any circle is the
+
+ align:start position:0%
+value at the center of any circle is the
+ 
+
+ align:start position:0%
+value at the center of any circle is the
+average of the value around the circle
+
+ align:start position:0%
+average of the value around the circle
+ 
+
+ align:start position:0%
+average of the value around the circle
+now say look at the big circle where
+
+ align:start position:0%
+now say look at the big circle where
+ 
+
+ align:start position:0%
+now say look at the big circle where
+will the maximum value of U occur
+
+ align:start position:0%
+will the maximum value of U occur
+ 
+
+ align:start position:0%
+will the maximum value of U occur
+somewhere the somewhere on the boundary
+
+ align:start position:0%
+somewhere the somewhere on the boundary
+ 
+
+ align:start position:0%
+somewhere the somewhere on the boundary
+it couldn't occur inside this the
+
+ align:start position:0%
+it couldn't occur inside this the
+ 
+
+ align:start position:0%
+it couldn't occur inside this the
+maximum can't occur there because it's
+
+ align:start position:0%
+maximum can't occur there because it's
+ 
+
+ align:start position:0%
+maximum can't occur there because it's
+the because that value U at that point
+
+ align:start position:0%
+the because that value U at that point
+ 
+
+ align:start position:0%
+the because that value U at that point
+is the average of the of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those so that couldn't be bigger than
+
+ align:start position:0%
+those so that couldn't be bigger than
+ 
+
+ align:start position:0%
+those so that couldn't be bigger than
+all these points and those couldn't be
+
+ align:start position:0%
+all these points and those couldn't be
+ 
+
+ align:start position:0%
+all these points and those couldn't be
+bigger than all the points around them
+
+ align:start position:0%
+bigger than all the points around them
+ 
+
+ align:start position:0%
+bigger than all the points around them
+so the only place that can be biggest is
+
+ align:start position:0%
+so the only place that can be biggest is
+ 
+
+ align:start position:0%
+so the only place that can be biggest is
+out at the boundary well of course in
+
+ align:start position:0%
+out at the boundary well of course in
+ 
+
+ align:start position:0%
+out at the boundary well of course in
+this example it's really the biggest
+
+ align:start position:0%
+this example it's really the biggest
+ 
+
+ align:start position:0%
+this example it's really the biggest
+it's it's blows completely up but uh so
+
+ align:start position:0%
+it's it's blows completely up but uh so
+ 
+
+ align:start position:0%
+it's it's blows completely up but uh so
+that's a general interesting fact that
+
+ align:start position:0%
+that's a general interesting fact that
+ 
+
+ align:start position:0%
+that's a general interesting fact that
+this maximum principle and of course it
+
+ align:start position:0%
+this maximum principle and of course it
+ 
+
+ align:start position:0%
+this maximum principle and of course it
+makes total sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if yeah now a Delta function of the
+
+ align:start position:0%
+if yeah now a Delta function of the
+ 
+
+ align:start position:0%
+if yeah now a Delta function of the
+center that would put a source in so
+
+ align:start position:0%
+center that would put a source in so
+ 
+
+ align:start position:0%
+center that would put a source in so
+this this maximum principle applies to
+
+ align:start position:0%
+this this maximum principle applies to
+ 
+
+ align:start position:0%
+this this maximum principle applies to
+any any uh any U equals U any is given
+
+ align:start position:0%
+any any uh any U equals U any is given
+ 
+
+ align:start position:0%
+any any uh any U equals U any is given
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+boundary on the
+
+ align:start position:0%
+boundary on the
+ 
+
+ align:start position:0%
+boundary on the
+boundary yeah so it's totally natural
+
+ align:start position:0%
+boundary yeah so it's totally natural
+ 
+
+ align:start position:0%
+boundary yeah so it's totally natural
+suppose I have my
+
+ align:start position:0%
+suppose I have my
+ 
+
+ align:start position:0%
+suppose I have my
+circle and I hold the boundary at
+
+ align:start position:0%
+circle and I hold the boundary at
+ 
+
+ align:start position:0%
+circle and I hold the boundary at
+certain
+
+ align:start position:0%
+certain
+ 
+
+ align:start position:0%
+certain
+temperatures then what would you tell me
+
+ align:start position:0%
+temperatures then what would you tell me
+ 
+
+ align:start position:0%
+temperatures then what would you tell me
+about the temperature temp
+
+ align:start position:0%
+about the temperature temp
+ 
+
+ align:start position:0%
+about the temperature temp
+inside it's it's going to be in between
+
+ align:start position:0%
+inside it's it's going to be in between
+ 
+
+ align:start position:0%
+inside it's it's going to be in between
+right the temperature inside is going to
+
+ align:start position:0%
+right the temperature inside is going to
+ 
+
+ align:start position:0%
+right the temperature inside is going to
+be in between if I hold it at some
+
+ align:start position:0%
+be in between if I hold it at some
+ 
+
+ align:start position:0%
+be in between if I hold it at some
+varying temperature here that maybe
+
+ align:start position:0%
+varying temperature here that maybe
+ 
+
+ align:start position:0%
+varying temperature here that maybe
+varies from 3° to
+
+ align:start position:0%
+varies from 3° to
+ 
+
+ align:start position:0%
+varies from 3° to
+55° then inside it will be somewhere
+
+ align:start position:0%
+55° then inside it will be somewhere
+ 
+
+ align:start position:0%
+55° then inside it will be somewhere
+between 3 and 55 I'm not going to see a
+
+ align:start position:0%
+between 3 and 55 I'm not going to see a
+ 
+
+ align:start position:0%
+between 3 and 55 I'm not going to see a
+56 degree temperature inside if there
+
+ align:start position:0%
+56 degree temperature inside if there
+ 
+
+ align:start position:0%
+56 degree temperature inside if there
+are no Source terms so that's so I'm
+
+ align:start position:0%
+are no Source terms so that's so I'm
+ 
+
+ align:start position:0%
+are no Source terms so that's so I'm
+thinking here of no Source terms so I've
+
+ align:start position:0%
+thinking here of no Source terms so I've
+ 
+
+ align:start position:0%
+thinking here of no Source terms so I've
+got I've had that chance to menion the
+
+ align:start position:0%
+got I've had that chance to menion the
+ 
+
+ align:start position:0%
+got I've had that chance to menion the
+maximum principle and the idea that I
+
+ align:start position:0%
+maximum principle and the idea that I
+ 
+
+ align:start position:0%
+maximum principle and the idea that I
+could you know the temperature will vary
+
+ align:start position:0%
+could you know the temperature will vary
+ 
+
+ align:start position:0%
+could you know the temperature will vary
+according to whatever I like on the
+
+ align:start position:0%
+according to whatever I like on the
+ 
+
+ align:start position:0%
+according to whatever I like on the
+outside and the inside it's a lot
+
+ align:start position:0%
+outside and the inside it's a lot
+ 
+
+ align:start position:0%
+outside and the inside it's a lot
+smoother the the the the equilibrium
+
+ align:start position:0%
+smoother the the the the equilibrium
+ 
+
+ align:start position:0%
+smoother the the the the equilibrium
+tends to be to smooth out the Hills and
+
+ align:start position:0%
+tends to be to smooth out the Hills and
+ 
+
+ align:start position:0%
+tends to be to smooth out the Hills and
+Valleys you know if it's three here and
+
+ align:start position:0%
+Valleys you know if it's three here and
+ 
+
+ align:start position:0%
+Valleys you know if it's three here and
+then 55 here and three here and 55 here
+
+ align:start position:0%
+then 55 here and three here and 55 here
+ 
+
+ align:start position:0%
+then 55 here and three here and 55 here
+then in between it'll stay
+
+ align:start position:0%
+then in between it'll stay
+ 
+
+ align:start position:0%
+then in between it'll stay
+around whatever the average is 29 or
+
+ align:start position:0%
+around whatever the average is 29 or
+ 
+
+ align:start position:0%
+around whatever the average is 29 or
+something uh quite a bit is that but I
+
+ align:start position:0%
+something uh quite a bit is that but I
+ 
+
+ align:start position:0%
+something uh quite a bit is that but I
+can't have any other sources yeah if
+
+ align:start position:0%
+can't have any other sources yeah if
+ 
+
+ align:start position:0%
+can't have any other sources yeah if
+there was another source then of course
+
+ align:start position:0%
+there was another source then of course
+ 
+
+ align:start position:0%
+there was another source then of course
+that's making something special happen
+
+ align:start position:0%
+that's making something special happen
+ 
+
+ align:start position:0%
+that's making something special happen
+inside so my maximum principle is for no
+
+ align:start position:0%
+inside so my maximum principle is for no
+ 
+
+ align:start position:0%
+inside so my maximum principle is for no
+source and my maximum principle says if
+
+ align:start position:0%
+source and my maximum principle says if
+ 
+
+ align:start position:0%
+source and my maximum principle says if
+there's no Source then then uh every
+
+ align:start position:0%
+there's no Source then then uh every
+ 
+
+ align:start position:0%
+there's no Source then then uh every
+value is the a average of any circle
+
+ align:start position:0%
+value is the a average of any circle
+ 
+
+ align:start position:0%
+value is the a average of any circle
+around it and it all just it's smooth
+
+ align:start position:0%
+around it and it all just it's smooth
+ 
+
+ align:start position:0%
+around it and it all just it's smooth
+the equation is like smoothing things
+
+ align:start position:0%
+the equation is like smoothing things
+ 
+
+ align:start position:0%
+the equation is like smoothing things
+out yeah and we could derive that fact
+
+ align:start position:0%
+out yeah and we could derive that fact
+ 
+
+ align:start position:0%
+out yeah and we could derive that fact
+but I think maybe maybe that's a that's
+
+ align:start position:0%
+but I think maybe maybe that's a that's
+ 
+
+ align:start position:0%
+but I think maybe maybe that's a that's
+that's a nutshell um discussion but I
+
+ align:start position:0%
+that's a nutshell um discussion but I
+ 
+
+ align:start position:0%
+that's a nutshell um discussion but I
+guess I'm my conscience is telling me
+
+ align:start position:0%
+guess I'm my conscience is telling me
+ 
+
+ align:start position:0%
+guess I'm my conscience is telling me
+that I've got number two still to
+
+ align:start position:0%
+that I've got number two still to
+ 
+
+ align:start position:0%
+that I've got number two still to
+mention and let me tell you how number
+
+ align:start position:0%
+mention and let me tell you how number
+ 
+
+ align:start position:0%
+mention and let me tell you how number
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+works okay now I'm back to a source
+
+ align:start position:0%
+works okay now I'm back to a source
+ 
+
+ align:start position:0%
+works okay now I'm back to a source
+inside but not at the origin where I was
+
+ align:start position:0%
+inside but not at the origin where I was
+ 
+
+ align:start position:0%
+inside but not at the origin where I was
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+happy so the idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is do a mapping change the change to
+
+ align:start position:0%
+is do a mapping change the change to
+ 
+
+ align:start position:0%
+is do a mapping change the change to
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+variables that that bring that Source
+
+ align:start position:0%
+variables that that bring that Source
+ 
+
+ align:start position:0%
+variables that that bring that Source
+into the
+
+ align:start position:0%
+into the
+ 
+
+ align:start position:0%
+into the
+center so I going to change so I'm not
+
+ align:start position:0%
+center so I going to change so I'm not
+ 
+
+ align:start position:0%
+center so I going to change so I'm not
+going to do it but I'm going to say how
+
+ align:start position:0%
+going to do it but I'm going to say how
+ 
+
+ align:start position:0%
+going to do it but I'm going to say how
+to do it uh I I this is the XY plane
+
+ align:start position:0%
+to do it uh I I this is the XY plane
+ 
+
+ align:start position:0%
+to do it uh I I this is the XY plane
+with some Source at some point and the
+
+ align:start position:0%
+with some Source at some point and the
+ 
+
+ align:start position:0%
+with some Source at some point and the
+idea will be that I'll that I'll change
+
+ align:start position:0%
+idea will be that I'll that I'll change
+ 
+
+ align:start position:0%
+idea will be that I'll that I'll change
+to some new variables X of X and Y and Y
+
+ align:start position:0%
+to some new variables X of X and Y and Y
+ 
+
+ align:start position:0%
+to some new variables X of X and Y and Y
+of X and Y which will bring that point
+
+ align:start position:0%
+of X and Y which will bring that point
+ 
+
+ align:start position:0%
+of X and Y which will bring that point
+to the center so in the capital
+
+ align:start position:0%
+to the center so in the capital
+ 
+
+ align:start position:0%
+to the center so in the capital
+variables capital x capital Y that point
+
+ align:start position:0%
+variables capital x capital Y that point
+ 
+
+ align:start position:0%
+variables capital x capital Y that point
+will become 0 0 so I'll be in the in the
+
+ align:start position:0%
+will become 0 0 so I'll be in the in the
+ 
+
+ align:start position:0%
+will become 0 0 so I'll be in the in the
+capital x capital Y plane I'll be back
+
+ align:start position:0%
+capital x capital Y plane I'll be back
+ 
+
+ align:start position:0%
+capital x capital Y plane I'll be back
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+here which is great provided the
+
+ align:start position:0%
+here which is great provided the
+ 
+
+ align:start position:0%
+here which is great provided the
+equation didn't change on me right like
+
+ align:start position:0%
+equation didn't change on me right like
+ 
+
+ align:start position:0%
+equation didn't change on me right like
+I'm I'm I'm happy to think that that
+
+ align:start position:0%
+I'm I'm I'm happy to think that that
+ 
+
+ align:start position:0%
+I'm I'm I'm happy to think that that
+Source would be centered there but I
+
+ align:start position:0%
+Source would be centered there but I
+ 
+
+ align:start position:0%
+Source would be centered there but I
+want to use what I already knew and I
+
+ align:start position:0%
+want to use what I already knew and I
+ 
+
+ align:start position:0%
+want to use what I already knew and I
+can only do that if the equation didn't
+
+ align:start position:0%
+can only do that if the equation didn't
+ 
+
+ align:start position:0%
+can only do that if the equation didn't
+change so the trick the beauty is that
+
+ align:start position:0%
+change so the trick the beauty is that
+ 
+
+ align:start position:0%
+change so the trick the beauty is that
+the equation the pl equation doesn't
+
+ align:start position:0%
+the equation the pl equation doesn't
+ 
+
+ align:start position:0%
+the equation the pl equation doesn't
+change if your if these
+
+ align:start position:0%
+change if your if these
+ 
+
+ align:start position:0%
+change if your if these
+are real and imaginary parts
+
+ align:start position:0%
+are real and imaginary parts
+ 
+
+ align:start position:0%
+are real and imaginary parts
+of our analytic function if they're if
+
+ align:start position:0%
+of our analytic function if they're if
+ 
+
+ align:start position:0%
+of our analytic function if they're if
+they solve L pla's equation if the if
+
+ align:start position:0%
+they solve L pla's equation if the if
+ 
+
+ align:start position:0%
+they solve L pla's equation if the if
+the change of it I won't carry through
+
+ align:start position:0%
+the change of it I won't carry through
+ 
+
+ align:start position:0%
+the change of it I won't carry through
+that step but then so this is called a
+
+ align:start position:0%
+that step but then so this is called a
+ 
+
+ align:start position:0%
+that step but then so this is called a
+conformal mapping so this is the last
+
+ align:start position:0%
+conformal mapping so this is the last
+ 
+
+ align:start position:0%
+conformal mapping so this is the last
+word in the in the uh in the outline
+
+ align:start position:0%
+word in the in the uh in the outline
+ 
+
+ align:start position:0%
+word in the in the uh in the outline
+this is a a change of variables and it's
+
+ align:start position:0%
+this is a a change of variables and it's
+ 
+
+ align:start position:0%
+this is a a change of variables and it's
+called conformal that means what that
+
+ align:start position:0%
+called conformal that means what that
+ 
+
+ align:start position:0%
+called conformal that means what that
+means something like angles don't
+
+ align:start position:0%
+means something like angles don't
+ 
+
+ align:start position:0%
+means something like angles don't
+change and it's given by solute so if I
+
+ align:start position:0%
+change and it's given by solute so if I
+ 
+
+ align:start position:0%
+change and it's given by solute so if I
+can figure out a solution to the plaza
+
+ align:start position:0%
+can figure out a solution to the plaza
+ 
+
+ align:start position:0%
+can figure out a solution to the plaza
+equation that that for which this this
+
+ align:start position:0%
+equation that that for which this this
+ 
+
+ align:start position:0%
+equation that that for which this this
+particular point I get zero and zero
+
+ align:start position:0%
+particular point I get zero and zero
+ 
+
+ align:start position:0%
+particular point I get zero and zero
+that will move then in the new in the
+
+ align:start position:0%
+that will move then in the new in the
+ 
+
+ align:start position:0%
+that will move then in the new in the
+new variables my my source will be at
+
+ align:start position:0%
+new variables my my source will be at
+ 
+
+ align:start position:0%
+new variables my my source will be at
+the center point and then it'll be the
+
+ align:start position:0%
+the center point and then it'll be the
+ 
+
+ align:start position:0%
+the center point and then it'll be the
+log of and then the in the new variables
+
+ align:start position:0%
+log of and then the in the new variables
+ 
+
+ align:start position:0%
+log of and then the in the new variables
+it'll be x^2 +
+
+ align:start position:0%
+it'll be x^2 +
+ 
+
+ align:start position:0%
+it'll be x^2 +
+y^2 and capital Y over capital x
+
+ align:start position:0%
+y^2 and capital Y over capital x
+ 
+
+ align:start position:0%
+y^2 and capital Y over capital x
+I'm I'm uh touching here A whole subject
+
+ align:start position:0%
+I'm I'm uh touching here A whole subject
+ 
+
+ align:start position:0%
+I'm I'm uh touching here A whole subject
+of mathemat I mean a whole course of
+
+ align:start position:0%
+of mathemat I mean a whole course of
+ 
+
+ align:start position:0%
+of mathemat I mean a whole course of
+mathematics functions analytic functions
+
+ align:start position:0%
+mathematics functions analytic functions
+ 
+
+ align:start position:0%
+mathematics functions analytic functions
+functions of a complex variable it's a
+
+ align:start position:0%
+functions of a complex variable it's a
+ 
+
+ align:start position:0%
+functions of a complex variable it's a
+whole world and I think let's just open
+
+ align:start position:0%
+whole world and I think let's just open
+ 
+
+ align:start position:0%
+whole world and I think let's just open
+that door look in and close the door
+
+ align:start position:0%
+that door look in and close the door
+ 
+
+ align:start position:0%
+that door look in and close the door
+again because uh well it's very
+
+ align:start position:0%
+again because uh well it's very
+ 
+
+ align:start position:0%
+again because uh well it's very
+important but um well we don't have time
+
+ align:start position:0%
+important but um well we don't have time
+ 
+
+ align:start position:0%
+important but um well we don't have time
+for it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you oh I don't know I know I don't want
+
+ align:start position:0%
+you oh I don't know I know I don't want
+ 
+
+ align:start position:0%
+you oh I don't know I know I don't want
+to I yeah oh I didn't even say that I
+
+ align:start position:0%
+to I yeah oh I didn't even say that I
+ 
+
+ align:start position:0%
+to I yeah oh I didn't even say that I
+want to keep the boundary the same of
+
+ align:start position:0%
+want to keep the boundary the same of
+ 
+
+ align:start position:0%
+want to keep the boundary the same of
+course because I want to get back to
+
+ align:start position:0%
+course because I want to get back to
+ 
+
+ align:start position:0%
+course because I want to get back to
+this problem yeah so I'm so my my my
+
+ align:start position:0%
+this problem yeah so I'm so my my my
+ 
+
+ align:start position:0%
+this problem yeah so I'm so my my my
+clever my my conformal change of
+
+ align:start position:0%
+clever my my conformal change of
+ 
+
+ align:start position:0%
+clever my my conformal change of
+variables the idea is to and and I could
+
+ align:start position:0%
+variables the idea is to and and I could
+ 
+
+ align:start position:0%
+variables the idea is to and and I could
+write it down actually I'll put it in
+
+ align:start position:0%
+write it down actually I'll put it in
+ 
+
+ align:start position:0%
+write it down actually I'll put it in
+the notes the one that works it's it's
+
+ align:start position:0%
+the notes the one that works it's it's
+ 
+
+ align:start position:0%
+the notes the one that works it's it's
+in this section
+
+ align:start position:0%
+in this section
+ 
+
+ align:start position:0%
+in this section
+4.4 the the change of variables so
+
+ align:start position:0%
+4.4 the the change of variables so
+ 
+
+ align:start position:0%
+4.4 the the change of variables so
+that's the place
+
+ align:start position:0%
+that's the place
+ 
+
+ align:start position:0%
+that's the place
+to look for this topic so the idea is
+
+ align:start position:0%
+to look for this topic so the idea is
+ 
+
+ align:start position:0%
+to look for this topic so the idea is
+bring this guy into the center but leave
+
+ align:start position:0%
+bring this guy into the center but leave
+ 
+
+ align:start position:0%
+bring this guy into the center but leave
+the circle
+
+ align:start position:0%
+the circle
+ 
+
+ align:start position:0%
+the circle
+alone and uh people spent like you know
+
+ align:start position:0%
+alone and uh people spent like you know
+ 
+
+ align:start position:0%
+alone and uh people spent like you know
+lifetimes figuring out how to do that
+
+ align:start position:0%
+lifetimes figuring out how to do that
+ 
+
+ align:start position:0%
+lifetimes figuring out how to do that
+for different regions for a circle not
+
+ align:start position:0%
+for different regions for a circle not
+ 
+
+ align:start position:0%
+for different regions for a circle not
+not it's not too hard and and it's right
+
+ align:start position:0%
+not it's not too hard and and it's right
+ 
+
+ align:start position:0%
+not it's not too hard and and it's right
+there and it'll be in the on the web
+
+ align:start position:0%
+there and it'll be in the on the web
+ 
+
+ align:start position:0%
+there and it'll be in the on the web
+page but uh for other
+
+ align:start position:0%
+page but uh for other
+ 
+
+ align:start position:0%
+page but uh for other
+regions uh people
+
+ align:start position:0%
+regions uh people
+ 
+
+ align:start position:0%
+regions uh people
+you know like if you came up with a new
+
+ align:start position:0%
+you know like if you came up with a new
+ 
+
+ align:start position:0%
+you know like if you came up with a new
+region that you could move to a circle
+
+ align:start position:0%
+region that you could move to a circle
+ 
+
+ align:start position:0%
+region that you could move to a circle
+oh and then then oh I mentioned reman
+
+ align:start position:0%
+oh and then then oh I mentioned reman
+ 
+
+ align:start position:0%
+oh and then then oh I mentioned reman
+sorry there's so much in this subject if
+
+ align:start position:0%
+sorry there's so much in this subject if
+ 
+
+ align:start position:0%
+sorry there's so much in this subject if
+I get started uh
+
+ align:start position:0%
+I get started uh
+ 
+
+ align:start position:0%
+I get started uh
+reman there's a great theorem of reman
+
+ align:start position:0%
+reman there's a great theorem of reman
+ 
+
+ align:start position:0%
+reman there's a great theorem of reman
+probably the most famous one of the most
+
+ align:start position:0%
+probably the most famous one of the most
+ 
+
+ align:start position:0%
+probably the most famous one of the most
+famous theorems of his reman mapping
+
+ align:start position:0%
+famous theorems of his reman mapping
+ 
+
+ align:start position:0%
+famous theorems of his reman mapping
+theorem which says that any region can
+
+ align:start position:0%
+theorem which says that any region can
+ 
+
+ align:start position:0%
+theorem which says that any region can
+be mapped to a circle by one of
+
+ align:start position:0%
+be mapped to a circle by one of
+ 
+
+ align:start position:0%
+be mapped to a circle by one of
+these by one of
+
+ align:start position:0%
+these by one of
+ 
+
+ align:start position:0%
+these by one of
+these speak into that uh by one of these
+
+ align:start position:0%
+these speak into that uh by one of these
+ 
+
+ align:start position:0%
+these speak into that uh by one of these
+uh conformal
+
+ align:start position:0%
+uh conformal
+ 
+
+ align:start position:0%
+uh conformal
+mappings so if you can find there is one
+
+ align:start position:0%
+mappings so if you can find there is one
+ 
+
+ align:start position:0%
+mappings so if you can find there is one
+out there and if you can find it you can
+
+ align:start position:0%
+out there and if you can find it you can
+ 
+
+ align:start position:0%
+out there and if you can find it you can
+reduce to a problem that you already
+
+ align:start position:0%
+reduce to a problem that you already
+ 
+
+ align:start position:0%
+reduce to a problem that you already
+like and um you have the solution to
+
+ align:start position:0%
+like and um you have the solution to
+ 
+
+ align:start position:0%
+like and um you have the solution to
+your to your uh other to your given
+
+ align:start position:0%
+your to your uh other to your given
+ 
+
+ align:start position:0%
+your to your uh other to your given
+problem okay that's so I was going to
+
+ align:start position:0%
+problem okay that's so I was going to
+ 
+
+ align:start position:0%
+problem okay that's so I was going to
+comment this opens a beautiful world of
+
+ align:start position:0%
+comment this opens a beautiful world of
+ 
+
+ align:start position:0%
+comment this opens a beautiful world of
+of uh
+
+ align:start position:0%
+of uh
+ 
+
+ align:start position:0%
+of uh
+analysis but it's not it's a different
+
+ align:start position:0%
+analysis but it's not it's a different
+ 
+
+ align:start position:0%
+analysis but it's not it's a different
+world from
+
+ align:start position:0%
+world from
+ 
+
+ align:start position:0%
+world from
+computations if I give if you gave me
+
+ align:start position:0%
+computations if I give if you gave me
+ 
+
+ align:start position:0%
+computations if I give if you gave me
+ll's
+
+ align:start position:0%
+ll's
+ 
+
+ align:start position:0%
+ll's
+equation with some Source term and some
+
+ align:start position:0%
+equation with some Source term and some
+ 
+
+ align:start position:0%
+equation with some Source term and some
+boundary conditions chances are I would
+
+ align:start position:0%
+boundary conditions chances are I would
+ 
+
+ align:start position:0%
+boundary conditions chances are I would
+say okay is that on my little list of
+
+ align:start position:0%
+say okay is that on my little list of
+ 
+
+ align:start position:0%
+say okay is that on my little list of
+easy of of of perfect ones chances are
+
+ align:start position:0%
+easy of of of perfect ones chances are
+ 
+
+ align:start position:0%
+easy of of of perfect ones chances are
+no the region wouldn't if the region
+
+ align:start position:0%
+no the region wouldn't if the region
+ 
+
+ align:start position:0%
+no the region wouldn't if the region
+wasn't a circle it wouldn't be on my
+
+ align:start position:0%
+wasn't a circle it wouldn't be on my
+ 
+
+ align:start position:0%
+wasn't a circle it wouldn't be on my
+list well a square might be but but some
+
+ align:start position:0%
+list well a square might be but but some
+ 
+
+ align:start position:0%
+list well a square might be but but some
+other region wouldn't be so what would I
+
+ align:start position:0%
+other region wouldn't be so what would I
+ 
+
+ align:start position:0%
+other region wouldn't be so what would I
+do I would use finite differences or
+
+ align:start position:0%
+do I would use finite differences or
+ 
+
+ align:start position:0%
+do I would use finite differences or
+finite elements and that's so that's the
+
+ align:start position:0%
+finite elements and that's so that's the
+ 
+
+ align:start position:0%
+finite elements and that's so that's the
+scientific Computing part of these
+
+ align:start position:0%
+scientific Computing part of these
+ 
+
+ align:start position:0%
+scientific Computing part of these
+lectures that's coming next so what
+
+ align:start position:0%
+lectures that's coming next so what
+ 
+
+ align:start position:0%
+lectures that's coming next so what
+you're seeing here is like you could say
+
+ align:start position:0%
+you're seeing here is like you could say
+ 
+
+ align:start position:0%
+you're seeing here is like you could say
+the applied math the the math analysis
+
+ align:start position:0%
+the applied math the the math analysis
+ 
+
+ align:start position:0%
+the applied math the the math analysis
+part of lass's
+
+ align:start position:0%
+part of lass's
+ 
+
+ align:start position:0%
+part of lass's
+equation and it's amazing how far you
+
+ align:start position:0%
+equation and it's amazing how far you
+ 
+
+ align:start position:0%
+equation and it's amazing how far you
+can get but
+
+ align:start position:0%
+can get but
+ 
+
+ align:start position:0%
+can get but
+still a typical General problem would
+
+ align:start position:0%
+still a typical General problem would
+ 
+
+ align:start position:0%
+still a typical General problem would
+have a region you know funny shaped
+
+ align:start position:0%
+have a region you know funny shaped
+ 
+
+ align:start position:0%
+have a region you know funny shaped
+region the fuselage of a plane or the or
+
+ align:start position:0%
+region the fuselage of a plane or the or
+ 
+
+ align:start position:0%
+region the fuselage of a plane or the or
+the shape of any uh of of a missile and
+
+ align:start position:0%
+the shape of any uh of of a missile and
+ 
+
+ align:start position:0%
+the shape of any uh of of a missile and
+uh if you wanted to know the heat
+
+ align:start position:0%
+uh if you wanted to know the heat
+ 
+
+ align:start position:0%
+uh if you wanted to know the heat
+Distribution on that surface of that
+
+ align:start position:0%
+Distribution on that surface of that
+ 
+
+ align:start position:0%
+Distribution on that surface of that
+missile
+
+ align:start position:0%
+missile
+ 
+
+ align:start position:0%
+missile
+uh you couldn't it wouldn't be a circle
+
+ align:start position:0%
+uh you couldn't it wouldn't be a circle
+ 
+
+ align:start position:0%
+uh you couldn't it wouldn't be a circle
+and you would end up using finite
+
+ align:start position:0%
+and you would end up using finite
+ 
+
+ align:start position:0%
+and you would end up using finite
+differences or finite elements so that
+
+ align:start position:0%
+differences or finite elements so that
+ 
+
+ align:start position:0%
+differences or finite elements so that
+that's central part of scientific
+
+ align:start position:0%
+that's central part of scientific
+ 
+
+ align:start position:0%
+that's central part of scientific
+Computing how to solve lassus equation
+
+ align:start position:0%
+Computing how to solve lassus equation
+ 
+
+ align:start position:0%
+Computing how to solve lassus equation
+approximately by difference methods or
+
+ align:start position:0%
+approximately by difference methods or
+ 
+
+ align:start position:0%
+approximately by difference methods or
+finite element methods okay that's uh
+
+ align:start position:0%
+finite element methods okay that's uh
+ 
+
+ align:start position:0%
+finite element methods okay that's uh
+lecture nine completed lecture 10 as I
+
+ align:start position:0%
+lecture nine completed lecture 10 as I
+ 
+
+ align:start position:0%
+lecture nine completed lecture 10 as I
+mentioned on on the web page is going to
+
+ align:start position:0%
+mentioned on on the web page is going to
+ 
+
+ align:start position:0%
+mentioned on on the web page is going to
+go back to onedimensional to those
+
+ align:start position:0%
+go back to onedimensional to those
+ 
+
+ align:start position:0%
+go back to onedimensional to those
+special matrices that we started with
+
+ align:start position:0%
+special matrices that we started with
+ 
+
+ align:start position:0%
+special matrices that we started with
+and uh really try to understand them
+
+ align:start position:0%
+and uh really try to understand them
+ 
+
+ align:start position:0%
+and uh really try to understand them
+okay so we're at 3:15 so 3:30 for that
+
+ align:start position:0%
+okay so we're at 3:15 so 3:30 for that
+ 
+
+ align:start position:0%
+okay so we're at 3:15 so 3:30 for that
+thanks
\ No newline at end of file
diff --git a/8dTMUigqBHM.txt b/8dTMUigqBHM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e12978e1bf287910ef5a258858696046ebad77fe
--- /dev/null
+++ b/8dTMUigqBHM.txt
@@ -0,0 +1,4045 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+SAMAN AMARASINGHE: Today I'm
+going to talk a little bit
+
+about computer architecture.
+
+And how computer architecture
+impacts performance
+
+engineering.
+
+So the main part of this is
+going through a long overview
+
+of the Pentium, the Nahalem
+architecture that in the
+
+machines that you guys
+are using, which
+
+is hot off the press.
+
+Six core processor that's
+out there now.
+
+And then I will talk a little
+bit about profiling a program.
+
+And then the next lecture, the
+TAs are going to demonstrate
+
+how to use some of those
+profiling tools that you guys
+
+are supposed to use for
+the project two.
+
+And I guess the project two will
+probably appear, since we
+
+had a delay, so probably
+be up here 24 delayed.
+
+We'll release the project,
+too, up there.
+
+And then at the end of the talk,
+end of the lecture, I'm
+
+going to talk about a little
+bit of example.
+
+Go to some program and show what
+you can gain by looking
+
+at things like profiling,
+and what
+
+information that you gain.
+
+Just kind of do a
+high level view.
+
+So let's start something.
+
+So how many of you have had
+a chip in your hand.
+
+Microprocessor in your hand.
+
+Some.
+
+There's some people
+who haven't.
+
+So I brought some show
+and tell things.
+
+So what I'm going to do
+is pass them around.
+
+And there are two things that
+are actually very valuable
+
+that I want to tell you and then
+make sure that they don't
+
+get damaged.
+
+So this is a Pentium 3 that's
+already in a big
+
+heat sink in there.
+
+So you can't see that much, but
+they're really cute and
+
+they created a hologram of the
+chip and put it there so you
+
+can catch, I guess, people who
+are trying to use counterfeit
+
+and stuff like that.
+
+So this is MDK 6 with
+the packaging.
+
+I'm going to send it
+around in there.
+
+And this is a Pentium Pro.
+
+Normally what happens is that
+when the first dye comes out,
+
+this is humongous,
+giganiticized.
+
+But after a couple of
+generations, what you do is
+
+you take the same circuit and
+you shrink it and shrink it.
+
+This is probably what
+two shrinks--
+
+so the actual dye right now is
+very small because this is
+
+copper [UNINTELLIGIBLE PHRASE]
+
+later process that things
+have been shrunk.
+
+This is a Core Two Duo
+So I think there's a
+
+two cores in there.
+
+So I didn't want to bring
+anything newer because those
+
+chips are darn expensive, and
+if you touch it, basically
+
+just static will basically
+destroy the process.
+
+So these are something that
+came out of things that
+
+doesn't work.
+
+The next two things.
+
+These are--
+
+I really need to get this
+[UNINTELLIGIBLE] because these
+
+are like the only thing
+that's the one
+
+available in this world.
+
+Basically there's only
+one of item.
+
+So at MIT, we build a process a
+couple of years ago called a
+
+row processor.
+
+So here's a row dye before
+it's being mounted.
+
+So this is what comes out after
+all the fabrication,
+
+before it goes into this
+mounting with all the pins.
+
+If you look at the top of this
+one, what do you see?
+
+It's all these dots, which
+are basically where
+
+all the pins go.
+
+So you don't actually even see
+inside the dye in this one.
+
+However, then you pay a bunch
+of money to these people who
+
+go and grind that chip.
+
+You take a real working chip and
+you grind it, and expose
+
+insides of the chip.
+
+So this is a ground chip that's
+
+exposed the metal layering.
+
+In fact, this you can see real
+circuits in the chip.
+
+So I don't think anybody has the
+mission that's required to
+
+see the transistors or
+even the circuits.
+
+But it's kind of interesting
+to see.
+
+So here are these two
+things, so some show
+
+and tell like that.
+
+Ah-ha.
+
+And this.
+
+This is entire reason that
+microprocessor not getting
+
+faster anymore.
+
+Because this is one humongo heap
+thing that you put in the
+
+modern machines, and there's a
+huge fan that goes above that.
+
+And you can't keep building
+larger and larger heat things
+
+to get the heat out.
+
+And so that this why the heat
+is paramount, and that's why
+
+we can't run 4 gigahertz,
+10 gigahertz process.
+
+We are thick into the current
+kind of gigahertz train, and
+
+then we [UNINTELLIGIBLE]
+
+multiple cores.
+
+So it's a big, humongo block
+in there, and then some
+
+actually might even have
+a bigger block.
+
+So while this go around, let's
+start the lecture.
+
+So computer architecting
+includes
+
+many different things.
+
+You are doing instructions,
+memory, IEO Bus, disk systems,
+
+GPU, graphics, all
+of those things.
+
+But we are not getting
+into beyond
+
+instruction and memory system.
+
+So we are going to focus on
+that, but if you really want
+
+to understand the full end to
+end performance, you have to
+
+worry about all those
+other things.
+
+So that said, let's go into
+instructions and memory.
+
+So here is the Nehalem
+processor.
+
+And there's a beautiful
+picture of the
+
+processor in the left.
+
+This as kind of the role
+chip that I'm showing.
+
+They have ground out the upper
+layers and showed some of the
+
+layers in there.
+
+So that's what you get when
+you buy the Nehalem.
+
+And this very complicated
+diagram in the right side,
+
+it's an abstract notion of
+what's happening inside.
+
+So what you do is go a little
+bit into this [UNINTELLIGIBLE]
+
+diagram, and trying to
+understand what impact it
+
+would have on you.
+
+This is not architecture class,
+but you, as trying to
+
+get performance, has to make
+sure all these components
+
+works pretty well.
+
+That said, it's very hard to
+understand in a modern
+
+microprocessor exactly
+what's going on.
+
+Not even Intel understand
+what's going
+
+on most of the time.
+
+And so a lot of things
+[UNINTELLIGIBLE].
+
+So you can't ask tell
+me exactly what
+
+happened or get there.
+
+So you can be fussy.
+
+On the other hand, being fussy
+means there's a level of
+
+abstraction that you
+have to live with.
+
+And what that means is when
+something hit their head very
+
+hard, and have a really bad
+situation you can see that and
+
+you can react to that.
+
+But there are a lot of small
+things that happen.
+
+These things interact in
+very complex ways.
+
+So you don't understand exactly
+the minor detail
+
+what's going on in these
+microprocessor for a given
+
+application.
+
+A lot of different things might
+work different ways.
+
+So that's it.
+
+So if we look at what you learn
+from 004, so what that
+
+means is instruction.
+
+You have here two
+instructions.
+
+One after the other.
+
+So if the instructions
+take [UNINTELLIGIBLE]
+
+cycle.
+
+So we see the
+non-[UNINTELLIGIBLE]
+
+method.
+
+So you look at why it's probably
+taking five cycles.
+
+So that's because it's doing
+different things.
+
+You are doing instruction fetch,
+instruction decode,
+
+after that execute.
+
+Then you do some memory
+[UNINTELLIGIBLE] and then find
+
+the right packet in there.
+
+So you do all those things
+[UNINTELLIGIBLE]
+
+instruction, and then
+you start the next
+
+[UNINTELLIGIBLE] cycle.
+
+Of course, this is
+very necessary.
+
+So the first two people
+[UNINTELLIGIBLE].
+
+After I do instruction fetch,
+that logic that's doing
+
+instruction fetch is not doing
+anything for a while.
+
+Why don't I start the next
+instruction phase immediately
+
+because you are doing the same
+circuit, and then recycle,
+
+that's so it can go do the next
+thing, and next thing,
+
+and next thing.
+
+And by doing that, well I can
+basically recycle, I can get
+
+the instruction through
+the system.
+
+So this looks very nice and
+simple and you can get.
+
+So what are they
+choosing here?
+
+Is the world this
+nice and simple?
+
+No.
+
+OK, what might happen?
+
+AUDIENCE: [INAUDIBLE PHRASE]
+
+SAMAN AMARASINGHE: You have a
+lot of issues that normally
+
+cause hazards.
+
+So there could be three
+different type of hazard.
+
+There's a thing called
+structural hazard.
+
+What you are trying to do is
+attempt to use the same
+
+hardware, do two things, but
+there's only one hardware.
+
+You can't get two things done.
+
+One has to be after another.
+
+And there's a thing called
+data hazards.
+
+That means you're trying to
+run these things, one now
+
+another, but in logically.
+
+They have to run sequence
+serially.
+
+So that means that's a data
+dependence, I'll get into,
+
+that makes it impossible to make
+these things run in the
+
+pipeline fashion.
+
+And finally, this control has
+things like branches and
+
+things like that,
+[UNINTELLIGIBLE]
+
+interfere with that.
+
+So let me get a little
+bit detail down here.
+
+So the first thing we have is
+what we call data hazard.
+
+I will talk about two
+different hazards.
+
+So before I go there, I will
+share a little bit about this
+
+assembly representation.
+
+In two lectures, you're going
+to get a more deep drilling
+
+into the how to go from
+C to Assembly.
+
+But before that, so what this
+instruction says, this is the
+
+normal x86 form.
+
+We are doing add long.
+
+Add in to the values in this
+rbx and rax and put the
+
+results back into rax.
+
+So you are doing rbx plus rax
+and get the result into rax.
+
+You are subjecting rax
+with rcx and put the
+
+results into rcx.
+
+So basically all the rest of
+the results are in the
+
+right-hand side.
+
+Two [UNINTELLIGIBLE]
+
+are basically the first
+and second.
+
+So the last one gets
+read and modified.
+
+So that's the way
+it's weighted.
+
+So while you have two is--
+
+question?
+
+AUDIENCE: [INAUDIBLE PHRASE]
+
+SAMAN AMARASINGHE: Instruction,
+yeah.
+
+It's different concept.
+
+The second instruction is data
+dependent, of course.
+
+What's happening is I am writing
+this value here, which
+
+will be read by this guy here.
+
+So I write something
+and the next
+
+instruction is reading that.
+
+The problem is it's the right
+thing must not be available
+
+until very late in
+the pipeline.
+
+So they cannot execute
+simultaneously and all that
+
+thing basically of
+this dependence.
+
+This is called basically read
+after write, because I'm going
+
+to read after it's
+been written.
+
+And if you look at the pipeline
+here, what happens is
+
+the write happens here, and the
+next feed has to happen
+
+somewhere down here.
+
+So until this one, this
+slide [UNINTELLIGIBLE]
+
+so this status has to get
+delayed after this point.
+
+This make sense?
+
+Because I'm trying to in here
+read something that's not
+
+going to be produced for
+two more clock cycles.
+
+So that's not available
+and I can't do that.
+
+Make sense?
+
+OK.
+
+So this next cycle dependence
+is called name dependence.
+
+That's the dependence
+and anti-dependence.
+
+Basically what it's doing is two
+instructions are using the
+
+same register.
+
+And because of that I can't
+start to see the radius there
+
+until the other one switches
+off with the register.
+
+So in here, what's happening
+here is I am
+
+subtracting rax and rbx.
+
+I'm putting the value in rbx.
+
+And here I am adding rcx to
+rax, and basically start
+
+putting the value in rax.
+
+The problem here is I cannot
+modify rax before this guy has
+
+[UNINTELLIGIBLE]
+
+the value in here.
+
+So that means I'm trying to go
+modify it, and say no, no, no.
+
+You can't touch it because
+somebody will still want to
+
+get the value, and I can't
+go destroy the value.
+
+And I had to [UNINTELLIGIBLE].
+
+That's the first type of what
+you call anti-dependence.
+
+And because of this, you
+both are using rax.
+
+There's no real data movement,
+but it basically
+
+has the same space.
+
+I had to wait till the other
+person can be evicted before I
+
+can read that register.
+
+So these are called write
+after read hazard.
+
+The other type of dependence is
+called output dependence.
+
+So I am updating rax twice, and
+of course in this simple
+
+example we can probably even
+drop this instruction because
+
+it doesn't matter because
+I'm re-writing it.
+
+But if there's something in
+between also reading, what
+
+happens is I can't do
+this in wrong order.
+
+The last value that updated has
+to be this instruction.
+
+So we had to make sure this
+instruction happens after this
+
+instruction.
+
+So we have a dependence, so
+there's some ordering in here
+
+that has to be maintained.
+
+And this is call write
+after write hazard.
+
+So instructions that have medium
+dependence, we can
+
+actually get rid of the
+dependent by what we call
+
+register renaming.
+
+So everybody uses rax, so that's
+kind of artifact of
+
+good old inter [UNINTELLIGIBLE]
+
+architecture sometimes
+[UNINTELLIGIBLE]
+
+when register, so you have to
+use the same register for
+
+many, many things.
+
+So in a modern--
+
+inside the hardware
+there's what we
+
+call a register renaming.
+
+You have lots more slots for the
+same registers, and even
+
+when you're using rax, this is
+an old one, this is a new one,
+
+use a different location
+for the new one.
+
+So I can do renaming.
+
+And then basically hardware
+can get rid of that.
+
+The next interesting thing
+is control hazard.
+
+So here what we see, if you had
+this kind of a loop, s1,
+
+it's control dependent on p1.
+
+So we can't do s1 until
+p1 is done.
+
+Or s2 until p2 is done.
+
+So we are [UNINTELLIGIBLE]
+
+the p1 condition is
+[UNINTELLIGIBLE]
+
+before you can do s1 and
+[UNINTELLIGIBLE]
+
+for the next one.
+
+So the interesting thing is
+control dependence also we can
+
+get rid of it by doing
+speculation.
+
+So the idea there what hardware
+does is it will say
+
+wait a minute.
+
+I know I have to wait till p1 is
+[UNINTELLIGIBLE] to do s1.
+
+But I'm going to do s1 anyway.
+
+I will just go to s1,
+speculatively.
+
+And then at the end of doing
+that, at some time when p1 is
+
+calculated, and I know
+what the p1, I
+
+said did I do it right?
+
+If I did it right, I'm good.
+
+If I did something wrong,
+I have done some
+
+[UNINTELLIGIBLE]
+
+that is not useful for that.
+
+Question?
+
+AUDIENCE: [INAUDIBLE PHRASE]
+
+SAMAN AMARASINGHE: So what
+happens is there's this thing
+
+called a write buffer.
+
+The complex thing is at the
+end of the day, the
+
+instructions have to
+be get committed in
+
+the order they arrive.
+
+So before committing, you keep
+the state in buffers without
+
+[UNINTELLIGIBLE]
+
+into the main one.
+
+AUDIENCE: [INAUDIBLE PHRASE]
+
+SAMAN AMARASINGHE: So right
+back into memory doesn't
+
+happen until the commit point.
+
+But when you read something,
+before reading the memory, say
+
+OK, I have updated something,
+is it in the right buffer?
+
+So I read things from the
+right buffer in there.
+
+So you had to go in
+order commitment.
+
+Because you can't do out of
+order commitment, that can do
+
+crazy things.
+
+You do in order commitment, but
+inside the metrics things
+
+can go easier.
+
+I'm just kind of jumping
+the gun a little bit.
+
+So in a modern Nehalem
+processor, these are kind of
+
+Intel [UNINTELLIGIBLE], so you
+don't know exactly what it is.
+
+In some place it says it
+has 16 clock cycles.
+
+So it says it might be 16
+stages of pipeline.
+
+And another place it says 20
+to 24 stages of pipeline.
+
+OK, if you work for Intel and
+sign the NDA you will get the
+
+exact number.
+
+But it doesn't matter.
+
+It's a lot of pipeline
+stages, so that's
+
+all you need to know.
+
+So what happens is if you are
+doing this in sort of five
+
+stage, like what you did
+in probably beta.
+
+You do instruction decode,
+instruction queue, pre-record
+
+queue, decode, register rename,
+
+and allocate registers.
+
+And then there's thing called
+reservation and stations that
+
+wait for when data's available
+to execute that instruction.
+
+And then execute, and then
+basically go there.
+
+This is what normally
+instruction life would be, if
+
+everything goes one after
+another after another.
+
+So what to get out of this is
+the pipelines are long.
+
+So pipeline stores and stuff
+can be expensive.
+
+So the other thing you can
+do in abstract way
+
+is do multiple issue.
+
+So if you do pipeline, what
+happens is you do one at a
+
+time so you can use the pipeline
+stages nicely.
+
+How about instead of having one
+unit, if you have integer
+
+unit and a floating
+point unit.
+
+And every clock cycle you
+can basically abstract.
+
+You could say look, I'm taking
+interger instruction, I'm
+
+taking floating point
+instruction, and take them
+
+both together [UNINTELLIGIBLE].
+
+And then whala, at the end of
+the day in one clock cycle I
+
+can [UNINTELLIGIBLE]
+
+two instructions, one integer,
+one floating point, if you
+
+have two different
+sets in there.
+
+So this is also very nice.
+
+You can get a lot of what we
+call super scaler performance.
+
+However, it's called instruction
+level parallelism.
+
+There's a lot of problems, also
+things that you worry.
+
+Well first of all, you have to
+have enough instruction in
+
+level parallel.
+
+Because the instruction you get
+is the sequence history,
+
+and you see one after another.
+
+I mean you write your
+program and compile.
+
+It looks like you run one
+instruction, finish it, run
+
+another, run another.
+
+So in order to form parallely,
+you're to find things.
+
+You can actually do parallel.
+
+That takes time.
+
+And of course, between hardware
+and software you are
+
+to maintain that preserve order
+of instructions, because
+
+you want to make sure that it
+looks like and it feels like
+
+you ran one after another
+after another.
+
+You don't want things to run in
+a haphazard way and create
+
+arbitrary result.
+
+And so you have to, again,
+things like this, data
+
+dependences, control dependences
+have to be
+
+satisfied when you're getting
+this parallelism.
+
+So data dependency, there's a
+hazard, and determining which
+
+order you can run things.
+
+So for example, output
+dependence.
+
+Say look, I can't just
+run them parallel.
+
+I have to make one after
+another after another.
+
+You're to get all those
+things done.
+
+And also if you're lot of
+dependency kind of gives you
+
+bounds, how much parallelism
+you can get.
+
+If things are all one dependent
+against one after
+
+another, you can't run
+them parallel.
+
+You have to wait to run
+things to another one.
+
+So by looking at data
+dependence, as you can figure
+
+out, OK look, did I get good
+performance, good ILT or not?
+
+So what we want to do is exploit
+this parallelism like
+
+we see in the program order.
+
+And basically make sure that
+you always get the
+
+same result on that.
+
+One way of getting parallelism
+that is in modern process is
+
+called multimedia instruction.
+
+It's called SIMD in academic
+circle, something like Single
+
+Instruction Multiple Data, and
+it's called data level
+
+parallelism, and Intel, of
+course, has to give the
+
+[UNINTELLIGIBLE] name
+they call SSE, they
+
+just call it MMX.
+
+So the idea there is
+look, they are
+
+building this wide measure.
+
+They can easily build 128
+bit wide register.
+
+But you most probably don't
+need 128 bit data, because
+
+that's too big.
+
+But they can build this large.
+
+And most will tell you about
+happy with about 32 bit data.
+
+So what?
+
+[UNINTELLIGIBLE]
+
+wait a minute.
+
+You build this wide thing.
+
+But you can chop it into four
+pieces or eight pieces or two
+
+pieces, what you want.
+
+So here we chop that large
+thing into four pieces.
+
+And then what you can do is in
+a single instruction, you can
+
+instead of doing one large add,
+the same type of adder,
+
+you can add four separate
+things.
+
+Four small parts.
+
+So you're assuring add, but
+instead of adding 228 bit
+
+data, what you are doing is
+adding here, four 32 bit data.
+
+The entire architecture
+looks very identical
+
+to an 228 bit data.
+
+It's basically to remember
+your double
+
+004, it's like a carry.
+
+Then just have to
+come the carry.
+
+You don't carry from here
+to here, and do that.
+
+So this is you're loading this
+large chunk, and you are just
+
+working on these things.
+
+And whala, by doing that,
+having the same kind of
+
+circuitry, you get much
+better parallelism.
+
+And if you have like 8 bit data,
+boy, you can get lots of
+
+parallelism.
+
+So there's all these multiple
+instructions in there.
+
+And so what you can do is you
+can have a loop like this.
+
+So you can, in every situation,
+you can add the I
+
+to BI, and create pretty
+good [UNINTELLIGIBLE].
+
+So you can do one at a time.
+
+But assume you have
+32 bit values.
+
+Instead of doing-- single
+instruction you can load 0 to
+
+8 3 in one go.
+
+B0 to BC in one go.
+
+Just do the add of all four in
+one, go [UNINTELLIGIBLE].
+
+So in single time you get
+four things done.
+
+So this is really cool.
+
+And if you remember my first
+lecture, we showed this matrix
+
+multiplier.
+
+If you get [UNINTELLIGIBLE]
+
+in there, you get a lot less
+instructions executed.
+
+We got a nice [UNINTELLIGIBLE].
+
+So I'm going down, so the top
+path I'm showing, the C code--
+
+for that loop, and then the
+bottom half in there, I'm
+
+showing the normal
+assembly that we
+
+[UNINTELLIGIBLE], what you see.
+
+And once you start understanding
+assembly a
+
+little bit more, you can go
+ahead and read this and see
+
+what's going on.
+
+And then if you
+[UNINTELLIGIBLE], you get a
+
+humongous beast like this.
+
+This has unrolled
+[UNINTELLIGIBLE], whatever.
+
+And this is the kind of code
+that we generated by
+
+[UNINTELLIGIBLE].
+
+And that's just much,
+much faster than
+
+the one on the left.
+
+Any questions so far?
+
+OK.
+
+So when we have this superscalar
+[UNINTELLIGIBLE],
+
+with multiple execution, so what
+you can do is in a clock
+
+cycle, you can do
+a lot of things.
+
+So in the [UNINTELLIGIBLE]
+processor, you have basically
+
+six things, six execution things
+that can happen in one
+
+clock cycle.
+
+It's not the same thing, so
+you can do a data store.
+
+You can store address, load
+address from there, and then
+
+you can do three different
+type of executions.
+
+There are three units in here.
+
+In here you can do either
+integer or SSE, add or move
+
+instruction, this unit can do
+this kind of instruction, you
+
+can have a floating point
+add-in around here.
+
+This one needs to also have this
+bunch of different things
+
+you can do.
+
+So this complex hardware, we'll
+kind of figure out, OK,
+
+if you have these instructions,
+figure out what
+
+of these [UNINTELLIGIBLE]
+
+are available.
+
+If the instruction is able to
+execute, it will put it into
+
+one of these and het
+the results out.
+
+So if you're lucky, what you
+can see is, you might get
+
+about six instructions
+going each cycle.
+
+So if you look at the mesh
+here, what we call clock
+
+[UNINTELLIGIBLE] instruction,
+it could be 1/6.
+
+If you're lucky.
+
+If you can run the mesh into
+the metal, that means
+
+everything is working
+all the time.
+
+It's very hard to find that
+kind of program, but
+
+[UNINTELLIGIBLE]
+
+can get something like that.
+
+That's really cool.
+
+So what happens is to get this
+thing, they do things called
+
+out-of-order instruction.
+
+So what that means is, issuing
+this varying number of
+
+instructions in the clock,
+in here, in the Nehalem
+
+processor, you can store 128
+instructions in this core
+
+instruction buffer.
+
+[INAUDIBLE]
+
+better name than instruction
+buffer.
+
+If you can see that, [INAUDIBLE]
+very far.
+
+But [INAUDIBLE] up
+there, sorry.
+
+Here.
+
+It's called reservation
+stations.
+
+So when you put it in, all
+those [UNINTELLIGIBLE],
+
+reformation [UNINTELLIGIBLE],
+ready to get, and the minute
+
+it becomes available, that means
+all the data is ready
+
+for it to run, you can basically
+issue that and run.
+
+So what they're doing is,
+in these hundreds of
+
+instructions, you're figuring
+out the patterns you can run.
+
+And a minute some part is
+available, the data becomes
+
+available, you can run that.
+
+And so that means the program
+might have instructions in
+
+certain order.
+
+It gets executed in very
+different orders than what the
+
+program has.
+
+So that's what call you
+can give things like
+
+[UNINTELLIGIBLE]
+
+register, [UNINTELLIGIBLE]
+dependencies, [UNINTELLIGIBLE]
+
+execution.
+
+And sometimes you might
+run speculator.
+
+You might not know.
+
+You might have the data, but
+there might be controlled
+
+dependence.
+
+You might not know that it's
+actually is supposed to
+
+happen, but it says
+wait a minute, I
+
+have execution available.
+
+It's not doing anything.
+
+OK, let's run it and keep the
+results, and if it is actually
+
+useful, we'll use it.
+
+Otherwise, we'll
+throw it away.
+
+You can do things like that.
+
+And that's a speculation.
+
+So another type of
+speculation--
+
+speculation mostly means, you
+want to do something, but you
+
+don't know whether
+you can do it.
+
+So how do you go about
+doing that?
+
+The way that interprocess and
+modern processor do, is they
+
+do a lot of predictions.
+
+It has like this is
+[UNINTELLIGIBLE] say, look at
+
+the crystal ball and say,
+aha, this is the future.
+
+And it does that
+[UNINTELLIGIBLE]
+
+really many things.
+
+So it does things like branch
+prediction, value prediction,
+
+prefetching.
+
+So it says, aha, I don't know
+where you're going, but I
+
+think you are going home
+after the class.
+
+And then probably if I said
+something like this, it's
+
+probably right for most
+of the people.
+
+And actually, no, in this class,
+most of you, again,
+
+will probably go to sleep after
+the class, because of
+
+the project.
+
+So if I do that probably I do
+a very good prediction.
+
+How many of you are going to go
+to sleep after the class?
+
+Huh, my prediction
+is not that good.
+
+OK.
+
+We'll see.
+
+So you can go all these kinds
+of things, identify normal
+
+behavior programs to
+deal with that.
+
+Ad what prefetching says is,
+if I look at what you have
+
+been taking from the money,
+there are some patterns, and
+
+I'm expecting you to
+[UNINTELLIGIBLE]
+
+that pattern, and I will
+basically get the data, even
+
+though you don't ask for it,
+because I'm expecting you to
+
+be doing that.
+
+It's like a very good butler who
+can really think, you ask
+
+something, have that ready
+for you, basically.
+
+So by doing that, you can get
+much better parallelism,
+
+because now you're not waiting
+for that to be sure
+
+that you can do it.
+
+You're just kind of doing this,
+assuming you might be
+
+using it, and if you do it
+really well, you're actually
+
+going to use it.
+
+And that will be useful.
+
+So for example, even things
+like value prediction.
+
+Value prediction says,
+[UNINTELLIGIBLE]
+
+to get out, you know when you
+do this complex calculation,
+
+most of the time,
+data is zero.
+
+You multiply and add a lot of
+zeroes, and if you're doing
+
+spreadsheets, all it is
+[UNINTELLIGIBLE] calculations.
+
+So if I don't know the value,
+let me assume it's 0.
+
+And that actually works
+most of the time.
+
+Or you look at the last couple
+of times, what has happened to
+
+that [UNINTELLIGIBLE],
+and there,
+
+let me predict something.
+
+And people to find these kind
+of things that are a lot of
+
+patterns in [UNINTELLIGIBLE]
+program.
+
+And if it works, that's
+really great.
+
+So in speculation, what you do
+is first issue and execute.
+
+As if the branch was--
+
+I already knew where it is
+going, just by using the
+
+prediction.
+
+And if I just know dynamic
+scheduling, I am only doing
+
+[UNINTELLIGIBLE]
+
+issues, I am not going to
+execute until I know
+
+everything is [UNINTELLIGIBLE].
+
+So it's speculation goes
+one step beyond.
+
+It's what we call a data
+flow execution
+
+model, the dynamic schedule.
+
+And that means, the minute the
+data is ready and everything
+
+is ready, you can execute, even
+though it might not mean
+
+the same mode of the program.
+
+It might be much later
+instruction.
+
+But implicitly, you
+can execute that.
+
+So again, the [UNINTELLIGIBLE]
+
+pipeline, you can do
+20 to 24 stage or
+
+16, whatever is correct.
+
+The other thing it does is
+this crazy thing called
+
+micro-ops that puts everybody
+out to a loop.
+
+So what happened was-- this
+is kind of historical--
+
+Intel, a long time ago, came up
+with the x86 architecture.
+
+They came up with this
+instruction set.
+
+That instruction set is called
+a CISC instruction set.
+
+It's a complex instruction
+set architecture.
+
+What that means is there are
+these instructions there are
+
+that are really,
+really complex.
+
+You can move an entire string
+from one place to another in
+
+one instruction.
+
+The problem is, most
+instructions cannot
+
+be done in one cycle.
+
+So what modern [UNINTELLIGIBLE]
+
+did was, they built a
+[UNINTELLIGIBLE] compiler into
+
+the hardware.
+
+So what happens inside this
+process is, take this CISC
+
+instruction and compile them
+down to these particular
+
+micro-operations, that each
+operation is small can be done
+
+in basically one cycle.
+
+So it's doing this
+mapping in there.
+
+And then inside the computer,
+it's basically
+
+dealing with micro-ops.
+
+So up to here, it's dealing with
+these long instructions,
+
+and here it's precoding and
+decoding into micro-ops.
+
+So after that, so what that
+means, every cycle, it can
+
+issue 6 micro-ops.
+
+So there might be 6 instructions
+you know, 3, or
+
+even 1, depending on how many
+micro-ops [UNINTELLIGIBLE].
+
+So if you look at instruction
+manual in the
+
+[UNINTELLIGIBLE], you can
+see how many micro-op
+
+[UNINTELLIGIBLE] instruction
+it's going into, and if it's
+
+large, that means those
+instructions are slow.
+
+And you can have this 120
+micro-op waiting to be
+
+executed, sitting in this
+reservation station.
+
+Basically, they are
+waiting there.
+
+The minute the data is
+available, and then a slot
+
+available, it will go down, get
+executed, and come back.
+
+So branch prediction,
+basically--
+
+the problem with branches is
+if you have this very nice
+
+pipeline, what happens is,
+branch target is not known
+
+until this target
+detection time.
+
+Where is my mouse?
+
+OK.
+
+Until this point, I don't know
+whether the branch, where I am
+
+supposed to go.
+
+And so how do I go ahead and get
+the instruction, because I
+
+don't know where I'm going
+until this point.
+
+Even worse, I might not
+even know address.
+
+Some [UNINTELLIGIBLE]
+
+you are going AOB, you are
+taken or not taken.
+
+But sometimes there might
+be [UNINTELLIGIBLE]
+
+branches.
+
+I don't even, if I'm returning
+the return
+
+address in the stack.
+
+Until I go fit the stack and
+load it and all those things,
+
+I don't know where I'm
+going, so I had to
+
+wait until this point.
+
+So if I do it, basically
+I have to
+
+wait until this pipeline.
+
+All these things are
+going to stalled.
+
+Nothing happens in here.
+
+This is first stage.
+
+You can have a interested
+pipeline.
+
+You are waiting 20 stages, just
+stalled, doing nothing.
+
+And then there's superscalar
+plus 20.
+
+So that means 20 cycles without
+the [? 6 issues ?]
+
+you can do.
+
+So 6 plus 20 is 120 possible
+instructions wasted, and it's
+
+a lot of waste.
+
+So you don't want to do that.
+
+So what you do is, you build a
+predictor to figure out which
+
+direction the brand is going.
+
+And depending on what the
+predictor do, and the neat
+
+thing is, these days, these
+predictions are
+
+really, really good.
+
+They can predict up to 99 points
+plus [UNINTELLIGIBLE]
+
+where you're going.
+
+So it's like me telling you,
+you guys are all going to
+
+sleep afterwards, and this
+is going to sleep on me.
+
+So what you can predict,
+I will say, aha!
+
+I tell you, you are going
+in that direction.
+
+This is like going to
+[UNINTELLIGIBLE].
+
+I think you're going
+that direction, and
+
+then you just go there.
+
+And 99% of the time, you're OK,
+and when [UNINTELLIGIBLE]
+
+finally decided, you can say,
+oh, that was slight.
+
+If you're wrong, you squash
+everything and restart.
+
+And so modern predictors are
+this very complicated beast.
+
+It looks at things like what
+happened previously.
+
+It looks at [UNINTELLIGIBLE]
+call stack where are the call
+
+stack, what went into
+the call stack.
+
+And then when you're returning,
+you can predict
+
+where we might be returning.
+
+A lot of different things go in
+there, and in fact, we see
+
+the core microarchitecture that
+came before Nehalem's
+
+predictor, and Nehalem
+[UNINTELLIGIBLE], oh, it even
+
+has more things, and so it's
+even more different.
+
+So these guys are doing
+these complex things.
+
+What that means is, sometimes
+it affects program in a way
+
+that you think, oh, huh, this is
+something that I don't know
+
+what might happen.
+
+[UNINTELLIGIBLE]
+
+this condition, I might not
+know what might happen.
+
+But model prediction sometimes
+surprises you.
+
+Aha, I know there's a pattern,
+I recognize that pattern, and
+
+I go about that.
+
+And every architecture, I try
+different kinds of patterns,
+
+and I find the architectures
+get better and better.
+
+So for example, at some point,
+if you go odd-even, odd-even
+
+branches, if you assume I have
+a loop, I say, if i is odd,
+
+going one direction,
+otherwise not.
+
+Pentium 3 type thing, OK.
+
+It just screw up
+[UNINTELLIGIBLE]
+
+with every time it's doing
+something different.
+
+I don't know what's going on.
+
+[UNINTELLIGIBLE]
+
+Pentium I'd probably say aha,
+there's a pattern, odd-even,
+
+odd-even, it figure out.
+
+I core 2 figures out things like
+every third, every fourth
+
+type pattern it figures out.
+
+And then things get
+better and better.
+
+There's very complicated
+patterns you do, these guys
+
+manage to figure out.
+
+Which is kind of fun, to
+see what it can figure
+
+out, what it can't.
+
+By writing a very small program,
+you can get that.
+
+I show some of that.
+
+So the next thing that you have
+to worry about is the
+
+memory system.
+
+So the memory system, if you
+want to be the computer, what
+
+you want to do is have a
+lot of very fast memory
+
+very close to you.
+
+You can do that.
+
+It's going to be
+very expensive.
+
+Sometimes through SQL you
+can't even attain that,
+
+because by the time you build a
+lot of things, it's actually
+
+already far away from
+you, because we are
+
+running very fast here.
+
+So the way you deal with that
+is building caches.
+
+That means you keep a small
+amount of things close to you
+
+in there, and you put things
+in that cache in a way that
+
+hopefully, those are
+the things you
+
+will be using anyways.
+
+So it works very nicely.
+
+So the reason that can be done
+is in programming, when you
+
+run a program, there are two
+types of behaviors that it
+
+[UNINTELLIGIBLE] to
+take advantage of.
+
+One thing is called
+temporal locality.
+
+What that means is, most
+programs, if you use you some
+
+data, there's a good chance you
+are going to use the same
+
+data very soon.
+
+Because normally, there's a
+thing called a working set.
+
+I am working with a certain
+set of data.
+
+I'm basically touching these
+things again and again.
+
+So if I use that, I'm going
+to use that data again.
+
+So that means I want to keep the
+data that I used close by.
+
+Other one is called
+special locality.
+
+That means, if I use some
+data, I have a very good
+
+chance that I might be using
+a neighboring data item.
+
+Because if I am accessing a
+structure or an array, if I'm
+
+accessing something, I
+might be accessing a
+
+[UNINTELLIGIBLE] neighbor
+thing next.
+
+So there's what's called
+partial locality.
+
+And taking advantage of these
+two, you can build this very
+
+fast memory system that feels
+like you have a huge amount of
+
+memory very close to you.
+
+Of course, the opposite
+is true.
+
+If your program doesn't behave
+like that, it looks like you
+
+have lots of memory very far
+from you, and the program
+
+becomes very, very slow.
+
+Because memories didn't speed
+up as fast as processors.
+
+So what that means is, every
+generation, the memory
+
+[UNINTELLIGIBLE] further and
+further away, slower and
+
+slower and slower.
+
+And this is how we manage
+to keep the
+
+machines running fast.
+
+So if you look at what's going
+on every level, I just gave
+
+you a diagram.
+
+I won't go through detail.
+
+You can look at it later.
+
+There are caches, and higher
+levels you can
+
+only keep very small.
+
+And one like [UNINTELLIGIBLE],
+you can only keep a couple of
+
+hundred bytes in
+the registers.
+
+But very fast exercise.
+
+Then you go to cache.
+
+I see on-chip stuff.
+
+We can keep a little bit more,
+access time go down, and then
+
+finally when you go to main
+memory, you can keep a huge
+
+amount, slow access.
+
+And even at the end, something
+like tape, you can keep a huge
+
+amount of stuff.
+
+Almost infinite amount
+of stuff.
+
+But it takes hours to get
+the tape access is not
+
+[UNINTELLIGIBLE].
+
+So there's this hierarchy, and
+there are a certain amount
+
+things you want.
+
+You are using [UNINTELLIGIBLE]
+
+very fast.
+
+You don't want to
+put it in tape.
+
+But you know something that you
+might access in a year,
+
+that's probably a good
+place to put it.
+
+So there's this hierarchy
+there.
+
+And then you have cache, what
+happens is, you want to give
+
+the illusion everything is
+there, but when you go to
+
+access it, the data might
+not be there.
+
+There are many reasons it might
+not be there, so let's
+
+go through some of
+the reasons.
+
+So one thing is called
+cold miss.
+
+That means it's the first time
+I've seen that data.
+
+So it cannot be in the cache.
+
+If it's the first time I was
+asking the disk, it's probably
+
+sitting very back in main
+memory, or somewhere in the
+
+disk, and I have to go get it.
+
+One way to get around this
+problem is prefetching.
+
+So if I keep accessing
+this I say, aha.
+
+You're accessing this
+in this pattern.
+
+And there's a good probability
+the next pattern is here, and
+
+OK, go get it very fast, because
+you're coming in that
+
+sort of direction.
+
+So by doing prefetching, you
+might be able to get rid of
+
+[UNINTELLIGIBLE] is happening.
+
+Then there's a thing called
+capacity miss.
+
+What that means is, you're
+accessing a lot of data.
+
+At some point, you have
+accessed enough data,
+
+everything you accessed cannot
+be fit in the cache, and you
+
+have to throw out some of the
+data to put the next one.
+
+So most caches use the
+a policy called
+
+least recently used.
+
+That means the data that you
+unpacked for the longest time
+
+gets thrown out of the cache.
+
+But the problem is, at some
+point, you're going to come
+
+back to it.
+
+And if you come back to it after
+a long time, that thing
+
+has been out of that
+level of cache.
+
+This happened at every level.
+
+So what that means is, you have
+a thing called a working
+
+set, that you keep working
+again and using.
+
+If the working set is a little
+bit larger than the cache,
+
+when you come back to that,
+the data is gone.
+
+It's not in the cache.
+
+So you want to kind of create a
+working set that fits in the
+
+cache nicely, at ever
+level, basically.
+
+You can do something like
+pre-fetching and gets around
+
+it, but if you can avoid
+[UNINTELLIGIBLE], that's
+
+really nice.
+
+Then there's a thing called
+a conflict miss.
+
+One way of cache work-- it
+doesn't let you store
+
+everything in every location.
+
+Sometimes there are some
+locations in cache
+
+[UNINTELLIGIBLE]
+
+associated with it.
+
+Did you get [UNINTELLIGIBLE]
+associated in 004??
+
+Associativity?
+
+OK.
+
+Again, I will talk about cache
+associated [UNINTELLIGIBLE],
+
+but I'm going to talk about
+memory system later and
+
+[UNINTELLIGIBLE] there.
+
+And what that means is, this
+is a really bad behavior,
+
+because you are only accessing
+a small amount of things, but
+
+all of the data, all
+the aggregate can't
+
+fit into the cache.
+
+The pattern makes it only fit
+into a small part of the
+
+cache, so you had to
+throw the data out.
+
+I'll get back to this.
+
+I'm just going to
+put it there.
+
+And then in a multiprocess
+system, [UNINTELLIGIBLE]
+
+multicourse, there's a thing
+called true sharing.
+
+That means I [UNINTELLIGIBLE]
+data [UNINTELLIGIBLE], and the
+
+next time [UNINTELLIGIBLE]
+
+want to trust the data.
+
+So I have to give the data to
+you, so you're getting cache.
+
+And then when I want to use my
+data, it's [UNINTELLIGIBLE].
+
+I have to get it back to me.
+
+So I'm kind of using data back
+and forth, back and forth.
+
+So that's called true sharing.
+
+And a more hideous form of that
+is called false sharing.
+
+That means most of the data
+is in a cache line.
+
+When you move data you
+move the cache line.
+
+So what I'm doing, is I'm using
+my data myself, and you
+
+are using some other data, but
+unfortunately, they're in the
+
+same cache line.
+
+So when I say, OK, I want my
+data, I get the entire cache
+
+line, including your
+data, and then you
+
+want to use your data.
+
+You say, oops, it's
+not with me.
+
+And I then that means
+you [UNINTELLIGIBLE]
+
+go to you, and at that
+point, I don't have
+
+my data in my cache.
+
+So this data is going
+back and forth.
+
+Even though I never touch your
+data, we have two separate
+
+data, but it's going back.
+
+I will get this things in a
+lot more detail in later
+
+lectures, so this is kind
+of giving [INAUDIBLE].
+
+So there are all of these
+different ways that the data
+
+can be not in the cache.
+
+So here is what the
+processor you are
+
+working with looks like.
+
+There are 6 cores, and there
+are L1 separate instruction
+
+and data caches, and then
+there's L2 unified cache,
+
+[UNINTELLIGIBLE]
+
+L3 cache or [UNINTELLIGIBLE],
+and then there's main memory.
+
+So it's even this deep,
+deep, deep cache
+
+hierarchy going on then.
+
+And then right-hand side, I kind
+of showed the difference.
+
+And the interesting thing to
+realize is, the L1 cache
+
+delays about 4 nanoseconds.
+
+It gets a little bit, 2 1/2
+times slower when you go to L2
+
+cache, and [? 12 ?] times
+slower when you go to L3
+
+cache, and even more slow when
+you go to main memory.
+
+So every time you go down,
+it gets slower
+
+and slower and slower.
+
+That's basically the
+gist of it in here.
+
+Question?
+
+AUDIENCE: Each core has two L1
+cache for instructions and
+
+[INAUDIBLE]?
+
+SAMAN AMARASINGHE: And
+instruction data.
+
+So instruction goes
+one direction,
+
+data goes in one direction.
+
+So next I want to talk a little
+bit about profiling.
+
+So predictor who is
+going to be--
+
+the first part of the predictor
+
+is all about profiling.
+
+Profiling is very important,
+because you run a program.
+
+It doesn't do well.
+
+So how do you know
+what's going on?
+
+First of all, you do know, even
+if it's not doing well.
+
+And if it's not doing well,
+what's the reason?
+
+So just having one number,
+that then saying it's
+
+[UNINTELLIGIBLE] in 10 minutes,
+[UNINTELLIGIBLE]
+
+5 minutes, doesn't tell
+you too much.
+
+You know what to look if you
+have a large program.
+
+The profiling means going,
+looking at what the program is
+
+doing to get an understanding
+in there.
+
+So what you want to do was
+collect this performance data
+
+while running the application,
+and then if you're a large
+
+application, you want to
+organize and display data in
+
+that a variety of ways, and a
+lot of times, relate that data
+
+to source code, and see
+what that means in the
+
+[UNINTELLIGIBLE]
+
+code.
+
+And hopefully by looking at this
+one, you can identify,
+
+ha, there's a problem here.
+
+So there are a bunch of tools.
+
+Intel Vtune, gprof,
+oprofile, perf.
+
+So you guys are going to use
+mainly perf, and we will
+
+probably talk a little
+bit about gprof.
+
+And next time when you come,
+next lecture we'll talk about
+
+this a lot more.
+
+So profiling is mainly to find
+where in an application or a
+
+system there is a significant
+amount of activity.
+
+And when the significant amount
+of activity you want to
+
+know whether those activity can
+be avoided, or there's a
+
+problem here.
+
+So there are some
+[UNINTELLIGIBLE]
+
+significant to what's there,
+it could be anywhere.
+
+It might be addressed
+in the memory,
+
+something might be happening.
+
+It might be in the
+[UNINTELLIGIBLE]
+
+system, some kind of process in
+the operating system might
+
+be happening in one thread, it
+might be happening in an
+
+executable file or a module.
+
+If you know the symbol of
+something, you can say, oh,
+
+huh, that mode, that actually
+is this function, and if you
+
+know even more information about
+the program, you can
+
+say, aha, that's false,
+and in fact it's
+
+this line of the program.
+
+So you get this information from
+the application when you
+
+compile that you can say debug
+information, say aha, this
+
+happens in this line
+of the program
+
+that's having this problem.
+
+So you can break it down and
+get that info like that.
+
+[PHONE RINGING]
+
+Somebody's trying to call me.
+
+Hold on.
+
+OK.
+
+Secondly, we care about
+significant activity.
+
+If the activity just happened
+only a few times, happened
+
+only nanoseconds of execution
+time, who cares?
+
+You don't want to do that.
+
+You want to focus on
+things that matter.
+
+And the key thing about
+this [UNINTELLIGIBLE].
+
+If you spend most of your time
+in insignificant things, you
+
+would get insignificant
+performance improvement.
+
+If you found the significant
+part and work on that, you can
+
+get significant gains.
+
+So the key thing is to find
+the significant ones.
+
+[PHONE RINGING]
+
+Excuse me.
+
+OK.
+
+And the final activity.
+
+So activity means time is spent
+in doing something, and
+
+some activities are bad ones.
+
+Like if you actually do running
+
+instruction, that's good.
+
+If your running is useful
+instruction, a long
+
+time, you're OK.
+
+But you might doing actually
+[UNINTELLIGIBLE],
+
+[UNINTELLIGIBLE]
+
+[? misprediction ?], stuff like
+
+that, that's bad activity.
+
+You [UNINTELLIGIBLE] say, aha.
+
+I am spending a lot of time
+doing something that I can
+
+avoid, and how do
+I avoid that?
+
+So that's what you
+want to look at.
+
+And you have two ways of doing
+that, and I want to give you
+
+an analogy to figure
+out what it is.
+
+So assume you are going,
+visiting a bunch
+
+of different places.
+
+You're on a city tour.
+
+You are visiting different
+parts of the city.
+
+And I want to figure out,
+where do you spend
+
+most of your time?
+
+And that's a hard problem,
+because I am sitting in my
+
+office, and say, OK, you're
+going [UNINTELLIGIBLE]
+
+the city.
+
+I want to figure out where you
+spend most of the time.
+
+I have two ways of doing that.
+
+I'm a busy person.
+
+What I can do is every 30
+minutes, I can call you and
+
+say, where are you?
+
+And you say, OK, I'm in this
+library, I'm in this--
+
+and then at that point, I can
+have a histogram and say, he's
+
+still in the library.
+
+And I can call again,
+where are you?
+
+And I can log that.
+
+And at some point, at the end
+of the day, I'll have a
+
+histogram saying, every time I
+call, you found something.
+
+If you spend a lot of time in
+the science museum, I will
+
+have a bunch of
+[UNINTELLIGIBLE].
+
+We'll see [UNINTELLIGIBLE]
+
+become then, and if you are not
+[UNINTELLIGIBLE], if you
+
+have only one [UNINTELLIGIBLE]
+
+find out, OK, you're not
+spending time there.
+
+That's one way to do that.
+
+Let's go [UNINTELLIGIBLE]
+
+saying, for every landmark, I
+create a telephone booth.
+
+And every time you enter a
+landmark, you [UNINTELLIGIBLE]
+
+the telephone booth, you've got
+to call an operator and
+
+say what time it is, so
+[UNINTELLIGIBLE].
+
+And then you call me and say,
+aha, I'm entering this
+
+landmark, the time now is 5:50,
+and I write it down.
+
+And every time you exit the
+landmark, you call me and say,
+
+I'm exiting this landmark.
+
+Time now is--
+
+I write it down.
+
+OK?
+
+These are kind of two
+ways of doing that.
+
+That's like an instrumentation
+solution.
+
+So the sampling collector-based
+periodically
+
+interupt the processor and look
+at where you are, and
+
+depending on where you are,
+you can mark that off.
+
+And it's called time-based
+sampling means every time,
+
+every 100 milliseconds or
+something, in [UNINTELLIGIBLE]
+
+processing, you stop and
+say where you are.
+
+Event-based sampling means you
+are counting number of events
+
+like cache meters.
+
+Every hundred cache meters, you
+stop and say, OK, where
+
+has this happened?
+
+Of course, if the cache misses
+happen in a regular pattern,
+
+you might be in trouble, because
+every hundred, you
+
+might be the same place, then
+you would get a skewed number.
+
+But most probably, there's
+a statistical
+
+variation in there.
+
+You can get [? account index ?]
+
+and figure out where these
+things happen.
+
+So if you're looking at where
+all the cache [UNINTELLIGIBLE]
+
+is happening, you don't look at
+every miss, because there
+
+are millions of miss.
+
+Every 10,000 miss, you figure
+out where you are, and
+
+statistically, one is missing
+many times, that will adapt in
+
+that column.
+
+And nice thing about
+that is, there's
+
+nothing you need to do.
+
+Now installation, no changes to
+application you need to do.
+
+[UNINTELLIGIBLE] here, you know
+how to go in changes,
+
+phone booth everywhere.
+
+Wide coverage.
+
+You can cover everything.
+
+So that means, assume you
+install phone booth in all the
+
+fixed landmarks, but there's a
+service [UNINTELLIGIBLE] down.
+
+I didn't see.
+
+I don't have a phone
+booth there.
+
+But here, if I'm calling you,
+I know I'm [UNINTELLIGIBLE]
+
+you, anyplace you are, I will
+cover, even though I haven't
+
+anticipated that point.
+
+Very low overhead, because I can
+decide to call you every
+
+30 minutes or call you every 1
+minute, if I really care or
+
+worry about you, and I can
+control the overhead that I'm
+
+looking at, basically.
+
+The problem is its approximate
+position.
+
+Because if you spend 5 hours
+at MIT and 30 seconds at
+
+Harvard, I will never know
+that you went to Harvard,
+
+because I might have not called
+you while you were
+
+there at Harvard.
+
+You might think it's boring
+and come back, and I never
+
+knew that you did that.
+
+And also, the other thing is, I
+don't know exactly how many
+
+times you went to a place,
+because I might have called
+
+you 10 times, and I found you
+in the museum of the science
+
+10 times, but you might have
+gone there 20 times, and I
+
+might have missed you under the
+times I didn't call, or
+
+you might have gone there only
+five times and stayed for a
+
+long time, and I might have
+called multiple times.
+
+I don't know that, and I don't
+know the count of times you
+
+are gone, which is
+hard to know.
+
+So the main thing is there might
+be things that are not
+
+that statistically significant
+that you might miss.
+
+And if you care about that,
+it's not a good bet.
+
+But most of the time we care
+about the really statistically
+
+significant things, so this
+is a really good method.
+
+The other part is perfect
+accuracy, because every time
+
+you go somewhere, you have to
+call me, and I know how many
+
+times you went to the
+museum of science.
+
+I know exactly the time
+you enter and exited a
+
+[UNINTELLIGIBLE].
+
+I know all of those things
+[INAUDIBLE].
+
+The problem of that is kind
+of low granularity.
+
+I can't put phone booth at every
+corner, and if you had
+
+called me at every corner,
+it's going
+
+to be way too expensive.
+
+So I have low granularity, very
+good information, and
+
+also high overhead.
+
+Because if you're going in and
+out a lot to a building, you
+
+have to call, you have
+to stop and call,
+
+it's very high overhead.
+
+And there's not much of a way
+for me to control that.
+
+And it's also high touch.
+
+That means I have to build all
+that infrastructure, I have to
+
+go and modify your application,
+basically, in
+
+something [UNINTELLIGIBLE]
+
+compile time application, get
+modified to basically have all
+
+these [UNINTELLIGIBLE]
+
+installed into the
+application.
+
+So you can look a lot of
+different types of events.
+
+So in Intel, if you look at
+core performance counters,
+
+there are hundreds of
+performance counters.
+
+And some of these performance
+counters have no sense
+
+whatsoever.
+
+So for example, Intel has
+this counter called
+
+number of bogus branches.
+
+What's a bogus branch?
+
+I mean, why should Intel be
+doing anything bogus?
+
+It's some [UNINTELLIGIBLE]
+
+came out.
+
+But there are some counters
+that are useful, so you're
+
+sort of getting [UNINTELLIGIBLE]
+
+by thousands of things
+available, we focus on things
+
+that we care about.
+
+Things like branch events,
+load store events, cache
+
+meter, prefetchers.
+
+Those are the important things,
+and some multicore
+
+events that we can look at,
+and get some interesting
+
+information.
+
+And a lot of times, just by
+looking at numbers doesn't
+
+make too much sense.
+
+You know you had $5 billion,
+$300 million branches missed.
+
+Is it a good high or low?
+
+You have no idea.
+
+The right thing is, OK.
+
+[UNINTELLIGIBLE]
+
+to number of instruction
+executed how much it would be.
+
+The most important numbers
+are ratios.
+
+So from the branches executed,
+how many were missed?
+
+That's a lot more important
+than, you have 5 billion
+
+branch misses.
+
+That doesn't say
+anything to me.
+
+So most of the time, you have
+to figure out the right
+
+ratios, and what makes sense
+to look at those ratios.
+
+So now what I want to do is
+to go through a couple of
+
+examples and show what
+I can see in these
+
+different program behaviors.
+
+Any questions so far?
+
+Next lecture we are going to go
+through hands-on examples,
+
+going through some of these
+profiling tools.
+
+So it's kind of fun--
+
+what I did was finally discover
+what architecture is
+
+doing, and what is the modern
+multicore is capable of doing.
+
+In fact, some of these examples,
+so this set of
+
+examples were done
+on a Core Two.
+
+So some of the numbers might
+be very different in
+
+[UNINTELLIGIBLE], because the
+architecture might do better
+
+in some special prediction
+stuff.
+
+I don't know.
+
+It might be fun to
+move it it again.
+
+So what I have is a program
+that I first created two
+
+interesting arrays to
+access this array.
+
+One array has numbers 1 to n,
+MAXA, is stored in this array.
+
+This has 1 to MAXA in random
+order stored in this array.
+
+So when I use this as a way to
+access the main array, and if
+
+I use this in [UNINTELLIGIBLE]
+
+0 to n, I will actually access
+A [UNINTELLIGIBLE]
+
+0.
+
+It's almost like saying AI.
+
+But I use this here.
+
+But if I use this one, I'm doing
+random [UNINTELLIGIBLE].
+
+Well, the first program I'm
+doing is just nothing but
+
+going through this one.
+
+I will have autoloop that will
+go through many, many times,
+
+so I can actually
+[UNINTELLIGIBLE]
+
+time.
+
+So I just go through--
+
+just nothing but trying to
+just go through that.
+
+Second thing I did, I just
+put a condition.
+
+Say, j is than MAXA half.
+
+That means halfway through
+the program, I will go
+
+and update this one.
+
+Another half, I'm not
+doing anything.
+
+Then I said, OK, look.
+
+I divide by every fourth
+[UNINTELLIGIBLE].
+
+So what I is j and
+with 03 in there.
+
+That means 3 means [? 2b ?]
+
+in the 1 1.
+
+So we study 0.
+
+That means last two
+[UNINTELLIGIBLE] has to be 0.
+
+To form in delta every fourth
+element, I will update.
+
+Otherwise I won't.
+
+And the next thing I
+did was I updated--
+
+OK.
+
+Let me ask you a question.
+
+So this program, the output--
+
+that means what happened
+to A--
+
+the output of A is equivalent to
+some other program, one of
+
+these three programs.
+
+Which one is the [? outward ?]
+
+equivalent?
+
+See what you can make up.
+
+So first three programs or
+each will have separate
+
+different outputs.
+
+A at A would be different
+if you run it.
+
+Except the fourth program will
+produce the exact same results
+
+as some other program, on the
+first three programs.
+
+Which one?
+
+Wake up, wake up, wake up!
+
+I hear something.
+
+I hear some--
+
+second one.
+
+Somebody said the second one.
+
+How many people agree
+with that?
+
+How many people disagree?
+
+OK.
+
+This is not a statistical
+example.
+
+It can be exact.
+
+Why say the second one?
+
+Second one is right.
+
+So what that means is, in fact,
+instead of a j, I'm
+
+using inc j.
+
+Inc j is exactly j, because it
+goes, inc 0 is 0, inc 1 is 1,
+
+inc 2 is 2.
+
+I just created the same
+[UNINTELLIGIBLE]
+
+array in here.
+
+This is something to get that.
+
+And finally, I am doing
+the [UNINTELLIGIBLE]
+
+A basically from x.
+
+So what that means, I'm using
+the same amount of data will
+
+get updated, but it's very
+different order in there.
+
+So now, before I go to
+the next slide--
+
+question?
+
+AUDIENCE: Maybe you said this,
+but what is the A array?
+
+SAMAN AMARASINGHE: Yeah,
+it's some numbers.
+
+Some random set of numbers.
+
+I don't care about that.
+
+I just updated this one.
+
+So in here, which program do
+we think run the faster?
+
+So let me ask you this--
+
+which program updated the least
+amount of updates for A?
+
+Third one, yeah, because
+it's only doing
+
+every fourth element.
+
+Which did the most?
+
+First one is doing every
+element, and everybody else
+
+will do probably half
+of the updates.
+
+So knowing that, which program
+will run faster?
+
+First one is updating
+everything.
+
+[UNINTELLIGIBLE], OK.
+
+[UNINTELLIGIBLE]
+
+plus 1, OK.
+
+Which program will run slow?
+
+Last one.
+
+You guys are onto something.
+
+You have seen my slide, you
+actually know what the
+
+hell is going on.
+
+So what I show here is, you
+can't read this one, but I
+
+[UNINTELLIGIBLE]
+
+on time, and then I
+create a ratio.
+
+So if you look at the ratio--
+
+so aha.
+
+The first program, I always
+normalize to that, runs 1, and
+
+that runs the fastest, if you
+tried, and the last program
+
+ran the slowest.
+
+And the interesting thing is,
+the [UNINTELLIGIBLE], the
+
+other, the two, the second and
+fourth one, that wrote about
+
+half [UNINTELLIGIBLE], basically
+ran all of the same.
+
+But the one that wrote every
+fourth element was actually
+
+slower than others.
+
+Why is it going on?
+
+So what you can do is, first
+look at how many instructions
+
+would it add up, and how many
+instruction were executed?
+
+So if you look at that, what
+you see is, the first one
+
+executes the least amount of
+instructions, because it
+
+doesn't have to do all
+this [UNINTELLIGIBLE]
+
+when it's updating.
+
+The interesting thing is, the
+one that wrote half has the
+
+most amount of instructions.
+
+One that wrote only 1/4 has
+middle amount of instructions.
+
+That kind of makes
+sense in here.
+
+But this still doesn't
+explain the slowdown.
+
+That means if this is the only
+case, the divide by 4 should
+
+run faster than the
+other three.
+
+That doesn't make sense.
+
+And then what you look at,
+look at [UNINTELLIGIBLE]
+
+branches in there, and if you
+look at the branches,
+
+what you see is--
+
+Let me skip this
+one, actually.
+
+I want to get this one.
+
+This is called clocks
+per instruction.
+
+What this is is, if the
+instructions ran slow, these
+
+instructions will take a
+lot more clock cycles.
+
+That means the instructions
+are not doing well.
+
+That means they are
+stalling, they are
+
+taking a lot more time.
+
+Normally, we should be able
+to run [UNINTELLIGIBLE]
+
+about four instruction
+[UNINTELLIGIBLE] cycles should
+
+get a CPA of 0.25, but that's
+very rare, and if you look at
+
+that, if I normalize, I get
+1 in here normalized.
+
+And then what you see is second
+and fourth test, almost
+
+the same CPI, and the third has
+worse, and the last one is
+
+even worse.
+
+So why is that?
+
+Why are those instructions
+doing bad?
+
+And then you can go look
+at that misprediction
+
+instruction, and this is
+exactly what happens.
+
+Divide by 4.
+
+This is a condition.
+
+The branch predictor couldn't
+predict it that well, because
+
+[UNINTELLIGIBLE]
+
+predicted in the first three,
+and it's [UNINTELLIGIBLE]
+
+predicted, OK, after three,
+next one is also going 1
+
+direction, oops, it's in
+another direction.
+
+OK, going first three
+predictions, going one
+
+direction, knowing
+that information.
+
+So divide by 4, looks really
+bad, then predict 3.
+
+And then the random one was
+just completely off.
+
+Random one, basically
+predictions of three
+
+[INAUDIBLE].
+
+That's why this is.
+
+So in fact, if you just want to
+calculate the run time, if
+
+you think every misprediction
+cost you 21 instructions, you
+
+kind of get the exact
+total first.
+
+You can't help it.
+
+So after you meet the
+instruction, take one cycle,
+
+and everybody misprediction
+instruction, take 21 cycles,
+
+and you just calculate that.
+
+And this [UNINTELLIGIBLE], I
+just came, took it out of a
+
+hat, and then voila, I get
+a number that's very
+
+close to run time.
+
+So what that means is, I can
+kind of understand what the
+
+behavior, this explains
+what's going on.
+
+So I can have a model in my
+head for what's going on.
+
+So it's all about misprediction
+in here.
+
+I did two other experiments
+in here.
+
+I have the slide sitting here,
+but I don't think I have too
+
+much time to go.
+
+I want to go to the
+numbers in there.
+
+Are you ready, [UNINTELLIGIBLE]?
+
+OK.
+
+Why don't you go put
+your laptop in.
+
+You have the dongle?
+
+AUDIENCE: [INAUDIBLE]
+
+SAMAN AMARASINGHE: OK.
+
+So voila.
+
+So something you guys waited all
+this time, and were up all
+
+these days developing.
+
+So let's see how
+everybody did.
+
+OK, without further ado.
+
+I haven't even seen
+these numbers.
+
+OK, what happened?
+
+He's trying to--
+
+OK, good.
+
+This is [UNINTELLIGIBLE]
+
+screen, OK.
+
+Do you have it?
+
+OK.
+
+AUDIENCE: OK.
+
+Something to keep in mind
+is, we haven't actually
+
+investigated what's causing
+people to have build failures
+
+or crashes yet.
+
+So it could be your fault,
+it could be ours.
+
+We'll figure that out.
+
+SAMAN AMARASINGHE: So if
+smaller, better or higher,
+
+better, what's--
+
+AUDIENCE: [INAUDIBLE] better.
+
+This is run time.
+
+That
+
+SAMAN AMARASINGHE: This
+is really good!
+
+This is actually--
+
+AUDIENCE: [INAUDIBLE]
+
+The baseline is the flat code
+that you see in the middle.
+
+SAMAN AMARASINGHE: So
+this is really good.
+
+That means there were
+kind of two groups.
+
+Most of the people got
+everything right, and they're
+
+now the bottom.
+
+And there's another group that
+missed something, and it's in
+
+the second camp.
+
+AUDIENCE: I think some of these
+projects are from people
+
+who dropped the class
+at some point.
+
+So there's probably
+[INAUDIBLE]
+
+might not be actually
+representative of the class.
+
+SAMAN AMARASINGHE: So last
+year, we got like almost
+
+exponential curve, actually.
+
+Last year, what happened was
+there were a couple of people
+
+at the bottom, and everybody
+worked at the top, basically.
+
+Which is actually good.
+
+So you guys actually figured
+out what's going on.
+
+AUDIENCE: So next one is
+even more interesting.
+
+SAMAN AMARASINGHE: Wow!
+
+AUDIENCE: So this
+is [INAUDIBLE]
+
+that we gave you guys.
+
+Most of you optimized it
+down to 0 seconds.
+
+So I coded in a harder
+test case, and here's
+
+the results on that.
+
+Still pretty good.
+
+[INAUDIBLE]
+
+There's some very specific
+optimizations [INAUDIBLE].
+
+Yeah.
+
+SAMAN AMARASINGHE: So exactly.
+
+There are people who are
+climbing up, I don't know
+
+exactly what, but it's very
+clear that [UNINTELLIGIBLE],
+
+probably data representation
+tag that
+
+people missed in here.
+
+Which is really now
+interesting.
+
+Yes.
+
+AUDIENCE: And for Pentominos,
+this is very incomplete,
+
+because the set of tests that
+we wanted to run are still
+
+currently running.
+
+So I just picked a random test
+case, just to give everybody
+
+an idea of how everybody did,
+and set the time out very low
+
+so that I could actually finish
+it during this lecture.
+
+And what's [INAUDIBLE]?
+
+Yes.
+
+Somebody solved it
+instantaneously, and it
+
+searches for the first 5,000
+solutions to some random
+
+puzzle that I pulled out.
+
+SAMAN AMARASINGHE: So
+[UNINTELLIGIBLE]?
+
+AUDIENCE: That I haven't
+verified yet.
+
+SAMAN AMARASINGHE: Aha.
+
+So it might be, there might be
+just the scratchings, so we
+
+don't know that, and then that
+could be correct answer, but--
+
+AUDIENCE: Which one
+is the baseline?
+
+The baseline is actually
+the 90-second mark.
+
+[INAUDIBLE]
+
+SAMAN AMARASINGHE:
+[UNINTELLIGIBLE]
+
+the baseline?
+
+AUDIENCE: No.
+
+10 seconds and above are either
+timeout or [INAUDIBLE].
+
+SAMAN AMARASINGHE: Oh, they're
+probably mostly timeouts.
+
+AUDIENCE: [INAUDIBLE]
+
+SAMAN AMARASINGHE: Yes.
+
+So there you are.
+
+This one, people would have some
+work to do, I guess, to
+
+get the performance down.
+
+But this is pretty good.
+
+This is not like
+[UNINTELLIGIBLE].
+
+I mean, last couple of
+years, we had people,
+
+[UNINTELLIGIBLE]
+
+someone who was 1,000
+[UNINTELLIGIBLE], you had to
+
+plot it in a log thing.
+
+So in fact, if I do a square
+root within the grid, this is
+
+pretty nice.
+
+So [UNINTELLIGIBLE]
+
+is not that bad.
+
+So this is great.
+
+This is where you get
+[UNINTELLIGIBLE]
+
+performance wise And if you are
+in the bottom, you can go
+
+have a beer.
+
+Otherwise, you might have to
+go back and figure out what
+
+you missed.
+
+AUDIENCE: [INAUDIBLE]
+
+SAMAN AMARASINGHE: Oh, if
+you're [UNINTELLIGIBLE].
+
+Yes, exactly yes.
+
+I should say that.
\ No newline at end of file
diff --git a/96RHvPVlxN8.txt b/96RHvPVlxN8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9d40bf2d67d8d43b7024c246bea889cb1e54392c
--- /dev/null
+++ b/96RHvPVlxN8.txt
@@ -0,0 +1,691 @@
+align:start position:0%
+ 
+welcome back to a20 in this short video
+
+ align:start position:0%
+welcome back to a20 in this short video
+ 
+
+ align:start position:0%
+welcome back to a20 in this short video
+you want to discuss length contraction
+
+ align:start position:0%
+you want to discuss length contraction
+ 
+
+ align:start position:0%
+you want to discuss length contraction
+we want to actually derive length
+
+ align:start position:0%
+we want to actually derive length
+ 
+
+ align:start position:0%
+we want to actually derive length
+contraction
+
+ align:start position:0%
+contraction
+ 
+
+ align:start position:0%
+contraction
+and we do this with an experiment the
+
+ align:start position:0%
+and we do this with an experiment the
+ 
+
+ align:start position:0%
+and we do this with an experiment the
+question is how long is bob spacecraft
+
+ align:start position:0%
+question is how long is bob spacecraft
+ 
+
+ align:start position:0%
+question is how long is bob spacecraft
+the experiment is conducted by taking
+
+ align:start position:0%
+the experiment is conducted by taking
+ 
+
+ align:start position:0%
+the experiment is conducted by taking
+two pictures so illustrated here the
+
+ align:start position:0%
+two pictures so illustrated here the
+ 
+
+ align:start position:0%
+two pictures so illustrated here the
+first picture is when
+
+ align:start position:0%
+first picture is when
+ 
+
+ align:start position:0%
+first picture is when
+alice's and bob spacecrafts just start
+
+ align:start position:0%
+alice's and bob spacecrafts just start
+ 
+
+ align:start position:0%
+alice's and bob spacecrafts just start
+to meet
+
+ align:start position:0%
+to meet
+ 
+
+ align:start position:0%
+to meet
+um bob's relative to analysis is moving
+
+ align:start position:0%
+um bob's relative to analysis is moving
+ 
+
+ align:start position:0%
+um bob's relative to analysis is moving
+with the velocity v and we take the
+
+ align:start position:0%
+with the velocity v and we take the
+ 
+
+ align:start position:0%
+with the velocity v and we take the
+second picture when the back of bob's
+
+ align:start position:0%
+second picture when the back of bob's
+ 
+
+ align:start position:0%
+second picture when the back of bob's
+spacecraft is meeting the front of
+
+ align:start position:0%
+spacecraft is meeting the front of
+ 
+
+ align:start position:0%
+spacecraft is meeting the front of
+alice's just like it's shown here
+
+ align:start position:0%
+alice's just like it's shown here
+ 
+
+ align:start position:0%
+alice's just like it's shown here
+and the pictures
+
+ align:start position:0%
+and the pictures
+ 
+
+ align:start position:0%
+and the pictures
+take pictures of clocks
+
+ align:start position:0%
+take pictures of clocks
+ 
+
+ align:start position:0%
+take pictures of clocks
+so in the first picture we we see
+
+ align:start position:0%
+so in the first picture we we see
+ 
+
+ align:start position:0%
+so in the first picture we we see
+alice's clock show a ta1
+
+ align:start position:0%
+alice's clock show a ta1
+ 
+
+ align:start position:0%
+alice's clock show a ta1
+and bob's
+
+ align:start position:0%
+and bob's
+ 
+
+ align:start position:0%
+and bob's
+tb1 and for the second equivalently we
+
+ align:start position:0%
+tb1 and for the second equivalently we
+ 
+
+ align:start position:0%
+tb1 and for the second equivalently we
+see ta2 and tb2
+
+ align:start position:0%
+see ta2 and tb2
+ 
+
+ align:start position:0%
+see ta2 and tb2
+so your task is now to express the
+
+ align:start position:0%
+so your task is now to express the
+ 
+
+ align:start position:0%
+so your task is now to express the
+length of bob's spacecraft
+
+ align:start position:0%
+length of bob's spacecraft
+ 
+
+ align:start position:0%
+length of bob's spacecraft
+for as alice sees this from these
+
+ align:start position:0%
+for as alice sees this from these
+ 
+
+ align:start position:0%
+for as alice sees this from these
+pictures and as bob does see it from his
+
+ align:start position:0%
+pictures and as bob does see it from his
+ 
+
+ align:start position:0%
+pictures and as bob does see it from his
+own pictures
+
+ align:start position:0%
+own pictures
+ 
+
+ align:start position:0%
+own pictures
+by comparing the time and the velocity
+
+ align:start position:0%
+by comparing the time and the velocity
+ 
+
+ align:start position:0%
+by comparing the time and the velocity
+pause the video and try to work this out
+
+ align:start position:0%
+pause the video and try to work this out
+ 
+
+ align:start position:0%
+pause the video and try to work this out
+so i did this here for you
+
+ align:start position:0%
+so i did this here for you
+ 
+
+ align:start position:0%
+so i did this here for you
+you calculate um
+
+ align:start position:0%
+you calculate um
+ 
+
+ align:start position:0%
+you calculate um
+the length we can do this with the
+
+ align:start position:0%
+the length we can do this with the
+ 
+
+ align:start position:0%
+the length we can do this with the
+velocity and simply the product of the
+
+ align:start position:0%
+velocity and simply the product of the
+ 
+
+ align:start position:0%
+velocity and simply the product of the
+velocity and the time difference in the
+
+ align:start position:0%
+velocity and the time difference in the
+ 
+
+ align:start position:0%
+velocity and the time difference in the
+pictures as shown
+
+ align:start position:0%
+pictures as shown
+ 
+
+ align:start position:0%
+pictures as shown
+of those two clocks we see this for
+
+ align:start position:0%
+of those two clocks we see this for
+ 
+
+ align:start position:0%
+of those two clocks we see this for
+alice
+
+ align:start position:0%
+alice
+ 
+
+ align:start position:0%
+alice
+and we see this for bob
+
+ align:start position:0%
+and we see this for bob
+ 
+
+ align:start position:0%
+and we see this for bob
+and now we can start to compare
+
+ align:start position:0%
+and now we can start to compare
+ 
+
+ align:start position:0%
+and now we can start to compare
+for bob ls now is moving
+
+ align:start position:0%
+for bob ls now is moving
+ 
+
+ align:start position:0%
+for bob ls now is moving
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+the time difference
+
+ align:start position:0%
+the time difference
+ 
+
+ align:start position:0%
+the time difference
+in alice's
+
+ align:start position:0%
+in alice's
+ 
+
+ align:start position:0%
+in alice's
+clock will be smaller by one over gamma
+
+ align:start position:0%
+clock will be smaller by one over gamma
+ 
+
+ align:start position:0%
+clock will be smaller by one over gamma
+compared to what bob sees in his own
+
+ align:start position:0%
+compared to what bob sees in his own
+ 
+
+ align:start position:0%
+compared to what bob sees in his own
+clocks so for bob says or bob says
+
+ align:start position:0%
+clocks so for bob says or bob says
+ 
+
+ align:start position:0%
+clocks so for bob says or bob says
+your clock is slow
+
+ align:start position:0%
+your clock is slow
+ 
+
+ align:start position:0%
+your clock is slow
+um so we can use this we can then
+
+ align:start position:0%
+um so we can use this we can then
+ 
+
+ align:start position:0%
+um so we can use this we can then
+calculate um the length of the
+
+ align:start position:0%
+calculate um the length of the
+ 
+
+ align:start position:0%
+calculate um the length of the
+spacecraft
+
+ align:start position:0%
+spacecraft
+ 
+
+ align:start position:0%
+spacecraft
+as alice sees it
+
+ align:start position:0%
+as alice sees it
+ 
+
+ align:start position:0%
+as alice sees it
+equal to v times delta ta
+
+ align:start position:0%
+equal to v times delta ta
+ 
+
+ align:start position:0%
+equal to v times delta ta
+and we just use the time relation here
+
+ align:start position:0%
+and we just use the time relation here
+ 
+
+ align:start position:0%
+and we just use the time relation here
+in this equation and we find that the
+
+ align:start position:0%
+in this equation and we find that the
+ 
+
+ align:start position:0%
+in this equation and we find that the
+lengths are actually not the same the
+
+ align:start position:0%
+lengths are actually not the same the
+ 
+
+ align:start position:0%
+lengths are actually not the same the
+length as ls is one over gamma times the
+
+ align:start position:0%
+length as ls is one over gamma times the
+ 
+
+ align:start position:0%
+length as ls is one over gamma times the
+length as prophecies of the very same
+
+ align:start position:0%
+length as prophecies of the very same
+ 
+
+ align:start position:0%
+length as prophecies of the very same
+spacecraft
+
+ align:start position:0%
+spacecraft
+ 
+
+ align:start position:0%
+spacecraft
+so the lengths
+
+ align:start position:0%
+so the lengths
+ 
+
+ align:start position:0%
+so the lengths
+of the spacecraft are not the same as
+
+ align:start position:0%
+of the spacecraft are not the same as
+ 
+
+ align:start position:0%
+of the spacecraft are not the same as
+seen by alice
+
+ align:start position:0%
+seen by alice
+ 
+
+ align:start position:0%
+seen by alice
+and seen by bob
+
+ align:start position:0%
+and seen by bob
+ 
+
+ align:start position:0%
+and seen by bob
+now here you have to see that in this
+
+ align:start position:0%
+now here you have to see that in this
+ 
+
+ align:start position:0%
+now here you have to see that in this
+example what i just did
+
+ align:start position:0%
+example what i just did
+ 
+
+ align:start position:0%
+example what i just did
+is i changed around who's moving and was
+
+ align:start position:0%
+is i changed around who's moving and was
+ 
+
+ align:start position:0%
+is i changed around who's moving and was
+resting so here the observation of alice
+
+ align:start position:0%
+resting so here the observation of alice
+ 
+
+ align:start position:0%
+resting so here the observation of alice
+of bob spacecraft is that of the moving
+
+ align:start position:0%
+of bob spacecraft is that of the moving
+ 
+
+ align:start position:0%
+of bob spacecraft is that of the moving
+spacecraft so ls sees a moving
+
+ align:start position:0%
+spacecraft so ls sees a moving
+ 
+
+ align:start position:0%
+spacecraft so ls sees a moving
+spacecraft which is shorter than the
+
+ align:start position:0%
+spacecraft which is shorter than the
+ 
+
+ align:start position:0%
+spacecraft which is shorter than the
+spacecraft itself at length at rest
+
+ align:start position:0%
+spacecraft itself at length at rest
+ 
+
+ align:start position:0%
+spacecraft itself at length at rest
+so how can we resolve this um alice will
+
+ align:start position:0%
+so how can we resolve this um alice will
+ 
+
+ align:start position:0%
+so how can we resolve this um alice will
+argue that the two clocks bob used are
+
+ align:start position:0%
+argue that the two clocks bob used are
+ 
+
+ align:start position:0%
+argue that the two clocks bob used are
+actually not synchronized
+
+ align:start position:0%
+actually not synchronized
+ 
+
+ align:start position:0%
+actually not synchronized
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if you paid a lot of attention you see
+
+ align:start position:0%
+if you paid a lot of attention you see
+ 
+
+ align:start position:0%
+if you paid a lot of attention you see
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+i'm actually not looking at the same
+
+ align:start position:0%
+i'm actually not looking at the same
+ 
+
+ align:start position:0%
+i'm actually not looking at the same
+clock i'm having i had a look at the
+
+ align:start position:0%
+clock i'm having i had a look at the
+ 
+
+ align:start position:0%
+clock i'm having i had a look at the
+clock at the beginning of the spacecraft
+
+ align:start position:0%
+clock at the beginning of the spacecraft
+ 
+
+ align:start position:0%
+clock at the beginning of the spacecraft
+at the end of the spacecraft
+
+ align:start position:0%
+at the end of the spacecraft
+ 
+
+ align:start position:0%
+at the end of the spacecraft
+and while they are synchronized for bob
+
+ align:start position:0%
+and while they are synchronized for bob
+ 
+
+ align:start position:0%
+and while they are synchronized for bob
+they're not synchronized for alice
+
+ align:start position:0%
+they're not synchronized for alice
+ 
+
+ align:start position:0%
+they're not synchronized for alice
+who's right
+
+ align:start position:0%
+who's right
+ 
+
+ align:start position:0%
+who's right
+both are right they're just observing
+
+ align:start position:0%
+both are right they're just observing
+ 
+
+ align:start position:0%
+both are right they're just observing
+events or sequences events with two
+
+ align:start position:0%
+events or sequences events with two
+ 
+
+ align:start position:0%
+events or sequences events with two
+different reference frames
\ No newline at end of file
diff --git a/9SvAZgd0J_A.txt b/9SvAZgd0J_A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6276f48cf9cda1057eb7eac282f4221441d98f96
--- /dev/null
+++ b/9SvAZgd0J_A.txt
@@ -0,0 +1,10131 @@
+align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+today we are going to continue um
+
+ align:start position:0%
+today we are going to continue um
+ 
+
+ align:start position:0%
+today we are going to continue um
+thinking about reactions um
+
+ align:start position:0%
+thinking about reactions um
+ 
+
+ align:start position:0%
+thinking about reactions um
+just to remind you what did we do on
+
+ align:start position:0%
+just to remind you what did we do on
+ 
+
+ align:start position:0%
+just to remind you what did we do on
+friday so we introduced here's what we
+
+ align:start position:0%
+friday so we introduced here's what we
+ 
+
+ align:start position:0%
+friday so we introduced here's what we
+did last time
+
+ align:start position:0%
+did last time
+ 
+
+ align:start position:0%
+did last time
+we talked about constant we talked about
+
+ align:start position:0%
+we talked about constant we talked about
+ 
+
+ align:start position:0%
+we talked about constant we talked about
+reactions okay and there
+
+ align:start position:0%
+reactions okay and there
+ 
+
+ align:start position:0%
+reactions okay and there
+on on friday we were really interested
+
+ align:start position:0%
+on on friday we were really interested
+ 
+
+ align:start position:0%
+on on friday we were really interested
+in rates
+
+ align:start position:0%
+in rates
+ 
+
+ align:start position:0%
+in rates
+you know how fast is it happening so we
+
+ align:start position:0%
+you know how fast is it happening so we
+ 
+
+ align:start position:0%
+you know how fast is it happening so we
+talked about things that affect the
+
+ align:start position:0%
+talked about things that affect the
+ 
+
+ align:start position:0%
+talked about things that affect the
+reaction rate
+
+ align:start position:0%
+reaction rate
+ 
+
+ align:start position:0%
+reaction rate
+right like concentration okay
+
+ align:start position:0%
+right like concentration okay
+ 
+
+ align:start position:0%
+right like concentration okay
+concentration versus time
+
+ align:start position:0%
+concentration versus time
+ 
+
+ align:start position:0%
+concentration versus time
+and and how you can measure that and
+
+ align:start position:0%
+and and how you can measure that and
+ 
+
+ align:start position:0%
+and and how you can measure that and
+then and and you can have
+
+ align:start position:0%
+then and and you can have
+ 
+
+ align:start position:0%
+then and and you can have
+rate laws based on experimental
+
+ align:start position:0%
+rate laws based on experimental
+ 
+
+ align:start position:0%
+rate laws based on experimental
+measurements
+
+ align:start position:0%
+measurements
+ 
+
+ align:start position:0%
+measurements
+okay and and and that that can tell you
+
+ align:start position:0%
+okay and and and that that can tell you
+ 
+
+ align:start position:0%
+okay and and and that that can tell you
+the reaction order
+
+ align:start position:0%
+the reaction order
+ 
+
+ align:start position:0%
+the reaction order
+we talked about zeroth first second
+
+ align:start position:0%
+we talked about zeroth first second
+ 
+
+ align:start position:0%
+we talked about zeroth first second
+order reactions uh the rate constant
+
+ align:start position:0%
+order reactions uh the rate constant
+ 
+
+ align:start position:0%
+order reactions uh the rate constant
+and then we also talked about the
+
+ align:start position:0%
+and then we also talked about the
+ 
+
+ align:start position:0%
+and then we also talked about the
+temperature dependence
+
+ align:start position:0%
+temperature dependence
+ 
+
+ align:start position:0%
+temperature dependence
+um and the very end the role of a
+
+ align:start position:0%
+um and the very end the role of a
+ 
+
+ align:start position:0%
+um and the very end the role of a
+catalyst and lowering that
+
+ align:start position:0%
+catalyst and lowering that
+ 
+
+ align:start position:0%
+catalyst and lowering that
+activation barrier today
+
+ align:start position:0%
+activation barrier today
+ 
+
+ align:start position:0%
+activation barrier today
+we're going to talk about how things
+
+ align:start position:0%
+we're going to talk about how things
+ 
+
+ align:start position:0%
+we're going to talk about how things
+dissolve so we're going to talk about
+
+ align:start position:0%
+dissolve so we're going to talk about
+ 
+
+ align:start position:0%
+dissolve so we're going to talk about
+solubility okay
+
+ align:start position:0%
+solubility okay
+ 
+
+ align:start position:0%
+solubility okay
+and this has to do with reactions
+
+ align:start position:0%
+and this has to do with reactions
+ 
+
+ align:start position:0%
+and this has to do with reactions
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+something dissolving is a reaction
+
+ align:start position:0%
+something dissolving is a reaction
+ 
+
+ align:start position:0%
+something dissolving is a reaction
+but but what's going to happen is we're
+
+ align:start position:0%
+but but what's going to happen is we're
+ 
+
+ align:start position:0%
+but but what's going to happen is we're
+going to talk about how that reaction
+
+ align:start position:0%
+going to talk about how that reaction
+ 
+
+ align:start position:0%
+going to talk about how that reaction
+finds its happy place and we know
+
+ align:start position:0%
+finds its happy place and we know
+ 
+
+ align:start position:0%
+finds its happy place and we know
+happy place is a good thing and and it's
+
+ align:start position:0%
+happy place is a good thing and and it's
+ 
+
+ align:start position:0%
+happy place is a good thing and and it's
+called equilibrium
+
+ align:start position:0%
+called equilibrium
+ 
+
+ align:start position:0%
+called equilibrium
+right uh and so that's going to involve
+
+ align:start position:0%
+right uh and so that's going to involve
+ 
+
+ align:start position:0%
+right uh and so that's going to involve
+talking about things like
+
+ align:start position:0%
+talking about things like
+ 
+
+ align:start position:0%
+talking about things like
+oh equilibrium constants uh the
+
+ align:start position:0%
+oh equilibrium constants uh the
+ 
+
+ align:start position:0%
+oh equilibrium constants uh the
+dissolution
+
+ align:start position:0%
+dissolution
+ 
+
+ align:start position:0%
+dissolution
+we're going to look at some examples
+
+ align:start position:0%
+we're going to look at some examples
+ 
+
+ align:start position:0%
+we're going to look at some examples
+with ionic compounds so salts we're
+
+ align:start position:0%
+with ionic compounds so salts we're
+ 
+
+ align:start position:0%
+with ionic compounds so salts we're
+going to be dissolving salts in
+
+ align:start position:0%
+going to be dissolving salts in
+ 
+
+ align:start position:0%
+going to be dissolving salts in
+in water and and looking at how to think
+
+ align:start position:0%
+in water and and looking at how to think
+ 
+
+ align:start position:0%
+in water and and looking at how to think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+how much of that dissolves in terms of
+
+ align:start position:0%
+how much of that dissolves in terms of
+ 
+
+ align:start position:0%
+how much of that dissolves in terms of
+the equilibrium constant for the
+
+ align:start position:0%
+the equilibrium constant for the
+ 
+
+ align:start position:0%
+the equilibrium constant for the
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+okay so that's the goal today i want to
+
+ align:start position:0%
+okay so that's the goal today i want to
+ 
+
+ align:start position:0%
+okay so that's the goal today i want to
+start though
+
+ align:start position:0%
+start though
+ 
+
+ align:start position:0%
+start though
+uh by talking about why this matters
+
+ align:start position:0%
+uh by talking about why this matters
+ 
+
+ align:start position:0%
+uh by talking about why this matters
+and that's directly related to your
+
+ align:start position:0%
+and that's directly related to your
+ 
+
+ align:start position:0%
+and that's directly related to your
+goody bag
+
+ align:start position:0%
+goody bag
+ 
+
+ align:start position:0%
+goody bag
+okay so this is uh this is
+
+ align:start position:0%
+okay so this is uh this is
+ 
+
+ align:start position:0%
+okay so this is uh this is
+something some of you may have seen uh
+
+ align:start position:0%
+something some of you may have seen uh
+ 
+
+ align:start position:0%
+something some of you may have seen uh
+the data here
+
+ align:start position:0%
+the data here
+ 
+
+ align:start position:0%
+the data here
+from the 50s is from the mauna loa
+
+ align:start position:0%
+from the 50s is from the mauna loa
+ 
+
+ align:start position:0%
+from the 50s is from the mauna loa
+measurements the top of the volcano
+
+ align:start position:0%
+measurements the top of the volcano
+ 
+
+ align:start position:0%
+measurements the top of the volcano
+and uh and and this is co2 concentration
+
+ align:start position:0%
+and uh and and this is co2 concentration
+ 
+
+ align:start position:0%
+and uh and and this is co2 concentration
+parts per million in the atmosphere
+
+ align:start position:0%
+parts per million in the atmosphere
+ 
+
+ align:start position:0%
+parts per million in the atmosphere
+and but if you dig into the ice you know
+
+ align:start position:0%
+and but if you dig into the ice you know
+ 
+
+ align:start position:0%
+and but if you dig into the ice you know
+we're gonna be doing a lot of that here
+
+ align:start position:0%
+we're gonna be doing a lot of that here
+ 
+
+ align:start position:0%
+we're gonna be doing a lot of that here
+in boston over the next three months
+
+ align:start position:0%
+in boston over the next three months
+ 
+
+ align:start position:0%
+in boston over the next three months
+but if you dig deeper into the ice in
+
+ align:start position:0%
+but if you dig deeper into the ice in
+ 
+
+ align:start position:0%
+but if you dig deeper into the ice in
+the cores
+
+ align:start position:0%
+the cores
+ 
+
+ align:start position:0%
+the cores
+you go back in time it's a beautiful
+
+ align:start position:0%
+you go back in time it's a beautiful
+ 
+
+ align:start position:0%
+you go back in time it's a beautiful
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+the ice as you go down is ancient
+
+ align:start position:0%
+the ice as you go down is ancient
+ 
+
+ align:start position:0%
+the ice as you go down is ancient
+atmosphere
+
+ align:start position:0%
+atmosphere
+ 
+
+ align:start position:0%
+atmosphere
+that's cool because there's little
+
+ align:start position:0%
+that's cool because there's little
+ 
+
+ align:start position:0%
+that's cool because there's little
+bubbles remember like like
+
+ align:start position:0%
+bubbles remember like like
+ 
+
+ align:start position:0%
+bubbles remember like like
+you know there remember we talked about
+
+ align:start position:0%
+you know there remember we talked about
+ 
+
+ align:start position:0%
+you know there remember we talked about
+like the half-life of carbon 14
+
+ align:start position:0%
+like the half-life of carbon 14
+ 
+
+ align:start position:0%
+like the half-life of carbon 14
+that's trapped from say a living thing
+
+ align:start position:0%
+that's trapped from say a living thing
+ 
+
+ align:start position:0%
+that's trapped from say a living thing
+breathing it in
+
+ align:start position:0%
+breathing it in
+ 
+
+ align:start position:0%
+breathing it in
+right well you can trap directly the
+
+ align:start position:0%
+right well you can trap directly the
+ 
+
+ align:start position:0%
+right well you can trap directly the
+little bubbles of atmosphere
+
+ align:start position:0%
+little bubbles of atmosphere
+ 
+
+ align:start position:0%
+little bubbles of atmosphere
+in the ice and that's what happens and
+
+ align:start position:0%
+in the ice and that's what happens and
+ 
+
+ align:start position:0%
+in the ice and that's what happens and
+that's why we know what co2 levels were
+
+ align:start position:0%
+that's why we know what co2 levels were
+ 
+
+ align:start position:0%
+that's why we know what co2 levels were
+going back a million almost a million
+
+ align:start position:0%
+going back a million almost a million
+ 
+
+ align:start position:0%
+going back a million almost a million
+years here it's 800 thousand years of
+
+ align:start position:0%
+years here it's 800 thousand years of
+ 
+
+ align:start position:0%
+years here it's 800 thousand years of
+data
+
+ align:start position:0%
+data
+ 
+
+ align:start position:0%
+data
+and uh this is a graph that i think many
+
+ align:start position:0%
+and uh this is a graph that i think many
+ 
+
+ align:start position:0%
+and uh this is a graph that i think many
+of you see if we can't you know
+
+ align:start position:0%
+of you see if we can't you know
+ 
+
+ align:start position:0%
+of you see if we can't you know
+so so okay it's going up a lot right
+
+ align:start position:0%
+so so okay it's going up a lot right
+ 
+
+ align:start position:0%
+so so okay it's going up a lot right
+okay uh and here it is now this is just
+
+ align:start position:0%
+okay uh and here it is now this is just
+ 
+
+ align:start position:0%
+okay uh and here it is now this is just
+zooming in on the last
+
+ align:start position:0%
+zooming in on the last
+ 
+
+ align:start position:0%
+zooming in on the last
+uh uh 50 years so this is just the data
+
+ align:start position:0%
+uh uh 50 years so this is just the data
+ 
+
+ align:start position:0%
+uh uh 50 years so this is just the data
+the monolith
+
+ align:start position:0%
+the monolith
+ 
+
+ align:start position:0%
+the monolith
+load data uh and and the reason is
+
+ align:start position:0%
+load data uh and and the reason is
+ 
+
+ align:start position:0%
+load data uh and and the reason is
+because here we also have another kind
+
+ align:start position:0%
+because here we also have another kind
+ 
+
+ align:start position:0%
+because here we also have another kind
+of data so there's a lot of attention
+
+ align:start position:0%
+of data so there's a lot of attention
+ 
+
+ align:start position:0%
+of data so there's a lot of attention
+paid
+
+ align:start position:0%
+paid
+ 
+
+ align:start position:0%
+paid
+on co2 and there should be there's a lot
+
+ align:start position:0%
+on co2 and there should be there's a lot
+ 
+
+ align:start position:0%
+on co2 and there should be there's a lot
+less attention paid to what that is
+
+ align:start position:0%
+less attention paid to what that is
+ 
+
+ align:start position:0%
+less attention paid to what that is
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+to our oceans and this is a reaction
+
+ align:start position:0%
+to our oceans and this is a reaction
+ 
+
+ align:start position:0%
+to our oceans and this is a reaction
+that we will talk about more
+
+ align:start position:0%
+that we will talk about more
+ 
+
+ align:start position:0%
+that we will talk about more
+when we talk about acidification so when
+
+ align:start position:0%
+when we talk about acidification so when
+ 
+
+ align:start position:0%
+when we talk about acidification so when
+we talk about acids and bases which is
+
+ align:start position:0%
+we talk about acids and bases which is
+ 
+
+ align:start position:0%
+we talk about acids and bases which is
+coming up later
+
+ align:start position:0%
+coming up later
+ 
+
+ align:start position:0%
+coming up later
+later being wednesday and next week
+
+ align:start position:0%
+later being wednesday and next week
+ 
+
+ align:start position:0%
+later being wednesday and next week
+we'll talk more about this but i just
+
+ align:start position:0%
+we'll talk more about this but i just
+ 
+
+ align:start position:0%
+we'll talk more about this but i just
+want to tell you that when when you have
+
+ align:start position:0%
+want to tell you that when when you have
+ 
+
+ align:start position:0%
+want to tell you that when when you have
+co2 in the atmosphere going up
+
+ align:start position:0%
+co2 in the atmosphere going up
+ 
+
+ align:start position:0%
+co2 in the atmosphere going up
+then you also have co2 in the ocean
+
+ align:start position:0%
+then you also have co2 in the ocean
+ 
+
+ align:start position:0%
+then you also have co2 in the ocean
+going up so the co2 in the ocean co2 in
+
+ align:start position:0%
+going up so the co2 in the ocean co2 in
+ 
+
+ align:start position:0%
+going up so the co2 in the ocean co2 in
+the atmosphere
+
+ align:start position:0%
+the atmosphere
+ 
+
+ align:start position:0%
+the atmosphere
+is getting absorbed by the ocean
+
+ align:start position:0%
+is getting absorbed by the ocean
+ 
+
+ align:start position:0%
+is getting absorbed by the ocean
+okay so what no it's it's a lot
+
+ align:start position:0%
+okay so what no it's it's a lot
+ 
+
+ align:start position:0%
+okay so what no it's it's a lot
+of what because what happens is
+
+ align:start position:0%
+of what because what happens is
+ 
+
+ align:start position:0%
+of what because what happens is
+the co2 in the ocean the more co2 in the
+
+ align:start position:0%
+the co2 in the ocean the more co2 in the
+ 
+
+ align:start position:0%
+the co2 in the ocean the more co2 in the
+ocean
+
+ align:start position:0%
+ocean
+ 
+
+ align:start position:0%
+ocean
+is making the ocean more acidic now so
+
+ align:start position:0%
+is making the ocean more acidic now so
+ 
+
+ align:start position:0%
+is making the ocean more acidic now so
+so if you if you just write this number
+
+ align:start position:0%
+so if you if you just write this number
+ 
+
+ align:start position:0%
+so if you if you just write this number
+down because it's
+
+ align:start position:0%
+down because it's
+ 
+
+ align:start position:0%
+down because it's
+so astonishing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay past
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+past 200 years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the ocean has become
+
+ align:start position:0%
+the ocean has become
+ 
+
+ align:start position:0%
+the ocean has become
+30 percent more acidic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now that is the faster fastest
+
+ align:start position:0%
+now that is the faster fastest
+ 
+
+ align:start position:0%
+now that is the faster fastest
+fastest known change
+
+ align:start position:0%
+fastest known change
+ 
+
+ align:start position:0%
+fastest known change
+fastest known change in the ocean
+
+ align:start position:0%
+fastest known change in the ocean
+ 
+
+ align:start position:0%
+fastest known change in the ocean
+chemistry in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+50 million years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a big and very sudden change
+
+ align:start position:0%
+that's a big and very sudden change
+ 
+
+ align:start position:0%
+that's a big and very sudden change
+so the ocean is is absorbing about 22
+
+ align:start position:0%
+so the ocean is is absorbing about 22
+ 
+
+ align:start position:0%
+so the ocean is is absorbing about 22
+million tons per day
+
+ align:start position:0%
+million tons per day
+ 
+
+ align:start position:0%
+million tons per day
+of co2 and that number is going to say
+
+ align:start position:0%
+of co2 and that number is going to say
+ 
+
+ align:start position:0%
+of co2 and that number is going to say
+well okay why does that matter
+
+ align:start position:0%
+well okay why does that matter
+ 
+
+ align:start position:0%
+well okay why does that matter
+isn't it again maybe it'll do the oceans
+
+ align:start position:0%
+isn't it again maybe it'll do the oceans
+ 
+
+ align:start position:0%
+isn't it again maybe it'll do the oceans
+what it's doing to the atmosphere making
+
+ align:start position:0%
+what it's doing to the atmosphere making
+ 
+
+ align:start position:0%
+what it's doing to the atmosphere making
+things a little more
+
+ align:start position:0%
+things a little more
+ 
+
+ align:start position:0%
+things a little more
+no it's doing more because when it
+
+ align:start position:0%
+no it's doing more because when it
+ 
+
+ align:start position:0%
+no it's doing more because when it
+acidifies
+
+ align:start position:0%
+acidifies
+ 
+
+ align:start position:0%
+acidifies
+then it has a direct impact on things
+
+ align:start position:0%
+then it has a direct impact on things
+ 
+
+ align:start position:0%
+then it has a direct impact on things
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+which is a a terror pot and this is one
+
+ align:start position:0%
+which is a a terror pot and this is one
+ 
+
+ align:start position:0%
+which is a a terror pot and this is one
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+you you look at the the food chain of
+
+ align:start position:0%
+you you look at the the food chain of
+ 
+
+ align:start position:0%
+you you look at the the food chain of
+the ocean there's like three things at
+
+ align:start position:0%
+the ocean there's like three things at
+ 
+
+ align:start position:0%
+the ocean there's like three things at
+the bottom
+
+ align:start position:0%
+the bottom
+ 
+
+ align:start position:0%
+the bottom
+that's one of them i mean there's plants
+
+ align:start position:0%
+that's one of them i mean there's plants
+ 
+
+ align:start position:0%
+that's one of them i mean there's plants
+right there's there's photosynthesis and
+
+ align:start position:0%
+right there's there's photosynthesis and
+ 
+
+ align:start position:0%
+right there's there's photosynthesis and
+then there's the bottom
+
+ align:start position:0%
+then there's the bottom
+ 
+
+ align:start position:0%
+then there's the bottom
+of the food chain now you know what
+
+ align:start position:0%
+of the food chain now you know what
+ 
+
+ align:start position:0%
+of the food chain now you know what
+what's going to happen when the bottom
+
+ align:start position:0%
+what's going to happen when the bottom
+ 
+
+ align:start position:0%
+what's going to happen when the bottom
+of the food chain
+
+ align:start position:0%
+of the food chain
+ 
+
+ align:start position:0%
+of the food chain
+uh disappears right this is one of
+
+ align:start position:0%
+uh disappears right this is one of
+ 
+
+ align:start position:0%
+uh disappears right this is one of
+one of the main kinds of animals that
+
+ align:start position:0%
+one of the main kinds of animals that
+ 
+
+ align:start position:0%
+one of the main kinds of animals that
+lives at the bottom of which
+
+ align:start position:0%
+lives at the bottom of which
+ 
+
+ align:start position:0%
+lives at the bottom of which
+they've got these very small calcium
+
+ align:start position:0%
+they've got these very small calcium
+ 
+
+ align:start position:0%
+they've got these very small calcium
+carbonate shells
+
+ align:start position:0%
+carbonate shells
+ 
+
+ align:start position:0%
+carbonate shells
+if you make the ocean just a little more
+
+ align:start position:0%
+if you make the ocean just a little more
+ 
+
+ align:start position:0%
+if you make the ocean just a little more
+acidic
+
+ align:start position:0%
+acidic
+ 
+
+ align:start position:0%
+acidic
+like we're doing those shells don't
+
+ align:start position:0%
+like we're doing those shells don't
+ 
+
+ align:start position:0%
+like we're doing those shells don't
+survive
+
+ align:start position:0%
+survive
+ 
+
+ align:start position:0%
+survive
+and those animals don't survive right
+
+ align:start position:0%
+and those animals don't survive right
+ 
+
+ align:start position:0%
+and those animals don't survive right
+so that's what happens to a pteropod
+
+ align:start position:0%
+so that's what happens to a pteropod
+ 
+
+ align:start position:0%
+so that's what happens to a pteropod
+at the rate we're going in like
+
+ align:start position:0%
+at the rate we're going in like
+ 
+
+ align:start position:0%
+at the rate we're going in like
+decades of time from now that's what
+
+ align:start position:0%
+decades of time from now that's what
+ 
+
+ align:start position:0%
+decades of time from now that's what
+happens right
+
+ align:start position:0%
+happens right
+ 
+
+ align:start position:0%
+happens right
+45 days so what you have in your goodie
+
+ align:start position:0%
+45 days so what you have in your goodie
+ 
+
+ align:start position:0%
+45 days so what you have in your goodie
+bag
+
+ align:start position:0%
+bag
+ 
+
+ align:start position:0%
+bag
+is a way to see this a little bit more
+
+ align:start position:0%
+is a way to see this a little bit more
+ 
+
+ align:start position:0%
+is a way to see this a little bit more
+accelerated
+
+ align:start position:0%
+accelerated
+ 
+
+ align:start position:0%
+accelerated
+right so so here's your goodie bag okay
+
+ align:start position:0%
+right so so here's your goodie bag okay
+ 
+
+ align:start position:0%
+right so so here's your goodie bag okay
+so i wanted you to
+
+ align:start position:0%
+so i wanted you to
+ 
+
+ align:start position:0%
+so i wanted you to
+i wanted you to see what's happening in
+
+ align:start position:0%
+i wanted you to see what's happening in
+ 
+
+ align:start position:0%
+i wanted you to see what's happening in
+the ocean
+
+ align:start position:0%
+the ocean
+ 
+
+ align:start position:0%
+the ocean
+and you have now the tools to do that so
+
+ align:start position:0%
+and you have now the tools to do that so
+ 
+
+ align:start position:0%
+and you have now the tools to do that so
+in your goody bag you've got
+
+ align:start position:0%
+in your goody bag you've got
+ 
+
+ align:start position:0%
+in your goody bag you've got
+uh citric powder imagine you take a lot
+
+ align:start position:0%
+uh citric powder imagine you take a lot
+ 
+
+ align:start position:0%
+uh citric powder imagine you take a lot
+of limes and you squeeze them and then
+
+ align:start position:0%
+of limes and you squeeze them and then
+ 
+
+ align:start position:0%
+of limes and you squeeze them and then
+you dry it all out and that's what you
+
+ align:start position:0%
+you dry it all out and that's what you
+ 
+
+ align:start position:0%
+you dry it all out and that's what you
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+right citric acid okay now you're gonna
+
+ align:start position:0%
+right citric acid okay now you're gonna
+ 
+
+ align:start position:0%
+right citric acid okay now you're gonna
+mix that
+
+ align:start position:0%
+mix that
+ 
+
+ align:start position:0%
+mix that
+with water to change the ph and that's
+
+ align:start position:0%
+with water to change the ph and that's
+ 
+
+ align:start position:0%
+with water to change the ph and that's
+going to so you're going to dissolve
+
+ align:start position:0%
+going to so you're going to dissolve
+ 
+
+ align:start position:0%
+going to so you're going to dissolve
+this powder
+
+ align:start position:0%
+this powder
+ 
+
+ align:start position:0%
+this powder
+that's the topic of today's lectures
+
+ align:start position:0%
+that's the topic of today's lectures
+ 
+
+ align:start position:0%
+that's the topic of today's lectures
+dissolution right in equilibrium
+
+ align:start position:0%
+dissolution right in equilibrium
+ 
+
+ align:start position:0%
+dissolution right in equilibrium
+so you're going to mix that into water
+
+ align:start position:0%
+so you're going to mix that into water
+ 
+
+ align:start position:0%
+so you're going to mix that into water
+and you've got a scale
+
+ align:start position:0%
+and you've got a scale
+ 
+
+ align:start position:0%
+and you've got a scale
+from a previous goodie bag
+
+ align:start position:0%
+from a previous goodie bag
+ 
+
+ align:start position:0%
+from a previous goodie bag
+so my hope is that you've been using
+
+ align:start position:0%
+so my hope is that you've been using
+ 
+
+ align:start position:0%
+so my hope is that you've been using
+that on a daily basis you take it with
+
+ align:start position:0%
+that on a daily basis you take it with
+ 
+
+ align:start position:0%
+that on a daily basis you take it with
+you places
+
+ align:start position:0%
+you places
+ 
+
+ align:start position:0%
+you places
+and you can use that again here and
+
+ align:start position:0%
+and you can use that again here and
+ 
+
+ align:start position:0%
+and you can use that again here and
+you'll need that because i want you to
+
+ align:start position:0%
+you'll need that because i want you to
+ 
+
+ align:start position:0%
+you'll need that because i want you to
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+how these shells dissolve and if you
+
+ align:start position:0%
+how these shells dissolve and if you
+ 
+
+ align:start position:0%
+how these shells dissolve and if you
+lower
+
+ align:start position:0%
+lower
+ 
+
+ align:start position:0%
+lower
+the acidity more you know you we we
+
+ align:start position:0%
+the acidity more you know you we we
+ 
+
+ align:start position:0%
+the acidity more you know you we we
+don't want to wait 40 but you can't wait
+
+ align:start position:0%
+don't want to wait 40 but you can't wait
+ 
+
+ align:start position:0%
+don't want to wait 40 but you can't wait
+45 days but i want to i want you to be
+
+ align:start position:0%
+45 days but i want to i want you to be
+ 
+
+ align:start position:0%
+45 days but i want to i want you to be
+able to do these experiments in minutes
+
+ align:start position:0%
+able to do these experiments in minutes
+ 
+
+ align:start position:0%
+able to do these experiments in minutes
+so we're going to go a little lower in
+
+ align:start position:0%
+so we're going to go a little lower in
+ 
+
+ align:start position:0%
+so we're going to go a little lower in
+acidity in ph
+
+ align:start position:0%
+acidity in ph
+ 
+
+ align:start position:0%
+acidity in ph
+right but you're going to get the same
+
+ align:start position:0%
+right but you're going to get the same
+ 
+
+ align:start position:0%
+right but you're going to get the same
+result you're going to dissolve these
+
+ align:start position:0%
+result you're going to dissolve these
+ 
+
+ align:start position:0%
+result you're going to dissolve these
+shells
+
+ align:start position:0%
+shells
+ 
+
+ align:start position:0%
+shells
+okay now this is okay now uh
+
+ align:start position:0%
+okay now this is okay now uh
+ 
+
+ align:start position:0%
+okay now this is okay now uh
+please some of you are going on planes
+
+ align:start position:0%
+please some of you are going on planes
+ 
+
+ align:start position:0%
+please some of you are going on planes
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there's white powder and a scale
+
+ align:start position:0%
+there's white powder and a scale
+ 
+
+ align:start position:0%
+there's white powder and a scale
+involved in this goodie bag
+
+ align:start position:0%
+involved in this goodie bag
+ 
+
+ align:start position:0%
+involved in this goodie bag
+please don't put that in your carry-on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's just not a good it really isn't a
+
+ align:start position:0%
+it's just not a good it really isn't a
+ 
+
+ align:start position:0%
+it's just not a good it really isn't a
+good idea like we have data
+
+ align:start position:0%
+good idea like we have data
+ 
+
+ align:start position:0%
+good idea like we have data
+from students sending me pictures
+
+ align:start position:0%
+from students sending me pictures
+ 
+
+ align:start position:0%
+from students sending me pictures
+with the airport screening person
+
+ align:start position:0%
+with the airport screening person
+ 
+
+ align:start position:0%
+with the airport screening person
+so i i love the excitement of
+
+ align:start position:0%
+so i i love the excitement of
+ 
+
+ align:start position:0%
+so i i love the excitement of
+thinking about this over thanksgiving
+
+ align:start position:0%
+thinking about this over thanksgiving
+ 
+
+ align:start position:0%
+thinking about this over thanksgiving
+but put it in your suitcase
+
+ align:start position:0%
+but put it in your suitcase
+ 
+
+ align:start position:0%
+but put it in your suitcase
+if you're gonna take it home okay that's
+
+ align:start position:0%
+if you're gonna take it home okay that's
+ 
+
+ align:start position:0%
+if you're gonna take it home okay that's
+my why this matters
+
+ align:start position:0%
+my why this matters
+ 
+
+ align:start position:0%
+my why this matters
+well so we're dissolving stuff today
+
+ align:start position:0%
+well so we're dissolving stuff today
+ 
+
+ align:start position:0%
+well so we're dissolving stuff today
+that's the topic how do things dissolve
+
+ align:start position:0%
+that's the topic how do things dissolve
+ 
+
+ align:start position:0%
+that's the topic how do things dissolve
+yeah there's a citric powder that's
+
+ align:start position:0%
+yeah there's a citric powder that's
+ 
+
+ align:start position:0%
+yeah there's a citric powder that's
+citric
+
+ align:start position:0%
+citric
+ 
+
+ align:start position:0%
+citric
+acid that's gonna make water more acidic
+
+ align:start position:0%
+acid that's gonna make water more acidic
+ 
+
+ align:start position:0%
+acid that's gonna make water more acidic
+and again we're going to move into acids
+
+ align:start position:0%
+and again we're going to move into acids
+ 
+
+ align:start position:0%
+and again we're going to move into acids
+and bases next they were just talking
+
+ align:start position:0%
+and bases next they were just talking
+ 
+
+ align:start position:0%
+and bases next they were just talking
+about dissolution
+
+ align:start position:0%
+about dissolution
+ 
+
+ align:start position:0%
+about dissolution
+and so here's here's citric acid there
+
+ align:start position:0%
+and so here's here's citric acid there
+ 
+
+ align:start position:0%
+and so here's here's citric acid there
+it is now over thanksgiving i thought
+
+ align:start position:0%
+it is now over thanksgiving i thought
+ 
+
+ align:start position:0%
+it is now over thanksgiving i thought
+i'd throw this in because you might have
+
+ align:start position:0%
+i'd throw this in because you might have
+ 
+
+ align:start position:0%
+i'd throw this in because you might have
+sugar
+
+ align:start position:0%
+sugar
+ 
+
+ align:start position:0%
+sugar
+at the table you know to call it
+
+ align:start position:0%
+at the table you know to call it
+ 
+
+ align:start position:0%
+at the table you know to call it
+c12h22o11
+
+ align:start position:0%
+c12h22o11
+ 
+
+ align:start position:0%
+c12h22o11
+don't ask for the sugar if you want to
+
+ align:start position:0%
+don't ask for the sugar if you want to
+ 
+
+ align:start position:0%
+don't ask for the sugar if you want to
+add some sugar to something
+
+ align:start position:0%
+add some sugar to something
+ 
+
+ align:start position:0%
+add some sugar to something
+ask for it by molecular name now but the
+
+ align:start position:0%
+ask for it by molecular name now but the
+ 
+
+ align:start position:0%
+ask for it by molecular name now but the
+question is why do these things dissolve
+
+ align:start position:0%
+question is why do these things dissolve
+ 
+
+ align:start position:0%
+question is why do these things dissolve
+in the first place
+
+ align:start position:0%
+in the first place
+ 
+
+ align:start position:0%
+in the first place
+there's acetic acid citric acid
+
+ align:start position:0%
+there's acetic acid citric acid
+ 
+
+ align:start position:0%
+there's acetic acid citric acid
+um uh there's sugar right these are
+
+ align:start position:0%
+um uh there's sugar right these are
+ 
+
+ align:start position:0%
+um uh there's sugar right these are
+molecules that look like that
+
+ align:start position:0%
+molecules that look like that
+ 
+
+ align:start position:0%
+molecules that look like that
+why did they dissolve in the first place
+
+ align:start position:0%
+why did they dissolve in the first place
+ 
+
+ align:start position:0%
+why did they dissolve in the first place
+and the answer
+
+ align:start position:0%
+and the answer
+ 
+
+ align:start position:0%
+and the answer
+is because of all the things that we've
+
+ align:start position:0%
+is because of all the things that we've
+ 
+
+ align:start position:0%
+is because of all the things that we've
+learned
+
+ align:start position:0%
+learned
+ 
+
+ align:start position:0%
+learned
+about bonding right and about things
+
+ align:start position:0%
+about bonding right and about things
+ 
+
+ align:start position:0%
+about bonding right and about things
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+like whether a molecule is polar or not
+
+ align:start position:0%
+like whether a molecule is polar or not
+ 
+
+ align:start position:0%
+like whether a molecule is polar or not
+or in this case whether you've got the
+
+ align:start position:0%
+or in this case whether you've got the
+ 
+
+ align:start position:0%
+or in this case whether you've got the
+possibility
+
+ align:start position:0%
+possibility
+ 
+
+ align:start position:0%
+possibility
+to hydrogen bond or not
+
+ align:start position:0%
+to hydrogen bond or not
+ 
+
+ align:start position:0%
+to hydrogen bond or not
+right and so if you look at both of
+
+ align:start position:0%
+right and so if you look at both of
+ 
+
+ align:start position:0%
+right and so if you look at both of
+these that you can see
+
+ align:start position:0%
+these that you can see
+ 
+
+ align:start position:0%
+these that you can see
+that they both have a whole bunch of
+
+ align:start position:0%
+that they both have a whole bunch of
+ 
+
+ align:start position:0%
+that they both have a whole bunch of
+little oh groups
+
+ align:start position:0%
+little oh groups
+ 
+
+ align:start position:0%
+little oh groups
+that look a whole lot like things we've
+
+ align:start position:0%
+that look a whole lot like things we've
+ 
+
+ align:start position:0%
+that look a whole lot like things we've
+seen
+
+ align:start position:0%
+seen
+ 
+
+ align:start position:0%
+seen
+that like to hydrogen bond all right you
+
+ align:start position:0%
+that like to hydrogen bond all right you
+ 
+
+ align:start position:0%
+that like to hydrogen bond all right you
+see those ohs on the end there
+
+ align:start position:0%
+see those ohs on the end there
+ 
+
+ align:start position:0%
+see those ohs on the end there
+both for sugar right around the outside
+
+ align:start position:0%
+both for sugar right around the outside
+ 
+
+ align:start position:0%
+both for sugar right around the outside
+and for citric acid and and so what
+
+ align:start position:0%
+and for citric acid and and so what
+ 
+
+ align:start position:0%
+and for citric acid and and so what
+happens is if
+
+ align:start position:0%
+happens is if
+ 
+
+ align:start position:0%
+happens is if
+i put a sugar molecule into water here's
+
+ align:start position:0%
+i put a sugar molecule into water here's
+ 
+
+ align:start position:0%
+i put a sugar molecule into water here's
+a picture of it
+
+ align:start position:0%
+a picture of it
+ 
+
+ align:start position:0%
+a picture of it
+okay there's a picture of it so there's
+
+ align:start position:0%
+okay there's a picture of it so there's
+ 
+
+ align:start position:0%
+okay there's a picture of it so there's
+sugar molecules there now they start in
+
+ align:start position:0%
+sugar molecules there now they start in
+ 
+
+ align:start position:0%
+sugar molecules there now they start in
+a crystal of sugar
+
+ align:start position:0%
+a crystal of sugar
+ 
+
+ align:start position:0%
+a crystal of sugar
+right little you know you pour your
+
+ align:start position:0%
+right little you know you pour your
+ 
+
+ align:start position:0%
+right little you know you pour your
+sugar in a teaspoon of sugar
+
+ align:start position:0%
+sugar in a teaspoon of sugar
+ 
+
+ align:start position:0%
+sugar in a teaspoon of sugar
+and and then and it's in a solid but
+
+ align:start position:0%
+and and then and it's in a solid but
+ 
+
+ align:start position:0%
+and and then and it's in a solid but
+then it goes off and it breaks away
+
+ align:start position:0%
+then it goes off and it breaks away
+ 
+
+ align:start position:0%
+then it goes off and it breaks away
+into the water and those those little
+
+ align:start position:0%
+into the water and those those little
+ 
+
+ align:start position:0%
+into the water and those those little
+ones are the water molecules
+
+ align:start position:0%
+ones are the water molecules
+ 
+
+ align:start position:0%
+ones are the water molecules
+why because the water was bonding to
+
+ align:start position:0%
+why because the water was bonding to
+ 
+
+ align:start position:0%
+why because the water was bonding to
+itself
+
+ align:start position:0%
+itself
+ 
+
+ align:start position:0%
+itself
+the water has dipoles dipole-dipole
+
+ align:start position:0%
+the water has dipoles dipole-dipole
+ 
+
+ align:start position:0%
+the water has dipoles dipole-dipole
+remember that the water has
+
+ align:start position:0%
+remember that the water has
+ 
+
+ align:start position:0%
+remember that the water has
+uh hydrogen bonds
+
+ align:start position:0%
+uh hydrogen bonds
+ 
+
+ align:start position:0%
+uh hydrogen bonds
+but the sugar does too the sugar does
+
+ align:start position:0%
+but the sugar does too the sugar does
+ 
+
+ align:start position:0%
+but the sugar does too the sugar does
+too
+
+ align:start position:0%
+too
+ 
+
+ align:start position:0%
+too
+and so the water sees this this crystal
+
+ align:start position:0%
+and so the water sees this this crystal
+ 
+
+ align:start position:0%
+and so the water sees this this crystal
+of sugar and it says well hang on
+
+ align:start position:0%
+of sugar and it says well hang on
+ 
+
+ align:start position:0%
+of sugar and it says well hang on
+you know if you come out um we we could
+
+ align:start position:0%
+you know if you come out um we we could
+ 
+
+ align:start position:0%
+you know if you come out um we we could
+bond together
+
+ align:start position:0%
+bond together
+ 
+
+ align:start position:0%
+bond together
+in much the same way that we're already
+
+ align:start position:0%
+in much the same way that we're already
+ 
+
+ align:start position:0%
+in much the same way that we're already
+bonding with each other the water
+
+ align:start position:0%
+bonding with each other the water
+ 
+
+ align:start position:0%
+bonding with each other the water
+molecules are already bonding
+
+ align:start position:0%
+molecules are already bonding
+ 
+
+ align:start position:0%
+molecules are already bonding
+hydrogen dipole sugar is like well i got
+
+ align:start position:0%
+hydrogen dipole sugar is like well i got
+ 
+
+ align:start position:0%
+hydrogen dipole sugar is like well i got
+hydrogen i got dipole
+
+ align:start position:0%
+hydrogen i got dipole
+ 
+
+ align:start position:0%
+hydrogen i got dipole
+and and so it can break off and it
+
+ align:start position:0%
+and and so it can break off and it
+ 
+
+ align:start position:0%
+and and so it can break off and it
+doesn't cost
+
+ align:start position:0%
+doesn't cost
+ 
+
+ align:start position:0%
+doesn't cost
+that much energy in fact it gains energy
+
+ align:start position:0%
+that much energy in fact it gains energy
+ 
+
+ align:start position:0%
+that much energy in fact it gains energy
+by doing this
+
+ align:start position:0%
+by doing this
+ 
+
+ align:start position:0%
+by doing this
+right it can gain and so this can
+
+ align:start position:0%
+right it can gain and so this can
+ 
+
+ align:start position:0%
+right it can gain and so this can
+actually be
+
+ align:start position:0%
+actually be
+ 
+
+ align:start position:0%
+actually be
+a lower energy state overall
+
+ align:start position:0%
+a lower energy state overall
+ 
+
+ align:start position:0%
+a lower energy state overall
+now that's because
+
+ align:start position:0%
+now that's because
+ 
+
+ align:start position:0%
+now that's because
+of something that many of you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have probably heard and now we can put
+
+ align:start position:0%
+have probably heard and now we can put
+ 
+
+ align:start position:0%
+have probably heard and now we can put
+some bonding to it but it's because like
+
+ align:start position:0%
+some bonding to it but it's because like
+ 
+
+ align:start position:0%
+some bonding to it but it's because like
+dissolves like oh yeah that's technical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's technical because now we know
+
+ align:start position:0%
+that's technical because now we know
+ 
+
+ align:start position:0%
+that's technical because now we know
+what like means like means a type of
+
+ align:start position:0%
+what like means like means a type of
+ 
+
+ align:start position:0%
+what like means like means a type of
+bonding
+
+ align:start position:0%
+bonding
+ 
+
+ align:start position:0%
+bonding
+right like means a type of so there you
+
+ align:start position:0%
+right like means a type of so there you
+ 
+
+ align:start position:0%
+right like means a type of so there you
+go it's like
+
+ align:start position:0%
+go it's like
+ 
+
+ align:start position:0%
+go it's like
+water it has hydrogen bonding potential
+
+ align:start position:0%
+water it has hydrogen bonding potential
+ 
+
+ align:start position:0%
+water it has hydrogen bonding potential
+therefore
+
+ align:start position:0%
+therefore
+ 
+
+ align:start position:0%
+therefore
+it's able to dissolve in the water
+
+ align:start position:0%
+it's able to dissolve in the water
+ 
+
+ align:start position:0%
+it's able to dissolve in the water
+right so water water has
+
+ align:start position:0%
+right so water water has
+ 
+
+ align:start position:0%
+right so water water has
+well what does water have it's got
+
+ align:start position:0%
+well what does water have it's got
+ 
+
+ align:start position:0%
+well what does water have it's got
+dipoles
+
+ align:start position:0%
+dipoles
+ 
+
+ align:start position:0%
+dipoles
+right so it can do dipole-dipole stuff
+
+ align:start position:0%
+right so it can do dipole-dipole stuff
+ 
+
+ align:start position:0%
+right so it can do dipole-dipole stuff
+it's got h-bonds
+
+ align:start position:0%
+it's got h-bonds
+ 
+
+ align:start position:0%
+it's got h-bonds
+oh everything has london
+
+ align:start position:0%
+oh everything has london
+ 
+
+ align:start position:0%
+oh everything has london
+everything has london right
+
+ align:start position:0%
+everything has london right
+ 
+
+ align:start position:0%
+everything has london right
+yeah so if you got those ingredients if
+
+ align:start position:0%
+yeah so if you got those ingredients if
+ 
+
+ align:start position:0%
+yeah so if you got those ingredients if
+you got that ability
+
+ align:start position:0%
+you got that ability
+ 
+
+ align:start position:0%
+you got that ability
+if you got those likes then you might be
+
+ align:start position:0%
+if you got those likes then you might be
+ 
+
+ align:start position:0%
+if you got those likes then you might be
+able to dissolve
+
+ align:start position:0%
+able to dissolve
+ 
+
+ align:start position:0%
+able to dissolve
+okay well this is called a polar solvent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because the molecules that make it up
+
+ align:start position:0%
+because the molecules that make it up
+ 
+
+ align:start position:0%
+because the molecules that make it up
+are polar
+
+ align:start position:0%
+are polar
+ 
+
+ align:start position:0%
+are polar
+right okay they've got dipole you know
+
+ align:start position:0%
+right okay they've got dipole you know
+ 
+
+ align:start position:0%
+right okay they've got dipole you know
+actually and
+
+ align:start position:0%
+actually and
+ 
+
+ align:start position:0%
+actually and
+and so we're very interested in in
+
+ align:start position:0%
+and so we're very interested in in
+ 
+
+ align:start position:0%
+and so we're very interested in in
+understanding how things mix with other
+
+ align:start position:0%
+understanding how things mix with other
+ 
+
+ align:start position:0%
+understanding how things mix with other
+things and why they mix with other
+
+ align:start position:0%
+things and why they mix with other
+ 
+
+ align:start position:0%
+things and why they mix with other
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+um let's take a look at another example
+
+ align:start position:0%
+um let's take a look at another example
+ 
+
+ align:start position:0%
+um let's take a look at another example
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so here we have ethanol i keep on
+
+ align:start position:0%
+so here we have ethanol i keep on
+ 
+
+ align:start position:0%
+so here we have ethanol i keep on
+bringing up ethanol
+
+ align:start position:0%
+bringing up ethanol
+ 
+
+ align:start position:0%
+bringing up ethanol
+there might be some served and if you're
+
+ align:start position:0%
+there might be some served and if you're
+ 
+
+ align:start position:0%
+there might be some served and if you're
+21 or over you can have some
+
+ align:start position:0%
+21 or over you can have some
+ 
+
+ align:start position:0%
+21 or over you can have some
+otherwise it's illegal
+
+ align:start position:0%
+otherwise it's illegal
+ 
+
+ align:start position:0%
+otherwise it's illegal
+ethanol up there at the top thank
+
+ align:start position:0%
+ethanol up there at the top thank
+ 
+
+ align:start position:0%
+ethanol up there at the top thank
+goodness
+
+ align:start position:0%
+goodness
+ 
+
+ align:start position:0%
+goodness
+you will say at your thanksgiving table
+
+ align:start position:0%
+you will say at your thanksgiving table
+ 
+
+ align:start position:0%
+you will say at your thanksgiving table
+it is not methoxymethane
+
+ align:start position:0%
+it is not methoxymethane
+ 
+
+ align:start position:0%
+it is not methoxymethane
+and because if it were it would be the
+
+ align:start position:0%
+and because if it were it would be the
+ 
+
+ align:start position:0%
+and because if it were it would be the
+same chemical formula
+
+ align:start position:0%
+same chemical formula
+ 
+
+ align:start position:0%
+same chemical formula
+but the oh the o would be in the middle
+
+ align:start position:0%
+but the oh the o would be in the middle
+ 
+
+ align:start position:0%
+but the oh the o would be in the middle
+of the two c's with the ch3s on the ends
+
+ align:start position:0%
+of the two c's with the ch3s on the ends
+ 
+
+ align:start position:0%
+of the two c's with the ch3s on the ends
+and it wouldn't be able to hydrogen
+
+ align:start position:0%
+and it wouldn't be able to hydrogen
+ 
+
+ align:start position:0%
+and it wouldn't be able to hydrogen
+bonding or all this be vapor
+
+ align:start position:0%
+bonding or all this be vapor
+ 
+
+ align:start position:0%
+bonding or all this be vapor
+it'd be vapor no but it's ethanol
+
+ align:start position:0%
+it'd be vapor no but it's ethanol
+ 
+
+ align:start position:0%
+it'd be vapor no but it's ethanol
+because it has hydrogen bonding
+
+ align:start position:0%
+because it has hydrogen bonding
+ 
+
+ align:start position:0%
+because it has hydrogen bonding
+capabilities but look at what happens if
+
+ align:start position:0%
+capabilities but look at what happens if
+ 
+
+ align:start position:0%
+capabilities but look at what happens if
+it's heptanol so all i've done now is
+
+ align:start position:0%
+it's heptanol so all i've done now is
+ 
+
+ align:start position:0%
+it's heptanol so all i've done now is
+i've taken the same
+
+ align:start position:0%
+i've taken the same
+ 
+
+ align:start position:0%
+i've taken the same
+n group and i've given it more of a
+
+ align:start position:0%
+n group and i've given it more of a
+ 
+
+ align:start position:0%
+n group and i've given it more of a
+carbon chain
+
+ align:start position:0%
+carbon chain
+ 
+
+ align:start position:0%
+carbon chain
+how is that going to affect how it
+
+ align:start position:0%
+how is that going to affect how it
+ 
+
+ align:start position:0%
+how is that going to affect how it
+dissolves given what we just talked
+
+ align:start position:0%
+dissolves given what we just talked
+ 
+
+ align:start position:0%
+dissolves given what we just talked
+about that like dissolves
+
+ align:start position:0%
+about that like dissolves
+ 
+
+ align:start position:0%
+about that like dissolves
+but they both have hydrogen bond
+
+ align:start position:0%
+but they both have hydrogen bond
+ 
+
+ align:start position:0%
+but they both have hydrogen bond
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+they both have high but look more and
+
+ align:start position:0%
+they both have high but look more and
+ 
+
+ align:start position:0%
+they both have high but look more and
+more of it as you go from methanol to
+
+ align:start position:0%
+more of it as you go from methanol to
+ 
+
+ align:start position:0%
+more of it as you go from methanol to
+heptanol
+
+ align:start position:0%
+heptanol
+ 
+
+ align:start position:0%
+heptanol
+more more and more of it is something
+
+ align:start position:0%
+more more and more of it is something
+ 
+
+ align:start position:0%
+more more and more of it is something
+else
+
+ align:start position:0%
+else
+ 
+
+ align:start position:0%
+else
+it's only london
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's going to happen now if i put
+
+ align:start position:0%
+so what's going to happen now if i put
+ 
+
+ align:start position:0%
+so what's going to happen now if i put
+this in the water
+
+ align:start position:0%
+this in the water
+ 
+
+ align:start position:0%
+this in the water
+well we can see let's go in series
+
+ align:start position:0%
+well we can see let's go in series
+ 
+
+ align:start position:0%
+well we can see let's go in series
+here's methanol
+
+ align:start position:0%
+here's methanol
+ 
+
+ align:start position:0%
+here's methanol
+ethanol propanol right butanol pentanol
+
+ align:start position:0%
+ethanol propanol right butanol pentanol
+ 
+
+ align:start position:0%
+ethanol propanol right butanol pentanol
+hexanol heptanol is down at the bottom
+
+ align:start position:0%
+hexanol heptanol is down at the bottom
+ 
+
+ align:start position:0%
+hexanol heptanol is down at the bottom
+and there's the water
+
+ align:start position:0%
+and there's the water
+ 
+
+ align:start position:0%
+and there's the water
+solubility all we got to write that down
+
+ align:start position:0%
+solubility all we got to write that down
+ 
+
+ align:start position:0%
+solubility all we got to write that down
+solubility solubility
+
+ align:start position:0%
+solubility solubility
+ 
+
+ align:start position:0%
+solubility solubility
+okay so solubility is
+
+ align:start position:0%
+okay so solubility is
+ 
+
+ align:start position:0%
+okay so solubility is
+kind of what it sounds like the ability
+
+ align:start position:0%
+kind of what it sounds like the ability
+ 
+
+ align:start position:0%
+kind of what it sounds like the ability
+for a solute
+
+ align:start position:0%
+for a solute
+ 
+
+ align:start position:0%
+for a solute
+that's the thing we're dissolving
+
+ align:start position:0%
+that's the thing we're dissolving
+ 
+
+ align:start position:0%
+that's the thing we're dissolving
+okay to dissolve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a solvent
+
+ align:start position:0%
+in a solvent
+ 
+
+ align:start position:0%
+in a solvent
+that's the thing we're trying to
+
+ align:start position:0%
+that's the thing we're trying to
+ 
+
+ align:start position:0%
+that's the thing we're trying to
+dissolve it into
+
+ align:start position:0%
+dissolve it into
+ 
+
+ align:start position:0%
+dissolve it into
+that's the solubility and we'll be
+
+ align:start position:0%
+that's the solubility and we'll be
+ 
+
+ align:start position:0%
+that's the solubility and we'll be
+talking about the maximum solubility in
+
+ align:start position:0%
+talking about the maximum solubility in
+ 
+
+ align:start position:0%
+talking about the maximum solubility in
+just a few minutes which is what we
+
+ align:start position:0%
+just a few minutes which is what we
+ 
+
+ align:start position:0%
+just a few minutes which is what we
+usually
+
+ align:start position:0%
+usually
+ 
+
+ align:start position:0%
+usually
+say what's the solubility we often mean
+
+ align:start position:0%
+say what's the solubility we often mean
+ 
+
+ align:start position:0%
+say what's the solubility we often mean
+the maximum
+
+ align:start position:0%
+the maximum
+ 
+
+ align:start position:0%
+the maximum
+well that's what's listed here the
+
+ align:start position:0%
+well that's what's listed here the
+ 
+
+ align:start position:0%
+well that's what's listed here the
+maximum right so what
+
+ align:start position:0%
+maximum right so what
+ 
+
+ align:start position:0%
+maximum right so what
+okay oh okay uh methanol ethanol
+
+ align:start position:0%
+okay oh okay uh methanol ethanol
+ 
+
+ align:start position:0%
+okay oh okay uh methanol ethanol
+miscible
+
+ align:start position:0%
+miscible
+ 
+
+ align:start position:0%
+miscible
+so you can put as much as you want and
+
+ align:start position:0%
+so you can put as much as you want and
+ 
+
+ align:start position:0%
+so you can put as much as you want and
+it'll always
+
+ align:start position:0%
+it'll always
+ 
+
+ align:start position:0%
+it'll always
+get you know keep mixing in with the
+
+ align:start position:0%
+get you know keep mixing in with the
+ 
+
+ align:start position:0%
+get you know keep mixing in with the
+water but now look
+
+ align:start position:0%
+water but now look
+ 
+
+ align:start position:0%
+water but now look
+once you get to butanol pentanol hexanol
+
+ align:start position:0%
+once you get to butanol pentanol hexanol
+ 
+
+ align:start position:0%
+once you get to butanol pentanol hexanol
+it starts going down
+
+ align:start position:0%
+it starts going down
+ 
+
+ align:start position:0%
+it starts going down
+you can't mix as much as you want in
+
+ align:start position:0%
+you can't mix as much as you want in
+ 
+
+ align:start position:0%
+you can't mix as much as you want in
+fact it's less and less and less and the
+
+ align:start position:0%
+fact it's less and less and less and the
+ 
+
+ align:start position:0%
+fact it's less and less and less and the
+reason
+
+ align:start position:0%
+reason
+ 
+
+ align:start position:0%
+reason
+we now know is because of what i just
+
+ align:start position:0%
+we now know is because of what i just
+ 
+
+ align:start position:0%
+we now know is because of what i just
+said
+
+ align:start position:0%
+said
+ 
+
+ align:start position:0%
+said
+right as you go down the hydrogen bond
+
+ align:start position:0%
+right as you go down the hydrogen bond
+ 
+
+ align:start position:0%
+right as you go down the hydrogen bond
+and dipole dipole-dipole
+
+ align:start position:0%
+and dipole dipole-dipole
+ 
+
+ align:start position:0%
+and dipole dipole-dipole
+becomes less important because you've
+
+ align:start position:0%
+becomes less important because you've
+ 
+
+ align:start position:0%
+becomes less important because you've
+got more and more of the molecule
+
+ align:start position:0%
+got more and more of the molecule
+ 
+
+ align:start position:0%
+got more and more of the molecule
+that's only london and so it's less
+
+ align:start position:0%
+that's only london and so it's less
+ 
+
+ align:start position:0%
+that's only london and so it's less
+like the water environment the bonding
+
+ align:start position:0%
+like the water environment the bonding
+ 
+
+ align:start position:0%
+like the water environment the bonding
+environment that the water liked
+
+ align:start position:0%
+environment that the water liked
+ 
+
+ align:start position:0%
+environment that the water liked
+with itself and so it has
+
+ align:start position:0%
+with itself and so it has
+ 
+
+ align:start position:0%
+with itself and so it has
+more of a trouble more trouble
+
+ align:start position:0%
+more of a trouble more trouble
+ 
+
+ align:start position:0%
+more of a trouble more trouble
+dissolving and being energetically
+
+ align:start position:0%
+dissolving and being energetically
+ 
+
+ align:start position:0%
+dissolving and being energetically
+favorable
+
+ align:start position:0%
+favorable
+ 
+
+ align:start position:0%
+favorable
+isolated by those water molecules by the
+
+ align:start position:0%
+isolated by those water molecules by the
+ 
+
+ align:start position:0%
+isolated by those water molecules by the
+way does anybody know the origin
+
+ align:start position:0%
+way does anybody know the origin
+ 
+
+ align:start position:0%
+way does anybody know the origin
+of the word proof speaking of ethanol
+
+ align:start position:0%
+of the word proof speaking of ethanol
+ 
+
+ align:start position:0%
+of the word proof speaking of ethanol
+if you buy a bottle of ethanol uh
+
+ align:start position:0%
+if you buy a bottle of ethanol uh
+ 
+
+ align:start position:0%
+if you buy a bottle of ethanol uh
+at the at the supermarket okay so
+
+ align:start position:0%
+at the at the supermarket okay so
+ 
+
+ align:start position:0%
+at the at the supermarket okay so
+there's gin
+
+ align:start position:0%
+there's gin
+ 
+
+ align:start position:0%
+there's gin
+or vodka or whatever and and it says
+
+ align:start position:0%
+or vodka or whatever and and it says
+ 
+
+ align:start position:0%
+or vodka or whatever and and it says
+it's something percent out here 20
+
+ align:start position:0%
+it's something percent out here 20
+ 
+
+ align:start position:0%
+it's something percent out here 20
+alcohol 40 proof
+
+ align:start position:0%
+alcohol 40 proof
+ 
+
+ align:start position:0%
+alcohol 40 proof
+does anybody know where that comes from
+
+ align:start position:0%
+does anybody know where that comes from
+ 
+
+ align:start position:0%
+does anybody know where that comes from
+it's this it's just
+
+ align:start position:0%
+it's this it's just
+ 
+
+ align:start position:0%
+it's this it's just
+but what they did they didn't know if
+
+ align:start position:0%
+but what they did they didn't know if
+ 
+
+ align:start position:0%
+but what they did they didn't know if
+you were making good alcohol back at the
+
+ align:start position:0%
+you were making good alcohol back at the
+ 
+
+ align:start position:0%
+you were making good alcohol back at the
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+and they said well i don't i don't have
+
+ align:start position:0%
+and they said well i don't i don't have
+ 
+
+ align:start position:0%
+and they said well i don't i don't have
+all these detailed abilities to measure
+
+ align:start position:0%
+all these detailed abilities to measure
+ 
+
+ align:start position:0%
+all these detailed abilities to measure
+and quantify it so
+
+ align:start position:0%
+and quantify it so
+ 
+
+ align:start position:0%
+and quantify it so
+i'm just going to light it on fire that
+
+ align:start position:0%
+i'm just going to light it on fire that
+ 
+
+ align:start position:0%
+i'm just going to light it on fire that
+is exactly what
+
+ align:start position:0%
+is exactly what
+ 
+
+ align:start position:0%
+is exactly what
+p is this a good bottle of gin i don't
+
+ align:start position:0%
+p is this a good bottle of gin i don't
+ 
+
+ align:start position:0%
+p is this a good bottle of gin i don't
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+let's light it on fire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's what they did and it turns out
+
+ align:start position:0%
+that's what they did and it turns out
+ 
+
+ align:start position:0%
+that's what they did and it turns out
+that if ethanol and water
+
+ align:start position:0%
+that if ethanol and water
+ 
+
+ align:start position:0%
+that if ethanol and water
+are at 50 50 mixture or more
+
+ align:start position:0%
+are at 50 50 mixture or more
+ 
+
+ align:start position:0%
+are at 50 50 mixture or more
+it will light on fire don't try that
+
+ align:start position:0%
+it will light on fire don't try that
+ 
+
+ align:start position:0%
+it will light on fire don't try that
+please
+
+ align:start position:0%
+please
+ 
+
+ align:start position:0%
+please
+don't do these experiments but so
+
+ align:start position:0%
+don't do these experiments but so
+ 
+
+ align:start position:0%
+don't do these experiments but so
+that meant that mint is this a good
+
+ align:start position:0%
+that meant that mint is this a good
+ 
+
+ align:start position:0%
+that meant that mint is this a good
+bottle of gin
+
+ align:start position:0%
+bottle of gin
+ 
+
+ align:start position:0%
+bottle of gin
+well if it's 50 50 i'm gonna say it's a
+
+ align:start position:0%
+well if it's 50 50 i'm gonna say it's a
+ 
+
+ align:start position:0%
+well if it's 50 50 i'm gonna say it's a
+good bottle of gin
+
+ align:start position:0%
+good bottle of gin
+ 
+
+ align:start position:0%
+good bottle of gin
+so let's light it on fire oh it lit on
+
+ align:start position:0%
+so let's light it on fire oh it lit on
+ 
+
+ align:start position:0%
+so let's light it on fire oh it lit on
+fire that's 100
+
+ align:start position:0%
+fire that's 100
+ 
+
+ align:start position:0%
+fire that's 100
+proof that it's good
+
+ align:start position:0%
+proof that it's good
+ 
+
+ align:start position:0%
+proof that it's good
+that is true that is the origin of the
+
+ align:start position:0%
+that is true that is the origin of the
+ 
+
+ align:start position:0%
+that is true that is the origin of the
+word proof
+
+ align:start position:0%
+word proof
+ 
+
+ align:start position:0%
+word proof
+it is proof that it's mixed well
+
+ align:start position:0%
+it is proof that it's mixed well
+ 
+
+ align:start position:0%
+it is proof that it's mixed well
+and it's good stuff okay
+
+ align:start position:0%
+and it's good stuff okay
+ 
+
+ align:start position:0%
+and it's good stuff okay
+mix dissolution dissolution
+
+ align:start position:0%
+mix dissolution dissolution
+ 
+
+ align:start position:0%
+mix dissolution dissolution
+oh what else can we try to dissolve okay
+
+ align:start position:0%
+oh what else can we try to dissolve okay
+ 
+
+ align:start position:0%
+oh what else can we try to dissolve okay
+we're dissolving alcohol we're going
+
+ align:start position:0%
+we're dissolving alcohol we're going
+ 
+
+ align:start position:0%
+we're dissolving alcohol we're going
+down to heptanol we're lucky it's not
+
+ align:start position:0%
+down to heptanol we're lucky it's not
+ 
+
+ align:start position:0%
+down to heptanol we're lucky it's not
+methoxy methane
+
+ align:start position:0%
+methoxy methane
+ 
+
+ align:start position:0%
+methoxy methane
+um we talked about sugar you know so
+
+ align:start position:0%
+um we talked about sugar you know so
+ 
+
+ align:start position:0%
+um we talked about sugar you know so
+we got to have a framework by the way so
+
+ align:start position:0%
+we got to have a framework by the way so
+ 
+
+ align:start position:0%
+we got to have a framework by the way so
+okay solubility the ability for solute
+
+ align:start position:0%
+okay solubility the ability for solute
+ 
+
+ align:start position:0%
+okay solubility the ability for solute
+to dissolve
+
+ align:start position:0%
+to dissolve
+ 
+
+ align:start position:0%
+to dissolve
+and now okay there's a context here
+
+ align:start position:0%
+and now okay there's a context here
+ 
+
+ align:start position:0%
+and now okay there's a context here
+right let's suppose i'm dissolving
+
+ align:start position:0%
+right let's suppose i'm dissolving
+ 
+
+ align:start position:0%
+right let's suppose i'm dissolving
+sugar right so so sugar
+
+ align:start position:0%
+sugar right so so sugar
+ 
+
+ align:start position:0%
+sugar right so so sugar
+how are we going to write this
+
+ align:start position:0%
+how are we going to write this
+ 
+
+ align:start position:0%
+how are we going to write this
+dissolving down
+
+ align:start position:0%
+dissolving down
+ 
+
+ align:start position:0%
+dissolving down
+well sugar is c12 okay
+
+ align:start position:0%
+well sugar is c12 okay
+ 
+
+ align:start position:0%
+well sugar is c12 okay
+h22011
+
+ align:start position:0%
+h22011
+ 
+
+ align:start position:0%
+h22011
+and and if we put it in water well you
+
+ align:start position:0%
+and and if we put it in water well you
+ 
+
+ align:start position:0%
+and and if we put it in water well you
+know we could we could formally write
+
+ align:start position:0%
+know we could we could formally write
+ 
+
+ align:start position:0%
+know we could we could formally write
+the whole thing out
+
+ align:start position:0%
+the whole thing out
+ 
+
+ align:start position:0%
+the whole thing out
+right we can write it out we can say
+
+ align:start position:0%
+right we can write it out we can say
+ 
+
+ align:start position:0%
+right we can write it out we can say
+well i'm going to add water to it
+
+ align:start position:0%
+well i'm going to add water to it
+ 
+
+ align:start position:0%
+well i'm going to add water to it
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's going to go to well okay it's
+
+ align:start position:0%
+and that's going to go to well okay it's
+ 
+
+ align:start position:0%
+and that's going to go to well okay it's
+going to go to c12
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus more water but there's something
+
+ align:start position:0%
+plus more water but there's something
+ 
+
+ align:start position:0%
+plus more water but there's something
+very important that i'm leaving out
+
+ align:start position:0%
+very important that i'm leaving out
+ 
+
+ align:start position:0%
+very important that i'm leaving out
+and when you think about dissolution you
+
+ align:start position:0%
+and when you think about dissolution you
+ 
+
+ align:start position:0%
+and when you think about dissolution you
+got to keep track
+
+ align:start position:0%
+got to keep track
+ 
+
+ align:start position:0%
+got to keep track
+what was it was it a solid was it a
+
+ align:start position:0%
+what was it was it a solid was it a
+ 
+
+ align:start position:0%
+what was it was it a solid was it a
+liquid or was it something dissolved in
+
+ align:start position:0%
+liquid or was it something dissolved in
+ 
+
+ align:start position:0%
+liquid or was it something dissolved in
+a liquid
+
+ align:start position:0%
+a liquid
+ 
+
+ align:start position:0%
+a liquid
+right so this started as a solid so we
+
+ align:start position:0%
+right so this started as a solid so we
+ 
+
+ align:start position:0%
+right so this started as a solid so we
+put an s there
+
+ align:start position:0%
+put an s there
+ 
+
+ align:start position:0%
+put an s there
+this started as a liquid this is the
+
+ align:start position:0%
+this started as a liquid this is the
+ 
+
+ align:start position:0%
+this started as a liquid this is the
+dissolved thing so we put an aq
+
+ align:start position:0%
+dissolved thing so we put an aq
+ 
+
+ align:start position:0%
+dissolved thing so we put an aq
+and the aq means aqueous it is in an
+
+ align:start position:0%
+and the aq means aqueous it is in an
+ 
+
+ align:start position:0%
+and the aq means aqueous it is in an
+aqueous solution it is a dissolved
+
+ align:start position:0%
+aqueous solution it is a dissolved
+ 
+
+ align:start position:0%
+aqueous solution it is a dissolved
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+right and so and so here this is a
+
+ align:start position:0%
+right and so and so here this is a
+ 
+
+ align:start position:0%
+right and so and so here this is a
+liquid now the other thing that
+
+ align:start position:0%
+liquid now the other thing that
+ 
+
+ align:start position:0%
+liquid now the other thing that
+that happens
+
+ align:start position:0%
+that happens
+ 
+
+ align:start position:0%
+that happens
+is well okay the h2o is kind of there
+
+ align:start position:0%
+is well okay the h2o is kind of there
+ 
+
+ align:start position:0%
+is well okay the h2o is kind of there
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+it's all over the place it's the solvent
+
+ align:start position:0%
+it's all over the place it's the solvent
+ 
+
+ align:start position:0%
+it's all over the place it's the solvent
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and so we often leave it out because
+
+ align:start position:0%
+and so we often leave it out because
+ 
+
+ align:start position:0%
+and so we often leave it out because
+it's everywhere on both sides right
+
+ align:start position:0%
+it's everywhere on both sides right
+ 
+
+ align:start position:0%
+it's everywhere on both sides right
+and so often what you'll see and we'll
+
+ align:start position:0%
+and so often what you'll see and we'll
+ 
+
+ align:start position:0%
+and so often what you'll see and we'll
+write more of these
+
+ align:start position:0%
+write more of these
+ 
+
+ align:start position:0%
+write more of these
+coming is that you might write a
+
+ align:start position:0%
+coming is that you might write a
+ 
+
+ align:start position:0%
+coming is that you might write a
+dissolution
+
+ align:start position:0%
+dissolution
+ 
+
+ align:start position:0%
+dissolution
+of sugar as this
+
+ align:start position:0%
+of sugar as this
+ 
+
+ align:start position:0%
+of sugar as this
+solid and it just goes to something
+
+ align:start position:0%
+solid and it just goes to something
+ 
+
+ align:start position:0%
+solid and it just goes to something
+that is dissolved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you know that what happened there is
+
+ align:start position:0%
+and you know that what happened there is
+ 
+
+ align:start position:0%
+and you know that what happened there is
+sometimes you'll also see it like this
+
+ align:start position:0%
+sometimes you'll also see it like this
+ 
+
+ align:start position:0%
+sometimes you'll also see it like this
+what'd you do on the arrow i added water
+
+ align:start position:0%
+what'd you do on the arrow i added water
+ 
+
+ align:start position:0%
+what'd you do on the arrow i added water
+that's what the arrow did okay so i'm
+
+ align:start position:0%
+that's what the arrow did okay so i'm
+ 
+
+ align:start position:0%
+that's what the arrow did okay so i'm
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+just getting comfortable with writing
+
+ align:start position:0%
+just getting comfortable with writing
+ 
+
+ align:start position:0%
+just getting comfortable with writing
+these dissolution reactions
+
+ align:start position:0%
+these dissolution reactions
+ 
+
+ align:start position:0%
+these dissolution reactions
+okay now what else can i dissolve well
+
+ align:start position:0%
+okay now what else can i dissolve well
+ 
+
+ align:start position:0%
+okay now what else can i dissolve well
+here's another good example vitamin a
+
+ align:start position:0%
+here's another good example vitamin a
+ 
+
+ align:start position:0%
+here's another good example vitamin a
+vitamins
+
+ align:start position:0%
+vitamins
+ 
+
+ align:start position:0%
+vitamins
+there's some vitamins you can have as
+
+ align:start position:0%
+there's some vitamins you can have as
+ 
+
+ align:start position:0%
+there's some vitamins you can have as
+much as you want pretty much
+
+ align:start position:0%
+much as you want pretty much
+ 
+
+ align:start position:0%
+much as you want pretty much
+why because they're water soluble
+
+ align:start position:0%
+why because they're water soluble
+ 
+
+ align:start position:0%
+why because they're water soluble
+and other vitamins are fat soluble that
+
+ align:start position:0%
+and other vitamins are fat soluble that
+ 
+
+ align:start position:0%
+and other vitamins are fat soluble that
+means they they
+
+ align:start position:0%
+means they they
+ 
+
+ align:start position:0%
+means they they
+they just they don't like water as much
+
+ align:start position:0%
+they just they don't like water as much
+ 
+
+ align:start position:0%
+they just they don't like water as much
+as they like the hydrophobic
+
+ align:start position:0%
+as they like the hydrophobic
+ 
+
+ align:start position:0%
+as they like the hydrophobic
+hydrophobic molecules of fat cells
+
+ align:start position:0%
+hydrophobic molecules of fat cells
+ 
+
+ align:start position:0%
+hydrophobic molecules of fat cells
+and so they go into fatty tissue
+
+ align:start position:0%
+and so they go into fatty tissue
+ 
+
+ align:start position:0%
+and so they go into fatty tissue
+where they don't come out that's why
+
+ align:start position:0%
+where they don't come out that's why
+ 
+
+ align:start position:0%
+where they don't come out that's why
+don't have do not have unlimited amounts
+
+ align:start position:0%
+don't have do not have unlimited amounts
+ 
+
+ align:start position:0%
+don't have do not have unlimited amounts
+of vitamin a
+
+ align:start position:0%
+of vitamin a
+ 
+
+ align:start position:0%
+of vitamin a
+that's not good for you but vitamin c
+
+ align:start position:0%
+that's not good for you but vitamin c
+ 
+
+ align:start position:0%
+that's not good for you but vitamin c
+no problem no problem because it's going
+
+ align:start position:0%
+no problem no problem because it's going
+ 
+
+ align:start position:0%
+no problem no problem because it's going
+to dissolve in water
+
+ align:start position:0%
+to dissolve in water
+ 
+
+ align:start position:0%
+to dissolve in water
+right and so your body can take in and
+
+ align:start position:0%
+right and so your body can take in and
+ 
+
+ align:start position:0%
+right and so your body can take in and
+get rid of as much of it as you want but
+
+ align:start position:0%
+get rid of as much of it as you want but
+ 
+
+ align:start position:0%
+get rid of as much of it as you want but
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+get if it's dissolved in fat cells
+
+ align:start position:0%
+get if it's dissolved in fat cells
+ 
+
+ align:start position:0%
+get if it's dissolved in fat cells
+that's a different thing so vitamin a
+
+ align:start position:0%
+that's a different thing so vitamin a
+ 
+
+ align:start position:0%
+that's a different thing so vitamin a
+vitamin c and you can see it right there
+
+ align:start position:0%
+vitamin c and you can see it right there
+ 
+
+ align:start position:0%
+vitamin c and you can see it right there
+from the chemistry
+
+ align:start position:0%
+from the chemistry
+ 
+
+ align:start position:0%
+from the chemistry
+this is it look at all those oh groups
+
+ align:start position:0%
+this is it look at all those oh groups
+ 
+
+ align:start position:0%
+this is it look at all those oh groups
+in vitamin c
+
+ align:start position:0%
+in vitamin c
+ 
+
+ align:start position:0%
+in vitamin c
+look at that oh that's gonna love
+
+ align:start position:0%
+look at that oh that's gonna love
+ 
+
+ align:start position:0%
+look at that oh that's gonna love
+hydrogen bonding
+
+ align:start position:0%
+hydrogen bonding
+ 
+
+ align:start position:0%
+hydrogen bonding
+and on vitamin a you just got the one
+
+ align:start position:0%
+and on vitamin a you just got the one
+ 
+
+ align:start position:0%
+and on vitamin a you just got the one
+all the way down there at the bottom
+
+ align:start position:0%
+all the way down there at the bottom
+ 
+
+ align:start position:0%
+all the way down there at the bottom
+it's hydrophobic by the way
+
+ align:start position:0%
+it's hydrophobic by the way
+ 
+
+ align:start position:0%
+it's hydrophobic by the way
+in this class we do not say the words
+
+ align:start position:0%
+in this class we do not say the words
+ 
+
+ align:start position:0%
+in this class we do not say the words
+hydrophobic interaction because that
+
+ align:start position:0%
+hydrophobic interaction because that
+ 
+
+ align:start position:0%
+hydrophobic interaction because that
+doesn't make sense
+
+ align:start position:0%
+doesn't make sense
+ 
+
+ align:start position:0%
+doesn't make sense
+there's no such thing as a hydrophobic
+
+ align:start position:0%
+there's no such thing as a hydrophobic
+ 
+
+ align:start position:0%
+there's no such thing as a hydrophobic
+interaction
+
+ align:start position:0%
+interaction
+ 
+
+ align:start position:0%
+interaction
+no hydrophobic interaction is misused
+
+ align:start position:0%
+no hydrophobic interaction is misused
+ 
+
+ align:start position:0%
+no hydrophobic interaction is misused
+what it really means is that something
+
+ align:start position:0%
+what it really means is that something
+ 
+
+ align:start position:0%
+what it really means is that something
+that's hydrophobic likes itself
+
+ align:start position:0%
+that's hydrophobic likes itself
+ 
+
+ align:start position:0%
+that's hydrophobic likes itself
+more you know being together with itself
+
+ align:start position:0%
+more you know being together with itself
+ 
+
+ align:start position:0%
+more you know being together with itself
+more than than it likes being in the
+
+ align:start position:0%
+more than than it likes being in the
+ 
+
+ align:start position:0%
+more than than it likes being in the
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+or something hydrophilic that's what is
+
+ align:start position:0%
+or something hydrophilic that's what is
+ 
+
+ align:start position:0%
+or something hydrophilic that's what is
+meant but there's no actual interaction
+
+ align:start position:0%
+meant but there's no actual interaction
+ 
+
+ align:start position:0%
+meant but there's no actual interaction
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+okay hydrophobic hydrophilic those now
+
+ align:start position:0%
+okay hydrophobic hydrophilic those now
+ 
+
+ align:start position:0%
+okay hydrophobic hydrophilic those now
+okay well those are other things you can
+
+ align:start position:0%
+okay well those are other things you can
+ 
+
+ align:start position:0%
+okay well those are other things you can
+think about dissolving
+
+ align:start position:0%
+think about dissolving
+ 
+
+ align:start position:0%
+think about dissolving
+you could also dissolve salt
+
+ align:start position:0%
+you could also dissolve salt
+ 
+
+ align:start position:0%
+you could also dissolve salt
+and this is what we're going to use as
+
+ align:start position:0%
+and this is what we're going to use as
+ 
+
+ align:start position:0%
+and this is what we're going to use as
+examples
+
+ align:start position:0%
+examples
+ 
+
+ align:start position:0%
+examples
+and this is a picture of a salt crystal
+
+ align:start position:0%
+and this is a picture of a salt crystal
+ 
+
+ align:start position:0%
+and this is a picture of a salt crystal
+so we showed the sugar
+
+ align:start position:0%
+so we showed the sugar
+ 
+
+ align:start position:0%
+so we showed the sugar
+now here's salt now so the thing about
+
+ align:start position:0%
+now here's salt now so the thing about
+ 
+
+ align:start position:0%
+now here's salt now so the thing about
+salt
+
+ align:start position:0%
+salt
+ 
+
+ align:start position:0%
+salt
+where's my sugar there's the sugar and
+
+ align:start position:0%
+where's my sugar there's the sugar and
+ 
+
+ align:start position:0%
+where's my sugar there's the sugar and
+let's put salt underneath it
+
+ align:start position:0%
+let's put salt underneath it
+ 
+
+ align:start position:0%
+let's put salt underneath it
+the thing about salt
+
+ align:start position:0%
+the thing about salt
+ 
+
+ align:start position:0%
+the thing about salt
+which is really just a general term for
+
+ align:start position:0%
+which is really just a general term for
+ 
+
+ align:start position:0%
+which is really just a general term for
+when you have an ionic solid that
+
+ align:start position:0%
+when you have an ionic solid that
+ 
+
+ align:start position:0%
+when you have an ionic solid that
+that can be made from a mixture of acids
+
+ align:start position:0%
+that can be made from a mixture of acids
+ 
+
+ align:start position:0%
+that can be made from a mixture of acids
+and bases and dissolves
+
+ align:start position:0%
+and bases and dissolves
+ 
+
+ align:start position:0%
+and bases and dissolves
+oftentimes a little bit at least in
+
+ align:start position:0%
+oftentimes a little bit at least in
+ 
+
+ align:start position:0%
+oftentimes a little bit at least in
+water right
+
+ align:start position:0%
+water right
+ 
+
+ align:start position:0%
+water right
+okay so so a salt uh let's see
+
+ align:start position:0%
+okay so so a salt uh let's see
+ 
+
+ align:start position:0%
+okay so so a salt uh let's see
+a salt or like an ionic solid let's say
+
+ align:start position:0%
+a salt or like an ionic solid let's say
+ 
+
+ align:start position:0%
+a salt or like an ionic solid let's say
+for now
+
+ align:start position:0%
+for now
+ 
+
+ align:start position:0%
+for now
+okay this gives
+
+ align:start position:0%
+okay this gives
+ 
+
+ align:start position:0%
+okay this gives
+something different because this breaks
+
+ align:start position:0%
+something different because this breaks
+ 
+
+ align:start position:0%
+something different because this breaks
+apart
+
+ align:start position:0%
+apart
+ 
+
+ align:start position:0%
+apart
+into positive and negative
+
+ align:start position:0%
+into positive and negative
+ 
+
+ align:start position:0%
+into positive and negative
+ions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that they contain right so in the case
+
+ align:start position:0%
+that they contain right so in the case
+ 
+
+ align:start position:0%
+that they contain right so in the case
+of sodium
+
+ align:start position:0%
+of sodium
+ 
+
+ align:start position:0%
+of sodium
+and chlorine sodium chloride well that's
+
+ align:start position:0%
+and chlorine sodium chloride well that's
+ 
+
+ align:start position:0%
+and chlorine sodium chloride well that's
+going to dissociate if you pour
+
+ align:start position:0%
+going to dissociate if you pour
+ 
+
+ align:start position:0%
+going to dissociate if you pour
+salt in water then here's the reaction
+
+ align:start position:0%
+salt in water then here's the reaction
+ 
+
+ align:start position:0%
+salt in water then here's the reaction
+for that you got sodium chloride solid
+
+ align:start position:0%
+for that you got sodium chloride solid
+ 
+
+ align:start position:0%
+for that you got sodium chloride solid
+okay we put it in water that's going to
+
+ align:start position:0%
+okay we put it in water that's going to
+ 
+
+ align:start position:0%
+okay we put it in water that's going to
+go into ions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so i put that in water it and it's
+
+ align:start position:0%
+okay so i put that in water it and it's
+ 
+
+ align:start position:0%
+okay so i put that in water it and it's
+it's different in the sense that it
+
+ align:start position:0%
+it's different in the sense that it
+ 
+
+ align:start position:0%
+it's different in the sense that it
+doesn't
+
+ align:start position:0%
+doesn't
+ 
+
+ align:start position:0%
+doesn't
+break down into the molecules that made
+
+ align:start position:0%
+break down into the molecules that made
+ 
+
+ align:start position:0%
+break down into the molecules that made
+up the sugar
+
+ align:start position:0%
+up the sugar
+ 
+
+ align:start position:0%
+up the sugar
+does that have a particle of sugar
+
+ align:start position:0%
+does that have a particle of sugar
+ 
+
+ align:start position:0%
+does that have a particle of sugar
+that's got millions and millions of
+
+ align:start position:0%
+that's got millions and millions of
+ 
+
+ align:start position:0%
+that's got millions and millions of
+molecules in it
+
+ align:start position:0%
+molecules in it
+ 
+
+ align:start position:0%
+molecules in it
+now they dissociate that's what the aq
+
+ align:start position:0%
+now they dissociate that's what the aq
+ 
+
+ align:start position:0%
+now they dissociate that's what the aq
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+okay those are neutral here they're it's
+
+ align:start position:0%
+okay those are neutral here they're it's
+ 
+
+ align:start position:0%
+okay those are neutral here they're it's
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+it's a solid but you can understand this
+
+ align:start position:0%
+it's a solid but you can understand this
+ 
+
+ align:start position:0%
+it's a solid but you can understand this
+from looking at it and thinking about it
+
+ align:start position:0%
+from looking at it and thinking about it
+ 
+
+ align:start position:0%
+from looking at it and thinking about it
+look at the way those water molecules
+
+ align:start position:0%
+look at the way those water molecules
+ 
+
+ align:start position:0%
+look at the way those water molecules
+are oriented
+
+ align:start position:0%
+are oriented
+ 
+
+ align:start position:0%
+are oriented
+right they're they're pointing to the cl
+
+ align:start position:0%
+right they're they're pointing to the cl
+ 
+
+ align:start position:0%
+right they're they're pointing to the cl
+with their positivity
+
+ align:start position:0%
+with their positivity
+ 
+
+ align:start position:0%
+with their positivity
+what positive charge and they're
+
+ align:start position:0%
+what positive charge and they're
+ 
+
+ align:start position:0%
+what positive charge and they're
+pointing to their the sodium
+
+ align:start position:0%
+pointing to their the sodium
+ 
+
+ align:start position:0%
+pointing to their the sodium
+with the negative and that's how they
+
+ align:start position:0%
+with the negative and that's how they
+ 
+
+ align:start position:0%
+with the negative and that's how they
+find happiness
+
+ align:start position:0%
+find happiness
+ 
+
+ align:start position:0%
+find happiness
+in water because they're ions
+
+ align:start position:0%
+in water because they're ions
+ 
+
+ align:start position:0%
+in water because they're ions
+and water can be either way yeah it can
+
+ align:start position:0%
+and water can be either way yeah it can
+ 
+
+ align:start position:0%
+and water can be either way yeah it can
+point its dipole in neither
+
+ align:start position:0%
+point its dipole in neither
+ 
+
+ align:start position:0%
+point its dipole in neither
+and so it can actually bond remember the
+
+ align:start position:0%
+and so it can actually bond remember the
+ 
+
+ align:start position:0%
+and so it can actually bond remember the
+hydrogen's got a little positive charge
+
+ align:start position:0%
+hydrogen's got a little positive charge
+ 
+
+ align:start position:0%
+hydrogen's got a little positive charge
+because oxygen took it
+
+ align:start position:0%
+because oxygen took it
+ 
+
+ align:start position:0%
+because oxygen took it
+right and so that's what the you know it
+
+ align:start position:0%
+right and so that's what the you know it
+ 
+
+ align:start position:0%
+right and so that's what the you know it
+has a dipole and that's able to
+
+ align:start position:0%
+has a dipole and that's able to
+ 
+
+ align:start position:0%
+has a dipole and that's able to
+to turn around and bond and be happy
+
+ align:start position:0%
+to turn around and bond and be happy
+ 
+
+ align:start position:0%
+to turn around and bond and be happy
+with each of these ions that's why salt
+
+ align:start position:0%
+with each of these ions that's why salt
+ 
+
+ align:start position:0%
+with each of these ions that's why salt
+dissolves
+
+ align:start position:0%
+dissolves
+ 
+
+ align:start position:0%
+dissolves
+right because it can find a happy place
+
+ align:start position:0%
+right because it can find a happy place
+ 
+
+ align:start position:0%
+right because it can find a happy place
+other reasons exist outside of this
+
+ align:start position:0%
+other reasons exist outside of this
+ 
+
+ align:start position:0%
+other reasons exist outside of this
+class like entropy
+
+ align:start position:0%
+class like entropy
+ 
+
+ align:start position:0%
+class like entropy
+thermodynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this is how we're going to picture
+
+ align:start position:0%
+but this is how we're going to picture
+ 
+
+ align:start position:0%
+but this is how we're going to picture
+it as energetically happy
+
+ align:start position:0%
+it as energetically happy
+ 
+
+ align:start position:0%
+it as energetically happy
+it can become happy now
+
+ align:start position:0%
+it can become happy now
+ 
+
+ align:start position:0%
+it can become happy now
+um okay so we've dissolved some things
+
+ align:start position:0%
+um okay so we've dissolved some things
+ 
+
+ align:start position:0%
+um okay so we've dissolved some things
+we got to start thinking about the thing
+
+ align:start position:0%
+we got to start thinking about the thing
+ 
+
+ align:start position:0%
+we got to start thinking about the thing
+that i mentioned before which is
+
+ align:start position:0%
+that i mentioned before which is
+ 
+
+ align:start position:0%
+that i mentioned before which is
+how much can i dissolve how much can i
+
+ align:start position:0%
+how much can i dissolve how much can i
+ 
+
+ align:start position:0%
+how much can i dissolve how much can i
+dissolve
+
+ align:start position:0%
+dissolve
+ 
+
+ align:start position:0%
+dissolve
+and and that you know it gets into this
+
+ align:start position:0%
+and and that you know it gets into this
+ 
+
+ align:start position:0%
+and and that you know it gets into this
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this table here right okay there it is
+
+ align:start position:0%
+this table here right okay there it is
+ 
+
+ align:start position:0%
+this table here right okay there it is
+so that's how much
+
+ align:start position:0%
+so that's how much
+ 
+
+ align:start position:0%
+so that's how much
+and and you you see it's listed there as
+
+ align:start position:0%
+and and you you see it's listed there as
+ 
+
+ align:start position:0%
+and and you you see it's listed there as
+moles per 100 grams
+
+ align:start position:0%
+moles per 100 grams
+ 
+
+ align:start position:0%
+moles per 100 grams
+all right and so that's one way to write
+
+ align:start position:0%
+all right and so that's one way to write
+ 
+
+ align:start position:0%
+all right and so that's one way to write
+it you could write it
+
+ align:start position:0%
+it you could write it
+ 
+
+ align:start position:0%
+it you could write it
+as uh so so like it's often like the max
+
+ align:start position:0%
+as uh so so like it's often like the max
+ 
+
+ align:start position:0%
+as uh so so like it's often like the max
+the max solubility
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is often
+
+ align:start position:0%
+is often
+ 
+
+ align:start position:0%
+is often
+what we're interested in and and you
+
+ align:start position:0%
+what we're interested in and and you
+ 
+
+ align:start position:0%
+what we're interested in and and you
+could write it in in
+
+ align:start position:0%
+could write it in in
+ 
+
+ align:start position:0%
+could write it in in
+uh okay moles per 100 grams you could
+
+ align:start position:0%
+uh okay moles per 100 grams you could
+ 
+
+ align:start position:0%
+uh okay moles per 100 grams you could
+write it in
+
+ align:start position:0%
+write it in
+ 
+
+ align:start position:0%
+write it in
+uh moles per liter well that's a
+
+ align:start position:0%
+uh moles per liter well that's a
+ 
+
+ align:start position:0%
+uh moles per liter well that's a
+that's something that we've already
+
+ align:start position:0%
+that's something that we've already
+ 
+
+ align:start position:0%
+that's something that we've already
+learned right that's m
+
+ align:start position:0%
+learned right that's m
+ 
+
+ align:start position:0%
+learned right that's m
+from from last friday the molarity or it
+
+ align:start position:0%
+from from last friday the molarity or it
+ 
+
+ align:start position:0%
+from from last friday the molarity or it
+could be in like grams
+
+ align:start position:0%
+could be in like grams
+ 
+
+ align:start position:0%
+could be in like grams
+sometimes you'll see it in grams per
+
+ align:start position:0%
+sometimes you'll see it in grams per
+ 
+
+ align:start position:0%
+sometimes you'll see it in grams per
+liter right so don't get
+
+ align:start position:0%
+liter right so don't get
+ 
+
+ align:start position:0%
+liter right so don't get
+don't get bogged down but but you know
+
+ align:start position:0%
+don't get bogged down but but you know
+ 
+
+ align:start position:0%
+don't get bogged down but but you know
+by the units
+
+ align:start position:0%
+by the units
+ 
+
+ align:start position:0%
+by the units
+it's just how much of this stuff were
+
+ align:start position:0%
+it's just how much of this stuff were
+ 
+
+ align:start position:0%
+it's just how much of this stuff were
+you able
+
+ align:start position:0%
+you able
+ 
+
+ align:start position:0%
+you able
+to to dissolve and
+
+ align:start position:0%
+to to dissolve and
+ 
+
+ align:start position:0%
+to to dissolve and
+and you know if we look at say sugar
+
+ align:start position:0%
+and you know if we look at say sugar
+ 
+
+ align:start position:0%
+and you know if we look at say sugar
+okay here's sugar here's salt
+
+ align:start position:0%
+okay here's sugar here's salt
+ 
+
+ align:start position:0%
+okay here's sugar here's salt
+how much sugar can dissolve okay
+
+ align:start position:0%
+how much sugar can dissolve okay
+ 
+
+ align:start position:0%
+how much sugar can dissolve okay
+if you so
+
+ align:start position:0%
+if you so
+ 
+
+ align:start position:0%
+if you so
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+i'll just i'm not going to cram it in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for sugar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the max is
+
+ align:start position:0%
+the max is
+ 
+
+ align:start position:0%
+the max is
+1800 so i'm going to
+
+ align:start position:0%
+1800 so i'm going to
+ 
+
+ align:start position:0%
+1800 so i'm going to
+do both those units 1800 grams per liter
+
+ align:start position:0%
+do both those units 1800 grams per liter
+ 
+
+ align:start position:0%
+do both those units 1800 grams per liter
+and if you convert that it's 5.26
+
+ align:start position:0%
+and if you convert that it's 5.26
+ 
+
+ align:start position:0%
+and if you convert that it's 5.26
+moles per liter that's how much sugar
+
+ align:start position:0%
+moles per liter that's how much sugar
+ 
+
+ align:start position:0%
+moles per liter that's how much sugar
+you can dissolve in water
+
+ align:start position:0%
+you can dissolve in water
+ 
+
+ align:start position:0%
+you can dissolve in water
+by the way i did a quick calculation and
+
+ align:start position:0%
+by the way i did a quick calculation and
+ 
+
+ align:start position:0%
+by the way i did a quick calculation and
+that's 429 teaspoons
+
+ align:start position:0%
+that's 429 teaspoons
+ 
+
+ align:start position:0%
+that's 429 teaspoons
+that's 429 teaspoons i don't know what
+
+ align:start position:0%
+that's 429 teaspoons i don't know what
+ 
+
+ align:start position:0%
+that's 429 teaspoons i don't know what
+everybody's saying
+
+ align:start position:0%
+everybody's saying
+ 
+
+ align:start position:0%
+everybody's saying
+you know coke has so much sugar
+
+ align:start position:0%
+you know coke has so much sugar
+ 
+
+ align:start position:0%
+you know coke has so much sugar
+coke's got only 26 teaspoons per liter
+
+ align:start position:0%
+coke's got only 26 teaspoons per liter
+ 
+
+ align:start position:0%
+coke's got only 26 teaspoons per liter
+you could put a lot more in if they
+
+ align:start position:0%
+you could put a lot more in if they
+ 
+
+ align:start position:0%
+you could put a lot more in if they
+wanted
+
+ align:start position:0%
+wanted
+ 
+
+ align:start position:0%
+wanted
+i'll go the other way i challenge them
+
+ align:start position:0%
+i'll go the other way i challenge them
+ 
+
+ align:start position:0%
+i'll go the other way i challenge them
+to go near the solubility limit
+
+ align:start position:0%
+to go near the solubility limit
+ 
+
+ align:start position:0%
+to go near the solubility limit
+they're not even close too much sugar
+
+ align:start position:0%
+they're not even close too much sugar
+ 
+
+ align:start position:0%
+they're not even close too much sugar
+so salt you can also look at salt okay
+
+ align:start position:0%
+so salt you can also look at salt okay
+ 
+
+ align:start position:0%
+so salt you can also look at salt okay
+salt is uh
+
+ align:start position:0%
+salt is uh
+ 
+
+ align:start position:0%
+salt is uh
+for salt what is it salt is 359
+
+ align:start position:0%
+for salt what is it salt is 359
+ 
+
+ align:start position:0%
+for salt what is it salt is 359
+grams per liter and then that's it
+
+ align:start position:0%
+grams per liter and then that's it
+ 
+
+ align:start position:0%
+grams per liter and then that's it
+that's 6.14
+
+ align:start position:0%
+that's 6.14
+ 
+
+ align:start position:0%
+that's 6.14
+this is nacl
+
+ align:start position:0%
+this is nacl
+ 
+
+ align:start position:0%
+this is nacl
+you know it's interesting if you compare
+
+ align:start position:0%
+you know it's interesting if you compare
+ 
+
+ align:start position:0%
+you know it's interesting if you compare
+with sodium chloride with say sodium
+
+ align:start position:0%
+with sodium chloride with say sodium
+ 
+
+ align:start position:0%
+with sodium chloride with say sodium
+bromide
+
+ align:start position:0%
+bromide
+ 
+
+ align:start position:0%
+bromide
+right so if you look at sodium bromide
+
+ align:start position:0%
+right so if you look at sodium bromide
+ 
+
+ align:start position:0%
+right so if you look at sodium bromide
+it's going to be 8.9
+
+ align:start position:0%
+it's going to be 8.9
+ 
+
+ align:start position:0%
+it's going to be 8.9
+and sodium fluoride is only going to be
+
+ align:start position:0%
+and sodium fluoride is only going to be
+ 
+
+ align:start position:0%
+and sodium fluoride is only going to be
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why because it comes right down to the
+
+ align:start position:0%
+why because it comes right down to the
+ 
+
+ align:start position:0%
+why because it comes right down to the
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+i've got to make these happier i've got
+
+ align:start position:0%
+i've got to make these happier i've got
+ 
+
+ align:start position:0%
+i've got to make these happier i've got
+to make them happier well
+
+ align:start position:0%
+to make them happier well
+ 
+
+ align:start position:0%
+to make them happier well
+you got the ions there and the water
+
+ align:start position:0%
+you got the ions there and the water
+ 
+
+ align:start position:0%
+you got the ions there and the water
+likes it but what if they really didn't
+
+ align:start position:0%
+likes it but what if they really didn't
+ 
+
+ align:start position:0%
+likes it but what if they really didn't
+have as strong of an ionic bond to start
+
+ align:start position:0%
+have as strong of an ionic bond to start
+ 
+
+ align:start position:0%
+have as strong of an ionic bond to start
+with we can imagine you might be able to
+
+ align:start position:0%
+with we can imagine you might be able to
+ 
+
+ align:start position:0%
+with we can imagine you might be able to
+get to a higher
+
+ align:start position:0%
+get to a higher
+ 
+
+ align:start position:0%
+get to a higher
+amount of dissociation oh what if they
+
+ align:start position:0%
+amount of dissociation oh what if they
+ 
+
+ align:start position:0%
+amount of dissociation oh what if they
+had a very strong
+
+ align:start position:0%
+had a very strong
+ 
+
+ align:start position:0%
+had a very strong
+ionic bond you might imagine that less
+
+ align:start position:0%
+ionic bond you might imagine that less
+ 
+
+ align:start position:0%
+ionic bond you might imagine that less
+of it you got a lower
+
+ align:start position:0%
+of it you got a lower
+ 
+
+ align:start position:0%
+of it you got a lower
+maximum solubility so it all kind of
+
+ align:start position:0%
+maximum solubility so it all kind of
+ 
+
+ align:start position:0%
+maximum solubility so it all kind of
+goes together with the things that we've
+
+ align:start position:0%
+goes together with the things that we've
+ 
+
+ align:start position:0%
+goes together with the things that we've
+learned
+
+ align:start position:0%
+learned
+ 
+
+ align:start position:0%
+learned
+okay all right but what we're really
+
+ align:start position:0%
+okay all right but what we're really
+ 
+
+ align:start position:0%
+okay all right but what we're really
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+is what i need to tell you about next
+
+ align:start position:0%
+is what i need to tell you about next
+ 
+
+ align:start position:0%
+is what i need to tell you about next
+and that is
+
+ align:start position:0%
+and that is
+ 
+
+ align:start position:0%
+and that is
+this idea that we've reached a dynamic
+
+ align:start position:0%
+this idea that we've reached a dynamic
+ 
+
+ align:start position:0%
+this idea that we've reached a dynamic
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+we've reached a dynamic equilibrium so
+
+ align:start position:0%
+we've reached a dynamic equilibrium so
+ 
+
+ align:start position:0%
+we've reached a dynamic equilibrium so
+what what does that mean well if it's
+
+ align:start position:0%
+what what does that mean well if it's
+ 
+
+ align:start position:0%
+what what does that mean well if it's
+unsaturated
+
+ align:start position:0%
+unsaturated
+ 
+
+ align:start position:0%
+unsaturated
+so if it's unsaturated i'm way before
+
+ align:start position:0%
+so if it's unsaturated i'm way before
+ 
+
+ align:start position:0%
+so if it's unsaturated i'm way before
+this limit
+
+ align:start position:0%
+this limit
+ 
+
+ align:start position:0%
+this limit
+right this is salt that's the limit max
+
+ align:start position:0%
+right this is salt that's the limit max
+ 
+
+ align:start position:0%
+right this is salt that's the limit max
+max what does it mean
+
+ align:start position:0%
+max what does it mean
+ 
+
+ align:start position:0%
+max what does it mean
+what does it mean to to be below what
+
+ align:start position:0%
+what does it mean to to be below what
+ 
+
+ align:start position:0%
+what does it mean to to be below what
+does it mean to even have reached
+
+ align:start position:0%
+does it mean to even have reached
+ 
+
+ align:start position:0%
+does it mean to even have reached
+the maximum itself okay
+
+ align:start position:0%
+the maximum itself okay
+ 
+
+ align:start position:0%
+the maximum itself okay
+what it means is not that things aren't
+
+ align:start position:0%
+what it means is not that things aren't
+ 
+
+ align:start position:0%
+what it means is not that things aren't
+dissolving
+
+ align:start position:0%
+dissolving
+ 
+
+ align:start position:0%
+dissolving
+what it means is that things are
+
+ align:start position:0%
+what it means is that things are
+ 
+
+ align:start position:0%
+what it means is that things are
+reforming recrystallizing
+
+ align:start position:0%
+reforming recrystallizing
+ 
+
+ align:start position:0%
+reforming recrystallizing
+at the same rate that they're dissolving
+
+ align:start position:0%
+at the same rate that they're dissolving
+ 
+
+ align:start position:0%
+at the same rate that they're dissolving
+that's what the maximum means and that's
+
+ align:start position:0%
+that's what the maximum means and that's
+ 
+
+ align:start position:0%
+that's what the maximum means and that's
+an equilibrium and that's what we're
+
+ align:start position:0%
+an equilibrium and that's what we're
+ 
+
+ align:start position:0%
+an equilibrium and that's what we're
+going to talk about next right
+
+ align:start position:0%
+going to talk about next right
+ 
+
+ align:start position:0%
+going to talk about next right
+so if it's unsaturated there's a nice
+
+ align:start position:0%
+so if it's unsaturated there's a nice
+ 
+
+ align:start position:0%
+so if it's unsaturated there's a nice
+little molecular picture right there's
+
+ align:start position:0%
+little molecular picture right there's
+ 
+
+ align:start position:0%
+little molecular picture right there's
+the thing you're dissolving
+
+ align:start position:0%
+the thing you're dissolving
+ 
+
+ align:start position:0%
+the thing you're dissolving
+and look at them they're going away into
+
+ align:start position:0%
+and look at them they're going away into
+ 
+
+ align:start position:0%
+and look at them they're going away into
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+maybe it's salt breaking up into ions
+
+ align:start position:0%
+maybe it's salt breaking up into ions
+ 
+
+ align:start position:0%
+maybe it's salt breaking up into ions
+maybe it's sugar
+
+ align:start position:0%
+maybe it's sugar
+ 
+
+ align:start position:0%
+maybe it's sugar
+they're going into solution and finding
+
+ align:start position:0%
+they're going into solution and finding
+ 
+
+ align:start position:0%
+they're going into solution and finding
+a happy place around the water but once
+
+ align:start position:0%
+a happy place around the water but once
+ 
+
+ align:start position:0%
+a happy place around the water but once
+in a while one of them comes back you
+
+ align:start position:0%
+in a while one of them comes back you
+ 
+
+ align:start position:0%
+in a while one of them comes back you
+see that
+
+ align:start position:0%
+see that
+ 
+
+ align:start position:0%
+see that
+little particle there coming back that
+
+ align:start position:0%
+little particle there coming back that
+ 
+
+ align:start position:0%
+little particle there coming back that
+happens but
+
+ align:start position:0%
+happens but
+ 
+
+ align:start position:0%
+happens but
+but much more they're dissolving
+
+ align:start position:0%
+but much more they're dissolving
+ 
+
+ align:start position:0%
+but much more they're dissolving
+then you reach this point of saturation
+
+ align:start position:0%
+then you reach this point of saturation
+ 
+
+ align:start position:0%
+then you reach this point of saturation
+where it cannot where it's going to
+
+ align:start position:0%
+where it cannot where it's going to
+ 
+
+ align:start position:0%
+where it cannot where it's going to
+recrystallize reform the solid at the
+
+ align:start position:0%
+recrystallize reform the solid at the
+ 
+
+ align:start position:0%
+recrystallize reform the solid at the
+same rate that you dissolve and that's
+
+ align:start position:0%
+same rate that you dissolve and that's
+ 
+
+ align:start position:0%
+same rate that you dissolve and that's
+the place
+
+ align:start position:0%
+the place
+ 
+
+ align:start position:0%
+the place
+where you can't dissolve anymore
+
+ align:start position:0%
+where you can't dissolve anymore
+ 
+
+ align:start position:0%
+where you can't dissolve anymore
+all right so what's really happening is
+
+ align:start position:0%
+all right so what's really happening is
+ 
+
+ align:start position:0%
+all right so what's really happening is
+that you have a solute
+
+ align:start position:0%
+that you have a solute
+ 
+
+ align:start position:0%
+that you have a solute
+plus a solvent and it's not
+
+ align:start position:0%
+plus a solvent and it's not
+ 
+
+ align:start position:0%
+plus a solvent and it's not
+going one way as we've been dr uh
+
+ align:start position:0%
+going one way as we've been dr uh
+ 
+
+ align:start position:0%
+going one way as we've been dr uh
+writing it down it's going both ways so
+
+ align:start position:0%
+writing it down it's going both ways so
+ 
+
+ align:start position:0%
+writing it down it's going both ways so
+it's actually the solute plus the
+
+ align:start position:0%
+it's actually the solute plus the
+ 
+
+ align:start position:0%
+it's actually the solute plus the
+solvent
+
+ align:start position:0%
+solvent
+ 
+
+ align:start position:0%
+solvent
+goes like this that is what we've been
+
+ align:start position:0%
+goes like this that is what we've been
+ 
+
+ align:start position:0%
+goes like this that is what we've been
+talking about that's dissolution
+
+ align:start position:0%
+talking about that's dissolution
+ 
+
+ align:start position:0%
+talking about that's dissolution
+and that's the predominant mechanism on
+
+ align:start position:0%
+and that's the predominant mechanism on
+ 
+
+ align:start position:0%
+and that's the predominant mechanism on
+the left before you've saturated
+
+ align:start position:0%
+the left before you've saturated
+ 
+
+ align:start position:0%
+the left before you've saturated
+yeah but but see and that goes to some
+
+ align:start position:0%
+yeah but but see and that goes to some
+ 
+
+ align:start position:0%
+yeah but but see and that goes to some
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+but see you can also precipitate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+precipitate sun
+
+ align:start position:0%
+precipitate sun
+ 
+
+ align:start position:0%
+precipitate sun
+precipitation right
+
+ align:start position:0%
+precipitation right
+ 
+
+ align:start position:0%
+precipitation right
+and and so the sat at the saturated
+
+ align:start position:0%
+and and so the sat at the saturated
+ 
+
+ align:start position:0%
+and and so the sat at the saturated
+solution you have
+
+ align:start position:0%
+solution you have
+ 
+
+ align:start position:0%
+solution you have
+and if it's saturated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then that's another way of saying we've
+
+ align:start position:0%
+then that's another way of saying we've
+ 
+
+ align:start position:0%
+then that's another way of saying we've
+reached the max
+
+ align:start position:0%
+reached the max
+ 
+
+ align:start position:0%
+reached the max
+possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concentration of the solute
+
+ align:start position:0%
+concentration of the solute
+ 
+
+ align:start position:0%
+concentration of the solute
+remember little brackets means
+
+ align:start position:0%
+remember little brackets means
+ 
+
+ align:start position:0%
+remember little brackets means
+concentration molarity
+
+ align:start position:0%
+concentration molarity
+ 
+
+ align:start position:0%
+concentration molarity
+okay it means
+
+ align:start position:0%
+okay it means
+ 
+
+ align:start position:0%
+okay it means
+that these rates thinking back to friday
+
+ align:start position:0%
+that these rates thinking back to friday
+ 
+
+ align:start position:0%
+that these rates thinking back to friday
+are the same it means these rates are
+
+ align:start position:0%
+are the same it means these rates are
+ 
+
+ align:start position:0%
+are the same it means these rates are
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+this is a dynamic equilibrium and so
+
+ align:start position:0%
+this is a dynamic equilibrium and so
+ 
+
+ align:start position:0%
+this is a dynamic equilibrium and so
+that's what we need now
+
+ align:start position:0%
+that's what we need now
+ 
+
+ align:start position:0%
+that's what we need now
+the tools to talk about and so we're
+
+ align:start position:0%
+the tools to talk about and so we're
+ 
+
+ align:start position:0%
+the tools to talk about and so we're
+going to talk about three
+
+ align:start position:0%
+going to talk about three
+ 
+
+ align:start position:0%
+going to talk about three
+three things the reaction quotient
+
+ align:start position:0%
+three things the reaction quotient
+ 
+
+ align:start position:0%
+three things the reaction quotient
+the equilibrium constant k chemical
+
+ align:start position:0%
+the equilibrium constant k chemical
+ 
+
+ align:start position:0%
+the equilibrium constant k chemical
+equilibrium and then the solubility
+
+ align:start position:0%
+equilibrium and then the solubility
+ 
+
+ align:start position:0%
+equilibrium and then the solubility
+product okay now if you think about
+
+ align:start position:0%
+product okay now if you think about
+ 
+
+ align:start position:0%
+product okay now if you think about
+react so
+
+ align:start position:0%
+react so
+ 
+
+ align:start position:0%
+react so
+i just said this is like the forward
+
+ align:start position:0%
+i just said this is like the forward
+ 
+
+ align:start position:0%
+i just said this is like the forward
+reaction is going in the same
+
+ align:start position:0%
+reaction is going in the same
+ 
+
+ align:start position:0%
+reaction is going in the same
+it's happening in the same rate as the
+
+ align:start position:0%
+it's happening in the same rate as the
+ 
+
+ align:start position:0%
+it's happening in the same rate as the
+reverse and so if you think about this
+
+ align:start position:0%
+reverse and so if you think about this
+ 
+
+ align:start position:0%
+reverse and so if you think about this
+as like a graph okay
+
+ align:start position:0%
+as like a graph okay
+ 
+
+ align:start position:0%
+as like a graph okay
+of concentrations so i'll just put here
+
+ align:start position:0%
+of concentrations so i'll just put here
+ 
+
+ align:start position:0%
+of concentrations so i'll just put here
+concentrations right and time
+
+ align:start position:0%
+concentrations right and time
+ 
+
+ align:start position:0%
+concentrations right and time
+then then maybe i have started i put my
+
+ align:start position:0%
+then then maybe i have started i put my
+ 
+
+ align:start position:0%
+then then maybe i have started i put my
+my salt okay i pour a teaspoon of salt
+
+ align:start position:0%
+my salt okay i pour a teaspoon of salt
+ 
+
+ align:start position:0%
+my salt okay i pour a teaspoon of salt
+in water
+
+ align:start position:0%
+in water
+ 
+
+ align:start position:0%
+in water
+and and the the the salt is is
+
+ align:start position:0%
+and and the the the salt is is
+ 
+
+ align:start position:0%
+and and the the the salt is is
+dissolving
+
+ align:start position:0%
+dissolving
+ 
+
+ align:start position:0%
+dissolving
+right so so it's going into the products
+
+ align:start position:0%
+right so so it's going into the products
+ 
+
+ align:start position:0%
+right so so it's going into the products
+it starts out at zero in solution and
+
+ align:start position:0%
+it starts out at zero in solution and
+ 
+
+ align:start position:0%
+it starts out at zero in solution and
+then it becomes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+products
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but at the same time
+
+ align:start position:0%
+okay but at the same time
+ 
+
+ align:start position:0%
+okay but at the same time
+maybe maybe i've started it up here and
+
+ align:start position:0%
+maybe maybe i've started it up here and
+ 
+
+ align:start position:0%
+maybe maybe i've started it up here and
+these are the reactants because
+
+ align:start position:0%
+these are the reactants because
+ 
+
+ align:start position:0%
+these are the reactants because
+in tight that look like this because in
+
+ align:start position:0%
+in tight that look like this because in
+ 
+
+ align:start position:0%
+in tight that look like this because in
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+and those would be the reactants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the concentrations of these things at
+
+ align:start position:0%
+so the concentrations of these things at
+ 
+
+ align:start position:0%
+so the concentrations of these things at
+a certain point they're changing
+
+ align:start position:0%
+a certain point they're changing
+ 
+
+ align:start position:0%
+a certain point they're changing
+and then at a certain point they're not
+
+ align:start position:0%
+and then at a certain point they're not
+ 
+
+ align:start position:0%
+and then at a certain point they're not
+changing
+
+ align:start position:0%
+changing
+ 
+
+ align:start position:0%
+changing
+but there's still reactions happening
+
+ align:start position:0%
+but there's still reactions happening
+ 
+
+ align:start position:0%
+but there's still reactions happening
+back and forth like i just showed you
+
+ align:start position:0%
+back and forth like i just showed you
+ 
+
+ align:start position:0%
+back and forth like i just showed you
+it's a dynamic equilibrium
+
+ align:start position:0%
+it's a dynamic equilibrium
+ 
+
+ align:start position:0%
+it's a dynamic equilibrium
+okay now what we do is we write down for
+
+ align:start position:0%
+okay now what we do is we write down for
+ 
+
+ align:start position:0%
+okay now what we do is we write down for
+some arbitrary reaction
+
+ align:start position:0%
+some arbitrary reaction
+ 
+
+ align:start position:0%
+some arbitrary reaction
+a a plus so let's go back to this one
+
+ align:start position:0%
+a a plus so let's go back to this one
+ 
+
+ align:start position:0%
+a a plus so let's go back to this one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but now we're going to write it going
+
+ align:start position:0%
+but now we're going to write it going
+ 
+
+ align:start position:0%
+but now we're going to write it going
+both ways
+
+ align:start position:0%
+both ways
+ 
+
+ align:start position:0%
+both ways
+cc plus db
+
+ align:start position:0%
+cc plus db
+ 
+
+ align:start position:0%
+cc plus db
+you can define the reaction quotient q
+
+ align:start position:0%
+you can define the reaction quotient q
+ 
+
+ align:start position:0%
+you can define the reaction quotient q
+that's the first thing
+
+ align:start position:0%
+that's the first thing
+ 
+
+ align:start position:0%
+that's the first thing
+as the concentrations a
+
+ align:start position:0%
+as the concentrations a
+ 
+
+ align:start position:0%
+as the concentrations a
+c of the products c to the c
+
+ align:start position:0%
+c of the products c to the c
+ 
+
+ align:start position:0%
+c of the products c to the c
+d to the d over
+
+ align:start position:0%
+d to the d over
+ 
+
+ align:start position:0%
+d to the d over
+a to the a
+
+ align:start position:0%
+a to the a
+ 
+
+ align:start position:0%
+a to the a
+b to the b please
+
+ align:start position:0%
+b to the b please
+ 
+
+ align:start position:0%
+b to the b please
+do not confuse this with the rates
+
+ align:start position:0%
+do not confuse this with the rates
+ 
+
+ align:start position:0%
+do not confuse this with the rates
+yeah i've been talking about like the
+
+ align:start position:0%
+yeah i've been talking about like the
+ 
+
+ align:start position:0%
+yeah i've been talking about like the
+rates being equal
+
+ align:start position:0%
+rates being equal
+ 
+
+ align:start position:0%
+rates being equal
+that's not from the rates remember the
+
+ align:start position:0%
+that's not from the rates remember the
+ 
+
+ align:start position:0%
+that's not from the rates remember the
+exponents of the rate law
+
+ align:start position:0%
+exponents of the rate law
+ 
+
+ align:start position:0%
+exponents of the rate law
+come from experimental measurements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the reaction quotient comes from the
+
+ align:start position:0%
+the reaction quotient comes from the
+ 
+
+ align:start position:0%
+the reaction quotient comes from the
+stoichiometric coefficients
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why the these these exponents here
+
+ align:start position:0%
+why the these these exponents here
+ 
+
+ align:start position:0%
+why the these these exponents here
+have to do literally with probabilities
+
+ align:start position:0%
+have to do literally with probabilities
+ 
+
+ align:start position:0%
+have to do literally with probabilities
+of reaction
+
+ align:start position:0%
+of reaction
+ 
+
+ align:start position:0%
+of reaction
+of reacting it has to do with the fact
+
+ align:start position:0%
+of reacting it has to do with the fact
+ 
+
+ align:start position:0%
+of reacting it has to do with the fact
+that if i've got
+
+ align:start position:0%
+that if i've got
+ 
+
+ align:start position:0%
+that if i've got
+two of c then you multiply the amount of
+
+ align:start position:0%
+two of c then you multiply the amount of
+ 
+
+ align:start position:0%
+two of c then you multiply the amount of
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+times another amount of c in the same
+
+ align:start position:0%
+times another amount of c in the same
+ 
+
+ align:start position:0%
+times another amount of c in the same
+volume
+
+ align:start position:0%
+volume
+ 
+
+ align:start position:0%
+volume
+it has to do with probabilities of
+
+ align:start position:0%
+it has to do with probabilities of
+ 
+
+ align:start position:0%
+it has to do with probabilities of
+reacting that's where you get those
+
+ align:start position:0%
+reacting that's where you get those
+ 
+
+ align:start position:0%
+reacting that's where you get those
+exponents
+
+ align:start position:0%
+exponents
+ 
+
+ align:start position:0%
+exponents
+and they're directly from the
+
+ align:start position:0%
+and they're directly from the
+ 
+
+ align:start position:0%
+and they're directly from the
+stoichiometric coefficients they do not
+
+ align:start position:0%
+stoichiometric coefficients they do not
+ 
+
+ align:start position:0%
+stoichiometric coefficients they do not
+need to be
+
+ align:start position:0%
+need to be
+ 
+
+ align:start position:0%
+need to be
+experimentally measured once you have
+
+ align:start position:0%
+experimentally measured once you have
+ 
+
+ align:start position:0%
+experimentally measured once you have
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+you have the reaction quotient okay
+
+ align:start position:0%
+you have the reaction quotient okay
+ 
+
+ align:start position:0%
+you have the reaction quotient okay
+now why is this useful this reaction
+
+ align:start position:0%
+now why is this useful this reaction
+ 
+
+ align:start position:0%
+now why is this useful this reaction
+quotient well it's useful because
+
+ align:start position:0%
+quotient well it's useful because
+ 
+
+ align:start position:0%
+quotient well it's useful because
+there's a very special place where
+
+ align:start position:0%
+there's a very special place where
+ 
+
+ align:start position:0%
+there's a very special place where
+now it doesn't change anymore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these concentrations aren't changing
+
+ align:start position:0%
+these concentrations aren't changing
+ 
+
+ align:start position:0%
+these concentrations aren't changing
+reactions are still happening but the
+
+ align:start position:0%
+reactions are still happening but the
+ 
+
+ align:start position:0%
+reactions are still happening but the
+concentrations aren't changing
+
+ align:start position:0%
+concentrations aren't changing
+ 
+
+ align:start position:0%
+concentrations aren't changing
+no change
+
+ align:start position:0%
+no change
+ 
+
+ align:start position:0%
+no change
+if there's no change then gazoom type
+
+ align:start position:0%
+if there's no change then gazoom type
+ 
+
+ align:start position:0%
+if there's no change then gazoom type
+then q isn't changing because it's just
+
+ align:start position:0%
+then q isn't changing because it's just
+ 
+
+ align:start position:0%
+then q isn't changing because it's just
+a ratio of concentrations
+
+ align:start position:0%
+a ratio of concentrations
+ 
+
+ align:start position:0%
+a ratio of concentrations
+it's a ratio of concentrations right
+
+ align:start position:0%
+it's a ratio of concentrations right
+ 
+
+ align:start position:0%
+it's a ratio of concentrations right
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+equal to this whole thing not just the
+
+ align:start position:0%
+equal to this whole thing not just the
+ 
+
+ align:start position:0%
+equal to this whole thing not just the
+top line
+
+ align:start position:0%
+top line
+ 
+
+ align:start position:0%
+top line
+the reaction quotient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is related to the concentration so if
+
+ align:start position:0%
+is related to the concentration so if
+ 
+
+ align:start position:0%
+is related to the concentration so if
+the concentrations don't change even if
+
+ align:start position:0%
+the concentrations don't change even if
+ 
+
+ align:start position:0%
+the concentrations don't change even if
+reactions are happening still
+
+ align:start position:0%
+reactions are happening still
+ 
+
+ align:start position:0%
+reactions are happening still
+it's a constant so at this point
+
+ align:start position:0%
+it's a constant so at this point
+ 
+
+ align:start position:0%
+it's a constant so at this point
+q equals a constant
+
+ align:start position:0%
+q equals a constant
+ 
+
+ align:start position:0%
+q equals a constant
+and that is an equilibrium constant so
+
+ align:start position:0%
+and that is an equilibrium constant so
+ 
+
+ align:start position:0%
+and that is an equilibrium constant so
+we'll call it k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eq
+
+ align:start position:0%
+eq
+ 
+
+ align:start position:0%
+eq
+it's a dynamic equilibrium k represents
+
+ align:start position:0%
+it's a dynamic equilibrium k represents
+ 
+
+ align:start position:0%
+it's a dynamic equilibrium k represents
+a dynamic equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what's really useful about k
+
+ align:start position:0%
+and what's really useful about k
+ 
+
+ align:start position:0%
+and what's really useful about k
+is that for a given reaction k
+
+ align:start position:0%
+is that for a given reaction k
+ 
+
+ align:start position:0%
+is that for a given reaction k
+is a constant i just said it but it
+
+ align:start position:0%
+is a constant i just said it but it
+ 
+
+ align:start position:0%
+is a constant i just said it but it
+doesn't matter
+
+ align:start position:0%
+doesn't matter
+ 
+
+ align:start position:0%
+doesn't matter
+for oh it depends on temperature but if
+
+ align:start position:0%
+for oh it depends on temperature but if
+ 
+
+ align:start position:0%
+for oh it depends on temperature but if
+i keep the temperature fixed
+
+ align:start position:0%
+i keep the temperature fixed
+ 
+
+ align:start position:0%
+i keep the temperature fixed
+k won't change it's a constant
+
+ align:start position:0%
+k won't change it's a constant
+ 
+
+ align:start position:0%
+k won't change it's a constant
+it's it's it's the constant that tells
+
+ align:start position:0%
+it's it's it's the constant that tells
+ 
+
+ align:start position:0%
+it's it's it's the constant that tells
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+where equilibrium is it's a constant
+
+ align:start position:0%
+where equilibrium is it's a constant
+ 
+
+ align:start position:0%
+where equilibrium is it's a constant
+that tells me where equilibrium is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now there's one more thing that we
+
+ align:start position:0%
+okay now there's one more thing that we
+ 
+
+ align:start position:0%
+okay now there's one more thing that we
+got to write down
+
+ align:start position:0%
+got to write down
+ 
+
+ align:start position:0%
+got to write down
+which is that third one there i'm going
+
+ align:start position:0%
+which is that third one there i'm going
+ 
+
+ align:start position:0%
+which is that third one there i'm going
+to put it on here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so k is an equilibrium constant that's a
+
+ align:start position:0%
+so k is an equilibrium constant that's a
+ 
+
+ align:start position:0%
+so k is an equilibrium constant that's a
+general constant
+
+ align:start position:0%
+general constant
+ 
+
+ align:start position:0%
+general constant
+but now i'm going to turn my attention
+
+ align:start position:0%
+but now i'm going to turn my attention
+ 
+
+ align:start position:0%
+but now i'm going to turn my attention
+from any old reaction
+
+ align:start position:0%
+from any old reaction
+ 
+
+ align:start position:0%
+from any old reaction
+like k is actually a very general
+
+ align:start position:0%
+like k is actually a very general
+ 
+
+ align:start position:0%
+like k is actually a very general
+concept for equilibrium
+
+ align:start position:0%
+concept for equilibrium
+ 
+
+ align:start position:0%
+concept for equilibrium
+we are in this class going to use it for
+
+ align:start position:0%
+we are in this class going to use it for
+ 
+
+ align:start position:0%
+we are in this class going to use it for
+solubility
+
+ align:start position:0%
+solubility
+ 
+
+ align:start position:0%
+solubility
+that's how we are using the equilibrium
+
+ align:start position:0%
+that's how we are using the equilibrium
+ 
+
+ align:start position:0%
+that's how we are using the equilibrium
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+no okay and so and so the ksp
+
+ align:start position:0%
+no okay and so and so the ksp
+ 
+
+ align:start position:0%
+no okay and so and so the ksp
+is the solubility product
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's an equilibrium constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is related to
+
+ align:start position:0%
+that is related to
+ 
+
+ align:start position:0%
+that is related to
+solubility
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is literally the product of
+
+ align:start position:0%
+it is literally the product of
+ 
+
+ align:start position:0%
+it is literally the product of
+solubilities in equilibrium that is
+
+ align:start position:0%
+solubilities in equilibrium that is
+ 
+
+ align:start position:0%
+solubilities in equilibrium that is
+literally what it means so we're going
+
+ align:start position:0%
+literally what it means so we're going
+ 
+
+ align:start position:0%
+literally what it means so we're going
+to do some examples to see that
+
+ align:start position:0%
+to do some examples to see that
+ 
+
+ align:start position:0%
+to do some examples to see that
+it's an equilibrium so it's a constant
+
+ align:start position:0%
+it's an equilibrium so it's a constant
+ 
+
+ align:start position:0%
+it's an equilibrium so it's a constant
+of equilibrium
+
+ align:start position:0%
+of equilibrium
+ 
+
+ align:start position:0%
+of equilibrium
+and it's called the gazentite it's
+
+ align:start position:0%
+and it's called the gazentite it's
+ 
+
+ align:start position:0%
+and it's called the gazentite it's
+called the solubility product because
+
+ align:start position:0%
+called the solubility product because
+ 
+
+ align:start position:0%
+called the solubility product because
+it's related to
+
+ align:start position:0%
+it's related to
+ 
+
+ align:start position:0%
+it's related to
+the equilibrium of dissolving something
+
+ align:start position:0%
+the equilibrium of dissolving something
+ 
+
+ align:start position:0%
+the equilibrium of dissolving something
+dissolving some solute in a solvent so
+
+ align:start position:0%
+dissolving some solute in a solvent so
+ 
+
+ align:start position:0%
+dissolving some solute in a solvent so
+we're going to do something
+
+ align:start position:0%
+we're going to do something
+ 
+
+ align:start position:0%
+we're going to do something
+now we're going to do examples with
+
+ align:start position:0%
+now we're going to do examples with
+ 
+
+ align:start position:0%
+now we're going to do examples with
+salts
+
+ align:start position:0%
+salts
+ 
+
+ align:start position:0%
+salts
+okay so we're going to be dissolving
+
+ align:start position:0%
+okay so we're going to be dissolving
+ 
+
+ align:start position:0%
+okay so we're going to be dissolving
+salts and talking about equilibrium
+
+ align:start position:0%
+salts and talking about equilibrium
+ 
+
+ align:start position:0%
+salts and talking about equilibrium
+constants in that dissolution otherwise
+
+ align:start position:0%
+constants in that dissolution otherwise
+ 
+
+ align:start position:0%
+constants in that dissolution otherwise
+known as the solubility product it's
+
+ align:start position:0%
+known as the solubility product it's
+ 
+
+ align:start position:0%
+known as the solubility product it's
+just an equilibrium constant
+
+ align:start position:0%
+just an equilibrium constant
+ 
+
+ align:start position:0%
+just an equilibrium constant
+there are many this is the one we're
+
+ align:start position:0%
+there are many this is the one we're
+ 
+
+ align:start position:0%
+there are many this is the one we're
+going to care about and we're going to
+
+ align:start position:0%
+going to care about and we're going to
+ 
+
+ align:start position:0%
+going to care about and we're going to
+do it for salts and so
+
+ align:start position:0%
+do it for salts and so
+ 
+
+ align:start position:0%
+do it for salts and so
+one of the things you got to you know so
+
+ align:start position:0%
+one of the things you got to you know so
+ 
+
+ align:start position:0%
+one of the things you got to you know so
+nacl that was kind of easy
+
+ align:start position:0%
+nacl that was kind of easy
+ 
+
+ align:start position:0%
+nacl that was kind of easy
+right that became a cation and an anion
+
+ align:start position:0%
+right that became a cation and an anion
+ 
+
+ align:start position:0%
+right that became a cation and an anion
+in solution
+
+ align:start position:0%
+in solution
+ 
+
+ align:start position:0%
+in solution
+right yeah but salts can be made of many
+
+ align:start position:0%
+right yeah but salts can be made of many
+ 
+
+ align:start position:0%
+right yeah but salts can be made of many
+many different types of cations and
+
+ align:start position:0%
+many different types of cations and
+ 
+
+ align:start position:0%
+many different types of cations and
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+lists that go on and on and on um here
+
+ align:start position:0%
+lists that go on and on and on um here
+ 
+
+ align:start position:0%
+lists that go on and on and on um here
+are some
+
+ align:start position:0%
+are some
+ 
+
+ align:start position:0%
+are some
+and they get named right so here's like
+
+ align:start position:0%
+and they get named right so here's like
+ 
+
+ align:start position:0%
+and they get named right so here's like
+some of the
+
+ align:start position:0%
+some of the
+ 
+
+ align:start position:0%
+some of the
+the anions oh chlorine we just did that
+
+ align:start position:0%
+the anions oh chlorine we just did that
+ 
+
+ align:start position:0%
+the anions oh chlorine we just did that
+one okay okay
+
+ align:start position:0%
+one okay okay
+ 
+
+ align:start position:0%
+one okay okay
+uh bromine oh uh you could also have a
+
+ align:start position:0%
+uh bromine oh uh you could also have a
+ 
+
+ align:start position:0%
+uh bromine oh uh you could also have a
+carbonate
+
+ align:start position:0%
+carbonate
+ 
+
+ align:start position:0%
+carbonate
+you could have chromates hydroxides
+
+ align:start position:0%
+you could have chromates hydroxides
+ 
+
+ align:start position:0%
+you could have chromates hydroxides
+oxalates sulfates sulfides
+
+ align:start position:0%
+oxalates sulfates sulfides
+ 
+
+ align:start position:0%
+oxalates sulfates sulfides
+and then the list goes on and on and on
+
+ align:start position:0%
+and then the list goes on and on and on
+ 
+
+ align:start position:0%
+and then the list goes on and on and on
+right there are many many of these
+
+ align:start position:0%
+right there are many many of these
+ 
+
+ align:start position:0%
+right there are many many of these
+they don't have to be a single atom it
+
+ align:start position:0%
+they don't have to be a single atom it
+ 
+
+ align:start position:0%
+they don't have to be a single atom it
+can be a part
+
+ align:start position:0%
+can be a part
+ 
+
+ align:start position:0%
+can be a part
+of a salt that breaks off and has a
+
+ align:start position:0%
+of a salt that breaks off and has a
+ 
+
+ align:start position:0%
+of a salt that breaks off and has a
+negative charge that's an anion and
+
+ align:start position:0%
+negative charge that's an anion and
+ 
+
+ align:start position:0%
+negative charge that's an anion and
+here are some of the cations sodium
+
+ align:start position:0%
+here are some of the cations sodium
+ 
+
+ align:start position:0%
+here are some of the cations sodium
+potassium calcium
+
+ align:start position:0%
+potassium calcium
+ 
+
+ align:start position:0%
+potassium calcium
+right and you know about these things
+
+ align:start position:0%
+right and you know about these things
+ 
+
+ align:start position:0%
+right and you know about these things
+we've been talking about these things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you know like if it's sodium then
+
+ align:start position:0%
+and you know like if it's sodium then
+ 
+
+ align:start position:0%
+and you know like if it's sodium then
+you know it's only going to lose it's
+
+ align:start position:0%
+you know it's only going to lose it's
+ 
+
+ align:start position:0%
+you know it's only going to lose it's
+only going to be an a plus
+
+ align:start position:0%
+only going to be an a plus
+ 
+
+ align:start position:0%
+only going to be an a plus
+it doesn't have a second weekly bond
+
+ align:start position:0%
+it doesn't have a second weekly bond
+ 
+
+ align:start position:0%
+it doesn't have a second weekly bond
+bonded electron
+
+ align:start position:0%
+bonded electron
+ 
+
+ align:start position:0%
+bonded electron
+to lose so it's really only going to be
+
+ align:start position:0%
+to lose so it's really only going to be
+ 
+
+ align:start position:0%
+to lose so it's really only going to be
+an a plus
+
+ align:start position:0%
+an a plus
+ 
+
+ align:start position:0%
+an a plus
+but but then you get and calcium is
+
+ align:start position:0%
+but but then you get and calcium is
+ 
+
+ align:start position:0%
+but but then you get and calcium is
+going to be calcium 2 plus
+
+ align:start position:0%
+going to be calcium 2 plus
+ 
+
+ align:start position:0%
+going to be calcium 2 plus
+right it's got two magnesium two and and
+
+ align:start position:0%
+right it's got two magnesium two and and
+ 
+
+ align:start position:0%
+right it's got two magnesium two and and
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+iron you know transition metals a little
+
+ align:start position:0%
+iron you know transition metals a little
+ 
+
+ align:start position:0%
+iron you know transition metals a little
+more complicated
+
+ align:start position:0%
+more complicated
+ 
+
+ align:start position:0%
+more complicated
+right they can be a little more
+
+ align:start position:0%
+right they can be a little more
+ 
+
+ align:start position:0%
+right they can be a little more
+complicated uh so like iron could be two
+
+ align:start position:0%
+complicated uh so like iron could be two
+ 
+
+ align:start position:0%
+complicated uh so like iron could be two
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+or three plus or depends right and on
+
+ align:start position:0%
+or three plus or depends right and on
+ 
+
+ align:start position:0%
+or three plus or depends right and on
+and on and on for those
+
+ align:start position:0%
+and on and on for those
+ 
+
+ align:start position:0%
+and on and on for those
+right and and so so we'll do a few
+
+ align:start position:0%
+right and and so so we'll do a few
+ 
+
+ align:start position:0%
+right and and so so we'll do a few
+examples
+
+ align:start position:0%
+examples
+ 
+
+ align:start position:0%
+examples
+we'll do a few examples so we'll get our
+
+ align:start position:0%
+we'll do a few examples so we'll get our
+ 
+
+ align:start position:0%
+we'll do a few examples so we'll get our
+kind of uh uh
+
+ align:start position:0%
+kind of uh uh
+ 
+
+ align:start position:0%
+kind of uh uh
+you know we'll get into the mood
+
+ align:start position:0%
+you know we'll get into the mood
+ 
+
+ align:start position:0%
+you know we'll get into the mood
+and i want to do it first i'm going to
+
+ align:start position:0%
+and i want to do it first i'm going to
+ 
+
+ align:start position:0%
+and i want to do it first i'm going to
+do an example that's actually a classic
+
+ align:start position:0%
+do an example that's actually a classic
+ 
+
+ align:start position:0%
+do an example that's actually a classic
+example because it's not it doesn't
+
+ align:start position:0%
+example because it's not it doesn't
+ 
+
+ align:start position:0%
+example because it's not it doesn't
+dissolve
+
+ align:start position:0%
+dissolve
+ 
+
+ align:start position:0%
+dissolve
+very well but it's silver chloride now
+
+ align:start position:0%
+very well but it's silver chloride now
+ 
+
+ align:start position:0%
+very well but it's silver chloride now
+sodium chloride
+
+ align:start position:0%
+sodium chloride
+ 
+
+ align:start position:0%
+sodium chloride
+is sodium chloride goes all the way
+
+ align:start position:0%
+is sodium chloride goes all the way
+ 
+
+ align:start position:0%
+is sodium chloride goes all the way
+to the point where it it it basically it
+
+ align:start position:0%
+to the point where it it it basically it
+ 
+
+ align:start position:0%
+to the point where it it it basically it
+dissolves
+
+ align:start position:0%
+dissolves
+ 
+
+ align:start position:0%
+dissolves
+so well right
+
+ align:start position:0%
+so well right
+ 
+
+ align:start position:0%
+so well right
+now so you can imagine the equilibrium
+
+ align:start position:0%
+now so you can imagine the equilibrium
+ 
+
+ align:start position:0%
+now so you can imagine the equilibrium
+for sodium chloride goes way to the
+
+ align:start position:0%
+for sodium chloride goes way to the
+ 
+
+ align:start position:0%
+for sodium chloride goes way to the
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+yeah but for silver chloride it's it's
+
+ align:start position:0%
+yeah but for silver chloride it's it's
+ 
+
+ align:start position:0%
+yeah but for silver chloride it's it's
+different for silver chloride it's
+
+ align:start position:0%
+different for silver chloride it's
+ 
+
+ align:start position:0%
+different for silver chloride it's
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+so we're going to look at this curve
+
+ align:start position:0%
+so we're going to look at this curve
+ 
+
+ align:start position:0%
+so we're going to look at this curve
+okay and i'll talk about this curve
+
+ align:start position:0%
+okay and i'll talk about this curve
+ 
+
+ align:start position:0%
+okay and i'll talk about this curve
+don't worry
+
+ align:start position:0%
+don't worry
+ 
+
+ align:start position:0%
+don't worry
+we're coming to it we are coming to it
+
+ align:start position:0%
+we're coming to it we are coming to it
+ 
+
+ align:start position:0%
+we're coming to it we are coming to it
+let me
+
+ align:start position:0%
+let me
+ 
+
+ align:start position:0%
+let me
+start in the middle again because
+
+ align:start position:0%
+start in the middle again because
+ 
+
+ align:start position:0%
+start in the middle again because
+what the equilibrium constant does given
+
+ align:start position:0%
+what the equilibrium constant does given
+ 
+
+ align:start position:0%
+what the equilibrium constant does given
+the definition that i have just hidden
+
+ align:start position:0%
+the definition that i have just hidden
+ 
+
+ align:start position:0%
+the definition that i have just hidden
+unfortunately
+
+ align:start position:0%
+unfortunately
+ 
+
+ align:start position:0%
+unfortunately
+is it allows us to go back and forth if
+
+ align:start position:0%
+is it allows us to go back and forth if
+ 
+
+ align:start position:0%
+is it allows us to go back and forth if
+i know the equilibrium constant
+
+ align:start position:0%
+i know the equilibrium constant
+ 
+
+ align:start position:0%
+i know the equilibrium constant
+then i can get how much
+
+ align:start position:0%
+then i can get how much
+ 
+
+ align:start position:0%
+then i can get how much
+one of these ions is soluble i can get
+
+ align:start position:0%
+one of these ions is soluble i can get
+ 
+
+ align:start position:0%
+one of these ions is soluble i can get
+the solubility maximum solubility
+
+ align:start position:0%
+the solubility maximum solubility
+ 
+
+ align:start position:0%
+the solubility maximum solubility
+of it right so let's take an example so
+
+ align:start position:0%
+of it right so let's take an example so
+ 
+
+ align:start position:0%
+of it right so let's take an example so
+here here's a here's the question right
+
+ align:start position:0%
+here here's a here's the question right
+ 
+
+ align:start position:0%
+here here's a here's the question right
+how much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a g cl cl
+
+ align:start position:0%
+a g cl cl
+ 
+
+ align:start position:0%
+a g cl cl
+dissolves in
+
+ align:start position:0%
+dissolves in
+ 
+
+ align:start position:0%
+dissolves in
+one liter of water that's
+
+ align:start position:0%
+one liter of water that's
+ 
+
+ align:start position:0%
+one liter of water that's
+such a good question i don't know
+
+ align:start position:0%
+such a good question i don't know
+ 
+
+ align:start position:0%
+such a good question i don't know
+but i do know that the solubility
+
+ align:start position:0%
+but i do know that the solubility
+ 
+
+ align:start position:0%
+but i do know that the solubility
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+that this equilibrium constant for
+
+ align:start position:0%
+that this equilibrium constant for
+ 
+
+ align:start position:0%
+that this equilibrium constant for
+sodium chloride is 1.7
+
+ align:start position:0%
+sodium chloride is 1.7
+ 
+
+ align:start position:0%
+sodium chloride is 1.7
+times 10 to the minus 10.
+
+ align:start position:0%
+times 10 to the minus 10.
+ 
+
+ align:start position:0%
+times 10 to the minus 10.
+now if i write down the
+
+ align:start position:0%
+now if i write down the
+ 
+
+ align:start position:0%
+now if i write down the
+the dissolution reaction sodium chloride
+
+ align:start position:0%
+the dissolution reaction sodium chloride
+ 
+
+ align:start position:0%
+the dissolution reaction sodium chloride
+solid is going to go
+
+ align:start position:0%
+solid is going to go
+ 
+
+ align:start position:0%
+solid is going to go
+to i'm sorry
+
+ align:start position:0%
+to i'm sorry
+ 
+
+ align:start position:0%
+to i'm sorry
+sodium silver silver plus
+
+ align:start position:0%
+sodium silver silver plus
+ 
+
+ align:start position:0%
+sodium silver silver plus
+in solution so we put the aqueous plus
+
+ align:start position:0%
+in solution so we put the aqueous plus
+ 
+
+ align:start position:0%
+in solution so we put the aqueous plus
+chlorine
+
+ align:start position:0%
+chlorine
+ 
+
+ align:start position:0%
+chlorine
+minus in solution okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's going to go back and forth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so the ksp for this is going to
+
+ align:start position:0%
+and so the ksp for this is going to
+ 
+
+ align:start position:0%
+and so the ksp for this is going to
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+i'm going to go with the equation that i
+
+ align:start position:0%
+i'm going to go with the equation that i
+ 
+
+ align:start position:0%
+i'm going to go with the equation that i
+wrote down the concentration of silver
+
+ align:start position:0%
+wrote down the concentration of silver
+ 
+
+ align:start position:0%
+wrote down the concentration of silver
+to the 1
+
+ align:start position:0%
+to the 1
+ 
+
+ align:start position:0%
+to the 1
+times the concentration of chlorine
+
+ align:start position:0%
+times the concentration of chlorine
+ 
+
+ align:start position:0%
+times the concentration of chlorine
+minus these are ions
+
+ align:start position:0%
+minus these are ions
+ 
+
+ align:start position:0%
+minus these are ions
+divided by the concentration of silver
+
+ align:start position:0%
+divided by the concentration of silver
+ 
+
+ align:start position:0%
+divided by the concentration of silver
+chloride
+
+ align:start position:0%
+chloride
+ 
+
+ align:start position:0%
+chloride
+solid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh ho ho now we get to another thing
+
+ align:start position:0%
+oh ho ho now we get to another thing
+ 
+
+ align:start position:0%
+oh ho ho now we get to another thing
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+i got rid of water because water's
+
+ align:start position:0%
+i got rid of water because water's
+ 
+
+ align:start position:0%
+i got rid of water because water's
+everywhere
+
+ align:start position:0%
+everywhere
+ 
+
+ align:start position:0%
+everywhere
+it's the solvent so you don't need to
+
+ align:start position:0%
+it's the solvent so you don't need to
+ 
+
+ align:start position:0%
+it's the solvent so you don't need to
+put it into these equilibrium
+
+ align:start position:0%
+put it into these equilibrium
+ 
+
+ align:start position:0%
+put it into these equilibrium
+calculations
+
+ align:start position:0%
+calculations
+ 
+
+ align:start position:0%
+calculations
+yeah well it's the same thing with
+
+ align:start position:0%
+yeah well it's the same thing with
+ 
+
+ align:start position:0%
+yeah well it's the same thing with
+the solid so if i
+
+ align:start position:0%
+the solid so if i
+ 
+
+ align:start position:0%
+the solid so if i
+think about this a little bit this
+
+ align:start position:0%
+think about this a little bit this
+ 
+
+ align:start position:0%
+think about this a little bit this
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+is between dissolved
+
+ align:start position:0%
+is between dissolved
+ 
+
+ align:start position:0%
+is between dissolved
+it's between the the ions that are
+
+ align:start position:0%
+it's between the the ions that are
+ 
+
+ align:start position:0%
+it's between the the ions that are
+dissolving
+
+ align:start position:0%
+dissolving
+ 
+
+ align:start position:0%
+dissolving
+but there from this from this reaction
+
+ align:start position:0%
+but there from this from this reaction
+ 
+
+ align:start position:0%
+but there from this from this reaction
+from the way it's written there i've got
+
+ align:start position:0%
+from the way it's written there i've got
+ 
+
+ align:start position:0%
+from the way it's written there i've got
+a solid form of silver chloride
+
+ align:start position:0%
+a solid form of silver chloride
+ 
+
+ align:start position:0%
+a solid form of silver chloride
+so this is not so this is the
+
+ align:start position:0%
+so this is not so this is the
+ 
+
+ align:start position:0%
+so this is not so this is the
+concentration
+
+ align:start position:0%
+concentration
+ 
+
+ align:start position:0%
+concentration
+of solid silver chloride in the solid
+
+ align:start position:0%
+of solid silver chloride in the solid
+ 
+
+ align:start position:0%
+of solid silver chloride in the solid
+that's just a constant that's not going
+
+ align:start position:0%
+that's just a constant that's not going
+ 
+
+ align:start position:0%
+that's just a constant that's not going
+to change
+
+ align:start position:0%
+to change
+ 
+
+ align:start position:0%
+to change
+that's not going to change common
+
+ align:start position:0%
+that's not going to change common
+ 
+
+ align:start position:0%
+that's not going to change common
+misunderstanding
+
+ align:start position:0%
+misunderstanding
+ 
+
+ align:start position:0%
+misunderstanding
+it doesn't change so we get rid of it
+
+ align:start position:0%
+it doesn't change so we get rid of it
+ 
+
+ align:start position:0%
+it doesn't change so we get rid of it
+because it gets folded into the constant
+
+ align:start position:0%
+because it gets folded into the constant
+ 
+
+ align:start position:0%
+because it gets folded into the constant
+that's always the same the concentration
+
+ align:start position:0%
+that's always the same the concentration
+ 
+
+ align:start position:0%
+that's always the same the concentration
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+is always the same right and so we get
+
+ align:start position:0%
+is always the same right and so we get
+ 
+
+ align:start position:0%
+is always the same right and so we get
+rid of it
+
+ align:start position:0%
+rid of it
+ 
+
+ align:start position:0%
+rid of it
+so now we have the ksp k
+
+ align:start position:0%
+so now we have the ksp k
+ 
+
+ align:start position:0%
+so now we have the ksp k
+is equal to in this case a g plus
+
+ align:start position:0%
+is equal to in this case a g plus
+ 
+
+ align:start position:0%
+is equal to in this case a g plus
+times cl minus talk about solubility
+
+ align:start position:0%
+times cl minus talk about solubility
+ 
+
+ align:start position:0%
+times cl minus talk about solubility
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+concentrate right solubility is when
+
+ align:start position:0%
+concentrate right solubility is when
+ 
+
+ align:start position:0%
+concentrate right solubility is when
+when i add this in it reaches some
+
+ align:start position:0%
+when i add this in it reaches some
+ 
+
+ align:start position:0%
+when i add this in it reaches some
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+where they're dissolving and reforming i
+
+ align:start position:0%
+where they're dissolving and reforming i
+ 
+
+ align:start position:0%
+where they're dissolving and reforming i
+wanted to know at what point that is
+
+ align:start position:0%
+wanted to know at what point that is
+ 
+
+ align:start position:0%
+wanted to know at what point that is
+what concentrations
+
+ align:start position:0%
+what concentrations
+ 
+
+ align:start position:0%
+what concentrations
+is that going to be this is them
+
+ align:start position:0%
+is that going to be this is them
+ 
+
+ align:start position:0%
+is that going to be this is them
+right and so solubility product right
+
+ align:start position:0%
+right and so solubility product right
+ 
+
+ align:start position:0%
+right and so solubility product right
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+now okay well that now oh
+
+ align:start position:0%
+now okay well that now oh
+ 
+
+ align:start position:0%
+now okay well that now oh
+okay i used i used the definition of an
+
+ align:start position:0%
+okay i used i used the definition of an
+ 
+
+ align:start position:0%
+okay i used i used the definition of an
+equilibrium constant
+
+ align:start position:0%
+equilibrium constant
+ 
+
+ align:start position:0%
+equilibrium constant
+and now i can use this reaction
+
+ align:start position:0%
+and now i can use this reaction
+ 
+
+ align:start position:0%
+and now i can use this reaction
+i can use this reaction because the
+
+ align:start position:0%
+i can use this reaction because the
+ 
+
+ align:start position:0%
+i can use this reaction because the
+stoichiometric coefficients
+
+ align:start position:0%
+stoichiometric coefficients
+ 
+
+ align:start position:0%
+stoichiometric coefficients
+tell me they tell me both what the
+
+ align:start position:0%
+tell me they tell me both what the
+ 
+
+ align:start position:0%
+tell me they tell me both what the
+exponents there are
+
+ align:start position:0%
+exponents there are
+ 
+
+ align:start position:0%
+exponents there are
+one but they also tell me the relative
+
+ align:start position:0%
+one but they also tell me the relative
+ 
+
+ align:start position:0%
+one but they also tell me the relative
+molar amounts of these things is the
+
+ align:start position:0%
+molar amounts of these things is the
+ 
+
+ align:start position:0%
+molar amounts of these things is the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+so if x equals the concentration of
+
+ align:start position:0%
+so if x equals the concentration of
+ 
+
+ align:start position:0%
+so if x equals the concentration of
+silver plus
+
+ align:start position:0%
+silver plus
+ 
+
+ align:start position:0%
+silver plus
+then it must also must
+
+ align:start position:0%
+then it must also must
+ 
+
+ align:start position:0%
+then it must also must
+also equal the concentration
+
+ align:start position:0%
+also equal the concentration
+ 
+
+ align:start position:0%
+also equal the concentration
+of cl minus if you just let x equal the
+
+ align:start position:0%
+of cl minus if you just let x equal the
+ 
+
+ align:start position:0%
+of cl minus if you just let x equal the
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+that comes from the reaction one in
+
+ align:start position:0%
+that comes from the reaction one in
+ 
+
+ align:start position:0%
+that comes from the reaction one in
+front of silver one in front of chlorine
+
+ align:start position:0%
+front of silver one in front of chlorine
+ 
+
+ align:start position:0%
+front of silver one in front of chlorine
+and so that means now that you can solve
+
+ align:start position:0%
+and so that means now that you can solve
+ 
+
+ align:start position:0%
+and so that means now that you can solve
+it because
+
+ align:start position:0%
+it because
+ 
+
+ align:start position:0%
+it because
+x squared is equal to
+
+ align:start position:0%
+x squared is equal to
+ 
+
+ align:start position:0%
+x squared is equal to
+one point seven times ten
+
+ align:start position:0%
+one point seven times ten
+ 
+
+ align:start position:0%
+one point seven times ten
+to the minus tenth and
+
+ align:start position:0%
+to the minus tenth and
+ 
+
+ align:start position:0%
+to the minus tenth and
+x equals 1.3
+
+ align:start position:0%
+x equals 1.3
+ 
+
+ align:start position:0%
+x equals 1.3
+times 10 to the minus fifth
+
+ align:start position:0%
+times 10 to the minus fifth
+ 
+
+ align:start position:0%
+times 10 to the minus fifth
+m and that equals these concentrations
+
+ align:start position:0%
+m and that equals these concentrations
+ 
+
+ align:start position:0%
+m and that equals these concentrations
+right that equals the concentration of
+
+ align:start position:0%
+right that equals the concentration of
+ 
+
+ align:start position:0%
+right that equals the concentration of
+silver plus so that is how much
+
+ align:start position:0%
+silver plus so that is how much
+ 
+
+ align:start position:0%
+silver plus so that is how much
+in equilibrium this is an equilibrium
+
+ align:start position:0%
+in equilibrium this is an equilibrium
+ 
+
+ align:start position:0%
+in equilibrium this is an equilibrium
+constant that is how much
+
+ align:start position:0%
+constant that is how much
+ 
+
+ align:start position:0%
+constant that is how much
+you will get of these ions dissolved in
+
+ align:start position:0%
+you will get of these ions dissolved in
+ 
+
+ align:start position:0%
+you will get of these ions dissolved in
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+now there's a nice way to set this up
+
+ align:start position:0%
+now there's a nice way to set this up
+ 
+
+ align:start position:0%
+now there's a nice way to set this up
+that um
+
+ align:start position:0%
+that um
+ 
+
+ align:start position:0%
+that um
+that is taught is often taught in high
+
+ align:start position:0%
+that is taught is often taught in high
+ 
+
+ align:start position:0%
+that is taught is often taught in high
+school i like it i think it's a good way
+
+ align:start position:0%
+school i like it i think it's a good way
+ 
+
+ align:start position:0%
+school i like it i think it's a good way
+to kind of
+
+ align:start position:0%
+to kind of
+ 
+
+ align:start position:0%
+to kind of
+keep track right and so if you were uh
+
+ align:start position:0%
+keep track right and so if you were uh
+ 
+
+ align:start position:0%
+keep track right and so if you were uh
+wanting to keep track and you like
+
+ align:start position:0%
+wanting to keep track and you like
+ 
+
+ align:start position:0%
+wanting to keep track and you like
+tables there's something called
+
+ align:start position:0%
+tables there's something called
+ 
+
+ align:start position:0%
+tables there's something called
+the ice table now in this case it's
+
+ align:start position:0%
+the ice table now in this case it's
+ 
+
+ align:start position:0%
+the ice table now in this case it's
+it's a little bit boring but
+
+ align:start position:0%
+it's a little bit boring but
+ 
+
+ align:start position:0%
+it's a little bit boring but
+as you'll see it can actually wind up
+
+ align:start position:0%
+as you'll see it can actually wind up
+ 
+
+ align:start position:0%
+as you'll see it can actually wind up
+being pretty useful especially when
+
+ align:start position:0%
+being pretty useful especially when
+ 
+
+ align:start position:0%
+being pretty useful especially when
+we add other ions which are going to do
+
+ align:start position:0%
+we add other ions which are going to do
+ 
+
+ align:start position:0%
+we add other ions which are going to do
+soon so ice is initial
+
+ align:start position:0%
+soon so ice is initial
+ 
+
+ align:start position:0%
+soon so ice is initial
+change equilibrium initial
+
+ align:start position:0%
+change equilibrium initial
+ 
+
+ align:start position:0%
+change equilibrium initial
+change equilibrium it's just a way of
+
+ align:start position:0%
+change equilibrium it's just a way of
+ 
+
+ align:start position:0%
+change equilibrium it's just a way of
+keeping track of what i just did
+
+ align:start position:0%
+keeping track of what i just did
+ 
+
+ align:start position:0%
+keeping track of what i just did
+because i started with some amount of
+
+ align:start position:0%
+because i started with some amount of
+ 
+
+ align:start position:0%
+because i started with some amount of
+solid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and i had zero i put it into water
+
+ align:start position:0%
+okay and i had zero i put it into water
+ 
+
+ align:start position:0%
+okay and i had zero i put it into water
+i had zero
+
+ align:start position:0%
+i had zero
+ 
+
+ align:start position:0%
+i had zero
+but then i added 1.3
+
+ align:start position:0%
+but then i added 1.3
+ 
+
+ align:start position:0%
+but then i added 1.3
+times 10 to the minus fifth and i added
+
+ align:start position:0%
+times 10 to the minus fifth and i added
+ 
+
+ align:start position:0%
+times 10 to the minus fifth and i added
+1.3 times 10 to the minus fifth
+
+ align:start position:0%
+1.3 times 10 to the minus fifth
+ 
+
+ align:start position:0%
+1.3 times 10 to the minus fifth
+and so my equilibrium is a little less
+
+ align:start position:0%
+and so my equilibrium is a little less
+ 
+
+ align:start position:0%
+and so my equilibrium is a little less
+a little less
+
+ align:start position:0%
+a little less
+ 
+
+ align:start position:0%
+a little less
+solid and over here
+
+ align:start position:0%
+solid and over here
+ 
+
+ align:start position:0%
+solid and over here
+it's just these numbers okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that was indeed boring but
+
+ align:start position:0%
+that was indeed boring but
+ 
+
+ align:start position:0%
+that was indeed boring but
+have no fear it becomes helpful
+
+ align:start position:0%
+have no fear it becomes helpful
+ 
+
+ align:start position:0%
+have no fear it becomes helpful
+and it becomes helpful because what
+
+ align:start position:0%
+and it becomes helpful because what
+ 
+
+ align:start position:0%
+and it becomes helpful because what
+we're going to do next not right now
+
+ align:start position:0%
+we're going to do next not right now
+ 
+
+ align:start position:0%
+we're going to do next not right now
+but on wednesday what we're going to do
+
+ align:start position:0%
+but on wednesday what we're going to do
+ 
+
+ align:start position:0%
+but on wednesday what we're going to do
+is we're going to
+
+ align:start position:0%
+is we're going to
+ 
+
+ align:start position:0%
+is we're going to
+we're going to mess with this
+
+ align:start position:0%
+we're going to mess with this
+ 
+
+ align:start position:0%
+we're going to mess with this
+equilibrium we say
+
+ align:start position:0%
+equilibrium we say
+ 
+
+ align:start position:0%
+equilibrium we say
+oh equilibrium i'm going to throw you
+
+ align:start position:0%
+oh equilibrium i'm going to throw you
+ 
+
+ align:start position:0%
+oh equilibrium i'm going to throw you
+off an equilibrium and say no you're not
+
+ align:start position:0%
+off an equilibrium and say no you're not
+ 
+
+ align:start position:0%
+off an equilibrium and say no you're not
+because i'm equilibrium and i will
+
+ align:start position:0%
+because i'm equilibrium and i will
+ 
+
+ align:start position:0%
+because i'm equilibrium and i will
+always be found
+
+ align:start position:0%
+always be found
+ 
+
+ align:start position:0%
+always be found
+and that's called le chatelier's
+
+ align:start position:0%
+and that's called le chatelier's
+ 
+
+ align:start position:0%
+and that's called le chatelier's
+principle and and what that does is it
+
+ align:start position:0%
+principle and and what that does is it
+ 
+
+ align:start position:0%
+principle and and what that does is it
+allows us to really go back and forth
+
+ align:start position:0%
+allows us to really go back and forth
+ 
+
+ align:start position:0%
+allows us to really go back and forth
+we get to actually let's say add a bunch
+
+ align:start position:0%
+we get to actually let's say add a bunch
+ 
+
+ align:start position:0%
+we get to actually let's say add a bunch
+of chlorine ions to this
+
+ align:start position:0%
+of chlorine ions to this
+ 
+
+ align:start position:0%
+of chlorine ions to this
+and we're going to see what happens to
+
+ align:start position:0%
+and we're going to see what happens to
+ 
+
+ align:start position:0%
+and we're going to see what happens to
+this balance
+
+ align:start position:0%
+this balance
+ 
+
+ align:start position:0%
+this balance
+it will find equilibrium and we have the
+
+ align:start position:0%
+it will find equilibrium and we have the
+ 
+
+ align:start position:0%
+it will find equilibrium and we have the
+tools now to know
+
+ align:start position:0%
+tools now to know
+ 
+
+ align:start position:0%
+tools now to know
+how to find it that's that green curve
+
+ align:start position:0%
+how to find it that's that green curve
+ 
+
+ align:start position:0%
+how to find it that's that green curve
+there you see this is what we're going
+
+ align:start position:0%
+there you see this is what we're going
+ 
+
+ align:start position:0%
+there you see this is what we're going
+to work with
+
+ align:start position:0%
+to work with
+ 
+
+ align:start position:0%
+to work with
+there's the concentration of chlorine
+
+ align:start position:0%
+there's the concentration of chlorine
+ 
+
+ align:start position:0%
+there's the concentration of chlorine
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now is it there's the concentration of
+
+ align:start position:0%
+now is it there's the concentration of
+ 
+
+ align:start position:0%
+now is it there's the concentration of
+silver
+
+ align:start position:0%
+silver
+ 
+
+ align:start position:0%
+silver
+in ions the dissolved chlorine on the
+
+ align:start position:0%
+in ions the dissolved chlorine on the
+ 
+
+ align:start position:0%
+in ions the dissolved chlorine on the
+x-axis dissolve silver on the wax and
+
+ align:start position:0%
+x-axis dissolve silver on the wax and
+ 
+
+ align:start position:0%
+x-axis dissolve silver on the wax and
+look at that
+
+ align:start position:0%
+look at that
+ 
+
+ align:start position:0%
+look at that
+i've got that point b there
+
+ align:start position:0%
+i've got that point b there
+ 
+
+ align:start position:0%
+i've got that point b there
+that is where these things have found
+
+ align:start position:0%
+that is where these things have found
+ 
+
+ align:start position:0%
+that is where these things have found
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+when it's not messed with now the thing
+
+ align:start position:0%
+when it's not messed with now the thing
+ 
+
+ align:start position:0%
+when it's not messed with now the thing
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+if you were a reaction happening and you
+
+ align:start position:0%
+if you were a reaction happening and you
+ 
+
+ align:start position:0%
+if you were a reaction happening and you
+hadn't
+
+ align:start position:0%
+hadn't
+ 
+
+ align:start position:0%
+hadn't
+gotten to equilibrium yet so i hadn't
+
+ align:start position:0%
+gotten to equilibrium yet so i hadn't
+ 
+
+ align:start position:0%
+gotten to equilibrium yet so i hadn't
+added much silver chloride
+
+ align:start position:0%
+added much silver chloride
+ 
+
+ align:start position:0%
+added much silver chloride
+if that was the case then you might be
+
+ align:start position:0%
+if that was the case then you might be
+ 
+
+ align:start position:0%
+if that was the case then you might be
+at point d
+
+ align:start position:0%
+at point d
+ 
+
+ align:start position:0%
+at point d
+does it notice that the reaction
+
+ align:start position:0%
+does it notice that the reaction
+ 
+
+ align:start position:0%
+does it notice that the reaction
+quotient q
+
+ align:start position:0%
+quotient q
+ 
+
+ align:start position:0%
+quotient q
+is less than the equilibrium quotient
+
+ align:start position:0%
+is less than the equilibrium quotient
+ 
+
+ align:start position:0%
+is less than the equilibrium quotient
+the equilibrium constant
+
+ align:start position:0%
+the equilibrium constant
+ 
+
+ align:start position:0%
+the equilibrium constant
+q is less that means it's going to be
+
+ align:start position:0%
+q is less that means it's going to be
+ 
+
+ align:start position:0%
+q is less that means it's going to be
+driven to dissolve
+
+ align:start position:0%
+driven to dissolve
+ 
+
+ align:start position:0%
+driven to dissolve
+more than it precipitates until it gets
+
+ align:start position:0%
+more than it precipitates until it gets
+ 
+
+ align:start position:0%
+more than it precipitates until it gets
+to point b
+
+ align:start position:0%
+to point b
+ 
+
+ align:start position:0%
+to point b
+on this curve you could also be way way
+
+ align:start position:0%
+on this curve you could also be way way
+ 
+
+ align:start position:0%
+on this curve you could also be way way
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+right with a much higher q point e and
+
+ align:start position:0%
+right with a much higher q point e and
+ 
+
+ align:start position:0%
+right with a much higher q point e and
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+it's got to find equilibrium it's going
+
+ align:start position:0%
+it's got to find equilibrium it's going
+ 
+
+ align:start position:0%
+it's got to find equilibrium it's going
+to find equilibrium which is what we
+
+ align:start position:0%
+to find equilibrium which is what we
+ 
+
+ align:start position:0%
+to find equilibrium which is what we
+just calculated
+
+ align:start position:0%
+just calculated
+ 
+
+ align:start position:0%
+just calculated
+those are the concentrations of
+
+ align:start position:0%
+those are the concentrations of
+ 
+
+ align:start position:0%
+those are the concentrations of
+equilibrium it's got to get back to
+
+ align:start position:0%
+equilibrium it's got to get back to
+ 
+
+ align:start position:0%
+equilibrium it's got to get back to
+point b it's going to do it by
+
+ align:start position:0%
+point b it's going to do it by
+ 
+
+ align:start position:0%
+point b it's going to do it by
+precipitating out
+
+ align:start position:0%
+precipitating out
+ 
+
+ align:start position:0%
+precipitating out
+solid it's gone too far
+
+ align:start position:0%
+solid it's gone too far
+ 
+
+ align:start position:0%
+solid it's gone too far
+right but but you can see that
+
+ align:start position:0%
+right but but you can see that
+ 
+
+ align:start position:0%
+right but but you can see that
+equilibrium can also be had and will be
+
+ align:start position:0%
+equilibrium can also be had and will be
+ 
+
+ align:start position:0%
+equilibrium can also be had and will be
+had it
+
+ align:start position:0%
+had it
+ 
+
+ align:start position:0%
+had it
+shall be had because k never changes if
+
+ align:start position:0%
+shall be had because k never changes if
+ 
+
+ align:start position:0%
+shall be had because k never changes if
+you fix the temperature k is the same
+
+ align:start position:0%
+you fix the temperature k is the same
+ 
+
+ align:start position:0%
+you fix the temperature k is the same
+so i can mess with this in other ways i
+
+ align:start position:0%
+so i can mess with this in other ways i
+ 
+
+ align:start position:0%
+so i can mess with this in other ways i
+could go and add a whole bunch of
+
+ align:start position:0%
+could go and add a whole bunch of
+ 
+
+ align:start position:0%
+could go and add a whole bunch of
+chlorine
+
+ align:start position:0%
+chlorine
+ 
+
+ align:start position:0%
+chlorine
+and it will come back down onto that
+
+ align:start position:0%
+and it will come back down onto that
+ 
+
+ align:start position:0%
+and it will come back down onto that
+green curve it will come back down onto
+
+ align:start position:0%
+green curve it will come back down onto
+ 
+
+ align:start position:0%
+green curve it will come back down onto
+that green curve
+
+ align:start position:0%
+that green curve
+ 
+
+ align:start position:0%
+that green curve
+which is the curve that guarantees k is
+
+ align:start position:0%
+which is the curve that guarantees k is
+ 
+
+ align:start position:0%
+which is the curve that guarantees k is
+the same constant
+
+ align:start position:0%
+the same constant
+ 
+
+ align:start position:0%
+the same constant
+that's what that green curve is okay
+
+ align:start position:0%
+that's what that green curve is okay
+ 
+
+ align:start position:0%
+that's what that green curve is okay
+there's one last point i'm going to make
+
+ align:start position:0%
+there's one last point i'm going to make
+ 
+
+ align:start position:0%
+there's one last point i'm going to make
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+and that is units right units
+
+ align:start position:0%
+and that is units right units
+ 
+
+ align:start position:0%
+and that is units right units
+of k
+
+ align:start position:0%
+of k
+ 
+
+ align:start position:0%
+of k
+depend it was like the rate law it
+
+ align:start position:0%
+depend it was like the rate law it
+ 
+
+ align:start position:0%
+depend it was like the rate law it
+depends
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the reaction
+
+ align:start position:0%
+on the reaction
+ 
+
+ align:start position:0%
+on the reaction
+look a concentration is a concentration
+
+ align:start position:0%
+look a concentration is a concentration
+ 
+
+ align:start position:0%
+look a concentration is a concentration
+that was deep units are capital m
+
+ align:start position:0%
+that was deep units are capital m
+ 
+
+ align:start position:0%
+that was deep units are capital m
+moles per liter right but that means
+
+ align:start position:0%
+moles per liter right but that means
+ 
+
+ align:start position:0%
+moles per liter right but that means
+that k
+
+ align:start position:0%
+that k
+ 
+
+ align:start position:0%
+that k
+right k is is is two of those multiplied
+
+ align:start position:0%
+right k is is is two of those multiplied
+ 
+
+ align:start position:0%
+right k is is is two of those multiplied
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+so in this case k has
+
+ align:start position:0%
+so in this case k has
+ 
+
+ align:start position:0%
+so in this case k has
+units of m squared
+
+ align:start position:0%
+units of m squared
+ 
+
+ align:start position:0%
+units of m squared
+it must or it wouldn't work k
+
+ align:start position:0%
+it must or it wouldn't work k
+ 
+
+ align:start position:0%
+it must or it wouldn't work k
+can have units of m cubed right
+
+ align:start position:0%
+can have units of m cubed right
+ 
+
+ align:start position:0%
+can have units of m cubed right
+we will pick up here on wednesday and
+
+ align:start position:0%
+we will pick up here on wednesday and
+ 
+
+ align:start position:0%
+we will pick up here on wednesday and
+we'll cover
+
+ align:start position:0%
+we'll cover
+ 
+
+ align:start position:0%
+we'll cover
+more of this more examples before we
+
+ align:start position:0%
+more of this more examples before we
+ 
+
+ align:start position:0%
+more of this more examples before we
+move on to acids and bases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/9T89uDdO7UI.txt b/9T89uDdO7UI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..91004558cce3a073ff8cae3b95395657098c0582
--- /dev/null
+++ b/9T89uDdO7UI.txt
@@ -0,0 +1,6563 @@
+align:start position:0%
+ 
+welcome everyone it's good to have you
+
+ align:start position:0%
+welcome everyone it's good to have you
+ 
+
+ align:start position:0%
+welcome everyone it's good to have you
+here I see some familiar faces and some
+
+ align:start position:0%
+here I see some familiar faces and some
+ 
+
+ align:start position:0%
+here I see some familiar faces and some
+less familiar faces so that's that's
+
+ align:start position:0%
+less familiar faces so that's that's
+ 
+
+ align:start position:0%
+less familiar faces so that's that's
+fantastic so what I wanted to do is
+
+ align:start position:0%
+fantastic so what I wanted to do is
+ 
+
+ align:start position:0%
+fantastic so what I wanted to do is
+prepare to talk and within the talk have
+
+ align:start position:0%
+prepare to talk and within the talk have
+ 
+
+ align:start position:0%
+prepare to talk and within the talk have
+some images a few videos to look at and
+
+ align:start position:0%
+some images a few videos to look at and
+ 
+
+ align:start position:0%
+some images a few videos to look at and
+there's also a audience participation
+
+ align:start position:0%
+there's also a audience participation
+ 
+
+ align:start position:0%
+there's also a audience participation
+component because that's just how I roll
+
+ align:start position:0%
+component because that's just how I roll
+ 
+
+ align:start position:0%
+component because that's just how I roll
+we have to practice what we're up to so
+
+ align:start position:0%
+we have to practice what we're up to so
+ 
+
+ align:start position:0%
+we have to practice what we're up to so
+this segment this talk is one that is
+
+ align:start position:0%
+this segment this talk is one that is
+ 
+
+ align:start position:0%
+this segment this talk is one that is
+looking at pedagogy as not simply
+
+ align:start position:0%
+looking at pedagogy as not simply
+ 
+
+ align:start position:0%
+looking at pedagogy as not simply
+pedagogical strategies in general but to
+
+ align:start position:0%
+pedagogical strategies in general but to
+ 
+
+ align:start position:0%
+pedagogical strategies in general but to
+look more at the ways that I translate
+
+ align:start position:0%
+look more at the ways that I translate
+ 
+
+ align:start position:0%
+look more at the ways that I translate
+this idea of pedagogy through lenses or
+
+ align:start position:0%
+this idea of pedagogy through lenses or
+ 
+
+ align:start position:0%
+this idea of pedagogy through lenses or
+filters of disruption or criticality and
+
+ align:start position:0%
+filters of disruption or criticality and
+ 
+
+ align:start position:0%
+filters of disruption or criticality and
+so part of the work that I do
+
+ align:start position:0%
+so part of the work that I do
+ 
+
+ align:start position:0%
+so part of the work that I do
+professionally is prepare teachers of
+
+ align:start position:0%
+professionally is prepare teachers of
+ 
+
+ align:start position:0%
+professionally is prepare teachers of
+art for k-12 but also work with graduate
+
+ align:start position:0%
+art for k-12 but also work with graduate
+ 
+
+ align:start position:0%
+art for k-12 but also work with graduate
+students to be as a conductor research
+
+ align:start position:0%
+students to be as a conductor research
+ 
+
+ align:start position:0%
+students to be as a conductor research
+and I also do my own research in
+
+ align:start position:0%
+and I also do my own research in
+ 
+
+ align:start position:0%
+and I also do my own research in
+scholarly kinds of moves about the ways
+
+ align:start position:0%
+scholarly kinds of moves about the ways
+ 
+
+ align:start position:0%
+scholarly kinds of moves about the ways
+in which visual imagery visual art
+
+ align:start position:0%
+in which visual imagery visual art
+ 
+
+ align:start position:0%
+in which visual imagery visual art
+visual cultural production functions as
+
+ align:start position:0%
+visual cultural production functions as
+ 
+
+ align:start position:0%
+visual cultural production functions as
+modes or spaces for teaching and
+
+ align:start position:0%
+modes or spaces for teaching and
+ 
+
+ align:start position:0%
+modes or spaces for teaching and
+learning Jasper Johns a pop artist
+
+ align:start position:0%
+learning Jasper Johns a pop artist
+ 
+
+ align:start position:0%
+learning Jasper Johns a pop artist
+someone who's been relegated into that
+
+ align:start position:0%
+someone who's been relegated into that
+ 
+
+ align:start position:0%
+someone who's been relegated into that
+space by some critics and historians
+
+ align:start position:0%
+space by some critics and historians
+ 
+
+ align:start position:0%
+space by some critics and historians
+this is something that's a statement he
+
+ align:start position:0%
+this is something that's a statement he
+ 
+
+ align:start position:0%
+this is something that's a statement he
+made about his art practice like how do
+
+ align:start position:0%
+made about his art practice like how do
+ 
+
+ align:start position:0%
+made about his art practice like how do
+you make your art what's your approach I
+
+ align:start position:0%
+you make your art what's your approach I
+ 
+
+ align:start position:0%
+you make your art what's your approach I
+take an object do something to it
+
+ align:start position:0%
+take an object do something to it
+ 
+
+ align:start position:0%
+take an object do something to it
+and I do something else do it really
+
+ align:start position:0%
+and I do something else do it really
+ 
+
+ align:start position:0%
+and I do something else do it really
+well yeah I mean that seems really
+
+ align:start position:0%
+well yeah I mean that seems really
+ 
+
+ align:start position:0%
+well yeah I mean that seems really
+simplified but for me that's really
+
+ align:start position:0%
+simplified but for me that's really
+ 
+
+ align:start position:0%
+simplified but for me that's really
+interesting and quite powerful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+methodology your method to use you take
+
+ align:start position:0%
+methodology your method to use you take
+ 
+
+ align:start position:0%
+methodology your method to use you take
+something and then that thing is not
+
+ align:start position:0%
+something and then that thing is not
+ 
+
+ align:start position:0%
+something and then that thing is not
+just it's not finished it's not done
+
+ align:start position:0%
+just it's not finished it's not done
+ 
+
+ align:start position:0%
+just it's not finished it's not done
+being whatever it could be and then do
+
+ align:start position:0%
+being whatever it could be and then do
+ 
+
+ align:start position:0%
+being whatever it could be and then do
+something to it okay I did but then
+
+ align:start position:0%
+something to it okay I did but then
+ 
+
+ align:start position:0%
+something to it okay I did but then
+let's keep it going do something else to
+
+ align:start position:0%
+let's keep it going do something else to
+ 
+
+ align:start position:0%
+let's keep it going do something else to
+it so for me the doing can happen in a
+
+ align:start position:0%
+it so for me the doing can happen in a
+ 
+
+ align:start position:0%
+it so for me the doing can happen in a
+number of ways you can alter it you can
+
+ align:start position:0%
+number of ways you can alter it you can
+ 
+
+ align:start position:0%
+number of ways you can alter it you can
+modify you can throw it you can add
+
+ align:start position:0%
+modify you can throw it you can add
+ 
+
+ align:start position:0%
+modify you can throw it you can add
+something to it you can take something
+
+ align:start position:0%
+something to it you can take something
+ 
+
+ align:start position:0%
+something to it you can take something
+away but we can also as viewers
+
+ align:start position:0%
+away but we can also as viewers
+ 
+
+ align:start position:0%
+away but we can also as viewers
+or people who are engaging with that
+
+ align:start position:0%
+or people who are engaging with that
+ 
+
+ align:start position:0%
+or people who are engaging with that
+object we might ask questions so asking
+
+ align:start position:0%
+object we might ask questions so asking
+ 
+
+ align:start position:0%
+object we might ask questions so asking
+the asking of questions is a form of
+
+ align:start position:0%
+the asking of questions is a form of
+ 
+
+ align:start position:0%
+the asking of questions is a form of
+doing and so for me
+
+ align:start position:0%
+doing and so for me
+ 
+
+ align:start position:0%
+doing and so for me
+Johnson's quotation is is nice is for me
+
+ align:start position:0%
+Johnson's quotation is is nice is for me
+ 
+
+ align:start position:0%
+Johnson's quotation is is nice is for me
+as a bridge from a more modernist
+
+ align:start position:0%
+as a bridge from a more modernist
+ 
+
+ align:start position:0%
+as a bridge from a more modernist
+mindset or approach where it's about the
+
+ align:start position:0%
+mindset or approach where it's about the
+ 
+
+ align:start position:0%
+mindset or approach where it's about the
+object and it's about the making in the
+
+ align:start position:0%
+object and it's about the making in the
+ 
+
+ align:start position:0%
+object and it's about the making in the
+process of making to some folks might
+
+ align:start position:0%
+process of making to some folks might
+ 
+
+ align:start position:0%
+process of making to some folks might
+talk about the slide into post-modernism
+
+ align:start position:0%
+talk about the slide into post-modernism
+ 
+
+ align:start position:0%
+talk about the slide into post-modernism
+or other post spaces where we move
+
+ align:start position:0%
+or other post spaces where we move
+ 
+
+ align:start position:0%
+or other post spaces where we move
+beyond object Nisour material nests to
+
+ align:start position:0%
+beyond object Nisour material nests to
+ 
+
+ align:start position:0%
+beyond object Nisour material nests to
+other realms that have more conceptual
+
+ align:start position:0%
+other realms that have more conceptual
+ 
+
+ align:start position:0%
+other realms that have more conceptual
+content and interest that notion of
+
+ align:start position:0%
+content and interest that notion of
+ 
+
+ align:start position:0%
+content and interest that notion of
+asking questions are taking object doing
+
+ align:start position:0%
+asking questions are taking object doing
+ 
+
+ align:start position:0%
+asking questions are taking object doing
+something who are doing something else
+
+ align:start position:0%
+something who are doing something else
+ 
+
+ align:start position:0%
+something who are doing something else
+to it
+
+ align:start position:0%
+to it
+ 
+
+ align:start position:0%
+to it
+you could engage learners like that
+
+ align:start position:0%
+you could engage learners like that
+ 
+
+ align:start position:0%
+you could engage learners like that
+right that's one way to engage learners
+
+ align:start position:0%
+right that's one way to engage learners
+ 
+
+ align:start position:0%
+right that's one way to engage learners
+so if we think about learners we should
+
+ align:start position:0%
+so if we think about learners we should
+ 
+
+ align:start position:0%
+so if we think about learners we should
+also think about curriculum now this is
+
+ align:start position:0%
+also think about curriculum now this is
+ 
+
+ align:start position:0%
+also think about curriculum now this is
+an image this is not one that I drew but
+
+ align:start position:0%
+an image this is not one that I drew but
+ 
+
+ align:start position:0%
+an image this is not one that I drew but
+it's a cartoon for one a single cartoon
+
+ align:start position:0%
+it's a cartoon for one a single cartoon
+ 
+
+ align:start position:0%
+it's a cartoon for one a single cartoon
+panel from non sequitur and I use this
+
+ align:start position:0%
+panel from non sequitur and I use this
+ 
+
+ align:start position:0%
+panel from non sequitur and I use this
+image when I teach curriculum classes so
+
+ align:start position:0%
+image when I teach curriculum classes so
+ 
+
+ align:start position:0%
+image when I teach curriculum classes so
+on the right we have this larger fish
+
+ align:start position:0%
+on the right we have this larger fish
+ 
+
+ align:start position:0%
+on the right we have this larger fish
+with kind of sharp teeth and there's
+
+ align:start position:0%
+with kind of sharp teeth and there's
+ 
+
+ align:start position:0%
+with kind of sharp teeth and there's
+stuff falling down from the fish's mouth
+
+ align:start position:0%
+stuff falling down from the fish's mouth
+ 
+
+ align:start position:0%
+stuff falling down from the fish's mouth
+and then there are these three smaller
+
+ align:start position:0%
+and then there are these three smaller
+ 
+
+ align:start position:0%
+and then there are these three smaller
+fish and then there's a another fish
+
+ align:start position:0%
+fish and then there's a another fish
+ 
+
+ align:start position:0%
+fish and then there's a another fish
+that's kind of medium-sized and that one
+
+ align:start position:0%
+that's kind of medium-sized and that one
+ 
+
+ align:start position:0%
+that's kind of medium-sized and that one
+actually knows how to talk which i think
+
+ align:start position:0%
+actually knows how to talk which i think
+ 
+
+ align:start position:0%
+actually knows how to talk which i think
+is an interesting thing so we're able to
+
+ align:start position:0%
+is an interesting thing so we're able to
+ 
+
+ align:start position:0%
+is an interesting thing so we're able to
+fish saying that the medium-sized fish
+
+ align:start position:0%
+fish saying that the medium-sized fish
+ 
+
+ align:start position:0%
+fish saying that the medium-sized fish
+says no we can't swim any faster the
+
+ align:start position:0%
+says no we can't swim any faster the
+ 
+
+ align:start position:0%
+says no we can't swim any faster the
+school curriculum is geared for the
+
+ align:start position:0%
+school curriculum is geared for the
+ 
+
+ align:start position:0%
+school curriculum is geared for the
+slower swimmers so that ten of you have
+
+ align:start position:0%
+slower swimmers so that ten of you have
+ 
+
+ align:start position:0%
+slower swimmers so that ten of you have
+to wait for the others to catch up I
+
+ align:start position:0%
+to wait for the others to catch up I
+ 
+
+ align:start position:0%
+to wait for the others to catch up I
+don't know about you only see four other
+
+ align:start position:0%
+don't know about you only see four other
+ 
+
+ align:start position:0%
+don't know about you only see four other
+fish I only see four other fish I do see
+
+ align:start position:0%
+fish I only see four other fish I do see
+ 
+
+ align:start position:0%
+fish I only see four other fish I do see
+one fish that the little fish looks like
+
+ align:start position:0%
+one fish that the little fish looks like
+ 
+
+ align:start position:0%
+one fish that the little fish looks like
+little fish bits that are falling from
+
+ align:start position:0%
+little fish bits that are falling from
+ 
+
+ align:start position:0%
+little fish bits that are falling from
+this larger fish's mouth so where is the
+
+ align:start position:0%
+this larger fish's mouth so where is the
+ 
+
+ align:start position:0%
+this larger fish's mouth so where is the
+curriculum here is the curriculum this
+
+ align:start position:0%
+curriculum here is the curriculum this
+ 
+
+ align:start position:0%
+curriculum here is the curriculum this
+larger fish with the sharp teeth is the
+
+ align:start position:0%
+larger fish with the sharp teeth is the
+ 
+
+ align:start position:0%
+larger fish with the sharp teeth is the
+curriculum that the swimming is the
+
+ align:start position:0%
+curriculum that the swimming is the
+ 
+
+ align:start position:0%
+curriculum that the swimming is the
+curriculum the water itself this cartoon
+
+ align:start position:0%
+curriculum the water itself this cartoon
+ 
+
+ align:start position:0%
+curriculum the water itself this cartoon
+allows us to have multiple entry points
+
+ align:start position:0%
+allows us to have multiple entry points
+ 
+
+ align:start position:0%
+allows us to have multiple entry points
+to ask where the curriculum resides and
+
+ align:start position:0%
+to ask where the curriculum resides and
+ 
+
+ align:start position:0%
+to ask where the curriculum resides and
+if we think about that word curriculum
+
+ align:start position:0%
+if we think about that word curriculum
+ 
+
+ align:start position:0%
+if we think about that word curriculum
+it is derived from a Latin word karere
+
+ align:start position:0%
+it is derived from a Latin word karere
+ 
+
+ align:start position:0%
+it is derived from a Latin word karere
+and that's the infinitive to run
+
+ align:start position:0%
+and that's the infinitive to run
+ 
+
+ align:start position:0%
+and that's the infinitive to run
+so curriculum is to run it's the running
+
+ align:start position:0%
+so curriculum is to run it's the running
+ 
+
+ align:start position:0%
+so curriculum is to run it's the running
+of a course rather than a noun if we
+
+ align:start position:0%
+of a course rather than a noun if we
+ 
+
+ align:start position:0%
+of a course rather than a noun if we
+think about it in those terms right some
+
+ align:start position:0%
+think about it in those terms right some
+ 
+
+ align:start position:0%
+think about it in those terms right some
+curriculum theorists did work in the 70s
+
+ align:start position:0%
+curriculum theorists did work in the 70s
+ 
+
+ align:start position:0%
+curriculum theorists did work in the 70s
+and 80s to reconceptualize curriculum
+
+ align:start position:0%
+and 80s to reconceptualize curriculum
+ 
+
+ align:start position:0%
+and 80s to reconceptualize curriculum
+but and focus on this idea of curriculum
+
+ align:start position:0%
+but and focus on this idea of curriculum
+ 
+
+ align:start position:0%
+but and focus on this idea of curriculum
+as a verb to run so the running were in
+
+ align:start position:0%
+as a verb to run so the running were in
+ 
+
+ align:start position:0%
+as a verb to run so the running were in
+this case the swimming of the course is
+
+ align:start position:0%
+this case the swimming of the course is
+ 
+
+ align:start position:0%
+this case the swimming of the course is
+the curriculum so how they swim so
+
+ align:start position:0%
+the curriculum so how they swim so
+ 
+
+ align:start position:0%
+the curriculum so how they swim so
+apparently these that I'm assuming the
+
+ align:start position:0%
+apparently these that I'm assuming the
+ 
+
+ align:start position:0%
+apparently these that I'm assuming the
+medium sized fish is the teacher that um
+
+ align:start position:0%
+medium sized fish is the teacher that um
+ 
+
+ align:start position:0%
+medium sized fish is the teacher that um
+and could be could also be the you know
+
+ align:start position:0%
+and could be could also be the you know
+ 
+
+ align:start position:0%
+and could be could also be the you know
+the school principal or whoever's in
+
+ align:start position:0%
+the school principal or whoever's in
+ 
+
+ align:start position:0%
+the school principal or whoever's in
+charge there but the the middle three
+
+ align:start position:0%
+charge there but the the middle three
+ 
+
+ align:start position:0%
+charge there but the the middle three
+are probably or supposed to be maybe the
+
+ align:start position:0%
+are probably or supposed to be maybe the
+ 
+
+ align:start position:0%
+are probably or supposed to be maybe the
+students who seemed to know how to swim
+
+ align:start position:0%
+students who seemed to know how to swim
+ 
+
+ align:start position:0%
+students who seemed to know how to swim
+the course the way that it was designed
+
+ align:start position:0%
+the course the way that it was designed
+ 
+
+ align:start position:0%
+the course the way that it was designed
+maybe well this could be one of the
+
+ align:start position:0%
+maybe well this could be one of the
+ 
+
+ align:start position:0%
+maybe well this could be one of the
+learners to swimming adequately but
+
+ align:start position:0%
+learners to swimming adequately but
+ 
+
+ align:start position:0%
+learners to swimming adequately but
+sometimes when I have used this with my
+
+ align:start position:0%
+sometimes when I have used this with my
+ 
+
+ align:start position:0%
+sometimes when I have used this with my
+students in court in curriculum courses
+
+ align:start position:0%
+students in court in curriculum courses
+ 
+
+ align:start position:0%
+students in court in curriculum courses
+they talk about how this larger fish
+
+ align:start position:0%
+they talk about how this larger fish
+ 
+
+ align:start position:0%
+they talk about how this larger fish
+they often call it the Barracuda say
+
+ align:start position:0%
+they often call it the Barracuda say
+ 
+
+ align:start position:0%
+they often call it the Barracuda say
+that's the curriculum the curriculum
+
+ align:start position:0%
+that's the curriculum the curriculum
+ 
+
+ align:start position:0%
+that's the curriculum the curriculum
+eats up the swimmers who don't swim in
+
+ align:start position:0%
+eats up the swimmers who don't swim in
+ 
+
+ align:start position:0%
+eats up the swimmers who don't swim in
+predetermined ways okay so here at
+
+ align:start position:0%
+predetermined ways okay so here at
+ 
+
+ align:start position:0%
+predetermined ways okay so here at
+curriculum is a noun in an adversarial
+
+ align:start position:0%
+curriculum is a noun in an adversarial
+ 
+
+ align:start position:0%
+curriculum is a noun in an adversarial
+thing how depressing is that to be a
+
+ align:start position:0%
+thing how depressing is that to be a
+ 
+
+ align:start position:0%
+thing how depressing is that to be a
+teacher or a learner to think the
+
+ align:start position:0%
+teacher or a learner to think the
+ 
+
+ align:start position:0%
+teacher or a learner to think the
+curriculums after you you better stay in
+
+ align:start position:0%
+curriculums after you you better stay in
+ 
+
+ align:start position:0%
+curriculums after you you better stay in
+front of it but if we think of the
+
+ align:start position:0%
+front of it but if we think of the
+ 
+
+ align:start position:0%
+front of it but if we think of the
+curriculum as a verb in the ways in
+
+ align:start position:0%
+curriculum as a verb in the ways in
+ 
+
+ align:start position:0%
+curriculum as a verb in the ways in
+which we swim so maybe some swimmers
+
+ align:start position:0%
+which we swim so maybe some swimmers
+ 
+
+ align:start position:0%
+which we swim so maybe some swimmers
+swim higher in the water some some lower
+
+ align:start position:0%
+swim higher in the water some some lower
+ 
+
+ align:start position:0%
+swim higher in the water some some lower
+some swim sideways some swim faster and
+
+ align:start position:0%
+some swim sideways some swim faster and
+ 
+
+ align:start position:0%
+some swim sideways some swim faster and
+slower how might the curriculum allow
+
+ align:start position:0%
+slower how might the curriculum allow
+ 
+
+ align:start position:0%
+slower how might the curriculum allow
+for multiple swimmers rather than a
+
+ align:start position:0%
+for multiple swimmers rather than a
+ 
+
+ align:start position:0%
+for multiple swimmers rather than a
+predetermined and singular notion of
+
+ align:start position:0%
+predetermined and singular notion of
+ 
+
+ align:start position:0%
+predetermined and singular notion of
+what a learner could be but that's if we
+
+ align:start position:0%
+what a learner could be but that's if we
+ 
+
+ align:start position:0%
+what a learner could be but that's if we
+preface or that's if we privilege the
+
+ align:start position:0%
+preface or that's if we privilege the
+ 
+
+ align:start position:0%
+preface or that's if we privilege the
+idea of learning right we think about
+
+ align:start position:0%
+idea of learning right we think about
+ 
+
+ align:start position:0%
+idea of learning right we think about
+teaching we could just deliver I mean
+
+ align:start position:0%
+teaching we could just deliver I mean
+ 
+
+ align:start position:0%
+teaching we could just deliver I mean
+there are notions of teaching and
+
+ align:start position:0%
+there are notions of teaching and
+ 
+
+ align:start position:0%
+there are notions of teaching and
+curriculum that from the early 1900's
+
+ align:start position:0%
+curriculum that from the early 1900's
+ 
+
+ align:start position:0%
+curriculum that from the early 1900's
+and late 18-hundreds that would think
+
+ align:start position:0%
+and late 18-hundreds that would think
+ 
+
+ align:start position:0%
+and late 18-hundreds that would think
+that would proclaim that learners are
+
+ align:start position:0%
+that would proclaim that learners are
+ 
+
+ align:start position:0%
+that would proclaim that learners are
+empty vessels and the teacher has all
+
+ align:start position:0%
+empty vessels and the teacher has all
+ 
+
+ align:start position:0%
+empty vessels and the teacher has all
+the knowledge we just fill you up with
+
+ align:start position:0%
+the knowledge we just fill you up with
+ 
+
+ align:start position:0%
+the knowledge we just fill you up with
+knowledge and that says you're a learner
+
+ align:start position:0%
+knowledge and that says you're a learner
+ 
+
+ align:start position:0%
+knowledge and that says you're a learner
+you don't bring anything to the
+
+ align:start position:0%
+you don't bring anything to the
+ 
+
+ align:start position:0%
+you don't bring anything to the
+classroom but that's not the case you
+
+ align:start position:0%
+classroom but that's not the case you
+ 
+
+ align:start position:0%
+classroom but that's not the case you
+swim the way you swim bring that to the
+
+ align:start position:0%
+swim the way you swim bring that to the
+ 
+
+ align:start position:0%
+swim the way you swim bring that to the
+classroom
+
+ align:start position:0%
+classroom
+ 
+
+ align:start position:0%
+classroom
+so this idea of shifting from teaching
+
+ align:start position:0%
+so this idea of shifting from teaching
+ 
+
+ align:start position:0%
+so this idea of shifting from teaching
+to learning privileges or allows more
+
+ align:start position:0%
+to learning privileges or allows more
+ 
+
+ align:start position:0%
+to learning privileges or allows more
+attention to what learners bring to
+
+ align:start position:0%
+attention to what learners bring to
+ 
+
+ align:start position:0%
+attention to what learners bring to
+those spaces
+
+ align:start position:0%
+those spaces
+ 
+
+ align:start position:0%
+those spaces
+well another standardized approach that
+
+ align:start position:0%
+well another standardized approach that
+ 
+
+ align:start position:0%
+well another standardized approach that
+was very popular 100 years ago and still
+
+ align:start position:0%
+was very popular 100 years ago and still
+ 
+
+ align:start position:0%
+was very popular 100 years ago and still
+somehow is its popular within some
+
+ align:start position:0%
+somehow is its popular within some
+ 
+
+ align:start position:0%
+somehow is its popular within some
+circles in art at teaching and education
+
+ align:start position:0%
+circles in art at teaching and education
+ 
+
+ align:start position:0%
+circles in art at teaching and education
+are the elements of art and the
+
+ align:start position:0%
+are the elements of art and the
+ 
+
+ align:start position:0%
+are the elements of art and the
+principles of design some people call
+
+ align:start position:0%
+principles of design some people call
+ 
+
+ align:start position:0%
+principles of design some people call
+the elements and principles well it's
+
+ align:start position:0%
+the elements and principles well it's
+ 
+
+ align:start position:0%
+the elements and principles well it's
+the elements of art and principles of
+
+ align:start position:0%
+the elements of art and principles of
+ 
+
+ align:start position:0%
+the elements of art and principles of
+design and certainly these are ways to
+
+ align:start position:0%
+design and certainly these are ways to
+ 
+
+ align:start position:0%
+design and certainly these are ways to
+say look these are the things that are
+
+ align:start position:0%
+say look these are the things that are
+ 
+
+ align:start position:0%
+say look these are the things that are
+going on in visual imagery or material
+
+ align:start position:0%
+going on in visual imagery or material
+ 
+
+ align:start position:0%
+going on in visual imagery or material
+culture but they weren't intended to be
+
+ align:start position:0%
+culture but they weren't intended to be
+ 
+
+ align:start position:0%
+culture but they weren't intended to be
+the limitations they were intended to be
+
+ align:start position:0%
+the limitations they were intended to be
+ 
+
+ align:start position:0%
+the limitations they were intended to be
+ways to gain access to what we're seeing
+
+ align:start position:0%
+ways to gain access to what we're seeing
+ 
+
+ align:start position:0%
+ways to gain access to what we're seeing
+in front of us
+
+ align:start position:0%
+in front of us
+ 
+
+ align:start position:0%
+in front of us
+misinterpretation of that quite often
+
+ align:start position:0%
+misinterpretation of that quite often
+ 
+
+ align:start position:0%
+misinterpretation of that quite often
+teachers studio teachers are teachers
+
+ align:start position:0%
+teachers studio teachers are teachers
+ 
+
+ align:start position:0%
+teachers studio teachers are teachers
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+had 10 weeks to teach a course what 10
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+
+ align:start position:0%
+had 10 weeks to teach a course what 10
+topics would you teach you got to decide
+
+ align:start position:0%
+topics would you teach you got to decide
+ 
+
+ align:start position:0%
+topics would you teach you got to decide
+what doesn't get taught deciding what is
+
+ align:start position:0%
+what doesn't get taught deciding what is
+ 
+
+ align:start position:0%
+what doesn't get taught deciding what is
+not in the curriculum is part of the
+
+ align:start position:0%
+not in the curriculum is part of the
+ 
+
+ align:start position:0%
+not in the curriculum is part of the
+political acts part of the
+
+ align:start position:0%
+political acts part of the
+ 
+
+ align:start position:0%
+political acts part of the
+decision-making so these three prompts
+
+ align:start position:0%
+decision-making so these three prompts
+ 
+
+ align:start position:0%
+decision-making so these three prompts
+are ones that I've used for years and
+
+ align:start position:0%
+are ones that I've used for years and
+ 
+
+ align:start position:0%
+are ones that I've used for years and
+years and years to do exactly what we
+
+ align:start position:0%
+years and years to do exactly what we
+ 
+
+ align:start position:0%
+years and years to do exactly what we
+did you did it like 15 minutes
+
+ align:start position:0%
+did you did it like 15 minutes
+ 
+
+ align:start position:0%
+did you did it like 15 minutes
+I typically spend 15 minutes having the
+
+ align:start position:0%
+I typically spend 15 minutes having the
+ 
+
+ align:start position:0%
+I typically spend 15 minutes having the
+students generate the ideas then we
+
+ align:start position:0%
+students generate the ideas then we
+ 
+
+ align:start position:0%
+students generate the ideas then we
+spend 45 minutes critiquing and
+
+ align:start position:0%
+spend 45 minutes critiquing and
+ 
+
+ align:start position:0%
+spend 45 minutes critiquing and
+interpreting we're not going to spend 45
+
+ align:start position:0%
+interpreting we're not going to spend 45
+ 
+
+ align:start position:0%
+interpreting we're not going to spend 45
+minutes critiquing and interpreting but
+
+ align:start position:0%
+minutes critiquing and interpreting but
+ 
+
+ align:start position:0%
+minutes critiquing and interpreting but
+I'll lead you through some of the things
+
+ align:start position:0%
+I'll lead you through some of the things
+ 
+
+ align:start position:0%
+I'll lead you through some of the things
+that I'd like to do which prompt was
+
+ align:start position:0%
+that I'd like to do which prompt was
+ 
+
+ align:start position:0%
+that I'd like to do which prompt was
+this one this is events this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+creations what was this one creations
+
+ align:start position:0%
+creations what was this one creations
+ 
+
+ align:start position:0%
+creations what was this one creations
+women creations now notice the prompts
+
+ align:start position:0%
+women creations now notice the prompts
+ 
+
+ align:start position:0%
+women creations now notice the prompts
+our will talk about how I worded the
+
+ align:start position:0%
+our will talk about how I worded the
+ 
+
+ align:start position:0%
+our will talk about how I worded the
+prompts in a little bit I find it
+
+ align:start position:0%
+prompts in a little bit I find it
+ 
+
+ align:start position:0%
+prompts in a little bit I find it
+interesting this is just the way I'm
+
+ align:start position:0%
+interesting this is just the way I'm
+ 
+
+ align:start position:0%
+interesting this is just the way I'm
+reading with your lists one two three
+
+ align:start position:0%
+reading with your lists one two three
+ 
+
+ align:start position:0%
+reading with your lists one two three
+four of the five lists use numbers my
+
+ align:start position:0%
+four of the five lists use numbers my
+ 
+
+ align:start position:0%
+four of the five lists use numbers my
+assumption is that the one entry next to
+
+ align:start position:0%
+assumption is that the one entry next to
+ 
+
+ align:start position:0%
+assumption is that the one entry next to
+the number one is the most important
+
+ align:start position:0%
+the number one is the most important
+ 
+
+ align:start position:0%
+the number one is the most important
+only because it's lists if that's I'm
+
+ align:start position:0%
+only because it's lists if that's I'm
+ 
+
+ align:start position:0%
+only because it's lists if that's I'm
+just kind of culturally you know in that
+
+ align:start position:0%
+just kind of culturally you know in that
+ 
+
+ align:start position:0%
+just kind of culturally you know in that
+habit when I see a one I think of that
+
+ align:start position:0%
+habit when I see a one I think of that
+ 
+
+ align:start position:0%
+habit when I see a one I think of that
+being first usually first is most
+
+ align:start position:0%
+being first usually first is most
+ 
+
+ align:start position:0%
+being first usually first is most
+important unless you're David Letterman
+
+ align:start position:0%
+important unless you're David Letterman
+ 
+
+ align:start position:0%
+important unless you're David Letterman
+you reading your top ten list backwards
+
+ align:start position:0%
+you reading your top ten list backwards
+ 
+
+ align:start position:0%
+you reading your top ten list backwards
+if you had a last minute email from the
+
+ align:start position:0%
+if you had a last minute email from the
+ 
+
+ align:start position:0%
+if you had a last minute email from the
+publisher oh we just got some more money
+
+ align:start position:0%
+publisher oh we just got some more money
+ 
+
+ align:start position:0%
+publisher oh we just got some more money
+we could add another chapter to your
+
+ align:start position:0%
+we could add another chapter to your
+ 
+
+ align:start position:0%
+we could add another chapter to your
+textbook but you got to tell us by the
+
+ align:start position:0%
+textbook but you got to tell us by the
+ 
+
+ align:start position:0%
+textbook but you got to tell us by the
+end of the business day today could you
+
+ align:start position:0%
+end of the business day today could you
+ 
+
+ align:start position:0%
+end of the business day today could you
+come up with your number eleven right or
+
+ align:start position:0%
+come up with your number eleven right or
+ 
+
+ align:start position:0%
+come up with your number eleven right or
+oh I'm sorry our budget has been slashed
+
+ align:start position:0%
+oh I'm sorry our budget has been slashed
+ 
+
+ align:start position:0%
+oh I'm sorry our budget has been slashed
+we have to cut two chapters which two
+
+ align:start position:0%
+we have to cut two chapters which two
+ 
+
+ align:start position:0%
+we have to cut two chapters which two
+are the least important these are
+
+ align:start position:0%
+are the least important these are
+ 
+
+ align:start position:0%
+are the least important these are
+questions that curriculum designers
+
+ align:start position:0%
+questions that curriculum designers
+ 
+
+ align:start position:0%
+questions that curriculum designers
+curriculum developers make all the time
+
+ align:start position:0%
+curriculum developers make all the time
+ 
+
+ align:start position:0%
+curriculum developers make all the time
+teachers how much time do we have in the
+
+ align:start position:0%
+teachers how much time do we have in the
+ 
+
+ align:start position:0%
+teachers how much time do we have in the
+semester or the school year to teach oh
+
+ align:start position:0%
+semester or the school year to teach oh
+ 
+
+ align:start position:0%
+semester or the school year to teach oh
+we only got so far we got to hurry up
+
+ align:start position:0%
+we only got so far we got to hurry up
+ 
+
+ align:start position:0%
+we only got so far we got to hurry up
+and rush because this is more important
+
+ align:start position:0%
+and rush because this is more important
+ 
+
+ align:start position:0%
+and rush because this is more important
+and somebody else told us this was
+
+ align:start position:0%
+and somebody else told us this was
+ 
+
+ align:start position:0%
+and somebody else told us this was
+important so we got to teach well I'm
+
+ align:start position:0%
+important so we got to teach well I'm
+ 
+
+ align:start position:0%
+important so we got to teach well I'm
+not teaching that that seems less
+
+ align:start position:0%
+not teaching that that seems less
+ 
+
+ align:start position:0%
+not teaching that that seems less
+important I wanted these are political
+
+ align:start position:0%
+important I wanted these are political
+ 
+
+ align:start position:0%
+important I wanted these are political
+decisions but what is in is only there
+
+ align:start position:0%
+decisions but what is in is only there
+ 
+
+ align:start position:0%
+decisions but what is in is only there
+because it wasn't left out a critical
+
+ align:start position:0%
+because it wasn't left out a critical
+ 
+
+ align:start position:0%
+because it wasn't left out a critical
+pedagogy or pedagogy that I like to
+
+ align:start position:0%
+pedagogy or pedagogy that I like to
+ 
+
+ align:start position:0%
+pedagogy or pedagogy that I like to
+enact and encourage my students to use
+
+ align:start position:0%
+enact and encourage my students to use
+ 
+
+ align:start position:0%
+enact and encourage my students to use
+is one that asks these kinds of
+
+ align:start position:0%
+is one that asks these kinds of
+ 
+
+ align:start position:0%
+is one that asks these kinds of
+questions is constantly in this frame of
+
+ align:start position:0%
+questions is constantly in this frame of
+ 
+
+ align:start position:0%
+questions is constantly in this frame of
+asking even when we have our live
+
+ align:start position:0%
+asking even when we have our live
+ 
+
+ align:start position:0%
+asking even when we have our live
+even when we have our decision of what
+
+ align:start position:0%
+even when we have our decision of what
+ 
+
+ align:start position:0%
+even when we have our decision of what
+seems to be important well why is this
+
+ align:start position:0%
+seems to be important well why is this
+ 
+
+ align:start position:0%
+seems to be important well why is this
+on the list and where else does this
+
+ align:start position:0%
+on the list and where else does this
+ 
+
+ align:start position:0%
+on the list and where else does this
+allow us to go and if we take Toni
+
+ align:start position:0%
+allow us to go and if we take Toni
+ 
+
+ align:start position:0%
+allow us to go and if we take Toni
+Morrison what can we do with her work
+
+ align:start position:0%
+Morrison what can we do with her work
+ 
+
+ align:start position:0%
+Morrison what can we do with her work
+where does her work allow us to go
+
+ align:start position:0%
+where does her work allow us to go
+ 
+
+ align:start position:0%
+where does her work allow us to go
+following Jasper Johns and then where
+
+ align:start position:0%
+following Jasper Johns and then where
+ 
+
+ align:start position:0%
+following Jasper Johns and then where
+does that allow us to go right take Toni
+
+ align:start position:0%
+does that allow us to go right take Toni
+ 
+
+ align:start position:0%
+does that allow us to go right take Toni
+Morrison not an object but we can think
+
+ align:start position:0%
+Morrison not an object but we can think
+ 
+
+ align:start position:0%
+Morrison not an object but we can think
+it in those ways right take this entry
+
+ align:start position:0%
+it in those ways right take this entry
+ 
+
+ align:start position:0%
+it in those ways right take this entry
+do something to it do something else to
+
+ align:start position:0%
+do something to it do something else to
+ 
+
+ align:start position:0%
+do something to it do something else to
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+the word most doesn't appear in any of
+
+ align:start position:0%
+the word most doesn't appear in any of
+ 
+
+ align:start position:0%
+the word most doesn't appear in any of
+those prompts did you pick up on that
+
+ align:start position:0%
+those prompts did you pick up on that
+ 
+
+ align:start position:0%
+those prompts did you pick up on that
+why do you think I didn't put the word
+
+ align:start position:0%
+why do you think I didn't put the word
+ 
+
+ align:start position:0%
+why do you think I didn't put the word
+most in there too much pressure on me I
+
+ align:start position:0%
+most in there too much pressure on me I
+ 
+
+ align:start position:0%
+most in there too much pressure on me I
+could have easily written I'm fine with
+
+ align:start position:0%
+could have easily written I'm fine with
+ 
+
+ align:start position:0%
+could have easily written I'm fine with
+four-letter words I can just sew too
+
+ align:start position:0%
+four-letter words I can just sew too
+ 
+
+ align:start position:0%
+four-letter words I can just sew too
+much pressure for home even though I
+
+ align:start position:0%
+much pressure for home even though I
+ 
+
+ align:start position:0%
+much pressure for home even though I
+think we sort of try to do that is
+
+ align:start position:0%
+think we sort of try to do that is
+ 
+
+ align:start position:0%
+think we sort of try to do that is
+probably most of my that's the way in
+
+ align:start position:0%
+probably most of my that's the way in
+ 
+
+ align:start position:0%
+probably most of my that's the way in
+the way of the word important is if you
+
+ align:start position:0%
+the way of the word important is if you
+ 
+
+ align:start position:0%
+the way of the word important is if you
+don't have the most 30 things what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's kind of a pedagogical strategy
+
+ align:start position:0%
+so it's kind of a pedagogical strategy
+ 
+
+ align:start position:0%
+so it's kind of a pedagogical strategy
+to take some stress away to allow entry
+
+ align:start position:0%
+to take some stress away to allow entry
+ 
+
+ align:start position:0%
+to take some stress away to allow entry
+to remove some of the complications
+
+ align:start position:0%
+to remove some of the complications
+ 
+
+ align:start position:0%
+to remove some of the complications
+embedded in just working out the
+
+ align:start position:0%
+embedded in just working out the
+ 
+
+ align:start position:0%
+embedded in just working out the
+different values ahead of time anyway I
+
+ align:start position:0%
+different values ahead of time anyway I
+ 
+
+ align:start position:0%
+different values ahead of time anyway I
+mean certainly those are important
+
+ align:start position:0%
+mean certainly those are important
+ 
+
+ align:start position:0%
+mean certainly those are important
+conversations that not the stress I
+
+ align:start position:0%
+conversations that not the stress I
+ 
+
+ align:start position:0%
+conversations that not the stress I
+don't like them do stress in stables but
+
+ align:start position:0%
+don't like them do stress in stables but
+ 
+
+ align:start position:0%
+don't like them do stress in stables but
+to make an activity or allow an activity
+
+ align:start position:0%
+to make an activity or allow an activity
+ 
+
+ align:start position:0%
+to make an activity or allow an activity
+to have end points of entry for people
+
+ align:start position:0%
+to have end points of entry for people
+ 
+
+ align:start position:0%
+to have end points of entry for people
+where they feel like they can be part of
+
+ align:start position:0%
+where they feel like they can be part of
+ 
+
+ align:start position:0%
+where they feel like they can be part of
+that absolutely so it's not fixed
+
+ align:start position:0%
+that absolutely so it's not fixed
+ 
+
+ align:start position:0%
+that absolutely so it's not fixed
+absolutely that notion of curriculum for
+
+ align:start position:0%
+absolutely that notion of curriculum for
+ 
+
+ align:start position:0%
+absolutely that notion of curriculum for
+a lot of people it's fixed it's done
+
+ align:start position:0%
+a lot of people it's fixed it's done
+ 
+
+ align:start position:0%
+a lot of people it's fixed it's done
+it's a noun it's not a running it's not
+
+ align:start position:0%
+it's a noun it's not a running it's not
+ 
+
+ align:start position:0%
+it's a noun it's not a running it's not
+a continuation it's not a springboard
+
+ align:start position:0%
+a continuation it's not a springboard
+ 
+
+ align:start position:0%
+a continuation it's not a springboard
+and a prompt you're exactly right it's
+
+ align:start position:0%
+and a prompt you're exactly right it's
+ 
+
+ align:start position:0%
+and a prompt you're exactly right it's
+like a it's a point of continuous
+
+ align:start position:0%
+like a it's a point of continuous
+ 
+
+ align:start position:0%
+like a it's a point of continuous
+learning yeah
+
+ align:start position:0%
+learning yeah
+ 
+
+ align:start position:0%
+learning yeah
+good stuff all right so let's slide back
+
+ align:start position:0%
+good stuff all right so let's slide back
+ 
+
+ align:start position:0%
+good stuff all right so let's slide back
+up here wow this was 20 years ago and I
+
+ align:start position:0%
+up here wow this was 20 years ago and I
+ 
+
+ align:start position:0%
+up here wow this was 20 years ago and I
+was working with hypertext software
+
+ align:start position:0%
+was working with hypertext software
+ 
+
+ align:start position:0%
+was working with hypertext software
+story space so you kind of see that map
+
+ align:start position:0%
+story space so you kind of see that map
+ 
+
+ align:start position:0%
+story space so you kind of see that map
+in the upper left and my idea was I go
+
+ align:start position:0%
+in the upper left and my idea was I go
+ 
+
+ align:start position:0%
+in the upper left and my idea was I go
+to the barbershop and I get my haircut
+
+ align:start position:0%
+to the barbershop and I get my haircut
+ 
+
+ align:start position:0%
+to the barbershop and I get my haircut
+but I learn a lot of stuff in that
+
+ align:start position:0%
+but I learn a lot of stuff in that
+ 
+
+ align:start position:0%
+but I learn a lot of stuff in that
+barber shop
+
+ align:start position:0%
+barber shop
+ 
+
+ align:start position:0%
+barber shop
+I think this barber shop might be a
+
+ align:start position:0%
+I think this barber shop might be a
+ 
+
+ align:start position:0%
+I think this barber shop might be a
+curriculum might be an educational space
+
+ align:start position:0%
+curriculum might be an educational space
+ 
+
+ align:start position:0%
+curriculum might be an educational space
+no it's a hypertext there's a bunch of
+
+ align:start position:0%
+no it's a hypertext there's a bunch of
+ 
+
+ align:start position:0%
+no it's a hypertext there's a bunch of
+moving parts and different relationship
+
+ align:start position:0%
+moving parts and different relationship
+ 
+
+ align:start position:0%
+moving parts and different relationship
+maybe it's all of those things so I
+
+ align:start position:0%
+maybe it's all of those things so I
+ 
+
+ align:start position:0%
+maybe it's all of those things so I
+started to overlap there's different
+
+ align:start position:0%
+started to overlap there's different
+ 
+
+ align:start position:0%
+started to overlap there's different
+thoughts into a piece called Pat's
+
+ align:start position:0%
+thoughts into a piece called Pat's
+ 
+
+ align:start position:0%
+thoughts into a piece called Pat's
+barber shop one day I asked the
+
+ align:start position:0%
+barber shop one day I asked the
+ 
+
+ align:start position:0%
+barber shop one day I asked the
+gathering of barbers and clients what
+
+ align:start position:0%
+gathering of barbers and clients what
+ 
+
+ align:start position:0%
+gathering of barbers and clients what
+can someone learn in here meaning what
+
+ align:start position:0%
+can someone learn in here meaning what
+ 
+
+ align:start position:0%
+can someone learn in here meaning what
+can someone learn in this barber shop
+
+ align:start position:0%
+can someone learn in this barber shop
+ 
+
+ align:start position:0%
+can someone learn in this barber shop
+and this barber shop is in Norfolk
+
+ align:start position:0%
+and this barber shop is in Norfolk
+ 
+
+ align:start position:0%
+and this barber shop is in Norfolk
+Virginia predominantly african-american
+
+ align:start position:0%
+Virginia predominantly african-american
+ 
+
+ align:start position:0%
+Virginia predominantly african-american
+segment of Norfolk this was when I was
+
+ align:start position:0%
+segment of Norfolk this was when I was
+ 
+
+ align:start position:0%
+segment of Norfolk this was when I was
+on faculty at you know many immune
+
+ align:start position:0%
+on faculty at you know many immune
+ 
+
+ align:start position:0%
+on faculty at you know many immune
+Aversa T so as Pat the owner and lead
+
+ align:start position:0%
+Aversa T so as Pat the owner and lead
+ 
+
+ align:start position:0%
+Aversa T so as Pat the owner and lead
+barber what can somebody learn here and
+
+ align:start position:0%
+barber what can somebody learn here and
+ 
+
+ align:start position:0%
+barber what can somebody learn here and
+according to Pat people learn a lot
+
+ align:start position:0%
+according to Pat people learn a lot
+ 
+
+ align:start position:0%
+according to Pat people learn a lot
+about life
+
+ align:start position:0%
+about life
+ 
+
+ align:start position:0%
+about life
+education business the street the whole
+
+ align:start position:0%
+education business the street the whole
+ 
+
+ align:start position:0%
+education business the street the whole
+nine someone else noted with the smirk
+
+ align:start position:0%
+nine someone else noted with the smirk
+ 
+
+ align:start position:0%
+nine someone else noted with the smirk
+they learn what a gram is he was talking
+
+ align:start position:0%
+they learn what a gram is he was talking
+ 
+
+ align:start position:0%
+they learn what a gram is he was talking
+about illicit substances how much you
+
+ align:start position:0%
+about illicit substances how much you
+ 
+
+ align:start position:0%
+about illicit substances how much you
+can get for a stolen TV and that they
+
+ align:start position:0%
+can get for a stolen TV and that they
+ 
+
+ align:start position:0%
+can get for a stolen TV and that they
+can learn that crack is good
+
+ align:start position:0%
+can learn that crack is good
+ 
+
+ align:start position:0%
+can learn that crack is good
+we love crackheads what he meant was the
+
+ align:start position:0%
+we love crackheads what he meant was the
+ 
+
+ align:start position:0%
+we love crackheads what he meant was the
+first part he was actually being
+
+ align:start position:0%
+first part he was actually being
+ 
+
+ align:start position:0%
+first part he was actually being
+sarcastic but the second part was he was
+
+ align:start position:0%
+sarcastic but the second part was he was
+ 
+
+ align:start position:0%
+sarcastic but the second part was he was
+being more supportive in a
+
+ align:start position:0%
+being more supportive in a
+ 
+
+ align:start position:0%
+being more supportive in a
+matter-of-fact tone one of the barbers
+
+ align:start position:0%
+matter-of-fact tone one of the barbers
+ 
+
+ align:start position:0%
+matter-of-fact tone one of the barbers
+commented if you could put a camera in
+
+ align:start position:0%
+commented if you could put a camera in
+ 
+
+ align:start position:0%
+commented if you could put a camera in
+here for a week you could make a movie
+
+ align:start position:0%
+here for a week you could make a movie
+ 
+
+ align:start position:0%
+here for a week you could make a movie
+at one point Pat himself responded to my
+
+ align:start position:0%
+at one point Pat himself responded to my
+ 
+
+ align:start position:0%
+at one point Pat himself responded to my
+question in a melodic chant Oh Jay did
+
+ align:start position:0%
+question in a melodic chant Oh Jay did
+ 
+
+ align:start position:0%
+question in a melodic chant Oh Jay did
+it Oh Jay did it a reference to a scene
+
+ align:start position:0%
+it Oh Jay did it a reference to a scene
+ 
+
+ align:start position:0%
+it Oh Jay did it a reference to a scene
+in the movie barbershop in the famous
+
+ align:start position:0%
+in the movie barbershop in the famous
+ 
+
+ align:start position:0%
+in the movie barbershop in the famous
+court trial later in a more serious tone
+
+ align:start position:0%
+court trial later in a more serious tone
+ 
+
+ align:start position:0%
+court trial later in a more serious tone
+Pat proudly stated younger teenagers
+
+ align:start position:0%
+Pat proudly stated younger teenagers
+ 
+
+ align:start position:0%
+Pat proudly stated younger teenagers
+learn from me don't sell drugs be
+
+ align:start position:0%
+learn from me don't sell drugs be
+ 
+
+ align:start position:0%
+learn from me don't sell drugs be
+successful keep a straight head Pat
+
+ align:start position:0%
+successful keep a straight head Pat
+ 
+
+ align:start position:0%
+successful keep a straight head Pat
+admitted that in his place you learn
+
+ align:start position:0%
+admitted that in his place you learn
+ 
+
+ align:start position:0%
+admitted that in his place you learn
+about everyday life and this project
+
+ align:start position:0%
+about everyday life and this project
+ 
+
+ align:start position:0%
+about everyday life and this project
+went on for years going in the coming
+
+ align:start position:0%
+went on for years going in the coming
+ 
+
+ align:start position:0%
+went on for years going in the coming
+professor well hey professor guess what
+
+ align:start position:0%
+professor well hey professor guess what
+ 
+
+ align:start position:0%
+professor well hey professor guess what
+this and they would start to tell me
+
+ align:start position:0%
+this and they would start to tell me
+ 
+
+ align:start position:0%
+this and they would start to tell me
+what they learned recently and so I'd
+
+ align:start position:0%
+what they learned recently and so I'd
+ 
+
+ align:start position:0%
+what they learned recently and so I'd
+get new lessons and so this article is
+
+ align:start position:0%
+get new lessons and so this article is
+ 
+
+ align:start position:0%
+get new lessons and so this article is
+filled with different ways to think
+
+ align:start position:0%
+filled with different ways to think
+ 
+
+ align:start position:0%
+filled with different ways to think
+about that barber shop as a hypertext
+
+ align:start position:0%
+about that barber shop as a hypertext
+ 
+
+ align:start position:0%
+about that barber shop as a hypertext
+looking at other a subsequent work not
+
+ align:start position:0%
+looking at other a subsequent work not
+ 
+
+ align:start position:0%
+looking at other a subsequent work not
+only my artists and residents here at
+
+ align:start position:0%
+only my artists and residents here at
+ 
+
+ align:start position:0%
+only my artists and residents here at
+MIT this year but I'm also an artist in
+
+ align:start position:0%
+MIT this year but I'm also an artist in
+ 
+
+ align:start position:0%
+MIT this year but I'm also an artist in
+residence at a local elementary school
+
+ align:start position:0%
+residence at a local elementary school
+ 
+
+ align:start position:0%
+residence at a local elementary school
+back where I live I've been working with
+
+ align:start position:0%
+back where I live I've been working with
+ 
+
+ align:start position:0%
+back where I live I've been working with
+first graders and third graders so you
+
+ align:start position:0%
+first graders and third graders so you
+ 
+
+ align:start position:0%
+first graders and third graders so you
+know what I did a few weeks ago I talked
+
+ align:start position:0%
+know what I did a few weeks ago I talked
+ 
+
+ align:start position:0%
+know what I did a few weeks ago I talked
+to third graders about epidemiology
+
+ align:start position:0%
+to third graders about epidemiology
+ 
+
+ align:start position:0%
+to third graders about epidemiology
+which is what you do right showed them
+
+ align:start position:0%
+which is what you do right showed them
+ 
+
+ align:start position:0%
+which is what you do right showed them
+this map my intention wasn't to talk
+
+ align:start position:0%
+this map my intention wasn't to talk
+ 
+
+ align:start position:0%
+this map my intention wasn't to talk
+specifically about epidemiology my
+
+ align:start position:0%
+specifically about epidemiology my
+ 
+
+ align:start position:0%
+specifically about epidemiology my
+intention was to talk about how the
+
+ align:start position:0%
+intention was to talk about how the
+ 
+
+ align:start position:0%
+intention was to talk about how the
+visual representation of ideas or how
+
+ align:start position:0%
+visual representation of ideas or how
+ 
+
+ align:start position:0%
+visual representation of ideas or how
+the visual representation of data the
+
+ align:start position:0%
+the visual representation of data the
+ 
+
+ align:start position:0%
+the visual representation of data the
+visual representation of information
+
+ align:start position:0%
+visual representation of information
+ 
+
+ align:start position:0%
+visual representation of information
+might allow us access to ways of knowing
+
+ align:start position:0%
+might allow us access to ways of knowing
+ 
+
+ align:start position:0%
+might allow us access to ways of knowing
+and understanding that we wouldn't have
+
+ align:start position:0%
+and understanding that we wouldn't have
+ 
+
+ align:start position:0%
+and understanding that we wouldn't have
+without those visual representations so
+
+ align:start position:0%
+without those visual representations so
+ 
+
+ align:start position:0%
+without those visual representations so
+here we have a segment of London and you
+
+ align:start position:0%
+here we have a segment of London and you
+ 
+
+ align:start position:0%
+here we have a segment of London and you
+see a bunch of dots there and those dots
+
+ align:start position:0%
+see a bunch of dots there and those dots
+ 
+
+ align:start position:0%
+see a bunch of dots there and those dots
+essentially are the
+
+ align:start position:0%
+essentially are the
+ 
+
+ align:start position:0%
+essentially are the
+the places where Jon Snow in the late
+
+ align:start position:0%
+the places where Jon Snow in the late
+ 
+
+ align:start position:0%
+the places where Jon Snow in the late
+1800s identified people who had died
+
+ align:start position:0%
+1800s identified people who had died
+ 
+
+ align:start position:0%
+1800s identified people who had died
+from cholera and his theory which was
+
+ align:start position:0%
+from cholera and his theory which was
+ 
+
+ align:start position:0%
+from cholera and his theory which was
+different than the local theory and the
+
+ align:start position:0%
+different than the local theory and the
+ 
+
+ align:start position:0%
+different than the local theory and the
+common theory at that point his theory
+
+ align:start position:0%
+common theory at that point his theory
+ 
+
+ align:start position:0%
+common theory at that point his theory
+was people were getting color from the
+
+ align:start position:0%
+was people were getting color from the
+ 
+
+ align:start position:0%
+was people were getting color from the
+walk from water everybody else know it's
+
+ align:start position:0%
+walk from water everybody else know it's
+ 
+
+ align:start position:0%
+walk from water everybody else know it's
+in the air or it's divine intervention
+
+ align:start position:0%
+in the air or it's divine intervention
+ 
+
+ align:start position:0%
+in the air or it's divine intervention
+or something else go in a John you don't
+
+ align:start position:0%
+or something else go in a John you don't
+ 
+
+ align:start position:0%
+or something else go in a John you don't
+know what you're talking about so I told
+
+ align:start position:0%
+know what you're talking about so I told
+ 
+
+ align:start position:0%
+know what you're talking about so I told
+the kids this my I didn't tell them this
+
+ align:start position:0%
+the kids this my I didn't tell them this
+ 
+
+ align:start position:0%
+the kids this my I didn't tell them this
+yet I said here's a map what do you what
+
+ align:start position:0%
+yet I said here's a map what do you what
+ 
+
+ align:start position:0%
+yet I said here's a map what do you what
+do you see how it's a map okay
+
+ align:start position:0%
+do you see how it's a map okay
+ 
+
+ align:start position:0%
+do you see how it's a map okay
+you know what else you see well I see a
+
+ align:start position:0%
+you know what else you see well I see a
+ 
+
+ align:start position:0%
+you know what else you see well I see a
+bunch of dots what do you think those
+
+ align:start position:0%
+bunch of dots what do you think those
+ 
+
+ align:start position:0%
+bunch of dots what do you think those
+that don't those are the people that's
+
+ align:start position:0%
+that don't those are the people that's
+ 
+
+ align:start position:0%
+that don't those are the people that's
+where they live or maybe that's where
+
+ align:start position:0%
+where they live or maybe that's where
+ 
+
+ align:start position:0%
+where they live or maybe that's where
+something happened why are there more
+
+ align:start position:0%
+something happened why are there more
+ 
+
+ align:start position:0%
+something happened why are there more
+dots here none of that I don't know they
+
+ align:start position:0%
+dots here none of that I don't know they
+ 
+
+ align:start position:0%
+dots here none of that I don't know they
+say oh wait there's some X's what do you
+
+ align:start position:0%
+say oh wait there's some X's what do you
+ 
+
+ align:start position:0%
+say oh wait there's some X's what do you
+think those X's are they had all these
+
+ align:start position:0%
+think those X's are they had all these
+ 
+
+ align:start position:0%
+think those X's are they had all these
+ideas well you don't see the X's here
+
+ align:start position:0%
+ideas well you don't see the X's here
+ 
+
+ align:start position:0%
+ideas well you don't see the X's here
+the x's the X is a year oh okay that's
+
+ align:start position:0%
+the x's the X is a year oh okay that's
+ 
+
+ align:start position:0%
+the x's the X is a year oh okay that's
+helpful Thanks so what's going on tell
+
+ align:start position:0%
+helpful Thanks so what's going on tell
+ 
+
+ align:start position:0%
+helpful Thanks so what's going on tell
+me about the relationship between the
+
+ align:start position:0%
+me about the relationship between the
+ 
+
+ align:start position:0%
+me about the relationship between the
+X's in the dots oh well most of the dots
+
+ align:start position:0%
+X's in the dots oh well most of the dots
+ 
+
+ align:start position:0%
+X's in the dots oh well most of the dots
+are in the middle and 'muslim around
+
+ align:start position:0%
+are in the middle and 'muslim around
+ 
+
+ align:start position:0%
+are in the middle and 'muslim around
+that green dot in the center I said oh
+
+ align:start position:0%
+that green dot in the center I said oh
+ 
+
+ align:start position:0%
+that green dot in the center I said oh
+you know what
+
+ align:start position:0%
+you know what
+ 
+
+ align:start position:0%
+you know what
+that's what Jon Snow thought to guess
+
+ align:start position:0%
+that's what Jon Snow thought to guess
+ 
+
+ align:start position:0%
+that's what Jon Snow thought to guess
+what he figured out that's where the
+
+ align:start position:0%
+what he figured out that's where the
+ 
+
+ align:start position:0%
+what he figured out that's where the
+people were getting sick that's what the
+
+ align:start position:0%
+people were getting sick that's what the
+ 
+
+ align:start position:0%
+people were getting sick that's what the
+people were dying because they were
+
+ align:start position:0%
+people were dying because they were
+ 
+
+ align:start position:0%
+people were dying because they were
+drinking the water and it was because he
+
+ align:start position:0%
+drinking the water and it was because he
+ 
+
+ align:start position:0%
+drinking the water and it was because he
+was able to visually represent the data
+
+ align:start position:0%
+was able to visually represent the data
+ 
+
+ align:start position:0%
+was able to visually represent the data
+he could get to this this observation
+
+ align:start position:0%
+he could get to this this observation
+ 
+
+ align:start position:0%
+he could get to this this observation
+they thought that was pretty cool then I
+
+ align:start position:0%
+they thought that was pretty cool then I
+ 
+
+ align:start position:0%
+they thought that was pretty cool then I
+told him so now here's a new word
+
+ align:start position:0%
+told him so now here's a new word
+ 
+
+ align:start position:0%
+told him so now here's a new word
+epidemiology but two eight nine year old
+
+ align:start position:0%
+epidemiology but two eight nine year old
+ 
+
+ align:start position:0%
+epidemiology but two eight nine year old
+saying epidemiology it's great but they
+
+ align:start position:0%
+saying epidemiology it's great but they
+ 
+
+ align:start position:0%
+saying epidemiology it's great but they
+start to understand how visual
+
+ align:start position:0%
+start to understand how visual
+ 
+
+ align:start position:0%
+start to understand how visual
+representation of information allows
+
+ align:start position:0%
+representation of information allows
+ 
+
+ align:start position:0%
+representation of information allows
+access to ideas in different ways and I
+
+ align:start position:0%
+access to ideas in different ways and I
+ 
+
+ align:start position:0%
+access to ideas in different ways and I
+said if you like this map what about
+
+ align:start position:0%
+said if you like this map what about
+ 
+
+ align:start position:0%
+said if you like this map what about
+this one other people thought that that
+
+ align:start position:0%
+this one other people thought that that
+ 
+
+ align:start position:0%
+this one other people thought that that
+map was interesting too how many
+
+ align:start position:0%
+map was interesting too how many
+ 
+
+ align:start position:0%
+map was interesting too how many
+different ways could you represent data
+
+ align:start position:0%
+different ways could you represent data
+ 
+
+ align:start position:0%
+different ways could you represent data
+visually using a map other people
+
+ align:start position:0%
+visually using a map other people
+ 
+
+ align:start position:0%
+visually using a map other people
+thought John snows idea was really cool
+
+ align:start position:0%
+thought John snows idea was really cool
+ 
+
+ align:start position:0%
+thought John snows idea was really cool
+they came up oh and then as soon as I
+
+ align:start position:0%
+they came up oh and then as soon as I
+ 
+
+ align:start position:0%
+they came up oh and then as soon as I
+showed this
+
+ align:start position:0%
+showed this
+ 
+
+ align:start position:0%
+showed this
+oh that's Google Maps eight nine year
+
+ align:start position:0%
+oh that's Google Maps eight nine year
+ 
+
+ align:start position:0%
+oh that's Google Maps eight nine year
+olds know about Google Maps yeah hmm so
+
+ align:start position:0%
+olds know about Google Maps yeah hmm so
+ 
+
+ align:start position:0%
+olds know about Google Maps yeah hmm so
+now how does Google Maps play into how
+
+ align:start position:0%
+now how does Google Maps play into how
+ 
+
+ align:start position:0%
+now how does Google Maps play into how
+we might teach in elementary school
+
+ align:start position:0%
+we might teach in elementary school
+ 
+
+ align:start position:0%
+we might teach in elementary school
+about space about visual representation
+
+ align:start position:0%
+about space about visual representation
+ 
+
+ align:start position:0%
+about space about visual representation
+just taking an object and doing
+
+ align:start position:0%
+just taking an object and doing
+ 
+
+ align:start position:0%
+just taking an object and doing
+something to it
+
+ align:start position:0%
+something to it
+ 
+
+ align:start position:0%
+something to it
+something else too I do something
+
+ align:start position:0%
+something else too I do something
+ 
+
+ align:start position:0%
+something else too I do something
+similar with my pre-service teachers as
+
+ align:start position:0%
+similar with my pre-service teachers as
+ 
+
+ align:start position:0%
+similar with my pre-service teachers as
+they're preparing to become teachers of
+
+ align:start position:0%
+they're preparing to become teachers of
+ 
+
+ align:start position:0%
+they're preparing to become teachers of
+preparing to go out into classrooms to
+
+ align:start position:0%
+preparing to go out into classrooms to
+ 
+
+ align:start position:0%
+preparing to go out into classrooms to
+do their student teaching when they're
+
+ align:start position:0%
+do their student teaching when they're
+ 
+
+ align:start position:0%
+do their student teaching when they're
+trying to figure out how learning and
+
+ align:start position:0%
+trying to figure out how learning and
+ 
+
+ align:start position:0%
+trying to figure out how learning and
+teaching happens in educational spaces
+
+ align:start position:0%
+teaching happens in educational spaces
+ 
+
+ align:start position:0%
+teaching happens in educational spaces
+one of the tasks I give them is all
+
+ align:start position:0%
+one of the tasks I give them is all
+ 
+
+ align:start position:0%
+one of the tasks I give them is all
+right go ahead and do your next
+
+ align:start position:0%
+right go ahead and do your next
+ 
+
+ align:start position:0%
+right go ahead and do your next
+observation whatever what you do is when
+
+ align:start position:0%
+observation whatever what you do is when
+ 
+
+ align:start position:0%
+observation whatever what you do is when
+you sit down I want you to draw a map of
+
+ align:start position:0%
+you sit down I want you to draw a map of
+ 
+
+ align:start position:0%
+you sit down I want you to draw a map of
+the classroom on a piece of paper and
+
+ align:start position:0%
+the classroom on a piece of paper and
+ 
+
+ align:start position:0%
+the classroom on a piece of paper and
+take with you a marker that you know
+
+ align:start position:0%
+take with you a marker that you know
+ 
+
+ align:start position:0%
+take with you a marker that you know
+will bleed if you leave it too long on
+
+ align:start position:0%
+will bleed if you leave it too long on
+ 
+
+ align:start position:0%
+will bleed if you leave it too long on
+the piece of paper what I want you to do
+
+ align:start position:0%
+the piece of paper what I want you to do
+ 
+
+ align:start position:0%
+the piece of paper what I want you to do
+is I want you to make a note of where
+
+ align:start position:0%
+is I want you to make a note of where
+ 
+
+ align:start position:0%
+is I want you to make a note of where
+all of the furniture is in the room
+
+ align:start position:0%
+all of the furniture is in the room
+ 
+
+ align:start position:0%
+all of the furniture is in the room
+entry points exit points which indicate
+
+ align:start position:0%
+entry points exit points which indicate
+ 
+
+ align:start position:0%
+entry points exit points which indicate
+where the students are when you enter
+
+ align:start position:0%
+where the students are when you enter
+ 
+
+ align:start position:0%
+where the students are when you enter
+the room and indicate where the teacher
+
+ align:start position:0%
+the room and indicate where the teacher
+ 
+
+ align:start position:0%
+the room and indicate where the teacher
+is by putting your marker down and the
+
+ align:start position:0%
+is by putting your marker down and the
+ 
+
+ align:start position:0%
+is by putting your marker down and the
+entire time that you're there you move
+
+ align:start position:0%
+entire time that you're there you move
+ 
+
+ align:start position:0%
+entire time that you're there you move
+your marker wherever the teacher moves
+
+ align:start position:0%
+your marker wherever the teacher moves
+ 
+
+ align:start position:0%
+your marker wherever the teacher moves
+when the teacher stops you stop your
+
+ align:start position:0%
+when the teacher stops you stop your
+ 
+
+ align:start position:0%
+when the teacher stops you stop your
+marker when the teacher starts moving
+
+ align:start position:0%
+marker when the teacher starts moving
+ 
+
+ align:start position:0%
+marker when the teacher starts moving
+you move the market so if the marker if
+
+ align:start position:0%
+you move the market so if the marker if
+ 
+
+ align:start position:0%
+you move the market so if the marker if
+the teacher stops the marker stops if
+
+ align:start position:0%
+the teacher stops the marker stops if
+ 
+
+ align:start position:0%
+the teacher stops the marker stops if
+the marker stops the marker starts to
+
+ align:start position:0%
+the marker stops the marker starts to
+ 
+
+ align:start position:0%
+the marker stops the marker starts to
+bleed it starts to over time take up
+
+ align:start position:0%
+bleed it starts to over time take up
+ 
+
+ align:start position:0%
+bleed it starts to over time take up
+more and more space and then I collect
+
+ align:start position:0%
+more and more space and then I collect
+ 
+
+ align:start position:0%
+more and more space and then I collect
+these maps and we look at them we start
+
+ align:start position:0%
+these maps and we look at them we start
+ 
+
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+
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+you some other maps this person didn't
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+use a marker so they just kind of kept
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+scribbling and overlapping this is
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+happening among the learners to what
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+
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+
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+have to do with the ways in which
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+
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+have to do with the ways in which
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+
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+
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+teacher
+
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+ 
+ 
+
+ align:start position:0%
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+ 
+
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+do with all the students but I don't
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+know if you have enough fingers to move
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+
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+know if you have enough fingers to move
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+
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+all the kids around right interpretation
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+the construction of meaning or the
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+attending to the construction of
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+meanings by talking about it making
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+
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+ 
+
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+sense of works of art ooh you know about
+America rock and Schoolhouse Rock when I
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+America rock and Schoolhouse Rock when I
+ 
+
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+America rock and Schoolhouse Rock when I
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+
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+was a kid these shows would come on
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+
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+was a kid these shows would come on
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+television between the cartoon two or
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+
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+three minute videos Schoolhouse Rock in
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+
+ align:start position:0%
+three minute videos Schoolhouse Rock in
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+
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+America Rock America Rock was a way for
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+
+ align:start position:0%
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+
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+
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+of the United States or a history of the
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+of the United States or a history of the
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+United States so here you see some of
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+
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+United States so here you see some of
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+the episodes no more Kings the founding
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+
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+the episodes no more Kings the founding
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+
+ align:start position:0%
+of America fireworks the Declaration of
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+
+ align:start position:0%
+of America fireworks the Declaration of
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+
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+
+ align:start position:0%
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+
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+
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+preamble because I watch School House
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+preamble because I watch School House
+ 
+
+ align:start position:0%
+preamble because I watch School House
+Rock We the People in order for a more
+
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+Rock We the People in order for a more
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+
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+Rock We the People in order for a more
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+
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+
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+
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+ 
+
+ align:start position:0%
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+middle ooh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Boston Tea Party is that big cup still
+
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+Boston Tea Party is that big cup still
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+
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+Boston Tea Party is that big cup still
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+
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+here in the water no the one on the
+ 
+
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+bottom this is called elbow room elbow
+
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+
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+
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+
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+
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+
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+the word manifest destiny or the term
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+is the melting pot shaped in the form of
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+
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+the United Continental United States
+ 
+
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+the United Continental United States
+little guy just jumps right in it
+
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+ 
+
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+
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+ 
+
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+the lyrics
+
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+the lyrics
+ 
+
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+the lyrics
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they swore their loyalty until the very
+
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+they swore their loyalty until the very
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+
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+end and you taking your own
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
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+this team they wanted no more mother
+
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+this team they wanted no more mother
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+[Applause]
+
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+[Applause]
+ 
+
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+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
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+
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+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
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+ 
+what a great place to live I mean the
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+
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+like what else did you learn from that I
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+
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+like what else did you learn from that I
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+what else did you learn about this
+ 
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+what else did you learn about this
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+
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+video what else did you learn pilgrims
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+
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+in the colonists didn't pay any
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+something Oh things that we didn't learn
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+that this video wildly misrepresented
+
+ align:start position:0%
+that this video wildly misrepresented
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+
+ align:start position:0%
+that this video wildly misrepresented
+and erased a crucial part of history
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+and erased a crucial part of history
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+for white males but it paints a very
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+nice easy picture of what history was
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+but is not true and it has repercussions
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+but is not true and it has repercussions
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+now because of a pulse well I mean they
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+
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+now because of a pulse well I mean they
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+
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+that no they only had three minutes how
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+
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+that no they only had three minutes how
+can we put all that stuff in Bing you
+
+ align:start position:0%
+can we put all that stuff in Bing you
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+
+ align:start position:0%
+can we put all that stuff in Bing you
+know so if you're an art teacher and
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+know so if you're an art teacher and
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+let's say you're assigned to or you're
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+
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+let's say you're assigned to or you're
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+justify showing this video I mean
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+
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+justify showing this video I mean
+illustration video video production can
+
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+illustration video video production can
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+
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+illustration video video production can
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+be taught through the art classroom the
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+
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+
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+there's history being taught I could
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+
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+justify following a prescribed
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+teach together yeah okay we're watching
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+ align:start position:0%
+teach together yeah okay we're watching
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+
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+teach together yeah okay we're watching
+some Schoolhouse Rock and we're going to
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+some Schoolhouse Rock and we're going to
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+ align:start position:0%
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+pedagogical lenses that well you were
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+and we were applying many of them in our
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+and we were applying many of them in our
+reading of that list so as an art
+
+ align:start position:0%
+reading of that list so as an art
+ 
+
+ align:start position:0%
+reading of that list so as an art
+teacher or just a teacher who likes to
+
+ align:start position:0%
+teacher or just a teacher who likes to
+ 
+
+ align:start position:0%
+teacher or just a teacher who likes to
+cause trouble or ask questions or
+
+ align:start position:0%
+cause trouble or ask questions or
+ 
+
+ align:start position:0%
+cause trouble or ask questions or
+promote critical thinking we could show
+
+ align:start position:0%
+promote critical thinking we could show
+ 
+
+ align:start position:0%
+promote critical thinking we could show
+these videos like this so you can show
+
+ align:start position:0%
+these videos like this so you can show
+ 
+
+ align:start position:0%
+these videos like this so you can show
+any visual culture example and interpret
+
+ align:start position:0%
+any visual culture example and interpret
+ 
+
+ align:start position:0%
+any visual culture example and interpret
+and critique through those different
+
+ align:start position:0%
+and critique through those different
+ 
+
+ align:start position:0%
+and critique through those different
+lenses just want to show you a couple of
+
+ align:start position:0%
+lenses just want to show you a couple of
+ 
+
+ align:start position:0%
+lenses just want to show you a couple of
+assignments this assignment is by
+
+ align:start position:0%
+assignments this assignment is by
+ 
+
+ align:start position:0%
+assignments this assignment is by
+another colleague Andres Hernandez who
+
+ align:start position:0%
+another colleague Andres Hernandez who
+ 
+
+ align:start position:0%
+another colleague Andres Hernandez who
+teaches at school of the Art Institute
+
+ align:start position:0%
+teaches at school of the Art Institute
+ 
+
+ align:start position:0%
+teaches at school of the Art Institute
+in Chicago and so this is a project that
+
+ align:start position:0%
+in Chicago and so this is a project that
+ 
+
+ align:start position:0%
+in Chicago and so this is a project that
+he engaged as two students to do where
+
+ align:start position:0%
+he engaged as two students to do where
+ 
+
+ align:start position:0%
+he engaged as two students to do where
+he he uses this quotation to talk about
+
+ align:start position:0%
+he he uses this quotation to talk about
+ 
+
+ align:start position:0%
+he he uses this quotation to talk about
+this and to question this term informal
+
+ align:start position:0%
+this and to question this term informal
+ 
+
+ align:start position:0%
+this and to question this term informal
+sediment settlements now you think about
+
+ align:start position:0%
+sediment settlements now you think about
+ 
+
+ align:start position:0%
+sediment settlements now you think about
+refugees you think about people who've
+
+ align:start position:0%
+refugees you think about people who've
+ 
+
+ align:start position:0%
+refugees you think about people who've
+been displaced and to think about the
+
+ align:start position:0%
+been displaced and to think about the
+ 
+
+ align:start position:0%
+been displaced and to think about the
+housing that they have constructed for
+
+ align:start position:0%
+housing that they have constructed for
+ 
+
+ align:start position:0%
+housing that they have constructed for
+themselves as informal really it's as
+
+ align:start position:0%
+themselves as informal really it's as
+ 
+
+ align:start position:0%
+themselves as informal really it's as
+formal as it's going to get for those
+
+ align:start position:0%
+formal as it's going to get for those
+ 
+
+ align:start position:0%
+formal as it's going to get for those
+folks in that moment I mean the
+
+ align:start position:0%
+folks in that moment I mean the
+ 
+
+ align:start position:0%
+folks in that moment I mean the
+terminology itself is problematic and so
+
+ align:start position:0%
+terminology itself is problematic and so
+ 
+
+ align:start position:0%
+terminology itself is problematic and so
+he wants he's thinking about this you
+
+ align:start position:0%
+he wants he's thinking about this you
+ 
+
+ align:start position:0%
+he wants he's thinking about this you
+know if you think about these kinds of
+
+ align:start position:0%
+know if you think about these kinds of
+ 
+
+ align:start position:0%
+know if you think about these kinds of
+places it says in fewer words the city
+
+ align:start position:0%
+places it says in fewer words the city
+ 
+
+ align:start position:0%
+places it says in fewer words the city
+produced by the people so inspired by
+
+ align:start position:0%
+produced by the people so inspired by
+ 
+
+ align:start position:0%
+produced by the people so inspired by
+the notion of a city produced by people
+
+ align:start position:0%
+the notion of a city produced by people
+ 
+
+ align:start position:0%
+the notion of a city produced by people
+he he tells the students who were
+
+ align:start position:0%
+he he tells the students who were
+ 
+
+ align:start position:0%
+he he tells the students who were
+learning to be art teachers and we have
+
+ align:start position:0%
+learning to be art teachers and we have
+ 
+
+ align:start position:0%
+learning to be art teachers and we have
+these open spaces at Vermont College of
+
+ align:start position:0%
+these open spaces at Vermont College of
+ 
+
+ align:start position:0%
+these open spaces at Vermont College of
+Fine Arts you're going to take one of
+
+ align:start position:0%
+Fine Arts you're going to take one of
+ 
+
+ align:start position:0%
+Fine Arts you're going to take one of
+the spaces and you're going to build a
+
+ align:start position:0%
+the spaces and you're going to build a
+ 
+
+ align:start position:0%
+the spaces and you're going to build a
+shelter out of cardboard and it has to
+
+ align:start position:0%
+shelter out of cardboard and it has to
+ 
+
+ align:start position:0%
+shelter out of cardboard and it has to
+have and there are certain criteria you
+
+ align:start position:0%
+have and there are certain criteria you
+ 
+
+ align:start position:0%
+have and there are certain criteria you
+have to have certain number of people in
+
+ align:start position:0%
+have to have certain number of people in
+ 
+
+ align:start position:0%
+have to have certain number of people in
+it and by doing that at the bottom you
+
+ align:start position:0%
+it and by doing that at the bottom you
+ 
+
+ align:start position:0%
+it and by doing that at the bottom you
+see the purpose of this assignment is
+
+ align:start position:0%
+see the purpose of this assignment is
+ 
+
+ align:start position:0%
+see the purpose of this assignment is
+that it's intuitive building using
+
+ align:start position:0%
+that it's intuitive building using
+ 
+
+ align:start position:0%
+that it's intuitive building using
+limited materials and is focused on a
+
+ align:start position:0%
+limited materials and is focused on a
+ 
+
+ align:start position:0%
+limited materials and is focused on a
+one-to-one scale or the scale of real
+
+ align:start position:0%
+one-to-one scale or the scale of real
+ 
+
+ align:start position:0%
+one-to-one scale or the scale of real
+life so right there because it's not a
+
+ align:start position:0%
+life so right there because it's not a
+ 
+
+ align:start position:0%
+life so right there because it's not a
+model because it's scaled at real life
+
+ align:start position:0%
+model because it's scaled at real life
+ 
+
+ align:start position:0%
+model because it's scaled at real life
+there's a way that our bodies enter into
+
+ align:start position:0%
+there's a way that our bodies enter into
+ 
+
+ align:start position:0%
+there's a way that our bodies enter into
+the reality and maybe into the reality
+
+ align:start position:0%
+the reality and maybe into the reality
+ 
+
+ align:start position:0%
+the reality and maybe into the reality
+of other people says further purpose is
+
+ align:start position:0%
+of other people says further purpose is
+ 
+
+ align:start position:0%
+of other people says further purpose is
+to design this design brief is a basic
+
+ align:start position:0%
+to design this design brief is a basic
+ 
+
+ align:start position:0%
+to design this design brief is a basic
+introduction of site specificity as well
+
+ align:start position:0%
+introduction of site specificity as well
+ 
+
+ align:start position:0%
+introduction of site specificity as well
+as full-scale prototyping and sketch
+
+ align:start position:0%
+as full-scale prototyping and sketch
+ 
+
+ align:start position:0%
+as full-scale prototyping and sketch
+modeling and then at the end you know it
+
+ align:start position:0%
+modeling and then at the end you know it
+ 
+
+ align:start position:0%
+modeling and then at the end you know it
+can be these models can be used to
+
+ align:start position:0%
+can be these models can be used to
+ 
+
+ align:start position:0%
+can be these models can be used to
+design to talk about principles of
+
+ align:start position:0%
+design to talk about principles of
+ 
+
+ align:start position:0%
+design to talk about principles of
+structure enclosure construction
+
+ align:start position:0%
+structure enclosure construction
+ 
+
+ align:start position:0%
+structure enclosure construction
+techniques all right so these are
+
+ align:start position:0%
+techniques all right so these are
+ 
+
+ align:start position:0%
+techniques all right so these are
+elements I would assume that are part of
+
+ align:start position:0%
+elements I would assume that are part of
+ 
+
+ align:start position:0%
+elements I would assume that are part of
+many other disciplines architecture
+
+ align:start position:0%
+many other disciplines architecture
+ 
+
+ align:start position:0%
+many other disciplines architecture
+urban planning and so forth but the idea
+
+ align:start position:0%
+urban planning and so forth but the idea
+ 
+
+ align:start position:0%
+urban planning and so forth but the idea
+is that he's drawing from a quotation
+
+ align:start position:0%
+is that he's drawing from a quotation
+ 
+
+ align:start position:0%
+is that he's drawing from a quotation
+from a theoretical argument focusing on
+
+ align:start position:0%
+from a theoretical argument focusing on
+ 
+
+ align:start position:0%
+from a theoretical argument focusing on
+a term and saying this term is
+
+ align:start position:0%
+a term and saying this term is
+ 
+
+ align:start position:0%
+a term and saying this term is
+problematic let's see what we might
+
+ align:start position:0%
+problematic let's see what we might
+ 
+
+ align:start position:0%
+problematic let's see what we might
+learn and how we might trouble this term
+
+ align:start position:0%
+learn and how we might trouble this term
+ 
+
+ align:start position:0%
+learn and how we might trouble this term
+through the act of making works of art
+
+ align:start position:0%
+through the act of making works of art
+ 
+
+ align:start position:0%
+through the act of making works of art
+and then those works of art allow us to
+
+ align:start position:0%
+and then those works of art allow us to
+ 
+
+ align:start position:0%
+and then those works of art allow us to
+gain literally entry points into them
+
+ align:start position:0%
+gain literally entry points into them
+ 
+
+ align:start position:0%
+gain literally entry points into them
+but also entry into the complications of
+
+ align:start position:0%
+but also entry into the complications of
+ 
+
+ align:start position:0%
+but also entry into the complications of
+what those terms mean
+
+ align:start position:0%
+what those terms mean
+ 
+
+ align:start position:0%
+what those terms mean
+here's another assignment Honduras
+
+ align:start position:0%
+here's another assignment Honduras
+ 
+
+ align:start position:0%
+here's another assignment Honduras
+provides the students find a building
+
+ align:start position:0%
+provides the students find a building
+ 
+
+ align:start position:0%
+provides the students find a building
+and engage with this spaces and then
+
+ align:start position:0%
+and engage with this spaces and then
+ 
+
+ align:start position:0%
+and engage with this spaces and then
+document it through photography so what
+
+ align:start position:0%
+document it through photography so what
+ 
+
+ align:start position:0%
+document it through photography so what
+do you learn about the spaces of what do
+
+ align:start position:0%
+do you learn about the spaces of what do
+ 
+
+ align:start position:0%
+do you learn about the spaces of what do
+you learn about the physicality of a
+
+ align:start position:0%
+you learn about the physicality of a
+ 
+
+ align:start position:0%
+you learn about the physicality of a
+building by becoming part of that
+
+ align:start position:0%
+building by becoming part of that
+ 
+
+ align:start position:0%
+building by becoming part of that
+building but by becoming part of the the
+
+ align:start position:0%
+building but by becoming part of the the
+ 
+
+ align:start position:0%
+building but by becoming part of the the
+negative spaces you could write about it
+
+ align:start position:0%
+negative spaces you could write about it
+ 
+
+ align:start position:0%
+negative spaces you could write about it
+you could measure it tape measure or
+
+ align:start position:0%
+you could measure it tape measure or
+ 
+
+ align:start position:0%
+you could measure it tape measure or
+your body could try to fit in there and
+
+ align:start position:0%
+your body could try to fit in there and
+ 
+
+ align:start position:0%
+your body could try to fit in there and
+understand what that space is about I
+
+ align:start position:0%
+understand what that space is about I
+ 
+
+ align:start position:0%
+understand what that space is about I
+know from teaching drawing one technique
+
+ align:start position:0%
+know from teaching drawing one technique
+ 
+
+ align:start position:0%
+know from teaching drawing one technique
+we can do we all had our drawing paper
+
+ align:start position:0%
+we can do we all had our drawing paper
+ 
+
+ align:start position:0%
+we can do we all had our drawing paper
+we could start drawing what we see now
+
+ align:start position:0%
+we could start drawing what we see now
+ 
+
+ align:start position:0%
+we could start drawing what we see now
+we get us so far but one strategy and
+
+ align:start position:0%
+we get us so far but one strategy and
+ 
+
+ align:start position:0%
+we get us so far but one strategy and
+our teacher will always do or often do
+
+ align:start position:0%
+our teacher will always do or often do
+ 
+
+ align:start position:0%
+our teacher will always do or often do
+and say I want you to draw what's not
+
+ align:start position:0%
+and say I want you to draw what's not
+ 
+
+ align:start position:0%
+and say I want you to draw what's not
+there I want you to draw the negative
+
+ align:start position:0%
+there I want you to draw the negative
+ 
+
+ align:start position:0%
+there I want you to draw the negative
+space and when you draw the negative
+
+ align:start position:0%
+space and when you draw the negative
+ 
+
+ align:start position:0%
+space and when you draw the negative
+spaces between the chair the spaces
+
+ align:start position:0%
+spaces between the chair the spaces
+ 
+
+ align:start position:0%
+spaces between the chair the spaces
+between the bars and the spaces between
+
+ align:start position:0%
+between the bars and the spaces between
+ 
+
+ align:start position:0%
+between the bars and the spaces between
+the handles and the rungs my drawing and
+
+ align:start position:0%
+the handles and the rungs my drawing and
+ 
+
+ align:start position:0%
+the handles and the rungs my drawing and
+rendering those negative spaces as
+
+ align:start position:0%
+rendering those negative spaces as
+ 
+
+ align:start position:0%
+rendering those negative spaces as
+accurately as possible
+
+ align:start position:0%
+accurately as possible
+ 
+
+ align:start position:0%
+accurately as possible
+you render the positive spaces so what
+
+ align:start position:0%
+you render the positive spaces so what
+ 
+
+ align:start position:0%
+you render the positive spaces so what
+do we learn by studying what is not
+
+ align:start position:0%
+do we learn by studying what is not
+ 
+
+ align:start position:0%
+do we learn by studying what is not
+there or the neglected spaces we learn
+
+ align:start position:0%
+there or the neglected spaces we learn
+ 
+
+ align:start position:0%
+there or the neglected spaces we learn
+more about the presence of the dominant
+
+ align:start position:0%
+more about the presence of the dominant
+ 
+
+ align:start position:0%
+more about the presence of the dominant
+structure so there are a number of books
+
+ align:start position:0%
+structure so there are a number of books
+ 
+
+ align:start position:0%
+structure so there are a number of books
+about pedagogy and about translating art
+
+ align:start position:0%
+about pedagogy and about translating art
+ 
+
+ align:start position:0%
+about pedagogy and about translating art
+practice and and pedagogical engagements
+
+ align:start position:0%
+practice and and pedagogical engagements
+ 
+
+ align:start position:0%
+practice and and pedagogical engagements
+in public spaces right so I'll just
+
+ align:start position:0%
+in public spaces right so I'll just
+ 
+
+ align:start position:0%
+in public spaces right so I'll just
+conclude here for some questions I can
+
+ align:start position:0%
+conclude here for some questions I can
+ 
+
+ align:start position:0%
+conclude here for some questions I can
+you know you can engage learners like
+
+ align:start position:0%
+you know you can engage learners like
+ 
+
+ align:start position:0%
+you know you can engage learners like
+this or you could do boring stuff it's
+
+ align:start position:0%
+this or you could do boring stuff it's
+ 
+
+ align:start position:0%
+this or you could do boring stuff it's
+up to you all right thanks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/A75xAGO3ZEY.txt b/A75xAGO3ZEY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cdce16141bb53088d8675c4c32e029324a5ac1bd
--- /dev/null
+++ b/A75xAGO3ZEY.txt
@@ -0,0 +1,3502 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Good afternoon.
+
+So it has been a little
+bit more than a week
+
+when we met the last time.
+
+Before I continue our
+discussion of metrology
+
+and interferometry.
+
+I just want to share
+something I saw on my visit
+
+to the Netherlands.
+
+When I visited the University of
+Delft and the Kavli Institute,
+
+they had just accomplished the
+entanglement of two NV centers.
+
+And we had just talked in
+class about the entanglement
+
+of two ions.
+
+So I'm sort of
+excited to show you
+
+that people have just
+taken the next step.
+
+And what often the
+next step means
+
+is that in atomic physics, we
+use pristine systems-- ions,
+
+neutral atoms in
+[INAUDIBLE] vacuum chamber.
+
+And we create new
+forms of entanglement.
+
+Or with quantum gases, new
+forms of quantum matter.
+
+But ultimately, we hope that
+those concepts, those methods,
+
+and this knowledge
+translates to some room
+
+temperature materials or
+solid state materials which
+
+can be handled more
+easily, and are therefore
+
+much closer to applications.
+
+So NV centers are kind of
+nature's natural ion trap,
+
+or nature's natural
+neutral atom trap.
+
+Let's not discuss whether
+this is neutral or ionized.
+
+It's a vacancy in nitrogen.
+
+And it has a spectrum
+which looks like an atom.
+
+So you can say once you have
+such a defect in nitrogen,
+
+you have an atom, a single
+atom in an atom trap
+
+or an ion in an ion trap.
+
+And you don't have
+to create the vacuum.
+
+It's there.
+
+Every time you look
+at it, it's there.
+
+And you can excite
+it with the laser.
+
+It has a spectrum
+similar to atoms.
+
+It has spin
+structure So you have
+
+these vacancies in diamond.
+
+So these are little
+quantum dots.
+
+But now you have two problems.
+
+One is you want to collect
+the light emitted by them.
+
+And what is best is to mill a
+lens right into the material.
+
+So this is the diamond material.
+
+A lens is milled.
+
+And that already gives
+some [? culmination ?]
+
+of the light emitted by it.
+
+But the bit problem
+until recently
+
+has been when you create
+those some people call it
+
+artificial atoms.
+
+Every atom is a
+little bit different,
+
+because it experience a
+slightly different environment.
+
+A crystal has strain, so if you
+have seemingly two identical
+
+defects in a diamond
+crystal, the two defects
+
+will have a
+resonance line, which
+
+is a few gigahertz difference.
+
+You would say, well, maybe
+it's just [? apart ?] in 10
+
+to the 5, but it means the
+photons are distinguishable.
+
+So if you want to do
+entanglement by having two such
+
+artificial atoms emitting a
+photon onto a beam splitter,
+
+and then by performing
+a measurement we project
+
+the atoms into Bell state-- I
+hope you all remember what we
+
+discussed for the trapped ions--
+then you have to make sure that
+
+fundamentally, those photons
+cannot be distinguished.
+
+And the trick here is that
+they put on some electrodes.
+
+And by adding an
+electric field, they
+
+can change the
+relative frequency.
+
+And therefore, within
+the frequency uncertainty
+
+given by Heisenberg's
+Uncertainty Relation,
+
+they can make the two
+photons identical.
+
+And when, let's say, experiment.
+
+Well, you have two NV
+centers, defects in diamond.
+
+You can manipulate with
+microwaves coherently the spin.
+
+You need lasers for
+initialization and readout.
+
+But then closer to what
+we want to discuss,
+
+you need laser beams which
+excite the NV center.
+
+And then the two NV
+centers emit photons.
+
+And what you see now is exactly
+what we discussed schematically
+
+and in context of the ions,
+that the two NV centers now
+
+emit photons.
+
+And by using polarization
+tricks and the beam splitter,
+
+you do a measurement
+after the beam splitter.
+
+And based on the outcome
+of the measurement,
+
+you have successfully
+projected the two NV centers
+
+into a [INAUDIBLE] state.
+
+OK, good.
+
+All right.
+
+Let me just summarize what our
+current discussion is about.
+
+This section is called
+Quantum Metrology.
+
+It is a section where we want
+to apply the concepts we have
+
+learned to precision
+measurements.
+
+It's actually a chapter
+which I find nice.
+
+We're not really
+introducing new concepts.
+
+We're using concepts
+previously introduced.
+
+And now you see how
+powerful those concepts
+
+are, what they can be used for.
+
+So we want to
+discuss the precision
+
+we can obtain in
+quantum measurement.
+
+We apply it here to an
+atom in the interferometer,
+
+to an optical interferometer.
+
+We could also
+discuss the precision
+
+of spectroscopic measurements.
+
+A lot of precision measurements
+have many things in common.
+
+So what we discuss here
+is as a generic example
+
+for precision measurement
+that we send light
+
+from our center interferometer.
+
+Here is a phase shift.
+
+And the question is,
+how accurately can we
+
+measure the phase shift when
+we use n photons as a resource?
+
+And of course, you
+are all familiar
+
+with the fundamental limit of
+standard measurements, which
+
+is short noise.
+
+And sort of as a warm up in
+our last class Wednesday,
+
+week ago, I showed you that when
+we use coherent states of light
+
+at the input of
+the interferometer,
+
+we obtain the short noise.
+
+Well, it may not be surprising,
+because coherent light
+
+is as close as possible, has
+similar to classical light.
+
+But then we discussed single
+mode, single photon input.
+
+And by using the formalism
+of the Mach-Zehnder
+
+interferometer, we've found that
+the phase uncertainty is again
+
+1 over square root n.
+
+So then the question is, how can
+we go to the Heisenberg limit,
+
+where we have an uncertainty
+in the phase of 1 over n?
+
+And just as a reminder,
+I find it very helpful.
+
+I told you that you can always
+envision if you have n photons
+
+and you multiply it, put
+the n photons together
+
+by multiplying the
+frequency by n,
+
+then you have one photon
+which [INAUDIBLE] with n times
+
+the frequency.
+
+And it's clear if you
+do a measurement at n
+
+times the frequency,
+your precision in phase
+
+is n times better.
+
+So what we have to do is
+we have to sort of put
+
+the n photons together.
+
+And then we can get a precision
+of the measurement, which
+
+is not square root n,
+but n times better.
+
+So this is what we
+want to continue today.
+
+This is the outline I gave
+you in the last class.
+
+If you have this
+optical interferometer,
+
+this Mach-Zehnder
+interferometer.
+
+And if you use coherent
+sets or single photons
+
+as the input state, we
+obtain the short noise.
+
+Now we have to change something.
+
+And we can change
+the input state,
+
+we can change the beam splitter,
+or we can change the readout.
+
+So we have to change something
+where we entangle the n
+
+photons, make sure in some sense
+they act as one giant photons,
+
+with either n times
+the frequency,
+
+but definitely with n times
+the sensitivity to phase shift.
+
+Any questions?
+
+Good.
+
+The first example, which
+we pretty much covered
+
+in the last class, was an
+entangled state interferometer.
+
+So instead of having the
+Mach-Zehnder interferometer
+
+as we had before, we have
+sort of a Bell state creation
+
+device.
+
+Then we provide the phase shift.
+
+And then we have a
+Bell analysis device.
+
+And I want to use here the
+formalism and the symbols
+
+we had introduced earlier.
+
+So just as a reminder, what
+we need is I need two gates.
+
+One is the Hadamard gate,
+which in matrix representation
+
+has this matrix form.
+
+And that means if you have
+a qubit which is either up
+
+or down and you apply
+the matrix to it,
+
+you put it in a superposition
+state of up and down.
+
+It's a single qubit rotation.
+
+You can say for the bloch
+on the Bloch sphere,
+
+it's a 90 degree rotation.
+
+The second gate we need
+is the controlled NOT.
+
+And the controlled NOT
+we discussed previously
+
+can be implemented by
+having an interferometer
+
+and using a non-linear Kerr
+medium coupling another photon
+
+to the interferometer
+in such a way
+
+that if you have a
+photon in mode C,
+
+it creates a phase shift
+with the interferometer.
+
+If there is no
+photon in mode C, it
+
+does not create an
+additional phase shift.
+
+And as we have
+discussed, this can
+
+implement the controlled NOT.
+
+So these are the ingredients.
+
+And at the end of
+the last class,
+
+I just showed you what those
+quantum gates can do for us.
+
+If you have two qubits at
+the input, we apply the--
+
+and I will assume they
+are both in logical 0--
+
+the Hadamard gate makes
+the coherent superposition.
+
+And then, we have
+a controlled NOT
+
+where this is the target gate.
+
+Well, if this is 0, if
+the control beat is 0,
+
+the target beat stays 0.
+
+So we get 0, 0.
+
+If the control beat is 1, the
+target beat is flipped to 1.
+
+So we get 1, 1.
+
+So the result is
+that we have now
+
+created a state 0, 0 plus 1, 1.
+
+And if we apply a phase shift
+to all the photons coming out
+
+on the right hand side, we get
+a phase shift which is too fine.
+
+So we already get the idea.
+
+If we take advantage
+of a state 1, 1,
+
+it has twice the [? face ?]
+sensitivity as a single photon.
+
+And we may therefore
+get the full benefit
+
+of the factor of 2, and
+not just square root 2.
+
+And this is what this
+discussion is about.
+
+Questions?
+
+OK, so that's where we ended.
+
+We can now use
+another controlled NOT
+
+and bring in the third qubit.
+
+So what we create here.
+
+Just make a reference, this
+is where we start today.
+
+So we create here the state,
+which is either all beats
+
+are 0, all beats are 1, and
+then the phase shift gives us
+
+three times the phase shift phi.
+
+And therefore, by bringing
+in more and more qubits,
+
+I've shown you n equals
+1, n equals 2, n equals 3.
+
+So now you can go to n.
+
+We obtain states which have n
+times the phase sensitivity.
+
+Let me just mention in
+passing that for n equals 3,
+
+the superposition of 0, 0, 0
+and 1, 1, 1 goes by the name
+
+not gigahertz, GHZ.
+
+Greenberger.
+
+This third one is Zeilinger.
+
+The second one is--
+
+AUDIENCE: Horne.
+
+PROFESSOR: Horne.
+
+Thank you.
+
+Greenberger-Horne-Zeilinger
+state.
+
+And those states play
+an important role
+
+in test of Bell's inequality.
+
+Or more generally, states which
+are macroscopically distinct
+
+are also regarded cat states
+or Schrodinger cat states.
+
+If we apply a phase
+shift and go now
+
+through the
+entangler in reverse,
+
+just a reverse sequence of
+CNOT gates and Hadamard gates,
+
+then we have all
+the other n minus,
+
+have the n minus 1 qubits.
+
+All the qubits except
+for the first reset to 0.
+
+But the first qubit is now
+in a superposition state
+
+where we have the
+phase into the power n.
+
+And now, we can
+make a measurement.
+
+And P is now the probability
+to find a single photon
+
+in the first qubit.
+
+So in other words,
+our measurement
+
+is exactly the same
+as we had before where
+
+we had the normal
+Mach-Zehnder interferometer.
+
+We put in one photon at a time.
+
+And we determined
+the probability.
+
+What is the photon at one of the
+outputs of the interferometer?
+
+But the only
+difference is that we
+
+have now a factor of n in the
+exponent for the phase shift.
+
+And I want to show you what
+is caused by this factor of n.
+
+Let me first remind
+you how we analyzed
+
+the sensitivity of
+an interferometer
+
+for single photon input before.
+
+So for a moment,
+set n equals 1 now.
+
+Then you get what we
+discussed two weeks ago.
+
+The probability is [INAUDIBLE]
+as an interferometer.
+
+Sine also, cosine also
+infringes with cosine phi.
+
+If you do measurements
+with a probability P,
+
+that's a binomial distribution.
+
+Then the deviation
+or the square root
+
+of the variance in the binomial
+distribution is P times 1
+
+minus P. And by inserting p
+here, we get sine phi over 2.
+
+The derivative of P, which
+is our signal, with a phase
+
+is given by that.
+
+And then just using
+error propagation,
+
+the uncertainty in the
+phase is the uncertainty
+
+in P divided by dp dt.
+
+So then we repeat the
+whole experiment n times,
+
+and if your binomial
+distribution and we
+
+do m [INAUDIBLE] of our
+[INAUDIBLE] with probability P,
+
+we get an m under
+the square root.
+
+And then we get 1
+over square root m.
+
+And this was what I
+showed you two weeks ago,
+
+the standard short noise limit.
+
+But now we have this
+additional factor of n
+
+here, which means that
+our probability has
+
+a cosine which goes with n phi.
+
+When we take the derivative,
+we get a factor of n here.
+
+And then dp d phi
+has the derivative.
+
+But then we have to
+use a chain rule, which
+
+has another factor of n.
+
+And therefore, we obtain now
+that the phase sensitivity
+
+goes as 1 over n.
+
+And therefore, we reach
+the Heisenberg limit.
+
+So if you have now your n
+photon entangler, the one I
+
+just-- the entanglement
+operation with these n cubits
+
+is special beam spreader
+replaced by the entangler,
+
+we have now a sensitivity,
+which goes 1 over n.
+
+And then of course,
+if you want, you
+
+can repeat the
+experiment n times.
+
+And whenever you
+repeat an experiment,
+
+you gain an addition with
+the square root of m.
+
+Just give me one second.
+
+We have this.
+
+OK, so this is an example where
+we had n qubits entangled,
+
+like here.
+
+And the sensitivity of
+this interferometer scales
+
+now as the Heisenberg
+limit with 1 over n.
+
+OK, I want to give you,
+because they're all nice
+
+and they're all special,
+I want to give you
+
+three more example how you can
+reach the Heisenberg limit.
+
+The next one goes by the name
+super beam splitter method.
+
+It's actually a very
+fancy beam splitter
+
+where you have two prods
+of your beam splitter.
+
+One has 0 and one has n photons.
+
+And behind the beam splitter,
+you have two options.
+
+Either all the n photons
+are in one state,
+
+or the n photons are
+in the other state.
+
+You never have
+any other mixture.
+
+Of course, you know your
+standard half silvered
+
+mirror will not do that for
+you, because it will split the n
+
+photon state with some
+Poissonian statistics
+
+or whatnot into the
+two arms and such.
+
+And you can calculate
+exactly what a normal beam
+
+splitter does to that.
+
+It's very, very different.
+
+This here is a very, very
+special beam splitter.
+
+Just to demystify this
+beam splitter a little bit,
+
+I want to show you that, at
+least conceptually, there
+
+is an easy implementation
+with atoms.
+
+I really like in this section
+to grab an example from atoms
+
+and to grab an example for
+photons, because it really
+
+brings out that the
+language may develop equally
+
+applies to atoms and photon.
+
+So if I take now
+an easy example,
+
+if I take an example of the
+Bose-Einstein condensate with n
+
+atoms, let's assume
+we have a double well.
+
+But now we have
+attractive interactions.
+
+This is not your standard BEC.
+
+Your standard
+Bose-Einstein condensate
+
+has repulsive interaction,
+with attractive interaction.
+
+If you go beyond a certain
+size, certain a atom number,
+
+the condensate will collapse.
+
+So let's assume we have a
+Bose-Einstein condensate with n
+
+atoms.
+
+There are some
+attractive interactions,
+
+but we stay within
+the stability diagram
+
+that those atoms do not-- that
+those atoms do not collapse.
+
+So now, if the atoms
+are attractive,
+
+they all want to be together.
+
+Because then they lower
+the energy of each other.
+
+So if you have something
+with attractive interaction,
+
+you want to have
+n atoms together.
+
+But if your double
+well potential
+
+is absolutely symmetric,
+there is no symmetry breaking,
+
+and you have an equal
+amplitude for all the atoms
+
+to be in the other well.
+
+So therefore, under the
+very idealized situation
+
+I described here,
+you will actually
+
+create a superposition
+state of n atoms
+
+in one well with n
+atoms in the other well.
+
+And this is exactly
+what we tried
+
+to accomplish with
+this beam splitter.
+
+OK, so if we have this
+special beam splitter, which
+
+creates that state,
+then when we add a phase
+
+shift to one arm of
+the interferometer,
+
+we obtain-- which looks very
+promising-- a phase shift
+
+phi multiplied by n.
+
+And if we read it
+out, we have now
+
+if you pass it through the
+other super beam splitter,
+
+we create again a
+superposition of n0 and 0n.
+
+But now, because
+of the phase shift
+
+with cosine and sine factors,
+which involve n times
+
+the phase shift.
+
+For obvious reasons,
+those states
+
+also go by the name noon states.
+
+That's the name which everybody
+uses for those states,
+
+because if you just read
+n00n, it gives noon.
+
+So this is the
+famous noon state.
+
+So it seems it smells
+already, right,
+
+because it has a
+phase shift of n phi.
+
+Let me just convince you
+that this is indeed the case.
+
+So the probability
+of reading out
+
+0 photons in one arm
+of the interferometer
+
+scales now with
+the cosine square.
+
+If you do one
+single measurement,
+
+the binomial
+distribution is the same
+
+as before, but
+with a factor of n.
+
+The derivative has
+those factors of n.
+
+And that means that the variance
+in the phase measurement
+
+is now 1 over n.
+
+If you want a reference,
+I put it down here.
+
+As far as I know,
+the experiment has
+
+been done with three
+photons, but not
+
+with larger photon number.
+
+Questions?
+
+Collin.
+
+AUDIENCE: This picture
+with the double well,
+
+isn't there going to be-- all
+right, some people would say
+
+you spontaneously break the
+symmetry and [INAUDIBLE]
+
+either ends up in one
+side or the other.
+
+Like isn't this [INAUDIBLE]?
+
+PROFESSOR: Well,
+Bose-Einstein condensation
+
+with attractive interactions
+was observed in 1995.
+
+And now, 18 years later, nobody
+has done this seemingly simple
+
+experiment.
+
+And what happens
+is really that you
+
+have to be very,
+very careful against
+
+any experimental imperfection.
+
+If the two double well
+potentials are not
+
+exactly identical,
+the bosons always
+
+want to go to the
+lowest quantum state.
+
+Well, that's their
+job, so to speak.
+
+That's their job description.
+
+And if you have a
+minuscule difference
+
+between the two, the
+dates of the two wells,
+
+you will not get a
+superposition state.
+
+You will simply
+populate one state.
+
+And how to make it
+experimentally [INAUDIBLE],
+
+this is a really big challenge.
+
+[? Tino ?].
+
+AUDIENCE: I have a question.
+
+Let's say we're somehow
+able to make the double well
+
+potential perfect.
+
+But if we didn't have
+attractive interactions,
+
+then wouldn't he just
+get a big product state
+
+of each atom being
+in either well?
+
+PROFESSOR: OK, if you're
+a non-interacting system,
+
+the ground state of a
+double well potential
+
+is just your metric state 1
+plus 2 over square root 2.
+
+And for non-interactive
+BEC, you figure out
+
+what is the ground
+state for one particle
+
+and then take it to the power n.
+
+This is the non-interactive BEC.
+
+STUDENT: So then entanglement
+is because of the interaction,
+
+right?
+
+PROFESSOR: If you have
+strong repulsive interaction,
+
+you have something
+which should remind you
+
+of the [INAUDIBLE] insulator.
+
+You have n atoms.
+
+And n over 2 atoms go
+to one well. n over 2 go
+
+to the other well.
+
+Because any form of number
+fluctuations would be costly.
+
+It will cost you additional
+repulsive interaction.
+
+So therefore, the
+condensate wants
+
+to break up into
+two equal parts.
+
+So that's actually
+a way how you would
+
+create another non-classical
+state, the dual flux
+
+state of n over 2,
+n over 2 particle.
+
+And for attractive
+interactions, well you
+
+should create the known state.
+
+OK, so this was now
+a state n0 and 0n.
+
+There is another
+state, which you
+
+have encountered
+in your homework.
+
+And this is a superposition
+not of n0 and 0n and n0.
+
+It's a superposition of n
+minus 1n and n n minus 1.
+
+This state goes by the person
+I think who invented it,
+
+the [? Yerkey ?] state.
+
+And you showed in your homework
+that with that, you also
+
+reach Heisenberg Limited
+Interferometry, where
+
+the phase scales is 1 over n.
+
+What I want to add
+here to it is how
+
+one can create such
+a [? Yerkey ?] state.
+
+And again, I want
+to use the example
+
+with an atomic
+Bose-Einstein condensate.
+
+And here's the reference where
+this was very nicely discussed.
+
+So let's assume we can create
+two Bose-Einstein condensates.
+
+And they have exactly n atoms.
+
+And I would actually refer
+to [? Tino's ?] questions how
+
+to make them have
+two n atoms in a trap
+
+and then make a
+double well potential,
+
+deform the harmonic oscillator
+potential to a double well
+
+potential.
+
+Then for strong
+repulsive interactions,
+
+the condensate
+will symmetrically
+
+split into two flux states,
+each of which has n atoms.
+
+So now how can we create the
+[? Yerkey ?] state from that?
+
+Well, we simply have--
+we leak out atoms.
+
+We leak atoms out of the trap.
+
+My group demonstrated an RF
+beam splitter, how you can just
+
+split in very
+controlled way start
+
+rotating the cloud
+on non-trapped state.
+
+And then atoms slowly leak out.
+
+Well, when you can
+measure, of course,
+
+you can take an atom
+detector and measure
+
+that an atom has
+been out-coupled,
+
+that an atom has
+leaked out of the trap.
+
+If you don't like
+RF rotation, you
+
+can also think that there
+is a tunneling barrier,
+
+and atoms slowly leak out
+by whatever mechanism.
+
+And the moment you
+detect that an atom,
+
+you then project the state in
+the trap to n minus 1 atom,
+
+because you've measured
+that one atom has come out.
+
+But now you use a beam splitter.
+
+And a beam splitter could
+simply be a focused laser beam.
+
+And the atoms have
+a 50% probability
+
+of being reflected or
+end up tunneling through.
+
+So therefore, if you
+have now a detector
+
+which measures the
+atoms on one side
+
+and the atoms on the
+other side, then you
+
+don't know anymore when the
+detector makes click form which
+
+atom trap the atom came.
+
+Or more formally,
+a beam splitter
+
+transforms the two input modes
+ab into a plus b and a minus b
+
+normalized by square root 2.
+
+So therefore, if
+this detector clicks,
+
+when you project the remaining
+atoms into the symmetric state,
+
+here you detect one atom
+in the mode a plus b.
+
+And that means that
+the remaining atoms
+
+have been projected into
+the [? Yerkey ?] state.
+
+If the lower atom
+detector would click,
+
+well, you get a minus sign here.
+
+So that's one way how at
+least in a conceptually simple
+
+situation, you can prepare
+this highly non-classical state
+
+by starting with
+a dual flux state
+
+of Bose-Einstein
+condensates, and then using--
+
+and this is an ongoing theme
+here-- by using a measurement,
+
+and then the
+post-measurement state is
+
+the non-classical state
+you wanted to prepare.
+
+Question?
+
+Yes.
+
+AUDIENCE: How can you
+ensure that only one
+
+atom leaves the [INAUDIBLE]?
+
+PROFESSOR: The idea
+is that we leak atoms
+
+out very, very slowly.
+
+And then we have
+a detector, which
+
+we assume has 100%
+quantum efficiency.
+
+So therefore, we simply wait
+until the detector tells us
+
+that one atom has leaked out.
+
+And in an idealized experiment,
+we know the atoms either
+
+have been measured
+by the detector,
+
+or they are still in the trap.
+
+AUDIENCE: And also,
+is there a property
+
+that holds the [INAUDIBLE]
+you detect atoms [INAUDIBLE]?
+
+PROFESSOR: In principle
+yes, but the idea here
+
+is if you have a very
+slow leakage process,
+
+the probability that you detect
+two atoms at the same time
+
+is really zero.
+
+You leak them continuously
+and slowly, but then
+
+quantum mechanically, that
+means for most of the time,
+
+you measure nothing.
+
+That means the leakage
+hasn't taken place.
+
+The quantum mechanical
+system has not developed yet.
+
+But the moment you
+perform a measurement,
+
+you project-- it's
+really the same
+
+if you say you have
+n radioactive atoms.
+
+You have a detector.
+
+And when the
+detector makes click,
+
+you know you have n minus
+1 radioactive atoms left.
+
+It's just applied here
+to two atom types.
+
+Other questions?
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: No.
+
+And maybe I'll tell
+you now why not.
+
+We have discussed
+the noon state.
+
+And we have discussed here
+a highly non-classical
+
+superposition state.
+
+Let's just go back
+to the noon state.
+
+We have n atoms here, zero here,
+or n atoms, or the reverse.
+
+But now, assume a single atom
+is lost, is lost from your trap
+
+by some background
+gas collisions.
+
+And you have surrounded
+the trap with a detector.
+
+So if you have the noon state,
+the symmetric superposition
+
+state, all atoms here
+and all atoms there.
+
+But by your background process,
+by an inelastic collision,
+
+you lose one atom.
+
+And you detect it.
+
+You could set up your
+detectors that you
+
+know from which
+that you figure out
+
+from which trap was
+the particle lost.
+
+So therefore, a
+single particle lost
+
+if you localize from which
+trap the particle is lost
+
+would immediately project
+the noon state into a state
+
+where you know I have n or
+n minus 1 atoms in one well,
+
+and 0 in the other well.
+
+So I've already told
+you, with the attenuator,
+
+you can never assume
+an attenuator is just
+
+attenuating a beam.
+
+An attenuator can always
+regard it as a beam splitter.
+
+And you can do measurements at
+both arms of the beam splitter.
+
+Or you have to consider
+the vacuum noise which
+
+enters through the other
+part of the beam splitter.
+
+And if you are now add that
+those atoms, n atoms, in a trap
+
+have some natural loss
+by inelastic collision
+
+or background gas
+scattering, the loss
+
+is actually like a beam
+splitter that particles
+
+don't stay in the trap, but
+go out through the other part.
+
+And then you can measure it.
+
+So in other words,
+every loss process
+
+should be regarded as
+a possible measurement.
+
+And it doesn't
+matter whether you
+
+perform the measurement or not.
+
+And I think it's just obvious
+that the noon state, the moment
+
+one particle is lost and you
+reduce this particle to figure
+
+out if n particles are here
+or n particles are there,
+
+the whole superposition
+state is lost if you just
+
+lose one single atom out of n.
+
+So the lifetime of a noon state
+is then not your usual trap
+
+lifetime, where you
+lose half of the atoms,
+
+1 over e of the atoms.
+
+It is n times faster because
+it is the first atom lost,
+
+which is already
+completely removing
+
+the entanglement of your state.
+
+So more quantitatively, to
+say it more specifically,
+
+the limitation is loss.
+
+When you have a fully entangled
+state, maximally entangled
+
+state, usually a
+loss of one particle
+
+immediately removes
+the entanglement.
+
+We had the situa-- no,
+that's not a good example.
+
+But for the most
+entangled state,
+
+usually-- and for
+the noon state,
+
+it's trivial to see-- a
+single particle lost allows
+
+you to measure on which side
+of the potential barrier
+
+all the atoms are,
+and all the beauty
+
+of the non-classical
+state is lost.
+
+So if you assume that
+in a time window,
+
+you have an infinitesimal
+loss, a loss
+
+of epsilon, what
+usually happens is
+
+if you have an entanglement
+of n particles,
+
+then you lose your entanglement.
+
+If you expand 1
+minus epsilon to n,
+
+it becomes 1 minus
+n times epsilon.
+
+So that's one reason why
+people have not scaled up
+
+those schemes to a
+large number of photons,
+
+or a large number of atoms.
+
+Because the larger n
+is, the more sensitive
+
+you are to even very,
+very small losses.
+
+Questions?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yes.
+
+AUDIENCE: Or is that physically?
+
+PROFESSOR: The
+super beam splitter
+
+would create the noon state.
+
+I've not explained to
+you what it physically
+
+would be for photons,
+but I gave you
+
+the example for atoms
+to BECs in a double well
+
+potential with
+attractive interaction.
+
+So to start with
+the condensate in--
+
+AUDIENCE: Start with
+a bigger [INAUDIBLE].
+
+PROFESSOR: If you start with
+a double well potential,
+
+and you put in n
+atoms initially in,
+
+but then you switch
+on tunnel coupling,
+
+then you would
+create the noon state
+
+if the interactions
+are attractive,
+
+and if everything is idealized,
+that you have a completely
+
+symmetric double well potential.
+
+OK, the last example is the
+squeeze light Interferometer.
+
+I just want to
+mention it briefly,
+
+because we've talked so
+much about squeezed light.
+
+So now I want to show you
+that squeezed light can also
+
+be used to realize Heisenberg
+Limited Interferometery.
+
+So the idea is, when we plot
+the electric field versus time,
+
+and if you do squeezing
+in one quadrature,
+
+then for certain times,
+the electric field
+
+has lower noise
+and higher noise.
+
+We discussed that.
+
+And the idea is that if there is
+no noise at the zero crossing,
+
+that this means we can determine
+the zero crossing of the light,
+
+and therefore the phase
+shift with higher accuracy.
+
+You may also argue if you
+have this quasi-probabilities,
+
+and with squeezing, we have
+squeezed the coherent light
+
+into an ellipse.
+
+And things propagate
+with e to the i omega t.
+
+Then you can determine
+a phase shift,
+
+which is sort of an angular
+sector in this diagram,
+
+with higher precision
+if you have squeezed
+
+this circle into an
+ellipse like that.
+
+So that's the idea.
+
+And well, it's fairly clear that
+squeezing, if done correctly,
+
+can provide a better
+phase measurement.
+
+And what I want to show
+you here in a few minutes
+
+is how you can think about it.
+
+So we have discussed at length
+the optical Interferometer,
+
+where we have just a
+coherence state at the input.
+
+This is your standard
+laser Interferometer.
+
+But of course, very importantly,
+the second input port
+
+has the vacuum state.
+
+And we discussed the
+importance of that.
+
+So the one difference
+we want to do now
+
+is that we replace the
+vacuum at the second input
+
+by the squeezed
+vacuum where r is
+
+the parameter of
+the squeezed vacuum.
+
+OK, so that's pretty
+much what we do.
+
+We take this state, we
+plug it into our equation,
+
+we use exactly
+the same formalism
+
+we have used for
+coherence states.
+
+And the question,
+what is the result?
+
+Well, the result will be that
+the squeezing factor appears.
+
+Just as a reminder,
+for our Interferometer,
+
+we derived the sensitivity
+of the Interferometer.
+
+We had the quantities x and y.
+
+And the noise is delta in this
+y operator squared divided by x.
+
+This was the result when we
+operate the Interferometer
+
+at the phase shift
+of 90 degrees.
+
+Just a reminder.
+
+That's what we have done.
+
+That's how we
+analyze the situation
+
+with a coherent state.
+
+The signal x is
+now-- the signal x
+
+is the number
+measurement a dagger a.
+
+And we have now the input
+of the coherent state.
+
+And b dagger b.
+
+We have an input
+mode a and a mode b.
+
+They get split.
+
+And then we measure
+it at the output.
+
+And we can now at the
+output have photons--
+
+a dagger a, which come
+from the coherent state,
+
+and b dagger b, which come
+from the squeeze vacuum.
+
+So this is now using the
+beam splitter formalism
+
+applied to the Interferometer.
+
+So this is now the
+result we obtain.
+
+And in the strong local
+oscillator approximation,
+
+it is only the first
+part which contributes.
+
+And this is simply the number
+or photons in the coherent beam.
+
+The expectation value
+of y is 0, because it
+
+involves a b and
+b dagger operator.
+
+And the squeezed
+vacuum has only,
+
+if you write it down, in the
+n basis, in the flux basis,
+
+has only even n.
+
+So if you change
+n by one, you lose
+
+overlap with the
+squeezed vacuum.
+
+So therefore, this
+expectation value is 0.
+
+For the operator y squared,
+you take this and square it.
+
+And you get many, many terms,
+which I don't want to discuss.
+
+I use the strong
+local oscillator.
+
+Limited a dagger and
+a can be replaced
+
+by the eigenvalue alpha
+of the coherent state.
+
+So therefore, I factor
+out alpha squared
+
+in the strong local
+oscillator limit.
+
+And then what is left is
+b plus b dagger squared.
+
+And since we have
+squeezed the vacuum,
+
+this gives us a factor
+into the minus r.
+
+So if we put all those
+results together,
+
+we find that the phase
+uncertainty is now
+
+what we obtained when
+we had a coherent state
+
+with the ordinary vacuum.
+
+And in the strong
+local oscillator limit,
+
+the only difference
+to the ordinary vacuum
+
+is that in this term, we've
+got the exponential factor e
+
+to the minus r.
+
+And since we have
+taken a square root,
+
+it's e to the minus r over 2.
+
+So that result would
+actually suggest
+
+that the more we squeeze,
+that delta phi should go to 0.
+
+So it seems even better
+than the Heisenberg limit.
+
+However-- well, this is
+too good to be true--
+
+what I've neglected here
+is just the following.
+
+When you squeeze more
+and more, the more you
+
+squeeze the vacuum,
+the more photons
+
+are in the squeezed vacuum,
+because this ellipse stitches
+
+further and further out and
+has overlap with flux states
+
+at higher and higher
+photon number.
+
+So therefore, when you go to
+the limit of infinite squeezing,
+
+you squeeze out
+of the limit where
+
+you can regard the local
+oscillator as strong,
+
+because the squeezed
+vacuum has more photons
+
+than your local oscillator.
+
+And then you have to
+consider additional terms.
+
+So let me just write that down.
+
+However, the squeezed vacuum has
+non-zero average photon number.
+
+And the photon number
+of the squeezed vacuum
+
+is, of course, apply b dagger
+b to the squeezed vacuum.
+
+This gives us a sinc function.
+
+And we can call this
+the number of photons
+
+in the squeezed vacuum.
+
+So we have to consider now
+this contribution to y square.
+
+So we have to
+consider the quadrator
+
+of the ellipse, the long
+part of the ellipse,
+
+the non-squeezed
+quadrator component.
+
+And we have to
+consider that when
+
+we calculate the expectation
+value of y square.
+
+And then we find
+additional terms,
+
+which I don't want
+to derive here.
+
+And the question is then, if
+you squeeze too much, you lose.
+
+So there's an optimal
+amount of squeezing.
+
+And for this optimal
+amount of squeezing,
+
+the phase uncertainty
+becomes approximately one
+
+over the number of photons
+in the coherent state,
+
+plus the number of photons
+in your squeeze vacuum.
+
+So this is, again, very close
+to the Heisenberg limit.
+
+So the situation
+with squeezed light
+
+is less elegant, because
+if you squeeze too much,
+
+you have to consider
+additional terms.
+
+This is why I gave you the
+example of the squeezed light
+
+and the squeezed
+vacuum as the last.
+
+But again, the Heisenberg
+limit is very fundamental
+
+as we discussed.
+
+And for an optimum
+arrangement of the squeezing,
+
+you can also use a
+squeezed vacuum input
+
+to the Interferometer to
+realize the Heisenberg limit.
+
+Any questions?
+
+Why is squeezing important?
+
+Well, squeezing caught the
+attention of the physics
+
+community when it was
+suggested in connection
+
+with gravitational--
+with the detection
+
+of gravitational waves.
+
+As you know, the
+laser Interferometer,
+
+the most advanced one is
+LIGO, has a monumental task
+
+in detecting a
+very small signal.
+
+And pretty much everything which
+precision metrology can provide
+
+is being implemented
+for that purpose.
+
+So you can see, this is
+like precision measurement.
+
+Like maybe the trip
+to the moon was
+
+for aviation in
+several decades ago.
+
+So everything is really--
+a lot of things pushing
+
+the frontier of
+precision measurement
+
+is motivated by the precision
+needed for gravitational wave
+
+detection.
+
+And what I want to show
+you here is a diagram
+
+for what is called
+advanced LIGO.
+
+LIGO is currently
+operating, but there
+
+is an upgrade to LIGO
+called advanced LIGO.
+
+And what you
+recognize here is we
+
+have a laser which goes into
+a Michelson Interferometer.
+
+And this is how you want to
+detect gravitational waves.
+
+But now you realize
+that the addition here
+
+is a squeezed source.
+
+And what you are
+squeezing is not,
+
+while it should be
+clear to you now,
+
+we're not squeezing
+the laser beam.
+
+This would be much, much harder,
+because many, many photons are
+
+involved.
+
+But it is sufficient to
+squeeze the vacuum and couple
+
+in squeezed vacuum into your
+cavitational wave detector.
+
+If you wonder, it's a
+little bit more complicated
+
+because people want to
+recycle light and have
+
+put in other bells and whistles.
+
+But in essence, a
+squeezed vacuum source
+
+is a major addition
+to advanced LIGO.
+
+Yes.
+
+AUDIENCE: Where is
+the squeeze actually
+
+coming into the system?
+
+I see where it's drawn,
+but where is it actually
+
+entering the interferometer?
+
+At that first beam splitter?
+
+PROFESSOR: OK.
+
+We have to now-- there are
+more things added here.
+
+Ideally, you would think you
+have a beam splitter here,
+
+the laser comes in
+here, and you simply
+
+want to enter the
+squeezed vacuum here.
+
+And this is how we
+have explained it.
+
+We have one beam splitter
+in our Interferometer.
+
+There is an input
+port and an open port.
+
+But what is important
+here is also
+
+that the measurement--
+here you have
+
+a detector for reading
+out the Interferometer.
+
+And what is important
+is that the phase
+
+is balanced close to the point
+where no light is coming out.
+
+So you're measuring the
+zero crossing of a fringe.
+
+But that would mean
+most of the light
+
+would then exit
+the Interferometer
+
+at the other port.
+
+But high power lasers are
+very important for keeping
+
+the classical short noise down.
+
+So you want to work with
+the highest power possible.
+
+And therefore, you can't
+allow the light to exit.
+
+You want to recycle it.
+
+You want to use
+enhancement cavities.
+
+And what I can tell you is that
+this set up here integrates,
+
+I think, the signal
+recycling, the measurement
+
+at the zero fringe.
+
+And you see that kind
+of those different parts
+
+are copied in a
+way which I didn't
+
+prepare to explain it to you.
+
+All I wanted you to
+do is pretty much
+
+recognize that a squeeze
+light generator is important.
+
+And this enters
+the interferometer
+
+as a squeezed vacuum.
+
+What I find very
+interesting, and this
+
+is what I want to
+discuss now is,
+
+that when you have an
+interferometer like LIGO,
+
+cavitational wave
+interferometer,
+
+and now you want to squeeze.
+
+Does it really help to squeeze?
+
+Does it always help to squeeze?
+
+Or what is the situation?
+
+And this is what I want
+to discuss with you.
+
+So let's forget about signal
+recycling and enhancement
+
+cavities and things like this.
+
+Let's just discuss the basic
+cavitation wave detector, where
+
+we have an input,
+we have the two arms
+
+of the Michelson interferometer.
+
+And to have more
+sensitivity, the light
+
+bounces back and forth
+in an enhancement cavity.
+
+You can say if the light bounces
+back and forth 100 times,
+
+it is as if you had
+an arm length which
+
+is 100 times larger.
+
+And now we put in
+squeezed vacuum
+
+at the open part of
+the interferometer.
+
+And here we have
+our photo-diodes
+
+to perform the measurement.
+
+So the goal is to measure
+a small length scale.
+
+If a cavitation wave comes
+by, cavitational waves
+
+have quadrupolar character.
+
+So the metric will
+be such that there's
+
+a quadrupolar perturbation
+in the metric of space.
+
+And that means that, in
+essence, one of the mirrors
+
+is slightly moving out.
+
+The other mirror is
+slightly moving in.
+
+So therefore, the interferometer
+needs a very, very high
+
+sensitivity to displacement
+of one of the mirrors
+
+by an amount delta z.
+
+And if you normalize
+delta z to the arm length,
+
+or the arm length times
+the number of bounces,
+
+the task is to
+measure sensitivity
+
+in a length displacement
+of 10 to the minus 21.
+
+That's one of the
+smallest numbers
+
+which have ever been measured.
+
+And therefore, it is clear
+that this interferometer
+
+should operate as close
+as possible to the quantum
+
+limit of measurement.
+
+So what you want to measure here
+is, with the highest accuracy
+
+possible, the displacement
+of an object delta z.
+
+However, your object fulfills
+and uncertainty relationship,
+
+that if you want to measure
+the position very accurately,
+
+you also have to consider that
+it has a momentum uncertainty.
+
+And this fulfills Heisenberg's
+uncertainty relation.
+
+You will say, well, why should
+I care about the momentum
+
+uncertainty if all I want
+to measure is the position.
+
+Well, you should care
+because momentum uncertainty
+
+after a time tau turns
+into position uncertainty,
+
+because position uncertainty
+is uncertainty in velocity.
+
+And if I multiply
+it by the time tau
+
+it takes you to perform
+the measurement,
+
+you have now an
+uncertainty in position,
+
+which comes from the original
+uncertainty in momentum.
+
+So if I use the expression
+for Heisenberg's Uncertainty
+
+Relation, I find this.
+
+And now, what we
+have to minimize
+
+to get the highest precision
+is the total uncertainty
+
+in position, which is
+the original uncertainty,
+
+plus the uncertainty due
+to the motion of the mirror
+
+during the measurement process.
+
+So what we have here
+is we have delta z.
+
+We have a contribution which
+scores as 1 over delta z.
+
+And by just finding out what is
+the optimum choice of delta z,
+
+you find the result above.
+
+Or if you want to say you
+want that this delta z tau is
+
+comparable to delta z, just
+set this equal to delta z,
+
+solve for delta z, and
+you find the quantum limit
+
+for the interferometer,
+which is given up there.
+
+So this has nothing
+to do with squeezing.
+
+And you cannot improve on this
+quantum limit by squeezing.
+
+This is what you got.
+
+It only depends on the
+duration of the measurement.
+
+And it depends on the
+mass of the mirror.
+
+Now-- just get my
+notes ready-- there
+
+is a very influential
+and seminal paper
+
+by Caves-- the reference
+is given here--
+
+which was really
+laying out the concepts
+
+and the theory for quantum
+limited measurements with such
+
+an interferometer, and
+the use of squeezed light.
+
+Let me just summarize the
+most important findings.
+
+So this paper explains that
+you have two contributions
+
+to the noise, which
+depend on the laser
+
+power you use for
+your measurement.
+
+The first one is the
+photon counting noise.
+
+If you use more and
+more laser power,
+
+you have a better
+and better signal,
+
+and your short noise is reduced.
+
+So therefore, you have a better
+read out of the interferometer.
+
+And this is given here.
+
+Alpha is the eigenvalue
+of the coherent state.
+
+But there is a second
+aspect which you may not
+
+have thought about it,
+and this is the following.
+
+If you split a laser
+beam into two parts,
+
+you have fluctuations.
+
+The number of photons left
+and right are not identical.
+
+You have a coherent
+bean and you split it
+
+into two coherent
+beams, and then you
+
+have Poissonian
+fluctuations on either side.
+
+But if you have now Poissonian
+fluctuations in the photon
+
+number, if those photons
+are reflected off a mirror,
+
+they transfer photon
+recoil to the mirror.
+
+And the mirror is pushed
+by the radiation pressure.
+
+And it's pushed,
+and it has-- there
+
+is a differential motion
+of the two mirrors
+
+relative to each other due to
+the fluctuations in the photon
+
+number in the two arms
+of the interferometer.
+
+So therefore, what happens is
+you have a delta z deviation
+
+or variance in the measurement
+of the mirror, which
+
+comes from radiation pressure.
+
+It's a differential radiation
+pressure between the two arms.
+
+And what Caves
+showed in this paper
+
+is that the two effects
+which contribute
+
+to the precision
+of the measurement
+
+come from two different
+quadrature component.
+
+For the photon
+counting, we always
+
+want to squeeze the
+light in such a way
+
+that we have the narrow
+part of the ellipse
+
+in the quadrature component
+of our coherent beam.
+
+We've discussed
+it several times.
+
+So therefore, you want to
+squeeze it by e to the minus r.
+
+However, when what has a good
+effect for the photon counting
+
+has a bad effect
+for the fluctuations
+
+due to radiation pressure.
+
+So therefore, what
+happens is-- let's
+
+forget squeezing for a moment.
+
+If you have two contributions,
+one goes to the noise,
+
+one goes with alpha squared
+of the number of photons.
+
+One goes inverse with the square
+root of the number of photons.
+
+You will find out that
+even in the interferometer
+
+without squeezing, there
+is an optimum laser
+
+power, which you want to use.
+
+Because if you use
+two lower power,
+
+you lose in photon counting.
+
+If you use two higher
+power, you lose
+
+in the fluctuations of
+the radiation pressure.
+
+So even without squeezing,
+there is an optimum laser power.
+
+And for typical parameters,
+so there is an optimum power.
+
+And what we're
+shown in this paper
+
+is whenever you choose
+the optimum power which
+
+keeps a balance between
+photon counting and radiation
+
+pressure, then you reach
+the standard quantum
+
+limit of your interferometer.
+
+But it turns out that
+for typical parameters,
+
+this optimum is 8,000 watt.
+
+So that's why
+people at LIGO work
+
+harder and harder to develop
+more and more powerful
+
+lasers, because more
+laser power brings
+
+them closer and closer
+to the optimum power.
+
+But once they had
+the optimum power,
+
+additional squeezing
+will not help them
+
+because they are already at
+the fundamental quantum limit.
+
+So the one thing which
+squeezing does for you, it
+
+changes the optimum
+power in your input beam
+
+by a squeezing factor.
+
+So therefore, if you
+have lasers which
+
+have maybe 100 watt
+and not 8,000 watt,
+
+then squeezing helps you to
+reach the fundamental quantum
+
+limit of your interferometer.
+
+So that's pretty
+much all I wanted
+
+to say about precision
+measurements.
+
+I hope the last example--
+it's too complex to go
+
+through the whole analysis--
+but it gives you at least a
+
+feel that you have
+to keep your eye
+
+on both quadrature components.
+
+You can squeeze, you
+can get an improvement,
+
+in one physical
+effect, but you have
+
+to be careful to consider what
+happens in the other quadrature
+
+component.
+
+And in the end, you have to
+keep the two of them balanced.
+
+Any questions?
+
+Oops.
+
+OK.
+
+Well, we can get started with
+a very short chapter, which
+
+is about g2.
+
+The g2 measurement
+for light and atoms.
+
+I don't think you will
+find the discussion I
+
+want to present to
+you in any textbook.
+
+It is about whether g2 is 1 or
+2, whether we have fluctuations
+
+or not.
+
+And the discussion will be
+whether g2 of 2 and g2 of 1
+
+are quantum effect
+or classical effects.
+
+So I want to give you
+here in this discussion
+
+four different derivations of
+whether g2 is 1 or g2 is 2.
+
+And they look very,
+very different.
+
+Some are based on
+classical physics.
+
+Some are based on the
+concept of interference.
+
+And some are based on the
+quantum indistinguishability
+
+of particles.
+
+And once you see you all those
+four different explanations,
+
+I think you'll see
+the whole picture.
+
+And I hope you
+understand something.
+
+So again, it's a long
+story about factors of 2.
+
+But there are some factors of 2
+which are purely calculational,
+
+and there are other
+factors of 2 which
+
+involve a hell of
+a lot of physics.
+
+I mean, there are people
+who say the g2 factor of 2
+
+is really the difference between
+ordinary light and laser light.
+
+For light from a
+light bulb, g2 is 2.
+
+For light from a laser, g2 is 1.
+
+And this is the only
+fundamental difference
+
+between laser light
+and ordinary light.
+
+So this factor of
+2 is important.
+
+And I want to therefore have
+this additional discussion
+
+of the g2 function.
+
+So let me remind
+you that g2 of 0
+
+is the normalized probability
+to detect two photons or two
+
+particles simultaneously.
+
+And so far, we have
+discussed it for light.
+
+And the result we obtained by
+using our quantum formulation
+
+of light with creation
+annihilation operator,
+
+we found that g2 is 0.
+
+In the situation that we had
+black body radiation, which
+
+we can call thermal
+light, it's sometimes
+
+goes by the name chaotic light.
+
+Sometimes it's called
+classical light,
+
+but that may be a misnomer,
+because I regard the laser
+
+beam as a very
+classical form of light.
+
+This is sometimes
+called bunching
+
+because 2 is larger than 1.
+
+So pairs of photons
+appear bunched up.
+
+You have a higher probability
+than you would naively
+
+expect of detecting two
+photons simultaneously.
+
+And then we had the situation of
+laser light and coherent light
+
+where the g2 function was 1.
+
+And I want to shed some
+light on those two cases.
+
+We have discussed the extreme
+case of a single photon
+
+where the probability
+of detecting two photons
+
+is 0 for trivial reasons.
+
+So you have a g2 function of 0.
+
+But this is not what I
+want to discuss here.
+
+I want to shed some
+light on when do we
+
+get a g2 function of 1.
+
+When do we get a
+g2 function of 2.
+
+And one question
+we want to address,
+
+when we have a g2
+function of 2, is
+
+this a classical
+or quantum effect?
+
+Do you have an opinion?
+
+Who thinks-- question.
+
+AUDIENCE: When we did the
+homework problem where
+
+we had the linear's
+position, like alpha
+
+minus alpha
+[INAUDIBLE] plus alpha,
+
+we found that one can
+have a g2 greater than 1,
+
+and one can have
+a g2 less than 1.
+
+So maybe g2 isn't a
+great discriminator,
+
+whether it's very
+quantum or very classic.
+
+PROFESSOR: Let's hold
+this thought, yeah.
+
+You may be right.
+
+Let's come back to that.
+
+I think that's one opinion.
+
+The g2 function may
+not be a discriminator,
+
+because we can have g2 of 1
+and g2 of 2 purely classical.
+
+But why classical light
+behaves classically,
+
+maybe that's what we
+can understand there.
+
+And maybe what I
+want to tell you
+
+is that a lot of classical
+properties of classical light
+
+can be traced down to the
+indistinguishability of bosons,
+
+which are photons.
+
+So in other words, we
+shouldn't be surprised
+
+that something which
+seems purely classical
+
+is deeply rooted
+in quantum physics.
+
+But I'm ahead of my agenda.
+
+So let me start now.
+
+I want to offer you
+four different views.
+
+And the first one is that
+we have random intensity
+
+fluctuations.
+
+Think of a classical
+light source.
+
+And we assume that if
+things are really random,
+
+they are described by a
+Gaussian distribution.
+
+And if you switch on
+a light bulb, what
+
+you get if you measure the
+intensity when you measure what
+
+is the probability that the
+momentary intensity is I,
+
+well, you have to normalize
+it to the average intensity.
+
+But what you get is pretty much
+an exponential distribution.
+
+And this exponential
+distribution
+
+has a maximum at I equals 0.
+
+So the most probable
+intensity of all intensities
+
+when you switch
+on a light bulb is
+
+that you have 0 intensity
+at a given moment.
+
+But the average
+intensity is I average.
+
+So you can easily, for
+such a distribution,
+
+for such an exponential
+distribution,
+
+figure out what is the
+average of I to the power n.
+
+It is related to I
+average to the power n,
+
+but it has an n factorial.
+
+And what is important is the
+case for our discussion of n
+
+equals 2, where the
+square of the intensity
+
+averaged is two times the
+average intensity squared.
+
+And classically, g2
+is the probability
+
+of detecting two
+photons simultaneously,
+
+which is proportional
+to I square.
+
+We have to normalize it.
+
+And we normalize it
+by I average square.
+
+And this gives 2.
+
+So simply light with
+Gaussian fluctuations
+
+would give rise to
+a g2 function of 2.
+
+Since it's random fluctuations,
+it's also called chaotic light.
+
+And the physical pictures
+is the following.
+
+If you detect a photon,
+the light is fluctuating.
+
+But whenever you detect
+the first photon,
+
+it is more probable that you
+detect take the first photon
+
+when the intensity
+happened to be high.
+
+And then since the
+intensity is high,
+
+the probability
+for the next photon
+
+is higher than the
+average probability.
+
+So therefore, you get
+necessarily a g2 function of 2.
+
+So this is the physics of it.
+
+So let me just write that down.
+
+The first photon is more
+likely to be detected
+
+when the intensity
+fluctuation-- when
+
+intensity fluctuations
+give high intensity.
+
+And then we get this result.
+
+Yes.
+
+Let us discuss a second
+classical view, which
+
+I can call wave interference.
+
+This is really important.
+
+A lot of people get
+confused about it.
+
+If you have light
+in only one mode,
+
+this would be the
+laser of, for atoms,
+
+the Bose-Einstein condensate.
+
+One mode means a single wave.
+
+So if we have plain waves, we
+can describe all the photons
+
+or all the atoms by
+this wave function.
+
+So what is the g2 function
+for an object like this?
+
+AUDIENCE: 1.
+
+PROFESSOR: Trivially
+1, because if something
+
+is a clean wave, a single
+wave, all correlation functions
+
+factorize.
+
+You have the situation that
+I to the power n average
+
+is I average to the power n.
+
+And that means that
+gn is 1 for all n.
+
+OK, but let's now
+assume that we have two.
+
+We can also use more, but
+I want to restrict to two.
+
+That we have only two modes.
+
+And two modes can interfere.
+
+So let me apply to those
+two modes a simple model.
+
+And whether it's simple
+or not is relative.
+
+So it goes like as follows.
+
+If you have two modes,
+both of Unity intensity,
+
+then the average intensity is 2.
+
+But if you have interference,
+then the normalized intensity
+
+will vary between 0 and 4.
+
+Constructive interference
+means you get twice as much
+
+as average.
+
+Destructive means
+you get nothing.
+
+So therefore, the
+[? nt ?] squared
+
+will vary between 0 and 16.
+
+So if I just use the two
+extremes, it works out well.
+
+You have an I
+square, which is 8,
+
+the average of
+constructive interference
+
+and destructive interference.
+
+And this is two times
+the average intensity,
+
+which is 2 squared.
+
+So therefore, if you
+simply allow fluctuations
+
+due to the interference
+of two modes,
+
+we find that the
+g2 function is 2.
+
+So this demonstrates
+that g2 of 2
+
+has its deep origin
+in wave interference.
+
+And indeed, if you take a
+light bulb which emits photons,
+
+you have many, many atoms
+in your tungsten filament
+
+which can emit, re-emit waves.
+
+And since they have
+different positions,
+
+the waves arrive at your
+detector with random phases.
+
+And if you really write
+that down in a model--
+
+this is nicely done in
+the book by Loudon--
+
+you realize that
+random interference
+
+between waves results in
+an exponential distribution
+
+of intensity.
+
+So most people wouldn't
+make the connection.
+
+But there is a deep and
+fundamental relationship
+
+between random interference and
+the most random distribution,
+
+the exponential
+distribution, intensity
+
+which characterises thermal
+light or chaotic light.
+
+So let me just write that down.
+
+So the Gaussian intensity
+distribution-- actually
+
+it's an exponential
+intensity distribution.
+
+But if you write the
+intensity distribution
+
+as a distribution in
+the electric field,
+
+intensity becomes e square.
+
+Then it becomes a
+Gaussian [INAUDIBLE].
+
+So Gaussian or exponential
+intensity distribution
+
+in view number one is the
+result, is indeed the result,
+
+of interference.
+
+Any questions?
+
+So these are the
+two classical views.
+
+I think we should stop now.
+
+But on Wednesday, I will present
+you alternative derivations,
+
+which are completely
+focused on quantum operators
+
+and quantum counting statistics.
+
+Just a reminder, we have
+class today and Friday.
+
+And we have class
+this week on Friday.
\ No newline at end of file
diff --git a/A_hcPtESedQ.txt b/A_hcPtESedQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..345c948c8f1b0952f92758de99da690bd0c3830f
--- /dev/null
+++ b/A_hcPtESedQ.txt
@@ -0,0 +1,491 @@
+align:start position:0%
+ 
+okay um just real quickly um this Pond
+
+ align:start position:0%
+okay um just real quickly um this Pond
+ 
+
+ align:start position:0%
+okay um just real quickly um this Pond
+is because it's a glacial kettle Pond
+
+ align:start position:0%
+is because it's a glacial kettle Pond
+ 
+
+ align:start position:0%
+is because it's a glacial kettle Pond
+and it's it like I told you before it
+
+ align:start position:0%
+and it's it like I told you before it
+ 
+
+ align:start position:0%
+and it's it like I told you before it
+was like an outcrop of the water table
+
+ align:start position:0%
+was like an outcrop of the water table
+ 
+
+ align:start position:0%
+was like an outcrop of the water table
+it actually goes up and down seasonally
+
+ align:start position:0%
+it actually goes up and down seasonally
+ 
+
+ align:start position:0%
+it actually goes up and down seasonally
+with the water table during the summer
+
+ align:start position:0%
+with the water table during the summer
+ 
+
+ align:start position:0%
+with the water table during the summer
+when we have a lot of a vapid
+
+ align:start position:0%
+when we have a lot of a vapid
+ 
+
+ align:start position:0%
+when we have a lot of a vapid
+transpiration and and uh probably a
+
+ align:start position:0%
+transpiration and and uh probably a
+ 
+
+ align:start position:0%
+transpiration and and uh probably a
+little bit less
+
+ align:start position:0%
+little bit less
+ 
+
+ align:start position:0%
+little bit less
+rainfall groundwater levels tend to drop
+
+ align:start position:0%
+rainfall groundwater levels tend to drop
+ 
+
+ align:start position:0%
+rainfall groundwater levels tend to drop
+and during the winter when the trees
+
+ align:start position:0%
+and during the winter when the trees
+ 
+
+ align:start position:0%
+and during the winter when the trees
+have no leaves and all the rain that
+
+ align:start position:0%
+have no leaves and all the rain that
+ 
+
+ align:start position:0%
+have no leaves and all the rain that
+comes in as as precipitation can can
+
+ align:start position:0%
+comes in as as precipitation can can
+ 
+
+ align:start position:0%
+comes in as as precipitation can can
+recharge the aaer you actually have
+
+ align:start position:0%
+recharge the aaer you actually have
+ 
+
+ align:start position:0%
+recharge the aaer you actually have
+water levs rise so they go up and down
+
+ align:start position:0%
+water levs rise so they go up and down
+ 
+
+ align:start position:0%
+water levs rise so they go up and down
+seasonally and there are also droughts
+
+ align:start position:0%
+seasonally and there are also droughts
+ 
+
+ align:start position:0%
+seasonally and there are also droughts
+where it really drops and there are wet
+
+ align:start position:0%
+where it really drops and there are wet
+ 
+
+ align:start position:0%
+where it really drops and there are wet
+years where it really gets high okay so
+
+ align:start position:0%
+years where it really gets high okay so
+ 
+
+ align:start position:0%
+years where it really gets high okay so
+where you're standing right now just
+
+ align:start position:0%
+where you're standing right now just
+ 
+
+ align:start position:0%
+where you're standing right now just
+about 3 or 4 months ago was actually
+
+ align:start position:0%
+about 3 or 4 months ago was actually
+ 
+
+ align:start position:0%
+about 3 or 4 months ago was actually
+underwater the lake level was higher
+
+ align:start position:0%
+underwater the lake level was higher
+ 
+
+ align:start position:0%
+underwater the lake level was higher
+okay as the groundwater discharges to
+
+ align:start position:0%
+okay as the groundwater discharges to
+ 
+
+ align:start position:0%
+okay as the groundwater discharges to
+the aquifer from the aquifer into the
+
+ align:start position:0%
+the aquifer from the aquifer into the
+ 
+
+ align:start position:0%
+the aquifer from the aquifer into the
+pond and we talked about all those
+
+ align:start position:0%
+pond and we talked about all those
+ 
+
+ align:start position:0%
+pond and we talked about all those
+geochemical environments up in the
+
+ align:start position:0%
+geochemical environments up in the
+ 
+
+ align:start position:0%
+geochemical environments up in the
+Gravel Pit well you can imagine that
+
+ align:start position:0%
+Gravel Pit well you can imagine that
+ 
+
+ align:start position:0%
+Gravel Pit well you can imagine that
+water with zero dissolved oxygen where I
+
+ align:start position:0%
+water with zero dissolved oxygen where I
+ 
+
+ align:start position:0%
+water with zero dissolved oxygen where I
+had the real high iron remember that
+
+ align:start position:0%
+had the real high iron remember that
+ 
+
+ align:start position:0%
+had the real high iron remember that
+when the thing turned orange this
+
+ align:start position:0%
+when the thing turned orange this
+ 
+
+ align:start position:0%
+when the thing turned orange this
+discharging into the lake which of
+
+ align:start position:0%
+discharging into the lake which of
+ 
+
+ align:start position:0%
+discharging into the lake which of
+course is a surface water environment
+
+ align:start position:0%
+course is a surface water environment
+ 
+
+ align:start position:0%
+course is a surface water environment
+and there's dissolved oxygen in the lake
+
+ align:start position:0%
+and there's dissolved oxygen in the lake
+ 
+
+ align:start position:0%
+and there's dissolved oxygen in the lake
+cuz there'd be no fish otherwise okay
+
+ align:start position:0%
+cuz there'd be no fish otherwise okay
+ 
+
+ align:start position:0%
+cuz there'd be no fish otherwise okay
+turns out that in addition to dissolved
+
+ align:start position:0%
+turns out that in addition to dissolved
+ 
+
+ align:start position:0%
+turns out that in addition to dissolved
+iron there's no good fuel kit for it
+
+ align:start position:0%
+iron there's no good fuel kit for it
+ 
+
+ align:start position:0%
+iron there's no good fuel kit for it
+there's a lot of dissolved manganese it
+
+ align:start position:0%
+there's a lot of dissolved manganese it
+ 
+
+ align:start position:0%
+there's a lot of dissolved manganese it
+turns out the dissolved iron doesn't get
+
+ align:start position:0%
+turns out the dissolved iron doesn't get
+ 
+
+ align:start position:0%
+turns out the dissolved iron doesn't get
+this far south by the time we get this
+
+ align:start position:0%
+this far south by the time we get this
+ 
+
+ align:start position:0%
+this far south by the time we get this
+far sou all the organic carbon has been
+
+ align:start position:0%
+far sou all the organic carbon has been
+ 
+
+ align:start position:0%
+far sou all the organic carbon has been
+pretty much used up or a lot of it has
+
+ align:start position:0%
+pretty much used up or a lot of it has
+ 
+
+ align:start position:0%
+pretty much used up or a lot of it has
+and you don't have dissolved iron but
+
+ align:start position:0%
+and you don't have dissolved iron but
+ 
+
+ align:start position:0%
+and you don't have dissolved iron but
+you do have dissolved manganese and as
+
+ align:start position:0%
+you do have dissolved manganese and as
+ 
+
+ align:start position:0%
+you do have dissolved manganese and as
+the water discharges into the lake and
+
+ align:start position:0%
+the water discharges into the lake and
+ 
+
+ align:start position:0%
+the water discharges into the lake and
+hits the dissolved oxygen the manganese
+
+ align:start position:0%
+hits the dissolved oxygen the manganese
+ 
+
+ align:start position:0%
+hits the dissolved oxygen the manganese
+precipitates it back out and coats the
+
+ align:start position:0%
+precipitates it back out and coats the
+ 
+
+ align:start position:0%
+precipitates it back out and coats the
+Rocks black
+
+ align:start position:0%
+Rocks black
+ 
+
+ align:start position:0%
+Rocks black
+and so this is actually evidence of the
+
+ align:start position:0%
+and so this is actually evidence of the
+ 
+
+ align:start position:0%
+and so this is actually evidence of the
+groundwater that was containing
+
+ align:start position:0%
+groundwater that was containing
+ 
+
+ align:start position:0%
+groundwater that was containing
+manganese is discharging into the lake
+
+ align:start position:0%
+manganese is discharging into the lake
+ 
+
+ align:start position:0%
+manganese is discharging into the lake
+and when it hits that interface with the
+
+ align:start position:0%
+and when it hits that interface with the
+ 
+
+ align:start position:0%
+and when it hits that interface with the
+high DOL pond water the manganese
+
+ align:start position:0%
+high DOL pond water the manganese
+ 
+
+ align:start position:0%
+high DOL pond water the manganese
+precipitated out and you can actually
+
+ align:start position:0%
+precipitated out and you can actually
+ 
+
+ align:start position:0%
+precipitated out and you can actually
+see that if we dig
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here see how the black color is only
+
+ align:start position:0%
+here see how the black color is only
+ 
+
+ align:start position:0%
+here see how the black color is only
+just right at the surface and in fact if
+
+ align:start position:0%
+just right at the surface and in fact if
+ 
+
+ align:start position:0%
+just right at the surface and in fact if
+you take these rocks and break them open
+
+ align:start position:0%
+you take these rocks and break them open
+ 
+
+ align:start position:0%
+you take these rocks and break them open
+they're only black on the outside so
+
+ align:start position:0%
+they're only black on the outside so
+ 
+
+ align:start position:0%
+they're only black on the outside so
+it's really a coating I've been near of
+
+ align:start position:0%
+it's really a coating I've been near of
+ 
+
+ align:start position:0%
+it's really a coating I've been near of
+Manganese
+
+ align:start position:0%
+Manganese
+ 
+
+ align:start position:0%
+Manganese
+oxide so it's kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neat let's go a little further everybody
+
+ align:start position:0%
+neat let's go a little further everybody
+ 
+
+ align:start position:0%
+neat let's go a little further everybody
+call
\ No newline at end of file
diff --git a/AbK4bZhUk48.txt b/AbK4bZhUk48.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b0d07e8271357496a3ef0f543d35324129a87beb
--- /dev/null
+++ b/AbK4bZhUk48.txt
@@ -0,0 +1,9355 @@
+align:start position:0%
+ 
+well there's one bit of mystery left
+
+ align:start position:0%
+well there's one bit of mystery left
+ 
+
+ align:start position:0%
+well there's one bit of mystery left
+which I'd like to get rid of right now
+
+ align:start position:0%
+which I'd like to get rid of right now
+ 
+
+ align:start position:0%
+which I'd like to get rid of right now
+and that's that we've been blithely
+
+ align:start position:0%
+and that's that we've been blithely
+ 
+
+ align:start position:0%
+and that's that we've been blithely
+doing things like conses assuming
+
+ align:start position:0%
+doing things like conses assuming
+ 
+
+ align:start position:0%
+doing things like conses assuming
+there's always another one that we can
+
+ align:start position:0%
+there's always another one that we can
+ 
+
+ align:start position:0%
+there's always another one that we can
+that we've been doing these things like
+
+ align:start position:0%
+that we've been doing these things like
+ 
+
+ align:start position:0%
+that we've been doing these things like
+carring and could ring and assuming that
+
+ align:start position:0%
+carring and could ring and assuming that
+ 
+
+ align:start position:0%
+carring and could ring and assuming that
+we had some idea how this could be done
+
+ align:start position:0%
+we had some idea how this could be done
+ 
+
+ align:start position:0%
+we had some idea how this could be done
+now indeed we said that that's
+
+ align:start position:0%
+now indeed we said that that's
+ 
+
+ align:start position:0%
+now indeed we said that that's
+equivalent to having procedures okay but
+
+ align:start position:0%
+equivalent to having procedures okay but
+ 
+
+ align:start position:0%
+equivalent to having procedures okay but
+that doesn't really solve the problem
+
+ align:start position:0%
+that doesn't really solve the problem
+ 
+
+ align:start position:0%
+that doesn't really solve the problem
+because the procedures need all sorts of
+
+ align:start position:0%
+because the procedures need all sorts of
+ 
+
+ align:start position:0%
+because the procedures need all sorts of
+complicated mechanism like environment
+
+ align:start position:0%
+complicated mechanism like environment
+ 
+
+ align:start position:0%
+complicated mechanism like environment
+structures and things like that to work
+
+ align:start position:0%
+structures and things like that to work
+ 
+
+ align:start position:0%
+structures and things like that to work
+and those were ultimately made out of
+
+ align:start position:0%
+and those were ultimately made out of
+ 
+
+ align:start position:0%
+and those were ultimately made out of
+constants in the in the model that we
+
+ align:start position:0%
+constants in the in the model that we
+ 
+
+ align:start position:0%
+constants in the in the model that we
+had so that really doesn't solve the
+
+ align:start position:0%
+had so that really doesn't solve the
+ 
+
+ align:start position:0%
+had so that really doesn't solve the
+problem and now the problem here is is
+
+ align:start position:0%
+problem and now the problem here is is
+ 
+
+ align:start position:0%
+problem and now the problem here is is
+the glue that data structure is made out
+
+ align:start position:0%
+the glue that data structure is made out
+ 
+
+ align:start position:0%
+the glue that data structure is made out
+of what kind of possible thing could be
+
+ align:start position:0%
+of what kind of possible thing could be
+ 
+
+ align:start position:0%
+of what kind of possible thing could be
+and we've been showing you things like a
+
+ align:start position:0%
+and we've been showing you things like a
+ 
+
+ align:start position:0%
+and we've been showing you things like a
+machine a computer that has a controller
+
+ align:start position:0%
+machine a computer that has a controller
+ 
+
+ align:start position:0%
+machine a computer that has a controller
+and some registers and maybe a stack and
+
+ align:start position:0%
+and some registers and maybe a stack and
+ 
+
+ align:start position:0%
+and some registers and maybe a stack and
+we haven't said anything about for
+
+ align:start position:0%
+we haven't said anything about for
+ 
+
+ align:start position:0%
+we haven't said anything about for
+example its larger memory and I think
+
+ align:start position:0%
+example its larger memory and I think
+ 
+
+ align:start position:0%
+example its larger memory and I think
+that's what we have to worry about right
+
+ align:start position:0%
+that's what we have to worry about right
+ 
+
+ align:start position:0%
+that's what we have to worry about right
+now but just for just to make it
+
+ align:start position:0%
+now but just for just to make it
+ 
+
+ align:start position:0%
+now but just for just to make it
+perfectly clear that this is an
+
+ align:start position:0%
+perfectly clear that this is an
+ 
+
+ align:start position:0%
+perfectly clear that this is an
+essential purely if whatever
+
+ align:start position:0%
+essential purely if whatever
+ 
+
+ align:start position:0%
+essential purely if whatever
+implementational thing I like to show
+
+ align:start position:0%
+implementational thing I like to show
+ 
+
+ align:start position:0%
+implementational thing I like to show
+you for example how you could do it all
+
+ align:start position:0%
+you for example how you could do it all
+ 
+
+ align:start position:0%
+you for example how you could do it all
+with numbers that's an easy one
+
+ align:start position:0%
+with numbers that's an easy one
+ 
+
+ align:start position:0%
+with numbers that's an easy one
+famous fella by the name of girdle a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+logician of en over the 1930s
+
+ align:start position:0%
+logician of en over the 1930s
+ 
+
+ align:start position:0%
+logician of en over the 1930s
+invented a very clever way of encoding
+
+ align:start position:0%
+invented a very clever way of encoding
+ 
+
+ align:start position:0%
+invented a very clever way of encoding
+the complicated expressions as numbers
+
+ align:start position:0%
+the complicated expressions as numbers
+ 
+
+ align:start position:0%
+the complicated expressions as numbers
+for example and I'm not saying exactly
+
+ align:start position:0%
+for example and I'm not saying exactly
+ 
+
+ align:start position:0%
+for example and I'm not saying exactly
+what kernels scheme is because he didn't
+
+ align:start position:0%
+what kernels scheme is because he didn't
+ 
+
+ align:start position:0%
+what kernels scheme is because he didn't
+use words like cons he had other kinds
+
+ align:start position:0%
+use words like cons he had other kinds
+ 
+
+ align:start position:0%
+use words like cons he had other kinds
+of ways to combine to make expressions
+
+ align:start position:0%
+of ways to combine to make expressions
+ 
+
+ align:start position:0%
+of ways to combine to make expressions
+but he said I'm going to assign a number
+
+ align:start position:0%
+but he said I'm going to assign a number
+ 
+
+ align:start position:0%
+but he said I'm going to assign a number
+to every algebraic expression and the
+
+ align:start position:0%
+to every algebraic expression and the
+ 
+
+ align:start position:0%
+to every algebraic expression and the
+way I'm going to manufacture these
+
+ align:start position:0%
+way I'm going to manufacture these
+ 
+
+ align:start position:0%
+way I'm going to manufacture these
+numbers is by combining the numbers of
+
+ align:start position:0%
+numbers is by combining the numbers of
+ 
+
+ align:start position:0%
+numbers is by combining the numbers of
+the parts so for example if we what we
+
+ align:start position:0%
+the parts so for example if we what we
+ 
+
+ align:start position:0%
+the parts so for example if we what we
+were doing in our world we could say
+
+ align:start position:0%
+were doing in our world we could say
+ 
+
+ align:start position:0%
+were doing in our world we could say
+that if if objects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are represented by numbers numbers then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cons of X&Y
+
+ align:start position:0%
+cons of X&Y
+ 
+
+ align:start position:0%
+cons of X&Y
+could be represented by could be
+
+ align:start position:0%
+could be represented by could be
+ 
+
+ align:start position:0%
+could be represented by could be
+represented by 2 to the X times 3 to the
+
+ align:start position:0%
+represented by 2 to the X times 3 to the
+ 
+
+ align:start position:0%
+represented by 2 to the X times 3 to the
+Y because then we could extract the
+
+ align:start position:0%
+Y because then we could extract the
+ 
+
+ align:start position:0%
+Y because then we could extract the
+parts we could say for example that then
+
+ align:start position:0%
+parts we could say for example that then
+ 
+
+ align:start position:0%
+parts we could say for example that then
+car say X is the is the number of
+
+ align:start position:0%
+car say X is the is the number of
+ 
+
+ align:start position:0%
+car say X is the is the number of
+factors of 2 in X ok and of course
+
+ align:start position:0%
+factors of 2 in X ok and of course
+ 
+
+ align:start position:0%
+factors of 2 in X ok and of course
+cooter is the same thing it's the number
+
+ align:start position:0%
+cooter is the same thing it's the number
+ 
+
+ align:start position:0%
+cooter is the same thing it's the number
+of factors of 3 in X now this is a
+
+ align:start position:0%
+of factors of 3 in X now this is a
+ 
+
+ align:start position:0%
+of factors of 3 in X now this is a
+perfectly reasonable scheme except for
+
+ align:start position:0%
+perfectly reasonable scheme except for
+ 
+
+ align:start position:0%
+perfectly reasonable scheme except for
+the fact that the numbers rapidly get to
+
+ align:start position:0%
+the fact that the numbers rapidly get to
+ 
+
+ align:start position:0%
+the fact that the numbers rapidly get to
+be much larger in number of digits than
+
+ align:start position:0%
+be much larger in number of digits than
+ 
+
+ align:start position:0%
+be much larger in number of digits than
+the number of protons in the universe so
+
+ align:start position:0%
+the number of protons in the universe so
+ 
+
+ align:start position:0%
+the number of protons in the universe so
+there's no easy way to use this scheme
+
+ align:start position:0%
+there's no easy way to use this scheme
+ 
+
+ align:start position:0%
+there's no easy way to use this scheme
+other than a theoretical one on the
+
+ align:start position:0%
+other than a theoretical one on the
+ 
+
+ align:start position:0%
+other than a theoretical one on the
+other hand there are other ways of
+
+ align:start position:0%
+other hand there are other ways of
+ 
+
+ align:start position:0%
+other hand there are other ways of
+representing these things we have been
+
+ align:start position:0%
+representing these things we have been
+ 
+
+ align:start position:0%
+representing these things we have been
+thinking in terms of little blocks in
+
+ align:start position:0%
+thinking in terms of little blocks in
+ 
+
+ align:start position:0%
+thinking in terms of little blocks in
+boxes right we've been making we've been
+
+ align:start position:0%
+boxes right we've been making we've been
+ 
+
+ align:start position:0%
+boxes right we've been making we've been
+thinking about our constructors as
+
+ align:start position:0%
+thinking about our constructors as
+ 
+
+ align:start position:0%
+thinking about our constructors as
+looking sort of like this there are
+
+ align:start position:0%
+looking sort of like this there are
+ 
+
+ align:start position:0%
+looking sort of like this there are
+little pigeon holes with things in them
+
+ align:start position:0%
+little pigeon holes with things in them
+ 
+
+ align:start position:0%
+little pigeon holes with things in them
+and of course we arrange them in little
+
+ align:start position:0%
+and of course we arrange them in little
+ 
+
+ align:start position:0%
+and of course we arrange them in little
+trees I wish that the semiconductor
+
+ align:start position:0%
+trees I wish that the semiconductor
+ 
+
+ align:start position:0%
+trees I wish that the semiconductor
+manufacturers would supply me with
+
+ align:start position:0%
+manufacturers would supply me with
+ 
+
+ align:start position:0%
+manufacturers would supply me with
+something appropriate for this but
+
+ align:start position:0%
+something appropriate for this but
+ 
+
+ align:start position:0%
+something appropriate for this but
+actually what they do supply me with is
+
+ align:start position:0%
+actually what they do supply me with is
+ 
+
+ align:start position:0%
+actually what they do supply me with is
+a linear memory memory is sort of a big
+
+ align:start position:0%
+a linear memory memory is sort of a big
+ 
+
+ align:start position:0%
+a linear memory memory is sort of a big
+pile of pigeon holes pigeon holes like
+
+ align:start position:0%
+pile of pigeon holes pigeon holes like
+ 
+
+ align:start position:0%
+pile of pigeon holes pigeon holes like
+this each of which can hold a certain
+
+ align:start position:0%
+this each of which can hold a certain
+ 
+
+ align:start position:0%
+this each of which can hold a certain
+sized object a fixed size object so for
+
+ align:start position:0%
+sized object a fixed size object so for
+ 
+
+ align:start position:0%
+sized object a fixed size object so for
+example a complicated list with 25
+
+ align:start position:0%
+example a complicated list with 25
+ 
+
+ align:start position:0%
+example a complicated list with 25
+elements won't fit in one of these
+
+ align:start position:0%
+elements won't fit in one of these
+ 
+
+ align:start position:0%
+elements won't fit in one of these
+however each of these is indexed by an
+
+ align:start position:0%
+however each of these is indexed by an
+ 
+
+ align:start position:0%
+however each of these is indexed by an
+address
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the address might be 0 here 1 here 2
+
+ align:start position:0%
+so the address might be 0 here 1 here 2
+ 
+
+ align:start position:0%
+so the address might be 0 here 1 here 2
+here 3 here and so on
+
+ align:start position:0%
+here 3 here and so on
+ 
+
+ align:start position:0%
+here 3 here and so on
+that we write these down as numbers is
+
+ align:start position:0%
+that we write these down as numbers is
+ 
+
+ align:start position:0%
+that we write these down as numbers is
+unimportant what matters in their
+
+ align:start position:0%
+unimportant what matters in their
+ 
+
+ align:start position:0%
+unimportant what matters in their
+distinct and there's a way to get to the
+
+ align:start position:0%
+distinct and there's a way to get to the
+ 
+
+ align:start position:0%
+distinct and there's a way to get to the
+next one right and inside of each of
+
+ align:start position:0%
+next one right and inside of each of
+ 
+
+ align:start position:0%
+next one right and inside of each of
+these we can stuff something in each of
+
+ align:start position:0%
+these we can stuff something in each of
+ 
+
+ align:start position:0%
+these we can stuff something in each of
+these pigeon holes so that's what memory
+
+ align:start position:0%
+these pigeon holes so that's what memory
+ 
+
+ align:start position:0%
+these pigeon holes so that's what memory
+is like for those of you who haven't
+
+ align:start position:0%
+is like for those of you who haven't
+ 
+
+ align:start position:0%
+is like for those of you who haven't
+built a computer now now the problem is
+
+ align:start position:0%
+built a computer now now the problem is
+ 
+
+ align:start position:0%
+built a computer now now the problem is
+how are we going to impose on this type
+
+ align:start position:0%
+how are we going to impose on this type
+ 
+
+ align:start position:0%
+how are we going to impose on this type
+of structure this nice tree structure
+
+ align:start position:0%
+of structure this nice tree structure
+ 
+
+ align:start position:0%
+of structure this nice tree structure
+well it's not very hard and there have
+
+ align:start position:0%
+well it's not very hard and there have
+ 
+
+ align:start position:0%
+well it's not very hard and there have
+been numerous schemes involved in this
+
+ align:start position:0%
+been numerous schemes involved in this
+ 
+
+ align:start position:0%
+been numerous schemes involved in this
+the most important one is to say well
+
+ align:start position:0%
+the most important one is to say well
+ 
+
+ align:start position:0%
+the most important one is to say well
+assuming that the semiconductor
+
+ align:start position:0%
+assuming that the semiconductor
+ 
+
+ align:start position:0%
+assuming that the semiconductor
+manufacturer allows me to rearrange my
+
+ align:start position:0%
+manufacturer allows me to rearrange my
+ 
+
+ align:start position:0%
+manufacturer allows me to rearrange my
+memory so that one of these pigeonholes
+
+ align:start position:0%
+memory so that one of these pigeonholes
+ 
+
+ align:start position:0%
+memory so that one of these pigeonholes
+is big enough to hold the address of
+
+ align:start position:0%
+is big enough to hold the address of
+ 
+
+ align:start position:0%
+is big enough to hold the address of
+another ok I've haven't made now it
+
+ align:start position:0%
+another ok I've haven't made now it
+ 
+
+ align:start position:0%
+another ok I've haven't made now it
+actually has to be a little bit bigger
+
+ align:start position:0%
+actually has to be a little bit bigger
+ 
+
+ align:start position:0%
+actually has to be a little bit bigger
+because I have to also install or store
+
+ align:start position:0%
+because I have to also install or store
+ 
+
+ align:start position:0%
+because I have to also install or store
+some some information as to a tag which
+
+ align:start position:0%
+some some information as to a tag which
+ 
+
+ align:start position:0%
+some some information as to a tag which
+describes the kind of thing that's there
+
+ align:start position:0%
+describes the kind of thing that's there
+ 
+
+ align:start position:0%
+describes the kind of thing that's there
+and we'll see that in a second and of
+
+ align:start position:0%
+and we'll see that in a second and of
+ 
+
+ align:start position:0%
+and we'll see that in a second and of
+course the semiconductor manufacturer
+
+ align:start position:0%
+course the semiconductor manufacturer
+ 
+
+ align:start position:0%
+course the semiconductor manufacturer
+doesn't arrange it so that I can do that
+
+ align:start position:0%
+doesn't arrange it so that I can do that
+ 
+
+ align:start position:0%
+doesn't arrange it so that I can do that
+then of course I can with some
+
+ align:start position:0%
+then of course I can with some
+ 
+
+ align:start position:0%
+then of course I can with some
+cleverness arrange combinations of these
+
+ align:start position:0%
+cleverness arrange combinations of these
+ 
+
+ align:start position:0%
+cleverness arrange combinations of these
+to fit together in that way so we're
+
+ align:start position:0%
+to fit together in that way so we're
+ 
+
+ align:start position:0%
+to fit together in that way so we're
+going to have to we're gonna have to
+
+ align:start position:0%
+going to have to we're gonna have to
+ 
+
+ align:start position:0%
+going to have to we're gonna have to
+imagine imposing this complicated tree
+
+ align:start position:0%
+imagine imposing this complicated tree
+ 
+
+ align:start position:0%
+imagine imposing this complicated tree
+structure on our nice linear memory if
+
+ align:start position:0%
+structure on our nice linear memory if
+ 
+
+ align:start position:0%
+structure on our nice linear memory if
+we look at the first still store we see
+
+ align:start position:0%
+we look at the first still store we see
+ 
+
+ align:start position:0%
+we look at the first still store we see
+the a classic scheme for doing that and
+
+ align:start position:0%
+the a classic scheme for doing that and
+ 
+
+ align:start position:0%
+the a classic scheme for doing that and
+it's a standard way of representing list
+
+ align:start position:0%
+it's a standard way of representing list
+ 
+
+ align:start position:0%
+it's a standard way of representing list
+structures in in a linear memory what we
+
+ align:start position:0%
+structures in in a linear memory what we
+ 
+
+ align:start position:0%
+structures in in a linear memory what we
+do is we divide this memory it's a into
+
+ align:start position:0%
+do is we divide this memory it's a into
+ 
+
+ align:start position:0%
+do is we divide this memory it's a into
+two parts an array called the cars and
+
+ align:start position:0%
+two parts an array called the cars and
+ 
+
+ align:start position:0%
+two parts an array called the cars and
+an array called the cutters now whether
+
+ align:start position:0%
+an array called the cutters now whether
+ 
+
+ align:start position:0%
+an array called the cutters now whether
+those happen to be sequential addresses
+
+ align:start position:0%
+those happen to be sequential addresses
+ 
+
+ align:start position:0%
+those happen to be sequential addresses
+or whatever it's not important that
+
+ align:start position:0%
+or whatever it's not important that
+ 
+
+ align:start position:0%
+or whatever it's not important that
+somebody's implementation details but
+
+ align:start position:0%
+somebody's implementation details but
+ 
+
+ align:start position:0%
+somebody's implementation details but
+there are two there are two it arrays
+
+ align:start position:0%
+there are two there are two it arrays
+ 
+
+ align:start position:0%
+there are two there are two it arrays
+here linear arrays indexed by sequential
+
+ align:start position:0%
+here linear arrays indexed by sequential
+ 
+
+ align:start position:0%
+here linear arrays indexed by sequential
+indices like this what is stored in each
+
+ align:start position:0%
+indices like this what is stored in each
+ 
+
+ align:start position:0%
+indices like this what is stored in each
+of these pigeonholes is a typed object
+
+ align:start position:0%
+of these pigeonholes is a typed object
+ 
+
+ align:start position:0%
+of these pigeonholes is a typed object
+and what we have here are types which
+
+ align:start position:0%
+and what we have here are types which
+ 
+
+ align:start position:0%
+and what we have here are types which
+are begin with letters like P
+
+ align:start position:0%
+are begin with letters like P
+ 
+
+ align:start position:0%
+are begin with letters like P
+standing for a pair or n standing for a
+
+ align:start position:0%
+standing for a pair or n standing for a
+ 
+
+ align:start position:0%
+standing for a pair or n standing for a
+number or east and for an empty list the
+
+ align:start position:0%
+number or east and for an empty list the
+ 
+
+ align:start position:0%
+number or east and for an empty list the
+end of the list so if we wish to
+
+ align:start position:0%
+end of the list so if we wish to
+ 
+
+ align:start position:0%
+end of the list so if we wish to
+represent an object like this list
+
+ align:start position:0%
+represent an object like this list
+ 
+
+ align:start position:0%
+represent an object like this list
+beginning with one two and then having a
+
+ align:start position:0%
+beginning with one two and then having a
+ 
+
+ align:start position:0%
+beginning with one two and then having a
+3 and a 4 as its second and third
+
+ align:start position:0%
+3 and a 4 as its second and third
+ 
+
+ align:start position:0%
+3 and a 4 as its second and third
+elements a list containing a list as its
+
+ align:start position:0%
+elements a list containing a list as its
+ 
+
+ align:start position:0%
+elements a list containing a list as its
+first part and then two numbers as the
+
+ align:start position:0%
+first part and then two numbers as the
+ 
+
+ align:start position:0%
+first part and then two numbers as the
+second and third parts then of course we
+
+ align:start position:0%
+second and third parts then of course we
+ 
+
+ align:start position:0%
+second and third parts then of course we
+draw it sort of like this these days in
+
+ align:start position:0%
+draw it sort of like this these days in
+ 
+
+ align:start position:0%
+draw it sort of like this these days in
+box and pointer notation and you see
+
+ align:start position:0%
+box and pointer notation and you see
+ 
+
+ align:start position:0%
+box and pointer notation and you see
+these are the three the three cells that
+
+ align:start position:0%
+these are the three the three cells that
+ 
+
+ align:start position:0%
+these are the three the three cells that
+have that as their car pointer the
+
+ align:start position:0%
+have that as their car pointer the
+ 
+
+ align:start position:0%
+have that as their car pointer the
+object which is either one two or three
+
+ align:start position:0%
+object which is either one two or three
+ 
+
+ align:start position:0%
+object which is either one two or three
+or four and then of course the one to
+
+ align:start position:0%
+or four and then of course the one to
+ 
+
+ align:start position:0%
+or four and then of course the one to
+the car of this entire structure is
+
+ align:start position:0%
+the car of this entire structure is
+ 
+
+ align:start position:0%
+the car of this entire structure is
+itself a sub structure which contains a
+
+ align:start position:0%
+itself a sub structure which contains a
+ 
+
+ align:start position:0%
+itself a sub structure which contains a
+sub list like that and what I'm about to
+
+ align:start position:0%
+sub list like that and what I'm about to
+ 
+
+ align:start position:0%
+sub list like that and what I'm about to
+do is put down places which are I'm
+
+ align:start position:0%
+do is put down places which are I'm
+ 
+
+ align:start position:0%
+do is put down places which are I'm
+going to assign indices like this one
+
+ align:start position:0%
+going to assign indices like this one
+ 
+
+ align:start position:0%
+going to assign indices like this one
+over here represents the the index of
+
+ align:start position:0%
+over here represents the the index of
+ 
+
+ align:start position:0%
+over here represents the the index of
+this cell but that pointer that we see
+
+ align:start position:0%
+this cell but that pointer that we see
+ 
+
+ align:start position:0%
+this cell but that pointer that we see
+here is a reference to the pigeon the
+
+ align:start position:0%
+here is a reference to the pigeon the
+ 
+
+ align:start position:0%
+here is a reference to the pigeon the
+pair of pigeon holes and the cars and
+
+ align:start position:0%
+pair of pigeon holes and the cars and
+ 
+
+ align:start position:0%
+pair of pigeon holes and the cars and
+the critters that are labeled by one in
+
+ align:start position:0%
+the critters that are labeled by one in
+ 
+
+ align:start position:0%
+the critters that are labeled by one in
+my linear memory down here so if I wish
+
+ align:start position:0%
+my linear memory down here so if I wish
+ 
+
+ align:start position:0%
+my linear memory down here so if I wish
+to impose this structure on my linear
+
+ align:start position:0%
+to impose this structure on my linear
+ 
+
+ align:start position:0%
+to impose this structure on my linear
+memory what I do is I say oh yes why
+
+ align:start position:0%
+memory what I do is I say oh yes why
+ 
+
+ align:start position:0%
+memory what I do is I say oh yes why
+don't we drop this why we drop this into
+
+ align:start position:0%
+don't we drop this why we drop this into
+ 
+
+ align:start position:0%
+don't we drop this why we drop this into
+cell one as I pick one there's one okay
+
+ align:start position:0%
+cell one as I pick one there's one okay
+ 
+
+ align:start position:0%
+cell one as I pick one there's one okay
+and that says that it's car I'm going to
+
+ align:start position:0%
+and that says that it's car I'm going to
+ 
+
+ align:start position:0%
+and that says that it's car I'm going to
+assign it to be a pair it's a pair which
+
+ align:start position:0%
+assign it to be a pair it's a pair which
+ 
+
+ align:start position:0%
+assign it to be a pair it's a pair which
+is an index five and the cutter which is
+
+ align:start position:0%
+is an index five and the cutter which is
+ 
+
+ align:start position:0%
+is an index five and the cutter which is
+this one over here is a pair which I'm
+
+ align:start position:0%
+this one over here is a pair which I'm
+ 
+
+ align:start position:0%
+this one over here is a pair which I'm
+going to stick into place to p2 and take
+
+ align:start position:0%
+going to stick into place to p2 and take
+ 
+
+ align:start position:0%
+going to stick into place to p2 and take
+a look at p2 oh yes well p2 is a thing
+
+ align:start position:0%
+a look at p2 oh yes well p2 is a thing
+ 
+
+ align:start position:0%
+a look at p2 oh yes well p2 is a thing
+whose car is the number three so that's
+
+ align:start position:0%
+whose car is the number three so that's
+ 
+
+ align:start position:0%
+whose car is the number three so that's
+you see an n3 and who is Qatar over here
+
+ align:start position:0%
+you see an n3 and who is Qatar over here
+ 
+
+ align:start position:0%
+you see an n3 and who is Qatar over here
+is a pair which is lives in place for so
+
+ align:start position:0%
+is a pair which is lives in place for so
+ 
+
+ align:start position:0%
+is a pair which is lives in place for so
+that's what this p4 is p4 is a number
+
+ align:start position:0%
+that's what this p4 is p4 is a number
+ 
+
+ align:start position:0%
+that's what this p4 is p4 is a number
+whose value is 4 in its car and whose
+
+ align:start position:0%
+whose value is 4 in its car and whose
+ 
+
+ align:start position:0%
+whose value is 4 in its car and whose
+cooter is an empty list right there
+
+ align:start position:0%
+cooter is an empty list right there
+ 
+
+ align:start position:0%
+cooter is an empty list right there
+and that ends it so this is this is the
+
+ align:start position:0%
+and that ends it so this is this is the
+ 
+
+ align:start position:0%
+and that ends it so this is this is the
+traditional way of representing this
+
+ align:start position:0%
+traditional way of representing this
+ 
+
+ align:start position:0%
+traditional way of representing this
+kind of binary tree in a in a linear
+
+ align:start position:0%
+kind of binary tree in a in a linear
+ 
+
+ align:start position:0%
+kind of binary tree in a in a linear
+memory now now next question of course
+
+ align:start position:0%
+memory now now next question of course
+ 
+
+ align:start position:0%
+memory now now next question of course
+that we might want to worry about is
+
+ align:start position:0%
+that we might want to worry about is
+ 
+
+ align:start position:0%
+that we might want to worry about is
+just a little bit of implementation that
+
+ align:start position:0%
+just a little bit of implementation that
+ 
+
+ align:start position:0%
+just a little bit of implementation that
+means that when I write procedures of
+
+ align:start position:0%
+means that when I write procedures of
+ 
+
+ align:start position:0%
+means that when I write procedures of
+the form assign assigned a some
+
+ align:start position:0%
+the form assign assigned a some
+ 
+
+ align:start position:0%
+the form assign assigned a some
+procedures lines of register machine
+
+ align:start position:0%
+procedures lines of register machine
+ 
+
+ align:start position:0%
+procedures lines of register machine
+code of the form assigned a the car
+
+ align:start position:0%
+code of the form assigned a the car
+ 
+
+ align:start position:0%
+code of the form assigned a the car
+fetch of B what I really mean is
+
+ align:start position:0%
+fetch of B what I really mean is
+ 
+
+ align:start position:0%
+fetch of B what I really mean is
+something is addressing these addressing
+
+ align:start position:0%
+something is addressing these addressing
+ 
+
+ align:start position:0%
+something is addressing these addressing
+these elements and so whether it's going
+
+ align:start position:0%
+these elements and so whether it's going
+ 
+
+ align:start position:0%
+these elements and so whether it's going
+to think of that as a abbreviation for
+
+ align:start position:0%
+to think of that as a abbreviation for
+ 
+
+ align:start position:0%
+to think of that as a abbreviation for
+it now of course in order to write that
+
+ align:start position:0%
+it now of course in order to write that
+ 
+
+ align:start position:0%
+it now of course in order to write that
+down I'm going to introduce some sort of
+
+ align:start position:0%
+down I'm going to introduce some sort of
+ 
+
+ align:start position:0%
+down I'm going to introduce some sort of
+structure called a vector okay and we're
+
+ align:start position:0%
+structure called a vector okay and we're
+ 
+
+ align:start position:0%
+structure called a vector okay and we're
+gonna have something which you'll
+
+ align:start position:0%
+gonna have something which you'll
+ 
+
+ align:start position:0%
+gonna have something which you'll
+reference a vector just so we can write
+
+ align:start position:0%
+reference a vector just so we can write
+ 
+
+ align:start position:0%
+reference a vector just so we can write
+it down which takes the name of the
+
+ align:start position:0%
+it down which takes the name of the
+ 
+
+ align:start position:0%
+it down which takes the name of the
+vector or the that's the new name is the
+
+ align:start position:0%
+vector or the that's the new name is the
+ 
+
+ align:start position:0%
+vector or the that's the new name is the
+right word which takes the vector and
+
+ align:start position:0%
+right word which takes the vector and
+ 
+
+ align:start position:0%
+right word which takes the vector and
+the an index and I have to have a way of
+
+ align:start position:0%
+the an index and I have to have a way of
+ 
+
+ align:start position:0%
+the an index and I have to have a way of
+setting one of those with something
+
+ align:start position:0%
+setting one of those with something
+ 
+
+ align:start position:0%
+setting one of those with something
+called a vector set I don't really care
+
+ align:start position:0%
+called a vector set I don't really care
+ 
+
+ align:start position:0%
+called a vector set I don't really care
+but let's look for example at then that
+
+ align:start position:0%
+but let's look for example at then that
+ 
+
+ align:start position:0%
+but let's look for example at then that
+kind of implementation of car and cutter
+
+ align:start position:0%
+kind of implementation of car and cutter
+ 
+
+ align:start position:0%
+kind of implementation of car and cutter
+okay so for example if I happen to have
+
+ align:start position:0%
+okay so for example if I happen to have
+ 
+
+ align:start position:0%
+okay so for example if I happen to have
+a register B which contains the index
+
+ align:start position:0%
+a register B which contains the index
+ 
+
+ align:start position:0%
+a register B which contains the index
+the typed index of a pair and therefore
+
+ align:start position:0%
+the typed index of a pair and therefore
+ 
+
+ align:start position:0%
+the typed index of a pair and therefore
+it is the pointer to a pair then I can
+
+ align:start position:0%
+it is the pointer to a pair then I can
+ 
+
+ align:start position:0%
+it is the pointer to a pair then I can
+take the car of that okay and I in fry
+
+ align:start position:0%
+take the car of that okay and I in fry
+ 
+
+ align:start position:0%
+take the car of that okay and I in fry
+it right to stand I might put that in
+
+ align:start position:0%
+it right to stand I might put that in
+ 
+
+ align:start position:0%
+it right to stand I might put that in
+register a what that really is is a
+
+ align:start position:0%
+register a what that really is is a
+ 
+
+ align:start position:0%
+register a what that really is is a
+representation of the the assigned to a
+
+ align:start position:0%
+representation of the the assigned to a
+ 
+
+ align:start position:0%
+representation of the the assigned to a
+the value of vector reffing or array
+
+ align:start position:0%
+the value of vector reffing or array
+ 
+
+ align:start position:0%
+the value of vector reffing or array
+indexing if you will or something the
+
+ align:start position:0%
+indexing if you will or something the
+ 
+
+ align:start position:0%
+indexing if you will or something the
+cars the cars object whatever that is
+
+ align:start position:0%
+cars the cars object whatever that is
+ 
+
+ align:start position:0%
+cars the cars object whatever that is
+with the index B and similarly for Qatar
+
+ align:start position:0%
+with the index B and similarly for Qatar
+ 
+
+ align:start position:0%
+with the index B and similarly for Qatar
+and we can do the same thing for
+
+ align:start position:0%
+and we can do the same thing for
+ 
+
+ align:start position:0%
+and we can do the same thing for
+assignment two data structures if we
+
+ align:start position:0%
+assignment two data structures if we
+ 
+
+ align:start position:0%
+assignment two data structures if we
+need to do that sort of thing at all
+
+ align:start position:0%
+need to do that sort of thing at all
+ 
+
+ align:start position:0%
+need to do that sort of thing at all
+it's not too hard to build that well now
+
+ align:start position:0%
+it's not too hard to build that well now
+ 
+
+ align:start position:0%
+it's not too hard to build that well now
+the next question is how we gonna do
+
+ align:start position:0%
+the next question is how we gonna do
+ 
+
+ align:start position:0%
+the next question is how we gonna do
+allocation I'm every so often I say I
+
+ align:start position:0%
+allocation I'm every so often I say I
+ 
+
+ align:start position:0%
+allocation I'm every so often I say I
+want a cons now Constance don't grow on
+
+ align:start position:0%
+want a cons now Constance don't grow on
+ 
+
+ align:start position:0%
+want a cons now Constance don't grow on
+trees or maybe they should but I act out
+
+ align:start position:0%
+trees or maybe they should but I act out
+ 
+
+ align:start position:0%
+trees or maybe they should but I act out
+some way if I have to have some way of
+
+ align:start position:0%
+some way if I have to have some way of
+ 
+
+ align:start position:0%
+some way if I have to have some way of
+getting next one I have to have some
+
+ align:start position:0%
+getting next one I have to have some
+ 
+
+ align:start position:0%
+getting next one I have to have some
+idea of is there memory that is unused
+
+ align:start position:0%
+idea of is there memory that is unused
+ 
+
+ align:start position:0%
+idea of is there memory that is unused
+but I might want to allocate from and
+
+ align:start position:0%
+but I might want to allocate from and
+ 
+
+ align:start position:0%
+but I might want to allocate from and
+there are many schemes for doing this
+
+ align:start position:0%
+there are many schemes for doing this
+ 
+
+ align:start position:0%
+there are many schemes for doing this
+and the particular thing I'm showing you
+
+ align:start position:0%
+and the particular thing I'm showing you
+ 
+
+ align:start position:0%
+and the particular thing I'm showing you
+right now is not essential however it's
+
+ align:start position:0%
+right now is not essential however it's
+ 
+
+ align:start position:0%
+right now is not essential however it's
+convenient and has been done many times
+
+ align:start position:0%
+convenient and has been done many times
+ 
+
+ align:start position:0%
+convenient and has been done many times
+there's a one schemes called the free
+
+ align:start position:0%
+there's a one schemes called the free
+ 
+
+ align:start position:0%
+there's a one schemes called the free
+list allocation scheme and what that
+
+ align:start position:0%
+list allocation scheme and what that
+ 
+
+ align:start position:0%
+list allocation scheme and what that
+means is that all of the free memory
+
+ align:start position:0%
+means is that all of the free memory
+ 
+
+ align:start position:0%
+means is that all of the free memory
+that there is in the world is linked
+
+ align:start position:0%
+that there is in the world is linked
+ 
+
+ align:start position:0%
+that there is in the world is linked
+together in a linked list just like all
+
+ align:start position:0%
+together in a linked list just like all
+ 
+
+ align:start position:0%
+together in a linked list just like all
+the other stuff and whenever you need a
+
+ align:start position:0%
+the other stuff and whenever you need a
+ 
+
+ align:start position:0%
+the other stuff and whenever you need a
+free cell to make a new cons
+
+ align:start position:0%
+free cell to make a new cons
+ 
+
+ align:start position:0%
+free cell to make a new cons
+you grab the first one make the free
+
+ align:start position:0%
+you grab the first one make the free
+ 
+
+ align:start position:0%
+you grab the first one make the free
+list be the could or of it and then I
+
+ align:start position:0%
+list be the could or of it and then I
+ 
+
+ align:start position:0%
+list be the could or of it and then I
+allocate that and so what that looks
+
+ align:start position:0%
+allocate that and so what that looks
+ 
+
+ align:start position:0%
+allocate that and so what that looks
+like is something like this here we have
+
+ align:start position:0%
+like is something like this here we have
+ 
+
+ align:start position:0%
+like is something like this here we have
+the free list here we have the free list
+
+ align:start position:0%
+the free list here we have the free list
+ 
+
+ align:start position:0%
+the free list here we have the free list
+starting in F in six okay and what that
+
+ align:start position:0%
+starting in F in six okay and what that
+ 
+
+ align:start position:0%
+starting in F in six okay and what that
+is is a pointer off to say 8 so what it
+
+ align:start position:0%
+is is a pointer off to say 8 so what it
+ 
+
+ align:start position:0%
+is is a pointer off to say 8 so what it
+says is this one is free and the next
+
+ align:start position:0%
+says is this one is free and the next
+ 
+
+ align:start position:0%
+says is this one is free and the next
+one is an eight this one is free and the
+
+ align:start position:0%
+one is an eight this one is free and the
+ 
+
+ align:start position:0%
+one is an eight this one is free and the
+next one is in is in three the next one
+
+ align:start position:0%
+next one is in is in three the next one
+ 
+
+ align:start position:0%
+next one is in is in three the next one
+that's free that one's free and the next
+
+ align:start position:0%
+that's free that one's free and the next
+ 
+
+ align:start position:0%
+that's free that one's free and the next
+one is in zero that one's free in the
+
+ align:start position:0%
+one is in zero that one's free in the
+ 
+
+ align:start position:0%
+one is in zero that one's free in the
+next one's in 15 something like that and
+
+ align:start position:0%
+next one's in 15 something like that and
+ 
+
+ align:start position:0%
+next one's in 15 something like that and
+we can imagine having such a structure
+
+ align:start position:0%
+we can imagine having such a structure
+ 
+
+ align:start position:0%
+we can imagine having such a structure
+given that we have something like that
+
+ align:start position:0%
+given that we have something like that
+ 
+
+ align:start position:0%
+given that we have something like that
+then it's possible to just get one when
+
+ align:start position:0%
+then it's possible to just get one when
+ 
+
+ align:start position:0%
+then it's possible to just get one when
+you need it and so a program a program
+
+ align:start position:0%
+you need it and so a program a program
+ 
+
+ align:start position:0%
+you need it and so a program a program
+for doing cons this is what constantly
+
+ align:start position:0%
+for doing cons this is what constantly
+ 
+
+ align:start position:0%
+for doing cons this is what constantly
+turn into to assign to a register a the
+
+ align:start position:0%
+turn into to assign to a register a the
+ 
+
+ align:start position:0%
+turn into to assign to a register a the
+result of Consing the of B onto a see
+
+ align:start position:0%
+result of Consing the of B onto a see
+ 
+
+ align:start position:0%
+result of Consing the of B onto a see
+the value and it's contained beyond and
+
+ align:start position:0%
+the value and it's contained beyond and
+ 
+
+ align:start position:0%
+the value and it's contained beyond and
+the value of contains see what we have
+
+ align:start position:0%
+the value of contains see what we have
+ 
+
+ align:start position:0%
+the value of contains see what we have
+to do is get the current tie a head of
+
+ align:start position:0%
+to do is get the current tie a head of
+ 
+
+ align:start position:0%
+to do is get the current tie a head of
+the free list make the free list B it's
+
+ align:start position:0%
+the free list make the free list B it's
+ 
+
+ align:start position:0%
+the free list make the free list B it's
+could or then we have to change the cars
+
+ align:start position:0%
+could or then we have to change the cars
+ 
+
+ align:start position:0%
+could or then we have to change the cars
+to be the of the the thing we're making
+
+ align:start position:0%
+to be the of the the thing we're making
+ 
+
+ align:start position:0%
+to be the of the the thing we're making
+up to be in a to be the B the thing in B
+
+ align:start position:0%
+up to be in a to be the B the thing in B
+ 
+
+ align:start position:0%
+up to be in a to be the B the thing in B
+and we have to make change the Cooter's
+
+ align:start position:0%
+and we have to make change the Cooter's
+ 
+
+ align:start position:0%
+and we have to make change the Cooter's
+of the thing that's in a to be city so
+
+ align:start position:0%
+of the thing that's in a to be city so
+ 
+
+ align:start position:0%
+of the thing that's in a to be city so
+and then what we have an a is the right
+
+ align:start position:0%
+and then what we have an a is the right
+ 
+
+ align:start position:0%
+and then what we have an a is the right
+new frob whatever it is the object that
+
+ align:start position:0%
+new frob whatever it is the object that
+ 
+
+ align:start position:0%
+new frob whatever it is the object that
+we want now one there's a little bit of
+
+ align:start position:0%
+we want now one there's a little bit of
+ 
+
+ align:start position:0%
+we want now one there's a little bit of
+a cheat here that I haven't told you
+
+ align:start position:0%
+a cheat here that I haven't told you
+ 
+
+ align:start position:0%
+a cheat here that I haven't told you
+about which is somewhere around here I
+
+ align:start position:0%
+about which is somewhere around here I
+ 
+
+ align:start position:0%
+about which is somewhere around here I
+haven't set the type of the thing that
+
+ align:start position:0%
+haven't set the type of the thing that
+ 
+
+ align:start position:0%
+haven't set the type of the thing that
+I've the the type of the the thing that
+
+ align:start position:0%
+I've the the type of the the thing that
+ 
+
+ align:start position:0%
+I've the the type of the the thing that
+I'm consoling up to be a pair and I
+
+ align:start position:0%
+I'm consoling up to be a pair and I
+ 
+
+ align:start position:0%
+I'm consoling up to be a pair and I
+ought to so there should be some sort of
+
+ align:start position:0%
+ought to so there should be some sort of
+ 
+
+ align:start position:0%
+ought to so there should be some sort of
+bits here are being set and I just
+
+ align:start position:0%
+bits here are being set and I just
+ 
+
+ align:start position:0%
+bits here are being set and I just
+haven't written that down we could have
+
+ align:start position:0%
+haven't written that down we could have
+ 
+
+ align:start position:0%
+haven't written that down we could have
+arranged it of course for the free list
+
+ align:start position:0%
+arranged it of course for the free list
+ 
+
+ align:start position:0%
+arranged it of course for the free list
+to be made out of pairs and so then
+
+ align:start position:0%
+to be made out of pairs and so then
+ 
+
+ align:start position:0%
+to be made out of pairs and so then
+there's no problem with that but that's
+
+ align:start position:0%
+there's no problem with that but that's
+ 
+
+ align:start position:0%
+there's no problem with that but that's
+sort of again an essential detail of the
+
+ align:start position:0%
+sort of again an essential detail of the
+ 
+
+ align:start position:0%
+sort of again an essential detail of the
+way the way some particular programmer
+
+ align:start position:0%
+way the way some particular programmer
+ 
+
+ align:start position:0%
+way the way some particular programmer
+or architect or whatever might
+
+ align:start position:0%
+or architect or whatever might
+ 
+
+ align:start position:0%
+or architect or whatever might
+manufacture his machine or or a lisp
+
+ align:start position:0%
+manufacture his machine or or a lisp
+ 
+
+ align:start position:0%
+manufacture his machine or or a lisp
+system so for example just looking at
+
+ align:start position:0%
+system so for example just looking at
+ 
+
+ align:start position:0%
+system so for example just looking at
+this to allocate the allocate given that
+
+ align:start position:0%
+this to allocate the allocate given that
+ 
+
+ align:start position:0%
+this to allocate the allocate given that
+I had already the structure that I that
+
+ align:start position:0%
+I had already the structure that I that
+ 
+
+ align:start position:0%
+I had already the structure that I that
+you saw before
+
+ align:start position:0%
+you saw before
+ 
+
+ align:start position:0%
+you saw before
+supposing I wanted to allocate a new a
+
+ align:start position:0%
+supposing I wanted to allocate a new a
+ 
+
+ align:start position:0%
+supposing I wanted to allocate a new a
+new cell which is going to be
+
+ align:start position:0%
+new cell which is going to be
+ 
+
+ align:start position:0%
+new cell which is going to be
+representation of the list 1 1 2 we're
+
+ align:start position:0%
+representation of the list 1 1 2 we're
+ 
+
+ align:start position:0%
+representation of the list 1 1 2 we're
+already one 2 was the car of the
+
+ align:start position:0%
+already one 2 was the car of the
+ 
+
+ align:start position:0%
+already one 2 was the car of the
+original list we were playing with
+
+ align:start position:0%
+original list we were playing with
+ 
+
+ align:start position:0%
+original list we were playing with
+before well that's not so hard I stored
+
+ align:start position:0%
+before well that's not so hard I stored
+ 
+
+ align:start position:0%
+before well that's not so hard I stored
+that one in 1 so app1 is the
+
+ align:start position:0%
+that one in 1 so app1 is the
+ 
+
+ align:start position:0%
+that one in 1 so app1 is the
+representation of this this is p5 that's
+
+ align:start position:0%
+representation of this this is p5 that's
+ 
+
+ align:start position:0%
+representation of this this is p5 that's
+going to be the cooter of this now we're
+
+ align:start position:0%
+going to be the cooter of this now we're
+ 
+
+ align:start position:0%
+going to be the cooter of this now we're
+going to pull something off the free
+
+ align:start position:0%
+going to pull something off the free
+ 
+
+ align:start position:0%
+going to pull something off the free
+list but remember the free list started
+
+ align:start position:0%
+list but remember the free list started
+ 
+
+ align:start position:0%
+list but remember the free list started
+at 6 the new free list after this
+
+ align:start position:0%
+at 6 the new free list after this
+ 
+
+ align:start position:0%
+at 6 the new free list after this
+allocation is 8 is that a free list
+
+ align:start position:0%
+allocation is 8 is that a free list
+ 
+
+ align:start position:0%
+allocation is 8 is that a free list
+beginning and 8 and of course in 6 now
+
+ align:start position:0%
+beginning and 8 and of course in 6 now
+ 
+
+ align:start position:0%
+beginning and 8 and of course in 6 now
+we have a number 1 which is what we
+
+ align:start position:0%
+we have a number 1 which is what we
+ 
+
+ align:start position:0%
+we have a number 1 which is what we
+wanted with its could or being the pair
+
+ align:start position:0%
+wanted with its could or being the pair
+ 
+
+ align:start position:0%
+wanted with its could or being the pair
+starting in location 5 and that's no big
+
+ align:start position:0%
+starting in location 5 and that's no big
+ 
+
+ align:start position:0%
+starting in location 5 and that's no big
+deal
+
+ align:start position:0%
+deal
+ 
+
+ align:start position:0%
+deal
+so the only the only problem really a
+
+ align:start position:0%
+so the only the only problem really a
+ 
+
+ align:start position:0%
+so the only the only problem really a
+remaining here is well I don't have an
+
+ align:start position:0%
+remaining here is well I don't have an
+ 
+
+ align:start position:0%
+remaining here is well I don't have an
+infinitely large memory I mean if I do
+
+ align:start position:0%
+infinitely large memory I mean if I do
+ 
+
+ align:start position:0%
+infinitely large memory I mean if I do
+this for a little while
+
+ align:start position:0%
+this for a little while
+ 
+
+ align:start position:0%
+this for a little while
+say for example supposing it takes me a
+
+ align:start position:0%
+say for example supposing it takes me a
+ 
+
+ align:start position:0%
+say for example supposing it takes me a
+microsecond to do a conce and if I have
+
+ align:start position:0%
+microsecond to do a conce and if I have
+ 
+
+ align:start position:0%
+microsecond to do a conce and if I have
+a million cons memory then I'm only
+
+ align:start position:0%
+a million cons memory then I'm only
+ 
+
+ align:start position:0%
+a million cons memory then I'm only
+going to run out in a second and that's
+
+ align:start position:0%
+going to run out in a second and that's
+ 
+
+ align:start position:0%
+going to run out in a second and that's
+pretty bad
+
+ align:start position:0%
+pretty bad
+ 
+
+ align:start position:0%
+pretty bad
+so what we do but to prevent that
+
+ align:start position:0%
+so what we do but to prevent that
+ 
+
+ align:start position:0%
+so what we do but to prevent that
+disaster the ecological disaster talk
+
+ align:start position:0%
+disaster the ecological disaster talk
+ 
+
+ align:start position:0%
+disaster the ecological disaster talk
+about right after questions are there
+
+ align:start position:0%
+about right after questions are there
+ 
+
+ align:start position:0%
+about right after questions are there
+any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes in the environment diagrams that we
+
+ align:start position:0%
+yes in the environment diagrams that we
+ 
+
+ align:start position:0%
+yes in the environment diagrams that we
+were drawing you know we would use the
+
+ align:start position:0%
+were drawing you know we would use the
+ 
+
+ align:start position:0%
+were drawing you know we would use the
+body of procedures and you would
+
+ align:start position:0%
+body of procedures and you would
+ 
+
+ align:start position:0%
+body of procedures and you would
+eventually wind up with things that were
+
+ align:start position:0%
+eventually wind up with things that were
+ 
+
+ align:start position:0%
+eventually wind up with things that were
+no longer useful in that structure yes
+
+ align:start position:0%
+no longer useful in that structure yes
+ 
+
+ align:start position:0%
+no longer useful in that structure yes
+ma'am
+
+ align:start position:0%
+ma'am
+ 
+
+ align:start position:0%
+ma'am
+how does how is that represented
+
+ align:start position:0%
+how does how is that represented
+ 
+
+ align:start position:0%
+how does how is that represented
+problems here okay when you were asking
+
+ align:start position:0%
+problems here okay when you were asking
+ 
+
+ align:start position:0%
+problems here okay when you were asking
+is that material becomes unemployed are
+
+ align:start position:0%
+is that material becomes unemployed are
+ 
+
+ align:start position:0%
+is that material becomes unemployed are
+you slit we'll talk about that a second
+
+ align:start position:0%
+you slit we'll talk about that a second
+ 
+
+ align:start position:0%
+you slit we'll talk about that a second
+that has to do with how to prevent eka
+
+ align:start position:0%
+that has to do with how to prevent eka
+ 
+
+ align:start position:0%
+that has to do with how to prevent eka
+logical disasters right if I make a lot
+
+ align:start position:0%
+logical disasters right if I make a lot
+ 
+
+ align:start position:0%
+logical disasters right if I make a lot
+of garbage I have to somehow be able to
+
+ align:start position:0%
+of garbage I have to somehow be able to
+ 
+
+ align:start position:0%
+of garbage I have to somehow be able to
+clean up after myself and we'll talk
+
+ align:start position:0%
+clean up after myself and we'll talk
+ 
+
+ align:start position:0%
+clean up after myself and we'll talk
+about that in a second
+
+ align:start position:0%
+about that in a second
+ 
+
+ align:start position:0%
+about that in a second
+the other question you're asking is how
+
+ align:start position:0%
+the other question you're asking is how
+ 
+
+ align:start position:0%
+the other question you're asking is how
+you represent the environments I think
+
+ align:start position:0%
+you represent the environments I think
+ 
+
+ align:start position:0%
+you represent the environments I think
+okay and the environment structures can
+
+ align:start position:0%
+okay and the environment structures can
+ 
+
+ align:start position:0%
+okay and the environment structures can
+be represented in arbitrary ways there
+
+ align:start position:0%
+be represented in arbitrary ways there
+ 
+
+ align:start position:0%
+be represented in arbitrary ways there
+are lots of them I mean here I'm just
+
+ align:start position:0%
+are lots of them I mean here I'm just
+ 
+
+ align:start position:0%
+are lots of them I mean here I'm just
+telling you about list cells of course
+
+ align:start position:0%
+telling you about list cells of course
+ 
+
+ align:start position:0%
+telling you about list cells of course
+every real system has vectors of
+
+ align:start position:0%
+every real system has vectors of
+ 
+
+ align:start position:0%
+every real system has vectors of
+arbitrary length as well as the vectors
+
+ align:start position:0%
+arbitrary length as well as the vectors
+ 
+
+ align:start position:0%
+arbitrary length as well as the vectors
+of length two which represent list cells
+
+ align:start position:0%
+of length two which represent list cells
+ 
+
+ align:start position:0%
+of length two which represent list cells
+and the environment structures that one
+
+ align:start position:0%
+and the environment structures that one
+ 
+
+ align:start position:0%
+and the environment structures that one
+uses in a in a professionally written
+
+ align:start position:0%
+uses in a in a professionally written
+ 
+
+ align:start position:0%
+uses in a in a professionally written
+Lisp system tend to be vectors which
+
+ align:start position:0%
+Lisp system tend to be vectors which
+ 
+
+ align:start position:0%
+Lisp system tend to be vectors which
+contain a number of elements
+
+ align:start position:0%
+contain a number of elements
+ 
+
+ align:start position:0%
+contain a number of elements
+approximately equal to the number of
+
+ align:start position:0%
+approximately equal to the number of
+ 
+
+ align:start position:0%
+approximately equal to the number of
+arguments a little bit more because
+
+ align:start position:0%
+arguments a little bit more because
+ 
+
+ align:start position:0%
+arguments a little bit more because
+because you need certain glue okay and
+
+ align:start position:0%
+because you need certain glue okay and
+ 
+
+ align:start position:0%
+because you need certain glue okay and
+that so you remember the environment
+
+ align:start position:0%
+that so you remember the environment
+ 
+
+ align:start position:0%
+that so you remember the environment
+amended frames the frames are
+
+ align:start position:0%
+amended frames the frames are
+ 
+
+ align:start position:0%
+amended frames the frames are
+constructed by applying a procedure in
+
+ align:start position:0%
+constructed by applying a procedure in
+ 
+
+ align:start position:0%
+constructed by applying a procedure in
+doing so an allocation is made of a
+
+ align:start position:0%
+doing so an allocation is made of a
+ 
+
+ align:start position:0%
+doing so an allocation is made of a
+place which can is the number of
+
+ align:start position:0%
+place which can is the number of
+ 
+
+ align:start position:0%
+place which can is the number of
+arguments long plus some glue that gets
+
+ align:start position:0%
+arguments long plus some glue that gets
+ 
+
+ align:start position:0%
+arguments long plus some glue that gets
+linked into a chain okay just it's just
+
+ align:start position:0%
+linked into a chain okay just it's just
+ 
+
+ align:start position:0%
+linked into a chain okay just it's just
+like Algol at that level there any other
+
+ align:start position:0%
+like Algol at that level there any other
+ 
+
+ align:start position:0%
+like Algol at that level there any other
+questions okay thank you and let's take
+
+ align:start position:0%
+questions okay thank you and let's take
+ 
+
+ align:start position:0%
+questions okay thank you and let's take
+a short break
+
+ align:start position:0%
+a short break
+ 
+
+ align:start position:0%
+a short break
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well as I just said computer memories
+
+ align:start position:0%
+well as I just said computer memories
+ 
+
+ align:start position:0%
+well as I just said computer memories
+supplied by the semiconductor
+
+ align:start position:0%
+supplied by the semiconductor
+ 
+
+ align:start position:0%
+supplied by the semiconductor
+manufacturers are finite and that's
+
+ align:start position:0%
+manufacturers are finite and that's
+ 
+
+ align:start position:0%
+manufacturers are finite and that's
+quite a pity it might not always be that
+
+ align:start position:0%
+quite a pity it might not always be that
+ 
+
+ align:start position:0%
+quite a pity it might not always be that
+way just for a quick calculation you can
+
+ align:start position:0%
+way just for a quick calculation you can
+ 
+
+ align:start position:0%
+way just for a quick calculation you can
+see that it's possible that if memories
+
+ align:start position:0%
+see that it's possible that if memories
+ 
+
+ align:start position:0%
+see that it's possible that if memories
+prices keep going to help the rate
+
+ align:start position:0%
+prices keep going to help the rate
+ 
+
+ align:start position:0%
+prices keep going to help the rate
+they're going that if you took still
+
+ align:start position:0%
+they're going that if you took still
+ 
+
+ align:start position:0%
+they're going that if you took still
+took a microsecond to do a Const then
+
+ align:start position:0%
+took a microsecond to do a Const then
+ 
+
+ align:start position:0%
+took a microsecond to do a Const then
+first of all everybody should know that
+
+ align:start position:0%
+first of all everybody should know that
+ 
+
+ align:start position:0%
+first of all everybody should know that
+there was bad pie times 10 to the 7
+
+ align:start position:0%
+there was bad pie times 10 to the 7
+ 
+
+ align:start position:0%
+there was bad pie times 10 to the 7
+seconds in a year and so that would be
+
+ align:start position:0%
+seconds in a year and so that would be
+ 
+
+ align:start position:0%
+seconds in a year and so that would be
+10 to the seventh plus 10 - 6 - 10 to
+
+ align:start position:0%
+10 to the seventh plus 10 - 6 - 10 to
+ 
+
+ align:start position:0%
+10 to the seventh plus 10 - 6 - 10 to
+the 13th so it's maybe 10 to the 14th
+
+ align:start position:0%
+the 13th so it's maybe 10 to the 14th
+ 
+
+ align:start position:0%
+the 13th so it's maybe 10 to the 14th
+constants in the life of the Machine if
+
+ align:start position:0%
+constants in the life of the Machine if
+ 
+
+ align:start position:0%
+constants in the life of the Machine if
+there was 10 to the 14th words of memory
+
+ align:start position:0%
+there was 10 to the 14th words of memory
+ 
+
+ align:start position:0%
+there was 10 to the 14th words of memory
+on your machine you'd never run out ok
+
+ align:start position:0%
+on your machine you'd never run out ok
+ 
+
+ align:start position:0%
+on your machine you'd never run out ok
+so that would be and that's not
+
+ align:start position:0%
+so that would be and that's not
+ 
+
+ align:start position:0%
+so that would be and that's not
+completely unreasonable 10 to the 14th
+
+ align:start position:0%
+completely unreasonable 10 to the 14th
+ 
+
+ align:start position:0%
+completely unreasonable 10 to the 14th
+is not a very large number ok I'm even
+
+ align:start position:0%
+is not a very large number ok I'm even
+ 
+
+ align:start position:0%
+is not a very large number ok I'm even
+for it I don't think it is but then
+
+ align:start position:0%
+for it I don't think it is but then
+ 
+
+ align:start position:0%
+for it I don't think it is but then
+again I like to play with astronomy so
+
+ align:start position:0%
+again I like to play with astronomy so
+ 
+
+ align:start position:0%
+again I like to play with astronomy so
+it's at least 10 to the 18 centimeters
+
+ align:start position:0%
+it's at least 10 to the 18 centimeters
+ 
+
+ align:start position:0%
+it's at least 10 to the 18 centimeters
+between us and the nearest star but the
+
+ align:start position:0%
+between us and the nearest star but the
+ 
+
+ align:start position:0%
+between us and the nearest star but the
+the thing I'm about to worry about is at
+
+ align:start position:0%
+the thing I'm about to worry about is at
+ 
+
+ align:start position:0%
+the thing I'm about to worry about is at
+least in the current economic state of
+
+ align:start position:0%
+least in the current economic state of
+ 
+
+ align:start position:0%
+least in the current economic state of
+affairs 10 to the 14th pieces of memory
+
+ align:start position:0%
+affairs 10 to the 14th pieces of memory
+ 
+
+ align:start position:0%
+affairs 10 to the 14th pieces of memory
+is expensive and so I suppose that we
+
+ align:start position:0%
+is expensive and so I suppose that we
+ 
+
+ align:start position:0%
+is expensive and so I suppose that we
+have to do is make do with much smaller
+
+ align:start position:0%
+have to do is make do with much smaller
+ 
+
+ align:start position:0%
+have to do is make do with much smaller
+memories now in general we want to have
+
+ align:start position:0%
+memories now in general we want to have
+ 
+
+ align:start position:0%
+memories now in general we want to have
+an illusion of infinity all we need to
+
+ align:start position:0%
+an illusion of infinity all we need to
+ 
+
+ align:start position:0%
+an illusion of infinity all we need to
+do is arrange it so that whenever you
+
+ align:start position:0%
+do is arrange it so that whenever you
+ 
+
+ align:start position:0%
+do is arrange it so that whenever you
+look the thing is there and that's
+
+ align:start position:0%
+look the thing is there and that's
+ 
+
+ align:start position:0%
+look the thing is there and that's
+that's really an important idea a person
+
+ align:start position:0%
+that's really an important idea a person
+ 
+
+ align:start position:0%
+that's really an important idea a person
+or a computer lives only a finite amount
+
+ align:start position:0%
+or a computer lives only a finite amount
+ 
+
+ align:start position:0%
+or a computer lives only a finite amount
+of time and can only take a finite
+
+ align:start position:0%
+of time and can only take a finite
+ 
+
+ align:start position:0%
+of time and can only take a finite
+number of looks at something and so you
+
+ align:start position:0%
+number of looks at something and so you
+ 
+
+ align:start position:0%
+number of looks at something and so you
+really only need a finite amount of
+
+ align:start position:0%
+really only need a finite amount of
+ 
+
+ align:start position:0%
+really only need a finite amount of
+stuff but you have to arrange it so no
+
+ align:start position:0%
+stuff but you have to arrange it so no
+ 
+
+ align:start position:0%
+stuff but you have to arrange it so no
+matter how much there is that your momís
+
+ align:start position:0%
+matter how much there is that your momís
+ 
+
+ align:start position:0%
+matter how much there is that your momís
+you really claim there is there's always
+
+ align:start position:0%
+you really claim there is there's always
+ 
+
+ align:start position:0%
+you really claim there is there's always
+enough stuff so that when you make a
+
+ align:start position:0%
+enough stuff so that when you make a
+ 
+
+ align:start position:0%
+enough stuff so that when you make a
+look it's there and so you'll need to
+
+ align:start position:0%
+look it's there and so you'll need to
+ 
+
+ align:start position:0%
+look it's there and so you'll need to
+find an amount but let's let's see one
+
+ align:start position:0%
+find an amount but let's let's see one
+ 
+
+ align:start position:0%
+find an amount but let's let's see one
+problem is as was brought up that there
+
+ align:start position:0%
+problem is as was brought up that there
+ 
+
+ align:start position:0%
+problem is as was brought up that there
+are possible ways that that there are
+
+ align:start position:0%
+are possible ways that that there are
+ 
+
+ align:start position:0%
+are possible ways that that there are
+lots of stuff that we make that we don't
+
+ align:start position:0%
+lots of stuff that we make that we don't
+ 
+
+ align:start position:0%
+lots of stuff that we make that we don't
+need and we could recycle the material
+
+ align:start position:0%
+need and we could recycle the material
+ 
+
+ align:start position:0%
+need and we could recycle the material
+on which it's made an example
+
+ align:start position:0%
+on which it's made an example
+ 
+
+ align:start position:0%
+on which it's made an example
+for is the fact that when we were
+
+ align:start position:0%
+for is the fact that when we were
+ 
+
+ align:start position:0%
+for is the fact that when we were
+building environment structures and we
+
+ align:start position:0%
+building environment structures and we
+ 
+
+ align:start position:0%
+building environment structures and we
+do so every time we call a procedure we
+
+ align:start position:0%
+do so every time we call a procedure we
+ 
+
+ align:start position:0%
+do so every time we call a procedure we
+in build in a environment frame that
+
+ align:start position:0%
+in build in a environment frame that
+ 
+
+ align:start position:0%
+in build in a environment frame that
+environment frame doesn't necessarily
+
+ align:start position:0%
+environment frame doesn't necessarily
+ 
+
+ align:start position:0%
+environment frame doesn't necessarily
+have a very long lifetime its life time
+
+ align:start position:0%
+have a very long lifetime its life time
+ 
+
+ align:start position:0%
+have a very long lifetime its life time
+meaning its youthfulness may exist only
+
+ align:start position:0%
+meaning its youthfulness may exist only
+ 
+
+ align:start position:0%
+meaning its youthfulness may exist only
+over the the invocation of the procedure
+
+ align:start position:0%
+over the the invocation of the procedure
+ 
+
+ align:start position:0%
+over the the invocation of the procedure
+or if the procedure exports another
+
+ align:start position:0%
+or if the procedure exports another
+ 
+
+ align:start position:0%
+or if the procedure exports another
+procedure by returning it as a value and
+
+ align:start position:0%
+procedure by returning it as a value and
+ 
+
+ align:start position:0%
+procedure by returning it as a value and
+that procedure was defined inside of it
+
+ align:start position:0%
+that procedure was defined inside of it
+ 
+
+ align:start position:0%
+that procedure was defined inside of it
+well then the lifetime of the frame of
+
+ align:start position:0%
+well then the lifetime of the frame of
+ 
+
+ align:start position:0%
+well then the lifetime of the frame of
+the out of procedure still is only the
+
+ align:start position:0%
+the out of procedure still is only the
+ 
+
+ align:start position:0%
+the out of procedure still is only the
+lifetime of the percent of the procedure
+
+ align:start position:0%
+lifetime of the percent of the procedure
+ 
+
+ align:start position:0%
+lifetime of the percent of the procedure
+which was exported and so ultimately a
+
+ align:start position:0%
+which was exported and so ultimately a
+ 
+
+ align:start position:0%
+which was exported and so ultimately a
+lot of that is garbage okay there are
+
+ align:start position:0%
+lot of that is garbage okay there are
+ 
+
+ align:start position:0%
+lot of that is garbage okay there are
+other ways of producing garbage as well
+
+ align:start position:0%
+other ways of producing garbage as well
+ 
+
+ align:start position:0%
+other ways of producing garbage as well
+users produce garbage an example of user
+
+ align:start position:0%
+users produce garbage an example of user
+ 
+
+ align:start position:0%
+users produce garbage an example of user
+garbage is something like this if we
+
+ align:start position:0%
+garbage is something like this if we
+ 
+
+ align:start position:0%
+garbage is something like this if we
+write a program to for example a pen two
+
+ align:start position:0%
+write a program to for example a pen two
+ 
+
+ align:start position:0%
+write a program to for example a pen two
+lists together well one way to do it is
+
+ align:start position:0%
+lists together well one way to do it is
+ 
+
+ align:start position:0%
+lists together well one way to do it is
+to reverse the first list onto the empty
+
+ align:start position:0%
+to reverse the first list onto the empty
+ 
+
+ align:start position:0%
+to reverse the first list onto the empty
+list and reverse that onto the second
+
+ align:start position:0%
+list and reverse that onto the second
+ 
+
+ align:start position:0%
+list and reverse that onto the second
+list now that's not a terribly bad way
+
+ align:start position:0%
+list now that's not a terribly bad way
+ 
+
+ align:start position:0%
+list now that's not a terribly bad way
+of doing it okay and however the
+
+ align:start position:0%
+of doing it okay and however the
+ 
+
+ align:start position:0%
+of doing it okay and however the
+intermediate result which is the
+
+ align:start position:0%
+intermediate result which is the
+ 
+
+ align:start position:0%
+intermediate result which is the
+reversal of the first list as done by
+
+ align:start position:0%
+reversal of the first list as done by
+ 
+
+ align:start position:0%
+reversal of the first list as done by
+this program is never going to be
+
+ align:start position:0%
+this program is never going to be
+ 
+
+ align:start position:0%
+this program is never going to be
+accessed ever again after it's copied
+
+ align:start position:0%
+accessed ever again after it's copied
+ 
+
+ align:start position:0%
+accessed ever again after it's copied
+back onto the second it's an
+
+ align:start position:0%
+back onto the second it's an
+ 
+
+ align:start position:0%
+back onto the second it's an
+intermediate result it's going to be
+
+ align:start position:0%
+intermediate result it's going to be
+ 
+
+ align:start position:0%
+intermediate result it's going to be
+hard to ever see how anybody would ever
+
+ align:start position:0%
+hard to ever see how anybody would ever
+ 
+
+ align:start position:0%
+hard to ever see how anybody would ever
+be able to access it in fact it will go
+
+ align:start position:0%
+be able to access it in fact it will go
+ 
+
+ align:start position:0%
+be able to access it in fact it will go
+away now if we make a lot of garbage
+
+ align:start position:0%
+away now if we make a lot of garbage
+ 
+
+ align:start position:0%
+away now if we make a lot of garbage
+like that and we should be allowed to
+
+ align:start position:0%
+like that and we should be allowed to
+ 
+
+ align:start position:0%
+like that and we should be allowed to
+then there's got to be some way to
+
+ align:start position:0%
+then there's got to be some way to
+ 
+
+ align:start position:0%
+then there's got to be some way to
+reclaim that garbage well what I'd like
+
+ align:start position:0%
+reclaim that garbage well what I'd like
+ 
+
+ align:start position:0%
+reclaim that garbage well what I'd like
+to tell you about now is a very clever
+
+ align:start position:0%
+to tell you about now is a very clever
+ 
+
+ align:start position:0%
+to tell you about now is a very clever
+technique whereby a list system can
+
+ align:start position:0%
+technique whereby a list system can
+ 
+
+ align:start position:0%
+technique whereby a list system can
+prove a small theorem every so often of
+
+ align:start position:0%
+prove a small theorem every so often of
+ 
+
+ align:start position:0%
+prove a small theorem every so often of
+the form the following piece of junk
+
+ align:start position:0%
+the form the following piece of junk
+ 
+
+ align:start position:0%
+the form the following piece of junk
+will never be accessed again it can have
+
+ align:start position:0%
+will never be accessed again it can have
+ 
+
+ align:start position:0%
+will never be accessed again it can have
+no effect on the future of a computation
+
+ align:start position:0%
+no effect on the future of a computation
+ 
+
+ align:start position:0%
+no effect on the future of a computation
+it's actually based on a very simple
+
+ align:start position:0%
+it's actually based on a very simple
+ 
+
+ align:start position:0%
+it's actually based on a very simple
+idea and we've designed our computers to
+
+ align:start position:0%
+idea and we've designed our computers to
+ 
+
+ align:start position:0%
+idea and we've designed our computers to
+look sort of like this there's some data
+
+ align:start position:0%
+look sort of like this there's some data
+ 
+
+ align:start position:0%
+look sort of like this there's some data
+path
+
+ align:start position:0%
+path
+ 
+
+ align:start position:0%
+path
+which contains some registers you know
+
+ align:start position:0%
+which contains some registers you know
+ 
+
+ align:start position:0%
+which contains some registers you know
+with everything's like X and and and Val
+
+ align:start position:0%
+with everything's like X and and and Val
+ 
+
+ align:start position:0%
+with everything's like X and and and Val
+and so on and there's one here called
+
+ align:start position:0%
+and so on and there's one here called
+ 
+
+ align:start position:0%
+and so on and there's one here called
+the stack some sort which points off to
+
+ align:start position:0%
+the stack some sort which points off to
+ 
+
+ align:start position:0%
+the stack some sort which points off to
+a structure somewhere which is the stack
+
+ align:start position:0%
+a structure somewhere which is the stack
+ 
+
+ align:start position:0%
+a structure somewhere which is the stack
+and we'll worry about the second there's
+
+ align:start position:0%
+and we'll worry about the second there's
+ 
+
+ align:start position:0%
+and we'll worry about the second there's
+some finite in the street controller
+
+ align:start position:0%
+some finite in the street controller
+ 
+
+ align:start position:0%
+some finite in the street controller
+finite state machine controller and
+
+ align:start position:0%
+finite state machine controller and
+ 
+
+ align:start position:0%
+finite state machine controller and
+there's some control signals that go
+
+ align:start position:0%
+there's some control signals that go
+ 
+
+ align:start position:0%
+there's some control signals that go
+this way and predicate results that come
+
+ align:start position:0%
+this way and predicate results that come
+ 
+
+ align:start position:0%
+this way and predicate results that come
+this way not the interesting part this
+
+ align:start position:0%
+this way not the interesting part this
+ 
+
+ align:start position:0%
+this way not the interesting part this
+is all there's some some structured
+
+ align:start position:0%
+is all there's some some structured
+ 
+
+ align:start position:0%
+is all there's some some structured
+memory which I just told you how to make
+
+ align:start position:0%
+memory which I just told you how to make
+ 
+
+ align:start position:0%
+memory which I just told you how to make
+which may contain a stack I didn't tell
+
+ align:start position:0%
+which may contain a stack I didn't tell
+ 
+
+ align:start position:0%
+which may contain a stack I didn't tell
+you how to make things of arbitrary
+
+ align:start position:0%
+you how to make things of arbitrary
+ 
+
+ align:start position:0%
+you how to make things of arbitrary
+shape only pairs but in fact with what I
+
+ align:start position:0%
+shape only pairs but in fact with what I
+ 
+
+ align:start position:0%
+shape only pairs but in fact with what I
+told you you could simulate a stack by a
+
+ align:start position:0%
+told you you could simulate a stack by a
+ 
+
+ align:start position:0%
+told you you could simulate a stack by a
+big list I don't plan to do that it's
+
+ align:start position:0%
+big list I don't plan to do that it's
+ 
+
+ align:start position:0%
+big list I don't plan to do that it's
+not a nice way to do it but we could
+
+ align:start position:0%
+not a nice way to do it but we could
+ 
+
+ align:start position:0%
+not a nice way to do it but we could
+might have something like that we have
+
+ align:start position:0%
+might have something like that we have
+ 
+
+ align:start position:0%
+might have something like that we have
+all sorts of little data structures in
+
+ align:start position:0%
+all sorts of little data structures in
+ 
+
+ align:start position:0%
+all sorts of little data structures in
+here you know that are hooked together
+
+ align:start position:0%
+here you know that are hooked together
+ 
+
+ align:start position:0%
+here you know that are hooked together
+in funny ways okay connect to other
+
+ align:start position:0%
+in funny ways okay connect to other
+ 
+
+ align:start position:0%
+in funny ways okay connect to other
+things and so on and ultimately things
+
+ align:start position:0%
+things and so on and ultimately things
+ 
+
+ align:start position:0%
+things and so on and ultimately things
+up there are pointers to these the
+
+ align:start position:0%
+up there are pointers to these the
+ 
+
+ align:start position:0%
+up there are pointers to these the
+things that are in the registers are
+
+ align:start position:0%
+things that are in the registers are
+ 
+
+ align:start position:0%
+things that are in the registers are
+pointers off to the data structures that
+
+ align:start position:0%
+pointers off to the data structures that
+ 
+
+ align:start position:0%
+pointers off to the data structures that
+live in this list structure memory now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the truth of the matter is that the
+
+ align:start position:0%
+the truth of the matter is that the
+ 
+
+ align:start position:0%
+the truth of the matter is that the
+Contin tire consciousness of this
+
+ align:start position:0%
+Contin tire consciousness of this
+ 
+
+ align:start position:0%
+Contin tire consciousness of this
+machine is in these registers okay there
+
+ align:start position:0%
+machine is in these registers okay there
+ 
+
+ align:start position:0%
+machine is in these registers okay there
+is no possible way that the Machine if
+
+ align:start position:0%
+is no possible way that the Machine if
+ 
+
+ align:start position:0%
+is no possible way that the Machine if
+done correctly if built correctly can
+
+ align:start position:0%
+done correctly if built correctly can
+ 
+
+ align:start position:0%
+done correctly if built correctly can
+access anything in this list structure
+
+ align:start position:0%
+access anything in this list structure
+ 
+
+ align:start position:0%
+access anything in this list structure
+memory unless the thing in that list
+
+ align:start position:0%
+memory unless the thing in that list
+ 
+
+ align:start position:0%
+memory unless the thing in that list
+structure memory is is connected by a
+
+ align:start position:0%
+structure memory is is connected by a
+ 
+
+ align:start position:0%
+structure memory is is connected by a
+sequence of data structures to to the
+
+ align:start position:0%
+sequence of data structures to to the
+ 
+
+ align:start position:0%
+sequence of data structures to to the
+registers if it's accessible by
+
+ align:start position:0%
+registers if it's accessible by
+ 
+
+ align:start position:0%
+registers if it's accessible by
+legitimate data structure selectors from
+
+ align:start position:0%
+legitimate data structure selectors from
+ 
+
+ align:start position:0%
+legitimate data structure selectors from
+the pointers that are stored in these
+
+ align:start position:0%
+the pointers that are stored in these
+ 
+
+ align:start position:0%
+the pointers that are stored in these
+registers things like array references
+
+ align:start position:0%
+registers things like array references
+ 
+
+ align:start position:0%
+registers things like array references
+perhaps or cons cell references cars and
+
+ align:start position:0%
+perhaps or cons cell references cars and
+ 
+
+ align:start position:0%
+perhaps or cons cell references cars and
+quitters but I can't just talk about a
+
+ align:start position:0%
+quitters but I can't just talk about a
+ 
+
+ align:start position:0%
+quitters but I can't just talk about a
+random place in this memory because I
+
+ align:start position:0%
+random place in this memory because I
+ 
+
+ align:start position:0%
+random place in this memory because I
+can't get to it these are being
+
+ align:start position:0%
+can't get to it these are being
+ 
+
+ align:start position:0%
+can't get to it these are being
+arbitrary names I'm not allowed to count
+
+ align:start position:0%
+arbitrary names I'm not allowed to count
+ 
+
+ align:start position:0%
+arbitrary names I'm not allowed to count
+okay at least as I'm Val you ating
+
+ align:start position:0%
+okay at least as I'm Val you ating
+ 
+
+ align:start position:0%
+okay at least as I'm Val you ating
+expressions if that's the case okay then
+
+ align:start position:0%
+expressions if that's the case okay then
+ 
+
+ align:start position:0%
+expressions if that's the case okay then
+there's a very simple theorem to be
+
+ align:start position:0%
+there's a very simple theorem to be
+ 
+
+ align:start position:0%
+there's a very simple theorem to be
+proved
+
+ align:start position:0%
+proved
+ 
+
+ align:start position:0%
+proved
+which is if I start with all the weak
+
+ align:start position:0%
+which is if I start with all the weak
+ 
+
+ align:start position:0%
+which is if I start with all the weak
+pointers that are in all these registers
+
+ align:start position:0%
+pointers that are in all these registers
+ 
+
+ align:start position:0%
+pointers that are in all these registers
+and recursively chase out marking all
+
+ align:start position:0%
+and recursively chase out marking all
+ 
+
+ align:start position:0%
+and recursively chase out marking all
+the places I can get to by selectors
+
+ align:start position:0%
+the places I can get to by selectors
+ 
+
+ align:start position:0%
+the places I can get to by selectors
+then eventually I mark everything that
+
+ align:start position:0%
+then eventually I mark everything that
+ 
+
+ align:start position:0%
+then eventually I mark everything that
+can be gotten to
+
+ align:start position:0%
+can be gotten to
+ 
+
+ align:start position:0%
+can be gotten to
+anything which is not so marked is
+
+ align:start position:0%
+anything which is not so marked is
+ 
+
+ align:start position:0%
+anything which is not so marked is
+garbage and can be recycled
+
+ align:start position:0%
+garbage and can be recycled
+ 
+
+ align:start position:0%
+garbage and can be recycled
+very simple cannot affect the future of
+
+ align:start position:0%
+very simple cannot affect the future of
+ 
+
+ align:start position:0%
+very simple cannot affect the future of
+the computation so let me show you that
+
+ align:start position:0%
+the computation so let me show you that
+ 
+
+ align:start position:0%
+the computation so let me show you that
+in that particular in a particular
+
+ align:start position:0%
+in that particular in a particular
+ 
+
+ align:start position:0%
+in that particular in a particular
+example that means I'm going to have to
+
+ align:start position:0%
+example that means I'm going to have to
+ 
+
+ align:start position:0%
+example that means I'm going to have to
+append to my description of the list
+
+ align:start position:0%
+append to my description of the list
+ 
+
+ align:start position:0%
+append to my description of the list
+structure a mark and so here for example
+
+ align:start position:0%
+structure a mark and so here for example
+ 
+
+ align:start position:0%
+structure a mark and so here for example
+is a list ruptured memory and in this
+
+ align:start position:0%
+is a list ruptured memory and in this
+ 
+
+ align:start position:0%
+is a list ruptured memory and in this
+list structured memory is some list
+
+ align:start position:0%
+list structured memory is some list
+ 
+
+ align:start position:0%
+list structured memory is some list
+structure beginning at a place I'm going
+
+ align:start position:0%
+structure beginning at a place I'm going
+ 
+
+ align:start position:0%
+structure beginning at a place I'm going
+to call this is the root now it doesn't
+
+ align:start position:0%
+to call this is the root now it doesn't
+ 
+
+ align:start position:0%
+to call this is the root now it doesn't
+really have to have a root it could be a
+
+ align:start position:0%
+really have to have a root it could be a
+ 
+
+ align:start position:0%
+really have to have a root it could be a
+bunch of them like all the registers
+
+ align:start position:0%
+bunch of them like all the registers
+ 
+
+ align:start position:0%
+bunch of them like all the registers
+well I could cleverly arranged it so all
+
+ align:start position:0%
+well I could cleverly arranged it so all
+ 
+
+ align:start position:0%
+well I could cleverly arranged it so all
+the registers all the things that run
+
+ align:start position:0%
+the registers all the things that run
+ 
+
+ align:start position:0%
+the registers all the things that run
+all the registers are also at the right
+
+ align:start position:0%
+all the registers are also at the right
+ 
+
+ align:start position:0%
+all the registers are also at the right
+moment put into this into this root
+
+ align:start position:0%
+moment put into this into this root
+ 
+
+ align:start position:0%
+moment put into this into this root
+structure and then we got one pointer to
+
+ align:start position:0%
+structure and then we got one pointer to
+ 
+
+ align:start position:0%
+structure and then we got one pointer to
+it I don't really care so the idea is
+
+ align:start position:0%
+it I don't really care so the idea is
+ 
+
+ align:start position:0%
+it I don't really care so the idea is
+we're going to concept stuff until
+
+ align:start position:0%
+we're going to concept stuff until
+ 
+
+ align:start position:0%
+we're going to concept stuff until
+though our free list is empty we've run
+
+ align:start position:0%
+though our free list is empty we've run
+ 
+
+ align:start position:0%
+though our free list is empty we've run
+out of things now we're going to do this
+
+ align:start position:0%
+out of things now we're going to do this
+ 
+
+ align:start position:0%
+out of things now we're going to do this
+process of proving the theorem that a
+
+ align:start position:0%
+process of proving the theorem that a
+ 
+
+ align:start position:0%
+process of proving the theorem that a
+certain percentage of the memory is got
+
+ align:start position:0%
+certain percentage of the memory is got
+ 
+
+ align:start position:0%
+certain percentage of the memory is got
+crap in it and then we recycle that to
+
+ align:start position:0%
+crap in it and then we recycle that to
+ 
+
+ align:start position:0%
+crap in it and then we recycle that to
+grow new trees a standard use of of such
+
+ align:start position:0%
+grow new trees a standard use of of such
+ 
+
+ align:start position:0%
+grow new trees a standard use of of such
+garbage so in any case what do we have
+
+ align:start position:0%
+garbage so in any case what do we have
+ 
+
+ align:start position:0%
+garbage so in any case what do we have
+here well we have some data structure
+
+ align:start position:0%
+here well we have some data structure
+ 
+
+ align:start position:0%
+here well we have some data structure
+which starts out over here in p5 and
+
+ align:start position:0%
+which starts out over here in p5 and
+ 
+
+ align:start position:0%
+which starts out over here in p5 and
+well sorry starts out in 1 and in fact
+
+ align:start position:0%
+well sorry starts out in 1 and in fact
+ 
+
+ align:start position:0%
+well sorry starts out in 1 and in fact
+it it has a car in P + 5 and it scooter
+
+ align:start position:0%
+it it has a car in P + 5 and it scooter
+ 
+
+ align:start position:0%
+it it has a car in P + 5 and it scooter
+is in 2 and all the marks start out at 0
+
+ align:start position:0%
+is in 2 and all the marks start out at 0
+ 
+
+ align:start position:0%
+is in 2 and all the marks start out at 0
+let's start marking just to play this
+
+ align:start position:0%
+let's start marking just to play this
+ 
+
+ align:start position:0%
+let's start marking just to play this
+game ok so for example so the pen side
+
+ align:start position:0%
+game ok so for example so the pen side
+ 
+
+ align:start position:0%
+game ok so for example so the pen side
+can assess one from the root I will mark
+
+ align:start position:0%
+can assess one from the root I will mark
+ 
+
+ align:start position:0%
+can assess one from the root I will mark
+that let me mark it
+
+ align:start position:0%
+that let me mark it
+ 
+
+ align:start position:0%
+that let me mark it
+bang okay so that's marked okay now
+
+ align:start position:0%
+bang okay so that's marked okay now
+ 
+
+ align:start position:0%
+bang okay so that's marked okay now
+since I can since I have a five year I
+
+ align:start position:0%
+since I can since I have a five year I
+ 
+
+ align:start position:0%
+since I can since I have a five year I
+can go to five and see well marked that
+
+ align:start position:0%
+can go to five and see well marked that
+ 
+
+ align:start position:0%
+can go to five and see well marked that
+bang that's useful stuff but five
+
+ align:start position:0%
+bang that's useful stuff but five
+ 
+
+ align:start position:0%
+bang that's useful stuff but five
+references as a number in its car I'm
+
+ align:start position:0%
+references as a number in its car I'm
+ 
+
+ align:start position:0%
+references as a number in its car I'm
+not interested in marking numbers but
+
+ align:start position:0%
+not interested in marking numbers but
+ 
+
+ align:start position:0%
+not interested in marking numbers but
+it's could or seven so I can mark that
+
+ align:start position:0%
+it's could or seven so I can mark that
+ 
+
+ align:start position:0%
+it's could or seven so I can mark that
+bang okay seven is the empty list all
+
+ align:start position:0%
+bang okay seven is the empty list all
+ 
+
+ align:start position:0%
+bang okay seven is the empty list all
+the only thing at references and it's
+
+ align:start position:0%
+the only thing at references and it's
+ 
+
+ align:start position:0%
+the only thing at references and it's
+got a number in its car not interesting
+
+ align:start position:0%
+got a number in its car not interesting
+ 
+
+ align:start position:0%
+got a number in its car not interesting
+okay well now let's go back here I
+
+ align:start position:0%
+okay well now let's go back here I
+ 
+
+ align:start position:0%
+okay well now let's go back here I
+forgot about something to see in other
+
+ align:start position:0%
+forgot about something to see in other
+ 
+
+ align:start position:0%
+forgot about something to see in other
+words if I'm looking at cell one cell
+
+ align:start position:0%
+words if I'm looking at cell one cell
+ 
+
+ align:start position:0%
+words if I'm looking at cell one cell
+one contains a contains a two right over
+
+ align:start position:0%
+one contains a contains a two right over
+ 
+
+ align:start position:0%
+one contains a contains a two right over
+here of reference to two that means I
+
+ align:start position:0%
+here of reference to two that means I
+ 
+
+ align:start position:0%
+here of reference to two that means I
+should go mark mark to bang to contains
+
+ align:start position:0%
+should go mark mark to bang to contains
+ 
+
+ align:start position:0%
+should go mark mark to bang to contains
+a reference to four it's got a number in
+
+ align:start position:0%
+a reference to four it's got a number in
+ 
+
+ align:start position:0%
+a reference to four it's got a number in
+its car I'm not interested in that so
+
+ align:start position:0%
+its car I'm not interested in that so
+ 
+
+ align:start position:0%
+its car I'm not interested in that so
+I'm going to go and walk that for all
+
+ align:start position:0%
+I'm going to go and walk that for all
+ 
+
+ align:start position:0%
+I'm going to go and walk that for all
+refers to seven through its car and
+
+ align:start position:0%
+refers to seven through its car and
+ 
+
+ align:start position:0%
+refers to seven through its car and
+there's the attempting that's could er
+
+ align:start position:0%
+there's the attempting that's could er
+ 
+
+ align:start position:0%
+there's the attempting that's could er
+but I've already marked that one so I
+
+ align:start position:0%
+but I've already marked that one so I
+ 
+
+ align:start position:0%
+but I've already marked that one so I
+don't have the market again this is all
+
+ align:start position:0%
+don't have the market again this is all
+ 
+
+ align:start position:0%
+don't have the market again this is all
+the accessible structure from that place
+
+ align:start position:0%
+the accessible structure from that place
+ 
+
+ align:start position:0%
+the accessible structure from that place
+simple recursive mark algorithm now
+
+ align:start position:0%
+simple recursive mark algorithm now
+ 
+
+ align:start position:0%
+simple recursive mark algorithm now
+there are some unhappiness is about that
+
+ align:start position:0%
+there are some unhappiness is about that
+ 
+
+ align:start position:0%
+there are some unhappiness is about that
+algorithm and we can worry about that in
+
+ align:start position:0%
+algorithm and we can worry about that in
+ 
+
+ align:start position:0%
+algorithm and we can worry about that in
+a second but basically you'll see that
+
+ align:start position:0%
+a second but basically you'll see that
+ 
+
+ align:start position:0%
+a second but basically you'll see that
+all the things that have not been marked
+
+ align:start position:0%
+all the things that have not been marked
+ 
+
+ align:start position:0%
+all the things that have not been marked
+are our places that are free and I could
+
+ align:start position:0%
+are our places that are free and I could
+ 
+
+ align:start position:0%
+are our places that are free and I could
+recycle so the next stage after that is
+
+ align:start position:0%
+recycle so the next stage after that is
+ 
+
+ align:start position:0%
+recycle so the next stage after that is
+going to be scan through all of my
+
+ align:start position:0%
+going to be scan through all of my
+ 
+
+ align:start position:0%
+going to be scan through all of my
+memory looking for looking for things
+
+ align:start position:0%
+memory looking for looking for things
+ 
+
+ align:start position:0%
+memory looking for looking for things
+that are not marked every time I come
+
+ align:start position:0%
+that are not marked every time I come
+ 
+
+ align:start position:0%
+that are not marked every time I come
+across a marketing I unmarked it and
+
+ align:start position:0%
+across a marketing I unmarked it and
+ 
+
+ align:start position:0%
+across a marketing I unmarked it and
+every time I come across an unmarked
+
+ align:start position:0%
+every time I come across an unmarked
+ 
+
+ align:start position:0%
+every time I come across an unmarked
+thing I'm going to link it together into
+
+ align:start position:0%
+thing I'm going to link it together into
+ 
+
+ align:start position:0%
+thing I'm going to link it together into
+my free list classic very simple
+
+ align:start position:0%
+my free list classic very simple
+ 
+
+ align:start position:0%
+my free list classic very simple
+algorithm so let's see is that very
+
+ align:start position:0%
+algorithm so let's see is that very
+ 
+
+ align:start position:0%
+algorithm so let's see is that very
+simple yes it is I'm not going to go
+
+ align:start position:0%
+simple yes it is I'm not going to go
+ 
+
+ align:start position:0%
+simple yes it is I'm not going to go
+through the code in any detail but I
+
+ align:start position:0%
+through the code in any detail but I
+ 
+
+ align:start position:0%
+through the code in any detail but I
+just want to show you about how long it
+
+ align:start position:0%
+just want to show you about how long it
+ 
+
+ align:start position:0%
+just want to show you about how long it
+is let's look at the mark phase here's
+
+ align:start position:0%
+is let's look at the mark phase here's
+ 
+
+ align:start position:0%
+is let's look at the mark phase here's
+the first here's the first part of the
+
+ align:start position:0%
+the first here's the first part of the
+ 
+
+ align:start position:0%
+the first here's the first part of the
+mark phase we pick up the route we're
+
+ align:start position:0%
+mark phase we pick up the route we're
+ 
+
+ align:start position:0%
+mark phase we pick up the route we're
+going to have to do some we're going to
+
+ align:start position:0%
+going to have to do some we're going to
+ 
+
+ align:start position:0%
+going to have to do some we're going to
+use that as a recursive procedure call
+
+ align:start position:0%
+use that as a recursive procedure call
+ 
+
+ align:start position:0%
+use that as a recursive procedure call
+we're going to sweep from there after
+
+ align:start position:0%
+we're going to sweep from there after
+ 
+
+ align:start position:0%
+we're going to sweep from there after
+when we're done with marking and then
+
+ align:start position:0%
+when we're done with marking and then
+ 
+
+ align:start position:0%
+when we're done with marking and then
+we're going to do a little a couple of
+
+ align:start position:0%
+we're going to do a little a couple of
+ 
+
+ align:start position:0%
+we're going to do a little a couple of
+instructions that do this checking out
+
+ align:start position:0%
+instructions that do this checking out
+ 
+
+ align:start position:0%
+instructions that do this checking out
+of the marks and changing the marks and
+
+ align:start position:0%
+of the marks and changing the marks and
+ 
+
+ align:start position:0%
+of the marks and changing the marks and
+things like that according to the
+
+ align:start position:0%
+things like that according to the
+ 
+
+ align:start position:0%
+things like that according to the
+algorithm I
+
+ align:start position:0%
+algorithm I
+ 
+
+ align:start position:0%
+algorithm I
+just shown you okay it comes out here
+
+ align:start position:0%
+just shown you okay it comes out here
+ 
+
+ align:start position:0%
+just shown you okay it comes out here
+you have to mark the cars of things and
+
+ align:start position:0%
+you have to mark the cars of things and
+ 
+
+ align:start position:0%
+you have to mark the cars of things and
+you also have to be able to mark the
+
+ align:start position:0%
+you also have to be able to mark the
+ 
+
+ align:start position:0%
+you also have to be able to mark the
+Cooter's of things that's the entire
+
+ align:start position:0%
+Cooter's of things that's the entire
+ 
+
+ align:start position:0%
+Cooter's of things that's the entire
+mark face now I'm going to tell you a
+
+ align:start position:0%
+mark face now I'm going to tell you a
+ 
+
+ align:start position:0%
+mark face now I'm going to tell you a
+little story about this the old deck PDP
+
+ align:start position:0%
+little story about this the old deck PDP
+ 
+
+ align:start position:0%
+little story about this the old deck PDP
+six computer this was the way that the
+
+ align:start position:0%
+six computer this was the way that the
+ 
+
+ align:start position:0%
+six computer this was the way that the
+mark sweet garbage collectors it was was
+
+ align:start position:0%
+mark sweet garbage collectors it was was
+ 
+
+ align:start position:0%
+mark sweet garbage collectors it was was
+written the program was so small that
+
+ align:start position:0%
+written the program was so small that
+ 
+
+ align:start position:0%
+written the program was so small that
+with the data that it read they needed
+
+ align:start position:0%
+with the data that it read they needed
+ 
+
+ align:start position:0%
+with the data that it read they needed
+with the registers that needed to
+
+ align:start position:0%
+with the registers that needed to
+ 
+
+ align:start position:0%
+with the registers that needed to
+manipulate the memory it fit into the
+
+ align:start position:0%
+manipulate the memory it fit into the
+ 
+
+ align:start position:0%
+manipulate the memory it fit into the
+fast registers of the machine which were
+
+ align:start position:0%
+fast registers of the machine which were
+ 
+
+ align:start position:0%
+fast registers of the machine which were
+16 the whole program and you could
+
+ align:start position:0%
+16 the whole program and you could
+ 
+
+ align:start position:0%
+16 the whole program and you could
+execute instructions and the fast
+
+ align:start position:0%
+execute instructions and the fast
+ 
+
+ align:start position:0%
+execute instructions and the fast
+registers so there's an extremely small
+
+ align:start position:0%
+registers so there's an extremely small
+ 
+
+ align:start position:0%
+registers so there's an extremely small
+program and you could run very fast
+
+ align:start position:0%
+program and you could run very fast
+ 
+
+ align:start position:0%
+program and you could run very fast
+now unfortunately of course this program
+
+ align:start position:0%
+now unfortunately of course this program
+ 
+
+ align:start position:0%
+now unfortunately of course this program
+because of the fact that it's recursive
+
+ align:start position:0%
+because of the fact that it's recursive
+ 
+
+ align:start position:0%
+because of the fact that it's recursive
+in the way that in the way that you do
+
+ align:start position:0%
+in the way that in the way that you do
+ 
+
+ align:start position:0%
+in the way that in the way that you do
+something first and then you do
+
+ align:start position:0%
+something first and then you do
+ 
+
+ align:start position:0%
+something first and then you do
+something after that you have to work on
+
+ align:start position:0%
+something after that you have to work on
+ 
+
+ align:start position:0%
+something after that you have to work on
+the cars and then the cutters it
+
+ align:start position:0%
+the cars and then the cutters it
+ 
+
+ align:start position:0%
+the cars and then the cutters it
+requires auxiliary memory so solicit
+
+ align:start position:0%
+requires auxiliary memory so solicit
+ 
+
+ align:start position:0%
+requires auxiliary memory so solicit
+Lisp systems you know those requires and
+
+ align:start position:0%
+Lisp systems you know those requires and
+ 
+
+ align:start position:0%
+Lisp systems you know those requires and
+stack for mocking Lisp systems that are
+
+ align:start position:0%
+stack for mocking Lisp systems that are
+ 
+
+ align:start position:0%
+stack for mocking Lisp systems that are
+built this way have a limit to the depth
+
+ align:start position:0%
+built this way have a limit to the depth
+ 
+
+ align:start position:0%
+built this way have a limit to the depth
+of recursion you can have in data
+
+ align:start position:0%
+of recursion you can have in data
+ 
+
+ align:start position:0%
+of recursion you can have in data
+structures in either the car or the
+
+ align:start position:0%
+structures in either the car or the
+ 
+
+ align:start position:0%
+structures in either the car or the
+cutter and that doesn't work very nicely
+
+ align:start position:0%
+cutter and that doesn't work very nicely
+ 
+
+ align:start position:0%
+cutter and that doesn't work very nicely
+on the other hand you never notice it if
+
+ align:start position:0%
+on the other hand you never notice it if
+ 
+
+ align:start position:0%
+on the other hand you never notice it if
+it's big enough and that certainly been
+
+ align:start position:0%
+it's big enough and that certainly been
+ 
+
+ align:start position:0%
+it's big enough and that certainly been
+that's certainly been the case for most
+
+ align:start position:0%
+that's certainly been the case for most
+ 
+
+ align:start position:0%
+that's certainly been the case for most
+mac lists for example which ran maxima
+
+ align:start position:0%
+mac lists for example which ran maxima
+ 
+
+ align:start position:0%
+mac lists for example which ran maxima
+where you could deal with expressions of
+
+ align:start position:0%
+where you could deal with expressions of
+ 
+
+ align:start position:0%
+where you could deal with expressions of
+thousands of elements long these are
+
+ align:start position:0%
+thousands of elements long these are
+ 
+
+ align:start position:0%
+thousands of elements long these are
+algebraic expressions with thousands of
+
+ align:start position:0%
+algebraic expressions with thousands of
+ 
+
+ align:start position:0%
+algebraic expressions with thousands of
+terms there's no problem with that such
+
+ align:start position:0%
+terms there's no problem with that such
+ 
+
+ align:start position:0%
+terms there's no problem with that such
+the garbage collector does work on the
+
+ align:start position:0%
+the garbage collector does work on the
+ 
+
+ align:start position:0%
+the garbage collector does work on the
+other hand is a very clever modification
+
+ align:start position:0%
+other hand is a very clever modification
+ 
+
+ align:start position:0%
+other hand is a very clever modification
+to this algorithm which i will not
+
+ align:start position:0%
+to this algorithm which i will not
+ 
+
+ align:start position:0%
+to this algorithm which i will not
+describe by Peter Deutsch and Shore and
+
+ align:start position:0%
+describe by Peter Deutsch and Shore and
+ 
+
+ align:start position:0%
+describe by Peter Deutsch and Shore and
+waste herbs or from IBM and wait who I
+
+ align:start position:0%
+waste herbs or from IBM and wait who I
+ 
+
+ align:start position:0%
+waste herbs or from IBM and wait who I
+don't know where that out that algorithm
+
+ align:start position:0%
+don't know where that out that algorithm
+ 
+
+ align:start position:0%
+don't know where that out that algorithm
+allows you to build you can do this
+
+ align:start position:0%
+allows you to build you can do this
+ 
+
+ align:start position:0%
+allows you to build you can do this
+without auxiliary memory by remembering
+
+ align:start position:0%
+without auxiliary memory by remembering
+ 
+
+ align:start position:0%
+without auxiliary memory by remembering
+as you walk the data structures where
+
+ align:start position:0%
+as you walk the data structures where
+ 
+
+ align:start position:0%
+as you walk the data structures where
+you came from by reversing the pointers
+
+ align:start position:0%
+you came from by reversing the pointers
+ 
+
+ align:start position:0%
+you came from by reversing the pointers
+as you go down and crawling up the
+
+ align:start position:0%
+as you go down and crawling up the
+ 
+
+ align:start position:0%
+as you go down and crawling up the
+reverse pointers as you go up to rather
+
+ align:start position:0%
+reverse pointers as you go up to rather
+ 
+
+ align:start position:0%
+reverse pointers as you go up to rather
+tricky algorithm the first time you
+
+ align:start position:0%
+tricky algorithm the first time you
+ 
+
+ align:start position:0%
+tricky algorithm the first time you
+write it back to three first three times
+
+ align:start position:0%
+write it back to three first three times
+ 
+
+ align:start position:0%
+write it back to three first three times
+you write it has a terrible bug in it
+
+ align:start position:0%
+you write it has a terrible bug in it
+ 
+
+ align:start position:0%
+you write it has a terrible bug in it
+and it's also about square rather slow
+
+ align:start position:0%
+and it's also about square rather slow
+ 
+
+ align:start position:0%
+and it's also about square rather slow
+because it's complicated it takes about
+
+ align:start position:0%
+because it's complicated it takes about
+ 
+
+ align:start position:0%
+because it's complicated it takes about
+six times as many rare memory references
+
+ align:start position:0%
+six times as many rare memory references
+ 
+
+ align:start position:0%
+six times as many rare memory references
+to do the sorts of things that we're
+
+ align:start position:0%
+to do the sorts of things that we're
+ 
+
+ align:start position:0%
+to do the sorts of things that we're
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+well now once I've done this marking
+
+ align:start position:0%
+well now once I've done this marking
+ 
+
+ align:start position:0%
+well now once I've done this marking
+phase and I get into a position where
+
+ align:start position:0%
+phase and I get into a position where
+ 
+
+ align:start position:0%
+phase and I get into a position where
+things look like this let's look yes
+
+ align:start position:0%
+things look like this let's look yes
+ 
+
+ align:start position:0%
+things look like this let's look yes
+here we have some here we have the mark
+
+ align:start position:0%
+here we have some here we have the mark
+ 
+
+ align:start position:0%
+here we have some here we have the mark
+done just as I did it now we have to
+
+ align:start position:0%
+done just as I did it now we have to
+ 
+
+ align:start position:0%
+done just as I did it now we have to
+perform the sweep phase and I describe
+
+ align:start position:0%
+perform the sweep phase and I describe
+ 
+
+ align:start position:0%
+perform the sweep phase and I describe
+to you what the sweeteners like I'm
+
+ align:start position:0%
+to you what the sweeteners like I'm
+ 
+
+ align:start position:0%
+to you what the sweeteners like I'm
+going to walk down from one end of
+
+ align:start position:0%
+going to walk down from one end of
+ 
+
+ align:start position:0%
+going to walk down from one end of
+memory or the other I don't care we're
+
+ align:start position:0%
+memory or the other I don't care we're
+ 
+
+ align:start position:0%
+memory or the other I don't care we're
+scanning every cell that's in the memory
+
+ align:start position:0%
+scanning every cell that's in the memory
+ 
+
+ align:start position:0%
+scanning every cell that's in the memory
+and as I scan these cells I'm going to
+
+ align:start position:0%
+and as I scan these cells I'm going to
+ 
+
+ align:start position:0%
+and as I scan these cells I'm going to
+link them together if they are free into
+
+ align:start position:0%
+link them together if they are free into
+ 
+
+ align:start position:0%
+link them together if they are free into
+the free list and if they're not free
+
+ align:start position:0%
+the free list and if they're not free
+ 
+
+ align:start position:0%
+the free list and if they're not free
+I'm going to unmarked them so the marks
+
+ align:start position:0%
+I'm going to unmarked them so the marks
+ 
+
+ align:start position:0%
+I'm going to unmarked them so the marks
+become zero and in fact what I get well
+
+ align:start position:0%
+become zero and in fact what I get well
+ 
+
+ align:start position:0%
+become zero and in fact what I get well
+the program is not very complicated it
+
+ align:start position:0%
+the program is not very complicated it
+ 
+
+ align:start position:0%
+the program is not very complicated it
+looks sort of like this it's a little
+
+ align:start position:0%
+looks sort of like this it's a little
+ 
+
+ align:start position:0%
+looks sort of like this it's a little
+longer you're the first piece of it this
+
+ align:start position:0%
+longer you're the first piece of it this
+ 
+
+ align:start position:0%
+longer you're the first piece of it this
+one's coming down from the top of memory
+
+ align:start position:0%
+one's coming down from the top of memory
+ 
+
+ align:start position:0%
+one's coming down from the top of memory
+I don't want you to try to understand
+
+ align:start position:0%
+I don't want you to try to understand
+ 
+
+ align:start position:0%
+I don't want you to try to understand
+this at this point it's rather simple
+
+ align:start position:0%
+this at this point it's rather simple
+ 
+
+ align:start position:0%
+this at this point it's rather simple
+it's a very simple algorithm but there's
+
+ align:start position:0%
+it's a very simple algorithm but there's
+ 
+
+ align:start position:0%
+it's a very simple algorithm but there's
+pieces of it that just sort of look like
+
+ align:start position:0%
+pieces of it that just sort of look like
+ 
+
+ align:start position:0%
+pieces of it that just sort of look like
+this they're all on sort of obvious and
+
+ align:start position:0%
+this they're all on sort of obvious and
+ 
+
+ align:start position:0%
+this they're all on sort of obvious and
+then after we've done the sweep we get
+
+ align:start position:0%
+then after we've done the sweep we get
+ 
+
+ align:start position:0%
+then after we've done the sweep we get
+an answer that looks like that now there
+
+ align:start position:0%
+an answer that looks like that now there
+ 
+
+ align:start position:0%
+an answer that looks like that now there
+are some disadvantages with mark-sweep
+
+ align:start position:0%
+are some disadvantages with mark-sweep
+ 
+
+ align:start position:0%
+are some disadvantages with mark-sweep
+algorithms of this sort serious ones one
+
+ align:start position:0%
+algorithms of this sort serious ones one
+ 
+
+ align:start position:0%
+algorithms of this sort serious ones one
+that one important disadvantage is that
+
+ align:start position:0%
+that one important disadvantage is that
+ 
+
+ align:start position:0%
+that one important disadvantage is that
+your memories get larger and larger as
+
+ align:start position:0%
+your memories get larger and larger as
+ 
+
+ align:start position:0%
+your memories get larger and larger as
+you say address spaces get larger and
+
+ align:start position:0%
+you say address spaces get larger and
+ 
+
+ align:start position:0%
+you say address spaces get larger and
+larger you're willing to represent more
+
+ align:start position:0%
+larger you're willing to represent more
+ 
+
+ align:start position:0%
+larger you're willing to represent more
+and more stuff then it gets very costly
+
+ align:start position:0%
+and more stuff then it gets very costly
+ 
+
+ align:start position:0%
+and more stuff then it gets very costly
+to scan all of memory what you'd really
+
+ align:start position:0%
+to scan all of memory what you'd really
+ 
+
+ align:start position:0%
+to scan all of memory what you'd really
+like to do is only scan the useful stuff
+
+ align:start position:0%
+like to do is only scan the useful stuff
+ 
+
+ align:start position:0%
+like to do is only scan the useful stuff
+it would even be better if you realize
+
+ align:start position:0%
+it would even be better if you realize
+ 
+
+ align:start position:0%
+it would even be better if you realize
+that some stuff was was known to be good
+
+ align:start position:0%
+that some stuff was was known to be good
+ 
+
+ align:start position:0%
+that some stuff was was known to be good
+and useful and you don't have to look at
+
+ align:start position:0%
+and useful and you don't have to look at
+ 
+
+ align:start position:0%
+and useful and you don't have to look at
+it more than once or twice or very
+
+ align:start position:0%
+it more than once or twice or very
+ 
+
+ align:start position:0%
+it more than once or twice or very
+rarely whereas other stuff that is not
+
+ align:start position:0%
+rarely whereas other stuff that is not
+ 
+
+ align:start position:0%
+rarely whereas other stuff that is not
+you're not so sure about you can look at
+
+ align:start position:0%
+you're not so sure about you can look at
+ 
+
+ align:start position:0%
+you're not so sure about you can look at
+in more detail every time you want to do
+
+ align:start position:0%
+in more detail every time you want to do
+ 
+
+ align:start position:0%
+in more detail every time you want to do
+this what a garbage collect well there
+
+ align:start position:0%
+this what a garbage collect well there
+ 
+
+ align:start position:0%
+this what a garbage collect well there
+there are algorithms that are organized
+
+ align:start position:0%
+there are algorithms that are organized
+ 
+
+ align:start position:0%
+there are algorithms that are organized
+in this way let me tell you about a
+
+ align:start position:0%
+in this way let me tell you about a
+ 
+
+ align:start position:0%
+in this way let me tell you about a
+famous old algorithm which allows you to
+
+ align:start position:0%
+famous old algorithm which allows you to
+ 
+
+ align:start position:0%
+famous old algorithm which allows you to
+only look at the part of memory which is
+
+ align:start position:0%
+only look at the part of memory which is
+ 
+
+ align:start position:0%
+only look at the part of memory which is
+known to be useful and which happens to
+
+ align:start position:0%
+known to be useful and which happens to
+ 
+
+ align:start position:0%
+known to be useful and which happens to
+be the fastest known garbage collector
+
+ align:start position:0%
+be the fastest known garbage collector
+ 
+
+ align:start position:0%
+be the fastest known garbage collector
+algorithm this is the Minsky
+
+ align:start position:0%
+algorithm this is the Minsky
+ 
+
+ align:start position:0%
+algorithm this is the Minsky
+seneschal yochelson garbage collector
+
+ align:start position:0%
+seneschal yochelson garbage collector
+ 
+
+ align:start position:0%
+seneschal yochelson garbage collector
+algorithm it was invented by by Minsky
+
+ align:start position:0%
+algorithm it was invented by by Minsky
+ 
+
+ align:start position:0%
+algorithm it was invented by by Minsky
+in 1961 or 60 or something for the RLE
+
+ align:start position:0%
+in 1961 or 60 or something for the RLE
+ 
+
+ align:start position:0%
+in 1961 or 60 or something for the RLE
+pdp-1 list which had 4096 words of a
+
+ align:start position:0%
+pdp-1 list which had 4096 words of a
+ 
+
+ align:start position:0%
+pdp-1 list which had 4096 words of a
+list memory and a drum and the whole
+
+ align:start position:0%
+list memory and a drum and the whole
+ 
+
+ align:start position:0%
+list memory and a drum and the whole
+idea was to garbage collect this
+
+ align:start position:0%
+idea was to garbage collect this
+ 
+
+ align:start position:0%
+idea was to garbage collect this
+terrible memory what this key realized
+
+ align:start position:0%
+terrible memory what this key realized
+ 
+
+ align:start position:0%
+terrible memory what this key realized
+was the easiest way to do this is to
+
+ align:start position:0%
+was the easiest way to do this is to
+ 
+
+ align:start position:0%
+was the easiest way to do this is to
+scan the memory in the same sense
+
+ align:start position:0%
+scan the memory in the same sense
+ 
+
+ align:start position:0%
+scan the memory in the same sense
+walking the the good structure copying
+
+ align:start position:0%
+walking the the good structure copying
+ 
+
+ align:start position:0%
+walking the the good structure copying
+it out into the drum compacted and then
+
+ align:start position:0%
+it out into the drum compacted and then
+ 
+
+ align:start position:0%
+it out into the drum compacted and then
+when it was that we were done copying it
+
+ align:start position:0%
+when it was that we were done copying it
+ 
+
+ align:start position:0%
+when it was that we were done copying it
+all out then you swapped that back into
+
+ align:start position:0%
+all out then you swapped that back into
+ 
+
+ align:start position:0%
+all out then you swapped that back into
+your memory now whether you do not use a
+
+ align:start position:0%
+your memory now whether you do not use a
+ 
+
+ align:start position:0%
+your memory now whether you do not use a
+drum or another piece of memory or
+
+ align:start position:0%
+drum or another piece of memory or
+ 
+
+ align:start position:0%
+drum or another piece of memory or
+something like that isn't important in
+
+ align:start position:0%
+something like that isn't important in
+ 
+
+ align:start position:0%
+something like that isn't important in
+fact I don't think people use drums
+
+ align:start position:0%
+fact I don't think people use drums
+ 
+
+ align:start position:0%
+fact I don't think people use drums
+anymore for anything but this algorithm
+
+ align:start position:0%
+anymore for anything but this algorithm
+ 
+
+ align:start position:0%
+anymore for anything but this algorithm
+basically depends upon having about
+
+ align:start position:0%
+basically depends upon having about
+ 
+
+ align:start position:0%
+basically depends upon having about
+twice as much address space as you're
+
+ align:start position:0%
+twice as much address space as you're
+ 
+
+ align:start position:0%
+twice as much address space as you're
+actually using and so what you have is
+
+ align:start position:0%
+actually using and so what you have is
+ 
+
+ align:start position:0%
+actually using and so what you have is
+some initially some mixture of of useful
+
+ align:start position:0%
+some initially some mixture of of useful
+ 
+
+ align:start position:0%
+some initially some mixture of of useful
+data and garbage so this is your called
+
+ align:start position:0%
+data and garbage so this is your called
+ 
+
+ align:start position:0%
+data and garbage so this is your called
+from space and this is a mixture of crud
+
+ align:start position:0%
+from space and this is a mixture of crud
+ 
+
+ align:start position:0%
+from space and this is a mixture of crud
+some of its important and some of it
+
+ align:start position:0%
+some of its important and some of it
+ 
+
+ align:start position:0%
+some of its important and some of it
+isn't
+
+ align:start position:0%
+isn't
+ 
+
+ align:start position:0%
+isn't
+now there's a another place which is
+
+ align:start position:0%
+now there's a another place which is
+ 
+
+ align:start position:0%
+now there's a another place which is
+hopefully big enough if we will call to
+
+ align:start position:0%
+hopefully big enough if we will call to
+ 
+
+ align:start position:0%
+hopefully big enough if we will call to
+space which is where we're copying to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what happens is and I'm not going to
+
+ align:start position:0%
+and what happens is and I'm not going to
+ 
+
+ align:start position:0%
+and what happens is and I'm not going to
+go through this in detail it's in it's
+
+ align:start position:0%
+go through this in detail it's in it's
+ 
+
+ align:start position:0%
+go through this in detail it's in it's
+in our book quite explicitly there's a a
+
+ align:start position:0%
+in our book quite explicitly there's a a
+ 
+
+ align:start position:0%
+in our book quite explicitly there's a a
+root pointer you start from and the idea
+
+ align:start position:0%
+root pointer you start from and the idea
+ 
+
+ align:start position:0%
+root pointer you start from and the idea
+is that you try if I start with the root
+
+ align:start position:0%
+is that you try if I start with the root
+ 
+
+ align:start position:0%
+is that you try if I start with the root
+you copy the first thing that you see
+
+ align:start position:0%
+you copy the first thing that you see
+ 
+
+ align:start position:0%
+you copy the first thing that you see
+the first thing that the root points at
+
+ align:start position:0%
+the first thing that the root points at
+ 
+
+ align:start position:0%
+the first thing that the root points at
+to the beginning of to space the first
+
+ align:start position:0%
+to the beginning of to space the first
+ 
+
+ align:start position:0%
+to the beginning of to space the first
+thing is a pair of sum or something like
+
+ align:start position:0%
+thing is a pair of sum or something like
+ 
+
+ align:start position:0%
+thing is a pair of sum or something like
+that a data structure you then you then
+
+ align:start position:0%
+that a data structure you then you then
+ 
+
+ align:start position:0%
+that a data structure you then you then
+also leave behind a broken heart saying
+
+ align:start position:0%
+also leave behind a broken heart saying
+ 
+
+ align:start position:0%
+also leave behind a broken heart saying
+I move this object from here to here
+
+ align:start position:0%
+I move this object from here to here
+ 
+
+ align:start position:0%
+I move this object from here to here
+giving the place where it moved to this
+
+ align:start position:0%
+giving the place where it moved to this
+ 
+
+ align:start position:0%
+giving the place where it moved to this
+is called a broken heart because a
+
+ align:start position:0%
+is called a broken heart because a
+ 
+
+ align:start position:0%
+is called a broken heart because a
+friend of mine who implemented one of
+
+ align:start position:0%
+friend of mine who implemented one of
+ 
+
+ align:start position:0%
+friend of mine who implemented one of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+in 1966 I was a very romantic character
+
+ align:start position:0%
+in 1966 I was a very romantic character
+ 
+
+ align:start position:0%
+in 1966 I was a very romantic character
+and called it a broken heart but in any
+
+ align:start position:0%
+and called it a broken heart but in any
+ 
+
+ align:start position:0%
+and called it a broken heart but in any
+case the the next thing you do is now
+
+ align:start position:0%
+case the the next thing you do is now
+ 
+
+ align:start position:0%
+case the the next thing you do is now
+you have a new free pointer which is
+
+ align:start position:0%
+you have a new free pointer which is
+ 
+
+ align:start position:0%
+you have a new free pointer which is
+here and you start scanning you scan
+
+ align:start position:0%
+here and you start scanning you scan
+ 
+
+ align:start position:0%
+here and you start scanning you scan
+this you scan this data structure you
+
+ align:start position:0%
+this you scan this data structure you
+ 
+
+ align:start position:0%
+this you scan this data structure you
+just copied and every time you encounter
+
+ align:start position:0%
+just copied and every time you encounter
+ 
+
+ align:start position:0%
+just copied and every time you encounter
+a pointer in it you're treated as if it
+
+ align:start position:0%
+a pointer in it you're treated as if it
+ 
+
+ align:start position:0%
+a pointer in it you're treated as if it
+was the root pointer here oh I'm sorry
+
+ align:start position:0%
+was the root pointer here oh I'm sorry
+ 
+
+ align:start position:0%
+was the root pointer here oh I'm sorry
+to let the other thing you do is you now
+
+ align:start position:0%
+to let the other thing you do is you now
+ 
+
+ align:start position:0%
+to let the other thing you do is you now
+move the root pointer to there okay so
+
+ align:start position:0%
+move the root pointer to there okay so
+ 
+
+ align:start position:0%
+move the root pointer to there okay so
+now you scan this and everything you see
+
+ align:start position:0%
+now you scan this and everything you see
+ 
+
+ align:start position:0%
+now you scan this and everything you see
+you treat it as if it were the root
+
+ align:start position:0%
+you treat it as if it were the root
+ 
+
+ align:start position:0%
+you treat it as if it were the root
+pointer the see if you see something
+
+ align:start position:0%
+pointer the see if you see something
+ 
+
+ align:start position:0%
+pointer the see if you see something
+well it points up into there somewhere
+
+ align:start position:0%
+well it points up into there somewhere
+ 
+
+ align:start position:0%
+well it points up into there somewhere
+is it pointing at the thing which you've
+
+ align:start position:0%
+is it pointing at the thing which you've
+ 
+
+ align:start position:0%
+is it pointing at the thing which you've
+not copied yet is there a broken heart
+
+ align:start position:0%
+not copied yet is there a broken heart
+ 
+
+ align:start position:0%
+not copied yet is there a broken heart
+there if there's a broken heart there
+
+ align:start position:0%
+there if there's a broken heart there
+ 
+
+ align:start position:0%
+there if there's a broken heart there
+and it's something you have copied you
+
+ align:start position:0%
+and it's something you have copied you
+ 
+
+ align:start position:0%
+and it's something you have copied you
+just replace this pointer with the thing
+
+ align:start position:0%
+just replace this pointer with the thing
+ 
+
+ align:start position:0%
+just replace this pointer with the thing
+the broken heart points that if this is
+
+ align:start position:0%
+the broken heart points that if this is
+ 
+
+ align:start position:0%
+the broken heart points that if this is
+not if this thing has not been copied
+
+ align:start position:0%
+not if this thing has not been copied
+ 
+
+ align:start position:0%
+not if this thing has not been copied
+you copy it to the next place over here
+
+ align:start position:0%
+you copy it to the next place over here
+ 
+
+ align:start position:0%
+you copy it to the next place over here
+move your free pointer over here okay
+
+ align:start position:0%
+move your free pointer over here okay
+ 
+
+ align:start position:0%
+move your free pointer over here okay
+and then and then leave a broken heart
+
+ align:start position:0%
+and then and then leave a broken heart
+ 
+
+ align:start position:0%
+and then and then leave a broken heart
+behind and scan and if eventually when
+
+ align:start position:0%
+behind and scan and if eventually when
+ 
+
+ align:start position:0%
+behind and scan and if eventually when
+the Scan pointer hits the free pointer
+
+ align:start position:0%
+the Scan pointer hits the free pointer
+ 
+
+ align:start position:0%
+the Scan pointer hits the free pointer
+everything in memory has been copied and
+
+ align:start position:0%
+everything in memory has been copied and
+ 
+
+ align:start position:0%
+everything in memory has been copied and
+then there's a whole bunch of empty
+
+ align:start position:0%
+then there's a whole bunch of empty
+ 
+
+ align:start position:0%
+then there's a whole bunch of empty
+space up here which you could either
+
+ align:start position:0%
+space up here which you could either
+ 
+
+ align:start position:0%
+space up here which you could either
+make into a free list if that's what you
+
+ align:start position:0%
+make into a free list if that's what you
+ 
+
+ align:start position:0%
+make into a free list if that's what you
+want to do but generally you don't in
+
+ align:start position:0%
+want to do but generally you don't in
+ 
+
+ align:start position:0%
+want to do but generally you don't in
+this kind of system in this system you
+
+ align:start position:0%
+this kind of system in this system you
+ 
+
+ align:start position:0%
+this kind of system in this system you
+sequential II allocate your memory that
+
+ align:start position:0%
+sequential II allocate your memory that
+ 
+
+ align:start position:0%
+sequential II allocate your memory that
+is a very very nice algorithm and sort
+
+ align:start position:0%
+is a very very nice algorithm and sort
+ 
+
+ align:start position:0%
+is a very very nice algorithm and sort
+of the one we use in the scheme that
+
+ align:start position:0%
+of the one we use in the scheme that
+ 
+
+ align:start position:0%
+of the one we use in the scheme that
+you've been using and known to be
+
+ align:start position:0%
+you've been using and known to be
+ 
+
+ align:start position:0%
+you've been using and known to be
+expected I believe it's no one has found
+
+ align:start position:0%
+expected I believe it's no one has found
+ 
+
+ align:start position:0%
+expected I believe it's no one has found
+a faster algorithm than that there are
+
+ align:start position:0%
+a faster algorithm than that there are
+ 
+
+ align:start position:0%
+a faster algorithm than that there are
+very simple modifications to this
+
+ align:start position:0%
+very simple modifications to this
+ 
+
+ align:start position:0%
+very simple modifications to this
+algorithm invented by Henry Baker which
+
+ align:start position:0%
+algorithm invented by Henry Baker which
+ 
+
+ align:start position:0%
+algorithm invented by Henry Baker which
+allowed one to run this algorithm in
+
+ align:start position:0%
+allowed one to run this algorithm in
+ 
+
+ align:start position:0%
+allowed one to run this algorithm in
+real time meaning you don't have to stop
+
+ align:start position:0%
+real time meaning you don't have to stop
+ 
+
+ align:start position:0%
+real time meaning you don't have to stop
+the garbage collect but you can
+
+ align:start position:0%
+the garbage collect but you can
+ 
+
+ align:start position:0%
+the garbage collect but you can
+interleave the Consing that meant the
+
+ align:start position:0%
+interleave the Consing that meant the
+ 
+
+ align:start position:0%
+interleave the Consing that meant the
+machine does when it's running with
+
+ align:start position:0%
+machine does when it's running with
+ 
+
+ align:start position:0%
+machine does when it's running with
+steps of the garbage collection process
+
+ align:start position:0%
+steps of the garbage collection process
+ 
+
+ align:start position:0%
+steps of the garbage collection process
+so that the thing that this garbage
+
+ align:start position:0%
+so that the thing that this garbage
+ 
+
+ align:start position:0%
+so that the thing that this garbage
+collection is distributed in the machine
+
+ align:start position:0%
+collection is distributed in the machine
+ 
+
+ align:start position:0%
+collection is distributed in the machine
+doesn't have to stop and garbage
+
+ align:start position:0%
+doesn't have to stop and garbage
+ 
+
+ align:start position:0%
+doesn't have to stop and garbage
+collecting start of course in the case
+
+ align:start position:0%
+collecting start of course in the case
+ 
+
+ align:start position:0%
+collecting start of course in the case
+of of machines with virtual memory where
+
+ align:start position:0%
+of of machines with virtual memory where
+ 
+
+ align:start position:0%
+of of machines with virtual memory where
+where a lot of it is in inaccessible
+
+ align:start position:0%
+where a lot of it is in inaccessible
+ 
+
+ align:start position:0%
+where a lot of it is in inaccessible
+places this becomes a very expensive
+
+ align:start position:0%
+places this becomes a very expensive
+ 
+
+ align:start position:0%
+places this becomes a very expensive
+process and there have been numerous
+
+ align:start position:0%
+process and there have been numerous
+ 
+
+ align:start position:0%
+process and there have been numerous
+attempts to make this much better there
+
+ align:start position:0%
+attempts to make this much better there
+ 
+
+ align:start position:0%
+attempts to make this much better there
+is a a nice paper for those of our
+
+ align:start position:0%
+is a a nice paper for those of our
+ 
+
+ align:start position:0%
+is a a nice paper for those of our
+viewing by moon and other piece
+
+ align:start position:0%
+viewing by moon and other piece
+ 
+
+ align:start position:0%
+viewing by moon and other piece
+well which describes a modification to
+
+ align:start position:0%
+well which describes a modification to
+ 
+
+ align:start position:0%
+well which describes a modification to
+the incremental Minsky facial yochelson
+
+ align:start position:0%
+the incremental Minsky facial yochelson
+ 
+
+ align:start position:0%
+the incremental Minsky facial yochelson
+algorithm a modification of the Bakker
+
+ align:start position:0%
+algorithm a modification of the Bakker
+ 
+
+ align:start position:0%
+algorithm a modification of the Bakker
+algorithm which which is more efficient
+
+ align:start position:0%
+algorithm which which is more efficient
+ 
+
+ align:start position:0%
+algorithm which which is more efficient
+for virtual memory systems well I think
+
+ align:start position:0%
+for virtual memory systems well I think
+ 
+
+ align:start position:0%
+for virtual memory systems well I think
+now the mystery to this is sort of gone
+
+ align:start position:0%
+now the mystery to this is sort of gone
+ 
+
+ align:start position:0%
+now the mystery to this is sort of gone
+and I'd like to see if there any
+
+ align:start position:0%
+and I'd like to see if there any
+ 
+
+ align:start position:0%
+and I'd like to see if there any
+questions yes I thought one of you run
+
+ align:start position:0%
+questions yes I thought one of you run
+ 
+
+ align:start position:0%
+questions yes I thought one of you run
+the garbage collector on the systems
+
+ align:start position:0%
+the garbage collector on the systems
+ 
+
+ align:start position:0%
+the garbage collector on the systems
+upstairs and it seemed to me to run
+
+ align:start position:0%
+upstairs and it seemed to me to run
+ 
+
+ align:start position:0%
+upstairs and it seemed to me to run
+extremely fast yes did the whole thing
+
+ align:start position:0%
+extremely fast yes did the whole thing
+ 
+
+ align:start position:0%
+extremely fast yes did the whole thing
+take sweep through all of memory and no
+
+ align:start position:0%
+take sweep through all of memory and no
+ 
+
+ align:start position:0%
+take sweep through all of memory and no
+and sweep this went through exactly what
+
+ align:start position:0%
+and sweep this went through exactly what
+ 
+
+ align:start position:0%
+and sweep this went through exactly what
+was needed to copy the youthful
+
+ align:start position:0%
+was needed to copy the youthful
+ 
+
+ align:start position:0%
+was needed to copy the youthful
+structure it's a copying collector okay
+
+ align:start position:0%
+structure it's a copying collector okay
+ 
+
+ align:start position:0%
+structure it's a copying collector okay
+and it's rather and it is very fast on
+
+ align:start position:0%
+and it's rather and it is very fast on
+ 
+
+ align:start position:0%
+and it's rather and it is very fast on
+the whole I suppose to copy in a bobcat
+
+ align:start position:0%
+the whole I suppose to copy in a bobcat
+ 
+
+ align:start position:0%
+the whole I suppose to copy in a bobcat
+to copy I think a couple of three or
+
+ align:start position:0%
+to copy I think a couple of three or
+ 
+
+ align:start position:0%
+to copy I think a couple of three or
+four three megabyte thing or something
+
+ align:start position:0%
+four three megabyte thing or something
+ 
+
+ align:start position:0%
+four three megabyte thing or something
+is less than a second a real-time I mean
+
+ align:start position:0%
+is less than a second a real-time I mean
+ 
+
+ align:start position:0%
+is less than a second a real-time I mean
+really these are very small programs one
+
+ align:start position:0%
+really these are very small programs one
+ 
+
+ align:start position:0%
+really these are very small programs one
+thing you should realize is that is that
+
+ align:start position:0%
+thing you should realize is that is that
+ 
+
+ align:start position:0%
+thing you should realize is that is that
+garbage collectors have to be small not
+
+ align:start position:0%
+garbage collectors have to be small not
+ 
+
+ align:start position:0%
+garbage collectors have to be small not
+because they have to be fast but because
+
+ align:start position:0%
+because they have to be fast but because
+ 
+
+ align:start position:0%
+because they have to be fast but because
+no one can debug a complicated garbage
+
+ align:start position:0%
+no one can debug a complicated garbage
+ 
+
+ align:start position:0%
+no one can debug a complicated garbage
+collector a garbage collector if it
+
+ align:start position:0%
+collector a garbage collector if it
+ 
+
+ align:start position:0%
+collector a garbage collector if it
+doesn't work will trash your memory in
+
+ align:start position:0%
+doesn't work will trash your memory in
+ 
+
+ align:start position:0%
+doesn't work will trash your memory in
+such a way that you cannot figure out
+
+ align:start position:0%
+such a way that you cannot figure out
+ 
+
+ align:start position:0%
+such a way that you cannot figure out
+what the hell happened
+
+ align:start position:0%
+what the hell happened
+ 
+
+ align:start position:0%
+what the hell happened
+you need an audit trail because it's
+
+ align:start position:0%
+you need an audit trail because it's
+ 
+
+ align:start position:0%
+you need an audit trail because it's
+agree arranges everything and how do you
+
+ align:start position:0%
+agree arranges everything and how do you
+ 
+
+ align:start position:0%
+agree arranges everything and how do you
+know what happened there so this is the
+
+ align:start position:0%
+know what happened there so this is the
+ 
+
+ align:start position:0%
+know what happened there so this is the
+only kind of program that it really
+
+ align:start position:0%
+only kind of program that it really
+ 
+
+ align:start position:0%
+only kind of program that it really
+seriously matters if you stare at it
+
+ align:start position:0%
+seriously matters if you stare at it
+ 
+
+ align:start position:0%
+seriously matters if you stare at it
+long enough so that you believe that it
+
+ align:start position:0%
+long enough so that you believe that it
+ 
+
+ align:start position:0%
+long enough so that you believe that it
+works and that means and then you prove
+
+ align:start position:0%
+works and that means and then you prove
+ 
+
+ align:start position:0%
+works and that means and then you prove
+it to yourself and not that there's no
+
+ align:start position:0%
+it to yourself and not that there's no
+ 
+
+ align:start position:0%
+it to yourself and not that there's no
+way to debug it and that takes that
+
+ align:start position:0%
+way to debug it and that takes that
+ 
+
+ align:start position:0%
+way to debug it and that takes that
+takes it being small enough so you can
+
+ align:start position:0%
+takes it being small enough so you can
+ 
+
+ align:start position:0%
+takes it being small enough so you can
+hold it in your head so garbage
+
+ align:start position:0%
+hold it in your head so garbage
+ 
+
+ align:start position:0%
+hold it in your head so garbage
+collectors are special in this way so
+
+ align:start position:0%
+collectors are special in this way so
+ 
+
+ align:start position:0%
+collectors are special in this way so
+every reasonable garbage collector has
+
+ align:start position:0%
+every reasonable garbage collector has
+ 
+
+ align:start position:0%
+every reasonable garbage collector has
+gotten small and generally small
+
+ align:start position:0%
+gotten small and generally small
+ 
+
+ align:start position:0%
+gotten small and generally small
+programs are fast yes beep the name of
+
+ align:start position:0%
+programs are fast yes beep the name of
+ 
+
+ align:start position:0%
+programs are fast yes beep the name of
+this technique once again that's the
+
+ align:start position:0%
+this technique once again that's the
+ 
+
+ align:start position:0%
+this technique once again that's the
+Minsky initial yochelson garbage
+
+ align:start position:0%
+Minsky initial yochelson garbage
+ 
+
+ align:start position:0%
+Minsky initial yochelson garbage
+collector
+
+ align:start position:0%
+collector
+ 
+
+ align:start position:0%
+collector
+Minsky invented in 61 for the r-la pdp-1
+
+ align:start position:0%
+Minsky invented in 61 for the r-la pdp-1
+ 
+
+ align:start position:0%
+Minsky invented in 61 for the r-la pdp-1
+a version of it was was developed and
+
+ align:start position:0%
+a version of it was was developed and
+ 
+
+ align:start position:0%
+a version of it was was developed and
+they Mel aberrated
+
+ align:start position:0%
+they Mel aberrated
+ 
+
+ align:start position:0%
+they Mel aberrated
+to be used in multicam at a Mac Lisp
+
+ align:start position:0%
+to be used in multicam at a Mac Lisp
+ 
+
+ align:start position:0%
+to be used in multicam at a Mac Lisp
+potential in yochelson and are somewhere
+
+ align:start position:0%
+potential in yochelson and are somewhere
+ 
+
+ align:start position:0%
+potential in yochelson and are somewhere
+around 1968 or 69 okay let's take a
+
+ align:start position:0%
+around 1968 or 69 okay let's take a
+ 
+
+ align:start position:0%
+around 1968 or 69 okay let's take a
+break
+
+ align:start position:0%
+break
+ 
+
+ align:start position:0%
+break
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we've come to the end of this
+
+ align:start position:0%
+well we've come to the end of this
+ 
+
+ align:start position:0%
+well we've come to the end of this
+subject and we've already shown you a
+
+ align:start position:0%
+subject and we've already shown you a
+ 
+
+ align:start position:0%
+subject and we've already shown you a
+universal machine which is down to the
+
+ align:start position:0%
+universal machine which is down to the
+ 
+
+ align:start position:0%
+universal machine which is down to the
+low value ater adapted level of detail
+
+ align:start position:0%
+low value ater adapted level of detail
+ 
+
+ align:start position:0%
+low value ater adapted level of detail
+you could imagine you could make one
+
+ align:start position:0%
+you could imagine you could make one
+ 
+
+ align:start position:0%
+you could imagine you could make one
+this is a particular implementation of
+
+ align:start position:0%
+this is a particular implementation of
+ 
+
+ align:start position:0%
+this is a particular implementation of
+Lisp built on one of those scheme chips
+
+ align:start position:0%
+Lisp built on one of those scheme chips
+ 
+
+ align:start position:0%
+Lisp built on one of those scheme chips
+that was talked about yesterday sitting
+
+ align:start position:0%
+that was talked about yesterday sitting
+ 
+
+ align:start position:0%
+that was talked about yesterday sitting
+over here this is mostly interface to
+
+ align:start position:0%
+over here this is mostly interface to
+ 
+
+ align:start position:0%
+over here this is mostly interface to
+somebody's memory with a little bit of
+
+ align:start position:0%
+somebody's memory with a little bit of
+ 
+
+ align:start position:0%
+somebody's memory with a little bit of
+timing and other such stuff but this
+
+ align:start position:0%
+timing and other such stuff but this
+ 
+
+ align:start position:0%
+timing and other such stuff but this
+fellow actually ran Lisp and a fairly
+
+ align:start position:0%
+fellow actually ran Lisp and a fairly
+ 
+
+ align:start position:0%
+fellow actually ran Lisp and a fairly
+reasonable rate as interpretive it ran
+
+ align:start position:0%
+reasonable rate as interpretive it ran
+ 
+
+ align:start position:0%
+reasonable rate as interpretive it ran
+the Lisp as fast as a dec pdp-10 back in
+
+ align:start position:0%
+the Lisp as fast as a dec pdp-10 back in
+ 
+
+ align:start position:0%
+the Lisp as fast as a dec pdp-10 back in
+1979 and so it gotten pretty pretty
+
+ align:start position:0%
+1979 and so it gotten pretty pretty
+ 
+
+ align:start position:0%
+1979 and so it gotten pretty pretty
+Hardware pretty concrete mmm we've also
+
+ align:start position:0%
+Hardware pretty concrete mmm we've also
+ 
+
+ align:start position:0%
+Hardware pretty concrete mmm we've also
+download you a bit with the things you
+
+ align:start position:0%
+download you a bit with the things you
+ 
+
+ align:start position:0%
+download you a bit with the things you
+can compute but is it the case that
+
+ align:start position:0%
+can compute but is it the case that
+ 
+
+ align:start position:0%
+can compute but is it the case that
+there are things we can't compute and so
+
+ align:start position:0%
+there are things we can't compute and so
+ 
+
+ align:start position:0%
+there are things we can't compute and so
+I'd like to end this with showing you
+
+ align:start position:0%
+I'd like to end this with showing you
+ 
+
+ align:start position:0%
+I'd like to end this with showing you
+some things that you'd like to be able
+
+ align:start position:0%
+some things that you'd like to be able
+ 
+
+ align:start position:0%
+some things that you'd like to be able
+to compute then you can't the answer is
+
+ align:start position:0%
+to compute then you can't the answer is
+ 
+
+ align:start position:0%
+to compute then you can't the answer is
+yes you there are things you can't
+
+ align:start position:0%
+yes you there are things you can't
+ 
+
+ align:start position:0%
+yes you there are things you can't
+compute and for example something you'd
+
+ align:start position:0%
+compute and for example something you'd
+ 
+
+ align:start position:0%
+compute and for example something you'd
+really like is in your if you're writing
+
+ align:start position:0%
+really like is in your if you're writing
+ 
+
+ align:start position:0%
+really like is in your if you're writing
+a compiler you'd like a program that
+
+ align:start position:0%
+a compiler you'd like a program that
+ 
+
+ align:start position:0%
+a compiler you'd like a program that
+would check that a thing you're going to
+
+ align:start position:0%
+would check that a thing you're going to
+ 
+
+ align:start position:0%
+would check that a thing you're going to
+do will work wouldn't that be nice you'd
+
+ align:start position:0%
+do will work wouldn't that be nice you'd
+ 
+
+ align:start position:0%
+do will work wouldn't that be nice you'd
+like something that would catch infinite
+
+ align:start position:0%
+like something that would catch infinite
+ 
+
+ align:start position:0%
+like something that would catch infinite
+loops for example in programs that were
+
+ align:start position:0%
+loops for example in programs that were
+ 
+
+ align:start position:0%
+loops for example in programs that were
+written by my users button generally you
+
+ align:start position:0%
+written by my users button generally you
+ 
+
+ align:start position:0%
+written by my users button generally you
+can't write such a program that'll read
+
+ align:start position:0%
+can't write such a program that'll read
+ 
+
+ align:start position:0%
+can't write such a program that'll read
+any program and determine whether or not
+
+ align:start position:0%
+any program and determine whether or not
+ 
+
+ align:start position:0%
+any program and determine whether or not
+it's an infant loop let me show you that
+
+ align:start position:0%
+it's an infant loop let me show you that
+ 
+
+ align:start position:0%
+it's an infant loop let me show you that
+it's a little bit of a minor mathematics
+
+ align:start position:0%
+it's a little bit of a minor mathematics
+ 
+
+ align:start position:0%
+it's a little bit of a minor mathematics
+hmm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's imagine that we just had a
+
+ align:start position:0%
+let's imagine that we just had a
+ 
+
+ align:start position:0%
+let's imagine that we just had a
+mathematical function before we start
+
+ align:start position:0%
+mathematical function before we start
+ 
+
+ align:start position:0%
+mathematical function before we start
+and there is one called s which takes a
+
+ align:start position:0%
+and there is one called s which takes a
+ 
+
+ align:start position:0%
+and there is one called s which takes a
+procedure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+and it's argument a and what s does is
+
+ align:start position:0%
+and it's argument a and what s does is
+ 
+
+ align:start position:0%
+and it's argument a and what s does is
+it determines whether or not it's safe
+
+ align:start position:0%
+it determines whether or not it's safe
+ 
+
+ align:start position:0%
+it determines whether or not it's safe
+to run P on a and what I mean by that is
+
+ align:start position:0%
+to run P on a and what I mean by that is
+ 
+
+ align:start position:0%
+to run P on a and what I mean by that is
+this it's true if he applied to a will
+
+ align:start position:0%
+this it's true if he applied to a will
+ 
+
+ align:start position:0%
+this it's true if he applied to a will
+converge to a value without an error and
+
+ align:start position:0%
+converge to a value without an error and
+ 
+
+ align:start position:0%
+converge to a value without an error and
+it's false if P of a loops forever
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before it makes an error now that's
+
+ align:start position:0%
+before it makes an error now that's
+ 
+
+ align:start position:0%
+before it makes an error now that's
+surely a function there is some for
+
+ align:start position:0%
+surely a function there is some for
+ 
+
+ align:start position:0%
+surely a function there is some for
+every procedure and for every argument
+
+ align:start position:0%
+every procedure and for every argument
+ 
+
+ align:start position:0%
+every procedure and for every argument
+you could give it that is either true or
+
+ align:start position:0%
+you could give it that is either true or
+ 
+
+ align:start position:0%
+you could give it that is either true or
+false that it converges with a mouth
+
+ align:start position:0%
+false that it converges with a mouth
+ 
+
+ align:start position:0%
+false that it converges with a mouth
+making an error and you could make a
+
+ align:start position:0%
+making an error and you could make a
+ 
+
+ align:start position:0%
+making an error and you could make a
+giant table of them but the question is
+
+ align:start position:0%
+giant table of them but the question is
+ 
+
+ align:start position:0%
+giant table of them but the question is
+can you write a procedure that computes
+
+ align:start position:0%
+can you write a procedure that computes
+ 
+
+ align:start position:0%
+can you write a procedure that computes
+the values of this function well let's
+
+ align:start position:0%
+the values of this function well let's
+ 
+
+ align:start position:0%
+the values of this function well let's
+assume that we can suppose that we have
+
+ align:start position:0%
+assume that we can suppose that we have
+ 
+
+ align:start position:0%
+assume that we can suppose that we have
+a procedure procedure called safe that
+
+ align:start position:0%
+a procedure procedure called safe that
+ 
+
+ align:start position:0%
+a procedure procedure called safe that
+computes the value of s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay then I'm going to show you by
+
+ align:start position:0%
+okay then I'm going to show you by
+ 
+
+ align:start position:0%
+okay then I'm going to show you by
+several methods that you can't that you
+
+ align:start position:0%
+several methods that you can't that you
+ 
+
+ align:start position:0%
+several methods that you can't that you
+can't do this the easiest one or the
+
+ align:start position:0%
+can't do this the easiest one or the
+ 
+
+ align:start position:0%
+can't do this the easiest one or the
+first one let's define a procedure
+
+ align:start position:0%
+first one let's define a procedure
+ 
+
+ align:start position:0%
+first one let's define a procedure
+called diag1 given that we have say we
+
+ align:start position:0%
+called diag1 given that we have say we
+ 
+
+ align:start position:0%
+called diag1 given that we have say we
+can define the ag-1 diag1 to be the
+
+ align:start position:0%
+can define the ag-1 diag1 to be the
+ 
+
+ align:start position:0%
+can define the ag-1 diag1 to be the
+procedure of one argument P which has
+
+ align:start position:0%
+procedure of one argument P which has
+ 
+
+ align:start position:0%
+procedure of one argument P which has
+the following properties
+
+ align:start position:0%
+the following properties
+ 
+
+ align:start position:0%
+the following properties
+if say if it's safe to apply P to itself
+
+ align:start position:0%
+if say if it's safe to apply P to itself
+ 
+
+ align:start position:0%
+if say if it's safe to apply P to itself
+right then I wish to have an infinite
+
+ align:start position:0%
+right then I wish to have an infinite
+ 
+
+ align:start position:0%
+right then I wish to have an infinite
+loop otherwise I'm going to return three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe it was 42 what's the answer to the
+
+ align:start position:0%
+maybe it was 42 what's the answer to the
+ 
+
+ align:start position:0%
+maybe it was 42 what's the answer to the
+big question where of course we know it
+
+ align:start position:0%
+big question where of course we know it
+ 
+
+ align:start position:0%
+big question where of course we know it
+an infinite loop is an infinite loop to
+
+ align:start position:0%
+an infinite loop is an infinite loop to
+ 
+
+ align:start position:0%
+an infinite loop is an infinite loop to
+be a procedure of no arguments which is
+
+ align:start position:0%
+be a procedure of no arguments which is
+ 
+
+ align:start position:0%
+be a procedure of no arguments which is
+that nice lambda calculus loop land
+
+ align:start position:0%
+that nice lambda calculus loop land
+ 
+
+ align:start position:0%
+that nice lambda calculus loop land
+attacks X of x applied to lambda of X X
+
+ align:start position:0%
+attacks X of x applied to lambda of X X
+ 
+
+ align:start position:0%
+attacks X of x applied to lambda of X X
+of X so there's nothing left to the
+
+ align:start position:0%
+of X so there's nothing left to the
+ 
+
+ align:start position:0%
+of X so there's nothing left to the
+imagination here okay well let's see
+
+ align:start position:0%
+imagination here okay well let's see
+ 
+
+ align:start position:0%
+imagination here okay well let's see
+what the story is I'm supposing it's the
+
+ align:start position:0%
+what the story is I'm supposing it's the
+ 
+
+ align:start position:0%
+what the story is I'm supposing it's the
+case that we worry about the procedure
+
+ align:start position:0%
+case that we worry about the procedure
+ 
+
+ align:start position:0%
+case that we worry about the procedure
+called by AG 1 applied to diag1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well what could it possibly be well I
+
+ align:start position:0%
+well what could it possibly be well I
+ 
+
+ align:start position:0%
+well what could it possibly be well I
+don't know we're going to substitute
+
+ align:start position:0%
+don't know we're going to substitute
+ 
+
+ align:start position:0%
+don't know we're going to substitute
+diag1 for FP in the body here well is it
+
+ align:start position:0%
+diag1 for FP in the body here well is it
+ 
+
+ align:start position:0%
+diag1 for FP in the body here well is it
+safe to compute the ag-1 today I want I
+
+ align:start position:0%
+safe to compute the ag-1 today I want I
+ 
+
+ align:start position:0%
+safe to compute the ag-1 today I want I
+don't know there are two possibilities
+
+ align:start position:0%
+don't know there are two possibilities
+ 
+
+ align:start position:0%
+don't know there are two possibilities
+if it's safe to compute diag1 of diag1
+
+ align:start position:0%
+if it's safe to compute diag1 of diag1
+ 
+
+ align:start position:0%
+if it's safe to compute diag1 of diag1
+that means it shouldn't loop oh that
+
+ align:start position:0%
+that means it shouldn't loop oh that
+ 
+
+ align:start position:0%
+that means it shouldn't loop oh that
+means I go to here but then I produce an
+
+ align:start position:0%
+means I go to here but then I produce an
+ 
+
+ align:start position:0%
+means I go to here but then I produce an
+infinite loop so it can't be safe but if
+
+ align:start position:0%
+infinite loop so it can't be safe but if
+ 
+
+ align:start position:0%
+infinite loop so it can't be safe but if
+it's not safe to compute the ag-1 of
+
+ align:start position:0%
+it's not safe to compute the ag-1 of
+ 
+
+ align:start position:0%
+it's not safe to compute the ag-1 of
+diag1 then the answer to this
+
+ align:start position:0%
+diag1 then the answer to this
+ 
+
+ align:start position:0%
+diag1 then the answer to this
+but that's the ag-1 of diag1 so it had
+
+ align:start position:0%
+but that's the ag-1 of diag1 so it had
+ 
+
+ align:start position:0%
+but that's the ag-1 of diag1 so it had
+to be saved so therefore you therefore
+
+ align:start position:0%
+to be saved so therefore you therefore
+ 
+
+ align:start position:0%
+to be saved so therefore you therefore
+by contradiction you cannot produce safe
+
+ align:start position:0%
+by contradiction you cannot produce safe
+ 
+
+ align:start position:0%
+by contradiction you cannot produce safe
+for those of you who are boggled by that
+
+ align:start position:0%
+for those of you who are boggled by that
+ 
+
+ align:start position:0%
+for those of you who are boggled by that
+one I'm going to say it again a
+
+ align:start position:0%
+one I'm going to say it again a
+ 
+
+ align:start position:0%
+one I'm going to say it again a
+different way just know one more
+
+ align:start position:0%
+different way just know one more
+ 
+
+ align:start position:0%
+different way just know one more
+alternative
+
+ align:start position:0%
+alternative
+ 
+
+ align:start position:0%
+alternative
+let's define diag to these named diag
+
+ align:start position:0%
+let's define diag to these named diag
+ 
+
+ align:start position:0%
+let's define diag to these named diag
+because because of Cantor's diagonal
+
+ align:start position:0%
+because because of Cantor's diagonal
+ 
+
+ align:start position:0%
+because because of Cantor's diagonal
+argument this is these are instances of
+
+ align:start position:0%
+argument this is these are instances of
+ 
+
+ align:start position:0%
+argument this is these are instances of
+a famous argument which was originally
+
+ align:start position:0%
+a famous argument which was originally
+ 
+
+ align:start position:0%
+a famous argument which was originally
+used by Cantor in the late part of the
+
+ align:start position:0%
+used by Cantor in the late part of the
+ 
+
+ align:start position:0%
+used by Cantor in the late part of the
+last century to prove that the real
+
+ align:start position:0%
+last century to prove that the real
+ 
+
+ align:start position:0%
+last century to prove that the real
+numbers were not countable that there
+
+ align:start position:0%
+numbers were not countable that there
+ 
+
+ align:start position:0%
+numbers were not countable that there
+are too many real numbers to be counted
+
+ align:start position:0%
+are too many real numbers to be counted
+ 
+
+ align:start position:0%
+are too many real numbers to be counted
+by integers that there are more points
+
+ align:start position:0%
+by integers that there are more points
+ 
+
+ align:start position:0%
+by integers that there are more points
+on a line for example than there are
+
+ align:start position:0%
+on a line for example than there are
+ 
+
+ align:start position:0%
+on a line for example than there are
+counting numbers and may or may not be
+
+ align:start position:0%
+counting numbers and may or may not be
+ 
+
+ align:start position:0%
+counting numbers and may or may not be
+obvious and I don't want to get into
+
+ align:start position:0%
+obvious and I don't want to get into
+ 
+
+ align:start position:0%
+obvious and I don't want to get into
+that now but diag 2 is again a procedure
+
+ align:start position:0%
+that now but diag 2 is again a procedure
+ 
+
+ align:start position:0%
+that now but diag 2 is again a procedure
+of one argument P and almost the same as
+
+ align:start position:0%
+of one argument P and almost the same as
+ 
+
+ align:start position:0%
+of one argument P and almost the same as
+the previous one which is if it's safe
+
+ align:start position:0%
+the previous one which is if it's safe
+ 
+
+ align:start position:0%
+the previous one which is if it's safe
+to compute P on P then I'm going to
+
+ align:start position:0%
+to compute P on P then I'm going to
+ 
+
+ align:start position:0%
+to compute P on P then I'm going to
+produce oops
+
+ align:start position:0%
+produce oops
+ 
+
+ align:start position:0%
+produce oops
+yeah then I want to compute some other
+
+ align:start position:0%
+yeah then I want to compute some other
+ 
+
+ align:start position:0%
+yeah then I want to compute some other
+thing other than P of P otherwise I'm
+
+ align:start position:0%
+thing other than P of P otherwise I'm
+ 
+
+ align:start position:0%
+thing other than P of P otherwise I'm
+gonna put out false where other than it
+
+ align:start position:0%
+gonna put out false where other than it
+ 
+
+ align:start position:0%
+gonna put out false where other than it
+says whatever P of P is I'm gonna put
+
+ align:start position:0%
+says whatever P of P is I'm gonna put
+ 
+
+ align:start position:0%
+says whatever P of P is I'm gonna put
+out something else I can give you an
+
+ align:start position:0%
+out something else I can give you an
+ 
+
+ align:start position:0%
+out something else I can give you an
+example of a definition of other than
+
+ align:start position:0%
+example of a definition of other than
+ 
+
+ align:start position:0%
+example of a definition of other than
+which I think works let's see yes where
+
+ align:start position:0%
+which I think works let's see yes where
+ 
+
+ align:start position:0%
+which I think works let's see yes where
+other than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the a procedure of one argument X which
+
+ align:start position:0%
+the a procedure of one argument X which
+ 
+
+ align:start position:0%
+the a procedure of one argument X which
+says if it's EQ X to say quote a then
+
+ align:start position:0%
+says if it's EQ X to say quote a then
+ 
+
+ align:start position:0%
+says if it's EQ X to say quote a then
+the answer is called C otherwise its
+
+ align:start position:0%
+the answer is called C otherwise its
+ 
+
+ align:start position:0%
+the answer is called C otherwise its
+quote a that always produces something
+
+ align:start position:0%
+quote a that always produces something
+ 
+
+ align:start position:0%
+quote a that always produces something
+which is not what its argument is that's
+
+ align:start position:0%
+which is not what its argument is that's
+ 
+
+ align:start position:0%
+which is not what its argument is that's
+all it is that's all I wanted well now
+
+ align:start position:0%
+all it is that's all I wanted well now
+ 
+
+ align:start position:0%
+all it is that's all I wanted well now
+let's consider this one diag two of diag
+
+ align:start position:0%
+let's consider this one diag two of diag
+ 
+
+ align:start position:0%
+let's consider this one diag two of diag
+two well look this only does something
+
+ align:start position:0%
+two well look this only does something
+ 
+
+ align:start position:0%
+two well look this only does something
+dangerous like calling P of P if it's
+
+ align:start position:0%
+dangerous like calling P of P if it's
+ 
+
+ align:start position:0%
+dangerous like calling P of P if it's
+safe to do so
+
+ align:start position:0%
+safe to do so
+ 
+
+ align:start position:0%
+safe to do so
+so if safe is defined at all if as you
+
+ align:start position:0%
+so if safe is defined at all if as you
+ 
+
+ align:start position:0%
+so if safe is defined at all if as you
+can define such a procedure safe then
+
+ align:start position:0%
+can define such a procedure safe then
+ 
+
+ align:start position:0%
+can define such a procedure safe then
+this procedure is always defined in
+
+ align:start position:0%
+this procedure is always defined in
+ 
+
+ align:start position:0%
+this procedure is always defined in
+therefore safe on any inputs okay so
+
+ align:start position:0%
+therefore safe on any inputs okay so
+ 
+
+ align:start position:0%
+therefore safe on any inputs okay so
+diag to of die i to must reduce to other
+
+ align:start position:0%
+diag to of die i to must reduce to other
+ 
+
+ align:start position:0%
+diag to of die i to must reduce to other
+then diag to of diag to and that doesn't
+
+ align:start position:0%
+then diag to of diag to and that doesn't
+ 
+
+ align:start position:0%
+then diag to of diag to and that doesn't
+make sense so we've a contradiction and
+
+ align:start position:0%
+make sense so we've a contradiction and
+ 
+
+ align:start position:0%
+make sense so we've a contradiction and
+therefore we can't define say i just
+
+ align:start position:0%
+therefore we can't define say i just
+ 
+
+ align:start position:0%
+therefore we can't define say i just
+want to do that twice slightly
+
+ align:start position:0%
+want to do that twice slightly
+ 
+
+ align:start position:0%
+want to do that twice slightly
+differently so you wouldn't feel you
+
+ align:start position:0%
+differently so you wouldn't feel you
+ 
+
+ align:start position:0%
+differently so you wouldn't feel you
+wouldn't feel that the first one was a
+
+ align:start position:0%
+wouldn't feel that the first one was a
+ 
+
+ align:start position:0%
+wouldn't feel that the first one was a
+trick okay they made both tricks was
+
+ align:start position:0%
+trick okay they made both tricks was
+ 
+
+ align:start position:0%
+trick okay they made both tricks was
+there at least slightly different so I
+
+ align:start position:0%
+there at least slightly different so I
+ 
+
+ align:start position:0%
+there at least slightly different so I
+suppose that pretty much wraps it up I'm
+
+ align:start position:0%
+suppose that pretty much wraps it up I'm
+ 
+
+ align:start position:0%
+suppose that pretty much wraps it up I'm
+just pretty what we call the halting
+
+ align:start position:0%
+just pretty what we call the halting
+ 
+
+ align:start position:0%
+just pretty what we call the halting
+theorem I suppose with that we're gonna
+
+ align:start position:0%
+theorem I suppose with that we're gonna
+ 
+
+ align:start position:0%
+theorem I suppose with that we're gonna
+halt I hope you have a good time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are there any questions yes what is the
+
+ align:start position:0%
+are there any questions yes what is the
+ 
+
+ align:start position:0%
+are there any questions yes what is the
+value of s of diag1 of what s of diag1
+
+ align:start position:0%
+value of s of diag1 of what s of diag1
+ 
+
+ align:start position:0%
+value of s of diag1 of what s of diag1
+if you said s is the function and we can
+
+ align:start position:0%
+if you said s is the function and we can
+ 
+
+ align:start position:0%
+if you said s is the function and we can
+oh I don't know I don't know it's a
+
+ align:start position:0%
+oh I don't know I don't know it's a
+ 
+
+ align:start position:0%
+oh I don't know I don't know it's a
+function but I don't know how to compute
+
+ align:start position:0%
+function but I don't know how to compute
+ 
+
+ align:start position:0%
+function but I don't know how to compute
+it I'm I can't do it I'm just a machine
+
+ align:start position:0%
+it I'm I can't do it I'm just a machine
+ 
+
+ align:start position:0%
+it I'm I can't do it I'm just a machine
+to write and there's no machine that in
+
+ align:start position:0%
+to write and there's no machine that in
+ 
+
+ align:start position:0%
+to write and there's no machine that in
+principle it might be that in that
+
+ align:start position:0%
+principle it might be that in that
+ 
+
+ align:start position:0%
+principle it might be that in that
+particular case you just asked with some
+
+ align:start position:0%
+particular case you just asked with some
+ 
+
+ align:start position:0%
+particular case you just asked with some
+thinking I could figure it out but in
+
+ align:start position:0%
+thinking I could figure it out but in
+ 
+
+ align:start position:0%
+thinking I could figure it out but in
+general I can't compute the value of s
+
+ align:start position:0%
+general I can't compute the value of s
+ 
+
+ align:start position:0%
+general I can't compute the value of s
+any better than the other machine can
+
+ align:start position:0%
+any better than the other machine can
+ 
+
+ align:start position:0%
+any better than the other machine can
+there is such a function it's just that
+
+ align:start position:0%
+there is such a function it's just that
+ 
+
+ align:start position:0%
+there is such a function it's just that
+no machine can be built the computer now
+
+ align:start position:0%
+no machine can be built the computer now
+ 
+
+ align:start position:0%
+no machine can be built the computer now
+there's a way of saying that that should
+
+ align:start position:0%
+there's a way of saying that that should
+ 
+
+ align:start position:0%
+there's a way of saying that that should
+not be surprising going through this I
+
+ align:start position:0%
+not be surprising going through this I
+ 
+
+ align:start position:0%
+not be surprising going through this I
+mean I don't have time to do this here
+
+ align:start position:0%
+mean I don't have time to do this here
+ 
+
+ align:start position:0%
+mean I don't have time to do this here
+but the number of functions is very
+
+ align:start position:0%
+but the number of functions is very
+ 
+
+ align:start position:0%
+but the number of functions is very
+large okay if there's a certain number
+
+ align:start position:0%
+large okay if there's a certain number
+ 
+
+ align:start position:0%
+large okay if there's a certain number
+of answers possible and a certain number
+
+ align:start position:0%
+of answers possible and a certain number
+ 
+
+ align:start position:0%
+of answers possible and a certain number
+of inputs possible that's the number of
+
+ align:start position:0%
+of inputs possible that's the number of
+ 
+
+ align:start position:0%
+of inputs possible that's the number of
+answers raised to the number inputs
+
+ align:start position:0%
+answers raised to the number inputs
+ 
+
+ align:start position:0%
+answers raised to the number inputs
+there's a number of possible functions
+
+ align:start position:0%
+there's a number of possible functions
+ 
+
+ align:start position:0%
+there's a number of possible functions
+hey I'm one variable
+
+ align:start position:0%
+hey I'm one variable
+ 
+
+ align:start position:0%
+hey I'm one variable
+now now that's always bigger than the
+
+ align:start position:0%
+now now that's always bigger than the
+ 
+
+ align:start position:0%
+now now that's always bigger than the
+then-then-then the thing you're raising
+
+ align:start position:0%
+then-then-then the thing you're raising
+ 
+
+ align:start position:0%
+then-then-then the thing you're raising
+to and the exponent the number of
+
+ align:start position:0%
+to and the exponent the number of
+ 
+
+ align:start position:0%
+to and the exponent the number of
+functions is larger than the number of
+
+ align:start position:0%
+functions is larger than the number of
+ 
+
+ align:start position:0%
+functions is larger than the number of
+number of programs that one can write by
+
+ align:start position:0%
+number of programs that one can write by
+ 
+
+ align:start position:0%
+number of programs that one can write by
+an infinity counting argument so there
+
+ align:start position:0%
+an infinity counting argument so there
+ 
+
+ align:start position:0%
+an infinity counting argument so there
+must Adan's much larger so there must be
+
+ align:start position:0%
+must Adan's much larger so there must be
+ 
+
+ align:start position:0%
+must Adan's much larger so there must be
+a lot of a lot of functions that can't
+
+ align:start position:0%
+a lot of a lot of functions that can't
+ 
+
+ align:start position:0%
+a lot of a lot of functions that can't
+be computed by programs yeah you're
+
+ align:start position:0%
+be computed by programs yeah you're
+ 
+
+ align:start position:0%
+be computed by programs yeah you're
+talking about specifications an
+
+ align:start position:0%
+talking about specifications an
+ 
+
+ align:start position:0%
+talking about specifications an
+automatic generation and solution do you
+
+ align:start position:0%
+automatic generation and solution do you
+ 
+
+ align:start position:0%
+automatic generation and solution do you
+see any steps between specifications and
+
+ align:start position:0%
+see any steps between specifications and
+ 
+
+ align:start position:0%
+see any steps between specifications and
+solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+steps between you mean you're saying how
+
+ align:start position:0%
+steps between you mean you're saying how
+ 
+
+ align:start position:0%
+steps between you mean you're saying how
+you go about constructing constructing
+
+ align:start position:0%
+you go about constructing constructing
+ 
+
+ align:start position:0%
+you go about constructing constructing
+devices given that you have
+
+ align:start position:0%
+devices given that you have
+ 
+
+ align:start position:0%
+devices given that you have
+specification for the device there's a
+
+ align:start position:0%
+specification for the device there's a
+ 
+
+ align:start position:0%
+specification for the device there's a
+longer software engineering that goes
+
+ align:start position:0%
+longer software engineering that goes
+ 
+
+ align:start position:0%
+longer software engineering that goes
+from specifications through many layers
+
+ align:start position:0%
+from specifications through many layers
+ 
+
+ align:start position:0%
+from specifications through many layers
+of design and then implementation yes
+
+ align:start position:0%
+of design and then implementation yes
+ 
+
+ align:start position:0%
+of design and then implementation yes
+it's curious if you think that's
+
+ align:start position:0%
+it's curious if you think that's
+ 
+
+ align:start position:0%
+it's curious if you think that's
+realistic well I think that some of its
+
+ align:start position:0%
+realistic well I think that some of its
+ 
+
+ align:start position:0%
+realistic well I think that some of its
+realistic and some of it isn't I mean
+
+ align:start position:0%
+realistic and some of it isn't I mean
+ 
+
+ align:start position:0%
+realistic and some of it isn't I mean
+surely if I want to build an electrical
+
+ align:start position:0%
+surely if I want to build an electrical
+ 
+
+ align:start position:0%
+surely if I want to build an electrical
+filter okay and I have a rather
+
+ align:start position:0%
+filter okay and I have a rather
+ 
+
+ align:start position:0%
+filter okay and I have a rather
+interesting possibility right supposing
+
+ align:start position:0%
+interesting possibility right supposing
+ 
+
+ align:start position:0%
+interesting possibility right supposing
+I have I want to build a thing that
+
+ align:start position:0%
+I have I want to build a thing that
+ 
+
+ align:start position:0%
+I have I want to build a thing that
+matches that matches some power output
+
+ align:start position:0%
+matches that matches some power output
+ 
+
+ align:start position:0%
+matches that matches some power output
+to a radio transmitter right to a to
+
+ align:start position:0%
+to a radio transmitter right to a to
+ 
+
+ align:start position:0%
+to a radio transmitter right to a to
+some to some antenna and I'm really add
+
+ align:start position:0%
+some to some antenna and I'm really add
+ 
+
+ align:start position:0%
+some to some antenna and I'm really add
+this power I pray just helpless too bad
+
+ align:start position:0%
+this power I pray just helpless too bad
+ 
+
+ align:start position:0%
+this power I pray just helpless too bad
+here and the problem is they have
+
+ align:start position:0%
+here and the problem is they have
+ 
+
+ align:start position:0%
+here and the problem is they have
+different impedances I want them to
+
+ align:start position:0%
+different impedances I want them to
+ 
+
+ align:start position:0%
+different impedances I want them to
+match the impedances I also want to make
+
+ align:start position:0%
+match the impedances I also want to make
+ 
+
+ align:start position:0%
+match the impedances I also want to make
+a filter in there which is going to get
+
+ align:start position:0%
+a filter in there which is going to get
+ 
+
+ align:start position:0%
+a filter in there which is going to get
+rid of some harmonic radiation well one
+
+ align:start position:0%
+rid of some harmonic radiation well one
+ 
+
+ align:start position:0%
+rid of some harmonic radiation well one
+one old-fashioned technique for doing
+
+ align:start position:0%
+one old-fashioned technique for doing
+ 
+
+ align:start position:0%
+one old-fashioned technique for doing
+this is called image impedances or
+
+ align:start position:0%
+this is called image impedances or
+ 
+
+ align:start position:0%
+this is called image impedances or
+something like that and what you do is
+
+ align:start position:0%
+something like that and what you do is
+ 
+
+ align:start position:0%
+something like that and what you do is
+you say you have a basic module called
+
+ align:start position:0%
+you say you have a basic module called
+ 
+
+ align:start position:0%
+you say you have a basic module called
+an L section looks like this and this if
+
+ align:start position:0%
+an L section looks like this and this if
+ 
+
+ align:start position:0%
+an L section looks like this and this if
+I happen to connect this to some
+
+ align:start position:0%
+I happen to connect this to some
+ 
+
+ align:start position:0%
+I happen to connect this to some
+resistance R and if I make this
+
+ align:start position:0%
+resistance R and if I make this
+ 
+
+ align:start position:0%
+resistance R and if I make this
+impedance XXL and if it happens to be Q
+
+ align:start position:0%
+impedance XXL and if it happens to be Q
+ 
+
+ align:start position:0%
+impedance XXL and if it happens to be Q
+times R then this transit this produces
+
+ align:start position:0%
+times R then this transit this produces
+ 
+
+ align:start position:0%
+times R then this transit this produces
+a a low-pass filter with a Q square plus
+
+ align:start position:0%
+a a low-pass filter with a Q square plus
+ 
+
+ align:start position:0%
+a a low-pass filter with a Q square plus
+one impedance match okay just what I
+
+ align:start position:0%
+one impedance match okay just what I
+ 
+
+ align:start position:0%
+one impedance match okay just what I
+need because now I can take two of these
+
+ align:start position:0%
+need because now I can take two of these
+ 
+
+ align:start position:0%
+need because now I can take two of these
+hook them together like this
+
+ align:start position:0%
+hook them together like this
+ 
+
+ align:start position:0%
+hook them together like this
+okay okay and I take another one okay
+
+ align:start position:0%
+okay okay and I take another one okay
+ 
+
+ align:start position:0%
+okay okay and I take another one okay
+and then I'll hook them together like
+
+ align:start position:0%
+and then I'll hook them together like
+ 
+
+ align:start position:0%
+and then I'll hook them together like
+that and I have two L sections hooked
+
+ align:start position:0%
+that and I have two L sections hooked
+ 
+
+ align:start position:0%
+that and I have two L sections hooked
+together and this little step the
+
+ align:start position:0%
+together and this little step the
+ 
+
+ align:start position:0%
+together and this little step the
+impedance down to one that I know and
+
+ align:start position:0%
+impedance down to one that I know and
+ 
+
+ align:start position:0%
+impedance down to one that I know and
+this will step it up to one I know each
+
+ align:start position:0%
+this will step it up to one I know each
+ 
+
+ align:start position:0%
+this will step it up to one I know each
+of these the low pass filter getting rid
+
+ align:start position:0%
+of these the low pass filter getting rid
+ 
+
+ align:start position:0%
+of these the low pass filter getting rid
+of some harmonics
+
+ align:start position:0%
+of some harmonics
+ 
+
+ align:start position:0%
+of some harmonics
+it's a good filter it's called apply
+
+ align:start position:0%
+it's a good filter it's called apply
+ 
+
+ align:start position:0%
+it's a good filter it's called apply
+section filter great okay except for the
+
+ align:start position:0%
+section filter great okay except for the
+ 
+
+ align:start position:0%
+section filter great okay except for the
+fact that in doing what I just did I've
+
+ align:start position:0%
+fact that in doing what I just did I've
+ 
+
+ align:start position:0%
+fact that in doing what I just did I've
+made a terrible I've made a terrible
+
+ align:start position:0%
+made a terrible I've made a terrible
+ 
+
+ align:start position:0%
+made a terrible I've made a terrible
+inefficiency in this system I've made
+
+ align:start position:0%
+inefficiency in this system I've made
+ 
+
+ align:start position:0%
+inefficiency in this system I've made
+two coils where I should have made one
+
+ align:start position:0%
+two coils where I should have made one
+ 
+
+ align:start position:0%
+two coils where I should have made one
+and the problem with most software
+
+ align:start position:0%
+and the problem with most software
+ 
+
+ align:start position:0%
+and the problem with most software
+engineering arms is that there's no
+
+ align:start position:0%
+engineering arms is that there's no
+ 
+
+ align:start position:0%
+engineering arms is that there's no
+matter there's no mechanism other than
+
+ align:start position:0%
+matter there's no mechanism other than
+ 
+
+ align:start position:0%
+matter there's no mechanism other than
+people optimization and
+
+ align:start position:0%
+people optimization and
+ 
+
+ align:start position:0%
+people optimization and
+Wyler's for getting rid of the redundant
+
+ align:start position:0%
+Wyler's for getting rid of the redundant
+ 
+
+ align:start position:0%
+Wyler's for getting rid of the redundant
+parts that constructed when doing
+
+ align:start position:0%
+parts that constructed when doing
+ 
+
+ align:start position:0%
+parts that constructed when doing
+top-down design okay and it's even worse
+
+ align:start position:0%
+top-down design okay and it's even worse
+ 
+
+ align:start position:0%
+top-down design okay and it's even worse
+there are lots of very important
+
+ align:start position:0%
+there are lots of very important
+ 
+
+ align:start position:0%
+there are lots of very important
+structures that you can construct it all
+
+ align:start position:0%
+structures that you can construct it all
+ 
+
+ align:start position:0%
+structures that you can construct it all
+this way yeah so I think that I think
+
+ align:start position:0%
+this way yeah so I think that I think
+ 
+
+ align:start position:0%
+this way yeah so I think that I think
+that the standard top-down design is a
+
+ align:start position:0%
+that the standard top-down design is a
+ 
+
+ align:start position:0%
+that the standard top-down design is a
+rather shallow business doesn't really
+
+ align:start position:0%
+rather shallow business doesn't really
+ 
+
+ align:start position:0%
+rather shallow business doesn't really
+capture what people want to do in design
+
+ align:start position:0%
+capture what people want to do in design
+ 
+
+ align:start position:0%
+capture what people want to do in design
+give you another electrical example
+
+ align:start position:0%
+give you another electrical example
+ 
+
+ align:start position:0%
+give you another electrical example
+Electrical examples is so much clearer
+
+ align:start position:0%
+Electrical examples is so much clearer
+ 
+
+ align:start position:0%
+Electrical examples is so much clearer
+than computational examples because
+
+ align:start position:0%
+than computational examples because
+ 
+
+ align:start position:0%
+than computational examples because
+computational examples require a certain
+
+ align:start position:0%
+computational examples require a certain
+ 
+
+ align:start position:0%
+computational examples require a certain
+degree of complexity to explain them but
+
+ align:start position:0%
+degree of complexity to explain them but
+ 
+
+ align:start position:0%
+degree of complexity to explain them but
+one of my favorite examples in the
+
+ align:start position:0%
+one of my favorite examples in the
+ 
+
+ align:start position:0%
+one of my favorite examples in the
+electrical world and how would I ever
+
+ align:start position:0%
+electrical world and how would I ever
+ 
+
+ align:start position:0%
+electrical world and how would I ever
+come up with the output stage and that's
+
+ align:start position:0%
+come up with the output stage and that's
+ 
+
+ align:start position:0%
+come up with the output stage and that's
+this interstage connection in an if'
+
+ align:start position:0%
+this interstage connection in an if'
+ 
+
+ align:start position:0%
+this interstage connection in an if'
+amplifier that some little transistor
+
+ align:start position:0%
+amplifier that some little transistor
+ 
+
+ align:start position:0%
+amplifier that some little transistor
+here and oh let's see well I'm gonna
+
+ align:start position:0%
+here and oh let's see well I'm gonna
+ 
+
+ align:start position:0%
+here and oh let's see well I'm gonna
+have a tank and I'm gonna hook this up
+
+ align:start position:0%
+have a tank and I'm gonna hook this up
+ 
+
+ align:start position:0%
+have a tank and I'm gonna hook this up
+to say I'm gonna link couple that to the
+
+ align:start position:0%
+to say I'm gonna link couple that to the
+ 
+
+ align:start position:0%
+to say I'm gonna link couple that to the
+input of the next stage okay here's a
+
+ align:start position:0%
+input of the next stage okay here's a
+ 
+
+ align:start position:0%
+input of the next stage okay here's a
+perfectly plausible plan well except for
+
+ align:start position:0%
+perfectly plausible plan well except for
+ 
+
+ align:start position:0%
+perfectly plausible plan well except for
+the fact that since I put that going up
+
+ align:start position:0%
+the fact that since I put that going up
+ 
+
+ align:start position:0%
+the fact that since I put that going up
+I should make that going that way okay
+
+ align:start position:0%
+I should make that going that way okay
+ 
+
+ align:start position:0%
+I should make that going that way okay
+here's a perfectly plausible plan for a
+
+ align:start position:0%
+here's a perfectly plausible plan for a
+ 
+
+ align:start position:0%
+here's a perfectly plausible plan for a
+no I shouldn't I'm done excuse me it
+
+ align:start position:0%
+no I shouldn't I'm done excuse me it
+ 
+
+ align:start position:0%
+no I shouldn't I'm done excuse me it
+doesn't matter the points use a
+
+ align:start position:0%
+doesn't matter the points use a
+ 
+
+ align:start position:0%
+doesn't matter the points use a
+perfectly flowing plan for coupling two
+
+ align:start position:0%
+perfectly flowing plan for coupling two
+ 
+
+ align:start position:0%
+perfectly flowing plan for coupling two
+stages together okay now what problem is
+
+ align:start position:0%
+stages together okay now what problem is
+ 
+
+ align:start position:0%
+stages together okay now what problem is
+is what's this hierarchically it's not
+
+ align:start position:0%
+is what's this hierarchically it's not
+ 
+
+ align:start position:0%
+is what's this hierarchically it's not
+one thing and hierarchically it doesn't
+
+ align:start position:0%
+one thing and hierarchically it doesn't
+ 
+
+ align:start position:0%
+one thing and hierarchically it doesn't
+make any sense at all it's the it's the
+
+ align:start position:0%
+make any sense at all it's the it's the
+ 
+
+ align:start position:0%
+make any sense at all it's the it's the
+inductance of a tuned circuit it's the
+
+ align:start position:0%
+inductance of a tuned circuit it's the
+ 
+
+ align:start position:0%
+inductance of a tuned circuit it's the
+it's the primary of a transformer and
+
+ align:start position:0%
+it's the primary of a transformer and
+ 
+
+ align:start position:0%
+it's the primary of a transformer and
+it's also the DC path by which bias
+
+ align:start position:0%
+it's also the DC path by which bias
+ 
+
+ align:start position:0%
+it's also the DC path by which bias
+conditions get to the collector of that
+
+ align:start position:0%
+conditions get to the collector of that
+ 
+
+ align:start position:0%
+conditions get to the collector of that
+transistor and there's no simple
+
+ align:start position:0%
+transistor and there's no simple
+ 
+
+ align:start position:0%
+transistor and there's no simple
+top-down design that's going to produce
+
+ align:start position:0%
+top-down design that's going to produce
+ 
+
+ align:start position:0%
+top-down design that's going to produce
+a structure like that with so many
+
+ align:start position:0%
+a structure like that with so many
+ 
+
+ align:start position:0%
+a structure like that with so many
+overlapping from overlapping uses for a
+
+ align:start position:0%
+overlapping from overlapping uses for a
+ 
+
+ align:start position:0%
+overlapping from overlapping uses for a
+particular thing playing playing
+
+ align:start position:0%
+particular thing playing playing
+ 
+
+ align:start position:0%
+particular thing playing playing
+Scrabble we have to do triple word
+
+ align:start position:0%
+Scrabble we have to do triple word
+ 
+
+ align:start position:0%
+Scrabble we have to do triple word
+scores or whatever it's not so easy and
+
+ align:start position:0%
+scores or whatever it's not so easy and
+ 
+
+ align:start position:0%
+scores or whatever it's not so easy and
+top-down design top-down design strategy
+
+ align:start position:0%
+top-down design top-down design strategy
+ 
+
+ align:start position:0%
+top-down design top-down design strategy
+yet most of real engineering is based on
+
+ align:start position:0%
+yet most of real engineering is based on
+ 
+
+ align:start position:0%
+yet most of real engineering is based on
+on getting the most for for effort and
+
+ align:start position:0%
+on getting the most for for effort and
+ 
+
+ align:start position:0%
+on getting the most for for effort and
+that's what you're seeing here is this
+
+ align:start position:0%
+that's what you're seeing here is this
+ 
+
+ align:start position:0%
+that's what you're seeing here is this
+the last question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+apparently so thank you
+
+ align:start position:0%
+apparently so thank you
+ 
+
+ align:start position:0%
+apparently so thank you
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+[Music]
\ No newline at end of file
diff --git a/AbbajZZZxVE.txt b/AbbajZZZxVE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..52244fad31013c404b082d7a1fc9e56b736055e9
--- /dev/null
+++ b/AbbajZZZxVE.txt
@@ -0,0 +1,7600 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this I'm
+
+ align:start position:0%
+this I'm
+ 
+
+ align:start position:0%
+this I'm
+impressed um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good morning morning I'm not Don sadway
+
+ align:start position:0%
+good morning morning I'm not Don sadway
+ 
+
+ align:start position:0%
+good morning morning I'm not Don sadway
+as you can tell he's at a conference I'm
+
+ align:start position:0%
+as you can tell he's at a conference I'm
+ 
+
+ align:start position:0%
+as you can tell he's at a conference I'm
+not sure I think it's in
+
+ align:start position:0%
+not sure I think it's in
+ 
+
+ align:start position:0%
+not sure I think it's in
+Halifax no what the heck can you have in
+
+ align:start position:0%
+Halifax no what the heck can you have in
+ 
+
+ align:start position:0%
+Halifax no what the heck can you have in
+Halifax education okay um a couple of
+
+ align:start position:0%
+Halifax education okay um a couple of
+ 
+
+ align:start position:0%
+Halifax education okay um a couple of
+announcements the obvious the first test
+
+ align:start position:0%
+announcements the obvious the first test
+ 
+
+ align:start position:0%
+announcements the obvious the first test
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+Wednesday um maybe not so obvious but
+
+ align:start position:0%
+Wednesday um maybe not so obvious but
+ 
+
+ align:start position:0%
+Wednesday um maybe not so obvious but
+it's posted on the uh on the website uh
+
+ align:start position:0%
+it's posted on the uh on the website uh
+ 
+
+ align:start position:0%
+it's posted on the uh on the website uh
+there'll be a review session for those
+
+ align:start position:0%
+there'll be a review session for those
+ 
+
+ align:start position:0%
+there'll be a review session for those
+of you who care to come uh given by
+
+ align:start position:0%
+of you who care to come uh given by
+ 
+
+ align:start position:0%
+of you who care to come uh given by
+myself in
+
+ align:start position:0%
+myself in
+ 
+
+ align:start position:0%
+myself in
+26100 tomorrow night starting at 700
+
+ align:start position:0%
+26100 tomorrow night starting at 700
+ 
+
+ align:start position:0%
+26100 tomorrow night starting at 700
+p.m. uh going until the last question is
+
+ align:start position:0%
+p.m. uh going until the last question is
+ 
+
+ align:start position:0%
+p.m. uh going until the last question is
+answered that's why the
+
+ align:start position:0%
+answered that's why the
+ 
+
+ align:start position:0%
+answered that's why the
+infinity um please don't show up at
+
+ align:start position:0%
+infinity um please don't show up at
+ 
+
+ align:start position:0%
+infinity um please don't show up at
+10:30 or 11: and start asking questions
+
+ align:start position:0%
+10:30 or 11: and start asking questions
+ 
+
+ align:start position:0%
+10:30 or 11: and start asking questions
+I just flew in from Beijing for those of
+
+ align:start position:0%
+I just flew in from Beijing for those of
+ 
+
+ align:start position:0%
+I just flew in from Beijing for those of
+you uh who don't realize that it's now
+
+ align:start position:0%
+you uh who don't realize that it's now
+ 
+
+ align:start position:0%
+you uh who don't realize that it's now
+about 12 o'clock in the evening tomorrow
+
+ align:start position:0%
+about 12 o'clock in the evening tomorrow
+ 
+
+ align:start position:0%
+about 12 o'clock in the evening tomorrow
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+Beijing yeah so um anyway I'll probably
+
+ align:start position:0%
+Beijing yeah so um anyway I'll probably
+ 
+
+ align:start position:0%
+Beijing yeah so um anyway I'll probably
+fall asleep by about
+
+ align:start position:0%
+fall asleep by about
+ 
+
+ align:start position:0%
+fall asleep by about
+10:30 anyway okay uh one one little
+
+ align:start position:0%
+10:30 anyway okay uh one one little
+ 
+
+ align:start position:0%
+10:30 anyway okay uh one one little
+thing about the quiz U Professor sway
+
+ align:start position:0%
+thing about the quiz U Professor sway
+ 
+
+ align:start position:0%
+thing about the quiz U Professor sway
+always gives um some admonitions about
+
+ align:start position:0%
+always gives um some admonitions about
+ 
+
+ align:start position:0%
+always gives um some admonitions about
+how to take these quizzes and um one
+
+ align:start position:0%
+how to take these quizzes and um one
+ 
+
+ align:start position:0%
+how to take these quizzes and um one
+thing that I'd like to add to it and
+
+ align:start position:0%
+thing that I'd like to add to it and
+ 
+
+ align:start position:0%
+thing that I'd like to add to it and
+that is and I've told this to my
+
+ align:start position:0%
+that is and I've told this to my
+ 
+
+ align:start position:0%
+that is and I've told this to my
+recitation sections that when you do
+
+ align:start position:0%
+recitation sections that when you do
+ 
+
+ align:start position:0%
+recitation sections that when you do
+these quizzes in spite of the fact that
+
+ align:start position:0%
+these quizzes in spite of the fact that
+ 
+
+ align:start position:0%
+these quizzes in spite of the fact that
+it might be trivial in some some cases
+
+ align:start position:0%
+it might be trivial in some some cases
+ 
+
+ align:start position:0%
+it might be trivial in some some cases
+make sure you carry the units through if
+
+ align:start position:0%
+make sure you carry the units through if
+ 
+
+ align:start position:0%
+make sure you carry the units through if
+you got a if you got a problem that has
+
+ align:start position:0%
+you got a if you got a problem that has
+ 
+
+ align:start position:0%
+you got a if you got a problem that has
+units associated with it do the exercise
+
+ align:start position:0%
+units associated with it do the exercise
+ 
+
+ align:start position:0%
+units associated with it do the exercise
+of carrying the units through because
+
+ align:start position:0%
+of carrying the units through because
+ 
+
+ align:start position:0%
+of carrying the units through because
+guess
+
+ align:start position:0%
+guess
+ 
+
+ align:start position:0%
+guess
+what if you if the units come out are
+
+ align:start position:0%
+what if you if the units come out are
+ 
+
+ align:start position:0%
+what if you if the units come out are
+supposed to come out in meters per
+
+ align:start position:0%
+supposed to come out in meters per
+ 
+
+ align:start position:0%
+supposed to come out in meters per
+second and you get seconds per meter
+
+ align:start position:0%
+second and you get seconds per meter
+ 
+
+ align:start position:0%
+second and you get seconds per meter
+what do you figure the chances of that
+
+ align:start position:0%
+what do you figure the chances of that
+ 
+
+ align:start position:0%
+what do you figure the chances of that
+problem being
+
+ align:start position:0%
+problem being
+ 
+
+ align:start position:0%
+problem being
+RAR zero all right if the units come out
+
+ align:start position:0%
+RAR zero all right if the units come out
+ 
+
+ align:start position:0%
+RAR zero all right if the units come out
+meters per second you'll quickly
+
+ align:start position:0%
+meters per second you'll quickly
+ 
+
+ align:start position:0%
+meters per second you'll quickly
+discover that the problem in 3091 are
+
+ align:start position:0%
+discover that the problem in 3091 are
+ 
+
+ align:start position:0%
+discover that the problem in 3091 are
+just not that
+
+ align:start position:0%
+just not that
+ 
+
+ align:start position:0%
+just not that
+complicated and so even by units
+
+ align:start position:0%
+complicated and so even by units
+ 
+
+ align:start position:0%
+complicated and so even by units
+analysis if the units come out right you
+
+ align:start position:0%
+analysis if the units come out right you
+ 
+
+ align:start position:0%
+analysis if the units come out right you
+got a good shot that unless unless
+
+ align:start position:0%
+got a good shot that unless unless
+ 
+
+ align:start position:0%
+got a good shot that unless unless
+you've really really messed up that the
+
+ align:start position:0%
+you've really really messed up that the
+ 
+
+ align:start position:0%
+you've really really messed up that the
+uh that the answer is going to be right
+
+ align:start position:0%
+uh that the answer is going to be right
+ 
+
+ align:start position:0%
+uh that the answer is going to be right
+the second thing is uh ballark it that
+
+ align:start position:0%
+the second thing is uh ballark it that
+ 
+
+ align:start position:0%
+the second thing is uh ballark it that
+is to say guess the answer ahead of time
+
+ align:start position:0%
+is to say guess the answer ahead of time
+ 
+
+ align:start position:0%
+is to say guess the answer ahead of time
+strip all the decimal places off just go
+
+ align:start position:0%
+strip all the decimal places off just go
+ 
+
+ align:start position:0%
+strip all the decimal places off just go
+go with powers of 10 and then seeing
+
+ align:start position:0%
+go with powers of 10 and then seeing
+ 
+
+ align:start position:0%
+go with powers of 10 and then seeing
+what the answer should be and you'll be
+
+ align:start position:0%
+what the answer should be and you'll be
+ 
+
+ align:start position:0%
+what the answer should be and you'll be
+within 25 or 30% every time
+
+ align:start position:0%
+within 25 or 30% every time
+ 
+
+ align:start position:0%
+within 25 or 30% every time
+and that's a good thing to know because
+
+ align:start position:0%
+and that's a good thing to know because
+ 
+
+ align:start position:0%
+and that's a good thing to know because
+if you come out with an answer that's
+
+ align:start position:0%
+if you come out with an answer that's
+ 
+
+ align:start position:0%
+if you come out with an answer that's
+somewhere near the diameter of the
+
+ align:start position:0%
+somewhere near the diameter of the
+ 
+
+ align:start position:0%
+somewhere near the diameter of the
+universe and it's supposed to be the
+
+ align:start position:0%
+universe and it's supposed to be the
+ 
+
+ align:start position:0%
+universe and it's supposed to be the
+diameter of an atom then you'll know
+
+ align:start position:0%
+diameter of an atom then you'll know
+ 
+
+ align:start position:0%
+diameter of an atom then you'll know
+that you probably made a mistake so
+
+ align:start position:0%
+that you probably made a mistake so
+ 
+
+ align:start position:0%
+that you probably made a mistake so
+those are two pieces of
+
+ align:start position:0%
+those are two pieces of
+ 
+
+ align:start position:0%
+those are two pieces of
+advice okay last day um uh you talked
+
+ align:start position:0%
+advice okay last day um uh you talked
+ 
+
+ align:start position:0%
+advice okay last day um uh you talked
+about the borne Hab cycle uh an octet
+
+ align:start position:0%
+about the borne Hab cycle uh an octet
+ 
+
+ align:start position:0%
+about the borne Hab cycle uh an octet
+stability via electron transfer uh the
+
+ align:start position:0%
+stability via electron transfer uh the
+ 
+
+ align:start position:0%
+stability via electron transfer uh the
+born haer cycle was designed to allow us
+
+ align:start position:0%
+born haer cycle was designed to allow us
+ 
+
+ align:start position:0%
+born haer cycle was designed to allow us
+to calculate the
+
+ align:start position:0%
+to calculate the
+ 
+
+ align:start position:0%
+to calculate the
+energetics of uh in particular the ionic
+
+ align:start position:0%
+energetics of uh in particular the ionic
+ 
+
+ align:start position:0%
+energetics of uh in particular the ionic
+Bond and the thing we need to remember
+
+ align:start position:0%
+Bond and the thing we need to remember
+ 
+
+ align:start position:0%
+Bond and the thing we need to remember
+or a couple of things at least and that
+
+ align:start position:0%
+or a couple of things at least and that
+ 
+
+ align:start position:0%
+or a couple of things at least and that
+is is that the lattice energy as is um
+
+ align:start position:0%
+is is that the lattice energy as is um
+ 
+
+ align:start position:0%
+is is that the lattice energy as is um
+depicted by the madin constant is
+
+ align:start position:0%
+depicted by the madin constant is
+ 
+
+ align:start position:0%
+depicted by the madin constant is
+dominant and that the mlin constant what
+
+ align:start position:0%
+dominant and that the mlin constant what
+ 
+
+ align:start position:0%
+dominant and that the mlin constant what
+does it represent it represents it's a
+
+ align:start position:0%
+does it represent it represents it's a
+ 
+
+ align:start position:0%
+does it represent it represents it's a
+geometric Factor That's Unique for each
+
+ align:start position:0%
+geometric Factor That's Unique for each
+ 
+
+ align:start position:0%
+geometric Factor That's Unique for each
+crystal structure so that's something
+
+ align:start position:0%
+crystal structure so that's something
+ 
+
+ align:start position:0%
+crystal structure so that's something
+you go and look up so you go and look
+
+ align:start position:0%
+you go and look up so you go and look
+ 
+
+ align:start position:0%
+you go and look up so you go and look
+that up and um and those are the key uh
+
+ align:start position:0%
+that up and um and those are the key uh
+ 
+
+ align:start position:0%
+that up and um and those are the key uh
+those are the key things and and as a
+
+ align:start position:0%
+those are the key things and and as a
+ 
+
+ align:start position:0%
+those are the key things and and as a
+result of that
+
+ align:start position:0%
+result of that
+ 
+
+ align:start position:0%
+result of that
+uh the um achieving of octed stability
+
+ align:start position:0%
+uh the um achieving of octed stability
+ 
+
+ align:start position:0%
+uh the um achieving of octed stability
+VI electrons transfer we tumbled to the
+
+ align:start position:0%
+VI electrons transfer we tumbled to the
+ 
+
+ align:start position:0%
+VI electrons transfer we tumbled to the
+idea of an ionic bond an ionic bond
+
+ align:start position:0%
+idea of an ionic bond an ionic bond
+ 
+
+ align:start position:0%
+idea of an ionic bond an ionic bond
+where one atom donates an electron
+
+ align:start position:0%
+where one atom donates an electron
+ 
+
+ align:start position:0%
+where one atom donates an electron
+completely to the other atom sort of
+
+ align:start position:0%
+completely to the other atom sort of
+ 
+
+ align:start position:0%
+completely to the other atom sort of
+like servanthood one donates yourself
+
+ align:start position:0%
+like servanthood one donates yourself
+ 
+
+ align:start position:0%
+like servanthood one donates yourself
+completely to a to another okay so
+
+ align:start position:0%
+completely to a to another okay so
+ 
+
+ align:start position:0%
+completely to a to another okay so
+that's where we are but um we got a few
+
+ align:start position:0%
+that's where we are but um we got a few
+ 
+
+ align:start position:0%
+that's where we are but um we got a few
+problems okay sodium chloride Works
+
+ align:start position:0%
+problems okay sodium chloride Works
+ 
+
+ align:start position:0%
+problems okay sodium chloride Works
+magnesium chloride chloride Works
+
+ align:start position:0%
+magnesium chloride chloride Works
+ 
+
+ align:start position:0%
+magnesium chloride chloride Works
+magnesium oxide works all of these from
+
+ align:start position:0%
+magnesium oxide works all of these from
+ 
+
+ align:start position:0%
+magnesium oxide works all of these from
+the group one and two through the group
+
+ align:start position:0%
+the group one and two through the group
+ 
+
+ align:start position:0%
+the group one and two through the group
+U group five and six elements but what
+
+ align:start position:0%
+U group five and six elements but what
+ 
+
+ align:start position:0%
+U group five and six elements but what
+about what about elements what about
+
+ align:start position:0%
+about what about elements what about
+ 
+
+ align:start position:0%
+about what about elements what about
+molecules like hydrogen or nitrogen or
+
+ align:start position:0%
+molecules like hydrogen or nitrogen or
+ 
+
+ align:start position:0%
+molecules like hydrogen or nitrogen or
+maybe oxygen or we can keep on going
+
+ align:start position:0%
+maybe oxygen or we can keep on going
+ 
+
+ align:start position:0%
+maybe oxygen or we can keep on going
+chlorine all right we know these are
+
+ align:start position:0%
+chlorine all right we know these are
+ 
+
+ align:start position:0%
+chlorine all right we know these are
+stable um we know these are stable and
+
+ align:start position:0%
+stable um we know these are stable and
+ 
+
+ align:start position:0%
+stable um we know these are stable and
+if we wanted to try to try to fit say
+
+ align:start position:0%
+if we wanted to try to try to fit say
+ 
+
+ align:start position:0%
+if we wanted to try to try to fit say
+hydrogen into this scheme that we have
+
+ align:start position:0%
+hydrogen into this scheme that we have
+ 
+
+ align:start position:0%
+hydrogen into this scheme that we have
+we'd have to do what we'd have to figure
+
+ align:start position:0%
+we'd have to do what we'd have to figure
+ 
+
+ align:start position:0%
+we'd have to do what we'd have to figure
+out a way to achieve octet stability by
+
+ align:start position:0%
+out a way to achieve octet stability by
+ 
+
+ align:start position:0%
+out a way to achieve octet stability by
+electron transfer well we've got two
+
+ align:start position:0%
+electron transfer well we've got two
+ 
+
+ align:start position:0%
+electron transfer well we've got two
+hydrogen we got two hydrogen atoms here
+
+ align:start position:0%
+hydrogen we got two hydrogen atoms here
+ 
+
+ align:start position:0%
+hydrogen we got two hydrogen atoms here
+and well what would have to happen Well
+
+ align:start position:0%
+and well what would have to happen Well
+ 
+
+ align:start position:0%
+and well what would have to happen Well
+we'd have to have one of these hydrogen
+
+ align:start position:0%
+we'd have to have one of these hydrogen
+ 
+
+ align:start position:0%
+we'd have to have one of these hydrogen
+atoms go to a to an H+ plus an electron
+
+ align:start position:0%
+atoms go to a to an H+ plus an electron
+ 
+
+ align:start position:0%
+atoms go to a to an H+ plus an electron
+right so now we
+
+ align:start position:0%
+right so now we
+ 
+
+ align:start position:0%
+right so now we
+have a hydrogen ion here but at the same
+
+ align:start position:0%
+have a hydrogen ion here but at the same
+ 
+
+ align:start position:0%
+have a hydrogen ion here but at the same
+time another hydrogen would have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would have to do that and clearly we
+
+ align:start position:0%
+would have to do that and clearly we
+ 
+
+ align:start position:0%
+would have to do that and clearly we
+can't do
+
+ align:start position:0%
+can't do
+ 
+
+ align:start position:0%
+can't do
+both this one
+
+ align:start position:0%
+both this one
+ 
+
+ align:start position:0%
+both this one
+here is what hydrogen with an added
+
+ align:start position:0%
+here is what hydrogen with an added
+ 
+
+ align:start position:0%
+here is what hydrogen with an added
+electron that's ISO electronic with
+
+ align:start position:0%
+electron that's ISO electronic with
+ 
+
+ align:start position:0%
+electron that's ISO electronic with
+helium this thing here this is just a
+
+ align:start position:0%
+helium this thing here this is just a
+ 
+
+ align:start position:0%
+helium this thing here this is just a
+naked proton so it doesn't it doesn't
+
+ align:start position:0%
+naked proton so it doesn't it doesn't
+ 
+
+ align:start position:0%
+naked proton so it doesn't it doesn't
+work it doesn't work so we need to find
+
+ align:start position:0%
+work it doesn't work so we need to find
+ 
+
+ align:start position:0%
+work it doesn't work so we need to find
+another scheme
+
+ align:start position:0%
+another scheme
+ 
+
+ align:start position:0%
+another scheme
+and that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution was provided for us by GN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lewis right GN Lewis and he asked the
+
+ align:start position:0%
+Lewis right GN Lewis and he asked the
+ 
+
+ align:start position:0%
+Lewis right GN Lewis and he asked the
+question what
+
+ align:start position:0%
+question what
+ 
+
+ align:start position:0%
+question what
+if if we
+
+ align:start position:0%
+if if we
+ 
+
+ align:start position:0%
+if if we
+could
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+share electrons and by now I'm meaning
+
+ align:start position:0%
+share electrons and by now I'm meaning
+ 
+
+ align:start position:0%
+share electrons and by now I'm meaning
+the veence electrons all right what if
+
+ align:start position:0%
+the veence electrons all right what if
+ 
+
+ align:start position:0%
+the veence electrons all right what if
+we could share what if we could share
+
+ align:start position:0%
+we could share what if we could share
+ 
+
+ align:start position:0%
+we could share what if we could share
+electrons well let's look at hydrogen
+
+ align:start position:0%
+electrons well let's look at hydrogen
+ 
+
+ align:start position:0%
+electrons well let's look at hydrogen
+and see what would happen well we know
+
+ align:start position:0%
+and see what would happen well we know
+ 
+
+ align:start position:0%
+and see what would happen well we know
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+hydrogen is 1s right so if we take
+
+ align:start position:0%
+hydrogen is 1s right so if we take
+ 
+
+ align:start position:0%
+hydrogen is 1s right so if we take
+another hydrogen we stick it over here 1
+
+ align:start position:0%
+another hydrogen we stick it over here 1
+ 
+
+ align:start position:0%
+another hydrogen we stick it over here 1
+s we know we have an electron here and
+
+ align:start position:0%
+s we know we have an electron here and
+ 
+
+ align:start position:0%
+s we know we have an electron here and
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+say the X denotes the other the electron
+
+ align:start position:0%
+say the X denotes the other the electron
+ 
+
+ align:start position:0%
+say the X denotes the other the electron
+from this hydrogen and now we
+
+ align:start position:0%
+from this hydrogen and now we
+ 
+
+ align:start position:0%
+from this hydrogen and now we
+form a bond
+
+ align:start position:0%
+form a bond
+ 
+
+ align:start position:0%
+form a bond
+and what do we have well this
+
+ align:start position:0%
+and what do we have well this
+ 
+
+ align:start position:0%
+and what do we have well this
+is isoelectronic with helium right and
+
+ align:start position:0%
+is isoelectronic with helium right and
+ 
+
+ align:start position:0%
+is isoelectronic with helium right and
+so is
+
+ align:start position:0%
+so is
+ 
+
+ align:start position:0%
+so is
+this ISO electronic with helium and so
+
+ align:start position:0%
+this ISO electronic with helium and so
+ 
+
+ align:start position:0%
+this ISO electronic with helium and so
+we think we and we have a uh both each
+
+ align:start position:0%
+we think we and we have a uh both each
+ 
+
+ align:start position:0%
+we think we and we have a uh both each
+hydrogen has access to each
+
+ align:start position:0%
+hydrogen has access to each
+ 
+
+ align:start position:0%
+hydrogen has access to each
+electron and now we have a satisfied
+
+ align:start position:0%
+electron and now we have a satisfied
+ 
+
+ align:start position:0%
+electron and now we have a satisfied
+system now we could do the same thing
+
+ align:start position:0%
+system now we could do the same thing
+ 
+
+ align:start position:0%
+system now we could do the same thing
+with well we're going to do it do it
+
+ align:start position:0%
+with well we're going to do it do it
+ 
+
+ align:start position:0%
+with well we're going to do it do it
+with nitrogen in a minute but this is a
+
+ align:start position:0%
+with nitrogen in a minute but this is a
+ 
+
+ align:start position:0%
+with nitrogen in a minute but this is a
+case where we have we have two two atoms
+
+ align:start position:0%
+case where we have we have two two atoms
+ 
+
+ align:start position:0%
+case where we have we have two two atoms
+sharing electrons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in general what we have is sharing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to sharing to achieve electron of octet
+
+ align:start position:0%
+to sharing to achieve electron of octet
+ 
+
+ align:start position:0%
+to sharing to achieve electron of octet
+stability let's take a look at let's
+
+ align:start position:0%
+stability let's take a look at let's
+ 
+
+ align:start position:0%
+stability let's take a look at let's
+look at nitrogen to see if it goes a to
+
+ align:start position:0%
+look at nitrogen to see if it goes a to
+ 
+
+ align:start position:0%
+look at nitrogen to see if it goes a to
+see to see if it it applies it applies
+
+ align:start position:0%
+see to see if it it applies it applies
+ 
+
+ align:start position:0%
+see to see if it it applies it applies
+there as well well we know nitrogen has
+
+ align:start position:0%
+there as well well we know nitrogen has
+ 
+
+ align:start position:0%
+there as well well we know nitrogen has
+what nitrogen is uh 1 S2 2
+
+ align:start position:0%
+what nitrogen is uh 1 S2 2
+ 
+
+ align:start position:0%
+what nitrogen is uh 1 S2 2
+S2
+
+ align:start position:0%
+S2
+ 
+
+ align:start position:0%
+S2
+2p3
+
+ align:start position:0%
+2p3
+ 
+
+ align:start position:0%
+2p3
+so we've got five electrons here in the
+
+ align:start position:0%
+so we've got five electrons here in the
+ 
+
+ align:start position:0%
+so we've got five electrons here in the
+v in the veent Shell if we take
+
+ align:start position:0%
+v in the veent Shell if we take
+ 
+
+ align:start position:0%
+v in the veent Shell if we take
+nitrogen we've got n N2 and let's just
+
+ align:start position:0%
+nitrogen we've got n N2 and let's just
+ 
+
+ align:start position:0%
+nitrogen we've got n N2 and let's just
+we go one two three whoops four
+
+ align:start position:0%
+we go one two three whoops four
+ 
+
+ align:start position:0%
+we go one two three whoops four
+five one 2 3 four five 1 2 3 4 5 6 7even
+
+ align:start position:0%
+five one 2 3 four five 1 2 3 4 5 6 7even
+ 
+
+ align:start position:0%
+five one 2 3 four five 1 2 3 4 5 6 7even
+eight right 1 2 3 4 5 6 7 8 here we
+
+ align:start position:0%
+eight right 1 2 3 4 5 6 7 8 here we
+ 
+
+ align:start position:0%
+eight right 1 2 3 4 5 6 7 8 here we
+go we've got two cases where each one of
+
+ align:start position:0%
+go we've got two cases where each one of
+ 
+
+ align:start position:0%
+go we've got two cases where each one of
+those things
+
+ align:start position:0%
+those things
+ 
+
+ align:start position:0%
+those things
+now is isoelectric with NE
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neon and we have achieved octet
+
+ align:start position:0%
+neon and we have achieved octet
+ 
+
+ align:start position:0%
+neon and we have achieved octet
+stability
+
+ align:start position:0%
+stability
+ 
+
+ align:start position:0%
+stability
+um in the in the same way all right
+
+ align:start position:0%
+um in the in the same way all right
+ 
+
+ align:start position:0%
+um in the in the same way all right
+so Lewis called
+
+ align:start position:0%
+so Lewis called
+ 
+
+ align:start position:0%
+so Lewis called
+this he called what did he he called it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cooperative Co exact
+
+ align:start position:0%
+Cooperative Co exact
+ 
+
+ align:start position:0%
+Cooperative Co exact
+use of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+veence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrons right so you take the co here
+
+ align:start position:0%
+electrons right so you take the co here
+ 
+
+ align:start position:0%
+electrons right so you take the co here
+and we take the veence here and out of
+
+ align:start position:0%
+and we take the veence here and out of
+ 
+
+ align:start position:0%
+and we take the veence here and out of
+that comes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coent all right coent all right and
+
+ align:start position:0%
+coent all right coent all right and
+ 
+
+ align:start position:0%
+coent all right coent all right and
+let's be a little now we need to put a
+
+ align:start position:0%
+let's be a little now we need to put a
+ 
+
+ align:start position:0%
+let's be a little now we need to put a
+little um a little terminology here
+
+ align:start position:0%
+little um a little terminology here
+ 
+
+ align:start position:0%
+little um a little terminology here
+these this region in here contained the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bonding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+domains right and the non-bonding
+
+ align:start position:0%
+domains right and the non-bonding
+ 
+
+ align:start position:0%
+domains right and the non-bonding
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+non
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bonding non-bonding domains and this
+
+ align:start position:0%
+bonding non-bonding domains and this
+ 
+
+ align:start position:0%
+bonding non-bonding domains and this
+structure that's that I've depicted here
+
+ align:start position:0%
+structure that's that I've depicted here
+ 
+
+ align:start position:0%
+structure that's that I've depicted here
+using the X's and O's um is called the
+
+ align:start position:0%
+using the X's and O's um is called the
+ 
+
+ align:start position:0%
+using the X's and O's um is called the
+Lewis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure right it's called the it's
+
+ align:start position:0%
+structure right it's called the it's
+ 
+
+ align:start position:0%
+structure right it's called the it's
+called the Lewis structure
+
+ align:start position:0%
+called the Lewis structure
+ 
+
+ align:start position:0%
+called the Lewis structure
+and let's
+
+ align:start position:0%
+and let's
+ 
+
+ align:start position:0%
+and let's
+see this is actually from Lewis's notes
+
+ align:start position:0%
+see this is actually from Lewis's notes
+ 
+
+ align:start position:0%
+see this is actually from Lewis's notes
+now remember uh this is 1902 so there
+
+ align:start position:0%
+now remember uh this is 1902 so there
+ 
+
+ align:start position:0%
+now remember uh this is 1902 so there
+wasn't a whole lot going on there was a
+
+ align:start position:0%
+wasn't a whole lot going on there was a
+ 
+
+ align:start position:0%
+wasn't a whole lot going on there was a
+lot of physics going on but we didn't
+
+ align:start position:0%
+lot of physics going on but we didn't
+ 
+
+ align:start position:0%
+lot of physics going on but we didn't
+know a whole lot about atomic structure
+
+ align:start position:0%
+know a whole lot about atomic structure
+ 
+
+ align:start position:0%
+know a whole lot about atomic structure
+back in those days but you can see this
+
+ align:start position:0%
+back in those days but you can see this
+ 
+
+ align:start position:0%
+back in those days but you can see this
+is right out of his right out of his
+
+ align:start position:0%
+is right out of his right out of his
+ 
+
+ align:start position:0%
+is right out of his right out of his
+notebook and you can see he's arranged
+
+ align:start position:0%
+notebook and you can see he's arranged
+ 
+
+ align:start position:0%
+notebook and you can see he's arranged
+the atoms by row and he's trying to
+
+ align:start position:0%
+the atoms by row and he's trying to
+ 
+
+ align:start position:0%
+the atoms by row and he's trying to
+figure out see lithium has one buril
+
+ align:start position:0%
+figure out see lithium has one buril
+ 
+
+ align:start position:0%
+figure out see lithium has one buril
+uh magnesium have two Boron aluminum
+
+ align:start position:0%
+uh magnesium have two Boron aluminum
+ 
+
+ align:start position:0%
+uh magnesium have two Boron aluminum
+have three and he's trying to figure out
+
+ align:start position:0%
+have three and he's trying to figure out
+ 
+
+ align:start position:0%
+have three and he's trying to figure out
+how to arrange these things this is
+
+ align:start position:0%
+how to arrange these things this is
+ 
+
+ align:start position:0%
+how to arrange these things this is
+right out of his right out of his
+
+ align:start position:0%
+right out of his right out of his
+ 
+
+ align:start position:0%
+right out of his right out of his
+notebook and look up at the top
+
+ align:start position:0%
+notebook and look up at the top
+ 
+
+ align:start position:0%
+notebook and look up at the top
+here he's got a bit of a mistake he's
+
+ align:start position:0%
+here he's got a bit of a mistake he's
+ 
+
+ align:start position:0%
+here he's got a bit of a mistake he's
+trying to make helium octet stable he's
+
+ align:start position:0%
+trying to make helium octet stable he's
+ 
+
+ align:start position:0%
+trying to make helium octet stable he's
+trying to put eight electrons around
+
+ align:start position:0%
+trying to put eight electrons around
+ 
+
+ align:start position:0%
+trying to put eight electrons around
+helium and it ain't working right but
+
+ align:start position:0%
+helium and it ain't working right but
+ 
+
+ align:start position:0%
+helium and it ain't working right but
+look down
+
+ align:start position:0%
+look down
+ 
+
+ align:start position:0%
+look down
+here he's got a box within a box this is
+
+ align:start position:0%
+here he's got a box within a box this is
+ 
+
+ align:start position:0%
+here he's got a box within a box this is
+1902 this is reminiscent of what
+
+ align:start position:0%
+1902 this is reminiscent of what
+ 
+
+ align:start position:0%
+1902 this is reminiscent of what
+the shell structure which people hadn't
+
+ align:start position:0%
+the shell structure which people hadn't
+ 
+
+ align:start position:0%
+the shell structure which people hadn't
+even thought of so this is in his notes
+
+ align:start position:0%
+even thought of so this is in his notes
+ 
+
+ align:start position:0%
+even thought of so this is in his notes
+he didn't uh publish uh he didn't
+
+ align:start position:0%
+he didn't uh publish uh he didn't
+ 
+
+ align:start position:0%
+he didn't uh publish uh he didn't
+publish uh these notes and he didn't
+
+ align:start position:0%
+publish uh these notes and he didn't
+ 
+
+ align:start position:0%
+publish uh these notes and he didn't
+publish anything related to the Lewis
+
+ align:start position:0%
+publish anything related to the Lewis
+ 
+
+ align:start position:0%
+publish anything related to the Lewis
+structure until about 1912 or 1913 but
+
+ align:start position:0%
+structure until about 1912 or 1913 but
+ 
+
+ align:start position:0%
+structure until about 1912 or 1913 but
+you can see that he was
+
+ align:start position:0%
+you can see that he was
+ 
+
+ align:start position:0%
+you can see that he was
+thinking about this structure for all
+
+ align:start position:0%
+thinking about this structure for all
+ 
+
+ align:start position:0%
+thinking about this structure for all
+along whoops let's see if I can get this
+
+ align:start position:0%
+along whoops let's see if I can get this
+ 
+
+ align:start position:0%
+along whoops let's see if I can get this
+to let's see okay now this is a more
+
+ align:start position:0%
+to let's see okay now this is a more
+ 
+
+ align:start position:0%
+to let's see okay now this is a more
+formal look at that structure and you
+
+ align:start position:0%
+formal look at that structure and you
+ 
+
+ align:start position:0%
+formal look at that structure and you
+can see what you can see what he's done
+
+ align:start position:0%
+can see what you can see what he's done
+ 
+
+ align:start position:0%
+can see what you can see what he's done
+this is um I don't know what the dates
+
+ align:start position:0%
+this is um I don't know what the dates
+ 
+
+ align:start position:0%
+this is um I don't know what the dates
+say 1916 excuse me it's at 1916 and you
+
+ align:start position:0%
+say 1916 excuse me it's at 1916 and you
+ 
+
+ align:start position:0%
+say 1916 excuse me it's at 1916 and you
+can see what he's done he's taken the
+
+ align:start position:0%
+can see what he's done he's taken the
+ 
+
+ align:start position:0%
+can see what he's done he's taken the
+elements and he's arranged them and he's
+
+ align:start position:0%
+elements and he's arranged them and he's
+ 
+
+ align:start position:0%
+elements and he's arranged them and he's
+stripped off all of the nonvalence
+
+ align:start position:0%
+stripped off all of the nonvalence
+ 
+
+ align:start position:0%
+stripped off all of the nonvalence
+electrons and all he's done is leave the
+
+ align:start position:0%
+electrons and all he's done is leave the
+ 
+
+ align:start position:0%
+electrons and all he's done is leave the
+veence electrons Associated so you can
+
+ align:start position:0%
+veence electrons Associated so you can
+ 
+
+ align:start position:0%
+veence electrons Associated so you can
+see the alkali metals here lithium one
+
+ align:start position:0%
+see the alkali metals here lithium one
+ 
+
+ align:start position:0%
+see the alkali metals here lithium one
+electron and then brillium magnesium uh
+
+ align:start position:0%
+electron and then brillium magnesium uh
+ 
+
+ align:start position:0%
+electron and then brillium magnesium uh
+two electrons all the way over here to
+
+ align:start position:0%
+two electrons all the way over here to
+ 
+
+ align:start position:0%
+two electrons all the way over here to
+neon and argon where you have stability
+
+ align:start position:0%
+neon and argon where you have stability
+ 
+
+ align:start position:0%
+neon and argon where you have stability
+there's Florine and Chlor where you have
+
+ align:start position:0%
+there's Florine and Chlor where you have
+ 
+
+ align:start position:0%
+there's Florine and Chlor where you have
+where you have seven electrons so that's
+
+ align:start position:0%
+where you have seven electrons so that's
+ 
+
+ align:start position:0%
+where you have seven electrons so that's
+the um that's his that's his um his his
+
+ align:start position:0%
+the um that's his that's his um his his
+ 
+
+ align:start position:0%
+the um that's his that's his um his his
+gift his gift to us the Lewis structure
+
+ align:start position:0%
+gift his gift to us the Lewis structure
+ 
+
+ align:start position:0%
+gift his gift to us the Lewis structure
+and the and the the idea that you could
+
+ align:start position:0%
+and the and the the idea that you could
+ 
+
+ align:start position:0%
+and the and the the idea that you could
+share electrons and form a Cove valent
+
+ align:start position:0%
+share electrons and form a Cove valent
+ 
+
+ align:start position:0%
+share electrons and form a Cove valent
+Cove valent Bond now we need to go a
+
+ align:start position:0%
+Cove valent Bond now we need to go a
+ 
+
+ align:start position:0%
+Cove valent Bond now we need to go a
+little bit further to to put some more
+
+ align:start position:0%
+little bit further to to put some more
+ 
+
+ align:start position:0%
+little bit further to to put some more
+meat on this thing because we haven't
+
+ align:start position:0%
+meat on this thing because we haven't
+ 
+
+ align:start position:0%
+meat on this thing because we haven't
+Quantified it Quantified it yet we've
+
+ align:start position:0%
+Quantified it Quantified it yet we've
+ 
+
+ align:start position:0%
+Quantified it Quantified it yet we've
+got the concept but we haven't
+
+ align:start position:0%
+got the concept but we haven't
+ 
+
+ align:start position:0%
+got the concept but we haven't
+Quantified it yet but let's take a look
+
+ align:start position:0%
+Quantified it yet but let's take a look
+ 
+
+ align:start position:0%
+Quantified it yet but let's take a look
+and see about water
+
+ align:start position:0%
+and see about water
+ 
+
+ align:start position:0%
+and see about water
+let's take a these
+
+ align:start position:0%
+let's take a these
+ 
+
+ align:start position:0%
+let's take a these
+are so-called homopolar molecules the mo
+
+ align:start position:0%
+are so-called homopolar molecules the mo
+ 
+
+ align:start position:0%
+are so-called homopolar molecules the mo
+the atoms are the same in each in each
+
+ align:start position:0%
+the atoms are the same in each in each
+ 
+
+ align:start position:0%
+the atoms are the same in each in each
+one and let's try one with uh with with
+
+ align:start position:0%
+one and let's try one with uh with with
+ 
+
+ align:start position:0%
+one and let's try one with uh with with
+non two different two different atoms
+
+ align:start position:0%
+non two different two different atoms
+ 
+
+ align:start position:0%
+non two different two different atoms
+let's take a look at Water we know that
+
+ align:start position:0%
+let's take a look at Water we know that
+ 
+
+ align:start position:0%
+let's take a look at Water we know that
+hydrogen is 1 S1 and oxygen is 1 S2 2p
+
+ align:start position:0%
+hydrogen is 1 S1 and oxygen is 1 S2 2p
+ 
+
+ align:start position:0%
+hydrogen is 1 S1 and oxygen is 1 S2 2p
+whoops S2 2p 4 so there's six electon El
+
+ align:start position:0%
+whoops S2 2p 4 so there's six electon El
+ 
+
+ align:start position:0%
+whoops S2 2p 4 so there's six electon El
+Rons in the veence in the ve in the
+
+ align:start position:0%
+Rons in the veence in the ve in the
+ 
+
+ align:start position:0%
+Rons in the veence in the ve in the
+veence in the veence shell and let's try
+
+ align:start position:0%
+veence in the veence shell and let's try
+ 
+
+ align:start position:0%
+veence in the veence shell and let's try
+oxygen well oxygen we'll put a hydrogen
+
+ align:start position:0%
+oxygen well oxygen we'll put a hydrogen
+ 
+
+ align:start position:0%
+oxygen well oxygen we'll put a hydrogen
+here hydrogen here and one two 3 4 uh
+
+ align:start position:0%
+here hydrogen here and one two 3 4 uh
+ 
+
+ align:start position:0%
+here hydrogen here and one two 3 4 uh
+we've got to put six electrons around it
+
+ align:start position:0%
+we've got to put six electrons around it
+ 
+
+ align:start position:0%
+we've got to put six electrons around it
+so let's put one here and one here we've
+
+ align:start position:0%
+so let's put one here and one here we've
+ 
+
+ align:start position:0%
+so let's put one here and one here we've
+got an electron from each of the
+
+ align:start position:0%
+got an electron from each of the
+ 
+
+ align:start position:0%
+got an electron from each of the
+hydrogens so let's put that here and
+
+ align:start position:0%
+hydrogens so let's put that here and
+ 
+
+ align:start position:0%
+hydrogens so let's put that here and
+that's there and that works so now we
+
+ align:start position:0%
+that's there and that works so now we
+ 
+
+ align:start position:0%
+that's there and that works so now we
+have what we have two well let me draw
+
+ align:start position:0%
+have what we have two well let me draw
+ 
+
+ align:start position:0%
+have what we have two well let me draw
+this as a square we have two
+
+ align:start position:0%
+this as a square we have two
+ 
+
+ align:start position:0%
+this as a square we have two
+bonding domains right two bonding
+
+ align:start position:0%
+bonding domains right two bonding
+ 
+
+ align:start position:0%
+bonding domains right two bonding
+domains and we have uh
+
+ align:start position:0%
+domains and we have uh
+ 
+
+ align:start position:0%
+domains and we have uh
+two non-bonding domains now we know that
+
+ align:start position:0%
+two non-bonding domains now we know that
+ 
+
+ align:start position:0%
+two non-bonding domains now we know that
+there's more structure to this uh to
+
+ align:start position:0%
+there's more structure to this uh to
+ 
+
+ align:start position:0%
+there's more structure to this uh to
+this molecule water is a pretty uh very
+
+ align:start position:0%
+this molecule water is a pretty uh very
+ 
+
+ align:start position:0%
+this molecule water is a pretty uh very
+unique unique molecule uh it's one of
+
+ align:start position:0%
+unique unique molecule uh it's one of
+ 
+
+ align:start position:0%
+unique unique molecule uh it's one of
+the only only compounds there's only I
+
+ align:start position:0%
+the only only compounds there's only I
+ 
+
+ align:start position:0%
+the only only compounds there's only I
+think three
+
+ align:start position:0%
+think three
+ 
+
+ align:start position:0%
+think three
+where the density actually goes
+
+ align:start position:0%
+where the density actually goes
+ 
+
+ align:start position:0%
+where the density actually goes
+down when it freezes think about that
+
+ align:start position:0%
+down when it freezes think about that
+ 
+
+ align:start position:0%
+down when it freezes think about that
+think of anything else where the density
+
+ align:start position:0%
+think of anything else where the density
+ 
+
+ align:start position:0%
+think of anything else where the density
+goes down when it freezes and think
+
+ align:start position:0%
+goes down when it freezes and think
+ 
+
+ align:start position:0%
+goes down when it freezes and think
+about where we would be um if if that
+
+ align:start position:0%
+about where we would be um if if that
+ 
+
+ align:start position:0%
+about where we would be um if if that
+wasn't the
+
+ align:start position:0%
+wasn't the
+ 
+
+ align:start position:0%
+wasn't the
+case ponds would freeze from the bottom
+
+ align:start position:0%
+case ponds would freeze from the bottom
+ 
+
+ align:start position:0%
+case ponds would freeze from the bottom
+up that would be a bummer all the fish
+
+ align:start position:0%
+up that would be a bummer all the fish
+ 
+
+ align:start position:0%
+up that would be a bummer all the fish
+would freeze in the
+
+ align:start position:0%
+would freeze in the
+ 
+
+ align:start position:0%
+would freeze in the
+wintertime um water has some pretty
+
+ align:start position:0%
+wintertime um water has some pretty
+ 
+
+ align:start position:0%
+wintertime um water has some pretty
+unique properties which we'll we'll deal
+
+ align:start position:0%
+unique properties which we'll we'll deal
+ 
+
+ align:start position:0%
+unique properties which we'll we'll deal
+with a little bit a little bit later but
+
+ align:start position:0%
+with a little bit a little bit later but
+ 
+
+ align:start position:0%
+with a little bit a little bit later but
+it all relates to the bonding all
+
+ align:start position:0%
+it all relates to the bonding all
+ 
+
+ align:start position:0%
+it all relates to the bonding all
+relates to the
+
+ align:start position:0%
+relates to the
+ 
+
+ align:start position:0%
+relates to the
+bonding okay um and now Lewis actually
+
+ align:start position:0%
+bonding okay um and now Lewis actually
+ 
+
+ align:start position:0%
+bonding okay um and now Lewis actually
+listed some rules and let's what we want
+
+ align:start position:0%
+listed some rules and let's what we want
+ 
+
+ align:start position:0%
+listed some rules and let's what we want
+to do is go by example here all right
+
+ align:start position:0%
+to do is go by example here all right
+ 
+
+ align:start position:0%
+to do is go by example here all right
+and these are these by the way are
+
+ align:start position:0%
+and these are these by the way are
+ 
+
+ align:start position:0%
+and these are these by the way are
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+Lewis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structures Lewis structures all right
+
+ align:start position:0%
+structures Lewis structures all right
+ 
+
+ align:start position:0%
+structures Lewis structures all right
+and so he he came up with a set of rules
+
+ align:start position:0%
+and so he he came up with a set of rules
+ 
+
+ align:start position:0%
+and so he he came up with a set of rules
+and let's take a let's take an example
+
+ align:start position:0%
+and let's take a let's take an example
+ 
+
+ align:start position:0%
+and let's take a let's take an example
+and um uh and see how these apply and as
+
+ align:start position:0%
+and um uh and see how these apply and as
+ 
+
+ align:start position:0%
+and um uh and see how these apply and as
+an example let's take um sulfur
+
+ align:start position:0%
+an example let's take um sulfur
+ 
+
+ align:start position:0%
+an example let's take um sulfur
+chloride s O2 make it a little
+
+ align:start position:0%
+chloride s O2 make it a little
+ 
+
+ align:start position:0%
+chloride s O2 make it a little
+complicated cl2 all right so don't worry
+
+ align:start position:0%
+complicated cl2 all right so don't worry
+ 
+
+ align:start position:0%
+complicated cl2 all right so don't worry
+about these compounds and uh we'll tell
+
+ align:start position:0%
+about these compounds and uh we'll tell
+ 
+
+ align:start position:0%
+about these compounds and uh we'll tell
+you all you need to know if we have
+
+ align:start position:0%
+you all you need to know if we have
+ 
+
+ align:start position:0%
+you all you need to know if we have
+except for how to draw them and it says
+
+ align:start position:0%
+except for how to draw them and it says
+ 
+
+ align:start position:0%
+except for how to draw them and it says
+okay Center the element with the lowest
+
+ align:start position:0%
+okay Center the element with the lowest
+ 
+
+ align:start position:0%
+okay Center the element with the lowest
+average veence electron energy well if
+
+ align:start position:0%
+average veence electron energy well if
+ 
+
+ align:start position:0%
+average veence electron energy well if
+you look in your sulfur is less than
+
+ align:start position:0%
+you look in your sulfur is less than
+ 
+
+ align:start position:0%
+you look in your sulfur is less than
+chlorine Which is less than oxygen so
+
+ align:start position:0%
+chlorine Which is less than oxygen so
+ 
+
+ align:start position:0%
+chlorine Which is less than oxygen so
+sulfur has the lowest average veence
+
+ align:start position:0%
+sulfur has the lowest average veence
+ 
+
+ align:start position:0%
+sulfur has the lowest average veence
+electron energy so that says put the
+
+ align:start position:0%
+electron energy so that says put the
+ 
+
+ align:start position:0%
+electron energy so that says put the
+sulfur in the center all right all right
+
+ align:start position:0%
+sulfur in the center all right all right
+ 
+
+ align:start position:0%
+sulfur in the center all right all right
+so put the sulfur in the center then it
+
+ align:start position:0%
+so put the sulfur in the center then it
+ 
+
+ align:start position:0%
+so put the sulfur in the center then it
+says count all the veence electrons well
+
+ align:start position:0%
+says count all the veence electrons well
+ 
+
+ align:start position:0%
+says count all the veence electrons well
+sulfur has six that's 3
+
+ align:start position:0%
+sulfur has six that's 3
+ 
+
+ align:start position:0%
+sulfur has six that's 3
+S2 uh 3
+
+ align:start position:0%
+S2 uh 3
+ 
+
+ align:start position:0%
+S2 uh 3
+P4 uh
+
+ align:start position:0%
+P4 uh
+ 
+
+ align:start position:0%
+P4 uh
+oxygen uh 2 * oxygen that's 12
+
+ align:start position:0%
+oxygen uh 2 * oxygen that's 12
+ 
+
+ align:start position:0%
+oxygen uh 2 * oxygen that's 12
+because it's sulfur is 2 S2
+
+ align:start position:0%
+because it's sulfur is 2 S2
+ 
+
+ align:start position:0%
+because it's sulfur is 2 S2
+2p4 and chlorine there's two of
+
+ align:start position:0%
+2p4 and chlorine there's two of
+ 
+
+ align:start position:0%
+2p4 and chlorine there's two of
+those that gives us
+
+ align:start position:0%
+those that gives us
+ 
+
+ align:start position:0%
+those that gives us
+14 and that's 3 S2 3 P5 and so we got to
+
+ align:start position:0%
+14 and that's 3 S2 3 P5 and so we got to
+ 
+
+ align:start position:0%
+14 and that's 3 S2 3 P5 and so we got to
+come up with we have 32 electrons that
+
+ align:start position:0%
+come up with we have 32 electrons that
+ 
+
+ align:start position:0%
+come up with we have 32 electrons that
+we have to
+
+ align:start position:0%
+we have to
+ 
+
+ align:start position:0%
+we have to
+use okay and it says draw a single bond
+
+ align:start position:0%
+use okay and it says draw a single bond
+ 
+
+ align:start position:0%
+use okay and it says draw a single bond
+from each surrounding atom to the
+
+ align:start position:0%
+from each surrounding atom to the
+ 
+
+ align:start position:0%
+from each surrounding atom to the
+central atom and subtract two two veence
+
+ align:start position:0%
+central atom and subtract two two veence
+ 
+
+ align:start position:0%
+central atom and subtract two two veence
+electrons okay and let's just put
+
+ align:start position:0%
+electrons okay and let's just put
+ 
+
+ align:start position:0%
+electrons okay and let's just put
+chlorine here carine here oxygen here
+
+ align:start position:0%
+chlorine here carine here oxygen here
+ 
+
+ align:start position:0%
+chlorine here carine here oxygen here
+oxygen here so 2 4 6 8 minus 8 uh that
+
+ align:start position:0%
+oxygen here so 2 4 6 8 minus 8 uh that
+ 
+
+ align:start position:0%
+oxygen here so 2 4 6 8 minus 8 uh that
+gives
+
+ align:start position:0%
+gives
+ 
+
+ align:start position:0%
+gives
+us 24 so we have 24 electrons that we
+
+ align:start position:0%
+us 24 so we have 24 electrons that we
+ 
+
+ align:start position:0%
+us 24 so we have 24 electrons that we
+have to we have to come up with and then
+
+ align:start position:0%
+have to we have to come up with and then
+ 
+
+ align:start position:0%
+have to we have to come up with and then
+it says okay distribute the remaining
+
+ align:start position:0%
+it says okay distribute the remaining
+ 
+
+ align:start position:0%
+it says okay distribute the remaining
+electrons in pairs so that each atom has
+
+ align:start position:0%
+electrons in pairs so that each atom has
+ 
+
+ align:start position:0%
+electrons in pairs so that each atom has
+eight place the non-bonding pairs on
+
+ align:start position:0%
+eight place the non-bonding pairs on
+ 
+
+ align:start position:0%
+eight place the non-bonding pairs on
+peripheral atoms first which the higher
+
+ align:start position:0%
+peripheral atoms first which the higher
+ 
+
+ align:start position:0%
+peripheral atoms first which the higher
+average veence electron energy all right
+
+ align:start position:0%
+average veence electron energy all right
+ 
+
+ align:start position:0%
+average veence electron energy all right
+well oxygen has the highest veence
+
+ align:start position:0%
+well oxygen has the highest veence
+ 
+
+ align:start position:0%
+well oxygen has the highest veence
+electron energy so let's go and put the
+
+ align:start position:0%
+electron energy so let's go and put the
+ 
+
+ align:start position:0%
+electron energy so let's go and put the
+one two three four five six here let's
+
+ align:start position:0%
+one two three four five six here let's
+ 
+
+ align:start position:0%
+one two three four five six here let's
+do one two three four five six here and
+
+ align:start position:0%
+do one two three four five six here and
+ 
+
+ align:start position:0%
+do one two three four five six here and
+okay and let's uh put the atoms put the
+
+ align:start position:0%
+okay and let's uh put the atoms put the
+ 
+
+ align:start position:0%
+okay and let's uh put the atoms put the
+atoms around now we'll do the chlorines
+
+ align:start position:0%
+atoms around now we'll do the chlorines
+ 
+
+ align:start position:0%
+atoms around now we'll do the chlorines
+chlorines have seven right so uh one two
+
+ align:start position:0%
+chlorines have seven right so uh one two
+ 
+
+ align:start position:0%
+chlorines have seven right so uh one two
+three four five six seven right one two
+
+ align:start position:0%
+three four five six seven right one two
+ 
+
+ align:start position:0%
+three four five six seven right one two
+three four five six seven okay so now
+
+ align:start position:0%
+three four five six seven okay so now
+ 
+
+ align:start position:0%
+three four five six seven okay so now
+we've
+
+ align:start position:0%
+we've
+ 
+
+ align:start position:0%
+we've
+got take an an electron from that sulfur
+
+ align:start position:0%
+got take an an electron from that sulfur
+ 
+
+ align:start position:0%
+got take an an electron from that sulfur
+put it here an electron from that sulfur
+
+ align:start position:0%
+put it here an electron from that sulfur
+ 
+
+ align:start position:0%
+put it here an electron from that sulfur
+put it here so how many we got in the
+
+ align:start position:0%
+put it here so how many we got in the
+ 
+
+ align:start position:0%
+put it here so how many we got in the
+sulfur we got one two
+
+ align:start position:0%
+sulfur we got one two
+ 
+
+ align:start position:0%
+sulfur we got one two
+3 four 5 six set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well son of a gun 1 two 3 four five six
+
+ align:start position:0%
+well son of a gun 1 two 3 four five six
+ 
+
+ align:start position:0%
+well son of a gun 1 two 3 four five six
+sulfur one two six we got six we've used
+
+ align:start position:0%
+sulfur one two six we got six we've used
+ 
+
+ align:start position:0%
+sulfur one two six we got six we've used
+all the
+
+ align:start position:0%
+all the
+ 
+
+ align:start position:0%
+all the
+electrons but what do we have here well
+
+ align:start position:0%
+electrons but what do we have here well
+ 
+
+ align:start position:0%
+electrons but what do we have here well
+this chlorine has taken one electron
+
+ align:start position:0%
+this chlorine has taken one electron
+ 
+
+ align:start position:0%
+this chlorine has taken one electron
+from The
+
+ align:start position:0%
+from The
+ 
+
+ align:start position:0%
+from The
+sulfur but the oxygen has taken two
+
+ align:start position:0%
+sulfur but the oxygen has taken two
+ 
+
+ align:start position:0%
+sulfur but the oxygen has taken two
+electrons from The sulfur this is a kind
+
+ align:start position:0%
+electrons from The sulfur this is a kind
+ 
+
+ align:start position:0%
+electrons from The sulfur this is a kind
+of a special uh when and you might
+
+ align:start position:0%
+of a special uh when and you might
+ 
+
+ align:start position:0%
+of a special uh when and you might
+expect that oxygen has the highest
+
+ align:start position:0%
+expect that oxygen has the highest
+ 
+
+ align:start position:0%
+expect that oxygen has the highest
+average veence electron energy so it's
+
+ align:start position:0%
+average veence electron energy so it's
+ 
+
+ align:start position:0%
+average veence electron energy so it's
+going to want to scarf and take these uh
+
+ align:start position:0%
+going to want to scarf and take these uh
+ 
+
+ align:start position:0%
+going to want to scarf and take these uh
+and take these electrons this is called
+
+ align:start position:0%
+and take these electrons this is called
+ 
+
+ align:start position:0%
+and take these electrons this is called
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+dative
+
+ align:start position:0%
+dative
+ 
+
+ align:start position:0%
+dative
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+Bond it's it's what it's called when
+
+ align:start position:0%
+Bond it's it's what it's called when
+ 
+
+ align:start position:0%
+Bond it's it's what it's called when
+when an atom takes both electrons in the
+
+ align:start position:0%
+when an atom takes both electrons in the
+ 
+
+ align:start position:0%
+when an atom takes both electrons in the
+bond all right so what do we have we
+
+ align:start position:0%
+bond all right so what do we have we
+ 
+
+ align:start position:0%
+bond all right so what do we have we
+have one
+
+ align:start position:0%
+have one
+ 
+
+ align:start position:0%
+have one
+two we have one four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bonding bonding domains and how many
+
+ align:start position:0%
+bonding bonding domains and how many
+ 
+
+ align:start position:0%
+bonding bonding domains and how many
+non-bonding well 1 two 3 four 5 6 7 8 9
+
+ align:start position:0%
+non-bonding well 1 two 3 four 5 6 7 8 9
+ 
+
+ align:start position:0%
+non-bonding well 1 two 3 four 5 6 7 8 9
+10 11
+
+ align:start position:0%
+10 11
+ 
+
+ align:start position:0%
+10 11
+12 12 non
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bonding non-bonding 12 non-bonding
+
+ align:start position:0%
+bonding non-bonding 12 non-bonding
+ 
+
+ align:start position:0%
+bonding non-bonding 12 non-bonding
+domains
+
+ align:start position:0%
+domains
+ 
+
+ align:start position:0%
+domains
+okay so this is looking pretty good we
+
+ align:start position:0%
+okay so this is looking pretty good we
+ 
+
+ align:start position:0%
+okay so this is looking pretty good we
+now have we've got octet stability we've
+
+ align:start position:0%
+now have we've got octet stability we've
+ 
+
+ align:start position:0%
+now have we've got octet stability we've
+got uh each each one is um has a has a
+
+ align:start position:0%
+got uh each each one is um has a has a
+ 
+
+ align:start position:0%
+got uh each each one is um has a has a
+an inert electronic
+
+ align:start position:0%
+an inert electronic
+ 
+
+ align:start position:0%
+an inert electronic
+structure but a few things to note we
+
+ align:start position:0%
+structure but a few things to note we
+ 
+
+ align:start position:0%
+structure but a few things to note we
+know that because the sulfur and the
+
+ align:start position:0%
+know that because the sulfur and the
+ 
+
+ align:start position:0%
+know that because the sulfur and the
+chlorine and the oxygen have different
+
+ align:start position:0%
+chlorine and the oxygen have different
+ 
+
+ align:start position:0%
+chlorine and the oxygen have different
+average veence electron energies they'll
+
+ align:start position:0%
+average veence electron energies they'll
+ 
+
+ align:start position:0%
+average veence electron energies they'll
+have different electron
+
+ align:start position:0%
+have different electron
+ 
+
+ align:start position:0%
+have different electron
+affinities
+
+ align:start position:0%
+affinities
+ 
+
+ align:start position:0%
+affinities
+so this bond is going to be a little bit
+
+ align:start position:0%
+so this bond is going to be a little bit
+ 
+
+ align:start position:0%
+so this bond is going to be a little bit
+different than this Bond we have to
+
+ align:start position:0%
+different than this Bond we have to
+ 
+
+ align:start position:0%
+different than this Bond we have to
+account for that in some way because we
+
+ align:start position:0%
+account for that in some way because we
+ 
+
+ align:start position:0%
+account for that in some way because we
+know they don't have identical average
+
+ align:start position:0%
+know they don't have identical average
+ 
+
+ align:start position:0%
+know they don't have identical average
+veence electron energies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's start over
+
+ align:start position:0%
+okay let's start over
+ 
+
+ align:start position:0%
+okay let's start over
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops okay let's try another
+
+ align:start position:0%
+oops okay let's try another
+ 
+
+ align:start position:0%
+oops okay let's try another
+one let's try something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four which is what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+methane methane what do we know about
+
+ align:start position:0%
+methane methane what do we know about
+ 
+
+ align:start position:0%
+methane methane what do we know about
+methane well we know it's
+
+ align:start position:0%
+methane well we know it's
+ 
+
+ align:start position:0%
+methane well we know it's
+stable um um but we also know that it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetric right it's symmetric we know
+
+ align:start position:0%
+symmetric right it's symmetric we know
+ 
+
+ align:start position:0%
+symmetric right it's symmetric we know
+that it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+non it's non-polar all right so those
+
+ align:start position:0%
+non it's non-polar all right so those
+ 
+
+ align:start position:0%
+non it's non-polar all right so those
+are the things that we those are the
+
+ align:start position:0%
+are the things that we those are the
+ 
+
+ align:start position:0%
+are the things that we those are the
+things that we know about it we also
+
+ align:start position:0%
+things that we know about it we also
+ 
+
+ align:start position:0%
+things that we know about it we also
+know that
+
+ align:start position:0%
+know that
+ 
+
+ align:start position:0%
+know that
+carbon is uh 1 S2 2 S2 2
+
+ align:start position:0%
+carbon is uh 1 S2 2 S2 2
+ 
+
+ align:start position:0%
+carbon is uh 1 S2 2 S2 2
+P2 and we know what Hydro we know what
+
+ align:start position:0%
+P2 and we know what Hydro we know what
+ 
+
+ align:start position:0%
+P2 and we know what Hydro we know what
+hydrogen is and so if we look at our our
+
+ align:start position:0%
+hydrogen is and so if we look at our our
+ 
+
+ align:start position:0%
+hydrogen is and so if we look at our our
+box our box notation right we've got
+
+ align:start position:0%
+box our box notation right we've got
+ 
+
+ align:start position:0%
+box our box notation right we've got
+three states in the p orbital we' got
+
+ align:start position:0%
+three states in the p orbital we' got
+ 
+
+ align:start position:0%
+three states in the p orbital we' got
+one in the in the S orbital if we apply
+
+ align:start position:0%
+one in the in the S orbital if we apply
+ 
+
+ align:start position:0%
+one in the in the S orbital if we apply
+the hund the hund the hund rule uh we've
+
+ align:start position:0%
+the hund the hund the hund rule uh we've
+ 
+
+ align:start position:0%
+the hund the hund the hund rule uh we've
+got up arrow down arrow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right but there's something else that we
+
+ align:start position:0%
+right but there's something else that we
+ 
+
+ align:start position:0%
+right but there's something else that we
+know all right we somehow have to take
+
+ align:start position:0%
+know all right we somehow have to take
+ 
+
+ align:start position:0%
+know all right we somehow have to take
+hydrogen attach it to carbon and we have
+
+ align:start position:0%
+hydrogen attach it to carbon and we have
+ 
+
+ align:start position:0%
+hydrogen attach it to carbon and we have
+to make it symmetric and we have to make
+
+ align:start position:0%
+to make it symmetric and we have to make
+ 
+
+ align:start position:0%
+to make it symmetric and we have to make
+it non we have to make it
+
+ align:start position:0%
+it non we have to make it
+ 
+
+ align:start position:0%
+it non we have to make it
+non-polar and yet we know that the shape
+
+ align:start position:0%
+non-polar and yet we know that the shape
+ 
+
+ align:start position:0%
+non-polar and yet we know that the shape
+the shape of the S orbitals is
+
+ align:start position:0%
+the shape of the S orbitals is
+ 
+
+ align:start position:0%
+the shape of the S orbitals is
+spherical the shape of the P orbitals is
+
+ align:start position:0%
+spherical the shape of the P orbitals is
+ 
+
+ align:start position:0%
+spherical the shape of the P orbitals is
+however not spherical is it it's
+
+ align:start position:0%
+however not spherical is it it's
+ 
+
+ align:start position:0%
+however not spherical is it it's
+asymmetric and moreover they're at right
+
+ align:start position:0%
+asymmetric and moreover they're at right
+ 
+
+ align:start position:0%
+asymmetric and moreover they're at right
+angles to one another that we've learned
+
+ align:start position:0%
+angles to one another that we've learned
+ 
+
+ align:start position:0%
+angles to one another that we've learned
+so somehow we have to figure out a way
+
+ align:start position:0%
+so somehow we have to figure out a way
+ 
+
+ align:start position:0%
+so somehow we have to figure out a way
+to take orbitals that are
+
+ align:start position:0%
+to take orbitals that are
+ 
+
+ align:start position:0%
+to take orbitals that are
+non-symmetric and convert them into
+
+ align:start position:0%
+non-symmetric and convert them into
+ 
+
+ align:start position:0%
+non-symmetric and convert them into
+orbitals that are symmetric now what
+
+ align:start position:0%
+orbitals that are symmetric now what
+ 
+
+ align:start position:0%
+orbitals that are symmetric now what
+does that mean if it's symmetric that
+
+ align:start position:0%
+does that mean if it's symmetric that
+ 
+
+ align:start position:0%
+does that mean if it's symmetric that
+means that each bond has exactly the
+
+ align:start position:0%
+means that each bond has exactly the
+ 
+
+ align:start position:0%
+means that each bond has exactly the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+energy same Bond symmetric bonds means
+
+ align:start position:0%
+energy same Bond symmetric bonds means
+ 
+
+ align:start position:0%
+energy same Bond symmetric bonds means
+equal equal energy which means equal
+
+ align:start position:0%
+equal equal energy which means equal
+ 
+
+ align:start position:0%
+equal equal energy which means equal
+lengths if we can do that we'll end up
+
+ align:start position:0%
+lengths if we can do that we'll end up
+ 
+
+ align:start position:0%
+lengths if we can do that we'll end up
+with a symmetric non-polar uh non-polar
+
+ align:start position:0%
+with a symmetric non-polar uh non-polar
+ 
+
+ align:start position:0%
+with a symmetric non-polar uh non-polar
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+well this stumped people for a while
+
+ align:start position:0%
+well this stumped people for a while
+ 
+
+ align:start position:0%
+well this stumped people for a while
+until another fellow came along
+
+ align:start position:0%
+until another fellow came along
+ 
+
+ align:start position:0%
+until another fellow came along
+lonus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pauling he's famous for a lot of things
+
+ align:start position:0%
+Pauling he's famous for a lot of things
+ 
+
+ align:start position:0%
+Pauling he's famous for a lot of things
+one of which is one of which is calent
+
+ align:start position:0%
+one of which is one of which is calent
+ 
+
+ align:start position:0%
+one of which is one of which is calent
+bonding and he said to he said well let
+
+ align:start position:0%
+bonding and he said to he said well let
+ 
+
+ align:start position:0%
+bonding and he said to he said well let
+me take a look at this what if I were
+
+ align:start position:0%
+me take a look at this what if I were
+ 
+
+ align:start position:0%
+me take a look at this what if I were
+able to
+
+ align:start position:0%
+able to
+ 
+
+ align:start position:0%
+able to
+mix what if I were able to mix the
+
+ align:start position:0%
+mix what if I were able to mix the
+ 
+
+ align:start position:0%
+mix what if I were able to mix the
+orbitals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right what if I were able to mix mix
+
+ align:start position:0%
+all right what if I were able to mix mix
+ 
+
+ align:start position:0%
+all right what if I were able to mix mix
+these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orbitals and
+
+ align:start position:0%
+orbitals and
+ 
+
+ align:start position:0%
+orbitals and
+produce what he called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hybrid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bonds right hybrid
+
+ align:start position:0%
+bonds right hybrid
+ 
+
+ align:start position:0%
+bonds right hybrid
+bonds and how would he do that well this
+
+ align:start position:0%
+bonds and how would he do that well this
+ 
+
+ align:start position:0%
+bonds and how would he do that well this
+is where the thinking cames in he say
+
+ align:start position:0%
+is where the thinking cames in he say
+ 
+
+ align:start position:0%
+is where the thinking cames in he say
+let's just mix let's just mix the 2s and
+
+ align:start position:0%
+let's just mix let's just mix the 2s and
+ 
+
+ align:start position:0%
+let's just mix let's just mix the 2s and
+the 2 p orbitals right right 2 S 2 p
+
+ align:start position:0%
+the 2 p orbitals right right 2 S 2 p
+ 
+
+ align:start position:0%
+the 2 p orbitals right right 2 S 2 p
+orbitals and I need I know I need to
+
+ align:start position:0%
+orbitals and I need I know I need to
+ 
+
+ align:start position:0%
+orbitals and I need I know I need to
+come up with with four symmetric equil
+
+ align:start position:0%
+come up with with four symmetric equil
+ 
+
+ align:start position:0%
+come up with with four symmetric equil
+length bonds and well let's just see
+
+ align:start position:0%
+length bonds and well let's just see
+ 
+
+ align:start position:0%
+length bonds and well let's just see
+let's draw the structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and so I take it I mix the 2s and
+
+ align:start position:0%
+here and so I take it I mix the 2s and
+ 
+
+ align:start position:0%
+here and so I take it I mix the 2s and
+the two PS and I then by my hund rule if
+
+ align:start position:0%
+the two PS and I then by my hund rule if
+ 
+
+ align:start position:0%
+the two PS and I then by my hund rule if
+I can come up with four I've got what
+
+ align:start position:0%
+I can come up with four I've got what
+ 
+
+ align:start position:0%
+I can come up with four I've got what
+have I've got I've got two states here
+
+ align:start position:0%
+have I've got I've got two states here
+ 
+
+ align:start position:0%
+have I've got I've got two states here
+three states here two here I need four
+
+ align:start position:0%
+three states here two here I need four
+ 
+
+ align:start position:0%
+three states here two here I need four
+and if I can come up with these bonds
+
+ align:start position:0%
+and if I can come up with these bonds
+ 
+
+ align:start position:0%
+and if I can come up with these bonds
+four by the hund rule I fill them like
+
+ align:start position:0%
+four by the hund rule I fill them like
+ 
+
+ align:start position:0%
+four by the hund rule I fill them like
+this and there I have it I have I have
+
+ align:start position:0%
+this and there I have it I have I have
+ 
+
+ align:start position:0%
+this and there I have it I have I have
+four um bonds that are of equal uh equal
+
+ align:start position:0%
+four um bonds that are of equal uh equal
+ 
+
+ align:start position:0%
+four um bonds that are of equal uh equal
+energy and he called this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sp3 an sp3 hybrid right an S3 sp3 hybrid
+
+ align:start position:0%
+sp3 an sp3 hybrid right an S3 sp3 hybrid
+ 
+
+ align:start position:0%
+sp3 an sp3 hybrid right an S3 sp3 hybrid
+and now I
+
+ align:start position:0%
+and now I
+ 
+
+ align:start position:0%
+and now I
+can't do the drawing Justice
+
+ align:start position:0%
+can't do the drawing Justice
+ 
+
+ align:start position:0%
+can't do the drawing Justice
+but let's take a look at how how we do
+
+ align:start position:0%
+but let's take a look at how how we do
+ 
+
+ align:start position:0%
+but let's take a look at how how we do
+this this is a the the the the the graph
+
+ align:start position:0%
+this this is a the the the the the graph
+ 
+
+ align:start position:0%
+this this is a the the the the the graph
+to the left this is the S orbital
+
+ align:start position:0%
+to the left this is the S orbital
+ 
+
+ align:start position:0%
+to the left this is the S orbital
+symmetric these are the P orbitals and
+
+ align:start position:0%
+symmetric these are the P orbitals and
+ 
+
+ align:start position:0%
+symmetric these are the P orbitals and
+these are what these are the probability
+
+ align:start position:0%
+these are what these are the probability
+ 
+
+ align:start position:0%
+these are what these are the probability
+densities right our friend uh schinger
+
+ align:start position:0%
+densities right our friend uh schinger
+ 
+
+ align:start position:0%
+densities right our friend uh schinger
+told us that this is what the if you
+
+ align:start position:0%
+told us that this is what the if you
+ 
+
+ align:start position:0%
+told us that this is what the if you
+solve for the wave function this is what
+
+ align:start position:0%
+solve for the wave function this is what
+ 
+
+ align:start position:0%
+solve for the wave function this is what
+the probability densities look like if I
+
+ align:start position:0%
+the probability densities look like if I
+ 
+
+ align:start position:0%
+the probability densities look like if I
+now hybridize these if I take these and
+
+ align:start position:0%
+now hybridize these if I take these and
+ 
+
+ align:start position:0%
+now hybridize these if I take these and
+I make four symmetric now these are just
+
+ align:start position:0%
+I make four symmetric now these are just
+ 
+
+ align:start position:0%
+I make four symmetric now these are just
+the just the um the sp3 orbitals the
+
+ align:start position:0%
+the just the um the sp3 orbitals the
+ 
+
+ align:start position:0%
+the just the um the sp3 orbitals the
+hydrogen is not on there yet notice this
+
+ align:start position:0%
+hydrogen is not on there yet notice this
+ 
+
+ align:start position:0%
+hydrogen is not on there yet notice this
+uh the orbital looks kind of funny it's
+
+ align:start position:0%
+uh the orbital looks kind of funny it's
+ 
+
+ align:start position:0%
+uh the orbital looks kind of funny it's
+got a big big lobe and a little lobe and
+
+ align:start position:0%
+got a big big lobe and a little lobe and
+ 
+
+ align:start position:0%
+got a big big lobe and a little lobe and
+they're sort of backed into it so this
+
+ align:start position:0%
+they're sort of backed into it so this
+ 
+
+ align:start position:0%
+they're sort of backed into it so this
+forms a
+
+ align:start position:0%
+forms a
+ 
+
+ align:start position:0%
+forms a
+tetrahedron which forms the sp3 hybrid
+
+ align:start position:0%
+tetrahedron which forms the sp3 hybrid
+ 
+
+ align:start position:0%
+tetrahedron which forms the sp3 hybrid
+orbitals now the hydrogen on the other
+
+ align:start position:0%
+orbitals now the hydrogen on the other
+ 
+
+ align:start position:0%
+orbitals now the hydrogen on the other
+hand the hydrogen has uh symmetric s
+
+ align:start position:0%
+hand the hydrogen has uh symmetric s
+ 
+
+ align:start position:0%
+hand the hydrogen has uh symmetric s
+orbitals and now we take and this this
+
+ align:start position:0%
+orbitals and now we take and this this
+ 
+
+ align:start position:0%
+orbitals and now we take and this this
+is another just another way to look at
+
+ align:start position:0%
+is another just another way to look at
+ 
+
+ align:start position:0%
+is another just another way to look at
+whoops my little another way to look at
+
+ align:start position:0%
+whoops my little another way to look at
+ 
+
+ align:start position:0%
+whoops my little another way to look at
+it you take these sp3 hybridized
+
+ align:start position:0%
+it you take these sp3 hybridized
+ 
+
+ align:start position:0%
+it you take these sp3 hybridized
+orbitals and you add a hydrogen to each
+
+ align:start position:0%
+orbitals and you add a hydrogen to each
+ 
+
+ align:start position:0%
+orbitals and you add a hydrogen to each
+one and now what do you have you have
+
+ align:start position:0%
+one and now what do you have you have
+ 
+
+ align:start position:0%
+one and now what do you have you have
+you have a symmetric um um symmetric
+
+ align:start position:0%
+you have a symmetric um um symmetric
+ 
+
+ align:start position:0%
+you have a symmetric um um symmetric
+molecule and let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see whoops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have a molecule where we put the put
+
+ align:start position:0%
+you have a molecule where we put the put
+ 
+
+ align:start position:0%
+you have a molecule where we put the put
+the carbon put the carbon in the center
+
+ align:start position:0%
+the carbon put the carbon in the center
+ 
+
+ align:start position:0%
+the carbon put the carbon in the center
+and we go up like this like this and out
+
+ align:start position:0%
+and we go up like this like this and out
+ 
+
+ align:start position:0%
+and we go up like this like this and out
+the back and now you have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tetrahedron with equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal equal length equal length um uh
+
+ align:start position:0%
+equal equal length equal length um uh
+ 
+
+ align:start position:0%
+equal equal length equal length um uh
+equal length bonds and um and it's going
+
+ align:start position:0%
+equal length bonds and um and it's going
+ 
+
+ align:start position:0%
+equal length bonds and um and it's going
+to be symmetric now will it be will it
+
+ align:start position:0%
+to be symmetric now will it be will it
+ 
+
+ align:start position:0%
+to be symmetric now will it be will it
+be polar or non-polar we're getting a
+
+ align:start position:0%
+be polar or non-polar we're getting a
+ 
+
+ align:start position:0%
+be polar or non-polar we're getting a
+little ahead of ourselves what makes
+
+ align:start position:0%
+little ahead of ourselves what makes
+ 
+
+ align:start position:0%
+little ahead of ourselves what makes
+something polar versus
+
+ align:start position:0%
+something polar versus
+ 
+
+ align:start position:0%
+something polar versus
+non-polar
+
+ align:start position:0%
+non-polar
+ 
+
+ align:start position:0%
+non-polar
+well if this is if this bond has
+
+ align:start position:0%
+well if this is if this bond has
+ 
+
+ align:start position:0%
+well if this is if this bond has
+completely identically equal sharing of
+
+ align:start position:0%
+completely identically equal sharing of
+ 
+
+ align:start position:0%
+completely identically equal sharing of
+electrons then this Bond will be will be
+
+ align:start position:0%
+electrons then this Bond will be will be
+ 
+
+ align:start position:0%
+electrons then this Bond will be will be
+non-polar however we're going to see
+
+ align:start position:0%
+non-polar however we're going to see
+ 
+
+ align:start position:0%
+non-polar however we're going to see
+that that's not the case for hydrogen
+
+ align:start position:0%
+that that's not the case for hydrogen
+ 
+
+ align:start position:0%
+that that's not the case for hydrogen
+and carbon these this Bond will be will
+
+ align:start position:0%
+and carbon these this Bond will be will
+ 
+
+ align:start position:0%
+and carbon these this Bond will be will
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+non-polar so that means we got one two
+
+ align:start position:0%
+non-polar so that means we got one two
+ 
+
+ align:start position:0%
+non-polar so that means we got one two
+three four non-polar Bonds in here and
+
+ align:start position:0%
+three four non-polar Bonds in here and
+ 
+
+ align:start position:0%
+three four non-polar Bonds in here and
+yet the molecule is
+
+ align:start position:0%
+yet the molecule is
+ 
+
+ align:start position:0%
+yet the molecule is
+symmetric and non-polar what's going on
+
+ align:start position:0%
+symmetric and non-polar what's going on
+ 
+
+ align:start position:0%
+symmetric and non-polar what's going on
+well what's going on is the carbon is at
+
+ align:start position:0%
+well what's going on is the carbon is at
+ 
+
+ align:start position:0%
+well what's going on is the carbon is at
+the exact center of the tetrahedron so
+
+ align:start position:0%
+the exact center of the tetrahedron so
+ 
+
+ align:start position:0%
+the exact center of the tetrahedron so
+the non-polar bonds cancel each other
+
+ align:start position:0%
+the non-polar bonds cancel each other
+ 
+
+ align:start position:0%
+the non-polar bonds cancel each other
+out the two sources of charge cancel
+
+ align:start position:0%
+out the two sources of charge cancel
+ 
+
+ align:start position:0%
+out the two sources of charge cancel
+each other out and you get a non-polar
+
+ align:start position:0%
+each other out and you get a non-polar
+ 
+
+ align:start position:0%
+each other out and you get a non-polar
+you get a non-polar molecule okay so
+
+ align:start position:0%
+you get a non-polar molecule okay so
+ 
+
+ align:start position:0%
+you get a non-polar molecule okay so
+that's what that's what um that's what
+
+ align:start position:0%
+that's what that's what um that's what
+ 
+
+ align:start position:0%
+that's what that's what um that's what
+Pauling did but he did uh a little bit
+
+ align:start position:0%
+Pauling did but he did uh a little bit
+ 
+
+ align:start position:0%
+Pauling did but he did uh a little bit
+better um Lewis by the way didn't get a
+
+ align:start position:0%
+better um Lewis by the way didn't get a
+ 
+
+ align:start position:0%
+better um Lewis by the way didn't get a
+Nobel Prize but Pauling did get a Nobel
+
+ align:start position:0%
+Nobel Prize but Pauling did get a Nobel
+ 
+
+ align:start position:0%
+Nobel Prize but Pauling did get a Nobel
+Prize so you say to yourself well lwis
+
+ align:start position:0%
+Prize so you say to yourself well lwis
+ 
+
+ align:start position:0%
+Prize so you say to yourself well lwis
+is the guy that came up with the came up
+
+ align:start position:0%
+is the guy that came up with the came up
+ 
+
+ align:start position:0%
+is the guy that came up with the came up
+with the the idea why didn't he get The
+
+ align:start position:0%
+with the the idea why didn't he get The
+ 
+
+ align:start position:0%
+with the the idea why didn't he get The
+Nobel Prize well he came up with the
+
+ align:start position:0%
+Nobel Prize well he came up with the
+ 
+
+ align:start position:0%
+Nobel Prize well he came up with the
+theory but he did didn't reduce it
+
+ align:start position:0%
+theory but he did didn't reduce it
+ 
+
+ align:start position:0%
+theory but he did didn't reduce it
+reduce it to something quantitative
+
+ align:start position:0%
+reduce it to something quantitative
+ 
+
+ align:start position:0%
+reduce it to something quantitative
+Pauling did that and so let's go back
+
+ align:start position:0%
+Pauling did that and so let's go back
+ 
+
+ align:start position:0%
+Pauling did that and so let's go back
+and take a look at the energetics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again let's look let's take another look
+
+ align:start position:0%
+again let's look let's take another look
+ 
+
+ align:start position:0%
+again let's look let's take another look
+at the energetics now last day uh we we
+
+ align:start position:0%
+at the energetics now last day uh we we
+ 
+
+ align:start position:0%
+at the energetics now last day uh we we
+took it looked at the energetics of the
+
+ align:start position:0%
+took it looked at the energetics of the
+ 
+
+ align:start position:0%
+took it looked at the energetics of the
+ionic bond right and we wrote something
+
+ align:start position:0%
+ionic bond right and we wrote something
+ 
+
+ align:start position:0%
+ionic bond right and we wrote something
+that looks uh the energy is equal to
+
+ align:start position:0%
+that looks uh the energy is equal to
+ 
+
+ align:start position:0%
+that looks uh the energy is equal to
+minus the melin constant
+
+ align:start position:0%
+minus the melin constant
+ 
+
+ align:start position:0%
+minus the melin constant
+times avagadro's number q1 Q2 over 4 pi
+
+ align:start position:0%
+times avagadro's number q1 Q2 over 4 pi
+ 
+
+ align:start position:0%
+times avagadro's number q1 Q2 over 4 pi
+epsilon0
+
+ align:start position:0%
+epsilon0
+ 
+
+ align:start position:0%
+epsilon0
+r0 and we knew that if we know the
+
+ align:start position:0%
+r0 and we knew that if we know the
+ 
+
+ align:start position:0%
+r0 and we knew that if we know the
+crystal structure we can get the madin
+
+ align:start position:0%
+crystal structure we can get the madin
+ 
+
+ align:start position:0%
+crystal structure we can get the madin
+constant not a problem and what we need
+
+ align:start position:0%
+constant not a problem and what we need
+ 
+
+ align:start position:0%
+constant not a problem and what we need
+to do is to get this well how do we get
+
+ align:start position:0%
+to do is to get this well how do we get
+ 
+
+ align:start position:0%
+to do is to get this well how do we get
+that well if we have a if we just take
+
+ align:start position:0%
+that well if we have a if we just take
+ 
+
+ align:start position:0%
+that well if we have a if we just take
+for example mg and let's
+
+ align:start position:0%
+for example mg and let's
+ 
+
+ align:start position:0%
+for example mg and let's
+try
+
+ align:start position:0%
+try
+ 
+
+ align:start position:0%
+try
+mg magnesium chloride just as an example
+
+ align:start position:0%
+mg magnesium chloride just as an example
+ 
+
+ align:start position:0%
+mg magnesium chloride just as an example
+we can put the
+
+ align:start position:0%
+we can put the
+ 
+
+ align:start position:0%
+we can put the
+Magnesium 2+ here and then we put the
+
+ align:start position:0%
+Magnesium 2+ here and then we put the
+ 
+
+ align:start position:0%
+Magnesium 2+ here and then we put the
+oxygen
+
+ align:start position:0%
+oxygen
+ 
+
+ align:start position:0%
+oxygen
+here O2 minus and we know that this
+
+ align:start position:0%
+here O2 minus and we know that this
+ 
+
+ align:start position:0%
+here O2 minus and we know that this
+gives us our R
+
+ align:start position:0%
+gives us our R
+ 
+
+ align:start position:0%
+gives us our R
+zero right so we can go and measure that
+
+ align:start position:0%
+zero right so we can go and measure that
+ 
+
+ align:start position:0%
+zero right so we can go and measure that
+we haven't said much about how to
+
+ align:start position:0%
+we haven't said much about how to
+ 
+
+ align:start position:0%
+we haven't said much about how to
+measure it but you can measure
+
+ align:start position:0%
+measure it but you can measure
+ 
+
+ align:start position:0%
+measure it but you can measure
+it um if we wanted to get the chlorine
+
+ align:start position:0%
+it um if we wanted to get the chlorine
+ 
+
+ align:start position:0%
+it um if we wanted to get the chlorine
+we could just put the chlorine over here
+
+ align:start position:0%
+we could just put the chlorine over here
+ 
+
+ align:start position:0%
+we could just put the chlorine over here
+and we'd measure another
+
+ align:start position:0%
+and we'd measure another
+ 
+
+ align:start position:0%
+and we'd measure another
+another another radius there and we
+
+ align:start position:0%
+another another radius there and we
+ 
+
+ align:start position:0%
+another another radius there and we
+could easily calculate the easily
+
+ align:start position:0%
+could easily calculate the easily
+ 
+
+ align:start position:0%
+could easily calculate the easily
+calculate the energies but with Cove
+
+ align:start position:0%
+calculate the energies but with Cove
+ 
+
+ align:start position:0%
+calculate the energies but with Cove
+valent bonding it's not so simple all
+
+ align:start position:0%
+valent bonding it's not so simple all
+ 
+
+ align:start position:0%
+valent bonding it's not so simple all
+right it's not so simple and so let's
+
+ align:start position:0%
+right it's not so simple and so let's
+ 
+
+ align:start position:0%
+right it's not so simple and so let's
+see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how let's take an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example and let's take an example
+
+ align:start position:0%
+example and let's take an example
+ 
+
+ align:start position:0%
+example and let's take an example
+HF hydrop Floric acid right um well if
+
+ align:start position:0%
+HF hydrop Floric acid right um well if
+ 
+
+ align:start position:0%
+HF hydrop Floric acid right um well if
+we want to draw that we have
+
+ align:start position:0%
+we want to draw that we have
+ 
+
+ align:start position:0%
+we want to draw that we have
+HF
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whoops it would look something look
+
+ align:start position:0%
+whoops it would look something look
+ 
+
+ align:start position:0%
+whoops it would look something look
+something like that but let's say we
+
+ align:start position:0%
+something like that but let's say we
+ 
+
+ align:start position:0%
+something like that but let's say we
+wanted to calculate the energy now
+
+ align:start position:0%
+wanted to calculate the energy now
+ 
+
+ align:start position:0%
+wanted to calculate the energy now
+Pauling was trying to figure out how to
+
+ align:start position:0%
+Pauling was trying to figure out how to
+ 
+
+ align:start position:0%
+Pauling was trying to figure out how to
+do this and he said well what if I were
+
+ align:start position:0%
+do this and he said well what if I were
+ 
+
+ align:start position:0%
+do this and he said well what if I were
+to take and just
+
+ align:start position:0%
+to take and just
+ 
+
+ align:start position:0%
+to take and just
+somehow add up bonds for the energies of
+
+ align:start position:0%
+somehow add up bonds for the energies of
+ 
+
+ align:start position:0%
+somehow add up bonds for the energies of
+bonds or or derive this energy from
+
+ align:start position:0%
+bonds or or derive this energy from
+ 
+
+ align:start position:0%
+bonds or or derive this energy from
+energies that I do know all right and so
+
+ align:start position:0%
+energies that I do know all right and so
+ 
+
+ align:start position:0%
+energies that I do know all right and so
+let's take
+
+ align:start position:0%
+let's take
+ 
+
+ align:start position:0%
+let's take
+H H the HH Bond more
+
+ align:start position:0%
+H H the HH Bond more
+ 
+
+ align:start position:0%
+H H the HH Bond more
+particularly the the H H um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bond right and let's ask what the energy
+
+ align:start position:0%
+Bond right and let's ask what the energy
+ 
+
+ align:start position:0%
+Bond right and let's ask what the energy
+of that is well we can look that up and
+
+ align:start position:0%
+of that is well we can look that up and
+ 
+
+ align:start position:0%
+of that is well we can look that up and
+that's table in your text by the way
+
+ align:start position:0%
+that's table in your text by the way
+ 
+
+ align:start position:0%
+that's table in your text by the way
+B b14 in your text all right and we can
+
+ align:start position:0%
+B b14 in your text all right and we can
+ 
+
+ align:start position:0%
+B b14 in your text all right and we can
+come up with a number of 435
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kles per
+
+ align:start position:0%
+kles per
+ 
+
+ align:start position:0%
+kles per
+mole right
+
+ align:start position:0%
+mole right
+ 
+
+ align:start position:0%
+mole right
+435 well if we want to get HF let's see
+
+ align:start position:0%
+435 well if we want to get HF let's see
+ 
+
+ align:start position:0%
+435 well if we want to get HF let's see
+what F the FF bond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is well you go look in your table and
+
+ align:start position:0%
+is well you go look in your table and
+ 
+
+ align:start position:0%
+is well you go look in your table and
+you come up with
+
+ align:start position:0%
+you come up with
+ 
+
+ align:start position:0%
+you come up with
+h60 K per mole so if I had to
+
+ align:start position:0%
+h60 K per mole so if I had to
+ 
+
+ align:start position:0%
+h60 K per mole so if I had to
+guess what would you guess the bond
+
+ align:start position:0%
+guess what would you guess the bond
+ 
+
+ align:start position:0%
+guess what would you guess the bond
+energy would be in HF well 435
+
+ align:start position:0%
+energy would be in HF well 435
+ 
+
+ align:start position:0%
+energy would be in HF well 435
+160 take 435 add it to 160 divide by two
+
+ align:start position:0%
+160 take 435 add it to 160 divide by two
+ 
+
+ align:start position:0%
+160 take 435 add it to 160 divide by two
+maybe that would be a guess or I could
+
+ align:start position:0%
+maybe that would be a guess or I could
+ 
+
+ align:start position:0%
+maybe that would be a guess or I could
+come up with some other scheme but you
+
+ align:start position:0%
+come up with some other scheme but you
+ 
+
+ align:start position:0%
+come up with some other scheme but you
+would kind of guess that it would be
+
+ align:start position:0%
+would kind of guess that it would be
+ 
+
+ align:start position:0%
+would kind of guess that it would be
+somewhere in between right it would be
+
+ align:start position:0%
+somewhere in between right it would be
+ 
+
+ align:start position:0%
+somewhere in between right it would be
+somewhere somewhere in between well
+
+ align:start position:0%
+somewhere somewhere in between well
+ 
+
+ align:start position:0%
+somewhere somewhere in between well
+what's the
+
+ align:start position:0%
+what's the
+ 
+
+ align:start position:0%
+what's the
+actual value well the
+
+ align:start position:0%
+actual value well the
+ 
+
+ align:start position:0%
+actual value well the
+HF
+
+ align:start position:0%
+HF
+ 
+
+ align:start position:0%
+HF
+fond energy is actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+569 k per mole so we have a problem the
+
+ align:start position:0%
+569 k per mole so we have a problem the
+ 
+
+ align:start position:0%
+569 k per mole so we have a problem the
+problem is we can't add these two
+
+ align:start position:0%
+problem is we can't add these two
+ 
+
+ align:start position:0%
+problem is we can't add these two
+together we can't come there's no way
+
+ align:start position:0%
+together we can't come there's no way
+ 
+
+ align:start position:0%
+together we can't come there's no way
+that we can get from here to here to
+
+ align:start position:0%
+that we can get from here to here to
+ 
+
+ align:start position:0%
+that we can get from here to here to
+here without knowing a little bit more
+
+ align:start position:0%
+here without knowing a little bit more
+ 
+
+ align:start position:0%
+here without knowing a little bit more
+information and well we get that
+
+ align:start position:0%
+information and well we get that
+ 
+
+ align:start position:0%
+information and well we get that
+information by going back to the
+
+ align:start position:0%
+information by going back to the
+ 
+
+ align:start position:0%
+information by going back to the
+definition what was it what's a the
+
+ align:start position:0%
+definition what was it what's a the
+ 
+
+ align:start position:0%
+definition what was it what's a the
+definition of a calent bond sharing of
+
+ align:start position:0%
+definition of a calent bond sharing of
+ 
+
+ align:start position:0%
+definition of a calent bond sharing of
+electrons well they don't have to share
+
+ align:start position:0%
+electrons well they don't have to share
+ 
+
+ align:start position:0%
+electrons well they don't have to share
+equally do they and if they don't share
+
+ align:start position:0%
+equally do they and if they don't share
+ 
+
+ align:start position:0%
+equally do they and if they don't share
+equally then the individual bonds might
+
+ align:start position:0%
+equally then the individual bonds might
+ 
+
+ align:start position:0%
+equally then the individual bonds might
+be might have might have different
+
+ align:start position:0%
+be might have might have different
+ 
+
+ align:start position:0%
+be might have might have different
+energies and so that's exactly what what
+
+ align:start position:0%
+energies and so that's exactly what what
+ 
+
+ align:start position:0%
+energies and so that's exactly what what
+Pauling proposed right and he actually
+
+ align:start position:0%
+Pauling proposed right and he actually
+ 
+
+ align:start position:0%
+Pauling proposed right and he actually
+um um proposed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sharing unequal sharing of
+
+ align:start position:0%
+sharing unequal sharing of
+ 
+
+ align:start position:0%
+sharing unequal sharing of
+electrons and what did he use for a um
+
+ align:start position:0%
+electrons and what did he use for a um
+ 
+
+ align:start position:0%
+electrons and what did he use for a um
+he wanted he needed to get quantitative
+
+ align:start position:0%
+he wanted he needed to get quantitative
+ 
+
+ align:start position:0%
+he wanted he needed to get quantitative
+and he defined a term called the electr
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negativity and in your
+
+ align:start position:0%
+negativity and in your
+ 
+
+ align:start position:0%
+negativity and in your
+text it's e subn but in most chemistry
+
+ align:start position:0%
+text it's e subn but in most chemistry
+ 
+
+ align:start position:0%
+text it's e subn but in most chemistry
+texts it's also Kai That's the more
+
+ align:start position:0%
+texts it's also Kai That's the more
+ 
+
+ align:start position:0%
+texts it's also Kai That's the more
+common that's the more common the more
+
+ align:start position:0%
+common that's the more common the more
+ 
+
+ align:start position:0%
+common that's the more common the more
+common term and it represents the
+
+ align:start position:0%
+common term and it represents the
+ 
+
+ align:start position:0%
+common term and it represents the
+ability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of an
+
+ align:start position:0%
+of an
+ 
+
+ align:start position:0%
+of an
+atom to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attract
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+bond all right the ability of an El of a
+
+ align:start position:0%
+bond all right the ability of an El of a
+ 
+
+ align:start position:0%
+bond all right the ability of an El of a
+the ability of an atom to to attract
+
+ align:start position:0%
+the ability of an atom to to attract
+ 
+
+ align:start position:0%
+the ability of an atom to to attract
+electrons and in
+
+ align:start position:0%
+electrons and in
+ 
+
+ align:start position:0%
+electrons and in
+particular in a Cove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+valent in a calent bond all right and he
+
+ align:start position:0%
+valent in a calent bond all right and he
+ 
+
+ align:start position:0%
+valent in a calent bond all right and he
+came up with a
+
+ align:start position:0%
+came up with a
+ 
+
+ align:start position:0%
+came up with a
+scheme
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is uh how he ranked things and
+
+ align:start position:0%
+and this is uh how he ranked things and
+ 
+
+ align:start position:0%
+and this is uh how he ranked things and
+you can see what you can see um a
+
+ align:start position:0%
+you can see what you can see um a
+ 
+
+ align:start position:0%
+you can see what you can see um a
+parallel if you take a look at uh last
+
+ align:start position:0%
+parallel if you take a look at uh last
+ 
+
+ align:start position:0%
+parallel if you take a look at uh last
+day or the day before you'll see we
+
+ align:start position:0%
+day or the day before you'll see we
+ 
+
+ align:start position:0%
+day or the day before you'll see we
+talked about average veence electron
+
+ align:start position:0%
+talked about average veence electron
+ 
+
+ align:start position:0%
+talked about average veence electron
+energy there's a striking parallel here
+
+ align:start position:0%
+energy there's a striking parallel here
+ 
+
+ align:start position:0%
+energy there's a striking parallel here
+and that the the group one elements have
+
+ align:start position:0%
+and that the the group one elements have
+ 
+
+ align:start position:0%
+and that the the group one elements have
+a tendency to want to give up electrons
+
+ align:start position:0%
+a tendency to want to give up electrons
+ 
+
+ align:start position:0%
+a tendency to want to give up electrons
+where whereas the Florine chlorine and
+
+ align:start position:0%
+where whereas the Florine chlorine and
+ 
+
+ align:start position:0%
+where whereas the Florine chlorine and
+those and bromine have a tendency to
+
+ align:start position:0%
+those and bromine have a tendency to
+ 
+
+ align:start position:0%
+those and bromine have a tendency to
+attract electrons and so this is a a
+
+ align:start position:0%
+attract electrons and so this is a a
+ 
+
+ align:start position:0%
+attract electrons and so this is a a
+schematic of the electric electric NE
+
+ align:start position:0%
+schematic of the electric electric NE
+ 
+
+ align:start position:0%
+schematic of the electric electric NE
+negativity scale now Pauling originally
+
+ align:start position:0%
+negativity scale now Pauling originally
+ 
+
+ align:start position:0%
+negativity scale now Pauling originally
+assumed that Florine was the most
+
+ align:start position:0%
+assumed that Florine was the most
+ 
+
+ align:start position:0%
+assumed that Florine was the most
+electronegative element so he assumed he
+
+ align:start position:0%
+electronegative element so he assumed he
+ 
+
+ align:start position:0%
+electronegative element so he assumed he
+referenced or normalized everything to
+
+ align:start position:0%
+referenced or normalized everything to
+ 
+
+ align:start position:0%
+referenced or normalized everything to
+Florine since that time we've been able
+
+ align:start position:0%
+Florine since that time we've been able
+ 
+
+ align:start position:0%
+Florine since that time we've been able
+to actually measure these Bond strengths
+
+ align:start position:0%
+to actually measure these Bond strengths
+ 
+
+ align:start position:0%
+to actually measure these Bond strengths
+by PES photo electron spectroscopy and
+
+ align:start position:0%
+by PES photo electron spectroscopy and
+ 
+
+ align:start position:0%
+by PES photo electron spectroscopy and
+when you do that it turns out that
+
+ align:start position:0%
+when you do that it turns out that
+ 
+
+ align:start position:0%
+when you do that it turns out that
+Florine doesn't come out to exactly four
+
+ align:start position:0%
+Florine doesn't come out to exactly four
+ 
+
+ align:start position:0%
+Florine doesn't come out to exactly four
+and this is a figure out of your text
+
+ align:start position:0%
+and this is a figure out of your text
+ 
+
+ align:start position:0%
+and this is a figure out of your text
+and you can see that Florine instead of
+
+ align:start position:0%
+and you can see that Florine instead of
+ 
+
+ align:start position:0%
+and you can see that Florine instead of
+four it's about 4 point 4.19 but it's as
+
+ align:start position:0%
+four it's about 4 point 4.19 but it's as
+ 
+
+ align:start position:0%
+four it's about 4 point 4.19 but it's as
+you would expect the most
+
+ align:start position:0%
+you would expect the most
+ 
+
+ align:start position:0%
+you would expect the most
+electronegative elements Florine
+
+ align:start position:0%
+electronegative elements Florine
+ 
+
+ align:start position:0%
+electronegative elements Florine
+chlorine oxygen are over here uh the
+
+ align:start position:0%
+chlorine oxygen are over here uh the
+ 
+
+ align:start position:0%
+chlorine oxygen are over here uh the
+highest one is is neon but the lowest
+
+ align:start position:0%
+highest one is is neon but the lowest
+ 
+
+ align:start position:0%
+highest one is is neon but the lowest
+one is way down here cesium and you
+
+ align:start position:0%
+one is way down here cesium and you
+ 
+
+ align:start position:0%
+one is way down here cesium and you
+would expect that the group one absent
+
+ align:start position:0%
+would expect that the group one absent
+ 
+
+ align:start position:0%
+would expect that the group one absent
+hydrogen would be the ones that would um
+
+ align:start position:0%
+hydrogen would be the ones that would um
+ 
+
+ align:start position:0%
+hydrogen would be the ones that would um
+that would have the least now remember
+
+ align:start position:0%
+that would have the least now remember
+ 
+
+ align:start position:0%
+that would have the least now remember
+the formation of the ionic bonds was
+
+ align:start position:0%
+the formation of the ionic bonds was
+ 
+
+ align:start position:0%
+the formation of the ionic bonds was
+from group one and group two and over
+
+ align:start position:0%
+from group one and group two and over
+ 
+
+ align:start position:0%
+from group one and group two and over
+here with um uh group six and seven so
+
+ align:start position:0%
+here with um uh group six and seven so
+ 
+
+ align:start position:0%
+here with um uh group six and seven so
+those are the ones that are most most
+
+ align:start position:0%
+those are the ones that are most most
+ 
+
+ align:start position:0%
+those are the ones that are most most
+likely form ionic
+
+ align:start position:0%
+likely form ionic
+ 
+
+ align:start position:0%
+likely form ionic
+bonds okay not only did he propose it he
+
+ align:start position:0%
+bonds okay not only did he propose it he
+ 
+
+ align:start position:0%
+bonds okay not only did he propose it he
+Quantified it and um he did something
+
+ align:start position:0%
+Quantified it and um he did something
+ 
+
+ align:start position:0%
+Quantified it and um he did something
+even even better let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+defined something called how much time
+
+ align:start position:0%
+defined something called how much time
+ 
+
+ align:start position:0%
+defined something called how much time
+do we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charge right now this is what got him
+
+ align:start position:0%
+charge right now this is what got him
+ 
+
+ align:start position:0%
+charge right now this is what got him
+this is what got him the Nobel Prize
+
+ align:start position:0%
+this is what got him the Nobel Prize
+ 
+
+ align:start position:0%
+this is what got him the Nobel Prize
+and he to find partial charge and I'll
+
+ align:start position:0%
+and he to find partial charge and I'll
+ 
+
+ align:start position:0%
+and he to find partial charge and I'll
+give you the formula G subx this is in
+
+ align:start position:0%
+give you the formula G subx this is in
+ 
+
+ align:start position:0%
+give you the formula G subx this is in
+your text that's of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X in an XY Bond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right um Kai sub X Plus Kai sub y right
+
+ align:start position:0%
+right um Kai sub X Plus Kai sub y right
+ 
+
+ align:start position:0%
+right um Kai sub X Plus Kai sub y right
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+G
+
+ align:start position:0%
+G
+ 
+
+ align:start position:0%
+G
+subx is the group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number right n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subx is the number of non
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bonding non-bonding
+
+ align:start position:0%
+bonding non-bonding
+ 
+
+ align:start position:0%
+bonding non-bonding
+electrons and B
+
+ align:start position:0%
+electrons and B
+ 
+
+ align:start position:0%
+electrons and B
+subx is the number of bonding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bonding electrons okay now let's take
+
+ align:start position:0%
+bonding electrons okay now let's take
+ 
+
+ align:start position:0%
+bonding electrons okay now let's take
+this and look at what what we get if we
+
+ align:start position:0%
+this and look at what what we get if we
+ 
+
+ align:start position:0%
+this and look at what what we get if we
+try HF all right we know this is what we
+
+ align:start position:0%
+try HF all right we know this is what we
+ 
+
+ align:start position:0%
+try HF all right we know this is what we
+this is what it comes out to this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H right we got one X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we know that this is going to be by
+
+ align:start position:0%
+here we know that this is going to be by
+ 
+
+ align:start position:0%
+here we know that this is going to be by
+measurement this is going to be plus and
+
+ align:start position:0%
+measurement this is going to be plus and
+ 
+
+ align:start position:0%
+measurement this is going to be plus and
+this is going to be minus it's going to
+
+ align:start position:0%
+this is going to be minus it's going to
+ 
+
+ align:start position:0%
+this is going to be minus it's going to
+be D it's going to be a dipole this is
+
+ align:start position:0%
+be D it's going to be a dipole this is
+ 
+
+ align:start position:0%
+be D it's going to be a dipole this is
+plus this is minus
+
+ align:start position:0%
+plus this is minus
+ 
+
+ align:start position:0%
+plus this is minus
+and we know that Kai of the Florine is
+
+ align:start position:0%
+and we know that Kai of the Florine is
+ 
+
+ align:start position:0%
+and we know that Kai of the Florine is
+4 1
+
+ align:start position:0%
+4 1
+ 
+
+ align:start position:0%
+4 1
+n and Kai of the hydrogen is equal to
+
+ align:start position:0%
+n and Kai of the hydrogen is equal to
+ 
+
+ align:start position:0%
+n and Kai of the hydrogen is equal to
+2.3
+
+ align:start position:0%
+2.3
+ 
+
+ align:start position:0%
+2.3
+Z okay well if we plug that in let me
+
+ align:start position:0%
+Z okay well if we plug that in let me
+ 
+
+ align:start position:0%
+Z okay well if we plug that in let me
+just do one of
+
+ align:start position:0%
+just do one of
+ 
+
+ align:start position:0%
+just do one of
+them for just do the Florine and by the
+
+ align:start position:0%
+them for just do the Florine and by the
+ 
+
+ align:start position:0%
+them for just do the Florine and by the
+way the if you do this for the hydrogen
+
+ align:start position:0%
+way the if you do this for the hydrogen
+ 
+
+ align:start position:0%
+way the if you do this for the hydrogen
+it ought to come out the same that's
+
+ align:start position:0%
+it ought to come out the same that's
+ 
+
+ align:start position:0%
+it ought to come out the same that's
+equal to 7us - 6 -
+
+ align:start position:0%
+equal to 7us - 6 -
+ 
+
+ align:start position:0%
+equal to 7us - 6 -
+2 *
+
+ align:start position:0%
+2 *
+ 
+
+ align:start position:0%
+2 *
+4.19 over
+
+ align:start position:0%
+4.19 over
+ 
+
+ align:start position:0%
+4.19 over
+4.19 plus
+
+ align:start position:0%
+4.19 plus
+ 
+
+ align:start position:0%
+4.19 plus
+2.3 and that gives you a
+
+ align:start position:0%
+2.3 and that gives you a
+ 
+
+ align:start position:0%
+2.3 and that gives you a
+number for the Florine minus
+
+ align:start position:0%
+number for the Florine minus
+ 
+
+ align:start position:0%
+number for the Florine minus
+0.29 all right now if you do the same do
+
+ align:start position:0%
+0.29 all right now if you do the same do
+ 
+
+ align:start position:0%
+0.29 all right now if you do the same do
+the same for the uh for the for the
+
+ align:start position:0%
+the same for the uh for the for the
+ 
+
+ align:start position:0%
+the same for the uh for the for the
+hydrogen you'll come out with the same
+
+ align:start position:0%
+hydrogen you'll come out with the same
+ 
+
+ align:start position:0%
+hydrogen you'll come out with the same
+number but it'll be plus
+
+ align:start position:0%
+number but it'll be plus
+ 
+
+ align:start position:0%
+number but it'll be plus
+all right but it but it'll be plus and
+
+ align:start position:0%
+all right but it but it'll be plus and
+ 
+
+ align:start position:0%
+all right but it but it'll be plus and
+so then that what that tells us is HF is
+
+ align:start position:0%
+so then that what that tells us is HF is
+ 
+
+ align:start position:0%
+so then that what that tells us is HF is
+polar HF is HF is
+
+ align:start position:0%
+polar HF is HF is
+ 
+
+ align:start position:0%
+polar HF is HF is
+polar okay so we did that and um now
+
+ align:start position:0%
+polar okay so we did that and um now
+ 
+
+ align:start position:0%
+polar okay so we did that and um now
+let's go back to whoops I'm running out
+
+ align:start position:0%
+let's go back to whoops I'm running out
+ 
+
+ align:start position:0%
+let's go back to whoops I'm running out
+of space let's go back to let's go back
+
+ align:start position:0%
+of space let's go back to let's go back
+ 
+
+ align:start position:0%
+of space let's go back to let's go back
+to methane and see what happens see what
+
+ align:start position:0%
+to methane and see what happens see what
+ 
+
+ align:start position:0%
+to methane and see what happens see what
+happens there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's go back let's go back to methane
+
+ align:start position:0%
+let's go back let's go back to methane
+ 
+
+ align:start position:0%
+let's go back let's go back to methane
+well the kai of the carbon is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2.54 Kai of the hydrogen again is what
+
+ align:start position:0%
+2.54 Kai of the hydrogen again is what
+ 
+
+ align:start position:0%
+2.54 Kai of the hydrogen again is what
+2.3 and
+
+ align:start position:0%
+2.3 and
+ 
+
+ align:start position:0%
+2.3 and
+um so what this tells us since these
+
+ align:start position:0%
+um so what this tells us since these
+ 
+
+ align:start position:0%
+um so what this tells us since these
+aren't equal that tells us that the
+
+ align:start position:0%
+aren't equal that tells us that the
+ 
+
+ align:start position:0%
+aren't equal that tells us that the
+carbon hydrogen
+
+ align:start position:0%
+carbon hydrogen
+ 
+
+ align:start position:0%
+carbon hydrogen
+bond is
+
+ align:start position:0%
+bond is
+ 
+
+ align:start position:0%
+bond is
+not well better way to look at
+
+ align:start position:0%
+not well better way to look at
+ 
+
+ align:start position:0%
+not well better way to look at
+it is
+
+ align:start position:0%
+it is
+ 
+
+ align:start position:0%
+it is
+polar right hydrogen bond is polar and
+
+ align:start position:0%
+polar right hydrogen bond is polar and
+ 
+
+ align:start position:0%
+polar right hydrogen bond is polar and
+so if we go and we draw this again if
+
+ align:start position:0%
+so if we go and we draw this again if
+ 
+
+ align:start position:0%
+so if we go and we draw this again if
+this is the carbon here
+
+ align:start position:0%
+this is the carbon here
+ 
+
+ align:start position:0%
+this is the carbon here
+hydrogen
+
+ align:start position:0%
+hydrogen
+ 
+
+ align:start position:0%
+hydrogen
+hydrogen
+
+ align:start position:0%
+hydrogen
+ 
+
+ align:start position:0%
+hydrogen
+hydrogen hydrogen like this
+
+ align:start position:0%
+hydrogen hydrogen like this
+ 
+
+ align:start position:0%
+hydrogen hydrogen like this
+then this is going to be a little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus right little whoops plus and this
+
+ align:start position:0%
+plus right little whoops plus and this
+ 
+
+ align:start position:0%
+plus right little whoops plus and this
+end is going to be negative all right so
+
+ align:start position:0%
+end is going to be negative all right so
+ 
+
+ align:start position:0%
+end is going to be negative all right so
+we know from our calculation that we can
+
+ align:start position:0%
+we know from our calculation that we can
+ 
+
+ align:start position:0%
+we know from our calculation that we can
+do over here that this this
+
+ align:start position:0%
+do over here that this this
+ 
+
+ align:start position:0%
+do over here that this this
+bond is
+
+ align:start position:0%
+bond is
+ 
+
+ align:start position:0%
+bond is
+polar right this bond is polar but again
+
+ align:start position:0%
+polar right this bond is polar but again
+ 
+
+ align:start position:0%
+polar right this bond is polar but again
+as I alluded to
+
+ align:start position:0%
+as I alluded to
+ 
+
+ align:start position:0%
+as I alluded to
+earlier because the carbon is centered
+
+ align:start position:0%
+earlier because the carbon is centered
+ 
+
+ align:start position:0%
+earlier because the carbon is centered
+in the tetrahedron because of the sp3
+
+ align:start position:0%
+in the tetrahedron because of the sp3
+ 
+
+ align:start position:0%
+in the tetrahedron because of the sp3
+hybridization the molecule itself is
+
+ align:start position:0%
+hybridization the molecule itself is
+ 
+
+ align:start position:0%
+hybridization the molecule itself is
+symmetric and
+
+ align:start position:0%
+symmetric and
+ 
+
+ align:start position:0%
+symmetric and
+non-polar okay and for this he got a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Nobel in I think 19
+
+ align:start position:0%
+Nobel in I think 19
+ 
+
+ align:start position:0%
+Nobel in I think 19
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+1954 okay now one last thing that he did
+
+ align:start position:0%
+1954 okay now one last thing that he did
+ 
+
+ align:start position:0%
+1954 okay now one last thing that he did
+is that he said okay what's going on
+
+ align:start position:0%
+is that he said okay what's going on
+ 
+
+ align:start position:0%
+is that he said okay what's going on
+here well on the one hand we have ionic
+
+ align:start position:0%
+here well on the one hand we have ionic
+ 
+
+ align:start position:0%
+here well on the one hand we have ionic
+bonding where we have complete sharing
+
+ align:start position:0%
+bonding where we have complete sharing
+ 
+
+ align:start position:0%
+bonding where we have complete sharing
+on the other hand if we have a perfect
+
+ align:start position:0%
+on the other hand if we have a perfect
+ 
+
+ align:start position:0%
+on the other hand if we have a perfect
+Cove valence Bond we have identical ABS
+
+ align:start position:0%
+Cove valence Bond we have identical ABS
+ 
+
+ align:start position:0%
+Cove valence Bond we have identical ABS
+equal sharing but we know that that just
+
+ align:start position:0%
+equal sharing but we know that that just
+ 
+
+ align:start position:0%
+equal sharing but we know that that just
+by this calculation that we don't have
+
+ align:start position:0%
+by this calculation that we don't have
+ 
+
+ align:start position:0%
+by this calculation that we don't have
+equal sharing so somewhere in between
+
+ align:start position:0%
+equal sharing so somewhere in between
+ 
+
+ align:start position:0%
+equal sharing so somewhere in between
+the bonds are we have a range of bonds
+
+ align:start position:0%
+the bonds are we have a range of bonds
+ 
+
+ align:start position:0%
+the bonds are we have a range of bonds
+between ionic on the one hand and
+
+ align:start position:0%
+between ionic on the one hand and
+ 
+
+ align:start position:0%
+between ionic on the one hand and
+perfectly Cove valent on the other hand
+
+ align:start position:0%
+perfectly Cove valent on the other hand
+ 
+
+ align:start position:0%
+perfectly Cove valent on the other hand
+but there's a whole range in between so
+
+ align:start position:0%
+but there's a whole range in between so
+ 
+
+ align:start position:0%
+but there's a whole range in between so
+what's going on there well
+
+ align:start position:0%
+what's going on there well
+ 
+
+ align:start position:0%
+what's going on there well
+he Pauling also suggests that for that
+
+ align:start position:0%
+he Pauling also suggests that for that
+ 
+
+ align:start position:0%
+he Pauling also suggests that for that
+case that the bonds are partially ionic
+
+ align:start position:0%
+case that the bonds are partially ionic
+ 
+
+ align:start position:0%
+case that the bonds are partially ionic
+and partially calent and he came up with
+
+ align:start position:0%
+and partially calent and he came up with
+ 
+
+ align:start position:0%
+and partially calent and he came up with
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relationship to calculate the percent
+
+ align:start position:0%
+relationship to calculate the percent
+ 
+
+ align:start position:0%
+relationship to calculate the percent
+ionic character all right and I'll just
+
+ align:start position:0%
+ionic character all right and I'll just
+ 
+
+ align:start position:0%
+ionic character all right and I'll just
+give it to you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared to give you percent all right so
+
+ align:start position:0%
+squared to give you percent all right so
+ 
+
+ align:start position:0%
+squared to give you percent all right so
+this is a relationship and so you can
+
+ align:start position:0%
+this is a relationship and so you can
+ 
+
+ align:start position:0%
+this is a relationship and so you can
+see where Kai comes in where Kai comes
+
+ align:start position:0%
+see where Kai comes in where Kai comes
+ 
+
+ align:start position:0%
+see where Kai comes in where Kai comes
+in here and this is the the difference
+
+ align:start position:0%
+in here and this is the the difference
+ 
+
+ align:start position:0%
+in here and this is the the difference
+in electr negativity between the two
+
+ align:start position:0%
+in electr negativity between the two
+ 
+
+ align:start position:0%
+in electr negativity between the two
+between the two the two elements all
+
+ align:start position:0%
+between the two the two elements all
+ 
+
+ align:start position:0%
+between the two the two elements all
+right let's see how much
+
+ align:start position:0%
+right let's see how much
+ 
+
+ align:start position:0%
+right let's see how much
+time okay he also
+
+ align:start position:0%
+time okay he also
+ 
+
+ align:start position:0%
+time okay he also
+uh let me see he also lastly to to close
+
+ align:start position:0%
+uh let me see he also lastly to to close
+ 
+
+ align:start position:0%
+uh let me see he also lastly to to close
+this out he
+
+ align:start position:0%
+this out he
+ 
+
+ align:start position:0%
+this out he
+also developed an analytical expression
+
+ align:start position:0%
+also developed an analytical expression
+ 
+
+ align:start position:0%
+also developed an analytical expression
+for the energy of that Cove valent bond
+
+ align:start position:0%
+for the energy of that Cove valent bond
+ 
+
+ align:start position:0%
+for the energy of that Cove valent bond
+which is really what we
+
+ align:start position:0%
+which is really what we
+ 
+
+ align:start position:0%
+which is really what we
+want all right so the the type of um um
+
+ align:start position:0%
+want all right so the the type of um um
+ 
+
+ align:start position:0%
+want all right so the the type of um um
+uh Bond energies that we can go and look
+
+ align:start position:0%
+uh Bond energies that we can go and look
+ 
+
+ align:start position:0%
+uh Bond energies that we can go and look
+up in the in tables are individual atom
+
+ align:start position:0%
+up in the in tables are individual atom
+ 
+
+ align:start position:0%
+up in the in tables are individual atom
+bonds HH FF and the like but he said the
+
+ align:start position:0%
+bonds HH FF and the like but he said the
+ 
+
+ align:start position:0%
+bonds HH FF and the like but he said the
+energy of a of a of an XY bond is going
+
+ align:start position:0%
+energy of a of a of an XY bond is going
+ 
+
+ align:start position:0%
+energy of a of a of an XY bond is going
+to be equal to the square root
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say right so the XX Bond and the y y
+
+ align:start position:0%
+say right so the XX Bond and the y y
+ 
+
+ align:start position:0%
+say right so the XX Bond and the y y
+Bond we can look up those
+
+ align:start position:0%
+Bond we can look up those
+ 
+
+ align:start position:0%
+Bond we can look up those
+energies plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+96.3 Delta K squared in
+
+ align:start position:0%
+96.3 Delta K squared in
+ 
+
+ align:start position:0%
+96.3 Delta K squared in
+the kiles per mole where's the 96.3 come
+
+ align:start position:0%
+the kiles per mole where's the 96.3 come
+ 
+
+ align:start position:0%
+the kiles per mole where's the 96.3 come
+from well it's a conversion factor
+
+ align:start position:0%
+from well it's a conversion factor
+ 
+
+ align:start position:0%
+from well it's a conversion factor
+so this gives you the uh um the energy
+
+ align:start position:0%
+so this gives you the uh um the energy
+ 
+
+ align:start position:0%
+so this gives you the uh um the energy
+of the bond now if we plug in the
+
+ align:start position:0%
+of the bond now if we plug in the
+ 
+
+ align:start position:0%
+of the bond now if we plug in the
+numbers we plug in the numbers for uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+HF what do we get well we get uh Square
+
+ align:start position:0%
+HF what do we get well we get uh Square
+ 
+
+ align:start position:0%
+HF what do we get well we get uh Square
+< TK of
+
+ align:start position:0%
+< TK of
+ 
+
+ align:start position:0%
+< TK of
+435 *
+
+ align:start position:0%
+435 *
+ 
+
+ align:start position:0%
+435 *
+160 plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+96.3 uh times
+
+ align:start position:0%
+96.3 uh times
+ 
+
+ align:start position:0%
+96.3 uh times
+I hus K carbon
+
+ align:start position:0%
+I hus K carbon
+ 
+
+ align:start position:0%
+I hus K carbon
+whoops squared and you get this number
+
+ align:start position:0%
+whoops squared and you get this number
+ 
+
+ align:start position:0%
+whoops squared and you get this number
+here is 2.3 this is
+
+ align:start position:0%
+here is 2.3 this is
+ 
+
+ align:start position:0%
+here is 2.3 this is
+4.19 you get the E of the
+
+ align:start position:0%
+4.19 you get the E of the
+ 
+
+ align:start position:0%
+4.19 you get the E of the
+HF is equal to
+
+ align:start position:0%
+HF is equal to
+ 
+
+ align:start position:0%
+HF is equal to
+608 okay now where's my other one
+
+ align:start position:0%
+608 okay now where's my other one
+ 
+
+ align:start position:0%
+608 okay now where's my other one
+somewhere here
+
+ align:start position:0%
+somewhere here
+ 
+
+ align:start position:0%
+somewhere here
+569 over here K per mole
+
+ align:start position:0%
+569 over here K per mole
+ 
+
+ align:start position:0%
+569 over here K per mole
+and by his formula he gets 608 which
+
+ align:start position:0%
+and by his formula he gets 608 which
+ 
+
+ align:start position:0%
+and by his formula he gets 608 which
+isn't bad which really which really
+
+ align:start position:0%
+isn't bad which really which really
+ 
+
+ align:start position:0%
+isn't bad which really which really
+isn't bad isn't bad at
+
+ align:start position:0%
+isn't bad isn't bad at
+ 
+
+ align:start position:0%
+isn't bad isn't bad at
+all okay so what we've gone through
+
+ align:start position:0%
+all okay so what we've gone through
+ 
+
+ align:start position:0%
+all okay so what we've gone through
+today is we've introduced covalent
+
+ align:start position:0%
+today is we've introduced covalent
+ 
+
+ align:start position:0%
+today is we've introduced covalent
+bonding and we figured out a way to
+
+ align:start position:0%
+bonding and we figured out a way to
+ 
+
+ align:start position:0%
+bonding and we figured out a way to
+quantify it not only did we figure out a
+
+ align:start position:0%
+quantify it not only did we figure out a
+ 
+
+ align:start position:0%
+quantify it not only did we figure out a
+way to did we describe how we quantify
+
+ align:start position:0%
+way to did we describe how we quantify
+ 
+
+ align:start position:0%
+way to did we describe how we quantify
+it but we've also Quantified how we tell
+
+ align:start position:0%
+it but we've also Quantified how we tell
+ 
+
+ align:start position:0%
+it but we've also Quantified how we tell
+the difference between calent ionic and
+
+ align:start position:0%
+the difference between calent ionic and
+ 
+
+ align:start position:0%
+the difference between calent ionic and
+percen ionic character so those are the
+
+ align:start position:0%
+percen ionic character so those are the
+ 
+
+ align:start position:0%
+percen ionic character so those are the
+key things to remember for today but
+
+ align:start position:0%
+key things to remember for today but
+ 
+
+ align:start position:0%
+key things to remember for today but
+hold on a minute what we got got a few
+
+ align:start position:0%
+hold on a minute what we got got a few
+ 
+
+ align:start position:0%
+hold on a minute what we got got a few
+minutes
+
+ align:start position:0%
+minutes
+ 
+
+ align:start position:0%
+minutes
+here let's give you an
+
+ align:start position:0%
+here let's give you an
+ 
+
+ align:start position:0%
+here let's give you an
+example of
+
+ align:start position:0%
+example of
+ 
+
+ align:start position:0%
+example of
+uh sp3
+
+ align:start position:0%
+uh sp3
+ 
+
+ align:start position:0%
+uh sp3
+hybridization um there's a scientist
+
+ align:start position:0%
+hybridization um there's a scientist
+ 
+
+ align:start position:0%
+hybridization um there's a scientist
+Thomas Midgley and uh Professor sway
+
+ align:start position:0%
+Thomas Midgley and uh Professor sway
+ 
+
+ align:start position:0%
+Thomas Midgley and uh Professor sway
+calls him sp3 Midgley he developed a
+
+ align:start position:0%
+calls him sp3 Midgley he developed a
+ 
+
+ align:start position:0%
+calls him sp3 Midgley he developed a
+whole lot of compounds based on sp3
+
+ align:start position:0%
+whole lot of compounds based on sp3
+ 
+
+ align:start position:0%
+whole lot of compounds based on sp3
+hybridization and this one here you
+
+ align:start position:0%
+hybridization and this one here you
+ 
+
+ align:start position:0%
+hybridization and this one here you
+might some of you might recog recognize
+
+ align:start position:0%
+might some of you might recog recognize
+ 
+
+ align:start position:0%
+might some of you might recog recognize
+is um uh uh Doro dioro methane it's also
+
+ align:start position:0%
+is um uh uh Doro dioro methane it's also
+ 
+
+ align:start position:0%
+is um uh uh Doro dioro methane it's also
+known as a
+
+ align:start position:0%
+known as a
+ 
+
+ align:start position:0%
+known as a
+CFC and this is the shape it's sp3
+
+ align:start position:0%
+CFC and this is the shape it's sp3
+ 
+
+ align:start position:0%
+CFC and this is the shape it's sp3
+hybridized now um it's not going to be
+
+ align:start position:0%
+hybridized now um it's not going to be
+ 
+
+ align:start position:0%
+hybridized now um it's not going to be
+symmetric is it because there's two
+
+ align:start position:0%
+symmetric is it because there's two
+ 
+
+ align:start position:0%
+symmetric is it because there's two
+flines and two chlorines so it's a non
+
+ align:start position:0%
+flines and two chlorines so it's a non
+ 
+
+ align:start position:0%
+flines and two chlorines so it's a non
+symmetric nonsymmetric molecule but what
+
+ align:start position:0%
+symmetric nonsymmetric molecule but what
+ 
+
+ align:start position:0%
+symmetric nonsymmetric molecule but what
+is uh what is good about what is what is
+
+ align:start position:0%
+is uh what is good about what is what is
+ 
+
+ align:start position:0%
+is uh what is good about what is what is
+so unusual about this well up until
+
+ align:start position:0%
+so unusual about this well up until
+ 
+
+ align:start position:0%
+so unusual about this well up until
+probably 10 years ago this was the
+
+ align:start position:0%
+probably 10 years ago this was the
+ 
+
+ align:start position:0%
+probably 10 years ago this was the
+primary propellant in just about every
+
+ align:start position:0%
+primary propellant in just about every
+ 
+
+ align:start position:0%
+primary propellant in just about every
+kind of can every kind of spray thing
+
+ align:start position:0%
+kind of can every kind of spray thing
+ 
+
+ align:start position:0%
+kind of can every kind of spray thing
+that we had hairspray everything it was
+
+ align:start position:0%
+that we had hairspray everything it was
+ 
+
+ align:start position:0%
+that we had hairspray everything it was
+it's called Freon it's also used in air
+
+ align:start position:0%
+it's called Freon it's also used in air
+ 
+
+ align:start position:0%
+it's called Freon it's also used in air
+conditioners also used in air
+
+ align:start position:0%
+conditioners also used in air
+ 
+
+ align:start position:0%
+conditioners also used in air
+conditioners what was neat about it is
+
+ align:start position:0%
+conditioners what was neat about it is
+ 
+
+ align:start position:0%
+conditioners what was neat about it is
+before that time the the predominant um
+
+ align:start position:0%
+before that time the the predominant um
+ 
+
+ align:start position:0%
+before that time the the predominant um
+species to use for air conditioning or
+
+ align:start position:0%
+species to use for air conditioning or
+ 
+
+ align:start position:0%
+species to use for air conditioning or
+Refrigeration was ammonia and not too
+
+ align:start position:0%
+Refrigeration was ammonia and not too
+ 
+
+ align:start position:0%
+Refrigeration was ammonia and not too
+many people actually if you look talk to
+
+ align:start position:0%
+many people actually if you look talk to
+ 
+
+ align:start position:0%
+many people actually if you look talk to
+your grandmother or grandfather and
+
+ align:start position:0%
+your grandmother or grandfather and
+ 
+
+ align:start position:0%
+your grandmother or grandfather and
+there were some refrigerators that were
+
+ align:start position:0%
+there were some refrigerators that were
+ 
+
+ align:start position:0%
+there were some refrigerators that were
+actually made that used ammonia but when
+
+ align:start position:0%
+actually made that used ammonia but when
+ 
+
+ align:start position:0%
+actually made that used ammonia but when
+they sprung a leak you had a problem and
+
+ align:start position:0%
+they sprung a leak you had a problem and
+ 
+
+ align:start position:0%
+they sprung a leak you had a problem and
+so by and large until these uh fre fron
+
+ align:start position:0%
+so by and large until these uh fre fron
+ 
+
+ align:start position:0%
+so by and large until these uh fre fron
+was invented by midy there wasn't uh a
+
+ align:start position:0%
+was invented by midy there wasn't uh a
+ 
+
+ align:start position:0%
+was invented by midy there wasn't uh a
+good um G gas that had the right
+
+ align:start position:0%
+good um G gas that had the right
+ 
+
+ align:start position:0%
+good um G gas that had the right
+properties to be used for a refrigerant
+
+ align:start position:0%
+properties to be used for a refrigerant
+ 
+
+ align:start position:0%
+properties to be used for a refrigerant
+and so this was good as a refrigerant
+
+ align:start position:0%
+and so this was good as a refrigerant
+ 
+
+ align:start position:0%
+and so this was good as a refrigerant
+but something else can happen with these
+
+ align:start position:0%
+but something else can happen with these
+ 
+
+ align:start position:0%
+but something else can happen with these
+things and I think this is uh you hear
+
+ align:start position:0%
+things and I think this is uh you hear
+ 
+
+ align:start position:0%
+things and I think this is uh you hear
+about this in the news a lot if you get
+
+ align:start position:0%
+about this in the news a lot if you get
+ 
+
+ align:start position:0%
+about this in the news a lot if you get
+some of these uh these in the upper
+
+ align:start position:0%
+some of these uh these in the upper
+ 
+
+ align:start position:0%
+some of these uh these in the upper
+atmosphere this um a photon an ultrav
+
+ align:start position:0%
+atmosphere this um a photon an ultrav
+ 
+
+ align:start position:0%
+atmosphere this um a photon an ultrav
+ENT Photon has an energy capable of
+
+ align:start position:0%
+ENT Photon has an energy capable of
+ 
+
+ align:start position:0%
+ENT Photon has an energy capable of
+breaking this Bond when it breaks this
+
+ align:start position:0%
+breaking this Bond when it breaks this
+ 
+
+ align:start position:0%
+breaking this Bond when it breaks this
+bond that Flor that chlorine atom a free
+
+ align:start position:0%
+bond that Flor that chlorine atom a free
+ 
+
+ align:start position:0%
+bond that Flor that chlorine atom a free
+chlorine atom comes down and reacts with
+
+ align:start position:0%
+chlorine atom comes down and reacts with
+ 
+
+ align:start position:0%
+chlorine atom comes down and reacts with
+the this is Ozone with the ozone in the
+
+ align:start position:0%
+the this is Ozone with the ozone in the
+ 
+
+ align:start position:0%
+the this is Ozone with the ozone in the
+upper atmosphere and you end up with a
+
+ align:start position:0%
+upper atmosphere and you end up with a
+ 
+
+ align:start position:0%
+upper atmosphere and you end up with a
+destruction of the ozone layer and this
+
+ align:start position:0%
+destruction of the ozone layer and this
+ 
+
+ align:start position:0%
+destruction of the ozone layer and this
+is what you hear a lot about in the news
+
+ align:start position:0%
+is what you hear a lot about in the news
+ 
+
+ align:start position:0%
+is what you hear a lot about in the news
+um Kyoto and all this kind of thing
+
+ align:start position:0%
+um Kyoto and all this kind of thing
+ 
+
+ align:start position:0%
+um Kyoto and all this kind of thing
+about destruction of the ozone the ozone
+
+ align:start position:0%
+about destruction of the ozone the ozone
+ 
+
+ align:start position:0%
+about destruction of the ozone the ozone
+layer well this uh Mario Molina who's a
+
+ align:start position:0%
+layer well this uh Mario Molina who's a
+ 
+
+ align:start position:0%
+layer well this uh Mario Molina who's a
+faculty member here at MIT won a Nobel
+
+ align:start position:0%
+faculty member here at MIT won a Nobel
+ 
+
+ align:start position:0%
+faculty member here at MIT won a Nobel
+Prize for describing this um um this
+
+ align:start position:0%
+Prize for describing this um um this
+ 
+
+ align:start position:0%
+Prize for describing this um um this
+process he wasn't here at MIT when he um
+
+ align:start position:0%
+process he wasn't here at MIT when he um
+ 
+
+ align:start position:0%
+process he wasn't here at MIT when he um
+when he won the prize but here's the
+
+ align:start position:0%
+when he won the prize but here's the
+ 
+
+ align:start position:0%
+when he won the prize but here's the
+here's the paper the actual paper now uh
+
+ align:start position:0%
+here's the paper the actual paper now uh
+ 
+
+ align:start position:0%
+here's the paper the actual paper now uh
+you think you can make a mistake on your
+
+ align:start position:0%
+you think you can make a mistake on your
+ 
+
+ align:start position:0%
+you think you can make a mistake on your
+exam take a look at this up here and
+
+ align:start position:0%
+exam take a look at this up here and
+ 
+
+ align:start position:0%
+exam take a look at this up here and
+tell me what that all is I have no
+
+ align:start position:0%
+tell me what that all is I have no
+ 
+
+ align:start position:0%
+tell me what that all is I have no
+idea that's exactly the the actual the
+
+ align:start position:0%
+idea that's exactly the the actual the
+ 
+
+ align:start position:0%
+idea that's exactly the the actual the
+actual paper it's actually should be
+
+ align:start position:0%
+actual paper it's actually should be
+ 
+
+ align:start position:0%
+actual paper it's actually should be
+chlorine catalyzed shouldn't it but who
+
+ align:start position:0%
+chlorine catalyzed shouldn't it but who
+ 
+
+ align:start position:0%
+chlorine catalyzed shouldn't it but who
+cares he got the Nobel
+
+ align:start position:0%
+cares he got the Nobel
+ 
+
+ align:start position:0%
+cares he got the Nobel
+Prize and I'm sure he's not worried
+
+ align:start position:0%
+Prize and I'm sure he's not worried
+ 
+
+ align:start position:0%
+Prize and I'm sure he's not worried
+about it at all okay good luck on your
+
+ align:start position:0%
+about it at all okay good luck on your
+ 
+
+ align:start position:0%
+about it at all okay good luck on your
+on your test and uh remember the review
+
+ align:start position:0%
+on your test and uh remember the review
+ 
+
+ align:start position:0%
+on your test and uh remember the review
+session if you care
\ No newline at end of file
diff --git a/Amd_bNYzgUw.txt b/Amd_bNYzgUw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fa4d1792960313c74d716200d1866bbd19f70fd6
--- /dev/null
+++ b/Amd_bNYzgUw.txt
@@ -0,0 +1,1883 @@
+align:start position:0%
+ 
+so let's look now at the mathematical
+
+ align:start position:0%
+so let's look now at the mathematical
+ 
+
+ align:start position:0%
+so let's look now at the mathematical
+foundations of probability theory the
+
+ align:start position:0%
+foundations of probability theory the
+ 
+
+ align:start position:0%
+foundations of probability theory the
+basic definitions of which we've just
+
+ align:start position:0%
+basic definitions of which we've just
+ 
+
+ align:start position:0%
+basic definitions of which we've just
+been doing examples up until now so a
+
+ align:start position:0%
+been doing examples up until now so a
+ 
+
+ align:start position:0%
+been doing examples up until now so a
+key concept is a probability space and
+
+ align:start position:0%
+key concept is a probability space and
+ 
+
+ align:start position:0%
+key concept is a probability space and
+that's what we're going to talk about in
+
+ align:start position:0%
+that's what we're going to talk about in
+ 
+
+ align:start position:0%
+that's what we're going to talk about in
+this segment so this the abstract
+
+ align:start position:0%
+this segment so this the abstract
+ 
+
+ align:start position:0%
+this segment so this the abstract
+setting of a probability space is the
+
+ align:start position:0%
+setting of a probability space is the
+ 
+
+ align:start position:0%
+setting of a probability space is the
+first thing you start off with is the
+
+ align:start position:0%
+first thing you start off with is the
+ 
+
+ align:start position:0%
+first thing you start off with is the
+set of outcomes which is what we were
+
+ align:start position:0%
+set of outcomes which is what we were
+ 
+
+ align:start position:0%
+set of outcomes which is what we were
+saw we were doing with the tree models
+
+ align:start position:0%
+saw we were doing with the tree models
+ 
+
+ align:start position:0%
+saw we were doing with the tree models
+in the previous videos and the condition
+
+ align:start position:0%
+in the previous videos and the condition
+ 
+
+ align:start position:0%
+in the previous videos and the condition
+that we require is that there should be
+
+ align:start position:0%
+that we require is that there should be
+ 
+
+ align:start position:0%
+that we require is that there should be
+a countable set of outcomes so there's
+
+ align:start position:0%
+a countable set of outcomes so there's
+ 
+
+ align:start position:0%
+a countable set of outcomes so there's
+something called the sample space and
+
+ align:start position:0%
+something called the sample space and
+ 
+
+ align:start position:0%
+something called the sample space and
+the sample space is designed to describe
+
+ align:start position:0%
+the sample space is designed to describe
+ 
+
+ align:start position:0%
+the sample space is designed to describe
+to model all the possible things that
+
+ align:start position:0%
+to model all the possible things that
+ 
+
+ align:start position:0%
+to model all the possible things that
+can happen as the result of your random
+
+ align:start position:0%
+can happen as the result of your random
+ 
+
+ align:start position:0%
+can happen as the result of your random
+experiment all the possible outcomes and
+
+ align:start position:0%
+experiment all the possible outcomes and
+ 
+
+ align:start position:0%
+experiment all the possible outcomes and
+we required that there be a countable
+
+ align:start position:0%
+we required that there be a countable
+ 
+
+ align:start position:0%
+we required that there be a countable
+number now the examples that we've seen
+
+ align:start position:0%
+number now the examples that we've seen
+ 
+
+ align:start position:0%
+number now the examples that we've seen
+so far have only had a finite number but
+
+ align:start position:0%
+so far have only had a finite number but
+ 
+
+ align:start position:0%
+so far have only had a finite number but
+we will shortly see a bunch of examples
+
+ align:start position:0%
+we will shortly see a bunch of examples
+ 
+
+ align:start position:0%
+we will shortly see a bunch of examples
+where we really need an infinite number
+
+ align:start position:0%
+where we really need an infinite number
+ 
+
+ align:start position:0%
+where we really need an infinite number
+but only a countable infinite number
+
+ align:start position:0%
+but only a countable infinite number
+ 
+
+ align:start position:0%
+but only a countable infinite number
+that's part of the definition of a
+
+ align:start position:0%
+that's part of the definition of a
+ 
+
+ align:start position:0%
+that's part of the definition of a
+probability space the set of outcomes
+
+ align:start position:0%
+probability space the set of outcomes
+ 
+
+ align:start position:0%
+probability space the set of outcomes
+the next thing is a probability function
+
+ align:start position:0%
+the next thing is a probability function
+ 
+
+ align:start position:0%
+the next thing is a probability function
+whose task is to assign probabilities to
+
+ align:start position:0%
+whose task is to assign probabilities to
+ 
+
+ align:start position:0%
+whose task is to assign probabilities to
+the outcomes so the condition is that
+
+ align:start position:0%
+the outcomes so the condition is that
+ 
+
+ align:start position:0%
+the outcomes so the condition is that
+the probability function PR gives the
+
+ align:start position:0%
+the probability function PR gives the
+ 
+
+ align:start position:0%
+the probability function PR gives the
+every element in s every outcome is
+
+ align:start position:0%
+every element in s every outcome is
+ 
+
+ align:start position:0%
+every element in s every outcome is
+going to be assigned a probability of
+
+ align:start position:0%
+going to be assigned a probability of
+ 
+
+ align:start position:0%
+going to be assigned a probability of
+between 0 and 1 inclusive yeah so every
+
+ align:start position:0%
+between 0 and 1 inclusive yeah so every
+ 
+
+ align:start position:0%
+between 0 and 1 inclusive yeah so every
+outcome gets a probability between 0 and
+
+ align:start position:0%
+outcome gets a probability between 0 and
+ 
+
+ align:start position:0%
+outcome gets a probability between 0 and
+1 and but the constraint on the
+
+ align:start position:0%
+1 and but the constraint on the
+ 
+
+ align:start position:0%
+1 and but the constraint on the
+probability function is that if I sum up
+
+ align:start position:0%
+probability function is that if I sum up
+ 
+
+ align:start position:0%
+probability function is that if I sum up
+with the probabilities of all the
+
+ align:start position:0%
+with the probabilities of all the
+ 
+
+ align:start position:0%
+with the probabilities of all the
+outcomes Omega R is an outcome in the
+
+ align:start position:0%
+outcomes Omega R is an outcome in the
+ 
+
+ align:start position:0%
+outcomes Omega R is an outcome in the
+sample space s and I take the sum of all
+
+ align:start position:0%
+sample space s and I take the sum of all
+ 
+
+ align:start position:0%
+sample space s and I take the sum of all
+of those probabilities of Omega they
+
+ align:start position:0%
+of those probabilities of Omega they
+ 
+
+ align:start position:0%
+of those probabilities of Omega they
+have to sum to 1 that's the crucial
+
+ align:start position:0%
+have to sum to 1 that's the crucial
+ 
+
+ align:start position:0%
+have to sum to 1 that's the crucial
+condition that defines a probability
+
+ align:start position:0%
+condition that defines a probability
+ 
+
+ align:start position:0%
+condition that defines a probability
+function on a probability on a sample
+
+ align:start position:0%
+function on a probability on a sample
+ 
+
+ align:start position:0%
+function on a probability on a sample
+space and the two together are what are
+
+ align:start position:0%
+space and the two together are what are
+ 
+
+ align:start position:0%
+space and the two together are what are
+called a probability space a sample
+
+ align:start position:0%
+called a probability space a sample
+ 
+
+ align:start position:0%
+called a probability space a sample
+space with a probability function is a
+
+ align:start position:0%
+space with a probability function is a
+ 
+
+ align:start position:0%
+space with a probability function is a
+probability space so the purpose of the
+
+ align:start position:0%
+probability space so the purpose of the
+ 
+
+ align:start position:0%
+probability space so the purpose of the
+tree model that we were using is really
+
+ align:start position:0%
+tree model that we were using is really
+ 
+
+ align:start position:0%
+tree model that we were using is really
+to figure out which probability space to
+
+ align:start position:0%
+to figure out which probability space to
+ 
+
+ align:start position:0%
+to figure out which probability space to
+use and the math the mathematics doesn't
+
+ align:start position:0%
+use and the math the mathematics doesn't
+ 
+
+ align:start position:0%
+use and the math the mathematics doesn't
+really start until you have the
+
+ align:start position:0%
+really start until you have the
+ 
+
+ align:start position:0%
+really start until you have the
+probability space up until that it's the
+
+ align:start position:0%
+probability space up until that it's the
+ 
+
+ align:start position:0%
+probability space up until that it's the
+modeling part that's very important
+
+ align:start position:0%
+modeling part that's very important
+ 
+
+ align:start position:0%
+modeling part that's very important
+automatically but you can't say that the
+
+ align:start position:0%
+automatically but you can't say that the
+ 
+
+ align:start position:0%
+automatically but you can't say that the
+model is right or wrong it's a model and
+
+ align:start position:0%
+model is right or wrong it's a model and
+ 
+
+ align:start position:0%
+model is right or wrong it's a model and
+it's rightness or wrongness is a matter
+
+ align:start position:0%
+it's rightness or wrongness is a matter
+ 
+
+ align:start position:0%
+it's rightness or wrongness is a matter
+of judgment and comparison to how it it
+
+ align:start position:0%
+of judgment and comparison to how it it
+ 
+
+ align:start position:0%
+of judgment and comparison to how it it
+stacks up against reality and things
+
+ align:start position:0%
+stacks up against reality and things
+ 
+
+ align:start position:0%
+stacks up against reality and things
+that we care about when we're using the
+
+ align:start position:0%
+that we care about when we're using the
+ 
+
+ align:start position:0%
+that we care about when we're using the
+tree model it's the leaves of the tree
+
+ align:start position:0%
+tree model it's the leaves of the tree
+ 
+
+ align:start position:0%
+tree model it's the leaves of the tree
+that correspond to the outcomes and the
+
+ align:start position:0%
+that correspond to the outcomes and the
+ 
+
+ align:start position:0%
+that correspond to the outcomes and the
+outcome probabilities which are crucial
+
+ align:start position:0%
+outcome probabilities which are crucial
+ 
+
+ align:start position:0%
+outcome probabilities which are crucial
+for having a probability space we got by
+
+ align:start position:0%
+for having a probability space we got by
+ 
+
+ align:start position:0%
+for having a probability space we got by
+reasoning about the probabilities to
+
+ align:start position:0%
+reasoning about the probabilities to
+ 
+
+ align:start position:0%
+reasoning about the probabilities to
+assign to each possible branch of the
+
+ align:start position:0%
+assign to each possible branch of the
+ 
+
+ align:start position:0%
+assign to each possible branch of the
+tree as you worked your way from root to
+
+ align:start position:0%
+tree as you worked your way from root to
+ 
+
+ align:start position:0%
+tree as you worked your way from root to
+leaf so the other key concept that we
+
+ align:start position:0%
+leaf so the other key concept that we
+ 
+
+ align:start position:0%
+leaf so the other key concept that we
+saw already is the idea of an event an
+
+ align:start position:0%
+saw already is the idea of an event an
+ 
+
+ align:start position:0%
+saw already is the idea of an event an
+event formally is nothing but a subset
+
+ align:start position:0%
+event formally is nothing but a subset
+ 
+
+ align:start position:0%
+event formally is nothing but a subset
+of the sample space it's the event is
+
+ align:start position:0%
+of the sample space it's the event is
+ 
+
+ align:start position:0%
+of the sample space it's the event is
+some set of outcomes presumably the
+
+ align:start position:0%
+some set of outcomes presumably the
+ 
+
+ align:start position:0%
+some set of outcomes presumably the
+event is an event that you're interested
+
+ align:start position:0%
+event is an event that you're interested
+ 
+
+ align:start position:0%
+event is an event that you're interested
+in like winning and the definition of
+
+ align:start position:0%
+in like winning and the definition of
+ 
+
+ align:start position:0%
+in like winning and the definition of
+the probability of an event is simply
+
+ align:start position:0%
+the probability of an event is simply
+ 
+
+ align:start position:0%
+the probability of an event is simply
+the sum of the probabilities of all the
+
+ align:start position:0%
+the sum of the probabilities of all the
+ 
+
+ align:start position:0%
+the sum of the probabilities of all the
+outcomes in the event and we were using
+
+ align:start position:0%
+outcomes in the event and we were using
+ 
+
+ align:start position:0%
+outcomes in the event and we were using
+this already for both Monty Hall and for
+
+ align:start position:0%
+this already for both Monty Hall and for
+ 
+
+ align:start position:0%
+this already for both Monty Hall and for
+the poker hands but this is the official
+
+ align:start position:0%
+the poker hands but this is the official
+ 
+
+ align:start position:0%
+the poker hands but this is the official
+general definition that once we have a
+
+ align:start position:0%
+general definition that once we have a
+ 
+
+ align:start position:0%
+general definition that once we have a
+probability function that assigns
+
+ align:start position:0%
+probability function that assigns
+ 
+
+ align:start position:0%
+probability function that assigns
+probabilities to outcomes then we can
+
+ align:start position:0%
+probabilities to outcomes then we can
+ 
+
+ align:start position:0%
+probabilities to outcomes then we can
+use that to define the probability of an
+
+ align:start position:0%
+use that to define the probability of an
+ 
+
+ align:start position:0%
+use that to define the probability of an
+event this is the definition of the
+
+ align:start position:0%
+event this is the definition of the
+ 
+
+ align:start position:0%
+event this is the definition of the
+probability of an event is simply the
+
+ align:start position:0%
+probability of an event is simply the
+ 
+
+ align:start position:0%
+probability of an event is simply the
+sum of the outcome probabilities and as
+
+ align:start position:0%
+sum of the outcome probabilities and as
+ 
+
+ align:start position:0%
+sum of the outcome probabilities and as
+an immediate corollary of this
+
+ align:start position:0%
+an immediate corollary of this
+ 
+
+ align:start position:0%
+an immediate corollary of this
+definition what we get is something
+
+ align:start position:0%
+definition what we get is something
+ 
+
+ align:start position:0%
+definition what we get is something
+that's central to probability theory
+
+ align:start position:0%
+that's central to probability theory
+ 
+
+ align:start position:0%
+that's central to probability theory
+it's called the sum rule and it says
+
+ align:start position:0%
+it's called the sum rule and it says
+ 
+
+ align:start position:0%
+it's called the sum rule and it says
+that if you have a bunch of events that
+
+ align:start position:0%
+that if you have a bunch of events that
+ 
+
+ align:start position:0%
+that if you have a bunch of events that
+are pairwise disjoint so there's no
+
+ align:start position:0%
+are pairwise disjoint so there's no
+ 
+
+ align:start position:0%
+are pairwise disjoint so there's no
+outcome in common to a zero in it or a 1
+
+ align:start position:0%
+outcome in common to a zero in it or a 1
+ 
+
+ align:start position:0%
+outcome in common to a zero in it or a 1
+or a 1 and or a 2 and so on then the
+
+ align:start position:0%
+or a 1 and or a 2 and so on then the
+ 
+
+ align:start position:0%
+or a 1 and or a 2 and so on then the
+probability of the union of the a is the
+
+ align:start position:0%
+probability of the union of the a is the
+ 
+
+ align:start position:0%
+probability of the union of the a is the
+probability that one of these events
+
+ align:start position:0%
+probability that one of these events
+ 
+
+ align:start position:0%
+probability that one of these events
+occurs one or more of these events
+
+ align:start position:0%
+occurs one or more of these events
+ 
+
+ align:start position:0%
+occurs one or more of these events
+occurs is simply the sum of the
+
+ align:start position:0%
+occurs is simply the sum of the
+ 
+
+ align:start position:0%
+occurs is simply the sum of the
+individual probabilities and that is a
+
+ align:start position:0%
+individual probabilities and that is a
+ 
+
+ align:start position:0%
+individual probabilities and that is a
+rule that we'll be using all the time
+
+ align:start position:0%
+rule that we'll be using all the time
+ 
+
+ align:start position:0%
+rule that we'll be using all the time
+it's very convenient for computing
+
+ align:start position:0%
+it's very convenient for computing
+ 
+
+ align:start position:0%
+it's very convenient for computing
+things if you just break them up into
+
+ align:start position:0%
+things if you just break them up into
+ 
+
+ align:start position:0%
+things if you just break them up into
+into separate cases then you can handle
+
+ align:start position:0%
+into separate cases then you can handle
+ 
+
+ align:start position:0%
+into separate cases then you can handle
+the separate cases each a 0 a 1
+
+ align:start position:0%
+the separate cases each a 0 a 1
+ 
+
+ align:start position:0%
+the separate cases each a 0 a 1
+separately and then add up the
+
+ align:start position:0%
+separately and then add up the
+ 
+
+ align:start position:0%
+separately and then add up the
+probabilities
+
+ align:start position:0%
+probabilities
+ 
+
+ align:start position:0%
+probabilities
+and in some approaches of probability
+
+ align:start position:0%
+and in some approaches of probability
+ 
+
+ align:start position:0%
+and in some approaches of probability
+more general ones this is actually taken
+
+ align:start position:0%
+more general ones this is actually taken
+ 
+
+ align:start position:0%
+more general ones this is actually taken
+as an axiom
+
+ align:start position:0%
+as an axiom
+ 
+
+ align:start position:0%
+as an axiom
+it's the axiom that defines a
+
+ align:start position:0%
+it's the axiom that defines a
+ 
+
+ align:start position:0%
+it's the axiom that defines a
+probability space but where you start
+
+ align:start position:0%
+probability space but where you start
+ 
+
+ align:start position:0%
+probability space but where you start
+with an assignment of probabilities
+
+ align:start position:0%
+with an assignment of probabilities
+ 
+
+ align:start position:0%
+with an assignment of probabilities
+events but in the discrete case we don't
+
+ align:start position:0%
+events but in the discrete case we don't
+ 
+
+ align:start position:0%
+events but in the discrete case we don't
+have to worry about that
+
+ align:start position:0%
+have to worry about that
+ 
+
+ align:start position:0%
+have to worry about that
+it's a corollary of the way we define
+
+ align:start position:0%
+it's a corollary of the way we define
+ 
+
+ align:start position:0%
+it's a corollary of the way we define
+the probability and that of course is a
+
+ align:start position:0%
+the probability and that of course is a
+ 
+
+ align:start position:0%
+the probability and that of course is a
+crucial rule the sum rule sometimes
+
+ align:start position:0%
+crucial rule the sum rule sometimes
+ 
+
+ align:start position:0%
+crucial rule the sum rule sometimes
+called a countable sum rule but we're
+
+ align:start position:0%
+called a countable sum rule but we're
+ 
+
+ align:start position:0%
+called a countable sum rule but we're
+just gonna call it the sum rule
+
+ align:start position:0%
+just gonna call it the sum rule
+ 
+
+ align:start position:0%
+just gonna call it the sum rule
+expressed in concise notation it's the
+
+ align:start position:0%
+expressed in concise notation it's the
+ 
+
+ align:start position:0%
+expressed in concise notation it's the
+probability of the union of the AIS as
+
+ align:start position:0%
+probability of the union of the AIS as
+ 
+
+ align:start position:0%
+probability of the union of the AIS as
+AI ranges over the non-negative integers
+
+ align:start position:0%
+AI ranges over the non-negative integers
+ 
+
+ align:start position:0%
+AI ranges over the non-negative integers
+is simply the sum of the individual
+
+ align:start position:0%
+is simply the sum of the individual
+ 
+
+ align:start position:0%
+is simply the sum of the individual
+probabilities of those events
+
+ align:start position:0%
+probabilities of those events
+ 
+
+ align:start position:0%
+probabilities of those events
+now why it's called discrete probability
+
+ align:start position:0%
+now why it's called discrete probability
+ 
+
+ align:start position:0%
+now why it's called discrete probability
+that we're studying is because we have a
+
+ align:start position:0%
+that we're studying is because we have a
+ 
+
+ align:start position:0%
+that we're studying is because we have a
+countable sample space and as we saw
+
+ align:start position:0%
+countable sample space and as we saw
+ 
+
+ align:start position:0%
+countable sample space and as we saw
+that sort of discrete combinatorics is
+
+ align:start position:0%
+that sort of discrete combinatorics is
+ 
+
+ align:start position:0%
+that sort of discrete combinatorics is
+is the combinatorial countable and even
+
+ align:start position:0%
+is the combinatorial countable and even
+ 
+
+ align:start position:0%
+is the combinatorial countable and even
+finite sets really the crucial reason
+
+ align:start position:0%
+finite sets really the crucial reason
+ 
+
+ align:start position:0%
+finite sets really the crucial reason
+why we're sticking to discrete
+
+ align:start position:0%
+why we're sticking to discrete
+ 
+
+ align:start position:0%
+why we're sticking to discrete
+probability is that allows us to work
+
+ align:start position:0%
+probability is that allows us to work
+ 
+
+ align:start position:0%
+probability is that allows us to work
+with sums instead of integrals if you
+
+ align:start position:0%
+with sums instead of integrals if you
+ 
+
+ align:start position:0%
+with sums instead of integrals if you
+start allowing continuous intervals of
+
+ align:start position:0%
+start allowing continuous intervals of
+ 
+
+ align:start position:0%
+start allowing continuous intervals of
+time and the probability say of throwing
+
+ align:start position:0%
+time and the probability say of throwing
+ 
+
+ align:start position:0%
+time and the probability say of throwing
+a dart and it landing in a given
+
+ align:start position:0%
+a dart and it landing in a given
+ 
+
+ align:start position:0%
+a dart and it landing in a given
+interval on the line and a whole bunch
+
+ align:start position:0%
+interval on the line and a whole bunch
+ 
+
+ align:start position:0%
+interval on the line and a whole bunch
+of other situations where it's natural
+
+ align:start position:0%
+of other situations where it's natural
+ 
+
+ align:start position:0%
+of other situations where it's natural
+to want to use continuous probabilities
+
+ align:start position:0%
+to want to use continuous probabilities
+ 
+
+ align:start position:0%
+to want to use continuous probabilities
+you're forced into defining a
+
+ align:start position:0%
+you're forced into defining a
+ 
+
+ align:start position:0%
+you're forced into defining a
+probability in terms of integrals
+
+ align:start position:0%
+probability in terms of integrals
+ 
+
+ align:start position:0%
+probability in terms of integrals
+because every outcome has probability 0
+
+ align:start position:0%
+because every outcome has probability 0
+ 
+
+ align:start position:0%
+because every outcome has probability 0
+and the theoretical basis of it is
+
+ align:start position:0%
+and the theoretical basis of it is
+ 
+
+ align:start position:0%
+and the theoretical basis of it is
+considerably more complicated and we
+
+ align:start position:0%
+considerably more complicated and we
+ 
+
+ align:start position:0%
+considerably more complicated and we
+don't need it firm in fact virtually any
+
+ align:start position:0%
+don't need it firm in fact virtually any
+ 
+
+ align:start position:0%
+don't need it firm in fact virtually any
+purposes that come up in computer
+
+ align:start position:0%
+purposes that come up in computer
+ 
+
+ align:start position:0%
+purposes that come up in computer
+science and so we will happily not have
+
+ align:start position:0%
+science and so we will happily not have
+ 
+
+ align:start position:0%
+science and so we will happily not have
+to study integral calculus or measure
+
+ align:start position:0%
+to study integral calculus or measure
+ 
+
+ align:start position:0%
+to study integral calculus or measure
+theory really and just get by with sums
+
+ align:start position:0%
+theory really and just get by with sums
+ 
+
+ align:start position:0%
+theory really and just get by with sums
+so let's quickly point out some rules
+
+ align:start position:0%
+so let's quickly point out some rules
+ 
+
+ align:start position:0%
+so let's quickly point out some rules
+that are now corollaries that really
+
+ align:start position:0%
+that are now corollaries that really
+ 
+
+ align:start position:0%
+that are now corollaries that really
+derived rules of probability theory that
+
+ align:start position:0%
+derived rules of probability theory that
+ 
+
+ align:start position:0%
+derived rules of probability theory that
+follow as a consequence of the countable
+
+ align:start position:0%
+follow as a consequence of the countable
+ 
+
+ align:start position:0%
+follow as a consequence of the countable
+sum rule and the first one is the
+
+ align:start position:0%
+sum rule and the first one is the
+ 
+
+ align:start position:0%
+sum rule and the first one is the
+difference rule the probability of a
+
+ align:start position:0%
+difference rule the probability of a
+ 
+
+ align:start position:0%
+difference rule the probability of a
+minus B is simply equal to the
+
+ align:start position:0%
+minus B is simply equal to the
+ 
+
+ align:start position:0%
+minus B is simply equal to the
+probability of a minus the probability
+
+ align:start position:0%
+probability of a minus the probability
+ 
+
+ align:start position:0%
+probability of a minus the probability
+of a intersection B now notice how much
+
+ align:start position:0%
+of a intersection B now notice how much
+ 
+
+ align:start position:0%
+of a intersection B now notice how much
+this looks like the difference rule for
+
+ align:start position:0%
+this looks like the difference rule for
+ 
+
+ align:start position:0%
+this looks like the difference rule for
+cardinalities that the cardinality of
+
+ align:start position:0%
+cardinalities that the cardinality of
+ 
+
+ align:start position:0%
+cardinalities that the cardinality of
+the finite set a minus B is simply the
+
+ align:start position:0%
+the finite set a minus B is simply the
+ 
+
+ align:start position:0%
+the finite set a minus B is simply the
+cardinality of a minus
+
+ align:start position:0%
+cardinality of a minus
+ 
+
+ align:start position:0%
+cardinality of a minus
+the cardinality of a intersection B and
+
+ align:start position:0%
+the cardinality of a intersection B and
+ 
+
+ align:start position:0%
+the cardinality of a intersection B and
+indeed the proof of this is just like
+
+ align:start position:0%
+indeed the proof of this is just like
+ 
+
+ align:start position:0%
+indeed the proof of this is just like
+the proof of cardinality it follows
+
+ align:start position:0%
+the proof of cardinality it follows
+ 
+
+ align:start position:0%
+the proof of cardinality it follows
+directly from the sum rule for
+
+ align:start position:0%
+directly from the sum rule for
+ 
+
+ align:start position:0%
+directly from the sum rule for
+probabilities which corresponds of
+
+ align:start position:0%
+probabilities which corresponds of
+ 
+
+ align:start position:0%
+probabilities which corresponds of
+course to the sum rule for cardinalities
+
+ align:start position:0%
+course to the sum rule for cardinalities
+ 
+
+ align:start position:0%
+course to the sum rule for cardinalities
+namely by the sum rule for probabilities
+
+ align:start position:0%
+namely by the sum rule for probabilities
+ 
+
+ align:start position:0%
+namely by the sum rule for probabilities
+what we know is that the a is equal sets
+
+ align:start position:0%
+what we know is that the a is equal sets
+ 
+
+ align:start position:0%
+what we know is that the a is equal sets
+theoretically to a intersection B plus a
+
+ align:start position:0%
+theoretically to a intersection B plus a
+ 
+
+ align:start position:0%
+theoretically to a intersection B plus a
+minus B that is a breaks up into the
+
+ align:start position:0%
+minus B that is a breaks up into the
+ 
+
+ align:start position:0%
+minus B that is a breaks up into the
+points that it has in common with B and
+
+ align:start position:0%
+points that it has in common with B and
+ 
+
+ align:start position:0%
+points that it has in common with B and
+the points that it doesn't have in
+
+ align:start position:0%
+the points that it doesn't have in
+ 
+
+ align:start position:0%
+the points that it doesn't have in
+common with B since those are disjoint
+
+ align:start position:0%
+common with B since those are disjoint
+ 
+
+ align:start position:0%
+common with B since those are disjoint
+you can add them so the probability of a
+
+ align:start position:0%
+you can add them so the probability of a
+ 
+
+ align:start position:0%
+you can add them so the probability of a
+is equal to the probability of a
+
+ align:start position:0%
+is equal to the probability of a
+ 
+
+ align:start position:0%
+is equal to the probability of a
+intersection B plus probability of a
+
+ align:start position:0%
+intersection B plus probability of a
+ 
+
+ align:start position:0%
+intersection B plus probability of a
+minus B and so I just transpose the a
+
+ align:start position:0%
+minus B and so I just transpose the a
+ 
+
+ align:start position:0%
+minus B and so I just transpose the a
+minus B to the left-hand side and I get
+
+ align:start position:0%
+minus B to the left-hand side and I get
+ 
+
+ align:start position:0%
+minus B to the left-hand side and I get
+the difference rule which is a rule
+
+ align:start position:0%
+the difference rule which is a rule
+ 
+
+ align:start position:0%
+the difference rule which is a rule
+that's worth remembering similarly we
+
+ align:start position:0%
+that's worth remembering similarly we
+ 
+
+ align:start position:0%
+that's worth remembering similarly we
+have inclusion exclusion the if a and B
+
+ align:start position:0%
+have inclusion exclusion the if a and B
+ 
+
+ align:start position:0%
+have inclusion exclusion the if a and B
+are not disjoint then the probability of
+
+ align:start position:0%
+are not disjoint then the probability of
+ 
+
+ align:start position:0%
+are not disjoint then the probability of
+a union B is equal to the probability of
+
+ align:start position:0%
+a union B is equal to the probability of
+ 
+
+ align:start position:0%
+a union B is equal to the probability of
+a plus the probability of B minus the
+
+ align:start position:0%
+a plus the probability of B minus the
+ 
+
+ align:start position:0%
+a plus the probability of B minus the
+probability of the intersection and the
+
+ align:start position:0%
+probability of the intersection and the
+ 
+
+ align:start position:0%
+probability of the intersection and the
+proof is in fact exactly like the
+
+ align:start position:0%
+proof is in fact exactly like the
+ 
+
+ align:start position:0%
+proof is in fact exactly like the
+corresponding rule for cardinalities of
+
+ align:start position:0%
+corresponding rule for cardinalities of
+ 
+
+ align:start position:0%
+corresponding rule for cardinalities of
+finite sets and of course it generalizes
+
+ align:start position:0%
+finite sets and of course it generalizes
+ 
+
+ align:start position:0%
+finite sets and of course it generalizes
+two more sets this is an example of the
+
+ align:start position:0%
+two more sets this is an example of the
+ 
+
+ align:start position:0%
+two more sets this is an example of the
+inclusion exclusion for three sets in
+
+ align:start position:0%
+inclusion exclusion for three sets in
+ 
+
+ align:start position:0%
+inclusion exclusion for three sets in
+terms of probability another useful it
+
+ align:start position:0%
+terms of probability another useful it
+ 
+
+ align:start position:0%
+terms of probability another useful it
+turns out consequence is that the
+
+ align:start position:0%
+turns out consequence is that the
+ 
+
+ align:start position:0%
+turns out consequence is that the
+probability that a or B happens is
+
+ align:start position:0%
+probability that a or B happens is
+ 
+
+ align:start position:0%
+probability that a or B happens is
+guaranteed to be less than or equal to
+
+ align:start position:0%
+guaranteed to be less than or equal to
+ 
+
+ align:start position:0%
+guaranteed to be less than or equal to
+the probability that a happens plus the
+
+ align:start position:0%
+the probability that a happens plus the
+ 
+
+ align:start position:0%
+the probability that a happens plus the
+probability of B happens and this
+
+ align:start position:0%
+probability of B happens and this
+ 
+
+ align:start position:0%
+probability of B happens and this
+follows is a trivial consequence of the
+
+ align:start position:0%
+follows is a trivial consequence of the
+ 
+
+ align:start position:0%
+follows is a trivial consequence of the
+inclusion exclusion rule for two sets
+
+ align:start position:0%
+inclusion exclusion rule for two sets
+ 
+
+ align:start position:0%
+inclusion exclusion rule for two sets
+because the probability of a union B is
+
+ align:start position:0%
+because the probability of a union B is
+ 
+
+ align:start position:0%
+because the probability of a union B is
+equal to this Plus this minus some
+
+ align:start position:0%
+equal to this Plus this minus some
+ 
+
+ align:start position:0%
+equal to this Plus this minus some
+probability namely the probability of
+
+ align:start position:0%
+probability namely the probability of
+ 
+
+ align:start position:0%
+probability namely the probability of
+the intersection so you're taking away
+
+ align:start position:0%
+the intersection so you're taking away
+ 
+
+ align:start position:0%
+the intersection so you're taking away
+something non-negative from these two in
+
+ align:start position:0%
+something non-negative from these two in
+ 
+
+ align:start position:0%
+something non-negative from these two in
+order to equal that in particular then
+
+ align:start position:0%
+order to equal that in particular then
+ 
+
+ align:start position:0%
+order to equal that in particular then
+this must be less than or equal to that
+
+ align:start position:0%
+this must be less than or equal to that
+ 
+
+ align:start position:0%
+this must be less than or equal to that
+and the closely related phenomena is
+
+ align:start position:0%
+and the closely related phenomena is
+ 
+
+ align:start position:0%
+and the closely related phenomena is
+base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the probability that a or B happens is
+
+ align:start position:0%
+the probability that a or B happens is
+ 
+
+ align:start position:0%
+the probability that a or B happens is
+greater than or equal to the probability
+
+ align:start position:0%
+greater than or equal to the probability
+ 
+
+ align:start position:0%
+greater than or equal to the probability
+that a happens and finally we can
+
+ align:start position:0%
+that a happens and finally we can
+ 
+
+ align:start position:0%
+that a happens and finally we can
+generalize that to a countable
+
+ align:start position:0%
+generalize that to a countable
+ 
+
+ align:start position:0%
+generalize that to a countable
+collection of sets if I have a bunch of
+
+ align:start position:0%
+collection of sets if I have a bunch of
+ 
+
+ align:start position:0%
+collection of sets if I have a bunch of
+events a 0 a 1 and so on
+
+ align:start position:0%
+events a 0 a 1 and so on
+ 
+
+ align:start position:0%
+events a 0 a 1 and so on
+then the probability that at least one
+
+ align:start position:0%
+then the probability that at least one
+ 
+
+ align:start position:0%
+then the probability that at least one
+of them occurs the probability of the
+
+ align:start position:0%
+of them occurs the probability of the
+ 
+
+ align:start position:0%
+of them occurs the probability of the
+union of the AIS is less than or equal
+
+ align:start position:0%
+union of the AIS is less than or equal
+ 
+
+ align:start position:0%
+union of the AIS is less than or equal
+to the sum of their probabilities this
+
+ align:start position:0%
+to the sum of their probabilities this
+ 
+
+ align:start position:0%
+to the sum of their probabilities this
+is again another kind of obvious rule
+
+ align:start position:0%
+is again another kind of obvious rule
+ 
+
+ align:start position:0%
+is again another kind of obvious rule
+not hard to prove we're not gonna bother
+
+ align:start position:0%
+not hard to prove we're not gonna bother
+ 
+
+ align:start position:0%
+not hard to prove we're not gonna bother
+proving it because it really is obvious
+
+ align:start position:0%
+proving it because it really is obvious
+ 
+
+ align:start position:0%
+proving it because it really is obvious
+but we will get some mileage out of it
+
+ align:start position:0%
+but we will get some mileage out of it
+ 
+
+ align:start position:0%
+but we will get some mileage out of it
+later on so to summarize the key concept
+
+ align:start position:0%
+later on so to summarize the key concept
+ 
+
+ align:start position:0%
+later on so to summarize the key concept
+here is a probability space it consists
+
+ align:start position:0%
+here is a probability space it consists
+ 
+
+ align:start position:0%
+here is a probability space it consists
+of a countable set of outcomes the
+
+ align:start position:0%
+of a countable set of outcomes the
+ 
+
+ align:start position:0%
+of a countable set of outcomes the
+sample space and a probability function
+
+ align:start position:0%
+sample space and a probability function
+ 
+
+ align:start position:0%
+sample space and a probability function
+that assigns values between 0 and 1 to
+
+ align:start position:0%
+that assigns values between 0 and 1 to
+ 
+
+ align:start position:0%
+that assigns values between 0 and 1 to
+every outcomes such that the sum of the
+
+ align:start position:0%
+every outcomes such that the sum of the
+ 
+
+ align:start position:0%
+every outcomes such that the sum of the
+probabilities is 1 and when we're using
+
+ align:start position:0%
+probabilities is 1 and when we're using
+ 
+
+ align:start position:0%
+probabilities is 1 and when we're using
+our tree model and so on our objective
+
+ align:start position:0%
+our tree model and so on our objective
+ 
+
+ align:start position:0%
+our tree model and so on our objective
+is to construct one of these things
+
+ align:start position:0%
+is to construct one of these things
+ 
+
+ align:start position:0%
+is to construct one of these things
+usually the hard part will be verifying
+
+ align:start position:0%
+usually the hard part will be verifying
+ 
+
+ align:start position:0%
+usually the hard part will be verifying
+that in fact the way we've assigned
+
+ align:start position:0%
+that in fact the way we've assigned
+ 
+
+ align:start position:0%
+that in fact the way we've assigned
+probabilities has the property that the
+
+ align:start position:0%
+probabilities has the property that the
+ 
+
+ align:start position:0%
+probabilities has the property that the
+sum of them is equal to 1
\ No newline at end of file
diff --git a/AnzhigYawy8.txt b/AnzhigYawy8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c6d4d7da1babcda6af669c45de47f0b86684aaa8
--- /dev/null
+++ b/AnzhigYawy8.txt
@@ -0,0 +1,715 @@
+align:start position:0%
+ 
+it's a statement about the time
+
+ align:start position:0%
+it's a statement about the time
+ 
+
+ align:start position:0%
+it's a statement about the time
+dependence of the expectation values
+
+ align:start position:0%
+dependence of the expectation values
+ 
+
+ align:start position:0%
+dependence of the expectation values
+it's a pretty fundamental theorem so
+
+ align:start position:0%
+it's a pretty fundamental theorem so
+ 
+
+ align:start position:0%
+it's a pretty fundamental theorem so
+here it goes
+
+ align:start position:0%
+here it goes
+ 
+
+ align:start position:0%
+here it goes
+you have B DT of the expectation value
+
+ align:start position:0%
+you have B DT of the expectation value
+ 
+
+ align:start position:0%
+you have B DT of the expectation value
+of Q this is what we want to evaluate
+
+ align:start position:0%
+of Q this is what we want to evaluate
+ 
+
+ align:start position:0%
+of Q this is what we want to evaluate
+now this would be D DT of integral size
+
+ align:start position:0%
+now this would be D DT of integral size
+ 
+
+ align:start position:0%
+now this would be D DT of integral size
+star of X and T cube size of X and T and
+
+ align:start position:0%
+star of X and T cube size of X and T and
+ 
+
+ align:start position:0%
+star of X and T cube size of X and T and
+the DDT acts on the two of them so it
+
+ align:start position:0%
+the DDT acts on the two of them so it
+ 
+
+ align:start position:0%
+the DDT acts on the two of them so it
+gives you integral partial sized star DT
+
+ align:start position:0%
+gives you integral partial sized star DT
+ 
+
+ align:start position:0%
+gives you integral partial sized star DT
+q sy of X of T plus size star Q partial
+
+ align:start position:0%
+q sy of X of T plus size star Q partial
+ 
+
+ align:start position:0%
+q sy of X of T plus size star Q partial
+sy DT and this is the integral over DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you've seen that kind of stuff and what
+
+ align:start position:0%
+you've seen that kind of stuff and what
+ 
+
+ align:start position:0%
+you've seen that kind of stuff and what
+is it well integral DX this is the
+
+ align:start position:0%
+is it well integral DX this is the
+ 
+
+ align:start position:0%
+is it well integral DX this is the
+Schrodinger equation deep sigh star DT
+
+ align:start position:0%
+Schrodinger equation deep sigh star DT
+ 
+
+ align:start position:0%
+Schrodinger equation deep sigh star DT
+is I over H bar H sy star from the
+
+ align:start position:0%
+is I over H bar H sy star from the
+ 
+
+ align:start position:0%
+is I over H bar H sy star from the
+Schrodinger equation then you have the Q
+
+ align:start position:0%
+Schrodinger equation then you have the Q
+ 
+
+ align:start position:0%
+Schrodinger equation then you have the Q
+sy of X and T on this term you will have
+
+ align:start position:0%
+sy of X and T on this term you will have
+ 
+
+ align:start position:0%
+sy of X and T on this term you will have
+a very similar thing minus I over H bar
+
+ align:start position:0%
+a very similar thing minus I over H bar
+ 
+
+ align:start position:0%
+a very similar thing minus I over H bar
+this time size star Q
+
+ align:start position:0%
+this time size star Q
+ 
+
+ align:start position:0%
+this time size star Q
+each sigh of X and T so we use the
+
+ align:start position:0%
+each sigh of X and T so we use the
+ 
+
+ align:start position:0%
+each sigh of X and T so we use the
+Schrodinger equation in the form I deep
+
+ align:start position:0%
+Schrodinger equation in the form I deep
+ 
+
+ align:start position:0%
+Schrodinger equation in the form I deep
+sigh DT IH bar deep style T equal H side
+
+ align:start position:0%
+sigh DT IH bar deep style T equal H side
+ 
+
+ align:start position:0%
+sigh DT IH bar deep style T equal H side
+I used it twice so then it's actually
+
+ align:start position:0%
+I used it twice so then it's actually
+ 
+
+ align:start position:0%
+I used it twice so then it's actually
+convenient to multiply here by I h-bar D
+
+ align:start position:0%
+convenient to multiply here by I h-bar D
+ 
+
+ align:start position:0%
+convenient to multiply here by I h-bar D
+DT of Q so I multiply by IH bar and I
+
+ align:start position:0%
+DT of Q so I multiply by IH bar and I
+ 
+
+ align:start position:0%
+DT of Q so I multiply by IH bar and I
+will cancel the I and the H bar in this
+
+ align:start position:0%
+will cancel the I and the H bar in this
+ 
+
+ align:start position:0%
+will cancel the I and the H bar in this
+term minus then this term so we'll have
+
+ align:start position:0%
+term minus then this term so we'll have
+ 
+
+ align:start position:0%
+term minus then this term so we'll have
+V cubics
+
+ align:start position:0%
+V cubics
+ 
+
+ align:start position:0%
+V cubics
+sighs star Q H hat side minus H hot
+
+ align:start position:0%
+sighs star Q H hat side minus H hot
+ 
+
+ align:start position:0%
+sighs star Q H hat side minus H hot
+sighs star cube sigh okay things have
+
+ align:start position:0%
+sighs star cube sigh okay things have
+ 
+
+ align:start position:0%
+sighs star cube sigh okay things have
+simplified very nicely and there's just
+
+ align:start position:0%
+simplified very nicely and there's just
+ 
+
+ align:start position:0%
+simplified very nicely and there's just
+one more thing we can do
+
+ align:start position:0%
+one more thing we can do
+ 
+
+ align:start position:0%
+one more thing we can do
+look this is the product of Q and age
+
+ align:start position:0%
+look this is the product of Q and age
+ 
+
+ align:start position:0%
+look this is the product of Q and age
+but by hermiticity H in here can be
+
+ align:start position:0%
+but by hermiticity H in here can be
+ 
+
+ align:start position:0%
+but by hermiticity H in here can be
+brought to the other side to act on this
+
+ align:start position:0%
+brought to the other side to act on this
+ 
+
+ align:start position:0%
+brought to the other side to act on this
+wave function so this is actually equal
+
+ align:start position:0%
+wave function so this is actually equal
+ 
+
+ align:start position:0%
+wave function so this is actually equal
+to the integral D cubed DX well the X
+
+ align:start position:0%
+to the integral D cubed DX well the X
+ 
+
+ align:start position:0%
+to the integral D cubed DX well the X
+sized star Q H hot side - the H can go
+
+ align:start position:0%
+sized star Q H hot side - the H can go
+ 
+
+ align:start position:0%
+sized star Q H hot side - the H can go
+to the other side side star H cube sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then
+
+ align:start position:0%
+but then
+ 
+
+ align:start position:0%
+but then
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do we see there we recognize a
+
+ align:start position:0%
+what do we see there we recognize a
+ 
+
+ align:start position:0%
+what do we see there we recognize a
+commutator this commutator is just like
+
+ align:start position:0%
+commutator this commutator is just like
+ 
+
+ align:start position:0%
+commutator this commutator is just like
+we did for X and P and we started
+
+ align:start position:0%
+we did for X and P and we started
+ 
+
+ align:start position:0%
+we did for X and P and we started
+practicing how to compute them they show
+
+ align:start position:0%
+practicing how to compute them they show
+ 
+
+ align:start position:0%
+practicing how to compute them they show
+up here and this is maybe one of the
+
+ align:start position:0%
+up here and this is maybe one of the
+ 
+
+ align:start position:0%
+up here and this is maybe one of the
+reasons commentators are so important in
+
+ align:start position:0%
+reasons commentators are so important in
+ 
+
+ align:start position:0%
+reasons commentators are so important in
+quantum mechanics so what do we have
+
+ align:start position:0%
+quantum mechanics so what do we have
+ 
+
+ align:start position:0%
+quantum mechanics so what do we have
+here I h-bar D DT of the expectation
+
+ align:start position:0%
+here I h-bar D DT of the expectation
+ 
+
+ align:start position:0%
+here I h-bar D DT of the expectation
+value of Q is equal to the integral DX
+
+ align:start position:0%
+value of Q is equal to the integral DX
+ 
+
+ align:start position:0%
+value of Q is equal to the integral DX
+of psystar Q H minus H q sy and this is
+
+ align:start position:0%
+of psystar Q H minus H q sy and this is
+ 
+
+ align:start position:0%
+of psystar Q H minus H q sy and this is
+all of X and T well this is nothing else
+
+ align:start position:0%
+all of X and T well this is nothing else
+ 
+
+ align:start position:0%
+all of X and T well this is nothing else
+but the commutator of Q and H so our
+
+ align:start position:0%
+but the commutator of Q and H so our
+ 
+
+ align:start position:0%
+but the commutator of Q and H so our
+final result is that I h-bar D DT of the
+
+ align:start position:0%
+final result is that I h-bar D DT of the
+ 
+
+ align:start position:0%
+final result is that I h-bar D DT of the
+expectation value of Q is equal to look
+
+ align:start position:0%
+expectation value of Q is equal to look
+ 
+
+ align:start position:0%
+expectation value of Q is equal to look
+it's the expectation value of the
+
+ align:start position:0%
+it's the expectation value of the
+ 
+
+ align:start position:0%
+it's the expectation value of the
+commutator remember expectation value
+
+ align:start position:0%
+commutator remember expectation value
+ 
+
+ align:start position:0%
+commutator remember expectation value
+for an operator the operator and thing
+
+ align:start position:0%
+for an operator the operator and thing
+ 
+
+ align:start position:0%
+for an operator the operator and thing
+here so this is nothing else than the
+
+ align:start position:0%
+here so this is nothing else than the
+ 
+
+ align:start position:0%
+here so this is nothing else than the
+expectation value of Q with age this is
+
+ align:start position:0%
+expectation value of Q with age this is
+ 
+
+ align:start position:0%
+expectation value of Q with age this is
+actually a pretty important result it
+
+ align:start position:0%
+actually a pretty important result it
+ 
+
+ align:start position:0%
+actually a pretty important result it
+has all the dynamics of the physics in
+
+ align:start position:0%
+has all the dynamics of the physics in
+ 
+
+ align:start position:0%
+has all the dynamics of the physics in
+the observables look the wave functions
+
+ align:start position:0%
+the observables look the wave functions
+ 
+
+ align:start position:0%
+the observables look the wave functions
+used to change in time due to their
+
+ align:start position:0%
+used to change in time due to their
+ 
+
+ align:start position:0%
+used to change in time due to their
+change in time the expectation values of
+
+ align:start position:0%
+change in time the expectation values of
+ 
+
+ align:start position:0%
+change in time the expectation values of
+the operators change in time because
+
+ align:start position:0%
+the operators change in time because
+ 
+
+ align:start position:0%
+the operators change in time because
+this interval can depend on time but
+
+ align:start position:0%
+this interval can depend on time but
+ 
+
+ align:start position:0%
+this interval can depend on time but
+here what you have succeeded is to wrap
+
+ align:start position:0%
+here what you have succeeded is to wrap
+ 
+
+ align:start position:0%
+here what you have succeeded is to wrap
+percent the change in time of the
+
+ align:start position:0%
+percent the change in time of the
+ 
+
+ align:start position:0%
+percent the change in time of the
+expectation value the change in time of
+
+ align:start position:0%
+expectation value the change in time of
+ 
+
+ align:start position:0%
+expectation value the change in time of
+the position that you expect you find
+
+ align:start position:0%
+the position that you expect you find
+ 
+
+ align:start position:0%
+the position that you expect you find
+your particle in terms of the
+
+ align:start position:0%
+your particle in terms of the
+ 
+
+ align:start position:0%
+your particle in terms of the
+expectation value of a commutator with
+
+ align:start position:0%
+expectation value of a commutator with
+ 
+
+ align:start position:0%
+expectation value of a commutator with
+the Hamiltonian so if some quantity
+
+ align:start position:0%
+the Hamiltonian so if some quantity
+ 
+
+ align:start position:0%
+the Hamiltonian so if some quantity
+commutes with the Hamiltonian its
+
+ align:start position:0%
+commutes with the Hamiltonian its
+ 
+
+ align:start position:0%
+commutes with the Hamiltonian its
+expectation value will not change in
+
+ align:start position:0%
+expectation value will not change in
+ 
+
+ align:start position:0%
+expectation value will not change in
+time if you have a Hamiltonian say of a
+
+ align:start position:0%
+time if you have a Hamiltonian say of a
+ 
+
+ align:start position:0%
+time if you have a Hamiltonian say of a
+free particle
+
+ align:start position:0%
+free particle
+ 
+
+ align:start position:0%
+free particle
+well the momentum commutes with this
+
+ align:start position:0%
+well the momentum commutes with this
+ 
+
+ align:start position:0%
+well the momentum commutes with this
+therefore the expected value of the
+
+ align:start position:0%
+therefore the expected value of the
+ 
+
+ align:start position:0%
+therefore the expected value of the
+momentum you already know since the
+
+ align:start position:0%
+momentum you already know since the
+ 
+
+ align:start position:0%
+momentum you already know since the
+momentum commutes with H this is zero
+
+ align:start position:0%
+momentum commutes with H this is zero
+ 
+
+ align:start position:0%
+momentum commutes with H this is zero
+expected value of this is zero and the
+
+ align:start position:0%
+expected value of this is zero and the
+ 
+
+ align:start position:0%
+expected value of this is zero and the
+expected value of the momentum will not
+
+ align:start position:0%
+expected value of the momentum will not
+ 
+
+ align:start position:0%
+expected value of the momentum will not
+change will be conserved so conservation
+
+ align:start position:0%
+change will be conserved so conservation
+ 
+
+ align:start position:0%
+change will be conserved so conservation
+laws in quantum mechanics have to do
+
+ align:start position:0%
+laws in quantum mechanics have to do
+ 
+
+ align:start position:0%
+laws in quantum mechanics have to do
+with things that commute with the
+
+ align:start position:0%
+with things that commute with the
+ 
+
+ align:start position:0%
+with things that commute with the
+Hamiltonian and it's an idea we're gonna
+
+ align:start position:0%
+Hamiltonian and it's an idea we're gonna
+ 
+
+ align:start position:0%
+Hamiltonian and it's an idea we're gonna
+develop on
\ No newline at end of file
diff --git a/AtT59jxU9es.txt b/AtT59jxU9es.txt
new file mode 100644
index 0000000000000000000000000000000000000000..229a02804dc1eb39cc1ad2e90ca7a918baca1314
--- /dev/null
+++ b/AtT59jxU9es.txt
@@ -0,0 +1,15819 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common license. Your support
+
+ align:start position:0%
+a Creative Common license. Your support
+ 
+
+ align:start position:0%
+a Creative Common license. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or to view additional materials from
+
+ align:start position:0%
+or to view additional materials from
+ 
+
+ align:start position:0%
+or to view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let me begin by first asking whether
+
+ align:start position:0%
+Let me begin by first asking whether
+ 
+
+ align:start position:0%
+Let me begin by first asking whether
+there are any questions from last class
+
+ align:start position:0%
+there are any questions from last class
+ 
+
+ align:start position:0%
+there are any questions from last class
+which was uh a week ago. Hope you had a
+
+ align:start position:0%
+which was uh a week ago. Hope you had a
+ 
+
+ align:start position:0%
+which was uh a week ago. Hope you had a
+good break. Any any questions?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, before we begin Oh, today's topic
+
+ align:start position:0%
+Okay, before we begin Oh, today's topic
+ 
+
+ align:start position:0%
+Okay, before we begin Oh, today's topic
+question.
+
+ align:start position:0%
+question.
+ 
+
+ align:start position:0%
+question.
+No, before we begin today's uh topic on
+
+ align:start position:0%
+No, before we begin today's uh topic on
+ 
+
+ align:start position:0%
+No, before we begin today's uh topic on
+uh arbitrage and uh the pricing of
+
+ align:start position:0%
+uh arbitrage and uh the pricing of
+ 
+
+ align:start position:0%
+uh arbitrage and uh the pricing of
+multiple uh fixed income securities, I
+
+ align:start position:0%
+multiple uh fixed income securities, I
+ 
+
+ align:start position:0%
+multiple uh fixed income securities, I
+want to just uh take a few moments to
+
+ align:start position:0%
+want to just uh take a few moments to
+ 
+
+ align:start position:0%
+want to just uh take a few moments to
+talk a bit about what's going on in
+
+ align:start position:0%
+talk a bit about what's going on in
+ 
+
+ align:start position:0%
+talk a bit about what's going on in
+financial markets. Also to welcome the
+
+ align:start position:0%
+financial markets. Also to welcome the
+ 
+
+ align:start position:0%
+financial markets. Also to welcome the
+prospective students that we have uh
+
+ align:start position:0%
+prospective students that we have uh
+ 
+
+ align:start position:0%
+prospective students that we have uh
+sitting here in uh class today. So, uh,
+
+ align:start position:0%
+sitting here in uh class today. So, uh,
+ 
+
+ align:start position:0%
+sitting here in uh class today. So, uh,
+for once over the weekend, uh,
+
+ align:start position:0%
+for once over the weekend, uh,
+ 
+
+ align:start position:0%
+for once over the weekend, uh,
+unprecedented things didn't occur and,
+
+ align:start position:0%
+unprecedented things didn't occur and,
+ 
+
+ align:start position:0%
+unprecedented things didn't occur and,
+uh, so I'm glad to report that, uh,
+
+ align:start position:0%
+uh, so I'm glad to report that, uh,
+ 
+
+ align:start position:0%
+uh, so I'm glad to report that, uh,
+we're still here. Financial markets are
+
+ align:start position:0%
+we're still here. Financial markets are
+ 
+
+ align:start position:0%
+we're still here. Financial markets are
+still around. And as you know, the
+
+ align:start position:0%
+still around. And as you know, the
+ 
+
+ align:start position:0%
+still around. And as you know, the
+government has proposed, uh, some
+
+ align:start position:0%
+government has proposed, uh, some
+ 
+
+ align:start position:0%
+government has proposed, uh, some
+measures to deal with this current
+
+ align:start position:0%
+measures to deal with this current
+ 
+
+ align:start position:0%
+measures to deal with this current
+financial crisis.
+
+ align:start position:0%
+financial crisis.
+ 
+
+ align:start position:0%
+financial crisis.
+And at this point, it's still unclear as
+
+ align:start position:0%
+And at this point, it's still unclear as
+ 
+
+ align:start position:0%
+And at this point, it's still unclear as
+to what they're proposing, but we can
+
+ align:start position:0%
+to what they're proposing, but we can
+ 
+
+ align:start position:0%
+to what they're proposing, but we can
+actually see from the data what the
+
+ align:start position:0%
+actually see from the data what the
+ 
+
+ align:start position:0%
+actually see from the data what the
+market's reaction is. Last time remember
+
+ align:start position:0%
+market's reaction is. Last time remember
+ 
+
+ align:start position:0%
+market's reaction is. Last time remember
+we looked at the yield curve and uh
+
+ align:start position:0%
+we looked at the yield curve and uh
+ 
+
+ align:start position:0%
+we looked at the yield curve and uh
+literally it was just a week ago that
+
+ align:start position:0%
+literally it was just a week ago that
+ 
+
+ align:start position:0%
+literally it was just a week ago that
+the yield curve looked like this. Now
+
+ align:start position:0%
+the yield curve looked like this. Now
+ 
+
+ align:start position:0%
+the yield curve looked like this. Now
+remember that we focused on what
+
+ align:start position:0%
+remember that we focused on what
+ 
+
+ align:start position:0%
+remember that we focused on what
+happened at the very short end of the
+
+ align:start position:0%
+happened at the very short end of the
+ 
+
+ align:start position:0%
+happened at the very short end of the
+yield curve which is three-month
+
+ align:start position:0%
+yield curve which is three-month
+ 
+
+ align:start position:0%
+yield curve which is three-month
+treasury bills. And last week when we
+
+ align:start position:0%
+treasury bills. And last week when we
+ 
+
+ align:start position:0%
+treasury bills. And last week when we
+looked at this graph it was the yield
+
+ align:start position:0%
+looked at this graph it was the yield
+ 
+
+ align:start position:0%
+looked at this graph it was the yield
+was about three basis points uh for a
+
+ align:start position:0%
+was about three basis points uh for a
+ 
+
+ align:start position:0%
+was about three basis points uh for a
+three-month Treasury bill. And we
+
+ align:start position:0%
+three-month Treasury bill. And we
+ 
+
+ align:start position:0%
+three-month Treasury bill. And we
+pointed out that that was telling us
+
+ align:start position:0%
+pointed out that that was telling us
+ 
+
+ align:start position:0%
+pointed out that that was telling us
+something about the market. in
+
+ align:start position:0%
+something about the market. in
+ 
+
+ align:start position:0%
+something about the market. in
+particular it was telling us that the
+
+ align:start position:0%
+particular it was telling us that the
+ 
+
+ align:start position:0%
+particular it was telling us that the
+market was panicking. Yeah. um sort of
+
+ align:start position:0%
+market was panicking. Yeah. um sort of
+ 
+
+ align:start position:0%
+market was panicking. Yeah. um sort of
+are we sort of in this whole situation
+
+ align:start position:0%
+are we sort of in this whole situation
+ 
+
+ align:start position:0%
+are we sort of in this whole situation
+because looking at the market grossly
+
+ align:start position:0%
+because looking at the market grossly
+ 
+
+ align:start position:0%
+because looking at the market grossly
+pricing
+
+ align:start position:0%
+pricing
+ 
+
+ align:start position:0%
+pricing
+uh well I wouldn't say that it was
+
+ align:start position:0%
+uh well I wouldn't say that it was
+ 
+
+ align:start position:0%
+uh well I wouldn't say that it was
+looking at the market grossly mis the
+
+ align:start position:0%
+looking at the market grossly mis the
+ 
+
+ align:start position:0%
+looking at the market grossly mis the
+market obviously
+
+ align:start position:0%
+market obviously
+ 
+
+ align:start position:0%
+market obviously
+did not price this risk
+
+ align:start position:0%
+did not price this risk
+ 
+
+ align:start position:0%
+did not price this risk
+which looking at the market a year and a
+
+ align:start position:0%
+which looking at the market a year and a
+ 
+
+ align:start position:0%
+which looking at the market a year and a
+half ago
+
+ align:start position:0%
+half ago
+ 
+
+ align:start position:0%
+half ago
+you would have been oh there's this much
+
+ align:start position:0%
+you would have been oh there's this much
+ 
+
+ align:start position:0%
+you would have been oh there's this much
+risk
+
+ align:start position:0%
+risk
+ 
+
+ align:start position:0%
+risk
+they were totally Well, there are a
+
+ align:start position:0%
+they were totally Well, there are a
+ 
+
+ align:start position:0%
+they were totally Well, there are a
+number of things that are priced into a
+
+ align:start position:0%
+number of things that are priced into a
+ 
+
+ align:start position:0%
+number of things that are priced into a
+security. It's not just the risk, but
+
+ align:start position:0%
+security. It's not just the risk, but
+ 
+
+ align:start position:0%
+security. It's not just the risk, but
+it's also a reflection of supply and
+
+ align:start position:0%
+it's also a reflection of supply and
+ 
+
+ align:start position:0%
+it's also a reflection of supply and
+demand, right? So, in other words,
+
+ align:start position:0%
+demand, right? So, in other words,
+ 
+
+ align:start position:0%
+demand, right? So, in other words,
+what's going on here? The question that
+
+ align:start position:0%
+what's going on here? The question that
+ 
+
+ align:start position:0%
+what's going on here? The question that
+we want to answer from looking at the
+
+ align:start position:0%
+we want to answer from looking at the
+ 
+
+ align:start position:0%
+we want to answer from looking at the
+price is what do we know about what's
+
+ align:start position:0%
+price is what do we know about what's
+ 
+
+ align:start position:0%
+price is what do we know about what's
+going on in the marketplace based on
+
+ align:start position:0%
+going on in the marketplace based on
+ 
+
+ align:start position:0%
+going on in the marketplace based on
+that price? What is it telling us? The
+
+ align:start position:0%
+that price? What is it telling us? The
+ 
+
+ align:start position:0%
+that price? What is it telling us? The
+cost of borrowing over a 3-month period
+
+ align:start position:0%
+cost of borrowing over a 3-month period
+ 
+
+ align:start position:0%
+cost of borrowing over a 3-month period
+when it goes down to three basis points,
+
+ align:start position:0%
+when it goes down to three basis points,
+ 
+
+ align:start position:0%
+when it goes down to three basis points,
+that's telling you that the price of
+
+ align:start position:0%
+that's telling you that the price of
+ 
+
+ align:start position:0%
+that's telling you that the price of
+that security, the price of Treasury
+
+ align:start position:0%
+that security, the price of Treasury
+ 
+
+ align:start position:0%
+that security, the price of Treasury
+bills is extraordinarily high. relative
+
+ align:start position:0%
+bills is extraordinarily high. relative
+ 
+
+ align:start position:0%
+bills is extraordinarily high. relative
+to historical standards. Now, let's take
+
+ align:start position:0%
+to historical standards. Now, let's take
+ 
+
+ align:start position:0%
+to historical standards. Now, let's take
+a look at what happens uh more recently,
+
+ align:start position:0%
+a look at what happens uh more recently,
+ 
+
+ align:start position:0%
+a look at what happens uh more recently,
+in particular today. If we go to the u
+
+ align:start position:0%
+in particular today. If we go to the u
+ 
+
+ align:start position:0%
+in particular today. If we go to the u
+any of these websites, so in particular,
+
+ align:start position:0%
+any of these websites, so in particular,
+ 
+
+ align:start position:0%
+any of these websites, so in particular,
+let's go back to the Bloomberg site
+
+ align:start position:0%
+let's go back to the Bloomberg site
+ 
+
+ align:start position:0%
+let's go back to the Bloomberg site
+where we originally looked at this.
+
+ align:start position:0%
+where we originally looked at this.
+ 
+
+ align:start position:0%
+where we originally looked at this.
+First of all, this is now the yield
+
+ align:start position:0%
+First of all, this is now the yield
+ 
+
+ align:start position:0%
+First of all, this is now the yield
+curve. And it's hard to compare because
+
+ align:start position:0%
+curve. And it's hard to compare because
+ 
+
+ align:start position:0%
+curve. And it's hard to compare because
+I've got a different slide for the uh
+
+ align:start position:0%
+I've got a different slide for the uh
+ 
+
+ align:start position:0%
+I've got a different slide for the uh
+the last week's. This is just
+
+ align:start position:0%
+the last week's. This is just
+ 
+
+ align:start position:0%
+the last week's. This is just
+yesterday's the uh the orange, not uh
+
+ align:start position:0%
+yesterday's the uh the orange, not uh
+ 
+
+ align:start position:0%
+yesterday's the uh the orange, not uh
+not last week's. But the one thing
+
+ align:start position:0%
+not last week's. But the one thing
+ 
+
+ align:start position:0%
+not last week's. But the one thing
+you'll note is that at the very short
+
+ align:start position:0%
+you'll note is that at the very short
+ 
+
+ align:start position:0%
+you'll note is that at the very short
+end now instead of three basis points,
+
+ align:start position:0%
+end now instead of three basis points,
+ 
+
+ align:start position:0%
+end now instead of three basis points,
+the three-month Treasury is yielding 41
+
+ align:start position:0%
+the three-month Treasury is yielding 41
+ 
+
+ align:start position:0%
+the three-month Treasury is yielding 41
+basis points. What does that tell you
+
+ align:start position:0%
+basis points. What does that tell you
+ 
+
+ align:start position:0%
+basis points. What does that tell you
+about the price?
+
+ align:start position:0%
+about the price?
+ 
+
+ align:start position:0%
+about the price?
+Now, so Treasury securities, short-term
+
+ align:start position:0%
+Now, so Treasury securities, short-term
+ 
+
+ align:start position:0%
+Now, so Treasury securities, short-term
+Treasury securities have declined in
+
+ align:start position:0%
+Treasury securities have declined in
+ 
+
+ align:start position:0%
+Treasury securities have declined in
+price over the last week. And that's one
+
+ align:start position:0%
+price over the last week. And that's one
+ 
+
+ align:start position:0%
+price over the last week. And that's one
+sign that perhaps markets are not as
+
+ align:start position:0%
+sign that perhaps markets are not as
+ 
+
+ align:start position:0%
+sign that perhaps markets are not as
+panicked as they were last week. there
+
+ align:start position:0%
+panicked as they were last week. there
+ 
+
+ align:start position:0%
+panicked as they were last week. there
+isn't this mad rush to get into treasury
+
+ align:start position:0%
+isn't this mad rush to get into treasury
+ 
+
+ align:start position:0%
+isn't this mad rush to get into treasury
+securities in the short term. All right.
+
+ align:start position:0%
+securities in the short term. All right.
+ 
+
+ align:start position:0%
+securities in the short term. All right.
+So short-term yields have gone up. Yeah.
+
+ align:start position:0%
+So short-term yields have gone up. Yeah.
+ 
+
+ align:start position:0%
+So short-term yields have gone up. Yeah.
+So let me say you did a lot of work
+
+ align:start position:0%
+So let me say you did a lot of work
+ 
+
+ align:start position:0%
+So let me say you did a lot of work
+around the psychology of
+
+ align:start position:0%
+around the psychology of
+ 
+
+ align:start position:0%
+around the psychology of
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+So I'm just what I was wondering is when
+
+ align:start position:0%
+So I'm just what I was wondering is when
+ 
+
+ align:start position:0%
+So I'm just what I was wondering is when
+the p you know it seemed like as you
+
+ align:start position:0%
+the p you know it seemed like as you
+ 
+
+ align:start position:0%
+the p you know it seemed like as you
+said there's a flight to liquidity last
+
+ align:start position:0%
+said there's a flight to liquidity last
+ 
+
+ align:start position:0%
+said there's a flight to liquidity last
+week. Now,
+
+ align:start position:0%
+week. Now,
+ 
+
+ align:start position:0%
+week. Now,
+why was there such a huge movement or
+
+ align:start position:0%
+why was there such a huge movement or
+ 
+
+ align:start position:0%
+why was there such a huge movement or
+what led to the price dropping so much
+
+ align:start position:0%
+what led to the price dropping so much
+ 
+
+ align:start position:0%
+what led to the price dropping so much
+when I guess it could be reasonably
+
+ align:start position:0%
+when I guess it could be reasonably
+ 
+
+ align:start position:0%
+when I guess it could be reasonably
+expected that the price would come back
+
+ align:start position:0%
+expected that the price would come back
+ 
+
+ align:start position:0%
+expected that the price would come back
+up and so people would just wait it out
+
+ align:start position:0%
+up and so people would just wait it out
+ 
+
+ align:start position:0%
+up and so people would just wait it out
+and you know
+
+ align:start position:0%
+and you know
+ 
+
+ align:start position:0%
+and you know
+which price are you talking about
+
+ align:start position:0%
+which price are you talking about
+ 
+
+ align:start position:0%
+which price are you talking about
+dropping?
+
+ align:start position:0%
+dropping?
+ 
+
+ align:start position:0%
+dropping?
+I say I should probably say the yield
+
+ align:start position:0%
+I say I should probably say the yield
+ 
+
+ align:start position:0%
+I say I should probably say the yield
+the yield dropping and the price going
+
+ align:start position:0%
+the yield dropping and the price going
+ 
+
+ align:start position:0%
+the yield dropping and the price going
+up. Well, so there are are a number of
+
+ align:start position:0%
+up. Well, so there are are a number of
+ 
+
+ align:start position:0%
+up. Well, so there are are a number of
+factors at play, but the the
+
+ align:start position:0%
+factors at play, but the the
+ 
+
+ align:start position:0%
+factors at play, but the the
+current uh perspective that most of us
+
+ align:start position:0%
+current uh perspective that most of us
+ 
+
+ align:start position:0%
+current uh perspective that most of us
+have in financial markets about last
+
+ align:start position:0%
+have in financial markets about last
+ 
+
+ align:start position:0%
+have in financial markets about last
+week, and this is just perspective,
+
+ align:start position:0%
+week, and this is just perspective,
+ 
+
+ align:start position:0%
+week, and this is just perspective,
+remember last week is not that far away.
+
+ align:start position:0%
+remember last week is not that far away.
+ 
+
+ align:start position:0%
+remember last week is not that far away.
+Um what what happened last week by most
+
+ align:start position:0%
+Um what what happened last week by most
+ 
+
+ align:start position:0%
+Um what what happened last week by most
+accounts is that there was a a very
+
+ align:start position:0%
+accounts is that there was a a very
+ 
+
+ align:start position:0%
+accounts is that there was a a very
+significant rush to the exits by
+
+ align:start position:0%
+significant rush to the exits by
+ 
+
+ align:start position:0%
+significant rush to the exits by
+investors. By rushing to the exit exits,
+
+ align:start position:0%
+investors. By rushing to the exit exits,
+ 
+
+ align:start position:0%
+investors. By rushing to the exit exits,
+I mean getting out of risky securities
+
+ align:start position:0%
+I mean getting out of risky securities
+ 
+
+ align:start position:0%
+I mean getting out of risky securities
+and into safer securities. And at this
+
+ align:start position:0%
+and into safer securities. And at this
+ 
+
+ align:start position:0%
+and into safer securities. And at this
+point, it doesn't seem like there's much
+
+ align:start position:0%
+point, it doesn't seem like there's much
+ 
+
+ align:start position:0%
+point, it doesn't seem like there's much
+of a uh safe haven other than US
+
+ align:start position:0%
+of a uh safe haven other than US
+ 
+
+ align:start position:0%
+of a uh safe haven other than US
+Treasury securities and in particular
+
+ align:start position:0%
+Treasury securities and in particular
+ 
+
+ align:start position:0%
+Treasury securities and in particular
+short-term securities because you know
+
+ align:start position:0%
+short-term securities because you know
+ 
+
+ align:start position:0%
+short-term securities because you know
+you can get out get the money out uh
+
+ align:start position:0%
+you can get out get the money out uh
+ 
+
+ align:start position:0%
+you can get out get the money out uh
+over a relatively short period of time.
+
+ align:start position:0%
+over a relatively short period of time.
+ 
+
+ align:start position:0%
+over a relatively short period of time.
+So that's what the yield curve told us
+
+ align:start position:0%
+So that's what the yield curve told us
+ 
+
+ align:start position:0%
+So that's what the yield curve told us
+last week. That three basis points means
+
+ align:start position:0%
+last week. That three basis points means
+ 
+
+ align:start position:0%
+last week. That three basis points means
+that basically people didn't care about
+
+ align:start position:0%
+that basically people didn't care about
+ 
+
+ align:start position:0%
+that basically people didn't care about
+the yield. All they wanted to do was to
+
+ align:start position:0%
+the yield. All they wanted to do was to
+ 
+
+ align:start position:0%
+the yield. All they wanted to do was to
+get into US treasuries at at almost any
+
+ align:start position:0%
+get into US treasuries at at almost any
+ 
+
+ align:start position:0%
+get into US treasuries at at almost any
+price. Okay.
+
+ align:start position:0%
+price. Okay.
+ 
+
+ align:start position:0%
+price. Okay.
+This week it's different. In particular,
+
+ align:start position:0%
+This week it's different. In particular,
+ 
+
+ align:start position:0%
+This week it's different. In particular,
+not only has the short-term yield gone
+
+ align:start position:0%
+not only has the short-term yield gone
+ 
+
+ align:start position:0%
+not only has the short-term yield gone
+up, so now instead of three basis
+
+ align:start position:0%
+up, so now instead of three basis
+ 
+
+ align:start position:0%
+up, so now instead of three basis
+points, we're up to 41. But look at the
+
+ align:start position:0%
+points, we're up to 41. But look at the
+ 
+
+ align:start position:0%
+points, we're up to 41. But look at the
+long end of the yield curve. before the
+
+ align:start position:0%
+long end of the yield curve. before the
+ 
+
+ align:start position:0%
+long end of the yield curve. before the
+long end of the yield curve. Let me just
+
+ align:start position:0%
+long end of the yield curve. Let me just
+ 
+
+ align:start position:0%
+long end of the yield curve. Let me just
+go back and remind you what that looked
+
+ align:start position:0%
+go back and remind you what that looked
+ 
+
+ align:start position:0%
+go back and remind you what that looked
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+at the 30-year. A week ago, the 30-year
+
+ align:start position:0%
+at the 30-year. A week ago, the 30-year
+ 
+
+ align:start position:0%
+at the 30-year. A week ago, the 30-year
+yield was 4%. Okay, let's take a look at
+
+ align:start position:0%
+yield was 4%. Okay, let's take a look at
+ 
+
+ align:start position:0%
+yield was 4%. Okay, let's take a look at
+it what it is today.
+
+ align:start position:0%
+it what it is today.
+ 
+
+ align:start position:0%
+it what it is today.
+It's now uh the 30-year yield 4.37.
+
+ align:start position:0%
+It's now uh the 30-year yield 4.37.
+ 
+
+ align:start position:0%
+It's now uh the 30-year yield 4.37.
+That's another big movement. Why is
+
+ align:start position:0%
+That's another big movement. Why is
+ 
+
+ align:start position:0%
+That's another big movement. Why is
+that? Why would the yield for the
+
+ align:start position:0%
+that? Why would the yield for the
+ 
+
+ align:start position:0%
+that? Why would the yield for the
+long-term bond go up? What what is the
+
+ align:start position:0%
+long-term bond go up? What what is the
+ 
+
+ align:start position:0%
+long-term bond go up? What what is the
+market thinking today?
+
+ align:start position:0%
+market thinking today?
+ 
+
+ align:start position:0%
+market thinking today?
+They might be more worried about
+
+ align:start position:0%
+They might be more worried about
+ 
+
+ align:start position:0%
+They might be more worried about
+long-term inflation. The government has
+
+ align:start position:0%
+long-term inflation. The government has
+ 
+
+ align:start position:0%
+long-term inflation. The government has
+promised $700 billion.
+
+ align:start position:0%
+promised $700 billion.
+ 
+
+ align:start position:0%
+promised $700 billion.
+Okay, so inflation has now been
+
+ align:start position:0%
+Okay, so inflation has now been
+ 
+
+ align:start position:0%
+Okay, so inflation has now been
+incorporated just over the last seven
+
+ align:start position:0%
+incorporated just over the last seven
+ 
+
+ align:start position:0%
+incorporated just over the last seven
+days. So question, is this price correct
+
+ align:start position:0%
+days. So question, is this price correct
+ 
+
+ align:start position:0%
+days. So question, is this price correct
+or was last week's price correct?
+
+ align:start position:0%
+or was last week's price correct?
+ 
+
+ align:start position:0%
+or was last week's price correct?
+Getting to your point, I mean, what do
+
+ align:start position:0%
+Getting to your point, I mean, what do
+ 
+
+ align:start position:0%
+Getting to your point, I mean, what do
+we do? is is is the short end of the
+
+ align:start position:0%
+we do? is is is the short end of the
+ 
+
+ align:start position:0%
+we do? is is is the short end of the
+yield curve appropriate today at 41
+
+ align:start position:0%
+yield curve appropriate today at 41
+ 
+
+ align:start position:0%
+yield curve appropriate today at 41
+basis points or was it really
+
+ align:start position:0%
+basis points or was it really
+ 
+
+ align:start position:0%
+basis points or was it really
+appropriate at three basis points?
+
+ align:start position:0%
+appropriate at three basis points?
+ 
+
+ align:start position:0%
+appropriate at three basis points?
+There's no answer to that question
+
+ align:start position:0%
+There's no answer to that question
+ 
+
+ align:start position:0%
+There's no answer to that question
+because there's no right answer. These
+
+ align:start position:0%
+because there's no right answer. These
+ 
+
+ align:start position:0%
+because there's no right answer. These
+prices are a reflection of the current
+
+ align:start position:0%
+prices are a reflection of the current
+ 
+
+ align:start position:0%
+prices are a reflection of the current
+expectations of all the market
+
+ align:start position:0%
+expectations of all the market
+ 
+
+ align:start position:0%
+expectations of all the market
+participants.
+
+ align:start position:0%
+participants.
+ 
+
+ align:start position:0%
+participants.
+Right or wrong, it really reflects the
+
+ align:start position:0%
+Right or wrong, it really reflects the
+ 
+
+ align:start position:0%
+Right or wrong, it really reflects the
+combined either wisdom or fear or greed
+
+ align:start position:0%
+combined either wisdom or fear or greed
+ 
+
+ align:start position:0%
+combined either wisdom or fear or greed
+of the marketplace. And so our approach
+
+ align:start position:0%
+of the marketplace. And so our approach
+ 
+
+ align:start position:0%
+of the marketplace. And so our approach
+is to try to understand what that is. We
+
+ align:start position:0%
+is to try to understand what that is. We
+ 
+
+ align:start position:0%
+is to try to understand what that is. We
+want to explicate the information that
+
+ align:start position:0%
+want to explicate the information that
+ 
+
+ align:start position:0%
+want to explicate the information that
+happens to be in prices. But you have to
+
+ align:start position:0%
+happens to be in prices. But you have to
+ 
+
+ align:start position:0%
+happens to be in prices. But you have to
+understand that these are the same
+
+ align:start position:0%
+understand that these are the same
+ 
+
+ align:start position:0%
+understand that these are the same
+imperfect kind of prices that we came up
+
+ align:start position:0%
+imperfect kind of prices that we came up
+ 
+
+ align:start position:0%
+imperfect kind of prices that we came up
+with on day one when you bid for that
+
+ align:start position:0%
+with on day one when you bid for that
+ 
+
+ align:start position:0%
+with on day one when you bid for that
+little package. And you know it turned
+
+ align:start position:0%
+little package. And you know it turned
+ 
+
+ align:start position:0%
+little package. And you know it turned
+out that you got lucky and you know got
+
+ align:start position:0%
+out that you got lucky and you know got
+ 
+
+ align:start position:0%
+out that you got lucky and you know got
+an iPod for whatever $45.
+
+ align:start position:0%
+an iPod for whatever $45.
+ 
+
+ align:start position:0%
+an iPod for whatever $45.
+But it could have gone the other way.
+
+ align:start position:0%
+But it could have gone the other way.
+ 
+
+ align:start position:0%
+But it could have gone the other way.
+And in fact in the second class it did
+
+ align:start position:0%
+And in fact in the second class it did
+ 
+
+ align:start position:0%
+And in fact in the second class it did
+go the other way. So we we won't have we
+
+ align:start position:0%
+go the other way. So we we won't have we
+ 
+
+ align:start position:0%
+go the other way. So we we won't have we
+won't talk about that. Um the prices
+
+ align:start position:0%
+won't talk about that. Um the prices
+ 
+
+ align:start position:0%
+won't talk about that. Um the prices
+reflect all aspects of the economy, the
+
+ align:start position:0%
+reflect all aspects of the economy, the
+ 
+
+ align:start position:0%
+reflect all aspects of the economy, the
+rational as well as the irrational. And
+
+ align:start position:0%
+rational as well as the irrational. And
+ 
+
+ align:start position:0%
+rational as well as the irrational. And
+so last week, was it irrational for
+
+ align:start position:0%
+so last week, was it irrational for
+ 
+
+ align:start position:0%
+so last week, was it irrational for
+people to pull their money out from all
+
+ align:start position:0%
+people to pull their money out from all
+ 
+
+ align:start position:0%
+people to pull their money out from all
+sorts of investments and put them in the
+
+ align:start position:0%
+sorts of investments and put them in the
+ 
+
+ align:start position:0%
+sorts of investments and put them in the
+Treasury bills? Well, this goes to the
+
+ align:start position:0%
+Treasury bills? Well, this goes to the
+ 
+
+ align:start position:0%
+Treasury bills? Well, this goes to the
+heart of why the Treasury acted so
+
+ align:start position:0%
+heart of why the Treasury acted so
+ 
+
+ align:start position:0%
+heart of why the Treasury acted so
+quickly and why uh Chairman Bernani has
+
+ align:start position:0%
+quickly and why uh Chairman Bernani has
+ 
+
+ align:start position:0%
+quickly and why uh Chairman Bernani has
+said that he wants to get a quick
+
+ align:start position:0%
+said that he wants to get a quick
+ 
+
+ align:start position:0%
+said that he wants to get a quick
+resolution. Something very significant
+
+ align:start position:0%
+resolution. Something very significant
+ 
+
+ align:start position:0%
+resolution. Something very significant
+happened last week
+
+ align:start position:0%
+happened last week
+ 
+
+ align:start position:0%
+happened last week
+and I don't know how many of you really
+
+ align:start position:0%
+and I don't know how many of you really
+ 
+
+ align:start position:0%
+and I don't know how many of you really
+uh got wind of it. Um certainly the
+
+ align:start position:0%
+uh got wind of it. Um certainly the
+ 
+
+ align:start position:0%
+uh got wind of it. Um certainly the
+Treasury knew what was going on and the
+
+ align:start position:0%
+Treasury knew what was going on and the
+ 
+
+ align:start position:0%
+Treasury knew what was going on and the
+Fed did but it wasn't uh really
+
+ align:start position:0%
+Fed did but it wasn't uh really
+ 
+
+ align:start position:0%
+Fed did but it wasn't uh really
+highlighted in the newspapers in the way
+
+ align:start position:0%
+highlighted in the newspapers in the way
+ 
+
+ align:start position:0%
+highlighted in the newspapers in the way
+that uh that I would have thought it it
+
+ align:start position:0%
+that uh that I would have thought it it
+ 
+
+ align:start position:0%
+that uh that I would have thought it it
+should have been given the importance.
+
+ align:start position:0%
+should have been given the importance.
+ 
+
+ align:start position:0%
+should have been given the importance.
+Anybody know what I'm talking about?
+
+ align:start position:0%
+Anybody know what I'm talking about?
+ 
+
+ align:start position:0%
+Anybody know what I'm talking about?
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Um stopping the short selling.
+
+ align:start position:0%
+Um stopping the short selling.
+ 
+
+ align:start position:0%
+Um stopping the short selling.
+Well, that was one piece of news. The
+
+ align:start position:0%
+Well, that was one piece of news. The
+ 
+
+ align:start position:0%
+Well, that was one piece of news. The
+SEC mandated that for a period of time
+
+ align:start position:0%
+SEC mandated that for a period of time
+ 
+
+ align:start position:0%
+SEC mandated that for a period of time
+to be determined we are not allowed to
+
+ align:start position:0%
+to be determined we are not allowed to
+ 
+
+ align:start position:0%
+to be determined we are not allowed to
+short sell financial stocks because they
+
+ align:start position:0%
+short sell financial stocks because they
+ 
+
+ align:start position:0%
+short sell financial stocks because they
+wanted to stop the the kind of run that
+
+ align:start position:0%
+wanted to stop the the kind of run that
+ 
+
+ align:start position:0%
+wanted to stop the the kind of run that
+there's been on uh these securities. I'm
+
+ align:start position:0%
+there's been on uh these securities. I'm
+ 
+
+ align:start position:0%
+there's been on uh these securities. I'm
+going to come back and talk about it in
+
+ align:start position:0%
+going to come back and talk about it in
+ 
+
+ align:start position:0%
+going to come back and talk about it in
+the end of this lecture because we're
+
+ align:start position:0%
+the end of this lecture because we're
+ 
+
+ align:start position:0%
+the end of this lecture because we're
+going to talk about short sales but
+
+ align:start position:0%
+going to talk about short sales but
+ 
+
+ align:start position:0%
+going to talk about short sales but
+that's not what I was referring to.
+
+ align:start position:0%
+that's not what I was referring to.
+ 
+
+ align:start position:0%
+that's not what I was referring to.
+That's certainly a concern but that's
+
+ align:start position:0%
+That's certainly a concern but that's
+ 
+
+ align:start position:0%
+That's certainly a concern but that's
+not the major concern that I think the
+
+ align:start position:0%
+not the major concern that I think the
+ 
+
+ align:start position:0%
+not the major concern that I think the
+market was responding to. Yeah.
+
+ align:start position:0%
+market was responding to. Yeah.
+ 
+
+ align:start position:0%
+market was responding to. Yeah.
+Was the$8 billion redemption funds
+
+ align:start position:0%
+Was the$8 billion redemption funds
+ 
+
+ align:start position:0%
+Was the$8 billion redemption funds
+that's right? Where was that coming
+
+ align:start position:0%
+that's right? Where was that coming
+ 
+
+ align:start position:0%
+that's right? Where was that coming
+from? What what was going on with that?
+
+ align:start position:0%
+from? What what was going on with that?
+ 
+
+ align:start position:0%
+from? What what was going on with that?
+Why did that happen?
+
+ align:start position:0%
+Why did that happen?
+ 
+
+ align:start position:0%
+Why did that happen?
+These people are losing confidence in
+
+ align:start position:0%
+These people are losing confidence in
+ 
+
+ align:start position:0%
+These people are losing confidence in
+that short-term debt.
+
+ align:start position:0%
+that short-term debt.
+ 
+
+ align:start position:0%
+that short-term debt.
+And was there a reason for that loss of
+
+ align:start position:0%
+And was there a reason for that loss of
+ 
+
+ align:start position:0%
+And was there a reason for that loss of
+confidence? I mean, you know, money
+
+ align:start position:0%
+confidence? I mean, you know, money
+ 
+
+ align:start position:0%
+confidence? I mean, you know, money
+funds. What does that have to do with
+
+ align:start position:0%
+funds. What does that have to do with
+ 
+
+ align:start position:0%
+funds. What does that have to do with
+mortgages and Lehman and Goldman? What's
+
+ align:start position:0%
+mortgages and Lehman and Goldman? What's
+ 
+
+ align:start position:0%
+mortgages and Lehman and Goldman? What's
+there there's what's the connection?
+
+ align:start position:0%
+there there's what's the connection?
+ 
+
+ align:start position:0%
+there there's what's the connection?
+Well, I just think more is a
+
+ align:start position:0%
+Well, I just think more is a
+ 
+
+ align:start position:0%
+Well, I just think more is a
+psychological reaction than it was
+
+ align:start position:0%
+psychological reaction than it was
+ 
+
+ align:start position:0%
+psychological reaction than it was
+actual.
+
+ align:start position:0%
+actual.
+ 
+
+ align:start position:0%
+actual.
+Absolutely. It was a psychological
+
+ align:start position:0%
+Absolutely. It was a psychological
+ 
+
+ align:start position:0%
+Absolutely. It was a psychological
+reaction. But did did something trigger
+
+ align:start position:0%
+reaction. But did did something trigger
+ 
+
+ align:start position:0%
+reaction. But did did something trigger
+that? Is that psychological reaction
+
+ align:start position:0%
+that? Is that psychological reaction
+ 
+
+ align:start position:0%
+that? Is that psychological reaction
+completely unreasonable? If your
+
+ align:start position:0%
+completely unreasonable? If your
+ 
+
+ align:start position:0%
+completely unreasonable? If your
+grandmother asked you what she should do
+
+ align:start position:0%
+grandmother asked you what she should do
+ 
+
+ align:start position:0%
+grandmother asked you what she should do
+now with her money market fund, should
+
+ align:start position:0%
+now with her money market fund, should
+ 
+
+ align:start position:0%
+now with her money market fund, should
+you tell her don't worry about it, you
+
+ align:start position:0%
+you tell her don't worry about it, you
+ 
+
+ align:start position:0%
+you tell her don't worry about it, you
+know, just uh you know, stay the the uh
+
+ align:start position:0%
+know, just uh you know, stay the the uh
+ 
+
+ align:start position:0%
+know, just uh you know, stay the the uh
+the course and uh see what happens.
+
+ align:start position:0%
+the course and uh see what happens.
+ 
+
+ align:start position:0%
+the course and uh see what happens.
+Something happened last week that is
+
+ align:start position:0%
+Something happened last week that is
+ 
+
+ align:start position:0%
+Something happened last week that is
+related exactly to that issue. So,
+
+ align:start position:0%
+related exactly to that issue. So,
+ 
+
+ align:start position:0%
+related exactly to that issue. So,
+you're on to something. What is that,
+
+ align:start position:0%
+you're on to something. What is that,
+ 
+
+ align:start position:0%
+you're on to something. What is that,
+Megan?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Market funds broke the
+
+ align:start position:0%
+Market funds broke the
+ 
+
+ align:start position:0%
+Market funds broke the
+broke the buck. Exactly. Which money
+
+ align:start position:0%
+broke the buck. Exactly. Which money
+ 
+
+ align:start position:0%
+broke the buck. Exactly. Which money
+fund you remember?
+
+ align:start position:0%
+fund you remember?
+ 
+
+ align:start position:0%
+fund you remember?
+No, no, that
+
+ align:start position:0%
+No, no, that
+ 
+
+ align:start position:0%
+No, no, that
+it the reserve fund.
+
+ align:start position:0%
+it the reserve fund.
+ 
+
+ align:start position:0%
+it the reserve fund.
+What's the reserve?
+
+ align:start position:0%
+What's the reserve?
+ 
+
+ align:start position:0%
+What's the reserve?
+The reserve fund is one of the first, if
+
+ align:start position:0%
+The reserve fund is one of the first, if
+ 
+
+ align:start position:0%
+The reserve fund is one of the first, if
+not the first money market funds. And
+
+ align:start position:0%
+not the first money market funds. And
+ 
+
+ align:start position:0%
+not the first money market funds. And
+what is a money market fund? Do do we
+
+ align:start position:0%
+what is a money market fund? Do do we
+ 
+
+ align:start position:0%
+what is a money market fund? Do do we
+know what that is? You all know what
+
+ align:start position:0%
+know what that is? You all know what
+ 
+
+ align:start position:0%
+know what that is? You all know what
+that a money market fund is. You all
+
+ align:start position:0%
+that a money market fund is. You all
+ 
+
+ align:start position:0%
+that a money market fund is. You all
+probably have money in a money market
+
+ align:start position:0%
+probably have money in a money market
+ 
+
+ align:start position:0%
+probably have money in a money market
+fund whether you know it or not, right?
+
+ align:start position:0%
+fund whether you know it or not, right?
+ 
+
+ align:start position:0%
+fund whether you know it or not, right?
+Money market fund is a fund that
+
+ align:start position:0%
+Money market fund is a fund that
+ 
+
+ align:start position:0%
+Money market fund is a fund that
+contains relatively short-term and
+
+ align:start position:0%
+contains relatively short-term and
+ 
+
+ align:start position:0%
+contains relatively short-term and
+supposedly
+
+ align:start position:0%
+supposedly
+ 
+
+ align:start position:0%
+supposedly
+riskless securities like CDs,
+
+ align:start position:0%
+riskless securities like CDs,
+ 
+
+ align:start position:0%
+riskless securities like CDs,
+treasuries, and other kinds of very very
+
+ align:start position:0%
+treasuries, and other kinds of very very
+ 
+
+ align:start position:0%
+treasuries, and other kinds of very very
+safe assets. And what does it mean to
+
+ align:start position:0%
+safe assets. And what does it mean to
+ 
+
+ align:start position:0%
+safe assets. And what does it mean to
+break the buck?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Market funds had invested what they
+
+ align:start position:0%
+Market funds had invested what they
+ 
+
+ align:start position:0%
+Market funds had invested what they
+would be able to at that time,
+
+ align:start position:0%
+would be able to at that time,
+ 
+
+ align:start position:0%
+would be able to at that time,
+right? Breaking the buck means that when
+
+ align:start position:0%
+right? Breaking the buck means that when
+ 
+
+ align:start position:0%
+right? Breaking the buck means that when
+you put in a buck, money funds are
+
+ align:start position:0%
+you put in a buck, money funds are
+ 
+
+ align:start position:0%
+you put in a buck, money funds are
+supposed to be so safe that at the very
+
+ align:start position:0%
+supposed to be so safe that at the very
+ 
+
+ align:start position:0%
+supposed to be so safe that at the very
+least when you withdraw the money,
+
+ align:start position:0%
+least when you withdraw the money,
+ 
+
+ align:start position:0%
+least when you withdraw the money,
+you're going to get a buck back.
+
+ align:start position:0%
+you're going to get a buck back.
+ 
+
+ align:start position:0%
+you're going to get a buck back.
+Breaking the buck means that if you
+
+ align:start position:0%
+Breaking the buck means that if you
+ 
+
+ align:start position:0%
+Breaking the buck means that if you
+withdraw, there is a possibility that
+
+ align:start position:0%
+withdraw, there is a possibility that
+ 
+
+ align:start position:0%
+withdraw, there is a possibility that
+what you withdraw is less than a dollar.
+
+ align:start position:0%
+what you withdraw is less than a dollar.
+ 
+
+ align:start position:0%
+what you withdraw is less than a dollar.
+Now, that's scary because think about a
+
+ align:start position:0%
+Now, that's scary because think about a
+ 
+
+ align:start position:0%
+Now, that's scary because think about a
+bank. When you put your money into a
+
+ align:start position:0%
+bank. When you put your money into a
+ 
+
+ align:start position:0%
+bank. When you put your money into a
+banking, a checking account for a bank,
+
+ align:start position:0%
+banking, a checking account for a bank,
+ 
+
+ align:start position:0%
+banking, a checking account for a bank,
+you expect to get that money out. Maybe
+
+ align:start position:0%
+you expect to get that money out. Maybe
+ 
+
+ align:start position:0%
+you expect to get that money out. Maybe
+not with a lot of interest, maybe even
+
+ align:start position:0%
+not with a lot of interest, maybe even
+ 
+
+ align:start position:0%
+not with a lot of interest, maybe even
+with no interest if things don't go
+
+ align:start position:0%
+with no interest if things don't go
+ 
+
+ align:start position:0%
+with no interest if things don't go
+well, but you expect to get what you put
+
+ align:start position:0%
+well, but you expect to get what you put
+ 
+
+ align:start position:0%
+well, but you expect to get what you put
+in. You expect to get the principle
+
+ align:start position:0%
+in. You expect to get the principle
+ 
+
+ align:start position:0%
+in. You expect to get the principle
+back, right? Well, money market funds
+
+ align:start position:0%
+back, right? Well, money market funds
+ 
+
+ align:start position:0%
+back, right? Well, money market funds
+are very much the same way. People use
+
+ align:start position:0%
+are very much the same way. People use
+ 
+
+ align:start position:0%
+are very much the same way. People use
+them as if they were checking accounts.
+
+ align:start position:0%
+them as if they were checking accounts.
+ 
+
+ align:start position:0%
+them as if they were checking accounts.
+In fact, there are money market funds
+
+ align:start position:0%
+In fact, there are money market funds
+ 
+
+ align:start position:0%
+In fact, there are money market funds
+where you can write checks on them,
+
+ align:start position:0%
+where you can write checks on them,
+ 
+
+ align:start position:0%
+where you can write checks on them,
+right? And so breaking the buck has been
+
+ align:start position:0%
+right? And so breaking the buck has been
+ 
+
+ align:start position:0%
+right? And so breaking the buck has been
+a major concern not just among the the
+
+ align:start position:0%
+a major concern not just among the the
+ 
+
+ align:start position:0%
+a major concern not just among the the
+money funds but among regulators because
+
+ align:start position:0%
+money funds but among regulators because
+ 
+
+ align:start position:0%
+money funds but among regulators because
+if it turns out that retail investors,
+
+ align:start position:0%
+if it turns out that retail investors,
+ 
+
+ align:start position:0%
+if it turns out that retail investors,
+ordinary consumers are scared about
+
+ align:start position:0%
+ordinary consumers are scared about
+ 
+
+ align:start position:0%
+ordinary consumers are scared about
+what's going on with their money market
+
+ align:start position:0%
+what's going on with their money market
+ 
+
+ align:start position:0%
+what's going on with their money market
+accounts. they will do in mass what
+
+ align:start position:0%
+accounts. they will do in mass what
+ 
+
+ align:start position:0%
+accounts. they will do in mass what
+happened last week which is pull out
+
+ align:start position:0%
+happened last week which is pull out
+ 
+
+ align:start position:0%
+happened last week which is pull out
+huge sums of money from these money
+
+ align:start position:0%
+huge sums of money from these money
+ 
+
+ align:start position:0%
+huge sums of money from these money
+market funds and as I mentioned earlier
+
+ align:start position:0%
+market funds and as I mentioned earlier
+ 
+
+ align:start position:0%
+market funds and as I mentioned earlier
+no business can sustain a massive
+
+ align:start position:0%
+no business can sustain a massive
+ 
+
+ align:start position:0%
+no business can sustain a massive
+withdrawal of all capital all at once it
+
+ align:start position:0%
+withdrawal of all capital all at once it
+ 
+
+ align:start position:0%
+withdrawal of all capital all at once it
+it's just not possible for a business to
+
+ align:start position:0%
+it's just not possible for a business to
+ 
+
+ align:start position:0%
+it's just not possible for a business to
+be able to be conducted in that manner
+
+ align:start position:0%
+be able to be conducted in that manner
+ 
+
+ align:start position:0%
+be able to be conducted in that manner
+if that happens we will see mass
+
+ align:start position:0%
+if that happens we will see mass
+ 
+
+ align:start position:0%
+if that happens we will see mass
+failures of financial institutions that
+
+ align:start position:0%
+failures of financial institutions that
+ 
+
+ align:start position:0%
+failures of financial institutions that
+will make the last four weeks look like
+
+ align:start position:0%
+will make the last four weeks look like
+ 
+
+ align:start position:0%
+will make the last four weeks look like
+the good old days. Um, and that's what
+
+ align:start position:0%
+the good old days. Um, and that's what
+ 
+
+ align:start position:0%
+the good old days. Um, and that's what
+the Fed is concerned about. That's what
+
+ align:start position:0%
+the Fed is concerned about. That's what
+ 
+
+ align:start position:0%
+the Fed is concerned about. That's what
+the Treasury is concerned about. And so
+
+ align:start position:0%
+the Treasury is concerned about. And so
+ 
+
+ align:start position:0%
+the Treasury is concerned about. And so
+the hope is that the measures that they
+
+ align:start position:0%
+the hope is that the measures that they
+ 
+
+ align:start position:0%
+the hope is that the measures that they
+put in place will calm the fears of the
+
+ align:start position:0%
+put in place will calm the fears of the
+ 
+
+ align:start position:0%
+put in place will calm the fears of the
+public. That's the first order of
+
+ align:start position:0%
+public. That's the first order of
+ 
+
+ align:start position:0%
+public. That's the first order of
+business. It's calming the psychological
+
+ align:start position:0%
+business. It's calming the psychological
+ 
+
+ align:start position:0%
+business. It's calming the psychological
+kinds of effects that these headlines
+
+ align:start position:0%
+kinds of effects that these headlines
+ 
+
+ align:start position:0%
+kinds of effects that these headlines
+have produced. And so the hope is that
+
+ align:start position:0%
+have produced. And so the hope is that
+ 
+
+ align:start position:0%
+have produced. And so the hope is that
+once they put these measures in place,
+
+ align:start position:0%
+once they put these measures in place,
+ 
+
+ align:start position:0%
+once they put these measures in place,
+that will take care of the concerns.
+
+ align:start position:0%
+that will take care of the concerns.
+ 
+
+ align:start position:0%
+that will take care of the concerns.
+What they've done is to propose to
+
+ align:start position:0%
+What they've done is to propose to
+ 
+
+ align:start position:0%
+What they've done is to propose to
+guarantee money market funds the same
+
+ align:start position:0%
+guarantee money market funds the same
+ 
+
+ align:start position:0%
+guarantee money market funds the same
+way that the FDIC guarantees your uh
+
+ align:start position:0%
+way that the FDIC guarantees your uh
+ 
+
+ align:start position:0%
+way that the FDIC guarantees your uh
+banking accounts and the way that the
+
+ align:start position:0%
+banking accounts and the way that the
+ 
+
+ align:start position:0%
+banking accounts and the way that the
+SIPC guarantees your brokerage accounts.
+
+ align:start position:0%
+SIPC guarantees your brokerage accounts.
+ 
+
+ align:start position:0%
+SIPC guarantees your brokerage accounts.
+Uh and there are other measures that
+
+ align:start position:0%
+Uh and there are other measures that
+ 
+
+ align:start position:0%
+Uh and there are other measures that
+have been proposed. We won't have time
+
+ align:start position:0%
+have been proposed. We won't have time
+ 
+
+ align:start position:0%
+have been proposed. We won't have time
+to talk about them here, but over the
+
+ align:start position:0%
+to talk about them here, but over the
+ 
+
+ align:start position:0%
+to talk about them here, but over the
+next couple of weeks, the uh the finance
+
+ align:start position:0%
+next couple of weeks, the uh the finance
+ 
+
+ align:start position:0%
+next couple of weeks, the uh the finance
+group at the Sloan School will be
+
+ align:start position:0%
+group at the Sloan School will be
+ 
+
+ align:start position:0%
+group at the Sloan School will be
+putting together some kind of a panel
+
+ align:start position:0%
+putting together some kind of a panel
+ 
+
+ align:start position:0%
+putting together some kind of a panel
+discussion that will focus exactly on
+
+ align:start position:0%
+discussion that will focus exactly on
+ 
+
+ align:start position:0%
+discussion that will focus exactly on
+these issues. So, we'll let you know
+
+ align:start position:0%
+these issues. So, we'll let you know
+ 
+
+ align:start position:0%
+these issues. So, we'll let you know
+when that happens and we'll take on
+
+ align:start position:0%
+when that happens and we'll take on
+ 
+
+ align:start position:0%
+when that happens and we'll take on
+these issues head-on uh in that uh
+
+ align:start position:0%
+these issues head-on uh in that uh
+ 
+
+ align:start position:0%
+these issues head-on uh in that uh
+session. Okay. But it looks like for the
+
+ align:start position:0%
+session. Okay. But it looks like for the
+ 
+
+ align:start position:0%
+session. Okay. But it looks like for the
+moment, at least from the yield curves
+
+ align:start position:0%
+moment, at least from the yield curves
+ 
+
+ align:start position:0%
+moment, at least from the yield curves
+that we uh that we saw um that things
+
+ align:start position:0%
+that we uh that we saw um that things
+ 
+
+ align:start position:0%
+that we uh that we saw um that things
+are actually quieting down. Uh we'll
+
+ align:start position:0%
+are actually quieting down. Uh we'll
+ 
+
+ align:start position:0%
+are actually quieting down. Uh we'll
+we'll see on a day-by-day basis. So, you
+
+ align:start position:0%
+we'll see on a day-by-day basis. So, you
+ 
+
+ align:start position:0%
+we'll see on a day-by-day basis. So, you
+know, this is obviously last week. This
+
+ align:start position:0%
+know, this is obviously last week. This
+ 
+
+ align:start position:0%
+know, this is obviously last week. This
+week we have yields going up a little
+
+ align:start position:0%
+week we have yields going up a little
+ 
+
+ align:start position:0%
+week we have yields going up a little
+bit. So, that suggests that there isn't
+
+ align:start position:0%
+bit. So, that suggests that there isn't
+ 
+
+ align:start position:0%
+bit. So, that suggests that there isn't
+the same kind of pressure, but every day
+
+ align:start position:0%
+the same kind of pressure, but every day
+ 
+
+ align:start position:0%
+the same kind of pressure, but every day
+is, you know, another day and with
+
+ align:start position:0%
+is, you know, another day and with
+ 
+
+ align:start position:0%
+is, you know, another day and with
+another set of revelations. So by
+
+ align:start position:0%
+another set of revelations. So by
+ 
+
+ align:start position:0%
+another set of revelations. So by
+looking at these pieces of information,
+
+ align:start position:0%
+looking at these pieces of information,
+ 
+
+ align:start position:0%
+looking at these pieces of information,
+we can actually glean what the market is
+
+ align:start position:0%
+we can actually glean what the market is
+ 
+
+ align:start position:0%
+we can actually glean what the market is
+thinking. Is it right? Of course not.
+
+ align:start position:0%
+thinking. Is it right? Of course not.
+ 
+
+ align:start position:0%
+thinking. Is it right? Of course not.
+All forecasts are by construction
+
+ align:start position:0%
+All forecasts are by construction
+ 
+
+ align:start position:0%
+All forecasts are by construction
+incorrect to some degree. But it's a
+
+ align:start position:0%
+incorrect to some degree. But it's a
+ 
+
+ align:start position:0%
+incorrect to some degree. But it's a
+window on exactly what's going on in the
+
+ align:start position:0%
+window on exactly what's going on in the
+ 
+
+ align:start position:0%
+window on exactly what's going on in the
+marketplace and what people are
+
+ align:start position:0%
+marketplace and what people are
+ 
+
+ align:start position:0%
+marketplace and what people are
+thinking. Yeah. Right.
+
+ align:start position:0%
+thinking. Yeah. Right.
+ 
+
+ align:start position:0%
+thinking. Yeah. Right.
+Sorry, I missed the connection between
+
+ align:start position:0%
+Sorry, I missed the connection between
+ 
+
+ align:start position:0%
+Sorry, I missed the connection between
+this money market issue and the yield
+
+ align:start position:0%
+this money market issue and the yield
+ 
+
+ align:start position:0%
+this money market issue and the yield
+curve. Are you could you make that
+
+ align:start position:0%
+curve. Are you could you make that
+ 
+
+ align:start position:0%
+curve. Are you could you make that
+connection? I miss
+
+ align:start position:0%
+connection? I miss
+ 
+
+ align:start position:0%
+connection? I miss
+Yeah, sure. So the money market concern
+
+ align:start position:0%
+Yeah, sure. So the money market concern
+ 
+
+ align:start position:0%
+Yeah, sure. So the money market concern
+is that what people thought were safe
+
+ align:start position:0%
+is that what people thought were safe
+ 
+
+ align:start position:0%
+is that what people thought were safe
+apparently is not as safe as people
+
+ align:start position:0%
+apparently is not as safe as people
+ 
+
+ align:start position:0%
+apparently is not as safe as people
+thought. And the reserve fund breaking
+
+ align:start position:0%
+thought. And the reserve fund breaking
+ 
+
+ align:start position:0%
+thought. And the reserve fund breaking
+the buck by the way breaking the buck in
+
+ align:start position:0%
+the buck by the way breaking the buck in
+ 
+
+ align:start position:0%
+the buck by the way breaking the buck in
+that case meant that if you put in a
+
+ align:start position:0%
+that case meant that if you put in a
+ 
+
+ align:start position:0%
+that case meant that if you put in a
+dollar when you withdrew uh as of last
+
+ align:start position:0%
+dollar when you withdrew uh as of last
+ 
+
+ align:start position:0%
+dollar when you withdrew uh as of last
+week you would have withdrawn 97 cents.
+
+ align:start position:0%
+week you would have withdrawn 97 cents.
+ 
+
+ align:start position:0%
+week you would have withdrawn 97 cents.
+you'd lost three cents to the dollar,
+
+ align:start position:0%
+you'd lost three cents to the dollar,
+ 
+
+ align:start position:0%
+you'd lost three cents to the dollar,
+which may not seem like much, but if you
+
+ align:start position:0%
+which may not seem like much, but if you
+ 
+
+ align:start position:0%
+which may not seem like much, but if you
+went to your Bank of America ATM and you
+
+ align:start position:0%
+went to your Bank of America ATM and you
+ 
+
+ align:start position:0%
+went to your Bank of America ATM and you
+did a uh withdrawal and for every dollar
+
+ align:start position:0%
+did a uh withdrawal and for every dollar
+ 
+
+ align:start position:0%
+did a uh withdrawal and for every dollar
+you put in, you'd get 97 cents back,
+
+ align:start position:0%
+you put in, you'd get 97 cents back,
+ 
+
+ align:start position:0%
+you put in, you'd get 97 cents back,
+you'd be pretty ticked off, right? So,
+
+ align:start position:0%
+you'd be pretty ticked off, right? So,
+ 
+
+ align:start position:0%
+you'd be pretty ticked off, right? So,
+you know, it's something that is of
+
+ align:start position:0%
+you know, it's something that is of
+ 
+
+ align:start position:0%
+you know, it's something that is of
+great concern to retail investors.
+
+ align:start position:0%
+great concern to retail investors.
+ 
+
+ align:start position:0%
+great concern to retail investors.
+Anyway, so what happened last week was
+
+ align:start position:0%
+Anyway, so what happened last week was
+ 
+
+ align:start position:0%
+Anyway, so what happened last week was
+that actually the estimate, I think, is
+
+ align:start position:0%
+that actually the estimate, I think, is
+ 
+
+ align:start position:0%
+that actually the estimate, I think, is
+$90 billion. $90 billion of money came
+
+ align:start position:0%
+$90 billion. $90 billion of money came
+ 
+
+ align:start position:0%
+$90 billion. $90 billion of money came
+out of these funds in in a week and were
+
+ align:start position:0%
+out of these funds in in a week and were
+ 
+
+ align:start position:0%
+out of these funds in in a week and were
+put into either cash in the mattress or
+
+ align:start position:0%
+put into either cash in the mattress or
+ 
+
+ align:start position:0%
+put into either cash in the mattress or
+were put into uh treasury securities
+
+ align:start position:0%
+were put into uh treasury securities
+ 
+
+ align:start position:0%
+were put into uh treasury securities
+like the three-month T bills. That's
+
+ align:start position:0%
+like the three-month T bills. That's
+ 
+
+ align:start position:0%
+like the three-month T bills. That's
+what pushed the prices of those T bills
+
+ align:start position:0%
+what pushed the prices of those T bills
+ 
+
+ align:start position:0%
+what pushed the prices of those T bills
+up and therefore depressed the yields.
+
+ align:start position:0%
+up and therefore depressed the yields.
+ 
+
+ align:start position:0%
+up and therefore depressed the yields.
+And now we're back to a somewhat more uh
+
+ align:start position:0%
+And now we're back to a somewhat more uh
+ 
+
+ align:start position:0%
+And now we're back to a somewhat more uh
+reasonable level. I say reasonable
+
+ align:start position:0%
+reasonable level. I say reasonable
+ 
+
+ align:start position:0%
+reasonable level. I say reasonable
+having this kind of a short-term yield
+
+ align:start position:0%
+having this kind of a short-term yield
+ 
+
+ align:start position:0%
+having this kind of a short-term yield
+of 40 basis points by historical
+
+ align:start position:0%
+of 40 basis points by historical
+ 
+
+ align:start position:0%
+of 40 basis points by historical
+standards is still pretty low. So there
+
+ align:start position:0%
+standards is still pretty low. So there
+ 
+
+ align:start position:0%
+standards is still pretty low. So there
+are still many nervous investors out
+
+ align:start position:0%
+are still many nervous investors out
+ 
+
+ align:start position:0%
+are still many nervous investors out
+there uh that are trying to figure out
+
+ align:start position:0%
+there uh that are trying to figure out
+ 
+
+ align:start position:0%
+there uh that are trying to figure out
+what's going on and are waiting for the
+
+ align:start position:0%
+what's going on and are waiting for the
+ 
+
+ align:start position:0%
+what's going on and are waiting for the
+treasury to come up with something. This
+
+ align:start position:0%
+treasury to come up with something. This
+ 
+
+ align:start position:0%
+treasury to come up with something. This
+is another reason why uh chairman
+
+ align:start position:0%
+is another reason why uh chairman
+ 
+
+ align:start position:0%
+is another reason why uh chairman
+Bernani said we have to act quickly
+
+ align:start position:0%
+Bernani said we have to act quickly
+ 
+
+ align:start position:0%
+Bernani said we have to act quickly
+because markets are not going to stand
+
+ align:start position:0%
+because markets are not going to stand
+ 
+
+ align:start position:0%
+because markets are not going to stand
+and wait for the treasury or the Fed to
+
+ align:start position:0%
+and wait for the treasury or the Fed to
+ 
+
+ align:start position:0%
+and wait for the treasury or the Fed to
+do something. uh markets will react and
+
+ align:start position:0%
+do something. uh markets will react and
+ 
+
+ align:start position:0%
+do something. uh markets will react and
+if we wait too long the fear of this
+
+ align:start position:0%
+if we wait too long the fear of this
+ 
+
+ align:start position:0%
+if we wait too long the fear of this
+breaking the buck could actually return
+
+ align:start position:0%
+breaking the buck could actually return
+ 
+
+ align:start position:0%
+breaking the buck could actually return
+and then once you have a mass panic it's
+
+ align:start position:0%
+and then once you have a mass panic it's
+ 
+
+ align:start position:0%
+and then once you have a mass panic it's
+very very hard to stop that. Anybody
+
+ align:start position:0%
+very very hard to stop that. Anybody
+ 
+
+ align:start position:0%
+very very hard to stop that. Anybody
+who's uh uh ever seen a um uh you know
+
+ align:start position:0%
+who's uh uh ever seen a um uh you know
+ 
+
+ align:start position:0%
+who's uh uh ever seen a um uh you know
+one of these old animal kingdom type of
+
+ align:start position:0%
+one of these old animal kingdom type of
+ 
+
+ align:start position:0%
+one of these old animal kingdom type of
+movies about uh stampede, if you've got
+
+ align:start position:0%
+movies about uh stampede, if you've got
+ 
+
+ align:start position:0%
+movies about uh stampede, if you've got
+you know water buffalo stampeding, it's
+
+ align:start position:0%
+you know water buffalo stampeding, it's
+ 
+
+ align:start position:0%
+you know water buffalo stampeding, it's
+pretty hard to try to just say, "Oh,
+
+ align:start position:0%
+pretty hard to try to just say, "Oh,
+ 
+
+ align:start position:0%
+pretty hard to try to just say, "Oh,
+calm down. Stop it." you know, don't uh
+
+ align:start position:0%
+calm down. Stop it." you know, don't uh
+ 
+
+ align:start position:0%
+calm down. Stop it." you know, don't uh
+you know, slow down. You know, you you
+
+ align:start position:0%
+you know, slow down. You know, you you
+ 
+
+ align:start position:0%
+you know, slow down. You know, you you
+can't easily do that once it begins. So,
+
+ align:start position:0%
+can't easily do that once it begins. So,
+ 
+
+ align:start position:0%
+can't easily do that once it begins. So,
+you've got to stop it before it actually
+
+ align:start position:0%
+you've got to stop it before it actually
+ 
+
+ align:start position:0%
+you've got to stop it before it actually
+gets to that critical point and that's
+
+ align:start position:0%
+gets to that critical point and that's
+ 
+
+ align:start position:0%
+gets to that critical point and that's
+exactly what uh the government is trying
+
+ align:start position:0%
+exactly what uh the government is trying
+ 
+
+ align:start position:0%
+exactly what uh the government is trying
+to do. Yes.
+
+ align:start position:0%
+to do. Yes.
+ 
+
+ align:start position:0%
+to do. Yes.
+When you say that if interpret this like
+
+ align:start position:0%
+When you say that if interpret this like
+ 
+
+ align:start position:0%
+When you say that if interpret this like
+the prices went down so now there's less
+
+ align:start position:0%
+the prices went down so now there's less
+ 
+
+ align:start position:0%
+the prices went down so now there's less
+demand so it means people are more
+
+ align:start position:0%
+demand so it means people are more
+ 
+
+ align:start position:0%
+demand so it means people are more
+relaxed.
+
+ align:start position:0%
+relaxed.
+ 
+
+ align:start position:0%
+relaxed.
+Yeah. What if you say like if the
+
+ align:start position:0%
+Yeah. What if you say like if the
+ 
+
+ align:start position:0%
+Yeah. What if you say like if the
+interest rate went up it means they are
+
+ align:start position:0%
+interest rate went up it means they are
+ 
+
+ align:start position:0%
+interest rate went up it means they are
+considering the treasury bills to be
+
+ align:start position:0%
+considering the treasury bills to be
+ 
+
+ align:start position:0%
+considering the treasury bills to be
+more risky or riskier?
+
+ align:start position:0%
+more risky or riskier?
+ 
+
+ align:start position:0%
+more risky or riskier?
+Well um remember that treasury bills
+
+ align:start position:0%
+Well um remember that treasury bills
+ 
+
+ align:start position:0%
+Well um remember that treasury bills
+don't have any uh default risk uh at
+
+ align:start position:0%
+don't have any uh default risk uh at
+ 
+
+ align:start position:0%
+don't have any uh default risk uh at
+least as far as we know uh we have to be
+
+ align:start position:0%
+least as far as we know uh we have to be
+ 
+
+ align:start position:0%
+least as far as we know uh we have to be
+careful about staying stating all these
+
+ align:start position:0%
+careful about staying stating all these
+ 
+
+ align:start position:0%
+careful about staying stating all these
+unprecedented things have happened. The
+
+ align:start position:0%
+unprecedented things have happened. The
+ 
+
+ align:start position:0%
+unprecedented things have happened. The
+reason that treasury bills don't have
+
+ align:start position:0%
+reason that treasury bills don't have
+ 
+
+ align:start position:0%
+reason that treasury bills don't have
+any default risk is because what the
+
+ align:start position:0%
+any default risk is because what the
+ 
+
+ align:start position:0%
+any default risk is because what the
+Treasury security is is an IOU from the
+
+ align:start position:0%
+Treasury security is is an IOU from the
+ 
+
+ align:start position:0%
+Treasury security is is an IOU from the
+government that says I owe you a certain
+
+ align:start position:0%
+government that says I owe you a certain
+ 
+
+ align:start position:0%
+government that says I owe you a certain
+number of US dollars. And because the
+
+ align:start position:0%
+number of US dollars. And because the
+ 
+
+ align:start position:0%
+number of US dollars. And because the
+Treasury owns the printing press, they
+
+ align:start position:0%
+Treasury owns the printing press, they
+ 
+
+ align:start position:0%
+Treasury owns the printing press, they
+can always print out more dollars to
+
+ align:start position:0%
+can always print out more dollars to
+ 
+
+ align:start position:0%
+can always print out more dollars to
+give it to you as long as you're willing
+
+ align:start position:0%
+give it to you as long as you're willing
+ 
+
+ align:start position:0%
+give it to you as long as you're willing
+to take it. Okay? And at least from this
+
+ align:start position:0%
+to take it. Okay? And at least from this
+ 
+
+ align:start position:0%
+to take it. Okay? And at least from this
+graph, it seems like a lot of people are
+
+ align:start position:0%
+graph, it seems like a lot of people are
+ 
+
+ align:start position:0%
+graph, it seems like a lot of people are
+willing to take it. They really want
+
+ align:start position:0%
+willing to take it. They really want
+ 
+
+ align:start position:0%
+willing to take it. They really want
+Treasury bills right now and they're
+
+ align:start position:0%
+Treasury bills right now and they're
+ 
+
+ align:start position:0%
+Treasury bills right now and they're
+happy with that. Maybe they're not happy
+
+ align:start position:0%
+happy with that. Maybe they're not happy
+ 
+
+ align:start position:0%
+happy with that. Maybe they're not happy
+with it, but that's the sort of the less
+
+ align:start position:0%
+with it, but that's the sort of the less
+ 
+
+ align:start position:0%
+with it, but that's the sort of the less
+the the the smallest of all the evils
+
+ align:start position:0%
+the the the smallest of all the evils
+ 
+
+ align:start position:0%
+the the the smallest of all the evils
+that they can think of in terms of
+
+ align:start position:0%
+that they can think of in terms of
+ 
+
+ align:start position:0%
+that they can think of in terms of
+putting their money.
+
+ align:start position:0%
+putting their money.
+ 
+
+ align:start position:0%
+putting their money.
+So the increasing the yield in treasury
+
+ align:start position:0%
+So the increasing the yield in treasury
+ 
+
+ align:start position:0%
+So the increasing the yield in treasury
+uh in treasury bonds,
+
+ align:start position:0%
+uh in treasury bonds,
+ 
+
+ align:start position:0%
+uh in treasury bonds,
+yeah,
+
+ align:start position:0%
+yeah,
+ 
+
+ align:start position:0%
+yeah,
+do not mean an increase in the default.
+
+ align:start position:0%
+do not mean an increase in the default.
+ 
+
+ align:start position:0%
+do not mean an increase in the default.
+We we hope not. I mean, you know, I
+
+ align:start position:0%
+We we hope not. I mean, you know, I
+ 
+
+ align:start position:0%
+We we hope not. I mean, you know, I
+guess it could be possible that people
+
+ align:start position:0%
+guess it could be possible that people
+ 
+
+ align:start position:0%
+guess it could be possible that people
+are betting that the United States is
+
+ align:start position:0%
+are betting that the United States is
+ 
+
+ align:start position:0%
+are betting that the United States is
+going to default in 30 years. But uh my
+
+ align:start position:0%
+going to default in 30 years. But uh my
+ 
+
+ align:start position:0%
+going to default in 30 years. But uh my
+sense is that what's more likely given
+
+ align:start position:0%
+sense is that what's more likely given
+ 
+
+ align:start position:0%
+sense is that what's more likely given
+that these are default-free in in the
+
+ align:start position:0%
+that these are default-free in in the
+ 
+
+ align:start position:0%
+that these are default-free in in the
+sense that they're nominal bonds. So
+
+ align:start position:0%
+sense that they're nominal bonds. So
+ 
+
+ align:start position:0%
+sense that they're nominal bonds. So
+these bonds are going to be paid off in
+
+ align:start position:0%
+these bonds are going to be paid off in
+ 
+
+ align:start position:0%
+these bonds are going to be paid off in
+the little certificates called US
+
+ align:start position:0%
+the little certificates called US
+ 
+
+ align:start position:0%
+the little certificates called US
+dollars that the printing presses can
+
+ align:start position:0%
+dollars that the printing presses can
+ 
+
+ align:start position:0%
+dollars that the printing presses can
+always come up with. There's no risk
+
+ align:start position:0%
+always come up with. There's no risk
+ 
+
+ align:start position:0%
+always come up with. There's no risk
+that they can't print up more dollars.
+
+ align:start position:0%
+that they can't print up more dollars.
+ 
+
+ align:start position:0%
+that they can't print up more dollars.
+The risk is that a dollar 30 years from
+
+ align:start position:0%
+The risk is that a dollar 30 years from
+ 
+
+ align:start position:0%
+The risk is that a dollar 30 years from
+now isn't going to be worth as much as
+
+ align:start position:0%
+now isn't going to be worth as much as
+ 
+
+ align:start position:0%
+now isn't going to be worth as much as
+we thought it was going to be because of
+
+ align:start position:0%
+we thought it was going to be because of
+ 
+
+ align:start position:0%
+we thought it was going to be because of
+inflationary expectations. So as of
+
+ align:start position:0%
+inflationary expectations. So as of
+ 
+
+ align:start position:0%
+inflationary expectations. So as of
+today, that 30-year yield is not 4%,
+
+ align:start position:0%
+today, that 30-year yield is not 4%,
+ 
+
+ align:start position:0%
+today, that 30-year yield is not 4%,
+it's 4.37. and the.37
+
+ align:start position:0%
+it's 4.37. and the.37
+ 
+
+ align:start position:0%
+it's 4.37. and the.37
+one could attribute to a a an
+
+ align:start position:0%
+one could attribute to a a an
+ 
+
+ align:start position:0%
+one could attribute to a a an
+inflationary expectation by the
+
+ align:start position:0%
+inflationary expectation by the
+ 
+
+ align:start position:0%
+inflationary expectation by the
+marketplace.
+
+ align:start position:0%
+marketplace.
+ 
+
+ align:start position:0%
+marketplace.
+Do you think that the short-term change
+
+ align:start position:0%
+Do you think that the short-term change
+ 
+
+ align:start position:0%
+Do you think that the short-term change
+in the yield has anything to do with the
+
+ align:start position:0%
+in the yield has anything to do with the
+ 
+
+ align:start position:0%
+in the yield has anything to do with the
+recent devaluation of the dollar against
+
+ align:start position:0%
+recent devaluation of the dollar against
+ 
+
+ align:start position:0%
+recent devaluation of the dollar against
+foreign currencies?
+
+ align:start position:0%
+foreign currencies?
+ 
+
+ align:start position:0%
+foreign currencies?
+Uh, you know, it could be uh that
+
+ align:start position:0%
+Uh, you know, it could be uh that
+ 
+
+ align:start position:0%
+Uh, you know, it could be uh that
+because of that devaluation, dollars are
+
+ align:start position:0%
+because of that devaluation, dollars are
+ 
+
+ align:start position:0%
+because of that devaluation, dollars are
+cheaper and people are putting more
+
+ align:start position:0%
+cheaper and people are putting more
+ 
+
+ align:start position:0%
+cheaper and people are putting more
+money, you know, into US securities.
+
+ align:start position:0%
+money, you know, into US securities.
+ 
+
+ align:start position:0%
+money, you know, into US securities.
+That's also a possibility. But another
+
+ align:start position:0%
+That's also a possibility. But another
+ 
+
+ align:start position:0%
+That's also a possibility. But another
+way of putting that is that foreign
+
+ align:start position:0%
+way of putting that is that foreign
+ 
+
+ align:start position:0%
+way of putting that is that foreign
+investors are now finding treasuries
+
+ align:start position:0%
+investors are now finding treasuries
+ 
+
+ align:start position:0%
+investors are now finding treasuries
+more attractive for whatever reason. So
+
+ align:start position:0%
+more attractive for whatever reason. So
+ 
+
+ align:start position:0%
+more attractive for whatever reason. So
+yes, that's also part of that supply and
+
+ align:start position:0%
+yes, that's also part of that supply and
+ 
+
+ align:start position:0%
+yes, that's also part of that supply and
+demand story.
+
+ align:start position:0%
+demand story.
+ 
+
+ align:start position:0%
+demand story.
+Okay, last question. Yeah.
+
+ align:start position:0%
+Okay, last question. Yeah.
+ 
+
+ align:start position:0%
+Okay, last question. Yeah.
+Uh historically, what is a reasonable
+
+ align:start position:0%
+Uh historically, what is a reasonable
+ 
+
+ align:start position:0%
+Uh historically, what is a reasonable
+year? You mentioned that before like all
+
+ align:start position:0%
+year? You mentioned that before like all
+ 
+
+ align:start position:0%
+year? You mentioned that before like all
+this.
+
+ align:start position:0%
+this.
+ 
+
+ align:start position:0%
+this.
+Well, uh I'm glad you asked that
+
+ align:start position:0%
+Well, uh I'm glad you asked that
+ 
+
+ align:start position:0%
+Well, uh I'm glad you asked that
+question because we have a graph.
+
+ align:start position:0%
+question because we have a graph.
+ 
+
+ align:start position:0%
+question because we have a graph.
+These are the historical yields of the
+
+ align:start position:0%
+These are the historical yields of the
+ 
+
+ align:start position:0%
+These are the historical yields of the
+3month, 6 month, 1 year, 2 year, 5 year,
+
+ align:start position:0%
+3month, 6 month, 1 year, 2 year, 5 year,
+ 
+
+ align:start position:0%
+3month, 6 month, 1 year, 2 year, 5 year,
+10 year, 30-year from uh 1962
+
+ align:start position:0%
+10 year, 30-year from uh 1962
+ 
+
+ align:start position:0%
+10 year, 30-year from uh 1962
+to uh 19 or 200 and uh I think it's
+
+ align:start position:0%
+to uh 19 or 200 and uh I think it's
+ 
+
+ align:start position:0%
+to uh 19 or 200 and uh I think it's
+2004.
+
+ align:start position:0%
+2004.
+ 
+
+ align:start position:0%
+2004.
+And it depends on what flavor you're
+
+ align:start position:0%
+And it depends on what flavor you're
+ 
+
+ align:start position:0%
+And it depends on what flavor you're
+looking at. And it's I kind of hard to
+
+ align:start position:0%
+looking at. And it's I kind of hard to
+ 
+
+ align:start position:0%
+looking at. And it's I kind of hard to
+read this graph because of the colors,
+
+ align:start position:0%
+read this graph because of the colors,
+ 
+
+ align:start position:0%
+read this graph because of the colors,
+but if you look at the the dark blue
+
+ align:start position:0%
+but if you look at the the dark blue
+ 
+
+ align:start position:0%
+but if you look at the the dark blue
+line, um they actually all move together
+
+ align:start position:0%
+line, um they actually all move together
+ 
+
+ align:start position:0%
+line, um they actually all move together
+pretty much. But at one point that
+
+ align:start position:0%
+pretty much. But at one point that
+ 
+
+ align:start position:0%
+pretty much. But at one point that
+short-term yield was 4%.
+
+ align:start position:0%
+short-term yield was 4%.
+ 
+
+ align:start position:0%
+short-term yield was 4%.
+4% for a 3-month Treasury bill. Now,
+
+ align:start position:0%
+4% for a 3-month Treasury bill. Now,
+ 
+
+ align:start position:0%
+4% for a 3-month Treasury bill. Now,
+then these are all annualized, remember?
+
+ align:start position:0%
+then these are all annualized, remember?
+ 
+
+ align:start position:0%
+then these are all annualized, remember?
+So 4% doesn't mean 4% over 3 months. It
+
+ align:start position:0%
+So 4% doesn't mean 4% over 3 months. It
+ 
+
+ align:start position:0%
+So 4% doesn't mean 4% over 3 months. It
+means 4% on an annualized basis, which
+
+ align:start position:0%
+means 4% on an annualized basis, which
+ 
+
+ align:start position:0%
+means 4% on an annualized basis, which
+is why 41 basis points, that's an
+
+ align:start position:0%
+is why 41 basis points, that's an
+ 
+
+ align:start position:0%
+is why 41 basis points, that's an
+annualized yield for a 3-month loan,
+
+ align:start position:0%
+annualized yield for a 3-month loan,
+ 
+
+ align:start position:0%
+annualized yield for a 3-month loan,
+just seems ridiculously small by
+
+ align:start position:0%
+just seems ridiculously small by
+ 
+
+ align:start position:0%
+just seems ridiculously small by
+historical standards.
+
+ align:start position:0%
+historical standards.
+ 
+
+ align:start position:0%
+historical standards.
+But when people are scared about not
+
+ align:start position:0%
+But when people are scared about not
+ 
+
+ align:start position:0%
+But when people are scared about not
+getting paid, that kind of fear, that
+
+ align:start position:0%
+getting paid, that kind of fear, that
+ 
+
+ align:start position:0%
+getting paid, that kind of fear, that
+psychological pressure can be
+
+ align:start position:0%
+psychological pressure can be
+ 
+
+ align:start position:0%
+psychological pressure can be
+overwhelming. And do you believe in
+
+ align:start position:0%
+overwhelming. And do you believe in
+ 
+
+ align:start position:0%
+overwhelming. And do you believe in
+these prices? Does it make sense? Well,
+
+ align:start position:0%
+these prices? Does it make sense? Well,
+ 
+
+ align:start position:0%
+these prices? Does it make sense? Well,
+that I'm hoping to get you not to ask
+
+ align:start position:0%
+that I'm hoping to get you not to ask
+ 
+
+ align:start position:0%
+that I'm hoping to get you not to ask
+the question in that way, but rather to
+
+ align:start position:0%
+the question in that way, but rather to
+ 
+
+ align:start position:0%
+the question in that way, but rather to
+ask the question given market prices and
+
+ align:start position:0%
+ask the question given market prices and
+ 
+
+ align:start position:0%
+ask the question given market prices and
+what I know about it, what can I
+
+ align:start position:0%
+what I know about it, what can I
+ 
+
+ align:start position:0%
+what I know about it, what can I
+interpret from what's going on and what
+
+ align:start position:0%
+interpret from what's going on and what
+ 
+
+ align:start position:0%
+interpret from what's going on and what
+how does that affect me in terms of the
+
+ align:start position:0%
+how does that affect me in terms of the
+ 
+
+ align:start position:0%
+how does that affect me in terms of the
+financial decisions that I want to make?
+
+ align:start position:0%
+financial decisions that I want to make?
+ 
+
+ align:start position:0%
+financial decisions that I want to make?
+So if you are thinking about pricing
+
+ align:start position:0%
+So if you are thinking about pricing
+ 
+
+ align:start position:0%
+So if you are thinking about pricing
+other securities based upon these kinds
+
+ align:start position:0%
+other securities based upon these kinds
+ 
+
+ align:start position:0%
+other securities based upon these kinds
+of numbers, you need to ask yourself
+
+ align:start position:0%
+of numbers, you need to ask yourself
+ 
+
+ align:start position:0%
+of numbers, you need to ask yourself
+whether you believe the numbers make
+
+ align:start position:0%
+whether you believe the numbers make
+ 
+
+ align:start position:0%
+whether you believe the numbers make
+sense or are they just completely out of
+
+ align:start position:0%
+sense or are they just completely out of
+ 
+
+ align:start position:0%
+sense or are they just completely out of
+whack. And the only way to do that is to
+
+ align:start position:0%
+whack. And the only way to do that is to
+ 
+
+ align:start position:0%
+whack. And the only way to do that is to
+understand what the basis is for these
+
+ align:start position:0%
+understand what the basis is for these
+ 
+
+ align:start position:0%
+understand what the basis is for these
+numbers. So that's where we're going
+
+ align:start position:0%
+numbers. So that's where we're going
+ 
+
+ align:start position:0%
+numbers. So that's where we're going
+next in trying to understand how to
+
+ align:start position:0%
+next in trying to understand how to
+ 
+
+ align:start position:0%
+next in trying to understand how to
+measure the various different
+
+ align:start position:0%
+measure the various different
+ 
+
+ align:start position:0%
+measure the various different
+characteristics of these numbers to get
+
+ align:start position:0%
+characteristics of these numbers to get
+ 
+
+ align:start position:0%
+characteristics of these numbers to get
+a sense of what's reasonable, what's
+
+ align:start position:0%
+a sense of what's reasonable, what's
+ 
+
+ align:start position:0%
+a sense of what's reasonable, what's
+not. Question
+
+ align:start position:0%
+not. Question
+ 
+
+ align:start position:0%
+not. Question
+one on Treasury bills last week. Um, is
+
+ align:start position:0%
+one on Treasury bills last week. Um, is
+ 
+
+ align:start position:0%
+one on Treasury bills last week. Um, is
+that really individual people buying
+
+ align:start position:0%
+that really individual people buying
+ 
+
+ align:start position:0%
+that really individual people buying
+equity bills or is it more hedge funds
+
+ align:start position:0%
+equity bills or is it more hedge funds
+ 
+
+ align:start position:0%
+equity bills or is it more hedge funds
+and that sort of thing that are like
+
+ align:start position:0%
+and that sort of thing that are like
+ 
+
+ align:start position:0%
+and that sort of thing that are like
+systematically hedging the risk of some
+
+ align:start position:0%
+systematically hedging the risk of some
+ 
+
+ align:start position:0%
+systematically hedging the risk of some
+other securities that have the
+
+ align:start position:0%
+other securities that have the
+ 
+
+ align:start position:0%
+other securities that have the
+Well, you know, obviously it's very
+
+ align:start position:0%
+Well, you know, obviously it's very
+ 
+
+ align:start position:0%
+Well, you know, obviously it's very
+difficult to tell because we don't see
+
+ align:start position:0%
+difficult to tell because we don't see
+ 
+
+ align:start position:0%
+difficult to tell because we don't see
+who's making the purchases and sales.
+
+ align:start position:0%
+who's making the purchases and sales.
+ 
+
+ align:start position:0%
+who's making the purchases and sales.
+But we can tell from certain mutual
+
+ align:start position:0%
+But we can tell from certain mutual
+ 
+
+ align:start position:0%
+But we can tell from certain mutual
+funds and other money market flows that
+
+ align:start position:0%
+funds and other money market flows that
+ 
+
+ align:start position:0%
+funds and other money market flows that
+it seems like most of the flows last
+
+ align:start position:0%
+it seems like most of the flows last
+ 
+
+ align:start position:0%
+it seems like most of the flows last
+week came not from hedge funds, but
+
+ align:start position:0%
+week came not from hedge funds, but
+ 
+
+ align:start position:0%
+week came not from hedge funds, but
+rather from retail investors that were
+
+ align:start position:0%
+rather from retail investors that were
+ 
+
+ align:start position:0%
+rather from retail investors that were
+taking their money out of these money
+
+ align:start position:0%
+taking their money out of these money
+ 
+
+ align:start position:0%
+taking their money out of these money
+market accounts and then putting them
+
+ align:start position:0%
+market accounts and then putting them
+ 
+
+ align:start position:0%
+market accounts and then putting them
+into certain mutual funds that buy only
+
+ align:start position:0%
+into certain mutual funds that buy only
+ 
+
+ align:start position:0%
+into certain mutual funds that buy only
+treasury securities as well as uh
+
+ align:start position:0%
+treasury securities as well as uh
+ 
+
+ align:start position:0%
+treasury securities as well as uh
+treasury securities directly. You know,
+
+ align:start position:0%
+treasury securities directly. You know,
+ 
+
+ align:start position:0%
+treasury securities directly. You know,
+all of you can actually purchase
+
+ align:start position:0%
+all of you can actually purchase
+ 
+
+ align:start position:0%
+all of you can actually purchase
+treasury securities directly. There is a
+
+ align:start position:0%
+treasury securities directly. There is a
+ 
+
+ align:start position:0%
+treasury securities directly. There is a
+website called treasurydirect.gov
+
+ align:start position:0%
+website called treasurydirect.gov
+ 
+
+ align:start position:0%
+website called treasurydirect.gov
+and you can give me your credit card and
+
+ align:start position:0%
+and you can give me your credit card and
+ 
+
+ align:start position:0%
+and you can give me your credit card and
+register as a user and actually
+
+ align:start position:0%
+register as a user and actually
+ 
+
+ align:start position:0%
+register as a user and actually
+participate in treasury auctions and buy
+
+ align:start position:0%
+participate in treasury auctions and buy
+ 
+
+ align:start position:0%
+participate in treasury auctions and buy
+treasury securities. So it was a
+
+ align:start position:0%
+treasury securities. So it was a
+ 
+
+ align:start position:0%
+treasury securities. So it was a
+combination of those, but it really
+
+ align:start position:0%
+combination of those, but it really
+ 
+
+ align:start position:0%
+combination of those, but it really
+seemed like it was the retail sector,
+
+ align:start position:0%
+seemed like it was the retail sector,
+ 
+
+ align:start position:0%
+seemed like it was the retail sector,
+not institutions, not sophisticated
+
+ align:start position:0%
+not institutions, not sophisticated
+ 
+
+ align:start position:0%
+not institutions, not sophisticated
+hedge funds that were trying to do some
+
+ align:start position:0%
+hedge funds that were trying to do some
+ 
+
+ align:start position:0%
+hedge funds that were trying to do some
+kind of complex arbitrage. It was just
+
+ align:start position:0%
+kind of complex arbitrage. It was just
+ 
+
+ align:start position:0%
+kind of complex arbitrage. It was just
+investors saying, "I'm really scared. I
+
+ align:start position:0%
+investors saying, "I'm really scared. I
+ 
+
+ align:start position:0%
+investors saying, "I'm really scared. I
+want to put my money into something
+
+ align:start position:0%
+want to put my money into something
+ 
+
+ align:start position:0%
+want to put my money into something
+that's that's real and that will will be
+
+ align:start position:0%
+that's that's real and that will will be
+ 
+
+ align:start position:0%
+that's that's real and that will will be
+there. And so short-term treasury seemed
+
+ align:start position:0%
+there. And so short-term treasury seemed
+ 
+
+ align:start position:0%
+there. And so short-term treasury seemed
+like an answer. And as we saw from last
+
+ align:start position:0%
+like an answer. And as we saw from last
+ 
+
+ align:start position:0%
+like an answer. And as we saw from last
+week, gold was the other answer. It it's
+
+ align:start position:0%
+week, gold was the other answer. It it's
+ 
+
+ align:start position:0%
+week, gold was the other answer. It it's
+not an answer that I would propose for
+
+ align:start position:0%
+not an answer that I would propose for
+ 
+
+ align:start position:0%
+not an answer that I would propose for
+the typical investor because gold prices
+
+ align:start position:0%
+the typical investor because gold prices
+ 
+
+ align:start position:0%
+the typical investor because gold prices
+are quite volatile. And uh so you have
+
+ align:start position:0%
+are quite volatile. And uh so you have
+ 
+
+ align:start position:0%
+are quite volatile. And uh so you have
+to be very careful uh when you make an
+
+ align:start position:0%
+to be very careful uh when you make an
+ 
+
+ align:start position:0%
+to be very careful uh when you make an
+investment in that security or in that
+
+ align:start position:0%
+investment in that security or in that
+ 
+
+ align:start position:0%
+investment in that security or in that
+in that particular asset. But it is
+
+ align:start position:0%
+in that particular asset. But it is
+ 
+
+ align:start position:0%
+in that particular asset. But it is
+something that reflects the state of
+
+ align:start position:0%
+something that reflects the state of
+ 
+
+ align:start position:0%
+something that reflects the state of
+panic of the marketplace. And and by the
+
+ align:start position:0%
+panic of the marketplace. And and by the
+ 
+
+ align:start position:0%
+panic of the marketplace. And and by the
+way, I'm telling you something that you
+
+ align:start position:0%
+way, I'm telling you something that you
+ 
+
+ align:start position:0%
+way, I'm telling you something that you
+probably already know in the sense that
+
+ align:start position:0%
+probably already know in the sense that
+ 
+
+ align:start position:0%
+probably already know in the sense that
+my guess is that deep down inside all of
+
+ align:start position:0%
+my guess is that deep down inside all of
+ 
+
+ align:start position:0%
+my guess is that deep down inside all of
+you are feeling stressed out, right? I
+
+ align:start position:0%
+you are feeling stressed out, right? I
+ 
+
+ align:start position:0%
+you are feeling stressed out, right? I
+mean, you're probably stressed out about
+
+ align:start position:0%
+mean, you're probably stressed out about
+ 
+
+ align:start position:0%
+mean, you're probably stressed out about
+things like what does this mean for the
+
+ align:start position:0%
+things like what does this mean for the
+ 
+
+ align:start position:0%
+things like what does this mean for the
+job market uh for uh you know, career
+
+ align:start position:0%
+job market uh for uh you know, career
+ 
+
+ align:start position:0%
+job market uh for uh you know, career
+prospects and so on.
+
+ align:start position:0%
+prospects and so on.
+ 
+
+ align:start position:0%
+prospects and so on.
+I I would urge you all to uh take a deep
+
+ align:start position:0%
+I I would urge you all to uh take a deep
+ 
+
+ align:start position:0%
+I I would urge you all to uh take a deep
+breath and not not get uh panicked about
+
+ align:start position:0%
+breath and not not get uh panicked about
+ 
+
+ align:start position:0%
+breath and not not get uh panicked about
+that because as I said this is the kind
+
+ align:start position:0%
+that because as I said this is the kind
+ 
+
+ align:start position:0%
+that because as I said this is the kind
+of of dislocation that while very
+
+ align:start position:0%
+of of dislocation that while very
+ 
+
+ align:start position:0%
+of of dislocation that while very
+traumatic for market participants today
+
+ align:start position:0%
+traumatic for market participants today
+ 
+
+ align:start position:0%
+traumatic for market participants today
+and for those on the losing end there
+
+ align:start position:0%
+and for those on the losing end there
+ 
+
+ align:start position:0%
+and for those on the losing end there
+are as many opportunities created uh as
+
+ align:start position:0%
+are as many opportunities created uh as
+ 
+
+ align:start position:0%
+are as many opportunities created uh as
+there are uh taken away. And so my guess
+
+ align:start position:0%
+there are uh taken away. And so my guess
+ 
+
+ align:start position:0%
+there are uh taken away. And so my guess
+is that in a year's time uh the job
+
+ align:start position:0%
+is that in a year's time uh the job
+ 
+
+ align:start position:0%
+is that in a year's time uh the job
+market is going to look extraordinarily
+
+ align:start position:0%
+market is going to look extraordinarily
+ 
+
+ align:start position:0%
+market is going to look extraordinarily
+attractive particularly for those
+
+ align:start position:0%
+attractive particularly for those
+ 
+
+ align:start position:0%
+attractive particularly for those
+individuals that are trained in the uh
+
+ align:start position:0%
+individuals that are trained in the uh
+ 
+
+ align:start position:0%
+individuals that are trained in the uh
+the science and art of financial
+
+ align:start position:0%
+the science and art of financial
+ 
+
+ align:start position:0%
+the science and art of financial
+analysis. So you're all going to be very
+
+ align:start position:0%
+analysis. So you're all going to be very
+ 
+
+ align:start position:0%
+analysis. So you're all going to be very
+well equipped uh for that even though
+
+ align:start position:0%
+well equipped uh for that even though
+ 
+
+ align:start position:0%
+well equipped uh for that even though
+you may not feel that way right now
+
+ align:start position:0%
+you may not feel that way right now
+ 
+
+ align:start position:0%
+you may not feel that way right now
+because of what's going on in the
+
+ align:start position:0%
+because of what's going on in the
+ 
+
+ align:start position:0%
+because of what's going on in the
+marketplace. So uh I wouldn't panic
+
+ align:start position:0%
+marketplace. So uh I wouldn't panic
+ 
+
+ align:start position:0%
+marketplace. So uh I wouldn't panic
+certainly. Um and by the way you can see
+
+ align:start position:0%
+certainly. Um and by the way you can see
+ 
+
+ align:start position:0%
+certainly. Um and by the way you can see
+the opportunities that are already being
+
+ align:start position:0%
+the opportunities that are already being
+ 
+
+ align:start position:0%
+the opportunities that are already being
+created. You know, Warren Buffett just
+
+ align:start position:0%
+created. You know, Warren Buffett just
+ 
+
+ align:start position:0%
+created. You know, Warren Buffett just
+spent5 billion dollars uh purchasing a
+
+ align:start position:0%
+spent5 billion dollars uh purchasing a
+ 
+
+ align:start position:0%
+spent5 billion dollars uh purchasing a
+stake in Goldman Sachs. And we're going
+
+ align:start position:0%
+stake in Goldman Sachs. And we're going
+ 
+
+ align:start position:0%
+stake in Goldman Sachs. And we're going
+to talk about that in a couple of
+
+ align:start position:0%
+to talk about that in a couple of
+ 
+
+ align:start position:0%
+to talk about that in a couple of
+lectures when we do common stock because
+
+ align:start position:0%
+lectures when we do common stock because
+ 
+
+ align:start position:0%
+lectures when we do common stock because
+I want to use it as an example of
+
+ align:start position:0%
+I want to use it as an example of
+ 
+
+ align:start position:0%
+I want to use it as an example of
+getting a good deal uh you know in in
+
+ align:start position:0%
+getting a good deal uh you know in in
+ 
+
+ align:start position:0%
+getting a good deal uh you know in in
+markets. I mean, first of all, Warren
+
+ align:start position:0%
+markets. I mean, first of all, Warren
+ 
+
+ align:start position:0%
+markets. I mean, first of all, Warren
+Buffett given as the the success he's
+
+ align:start position:0%
+Buffett given as the the success he's
+ 
+
+ align:start position:0%
+Buffett given as the the success he's
+enjoyed as an investor, you know that
+
+ align:start position:0%
+enjoyed as an investor, you know that
+ 
+
+ align:start position:0%
+enjoyed as an investor, you know that
+when he plunks down five million5
+
+ align:start position:0%
+when he plunks down five million5
+ 
+
+ align:start position:0%
+when he plunks down five million5
+billion dollars in cash, he's probably
+
+ align:start position:0%
+billion dollars in cash, he's probably
+ 
+
+ align:start position:0%
+billion dollars in cash, he's probably
+doing it for a good reason, not out of
+
+ align:start position:0%
+doing it for a good reason, not out of
+ 
+
+ align:start position:0%
+doing it for a good reason, not out of
+charity. Um, and by the way, Goldman
+
+ align:start position:0%
+charity. Um, and by the way, Goldman
+ 
+
+ align:start position:0%
+charity. Um, and by the way, Goldman
+raised another $5 billion uh from
+
+ align:start position:0%
+raised another $5 billion uh from
+ 
+
+ align:start position:0%
+raised another $5 billion uh from
+additional uh rights issues. That's $10
+
+ align:start position:0%
+additional uh rights issues. That's $10
+ 
+
+ align:start position:0%
+additional uh rights issues. That's $10
+billion of capital that they raised
+
+ align:start position:0%
+billion of capital that they raised
+ 
+
+ align:start position:0%
+billion of capital that they raised
+relatively quickly. Uh, also Namura is
+
+ align:start position:0%
+relatively quickly. Uh, also Namura is
+ 
+
+ align:start position:0%
+relatively quickly. Uh, also Namura is
+in the negotiations to purchase certain
+
+ align:start position:0%
+in the negotiations to purchase certain
+ 
+
+ align:start position:0%
+in the negotiations to purchase certain
+assets of Lehman Brothers. Lehman has a
+
+ align:start position:0%
+assets of Lehman Brothers. Lehman has a
+ 
+
+ align:start position:0%
+assets of Lehman Brothers. Lehman has a
+terrific franchise and has some very
+
+ align:start position:0%
+terrific franchise and has some very
+ 
+
+ align:start position:0%
+terrific franchise and has some very
+significant operations in Asia as well
+
+ align:start position:0%
+significant operations in Asia as well
+ 
+
+ align:start position:0%
+significant operations in Asia as well
+as in the US and it's a very smart move
+
+ align:start position:0%
+as in the US and it's a very smart move
+ 
+
+ align:start position:0%
+as in the US and it's a very smart move
+on Namura's part to take advantage of
+
+ align:start position:0%
+on Namura's part to take advantage of
+ 
+
+ align:start position:0%
+on Namura's part to take advantage of
+that. So these are the kind of
+
+ align:start position:0%
+that. So these are the kind of
+ 
+
+ align:start position:0%
+that. So these are the kind of
+opportunities I'm talking about. And
+
+ align:start position:0%
+opportunities I'm talking about. And
+ 
+
+ align:start position:0%
+opportunities I'm talking about. And
+when Namora buys Leman, they're going to
+
+ align:start position:0%
+when Namora buys Leman, they're going to
+ 
+
+ align:start position:0%
+when Namora buys Leman, they're going to
+have to hire people in order to run the
+
+ align:start position:0%
+have to hire people in order to run the
+ 
+
+ align:start position:0%
+have to hire people in order to run the
+operations because you can bet that the
+
+ align:start position:0%
+operations because you can bet that the
+ 
+
+ align:start position:0%
+operations because you can bet that the
+whole dislocation ended up shaking loose
+
+ align:start position:0%
+whole dislocation ended up shaking loose
+ 
+
+ align:start position:0%
+whole dislocation ended up shaking loose
+a number of very talented uh um
+
+ align:start position:0%
+a number of very talented uh um
+ 
+
+ align:start position:0%
+a number of very talented uh um
+professionals from those organizations.
+
+ align:start position:0%
+professionals from those organizations.
+ 
+
+ align:start position:0%
+professionals from those organizations.
+So they got to hire. It's going to mean
+
+ align:start position:0%
+So they got to hire. It's going to mean
+ 
+
+ align:start position:0%
+So they got to hire. It's going to mean
+the next two or 3 months uh there may be
+
+ align:start position:0%
+the next two or 3 months uh there may be
+ 
+
+ align:start position:0%
+the next two or 3 months uh there may be
+some difficulties in getting the
+
+ align:start position:0%
+some difficulties in getting the
+ 
+
+ align:start position:0%
+some difficulties in getting the
+attention of these organizations because
+
+ align:start position:0%
+attention of these organizations because
+ 
+
+ align:start position:0%
+attention of these organizations because
+they're in the midst of trying to figure
+
+ align:start position:0%
+they're in the midst of trying to figure
+ 
+
+ align:start position:0%
+they're in the midst of trying to figure
+out uh exactly what kind of organization
+
+ align:start position:0%
+out uh exactly what kind of organization
+ 
+
+ align:start position:0%
+out uh exactly what kind of organization
+they are going to have when all of this
+
+ align:start position:0%
+they are going to have when all of this
+ 
+
+ align:start position:0%
+they are going to have when all of this
+when all the dust settles. But there are
+
+ align:start position:0%
+when all the dust settles. But there are
+ 
+
+ align:start position:0%
+when all the dust settles. But there are
+plenty of opportunities that are being
+
+ align:start position:0%
+plenty of opportunities that are being
+ 
+
+ align:start position:0%
+plenty of opportunities that are being
+created today including by the way the
+
+ align:start position:0%
+created today including by the way the
+ 
+
+ align:start position:0%
+created today including by the way the
+opportunity for the US government to
+
+ align:start position:0%
+opportunity for the US government to
+ 
+
+ align:start position:0%
+opportunity for the US government to
+take advantage of all of these
+
+ align:start position:0%
+take advantage of all of these
+ 
+
+ align:start position:0%
+take advantage of all of these
+distressed assets. So, one of the things
+
+ align:start position:0%
+distressed assets. So, one of the things
+ 
+
+ align:start position:0%
+distressed assets. So, one of the things
+that you should be careful about when
+
+ align:start position:0%
+that you should be careful about when
+ 
+
+ align:start position:0%
+that you should be careful about when
+you read that there's a $700 billion
+
+ align:start position:0%
+you read that there's a $700 billion
+ 
+
+ align:start position:0%
+you read that there's a $700 billion
+bailout that is somewhat misleading in
+
+ align:start position:0%
+bailout that is somewhat misleading in
+ 
+
+ align:start position:0%
+bailout that is somewhat misleading in
+the sense that first of all, we don't
+
+ align:start position:0%
+the sense that first of all, we don't
+ 
+
+ align:start position:0%
+the sense that first of all, we don't
+really know at this point exactly what
+
+ align:start position:0%
+really know at this point exactly what
+ 
+
+ align:start position:0%
+really know at this point exactly what
+the $700 billion will be for, how it
+
+ align:start position:0%
+the $700 billion will be for, how it
+ 
+
+ align:start position:0%
+the $700 billion will be for, how it
+will be used or how it's dispersed or is
+
+ align:start position:0%
+will be used or how it's dispersed or is
+ 
+
+ align:start position:0%
+will be used or how it's dispersed or is
+it really 700 billion. A lot of it
+
+ align:start position:0%
+it really 700 billion. A lot of it
+ 
+
+ align:start position:0%
+it really 700 billion. A lot of it
+depends upon how the money is spent and
+
+ align:start position:0%
+depends upon how the money is spent and
+ 
+
+ align:start position:0%
+depends upon how the money is spent and
+also what happens to housing markets.
+
+ align:start position:0%
+also what happens to housing markets.
+ 
+
+ align:start position:0%
+also what happens to housing markets.
+There is a scenario that I can imagine
+
+ align:start position:0%
+There is a scenario that I can imagine
+ 
+
+ align:start position:0%
+There is a scenario that I can imagine
+where the actual amount expended uh is
+
+ align:start position:0%
+where the actual amount expended uh is
+ 
+
+ align:start position:0%
+where the actual amount expended uh is
+either zero or negative. In other words,
+
+ align:start position:0%
+either zero or negative. In other words,
+ 
+
+ align:start position:0%
+either zero or negative. In other words,
+the government actually makes money uh
+
+ align:start position:0%
+the government actually makes money uh
+ 
+
+ align:start position:0%
+the government actually makes money uh
+from the current state of the markets
+
+ align:start position:0%
+from the current state of the markets
+ 
+
+ align:start position:0%
+from the current state of the markets
+because they can buy assets very
+
+ align:start position:0%
+because they can buy assets very
+ 
+
+ align:start position:0%
+because they can buy assets very
+cheaply, hold on to them forever until
+
+ align:start position:0%
+cheaply, hold on to them forever until
+ 
+
+ align:start position:0%
+cheaply, hold on to them forever until
+they pay off and then gain the kind of
+
+ align:start position:0%
+they pay off and then gain the kind of
+ 
+
+ align:start position:0%
+they pay off and then gain the kind of
+profit that the original uh uh financial
+
+ align:start position:0%
+profit that the original uh uh financial
+ 
+
+ align:start position:0%
+profit that the original uh uh financial
+engineers were expecting but could not
+
+ align:start position:0%
+engineers were expecting but could not
+ 
+
+ align:start position:0%
+engineers were expecting but could not
+take advantage of because of this
+
+ align:start position:0%
+take advantage of because of this
+ 
+
+ align:start position:0%
+take advantage of because of this
+liquidity crunch. So we'll talk about
+
+ align:start position:0%
+liquidity crunch. So we'll talk about
+ 
+
+ align:start position:0%
+liquidity crunch. So we'll talk about
+that uh over the next few lectures
+
+ align:start position:0%
+that uh over the next few lectures
+ 
+
+ align:start position:0%
+that uh over the next few lectures
+because we're going to develop some
+
+ align:start position:0%
+because we're going to develop some
+ 
+
+ align:start position:0%
+because we're going to develop some
+techniques to be able to to illustrate
+
+ align:start position:0%
+techniques to be able to to illustrate
+ 
+
+ align:start position:0%
+techniques to be able to to illustrate
+how these kind of uh arbitrage uh
+
+ align:start position:0%
+how these kind of uh arbitrage uh
+ 
+
+ align:start position:0%
+how these kind of uh arbitrage uh
+strategies work. Yeah.
+
+ align:start position:0%
+strategies work. Yeah.
+ 
+
+ align:start position:0%
+strategies work. Yeah.
+Namura uh is it more certain that it's
+
+ align:start position:0%
+Namura uh is it more certain that it's
+ 
+
+ align:start position:0%
+Namura uh is it more certain that it's
+going to happen or are there many banks
+
+ align:start position:0%
+going to happen or are there many banks
+ 
+
+ align:start position:0%
+going to happen or are there many banks
+that are trying to buy the
+
+ align:start position:0%
+that are trying to buy the
+ 
+
+ align:start position:0%
+that are trying to buy the
+Well, certainly there are a number of
+
+ align:start position:0%
+Well, certainly there are a number of
+ 
+
+ align:start position:0%
+Well, certainly there are a number of
+banks. I wouldn't say many simply
+
+ align:start position:0%
+banks. I wouldn't say many simply
+ 
+
+ align:start position:0%
+banks. I wouldn't say many simply
+because there aren't that many banks
+
+ align:start position:0%
+because there aren't that many banks
+ 
+
+ align:start position:0%
+because there aren't that many banks
+that are well capitalized enough to be
+
+ align:start position:0%
+that are well capitalized enough to be
+ 
+
+ align:start position:0%
+that are well capitalized enough to be
+able to take on, you know, a large unit
+
+ align:start position:0%
+able to take on, you know, a large unit
+ 
+
+ align:start position:0%
+able to take on, you know, a large unit
+of a business as big as Lehman Brothers.
+
+ align:start position:0%
+of a business as big as Lehman Brothers.
+ 
+
+ align:start position:0%
+of a business as big as Lehman Brothers.
+So, Numora is one of a handful of banks
+
+ align:start position:0%
+So, Numora is one of a handful of banks
+ 
+
+ align:start position:0%
+So, Numora is one of a handful of banks
+that are engaged, but they seem to be
+
+ align:start position:0%
+that are engaged, but they seem to be
+ 
+
+ align:start position:0%
+that are engaged, but they seem to be
+the front runner at this point.
+
+ align:start position:0%
+the front runner at this point.
+ 
+
+ align:start position:0%
+the front runner at this point.
+Generally, what I've heard kind of from
+
+ align:start position:0%
+Generally, what I've heard kind of from
+ 
+
+ align:start position:0%
+Generally, what I've heard kind of from
+the Asian
+
+ align:start position:0%
+the Asian
+ 
+
+ align:start position:0%
+the Asian
+analyst men that I spoken to is that
+
+ align:start position:0%
+analyst men that I spoken to is that
+ 
+
+ align:start position:0%
+analyst men that I spoken to is that
+it's quite likely that that might not go
+
+ align:start position:0%
+it's quite likely that that might not go
+ 
+
+ align:start position:0%
+it's quite likely that that might not go
+through as well because they find a lot
+
+ align:start position:0%
+through as well because they find a lot
+ 
+
+ align:start position:0%
+through as well because they find a lot
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Oh, absolutely. I mean there there are a
+
+ align:start position:0%
+Oh, absolutely. I mean there there are a
+ 
+
+ align:start position:0%
+Oh, absolutely. I mean there there are a
+number of issues that will come up in
+
+ align:start position:0%
+number of issues that will come up in
+ 
+
+ align:start position:0%
+number of issues that will come up in
+any kind of a deal and so you don't know
+
+ align:start position:0%
+any kind of a deal and so you don't know
+ 
+
+ align:start position:0%
+any kind of a deal and so you don't know
+whether or not something's going to go
+
+ align:start position:0%
+whether or not something's going to go
+ 
+
+ align:start position:0%
+whether or not something's going to go
+through until it actually goes through.
+
+ align:start position:0%
+through until it actually goes through.
+ 
+
+ align:start position:0%
+through until it actually goes through.
+The same thing uh could be said for what
+
+ align:start position:0%
+The same thing uh could be said for what
+ 
+
+ align:start position:0%
+The same thing uh could be said for what
+happened with uh uh Meil Lynch uh with
+
+ align:start position:0%
+happened with uh uh Meil Lynch uh with
+ 
+
+ align:start position:0%
+happened with uh uh Meil Lynch uh with
+uh uh AIG. All of these deals are sort
+
+ align:start position:0%
+uh uh AIG. All of these deals are sort
+ 
+
+ align:start position:0%
+uh uh AIG. All of these deals are sort
+of put together at the last minute and
+
+ align:start position:0%
+of put together at the last minute and
+ 
+
+ align:start position:0%
+of put together at the last minute and
+you know either they get consummated or
+
+ align:start position:0%
+you know either they get consummated or
+ 
+
+ align:start position:0%
+you know either they get consummated or
+there's some hitch at the end that makes
+
+ align:start position:0%
+there's some hitch at the end that makes
+ 
+
+ align:start position:0%
+there's some hitch at the end that makes
+it difficult. So yeah, I mean with a
+
+ align:start position:0%
+it difficult. So yeah, I mean with a
+ 
+
+ align:start position:0%
+it difficult. So yeah, I mean with a
+grain of salt, you should take all of
+
+ align:start position:0%
+grain of salt, you should take all of
+ 
+
+ align:start position:0%
+grain of salt, you should take all of
+these news reports and uh literally
+
+ align:start position:0%
+these news reports and uh literally
+ 
+
+ align:start position:0%
+these news reports and uh literally
+until the deal is signed, you will not
+
+ align:start position:0%
+until the deal is signed, you will not
+ 
+
+ align:start position:0%
+until the deal is signed, you will not
+know whether or not something's gone.
+
+ align:start position:0%
+know whether or not something's gone.
+ 
+
+ align:start position:0%
+know whether or not something's gone.
+But the point I'm illustrating is that
+
+ align:start position:0%
+But the point I'm illustrating is that
+ 
+
+ align:start position:0%
+But the point I'm illustrating is that
+these these assets are not completely
+
+ align:start position:0%
+these these assets are not completely
+ 
+
+ align:start position:0%
+these these assets are not completely
+worthless. What's happened is a very
+
+ align:start position:0%
+worthless. What's happened is a very
+ 
+
+ align:start position:0%
+worthless. What's happened is a very
+significant liquidity crunch and panic.
+
+ align:start position:0%
+significant liquidity crunch and panic.
+ 
+
+ align:start position:0%
+significant liquidity crunch and panic.
+When that happens, the pricing of all
+
+ align:start position:0%
+When that happens, the pricing of all
+ 
+
+ align:start position:0%
+When that happens, the pricing of all
+these assets becomes questionable. Okay,
+
+ align:start position:0%
+these assets becomes questionable. Okay,
+ 
+
+ align:start position:0%
+these assets becomes questionable. Okay,
+we're going to actually see an example
+
+ align:start position:0%
+we're going to actually see an example
+ 
+
+ align:start position:0%
+we're going to actually see an example
+of that. So if you wouldn't mind, let me
+
+ align:start position:0%
+of that. So if you wouldn't mind, let me
+ 
+
+ align:start position:0%
+of that. So if you wouldn't mind, let me
+put that off for a few minutes and then
+
+ align:start position:0%
+put that off for a few minutes and then
+ 
+
+ align:start position:0%
+put that off for a few minutes and then
+if you have further questions about
+
+ align:start position:0%
+if you have further questions about
+ 
+
+ align:start position:0%
+if you have further questions about
+this, we can come back to it. Let me
+
+ align:start position:0%
+this, we can come back to it. Let me
+ 
+
+ align:start position:0%
+this, we can come back to it. Let me
+start. Uh so this is lecture six and
+
+ align:start position:0%
+start. Uh so this is lecture six and
+ 
+
+ align:start position:0%
+start. Uh so this is lecture six and
+what I want to do is to start where we
+
+ align:start position:0%
+what I want to do is to start where we
+ 
+
+ align:start position:0%
+what I want to do is to start where we
+ended last time which was a discussion
+
+ align:start position:0%
+ended last time which was a discussion
+ 
+
+ align:start position:0%
+ended last time which was a discussion
+of coupon bonds and how you price coupon
+
+ align:start position:0%
+of coupon bonds and how you price coupon
+ 
+
+ align:start position:0%
+of coupon bonds and how you price coupon
+bonds simply as a package or a portfolio
+
+ align:start position:0%
+bonds simply as a package or a portfolio
+ 
+
+ align:start position:0%
+bonds simply as a package or a portfolio
+of pure discount bonds.
+
+ align:start position:0%
+of pure discount bonds.
+ 
+
+ align:start position:0%
+of pure discount bonds.
+Underlying this approach to pricing
+
+ align:start position:0%
+Underlying this approach to pricing
+ 
+
+ align:start position:0%
+Underlying this approach to pricing
+coupon bonds is a very important
+
+ align:start position:0%
+coupon bonds is a very important
+ 
+
+ align:start position:0%
+coupon bonds is a very important
+principle.
+
+ align:start position:0%
+principle.
+ 
+
+ align:start position:0%
+principle.
+That's a principle that was given to you
+
+ align:start position:0%
+That's a principle that was given to you
+ 
+
+ align:start position:0%
+That's a principle that was given to you
+in the very first day of class where we
+
+ align:start position:0%
+in the very first day of class where we
+ 
+
+ align:start position:0%
+in the very first day of class where we
+talked about the six fundamental
+
+ align:start position:0%
+talked about the six fundamental
+ 
+
+ align:start position:0%
+talked about the six fundamental
+principles of financial markets and it's
+
+ align:start position:0%
+principles of financial markets and it's
+ 
+
+ align:start position:0%
+principles of financial markets and it's
+the principle of the law of one price.
+
+ align:start position:0%
+the principle of the law of one price.
+ 
+
+ align:start position:0%
+the principle of the law of one price.
+So what I want to do today is to focus
+
+ align:start position:0%
+So what I want to do today is to focus
+ 
+
+ align:start position:0%
+So what I want to do today is to focus
+on that and talk about the law of one
+
+ align:start position:0%
+on that and talk about the law of one
+ 
+
+ align:start position:0%
+on that and talk about the law of one
+price and what it means for things like
+
+ align:start position:0%
+price and what it means for things like
+ 
+
+ align:start position:0%
+price and what it means for things like
+arbitrage,
+
+ align:start position:0%
+arbitrage,
+ 
+
+ align:start position:0%
+arbitrage,
+leverage, shortelling and relative
+
+ align:start position:0%
+leverage, shortelling and relative
+ 
+
+ align:start position:0%
+leverage, shortelling and relative
+pricing. Those are the key concepts
+
+ align:start position:0%
+pricing. Those are the key concepts
+ 
+
+ align:start position:0%
+pricing. Those are the key concepts
+we're going to cover today. So let me
+
+ align:start position:0%
+we're going to cover today. So let me
+ 
+
+ align:start position:0%
+we're going to cover today. So let me
+talk about the law of one price and
+
+ align:start position:0%
+talk about the law of one price and
+ 
+
+ align:start position:0%
+talk about the law of one price and
+remind you all what it is. It's a very
+
+ align:start position:0%
+remind you all what it is. It's a very
+ 
+
+ align:start position:0%
+remind you all what it is. It's a very
+simple idea. It's so simple that you
+
+ align:start position:0%
+simple idea. It's so simple that you
+ 
+
+ align:start position:0%
+simple idea. It's so simple that you
+might think it's obvious, but it's got
+
+ align:start position:0%
+might think it's obvious, but it's got
+ 
+
+ align:start position:0%
+might think it's obvious, but it's got
+some very, very dramatic implications.
+
+ align:start position:0%
+some very, very dramatic implications.
+ 
+
+ align:start position:0%
+some very, very dramatic implications.
+The law of one price says that
+
+ align:start position:0%
+The law of one price says that
+ 
+
+ align:start position:0%
+The law of one price says that
+two identical cash flows
+
+ align:start position:0%
+two identical cash flows
+ 
+
+ align:start position:0%
+two identical cash flows
+must have the same market price.
+
+ align:start position:0%
+must have the same market price.
+ 
+
+ align:start position:0%
+must have the same market price.
+Okay, let me repeat that. Two identical
+
+ align:start position:0%
+Okay, let me repeat that. Two identical
+ 
+
+ align:start position:0%
+Okay, let me repeat that. Two identical
+cash flows
+
+ align:start position:0%
+cash flows
+ 
+
+ align:start position:0%
+cash flows
+must have the same price.
+
+ align:start position:0%
+must have the same price.
+ 
+
+ align:start position:0%
+must have the same price.
+Now
+
+ align:start position:0%
+Now
+ 
+
+ align:start position:0%
+Now
+remember that when we think of an asset,
+
+ align:start position:0%
+remember that when we think of an asset,
+ 
+
+ align:start position:0%
+remember that when we think of an asset,
+we think of an asset as just a sequence
+
+ align:start position:0%
+we think of an asset as just a sequence
+ 
+
+ align:start position:0%
+we think of an asset as just a sequence
+of cash flows. That's what an asset is.
+
+ align:start position:0%
+of cash flows. That's what an asset is.
+ 
+
+ align:start position:0%
+of cash flows. That's what an asset is.
+So all I'm saying is that when you have
+
+ align:start position:0%
+So all I'm saying is that when you have
+ 
+
+ align:start position:0%
+So all I'm saying is that when you have
+two identical assets,
+
+ align:start position:0%
+two identical assets,
+ 
+
+ align:start position:0%
+two identical assets,
+they have to have the same price. That's
+
+ align:start position:0%
+they have to have the same price. That's
+ 
+
+ align:start position:0%
+they have to have the same price. That's
+not a very controversial statement. And
+
+ align:start position:0%
+not a very controversial statement. And
+ 
+
+ align:start position:0%
+not a very controversial statement. And
+this principle is one of the most
+
+ align:start position:0%
+this principle is one of the most
+ 
+
+ align:start position:0%
+this principle is one of the most
+important ideas in all of modern finance
+
+ align:start position:0%
+important ideas in all of modern finance
+ 
+
+ align:start position:0%
+important ideas in all of modern finance
+because it leads to the pricing of all
+
+ align:start position:0%
+because it leads to the pricing of all
+ 
+
+ align:start position:0%
+because it leads to the pricing of all
+sorts of securities including all the
+
+ align:start position:0%
+sorts of securities including all the
+ 
+
+ align:start position:0%
+sorts of securities including all the
+derivatives that have ever been priced
+
+ align:start position:0%
+derivatives that have ever been priced
+ 
+
+ align:start position:0%
+derivatives that have ever been priced
+on Wall Street. They use this idea of
+
+ align:start position:0%
+on Wall Street. They use this idea of
+ 
+
+ align:start position:0%
+on Wall Street. They use this idea of
+the law of one price. Okay. Yeah.
+
+ align:start position:0%
+the law of one price. Okay. Yeah.
+ 
+
+ align:start position:0%
+the law of one price. Okay. Yeah.
+But wouldn't you have to qualify that by
+
+ align:start position:0%
+But wouldn't you have to qualify that by
+ 
+
+ align:start position:0%
+But wouldn't you have to qualify that by
+saying it's an equilibrium?
+
+ align:start position:0%
+saying it's an equilibrium?
+ 
+
+ align:start position:0%
+saying it's an equilibrium?
+No. No, I don't have to qualify that at
+
+ align:start position:0%
+No. No, I don't have to qualify that at
+ 
+
+ align:start position:0%
+No. No, I don't have to qualify that at
+all. First, because this is a free
+
+ align:start position:0%
+all. First, because this is a free
+ 
+
+ align:start position:0%
+all. First, because this is a free
+country and I don't have to do anything
+
+ align:start position:0%
+country and I don't have to do anything
+ 
+
+ align:start position:0%
+country and I don't have to do anything
+I don't want to do.
+
+ align:start position:0%
+I don't want to do.
+ 
+
+ align:start position:0%
+I don't want to do.
+But but more importantly, it's because I
+
+ align:start position:0%
+But but more importantly, it's because I
+ 
+
+ align:start position:0%
+But but more importantly, it's because I
+I don't want to restrict it to an
+
+ align:start position:0%
+I don't want to restrict it to an
+ 
+
+ align:start position:0%
+I don't want to restrict it to an
+equilibrium. By equilibrium, you mean
+
+ align:start position:0%
+equilibrium. By equilibrium, you mean
+ 
+
+ align:start position:0%
+equilibrium. By equilibrium, you mean
+when supply equals demand, right?
+
+ align:start position:0%
+when supply equals demand, right?
+ 
+
+ align:start position:0%
+when supply equals demand, right?
+I don't care about supply and demand.
+
+ align:start position:0%
+I don't care about supply and demand.
+ 
+
+ align:start position:0%
+I don't care about supply and demand.
+Supply may very well not equal demand.
+
+ align:start position:0%
+Supply may very well not equal demand.
+ 
+
+ align:start position:0%
+Supply may very well not equal demand.
+That's okay with me.
+
+ align:start position:0%
+That's okay with me.
+ 
+
+ align:start position:0%
+That's okay with me.
+This principle of the law of one price
+
+ align:start position:0%
+This principle of the law of one price
+ 
+
+ align:start position:0%
+This principle of the law of one price
+that two identical cash flows have to
+
+ align:start position:0%
+that two identical cash flows have to
+ 
+
+ align:start position:0%
+that two identical cash flows have to
+have the same market price. The only
+
+ align:start position:0%
+have the same market price. The only
+ 
+
+ align:start position:0%
+have the same market price. The only
+assumption that I need in order for that
+
+ align:start position:0%
+assumption that I need in order for that
+ 
+
+ align:start position:0%
+assumption that I need in order for that
+law to be true
+
+ align:start position:0%
+law to be true
+ 
+
+ align:start position:0%
+law to be true
+is that people prefer more money to less
+
+ align:start position:0%
+is that people prefer more money to less
+ 
+
+ align:start position:0%
+is that people prefer more money to less
+money. And it's not even people. I just
+
+ align:start position:0%
+money. And it's not even people. I just
+ 
+
+ align:start position:0%
+money. And it's not even people. I just
+need one person in the economy that
+
+ align:start position:0%
+need one person in the economy that
+ 
+
+ align:start position:0%
+need one person in the economy that
+prefers more money to less money. And
+
+ align:start position:0%
+prefers more money to less money. And
+ 
+
+ align:start position:0%
+prefers more money to less money. And
+I'm happy to uh volunteer for that
+
+ align:start position:0%
+I'm happy to uh volunteer for that
+ 
+
+ align:start position:0%
+I'm happy to uh volunteer for that
+position. Okay. Why is that? It's
+
+ align:start position:0%
+position. Okay. Why is that? It's
+ 
+
+ align:start position:0%
+position. Okay. Why is that? It's
+because if that law is violated,
+
+ align:start position:0%
+because if that law is violated,
+ 
+
+ align:start position:0%
+because if that law is violated,
+if you can show me two identical cash
+
+ align:start position:0%
+if you can show me two identical cash
+ 
+
+ align:start position:0%
+if you can show me two identical cash
+flows
+
+ align:start position:0%
+flows
+ 
+
+ align:start position:0%
+flows
+that sell for different market prices,
+
+ align:start position:0%
+that sell for different market prices,
+ 
+
+ align:start position:0%
+that sell for different market prices,
+first of all, tell nobody but me about
+
+ align:start position:0%
+first of all, tell nobody but me about
+ 
+
+ align:start position:0%
+first of all, tell nobody but me about
+it. What I'm going to do is
+
+ align:start position:0%
+it. What I'm going to do is
+ 
+
+ align:start position:0%
+it. What I'm going to do is
+I'm going to buy the cheaper asset.
+
+ align:start position:0%
+I'm going to buy the cheaper asset.
+ 
+
+ align:start position:0%
+I'm going to buy the cheaper asset.
+I'm going to sell the more expensive
+
+ align:start position:0%
+I'm going to sell the more expensive
+ 
+
+ align:start position:0%
+I'm going to sell the more expensive
+asset. So as of today I make money,
+
+ align:start position:0%
+asset. So as of today I make money,
+ 
+
+ align:start position:0%
+asset. So as of today I make money,
+right? Because I bought the cheap, I
+
+ align:start position:0%
+right? Because I bought the cheap, I
+ 
+
+ align:start position:0%
+right? Because I bought the cheap, I
+sold the more expensive. That difference
+
+ align:start position:0%
+sold the more expensive. That difference
+ 
+
+ align:start position:0%
+sold the more expensive. That difference
+is positive for me.
+
+ align:start position:0%
+is positive for me.
+ 
+
+ align:start position:0%
+is positive for me.
+And then I argue that from that point
+
+ align:start position:0%
+And then I argue that from that point
+ 
+
+ align:start position:0%
+And then I argue that from that point
+on, I have no further risk and in fact
+
+ align:start position:0%
+on, I have no further risk and in fact
+ 
+
+ align:start position:0%
+on, I have no further risk and in fact
+no further obligations. I can just
+
+ align:start position:0%
+no further obligations. I can just
+ 
+
+ align:start position:0%
+no further obligations. I can just
+forget about the deal and take my money
+
+ align:start position:0%
+forget about the deal and take my money
+ 
+
+ align:start position:0%
+forget about the deal and take my money
+and spend it. Why? Because I've bought
+
+ align:start position:0%
+and spend it. Why? Because I've bought
+ 
+
+ align:start position:0%
+and spend it. Why? Because I've bought
+and sold identical cash flows. So from
+
+ align:start position:0%
+and sold identical cash flows. So from
+ 
+
+ align:start position:0%
+and sold identical cash flows. So from
+that point on in the future, all the
+
+ align:start position:0%
+that point on in the future, all the
+ 
+
+ align:start position:0%
+that point on in the future, all the
+cash flows cancel out.
+
+ align:start position:0%
+cash flows cancel out.
+ 
+
+ align:start position:0%
+cash flows cancel out.
+So I'm done. That's called an arbitrage
+
+ align:start position:0%
+So I'm done. That's called an arbitrage
+ 
+
+ align:start position:0%
+So I'm done. That's called an arbitrage
+or more technically a free lunch.
+
+ align:start position:0%
+or more technically a free lunch.
+ 
+
+ align:start position:0%
+or more technically a free lunch.
+I've been able to create money out of
+
+ align:start position:0%
+I've been able to create money out of
+ 
+
+ align:start position:0%
+I've been able to create money out of
+nothing. It doesn't assume supply equals
+
+ align:start position:0%
+nothing. It doesn't assume supply equals
+ 
+
+ align:start position:0%
+nothing. It doesn't assume supply equals
+demand. It doesn't assume any kind of
+
+ align:start position:0%
+demand. It doesn't assume any kind of
+ 
+
+ align:start position:0%
+demand. It doesn't assume any kind of
+mathematical uh formula for any kind of
+
+ align:start position:0%
+mathematical uh formula for any kind of
+ 
+
+ align:start position:0%
+mathematical uh formula for any kind of
+instrument. All it assumes is that more
+
+ align:start position:0%
+instrument. All it assumes is that more
+ 
+
+ align:start position:0%
+instrument. All it assumes is that more
+people prefer more money to less.
+
+ align:start position:0%
+people prefer more money to less.
+ 
+
+ align:start position:0%
+people prefer more money to less.
+I mean, so that day when you auctioned
+
+ align:start position:0%
+I mean, so that day when you auctioned
+ 
+
+ align:start position:0%
+I mean, so that day when you auctioned
+the iPod,
+
+ align:start position:0%
+the iPod,
+ 
+
+ align:start position:0%
+the iPod,
+Yes.
+
+ align:start position:0%
+Yes.
+ 
+
+ align:start position:0%
+Yes.
+then the only difference between an open
+
+ align:start position:0%
+then the only difference between an open
+ 
+
+ align:start position:0%
+then the only difference between an open
+package and the concealed package was
+
+ align:start position:0%
+package and the concealed package was
+ 
+
+ align:start position:0%
+package and the concealed package was
+that in one case you basically did not
+
+ align:start position:0%
+that in one case you basically did not
+ 
+
+ align:start position:0%
+that in one case you basically did not
+give enough information,
+
+ align:start position:0%
+give enough information,
+ 
+
+ align:start position:0%
+give enough information,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+Um, and it wasn't reaching a fair value.
+
+ align:start position:0%
+Um, and it wasn't reaching a fair value.
+ 
+
+ align:start position:0%
+Um, and it wasn't reaching a fair value.
+And so,
+
+ align:start position:0%
+And so,
+ 
+
+ align:start position:0%
+And so,
+well, wait, wait, wait, wait a minute.
+
+ align:start position:0%
+well, wait, wait, wait, wait a minute.
+ 
+
+ align:start position:0%
+well, wait, wait, wait, wait a minute.
+Well, when you say fair value, that's a
+
+ align:start position:0%
+Well, when you say fair value, that's a
+ 
+
+ align:start position:0%
+Well, when you say fair value, that's a
+loaded term. What do you mean by fair
+
+ align:start position:0%
+loaded term. What do you mean by fair
+ 
+
+ align:start position:0%
+loaded term. What do you mean by fair
+value? It was a fair value given all the
+
+ align:start position:0%
+value? It was a fair value given all the
+ 
+
+ align:start position:0%
+value? It was a fair value given all the
+information that the market had.
+
+ align:start position:0%
+information that the market had.
+ 
+
+ align:start position:0%
+information that the market had.
+But it's not the cash flow of that
+
+ align:start position:0%
+But it's not the cash flow of that
+ 
+
+ align:start position:0%
+But it's not the cash flow of that
+object. When the person buys object as
+
+ align:start position:0%
+object. When the person buys object as
+ 
+
+ align:start position:0%
+object. When the person buys object as
+packaged, once they open it, they'll
+
+ align:start position:0%
+packaged, once they open it, they'll
+ 
+
+ align:start position:0%
+packaged, once they open it, they'll
+know that the cash flow of that object
+
+ align:start position:0%
+know that the cash flow of that object
+ 
+
+ align:start position:0%
+know that the cash flow of that object
+is the same as if it were not packaged
+
+ align:start position:0%
+is the same as if it were not packaged
+ 
+
+ align:start position:0%
+is the same as if it were not packaged
+and they're going to reap the benefits
+
+ align:start position:0%
+and they're going to reap the benefits
+ 
+
+ align:start position:0%
+and they're going to reap the benefits
+as you just mentioned.
+
+ align:start position:0%
+as you just mentioned.
+ 
+
+ align:start position:0%
+as you just mentioned.
+That's right. But don't you think
+
+ align:start position:0%
+That's right. But don't you think
+ 
+
+ align:start position:0%
+That's right. But don't you think
+there's a difference between the package
+
+ align:start position:0%
+there's a difference between the package
+ 
+
+ align:start position:0%
+there's a difference between the package
+wrapped and the package unwrapped?
+
+ align:start position:0%
+wrapped and the package unwrapped?
+ 
+
+ align:start position:0%
+wrapped and the package unwrapped?
+Yeah. One of them is I mean it's just
+
+ align:start position:0%
+Yeah. One of them is I mean it's just
+ 
+
+ align:start position:0%
+Yeah. One of them is I mean it's just
+like a factory which will produce the
+
+ align:start position:0%
+like a factory which will produce the
+ 
+
+ align:start position:0%
+like a factory which will produce the
+same stuff, but it's valued at the
+
+ align:start position:0%
+same stuff, but it's valued at the
+ 
+
+ align:start position:0%
+same stuff, but it's valued at the
+market at a lower price than what it
+
+ align:start position:0%
+market at a lower price than what it
+ 
+
+ align:start position:0%
+market at a lower price than what it
+right. But what if one factory didn't
+
+ align:start position:0%
+right. But what if one factory didn't
+ 
+
+ align:start position:0%
+right. But what if one factory didn't
+tell you how it produced it and another
+
+ align:start position:0%
+tell you how it produced it and another
+ 
+
+ align:start position:0%
+tell you how it produced it and another
+factory did? Do you think that they
+
+ align:start position:0%
+factory did? Do you think that they
+ 
+
+ align:start position:0%
+factory did? Do you think that they
+would sell for the same price?
+
+ align:start position:0%
+would sell for the same price?
+ 
+
+ align:start position:0%
+would sell for the same price?
+The factories would input their future
+
+ align:start position:0%
+The factories would input their future
+ 
+
+ align:start position:0%
+The factories would input their future
+cash flow into a revenue which could be
+
+ align:start position:0%
+cash flow into a revenue which could be
+ 
+
+ align:start position:0%
+cash flow into a revenue which could be
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+only if it turns out that as a matter of
+
+ align:start position:0%
+only if it turns out that as a matter of
+ 
+
+ align:start position:0%
+only if it turns out that as a matter of
+fact it is identical. But you don't know
+
+ align:start position:0%
+fact it is identical. But you don't know
+ 
+
+ align:start position:0%
+fact it is identical. But you don't know
+that ahead of time. You can only price
+
+ align:start position:0%
+that ahead of time. You can only price
+ 
+
+ align:start position:0%
+that ahead of time. You can only price
+something with the information you have.
+
+ align:start position:0%
+something with the information you have.
+ 
+
+ align:start position:0%
+something with the information you have.
+Okay? So when I say two cash flows are
+
+ align:start position:0%
+Okay? So when I say two cash flows are
+ 
+
+ align:start position:0%
+Okay? So when I say two cash flows are
+identical, I'm saying that we
+
+ align:start position:0%
+identical, I'm saying that we
+ 
+
+ align:start position:0%
+identical, I'm saying that we
+acknowledge that the cash flows are in
+
+ align:start position:0%
+acknowledge that the cash flows are in
+ 
+
+ align:start position:0%
+acknowledge that the cash flows are in
+fact identical and we know that they're
+
+ align:start position:0%
+fact identical and we know that they're
+ 
+
+ align:start position:0%
+fact identical and we know that they're
+identical. If I put two packages up
+
+ align:start position:0%
+identical. If I put two packages up
+ 
+
+ align:start position:0%
+identical. If I put two packages up
+front in the room, one is an iPod and
+
+ align:start position:0%
+front in the room, one is an iPod and
+ 
+
+ align:start position:0%
+front in the room, one is an iPod and
+the other one is wrapped. So it looks
+
+ align:start position:0%
+the other one is wrapped. So it looks
+ 
+
+ align:start position:0%
+the other one is wrapped. So it looks
+like an iPod. It's got the same shape,
+
+ align:start position:0%
+like an iPod. It's got the same shape,
+ 
+
+ align:start position:0%
+like an iPod. It's got the same shape,
+the same dimensions, but it's wrapped.
+
+ align:start position:0%
+the same dimensions, but it's wrapped.
+ 
+
+ align:start position:0%
+the same dimensions, but it's wrapped.
+Would you say that they're identical?
+
+ align:start position:0%
+Would you say that they're identical?
+ 
+
+ align:start position:0%
+Would you say that they're identical?
+You can't know that. If you knew that,
+
+ align:start position:0%
+You can't know that. If you knew that,
+ 
+
+ align:start position:0%
+You can't know that. If you knew that,
+then you would price it accordingly. By
+
+ align:start position:0%
+then you would price it accordingly. By
+ 
+
+ align:start position:0%
+then you would price it accordingly. By
+the way, that gives you a very important
+
+ align:start position:0%
+the way, that gives you a very important
+ 
+
+ align:start position:0%
+the way, that gives you a very important
+piece of information. Suppose that I did
+
+ align:start position:0%
+piece of information. Suppose that I did
+ 
+
+ align:start position:0%
+piece of information. Suppose that I did
+that experiment. I had the iPod that was
+
+ align:start position:0%
+that experiment. I had the iPod that was
+ 
+
+ align:start position:0%
+that experiment. I had the iPod that was
+clearly unwrapped and it was an iPod.
+
+ align:start position:0%
+clearly unwrapped and it was an iPod.
+ 
+
+ align:start position:0%
+clearly unwrapped and it was an iPod.
+And then I had another package that was
+
+ align:start position:0%
+And then I had another package that was
+ 
+
+ align:start position:0%
+And then I had another package that was
+the identical dimension, but it was
+
+ align:start position:0%
+the identical dimension, but it was
+ 
+
+ align:start position:0%
+the identical dimension, but it was
+wrapped. Okay?
+
+ align:start position:0%
+wrapped. Okay?
+ 
+
+ align:start position:0%
+wrapped. Okay?
+And I auctioned them off. And it became
+
+ align:start position:0%
+And I auctioned them off. And it became
+ 
+
+ align:start position:0%
+And I auctioned them off. And it became
+clear initially
+
+ align:start position:0%
+clear initially
+ 
+
+ align:start position:0%
+clear initially
+that the two were priced at about the
+
+ align:start position:0%
+that the two were priced at about the
+ 
+
+ align:start position:0%
+that the two were priced at about the
+same.
+
+ align:start position:0%
+same.
+ 
+
+ align:start position:0%
+same.
+Well, if you saw that,
+
+ align:start position:0%
+Well, if you saw that,
+ 
+
+ align:start position:0%
+Well, if you saw that,
+you would then know
+
+ align:start position:0%
+you would then know
+ 
+
+ align:start position:0%
+you would then know
+that it was quite likely
+
+ align:start position:0%
+that it was quite likely
+ 
+
+ align:start position:0%
+that it was quite likely
+that what was in the wrapped package was
+
+ align:start position:0%
+that what was in the wrapped package was
+ 
+
+ align:start position:0%
+that what was in the wrapped package was
+the same as what was in the unwrapped
+
+ align:start position:0%
+the same as what was in the unwrapped
+ 
+
+ align:start position:0%
+the same as what was in the unwrapped
+package, right? But the only reason you
+
+ align:start position:0%
+package, right? But the only reason you
+ 
+
+ align:start position:0%
+package, right? But the only reason you
+would know that is because somebody in
+
+ align:start position:0%
+would know that is because somebody in
+ 
+
+ align:start position:0%
+would know that is because somebody in
+the audience apparently bid the same
+
+ align:start position:0%
+the audience apparently bid the same
+ 
+
+ align:start position:0%
+the audience apparently bid the same
+price. Now, why would they do that?
+
+ align:start position:0%
+price. Now, why would they do that?
+ 
+
+ align:start position:0%
+price. Now, why would they do that?
+Either they're knuckleheads
+
+ align:start position:0%
+Either they're knuckleheads
+ 
+
+ align:start position:0%
+Either they're knuckleheads
+or they know something that you don't
+
+ align:start position:0%
+or they know something that you don't
+ 
+
+ align:start position:0%
+or they know something that you don't
+know. And now that you looked at the
+
+ align:start position:0%
+know. And now that you looked at the
+ 
+
+ align:start position:0%
+know. And now that you looked at the
+price, you actually learned something
+
+ align:start position:0%
+price, you actually learned something
+ 
+
+ align:start position:0%
+price, you actually learned something
+about what's in there. So, what matters
+
+ align:start position:0%
+about what's in there. So, what matters
+ 
+
+ align:start position:0%
+about what's in there. So, what matters
+for pricing is what the entire market
+
+ align:start position:0%
+for pricing is what the entire market
+ 
+
+ align:start position:0%
+for pricing is what the entire market
+knows. Not just what you know, but what
+
+ align:start position:0%
+knows. Not just what you know, but what
+ 
+
+ align:start position:0%
+knows. Not just what you know, but what
+the entire market knows. Now, going back
+
+ align:start position:0%
+the entire market knows. Now, going back
+ 
+
+ align:start position:0%
+the entire market knows. Now, going back
+to this arbitrage, let's not worry about
+
+ align:start position:0%
+to this arbitrage, let's not worry about
+ 
+
+ align:start position:0%
+to this arbitrage, let's not worry about
+information asymmetries. So, let's
+
+ align:start position:0%
+information asymmetries. So, let's
+ 
+
+ align:start position:0%
+information asymmetries. So, let's
+assume that we all know exactly what
+
+ align:start position:0%
+assume that we all know exactly what
+ 
+
+ align:start position:0%
+assume that we all know exactly what
+there is to know, which is that these
+
+ align:start position:0%
+there is to know, which is that these
+ 
+
+ align:start position:0%
+there is to know, which is that these
+two securities have the same cash flow.
+
+ align:start position:0%
+two securities have the same cash flow.
+ 
+
+ align:start position:0%
+two securities have the same cash flow.
+If they have the same cash flow, they've
+
+ align:start position:0%
+If they have the same cash flow, they've
+ 
+
+ align:start position:0%
+If they have the same cash flow, they've
+got to have the same price. And that's
+
+ align:start position:0%
+got to have the same price. And that's
+ 
+
+ align:start position:0%
+got to have the same price. And that's
+exactly what we saw last time with this
+
+ align:start position:0%
+exactly what we saw last time with this
+ 
+
+ align:start position:0%
+exactly what we saw last time with this
+example, same cash flows, and therefore
+
+ align:start position:0%
+example, same cash flows, and therefore
+ 
+
+ align:start position:0%
+example, same cash flows, and therefore
+they have to have the same price. If
+
+ align:start position:0%
+they have to have the same price. If
+ 
+
+ align:start position:0%
+they have to have the same price. If
+they don't have the same price, then
+
+ align:start position:0%
+they don't have the same price, then
+ 
+
+ align:start position:0%
+they don't have the same price, then
+instead of feeling upset and despondent
+
+ align:start position:0%
+instead of feeling upset and despondent
+ 
+
+ align:start position:0%
+instead of feeling upset and despondent
+that somehow finance theory is in
+
+ align:start position:0%
+that somehow finance theory is in
+ 
+
+ align:start position:0%
+that somehow finance theory is in
+question, the most exciting thing for a
+
+ align:start position:0%
+question, the most exciting thing for a
+ 
+
+ align:start position:0%
+question, the most exciting thing for a
+finance professor is to see that this
+
+ align:start position:0%
+finance professor is to see that this
+ 
+
+ align:start position:0%
+finance professor is to see that this
+theory breaks down
+
+ align:start position:0%
+theory breaks down
+ 
+
+ align:start position:0%
+theory breaks down
+because then we actually can go transact
+
+ align:start position:0%
+because then we actually can go transact
+ 
+
+ align:start position:0%
+because then we actually can go transact
+in the marketplace and make money. So,
+
+ align:start position:0%
+in the marketplace and make money. So,
+ 
+
+ align:start position:0%
+in the marketplace and make money. So,
+if the law of one price fails, instead
+
+ align:start position:0%
+if the law of one price fails, instead
+ 
+
+ align:start position:0%
+if the law of one price fails, instead
+of calling me up and complaining about
+
+ align:start position:0%
+of calling me up and complaining about
+ 
+
+ align:start position:0%
+of calling me up and complaining about
+it, you should call me up and tell me
+
+ align:start position:0%
+it, you should call me up and tell me
+ 
+
+ align:start position:0%
+it, you should call me up and tell me
+what it is so I can take advantage of
+
+ align:start position:0%
+what it is so I can take advantage of
+ 
+
+ align:start position:0%
+what it is so I can take advantage of
+it. All right? It's a great thing. And
+
+ align:start position:0%
+it. All right? It's a great thing. And
+ 
+
+ align:start position:0%
+it. All right? It's a great thing. And
+here's the example. This price of a pure
+
+ align:start position:0%
+here's the example. This price of a pure
+ 
+
+ align:start position:0%
+here's the example. This price of a pure
+of a coup coupon bond is got to be equal
+
+ align:start position:0%
+of a coup coupon bond is got to be equal
+ 
+
+ align:start position:0%
+of a coup coupon bond is got to be equal
+to the prices of the discount bonds
+
+ align:start position:0%
+to the prices of the discount bonds
+ 
+
+ align:start position:0%
+to the prices of the discount bonds
+multiplied by the number of bonds you
+
+ align:start position:0%
+multiplied by the number of bonds you
+ 
+
+ align:start position:0%
+multiplied by the number of bonds you
+need in order to yield an identical cash
+
+ align:start position:0%
+need in order to yield an identical cash
+ 
+
+ align:start position:0%
+need in order to yield an identical cash
+flow.
+
+ align:start position:0%
+flow.
+ 
+
+ align:start position:0%
+flow.
+Okay. Now, if you have an identical cash
+
+ align:start position:0%
+Okay. Now, if you have an identical cash
+ 
+
+ align:start position:0%
+Okay. Now, if you have an identical cash
+flow, the lefthand side has to equal to
+
+ align:start position:0%
+flow, the lefthand side has to equal to
+ 
+
+ align:start position:0%
+flow, the lefthand side has to equal to
+the right hand side. If it doesn't, if
+
+ align:start position:0%
+the right hand side. If it doesn't, if
+ 
+
+ align:start position:0%
+the right hand side. If it doesn't, if
+the price of the left hand side is
+
+ align:start position:0%
+the price of the left hand side is
+ 
+
+ align:start position:0%
+the price of the left hand side is
+greater than the prices of the right
+
+ align:start position:0%
+greater than the prices of the right
+ 
+
+ align:start position:0%
+greater than the prices of the right
+hand side, then you should feel very
+
+ align:start position:0%
+hand side, then you should feel very
+ 
+
+ align:start position:0%
+hand side, then you should feel very
+happy because what you're going to do is
+
+ align:start position:0%
+happy because what you're going to do is
+ 
+
+ align:start position:0%
+happy because what you're going to do is
+to make money. Now, how much money are
+
+ align:start position:0%
+to make money. Now, how much money are
+ 
+
+ align:start position:0%
+to make money. Now, how much money are
+you going to make? Well, let's see. What
+
+ align:start position:0%
+you going to make? Well, let's see. What
+ 
+
+ align:start position:0%
+you going to make? Well, let's see. What
+you're going to do is you're gonna
+
+ align:start position:0%
+you're going to do is you're gonna
+ 
+
+ align:start position:0%
+you're going to do is you're gonna
+you're going to buy the right hand side,
+
+ align:start position:0%
+you're going to buy the right hand side,
+ 
+
+ align:start position:0%
+you're going to buy the right hand side,
+you're going to buy those bonds, and
+
+ align:start position:0%
+you're going to buy those bonds, and
+ 
+
+ align:start position:0%
+you're going to buy those bonds, and
+you're going to sell the lefthand side
+
+ align:start position:0%
+you're going to sell the lefthand side
+ 
+
+ align:start position:0%
+you're going to sell the lefthand side
+bond. So you what you make is that
+
+ align:start position:0%
+bond. So you what you make is that
+ 
+
+ align:start position:0%
+bond. So you what you make is that
+difference, right? Because you're buying
+
+ align:start position:0%
+difference, right? Because you're buying
+ 
+
+ align:start position:0%
+difference, right? Because you're buying
+you're spending a certain amount of
+
+ align:start position:0%
+you're spending a certain amount of
+ 
+
+ align:start position:0%
+you're spending a certain amount of
+money. That's the right-hand amount of
+
+ align:start position:0%
+money. That's the right-hand amount of
+ 
+
+ align:start position:0%
+money. That's the right-hand amount of
+money. And the left hand side is what
+
+ align:start position:0%
+money. And the left hand side is what
+ 
+
+ align:start position:0%
+money. And the left hand side is what
+you're going to get. And so you're
+
+ align:start position:0%
+you're going to get. And so you're
+ 
+
+ align:start position:0%
+you're going to get. And so you're
+actually going to you're actually going
+
+ align:start position:0%
+actually going to you're actually going
+ 
+
+ align:start position:0%
+actually going to you're actually going
+to be able to make that difference.
+
+ align:start position:0%
+to be able to make that difference.
+ 
+
+ align:start position:0%
+to be able to make that difference.
+But here's the key. When you make that
+
+ align:start position:0%
+But here's the key. When you make that
+ 
+
+ align:start position:0%
+But here's the key. When you make that
+difference, it's not a risky investment.
+
+ align:start position:0%
+difference, it's not a risky investment.
+ 
+
+ align:start position:0%
+difference, it's not a risky investment.
+There is no risk.
+
+ align:start position:0%
+There is no risk.
+ 
+
+ align:start position:0%
+There is no risk.
+By the way, how much money did you have
+
+ align:start position:0%
+By the way, how much money did you have
+ 
+
+ align:start position:0%
+By the way, how much money did you have
+to spend? How much of your own personal
+
+ align:start position:0%
+to spend? How much of your own personal
+ 
+
+ align:start position:0%
+to spend? How much of your own personal
+wealth did you have to commit to this
+
+ align:start position:0%
+wealth did you have to commit to this
+ 
+
+ align:start position:0%
+wealth did you have to commit to this
+trade?
+
+ align:start position:0%
+trade?
+ 
+
+ align:start position:0%
+trade?
+Just the risk.
+
+ align:start position:0%
+Just the risk.
+ 
+
+ align:start position:0%
+Just the risk.
+Just the risk. What risk?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Did you have to spend that?
+
+ align:start position:0%
+Did you have to spend that?
+ 
+
+ align:start position:0%
+Did you have to spend that?
+That's money that you get, not that you
+
+ align:start position:0%
+That's money that you get, not that you
+ 
+
+ align:start position:0%
+That's money that you get, not that you
+have to spend. Is there any money that
+
+ align:start position:0%
+have to spend. Is there any money that
+ 
+
+ align:start position:0%
+have to spend. Is there any money that
+comes out of your pocket to do this
+
+ align:start position:0%
+comes out of your pocket to do this
+ 
+
+ align:start position:0%
+comes out of your pocket to do this
+trade? No. because what you're buying is
+
+ align:start position:0%
+trade? No. because what you're buying is
+ 
+
+ align:start position:0%
+trade? No. because what you're buying is
+actually financed by what you sold. And
+
+ align:start position:0%
+actually financed by what you sold. And
+ 
+
+ align:start position:0%
+actually financed by what you sold. And
+then on top of that, you have a little
+
+ align:start position:0%
+then on top of that, you have a little
+ 
+
+ align:start position:0%
+then on top of that, you have a little
+extra left over. Okay?
+
+ align:start position:0%
+extra left over. Okay?
+ 
+
+ align:start position:0%
+extra left over. Okay?
+So, this is like one of these
+
+ align:start position:0%
+So, this is like one of these
+ 
+
+ align:start position:0%
+So, this is like one of these
+infomercials at 2:00 in the morning. You
+
+ align:start position:0%
+infomercials at 2:00 in the morning. You
+ 
+
+ align:start position:0%
+infomercials at 2:00 in the morning. You
+know, real estate, how to make a million
+
+ align:start position:0%
+know, real estate, how to make a million
+ 
+
+ align:start position:0%
+know, real estate, how to make a million
+dollars in real estate with no money
+
+ align:start position:0%
+dollars in real estate with no money
+ 
+
+ align:start position:0%
+dollars in real estate with no money
+down, right? You've put no money down.
+
+ align:start position:0%
+down, right? You've put no money down.
+ 
+
+ align:start position:0%
+down, right? You've put no money down.
+You haven't spent any money because what
+
+ align:start position:0%
+You haven't spent any money because what
+ 
+
+ align:start position:0%
+You haven't spent any money because what
+you've done is you've sold a bond and
+
+ align:start position:0%
+you've done is you've sold a bond and
+ 
+
+ align:start position:0%
+you've done is you've sold a bond and
+you've gotten this amount of cash. With
+
+ align:start position:0%
+you've gotten this amount of cash. With
+ 
+
+ align:start position:0%
+you've gotten this amount of cash. With
+that cash, you can buy these bonds. And
+
+ align:start position:0%
+that cash, you can buy these bonds. And
+ 
+
+ align:start position:0%
+that cash, you can buy these bonds. And
+how do you know you have money left
+
+ align:start position:0%
+how do you know you have money left
+ 
+
+ align:start position:0%
+how do you know you have money left
+over?
+
+ align:start position:0%
+over?
+ 
+
+ align:start position:0%
+over?
+By assumption. I'm assuming that this
+
+ align:start position:0%
+By assumption. I'm assuming that this
+ 
+
+ align:start position:0%
+By assumption. I'm assuming that this
+price is greater than that price. So now
+
+ align:start position:0%
+price is greater than that price. So now
+ 
+
+ align:start position:0%
+price is greater than that price. So now
+you have money left over. You've put no
+
+ align:start position:0%
+you have money left over. You've put no
+ 
+
+ align:start position:0%
+you have money left over. You've put no
+money down. You have cash in the pocket.
+
+ align:start position:0%
+money down. You have cash in the pocket.
+ 
+
+ align:start position:0%
+money down. You have cash in the pocket.
+You have no risk. You have no
+
+ align:start position:0%
+You have no risk. You have no
+ 
+
+ align:start position:0%
+You have no risk. You have no
+obligations because all the future cash
+
+ align:start position:0%
+obligations because all the future cash
+ 
+
+ align:start position:0%
+obligations because all the future cash
+flows that you owe are financed
+
+ align:start position:0%
+flows that you owe are financed
+ 
+
+ align:start position:0%
+flows that you owe are financed
+completely by the bonds that you bought.
+
+ align:start position:0%
+completely by the bonds that you bought.
+ 
+
+ align:start position:0%
+completely by the bonds that you bought.
+One for one, dollar for dollar, it
+
+ align:start position:0%
+One for one, dollar for dollar, it
+ 
+
+ align:start position:0%
+One for one, dollar for dollar, it
+matches. So literally as of today, you
+
+ align:start position:0%
+matches. So literally as of today, you
+ 
+
+ align:start position:0%
+matches. So literally as of today, you
+walk away from this transaction a richer
+
+ align:start position:0%
+walk away from this transaction a richer
+ 
+
+ align:start position:0%
+walk away from this transaction a richer
+individual. Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, that let me get back to that.
+
+ align:start position:0%
+Well, that let me get back to that.
+ 
+
+ align:start position:0%
+Well, that let me get back to that.
+That's a that's an interesting point.
+
+ align:start position:0%
+That's a that's an interesting point.
+ 
+
+ align:start position:0%
+That's a that's an interesting point.
+The question is, can these things really
+
+ align:start position:0%
+The question is, can these things really
+ 
+
+ align:start position:0%
+The question is, can these things really
+exist? Because once they do, it's almost
+
+ align:start position:0%
+exist? Because once they do, it's almost
+ 
+
+ align:start position:0%
+exist? Because once they do, it's almost
+too late because they're gone.
+
+ align:start position:0%
+too late because they're gone.
+ 
+
+ align:start position:0%
+too late because they're gone.
+And then follow up. Do is it just my
+
+ align:start position:0%
+And then follow up. Do is it just my
+ 
+
+ align:start position:0%
+And then follow up. Do is it just my
+imagination or do arbitrage desks exist?
+
+ align:start position:0%
+imagination or do arbitrage desks exist?
+ 
+
+ align:start position:0%
+imagination or do arbitrage desks exist?
+Arbitrage desks absolutely exist in
+
+ align:start position:0%
+Arbitrage desks absolutely exist in
+ 
+
+ align:start position:0%
+Arbitrage desks absolutely exist in
+financial firms
+
+ align:start position:0%
+financial firms
+ 
+
+ align:start position:0%
+financial firms
+and what they do is look for this stuff
+
+ align:start position:0%
+and what they do is look for this stuff
+ 
+
+ align:start position:0%
+and what they do is look for this stuff
+all day long. That's what they do. And
+
+ align:start position:0%
+all day long. That's what they do. And
+ 
+
+ align:start position:0%
+all day long. That's what they do. And
+so is it true that by the time you
+
+ align:start position:0%
+so is it true that by the time you
+ 
+
+ align:start position:0%
+so is it true that by the time you
+identify it's gone? Well, it's true if
+
+ align:start position:0%
+identify it's gone? Well, it's true if
+ 
+
+ align:start position:0%
+identify it's gone? Well, it's true if
+you're a finance academic um as well as
+
+ align:start position:0%
+you're a finance academic um as well as
+ 
+
+ align:start position:0%
+you're a finance academic um as well as
+a uh a retail investor.
+
+ align:start position:0%
+a uh a retail investor.
+ 
+
+ align:start position:0%
+a uh a retail investor.
+But you guys, you're going to go out in
+
+ align:start position:0%
+But you guys, you're going to go out in
+ 
+
+ align:start position:0%
+But you guys, you're going to go out in
+the job market and you're going to be
+
+ align:start position:0%
+the job market and you're going to be
+ 
+
+ align:start position:0%
+the job market and you're going to be
+hired by some of these arbitrage desks.
+
+ align:start position:0%
+hired by some of these arbitrage desks.
+ 
+
+ align:start position:0%
+hired by some of these arbitrage desks.
+So, you're going to be doing this. In
+
+ align:start position:0%
+So, you're going to be doing this. In
+ 
+
+ align:start position:0%
+So, you're going to be doing this. In
+fact, you're going to be doing something
+
+ align:start position:0%
+fact, you're going to be doing something
+ 
+
+ align:start position:0%
+fact, you're going to be doing something
+quite a bit more complicated. I'll get
+
+ align:start position:0%
+quite a bit more complicated. I'll get
+ 
+
+ align:start position:0%
+quite a bit more complicated. I'll get
+to that in one minute. Before I do that,
+
+ align:start position:0%
+to that in one minute. Before I do that,
+ 
+
+ align:start position:0%
+to that in one minute. Before I do that,
+I want to make sure that everybody's
+
+ align:start position:0%
+I want to make sure that everybody's
+ 
+
+ align:start position:0%
+I want to make sure that everybody's
+with me about this arbitrage. Yes.
+
+ align:start position:0%
+with me about this arbitrage. Yes.
+ 
+
+ align:start position:0%
+with me about this arbitrage. Yes.
+Um, is there any assumption that there's
+
+ align:start position:0%
+Um, is there any assumption that there's
+ 
+
+ align:start position:0%
+Um, is there any assumption that there's
+no transaction cost?
+
+ align:start position:0%
+no transaction cost?
+ 
+
+ align:start position:0%
+no transaction cost?
+Very good point. Yes. In this context,
+
+ align:start position:0%
+Very good point. Yes. In this context,
+ 
+
+ align:start position:0%
+Very good point. Yes. In this context,
+there's an assumption that you can buy
+
+ align:start position:0%
+there's an assumption that you can buy
+ 
+
+ align:start position:0%
+there's an assumption that you can buy
+and sell freely with no transactions
+
+ align:start position:0%
+and sell freely with no transactions
+ 
+
+ align:start position:0%
+and sell freely with no transactions
+cost. Obviously, in the real world,
+
+ align:start position:0%
+cost. Obviously, in the real world,
+ 
+
+ align:start position:0%
+cost. Obviously, in the real world,
+there are transactions costs. You got to
+
+ align:start position:0%
+there are transactions costs. You got to
+ 
+
+ align:start position:0%
+there are transactions costs. You got to
+stick those in and figure out whether
+
+ align:start position:0%
+stick those in and figure out whether
+ 
+
+ align:start position:0%
+stick those in and figure out whether
+you can still make money with
+
+ align:start position:0%
+you can still make money with
+ 
+
+ align:start position:0%
+you can still make money with
+transactions cost. Now, one form of
+
+ align:start position:0%
+transactions cost. Now, one form of
+ 
+
+ align:start position:0%
+transactions cost. Now, one form of
+transactions cost is a is not a a
+
+ align:start position:0%
+transactions cost is a is not a a
+ 
+
+ align:start position:0%
+transactions cost is a is not a a
+numerical cost, but it's a friction.
+
+ align:start position:0%
+numerical cost, but it's a friction.
+ 
+
+ align:start position:0%
+numerical cost, but it's a friction.
+What do you have to be able to do in
+
+ align:start position:0%
+What do you have to be able to do in
+ 
+
+ align:start position:0%
+What do you have to be able to do in
+order to do this transaction?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What financial
+
+ align:start position:0%
+What financial
+ 
+
+ align:start position:0%
+What financial
+operation do you need in order to be
+
+ align:start position:0%
+operation do you need in order to be
+ 
+
+ align:start position:0%
+operation do you need in order to be
+able to get this deal done? Yeah.
+
+ align:start position:0%
+able to get this deal done? Yeah.
+ 
+
+ align:start position:0%
+able to get this deal done? Yeah.
+Well, you have to be able to short sell.
+
+ align:start position:0%
+Well, you have to be able to short sell.
+ 
+
+ align:start position:0%
+Well, you have to be able to short sell.
+Short sell, right? Remember, we talked
+
+ align:start position:0%
+Short sell, right? Remember, we talked
+ 
+
+ align:start position:0%
+Short sell, right? Remember, we talked
+about short selling last time. That's
+
+ align:start position:0%
+about short selling last time. That's
+ 
+
+ align:start position:0%
+about short selling last time. That's
+selling something you don't own.
+
+ align:start position:0%
+selling something you don't own.
+ 
+
+ align:start position:0%
+selling something you don't own.
+So, you have to borrow the bond from
+
+ align:start position:0%
+So, you have to borrow the bond from
+ 
+
+ align:start position:0%
+So, you have to borrow the bond from
+somebody and then sell it and get those
+
+ align:start position:0%
+somebody and then sell it and get those
+ 
+
+ align:start position:0%
+somebody and then sell it and get those
+proceeds.
+
+ align:start position:0%
+proceeds.
+ 
+
+ align:start position:0%
+proceeds.
+What if it were the case that somebody
+
+ align:start position:0%
+What if it were the case that somebody
+ 
+
+ align:start position:0%
+What if it were the case that somebody
+imposed a constraint that you can't
+
+ align:start position:0%
+imposed a constraint that you can't
+ 
+
+ align:start position:0%
+imposed a constraint that you can't
+short sell? Who would ever do that?
+
+ align:start position:0%
+short sell? Who would ever do that?
+ 
+
+ align:start position:0%
+short sell? Who would ever do that?
+Well, we've seen what happens uh in the
+
+ align:start position:0%
+Well, we've seen what happens uh in the
+ 
+
+ align:start position:0%
+Well, we've seen what happens uh in the
+marketplace that can generate that kind
+
+ align:start position:0%
+marketplace that can generate that kind
+ 
+
+ align:start position:0%
+marketplace that can generate that kind
+of a constraint. What happens if you
+
+ align:start position:0%
+of a constraint. What happens if you
+ 
+
+ align:start position:0%
+of a constraint. What happens if you
+can't short sell? Yeah. need to put up
+
+ align:start position:0%
+can't short sell? Yeah. need to put up
+ 
+
+ align:start position:0%
+can't short sell? Yeah. need to put up
+the cost.
+
+ align:start position:0%
+the cost.
+ 
+
+ align:start position:0%
+the cost.
+What's that?
+
+ align:start position:0%
+What's that?
+ 
+
+ align:start position:0%
+What's that?
+You need to put up the cost of the
+
+ align:start position:0%
+You need to put up the cost of the
+ 
+
+ align:start position:0%
+You need to put up the cost of the
+Well, in fact, yes, you need to put up
+
+ align:start position:0%
+Well, in fact, yes, you need to put up
+ 
+
+ align:start position:0%
+Well, in fact, yes, you need to put up
+the cost, but it doesn't it really
+
+ align:start position:0%
+the cost, but it doesn't it really
+ 
+
+ align:start position:0%
+the cost, but it doesn't it really
+defeats the purpose because if you're
+
+ align:start position:0%
+defeats the purpose because if you're
+ 
+
+ align:start position:0%
+defeats the purpose because if you're
+going to buy the bond and then sell the
+
+ align:start position:0%
+going to buy the bond and then sell the
+ 
+
+ align:start position:0%
+going to buy the bond and then sell the
+bond, you haven't really done anything,
+
+ align:start position:0%
+bond, you haven't really done anything,
+ 
+
+ align:start position:0%
+bond, you haven't really done anything,
+right? This arbitrage argument relies on
+
+ align:start position:0%
+right? This arbitrage argument relies on
+ 
+
+ align:start position:0%
+right? This arbitrage argument relies on
+the fact that you can sell something you
+
+ align:start position:0%
+the fact that you can sell something you
+ 
+
+ align:start position:0%
+the fact that you can sell something you
+don't own by borrowing and shorting it
+
+ align:start position:0%
+don't own by borrowing and shorting it
+ 
+
+ align:start position:0%
+don't own by borrowing and shorting it
+and getting the proceeds and then giving
+
+ align:start position:0%
+and getting the proceeds and then giving
+ 
+
+ align:start position:0%
+and getting the proceeds and then giving
+it back to the person you borrowed
+
+ align:start position:0%
+it back to the person you borrowed
+ 
+
+ align:start position:0%
+it back to the person you borrowed
+whenever they want. Okay?
+
+ align:start position:0%
+whenever they want. Okay?
+ 
+
+ align:start position:0%
+whenever they want. Okay?
+If I don't allow you to short sell, this
+
+ align:start position:0%
+If I don't allow you to short sell, this
+ 
+
+ align:start position:0%
+If I don't allow you to short sell, this
+argument doesn't work anymore.
+
+ align:start position:0%
+argument doesn't work anymore.
+ 
+
+ align:start position:0%
+argument doesn't work anymore.
+And what that means is that this pricing
+
+ align:start position:0%
+And what that means is that this pricing
+ 
+
+ align:start position:0%
+And what that means is that this pricing
+relationship, this left-hand side has to
+
+ align:start position:0%
+relationship, this left-hand side has to
+ 
+
+ align:start position:0%
+relationship, this left-hand side has to
+equal the right hand side, that
+
+ align:start position:0%
+equal the right hand side, that
+ 
+
+ align:start position:0%
+equal the right hand side, that
+relationship goes out the window.
+
+ align:start position:0%
+relationship goes out the window.
+ 
+
+ align:start position:0%
+relationship goes out the window.
+For the next several weeks and possibly
+
+ align:start position:0%
+For the next several weeks and possibly
+ 
+
+ align:start position:0%
+For the next several weeks and possibly
+several months, finance theory is going
+
+ align:start position:0%
+several months, finance theory is going
+ 
+
+ align:start position:0%
+several months, finance theory is going
+to be on vacation uh because the
+
+ align:start position:0%
+to be on vacation uh because the
+ 
+
+ align:start position:0%
+to be on vacation uh because the
+government has suspended short sales for
+
+ align:start position:0%
+government has suspended short sales for
+ 
+
+ align:start position:0%
+government has suspended short sales for
+certain securities.
+
+ align:start position:0%
+certain securities.
+ 
+
+ align:start position:0%
+certain securities.
+And so the kind of force of markets that
+
+ align:start position:0%
+And so the kind of force of markets that
+ 
+
+ align:start position:0%
+And so the kind of force of markets that
+drive prices towards not an equilibrium
+
+ align:start position:0%
+drive prices towards not an equilibrium
+ 
+
+ align:start position:0%
+drive prices towards not an equilibrium
+but a pricing relationship that does not
+
+ align:start position:0%
+but a pricing relationship that does not
+ 
+
+ align:start position:0%
+but a pricing relationship that does not
+depend on equilibrium but depends on the
+
+ align:start position:0%
+depend on equilibrium but depends on the
+ 
+
+ align:start position:0%
+depend on equilibrium but depends on the
+law of one price
+
+ align:start position:0%
+law of one price
+ 
+
+ align:start position:0%
+law of one price
+that goes out the window if you can't
+
+ align:start position:0%
+that goes out the window if you can't
+ 
+
+ align:start position:0%
+that goes out the window if you can't
+short sell. Yeah. I guess I'm just going
+
+ align:start position:0%
+short sell. Yeah. I guess I'm just going
+ 
+
+ align:start position:0%
+short sell. Yeah. I guess I'm just going
+to understand why the Treasury um was
+
+ align:start position:0%
+to understand why the Treasury um was
+ 
+
+ align:start position:0%
+to understand why the Treasury um was
+looking for inpight on this. Why the
+
+ align:start position:0%
+looking for inpight on this. Why the
+ 
+
+ align:start position:0%
+looking for inpight on this. Why the
+Treasury wouldn't have just made the
+
+ align:start position:0%
+Treasury wouldn't have just made the
+ 
+
+ align:start position:0%
+Treasury wouldn't have just made the
+short interest on on their short sales
+
+ align:start position:0%
+short interest on on their short sales
+ 
+
+ align:start position:0%
+short interest on on their short sales
+so high that it was almost prohibited.
+
+ align:start position:0%
+so high that it was almost prohibited.
+ 
+
+ align:start position:0%
+so high that it was almost prohibited.
+But you really wanted to short focus um
+
+ align:start position:0%
+But you really wanted to short focus um
+ 
+
+ align:start position:0%
+But you really wanted to short focus um
+the instruments to hedge portfolios
+
+ align:start position:0%
+the instruments to hedge portfolios
+ 
+
+ align:start position:0%
+the instruments to hedge portfolios
+could do that if they wanted to pay
+
+ align:start position:0%
+could do that if they wanted to pay
+ 
+
+ align:start position:0%
+could do that if they wanted to pay
+that.
+
+ align:start position:0%
+that.
+ 
+
+ align:start position:0%
+that.
+You know that that's a fantastic
+
+ align:start position:0%
+You know that that's a fantastic
+ 
+
+ align:start position:0%
+You know that that's a fantastic
+alternative. I think that would have
+
+ align:start position:0%
+alternative. I think that would have
+ 
+
+ align:start position:0%
+alternative. I think that would have
+been far better. You're absolutely
+
+ align:start position:0%
+been far better. You're absolutely
+ 
+
+ align:start position:0%
+been far better. You're absolutely
+right. Increase the cost of shortselling
+
+ align:start position:0%
+right. Increase the cost of shortselling
+ 
+
+ align:start position:0%
+right. Increase the cost of shortselling
+by raising borrowing costs. By the way,
+
+ align:start position:0%
+by raising borrowing costs. By the way,
+ 
+
+ align:start position:0%
+by raising borrowing costs. By the way,
+when you short sell, as we said last
+
+ align:start position:0%
+when you short sell, as we said last
+ 
+
+ align:start position:0%
+when you short sell, as we said last
+time, it's not free. People aren't going
+
+ align:start position:0%
+time, it's not free. People aren't going
+ 
+
+ align:start position:0%
+time, it's not free. People aren't going
+to lend you the security for free.
+
+ align:start position:0%
+to lend you the security for free.
+ 
+
+ align:start position:0%
+to lend you the security for free.
+They're going to charge you for it. So,
+
+ align:start position:0%
+They're going to charge you for it. So,
+ 
+
+ align:start position:0%
+They're going to charge you for it. So,
+what if instead of
+
+ align:start position:0%
+what if instead of
+ 
+
+ align:start position:0%
+what if instead of
+forbidding it all together?
+
+ align:start position:0%
+forbidding it all together?
+ 
+
+ align:start position:0%
+forbidding it all together?
+Why not just triple the cost or
+
+ align:start position:0%
+Why not just triple the cost or
+ 
+
+ align:start position:0%
+Why not just triple the cost or
+quadruple the cost there? Therefore,
+
+ align:start position:0%
+quadruple the cost there? Therefore,
+ 
+
+ align:start position:0%
+quadruple the cost there? Therefore,
+only people who really really need to do
+
+ align:start position:0%
+only people who really really need to do
+ 
+
+ align:start position:0%
+only people who really really need to do
+it will do it. The problem with that is
+
+ align:start position:0%
+it will do it. The problem with that is
+ 
+
+ align:start position:0%
+it will do it. The problem with that is
+more of a political one. The political
+
+ align:start position:0%
+more of a political one. The political
+ 
+
+ align:start position:0%
+more of a political one. The political
+problem is that we want these evildoers,
+
+ align:start position:0%
+problem is that we want these evildoers,
+ 
+
+ align:start position:0%
+problem is that we want these evildoers,
+these uh uh short sellers that are
+
+ align:start position:0%
+these uh uh short sellers that are
+ 
+
+ align:start position:0%
+these uh uh short sellers that are
+driving the prices of financial
+
+ align:start position:0%
+driving the prices of financial
+ 
+
+ align:start position:0%
+driving the prices of financial
+securities to stop their bad activities.
+
+ align:start position:0%
+securities to stop their bad activities.
+ 
+
+ align:start position:0%
+securities to stop their bad activities.
+And so what we're going to do is to
+
+ align:start position:0%
+And so what we're going to do is to
+ 
+
+ align:start position:0%
+And so what we're going to do is to
+mandate by law that they can't do that.
+
+ align:start position:0%
+mandate by law that they can't do that.
+ 
+
+ align:start position:0%
+mandate by law that they can't do that.
+Now, that may be a reasonable thing from
+
+ align:start position:0%
+Now, that may be a reasonable thing from
+ 
+
+ align:start position:0%
+Now, that may be a reasonable thing from
+a political perspective, but it's not a
+
+ align:start position:0%
+a political perspective, but it's not a
+ 
+
+ align:start position:0%
+a political perspective, but it's not a
+reasonable thing from an economic
+
+ align:start position:0%
+reasonable thing from an economic
+ 
+
+ align:start position:0%
+reasonable thing from an economic
+perspective because what it does is it
+
+ align:start position:0%
+perspective because what it does is it
+ 
+
+ align:start position:0%
+perspective because what it does is it
+disrupts relationships like this,
+
+ align:start position:0%
+disrupts relationships like this,
+ 
+
+ align:start position:0%
+disrupts relationships like this,
+pricing relationships like this.
+
+ align:start position:0%
+pricing relationships like this.
+ 
+
+ align:start position:0%
+pricing relationships like this.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Can you actually change the borrowing
+
+ align:start position:0%
+Can you actually change the borrowing
+ 
+
+ align:start position:0%
+Can you actually change the borrowing
+cost for a few stocks or security?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean, shorting is a few stocks. Can
+
+ align:start position:0%
+I mean, shorting is a few stocks. Can
+ 
+
+ align:start position:0%
+I mean, shorting is a few stocks. Can
+you raise the interest rate?
+
+ align:start position:0%
+you raise the interest rate?
+ 
+
+ align:start position:0%
+you raise the interest rate?
+Well, um, if you're the government and
+
+ align:start position:0%
+Well, um, if you're the government and
+ 
+
+ align:start position:0%
+Well, um, if you're the government and
+you're in a time of crisis, it seems
+
+ align:start position:0%
+you're in a time of crisis, it seems
+ 
+
+ align:start position:0%
+you're in a time of crisis, it seems
+like you can do anything you want. Um,
+
+ align:start position:0%
+like you can do anything you want. Um,
+ 
+
+ align:start position:0%
+like you can do anything you want. Um,
+so I mean, practically, yes, you can say
+
+ align:start position:0%
+so I mean, practically, yes, you can say
+ 
+
+ align:start position:0%
+so I mean, practically, yes, you can say
+for all financial stocks that are on
+
+ align:start position:0%
+for all financial stocks that are on
+ 
+
+ align:start position:0%
+for all financial stocks that are on
+this list, we will now charge an extra
+
+ align:start position:0%
+this list, we will now charge an extra
+ 
+
+ align:start position:0%
+this list, we will now charge an extra
+high rate of of interest uh for
+
+ align:start position:0%
+high rate of of interest uh for
+ 
+
+ align:start position:0%
+high rate of of interest uh for
+borrowing those stocks. And in fact,
+
+ align:start position:0%
+borrowing those stocks. And in fact,
+ 
+
+ align:start position:0%
+borrowing those stocks. And in fact,
+there exists a mechanism even before
+
+ align:start position:0%
+there exists a mechanism even before
+ 
+
+ align:start position:0%
+there exists a mechanism even before
+this rule was put in place that for
+
+ align:start position:0%
+this rule was put in place that for
+ 
+
+ align:start position:0%
+this rule was put in place that for
+certain stocks that are quote hard to
+
+ align:start position:0%
+certain stocks that are quote hard to
+ 
+
+ align:start position:0%
+certain stocks that are quote hard to
+borrow, that's a technical term that
+
+ align:start position:0%
+borrow, that's a technical term that
+ 
+
+ align:start position:0%
+borrow, that's a technical term that
+Wall Street firms, brokerage firms use.
+
+ align:start position:0%
+Wall Street firms, brokerage firms use.
+ 
+
+ align:start position:0%
+Wall Street firms, brokerage firms use.
+Securities that are hard to borrow means
+
+ align:start position:0%
+Securities that are hard to borrow means
+ 
+
+ align:start position:0%
+Securities that are hard to borrow means
+that they're very actively traded and
+
+ align:start position:0%
+that they're very actively traded and
+ 
+
+ align:start position:0%
+that they're very actively traded and
+it's very hard to find a counterparty
+
+ align:start position:0%
+it's very hard to find a counterparty
+ 
+
+ align:start position:0%
+it's very hard to find a counterparty
+that's willing to let you borrow it from
+
+ align:start position:0%
+that's willing to let you borrow it from
+ 
+
+ align:start position:0%
+that's willing to let you borrow it from
+them. The hard to borrow stocks
+
+ align:start position:0%
+them. The hard to borrow stocks
+ 
+
+ align:start position:0%
+them. The hard to borrow stocks
+typically are lent out at a premium. So
+
+ align:start position:0%
+typically are lent out at a premium. So
+ 
+
+ align:start position:0%
+typically are lent out at a premium. So
+they are charged higher prices for those
+
+ align:start position:0%
+they are charged higher prices for those
+ 
+
+ align:start position:0%
+they are charged higher prices for those
+that are very very popular and you know
+
+ align:start position:0%
+that are very very popular and you know
+ 
+
+ align:start position:0%
+that are very very popular and you know
+by simply eliminating short sales you
+
+ align:start position:0%
+by simply eliminating short sales you
+ 
+
+ align:start position:0%
+by simply eliminating short sales you
+basically make those costs infinite.
+
+ align:start position:0%
+basically make those costs infinite.
+ 
+
+ align:start position:0%
+basically make those costs infinite.
+That's exactly what's going on. So it
+
+ align:start position:0%
+That's exactly what's going on. So it
+ 
+
+ align:start position:0%
+That's exactly what's going on. So it
+would have been better to make them
+
+ align:start position:0%
+would have been better to make them
+ 
+
+ align:start position:0%
+would have been better to make them
+finite but bigger uh that would have
+
+ align:start position:0%
+finite but bigger uh that would have
+ 
+
+ align:start position:0%
+finite but bigger uh that would have
+been better than than what they did
+
+ align:start position:0%
+been better than than what they did
+ 
+
+ align:start position:0%
+been better than than what they did
+which is making it infinite but from the
+
+ align:start position:0%
+which is making it infinite but from the
+ 
+
+ align:start position:0%
+which is making it infinite but from the
+purely financial markets perspective it
+
+ align:start position:0%
+purely financial markets perspective it
+ 
+
+ align:start position:0%
+purely financial markets perspective it
+would be best if there were no
+
+ align:start position:0%
+would be best if there were no
+ 
+
+ align:start position:0%
+would be best if there were no
+restrictions and no transactions cost at
+
+ align:start position:0%
+restrictions and no transactions cost at
+ 
+
+ align:start position:0%
+restrictions and no transactions cost at
+all. Obviously transactions costs are
+
+ align:start position:0%
+all. Obviously transactions costs are
+ 
+
+ align:start position:0%
+all. Obviously transactions costs are
+inevitable. So when you price these
+
+ align:start position:0%
+inevitable. So when you price these
+ 
+
+ align:start position:0%
+inevitable. So when you price these
+relationships,
+
+ align:start position:0%
+relationships,
+ 
+
+ align:start position:0%
+relationships,
+the equality is going to be up to
+
+ align:start position:0%
+the equality is going to be up to
+ 
+
+ align:start position:0%
+the equality is going to be up to
+transactions cost. There might be a
+
+ align:start position:0%
+transactions cost. There might be a
+ 
+
+ align:start position:0%
+transactions cost. There might be a
+little bit of a wedge between the lefth
+
+ align:start position:0%
+little bit of a wedge between the lefth
+ 
+
+ align:start position:0%
+little bit of a wedge between the lefth
+hand side and the right hand side but
+
+ align:start position:0%
+hand side and the right hand side but
+ 
+
+ align:start position:0%
+hand side and the right hand side but
+the difference will have to be small
+
+ align:start position:0%
+the difference will have to be small
+ 
+
+ align:start position:0%
+the difference will have to be small
+enough that uh apart from transactions
+
+ align:start position:0%
+enough that uh apart from transactions
+ 
+
+ align:start position:0%
+enough that uh apart from transactions
+cost they are not uh significantly
+
+ align:start position:0%
+cost they are not uh significantly
+ 
+
+ align:start position:0%
+cost they are not uh significantly
+different.
+
+ align:start position:0%
+different.
+ 
+
+ align:start position:0%
+different.
+Yeah. Could it be could it be that they
+
+ align:start position:0%
+Yeah. Could it be could it be that they
+ 
+
+ align:start position:0%
+Yeah. Could it be could it be that they
+also stopped the showing because of some
+
+ align:start position:0%
+also stopped the showing because of some
+ 
+
+ align:start position:0%
+also stopped the showing because of some
+illegal transactions or in information
+
+ align:start position:0%
+illegal transactions or in information
+ 
+
+ align:start position:0%
+illegal transactions or in information
+type?
+
+ align:start position:0%
+type?
+ 
+
+ align:start position:0%
+type?
+Well, if it were illegal transactions,
+
+ align:start position:0%
+Well, if it were illegal transactions,
+ 
+
+ align:start position:0%
+Well, if it were illegal transactions,
+the way they should have done it is to
+
+ align:start position:0%
+the way they should have done it is to
+ 
+
+ align:start position:0%
+the way they should have done it is to
+prosecute the illegal parties as opposed
+
+ align:start position:0%
+prosecute the illegal parties as opposed
+ 
+
+ align:start position:0%
+prosecute the illegal parties as opposed
+to stopping short sales for everybody,
+
+ align:start position:0%
+to stopping short sales for everybody,
+ 
+
+ align:start position:0%
+to stopping short sales for everybody,
+right? That would be a far more
+
+ align:start position:0%
+right? That would be a far more
+ 
+
+ align:start position:0%
+right? That would be a far more
+effective way of dealing with illegal
+
+ align:start position:0%
+effective way of dealing with illegal
+ 
+
+ align:start position:0%
+effective way of dealing with illegal
+activities. That's not what they were
+
+ align:start position:0%
+activities. That's not what they were
+ 
+
+ align:start position:0%
+activities. That's not what they were
+concerned about primarily. The SEC has
+
+ align:start position:0%
+concerned about primarily. The SEC has
+ 
+
+ align:start position:0%
+concerned about primarily. The SEC has
+an enforcement division whose sole job
+
+ align:start position:0%
+an enforcement division whose sole job
+ 
+
+ align:start position:0%
+an enforcement division whose sole job
+it is to check on all the kind of
+
+ align:start position:0%
+it is to check on all the kind of
+ 
+
+ align:start position:0%
+it is to check on all the kind of
+transactions that may have occurred to
+
+ align:start position:0%
+transactions that may have occurred to
+ 
+
+ align:start position:0%
+transactions that may have occurred to
+see whether or not there's any kind of
+
+ align:start position:0%
+see whether or not there's any kind of
+ 
+
+ align:start position:0%
+see whether or not there's any kind of
+illegal activity going on. It wasn't the
+
+ align:start position:0%
+illegal activity going on. It wasn't the
+ 
+
+ align:start position:0%
+illegal activity going on. It wasn't the
+illegal activity that prompted the short
+
+ align:start position:0%
+illegal activity that prompted the short
+ 
+
+ align:start position:0%
+illegal activity that prompted the short
+sales restriction. It was really the
+
+ align:start position:0%
+sales restriction. It was really the
+ 
+
+ align:start position:0%
+sales restriction. It was really the
+concern that financial firms were being
+
+ align:start position:0%
+concern that financial firms were being
+ 
+
+ align:start position:0%
+concern that financial firms were being
+pounded by short sellers that were
+
+ align:start position:0%
+pounded by short sellers that were
+ 
+
+ align:start position:0%
+pounded by short sellers that were
+betting on them failing. And the more
+
+ align:start position:0%
+betting on them failing. And the more
+ 
+
+ align:start position:0%
+betting on them failing. And the more
+pressure uh that they impose on the
+
+ align:start position:0%
+pressure uh that they impose on the
+ 
+
+ align:start position:0%
+pressure uh that they impose on the
+stock price going down down down, the
+
+ align:start position:0%
+stock price going down down down, the
+ 
+
+ align:start position:0%
+stock price going down down down, the
+more likely it is that people would lose
+
+ align:start position:0%
+more likely it is that people would lose
+ 
+
+ align:start position:0%
+more likely it is that people would lose
+confidence and then all of a sudden stop
+
+ align:start position:0%
+confidence and then all of a sudden stop
+ 
+
+ align:start position:0%
+confidence and then all of a sudden stop
+doing business with it. You know, in
+
+ align:start position:0%
+doing business with it. You know, in
+ 
+
+ align:start position:0%
+doing business with it. You know, in
+many ways that's what happened with Bear
+
+ align:start position:0%
+many ways that's what happened with Bear
+ 
+
+ align:start position:0%
+many ways that's what happened with Bear
+Sterns, at least from the historical
+
+ align:start position:0%
+Sterns, at least from the historical
+ 
+
+ align:start position:0%
+Sterns, at least from the historical
+record. It seems like what happened was
+
+ align:start position:0%
+record. It seems like what happened was
+ 
+
+ align:start position:0%
+record. It seems like what happened was
+that there was a rumor that Bear Sterns
+
+ align:start position:0%
+that there was a rumor that Bear Sterns
+ 
+
+ align:start position:0%
+that there was a rumor that Bear Sterns
+was not going to be uh solvent even
+
+ align:start position:0%
+was not going to be uh solvent even
+ 
+
+ align:start position:0%
+was not going to be uh solvent even
+though they didn't have any particular
+
+ align:start position:0%
+though they didn't have any particular
+ 
+
+ align:start position:0%
+though they didn't have any particular
+uh pressure to uh to pay certain debts
+
+ align:start position:0%
+uh pressure to uh to pay certain debts
+ 
+
+ align:start position:0%
+uh pressure to uh to pay certain debts
+at that point in time. And somehow that
+
+ align:start position:0%
+at that point in time. And somehow that
+ 
+
+ align:start position:0%
+at that point in time. And somehow that
+rumor grew into general fear and you
+
+ align:start position:0%
+rumor grew into general fear and you
+ 
+
+ align:start position:0%
+rumor grew into general fear and you
+know the short sellers got in and
+
+ align:start position:0%
+know the short sellers got in and
+ 
+
+ align:start position:0%
+know the short sellers got in and
+started shorting the stock. The stock
+
+ align:start position:0%
+started shorting the stock. The stock
+ 
+
+ align:start position:0%
+started shorting the stock. The stock
+price went down. People looked and said,
+
+ align:start position:0%
+price went down. People looked and said,
+ 
+
+ align:start position:0%
+price went down. People looked and said,
+"Oh my god, the stock's going down. I
+
+ align:start position:0%
+"Oh my god, the stock's going down. I
+ 
+
+ align:start position:0%
+"Oh my god, the stock's going down. I
+better take my business elsewhere and
+
+ align:start position:0%
+better take my business elsewhere and
+ 
+
+ align:start position:0%
+better take my business elsewhere and
+everybody started doing that. Once
+
+ align:start position:0%
+everybody started doing that. Once
+ 
+
+ align:start position:0%
+everybody started doing that. Once
+everybody started doing that, the firm
+
+ align:start position:0%
+everybody started doing that, the firm
+ 
+
+ align:start position:0%
+everybody started doing that, the firm
+began having great difficulties in
+
+ align:start position:0%
+began having great difficulties in
+ 
+
+ align:start position:0%
+began having great difficulties in
+maintaining a business."
+
+ align:start position:0%
+maintaining a business."
+ 
+
+ align:start position:0%
+maintaining a business."
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Even the case that selling is not
+
+ align:start position:0%
+Even the case that selling is not
+ 
+
+ align:start position:0%
+Even the case that selling is not
+allowed the investors who own the more
+
+ align:start position:0%
+allowed the investors who own the more
+ 
+
+ align:start position:0%
+allowed the investors who own the more
+expensive
+
+ align:start position:0%
+expensive
+ 
+
+ align:start position:0%
+expensive
+That's right.
+
+ align:start position:0%
+That's right.
+ 
+
+ align:start position:0%
+That's right.
+assets are going to sell them because
+
+ align:start position:0%
+assets are going to sell them because
+ 
+
+ align:start position:0%
+assets are going to sell them because
+they're going to think, "Okay, I'm
+
+ align:start position:0%
+they're going to think, "Okay, I'm
+ 
+
+ align:start position:0%
+they're going to think, "Okay, I'm
+selling today. combine here.
+
+ align:start position:0%
+selling today. combine here.
+ 
+
+ align:start position:0%
+selling today. combine here.
+That's right. That's right.
+
+ align:start position:0%
+That's right. That's right.
+ 
+
+ align:start position:0%
+That's right. That's right.
+So again, you have you do the uh demand
+
+ align:start position:0%
+So again, you have you do the uh demand
+ 
+
+ align:start position:0%
+So again, you have you do the uh demand
+and supplying, you have to
+
+ align:start position:0%
+and supplying, you have to
+ 
+
+ align:start position:0%
+and supplying, you have to
+you'll that's that's a very good point.
+
+ align:start position:0%
+you'll that's that's a very good point.
+ 
+
+ align:start position:0%
+you'll that's that's a very good point.
+Let me repeat it. The point is that even
+
+ align:start position:0%
+Let me repeat it. The point is that even
+ 
+
+ align:start position:0%
+Let me repeat it. The point is that even
+if you're not allowed to short sell,
+
+ align:start position:0%
+if you're not allowed to short sell,
+ 
+
+ align:start position:0%
+if you're not allowed to short sell,
+then the folks who own the left hand
+
+ align:start position:0%
+then the folks who own the left hand
+ 
+
+ align:start position:0%
+then the folks who own the left hand
+side, who own the coupon bond, they can
+
+ align:start position:0%
+side, who own the coupon bond, they can
+ 
+
+ align:start position:0%
+side, who own the coupon bond, they can
+say, "Hey, my coupon bond is worth 110,
+
+ align:start position:0%
+say, "Hey, my coupon bond is worth 110,
+ 
+
+ align:start position:0%
+say, "Hey, my coupon bond is worth 110,
+but I can get the exact same payoff by
+
+ align:start position:0%
+but I can get the exact same payoff by
+ 
+
+ align:start position:0%
+but I can get the exact same payoff by
+buying a bunch of pure discount bonds,
+
+ align:start position:0%
+buying a bunch of pure discount bonds,
+ 
+
+ align:start position:0%
+buying a bunch of pure discount bonds,
+and it's only going to cost me a hundred
+
+ align:start position:0%
+and it's only going to cost me a hundred
+ 
+
+ align:start position:0%
+and it's only going to cost me a hundred
+to buy them.
+
+ align:start position:0%
+to buy them.
+ 
+
+ align:start position:0%
+to buy them.
+I'm going to sell my coupon bond at 110
+
+ align:start position:0%
+I'm going to sell my coupon bond at 110
+ 
+
+ align:start position:0%
+I'm going to sell my coupon bond at 110
+and I'm going to buy $100 worth of these
+
+ align:start position:0%
+and I'm going to buy $100 worth of these
+ 
+
+ align:start position:0%
+and I'm going to buy $100 worth of these
+discount bonds and I just made 10 bucks.
+
+ align:start position:0%
+discount bonds and I just made 10 bucks.
+ 
+
+ align:start position:0%
+discount bonds and I just made 10 bucks.
+Now, that can happen as long as two
+
+ align:start position:0%
+Now, that can happen as long as two
+ 
+
+ align:start position:0%
+Now, that can happen as long as two
+things occur. One, the person who owns
+
+ align:start position:0%
+things occur. One, the person who owns
+ 
+
+ align:start position:0%
+things occur. One, the person who owns
+the bond knows about this.
+
+ align:start position:0%
+the bond knows about this.
+ 
+
+ align:start position:0%
+the bond knows about this.
+And two, they actually want to take the
+
+ align:start position:0%
+And two, they actually want to take the
+ 
+
+ align:start position:0%
+And two, they actually want to take the
+trouble to do the trade or they're able
+
+ align:start position:0%
+trouble to do the trade or they're able
+ 
+
+ align:start position:0%
+trouble to do the trade or they're able
+to do the trade. The problem is that
+
+ align:start position:0%
+to do the trade. The problem is that
+ 
+
+ align:start position:0%
+to do the trade. The problem is that
+most of the folks that bought the bond
+
+ align:start position:0%
+most of the folks that bought the bond
+ 
+
+ align:start position:0%
+most of the folks that bought the bond
+on the lefth hand side are pension funds
+
+ align:start position:0%
+on the lefth hand side are pension funds
+ 
+
+ align:start position:0%
+on the lefth hand side are pension funds
+that are not in the proc not in the
+
+ align:start position:0%
+that are not in the proc not in the
+ 
+
+ align:start position:0%
+that are not in the proc not in the
+business of doing these kind of
+
+ align:start position:0%
+business of doing these kind of
+ 
+
+ align:start position:0%
+business of doing these kind of
+arbitrage transactions. So they're not
+
+ align:start position:0%
+arbitrage transactions. So they're not
+ 
+
+ align:start position:0%
+arbitrage transactions. So they're not
+trying to do that. All they want to do
+
+ align:start position:0%
+trying to do that. All they want to do
+ 
+
+ align:start position:0%
+trying to do that. All they want to do
+is they they've got, you know, a bunch
+
+ align:start position:0%
+is they they've got, you know, a bunch
+ 
+
+ align:start position:0%
+is they they've got, you know, a bunch
+of uh pension plan uh participants. They
+
+ align:start position:0%
+of uh pension plan uh participants. They
+ 
+
+ align:start position:0%
+of uh pension plan uh participants. They
+need to pay out their benefits. They've
+
+ align:start position:0%
+need to pay out their benefits. They've
+ 
+
+ align:start position:0%
+need to pay out their benefits. They've
+got contributions. They just want to
+
+ align:start position:0%
+got contributions. They just want to
+ 
+
+ align:start position:0%
+got contributions. They just want to
+match assets to liabilities. They're not
+
+ align:start position:0%
+match assets to liabilities. They're not
+ 
+
+ align:start position:0%
+match assets to liabilities. They're not
+in the business of doing this kind of
+
+ align:start position:0%
+in the business of doing this kind of
+ 
+
+ align:start position:0%
+in the business of doing this kind of
+high-speed transaction.
+
+ align:start position:0%
+high-speed transaction.
+ 
+
+ align:start position:0%
+high-speed transaction.
+So what that means is that you're still
+
+ align:start position:0%
+So what that means is that you're still
+ 
+
+ align:start position:0%
+So what that means is that you're still
+right that if they realize this
+
+ align:start position:0%
+right that if they realize this
+ 
+
+ align:start position:0%
+right that if they realize this
+relationship is there and they are in a
+
+ align:start position:0%
+relationship is there and they are in a
+ 
+
+ align:start position:0%
+relationship is there and they are in a
+position to do the trades,
+
+ align:start position:0%
+position to do the trades,
+ 
+
+ align:start position:0%
+position to do the trades,
+they will sometimes and then that will
+
+ align:start position:0%
+they will sometimes and then that will
+ 
+
+ align:start position:0%
+they will sometimes and then that will
+force prices closer.
+
+ align:start position:0%
+force prices closer.
+ 
+
+ align:start position:0%
+force prices closer.
+But it's not going to be the same kind
+
+ align:start position:0%
+But it's not going to be the same kind
+ 
+
+ align:start position:0%
+But it's not going to be the same kind
+of numerical identity that has to hold
+
+ align:start position:0%
+of numerical identity that has to hold
+ 
+
+ align:start position:0%
+of numerical identity that has to hold
+when you've got greedy people uh like
+
+ align:start position:0%
+when you've got greedy people uh like
+ 
+
+ align:start position:0%
+when you've got greedy people uh like
+myself trying to do the trades and being
+
+ align:start position:0%
+myself trying to do the trades and being
+ 
+
+ align:start position:0%
+myself trying to do the trades and being
+able to do the trades uh at a moment's
+
+ align:start position:0%
+able to do the trades uh at a moment's
+ 
+
+ align:start position:0%
+able to do the trades uh at a moment's
+notice.
+
+ align:start position:0%
+notice.
+ 
+
+ align:start position:0%
+notice.
+Especially to that point
+
+ align:start position:0%
+Especially to that point
+ 
+
+ align:start position:0%
+Especially to that point
+market.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Exactly. Right. There are all sorts of
+
+ align:start position:0%
+Exactly. Right. There are all sorts of
+ 
+
+ align:start position:0%
+Exactly. Right. There are all sorts of
+additional complexities of being able to
+
+ align:start position:0%
+additional complexities of being able to
+ 
+
+ align:start position:0%
+additional complexities of being able to
+do the trade that as a pension plan
+
+ align:start position:0%
+do the trade that as a pension plan
+ 
+
+ align:start position:0%
+do the trade that as a pension plan
+you're not even allowed to do. Never
+
+ align:start position:0%
+you're not even allowed to do. Never
+ 
+
+ align:start position:0%
+you're not even allowed to do. Never
+mind whether you want to do them or not.
+
+ align:start position:0%
+mind whether you want to do them or not.
+ 
+
+ align:start position:0%
+mind whether you want to do them or not.
+So these are the kind of restrictions
+
+ align:start position:0%
+So these are the kind of restrictions
+ 
+
+ align:start position:0%
+So these are the kind of restrictions
+that would present the the uh this gap.
+
+ align:start position:0%
+that would present the the uh this gap.
+ 
+
+ align:start position:0%
+that would present the the uh this gap.
+Okay, but let's for now assume that
+
+ align:start position:0%
+Okay, but let's for now assume that
+ 
+
+ align:start position:0%
+Okay, but let's for now assume that
+there's no gap. We're going to assume
+
+ align:start position:0%
+there's no gap. We're going to assume
+ 
+
+ align:start position:0%
+there's no gap. We're going to assume
+that there's no frictions. We're going
+
+ align:start position:0%
+that there's no frictions. We're going
+ 
+
+ align:start position:0%
+that there's no frictions. We're going
+to assume that there's no short sales uh
+
+ align:start position:0%
+to assume that there's no short sales uh
+ 
+
+ align:start position:0%
+to assume that there's no short sales uh
+prohibitions. And when that happens,
+
+ align:start position:0%
+prohibitions. And when that happens,
+ 
+
+ align:start position:0%
+prohibitions. And when that happens,
+this pricing relationship has to hold.
+
+ align:start position:0%
+this pricing relationship has to hold.
+ 
+
+ align:start position:0%
+this pricing relationship has to hold.
+Now, I promised you I want to show you
+
+ align:start position:0%
+Now, I promised you I want to show you
+ 
+
+ align:start position:0%
+Now, I promised you I want to show you
+something more complicated that all of
+
+ align:start position:0%
+something more complicated that all of
+ 
+
+ align:start position:0%
+something more complicated that all of
+you may do when you get out of here. And
+
+ align:start position:0%
+you may do when you get out of here. And
+ 
+
+ align:start position:0%
+you may do when you get out of here. And
+that's this.
+
+ align:start position:0%
+that's this.
+ 
+
+ align:start position:0%
+that's this.
+Instead of looking at just one bond,
+
+ align:start position:0%
+Instead of looking at just one bond,
+ 
+
+ align:start position:0%
+Instead of looking at just one bond,
+what if we looked at a whole bunch of
+
+ align:start position:0%
+what if we looked at a whole bunch of
+ 
+
+ align:start position:0%
+what if we looked at a whole bunch of
+coupon bonds?
+
+ align:start position:0%
+coupon bonds?
+ 
+
+ align:start position:0%
+coupon bonds?
+Now,
+
+ align:start position:0%
+Now,
+ 
+
+ align:start position:0%
+Now,
+let's take a look using this pricing
+
+ align:start position:0%
+let's take a look using this pricing
+ 
+
+ align:start position:0%
+let's take a look using this pricing
+relationship that's based on the law of
+
+ align:start position:0%
+relationship that's based on the law of
+ 
+
+ align:start position:0%
+relationship that's based on the law of
+one price and basic greed.
+
+ align:start position:0%
+one price and basic greed.
+ 
+
+ align:start position:0%
+one price and basic greed.
+We've got n bonds here, one through n.
+
+ align:start position:0%
+We've got n bonds here, one through n.
+ 
+
+ align:start position:0%
+We've got n bonds here, one through n.
+And each has its own coupon, whatever
+
+ align:start position:0%
+And each has its own coupon, whatever
+ 
+
+ align:start position:0%
+And each has its own coupon, whatever
+that is. I'm just going to use notation
+
+ align:start position:0%
+that is. I'm just going to use notation
+ 
+
+ align:start position:0%
+that is. I'm just going to use notation
+to write down that each bond has its own
+
+ align:start position:0%
+to write down that each bond has its own
+ 
+
+ align:start position:0%
+to write down that each bond has its own
+particular coupon. Right? So, you've got
+
+ align:start position:0%
+particular coupon. Right? So, you've got
+ 
+
+ align:start position:0%
+particular coupon. Right? So, you've got
+a 3% 10-year bond, you've got a 4%
+
+ align:start position:0%
+a 3% 10-year bond, you've got a 4%
+ 
+
+ align:start position:0%
+a 3% 10-year bond, you've got a 4%
+30-year bond, you may have a 5 12% uh
+
+ align:start position:0%
+30-year bond, you may have a 5 12% uh
+ 
+
+ align:start position:0%
+30-year bond, you may have a 5 12% uh
+5-year bond. So, some of these coupons
+
+ align:start position:0%
+5-year bond. So, some of these coupons
+ 
+
+ align:start position:0%
+5-year bond. So, some of these coupons
+may be zero because capital T, I'm going
+
+ align:start position:0%
+may be zero because capital T, I'm going
+ 
+
+ align:start position:0%
+may be zero because capital T, I'm going
+to assume is the most extreme 30-year
+
+ align:start position:0%
+to assume is the most extreme 30-year
+ 
+
+ align:start position:0%
+to assume is the most extreme 30-year
+period, right? So, a five-year bond
+
+ align:start position:0%
+period, right? So, a five-year bond
+ 
+
+ align:start position:0%
+period, right? So, a five-year bond
+would have coupons for the first five
+
+ align:start position:0%
+would have coupons for the first five
+ 
+
+ align:start position:0%
+would have coupons for the first five
+years, and then for all of the coupon
+
+ align:start position:0%
+years, and then for all of the coupon
+ 
+
+ align:start position:0%
+years, and then for all of the coupon
+payments after that, I'm going to have
+
+ align:start position:0%
+payments after that, I'm going to have
+ 
+
+ align:start position:0%
+payments after that, I'm going to have
+000000. Right?
+
+ align:start position:0%
+000000. Right?
+ 
+
+ align:start position:0%
+000000. Right?
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+this should hearken back to your high
+
+ align:start position:0%
+this should hearken back to your high
+ 
+
+ align:start position:0%
+this should hearken back to your high
+school algebra days where you have
+
+ align:start position:0%
+school algebra days where you have
+ 
+
+ align:start position:0%
+school algebra days where you have
+multiple equations
+
+ align:start position:0%
+multiple equations
+ 
+
+ align:start position:0%
+multiple equations
+with multiple unknowns.
+
+ align:start position:0%
+with multiple unknowns.
+ 
+
+ align:start position:0%
+with multiple unknowns.
+Now, what's unknown here in these
+
+ align:start position:0%
+Now, what's unknown here in these
+ 
+
+ align:start position:0%
+Now, what's unknown here in these
+equations? What are the unknowns?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, you observe the prices, right,
+
+ align:start position:0%
+Well, you observe the prices, right,
+ 
+
+ align:start position:0%
+Well, you observe the prices, right,
+from the marketplace. So, the left hand
+
+ align:start position:0%
+from the marketplace. So, the left hand
+ 
+
+ align:start position:0%
+from the marketplace. So, the left hand
+side is not unknown.
+
+ align:start position:0%
+side is not unknown.
+ 
+
+ align:start position:0%
+side is not unknown.
+What about the right hand side? What are
+
+ align:start position:0%
+What about the right hand side? What are
+ 
+
+ align:start position:0%
+What about the right hand side? What are
+the unknowns? What do you What do you
+
+ align:start position:0%
+the unknowns? What do you What do you
+ 
+
+ align:start position:0%
+the unknowns? What do you What do you
+observe? What are the knowns? How about
+
+ align:start position:0%
+observe? What are the knowns? How about
+ 
+
+ align:start position:0%
+observe? What are the knowns? How about
+that? Let's start with that.
+
+ align:start position:0%
+that? Let's start with that.
+ 
+
+ align:start position:0%
+that? Let's start with that.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Uh the coupons.
+
+ align:start position:0%
+Uh the coupons.
+ 
+
+ align:start position:0%
+Uh the coupons.
+The coupons, right? If I tell you that
+
+ align:start position:0%
+The coupons, right? If I tell you that
+ 
+
+ align:start position:0%
+The coupons, right? If I tell you that
+I've got a 30-year 4 and a.5% bond, you
+
+ align:start position:0%
+I've got a 30-year 4 and a.5% bond, you
+ 
+
+ align:start position:0%
+I've got a 30-year 4 and a.5% bond, you
+know what the coupon's going to be,
+
+ align:start position:0%
+know what the coupon's going to be,
+ 
+
+ align:start position:0%
+know what the coupon's going to be,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+You don't know the
+
+ align:start position:0%
+You don't know the
+ 
+
+ align:start position:0%
+You don't know the
+What's that? The yield
+
+ align:start position:0%
+What's that? The yield
+ 
+
+ align:start position:0%
+What's that? The yield
+the yield is what we don't know.
+
+ align:start position:0%
+the yield is what we don't know.
+ 
+
+ align:start position:0%
+the yield is what we don't know.
+All right, that we either get from the
+
+ align:start position:0%
+All right, that we either get from the
+ 
+
+ align:start position:0%
+All right, that we either get from the
+marketplace or we can try to solve it
+
+ align:start position:0%
+marketplace or we can try to solve it
+ 
+
+ align:start position:0%
+marketplace or we can try to solve it
+from these prices.
+
+ align:start position:0%
+from these prices.
+ 
+
+ align:start position:0%
+from these prices.
+But how many different yields do we need
+
+ align:start position:0%
+But how many different yields do we need
+ 
+
+ align:start position:0%
+But how many different yields do we need
+in order to price each bond?
+
+ align:start position:0%
+in order to price each bond?
+ 
+
+ align:start position:0%
+in order to price each bond?
+These are t-year bonds. How many yields?
+
+ align:start position:0%
+These are t-year bonds. How many yields?
+ 
+
+ align:start position:0%
+These are t-year bonds. How many yields?
+Yeah, we need t yields, one for each
+
+ align:start position:0%
+Yeah, we need t yields, one for each
+ 
+
+ align:start position:0%
+Yeah, we need t yields, one for each
+year.
+
+ align:start position:0%
+year.
+ 
+
+ align:start position:0%
+year.
+We have T yields in these equations and
+
+ align:start position:0%
+We have T yields in these equations and
+ 
+
+ align:start position:0%
+We have T yields in these equations and
+they're the same across the different
+
+ align:start position:0%
+they're the same across the different
+ 
+
+ align:start position:0%
+they're the same across the different
+bonds, right? Because we're using the
+
+ align:start position:0%
+bonds, right? Because we're using the
+ 
+
+ align:start position:0%
+bonds, right? Because we're using the
+same pure discount bonds to replicate
+
+ align:start position:0%
+same pure discount bonds to replicate
+ 
+
+ align:start position:0%
+same pure discount bonds to replicate
+each of these coupon bonds.
+
+ align:start position:0%
+each of these coupon bonds.
+ 
+
+ align:start position:0%
+each of these coupon bonds.
+I've got T unknowns. How many equations
+
+ align:start position:0%
+I've got T unknowns. How many equations
+ 
+
+ align:start position:0%
+I've got T unknowns. How many equations
+do I have?
+
+ align:start position:0%
+do I have?
+ 
+
+ align:start position:0%
+do I have?
+N bonds. Right now, on any given day,
+
+ align:start position:0%
+N bonds. Right now, on any given day,
+ 
+
+ align:start position:0%
+N bonds. Right now, on any given day,
+you might have 200 to 300 bonds that are
+
+ align:start position:0%
+you might have 200 to 300 bonds that are
+ 
+
+ align:start position:0%
+you might have 200 to 300 bonds that are
+trading,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but you've only got 30 unknowns.
+
+ align:start position:0%
+but you've only got 30 unknowns.
+ 
+
+ align:start position:0%
+but you've only got 30 unknowns.
+So, let's think back to your high school
+
+ align:start position:0%
+So, let's think back to your high school
+ 
+
+ align:start position:0%
+So, let's think back to your high school
+algebra or college linear algebra days.
+
+ align:start position:0%
+algebra or college linear algebra days.
+ 
+
+ align:start position:0%
+algebra or college linear algebra days.
+If you've got 200 equations and 30
+
+ align:start position:0%
+If you've got 200 equations and 30
+ 
+
+ align:start position:0%
+If you've got 200 equations and 30
+unknowns,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many solutions do you have?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, let's let's get simpler. Suppose
+
+ align:start position:0%
+Well, let's let's get simpler. Suppose
+ 
+
+ align:start position:0%
+Well, let's let's get simpler. Suppose
+you had two equations and two unknowns.
+
+ align:start position:0%
+you had two equations and two unknowns.
+ 
+
+ align:start position:0%
+you had two equations and two unknowns.
+Just one solution.
+
+ align:start position:0%
+Just one solution.
+ 
+
+ align:start position:0%
+Just one solution.
+You have one solution. Assuming certain
+
+ align:start position:0%
+You have one solution. Assuming certain
+ 
+
+ align:start position:0%
+You have one solution. Assuming certain
+kind of conditions that hold like
+
+ align:start position:0%
+kind of conditions that hold like
+ 
+
+ align:start position:0%
+kind of conditions that hold like
+invertability, which we're going to talk
+
+ align:start position:0%
+invertability, which we're going to talk
+ 
+
+ align:start position:0%
+invertability, which we're going to talk
+about in a minute, two equations, two
+
+ align:start position:0%
+about in a minute, two equations, two
+ 
+
+ align:start position:0%
+about in a minute, two equations, two
+unknowns.
+
+ align:start position:0%
+unknowns.
+ 
+
+ align:start position:0%
+unknowns.
+You have one solution. How about uh one
+
+ align:start position:0%
+You have one solution. How about uh one
+ 
+
+ align:start position:0%
+You have one solution. How about uh one
+equation and two unknowns? How many
+
+ align:start position:0%
+equation and two unknowns? How many
+ 
+
+ align:start position:0%
+equation and two unknowns? How many
+solutions?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinite. Okay, that's right. Because
+
+ align:start position:0%
+Infinite. Okay, that's right. Because
+ 
+
+ align:start position:0%
+Infinite. Okay, that's right. Because
+you've got that extra degree of freedom,
+
+ align:start position:0%
+you've got that extra degree of freedom,
+ 
+
+ align:start position:0%
+you've got that extra degree of freedom,
+right? There's lots of different
+
+ align:start position:0%
+right? There's lots of different
+ 
+
+ align:start position:0%
+right? There's lots of different
+solutions. What about uh three equations
+
+ align:start position:0%
+solutions. What about uh three equations
+ 
+
+ align:start position:0%
+solutions. What about uh three equations
+and two unknowns?
+
+ align:start position:0%
+and two unknowns?
+ 
+
+ align:start position:0%
+and two unknowns?
+Now, how many solutions do you have?
+
+ align:start position:0%
+Now, how many solutions do you have?
+ 
+
+ align:start position:0%
+Now, how many solutions do you have?
+Yeah,
+
+ align:start position:0%
+Yeah,
+ 
+
+ align:start position:0%
+Yeah,
+because it's linear, you only have one.
+
+ align:start position:0%
+because it's linear, you only have one.
+ 
+
+ align:start position:0%
+because it's linear, you only have one.
+It's linear.
+
+ align:start position:0%
+It's linear.
+ 
+
+ align:start position:0%
+It's linear.
+Are you guaranteed to have one?
+
+ align:start position:0%
+Are you guaranteed to have one?
+ 
+
+ align:start position:0%
+Are you guaranteed to have one?
+You might have zero.
+
+ align:start position:0%
+You might have zero.
+ 
+
+ align:start position:0%
+You might have zero.
+You might have zero.
+
+ align:start position:0%
+You might have zero.
+ 
+
+ align:start position:0%
+You might have zero.
+What are the conditions under which you
+
+ align:start position:0%
+What are the conditions under which you
+ 
+
+ align:start position:0%
+What are the conditions under which you
+would have one?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The solution of the two equations
+
+ align:start position:0%
+The solution of the two equations
+ 
+
+ align:start position:0%
+The solution of the two equations
+applies for the third one.
+
+ align:start position:0%
+applies for the third one.
+ 
+
+ align:start position:0%
+applies for the third one.
+Right? There is a possibility you have
+
+ align:start position:0%
+Right? There is a possibility you have
+ 
+
+ align:start position:0%
+Right? There is a possibility you have
+one solution if the solution of the two
+
+ align:start position:0%
+one solution if the solution of the two
+ 
+
+ align:start position:0%
+one solution if the solution of the two
+equations actually applies to the third.
+
+ align:start position:0%
+equations actually applies to the third.
+ 
+
+ align:start position:0%
+equations actually applies to the third.
+Do you remember under what condition?
+
+ align:start position:0%
+Do you remember under what condition?
+ 
+
+ align:start position:0%
+Do you remember under what condition?
+Exhausted.
+
+ align:start position:0%
+Exhausted.
+ 
+
+ align:start position:0%
+Exhausted.
+That what?
+
+ align:start position:0%
+That what?
+ 
+
+ align:start position:0%
+That what?
+Exhausted.
+
+ align:start position:0%
+Exhausted.
+ 
+
+ align:start position:0%
+Exhausted.
+Exhausted. That's not quite the term
+
+ align:start position:0%
+Exhausted. That's not quite the term
+ 
+
+ align:start position:0%
+Exhausted. That's not quite the term
+that that mathematicians use. There's
+
+ align:start position:0%
+that that mathematicians use. There's
+ 
+
+ align:start position:0%
+that that mathematicians use. There's
+something called linear dependence.
+
+ align:start position:0%
+something called linear dependence.
+ 
+
+ align:start position:0%
+something called linear dependence.
+That's a very complicated word that
+
+ align:start position:0%
+That's a very complicated word that
+ 
+
+ align:start position:0%
+That's a very complicated word that
+describes the fact that if you have
+
+ align:start position:0%
+describes the fact that if you have
+ 
+
+ align:start position:0%
+describes the fact that if you have
+these two equations and two unknowns and
+
+ align:start position:0%
+these two equations and two unknowns and
+ 
+
+ align:start position:0%
+these two equations and two unknowns and
+you have one solution. You can just take
+
+ align:start position:0%
+you have one solution. You can just take
+ 
+
+ align:start position:0%
+you have one solution. You can just take
+an average of those two, a combination
+
+ align:start position:0%
+an average of those two, a combination
+ 
+
+ align:start position:0%
+an average of those two, a combination
+of those two and you'll get the third
+
+ align:start position:0%
+of those two and you'll get the third
+ 
+
+ align:start position:0%
+of those two and you'll get the third
+one. You can actually replicate the
+
+ align:start position:0%
+one. You can actually replicate the
+ 
+
+ align:start position:0%
+one. You can actually replicate the
+third equation
+
+ align:start position:0%
+third equation
+ 
+
+ align:start position:0%
+third equation
+from those two.
+
+ align:start position:0%
+from those two.
+ 
+
+ align:start position:0%
+from those two.
+What happens if you don't?
+
+ align:start position:0%
+What happens if you don't?
+ 
+
+ align:start position:0%
+What happens if you don't?
+What happens if you cannot take
+
+ align:start position:0%
+What happens if you cannot take
+ 
+
+ align:start position:0%
+What happens if you cannot take
+combinations of the first two equations
+
+ align:start position:0%
+combinations of the first two equations
+ 
+
+ align:start position:0%
+combinations of the first two equations
+to get the third? What does that mean?
+
+ align:start position:0%
+to get the third? What does that mean?
+ 
+
+ align:start position:0%
+to get the third? What does that mean?
+One of the numbers is wrong.
+
+ align:start position:0%
+One of the numbers is wrong.
+ 
+
+ align:start position:0%
+One of the numbers is wrong.
+One of the numbers is wrong. What do you
+
+ align:start position:0%
+One of the numbers is wrong. What do you
+ 
+
+ align:start position:0%
+One of the numbers is wrong. What do you
+mean by that?
+
+ align:start position:0%
+mean by that?
+ 
+
+ align:start position:0%
+mean by that?
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+it can't be a solution.
+
+ align:start position:0%
+it can't be a solution.
+ 
+
+ align:start position:0%
+it can't be a solution.
+It can't be a solution. Okay. Now, this
+
+ align:start position:0%
+It can't be a solution. Okay. Now, this
+ 
+
+ align:start position:0%
+It can't be a solution. Okay. Now, this
+is getting really interesting because on
+
+ align:start position:0%
+is getting really interesting because on
+ 
+
+ align:start position:0%
+is getting really interesting because on
+the one hand, you're probably getting
+
+ align:start position:0%
+the one hand, you're probably getting
+ 
+
+ align:start position:0%
+the one hand, you're probably getting
+confused about what any of this has to
+
+ align:start position:0%
+confused about what any of this has to
+ 
+
+ align:start position:0%
+confused about what any of this has to
+do with money. In a minute, I'm going to
+
+ align:start position:0%
+do with money. In a minute, I'm going to
+ 
+
+ align:start position:0%
+do with money. In a minute, I'm going to
+tell you it has everything to do with
+
+ align:start position:0%
+tell you it has everything to do with
+ 
+
+ align:start position:0%
+tell you it has everything to do with
+money, as you might expect.
+
+ align:start position:0%
+money, as you might expect.
+ 
+
+ align:start position:0%
+money, as you might expect.
+If we've got two equations and two
+
+ align:start position:0%
+If we've got two equations and two
+ 
+
+ align:start position:0%
+If we've got two equations and two
+unknowns, and we have one solution, that
+
+ align:start position:0%
+unknowns, and we have one solution, that
+ 
+
+ align:start position:0%
+unknowns, and we have one solution, that
+basically says that there are two
+
+ align:start position:0%
+basically says that there are two
+ 
+
+ align:start position:0%
+basically says that there are two
+yields, a one-year yield and a two-year
+
+ align:start position:0%
+yields, a one-year yield and a two-year
+ 
+
+ align:start position:0%
+yields, a one-year yield and a two-year
+yield
+
+ align:start position:0%
+yield
+ 
+
+ align:start position:0%
+yield
+that is able to price both bonds. And
+
+ align:start position:0%
+that is able to price both bonds. And
+ 
+
+ align:start position:0%
+that is able to price both bonds. And
+that better be the case because we're
+
+ align:start position:0%
+that better be the case because we're
+ 
+
+ align:start position:0%
+that better be the case because we're
+going to use these two yields to
+
+ align:start position:0%
+going to use these two yields to
+ 
+
+ align:start position:0%
+going to use these two yields to
+replicate the bonds. And so, this kind
+
+ align:start position:0%
+replicate the bonds. And so, this kind
+ 
+
+ align:start position:0%
+replicate the bonds. And so, this kind
+of a relationship has to hold. Now, if
+
+ align:start position:0%
+of a relationship has to hold. Now, if
+ 
+
+ align:start position:0%
+of a relationship has to hold. Now, if
+we add a third bond,
+
+ align:start position:0%
+we add a third bond,
+ 
+
+ align:start position:0%
+we add a third bond,
+if we add a third bond,
+
+ align:start position:0%
+if we add a third bond,
+ 
+
+ align:start position:0%
+if we add a third bond,
+and those same two yields that work for
+
+ align:start position:0%
+and those same two yields that work for
+ 
+
+ align:start position:0%
+and those same two yields that work for
+the first two bonds, they don't work for
+
+ align:start position:0%
+the first two bonds, they don't work for
+ 
+
+ align:start position:0%
+the first two bonds, they don't work for
+the third bond,
+
+ align:start position:0%
+the third bond,
+ 
+
+ align:start position:0%
+the third bond,
+something's wrong,
+
+ align:start position:0%
+something's wrong,
+ 
+
+ align:start position:0%
+something's wrong,
+right? It means that this third bond,
+
+ align:start position:0%
+right? It means that this third bond,
+ 
+
+ align:start position:0%
+right? It means that this third bond,
+its price
+
+ align:start position:0%
+its price
+ 
+
+ align:start position:0%
+its price
+does not satisfy
+
+ align:start position:0%
+does not satisfy
+ 
+
+ align:start position:0%
+does not satisfy
+the relationship
+
+ align:start position:0%
+the relationship
+ 
+
+ align:start position:0%
+the relationship
+between those two yields.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's evidence of a mispricing.
+
+ align:start position:0%
+That's evidence of a mispricing.
+ 
+
+ align:start position:0%
+That's evidence of a mispricing.
+Something is wrong. But in this case,
+
+ align:start position:0%
+Something is wrong. But in this case,
+ 
+
+ align:start position:0%
+Something is wrong. But in this case,
+what's wrong is that there's something
+
+ align:start position:0%
+what's wrong is that there's something
+ 
+
+ align:start position:0%
+what's wrong is that there's something
+mispriced between those two bonds
+
+ align:start position:0%
+mispriced between those two bonds
+ 
+
+ align:start position:0%
+mispriced between those two bonds
+and the third.
+
+ align:start position:0%
+and the third.
+ 
+
+ align:start position:0%
+and the third.
+So when you run into a situation like
+
+ align:start position:0%
+So when you run into a situation like
+ 
+
+ align:start position:0%
+So when you run into a situation like
+that, and we're going to give you an
+
+ align:start position:0%
+that, and we're going to give you an
+ 
+
+ align:start position:0%
+that, and we're going to give you an
+example in the problem set when you come
+
+ align:start position:0%
+example in the problem set when you come
+ 
+
+ align:start position:0%
+example in the problem set when you come
+across that, what that means is you
+
+ align:start position:0%
+across that, what that means is you
+ 
+
+ align:start position:0%
+across that, what that means is you
+should be extremely excited
+
+ align:start position:0%
+should be extremely excited
+ 
+
+ align:start position:0%
+should be extremely excited
+uh as opposed to depressed in math
+
+ align:start position:0%
+uh as opposed to depressed in math
+ 
+
+ align:start position:0%
+uh as opposed to depressed in math
+class. you know, geez, there's no
+
+ align:start position:0%
+class. you know, geez, there's no
+ 
+
+ align:start position:0%
+class. you know, geez, there's no
+solution in finance. What no solution
+
+ align:start position:0%
+solution in finance. What no solution
+ 
+
+ align:start position:0%
+solution in finance. What no solution
+means is that there is a transaction.
+
+ align:start position:0%
+means is that there is a transaction.
+ 
+
+ align:start position:0%
+means is that there is a transaction.
+There exists a linear combination of the
+
+ align:start position:0%
+There exists a linear combination of the
+ 
+
+ align:start position:0%
+There exists a linear combination of the
+first two bonds and the third that A
+
+ align:start position:0%
+first two bonds and the third that A
+ 
+
+ align:start position:0%
+first two bonds and the third that A
+cost you no money down. B will generate
+
+ align:start position:0%
+cost you no money down. B will generate
+ 
+
+ align:start position:0%
+cost you no money down. B will generate
+cash flow today. C will require no
+
+ align:start position:0%
+cash flow today. C will require no
+ 
+
+ align:start position:0%
+cash flow today. C will require no
+future payments of any sort. So, it's
+
+ align:start position:0%
+future payments of any sort. So, it's
+ 
+
+ align:start position:0%
+future payments of any sort. So, it's
+riskless.
+
+ align:start position:0%
+riskless.
+ 
+
+ align:start position:0%
+riskless.
+It is a free lunch. It is an arbitrage.
+
+ align:start position:0%
+It is a free lunch. It is an arbitrage.
+ 
+
+ align:start position:0%
+It is a free lunch. It is an arbitrage.
+Now that's with three equations and two
+
+ align:start position:0%
+Now that's with three equations and two
+ 
+
+ align:start position:0%
+Now that's with three equations and two
+unknowns. Anybody can do that, right?
+
+ align:start position:0%
+unknowns. Anybody can do that, right?
+ 
+
+ align:start position:0%
+unknowns. Anybody can do that, right?
+That's easy. What if it were 200
+
+ align:start position:0%
+That's easy. What if it were 200
+ 
+
+ align:start position:0%
+That's easy. What if it were 200
+equations and 30 unknowns? Now not so
+
+ align:start position:0%
+equations and 30 unknowns? Now not so
+ 
+
+ align:start position:0%
+equations and 30 unknowns? Now not so
+easy. Now you actually have to know
+
+ align:start position:0%
+easy. Now you actually have to know
+ 
+
+ align:start position:0%
+easy. Now you actually have to know
+something about linear algebra. Now the
+
+ align:start position:0%
+something about linear algebra. Now the
+ 
+
+ align:start position:0%
+something about linear algebra. Now the
+whole notion of what an invertible
+
+ align:start position:0%
+whole notion of what an invertible
+ 
+
+ align:start position:0%
+whole notion of what an invertible
+matrix is, what the igen values are, all
+
+ align:start position:0%
+matrix is, what the igen values are, all
+ 
+
+ align:start position:0%
+matrix is, what the igen values are, all
+the kind of infrastructure that you can
+
+ align:start position:0%
+the kind of infrastructure that you can
+ 
+
+ align:start position:0%
+the kind of infrastructure that you can
+build for understanding this becomes
+
+ align:start position:0%
+build for understanding this becomes
+ 
+
+ align:start position:0%
+build for understanding this becomes
+relevant as a quant trading on a
+
+ align:start position:0%
+relevant as a quant trading on a
+ 
+
+ align:start position:0%
+relevant as a quant trading on a
+proprietary trading desk.
+
+ align:start position:0%
+proprietary trading desk.
+ 
+
+ align:start position:0%
+proprietary trading desk.
+In the 1970s,
+
+ align:start position:0%
+In the 1970s,
+ 
+
+ align:start position:0%
+In the 1970s,
+a number of MIT graduates were hired by
+
+ align:start position:0%
+a number of MIT graduates were hired by
+ 
+
+ align:start position:0%
+a number of MIT graduates were hired by
+Solomon Brothers.
+
+ align:start position:0%
+Solomon Brothers.
+ 
+
+ align:start position:0%
+Solomon Brothers.
+They knew very little about fixed income
+
+ align:start position:0%
+They knew very little about fixed income
+ 
+
+ align:start position:0%
+They knew very little about fixed income
+securities. They knew the basics, which
+
+ align:start position:0%
+securities. They knew the basics, which
+ 
+
+ align:start position:0%
+securities. They knew the basics, which
+is what was was taught here, but they
+
+ align:start position:0%
+is what was was taught here, but they
+ 
+
+ align:start position:0%
+is what was was taught here, but they
+didn't know much about market realities
+
+ align:start position:0%
+didn't know much about market realities
+ 
+
+ align:start position:0%
+didn't know much about market realities
+in practice. And so when they went to
+
+ align:start position:0%
+in practice. And so when they went to
+ 
+
+ align:start position:0%
+in practice. And so when they went to
+solve their three equations and two
+
+ align:start position:0%
+solve their three equations and two
+ 
+
+ align:start position:0%
+solve their three equations and two
+unknowns,
+
+ align:start position:0%
+unknowns,
+ 
+
+ align:start position:0%
+unknowns,
+they observed inconsistencies.
+
+ align:start position:0%
+they observed inconsistencies.
+ 
+
+ align:start position:0%
+they observed inconsistencies.
+And they didn't do three equations and
+
+ align:start position:0%
+And they didn't do three equations and
+ 
+
+ align:start position:0%
+And they didn't do three equations and
+two unknowns. They did 200 equations in
+
+ align:start position:0%
+two unknowns. They did 200 equations in
+ 
+
+ align:start position:0%
+two unknowns. They did 200 equations in
+30 unknowns. And in the 1970s, that was
+
+ align:start position:0%
+30 unknowns. And in the 1970s, that was
+ 
+
+ align:start position:0%
+30 unknowns. And in the 1970s, that was
+not easy to do because we didn't have
+
+ align:start position:0%
+not easy to do because we didn't have
+ 
+
+ align:start position:0%
+not easy to do because we didn't have
+PCs, we didn't have Excel, we didn't
+
+ align:start position:0%
+PCs, we didn't have Excel, we didn't
+ 
+
+ align:start position:0%
+PCs, we didn't have Excel, we didn't
+have a lot of the tools that we have
+
+ align:start position:0%
+have a lot of the tools that we have
+ 
+
+ align:start position:0%
+have a lot of the tools that we have
+today. And what they did was they took
+
+ align:start position:0%
+today. And what they did was they took
+ 
+
+ align:start position:0%
+today. And what they did was they took
+these simultaneous linear equations.
+
+ align:start position:0%
+these simultaneous linear equations.
+ 
+
+ align:start position:0%
+these simultaneous linear equations.
+This is high school algebra. Even back
+
+ align:start position:0%
+This is high school algebra. Even back
+ 
+
+ align:start position:0%
+This is high school algebra. Even back
+then, it was high school algebra, okay?
+
+ align:start position:0%
+then, it was high school algebra, okay?
+ 
+
+ align:start position:0%
+then, it was high school algebra, okay?
+And they just cranked through and looked
+
+ align:start position:0%
+And they just cranked through and looked
+ 
+
+ align:start position:0%
+And they just cranked through and looked
+for mispricings, looked for no
+
+ align:start position:0%
+for mispricings, looked for no
+ 
+
+ align:start position:0%
+for mispricings, looked for no
+solutions. And they found a lot of cases
+
+ align:start position:0%
+solutions. And they found a lot of cases
+ 
+
+ align:start position:0%
+solutions. And they found a lot of cases
+with no solutions.
+
+ align:start position:0%
+with no solutions.
+ 
+
+ align:start position:0%
+with no solutions.
+In one of the years during the 1970s or
+
+ align:start position:0%
+In one of the years during the 1970s or
+ 
+
+ align:start position:0%
+In one of the years during the 1970s or
+80s, one of these MIT grads was paid an
+
+ align:start position:0%
+80s, one of these MIT grads was paid an
+ 
+
+ align:start position:0%
+80s, one of these MIT grads was paid an
+annual bonus of two $22 million
+
+ align:start position:0%
+annual bonus of two $22 million
+ 
+
+ align:start position:0%
+annual bonus of two $22 million
+for doing this for solving simultaneous
+
+ align:start position:0%
+for doing this for solving simultaneous
+ 
+
+ align:start position:0%
+for doing this for solving simultaneous
+linear equations. So this is an extra
+
+ align:start position:0%
+linear equations. So this is an extra
+ 
+
+ align:start position:0%
+linear equations. So this is an extra
+and and if that if that was what he got
+
+ align:start position:0%
+and and if that if that was what he got
+ 
+
+ align:start position:0%
+and and if that if that was what he got
+paid, you imagine what he generated for
+
+ align:start position:0%
+paid, you imagine what he generated for
+ 
+
+ align:start position:0%
+paid, you imagine what he generated for
+Solomon Brothers, it was a lot more than
+
+ align:start position:0%
+Solomon Brothers, it was a lot more than
+ 
+
+ align:start position:0%
+Solomon Brothers, it was a lot more than
+$22 million.
+
+ align:start position:0%
+$22 million.
+ 
+
+ align:start position:0%
+$22 million.
+This activity is known as fixed income
+
+ align:start position:0%
+This activity is known as fixed income
+ 
+
+ align:start position:0%
+This activity is known as fixed income
+arbitrage. There are many other versions
+
+ align:start position:0%
+arbitrage. There are many other versions
+ 
+
+ align:start position:0%
+arbitrage. There are many other versions
+of it, but this is the the plain vanilla
+
+ align:start position:0%
+of it, but this is the the plain vanilla
+ 
+
+ align:start position:0%
+of it, but this is the the plain vanilla
+version. And by the way, the plain
+
+ align:start position:0%
+version. And by the way, the plain
+ 
+
+ align:start position:0%
+version. And by the way, the plain
+vanilla version, it still works in the
+
+ align:start position:0%
+vanilla version, it still works in the
+ 
+
+ align:start position:0%
+vanilla version, it still works in the
+sense that occasionally, if you're quick
+
+ align:start position:0%
+sense that occasionally, if you're quick
+ 
+
+ align:start position:0%
+sense that occasionally, if you're quick
+enough and you have the right tools, you
+
+ align:start position:0%
+enough and you have the right tools, you
+ 
+
+ align:start position:0%
+enough and you have the right tools, you
+can identify mispricings and take
+
+ align:start position:0%
+can identify mispricings and take
+ 
+
+ align:start position:0%
+can identify mispricings and take
+advantage of them quickly. It doesn't
+
+ align:start position:0%
+advantage of them quickly. It doesn't
+ 
+
+ align:start position:0%
+advantage of them quickly. It doesn't
+last long. So, you're absolutely right.
+
+ align:start position:0%
+last long. So, you're absolutely right.
+ 
+
+ align:start position:0%
+last long. So, you're absolutely right.
+doesn't last long but the person who
+
+ align:start position:0%
+doesn't last long but the person who
+ 
+
+ align:start position:0%
+doesn't last long but the person who
+gets paid is the person who can do this
+
+ align:start position:0%
+gets paid is the person who can do this
+ 
+
+ align:start position:0%
+gets paid is the person who can do this
+the fastest and is able to understand uh
+
+ align:start position:0%
+the fastest and is able to understand uh
+ 
+
+ align:start position:0%
+the fastest and is able to understand uh
+the the inter relationships among these
+
+ align:start position:0%
+the the inter relationships among these
+ 
+
+ align:start position:0%
+the the inter relationships among these
+securities and you can understand now
+
+ align:start position:0%
+securities and you can understand now
+ 
+
+ align:start position:0%
+securities and you can understand now
+why retail investors have no chance of
+
+ align:start position:0%
+why retail investors have no chance of
+ 
+
+ align:start position:0%
+why retail investors have no chance of
+doing this kind of thing on their own
+
+ align:start position:0%
+doing this kind of thing on their own
+ 
+
+ align:start position:0%
+doing this kind of thing on their own
+this something you definitely don't want
+
+ align:start position:0%
+this something you definitely don't want
+ 
+
+ align:start position:0%
+this something you definitely don't want
+to try at home okay I know you guys have
+
+ align:start position:0%
+to try at home okay I know you guys have
+ 
+
+ align:start position:0%
+to try at home okay I know you guys have
+mat lab and you can do matrix inversions
+
+ align:start position:0%
+mat lab and you can do matrix inversions
+ 
+
+ align:start position:0%
+mat lab and you can do matrix inversions
+but there are lots of other uh frictions
+
+ align:start position:0%
+but there are lots of other uh frictions
+ 
+
+ align:start position:0%
+but there are lots of other uh frictions
+transactions costs and imperfections
+
+ align:start position:0%
+transactions costs and imperfections
+ 
+
+ align:start position:0%
+transactions costs and imperfections
+that you have to build into this
+
+ align:start position:0%
+that you have to build into this
+ 
+
+ align:start position:0%
+that you have to build into this
+analysis, but once you do, all sorts of
+
+ align:start position:0%
+analysis, but once you do, all sorts of
+ 
+
+ align:start position:0%
+analysis, but once you do, all sorts of
+interesting things start popping out. A
+
+ align:start position:0%
+interesting things start popping out. A
+ 
+
+ align:start position:0%
+interesting things start popping out. A
+question. Uh, yeah, there's a couple
+
+ align:start position:0%
+question. Uh, yeah, there's a couple
+ 
+
+ align:start position:0%
+question. Uh, yeah, there's a couple
+reasons why this does still exist. Like,
+
+ align:start position:0%
+reasons why this does still exist. Like,
+ 
+
+ align:start position:0%
+reasons why this does still exist. Like,
+why hasn't the arms race been everyone
+
+ align:start position:0%
+why hasn't the arms race been everyone
+ 
+
+ align:start position:0%
+why hasn't the arms race been everyone
+narrowed it down to basic efficiency?
+
+ align:start position:0%
+narrowed it down to basic efficiency?
+ 
+
+ align:start position:0%
+narrowed it down to basic efficiency?
+Well, it's actually much narrower now
+
+ align:start position:0%
+Well, it's actually much narrower now
+ 
+
+ align:start position:0%
+Well, it's actually much narrower now
+than it used to be. So, in fact, the
+
+ align:start position:0%
+than it used to be. So, in fact, the
+ 
+
+ align:start position:0%
+than it used to be. So, in fact, the
+market has gotten much much more
+
+ align:start position:0%
+market has gotten much much more
+ 
+
+ align:start position:0%
+market has gotten much much more
+competitive, but it's not down to zero
+
+ align:start position:0%
+competitive, but it's not down to zero
+ 
+
+ align:start position:0%
+competitive, but it's not down to zero
+precisely because there are frictions
+
+ align:start position:0%
+precisely because there are frictions
+ 
+
+ align:start position:0%
+precisely because there are frictions
+and other aspects. For example, some of
+
+ align:start position:0%
+and other aspects. For example, some of
+ 
+
+ align:start position:0%
+and other aspects. For example, some of
+these bonds, they have weird features
+
+ align:start position:0%
+these bonds, they have weird features
+ 
+
+ align:start position:0%
+these bonds, they have weird features
+like they're callable or in some cases,
+
+ align:start position:0%
+like they're callable or in some cases,
+ 
+
+ align:start position:0%
+like they're callable or in some cases,
+they may have uh certain types of of
+
+ align:start position:0%
+they may have uh certain types of of
+ 
+
+ align:start position:0%
+they may have uh certain types of of
+other requirements and market uh
+
+ align:start position:0%
+other requirements and market uh
+ 
+
+ align:start position:0%
+other requirements and market uh
+institutional imperfections that require
+
+ align:start position:0%
+institutional imperfections that require
+ 
+
+ align:start position:0%
+institutional imperfections that require
+you to build in those constraints when
+
+ align:start position:0%
+you to build in those constraints when
+ 
+
+ align:start position:0%
+you to build in those constraints when
+you do the analysis. And so, it's really
+
+ align:start position:0%
+you do the analysis. And so, it's really
+ 
+
+ align:start position:0%
+you do the analysis. And so, it's really
+about who has the better model. And
+
+ align:start position:0%
+about who has the better model. And
+ 
+
+ align:start position:0%
+about who has the better model. And
+frankly, there's an arms race that's
+
+ align:start position:0%
+frankly, there's an arms race that's
+ 
+
+ align:start position:0%
+frankly, there's an arms race that's
+been going on for the last three decades
+
+ align:start position:0%
+been going on for the last three decades
+ 
+
+ align:start position:0%
+been going on for the last three decades
+as to who has the the fastest computers.
+
+ align:start position:0%
+as to who has the the fastest computers.
+ 
+
+ align:start position:0%
+as to who has the the fastest computers.
+The first supercomputer that was ever
+
+ align:start position:0%
+The first supercomputer that was ever
+ 
+
+ align:start position:0%
+The first supercomputer that was ever
+installed on Wall Street, a Cray 2, was
+
+ align:start position:0%
+installed on Wall Street, a Cray 2, was
+ 
+
+ align:start position:0%
+installed on Wall Street, a Cray 2, was
+installed at Salomon Brothers doing
+
+ align:start position:0%
+installed at Salomon Brothers doing
+ 
+
+ align:start position:0%
+installed at Salomon Brothers doing
+simultaneous linear equations among
+
+ align:start position:0%
+simultaneous linear equations among
+ 
+
+ align:start position:0%
+simultaneous linear equations among
+other things. And so this is where
+
+ align:start position:0%
+other things. And so this is where
+ 
+
+ align:start position:0%
+other things. And so this is where
+technology has played a really big role
+
+ align:start position:0%
+technology has played a really big role
+ 
+
+ align:start position:0%
+technology has played a really big role
+in the developments of market prices.
+
+ align:start position:0%
+in the developments of market prices.
+ 
+
+ align:start position:0%
+in the developments of market prices.
+Another question. Okay. So
+
+ align:start position:0%
+Another question. Okay. So
+ 
+
+ align:start position:0%
+Another question. Okay. So
+this very very simple idea and you know
+
+ align:start position:0%
+this very very simple idea and you know
+ 
+
+ align:start position:0%
+this very very simple idea and you know
+it again it is simple has all sorts of
+
+ align:start position:0%
+it again it is simple has all sorts of
+ 
+
+ align:start position:0%
+it again it is simple has all sorts of
+important ramifications for the pricing
+
+ align:start position:0%
+important ramifications for the pricing
+ 
+
+ align:start position:0%
+important ramifications for the pricing
+of bonds and other securities.
+
+ align:start position:0%
+of bonds and other securities.
+ 
+
+ align:start position:0%
+of bonds and other securities.
+What that tells us is that market prices
+
+ align:start position:0%
+What that tells us is that market prices
+ 
+
+ align:start position:0%
+What that tells us is that market prices
+have all sorts of information that are
+
+ align:start position:0%
+have all sorts of information that are
+ 
+
+ align:start position:0%
+have all sorts of information that are
+incorporated into it. And one of the
+
+ align:start position:0%
+incorporated into it. And one of the
+ 
+
+ align:start position:0%
+incorporated into it. And one of the
+things that we want to understand is how
+
+ align:start position:0%
+things that we want to understand is how
+ 
+
+ align:start position:0%
+things that we want to understand is how
+to interpret that information. In
+
+ align:start position:0%
+to interpret that information. In
+ 
+
+ align:start position:0%
+to interpret that information. In
+particular, the first thing I want to do
+
+ align:start position:0%
+particular, the first thing I want to do
+ 
+
+ align:start position:0%
+particular, the first thing I want to do
+uh is to understand the risks. All
+
+ align:start position:0%
+uh is to understand the risks. All
+ 
+
+ align:start position:0%
+uh is to understand the risks. All
+right? Because we we talked about the
+
+ align:start position:0%
+right? Because we we talked about the
+ 
+
+ align:start position:0%
+right? Because we we talked about the
+fact that some of these market prices
+
+ align:start position:0%
+fact that some of these market prices
+ 
+
+ align:start position:0%
+fact that some of these market prices
+may have missed the risks that were
+
+ align:start position:0%
+may have missed the risks that were
+ 
+
+ align:start position:0%
+may have missed the risks that were
+implicit in some of the trades. And so
+
+ align:start position:0%
+implicit in some of the trades. And so
+ 
+
+ align:start position:0%
+implicit in some of the trades. And so
+the question is why and how how do we
+
+ align:start position:0%
+the question is why and how how do we
+ 
+
+ align:start position:0%
+the question is why and how how do we
+measure the risk of a bond portfolio? So
+
+ align:start position:0%
+measure the risk of a bond portfolio? So
+ 
+
+ align:start position:0%
+measure the risk of a bond portfolio? So
+what I want to do is to now look at the
+
+ align:start position:0%
+what I want to do is to now look at the
+ 
+
+ align:start position:0%
+what I want to do is to now look at the
+market price of a bond in terms of a
+
+ align:start position:0%
+market price of a bond in terms of a
+ 
+
+ align:start position:0%
+market price of a bond in terms of a
+function that has inputs and the price
+
+ align:start position:0%
+function that has inputs and the price
+ 
+
+ align:start position:0%
+function that has inputs and the price
+is the output and I want to ask the
+
+ align:start position:0%
+is the output and I want to ask the
+ 
+
+ align:start position:0%
+is the output and I want to ask the
+question what kind of fluctuation in the
+
+ align:start position:0%
+question what kind of fluctuation in the
+ 
+
+ align:start position:0%
+question what kind of fluctuation in the
+input will yield fluctuation in the
+
+ align:start position:0%
+input will yield fluctuation in the
+ 
+
+ align:start position:0%
+input will yield fluctuation in the
+output. You know we now know how to
+
+ align:start position:0%
+output. You know we now know how to
+ 
+
+ align:start position:0%
+output. You know we now know how to
+price these things. We now know how the
+
+ align:start position:0%
+price these things. We now know how the
+ 
+
+ align:start position:0%
+price these things. We now know how the
+relationships must work from a present
+
+ align:start position:0%
+relationships must work from a present
+ 
+
+ align:start position:0%
+relationships must work from a present
+value approach. And now what I want to
+
+ align:start position:0%
+value approach. And now what I want to
+ 
+
+ align:start position:0%
+value approach. And now what I want to
+do is to a ask whether we could measure
+
+ align:start position:0%
+do is to a ask whether we could measure
+ 
+
+ align:start position:0%
+do is to a ask whether we could measure
+the sensitivity. So, one way to do it is
+
+ align:start position:0%
+the sensitivity. So, one way to do it is
+ 
+
+ align:start position:0%
+the sensitivity. So, one way to do it is
+to just graph the price of a bond as a
+
+ align:start position:0%
+to just graph the price of a bond as a
+ 
+
+ align:start position:0%
+to just graph the price of a bond as a
+function of its yield. And we know that
+
+ align:start position:0%
+function of its yield. And we know that
+ 
+
+ align:start position:0%
+function of its yield. And we know that
+there's an inverse relationship, right?
+
+ align:start position:0%
+there's an inverse relationship, right?
+ 
+
+ align:start position:0%
+there's an inverse relationship, right?
+Just like we saw with treasuries this
+
+ align:start position:0%
+Just like we saw with treasuries this
+ 
+
+ align:start position:0%
+Just like we saw with treasuries this
+week versus last week, right? Last week
+
+ align:start position:0%
+week versus last week, right? Last week
+ 
+
+ align:start position:0%
+week versus last week, right? Last week
+there was a big run on treasuries. Lots
+
+ align:start position:0%
+there was a big run on treasuries. Lots
+ 
+
+ align:start position:0%
+there was a big run on treasuries. Lots
+of people wanted to get into them. Price
+
+ align:start position:0%
+of people wanted to get into them. Price
+ 
+
+ align:start position:0%
+of people wanted to get into them. Price
+goes up, yield goes down. And this week,
+
+ align:start position:0%
+goes up, yield goes down. And this week,
+ 
+
+ align:start position:0%
+goes up, yield goes down. And this week,
+less pressure, so we have yielding going
+
+ align:start position:0%
+less pressure, so we have yielding going
+ 
+
+ align:start position:0%
+less pressure, so we have yielding going
+up and the prices coming down. that
+
+ align:start position:0%
+up and the prices coming down. that
+ 
+
+ align:start position:0%
+up and the prices coming down. that
+provides us with one kind of measure of
+
+ align:start position:0%
+provides us with one kind of measure of
+ 
+
+ align:start position:0%
+provides us with one kind of measure of
+risk. So the kind of measure I'm talking
+
+ align:start position:0%
+risk. So the kind of measure I'm talking
+ 
+
+ align:start position:0%
+risk. So the kind of measure I'm talking
+about is the slope of this line, the
+
+ align:start position:0%
+about is the slope of this line, the
+ 
+
+ align:start position:0%
+about is the slope of this line, the
+instantaneous slope that tells us for a
+
+ align:start position:0%
+instantaneous slope that tells us for a
+ 
+
+ align:start position:0%
+instantaneous slope that tells us for a
+a bit of a tweak in interest rates or
+
+ align:start position:0%
+a bit of a tweak in interest rates or
+ 
+
+ align:start position:0%
+a bit of a tweak in interest rates or
+yield,
+
+ align:start position:0%
+yield,
+ 
+
+ align:start position:0%
+yield,
+what does that do to the market price?
+
+ align:start position:0%
+what does that do to the market price?
+ 
+
+ align:start position:0%
+what does that do to the market price?
+Because obviously when you're an
+
+ align:start position:0%
+Because obviously when you're an
+ 
+
+ align:start position:0%
+Because obviously when you're an
+investor, you're focusing on the price,
+
+ align:start position:0%
+investor, you're focusing on the price,
+ 
+
+ align:start position:0%
+investor, you're focusing on the price,
+right? Yield is a convenient way of
+
+ align:start position:0%
+right? Yield is a convenient way of
+ 
+
+ align:start position:0%
+right? Yield is a convenient way of
+summarizing the properties of a bond,
+
+ align:start position:0%
+summarizing the properties of a bond,
+ 
+
+ align:start position:0%
+summarizing the properties of a bond,
+but ultimately what you care about in
+
+ align:start position:0%
+but ultimately what you care about in
+ 
+
+ align:start position:0%
+but ultimately what you care about in
+your portfolio is price. And so the
+
+ align:start position:0%
+your portfolio is price. And so the
+ 
+
+ align:start position:0%
+your portfolio is price. And so the
+question is for a a move in the interest
+
+ align:start position:0%
+question is for a a move in the interest
+ 
+
+ align:start position:0%
+question is for a a move in the interest
+rate, what does that do to the price?
+
+ align:start position:0%
+rate, what does that do to the price?
+ 
+
+ align:start position:0%
+rate, what does that do to the price?
+Well, it turns out that there is one way
+
+ align:start position:0%
+Well, it turns out that there is one way
+ 
+
+ align:start position:0%
+Well, it turns out that there is one way
+to get at that um that is somewhat more
+
+ align:start position:0%
+to get at that um that is somewhat more
+ 
+
+ align:start position:0%
+to get at that um that is somewhat more
+intuitive than just looking at this kind
+
+ align:start position:0%
+intuitive than just looking at this kind
+ 
+
+ align:start position:0%
+intuitive than just looking at this kind
+of fluctuation. It's called duration and
+
+ align:start position:0%
+of fluctuation. It's called duration and
+ 
+
+ align:start position:0%
+of fluctuation. It's called duration and
+it's named after a person Macaulay who
+
+ align:start position:0%
+it's named after a person Macaulay who
+ 
+
+ align:start position:0%
+it's named after a person Macaulay who
+first proposed it as a way of measuring
+
+ align:start position:0%
+first proposed it as a way of measuring
+ 
+
+ align:start position:0%
+first proposed it as a way of measuring
+how risky a bond is.
+
+ align:start position:0%
+how risky a bond is.
+ 
+
+ align:start position:0%
+how risky a bond is.
+What Macaulay noted was that the longer
+
+ align:start position:0%
+What Macaulay noted was that the longer
+ 
+
+ align:start position:0%
+What Macaulay noted was that the longer
+the maturity of a bond, the more
+
+ align:start position:0%
+the maturity of a bond, the more
+ 
+
+ align:start position:0%
+the maturity of a bond, the more
+sensitive
+
+ align:start position:0%
+sensitive
+ 
+
+ align:start position:0%
+sensitive
+is the bond price to the yield. So, for
+
+ align:start position:0%
+is the bond price to the yield. So, for
+ 
+
+ align:start position:0%
+is the bond price to the yield. So, for
+example, a 30-year bond when you move
+
+ align:start position:0%
+example, a 30-year bond when you move
+ 
+
+ align:start position:0%
+example, a 30-year bond when you move
+the interest rate by one basis point
+
+ align:start position:0%
+the interest rate by one basis point
+ 
+
+ align:start position:0%
+the interest rate by one basis point
+will have a much much larger price
+
+ align:start position:0%
+will have a much much larger price
+ 
+
+ align:start position:0%
+will have a much much larger price
+fluctuation than a three-month bond,
+
+ align:start position:0%
+fluctuation than a three-month bond,
+ 
+
+ align:start position:0%
+fluctuation than a three-month bond,
+right? Why is that? Anybody give me some
+
+ align:start position:0%
+right? Why is that? Anybody give me some
+ 
+
+ align:start position:0%
+right? Why is that? Anybody give me some
+intuition for why that should be why
+
+ align:start position:0%
+intuition for why that should be why
+ 
+
+ align:start position:0%
+intuition for why that should be why
+that makes sense? Why should a longer
+
+ align:start position:0%
+that makes sense? Why should a longer
+ 
+
+ align:start position:0%
+that makes sense? Why should a longer
+maturity bond be more sensitive to
+
+ align:start position:0%
+maturity bond be more sensitive to
+ 
+
+ align:start position:0%
+maturity bond be more sensitive to
+changes in yield? Yeah, Ken,
+
+ align:start position:0%
+changes in yield? Yeah, Ken,
+ 
+
+ align:start position:0%
+changes in yield? Yeah, Ken,
+because you're hanging on because the
+
+ align:start position:0%
+because you're hanging on because the
+ 
+
+ align:start position:0%
+because you're hanging on because the
+cash is tied up long.
+
+ align:start position:0%
+cash is tied up long.
+ 
+
+ align:start position:0%
+cash is tied up long.
+Yeah. And and because
+
+ align:start position:0%
+Yeah. And and because
+ 
+
+ align:start position:0%
+Yeah. And and because
+uh the risk because the opportunity cost
+
+ align:start position:0%
+uh the risk because the opportunity cost
+ 
+
+ align:start position:0%
+uh the risk because the opportunity cost
+essentially of having that money tied up
+
+ align:start position:0%
+essentially of having that money tied up
+ 
+
+ align:start position:0%
+essentially of having that money tied up
+for that long means you can't spend it
+
+ align:start position:0%
+for that long means you can't spend it
+ 
+
+ align:start position:0%
+for that long means you can't spend it
+on all these on all these other things
+
+ align:start position:0%
+on all these on all these other things
+ 
+
+ align:start position:0%
+on all these on all these other things
+over those 30 years. That's right.
+
+ align:start position:0%
+over those 30 years. That's right.
+ 
+
+ align:start position:0%
+over those 30 years. That's right.
+You're investing for a longer period of
+
+ align:start position:0%
+You're investing for a longer period of
+ 
+
+ align:start position:0%
+You're investing for a longer period of
+time. So in fact the opportunity cost as
+
+ align:start position:0%
+time. So in fact the opportunity cost as
+ 
+
+ align:start position:0%
+time. So in fact the opportunity cost as
+measured by the foregone interest is
+
+ align:start position:0%
+measured by the foregone interest is
+ 
+
+ align:start position:0%
+measured by the foregone interest is
+going to be much larger. In other words,
+
+ align:start position:0%
+going to be much larger. In other words,
+ 
+
+ align:start position:0%
+going to be much larger. In other words,
+the discount rate that you use, this 1
+
+ align:start position:0%
+the discount rate that you use, this 1
+ 
+
+ align:start position:0%
+the discount rate that you use, this 1
+plus r, you've raised that to the 30th
+
+ align:start position:0%
+plus r, you've raised that to the 30th
+ 
+
+ align:start position:0%
+plus r, you've raised that to the 30th
+power, not to the one quarter power. And
+
+ align:start position:0%
+power, not to the one quarter power. And
+ 
+
+ align:start position:0%
+power, not to the one quarter power. And
+so something that's raised to the 30th
+
+ align:start position:0%
+so something that's raised to the 30th
+ 
+
+ align:start position:0%
+so something that's raised to the 30th
+power in the denominator, it has a much
+
+ align:start position:0%
+power in the denominator, it has a much
+ 
+
+ align:start position:0%
+power in the denominator, it has a much
+larger impact when you perturb that
+
+ align:start position:0%
+larger impact when you perturb that
+ 
+
+ align:start position:0%
+larger impact when you perturb that
+denominator by a little bit. Okay?
+
+ align:start position:0%
+denominator by a little bit. Okay?
+ 
+
+ align:start position:0%
+denominator by a little bit. Okay?
+Because you're actually increasing that
+
+ align:start position:0%
+Because you're actually increasing that
+ 
+
+ align:start position:0%
+Because you're actually increasing that
+uh that power uh you're increasing that
+
+ align:start position:0%
+uh that power uh you're increasing that
+ 
+
+ align:start position:0%
+uh that power uh you're increasing that
+quantity by that 30th power. Well, so if
+
+ align:start position:0%
+quantity by that 30th power. Well, so if
+ 
+
+ align:start position:0%
+quantity by that 30th power. Well, so if
+that's the case, if it's the case that
+
+ align:start position:0%
+that's the case, if it's the case that
+ 
+
+ align:start position:0%
+that's the case, if it's the case that
+the longer the maturity, the more at
+
+ align:start position:0%
+the longer the maturity, the more at
+ 
+
+ align:start position:0%
+the longer the maturity, the more at
+risk you are per basis point of interest
+
+ align:start position:0%
+risk you are per basis point of interest
+ 
+
+ align:start position:0%
+risk you are per basis point of interest
+rate fluctuation, then why don't we just
+
+ align:start position:0%
+rate fluctuation, then why don't we just
+ 
+
+ align:start position:0%
+rate fluctuation, then why don't we just
+measure the average
+
+ align:start position:0%
+measure the average
+ 
+
+ align:start position:0%
+measure the average
+duration
+
+ align:start position:0%
+duration
+ 
+
+ align:start position:0%
+duration
+of the bond? By average duration, I mean
+
+ align:start position:0%
+of the bond? By average duration, I mean
+ 
+
+ align:start position:0%
+of the bond? By average duration, I mean
+how long does the bond last when you
+
+ align:start position:0%
+how long does the bond last when you
+ 
+
+ align:start position:0%
+how long does the bond last when you
+weight it by the coupon payments that it
+
+ align:start position:0%
+weight it by the coupon payments that it
+ 
+
+ align:start position:0%
+weight it by the coupon payments that it
+pays you. So for a pure discount bond,
+
+ align:start position:0%
+pays you. So for a pure discount bond,
+ 
+
+ align:start position:0%
+pays you. So for a pure discount bond,
+the duration is simple. It's just the
+
+ align:start position:0%
+the duration is simple. It's just the
+ 
+
+ align:start position:0%
+the duration is simple. It's just the
+maturity date, right? If you've got a
+
+ align:start position:0%
+maturity date, right? If you've got a
+ 
+
+ align:start position:0%
+maturity date, right? If you've got a
+30-year strip that pays you a dollar in
+
+ align:start position:0%
+30-year strip that pays you a dollar in
+ 
+
+ align:start position:0%
+30-year strip that pays you a dollar in
+30 years, the duration of that bond is
+
+ align:start position:0%
+30 years, the duration of that bond is
+ 
+
+ align:start position:0%
+30 years, the duration of that bond is
+just 30 years. But what if you had a
+
+ align:start position:0%
+just 30 years. But what if you had a
+ 
+
+ align:start position:0%
+just 30 years. But what if you had a
+coupon bond that paid you coupons all
+
+ align:start position:0%
+coupon bond that paid you coupons all
+ 
+
+ align:start position:0%
+coupon bond that paid you coupons all
+along the way? Well, then you should
+
+ align:start position:0%
+along the way? Well, then you should
+ 
+
+ align:start position:0%
+along the way? Well, then you should
+take a weighted average of the 30 years
+
+ align:start position:0%
+take a weighted average of the 30 years
+ 
+
+ align:start position:0%
+take a weighted average of the 30 years
+and give some weight to the early years
+
+ align:start position:0%
+and give some weight to the early years
+ 
+
+ align:start position:0%
+and give some weight to the early years
+too because the early years are years
+
+ align:start position:0%
+too because the early years are years
+ 
+
+ align:start position:0%
+too because the early years are years
+where you're going to receive cash and
+
+ align:start position:0%
+where you're going to receive cash and
+ 
+
+ align:start position:0%
+where you're going to receive cash and
+therefore interest rate fluctuations are
+
+ align:start position:0%
+therefore interest rate fluctuations are
+ 
+
+ align:start position:0%
+therefore interest rate fluctuations are
+going to affect the value of those cash
+
+ align:start position:0%
+going to affect the value of those cash
+ 
+
+ align:start position:0%
+going to affect the value of those cash
+flows. So the weighted average term to
+
+ align:start position:0%
+flows. So the weighted average term to
+ 
+
+ align:start position:0%
+flows. So the weighted average term to
+maturity is simply equal to the sum of
+
+ align:start position:0%
+maturity is simply equal to the sum of
+ 
+
+ align:start position:0%
+maturity is simply equal to the sum of
+the date 1 2 3 4 5 6 7 multiplied by a
+
+ align:start position:0%
+the date 1 2 3 4 5 6 7 multiplied by a
+ 
+
+ align:start position:0%
+the date 1 2 3 4 5 6 7 multiplied by a
+weight factor that sums to one. And
+
+ align:start position:0%
+weight factor that sums to one. And
+ 
+
+ align:start position:0%
+weight factor that sums to one. And
+let's just use as a weight factor
+
+ align:start position:0%
+let's just use as a weight factor
+ 
+
+ align:start position:0%
+let's just use as a weight factor
+the proportion of present value of cash
+
+ align:start position:0%
+the proportion of present value of cash
+ 
+
+ align:start position:0%
+the proportion of present value of cash
+flow on that date. Okay.
+
+ align:start position:0%
+flow on that date. Okay.
+ 
+
+ align:start position:0%
+flow on that date. Okay.
+So if you take the weighted average
+
+ align:start position:0%
+So if you take the weighted average
+ 
+
+ align:start position:0%
+So if you take the weighted average
+where you take the weights as the
+
+ align:start position:0%
+where you take the weights as the
+ 
+
+ align:start position:0%
+where you take the weights as the
+present value of the coupon divided by
+
+ align:start position:0%
+present value of the coupon divided by
+ 
+
+ align:start position:0%
+present value of the coupon divided by
+the present value of the bond those
+
+ align:start position:0%
+the present value of the bond those
+ 
+
+ align:start position:0%
+the present value of the bond those
+weights certainly sum to one
+
+ align:start position:0%
+weights certainly sum to one
+ 
+
+ align:start position:0%
+weights certainly sum to one
+and then you're waiting that by the date
+
+ align:start position:0%
+and then you're waiting that by the date
+ 
+
+ align:start position:0%
+and then you're waiting that by the date
+the year that you get paid that number
+
+ align:start position:0%
+the year that you get paid that number
+ 
+
+ align:start position:0%
+the year that you get paid that number
+will give you what's called macau
+
+ align:start position:0%
+will give you what's called macau
+ 
+
+ align:start position:0%
+will give you what's called macau
+duration. Okay.
+
+ align:start position:0%
+duration. Okay.
+ 
+
+ align:start position:0%
+duration. Okay.
+So it turns out that the reason the
+
+ align:start position:0%
+So it turns out that the reason the
+ 
+
+ align:start position:0%
+So it turns out that the reason the
+macau duration is interesting is that
+
+ align:start position:0%
+macau duration is interesting is that
+ 
+
+ align:start position:0%
+macau duration is interesting is that
+when you take a look at bond prices and
+
+ align:start position:0%
+when you take a look at bond prices and
+ 
+
+ align:start position:0%
+when you take a look at bond prices and
+you ask the question for a certain
+
+ align:start position:0%
+you ask the question for a certain
+ 
+
+ align:start position:0%
+you ask the question for a certain
+percentage change a certain basis point
+
+ align:start position:0%
+percentage change a certain basis point
+ 
+
+ align:start position:0%
+percentage change a certain basis point
+change in the interest rate what does
+
+ align:start position:0%
+change in the interest rate what does
+ 
+
+ align:start position:0%
+change in the interest rate what does
+that do to the bond price as a
+
+ align:start position:0%
+that do to the bond price as a
+ 
+
+ align:start position:0%
+that do to the bond price as a
+percentage of its current price. So this
+
+ align:start position:0%
+percentage of its current price. So this
+ 
+
+ align:start position:0%
+percentage of its current price. So this
+is the sensitivity.
+
+ align:start position:0%
+is the sensitivity.
+ 
+
+ align:start position:0%
+is the sensitivity.
+It turns out that you can show that at
+
+ align:start position:0%
+It turns out that you can show that at
+ 
+
+ align:start position:0%
+It turns out that you can show that at
+that's actually the negative of the
+
+ align:start position:0%
+that's actually the negative of the
+ 
+
+ align:start position:0%
+that's actually the negative of the
+macau duration divided by one plus the
+
+ align:start position:0%
+macau duration divided by one plus the
+ 
+
+ align:start position:0%
+macau duration divided by one plus the
+bond yield.
+
+ align:start position:0%
+bond yield.
+ 
+
+ align:start position:0%
+bond yield.
+So this is a long way of stating that
+
+ align:start position:0%
+So this is a long way of stating that
+ 
+
+ align:start position:0%
+So this is a long way of stating that
+the duration gives you a measure of how
+
+ align:start position:0%
+the duration gives you a measure of how
+ 
+
+ align:start position:0%
+the duration gives you a measure of how
+sensitive the bond price is to changes
+
+ align:start position:0%
+sensitive the bond price is to changes
+ 
+
+ align:start position:0%
+sensitive the bond price is to changes
+in yield.
+
+ align:start position:0%
+in yield.
+ 
+
+ align:start position:0%
+in yield.
+Okay, the longer the duration,
+
+ align:start position:0%
+Okay, the longer the duration,
+ 
+
+ align:start position:0%
+Okay, the longer the duration,
+the more sensitive the bond is to
+
+ align:start position:0%
+the more sensitive the bond is to
+ 
+
+ align:start position:0%
+the more sensitive the bond is to
+changes in yield. And duration now just
+
+ align:start position:0%
+changes in yield. And duration now just
+ 
+
+ align:start position:0%
+changes in yield. And duration now just
+means a weighted average of all of the
+
+ align:start position:0%
+means a weighted average of all of the
+ 
+
+ align:start position:0%
+means a weighted average of all of the
+payout dates that a bond will have. If a
+
+ align:start position:0%
+payout dates that a bond will have. If a
+ 
+
+ align:start position:0%
+payout dates that a bond will have. If a
+bond pays a lot of its cash upfront and
+
+ align:start position:0%
+bond pays a lot of its cash upfront and
+ 
+
+ align:start position:0%
+bond pays a lot of its cash upfront and
+very little in later periods,
+
+ align:start position:0%
+very little in later periods,
+ 
+
+ align:start position:0%
+very little in later periods,
+is a duration
+
+ align:start position:0%
+is a duration
+ 
+
+ align:start position:0%
+is a duration
+high or low?
+
+ align:start position:0%
+high or low?
+ 
+
+ align:start position:0%
+high or low?
+Low. And so if a duration is low, what
+
+ align:start position:0%
+Low. And so if a duration is low, what
+ 
+
+ align:start position:0%
+Low. And so if a duration is low, what
+that says is that there's not a lot of
+
+ align:start position:0%
+that says is that there's not a lot of
+ 
+
+ align:start position:0%
+that says is that there's not a lot of
+sensitivity to changes in yield on the
+
+ align:start position:0%
+sensitivity to changes in yield on the
+ 
+
+ align:start position:0%
+sensitivity to changes in yield on the
+bond price itself. If on the other hand,
+
+ align:start position:0%
+bond price itself. If on the other hand,
+ 
+
+ align:start position:0%
+bond price itself. If on the other hand,
+all of your payment is out in the
+
+ align:start position:0%
+all of your payment is out in the
+ 
+
+ align:start position:0%
+all of your payment is out in the
+future, way out in the future, that's
+
+ align:start position:0%
+future, way out in the future, that's
+ 
+
+ align:start position:0%
+future, way out in the future, that's
+going to make it very interest rate
+
+ align:start position:0%
+going to make it very interest rate
+ 
+
+ align:start position:0%
+going to make it very interest rate
+sensitive. Okay? And the negative number
+
+ align:start position:0%
+sensitive. Okay? And the negative number
+ 
+
+ align:start position:0%
+sensitive. Okay? And the negative number
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+indicates that there's an inverse
+
+ align:start position:0%
+indicates that there's an inverse
+ 
+
+ align:start position:0%
+indicates that there's an inverse
+relationship between price and yield. So
+
+ align:start position:0%
+relationship between price and yield. So
+ 
+
+ align:start position:0%
+relationship between price and yield. So
+when bond investors look at a particular
+
+ align:start position:0%
+when bond investors look at a particular
+ 
+
+ align:start position:0%
+when bond investors look at a particular
+portfolio of bonds, and this is key,
+
+ align:start position:0%
+portfolio of bonds, and this is key,
+ 
+
+ align:start position:0%
+portfolio of bonds, and this is key,
+they look at a portfolio of bonds
+
+ align:start position:0%
+they look at a portfolio of bonds
+ 
+
+ align:start position:0%
+they look at a portfolio of bonds
+because that's what they're going to be
+
+ align:start position:0%
+because that's what they're going to be
+ 
+
+ align:start position:0%
+because that's what they're going to be
+investing in. When you put your money in
+
+ align:start position:0%
+investing in. When you put your money in
+ 
+
+ align:start position:0%
+investing in. When you put your money in
+a money market fund or in a bond fund,
+
+ align:start position:0%
+a money market fund or in a bond fund,
+ 
+
+ align:start position:0%
+a money market fund or in a bond fund,
+medium-term, long-term, you're not
+
+ align:start position:0%
+medium-term, long-term, you're not
+ 
+
+ align:start position:0%
+medium-term, long-term, you're not
+putting it in one bond, you're putting
+
+ align:start position:0%
+putting it in one bond, you're putting
+ 
+
+ align:start position:0%
+putting it in one bond, you're putting
+it in a whole set of bonds. Your natural
+
+ align:start position:0%
+it in a whole set of bonds. Your natural
+ 
+
+ align:start position:0%
+it in a whole set of bonds. Your natural
+question is, how sensitive is that
+
+ align:start position:0%
+question is, how sensitive is that
+ 
+
+ align:start position:0%
+question is, how sensitive is that
+portfolio to changes in interest rates?
+
+ align:start position:0%
+portfolio to changes in interest rates?
+ 
+
+ align:start position:0%
+portfolio to changes in interest rates?
+And the answer is it's related to the
+
+ align:start position:0%
+And the answer is it's related to the
+ 
+
+ align:start position:0%
+And the answer is it's related to the
+duration. And so if I told you that this
+
+ align:start position:0%
+duration. And so if I told you that this
+ 
+
+ align:start position:0%
+duration. And so if I told you that this
+portfolio has a duration of 5 1/2 years,
+
+ align:start position:0%
+portfolio has a duration of 5 1/2 years,
+ 
+
+ align:start position:0%
+portfolio has a duration of 5 1/2 years,
+that will give you some intuition for
+
+ align:start position:0%
+that will give you some intuition for
+ 
+
+ align:start position:0%
+that will give you some intuition for
+how sensitive or how risky that
+
+ align:start position:0%
+how sensitive or how risky that
+ 
+
+ align:start position:0%
+how sensitive or how risky that
+portfolio is. So duration is a measure
+
+ align:start position:0%
+portfolio is. So duration is a measure
+ 
+
+ align:start position:0%
+portfolio is. So duration is a measure
+that I've defined for a bond, but you
+
+ align:start position:0%
+that I've defined for a bond, but you
+ 
+
+ align:start position:0%
+that I've defined for a bond, but you
+can define it for a portfolio of bonds,
+
+ align:start position:0%
+can define it for a portfolio of bonds,
+ 
+
+ align:start position:0%
+can define it for a portfolio of bonds,
+right? simply by taking the cash flows
+
+ align:start position:0%
+right? simply by taking the cash flows
+ 
+
+ align:start position:0%
+right? simply by taking the cash flows
+at every period
+
+ align:start position:0%
+at every period
+ 
+
+ align:start position:0%
+at every period
+and then computing a weighted average
+
+ align:start position:0%
+and then computing a weighted average
+ 
+
+ align:start position:0%
+and then computing a weighted average
+where the weights are the present value
+
+ align:start position:0%
+where the weights are the present value
+ 
+
+ align:start position:0%
+where the weights are the present value
+of those cash flows as a function of the
+
+ align:start position:0%
+of those cash flows as a function of the
+ 
+
+ align:start position:0%
+of those cash flows as a function of the
+entire portfolio.
+
+ align:start position:0%
+entire portfolio.
+ 
+
+ align:start position:0%
+entire portfolio.
+Okay, so here's an example uh where I've
+
+ align:start position:0%
+Okay, so here's an example uh where I've
+ 
+
+ align:start position:0%
+Okay, so here's an example uh where I've
+got a 4-year Treasury note with a face
+
+ align:start position:0%
+got a 4-year Treasury note with a face
+ 
+
+ align:start position:0%
+got a 4-year Treasury note with a face
+value of $100, 7% coupon selling at
+
+ align:start position:0%
+value of $100, 7% coupon selling at
+ 
+
+ align:start position:0%
+value of $100, 7% coupon selling at
+$103.50
+
+ align:start position:0%
+$103.50
+ 
+
+ align:start position:0%
+$103.50
+which yields 6%. That's the yield.
+
+ align:start position:0%
+which yields 6%. That's the yield.
+ 
+
+ align:start position:0%
+which yields 6%. That's the yield.
+That's the y that makes this 103.5 equal
+
+ align:start position:0%
+That's the y that makes this 103.5 equal
+ 
+
+ align:start position:0%
+That's the y that makes this 103.5 equal
+to the present value of all of those
+
+ align:start position:0%
+to the present value of all of those
+ 
+
+ align:start position:0%
+to the present value of all of those
+coupon payments plus the return of
+
+ align:start position:0%
+coupon payments plus the return of
+ 
+
+ align:start position:0%
+coupon payments plus the return of
+principal.
+
+ align:start position:0%
+principal.
+ 
+
+ align:start position:0%
+principal.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+And so here what I've done is to
+
+ align:start position:0%
+And so here what I've done is to
+ 
+
+ align:start position:0%
+And so here what I've done is to
+calculate for you the cash flows of the
+
+ align:start position:0%
+calculate for you the cash flows of the
+ 
+
+ align:start position:0%
+calculate for you the cash flows of the
+bond, the present value of those cash
+
+ align:start position:0%
+bond, the present value of those cash
+ 
+
+ align:start position:0%
+bond, the present value of those cash
+flows and then the respective product of
+
+ align:start position:0%
+flows and then the respective product of
+ 
+
+ align:start position:0%
+flows and then the respective product of
+t times the present value of cash flows.
+
+ align:start position:0%
+t times the present value of cash flows.
+ 
+
+ align:start position:0%
+t times the present value of cash flows.
+So you can actually compute for yourself
+
+ align:start position:0%
+So you can actually compute for yourself
+ 
+
+ align:start position:0%
+So you can actually compute for yourself
+that duration number and you can get a
+
+ align:start position:0%
+that duration number and you can get a
+ 
+
+ align:start position:0%
+that duration number and you can get a
+sense of exactly what that is.
+
+ align:start position:0%
+sense of exactly what that is.
+ 
+
+ align:start position:0%
+sense of exactly what that is.
+So the duration is about 7.13
+
+ align:start position:0%
+So the duration is about 7.13
+ 
+
+ align:start position:0%
+So the duration is about 7.13
+years. So duration is a a measurement
+
+ align:start position:0%
+years. So duration is a a measurement
+ 
+
+ align:start position:0%
+years. So duration is a a measurement
+that is in units of years or halfyear
+
+ align:start position:0%
+that is in units of years or halfyear
+ 
+
+ align:start position:0%
+that is in units of years or halfyear
+units sorry 7.13 halfyear units
+
+ align:start position:0%
+units sorry 7.13 halfyear units
+ 
+
+ align:start position:0%
+units sorry 7.13 halfyear units
+and the modified duration is going to be
+
+ align:start position:0%
+and the modified duration is going to be
+ 
+
+ align:start position:0%
+and the modified duration is going to be
+given by 6.92
+
+ align:start position:0%
+given by 6.92
+ 
+
+ align:start position:0%
+given by 6.92
+price risk at a yield of 3% therefore is
+
+ align:start position:0%
+price risk at a yield of 3% therefore is
+ 
+
+ align:start position:0%
+price risk at a yield of 3% therefore is
+going to be given by just this
+
+ align:start position:0%
+going to be given by just this
+ 
+
+ align:start position:0%
+going to be given by just this
+expression right here. What that says is
+
+ align:start position:0%
+expression right here. What that says is
+ 
+
+ align:start position:0%
+expression right here. What that says is
+that if the yield moves up by one uh a
+
+ align:start position:0%
+that if the yield moves up by one uh a
+ 
+
+ align:start position:0%
+that if the yield moves up by one uh a
+tenth of a percent or 10 basis points,
+
+ align:start position:0%
+tenth of a percent or 10 basis points,
+ 
+
+ align:start position:0%
+tenth of a percent or 10 basis points,
+the bond price is going to decrease by
+
+ align:start position:0%
+the bond price is going to decrease by
+ 
+
+ align:start position:0%
+the bond price is going to decrease by
+68 basis points. That will give you a
+
+ align:start position:0%
+68 basis points. That will give you a
+ 
+
+ align:start position:0%
+68 basis points. That will give you a
+sense of how exposed you are. If you
+
+ align:start position:0%
+sense of how exposed you are. If you
+ 
+
+ align:start position:0%
+sense of how exposed you are. If you
+have very long duration portfolios, that
+
+ align:start position:0%
+have very long duration portfolios, that
+ 
+
+ align:start position:0%
+have very long duration portfolios, that
+means that you're going to be in for a
+
+ align:start position:0%
+means that you're going to be in for a
+ 
+
+ align:start position:0%
+means that you're going to be in for a
+wild ride as interest rates swing around
+
+ align:start position:0%
+wild ride as interest rates swing around
+ 
+
+ align:start position:0%
+wild ride as interest rates swing around
+a lot. And if you're willing to take on
+
+ align:start position:0%
+a lot. And if you're willing to take on
+ 
+
+ align:start position:0%
+a lot. And if you're willing to take on
+that risk, that's great. But you're
+
+ align:start position:0%
+that risk, that's great. But you're
+ 
+
+ align:start position:0%
+that risk, that's great. But you're
+going to be at least uh uh uh
+
+ align:start position:0%
+going to be at least uh uh uh
+ 
+
+ align:start position:0%
+going to be at least uh uh uh
+compensated for that. Okay,
+
+ align:start position:0%
+compensated for that. Okay,
+ 
+
+ align:start position:0%
+compensated for that. Okay,
+macau duration uh you know you can
+
+ align:start position:0%
+macau duration uh you know you can
+ 
+
+ align:start position:0%
+macau duration uh you know you can
+compute it uh in this way uh for
+
+ align:start position:0%
+compute it uh in this way uh for
+ 
+
+ align:start position:0%
+compute it uh in this way uh for
+intra-ear coupons. That's a very
+
+ align:start position:0%
+intra-ear coupons. That's a very
+ 
+
+ align:start position:0%
+intra-ear coupons. That's a very
+straightforward calculation. So you want
+
+ align:start position:0%
+straightforward calculation. So you want
+ 
+
+ align:start position:0%
+straightforward calculation. So you want
+to make sure you know how to do that.
+
+ align:start position:0%
+to make sure you know how to do that.
+ 
+
+ align:start position:0%
+to make sure you know how to do that.
+You simply just use the usual
+
+ align:start position:0%
+You simply just use the usual
+ 
+
+ align:start position:0%
+You simply just use the usual
+discounting and uh dividing the yield by
+
+ align:start position:0%
+discounting and uh dividing the yield by
+ 
+
+ align:start position:0%
+discounting and uh dividing the yield by
+the appropriate payment periods.
+
+ align:start position:0%
+the appropriate payment periods.
+ 
+
+ align:start position:0%
+the appropriate payment periods.
+And now the uh the last concept that I
+
+ align:start position:0%
+And now the uh the last concept that I
+ 
+
+ align:start position:0%
+And now the uh the last concept that I
+want to cover today is
+
+ align:start position:0%
+want to cover today is
+ 
+
+ align:start position:0%
+want to cover today is
+convexity.
+
+ align:start position:0%
+convexity.
+ 
+
+ align:start position:0%
+convexity.
+Convexity is another measure of risk.
+
+ align:start position:0%
+Convexity is another measure of risk.
+ 
+
+ align:start position:0%
+Convexity is another measure of risk.
+It's the second derivative. What it
+
+ align:start position:0%
+It's the second derivative. What it
+ 
+
+ align:start position:0%
+It's the second derivative. What it
+measures is how the sensitivity
+
+ align:start position:0%
+measures is how the sensitivity
+ 
+
+ align:start position:0%
+measures is how the sensitivity
+itself changes.
+
+ align:start position:0%
+itself changes.
+ 
+
+ align:start position:0%
+itself changes.
+And it turns out that convexity as a
+
+ align:start position:0%
+And it turns out that convexity as a
+ 
+
+ align:start position:0%
+And it turns out that convexity as a
+measure gives you a sort of a higher
+
+ align:start position:0%
+measure gives you a sort of a higher
+ 
+
+ align:start position:0%
+measure gives you a sort of a higher
+order approximation both to the price of
+
+ align:start position:0%
+order approximation both to the price of
+ 
+
+ align:start position:0%
+order approximation both to the price of
+the bond as well as how the bond is
+
+ align:start position:0%
+the bond as well as how the bond is
+ 
+
+ align:start position:0%
+the bond as well as how the bond is
+going to move uh with respect to
+
+ align:start position:0%
+going to move uh with respect to
+ 
+
+ align:start position:0%
+going to move uh with respect to
+interest rates. So let me just show you
+
+ align:start position:0%
+interest rates. So let me just show you
+ 
+
+ align:start position:0%
+interest rates. So let me just show you
+what the derivation is. It's pretty
+
+ align:start position:0%
+what the derivation is. It's pretty
+ 
+
+ align:start position:0%
+what the derivation is. It's pretty
+straightforward. Uh but if you have any
+
+ align:start position:0%
+straightforward. Uh but if you have any
+ 
+
+ align:start position:0%
+straightforward. Uh but if you have any
+questions, happy to discuss it.
+
+ align:start position:0%
+questions, happy to discuss it.
+ 
+
+ align:start position:0%
+questions, happy to discuss it.
+You take the price of a bond and you
+
+ align:start position:0%
+You take the price of a bond and you
+ 
+
+ align:start position:0%
+You take the price of a bond and you
+take the second derivative with respect
+
+ align:start position:0%
+take the second derivative with respect
+ 
+
+ align:start position:0%
+take the second derivative with respect
+to the yield.
+
+ align:start position:0%
+to the yield.
+ 
+
+ align:start position:0%
+to the yield.
+What you're going to get out of it is an
+
+ align:start position:0%
+What you're going to get out of it is an
+ 
+
+ align:start position:0%
+What you're going to get out of it is an
+expression that looks like this. Now,
+
+ align:start position:0%
+expression that looks like this. Now,
+ 
+
+ align:start position:0%
+expression that looks like this. Now,
+that expression in and of itself has
+
+ align:start position:0%
+that expression in and of itself has
+ 
+
+ align:start position:0%
+that expression in and of itself has
+relatively little intuition.
+
+ align:start position:0%
+relatively little intuition.
+ 
+
+ align:start position:0%
+relatively little intuition.
+But let me just write down the
+
+ align:start position:0%
+But let me just write down the
+ 
+
+ align:start position:0%
+But let me just write down the
+percentage
+
+ align:start position:0%
+percentage
+ 
+
+ align:start position:0%
+percentage
+change in the first derivative as V
+
+ align:start position:0%
+change in the first derivative as V
+ 
+
+ align:start position:0%
+change in the first derivative as V
+subm. Okay? And then I'm going to show
+
+ align:start position:0%
+subm. Okay? And then I'm going to show
+ 
+
+ align:start position:0%
+subm. Okay? And then I'm going to show
+you an interesting relationship.
+
+ align:start position:0%
+you an interesting relationship.
+ 
+
+ align:start position:0%
+you an interesting relationship.
+This uh for those of you who remember
+
+ align:start position:0%
+This uh for those of you who remember
+ 
+
+ align:start position:0%
+This uh for those of you who remember
+your high school calculus or college
+
+ align:start position:0%
+your high school calculus or college
+ 
+
+ align:start position:0%
+your high school calculus or college
+calculus class, you'll remember there's
+
+ align:start position:0%
+calculus class, you'll remember there's
+ 
+
+ align:start position:0%
+calculus class, you'll remember there's
+something called a tailor approximation,
+
+ align:start position:0%
+something called a tailor approximation,
+ 
+
+ align:start position:0%
+something called a tailor approximation,
+right? Tailaylor series. This is a
+
+ align:start position:0%
+right? Tailaylor series. This is a
+ 
+
+ align:start position:0%
+right? Tailaylor series. This is a
+method of approximating nonlinear
+
+ align:start position:0%
+method of approximating nonlinear
+ 
+
+ align:start position:0%
+method of approximating nonlinear
+relationships using polomials, right?
+
+ align:start position:0%
+relationships using polomials, right?
+ 
+
+ align:start position:0%
+relationships using polomials, right?
+Powers of the variables in question. If
+
+ align:start position:0%
+Powers of the variables in question. If
+ 
+
+ align:start position:0%
+Powers of the variables in question. If
+you took the bond price as a function of
+
+ align:start position:0%
+you took the bond price as a function of
+ 
+
+ align:start position:0%
+you took the bond price as a function of
+the yield, right? It's a nonlinear
+
+ align:start position:0%
+the yield, right? It's a nonlinear
+ 
+
+ align:start position:0%
+the yield, right? It's a nonlinear
+function of course because you got that
+
+ align:start position:0%
+function of course because you got that
+ 
+
+ align:start position:0%
+function of course because you got that
+discounting going on.
+
+ align:start position:0%
+discounting going on.
+ 
+
+ align:start position:0%
+discounting going on.
+Then you can ask the question, how can I
+
+ align:start position:0%
+Then you can ask the question, how can I
+ 
+
+ align:start position:0%
+Then you can ask the question, how can I
+approximate the bond price as a function
+
+ align:start position:0%
+approximate the bond price as a function
+ 
+
+ align:start position:0%
+approximate the bond price as a function
+of the yield if I'm willing to take a
+
+ align:start position:0%
+of the yield if I'm willing to take a
+ 
+
+ align:start position:0%
+of the yield if I'm willing to take a
+couple of terms of the approximation.
+
+ align:start position:0%
+couple of terms of the approximation.
+ 
+
+ align:start position:0%
+couple of terms of the approximation.
+And when you do that, you get what may
+
+ align:start position:0%
+And when you do that, you get what may
+ 
+
+ align:start position:0%
+And when you do that, you get what may
+look like an awful expression, but
+
+ align:start position:0%
+look like an awful expression, but
+ 
+
+ align:start position:0%
+look like an awful expression, but
+actually it's quite beautiful in its own
+
+ align:start position:0%
+actually it's quite beautiful in its own
+ 
+
+ align:start position:0%
+actually it's quite beautiful in its own
+right. Uh what this says is that the
+
+ align:start position:0%
+right. Uh what this says is that the
+ 
+
+ align:start position:0%
+right. Uh what this says is that the
+price of the bond at a new interest rate
+
+ align:start position:0%
+price of the bond at a new interest rate
+ 
+
+ align:start position:0%
+price of the bond at a new interest rate
+at a new yield if the yield changes then
+
+ align:start position:0%
+at a new yield if the yield changes then
+ 
+
+ align:start position:0%
+at a new yield if the yield changes then
+the price of the whoops price of the
+
+ align:start position:0%
+the price of the whoops price of the
+ 
+
+ align:start position:0%
+the price of the whoops price of the
+bond at the new interest rate
+
+ align:start position:0%
+bond at the new interest rate
+ 
+
+ align:start position:0%
+bond at the new interest rate
+is going to be equal to the price of the
+
+ align:start position:0%
+is going to be equal to the price of the
+ 
+
+ align:start position:0%
+is going to be equal to the price of the
+bond at the old interest rate multiplied
+
+ align:start position:0%
+bond at the old interest rate multiplied
+ 
+
+ align:start position:0%
+bond at the old interest rate multiplied
+by a factor of something or other. And
+
+ align:start position:0%
+by a factor of something or other. And
+ 
+
+ align:start position:0%
+by a factor of something or other. And
+that factor is going to be given by one
+
+ align:start position:0%
+that factor is going to be given by one
+ 
+
+ align:start position:0%
+that factor is going to be given by one
+minus a term that's a linear function of
+
+ align:start position:0%
+minus a term that's a linear function of
+ 
+
+ align:start position:0%
+minus a term that's a linear function of
+the yield plus another term that is a
+
+ align:start position:0%
+the yield plus another term that is a
+ 
+
+ align:start position:0%
+the yield plus another term that is a
+quadratic function of the change in the
+
+ align:start position:0%
+quadratic function of the change in the
+ 
+
+ align:start position:0%
+quadratic function of the change in the
+yield. So this is what I mean when I say
+
+ align:start position:0%
+yield. So this is what I mean when I say
+ 
+
+ align:start position:0%
+yield. So this is what I mean when I say
+this is a second order approximation to
+
+ align:start position:0%
+this is a second order approximation to
+ 
+
+ align:start position:0%
+this is a second order approximation to
+the pricing relationship.
+
+ align:start position:0%
+the pricing relationship.
+ 
+
+ align:start position:0%
+the pricing relationship.
+And this basically gives us a way to
+
+ align:start position:0%
+And this basically gives us a way to
+ 
+
+ align:start position:0%
+And this basically gives us a way to
+figure out when yields move, what does
+
+ align:start position:0%
+figure out when yields move, what does
+ 
+
+ align:start position:0%
+figure out when yields move, what does
+that do to my portfolio?
+
+ align:start position:0%
+that do to my portfolio?
+ 
+
+ align:start position:0%
+that do to my portfolio?
+Now, you might be thinking, gee, this is
+
+ align:start position:0%
+Now, you might be thinking, gee, this is
+ 
+
+ align:start position:0%
+Now, you might be thinking, gee, this is
+an awful long way to go to try to figure
+
+ align:start position:0%
+an awful long way to go to try to figure
+ 
+
+ align:start position:0%
+an awful long way to go to try to figure
+that out. Can't we just, you know, use
+
+ align:start position:0%
+that out. Can't we just, you know, use
+ 
+
+ align:start position:0%
+that out. Can't we just, you know, use
+an Excel spreadsheet and then, you know,
+
+ align:start position:0%
+an Excel spreadsheet and then, you know,
+ 
+
+ align:start position:0%
+an Excel spreadsheet and then, you know,
+move the interest rate and then, you
+
+ align:start position:0%
+move the interest rate and then, you
+ 
+
+ align:start position:0%
+move the interest rate and then, you
+know, recalculate and see what that
+
+ align:start position:0%
+know, recalculate and see what that
+ 
+
+ align:start position:0%
+know, recalculate and see what that
+does? Today, you can, but in the 1970s,
+
+ align:start position:0%
+does? Today, you can, but in the 1970s,
+ 
+
+ align:start position:0%
+does? Today, you can, but in the 1970s,
+you couldn't. You didn't have that
+
+ align:start position:0%
+you couldn't. You didn't have that
+ 
+
+ align:start position:0%
+you couldn't. You didn't have that
+ability. So much of this framework was
+
+ align:start position:0%
+ability. So much of this framework was
+ 
+
+ align:start position:0%
+ability. So much of this framework was
+developed in the 1970s because people
+
+ align:start position:0%
+developed in the 1970s because people
+ 
+
+ align:start position:0%
+developed in the 1970s because people
+wanted to have easy ways of not only
+
+ align:start position:0%
+wanted to have easy ways of not only
+ 
+
+ align:start position:0%
+wanted to have easy ways of not only
+pricing bonds but figuring out what the
+
+ align:start position:0%
+pricing bonds but figuring out what the
+ 
+
+ align:start position:0%
+pricing bonds but figuring out what the
+risk of their positions were as bond
+
+ align:start position:0%
+risk of their positions were as bond
+ 
+
+ align:start position:0%
+risk of their positions were as bond
+traders and to do that quickly is very
+
+ align:start position:0%
+traders and to do that quickly is very
+ 
+
+ align:start position:0%
+traders and to do that quickly is very
+difficult. You remember the story I told
+
+ align:start position:0%
+difficult. You remember the story I told
+ 
+
+ align:start position:0%
+difficult. You remember the story I told
+you about when I got a mortgage uh you
+
+ align:start position:0%
+you about when I got a mortgage uh you
+ 
+
+ align:start position:0%
+you about when I got a mortgage uh you
+know 20 years ago and the u the bank
+
+ align:start position:0%
+know 20 years ago and the u the bank
+ 
+
+ align:start position:0%
+know 20 years ago and the u the bank
+loan officer you know just could not
+
+ align:start position:0%
+loan officer you know just could not
+ 
+
+ align:start position:0%
+loan officer you know just could not
+figure out what my mortgage payments
+
+ align:start position:0%
+figure out what my mortgage payments
+ 
+
+ align:start position:0%
+figure out what my mortgage payments
+were. she had to go look for a book and
+
+ align:start position:0%
+were. she had to go look for a book and
+ 
+
+ align:start position:0%
+were. she had to go look for a book and
+and try to thumb through what those
+
+ align:start position:0%
+and try to thumb through what those
+ 
+
+ align:start position:0%
+and try to thumb through what those
+calculations are. Well, imagine if
+
+ align:start position:0%
+calculations are. Well, imagine if
+ 
+
+ align:start position:0%
+calculations are. Well, imagine if
+you're a bond trader trading literally
+
+ align:start position:0%
+you're a bond trader trading literally
+ 
+
+ align:start position:0%
+you're a bond trader trading literally
+every minute of the day. And there was
+
+ align:start position:0%
+every minute of the day. And there was
+ 
+
+ align:start position:0%
+every minute of the day. And there was
+bond trading going on in the 1970s,
+
+ align:start position:0%
+bond trading going on in the 1970s,
+ 
+
+ align:start position:0%
+bond trading going on in the 1970s,
+believe it or not. Uh you have to figure
+
+ align:start position:0%
+believe it or not. Uh you have to figure
+ 
+
+ align:start position:0%
+believe it or not. Uh you have to figure
+out these pricing relationships. And it
+
+ align:start position:0%
+out these pricing relationships. And it
+ 
+
+ align:start position:0%
+out these pricing relationships. And it
+was not so easy. So a number of
+
+ align:start position:0%
+was not so easy. So a number of
+ 
+
+ align:start position:0%
+was not so easy. So a number of
+mathematicians came up with these kind
+
+ align:start position:0%
+mathematicians came up with these kind
+ 
+
+ align:start position:0%
+mathematicians came up with these kind
+of relationships for bond prices. In
+
+ align:start position:0%
+of relationships for bond prices. In
+ 
+
+ align:start position:0%
+of relationships for bond prices. In
+fact, it's funny. Bond pricing is
+
+ align:start position:0%
+fact, it's funny. Bond pricing is
+ 
+
+ align:start position:0%
+fact, it's funny. Bond pricing is
+actually quite a bit more of a
+
+ align:start position:0%
+actually quite a bit more of a
+ 
+
+ align:start position:0%
+actually quite a bit more of a
+mathematical art than equity pricing
+
+ align:start position:0%
+mathematical art than equity pricing
+ 
+
+ align:start position:0%
+mathematical art than equity pricing
+simply because with a bond there aren't
+
+ align:start position:0%
+simply because with a bond there aren't
+ 
+
+ align:start position:0%
+simply because with a bond there aren't
+that many moving parts and so they are
+
+ align:start position:0%
+that many moving parts and so they are
+ 
+
+ align:start position:0%
+that many moving parts and so they are
+subject to mathematical analysis like
+
+ align:start position:0%
+subject to mathematical analysis like
+ 
+
+ align:start position:0%
+subject to mathematical analysis like
+this. Whereas with stock prices since
+
+ align:start position:0%
+this. Whereas with stock prices since
+ 
+
+ align:start position:0%
+this. Whereas with stock prices since
+there are so many factors impinging on
+
+ align:start position:0%
+there are so many factors impinging on
+ 
+
+ align:start position:0%
+there are so many factors impinging on
+it the actual tools that we use are
+
+ align:start position:0%
+it the actual tools that we use are
+ 
+
+ align:start position:0%
+it the actual tools that we use are
+quite a bit less complex at least from a
+
+ align:start position:0%
+quite a bit less complex at least from a
+ 
+
+ align:start position:0%
+quite a bit less complex at least from a
+historical perspective.
+
+ align:start position:0%
+historical perspective.
+ 
+
+ align:start position:0%
+historical perspective.
+So um the purpose of this is really just
+
+ align:start position:0%
+So um the purpose of this is really just
+ 
+
+ align:start position:0%
+So um the purpose of this is really just
+to approximate the risk of a bond
+
+ align:start position:0%
+to approximate the risk of a bond
+ 
+
+ align:start position:0%
+to approximate the risk of a bond
+portfolio. You want to know when you
+
+ align:start position:0%
+portfolio. You want to know when you
+ 
+
+ align:start position:0%
+portfolio. You want to know when you
+change yields what that does to the
+
+ align:start position:0%
+change yields what that does to the
+ 
+
+ align:start position:0%
+change yields what that does to the
+portfolio and you also want to know if
+
+ align:start position:0%
+portfolio and you also want to know if
+ 
+
+ align:start position:0%
+portfolio and you also want to know if
+you if the yield changes in volatility
+
+ align:start position:0%
+you if the yield changes in volatility
+ 
+
+ align:start position:0%
+you if the yield changes in volatility
+what does that do to the portfolio. So
+
+ align:start position:0%
+what does that do to the portfolio. So
+ 
+
+ align:start position:0%
+what does that do to the portfolio. So
+this first term here this term tells you
+
+ align:start position:0%
+this first term here this term tells you
+ 
+
+ align:start position:0%
+this first term here this term tells you
+about shifts in the interest rate. What
+
+ align:start position:0%
+about shifts in the interest rate. What
+ 
+
+ align:start position:0%
+about shifts in the interest rate. What
+this term does is tell you about
+
+ align:start position:0%
+this term does is tell you about
+ 
+
+ align:start position:0%
+this term does is tell you about
+fluctuations or volatility of interest
+
+ align:start position:0%
+fluctuations or volatility of interest
+ 
+
+ align:start position:0%
+fluctuations or volatility of interest
+rates. And it turns out that volatility
+
+ align:start position:0%
+rates. And it turns out that volatility
+ 
+
+ align:start position:0%
+rates. And it turns out that volatility
+has an impact on bond portfolios as does
+
+ align:start position:0%
+has an impact on bond portfolios as does
+ 
+
+ align:start position:0%
+has an impact on bond portfolios as does
+uh changes in the level of interest
+
+ align:start position:0%
+uh changes in the level of interest
+ 
+
+ align:start position:0%
+uh changes in the level of interest
+rates. Just looking at this, can anybody
+
+ align:start position:0%
+rates. Just looking at this, can anybody
+ 
+
+ align:start position:0%
+rates. Just looking at this, can anybody
+tell me off the top of their head what
+
+ align:start position:0%
+tell me off the top of their head what
+ 
+
+ align:start position:0%
+tell me off the top of their head what
+direction this goes? In other words, if
+
+ align:start position:0%
+direction this goes? In other words, if
+ 
+
+ align:start position:0%
+direction this goes? In other words, if
+you are holding a bond and interest
+
+ align:start position:0%
+you are holding a bond and interest
+ 
+
+ align:start position:0%
+you are holding a bond and interest
+rates rise, we know that bond prices
+
+ align:start position:0%
+rates rise, we know that bond prices
+ 
+
+ align:start position:0%
+rates rise, we know that bond prices
+will fall.
+
+ align:start position:0%
+will fall.
+ 
+
+ align:start position:0%
+will fall.
+But what if the volatility of interest
+
+ align:start position:0%
+But what if the volatility of interest
+ 
+
+ align:start position:0%
+But what if the volatility of interest
+rates rise as they have over the last
+
+ align:start position:0%
+rates rise as they have over the last
+ 
+
+ align:start position:0%
+rates rise as they have over the last
+few weeks? Yields have bounced around a
+
+ align:start position:0%
+few weeks? Yields have bounced around a
+ 
+
+ align:start position:0%
+few weeks? Yields have bounced around a
+lot more lately than they have in the
+
+ align:start position:0%
+lot more lately than they have in the
+ 
+
+ align:start position:0%
+lot more lately than they have in the
+past. What does that do to a bond?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Does it make it more valuable or less
+
+ align:start position:0%
+Does it make it more valuable or less
+ 
+
+ align:start position:0%
+Does it make it more valuable or less
+valuable? Let's put it that way.
+
+ align:start position:0%
+valuable? Let's put it that way.
+ 
+
+ align:start position:0%
+valuable? Let's put it that way.
+How do you know? less more we have some
+
+ align:start position:0%
+How do you know? less more we have some
+ 
+
+ align:start position:0%
+How do you know? less more we have some
+volatility here. Okay,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take a look at that expression.
+
+ align:start position:0%
+take a look at that expression.
+ 
+
+ align:start position:0%
+take a look at that expression.
+V subm
+
+ align:start position:0%
+V subm
+ 
+
+ align:start position:0%
+V subm
+is going to be the second derivative.
+
+ align:start position:0%
+is going to be the second derivative.
+ 
+
+ align:start position:0%
+is going to be the second derivative.
+And then you've got a term there that's
+
+ align:start position:0%
+And then you've got a term there that's
+ 
+
+ align:start position:0%
+And then you've got a term there that's
+going to be the change in the yield,
+
+ align:start position:0%
+going to be the change in the yield,
+ 
+
+ align:start position:0%
+going to be the change in the yield,
+right? Squared.
+
+ align:start position:0%
+right? Squared.
+ 
+
+ align:start position:0%
+right? Squared.
+If the change in the yield squared goes
+
+ align:start position:0%
+If the change in the yield squared goes
+ 
+
+ align:start position:0%
+If the change in the yield squared goes
+up, other things equal
+
+ align:start position:0%
+up, other things equal
+ 
+
+ align:start position:0%
+up, other things equal
+and other things are never equal. But
+
+ align:start position:0%
+and other things are never equal. But
+ 
+
+ align:start position:0%
+and other things are never equal. But
+economists like to say other things
+
+ align:start position:0%
+economists like to say other things
+ 
+
+ align:start position:0%
+economists like to say other things
+equal,
+
+ align:start position:0%
+equal,
+ 
+
+ align:start position:0%
+equal,
+it actually makes bonds
+
+ align:start position:0%
+it actually makes bonds
+ 
+
+ align:start position:0%
+it actually makes bonds
+more valuable. In this respect, owning a
+
+ align:start position:0%
+more valuable. In this respect, owning a
+ 
+
+ align:start position:0%
+more valuable. In this respect, owning a
+bond
+
+ align:start position:0%
+bond
+ 
+
+ align:start position:0%
+bond
+actually is sort of like owning an
+
+ align:start position:0%
+actually is sort of like owning an
+ 
+
+ align:start position:0%
+actually is sort of like owning an
+option. Now, you don't know about
+
+ align:start position:0%
+option. Now, you don't know about
+ 
+
+ align:start position:0%
+option. Now, you don't know about
+options yet. We're going to come to that
+
+ align:start position:0%
+options yet. We're going to come to that
+ 
+
+ align:start position:0%
+options yet. We're going to come to that
+in a few lectures. But it turns out that
+
+ align:start position:0%
+in a few lectures. But it turns out that
+ 
+
+ align:start position:0%
+in a few lectures. But it turns out that
+having an option when volatility goes up
+
+ align:start position:0%
+having an option when volatility goes up
+ 
+
+ align:start position:0%
+having an option when volatility goes up
+can be very valuable. And similarly for
+
+ align:start position:0%
+can be very valuable. And similarly for
+ 
+
+ align:start position:0%
+can be very valuable. And similarly for
+bonds, bonds have option-like
+
+ align:start position:0%
+bonds, bonds have option-like
+ 
+
+ align:start position:0%
+bonds, bonds have option-like
+characteristics. And we see that here
+
+ align:start position:0%
+characteristics. And we see that here
+ 
+
+ align:start position:0%
+characteristics. And we see that here
+with this approximation,
+
+ align:start position:0%
+with this approximation,
+ 
+
+ align:start position:0%
+with this approximation,
+that second term uh will actually yield
+
+ align:start position:0%
+that second term uh will actually yield
+ 
+
+ align:start position:0%
+that second term uh will actually yield
+some actual value when volatility goes
+
+ align:start position:0%
+some actual value when volatility goes
+ 
+
+ align:start position:0%
+some actual value when volatility goes
+up. Now, I I do a numerical example here
+
+ align:start position:0%
+up. Now, I I do a numerical example here
+ 
+
+ align:start position:0%
+up. Now, I I do a numerical example here
+that I'd like you to look through on
+
+ align:start position:0%
+that I'd like you to look through on
+ 
+
+ align:start position:0%
+that I'd like you to look through on
+your own where I compute for you both
+
+ align:start position:0%
+your own where I compute for you both
+ 
+
+ align:start position:0%
+your own where I compute for you both
+the first and second terms of that
+
+ align:start position:0%
+the first and second terms of that
+ 
+
+ align:start position:0%
+the first and second terms of that
+approximation and you can actually see
+
+ align:start position:0%
+approximation and you can actually see
+ 
+
+ align:start position:0%
+approximation and you can actually see
+how good the approximation is. Okay? So,
+
+ align:start position:0%
+how good the approximation is. Okay? So,
+ 
+
+ align:start position:0%
+how good the approximation is. Okay? So,
+I'd like you to take a look at that,
+
+ align:start position:0%
+I'd like you to take a look at that,
+ 
+
+ align:start position:0%
+I'd like you to take a look at that,
+make sure you understand it, and next
+
+ align:start position:0%
+make sure you understand it, and next
+ 
+
+ align:start position:0%
+make sure you understand it, and next
+time be happy to answer questions about
+
+ align:start position:0%
+time be happy to answer questions about
+ 
+
+ align:start position:0%
+time be happy to answer questions about
+this. What we're going to cover on
+
+ align:start position:0%
+this. What we're going to cover on
+ 
+
+ align:start position:0%
+this. What we're going to cover on
+Monday is risky debt, which of course is
+
+ align:start position:0%
+Monday is risky debt, which of course is
+ 
+
+ align:start position:0%
+Monday is risky debt, which of course is
+directly related to what's going on in
+
+ align:start position:0%
+directly related to what's going on in
+ 
+
+ align:start position:0%
+directly related to what's going on in
+markets today. And so I I'd like you to
+
+ align:start position:0%
+markets today. And so I I'd like you to
+ 
+
+ align:start position:0%
+markets today. And so I I'd like you to
+to read up on uh that in the textbook.
+
+ align:start position:0%
+to read up on uh that in the textbook.
+ 
+
+ align:start position:0%
+to read up on uh that in the textbook.
+And when we come back on Monday, we're
+
+ align:start position:0%
+And when we come back on Monday, we're
+ 
+
+ align:start position:0%
+And when we come back on Monday, we're
+going to talk about debt ratings and
+
+ align:start position:0%
+going to talk about debt ratings and
+ 
+
+ align:start position:0%
+going to talk about debt ratings and
+possibly what went wrong with all of
+
+ align:start position:0%
+possibly what went wrong with all of
+ 
+
+ align:start position:0%
+possibly what went wrong with all of
+these subprime securities.
\ No newline at end of file
diff --git a/Azq6S6Hx0gU.txt b/Azq6S6Hx0gU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..847739a3b4e44e16adb739e23feb7dcf5dfb1972
--- /dev/null
+++ b/Azq6S6Hx0gU.txt
@@ -0,0 +1,13146 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu recap last night and give
+
+ align:start position:0%
+ocw.mit.edu recap last night and give
+ 
+
+ align:start position:0%
+ocw.mit.edu recap last night and give
+you remember what we had for an overview
+
+ align:start position:0%
+you remember what we had for an overview
+ 
+
+ align:start position:0%
+you remember what we had for an overview
+uh the first part was that um it's not
+
+ align:start position:0%
+uh the first part was that um it's not
+ 
+
+ align:start position:0%
+uh the first part was that um it's not
+about the business plan it's about
+
+ align:start position:0%
+about the business plan it's about
+ 
+
+ align:start position:0%
+about the business plan it's about
+planning that was the first point I hope
+
+ align:start position:0%
+planning that was the first point I hope
+ 
+
+ align:start position:0%
+planning that was the first point I hope
+you got uh the second one is that
+
+ align:start position:0%
+you got uh the second one is that
+ 
+
+ align:start position:0%
+you got uh the second one is that
+planning is not a static process it's
+
+ align:start position:0%
+planning is not a static process it's
+ 
+
+ align:start position:0%
+planning is not a static process it's
+Dynamic and therefore your plan is going
+
+ align:start position:0%
+Dynamic and therefore your plan is going
+ 
+
+ align:start position:0%
+Dynamic and therefore your plan is going
+to be dynamic however you uh you know
+
+ align:start position:0%
+to be dynamic however you uh you know
+ 
+
+ align:start position:0%
+to be dynamic however you uh you know
+write it down or or put it in slides
+
+ align:start position:0%
+write it down or or put it in slides
+ 
+
+ align:start position:0%
+write it down or or put it in slides
+that's the first set of
+
+ align:start position:0%
+that's the first set of
+ 
+
+ align:start position:0%
+that's the first set of
+points uh the second is the uh three
+
+ align:start position:0%
+points uh the second is the uh three
+ 
+
+ align:start position:0%
+points uh the second is the uh three
+wise or sorry the second is your goals
+
+ align:start position:0%
+wise or sorry the second is your goals
+ 
+
+ align:start position:0%
+wise or sorry the second is your goals
+and tasks in this whole process it's to
+
+ align:start position:0%
+and tasks in this whole process it's to
+ 
+
+ align:start position:0%
+and tasks in this whole process it's to
+create value and the second goal is to
+
+ align:start position:0%
+create value and the second goal is to
+ 
+
+ align:start position:0%
+create value and the second goal is to
+harvest some of the
+
+ align:start position:0%
+harvest some of the
+ 
+
+ align:start position:0%
+harvest some of the
+value and as we pointed out those are
+
+ align:start position:0%
+value and as we pointed out those are
+ 
+
+ align:start position:0%
+value and as we pointed out those are
+easy to say and it's increasingly hard
+
+ align:start position:0%
+easy to say and it's increasingly hard
+ 
+
+ align:start position:0%
+easy to say and it's increasingly hard
+to do uh the rest of the course will be
+
+ align:start position:0%
+to do uh the rest of the course will be
+ 
+
+ align:start position:0%
+to do uh the rest of the course will be
+telling you try to how to do those
+
+ align:start position:0%
+telling you try to how to do those
+ 
+
+ align:start position:0%
+telling you try to how to do those
+things the the questions that investors
+
+ align:start position:0%
+things the the questions that investors
+ 
+
+ align:start position:0%
+things the the questions that investors
+are going to be asking are the three
+
+ align:start position:0%
+are going to be asking are the three
+ 
+
+ align:start position:0%
+are going to be asking are the three
+wise why this why is this something
+
+ align:start position:0%
+wise why this why is this something
+ 
+
+ align:start position:0%
+wise why this why is this something
+important why now why is now the right
+
+ align:start position:0%
+important why now why is now the right
+ 
+
+ align:start position:0%
+important why now why is now the right
+time to do it and why this team why why
+
+ align:start position:0%
+time to do it and why this team why why
+ 
+
+ align:start position:0%
+time to do it and why this team why why
+is this group of people the right people
+
+ align:start position:0%
+is this group of people the right people
+ 
+
+ align:start position:0%
+is this group of people the right people
+and if they get through those the fourth
+
+ align:start position:0%
+and if they get through those the fourth
+ 
+
+ align:start position:0%
+and if they get through those the fourth
+one is why won't it work now I said that
+
+ align:start position:0%
+one is why won't it work now I said that
+ 
+
+ align:start position:0%
+one is why won't it work now I said that
+that's what investors ask and that's
+
+ align:start position:0%
+that's what investors ask and that's
+ 
+
+ align:start position:0%
+that's what investors ask and that's
+probably what you ought to be asking
+
+ align:start position:0%
+probably what you ought to be asking
+ 
+
+ align:start position:0%
+probably what you ought to be asking
+because the final point is the most
+
+ align:start position:0%
+because the final point is the most
+ 
+
+ align:start position:0%
+because the final point is the most
+scarce resource is not money it's your
+
+ align:start position:0%
+scarce resource is not money it's your
+ 
+
+ align:start position:0%
+scarce resource is not money it's your
+time so if you're not happy with those
+
+ align:start position:0%
+time so if you're not happy with those
+ 
+
+ align:start position:0%
+time so if you're not happy with those
+answers to those questions then you
+
+ align:start position:0%
+answers to those questions then you
+ 
+
+ align:start position:0%
+answers to those questions then you
+ought to iterate and find some new
+
+ align:start position:0%
+ought to iterate and find some new
+ 
+
+ align:start position:0%
+ought to iterate and find some new
+questions uh a new approach to those in
+
+ align:start position:0%
+questions uh a new approach to those in
+ 
+
+ align:start position:0%
+questions uh a new approach to those in
+fact tonight our speaker Bob has
+
+ align:start position:0%
+fact tonight our speaker Bob has
+ 
+
+ align:start position:0%
+fact tonight our speaker Bob has
+probably going to talk about how you've
+
+ align:start position:0%
+probably going to talk about how you've
+ 
+
+ align:start position:0%
+probably going to talk about how you've
+iterated few some things on that score
+
+ align:start position:0%
+iterated few some things on that score
+ 
+
+ align:start position:0%
+iterated few some things on that score
+okay so tonight uh we're starting down
+
+ align:start position:0%
+okay so tonight uh we're starting down
+ 
+
+ align:start position:0%
+okay so tonight uh we're starting down
+the path of filling in the business plan
+
+ align:start position:0%
+the path of filling in the business plan
+ 
+
+ align:start position:0%
+the path of filling in the business plan
+the first thing we said is you got to
+
+ align:start position:0%
+the first thing we said is you got to
+ 
+
+ align:start position:0%
+the first thing we said is you got to
+create value and one of the ways you can
+
+ align:start position:0%
+create value and one of the ways you can
+ 
+
+ align:start position:0%
+create value and one of the ways you can
+create value is to find a customer and
+
+ align:start position:0%
+create value is to find a customer and
+ 
+
+ align:start position:0%
+create value is to find a customer and
+Bob Jones who's one of our highly paid
+
+ align:start position:0%
+Bob Jones who's one of our highly paid
+ 
+
+ align:start position:0%
+Bob Jones who's one of our highly paid
+volunteers uh once again tripling your
+
+ align:start position:0%
+volunteers uh once again tripling your
+ 
+
+ align:start position:0%
+volunteers uh once again tripling your
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+income um Bob is um was a class ban of
+
+ align:start position:0%
+income um Bob is um was a class ban of
+ 
+
+ align:start position:0%
+income um Bob is um was a class ban of
+mine at Sloan uh people in the audience
+
+ align:start position:0%
+mine at Sloan uh people in the audience
+ 
+
+ align:start position:0%
+mine at Sloan uh people in the audience
+from Sloan do you know about the C
+
+ align:start position:0%
+from Sloan do you know about the C
+ 
+
+ align:start position:0%
+from Sloan do you know about the C
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+still going on you like that that's Bob
+
+ align:start position:0%
+still going on you like that that's Bob
+ 
+
+ align:start position:0%
+still going on you like that that's Bob
+he's the guy that organized the first C
+
+ align:start position:0%
+he's the guy that organized the first C
+ 
+
+ align:start position:0%
+he's the guy that organized the first C
+function um in addition to being a
+
+ align:start position:0%
+function um in addition to being a
+ 
+
+ align:start position:0%
+function um in addition to being a
+Serial entrepreneur
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah for those of you who are not from
+
+ align:start position:0%
+yeah for those of you who are not from
+ 
+
+ align:start position:0%
+yeah for those of you who are not from
+the Salone side of Campus the C function
+
+ align:start position:0%
+the Salone side of Campus the C function
+ 
+
+ align:start position:0%
+the Salone side of Campus the C function
+is consumption function in economics and
+
+ align:start position:0%
+is consumption function in economics and
+ 
+
+ align:start position:0%
+is consumption function in economics and
+you can picture what might be consumed
+
+ align:start position:0%
+you can picture what might be consumed
+ 
+
+ align:start position:0%
+you can picture what might be consumed
+at a Friday night uh consumption
+
+ align:start position:0%
+at a Friday night uh consumption
+ 
+
+ align:start position:0%
+at a Friday night uh consumption
+function so we'll leave it with that uh
+
+ align:start position:0%
+function so we'll leave it with that uh
+ 
+
+ align:start position:0%
+function so we'll leave it with that uh
+Bob's a Serial entrepreneur still at it
+
+ align:start position:0%
+Bob's a Serial entrepreneur still at it
+ 
+
+ align:start position:0%
+Bob's a Serial entrepreneur still at it
+like a lot lot of the speakers that
+
+ align:start position:0%
+like a lot lot of the speakers that
+ 
+
+ align:start position:0%
+like a lot lot of the speakers that
+we're going to hear from they're
+
+ align:start position:0%
+we're going to hear from they're
+ 
+
+ align:start position:0%
+we're going to hear from they're
+actually doing the very things they're
+
+ align:start position:0%
+actually doing the very things they're
+ 
+
+ align:start position:0%
+actually doing the very things they're
+talking to you about so this isn't just
+
+ align:start position:0%
+talking to you about so this isn't just
+ 
+
+ align:start position:0%
+talking to you about so this isn't just
+an academic exercise for them uh Bob's
+
+ align:start position:0%
+an academic exercise for them uh Bob's
+ 
+
+ align:start position:0%
+an academic exercise for them uh Bob's
+other uh claim to fame is he plays
+
+ align:start position:0%
+other uh claim to fame is he plays
+ 
+
+ align:start position:0%
+other uh claim to fame is he plays
+pretty good uh blues uh guitar and he
+
+ align:start position:0%
+pretty good uh blues uh guitar and he
+ 
+
+ align:start position:0%
+pretty good uh blues uh guitar and he
+has a blues band but U I'll let him
+
+ align:start position:0%
+has a blues band but U I'll let him
+ 
+
+ align:start position:0%
+has a blues band but U I'll let him
+decide whether he wants to say anything
+
+ align:start position:0%
+decide whether he wants to say anything
+ 
+
+ align:start position:0%
+decide whether he wants to say anything
+more about that and with that Bob the
+
+ align:start position:0%
+more about that and with that Bob the
+ 
+
+ align:start position:0%
+more about that and with that Bob the
+clicker is yours sir thanks
+
+ align:start position:0%
+clicker is yours sir thanks
+ 
+
+ align:start position:0%
+clicker is yours sir thanks
+Joe so good evening everybody i' like to
+
+ align:start position:0%
+Joe so good evening everybody i' like to
+ 
+
+ align:start position:0%
+Joe so good evening everybody i' like to
+congratulate you on the Good Sense
+
+ align:start position:0%
+congratulate you on the Good Sense
+ 
+
+ align:start position:0%
+congratulate you on the Good Sense
+required to sign up for one of the best
+
+ align:start position:0%
+required to sign up for one of the best
+ 
+
+ align:start position:0%
+required to sign up for one of the best
+courses that the Institute offers uh
+
+ align:start position:0%
+courses that the Institute offers uh
+ 
+
+ align:start position:0%
+courses that the Institute offers uh
+it's not the first course you you will
+
+ align:start position:0%
+it's not the first course you you will
+ 
+
+ align:start position:0%
+it's not the first course you you will
+take here that has you drinking from a
+
+ align:start position:0%
+take here that has you drinking from a
+ 
+
+ align:start position:0%
+take here that has you drinking from a
+fire hose but this one's pretty valuable
+
+ align:start position:0%
+fire hose but this one's pretty valuable
+ 
+
+ align:start position:0%
+fire hose but this one's pretty valuable
+stuff how many of you are in this
+
+ align:start position:0%
+stuff how many of you are in this
+ 
+
+ align:start position:0%
+stuff how many of you are in this
+because you're thinking of competing in
+
+ align:start position:0%
+because you're thinking of competing in
+ 
+
+ align:start position:0%
+because you're thinking of competing in
+the 100K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+competition good how many of you are
+
+ align:start position:0%
+competition good how many of you are
+ 
+
+ align:start position:0%
+competition good how many of you are
+contemplating making your living in
+
+ align:start position:0%
+contemplating making your living in
+ 
+
+ align:start position:0%
+contemplating making your living in
+entrepreneurship when you get out of
+
+ align:start position:0%
+entrepreneurship when you get out of
+ 
+
+ align:start position:0%
+entrepreneurship when you get out of
+here oh dear you poor
+
+ align:start position:0%
+here oh dear you poor
+ 
+
+ align:start position:0%
+here oh dear you poor
+things how many of you actually have
+
+ align:start position:0%
+things how many of you actually have
+ 
+
+ align:start position:0%
+things how many of you actually have
+something going right
+
+ align:start position:0%
+something going right
+ 
+
+ align:start position:0%
+something going right
+now wow well there's therapy available
+
+ align:start position:0%
+now wow well there's therapy available
+ 
+
+ align:start position:0%
+now wow well there's therapy available
+for you guys and and medication this is
+
+ align:start position:0%
+for you guys and and medication this is
+ 
+
+ align:start position:0%
+for you guys and and medication this is
+a little bit like a chronic illness you
+
+ align:start position:0%
+a little bit like a chronic illness you
+ 
+
+ align:start position:0%
+a little bit like a chronic illness you
+might be able to Tamp it down for a
+
+ align:start position:0%
+might be able to Tamp it down for a
+ 
+
+ align:start position:0%
+might be able to Tamp it down for a
+while and then it'll pop up again you
+
+ align:start position:0%
+while and then it'll pop up again you
+ 
+
+ align:start position:0%
+while and then it'll pop up again you
+won't be able to get rid of it once
+
+ align:start position:0%
+won't be able to get rid of it once
+ 
+
+ align:start position:0%
+won't be able to get rid of it once
+you're infected and Afflicted um I'd
+
+ align:start position:0%
+you're infected and Afflicted um I'd
+ 
+
+ align:start position:0%
+you're infected and Afflicted um I'd
+love some sense of what you guys are
+
+ align:start position:0%
+love some sense of what you guys are
+ 
+
+ align:start position:0%
+love some sense of what you guys are
+working on just some sense of the
+
+ align:start position:0%
+working on just some sense of the
+ 
+
+ align:start position:0%
+working on just some sense of the
+spectrum of who's doing what here do you
+
+ align:start position:0%
+spectrum of who's doing what here do you
+ 
+
+ align:start position:0%
+spectrum of who's doing what here do you
+have like a dog walking service for two
+
+ align:start position:0%
+have like a dog walking service for two
+ 
+
+ align:start position:0%
+have like a dog walking service for two
+income families or do you have something
+
+ align:start position:0%
+income families or do you have something
+ 
+
+ align:start position:0%
+income families or do you have something
+that detects the need for insulin and a
+
+ align:start position:0%
+that detects the need for insulin and a
+ 
+
+ align:start position:0%
+that detects the need for insulin and a
+patient with diabetes so somebody raise
+
+ align:start position:0%
+patient with diabetes so somebody raise
+ 
+
+ align:start position:0%
+patient with diabetes so somebody raise
+their hand and give me some sense of
+
+ align:start position:0%
+their hand and give me some sense of
+ 
+
+ align:start position:0%
+their hand and give me some sense of
+what it is you're working on
+
+ align:start position:0%
+what it is you're working on
+ 
+
+ align:start position:0%
+what it is you're working on
+please yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sir I'm sorry business what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what's broke that you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fix all right so you're sort of an
+
+ align:start position:0%
+fix all right so you're sort of an
+ 
+
+ align:start position:0%
+fix all right so you're sort of an
+Outsourcing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+service rent an expert
+
+ align:start position:0%
+service rent an expert
+ 
+
+ align:start position:0%
+service rent an expert
+good who else who else is working on
+
+ align:start position:0%
+good who else who else is working on
+ 
+
+ align:start position:0%
+good who else who else is working on
+something you can't all be it people yes
+
+ align:start position:0%
+something you can't all be it people yes
+ 
+
+ align:start position:0%
+something you can't all be it people yes
+sir I'm sorry say that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+personalized
+
+ align:start position:0%
+personalized
+ 
+
+ align:start position:0%
+personalized
+oh well tell us a little more about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that right I know that cancer is
+
+ align:start position:0%
+that right I know that cancer is
+ 
+
+ align:start position:0%
+that right I know that cancer is
+actually a family of disorders it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not so do you have like a set of
+
+ align:start position:0%
+not so do you have like a set of
+ 
+
+ align:start position:0%
+not so do you have like a set of
+molecular diagnostic tests which help
+
+ align:start position:0%
+molecular diagnostic tests which help
+ 
+
+ align:start position:0%
+molecular diagnostic tests which help
+determine which form they have and
+
+ align:start position:0%
+determine which form they have and
+ 
+
+ align:start position:0%
+determine which form they have and
+therefore which therapy they should get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and who will be your customer who will
+
+ align:start position:0%
+and who will be your customer who will
+ 
+
+ align:start position:0%
+and who will be your customer who will
+write you a check the patient the
+
+ align:start position:0%
+write you a check the patient the
+ 
+
+ align:start position:0%
+write you a check the patient the
+hospital the insurance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+company how many of you are thinking
+
+ align:start position:0%
+company how many of you are thinking
+ 
+
+ align:start position:0%
+company how many of you are thinking
+about working in the medical
+
+ align:start position:0%
+about working in the medical
+ 
+
+ align:start position:0%
+about working in the medical
+Arena yeah okay you you know then that
+
+ align:start position:0%
+Arena yeah okay you you know then that
+ 
+
+ align:start position:0%
+Arena yeah okay you you know then that
+there's a sort of a cluster of customers
+
+ align:start position:0%
+there's a sort of a cluster of customers
+ 
+
+ align:start position:0%
+there's a sort of a cluster of customers
+that you have to work with the doc has
+
+ align:start position:0%
+that you have to work with the doc has
+ 
+
+ align:start position:0%
+that you have to work with the doc has
+to request it then you have to go arm
+
+ align:start position:0%
+to request it then you have to go arm
+ 
+
+ align:start position:0%
+to request it then you have to go arm
+wrestle with the purchasing agent or the
+
+ align:start position:0%
+wrestle with the purchasing agent or the
+ 
+
+ align:start position:0%
+wrestle with the purchasing agent or the
+formulary committee or whatever it's
+
+ align:start position:0%
+formulary committee or whatever it's
+ 
+
+ align:start position:0%
+formulary committee or whatever it's
+really quite
+
+ align:start position:0%
+really quite
+ 
+
+ align:start position:0%
+really quite
+convoluted okay well that gives me at
+
+ align:start position:0%
+convoluted okay well that gives me at
+ 
+
+ align:start position:0%
+convoluted okay well that gives me at
+least some idea of uh how eclectic you
+
+ align:start position:0%
+least some idea of uh how eclectic you
+ 
+
+ align:start position:0%
+least some idea of uh how eclectic you
+guys are so what I'm going to try to do
+
+ align:start position:0%
+guys are so what I'm going to try to do
+ 
+
+ align:start position:0%
+guys are so what I'm going to try to do
+oh Joe tell me how I make this Gizmo
+
+ align:start position:0%
+oh Joe tell me how I make this Gizmo
+ 
+
+ align:start position:0%
+oh Joe tell me how I make this Gizmo
+work on oh God turn it
+
+ align:start position:0%
+work on oh God turn it
+ 
+
+ align:start position:0%
+work on oh God turn it
+on really demanding okay I'd like to
+
+ align:start position:0%
+on really demanding okay I'd like to
+ 
+
+ align:start position:0%
+on really demanding okay I'd like to
+know a little bit about you I think we
+
+ align:start position:0%
+know a little bit about you I think we
+ 
+
+ align:start position:0%
+know a little bit about you I think we
+covered that I'm going to try and
+
+ align:start position:0%
+covered that I'm going to try and
+ 
+
+ align:start position:0%
+covered that I'm going to try and
+provide you with a couple of Hot Tips in
+
+ align:start position:0%
+provide you with a couple of Hot Tips in
+ 
+
+ align:start position:0%
+provide you with a couple of Hot Tips in
+the course of this 90 minutes I have the
+
+ align:start position:0%
+the course of this 90 minutes I have the
+ 
+
+ align:start position:0%
+the course of this 90 minutes I have the
+sort of quaint notion that if I'm going
+
+ align:start position:0%
+sort of quaint notion that if I'm going
+ 
+
+ align:start position:0%
+sort of quaint notion that if I'm going
+to ask you to pay attention to me for an
+
+ align:start position:0%
+to ask you to pay attention to me for an
+ 
+
+ align:start position:0%
+to ask you to pay attention to me for an
+hour and a half I ought to try to give
+
+ align:start position:0%
+hour and a half I ought to try to give
+ 
+
+ align:start position:0%
+hour and a half I ought to try to give
+you something of value in return I
+
+ align:start position:0%
+you something of value in return I
+ 
+
+ align:start position:0%
+you something of value in return I
+realize that's sort of old school but uh
+
+ align:start position:0%
+realize that's sort of old school but uh
+ 
+
+ align:start position:0%
+realize that's sort of old school but uh
+I hope to help you find some customers
+
+ align:start position:0%
+I hope to help you find some customers
+ 
+
+ align:start position:0%
+I hope to help you find some customers
+and succeed with your businesses and I'm
+
+ align:start position:0%
+and succeed with your businesses and I'm
+ 
+
+ align:start position:0%
+and succeed with your businesses and I'm
+going to do that using a couple of
+
+ align:start position:0%
+going to do that using a couple of
+ 
+
+ align:start position:0%
+going to do that using a couple of
+product launches that I was involved
+
+ align:start position:0%
+product launches that I was involved
+ 
+
+ align:start position:0%
+product launches that I was involved
+with um there are times when people
+
+ align:start position:0%
+with um there are times when people
+ 
+
+ align:start position:0%
+with um there are times when people
+speak to you and they say well there's
+
+ align:start position:0%
+speak to you and they say well there's
+ 
+
+ align:start position:0%
+speak to you and they say well there's
+been 20 clinical trials done and the
+
+ align:start position:0%
+been 20 clinical trials done and the
+ 
+
+ align:start position:0%
+been 20 clinical trials done and the
+results are almost indisputable this is
+
+ align:start position:0%
+results are almost indisputable this is
+ 
+
+ align:start position:0%
+results are almost indisputable this is
+not one of those this is anecdotal
+
+ align:start position:0%
+not one of those this is anecdotal
+ 
+
+ align:start position:0%
+not one of those this is anecdotal
+you're not going to be hearing the voice
+
+ align:start position:0%
+you're not going to be hearing the voice
+ 
+
+ align:start position:0%
+you're not going to be hearing the voice
+of God you're going to be hearing my
+
+ align:start position:0%
+of God you're going to be hearing my
+ 
+
+ align:start position:0%
+of God you're going to be hearing my
+opinions and they may be wrong
+
+ align:start position:0%
+opinions and they may be wrong
+ 
+
+ align:start position:0%
+opinions and they may be wrong
+disclaimer but I'm going to walk you
+
+ align:start position:0%
+disclaimer but I'm going to walk you
+ 
+
+ align:start position:0%
+disclaimer but I'm going to walk you
+through a couple of product launches and
+
+ align:start position:0%
+through a couple of product launches and
+ 
+
+ align:start position:0%
+through a couple of product launches and
+some lessons that maybe you'll learn and
+
+ align:start position:0%
+some lessons that maybe you'll learn and
+ 
+
+ align:start position:0%
+some lessons that maybe you'll learn and
+uh there may be an opportunity for equal
+
+ align:start position:0%
+uh there may be an opportunity for equal
+ 
+
+ align:start position:0%
+uh there may be an opportunity for equal
+uh equal opport embarrassment in the
+
+ align:start position:0%
+uh equal opport embarrassment in the
+ 
+
+ align:start position:0%
+uh equal opport embarrassment in the
+course of this evening um I will fulfill
+
+ align:start position:0%
+course of this evening um I will fulfill
+ 
+
+ align:start position:0%
+course of this evening um I will fulfill
+the responsibilities of leadership by
+
+ align:start position:0%
+the responsibilities of leadership by
+ 
+
+ align:start position:0%
+the responsibilities of leadership by
+embarrassing myself first and then I'll
+
+ align:start position:0%
+embarrassing myself first and then I'll
+ 
+
+ align:start position:0%
+embarrassing myself first and then I'll
+offer you the chance to follow on so um
+
+ align:start position:0%
+offer you the chance to follow on so um
+ 
+
+ align:start position:0%
+offer you the chance to follow on so um
+I went to a couple of schools I had a
+
+ align:start position:0%
+I went to a couple of schools I had a
+ 
+
+ align:start position:0%
+I went to a couple of schools I had a
+couple of normal
+
+ align:start position:0%
+couple of normal
+ 
+
+ align:start position:0%
+couple of normal
+jobs and then I realized there was
+
+ align:start position:0%
+jobs and then I realized there was
+ 
+
+ align:start position:0%
+jobs and then I realized there was
+something wrong with me and left and
+
+ align:start position:0%
+something wrong with me and left and
+ 
+
+ align:start position:0%
+something wrong with me and left and
+went off and started up three different
+
+ align:start position:0%
+went off and started up three different
+ 
+
+ align:start position:0%
+went off and started up three different
+medical companies in a row and uh took a
+
+ align:start position:0%
+medical companies in a row and uh took a
+ 
+
+ align:start position:0%
+medical companies in a row and uh took a
+break from entrepreneurship to serve as
+
+ align:start position:0%
+break from entrepreneurship to serve as
+ 
+
+ align:start position:0%
+break from entrepreneurship to serve as
+CEO of a soy Foods company it was a
+
+ align:start position:0%
+CEO of a soy Foods company it was a
+ 
+
+ align:start position:0%
+CEO of a soy Foods company it was a
+turnaround company was a dreadful mess
+
+ align:start position:0%
+turnaround company was a dreadful mess
+ 
+
+ align:start position:0%
+turnaround company was a dreadful mess
+took a couple years to fix it had to
+
+ align:start position:0%
+took a couple years to fix it had to
+ 
+
+ align:start position:0%
+took a couple years to fix it had to
+fire 75 people in the process so it was
+
+ align:start position:0%
+fire 75 people in the process so it was
+ 
+
+ align:start position:0%
+fire 75 people in the process so it was
+a lot of sort of block and tackle work
+
+ align:start position:0%
+a lot of sort of block and tackle work
+ 
+
+ align:start position:0%
+a lot of sort of block and tackle work
+then I thought it would be kind of fun
+
+ align:start position:0%
+then I thought it would be kind of fun
+ 
+
+ align:start position:0%
+then I thought it would be kind of fun
+and relaxing to join a boutique
+
+ align:start position:0%
+and relaxing to join a boutique
+ 
+
+ align:start position:0%
+and relaxing to join a boutique
+consulting firm helping people do what I
+
+ align:start position:0%
+consulting firm helping people do what I
+ 
+
+ align:start position:0%
+consulting firm helping people do what I
+did uh and it was fun for a couple of
+
+ align:start position:0%
+did uh and it was fun for a couple of
+ 
+
+ align:start position:0%
+did uh and it was fun for a couple of
+years and then it got bored boring and I
+
+ align:start position:0%
+years and then it got bored boring and I
+ 
+
+ align:start position:0%
+years and then it got bored boring and I
+left and started up another company
+
+ align:start position:0%
+left and started up another company
+ 
+
+ align:start position:0%
+left and started up another company
+which I'll tell you about maybe a little
+
+ align:start position:0%
+which I'll tell you about maybe a little
+ 
+
+ align:start position:0%
+which I'll tell you about maybe a little
+bit in the course of the evening so a
+
+ align:start position:0%
+bit in the course of the evening so a
+ 
+
+ align:start position:0%
+bit in the course of the evening so a
+couple years ago the Wall Street Journal
+
+ align:start position:0%
+couple years ago the Wall Street Journal
+ 
+
+ align:start position:0%
+couple years ago the Wall Street Journal
+did a study uh during the last recession
+
+ align:start position:0%
+did a study uh during the last recession
+ 
+
+ align:start position:0%
+did a study uh during the last recession
+of who succeeded and who failed and did
+
+ align:start position:0%
+of who succeeded and who failed and did
+ 
+
+ align:start position:0%
+of who succeeded and who failed and did
+the people who succeeded aggregate
+
+ align:start position:0%
+the people who succeeded aggregate
+ 
+
+ align:start position:0%
+the people who succeeded aggregate
+around any particular plans and they did
+
+ align:start position:0%
+around any particular plans and they did
+ 
+
+ align:start position:0%
+around any particular plans and they did
+one group turned out to be cost leaders
+
+ align:start position:0%
+one group turned out to be cost leaders
+ 
+
+ align:start position:0%
+one group turned out to be cost leaders
+they aggressively cut their costs and
+
+ align:start position:0%
+they aggressively cut their costs and
+ 
+
+ align:start position:0%
+they aggressively cut their costs and
+that was their differentiator that's not
+
+ align:start position:0%
+that was their differentiator that's not
+ 
+
+ align:start position:0%
+that was their differentiator that's not
+you the other group were innovators and
+
+ align:start position:0%
+you the other group were innovators and
+ 
+
+ align:start position:0%
+you the other group were innovators and
+they focused on building brands that
+
+ align:start position:0%
+they focused on building brands that
+ 
+
+ align:start position:0%
+they focused on building brands that
+might be you but there was a fundament
+
+ align:start position:0%
+might be you but there was a fundament
+ 
+
+ align:start position:0%
+might be you but there was a fundament
+question that the successful ones ask
+
+ align:start position:0%
+question that the successful ones ask
+ 
+
+ align:start position:0%
+question that the successful ones ask
+which is how is your end user
+
+ align:start position:0%
+which is how is your end user
+ 
+
+ align:start position:0%
+which is how is your end user
+dissatisfied because that's where the
+
+ align:start position:0%
+dissatisfied because that's where the
+ 
+
+ align:start position:0%
+dissatisfied because that's where the
+opportunity
+
+ align:start position:0%
+opportunity
+ 
+
+ align:start position:0%
+opportunity
+lies and at an August institution like
+
+ align:start position:0%
+lies and at an August institution like
+ 
+
+ align:start position:0%
+lies and at an August institution like
+this one it's often thought that the
+
+ align:start position:0%
+this one it's often thought that the
+ 
+
+ align:start position:0%
+this one it's often thought that the
+answer is technology but it doesn't have
+
+ align:start position:0%
+answer is technology but it doesn't have
+ 
+
+ align:start position:0%
+answer is technology but it doesn't have
+to be if there's 50 kids in town that
+
+ align:start position:0%
+to be if there's 50 kids in town that
+ 
+
+ align:start position:0%
+to be if there's 50 kids in town that
+want a bicycle and there's no bicycle
+
+ align:start position:0%
+want a bicycle and there's no bicycle
+ 
+
+ align:start position:0%
+want a bicycle and there's no bicycle
+shop that could be your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+opportunity so I'm going to make an
+
+ align:start position:0%
+opportunity so I'm going to make an
+ 
+
+ align:start position:0%
+opportunity so I'm going to make an
+assertion right up front which is your
+
+ align:start position:0%
+assertion right up front which is your
+ 
+
+ align:start position:0%
+assertion right up front which is your
+business might survive but it won't
+
+ align:start position:0%
+business might survive but it won't
+ 
+
+ align:start position:0%
+business might survive but it won't
+Prosper until you know what are you
+
+ align:start position:0%
+Prosper until you know what are you
+ 
+
+ align:start position:0%
+Prosper until you know what are you
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+selling and there will be a couple of
+
+ align:start position:0%
+selling and there will be a couple of
+ 
+
+ align:start position:0%
+selling and there will be a couple of
+times tonight when I may interrogate you
+
+ align:start position:0%
+times tonight when I may interrogate you
+ 
+
+ align:start position:0%
+times tonight when I may interrogate you
+ruthlessly on this point who wants it so
+
+ align:start position:0%
+ruthlessly on this point who wants it so
+ 
+
+ align:start position:0%
+ruthlessly on this point who wants it so
+literally who
+
+ align:start position:0%
+literally who
+ 
+
+ align:start position:0%
+literally who
+cares and how do you find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them and I know that our friend Steve
+
+ align:start position:0%
+them and I know that our friend Steve
+ 
+
+ align:start position:0%
+them and I know that our friend Steve
+talked to you a little bit last night
+
+ align:start position:0%
+talked to you a little bit last night
+ 
+
+ align:start position:0%
+talked to you a little bit last night
+about raising Capital but it's kind of a
+
+ align:start position:0%
+about raising Capital but it's kind of a
+ 
+
+ align:start position:0%
+about raising Capital but it's kind of a
+dirty secret amongst investors that most
+
+ align:start position:0%
+dirty secret amongst investors that most
+ 
+
+ align:start position:0%
+dirty secret amongst investors that most
+of them really live in
+
+ align:start position:0%
+of them really live in
+ 
+
+ align:start position:0%
+of them really live in
+Terror because they know that if they
+
+ align:start position:0%
+Terror because they know that if they
+ 
+
+ align:start position:0%
+Terror because they know that if they
+invest in 10 of you
+
+ align:start position:0%
+invest in 10 of you
+ 
+
+ align:start position:0%
+invest in 10 of you
+guys eight of you are going to fail
+
+ align:start position:0%
+guys eight of you are going to fail
+ 
+
+ align:start position:0%
+guys eight of you are going to fail
+you're all smart good-look Charming I'm
+
+ align:start position:0%
+you're all smart good-look Charming I'm
+ 
+
+ align:start position:0%
+you're all smart good-look Charming I'm
+sure you're good to your parents and all
+
+ align:start position:0%
+sure you're good to your parents and all
+ 
+
+ align:start position:0%
+sure you're good to your parents and all
+of that but you're going to
+
+ align:start position:0%
+of that but you're going to
+ 
+
+ align:start position:0%
+of that but you're going to
+fail which means their investment's
+
+ align:start position:0%
+fail which means their investment's
+ 
+
+ align:start position:0%
+fail which means their investment's
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+evaporate and investors venture
+
+ align:start position:0%
+evaporate and investors venture
+ 
+
+ align:start position:0%
+evaporate and investors venture
+capitalist in particular raise money
+
+ align:start position:0%
+capitalist in particular raise money
+ 
+
+ align:start position:0%
+capitalist in particular raise money
+themselves they go around to Pension
+
+ align:start position:0%
+themselves they go around to Pension
+ 
+
+ align:start position:0%
+themselves they go around to Pension
+funds and say please contribute to our
+
+ align:start position:0%
+funds and say please contribute to our
+ 
+
+ align:start position:0%
+funds and say please contribute to our
+fund and if you lose their money they
+
+ align:start position:0%
+fund and if you lose their money they
+ 
+
+ align:start position:0%
+fund and if you lose their money they
+are unable to raise a fund next time and
+
+ align:start position:0%
+are unable to raise a fund next time and
+ 
+
+ align:start position:0%
+are unable to raise a fund next time and
+find themselves unemployed so oops the
+
+ align:start position:0%
+find themselves unemployed so oops the
+ 
+
+ align:start position:0%
+find themselves unemployed so oops the
+emperor is not wearing any clothes so
+
+ align:start position:0%
+emperor is not wearing any clothes so
+ 
+
+ align:start position:0%
+emperor is not wearing any clothes so
+when they look at you they want to try
+
+ align:start position:0%
+when they look at you they want to try
+ 
+
+ align:start position:0%
+when they look at you they want to try
+and figure out do you have a chance of
+
+ align:start position:0%
+and figure out do you have a chance of
+ 
+
+ align:start position:0%
+and figure out do you have a chance of
+succeeding with your business and the
+
+ align:start position:0%
+succeeding with your business and the
+ 
+
+ align:start position:0%
+succeeding with your business and the
+experienced ones know there's really One
+
+ align:start position:0%
+experienced ones know there's really One
+ 
+
+ align:start position:0%
+experienced ones know there's really One
+non-negotiable requirement and that's
+
+ align:start position:0%
+non-negotiable requirement and that's
+ 
+
+ align:start position:0%
+non-negotiable requirement and that's
+you have to have
+
+ align:start position:0%
+you have to have
+ 
+
+ align:start position:0%
+you have to have
+customers you don't need to be smart you
+
+ align:start position:0%
+customers you don't need to be smart you
+ 
+
+ align:start position:0%
+customers you don't need to be smart you
+don't need to be be good-look you don't
+
+ align:start position:0%
+don't need to be be good-look you don't
+ 
+
+ align:start position:0%
+don't need to be be good-look you don't
+need to get rich if you have
+
+ align:start position:0%
+need to get rich if you have
+ 
+
+ align:start position:0%
+need to get rich if you have
+customers people will think you're smart
+
+ align:start position:0%
+customers people will think you're smart
+ 
+
+ align:start position:0%
+customers people will think you're smart
+you will make money and if you make
+
+ align:start position:0%
+you will make money and if you make
+ 
+
+ align:start position:0%
+you will make money and if you make
+enough money they'll think you're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goodlooking so they want to know do you
+
+ align:start position:0%
+goodlooking so they want to know do you
+ 
+
+ align:start position:0%
+goodlooking so they want to know do you
+have any customers will you have any do
+
+ align:start position:0%
+have any customers will you have any do
+ 
+
+ align:start position:0%
+have any customers will you have any do
+you even know you need them and by the
+
+ align:start position:0%
+you even know you need them and by the
+ 
+
+ align:start position:0%
+you even know you need them and by the
+way have you done some homework how are
+
+ align:start position:0%
+way have you done some homework how are
+ 
+
+ align:start position:0%
+way have you done some homework how are
+you going to find them and how much are
+
+ align:start position:0%
+you going to find them and how much are
+ 
+
+ align:start position:0%
+you going to find them and how much are
+they worth are you going to spend $5 to
+
+ align:start position:0%
+they worth are you going to spend $5 to
+ 
+
+ align:start position:0%
+they worth are you going to spend $5 to
+acquire a customer whose lifetime value
+
+ align:start position:0%
+acquire a customer whose lifetime value
+ 
+
+ align:start position:0%
+acquire a customer whose lifetime value
+is $3 oops probably not a good idea how
+
+ align:start position:0%
+is $3 oops probably not a good idea how
+ 
+
+ align:start position:0%
+is $3 oops probably not a good idea how
+long is it going to take you to get
+
+ align:start position:0%
+long is it going to take you to get
+ 
+
+ align:start position:0%
+long is it going to take you to get
+there how many do you need in order to
+
+ align:start position:0%
+there how many do you need in order to
+ 
+
+ align:start position:0%
+there how many do you need in order to
+reach
+
+ align:start position:0%
+reach
+ 
+
+ align:start position:0%
+reach
+Prosperity I think there's two
+
+ align:start position:0%
+Prosperity I think there's two
+ 
+
+ align:start position:0%
+Prosperity I think there's two
+descriptors that you want you'd like to
+
+ align:start position:0%
+descriptors that you want you'd like to
+ 
+
+ align:start position:0%
+descriptors that you want you'd like to
+be important and you'd like to be unique
+
+ align:start position:0%
+be important and you'd like to be unique
+ 
+
+ align:start position:0%
+be important and you'd like to be unique
+and of course the sweet spot is when
+
+ align:start position:0%
+and of course the sweet spot is when
+ 
+
+ align:start position:0%
+and of course the sweet spot is when
+you're both so I think you can make a
+
+ align:start position:0%
+you're both so I think you can make a
+ 
+
+ align:start position:0%
+you're both so I think you can make a
+pretty good argument that air is
+
+ align:start position:0%
+pretty good argument that air is
+ 
+
+ align:start position:0%
+pretty good argument that air is
+important arguably not
+
+ align:start position:0%
+important arguably not
+ 
+
+ align:start position:0%
+important arguably not
+unique and I don't want to traumatize
+
+ align:start position:0%
+unique and I don't want to traumatize
+ 
+
+ align:start position:0%
+unique and I don't want to traumatize
+any of you but some would argue that MIT
+
+ align:start position:0%
+any of you but some would argue that MIT
+ 
+
+ align:start position:0%
+any of you but some would argue that MIT
+decals are unique but possibly not
+
+ align:start position:0%
+decals are unique but possibly not
+ 
+
+ align:start position:0%
+decals are unique but possibly not
+important possibly so can you make a a
+
+ align:start position:0%
+important possibly so can you make a a
+ 
+
+ align:start position:0%
+important possibly so can you make a a
+decent business selling either of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+well yes
+
+ align:start position:0%
+well yes
+ 
+
+ align:start position:0%
+well yes
+no people do people do give me an
+
+ align:start position:0%
+no people do people do give me an
+ 
+
+ align:start position:0%
+no people do people do give me an
+example of an opportunity to sell air
+
+ align:start position:0%
+example of an opportunity to sell air
+ 
+
+ align:start position:0%
+example of an opportunity to sell air
+Kims Kim labs okay that's a bit exotic
+
+ align:start position:0%
+Kims Kim labs okay that's a bit exotic
+ 
+
+ align:start position:0%
+Kims Kim labs okay that's a bit exotic
+any of you guys scuba
+
+ align:start position:0%
+any of you guys scuba
+ 
+
+ align:start position:0%
+any of you guys scuba
+dive I did my checkout dive off Catalina
+
+ align:start position:0%
+dive I did my checkout dive off Catalina
+ 
+
+ align:start position:0%
+dive I did my checkout dive off Catalina
+Island in California I was about 100
+
+ align:start position:0%
+Island in California I was about 100
+ 
+
+ align:start position:0%
+Island in California I was about 100
+feet down in the kelt
+
+ align:start position:0%
+feet down in the kelt
+ 
+
+ align:start position:0%
+feet down in the kelt
+beds o I've got about 15 minutes
+
+ align:start position:0%
+beds o I've got about 15 minutes
+ 
+
+ align:start position:0%
+beds o I've got about 15 minutes
+left I would have paid a lot for some
+
+ align:start position:0%
+left I would have paid a lot for some
+ 
+
+ align:start position:0%
+left I would have paid a lot for some
+air you know those packages that have
+
+ align:start position:0%
+air you know those packages that have
+ 
+
+ align:start position:0%
+air you know those packages that have
+all those little bubbles in them and you
+
+ align:start position:0%
+all those little bubbles in them and you
+ 
+
+ align:start position:0%
+all those little bubbles in them and you
+get really neurotic and pop them all you
+
+ align:start position:0%
+get really neurotic and pop them all you
+ 
+
+ align:start position:0%
+get really neurotic and pop them all you
+know what that company's called sealed
+
+ align:start position:0%
+know what that company's called sealed
+ 
+
+ align:start position:0%
+know what that company's called sealed
+air Corporation
+
+ align:start position:0%
+air Corporation
+ 
+
+ align:start position:0%
+air Corporation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+billion and of course the opportunity
+
+ align:start position:0%
+billion and of course the opportunity
+ 
+
+ align:start position:0%
+billion and of course the opportunity
+for to take 15 cents worth of material
+
+ align:start position:0%
+for to take 15 cents worth of material
+ 
+
+ align:start position:0%
+for to take 15 cents worth of material
+and sell it for four or five dollar
+
+ align:start position:0%
+and sell it for four or five dollar
+ 
+
+ align:start position:0%
+and sell it for four or five dollar
+obviously is picking the right
+
+ align:start position:0%
+obviously is picking the right
+ 
+
+ align:start position:0%
+obviously is picking the right
+positioning and the right opportunity so
+
+ align:start position:0%
+positioning and the right opportunity so
+ 
+
+ align:start position:0%
+positioning and the right opportunity so
+I'm being a little tongue and cheek here
+
+ align:start position:0%
+I'm being a little tongue and cheek here
+ 
+
+ align:start position:0%
+I'm being a little tongue and cheek here
+obviously but the point is to figure out
+
+ align:start position:0%
+obviously but the point is to figure out
+ 
+
+ align:start position:0%
+obviously but the point is to figure out
+who is going to find your offering
+
+ align:start position:0%
+who is going to find your offering
+ 
+
+ align:start position:0%
+who is going to find your offering
+unique and important so rather than
+
+ align:start position:0%
+unique and important so rather than
+ 
+
+ align:start position:0%
+unique and important so rather than
+start with how fabulous your product is
+
+ align:start position:0%
+start with how fabulous your product is
+ 
+
+ align:start position:0%
+start with how fabulous your product is
+who cares who actually thinks it's
+
+ align:start position:0%
+who cares who actually thinks it's
+ 
+
+ align:start position:0%
+who cares who actually thinks it's
+Unique who's
+
+ align:start position:0%
+Unique who's
+ 
+
+ align:start position:0%
+Unique who's
+important figure out how you're going to
+
+ align:start position:0%
+important figure out how you're going to
+ 
+
+ align:start position:0%
+important figure out how you're going to
+find them and tell them about what you
+
+ align:start position:0%
+find them and tell them about what you
+ 
+
+ align:start position:0%
+find them and tell them about what you
+got and then take their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+money now simple is not the same as easy
+
+ align:start position:0%
+money now simple is not the same as easy
+ 
+
+ align:start position:0%
+money now simple is not the same as easy
+this is simple it's not necessarily easy
+
+ align:start position:0%
+this is simple it's not necessarily easy
+ 
+
+ align:start position:0%
+this is simple it's not necessarily easy
+but what happens if you can't meet those
+
+ align:start position:0%
+but what happens if you can't meet those
+ 
+
+ align:start position:0%
+but what happens if you can't meet those
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+requirements I give you a hint kind of
+
+ align:start position:0%
+requirements I give you a hint kind of
+ 
+
+ align:start position:0%
+requirements I give you a hint kind of
+fish is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that right that's what's going to happen
+
+ align:start position:0%
+that right that's what's going to happen
+ 
+
+ align:start position:0%
+that right that's what's going to happen
+to you
+
+ align:start position:0%
+to you
+ 
+
+ align:start position:0%
+to you
+you will
+
+ align:start position:0%
+you will
+ 
+
+ align:start position:0%
+you will
+flounder so let me give you an example
+
+ align:start position:0%
+flounder so let me give you an example
+ 
+
+ align:start position:0%
+flounder so let me give you an example
+this was back in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+day I joined a company in California it
+
+ align:start position:0%
+day I joined a company in California it
+ 
+
+ align:start position:0%
+day I joined a company in California it
+had been 200 million in annual revenue
+
+ align:start position:0%
+had been 200 million in annual revenue
+ 
+
+ align:start position:0%
+had been 200 million in annual revenue
+for 12 straight years excuse me arguably
+
+ align:start position:0%
+for 12 straight years excuse me arguably
+ 
+
+ align:start position:0%
+for 12 straight years excuse me arguably
+a sleepy business and they got bought by
+
+ align:start position:0%
+a sleepy business and they got bought by
+ 
+
+ align:start position:0%
+a sleepy business and they got bought by
+an entrepreneur took them private
+
+ align:start position:0%
+an entrepreneur took them private
+ 
+
+ align:start position:0%
+an entrepreneur took them private
+leverage buyout said I want to kick up
+
+ align:start position:0%
+leverage buyout said I want to kick up
+ 
+
+ align:start position:0%
+leverage buyout said I want to kick up
+the sales of this outfit 50% in 3 years
+
+ align:start position:0%
+the sales of this outfit 50% in 3 years
+ 
+
+ align:start position:0%
+the sales of this outfit 50% in 3 years
+and take it public so he fired the
+
+ align:start position:0%
+and take it public so he fired the
+ 
+
+ align:start position:0%
+and take it public so he fired the
+senior management team brought in a
+
+ align:start position:0%
+senior management team brought in a
+ 
+
+ align:start position:0%
+senior management team brought in a
+bunch of ostensibly energetic
+
+ align:start position:0%
+bunch of ostensibly energetic
+ 
+
+ align:start position:0%
+bunch of ostensibly energetic
+entrepreneurs and gave everybody some
+
+ align:start position:0%
+entrepreneurs and gave everybody some
+ 
+
+ align:start position:0%
+entrepreneurs and gave everybody some
+stock so here's some stock for you and
+
+ align:start position:0%
+stock so here's some stock for you and
+ 
+
+ align:start position:0%
+stock so here's some stock for you and
+here's some stock for you and here's
+
+ align:start position:0%
+here's some stock for you and here's
+ 
+
+ align:start position:0%
+here's some stock for you and here's
+some stock for you and let's not
+
+ align:start position:0%
+some stock for you and let's not
+ 
+
+ align:start position:0%
+some stock for you and let's not
+argue let's make this worth something
+
+ align:start position:0%
+argue let's make this worth something
+ 
+
+ align:start position:0%
+argue let's make this worth something
+really a very good idea it was highly
+
+ align:start position:0%
+really a very good idea it was highly
+ 
+
+ align:start position:0%
+really a very good idea it was highly
+motivating I was running the clinical
+
+ align:start position:0%
+motivating I was running the clinical
+ 
+
+ align:start position:0%
+motivating I was running the clinical
+nutrition division really profitable we
+
+ align:start position:0%
+nutrition division really profitable we
+ 
+
+ align:start position:0%
+nutrition division really profitable we
+would make a leader of solution IV fluid
+
+ align:start position:0%
+would make a leader of solution IV fluid
+ 
+
+ align:start position:0%
+would make a leader of solution IV fluid
+for $3 sell it for 70 nice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+margins but I had a bad habit of going
+
+ align:start position:0%
+margins but I had a bad habit of going
+ 
+
+ align:start position:0%
+margins but I had a bad habit of going
+out in the marketplace and I did and I
+
+ align:start position:0%
+out in the marketplace and I did and I
+ 
+
+ align:start position:0%
+out in the marketplace and I did and I
+discovered that this business was going
+
+ align:start position:0%
+discovered that this business was going
+ 
+
+ align:start position:0%
+discovered that this business was going
+to go
+
+ align:start position:0%
+to go
+ 
+
+ align:start position:0%
+to go
+away Managed Care was coming changes and
+
+ align:start position:0%
+away Managed Care was coming changes and
+ 
+
+ align:start position:0%
+away Managed Care was coming changes and
+reimbursement structures Etc and it was
+
+ align:start position:0%
+reimbursement structures Etc and it was
+ 
+
+ align:start position:0%
+reimbursement structures Etc and it was
+going to go away before we had a chance
+
+ align:start position:0%
+going to go away before we had a chance
+ 
+
+ align:start position:0%
+going to go away before we had a chance
+to go public this was bad
+
+ align:start position:0%
+to go public this was bad
+ 
+
+ align:start position:0%
+to go public this was bad
+news I needed to find a new opportunity
+
+ align:start position:0%
+news I needed to find a new opportunity
+ 
+
+ align:start position:0%
+news I needed to find a new opportunity
+so I thought about it and I thought well
+
+ align:start position:0%
+so I thought about it and I thought well
+ 
+
+ align:start position:0%
+so I thought about it and I thought well
+this this science of nutrition is so
+
+ align:start position:0%
+this this science of nutrition is so
+ 
+
+ align:start position:0%
+this this science of nutrition is so
+awesome for people who are in the
+
+ align:start position:0%
+awesome for people who are in the
+ 
+
+ align:start position:0%
+awesome for people who are in the
+Intensive Care Unit it ought to be
+
+ align:start position:0%
+Intensive Care Unit it ought to be
+ 
+
+ align:start position:0%
+Intensive Care Unit it ought to be
+pretty good for people who are just out
+
+ align:start position:0%
+pretty good for people who are just out
+ 
+
+ align:start position:0%
+pretty good for people who are just out
+walking the
+
+ align:start position:0%
+walking the
+ 
+
+ align:start position:0%
+walking the
+street maybe we could reposition this go
+
+ align:start position:0%
+street maybe we could reposition this go
+ 
+
+ align:start position:0%
+street maybe we could reposition this go
+for a much broader Market nobody had
+
+ align:start position:0%
+for a much broader Market nobody had
+ 
+
+ align:start position:0%
+for a much broader Market nobody had
+done it power bar didn't exist none of
+
+ align:start position:0%
+done it power bar didn't exist none of
+ 
+
+ align:start position:0%
+done it power bar didn't exist none of
+those things happened but like most
+
+ align:start position:0%
+those things happened but like most
+ 
+
+ align:start position:0%
+those things happened but like most
+entrepreneurs I had uh it was a Triumph
+
+ align:start position:0%
+entrepreneurs I had uh it was a Triumph
+ 
+
+ align:start position:0%
+entrepreneurs I had uh it was a Triumph
+of energy over good sense I said let's
+
+ align:start position:0%
+of energy over good sense I said let's
+ 
+
+ align:start position:0%
+of energy over good sense I said let's
+try it even though no model for Success
+
+ align:start position:0%
+try it even though no model for Success
+ 
+
+ align:start position:0%
+try it even though no model for Success
+exist existed I had spent some time at
+
+ align:start position:0%
+exist existed I had spent some time at
+ 
+
+ align:start position:0%
+exist existed I had spent some time at
+Baxter and I knew something about the
+
+ align:start position:0%
+Baxter and I knew something about the
+ 
+
+ align:start position:0%
+Baxter and I knew something about the
+market for people who have kidney
+
+ align:start position:0%
+market for people who have kidney
+ 
+
+ align:start position:0%
+market for people who have kidney
+failure at the time there were 400,000
+
+ align:start position:0%
+failure at the time there were 400,000
+ 
+
+ align:start position:0%
+failure at the time there were 400,000
+of Market was growing like crazy and
+
+ align:start position:0%
+of Market was growing like crazy and
+ 
+
+ align:start position:0%
+of Market was growing like crazy and
+every one of the patients who was on
+
+ align:start position:0%
+every one of the patients who was on
+ 
+
+ align:start position:0%
+every one of the patients who was on
+dialysis went three times a week to one
+
+ align:start position:0%
+dialysis went three times a week to one
+ 
+
+ align:start position:0%
+dialysis went three times a week to one
+of 1300 dialysis centers in the country
+
+ align:start position:0%
+of 1300 dialysis centers in the country
+ 
+
+ align:start position:0%
+of 1300 dialysis centers in the country
+all of which are identified in a federal
+
+ align:start position:0%
+all of which are identified in a federal
+ 
+
+ align:start position:0%
+all of which are identified in a federal
+document so I knew where to find them I
+
+ align:start position:0%
+document so I knew where to find them I
+ 
+
+ align:start position:0%
+document so I knew where to find them I
+knew literally where they would be on
+
+ align:start position:0%
+knew literally where they would be on
+ 
+
+ align:start position:0%
+knew literally where they would be on
+Tuesday Thursday
+
+ align:start position:0%
+Tuesday Thursday
+ 
+
+ align:start position:0%
+Tuesday Thursday
+Saturday now when your kidneys fail you
+
+ align:start position:0%
+Saturday now when your kidneys fail you
+ 
+
+ align:start position:0%
+Saturday now when your kidneys fail you
+can't casually do something that so many
+
+ align:start position:0%
+can't casually do something that so many
+ 
+
+ align:start position:0%
+can't casually do something that so many
+of us do which is have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drink because you're unable to eliminate
+
+ align:start position:0%
+drink because you're unable to eliminate
+ 
+
+ align:start position:0%
+drink because you're unable to eliminate
+the fluids so it's not uncommon for a
+
+ align:start position:0%
+the fluids so it's not uncommon for a
+ 
+
+ align:start position:0%
+the fluids so it's not uncommon for a
+dialysis patient to gain 8 to 10 pounds
+
+ align:start position:0%
+dialysis patient to gain 8 to 10 pounds
+ 
+
+ align:start position:0%
+dialysis patient to gain 8 to 10 pounds
+between Monday and Wednesday part of
+
+ align:start position:0%
+between Monday and Wednesday part of
+ 
+
+ align:start position:0%
+between Monday and Wednesday part of
+what dialysis does is it rings out that
+
+ align:start position:0%
+what dialysis does is it rings out that
+ 
+
+ align:start position:0%
+what dialysis does is it rings out that
+extra fluid so these patients are fluid
+
+ align:start position:0%
+extra fluid so these patients are fluid
+ 
+
+ align:start position:0%
+extra fluid so these patients are fluid
+restricted for due to other things that
+
+ align:start position:0%
+restricted for due to other things that
+ 
+
+ align:start position:0%
+restricted for due to other things that
+your kidneys do for you many of them are
+
+ align:start position:0%
+your kidneys do for you many of them are
+ 
+
+ align:start position:0%
+your kidneys do for you many of them are
+clinically
+
+ align:start position:0%
+clinically
+ 
+
+ align:start position:0%
+clinically
+malnourished and the only nutrition
+
+ align:start position:0%
+malnourished and the only nutrition
+ 
+
+ align:start position:0%
+malnourished and the only nutrition
+supplements that were available were
+
+ align:start position:0%
+supplements that were available were
+ 
+
+ align:start position:0%
+supplements that were available were
+liquids insure things like that I said
+
+ align:start position:0%
+liquids insure things like that I said
+ 
+
+ align:start position:0%
+liquids insure things like that I said
+well duh what's wrong with
+
+ align:start position:0%
+well duh what's wrong with
+ 
+
+ align:start position:0%
+well duh what's wrong with
+that why don't we make a supplement
+
+ align:start position:0%
+that why don't we make a supplement
+ 
+
+ align:start position:0%
+that why don't we make a supplement
+that's high in the stuff they need
+
+ align:start position:0%
+that's high in the stuff they need
+ 
+
+ align:start position:0%
+that's high in the stuff they need
+doesn't have the stuff they don't need
+
+ align:start position:0%
+doesn't have the stuff they don't need
+ 
+
+ align:start position:0%
+doesn't have the stuff they don't need
+doesn't have any fluid Let's Make A
+
+ align:start position:0%
+doesn't have any fluid Let's Make A
+ 
+
+ align:start position:0%
+doesn't have any fluid Let's Make A
+nutrition
+
+ align:start position:0%
+nutrition
+ 
+
+ align:start position:0%
+nutrition
+bar we had the technology to do it we
+
+ align:start position:0%
+bar we had the technology to do it we
+ 
+
+ align:start position:0%
+bar we had the technology to do it we
+created something we called regain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we weren't required to do a clinical
+
+ align:start position:0%
+we weren't required to do a clinical
+ 
+
+ align:start position:0%
+we weren't required to do a clinical
+trial it was just food but we did Kaiser
+
+ align:start position:0%
+trial it was just food but we did Kaiser
+ 
+
+ align:start position:0%
+trial it was just food but we did Kaiser
+Permanente for those of you who live in
+
+ align:start position:0%
+Permanente for those of you who live in
+ 
+
+ align:start position:0%
+Permanente for those of you who live in
+California stuff worked got the results
+
+ align:start position:0%
+California stuff worked got the results
+ 
+
+ align:start position:0%
+California stuff worked got the results
+published in a The Archives of the
+
+ align:start position:0%
+published in a The Archives of the
+ 
+
+ align:start position:0%
+published in a The Archives of the
+National Kidney Foundation peerreview
+
+ align:start position:0%
+National Kidney Foundation peerreview
+ 
+
+ align:start position:0%
+National Kidney Foundation peerreview
+Journal good scientific support all the
+
+ align:start position:0%
+Journal good scientific support all the
+ 
+
+ align:start position:0%
+Journal good scientific support all the
+biomarkers improved patients got better
+
+ align:start position:0%
+biomarkers improved patients got better
+ 
+
+ align:start position:0%
+biomarkers improved patients got better
+we said well we know how to do this we
+
+ align:start position:0%
+we said well we know how to do this we
+ 
+
+ align:start position:0%
+we said well we know how to do this we
+know where to find them we know how to
+
+ align:start position:0%
+know where to find them we know how to
+ 
+
+ align:start position:0%
+know where to find them we know how to
+find the market leaders let's call the
+
+ align:start position:0%
+find the market leaders let's call the
+ 
+
+ align:start position:0%
+find the market leaders let's call the
+renal Physicians let's call the
+
+ align:start position:0%
+renal Physicians let's call the
+ 
+
+ align:start position:0%
+renal Physicians let's call the
+dietitians it's like we've developed
+
+ align:start position:0%
+dietitians it's like we've developed
+ 
+
+ align:start position:0%
+dietitians it's like we've developed
+something that's high in what your
+
+ align:start position:0%
+something that's high in what your
+ 
+
+ align:start position:0%
+something that's high in what your
+kidney failure patients ought to have
+
+ align:start position:0%
+kidney failure patients ought to have
+ 
+
+ align:start position:0%
+kidney failure patients ought to have
+and doesn't have any fluids in it what
+
+ align:start position:0%
+and doesn't have any fluids in it what
+ 
+
+ align:start position:0%
+and doesn't have any fluids in it what
+do you think the typical reaction
+
+ align:start position:0%
+do you think the typical reaction
+ 
+
+ align:start position:0%
+do you think the typical reaction
+was wish I thought of that so well how
+
+ align:start position:0%
+was wish I thought of that so well how
+ 
+
+ align:start position:0%
+was wish I thought of that so well how
+many of you patients do you think of
+
+ align:start position:0%
+many of you patients do you think of
+ 
+
+ align:start position:0%
+many of you patients do you think of
+your patients do you think this would be
+
+ align:start position:0%
+your patients do you think this would be
+ 
+
+ align:start position:0%
+your patients do you think this would be
+suitable
+
+ align:start position:0%
+suitable
+ 
+
+ align:start position:0%
+suitable
+for I'd say well all of
+
+ align:start position:0%
+for I'd say well all of
+ 
+
+ align:start position:0%
+for I'd say well all of
+them how many days a week would you
+
+ align:start position:0%
+them how many days a week would you
+ 
+
+ align:start position:0%
+them how many days a week would you
+recommend
+
+ align:start position:0%
+recommend
+ 
+
+ align:start position:0%
+recommend
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+seven say what how do you feel about $3
+
+ align:start position:0%
+seven say what how do you feel about $3
+ 
+
+ align:start position:0%
+seven say what how do you feel about $3
+a bar sounds right to us we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+said this pretty good little business
+
+ align:start position:0%
+said this pretty good little business
+ 
+
+ align:start position:0%
+said this pretty good little business
+here let's do
+
+ align:start position:0%
+here let's do
+ 
+
+ align:start position:0%
+here let's do
+it we said how you feel about the
+
+ align:start position:0%
+it we said how you feel about the
+ 
+
+ align:start position:0%
+it we said how you feel about the
+competition they said well yours is the
+
+ align:start position:0%
+competition they said well yours is the
+ 
+
+ align:start position:0%
+competition they said well yours is the
+only one doesn't have any liquid in it
+
+ align:start position:0%
+only one doesn't have any liquid in it
+ 
+
+ align:start position:0%
+only one doesn't have any liquid in it
+it's obviously going to have a strangle
+
+ align:start position:0%
+it's obviously going to have a strangle
+ 
+
+ align:start position:0%
+it's obviously going to have a strangle
+hold on this Market it's perfect so we
+
+ align:start position:0%
+hold on this Market it's perfect so we
+ 
+
+ align:start position:0%
+hold on this Market it's perfect so we
+said well this pretty good opportunity
+
+ align:start position:0%
+said well this pretty good opportunity
+ 
+
+ align:start position:0%
+said well this pretty good opportunity
+for their corporation it's going to
+
+ align:start position:0%
+for their corporation it's going to
+ 
+
+ align:start position:0%
+for their corporation it's going to
+replace some of the revenues let's make
+
+ align:start position:0%
+replace some of the revenues let's make
+ 
+
+ align:start position:0%
+replace some of the revenues let's make
+a whole bunch of it let's take the
+
+ align:start position:0%
+a whole bunch of it let's take the
+ 
+
+ align:start position:0%
+a whole bunch of it let's take the
+beauty shots and make the brochures
+
+ align:start position:0%
+beauty shots and make the brochures
+ 
+
+ align:start position:0%
+beauty shots and make the brochures
+let's haul in the Salesforce set up a
+
+ align:start position:0%
+let's haul in the Salesforce set up a
+ 
+
+ align:start position:0%
+let's haul in the Salesforce set up a
+commission plan train them on how to do
+
+ align:start position:0%
+commission plan train them on how to do
+ 
+
+ align:start position:0%
+commission plan train them on how to do
+it give them some incentives to go out
+
+ align:start position:0%
+it give them some incentives to go out
+ 
+
+ align:start position:0%
+it give them some incentives to go out
+there and sell it and let's launch which
+
+ align:start position:0%
+there and sell it and let's launch which
+ 
+
+ align:start position:0%
+there and sell it and let's launch which
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+did it was a complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disaster just an absolute failure
+
+ align:start position:0%
+disaster just an absolute failure
+ 
+
+ align:start position:0%
+disaster just an absolute failure
+revenues came in at less than 10% of
+
+ align:start position:0%
+revenues came in at less than 10% of
+ 
+
+ align:start position:0%
+revenues came in at less than 10% of
+what we forecasted and to make matters
+
+ align:start position:0%
+what we forecasted and to make matters
+ 
+
+ align:start position:0%
+what we forecasted and to make matters
+worse I was part of the senior
+
+ align:start position:0%
+worse I was part of the senior
+ 
+
+ align:start position:0%
+worse I was part of the senior
+management team and we would meet once a
+
+ align:start position:0%
+management team and we would meet once a
+ 
+
+ align:start position:0%
+management team and we would meet once a
+week conference room once a month we
+
+ align:start position:0%
+week conference room once a month we
+ 
+
+ align:start position:0%
+week conference room once a month we
+would go over how our business was
+
+ align:start position:0%
+would go over how our business was
+ 
+
+ align:start position:0%
+would go over how our business was
+doing so I'd have to stand up in front
+
+ align:start position:0%
+doing so I'd have to stand up in front
+ 
+
+ align:start position:0%
+doing so I'd have to stand up in front
+of my peers and say well our forcast for
+
+ align:start position:0%
+of my peers and say well our forcast for
+ 
+
+ align:start position:0%
+of my peers and say well our forcast for
+this month was $400,000 and we came in
+
+ align:start position:0%
+this month was $400,000 and we came in
+ 
+
+ align:start position:0%
+this month was $400,000 and we came in
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+32 they'd say Bob didn't quite
+
+ align:start position:0%
+32 they'd say Bob didn't quite
+ 
+
+ align:start position:0%
+32 they'd say Bob didn't quite
+understand you what was that number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+32 so what did I do wrong tell me why
+
+ align:start position:0%
+32 so what did I do wrong tell me why
+ 
+
+ align:start position:0%
+32 so what did I do wrong tell me why
+yes sir your customers didn't like
+
+ align:start position:0%
+yes sir your customers didn't like
+ 
+
+ align:start position:0%
+yes sir your customers didn't like
+it my customers didn't like it tell me
+
+ align:start position:0%
+it my customers didn't like it tell me
+ 
+
+ align:start position:0%
+it my customers didn't like it tell me
+more about
+
+ align:start position:0%
+more about
+ 
+
+ align:start position:0%
+more about
+that what didn't they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like they were happy with the liquid
+
+ align:start position:0%
+like they were happy with the liquid
+ 
+
+ align:start position:0%
+like they were happy with the liquid
+supplements that's a perfectly plausible
+
+ align:start position:0%
+supplements that's a perfectly plausible
+ 
+
+ align:start position:0%
+supplements that's a perfectly plausible
+answer but it's not the right one it's a
+
+ align:start position:0%
+answer but it's not the right one it's a
+ 
+
+ align:start position:0%
+answer but it's not the right one it's a
+very good speculation happens not to be
+
+ align:start position:0%
+very good speculation happens not to be
+ 
+
+ align:start position:0%
+very good speculation happens not to be
+the problem go ahead sir taste taste
+
+ align:start position:0%
+the problem go ahead sir taste taste
+ 
+
+ align:start position:0%
+the problem go ahead sir taste taste
+well that was a factor we thought it
+
+ align:start position:0%
+well that was a factor we thought it
+ 
+
+ align:start position:0%
+well that was a factor we thought it
+tasted pretty good but it turns out when
+
+ align:start position:0%
+tasted pretty good but it turns out when
+ 
+
+ align:start position:0%
+tasted pretty good but it turns out when
+your kidneys fail something shifts in
+
+ align:start position:0%
+your kidneys fail something shifts in
+ 
+
+ align:start position:0%
+your kidneys fail something shifts in
+your pallet and protein tastes like
+
+ align:start position:0%
+your pallet and protein tastes like
+ 
+
+ align:start position:0%
+your pallet and protein tastes like
+spoiled
+
+ align:start position:0%
+spoiled
+ 
+
+ align:start position:0%
+spoiled
+meat oops that was an issue what was the
+
+ align:start position:0%
+meat oops that was an issue what was the
+ 
+
+ align:start position:0%
+meat oops that was an issue what was the
+big issue what was the fundamental flaw
+
+ align:start position:0%
+big issue what was the fundamental flaw
+ 
+
+ align:start position:0%
+big issue what was the fundamental flaw
+the the most obvious thing that I did
+
+ align:start position:0%
+the the most obvious thing that I did
+ 
+
+ align:start position:0%
+the the most obvious thing that I did
+wrong in retrospect go ahead
+
+ align:start position:0%
+wrong in retrospect go ahead
+ 
+
+ align:start position:0%
+wrong in retrospect go ahead
+sir uh okay that's a pretty good
+
+ align:start position:0%
+sir uh okay that's a pretty good
+ 
+
+ align:start position:0%
+sir uh okay that's a pretty good
+question who paid for the product we're
+
+ align:start position:0%
+question who paid for the product we're
+ 
+
+ align:start position:0%
+question who paid for the product we're
+closing in on the
+
+ align:start position:0%
+closing in on the
+ 
+
+ align:start position:0%
+closing in on the
+issue okay here's a hint What's the
+
+ align:start position:0%
+issue okay here's a hint What's the
+ 
+
+ align:start position:0%
+issue okay here's a hint What's the
+title of my talk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tonight that was a clue okay so what did
+
+ align:start position:0%
+tonight that was a clue okay so what did
+ 
+
+ align:start position:0%
+tonight that was a clue okay so what did
+I do wrong yes sir
+
+ align:start position:0%
+I do wrong yes sir
+ 
+
+ align:start position:0%
+I do wrong yes sir
+misidentified I misidentified my
+
+ align:start position:0%
+misidentified I misidentified my
+ 
+
+ align:start position:0%
+misidentified I misidentified my
+customer you may be Exempted from the
+
+ align:start position:0%
+customer you may be Exempted from the
+ 
+
+ align:start position:0%
+customer you may be Exempted from the
+rest of the course that's exactly right
+
+ align:start position:0%
+rest of the course that's exactly right
+ 
+
+ align:start position:0%
+rest of the course that's exactly right
+who did I survey I surveyed the
+
+ align:start position:0%
+who did I survey I surveyed the
+ 
+
+ align:start position:0%
+who did I survey I surveyed the
+clinicians but they don't buy it and
+
+ align:start position:0%
+clinicians but they don't buy it and
+ 
+
+ align:start position:0%
+clinicians but they don't buy it and
+they don't put it in their mouth and eat
+
+ align:start position:0%
+they don't put it in their mouth and eat
+ 
+
+ align:start position:0%
+they don't put it in their mouth and eat
+it oops perfectly logical in the
+
+ align:start position:0%
+it oops perfectly logical in the
+ 
+
+ align:start position:0%
+it oops perfectly logical in the
+pharmaceutical world you call on the doc
+
+ align:start position:0%
+pharmaceutical world you call on the doc
+ 
+
+ align:start position:0%
+pharmaceutical world you call on the doc
+the doc writes a prescription doesn't
+
+ align:start position:0%
+the doc writes a prescription doesn't
+ 
+
+ align:start position:0%
+the doc writes a prescription doesn't
+matter whether you like it or
+
+ align:start position:0%
+matter whether you like it or
+ 
+
+ align:start position:0%
+matter whether you like it or
+not you got an earache take this stuff
+
+ align:start position:0%
+not you got an earache take this stuff
+ 
+
+ align:start position:0%
+not you got an earache take this stuff
+for five days your earache goes away too
+
+ align:start position:0%
+for five days your earache goes away too
+ 
+
+ align:start position:0%
+for five days your earache goes away too
+bad for you if it doesn't taste good if
+
+ align:start position:0%
+bad for you if it doesn't taste good if
+ 
+
+ align:start position:0%
+bad for you if it doesn't taste good if
+I get her to write the prescription I'm
+
+ align:start position:0%
+I get her to write the prescription I'm
+ 
+
+ align:start position:0%
+I get her to write the prescription I'm
+done not in this business in this
+
+ align:start position:0%
+done not in this business in this
+ 
+
+ align:start position:0%
+done not in this business in this
+business they have to go to the store
+
+ align:start position:0%
+business they have to go to the store
+ 
+
+ align:start position:0%
+business they have to go to the store
+themselves pay for it with their own
+
+ align:start position:0%
+themselves pay for it with their own
+ 
+
+ align:start position:0%
+themselves pay for it with their own
+money buy it eat it like it and buy it
+
+ align:start position:0%
+money buy it eat it like it and buy it
+ 
+
+ align:start position:0%
+money buy it eat it like it and buy it
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+well when we finally talked to them they
+
+ align:start position:0%
+well when we finally talked to them they
+ 
+
+ align:start position:0%
+well when we finally talked to them they
+didn't want
+
+ align:start position:0%
+didn't want
+ 
+
+ align:start position:0%
+didn't want
+it and they couldn't afford it okay who
+
+ align:start position:0%
+it and they couldn't afford it okay who
+ 
+
+ align:start position:0%
+it and they couldn't afford it okay who
+gets endstage renal
+
+ align:start position:0%
+gets endstage renal
+ 
+
+ align:start position:0%
+gets endstage renal
+disease well it turns out that 33% of
+
+ align:start position:0%
+disease well it turns out that 33% of
+ 
+
+ align:start position:0%
+disease well it turns out that 33% of
+them get there from a lifetime of
+
+ align:start position:0%
+them get there from a lifetime of
+ 
+
+ align:start position:0%
+them get there from a lifetime of
+mismanaging their diabetes and 44% of
+
+ align:start position:0%
+mismanaging their diabetes and 44% of
+ 
+
+ align:start position:0%
+mismanaging their diabetes and 44% of
+them get there from a lifetime of
+
+ align:start position:0%
+them get there from a lifetime of
+ 
+
+ align:start position:0%
+them get there from a lifetime of
+mismanaging their high blood pressure so
+
+ align:start position:0%
+mismanaging their high blood pressure so
+ 
+
+ align:start position:0%
+mismanaging their high blood pressure so
+three4 of my Target customers have not
+
+ align:start position:0%
+three4 of my Target customers have not
+ 
+
+ align:start position:0%
+three4 of my Target customers have not
+taken care of themselves for their
+
+ align:start position:0%
+taken care of themselves for their
+ 
+
+ align:start position:0%
+taken care of themselves for their
+entire life why would they start now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+furthermore once your kidneys fail and
+
+ align:start position:0%
+furthermore once your kidneys fail and
+ 
+
+ align:start position:0%
+furthermore once your kidneys fail and
+you end up on dialysis a well-intended
+
+ align:start position:0%
+you end up on dialysis a well-intended
+ 
+
+ align:start position:0%
+you end up on dialysis a well-intended
+social worker sort will say well Bob you
+
+ align:start position:0%
+social worker sort will say well Bob you
+ 
+
+ align:start position:0%
+social worker sort will say well Bob you
+got to be in here Tethered to this
+
+ align:start position:0%
+got to be in here Tethered to this
+ 
+
+ align:start position:0%
+got to be in here Tethered to this
+machine three days a week obviously you
+
+ align:start position:0%
+machine three days a week obviously you
+ 
+
+ align:start position:0%
+machine three days a week obviously you
+can't work so I'll put you on public aid
+
+ align:start position:0%
+can't work so I'll put you on public aid
+ 
+
+ align:start position:0%
+can't work so I'll put you on public aid
+well now you don't have any money if you
+
+ align:start position:0%
+well now you don't have any money if you
+ 
+
+ align:start position:0%
+well now you don't have any money if you
+do have $5 you're going to spend it on
+
+ align:start position:0%
+do have $5 you're going to spend it on
+ 
+
+ align:start position:0%
+do have $5 you're going to spend it on
+beer and cigarettes not on my
+
+ align:start position:0%
+beer and cigarettes not on my
+ 
+
+ align:start position:0%
+beer and cigarettes not on my
+product there was one final issue what
+
+ align:start position:0%
+product there was one final issue what
+ 
+
+ align:start position:0%
+product there was one final issue what
+was our sales Channel at the IV
+
+ align:start position:0%
+was our sales Channel at the IV
+ 
+
+ align:start position:0%
+was our sales Channel at the IV
+nutrition company we sold to
+
+ align:start position:0%
+nutrition company we sold to
+ 
+
+ align:start position:0%
+nutrition company we sold to
+hospitals with this business we had to
+
+ align:start position:0%
+hospitals with this business we had to
+ 
+
+ align:start position:0%
+hospitals with this business we had to
+sell to retail pharmacies and they
+
+ align:start position:0%
+sell to retail pharmacies and they
+ 
+
+ align:start position:0%
+sell to retail pharmacies and they
+wouldn't carry
+
+ align:start position:0%
+wouldn't carry
+ 
+
+ align:start position:0%
+wouldn't carry
+it well let's talk about that for a
+
+ align:start position:0%
+it well let's talk about that for a
+ 
+
+ align:start position:0%
+it well let's talk about that for a
+minute because that's kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fundamental if you
+
+ align:start position:0%
+fundamental if you
+ 
+
+ align:start position:0%
+fundamental if you
+ever want to have a laugh on a Saturday
+
+ align:start position:0%
+ever want to have a laugh on a Saturday
+ 
+
+ align:start position:0%
+ever want to have a laugh on a Saturday
+afternoon walk up to the pharmacist and
+
+ align:start position:0%
+afternoon walk up to the pharmacist and
+ 
+
+ align:start position:0%
+afternoon walk up to the pharmacist and
+your local Walgreens or CVS and say
+
+ align:start position:0%
+your local Walgreens or CVS and say
+ 
+
+ align:start position:0%
+your local Walgreens or CVS and say
+I've got a product you've never heard of
+
+ align:start position:0%
+I've got a product you've never heard of
+ 
+
+ align:start position:0%
+I've got a product you've never heard of
+from a company you've never done
+
+ align:start position:0%
+from a company you've never done
+ 
+
+ align:start position:0%
+from a company you've never done
+business with and I'd like you to carry
+
+ align:start position:0%
+business with and I'd like you to carry
+ 
+
+ align:start position:0%
+business with and I'd like you to carry
+it and watch as he falls on the floor
+
+ align:start position:0%
+it and watch as he falls on the floor
+ 
+
+ align:start position:0%
+it and watch as he falls on the floor
+and Hyster
+
+ align:start position:0%
+and Hyster
+ 
+
+ align:start position:0%
+and Hyster
+hysterics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why well I wasn't familiar with this I'd
+
+ align:start position:0%
+why well I wasn't familiar with this I'd
+ 
+
+ align:start position:0%
+why well I wasn't familiar with this I'd
+never had any exposure to this world and
+
+ align:start position:0%
+never had any exposure to this world and
+ 
+
+ align:start position:0%
+never had any exposure to this world and
+finally one day one of them kind of put
+
+ align:start position:0%
+finally one day one of them kind of put
+ 
+
+ align:start position:0%
+finally one day one of them kind of put
+his arm around me and said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bob come here see this foot of shelf
+
+ align:start position:0%
+Bob come here see this foot of shelf
+ 
+
+ align:start position:0%
+Bob come here see this foot of shelf
+space it's a linear foot right I have
+
+ align:start position:0%
+space it's a linear foot right I have
+ 
+
+ align:start position:0%
+space it's a linear foot right I have
+Crest toothpaste on that foot of shelf
+
+ align:start position:0%
+Crest toothpaste on that foot of shelf
+ 
+
+ align:start position:0%
+Crest toothpaste on that foot of shelf
+space I have all these complex
+
+ align:start position:0%
+space I have all these complex
+ 
+
+ align:start position:0%
+space I have all these complex
+algorithms that are going to tell me
+
+ align:start position:0%
+algorithms that are going to tell me
+ 
+
+ align:start position:0%
+algorithms that are going to tell me
+within a couple of dollars how much
+
+ align:start position:0%
+within a couple of dollars how much
+ 
+
+ align:start position:0%
+within a couple of dollars how much
+revenue this foot of shelf space going
+
+ align:start position:0%
+revenue this foot of shelf space going
+ 
+
+ align:start position:0%
+revenue this foot of shelf space going
+to generate for me each month now if I
+
+ align:start position:0%
+to generate for me each month now if I
+ 
+
+ align:start position:0%
+to generate for me each month now if I
+make room for your product and push
+
+ align:start position:0%
+make room for your product and push
+ 
+
+ align:start position:0%
+make room for your product and push
+Crest off there put your product on I
+
+ align:start position:0%
+Crest off there put your product on I
+ 
+
+ align:start position:0%
+Crest off there put your product on I
+don't want to lose any
+
+ align:start position:0%
+don't want to lose any
+ 
+
+ align:start position:0%
+don't want to lose any
+money so don't go to any trouble just
+
+ align:start position:0%
+money so don't go to any trouble just
+ 
+
+ align:start position:0%
+money so don't go to any trouble just
+write me a
+
+ align:start position:0%
+write me a
+ 
+
+ align:start position:0%
+write me a
+check they call it slotting fees you
+
+ align:start position:0%
+check they call it slotting fees you
+ 
+
+ align:start position:0%
+check they call it slotting fees you
+might call it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extortion with most of the major
+
+ align:start position:0%
+extortion with most of the major
+ 
+
+ align:start position:0%
+extortion with most of the major
+Pharmacy chains the tab is a million
+
+ align:start position:0%
+Pharmacy chains the tab is a million
+ 
+
+ align:start position:0%
+Pharmacy chains the tab is a million
+dollars a
+
+ align:start position:0%
+dollars a
+ 
+
+ align:start position:0%
+dollars a
+quarter plus 6% of your Topline
+
+ align:start position:0%
+quarter plus 6% of your Topline
+ 
+
+ align:start position:0%
+quarter plus 6% of your Topline
+revenues Plus guaranteed resale so if it
+
+ align:start position:0%
+revenues Plus guaranteed resale so if it
+ 
+
+ align:start position:0%
+revenues Plus guaranteed resale so if it
+doesn't sell they ship it back to you
+
+ align:start position:0%
+doesn't sell they ship it back to you
+ 
+
+ align:start position:0%
+doesn't sell they ship it back to you
+for full credit and you
+
+ align:start position:0%
+for full credit and you
+ 
+
+ align:start position:0%
+for full credit and you
+put one SKU in each of their stores and
+
+ align:start position:0%
+put one SKU in each of their stores and
+ 
+
+ align:start position:0%
+put one SKU in each of their stores and
+fill the entire pipeline for free
+
+ align:start position:0%
+fill the entire pipeline for free
+ 
+
+ align:start position:0%
+fill the entire pipeline for free
+they'll pay you if anybody reorders it
+
+ align:start position:0%
+they'll pay you if anybody reorders it
+ 
+
+ align:start position:0%
+they'll pay you if anybody reorders it
+pretty
+
+ align:start position:0%
+pretty
+ 
+
+ align:start position:0%
+pretty
+expensive well we couldn't afford that
+
+ align:start position:0%
+expensive well we couldn't afford that
+ 
+
+ align:start position:0%
+expensive well we couldn't afford that
+so we had a few problems with this
+
+ align:start position:0%
+so we had a few problems with this
+ 
+
+ align:start position:0%
+so we had a few problems with this
+business model that we' put together and
+
+ align:start position:0%
+business model that we' put together and
+ 
+
+ align:start position:0%
+business model that we' put together and
+we were trying to show Wall Street we
+
+ align:start position:0%
+we were trying to show Wall Street we
+ 
+
+ align:start position:0%
+we were trying to show Wall Street we
+were good candidate for a public
+
+ align:start position:0%
+were good candidate for a public
+ 
+
+ align:start position:0%
+were good candidate for a public
+offering and if we had our public
+
+ align:start position:0%
+offering and if we had our public
+ 
+
+ align:start position:0%
+offering and if we had our public
+offering the stock that we handed out
+
+ align:start position:0%
+offering the stock that we handed out
+ 
+
+ align:start position:0%
+offering the stock that we handed out
+was going to be worth something my
+
+ align:start position:0%
+was going to be worth something my
+ 
+
+ align:start position:0%
+was going to be worth something my
+failure was jeopardizing our ability to
+
+ align:start position:0%
+failure was jeopardizing our ability to
+ 
+
+ align:start position:0%
+failure was jeopardizing our ability to
+do that which meant Not only was I in
+
+ align:start position:0%
+do that which meant Not only was I in
+ 
+
+ align:start position:0%
+do that which meant Not only was I in
+the dogghouse with my boss but also with
+
+ align:start position:0%
+the dogghouse with my boss but also with
+ 
+
+ align:start position:0%
+the dogghouse with my boss but also with
+my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+peers and each month I would say well
+
+ align:start position:0%
+peers and each month I would say well
+ 
+
+ align:start position:0%
+peers and each month I would say well
+you know it's taking a little longer to
+
+ align:start position:0%
+you know it's taking a little longer to
+ 
+
+ align:start position:0%
+you know it's taking a little longer to
+take off than we thought give us a while
+
+ align:start position:0%
+take off than we thought give us a while
+ 
+
+ align:start position:0%
+take off than we thought give us a while
+to keep moving with the Salesforce and
+
+ align:start position:0%
+to keep moving with the Salesforce and
+ 
+
+ align:start position:0%
+to keep moving with the Salesforce and
+each month it continued to be a train
+
+ align:start position:0%
+each month it continued to be a train
+ 
+
+ align:start position:0%
+each month it continued to be a train
+wreck and it went on for an entire
+
+ align:start position:0%
+wreck and it went on for an entire
+ 
+
+ align:start position:0%
+wreck and it went on for an entire
+year ruined a year of my life because as
+
+ align:start position:0%
+year ruined a year of my life because as
+ 
+
+ align:start position:0%
+year ruined a year of my life because as
+this gentleman said over here I
+
+ align:start position:0%
+this gentleman said over here I
+ 
+
+ align:start position:0%
+this gentleman said over here I
+misidentified my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+customer so what do we do about
+
+ align:start position:0%
+customer so what do we do about
+ 
+
+ align:start position:0%
+customer so what do we do about
+it well we learned about inside sales we
+
+ align:start position:0%
+it well we learned about inside sales we
+ 
+
+ align:start position:0%
+it well we learned about inside sales we
+said 25% of these people take care of
+
+ align:start position:0%
+said 25% of these people take care of
+ 
+
+ align:start position:0%
+said 25% of these people take care of
+themselves we ought to be able to find
+
+ align:start position:0%
+themselves we ought to be able to find
+ 
+
+ align:start position:0%
+themselves we ought to be able to find
+them furthermore somebody ought to pay
+
+ align:start position:0%
+them furthermore somebody ought to pay
+ 
+
+ align:start position:0%
+them furthermore somebody ought to pay
+for this let's try Medicaid now you may
+
+ align:start position:0%
+for this let's try Medicaid now you may
+ 
+
+ align:start position:0%
+for this let's try Medicaid now you may
+or may not know that Medicare covers you
+
+ align:start position:0%
+or may not know that Medicare covers you
+ 
+
+ align:start position:0%
+or may not know that Medicare covers you
+if you're old it's a federal program
+
+ align:start position:0%
+if you're old it's a federal program
+ 
+
+ align:start position:0%
+if you're old it's a federal program
+Medicaid covers you if you're broke it's
+
+ align:start position:0%
+Medicaid covers you if you're broke it's
+ 
+
+ align:start position:0%
+Medicaid covers you if you're broke it's
+a state program what do you think are
+
+ align:start position:0%
+a state program what do you think are
+ 
+
+ align:start position:0%
+a state program what do you think are
+the chances that Illinois and Indiana
+
+ align:start position:0%
+the chances that Illinois and Indiana
+ 
+
+ align:start position:0%
+the chances that Illinois and Indiana
+have the same
+
+ align:start position:0%
+have the same
+ 
+
+ align:start position:0%
+have the same
+program Real Slim we got it reimbursed
+
+ align:start position:0%
+program Real Slim we got it reimbursed
+ 
+
+ align:start position:0%
+program Real Slim we got it reimbursed
+in 40 States it was almost as fun as 40
+
+ align:start position:0%
+in 40 States it was almost as fun as 40
+ 
+
+ align:start position:0%
+in 40 States it was almost as fun as 40
+consecutive Dental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extractions I said this is just a god-
+
+ align:start position:0%
+extractions I said this is just a god-
+ 
+
+ align:start position:0%
+extractions I said this is just a god-
+awful way to make a living sold the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+business parenthetically yes we did well
+
+ align:start position:0%
+business parenthetically yes we did well
+ 
+
+ align:start position:0%
+business parenthetically yes we did well
+enough in our group with our other
+
+ align:start position:0%
+enough in our group with our other
+ 
+
+ align:start position:0%
+enough in our group with our other
+products that we compensated for the
+
+ align:start position:0%
+products that we compensated for the
+ 
+
+ align:start position:0%
+products that we compensated for the
+shortfall with this and when we sold the
+
+ align:start position:0%
+shortfall with this and when we sold the
+ 
+
+ align:start position:0%
+shortfall with this and when we sold the
+business we didn't make any money but we
+
+ align:start position:0%
+business we didn't make any money but we
+ 
+
+ align:start position:0%
+business we didn't make any money but we
+recouped our investment so I escaped
+
+ align:start position:0%
+recouped our investment so I escaped
+ 
+
+ align:start position:0%
+recouped our investment so I escaped
+financially
+
+ align:start position:0%
+financially
+ 
+
+ align:start position:0%
+financially
+intact spiritually battered and
+
+ align:start position:0%
+intact spiritually battered and
+ 
+
+ align:start position:0%
+intact spiritually battered and
+abused much wiser but considerably
+
+ align:start position:0%
+abused much wiser but considerably
+ 
+
+ align:start position:0%
+abused much wiser but considerably
+sadder but let's fast forward a couple
+
+ align:start position:0%
+sadder but let's fast forward a couple
+ 
+
+ align:start position:0%
+sadder but let's fast forward a couple
+of years I did two more of these things
+
+ align:start position:0%
+of years I did two more of these things
+ 
+
+ align:start position:0%
+of years I did two more of these things
+and got better at it and after a while
+
+ align:start position:0%
+and got better at it and after a while
+ 
+
+ align:start position:0%
+and got better at it and after a while
+got recruited by a group of docs at
+
+ align:start position:0%
+got recruited by a group of docs at
+ 
+
+ align:start position:0%
+got recruited by a group of docs at
+Harvard Med school and they hauled Me In
+
+ align:start position:0%
+Harvard Med school and they hauled Me In
+ 
+
+ align:start position:0%
+Harvard Med school and they hauled Me In
+from California tough sales pitch to my
+
+ align:start position:0%
+from California tough sales pitch to my
+ 
+
+ align:start position:0%
+from California tough sales pitch to my
+family because we were in Southern
+
+ align:start position:0%
+family because we were in Southern
+ 
+
+ align:start position:0%
+family because we were in Southern
+California I said it snows in New
+
+ align:start position:0%
+California I said it snows in New
+ 
+
+ align:start position:0%
+California I said it snows in New
+England
+
+ align:start position:0%
+England
+ 
+
+ align:start position:0%
+England
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+does so we launched a new company with
+
+ align:start position:0%
+does so we launched a new company with
+ 
+
+ align:start position:0%
+does so we launched a new company with
+these guys we looked over all the stuff
+
+ align:start position:0%
+these guys we looked over all the stuff
+ 
+
+ align:start position:0%
+these guys we looked over all the stuff
+that they were working on figured out
+
+ align:start position:0%
+that they were working on figured out
+ 
+
+ align:start position:0%
+that they were working on figured out
+none of it was going to come to Market
+
+ align:start position:0%
+none of it was going to come to Market
+ 
+
+ align:start position:0%
+none of it was going to come to Market
+before we ran out of money said well how
+
+ align:start position:0%
+before we ran out of money said well how
+ 
+
+ align:start position:0%
+before we ran out of money said well how
+you guys feel about diabetes
+
+ align:start position:0%
+you guys feel about diabetes
+ 
+
+ align:start position:0%
+you guys feel about diabetes
+the answer was well we like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diabetes okay well we need to be in a
+
+ align:start position:0%
+diabetes okay well we need to be in a
+ 
+
+ align:start position:0%
+diabetes okay well we need to be in a
+field that's big enough to get us
+
+ align:start position:0%
+field that's big enough to get us
+ 
+
+ align:start position:0%
+field that's big enough to get us
+noticed in a need that's small enough
+
+ align:start position:0%
+noticed in a need that's small enough
+ 
+
+ align:start position:0%
+noticed in a need that's small enough
+that we can handle it with one poor
+
+ align:start position:0%
+that we can handle it with one poor
+ 
+
+ align:start position:0%
+that we can handle it with one poor
+underpaid
+
+ align:start position:0%
+underpaid
+ 
+
+ align:start position:0%
+underpaid
+employee so I had an intuition that
+
+ align:start position:0%
+employee so I had an intuition that
+ 
+
+ align:start position:0%
+employee so I had an intuition that
+there was something they needed and
+
+ align:start position:0%
+there was something they needed and
+ 
+
+ align:start position:0%
+there was something they needed and
+weren't
+
+ align:start position:0%
+weren't
+ 
+
+ align:start position:0%
+weren't
+getting statistics at the time there
+
+ align:start position:0%
+getting statistics at the time there
+ 
+
+ align:start position:0%
+getting statistics at the time there
+were 10 million people diagnosed with
+
+ align:start position:0%
+were 10 million people diagnosed with
+ 
+
+ align:start position:0%
+were 10 million people diagnosed with
+diabetes four million of them used
+
+ align:start position:0%
+diabetes four million of them used
+ 
+
+ align:start position:0%
+diabetes four million of them used
+insulin
+
+ align:start position:0%
+insulin
+ 
+
+ align:start position:0%
+insulin
+you have diabetes and you eat something
+
+ align:start position:0%
+you have diabetes and you eat something
+ 
+
+ align:start position:0%
+you have diabetes and you eat something
+your blood glucose goes up and it stays
+
+ align:start position:0%
+your blood glucose goes up and it stays
+ 
+
+ align:start position:0%
+your blood glucose goes up and it stays
+up because insulin incorporates it into
+
+ align:start position:0%
+up because insulin incorporates it into
+ 
+
+ align:start position:0%
+up because insulin incorporates it into
+the cells brings it back down and if
+
+ align:start position:0%
+the cells brings it back down and if
+ 
+
+ align:start position:0%
+the cells brings it back down and if
+your body stops generating insulin or if
+
+ align:start position:0%
+your body stops generating insulin or if
+ 
+
+ align:start position:0%
+your body stops generating insulin or if
+you stop being sensitive to insulin then
+
+ align:start position:0%
+you stop being sensitive to insulin then
+ 
+
+ align:start position:0%
+you stop being sensitive to insulin then
+it stays up and causes all manner of
+
+ align:start position:0%
+it stays up and causes all manner of
+ 
+
+ align:start position:0%
+it stays up and causes all manner of
+problems four million of these 10
+
+ align:start position:0%
+problems four million of these 10
+ 
+
+ align:start position:0%
+problems four million of these 10
+million people injected insulin to lower
+
+ align:start position:0%
+million people injected insulin to lower
+ 
+
+ align:start position:0%
+million people injected insulin to lower
+their blood sugar and if you get it
+
+ align:start position:0%
+their blood sugar and if you get it
+ 
+
+ align:start position:0%
+their blood sugar and if you get it
+wrong your blood sugar goes too
+
+ align:start position:0%
+wrong your blood sugar goes too
+ 
+
+ align:start position:0%
+wrong your blood sugar goes too
+low well most of the publicity for the
+
+ align:start position:0%
+low well most of the publicity for the
+ 
+
+ align:start position:0%
+low well most of the publicity for the
+damage that's done from diabetes comes
+
+ align:start position:0%
+damage that's done from diabetes comes
+ 
+
+ align:start position:0%
+damage that's done from diabetes comes
+from it being too high it's a leading
+
+ align:start position:0%
+from it being too high it's a leading
+ 
+
+ align:start position:0%
+from it being too high it's a leading
+cause of blindness kidney failure and
+
+ align:start position:0%
+cause of blindness kidney failure and
+ 
+
+ align:start position:0%
+cause of blindness kidney failure and
+peripheral amputations so it's
+
+ align:start position:0%
+peripheral amputations so it's
+ 
+
+ align:start position:0%
+peripheral amputations so it's
+catastrophic in introducing tight
+
+ align:start position:0%
+catastrophic in introducing tight
+ 
+
+ align:start position:0%
+catastrophic in introducing tight
+control that's three meals a day three
+
+ align:start position:0%
+control that's three meals a day three
+ 
+
+ align:start position:0%
+control that's three meals a day three
+small Stacks a day regular injections of
+
+ align:start position:0%
+small Stacks a day regular injections of
+ 
+
+ align:start position:0%
+small Stacks a day regular injections of
+insulin restricts the bandwidth good
+
+ align:start position:0%
+insulin restricts the bandwidth good
+ 
+
+ align:start position:0%
+insulin restricts the bandwidth good
+thing to do triples the incidence of low
+
+ align:start position:0%
+thing to do triples the incidence of low
+ 
+
+ align:start position:0%
+thing to do triples the incidence of low
+blood glucose and it must be treated
+
+ align:start position:0%
+blood glucose and it must be treated
+ 
+
+ align:start position:0%
+blood glucose and it must be treated
+right away because you faint
+
+ align:start position:0%
+right away because you faint
+ 
+
+ align:start position:0%
+right away because you faint
+which is bad if you're stuck in a
+
+ align:start position:0%
+which is bad if you're stuck in a
+ 
+
+ align:start position:0%
+which is bad if you're stuck in a
+traffic
+
+ align:start position:0%
+traffic
+ 
+
+ align:start position:0%
+traffic
+jam and it's particularly bad if it hits
+
+ align:start position:0%
+jam and it's particularly bad if it hits
+ 
+
+ align:start position:0%
+jam and it's particularly bad if it hits
+you while you're
+
+ align:start position:0%
+you while you're
+ 
+
+ align:start position:0%
+you while you're
+asleep if you're awake you start feeling
+
+ align:start position:0%
+asleep if you're awake you start feeling
+ 
+
+ align:start position:0%
+asleep if you're awake you start feeling
+clammy and tremulous and you know you've
+
+ align:start position:0%
+clammy and tremulous and you know you've
+ 
+
+ align:start position:0%
+clammy and tremulous and you know you've
+got a couple minutes to go drink some
+
+ align:start position:0%
+got a couple minutes to go drink some
+ 
+
+ align:start position:0%
+got a couple minutes to go drink some
+orange juice or eat a candy or whatever
+
+ align:start position:0%
+orange juice or eat a candy or whatever
+ 
+
+ align:start position:0%
+orange juice or eat a candy or whatever
+and elevate your blood glucose again but
+
+ align:start position:0%
+and elevate your blood glucose again but
+ 
+
+ align:start position:0%
+and elevate your blood glucose again but
+if you're asleep you may not wake
+
+ align:start position:0%
+if you're asleep you may not wake
+ 
+
+ align:start position:0%
+if you're asleep you may not wake
+up okay so what do they do about it well
+
+ align:start position:0%
+up okay so what do they do about it well
+ 
+
+ align:start position:0%
+up okay so what do they do about it well
+typically big injection of insulin big
+
+ align:start position:0%
+typically big injection of insulin big
+ 
+
+ align:start position:0%
+typically big injection of insulin big
+nighttime snack the hope that the two
+
+ align:start position:0%
+nighttime snack the hope that the two
+ 
+
+ align:start position:0%
+nighttime snack the hope that the two
+will balance each other in the course of
+
+ align:start position:0%
+will balance each other in the course of
+ 
+
+ align:start position:0%
+will balance each other in the course of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+evening unfortunately doesn't
+
+ align:start position:0%
+evening unfortunately doesn't
+ 
+
+ align:start position:0%
+evening unfortunately doesn't
+work because everything in the nighttime
+
+ align:start position:0%
+work because everything in the nighttime
+ 
+
+ align:start position:0%
+work because everything in the nighttime
+snack turns into glucose at the same
+
+ align:start position:0%
+snack turns into glucose at the same
+ 
+
+ align:start position:0%
+snack turns into glucose at the same
+time so the spike is higher but the
+
+ align:start position:0%
+time so the spike is higher but the
+ 
+
+ align:start position:0%
+time so the spike is higher but the
+duration no longer
+
+ align:start position:0%
+duration no longer
+ 
+
+ align:start position:0%
+duration no longer
+translation grossly
+
+ align:start position:0%
+translation grossly
+ 
+
+ align:start position:0%
+translation grossly
+oversimplified is that the food runs out
+
+ align:start position:0%
+oversimplified is that the food runs out
+ 
+
+ align:start position:0%
+oversimplified is that the food runs out
+at about 2 in the morning the insulin is
+
+ align:start position:0%
+at about 2 in the morning the insulin is
+ 
+
+ align:start position:0%
+at about 2 in the morning the insulin is
+still working and from 2 am until you
+
+ align:start position:0%
+still working and from 2 am until you
+ 
+
+ align:start position:0%
+still working and from 2 am until you
+get up is the danger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zone we had a bunch of f focus
+
+ align:start position:0%
+zone we had a bunch of f focus
+ 
+
+ align:start position:0%
+zone we had a bunch of f focus
+groups I lost control of myself threw
+
+ align:start position:0%
+groups I lost control of myself threw
+ 
+
+ align:start position:0%
+groups I lost control of myself threw
+the moderator out of the room walked in
+
+ align:start position:0%
+the moderator out of the room walked in
+ 
+
+ align:start position:0%
+the moderator out of the room walked in
+and said well now that we've explained
+
+ align:start position:0%
+and said well now that we've explained
+ 
+
+ align:start position:0%
+and said well now that we've explained
+this stuff to you tell me what your
+
+ align:start position:0%
+this stuff to you tell me what your
+ 
+
+ align:start position:0%
+this stuff to you tell me what your
+greatest fear really is what do you
+
+ align:start position:0%
+greatest fear really is what do you
+ 
+
+ align:start position:0%
+greatest fear really is what do you
+actually worry about and they all sort
+
+ align:start position:0%
+actually worry about and they all sort
+ 
+
+ align:start position:0%
+actually worry about and they all sort
+of said
+
+ align:start position:0%
+of said
+ 
+
+ align:start position:0%
+of said
+well I'm afraid I'll die in my sleep I
+
+ align:start position:0%
+well I'm afraid I'll die in my sleep I
+ 
+
+ align:start position:0%
+well I'm afraid I'll die in my sleep I
+sleep in that Lazy Boy in my living room
+
+ align:start position:0%
+sleep in that Lazy Boy in my living room
+ 
+
+ align:start position:0%
+sleep in that Lazy Boy in my living room
+or I have an alarm clock that goes off
+
+ align:start position:0%
+or I have an alarm clock that goes off
+ 
+
+ align:start position:0%
+or I have an alarm clock that goes off
+every hour or two just to make sure I
+
+ align:start position:0%
+every hour or two just to make sure I
+ 
+
+ align:start position:0%
+every hour or two just to make sure I
+don't have a good night's sleep ever
+
+ align:start position:0%
+don't have a good night's sleep ever
+ 
+
+ align:start position:0%
+don't have a good night's sleep ever
+thought well that's
+
+ align:start position:0%
+thought well that's
+ 
+
+ align:start position:0%
+thought well that's
+gripping and the
+
+ align:start position:0%
+gripping and the
+ 
+
+ align:start position:0%
+gripping and the
+parents of kids who had diabetes say
+
+ align:start position:0%
+parents of kids who had diabetes say
+ 
+
+ align:start position:0%
+parents of kids who had diabetes say
+every night I worry about my daughter I
+
+ align:start position:0%
+every night I worry about my daughter I
+ 
+
+ align:start position:0%
+every night I worry about my daughter I
+go in and I check on
+
+ align:start position:0%
+go in and I check on
+ 
+
+ align:start position:0%
+go in and I check on
+Jessica at two in the morning my wife
+
+ align:start position:0%
+Jessica at two in the morning my wife
+ 
+
+ align:start position:0%
+Jessica at two in the morning my wife
+and I stand there and say she awake I
+
+ align:start position:0%
+and I stand there and say she awake I
+ 
+
+ align:start position:0%
+and I stand there and say she awake I
+mean is she asleep or is she in a coma I
+
+ align:start position:0%
+mean is she asleep or is she in a coma I
+ 
+
+ align:start position:0%
+mean is she asleep or is she in a coma I
+don't know we say Jessica wake up what
+
+ align:start position:0%
+don't know we say Jessica wake up what
+ 
+
+ align:start position:0%
+don't know we say Jessica wake up what
+what you all right yeah I was asleep
+
+ align:start position:0%
+what you all right yeah I was asleep
+ 
+
+ align:start position:0%
+what you all right yeah I was asleep
+good go back to sleep it it sounds
+
+ align:start position:0%
+good go back to sleep it it sounds
+ 
+
+ align:start position:0%
+good go back to sleep it it sounds
+comical but it's quite gripping
+
+ align:start position:0%
+comical but it's quite gripping
+ 
+
+ align:start position:0%
+comical but it's quite gripping
+we said well we we've identified
+
+ align:start position:0%
+we said well we we've identified
+ 
+
+ align:start position:0%
+we said well we we've identified
+something emotional here so we put
+
+ align:start position:0%
+something emotional here so we put
+ 
+
+ align:start position:0%
+something emotional here so we put
+together a combination of nutrients that
+
+ align:start position:0%
+together a combination of nutrients that
+ 
+
+ align:start position:0%
+together a combination of nutrients that
+turned into glucose
+
+ align:start position:0%
+turned into glucose
+ 
+
+ align:start position:0%
+turned into glucose
+consecutively sucrose protein unco
+
+ align:start position:0%
+consecutively sucrose protein unco
+ 
+
+ align:start position:0%
+consecutively sucrose protein unco
+cornstarch being fundamentally a
+
+ align:start position:0%
+cornstarch being fundamentally a
+ 
+
+ align:start position:0%
+cornstarch being fundamentally a
+marketing guy of course I dubbed at time
+
+ align:start position:0%
+marketing guy of course I dubbed at time
+ 
+
+ align:start position:0%
+marketing guy of course I dubbed at time
+to release glucose right those
+
+ align:start position:0%
+to release glucose right those
+ 
+
+ align:start position:0%
+to release glucose right those
+ingredients are in a birthday
+
+ align:start position:0%
+ingredients are in a birthday
+ 
+
+ align:start position:0%
+ingredients are in a birthday
+cake but we managed to get a patent on
+
+ align:start position:0%
+cake but we managed to get a patent on
+ 
+
+ align:start position:0%
+cake but we managed to get a patent on
+it anyway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because if you use those ingredients in
+
+ align:start position:0%
+because if you use those ingredients in
+ 
+
+ align:start position:0%
+because if you use those ingredients in
+conjunction with materials that say
+
+ align:start position:0%
+conjunction with materials that say
+ 
+
+ align:start position:0%
+conjunction with materials that say
+diabetes you're violating my patent how
+
+ align:start position:0%
+diabetes you're violating my patent how
+ 
+
+ align:start position:0%
+diabetes you're violating my patent how
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+that novel and non obvious to a person
+
+ align:start position:0%
+that novel and non obvious to a person
+ 
+
+ align:start position:0%
+that novel and non obvious to a person
+of ordinary skill in the art and you
+
+ align:start position:0%
+of ordinary skill in the art and you
+ 
+
+ align:start position:0%
+of ordinary skill in the art and you
+have one of the great
+
+ align:start position:0%
+have one of the great
+ 
+
+ align:start position:0%
+have one of the great
+experts as one of your resources that's
+
+ align:start position:0%
+experts as one of your resources that's
+ 
+
+ align:start position:0%
+experts as one of your resources that's
+your host Joe hadzima I hope you'll talk
+
+ align:start position:0%
+your host Joe hadzima I hope you'll talk
+ 
+
+ align:start position:0%
+your host Joe hadzima I hope you'll talk
+about this a bit
+
+ align:start position:0%
+about this a bit
+ 
+
+ align:start position:0%
+about this a bit
+later
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we did make it taste good tasted sort
+
+ align:start position:0%
+so we did make it taste good tasted sort
+ 
+
+ align:start position:0%
+so we did make it taste good tasted sort
+of like fudge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we gave it a non-medical name would
+
+ align:start position:0%
+and we gave it a non-medical name would
+ 
+
+ align:start position:0%
+and we gave it a non-medical name would
+anybody care to guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why I heard I heard a murmur but I don't
+
+ align:start position:0%
+why I heard I heard a murmur but I don't
+ 
+
+ align:start position:0%
+why I heard I heard a murmur but I don't
+see a hand yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ma'am that is true but that was not the
+
+ align:start position:0%
+ma'am that is true but that was not the
+ 
+
+ align:start position:0%
+ma'am that is true but that was not the
+explanation
+
+ align:start position:0%
+explanation
+ 
+
+ align:start position:0%
+explanation
+sir again you not have to go through
+
+ align:start position:0%
+sir again you not have to go through
+ 
+
+ align:start position:0%
+sir again you not have to go through
+FDA well we didn't have to go to FDA but
+
+ align:start position:0%
+FDA well we didn't have to go to FDA but
+ 
+
+ align:start position:0%
+FDA well we didn't have to go to FDA but
+that's not why we did we gave it a
+
+ align:start position:0%
+that's not why we did we gave it a
+ 
+
+ align:start position:0%
+that's not why we did we gave it a
+non-medical name sir because you're
+
+ align:start position:0%
+non-medical name sir because you're
+ 
+
+ align:start position:0%
+non-medical name sir because you're
+trying
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+toce
+
+ align:start position:0%
+toce
+ 
+
+ align:start position:0%
+toce
+yes but perhaps not the fear that our
+
+ align:start position:0%
+yes but perhaps not the fear that our
+ 
+
+ align:start position:0%
+yes but perhaps not the fear that our
+audience would
+
+ align:start position:0%
+audience would
+ 
+
+ align:start position:0%
+audience would
+think we talk to our patients our
+
+ align:start position:0%
+think we talk to our patients our
+ 
+
+ align:start position:0%
+think we talk to our patients our
+customers something I'm going to
+
+ align:start position:0%
+customers something I'm going to
+ 
+
+ align:start position:0%
+customers something I'm going to
+encourage you to do and they said Bob
+
+ align:start position:0%
+encourage you to do and they said Bob
+ 
+
+ align:start position:0%
+encourage you to do and they said Bob
+I'm not a diabetic I am a person who has
+
+ align:start position:0%
+I'm not a diabetic I am a person who has
+ 
+
+ align:start position:0%
+I'm not a diabetic I am a person who has
+diabetes I'm a lawyer I'm a
+
+ align:start position:0%
+diabetes I'm a lawyer I'm a
+ 
+
+ align:start position:0%
+diabetes I'm a lawyer I'm a
+banker I'm a professional I have a
+
+ align:start position:0%
+banker I'm a professional I have a
+ 
+
+ align:start position:0%
+banker I'm a professional I have a
+condition but I manage it it just like
+
+ align:start position:0%
+condition but I manage it it just like
+ 
+
+ align:start position:0%
+condition but I manage it it just like
+you might have a headache but you manage
+
+ align:start position:0%
+you might have a headache but you manage
+ 
+
+ align:start position:0%
+you might have a headache but you manage
+it it's nobody's damn business whether
+
+ align:start position:0%
+it it's nobody's damn business whether
+ 
+
+ align:start position:0%
+it it's nobody's damn business whether
+or not I have diabetes and if I end up
+
+ align:start position:0%
+or not I have diabetes and if I end up
+ 
+
+ align:start position:0%
+or not I have diabetes and if I end up
+in a meeting that lasts half the night
+
+ align:start position:0%
+in a meeting that lasts half the night
+ 
+
+ align:start position:0%
+in a meeting that lasts half the night
+and I have to consume your product I
+
+ align:start position:0%
+and I have to consume your product I
+ 
+
+ align:start position:0%
+and I have to consume your product I
+don't want the other people around the
+
+ align:start position:0%
+don't want the other people around the
+ 
+
+ align:start position:0%
+don't want the other people around the
+conference table knowing I'm medicating
+
+ align:start position:0%
+conference table knowing I'm medicating
+ 
+
+ align:start position:0%
+conference table knowing I'm medicating
+it's none of their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+business thank
+
+ align:start position:0%
+business thank
+ 
+
+ align:start position:0%
+business thank
+you furthermore I had been arm wrestling
+
+ align:start position:0%
+you furthermore I had been arm wrestling
+ 
+
+ align:start position:0%
+you furthermore I had been arm wrestling
+with the FDA because I wanted to put
+
+ align:start position:0%
+with the FDA because I wanted to put
+ 
+
+ align:start position:0%
+with the FDA because I wanted to put
+four diabetes on the
+
+ align:start position:0%
+four diabetes on the
+ 
+
+ align:start position:0%
+four diabetes on the
+package and what our customers told me
+
+ align:start position:0%
+package and what our customers told me
+ 
+
+ align:start position:0%
+package and what our customers told me
+was if you do that I won't buy the
+
+ align:start position:0%
+was if you do that I won't buy the
+ 
+
+ align:start position:0%
+was if you do that I won't buy the
+product so I was trying very hard to do
+
+ align:start position:0%
+product so I was trying very hard to do
+ 
+
+ align:start position:0%
+product so I was trying very hard to do
+the one thing that would have scuttled
+
+ align:start position:0%
+the one thing that would have scuttled
+ 
+
+ align:start position:0%
+the one thing that would have scuttled
+the business fortunately our customers
+
+ align:start position:0%
+the business fortunately our customers
+ 
+
+ align:start position:0%
+the business fortunately our customers
+advised us and we listened and they said
+
+ align:start position:0%
+advised us and we listened and they said
+ 
+
+ align:start position:0%
+advised us and we listened and they said
+our kids have sleepovers and they have
+
+ align:start position:0%
+our kids have sleepovers and they have
+ 
+
+ align:start position:0%
+our kids have sleepovers and they have
+to do one of these at
+
+ align:start position:0%
+to do one of these at
+ 
+
+ align:start position:0%
+to do one of these at
+night and they would rather eat
+
+ align:start position:0%
+night and they would rather eat
+ 
+
+ align:start position:0%
+night and they would rather eat
+worms than be different from their peers
+
+ align:start position:0%
+worms than be different from their peers
+ 
+
+ align:start position:0%
+worms than be different from their peers
+so make it look like something they can
+
+ align:start position:0%
+so make it look like something they can
+ 
+
+ align:start position:0%
+so make it look like something they can
+offer for their friends like an energy
+
+ align:start position:0%
+offer for their friends like an energy
+ 
+
+ align:start position:0%
+offer for their friends like an energy
+bar Ed to release glucose hey guys you
+
+ align:start position:0%
+bar Ed to release glucose hey guys you
+ 
+
+ align:start position:0%
+bar Ed to release glucose hey guys you
+want one so I said okay we're bringing
+
+ align:start position:0%
+want one so I said okay we're bringing
+ 
+
+ align:start position:0%
+want one so I said okay we're bringing
+some consumer marketing in to all this
+
+ align:start position:0%
+some consumer marketing in to all this
+ 
+
+ align:start position:0%
+some consumer marketing in to all this
+science so this time around instead of
+
+ align:start position:0%
+science so this time around instead of
+ 
+
+ align:start position:0%
+science so this time around instead of
+just talking to clinicians they were
+
+ align:start position:0%
+just talking to clinicians they were
+ 
+
+ align:start position:0%
+just talking to clinicians they were
+important but they were not sufficient
+
+ align:start position:0%
+important but they were not sufficient
+ 
+
+ align:start position:0%
+important but they were not sufficient
+we talked to parents we talked to
+
+ align:start position:0%
+we talked to parents we talked to
+ 
+
+ align:start position:0%
+we talked to parents we talked to
+patients we went to all these things at
+
+ align:start position:0%
+patients we went to all these things at
+ 
+
+ align:start position:0%
+patients we went to all these things at
+elementary schools that parents of kids
+
+ align:start position:0%
+elementary schools that parents of kids
+ 
+
+ align:start position:0%
+elementary schools that parents of kids
+with diabetes would attend and you know
+
+ align:start position:0%
+with diabetes would attend and you know
+ 
+
+ align:start position:0%
+with diabetes would attend and you know
+those little bitty chairs sat there with
+
+ align:start position:0%
+those little bitty chairs sat there with
+ 
+
+ align:start position:0%
+those little bitty chairs sat there with
+our knees is banging against things and
+
+ align:start position:0%
+our knees is banging against things and
+ 
+
+ align:start position:0%
+our knees is banging against things and
+took lots of moms to lunch we learned an
+
+ align:start position:0%
+took lots of moms to lunch we learned an
+ 
+
+ align:start position:0%
+took lots of moms to lunch we learned an
+awful lot about this how many of you
+
+ align:start position:0%
+awful lot about this how many of you
+ 
+
+ align:start position:0%
+awful lot about this how many of you
+know someone who has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diabetes it's really important to go
+
+ align:start position:0%
+diabetes it's really important to go
+ 
+
+ align:start position:0%
+diabetes it's really important to go
+have these
+
+ align:start position:0%
+have these
+ 
+
+ align:start position:0%
+have these
+conversations and
+
+ align:start position:0%
+conversations and
+ 
+
+ align:start position:0%
+conversations and
+finally I said well what kind of
+
+ align:start position:0%
+finally I said well what kind of
+ 
+
+ align:start position:0%
+finally I said well what kind of
+advertising do these people see there
+
+ align:start position:0%
+advertising do these people see there
+ 
+
+ align:start position:0%
+advertising do these people see there
+are all sorts of diabetes magazines out
+
+ align:start position:0%
+are all sorts of diabetes magazines out
+ 
+
+ align:start position:0%
+are all sorts of diabetes magazines out
+there so I bought a half a dozen of them
+
+ align:start position:0%
+there so I bought a half a dozen of them
+ 
+
+ align:start position:0%
+there so I bought a half a dozen of them
+and the typical ad was on the back cover
+
+ align:start position:0%
+and the typical ad was on the back cover
+ 
+
+ align:start position:0%
+and the typical ad was on the back cover
+a full page blow up of a hypodermic
+
+ align:start position:0%
+a full page blow up of a hypodermic
+ 
+
+ align:start position:0%
+a full page blow up of a hypodermic
+needle just the thing to make you feel
+
+ align:start position:0%
+needle just the thing to make you feel
+ 
+
+ align:start position:0%
+needle just the thing to make you feel
+warm and resonant right I mean the copy
+
+ align:start position:0%
+warm and resonant right I mean the copy
+ 
+
+ align:start position:0%
+warm and resonant right I mean the copy
+would say my needle's sharper than his
+
+ align:start position:0%
+would say my needle's sharper than his
+ 
+
+ align:start position:0%
+would say my needle's sharper than his
+needle doesn't hurt as much buy
+
+ align:start position:0%
+needle doesn't hurt as much buy
+ 
+
+ align:start position:0%
+needle doesn't hurt as much buy
+mine I said
+
+ align:start position:0%
+mine I said
+ 
+
+ align:start position:0%
+mine I said
+ooh so we put together an ad with this
+
+ align:start position:0%
+ooh so we put together an ad with this
+ 
+
+ align:start position:0%
+ooh so we put together an ad with this
+agency that had flying
+
+ align:start position:0%
+agency that had flying
+ 
+
+ align:start position:0%
+agency that had flying
+pigs it was just so ludicrously out of
+
+ align:start position:0%
+pigs it was just so ludicrously out of
+ 
+
+ align:start position:0%
+pigs it was just so ludicrously out of
+place in this magazine nobody turned the
+
+ align:start position:0%
+place in this magazine nobody turned the
+ 
+
+ align:start position:0%
+place in this magazine nobody turned the
+page and there was some kind of lame
+
+ align:start position:0%
+page and there was some kind of lame
+ 
+
+ align:start position:0%
+page and there was some kind of lame
+copy about sleep per chance the dream
+
+ align:start position:0%
+copy about sleep per chance the dream
+ 
+
+ align:start position:0%
+copy about sleep per chance the dream
+Etc right everybody read it and we ran a
+
+ align:start position:0%
+Etc right everybody read it and we ran a
+ 
+
+ align:start position:0%
+Etc right everybody read it and we ran a
+little violator across the corner of the
+
+ align:start position:0%
+little violator across the corner of the
+ 
+
+ align:start position:0%
+little violator across the corner of the
+ad says for free sample call 1 800 and
+
+ align:start position:0%
+ad says for free sample call 1 800 and
+ 
+
+ align:start position:0%
+ad says for free sample call 1 800 and
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+number stuff started
+
+ align:start position:0%
+number stuff started
+ 
+
+ align:start position:0%
+number stuff started
+happening we were at 238 Main Street up
+
+ align:start position:0%
+happening we were at 238 Main Street up
+ 
+
+ align:start position:0%
+happening we were at 238 Main Street up
+above what was at the time a barber shop
+
+ align:start position:0%
+above what was at the time a barber shop
+ 
+
+ align:start position:0%
+above what was at the time a barber shop
+in a little ratty
+
+ align:start position:0%
+in a little ratty
+ 
+
+ align:start position:0%
+in a little ratty
+office when we started getting a 100
+
+ align:start position:0%
+office when we started getting a 100
+ 
+
+ align:start position:0%
+office when we started getting a 100
+calls a day we needed more
+
+ align:start position:0%
+calls a day we needed more
+ 
+
+ align:start position:0%
+calls a day we needed more
+phones 200 calls a day we said said gez
+
+ align:start position:0%
+phones 200 calls a day we said said gez
+ 
+
+ align:start position:0%
+phones 200 calls a day we said said gez
+we better get some people to answer the
+
+ align:start position:0%
+we better get some people to answer the
+ 
+
+ align:start position:0%
+we better get some people to answer the
+phone Kendall Square of course has more
+
+ align:start position:0%
+phone Kendall Square of course has more
+ 
+
+ align:start position:0%
+phone Kendall Square of course has more
+Geniuses per square foot than most
+
+ align:start position:0%
+Geniuses per square foot than most
+ 
+
+ align:start position:0%
+Geniuses per square foot than most
+places so we basically just went
+
+ align:start position:0%
+places so we basically just went
+ 
+
+ align:start position:0%
+places so we basically just went
+downstairs with the mirror and we held
+
+ align:start position:0%
+downstairs with the mirror and we held
+ 
+
+ align:start position:0%
+downstairs with the mirror and we held
+it under people's noses and if it fogged
+
+ align:start position:0%
+it under people's noses and if it fogged
+ 
+
+ align:start position:0%
+it under people's noses and if it fogged
+up we said would you like a
+
+ align:start position:0%
+up we said would you like a
+ 
+
+ align:start position:0%
+up we said would you like a
+job and fill the office 300 calls a day
+
+ align:start position:0%
+job and fill the office 300 calls a day
+ 
+
+ align:start position:0%
+job and fill the office 300 calls a day
+we said God we can't keep track of these
+
+ align:start position:0%
+we said God we can't keep track of these
+ 
+
+ align:start position:0%
+we said God we can't keep track of these
+people on index cards we better install
+
+ align:start position:0%
+people on index cards we better install
+ 
+
+ align:start position:0%
+people on index cards we better install
+a database 500 calls a day 500 calls a
+
+ align:start position:0%
+a database 500 calls a day 500 calls a
+ 
+
+ align:start position:0%
+a database 500 calls a day 500 calls a
+day we went off and rented some of these
+
+ align:start position:0%
+day we went off and rented some of these
+ 
+
+ align:start position:0%
+day we went off and rented some of these
+tables and stuck like three computers on
+
+ align:start position:0%
+tables and stuck like three computers on
+ 
+
+ align:start position:0%
+tables and stuck like three computers on
+a table and got all these people sitting
+
+ align:start position:0%
+a table and got all these people sitting
+ 
+
+ align:start position:0%
+a table and got all these people sitting
+there elbow to Elbow we said I think
+
+ align:start position:0%
+there elbow to Elbow we said I think
+ 
+
+ align:start position:0%
+there elbow to Elbow we said I think
+we're on to
+
+ align:start position:0%
+we're on to
+ 
+
+ align:start position:0%
+we're on to
+something I'm going to fast forward to
+
+ align:start position:0%
+something I'm going to fast forward to
+ 
+
+ align:start position:0%
+something I'm going to fast forward to
+something here we ended up in all of the
+
+ align:start position:0%
+something here we ended up in all of the
+ 
+
+ align:start position:0%
+something here we ended up in all of the
+major Pharmacy chains and all of the
+
+ align:start position:0%
+major Pharmacy chains and all of the
+ 
+
+ align:start position:0%
+major Pharmacy chains and all of the
+major wholesalers I'll tell you about
+
+ align:start position:0%
+major wholesalers I'll tell you about
+ 
+
+ align:start position:0%
+major wholesalers I'll tell you about
+that and the amount we paid for slotting
+
+ align:start position:0%
+that and the amount we paid for slotting
+ 
+
+ align:start position:0%
+that and the amount we paid for slotting
+fees was
+
+ align:start position:0%
+fees was
+ 
+
+ align:start position:0%
+fees was
+Zero unprecedented in our
+
+ align:start position:0%
+Zero unprecedented in our
+ 
+
+ align:start position:0%
+Zero unprecedented in our
+field I think the lesson is that
+
+ align:start position:0%
+field I think the lesson is that
+ 
+
+ align:start position:0%
+field I think the lesson is that
+understanding our customer as opposed to
+
+ align:start position:0%
+understanding our customer as opposed to
+ 
+
+ align:start position:0%
+understanding our customer as opposed to
+with regain thank you for your
+
+ align:start position:0%
+with regain thank you for your
+ 
+
+ align:start position:0%
+with regain thank you for your
+observation helped us build a better
+
+ align:start position:0%
+observation helped us build a better
+ 
+
+ align:start position:0%
+observation helped us build a better
+product and a successful business so how
+
+ align:start position:0%
+product and a successful business so how
+ 
+
+ align:start position:0%
+product and a successful business so how
+do we reach them
+
+ align:start position:0%
+do we reach them
+ 
+
+ align:start position:0%
+do we reach them
+well we said who influences them who's
+
+ align:start position:0%
+well we said who influences them who's
+ 
+
+ align:start position:0%
+well we said who influences them who's
+our customer who's their influencer how
+
+ align:start position:0%
+our customer who's their influencer how
+ 
+
+ align:start position:0%
+our customer who's their influencer how
+do we reach the influencer where do they
+
+ align:start position:0%
+do we reach the influencer where do they
+ 
+
+ align:start position:0%
+do we reach the influencer where do they
+spend their
+
+ align:start position:0%
+spend their
+ 
+
+ align:start position:0%
+spend their
+money and we
+
+ align:start position:0%
+money and we
+ 
+
+ align:start position:0%
+money and we
+discovered all right back up I hate to
+
+ align:start position:0%
+discovered all right back up I hate to
+ 
+
+ align:start position:0%
+discovered all right back up I hate to
+be crude but there are some people who
+
+ align:start position:0%
+be crude but there are some people who
+ 
+
+ align:start position:0%
+be crude but there are some people who
+have diabetes who are just determined
+
+ align:start position:0%
+have diabetes who are just determined
+ 
+
+ align:start position:0%
+have diabetes who are just determined
+not to take care of
+
+ align:start position:0%
+not to take care of
+ 
+
+ align:start position:0%
+not to take care of
+themselves so should we spend time and
+
+ align:start position:0%
+themselves so should we spend time and
+ 
+
+ align:start position:0%
+themselves so should we spend time and
+effort trying to reach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them so how do we find the ones who do
+
+ align:start position:0%
+them so how do we find the ones who do
+ 
+
+ align:start position:0%
+them so how do we find the ones who do
+take care of themselves and furthermore
+
+ align:start position:0%
+take care of themselves and furthermore
+ 
+
+ align:start position:0%
+take care of themselves and furthermore
+are willing to spend a little money on
+
+ align:start position:0%
+are willing to spend a little money on
+ 
+
+ align:start position:0%
+are willing to spend a little money on
+their care answer they're seeing a
+
+ align:start position:0%
+their care answer they're seeing a
+ 
+
+ align:start position:0%
+their care answer they're seeing a
+clinician the clinician called the
+
+ align:start position:0%
+clinician the clinician called the
+ 
+
+ align:start position:0%
+clinician the clinician called the
+certified diabetes educator and their
+
+ align:start position:0%
+certified diabetes educator and their
+ 
+
+ align:start position:0%
+certified diabetes educator and their
+Association I know this will astonish
+
+ align:start position:0%
+Association I know this will astonish
+ 
+
+ align:start position:0%
+Association I know this will astonish
+you is the American Association of
+
+ align:start position:0%
+you is the American Association of
+ 
+
+ align:start position:0%
+you is the American Association of
+diabetes
+
+ align:start position:0%
+diabetes
+ 
+
+ align:start position:0%
+diabetes
+Educators and if you go on their website
+
+ align:start position:0%
+Educators and if you go on their website
+ 
+
+ align:start position:0%
+Educators and if you go on their website
+there's little
+
+ align:start position:0%
+there's little
+ 
+
+ align:start position:0%
+there's little
+tab locate an educator you put in 02142
+
+ align:start position:0%
+tab locate an educator you put in 02142
+ 
+
+ align:start position:0%
+tab locate an educator you put in 02142
+out comes a list name contact
+
+ align:start position:0%
+out comes a list name contact
+ 
+
+ align:start position:0%
+out comes a list name contact
+information Etc we said
+
+ align:start position:0%
+information Etc we said
+ 
+
+ align:start position:0%
+information Etc we said
+well what do the Educators worry
+
+ align:start position:0%
+well what do the Educators worry
+ 
+
+ align:start position:0%
+well what do the Educators worry
+about we know what the patients worry
+
+ align:start position:0%
+about we know what the patients worry
+ 
+
+ align:start position:0%
+about we know what the patients worry
+about patients worry they're going to
+
+ align:start position:0%
+about patients worry they're going to
+ 
+
+ align:start position:0%
+about patients worry they're going to
+die in their sleep they go see an
+
+ align:start position:0%
+die in their sleep they go see an
+ 
+
+ align:start position:0%
+die in their sleep they go see an
+educator what does the educator worry
+
+ align:start position:0%
+educator what does the educator worry
+ 
+
+ align:start position:0%
+educator what does the educator worry
+about who would care to
+
+ align:start position:0%
+about who would care to
+ 
+
+ align:start position:0%
+about who would care to
+speculate what do the diabetes Educators
+
+ align:start position:0%
+speculate what do the diabetes Educators
+ 
+
+ align:start position:0%
+speculate what do the diabetes Educators
+worry about that we could hook on to in
+
+ align:start position:0%
+worry about that we could hook on to in
+ 
+
+ align:start position:0%
+worry about that we could hook on to in
+a phone call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well that's one they'd like to know that
+
+ align:start position:0%
+well that's one they'd like to know that
+ 
+
+ align:start position:0%
+well that's one they'd like to know that
+what you have works thank you what else
+
+ align:start position:0%
+what you have works thank you what else
+ 
+
+ align:start position:0%
+what you have works thank you what else
+when I asked them what's your greatest
+
+ align:start position:0%
+when I asked them what's your greatest
+ 
+
+ align:start position:0%
+when I asked them what's your greatest
+professional
+
+ align:start position:0%
+professional
+ 
+
+ align:start position:0%
+professional
+frustration anybody care to guess what
+
+ align:start position:0%
+frustration anybody care to guess what
+ 
+
+ align:start position:0%
+frustration anybody care to guess what
+their answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was yes
+
+ align:start position:0%
+was yes
+ 
+
+ align:start position:0%
+was yes
+sir oh my God that's absolutely right I
+
+ align:start position:0%
+sir oh my God that's absolutely right I
+ 
+
+ align:start position:0%
+sir oh my God that's absolutely right I
+tell them what to do and they don't do
+
+ align:start position:0%
+tell them what to do and they don't do
+ 
+
+ align:start position:0%
+tell them what to do and they don't do
+it drives me crazy
+
+ align:start position:0%
+it drives me crazy
+ 
+
+ align:start position:0%
+it drives me crazy
+we'd hear it over and over again single
+
+ align:start position:0%
+we'd hear it over and over again single
+ 
+
+ align:start position:0%
+we'd hear it over and over again single
+greatest professional frustration the
+
+ align:start position:0%
+greatest professional frustration the
+ 
+
+ align:start position:0%
+greatest professional frustration the
+medical term of course is compliance
+
+ align:start position:0%
+medical term of course is compliance
+ 
+
+ align:start position:0%
+medical term of course is compliance
+they don't
+
+ align:start position:0%
+they don't
+ 
+
+ align:start position:0%
+they don't
+comply
+
+ align:start position:0%
+comply
+ 
+
+ align:start position:0%
+comply
+so we said
+
+ align:start position:0%
+so we said
+ 
+
+ align:start position:0%
+so we said
+well we need to figure out how to
+
+ align:start position:0%
+well we need to figure out how to
+ 
+
+ align:start position:0%
+well we need to figure out how to
+address that so we'd call them up having
+
+ align:start position:0%
+address that so we'd call them up having
+ 
+
+ align:start position:0%
+address that so we'd call them up having
+located and by the way I know that these
+
+ align:start position:0%
+located and by the way I know that these
+ 
+
+ align:start position:0%
+located and by the way I know that these
+days an increasing number of people are
+
+ align:start position:0%
+days an increasing number of people are
+ 
+
+ align:start position:0%
+days an increasing number of people are
+terribly uncomfortable picking up the
+
+ align:start position:0%
+terribly uncomfortable picking up the
+ 
+
+ align:start position:0%
+terribly uncomfortable picking up the
+phone and calling someone without five
+
+ align:start position:0%
+phone and calling someone without five
+ 
+
+ align:start position:0%
+phone and calling someone without five
+emails to set up the appointment
+
+ align:start position:0%
+emails to set up the appointment
+ 
+
+ align:start position:0%
+emails to set up the appointment
+first so this may strike you as like
+
+ align:start position:0%
+first so this may strike you as like
+ 
+
+ align:start position:0%
+first so this may strike you as like
+emotionally difficult to just make cold
+
+ align:start position:0%
+emotionally difficult to just make cold
+ 
+
+ align:start position:0%
+emotionally difficult to just make cold
+calls but we
+
+ align:start position:0%
+calls but we
+ 
+
+ align:start position:0%
+calls but we
+did and when they'd answer the phone
+
+ align:start position:0%
+did and when they'd answer the phone
+ 
+
+ align:start position:0%
+did and when they'd answer the phone
+we'd
+
+ align:start position:0%
+we'd
+ 
+
+ align:start position:0%
+we'd
+say our company's worked with a group of
+
+ align:start position:0%
+say our company's worked with a group of
+ 
+
+ align:start position:0%
+say our company's worked with a group of
+docs out of Harvard Med school and we've
+
+ align:start position:0%
+docs out of Harvard Med school and we've
+ 
+
+ align:start position:0%
+docs out of Harvard Med school and we've
+invented what looks like a candy bar for
+
+ align:start position:0%
+invented what looks like a candy bar for
+ 
+
+ align:start position:0%
+invented what looks like a candy bar for
+addressing nocturnal
+
+ align:start position:0%
+addressing nocturnal
+ 
+
+ align:start position:0%
+addressing nocturnal
+hypoglycemia and the patients love it
+
+ align:start position:0%
+hypoglycemia and the patients love it
+ 
+
+ align:start position:0%
+hypoglycemia and the patients love it
+do you have 30
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds say
+
+ align:start position:0%
+seconds say
+ 
+
+ align:start position:0%
+seconds say
+again and we talk to him the last thing
+
+ align:start position:0%
+again and we talk to him the last thing
+ 
+
+ align:start position:0%
+again and we talk to him the last thing
+we would say in the conversation is who
+
+ align:start position:0%
+we would say in the conversation is who
+ 
+
+ align:start position:0%
+we would say in the conversation is who
+else that you know should we call oh you
+
+ align:start position:0%
+else that you know should we call oh you
+ 
+
+ align:start position:0%
+else that you know should we call oh you
+got to call my friend Susie cream cheese
+
+ align:start position:0%
+got to call my friend Susie cream cheese
+ 
+
+ align:start position:0%
+got to call my friend Susie cream cheese
+she would absolutely love this so we'd
+
+ align:start position:0%
+she would absolutely love this so we'd
+ 
+
+ align:start position:0%
+she would absolutely love this so we'd
+call Susie cream cheese and we say Susie
+
+ align:start position:0%
+call Susie cream cheese and we say Susie
+ 
+
+ align:start position:0%
+call Susie cream cheese and we say Susie
+Janet says we ought to call you oh how's
+
+ align:start position:0%
+Janet says we ought to call you oh how's
+ 
+
+ align:start position:0%
+Janet says we ought to call you oh how's
+Janet well you know her dogs's got a hip
+
+ align:start position:0%
+Janet well you know her dogs's got a hip
+ 
+
+ align:start position:0%
+Janet well you know her dogs's got a hip
+problem going to go in for surgery but
+
+ align:start position:0%
+problem going to go in for surgery but
+ 
+
+ align:start position:0%
+problem going to go in for surgery but
+other than that Janet oh she loves that
+
+ align:start position:0%
+other than that Janet oh she loves that
+ 
+
+ align:start position:0%
+other than that Janet oh she loves that
+dog yeah she does anyway she said we
+
+ align:start position:0%
+dog yeah she does anyway she said we
+ 
+
+ align:start position:0%
+dog yeah she does anyway she said we
+should call building relationships right
+
+ align:start position:0%
+should call building relationships right
+ 
+
+ align:start position:0%
+should call building relationships right
+so we started doing this stuff pretty
+
+ align:start position:0%
+so we started doing this stuff pretty
+ 
+
+ align:start position:0%
+so we started doing this stuff pretty
+soon we ended up with several thousand
+
+ align:start position:0%
+soon we ended up with several thousand
+ 
+
+ align:start position:0%
+soon we ended up with several thousand
+highly trained clinicians talking about
+
+ align:start position:0%
+highly trained clinicians talking about
+ 
+
+ align:start position:0%
+highly trained clinicians talking about
+our product on our behalf and their
+
+ align:start position:0%
+our product on our behalf and their
+ 
+
+ align:start position:0%
+our product on our behalf and their
+reward was not Financial their reward
+
+ align:start position:0%
+reward was not Financial their reward
+ 
+
+ align:start position:0%
+reward was not Financial their reward
+was that their patients came back to see
+
+ align:start position:0%
+was that their patients came back to see
+ 
+
+ align:start position:0%
+was that their patients came back to see
+them and said this stuff's awesome and
+
+ align:start position:0%
+them and said this stuff's awesome and
+ 
+
+ align:start position:0%
+them and said this stuff's awesome and
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+complied so we built a little float we
+
+ align:start position:0%
+complied so we built a little float we
+ 
+
+ align:start position:0%
+complied so we built a little float we
+said we have a Salesforce and we're
+
+ align:start position:0%
+said we have a Salesforce and we're
+ 
+
+ align:start position:0%
+said we have a Salesforce and we're
+calling on the Educators the Educators
+
+ align:start position:0%
+calling on the Educators the Educators
+ 
+
+ align:start position:0%
+calling on the Educators the Educators
+if we do this right will tell their
+
+ align:start position:0%
+if we do this right will tell their
+ 
+
+ align:start position:0%
+if we do this right will tell their
+patients the patients will call us and
+
+ align:start position:0%
+patients the patients will call us and
+ 
+
+ align:start position:0%
+patients the patients will call us and
+buy the product well that's
+
+ align:start position:0%
+buy the product well that's
+ 
+
+ align:start position:0%
+buy the product well that's
+attractive but it's not the path to
+
+ align:start position:0%
+attractive but it's not the path to
+ 
+
+ align:start position:0%
+attractive but it's not the path to
+financial Heaven because there's this
+
+ align:start position:0%
+financial Heaven because there's this
+ 
+
+ align:start position:0%
+financial Heaven because there's this
+group out there called
+
+ align:start position:0%
+group out there called
+ 
+
+ align:start position:0%
+group out there called
+retailers how do we get into the
+
+ align:start position:0%
+retailers how do we get into the
+ 
+
+ align:start position:0%
+retailers how do we get into the
+retailers maybe we could have the
+
+ align:start position:0%
+retailers maybe we could have the
+ 
+
+ align:start position:0%
+retailers maybe we could have the
+Educators call the retailers maybe we
+
+ align:start position:0%
+Educators call the retailers maybe we
+ 
+
+ align:start position:0%
+Educators call the retailers maybe we
+could have the patients call the
+
+ align:start position:0%
+could have the patients call the
+ 
+
+ align:start position:0%
+could have the patients call the
+retailers maybe then we could call the
+
+ align:start position:0%
+retailers maybe then we could call the
+ 
+
+ align:start position:0%
+retailers maybe then we could call the
+retailers and we'd make more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+money
+
+ align:start position:0%
+money
+ 
+
+ align:start position:0%
+money
+well this weekend if you have the
+
+ align:start position:0%
+well this weekend if you have the
+ 
+
+ align:start position:0%
+well this weekend if you have the
+opportunity stand in a pharmacy and
+
+ align:start position:0%
+opportunity stand in a pharmacy and
+ 
+
+ align:start position:0%
+opportunity stand in a pharmacy and
+watch the pharmacist when they answer
+
+ align:start position:0%
+watch the pharmacist when they answer
+ 
+
+ align:start position:0%
+watch the pharmacist when they answer
+the phone right they've got this phone
+
+ align:start position:0%
+the phone right they've got this phone
+ 
+
+ align:start position:0%
+the phone right they've got this phone
+tucked in the a
+
+ align:start position:0%
+tucked in the a
+ 
+
+ align:start position:0%
+tucked in the a
+pharmacy you got 12 seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how did we address this well people
+
+ align:start position:0%
+so how did we address this well people
+ 
+
+ align:start position:0%
+so how did we address this well people
+would call we'd send them a free
+
+ align:start position:0%
+would call we'd send them a free
+ 
+
+ align:start position:0%
+would call we'd send them a free
+sample by the way we had to put in some
+
+ align:start position:0%
+sample by the way we had to put in some
+ 
+
+ align:start position:0%
+sample by the way we had to put in some
+questions because we made it onto one of
+
+ align:start position:0%
+questions because we made it onto one of
+ 
+
+ align:start position:0%
+questions because we made it onto one of
+these web pages that said this outfit's
+
+ align:start position:0%
+these web pages that said this outfit's
+ 
+
+ align:start position:0%
+these web pages that said this outfit's
+given away free
+
+ align:start position:0%
+given away free
+ 
+
+ align:start position:0%
+given away free
+fudge so we got plenty of phone calls
+
+ align:start position:0%
+fudge so we got plenty of phone calls
+ 
+
+ align:start position:0%
+fudge so we got plenty of phone calls
+from people who were never going to be
+
+ align:start position:0%
+from people who were never going to be
+ 
+
+ align:start position:0%
+from people who were never going to be
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+customer so once we figured that out we
+
+ align:start position:0%
+customer so once we figured that out we
+ 
+
+ align:start position:0%
+customer so once we figured that out we
+had to start asking some qualified
+
+ align:start position:0%
+had to start asking some qualified
+ 
+
+ align:start position:0%
+had to start asking some qualified
+questions tell us what brand of insulin
+
+ align:start position:0%
+questions tell us what brand of insulin
+ 
+
+ align:start position:0%
+questions tell us what brand of insulin
+you're typically using if we heard how
+
+ align:start position:0%
+you're typically using if we heard how
+ 
+
+ align:start position:0%
+you're typically using if we heard how
+uh oh I'm sorry we don't have anything
+
+ align:start position:0%
+uh oh I'm sorry we don't have anything
+ 
+
+ align:start position:0%
+uh oh I'm sorry we don't have anything
+for you next right but we'd sent him a
+
+ align:start position:0%
+for you next right but we'd sent him a
+ 
+
+ align:start position:0%
+for you next right but we'd sent him a
+sample we'd follow it up did you get our
+
+ align:start position:0%
+sample we'd follow it up did you get our
+ 
+
+ align:start position:0%
+sample we'd follow it up did you get our
+product yes did you wake up dead no must
+
+ align:start position:0%
+product yes did you wake up dead no must
+ 
+
+ align:start position:0%
+product yes did you wake up dead no must
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+worked guys that was a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+joke we're providing free shipping if
+
+ align:start position:0%
+joke we're providing free shipping if
+ 
+
+ align:start position:0%
+joke we're providing free shipping if
+you'd care to order okay love it we'd
+
+ align:start position:0%
+you'd care to order okay love it we'd
+ 
+
+ align:start position:0%
+you'd care to order okay love it we'd
+take their order we'd track it carefully
+
+ align:start position:0%
+take their order we'd track it carefully
+ 
+
+ align:start position:0%
+take their order we'd track it carefully
+we'd call them back and say aren't you
+
+ align:start position:0%
+we'd call them back and say aren't you
+ 
+
+ align:start position:0%
+we'd call them back and say aren't you
+bow out don't you need some more why
+
+ align:start position:0%
+bow out don't you need some more why
+ 
+
+ align:start position:0%
+bow out don't you need some more why
+yes then one day we'd say you know this
+
+ align:start position:0%
+yes then one day we'd say you know this
+ 
+
+ align:start position:0%
+yes then one day we'd say you know this
+free shipping is coming to a close and
+
+ align:start position:0%
+free shipping is coming to a close and
+ 
+
+ align:start position:0%
+free shipping is coming to a close and
+we're going to have to start charging
+
+ align:start position:0%
+we're going to have to start charging
+ 
+
+ align:start position:0%
+we're going to have to start charging
+you for it and I know you go someplace
+
+ align:start position:0%
+you for it and I know you go someplace
+ 
+
+ align:start position:0%
+you for it and I know you go someplace
+to buy your insulin wouldn't it be more
+
+ align:start position:0%
+to buy your insulin wouldn't it be more
+ 
+
+ align:start position:0%
+to buy your insulin wouldn't it be more
+convenient to buy this stuff at the same
+
+ align:start position:0%
+convenient to buy this stuff at the same
+ 
+
+ align:start position:0%
+convenient to buy this stuff at the same
+place you buy your insulin well yeah it
+
+ align:start position:0%
+place you buy your insulin well yeah it
+ 
+
+ align:start position:0%
+place you buy your insulin well yeah it
+would okay we did some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+homework there's about 3% of the people
+
+ align:start position:0%
+homework there's about 3% of the people
+ 
+
+ align:start position:0%
+homework there's about 3% of the people
+in the country at the time had diabetes
+
+ align:start position:0%
+in the country at the time had diabetes
+ 
+
+ align:start position:0%
+in the country at the time had diabetes
+and they were worth about 24 4% of
+
+ align:start position:0%
+and they were worth about 24 4% of
+ 
+
+ align:start position:0%
+and they were worth about 24 4% of
+retail pharmacy
+
+ align:start position:0%
+retail pharmacy
+ 
+
+ align:start position:0%
+retail pharmacy
+purchases because you go in and buy
+
+ align:start position:0%
+purchases because you go in and buy
+ 
+
+ align:start position:0%
+purchases because you go in and buy
+toothpaste and a greeting card they go
+
+ align:start position:0%
+toothpaste and a greeting card they go
+ 
+
+ align:start position:0%
+toothpaste and a greeting card they go
+in and buy a blood glucose monitor
+
+ align:start position:0%
+in and buy a blood glucose monitor
+ 
+
+ align:start position:0%
+in and buy a blood glucose monitor
+strips right they're worth a lot of
+
+ align:start position:0%
+strips right they're worth a lot of
+ 
+
+ align:start position:0%
+strips right they're worth a lot of
+money so we'd say
+
+ align:start position:0%
+money so we'd say
+ 
+
+ align:start position:0%
+money so we'd say
+well why don't we set it up so you can
+
+ align:start position:0%
+well why don't we set it up so you can
+ 
+
+ align:start position:0%
+well why don't we set it up so you can
+pick it up wherever it is you buy your
+
+ align:start position:0%
+pick it up wherever it is you buy your
+ 
+
+ align:start position:0%
+pick it up wherever it is you buy your
+insulin where is that and they'd say oh
+
+ align:start position:0%
+insulin where is that and they'd say oh
+ 
+
+ align:start position:0%
+insulin where is that and they'd say oh
+Yos Pharmacy I say would you mind if we
+
+ align:start position:0%
+Yos Pharmacy I say would you mind if we
+ 
+
+ align:start position:0%
+Yos Pharmacy I say would you mind if we
+call Yos no no no you tell that turkey
+
+ align:start position:0%
+call Yos no no no you tell that turkey
+ 
+
+ align:start position:0%
+call Yos no no no you tell that turkey
+that Mabel wants to buy this stuff I've
+
+ align:start position:0%
+that Mabel wants to buy this stuff I've
+ 
+
+ align:start position:0%
+that Mabel wants to buy this stuff I've
+been buying from him for years hold on a
+
+ align:start position:0%
+been buying from him for years hold on a
+ 
+
+ align:start position:0%
+been buying from him for years hold on a
+second let me get you his phone
+
+ align:start position:0%
+second let me get you his phone
+ 
+
+ align:start position:0%
+second let me get you his phone
+number right
+
+ align:start position:0%
+number right
+ 
+
+ align:start position:0%
+number right
+so yast would answer the phone we'd say
+
+ align:start position:0%
+so yast would answer the phone we'd say
+ 
+
+ align:start position:0%
+so yast would answer the phone we'd say
+Yos we've just been selling our product
+
+ align:start position:0%
+Yos we've just been selling our product
+ 
+
+ align:start position:0%
+Yos we've just been selling our product
+to five of your customers that have
+
+ align:start position:0%
+to five of your customers that have
+ 
+
+ align:start position:0%
+to five of your customers that have
+diabetes they want to buy it from you
+
+ align:start position:0%
+diabetes they want to buy it from you
+ 
+
+ align:start position:0%
+diabetes they want to buy it from you
+and you don't have
+
+ align:start position:0%
+and you don't have
+ 
+
+ align:start position:0%
+and you don't have
+it what who is this okay let me back up
+
+ align:start position:0%
+it what who is this okay let me back up
+ 
+
+ align:start position:0%
+it what who is this okay let me back up
+ghost and I'd walk him through here's
+
+ align:start position:0%
+ghost and I'd walk him through here's
+ 
+
+ align:start position:0%
+ghost and I'd walk him through here's
+the five customers so what can we do
+
+ align:start position:0%
+the five customers so what can we do
+ 
+
+ align:start position:0%
+the five customers so what can we do
+about that ghost would say well you know
+
+ align:start position:0%
+about that ghost would say well you know
+ 
+
+ align:start position:0%
+about that ghost would say well you know
+we probably ought to have it but I can't
+
+ align:start position:0%
+we probably ought to have it but I can't
+ 
+
+ align:start position:0%
+we probably ought to have it but I can't
+possibly buy this without corporate
+
+ align:start position:0%
+possibly buy this without corporate
+ 
+
+ align:start position:0%
+possibly buy this without corporate
+approval I mean we're just one Walgreens
+
+ align:start position:0%
+approval I mean we're just one Walgreens
+ 
+
+ align:start position:0%
+approval I mean we're just one Walgreens
+right I mean you got to go to Deerfield
+
+ align:start position:0%
+right I mean you got to go to Deerfield
+ 
+
+ align:start position:0%
+right I mean you got to go to Deerfield
+to corporate
+
+ align:start position:0%
+to corporate
+ 
+
+ align:start position:0%
+to corporate
+headquarters Yos we know that but we
+
+ align:start position:0%
+headquarters Yos we know that but we
+ 
+
+ align:start position:0%
+headquarters Yos we know that but we
+also know that there's a level below
+
+ align:start position:0%
+also know that there's a level below
+ 
+
+ align:start position:0%
+also know that there's a level below
+which you can buy without corporate
+
+ align:start position:0%
+which you can buy without corporate
+ 
+
+ align:start position:0%
+which you can buy without corporate
+approval that number is probably
+
+ align:start position:0%
+approval that number is probably
+ 
+
+ align:start position:0%
+approval that number is probably
+$100 well yes it is well you'll be
+
+ align:start position:0%
+$100 well yes it is well you'll be
+ 
+
+ align:start position:0%
+$100 well yes it is well you'll be
+pleased to know that our initial starter
+
+ align:start position:0%
+pleased to know that our initial starter
+ 
+
+ align:start position:0%
+pleased to know that our initial starter
+pack cost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$99.95 and I can take your purchase
+
+ align:start position:0%
+$99.95 and I can take your purchase
+ 
+
+ align:start position:0%
+$99.95 and I can take your purchase
+order right now and by the way if it
+
+ align:start position:0%
+order right now and by the way if it
+ 
+
+ align:start position:0%
+order right now and by the way if it
+doesn't sell you don't need to ship it
+
+ align:start position:0%
+doesn't sell you don't need to ship it
+ 
+
+ align:start position:0%
+doesn't sell you don't need to ship it
+back to us for refund we'll take your
+
+ align:start position:0%
+back to us for refund we'll take your
+ 
+
+ align:start position:0%
+back to us for refund we'll take your
+word for it throw it in the the trash
+
+ align:start position:0%
+word for it throw it in the the trash
+ 
+
+ align:start position:0%
+word for it throw it in the the trash
+we'll send you back the
+
+ align:start position:0%
+we'll send you back the
+ 
+
+ align:start position:0%
+we'll send you back the
+money okay nobody ever mentioned
+
+ align:start position:0%
+money okay nobody ever mentioned
+ 
+
+ align:start position:0%
+money okay nobody ever mentioned
+slotting
+
+ align:start position:0%
+slotting
+ 
+
+ align:start position:0%
+slotting
+fees why not what did we have that gave
+
+ align:start position:0%
+fees why not what did we have that gave
+ 
+
+ align:start position:0%
+fees why not what did we have that gave
+us the ability to trample all over that
+
+ align:start position:0%
+us the ability to trample all over that
+ 
+
+ align:start position:0%
+us the ability to trample all over that
+convention who said
+
+ align:start position:0%
+convention who said
+ 
+
+ align:start position:0%
+convention who said
+customers Excuse me while my heart beats
+
+ align:start position:0%
+customers Excuse me while my heart beats
+ 
+
+ align:start position:0%
+customers Excuse me while my heart beats
+that's exactly
+
+ align:start position:0%
+that's exactly
+ 
+
+ align:start position:0%
+that's exactly
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so we've talked about this a bit
+
+ align:start position:0%
+so we've talked about this a bit
+ 
+
+ align:start position:0%
+so we've talked about this a bit
+the uh oh you know there was a neat
+
+ align:start position:0%
+the uh oh you know there was a neat
+ 
+
+ align:start position:0%
+the uh oh you know there was a neat
+thing we did a lot of these Educators
+
+ align:start position:0%
+thing we did a lot of these Educators
+ 
+
+ align:start position:0%
+thing we did a lot of these Educators
+would have a class on Saturdays one
+
+ align:start position:0%
+would have a class on Saturdays one
+ 
+
+ align:start position:0%
+would have a class on Saturdays one
+Saturday a month they'd bring in all of
+
+ align:start position:0%
+Saturday a month they'd bring in all of
+ 
+
+ align:start position:0%
+Saturday a month they'd bring in all of
+their people talk about new developments
+
+ align:start position:0%
+their people talk about new developments
+ 
+
+ align:start position:0%
+their people talk about new developments
+in Diabetes Care and like everybody
+
+ align:start position:0%
+in Diabetes Care and like everybody
+ 
+
+ align:start position:0%
+in Diabetes Care and like everybody
+who's got to write a monthly column or a
+
+ align:start position:0%
+who's got to write a monthly column or a
+ 
+
+ align:start position:0%
+who's got to write a monthly column or a
+blog or whatever it's hard to come up
+
+ align:start position:0%
+blog or whatever it's hard to come up
+ 
+
+ align:start position:0%
+blog or whatever it's hard to come up
+with content so we'd say well when's
+
+ align:start position:0%
+with content so we'd say well when's
+ 
+
+ align:start position:0%
+with content so we'd say well when's
+your next one of these oh it's a week
+
+ align:start position:0%
+your next one of these oh it's a week
+ 
+
+ align:start position:0%
+your next one of these oh it's a week
+and a half do you if you have your whole
+
+ align:start position:0%
+and a half do you if you have your whole
+ 
+
+ align:start position:0%
+and a half do you if you have your whole
+agenda set up yet no if you like this
+
+ align:start position:0%
+agenda set up yet no if you like this
+ 
+
+ align:start position:0%
+agenda set up yet no if you like this
+would this be something worth talking
+
+ align:start position:0%
+would this be something worth talking
+ 
+
+ align:start position:0%
+would this be something worth talking
+about to your patient population well
+
+ align:start position:0%
+about to your patient population well
+ 
+
+ align:start position:0%
+about to your patient population well
+yeah actually well we'll send you the
+
+ align:start position:0%
+yeah actually well we'll send you the
+ 
+
+ align:start position:0%
+yeah actually well we'll send you the
+stuff we'll send you the literature but
+
+ align:start position:0%
+stuff we'll send you the literature but
+ 
+
+ align:start position:0%
+stuff we'll send you the literature but
+let's suppose they do like it they're
+
+ align:start position:0%
+let's suppose they do like it they're
+ 
+
+ align:start position:0%
+let's suppose they do like it they're
+going to ask you three
+
+ align:start position:0%
+going to ask you three
+ 
+
+ align:start position:0%
+going to ask you three
+questions how's it taste how much does
+
+ align:start position:0%
+questions how's it taste how much does
+ 
+
+ align:start position:0%
+questions how's it taste how much does
+it cost where can I get
+
+ align:start position:0%
+it cost where can I get
+ 
+
+ align:start position:0%
+it cost where can I get
+it tastes like chocolate fudge you'll
+
+ align:start position:0%
+it tastes like chocolate fudge you'll
+ 
+
+ align:start position:0%
+it tastes like chocolate fudge you'll
+figure that out for yourself it's a
+
+ align:start position:0%
+figure that out for yourself it's a
+ 
+
+ align:start position:0%
+figure that out for yourself it's a
+dollar a bar how do we answer the third
+
+ align:start position:0%
+dollar a bar how do we answer the third
+ 
+
+ align:start position:0%
+dollar a bar how do we answer the third
+question oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+man there's a shop right I send all of
+
+ align:start position:0%
+man there's a shop right I send all of
+ 
+
+ align:start position:0%
+man there's a shop right I send all of
+my people
+
+ align:start position:0%
+my people
+ 
+
+ align:start position:0%
+my people
+too well can we call him and tell him
+
+ align:start position:0%
+too well can we call him and tell him
+ 
+
+ align:start position:0%
+too well can we call him and tell him
+that a week from now you're going to a
+
+ align:start position:0%
+that a week from now you're going to a
+ 
+
+ align:start position:0%
+that a week from now you're going to a
+week and a half from now you're going to
+
+ align:start position:0%
+week and a half from now you're going to
+ 
+
+ align:start position:0%
+week and a half from now you're going to
+be sending some people no we can do
+
+ align:start position:0%
+be sending some people no we can do
+ 
+
+ align:start position:0%
+be sending some people no we can do
+better than that tell that bonehead to
+
+ align:start position:0%
+better than that tell that bonehead to
+ 
+
+ align:start position:0%
+better than that tell that bonehead to
+get in here on Saturday morning he can
+
+ align:start position:0%
+get in here on Saturday morning he can
+ 
+
+ align:start position:0%
+get in here on Saturday morning he can
+stand up and talk to him himself and he
+
+ align:start position:0%
+stand up and talk to him himself and he
+ 
+
+ align:start position:0%
+stand up and talk to him himself and he
+can see what we're doing and he'll stock
+
+ align:start position:0%
+can see what we're doing and he'll stock
+ 
+
+ align:start position:0%
+can see what we're doing and he'll stock
+the product very cool pharmacists would
+
+ align:start position:0%
+the product very cool pharmacists would
+ 
+
+ align:start position:0%
+the product very cool pharmacists would
+agree nobody ever mentioned slotting
+
+ align:start position:0%
+agree nobody ever mentioned slotting
+ 
+
+ align:start position:0%
+agree nobody ever mentioned slotting
+fees and I bet you know you know why
+
+ align:start position:0%
+fees and I bet you know you know why
+ 
+
+ align:start position:0%
+fees and I bet you know you know why
+not so was good now we were in with the
+
+ align:start position:0%
+not so was good now we were in with the
+ 
+
+ align:start position:0%
+not so was good now we were in with the
+retailers but one day we discovered
+
+ align:start position:0%
+retailers but one day we discovered
+ 
+
+ align:start position:0%
+retailers but one day we discovered
+retailers really didn't want to deal
+
+ align:start position:0%
+retailers really didn't want to deal
+ 
+
+ align:start position:0%
+retailers really didn't want to deal
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+us they wanted to deal with
+
+ align:start position:0%
+us they wanted to deal with
+ 
+
+ align:start position:0%
+us they wanted to deal with
+wholesalers why
+
+ align:start position:0%
+wholesalers why
+ 
+
+ align:start position:0%
+wholesalers why
+not well there's about 5,000 different
+
+ align:start position:0%
+not well there's about 5,000 different
+ 
+
+ align:start position:0%
+not well there's about 5,000 different
+items in even a small drugstore and they
+
+ align:start position:0%
+items in even a small drugstore and they
+ 
+
+ align:start position:0%
+items in even a small drugstore and they
+don't want to be sending out 5,000
+
+ align:start position:0%
+don't want to be sending out 5,000
+ 
+
+ align:start position:0%
+don't want to be sending out 5,000
+taking in 5,000 invoices and sending out
+
+ align:start position:0%
+taking in 5,000 invoices and sending out
+ 
+
+ align:start position:0%
+taking in 5,000 invoices and sending out
+5,000 checks so wholesaler consolidates
+
+ align:start position:0%
+5,000 checks so wholesaler consolidates
+ 
+
+ align:start position:0%
+5,000 checks so wholesaler consolidates
+all that the truck comes brings them a
+
+ align:start position:0%
+all that the truck comes brings them a
+ 
+
+ align:start position:0%
+all that the truck comes brings them a
+bin sends them one
+
+ align:start position:0%
+bin sends them one
+ 
+
+ align:start position:0%
+bin sends them one
+bill now if you think getting into a
+
+ align:start position:0%
+bill now if you think getting into a
+ 
+
+ align:start position:0%
+bill now if you think getting into a
+retailer is difficult try the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wholesaler so we said
+
+ align:start position:0%
+wholesaler so we said
+ 
+
+ align:start position:0%
+wholesaler so we said
+well if we could do this oh my goodness
+
+ align:start position:0%
+well if we could do this oh my goodness
+ 
+
+ align:start position:0%
+well if we could do this oh my goodness
+we just need wheelbarrows to carry out
+
+ align:start position:0%
+we just need wheelbarrows to carry out
+ 
+
+ align:start position:0%
+we just need wheelbarrows to carry out
+all the
+
+ align:start position:0%
+all the
+ 
+
+ align:start position:0%
+all the
+money how do we do it we said well what
+
+ align:start position:0%
+money how do we do it we said well what
+ 
+
+ align:start position:0%
+money how do we do it we said well what
+do the wholesalers care
+
+ align:start position:0%
+do the wholesalers care
+ 
+
+ align:start position:0%
+do the wholesalers care
+about the wholesalers want to know know
+
+ align:start position:0%
+about the wholesalers want to know know
+ 
+
+ align:start position:0%
+about the wholesalers want to know know
+that there's an order already there that
+
+ align:start position:0%
+that there's an order already there that
+ 
+
+ align:start position:0%
+that there's an order already there that
+this is going to be painless they're
+
+ align:start position:0%
+this is going to be painless they're
+ 
+
+ align:start position:0%
+this is going to be painless they're
+fundamentally
+
+ align:start position:0%
+fundamentally
+ 
+
+ align:start position:0%
+fundamentally
+lazy make it easy for them we said
+
+ align:start position:0%
+lazy make it easy for them we said
+ 
+
+ align:start position:0%
+lazy make it easy for them we said
+okay what can we
+
+ align:start position:0%
+okay what can we
+ 
+
+ align:start position:0%
+okay what can we
+do we looked about and realized there
+
+ align:start position:0%
+do we looked about and realized there
+ 
+
+ align:start position:0%
+do we looked about and realized there
+was a trade show coming up in New
+
+ align:start position:0%
+was a trade show coming up in New
+ 
+
+ align:start position:0%
+was a trade show coming up in New
+Orleans we hadn't planned to go but we
+
+ align:start position:0%
+Orleans we hadn't planned to go but we
+ 
+
+ align:start position:0%
+Orleans we hadn't planned to go but we
+said we we ought to go and let's find
+
+ align:start position:0%
+said we we ought to go and let's find
+ 
+
+ align:start position:0%
+said we we ought to go and let's find
+the 25 drugstores I think it was
+
+ align:start position:0%
+the 25 drugstores I think it was
+ 
+
+ align:start position:0%
+the 25 drugstores I think it was
+Walgreens that are surrounding the
+
+ align:start position:0%
+Walgreens that are surrounding the
+ 
+
+ align:start position:0%
+Walgreens that are surrounding the
+area and let's tell them them that we're
+
+ align:start position:0%
+area and let's tell them them that we're
+ 
+
+ align:start position:0%
+area and let's tell them them that we're
+going to be at this show we're going to
+
+ align:start position:0%
+going to be at this show we're going to
+ 
+
+ align:start position:0%
+going to be at this show we're going to
+be meeting with the Educators and we're
+
+ align:start position:0%
+be meeting with the Educators and we're
+ 
+
+ align:start position:0%
+be meeting with the Educators and we're
+going to be pimping excuse me
+
+ align:start position:0%
+going to be pimping excuse me
+ 
+
+ align:start position:0%
+going to be pimping excuse me
+selling our product and that they should
+
+ align:start position:0%
+selling our product and that they should
+ 
+
+ align:start position:0%
+selling our product and that they should
+stock it and in fact they should
+
+ align:start position:0%
+stock it and in fact they should
+ 
+
+ align:start position:0%
+stock it and in fact they should
+pre-order it which we did they took the
+
+ align:start position:0%
+pre-order it which we did they took the
+ 
+
+ align:start position:0%
+pre-order it which we did they took the
+orders or pardon me they gave us their
+
+ align:start position:0%
+orders or pardon me they gave us their
+ 
+
+ align:start position:0%
+orders or pardon me they gave us their
+orders and then we called the wholesaler
+
+ align:start position:0%
+orders and then we called the wholesaler
+ 
+
+ align:start position:0%
+orders and then we called the wholesaler
+that Walgreens used and said you don't
+
+ align:start position:0%
+that Walgreens used and said you don't
+ 
+
+ align:start position:0%
+that Walgreens used and said you don't
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+me but I've sold a bunch of this product
+
+ align:start position:0%
+me but I've sold a bunch of this product
+ 
+
+ align:start position:0%
+me but I've sold a bunch of this product
+and I've built in a margin for
+
+ align:start position:0%
+and I've built in a margin for
+ 
+
+ align:start position:0%
+and I've built in a margin for
+you you don't have to do anything I'm
+
+ align:start position:0%
+you you don't have to do anything I'm
+ 
+
+ align:start position:0%
+you you don't have to do anything I'm
+going to take their order I'm going to
+
+ align:start position:0%
+going to take their order I'm going to
+ 
+
+ align:start position:0%
+going to take their order I'm going to
+ship their product I'm going to send you
+
+ align:start position:0%
+ship their product I'm going to send you
+ 
+
+ align:start position:0%
+ship their product I'm going to send you
+the money that you would have earned if
+
+ align:start position:0%
+the money that you would have earned if
+ 
+
+ align:start position:0%
+the money that you would have earned if
+You' done this even though you haven't
+
+ align:start position:0%
+You' done this even though you haven't
+ 
+
+ align:start position:0%
+You' done this even though you haven't
+earned it and you haven't done anything
+
+ align:start position:0%
+earned it and you haven't done anything
+ 
+
+ align:start position:0%
+earned it and you haven't done anything
+what I want is for you to put us in your
+
+ align:start position:0%
+what I want is for you to put us in your
+ 
+
+ align:start position:0%
+what I want is for you to put us in your
+system just key Us in the system so that
+
+ align:start position:0%
+system just key Us in the system so that
+ 
+
+ align:start position:0%
+system just key Us in the system so that
+if they reorder they can call you and
+
+ align:start position:0%
+if they reorder they can call you and
+ 
+
+ align:start position:0%
+if they reorder they can call you and
+I've built a business for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you tell me that again
+
+ align:start position:0%
+you tell me that again
+ 
+
+ align:start position:0%
+you tell me that again
+right but I wanted to be able to say to
+
+ align:start position:0%
+right but I wanted to be able to say to
+ 
+
+ align:start position:0%
+right but I wanted to be able to say to
+the Walgreens when they said GE we've
+
+ align:start position:0%
+the Walgreens when they said GE we've
+ 
+
+ align:start position:0%
+the Walgreens when they said GE we've
+sold all that stuff we could say great
+
+ align:start position:0%
+sold all that stuff we could say great
+ 
+
+ align:start position:0%
+sold all that stuff we could say great
+call your wholesaler he's got it of
+
+ align:start position:0%
+call your wholesaler he's got it of
+ 
+
+ align:start position:0%
+call your wholesaler he's got it of
+course he didn't but he was in the
+
+ align:start position:0%
+course he didn't but he was in the
+ 
+
+ align:start position:0%
+course he didn't but he was in the
+system wholesaler called us
+
+ align:start position:0%
+system wholesaler called us
+ 
+
+ align:start position:0%
+system wholesaler called us
+poof off we went one last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example we got a letter one day sitting
+
+ align:start position:0%
+example we got a letter one day sitting
+ 
+
+ align:start position:0%
+example we got a letter one day sitting
+in the office from a major Retail
+
+ align:start position:0%
+in the office from a major Retail
+ 
+
+ align:start position:0%
+in the office from a major Retail
+Pharmacy chain headquarted in clear
+
+ align:start position:0%
+Pharmacy chain headquarted in clear
+ 
+
+ align:start position:0%
+Pharmacy chain headquarted in clear
+waterer
+
+ align:start position:0%
+waterer
+ 
+
+ align:start position:0%
+waterer
+Florida we're drawing up our planogram
+
+ align:start position:0%
+Florida we're drawing up our planogram
+ 
+
+ align:start position:0%
+Florida we're drawing up our planogram
+for the coming year who can tell us what
+
+ align:start position:0%
+for the coming year who can tell us what
+ 
+
+ align:start position:0%
+for the coming year who can tell us what
+a planogram
+
+ align:start position:0%
+a planogram
+ 
+
+ align:start position:0%
+a planogram
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sir that's exactly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right when you walk in and you see all
+
+ align:start position:0%
+right when you walk in and you see all
+ 
+
+ align:start position:0%
+right when you walk in and you see all
+these products at different places
+
+ align:start position:0%
+these products at different places
+ 
+
+ align:start position:0%
+these products at different places
+they've got that laid out like a
+
+ align:start position:0%
+they've got that laid out like a
+ 
+
+ align:start position:0%
+they've got that laid out like a
+blueprint and many places in fact have a
+
+ align:start position:0%
+blueprint and many places in fact have a
+ 
+
+ align:start position:0%
+blueprint and many places in fact have a
+room somewhere near their corporate
+
+ align:start position:0%
+room somewhere near their corporate
+ 
+
+ align:start position:0%
+room somewhere near their corporate
+headquarters with shelves and they put
+
+ align:start position:0%
+headquarters with shelves and they put
+ 
+
+ align:start position:0%
+headquarters with shelves and they put
+stuff on it and they step back to look
+
+ align:start position:0%
+stuff on it and they step back to look
+ 
+
+ align:start position:0%
+stuff on it and they step back to look
+at it and they photograph it and I mean
+
+ align:start position:0%
+at it and they photograph it and I mean
+ 
+
+ align:start position:0%
+at it and they photograph it and I mean
+there's of analysis we're putting
+
+ align:start position:0%
+there's of analysis we're putting
+ 
+
+ align:start position:0%
+there's of analysis we're putting
+together our planogram for the coming
+
+ align:start position:0%
+together our planogram for the coming
+ 
+
+ align:start position:0%
+together our planogram for the coming
+year if you'd like to be a part of it
+
+ align:start position:0%
+year if you'd like to be a part of it
+ 
+
+ align:start position:0%
+year if you'd like to be a part of it
+you have to come to Clearwater Florida
+
+ align:start position:0%
+you have to come to Clearwater Florida
+ 
+
+ align:start position:0%
+you have to come to Clearwater Florida
+for a 15minute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+meeting we didn't solicit this letter
+
+ align:start position:0%
+meeting we didn't solicit this letter
+ 
+
+ align:start position:0%
+meeting we didn't solicit this letter
+just sort of washed in they evidently
+
+ align:start position:0%
+just sort of washed in they evidently
+ 
+
+ align:start position:0%
+just sort of washed in they evidently
+had heard about
+
+ align:start position:0%
+had heard about
+ 
+
+ align:start position:0%
+had heard about
+us
+
+ align:start position:0%
+us
+ 
+
+ align:start position:0%
+us
+so I
+
+ align:start position:0%
+so I
+ 
+
+ align:start position:0%
+so I
+said who runs this meeting well it's a
+
+ align:start position:0%
+said who runs this meeting well it's a
+ 
+
+ align:start position:0%
+said who runs this meeting well it's a
+guy named Jeff I called a few people I
+
+ align:start position:0%
+guy named Jeff I called a few people I
+ 
+
+ align:start position:0%
+guy named Jeff I called a few people I
+knew in the industry and said how is
+
+ align:start position:0%
+knew in the industry and said how is
+ 
+
+ align:start position:0%
+knew in the industry and said how is
+Jeff rewarded for this they said Jeff
+
+ align:start position:0%
+Jeff rewarded for this they said Jeff
+ 
+
+ align:start position:0%
+Jeff rewarded for this they said Jeff
+spends a whole week having one 15minute
+
+ align:start position:0%
+spends a whole week having one 15minute
+ 
+
+ align:start position:0%
+spends a whole week having one 15minute
+conversation after another all day long
+
+ align:start position:0%
+conversation after another all day long
+ 
+
+ align:start position:0%
+conversation after another all day long
+five straight days oh my God this sounds
+
+ align:start position:0%
+five straight days oh my God this sounds
+ 
+
+ align:start position:0%
+five straight days oh my God this sounds
+like something out of Dante's Inferno or
+
+ align:start position:0%
+like something out of Dante's Inferno or
+ 
+
+ align:start position:0%
+like something out of Dante's Inferno or
+something this is terrible but he's
+
+ align:start position:0%
+something this is terrible but he's
+ 
+
+ align:start position:0%
+something this is terrible but he's
+rewarded by the amount of slotting fees
+
+ align:start position:0%
+rewarded by the amount of slotting fees
+ 
+
+ align:start position:0%
+rewarded by the amount of slotting fees
+that he can extort from these eager
+
+ align:start position:0%
+that he can extort from these eager
+ 
+
+ align:start position:0%
+that he can extort from these eager
+vendors I said well we don't have any
+
+ align:start position:0%
+vendors I said well we don't have any
+ 
+
+ align:start position:0%
+vendors I said well we don't have any
+money
+
+ align:start position:0%
+money
+ 
+
+ align:start position:0%
+money
+but let's do it
+
+ align:start position:0%
+but let's do it
+ 
+
+ align:start position:0%
+but let's do it
+anyway so we went down there and we're
+
+ align:start position:0%
+anyway so we went down there and we're
+ 
+
+ align:start position:0%
+anyway so we went down there and we're
+sitting in this huge Lobby and there are
+
+ align:start position:0%
+sitting in this huge Lobby and there are
+ 
+
+ align:start position:0%
+sitting in this huge Lobby and there are
+all these people with these like poster
+
+ align:start position:0%
+all these people with these like poster
+ 
+
+ align:start position:0%
+all these people with these like poster
+boards that look like endcaps and
+
+ align:start position:0%
+boards that look like endcaps and
+ 
+
+ align:start position:0%
+boards that look like endcaps and
+briefcases that open out to be these
+
+ align:start position:0%
+briefcases that open out to be these
+ 
+
+ align:start position:0%
+briefcases that open out to be these
+fabulous displays and they're all
+
+ align:start position:0%
+fabulous displays and they're all
+ 
+
+ align:start position:0%
+fabulous displays and they're all
+sitting there like God can I walk your
+
+ align:start position:0%
+sitting there like God can I walk your
+ 
+
+ align:start position:0%
+sitting there like God can I walk your
+dog can I pick up your dry cleaning
+
+ align:start position:0%
+dog can I pick up your dry cleaning
+ 
+
+ align:start position:0%
+dog can I pick up your dry cleaning
+please put me on your
+
+ align:start position:0%
+please put me on your
+ 
+
+ align:start position:0%
+please put me on your
+shelves there were two of us there and
+
+ align:start position:0%
+shelves there were two of us there and
+ 
+
+ align:start position:0%
+shelves there were two of us there and
+we were
+
+ align:start position:0%
+we were
+ 
+
+ align:start position:0%
+we were
+empty-handed other than one little
+
+ align:start position:0%
+empty-handed other than one little
+ 
+
+ align:start position:0%
+empty-handed other than one little
+portfolio we came in and we said this
+
+ align:start position:0%
+portfolio we came in and we said this
+ 
+
+ align:start position:0%
+portfolio we came in and we said this
+isn't going to be like your other
+
+ align:start position:0%
+isn't going to be like your other
+ 
+
+ align:start position:0%
+isn't going to be like your other
+15minute meetings this week because
+
+ align:start position:0%
+15minute meetings this week because
+ 
+
+ align:start position:0%
+15minute meetings this week because
+we're startup we don't have any money
+
+ align:start position:0%
+we're startup we don't have any money
+ 
+
+ align:start position:0%
+we're startup we don't have any money
+we're not going to give you a
+
+ align:start position:0%
+we're not going to give you a
+ 
+
+ align:start position:0%
+we're not going to give you a
+nickel but we propose to spend five
+
+ align:start position:0%
+nickel but we propose to spend five
+ 
+
+ align:start position:0%
+nickel but we propose to spend five
+minutes telling you who we are five
+
+ align:start position:0%
+minutes telling you who we are five
+ 
+
+ align:start position:0%
+minutes telling you who we are five
+minutes telling you what our product is
+
+ align:start position:0%
+minutes telling you what our product is
+ 
+
+ align:start position:0%
+minutes telling you what our product is
+and five minutes telling you why you
+
+ align:start position:0%
+and five minutes telling you why you
+ 
+
+ align:start position:0%
+and five minutes telling you why you
+want us on your shelves
+
+ align:start position:0%
+want us on your shelves
+ 
+
+ align:start position:0%
+want us on your shelves
+anyway and he sort of kicked back in his
+
+ align:start position:0%
+anyway and he sort of kicked back in his
+ 
+
+ align:start position:0%
+anyway and he sort of kicked back in his
+chair and he said well it's your 15
+
+ align:start position:0%
+chair and he said well it's your 15
+ 
+
+ align:start position:0%
+chair and he said well it's your 15
+minutes sport whatever you want to
+
+ align:start position:0%
+minutes sport whatever you want to
+ 
+
+ align:start position:0%
+minutes sport whatever you want to
+do so
+
+ align:start position:0%
+do so
+ 
+
+ align:start position:0%
+do so
+we spent the first 10 minutes saying
+
+ align:start position:0%
+we spent the first 10 minutes saying
+ 
+
+ align:start position:0%
+we spent the first 10 minutes saying
+we're so fabulous as you would
+
+ align:start position:0%
+we're so fabulous as you would
+ 
+
+ align:start position:0%
+we're so fabulous as you would
+expect and in the last five minutes we
+
+ align:start position:0%
+expect and in the last five minutes we
+ 
+
+ align:start position:0%
+expect and in the last five minutes we
+said Jeff this print out is of the
+
+ align:start position:0%
+said Jeff this print out is of the
+ 
+
+ align:start position:0%
+said Jeff this print out is of the
+people with
+
+ align:start position:0%
+people with
+ 
+
+ align:start position:0%
+people with
+diabetes that have contacted us in the
+
+ align:start position:0%
+diabetes that have contacted us in the
+ 
+
+ align:start position:0%
+diabetes that have contacted us in the
+states where you have
+
+ align:start position:0%
+states where you have
+ 
+
+ align:start position:0%
+states where you have
+stores there's 10,000 of
+
+ align:start position:0%
+stores there's 10,000 of
+ 
+
+ align:start position:0%
+stores there's 10,000 of
+them all of us are asking us the same
+
+ align:start position:0%
+them all of us are asking us the same
+ 
+
+ align:start position:0%
+them all of us are asking us the same
+question where can I go
+
+ align:start position:0%
+question where can I go
+ 
+
+ align:start position:0%
+question where can I go
+to buy your product how would you like
+
+ align:start position:0%
+to buy your product how would you like
+ 
+
+ align:start position:0%
+to buy your product how would you like
+us to answer their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question he sat
+
+ align:start position:0%
+question he sat
+ 
+
+ align:start position:0%
+question he sat
+there and he looked at us for almost a
+
+ align:start position:0%
+there and he looked at us for almost a
+ 
+
+ align:start position:0%
+there and he looked at us for almost a
+minute which is like I'm hold your
+
+ align:start position:0%
+minute which is like I'm hold your
+ 
+
+ align:start position:0%
+minute which is like I'm hold your
+breath for a minute sometime it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+agonizing and he started grinning and he
+
+ align:start position:0%
+agonizing and he started grinning and he
+ 
+
+ align:start position:0%
+agonizing and he started grinning and he
+said okay you're
+
+ align:start position:0%
+said okay you're
+ 
+
+ align:start position:0%
+said okay you're
+in so he said well you know we want to
+
+ align:start position:0%
+in so he said well you know we want to
+ 
+
+ align:start position:0%
+in so he said well you know we want to
+Stage this we'll go in where we built
+
+ align:start position:0%
+Stage this we'll go in where we built
+ 
+
+ align:start position:0%
+Stage this we'll go in where we built
+the demand I hate returns and Etc but
+
+ align:start position:0%
+the demand I hate returns and Etc but
+ 
+
+ align:start position:0%
+the demand I hate returns and Etc but
+Nar a word about slotting fees I bet you
+
+ align:start position:0%
+Nar a word about slotting fees I bet you
+ 
+
+ align:start position:0%
+Nar a word about slotting fees I bet you
+can guess the next thing that's going to
+
+ align:start position:0%
+can guess the next thing that's going to
+ 
+
+ align:start position:0%
+can guess the next thing that's going to
+pop up why not what gave us that
+
+ align:start position:0%
+pop up why not what gave us that
+ 
+
+ align:start position:0%
+pop up why not what gave us that
+negotiating power we
+
+ align:start position:0%
+negotiating power we
+ 
+
+ align:start position:0%
+negotiating power we
+had thank
+
+ align:start position:0%
+had thank
+ 
+
+ align:start position:0%
+had thank
+you it wasn't for being smart or
+
+ align:start position:0%
+you it wasn't for being smart or
+ 
+
+ align:start position:0%
+you it wasn't for being smart or
+charming or anything else it was just
+
+ align:start position:0%
+charming or anything else it was just
+ 
+
+ align:start position:0%
+charming or anything else it was just
+good old hard work but we came in there
+
+ align:start position:0%
+good old hard work but we came in there
+ 
+
+ align:start position:0%
+good old hard work but we came in there
+and essentially
+
+ align:start position:0%
+and essentially
+ 
+
+ align:start position:0%
+and essentially
+said you're not generating the demand we
+
+ align:start position:0%
+said you're not generating the demand we
+ 
+
+ align:start position:0%
+said you're not generating the demand we
+we are so we're not paying you for it
+
+ align:start position:0%
+we are so we're not paying you for it
+ 
+
+ align:start position:0%
+we are so we're not paying you for it
+we're bringing you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+business so impressive growth in sales
+
+ align:start position:0%
+business so impressive growth in sales
+ 
+
+ align:start position:0%
+business so impressive growth in sales
+real high reorder rate a lot of good
+
+ align:start position:0%
+real high reorder rate a lot of good
+ 
+
+ align:start position:0%
+real high reorder rate a lot of good
+publicity ended up selling the business
+
+ align:start position:0%
+publicity ended up selling the business
+ 
+
+ align:start position:0%
+publicity ended up selling the business
+to a billion dooll pharmaceutical
+
+ align:start position:0%
+to a billion dooll pharmaceutical
+ 
+
+ align:start position:0%
+to a billion dooll pharmaceutical
+firm everybody was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I was 10 years older at the end of
+
+ align:start position:0%
+so I was 10 years older at the end of
+ 
+
+ align:start position:0%
+so I was 10 years older at the end of
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+years but I learned a
+
+ align:start position:0%
+years but I learned a
+ 
+
+ align:start position:0%
+years but I learned a
+lot so tell me what should I have
+
+ align:start position:0%
+lot so tell me what should I have
+ 
+
+ align:start position:0%
+lot so tell me what should I have
+learned from this what might you have
+
+ align:start position:0%
+learned from this what might you have
+ 
+
+ align:start position:0%
+learned from this what might you have
+learned given that many of you raised
+
+ align:start position:0%
+learned given that many of you raised
+ 
+
+ align:start position:0%
+learned given that many of you raised
+your hands when you said you were in
+
+ align:start position:0%
+your hands when you said you were in
+ 
+
+ align:start position:0%
+your hands when you said you were in
+process of doing all this stuff what
+
+ align:start position:0%
+process of doing all this stuff what
+ 
+
+ align:start position:0%
+process of doing all this stuff what
+should I have learned what should you
+
+ align:start position:0%
+should I have learned what should you
+ 
+
+ align:start position:0%
+should I have learned what should you
+have learned that will help facilitate
+
+ align:start position:0%
+have learned that will help facilitate
+ 
+
+ align:start position:0%
+have learned that will help facilitate
+your progress with your business and my
+
+ align:start position:0%
+your progress with your business and my
+ 
+
+ align:start position:0%
+your progress with your business and my
+current Venture so let's have some hands
+
+ align:start position:0%
+current Venture so let's have some hands
+ 
+
+ align:start position:0%
+current Venture so let's have some hands
+tell me what I what I should have
+
+ align:start position:0%
+tell me what I what I should have
+ 
+
+ align:start position:0%
+tell me what I what I should have
+learned from this and which maybe you
+
+ align:start position:0%
+learned from this and which maybe you
+ 
+
+ align:start position:0%
+learned from this and which maybe you
+can have gleaned what mistakes should I
+
+ align:start position:0%
+can have gleaned what mistakes should I
+ 
+
+ align:start position:0%
+can have gleaned what mistakes should I
+avoid going forward what things should I
+
+ align:start position:0%
+avoid going forward what things should I
+ 
+
+ align:start position:0%
+avoid going forward what things should I
+do that were right help me
+
+ align:start position:0%
+do that were right help me
+ 
+
+ align:start position:0%
+do that were right help me
+out in the back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes did everybody hear that
+
+ align:start position:0%
+yes did everybody hear that
+ 
+
+ align:start position:0%
+yes did everybody hear that
+okay let me paraphrase with the first
+
+ align:start position:0%
+okay let me paraphrase with the first
+ 
+
+ align:start position:0%
+okay let me paraphrase with the first
+one the disaster I did focus on some of
+
+ align:start position:0%
+one the disaster I did focus on some of
+ 
+
+ align:start position:0%
+one the disaster I did focus on some of
+the stakeholders but not the key ones
+
+ align:start position:0%
+the stakeholders but not the key ones
+ 
+
+ align:start position:0%
+the stakeholders but not the key ones
+not the customers who are actually going
+
+ align:start position:0%
+not the customers who are actually going
+ 
+
+ align:start position:0%
+not the customers who are actually going
+to buy it it's important to know and I
+
+ align:start position:0%
+to buy it it's important to know and I
+ 
+
+ align:start position:0%
+to buy it it's important to know and I
+think I asked this question of one of
+
+ align:start position:0%
+think I asked this question of one of
+ 
+
+ align:start position:0%
+think I asked this question of one of
+you who's going to write the check who's
+
+ align:start position:0%
+you who's going to write the check who's
+ 
+
+ align:start position:0%
+you who's going to write the check who's
+actually going to put their money on the
+
+ align:start position:0%
+actually going to put their money on the
+ 
+
+ align:start position:0%
+actually going to put their money on the
+table for this and then who influences
+
+ align:start position:0%
+table for this and then who influences
+ 
+
+ align:start position:0%
+table for this and then who influences
+them so that's uh certainly one of the
+
+ align:start position:0%
+them so that's uh certainly one of the
+ 
+
+ align:start position:0%
+them so that's uh certainly one of the
+more painful but crucial lessons
+
+ align:start position:0%
+more painful but crucial lessons
+ 
+
+ align:start position:0%
+more painful but crucial lessons
+anything else
+
+ align:start position:0%
+anything else
+ 
+
+ align:start position:0%
+anything else
+else that's fundamentally it by the way
+
+ align:start position:0%
+else that's fundamentally it by the way
+ 
+
+ align:start position:0%
+else that's fundamentally it by the way
+but if if you got nothing else listen to
+
+ align:start position:0%
+but if if you got nothing else listen to
+ 
+
+ align:start position:0%
+but if if you got nothing else listen to
+that yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sir well we certainly
+
+ align:start position:0%
+sir well we certainly
+ 
+
+ align:start position:0%
+sir well we certainly
+tried this gentleman said we made it
+
+ align:start position:0%
+tried this gentleman said we made it
+ 
+
+ align:start position:0%
+tried this gentleman said we made it
+almost impossible for everyone we
+
+ align:start position:0%
+almost impossible for everyone we
+ 
+
+ align:start position:0%
+almost impossible for everyone we
+contacted to say no how did we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that go ahead
+
+ align:start position:0%
+that go ahead
+ 
+
+ align:start position:0%
+that go ahead
+sir that was part of it but each time I
+
+ align:start position:0%
+sir that was part of it but each time I
+ 
+
+ align:start position:0%
+sir that was part of it but each time I
+call somebody that didn't know me what
+
+ align:start position:0%
+call somebody that didn't know me what
+ 
+
+ align:start position:0%
+call somebody that didn't know me what
+homework did I do
+
+ align:start position:0%
+homework did I do
+ 
+
+ align:start position:0%
+homework did I do
+first pardon me filing out what
+
+ align:start position:0%
+first pardon me filing out what
+ 
+
+ align:start position:0%
+first pardon me filing out what
+motivates them what do they care about
+
+ align:start position:0%
+motivates them what do they care about
+ 
+
+ align:start position:0%
+motivates them what do they care about
+all right people think of
+
+ align:start position:0%
+all right people think of
+ 
+
+ align:start position:0%
+all right people think of
+selling as this sort of Tainted activity
+
+ align:start position:0%
+selling as this sort of Tainted activity
+ 
+
+ align:start position:0%
+selling as this sort of Tainted activity
+and it can
+
+ align:start position:0%
+and it can
+ 
+
+ align:start position:0%
+and it can
+be but a hugely important component of
+
+ align:start position:0%
+be but a hugely important component of
+ 
+
+ align:start position:0%
+be but a hugely important component of
+it is just finding out what people
+
+ align:start position:0%
+it is just finding out what people
+ 
+
+ align:start position:0%
+it is just finding out what people
+want okay I think you need to know what
+
+ align:start position:0%
+want okay I think you need to know what
+ 
+
+ align:start position:0%
+want okay I think you need to know what
+they're really buying
+
+ align:start position:0%
+they're really buying
+ 
+
+ align:start position:0%
+they're really buying
+and I think you have to have some
+
+ align:start position:0%
+and I think you have to have some
+ 
+
+ align:start position:0%
+and I think you have to have some
+positioning I think if you have a
+
+ align:start position:0%
+positioning I think if you have a
+ 
+
+ align:start position:0%
+positioning I think if you have a
+product that's for everyone I'm sorry to
+
+ align:start position:0%
+product that's for everyone I'm sorry to
+ 
+
+ align:start position:0%
+product that's for everyone I'm sorry to
+tell you this but it's my opinion that
+
+ align:start position:0%
+tell you this but it's my opinion that
+ 
+
+ align:start position:0%
+tell you this but it's my opinion that
+it's not actually for anyone you need
+
+ align:start position:0%
+it's not actually for anyone you need
+ 
+
+ align:start position:0%
+it's not actually for anyone you need
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+focus and I'm also sorry to tell you
+
+ align:start position:0%
+focus and I'm also sorry to tell you
+ 
+
+ align:start position:0%
+focus and I'm also sorry to tell you
+nobody actually needs your product they
+
+ align:start position:0%
+nobody actually needs your product they
+ 
+
+ align:start position:0%
+nobody actually needs your product they
+might need the benefits I actually don't
+
+ align:start position:0%
+might need the benefits I actually don't
+ 
+
+ align:start position:0%
+might need the benefits I actually don't
+need these
+
+ align:start position:0%
+need these
+ 
+
+ align:start position:0%
+need these
+glasses what I need is to see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+better so I hired in the consumer sense
+
+ align:start position:0%
+better so I hired in the consumer sense
+ 
+
+ align:start position:0%
+better so I hired in the consumer sense
+of the term I hired glass
+
+ align:start position:0%
+of the term I hired glass
+ 
+
+ align:start position:0%
+of the term I hired glass
+some of you hired contact lenses some of
+
+ align:start position:0%
+some of you hired contact lenses some of
+ 
+
+ align:start position:0%
+some of you hired contact lenses some of
+you I'm willing to bet hired the surgeon
+
+ align:start position:0%
+you I'm willing to bet hired the surgeon
+ 
+
+ align:start position:0%
+you I'm willing to bet hired the surgeon
+to do the little laser procedure but all
+
+ align:start position:0%
+to do the little laser procedure but all
+ 
+
+ align:start position:0%
+to do the little laser procedure but all
+of us had the same fundamental need we
+
+ align:start position:0%
+of us had the same fundamental need we
+ 
+
+ align:start position:0%
+of us had the same fundamental need we
+wanted to see better we just took
+
+ align:start position:0%
+wanted to see better we just took
+ 
+
+ align:start position:0%
+wanted to see better we just took
+different routes to get
+
+ align:start position:0%
+different routes to get
+ 
+
+ align:start position:0%
+different routes to get
+there so sell the benefits first and I'm
+
+ align:start position:0%
+there so sell the benefits first and I'm
+ 
+
+ align:start position:0%
+there so sell the benefits first and I'm
+a huge believer in Market segmentation I
+
+ align:start position:0%
+a huge believer in Market segmentation I
+ 
+
+ align:start position:0%
+a huge believer in Market segmentation I
+don't think everybody in the market is
+
+ align:start position:0%
+don't think everybody in the market is
+ 
+
+ align:start position:0%
+don't think everybody in the market is
+equal and I think there's a lot of them
+
+ align:start position:0%
+equal and I think there's a lot of them
+ 
+
+ align:start position:0%
+equal and I think there's a lot of them
+who aren't going to be your customer and
+
+ align:start position:0%
+who aren't going to be your customer and
+ 
+
+ align:start position:0%
+who aren't going to be your customer and
+I like to segment them by motivation to
+
+ align:start position:0%
+I like to segment them by motivation to
+ 
+
+ align:start position:0%
+I like to segment them by motivation to
+buy bu what I have I think there's a
+
+ align:start position:0%
+buy bu what I have I think there's a
+ 
+
+ align:start position:0%
+buy bu what I have I think there's a
+small group at the top feeling the pain
+
+ align:start position:0%
+small group at the top feeling the pain
+ 
+
+ align:start position:0%
+small group at the top feeling the pain
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+now underneath that I don't know let's
+
+ align:start position:0%
+now underneath that I don't know let's
+ 
+
+ align:start position:0%
+now underneath that I don't know let's
+say I have something that reduces the
+
+ align:start position:0%
+say I have something that reduces the
+ 
+
+ align:start position:0%
+say I have something that reduces the
+likelihood of heart attacks so if you
+
+ align:start position:0%
+likelihood of heart attacks so if you
+ 
+
+ align:start position:0%
+likelihood of heart attacks so if you
+had a heart attack yesterday and you're
+
+ align:start position:0%
+had a heart attack yesterday and you're
+ 
+
+ align:start position:0%
+had a heart attack yesterday and you're
+still alive you could be a good customer
+
+ align:start position:0%
+still alive you could be a good customer
+ 
+
+ align:start position:0%
+still alive you could be a good customer
+for me if you're not alive I'm sorry we
+
+ align:start position:0%
+for me if you're not alive I'm sorry we
+ 
+
+ align:start position:0%
+for me if you're not alive I'm sorry we
+won't do any business
+
+ align:start position:0%
+won't do any business
+ 
+
+ align:start position:0%
+won't do any business
+together his immediate
+
+ align:start position:0%
+together his immediate
+ 
+
+ align:start position:0%
+together his immediate
+family they're in the second tier
+
+ align:start position:0%
+family they're in the second tier
+ 
+
+ align:start position:0%
+family they're in the second tier
+they're worried gez maybe we should pay
+
+ align:start position:0%
+they're worried gez maybe we should pay
+ 
+
+ align:start position:0%
+they're worried gez maybe we should pay
+attention to this down below that people
+
+ align:start position:0%
+attention to this down below that people
+ 
+
+ align:start position:0%
+attention to this down below that people
+who are kind of vigilant and then
+
+ align:start position:0%
+who are kind of vigilant and then
+ 
+
+ align:start position:0%
+who are kind of vigilant and then
+there's a huge bunch of people that's
+
+ align:start position:0%
+there's a huge bunch of people that's
+ 
+
+ align:start position:0%
+there's a huge bunch of people that's
+just a graveyard for you don't go there
+
+ align:start position:0%
+just a graveyard for you don't go there
+ 
+
+ align:start position:0%
+just a graveyard for you don't go there
+start at the
+
+ align:start position:0%
+start at the
+ 
+
+ align:start position:0%
+start at the
+top couple reasons if you can't build a
+
+ align:start position:0%
+top couple reasons if you can't build a
+ 
+
+ align:start position:0%
+top couple reasons if you can't build a
+business there time for your next
+
+ align:start position:0%
+business there time for your next
+ 
+
+ align:start position:0%
+business there time for your next
+idea think of yourself as a jockey not
+
+ align:start position:0%
+idea think of yourself as a jockey not
+ 
+
+ align:start position:0%
+idea think of yourself as a jockey not
+as a
+
+ align:start position:0%
+as a
+ 
+
+ align:start position:0%
+as a
+horse if you start at the top and you
+
+ align:start position:0%
+horse if you start at the top and you
+ 
+
+ align:start position:0%
+horse if you start at the top and you
+fail you might be a very good jockey you
+
+ align:start position:0%
+fail you might be a very good jockey you
+ 
+
+ align:start position:0%
+fail you might be a very good jockey you
+just picked the wrong
+
+ align:start position:0%
+just picked the wrong
+ 
+
+ align:start position:0%
+just picked the wrong
+horse pick another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+horse oh also by the way if you're
+
+ align:start position:0%
+horse oh also by the way if you're
+ 
+
+ align:start position:0%
+horse oh also by the way if you're
+thinking one day you might sell your
+
+ align:start position:0%
+thinking one day you might sell your
+ 
+
+ align:start position:0%
+thinking one day you might sell your
+Venture you can go to big company X
+
+ align:start position:0%
+Venture you can go to big company X
+ 
+
+ align:start position:0%
+Venture you can go to big company X
+Johnson and Johnson and say guys I spent
+
+ align:start position:0%
+Johnson and Johnson and say guys I spent
+ 
+
+ align:start position:0%
+Johnson and Johnson and say guys I spent
+$1.98 and penetrated that block at the
+
+ align:start position:0%
+$1.98 and penetrated that block at the
+ 
+
+ align:start position:0%
+$1.98 and penetrated that block at the
+top you have a
+
+ align:start position:0%
+top you have a
+ 
+
+ align:start position:0%
+top you have a
+million you can take it further down you
+
+ align:start position:0%
+million you can take it further down you
+ 
+
+ align:start position:0%
+million you can take it further down you
+can do the math let's talk about the
+
+ align:start position:0%
+can do the math let's talk about the
+ 
+
+ align:start position:0%
+can do the math let's talk about the
+discounted value future earnings and
+
+ align:start position:0%
+discounted value future earnings and
+ 
+
+ align:start position:0%
+discounted value future earnings and
+pull together a little purchase package
+
+ align:start position:0%
+pull together a little purchase package
+ 
+
+ align:start position:0%
+pull together a little purchase package
+right if you can't succeed at the top
+
+ align:start position:0%
+right if you can't succeed at the top
+ 
+
+ align:start position:0%
+right if you can't succeed at the top
+you don't have a
+
+ align:start position:0%
+you don't have a
+ 
+
+ align:start position:0%
+you don't have a
+story but if you want to change your
+
+ align:start position:0%
+story but if you want to change your
+ 
+
+ align:start position:0%
+story but if you want to change your
+buying habits it requires a lot of
+
+ align:start position:0%
+buying habits it requires a lot of
+ 
+
+ align:start position:0%
+buying habits it requires a lot of
+motivation and I'm sorry if this sounds
+
+ align:start position:0%
+motivation and I'm sorry if this sounds
+ 
+
+ align:start position:0%
+motivation and I'm sorry if this sounds
+manipulative it's just blunt I think
+
+ align:start position:0%
+manipulative it's just blunt I think
+ 
+
+ align:start position:0%
+manipulative it's just blunt I think
+pain is very motivational
+
+ align:start position:0%
+pain is very motivational
+ 
+
+ align:start position:0%
+pain is very motivational
+fear greed vanity these are I mean I'm
+
+ align:start position:0%
+fear greed vanity these are I mean I'm
+ 
+
+ align:start position:0%
+fear greed vanity these are I mean I'm
+not trying to list the seven deadly sins
+
+ align:start position:0%
+not trying to list the seven deadly sins
+ 
+
+ align:start position:0%
+not trying to list the seven deadly sins
+here but but ask
+
+ align:start position:0%
+here but but ask
+ 
+
+ align:start position:0%
+here but but ask
+yourself what would cause people to stop
+
+ align:start position:0%
+yourself what would cause people to stop
+ 
+
+ align:start position:0%
+yourself what would cause people to stop
+doing what they're doing now and buy
+
+ align:start position:0%
+doing what they're doing now and buy
+ 
+
+ align:start position:0%
+doing what they're doing now and buy
+what you have are they dissatisfied with
+
+ align:start position:0%
+what you have are they dissatisfied with
+ 
+
+ align:start position:0%
+what you have are they dissatisfied with
+their current Cancer Care are they
+
+ align:start position:0%
+their current Cancer Care are they
+ 
+
+ align:start position:0%
+their current Cancer Care are they
+dissatisfied with something that you've
+
+ align:start position:0%
+dissatisfied with something that you've
+ 
+
+ align:start position:0%
+dissatisfied with something that you've
+got what's going to motivate them to
+
+ align:start position:0%
+got what's going to motivate them to
+ 
+
+ align:start position:0%
+got what's going to motivate them to
+change their buying habits and I got to
+
+ align:start position:0%
+change their buying habits and I got to
+ 
+
+ align:start position:0%
+change their buying habits and I got to
+tell you virtue is a tough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sell buy my vitamins because 20 years
+
+ align:start position:0%
+sell buy my vitamins because 20 years
+ 
+
+ align:start position:0%
+sell buy my vitamins because 20 years
+from now the antioxidants will have
+
+ align:start position:0%
+from now the antioxidants will have
+ 
+
+ align:start position:0%
+from now the antioxidants will have
+caused you to have few
+
+ align:start position:0%
+caused you to have few
+ 
+
+ align:start position:0%
+caused you to have few
+mutations at the end of your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chromosomes I don't think
+
+ align:start position:0%
+chromosomes I don't think
+ 
+
+ align:start position:0%
+chromosomes I don't think
+so so with that as a context what was I
+
+ align:start position:0%
+so so with that as a context what was I
+ 
+
+ align:start position:0%
+so so with that as a context what was I
+really selling with the one that
+
+ align:start position:0%
+really selling with the one that
+ 
+
+ align:start position:0%
+really selling with the one that
+failed I was selling virtue take this
+
+ align:start position:0%
+failed I was selling virtue take this
+ 
+
+ align:start position:0%
+failed I was selling virtue take this
+stuff and your biomarkers will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+improve what was I really selling with
+
+ align:start position:0%
+improve what was I really selling with
+ 
+
+ align:start position:0%
+improve what was I really selling with
+nightbite by the way answer that
+
+ align:start position:0%
+nightbite by the way answer that
+ 
+
+ align:start position:0%
+nightbite by the way answer that
+question for me what was I really
+
+ align:start position:0%
+question for me what was I really
+ 
+
+ align:start position:0%
+question for me what was I really
+selling with
+
+ align:start position:0%
+selling with
+ 
+
+ align:start position:0%
+selling with
+nightbite sir Peace of Mind peace of
+
+ align:start position:0%
+nightbite sir Peace of Mind peace of
+ 
+
+ align:start position:0%
+nightbite sir Peace of Mind peace of
+mind that's exactly right in fact once
+
+ align:start position:0%
+mind that's exactly right in fact once
+ 
+
+ align:start position:0%
+mind that's exactly right in fact once
+we figured that out all the lights went
+
+ align:start position:0%
+we figured that out all the lights went
+ 
+
+ align:start position:0%
+we figured that out all the lights went
+on and the ad copy wrote itself it was
+
+ align:start position:0%
+on and the ad copy wrote itself it was
+ 
+
+ align:start position:0%
+on and the ad copy wrote itself it was
+corny one bite and the rest is easy
+
+ align:start position:0%
+corny one bite and the rest is easy
+ 
+
+ align:start position:0%
+corny one bite and the rest is easy
+right but we got it that's exactly what
+
+ align:start position:0%
+right but we got it that's exactly what
+ 
+
+ align:start position:0%
+right but we got it that's exactly what
+we were
+
+ align:start position:0%
+we were
+ 
+
+ align:start position:0%
+we were
+selling
+
+ align:start position:0%
+selling
+ 
+
+ align:start position:0%
+selling
+so with no disrespect whatsoever you
+
+ align:start position:0%
+so with no disrespect whatsoever you
+ 
+
+ align:start position:0%
+so with no disrespect whatsoever you
+have a question question um going back a
+
+ align:start position:0%
+have a question question um going back a
+ 
+
+ align:start position:0%
+have a question question um going back a
+little toal how do you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that well I knew in fact that slotting
+
+ align:start position:0%
+that well I knew in fact that slotting
+ 
+
+ align:start position:0%
+that well I knew in fact that slotting
+fees were a big part of their revenue
+
+ align:start position:0%
+fees were a big part of their revenue
+ 
+
+ align:start position:0%
+fees were a big part of their revenue
+and not having them normally would make
+
+ align:start position:0%
+and not having them normally would make
+ 
+
+ align:start position:0%
+and not having them normally would make
+for a no-o but what I produced for them
+
+ align:start position:0%
+for a no-o but what I produced for them
+ 
+
+ align:start position:0%
+for a no-o but what I produced for them
+was a pretty nearly guaranteed income
+
+ align:start position:0%
+was a pretty nearly guaranteed income
+ 
+
+ align:start position:0%
+was a pretty nearly guaranteed income
+stream which exceeded the value of the
+
+ align:start position:0%
+stream which exceeded the value of the
+ 
+
+ align:start position:0%
+stream which exceeded the value of the
+slotting fees I also introduced the
+
+ align:start position:0%
+slotting fees I also introduced the
+ 
+
+ align:start position:0%
+slotting fees I also introduced the
+topic of
+
+ align:start position:0%
+topic of
+ 
+
+ align:start position:0%
+topic of
+competition I
+
+ align:start position:0%
+competition I
+ 
+
+ align:start position:0%
+competition I
+said our customers have mentioned you as
+
+ align:start position:0%
+said our customers have mentioned you as
+ 
+
+ align:start position:0%
+said our customers have mentioned you as
+their favorite
+
+ align:start position:0%
+their favorite
+ 
+
+ align:start position:0%
+their favorite
+Pharmacy or the our customer the
+
+ align:start position:0%
+Pharmacy or the our customer the
+ 
+
+ align:start position:0%
+Pharmacy or the our customer the
+pharmacist have mentioned that the
+
+ align:start position:0%
+pharmacist have mentioned that the
+ 
+
+ align:start position:0%
+pharmacist have mentioned that the
+wholesaler they most like to do business
+
+ align:start position:0%
+wholesaler they most like to do business
+ 
+
+ align:start position:0%
+wholesaler they most like to do business
+with is you they have of course other
+
+ align:start position:0%
+with is you they have of course other
+ 
+
+ align:start position:0%
+with is you they have of course other
+wholesalers they don't concentrate all
+
+ align:start position:0%
+wholesalers they don't concentrate all
+ 
+
+ align:start position:0%
+wholesalers they don't concentrate all
+of their eggs in one basket I'm hopeful
+
+ align:start position:0%
+of their eggs in one basket I'm hopeful
+ 
+
+ align:start position:0%
+of their eggs in one basket I'm hopeful
+that we can do business because
+
+ align:start position:0%
+that we can do business because
+ 
+
+ align:start position:0%
+that we can do business because
+otherwise I will have to go to number
+
+ align:start position:0%
+otherwise I will have to go to number
+ 
+
+ align:start position:0%
+otherwise I will have to go to number
+two so how would you like me to hand
+
+ align:start position:0%
+two so how would you like me to hand
+ 
+
+ align:start position:0%
+two so how would you like me to hand
+their need can we work
+
+ align:start position:0%
+their need can we work
+ 
+
+ align:start position:0%
+their need can we work
+together right again it don't get me
+
+ align:start position:0%
+together right again it don't get me
+ 
+
+ align:start position:0%
+together right again it don't get me
+wrong we did get told to hold no from
+
+ align:start position:0%
+wrong we did get told to hold no from
+ 
+
+ align:start position:0%
+wrong we did get told to hold no from
+time to time and and in fact if you're
+
+ align:start position:0%
+time to time and and in fact if you're
+ 
+
+ align:start position:0%
+time to time and and in fact if you're
+going to be an entrepreneur I hate to
+
+ align:start position:0%
+going to be an entrepreneur I hate to
+ 
+
+ align:start position:0%
+going to be an entrepreneur I hate to
+tell you this you will kiss a few frogs
+
+ align:start position:0%
+tell you this you will kiss a few frogs
+ 
+
+ align:start position:0%
+tell you this you will kiss a few frogs
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+there nature of the Beast right okay as
+
+ align:start position:0%
+there nature of the Beast right okay as
+ 
+
+ align:start position:0%
+there nature of the Beast right okay as
+I started to say some of you are
+
+ align:start position:0%
+I started to say some of you are
+ 
+
+ align:start position:0%
+I started to say some of you are
+taking MBA courses that are focused on
+
+ align:start position:0%
+taking MBA courses that are focused on
+ 
+
+ align:start position:0%
+taking MBA courses that are focused on
+marketing I'm going to give you an
+
+ align:start position:0%
+marketing I'm going to give you an
+ 
+
+ align:start position:0%
+marketing I'm going to give you an
+entire year of business school level
+
+ align:start position:0%
+entire year of business school level
+ 
+
+ align:start position:0%
+entire year of business school level
+marketing and two bullet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points find out what your customers
+
+ align:start position:0%
+points find out what your customers
+ 
+
+ align:start position:0%
+points find out what your customers
+want give it to
+
+ align:start position:0%
+want give it to
+ 
+
+ align:start position:0%
+want give it to
+them end of
+
+ align:start position:0%
+them end of
+ 
+
+ align:start position:0%
+them end of
+lecture now there's all manner of
+
+ align:start position:0%
+lecture now there's all manner of
+ 
+
+ align:start position:0%
+lecture now there's all manner of
+sophisticated regression analysis and
+
+ align:start position:0%
+sophisticated regression analysis and
+ 
+
+ align:start position:0%
+sophisticated regression analysis and
+etc etc that can be employed to do this
+
+ align:start position:0%
+etc etc that can be employed to do this
+ 
+
+ align:start position:0%
+etc etc that can be employed to do this
+but if you lose track of these two
+
+ align:start position:0%
+but if you lose track of these two
+ 
+
+ align:start position:0%
+but if you lose track of these two
+fundamental points you've missed the
+
+ align:start position:0%
+fundamental points you've missed the
+ 
+
+ align:start position:0%
+fundamental points you've missed the
+point so Focus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I hated the boss I had that said
+
+ align:start position:0%
+and I hated the boss I had that said
+ 
+
+ align:start position:0%
+and I hated the boss I had that said
+this to me because I could never get it
+
+ align:start position:0%
+this to me because I could never get it
+ 
+
+ align:start position:0%
+this to me because I could never get it
+out of my head drove me nuts it was so
+
+ align:start position:0%
+out of my head drove me nuts it was so
+ 
+
+ align:start position:0%
+out of my head drove me nuts it was so
+corny he'd say Jones there is no Hocus
+
+ align:start position:0%
+corny he'd say Jones there is no Hocus
+ 
+
+ align:start position:0%
+corny he'd say Jones there is no Hocus
+Pocus that takes the place of focus I
+
+ align:start position:0%
+Pocus that takes the place of focus I
+ 
+
+ align:start position:0%
+Pocus that takes the place of focus I
+think you're killing me but it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true so a different way of looking at
+
+ align:start position:0%
+true so a different way of looking at
+ 
+
+ align:start position:0%
+true so a different way of looking at
+this it's not sales it's detective
+
+ align:start position:0%
+this it's not sales it's detective
+ 
+
+ align:start position:0%
+this it's not sales it's detective
+work if you were to succeed do some
+
+ align:start position:0%
+work if you were to succeed do some
+ 
+
+ align:start position:0%
+work if you were to succeed do some
+detective work find your customer rather
+
+ align:start position:0%
+detective work find your customer rather
+ 
+
+ align:start position:0%
+detective work find your customer rather
+than promote your product because your
+
+ align:start position:0%
+than promote your product because your
+ 
+
+ align:start position:0%
+than promote your product because your
+customers hire these things to do a
+
+ align:start position:0%
+customers hire these things to do a
+ 
+
+ align:start position:0%
+customers hire these things to do a
+specific job design your product to do
+
+ align:start position:0%
+specific job design your product to do
+ 
+
+ align:start position:0%
+specific job design your product to do
+the job they want for a specific
+
+ align:start position:0%
+the job they want for a specific
+ 
+
+ align:start position:0%
+the job they want for a specific
+customer go find them and if you've done
+
+ align:start position:0%
+customer go find them and if you've done
+ 
+
+ align:start position:0%
+customer go find them and if you've done
+this right the selling will be
+
+ align:start position:0%
+this right the selling will be
+ 
+
+ align:start position:0%
+this right the selling will be
+easy how do you do it talk with
+
+ align:start position:0%
+easy how do you do it talk with
+ 
+
+ align:start position:0%
+easy how do you do it talk with
+them coold calls oh God literally phone
+
+ align:start position:0%
+them coold calls oh God literally phone
+ 
+
+ align:start position:0%
+them coold calls oh God literally phone
+calls emails are helpful but they're not
+
+ align:start position:0%
+calls emails are helpful but they're not
+ 
+
+ align:start position:0%
+calls emails are helpful but they're not
+adequate talk to them serve surveys are
+
+ align:start position:0%
+adequate talk to them serve surveys are
+ 
+
+ align:start position:0%
+adequate talk to them serve surveys are
+helpful they're not adequate talk to
+
+ align:start position:0%
+helpful they're not adequate talk to
+ 
+
+ align:start position:0%
+helpful they're not adequate talk to
+them some years ago I wanted to do a
+
+ align:start position:0%
+them some years ago I wanted to do a
+ 
+
+ align:start position:0%
+them some years ago I wanted to do a
+deal with a group in Finland that had
+
+ align:start position:0%
+deal with a group in Finland that had
+ 
+
+ align:start position:0%
+deal with a group in Finland that had
+invented a margarine that lowered
+
+ align:start position:0%
+invented a margarine that lowered
+ 
+
+ align:start position:0%
+invented a margarine that lowered
+cholesterol and I was intrigued Johnson
+
+ align:start position:0%
+cholesterol and I was intrigued Johnson
+ 
+
+ align:start position:0%
+cholesterol and I was intrigued Johnson
+and Johnson offered them a huge sack
+
+ align:start position:0%
+and Johnson offered them a huge sack
+ 
+
+ align:start position:0%
+and Johnson offered them a huge sack
+full of money our startup couldn't
+
+ align:start position:0%
+full of money our startup couldn't
+ 
+
+ align:start position:0%
+full of money our startup couldn't
+compete we
+
+ align:start position:0%
+compete we
+ 
+
+ align:start position:0%
+compete we
+lost but I watched what J&J did
+
+ align:start position:0%
+lost but I watched what J&J did
+ 
+
+ align:start position:0%
+lost but I watched what J&J did
+and I went into a number of supermarkets
+
+ align:start position:0%
+and I went into a number of supermarkets
+ 
+
+ align:start position:0%
+and I went into a number of supermarkets
+it's actually didn't take long I stood
+
+ align:start position:0%
+it's actually didn't take long I stood
+ 
+
+ align:start position:0%
+it's actually didn't take long I stood
+off to the side next to near where
+
+ align:start position:0%
+off to the side next to near where
+ 
+
+ align:start position:0%
+off to the side next to near where
+people had the
+
+ align:start position:0%
+people had the
+ 
+
+ align:start position:0%
+people had the
+margarine and I would watch customers
+
+ align:start position:0%
+margarine and I would watch customers
+ 
+
+ align:start position:0%
+margarine and I would watch customers
+come in the stuff that Jay and Jay had
+
+ align:start position:0%
+come in the stuff that Jay and Jay had
+ 
+
+ align:start position:0%
+come in the stuff that Jay and Jay had
+was about eight times as expensive as
+
+ align:start position:0%
+was about eight times as expensive as
+ 
+
+ align:start position:0%
+was about eight times as expensive as
+traditional margarine margarine Shoppers
+
+ align:start position:0%
+traditional margarine margarine Shoppers
+ 
+
+ align:start position:0%
+traditional margarine margarine Shoppers
+would come in and they'd look let's see1
+
+ align:start position:0%
+would come in and they'd look let's see1
+ 
+
+ align:start position:0%
+would come in and they'd look let's see1
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+19139 $8 dollar for doll4 I'll take the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$139 so I would stop these people and
+
+ align:start position:0%
+$139 so I would stop these people and
+ 
+
+ align:start position:0%
+$139 so I would stop these people and
+say excuse me I was thinking of buying
+
+ align:start position:0%
+say excuse me I was thinking of buying
+ 
+
+ align:start position:0%
+say excuse me I was thinking of buying
+this $8 stuff and I noticed you didn't
+
+ align:start position:0%
+this $8 stuff and I noticed you didn't
+ 
+
+ align:start position:0%
+this $8 stuff and I noticed you didn't
+how come you didn't oh man I got all
+
+ align:start position:0%
+how come you didn't oh man I got all
+ 
+
+ align:start position:0%
+how come you didn't oh man I got all
+manner of other ways to take care of my
+
+ align:start position:0%
+manner of other ways to take care of my
+ 
+
+ align:start position:0%
+manner of other ways to take care of my
+cholesterol besides I don't feel
+
+ align:start position:0%
+cholesterol besides I don't feel
+ 
+
+ align:start position:0%
+cholesterol besides I don't feel
+bad so talk to them know them how do
+
+ align:start position:0%
+bad so talk to them know them how do
+ 
+
+ align:start position:0%
+bad so talk to them know them how do
+they view their problem and think about
+
+ align:start position:0%
+they view their problem and think about
+ 
+
+ align:start position:0%
+they view their problem and think about
+your service and ask yourself well how
+
+ align:start position:0%
+your service and ask yourself well how
+ 
+
+ align:start position:0%
+your service and ask yourself well how
+are they solving the problem now more
+
+ align:start position:0%
+are they solving the problem now more
+ 
+
+ align:start position:0%
+are they solving the problem now more
+importantly what are they spending their
+
+ align:start position:0%
+importantly what are they spending their
+ 
+
+ align:start position:0%
+importantly what are they spending their
+money on now to solve this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem and there's a great quote
+
+ align:start position:0%
+problem and there's a great quote
+ 
+
+ align:start position:0%
+problem and there's a great quote
+attributed to Henry
+
+ align:start position:0%
+attributed to Henry
+ 
+
+ align:start position:0%
+attributed to Henry
+Ford they said Henry do you ever ask
+
+ align:start position:0%
+Ford they said Henry do you ever ask
+ 
+
+ align:start position:0%
+Ford they said Henry do you ever ask
+your customers what they want and Henry
+
+ align:start position:0%
+your customers what they want and Henry
+ 
+
+ align:start position:0%
+your customers what they want and Henry
+said oh hell if I'd asked them what they
+
+ align:start position:0%
+said oh hell if I'd asked them what they
+ 
+
+ align:start position:0%
+said oh hell if I'd asked them what they
+wanted they'd have said Faster
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Horses right so understanding what's
+
+ align:start position:0%
+Horses right so understanding what's
+ 
+
+ align:start position:0%
+Horses right so understanding what's
+behind that was part of Henry's genius
+
+ align:start position:0%
+behind that was part of Henry's genius
+ 
+
+ align:start position:0%
+behind that was part of Henry's genius
+you do have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+competition
+
+ align:start position:0%
+competition
+ 
+
+ align:start position:0%
+competition
+okay my regain customers needed my
+
+ align:start position:0%
+okay my regain customers needed my
+ 
+
+ align:start position:0%
+okay my regain customers needed my
+product they didn't want it I couldn't
+
+ align:start position:0%
+product they didn't want it I couldn't
+ 
+
+ align:start position:0%
+product they didn't want it I couldn't
+sell
+
+ align:start position:0%
+sell
+ 
+
+ align:start position:0%
+sell
+so what matters is finding people who
+
+ align:start position:0%
+so what matters is finding people who
+ 
+
+ align:start position:0%
+so what matters is finding people who
+want it and figuring out how to
+
+ align:start position:0%
+want it and figuring out how to
+ 
+
+ align:start position:0%
+want it and figuring out how to
+communicate the benefits in just 30
+
+ align:start position:0%
+communicate the benefits in just 30
+ 
+
+ align:start position:0%
+communicate the benefits in just 30
+seconds and this is harder than you
+
+ align:start position:0%
+seconds and this is harder than you
+ 
+
+ align:start position:0%
+seconds and this is harder than you
+think because if you don't really
+
+ align:start position:0%
+think because if you don't really
+ 
+
+ align:start position:0%
+think because if you don't really
+understand the benefits good luck trying
+
+ align:start position:0%
+understand the benefits good luck trying
+ 
+
+ align:start position:0%
+understand the benefits good luck trying
+to put it into collateral material put
+
+ align:start position:0%
+to put it into collateral material put
+ 
+
+ align:start position:0%
+to put it into collateral material put
+it on your website any of that
+
+ align:start position:0%
+it on your website any of that
+ 
+
+ align:start position:0%
+it on your website any of that
+stuff and of course as Steve probably
+
+ align:start position:0%
+stuff and of course as Steve probably
+ 
+
+ align:start position:0%
+stuff and of course as Steve probably
+told you yesterday you're unlikely to
+
+ align:start position:0%
+told you yesterday you're unlikely to
+ 
+
+ align:start position:0%
+told you yesterday you're unlikely to
+raise money customers buy benefits so
+
+ align:start position:0%
+raise money customers buy benefits so
+ 
+
+ align:start position:0%
+raise money customers buy benefits so
+some of the questions what's broke that
+
+ align:start position:0%
+some of the questions what's broke that
+ 
+
+ align:start position:0%
+some of the questions what's broke that
+we fix who
+
+ align:start position:0%
+we fix who
+ 
+
+ align:start position:0%
+we fix who
+cares do they have any
+
+ align:start position:0%
+cares do they have any
+ 
+
+ align:start position:0%
+cares do they have any
+money as a working musician I know that
+
+ align:start position:0%
+money as a working musician I know that
+ 
+
+ align:start position:0%
+money as a working musician I know that
+it's just feudal to try and make
+
+ align:start position:0%
+it's just feudal to try and make
+ 
+
+ align:start position:0%
+it's just feudal to try and make
+something for that market guitar players
+
+ align:start position:0%
+something for that market guitar players
+ 
+
+ align:start position:0%
+something for that market guitar players
+are all
+
+ align:start position:0%
+are all
+ 
+
+ align:start position:0%
+are all
+starving how do you find them how are
+
+ align:start position:0%
+starving how do you find them how are
+ 
+
+ align:start position:0%
+starving how do you find them how are
+they solving it why is what we have
+
+ align:start position:0%
+they solving it why is what we have
+ 
+
+ align:start position:0%
+they solving it why is what we have
+better um I'm going to zap through a
+
+ align:start position:0%
+better um I'm going to zap through a
+ 
+
+ align:start position:0%
+better um I'm going to zap through a
+couple of these
+
+ align:start position:0%
+couple of these
+ 
+
+ align:start position:0%
+couple of these
+um I want to spend a second on this
+
+ align:start position:0%
+um I want to spend a second on this
+ 
+
+ align:start position:0%
+um I want to spend a second on this
+though this all right all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something that we're doing with our
+
+ align:start position:0%
+something that we're doing with our
+ 
+
+ align:start position:0%
+something that we're doing with our
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+outfit we said let's and we're not the
+
+ align:start position:0%
+outfit we said let's and we're not the
+ 
+
+ align:start position:0%
+outfit we said let's and we're not the
+only ones doing this mind you but we are
+
+ align:start position:0%
+only ones doing this mind you but we are
+ 
+
+ align:start position:0%
+only ones doing this mind you but we are
+applying this start with the ideas
+
+ align:start position:0%
+applying this start with the ideas
+ 
+
+ align:start position:0%
+applying this start with the ideas
+Identify some unmet needs Etc go
+
+ align:start position:0%
+Identify some unmet needs Etc go
+ 
+
+ align:start position:0%
+Identify some unmet needs Etc go
+interview people who might want it and
+
+ align:start position:0%
+interview people who might want it and
+ 
+
+ align:start position:0%
+interview people who might want it and
+then make a Bare Bones version of the
+
+ align:start position:0%
+then make a Bare Bones version of the
+ 
+
+ align:start position:0%
+then make a Bare Bones version of the
+product we're making a 2 and a half
+
+ align:start position:0%
+product we're making a 2 and a half
+ 
+
+ align:start position:0%
+product we're making a 2 and a half
+ounce beverage that helps you sleep at
+
+ align:start position:0%
+ounce beverage that helps you sleep at
+ 
+
+ align:start position:0%
+ounce beverage that helps you sleep at
+night and we made a little prototype and
+
+ align:start position:0%
+night and we made a little prototype and
+ 
+
+ align:start position:0%
+night and we made a little prototype and
+it looks bad it tastes bad and you can't
+
+ align:start position:0%
+it looks bad it tastes bad and you can't
+ 
+
+ align:start position:0%
+it looks bad it tastes bad and you can't
+get the cap
+
+ align:start position:0%
+get the cap
+ 
+
+ align:start position:0%
+get the cap
+off arguably this is not a good profile
+
+ align:start position:0%
+off arguably this is not a good profile
+ 
+
+ align:start position:0%
+off arguably this is not a good profile
+for a retail product but we had one
+
+ align:start position:0%
+for a retail product but we had one
+ 
+
+ align:start position:0%
+for a retail product but we had one
+primary concern does it work if we give
+
+ align:start position:0%
+primary concern does it work if we give
+ 
+
+ align:start position:0%
+primary concern does it work if we give
+it to 30 people and nobody goes to sleep
+
+ align:start position:0%
+it to 30 people and nobody goes to sleep
+ 
+
+ align:start position:0%
+it to 30 people and nobody goes to sleep
+well then we stop right there silly to
+
+ align:start position:0%
+well then we stop right there silly to
+ 
+
+ align:start position:0%
+well then we stop right there silly to
+have spent any time making it look good
+
+ align:start position:0%
+have spent any time making it look good
+ 
+
+ align:start position:0%
+have spent any time making it look good
+so go out there and see if you can
+
+ align:start position:0%
+so go out there and see if you can
+ 
+
+ align:start position:0%
+so go out there and see if you can
+identify customers for launch and in
+
+ align:start position:0%
+identify customers for launch and in
+ 
+
+ align:start position:0%
+identify customers for launch and in
+fact the first group of customers that
+
+ align:start position:0%
+fact the first group of customers that
+ 
+
+ align:start position:0%
+fact the first group of customers that
+we thought would be suitable for our
+
+ align:start position:0%
+we thought would be suitable for our
+ 
+
+ align:start position:0%
+we thought would be suitable for our
+business turned out to be wrong I had a
+
+ align:start position:0%
+business turned out to be wrong I had a
+ 
+
+ align:start position:0%
+business turned out to be wrong I had a
+really bad five or six weeks where I got
+
+ align:start position:0%
+really bad five or six weeks where I got
+ 
+
+ align:start position:0%
+really bad five or six weeks where I got
+told no all day day every day for five
+
+ align:start position:0%
+told no all day day every day for five
+ 
+
+ align:start position:0%
+told no all day day every day for five
+or six straight weeks finally figured
+
+ align:start position:0%
+or six straight weeks finally figured
+ 
+
+ align:start position:0%
+or six straight weeks finally figured
+out they don't want it they might need
+
+ align:start position:0%
+out they don't want it they might need
+ 
+
+ align:start position:0%
+out they don't want it they might need
+it but time to iterate once you get it
+
+ align:start position:0%
+it but time to iterate once you get it
+ 
+
+ align:start position:0%
+it but time to iterate once you get it
+right then you can get about the
+
+ align:start position:0%
+right then you can get about the
+ 
+
+ align:start position:0%
+right then you can get about the
+business of doing your branding and
+
+ align:start position:0%
+business of doing your branding and
+ 
+
+ align:start position:0%
+business of doing your branding and
+packaging more formally and then you can
+
+ align:start position:0%
+packaging more formally and then you can
+ 
+
+ align:start position:0%
+packaging more formally and then you can
+get about the business of growing the
+
+ align:start position:0%
+get about the business of growing the
+ 
+
+ align:start position:0%
+get about the business of growing the
+company and by the way you might be able
+
+ align:start position:0%
+company and by the way you might be able
+ 
+
+ align:start position:0%
+company and by the way you might be able
+to raise a little money at a couple of
+
+ align:start position:0%
+to raise a little money at a couple of
+ 
+
+ align:start position:0%
+to raise a little money at a couple of
+those points a little money to build
+
+ align:start position:0%
+those points a little money to build
+ 
+
+ align:start position:0%
+those points a little money to build
+your prototype and then once you figure
+
+ align:start position:0%
+your prototype and then once you figure
+ 
+
+ align:start position:0%
+your prototype and then once you figure
+out what you're doing a little money to
+
+ align:start position:0%
+out what you're doing a little money to
+ 
+
+ align:start position:0%
+out what you're doing a little money to
+actually take something to to the
+
+ align:start position:0%
+actually take something to to the
+ 
+
+ align:start position:0%
+actually take something to to the
+marketplace because you have reduced the
+
+ align:start position:0%
+marketplace because you have reduced the
+ 
+
+ align:start position:0%
+marketplace because you have reduced the
+risk but that stage of the game is
+
+ align:start position:0%
+risk but that stage of the game is
+ 
+
+ align:start position:0%
+risk but that stage of the game is
+hugely useful and I submit that that's
+
+ align:start position:0%
+hugely useful and I submit that that's
+ 
+
+ align:start position:0%
+hugely useful and I submit that that's
+what a and his team have done already
+
+ align:start position:0%
+what a and his team have done already
+ 
+
+ align:start position:0%
+what a and his team have done already
+they've made a minimum viable product
+
+ align:start position:0%
+they've made a minimum viable product
+ 
+
+ align:start position:0%
+they've made a minimum viable product
+they're circulating a pancake mix and
+
+ align:start position:0%
+they're circulating a pancake mix and
+ 
+
+ align:start position:0%
+they're circulating a pancake mix and
+they're getting valuable customer
+
+ align:start position:0%
+they're getting valuable customer
+ 
+
+ align:start position:0%
+they're getting valuable customer
+feedback Al your recipe calls for
+
+ align:start position:0%
+feedback Al your recipe calls for
+ 
+
+ align:start position:0%
+feedback Al your recipe calls for
+sparkling water I don't keep sparkling
+
+ align:start position:0%
+sparkling water I don't keep sparkling
+ 
+
+ align:start position:0%
+sparkling water I don't keep sparkling
+water at home how can I make pancakes
+
+ align:start position:0%
+water at home how can I make pancakes
+ 
+
+ align:start position:0%
+water at home how can I make pancakes
+without sparkling water oh useful right
+
+ align:start position:0%
+without sparkling water oh useful right
+ 
+
+ align:start position:0%
+without sparkling water oh useful right
+okay so we're going to skip what I'm
+
+ align:start position:0%
+okay so we're going to skip what I'm
+ 
+
+ align:start position:0%
+okay so we're going to skip what I'm
+doing now
+
+ align:start position:0%
+doing now
+ 
+
+ align:start position:0%
+doing now
+um though of course it's
+
+ align:start position:0%
+um though of course it's
+ 
+
+ align:start position:0%
+um though of course it's
+fascinating we're out of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+so I have one set of final questions
+
+ align:start position:0%
+so I have one set of final questions
+ 
+
+ align:start position:0%
+so I have one set of final questions
+where customers go for help how are you
+
+ align:start position:0%
+where customers go for help how are you
+ 
+
+ align:start position:0%
+where customers go for help how are you
+going to reach them paint a picture of
+
+ align:start position:0%
+going to reach them paint a picture of
+ 
+
+ align:start position:0%
+going to reach them paint a picture of
+who's going to write you that first
+
+ align:start position:0%
+who's going to write you that first
+ 
+
+ align:start position:0%
+who's going to write you that first
+check what evidence do you have that
+
+ align:start position:0%
+check what evidence do you have that
+ 
+
+ align:start position:0%
+check what evidence do you have that
+they will pay for your product this was
+
+ align:start position:0%
+they will pay for your product this was
+ 
+
+ align:start position:0%
+they will pay for your product this was
+crucial to me for the gentleman talking
+
+ align:start position:0%
+crucial to me for the gentleman talking
+ 
+
+ align:start position:0%
+crucial to me for the gentleman talking
+about calling on IBM and calling on
+
+ align:start position:0%
+about calling on IBM and calling on
+ 
+
+ align:start position:0%
+about calling on IBM and calling on
+people who would want his augmentation
+
+ align:start position:0%
+people who would want his augmentation
+ 
+
+ align:start position:0%
+people who would want his augmentation
+of Google what evidence you have that
+
+ align:start position:0%
+of Google what evidence you have that
+ 
+
+ align:start position:0%
+of Google what evidence you have that
+somebody's going to pay for it how much
+
+ align:start position:0%
+somebody's going to pay for it how much
+ 
+
+ align:start position:0%
+somebody's going to pay for it how much
+and then it calls for someone who's I
+
+ align:start position:0%
+and then it calls for someone who's I
+ 
+
+ align:start position:0%
+and then it calls for someone who's I
+don't know kind of a pervert to actually
+
+ align:start position:0%
+don't know kind of a pervert to actually
+ 
+
+ align:start position:0%
+don't know kind of a pervert to actually
+be responsible for sales although some
+
+ align:start position:0%
+be responsible for sales although some
+ 
+
+ align:start position:0%
+be responsible for sales although some
+of us like it who's going to do
+
+ align:start position:0%
+of us like it who's going to do
+ 
+
+ align:start position:0%
+of us like it who's going to do
+it I don't think we have time for any
+
+ align:start position:0%
+it I don't think we have time for any
+ 
+
+ align:start position:0%
+it I don't think we have time for any
+more of your questions with regret so
+
+ align:start position:0%
+more of your questions with regret so
+ 
+
+ align:start position:0%
+more of your questions with regret so
+let me summarize the only non-negotiable
+
+ align:start position:0%
+let me summarize the only non-negotiable
+ 
+
+ align:start position:0%
+let me summarize the only non-negotiable
+requirement for successful business is
+
+ align:start position:0%
+requirement for successful business is
+ 
+
+ align:start position:0%
+requirement for successful business is
+your customers and if you're going to
+
+ align:start position:0%
+your customers and if you're going to
+ 
+
+ align:start position:0%
+your customers and if you're going to
+succeed you have to have something
+
+ align:start position:0%
+succeed you have to have something
+ 
+
+ align:start position:0%
+succeed you have to have something
+that's unique and important for someone
+
+ align:start position:0%
+that's unique and important for someone
+ 
+
+ align:start position:0%
+that's unique and important for someone
+you gave us a great example of pivoting
+
+ align:start position:0%
+you gave us a great example of pivoting
+ 
+
+ align:start position:0%
+you gave us a great example of pivoting
+that from the head of IBM to college
+
+ align:start position:0%
+that from the head of IBM to college
+ 
+
+ align:start position:0%
+that from the head of IBM to college
+students all right it's got to be
+
+ align:start position:0%
+students all right it's got to be
+ 
+
+ align:start position:0%
+students all right it's got to be
+important to someone so figure out who
+
+ align:start position:0%
+important to someone so figure out who
+ 
+
+ align:start position:0%
+important to someone so figure out who
+can't live without it go find them and
+
+ align:start position:0%
+can't live without it go find them and
+ 
+
+ align:start position:0%
+can't live without it go find them and
+tell them about it and take their money
+
+ align:start position:0%
+tell them about it and take their money
+ 
+
+ align:start position:0%
+tell them about it and take their money
+thank you very much
\ No newline at end of file
diff --git a/BChhAS1sFvA.txt b/BChhAS1sFvA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dddde1faa46eaeec48d86c4a0ebdba3885b3ebe4
--- /dev/null
+++ b/BChhAS1sFvA.txt
@@ -0,0 +1,4776 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right so let's try to
+
+ align:start position:0%
+ocw.mit.edu all right so let's try to
+ 
+
+ align:start position:0%
+ocw.mit.edu all right so let's try to
+do okay so let's try to discuss a bit
+
+ align:start position:0%
+do okay so let's try to discuss a bit
+ 
+
+ align:start position:0%
+do okay so let's try to discuss a bit
+how things relate to
+
+ align:start position:0%
+how things relate to
+ 
+
+ align:start position:0%
+how things relate to
+physics okay
+
+ align:start position:0%
+physics okay
+ 
+
+ align:start position:0%
+physics okay
+so there's two main things I want to
+
+ align:start position:0%
+so there's two main things I want to
+ 
+
+ align:start position:0%
+so there's two main things I want to
+discuss one of them is what curl says
+
+ align:start position:0%
+discuss one of them is what curl says
+ 
+
+ align:start position:0%
+discuss one of them is what curl says
+about force fields and in
+
+ align:start position:0%
+about force fields and in
+ 
+
+ align:start position:0%
+about force fields and in
+particular uh nice
+
+ align:start position:0%
+particular uh nice
+ 
+
+ align:start position:0%
+particular uh nice
+consequence of that concerning
+
+ align:start position:0%
+consequence of that concerning
+ 
+
+ align:start position:0%
+consequence of that concerning
+gravitational
+
+ align:start position:0%
+gravitational
+ 
+
+ align:start position:0%
+gravitational
+attraction okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so more about curve first so we've seen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we have a velocity
+
+ align:start position:0%
+if we have a velocity
+ 
+
+ align:start position:0%
+if we have a velocity
+field then we've seen that the curl
+
+ align:start position:0%
+field then we've seen that the curl
+ 
+
+ align:start position:0%
+field then we've seen that the curl
+measures the rotation effect more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+precisely Cur
+
+ align:start position:0%
+precisely Cur
+ 
+
+ align:start position:0%
+precisely Cur
+V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measures twice the angular velocity or
+
+ align:start position:0%
+measures twice the angular velocity or
+ 
+
+ align:start position:0%
+measures twice the angular velocity or
+maybe I should say the angular velocity
+
+ align:start position:0%
+maybe I should say the angular velocity
+ 
+
+ align:start position:0%
+maybe I should say the angular velocity
+Vector because it also includes the axis
+
+ align:start position:0%
+Vector because it also includes the axis
+ 
+
+ align:start position:0%
+Vector because it also includes the axis
+of rotation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I should say maybe for
+
+ align:start position:0%
+okay so I should say maybe for
+ 
+
+ align:start position:0%
+okay so I should say maybe for
+the rotation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion so for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example just to remind you I mean we've
+
+ align:start position:0%
+example just to remind you I mean we've
+ 
+
+ align:start position:0%
+example just to remind you I mean we've
+seen this guy a couple of times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if I give you a uniform rotation
+
+ align:start position:0%
+but if I give you a uniform rotation
+ 
+
+ align:start position:0%
+but if I give you a uniform rotation
+motion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z-axis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's a vector field in which the
+
+ align:start position:0%
+so that's a vector field in which the
+ 
+
+ align:start position:0%
+so that's a vector field in which the
+trajectories are going to be circles
+
+ align:start position:0%
+trajectories are going to be circles
+ 
+
+ align:start position:0%
+trajectories are going to be circles
+centered in the z-axis and our Vector
+
+ align:start position:0%
+centered in the z-axis and our Vector
+ 
+
+ align:start position:0%
+centered in the z-axis and our Vector
+field is just going to be tangent to
+
+ align:start position:0%
+field is just going to be tangent to
+ 
+
+ align:start position:0%
+field is just going to be tangent to
+each of these
+
+ align:start position:0%
+each of these
+ 
+
+ align:start position:0%
+each of these
+circles and if you look at it from above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you'll have this rotation Vector
+
+ align:start position:0%
+then you'll have this rotation Vector
+ 
+
+ align:start position:0%
+then you'll have this rotation Vector
+field that we've seen many
+
+ align:start position:0%
+field that we've seen many
+ 
+
+ align:start position:0%
+field that we've seen many
+times so typically the velocity Vector
+
+ align:start position:0%
+times so typically the velocity Vector
+ 
+
+ align:start position:0%
+times so typically the velocity Vector
+for this would be minus y i+ XJ times
+
+ align:start position:0%
+for this would be minus y i+ XJ times
+ 
+
+ align:start position:0%
+for this would be minus y i+ XJ times
+maybe the a number which represents how
+
+ align:start position:0%
+maybe the a number which represents how
+ 
+
+ align:start position:0%
+maybe the a number which represents how
+fast we're spinning the angular velocity
+
+ align:start position:0%
+fast we're spinning the angular velocity
+ 
+
+ align:start position:0%
+fast we're spinning the angular velocity
+in radians per
+
+ align:start position:0%
+in radians per
+ 
+
+ align:start position:0%
+in radians per
+second and then
+
+ align:start position:0%
+second and then
+ 
+
+ align:start position:0%
+second and then
+no if you compute the curl of this you
+
+ align:start position:0%
+no if you compute the curl of this you
+ 
+
+ align:start position:0%
+no if you compute the curl of this you
+will end up with 2 Omega *
+
+ align:start position:0%
+will end up with 2 Omega *
+ 
+
+ align:start position:0%
+will end up with 2 Omega *
+K so now the other kinds of vector
+
+ align:start position:0%
+K so now the other kinds of vector
+ 
+
+ align:start position:0%
+K so now the other kinds of vector
+Fields we've seen physically are force
+
+ align:start position:0%
+Fields we've seen physically are force
+ 
+
+ align:start position:0%
+Fields we've seen physically are force
+fields so the question is what does the
+
+ align:start position:0%
+fields so the question is what does the
+ 
+
+ align:start position:0%
+fields so the question is what does the
+curl of a force field
+
+ align:start position:0%
+curl of a force field
+ 
+
+ align:start position:0%
+curl of a force field
+mean what can we say about that so the
+
+ align:start position:0%
+mean what can we say about that so the
+ 
+
+ align:start position:0%
+mean what can we say about that so the
+interpretation is a little bit less
+
+ align:start position:0%
+interpretation is a little bit less
+ 
+
+ align:start position:0%
+interpretation is a little bit less
+obvious but let's try to get some idea
+
+ align:start position:0%
+obvious but let's try to get some idea
+ 
+
+ align:start position:0%
+obvious but let's try to get some idea
+of what it might be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I want to remind you that if we
+
+ align:start position:0%
+okay so I want to remind you that if we
+ 
+
+ align:start position:0%
+okay so I want to remind you that if we
+have a solid in a force field we can
+
+ align:start position:0%
+have a solid in a force field we can
+ 
+
+ align:start position:0%
+have a solid in a force field we can
+measure the torque of the
+
+ align:start position:0%
+measure the torque of the
+ 
+
+ align:start position:0%
+measure the torque of the
+force the torque exerted by the force on
+
+ align:start position:0%
+force the torque exerted by the force on
+ 
+
+ align:start position:0%
+force the torque exerted by the force on
+the solid
+
+ align:start position:0%
+the solid
+ 
+
+ align:start position:0%
+the solid
+so maybe first I should remind you about
+
+ align:start position:0%
+so maybe first I should remind you about
+ 
+
+ align:start position:0%
+so maybe first I should remind you about
+what torque is in space so let's say
+
+ align:start position:0%
+what torque is in space so let's say
+ 
+
+ align:start position:0%
+what torque is in space so let's say
+that I have a piece of solid with a mass
+
+ align:start position:0%
+that I have a piece of solid with a mass
+ 
+
+ align:start position:0%
+that I have a piece of solid with a mass
+Delta m for example and I have a force
+
+ align:start position:0%
+Delta m for example and I have a force
+ 
+
+ align:start position:0%
+Delta m for example and I have a force
+that's being exerted to
+
+ align:start position:0%
+that's being exerted to
+ 
+
+ align:start position:0%
+that's being exerted to
+it so let's say that maybe my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Force might
+
+ align:start position:0%
+Force might
+ 
+
+ align:start position:0%
+Force might
+be F time Delta M if you think for
+
+ align:start position:0%
+be F time Delta M if you think for
+ 
+
+ align:start position:0%
+be F time Delta M if you think for
+example of a gravitational field you
+
+ align:start position:0%
+example of a gravitational field you
+ 
+
+ align:start position:0%
+example of a gravitational field you
+know the gravitational force is actually
+
+ align:start position:0%
+know the gravitational force is actually
+ 
+
+ align:start position:0%
+know the gravitational force is actually
+the gravitational field times the
+
+ align:start position:0%
+the gravitational field times the
+ 
+
+ align:start position:0%
+the gravitational field times the
+mass I me you can forget Delta M if you
+
+ align:start position:0%
+mass I me you can forget Delta M if you
+ 
+
+ align:start position:0%
+mass I me you can forget Delta M if you
+don't like
+
+ align:start position:0%
+don't like
+ 
+
+ align:start position:0%
+don't like
+it and let's say that the position
+
+ align:start position:0%
+it and let's say that the position
+ 
+
+ align:start position:0%
+it and let's say that the position
+Vector oops should be aiming for the
+
+ align:start position:0%
+Vector oops should be aiming for the
+ 
+
+ align:start position:0%
+Vector oops should be aiming for the
+origin the position Vector R is here and
+
+ align:start position:0%
+origin the position Vector R is here and
+ 
+
+ align:start position:0%
+origin the position Vector R is here and
+now let's say that maybe this guy is at
+
+ align:start position:0%
+now let's say that maybe this guy is at
+ 
+
+ align:start position:0%
+now let's say that maybe this guy is at
+the end of some arm or some you know
+
+ align:start position:0%
+the end of some arm or some you know
+ 
+
+ align:start position:0%
+the end of some arm or some you know
+metal thing and I want to hold it in
+
+ align:start position:0%
+metal thing and I want to hold it in
+ 
+
+ align:start position:0%
+metal thing and I want to hold it in
+place so the force is going to exert a
+
+ align:start position:0%
+place so the force is going to exert a
+ 
+
+ align:start position:0%
+place so the force is going to exert a
+torque relative to the origin that will
+
+ align:start position:0%
+torque relative to the origin that will
+ 
+
+ align:start position:0%
+torque relative to the origin that will
+try to measure you know how much I'm
+
+ align:start position:0%
+try to measure you know how much I'm
+ 
+
+ align:start position:0%
+try to measure you know how much I'm
+trying to swing this guy around the
+
+ align:start position:0%
+trying to swing this guy around the
+ 
+
+ align:start position:0%
+trying to swing this guy around the
+origin and consequently how much effort
+
+ align:start position:0%
+origin and consequently how much effort
+ 
+
+ align:start position:0%
+origin and consequently how much effort
+I have to exert if I want to actually
+
+ align:start position:0%
+I have to exert if I want to actually
+ 
+
+ align:start position:0%
+I have to exert if I want to actually
+maintain it at its place but by just
+
+ align:start position:0%
+maintain it at its place but by just
+ 
+
+ align:start position:0%
+maintain it at its place but by just
+holding it at the end of a stick
+
+ align:start position:0%
+holding it at the end of a stick
+ 
+
+ align:start position:0%
+holding it at the end of a stick
+here okay so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talk is now a vector which is just the
+
+ align:start position:0%
+talk is now a vector which is just the
+ 
+
+ align:start position:0%
+talk is now a vector which is just the
+cross product of a position Vector with
+
+ align:start position:0%
+cross product of a position Vector with
+ 
+
+ align:start position:0%
+cross product of a position Vector with
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+force and so what a measures again is
+
+ align:start position:0%
+force and so what a measures again is
+ 
+
+ align:start position:0%
+force and so what a measures again is
+the rotation effects of the force and
+
+ align:start position:0%
+the rotation effects of the force and
+ 
+
+ align:start position:0%
+the rotation effects of the force and
+you know if you
+
+ align:start position:0%
+you know if you
+ 
+
+ align:start position:0%
+you know if you
+remember the principle
+
+ align:start position:0%
+remember the principle
+ 
+
+ align:start position:0%
+remember the principle
+that the derivative of velocity which is
+
+ align:start position:0%
+that the derivative of velocity which is
+ 
+
+ align:start position:0%
+that the derivative of velocity which is
+acceleration is force divided by
+
+ align:start position:0%
+acceleration is force divided by
+ 
+
+ align:start position:0%
+acceleration is force divided by
+mass then the derivative of angular
+
+ align:start position:0%
+mass then the derivative of angular
+ 
+
+ align:start position:0%
+mass then the derivative of angular
+velocity should be angular acceleration
+
+ align:start position:0%
+velocity should be angular acceleration
+ 
+
+ align:start position:0%
+velocity should be angular acceleration
+which is related to the torque per unit
+
+ align:start position:0%
+which is related to the torque per unit
+ 
+
+ align:start position:0%
+which is related to the torque per unit
+mass and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me just remind you if I look at
+
+ align:start position:0%
+let me just remind you if I look at
+ 
+
+ align:start position:0%
+let me just remind you if I look at
+translation motions you know say I'm
+
+ align:start position:0%
+translation motions you know say I'm
+ 
+
+ align:start position:0%
+translation motions you know say I'm
+just looking at a point Mass so there's
+
+ align:start position:0%
+just looking at a point Mass so there's
+ 
+
+ align:start position:0%
+just looking at a point Mass so there's
+no rotation
+
+ align:start position:0%
+no rotation
+ 
+
+ align:start position:0%
+no rotation
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+then Force divided by
+
+ align:start position:0%
+then Force divided by
+ 
+
+ align:start position:0%
+then Force divided by
+mass is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceleration which is the
+
+ align:start position:0%
+acceleration which is the
+ 
+
+ align:start position:0%
+acceleration which is the
+derivative of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+velocity and so what I'm claiming is
+
+ align:start position:0%
+velocity and so what I'm claiming is
+ 
+
+ align:start position:0%
+velocity and so what I'm claiming is
+that for rotation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+effects we have a similar low which
+
+ align:start position:0%
+effects we have a similar low which
+ 
+
+ align:start position:0%
+effects we have a similar low which
+maybe you've seen in
+
+ align:start position:0%
+maybe you've seen in
+ 
+
+ align:start position:0%
+maybe you've seen in
+801 uh at least well it's one of the
+
+ align:start position:0%
+801 uh at least well it's one of the
+ 
+
+ align:start position:0%
+801 uh at least well it's one of the
+important things of solid mechanics
+
+ align:start position:0%
+important things of solid mechanics
+ 
+
+ align:start position:0%
+important things of solid mechanics
+which is that the torque of the force
+
+ align:start position:0%
+which is that the torque of the force
+ 
+
+ align:start position:0%
+which is that the torque of the force
+divided by the moment of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inertia I'm cheating a little bit here
+
+ align:start position:0%
+inertia I'm cheating a little bit here
+ 
+
+ align:start position:0%
+inertia I'm cheating a little bit here
+but if you can see how I'm cheating then
+
+ align:start position:0%
+but if you can see how I'm cheating then
+ 
+
+ align:start position:0%
+but if you can see how I'm cheating then
+I'm sure you know how to State it
+
+ align:start position:0%
+I'm sure you know how to State it
+ 
+
+ align:start position:0%
+I'm sure you know how to State it
+correctly and if you don't see how I'm
+
+ align:start position:0%
+correctly and if you don't see how I'm
+ 
+
+ align:start position:0%
+correctly and if you don't see how I'm
+cheating then let's just ignore the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+details is angular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acceleration and angular acceleration is
+
+ align:start position:0%
+acceleration and angular acceleration is
+ 
+
+ align:start position:0%
+acceleration and angular acceleration is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+derivative of angular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+velocity okay so now if I think of
+
+ align:start position:0%
+velocity okay so now if I think of
+ 
+
+ align:start position:0%
+velocity okay so now if I think of
+curl as an operation which from a
+
+ align:start position:0%
+curl as an operation which from a
+ 
+
+ align:start position:0%
+curl as an operation which from a
+velocity field gives the angular
+
+ align:start position:0%
+velocity field gives the angular
+ 
+
+ align:start position:0%
+velocity field gives the angular
+velocity of its rotation
+
+ align:start position:0%
+velocity of its rotation
+ 
+
+ align:start position:0%
+velocity of its rotation
+effects then you see that the curl of an
+
+ align:start position:0%
+effects then you see that the curl of an
+ 
+
+ align:start position:0%
+effects then you see that the curl of an
+acceleration
+
+ align:start position:0%
+acceleration
+ 
+
+ align:start position:0%
+acceleration
+field gives the angular acceleration in
+
+ align:start position:0%
+field gives the angular acceleration in
+ 
+
+ align:start position:0%
+field gives the angular acceleration in
+the rotation part of the acceleration
+
+ align:start position:0%
+the rotation part of the acceleration
+ 
+
+ align:start position:0%
+the rotation part of the acceleration
+effect and
+
+ align:start position:0%
+effect and
+ 
+
+ align:start position:0%
+effect and
+therefore the curl of a force field
+
+ align:start position:0%
+therefore the curl of a force field
+ 
+
+ align:start position:0%
+therefore the curl of a force field
+measures the torque per unit moment of
+
+ align:start position:0%
+measures the torque per unit moment of
+ 
+
+ align:start position:0%
+measures the torque per unit moment of
+inertia
+
+ align:start position:0%
+inertia
+ 
+
+ align:start position:0%
+inertia
+so it measures how much torque this
+
+ align:start position:0%
+so it measures how much torque this
+ 
+
+ align:start position:0%
+so it measures how much torque this
+force field exerts on a small test solid
+
+ align:start position:0%
+force field exerts on a small test solid
+ 
+
+ align:start position:0%
+force field exerts on a small test solid
+placed in it so if you you know you have
+
+ align:start position:0%
+placed in it so if you you know you have
+ 
+
+ align:start position:0%
+placed in it so if you you know you have
+a small solid somewhere the curl will
+
+ align:start position:0%
+a small solid somewhere the curl will
+ 
+
+ align:start position:0%
+a small solid somewhere the curl will
+just measure how much your solid starts
+
+ align:start position:0%
+just measure how much your solid starts
+ 
+
+ align:start position:0%
+just measure how much your solid starts
+spinning if you leave it in this force
+
+ align:start position:0%
+spinning if you leave it in this force
+ 
+
+ align:start position:0%
+spinning if you leave it in this force
+field so in particular a force field
+
+ align:start position:0%
+field so in particular a force field
+ 
+
+ align:start position:0%
+field so in particular a force field
+with no curl is a force field that does
+
+ align:start position:0%
+with no curl is a force field that does
+ 
+
+ align:start position:0%
+with no curl is a force field that does
+not generate any rotation motion so that
+
+ align:start position:0%
+not generate any rotation motion so that
+ 
+
+ align:start position:0%
+not generate any rotation motion so that
+means you know if you put an object in
+
+ align:start position:0%
+means you know if you put an object in
+ 
+
+ align:start position:0%
+means you know if you put an object in
+there that's completely immobile and you
+
+ align:start position:0%
+there that's completely immobile and you
+ 
+
+ align:start position:0%
+there that's completely immobile and you
+leave it in that force field well of
+
+ align:start position:0%
+leave it in that force field well of
+ 
+
+ align:start position:0%
+leave it in that force field well of
+course it might accelerate in some
+
+ align:start position:0%
+course it might accelerate in some
+ 
+
+ align:start position:0%
+course it might accelerate in some
+Direction but it won't start
+
+ align:start position:0%
+Direction but it won't start
+ 
+
+ align:start position:0%
+Direction but it won't start
+spinning while if you put it in there
+
+ align:start position:0%
+spinning while if you put it in there
+ 
+
+ align:start position:0%
+spinning while if you put it in there
+spinning already in some direction then
+
+ align:start position:0%
+spinning already in some direction then
+ 
+
+ align:start position:0%
+spinning already in some direction then
+well it should continue to spin in the
+
+ align:start position:0%
+well it should continue to spin in the
+ 
+
+ align:start position:0%
+well it should continue to spin in the
+same way of course maybe there will be
+
+ align:start position:0%
+same way of course maybe there will be
+ 
+
+ align:start position:0%
+same way of course maybe there will be
+you know friction and things like that
+
+ align:start position:0%
+you know friction and things like that
+ 
+
+ align:start position:0%
+you know friction and things like that
+that will slow it down but this force
+
+ align:start position:0%
+that will slow it down but this force
+ 
+
+ align:start position:0%
+that will slow it down but this force
+field is not responsible for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay so
+
+ align:start position:0%
+it okay so
+ 
+
+ align:start position:0%
+it okay so
+the cool consequence of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this if a force field F derives from a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential okay so that's what we've seen
+
+ align:start position:0%
+potential okay so that's what we've seen
+ 
+
+ align:start position:0%
+potential okay so that's what we've seen
+about conservative
+
+ align:start position:0%
+about conservative
+ 
+
+ align:start position:0%
+about conservative
+forces so our main concern so far has
+
+ align:start position:0%
+forces so our main concern so far has
+ 
+
+ align:start position:0%
+forces so our main concern so far has
+been to say if we have a conservative
+
+ align:start position:0%
+been to say if we have a conservative
+ 
+
+ align:start position:0%
+been to say if we have a conservative
+force field it means that the work of a
+
+ align:start position:0%
+force field it means that the work of a
+ 
+
+ align:start position:0%
+force field it means that the work of a
+force is the change in the energy and in
+
+ align:start position:0%
+force is the change in the energy and in
+ 
+
+ align:start position:0%
+force is the change in the energy and in
+particular we can't get energy for free
+
+ align:start position:0%
+particular we can't get energy for free
+ 
+
+ align:start position:0%
+particular we can't get energy for free
+out of it and you know that the change
+
+ align:start position:0%
+out of it and you know that the change
+ 
+
+ align:start position:0%
+out of it and you know that the change
+in potential energy is going to be
+
+ align:start position:0%
+in potential energy is going to be
+ 
+
+ align:start position:0%
+in potential energy is going to be
+related to the change in kinetic energy
+
+ align:start position:0%
+related to the change in kinetic energy
+ 
+
+ align:start position:0%
+related to the change in kinetic energy
+so that's you know you have conservation
+
+ align:start position:0%
+so that's you know you have conservation
+ 
+
+ align:start position:0%
+so that's you know you have conservation
+of energy principles well there's
+
+ align:start position:0%
+of energy principles well there's
+ 
+
+ align:start position:0%
+of energy principles well there's
+another thing that we know now because
+
+ align:start position:0%
+another thing that we know now because
+ 
+
+ align:start position:0%
+another thing that we know now because
+if a force deres from potential then
+
+ align:start position:0%
+if a force deres from potential then
+ 
+
+ align:start position:0%
+if a force deres from potential then
+that means that its
+
+ align:start position:0%
+that means that its
+ 
+
+ align:start position:0%
+that means that its
+curl is zero that's the Criterion we've
+
+ align:start position:0%
+curl is zero that's the Criterion we've
+ 
+
+ align:start position:0%
+curl is zero that's the Criterion we've
+seen for a force to derive from for a
+
+ align:start position:0%
+seen for a force to derive from for a
+ 
+
+ align:start position:0%
+seen for a force to derive from for a
+vector field to derive from a
+
+ align:start position:0%
+vector field to derive from a
+ 
+
+ align:start position:0%
+vector field to derive from a
+potential and
+
+ align:start position:0%
+potential and
+ 
+
+ align:start position:0%
+potential and
+if the curl is zero then it means that
+
+ align:start position:0%
+if the curl is zero then it means that
+ 
+
+ align:start position:0%
+if the curl is zero then it means that
+actually this force does not generate
+
+ align:start position:0%
+actually this force does not generate
+ 
+
+ align:start position:0%
+actually this force does not generate
+any rotation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+effects so for
+
+ align:start position:0%
+effects so for
+ 
+
+ align:start position:0%
+effects so for
+example you know if you try to
+
+ align:start position:0%
+example you know if you try to
+ 
+
+ align:start position:0%
+example you know if you try to
+understand where does the Earth come
+
+ align:start position:0%
+understand where does the Earth come
+ 
+
+ align:start position:0%
+understand where does the Earth come
+from well the Earth is spinning on
+
+ align:start position:0%
+from well the Earth is spinning on
+ 
+
+ align:start position:0%
+from well the Earth is spinning on
+itself as it goes around the
+
+ align:start position:0%
+itself as it goes around the
+ 
+
+ align:start position:0%
+itself as it goes around the
+Sun and you might wonder where does that
+
+ align:start position:0%
+Sun and you might wonder where does that
+ 
+
+ align:start position:0%
+Sun and you might wonder where does that
+come from is that caused by
+
+ align:start position:0%
+come from is that caused by
+ 
+
+ align:start position:0%
+come from is that caused by
+gravitational attraction and while the
+
+ align:start position:0%
+gravitational attraction and while the
+ 
+
+ align:start position:0%
+gravitational attraction and while the
+answer is no gravitational attraction in
+
+ align:start position:0%
+answer is no gravitational attraction in
+ 
+
+ align:start position:0%
+answer is no gravitational attraction in
+itself cannot cause the Earth to start
+
+ align:start position:0%
+itself cannot cause the Earth to start
+ 
+
+ align:start position:0%
+itself cannot cause the Earth to start
+spinning faster or
+
+ align:start position:0%
+spinning faster or
+ 
+
+ align:start position:0%
+spinning faster or
+slower at least if you assume the Earth
+
+ align:start position:0%
+slower at least if you assume the Earth
+ 
+
+ align:start position:0%
+slower at least if you assume the Earth
+to be a solid which actually is
+
+ align:start position:0%
+to be a solid which actually is
+ 
+
+ align:start position:0%
+to be a solid which actually is
+false okay but still it doesn't explain
+
+ align:start position:0%
+false okay but still it doesn't explain
+ 
+
+ align:start position:0%
+false okay but still it doesn't explain
+I mean basically the reason why the
+
+ align:start position:0%
+I mean basically the reason why the
+ 
+
+ align:start position:0%
+I mean basically the reason why the
+Earth is spinning is because it was
+
+ align:start position:0%
+Earth is spinning is because it was
+ 
+
+ align:start position:0%
+Earth is spinning is because it was
+formed spinning
+
+ align:start position:0%
+formed spinning
+ 
+
+ align:start position:0%
+formed spinning
+it didn't start spinning because of
+
+ align:start position:0%
+it didn't start spinning because of
+ 
+
+ align:start position:0%
+it didn't start spinning because of
+gravitational effect and that's you
+
+ align:start position:0%
+gravitational effect and that's you
+ 
+
+ align:start position:0%
+gravitational effect and that's you
+know a rather deep purely mathematical
+
+ align:start position:0%
+know a rather deep purely mathematical
+ 
+
+ align:start position:0%
+know a rather deep purely mathematical
+consequence of understanding gravitation
+
+ align:start position:0%
+consequence of understanding gravitation
+ 
+
+ align:start position:0%
+consequence of understanding gravitation
+in this way so it's quite spectacular
+
+ align:start position:0%
+in this way so it's quite spectacular
+ 
+
+ align:start position:0%
+in this way so it's quite spectacular
+that just you know by abstract thinking
+
+ align:start position:0%
+that just you know by abstract thinking
+ 
+
+ align:start position:0%
+that just you know by abstract thinking
+we got there so actually what's the
+
+ align:start position:0%
+we got there so actually what's the
+ 
+
+ align:start position:0%
+we got there so actually what's the
+truth well the truth is actually the
+
+ align:start position:0%
+truth well the truth is actually the
+ 
+
+ align:start position:0%
+truth well the truth is actually the
+Earth the moon and everything is
+
+ align:start position:0%
+Earth the moon and everything is
+ 
+
+ align:start position:0%
+Earth the moon and everything is
+actually slightly deformable and so
+
+ align:start position:0%
+actually slightly deformable and so
+ 
+
+ align:start position:0%
+actually slightly deformable and so
+there's deformation friction effects
+
+ align:start position:0%
+there's deformation friction effects
+ 
+
+ align:start position:0%
+there's deformation friction effects
+tidal effects and so on and these
+
+ align:start position:0%
+tidal effects and so on and these
+ 
+
+ align:start position:0%
+tidal effects and so on and these
+actually cause rotations to get slightly
+
+ align:start position:0%
+actually cause rotations to get slightly
+ 
+
+ align:start position:0%
+actually cause rotations to get slightly
+synchronized with each other so for
+
+ align:start position:0%
+synchronized with each other so for
+ 
+
+ align:start position:0%
+synchronized with each other so for
+example if you want to explain why the
+
+ align:start position:0%
+example if you want to explain why the
+ 
+
+ align:start position:0%
+example if you want to explain why the
+Moon is always showing the same face to
+
+ align:start position:0%
+Moon is always showing the same face to
+ 
+
+ align:start position:0%
+Moon is always showing the same face to
+the Earth so why the rotation of a moon
+
+ align:start position:0%
+the Earth so why the rotation of a moon
+ 
+
+ align:start position:0%
+the Earth so why the rotation of a moon
+on itself is synchronized with its
+
+ align:start position:0%
+on itself is synchronized with its
+ 
+
+ align:start position:0%
+on itself is synchronized with its
+revolution around the earth that is
+
+ align:start position:0%
+revolution around the earth that is
+ 
+
+ align:start position:0%
+revolution around the earth that is
+actually explained by friction effect
+
+ align:start position:0%
+actually explained by friction effect
+ 
+
+ align:start position:0%
+actually explained by friction effect
+over time and the gravitational
+
+ align:start position:0%
+over time and the gravitational
+ 
+
+ align:start position:0%
+over time and the gravitational
+attraction of the Earth and the moon so
+
+ align:start position:0%
+attraction of the Earth and the moon so
+ 
+
+ align:start position:0%
+attraction of the Earth and the moon so
+there is something there but if you took
+
+ align:start position:0%
+there is something there but if you took
+ 
+
+ align:start position:0%
+there is something there but if you took
+perfectly solid you know perfectly rigid
+
+ align:start position:0%
+perfectly solid you know perfectly rigid
+ 
+
+ align:start position:0%
+perfectly solid you know perfectly rigid
+solid bodies then gravitation would
+
+ align:start position:0%
+solid bodies then gravitation would
+ 
+
+ align:start position:0%
+solid bodies then gravitation would
+never cause any rotation effect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so of course that tells us that we
+
+ align:start position:0%
+okay so of course that tells us that we
+ 
+
+ align:start position:0%
+okay so of course that tells us that we
+don't know how to answer the question of
+
+ align:start position:0%
+don't know how to answer the question of
+ 
+
+ align:start position:0%
+don't know how to answer the question of
+why is the Earth spinning
+
+ align:start position:0%
+why is the Earth spinning
+ 
+
+ align:start position:0%
+why is the Earth spinning
+and well that will be left for another
+
+ align:start position:0%
+and well that will be left for another
+ 
+
+ align:start position:0%
+and well that will be left for another
+physics class I I don't have a good
+
+ align:start position:0%
+physics class I I don't have a good
+ 
+
+ align:start position:0%
+physics class I I don't have a good
+answer to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that was kind of 801 is uh let me now
+
+ align:start position:0%
+so that was kind of 801 is uh let me now
+ 
+
+ align:start position:0%
+so that was kind of 801 is uh let me now
+move forward to 802
+
+ align:start position:0%
+move forward to 802
+ 
+
+ align:start position:0%
+move forward to 802
+stuff so I want to tell you things about
+
+ align:start position:0%
+stuff so I want to tell you things about
+ 
+
+ align:start position:0%
+stuff so I want to tell you things about
+electric and magnetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fields
+
+ align:start position:0%
+fields
+ 
+
+ align:start position:0%
+fields
+and in fact something that's known as
+
+ align:start position:0%
+and in fact something that's known as
+ 
+
+ align:start position:0%
+and in fact something that's known as
+Maxwell's equ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just a quick poll if you have been
+
+ align:start position:0%
+so just a quick poll if you have been
+ 
+
+ align:start position:0%
+so just a quick poll if you have been
+taking first of all how many of you have
+
+ align:start position:0%
+taking first of all how many of you have
+ 
+
+ align:start position:0%
+taking first of all how many of you have
+been taking 8 to2 or something like that
+
+ align:start position:0%
+been taking 8 to2 or something like that
+ 
+
+ align:start position:0%
+been taking 8 to2 or something like that
+okay so that's not very many so for most
+
+ align:start position:0%
+okay so that's not very many so for most
+ 
+
+ align:start position:0%
+okay so that's not very many so for most
+of you this is a preview if you've been
+
+ align:start position:0%
+of you this is a preview if you've been
+ 
+
+ align:start position:0%
+of you this is a preview if you've been
+taking 802 have you seen Maxwell's
+
+ align:start position:0%
+taking 802 have you seen Maxwell's
+ 
+
+ align:start position:0%
+taking 802 have you seen Maxwell's
+equations at least part of them yeah
+
+ align:start position:0%
+equations at least part of them yeah
+ 
+
+ align:start position:0%
+equations at least part of them yeah
+okay so then I'm sure in that case you
+
+ align:start position:0%
+okay so then I'm sure in that case you
+ 
+
+ align:start position:0%
+okay so then I'm sure in that case you
+know better than me what I'm going to
+
+ align:start position:0%
+know better than me what I'm going to
+ 
+
+ align:start position:0%
+know better than me what I'm going to
+talk about because I'm not a physicist
+
+ align:start position:0%
+talk about because I'm not a physicist
+ 
+
+ align:start position:0%
+talk about because I'm not a physicist
+but just in case um
+
+ align:start position:0%
+but just in case um
+ 
+
+ align:start position:0%
+but just in case um
+so Maxwell's equations govern how
+
+ align:start position:0%
+so Maxwell's equations govern how
+ 
+
+ align:start position:0%
+so Maxwell's equations govern how
+electric and magnetic fields behave how
+
+ align:start position:0%
+electric and magnetic fields behave how
+ 
+
+ align:start position:0%
+electric and magnetic fields behave how
+they're caused by charge electric
+
+ align:start position:0%
+they're caused by charge electric
+ 
+
+ align:start position:0%
+they're caused by charge electric
+charges and their motions and in
+
+ align:start position:0%
+charges and their motions and in
+ 
+
+ align:start position:0%
+charges and their motions and in
+particular they explain a lot of things
+
+ align:start position:0%
+particular they explain a lot of things
+ 
+
+ align:start position:0%
+particular they explain a lot of things
+such as you know how electrical devices
+
+ align:start position:0%
+such as you know how electrical devices
+ 
+
+ align:start position:0%
+such as you know how electrical devices
+work but also how electromagnetic waves
+
+ align:start position:0%
+work but also how electromagnetic waves
+ 
+
+ align:start position:0%
+work but also how electromagnetic waves
+propagate so in particular that explains
+
+ align:start position:0%
+propagate so in particular that explains
+ 
+
+ align:start position:0%
+propagate so in particular that explains
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+um and um you know all sorts of waves so
+
+ align:start position:0%
+um and um you know all sorts of waves so
+ 
+
+ align:start position:0%
+um and um you know all sorts of waves so
+it's thanks to them that you know your
+
+ align:start position:0%
+it's thanks to them that you know your
+ 
+
+ align:start position:0%
+it's thanks to them that you know your
+cell phone and your
+
+ align:start position:0%
+cell phone and your
+ 
+
+ align:start position:0%
+cell phone and your
+laptop and things like that work but
+
+ align:start position:0%
+laptop and things like that work but
+ 
+
+ align:start position:0%
+laptop and things like that work but
+anyway okay
+
+ align:start position:0%
+anyway okay
+ 
+
+ align:start position:0%
+anyway okay
+so hopefully most of you know that the
+
+ align:start position:0%
+so hopefully most of you know that the
+ 
+
+ align:start position:0%
+so hopefully most of you know that the
+electric field is a vector field that
+
+ align:start position:0%
+electric field is a vector field that
+ 
+
+ align:start position:0%
+electric field is a vector field that
+basically tells you what kind of force
+
+ align:start position:0%
+basically tells you what kind of force
+ 
+
+ align:start position:0%
+basically tells you what kind of force
+will be exerted on a Charged particle
+
+ align:start position:0%
+will be exerted on a Charged particle
+ 
+
+ align:start position:0%
+will be exerted on a Charged particle
+that you put in it so if you have a
+
+ align:start position:0%
+that you put in it so if you have a
+ 
+
+ align:start position:0%
+that you put in it so if you have a
+particle carrying an electric
+
+ align:start position:0%
+particle carrying an electric
+ 
+
+ align:start position:0%
+particle carrying an electric
+charge then this Vector field will tell
+
+ align:start position:0%
+charge then this Vector field will tell
+ 
+
+ align:start position:0%
+charge then this Vector field will tell
+you basically there will be an electric
+
+ align:start position:0%
+you basically there will be an electric
+ 
+
+ align:start position:0%
+you basically there will be an electric
+force which is the charge times e that
+
+ align:start position:0%
+force which is the charge times e that
+ 
+
+ align:start position:0%
+force which is the charge times e that
+will be exerted on that particle and
+
+ align:start position:0%
+will be exerted on that particle and
+ 
+
+ align:start position:0%
+will be exerted on that particle and
+that's what's responsible for example
+
+ align:start position:0%
+that's what's responsible for example
+ 
+
+ align:start position:0%
+that's what's responsible for example
+for the flow of electrons when you have
+
+ align:start position:0%
+for the flow of electrons when you have
+ 
+
+ align:start position:0%
+for the flow of electrons when you have
+a voltage difference because
+
+ align:start position:0%
+a voltage difference because
+ 
+
+ align:start position:0%
+a voltage difference because
+classically this guy is actually the
+
+ align:start position:0%
+classically this guy is actually the
+ 
+
+ align:start position:0%
+classically this guy is actually the
+gradient of a potential and that that
+
+ align:start position:0%
+gradient of a potential and that that
+ 
+
+ align:start position:0%
+gradient of a potential and that that
+potential is just electric
+
+ align:start position:0%
+potential is just electric
+ 
+
+ align:start position:0%
+potential is just electric
+voltage the magnetic field is a little
+
+ align:start position:0%
+voltage the magnetic field is a little
+ 
+
+ align:start position:0%
+voltage the magnetic field is a little
+bit harder to think about if you never
+
+ align:start position:0%
+bit harder to think about if you never
+ 
+
+ align:start position:0%
+bit harder to think about if you never
+seen it in physics but you know it's
+
+ align:start position:0%
+seen it in physics but you know it's
+ 
+
+ align:start position:0%
+seen it in physics but you know it's
+what's
+
+ align:start position:0%
+what's
+ 
+
+ align:start position:0%
+what's
+causing for example magnets to work
+
+ align:start position:0%
+causing for example magnets to work
+ 
+
+ align:start position:0%
+causing for example magnets to work
+and well basically it's a force that's
+
+ align:start position:0%
+and well basically it's a force that's
+ 
+
+ align:start position:0%
+and well basically it's a force that's
+also expressed in terms of a of a vector
+
+ align:start position:0%
+also expressed in terms of a of a vector
+ 
+
+ align:start position:0%
+also expressed in terms of a of a vector
+field usually called B some people call
+
+ align:start position:0%
+field usually called B some people call
+ 
+
+ align:start position:0%
+field usually called B some people call
+it h but I'm going to use
+
+ align:start position:0%
+it h but I'm going to use
+ 
+
+ align:start position:0%
+it h but I'm going to use
+B and that Force tends to cause if you
+
+ align:start position:0%
+B and that Force tends to cause if you
+ 
+
+ align:start position:0%
+B and that Force tends to cause if you
+have a moving charged particle then that
+
+ align:start position:0%
+have a moving charged particle then that
+ 
+
+ align:start position:0%
+have a moving charged particle then that
+will cause it to deflect its trajectory
+
+ align:start position:0%
+will cause it to deflect its trajectory
+ 
+
+ align:start position:0%
+will cause it to deflect its trajectory
+and start rotating in the magnetic field
+
+ align:start position:0%
+and start rotating in the magnetic field
+ 
+
+ align:start position:0%
+and start rotating in the magnetic field
+so what it does is not quite as easy as
+
+ align:start position:0%
+so what it does is not quite as easy as
+ 
+
+ align:start position:0%
+so what it does is not quite as easy as
+what the electric field does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um just
+
+ align:start position:0%
+um just
+ 
+
+ align:start position:0%
+um just
+to give you formulas the force caused by
+
+ align:start position:0%
+to give you formulas the force caused by
+ 
+
+ align:start position:0%
+to give you formulas the force caused by
+the electric field is the charge time
+
+ align:start position:0%
+the electric field is the charge time
+ 
+
+ align:start position:0%
+the electric field is the charge time
+the electric field and the force caused
+
+ align:start position:0%
+the electric field and the force caused
+ 
+
+ align:start position:0%
+the electric field and the force caused
+by the magnetic field is well I always
+
+ align:start position:0%
+by the magnetic field is well I always
+ 
+
+ align:start position:0%
+by the magnetic field is well I always
+I'm never sure about the sign is that
+
+ align:start position:0%
+I'm never sure about the sign is that
+ 
+
+ align:start position:0%
+I'm never sure about the sign is that
+the correct sign good
+
+ align:start position:0%
+the correct sign good
+ 
+
+ align:start position:0%
+the correct sign good
+okay so now the question is we need to
+
+ align:start position:0%
+okay so now the question is we need to
+ 
+
+ align:start position:0%
+okay so now the question is we need to
+understand how these fields themselves
+
+ align:start position:0%
+understand how these fields themselves
+ 
+
+ align:start position:0%
+understand how these fields themselves
+are caused by the by the charge
+
+ align:start position:0%
+are caused by the by the charge
+ 
+
+ align:start position:0%
+are caused by the by the charge
+particles that are placed in them
+
+ align:start position:0%
+particles that are placed in them
+ 
+
+ align:start position:0%
+particles that are placed in them
+and so there's various laws in there
+
+ align:start position:0%
+and so there's various laws in there
+ 
+
+ align:start position:0%
+and so there's various laws in there
+that explain what's going on so let me
+
+ align:start position:0%
+that explain what's going on so let me
+ 
+
+ align:start position:0%
+that explain what's going on so let me
+Focus today on the electric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+so Maxwell's equations actually tell you
+
+ align:start position:0%
+so Maxwell's equations actually tell you
+ 
+
+ align:start position:0%
+so Maxwell's equations actually tell you
+about da and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cur of this
+
+ align:start position:0%
+Cur of this
+ 
+
+ align:start position:0%
+Cur of this
+Fields so let's look at div and curl of
+
+ align:start position:0%
+Fields so let's look at div and curl of
+ 
+
+ align:start position:0%
+Fields so let's look at div and curl of
+the electric
+
+ align:start position:0%
+the electric
+ 
+
+ align:start position:0%
+the electric
+field so the first equation
+
+ align:start position:0%
+field so the first equation
+ 
+
+ align:start position:0%
+field so the first equation
+is called the G
+
+ align:start position:0%
+is called the G
+ 
+
+ align:start position:0%
+is called the G
+Kum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+law and it says that the Divergence of
+
+ align:start position:0%
+law and it says that the Divergence of
+ 
+
+ align:start position:0%
+law and it says that the Divergence of
+the electric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field is equal
+
+ align:start position:0%
+field is equal
+ 
+
+ align:start position:0%
+field is equal
+to so this
+
+ align:start position:0%
+to so this
+ 
+
+ align:start position:0%
+to so this
+is just a physical
+
+ align:start position:0%
+is just a physical
+ 
+
+ align:start position:0%
+is just a physical
+constant what it's equal to depends on
+
+ align:start position:0%
+constant what it's equal to depends on
+ 
+
+ align:start position:0%
+constant what it's equal to depends on
+what units you're
+
+ align:start position:0%
+what units you're
+ 
+
+ align:start position:0%
+what units you're
+using and this guy ho well it's not the
+
+ align:start position:0%
+using and this guy ho well it's not the
+ 
+
+ align:start position:0%
+using and this guy ho well it's not the
+same row as in spherical coordinates
+
+ align:start position:0%
+same row as in spherical coordinates
+ 
+
+ align:start position:0%
+same row as in spherical coordinates
+because physicists somehow patented the
+
+ align:start position:0%
+because physicists somehow patented the
+ 
+
+ align:start position:0%
+because physicists somehow patented the
+use of head letter first uh it's the
+
+ align:start position:0%
+use of head letter first uh it's the
+ 
+
+ align:start position:0%
+use of head letter first uh it's the
+actually the electric charge density so
+
+ align:start position:0%
+actually the electric charge density so
+ 
+
+ align:start position:0%
+actually the electric charge density so
+it's the amount of electric
+
+ align:start position:0%
+it's the amount of electric
+ 
+
+ align:start position:0%
+it's the amount of electric
+charge per unit
+
+ align:start position:0%
+charge per unit
+ 
+
+ align:start position:0%
+charge per unit
+volume so what it tells you what this
+
+ align:start position:0%
+volume so what it tells you what this
+ 
+
+ align:start position:0%
+volume so what it tells you what this
+tells you is that Divergence of e is
+
+ align:start position:0%
+tells you is that Divergence of e is
+ 
+
+ align:start position:0%
+tells you is that Divergence of e is
+caused by the presence of electric
+
+ align:start position:0%
+caused by the presence of electric
+ 
+
+ align:start position:0%
+caused by the presence of electric
+charge in particular if you have an
+
+ align:start position:0%
+charge in particular if you have an
+ 
+
+ align:start position:0%
+charge in particular if you have an
+empty region of
+
+ align:start position:0%
+empty region of
+ 
+
+ align:start position:0%
+empty region of
+space or region where nothing has
+
+ align:start position:0%
+space or region where nothing has
+ 
+
+ align:start position:0%
+space or region where nothing has
+electrical charge then e has
+
+ align:start position:0%
+electrical charge then e has
+ 
+
+ align:start position:0%
+electrical charge then e has
+as Divergence equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero so now that looks like a very
+
+ align:start position:0%
+zero so now that looks like a very
+ 
+
+ align:start position:0%
+zero so now that looks like a very
+abstract strange equation I mean
+
+ align:start position:0%
+abstract strange equation I mean
+ 
+
+ align:start position:0%
+abstract strange equation I mean
+actually it's a partial differential
+
+ align:start position:0%
+actually it's a partial differential
+ 
+
+ align:start position:0%
+actually it's a partial differential
+equation Satisfied by the electric field
+
+ align:start position:0%
+equation Satisfied by the electric field
+ 
+
+ align:start position:0%
+equation Satisfied by the electric field
+e and that's not very intuitive in any
+
+ align:start position:0%
+e and that's not very intuitive in any
+ 
+
+ align:start position:0%
+e and that's not very intuitive in any
+way okay
+
+ align:start position:0%
+way okay
+ 
+
+ align:start position:0%
+way okay
+so what's actually more
+
+ align:start position:0%
+so what's actually more
+ 
+
+ align:start position:0%
+so what's actually more
+intuitive is what we get if we apply the
+
+ align:start position:0%
+intuitive is what we get if we apply the
+ 
+
+ align:start position:0%
+intuitive is what we get if we apply the
+Divergence Theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to this
+
+ align:start position:0%
+to this
+ 
+
+ align:start position:0%
+to this
+equation okay
+
+ align:start position:0%
+equation okay
+ 
+
+ align:start position:0%
+equation okay
+so if I think now about any closed
+
+ align:start position:0%
+so if I think now about any closed
+ 
+
+ align:start position:0%
+so if I think now about any closed
+surface okay and I want to think about
+
+ align:start position:0%
+surface okay and I want to think about
+ 
+
+ align:start position:0%
+surface okay and I want to think about
+the flux of the electric field out of
+
+ align:start position:0%
+the flux of the electric field out of
+ 
+
+ align:start position:0%
+the flux of the electric field out of
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface so we haven't really thought
+
+ align:start position:0%
+surface so we haven't really thought
+ 
+
+ align:start position:0%
+surface so we haven't really thought
+about what the flux of a force field
+
+ align:start position:0%
+about what the flux of a force field
+ 
+
+ align:start position:0%
+about what the flux of a force field
+does and I don't want to get into that
+
+ align:start position:0%
+does and I don't want to get into that
+ 
+
+ align:start position:0%
+does and I don't want to get into that
+because there's no very easy answer in
+
+ align:start position:0%
+because there's no very easy answer in
+ 
+
+ align:start position:0%
+because there's no very easy answer in
+general but I'm going to explain soon
+
+ align:start position:0%
+general but I'm going to explain soon
+ 
+
+ align:start position:0%
+general but I'm going to explain soon
+how this can be useful
+
+ align:start position:0%
+how this can be useful
+ 
+
+ align:start position:0%
+how this can be useful
+sometimes but so let's say that we want
+
+ align:start position:0%
+sometimes but so let's say that we want
+ 
+
+ align:start position:0%
+sometimes but so let's say that we want
+to find the flux of the electric field
+
+ align:start position:0%
+to find the flux of the electric field
+ 
+
+ align:start position:0%
+to find the flux of the electric field
+out of a closed
+
+ align:start position:0%
+out of a closed
+ 
+
+ align:start position:0%
+out of a closed
+surface then by the Divergence
+
+ align:start position:0%
+surface then by the Divergence
+ 
+
+ align:start position:0%
+surface then by the Divergence
+Theorem that's equal to the triple
+
+ align:start position:0%
+Theorem that's equal to the triple
+ 
+
+ align:start position:0%
+Theorem that's equal to the triple
+integral of the region inside of D
+
+ align:start position:0%
+integral of the region inside of D
+ 
+
+ align:start position:0%
+integral of the region inside of D
+DV which is by the
+
+ align:start position:0%
+DV which is by the
+ 
+
+ align:start position:0%
+DV which is by the
+equation one of our 0 that's this
+
+ align:start position:0%
+equation one of our 0 that's this
+ 
+
+ align:start position:0%
+equation one of our 0 that's this
+constant the triple
+
+ align:start position:0%
+constant the triple
+ 
+
+ align:start position:0%
+constant the triple
+integral of row DV but now if I
+
+ align:start position:0%
+integral of row DV but now if I
+ 
+
+ align:start position:0%
+integral of row DV but now if I
+integrate the charge density over the
+
+ align:start position:0%
+integrate the charge density over the
+ 
+
+ align:start position:0%
+integrate the charge density over the
+entire region then what I will get is
+
+ align:start position:0%
+entire region then what I will get is
+ 
+
+ align:start position:0%
+entire region then what I will get is
+actually the total amount of electric
+
+ align:start position:0%
+actually the total amount of electric
+ 
+
+ align:start position:0%
+actually the total amount of electric
+charge inside the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+region okay so that's the electric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charge in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+D so
+
+ align:start position:0%
+D so
+ 
+
+ align:start position:0%
+D so
+this one tells us in a more concrete way
+
+ align:start position:0%
+this one tells us in a more concrete way
+ 
+
+ align:start position:0%
+this one tells us in a more concrete way
+how electric charges placed in here
+
+ align:start position:0%
+how electric charges placed in here
+ 
+
+ align:start position:0%
+how electric charges placed in here
+influence the electric field around them
+
+ align:start position:0%
+influence the electric field around them
+ 
+
+ align:start position:0%
+influence the electric field around them
+in particular one application of that is
+
+ align:start position:0%
+in particular one application of that is
+ 
+
+ align:start position:0%
+in particular one application of that is
+if you want to study capacitors so
+
+ align:start position:0%
+if you want to study capacitors so
+ 
+
+ align:start position:0%
+if you want to study capacitors so
+capacitors are these things that store
+
+ align:start position:0%
+capacitors are these things that store
+ 
+
+ align:start position:0%
+capacitors are these things that store
+energy by basically you have two plates
+
+ align:start position:0%
+energy by basically you have two plates
+ 
+
+ align:start position:0%
+energy by basically you have two plates
+one that contains positive charge the
+
+ align:start position:0%
+one that contains positive charge the
+ 
+
+ align:start position:0%
+one that contains positive charge the
+other negative charge and then you have
+
+ align:start position:0%
+other negative charge and then you have
+ 
+
+ align:start position:0%
+other negative charge and then you have
+a voltage between these plates and that
+
+ align:start position:0%
+a voltage between these plates and that
+ 
+
+ align:start position:0%
+a voltage between these plates and that
+can act basically that can provide
+
+ align:start position:0%
+can act basically that can provide
+ 
+
+ align:start position:0%
+can act basically that can provide
+electrical energy
+
+ align:start position:0%
+electrical energy
+ 
+
+ align:start position:0%
+electrical energy
+to power Maybe an electrical
+
+ align:start position:0%
+to power Maybe an electrical
+ 
+
+ align:start position:0%
+to power Maybe an electrical
+circuit and so you know that's kind of
+
+ align:start position:0%
+circuit and so you know that's kind of
+ 
+
+ align:start position:0%
+circuit and so you know that's kind of
+it's not really a battery because it
+
+ align:start position:0%
+it's not really a battery because it
+ 
+
+ align:start position:0%
+it's not really a battery because it
+doesn't store energy in large enough
+
+ align:start position:0%
+doesn't store energy in large enough
+ 
+
+ align:start position:0%
+doesn't store energy in large enough
+amounts for that but for example that's
+
+ align:start position:0%
+amounts for that but for example that's
+ 
+
+ align:start position:0%
+amounts for that but for example that's
+why you know when you switch your
+
+ align:start position:0%
+why you know when you switch your
+ 
+
+ align:start position:0%
+why you know when you switch your
+favorite Gadget off it doesn't actually
+
+ align:start position:0%
+favorite Gadget off it doesn't actually
+ 
+
+ align:start position:0%
+favorite Gadget off it doesn't actually
+go off immediately but somehow you see
+
+ align:start position:0%
+go off immediately but somehow you see
+ 
+
+ align:start position:0%
+go off immediately but somehow you see
+things diming progressively there's a
+
+ align:start position:0%
+things diming progressively there's a
+ 
+
+ align:start position:0%
+things diming progressively there's a
+capacitor in there so if you want to
+
+ align:start position:0%
+capacitor in there so if you want to
+ 
+
+ align:start position:0%
+capacitor in there so if you want to
+understand how the voltage and the
+
+ align:start position:0%
+understand how the voltage and the
+ 
+
+ align:start position:0%
+understand how the voltage and the
+charge relate to each other well the
+
+ align:start position:0%
+charge relate to each other well the
+ 
+
+ align:start position:0%
+charge relate to each other well the
+voltage is obtained by integrating the
+
+ align:start position:0%
+voltage is obtained by integrating the
+ 
+
+ align:start position:0%
+voltage is obtained by integrating the
+electric field from one plate to the
+
+ align:start position:0%
+electric field from one plate to the
+ 
+
+ align:start position:0%
+electric field from one plate to the
+other plate and the force sorry the
+
+ align:start position:0%
+other plate and the force sorry the
+ 
+
+ align:start position:0%
+other plate and the force sorry the
+charges in the plates are what causes
+
+ align:start position:0%
+charges in the plates are what causes
+ 
+
+ align:start position:0%
+charges in the plates are what causes
+the electric field between the plates so
+
+ align:start position:0%
+the electric field between the plates so
+ 
+
+ align:start position:0%
+the electric field between the plates so
+that's how you can get the relation
+
+ align:start position:0%
+that's how you can get the relation
+ 
+
+ align:start position:0%
+that's how you can get the relation
+between voltage and charge in these guys
+
+ align:start position:0%
+between voltage and charge in these guys
+ 
+
+ align:start position:0%
+between voltage and charge in these guys
+that's an example of application of
+
+ align:start position:0%
+that's an example of application of
+ 
+
+ align:start position:0%
+that's an example of application of
+that okay now of course if you haven't
+
+ align:start position:0%
+that okay now of course if you haven't
+ 
+
+ align:start position:0%
+that okay now of course if you haven't
+seen any of this then maybe it's a
+
+ align:start position:0%
+seen any of this then maybe it's a
+ 
+
+ align:start position:0%
+seen any of this then maybe it's a
+little bit esoteric but that will tell
+
+ align:start position:0%
+little bit esoteric but that will tell
+ 
+
+ align:start position:0%
+little bit esoteric but that will tell
+you you know part of what you will see
+
+ align:start position:0%
+you you know part of what you will see
+ 
+
+ align:start position:0%
+you you know part of what you will see
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay questions
+
+ align:start position:0%
+okay questions
+ 
+
+ align:start position:0%
+okay questions
+I see some confused
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+faces okay well don't worry it will make
+
+ align:start position:0%
+faces okay well don't worry it will make
+ 
+
+ align:start position:0%
+faces okay well don't worry it will make
+sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+someday so the next one I want to tell
+
+ align:start position:0%
+someday so the next one I want to tell
+ 
+
+ align:start position:0%
+someday so the next one I want to tell
+you about is far's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+low so in case you're confused by the
+
+ align:start position:0%
+low so in case you're confused by the
+ 
+
+ align:start position:0%
+low so in case you're confused by the
+way I should say Maxwell's equations so
+
+ align:start position:0%
+way I should say Maxwell's equations so
+ 
+
+ align:start position:0%
+way I should say Maxwell's equations so
+there's four equations in the set of Max
+
+ align:start position:0%
+there's four equations in the set of Max
+ 
+
+ align:start position:0%
+there's four equations in the set of Max
+equations and most of them don't carry
+
+ align:start position:0%
+equations and most of them don't carry
+ 
+
+ align:start position:0%
+equations and most of them don't carry
+Maxwell's name I mean
+
+ align:start position:0%
+Maxwell's name I mean
+ 
+
+ align:start position:0%
+Maxwell's name I mean
+that's Qui feature of
+
+ align:start position:0%
+that's Qui feature of
+ 
+
+ align:start position:0%
+that's Qui feature of
+them so that one tells you about the
+
+ align:start position:0%
+them so that one tells you about the
+ 
+
+ align:start position:0%
+them so that one tells you about the
+curl of the electric
+
+ align:start position:0%
+curl of the electric
+ 
+
+ align:start position:0%
+curl of the electric
+field so now depending on your knowledge
+
+ align:start position:0%
+field so now depending on your knowledge
+ 
+
+ align:start position:0%
+field so now depending on your knowledge
+you might start telling me well the curl
+
+ align:start position:0%
+you might start telling me well the curl
+ 
+
+ align:start position:0%
+you might start telling me well the curl
+of the electric field has to be zero
+
+ align:start position:0%
+of the electric field has to be zero
+ 
+
+ align:start position:0%
+of the electric field has to be zero
+because it derives it derives from
+
+ align:start position:0%
+because it derives it derives from
+ 
+
+ align:start position:0%
+because it derives it derives from
+actually it's the gradient of the
+
+ align:start position:0%
+actually it's the gradient of the
+ 
+
+ align:start position:0%
+actually it's the gradient of the
+electric potential I told you this stuff
+
+ align:start position:0%
+electric potential I told you this stuff
+ 
+
+ align:start position:0%
+electric potential I told you this stuff
+about voltage well that doesn't account
+
+ align:start position:0%
+about voltage well that doesn't account
+ 
+
+ align:start position:0%
+about voltage well that doesn't account
+for the fact that sometimes you can
+
+ align:start position:0%
+for the fact that sometimes you can
+ 
+
+ align:start position:0%
+for the fact that sometimes you can
+create voltage
+
+ align:start position:0%
+create voltage
+ 
+
+ align:start position:0%
+create voltage
+out of nowhere using magnetic fields and
+
+ align:start position:0%
+out of nowhere using magnetic fields and
+ 
+
+ align:start position:0%
+out of nowhere using magnetic fields and
+in fact you have a faure of
+
+ align:start position:0%
+in fact you have a faure of
+ 
+
+ align:start position:0%
+in fact you have a faure of
+conservativity of the electric force if
+
+ align:start position:0%
+conservativity of the electric force if
+ 
+
+ align:start position:0%
+conservativity of the electric force if
+you have a magnetic
+
+ align:start position:0%
+you have a magnetic
+ 
+
+ align:start position:0%
+you have a magnetic
+field so what this one says is actually
+
+ align:start position:0%
+field so what this one says is actually
+ 
+
+ align:start position:0%
+field so what this one says is actually
+the curl of e is not zero but rather
+
+ align:start position:0%
+the curl of e is not zero but rather
+ 
+
+ align:start position:0%
+the curl of e is not zero but rather
+it's the derivative of the magnetic
+
+ align:start position:0%
+it's the derivative of the magnetic
+ 
+
+ align:start position:0%
+it's the derivative of the magnetic
+field with respect to
+
+ align:start position:0%
+field with respect to
+ 
+
+ align:start position:0%
+field with respect to
+time okay so more precisely it tells you
+
+ align:start position:0%
+time okay so more precisely it tells you
+ 
+
+ align:start position:0%
+time okay so more precisely it tells you
+that what you might have learned about
+
+ align:start position:0%
+that what you might have learned about
+ 
+
+ align:start position:0%
+that what you might have learned about
+electric Fields deriving from electric
+
+ align:start position:0%
+electric Fields deriving from electric
+ 
+
+ align:start position:0%
+electric Fields deriving from electric
+potential becomes false if you have a
+
+ align:start position:0%
+potential becomes false if you have a
+ 
+
+ align:start position:0%
+potential becomes false if you have a
+variable magnetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field and just to tell
+
+ align:start position:0%
+field and just to tell
+ 
+
+ align:start position:0%
+field and just to tell
+you you know that's again a strange
+
+ align:start position:0%
+you you know that's again a strange
+ 
+
+ align:start position:0%
+you you know that's again a strange
+partial differential equation relating
+
+ align:start position:0%
+partial differential equation relating
+ 
+
+ align:start position:0%
+partial differential equation relating
+these two Vector Fields
+
+ align:start position:0%
+these two Vector Fields
+ 
+
+ align:start position:0%
+these two Vector Fields
+so to make sense of it one should use
+
+ align:start position:0%
+so to make sense of it one should use
+ 
+
+ align:start position:0%
+so to make sense of it one should use
+Stokes theorem okay so if we apply
+
+ align:start position:0%
+Stokes theorem okay so if we apply
+ 
+
+ align:start position:0%
+Stokes theorem okay so if we apply
+Stokes
+
+ align:start position:0%
+Stokes
+ 
+
+ align:start position:0%
+Stokes
+theorem to compute the work done by the
+
+ align:start position:0%
+theorem to compute the work done by the
+ 
+
+ align:start position:0%
+theorem to compute the work done by the
+electric field around a closed curve
+
+ align:start position:0%
+electric field around a closed curve
+ 
+
+ align:start position:0%
+electric field around a closed curve
+so that means you know you have a wire
+
+ align:start position:0%
+so that means you know you have a wire
+ 
+
+ align:start position:0%
+so that means you know you have a wire
+in there and you want to find the
+
+ align:start position:0%
+in there and you want to find the
+ 
+
+ align:start position:0%
+in there and you want to find the
+voltage along the wire so now there's a
+
+ align:start position:0%
+voltage along the wire so now there's a
+ 
+
+ align:start position:0%
+voltage along the wire so now there's a
+strange thing because classically you
+
+ align:start position:0%
+strange thing because classically you
+ 
+
+ align:start position:0%
+strange thing because classically you
+would say well if I just have a wire
+
+ align:start position:0%
+would say well if I just have a wire
+ 
+
+ align:start position:0%
+would say well if I just have a wire
+with nothing in it there's no voltage on
+
+ align:start position:0%
+with nothing in it there's no voltage on
+ 
+
+ align:start position:0%
+with nothing in it there's no voltage on
+it well small change in plans if you
+
+ align:start position:0%
+it well small change in plans if you
+ 
+
+ align:start position:0%
+it well small change in plans if you
+actually have a varying a varying
+
+ align:start position:0%
+actually have a varying a varying
+ 
+
+ align:start position:0%
+actually have a varying a varying
+magnetic field that passes through that
+
+ align:start position:0%
+magnetic field that passes through that
+ 
+
+ align:start position:0%
+magnetic field that passes through that
+wire then that will actually generate
+
+ align:start position:0%
+wire then that will actually generate
+ 
+
+ align:start position:0%
+wire then that will actually generate
+voltage in it and that's how a
+
+ align:start position:0%
+voltage in it and that's how a
+ 
+
+ align:start position:0%
+voltage in it and that's how a
+Transformer works so a Transformer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know when you plug your laptop into
+
+ align:start position:0%
+you know when you plug your laptop into
+ 
+
+ align:start position:0%
+you know when you plug your laptop into
+the wall circuit you don't actually feed
+
+ align:start position:0%
+the wall circuit you don't actually feed
+ 
+
+ align:start position:0%
+the wall circuit you don't actually feed
+it directly 110 volts or 120 volts or
+
+ align:start position:0%
+it directly 110 volts or 120 volts or
+ 
+
+ align:start position:0%
+it directly 110 volts or 120 volts or
+whatever there's a transformer in there
+
+ align:start position:0%
+whatever there's a transformer in there
+ 
+
+ align:start position:0%
+whatever there's a transformer in there
+what the Transformer does is it takes
+
+ align:start position:0%
+what the Transformer does is it takes
+ 
+
+ align:start position:0%
+what the Transformer does is it takes
+some input voltage and it passes that
+
+ align:start position:0%
+some input voltage and it passes that
+ 
+
+ align:start position:0%
+some input voltage and it passes that
+through basically a loop of
+
+ align:start position:0%
+through basically a loop of
+ 
+
+ align:start position:0%
+through basically a loop of
+wire okay not much seems to be happening
+
+ align:start position:0%
+wire okay not much seems to be happening
+ 
+
+ align:start position:0%
+wire okay not much seems to be happening
+but now you have another loop of wire
+
+ align:start position:0%
+but now you have another loop of wire
+ 
+
+ align:start position:0%
+but now you have another loop of wire
+that is intertwined with it and somehow
+
+ align:start position:0%
+that is intertwined with it and somehow
+ 
+
+ align:start position:0%
+that is intertwined with it and somehow
+the magnetic field generated by so it
+
+ align:start position:0%
+the magnetic field generated by so it
+ 
+
+ align:start position:0%
+the magnetic field generated by so it
+has to be alternating current the
+
+ align:start position:0%
+has to be alternating current the
+ 
+
+ align:start position:0%
+has to be alternating current the
+alternating current varies over time in
+
+ align:start position:0%
+alternating current varies over time in
+ 
+
+ align:start position:0%
+alternating current varies over time in
+the first wire that generates a magnetic
+
+ align:start position:0%
+the first wire that generates a magnetic
+ 
+
+ align:start position:0%
+the first wire that generates a magnetic
+field that varies over time so that
+
+ align:start position:0%
+field that varies over time so that
+ 
+
+ align:start position:0%
+field that varies over time so that
+causes DB by DT and that causes curl of
+
+ align:start position:0%
+causes DB by DT and that causes curl of
+ 
+
+ align:start position:0%
+causes DB by DT and that causes curl of
+the electric field and the curl of the
+
+ align:start position:0%
+the electric field and the curl of the
+ 
+
+ align:start position:0%
+the electric field and the curl of the
+electric field will generate voltage
+
+ align:start position:0%
+electric field will generate voltage
+ 
+
+ align:start position:0%
+electric field will generate voltage
+between these two
+
+ align:start position:0%
+between these two
+ 
+
+ align:start position:0%
+between these two
+guys and that's how a Transformer works
+
+ align:start position:0%
+guys and that's how a Transformer works
+ 
+
+ align:start position:0%
+guys and that's how a Transformer works
+it uses Stokes
+
+ align:start position:0%
+it uses Stokes
+ 
+
+ align:start position:0%
+it uses Stokes
+theorem okay so more precisely how do we
+
+ align:start position:0%
+theorem okay so more precisely how do we
+ 
+
+ align:start position:0%
+theorem okay so more precisely how do we
+find the voltage between these two
+
+ align:start position:0%
+find the voltage between these two
+ 
+
+ align:start position:0%
+find the voltage between these two
+points let's close the loop and let's
+
+ align:start position:0%
+points let's close the loop and let's
+ 
+
+ align:start position:0%
+points let's close the loop and let's
+try to figure out the voltage inside
+
+ align:start position:0%
+try to figure out the voltage inside
+ 
+
+ align:start position:0%
+try to figure out the voltage inside
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+Loop so to find the voltage along a
+
+ align:start position:0%
+Loop so to find the voltage along a
+ 
+
+ align:start position:0%
+Loop so to find the voltage along a
+closed curve placed in a varing magnetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field so we have to do the line
+
+ align:start position:0%
+field so we have to do the line
+ 
+
+ align:start position:0%
+field so we have to do the line
+integral along a closed curve of the
+
+ align:start position:0%
+integral along a closed curve of the
+ 
+
+ align:start position:0%
+integral along a closed curve of the
+electric field and you should think of
+
+ align:start position:0%
+electric field and you should think of
+ 
+
+ align:start position:0%
+electric field and you should think of
+this as the voltage generated in this
+
+ align:start position:0%
+this as the voltage generated in this
+ 
+
+ align:start position:0%
+this as the voltage generated in this
+circuit that will be the flux
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through this surface bounded by the
+
+ align:start position:0%
+through this surface bounded by the
+ 
+
+ align:start position:0%
+through this surface bounded by the
+curve of Cur
+
+ align:start position:0%
+curve of Cur
+ 
+
+ align:start position:0%
+curve of Cur
+e DS that's what Stokes theorem says and
+
+ align:start position:0%
+e DS that's what Stokes theorem says and
+ 
+
+ align:start position:0%
+e DS that's what Stokes theorem says and
+now if you combine with farad law you
+
+ align:start position:0%
+now if you combine with farad law you
+ 
+
+ align:start position:0%
+now if you combine with farad law you
+end up with the flux through S
+
+ align:start position:0%
+end up with the flux through S
+ 
+
+ align:start position:0%
+end up with the flux through S
+of minus
+
+ align:start position:0%
+of minus
+ 
+
+ align:start position:0%
+of minus
+dbdt and of course you could take if
+
+ align:start position:0%
+dbdt and of course you could take if
+ 
+
+ align:start position:0%
+dbdt and of course you could take if
+your Loop doesn't move over time so I
+
+ align:start position:0%
+your Loop doesn't move over time so I
+ 
+
+ align:start position:0%
+your Loop doesn't move over time so I
+mean actually there's there's a
+
+ align:start position:0%
+mean actually there's there's a
+ 
+
+ align:start position:0%
+mean actually there's there's a
+different story if you start somehow
+
+ align:start position:0%
+different story if you start somehow
+ 
+
+ align:start position:0%
+different story if you start somehow
+taking your wire and somehow moving it
+
+ align:start position:0%
+taking your wire and somehow moving it
+ 
+
+ align:start position:0%
+taking your wire and somehow moving it
+inside the field but if you don't do
+
+ align:start position:0%
+inside the field but if you don't do
+ 
+
+ align:start position:0%
+inside the field but if you don't do
+that if it's the field that's moving
+
+ align:start position:0%
+that if it's the field that's moving
+ 
+
+ align:start position:0%
+that if it's the field that's moving
+then you just can take the d by DT
+
+ align:start position:0%
+then you just can take the d by DT
+ 
+
+ align:start position:0%
+then you just can take the d by DT
+outside but let's not
+
+ align:start position:0%
+outside but let's not
+ 
+
+ align:start position:0%
+outside but let's not
+bother okay
+
+ align:start position:0%
+bother okay
+ 
+
+ align:start position:0%
+bother okay
+so again what this equation tells you is
+
+ align:start position:0%
+so again what this equation tells you is
+ 
+
+ align:start position:0%
+so again what this equation tells you is
+that if magnetic field changes over time
+
+ align:start position:0%
+that if magnetic field changes over time
+ 
+
+ align:start position:0%
+that if magnetic field changes over time
+then it creates just out of nowhere an
+
+ align:start position:0%
+then it creates just out of nowhere an
+ 
+
+ align:start position:0%
+then it creates just out of nowhere an
+electric field and that electric field
+
+ align:start position:0%
+electric field and that electric field
+ 
+
+ align:start position:0%
+electric field and that electric field
+can be used to power things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I don't really claim that I've given
+
+ align:start position:0%
+so I don't really claim that I've given
+ 
+
+ align:start position:0%
+so I don't really claim that I've given
+you enough details to understand how
+
+ align:start position:0%
+you enough details to understand how
+ 
+
+ align:start position:0%
+you enough details to understand how
+they work but basically these equations
+
+ align:start position:0%
+they work but basically these equations
+ 
+
+ align:start position:0%
+they work but basically these equations
+are at the heart of understanding how
+
+ align:start position:0%
+are at the heart of understanding how
+ 
+
+ align:start position:0%
+are at the heart of understanding how
+things like capacitors and Transformers
+
+ align:start position:0%
+things like capacitors and Transformers
+ 
+
+ align:start position:0%
+things like capacitors and Transformers
+work and they also explain a lot of
+
+ align:start position:0%
+work and they also explain a lot of
+ 
+
+ align:start position:0%
+work and they also explain a lot of
+other things but I will leave that to
+
+ align:start position:0%
+other things but I will leave that to
+ 
+
+ align:start position:0%
+other things but I will leave that to
+your physics teachers uh just for
+
+ align:start position:0%
+your physics teachers uh just for
+ 
+
+ align:start position:0%
+your physics teachers uh just for
+completeness
+
+ align:start position:0%
+completeness
+ 
+
+ align:start position:0%
+completeness
+let me just give you the last two
+
+ align:start position:0%
+let me just give you the last two
+ 
+
+ align:start position:0%
+let me just give you the last two
+equations in that I'm not just I'm not
+
+ align:start position:0%
+equations in that I'm not just I'm not
+ 
+
+ align:start position:0%
+equations in that I'm not just I'm not
+even going to try to explain them too
+
+ align:start position:0%
+even going to try to explain them too
+ 
+
+ align:start position:0%
+even going to try to explain them too
+much so one of them says that the
+
+ align:start position:0%
+much so one of them says that the
+ 
+
+ align:start position:0%
+much so one of them says that the
+Divergence of the magnetic field is zero
+
+ align:start position:0%
+Divergence of the magnetic field is zero
+ 
+
+ align:start position:0%
+Divergence of the magnetic field is zero
+which somehow is fortunate because
+
+ align:start position:0%
+which somehow is fortunate because
+ 
+
+ align:start position:0%
+which somehow is fortunate because
+otherwise you would run into trouble
+
+ align:start position:0%
+otherwise you would run into trouble
+ 
+
+ align:start position:0%
+otherwise you would run into trouble
+trying to understand surface
+
+ align:start position:0%
+trying to understand surface
+ 
+
+ align:start position:0%
+trying to understand surface
+Independence when you apply Stokes
+
+ align:start position:0%
+Independence when you apply Stokes
+ 
+
+ align:start position:0%
+Independence when you apply Stokes
+theorem in
+
+ align:start position:0%
+theorem in
+ 
+
+ align:start position:0%
+theorem in
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and the last one tells you how the curl
+
+ align:start position:0%
+and the last one tells you how the curl
+ 
+
+ align:start position:0%
+and the last one tells you how the curl
+of the magnetic field is caused by
+
+ align:start position:0%
+of the magnetic field is caused by
+ 
+
+ align:start position:0%
+of the magnetic field is caused by
+motion of charged particles so in
+
+ align:start position:0%
+motion of charged particles so in
+ 
+
+ align:start position:0%
+motion of charged particles so in
+fact it says that the curl of
+
+ align:start position:0%
+fact it says that the curl of
+ 
+
+ align:start position:0%
+fact it says that the curl of
+J sorry the curl of
+
+ align:start position:0%
+J sorry the curl of
+ 
+
+ align:start position:0%
+J sorry the curl of
+B is given by this kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula where J is What's called the
+
+ align:start position:0%
+formula where J is What's called the
+ 
+
+ align:start position:0%
+formula where J is What's called the
+vector current density so it it measures
+
+ align:start position:0%
+vector current density so it it measures
+ 
+
+ align:start position:0%
+vector current density so it it measures
+the flow of electrically charged
+
+ align:start position:0%
+the flow of electrically charged
+ 
+
+ align:start position:0%
+the flow of electrically charged
+particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so you get this guy when you start
+
+ align:start position:0%
+okay so you get this guy when you start
+ 
+
+ align:start position:0%
+okay so you get this guy when you start
+taking charged particles like electrons
+
+ align:start position:0%
+taking charged particles like electrons
+ 
+
+ align:start position:0%
+taking charged particles like electrons
+maybe and moving them
+
+ align:start position:0%
+maybe and moving them
+ 
+
+ align:start position:0%
+maybe and moving them
+around and of course that's actually
+
+ align:start position:0%
+around and of course that's actually
+ 
+
+ align:start position:0%
+around and of course that's actually
+part of how Transformers work because
+
+ align:start position:0%
+part of how Transformers work because
+ 
+
+ align:start position:0%
+part of how Transformers work because
+I've told you you know running the AC
+
+ align:start position:0%
+I've told you you know running the AC
+ 
+
+ align:start position:0%
+I've told you you know running the AC
+through the first Loop generates a
+
+ align:start position:0%
+through the first Loop generates a
+ 
+
+ align:start position:0%
+through the first Loop generates a
+magnetic field well how does it do that
+
+ align:start position:0%
+magnetic field well how does it do that
+ 
+
+ align:start position:0%
+magnetic field well how does it do that
+it's thanks to this equation if you have
+
+ align:start position:0%
+it's thanks to this equation if you have
+ 
+
+ align:start position:0%
+it's thanks to this equation if you have
+a current passing in the loop that
+
+ align:start position:0%
+a current passing in the loop that
+ 
+
+ align:start position:0%
+a current passing in the loop that
+causes a magnetic field and in turn
+
+ align:start position:0%
+causes a magnetic field and in turn
+ 
+
+ align:start position:0%
+causes a magnetic field and in turn
+through the other equation that causes
+
+ align:start position:0%
+through the other equation that causes
+ 
+
+ align:start position:0%
+through the other equation that causes
+an electric field which in turns causes
+
+ align:start position:0%
+an electric field which in turns causes
+ 
+
+ align:start position:0%
+an electric field which in turns causes
+urrent so it's all somehow intertwined
+
+ align:start position:0%
+urrent so it's all somehow intertwined
+ 
+
+ align:start position:0%
+urrent so it's all somehow intertwined
+in a very intricate way and it's really
+
+ align:start position:0%
+in a very intricate way and it's really
+ 
+
+ align:start position:0%
+in a very intricate way and it's really
+remarkable how well that works in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+practice okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I think that's basically all I wanted
+
+ align:start position:0%
+so I think that's basically all I wanted
+ 
+
+ align:start position:0%
+so I think that's basically all I wanted
+to say about 802 I don't want to you
+
+ align:start position:0%
+to say about 802 I don't want to you
+ 
+
+ align:start position:0%
+to say about 802 I don't want to you
+know put your physics teachers out of a
+
+ align:start position:0%
+know put your physics teachers out of a
+ 
+
+ align:start position:0%
+know put your physics teachers out of a
+job
+
+ align:start position:0%
+job
+ 
+
+ align:start position:0%
+job
+so um if you haven't seen any of this
+
+ align:start position:0%
+so um if you haven't seen any of this
+ 
+
+ align:start position:0%
+so um if you haven't seen any of this
+before I understand that this is
+
+ align:start position:0%
+before I understand that this is
+ 
+
+ align:start position:0%
+before I understand that this is
+probably not detailed enough to be
+
+ align:start position:0%
+probably not detailed enough to be
+ 
+
+ align:start position:0%
+probably not detailed enough to be
+really understandable but hopefully it
+
+ align:start position:0%
+really understandable but hopefully it
+ 
+
+ align:start position:0%
+really understandable but hopefully it
+makes you it will make you a bit curious
+
+ align:start position:0%
+makes you it will make you a bit curious
+ 
+
+ align:start position:0%
+makes you it will make you a bit curious
+about that and prompt you to you know
+
+ align:start position:0%
+about that and prompt you to you know
+ 
+
+ align:start position:0%
+about that and prompt you to you know
+take that class someday and maybe even
+
+ align:start position:0%
+take that class someday and maybe even
+ 
+
+ align:start position:0%
+take that class someday and maybe even
+remember how it relates to 1802
\ No newline at end of file
diff --git a/BFwc2XA8rSk.txt b/BFwc2XA8rSk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c2dbee278788370ff10447f5c522e08802a2615f
--- /dev/null
+++ b/BFwc2XA8rSk.txt
@@ -0,0 +1,13963 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so today I'll talk about coin join
+
+ align:start position:0%
+okay so today I'll talk about coin join
+ 
+
+ align:start position:0%
+okay so today I'll talk about coin join
+signature aggregation sort of well
+
+ align:start position:0%
+signature aggregation sort of well
+ 
+
+ align:start position:0%
+signature aggregation sort of well
+before that privacy but privacy coin
+
+ align:start position:0%
+before that privacy but privacy coin
+ 
+
+ align:start position:0%
+before that privacy but privacy coin
+join clone shuffle signature aggregation
+
+ align:start position:0%
+join clone shuffle signature aggregation
+ 
+
+ align:start position:0%
+join clone shuffle signature aggregation
+and how these all connect it's a little
+
+ align:start position:0%
+and how these all connect it's a little
+ 
+
+ align:start position:0%
+and how these all connect it's a little
+bit of a leap to put these boats in the
+
+ align:start position:0%
+bit of a leap to put these boats in the
+ 
+
+ align:start position:0%
+bit of a leap to put these boats in the
+same class but not really they're there
+
+ align:start position:0%
+same class but not really they're there
+ 
+
+ align:start position:0%
+same class but not really they're there
+they're connected but there are some
+
+ align:start position:0%
+they're connected but there are some
+ 
+
+ align:start position:0%
+they're connected but there are some
+somewhat separate things today talk
+
+ align:start position:0%
+somewhat separate things today talk
+ 
+
+ align:start position:0%
+somewhat separate things today talk
+about privacy coin join and various ways
+
+ align:start position:0%
+about privacy coin join and various ways
+ 
+
+ align:start position:0%
+about privacy coin join and various ways
+to do that and then aggregate signatures
+
+ align:start position:0%
+to do that and then aggregate signatures
+ 
+
+ align:start position:0%
+to do that and then aggregate signatures
+so Schnoor multi signatures and then
+
+ align:start position:0%
+so Schnoor multi signatures and then
+ 
+
+ align:start position:0%
+so Schnoor multi signatures and then
+aggregation and attacks on this system
+
+ align:start position:0%
+aggregation and attacks on this system
+ 
+
+ align:start position:0%
+aggregation and attacks on this system
+okay so the idea is privacy and there's
+
+ align:start position:0%
+okay so the idea is privacy and there's
+ 
+
+ align:start position:0%
+okay so the idea is privacy and there's
+a bunch of terms we can use here like
+
+ align:start position:0%
+a bunch of terms we can use here like
+ 
+
+ align:start position:0%
+a bunch of terms we can use here like
+anonymity and fungibility and whatever
+
+ align:start position:0%
+anonymity and fungibility and whatever
+ 
+
+ align:start position:0%
+anonymity and fungibility and whatever
+the term for this I don't need any
+
+ align:start position:0%
+the term for this I don't need any
+ 
+
+ align:start position:0%
+the term for this I don't need any
+because I have nothing to hide so I
+
+ align:start position:0%
+because I have nothing to hide so I
+ 
+
+ align:start position:0%
+because I have nothing to hide so I
+don't need any privacy I don't need any
+
+ align:start position:0%
+don't need any privacy I don't need any
+ 
+
+ align:start position:0%
+don't need any privacy I don't need any
+anonymity I'm a good person I don't
+
+ align:start position:0%
+anonymity I'm a good person I don't
+ 
+
+ align:start position:0%
+anonymity I'm a good person I don't
+break the law I'm boring guy I don't do
+
+ align:start position:0%
+break the law I'm boring guy I don't do
+ 
+
+ align:start position:0%
+break the law I'm boring guy I don't do
+anything crazy I'm joking but no I'm not
+
+ align:start position:0%
+anything crazy I'm joking but no I'm not
+ 
+
+ align:start position:0%
+anything crazy I'm joking but no I'm not
+joking about being boring and not doing
+
+ align:start position:0%
+joking about being boring and not doing
+ 
+
+ align:start position:0%
+joking about being boring and not doing
+anything crazy that is actually pretty
+
+ align:start position:0%
+anything crazy that is actually pretty
+ 
+
+ align:start position:0%
+anything crazy that is actually pretty
+true I mostly just work on this stuff
+
+ align:start position:0%
+true I mostly just work on this stuff
+ 
+
+ align:start position:0%
+true I mostly just work on this stuff
+but yeah that's a fairly common thing
+
+ align:start position:0%
+but yeah that's a fairly common thing
+ 
+
+ align:start position:0%
+but yeah that's a fairly common thing
+that people say and the biggest thing
+
+ align:start position:0%
+that people say and the biggest thing
+ 
+
+ align:start position:0%
+that people say and the biggest thing
+that sort of clearest example is it
+
+ align:start position:0%
+that sort of clearest example is it
+ 
+
+ align:start position:0%
+that sort of clearest example is it
+won't have anything to hide you don't
+
+ align:start position:0%
+won't have anything to hide you don't
+ 
+
+ align:start position:0%
+won't have anything to hide you don't
+have any Bitcoin because like literally
+
+ align:start position:0%
+have any Bitcoin because like literally
+ 
+
+ align:start position:0%
+have any Bitcoin because like literally
+if you don't hide your private key and
+
+ align:start position:0%
+if you don't hide your private key and
+ 
+
+ align:start position:0%
+if you don't hide your private key and
+someone will just immediately take your
+
+ align:start position:0%
+someone will just immediately take your
+ 
+
+ align:start position:0%
+someone will just immediately take your
+bitcoins so so you do have secrets right
+
+ align:start position:0%
+bitcoins so so you do have secrets right
+ 
+
+ align:start position:0%
+bitcoins so so you do have secrets right
+your secret is your private key and your
+
+ align:start position:0%
+your secret is your private key and your
+ 
+
+ align:start position:0%
+your secret is your private key and your
+password and if bitcoin and these types
+
+ align:start position:0%
+password and if bitcoin and these types
+ 
+
+ align:start position:0%
+password and if bitcoin and these types
+of systems really take off potentially
+
+ align:start position:0%
+of systems really take off potentially
+ 
+
+ align:start position:0%
+of systems really take off potentially
+most of your money and a lot of your
+
+ align:start position:0%
+most of your money and a lot of your
+ 
+
+ align:start position:0%
+most of your money and a lot of your
+wealth could be tied up in what is you
+
+ align:start position:0%
+wealth could be tied up in what is you
+ 
+
+ align:start position:0%
+wealth could be tied up in what is you
+know a secret so if you're not able to
+
+ align:start position:0%
+know a secret so if you're not able to
+ 
+
+ align:start position:0%
+know a secret so if you're not able to
+keep your secrets you could lose a lot
+
+ align:start position:0%
+keep your secrets you could lose a lot
+ 
+
+ align:start position:0%
+keep your secrets you could lose a lot
+of money and larger like I sort of think
+
+ align:start position:0%
+of money and larger like I sort of think
+ 
+
+ align:start position:0%
+of money and larger like I sort of think
+that going for you know this is very
+
+ align:start position:0%
+that going for you know this is very
+ 
+
+ align:start position:0%
+that going for you know this is very
+sort of thought leader II future kind of
+
+ align:start position:0%
+sort of thought leader II future kind of
+ 
+
+ align:start position:0%
+sort of thought leader II future kind of
+thing but going forward it seems like
+
+ align:start position:0%
+thing but going forward it seems like
+ 
+
+ align:start position:0%
+thing but going forward it seems like
+sort of all you have is your secrets to
+
+ align:start position:0%
+sort of all you have is your secrets to
+ 
+
+ align:start position:0%
+sort of all you have is your secrets to
+the extent that you can own anything the
+
+ align:start position:0%
+the extent that you can own anything the
+ 
+
+ align:start position:0%
+the extent that you can own anything the
+thing that you really have control over
+
+ align:start position:0%
+thing that you really have control over
+ 
+
+ align:start position:0%
+thing that you really have control over
+got these things in my head that no one
+
+ align:start position:0%
+got these things in my head that no one
+ 
+
+ align:start position:0%
+got these things in my head that no one
+else knows and I might not you know
+
+ align:start position:0%
+else knows and I might not you know
+ 
+
+ align:start position:0%
+else knows and I might not you know
+maybe I own my car but that's also sort
+
+ align:start position:0%
+maybe I own my car but that's also sort
+ 
+
+ align:start position:0%
+maybe I own my car but that's also sort
+of property rights and legal systems and
+
+ align:start position:0%
+of property rights and legal systems and
+ 
+
+ align:start position:0%
+of property rights and legal systems and
+maybe it can get repossessed maybe I own
+
+ align:start position:0%
+maybe it can get repossessed maybe I own
+ 
+
+ align:start position:0%
+maybe it can get repossessed maybe I own
+this Lane
+
+ align:start position:0%
+this Lane
+ 
+
+ align:start position:0%
+this Lane
+but again that's sort of this thing with
+
+ align:start position:0%
+but again that's sort of this thing with
+ 
+
+ align:start position:0%
+but again that's sort of this thing with
+the state but I definitely really have
+
+ align:start position:0%
+the state but I definitely really have
+ 
+
+ align:start position:0%
+the state but I definitely really have
+the stuff in my head and I can at least
+
+ align:start position:0%
+the stuff in my head and I can at least
+ 
+
+ align:start position:0%
+the stuff in my head and I can at least
+you know try to keep keep that so even
+
+ align:start position:0%
+you know try to keep keep that so even
+ 
+
+ align:start position:0%
+you know try to keep keep that so even
+if you think you have nothing to hide
+
+ align:start position:0%
+if you think you have nothing to hide
+ 
+
+ align:start position:0%
+if you think you have nothing to hide
+you do have your private keys to hide
+
+ align:start position:0%
+you do have your private keys to hide
+ 
+
+ align:start position:0%
+you do have your private keys to hide
+and that's sort of the obvious one but
+
+ align:start position:0%
+and that's sort of the obvious one but
+ 
+
+ align:start position:0%
+and that's sort of the obvious one but
+but larger you want privacy because in
+
+ align:start position:0%
+but larger you want privacy because in
+ 
+
+ align:start position:0%
+but larger you want privacy because in
+general you don't want to reveal stuff
+
+ align:start position:0%
+general you don't want to reveal stuff
+ 
+
+ align:start position:0%
+general you don't want to reveal stuff
+about your coins this is you know
+
+ align:start position:0%
+about your coins this is you know
+ 
+
+ align:start position:0%
+about your coins this is you know
+specific to Bitcoin but like my
+
+ align:start position:0%
+specific to Bitcoin but like my
+ 
+
+ align:start position:0%
+specific to Bitcoin but like my
+philosophy is I generally don't want to
+
+ align:start position:0%
+philosophy is I generally don't want to
+ 
+
+ align:start position:0%
+philosophy is I generally don't want to
+reveal stuff ever and a lot of times it
+
+ align:start position:0%
+reveal stuff ever and a lot of times it
+ 
+
+ align:start position:0%
+reveal stuff ever and a lot of times it
+stores I remember like RadioShack when
+
+ align:start position:0%
+stores I remember like RadioShack when
+ 
+
+ align:start position:0%
+stores I remember like RadioShack when
+it was still a thing and I was in like
+
+ align:start position:0%
+it was still a thing and I was in like
+ 
+
+ align:start position:0%
+it was still a thing and I was in like
+high school they would always ask you
+
+ align:start position:0%
+high school they would always ask you
+ 
+
+ align:start position:0%
+high school they would always ask you
+your phone number when you bought
+
+ align:start position:0%
+your phone number when you bought
+ 
+
+ align:start position:0%
+your phone number when you bought
+anything and when I was little I would
+
+ align:start position:0%
+anything and when I was little I would
+ 
+
+ align:start position:0%
+anything and when I was little I would
+just tell them my parents phone number
+
+ align:start position:0%
+just tell them my parents phone number
+ 
+
+ align:start position:0%
+just tell them my parents phone number
+at my house cuz like I don't know they
+
+ align:start position:0%
+at my house cuz like I don't know they
+ 
+
+ align:start position:0%
+at my house cuz like I don't know they
+asked but then once I was in like
+
+ align:start position:0%
+asked but then once I was in like
+ 
+
+ align:start position:0%
+asked but then once I was in like
+college I was like wait no I'm just
+
+ align:start position:0%
+college I was like wait no I'm just
+ 
+
+ align:start position:0%
+college I was like wait no I'm just
+gonna make something up and and now I do
+
+ align:start position:0%
+gonna make something up and and now I do
+ 
+
+ align:start position:0%
+gonna make something up and and now I do
+that all the time and it sometimes gets
+
+ align:start position:0%
+that all the time and it sometimes gets
+ 
+
+ align:start position:0%
+that all the time and it sometimes gets
+a million for other people because I
+
+ align:start position:0%
+a million for other people because I
+ 
+
+ align:start position:0%
+a million for other people because I
+would like go to a restaurant they ask
+
+ align:start position:0%
+would like go to a restaurant they ask
+ 
+
+ align:start position:0%
+would like go to a restaurant they ask
+you know I put my name down I'll say I'm
+
+ align:start position:0%
+you know I put my name down I'll say I'm
+ 
+
+ align:start position:0%
+you know I put my name down I'll say I'm
+Fred and then my other friend comes and
+
+ align:start position:0%
+Fred and then my other friend comes and
+ 
+
+ align:start position:0%
+Fred and then my other friend comes and
+she was like wait you're not listed like
+
+ align:start position:0%
+she was like wait you're not listed like
+ 
+
+ align:start position:0%
+she was like wait you're not listed like
+and then she put her name in and like no
+
+ align:start position:0%
+and then she put her name in and like no
+ 
+
+ align:start position:0%
+and then she put her name in and like no
+no no I'm already there I'm Fred and you
+
+ align:start position:0%
+no no I'm already there I'm Fred and you
+ 
+
+ align:start position:0%
+no no I'm already there I'm Fred and you
+know like confusing things like that and
+
+ align:start position:0%
+know like confusing things like that and
+ 
+
+ align:start position:0%
+know like confusing things like that and
+I hope and I horse sort of think that
+
+ align:start position:0%
+I hope and I horse sort of think that
+ 
+
+ align:start position:0%
+I hope and I horse sort of think that
+that we're starting to see this kind of
+
+ align:start position:0%
+that we're starting to see this kind of
+ 
+
+ align:start position:0%
+that we're starting to see this kind of
+thing like there's like facebook
+
+ align:start position:0%
+thing like there's like facebook
+ 
+
+ align:start position:0%
+thing like there's like facebook
+hearings now and people are all shocked
+
+ align:start position:0%
+hearings now and people are all shocked
+ 
+
+ align:start position:0%
+hearings now and people are all shocked
+that like the company Facebook can read
+
+ align:start position:0%
+that like the company Facebook can read
+ 
+
+ align:start position:0%
+that like the company Facebook can read
+everyone's messages and see everything
+
+ align:start position:0%
+everyone's messages and see everything
+ 
+
+ align:start position:0%
+everyone's messages and see everything
+well yeah that's how it works right
+
+ align:start position:0%
+well yeah that's how it works right
+ 
+
+ align:start position:0%
+well yeah that's how it works right
+you're giving it all to their servers so
+
+ align:start position:0%
+you're giving it all to their servers so
+ 
+
+ align:start position:0%
+you're giving it all to their servers so
+so I think it's starting to be like
+
+ align:start position:0%
+so I think it's starting to be like
+ 
+
+ align:start position:0%
+so I think it's starting to be like
+we're before companies would all be like
+
+ align:start position:0%
+we're before companies would all be like
+ 
+
+ align:start position:0%
+we're before companies would all be like
+we just want to get all the user data
+
+ align:start position:0%
+we just want to get all the user data
+ 
+
+ align:start position:0%
+we just want to get all the user data
+possible hopefully going forward data
+
+ align:start position:0%
+possible hopefully going forward data
+ 
+
+ align:start position:0%
+possible hopefully going forward data
+will be seen more as a liability and
+
+ align:start position:0%
+will be seen more as a liability and
+ 
+
+ align:start position:0%
+will be seen more as a liability and
+less as an asset it means we're not
+
+ align:start position:0%
+less as an asset it means we're not
+ 
+
+ align:start position:0%
+less as an asset it means we're not
+there yet
+
+ align:start position:0%
+there yet
+ 
+
+ align:start position:0%
+there yet
+right because the companies who get sort
+
+ align:start position:0%
+right because the companies who get sort
+ 
+
+ align:start position:0%
+right because the companies who get sort
+of hacked and lose all this user data
+
+ align:start position:0%
+of hacked and lose all this user data
+ 
+
+ align:start position:0%
+of hacked and lose all this user data
+don't really get punished
+
+ align:start position:0%
+don't really get punished
+ 
+
+ align:start position:0%
+don't really get punished
+so like the Equifax thing and like all
+
+ align:start position:0%
+so like the Equifax thing and like all
+ 
+
+ align:start position:0%
+so like the Equifax thing and like all
+these different data breaches there's
+
+ align:start position:0%
+these different data breaches there's
+ 
+
+ align:start position:0%
+these different data breaches there's
+not a ton of consequences yet maybe
+
+ align:start position:0%
+not a ton of consequences yet maybe
+ 
+
+ align:start position:0%
+not a ton of consequences yet maybe
+there will be in the future and maybe
+
+ align:start position:0%
+there will be in the future and maybe
+ 
+
+ align:start position:0%
+there will be in the future and maybe
+companies will start to like not want
+
+ align:start position:0%
+companies will start to like not want
+ 
+
+ align:start position:0%
+companies will start to like not want
+all this data but you know it's it's
+
+ align:start position:0%
+all this data but you know it's it's
+ 
+
+ align:start position:0%
+all this data but you know it's it's
+it's not as clean-cut as like well I
+
+ align:start position:0%
+it's not as clean-cut as like well I
+ 
+
+ align:start position:0%
+it's not as clean-cut as like well I
+have no I didn't do anything wrong so I
+
+ align:start position:0%
+have no I didn't do anything wrong so I
+ 
+
+ align:start position:0%
+have no I didn't do anything wrong so I
+don't want to hide it
+
+ align:start position:0%
+don't want to hide it
+ 
+
+ align:start position:0%
+don't want to hide it
+sort of default hide is my stance and
+
+ align:start position:0%
+sort of default hide is my stance and
+ 
+
+ align:start position:0%
+sort of default hide is my stance and
+there's and there's so many conflicting
+
+ align:start position:0%
+there's and there's so many conflicting
+ 
+
+ align:start position:0%
+there's and there's so many conflicting
+interests where every time you're on the
+
+ align:start position:0%
+interests where every time you're on the
+ 
+
+ align:start position:0%
+interests where every time you're on the
+websites it's like this website wants to
+
+ align:start position:0%
+websites it's like this website wants to
+ 
+
+ align:start position:0%
+websites it's like this website wants to
+your location any like wait how do I
+
+ align:start position:0%
+your location any like wait how do I
+ 
+
+ align:start position:0%
+your location any like wait how do I
+always disable that I don't I don't know
+
+ align:start position:0%
+always disable that I don't I don't know
+ 
+
+ align:start position:0%
+always disable that I don't I don't know
+no the settings but everyone wants this
+
+ align:start position:0%
+no the settings but everyone wants this
+ 
+
+ align:start position:0%
+no the settings but everyone wants this
+stuff so another reason especially you
+
+ align:start position:0%
+stuff so another reason especially you
+ 
+
+ align:start position:0%
+stuff so another reason especially you
+know specifically in the case of money
+
+ align:start position:0%
+know specifically in the case of money
+ 
+
+ align:start position:0%
+know specifically in the case of money
+is what's called fungibility and sounds
+
+ align:start position:0%
+is what's called fungibility and sounds
+ 
+
+ align:start position:0%
+is what's called fungibility and sounds
+like a weird word it just means that
+
+ align:start position:0%
+like a weird word it just means that
+ 
+
+ align:start position:0%
+like a weird word it just means that
+every Bitcoin is the same or every
+
+ align:start position:0%
+every Bitcoin is the same or every
+ 
+
+ align:start position:0%
+every Bitcoin is the same or every
+dollar is the same right so dollars are
+
+ align:start position:0%
+dollar is the same right so dollars are
+ 
+
+ align:start position:0%
+dollar is the same right so dollars are
+fungible in that you know physically
+
+ align:start position:0%
+fungible in that you know physically
+ 
+
+ align:start position:0%
+fungible in that you know physically
+okay this twenty dollar bill and this
+
+ align:start position:0%
+okay this twenty dollar bill and this
+ 
+
+ align:start position:0%
+okay this twenty dollar bill and this
+twenty dollar bill are worth the same
+
+ align:start position:0%
+twenty dollar bill are worth the same
+ 
+
+ align:start position:0%
+twenty dollar bill are worth the same
+and different denominations so I will
+
+ align:start position:0%
+and different denominations so I will
+ 
+
+ align:start position:0%
+and different denominations so I will
+give you a twenty four to ten and anyone
+
+ align:start position:0%
+give you a twenty four to ten and anyone
+ 
+
+ align:start position:0%
+give you a twenty four to ten and anyone
+will do that they're worth the same you
+
+ align:start position:0%
+will do that they're worth the same you
+ 
+
+ align:start position:0%
+will do that they're worth the same you
+don't have sort of well this dollars not
+
+ align:start position:0%
+don't have sort of well this dollars not
+ 
+
+ align:start position:0%
+don't have sort of well this dollars not
+worth quite as much and sometimes that
+
+ align:start position:0%
+worth quite as much and sometimes that
+ 
+
+ align:start position:0%
+worth quite as much and sometimes that
+happens right even with dollar bills
+
+ align:start position:0%
+happens right even with dollar bills
+ 
+
+ align:start position:0%
+happens right even with dollar bills
+like when in other countries when the
+
+ align:start position:0%
+like when in other countries when the
+ 
+
+ align:start position:0%
+like when in other countries when the
+new hundred dollar I think in the
+
+ align:start position:0%
+new hundred dollar I think in the
+ 
+
+ align:start position:0%
+new hundred dollar I think in the
+Philippines when the new hundred dollar
+
+ align:start position:0%
+Philippines when the new hundred dollar
+ 
+
+ align:start position:0%
+Philippines when the new hundred dollar
+bills were issued that have the like
+
+ align:start position:0%
+bills were issued that have the like
+ 
+
+ align:start position:0%
+bills were issued that have the like
+little blue shiny thing people didn't
+
+ align:start position:0%
+little blue shiny thing people didn't
+ 
+
+ align:start position:0%
+little blue shiny thing people didn't
+like them and people were like no I
+
+ align:start position:0%
+like them and people were like no I
+ 
+
+ align:start position:0%
+like them and people were like no I
+won't trade my old hundred dollar bill
+
+ align:start position:0%
+won't trade my old hundred dollar bill
+ 
+
+ align:start position:0%
+won't trade my old hundred dollar bill
+for your new hundred dollar bill I don't
+
+ align:start position:0%
+for your new hundred dollar bill I don't
+ 
+
+ align:start position:0%
+for your new hundred dollar bill I don't
+trust this new one eventually they got
+
+ align:start position:0%
+trust this new one eventually they got
+ 
+
+ align:start position:0%
+trust this new one eventually they got
+used to it but there's there's things
+
+ align:start position:0%
+used to it but there's there's things
+ 
+
+ align:start position:0%
+used to it but there's there's things
+that even money can be not fungible but
+
+ align:start position:0%
+that even money can be not fungible but
+ 
+
+ align:start position:0%
+that even money can be not fungible but
+so the classic example is like okay gold
+
+ align:start position:0%
+so the classic example is like okay gold
+ 
+
+ align:start position:0%
+so the classic example is like okay gold
+is fungible diamonds are not diamonds I
+
+ align:start position:0%
+is fungible diamonds are not diamonds I
+ 
+
+ align:start position:0%
+is fungible diamonds are not diamonds I
+have little experience with diamonds
+
+ align:start position:0%
+have little experience with diamonds
+ 
+
+ align:start position:0%
+have little experience with diamonds
+they seem kind of silly but like they're
+
+ align:start position:0%
+they seem kind of silly but like they're
+ 
+
+ align:start position:0%
+they seem kind of silly but like they're
+all unique right they've got different
+
+ align:start position:0%
+all unique right they've got different
+ 
+
+ align:start position:0%
+all unique right they've got different
+grades and different cuts and different
+
+ align:start position:0%
+grades and different cuts and different
+ 
+
+ align:start position:0%
+grades and different cuts and different
+sizes and carrots and little inclusions
+
+ align:start position:0%
+sizes and carrots and little inclusions
+ 
+
+ align:start position:0%
+sizes and carrots and little inclusions
+and imperfections and you've got this
+
+ align:start position:0%
+and imperfections and you've got this
+ 
+
+ align:start position:0%
+and imperfections and you've got this
+whole industry where you know people
+
+ align:start position:0%
+whole industry where you know people
+ 
+
+ align:start position:0%
+whole industry where you know people
+with these little eye things like look
+
+ align:start position:0%
+with these little eye things like look
+ 
+
+ align:start position:0%
+with these little eye things like look
+at the diamonds and figure out oh this
+
+ align:start position:0%
+at the diamonds and figure out oh this
+ 
+
+ align:start position:0%
+at the diamonds and figure out oh this
+is a good one or this one so so whereas
+
+ align:start position:0%
+is a good one or this one so so whereas
+ 
+
+ align:start position:0%
+is a good one or this one so so whereas
+gold is well sort of also has essayists
+
+ align:start position:0%
+gold is well sort of also has essayists
+ 
+
+ align:start position:0%
+gold is well sort of also has essayists
+and good delivery standards and all
+
+ align:start position:0%
+and good delivery standards and all
+ 
+
+ align:start position:0%
+and good delivery standards and all
+these things for the gold bars but it's
+
+ align:start position:0%
+these things for the gold bars but it's
+ 
+
+ align:start position:0%
+these things for the gold bars but it's
+much more of a standard and there's no
+
+ align:start position:0%
+much more of a standard and there's no
+ 
+
+ align:start position:0%
+much more of a standard and there's no
+judgment call it's like okay this is
+
+ align:start position:0%
+judgment call it's like okay this is
+ 
+
+ align:start position:0%
+judgment call it's like okay this is
+gold
+
+ align:start position:0%
+gold
+ 
+
+ align:start position:0%
+gold
+it's 99.95% pure its weighs this much
+
+ align:start position:0%
+it's 99.95% pure its weighs this much
+ 
+
+ align:start position:0%
+it's 99.95% pure its weighs this much
+this is how much it's worth and you can
+
+ align:start position:0%
+this is how much it's worth and you can
+ 
+
+ align:start position:0%
+this is how much it's worth and you can
+chop gold up and okay sorry divisibility
+
+ align:start position:0%
+chop gold up and okay sorry divisibility
+ 
+
+ align:start position:0%
+chop gold up and okay sorry divisibility
+is different than fungibility right so
+
+ align:start position:0%
+is different than fungibility right so
+ 
+
+ align:start position:0%
+is different than fungibility right so
+if diamonds were all identical but not
+
+ align:start position:0%
+if diamonds were all identical but not
+ 
+
+ align:start position:0%
+if diamonds were all identical but not
+divisible they could still maybe
+
+ align:start position:0%
+divisible they could still maybe
+ 
+
+ align:start position:0%
+divisible they could still maybe
+function as money you just need a lot of
+
+ align:start position:0%
+function as money you just need a lot of
+ 
+
+ align:start position:0%
+function as money you just need a lot of
+little diamonds but the fact that Gold's
+
+ align:start position:0%
+little diamonds but the fact that Gold's
+ 
+
+ align:start position:0%
+little diamonds but the fact that Gold's
+also divisible is really is
+
+ align:start position:0%
+also divisible is really is
+ 
+
+ align:start position:0%
+also divisible is really is
+but the fungibility is really what's
+
+ align:start position:0%
+but the fungibility is really what's
+ 
+
+ align:start position:0%
+but the fungibility is really what's
+nice about it and what makes it sort of
+
+ align:start position:0%
+nice about it and what makes it sort of
+ 
+
+ align:start position:0%
+nice about it and what makes it sort of
+used as money currencies fungibility is
+
+ align:start position:0%
+used as money currencies fungibility is
+ 
+
+ align:start position:0%
+used as money currencies fungibility is
+actually I'm not a lawyer but I hang out
+
+ align:start position:0%
+actually I'm not a lawyer but I hang out
+ 
+
+ align:start position:0%
+actually I'm not a lawyer but I hang out
+with them it's it's enforced by the law
+
+ align:start position:0%
+with them it's it's enforced by the law
+ 
+
+ align:start position:0%
+with them it's it's enforced by the law
+itself so it's an interesting case
+
+ align:start position:0%
+itself so it's an interesting case
+ 
+
+ align:start position:0%
+itself so it's an interesting case
+Crawford versus the Royal Bank in
+
+ align:start position:0%
+Crawford versus the Royal Bank in
+ 
+
+ align:start position:0%
+Crawford versus the Royal Bank in
+Scotland a couple hundred years ago
+
+ align:start position:0%
+Scotland a couple hundred years ago
+ 
+
+ align:start position:0%
+Scotland a couple hundred years ago
+where there was a guy and he wrote his
+
+ align:start position:0%
+where there was a guy and he wrote his
+ 
+
+ align:start position:0%
+where there was a guy and he wrote his
+name on a twenty pound to note it's like
+
+ align:start position:0%
+name on a twenty pound to note it's like
+ 
+
+ align:start position:0%
+name on a twenty pound to note it's like
+Crawford you know this is his money and
+
+ align:start position:0%
+Crawford you know this is his money and
+ 
+
+ align:start position:0%
+Crawford you know this is his money and
+I think he was trying to mail it someone
+
+ align:start position:0%
+I think he was trying to mail it someone
+ 
+
+ align:start position:0%
+I think he was trying to mail it someone
+he lost it years later the note shows up
+
+ align:start position:0%
+he lost it years later the note shows up
+ 
+
+ align:start position:0%
+he lost it years later the note shows up
+at a bank and he's like no see that was
+
+ align:start position:0%
+at a bank and he's like no see that was
+ 
+
+ align:start position:0%
+at a bank and he's like no see that was
+my money and I lost it
+
+ align:start position:0%
+my money and I lost it
+ 
+
+ align:start position:0%
+my money and I lost it
+and he demands the money back right i I
+
+ align:start position:0%
+and he demands the money back right i I
+ 
+
+ align:start position:0%
+and he demands the money back right i I
+lost that money this is my property give
+
+ align:start position:0%
+lost that money this is my property give
+ 
+
+ align:start position:0%
+lost that money this is my property give
+it back it's got my name on it I can
+
+ align:start position:0%
+it back it's got my name on it I can
+ 
+
+ align:start position:0%
+it back it's got my name on it I can
+prove it and then the court says no no
+
+ align:start position:0%
+prove it and then the court says no no
+ 
+
+ align:start position:0%
+prove it and then the court says no no
+that's not how money works right the
+
+ align:start position:0%
+that's not how money works right the
+ 
+
+ align:start position:0%
+that's not how money works right the
+bank has the money you can't you can't
+
+ align:start position:0%
+bank has the money you can't you can't
+ 
+
+ align:start position:0%
+bank has the money you can't you can't
+just write your name on money and then
+
+ align:start position:0%
+just write your name on money and then
+ 
+
+ align:start position:0%
+just write your name on money and then
+have it be yours because you know and
+
+ align:start position:0%
+have it be yours because you know and
+ 
+
+ align:start position:0%
+have it be yours because you know and
+and this is this is very different from
+
+ align:start position:0%
+and this is this is very different from
+ 
+
+ align:start position:0%
+and this is this is very different from
+property right so if you steal a bicycle
+
+ align:start position:0%
+property right so if you steal a bicycle
+ 
+
+ align:start position:0%
+property right so if you steal a bicycle
+and then you go sell it on well sorry if
+
+ align:start position:0%
+and then you go sell it on well sorry if
+ 
+
+ align:start position:0%
+and then you go sell it on well sorry if
+someone steals a bicycle sells it on
+
+ align:start position:0%
+someone steals a bicycle sells it on
+ 
+
+ align:start position:0%
+someone steals a bicycle sells it on
+Craigslist and you buy it and you didn't
+
+ align:start position:0%
+Craigslist and you buy it and you didn't
+ 
+
+ align:start position:0%
+Craigslist and you buy it and you didn't
+know right it's just whatever some guys
+
+ align:start position:0%
+know right it's just whatever some guys
+ 
+
+ align:start position:0%
+know right it's just whatever some guys
+selling a bike on Craigslist the police
+
+ align:start position:0%
+selling a bike on Craigslist the police
+ 
+
+ align:start position:0%
+selling a bike on Craigslist the police
+show up and say hey that bicycle stolen
+
+ align:start position:0%
+show up and say hey that bicycle stolen
+ 
+
+ align:start position:0%
+show up and say hey that bicycle stolen
+we're taking it back and you're like
+
+ align:start position:0%
+we're taking it back and you're like
+ 
+
+ align:start position:0%
+we're taking it back and you're like
+well I didn't know you know I just
+
+ align:start position:0%
+well I didn't know you know I just
+ 
+
+ align:start position:0%
+well I didn't know you know I just
+bought on Craigslist I paid a couple
+
+ align:start position:0%
+bought on Craigslist I paid a couple
+ 
+
+ align:start position:0%
+bought on Craigslist I paid a couple
+hundred bucks police are like sorry
+
+ align:start position:0%
+hundred bucks police are like sorry
+ 
+
+ align:start position:0%
+hundred bucks police are like sorry
+we're taking you no you're not you're
+
+ align:start position:0%
+we're taking you no you're not you're
+ 
+
+ align:start position:0%
+we're taking you no you're not you're
+not in trouble right we're not gonna
+
+ align:start position:0%
+not in trouble right we're not gonna
+ 
+
+ align:start position:0%
+not in trouble right we're not gonna
+charge you with a crime but this these
+
+ align:start position:0%
+charge you with a crime but this these
+ 
+
+ align:start position:0%
+charge you with a crime but this these
+are stolen goods we're taking them back
+
+ align:start position:0%
+are stolen goods we're taking them back
+ 
+
+ align:start position:0%
+are stolen goods we're taking them back
+giving it to the rightful one owner and
+
+ align:start position:0%
+giving it to the rightful one owner and
+ 
+
+ align:start position:0%
+giving it to the rightful one owner and
+that's how the law works you're not if
+
+ align:start position:0%
+that's how the law works you're not if
+ 
+
+ align:start position:0%
+that's how the law works you're not if
+you can try to complain about it but
+
+ align:start position:0%
+you can try to complain about it but
+ 
+
+ align:start position:0%
+you can try to complain about it but
+they're taking it money's different
+
+ align:start position:0%
+they're taking it money's different
+ 
+
+ align:start position:0%
+they're taking it money's different
+right if you're running a pizza store
+
+ align:start position:0%
+right if you're running a pizza store
+ 
+
+ align:start position:0%
+right if you're running a pizza store
+someone comes in gives you a 20 by so
+
+ align:start position:0%
+someone comes in gives you a 20 by so
+ 
+
+ align:start position:0%
+someone comes in gives you a 20 by so
+pizza and then presumably eats it or
+
+ align:start position:0%
+pizza and then presumably eats it or
+ 
+
+ align:start position:0%
+pizza and then presumably eats it or
+whatever and then a couple hours later
+
+ align:start position:0%
+whatever and then a couple hours later
+ 
+
+ align:start position:0%
+whatever and then a couple hours later
+the police come in and say hey that guy
+
+ align:start position:0%
+the police come in and say hey that guy
+ 
+
+ align:start position:0%
+the police come in and say hey that guy
+stole that 20 dollar bill and we're
+
+ align:start position:0%
+stole that 20 dollar bill and we're
+ 
+
+ align:start position:0%
+stole that 20 dollar bill and we're
+taking it back and giving it to its
+
+ align:start position:0%
+taking it back and giving it to its
+ 
+
+ align:start position:0%
+taking it back and giving it to its
+rightful owner as the shopkeeper like
+
+ align:start position:0%
+rightful owner as the shopkeeper like
+ 
+
+ align:start position:0%
+rightful owner as the shopkeeper like
+well which I don't even know which 20
+
+ align:start position:0%
+well which I don't even know which 20
+ 
+
+ align:start position:0%
+well which I don't even know which 20
+dollar bill even though they're serial
+
+ align:start position:0%
+dollar bill even though they're serial
+ 
+
+ align:start position:0%
+dollar bill even though they're serial
+numbers and the police could say no it
+
+ align:start position:0%
+numbers and the police could say no it
+ 
+
+ align:start position:0%
+numbers and the police could say no it
+was this twenty dollar bill we're taking
+
+ align:start position:0%
+was this twenty dollar bill we're taking
+ 
+
+ align:start position:0%
+was this twenty dollar bill we're taking
+it back returning it to the person he
+
+ align:start position:0%
+it back returning it to the person he
+ 
+
+ align:start position:0%
+it back returning it to the person he
+stole it from legally they can't do that
+
+ align:start position:0%
+stole it from legally they can't do that
+ 
+
+ align:start position:0%
+stole it from legally they can't do that
+right I'm
+
+ align:start position:0%
+right I'm
+ 
+
+ align:start position:0%
+right I'm
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+but so this is from talking to lawyer
+
+ align:start position:0%
+but so this is from talking to lawyer
+ 
+
+ align:start position:0%
+but so this is from talking to lawyer
+people so so money's different money's
+
+ align:start position:0%
+people so so money's different money's
+ 
+
+ align:start position:0%
+people so so money's different money's
+not property in the same sense and and
+
+ align:start position:0%
+not property in the same sense and and
+ 
+
+ align:start position:0%
+not property in the same sense and and
+the fungibility is enforced by the state
+
+ align:start position:0%
+the fungibility is enforced by the state
+ 
+
+ align:start position:0%
+the fungibility is enforced by the state
+and it's also enforced the divisibility
+
+ align:start position:0%
+and it's also enforced the divisibility
+ 
+
+ align:start position:0%
+and it's also enforced the divisibility
+and fungibility are enforced by the
+
+ align:start position:0%
+and fungibility are enforced by the
+ 
+
+ align:start position:0%
+and fungibility are enforced by the
+banks and that like the the US dollar
+
+ align:start position:0%
+banks and that like the the US dollar
+ 
+
+ align:start position:0%
+banks and that like the the US dollar
+isn't like worth anything in that the
+
+ align:start position:0%
+isn't like worth anything in that the
+ 
+
+ align:start position:0%
+isn't like worth anything in that the
+government and the banks don't have to
+
+ align:start position:0%
+government and the banks don't have to
+ 
+
+ align:start position:0%
+government and the banks don't have to
+give you anything for a dollar like they
+
+ align:start position:0%
+give you anything for a dollar like they
+ 
+
+ align:start position:0%
+give you anything for a dollar like they
+used to sort of have this agreement
+
+ align:start position:0%
+used to sort of have this agreement
+ 
+
+ align:start position:0%
+used to sort of have this agreement
+where okay you give us was it twenty
+
+ align:start position:0%
+where okay you give us was it twenty
+ 
+
+ align:start position:0%
+where okay you give us was it twenty
+five thirty five dollars and we'll give
+
+ align:start position:0%
+five thirty five dollars and we'll give
+ 
+
+ align:start position:0%
+five thirty five dollars and we'll give
+you an ounce of gold that the government
+
+ align:start position:0%
+you an ounce of gold that the government
+ 
+
+ align:start position:0%
+you an ounce of gold that the government
+no longer is in place but they do have
+
+ align:start position:0%
+no longer is in place but they do have
+ 
+
+ align:start position:0%
+no longer is in place but they do have
+to give you change
+
+ align:start position:0%
+to give you change
+ 
+
+ align:start position:0%
+to give you change
+right so they do have a duty where if
+
+ align:start position:0%
+right so they do have a duty where if
+ 
+
+ align:start position:0%
+right so they do have a duty where if
+you have a bunch of old beat-up 20
+
+ align:start position:0%
+you have a bunch of old beat-up 20
+ 
+
+ align:start position:0%
+you have a bunch of old beat-up 20
+dollar bills the bank sort of does have
+
+ align:start position:0%
+dollar bills the bank sort of does have
+ 
+
+ align:start position:0%
+dollar bills the bank sort of does have
+to honor those and give you new $20
+
+ align:start position:0%
+to honor those and give you new $20
+ 
+
+ align:start position:0%
+to honor those and give you new $20
+bills and that's one of the things that
+
+ align:start position:0%
+bills and that's one of the things that
+ 
+
+ align:start position:0%
+bills and that's one of the things that
+the Bureau of Engraving and printing and
+
+ align:start position:0%
+the Bureau of Engraving and printing and
+ 
+
+ align:start position:0%
+the Bureau of Engraving and printing and
+the Fed they all have this system so
+
+ align:start position:0%
+the Fed they all have this system so
+ 
+
+ align:start position:0%
+the Fed they all have this system so
+they maintain the currency in that
+
+ align:start position:0%
+they maintain the currency in that
+ 
+
+ align:start position:0%
+they maintain the currency in that
+system in that sense so there's all
+
+ align:start position:0%
+system in that sense so there's all
+ 
+
+ align:start position:0%
+system in that sense so there's all
+these things that like you don't really
+
+ align:start position:0%
+these things that like you don't really
+ 
+
+ align:start position:0%
+these things that like you don't really
+think about in that how money operates
+
+ align:start position:0%
+think about in that how money operates
+ 
+
+ align:start position:0%
+think about in that how money operates
+but fungibility divisibility those are
+
+ align:start position:0%
+but fungibility divisibility those are
+ 
+
+ align:start position:0%
+but fungibility divisibility those are
+like really important and most of it is
+
+ align:start position:0%
+like really important and most of it is
+ 
+
+ align:start position:0%
+like really important and most of it is
+enforced by the legal system Bitcoin
+
+ align:start position:0%
+enforced by the legal system Bitcoin
+ 
+
+ align:start position:0%
+enforced by the legal system Bitcoin
+does not have these legal protections
+
+ align:start position:0%
+does not have these legal protections
+ 
+
+ align:start position:0%
+does not have these legal protections
+you want you want Bitcoin to work even
+
+ align:start position:0%
+you want you want Bitcoin to work even
+ 
+
+ align:start position:0%
+you want you want Bitcoin to work even
+where it's not legally recognized as
+
+ align:start position:0%
+where it's not legally recognized as
+ 
+
+ align:start position:0%
+where it's not legally recognized as
+being money and our goal is to make it
+
+ align:start position:0%
+being money and our goal is to make it
+ 
+
+ align:start position:0%
+being money and our goal is to make it
+like money so yeah if they're stolen
+
+ align:start position:0%
+like money so yeah if they're stolen
+ 
+
+ align:start position:0%
+like money so yeah if they're stolen
+bitcoins and you can trace them the you
+
+ align:start position:0%
+bitcoins and you can trace them the you
+ 
+
+ align:start position:0%
+bitcoins and you can trace them the you
+know law enforcement could say no those
+
+ align:start position:0%
+know law enforcement could say no those
+ 
+
+ align:start position:0%
+know law enforcement could say no those
+bitcoins are stolen were recovering them
+
+ align:start position:0%
+bitcoins are stolen were recovering them
+ 
+
+ align:start position:0%
+bitcoins are stolen were recovering them
+so it's it's not treated as a currency
+
+ align:start position:0%
+so it's it's not treated as a currency
+ 
+
+ align:start position:0%
+so it's it's not treated as a currency
+it's also not contribute as fungible
+
+ align:start position:0%
+it's also not contribute as fungible
+ 
+
+ align:start position:0%
+it's also not contribute as fungible
+right so so in the in the absence of
+
+ align:start position:0%
+right so so in the in the absence of
+ 
+
+ align:start position:0%
+right so so in the in the absence of
+these sort of protections from the legal
+
+ align:start position:0%
+these sort of protections from the legal
+ 
+
+ align:start position:0%
+these sort of protections from the legal
+system the software needs to help
+
+ align:start position:0%
+system the software needs to help
+ 
+
+ align:start position:0%
+system the software needs to help
+enforce the fungibility and divisibility
+
+ align:start position:0%
+enforce the fungibility and divisibility
+ 
+
+ align:start position:0%
+enforce the fungibility and divisibility
+of these things right so you can sort of
+
+ align:start position:0%
+of these things right so you can sort of
+ 
+
+ align:start position:0%
+of these things right so you can sort of
+treat the Bitcoin software and rule set
+
+ align:start position:0%
+treat the Bitcoin software and rule set
+ 
+
+ align:start position:0%
+treat the Bitcoin software and rule set
+as a sort of only it's not a legal
+
+ align:start position:0%
+as a sort of only it's not a legal
+ 
+
+ align:start position:0%
+as a sort of only it's not a legal
+system but it's a system of rules that
+
+ align:start position:0%
+system but it's a system of rules that
+ 
+
+ align:start position:0%
+system but it's a system of rules that
+governs how the Bitcoin transactions
+
+ align:start position:0%
+governs how the Bitcoin transactions
+ 
+
+ align:start position:0%
+governs how the Bitcoin transactions
+work and so the fungibility is has got
+
+ align:start position:0%
+work and so the fungibility is has got
+ 
+
+ align:start position:0%
+work and so the fungibility is has got
+to be in the system right so simple so
+
+ align:start position:0%
+to be in the system right so simple so
+ 
+
+ align:start position:0%
+to be in the system right so simple so
+gold for example they don't have oh they
+
+ align:start position:0%
+gold for example they don't have oh they
+ 
+
+ align:start position:0%
+gold for example they don't have oh they
+might I don't want to say they don't
+
+ align:start position:0%
+might I don't want to say they don't
+ 
+
+ align:start position:0%
+might I don't want to say they don't
+have rules about gold there's probably
+
+ align:start position:0%
+have rules about gold there's probably
+ 
+
+ align:start position:0%
+have rules about gold there's probably
+all sorts of old laws about gold but uh
+
+ align:start position:0%
+all sorts of old laws about gold but uh
+ 
+
+ align:start position:0%
+all sorts of old laws about gold but uh
+but you don't really need a law
+
+ align:start position:0%
+but you don't really need a law
+ 
+
+ align:start position:0%
+but you don't really need a law
+enforcing the fungibility of gold in
+
+ align:start position:0%
+enforcing the fungibility of gold in
+ 
+
+ align:start position:0%
+enforcing the fungibility of gold in
+that you can sort of melt it down and
+
+ align:start position:0%
+that you can sort of melt it down and
+ 
+
+ align:start position:0%
+that you can sort of melt it down and
+it's untraceable right if you you have
+
+ align:start position:0%
+it's untraceable right if you you have
+ 
+
+ align:start position:0%
+it's untraceable right if you you have
+this old gold coin from this Empire and
+
+ align:start position:0%
+this old gold coin from this Empire and
+ 
+
+ align:start position:0%
+this old gold coin from this Empire and
+this other
+
+ align:start position:0%
+this other
+ 
+
+ align:start position:0%
+this other
+from this empire you melt the gold you
+
+ align:start position:0%
+from this empire you melt the gold you
+ 
+
+ align:start position:0%
+from this empire you melt the gold you
+put it into a new coin no one can tell
+
+ align:start position:0%
+put it into a new coin no one can tell
+ 
+
+ align:start position:0%
+put it into a new coin no one can tell
+so so similarly Bitcoin needs to enforce
+
+ align:start position:0%
+so so similarly Bitcoin needs to enforce
+ 
+
+ align:start position:0%
+so so similarly Bitcoin needs to enforce
+punch ability that way okay so any
+
+ align:start position:0%
+punch ability that way okay so any
+ 
+
+ align:start position:0%
+punch ability that way okay so any
+questions so far about these definitions
+
+ align:start position:0%
+questions so far about these definitions
+ 
+
+ align:start position:0%
+questions so far about these definitions
+or objections I don't think Bitcoin
+
+ align:start position:0%
+or objections I don't think Bitcoin
+ 
+
+ align:start position:0%
+or objections I don't think Bitcoin
+should be fungible they're not they're
+
+ align:start position:0%
+should be fungible they're not they're
+ 
+
+ align:start position:0%
+should be fungible they're not they're
+not valued the same because they haven't
+
+ align:start position:0%
+not valued the same because they haven't
+ 
+
+ align:start position:0%
+not valued the same because they haven't
+been fully confirmed yeah no that's an
+
+ align:start position:0%
+been fully confirmed yeah no that's an
+ 
+
+ align:start position:0%
+been fully confirmed yeah no that's an
+interesting way to look at it I mean I'm
+
+ align:start position:0%
+interesting way to look at it I mean I'm
+ 
+
+ align:start position:0%
+interesting way to look at it I mean I'm
+not talking about sort of the time-based
+
+ align:start position:0%
+not talking about sort of the time-based
+ 
+
+ align:start position:0%
+not talking about sort of the time-based
+things here because I guess in in many
+
+ align:start position:0%
+things here because I guess in in many
+ 
+
+ align:start position:0%
+things here because I guess in in many
+cases you say okay I'm gonna weigh today
+
+ align:start position:0%
+cases you say okay I'm gonna weigh today
+ 
+
+ align:start position:0%
+cases you say okay I'm gonna weigh today
+and if it's got a hundred confirmations
+
+ align:start position:0%
+and if it's got a hundred confirmations
+ 
+
+ align:start position:0%
+and if it's got a hundred confirmations
+it's good right I'll consider it fully
+
+ align:start position:0%
+it's good right I'll consider it fully
+ 
+
+ align:start position:0%
+it's good right I'll consider it fully
+value but yeah there could be things
+
+ align:start position:0%
+value but yeah there could be things
+ 
+
+ align:start position:0%
+value but yeah there could be things
+where you look at the probability of a
+
+ align:start position:0%
+where you look at the probability of a
+ 
+
+ align:start position:0%
+where you look at the probability of a
+double spend and then sort of assigned
+
+ align:start position:0%
+double spend and then sort of assigned
+ 
+
+ align:start position:0%
+double spend and then sort of assigned
+value to it increasing as time passes or
+
+ align:start position:0%
+value to it increasing as time passes or
+ 
+
+ align:start position:0%
+value to it increasing as time passes or
+something that's sort of a unique thing
+
+ align:start position:0%
+something that's sort of a unique thing
+ 
+
+ align:start position:0%
+something that's sort of a unique thing
+to Bitcoin where the transfers the the
+
+ align:start position:0%
+to Bitcoin where the transfers the the
+ 
+
+ align:start position:0%
+to Bitcoin where the transfers the the
+sort of finality of the transfer
+
+ align:start position:0%
+sort of finality of the transfer
+ 
+
+ align:start position:0%
+sort of finality of the transfer
+increases with time which is not really
+
+ align:start position:0%
+increases with time which is not really
+ 
+
+ align:start position:0%
+increases with time which is not really
+the case with like gold or dollars we're
+
+ align:start position:0%
+the case with like gold or dollars we're
+ 
+
+ align:start position:0%
+the case with like gold or dollars we're
+like okay I got it
+
+ align:start position:0%
+like okay I got it
+ 
+
+ align:start position:0%
+like okay I got it
+like the fact that I've had it for one
+
+ align:start position:0%
+like the fact that I've had it for one
+ 
+
+ align:start position:0%
+like the fact that I've had it for one
+minute or 10 minutes doesn't really
+
+ align:start position:0%
+minute or 10 minutes doesn't really
+ 
+
+ align:start position:0%
+minute or 10 minutes doesn't really
+change that I've got it so so yeah that
+
+ align:start position:0%
+change that I've got it so so yeah that
+ 
+
+ align:start position:0%
+change that I've got it so so yeah that
+that's that's an interesting point um
+
+ align:start position:0%
+that's that's an interesting point um
+ 
+
+ align:start position:0%
+that's that's an interesting point um
+not really addressing it here I'm sort
+
+ align:start position:0%
+not really addressing it here I'm sort
+ 
+
+ align:start position:0%
+not really addressing it here I'm sort
+of you know in this in this conversation
+
+ align:start position:0%
+of you know in this in this conversation
+ 
+
+ align:start position:0%
+of you know in this in this conversation
+just assume you wait a day and then all
+
+ align:start position:0%
+just assume you wait a day and then all
+ 
+
+ align:start position:0%
+just assume you wait a day and then all
+the the probability of it going back is
+
+ align:start position:0%
+the the probability of it going back is
+ 
+
+ align:start position:0%
+the the probability of it going back is
+sort of negligible but it's more the
+
+ align:start position:0%
+sort of negligible but it's more the
+ 
+
+ align:start position:0%
+sort of negligible but it's more the
+fungibility in that like you can trace
+
+ align:start position:0%
+fungibility in that like you can trace
+ 
+
+ align:start position:0%
+fungibility in that like you can trace
+where it came from and you know assign
+
+ align:start position:0%
+where it came from and you know assign
+ 
+
+ align:start position:0%
+where it came from and you know assign
+values to different coins based on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's a real-world example of this
+
+ align:start position:0%
+so there's a real-world example of this
+ 
+
+ align:start position:0%
+so there's a real-world example of this
+I don't want to name specific names but
+
+ align:start position:0%
+I don't want to name specific names but
+ 
+
+ align:start position:0%
+I don't want to name specific names but
+customer buy some coins you go to
+
+ align:start position:0%
+customer buy some coins you go to
+ 
+
+ align:start position:0%
+customer buy some coins you go to
+exchange you send them a couple hundred
+
+ align:start position:0%
+exchange you send them a couple hundred
+ 
+
+ align:start position:0%
+exchange you send them a couple hundred
+bucks you say I want to buy some
+
+ align:start position:0%
+bucks you say I want to buy some
+ 
+
+ align:start position:0%
+bucks you say I want to buy some
+bitcoins and the customer buy the buys
+
+ align:start position:0%
+bitcoins and the customer buy the buys
+ 
+
+ align:start position:0%
+bitcoins and the customer buy the buys
+the bitcoins and then transfers the
+
+ align:start position:0%
+the bitcoins and then transfers the
+ 
+
+ align:start position:0%
+the bitcoins and then transfers the
+coins to a betting shop a betting
+
+ align:start position:0%
+coins to a betting shop a betting
+ 
+
+ align:start position:0%
+coins to a betting shop a betting
+company in the UK
+
+ align:start position:0%
+company in the UK
+ 
+
+ align:start position:0%
+company in the UK
+and bets on a soccer game for example
+
+ align:start position:0%
+and bets on a soccer game for example
+ 
+
+ align:start position:0%
+and bets on a soccer game for example
+any wins great so he you know bought a
+
+ align:start position:0%
+any wins great so he you know bought a
+ 
+
+ align:start position:0%
+any wins great so he you know bought a
+coin sent it over to this UK gambling
+
+ align:start position:0%
+coin sent it over to this UK gambling
+ 
+
+ align:start position:0%
+coin sent it over to this UK gambling
+company bet on a soccer game or a
+
+ align:start position:0%
+company bet on a soccer game or a
+ 
+
+ align:start position:0%
+company bet on a soccer game or a
+football I guess they call it wins now
+
+ align:start position:0%
+football I guess they call it wins now
+ 
+
+ align:start position:0%
+football I guess they call it wins now
+he has two coins transfers those two
+
+ align:start position:0%
+he has two coins transfers those two
+ 
+
+ align:start position:0%
+he has two coins transfers those two
+coins back to the u.s. exchange and he
+
+ align:start position:0%
+coins back to the u.s. exchange and he
+ 
+
+ align:start position:0%
+coins back to the u.s. exchange and he
+wants to sell them before he can click
+
+ align:start position:0%
+wants to sell them before he can click
+ 
+
+ align:start position:0%
+wants to sell them before he can click
+sell his account is closed and the
+
+ align:start position:0%
+sell his account is closed and the
+ 
+
+ align:start position:0%
+sell his account is closed and the
+exchange website says nope you violated
+
+ align:start position:0%
+exchange website says nope you violated
+ 
+
+ align:start position:0%
+exchange website says nope you violated
+our Terms of Service we're closing your
+
+ align:start position:0%
+our Terms of Service we're closing your
+ 
+
+ align:start position:0%
+our Terms of Service we're closing your
+account you know take your bitcoins take
+
+ align:start position:0%
+account you know take your bitcoins take
+ 
+
+ align:start position:0%
+account you know take your bitcoins take
+me we've sent all your dollars back to
+
+ align:start position:0%
+me we've sent all your dollars back to
+ 
+
+ align:start position:0%
+me we've sent all your dollars back to
+your bank you know withdraw your
+
+ align:start position:0%
+your bank you know withdraw your
+ 
+
+ align:start position:0%
+your bank you know withdraw your
+bitcoins we're out this happens so this
+
+ align:start position:0%
+bitcoins we're out this happens so this
+ 
+
+ align:start position:0%
+bitcoins we're out this happens so this
+is it Rob I mean whether you agree with
+
+ align:start position:0%
+is it Rob I mean whether you agree with
+ 
+
+ align:start position:0%
+is it Rob I mean whether you agree with
+gambling being legal you know so in the
+
+ align:start position:0%
+gambling being legal you know so in the
+ 
+
+ align:start position:0%
+gambling being legal you know so in the
+UK Harvard there's no law violated right
+
+ align:start position:0%
+UK Harvard there's no law violated right
+ 
+
+ align:start position:0%
+UK Harvard there's no law violated right
+and as a United States so this is sort
+
+ align:start position:0%
+and as a United States so this is sort
+ 
+
+ align:start position:0%
+and as a United States so this is sort
+of a gray area I'm pretty sure that if
+
+ align:start position:0%
+of a gray area I'm pretty sure that if
+ 
+
+ align:start position:0%
+of a gray area I'm pretty sure that if
+I'm a US citizen I take a plane over to
+
+ align:start position:0%
+I'm a US citizen I take a plane over to
+ 
+
+ align:start position:0%
+I'm a US citizen I take a plane over to
+London I go to a I don't know the lingo
+
+ align:start position:0%
+London I go to a I don't know the lingo
+ 
+
+ align:start position:0%
+London I go to a I don't know the lingo
+punters shop betting shop yeah there's
+
+ align:start position:0%
+punters shop betting shop yeah there's
+ 
+
+ align:start position:0%
+punters shop betting shop yeah there's
+also and then I bet on something and I
+
+ align:start position:0%
+also and then I bet on something and I
+ 
+
+ align:start position:0%
+also and then I bet on something and I
+win well I'm pretty sure I have to you
+
+ align:start position:0%
+win well I'm pretty sure I have to you
+ 
+
+ align:start position:0%
+win well I'm pretty sure I have to you
+have to pay capital gains on those
+
+ align:start position:0%
+have to pay capital gains on those
+ 
+
+ align:start position:0%
+have to pay capital gains on those
+winnings to the US IRS but I haven't
+
+ align:start position:0%
+winnings to the US IRS but I haven't
+ 
+
+ align:start position:0%
+winnings to the US IRS but I haven't
+broken a law right because I'm not in
+
+ align:start position:0%
+broken a law right because I'm not in
+ 
+
+ align:start position:0%
+broken a law right because I'm not in
+the US when I'm doing this thing so
+
+ align:start position:0%
+the US when I'm doing this thing so
+ 
+
+ align:start position:0%
+the US when I'm doing this thing so
+similarly how you know if casino
+
+ align:start position:0%
+similarly how you know if casino
+ 
+
+ align:start position:0%
+similarly how you know if casino
+gambling is illegal in Massachusetts
+
+ align:start position:0%
+gambling is illegal in Massachusetts
+ 
+
+ align:start position:0%
+gambling is illegal in Massachusetts
+sort of I can go to Las Vegas I can
+
+ align:start position:0%
+sort of I can go to Las Vegas I can
+ 
+
+ align:start position:0%
+sort of I can go to Las Vegas I can
+gamble and I can come back to the
+
+ align:start position:0%
+gamble and I can come back to the
+ 
+
+ align:start position:0%
+gamble and I can come back to the
+Massachusetts and it's okay so this is
+
+ align:start position:0%
+Massachusetts and it's okay so this is
+ 
+
+ align:start position:0%
+Massachusetts and it's okay so this is
+probably a gray area I don't know if
+
+ align:start position:0%
+probably a gray area I don't know if
+ 
+
+ align:start position:0%
+probably a gray area I don't know if
+there's actual court cases about this
+
+ align:start position:0%
+there's actual court cases about this
+ 
+
+ align:start position:0%
+there's actual court cases about this
+where you're still sitting in
+
+ align:start position:0%
+where you're still sitting in
+ 
+
+ align:start position:0%
+where you're still sitting in
+Massachusetts at your computer but
+
+ align:start position:0%
+Massachusetts at your computer but
+ 
+
+ align:start position:0%
+Massachusetts at your computer but
+you've sent your money to the United
+
+ align:start position:0%
+you've sent your money to the United
+ 
+
+ align:start position:0%
+you've sent your money to the United
+Kingdom you I don't know I don't I don't
+
+ align:start position:0%
+Kingdom you I don't know I don't I don't
+ 
+
+ align:start position:0%
+Kingdom you I don't know I don't I don't
+think I don't know of anyone who's
+
+ align:start position:0%
+think I don't know of anyone who's
+ 
+
+ align:start position:0%
+think I don't know of anyone who's
+gotten in trouble for this I don't know
+
+ align:start position:0%
+gotten in trouble for this I don't know
+ 
+
+ align:start position:0%
+gotten in trouble for this I don't know
+if there's been prosecution like against
+
+ align:start position:0%
+if there's been prosecution like against
+ 
+
+ align:start position:0%
+if there's been prosecution like against
+UK betting shops for this kind of thing
+
+ align:start position:0%
+UK betting shops for this kind of thing
+ 
+
+ align:start position:0%
+UK betting shops for this kind of thing
+but this happens a lot of a lot of
+
+ align:start position:0%
+but this happens a lot of a lot of
+ 
+
+ align:start position:0%
+but this happens a lot of a lot of
+companies run betting shops like this
+
+ align:start position:0%
+companies run betting shops like this
+ 
+
+ align:start position:0%
+companies run betting shops like this
+but I have seen that US exchanges will
+
+ align:start position:0%
+but I have seen that US exchanges will
+ 
+
+ align:start position:0%
+but I have seen that US exchanges will
+shut down accounts because of this they
+
+ align:start position:0%
+shut down accounts because of this they
+ 
+
+ align:start position:0%
+shut down accounts because of this they
+say look you can buy bitcoins but if
+
+ align:start position:0%
+say look you can buy bitcoins but if
+ 
+
+ align:start position:0%
+say look you can buy bitcoins but if
+you're using these to gamble we don't we
+
+ align:start position:0%
+you're using these to gamble we don't we
+ 
+
+ align:start position:0%
+you're using these to gamble we don't we
+want to get involved it's just more risk
+
+ align:start position:0%
+want to get involved it's just more risk
+ 
+
+ align:start position:0%
+want to get involved it's just more risk
+for us and so they close their accounts
+
+ align:start position:0%
+for us and so they close their accounts
+ 
+
+ align:start position:0%
+for us and so they close their accounts
+so the problem here is what did I say
+
+ align:start position:0%
+so the problem here is what did I say
+ 
+
+ align:start position:0%
+so the problem here is what did I say
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+yeah what's from from the perspective of
+
+ align:start position:0%
+yeah what's from from the perspective of
+ 
+
+ align:start position:0%
+yeah what's from from the perspective of
+like the legal system for
+
+ align:start position:0%
+like the legal system for
+ 
+
+ align:start position:0%
+like the legal system for
+user it's obviously problems because
+
+ align:start position:0%
+user it's obviously problems because
+ 
+
+ align:start position:0%
+user it's obviously problems because
+it's annoying what's the problem for
+
+ align:start position:0%
+it's annoying what's the problem for
+ 
+
+ align:start position:0%
+it's annoying what's the problem for
+Bitcoin here why should care about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+back but yeah the real thing is these
+
+ align:start position:0%
+back but yeah the real thing is these
+ 
+
+ align:start position:0%
+back but yeah the real thing is these
+two bitcoins are sort of worth less than
+
+ align:start position:0%
+two bitcoins are sort of worth less than
+ 
+
+ align:start position:0%
+two bitcoins are sort of worth less than
+two other bitcoins right now you've got
+
+ align:start position:0%
+two other bitcoins right now you've got
+ 
+
+ align:start position:0%
+two other bitcoins right now you've got
+a sort of different value for these
+
+ align:start position:0%
+a sort of different value for these
+ 
+
+ align:start position:0%
+a sort of different value for these
+where these two bitcoins are hot and I
+
+ align:start position:0%
+where these two bitcoins are hot and I
+ 
+
+ align:start position:0%
+where these two bitcoins are hot and I
+need to you know get rid of them and
+
+ align:start position:0%
+need to you know get rid of them and
+ 
+
+ align:start position:0%
+need to you know get rid of them and
+launder them or something right and you
+
+ align:start position:0%
+launder them or something right and you
+ 
+
+ align:start position:0%
+launder them or something right and you
+just walk to the Bank of America and say
+
+ align:start position:0%
+just walk to the Bank of America and say
+ 
+
+ align:start position:0%
+just walk to the Bank of America and say
+here I want to deposit this probably
+
+ align:start position:0%
+here I want to deposit this probably
+ 
+
+ align:start position:0%
+here I want to deposit this probably
+you've got some problems okay actual
+
+ align:start position:0%
+you've got some problems okay actual
+ 
+
+ align:start position:0%
+you've got some problems okay actual
+physical currency notes so yeah so this
+
+ align:start position:0%
+physical currency notes so yeah so this
+ 
+
+ align:start position:0%
+physical currency notes so yeah so this
+now now you've got the sort of money
+
+ align:start position:0%
+now now you've got the sort of money
+ 
+
+ align:start position:0%
+now now you've got the sort of money
+laundering that now people are gonna try
+
+ align:start position:0%
+laundering that now people are gonna try
+ 
+
+ align:start position:0%
+laundering that now people are gonna try
+to do using Bitcoin it'd be preferable
+
+ align:start position:0%
+to do using Bitcoin it'd be preferable
+ 
+
+ align:start position:0%
+to do using Bitcoin it'd be preferable
+if it was so the the way that they can
+
+ align:start position:0%
+if it was so the the way that they can
+ 
+
+ align:start position:0%
+if it was so the the way that they can
+tell about this is that people reuse a
+
+ align:start position:0%
+tell about this is that people reuse a
+ 
+
+ align:start position:0%
+tell about this is that people reuse a
+dresses Bitcoin is not inherently as
+
+ align:start position:0%
+dresses Bitcoin is not inherently as
+ 
+
+ align:start position:0%
+dresses Bitcoin is not inherently as
+fungible as say gold or or even dollar
+
+ align:start position:0%
+fungible as say gold or or even dollar
+ 
+
+ align:start position:0%
+fungible as say gold or or even dollar
+but dollar bills have these serial
+
+ align:start position:0%
+but dollar bills have these serial
+ 
+
+ align:start position:0%
+but dollar bills have these serial
+numbers right and I don't know to what
+
+ align:start position:0%
+numbers right and I don't know to what
+ 
+
+ align:start position:0%
+numbers right and I don't know to what
+extent people tracked these things but
+
+ align:start position:0%
+extent people tracked these things but
+ 
+
+ align:start position:0%
+extent people tracked these things but
+bitcoins are much more like the dollar
+
+ align:start position:0%
+bitcoins are much more like the dollar
+ 
+
+ align:start position:0%
+bitcoins are much more like the dollar
+bills with serial numbers and it's all
+
+ align:start position:0%
+bills with serial numbers and it's all
+ 
+
+ align:start position:0%
+bills with serial numbers and it's all
+on on the internet it's all on the
+
+ align:start position:0%
+on on the internet it's all on the
+ 
+
+ align:start position:0%
+on on the internet it's all on the
+computer so it's really easy to track
+
+ align:start position:0%
+computer so it's really easy to track
+ 
+
+ align:start position:0%
+computer so it's really easy to track
+things this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and no one could stop him yes or no
+
+ align:start position:0%
+and no one could stop him yes or no
+ 
+
+ align:start position:0%
+and no one could stop him yes or no
+right so you say okay the bitcoins are
+
+ align:start position:0%
+right so you say okay the bitcoins are
+ 
+
+ align:start position:0%
+right so you say okay the bitcoins are
+you know I'm at the exchange they've got
+
+ align:start position:0%
+you know I'm at the exchange they've got
+ 
+
+ align:start position:0%
+you know I'm at the exchange they've got
+a giant pool of addresses I transfer to
+
+ align:start position:0%
+a giant pool of addresses I transfer to
+ 
+
+ align:start position:0%
+a giant pool of addresses I transfer to
+you know the the casino and then the
+
+ align:start position:0%
+you know the the casino and then the
+ 
+
+ align:start position:0%
+you know the the casino and then the
+casino in this in many of these cases
+
+ align:start position:0%
+casino in this in many of these cases
+ 
+
+ align:start position:0%
+casino in this in many of these cases
+uses reuses addresses extensively so
+
+ align:start position:0%
+uses reuses addresses extensively so
+ 
+
+ align:start position:0%
+uses reuses addresses extensively so
+it's really easy to see that this is the
+
+ align:start position:0%
+it's really easy to see that this is the
+ 
+
+ align:start position:0%
+it's really easy to see that this is the
+casino and then from the casino goes to
+
+ align:start position:0%
+casino and then from the casino goes to
+ 
+
+ align:start position:0%
+casino and then from the casino goes to
+the exchange again exchange flags that
+
+ align:start position:0%
+the exchange again exchange flags that
+ 
+
+ align:start position:0%
+the exchange again exchange flags that
+and says hey no we know where this came
+
+ align:start position:0%
+and says hey no we know where this came
+ 
+
+ align:start position:0%
+and says hey no we know where this came
+from instead you say okay I go to user a
+
+ align:start position:0%
+from instead you say okay I go to user a
+ 
+
+ align:start position:0%
+from instead you say okay I go to user a
+and then I go to the exchange in some
+
+ align:start position:0%
+and then I go to the exchange in some
+ 
+
+ align:start position:0%
+and then I go to the exchange in some
+cases that might you know if there
+
+ align:start position:0%
+cases that might you know if there
+ 
+
+ align:start position:0%
+cases that might you know if there
+algorithm is hey just look at where it
+
+ align:start position:0%
+algorithm is hey just look at where it
+ 
+
+ align:start position:0%
+algorithm is hey just look at where it
+came from
+
+ align:start position:0%
+came from
+ 
+
+ align:start position:0%
+came from
+sure but if you say wait there was one
+
+ align:start position:0%
+sure but if you say wait there was one
+ 
+
+ align:start position:0%
+sure but if you say wait there was one
+output
+
+ align:start position:0%
+output
+ 
+
+ align:start position:0%
+output
+you know this transaction is one input
+
+ align:start position:0%
+you know this transaction is one input
+ 
+
+ align:start position:0%
+you know this transaction is one input
+one output so we know exactly where it
+
+ align:start position:0%
+one output so we know exactly where it
+ 
+
+ align:start position:0%
+one output so we know exactly where it
+came from you can trace it back that way
+
+ align:start position:0%
+came from you can trace it back that way
+ 
+
+ align:start position:0%
+came from you can trace it back that way
+so it depends the coins being worth less
+
+ align:start position:0%
+so it depends the coins being worth less
+ 
+
+ align:start position:0%
+so it depends the coins being worth less
+you know this is unmown alike and since
+
+ align:start position:0%
+you know this is unmown alike and since
+ 
+
+ align:start position:0%
+you know this is unmown alike and since
+legal tender is a whole other thing and
+
+ align:start position:0%
+legal tender is a whole other thing and
+ 
+
+ align:start position:0%
+legal tender is a whole other thing and
+I'm pretty sure a Bitcoin will never be
+
+ align:start position:0%
+I'm pretty sure a Bitcoin will never be
+ 
+
+ align:start position:0%
+I'm pretty sure a Bitcoin will never be
+legal tender anywhere in terms of like
+
+ align:start position:0%
+legal tender anywhere in terms of like
+ 
+
+ align:start position:0%
+legal tender anywhere in terms of like
+that's gonna be settled it but at least
+
+ align:start position:0%
+that's gonna be settled it but at least
+ 
+
+ align:start position:0%
+that's gonna be settled it but at least
+fungibility we want that so if we want
+
+ align:start position:0%
+fungibility we want that so if we want
+ 
+
+ align:start position:0%
+fungibility we want that so if we want
+to make Bitcoin more money like how do
+
+ align:start position:0%
+to make Bitcoin more money like how do
+ 
+
+ align:start position:0%
+to make Bitcoin more money like how do
+we fix this
+
+ align:start position:0%
+we fix this
+ 
+
+ align:start position:0%
+we fix this
+the first and and simplest and possibly
+
+ align:start position:0%
+the first and and simplest and possibly
+ 
+
+ align:start position:0%
+the first and and simplest and possibly
+the biggest is address reuse so if the
+
+ align:start position:0%
+the biggest is address reuse so if the
+ 
+
+ align:start position:0%
+the biggest is address reuse so if the
+casino keeps using the same address over
+
+ align:start position:0%
+casino keeps using the same address over
+ 
+
+ align:start position:0%
+casino keeps using the same address over
+and over it's really obvious and so
+
+ align:start position:0%
+and over it's really obvious and so
+ 
+
+ align:start position:0%
+and over it's really obvious and so
+things like vanity addresses so a lot of
+
+ align:start position:0%
+things like vanity addresses so a lot of
+ 
+
+ align:start position:0%
+things like vanity addresses so a lot of
+them will use vanity addresses a vanity
+
+ align:start position:0%
+them will use vanity addresses a vanity
+ 
+
+ align:start position:0%
+them will use vanity addresses a vanity
+address is when you continually perform
+
+ align:start position:0%
+address is when you continually perform
+ 
+
+ align:start position:0%
+address is when you continually perform
+computations to try to get a human
+
+ align:start position:0%
+computations to try to get a human
+ 
+
+ align:start position:0%
+computations to try to get a human
+readable address right the addresses are
+
+ align:start position:0%
+readable address right the addresses are
+ 
+
+ align:start position:0%
+readable address right the addresses are
+random numbers though for example I
+
+ align:start position:0%
+random numbers though for example I
+ 
+
+ align:start position:0%
+random numbers though for example I
+taint rich so Greg Maxwell has this
+
+ align:start position:0%
+taint rich so Greg Maxwell has this
+ 
+
+ align:start position:0%
+taint rich so Greg Maxwell has this
+address which is 1g Maxwell boa MD
+
+ align:start position:0%
+address which is 1g Maxwell boa MD
+ 
+
+ align:start position:0%
+address which is 1g Maxwell boa MD
+accident so you can see that the first
+
+ align:start position:0%
+accident so you can see that the first
+ 
+
+ align:start position:0%
+accident so you can see that the first
+you know the first part of that address
+
+ align:start position:0%
+you know the first part of that address
+ 
+
+ align:start position:0%
+you know the first part of that address
+is to you Maxwell and you get that just
+
+ align:start position:0%
+is to you Maxwell and you get that just
+ 
+
+ align:start position:0%
+is to you Maxwell and you get that just
+by continually attempting millions and
+
+ align:start position:0%
+by continually attempting millions and
+ 
+
+ align:start position:0%
+by continually attempting millions and
+millions or billions of different keys
+
+ align:start position:0%
+millions or billions of different keys
+ 
+
+ align:start position:0%
+millions or billions of different keys
+and seeing which turn into the address
+
+ align:start position:0%
+and seeing which turn into the address
+ 
+
+ align:start position:0%
+and seeing which turn into the address
+you want so people do that people spend
+
+ align:start position:0%
+you want so people do that people spend
+ 
+
+ align:start position:0%
+you want so people do that people spend
+a lot of resources on making cool
+
+ align:start position:0%
+a lot of resources on making cool
+ 
+
+ align:start position:0%
+a lot of resources on making cool
+addresses and then the casino can say
+
+ align:start position:0%
+addresses and then the casino can say
+ 
+
+ align:start position:0%
+addresses and then the casino can say
+okay this is my address but that really
+
+ align:start position:0%
+okay this is my address but that really
+ 
+
+ align:start position:0%
+okay this is my address but that really
+hurts the fungibility and privacy
+
+ align:start position:0%
+hurts the fungibility and privacy
+ 
+
+ align:start position:0%
+hurts the fungibility and privacy
+because now it's clear what when you
+
+ align:start position:0%
+because now it's clear what when you
+ 
+
+ align:start position:0%
+because now it's clear what when you
+know I want a customer sends to that
+
+ align:start position:0%
+know I want a customer sends to that
+ 
+
+ align:start position:0%
+know I want a customer sends to that
+address every
+
+ align:start position:0%
+address every
+ 
+
+ align:start position:0%
+address every
+one in the world can see its breathing
+
+ align:start position:0%
+one in the world can see its breathing
+ 
+
+ align:start position:0%
+one in the world can see its breathing
+you know but yeah like Satoshi dice does
+
+ align:start position:0%
+you know but yeah like Satoshi dice does
+ 
+
+ align:start position:0%
+you know but yeah like Satoshi dice does
+this too right or did one yeah so these
+
+ align:start position:0%
+this too right or did one yeah so these
+ 
+
+ align:start position:0%
+this too right or did one yeah so these
+social Satoshi dice addresses Satoshi
+
+ align:start position:0%
+social Satoshi dice addresses Satoshi
+ 
+
+ align:start position:0%
+social Satoshi dice addresses Satoshi
+dry spinning yeah it always starts with
+
+ align:start position:0%
+dry spinning yeah it always starts with
+ 
+
+ align:start position:0%
+dry spinning yeah it always starts with
+one dice nine in one day yeah so like
+
+ align:start position:0%
+one dice nine in one day yeah so like
+ 
+
+ align:start position:0%
+one dice nine in one day yeah so like
+branding I guess makes it easier for it
+
+ align:start position:0%
+branding I guess makes it easier for it
+ 
+
+ align:start position:0%
+branding I guess makes it easier for it
+does make it easier for people to
+
+ align:start position:0%
+does make it easier for people to
+ 
+
+ align:start position:0%
+does make it easier for people to
+recognize and if they have a list of the
+
+ align:start position:0%
+recognize and if they have a list of the
+ 
+
+ align:start position:0%
+recognize and if they have a list of the
+addresses they're like oh that's the
+
+ align:start position:0%
+addresses they're like oh that's the
+ 
+
+ align:start position:0%
+addresses they're like oh that's the
+casino dress I want to deposit to the
+
+ align:start position:0%
+casino dress I want to deposit to the
+ 
+
+ align:start position:0%
+casino dress I want to deposit to the
+casino and just copy and paste that in
+
+ align:start position:0%
+casino and just copy and paste that in
+ 
+
+ align:start position:0%
+casino and just copy and paste that in
+there so so like it is a use it it does
+
+ align:start position:0%
+there so so like it is a use it it does
+ 
+
+ align:start position:0%
+there so so like it is a use it it does
+help usability and that's one of the
+
+ align:start position:0%
+help usability and that's one of the
+ 
+
+ align:start position:0%
+help usability and that's one of the
+issues in Bitcoin it's like having these
+
+ align:start position:0%
+issues in Bitcoin it's like having these
+ 
+
+ align:start position:0%
+issues in Bitcoin it's like having these
+giant ugly addresses that you have to
+
+ align:start position:0%
+giant ugly addresses that you have to
+ 
+
+ align:start position:0%
+giant ugly addresses that you have to
+get right and not sent to the wrong one
+
+ align:start position:0%
+get right and not sent to the wrong one
+ 
+
+ align:start position:0%
+get right and not sent to the wrong one
+it's it's not a great user experience
+
+ align:start position:0%
+it's it's not a great user experience
+ 
+
+ align:start position:0%
+it's it's not a great user experience
+kind of thing so I can see that vanity
+
+ align:start position:0%
+kind of thing so I can see that vanity
+ 
+
+ align:start position:0%
+kind of thing so I can see that vanity
+addresses do improve improve the user
+
+ align:start position:0%
+addresses do improve improve the user
+ 
+
+ align:start position:0%
+addresses do improve improve the user
+experience a little bit but it really
+
+ align:start position:0%
+experience a little bit but it really
+ 
+
+ align:start position:0%
+experience a little bit but it really
+hurts the privacy of the system so an
+
+ align:start position:0%
+hurts the privacy of the system so an
+ 
+
+ align:start position:0%
+hurts the privacy of the system so an
+address race is a problem because people
+
+ align:start position:0%
+address race is a problem because people
+ 
+
+ align:start position:0%
+address race is a problem because people
+keep using it it looks cool also web
+
+ align:start position:0%
+keep using it it looks cool also web
+ 
+
+ align:start position:0%
+keep using it it looks cool also web
+explorers in for scoops a lot like so if
+
+ align:start position:0%
+explorers in for scoops a lot like so if
+ 
+
+ align:start position:0%
+explorers in for scoops a lot like so if
+you look at um you know if you just look
+
+ align:start position:0%
+you look at um you know if you just look
+ 
+
+ align:start position:0%
+you look at um you know if you just look
+at blockchain on info right you'll have
+
+ align:start position:0%
+at blockchain on info right you'll have
+ 
+
+ align:start position:0%
+at blockchain on info right you'll have
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+this is Advanced Mode enable disable I
+
+ align:start position:0%
+this is Advanced Mode enable disable I
+ 
+
+ align:start position:0%
+this is Advanced Mode enable disable I
+don't know
+
+ align:start position:0%
+don't know
+ 
+
+ align:start position:0%
+don't know
+even with Advanced Mode yeah okay it'll
+
+ align:start position:0%
+even with Advanced Mode yeah okay it'll
+ 
+
+ align:start position:0%
+even with Advanced Mode yeah okay it'll
+it'll give you a link to the output so
+
+ align:start position:0%
+it'll give you a link to the output so
+ 
+
+ align:start position:0%
+it'll give you a link to the output so
+no one's gonna click that anyway so the
+
+ align:start position:0%
+no one's gonna click that anyway so the
+ 
+
+ align:start position:0%
+no one's gonna click that anyway so the
+idea is this shows
+
+ align:start position:0%
+idea is this shows
+ 
+
+ align:start position:0%
+idea is this shows
+oh here's the transaction it's coming
+
+ align:start position:0%
+oh here's the transaction it's coming
+ 
+
+ align:start position:0%
+oh here's the transaction it's coming
+from two addresses sending to two
+
+ align:start position:0%
+from two addresses sending to two
+ 
+
+ align:start position:0%
+from two addresses sending to two
+addresses and it even gives you a
+
+ align:start position:0%
+addresses and it even gives you a
+ 
+
+ align:start position:0%
+addresses and it even gives you a
+helpful hey this is this is greg maxwell
+
+ align:start position:0%
+helpful hey this is this is greg maxwell
+ 
+
+ align:start position:0%
+helpful hey this is this is greg maxwell
+right and i'll give you a link to where
+
+ align:start position:0%
+right and i'll give you a link to where
+ 
+
+ align:start position:0%
+right and i'll give you a link to where
+does this go you're being redirected
+
+ align:start position:0%
+does this go you're being redirected
+ 
+
+ align:start position:0%
+does this go you're being redirected
+okay well go for it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+GMAX okay so it's Greg's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Gregg's little account on Bitcoin talk
+
+ align:start position:0%
+Gregg's little account on Bitcoin talk
+ 
+
+ align:start position:0%
+Gregg's little account on Bitcoin talk
+interesting but so this is you know you
+
+ align:start position:0%
+interesting but so this is you know you
+ 
+
+ align:start position:0%
+interesting but so this is you know you
+guys know enough about this system now
+
+ align:start position:0%
+guys know enough about this system now
+ 
+
+ align:start position:0%
+guys know enough about this system now
+that this is not true right if you click
+
+ align:start position:0%
+that this is not true right if you click
+ 
+
+ align:start position:0%
+that this is not true right if you click
+on an address and now it gives you all
+
+ align:start position:0%
+on an address and now it gives you all
+ 
+
+ align:start position:0%
+on an address and now it gives you all
+the transactions way too many that were
+
+ align:start position:0%
+the transactions way too many that were
+ 
+
+ align:start position:0%
+the transactions way too many that were
+involved in this but if you if you click
+
+ align:start position:0%
+involved in this but if you if you click
+ 
+
+ align:start position:0%
+involved in this but if you if you click
+on a transaction it's it's not spending
+
+ align:start position:0%
+on a transaction it's it's not spending
+ 
+
+ align:start position:0%
+on a transaction it's it's not spending
+from addresses in to addresses its
+
+ align:start position:0%
+from addresses in to addresses its
+ 
+
+ align:start position:0%
+from addresses in to addresses its
+spending from transaction outputs and
+
+ align:start position:0%
+spending from transaction outputs and
+ 
+
+ align:start position:0%
+spending from transaction outputs and
+spending to addresses that can later be
+
+ align:start position:0%
+spending to addresses that can later be
+ 
+
+ align:start position:0%
+spending to addresses that can later be
+consumed so the way that web explores
+
+ align:start position:0%
+consumed so the way that web explores
+ 
+
+ align:start position:0%
+consumed so the way that web explores
+and it'll show a balance right if I
+
+ align:start position:0%
+and it'll show a balance right if I
+ 
+
+ align:start position:0%
+and it'll show a balance right if I
+clicked on an address it says hey here's
+
+ align:start position:0%
+clicked on an address it says hey here's
+ 
+
+ align:start position:0%
+clicked on an address it says hey here's
+the number of transactions involved
+
+ align:start position:0%
+the number of transactions involved
+ 
+
+ align:start position:0%
+the number of transactions involved
+here's the final balance you know and
+
+ align:start position:0%
+here's the final balance you know and
+ 
+
+ align:start position:0%
+here's the final balance you know and
+you can look at the current balance and
+
+ align:start position:0%
+you can look at the current balance and
+ 
+
+ align:start position:0%
+you can look at the current balance and
+things like that but that's not actually
+
+ align:start position:0%
+things like that but that's not actually
+ 
+
+ align:start position:0%
+things like that but that's not actually
+how the system works and it hurts hurts
+
+ align:start position:0%
+how the system works and it hurts hurts
+ 
+
+ align:start position:0%
+how the system works and it hurts hurts
+privacy and fungibility to have this
+
+ align:start position:0%
+privacy and fungibility to have this
+ 
+
+ align:start position:0%
+privacy and fungibility to have this
+idea of oh this is sort of my account
+
+ align:start position:0%
+idea of oh this is sort of my account
+ 
+
+ align:start position:0%
+idea of oh this is sort of my account
+and it's got a balance that can increase
+
+ align:start position:0%
+and it's got a balance that can increase
+ 
+
+ align:start position:0%
+and it's got a balance that can increase
+and decrease because then that implies
+
+ align:start position:0%
+and decrease because then that implies
+ 
+
+ align:start position:0%
+and decrease because then that implies
+that I'm gonna keep using it whereas
+
+ align:start position:0%
+that I'm gonna keep using it whereas
+ 
+
+ align:start position:0%
+that I'm gonna keep using it whereas
+really they if they're one-time use that
+
+ align:start position:0%
+really they if they're one-time use that
+ 
+
+ align:start position:0%
+really they if they're one-time use that
+hurts that really makes it harder to
+
+ align:start position:0%
+hurts that really makes it harder to
+ 
+
+ align:start position:0%
+hurts that really makes it harder to
+trace things okay so another aspect that
+
+ align:start position:0%
+trace things okay so another aspect that
+ 
+
+ align:start position:0%
+trace things okay so another aspect that
+hurts this if you want to trace things
+
+ align:start position:0%
+hurts this if you want to trace things
+ 
+
+ align:start position:0%
+hurts this if you want to trace things
+so if it's one input one output right
+
+ align:start position:0%
+so if it's one input one output right
+ 
+
+ align:start position:0%
+so if it's one input one output right
+here it's real easy but even if it's not
+
+ align:start position:0%
+here it's real easy but even if it's not
+ 
+
+ align:start position:0%
+here it's real easy but even if it's not
+one input one output so for example
+
+ align:start position:0%
+one input one output so for example
+ 
+
+ align:start position:0%
+one input one output so for example
+imagine a transaction where the input
+
+ align:start position:0%
+imagine a transaction where the input
+ 
+
+ align:start position:0%
+imagine a transaction where the input
+has ten coins in it there's output a
+
+ align:start position:0%
+has ten coins in it there's output a
+ 
+
+ align:start position:0%
+has ten coins in it there's output a
+which is one coin output B which is
+
+ align:start position:0%
+which is one coin output B which is
+ 
+
+ align:start position:0%
+which is one coin output B which is
+eight point nine nine seven nine nine
+
+ align:start position:0%
+eight point nine nine seven nine nine
+ 
+
+ align:start position:0%
+eight point nine nine seven nine nine
+seven coins which do you think is the
+
+ align:start position:0%
+seven coins which do you think is the
+ 
+
+ align:start position:0%
+seven coins which do you think is the
+change address right there all different
+
+ align:start position:0%
+change address right there all different
+ 
+
+ align:start position:0%
+change address right there all different
+addresses but the eight point nine seven
+
+ align:start position:0%
+addresses but the eight point nine seven
+ 
+
+ align:start position:0%
+addresses but the eight point nine seven
+right I mean it's it's okay he's you
+
+ align:start position:0%
+right I mean it's it's okay he's you
+ 
+
+ align:start position:0%
+right I mean it's it's okay he's you
+know whoever's doing this they're
+
+ align:start position:0%
+know whoever's doing this they're
+ 
+
+ align:start position:0%
+know whoever's doing this they're
+sending one coin and the remainder minus
+
+ align:start position:0%
+sending one coin and the remainder minus
+ 
+
+ align:start position:0%
+sending one coin and the remainder minus
+the fee is this so it's often pretty
+
+ align:start position:0%
+the fee is this so it's often pretty
+ 
+
+ align:start position:0%
+the fee is this so it's often pretty
+clear even though looking at it all the
+
+ align:start position:0%
+clear even though looking at it all the
+ 
+
+ align:start position:0%
+clear even though looking at it all the
+addresses are different okay is it are
+
+ align:start position:0%
+addresses are different okay is it are
+ 
+
+ align:start position:0%
+addresses are different okay is it are
+any of these change the dresses is it
+
+ align:start position:0%
+any of these change the dresses is it
+ 
+
+ align:start position:0%
+any of these change the dresses is it
+just a sending to B and C is it a
+
+ align:start position:0%
+just a sending to B and C is it a
+ 
+
+ align:start position:0%
+just a sending to B and C is it a
+sending to B and back to a I'll often
+
+ align:start position:0%
+sending to B and back to a I'll often
+ 
+
+ align:start position:0%
+sending to B and back to a I'll often
+it's pretty easy to figure out and
+
+ align:start position:0%
+it's pretty easy to figure out and
+ 
+
+ align:start position:0%
+it's pretty easy to figure out and
+you're guessing but you can get the
+
+ align:start position:0%
+you're guessing but you can get the
+ 
+
+ align:start position:0%
+you're guessing but you can get the
+guessing pretty pretty good okay so what
+
+ align:start position:0%
+guessing pretty pretty good okay so what
+ 
+
+ align:start position:0%
+guessing pretty pretty good okay so what
+we're gonna talk about now anonymity
+
+ align:start position:0%
+we're gonna talk about now anonymity
+ 
+
+ align:start position:0%
+we're gonna talk about now anonymity
+sense so bitcoin is not actually
+
+ align:start position:0%
+sense so bitcoin is not actually
+ 
+
+ align:start position:0%
+sense so bitcoin is not actually
+anonymous right there are sort of
+
+ align:start position:0%
+anonymous right there are sort of
+ 
+
+ align:start position:0%
+anonymous right there are sort of
+identities attached to these things in
+
+ align:start position:0%
+identities attached to these things in
+ 
+
+ align:start position:0%
+identities attached to these things in
+it you have addresses the addresses are
+
+ align:start position:0%
+it you have addresses the addresses are
+ 
+
+ align:start position:0%
+it you have addresses the addresses are
+not your name but you can think of them
+
+ align:start position:0%
+not your name but you can think of them
+ 
+
+ align:start position:0%
+not your name but you can think of them
+as a pseudonym right and you can
+
+ align:start position:0%
+as a pseudonym right and you can
+ 
+
+ align:start position:0%
+as a pseudonym right and you can
+create a bunch of pseudonyms but they
+
+ align:start position:0%
+create a bunch of pseudonyms but they
+ 
+
+ align:start position:0%
+create a bunch of pseudonyms but they
+there are these keys there are these
+
+ align:start position:0%
+there are these keys there are these
+ 
+
+ align:start position:0%
+there are these keys there are these
+publicly seen you know known addresses
+
+ align:start position:0%
+publicly seen you know known addresses
+ 
+
+ align:start position:0%
+publicly seen you know known addresses
+and so we want to expand an anonymity
+
+ align:start position:0%
+and so we want to expand an anonymity
+ 
+
+ align:start position:0%
+and so we want to expand an anonymity
+set and so the idea of annum anonymity
+
+ align:start position:0%
+set and so the idea of annum anonymity
+ 
+
+ align:start position:0%
+set and so the idea of annum anonymity
+set is how many possible different you
+
+ align:start position:0%
+set is how many possible different you
+ 
+
+ align:start position:0%
+set is how many possible different you
+know identities could be the owner of
+
+ align:start position:0%
+know identities could be the owner of
+ 
+
+ align:start position:0%
+know identities could be the owner of
+these coins so and the idea of expanding
+
+ align:start position:0%
+these coins so and the idea of expanding
+ 
+
+ align:start position:0%
+these coins so and the idea of expanding
+your anonymity set so even if Bitcoin
+
+ align:start position:0%
+your anonymity set so even if Bitcoin
+ 
+
+ align:start position:0%
+your anonymity set so even if Bitcoin
+were perfectly anonymous in terms of the
+
+ align:start position:0%
+were perfectly anonymous in terms of the
+ 
+
+ align:start position:0%
+were perfectly anonymous in terms of the
+anonymity set was everyone who had
+
+ align:start position:0%
+anonymity set was everyone who had
+ 
+
+ align:start position:0%
+anonymity set was everyone who had
+Bitcoin that's still actually not that
+
+ align:start position:0%
+Bitcoin that's still actually not that
+ 
+
+ align:start position:0%
+Bitcoin that's still actually not that
+many people so if you see a Bitcoin
+
+ align:start position:0%
+many people so if you see a Bitcoin
+ 
+
+ align:start position:0%
+many people so if you see a Bitcoin
+you're like well I don't know who owns
+
+ align:start position:0%
+you're like well I don't know who owns
+ 
+
+ align:start position:0%
+you're like well I don't know who owns
+it but I know that the person who owns
+
+ align:start position:0%
+it but I know that the person who owns
+ 
+
+ align:start position:0%
+it but I know that the person who owns
+it owns Bitcoin and actually there's not
+
+ align:start position:0%
+it owns Bitcoin and actually there's not
+ 
+
+ align:start position:0%
+it owns Bitcoin and actually there's not
+that many people who own Bitcoin so I've
+
+ align:start position:0%
+that many people who own Bitcoin so I've
+ 
+
+ align:start position:0%
+that many people who own Bitcoin so I've
+just eliminated 99% of the people my
+
+ align:start position:0%
+just eliminated 99% of the people my
+ 
+
+ align:start position:0%
+just eliminated 99% of the people my
+suspects right just just by doing that
+
+ align:start position:0%
+suspects right just just by doing that
+ 
+
+ align:start position:0%
+suspects right just just by doing that
+so just having more people using Bitcoin
+
+ align:start position:0%
+so just having more people using Bitcoin
+ 
+
+ align:start position:0%
+so just having more people using Bitcoin
+makes it more anonymous in that sense
+
+ align:start position:0%
+makes it more anonymous in that sense
+ 
+
+ align:start position:0%
+makes it more anonymous in that sense
+right if it's very niche kind of thing
+
+ align:start position:0%
+right if it's very niche kind of thing
+ 
+
+ align:start position:0%
+right if it's very niche kind of thing
+and then the police say okay well
+
+ align:start position:0%
+and then the police say okay well
+ 
+
+ align:start position:0%
+and then the police say okay well
+whoever did this crime they're a Bitcoin
+
+ align:start position:0%
+whoever did this crime they're a Bitcoin
+ 
+
+ align:start position:0%
+whoever did this crime they're a Bitcoin
+user
+
+ align:start position:0%
+user
+ 
+
+ align:start position:0%
+user
+well now you can find there's not that
+
+ align:start position:0%
+well now you can find there's not that
+ 
+
+ align:start position:0%
+well now you can find there's not that
+many Bitcoin users so you want to try to
+
+ align:start position:0%
+many Bitcoin users so you want to try to
+ 
+
+ align:start position:0%
+many Bitcoin users so you want to try to
+increase your anonymity set for a
+
+ align:start position:0%
+increase your anonymity set for a
+ 
+
+ align:start position:0%
+increase your anonymity set for a
+specific transaction okay so the
+
+ align:start position:0%
+specific transaction okay so the
+ 
+
+ align:start position:0%
+specific transaction okay so the
+traditional I don't want to say
+
+ align:start position:0%
+traditional I don't want to say
+ 
+
+ align:start position:0%
+traditional I don't want to say
+traditional the way you do this is
+
+ align:start position:0%
+traditional the way you do this is
+ 
+
+ align:start position:0%
+traditional the way you do this is
+basically monitoring laundering it's a
+
+ align:start position:0%
+basically monitoring laundering it's a
+ 
+
+ align:start position:0%
+basically monitoring laundering it's a
+Bitcoin mixer and these mixers still
+
+ align:start position:0%
+Bitcoin mixer and these mixers still
+ 
+
+ align:start position:0%
+Bitcoin mixer and these mixers still
+exist I'm pretty sure right James you
+
+ align:start position:0%
+exist I'm pretty sure right James you
+ 
+
+ align:start position:0%
+exist I'm pretty sure right James you
+know they're still around they're still
+
+ align:start position:0%
+know they're still around they're still
+ 
+
+ align:start position:0%
+know they're still around they're still
+around I don't know why but a lot of
+
+ align:start position:0%
+around I don't know why but a lot of
+ 
+
+ align:start position:0%
+around I don't know why but a lot of
+times these tor well I mean I know why
+
+ align:start position:0%
+times these tor well I mean I know why
+ 
+
+ align:start position:0%
+times these tor well I mean I know why
+but it's like there's so many better
+
+ align:start position:0%
+but it's like there's so many better
+ 
+
+ align:start position:0%
+but it's like there's so many better
+ways to do this so you've got coins that
+
+ align:start position:0%
+ways to do this so you've got coins that
+ 
+
+ align:start position:0%
+ways to do this so you've got coins that
+address a and you say okay I'm gonna
+
+ align:start position:0%
+address a and you say okay I'm gonna
+ 
+
+ align:start position:0%
+address a and you say okay I'm gonna
+send ten coins to the mixer which does
+
+ align:start position:0%
+send ten coins to the mixer which does
+ 
+
+ align:start position:0%
+send ten coins to the mixer which does
+address B and then later some different
+
+ align:start position:0%
+address B and then later some different
+ 
+
+ align:start position:0%
+address B and then later some different
+not from that output but somewhere else
+
+ align:start position:0%
+not from that output but somewhere else
+ 
+
+ align:start position:0%
+not from that output but somewhere else
+in this sort of giant mixer account for
+
+ align:start position:0%
+in this sort of giant mixer account for
+ 
+
+ align:start position:0%
+in this sort of giant mixer account for
+coins get sent to address C and for
+
+ align:start position:0%
+coins get sent to address C and for
+ 
+
+ align:start position:0%
+coins get sent to address C and for
+coins six going to address D so you've
+
+ align:start position:0%
+coins six going to address D so you've
+ 
+
+ align:start position:0%
+coins six going to address D so you've
+now expect you know you basically pool
+
+ align:start position:0%
+now expect you know you basically pool
+ 
+
+ align:start position:0%
+now expect you know you basically pool
+all the coins into this mixer which uses
+
+ align:start position:0%
+all the coins into this mixer which uses
+ 
+
+ align:start position:0%
+all the coins into this mixer which uses
+lots of different addresses and then
+
+ align:start position:0%
+lots of different addresses and then
+ 
+
+ align:start position:0%
+lots of different addresses and then
+split it up over time different amounts
+
+ align:start position:0%
+split it up over time different amounts
+ 
+
+ align:start position:0%
+split it up over time different amounts
+and it gets really hard to figure out
+
+ align:start position:0%
+and it gets really hard to figure out
+ 
+
+ align:start position:0%
+and it gets really hard to figure out
+where the coins came from so you're in
+
+ align:start position:0%
+where the coins came from so you're in
+ 
+
+ align:start position:0%
+where the coins came from so you're in
+and we said is bigger the the problem is
+
+ align:start position:0%
+and we said is bigger the the problem is
+ 
+
+ align:start position:0%
+and we said is bigger the the problem is
+mixers work well potential a nativity
+
+ align:start position:0%
+mixers work well potential a nativity
+ 
+
+ align:start position:0%
+mixers work well potential a nativity
+set is all the other users of the mixer
+
+ align:start position:0%
+set is all the other users of the mixer
+ 
+
+ align:start position:0%
+set is all the other users of the mixer
+if it's well designed the problem the
+
+ align:start position:0%
+if it's well designed the problem the
+ 
+
+ align:start position:0%
+if it's well designed the problem the
+mixer is a sphere with everyone's money
+
+ align:start position:0%
+mixer is a sphere with everyone's money
+ 
+
+ align:start position:0%
+mixer is a sphere with everyone's money
+very consistently the mixers are not
+
+ align:start position:0%
+very consistently the mixers are not
+ 
+
+ align:start position:0%
+very consistently the mixers are not
+certainly not publicly regulated company
+
+ align:start position:0%
+certainly not publicly regulated company
+ 
+
+ align:start position:0%
+certainly not publicly regulated company
+I'm pretty sure you couldn't do that so
+
+ align:start position:0%
+I'm pretty sure you couldn't do that so
+ 
+
+ align:start position:0%
+I'm pretty sure you couldn't do that so
+they're just sort of these anonymous
+
+ align:start position:0%
+they're just sort of these anonymous
+ 
+
+ align:start position:0%
+they're just sort of these anonymous
+like hey I'm a mixer Bitcoin cloud or
+
+ align:start position:0%
+like hey I'm a mixer Bitcoin cloud or
+ 
+
+ align:start position:0%
+like hey I'm a mixer Bitcoin cloud or
+Bitcoin fog or whatever and the a lot of
+
+ align:start position:0%
+Bitcoin fog or whatever and the a lot of
+ 
+
+ align:start position:0%
+Bitcoin fog or whatever and the a lot of
+times they're on tour so you don't even
+
+ align:start position:0%
+times they're on tour so you don't even
+ 
+
+ align:start position:0%
+times they're on tour so you don't even
+know where the mixer exists and you just
+
+ align:start position:0%
+know where the mixer exists and you just
+ 
+
+ align:start position:0%
+know where the mixer exists and you just
+sort of hope for the best and send your
+
+ align:start position:0%
+sort of hope for the best and send your
+ 
+
+ align:start position:0%
+sort of hope for the best and send your
+money in yeah yeah some of them take
+
+ align:start position:0%
+money in yeah yeah some of them take
+ 
+
+ align:start position:0%
+money in yeah yeah some of them take
+these the big fee is when they keep all
+
+ align:start position:0%
+these the big fee is when they keep all
+ 
+
+ align:start position:0%
+these the big fee is when they keep all
+your money and don't give it back but
+
+ align:start position:0%
+your money and don't give it back but
+ 
+
+ align:start position:0%
+your money and don't give it back but
+but yeah a lot of times they will take a
+
+ align:start position:0%
+but yeah a lot of times they will take a
+ 
+
+ align:start position:0%
+but yeah a lot of times they will take a
+small small cut but it's it's not
+
+ align:start position:0%
+small small cut but it's it's not
+ 
+
+ align:start position:0%
+small small cut but it's it's not
+actually hard to write the cost is
+
+ align:start position:0%
+actually hard to write the cost is
+ 
+
+ align:start position:0%
+actually hard to write the cost is
+pretty minimal in that you you need some
+
+ align:start position:0%
+pretty minimal in that you you need some
+ 
+
+ align:start position:0%
+pretty minimal in that you you need some
+kind of tour service and then you just
+
+ align:start position:0%
+kind of tour service and then you just
+ 
+
+ align:start position:0%
+kind of tour service and then you just
+have some software that just runs this
+
+ align:start position:0%
+have some software that just runs this
+ 
+
+ align:start position:0%
+have some software that just runs this
+and you know allows deposits and
+
+ align:start position:0%
+and you know allows deposits and
+ 
+
+ align:start position:0%
+and you know allows deposits and
+withdrawals the conference in Puerto
+
+ align:start position:0%
+withdrawals the conference in Puerto
+ 
+
+ align:start position:0%
+withdrawals the conference in Puerto
+Rico financial crypto so there was a
+
+ align:start position:0%
+Rico financial crypto so there was a
+ 
+
+ align:start position:0%
+Rico financial crypto so there was a
+talk about a what was the word they used
+
+ align:start position:0%
+talk about a what was the word they used
+ 
+
+ align:start position:0%
+talk about a what was the word they used
+not traceable a reputable a mixer that
+
+ align:start position:0%
+not traceable a reputable a mixer that
+ 
+
+ align:start position:0%
+not traceable a reputable a mixer that
+you could prove defrauded you right so
+
+ align:start position:0%
+you could prove defrauded you right so
+ 
+
+ align:start position:0%
+you could prove defrauded you right so
+you had you know you could you could
+
+ align:start position:0%
+you had you know you could you could
+ 
+
+ align:start position:0%
+you had you know you could you could
+have these proofs that like oh I can
+
+ align:start position:0%
+have these proofs that like oh I can
+ 
+
+ align:start position:0%
+have these proofs that like oh I can
+prove that they stole my coins that I
+
+ align:start position:0%
+prove that they stole my coins that I
+ 
+
+ align:start position:0%
+prove that they stole my coins that I
+which is I don't know I thought was kind
+
+ align:start position:0%
+which is I don't know I thought was kind
+ 
+
+ align:start position:0%
+which is I don't know I thought was kind
+of useless because the whole idea is
+
+ align:start position:0%
+of useless because the whole idea is
+ 
+
+ align:start position:0%
+of useless because the whole idea is
+they're anonymous and maybe you can
+
+ align:start position:0%
+they're anonymous and maybe you can
+ 
+
+ align:start position:0%
+they're anonymous and maybe you can
+prove that they ripped you off but they
+
+ align:start position:0%
+prove that they ripped you off but they
+ 
+
+ align:start position:0%
+prove that they ripped you off but they
+still ripped you off okay so then the
+
+ align:start position:0%
+still ripped you off okay so then the
+ 
+
+ align:start position:0%
+still ripped you off okay so then the
+better idea than a mixer is I taint rich
+
+ align:start position:0%
+better idea than a mixer is I taint rich
+ 
+
+ align:start position:0%
+better idea than a mixer is I taint rich
+was a blog post from Greg that's why
+
+ align:start position:0%
+was a blog post from Greg that's why
+ 
+
+ align:start position:0%
+was a blog post from Greg that's why
+I've got this up in 2013 it was kind of
+
+ align:start position:0%
+I've got this up in 2013 it was kind of
+ 
+
+ align:start position:0%
+I've got this up in 2013 it was kind of
+fun ever since I was a wee lad I had a
+
+ align:start position:0%
+fun ever since I was a wee lad I had a
+ 
+
+ align:start position:0%
+fun ever since I was a wee lad I had a
+dream my dream being incorrectly acestus
+
+ align:start position:0%
+dream my dream being incorrectly acestus
+ 
+
+ align:start position:0%
+dream my dream being incorrectly acestus
+and possibly rich by brain-dead
+
+ align:start position:0%
+and possibly rich by brain-dead
+ 
+
+ align:start position:0%
+and possibly rich by brain-dead
+automated analysis now with your help I
+
+ align:start position:0%
+automated analysis now with your help I
+ 
+
+ align:start position:0%
+automated analysis now with your help I
+can be so he wanted to mix inputs from
+
+ align:start position:0%
+can be so he wanted to mix inputs from
+ 
+
+ align:start position:0%
+can be so he wanted to mix inputs from
+different people within the same
+
+ align:start position:0%
+different people within the same
+ 
+
+ align:start position:0%
+different people within the same
+transaction so you could have two
+
+ align:start position:0%
+transaction so you could have two
+ 
+
+ align:start position:0%
+transaction so you could have two
+different people in the same transaction
+
+ align:start position:0%
+different people in the same transaction
+ 
+
+ align:start position:0%
+different people in the same transaction
+and in Bitcoin this is secure because
+
+ align:start position:0%
+and in Bitcoin this is secure because
+ 
+
+ align:start position:0%
+and in Bitcoin this is secure because
+the signature signs the whole
+
+ align:start position:0%
+the signature signs the whole
+ 
+
+ align:start position:0%
+the signature signs the whole
+transaction so you say okay I'm user a I
+
+ align:start position:0%
+transaction so you say okay I'm user a I
+ 
+
+ align:start position:0%
+transaction so you say okay I'm user a I
+put you know have my 10 coin input I'll
+
+ align:start position:0%
+put you know have my 10 coin input I'll
+ 
+
+ align:start position:0%
+put you know have my 10 coin input I'll
+match up with user B who's got his to
+
+ align:start position:0%
+match up with user B who's got his to
+ 
+
+ align:start position:0%
+match up with user B who's got his to
+coin input and we both signed this whole
+
+ align:start position:0%
+coin input and we both signed this whole
+ 
+
+ align:start position:0%
+coin input and we both signed this whole
+transaction which sends two points to C
+
+ align:start position:0%
+transaction which sends two points to C
+ 
+
+ align:start position:0%
+transaction which sends two points to C
+and ten coins to D so now you can't
+
+ align:start position:0%
+and ten coins to D so now you can't
+ 
+
+ align:start position:0%
+and ten coins to D so now you can't
+trace where these coins went right well
+
+ align:start position:0%
+trace where these coins went right well
+ 
+
+ align:start position:0%
+trace where these coins went right well
+sort of can but but it's but if you just
+
+ align:start position:0%
+sort of can but but it's but if you just
+ 
+
+ align:start position:0%
+sort of can but but it's but if you just
+look at the graph of transactions it's
+
+ align:start position:0%
+look at the graph of transactions it's
+ 
+
+ align:start position:0%
+look at the graph of transactions it's
+not as obvious so the first transactions
+
+ align:start position:0%
+not as obvious so the first transactions
+ 
+
+ align:start position:0%
+not as obvious so the first transactions
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+fun I remember seeing this so there's
+
+ align:start position:0%
+fun I remember seeing this so there's
+ 
+
+ align:start position:0%
+fun I remember seeing this so there's
+there's three inputs 40,000 bitcoins
+
+ align:start position:0%
+there's three inputs 40,000 bitcoins
+ 
+
+ align:start position:0%
+there's three inputs 40,000 bitcoins
+0.133 seven bitcoins and one Bitcoin
+
+ align:start position:0%
+0.133 seven bitcoins and one Bitcoin
+ 
+
+ align:start position:0%
+0.133 seven bitcoins and one Bitcoin
+from Gregg's and then 40,000 and three
+
+ align:start position:0%
+from Gregg's and then 40,000 and three
+ 
+
+ align:start position:0%
+from Gregg's and then 40,000 and three
+one three three and then 0.82 for some
+
+ align:start position:0%
+one three three and then 0.82 for some
+ 
+
+ align:start position:0%
+one three three and then 0.82 for some
+reason it was even more like yeah 40,000
+
+ align:start position:0%
+reason it was even more like yeah 40,000
+ 
+
+ align:start position:0%
+reason it was even more like yeah 40,000
+bitcoins is pretty good today it was no
+
+ align:start position:0%
+bitcoins is pretty good today it was no
+ 
+
+ align:start position:0%
+bitcoins is pretty good today it was no
+less impressive at the time in 2013 even
+
+ align:start position:0%
+less impressive at the time in 2013 even
+ 
+
+ align:start position:0%
+less impressive at the time in 2013 even
+though I guess it was only worth about
+
+ align:start position:0%
+though I guess it was only worth about
+ 
+
+ align:start position:0%
+though I guess it was only worth about
+half a million dollars at that time but
+
+ align:start position:0%
+half a million dollars at that time but
+ 
+
+ align:start position:0%
+half a million dollars at that time but
+but it was like it was pretty cool and
+
+ align:start position:0%
+but it was like it was pretty cool and
+ 
+
+ align:start position:0%
+but it was like it was pretty cool and
+then Gregg was like wow I've never seen
+
+ align:start position:0%
+then Gregg was like wow I've never seen
+ 
+
+ align:start position:0%
+then Gregg was like wow I've never seen
+that much money wait where did ya loaded
+
+ align:start position:0%
+that much money wait where did ya loaded
+ 
+
+ align:start position:0%
+that much money wait where did ya loaded
+so the guy who posted the 40 thousand
+
+ align:start position:0%
+so the guy who posted the 40 thousand
+ 
+
+ align:start position:0%
+so the guy who posted the 40 thousand
+coins he's called loaded and nobody
+
+ align:start position:0%
+coins he's called loaded and nobody
+ 
+
+ align:start position:0%
+coins he's called loaded and nobody
+knows who he is but he shows up from
+
+ align:start position:0%
+knows who he is but he shows up from
+ 
+
+ align:start position:0%
+knows who he is but he shows up from
+time to time and has a lot of money and
+
+ align:start position:0%
+time to time and has a lot of money and
+ 
+
+ align:start position:0%
+time to time and has a lot of money and
+so yeah then Gregg you know made a
+
+ align:start position:0%
+so yeah then Gregg you know made a
+ 
+
+ align:start position:0%
+so yeah then Gregg you know made a
+transaction uploaded I've handled prices
+
+ align:start position:0%
+transaction uploaded I've handled prices
+ 
+
+ align:start position:0%
+transaction uploaded I've handled prices
+before the most I've ever moved how to
+
+ align:start position:0%
+before the most I've ever moved how to
+ 
+
+ align:start position:0%
+before the most I've ever moved how to
+move on a single key press so very cool
+
+ align:start position:0%
+move on a single key press so very cool
+ 
+
+ align:start position:0%
+move on a single key press so very cool
+so it's pretty cool you can now you know
+
+ align:start position:0%
+so it's pretty cool you can now you know
+ 
+
+ align:start position:0%
+so it's pretty cool you can now you know
+you can put this was very manual right
+
+ align:start position:0%
+you can put this was very manual right
+ 
+
+ align:start position:0%
+you can put this was very manual right
+that was on a message board sort of
+
+ align:start position:0%
+that was on a message board sort of
+ 
+
+ align:start position:0%
+that was on a message board sort of
+goofing around but there's no risk
+
+ align:start position:0%
+goofing around but there's no risk
+ 
+
+ align:start position:0%
+goofing around but there's no risk
+you're not sending money to someone and
+
+ align:start position:0%
+you're not sending money to someone and
+ 
+
+ align:start position:0%
+you're not sending money to someone and
+then getting it back you're just saying
+
+ align:start position:0%
+then getting it back you're just saying
+ 
+
+ align:start position:0%
+then getting it back you're just saying
+oh Moo you know I'll sign off on this
+
+ align:start position:0%
+oh Moo you know I'll sign off on this
+ 
+
+ align:start position:0%
+oh Moo you know I'll sign off on this
+transaction and them transactions are
+
+ align:start position:0%
+transaction and them transactions are
+ 
+
+ align:start position:0%
+transaction and them transactions are
+atomic right you can't say oh I'm gonna
+
+ align:start position:0%
+atomic right you can't say oh I'm gonna
+ 
+
+ align:start position:0%
+atomic right you can't say oh I'm gonna
+cut off this bottom part and only have
+
+ align:start position:0%
+cut off this bottom part and only have
+ 
+
+ align:start position:0%
+cut off this bottom part and only have
+ten coins go in and two coins come out
+
+ align:start position:0%
+ten coins go in and two coins come out
+ 
+
+ align:start position:0%
+ten coins go in and two coins come out
+right the whole transaction is the thing
+
+ align:start position:0%
+right the whole transaction is the thing
+ 
+
+ align:start position:0%
+right the whole transaction is the thing
+that gets signed okay so what's the
+
+ align:start position:0%
+that gets signed okay so what's the
+ 
+
+ align:start position:0%
+that gets signed okay so what's the
+problem with this model anyway to tell
+
+ align:start position:0%
+problem with this model anyway to tell
+ 
+
+ align:start position:0%
+problem with this model anyway to tell
+any way to get a mapping from C and D to
+
+ align:start position:0%
+any way to get a mapping from C and D to
+ 
+
+ align:start position:0%
+any way to get a mapping from C and D to
+a and B there's one really obvious one
+
+ align:start position:0%
+a and B there's one really obvious one
+ 
+
+ align:start position:0%
+a and B there's one really obvious one
+on this great it's an X right yeah well
+
+ align:start position:0%
+on this great it's an X right yeah well
+ 
+
+ align:start position:0%
+on this great it's an X right yeah well
+gee I think it's a goes to D and B goes
+
+ align:start position:0%
+gee I think it's a goes to D and B goes
+ 
+
+ align:start position:0%
+gee I think it's a goes to D and B goes
+to C because the amounts are completely
+
+ align:start position:0%
+to C because the amounts are completely
+ 
+
+ align:start position:0%
+to C because the amounts are completely
+different and actually we'll talk about
+
+ align:start position:0%
+different and actually we'll talk about
+ 
+
+ align:start position:0%
+different and actually we'll talk about
+amounts next week but yeah so how about
+
+ align:start position:0%
+amounts next week but yeah so how about
+ 
+
+ align:start position:0%
+amounts next week but yeah so how about
+this well you've got ten coins coming in
+
+ align:start position:0%
+this well you've got ten coins coming in
+ 
+
+ align:start position:0%
+this well you've got ten coins coming in
+two coins coming in here here and I've
+
+ align:start position:0%
+two coins coming in here here and I've
+ 
+
+ align:start position:0%
+two coins coming in here here and I've
+got address CDV enough one seven one and
+
+ align:start position:0%
+got address CDV enough one seven one and
+ 
+
+ align:start position:0%
+got address CDV enough one seven one and
+three better maybe no no nice right you
+
+ align:start position:0%
+three better maybe no no nice right you
+ 
+
+ align:start position:0%
+three better maybe no no nice right you
+can still easily write the seven goes to
+
+ align:start position:0%
+can still easily write the seven goes to
+ 
+
+ align:start position:0%
+can still easily write the seven goes to
+the ten the you know seven three the one
+
+ align:start position:0%
+the ten the you know seven three the one
+ 
+
+ align:start position:0%
+the ten the you know seven three the one
+and one there's no
+
+ align:start position:0%
+and one there's no
+ 
+
+ align:start position:0%
+and one there's no
+I don't think there's any way it could
+
+ align:start position:0%
+I don't think there's any way it could
+ 
+
+ align:start position:0%
+I don't think there's any way it could
+be anything else yeah how about this
+
+ align:start position:0%
+be anything else yeah how about this
+ 
+
+ align:start position:0%
+be anything else yeah how about this
+address cs2 coins address ds2 coins
+
+ align:start position:0%
+address cs2 coins address ds2 coins
+ 
+
+ align:start position:0%
+address cs2 coins address ds2 coins
+address he has eight points
+
+ align:start position:0%
+address he has eight points
+ 
+
+ align:start position:0%
+address he has eight points
+well now that actually works right it's
+
+ align:start position:0%
+well now that actually works right it's
+ 
+
+ align:start position:0%
+well now that actually works right it's
+not clear if C is from A or B same with
+
+ align:start position:0%
+not clear if C is from A or B same with
+ 
+
+ align:start position:0%
+not clear if C is from A or B same with
+D right these two have some anonymity in
+
+ align:start position:0%
+D right these two have some anonymity in
+ 
+
+ align:start position:0%
+D right these two have some anonymity in
+that you're not sure which of which user
+
+ align:start position:0%
+that you're not sure which of which user
+ 
+
+ align:start position:0%
+that you're not sure which of which user
+it's from he on the other hand is
+
+ align:start position:0%
+it's from he on the other hand is
+ 
+
+ align:start position:0%
+it's from he on the other hand is
+obviously for me but these coins are now
+
+ align:start position:0%
+obviously for me but these coins are now
+ 
+
+ align:start position:0%
+obviously for me but these coins are now
+sort of in deterring you know the
+
+ align:start position:0%
+sort of in deterring you know the
+ 
+
+ align:start position:0%
+sort of in deterring you know the
+anonymity set has gone has doubled right
+
+ align:start position:0%
+anonymity set has gone has doubled right
+ 
+
+ align:start position:0%
+anonymity set has gone has doubled right
+you don't know whether it's C or D right
+
+ align:start position:0%
+you don't know whether it's C or D right
+ 
+
+ align:start position:0%
+you don't know whether it's C or D right
+these addresses now unclear so that's
+
+ align:start position:0%
+these addresses now unclear so that's
+ 
+
+ align:start position:0%
+these addresses now unclear so that's
+kind of cool how do we you know scale
+
+ align:start position:0%
+kind of cool how do we you know scale
+ 
+
+ align:start position:0%
+kind of cool how do we you know scale
+this well have more users and a bigger
+
+ align:start position:0%
+this well have more users and a bigger
+ 
+
+ align:start position:0%
+this well have more users and a bigger
+anonymity set so one issue with this is
+
+ align:start position:0%
+anonymity set so one issue with this is
+ 
+
+ align:start position:0%
+anonymity set so one issue with this is
+the users them as you scale to more
+
+ align:start position:0%
+the users them as you scale to more
+ 
+
+ align:start position:0%
+the users them as you scale to more
+users let's say you do ten different
+
+ align:start position:0%
+users let's say you do ten different
+ 
+
+ align:start position:0%
+users let's say you do ten different
+users where they all put in their inputs
+
+ align:start position:0%
+users where they all put in their inputs
+ 
+
+ align:start position:0%
+users where they all put in their inputs
+they all put in their set of outputs and
+
+ align:start position:0%
+they all put in their set of outputs and
+ 
+
+ align:start position:0%
+they all put in their set of outputs and
+now you've got this big transaction
+
+ align:start position:0%
+now you've got this big transaction
+ 
+
+ align:start position:0%
+now you've got this big transaction
+where they can sort of it's hard to tell
+
+ align:start position:0%
+where they can sort of it's hard to tell
+ 
+
+ align:start position:0%
+where they can sort of it's hard to tell
+what the mapping is the promise you gain
+
+ align:start position:0%
+what the mapping is the promise you gain
+ 
+
+ align:start position:0%
+what the mapping is the promise you gain
+numbers of inputs and numbers of users
+
+ align:start position:0%
+numbers of inputs and numbers of users
+ 
+
+ align:start position:0%
+numbers of inputs and numbers of users
+the users themselves know the mapping
+
+ align:start position:0%
+the users themselves know the mapping
+ 
+
+ align:start position:0%
+the users themselves know the mapping
+right because someone's actually doing
+
+ align:start position:0%
+right because someone's actually doing
+ 
+
+ align:start position:0%
+right because someone's actually doing
+the you know I put in my thing and put
+
+ align:start position:0%
+the you know I put in my thing and put
+ 
+
+ align:start position:0%
+the you know I put in my thing and put
+in yours so there's a user that knows
+
+ align:start position:0%
+in yours so there's a user that knows
+ 
+
+ align:start position:0%
+in yours so there's a user that knows
+the mapping and they can leak that info
+
+ align:start position:0%
+the mapping and they can leak that info
+ 
+
+ align:start position:0%
+the mapping and they can leak that info
+and that hurts the enemy right so maybe
+
+ align:start position:0%
+and that hurts the enemy right so maybe
+ 
+
+ align:start position:0%
+and that hurts the enemy right so maybe
+just hurting just the transaction graph
+
+ align:start position:0%
+just hurting just the transaction graph
+ 
+
+ align:start position:0%
+just hurting just the transaction graph
+itself won't tell you but somebody knows
+
+ align:start position:0%
+itself won't tell you but somebody knows
+ 
+
+ align:start position:0%
+itself won't tell you but somebody knows
+and they can reveal that at a later date
+
+ align:start position:0%
+and they can reveal that at a later date
+ 
+
+ align:start position:0%
+and they can reveal that at a later date
+so that's not good so there's a really
+
+ align:start position:0%
+so that's not good so there's a really
+ 
+
+ align:start position:0%
+so that's not good so there's a really
+cool really cool protocol called coin
+
+ align:start position:0%
+cool really cool protocol called coin
+ 
+
+ align:start position:0%
+cool really cool protocol called coin
+shuffle so pre coin join messaging to
+
+ align:start position:0%
+shuffle so pre coin join messaging to
+ 
+
+ align:start position:0%
+shuffle so pre coin join messaging to
+shuffle the inputs and outputs and this
+
+ align:start position:0%
+shuffle the inputs and outputs and this
+ 
+
+ align:start position:0%
+shuffle the inputs and outputs and this
+allows you to have ten twenty thirty
+
+ align:start position:0%
+allows you to have ten twenty thirty
+ 
+
+ align:start position:0%
+allows you to have ten twenty thirty
+different people doing it and if least
+
+ align:start position:0%
+different people doing it and if least
+ 
+
+ align:start position:0%
+different people doing it and if least
+if at least two participants are honest
+
+ align:start position:0%
+if at least two participants are honest
+ 
+
+ align:start position:0%
+if at least two participants are honest
+then the mapping cannot be determined
+
+ align:start position:0%
+then the mapping cannot be determined
+ 
+
+ align:start position:0%
+then the mapping cannot be determined
+the way it works like this is super
+
+ align:start position:0%
+the way it works like this is super
+ 
+
+ align:start position:0%
+the way it works like this is super
+quick because I don't have time that
+
+ align:start position:0%
+quick because I don't have time that
+ 
+
+ align:start position:0%
+quick because I don't have time that
+everyone has their inputs right that
+
+ align:start position:0%
+everyone has their inputs right that
+ 
+
+ align:start position:0%
+everyone has their inputs right that
+they want to put into the transaction
+
+ align:start position:0%
+they want to put into the transaction
+ 
+
+ align:start position:0%
+they want to put into the transaction
+and they also have the output addresses
+
+ align:start position:0%
+and they also have the output addresses
+ 
+
+ align:start position:0%
+and they also have the output addresses
+that they want as their outputs so they
+
+ align:start position:0%
+that they want as their outputs so they
+ 
+
+ align:start position:0%
+that they want as their outputs so they
+they make a new set of public keys that
+
+ align:start position:0%
+they make a new set of public keys that
+ 
+
+ align:start position:0%
+they make a new set of public keys that
+they're not going to use on Bitcoin at
+
+ align:start position:0%
+they're not going to use on Bitcoin at
+ 
+
+ align:start position:0%
+they're not going to use on Bitcoin at
+all right they're just making public
+
+ align:start position:0%
+all right they're just making public
+ 
+
+ align:start position:0%
+all right they're just making public
+keys for encryption purposes for this
+
+ align:start position:0%
+keys for encryption purposes for this
+ 
+
+ align:start position:0%
+keys for encryption purposes for this
+this game and they also tell everyone
+
+ align:start position:0%
+this game and they also tell everyone
+ 
+
+ align:start position:0%
+this game and they also tell everyone
+here's my inputs right
+
+ align:start position:0%
+here's my inputs right
+ 
+
+ align:start position:0%
+here's my inputs right
+my input is a my input is B so the
+
+ align:start position:0%
+my input is a my input is B so the
+ 
+
+ align:start position:0%
+my input is a my input is B so the
+inputs are publicly known or not
+
+ align:start position:0%
+inputs are publicly known or not
+ 
+
+ align:start position:0%
+inputs are publicly known or not
+publicly pumped to the people
+
+ align:start position:0%
+publicly pumped to the people
+ 
+
+ align:start position:0%
+publicly pumped to the people
+participating and then the idea is okay
+
+ align:start position:0%
+participating and then the idea is okay
+ 
+
+ align:start position:0%
+participating and then the idea is okay
+I know everyone's public key that
+
+ align:start position:0%
+I know everyone's public key that
+ 
+
+ align:start position:0%
+I know everyone's public key that
+they've given so I encrypt my output so
+
+ align:start position:0%
+they've given so I encrypt my output so
+ 
+
+ align:start position:0%
+they've given so I encrypt my output so
+I've got an input I told everyone I've
+
+ align:start position:0%
+I've got an input I told everyone I've
+ 
+
+ align:start position:0%
+I've got an input I told everyone I've
+got my output and I encrypt that the
+
+ align:start position:0%
+got my output and I encrypt that the
+ 
+
+ align:start position:0%
+got my output and I encrypt that the
+address itself and the amount with
+
+ align:start position:0%
+address itself and the amount with
+ 
+
+ align:start position:0%
+address itself and the amount with
+everyone's public keys sequentially so
+
+ align:start position:0%
+everyone's public keys sequentially so
+ 
+
+ align:start position:0%
+everyone's public keys sequentially so
+for example I use encryption you know
+
+ align:start position:0%
+for example I use encryption you know
+ 
+
+ align:start position:0%
+for example I use encryption you know
+encryption on key C to encrypt the thing
+
+ align:start position:0%
+encryption on key C to encrypt the thing
+ 
+
+ align:start position:0%
+encryption on key C to encrypt the thing
+on encryption on key B encrypt the
+
+ align:start position:0%
+on encryption on key B encrypt the
+ 
+
+ align:start position:0%
+on encryption on key B encrypt the
+encryption on PA of my output and then I
+
+ align:start position:0%
+encryption on PA of my output and then I
+ 
+
+ align:start position:0%
+encryption on PA of my output and then I
+hand this to user a okay so this is like
+
+ align:start position:0%
+hand this to user a okay so this is like
+ 
+
+ align:start position:0%
+hand this to user a okay so this is like
+Onion Routing sort of onion encryption
+
+ align:start position:0%
+Onion Routing sort of onion encryption
+ 
+
+ align:start position:0%
+Onion Routing sort of onion encryption
+where you take a plaintext encrypt it
+
+ align:start position:0%
+where you take a plaintext encrypt it
+ 
+
+ align:start position:0%
+where you take a plaintext encrypt it
+encrypt it again and encrypt it again
+
+ align:start position:0%
+encrypt it again and encrypt it again
+ 
+
+ align:start position:0%
+encrypt it again and encrypt it again
+so I receive these encrypted outputs I
+
+ align:start position:0%
+so I receive these encrypted outputs I
+ 
+
+ align:start position:0%
+so I receive these encrypted outputs I
+shuffle them write I received one from a
+
+ align:start position:0%
+shuffle them write I received one from a
+ 
+
+ align:start position:0%
+shuffle them write I received one from a
+1 from B 1 from C you know I receive
+
+ align:start position:0%
+1 from B 1 from C you know I receive
+ 
+
+ align:start position:0%
+1 from B 1 from C you know I receive
+Eric's actually I received the whole set
+
+ align:start position:0%
+Eric's actually I received the whole set
+ 
+
+ align:start position:0%
+Eric's actually I received the whole set
+I shuffle the order and then I put use
+
+ align:start position:0%
+I shuffle the order and then I put use
+ 
+
+ align:start position:0%
+I shuffle the order and then I put use
+my key to decrypt one layer right it's
+
+ align:start position:0%
+my key to decrypt one layer right it's
+ 
+
+ align:start position:0%
+my key to decrypt one layer right it's
+still gonna be encrypted because I just
+
+ align:start position:0%
+still gonna be encrypted because I just
+ 
+
+ align:start position:0%
+still gonna be encrypted because I just
+see here's a bunch of encrypted data i
+
+ align:start position:0%
+see here's a bunch of encrypted data i
+ 
+
+ align:start position:0%
+see here's a bunch of encrypted data i
+decrypt it it's still encrypted with the
+
+ align:start position:0%
+decrypt it it's still encrypted with the
+ 
+
+ align:start position:0%
+decrypt it it's still encrypted with the
+next person's key and then I hand it to
+
+ align:start position:0%
+next person's key and then I hand it to
+ 
+
+ align:start position:0%
+next person's key and then I hand it to
+them and they shuffle decrypt so the
+
+ align:start position:0%
+them and they shuffle decrypt so the
+ 
+
+ align:start position:0%
+them and they shuffle decrypt so the
+final user gets the outputs and you know
+
+ align:start position:0%
+final user gets the outputs and you know
+ 
+
+ align:start position:0%
+final user gets the outputs and you know
+the final user so in this case user C
+
+ align:start position:0%
+the final user so in this case user C
+ 
+
+ align:start position:0%
+the final user so in this case user C
+can decrypt and now he's got my output
+
+ align:start position:0%
+can decrypt and now he's got my output
+ 
+
+ align:start position:0%
+can decrypt and now he's got my output
+but it's annulled around with everyone
+
+ align:start position:0%
+but it's annulled around with everyone
+ 
+
+ align:start position:0%
+but it's annulled around with everyone
+else's output at every step of the way
+
+ align:start position:0%
+else's output at every step of the way
+ 
+
+ align:start position:0%
+else's output at every step of the way
+so they can't tell whose went to whom
+
+ align:start position:0%
+so they can't tell whose went to whom
+ 
+
+ align:start position:0%
+so they can't tell whose went to whom
+and then they have this final
+
+ align:start position:0%
+and then they have this final
+ 
+
+ align:start position:0%
+and then they have this final
+transaction which has all the outputs in
+
+ align:start position:0%
+transaction which has all the outputs in
+ 
+
+ align:start position:0%
+transaction which has all the outputs in
+some random order because everyone
+
+ align:start position:0%
+some random order because everyone
+ 
+
+ align:start position:0%
+some random order because everyone
+contributed to randomizing the order of
+
+ align:start position:0%
+contributed to randomizing the order of
+ 
+
+ align:start position:0%
+contributed to randomizing the order of
+the outputs so this is really cool as
+
+ align:start position:0%
+the outputs so this is really cool as
+ 
+
+ align:start position:0%
+the outputs so this is really cool as
+long as two parties are honest if
+
+ align:start position:0%
+long as two parties are honest if
+ 
+
+ align:start position:0%
+long as two parties are honest if
+there's only one honest party it doesn't
+
+ align:start position:0%
+there's only one honest party it doesn't
+ 
+
+ align:start position:0%
+there's only one honest party it doesn't
+work because then every dishonest party
+
+ align:start position:0%
+work because then every dishonest party
+ 
+
+ align:start position:0%
+work because then every dishonest party
+colludes and says well you know we know
+
+ align:start position:0%
+colludes and says well you know we know
+ 
+
+ align:start position:0%
+colludes and says well you know we know
+everything but the honest parties output
+
+ align:start position:0%
+everything but the honest parties output
+ 
+
+ align:start position:0%
+everything but the honest parties output
+so we can figure out which one it is but
+
+ align:start position:0%
+so we can figure out which one it is but
+ 
+
+ align:start position:0%
+so we can figure out which one it is but
+if there's two users then you can't
+
+ align:start position:0%
+if there's two users then you can't
+ 
+
+ align:start position:0%
+if there's two users then you can't
+determine two users actually doing this
+
+ align:start position:0%
+determine two users actually doing this
+ 
+
+ align:start position:0%
+determine two users actually doing this
+then you can't determine the order so
+
+ align:start position:0%
+then you can't determine the order so
+ 
+
+ align:start position:0%
+then you can't determine the order so
+that's pretty cool I think it's being
+
+ align:start position:0%
+that's pretty cool I think it's being
+ 
+
+ align:start position:0%
+that's pretty cool I think it's being
+used for join market thank you something
+
+ align:start position:0%
+used for join market thank you something
+ 
+
+ align:start position:0%
+used for join market thank you something
+like this I don't know so there's like
+
+ align:start position:0%
+like this I don't know so there's like
+ 
+
+ align:start position:0%
+like this I don't know so there's like
+cool techniques for this kind of thing
+
+ align:start position:0%
+cool techniques for this kind of thing
+ 
+
+ align:start position:0%
+cool techniques for this kind of thing
+okay real-world though some people use
+
+ align:start position:0%
+okay real-world though some people use
+ 
+
+ align:start position:0%
+okay real-world though some people use
+this right join market exists
+
+ align:start position:0%
+this right join market exists
+ 
+
+ align:start position:0%
+this right join market exists
+I don't know how popular it is problem
+
+ align:start position:0%
+I don't know how popular it is problem
+ 
+
+ align:start position:0%
+I don't know how popular it is problem
+which people use this who uses this it's
+
+ align:start position:0%
+which people use this who uses this it's
+ 
+
+ align:start position:0%
+which people use this who uses this it's
+got a limited anonymity set of the
+
+ align:start position:0%
+got a limited anonymity set of the
+ 
+
+ align:start position:0%
+got a limited anonymity set of the
+people who really want anonymity which
+
+ align:start position:0%
+people who really want anonymity which
+ 
+
+ align:start position:0%
+people who really want anonymity which
+is not the anonymity set the people who
+
+ align:start position:0%
+is not the anonymity set the people who
+ 
+
+ align:start position:0%
+is not the anonymity set the people who
+want in any buddy want it's just kind of
+
+ align:start position:0%
+want in any buddy want it's just kind of
+ 
+
+ align:start position:0%
+want in any buddy want it's just kind of
+confusing but the idea is I don't want
+
+ align:start position:0%
+confusing but the idea is I don't want
+ 
+
+ align:start position:0%
+confusing but the idea is I don't want
+to just be in this group of people who
+
+ align:start position:0%
+to just be in this group of people who
+ 
+
+ align:start position:0%
+to just be in this group of people who
+want anonymity because those are the
+
+ align:start position:0%
+want anonymity because those are the
+ 
+
+ align:start position:0%
+want anonymity because those are the
+people I don't want to be associated
+
+ align:start position:0%
+people I don't want to be associated
+ 
+
+ align:start position:0%
+people I don't want to be associated
+I would rather associate myself with the
+
+ align:start position:0%
+I would rather associate myself with the
+ 
+
+ align:start position:0%
+I would rather associate myself with the
+people who don't particularly want
+
+ align:start position:0%
+people who don't particularly want
+ 
+
+ align:start position:0%
+people who don't particularly want
+anonymity this is a big problem right
+
+ align:start position:0%
+anonymity this is a big problem right
+ 
+
+ align:start position:0%
+anonymity this is a big problem right
+how do you people don't want if you
+
+ align:start position:0%
+how do you people don't want if you
+ 
+
+ align:start position:0%
+how do you people don't want if you
+people don't care about privacy people
+
+ align:start position:0%
+people don't care about privacy people
+ 
+
+ align:start position:0%
+people don't care about privacy people
+don't want to do these kinds of things
+
+ align:start position:0%
+don't want to do these kinds of things
+ 
+
+ align:start position:0%
+don't want to do these kinds of things
+and and this costs money too in this
+
+ align:start position:0%
+and and this costs money too in this
+ 
+
+ align:start position:0%
+and and this costs money too in this
+case like if you're doing these
+
+ align:start position:0%
+case like if you're doing these
+ 
+
+ align:start position:0%
+case like if you're doing these
+transactions this isn't really a payment
+
+ align:start position:0%
+transactions this isn't really a payment
+ 
+
+ align:start position:0%
+transactions this isn't really a payment
+this is just a superfluous transaction
+
+ align:start position:0%
+this is just a superfluous transaction
+ 
+
+ align:start position:0%
+this is just a superfluous transaction
+to turn your money around to get some
+
+ align:start position:0%
+to turn your money around to get some
+ 
+
+ align:start position:0%
+to turn your money around to get some
+more privacy this is one of the big
+
+ align:start position:0%
+more privacy this is one of the big
+ 
+
+ align:start position:0%
+more privacy this is one of the big
+issues with okay we want anonymity but
+
+ align:start position:0%
+issues with okay we want anonymity but
+ 
+
+ align:start position:0%
+issues with okay we want anonymity but
+if it if anonymity is opt-in it's not
+
+ align:start position:0%
+if it if anonymity is opt-in it's not
+ 
+
+ align:start position:0%
+if it if anonymity is opt-in it's not
+very useful right because then it's it's
+
+ align:start position:0%
+very useful right because then it's it's
+ 
+
+ align:start position:0%
+very useful right because then it's it's
+sort of like tor where if I'm using tor
+
+ align:start position:0%
+sort of like tor where if I'm using tor
+ 
+
+ align:start position:0%
+sort of like tor where if I'm using tor
+everyone's like why are you using tor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and so yeah well at this point
+
+ align:start position:0%
+and and so yeah well at this point
+ 
+
+ align:start position:0%
+and and so yeah well at this point
+encryption is now sort of ubiquitous and
+
+ align:start position:0%
+encryption is now sort of ubiquitous and
+ 
+
+ align:start position:0%
+encryption is now sort of ubiquitous and
+it's like the standard but yeah most
+
+ align:start position:0%
+it's like the standard but yeah most
+ 
+
+ align:start position:0%
+it's like the standard but yeah most
+trends are actual Bitcoin transactions
+
+ align:start position:0%
+trends are actual Bitcoin transactions
+ 
+
+ align:start position:0%
+trends are actual Bitcoin transactions
+are ending up from exchanges I don't
+
+ align:start position:0%
+are ending up from exchanges I don't
+ 
+
+ align:start position:0%
+are ending up from exchanges I don't
+know there's a lot but I don't know if
+
+ align:start position:0%
+know there's a lot but I don't know if
+ 
+
+ align:start position:0%
+know there's a lot but I don't know if
+it's majority I think it's I think it's
+
+ align:start position:0%
+it's majority I think it's I think it's
+ 
+
+ align:start position:0%
+it's majority I think it's I think it's
+like a decent percentage but I think
+
+ align:start position:0%
+like a decent percentage but I think
+ 
+
+ align:start position:0%
+like a decent percentage but I think
+it's less than half but yeah there's a
+
+ align:start position:0%
+it's less than half but yeah there's a
+ 
+
+ align:start position:0%
+it's less than half but yeah there's a
+lot
+
+ align:start position:0%
+lot
+ 
+
+ align:start position:0%
+lot
+it's it'd be awesome so exchanges are
+
+ align:start position:0%
+it's it'd be awesome so exchanges are
+ 
+
+ align:start position:0%
+it's it'd be awesome so exchanges are
+actually uniquely positioned where
+
+ align:start position:0%
+actually uniquely positioned where
+ 
+
+ align:start position:0%
+actually uniquely positioned where
+something like coin shuffle you could
+
+ align:start position:0%
+something like coin shuffle you could
+ 
+
+ align:start position:0%
+something like coin shuffle you could
+really easily do a like oblivious
+
+ align:start position:0%
+really easily do a like oblivious
+ 
+
+ align:start position:0%
+really easily do a like oblivious
+withdrawal where you say I want to
+
+ align:start position:0%
+withdrawal where you say I want to
+ 
+
+ align:start position:0%
+withdrawal where you say I want to
+withdraw my coins and I'm not gonna tell
+
+ align:start position:0%
+withdraw my coins and I'm not gonna tell
+ 
+
+ align:start position:0%
+withdraw my coins and I'm not gonna tell
+you where to but I'll give you this
+
+ align:start position:0%
+you where to but I'll give you this
+ 
+
+ align:start position:0%
+you where to but I'll give you this
+encrypted thing that gets shuffled
+
+ align:start position:0%
+encrypted thing that gets shuffled
+ 
+
+ align:start position:0%
+encrypted thing that gets shuffled
+around with different users and then at
+
+ align:start position:0%
+around with different users and then at
+ 
+
+ align:start position:0%
+around with different users and then at
+the end I sign off on it and the
+
+ align:start position:0%
+the end I sign off on it and the
+ 
+
+ align:start position:0%
+the end I sign off on it and the
+exchange can say well we're fulfilling
+
+ align:start position:0%
+exchange can say well we're fulfilling
+ 
+
+ align:start position:0%
+exchange can say well we're fulfilling
+all our customers withdrawals but we
+
+ align:start position:0%
+all our customers withdrawals but we
+ 
+
+ align:start position:0%
+all our customers withdrawals but we
+don't know where
+
+ align:start position:0%
+don't know where
+ 
+
+ align:start position:0%
+don't know where
+the coins are going you could totally do
+
+ align:start position:0%
+the coins are going you could totally do
+ 
+
+ align:start position:0%
+the coins are going you could totally do
+that I that's not a conversation that
+
+ align:start position:0%
+that I that's not a conversation that
+ 
+
+ align:start position:0%
+that I that's not a conversation that
+happens at any exchange here's this you
+
+ align:start position:0%
+happens at any exchange here's this you
+ 
+
+ align:start position:0%
+happens at any exchange here's this you
+know users name and address you know his
+
+ align:start position:0%
+know users name and address you know his
+ 
+
+ align:start position:0%
+know users name and address you know his
+house home address and his social
+
+ align:start position:0%
+house home address and his social
+ 
+
+ align:start position:0%
+house home address and his social
+security number
+
+ align:start position:0%
+security number
+ 
+
+ align:start position:0%
+security number
+and here's what he bought and sold
+
+ align:start position:0%
+and here's what he bought and sold
+ 
+
+ align:start position:0%
+and here's what he bought and sold
+versus does that also have and here's
+
+ align:start position:0%
+versus does that also have and here's
+ 
+
+ align:start position:0%
+versus does that also have and here's
+where the addresses where he withdrew
+
+ align:start position:0%
+where the addresses where he withdrew
+ 
+
+ align:start position:0%
+where the addresses where he withdrew
+his coins to that you know I don't I
+
+ align:start position:0%
+his coins to that you know I don't I
+ 
+
+ align:start position:0%
+his coins to that you know I don't I
+don't think the IRA like the IRS thing I
+
+ align:start position:0%
+don't think the IRA like the IRS thing I
+ 
+
+ align:start position:0%
+don't think the IRA like the IRS thing I
+think it was mostly we want to get
+
+ align:start position:0%
+think it was mostly we want to get
+ 
+
+ align:start position:0%
+think it was mostly we want to get
+people for not reporting their games I
+
+ align:start position:0%
+people for not reporting their games I
+ 
+
+ align:start position:0%
+people for not reporting their games I
+don't think it was right FinCEN the to
+
+ align:start position:0%
+don't think it was right FinCEN the to
+ 
+
+ align:start position:0%
+don't think it was right FinCEN the to
+map Bitcoin addresses to human names so
+
+ align:start position:0%
+map Bitcoin addresses to human names so
+ 
+
+ align:start position:0%
+map Bitcoin addresses to human names so
+they could see who did what
+
+ align:start position:0%
+they could see who did what
+ 
+
+ align:start position:0%
+they could see who did what
+I don't yeah IRS just wants to know who
+
+ align:start position:0%
+I don't yeah IRS just wants to know who
+ 
+
+ align:start position:0%
+I don't yeah IRS just wants to know who
+sold and didn't report gates by the way
+
+ align:start position:0%
+sold and didn't report gates by the way
+ 
+
+ align:start position:0%
+sold and didn't report gates by the way
+next to this weekend if you sold any
+
+ align:start position:0%
+next to this weekend if you sold any
+ 
+
+ align:start position:0%
+next to this weekend if you sold any
+coins last year you gotta tell the IRS
+
+ align:start position:0%
+coins last year you gotta tell the IRS
+ 
+
+ align:start position:0%
+coins last year you gotta tell the IRS
+I'm actually gonna pay a little bit of
+
+ align:start position:0%
+I'm actually gonna pay a little bit of
+ 
+
+ align:start position:0%
+I'm actually gonna pay a little bit of
+tax on that so yeah so so in anybody's
+
+ align:start position:0%
+tax on that so yeah so so in anybody's
+ 
+
+ align:start position:0%
+tax on that so yeah so so in anybody's
+tricky yeah like you could try to go
+
+ align:start position:0%
+tricky yeah like you could try to go
+ 
+
+ align:start position:0%
+tricky yeah like you could try to go
+through exchanges probably not the best
+
+ align:start position:0%
+through exchanges probably not the best
+ 
+
+ align:start position:0%
+through exchanges probably not the best
+it's just not like they're not gonna do
+
+ align:start position:0%
+it's just not like they're not gonna do
+ 
+
+ align:start position:0%
+it's just not like they're not gonna do
+it it's it's hard to do even research on
+
+ align:start position:0%
+it it's it's hard to do even research on
+ 
+
+ align:start position:0%
+it it's it's hard to do even research on
+this kind of stuff when you're a company
+
+ align:start position:0%
+this kind of stuff when you're a company
+ 
+
+ align:start position:0%
+this kind of stuff when you're a company
+there's a lot of sort of chilling
+
+ align:start position:0%
+there's a lot of sort of chilling
+ 
+
+ align:start position:0%
+there's a lot of sort of chilling
+effects itself that's sort of why I like
+
+ align:start position:0%
+effects itself that's sort of why I like
+ 
+
+ align:start position:0%
+effects itself that's sort of why I like
+working at MIT in that if I want to
+
+ align:start position:0%
+working at MIT in that if I want to
+ 
+
+ align:start position:0%
+working at MIT in that if I want to
+research crazy anonymity stuff totally
+
+ align:start position:0%
+research crazy anonymity stuff totally
+ 
+
+ align:start position:0%
+research crazy anonymity stuff totally
+fine whereas if I'm working at a VC
+
+ align:start position:0%
+fine whereas if I'm working at a VC
+ 
+
+ align:start position:0%
+fine whereas if I'm working at a VC
+funded company in San Francisco and I'm
+
+ align:start position:0%
+funded company in San Francisco and I'm
+ 
+
+ align:start position:0%
+funded company in San Francisco and I'm
+like hey we're making you know these
+
+ align:start position:0%
+like hey we're making you know these
+ 
+
+ align:start position:0%
+like hey we're making you know these
+anonymity protocols you sure you want to
+
+ align:start position:0%
+anonymity protocols you sure you want to
+ 
+
+ align:start position:0%
+anonymity protocols you sure you want to
+do it like it could be an awkward
+
+ align:start position:0%
+do it like it could be an awkward
+ 
+
+ align:start position:0%
+do it like it could be an awkward
+conversation in some cases okay so yeah
+
+ align:start position:0%
+conversation in some cases okay so yeah
+ 
+
+ align:start position:0%
+conversation in some cases okay so yeah
+people don't care about privacy it's
+
+ align:start position:0%
+people don't care about privacy it's
+ 
+
+ align:start position:0%
+people don't care about privacy it's
+sort of an externality if you say well
+
+ align:start position:0%
+sort of an externality if you say well
+ 
+
+ align:start position:0%
+sort of an externality if you say well
+I'm using addresses but that only hurts
+
+ align:start position:0%
+I'm using addresses but that only hurts
+ 
+
+ align:start position:0%
+I'm using addresses but that only hurts
+my privacy that's naturally not true
+
+ align:start position:0%
+my privacy that's naturally not true
+ 
+
+ align:start position:0%
+my privacy that's naturally not true
+right in the simplest sense
+
+ align:start position:0%
+right in the simplest sense
+ 
+
+ align:start position:0%
+right in the simplest sense
+you're reducing the anonymity set for
+
+ align:start position:0%
+you're reducing the anonymity set for
+ 
+
+ align:start position:0%
+you're reducing the anonymity set for
+everyone else right so if I have point
+
+ align:start position:0%
+everyone else right so if I have point
+ 
+
+ align:start position:0%
+everyone else right so if I have point
+you know if I say okay where are James's
+
+ align:start position:0%
+you know if I say okay where are James's
+ 
+
+ align:start position:0%
+you know if I say okay where are James's
+coins well I know they're not at 1g
+
+ align:start position:0%
+coins well I know they're not at 1g
+ 
+
+ align:start position:0%
+coins well I know they're not at 1g
+Maxwell 909 because that's Greg
+
+ align:start position:0%
+Maxwell 909 because that's Greg
+ 
+
+ align:start position:0%
+Maxwell 909 because that's Greg
+Maxwell's coins so it can't so I'm you
+
+ align:start position:0%
+Maxwell's coins so it can't so I'm you
+ 
+
+ align:start position:0%
+Maxwell's coins so it can't so I'm you
+know when you use publicly identifiable
+
+ align:start position:0%
+know when you use publicly identifiable
+ 
+
+ align:start position:0%
+know when you use publicly identifiable
+addresses and vanity addresses you're
+
+ align:start position:0%
+addresses and vanity addresses you're
+ 
+
+ align:start position:0%
+addresses and vanity addresses you're
+actually reducing the anonymity set for
+
+ align:start position:0%
+actually reducing the anonymity set for
+ 
+
+ align:start position:0%
+actually reducing the anonymity set for
+everyone else it's sort of an
+
+ align:start position:0%
+everyone else it's sort of an
+ 
+
+ align:start position:0%
+everyone else it's sort of an
+externality where the people who say I
+
+ align:start position:0%
+externality where the people who say I
+ 
+
+ align:start position:0%
+externality where the people who say I
+don't care about privacy are not paying
+
+ align:start position:0%
+don't care about privacy are not paying
+ 
+
+ align:start position:0%
+don't care about privacy are not paying
+the cost of harming the people who don't
+
+ align:start position:0%
+the cost of harming the people who don't
+ 
+
+ align:start position:0%
+the cost of harming the people who don't
+care about privacy so this is a tricky
+
+ align:start position:0%
+care about privacy so this is a tricky
+ 
+
+ align:start position:0%
+care about privacy so this is a tricky
+problem and the solution it's there's no
+
+ align:start position:0%
+problem and the solution it's there's no
+ 
+
+ align:start position:0%
+problem and the solution it's there's no
+solution but one one cool thing one way
+
+ align:start position:0%
+solution but one one cool thing one way
+ 
+
+ align:start position:0%
+solution but one one cool thing one way
+forward is well everyone likes cheaper
+
+ align:start position:0%
+forward is well everyone likes cheaper
+ 
+
+ align:start position:0%
+forward is well everyone likes cheaper
+transactions right everyone likes saving
+
+ align:start position:0%
+transactions right everyone likes saving
+ 
+
+ align:start position:0%
+transactions right everyone likes saving
+one so can we make it cheaper to improve
+
+ align:start position:0%
+one so can we make it cheaper to improve
+ 
+
+ align:start position:0%
+one so can we make it cheaper to improve
+in an image and so privacy and
+
+ align:start position:0%
+in an image and so privacy and
+ 
+
+ align:start position:0%
+in an image and so privacy and
+scalability in some cases are at odds
+
+ align:start position:0%
+scalability in some cases are at odds
+ 
+
+ align:start position:0%
+scalability in some cases are at odds
+right so in things like ring signatures
+
+ align:start position:0%
+right so in things like ring signatures
+ 
+
+ align:start position:0%
+right so in things like ring signatures
+which is maybe I'll I don't think I have
+
+ align:start position:0%
+which is maybe I'll I don't think I have
+ 
+
+ align:start position:0%
+which is maybe I'll I don't think I have
+time to go but but Monaro is a sort of
+
+ align:start position:0%
+time to go but but Monaro is a sort of
+ 
+
+ align:start position:0%
+time to go but but Monaro is a sort of
+privacy focused currency that uses ring
+
+ align:start position:0%
+privacy focused currency that uses ring
+ 
+
+ align:start position:0%
+privacy focused currency that uses ring
+signatures where you can point to a ring
+
+ align:start position:0%
+signatures where you can point to a ring
+ 
+
+ align:start position:0%
+signatures where you can point to a ring
+signatures I can point to two public
+
+ align:start position:0%
+signatures I can point to two public
+ 
+
+ align:start position:0%
+signatures I can point to two public
+keys and say okay there's public key a
+
+ align:start position:0%
+keys and say okay there's public key a
+ 
+
+ align:start position:0%
+keys and say okay there's public key a
+in public he be I'm signing message m on
+
+ align:start position:0%
+in public he be I'm signing message m on
+ 
+
+ align:start position:0%
+in public he be I'm signing message m on
+one of those two public keys but I'm not
+
+ align:start position:0%
+one of those two public keys but I'm not
+ 
+
+ align:start position:0%
+one of those two public keys but I'm not
+telling you which and you can verify
+
+ align:start position:0%
+telling you which and you can verify
+ 
+
+ align:start position:0%
+telling you which and you can verify
+that okay one of these keys signed but I
+
+ align:start position:0%
+that okay one of these keys signed but I
+ 
+
+ align:start position:0%
+that okay one of these keys signed but I
+you know I don't know which and the
+
+ align:start position:0%
+you know I don't know which and the
+ 
+
+ align:start position:0%
+you know I don't know which and the
+signer had to have one of the private
+
+ align:start position:0%
+signer had to have one of the private
+ 
+
+ align:start position:0%
+signer had to have one of the private
+keys or both right it's easy to if you
+
+ align:start position:0%
+keys or both right it's easy to if you
+ 
+
+ align:start position:0%
+keys or both right it's easy to if you
+have both keys you can obviously make a
+
+ align:start position:0%
+have both keys you can obviously make a
+ 
+
+ align:start position:0%
+have both keys you can obviously make a
+ring signature and it doesn't have to be
+
+ align:start position:0%
+ring signature and it doesn't have to be
+ 
+
+ align:start position:0%
+ring signature and it doesn't have to be
+two it can be five ten whatever a bunch
+
+ align:start position:0%
+two it can be five ten whatever a bunch
+ 
+
+ align:start position:0%
+two it can be five ten whatever a bunch
+of you know you pick a bunch of public
+
+ align:start position:0%
+of you know you pick a bunch of public
+ 
+
+ align:start position:0%
+of you know you pick a bunch of public
+keys sign with one of them so that's
+
+ align:start position:0%
+keys sign with one of them so that's
+ 
+
+ align:start position:0%
+keys sign with one of them so that's
+pretty cool that expands the size of
+
+ align:start position:0%
+pretty cool that expands the size of
+ 
+
+ align:start position:0%
+pretty cool that expands the size of
+signatures I believe with like o of n so
+
+ align:start position:0%
+signatures I believe with like o of n so
+ 
+
+ align:start position:0%
+signatures I believe with like o of n so
+if I have ten keys you're pointing to
+
+ align:start position:0%
+if I have ten keys you're pointing to
+ 
+
+ align:start position:0%
+if I have ten keys you're pointing to
+and you make a signature on one of them
+
+ align:start position:0%
+and you make a signature on one of them
+ 
+
+ align:start position:0%
+and you make a signature on one of them
+the signature actually gets bigger and
+
+ align:start position:0%
+the signature actually gets bigger and
+ 
+
+ align:start position:0%
+the signature actually gets bigger and
+so there's so like for Manero they use
+
+ align:start position:0%
+so there's so like for Manero they use
+ 
+
+ align:start position:0%
+so there's so like for Manero they use
+all these different systems and
+
+ align:start position:0%
+all these different systems and
+ 
+
+ align:start position:0%
+all these different systems and
+scalability is one of the big problems
+
+ align:start position:0%
+scalability is one of the big problems
+ 
+
+ align:start position:0%
+scalability is one of the big problems
+with there I mean it's a problem with
+
+ align:start position:0%
+with there I mean it's a problem with
+ 
+
+ align:start position:0%
+with there I mean it's a problem with
+Bitcoin as well it's problem with
+
+ align:start position:0%
+Bitcoin as well it's problem with
+ 
+
+ align:start position:0%
+Bitcoin as well it's problem with
+everything but it's it's even worse in
+
+ align:start position:0%
+everything but it's it's even worse in
+ 
+
+ align:start position:0%
+everything but it's it's even worse in
+manera because of the choices and like
+
+ align:start position:0%
+manera because of the choices and like
+ 
+
+ align:start position:0%
+manera because of the choices and like
+the different algorithms they use so in
+
+ align:start position:0%
+the different algorithms they use so in
+ 
+
+ align:start position:0%
+the different algorithms they use so in
+some cases privacy and scalability
+
+ align:start position:0%
+some cases privacy and scalability
+ 
+
+ align:start position:0%
+some cases privacy and scalability
+scalability are at odds but in some
+
+ align:start position:0%
+scalability are at odds but in some
+ 
+
+ align:start position:0%
+scalability are at odds but in some
+cases it works together where you can
+
+ align:start position:0%
+cases it works together where you can
+ 
+
+ align:start position:0%
+cases it works together where you can
+say look we just we want to have less
+
+ align:start position:0%
+say look we just we want to have less
+ 
+
+ align:start position:0%
+say look we just we want to have less
+information about these transactions so
+
+ align:start position:0%
+information about these transactions so
+ 
+
+ align:start position:0%
+information about these transactions so
+if you have left's information to store
+
+ align:start position:0%
+if you have left's information to store
+ 
+
+ align:start position:0%
+if you have left's information to store
+theirs
+
+ align:start position:0%
+theirs
+ 
+
+ align:start position:0%
+theirs
+information to link the users to their
+
+ align:start position:0%
+information to link the users to their
+ 
+
+ align:start position:0%
+information to link the users to their
+coins okay so an idea here is aggregate
+
+ align:start position:0%
+coins okay so an idea here is aggregate
+ 
+
+ align:start position:0%
+coins okay so an idea here is aggregate
+signatures so currently when you sign
+
+ align:start position:0%
+signatures so currently when you sign
+ 
+
+ align:start position:0%
+signatures so currently when you sign
+you have this input you say okay here's
+
+ align:start position:0%
+you have this input you say okay here's
+ 
+
+ align:start position:0%
+you have this input you say okay here's
+users a signature here's users B
+
+ align:start position:0%
+users a signature here's users B
+ 
+
+ align:start position:0%
+users a signature here's users B
+signature and you're doing this like
+
+ align:start position:0%
+signature and you're doing this like
+ 
+
+ align:start position:0%
+signature and you're doing this like
+ineffective coin joint thing here the
+
+ align:start position:0%
+ineffective coin joint thing here the
+ 
+
+ align:start position:0%
+ineffective coin joint thing here the
+goal would be we want to aggregate these
+
+ align:start position:0%
+goal would be we want to aggregate these
+ 
+
+ align:start position:0%
+goal would be we want to aggregate these
+signatures so we don't have a signature
+
+ align:start position:0%
+signatures so we don't have a signature
+ 
+
+ align:start position:0%
+signatures so we don't have a signature
+for this input we just have a single
+
+ align:start position:0%
+for this input we just have a single
+ 
+
+ align:start position:0%
+for this input we just have a single
+signature on key C which is just somehow
+
+ align:start position:0%
+signature on key C which is just somehow
+ 
+
+ align:start position:0%
+signature on key C which is just somehow
+the combination of a and B's signature
+
+ align:start position:0%
+the combination of a and B's signature
+ 
+
+ align:start position:0%
+the combination of a and B's signature
+and then you can save space because
+
+ align:start position:0%
+and then you can save space because
+ 
+
+ align:start position:0%
+and then you can save space because
+there's only one signature that stays
+
+ align:start position:0%
+there's only one signature that stays
+ 
+
+ align:start position:0%
+there's only one signature that stays
+the same size but still prove that both
+
+ align:start position:0%
+the same size but still prove that both
+ 
+
+ align:start position:0%
+the same size but still prove that both
+a so this is not a ring signature right
+
+ align:start position:0%
+a so this is not a ring signature right
+ 
+
+ align:start position:0%
+a so this is not a ring signature right
+this is aggregate is a and B both signed
+
+ align:start position:0%
+this is aggregate is a and B both signed
+ 
+
+ align:start position:0%
+this is aggregate is a and B both signed
+and produced a single signature together
+
+ align:start position:0%
+and produced a single signature together
+ 
+
+ align:start position:0%
+and produced a single signature together
+and that can validate the whole thing
+
+ align:start position:0%
+and that can validate the whole thing
+ 
+
+ align:start position:0%
+and that can validate the whole thing
+okay so how can we make this signature
+
+ align:start position:0%
+okay so how can we make this signature
+ 
+
+ align:start position:0%
+okay so how can we make this signature
+we know pump Keys a and B they're both
+
+ align:start position:0%
+we know pump Keys a and B they're both
+ 
+
+ align:start position:0%
+we know pump Keys a and B they're both
+signing the same message which is really
+
+ align:start position:0%
+signing the same message which is really
+ 
+
+ align:start position:0%
+signing the same message which is really
+important there's other the terms for
+
+ align:start position:0%
+important there's other the terms for
+ 
+
+ align:start position:0%
+important there's other the terms for
+these things there's like multi
+
+ align:start position:0%
+these things there's like multi
+ 
+
+ align:start position:0%
+these things there's like multi
+signatures aggregate signatures key
+
+ align:start position:0%
+signatures aggregate signatures key
+ 
+
+ align:start position:0%
+signatures aggregate signatures key
+aggregation like and no one agrees on
+
+ align:start position:0%
+aggregation like and no one agrees on
+ 
+
+ align:start position:0%
+aggregation like and no one agrees on
+I've had arguments like I've had
+
+ align:start position:0%
+I've had arguments like I've had
+ 
+
+ align:start position:0%
+I've had arguments like I've had
+discussions with people and I'm like
+
+ align:start position:0%
+discussions with people and I'm like
+ 
+
+ align:start position:0%
+discussions with people and I'm like
+wait that's what you call it I was
+
+ align:start position:0%
+wait that's what you call it I was
+ 
+
+ align:start position:0%
+wait that's what you call it I was
+calling it something else and there's
+
+ align:start position:0%
+calling it something else and there's
+ 
+
+ align:start position:0%
+calling it something else and there's
+not really good terms for this but in
+
+ align:start position:0%
+not really good terms for this but in
+ 
+
+ align:start position:0%
+not really good terms for this but in
+this case what we want is we're signing
+
+ align:start position:0%
+this case what we want is we're signing
+ 
+
+ align:start position:0%
+this case what we want is we're signing
+the same message so that makes it easier
+
+ align:start position:0%
+the same message so that makes it easier
+ 
+
+ align:start position:0%
+the same message so that makes it easier
+right we're not we're not trying to
+
+ align:start position:0%
+right we're not we're not trying to
+ 
+
+ align:start position:0%
+right we're not we're not trying to
+combine different messages different
+
+ align:start position:0%
+combine different messages different
+ 
+
+ align:start position:0%
+combine different messages different
+signatures on different messages from
+
+ align:start position:0%
+signatures on different messages from
+ 
+
+ align:start position:0%
+signatures on different messages from
+different pub keys and combine it to the
+
+ align:start position:0%
+different pub keys and combine it to the
+ 
+
+ align:start position:0%
+different pub keys and combine it to the
+same signature that's even harder
+
+ align:start position:0%
+same signature that's even harder
+ 
+
+ align:start position:0%
+same signature that's even harder
+although that is possible in some some
+
+ align:start position:0%
+although that is possible in some some
+ 
+
+ align:start position:0%
+although that is possible in some some
+ways but in this case a and B are
+
+ align:start position:0%
+ways but in this case a and B are
+ 
+
+ align:start position:0%
+ways but in this case a and B are
+signing the same message with they're
+
+ align:start position:0%
+signing the same message with they're
+ 
+
+ align:start position:0%
+signing the same message with they're
+two different keys and they need one
+
+ align:start position:0%
+two different keys and they need one
+ 
+
+ align:start position:0%
+two different keys and they need one
+signature and the signature is going to
+
+ align:start position:0%
+signature and the signature is going to
+ 
+
+ align:start position:0%
+signature and the signature is going to
+be RNs right so the equation that we had
+
+ align:start position:0%
+be RNs right so the equation that we had
+ 
+
+ align:start position:0%
+be RNs right so the equation that we had
+that we've done a couple times you know
+
+ align:start position:0%
+that we've done a couple times you know
+ 
+
+ align:start position:0%
+that we've done a couple times you know
+the signature is K some random number
+
+ align:start position:0%
+the signature is K some random number
+ 
+
+ align:start position:0%
+the signature is K some random number
+minus the hash of the message and K
+
+ align:start position:0%
+minus the hash of the message and K
+ 
+
+ align:start position:0%
+minus the hash of the message and K
+times G R times the private key and to
+
+ align:start position:0%
+times G R times the private key and to
+ 
+
+ align:start position:0%
+times G R times the private key and to
+verify you you know R minus the hash of
+
+ align:start position:0%
+verify you you know R minus the hash of
+ 
+
+ align:start position:0%
+verify you you know R minus the hash of
+the message in R times the public key
+
+ align:start position:0%
+the message in R times the public key
+ 
+
+ align:start position:0%
+the message in R times the public key
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you share the private keys with each
+
+ align:start position:0%
+if you share the private keys with each
+ 
+
+ align:start position:0%
+if you share the private keys with each
+other it's kind of easy right you say
+
+ align:start position:0%
+other it's kind of easy right you say
+ 
+
+ align:start position:0%
+other it's kind of easy right you say
+hey Alice just says here's my key Bob
+
+ align:start position:0%
+hey Alice just says here's my key Bob
+ 
+
+ align:start position:0%
+hey Alice just says here's my key Bob
+and then the Bob can compute everything
+
+ align:start position:0%
+and then the Bob can compute everything
+ 
+
+ align:start position:0%
+and then the Bob can compute everything
+you can do that was ECDSA but you really
+
+ align:start position:0%
+you can do that was ECDSA but you really
+ 
+
+ align:start position:0%
+you can do that was ECDSA but you really
+don't want to share private keys because
+
+ align:start position:0%
+don't want to share private keys because
+ 
+
+ align:start position:0%
+don't want to share private keys because
+as soon as you give someone else your
+
+ align:start position:0%
+as soon as you give someone else your
+ 
+
+ align:start position:0%
+as soon as you give someone else your
+private key maybe they don't sign this
+
+ align:start position:0%
+private key maybe they don't sign this
+ 
+
+ align:start position:0%
+private key maybe they don't sign this
+aggregate signature of the thing you
+
+ align:start position:0%
+aggregate signature of the thing you
+ 
+
+ align:start position:0%
+aggregate signature of the thing you
+want to sign they sign something else
+
+ align:start position:0%
+want to sign they sign something else
+ 
+
+ align:start position:0%
+want to sign they sign something else
+giving them all the money so you want to
+
+ align:start position:0%
+giving them all the money so you want to
+ 
+
+ align:start position:0%
+giving them all the money so you want to
+be involved in this process okay so the
+
+ align:start position:0%
+be involved in this process okay so the
+ 
+
+ align:start position:0%
+be involved in this process okay so the
+simplest sort of multi signature system
+
+ align:start position:0%
+simplest sort of multi signature system
+ 
+
+ align:start position:0%
+simplest sort of multi signature system
+for signatures first you want to share
+
+ align:start position:0%
+for signatures first you want to share
+ 
+
+ align:start position:0%
+for signatures first you want to share
+an R value but so this this R is also
+
+ align:start position:0%
+an R value but so this this R is also
+ 
+
+ align:start position:0%
+an R value but so this this R is also
+gonna have to have contributions from
+
+ align:start position:0%
+gonna have to have contributions from
+ 
+
+ align:start position:0%
+gonna have to have contributions from
+both users right who comes up with what
+
+ align:start position:0%
+both users right who comes up with what
+ 
+
+ align:start position:0%
+both users right who comes up with what
+here if C is the combination of both
+
+ align:start position:0%
+here if C is the combination of both
+ 
+
+ align:start position:0%
+here if C is the combination of both
+Alice and Bob's public key well the
+
+ align:start position:0%
+Alice and Bob's public key well the
+ 
+
+ align:start position:0%
+Alice and Bob's public key well the
+message we have already agreed on but
+
+ align:start position:0%
+message we have already agreed on but
+ 
+
+ align:start position:0%
+message we have already agreed on but
+this R value is the question so the idea
+
+ align:start position:0%
+this R value is the question so the idea
+ 
+
+ align:start position:0%
+this R value is the question so the idea
+is Alice comes up with k sub a computes
+
+ align:start position:0%
+is Alice comes up with k sub a computes
+ 
+
+ align:start position:0%
+is Alice comes up with k sub a computes
+R sub a and gives it to Bob Bob makes K
+
+ align:start position:0%
+R sub a and gives it to Bob Bob makes K
+ 
+
+ align:start position:0%
+R sub a and gives it to Bob Bob makes K
+sub B computes R sub B and gives that to
+
+ align:start position:0%
+sub B computes R sub B and gives that to
+ 
+
+ align:start position:0%
+sub B computes R sub B and gives that to
+Alice then both of them can say okay
+
+ align:start position:0%
+Alice then both of them can say okay
+ 
+
+ align:start position:0%
+Alice then both of them can say okay
+well we know the real r that we're gonna
+
+ align:start position:0%
+well we know the real r that we're gonna
+ 
+
+ align:start position:0%
+well we know the real r that we're gonna
+use for the signature is the sum of R
+
+ align:start position:0%
+use for the signature is the sum of R
+ 
+
+ align:start position:0%
+use for the signature is the sum of R
+sub a and R sub B then they want to
+
+ align:start position:0%
+sub a and R sub B then they want to
+ 
+
+ align:start position:0%
+sub a and R sub B then they want to
+compute their own SS I don't know how to
+
+ align:start position:0%
+compute their own SS I don't know how to
+ 
+
+ align:start position:0%
+compute their own SS I don't know how to
+ask
+
+ align:start position:0%
+ask
+ 
+
+ align:start position:0%
+ask
+so for Alice S sub a is gonna be equal
+
+ align:start position:0%
+so for Alice S sub a is gonna be equal
+ 
+
+ align:start position:0%
+so for Alice S sub a is gonna be equal
+to K sub a that only she knows right she
+
+ align:start position:0%
+to K sub a that only she knows right she
+ 
+
+ align:start position:0%
+to K sub a that only she knows right she
+shared R sub a but not case of a with
+
+ align:start position:0%
+shared R sub a but not case of a with
+ 
+
+ align:start position:0%
+shared R sub a but not case of a with
+Bob - the hash of the message and this
+
+ align:start position:0%
+Bob - the hash of the message and this
+ 
+
+ align:start position:0%
+Bob - the hash of the message and this
+aggregate you know the summed R times
+
+ align:start position:0%
+aggregate you know the summed R times
+ 
+
+ align:start position:0%
+aggregate you know the summed R times
+her private key for Bob its SMB equals
+
+ align:start position:0%
+her private key for Bob its SMB equals
+ 
+
+ align:start position:0%
+her private key for Bob its SMB equals
+case of me - the hash of the message in
+
+ align:start position:0%
+case of me - the hash of the message in
+ 
+
+ align:start position:0%
+case of me - the hash of the message in
+our times little B and then they give
+
+ align:start position:0%
+our times little B and then they give
+ 
+
+ align:start position:0%
+our times little B and then they give
+each other or really only one party
+
+ align:start position:0%
+each other or really only one party
+ 
+
+ align:start position:0%
+each other or really only one party
+needs to do this right either Alice
+
+ align:start position:0%
+needs to do this right either Alice
+ 
+
+ align:start position:0%
+needs to do this right either Alice
+gives S sub a to Bob or Bob gives s sub
+
+ align:start position:0%
+gives S sub a to Bob or Bob gives s sub
+ 
+
+ align:start position:0%
+gives S sub a to Bob or Bob gives s sub
+a to Alice but they don't have to both
+
+ align:start position:0%
+a to Alice but they don't have to both
+ 
+
+ align:start position:0%
+a to Alice but they don't have to both
+do it because then the final step is you
+
+ align:start position:0%
+do it because then the final step is you
+ 
+
+ align:start position:0%
+do it because then the final step is you
+just add the SS right so this sum you
+
+ align:start position:0%
+just add the SS right so this sum you
+ 
+
+ align:start position:0%
+just add the SS right so this sum you
+know this aggregate s is s ma + s sub B
+
+ align:start position:0%
+know this aggregate s is s ma + s sub B
+ 
+
+ align:start position:0%
+know this aggregate s is s ma + s sub B
+which is case of a plus K sub B - the
+
+ align:start position:0%
+which is case of a plus K sub B - the
+ 
+
+ align:start position:0%
+which is case of a plus K sub B - the
+hash of M + R times a - the hash of M +
+
+ align:start position:0%
+hash of M + R times a - the hash of M +
+ 
+
+ align:start position:0%
+hash of M + R times a - the hash of M +
+R times B which is you can call this K
+
+ align:start position:0%
+R times B which is you can call this K
+ 
+
+ align:start position:0%
+R times B which is you can call this K
+right that's the discrete log of R
+
+ align:start position:0%
+right that's the discrete log of R
+ 
+
+ align:start position:0%
+right that's the discrete log of R
+because they summed it and then you can
+
+ align:start position:0%
+because they summed it and then you can
+ 
+
+ align:start position:0%
+because they summed it and then you can
+factor out the a and B here and so this
+
+ align:start position:0%
+factor out the a and B here and so this
+ 
+
+ align:start position:0%
+factor out the a and B here and so this
+is the sum of their private keys this is
+
+ align:start position:0%
+is the sum of their private keys this is
+ 
+
+ align:start position:0%
+is the sum of their private keys this is
+the sum of their K values and then the
+
+ align:start position:0%
+the sum of their K values and then the
+ 
+
+ align:start position:0%
+the sum of their K values and then the
+signal verification step will work and
+
+ align:start position:0%
+signal verification step will work and
+ 
+
+ align:start position:0%
+signal verification step will work and
+that works awesome okay questions about
+
+ align:start position:0%
+that works awesome okay questions about
+ 
+
+ align:start position:0%
+that works awesome okay questions about
+this basic basically makes sense there's
+
+ align:start position:0%
+this basic basically makes sense there's
+ 
+
+ align:start position:0%
+this basic basically makes sense there's
+all sorts of minefield caveat sort of
+
+ align:start position:0%
+all sorts of minefield caveat sort of
+ 
+
+ align:start position:0%
+all sorts of minefield caveat sort of
+watch out things for example if they
+
+ align:start position:0%
+watch out things for example if they
+ 
+
+ align:start position:0%
+watch out things for example if they
+learn your K value they will learn your
+
+ align:start position:0%
+learn your K value they will learn your
+ 
+
+ align:start position:0%
+learn your K value they will learn your
+private key once they get us
+
+ align:start position:0%
+private key once they get us
+ 
+
+ align:start position:0%
+private key once they get us
+normally you make normally you make
+
+ align:start position:0%
+normally you make normally you make
+ 
+
+ align:start position:0%
+normally you make normally you make
+deterministic K values where you compute
+
+ align:start position:0%
+deterministic K values where you compute
+ 
+
+ align:start position:0%
+deterministic K values where you compute
+K as like the hash of your message being
+
+ align:start position:0%
+K as like the hash of your message being
+ 
+
+ align:start position:0%
+K as like the hash of your message being
+signed and your private key that's
+
+ align:start position:0%
+signed and your private key that's
+ 
+
+ align:start position:0%
+signed and your private key that's
+dangerous to do in this case because
+
+ align:start position:0%
+dangerous to do in this case because
+ 
+
+ align:start position:0%
+dangerous to do in this case because
+they might get a K value from you and
+
+ align:start position:0%
+they might get a K value from you and
+ 
+
+ align:start position:0%
+they might get a K value from you and
+then get and then give you a different R
+
+ align:start position:0%
+then get and then give you a different R
+ 
+
+ align:start position:0%
+then get and then give you a different R
+value and get another K value and like
+
+ align:start position:0%
+value and get another K value and like
+ 
+
+ align:start position:0%
+value and get another K value and like
+find your private key so there's all
+
+ align:start position:0%
+find your private key so there's all
+ 
+
+ align:start position:0%
+find your private key so there's all
+sorts of like watch out things okay so
+
+ align:start position:0%
+sorts of like watch out things okay so
+ 
+
+ align:start position:0%
+sorts of like watch out things okay so
+the the idea is okay now cool
+
+ align:start position:0%
+the the idea is okay now cool
+ 
+
+ align:start position:0%
+the the idea is okay now cool
+we've got address you know we've got
+
+ align:start position:0%
+we've got address you know we've got
+ 
+
+ align:start position:0%
+we've got address you know we've got
+output which needs a signature from a
+
+ align:start position:0%
+output which needs a signature from a
+ 
+
+ align:start position:0%
+output which needs a signature from a
+we've got an output which needs a
+
+ align:start position:0%
+we've got an output which needs a
+ 
+
+ align:start position:0%
+we've got an output which needs a
+signature from B we'll use those as
+
+ align:start position:0%
+signature from B we'll use those as
+ 
+
+ align:start position:0%
+signature from B we'll use those as
+inputs and just have this sum C
+
+ align:start position:0%
+inputs and just have this sum C
+ 
+
+ align:start position:0%
+inputs and just have this sum C
+signature and that shows that both
+
+ align:start position:0%
+signature and that shows that both
+ 
+
+ align:start position:0%
+signature and that shows that both
+parties signed right so we're good now
+
+ align:start position:0%
+parties signed right so we're good now
+ 
+
+ align:start position:0%
+parties signed right so we're good now
+we have way less data right these
+
+ align:start position:0%
+we have way less data right these
+ 
+
+ align:start position:0%
+we have way less data right these
+signatures are like 60 something 65
+
+ align:start position:0%
+signatures are like 60 something 65
+ 
+
+ align:start position:0%
+signatures are like 60 something 65
+bytes so instead of having it twice you
+
+ align:start position:0%
+bytes so instead of having it twice you
+ 
+
+ align:start position:0%
+bytes so instead of having it twice you
+just have one that covers the whole
+
+ align:start position:0%
+just have one that covers the whole
+ 
+
+ align:start position:0%
+just have one that covers the whole
+transaction great and it can it doesn't
+
+ align:start position:0%
+transaction great and it can it doesn't
+ 
+
+ align:start position:0%
+transaction great and it can it doesn't
+have to be a it doesn't have to be two
+
+ align:start position:0%
+have to be a it doesn't have to be two
+ 
+
+ align:start position:0%
+have to be a it doesn't have to be two
+right you can see how this would extend
+
+ align:start position:0%
+right you can see how this would extend
+ 
+
+ align:start position:0%
+right you can see how this would extend
+to three four or five different people
+
+ align:start position:0%
+to three four or five different people
+ 
+
+ align:start position:0%
+to three four or five different people
+they would all have to compute their own
+
+ align:start position:0%
+they would all have to compute their own
+ 
+
+ align:start position:0%
+they would all have to compute their own
+K value give it to everyone else
+
+ align:start position:0%
+K value give it to everyone else
+ 
+
+ align:start position:0%
+K value give it to everyone else
+everyone compute computes this combined
+
+ align:start position:0%
+everyone compute computes this combined
+ 
+
+ align:start position:0%
+everyone compute computes this combined
+R value and then does their own s's and
+
+ align:start position:0%
+R value and then does their own s's and
+ 
+
+ align:start position:0%
+R value and then does their own s's and
+then sums them all up and this would
+
+ align:start position:0%
+then sums them all up and this would
+ 
+
+ align:start position:0%
+then sums them all up and this would
+work with any number of participants
+
+ align:start position:0%
+work with any number of participants
+ 
+
+ align:start position:0%
+work with any number of participants
+problem you've got a bunch of coins that
+
+ align:start position:0%
+problem you've got a bunch of coins that
+ 
+
+ align:start position:0%
+problem you've got a bunch of coins that
+40,000 coins from before and then one
+
+ align:start position:0%
+40,000 coins from before and then one
+ 
+
+ align:start position:0%
+40,000 coins from before and then one
+day you see wait I'm user a user beam
+
+ align:start position:0%
+day you see wait I'm user a user beam
+ 
+
+ align:start position:0%
+day you see wait I'm user a user beam
+came up with a user a and B signature
+
+ align:start position:0%
+came up with a user a and B signature
+ 
+
+ align:start position:0%
+came up with a user a and B signature
+and sent it all to address
+
+ align:start position:0%
+and sent it all to address
+ 
+
+ align:start position:0%
+and sent it all to address
+II I never signed anything I didn't do
+
+ align:start position:0%
+II I never signed anything I didn't do
+ 
+
+ align:start position:0%
+II I never signed anything I didn't do
+this process with him how did he steal
+
+ align:start position:0%
+this process with him how did he steal
+ 
+
+ align:start position:0%
+this process with him how did he steal
+all my coins this is bad so any idea of
+
+ align:start position:0%
+all my coins this is bad so any idea of
+ 
+
+ align:start position:0%
+all my coins this is bad so any idea of
+how you could do this with the equations
+
+ align:start position:0%
+how you could do this with the equations
+ 
+
+ align:start position:0%
+how you could do this with the equations
+we okay so what you do is you say hey
+
+ align:start position:0%
+we okay so what you do is you say hey
+ 
+
+ align:start position:0%
+we okay so what you do is you say hey
+here's key a on the network and and
+
+ align:start position:0%
+here's key a on the network and and
+ 
+
+ align:start position:0%
+here's key a on the network and and
+normally you see pub key hashes but a
+
+ align:start position:0%
+normally you see pub key hashes but a
+ 
+
+ align:start position:0%
+normally you see pub key hashes but a
+lot of times you see pub keys and anyway
+
+ align:start position:0%
+lot of times you see pub keys and anyway
+ 
+
+ align:start position:0%
+lot of times you see pub keys and anyway
+you definitely see the pub key once
+
+ align:start position:0%
+you definitely see the pub key once
+ 
+
+ align:start position:0%
+you definitely see the pub key once
+people try to spend it so maybe if you
+
+ align:start position:0%
+people try to spend it so maybe if you
+ 
+
+ align:start position:0%
+people try to spend it so maybe if you
+maybe you have to do this quickly but
+
+ align:start position:0%
+maybe you have to do this quickly but
+ 
+
+ align:start position:0%
+maybe you have to do this quickly but
+you can do this real quick so you say
+
+ align:start position:0%
+you can do this real quick so you say
+ 
+
+ align:start position:0%
+you can do this real quick so you say
+okay I'm gonna make you a random you
+
+ align:start position:0%
+okay I'm gonna make you a random you
+ 
+
+ align:start position:0%
+okay I'm gonna make you a random you
+know a random private key compute Q
+
+ align:start position:0%
+know a random private key compute Q
+ 
+
+ align:start position:0%
+know a random private key compute Q
+times G to be big Q and then I'll
+
+ align:start position:0%
+times G to be big Q and then I'll
+ 
+
+ align:start position:0%
+times G to be big Q and then I'll
+compute key B which is Q minus a and
+
+ align:start position:0%
+compute key B which is Q minus a and
+ 
+
+ align:start position:0%
+compute key B which is Q minus a and
+then I will send some coins to be and
+
+ align:start position:0%
+then I will send some coins to be and
+ 
+
+ align:start position:0%
+then I will send some coins to be and
+now note that I don't know the private
+
+ align:start position:0%
+now note that I don't know the private
+ 
+
+ align:start position:0%
+now note that I don't know the private
+key for B write the private key for B is
+
+ align:start position:0%
+key for B write the private key for B is
+ 
+
+ align:start position:0%
+key for B write the private key for B is
+gonna be this little Q minus little a I
+
+ align:start position:0%
+gonna be this little Q minus little a I
+ 
+
+ align:start position:0%
+gonna be this little Q minus little a I
+don't know a little a so I don't know
+
+ align:start position:0%
+don't know a little a so I don't know
+ 
+
+ align:start position:0%
+don't know a little a so I don't know
+what little B is but that's okay so it's
+
+ align:start position:0%
+what little B is but that's okay so it's
+ 
+
+ align:start position:0%
+what little B is but that's okay so it's
+I don't I don't send too many coins to
+
+ align:start position:0%
+I don't I don't send too many coins to
+ 
+
+ align:start position:0%
+I don't I don't send too many coins to
+key B and anyway I'll get him back
+
+ align:start position:0%
+key B and anyway I'll get him back
+ 
+
+ align:start position:0%
+key B and anyway I'll get him back
+I don't know B I can't sign with it
+
+ align:start position:0%
+I don't know B I can't sign with it
+ 
+
+ align:start position:0%
+I don't know B I can't sign with it
+however I want to spend from B and a
+
+ align:start position:0%
+however I want to spend from B and a
+ 
+
+ align:start position:0%
+however I want to spend from B and a
+together I don't know little B I don't
+
+ align:start position:0%
+together I don't know little B I don't
+ 
+
+ align:start position:0%
+together I don't know little B I don't
+little away I don't know the private key
+
+ align:start position:0%
+little away I don't know the private key
+ 
+
+ align:start position:0%
+little away I don't know the private key
+for either but I do know the private key
+
+ align:start position:0%
+for either but I do know the private key
+ 
+
+ align:start position:0%
+for either but I do know the private key
+for both which is sort of confusing but
+
+ align:start position:0%
+for both which is sort of confusing but
+ 
+
+ align:start position:0%
+for both which is sort of confusing but
+the idea is well C is gonna be a plus B
+
+ align:start position:0%
+the idea is well C is gonna be a plus B
+ 
+
+ align:start position:0%
+the idea is well C is gonna be a plus B
+which is a plus Q minus a which is just
+
+ align:start position:0%
+which is a plus Q minus a which is just
+ 
+
+ align:start position:0%
+which is a plus Q minus a which is just
+Q right so in this case I can observe a
+
+ align:start position:0%
+Q right so in this case I can observe a
+ 
+
+ align:start position:0%
+Q right so in this case I can observe a
+key find you know make this rogue key
+
+ align:start position:0%
+key find you know make this rogue key
+ 
+
+ align:start position:0%
+key find you know make this rogue key
+and then spend from both of them without
+
+ align:start position:0%
+and then spend from both of them without
+ 
+
+ align:start position:0%
+and then spend from both of them without
+knowing the actual key that I I wanted
+
+ align:start position:0%
+knowing the actual key that I I wanted
+ 
+
+ align:start position:0%
+knowing the actual key that I I wanted
+to steal from so this is a huge problem
+
+ align:start position:0%
+to steal from so this is a huge problem
+ 
+
+ align:start position:0%
+to steal from so this is a huge problem
+right you can't have this this would
+
+ align:start position:0%
+right you can't have this this would
+ 
+
+ align:start position:0%
+right you can't have this this would
+make signature aggregation completely
+
+ align:start position:0%
+make signature aggregation completely
+ 
+
+ align:start position:0%
+make signature aggregation completely
+insecure what are some ideas of how to
+
+ align:start position:0%
+insecure what are some ideas of how to
+ 
+
+ align:start position:0%
+insecure what are some ideas of how to
+how to fix that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any so the interesting thing is in all
+
+ align:start position:0%
+any so the interesting thing is in all
+ 
+
+ align:start position:0%
+any so the interesting thing is in all
+the literature about multi signature
+
+ align:start position:0%
+the literature about multi signature
+ 
+
+ align:start position:0%
+the literature about multi signature
+this problem sort of still persists and
+
+ align:start position:0%
+this problem sort of still persists and
+ 
+
+ align:start position:0%
+this problem sort of still persists and
+the new reason the new papers about how
+
+ align:start position:0%
+the new reason the new papers about how
+ 
+
+ align:start position:0%
+the new reason the new papers about how
+to use this in Bitcoin are the ones that
+
+ align:start position:0%
+to use this in Bitcoin are the ones that
+ 
+
+ align:start position:0%
+to use this in Bitcoin are the ones that
+are actually addressing it so the
+
+ align:start position:0%
+are actually addressing it so the
+ 
+
+ align:start position:0%
+are actually addressing it so the
+general idea was well make B sign right
+
+ align:start position:0%
+general idea was well make B sign right
+ 
+
+ align:start position:0%
+general idea was well make B sign right
+make B prove that he actually can sign
+
+ align:start position:0%
+make B prove that he actually can sign
+ 
+
+ align:start position:0%
+make B prove that he actually can sign
+with with key B before you start doing
+
+ align:start position:0%
+with with key B before you start doing
+ 
+
+ align:start position:0%
+with with key B before you start doing
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+have Alice and Bob talk to each other
+
+ align:start position:0%
+have Alice and Bob talk to each other
+ 
+
+ align:start position:0%
+have Alice and Bob talk to each other
+and Bob says okay here's a signature
+
+ align:start position:0%
+and Bob says okay here's a signature
+ 
+
+ align:start position:0%
+and Bob says okay here's a signature
+with with key B and al says okay here's
+
+ align:start position:0%
+with with key B and al says okay here's
+ 
+
+ align:start position:0%
+with with key B and al says okay here's
+the signature with key a and now you've
+
+ align:start position:0%
+the signature with key a and now you've
+ 
+
+ align:start position:0%
+the signature with key a and now you've
+proven that that they actually can sign
+
+ align:start position:0%
+proven that that they actually can sign
+ 
+
+ align:start position:0%
+proven that that they actually can sign
+and they're not doing these kinds of
+
+ align:start position:0%
+and they're not doing these kinds of
+ 
+
+ align:start position:0%
+and they're not doing these kinds of
+rogue attacks right so that's the
+
+ align:start position:0%
+rogue attacks right so that's the
+ 
+
+ align:start position:0%
+rogue attacks right so that's the
+straight straightforward way to do it
+
+ align:start position:0%
+straight straightforward way to do it
+ 
+
+ align:start position:0%
+straight straightforward way to do it
+right we're okay
+
+ align:start position:0%
+right we're okay
+ 
+
+ align:start position:0%
+right we're okay
+you know if you don't know B and can't
+
+ align:start position:0%
+you know if you don't know B and can't
+ 
+
+ align:start position:0%
+you know if you don't know B and can't
+sign we're not going to continue with
+
+ align:start position:0%
+sign we're not going to continue with
+ 
+
+ align:start position:0%
+sign we're not going to continue with
+this process that's interactive though
+
+ align:start position:0%
+this process that's interactive though
+ 
+
+ align:start position:0%
+this process that's interactive though
+so yeah make me sign a message before
+
+ align:start position:0%
+so yeah make me sign a message before
+ 
+
+ align:start position:0%
+so yeah make me sign a message before
+combining keys easy that's what people
+
+ align:start position:0%
+combining keys easy that's what people
+ 
+
+ align:start position:0%
+combining keys easy that's what people
+sort of thought about for years but the
+
+ align:start position:0%
+sort of thought about for years but the
+ 
+
+ align:start position:0%
+sort of thought about for years but the
+whole point here is to aggregate
+
+ align:start position:0%
+whole point here is to aggregate
+ 
+
+ align:start position:0%
+whole point here is to aggregate
+signatures and so if you require B to
+
+ align:start position:0%
+signatures and so if you require B to
+ 
+
+ align:start position:0%
+signatures and so if you require B to
+create a signature and post it into the
+
+ align:start position:0%
+create a signature and post it into the
+ 
+
+ align:start position:0%
+create a signature and post it into the
+transaction you've just eliminated all
+
+ align:start position:0%
+transaction you've just eliminated all
+ 
+
+ align:start position:0%
+transaction you've just eliminated all
+the games all the space-saving for this
+
+ align:start position:0%
+the games all the space-saving for this
+ 
+
+ align:start position:0%
+the games all the space-saving for this
+technique so we can't have that we want
+
+ align:start position:0%
+technique so we can't have that we want
+ 
+
+ align:start position:0%
+technique so we can't have that we want
+it to be non interactive we want any
+
+ align:start position:0%
+it to be non interactive we want any
+ 
+
+ align:start position:0%
+it to be non interactive we want any
+existing keys to be usable in this
+
+ align:start position:0%
+existing keys to be usable in this
+ 
+
+ align:start position:0%
+existing keys to be usable in this
+system without free committing to
+
+ align:start position:0%
+system without free committing to
+ 
+
+ align:start position:0%
+system without free committing to
+anything you could also make it
+
+ align:start position:0%
+anything you could also make it
+ 
+
+ align:start position:0%
+anything you could also make it
+interactive where well anyway it's
+
+ align:start position:0%
+interactive where well anyway it's
+ 
+
+ align:start position:0%
+interactive where well anyway it's
+actually the better way to do it
+
+ align:start position:0%
+actually the better way to do it
+ 
+
+ align:start position:0%
+actually the better way to do it
+ud linearize the signatures so you
+
+ align:start position:0%
+ud linearize the signatures so you
+ 
+
+ align:start position:0%
+ud linearize the signatures so you
+redefine the signatures you still send
+
+ align:start position:0%
+redefine the signatures you still send
+ 
+
+ align:start position:0%
+redefine the signatures you still send
+to for example key a or key B you know
+
+ align:start position:0%
+to for example key a or key B you know
+ 
+
+ align:start position:0%
+to for example key a or key B you know
+your outputs are still pump keys but
+
+ align:start position:0%
+your outputs are still pump keys but
+ 
+
+ align:start position:0%
+your outputs are still pump keys but
+when you require a signature you don't
+
+ align:start position:0%
+when you require a signature you don't
+ 
+
+ align:start position:0%
+when you require a signature you don't
+require a signature from that pub key
+
+ align:start position:0%
+require a signature from that pub key
+ 
+
+ align:start position:0%
+require a signature from that pub key
+you you require a signature from that
+
+ align:start position:0%
+you you require a signature from that
+ 
+
+ align:start position:0%
+you you require a signature from that
+pub key times the hash of that pump key
+
+ align:start position:0%
+pub key times the hash of that pump key
+ 
+
+ align:start position:0%
+pub key times the hash of that pump key
+right so you say okay I'm sending to any
+
+ align:start position:0%
+right so you say okay I'm sending to any
+ 
+
+ align:start position:0%
+right so you say okay I'm sending to any
+but when normally I have Sig a saying
+
+ align:start position:0%
+but when normally I have Sig a saying
+ 
+
+ align:start position:0%
+but when normally I have Sig a saying
+you know signature from key a instead I
+
+ align:start position:0%
+you know signature from key a instead I
+ 
+
+ align:start position:0%
+you know signature from key a instead I
+say no I want a signature from a time's
+
+ align:start position:0%
+say no I want a signature from a time's
+ 
+
+ align:start position:0%
+say no I want a signature from a time's
+the hash of a this is so anyone who
+
+ align:start position:0%
+the hash of a this is so anyone who
+ 
+
+ align:start position:0%
+the hash of a this is so anyone who
+knows the private key for a will know
+
+ align:start position:0%
+knows the private key for a will know
+ 
+
+ align:start position:0%
+knows the private key for a will know
+the private key for this because this is
+
+ align:start position:0%
+the private key for this because this is
+ 
+
+ align:start position:0%
+the private key for this because this is
+public right everyone can see what the
+
+ align:start position:0%
+public right everyone can see what the
+ 
+
+ align:start position:0%
+public right everyone can see what the
+hash of a is and then so it's just
+
+ align:start position:0%
+hash of a is and then so it's just
+ 
+
+ align:start position:0%
+hash of a is and then so it's just
+little a times hash of little a right
+
+ align:start position:0%
+little a times hash of little a right
+ 
+
+ align:start position:0%
+little a times hash of little a right
+you just multiple you know this is a
+
+ align:start position:0%
+you just multiple you know this is a
+ 
+
+ align:start position:0%
+you just multiple you know this is a
+scalar multiplication so the scalar
+
+ align:start position:0%
+scalar multiplication so the scalar
+ 
+
+ align:start position:0%
+scalar multiplication so the scalar
+multiplication works the same for the
+
+ align:start position:0%
+multiplication works the same for the
+ 
+
+ align:start position:0%
+multiplication works the same for the
+mean sorry this is the you know the
+
+ align:start position:0%
+mean sorry this is the you know the
+ 
+
+ align:start position:0%
+mean sorry this is the you know the
+point multiplication and it works the
+
+ align:start position:0%
+point multiplication and it works the
+ 
+
+ align:start position:0%
+point multiplication and it works the
+same for the scalar down here so this is
+
+ align:start position:0%
+same for the scalar down here so this is
+ 
+
+ align:start position:0%
+same for the scalar down here so this is
+it doesn't hurt it doesn't make it any
+
+ align:start position:0%
+it doesn't hurt it doesn't make it any
+ 
+
+ align:start position:0%
+it doesn't hurt it doesn't make it any
+harder to sign you just have to perform
+
+ align:start position:0%
+harder to sign you just have to perform
+ 
+
+ align:start position:0%
+harder to sign you just have to perform
+a hash operation and a multiplication
+
+ align:start position:0%
+a hash operation and a multiplication
+ 
+
+ align:start position:0%
+a hash operation and a multiplication
+which is quick but what it does
+
+ align:start position:0%
+which is quick but what it does
+ 
+
+ align:start position:0%
+which is quick but what it does
+is it prevents this kind of attack so
+
+ align:start position:0%
+is it prevents this kind of attack so
+ 
+
+ align:start position:0%
+is it prevents this kind of attack so
+instead of signing with a plus B sign
+
+ align:start position:0%
+instead of signing with a plus B sign
+ 
+
+ align:start position:0%
+instead of signing with a plus B sign
+with a times the hash of a plus B times
+
+ align:start position:0%
+with a times the hash of a plus B times
+ 
+
+ align:start position:0%
+with a times the hash of a plus B times
+the hash of B since in this case in
+
+ align:start position:0%
+the hash of B since in this case in
+ 
+
+ align:start position:0%
+the hash of B since in this case in
+Bitcoin the public key is that you know
+
+ align:start position:0%
+Bitcoin the public key is that you know
+ 
+
+ align:start position:0%
+Bitcoin the public key is that you know
+you know you can see what public keys
+
+ align:start position:0%
+you know you can see what public keys
+ 
+
+ align:start position:0%
+you know you can see what public keys
+are being signed and aggregated so you
+
+ align:start position:0%
+are being signed and aggregated so you
+ 
+
+ align:start position:0%
+are being signed and aggregated so you
+say okay well I'm gonna try to do this
+
+ align:start position:0%
+say okay well I'm gonna try to do this
+ 
+
+ align:start position:0%
+say okay well I'm gonna try to do this
+technique C is a times the hash of a
+
+ align:start position:0%
+technique C is a times the hash of a
+ 
+
+ align:start position:0%
+technique C is a times the hash of a
+plus B times the hash of B the private
+
+ align:start position:0%
+plus B times the hash of B the private
+ 
+
+ align:start position:0%
+plus B times the hash of B the private
+key is gonna be a times the hash of the
+
+ align:start position:0%
+key is gonna be a times the hash of the
+ 
+
+ align:start position:0%
+key is gonna be a times the hash of the
+pump QA plus little B times the hash of
+
+ align:start position:0%
+pump QA plus little B times the hash of
+ 
+
+ align:start position:0%
+pump QA plus little B times the hash of
+punky Big B I know B which is Q minus a
+
+ align:start position:0%
+punky Big B I know B which is Q minus a
+ 
+
+ align:start position:0%
+punky Big B I know B which is Q minus a
+or sorry I don't
+
+ align:start position:0%
+or sorry I don't
+ 
+
+ align:start position:0%
+or sorry I don't
+well I compute it I don't know B this is
+
+ align:start position:0%
+well I compute it I don't know B this is
+ 
+
+ align:start position:0%
+well I compute it I don't know B this is
+I know Q right and I I constructed sort
+
+ align:start position:0%
+I know Q right and I I constructed sort
+ 
+
+ align:start position:0%
+I know Q right and I I constructed sort
+of this B is Q minus a but I don't know
+
+ align:start position:0%
+of this B is Q minus a but I don't know
+ 
+
+ align:start position:0%
+of this B is Q minus a but I don't know
+it so C is now going to be a times the
+
+ align:start position:0%
+it so C is now going to be a times the
+ 
+
+ align:start position:0%
+it so C is now going to be a times the
+hash of a plus Q minus a times the hash
+
+ align:start position:0%
+hash of a plus Q minus a times the hash
+ 
+
+ align:start position:0%
+hash of a plus Q minus a times the hash
+of Q minus a right that's what B is I
+
+ align:start position:0%
+of Q minus a right that's what B is I
+ 
+
+ align:start position:0%
+of Q minus a right that's what B is I
+can't cancel out this little a anymore
+
+ align:start position:0%
+can't cancel out this little a anymore
+ 
+
+ align:start position:0%
+can't cancel out this little a anymore
+right because it's got a different
+
+ align:start position:0%
+right because it's got a different
+ 
+
+ align:start position:0%
+right because it's got a different
+coefficient maybe it's easier if you
+
+ align:start position:0%
+coefficient maybe it's easier if you
+ 
+
+ align:start position:0%
+coefficient maybe it's easier if you
+sort of move them on the other side
+
+ align:start position:0%
+sort of move them on the other side
+ 
+
+ align:start position:0%
+sort of move them on the other side
+right I've now got these coefficients in
+
+ align:start position:0%
+right I've now got these coefficients in
+ 
+
+ align:start position:0%
+right I've now got these coefficients in
+front of my private keys that are not
+
+ align:start position:0%
+front of my private keys that are not
+ 
+
+ align:start position:0%
+front of my private keys that are not
+the same and won't cancel out anymore
+
+ align:start position:0%
+the same and won't cancel out anymore
+ 
+
+ align:start position:0%
+the same and won't cancel out anymore
+before if the code you know I sue before
+
+ align:start position:0%
+before if the code you know I sue before
+ 
+
+ align:start position:0%
+before if the code you know I sue before
+it's the same like before the system is
+
+ align:start position:0%
+it's the same like before the system is
+ 
+
+ align:start position:0%
+it's the same like before the system is
+x one right so the idea was a times 1
+
+ align:start position:0%
+x one right so the idea was a times 1
+ 
+
+ align:start position:0%
+x one right so the idea was a times 1
+plus Q minus a times 1 since the
+
+ align:start position:0%
+plus Q minus a times 1 since the
+ 
+
+ align:start position:0%
+plus Q minus a times 1 since the
+coefficients are the same one I can
+
+ align:start position:0%
+coefficients are the same one I can
+ 
+
+ align:start position:0%
+coefficients are the same one I can
+factor them out and now you know apply
+
+ align:start position:0%
+factor them out and now you know apply
+ 
+
+ align:start position:0%
+factor them out and now you know apply
+these and remove the a so if the
+
+ align:start position:0%
+these and remove the a so if the
+ 
+
+ align:start position:0%
+these and remove the a so if the
+coefficients are the same if it moves it
+
+ align:start position:0%
+coefficients are the same if it moves it
+ 
+
+ align:start position:0%
+coefficients are the same if it moves it
+was a times the hash of a plus Q minus a
+
+ align:start position:0%
+was a times the hash of a plus Q minus a
+ 
+
+ align:start position:0%
+was a times the hash of a plus Q minus a
+times the hash of a I'm good
+
+ align:start position:0%
+times the hash of a I'm good
+ 
+
+ align:start position:0%
+times the hash of a I'm good
+I can still factor out that coefficient
+
+ align:start position:0%
+I can still factor out that coefficient
+ 
+
+ align:start position:0%
+I can still factor out that coefficient
+and cancel out a but now the
+
+ align:start position:0%
+and cancel out a but now the
+ 
+
+ align:start position:0%
+and cancel out a but now the
+coefficients are different and so I
+
+ align:start position:0%
+coefficients are different and so I
+ 
+
+ align:start position:0%
+coefficients are different and so I
+can't do that subtraction right and now
+
+ align:start position:0%
+can't do that subtraction right and now
+ 
+
+ align:start position:0%
+can't do that subtraction right and now
+I'm stuck I cannot sign with this little
+
+ align:start position:0%
+I'm stuck I cannot sign with this little
+ 
+
+ align:start position:0%
+I'm stuck I cannot sign with this little
+C just from knowing Q questions about
+
+ align:start position:0%
+C just from knowing Q questions about
+ 
+
+ align:start position:0%
+C just from knowing Q questions about
+this yeah
+
+ align:start position:0%
+this yeah
+ 
+
+ align:start position:0%
+this yeah
+Oh everything there is in this attack Q
+
+ align:start position:0%
+Oh everything there is in this attack Q
+ 
+
+ align:start position:0%
+Oh everything there is in this attack Q
+is just any random number right but the
+
+ align:start position:0%
+is just any random number right but the
+ 
+
+ align:start position:0%
+is just any random number right but the
+idea is here Q being any random number
+
+ align:start position:0%
+idea is here Q being any random number
+ 
+
+ align:start position:0%
+idea is here Q being any random number
+doesn't help you right because you
+
+ align:start position:0%
+doesn't help you right because you
+ 
+
+ align:start position:0%
+doesn't help you right because you
+you've sent money to be you're trying to
+
+ align:start position:0%
+you've sent money to be you're trying to
+ 
+
+ align:start position:0%
+you've sent money to be you're trying to
+sign from you're trying to sign with Q
+
+ align:start position:0%
+sign from you're trying to sign with Q
+ 
+
+ align:start position:0%
+sign from you're trying to sign with Q
+minus a but you don't actually know the
+
+ align:start position:0%
+minus a but you don't actually know the
+ 
+
+ align:start position:0%
+minus a but you don't actually know the
+private key q minus a so you're stuck I
+
+ align:start position:0%
+private key q minus a so you're stuck I
+ 
+
+ align:start position:0%
+private key q minus a so you're stuck I
+mean even even if you did in this case
+
+ align:start position:0%
+mean even even if you did in this case
+ 
+
+ align:start position:0%
+mean even even if you did in this case
+it wouldn't help right because you still
+
+ align:start position:0%
+it wouldn't help right because you still
+ 
+
+ align:start position:0%
+it wouldn't help right because you still
+have that a there so this prevents that
+
+ align:start position:0%
+have that a there so this prevents that
+ 
+
+ align:start position:0%
+have that a there so this prevents that
+kind of straightforward you know so your
+
+ align:start position:0%
+kind of straightforward you know so your
+ 
+
+ align:start position:0%
+kind of straightforward you know so your
+attack can't get rid of the a times H a
+
+ align:start position:0%
+attack can't get rid of the a times H a
+ 
+
+ align:start position:0%
+attack can't get rid of the a times H a
+term this actually is not enough there's
+
+ align:start position:0%
+term this actually is not enough there's
+ 
+
+ align:start position:0%
+term this actually is not enough there's
+a paper called Wagner Wagner's paper
+
+ align:start position:0%
+a paper called Wagner Wagner's paper
+ 
+
+ align:start position:0%
+a paper called Wagner Wagner's paper
+some guy in California UC Berkeley I
+
+ align:start position:0%
+some guy in California UC Berkeley I
+ 
+
+ align:start position:0%
+some guy in California UC Berkeley I
+think a generalized birthday problem and
+
+ align:start position:0%
+think a generalized birthday problem and
+ 
+
+ align:start position:0%
+think a generalized birthday problem and
+it's a hard paper to read but if you're
+
+ align:start position:0%
+it's a hard paper to read but if you're
+ 
+
+ align:start position:0%
+it's a hard paper to read but if you're
+working on these kinds of things it's a
+
+ align:start position:0%
+working on these kinds of things it's a
+ 
+
+ align:start position:0%
+working on these kinds of things it's a
+good paper to read because it comes up
+
+ align:start position:0%
+good paper to read because it comes up
+ 
+
+ align:start position:0%
+good paper to read because it comes up
+again and again with these kinds of
+
+ align:start position:0%
+again and again with these kinds of
+ 
+
+ align:start position:0%
+again and again with these kinds of
+attacks collisions did we talk about I
+
+ align:start position:0%
+attacks collisions did we talk about I
+ 
+
+ align:start position:0%
+attacks collisions did we talk about I
+don't think we ever talked about okay so
+
+ align:start position:0%
+don't think we ever talked about okay so
+ 
+
+ align:start position:0%
+don't think we ever talked about okay so
+the idea of colliding for example a hash
+
+ align:start position:0%
+the idea of colliding for example a hash
+ 
+
+ align:start position:0%
+the idea of colliding for example a hash
+function or in this case public heat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+usually it takes half this the work that
+
+ align:start position:0%
+usually it takes half this the work that
+ 
+
+ align:start position:0%
+usually it takes half this the work that
+you the reason it's called like a
+
+ align:start position:0%
+you the reason it's called like a
+ 
+
+ align:start position:0%
+you the reason it's called like a
+birthday paradox is because what's do
+
+ align:start position:0%
+birthday paradox is because what's do
+ 
+
+ align:start position:0%
+birthday paradox is because what's do
+people know this birthday thing like how
+
+ align:start position:0%
+people know this birthday thing like how
+ 
+
+ align:start position:0%
+people know this birthday thing like how
+many people need to be in a room before
+
+ align:start position:0%
+many people need to be in a room before
+ 
+
+ align:start position:0%
+many people need to be in a room before
+two people have the same birthday and
+
+ align:start position:0%
+two people have the same birthday and
+ 
+
+ align:start position:0%
+two people have the same birthday and
+it's like 22 or something it's like
+
+ align:start position:0%
+it's like 22 or something it's like
+ 
+
+ align:start position:0%
+it's like 22 or something it's like
+really low and and it's surprising
+
+ align:start position:0%
+really low and and it's surprising
+ 
+
+ align:start position:0%
+really low and and it's surprising
+because you'd think well maybe 365
+
+ align:start position:0%
+because you'd think well maybe 365
+ 
+
+ align:start position:0%
+because you'd think well maybe 365
+divided by 2 so like a hundred something
+
+ align:start position:0%
+divided by 2 so like a hundred something
+ 
+
+ align:start position:0%
+divided by 2 so like a hundred something
+you know 180 or something but it's
+
+ align:start position:0%
+you know 180 or something but it's
+ 
+
+ align:start position:0%
+you know 180 or something but it's
+actually 22 I think because of the way
+
+ align:start position:0%
+actually 22 I think because of the way
+ 
+
+ align:start position:0%
+actually 22 I think because of the way
+like for every new person added there's
+
+ align:start position:0%
+like for every new person added there's
+ 
+
+ align:start position:0%
+like for every new person added there's
+a possibility they collide with every
+
+ align:start position:0%
+a possibility they collide with every
+ 
+
+ align:start position:0%
+a possibility they collide with every
+already existing person's birthday and
+
+ align:start position:0%
+already existing person's birthday and
+ 
+
+ align:start position:0%
+already existing person's birthday and
+so the collisions are like more common
+
+ align:start position:0%
+so the collisions are like more common
+ 
+
+ align:start position:0%
+so the collisions are like more common
+than you think
+
+ align:start position:0%
+than you think
+ 
+
+ align:start position:0%
+than you think
+so in the case of colliding a hash
+
+ align:start position:0%
+so in the case of colliding a hash
+ 
+
+ align:start position:0%
+so in the case of colliding a hash
+function even though if even if the hash
+
+ align:start position:0%
+function even though if even if the hash
+ 
+
+ align:start position:0%
+function even though if even if the hash
+function is 2 to the 256 bits you only
+
+ align:start position:0%
+function is 2 to the 256 bits you only
+ 
+
+ align:start position:0%
+function is 2 to the 256 bits you only
+need two to the 128 attempts to collide
+
+ align:start position:0%
+need two to the 128 attempts to collide
+ 
+
+ align:start position:0%
+need two to the 128 attempts to collide
+and find two that are there that are the
+
+ align:start position:0%
+and find two that are there that are the
+ 
+
+ align:start position:0%
+and find two that are there that are the
+same and that's if you store all the old
+
+ align:start position:0%
+same and that's if you store all the old
+ 
+
+ align:start position:0%
+same and that's if you store all the old
+hashes and so
+
+ align:start position:0%
+hashes and so
+ 
+
+ align:start position:0%
+hashes and so
+I keep coming up with new ones after the
+
+ align:start position:0%
+I keep coming up with new ones after the
+ 
+
+ align:start position:0%
+I keep coming up with new ones after the
+square root of the number of attempts
+
+ align:start position:0%
+square root of the number of attempts
+ 
+
+ align:start position:0%
+square root of the number of attempts
+you'll find it and then there's some
+
+ align:start position:0%
+you'll find it and then there's some
+ 
+
+ align:start position:0%
+you'll find it and then there's some
+techniques with like cycle finding where
+
+ align:start position:0%
+techniques with like cycle finding where
+ 
+
+ align:start position:0%
+techniques with like cycle finding where
+you don't have to store them all things
+
+ align:start position:0%
+you don't have to store them all things
+ 
+
+ align:start position:0%
+you don't have to store them all things
+like that so usually you think ok 2 to
+
+ align:start position:0%
+like that so usually you think ok 2 to
+ 
+
+ align:start position:0%
+like that so usually you think ok 2 to
+the N over 2 time to find a collision
+
+ align:start position:0%
+the N over 2 time to find a collision
+ 
+
+ align:start position:0%
+the N over 2 time to find a collision
+but that's a collision between two
+
+ align:start position:0%
+but that's a collision between two
+ 
+
+ align:start position:0%
+but that's a collision between two
+things and Wagner's attack is sort of
+
+ align:start position:0%
+things and Wagner's attack is sort of
+ 
+
+ align:start position:0%
+things and Wagner's attack is sort of
+yeah find a and B such that a equals B
+
+ align:start position:0%
+yeah find a and B such that a equals B
+ 
+
+ align:start position:0%
+yeah find a and B such that a equals B
+kind of the normal vision now find a0 a1
+
+ align:start position:0%
+kind of the normal vision now find a0 a1
+ 
+
+ align:start position:0%
+kind of the normal vision now find a0 a1
+up to a I so find I things on this side
+
+ align:start position:0%
+up to a I so find I things on this side
+ 
+
+ align:start position:0%
+up to a I so find I things on this side
+and J things on this side such as the
+
+ align:start position:0%
+and J things on this side such as the
+ 
+
+ align:start position:0%
+and J things on this side such as the
+sum of a equals the sum of B and in the
+
+ align:start position:0%
+sum of a equals the sum of B and in the
+ 
+
+ align:start position:0%
+sum of a equals the sum of B and in the
+case of elliptic curve points it would
+
+ align:start position:0%
+case of elliptic curve points it would
+ 
+
+ align:start position:0%
+case of elliptic curve points it would
+actually be the sum you do addition in
+
+ align:start position:0%
+actually be the sum you do addition in
+ 
+
+ align:start position:0%
+actually be the sum you do addition in
+the case of hashes it might be X or or
+
+ align:start position:0%
+the case of hashes it might be X or or
+ 
+
+ align:start position:0%
+the case of hashes it might be X or or
+some other operation but the idea is if
+
+ align:start position:0%
+some other operation but the idea is if
+ 
+
+ align:start position:0%
+some other operation but the idea is if
+you have a lot of different things and
+
+ align:start position:0%
+you have a lot of different things and
+ 
+
+ align:start position:0%
+you have a lot of different things and
+you can pick and choose on both sides
+
+ align:start position:0%
+you can pick and choose on both sides
+ 
+
+ align:start position:0%
+you can pick and choose on both sides
+you can potentially find collisions when
+
+ align:start position:0%
+you can potentially find collisions when
+ 
+
+ align:start position:0%
+you can potentially find collisions when
+what much less time and in the case of
+
+ align:start position:0%
+what much less time and in the case of
+ 
+
+ align:start position:0%
+what much less time and in the case of
+these elliptic curve points it probably
+
+ align:start position:0%
+these elliptic curve points it probably
+ 
+
+ align:start position:0%
+these elliptic curve points it probably
+would be practical you'd need I don't
+
+ align:start position:0%
+would be practical you'd need I don't
+ 
+
+ align:start position:0%
+would be practical you'd need I don't
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+dozens 20 30 40 different keys but you
+
+ align:start position:0%
+dozens 20 30 40 different keys but you
+ 
+
+ align:start position:0%
+dozens 20 30 40 different keys but you
+could potentially say ok there's a key
+
+ align:start position:0%
+could potentially say ok there's a key
+ 
+
+ align:start position:0%
+could potentially say ok there's a key
+with a lot of coins I'm going to find a
+
+ align:start position:0%
+with a lot of coins I'm going to find a
+ 
+
+ align:start position:0%
+with a lot of coins I'm going to find a
+whole bunch a set of a whole bunch of
+
+ align:start position:0%
+whole bunch a set of a whole bunch of
+ 
+
+ align:start position:0%
+whole bunch a set of a whole bunch of
+keys such that that I can cancel that
+
+ align:start position:0%
+keys such that that I can cancel that
+ 
+
+ align:start position:0%
+keys such that that I can cancel that
+key out even with this multiplying by a
+
+ align:start position:0%
+key out even with this multiplying by a
+ 
+
+ align:start position:0%
+key out even with this multiplying by a
+different coefficient because I've got
+
+ align:start position:0%
+different coefficient because I've got
+ 
+
+ align:start position:0%
+different coefficient because I've got
+like so many you know so much search
+
+ align:start position:0%
+like so many you know so much search
+ 
+
+ align:start position:0%
+like so many you know so much search
+space III can't like it's a kind of kind
+
+ align:start position:0%
+space III can't like it's a kind of kind
+ 
+
+ align:start position:0%
+space III can't like it's a kind of kind
+of it's a cool paper you should look
+
+ align:start position:0%
+of it's a cool paper you should look
+ 
+
+ align:start position:0%
+of it's a cool paper you should look
+through it if you're interested but
+
+ align:start position:0%
+through it if you're interested but
+ 
+
+ align:start position:0%
+through it if you're interested but
+that's a problem you can you can sort of
+
+ align:start position:0%
+that's a problem you can you can sort of
+ 
+
+ align:start position:0%
+that's a problem you can you can sort of
+make progress is the basic idea is that
+
+ align:start position:0%
+make progress is the basic idea is that
+ 
+
+ align:start position:0%
+make progress is the basic idea is that
+I can keep getting closer and closer to
+
+ align:start position:0%
+I can keep getting closer and closer to
+ 
+
+ align:start position:0%
+I can keep getting closer and closer to
+canceling this thing out so instead we
+
+ align:start position:0%
+canceling this thing out so instead we
+ 
+
+ align:start position:0%
+canceling this thing out so instead we
+have these improved D linearization and
+
+ align:start position:0%
+have these improved D linearization and
+ 
+
+ align:start position:0%
+have these improved D linearization and
+this is talked about in the music paper
+
+ align:start position:0%
+this is talked about in the music paper
+ 
+
+ align:start position:0%
+this is talked about in the music paper
+or from like January you take the hash
+
+ align:start position:0%
+or from like January you take the hash
+ 
+
+ align:start position:0%
+or from like January you take the hash
+of all the keys concatenated together in
+
+ align:start position:0%
+of all the keys concatenated together in
+ 
+
+ align:start position:0%
+of all the keys concatenated together in
+some specified order all right so you
+
+ align:start position:0%
+some specified order all right so you
+ 
+
+ align:start position:0%
+some specified order all right so you
+sort the keys some way and you say ok Z
+
+ align:start position:0%
+sort the keys some way and you say ok Z
+ 
+
+ align:start position:0%
+sort the keys some way and you say ok Z
+is the hash of a and B or if there's
+
+ align:start position:0%
+is the hash of a and B or if there's
+ 
+
+ align:start position:0%
+is the hash of a and B or if there's
+more keys a and B and C you know just
+
+ align:start position:0%
+more keys a and B and C you know just
+ 
+
+ align:start position:0%
+more keys a and B and C you know just
+all concatenated and then you sign with
+
+ align:start position:0%
+all concatenated and then you sign with
+ 
+
+ align:start position:0%
+all concatenated and then you sign with
+a time's the hash of Z and a 0 plus B
+
+ align:start position:0%
+a time's the hash of Z and a 0 plus B
+ 
+
+ align:start position:0%
+a time's the hash of Z and a 0 plus B
+times the hash of Z and a 1 so you make
+
+ align:start position:0%
+times the hash of Z and a 1 so you make
+ 
+
+ align:start position:0%
+times the hash of Z and a 1 so you make
+the coefficients distinct but you also
+
+ align:start position:0%
+the coefficients distinct but you also
+ 
+
+ align:start position:0%
+the coefficients distinct but you also
+make the coefficients
+
+ align:start position:0%
+make the coefficients
+ 
+
+ align:start position:0%
+make the coefficients
+MIT to every single part of the set
+
+ align:start position:0%
+MIT to every single part of the set
+ 
+
+ align:start position:0%
+MIT to every single part of the set
+right every key in the set needs to be
+
+ align:start position:0%
+right every key in the set needs to be
+ 
+
+ align:start position:0%
+right every key in the set needs to be
+in this coefficient and the music sort
+
+ align:start position:0%
+in this coefficient and the music sort
+ 
+
+ align:start position:0%
+in this coefficient and the music sort
+of explains why that works so the the
+
+ align:start position:0%
+of explains why that works so the the
+ 
+
+ align:start position:0%
+of explains why that works so the the
+attack right in in this case is well
+
+ align:start position:0%
+attack right in in this case is well
+ 
+
+ align:start position:0%
+attack right in in this case is well
+I've got these different coefficients
+
+ align:start position:0%
+I've got these different coefficients
+ 
+
+ align:start position:0%
+I've got these different coefficients
+right but the coefficient here only
+
+ align:start position:0%
+right but the coefficient here only
+ 
+
+ align:start position:0%
+right but the coefficient here only
+depends on this key here so maybe I can
+
+ align:start position:0%
+depends on this key here so maybe I can
+ 
+
+ align:start position:0%
+depends on this key here so maybe I can
+find a bunch of different keys with
+
+ align:start position:0%
+find a bunch of different keys with
+ 
+
+ align:start position:0%
+find a bunch of different keys with
+different coefficients such that these
+
+ align:start position:0%
+different coefficients such that these
+ 
+
+ align:start position:0%
+different coefficients such that these
+coefficients will cancel out or you know
+
+ align:start position:0%
+coefficients will cancel out or you know
+ 
+
+ align:start position:0%
+coefficients will cancel out or you know
+these coefficients will sum or multiply
+
+ align:start position:0%
+these coefficients will sum or multiply
+ 
+
+ align:start position:0%
+these coefficients will sum or multiply
+you know sum up to hash of a so it seems
+
+ align:start position:0%
+you know sum up to hash of a so it seems
+ 
+
+ align:start position:0%
+you know sum up to hash of a so it seems
+like hard right I can't find something I
+
+ align:start position:0%
+like hard right I can't find something I
+ 
+
+ align:start position:0%
+like hard right I can't find something I
+can't find different hashes that will
+
+ align:start position:0%
+can't find different hashes that will
+ 
+
+ align:start position:0%
+can't find different hashes that will
+equal the hash of a right that's a hash
+
+ align:start position:0%
+equal the hash of a right that's a hash
+ 
+
+ align:start position:0%
+equal the hash of a right that's a hash
+collision but if I have any number of
+
+ align:start position:0%
+collision but if I have any number of
+ 
+
+ align:start position:0%
+collision but if I have any number of
+different things I may be able to and so
+
+ align:start position:0%
+different things I may be able to and so
+ 
+
+ align:start position:0%
+different things I may be able to and so
+the idea is if you do this well now
+
+ align:start position:0%
+the idea is if you do this well now
+ 
+
+ align:start position:0%
+the idea is if you do this well now
+every time I'm adding or removing a key
+
+ align:start position:0%
+every time I'm adding or removing a key
+ 
+
+ align:start position:0%
+every time I'm adding or removing a key
+from my attempt I still I have to change
+
+ align:start position:0%
+from my attempt I still I have to change
+ 
+
+ align:start position:0%
+from my attempt I still I have to change
+Z so I can't leave this here and start
+
+ align:start position:0%
+Z so I can't leave this here and start
+ 
+
+ align:start position:0%
+Z so I can't leave this here and start
+adding things and try to try to work on
+
+ align:start position:0%
+adding things and try to try to work on
+ 
+
+ align:start position:0%
+adding things and try to try to work on
+it that way because every time I add of
+
+ align:start position:0%
+it that way because every time I add of
+ 
+
+ align:start position:0%
+it that way because every time I add of
+C or D Z changes and so I have to start
+
+ align:start position:0%
+C or D Z changes and so I have to start
+ 
+
+ align:start position:0%
+C or D Z changes and so I have to start
+over from scratch
+
+ align:start position:0%
+over from scratch
+ 
+
+ align:start position:0%
+over from scratch
+so that's the anyway that's my general
+
+ align:start position:0%
+so that's the anyway that's my general
+ 
+
+ align:start position:0%
+so that's the anyway that's my general
+intuition of how the de linearization
+
+ align:start position:0%
+intuition of how the de linearization
+ 
+
+ align:start position:0%
+intuition of how the de linearization
+works for music and then yeah it used to
+
+ align:start position:0%
+works for music and then yeah it used to
+ 
+
+ align:start position:0%
+works for music and then yeah it used to
+be like Z and then put a in here because
+
+ align:start position:0%
+be like Z and then put a in here because
+ 
+
+ align:start position:0%
+be like Z and then put a in here because
+now that makes it unique but you can
+
+ align:start position:0%
+now that makes it unique but you can
+ 
+
+ align:start position:0%
+now that makes it unique but you can
+actually just number them you just need
+
+ align:start position:0%
+actually just number them you just need
+ 
+
+ align:start position:0%
+actually just number them you just need
+them to be distinct and since this hash
+
+ align:start position:0%
+them to be distinct and since this hash
+ 
+
+ align:start position:0%
+them to be distinct and since this hash
+function just say like 0 1 2 3 4 it's
+
+ align:start position:0%
+function just say like 0 1 2 3 4 it's
+ 
+
+ align:start position:0%
+function just say like 0 1 2 3 4 it's
+good enough ok any questions about this
+
+ align:start position:0%
+good enough ok any questions about this
+ 
+
+ align:start position:0%
+good enough ok any questions about this
+I realize it's kind of complicated and
+
+ align:start position:0%
+I realize it's kind of complicated and
+ 
+
+ align:start position:0%
+I realize it's kind of complicated and
+the software's kind of crazy but but the
+
+ align:start position:0%
+the software's kind of crazy but but the
+ 
+
+ align:start position:0%
+the software's kind of crazy but but the
+idea is that it prevents a bunch of
+
+ align:start position:0%
+idea is that it prevents a bunch of
+ 
+
+ align:start position:0%
+idea is that it prevents a bunch of
+these attacks so that you can securely
+
+ align:start position:0%
+these attacks so that you can securely
+ 
+
+ align:start position:0%
+these attacks so that you can securely
+use aggregate signatures questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hopefully yeah and you wouldn't have to
+
+ align:start position:0%
+hopefully yeah and you wouldn't have to
+ 
+
+ align:start position:0%
+hopefully yeah and you wouldn't have to
+program it but yeah so what you can do
+
+ align:start position:0%
+program it but yeah so what you can do
+ 
+
+ align:start position:0%
+program it but yeah so what you can do
+is you say okay
+
+ align:start position:0%
+is you say okay
+ 
+
+ align:start position:0%
+is you say okay
+it saves space right I've got my the the
+
+ align:start position:0%
+it saves space right I've got my the the
+ 
+
+ align:start position:0%
+it saves space right I've got my the the
+first use case will be in single wallets
+
+ align:start position:0%
+first use case will be in single wallets
+ 
+
+ align:start position:0%
+first use case will be in single wallets
+right non-internet it's it's interactive
+
+ align:start position:0%
+right non-internet it's it's interactive
+ 
+
+ align:start position:0%
+right non-internet it's it's interactive
+right so you have to do that thing where
+
+ align:start position:0%
+right so you have to do that thing where
+ 
+
+ align:start position:0%
+right so you have to do that thing where
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+up with different K values I share the
+
+ align:start position:0%
+up with different K values I share the
+ 
+
+ align:start position:0%
+up with different K values I share the
+different R values I come up with the s
+
+ align:start position:0%
+different R values I come up with the s
+ 
+
+ align:start position:0%
+different R values I come up with the s
+values I add those up sure if it's all
+
+ align:start position:0%
+values I add those up sure if it's all
+ 
+
+ align:start position:0%
+values I add those up sure if it's all
+doing it yourself where it's just there
+
+ align:start position:0%
+doing it yourself where it's just there
+ 
+
+ align:start position:0%
+doing it yourself where it's just there
+happened to be two different pub keys
+
+ align:start position:0%
+happened to be two different pub keys
+ 
+
+ align:start position:0%
+happened to be two different pub keys
+that you control both of you can
+
+ align:start position:0%
+that you control both of you can
+ 
+
+ align:start position:0%
+that you control both of you can
+basically skip all of that and you can
+
+ align:start position:0%
+basically skip all of that and you can
+ 
+
+ align:start position:0%
+basically skip all of that and you can
+just say no I'm just gonna you know I'm
+
+ align:start position:0%
+just say no I'm just gonna you know I'm
+ 
+
+ align:start position:0%
+just say no I'm just gonna you know I'm
+just gonna add the two points here and
+
+ align:start position:0%
+just gonna add the two points here and
+ 
+
+ align:start position:0%
+just gonna add the two points here and
+I'll use the same K value you know it's
+
+ align:start position:0%
+I'll use the same K value you know it's
+ 
+
+ align:start position:0%
+I'll use the same K value you know it's
+just me so this happens a lot in Bitcoin
+
+ align:start position:0%
+just me so this happens a lot in Bitcoin
+ 
+
+ align:start position:0%
+just me so this happens a lot in Bitcoin
+wallets where you're making a
+
+ align:start position:0%
+wallets where you're making a
+ 
+
+ align:start position:0%
+wallets where you're making a
+transaction with multiple inputs they're
+
+ align:start position:0%
+transaction with multiple inputs they're
+ 
+
+ align:start position:0%
+transaction with multiple inputs they're
+all controlled by you but you might have
+
+ align:start position:0%
+all controlled by you but you might have
+ 
+
+ align:start position:0%
+all controlled by you but you might have
+you know two coins here and three coins
+
+ align:start position:0%
+you know two coins here and three coins
+ 
+
+ align:start position:0%
+you know two coins here and three coins
+there and you want to send someone for
+
+ align:start position:0%
+there and you want to send someone for
+ 
+
+ align:start position:0%
+there and you want to send someone for
+coins so you got to use both of these
+
+ align:start position:0%
+coins so you got to use both of these
+ 
+
+ align:start position:0%
+coins so you got to use both of these
+inputs currently in Bitcoin you're gonna
+
+ align:start position:0%
+inputs currently in Bitcoin you're gonna
+ 
+
+ align:start position:0%
+inputs currently in Bitcoin you're gonna
+have multiple signatures with with this
+
+ align:start position:0%
+have multiple signatures with with this
+ 
+
+ align:start position:0%
+have multiple signatures with with this
+new signature aggregation you can say
+
+ align:start position:0%
+new signature aggregation you can say
+ 
+
+ align:start position:0%
+new signature aggregation you can say
+okay I'm picking these two inputs I'm
+
+ align:start position:0%
+okay I'm picking these two inputs I'm
+ 
+
+ align:start position:0%
+okay I'm picking these two inputs I'm
+signing for all of them with a single
+
+ align:start position:0%
+signing for all of them with a single
+ 
+
+ align:start position:0%
+signing for all of them with a single
+signature and in the case of it all
+
+ align:start position:0%
+signature and in the case of it all
+ 
+
+ align:start position:0%
+signature and in the case of it all
+being yours you don't even have to do
+
+ align:start position:0%
+being yours you don't even have to do
+ 
+
+ align:start position:0%
+being yours you don't even have to do
+you don't even have to do the two
+
+ align:start position:0%
+you don't even have to do the two
+ 
+
+ align:start position:0%
+you don't even have to do the two
+operations and add them right because
+
+ align:start position:0%
+operations and add them right because
+ 
+
+ align:start position:0%
+operations and add them right because
+you know the whole all the keys so
+
+ align:start position:0%
+you know the whole all the keys so
+ 
+
+ align:start position:0%
+you know the whole all the keys so
+that's gonna be the first use case and
+
+ align:start position:0%
+that's gonna be the first use case and
+ 
+
+ align:start position:0%
+that's gonna be the first use case and
+that's that's much easier to program
+
+ align:start position:0%
+that's that's much easier to program
+ 
+
+ align:start position:0%
+that's that's much easier to program
+because it's all just within the same
+
+ align:start position:0%
+because it's all just within the same
+ 
+
+ align:start position:0%
+because it's all just within the same
+computer and this is easy so that's cool
+
+ align:start position:0%
+computer and this is easy so that's cool
+ 
+
+ align:start position:0%
+computer and this is easy so that's cool
+and then a cool use is okay use it with
+
+ align:start position:0%
+and then a cool use is okay use it with
+ 
+
+ align:start position:0%
+and then a cool use is okay use it with
+coin joint where users a B C and D all
+
+ align:start position:0%
+coin joint where users a B C and D all
+ 
+
+ align:start position:0%
+coin joint where users a B C and D all
+contribute you know they all have an
+
+ align:start position:0%
+contribute you know they all have an
+ 
+
+ align:start position:0%
+contribute you know they all have an
+input with hey the same amount of coins
+
+ align:start position:0%
+input with hey the same amount of coins
+ 
+
+ align:start position:0%
+input with hey the same amount of coins
+great and they're doing coin shuffle to
+
+ align:start position:0%
+great and they're doing coin shuffle to
+ 
+
+ align:start position:0%
+great and they're doing coin shuffle to
+shuffle the order of these outputs so
+
+ align:start position:0%
+shuffle the order of these outputs so
+ 
+
+ align:start position:0%
+shuffle the order of these outputs so
+they're they know so a knows Oh mine is
+
+ align:start position:0%
+they're they know so a knows Oh mine is
+ 
+
+ align:start position:0%
+they're they know so a knows Oh mine is
+G but I have no idea about EF and H I
+
+ align:start position:0%
+G but I have no idea about EF and H I
+ 
+
+ align:start position:0%
+G but I have no idea about EF and H I
+don't know I don't know the mapping
+
+ align:start position:0%
+don't know I don't know the mapping
+ 
+
+ align:start position:0%
+don't know I don't know the mapping
+other than my own but hey my my output
+
+ align:start position:0%
+other than my own but hey my my output
+ 
+
+ align:start position:0%
+other than my own but hey my my output
+is in there
+
+ align:start position:0%
+is in there
+ 
+
+ align:start position:0%
+is in there
+cool so whatever everyone else is doing
+
+ align:start position:0%
+cool so whatever everyone else is doing
+ 
+
+ align:start position:0%
+cool so whatever everyone else is doing
+I don't care but I'm good with this
+
+ align:start position:0%
+I don't care but I'm good with this
+ 
+
+ align:start position:0%
+I don't care but I'm good with this
+transaction and they can contribute
+
+ align:start position:0%
+transaction and they can contribute
+ 
+
+ align:start position:0%
+transaction and they can contribute
+their own K value and their own s value
+
+ align:start position:0%
+their own K value and their own s value
+ 
+
+ align:start position:0%
+their own K value and their own s value
+and then finally then you put the
+
+ align:start position:0%
+and then finally then you put the
+ 
+
+ align:start position:0%
+and then finally then you put the
+signature at the bottom and it verifies
+
+ align:start position:0%
+signature at the bottom and it verifies
+ 
+
+ align:start position:0%
+signature at the bottom and it verifies
+that all these participants have signed
+
+ align:start position:0%
+that all these participants have signed
+ 
+
+ align:start position:0%
+that all these participants have signed
+and this is really nice because it's
+
+ align:start position:0%
+and this is really nice because it's
+ 
+
+ align:start position:0%
+and this is really nice because it's
+smaller right it used to be this would
+
+ align:start position:0%
+smaller right it used to be this would
+ 
+
+ align:start position:0%
+smaller right it used to be this would
+be what 200 something 250 bytes worth of
+
+ align:start position:0%
+be what 200 something 250 bytes worth of
+ 
+
+ align:start position:0%
+be what 200 something 250 bytes worth of
+signature data and now it's just 65
+
+ align:start position:0%
+signature data and now it's just 65
+ 
+
+ align:start position:0%
+signature data and now it's just 65
+bytes worth of signature data at the
+
+ align:start position:0%
+bytes worth of signature data at the
+ 
+
+ align:start position:0%
+bytes worth of signature data at the
+bottom so you save on fees you save on
+
+ align:start position:0%
+bottom so you save on fees you save on
+ 
+
+ align:start position:0%
+bottom so you save on fees you save on
+space every
+
+ align:start position:0%
+space every
+ 
+
+ align:start position:0%
+space every
+like this yeah it's cheaper than a solo
+
+ align:start position:0%
+like this yeah it's cheaper than a solo
+ 
+
+ align:start position:0%
+like this yeah it's cheaper than a solo
+transaction and so that potentially
+
+ align:start position:0%
+transaction and so that potentially
+ 
+
+ align:start position:0%
+transaction and so that potentially
+helps scalability and privacy and that
+
+ align:start position:0%
+helps scalability and privacy and that
+ 
+
+ align:start position:0%
+helps scalability and privacy and that
+if people say I want to do something
+
+ align:start position:0%
+if people say I want to do something
+ 
+
+ align:start position:0%
+if people say I want to do something
+cheaply I will connect to other people
+
+ align:start position:0%
+cheaply I will connect to other people
+ 
+
+ align:start position:0%
+cheaply I will connect to other people
+and aggregate my signature with theirs
+
+ align:start position:0%
+and aggregate my signature with theirs
+ 
+
+ align:start position:0%
+and aggregate my signature with theirs
+and so we save some space and save some
+
+ align:start position:0%
+and so we save some space and save some
+ 
+
+ align:start position:0%
+and so we save some space and save some
+money and maybe I don't really care
+
+ align:start position:0%
+money and maybe I don't really care
+ 
+
+ align:start position:0%
+money and maybe I don't really care
+about the anonymity thing maybe I'm you
+
+ align:start position:0%
+about the anonymity thing maybe I'm you
+ 
+
+ align:start position:0%
+about the anonymity thing maybe I'm you
+know entering into a transaction and
+
+ align:start position:0%
+know entering into a transaction and
+ 
+
+ align:start position:0%
+know entering into a transaction and
+there's some people doing shady deals in
+
+ align:start position:0%
+there's some people doing shady deals in
+ 
+
+ align:start position:0%
+there's some people doing shady deals in
+this transaction but I don't care right
+
+ align:start position:0%
+this transaction but I don't care right
+ 
+
+ align:start position:0%
+this transaction but I don't care right
+my thing gets in and out and I saved
+
+ align:start position:0%
+my thing gets in and out and I saved
+ 
+
+ align:start position:0%
+my thing gets in and out and I saved
+money so the extension of this would be
+
+ align:start position:0%
+money so the extension of this would be
+ 
+
+ align:start position:0%
+money so the extension of this would be
+what if you had just one giant
+
+ align:start position:0%
+what if you had just one giant
+ 
+
+ align:start position:0%
+what if you had just one giant
+transaction in every block which is all
+
+ align:start position:0%
+transaction in every block which is all
+ 
+
+ align:start position:0%
+transaction in every block which is all
+the inputs and all the outputs and
+
+ align:start position:0%
+the inputs and all the outputs and
+ 
+
+ align:start position:0%
+the inputs and all the outputs and
+there's a single signature that would be
+
+ align:start position:0%
+there's a single signature that would be
+ 
+
+ align:start position:0%
+there's a single signature that would be
+really cool
+
+ align:start position:0%
+really cool
+ 
+
+ align:start position:0%
+really cool
+we're not work there are techniques to
+
+ align:start position:0%
+we're not work there are techniques to
+ 
+
+ align:start position:0%
+we're not work there are techniques to
+do that there's so the issue is its
+
+ align:start position:0%
+do that there's so the issue is its
+ 
+
+ align:start position:0%
+do that there's so the issue is its
+interactive right in that you have to
+
+ align:start position:0%
+interactive right in that you have to
+ 
+
+ align:start position:0%
+interactive right in that you have to
+know about all the other inputs and all
+
+ align:start position:0%
+know about all the other inputs and all
+ 
+
+ align:start position:0%
+know about all the other inputs and all
+the other outputs so I can't if it were
+
+ align:start position:0%
+the other outputs so I can't if it were
+ 
+
+ align:start position:0%
+the other outputs so I can't if it were
+non interactive then I could say oh well
+
+ align:start position:0%
+non interactive then I could say oh well
+ 
+
+ align:start position:0%
+non interactive then I could say oh well
+there's this transaction where D is
+
+ align:start position:0%
+there's this transaction where D is
+ 
+
+ align:start position:0%
+there's this transaction where D is
+sending coins to H and there's also this
+
+ align:start position:0%
+sending coins to H and there's also this
+ 
+
+ align:start position:0%
+sending coins to H and there's also this
+other transaction where C sends coins to
+
+ align:start position:0%
+other transaction where C sends coins to
+ 
+
+ align:start position:0%
+other transaction where C sends coins to
+G and they've got their own signatures
+
+ align:start position:0%
+G and they've got their own signatures
+ 
+
+ align:start position:0%
+G and they've got their own signatures
+if I can take those two and you know I'm
+
+ align:start position:0%
+if I can take those two and you know I'm
+ 
+
+ align:start position:0%
+if I can take those two and you know I'm
+not either of these people I didn't do
+
+ align:start position:0%
+not either of these people I didn't do
+ 
+
+ align:start position:0%
+not either of these people I didn't do
+anything with these signatures but if I
+
+ align:start position:0%
+anything with these signatures but if I
+ 
+
+ align:start position:0%
+anything with these signatures but if I
+could take those two things and combine
+
+ align:start position:0%
+could take those two things and combine
+ 
+
+ align:start position:0%
+could take those two things and combine
+the signature not interactively then I
+
+ align:start position:0%
+the signature not interactively then I
+ 
+
+ align:start position:0%
+the signature not interactively then I
+could just basically take all the
+
+ align:start position:0%
+could just basically take all the
+ 
+
+ align:start position:0%
+could just basically take all the
+transactions in my men pool squish them
+
+ align:start position:0%
+transactions in my men pool squish them
+ 
+
+ align:start position:0%
+transactions in my men pool squish them
+into one transaction with one signature
+
+ align:start position:0%
+into one transaction with one signature
+ 
+
+ align:start position:0%
+into one transaction with one signature
+and put that in my block that would be
+
+ align:start position:0%
+and put that in my block that would be
+ 
+
+ align:start position:0%
+and put that in my block that would be
+really cool but the issue there is one
+
+ align:start position:0%
+really cool but the issue there is one
+ 
+
+ align:start position:0%
+really cool but the issue there is one
+the signatures have to be interactive
+
+ align:start position:0%
+the signatures have to be interactive
+ 
+
+ align:start position:0%
+the signatures have to be interactive
+and two they're on different messages
+
+ align:start position:0%
+and two they're on different messages
+ 
+
+ align:start position:0%
+and two they're on different messages
+right so in the case of cease sending to
+
+ align:start position:0%
+right so in the case of cease sending to
+ 
+
+ align:start position:0%
+right so in the case of cease sending to
+G it's a message of C to G and in D
+
+ align:start position:0%
+G it's a message of C to G and in D
+ 
+
+ align:start position:0%
+G it's a message of C to G and in D
+sending to H it's on that message there
+
+ align:start position:0%
+sending to H it's on that message there
+ 
+
+ align:start position:0%
+sending to H it's on that message there
+are techniques though so BLS signatures
+
+ align:start position:0%
+are techniques though so BLS signatures
+ 
+
+ align:start position:0%
+are techniques though so BLS signatures
+Bonet Lin Shaham signatures do allow you
+
+ align:start position:0%
+Bonet Lin Shaham signatures do allow you
+ 
+
+ align:start position:0%
+Bonet Lin Shaham signatures do allow you
+to do this
+
+ align:start position:0%
+to do this
+ 
+
+ align:start position:0%
+to do this
+so non-interactive aggregation of the
+
+ align:start position:0%
+so non-interactive aggregation of the
+ 
+
+ align:start position:0%
+so non-interactive aggregation of the
+signatures which would be really cool
+
+ align:start position:0%
+signatures which would be really cool
+ 
+
+ align:start position:0%
+signatures which would be really cool
+because then a block would only need one
+
+ align:start position:0%
+because then a block would only need one
+ 
+
+ align:start position:0%
+because then a block would only need one
+signature and in VLS signatures
+
+ align:start position:0%
+signature and in VLS signatures
+ 
+
+ align:start position:0%
+signature and in VLS signatures
+signatures themselves are a single point
+
+ align:start position:0%
+signatures themselves are a single point
+ 
+
+ align:start position:0%
+signatures themselves are a single point
+not a point and a scalar so it would
+
+ align:start position:0%
+not a point and a scalar so it would
+ 
+
+ align:start position:0%
+not a point and a scalar so it would
+just be 32 bytes well you'd probably use
+
+ align:start position:0%
+just be 32 bytes well you'd probably use
+ 
+
+ align:start position:0%
+just be 32 bytes well you'd probably use
+a different curve
+
+ align:start position:0%
+a different curve
+ 
+
+ align:start position:0%
+a different curve
+but um you have to but but yeah the idea
+
+ align:start position:0%
+but um you have to but but yeah the idea
+ 
+
+ align:start position:0%
+but um you have to but but yeah the idea
+of having these tiny signatures that
+
+ align:start position:0%
+of having these tiny signatures that
+ 
+
+ align:start position:0%
+of having these tiny signatures that
+satisfy proof for the entire set is
+
+ align:start position:0%
+satisfy proof for the entire set is
+ 
+
+ align:start position:0%
+satisfy proof for the entire set is
+really cool so this is yeah this is a
+
+ align:start position:0%
+really cool so this is yeah this is a
+ 
+
+ align:start position:0%
+really cool so this is yeah this is a
+cool idea there's so you're saying there
+
+ align:start position:0%
+cool idea there's so you're saying there
+ 
+
+ align:start position:0%
+cool idea there's so you're saying there
+isn't software you said like or that
+
+ align:start position:0%
+isn't software you said like or that
+ 
+
+ align:start position:0%
+isn't software you said like or that
+it's not on github okay yeah so the idea
+
+ align:start position:0%
+it's not on github okay yeah so the idea
+ 
+
+ align:start position:0%
+it's not on github okay yeah so the idea
+is there was a bunch of software for
+
+ align:start position:0%
+is there was a bunch of software for
+ 
+
+ align:start position:0%
+is there was a bunch of software for
+this that mostly sip so simply or Peter
+
+ align:start position:0%
+this that mostly sip so simply or Peter
+ 
+
+ align:start position:0%
+this that mostly sip so simply or Peter
+wool is his name on the Internet is CIPA
+
+ align:start position:0%
+wool is his name on the Internet is CIPA
+ 
+
+ align:start position:0%
+wool is his name on the Internet is CIPA
+and he told me what that stood for and
+
+ align:start position:0%
+and he told me what that stood for and
+ 
+
+ align:start position:0%
+and he told me what that stood for and
+it was some like super cheesy thing he
+
+ align:start position:0%
+it was some like super cheesy thing he
+ 
+
+ align:start position:0%
+it was some like super cheesy thing he
+made when he was in like middle school
+
+ align:start position:0%
+made when he was in like middle school
+ 
+
+ align:start position:0%
+made when he was in like middle school
+but anyway um he has been working on
+
+ align:start position:0%
+but anyway um he has been working on
+ 
+
+ align:start position:0%
+but anyway um he has been working on
+this kind of software so has so has
+
+ align:start position:0%
+this kind of software so has so has
+ 
+
+ align:start position:0%
+this kind of software so has so has
+Gregg that guy who you know five years
+
+ align:start position:0%
+Gregg that guy who you know five years
+ 
+
+ align:start position:0%
+Gregg that guy who you know five years
+ago wrote about this stuff and some
+
+ align:start position:0%
+ago wrote about this stuff and some
+ 
+
+ align:start position:0%
+ago wrote about this stuff and some
+other poster a couple of couple people
+
+ align:start position:0%
+other poster a couple of couple people
+ 
+
+ align:start position:0%
+other poster a couple of couple people
+have been working on this it's not
+
+ align:start position:0%
+have been working on this it's not
+ 
+
+ align:start position:0%
+have been working on this it's not
+publicly available code which is kind of
+
+ align:start position:0%
+publicly available code which is kind of
+ 
+
+ align:start position:0%
+publicly available code which is kind of
+weird but the reason is that they're
+
+ align:start position:0%
+weird but the reason is that they're
+ 
+
+ align:start position:0%
+weird but the reason is that they're
+working on Schnoor signatures and
+
+ align:start position:0%
+working on Schnoor signatures and
+ 
+
+ align:start position:0%
+working on Schnoor signatures and
+aggregation and it was on github in like
+
+ align:start position:0%
+aggregation and it was on github in like
+ 
+
+ align:start position:0%
+aggregation and it was on github in like
+a branch of glib SEC P that the repo
+
+ align:start position:0%
+a branch of glib SEC P that the repo
+ 
+
+ align:start position:0%
+a branch of glib SEC P that the repo
+they're using it and then all these alt
+
+ align:start position:0%
+they're using it and then all these alt
+ 
+
+ align:start position:0%
+they're using it and then all these alt
+coins were taking the code and putting
+
+ align:start position:0%
+coins were taking the code and putting
+ 
+
+ align:start position:0%
+coins were taking the code and putting
+it into their all coins and saying hey
+
+ align:start position:0%
+it into their all coins and saying hey
+ 
+
+ align:start position:0%
+it into their all coins and saying hey
+we support our signatures and so for
+
+ align:start position:0%
+we support our signatures and so for
+ 
+
+ align:start position:0%
+we support our signatures and so for
+example the road key attack like it was
+
+ align:start position:0%
+example the road key attack like it was
+ 
+
+ align:start position:0%
+example the road key attack like it was
+the simple version which didn't have
+
+ align:start position:0%
+the simple version which didn't have
+ 
+
+ align:start position:0%
+the simple version which didn't have
+this x the hash of the pub key and and
+
+ align:start position:0%
+this x the hash of the pub key and and
+ 
+
+ align:start position:0%
+this x the hash of the pub key and and
+they were like wait no don't you know
+
+ align:start position:0%
+they were like wait no don't you know
+ 
+
+ align:start position:0%
+they were like wait no don't you know
+we're working on this software but we
+
+ align:start position:0%
+we're working on this software but we
+ 
+
+ align:start position:0%
+we're working on this software but we
+know all of these problems with it
+
+ align:start position:0%
+know all of these problems with it
+ 
+
+ align:start position:0%
+know all of these problems with it
+right you can't actually use this for
+
+ align:start position:0%
+right you can't actually use this for
+ 
+
+ align:start position:0%
+right you can't actually use this for
+signature aggregation we're just sort of
+
+ align:start position:0%
+signature aggregation we're just sort of
+ 
+
+ align:start position:0%
+signature aggregation we're just sort of
+playing around and trying different
+
+ align:start position:0%
+playing around and trying different
+ 
+
+ align:start position:0%
+playing around and trying different
+things and so they actually pulled it
+
+ align:start position:0%
+things and so they actually pulled it
+ 
+
+ align:start position:0%
+things and so they actually pulled it
+from github and so it's like like I've
+
+ align:start position:0%
+from github and so it's like like I've
+ 
+
+ align:start position:0%
+from github and so it's like like I've
+seen it like I well that doesn't have
+
+ align:start position:0%
+seen it like I well that doesn't have
+ 
+
+ align:start position:0%
+seen it like I well that doesn't have
+any of this D linearization or the thing
+
+ align:start position:0%
+any of this D linearization or the thing
+ 
+
+ align:start position:0%
+any of this D linearization or the thing
+that prevent wagner's attack I like all
+
+ align:start position:0%
+that prevent wagner's attack I like all
+ 
+
+ align:start position:0%
+that prevent wagner's attack I like all
+of that stuff is not in there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay maybe that's a cool attack but
+
+ align:start position:0%
+so okay maybe that's a cool attack but
+ 
+
+ align:start position:0%
+so okay maybe that's a cool attack but
+they they were like oh shoot no like it
+
+ align:start position:0%
+they they were like oh shoot no like it
+ 
+
+ align:start position:0%
+they they were like oh shoot no like it
+but it's said in their repo like do not
+
+ align:start position:0%
+but it's said in their repo like do not
+ 
+
+ align:start position:0%
+but it's said in their repo like do not
+use this this is research code do not
+
+ align:start position:0%
+use this this is research code do not
+ 
+
+ align:start position:0%
+use this this is research code do not
+use this in production there are known
+
+ align:start position:0%
+use this in production there are known
+ 
+
+ align:start position:0%
+use this in production there are known
+vulnerabilities but people are like
+
+ align:start position:0%
+vulnerabilities but people are like
+ 
+
+ align:start position:0%
+vulnerabilities but people are like
+whatever I'm just you know people didn't
+
+ align:start position:0%
+whatever I'm just you know people didn't
+ 
+
+ align:start position:0%
+whatever I'm just you know people didn't
+care well yeah there's some esoteric
+
+ align:start position:0%
+care well yeah there's some esoteric
+ 
+
+ align:start position:0%
+care well yeah there's some esoteric
+educational durability but I'm gonna
+
+ align:start position:0%
+educational durability but I'm gonna
+ 
+
+ align:start position:0%
+educational durability but I'm gonna
+solve that because XYZ so they actually
+
+ align:start position:0%
+solve that because XYZ so they actually
+ 
+
+ align:start position:0%
+solve that because XYZ so they actually
+pulled the code they are working on the
+
+ align:start position:0%
+pulled the code they are working on the
+ 
+
+ align:start position:0%
+pulled the code they are working on the
+code and I mean the code works it's it's
+
+ align:start position:0%
+code and I mean the code works it's it's
+ 
+
+ align:start position:0%
+code and I mean the code works it's it's
+I've seen it but they are very sort of
+
+ align:start position:0%
+I've seen it but they are very sort of
+ 
+
+ align:start position:0%
+I've seen it but they are very sort of
+like we don't want to put it publicly
+
+ align:start position:0%
+like we don't want to put it publicly
+ 
+
+ align:start position:0%
+like we don't want to put it publicly
+until we're sort of saying okay here's
+
+ align:start position:0%
+until we're sort of saying okay here's
+ 
+
+ align:start position:0%
+until we're sort of saying okay here's
+our final version that we want to put in
+
+ align:start position:0%
+our final version that we want to put in
+ 
+
+ align:start position:0%
+our final version that we want to put in
+Bitcoin because they know as soon as
+
+ align:start position:0%
+Bitcoin because they know as soon as
+ 
+
+ align:start position:0%
+Bitcoin because they know as soon as
+they sort of put it out there for review
+
+ align:start position:0%
+they sort of put it out there for review
+ 
+
+ align:start position:0%
+they sort of put it out there for review
+all these all coins will take I mean you
+
+ align:start position:0%
+all these all coins will take I mean you
+ 
+
+ align:start position:0%
+all these all coins will take I mean you
+you've implemented this in yeah in not
+
+ align:start position:0%
+you've implemented this in yeah in not
+ 
+
+ align:start position:0%
+you've implemented this in yeah in not
+invert quite in a crypto kernel yeah so
+
+ align:start position:0%
+invert quite in a crypto kernel yeah so
+ 
+
+ align:start position:0%
+invert quite in a crypto kernel yeah so
+and you do use the music okay oh okay
+
+ align:start position:0%
+and you do use the music okay oh okay
+ 
+
+ align:start position:0%
+and you do use the music okay oh okay
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+now you know but yeah so there's um you
+
+ align:start position:0%
+now you know but yeah so there's um you
+ 
+
+ align:start position:0%
+now you know but yeah so there's um you
+know they know that people are gonna use
+
+ align:start position:0%
+know they know that people are gonna use
+ 
+
+ align:start position:0%
+know they know that people are gonna use
+this because it's a cool it's a cool
+
+ align:start position:0%
+this because it's a cool it's a cool
+ 
+
+ align:start position:0%
+this because it's a cool it's a cool
+signature scheme and once you have and
+
+ align:start position:0%
+signature scheme and once you have and
+ 
+
+ align:start position:0%
+signature scheme and once you have and
+I've talked about this multiple times
+
+ align:start position:0%
+I've talked about this multiple times
+ 
+
+ align:start position:0%
+I've talked about this multiple times
+before once you have this your signature
+
+ align:start position:0%
+before once you have this your signature
+ 
+
+ align:start position:0%
+before once you have this your signature
+equation there's all these other cool
+
+ align:start position:0%
+equation there's all these other cool
+ 
+
+ align:start position:0%
+equation there's all these other cool
+things you can do with your addresses
+
+ align:start position:0%
+things you can do with your addresses
+ 
+
+ align:start position:0%
+things you can do with your addresses
+and things like that and so that's the
+
+ align:start position:0%
+and things like that and so that's the
+ 
+
+ align:start position:0%
+and things like that and so that's the
+idea here is scalability is one that
+
+ align:start position:0%
+idea here is scalability is one that
+ 
+
+ align:start position:0%
+idea here is scalability is one that
+okay now we can combine things make it
+
+ align:start position:0%
+okay now we can combine things make it
+ 
+
+ align:start position:0%
+okay now we can combine things make it
+smaller and also we can hopefully help
+
+ align:start position:0%
+smaller and also we can hopefully help
+ 
+
+ align:start position:0%
+smaller and also we can hopefully help
+privacy this way and that people people
+
+ align:start position:0%
+privacy this way and that people people
+ 
+
+ align:start position:0%
+privacy this way and that people people
+who are not particularly concerned with
+
+ align:start position:0%
+who are not particularly concerned with
+ 
+
+ align:start position:0%
+who are not particularly concerned with
+their anonymity will say yeah I still
+
+ align:start position:0%
+their anonymity will say yeah I still
+ 
+
+ align:start position:0%
+their anonymity will say yeah I still
+want to use it because I say you know I
+
+ align:start position:0%
+want to use it because I say you know I
+ 
+
+ align:start position:0%
+want to use it because I say you know I
+can save a buck on fees so yeah I'll
+
+ align:start position:0%
+can save a buck on fees so yeah I'll
+ 
+
+ align:start position:0%
+can save a buck on fees so yeah I'll
+join this transaction with a bunch of
+
+ align:start position:0%
+join this transaction with a bunch of
+ 
+
+ align:start position:0%
+join this transaction with a bunch of
+other people and then you've got the
+
+ align:start position:0%
+other people and then you've got the
+ 
+
+ align:start position:0%
+other people and then you've got the
+people who actually want anonymity are
+
+ align:start position:0%
+people who actually want anonymity are
+ 
+
+ align:start position:0%
+people who actually want anonymity are
+like great these are exactly the people
+
+ align:start position:0%
+like great these are exactly the people
+ 
+
+ align:start position:0%
+like great these are exactly the people
+I want to be associated with the people
+
+ align:start position:0%
+I want to be associated with the people
+ 
+
+ align:start position:0%
+I want to be associated with the people
+who don't particularly care about
+
+ align:start position:0%
+who don't particularly care about
+ 
+
+ align:start position:0%
+who don't particularly care about
+anonymity so seems like a win-win right
+
+ align:start position:0%
+anonymity so seems like a win-win right
+ 
+
+ align:start position:0%
+anonymity so seems like a win-win right
+now all the software requires a regular
+
+ align:start position:0%
+now all the software requires a regular
+ 
+
+ align:start position:0%
+now all the software requires a regular
+old signature so for example if you have
+
+ align:start position:0%
+old signature so for example if you have
+ 
+
+ align:start position:0%
+old signature so for example if you have
+you know if these are regular if these
+
+ align:start position:0%
+you know if these are regular if these
+ 
+
+ align:start position:0%
+you know if these are regular if these
+are outputs that are currently being
+
+ align:start position:0%
+are outputs that are currently being
+ 
+
+ align:start position:0%
+are outputs that are currently being
+used and you do this I validate the
+
+ align:start position:0%
+used and you do this I validate the
+ 
+
+ align:start position:0%
+used and you do this I validate the
+output one at a time and I say okay I'm
+
+ align:start position:0%
+output one at a time and I say okay I'm
+ 
+
+ align:start position:0%
+output one at a time and I say okay I'm
+looking at this output you know look
+
+ align:start position:0%
+looking at this output you know look
+ 
+
+ align:start position:0%
+looking at this output you know look
+this input there's no signature at all
+
+ align:start position:0%
+this input there's no signature at all
+ 
+
+ align:start position:0%
+this input there's no signature at all
+fail okay the whole transaction fails so
+
+ align:start position:0%
+fail okay the whole transaction fails so
+ 
+
+ align:start position:0%
+fail okay the whole transaction fails so
+you need a new output type which says
+
+ align:start position:0%
+you need a new output type which says
+ 
+
+ align:start position:0%
+you need a new output type which says
+okay I'm using this new aggregate
+
+ align:start position:0%
+okay I'm using this new aggregate
+ 
+
+ align:start position:0%
+okay I'm using this new aggregate
+signature so actually look at all the
+
+ align:start position:0%
+signature so actually look at all the
+ 
+
+ align:start position:0%
+signature so actually look at all the
+inputs don't validate them at all and
+
+ align:start position:0%
+inputs don't validate them at all and
+ 
+
+ align:start position:0%
+inputs don't validate them at all and
+just validate at the end at the bottom
+
+ align:start position:0%
+just validate at the end at the bottom
+ 
+
+ align:start position:0%
+just validate at the end at the bottom
+so that's gonna be some different code
+
+ align:start position:0%
+so that's gonna be some different code
+ 
+
+ align:start position:0%
+so that's gonna be some different code
+and you you can't you can't
+
+ align:start position:0%
+and you you can't you can't
+ 
+
+ align:start position:0%
+and you you can't you can't
+retroactively lycée okay all the
+
+ align:start position:0%
+retroactively lycée okay all the
+ 
+
+ align:start position:0%
+retroactively lycée okay all the
+existing keys we can now spend you know
+
+ align:start position:0%
+existing keys we can now spend you know
+ 
+
+ align:start position:0%
+existing keys we can now spend you know
+all the existing outputs we can outspend
+
+ align:start position:0%
+all the existing outputs we can outspend
+ 
+
+ align:start position:0%
+all the existing outputs we can outspend
+with this new signature scheme you can't
+
+ align:start position:0%
+with this new signature scheme you can't
+ 
+
+ align:start position:0%
+with this new signature scheme you can't
+really do that so we'll have to make new
+
+ align:start position:0%
+really do that so we'll have to make new
+ 
+
+ align:start position:0%
+really do that so we'll have to make new
+addresses and the new addresses will be
+
+ align:start position:0%
+addresses and the new addresses will be
+ 
+
+ align:start position:0%
+addresses and the new addresses will be
+BC 1z instead of Q you know new address
+
+ align:start position:0%
+BC 1z instead of Q you know new address
+ 
+
+ align:start position:0%
+BC 1z instead of Q you know new address
+type and then we send to that now you're
+
+ align:start position:0%
+type and then we send to that now you're
+ 
+
+ align:start position:0%
+type and then we send to that now you're
+allowed to spend from it using aggregate
+
+ align:start position:0%
+allowed to spend from it using aggregate
+ 
+
+ align:start position:0%
+allowed to spend from it using aggregate
+signatures so all that software is
+
+ align:start position:0%
+signatures so all that software is
+ 
+
+ align:start position:0%
+signatures so all that software is
+mostly there but it might take a while
+
+ align:start position:0%
+mostly there but it might take a while
+ 
+
+ align:start position:0%
+mostly there but it might take a while
+for you got to get everyone on board I'm
+
+ align:start position:0%
+for you got to get everyone on board I'm
+ 
+
+ align:start position:0%
+for you got to get everyone on board I'm
+curious to see what people will complain
+
+ align:start position:0%
+curious to see what people will complain
+ 
+
+ align:start position:0%
+curious to see what people will complain
+about segue saying it was a little bit
+
+ align:start position:0%
+about segue saying it was a little bit
+ 
+
+ align:start position:0%
+about segue saying it was a little bit
+more like there's a lot to complain
+
+ align:start position:0%
+more like there's a lot to complain
+ 
+
+ align:start position:0%
+more like there's a lot to complain
+about even though I don't like parts of
+
+ align:start position:0%
+about even though I don't like parts of
+ 
+
+ align:start position:0%
+about even though I don't like parts of
+segments not even I there's a lot of
+
+ align:start position:0%
+segments not even I there's a lot of
+ 
+
+ align:start position:0%
+segments not even I there's a lot of
+parts I don't like it won't use but um
+
+ align:start position:0%
+parts I don't like it won't use but um
+ 
+
+ align:start position:0%
+parts I don't like it won't use but um
+but this seems like a sort of clear win
+
+ align:start position:0%
+but this seems like a sort of clear win
+ 
+
+ align:start position:0%
+but this seems like a sort of clear win
+where it's like great you can aggregate
+
+ align:start position:0%
+where it's like great you can aggregate
+ 
+
+ align:start position:0%
+where it's like great you can aggregate
+signatures do all these cool things I'm
+
+ align:start position:0%
+signatures do all these cool things I'm
+ 
+
+ align:start position:0%
+signatures do all these cool things I'm
+guessing there will be people saying
+
+ align:start position:0%
+guessing there will be people saying
+ 
+
+ align:start position:0%
+guessing there will be people saying
+this is bad and saying like no because
+
+ align:start position:0%
+this is bad and saying like no because
+ 
+
+ align:start position:0%
+this is bad and saying like no because
+Satoshi's vision is one signature one
+
+ align:start position:0%
+Satoshi's vision is one signature one
+ 
+
+ align:start position:0%
+Satoshi's vision is one signature one
+input you know a blockchain is a chain a
+
+ align:start position:0%
+input you know a blockchain is a chain a
+ 
+
+ align:start position:0%
+input you know a blockchain is a chain a
+coin is a chain of signatures and this
+
+ align:start position:0%
+coin is a chain of signatures and this
+ 
+
+ align:start position:0%
+coin is a chain of signatures and this
+coin has no signatures I don't I'm
+
+ align:start position:0%
+coin has no signatures I don't I'm
+ 
+
+ align:start position:0%
+coin has no signatures I don't I'm
+guessing I don't know what will happen
+
+ align:start position:0%
+guessing I don't know what will happen
+ 
+
+ align:start position:0%
+guessing I don't know what will happen
+but or maybe it might be smooth and
+
+ align:start position:0%
+but or maybe it might be smooth and
+ 
+
+ align:start position:0%
+but or maybe it might be smooth and
+everyone started like yeah this is
+
+ align:start position:0%
+everyone started like yeah this is
+ 
+
+ align:start position:0%
+everyone started like yeah this is
+obviously better great great paper great
+
+ align:start position:0%
+obviously better great great paper great
+ 
+
+ align:start position:0%
+obviously better great great paper great
+math great idea let's get it you know
+
+ align:start position:0%
+math great idea let's get it you know
+ 
+
+ align:start position:0%
+math great idea let's get it you know
+let's let's all activate it and use
+
+ align:start position:0%
+let's let's all activate it and use
+ 
+
+ align:start position:0%
+let's let's all activate it and use
+Bitcoin this way who knows so we'll see
+
+ align:start position:0%
+Bitcoin this way who knows so we'll see
+ 
+
+ align:start position:0%
+Bitcoin this way who knows so we'll see
+it's pretty cool software though and you
+
+ align:start position:0%
+it's pretty cool software though and you
+ 
+
+ align:start position:0%
+it's pretty cool software though and you
+can use it in other projects right so
+
+ align:start position:0%
+can use it in other projects right so
+ 
+
+ align:start position:0%
+can use it in other projects right so
+crypto kernels using signatures a
+
+ align:start position:0%
+crypto kernels using signatures a
+ 
+
+ align:start position:0%
+crypto kernels using signatures a
+probably a bunch of different coins who
+
+ align:start position:0%
+probably a bunch of different coins who
+ 
+
+ align:start position:0%
+probably a bunch of different coins who
+are sort of more agile in that it's
+
+ align:start position:0%
+are sort of more agile in that it's
+ 
+
+ align:start position:0%
+are sort of more agile in that it's
+easier to make changes will probably
+
+ align:start position:0%
+easier to make changes will probably
+ 
+
+ align:start position:0%
+easier to make changes will probably
+start using this I don't if they're I'm
+
+ align:start position:0%
+start using this I don't if they're I'm
+ 
+
+ align:start position:0%
+start using this I don't if they're I'm
+still ECDSA though right yeah no one no
+
+ align:start position:0%
+still ECDSA though right yeah no one no
+ 
+
+ align:start position:0%
+still ECDSA though right yeah no one no
+one's there's no coins that are actually
+
+ align:start position:0%
+one's there's no coins that are actually
+ 
+
+ align:start position:0%
+one's there's no coins that are actually
+implementing this yet sums whenever uses
+
+ align:start position:0%
+implementing this yet sums whenever uses
+ 
+
+ align:start position:0%
+implementing this yet sums whenever uses
+82 5 509 which is essentially a snorer
+
+ align:start position:0%
+82 5 509 which is essentially a snorer
+ 
+
+ align:start position:0%
+82 5 509 which is essentially a snorer
+signature and there saw and I think
+
+ align:start position:0%
+signature and there saw and I think
+ 
+
+ align:start position:0%
+signature and there saw and I think
+ripple can use
+
+ align:start position:0%
+ripple can use
+ 
+
+ align:start position:0%
+ripple can use
+8255 online so there's some different
+
+ align:start position:0%
+8255 online so there's some different
+ 
+
+ align:start position:0%
+8255 online so there's some different
+schemes that are more similar to this
+
+ align:start position:0%
+schemes that are more similar to this
+ 
+
+ align:start position:0%
+schemes that are more similar to this
+but still don't have the definitions for
+
+ align:start position:0%
+but still don't have the definitions for
+ 
+
+ align:start position:0%
+but still don't have the definitions for
+aggregation so anyway so this is cool
+
+ align:start position:0%
+aggregation so anyway so this is cool
+ 
+
+ align:start position:0%
+aggregation so anyway so this is cool
+stuff next time I will talk about the
+
+ align:start position:0%
+stuff next time I will talk about the
+ 
+
+ align:start position:0%
+stuff next time I will talk about the
+next one I'm not looking forward to
+
+ align:start position:0%
+next one I'm not looking forward to
+ 
+
+ align:start position:0%
+next one I'm not looking forward to
+making slides because it's like a really
+
+ align:start position:0%
+making slides because it's like a really
+ 
+
+ align:start position:0%
+making slides because it's like a really
+complicated one that I don't even
+
+ align:start position:0%
+complicated one that I don't even
+ 
+
+ align:start position:0%
+complicated one that I don't even
+understand like I sort of get it but
+
+ align:start position:0%
+understand like I sort of get it but
+ 
+
+ align:start position:0%
+understand like I sort of get it but
+it's like wait how okay but how to mix
+
+ align:start position:0%
+it's like wait how okay but how to mix
+ 
+
+ align:start position:0%
+it's like wait how okay but how to mix
+different amounts right so how to hide
+
+ align:start position:0%
+different amounts right so how to hide
+ 
+
+ align:start position:0%
+different amounts right so how to hide
+the it so the basic it's you know in
+
+ align:start position:0%
+the it so the basic it's you know in
+ 
+
+ align:start position:0%
+the it so the basic it's you know in
+this case hey it's great but in in many
+
+ align:start position:0%
+this case hey it's great but in in many
+ 
+
+ align:start position:0%
+this case hey it's great but in in many
+cases you can see right what I said the
+
+ align:start position:0%
+cases you can see right what I said the
+ 
+
+ align:start position:0%
+cases you can see right what I said the
+reason it doesn't work is because it's
+
+ align:start position:0%
+reason it doesn't work is because it's
+ 
+
+ align:start position:0%
+reason it doesn't work is because it's
+really obvious where the time you babies
+
+ align:start position:0%
+really obvious where the time you babies
+ 
+
+ align:start position:0%
+really obvious where the time you babies
+do tend to but what if you could hide
+
+ align:start position:0%
+do tend to but what if you could hide
+ 
+
+ align:start position:0%
+do tend to but what if you could hide
+the amounts but still enforce that the
+
+ align:start position:0%
+the amounts but still enforce that the
+ 
+
+ align:start position:0%
+the amounts but still enforce that the
+amounts were correct so that's the idea
+
+ align:start position:0%
+amounts were correct so that's the idea
+ 
+
+ align:start position:0%
+amounts were correct so that's the idea
+of confidential transactions which we'll
+
+ align:start position:0%
+of confidential transactions which we'll
+ 
+
+ align:start position:0%
+of confidential transactions which we'll
+talk about next time and then it leads
+
+ align:start position:0%
+talk about next time and then it leads
+ 
+
+ align:start position:0%
+talk about next time and then it leads
+to move a Wimble which is even more
+
+ align:start position:0%
+to move a Wimble which is even more
+ 
+
+ align:start position:0%
+to move a Wimble which is even more
+complicated and I'll I don't I'm not
+
+ align:start position:0%
+complicated and I'll I don't I'm not
+ 
+
+ align:start position:0%
+complicated and I'll I don't I'm not
+gonna promise then I'll explain the
+
+ align:start position:0%
+gonna promise then I'll explain the
+ 
+
+ align:start position:0%
+gonna promise then I'll explain the
+whole thing but I'll touch on the ideas
\ No newline at end of file
diff --git a/BOf_ZcJk-GU.txt b/BOf_ZcJk-GU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ba02934e019643e1d6971bd3bba652bcdca432ca
--- /dev/null
+++ b/BOf_ZcJk-GU.txt
@@ -0,0 +1,12581 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let us start
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so last time
+
+ align:start position:0%
+so last time
+ 
+
+ align:start position:0%
+so last time
+at the end of lecture we discussed
+
+ align:start position:0%
+at the end of lecture we discussed
+ 
+
+ align:start position:0%
+at the end of lecture we discussed
+writeavistic generation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the cross section
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we want to derive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+already visualization of the
+
+ align:start position:0%
+already visualization of the
+ 
+
+ align:start position:0%
+already visualization of the
+cross-section from some initial state to
+
+ align:start position:0%
+cross-section from some initial state to
+ 
+
+ align:start position:0%
+cross-section from some initial state to
+some final State okay so initial state
+
+ align:start position:0%
+some final State okay so initial state
+ 
+
+ align:start position:0%
+some final State okay so initial state
+divided by up is denoted by Alpha the
+
+ align:start position:0%
+divided by up is denoted by Alpha the
+ 
+
+ align:start position:0%
+divided by up is denoted by Alpha the
+final State denoted by Beta
+
+ align:start position:0%
+final State denoted by Beta
+ 
+
+ align:start position:0%
+final State denoted by Beta
+so we will for most physical process
+
+ align:start position:0%
+so we will for most physical process
+ 
+
+ align:start position:0%
+so we will for most physical process
+we will consider two particles
+
+ align:start position:0%
+we will consider two particles
+ 
+
+ align:start position:0%
+we will consider two particles
+scattering
+
+ align:start position:0%
+scattering
+ 
+
+ align:start position:0%
+scattering
+so this is just two particles and then
+
+ align:start position:0%
+so this is just two particles and then
+ 
+
+ align:start position:0%
+so this is just two particles and then
+scatter
+
+ align:start position:0%
+scatter
+ 
+
+ align:start position:0%
+scatter
+okay so this is our initial state
+
+ align:start position:0%
+okay so this is our initial state
+ 
+
+ align:start position:0%
+okay so this is our initial state
+always only have two particles
+
+ align:start position:0%
+always only have two particles
+ 
+
+ align:start position:0%
+always only have two particles
+but the final State can have actually
+
+ align:start position:0%
+but the final State can have actually
+ 
+
+ align:start position:0%
+but the final State can have actually
+lumbar particles okay
+
+ align:start position:0%
+lumbar particles okay
+ 
+
+ align:start position:0%
+lumbar particles okay
+I have uh uh uh however you've had a
+
+ align:start position:0%
+I have uh uh uh however you've had a
+ 
+
+ align:start position:0%
+I have uh uh uh however you've had a
+lumbar particles and it will then be
+
+ align:start position:0%
+lumbar particles and it will then be
+ 
+
+ align:start position:0%
+lumbar particles and it will then be
+defined
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we require
+
+ align:start position:0%
+so we require
+ 
+
+ align:start position:0%
+so we require
+that the Sigma Alpha Beta
+
+ align:start position:0%
+that the Sigma Alpha Beta
+ 
+
+ align:start position:0%
+that the Sigma Alpha Beta
+to be low renting warrant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we've got because the probability
+
+ align:start position:0%
+we've got because the probability
+ 
+
+ align:start position:0%
+we've got because the probability
+for yeah they should not depend on say
+
+ align:start position:0%
+for yeah they should not depend on say
+ 
+
+ align:start position:0%
+for yeah they should not depend on say
+say your frame we also want to uh or
+
+ align:start position:0%
+say your frame we also want to uh or
+ 
+
+ align:start position:0%
+say your frame we also want to uh or
+Define to be semi symmetric
+
+ align:start position:0%
+Define to be semi symmetric
+ 
+
+ align:start position:0%
+Define to be semi symmetric
+in one to two okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to make connection
+
+ align:start position:0%
+so to make connection
+ 
+
+ align:start position:0%
+so to make connection
+with the launch web
+
+ align:start position:0%
+with the launch web
+ 
+
+ align:start position:0%
+with the launch web
+non-relativistic story
+
+ align:start position:0%
+non-relativistic story
+ 
+
+ align:start position:0%
+non-relativistic story
+we can consider the rest frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so as a starting point we can consider
+
+ align:start position:0%
+so as a starting point we can consider
+ 
+
+ align:start position:0%
+so as a starting point we can consider
+the right frame of particle two
+
+ align:start position:0%
+the right frame of particle two
+ 
+
+ align:start position:0%
+the right frame of particle two
+okay you can always go to the reframe of
+
+ align:start position:0%
+okay you can always go to the reframe of
+ 
+
+ align:start position:0%
+okay you can always go to the reframe of
+particle two
+
+ align:start position:0%
+particle two
+ 
+
+ align:start position:0%
+particle two
+and then in that frame
+
+ align:start position:0%
+and then in that frame
+ 
+
+ align:start position:0%
+and then in that frame
+then we can Define this quantity
+
+ align:start position:0%
+then we can Define this quantity
+ 
+
+ align:start position:0%
+then we can Define this quantity
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+the probability
+
+ align:start position:0%
+the probability
+ 
+
+ align:start position:0%
+the probability
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+from alpha to Beta
+
+ align:start position:0%
+from alpha to Beta
+ 
+
+ align:start position:0%
+from alpha to Beta
+DT and then divided by the incident flux
+
+ align:start position:0%
+DT and then divided by the incident flux
+ 
+
+ align:start position:0%
+DT and then divided by the incident flux
+of particle 1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so this t p Alpha Beta t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the probability yeah
+
+ align:start position:0%
+is the probability yeah
+ 
+
+ align:start position:0%
+is the probability yeah
+let me just write it
+
+ align:start position:0%
+let me just write it
+ 
+
+ align:start position:0%
+let me just write it
+so this is the probability per unit time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for for this process from alpha to Beta
+
+ align:start position:0%
+for for this process from alpha to Beta
+ 
+
+ align:start position:0%
+for for this process from alpha to Beta
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the dn1 dtda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+the incident flux
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or particle one okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this expression is a large
+
+ align:start position:0%
+so this expression is a large
+ 
+
+ align:start position:0%
+so this expression is a large
+organization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to write basic context which in the rest
+
+ align:start position:0%
+to write basic context which in the rest
+ 
+
+ align:start position:0%
+to write basic context which in the rest
+frame of particle two okay in the rest
+
+ align:start position:0%
+frame of particle two okay in the rest
+ 
+
+ align:start position:0%
+frame of particle two okay in the rest
+frame of particle 2.
+
+ align:start position:0%
+frame of particle 2.
+ 
+
+ align:start position:0%
+frame of particle 2.
+and so so our strategy is to first work
+
+ align:start position:0%
+and so so our strategy is to first work
+ 
+
+ align:start position:0%
+and so so our strategy is to first work
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+this quantity
+
+ align:start position:0%
+this quantity
+ 
+
+ align:start position:0%
+this quantity
+in the rest frame of two
+
+ align:start position:0%
+in the rest frame of two
+ 
+
+ align:start position:0%
+in the rest frame of two
+and then we can and then we use the
+
+ align:start position:0%
+and then we can and then we use the
+ 
+
+ align:start position:0%
+and then we can and then we use the
+Lorent
+
+ align:start position:0%
+Lorent
+ 
+
+ align:start position:0%
+Lorent
+uh the requirement of the low renting
+
+ align:start position:0%
+uh the requirement of the low renting
+ 
+
+ align:start position:0%
+uh the requirement of the low renting
+warrant and the symmetric in one two to
+
+ align:start position:0%
+warrant and the symmetric in one two to
+ 
+
+ align:start position:0%
+warrant and the symmetric in one two to
+write it in the general frame okay so
+
+ align:start position:0%
+write it in the general frame okay so
+ 
+
+ align:start position:0%
+write it in the general frame okay so
+that's our strategy okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so um
+
+ align:start position:0%
+and so um
+ 
+
+ align:start position:0%
+and so um
+so first let's talk about this quantity
+
+ align:start position:0%
+so first let's talk about this quantity
+ 
+
+ align:start position:0%
+so first let's talk about this quantity
+this probability
+
+ align:start position:0%
+this probability
+ 
+
+ align:start position:0%
+this probability
+from alpha to Beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have a probability from alpha to
+
+ align:start position:0%
+so we have a probability from alpha to
+ 
+
+ align:start position:0%
+so we have a probability from alpha to
+Beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it can be
+
+ align:start position:0%
+so it can be
+ 
+
+ align:start position:0%
+so it can be
+so by definition is defined as a
+
+ align:start position:0%
+so by definition is defined as a
+ 
+
+ align:start position:0%
+so by definition is defined as a
+following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is we want to look at the transition
+
+ align:start position:0%
+is we want to look at the transition
+ 
+
+ align:start position:0%
+is we want to look at the transition
+amplitude
+
+ align:start position:0%
+amplitude
+ 
+
+ align:start position:0%
+amplitude
+which has which give you the beta State
+
+ align:start position:0%
+which has which give you the beta State
+ 
+
+ align:start position:0%
+which has which give you the beta State
+at time plus infinity
+
+ align:start position:0%
+at time plus infinity
+ 
+
+ align:start position:0%
+at time plus infinity
+and the form Alpha at time minus
+
+ align:start position:0%
+and the form Alpha at time minus
+ 
+
+ align:start position:0%
+and the form Alpha at time minus
+infinity okay so this is the amplitude
+
+ align:start position:0%
+infinity okay so this is the amplitude
+ 
+
+ align:start position:0%
+infinity okay so this is the amplitude
+and then we take the square
+
+ align:start position:0%
+and then we take the square
+ 
+
+ align:start position:0%
+and then we take the square
+okay and then we divide by the
+
+ align:start position:0%
+okay and then we divide by the
+ 
+
+ align:start position:0%
+okay and then we divide by the
+normalization
+
+ align:start position:0%
+normalization
+ 
+
+ align:start position:0%
+normalization
+of the beta itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+under the alpha itself okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we are divided by the normalization of
+
+ align:start position:0%
+we are divided by the normalization of
+ 
+
+ align:start position:0%
+we are divided by the normalization of
+the uh the beta and Alpha the state
+
+ align:start position:0%
+the uh the beta and Alpha the state
+ 
+
+ align:start position:0%
+the uh the beta and Alpha the state
+themselves okay so that's the hosting uh
+
+ align:start position:0%
+themselves okay so that's the hosting uh
+ 
+
+ align:start position:0%
+themselves okay so that's the hosting uh
+really Define the probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the upstairs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we already uh defined before so so
+
+ align:start position:0%
+we already uh defined before so so
+ 
+
+ align:start position:0%
+we already uh defined before so so
+previously we defined the beta Plus
+
+ align:start position:0%
+previously we defined the beta Plus
+ 
+
+ align:start position:0%
+previously we defined the beta Plus
+yeah a a Infinity Alpha minus infinity
+
+ align:start position:0%
+yeah a a Infinity Alpha minus infinity
+ 
+
+ align:start position:0%
+yeah a a Infinity Alpha minus infinity
+so this is by our previous definition
+
+ align:start position:0%
+so this is by our previous definition
+ 
+
+ align:start position:0%
+so this is by our previous definition
+is given by 2 pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to the power 4 Delta
+
+ align:start position:0%
+to the power 4 Delta
+ 
+
+ align:start position:0%
+to the power 4 Delta
+P Alpha P beta
+
+ align:start position:0%
+P Alpha P beta
+ 
+
+ align:start position:0%
+P Alpha P beta
+so the pr for prepaid is the total
+
+ align:start position:0%
+so the pr for prepaid is the total
+ 
+
+ align:start position:0%
+so the pr for prepaid is the total
+momentum of the ignition final States
+
+ align:start position:0%
+momentum of the ignition final States
+ 
+
+ align:start position:0%
+momentum of the ignition final States
+and the times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m alpha beta okay MF of beta is defined
+
+ align:start position:0%
+m alpha beta okay MF of beta is defined
+ 
+
+ align:start position:0%
+m alpha beta okay MF of beta is defined
+with the scattering amplitude from alpha
+
+ align:start position:0%
+with the scattering amplitude from alpha
+ 
+
+ align:start position:0%
+with the scattering amplitude from alpha
+to Beta okay
+
+ align:start position:0%
+to Beta okay
+ 
+
+ align:start position:0%
+to Beta okay
+okay so so this is what we uh this was
+
+ align:start position:0%
+okay so so this is what we uh this was
+ 
+
+ align:start position:0%
+okay so so this is what we uh this was
+essentially our definition of the
+
+ align:start position:0%
+essentially our definition of the
+ 
+
+ align:start position:0%
+essentially our definition of the
+scattering amplitude yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time yeah yeah it means that the uh uh
+
+ align:start position:0%
+time yeah yeah it means that the uh uh
+ 
+
+ align:start position:0%
+time yeah yeah it means that the uh uh
+the t equal to minus infinity yeah so
+
+ align:start position:0%
+the t equal to minus infinity yeah so
+ 
+
+ align:start position:0%
+the t equal to minus infinity yeah so
+this is the Heisenberg State okay so
+
+ align:start position:0%
+this is the Heisenberg State okay so
+ 
+
+ align:start position:0%
+this is the Heisenberg State okay so
+this is in the Heisenberg picture uh so
+
+ align:start position:0%
+this is in the Heisenberg picture uh so
+ 
+
+ align:start position:0%
+this is in the Heisenberg picture uh so
+this means that the t equal to minus
+
+ align:start position:0%
+this means that the t equal to minus
+ 
+
+ align:start position:0%
+this means that the t equal to minus
+infinity uh uh we have a free particle
+
+ align:start position:0%
+infinity uh uh we have a free particle
+ 
+
+ align:start position:0%
+infinity uh uh we have a free particle
+States uh described by Alpha and then
+
+ align:start position:0%
+States uh described by Alpha and then
+ 
+
+ align:start position:0%
+States uh described by Alpha and then
+the t equal to plus infinity uh we have
+
+ align:start position:0%
+the t equal to plus infinity uh we have
+ 
+
+ align:start position:0%
+the t equal to plus infinity uh we have
+three particle State defined uh uh given
+
+ align:start position:0%
+three particle State defined uh uh given
+ 
+
+ align:start position:0%
+three particle State defined uh uh given
+by Beta
+
+ align:start position:0%
+by Beta
+ 
+
+ align:start position:0%
+by Beta
+other questions
+
+ align:start position:0%
+other questions
+ 
+
+ align:start position:0%
+other questions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now let's take the square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now let's take the square
+
+ align:start position:0%
+okay now let's take the square
+ 
+
+ align:start position:0%
+okay now let's take the square
+so to remember
+
+ align:start position:0%
+so to remember
+ 
+
+ align:start position:0%
+so to remember
+so the Rhythm we need to put in
+
+ align:start position:0%
+so the Rhythm we need to put in
+ 
+
+ align:start position:0%
+so the Rhythm we need to put in
+downstairs you say why do we need to put
+
+ align:start position:0%
+downstairs you say why do we need to put
+ 
+
+ align:start position:0%
+downstairs you say why do we need to put
+the downstairs big because are they
+
+ align:start position:0%
+the downstairs big because are they
+ 
+
+ align:start position:0%
+the downstairs big because are they
+supposed to be normalized
+
+ align:start position:0%
+supposed to be normalized
+ 
+
+ align:start position:0%
+supposed to be normalized
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but in uh in practice when we do the
+
+ align:start position:0%
+but in uh in practice when we do the
+ 
+
+ align:start position:0%
+but in uh in practice when we do the
+calculation or in practice when we talk
+
+ align:start position:0%
+calculation or in practice when we talk
+ 
+
+ align:start position:0%
+calculation or in practice when we talk
+about the product three particles we use
+
+ align:start position:0%
+about the product three particles we use
+ 
+
+ align:start position:0%
+about the product three particles we use
+the plane wave basis okay but brainwave
+
+ align:start position:0%
+the plane wave basis okay but brainwave
+ 
+
+ align:start position:0%
+the plane wave basis okay but brainwave
+remember it's not normalizable
+
+ align:start position:0%
+remember it's not normalizable
+ 
+
+ align:start position:0%
+remember it's not normalizable
+it's only a loan either way as a data
+
+ align:start position:0%
+it's only a loan either way as a data
+ 
+
+ align:start position:0%
+it's only a loan either way as a data
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+okay so so they'll organize the
+
+ align:start position:0%
+okay so so they'll organize the
+ 
+
+ align:start position:0%
+okay so so they'll organize the
+realization is not equal to one okay
+
+ align:start position:0%
+realization is not equal to one okay
+ 
+
+ align:start position:0%
+realization is not equal to one okay
+exactly so we have to be careful okay so
+
+ align:start position:0%
+exactly so we have to be careful okay so
+ 
+
+ align:start position:0%
+exactly so we have to be careful okay so
+that's why we need to include them here
+
+ align:start position:0%
+that's why we need to include them here
+ 
+
+ align:start position:0%
+that's why we need to include them here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um yeah
+
+ align:start position:0%
+so um yeah
+ 
+
+ align:start position:0%
+so um yeah
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so now let's look at this quantity
+
+ align:start position:0%
+so now let's look at this quantity
+ 
+
+ align:start position:0%
+so now let's look at this quantity
+Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's just move it down
+
+ align:start position:0%
+so let's just move it down
+ 
+
+ align:start position:0%
+so let's just move it down
+so to save time I just want to copy it
+
+ align:start position:0%
+so to save time I just want to copy it
+ 
+
+ align:start position:0%
+so to save time I just want to copy it
+so this quantity Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then then just equal the right hand side
+
+ align:start position:0%
+then then just equal the right hand side
+ 
+
+ align:start position:0%
+then then just equal the right hand side
+Square okay so we will have 2 pi
+
+ align:start position:0%
+Square okay so we will have 2 pi
+ 
+
+ align:start position:0%
+Square okay so we will have 2 pi
+for the data function Square
+
+ align:start position:0%
+for the data function Square
+ 
+
+ align:start position:0%
+for the data function Square
+and then we have F of m alpha beta
+
+ align:start position:0%
+and then we have F of m alpha beta
+ 
+
+ align:start position:0%
+and then we have F of m alpha beta
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now let's look at the Delta function
+
+ align:start position:0%
+and now let's look at the Delta function
+ 
+
+ align:start position:0%
+and now let's look at the Delta function
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+so the data function squared will have
+
+ align:start position:0%
+so the data function squared will have
+ 
+
+ align:start position:0%
+so the data function squared will have
+two pieces
+
+ align:start position:0%
+two pieces
+ 
+
+ align:start position:0%
+two pieces
+so the uh so so the Delta function
+
+ align:start position:0%
+so the uh so so the Delta function
+ 
+
+ align:start position:0%
+so the uh so so the Delta function
+Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let me just save time so this
+
+ align:start position:0%
+okay let me just save time so this
+ 
+
+ align:start position:0%
+okay let me just save time so this
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+then we can take one piece
+
+ align:start position:0%
+then we can take one piece
+ 
+
+ align:start position:0%
+then we can take one piece
+one copy of it we just write it as P
+
+ align:start position:0%
+one copy of it we just write it as P
+ 
+
+ align:start position:0%
+one copy of it we just write it as P
+Alpha minus P beta
+
+ align:start position:0%
+Alpha minus P beta
+ 
+
+ align:start position:0%
+Alpha minus P beta
+and then the other piece
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will be just data four we can just
+
+ align:start position:0%
+will be just data four we can just
+ 
+
+ align:start position:0%
+will be just data four we can just
+divide it at zero
+
+ align:start position:0%
+divide it at zero
+ 
+
+ align:start position:0%
+divide it at zero
+okay because because the we already set
+
+ align:start position:0%
+okay because because the we already set
+ 
+
+ align:start position:0%
+okay because because the we already set
+uh the P of equal to P beta from the
+
+ align:start position:0%
+uh the P of equal to P beta from the
+ 
+
+ align:start position:0%
+uh the P of equal to P beta from the
+first set of function okay so the second
+
+ align:start position:0%
+first set of function okay so the second
+ 
+
+ align:start position:0%
+first set of function okay so the second
+uh Factor can be just become data zero
+
+ align:start position:0%
+uh Factor can be just become data zero
+ 
+
+ align:start position:0%
+uh Factor can be just become data zero
+so now we know how to so we have seen
+
+ align:start position:0%
+so now we know how to so we have seen
+ 
+
+ align:start position:0%
+so now we know how to so we have seen
+this before right
+
+ align:start position:0%
+this before right
+ 
+
+ align:start position:0%
+this before right
+so what is this object do you remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+yeah it's the total space-time volume
+
+ align:start position:0%
+yeah it's the total space-time volume
+ 
+
+ align:start position:0%
+yeah it's the total space-time volume
+okay the reading is that the 2 pi
+
+ align:start position:0%
+okay the reading is that the 2 pi
+ 
+
+ align:start position:0%
+okay the reading is that the 2 pi
+data four zero
+
+ align:start position:0%
+data four zero
+ 
+
+ align:start position:0%
+data four zero
+so this is a zero in momentum space okay
+
+ align:start position:0%
+so this is a zero in momentum space okay
+ 
+
+ align:start position:0%
+so this is a zero in momentum space okay
+so this is just equal to
+
+ align:start position:0%
+so this is just equal to
+ 
+
+ align:start position:0%
+so this is just equal to
+d4x
+
+ align:start position:0%
+d4x
+ 
+
+ align:start position:0%
+d4x
+expansion ikx
+
+ align:start position:0%
+expansion ikx
+ 
+
+ align:start position:0%
+expansion ikx
+divided k equal to zero
+
+ align:start position:0%
+divided k equal to zero
+ 
+
+ align:start position:0%
+divided k equal to zero
+okay value at the k equal to zero B
+
+ align:start position:0%
+okay value at the k equal to zero B
+ 
+
+ align:start position:0%
+okay value at the k equal to zero B
+because this is give you the two Pi
+
+ align:start position:0%
+because this is give you the two Pi
+ 
+
+ align:start position:0%
+because this is give you the two Pi
+Delta K and solid value k0 when you
+
+ align:start position:0%
+Delta K and solid value k0 when you
+ 
+
+ align:start position:0%
+Delta K and solid value k0 when you
+divide it at the K zero then of course
+
+ align:start position:0%
+divide it at the K zero then of course
+ 
+
+ align:start position:0%
+divide it at the K zero then of course
+this is just the space-time body
+
+ align:start position:0%
+this is just the space-time body
+ 
+
+ align:start position:0%
+this is just the space-time body
+okay so I take the spatial volume to be
+
+ align:start position:0%
+okay so I take the spatial volume to be
+ 
+
+ align:start position:0%
+okay so I take the spatial volume to be
+B and then this T is the time period
+
+ align:start position:0%
+B and then this T is the time period
+ 
+
+ align:start position:0%
+B and then this T is the time period
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+so so physically
+
+ align:start position:0%
+so so physically
+ 
+
+ align:start position:0%
+so so physically
+physically you can interpret the T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the duration
+
+ align:start position:0%
+as the duration
+ 
+
+ align:start position:0%
+as the duration
+uh the time duration we're actually
+
+ align:start position:0%
+uh the time duration we're actually
+ 
+
+ align:start position:0%
+uh the time duration we're actually
+doing the experiment okay because only
+
+ align:start position:0%
+doing the experiment okay because only
+ 
+
+ align:start position:0%
+doing the experiment okay because only
+that part is relevant uh for our uh uh
+
+ align:start position:0%
+that part is relevant uh for our uh uh
+ 
+
+ align:start position:0%
+that part is relevant uh for our uh uh
+for our experiment okay so this capital
+
+ align:start position:0%
+for our experiment okay so this capital
+ 
+
+ align:start position:0%
+for our experiment okay so this capital
+T can be interpreted uh um yeah
+
+ align:start position:0%
+T can be interpreted uh um yeah
+ 
+
+ align:start position:0%
+T can be interpreted uh um yeah
+okay good and now we can just replace
+
+ align:start position:0%
+okay good and now we can just replace
+ 
+
+ align:start position:0%
+okay good and now we can just replace
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we can just replace here
+
+ align:start position:0%
+so now we can just replace here
+ 
+
+ align:start position:0%
+so now we can just replace here
+by V times T okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we can just replace here by V times
+
+ align:start position:0%
+okay we can just replace here by V times
+ 
+
+ align:start position:0%
+okay we can just replace here by V times
+C okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's look at the downstairs okay
+
+ align:start position:0%
+so now let's look at the downstairs okay
+ 
+
+ align:start position:0%
+so now let's look at the downstairs okay
+now let's look at downstairs
+
+ align:start position:0%
+now let's look at downstairs
+ 
+
+ align:start position:0%
+now let's look at downstairs
+so downstairs
+
+ align:start position:0%
+so downstairs
+ 
+
+ align:start position:0%
+so downstairs
+so the Alpha and the beta will be just
+
+ align:start position:0%
+so the Alpha and the beta will be just
+ 
+
+ align:start position:0%
+so the Alpha and the beta will be just
+say uh yeah so the typical Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the alpha state would be say say if
+
+ align:start position:0%
+so the alpha state would be say say if
+ 
+
+ align:start position:0%
+so the alpha state would be say say if
+your initial momentum
+
+ align:start position:0%
+your initial momentum
+ 
+
+ align:start position:0%
+your initial momentum
+is P1 and the P2
+
+ align:start position:0%
+is P1 and the P2
+ 
+
+ align:start position:0%
+is P1 and the P2
+okay will be like this for for scalar
+
+ align:start position:0%
+okay will be like this for for scalar
+ 
+
+ align:start position:0%
+okay will be like this for for scalar
+particle just will be specified by P1
+
+ align:start position:0%
+particle just will be specified by P1
+ 
+
+ align:start position:0%
+particle just will be specified by P1
+and P2 and if you have polarizations
+
+ align:start position:0%
+and P2 and if you have polarizations
+ 
+
+ align:start position:0%
+and P2 and if you have polarizations
+then they'll be VIP polarizations okay
+
+ align:start position:0%
+then they'll be VIP polarizations okay
+ 
+
+ align:start position:0%
+then they'll be VIP polarizations okay
+uh here I just give you an example
+
+ align:start position:0%
+uh here I just give you an example
+ 
+
+ align:start position:0%
+uh here I just give you an example
+so now if you look at the normalization
+
+ align:start position:0%
+so now if you look at the normalization
+ 
+
+ align:start position:0%
+so now if you look at the normalization
+of this kind of states
+
+ align:start position:0%
+of this kind of states
+ 
+
+ align:start position:0%
+of this kind of states
+okay remember the P1 and P2 defined so
+
+ align:start position:0%
+okay remember the P1 and P2 defined so
+ 
+
+ align:start position:0%
+okay remember the P1 and P2 defined so
+remember if you have a single particle
+
+ align:start position:0%
+remember if you have a single particle
+ 
+
+ align:start position:0%
+remember if you have a single particle
+state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of momentum P so that is normalized to
+
+ align:start position:0%
+of momentum P so that is normalized to
+ 
+
+ align:start position:0%
+of momentum P so that is normalized to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+2 pi Cube
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+qp0
+
+ align:start position:0%
+qp0
+ 
+
+ align:start position:0%
+qp0
+Delta 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P minus P Prime
+
+ align:start position:0%
+P minus P Prime
+ 
+
+ align:start position:0%
+P minus P Prime
+okay because they're always on shell
+
+ align:start position:0%
+okay because they're always on shell
+ 
+
+ align:start position:0%
+okay because they're always on shell
+okay ignition final stay there and show
+
+ align:start position:0%
+okay ignition final stay there and show
+ 
+
+ align:start position:0%
+okay ignition final stay there and show
+so P0 are functions of P okay
+
+ align:start position:0%
+so P0 are functions of P okay
+ 
+
+ align:start position:0%
+so P0 are functions of P okay
+so that's how yeah we normalize them
+
+ align:start position:0%
+so that's how yeah we normalize them
+ 
+
+ align:start position:0%
+so that's how yeah we normalize them
+so p is normalized
+
+ align:start position:0%
+so p is normalized
+ 
+
+ align:start position:0%
+so p is normalized
+by square root Omega K
+
+ align:start position:0%
+by square root Omega K
+ 
+
+ align:start position:0%
+by square root Omega K
+Omega P say a p action
+
+ align:start position:0%
+Omega P say a p action
+ 
+
+ align:start position:0%
+Omega P say a p action
+zero okay
+
+ align:start position:0%
+zero okay
+ 
+
+ align:start position:0%
+zero okay
+and for example for scalar particle and
+
+ align:start position:0%
+and for example for scalar particle and
+ 
+
+ align:start position:0%
+and for example for scalar particle and
+then you look at the normalization just
+
+ align:start position:0%
+then you look at the normalization just
+ 
+
+ align:start position:0%
+then you look at the normalization just
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now if you look at the
+
+ align:start position:0%
+so now if you look at the
+ 
+
+ align:start position:0%
+so now if you look at the
+P which itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then you have P equal to P
+
+ align:start position:0%
+okay and then you have P equal to P
+ 
+
+ align:start position:0%
+okay and then you have P equal to P
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+and then you have the essentially just
+
+ align:start position:0%
+and then you have the essentially just
+ 
+
+ align:start position:0%
+and then you have the essentially just
+have q p 0 times V
+
+ align:start position:0%
+have q p 0 times V
+ 
+
+ align:start position:0%
+have q p 0 times V
+okay the V is the spatial volume because
+
+ align:start position:0%
+okay the V is the spatial volume because
+ 
+
+ align:start position:0%
+okay the V is the spatial volume because
+here you just have 2 pi Cube the Delta
+
+ align:start position:0%
+here you just have 2 pi Cube the Delta
+ 
+
+ align:start position:0%
+here you just have 2 pi Cube the Delta
+zero and Delta zero is in the spatial of
+
+ align:start position:0%
+zero and Delta zero is in the spatial of
+ 
+
+ align:start position:0%
+zero and Delta zero is in the spatial of
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+okay expression momentum for the same
+
+ align:start position:0%
+okay expression momentum for the same
+ 
+
+ align:start position:0%
+okay expression momentum for the same
+reason uh uh just gave you the space of
+
+ align:start position:0%
+reason uh uh just gave you the space of
+ 
+
+ align:start position:0%
+reason uh uh just gave you the space of
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so uh yeah and so now we can just
+
+ align:start position:0%
+and so uh yeah and so now we can just
+ 
+
+ align:start position:0%
+and so uh yeah and so now we can just
+apply these two uh to Alpha and the beta
+
+ align:start position:0%
+apply these two uh to Alpha and the beta
+ 
+
+ align:start position:0%
+apply these two uh to Alpha and the beta
+so the alpha
+
+ align:start position:0%
+so the alpha
+ 
+
+ align:start position:0%
+so the alpha
+so if I take the alpha you have momentum
+
+ align:start position:0%
+so if I take the alpha you have momentum
+ 
+
+ align:start position:0%
+so if I take the alpha you have momentum
+P1 P2
+
+ align:start position:0%
+P1 P2
+ 
+
+ align:start position:0%
+P1 P2
+you can see it's particle momentum pure
+
+ align:start position:0%
+you can see it's particle momentum pure
+ 
+
+ align:start position:0%
+you can see it's particle momentum pure
+and view on the beta to consist of
+
+ align:start position:0%
+and view on the beta to consist of
+ 
+
+ align:start position:0%
+and view on the beta to consist of
+momentum say K1
+
+ align:start position:0%
+momentum say K1
+ 
+
+ align:start position:0%
+momentum say K1
+and the k n suppose they are n particles
+
+ align:start position:0%
+and the k n suppose they are n particles
+ 
+
+ align:start position:0%
+and the k n suppose they are n particles
+okay so in
+
+ align:start position:0%
+okay so in
+ 
+
+ align:start position:0%
+okay so in
+can be arbitrary introduced
+
+ align:start position:0%
+can be arbitrary introduced
+ 
+
+ align:start position:0%
+can be arbitrary introduced
+and then then from here
+
+ align:start position:0%
+and then then from here
+ 
+
+ align:start position:0%
+and then then from here
+then then the alpha which itself
+
+ align:start position:0%
+then then the alpha which itself
+ 
+
+ align:start position:0%
+then then the alpha which itself
+would be just 2e1
+
+ align:start position:0%
+would be just 2e1
+ 
+
+ align:start position:0%
+would be just 2e1
+times the volume
+
+ align:start position:0%
+times the volume
+ 
+
+ align:start position:0%
+times the volume
+and QE2 times the volume okay if I need
+
+ align:start position:0%
+and QE2 times the volume okay if I need
+ 
+
+ align:start position:0%
+and QE2 times the volume okay if I need
+two other energy over the P1 and P2
+
+ align:start position:0%
+two other energy over the P1 and P2
+ 
+
+ align:start position:0%
+two other energy over the P1 and P2
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yeah so E1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to P1 and zero okay and EQ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and similarly the beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would be to take the product J from 1 to
+
+ align:start position:0%
+would be to take the product J from 1 to
+ 
+
+ align:start position:0%
+would be to take the product J from 1 to
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 k j
+
+ align:start position:0%
+2 k j
+ 
+
+ align:start position:0%
+2 k j
+erus component times V okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+and so so the k0 KJ 0 yeah for example
+
+ align:start position:0%
+and so so the k0 KJ 0 yeah for example
+ 
+
+ align:start position:0%
+and so so the k0 KJ 0 yeah for example
+just kg0
+
+ align:start position:0%
+just kg0
+ 
+
+ align:start position:0%
+just kg0
+just equal to
+
+ align:start position:0%
+just equal to
+ 
+
+ align:start position:0%
+just equal to
+KJ Square
+
+ align:start position:0%
+KJ Square
+ 
+
+ align:start position:0%
+KJ Square
+plus MJ squared
+
+ align:start position:0%
+plus MJ squared
+ 
+
+ align:start position:0%
+plus MJ squared
+okay so so different so here we allow
+
+ align:start position:0%
+okay so so different so here we allow
+ 
+
+ align:start position:0%
+okay so so different so here we allow
+the different particles you have
+
+ align:start position:0%
+the different particles you have
+ 
+
+ align:start position:0%
+the different particles you have
+different Mass okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh yeah similarly with P one zero
+
+ align:start position:0%
+and uh yeah similarly with P one zero
+ 
+
+ align:start position:0%
+and uh yeah similarly with P one zero
+and and P2 okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now it's not preparations now we can
+
+ align:start position:0%
+so now it's not preparations now we can
+ 
+
+ align:start position:0%
+so now it's not preparations now we can
+write down
+
+ align:start position:0%
+write down
+ 
+
+ align:start position:0%
+write down
+DPT
+
+ align:start position:0%
+DPT
+ 
+
+ align:start position:0%
+DPT
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so now the DP
+
+ align:start position:0%
+so now the DP
+ 
+
+ align:start position:0%
+so now the DP
+Alpha 2 Beta DT
+
+ align:start position:0%
+Alpha 2 Beta DT
+ 
+
+ align:start position:0%
+Alpha 2 Beta DT
+then essentially just equal to P Alpha
+
+ align:start position:0%
+then essentially just equal to P Alpha
+ 
+
+ align:start position:0%
+then essentially just equal to P Alpha
+Beta
+
+ align:start position:0%
+Beta
+ 
+
+ align:start position:0%
+Beta
+divided by T
+
+ align:start position:0%
+divided by T
+ 
+
+ align:start position:0%
+divided by T
+the total duration of your uh uh the
+
+ align:start position:0%
+the total duration of your uh uh the
+ 
+
+ align:start position:0%
+the total duration of your uh uh the
+physical process
+
+ align:start position:0%
+physical process
+ 
+
+ align:start position:0%
+physical process
+and so the reason they just related
+
+ align:start position:0%
+and so the reason they just related
+ 
+
+ align:start position:0%
+and so the reason they just related
+you say how can you do this okay
+
+ align:start position:0%
+you say how can you do this okay
+ 
+
+ align:start position:0%
+you say how can you do this okay
+this is a differential and how can you
+
+ align:start position:0%
+this is a differential and how can you
+ 
+
+ align:start position:0%
+this is a differential and how can you
+just divide it by the t
+
+ align:start position:0%
+just divide it by the t
+ 
+
+ align:start position:0%
+just divide it by the t
+a dual reason why we can just divide by
+
+ align:start position:0%
+a dual reason why we can just divide by
+ 
+
+ align:start position:0%
+a dual reason why we can just divide by
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+just because of yeah yeah uh uh uh
+
+ align:start position:0%
+just because of yeah yeah uh uh uh
+ 
+
+ align:start position:0%
+just because of yeah yeah uh uh uh
+that's a good statement yeah yeah but
+
+ align:start position:0%
+that's a good statement yeah yeah but
+ 
+
+ align:start position:0%
+that's a good statement yeah yeah but
+the statement I was
+
+ align:start position:0%
+the statement I was
+ 
+
+ align:start position:0%
+the statement I was
+wanting to you say is that the uh
+
+ align:start position:0%
+wanting to you say is that the uh
+ 
+
+ align:start position:0%
+wanting to you say is that the uh
+because the time translation symmetry
+
+ align:start position:0%
+because the time translation symmetry
+ 
+
+ align:start position:0%
+because the time translation symmetry
+and so so you would expect that the
+
+ align:start position:0%
+and so so you would expect that the
+ 
+
+ align:start position:0%
+and so so you would expect that the
+probability per unit time should be
+
+ align:start position:0%
+probability per unit time should be
+ 
+
+ align:start position:0%
+probability per unit time should be
+independent of time and so the
+
+ align:start position:0%
+independent of time and so the
+ 
+
+ align:start position:0%
+independent of time and so the
+probability say for duration of time and
+
+ align:start position:0%
+probability say for duration of time and
+ 
+
+ align:start position:0%
+probability say for duration of time and
+you can just multiply by the total time
+
+ align:start position:0%
+you can just multiply by the total time
+ 
+
+ align:start position:0%
+you can just multiply by the total time
+and indeed in order to make this
+
+ align:start position:0%
+and indeed in order to make this
+ 
+
+ align:start position:0%
+and indeed in order to make this
+equation make sense
+
+ align:start position:0%
+equation make sense
+ 
+
+ align:start position:0%
+equation make sense
+of course the P have to be small people
+
+ align:start position:0%
+of course the P have to be small people
+ 
+
+ align:start position:0%
+of course the P have to be small people
+because otherwise the uh if you multiply
+
+ align:start position:0%
+because otherwise the uh if you multiply
+ 
+
+ align:start position:0%
+because otherwise the uh if you multiply
+yeah this thing has to be small
+
+ align:start position:0%
+yeah this thing has to be small
+ 
+
+ align:start position:0%
+yeah this thing has to be small
+otherwise when you multiply by T of
+
+ align:start position:0%
+otherwise when you multiply by T of
+ 
+
+ align:start position:0%
+otherwise when you multiply by T of
+course it will be greater than one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yeah but but just to divide by T is
+
+ align:start position:0%
+okay yeah but but just to divide by T is
+ 
+
+ align:start position:0%
+okay yeah but but just to divide by T is
+from the time translation symmetry
+
+ align:start position:0%
+from the time translation symmetry
+ 
+
+ align:start position:0%
+from the time translation symmetry
+okay so so this is good because we know
+
+ align:start position:0%
+okay so so this is good because we know
+ 
+
+ align:start position:0%
+okay so so this is good because we know
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+from the Delta function there's a factor
+
+ align:start position:0%
+from the Delta function there's a factor
+ 
+
+ align:start position:0%
+from the Delta function there's a factor
+of t
+
+ align:start position:0%
+of t
+ 
+
+ align:start position:0%
+of t
+okay there's a fact of T so if we
+
+ align:start position:0%
+okay there's a fact of T so if we
+ 
+
+ align:start position:0%
+okay there's a fact of T so if we
+combine everything together
+
+ align:start position:0%
+combine everything together
+ 
+
+ align:start position:0%
+combine everything together
+so we combine everything together and
+
+ align:start position:0%
+so we combine everything together and
+ 
+
+ align:start position:0%
+so we combine everything together and
+then we can just then upstairs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is given by
+
+ align:start position:0%
+is given by
+ 
+
+ align:start position:0%
+is given by
+so we have the 2 pi
+
+ align:start position:0%
+so we have the 2 pi
+ 
+
+ align:start position:0%
+so we have the 2 pi
+power 4
+
+ align:start position:0%
+power 4
+ 
+
+ align:start position:0%
+power 4
+data 4 P r5p beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the m alpha to Beta squared
+
+ align:start position:0%
+the m alpha to Beta squared
+ 
+
+ align:start position:0%
+the m alpha to Beta squared
+times VT
+
+ align:start position:0%
+times VT
+ 
+
+ align:start position:0%
+times VT
+and the magnitude divided by T and then
+
+ align:start position:0%
+and the magnitude divided by T and then
+ 
+
+ align:start position:0%
+and the magnitude divided by T and then
+this T go away
+
+ align:start position:0%
+this T go away
+ 
+
+ align:start position:0%
+this T go away
+okay so I can just erase this t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is upstairs and then divided by
+
+ align:start position:0%
+so this is upstairs and then divided by
+ 
+
+ align:start position:0%
+so this is upstairs and then divided by
+T a capital T
+
+ align:start position:0%
+T a capital T
+ 
+
+ align:start position:0%
+T a capital T
+and then the downstairs we just copy
+
+ align:start position:0%
+and then the downstairs we just copy
+ 
+
+ align:start position:0%
+and then the downstairs we just copy
+these two expressions
+
+ align:start position:0%
+these two expressions
+ 
+
+ align:start position:0%
+these two expressions
+okay downstairs right
+
+ align:start position:0%
+okay downstairs right
+ 
+
+ align:start position:0%
+okay downstairs right
+I just copy this expression under this
+
+ align:start position:0%
+I just copy this expression under this
+ 
+
+ align:start position:0%
+I just copy this expression under this
+expression okay so so this is the
+
+ align:start position:0%
+expression okay so so this is the
+ 
+
+ align:start position:0%
+expression okay so so this is the
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+e 1 e 2 times B
+
+ align:start position:0%
+e 1 e 2 times B
+ 
+
+ align:start position:0%
+e 1 e 2 times B
+squared and then
+
+ align:start position:0%
+squared and then
+ 
+
+ align:start position:0%
+squared and then
+K from 1 to n
+
+ align:start position:0%
+K from 1 to n
+ 
+
+ align:start position:0%
+K from 1 to n
+2 K zero KJ 0. times B
+
+ align:start position:0%
+2 K zero KJ 0. times B
+ 
+
+ align:start position:0%
+2 K zero KJ 0. times B
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and yeah no it's not the detector it's
+
+ align:start position:0%
+and yeah no it's not the detector it's
+ 
+
+ align:start position:0%
+and yeah no it's not the detector it's
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we are Computing s Matrix right so
+
+ align:start position:0%
+we are Computing s Matrix right so
+ 
+
+ align:start position:0%
+we are Computing s Matrix right so
+asymmetrically always assume you wait
+
+ align:start position:0%
+asymmetrically always assume you wait
+ 
+
+ align:start position:0%
+asymmetrically always assume you wait
+for a long time so that your initial
+
+ align:start position:0%
+for a long time so that your initial
+ 
+
+ align:start position:0%
+for a long time so that your initial
+state is free and your final state is
+
+ align:start position:0%
+state is free and your final state is
+ 
+
+ align:start position:0%
+state is free and your final state is
+free yeah so of course it's much not uh
+
+ align:start position:0%
+free yeah so of course it's much not uh
+ 
+
+ align:start position:0%
+free yeah so of course it's much not uh
+uh is the it's it's the range of your
+
+ align:start position:0%
+uh is the it's it's the range of your
+ 
+
+ align:start position:0%
+uh is the it's it's the range of your
+detector
+
+ align:start position:0%
+detector
+ 
+
+ align:start position:0%
+detector
+yeah you have to put the director very
+
+ align:start position:0%
+yeah you have to put the director very
+ 
+
+ align:start position:0%
+yeah you have to put the director very
+far away in order to measure the
+
+ align:start position:0%
+far away in order to measure the
+ 
+
+ align:start position:0%
+far away in order to measure the
+particle yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you can imagine the V just
+
+ align:start position:0%
+yeah you can imagine the V just
+ 
+
+ align:start position:0%
+yeah you can imagine the V just
+essentially is the
+
+ align:start position:0%
+essentially is the
+ 
+
+ align:start position:0%
+essentially is the
+is the volume which is the the the the
+
+ align:start position:0%
+is the volume which is the the the the
+ 
+
+ align:start position:0%
+is the volume which is the the the the
+the the experiment is happening here
+
+ align:start position:0%
+the the experiment is happening here
+ 
+
+ align:start position:0%
+the the experiment is happening here
+other questions
+
+ align:start position:0%
+other questions
+ 
+
+ align:start position:0%
+other questions
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so you see there's all this V flying
+
+ align:start position:0%
+so you see there's all this V flying
+ 
+
+ align:start position:0%
+so you see there's all this V flying
+around okay so so they look very
+
+ align:start position:0%
+around okay so so they look very
+ 
+
+ align:start position:0%
+around okay so so they look very
+unpleasant
+
+ align:start position:0%
+unpleasant
+ 
+
+ align:start position:0%
+unpleasant
+but but don't worry later
+
+ align:start position:0%
+but but don't worry later
+ 
+
+ align:start position:0%
+but but don't worry later
+if you are doing the right thing then
+
+ align:start position:0%
+if you are doing the right thing then
+ 
+
+ align:start position:0%
+if you are doing the right thing then
+all these unpleasant scenes will go away
+
+ align:start position:0%
+all these unpleasant scenes will go away
+ 
+
+ align:start position:0%
+all these unpleasant scenes will go away
+okay so so that's the rule of physics
+
+ align:start position:0%
+okay so so that's the rule of physics
+ 
+
+ align:start position:0%
+okay so so that's the rule of physics
+and in the intermediate step you may see
+
+ align:start position:0%
+and in the intermediate step you may see
+ 
+
+ align:start position:0%
+and in the intermediate step you may see
+a lot of unpleasant scenes but if you
+
+ align:start position:0%
+a lot of unpleasant scenes but if you
+ 
+
+ align:start position:0%
+a lot of unpleasant scenes but if you
+are doing the right thing
+
+ align:start position:0%
+are doing the right thing
+ 
+
+ align:start position:0%
+are doing the right thing
+okay I understand oh this unpleasant
+
+ align:start position:0%
+okay I understand oh this unpleasant
+ 
+
+ align:start position:0%
+okay I understand oh this unpleasant
+thing will go away or say you say oh
+
+ align:start position:0%
+thing will go away or say you say oh
+ 
+
+ align:start position:0%
+thing will go away or say you say oh
+then I must be doing the right thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so here actually this
+
+ align:start position:0%
+okay so so here actually this
+ 
+
+ align:start position:0%
+okay so so here actually this
+probability is not the probability we
+
+ align:start position:0%
+probability is not the probability we
+ 
+
+ align:start position:0%
+probability is not the probability we
+actually measure
+
+ align:start position:0%
+actually measure
+ 
+
+ align:start position:0%
+actually measure
+because here I assume that the final
+
+ align:start position:0%
+because here I assume that the final
+ 
+
+ align:start position:0%
+because here I assume that the final
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+here I'll assume in the final States
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um yeah here I assume in the final
+
+ align:start position:0%
+um yeah here I assume in the final
+ 
+
+ align:start position:0%
+um yeah here I assume in the final
+states have precise momentum K1 and K N
+
+ align:start position:0%
+states have precise momentum K1 and K N
+ 
+
+ align:start position:0%
+states have precise momentum K1 and K N
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so in reality of course we will not be
+
+ align:start position:0%
+so in reality of course we will not be
+ 
+
+ align:start position:0%
+so in reality of course we will not be
+able to make in the precise measurements
+
+ align:start position:0%
+able to make in the precise measurements
+ 
+
+ align:start position:0%
+able to make in the precise measurements
+okay so so in real experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we always detectors have some fun at The
+
+ align:start position:0%
+we always detectors have some fun at The
+ 
+
+ align:start position:0%
+we always detectors have some fun at The
+Exchange have finally uh
+
+ align:start position:0%
+Exchange have finally uh
+ 
+
+ align:start position:0%
+Exchange have finally uh
+detectors
+
+ align:start position:0%
+detectors
+ 
+
+ align:start position:0%
+detectors
+have followed the resolutions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so what we measure is actually when we
+
+ align:start position:0%
+so what we measure is actually when we
+ 
+
+ align:start position:0%
+so what we measure is actually when we
+say the particle
+
+ align:start position:0%
+say the particle
+ 
+
+ align:start position:0%
+say the particle
+say have momentum K1
+
+ align:start position:0%
+say have momentum K1
+ 
+
+ align:start position:0%
+say have momentum K1
+we actually means that the particle one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is within
+
+ align:start position:0%
+is within
+ 
+
+ align:start position:0%
+is within
+some Decay
+
+ align:start position:0%
+some Decay
+ 
+
+ align:start position:0%
+some Decay
+one around A1 around K1 okay
+
+ align:start position:0%
+one around A1 around K1 okay
+ 
+
+ align:start position:0%
+one around A1 around K1 okay
+so there's always some finite
+
+ align:start position:0%
+so there's always some finite
+ 
+
+ align:start position:0%
+so there's always some finite
+neighborhood of K1 which are allowed by
+
+ align:start position:0%
+neighborhood of K1 which are allowed by
+ 
+
+ align:start position:0%
+neighborhood of K1 which are allowed by
+the biodetector
+
+ align:start position:0%
+the biodetector
+ 
+
+ align:start position:0%
+the biodetector
+or a resolution
+
+ align:start position:0%
+or a resolution
+ 
+
+ align:start position:0%
+or a resolution
+and similarly
+
+ align:start position:0%
+and similarly
+ 
+
+ align:start position:0%
+and similarly
+minority is particle 2 in DK2
+
+ align:start position:0%
+minority is particle 2 in DK2
+ 
+
+ align:start position:0%
+minority is particle 2 in DK2
+around K2
+
+ align:start position:0%
+around K2
+ 
+
+ align:start position:0%
+around K2
+Etc okay so the particle n is
+
+ align:start position:0%
+Etc okay so the particle n is
+ 
+
+ align:start position:0%
+Etc okay so the particle n is
+dkn
+
+ align:start position:0%
+dkn
+ 
+
+ align:start position:0%
+dkn
+run k n
+
+ align:start position:0%
+run k n
+ 
+
+ align:start position:0%
+run k n
+so then we actually leads to integrate
+
+ align:start position:0%
+so then we actually leads to integrate
+ 
+
+ align:start position:0%
+so then we actually leads to integrate
+over all uh uh uh all this uh uh
+
+ align:start position:0%
+over all uh uh uh all this uh uh
+ 
+
+ align:start position:0%
+over all uh uh uh all this uh uh
+resolutions okay
+
+ align:start position:0%
+resolutions okay
+ 
+
+ align:start position:0%
+resolutions okay
+so that means that we should multiply
+
+ align:start position:0%
+so that means that we should multiply
+ 
+
+ align:start position:0%
+so that means that we should multiply
+this DPT
+
+ align:start position:0%
+this DPT
+ 
+
+ align:start position:0%
+this DPT
+okay this corresponding to to Sharp
+
+ align:start position:0%
+okay this corresponding to to Sharp
+ 
+
+ align:start position:0%
+okay this corresponding to to Sharp
+fellow momentum okay sharp value
+
+ align:start position:0%
+fellow momentum okay sharp value
+ 
+
+ align:start position:0%
+fellow momentum okay sharp value
+momentum and we should multiply by those
+
+ align:start position:0%
+momentum and we should multiply by those
+ 
+
+ align:start position:0%
+momentum and we should multiply by those
+uncertainties okay so that means that
+
+ align:start position:0%
+uncertainties okay so that means that
+ 
+
+ align:start position:0%
+uncertainties okay so that means that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+say if I take this equation to be star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this equation to be star
+
+ align:start position:0%
+this equation to be star
+ 
+
+ align:start position:0%
+this equation to be star
+so the one actually is measured by the
+
+ align:start position:0%
+so the one actually is measured by the
+ 
+
+ align:start position:0%
+so the one actually is measured by the
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+when we say TI Alpha Beta DT
+
+ align:start position:0%
+when we say TI Alpha Beta DT
+ 
+
+ align:start position:0%
+when we say TI Alpha Beta DT
+from the real experiment is actually
+
+ align:start position:0%
+from the real experiment is actually
+ 
+
+ align:start position:0%
+from the real experiment is actually
+equals one into
+
+ align:start position:0%
+equals one into
+ 
+
+ align:start position:0%
+equals one into
+the star times
+
+ align:start position:0%
+the star times
+ 
+
+ align:start position:0%
+the star times
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh the so uh those uncertainties around
+
+ align:start position:0%
+uh the so uh those uncertainties around
+ 
+
+ align:start position:0%
+uh the so uh those uncertainties around
+the uh uh uh so so J
+
+ align:start position:0%
+the uh uh uh so so J
+ 
+
+ align:start position:0%
+the uh uh uh so so J
+equal to one
+
+ align:start position:0%
+equal to one
+ 
+
+ align:start position:0%
+equal to one
+to n
+
+ align:start position:0%
+to n
+ 
+
+ align:start position:0%
+to n
+d3k
+
+ align:start position:0%
+d3k
+ 
+
+ align:start position:0%
+d3k
+J
+
+ align:start position:0%
+J
+ 
+
+ align:start position:0%
+J
+2 pi Cube
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we need to multiply the number
+
+ align:start position:0%
+okay so we need to multiply the number
+ 
+
+ align:start position:0%
+okay so we need to multiply the number
+of states okay
+
+ align:start position:0%
+of states okay
+ 
+
+ align:start position:0%
+of states okay
+the number of states within each this uh
+
+ align:start position:0%
+the number of states within each this uh
+ 
+
+ align:start position:0%
+the number of states within each this uh
+Decay momentum Space volume
+
+ align:start position:0%
+Decay momentum Space volume
+ 
+
+ align:start position:0%
+Decay momentum Space volume
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the number of the state and the
+
+ align:start position:0%
+so the number of the state and the
+ 
+
+ align:start position:0%
+so the number of the state and the
+number of state is given by this
+
+ align:start position:0%
+number of state is given by this
+ 
+
+ align:start position:0%
+number of state is given by this
+times the volume okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so do you remember do you remember where
+
+ align:start position:0%
+so do you remember do you remember where
+ 
+
+ align:start position:0%
+so do you remember do you remember where
+this volume come from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+exactly so this gives you the density of
+
+ align:start position:0%
+exactly so this gives you the density of
+ 
+
+ align:start position:0%
+exactly so this gives you the density of
+State it's because the
+
+ align:start position:0%
+State it's because the
+ 
+
+ align:start position:0%
+State it's because the
+so if I just remind you remember if you
+
+ align:start position:0%
+so if I just remind you remember if you
+ 
+
+ align:start position:0%
+so if I just remind you remember if you
+so the way to think about it just
+
+ align:start position:0%
+so the way to think about it just
+ 
+
+ align:start position:0%
+so the way to think about it just
+imagine you put your uh uh put your uh
+
+ align:start position:0%
+imagine you put your uh uh put your uh
+ 
+
+ align:start position:0%
+imagine you put your uh uh put your uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+put your system in the Box
+
+ align:start position:0%
+put your system in the Box
+ 
+
+ align:start position:0%
+put your system in the Box
+and and then and then your uh
+
+ align:start position:0%
+and and then and then your uh
+ 
+
+ align:start position:0%
+and and then and then your uh
+your energy level will be quantized in
+
+ align:start position:0%
+your energy level will be quantized in
+ 
+
+ align:start position:0%
+your energy level will be quantized in
+terms of two Pi say 2 pi
+
+ align:start position:0%
+terms of two Pi say 2 pi
+ 
+
+ align:start position:0%
+terms of two Pi say 2 pi
+cubed divided by the volume okay so so
+
+ align:start position:0%
+cubed divided by the volume okay so so
+ 
+
+ align:start position:0%
+cubed divided by the volume okay so so
+this is the number of states in momentum
+
+ align:start position:0%
+this is the number of states in momentum
+ 
+
+ align:start position:0%
+this is the number of states in momentum
+space uh the density of states and then
+
+ align:start position:0%
+space uh the density of states and then
+ 
+
+ align:start position:0%
+space uh the density of states and then
+you multiply it by that decay okay and
+
+ align:start position:0%
+you multiply it by that decay okay and
+ 
+
+ align:start position:0%
+you multiply it by that decay okay and
+multiply that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so this is actually the quantity we
+
+ align:start position:0%
+so so this is actually the quantity we
+ 
+
+ align:start position:0%
+so so this is actually the quantity we
+are interested in
+
+ align:start position:0%
+are interested in
+ 
+
+ align:start position:0%
+are interested in
+okay this is a quantity we're interested
+
+ align:start position:0%
+okay this is a quantity we're interested
+ 
+
+ align:start position:0%
+okay this is a quantity we're interested
+any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's just plug the plug in that star
+
+ align:start position:0%
+let's just plug the plug in that star
+ 
+
+ align:start position:0%
+let's just plug the plug in that star
+into here
+
+ align:start position:0%
+into here
+ 
+
+ align:start position:0%
+into here
+okay so now the nice thing
+
+ align:start position:0%
+okay so now the nice thing
+ 
+
+ align:start position:0%
+okay so now the nice thing
+now we can count
+
+ align:start position:0%
+now we can count
+ 
+
+ align:start position:0%
+now we can count
+the number of V's okay if we are doing
+
+ align:start position:0%
+the number of V's okay if we are doing
+ 
+
+ align:start position:0%
+the number of V's okay if we are doing
+the right thing or the V
+
+ align:start position:0%
+the right thing or the V
+ 
+
+ align:start position:0%
+the right thing or the V
+should cancel okay except
+
+ align:start position:0%
+should cancel okay except
+ 
+
+ align:start position:0%
+should cancel okay except
+uh yeah
+
+ align:start position:0%
+uh yeah
+ 
+
+ align:start position:0%
+uh yeah
+but not quite yet okay uh so so so so
+
+ align:start position:0%
+but not quite yet okay uh so so so so
+ 
+
+ align:start position:0%
+but not quite yet okay uh so so so so
+upstairs we have 1V
+
+ align:start position:0%
+upstairs we have 1V
+ 
+
+ align:start position:0%
+upstairs we have 1V
+here we have V Square so let's first
+
+ align:start position:0%
+here we have V Square so let's first
+ 
+
+ align:start position:0%
+here we have V Square so let's first
+cancel this V
+
+ align:start position:0%
+cancel this V
+ 
+
+ align:start position:0%
+cancel this V
+so that we I don't have to worry about
+
+ align:start position:0%
+so that we I don't have to worry about
+ 
+
+ align:start position:0%
+so that we I don't have to worry about
+that okay so let's first cancel that V
+
+ align:start position:0%
+that okay so let's first cancel that V
+ 
+
+ align:start position:0%
+that okay so let's first cancel that V
+and now we have downstairs we have V for
+
+ align:start position:0%
+and now we have downstairs we have V for
+ 
+
+ align:start position:0%
+and now we have downstairs we have V for
+each J
+
+ align:start position:0%
+each J
+ 
+
+ align:start position:0%
+each J
+and the upstairs now we multiply this by
+
+ align:start position:0%
+and the upstairs now we multiply this by
+ 
+
+ align:start position:0%
+and the upstairs now we multiply this by
+this and then for each J I have one V so
+
+ align:start position:0%
+this and then for each J I have one V so
+ 
+
+ align:start position:0%
+this and then for each J I have one V so
+all this V will cancel that V
+
+ align:start position:0%
+all this V will cancel that V
+ 
+
+ align:start position:0%
+all this V will cancel that V
+okay all these will cancel that b so we
+
+ align:start position:0%
+okay all these will cancel that b so we
+ 
+
+ align:start position:0%
+okay all these will cancel that b so we
+left with
+
+ align:start position:0%
+left with
+ 
+
+ align:start position:0%
+left with
+only this single V okay
+
+ align:start position:0%
+only this single V okay
+ 
+
+ align:start position:0%
+only this single V okay
+this single V
+
+ align:start position:0%
+this single V
+ 
+
+ align:start position:0%
+this single V
+so so now we can write it the 14
+
+ align:start position:0%
+so so now we can write it the 14
+ 
+
+ align:start position:0%
+so so now we can write it the 14
+so I can write it this F
+
+ align:start position:0%
+so I can write it this F
+ 
+
+ align:start position:0%
+so I can write it this F
+m alpha beta Square so I just copy this
+
+ align:start position:0%
+m alpha beta Square so I just copy this
+ 
+
+ align:start position:0%
+m alpha beta Square so I just copy this
+and then I divide it by a let's keep
+
+ align:start position:0%
+and then I divide it by a let's keep
+ 
+
+ align:start position:0%
+and then I divide it by a let's keep
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+divided by
+
+ align:start position:0%
+divided by
+ 
+
+ align:start position:0%
+divided by
+4 e 1 e 2 times V
+
+ align:start position:0%
+4 e 1 e 2 times V
+ 
+
+ align:start position:0%
+4 e 1 e 2 times V
+and then I group everything else into
+
+ align:start position:0%
+and then I group everything else into
+ 
+
+ align:start position:0%
+and then I group everything else into
+what I call the MU okay
+
+ align:start position:0%
+what I call the MU okay
+ 
+
+ align:start position:0%
+what I call the MU okay
+and the MU is everything else
+
+ align:start position:0%
+and the MU is everything else
+ 
+
+ align:start position:0%
+and the MU is everything else
+the MU is defined to be
+
+ align:start position:0%
+the MU is defined to be
+ 
+
+ align:start position:0%
+the MU is defined to be
+this third function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+J from 1 to n
+
+ align:start position:0%
+J from 1 to n
+ 
+
+ align:start position:0%
+J from 1 to n
+d3k J
+
+ align:start position:0%
+d3k J
+ 
+
+ align:start position:0%
+d3k J
+2 pi Cube
+
+ align:start position:0%
+2 pi Cube
+ 
+
+ align:start position:0%
+2 pi Cube
+qkj 0.
+
+ align:start position:0%
+qkj 0.
+ 
+
+ align:start position:0%
+qkj 0.
+okay so I just combined these two
+
+ align:start position:0%
+okay so I just combined these two
+ 
+
+ align:start position:0%
+okay so I just combined these two
+products okay
+
+ align:start position:0%
+products okay
+ 
+
+ align:start position:0%
+products okay
+combine these two products okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the nice thing
+
+ align:start position:0%
+so the nice thing
+ 
+
+ align:start position:0%
+so the nice thing
+the redirect group all this together
+
+ align:start position:0%
+the redirect group all this together
+ 
+
+ align:start position:0%
+the redirect group all this together
+because not the MU
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now it's no renting warrant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is a lorenzing warrant
+
+ align:start position:0%
+okay so this is a lorenzing warrant
+ 
+
+ align:start position:0%
+okay so this is a lorenzing warrant
+measure
+
+ align:start position:0%
+measure
+ 
+
+ align:start position:0%
+measure
+because remember this is no renting
+
+ align:start position:0%
+because remember this is no renting
+ 
+
+ align:start position:0%
+because remember this is no renting
+warrant
+
+ align:start position:0%
+warrant
+ 
+
+ align:start position:0%
+warrant
+I remember this combination
+
+ align:start position:0%
+I remember this combination
+ 
+
+ align:start position:0%
+I remember this combination
+is also low renting warrant from your
+
+ align:start position:0%
+is also low renting warrant from your
+ 
+
+ align:start position:0%
+is also low renting warrant from your
+first day are essentially in qf t okay
+
+ align:start position:0%
+first day are essentially in qf t okay
+ 
+
+ align:start position:0%
+first day are essentially in qf t okay
+in your first P set you yeah so so now
+
+ align:start position:0%
+in your first P set you yeah so so now
+ 
+
+ align:start position:0%
+in your first P set you yeah so so now
+this nice thing is that this now it's a
+
+ align:start position:0%
+this nice thing is that this now it's a
+ 
+
+ align:start position:0%
+this nice thing is that this now it's a
+low renting worry
+
+ align:start position:0%
+low renting worry
+ 
+
+ align:start position:0%
+low renting worry
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we have this nice expression
+
+ align:start position:0%
+so now we have this nice expression
+ 
+
+ align:start position:0%
+so now we have this nice expression
+okay we have this nice expression
+
+ align:start position:0%
+okay we have this nice expression
+ 
+
+ align:start position:0%
+okay we have this nice expression
+we have this by definition is no renting
+
+ align:start position:0%
+we have this by definition is no renting
+ 
+
+ align:start position:0%
+we have this by definition is no renting
+warrant
+
+ align:start position:0%
+warrant
+ 
+
+ align:start position:0%
+warrant
+and then we have this four E1 and U2 and
+
+ align:start position:0%
+and then we have this four E1 and U2 and
+ 
+
+ align:start position:0%
+and then we have this four E1 and U2 and
+times V
+
+ align:start position:0%
+times V
+ 
+
+ align:start position:0%
+times V
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+for you one times B okay and now we want
+
+ align:start position:0%
+for you one times B okay and now we want
+ 
+
+ align:start position:0%
+for you one times B okay and now we want
+to write them into low renting warrants
+
+ align:start position:0%
+to write them into low renting warrants
+ 
+
+ align:start position:0%
+to write them into low renting warrants
+away okay
+
+ align:start position:0%
+away okay
+ 
+
+ align:start position:0%
+away okay
+but we haven't died this is only
+
+ align:start position:0%
+but we haven't died this is only
+ 
+
+ align:start position:0%
+but we haven't died this is only
+upstairs uh this by itself is not the
+
+ align:start position:0%
+upstairs uh this by itself is not the
+ 
+
+ align:start position:0%
+upstairs uh this by itself is not the
+renting one we have to divide it by the
+
+ align:start position:0%
+renting one we have to divide it by the
+ 
+
+ align:start position:0%
+renting one we have to divide it by the
+downstairs
+
+ align:start position:0%
+downstairs
+ 
+
+ align:start position:0%
+downstairs
+so the downstairs is the the flux
+
+ align:start position:0%
+so the downstairs is the the flux
+ 
+
+ align:start position:0%
+so the downstairs is the the flux
+okay is the flux
+
+ align:start position:0%
+okay is the flux
+ 
+
+ align:start position:0%
+okay is the flux
+so now in the rest frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of particle two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's calculate the the flux of the
+
+ align:start position:0%
+so let's calculate the the flux of the
+ 
+
+ align:start position:0%
+so let's calculate the the flux of the
+particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the so the flux of the particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the flux so we need to calculate
+
+ align:start position:0%
+okay so the flux so we need to calculate
+ 
+
+ align:start position:0%
+okay so the flux so we need to calculate
+the flux of particle one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so that's the thing we need to divide
+
+ align:start position:0%
+so so that's the thing we need to divide
+ 
+
+ align:start position:0%
+so so that's the thing we need to divide
+yeah so so this is the flux of the
+
+ align:start position:0%
+yeah so so this is the flux of the
+ 
+
+ align:start position:0%
+yeah so so this is the flux of the
+particle one okay
+
+ align:start position:0%
+particle one okay
+ 
+
+ align:start position:0%
+particle one okay
+so that flux is the longbow
+
+ align:start position:0%
+so that flux is the longbow
+ 
+
+ align:start position:0%
+so that flux is the longbow
+number of particles
+
+ align:start position:0%
+number of particles
+ 
+
+ align:start position:0%
+number of particles
+per unit time and per area
+
+ align:start position:0%
+per unit time and per area
+ 
+
+ align:start position:0%
+per unit time and per area
+okay a period time per area
+
+ align:start position:0%
+okay a period time per area
+ 
+
+ align:start position:0%
+okay a period time per area
+so this is the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the number of the particle number
+
+ align:start position:0%
+as the number of the particle number
+ 
+
+ align:start position:0%
+as the number of the particle number
+density of the particle 1 times the
+
+ align:start position:0%
+density of the particle 1 times the
+ 
+
+ align:start position:0%
+density of the particle 1 times the
+velocity of the particle one
+
+ align:start position:0%
+velocity of the particle one
+ 
+
+ align:start position:0%
+velocity of the particle one
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so remember the flux is essentially the
+
+ align:start position:0%
+so remember the flux is essentially the
+ 
+
+ align:start position:0%
+so remember the flux is essentially the
+density times the velocity okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this gives you the number of particle
+
+ align:start position:0%
+so this gives you the number of particle
+ 
+
+ align:start position:0%
+so this gives you the number of particle
+per volume
+
+ align:start position:0%
+per volume
+ 
+
+ align:start position:0%
+per volume
+and this is give you the uh the distance
+
+ align:start position:0%
+and this is give you the uh the distance
+ 
+
+ align:start position:0%
+and this is give you the uh the distance
+traveled per unit time and yeah so
+
+ align:start position:0%
+traveled per unit time and yeah so
+ 
+
+ align:start position:0%
+traveled per unit time and yeah so
+together they they give you that okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so yeah so so this is the velocity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the density of particle one
+
+ align:start position:0%
+so this is the density of particle one
+ 
+
+ align:start position:0%
+so this is the density of particle one
+so this is all in the rest frame of
+
+ align:start position:0%
+so this is all in the rest frame of
+ 
+
+ align:start position:0%
+so this is all in the rest frame of
+particle two okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now in this experiment we have two
+
+ align:start position:0%
+so now in this experiment we have two
+ 
+
+ align:start position:0%
+so now in this experiment we have two
+particle scattering so what do you think
+
+ align:start position:0%
+particle scattering so what do you think
+ 
+
+ align:start position:0%
+particle scattering so what do you think
+will be the density of one
+
+ align:start position:0%
+will be the density of one
+ 
+
+ align:start position:0%
+will be the density of one
+so what do you think is the N1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+exactly how many particles we have we
+
+ align:start position:0%
+exactly how many particles we have we
+ 
+
+ align:start position:0%
+exactly how many particles we have we
+don't have one particle so so this is
+
+ align:start position:0%
+don't have one particle so so this is
+ 
+
+ align:start position:0%
+don't have one particle so so this is
+just give a one more V okay
+
+ align:start position:0%
+just give a one more V okay
+ 
+
+ align:start position:0%
+just give a one more V okay
+so this is just given by one go V
+
+ align:start position:0%
+so this is just given by one go V
+ 
+
+ align:start position:0%
+so this is just given by one go V
+so so now we can find
+
+ align:start position:0%
+so so now we can find
+ 
+
+ align:start position:0%
+so so now we can find
+the D Sigma
+
+ align:start position:0%
+the D Sigma
+ 
+
+ align:start position:0%
+the D Sigma
+okay so the D Sigma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha 2 Beta
+
+ align:start position:0%
+Alpha 2 Beta
+ 
+
+ align:start position:0%
+Alpha 2 Beta
+then it's defined to be DP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT
+
+ align:start position:0%
+DT
+ 
+
+ align:start position:0%
+DT
+divided by the flux of one particle one
+
+ align:start position:0%
+divided by the flux of one particle one
+ 
+
+ align:start position:0%
+divided by the flux of one particle one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so now this is just given by
+
+ align:start position:0%
+so so now this is just given by
+ 
+
+ align:start position:0%
+so so now this is just given by
+now the volume cancel okay because M1
+
+ align:start position:0%
+now the volume cancel okay because M1
+ 
+
+ align:start position:0%
+now the volume cancel okay because M1
+is 1 over volume
+
+ align:start position:0%
+is 1 over volume
+ 
+
+ align:start position:0%
+is 1 over volume
+and then there's a volume here and now
+
+ align:start position:0%
+and then there's a volume here and now
+ 
+
+ align:start position:0%
+and then there's a volume here and now
+finally this volume cancel okay
+
+ align:start position:0%
+finally this volume cancel okay
+ 
+
+ align:start position:0%
+finally this volume cancel okay
+so now if we divide that by by the flux
+
+ align:start position:0%
+so now if we divide that by by the flux
+ 
+
+ align:start position:0%
+so now if we divide that by by the flux
+and the volume cancel and then we get
+
+ align:start position:0%
+and the volume cancel and then we get
+ 
+
+ align:start position:0%
+and the volume cancel and then we get
+m alpha
+
+ align:start position:0%
+m alpha
+ 
+
+ align:start position:0%
+m alpha
+beta Square
+
+ align:start position:0%
+beta Square
+ 
+
+ align:start position:0%
+beta Square
+the MU
+
+ align:start position:0%
+the MU
+ 
+
+ align:start position:0%
+the MU
+and then divided by E1
+
+ align:start position:0%
+and then divided by E1
+ 
+
+ align:start position:0%
+and then divided by E1
+E2 and V1 okay the velocity of the uh
+
+ align:start position:0%
+E2 and V1 okay the velocity of the uh
+ 
+
+ align:start position:0%
+E2 and V1 okay the velocity of the uh
+the the particle one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is the uh so view one of course
+
+ align:start position:0%
+so this is the uh so view one of course
+ 
+
+ align:start position:0%
+so this is the uh so view one of course
+can also be interpreted as a relative
+
+ align:start position:0%
+can also be interpreted as a relative
+ 
+
+ align:start position:0%
+can also be interpreted as a relative
+velocity between one and two okay
+
+ align:start position:0%
+velocity between one and two okay
+ 
+
+ align:start position:0%
+velocity between one and two okay
+anyway uh uh uh so this is expressing
+
+ align:start position:0%
+anyway uh uh uh so this is expressing
+ 
+
+ align:start position:0%
+anyway uh uh uh so this is expressing
+the uh assigned
+
+ align:start position:0%
+the uh assigned
+ 
+
+ align:start position:0%
+the uh assigned
+so this is expression in the rest frame
+
+ align:start position:0%
+so this is expression in the rest frame
+ 
+
+ align:start position:0%
+so this is expression in the rest frame
+of particle two okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so by definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so by definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we want
+
+ align:start position:0%
+we want
+ 
+
+ align:start position:0%
+we want
+this thing to be low rent environment
+
+ align:start position:0%
+this thing to be low rent environment
+ 
+
+ align:start position:0%
+this thing to be low rent environment
+and symmetric in one and two yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yeah yeah I think it's it's the similar
+
+ align:start position:0%
+yeah yeah I think it's it's the similar
+ 
+
+ align:start position:0%
+yeah yeah I think it's it's the similar
+uh it's the similar idea yeah because
+
+ align:start position:0%
+uh it's the similar idea yeah because
+ 
+
+ align:start position:0%
+uh it's the similar idea yeah because
+the let me see
+
+ align:start position:0%
+the let me see
+ 
+
+ align:start position:0%
+the let me see
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah yeah because essentially you get
+
+ align:start position:0%
+yeah yeah because essentially you get
+ 
+
+ align:start position:0%
+yeah yeah because essentially you get
+rid of that V yeah when you consider the
+
+ align:start position:0%
+rid of that V yeah when you consider the
+ 
+
+ align:start position:0%
+rid of that V yeah when you consider the
+wave package then you get then you get
+
+ align:start position:0%
+wave package then you get then you get
+ 
+
+ align:start position:0%
+wave package then you get then you get
+rid of
+
+ align:start position:0%
+rid of
+ 
+
+ align:start position:0%
+rid of
+then you get rid of this V yeah and then
+
+ align:start position:0%
+then you get rid of this V yeah and then
+ 
+
+ align:start position:0%
+then you get rid of this V yeah and then
+and then you also get rid of this V yeah
+
+ align:start position:0%
+and then you also get rid of this V yeah
+ 
+
+ align:start position:0%
+and then you also get rid of this V yeah
+yeah so you just get rid of the B one
+
+ align:start position:0%
+yeah so you just get rid of the B one
+ 
+
+ align:start position:0%
+yeah so you just get rid of the B one
+upstairs and went downstairs yeah that's
+
+ align:start position:0%
+upstairs and went downstairs yeah that's
+ 
+
+ align:start position:0%
+upstairs and went downstairs yeah that's
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now we want to write this in the
+
+ align:start position:0%
+so so now we want to write this in the
+ 
+
+ align:start position:0%
+so so now we want to write this in the
+Lorenz rents are in the form so so this
+
+ align:start position:0%
+Lorenz rents are in the form so so this
+ 
+
+ align:start position:0%
+Lorenz rents are in the form so so this
+is uh emphasize this is in the rest
+
+ align:start position:0%
+is uh emphasize this is in the rest
+ 
+
+ align:start position:0%
+is uh emphasize this is in the rest
+frame of two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now I look for object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now I want to look for object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which I will call Sigma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sigma
+
+ align:start position:0%
+the sigma
+ 
+
+ align:start position:0%
+the sigma
+is low renting warrant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah Sigma yeah let me write here Sigma
+
+ align:start position:0%
+yeah Sigma yeah let me write here Sigma
+ 
+
+ align:start position:0%
+yeah Sigma yeah let me write here Sigma
+is low renting warrant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the symmetric
+
+ align:start position:0%
+and the symmetric
+ 
+
+ align:start position:0%
+and the symmetric
+in one and two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in the rest frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of two
+
+ align:start position:0%
+of two
+ 
+
+ align:start position:0%
+of two
+then the sigma become this downstairs
+
+ align:start position:0%
+then the sigma become this downstairs
+ 
+
+ align:start position:0%
+then the sigma become this downstairs
+become this E1 E2 times V1
+
+ align:start position:0%
+become this E1 E2 times V1
+ 
+
+ align:start position:0%
+become this E1 E2 times V1
+okay so this is not the Manifest
+
+ align:start position:0%
+okay so this is not the Manifest
+ 
+
+ align:start position:0%
+okay so this is not the Manifest
+laurentine warrant object okay it's also
+
+ align:start position:0%
+laurentine warrant object okay it's also
+ 
+
+ align:start position:0%
+laurentine warrant object okay it's also
+like symmetric in one two
+
+ align:start position:0%
+like symmetric in one two
+ 
+
+ align:start position:0%
+like symmetric in one two
+but I should be able to find the object
+
+ align:start position:0%
+but I should be able to find the object
+ 
+
+ align:start position:0%
+but I should be able to find the object
+Sigma that is by itself is laurentine
+
+ align:start position:0%
+Sigma that is by itself is laurentine
+ 
+
+ align:start position:0%
+Sigma that is by itself is laurentine
+Warren symmetric in one two and in the
+
+ align:start position:0%
+Warren symmetric in one two and in the
+ 
+
+ align:start position:0%
+Warren symmetric in one two and in the
+rest frame of Q reduced to this object
+
+ align:start position:0%
+rest frame of Q reduced to this object
+ 
+
+ align:start position:0%
+rest frame of Q reduced to this object
+okay if I can find this object then I'm
+
+ align:start position:0%
+okay if I can find this object then I'm
+ 
+
+ align:start position:0%
+okay if I can find this object then I'm
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+okay in finding the cross act yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there should be a factor of four yeah
+
+ align:start position:0%
+there should be a factor of four yeah
+ 
+
+ align:start position:0%
+there should be a factor of four yeah
+yeah they should be thank you
+
+ align:start position:0%
+yeah they should be thank you
+ 
+
+ align:start position:0%
+yeah they should be thank you
+yeah yes some other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so I want to look for this object
+
+ align:start position:0%
+good so I want to look for this object
+ 
+
+ align:start position:0%
+good so I want to look for this object
+Sigma okay
+
+ align:start position:0%
+Sigma okay
+ 
+
+ align:start position:0%
+Sigma okay
+and so you can yeah you can do a little
+
+ align:start position:0%
+and so you can yeah you can do a little
+ 
+
+ align:start position:0%
+and so you can yeah you can do a little
+bit trial and arrow to find such a sigma
+
+ align:start position:0%
+bit trial and arrow to find such a sigma
+ 
+
+ align:start position:0%
+bit trial and arrow to find such a sigma
+so I will just write down the answer for
+
+ align:start position:0%
+so I will just write down the answer for
+ 
+
+ align:start position:0%
+so I will just write down the answer for
+you okay and to save the trouble uh
+
+ align:start position:0%
+you okay and to save the trouble uh
+ 
+
+ align:start position:0%
+you okay and to save the trouble uh
+yeah uh um I could have put it in your P
+
+ align:start position:0%
+yeah uh um I could have put it in your P
+ 
+
+ align:start position:0%
+yeah uh um I could have put it in your P
+set but I decided not to do it uh so so
+
+ align:start position:0%
+set but I decided not to do it uh so so
+ 
+
+ align:start position:0%
+set but I decided not to do it uh so so
+turned out the sigma is given by
+
+ align:start position:0%
+turned out the sigma is given by
+ 
+
+ align:start position:0%
+turned out the sigma is given by
+so when you write down the answer it's
+
+ align:start position:0%
+so when you write down the answer it's
+ 
+
+ align:start position:0%
+so when you write down the answer it's
+very simple
+
+ align:start position:0%
+very simple
+ 
+
+ align:start position:0%
+very simple
+you can almost cast it okay uh in the
+
+ align:start position:0%
+you can almost cast it okay uh in the
+ 
+
+ align:start position:0%
+you can almost cast it okay uh in the
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+so it's P1 dot P2
+
+ align:start position:0%
+so it's P1 dot P2
+ 
+
+ align:start position:0%
+so it's P1 dot P2
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+minus M1 squared times M2 squared okay
+
+ align:start position:0%
+minus M1 squared times M2 squared okay
+ 
+
+ align:start position:0%
+minus M1 squared times M2 squared okay
+my Q are the are the mass of the
+
+ align:start position:0%
+my Q are the are the mass of the
+ 
+
+ align:start position:0%
+my Q are the are the mass of the
+particle one okay
+
+ align:start position:0%
+particle one okay
+ 
+
+ align:start position:0%
+particle one okay
+so this object
+
+ align:start position:0%
+so this object
+ 
+
+ align:start position:0%
+so this object
+satisfy these three conditions
+
+ align:start position:0%
+satisfy these three conditions
+ 
+
+ align:start position:0%
+satisfy these three conditions
+okay this objectify this specific
+
+ align:start position:0%
+okay this objectify this specific
+ 
+
+ align:start position:0%
+okay this objectify this specific
+conditions also I will leave the
+
+ align:start position:0%
+conditions also I will leave the
+ 
+
+ align:start position:0%
+conditions also I will leave the
+exercise for yourself to check it okay
+
+ align:start position:0%
+exercise for yourself to check it okay
+ 
+
+ align:start position:0%
+exercise for yourself to check it okay
+it's very easy to check it so you just
+
+ align:start position:0%
+it's very easy to check it so you just
+ 
+
+ align:start position:0%
+it's very easy to check it so you just
+go to the right frame of Q and then you
+
+ align:start position:0%
+go to the right frame of Q and then you
+ 
+
+ align:start position:0%
+go to the right frame of Q and then you
+can check this reduced to that okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so now we almost have our final
+
+ align:start position:0%
+good so now we almost have our final
+ 
+
+ align:start position:0%
+good so now we almost have our final
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+for the cross action
+
+ align:start position:0%
+for the cross action
+ 
+
+ align:start position:0%
+for the cross action
+so the D Sigma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for this 2 2N scattering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we just collect our final result
+
+ align:start position:0%
+so now we just collect our final result
+ 
+
+ align:start position:0%
+so now we just collect our final result
+so we have the Sigma Alpha Beta
+
+ align:start position:0%
+so we have the Sigma Alpha Beta
+ 
+
+ align:start position:0%
+so we have the Sigma Alpha Beta
+9 is equal to
+
+ align:start position:0%
+9 is equal to
+ 
+
+ align:start position:0%
+9 is equal to
+m alpha beta Square
+
+ align:start position:0%
+m alpha beta Square
+ 
+
+ align:start position:0%
+m alpha beta Square
+D mu divided by 4
+
+ align:start position:0%
+D mu divided by 4
+ 
+
+ align:start position:0%
+D mu divided by 4
+Sigma
+
+ align:start position:0%
+Sigma
+ 
+
+ align:start position:0%
+Sigma
+okay just T mu
+
+ align:start position:0%
+okay just T mu
+ 
+
+ align:start position:0%
+okay just T mu
+okay so this is just our final answer
+
+ align:start position:0%
+okay so this is just our final answer
+ 
+
+ align:start position:0%
+okay so this is just our final answer
+and the sigma is given by that guy okay
+
+ align:start position:0%
+and the sigma is given by that guy okay
+ 
+
+ align:start position:0%
+and the sigma is given by that guy okay
+a capital Sigma just given by that guy
+
+ align:start position:0%
+a capital Sigma just given by that guy
+ 
+
+ align:start position:0%
+a capital Sigma just given by that guy
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so this is Manifesto renting warrant
+
+ align:start position:0%
+and so this is Manifesto renting warrant
+ 
+
+ align:start position:0%
+and so this is Manifesto renting warrant
+and the magnitude is symmetric on the
+
+ align:start position:0%
+and the magnitude is symmetric on the
+ 
+
+ align:start position:0%
+and the magnitude is symmetric on the
+one and two
+
+ align:start position:0%
+one and two
+ 
+
+ align:start position:0%
+one and two
+okay because Sigma is obviously
+
+ align:start position:0%
+okay because Sigma is obviously
+ 
+
+ align:start position:0%
+okay because Sigma is obviously
+symmetric on the one two
+
+ align:start position:0%
+symmetric on the one two
+ 
+
+ align:start position:0%
+symmetric on the one two
+okay and yeah
+
+ align:start position:0%
+okay and yeah
+ 
+
+ align:start position:0%
+okay and yeah
+and this is a very beautiful formula
+
+ align:start position:0%
+and this is a very beautiful formula
+ 
+
+ align:start position:0%
+and this is a very beautiful formula
+okay a um will be Burns through a lot of
+
+ align:start position:0%
+okay a um will be Burns through a lot of
+ 
+
+ align:start position:0%
+okay a um will be Burns through a lot of
+trouble
+
+ align:start position:0%
+trouble
+ 
+
+ align:start position:0%
+trouble
+I've been through a lot of v's and T's
+
+ align:start position:0%
+I've been through a lot of v's and T's
+ 
+
+ align:start position:0%
+I've been through a lot of v's and T's
+but but in the end we get a very
+
+ align:start position:0%
+but but in the end we get a very
+ 
+
+ align:start position:0%
+but but in the end we get a very
+beautiful answer okay
+
+ align:start position:0%
+beautiful answer okay
+ 
+
+ align:start position:0%
+beautiful answer okay
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so now let's consider some kinematic
+
+ align:start position:0%
+so now let's consider some kinematic
+ 
+
+ align:start position:0%
+so now let's consider some kinematic
+regimes of this formula
+
+ align:start position:0%
+regimes of this formula
+ 
+
+ align:start position:0%
+regimes of this formula
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so now let's talk about some
+
+ align:start position:0%
+so so now let's talk about some
+ 
+
+ align:start position:0%
+so so now let's talk about some
+kinematics of this formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so
+
+ align:start position:0%
+so so
+ 
+
+ align:start position:0%
+so so
+it's convenient so we have two particles
+
+ align:start position:0%
+it's convenient so we have two particles
+ 
+
+ align:start position:0%
+it's convenient so we have two particles
+two initial particles it's convenient to
+
+ align:start position:0%
+two initial particles it's convenient to
+ 
+
+ align:start position:0%
+two initial particles it's convenient to
+introduce the center of mass energy
+
+ align:start position:0%
+introduce the center of mass energy
+ 
+
+ align:start position:0%
+introduce the center of mass energy
+for the um for the um for the full
+
+ align:start position:0%
+for the um for the um for the full
+ 
+
+ align:start position:0%
+for the um for the um for the full
+system so so we can define something
+
+ align:start position:0%
+system so so we can define something
+ 
+
+ align:start position:0%
+system so so we can define something
+called s small s okay this is not big S
+
+ align:start position:0%
+called s small s okay this is not big S
+ 
+
+ align:start position:0%
+called s small s okay this is not big S
+so big S is reserved to action so this
+
+ align:start position:0%
+so big S is reserved to action so this
+ 
+
+ align:start position:0%
+so big S is reserved to action so this
+is small s
+
+ align:start position:0%
+is small s
+ 
+
+ align:start position:0%
+is small s
+P1 plus P2 squared
+
+ align:start position:0%
+P1 plus P2 squared
+ 
+
+ align:start position:0%
+P1 plus P2 squared
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so
+
+ align:start position:0%
+so so
+ 
+
+ align:start position:0%
+so so
+P1 and the plus P2 is like the total
+
+ align:start position:0%
+P1 and the plus P2 is like the total
+ 
+
+ align:start position:0%
+P1 and the plus P2 is like the total
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+of the initial state of course it's also
+
+ align:start position:0%
+of the initial state of course it's also
+ 
+
+ align:start position:0%
+of the initial state of course it's also
+total momentum of your fellow States uh
+
+ align:start position:0%
+total momentum of your fellow States uh
+ 
+
+ align:start position:0%
+total momentum of your fellow States uh
+uh just from the momentum conservation
+
+ align:start position:0%
+uh just from the momentum conservation
+ 
+
+ align:start position:0%
+uh just from the momentum conservation
+and today if I look at P1 and P2 Square
+
+ align:start position:0%
+and today if I look at P1 and P2 Square
+ 
+
+ align:start position:0%
+and today if I look at P1 and P2 Square
+and then this is just essentially the
+
+ align:start position:0%
+and then this is just essentially the
+ 
+
+ align:start position:0%
+and then this is just essentially the
+Umar in Mass
+
+ align:start position:0%
+Umar in Mass
+ 
+
+ align:start position:0%
+Umar in Mass
+for your uh uh uh for uh for your full
+
+ align:start position:0%
+for your uh uh uh for uh for your full
+ 
+
+ align:start position:0%
+for your uh uh uh for uh for your full
+full system okay
+
+ align:start position:0%
+full system okay
+ 
+
+ align:start position:0%
+full system okay
+so so this s is the so square root S
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the invariant mass is the effective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mass
+
+ align:start position:0%
+Mass
+ 
+
+ align:start position:0%
+Mass
+of the whole system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah of this the when I say the whole
+
+ align:start position:0%
+yeah of this the when I say the whole
+ 
+
+ align:start position:0%
+yeah of this the when I say the whole
+system I just mean the whole system
+
+ align:start position:0%
+system I just mean the whole system
+ 
+
+ align:start position:0%
+system I just mean the whole system
+or or particle one particle two and also
+
+ align:start position:0%
+or or particle one particle two and also
+ 
+
+ align:start position:0%
+or or particle one particle two and also
+the fellow States okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can also write the sigma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+turned out we can actually write Sigma
+
+ align:start position:0%
+turned out we can actually write Sigma
+ 
+
+ align:start position:0%
+turned out we can actually write Sigma
+in terms of s
+
+ align:start position:0%
+in terms of s
+ 
+
+ align:start position:0%
+in terms of s
+because the um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh because P1 dot P2
+
+ align:start position:0%
+so uh because P1 dot P2
+ 
+
+ align:start position:0%
+so uh because P1 dot P2
+can be written as one half
+
+ align:start position:0%
+can be written as one half
+ 
+
+ align:start position:0%
+can be written as one half
+P1 plus P2 Square minus
+
+ align:start position:0%
+P1 plus P2 Square minus
+ 
+
+ align:start position:0%
+P1 plus P2 Square minus
+P1 Square minus P2 squared
+
+ align:start position:0%
+P1 Square minus P2 squared
+ 
+
+ align:start position:0%
+P1 Square minus P2 squared
+foreign
+
+ align:start position:0%
+foreign
+ 
+
+ align:start position:0%
+foreign
+so this is just m Square so P1 squared
+
+ align:start position:0%
+so this is just m Square so P1 squared
+ 
+
+ align:start position:0%
+so this is just m Square so P1 squared
+just minus M1 squared P2 squared just
+
+ align:start position:0%
+just minus M1 squared P2 squared just
+ 
+
+ align:start position:0%
+just minus M1 squared P2 squared just
+minus M2 squared so this is just equal
+
+ align:start position:0%
+minus M2 squared so this is just equal
+ 
+
+ align:start position:0%
+minus M2 squared so this is just equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+minus one half
+
+ align:start position:0%
+minus one half
+ 
+
+ align:start position:0%
+minus one half
+okay as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+should be totaled
+
+ align:start position:0%
+should be totaled
+ 
+
+ align:start position:0%
+should be totaled
+s minus and one square minus M2 squared
+
+ align:start position:0%
+s minus and one square minus M2 squared
+ 
+
+ align:start position:0%
+s minus and one square minus M2 squared
+okay so so P1 p 2 squared just equal to
+
+ align:start position:0%
+okay so so P1 p 2 squared just equal to
+ 
+
+ align:start position:0%
+okay so so P1 p 2 squared just equal to
+minus s okay
+
+ align:start position:0%
+minus s okay
+ 
+
+ align:start position:0%
+minus s okay
+and then then then then then the sigma
+
+ align:start position:0%
+and then then then then then the sigma
+ 
+
+ align:start position:0%
+and then then then then then the sigma
+just then just can be expressed in terms
+
+ align:start position:0%
+just then just can be expressed in terms
+ 
+
+ align:start position:0%
+just then just can be expressed in terms
+of that okay
+
+ align:start position:0%
+of that okay
+ 
+
+ align:start position:0%
+of that okay
+so the sigma so let me just write down
+
+ align:start position:0%
+so the sigma so let me just write down
+ 
+
+ align:start position:0%
+so the sigma so let me just write down
+the final expression for the sigma
+
+ align:start position:0%
+the final expression for the sigma
+ 
+
+ align:start position:0%
+the final expression for the sigma
+in terms of s just equal to square root
+
+ align:start position:0%
+in terms of s just equal to square root
+ 
+
+ align:start position:0%
+in terms of s just equal to square root
+s Square
+
+ align:start position:0%
+s Square
+ 
+
+ align:start position:0%
+s Square
+to s
+
+ align:start position:0%
+to s
+ 
+
+ align:start position:0%
+to s
+and Y squared plus M2 Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus 1 squared minus M2 squared
+
+ align:start position:0%
+plus 1 squared minus M2 squared
+ 
+
+ align:start position:0%
+plus 1 squared minus M2 squared
+squared okay so I'll show you so the so
+
+ align:start position:0%
+squared okay so I'll show you so the so
+ 
+
+ align:start position:0%
+squared okay so I'll show you so the so
+so this whole kinematic factor of Sigma
+
+ align:start position:0%
+so this whole kinematic factor of Sigma
+ 
+
+ align:start position:0%
+so this whole kinematic factor of Sigma
+can be just expressed in terms of s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's uh around the thing
+
+ align:start position:0%
+so now let's uh around the thing
+ 
+
+ align:start position:0%
+so now let's uh around the thing
+he said often we are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's yeah even though this formula is
+
+ align:start position:0%
+it's yeah even though this formula is
+ 
+
+ align:start position:0%
+it's yeah even though this formula is
+can be used in any frame
+
+ align:start position:0%
+can be used in any frame
+ 
+
+ align:start position:0%
+can be used in any frame
+but sometimes depending on your question
+
+ align:start position:0%
+but sometimes depending on your question
+ 
+
+ align:start position:0%
+but sometimes depending on your question
+the the extraction is simply in some
+
+ align:start position:0%
+the the extraction is simply in some
+ 
+
+ align:start position:0%
+the the extraction is simply in some
+frame than some other frame okay so so
+
+ align:start position:0%
+frame than some other frame okay so so
+ 
+
+ align:start position:0%
+frame than some other frame okay so so
+one of the very frequently used frame is
+
+ align:start position:0%
+one of the very frequently used frame is
+ 
+
+ align:start position:0%
+one of the very frequently used frame is
+so called the center of Mass frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's called the center of Mass frame so
+
+ align:start position:0%
+it's called the center of Mass frame so
+ 
+
+ align:start position:0%
+it's called the center of Mass frame so
+in the sense of match frame
+
+ align:start position:0%
+in the sense of match frame
+ 
+
+ align:start position:0%
+in the sense of match frame
+so the Central Mass frame essentially
+
+ align:start position:0%
+so the Central Mass frame essentially
+ 
+
+ align:start position:0%
+so the Central Mass frame essentially
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+he said in this Frame
+
+ align:start position:0%
+he said in this Frame
+ 
+
+ align:start position:0%
+he said in this Frame
+that the uh the total Center of mass of
+
+ align:start position:0%
+that the uh the total Center of mass of
+ 
+
+ align:start position:0%
+that the uh the total Center of mass of
+the system does not move okay so means
+
+ align:start position:0%
+the system does not move okay so means
+ 
+
+ align:start position:0%
+the system does not move okay so means
+that the total momentum
+
+ align:start position:0%
+that the total momentum
+ 
+
+ align:start position:0%
+that the total momentum
+in the center of Mass frame total
+
+ align:start position:0%
+in the center of Mass frame total
+ 
+
+ align:start position:0%
+in the center of Mass frame total
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+let me see
+
+ align:start position:0%
+let me see
+ 
+
+ align:start position:0%
+let me see
+the total momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal to P1 and P2 is taken to be zero
+
+ align:start position:0%
+equal to P1 and P2 is taken to be zero
+ 
+
+ align:start position:0%
+equal to P1 and P2 is taken to be zero
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so the whole part so the full system
+
+ align:start position:0%
+so so the whole part so the full system
+ 
+
+ align:start position:0%
+so so the whole part so the full system
+is not moving
+
+ align:start position:0%
+is not moving
+ 
+
+ align:start position:0%
+is not moving
+and so that means we can take some means
+
+ align:start position:0%
+and so that means we can take some means
+ 
+
+ align:start position:0%
+and so that means we can take some means
+at p y equal to minus P2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so you could tune let's call it PCM
+
+ align:start position:0%
+so so you could tune let's call it PCM
+ 
+
+ align:start position:0%
+so so you could tune let's call it PCM
+okay it just means the center of mass
+
+ align:start position:0%
+okay it just means the center of mass
+ 
+
+ align:start position:0%
+okay it just means the center of mass
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now you can uh you can find the PCM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from from just solving the
+
+ align:start position:0%
+from from just solving the
+ 
+
+ align:start position:0%
+from from just solving the
+yeah say you can also Express the PCM in
+
+ align:start position:0%
+yeah say you can also Express the PCM in
+ 
+
+ align:start position:0%
+yeah say you can also Express the PCM in
+terms of the mass
+
+ align:start position:0%
+terms of the mass
+ 
+
+ align:start position:0%
+terms of the mass
+is because E1
+
+ align:start position:0%
+is because E1
+ 
+
+ align:start position:0%
+is because E1
+plus E2
+
+ align:start position:0%
+plus E2
+ 
+
+ align:start position:0%
+plus E2
+equal to square root S
+
+ align:start position:0%
+equal to square root S
+ 
+
+ align:start position:0%
+equal to square root S
+okay so this is the total so so in the
+
+ align:start position:0%
+okay so this is the total so so in the
+ 
+
+ align:start position:0%
+okay so this is the total so so in the
+Central Mass frame
+
+ align:start position:0%
+Central Mass frame
+ 
+
+ align:start position:0%
+Central Mass frame
+the total momentum is zero okay then
+
+ align:start position:0%
+the total momentum is zero okay then
+ 
+
+ align:start position:0%
+the total momentum is zero okay then
+then that means that each E1 and E2
+
+ align:start position:0%
+then that means that each E1 and E2
+ 
+
+ align:start position:0%
+then that means that each E1 and E2
+okay so so here there's no no spatial
+
+ align:start position:0%
+okay so so here there's no no spatial
+ 
+
+ align:start position:0%
+okay so so here there's no no spatial
+part contribution and here just have E1
+
+ align:start position:0%
+part contribution and here just have E1
+ 
+
+ align:start position:0%
+part contribution and here just have E1
+plus E2 squared equal to S okay so U1
+
+ align:start position:0%
+plus E2 squared equal to S okay so U1
+ 
+
+ align:start position:0%
+plus E2 squared equal to S okay so U1
+plus E2 equal to square root this
+
+ align:start position:0%
+plus E2 equal to square root this
+ 
+
+ align:start position:0%
+plus E2 equal to square root this
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then you can actually solve
+
+ align:start position:0%
+and then you can actually solve
+ 
+
+ align:start position:0%
+and then you can actually solve
+for the uh for p
+
+ align:start position:0%
+for the uh for p
+ 
+
+ align:start position:0%
+for the uh for p
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus M1 squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus mq Square equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+square root S
+
+ align:start position:0%
+square root S
+ 
+
+ align:start position:0%
+square root S
+okay so you now can now solve the uh
+
+ align:start position:0%
+okay so you now can now solve the uh
+ 
+
+ align:start position:0%
+okay so you now can now solve the uh
+signal mass in terms of s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when you so this is a simple equation
+
+ align:start position:0%
+so when you so this is a simple equation
+ 
+
+ align:start position:0%
+so when you so this is a simple equation
+which you can solve okay
+
+ align:start position:0%
+which you can solve okay
+ 
+
+ align:start position:0%
+which you can solve okay
+so this is a a a middle school equation
+
+ align:start position:0%
+so this is a a a middle school equation
+ 
+
+ align:start position:0%
+so this is a a a middle school equation
+but the result is very simple
+
+ align:start position:0%
+but the result is very simple
+ 
+
+ align:start position:0%
+but the result is very simple
+turns out
+
+ align:start position:0%
+turns out
+ 
+
+ align:start position:0%
+turns out
+the PCM
+
+ align:start position:0%
+the PCM
+ 
+
+ align:start position:0%
+the PCM
+the magnitude okay
+
+ align:start position:0%
+the magnitude okay
+ 
+
+ align:start position:0%
+the magnitude okay
+when you solve this equation
+
+ align:start position:0%
+when you solve this equation
+ 
+
+ align:start position:0%
+when you solve this equation
+you find this is precisely equal to
+
+ align:start position:0%
+you find this is precisely equal to
+ 
+
+ align:start position:0%
+you find this is precisely equal to
+this Sigma
+
+ align:start position:0%
+this Sigma
+ 
+
+ align:start position:0%
+this Sigma
+divided by square root S okay so this is
+
+ align:start position:0%
+divided by square root S okay so this is
+ 
+
+ align:start position:0%
+divided by square root S okay so this is
+a very beautiful simple formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given by Sigma divided by square root S
+
+ align:start position:0%
+given by Sigma divided by square root S
+ 
+
+ align:start position:0%
+given by Sigma divided by square root S
+or in other words the sigma can be
+
+ align:start position:0%
+or in other words the sigma can be
+ 
+
+ align:start position:0%
+or in other words the sigma can be
+written in terms of Center Mass momentum
+
+ align:start position:0%
+written in terms of Center Mass momentum
+ 
+
+ align:start position:0%
+written in terms of Center Mass momentum
+the magnitude times the square root S
+
+ align:start position:0%
+the magnitude times the square root S
+ 
+
+ align:start position:0%
+the magnitude times the square root S
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Times Square of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we can simplify
+
+ align:start position:0%
+so now we can simplify
+ 
+
+ align:start position:0%
+so now we can simplify
+that the expression in Central Mass
+
+ align:start position:0%
+that the expression in Central Mass
+ 
+
+ align:start position:0%
+that the expression in Central Mass
+frame
+
+ align:start position:0%
+frame
+ 
+
+ align:start position:0%
+frame
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so in the center of Mass frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we have in the center of mass
+
+ align:start position:0%
+now we have in the center of mass
+ 
+
+ align:start position:0%
+now we have in the center of mass
+frame
+
+ align:start position:0%
+frame
+ 
+
+ align:start position:0%
+frame
+now we have the sigma
+
+ align:start position:0%
+now we have the sigma
+ 
+
+ align:start position:0%
+now we have the sigma
+is equal to so let me just save the yeah
+
+ align:start position:0%
+is equal to so let me just save the yeah
+ 
+
+ align:start position:0%
+is equal to so let me just save the yeah
+just you should assume that the
+
+ align:start position:0%
+just you should assume that the
+ 
+
+ align:start position:0%
+just you should assume that the
+subscript Alpha to Beta
+
+ align:start position:0%
+subscript Alpha to Beta
+ 
+
+ align:start position:0%
+subscript Alpha to Beta
+the MU
+
+ align:start position:0%
+the MU
+ 
+
+ align:start position:0%
+the MU
+and then divided by 4
+
+ align:start position:0%
+and then divided by 4
+ 
+
+ align:start position:0%
+and then divided by 4
+Center of mass momentum magnitude of
+
+ align:start position:0%
+Center of mass momentum magnitude of
+ 
+
+ align:start position:0%
+Center of mass momentum magnitude of
+Central Mass of momentum Times Square
+
+ align:start position:0%
+Central Mass of momentum Times Square
+ 
+
+ align:start position:0%
+Central Mass of momentum Times Square
+Root s
+
+ align:start position:0%
+Root s
+ 
+
+ align:start position:0%
+Root s
+okay so we have a
+
+ align:start position:0%
+okay so we have a
+ 
+
+ align:start position:0%
+okay so we have a
+very simple formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the most of the time
+
+ align:start position:0%
+so the most of the time
+ 
+
+ align:start position:0%
+so the most of the time
+for most questions we are interested in
+
+ align:start position:0%
+for most questions we are interested in
+ 
+
+ align:start position:0%
+for most questions we are interested in
+as you will see
+
+ align:start position:0%
+as you will see
+ 
+
+ align:start position:0%
+as you will see
+in next lecture
+
+ align:start position:0%
+in next lecture
+ 
+
+ align:start position:0%
+in next lecture
+so most questions very interesting x
+
+ align:start position:0%
+so most questions very interesting x
+ 
+
+ align:start position:0%
+so most questions very interesting x
+equals one into two scattering so now
+
+ align:start position:0%
+equals one into two scattering so now
+ 
+
+ align:start position:0%
+equals one into two scattering so now
+let's specify uh two two two scatterings
+
+ align:start position:0%
+let's specify uh two two two scatterings
+ 
+
+ align:start position:0%
+let's specify uh two two two scatterings
+so the final state only also only
+
+ align:start position:0%
+so the final state only also only
+ 
+
+ align:start position:0%
+so the final state only also only
+contain two particles okay
+
+ align:start position:0%
+contain two particles okay
+ 
+
+ align:start position:0%
+contain two particles okay
+so so in this case we can simplify the D
+
+ align:start position:0%
+so so in this case we can simplify the D
+ 
+
+ align:start position:0%
+so so in this case we can simplify the D
+mu okay for the simplify T mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so so let's just write down the so in
+
+ align:start position:0%
+so so so let's just write down the so in
+ 
+
+ align:start position:0%
+so so so let's just write down the so in
+2D2 scattering essentially you have
+
+ align:start position:0%
+2D2 scattering essentially you have
+ 
+
+ align:start position:0%
+2D2 scattering essentially you have
+some particle come in
+
+ align:start position:0%
+some particle come in
+ 
+
+ align:start position:0%
+some particle come in
+say P1
+
+ align:start position:0%
+say P1
+ 
+
+ align:start position:0%
+say P1
+P2
+
+ align:start position:0%
+P2
+ 
+
+ align:start position:0%
+P2
+and then you have two phyllo particle K1
+
+ align:start position:0%
+and then you have two phyllo particle K1
+ 
+
+ align:start position:0%
+and then you have two phyllo particle K1
+and K2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then the intact okay
+
+ align:start position:0%
+okay and then the intact okay
+ 
+
+ align:start position:0%
+okay and then the intact okay
+intact
+
+ align:start position:0%
+intact
+ 
+
+ align:start position:0%
+intact
+so so now let's write down this the MU
+
+ align:start position:0%
+so so now let's write down this the MU
+ 
+
+ align:start position:0%
+so so now let's write down this the MU
+explicitly for this case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's write down the MU explicit for
+
+ align:start position:0%
+let's write down the MU explicit for
+ 
+
+ align:start position:0%
+let's write down the MU explicit for
+this case
+
+ align:start position:0%
+this case
+ 
+
+ align:start position:0%
+this case
+so the D mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is given by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so P1 plus P2 minus K1 minus K2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+D3 K1
+
+ align:start position:0%
+D3 K1
+ 
+
+ align:start position:0%
+D3 K1
+divided by 2 pi Cube
+
+ align:start position:0%
+divided by 2 pi Cube
+ 
+
+ align:start position:0%
+divided by 2 pi Cube
+q k 1 0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah let's just call q1 k0 E1 Prime
+
+ align:start position:0%
+yeah let's just call q1 k0 E1 Prime
+ 
+
+ align:start position:0%
+yeah let's just call q1 k0 E1 Prime
+and the D3 okay
+
+ align:start position:0%
+and the D3 okay
+ 
+
+ align:start position:0%
+and the D3 okay
+q q Pi Q
+
+ align:start position:0%
+q q Pi Q
+ 
+
+ align:start position:0%
+q q Pi Q
+then QE2 Prime
+
+ align:start position:0%
+then QE2 Prime
+ 
+
+ align:start position:0%
+then QE2 Prime
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the so the One Prime and in two prime
+
+ align:start position:0%
+so the so the One Prime and in two prime
+ 
+
+ align:start position:0%
+so the so the One Prime and in two prime
+they are just energy for K1 and K2 so E1
+
+ align:start position:0%
+they are just energy for K1 and K2 so E1
+ 
+
+ align:start position:0%
+they are just energy for K1 and K2 so E1
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+K one zero
+
+ align:start position:0%
+K one zero
+ 
+
+ align:start position:0%
+K one zero
+C2 Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah for example yeah so
+
+ align:start position:0%
+yeah for example yeah so
+ 
+
+ align:start position:0%
+yeah for example yeah so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so I will deload to the the mass
+
+ align:start position:0%
+yeah so I will deload to the the mass
+ 
+
+ align:start position:0%
+yeah so I will deload to the the mass
+for the two fellow particles M1 Prime
+
+ align:start position:0%
+for the two fellow particles M1 Prime
+ 
+
+ align:start position:0%
+for the two fellow particles M1 Prime
+and M2 Prime okay
+
+ align:start position:0%
+and M2 Prime okay
+ 
+
+ align:start position:0%
+and M2 Prime okay
+so I'm Prime two prime will be the mass
+
+ align:start position:0%
+so I'm Prime two prime will be the mass
+ 
+
+ align:start position:0%
+so I'm Prime two prime will be the mass
+of the two final particles okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so before simplify this uh a little bit
+
+ align:start position:0%
+so before simplify this uh a little bit
+ 
+
+ align:start position:0%
+so before simplify this uh a little bit
+further
+
+ align:start position:0%
+further
+ 
+
+ align:start position:0%
+further
+let us first introduce some notations
+
+ align:start position:0%
+let us first introduce some notations
+ 
+
+ align:start position:0%
+let us first introduce some notations
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so it's often convenient so many of you
+
+ align:start position:0%
+so it's often convenient so many of you
+ 
+
+ align:start position:0%
+so it's often convenient so many of you
+may have already seen this before
+
+ align:start position:0%
+may have already seen this before
+ 
+
+ align:start position:0%
+may have already seen this before
+often convenient to introduce
+
+ align:start position:0%
+often convenient to introduce
+ 
+
+ align:start position:0%
+often convenient to introduce
+the following quantities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so essentially they characterize all the
+
+ align:start position:0%
+so essentially they characterize all the
+ 
+
+ align:start position:0%
+so essentially they characterize all the
+low renting warrants quantities we can
+
+ align:start position:0%
+low renting warrants quantities we can
+ 
+
+ align:start position:0%
+low renting warrants quantities we can
+build up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from uh from
+
+ align:start position:0%
+from uh from
+ 
+
+ align:start position:0%
+from uh from
+P1 P2 K1 K2 okay so you can have
+
+ align:start position:0%
+P1 P2 K1 K2 okay so you can have
+ 
+
+ align:start position:0%
+P1 P2 K1 K2 okay so you can have
+so-called t
+
+ align:start position:0%
+so-called t
+ 
+
+ align:start position:0%
+so-called t
+is defined to be minus P1 minus K1
+
+ align:start position:0%
+is defined to be minus P1 minus K1
+ 
+
+ align:start position:0%
+is defined to be minus P1 minus K1
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+which is also the same from the momentum
+
+ align:start position:0%
+which is also the same from the momentum
+ 
+
+ align:start position:0%
+which is also the same from the momentum
+conversation P2 minus K2 Square
+
+ align:start position:0%
+conversation P2 minus K2 Square
+ 
+
+ align:start position:0%
+conversation P2 minus K2 Square
+so U
+
+ align:start position:0%
+so U
+ 
+
+ align:start position:0%
+so U
+minus P1 minus K2 Square
+
+ align:start position:0%
+minus P1 minus K2 Square
+ 
+
+ align:start position:0%
+minus P1 minus K2 Square
+same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus PQ minus K1 squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so so so let me just copy the S okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P1
+
+ align:start position:0%
+P1
+ 
+
+ align:start position:0%
+P1
+P2 Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so these are the quantities
+
+ align:start position:0%
+so so these are the quantities
+ 
+
+ align:start position:0%
+so so these are the quantities
+we are obviously already weren't
+
+ align:start position:0%
+we are obviously already weren't
+ 
+
+ align:start position:0%
+we are obviously already weren't
+and they are the low renting warrant you
+
+ align:start position:0%
+and they are the low renting warrant you
+ 
+
+ align:start position:0%
+and they are the low renting warrant you
+can build up
+
+ align:start position:0%
+can build up
+ 
+
+ align:start position:0%
+can build up
+the range environment quantities you can
+
+ align:start position:0%
+the range environment quantities you can
+ 
+
+ align:start position:0%
+the range environment quantities you can
+build up from say a P1 P2 K1 K2 okay so
+
+ align:start position:0%
+build up from say a P1 P2 K1 K2 okay so
+ 
+
+ align:start position:0%
+build up from say a P1 P2 K1 K2 okay so
+so any low range environment quantities
+
+ align:start position:0%
+so any low range environment quantities
+ 
+
+ align:start position:0%
+so any low range environment quantities
+which you can build from those
+
+ align:start position:0%
+which you can build from those
+ 
+
+ align:start position:0%
+which you can build from those
+four momentum
+
+ align:start position:0%
+four momentum
+ 
+
+ align:start position:0%
+four momentum
+can be expressed in terms of some
+
+ align:start position:0%
+can be expressed in terms of some
+ 
+
+ align:start position:0%
+can be expressed in terms of some
+combinations of Stu okay
+
+ align:start position:0%
+combinations of Stu okay
+ 
+
+ align:start position:0%
+combinations of Stu okay
+in fact Stu themselves a lot independent
+
+ align:start position:0%
+in fact Stu themselves a lot independent
+ 
+
+ align:start position:0%
+in fact Stu themselves a lot independent
+of each other there's only two
+
+ align:start position:0%
+of each other there's only two
+ 
+
+ align:start position:0%
+of each other there's only two
+independent Lowrance environments this
+
+ align:start position:0%
+independent Lowrance environments this
+ 
+
+ align:start position:0%
+independent Lowrance environments this
+momentum connotation the only two are
+
+ align:start position:0%
+momentum connotation the only two are
+ 
+
+ align:start position:0%
+momentum connotation the only two are
+independent or range environment you can
+
+ align:start position:0%
+independent or range environment you can
+ 
+
+ align:start position:0%
+independent or range environment you can
+introduce so so s plus T and the plus u
+
+ align:start position:0%
+introduce so so s plus T and the plus u
+ 
+
+ align:start position:0%
+introduce so so s plus T and the plus u
+it's actually not independent of each
+
+ align:start position:0%
+it's actually not independent of each
+ 
+
+ align:start position:0%
+it's actually not independent of each
+other you can show
+
+ align:start position:0%
+other you can show
+ 
+
+ align:start position:0%
+other you can show
+so this again I give you the exercise
+
+ align:start position:0%
+so this again I give you the exercise
+ 
+
+ align:start position:0%
+so this again I give you the exercise
+for yourself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can show that okay
+
+ align:start position:0%
+you can show that okay
+ 
+
+ align:start position:0%
+you can show that okay
+so if you load any of the two then you
+
+ align:start position:0%
+so if you load any of the two then you
+ 
+
+ align:start position:0%
+so if you load any of the two then you
+load the S you load the the other one
+
+ align:start position:0%
+load the S you load the the other one
+ 
+
+ align:start position:0%
+load the S you load the the other one
+and any anything can be expressed in
+
+ align:start position:0%
+and any anything can be expressed in
+ 
+
+ align:start position:0%
+and any anything can be expressed in
+terms of this uh uh uh this variable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do you mean how today
+
+ align:start position:0%
+what do you mean how today
+ 
+
+ align:start position:0%
+what do you mean how today
+oh yeah yeah then your family guidelines
+
+ align:start position:0%
+oh yeah yeah then your family guidelines
+ 
+
+ align:start position:0%
+oh yeah yeah then your family guidelines
+can be expressing it can be conveniently
+
+ align:start position:0%
+can be expressing it can be conveniently
+ 
+
+ align:start position:0%
+can be expressing it can be conveniently
+expressed in terms of them yeah as we
+
+ align:start position:0%
+expressed in terms of them yeah as we
+ 
+
+ align:start position:0%
+expressed in terms of them yeah as we
+will see next lecture and in homework
+
+ align:start position:0%
+will see next lecture and in homework
+ 
+
+ align:start position:0%
+will see next lecture and in homework
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah just uh
+
+ align:start position:0%
+yeah just uh
+ 
+
+ align:start position:0%
+yeah just uh
+so this quantity will be this quantity
+
+ align:start position:0%
+so this quantity will be this quantity
+ 
+
+ align:start position:0%
+so this quantity will be this quantity
+is low renting warrant
+
+ align:start position:0%
+is low renting warrant
+ 
+
+ align:start position:0%
+is low renting warrant
+so that can be conveniently expressed in
+
+ align:start position:0%
+so that can be conveniently expressed in
+ 
+
+ align:start position:0%
+so that can be conveniently expressed in
+terms of those quantities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so now yeah yeah including the demu
+
+ align:start position:0%
+so so now yeah yeah including the demu
+ 
+
+ align:start position:0%
+so so now yeah yeah including the demu
+okay the MU or uh yeah
+
+ align:start position:0%
+okay the MU or uh yeah
+ 
+
+ align:start position:0%
+okay the MU or uh yeah
+so now let's further simplify the mule
+
+ align:start position:0%
+so now let's further simplify the mule
+ 
+
+ align:start position:0%
+so now let's further simplify the mule
+in the center of Mass frame
+
+ align:start position:0%
+in the center of Mass frame
+ 
+
+ align:start position:0%
+in the center of Mass frame
+okay so this quantity we can try to
+
+ align:start position:0%
+okay so this quantity we can try to
+ 
+
+ align:start position:0%
+okay so this quantity we can try to
+simplify further
+
+ align:start position:0%
+simplify further
+ 
+
+ align:start position:0%
+simplify further
+so we can
+
+ align:start position:0%
+so we can
+ 
+
+ align:start position:0%
+so we can
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to do this in the center of Mass frame
+
+ align:start position:0%
+to do this in the center of Mass frame
+ 
+
+ align:start position:0%
+to do this in the center of Mass frame
+so in the center of Mass frame for 22
+
+ align:start position:0%
+so in the center of Mass frame for 22
+ 
+
+ align:start position:0%
+so in the center of Mass frame for 22
+scattering particularly simple
+
+ align:start position:0%
+scattering particularly simple
+ 
+
+ align:start position:0%
+scattering particularly simple
+because your income in particle have the
+
+ align:start position:0%
+because your income in particle have the
+ 
+
+ align:start position:0%
+because your income in particle have the
+update momentum
+
+ align:start position:0%
+update momentum
+ 
+
+ align:start position:0%
+update momentum
+okay so one is PCM
+
+ align:start position:0%
+okay so one is PCM
+ 
+
+ align:start position:0%
+okay so one is PCM
+and Y is will be minus PCM
+
+ align:start position:0%
+and Y is will be minus PCM
+ 
+
+ align:start position:0%
+and Y is will be minus PCM
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and uh uh a spatial momentum and then
+
+ align:start position:0%
+and uh uh a spatial momentum and then
+ 
+
+ align:start position:0%
+and uh uh a spatial momentum and then
+then the final particle
+
+ align:start position:0%
+then the final particle
+ 
+
+ align:start position:0%
+then the final particle
+they must also have updated momentum
+
+ align:start position:0%
+they must also have updated momentum
+ 
+
+ align:start position:0%
+they must also have updated momentum
+okay because the total momentum total
+
+ align:start position:0%
+okay because the total momentum total
+ 
+
+ align:start position:0%
+okay because the total momentum total
+spatial momentum in the signal match
+
+ align:start position:0%
+spatial momentum in the signal match
+ 
+
+ align:start position:0%
+spatial momentum in the signal match
+frame is zero okay so so this can call
+
+ align:start position:0%
+frame is zero okay so so this can call
+ 
+
+ align:start position:0%
+frame is zero okay so so this can call
+this uh k c n
+
+ align:start position:0%
+this uh k c n
+ 
+
+ align:start position:0%
+this uh k c n
+then this must be minus K cm
+
+ align:start position:0%
+then this must be minus K cm
+ 
+
+ align:start position:0%
+then this must be minus K cm
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+let's be minus KCM okay
+
+ align:start position:0%
+let's be minus KCM okay
+ 
+
+ align:start position:0%
+let's be minus KCM okay
+so so for Simplicity let's just call
+
+ align:start position:0%
+so so for Simplicity let's just call
+ 
+
+ align:start position:0%
+so so for Simplicity let's just call
+this KCM just k
+
+ align:start position:0%
+this KCM just k
+ 
+
+ align:start position:0%
+this KCM just k
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so now we can just uh acknowledge
+
+ align:start position:0%
+so so now we can just uh acknowledge
+ 
+
+ align:start position:0%
+so so now we can just uh acknowledge
+just with this in mind and let's just
+
+ align:start position:0%
+just with this in mind and let's just
+ 
+
+ align:start position:0%
+just with this in mind and let's just
+look at this demu okay
+
+ align:start position:0%
+look at this demu okay
+ 
+
+ align:start position:0%
+look at this demu okay
+look at distribute
+
+ align:start position:0%
+look at distribute
+ 
+
+ align:start position:0%
+look at distribute
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there are a few steps
+
+ align:start position:0%
+so there are a few steps
+ 
+
+ align:start position:0%
+so there are a few steps
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+maybe we don't want to go through all
+
+ align:start position:0%
+maybe we don't want to go through all
+ 
+
+ align:start position:0%
+maybe we don't want to go through all
+the details of these steps
+
+ align:start position:0%
+the details of these steps
+ 
+
+ align:start position:0%
+the details of these steps
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let me see I think
+
+ align:start position:0%
+um let me see I think
+ 
+
+ align:start position:0%
+um let me see I think
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah let me just outline some yeah so so
+
+ align:start position:0%
+yeah let me just outline some yeah so so
+ 
+
+ align:start position:0%
+yeah let me just outline some yeah so so
+we are not
+
+ align:start position:0%
+we are not
+ 
+
+ align:start position:0%
+we are not
+yeah I try to only go through some of
+
+ align:start position:0%
+yeah I try to only go through some of
+ 
+
+ align:start position:0%
+yeah I try to only go through some of
+the uh steps not to say doing all the
+
+ align:start position:0%
+the uh steps not to say doing all the
+ 
+
+ align:start position:0%
+the uh steps not to say doing all the
+steps okay
+
+ align:start position:0%
+steps okay
+ 
+
+ align:start position:0%
+steps okay
+so now in the Central Mass frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you find this the MU can be written
+
+ align:start position:0%
+then you find this the MU can be written
+ 
+
+ align:start position:0%
+then you find this the MU can be written
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first that these two Pi force and
+
+ align:start position:0%
+so first that these two Pi force and
+ 
+
+ align:start position:0%
+so first that these two Pi force and
+then you have two factors of two Pi Cube
+
+ align:start position:0%
+then you have two factors of two Pi Cube
+ 
+
+ align:start position:0%
+then you have two factors of two Pi Cube
+and then you cancel
+
+ align:start position:0%
+and then you cancel
+ 
+
+ align:start position:0%
+and then you cancel
+so you have this two Pi Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you have four
+
+ align:start position:0%
+then you have four
+ 
+
+ align:start position:0%
+then you have four
+E1 Prime
+
+ align:start position:0%
+E1 Prime
+ 
+
+ align:start position:0%
+E1 Prime
+E2 Prime
+
+ align:start position:0%
+E2 Prime
+ 
+
+ align:start position:0%
+E2 Prime
+then you have one restart of functions
+
+ align:start position:0%
+then you have one restart of functions
+ 
+
+ align:start position:0%
+then you have one restart of functions
+okay so you have
+
+ align:start position:0%
+okay so you have
+ 
+
+ align:start position:0%
+okay so you have
+K1
+
+ align:start position:0%
+K1
+ 
+
+ align:start position:0%
+K1
+you have E1 Prime
+
+ align:start position:0%
+you have E1 Prime
+ 
+
+ align:start position:0%
+you have E1 Prime
+plus E2 Prime
+
+ align:start position:0%
+plus E2 Prime
+ 
+
+ align:start position:0%
+plus E2 Prime
+minus square root S
+
+ align:start position:0%
+minus square root S
+ 
+
+ align:start position:0%
+minus square root S
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+beta 3
+
+ align:start position:0%
+beta 3
+ 
+
+ align:start position:0%
+beta 3
+K1 plus K2
+
+ align:start position:0%
+K1 plus K2
+ 
+
+ align:start position:0%
+K1 plus K2
+and D3 K1
+
+ align:start position:0%
+and D3 K1
+ 
+
+ align:start position:0%
+and D3 K1
+and this 3 K2 okay
+
+ align:start position:0%
+and this 3 K2 okay
+ 
+
+ align:start position:0%
+and this 3 K2 okay
+so as we said the K3 they have to be
+
+ align:start position:0%
+so as we said the K3 they have to be
+ 
+
+ align:start position:0%
+so as we said the K3 they have to be
+equal and update to each other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you can just evaluate one Delta
+
+ align:start position:0%
+and then you can just evaluate one Delta
+ 
+
+ align:start position:0%
+and then you can just evaluate one Delta
+function and then the other DK will
+
+ align:start position:0%
+function and then the other DK will
+ 
+
+ align:start position:0%
+function and then the other DK will
+remain okay the other Decay will remain
+
+ align:start position:0%
+remain okay the other Decay will remain
+ 
+
+ align:start position:0%
+remain okay the other Decay will remain
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so essentially you just have
+
+ align:start position:0%
+so essentially you just have
+ 
+
+ align:start position:0%
+so essentially you just have
+you say we can just forget about this
+
+ align:start position:0%
+you say we can just forget about this
+ 
+
+ align:start position:0%
+you say we can just forget about this
+and then you just have decay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I just have Decay okay d3k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this d3k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can intern write it as decay the
+
+ align:start position:0%
+you can intern write it as decay the
+ 
+
+ align:start position:0%
+you can intern write it as decay the
+magnitude of K and K square and then the
+
+ align:start position:0%
+magnitude of K and K square and then the
+ 
+
+ align:start position:0%
+magnitude of K and K square and then the
+center of mass
+
+ align:start position:0%
+center of mass
+ 
+
+ align:start position:0%
+center of mass
+uh solidango in the center of Mass frame
+
+ align:start position:0%
+uh solidango in the center of Mass frame
+ 
+
+ align:start position:0%
+uh solidango in the center of Mass frame
+okay so so this K Factor can be
+
+ align:start position:0%
+okay so so this K Factor can be
+ 
+
+ align:start position:0%
+okay so so this K Factor can be
+decomposed
+
+ align:start position:0%
+decomposed
+ 
+
+ align:start position:0%
+decomposed
+into the angular directions and the
+
+ align:start position:0%
+into the angular directions and the
+ 
+
+ align:start position:0%
+into the angular directions and the
+magnitude okay and then the now both E1
+
+ align:start position:0%
+magnitude okay and then the now both E1
+ 
+
+ align:start position:0%
+magnitude okay and then the now both E1
+and E2
+
+ align:start position:0%
+and E2
+ 
+
+ align:start position:0%
+and E2
+I expressed in terms of K Square
+
+ align:start position:0%
+I expressed in terms of K Square
+ 
+
+ align:start position:0%
+I expressed in terms of K Square
+plus M1 Prime Square
+
+ align:start position:0%
+plus M1 Prime Square
+ 
+
+ align:start position:0%
+plus M1 Prime Square
+and E2 Prime
+
+ align:start position:0%
+and E2 Prime
+ 
+
+ align:start position:0%
+and E2 Prime
+equal to K Square
+
+ align:start position:0%
+equal to K Square
+ 
+
+ align:start position:0%
+equal to K Square
+plus M2
+
+ align:start position:0%
+plus M2
+ 
+
+ align:start position:0%
+plus M2
+Prime squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now you can further evaluate this
+
+ align:start position:0%
+so now you can further evaluate this
+ 
+
+ align:start position:0%
+so now you can further evaluate this
+data function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now you can find a further evaluate
+
+ align:start position:0%
+okay now you can find a further evaluate
+ 
+
+ align:start position:0%
+okay now you can find a further evaluate
+this is the function big big because the
+
+ align:start position:0%
+this is the function big big because the
+ 
+
+ align:start position:0%
+this is the function big big because the
+E1 Prime and E2 Prime they just the
+
+ align:start position:0%
+E1 Prime and E2 Prime they just the
+ 
+
+ align:start position:0%
+E1 Prime and E2 Prime they just the
+functions of magnitude of K Square
+
+ align:start position:0%
+functions of magnitude of K Square
+ 
+
+ align:start position:0%
+functions of magnitude of K Square
+so you can evaluate this as a function
+
+ align:start position:0%
+so you can evaluate this as a function
+ 
+
+ align:start position:0%
+so you can evaluate this as a function
+you have decay of the magnitude of K
+
+ align:start position:0%
+you have decay of the magnitude of K
+ 
+
+ align:start position:0%
+you have decay of the magnitude of K
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you can do that so we're not going to
+
+ align:start position:0%
+so you can do that so we're not going to
+ 
+
+ align:start position:0%
+so you can do that so we're not going to
+detail okay I will not go into detail
+
+ align:start position:0%
+detail okay I will not go into detail
+ 
+
+ align:start position:0%
+detail okay I will not go into detail
+and so so when you do that when you
+
+ align:start position:0%
+and so so when you do that when you
+ 
+
+ align:start position:0%
+and so so when you do that when you
+solve that that's a function okay and
+
+ align:start position:0%
+solve that that's a function okay and
+ 
+
+ align:start position:0%
+solve that that's a function okay and
+then you find
+
+ align:start position:0%
+then you find
+ 
+
+ align:start position:0%
+then you find
+from here
+
+ align:start position:0%
+from here
+ 
+
+ align:start position:0%
+from here
+then you find that The Final Answer is
+
+ align:start position:0%
+then you find that The Final Answer is
+ 
+
+ align:start position:0%
+then you find that The Final Answer is
+given by
+
+ align:start position:0%
+given by
+ 
+
+ align:start position:0%
+given by
+okay do you find the final answer is
+
+ align:start position:0%
+okay do you find the final answer is
+ 
+
+ align:start position:0%
+okay do you find the final answer is
+given by very simple
+
+ align:start position:0%
+given by very simple
+ 
+
+ align:start position:0%
+given by very simple
+you find given by K
+
+ align:start position:0%
+you find given by K
+ 
+
+ align:start position:0%
+you find given by K
+c m divided by 14 pi squared
+
+ align:start position:0%
+c m divided by 14 pi squared
+ 
+
+ align:start position:0%
+c m divided by 14 pi squared
+square root S
+
+ align:start position:0%
+square root S
+ 
+
+ align:start position:0%
+square root S
+the Omega Center of mass okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this KCM is defined to be the
+
+ align:start position:0%
+and this KCM is defined to be the
+ 
+
+ align:start position:0%
+and this KCM is defined to be the
+solution of this equation
+
+ align:start position:0%
+solution of this equation
+ 
+
+ align:start position:0%
+solution of this equation
+so the so KCM
+
+ align:start position:0%
+so the so KCM
+ 
+
+ align:start position:0%
+so the so KCM
+is the solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to E1 prime plus V2 Prime equal to
+
+ align:start position:0%
+to E1 prime plus V2 Prime equal to
+ 
+
+ align:start position:0%
+to E1 prime plus V2 Prime equal to
+square base okay so again this is
+
+ align:start position:0%
+square base okay so again this is
+ 
+
+ align:start position:0%
+square base okay so again this is
+expressed in terms of the s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so yeah so through some type yeah
+
+ align:start position:0%
+okay so yeah so through some type yeah
+ 
+
+ align:start position:0%
+okay so yeah so through some type yeah
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+technically just evaluate this data
+
+ align:start position:0%
+technically just evaluate this data
+ 
+
+ align:start position:0%
+technically just evaluate this data
+function and yeah
+
+ align:start position:0%
+function and yeah
+ 
+
+ align:start position:0%
+function and yeah
+okay yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+so you only evaluate the K around the
+
+ align:start position:0%
+so you only evaluate the K around the
+ 
+
+ align:start position:0%
+so you only evaluate the K around the
+momentum shell right
+
+ align:start position:0%
+momentum shell right
+ 
+
+ align:start position:0%
+momentum shell right
+so so you can evaluate the data function
+
+ align:start position:0%
+so so you can evaluate the data function
+ 
+
+ align:start position:0%
+so so you can evaluate the data function
+because we always have a finite range of
+
+ align:start position:0%
+because we always have a finite range of
+ 
+
+ align:start position:0%
+because we always have a finite range of
+K to integrate over
+
+ align:start position:0%
+K to integrate over
+ 
+
+ align:start position:0%
+K to integrate over
+so it doesn't matter it doesn't matter
+
+ align:start position:0%
+so it doesn't matter it doesn't matter
+ 
+
+ align:start position:0%
+so it doesn't matter it doesn't matter
+how wide the range of this
+
+ align:start position:0%
+how wide the range of this
+ 
+
+ align:start position:0%
+how wide the range of this
+because the because the non-zero value
+
+ align:start position:0%
+because the because the non-zero value
+ 
+
+ align:start position:0%
+because the because the non-zero value
+of the MU is always around don't satisfy
+
+ align:start position:0%
+of the MU is always around don't satisfy
+ 
+
+ align:start position:0%
+of the MU is always around don't satisfy
+the momentum conversation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Does this answer your question
+
+ align:start position:0%
+Does this answer your question
+ 
+
+ align:start position:0%
+Does this answer your question
+yeah yeah good other questions
+
+ align:start position:0%
+yeah yeah good other questions
+ 
+
+ align:start position:0%
+yeah yeah good other questions
+yeah here I did in the right yeah I
+
+ align:start position:0%
+yeah here I did in the right yeah I
+ 
+
+ align:start position:0%
+yeah here I did in the right yeah I
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+you may Wonder here I didn't write the
+
+ align:start position:0%
+you may Wonder here I didn't write the
+ 
+
+ align:start position:0%
+you may Wonder here I didn't write the
+integral sign
+
+ align:start position:0%
+integral sign
+ 
+
+ align:start position:0%
+integral sign
+how can I just evaluate the data
+
+ align:start position:0%
+how can I just evaluate the data
+ 
+
+ align:start position:0%
+how can I just evaluate the data
+function okay you can the reason you you
+
+ align:start position:0%
+function okay you can the reason you you
+ 
+
+ align:start position:0%
+function okay you can the reason you you
+can evaluate the telephone is just no
+
+ align:start position:0%
+can evaluate the telephone is just no
+ 
+
+ align:start position:0%
+can evaluate the telephone is just no
+matter what is the range of Decay you
+
+ align:start position:0%
+matter what is the range of Decay you
+ 
+
+ align:start position:0%
+matter what is the range of Decay you
+integrate over
+
+ align:start position:0%
+integrate over
+ 
+
+ align:start position:0%
+integrate over
+uh uh and you always we always evaluate
+
+ align:start position:0%
+uh uh and you always we always evaluate
+ 
+
+ align:start position:0%
+uh uh and you always we always evaluate
+around those data functions okay and so
+
+ align:start position:0%
+around those data functions okay and so
+ 
+
+ align:start position:0%
+around those data functions okay and so
+you can always uh take care of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now if you combine this result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now we can write a a a simple
+
+ align:start position:0%
+and now we can write a a a simple
+ 
+
+ align:start position:0%
+and now we can write a a a simple
+expression for the sigma in the in the
+
+ align:start position:0%
+expression for the sigma in the in the
+ 
+
+ align:start position:0%
+expression for the sigma in the in the
+center of Mass frame okay
+
+ align:start position:0%
+center of Mass frame okay
+ 
+
+ align:start position:0%
+center of Mass frame okay
+so so if you combine them together then
+
+ align:start position:0%
+so so if you combine them together then
+ 
+
+ align:start position:0%
+so so if you combine them together then
+we find the sigma
+
+ align:start position:0%
+we find the sigma
+ 
+
+ align:start position:0%
+we find the sigma
+the Omega Center Mass frame
+
+ align:start position:0%
+the Omega Center Mass frame
+ 
+
+ align:start position:0%
+the Omega Center Mass frame
+is equal to
+
+ align:start position:0%
+is equal to
+ 
+
+ align:start position:0%
+is equal to
+m alpha beta Square
+
+ align:start position:0%
+m alpha beta Square
+ 
+
+ align:start position:0%
+m alpha beta Square
+divided by 16
+
+ align:start position:0%
+divided by 16
+ 
+
+ align:start position:0%
+divided by 16
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+Pi Square s
+
+ align:start position:0%
+Pi Square s
+ 
+
+ align:start position:0%
+Pi Square s
+and the KCM divided by PCA
+
+ align:start position:0%
+and the KCM divided by PCA
+ 
+
+ align:start position:0%
+and the KCM divided by PCA
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the KCM is the solution to this
+
+ align:start position:0%
+and the KCM is the solution to this
+ 
+
+ align:start position:0%
+and the KCM is the solution to this
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+and the PCM is the solution to this
+
+ align:start position:0%
+and the PCM is the solution to this
+ 
+
+ align:start position:0%
+and the PCM is the solution to this
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+so the PCM is the equation to this
+
+ align:start position:0%
+so the PCM is the equation to this
+ 
+
+ align:start position:0%
+so the PCM is the equation to this
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+okay so they are given by the same
+
+ align:start position:0%
+okay so they are given by the same
+ 
+
+ align:start position:0%
+okay so they are given by the same
+equation just you replace the M1 mq by
+
+ align:start position:0%
+equation just you replace the M1 mq by
+ 
+
+ align:start position:0%
+equation just you replace the M1 mq by
+M1 Prime the M2 Prime okay so this is
+
+ align:start position:0%
+M1 Prime the M2 Prime okay so this is
+ 
+
+ align:start position:0%
+M1 Prime the M2 Prime okay so this is
+the final answer
+
+ align:start position:0%
+the final answer
+ 
+
+ align:start position:0%
+the final answer
+for the differential cross-section for
+
+ align:start position:0%
+for the differential cross-section for
+ 
+
+ align:start position:0%
+for the differential cross-section for
+two to two scattering in the center of
+
+ align:start position:0%
+two to two scattering in the center of
+ 
+
+ align:start position:0%
+two to two scattering in the center of
+Mass frame
+
+ align:start position:0%
+Mass frame
+ 
+
+ align:start position:0%
+Mass frame
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+in the center of Mass frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so this is the expression which you
+
+ align:start position:0%
+and so this is the expression which you
+ 
+
+ align:start position:0%
+and so this is the expression which you
+will be a use later for uh uh of a
+
+ align:start position:0%
+will be a use later for uh uh of a
+ 
+
+ align:start position:0%
+will be a use later for uh uh of a
+certain yeah
+
+ align:start position:0%
+certain yeah
+ 
+
+ align:start position:0%
+certain yeah
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good
+
+ align:start position:0%
+okay good
+ 
+
+ align:start position:0%
+okay good
+so this concludes the discussion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the cross-section okay
+
+ align:start position:0%
+of the cross-section okay
+ 
+
+ align:start position:0%
+of the cross-section okay
+so it's finally over it's very over
+
+ align:start position:0%
+so it's finally over it's very over
+ 
+
+ align:start position:0%
+so it's finally over it's very over
+but we have to go through this because
+
+ align:start position:0%
+but we have to go through this because
+ 
+
+ align:start position:0%
+but we have to go through this because
+this is this kind of thing which we uh
+
+ align:start position:0%
+this is this kind of thing which we uh
+ 
+
+ align:start position:0%
+this is this kind of thing which we uh
+we compare with experiments okay
+
+ align:start position:0%
+we compare with experiments okay
+ 
+
+ align:start position:0%
+we compare with experiments okay
+and in particular if you calculate the
+
+ align:start position:0%
+and in particular if you calculate the
+ 
+
+ align:start position:0%
+and in particular if you calculate the
+total cross-section and then you can
+
+ align:start position:0%
+total cross-section and then you can
+ 
+
+ align:start position:0%
+total cross-section and then you can
+just integrate this over all the solid
+
+ align:start position:0%
+just integrate this over all the solid
+ 
+
+ align:start position:0%
+just integrate this over all the solid
+angle okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+so before now talking about the physical
+
+ align:start position:0%
+so before now talking about the physical
+ 
+
+ align:start position:0%
+so before now talking about the physical
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+there's one more thing we need to
+
+ align:start position:0%
+there's one more thing we need to
+ 
+
+ align:start position:0%
+there's one more thing we need to
+consider
+
+ align:start position:0%
+consider
+ 
+
+ align:start position:0%
+consider
+so here we consider the initial state
+
+ align:start position:0%
+so here we consider the initial state
+ 
+
+ align:start position:0%
+so here we consider the initial state
+to be one two two particles
+
+ align:start position:0%
+to be one two two particles
+ 
+
+ align:start position:0%
+to be one two two particles
+because we say we don't normally do
+
+ align:start position:0%
+because we say we don't normally do
+ 
+
+ align:start position:0%
+because we say we don't normally do
+scattering with more than two particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but there's a lot of situation
+
+ align:start position:0%
+but there's a lot of situation
+ 
+
+ align:start position:0%
+but there's a lot of situation
+which still often could uh happen
+
+ align:start position:0%
+which still often could uh happen
+ 
+
+ align:start position:0%
+which still often could uh happen
+okay so this is the situation
+
+ align:start position:0%
+okay so this is the situation
+ 
+
+ align:start position:0%
+okay so this is the situation
+which initial state only have one
+
+ align:start position:0%
+which initial state only have one
+ 
+
+ align:start position:0%
+which initial state only have one
+particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when your initials state only have
+
+ align:start position:0%
+so when your initials state only have
+ 
+
+ align:start position:0%
+so when your initials state only have
+one particle what do you have
+
+ align:start position:0%
+one particle what do you have
+ 
+
+ align:start position:0%
+one particle what do you have
+yeah then that goes one into K yeah so
+
+ align:start position:0%
+yeah then that goes one into K yeah so
+ 
+
+ align:start position:0%
+yeah then that goes one into K yeah so
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+you can still
+
+ align:start position:0%
+you can still
+ 
+
+ align:start position:0%
+you can still
+have the situation if you have an
+
+ align:start position:0%
+have the situation if you have an
+ 
+
+ align:start position:0%
+have the situation if you have an
+unstable particle
+
+ align:start position:0%
+unstable particle
+ 
+
+ align:start position:0%
+unstable particle
+then we can decay
+
+ align:start position:0%
+then we can decay
+ 
+
+ align:start position:0%
+then we can decay
+and then it's very important
+
+ align:start position:0%
+and then it's very important
+ 
+
+ align:start position:0%
+and then it's very important
+for many in many physical situations to
+
+ align:start position:0%
+for many in many physical situations to
+ 
+
+ align:start position:0%
+for many in many physical situations to
+calculate the Decay rates
+
+ align:start position:0%
+calculate the Decay rates
+ 
+
+ align:start position:0%
+calculate the Decay rates
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now
+
+ align:start position:0%
+so so now
+ 
+
+ align:start position:0%
+so so now
+so now we have P1
+
+ align:start position:0%
+so now we have P1
+ 
+
+ align:start position:0%
+so now we have P1
+say suppose this initial momentum and
+
+ align:start position:0%
+say suppose this initial momentum and
+ 
+
+ align:start position:0%
+say suppose this initial momentum and
+Decay into K one
+
+ align:start position:0%
+Decay into K one
+ 
+
+ align:start position:0%
+Decay into K one
+plus k n say follow in particles okay
+
+ align:start position:0%
+plus k n say follow in particles okay
+ 
+
+ align:start position:0%
+plus k n say follow in particles okay
+so now the the initial state only one
+
+ align:start position:0%
+so now the the initial state only one
+ 
+
+ align:start position:0%
+so now the the initial state only one
+particle and the final state is still K1
+
+ align:start position:0%
+particle and the final state is still K1
+ 
+
+ align:start position:0%
+particle and the final state is still K1
+okay so beta Remains the Same but Alpha
+
+ align:start position:0%
+okay so beta Remains the Same but Alpha
+ 
+
+ align:start position:0%
+okay so beta Remains the Same but Alpha
+only one particle okay and the Decay
+
+ align:start position:0%
+only one particle okay and the Decay
+ 
+
+ align:start position:0%
+only one particle okay and the Decay
+rate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is much simpler to Define
+
+ align:start position:0%
+is much simpler to Define
+ 
+
+ align:start position:0%
+is much simpler to Define
+it's just Dr DP
+
+ align:start position:0%
+it's just Dr DP
+ 
+
+ align:start position:0%
+it's just Dr DP
+Alpha Beta DT okay
+
+ align:start position:0%
+Alpha Beta DT okay
+ 
+
+ align:start position:0%
+Alpha Beta DT okay
+and we don't need to divide by flux all
+
+ align:start position:0%
+and we don't need to divide by flux all
+ 
+
+ align:start position:0%
+and we don't need to divide by flux all
+those scenes okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now let me explain a little bit
+
+ align:start position:0%
+so so now let me explain a little bit
+ 
+
+ align:start position:0%
+so so now let me explain a little bit
+again this DP Alpha Beta
+
+ align:start position:0%
+again this DP Alpha Beta
+ 
+
+ align:start position:0%
+again this DP Alpha Beta
+we always mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we mean that the probability
+
+ align:start position:0%
+we mean that the probability
+ 
+
+ align:start position:0%
+we mean that the probability
+of P1
+
+ align:start position:0%
+of P1
+ 
+
+ align:start position:0%
+of P1
+became
+
+ align:start position:0%
+became
+ 
+
+ align:start position:0%
+became
+into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unfollow particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particle 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+yeah with range
+
+ align:start position:0%
+yeah with range
+ 
+
+ align:start position:0%
+yeah with range
+with the decay one
+
+ align:start position:0%
+with the decay one
+ 
+
+ align:start position:0%
+with the decay one
+around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K1
+
+ align:start position:0%
+K1
+ 
+
+ align:start position:0%
+K1
+and the DK2
+
+ align:start position:0%
+and the DK2
+ 
+
+ align:start position:0%
+and the DK2
+around K2
+
+ align:start position:0%
+around K2
+ 
+
+ align:start position:0%
+around K2
+Etc okay and dkn around k n
+
+ align:start position:0%
+Etc okay and dkn around k n
+ 
+
+ align:start position:0%
+Etc okay and dkn around k n
+so so so when we write the Dr beta you
+
+ align:start position:0%
+so so so when we write the Dr beta you
+ 
+
+ align:start position:0%
+so so so when we write the Dr beta you
+should imagine this uh we already
+
+ align:start position:0%
+should imagine this uh we already
+ 
+
+ align:start position:0%
+should imagine this uh we already
+include that okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now we can just repeat what we did
+
+ align:start position:0%
+so so now we can just repeat what we did
+ 
+
+ align:start position:0%
+so so now we can just repeat what we did
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+so then this DP Alpha Beta
+
+ align:start position:0%
+so then this DP Alpha Beta
+ 
+
+ align:start position:0%
+so then this DP Alpha Beta
+DT
+
+ align:start position:0%
+DT
+ 
+
+ align:start position:0%
+DT
+DP Alpha Beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then just given by
+
+ align:start position:0%
+then just given by
+ 
+
+ align:start position:0%
+then just given by
+again this same square
+
+ align:start position:0%
+again this same square
+ 
+
+ align:start position:0%
+again this same square
+beta plus infinity square and Alpha
+
+ align:start position:0%
+beta plus infinity square and Alpha
+ 
+
+ align:start position:0%
+beta plus infinity square and Alpha
+minus infinity
+
+ align:start position:0%
+minus infinity
+ 
+
+ align:start position:0%
+minus infinity
+Square divided by
+
+ align:start position:0%
+Square divided by
+ 
+
+ align:start position:0%
+Square divided by
+beta
+
+ align:start position:0%
+beta
+ 
+
+ align:start position:0%
+beta
+and Alpha
+
+ align:start position:0%
+and Alpha
+ 
+
+ align:start position:0%
+and Alpha
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and times
+
+ align:start position:0%
+and times
+ 
+
+ align:start position:0%
+and times
+J from 1 to n
+
+ align:start position:0%
+J from 1 to n
+ 
+
+ align:start position:0%
+J from 1 to n
+V3
+
+ align:start position:0%
+V3
+ 
+
+ align:start position:0%
+V3
+KJ
+
+ align:start position:0%
+KJ
+ 
+
+ align:start position:0%
+KJ
+Q5 cubed times V okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now it's the same thing okay now it's
+
+ align:start position:0%
+so now it's the same thing okay now it's
+ 
+
+ align:start position:0%
+so now it's the same thing okay now it's
+same thing
+
+ align:start position:0%
+same thing
+ 
+
+ align:start position:0%
+same thing
+so so the only thing you need to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the other one
+
+ align:start position:0%
+and the other one
+ 
+
+ align:start position:0%
+and the other one
+say is
+
+ align:start position:0%
+say is
+ 
+
+ align:start position:0%
+say is
+everything else is the same okay so
+
+ align:start position:0%
+everything else is the same okay so
+ 
+
+ align:start position:0%
+everything else is the same okay so
+everything else it's the same so you
+
+ align:start position:0%
+everything else it's the same so you
+ 
+
+ align:start position:0%
+everything else it's the same so you
+just repeat our previous analysis which
+
+ align:start position:0%
+just repeat our previous analysis which
+ 
+
+ align:start position:0%
+just repeat our previous analysis which
+I will not repeat
+
+ align:start position:0%
+I will not repeat
+ 
+
+ align:start position:0%
+I will not repeat
+so the only thing different is just now
+
+ align:start position:0%
+so the only thing different is just now
+ 
+
+ align:start position:0%
+so the only thing different is just now
+the initial state is just two a single
+
+ align:start position:0%
+the initial state is just two a single
+ 
+
+ align:start position:0%
+the initial state is just two a single
+energy okay so you just repeat the whole
+
+ align:start position:0%
+energy okay so you just repeat the whole
+ 
+
+ align:start position:0%
+energy okay so you just repeat the whole
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+and then you find okay so I will not the
+
+ align:start position:0%
+and then you find okay so I will not the
+ 
+
+ align:start position:0%
+and then you find okay so I will not the
+then you find
+
+ align:start position:0%
+then you find
+ 
+
+ align:start position:0%
+then you find
+the gamma Alpha Beta
+
+ align:start position:0%
+the gamma Alpha Beta
+ 
+
+ align:start position:0%
+the gamma Alpha Beta
+equal to DP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha Beta
+
+ align:start position:0%
+Alpha Beta
+ 
+
+ align:start position:0%
+Alpha Beta
+divided by T
+
+ align:start position:0%
+divided by T
+ 
+
+ align:start position:0%
+divided by T
+and then you find that this is just
+
+ align:start position:0%
+and then you find that this is just
+ 
+
+ align:start position:0%
+and then you find that this is just
+given by
+
+ align:start position:0%
+given by
+ 
+
+ align:start position:0%
+given by
+qe1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha Beta
+
+ align:start position:0%
+Alpha Beta
+ 
+
+ align:start position:0%
+Alpha Beta
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+the MU okay the MU you defined in the
+
+ align:start position:0%
+the MU okay the MU you defined in the
+ 
+
+ align:start position:0%
+the MU okay the MU you defined in the
+same way
+
+ align:start position:0%
+same way
+ 
+
+ align:start position:0%
+same way
+okay the MU is defined the same way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this is the final answer
+
+ align:start position:0%
+so so this is the final answer
+ 
+
+ align:start position:0%
+so so this is the final answer
+for the uh for the Decay case
+
+ align:start position:0%
+for the uh for the Decay case
+ 
+
+ align:start position:0%
+for the uh for the Decay case
+and the total Decay rate
+
+ align:start position:0%
+and the total Decay rate
+ 
+
+ align:start position:0%
+and the total Decay rate
+will be you integrate just over all
+
+ align:start position:0%
+will be you integrate just over all
+ 
+
+ align:start position:0%
+will be you integrate just over all
+momentum okay
+
+ align:start position:0%
+momentum okay
+ 
+
+ align:start position:0%
+momentum okay
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so the total Decay rate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the total Decay rate
+
+ align:start position:0%
+so the total Decay rate
+ 
+
+ align:start position:0%
+so the total Decay rate
+is just gamma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+total rate
+
+ align:start position:0%
+total rate
+ 
+
+ align:start position:0%
+total rate
+then gamma is disarming over all
+
+ align:start position:0%
+then gamma is disarming over all
+ 
+
+ align:start position:0%
+then gamma is disarming over all
+possible choice of beta and then you
+
+ align:start position:0%
+possible choice of beta and then you
+ 
+
+ align:start position:0%
+possible choice of beta and then you
+integrate over all momentum
+
+ align:start position:0%
+integrate over all momentum
+ 
+
+ align:start position:0%
+integrate over all momentum
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the lifetime of the particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tau is just equal to one overcome
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one thing
+
+ align:start position:0%
+so one thing
+ 
+
+ align:start position:0%
+so one thing
+one difference with the cross-action
+
+ align:start position:0%
+one difference with the cross-action
+ 
+
+ align:start position:0%
+one difference with the cross-action
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+so the cross argument we mentioned
+
+ align:start position:0%
+so the cross argument we mentioned
+ 
+
+ align:start position:0%
+so the cross argument we mentioned
+before
+
+ align:start position:0%
+before
+ 
+
+ align:start position:0%
+before
+say it's low renting warrant
+
+ align:start position:0%
+say it's low renting warrant
+ 
+
+ align:start position:0%
+say it's low renting warrant
+but Decay rate is not
+
+ align:start position:0%
+but Decay rate is not
+ 
+
+ align:start position:0%
+but Decay rate is not
+and the carry does depend on the frame
+
+ align:start position:0%
+and the carry does depend on the frame
+ 
+
+ align:start position:0%
+and the carry does depend on the frame
+of the particle
+
+ align:start position:0%
+of the particle
+ 
+
+ align:start position:0%
+of the particle
+okay that's depend on the frame of the
+
+ align:start position:0%
+okay that's depend on the frame of the
+ 
+
+ align:start position:0%
+okay that's depend on the frame of the
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+so uh so Decay rate yeah so this knife
+
+ align:start position:0%
+so uh so Decay rate yeah so this knife
+ 
+
+ align:start position:0%
+so uh so Decay rate yeah so this knife
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+does depend on the uh the frame of the
+
+ align:start position:0%
+does depend on the uh the frame of the
+ 
+
+ align:start position:0%
+does depend on the uh the frame of the
+particle in the right frame of the
+
+ align:start position:0%
+particle in the right frame of the
+ 
+
+ align:start position:0%
+particle in the right frame of the
+particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because one into just E1 equal to M1
+
+ align:start position:0%
+because one into just E1 equal to M1
+ 
+
+ align:start position:0%
+because one into just E1 equal to M1
+okay just equal to mass over the
+
+ align:start position:0%
+okay just equal to mass over the
+ 
+
+ align:start position:0%
+okay just equal to mass over the
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+okay and so the rest frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Decay rate
+
+ align:start position:0%
+Decay rate
+ 
+
+ align:start position:0%
+Decay rate
+is the smallest among all possible Decay
+
+ align:start position:0%
+is the smallest among all possible Decay
+ 
+
+ align:start position:0%
+is the smallest among all possible Decay
+rates
+
+ align:start position:0%
+rates
+ 
+
+ align:start position:0%
+rates
+okay because the time dilation
+
+ align:start position:0%
+okay because the time dilation
+ 
+
+ align:start position:0%
+okay because the time dilation
+okay that the uh in the yeah yeah in all
+
+ align:start position:0%
+okay that the uh in the yeah yeah in all
+ 
+
+ align:start position:0%
+okay that the uh in the yeah yeah in all
+other moving frame because time time
+
+ align:start position:0%
+other moving frame because time time
+ 
+
+ align:start position:0%
+other moving frame because time time
+dilation the Decay rate become faster
+
+ align:start position:0%
+dilation the Decay rate become faster
+ 
+
+ align:start position:0%
+dilation the Decay rate become faster
+okay so that's what you
+
+ align:start position:0%
+okay so that's what you
+ 
+
+ align:start position:0%
+okay so that's what you
+then to that the particles moving and
+
+ align:start position:0%
+then to that the particles moving and
+ 
+
+ align:start position:0%
+then to that the particles moving and
+they have a longer lifetime okay
+
+ align:start position:0%
+they have a longer lifetime okay
+ 
+
+ align:start position:0%
+they have a longer lifetime okay
+they have a longer lifetime
+
+ align:start position:0%
+they have a longer lifetime
+ 
+
+ align:start position:0%
+they have a longer lifetime
+so this
+
+ align:start position:0%
+so this
+ 
+
+ align:start position:0%
+so this
+makes perfect sense okay so any
+
+ align:start position:0%
+makes perfect sense okay so any
+ 
+
+ align:start position:0%
+makes perfect sense okay so any
+questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah in general
+
+ align:start position:0%
+yeah in general
+ 
+
+ align:start position:0%
+yeah in general
+in general uh for the real
+
+ align:start position:0%
+in general uh for the real
+ 
+
+ align:start position:0%
+in general uh for the real
+you live low but but uh yeah basically
+
+ align:start position:0%
+you live low but but uh yeah basically
+ 
+
+ align:start position:0%
+you live low but but uh yeah basically
+is what we discover right
+
+ align:start position:0%
+is what we discover right
+ 
+
+ align:start position:0%
+is what we discover right
+yeah we observe what are the Decay
+
+ align:start position:0%
+yeah we observe what are the Decay
+ 
+
+ align:start position:0%
+yeah we observe what are the Decay
+fellow products
+
+ align:start position:0%
+fellow products
+ 
+
+ align:start position:0%
+fellow products
+yeah but you can also predict
+
+ align:start position:0%
+yeah but you can also predict
+ 
+
+ align:start position:0%
+yeah but you can also predict
+from your theory what are the possible
+
+ align:start position:0%
+from your theory what are the possible
+ 
+
+ align:start position:0%
+from your theory what are the possible
+decay
+
+ align:start position:0%
+decay
+ 
+
+ align:start position:0%
+decay
+but in real experiment there always
+
+ align:start position:0%
+but in real experiment there always
+ 
+
+ align:start position:0%
+but in real experiment there always
+maybe some particles
+
+ align:start position:0%
+maybe some particles
+ 
+
+ align:start position:0%
+maybe some particles
+we don't know yeah there may be some
+
+ align:start position:0%
+we don't know yeah there may be some
+ 
+
+ align:start position:0%
+we don't know yeah there may be some
+yeah some hidden interactions yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good
+
+ align:start position:0%
+okay good
+ 
+
+ align:start position:0%
+okay good
+good so that's finally concludes this
+
+ align:start position:0%
+good so that's finally concludes this
+ 
+
+ align:start position:0%
+good so that's finally concludes this
+discussion of this cross-section and
+
+ align:start position:0%
+discussion of this cross-section and
+ 
+
+ align:start position:0%
+discussion of this cross-section and
+Decay rate okay
+
+ align:start position:0%
+Decay rate okay
+ 
+
+ align:start position:0%
+Decay rate okay
+and now we can study some some process
+
+ align:start position:0%
+and now we can study some some process
+ 
+
+ align:start position:0%
+and now we can study some some process
+so we only have like 10 minutes to do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we will not really be able to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's just maybe to start it
+
+ align:start position:0%
+so it's just maybe to start it
+ 
+
+ align:start position:0%
+so it's just maybe to start it
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in general we will consider
+
+ align:start position:0%
+so in general we will consider
+ 
+
+ align:start position:0%
+so in general we will consider
+two to two scatterings okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in general you can see the 2D2
+
+ align:start position:0%
+okay in general you can see the 2D2
+ 
+
+ align:start position:0%
+okay in general you can see the 2D2
+scatterings
+
+ align:start position:0%
+scatterings
+ 
+
+ align:start position:0%
+scatterings
+and uh so so one remark you make
+
+ align:start position:0%
+and uh so so one remark you make
+ 
+
+ align:start position:0%
+and uh so so one remark you make
+and in that case we have this formula
+
+ align:start position:0%
+and in that case we have this formula
+ 
+
+ align:start position:0%
+and in that case we have this formula
+okay we have this very nice formula okay
+
+ align:start position:0%
+okay we have this very nice formula okay
+ 
+
+ align:start position:0%
+okay we have this very nice formula okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we spin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay see where the swing one half or
+
+ align:start position:0%
+okay see where the swing one half or
+ 
+
+ align:start position:0%
+okay see where the swing one half or
+swing one swing one half would be
+
+ align:start position:0%
+swing one swing one half would be
+ 
+
+ align:start position:0%
+swing one swing one half would be
+electrons protons
+
+ align:start position:0%
+electrons protons
+ 
+
+ align:start position:0%
+electrons protons
+Etc and spin one would be photon
+
+ align:start position:0%
+Etc and spin one would be photon
+ 
+
+ align:start position:0%
+Etc and spin one would be photon
+and the discussion amplitude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then will depend on the predation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of initial and fellow particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you mostly experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in most experiments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the
+
+ align:start position:0%
+so the
+ 
+
+ align:start position:0%
+so the
+the initial beam
+
+ align:start position:0%
+the initial beam
+ 
+
+ align:start position:0%
+the initial beam
+they are unpolarized okay it's not easy
+
+ align:start position:0%
+they are unpolarized okay it's not easy
+ 
+
+ align:start position:0%
+they are unpolarized okay it's not easy
+uh sometimes to do the polarized beam so
+
+ align:start position:0%
+uh sometimes to do the polarized beam so
+ 
+
+ align:start position:0%
+uh sometimes to do the polarized beam so
+initial state
+
+ align:start position:0%
+initial state
+ 
+
+ align:start position:0%
+initial state
+initial beams
+
+ align:start position:0%
+initial beams
+ 
+
+ align:start position:0%
+initial beams
+unpolarized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unpolarized means that just
+
+ align:start position:0%
+unpolarized means that just
+ 
+
+ align:start position:0%
+unpolarized means that just
+corresponding to a superposition
+
+ align:start position:0%
+corresponding to a superposition
+ 
+
+ align:start position:0%
+corresponding to a superposition
+of all possible kind of
+
+ align:start position:0%
+of all possible kind of
+ 
+
+ align:start position:0%
+of all possible kind of
+operations okay
+
+ align:start position:0%
+operations okay
+ 
+
+ align:start position:0%
+operations okay
+incoherence to a position
+
+ align:start position:0%
+incoherence to a position
+ 
+
+ align:start position:0%
+incoherence to a position
+and then the final
+
+ align:start position:0%
+and then the final
+ 
+
+ align:start position:0%
+and then the final
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+and the spin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+validation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or final state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normally cannot be detected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it's it's a difficult question
+
+ align:start position:0%
+okay it's it's a difficult question
+ 
+
+ align:start position:0%
+okay it's it's a difficult question
+to detect the polarization silver
+
+ align:start position:0%
+to detect the polarization silver
+ 
+
+ align:start position:0%
+to detect the polarization silver
+particle okay
+
+ align:start position:0%
+particle okay
+ 
+
+ align:start position:0%
+particle okay
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+actually it's not even say if you
+
+ align:start position:0%
+actually it's not even say if you
+ 
+
+ align:start position:0%
+actually it's not even say if you
+say Observer blue particle is not even
+
+ align:start position:0%
+say Observer blue particle is not even
+ 
+
+ align:start position:0%
+say Observer blue particle is not even
+easy to
+
+ align:start position:0%
+easy to
+ 
+
+ align:start position:0%
+easy to
+to tell whether this particle is both
+
+ align:start position:0%
+to tell whether this particle is both
+ 
+
+ align:start position:0%
+to tell whether this particle is both
+homophobia okay so so to to measure the
+
+ align:start position:0%
+homophobia okay so so to to measure the
+ 
+
+ align:start position:0%
+homophobia okay so so to to measure the
+specific partition is even harder okay
+
+ align:start position:0%
+specific partition is even harder okay
+ 
+
+ align:start position:0%
+specific partition is even harder okay
+anyway so so uh uh so the position of
+
+ align:start position:0%
+anyway so so uh uh so the position of
+ 
+
+ align:start position:0%
+anyway so so uh uh so the position of
+fellow particle fellow say that normally
+
+ align:start position:0%
+fellow particle fellow say that normally
+ 
+
+ align:start position:0%
+fellow particle fellow say that normally
+are not detected
+
+ align:start position:0%
+are not detected
+ 
+
+ align:start position:0%
+are not detected
+so in this case when we compare this
+
+ align:start position:0%
+so in this case when we compare this
+ 
+
+ align:start position:0%
+so in this case when we compare this
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+so when we calculate this kind of
+
+ align:start position:0%
+so when we calculate this kind of
+ 
+
+ align:start position:0%
+so when we calculate this kind of
+cross-section
+
+ align:start position:0%
+cross-section
+ 
+
+ align:start position:0%
+cross-section
+compare with experiments
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means that we should to compare
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we should sum over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some over polarizations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or final States
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the average
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+correlations of initial state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so so in one for the final State
+
+ align:start position:0%
+okay so so so in one for the final State
+ 
+
+ align:start position:0%
+okay so so so in one for the final State
+we need to sum over them because we need
+
+ align:start position:0%
+we need to sum over them because we need
+ 
+
+ align:start position:0%
+we need to sum over them because we need
+to sum of all possibilities
+
+ align:start position:0%
+to sum of all possibilities
+ 
+
+ align:start position:0%
+to sum of all possibilities
+but for the initial state
+
+ align:start position:0%
+but for the initial state
+ 
+
+ align:start position:0%
+but for the initial state
+all different organizations contribute
+
+ align:start position:0%
+all different organizations contribute
+ 
+
+ align:start position:0%
+all different organizations contribute
+so ability to average of them okay
+
+ align:start position:0%
+so ability to average of them okay
+ 
+
+ align:start position:0%
+so ability to average of them okay
+ability to average of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so for example
+
+ align:start position:0%
+so so for example
+ 
+
+ align:start position:0%
+so so for example
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for example if we consider such a
+
+ align:start position:0%
+so for example if we consider such a
+ 
+
+ align:start position:0%
+so for example if we consider such a
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+so very important process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say in QED is your violation of
+
+ align:start position:0%
+say in QED is your violation of
+ 
+
+ align:start position:0%
+say in QED is your violation of
+particles so if you have a particle on
+
+ align:start position:0%
+particles so if you have a particle on
+ 
+
+ align:start position:0%
+particles so if you have a particle on
+the anti-particle then they can allow it
+
+ align:start position:0%
+the anti-particle then they can allow it
+ 
+
+ align:start position:0%
+the anti-particle then they can allow it
+when they allow it then they are allow
+
+ align:start position:0%
+when they allow it then they are allow
+ 
+
+ align:start position:0%
+when they allow it then they are allow
+it into photon
+
+ align:start position:0%
+it into photon
+ 
+
+ align:start position:0%
+it into photon
+and the photon can split into some other
+
+ align:start position:0%
+and the photon can split into some other
+ 
+
+ align:start position:0%
+and the photon can split into some other
+particle antibarticle okay so this is a
+
+ align:start position:0%
+particle antibarticle okay so this is a
+ 
+
+ align:start position:0%
+particle antibarticle okay so this is a
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+of particle a come in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a a bar
+
+ align:start position:0%
+so this is a a bar
+ 
+
+ align:start position:0%
+so this is a a bar
+this is p and B Bar okay so this is a
+
+ align:start position:0%
+this is p and B Bar okay so this is a
+ 
+
+ align:start position:0%
+this is p and B Bar okay so this is a
+production the pair creation of B and B
+
+ align:start position:0%
+production the pair creation of B and B
+ 
+
+ align:start position:0%
+production the pair creation of B and B
+bar from crying a and this antibiotic
+
+ align:start position:0%
+bar from crying a and this antibiotic
+ 
+
+ align:start position:0%
+bar from crying a and this antibiotic
+okay so in real life
+
+ align:start position:0%
+okay so in real life
+ 
+
+ align:start position:0%
+okay so in real life
+in real life by clyding say for example
+
+ align:start position:0%
+in real life by clyding say for example
+ 
+
+ align:start position:0%
+in real life by clyding say for example
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+plus Photoshop
+
+ align:start position:0%
+plus Photoshop
+ 
+
+ align:start position:0%
+plus Photoshop
+then you can create many particles so
+
+ align:start position:0%
+then you can create many particles so
+ 
+
+ align:start position:0%
+then you can create many particles so
+this is the one of the uh most important
+
+ align:start position:0%
+this is the one of the uh most important
+ 
+
+ align:start position:0%
+this is the one of the uh most important
+way to discover new particles okay many
+
+ align:start position:0%
+way to discover new particles okay many
+ 
+
+ align:start position:0%
+way to discover new particles okay many
+new particles are discovered this way
+
+ align:start position:0%
+new particles are discovered this way
+ 
+
+ align:start position:0%
+new particles are discovered this way
+you just Collide the electron and the
+
+ align:start position:0%
+you just Collide the electron and the
+ 
+
+ align:start position:0%
+you just Collide the electron and the
+position
+
+ align:start position:0%
+position
+ 
+
+ align:start position:0%
+position
+and then you will be able to create new
+
+ align:start position:0%
+and then you will be able to create new
+ 
+
+ align:start position:0%
+and then you will be able to create new
+particles okay for example you can
+
+ align:start position:0%
+particles okay for example you can
+ 
+
+ align:start position:0%
+particles okay for example you can
+create muam
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you can create the clocks an
+
+ align:start position:0%
+and then you can create the clocks an
+ 
+
+ align:start position:0%
+and then you can create the clocks an
+antiquark
+
+ align:start position:0%
+antiquark
+ 
+
+ align:start position:0%
+antiquark
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+Etc okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so for such a so suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so in all this case both initial and
+
+ align:start position:0%
+so so in all this case both initial and
+ 
+
+ align:start position:0%
+so so in all this case both initial and
+phylo particles the the fermions
+
+ align:start position:0%
+phylo particles the the fermions
+ 
+
+ align:start position:0%
+phylo particles the the fermions
+so you need to specify their position so
+
+ align:start position:0%
+so you need to specify their position so
+ 
+
+ align:start position:0%
+so you need to specify their position so
+this one suppose we have P1 R1
+
+ align:start position:0%
+this one suppose we have P1 R1
+ 
+
+ align:start position:0%
+this one suppose we have P1 R1
+so here we have P2
+
+ align:start position:0%
+so here we have P2
+ 
+
+ align:start position:0%
+so here we have P2
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+say the uh since this is another
+
+ align:start position:0%
+say the uh since this is another
+ 
+
+ align:start position:0%
+say the uh since this is another
+particle it's called R2 bar
+
+ align:start position:0%
+particle it's called R2 bar
+ 
+
+ align:start position:0%
+particle it's called R2 bar
+and B would be because
+
+ align:start position:0%
+and B would be because
+ 
+
+ align:start position:0%
+and B would be because
+say this is k1 S1
+
+ align:start position:0%
+say this is k1 S1
+ 
+
+ align:start position:0%
+say this is k1 S1
+say this is K2 S2 bar okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then for the unpolarized process let
+
+ align:start position:0%
+and then for the unpolarized process let
+ 
+
+ align:start position:0%
+and then for the unpolarized process let
+me just write down one form one last
+
+ align:start position:0%
+me just write down one form one last
+ 
+
+ align:start position:0%
+me just write down one form one last
+formula
+
+ align:start position:0%
+formula
+ 
+
+ align:start position:0%
+formula
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you need to say suppose the
+
+ align:start position:0%
+so you need to say suppose the
+ 
+
+ align:start position:0%
+so you need to say suppose the
+scheduling amplitude is m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Square okay so m
+
+ align:start position:0%
+Square okay so m
+ 
+
+ align:start position:0%
+Square okay so m
+and then we need to for on polarized
+
+ align:start position:0%
+and then we need to for on polarized
+ 
+
+ align:start position:0%
+and then we need to for on polarized
+process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we need to consider we need to
+
+ align:start position:0%
+so we need to consider we need to
+ 
+
+ align:start position:0%
+so we need to consider we need to
+average initial spin R1
+
+ align:start position:0%
+average initial spin R1
+ 
+
+ align:start position:0%
+average initial spin R1
+an average over the finals uh the the R2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then we need to sum over S1
+
+ align:start position:0%
+okay and then we need to sum over S1
+ 
+
+ align:start position:0%
+okay and then we need to sum over S1
+and the sum of S2
+
+ align:start position:0%
+and the sum of S2
+ 
+
+ align:start position:0%
+and the sum of S2
+okay and then I have M Square
+
+ align:start position:0%
+okay and then I have M Square
+ 
+
+ align:start position:0%
+okay and then I have M Square
+okay so essentially
+
+ align:start position:0%
+okay so essentially
+ 
+
+ align:start position:0%
+okay so essentially
+this become one over four and sum over
+
+ align:start position:0%
+this become one over four and sum over
+ 
+
+ align:start position:0%
+this become one over four and sum over
+all possible spin polarizations of the M
+
+ align:start position:0%
+all possible spin polarizations of the M
+ 
+
+ align:start position:0%
+all possible spin polarizations of the M
+Square
+
+ align:start position:0%
+Square
+ 
+
+ align:start position:0%
+Square
+okay so this is the one we can say
+
+ align:start position:0%
+okay so this is the one we can say
+ 
+
+ align:start position:0%
+okay so this is the one we can say
+compare with experiments
+
+ align:start position:0%
+compare with experiments
+ 
+
+ align:start position:0%
+compare with experiments
+okay so next time we will we will write
+
+ align:start position:0%
+okay so next time we will we will write
+ 
+
+ align:start position:0%
+okay so next time we will we will write
+this down explicitly uh uh for this kind
+
+ align:start position:0%
+this down explicitly uh uh for this kind
+ 
+
+ align:start position:0%
+this down explicitly uh uh for this kind
+of process okay and uh yeah yeah so so
+
+ align:start position:0%
+of process okay and uh yeah yeah so so
+ 
+
+ align:start position:0%
+of process okay and uh yeah yeah so so
+let's stop here
\ No newline at end of file
diff --git a/Bcxyr_yBBQg.txt b/Bcxyr_yBBQg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c995366c9c7522df9970e485a2327e5ffdb0e961
--- /dev/null
+++ b/Bcxyr_yBBQg.txt
@@ -0,0 +1,2447 @@
+align:start position:0%
+ 
+Okay, so this is the first kanji for lesson 8. First
+
+ align:start position:0%
+Okay, so this is the first kanji for lesson 8. First
+ 
+
+ align:start position:0%
+Okay, so this is the first kanji for lesson 8. First
+of all, this kanji means
+
+ align:start position:0%
+of all, this kanji means
+ 
+
+ align:start position:0%
+of all, this kanji means
+ect or beeec.
+
+ align:start position:0%
+ect or beeec.
+ 
+
+ align:start position:0%
+ect or beeec.
+So, the part is component.
+
+ align:start position:0%
+So, the part is component.
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This part on the left side
+
+ align:start position:0%
+This part on the left side
+ 
+
+ align:start position:0%
+This part on the left side
+means exchange. For example, it
+
+ align:start position:0%
+means exchange. For example, it
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means international exchange. And
+
+ align:start position:0%
+means international exchange. And
+ 
+
+ align:start position:0%
+means international exchange. And
+then on the right side, everyone already knows this, right? It
+
+ align:start position:0%
+then on the right side, everyone already knows this, right? It
+ 
+
+ align:start position:0%
+then on the right side, everyone already knows this, right? It
+means power. So
+
+ align:start position:0%
+means power. So
+ 
+
+ align:start position:0%
+means power. So
+if you exchange your power, you can be more
+
+ align:start position:0%
+if you exchange your power, you can be more
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+effective. This feels like an E, which means
+
+ align:start position:0%
+effective. This feels like an E, which means
+ 
+
+ align:start position:0%
+effective. This feels like an E, which means
+active. As for the pronunciation, the main thing is the
+
+ align:start position:0%
+active. As for the pronunciation, the main thing is the
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+leading.
+
+ align:start position:0%
+leading.
+ 
+
+ align:start position:0%
+leading.
+For example, effect means result, then efficiency, and
+
+ align:start position:0%
+For example, effect means result, then efficiency, and
+ 
+
+ align:start position:0%
+For example, effect means result, then efficiency, and
+then effectiveness. This is an adjective,
+
+ align:start position:0%
+then effectiveness. This is an adjective,
+ 
+
+ align:start position:0%
+then effectiveness. This is an adjective,
+but active means active. And then,
+
+ align:start position:0%
+but active means active. And then,
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do you think about this kanji with the ya line? This is medicine, and
+
+ align:start position:0%
+what do you think about this kanji with the ya line? This is medicine, and
+ 
+
+ align:start position:0%
+what do you think about this kanji with the ya line? This is medicine, and
+then ect, so what does that
+
+ align:start position:0%
+then ect, so what does that
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean? Drug ect. And then, in the leading, there is hear.
+
+ align:start position:0%
+mean? Drug ect. And then, in the leading, there is hear.
+ 
+
+ align:start position:0%
+mean? Drug ect. And then, in the leading, there is hear.
+Hear, the medicine works, something works, something worked. Okay, so, the next
+
+ align:start position:0%
+Hear, the medicine works, something works, something worked. Okay, so, the next
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kanji is this kanji. The
+
+ align:start position:0%
+kanji is this kanji. The
+ 
+
+ align:start position:0%
+kanji is this kanji. The
+meaning is div, and then  It
+
+ align:start position:0%
+meaning is div, and then  It
+ 
+
+ align:start position:0%
+meaning is div, and then  It
+means subject of study, so it's a
+
+ align:start position:0%
+means subject of study, so it's a
+ 
+
+ align:start position:0%
+means subject of study, so it's a
+component. But
+
+ align:start position:0%
+component. But
+ 
+
+ align:start position:0%
+component. But
+first, this radical on the left side,
+
+ align:start position:0%
+first, this radical on the left side,
+ 
+
+ align:start position:0%
+first, this radical on the left side,
+this is called nogihen, and it
+
+ align:start position:0%
+this is called nogihen, and it
+ 
+
+ align:start position:0%
+this is called nogihen, and it
+means gray. Then on the left side, these
+
+ align:start position:0%
+means gray. Then on the left side, these
+ 
+
+ align:start position:0%
+means gray. Then on the left side, these
+kanji are WeUStousethissenseasaCOUNTERWhichislike18LButwenolongerusethisCOUNTERButYoucanIMAGINEastoryyouneedsomesortofCOUNTERorCinordertoDividegrains, and they're pronounced that way.
+
+ align:start position:0%
+kanji are WeUStousethissenseasaCOUNTERWhichislike18LButwenolongerusethisCOUNTERButYoucanIMAGINEastoryyouneedsomesortofCOUNTERorCinordertoDividegrains, and they're pronounced that way.
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But this is
+
+ align:start position:0%
+But this is
+ 
+
+ align:start position:0%
+But this is
+okay with just reading. For example, courseofsubjectsubject. And then
+
+ align:start position:0%
+okay with just reading. For example, courseofsubjectsubject. And then
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+science, be careful here.
+
+ align:start position:0%
+science, be careful here.
+ 
+
+ align:start position:0%
+science, be careful here.
+This science is science,
+
+ align:start position:0%
+This science is science,
+ 
+
+ align:start position:0%
+This science is science,
+botharereadasscience, but
+
+ align:start position:0%
+botharereadasscience, but
+ 
+
+ align:start position:0%
+botharereadasscience, but
+thischaractermeansCHEMISTRY, and
+
+ align:start position:0%
+thischaractermeansCHEMISTRY, and
+ 
+
+ align:start position:0%
+thischaractermeansCHEMISTRY, and
+then internal medicine.
+
+ align:start position:0%
+then internal medicine.
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Surgery
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+department. Then the next kanji,
+
+ align:start position:0%
+department. Then the next kanji,
+ 
+
+ align:start position:0%
+department. Then the next kanji,
+this kanji means decree, so it's a
+
+ align:start position:0%
+this kanji means decree, so it's a
+ 
+
+ align:start position:0%
+this kanji means decree, so it's a
+component. But also,
+
+ align:start position:0%
+component. But also,
+ 
+
+ align:start position:0%
+component. But also,
+this radical is
+
+ align:start position:0%
+this radical is
+ 
+
+ align:start position:0%
+this radical is
+okay, water. And then this
+
+ align:start position:0%
+okay, water. And then this
+ 
+
+ align:start position:0%
+okay, water. And then this
+part, this is you
+
+ align:start position:0%
+part, this is you
+ 
+
+ align:start position:0%
+part, this is you
+canIMAGINElikeWEAPONorsomethinglikesomeoneisactuallymakingWHwithaWEAPONSothatthewater
+
+ align:start position:0%
+canIMAGINElikeWEAPONorsomethinglikesomeoneisactuallymakingWHwithaWEAPONSothatthewater
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decreases, I
+
+ align:start position:0%
+decreases, I
+ 
+
+ align:start position:0%
+decreases, I
+think we can create a story like that, but the reading is,
+
+ align:start position:0%
+think we can create a story like that, but the reading is,
+ 
+
+ align:start position:0%
+think we can create a story like that, but the reading is,
+this is the present, it's
+
+ align:start position:0%
+this is the present, it's
+ 
+
+ align:start position:0%
+this is the present, it's
+called, ge. For example, decrease is okay,
+
+ align:start position:0%
+called, ge. For example, decrease is okay,
+ 
+
+ align:start position:0%
+called, ge. For example, decrease is okay,
+hey, decrease, and it becomes less, to
+
+ align:start position:0%
+hey, decrease, and it becomes less, to
+ 
+
+ align:start position:0%
+hey, decrease, and it becomes less, to
+decrease, the origin, this
+
+ align:start position:0%
+decrease, the origin, this
+ 
+
+ align:start position:0%
+decrease, the origin, this
+means point, so to
+
+ align:start position:0%
+means point, so to
+ 
+
+ align:start position:0%
+means point, so to
+decrease, it means
+
+ align:start position:0%
+decrease, it means
+ 
+
+ align:start position:0%
+decrease, it means
+reduction, and in
+
+ align:start position:0%
+reduction, and in
+ 
+
+ align:start position:0%
+reduction, and in
+principle, this "immediately"
+
+ align:start position:0%
+principle, this "immediately"
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means fast or speed, so speed means decrease. Tax
+
+ align:start position:0%
+means fast or speed, so speed means decrease. Tax
+ 
+
+ align:start position:0%
+means fast or speed, so speed means decrease. Tax
+reduction, this means tax, TsoTX, reduction.
+
+ align:start position:0%
+reduction, this means tax, TsoTX, reduction.
+ 
+
+ align:start position:0%
+reduction, this means tax, TsoTX, reduction.
+And in the
+
+ align:start position:0%
+And in the
+ 
+
+ align:start position:0%
+And in the
+reading, it's read as "decreased." For example, the population decreased,
+
+ align:start position:0%
+reading, it's read as "decreased." For example, the population decreased,
+ 
+
+ align:start position:0%
+reading, it's read as "decreased." For example, the population decreased,
+the PO, it means decreased. The
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next kanji, this kanji means "conry," so if you look at
+
+ align:start position:0%
+next kanji, this kanji means "conry," so if you look at
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this part, this radical,
+
+ align:start position:0%
+this part, this radical,
+ 
+
+ align:start position:0%
+this part, this radical,
+this think the
+
+ align:start position:0%
+this think the
+ 
+
+ align:start position:0%
+this think the
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+HOUSE, and then the next part, this part, this character
+
+ align:start position:0%
+HOUSE, and then the next part, this part, this character
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+itself
+
+ align:start position:0%
+itself
+ 
+
+ align:start position:0%
+itself
+means ORIGIN or BASE. For example, this is,
+
+ align:start position:0%
+means ORIGIN or BASE. For example, this is,
+ 
+
+ align:start position:0%
+means ORIGIN or BASE. For example, this is,
+THE ORIGIN of your
+
+ align:start position:0%
+THE ORIGIN of your
+ 
+
+ align:start position:0%
+THE ORIGIN of your
+Spirit, so you're fine, you
+
+ align:start position:0%
+Spirit, so you're fine, you
+ 
+
+ align:start position:0%
+Spirit, so you're fine, you
+can IMAGINE THE STORY, so THE BASE was attached to the ROOF, so the
+
+ align:start position:0%
+can IMAGINE THE STORY, so THE BASE was attached to the ROOF, so the
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+house is completed  So, it
+
+ align:start position:0%
+house is completed  So, it
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means "COMPLETE." It's how you read it, but in the
+
+ align:start position:0%
+means "COMPLETE." It's how you read it, but in the
+ 
+
+ align:start position:0%
+means "COMPLETE." It's how you read it, but in the
+reading, for example, "Complete" means "Completed." Then, "
+
+ align:start position:0%
+reading, for example, "Complete" means "Completed." Then, "
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Complete" also means "Complete." And then, "Complete"
+
+ align:start position:0%
+Complete" also means "Complete." And then, "Complete"
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means "Perfect." Then, the next kanji, this kanji,
+
+ align:start position:0%
+means "Perfect." Then, the next kanji, this kanji,
+ 
+
+ align:start position:0%
+means "Perfect." Then, the next kanji, this kanji,
+means "clim." It's a
+
+ align:start position:0%
+means "clim." It's a
+ 
+
+ align:start position:0%
+means "clim." It's a
+component, but the
+
+ align:start position:0%
+component, but the
+ 
+
+ align:start position:0%
+component, but the
+top part is "you can
+
+ align:start position:0%
+top part is "you can
+ 
+
+ align:start position:0%
+top part is "you can
+imagine."
+
+ align:start position:0%
+imagine."
+ 
+
+ align:start position:0%
+imagine."
+For example, "outed legs." And, for example, "Departure." A
+
+ align:start position:0%
+For example, "outed legs." And, for example, "Departure." A
+ 
+
+ align:start position:0%
+For example, "outed legs." And, for example, "Departure." A
+commonly used kanji is "to
+
+ align:start position:0%
+commonly used kanji is "to
+ 
+
+ align:start position:0%
+commonly used kanji is "to
+depart." It
+
+ align:start position:0%
+depart." It
+ 
+
+ align:start position:0%
+depart." It
+means "Depart." And then, the
+
+ align:start position:0%
+means "Depart." And then, the
+ 
+
+ align:start position:0%
+means "Depart." And then, the
+kanji in this one is "bean." So, you have to bring beans in order to climb high. Both of these together mean "climb."
+
+ align:start position:0%
+kanji in this one is "bean." So, you have to bring beans in order to climb high. Both of these together mean "climb."
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+For example, climbing Mount Fuji. This
+
+ align:start position:0%
+For example, climbing Mount Fuji. This
+ 
+
+ align:start position:0%
+For example, climbing Mount Fuji. This
+particle counter is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+school, so going to school. And then, for
+
+ align:start position:0%
+school, so going to school. And then, for
+ 
+
+ align:start position:0%
+school, so going to school. And then, for
+example,
+
+ align:start position:0%
+example,
+ 
+
+ align:start position:0%
+example,
+appearing in this play. This
+
+ align:start position:0%
+appearing in this play. This
+ 
+
+ align:start position:0%
+appearing in this play. This
+means "to appear." It
+
+ align:start position:0%
+means "to appear." It
+ 
+
+ align:start position:0%
+means "to appear." It
+means "place." So, it means going to that place. Then, the
+
+ align:start position:0%
+means "place." So, it means going to that place. Then, the
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next kanji, this kanji,
+
+ align:start position:0%
+next kanji, this kanji,
+ 
+
+ align:start position:0%
+next kanji, this kanji,
+means "public."  It
+
+ align:start position:0%
+means "public."  It
+ 
+
+ align:start position:0%
+means "public."  It
+means official, and
+
+ align:start position:0%
+means official, and
+ 
+
+ align:start position:0%
+means official, and
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+feeling, ASS with feeling, Simply,
+
+ align:start position:0%
+feeling, ASS with feeling, Simply,
+ 
+
+ align:start position:0%
+feeling, ASS with feeling, Simply,
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+katakana,
+
+ align:start position:0%
+katakana,
+ 
+
+ align:start position:0%
+katakana,
+those, and how to read it, but it's
+
+ align:start position:0%
+those, and how to read it, but it's
+ 
+
+ align:start position:0%
+those, and how to read it, but it's
+O-rin, for example, Park, this is okay,
+
+ align:start position:0%
+O-rin, for example, Park, this is okay,
+ 
+
+ align:start position:0%
+O-rin, for example, Park, this is okay,
+Pa, then Public University, this is PU,
+
+ align:start position:0%
+Pa, then Public University, this is PU,
+ 
+
+ align:start position:0%
+Pa, then Public University, this is PU,
+Unity, and then make public, this
+
+ align:start position:0%
+Unity, and then make public, this
+ 
+
+ align:start position:0%
+Unity, and then make public, this
+means PU, and it's the Kun
+
+ align:start position:0%
+means PU, and it's the Kun
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reading, but it's not used very often, but it can also be read as Dai,
+
+ align:start position:0%
+reading, but it's not used very often, but it can also be read as Dai,
+ 
+
+ align:start position:0%
+reading, but it's not used very often, but it can also be read as Dai,
+for example, made the incident big,
+
+ align:start position:0%
+for example, made the incident big,
+ 
+
+ align:start position:0%
+for example, made the incident big,
+this means the same as making the incident public, so, um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this feeling, the
+
+ align:start position:0%
+this feeling, the
+ 
+
+ align:start position:0%
+this feeling, the
+feeling means L, and it's a
+
+ align:start position:0%
+feeling means L, and it's a
+ 
+
+ align:start position:0%
+feeling means L, and it's a
+component, and this
+
+ align:start position:0%
+component, and this
+ 
+
+ align:start position:0%
+component, and this
+radical is okay, this is the
+
+ align:start position:0%
+radical is okay, this is the
+ 
+
+ align:start position:0%
+radical is okay, this is the
+radical of that person, and then
+
+ align:start position:0%
+radical of that person, and then
+ 
+
+ align:start position:0%
+radical of that person, and then
+this part,
+
+ align:start position:0%
+this part,
+ 
+
+ align:start position:0%
+this part,
+this feeling, by itself means
+
+ align:start position:0%
+this feeling, by itself means
+ 
+
+ align:start position:0%
+this feeling, by itself means
+TRIBE, or clan, So this is the person, Who is the
+
+ align:start position:0%
+TRIBE, or clan, So this is the person, Who is the
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lowest, one clan, in tri, it's
+
+ align:start position:0%
+lowest, one clan, in tri, it's
+ 
+
+ align:start position:0%
+lowest, one clan, in tri, it's
+L, and how to read it,
+
+ align:start position:0%
+L, and how to read it,
+ 
+
+ align:start position:0%
+L, and how to read it,
+first of all, it's the Kun reading, so it's
+
+ align:start position:0%
+first of all, it's the Kun reading, so it's
+ 
+
+ align:start position:0%
+first of all, it's the Kun reading, so it's
+low, it's okay, it's short, and then the temperature is low, it
+
+ align:start position:0%
+low, it's okay, it's short, and then the temperature is low, it
+ 
+
+ align:start position:0%
+low, it's okay, it's short, and then the temperature is low, it
+means LOW, it
+
+ align:start position:0%
+means LOW, it
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means short, and
+
+ align:start position:0%
+means short, and
+ 
+
+ align:start position:0%
+means short, and
+then bottom, this is the only reading,
+
+ align:start position:0%
+then bottom, this is the only reading,
+ 
+
+ align:start position:0%
+then bottom, this is the only reading,
+low, LOW, and then the lowest, this is the
+
+ align:start position:0%
+low, LOW, and then the lowest, this is the
+ 
+
+ align:start position:0%
+low, LOW, and then the lowest, this is the
+worst, it means the most.
+
+ align:start position:0%
+worst, it means the most.
+ 
+
+ align:start position:0%
+worst, it means the most.
+So, the worst, the opposite, can be
+
+ align:start position:0%
+So, the worst, the opposite, can be
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+used as the best. Now, the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next kanji, this kanji means
+
+ align:start position:0%
+next kanji, this kanji means
+ 
+
+ align:start position:0%
+next kanji, this kanji means
+reverse or coralie, and
+
+ align:start position:0%
+reverse or coralie, and
+ 
+
+ align:start position:0%
+reverse or coralie, and
+radical is this
+
+ align:start position:0%
+radical is this
+ 
+
+ align:start position:0%
+radical is this
+component, so this radical
+
+ align:start position:0%
+component, so this radical
+ 
+
+ align:start position:0%
+component, so this radical
+part, trust this, or
+
+ align:start position:0%
+part, trust this, or
+ 
+
+ align:start position:0%
+part, trust this, or
+intrusion, either is fine, but it also means legs or
+
+ align:start position:0%
+intrusion, either is fine, but it also means legs or
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something to do with
+
+ align:start position:0%
+something to do with
+ 
+
+ align:start position:0%
+something to do with
+legs. For example, take a look at this list. Street, road, right? So this is something to do with legs, and then you can imagine this, A person in a hand, Stand, so He must be going, opposite is reverse. I
+
+ align:start position:0%
+legs. For example, take a look at this list. Street, road, right? So this is something to do with legs, and then you can imagine this, A person in a hand, Stand, so He must be going, opposite is reverse. I
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wonder if that kind of story is okay. As for how to read it, it's
+
+ align:start position:0%
+wonder if that kind of story is okay. As for how to read it, it's
+ 
+
+ align:start position:0%
+wonder if that kind of story is okay. As for how to read it, it's
+reverse in the reading, for example, reverse, or
+
+ align:start position:0%
+reverse in the reading, for example, reverse, or
+ 
+
+ align:start position:0%
+reverse in the reading, for example, reverse, or
+oh, yeah. And paradox, this theory,
+
+ align:start position:0%
+oh, yeah. And paradox, this theory,
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has that meaning of explanation, so it's called paradox, and
+
+ align:start position:0%
+has that meaning of explanation, so it's called paradox, and
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it also means countercurrent, and there's also a word that isn't
+
+ align:start position:0%
+it also means countercurrent, and there's also a word that isn't
+ 
+
+ align:start position:0%
+it also means countercurrent, and there's also a word that isn't
+used very often, but it
+
+ align:start position:0%
+used very often, but it
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means handstand in the reading.
+
+ align:start position:0%
+means handstand in the reading.
+ 
+
+ align:start position:0%
+means handstand in the reading.
+First, the next feeling. This feeling
+
+ align:start position:0%
+First, the next feeling. This feeling
+ 
+
+ align:start position:0%
+First, the next feeling. This feeling
+means "point." So,
+
+ align:start position:0%
+means "point." So,
+ 
+
+ align:start position:0%
+means "point." So,
+this part. The
+
+ align:start position:0%
+this part. The
+ 
+
+ align:start position:0%
+this part. The
+feeling above means "fortune telling" or "fortune telling by itself." And
+
+ align:start position:0%
+feeling above means "fortune telling" or "fortune telling by itself." And
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then this radical below always means "
+
+ align:start position:0%
+then this radical below always means "
+ 
+
+ align:start position:0%
+then this radical below always means "
+fire." We have a good story to make for this character, but this one, this component, or this means "fortune telling" and this radical always means "fire." It's pronounced as "only reading."
+
+ align:start position:0%
+fire." We have a good story to make for this character, but this one, this component, or this means "fortune telling" and this radical always means "fire." It's pronounced as "only reading."
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+For example, "point" is the point of
+
+ align:start position:0%
+For example, "point" is the point of
+ 
+
+ align:start position:0%
+For example, "point" is the point of
+the EXAM,
+
+ align:start position:0%
+the EXAM,
+ 
+
+ align:start position:0%
+the EXAM,
+or test, and "score" is also "POINT."
+
+ align:start position:0%
+or test, and "score" is also "POINT."
+ 
+
+ align:start position:0%
+or test, and "score" is also "POINT."
+Grade test score, test point,
+
+ align:start position:0%
+Grade test score, test point,
+ 
+
+ align:start position:0%
+Grade test score, test point,
+both have the same meaning. And then,
+
+ align:start position:0%
+both have the same meaning. And then,
+ 
+
+ align:start position:0%
+both have the same meaning. And then,
+origin, which is a point that reduces points,
+
+ align:start position:0%
+origin, which is a point that reduces points,
+ 
+
+ align:start position:0%
+origin, which is a point that reduces points,
+is a dictionary of POINT. And defect, which is a
+
+ align:start position:0%
+is a dictionary of POINT. And defect, which is a
+ 
+
+ align:start position:0%
+is a dictionary of POINT. And defect, which is a
+defect. A person
+
+ align:start position:0%
+defect. A person
+ 
+
+ align:start position:0%
+defect. A person
+'s defect is that they speak well. It
+
+ align:start position:0%
+'s defect is that they speak well. It
+ 
+
+ align:start position:0%
+'s defect is that they speak well. It
+means something like "de." And then, I
+
+ align:start position:0%
+means something like "de." And then, I
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+think you often see this on trains. This is the terminal point. This is the last point.
+
+ align:start position:0%
+think you often see this on trains. This is the terminal point. This is the last point.
+ 
+
+ align:start position:0%
+think you often see this on trains. This is the terminal point. This is the last point.
+This is the ending point.
+
+ align:start position:0%
+This is the ending point.
+ 
+
+ align:start position:0%
+This is the ending point.
+For example, "the terminal point is Tokyo." This
+
+ align:start position:0%
+For example, "the terminal point is Tokyo." This
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means that the last station is Tokyo.  Okay, the
+
+ align:start position:0%
+means that the last station is Tokyo.  Okay, the
+ 
+
+ align:start position:0%
+means that the last station is Tokyo.  Okay, the
+next kanji, this one,
+
+ align:start position:0%
+next kanji, this one,
+ 
+
+ align:start position:0%
+next kanji, this one,
+means normal, regular, and
+
+ align:start position:0%
+means normal, regular, and
+ 
+
+ align:start position:0%
+means normal, regular, and
+always. Let's
+
+ align:start position:0%
+always. Let's
+ 
+
+ align:start position:0%
+always. Let's
+start from the bottom. It's a
+
+ align:start position:0%
+start from the bottom. It's a
+ 
+
+ align:start position:0%
+start from the bottom. It's a
+component,
+
+ align:start position:0%
+component,
+ 
+
+ align:start position:0%
+component,
+this one at the bottom, you
+
+ align:start position:0%
+this one at the bottom, you
+ 
+
+ align:start position:0%
+this one at the bottom, you
+can IMAGINE, some
+
+ align:start position:0%
+can IMAGINE, some
+ 
+
+ align:start position:0%
+can IMAGINE, some
+banner or flag, and it
+
+ align:start position:0%
+banner or flag, and it
+ 
+
+ align:start position:0%
+banner or flag, and it
+means something to do
+
+ align:start position:0%
+means something to do
+ 
+
+ align:start position:0%
+means something to do
+with CL. And then the next one in the middle, this is
+
+ align:start position:0%
+with CL. And then the next one in the middle, this is
+ 
+
+ align:start position:0%
+with CL. And then the next one in the middle, this is
+okay, right? mouth so
+
+ align:start position:0%
+okay, right? mouth so
+ 
+
+ align:start position:0%
+okay, right? mouth so
+IMAGINE, under normal
+
+ align:start position:0%
+IMAGINE, under normal
+ 
+
+ align:start position:0%
+IMAGINE, under normal
+circumstances, you always have to wear a mask, right THISIS PERFECT for our PANDEMIC
+
+ align:start position:0%
+circumstances, you always have to wear a mask, right THISIS PERFECT for our PANDEMIC
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PER. As for how to
+
+ align:start position:0%
+PER. As for how to
+ 
+
+ align:start position:0%
+PER. As for how to
+read it, there
+
+ align:start position:0%
+read it, there
+ 
+
+ align:start position:0%
+read it, there
+'s the "ji" in the reading,
+
+ align:start position:0%
+'s the "ji" in the reading,
+ 
+
+ align:start position:0%
+'s the "ji" in the reading,
+for example, "jiji," which means "always."
+
+ align:start position:0%
+for example, "jiji," which means "always."
+ 
+
+ align:start position:0%
+for example, "jiji," which means "always."
+Then there's "common sense," which means
+
+ align:start position:0%
+Then there's "common sense," which means
+ 
+
+ align:start position:0%
+Then there's "common sense," which means
+knowledge or sense. Then there's "
+
+ align:start position:0%
+knowledge or sense. Then there's "
+ 
+
+ align:start position:0%
+knowledge or sense. Then there's "
+abnormal," which means "
+
+ align:start position:0%
+abnormal," which means "
+ 
+
+ align:start position:0%
+abnormal," which means "
+always,"
+
+ align:start position:0%
+always,"
+ 
+
+ align:start position:0%
+always,"
+but this means "not," which means "diff." Then there's "
+
+ align:start position:0%
+but this means "not," which means "diff." Then there's "
+ 
+
+ align:start position:0%
+but this means "not," which means "diff." Then there's "
+soabnormal," which is the negative of "
+
+ align:start position:0%
+soabnormal," which is the negative of "
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solackof." And then there's "very," which
+
+ align:start position:0%
+solackof." And then there's "very," which
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means "very cold," which
+
+ align:start position:0%
+means "very cold," which
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means "very cold today." And then there's "emergency exits" that you often see in buildings.  It
+
+ align:start position:0%
+means "very cold today." And then there's "emergency exits" that you often see in buildings.  It
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means exit, and in the Kun
+
+ align:start position:0%
+means exit, and in the Kun
+ 
+
+ align:start position:0%
+means exit, and in the Kun
+reading, it
+
+ align:start position:0%
+reading, it
+ 
+
+ align:start position:0%
+reading, it
+means always.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now, the next kanji, this kanji, um, means
+
+ align:start position:0%
+Now, the next kanji, this kanji, um, means
+ 
+
+ align:start position:0%
+Now, the next kanji, this kanji, um, means
+copy, and
+
+ align:start position:0%
+copy, and
+ 
+
+ align:start position:0%
+copy, and
+this feeling, I
+
+ align:start position:0%
+this feeling, I
+ 
+
+ align:start position:0%
+this feeling, I
+have, please be careful, There is no D, on top of this, and
+
+ align:start position:0%
+have, please be careful, There is no D, on top of this, and
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+this part, this feeling itself
+
+ align:start position:0%
+this part, this feeling itself
+ 
+
+ align:start position:0%
+this part, this feeling itself
+means to give, and it is
+
+ align:start position:0%
+means to give, and it is
+ 
+
+ align:start position:0%
+means to give, and it is
+read as, this, in the
+
+ align:start position:0%
+read as, this, in the
+ 
+
+ align:start position:0%
+read as, this, in the
+on reading, S, for example, everyone is
+
+ align:start position:0%
+on reading, S, for example, everyone is
+ 
+
+ align:start position:0%
+on reading, S, for example, everyone is
+familiar with the word photograph, please take a photo, take a
+
+ align:start position:0%
+familiar with the word photograph, please take a photo, take a
+ 
+
+ align:start position:0%
+familiar with the word photograph, please take a photo, take a
+photo, and then to copy, this is a
+
+ align:start position:0%
+photo, and then to copy, this is a
+ 
+
+ align:start position:0%
+photo, and then to copy, this is a
+book, right? So,
+
+ align:start position:0%
+book, right? So,
+ 
+
+ align:start position:0%
+book, right? So,
+for example, if you were to copy the teachings of Buddhism, then
+
+ align:start position:0%
+for example, if you were to copy the teachings of Buddhism, then
+ 
+
+ align:start position:0%
+for example, if you were to copy the teachings of Buddhism, then
+radiate, this means to copy, and in the
+
+ align:start position:0%
+radiate, this means to copy, and in the
+ 
+
+ align:start position:0%
+radiate, this means to copy, and in the
+Kun reading, project,
+
+ align:start position:0%
+Kun reading, project,
+ 
+
+ align:start position:0%
+Kun reading, project,
+this is also to C, which
+
+ align:start position:0%
+this is also to C, which
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means to copy my friend's notes. Now, the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next kanji, this feeling, it means
+
+ align:start position:0%
+next kanji, this feeling, it means
+ 
+
+ align:start position:0%
+next kanji, this feeling, it means
+TRUE or genin. So, let's take a
+
+ align:start position:0%
+TRUE or genin. So, let's take a
+ 
+
+ align:start position:0%
+TRUE or genin. So, let's take a
+look at the components.
+
+ align:start position:0%
+look at the components.
+ 
+
+ align:start position:0%
+look at the components.
+This top one is good, this 10, and
+
+ align:start position:0%
+This top one is good, this 10, and
+ 
+
+ align:start position:0%
+This top one is good, this 10, and
+then these eyes, Eyes, are, Standing
+
+ align:start position:0%
+then these eyes, Eyes, are, Standing
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the podium, the truth, to find out what really is going on.
+
+ align:start position:0%
+on the podium, the truth, to find out what really is going on.
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This feeling means TRUE and then genen. It is
+
+ align:start position:0%
+This feeling means TRUE and then genen. It is
+ 
+
+ align:start position:0%
+This feeling means TRUE and then genen. It is
+pronounced as "
+
+ align:start position:0%
+pronounced as "
+ 
+
+ align:start position:0%
+pronounced as "
+shi" in the on reading.
+
+ align:start position:0%
+shi" in the on reading.
+ 
+
+ align:start position:0%
+shi" in the on reading.
+For example, "photograph" means copying a photo, or
+
+ align:start position:0%
+For example, "photograph" means copying a photo, or
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+taking a photo. Then "truth" means "real
+
+ align:start position:0%
+taking a photo. Then "truth" means "real
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intention." In the on reading, it is pronounced as "sumo." This is in the middle. Then "
+
+ align:start position:0%
+intention." In the on reading, it is pronounced as "sumo." This is in the middle. Then "
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right in the middle." Then "
+
+ align:start position:0%
+Right in the middle." Then "
+ 
+
+ align:start position:0%
+Right in the middle." Then "
+really white." Then "directly above,
+
+ align:start position:0%
+really white." Then "directly above,
+ 
+
+ align:start position:0%
+really white." Then "directly above,
+right, AB, directly below, right,
+
+ align:start position:0%
+right, AB, directly below, right,
+ 
+
+ align:start position:0%
+right, AB, directly below, right,
+Under. That's how it's used. Now, the
+
+ align:start position:0%
+Under. That's how it's used. Now, the
+ 
+
+ align:start position:0%
+Under. That's how it's used. Now, the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next feeling is this feeling. It
+
+ align:start position:0%
+next feeling is this feeling. It
+ 
+
+ align:start position:0%
+next feeling is this feeling. It
+means "C" or "verify." It is a
+
+ align:start position:0%
+means "C" or "verify." It is a
+ 
+
+ align:start position:0%
+means "C" or "verify." It is a
+component.
+
+ align:start position:0%
+component.
+ 
+
+ align:start position:0%
+component.
+First, this part on the far left is "Stone." Then
+
+ align:start position:0%
+First, this part on the far left is "Stone." Then
+ 
+
+ align:start position:0%
+First, this part on the far left is "Stone." Then
+this part has something to do with "A bard." So, you can make a story such that "make
+
+ align:start position:0%
+this part has something to do with "A bard." So, you can make a story such that "make
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure verify." Word can be "Safe" by putting a protection or "ROOF" and then putting a Stone on the left. It is pronounced as "on reading." For example, "sure."
+
+ align:start position:0%
+sure verify." Word can be "Safe" by putting a protection or "ROOF" and then putting a Stone on the left. It is pronounced as "on reading." For example, "sure."
+ 
+
+ align:start position:0%
+sure verify." Word can be "Safe" by putting a protection or "ROOF" and then putting a Stone on the left. It is pronounced as "on reading." For example, "sure."
+This is the adjective.
+
+ align:start position:0%
+This is the adjective.
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Probability is often used in mathematics, isn't it? Then there's clear,
+
+ align:start position:0%
+Probability is often used in mathematics, isn't it? Then there's clear,
+ 
+
+ align:start position:0%
+Probability is often used in mathematics, isn't it? Then there's clear,
+which is also active. Clear is,
+
+ align:start position:0%
+which is also active. Clear is,
+ 
+
+ align:start position:0%
+which is also active. Clear is,
+for example, please explain clearly.
+
+ align:start position:0%
+for example, please explain clearly.
+ 
+
+ align:start position:0%
+for example, please explain clearly.
+This is accurate. To
+
+ align:start position:0%
+This is accurate. To
+ 
+
+ align:start position:0%
+This is accurate. To
+believe
+
+ align:start position:0%
+believe
+ 
+
+ align:start position:0%
+believe
+firmly is to confirm.
+
+ align:start position:0%
+firmly is to confirm.
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Please confirm
+
+ align:start position:0%
+Please confirm
+ 
+
+ align:start position:0%
+Please confirm
+the time. It can be used
+
+ align:start position:0%
+the time. It can be used
+ 
+
+ align:start position:0%
+the time. It can be used
+in readings like this. Also,
+
+ align:start position:0%
+in readings like this. Also,
+ 
+
+ align:start position:0%
+in readings like this. Also,
+overify means,
+
+ align:start position:0%
+overify means,
+ 
+
+ align:start position:0%
+overify means,
+for example, please verify the time. Yes, the next one is like this. This is the
+
+ align:start position:0%
+for example, please verify the time. Yes, the next one is like this. This is the
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+last character in Lesson 8. This is like this,
+
+ align:start position:0%
+last character in Lesson 8. This is like this,
+ 
+
+ align:start position:0%
+last character in Lesson 8. This is like this,
+but it means
+
+ align:start position:0%
+but it means
+ 
+
+ align:start position:0%
+but it means
+vage.
+
+ align:start position:0%
+vage.
+ 
+
+ align:start position:0%
+vage.
+Component, is this okay?
+
+ align:start position:0%
+Component, is this okay?
+ 
+
+ align:start position:0%
+Component, is this okay?
+Then, on the right side, this is
+
+ align:start position:0%
+Then, on the right side, this is
+ 
+
+ align:start position:0%
+Then, on the right side, this is
+like, US have directly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+corresponded to
+
+ align:start position:0%
+corresponded to
+ 
+
+ align:start position:0%
+corresponded to
+English in you think about mean like OFF so in order to build a village you have to CH OFFLOT
+
+ align:start position:0%
+English in you think about mean like OFF so in order to build a village you have to CH OFFLOT
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Softrees. That's what it means. So, in the
+
+ align:start position:0%
+Softrees. That's what it means. So, in the
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reading,
+
+ align:start position:0%
+reading,
+ 
+
+ align:start position:0%
+reading,
+for example, noon, this is farm,
+
+ align:start position:0%
+for example, noon, this is farm,
+ 
+
+ align:start position:0%
+for example, noon, this is farm,
+vage. And in the
+
+ align:start position:0%
+vage. And in the
+ 
+
+ align:start position:0%
+vage. And in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reading, this is fishing village, and
+
+ align:start position:0%
+reading, this is fishing village, and
+ 
+
+ align:start position:0%
+reading, this is fishing village, and
+then villager, this
+
+ align:start position:0%
+then villager, this
+ 
+
+ align:start position:0%
+then villager, this
+means villager.
\ No newline at end of file
diff --git a/ByTlCmDoEnk.txt b/ByTlCmDoEnk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c62f5e97a8eedf38e0cf756f918256dd04cddfa8
--- /dev/null
+++ b/ByTlCmDoEnk.txt
@@ -0,0 +1,675 @@
+align:start position:0%
+ 
+we would now like to consider a system
+
+ align:start position:0%
+we would now like to consider a system
+ 
+
+ align:start position:0%
+we would now like to consider a system
+of particles and let's draw them as one
+
+ align:start position:0%
+of particles and let's draw them as one
+ 
+
+ align:start position:0%
+of particles and let's draw them as one
+two three and let's refer to this one as
+
+ align:start position:0%
+two three and let's refer to this one as
+ 
+
+ align:start position:0%
+two three and let's refer to this one as
+the jafe particle of mass M J and these
+
+ align:start position:0%
+the jafe particle of mass M J and these
+ 
+
+ align:start position:0%
+the jafe particle of mass M J and these
+particles system of particles is in a
+
+ align:start position:0%
+particles system of particles is in a
+ 
+
+ align:start position:0%
+particles system of particles is in a
+gravitational field and I would like to
+
+ align:start position:0%
+gravitational field and I would like to
+ 
+
+ align:start position:0%
+gravitational field and I would like to
+consider the torque about some point s
+
+ align:start position:0%
+consider the torque about some point s
+ 
+
+ align:start position:0%
+consider the torque about some point s
+for this system of particles and in
+
+ align:start position:0%
+for this system of particles and in
+ 
+
+ align:start position:0%
+for this system of particles and in
+particular I'd like to know how do I
+
+ align:start position:0%
+particular I'd like to know how do I
+ 
+
+ align:start position:0%
+particular I'd like to know how do I
+treat the gravitational force that's
+
+ align:start position:0%
+treat the gravitational force that's
+ 
+
+ align:start position:0%
+treat the gravitational force that's
+acting on all of these individual
+
+ align:start position:0%
+acting on all of these individual
+ 
+
+ align:start position:0%
+acting on all of these individual
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+well the way we'll analyze this is
+
+ align:start position:0%
+well the way we'll analyze this is
+ 
+
+ align:start position:0%
+well the way we'll analyze this is
+recall that the definition of torque
+
+ align:start position:0%
+recall that the definition of torque
+ 
+
+ align:start position:0%
+recall that the definition of torque
+about some point now we have J n
+
+ align:start position:0%
+about some point now we have J n
+ 
+
+ align:start position:0%
+about some point now we have J n
+particles labeled by index J it's a
+
+ align:start position:0%
+particles labeled by index J it's a
+ 
+
+ align:start position:0%
+particles labeled by index J it's a
+vector from the place where calculating
+
+ align:start position:0%
+vector from the place where calculating
+ 
+
+ align:start position:0%
+vector from the place where calculating
+the torque to where the J the particle
+
+ align:start position:0%
+the torque to where the J the particle
+ 
+
+ align:start position:0%
+the torque to where the J the particle
+is located so we draw that vector our s
+
+ align:start position:0%
+is located so we draw that vector our s
+ 
+
+ align:start position:0%
+is located so we draw that vector our s
+J and we cross that with the force
+
+ align:start position:0%
+J and we cross that with the force
+ 
+
+ align:start position:0%
+J and we cross that with the force
+that's acting on the J the particle
+
+ align:start position:0%
+that's acting on the J the particle
+ 
+
+ align:start position:0%
+that's acting on the J the particle
+which in this case is the gravitational
+
+ align:start position:0%
+which in this case is the gravitational
+ 
+
+ align:start position:0%
+which in this case is the gravitational
+force and J G and this is the torque
+
+ align:start position:0%
+force and J G and this is the torque
+ 
+
+ align:start position:0%
+force and J G and this is the torque
+about s and it's this complicated sum
+
+ align:start position:0%
+about s and it's this complicated sum
+ 
+
+ align:start position:0%
+about s and it's this complicated sum
+but the son will simplify in the
+
+ align:start position:0%
+but the son will simplify in the
+ 
+
+ align:start position:0%
+but the son will simplify in the
+following way let's just write out a
+
+ align:start position:0%
+following way let's just write out a
+ 
+
+ align:start position:0%
+following way let's just write out a
+couple terms to see what it actually
+
+ align:start position:0%
+couple terms to see what it actually
+ 
+
+ align:start position:0%
+couple terms to see what it actually
+looks like so we have our s 1 cross M 1
+
+ align:start position:0%
+looks like so we have our s 1 cross M 1
+ 
+
+ align:start position:0%
+looks like so we have our s 1 cross M 1
+G Plus rs2 across m 2g and we just keep
+
+ align:start position:0%
+G Plus rs2 across m 2g and we just keep
+ 
+
+ align:start position:0%
+G Plus rs2 across m 2g and we just keep
+on going for the n terms now the
+
+ align:start position:0%
+on going for the n terms now the
+ 
+
+ align:start position:0%
+on going for the n terms now the
+quantity m1 is a scalar units of
+
+ align:start position:0%
+quantity m1 is a scalar units of
+ 
+
+ align:start position:0%
+quantity m1 is a scalar units of
+kilograms in SI units but the cross
+
+ align:start position:0%
+kilograms in SI units but the cross
+ 
+
+ align:start position:0%
+kilograms in SI units but the cross
+product is between this vector and that
+
+ align:start position:0%
+product is between this vector and that
+ 
+
+ align:start position:0%
+product is between this vector and that
+vector so I can actually rewrite this as
+
+ align:start position:0%
+vector so I can actually rewrite this as
+ 
+
+ align:start position:0%
+vector so I can actually rewrite this as
+m1 RS 1 cross g plus m2 RS to cross G
+
+ align:start position:0%
+m1 RS 1 cross g plus m2 RS to cross G
+ 
+
+ align:start position:0%
+m1 RS 1 cross g plus m2 RS to cross G
+etc and you see that the Jeep term is
+
+ align:start position:0%
+etc and you see that the Jeep term is
+ 
+
+ align:start position:0%
+etc and you see that the Jeep term is
+the same for every single object so I
+
+ align:start position:0%
+the same for every single object so I
+ 
+
+ align:start position:0%
+the same for every single object so I
+can write this sum J goes from 1 to n as
+
+ align:start position:0%
+can write this sum J goes from 1 to n as
+ 
+
+ align:start position:0%
+can write this sum J goes from 1 to n as
+MJ r SJ and pull the G out of the sum
+
+ align:start position:0%
+MJ r SJ and pull the G out of the sum
+ 
+
+ align:start position:0%
+MJ r SJ and pull the G out of the sum
+because every term has the same gene in
+
+ align:start position:0%
+because every term has the same gene in
+ 
+
+ align:start position:0%
+because every term has the same gene in
+the cross product now let's focus on the
+
+ align:start position:0%
+the cross product now let's focus on the
+ 
+
+ align:start position:0%
+the cross product now let's focus on the
+meaning of this sum where we're waiting
+
+ align:start position:0%
+meaning of this sum where we're waiting
+ 
+
+ align:start position:0%
+meaning of this sum where we're waiting
+position by now
+
+ align:start position:0%
+position by now
+ 
+
+ align:start position:0%
+position by now
+recall that if you have the center of
+
+ align:start position:0%
+recall that if you have the center of
+ 
+
+ align:start position:0%
+recall that if you have the center of
+mass of an object and we want to find
+
+ align:start position:0%
+mass of an object and we want to find
+ 
+
+ align:start position:0%
+mass of an object and we want to find
+out where is the location of the center
+
+ align:start position:0%
+out where is the location of the center
+ 
+
+ align:start position:0%
+out where is the location of the center
+of mass with respect to point s then we
+
+ align:start position:0%
+of mass with respect to point s then we
+ 
+
+ align:start position:0%
+of mass with respect to point s then we
+can calculate this vector R SCM by our
+
+ align:start position:0%
+can calculate this vector R SCM by our
+ 
+
+ align:start position:0%
+can calculate this vector R SCM by our
+definition that the location of the
+
+ align:start position:0%
+definition that the location of the
+ 
+
+ align:start position:0%
+definition that the location of the
+center of mass with respect to s is
+
+ align:start position:0%
+center of mass with respect to s is
+ 
+
+ align:start position:0%
+center of mass with respect to s is
+given by the sum j goes from 1 to n of
+
+ align:start position:0%
+given by the sum j goes from 1 to n of
+ 
+
+ align:start position:0%
+given by the sum j goes from 1 to n of
+MJ r SJ and we divide that by the total
+
+ align:start position:0%
+MJ r SJ and we divide that by the total
+ 
+
+ align:start position:0%
+MJ r SJ and we divide that by the total
+mass and j will denote this term I am
+
+ align:start position:0%
+mass and j will denote this term I am
+ 
+
+ align:start position:0%
+mass and j will denote this term I am
+total for the total mass so what we see
+
+ align:start position:0%
+total for the total mass so what we see
+ 
+
+ align:start position:0%
+total for the total mass so what we see
+here is the total mass times RS cm is
+
+ align:start position:0%
+here is the total mass times RS cm is
+ 
+
+ align:start position:0%
+here is the total mass times RS cm is
+equal to exactly the sum that we have in
+
+ align:start position:0%
+equal to exactly the sum that we have in
+ 
+
+ align:start position:0%
+equal to exactly the sum that we have in
+that expression m j RS j that's
+
+ align:start position:0%
+that expression m j RS j that's
+ 
+
+ align:start position:0%
+that expression m j RS j that's
+precisely that term and so we can
+
+ align:start position:0%
+precisely that term and so we can
+ 
+
+ align:start position:0%
+precisely that term and so we can
+conclude that the torque about the
+
+ align:start position:0%
+conclude that the torque about the
+ 
+
+ align:start position:0%
+conclude that the torque about the
+center of mass is M total our s cm
+
+ align:start position:0%
+center of mass is M total our s cm
+ 
+
+ align:start position:0%
+center of mass is M total our s cm
+across G now remember again M total is a
+
+ align:start position:0%
+across G now remember again M total is a
+ 
+
+ align:start position:0%
+across G now remember again M total is a
+scalar the cross product is between
+
+ align:start position:0%
+scalar the cross product is between
+ 
+
+ align:start position:0%
+scalar the cross product is between
+these two vectors and so finally we
+
+ align:start position:0%
+these two vectors and so finally we
+ 
+
+ align:start position:0%
+these two vectors and so finally we
+write this as our s cm cross and total G
+
+ align:start position:0%
+write this as our s cm cross and total G
+ 
+
+ align:start position:0%
+write this as our s cm cross and total G
+and this is how we apply the
+
+ align:start position:0%
+and this is how we apply the
+ 
+
+ align:start position:0%
+and this is how we apply the
+gravitational force to a system of
+
+ align:start position:0%
+gravitational force to a system of
+ 
+
+ align:start position:0%
+gravitational force to a system of
+particles now what does that mean well
+
+ align:start position:0%
+particles now what does that mean well
+ 
+
+ align:start position:0%
+particles now what does that mean well
+let's just denote our system like this
+
+ align:start position:0%
+let's just denote our system like this
+ 
+
+ align:start position:0%
+let's just denote our system like this
+and let's say here's the center of mass
+
+ align:start position:0%
+and let's say here's the center of mass
+ 
+
+ align:start position:0%
+and let's say here's the center of mass
+and here's the point s so what we need
+
+ align:start position:0%
+and here's the point s so what we need
+ 
+
+ align:start position:0%
+and here's the point s so what we need
+to do is we need to draw the vector R as
+
+ align:start position:0%
+to do is we need to draw the vector R as
+ 
+
+ align:start position:0%
+to do is we need to draw the vector R as
+cm and apply all the gravitational force
+
+ align:start position:0%
+cm and apply all the gravitational force
+ 
+
+ align:start position:0%
+cm and apply all the gravitational force
+at the center of mass and then our
+
+ align:start position:0%
+at the center of mass and then our
+ 
+
+ align:start position:0%
+at the center of mass and then our
+torque about s is the vector RS to where
+
+ align:start position:0%
+torque about s is the vector RS to where
+ 
+
+ align:start position:0%
+torque about s is the vector RS to where
+the forces acting cross M total G so in
+
+ align:start position:0%
+the forces acting cross M total G so in
+ 
+
+ align:start position:0%
+the forces acting cross M total G so in
+conclusion when you have a rigid body or
+
+ align:start position:0%
+conclusion when you have a rigid body or
+ 
+
+ align:start position:0%
+conclusion when you have a rigid body or
+a system of particles and you want to
+
+ align:start position:0%
+a system of particles and you want to
+ 
+
+ align:start position:0%
+a system of particles and you want to
+calculate the torque due to a uniform
+
+ align:start position:0%
+calculate the torque due to a uniform
+ 
+
+ align:start position:0%
+calculate the torque due to a uniform
+gravitational field then we place all we
+
+ align:start position:0%
+gravitational field then we place all we
+ 
+
+ align:start position:0%
+gravitational field then we place all we
+act the total gravitational force is
+
+ align:start position:0%
+act the total gravitational force is
+ 
+
+ align:start position:0%
+act the total gravitational force is
+acting at the center of mass and that
+
+ align:start position:0%
+acting at the center of mass and that
+ 
+
+ align:start position:0%
+acting at the center of mass and that
+gives us the torque about s
+
+ align:start position:0%
+gives us the torque about s
+ 
+
+ align:start position:0%
+gives us the torque about s
+the individual torques of the system of
+
+ align:start position:0%
+the individual torques of the system of
+ 
+
+ align:start position:0%
+the individual torques of the system of
+the gravitational force about s all the
+
+ align:start position:0%
+the gravitational force about s all the
+ 
+
+ align:start position:0%
+the gravitational force about s all the
+force is placed at the center of mass
\ No newline at end of file
diff --git a/COg6Qzt1new.txt b/COg6Qzt1new.txt
new file mode 100644
index 0000000000000000000000000000000000000000..813873923c92b4cd53ffe7dc6f0f4d305b44b4a6
--- /dev/null
+++ b/COg6Qzt1new.txt
@@ -0,0 +1,14803 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+opencourseware under a Creative Commons
+
+ align:start position:0%
+opencourseware under a Creative Commons
+ 
+
+ align:start position:0%
+opencourseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay what I want to do for the first
+
+ align:start position:0%
+um okay what I want to do for the first
+ 
+
+ align:start position:0%
+um okay what I want to do for the first
+couple of minutes of today's lecture
+
+ align:start position:0%
+couple of minutes of today's lecture
+ 
+
+ align:start position:0%
+couple of minutes of today's lecture
+well I guess looking at the handout what
+
+ align:start position:0%
+well I guess looking at the handout what
+ 
+
+ align:start position:0%
+well I guess looking at the handout what
+I want to do is play fill in the blank
+
+ align:start position:0%
+I want to do is play fill in the blank
+ 
+
+ align:start position:0%
+I want to do is play fill in the blank
+with this great picture of a a neuron I
+
+ align:start position:0%
+with this great picture of a a neuron I
+ 
+
+ align:start position:0%
+with this great picture of a a neuron I
+got to talk about the gross structure of
+
+ align:start position:0%
+got to talk about the gross structure of
+ 
+
+ align:start position:0%
+got to talk about the gross structure of
+the brain last time but I didn't get to
+
+ align:start position:0%
+the brain last time but I didn't get to
+ 
+
+ align:start position:0%
+the brain last time but I didn't get to
+say anything about a neuron
+
+ align:start position:0%
+say anything about a neuron
+ 
+
+ align:start position:0%
+say anything about a neuron
+neurons are the are the
+
+ align:start position:0%
+neurons are the are the
+ 
+
+ align:start position:0%
+neurons are the are the
+um our brain cells not all of brain
+
+ align:start position:0%
+um our brain cells not all of brain
+ 
+
+ align:start position:0%
+um our brain cells not all of brain
+cells right this is going to be a
+
+ align:start position:0%
+cells right this is going to be a
+ 
+
+ align:start position:0%
+cells right this is going to be a
+a neuron at least
+
+ align:start position:0%
+a neuron at least
+ 
+
+ align:start position:0%
+a neuron at least
+half the cells in the brain would be in
+
+ align:start position:0%
+half the cells in the brain would be in
+ 
+
+ align:start position:0%
+half the cells in the brain would be in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+category of glia that's a word that
+
+ align:start position:0%
+category of glia that's a word that
+ 
+
+ align:start position:0%
+category of glia that's a word that
+comes from the word for glue and all the
+
+ align:start position:0%
+comes from the word for glue and all the
+ 
+
+ align:start position:0%
+comes from the word for glue and all the
+years I was learning about this stuff
+
+ align:start position:0%
+years I was learning about this stuff
+ 
+
+ align:start position:0%
+years I was learning about this stuff
+um glia kind of got shoved into the
+
+ align:start position:0%
+um glia kind of got shoved into the
+ 
+
+ align:start position:0%
+um glia kind of got shoved into the
+category of like support staff right
+
+ align:start position:0%
+category of like support staff right
+ 
+
+ align:start position:0%
+category of like support staff right
+these were the guys who cleaned up after
+
+ align:start position:0%
+these were the guys who cleaned up after
+ 
+
+ align:start position:0%
+these were the guys who cleaned up after
+the neurons who were doing all the cool
+
+ align:start position:0%
+the neurons who were doing all the cool
+ 
+
+ align:start position:0%
+the neurons who were doing all the cool
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+um but it's becoming increasingly clear
+
+ align:start position:0%
+um but it's becoming increasingly clear
+ 
+
+ align:start position:0%
+um but it's becoming increasingly clear
+that that
+
+ align:start position:0%
+that that
+ 
+
+ align:start position:0%
+that that
+um glia have many functions to play in
+
+ align:start position:0%
+um glia have many functions to play in
+ 
+
+ align:start position:0%
+um glia have many functions to play in
+brain function uh beyond the merely
+
+ align:start position:0%
+brain function uh beyond the merely
+ 
+
+ align:start position:0%
+brain function uh beyond the merely
+vegetative and if you go into
+
+ align:start position:0%
+vegetative and if you go into
+ 
+
+ align:start position:0%
+vegetative and if you go into
+Neuroscience odds are that you'll end up
+
+ align:start position:0%
+Neuroscience odds are that you'll end up
+ 
+
+ align:start position:0%
+Neuroscience odds are that you'll end up
+learning a lot more about Galia than I
+
+ align:start position:0%
+learning a lot more about Galia than I
+ 
+
+ align:start position:0%
+learning a lot more about Galia than I
+did when I was when I was taking the
+
+ align:start position:0%
+did when I was when I was taking the
+ 
+
+ align:start position:0%
+did when I was when I was taking the
+equivalent course but the main units the
+
+ align:start position:0%
+equivalent course but the main units the
+ 
+
+ align:start position:0%
+equivalent course but the main units the
+main if you like computational units for
+
+ align:start position:0%
+main if you like computational units for
+ 
+
+ align:start position:0%
+main if you like computational units for
+the brain are neurons and so here's a
+
+ align:start position:0%
+the brain are neurons and so here's a
+ 
+
+ align:start position:0%
+the brain are neurons and so here's a
+quick tour of a a sort of a canonical
+
+ align:start position:0%
+quick tour of a a sort of a canonical
+ 
+
+ align:start position:0%
+quick tour of a a sort of a canonical
+typical Neuron a typical neuron would
+
+ align:start position:0%
+typical Neuron a typical neuron would
+ 
+
+ align:start position:0%
+typical Neuron a typical neuron would
+collect information either from other
+
+ align:start position:0%
+collect information either from other
+ 
+
+ align:start position:0%
+collect information either from other
+neurons or from sense organs through its
+
+ align:start position:0%
+neurons or from sense organs through its
+ 
+
+ align:start position:0%
+neurons or from sense organs through its
+dendrites the word comes from uh
+
+ align:start position:0%
+dendrites the word comes from uh
+ 
+
+ align:start position:0%
+dendrites the word comes from uh
+tree-like because they're branching
+
+ align:start position:0%
+tree-like because they're branching
+ 
+
+ align:start position:0%
+tree-like because they're branching
+structure so all these little branches
+
+ align:start position:0%
+structure so all these little branches
+ 
+
+ align:start position:0%
+structure so all these little branches
+making connections with lots of other
+
+ align:start position:0%
+making connections with lots of other
+ 
+
+ align:start position:0%
+making connections with lots of other
+neurons or with sense organs in say the
+
+ align:start position:0%
+neurons or with sense organs in say the
+ 
+
+ align:start position:0%
+neurons or with sense organs in say the
+skin or something like that
+
+ align:start position:0%
+skin or something like that
+ 
+
+ align:start position:0%
+skin or something like that
+um and um the information that the the
+
+ align:start position:0%
+um and um the information that the the
+ 
+
+ align:start position:0%
+um and um the information that the the
+dendrites collect you can think of as
+
+ align:start position:0%
+dendrites collect you can think of as
+ 
+
+ align:start position:0%
+dendrites collect you can think of as
+being in the form of little pulses of
+
+ align:start position:0%
+being in the form of little pulses of
+ 
+
+ align:start position:0%
+being in the form of little pulses of
+excitation or inhibition they can be
+
+ align:start position:0%
+excitation or inhibition they can be
+ 
+
+ align:start position:0%
+excitation or inhibition they can be
+either positive or negative in nature
+
+ align:start position:0%
+either positive or negative in nature
+ 
+
+ align:start position:0%
+either positive or negative in nature
+they flow down towards the cell body
+
+ align:start position:0%
+they flow down towards the cell body
+ 
+
+ align:start position:0%
+they flow down towards the cell body
+here the neuron is a cell like other
+
+ align:start position:0%
+here the neuron is a cell like other
+ 
+
+ align:start position:0%
+here the neuron is a cell like other
+cells it does all those good cellular
+
+ align:start position:0%
+cells it does all those good cellular
+ 
+
+ align:start position:0%
+cells it does all those good cellular
+sorts of things but for the purposes for
+
+ align:start position:0%
+sorts of things but for the purposes for
+ 
+
+ align:start position:0%
+sorts of things but for the purposes for
+our purposes its big job is to act as a
+
+ align:start position:0%
+our purposes its big job is to act as a
+ 
+
+ align:start position:0%
+our purposes its big job is to act as a
+sort of a summator and to ask how
+
+ align:start position:0%
+sort of a summator and to ask how
+ 
+
+ align:start position:0%
+sort of a summator and to ask how
+excited am I am I you know if I sum up
+
+ align:start position:0%
+excited am I am I you know if I sum up
+ 
+
+ align:start position:0%
+excited am I am I you know if I sum up
+all these pluses and minuses am I
+
+ align:start position:0%
+all these pluses and minuses am I
+ 
+
+ align:start position:0%
+all these pluses and minuses am I
+excited enough to want to tell other
+
+ align:start position:0%
+excited enough to want to tell other
+ 
+
+ align:start position:0%
+excited enough to want to tell other
+neurons about my level of excitement
+
+ align:start position:0%
+neurons about my level of excitement
+ 
+
+ align:start position:0%
+neurons about my level of excitement
+here if the excitement passes a
+
+ align:start position:0%
+here if the excitement passes a
+ 
+
+ align:start position:0%
+here if the excitement passes a
+threshold old the neuron sends an action
+
+ align:start position:0%
+threshold old the neuron sends an action
+ 
+
+ align:start position:0%
+threshold old the neuron sends an action
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a signal action po
+
+ align:start position:0%
+a signal action po
+ 
+
+ align:start position:0%
+a signal action po
+potential no that doesn't look right
+
+ align:start position:0%
+potential no that doesn't look right
+ 
+
+ align:start position:0%
+potential no that doesn't look right
+does it well potent there we go this is
+
+ align:start position:0%
+does it well potent there we go this is
+ 
+
+ align:start position:0%
+does it well potent there we go this is
+why there's a handout right because I
+
+ align:start position:0%
+why there's a handout right because I
+ 
+
+ align:start position:0%
+why there's a handout right because I
+can't spell under good circumstances and
+
+ align:start position:0%
+can't spell under good circumstances and
+ 
+
+ align:start position:0%
+can't spell under good circumstances and
+I can't spell online at all anyway that
+
+ align:start position:0%
+I can't spell online at all anyway that
+ 
+
+ align:start position:0%
+I can't spell online at all anyway that
+should say potential it sends a signal
+
+ align:start position:0%
+should say potential it sends a signal
+ 
+
+ align:start position:0%
+should say potential it sends a signal
+down the axon the long wire of the
+
+ align:start position:0%
+down the axon the long wire of the
+ 
+
+ align:start position:0%
+down the axon the long wire of the
+neuron is the Axon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that action potential has a couple of
+
+ align:start position:0%
+um that action potential has a couple of
+ 
+
+ align:start position:0%
+um that action potential has a couple of
+important properties
+
+ align:start position:0%
+important properties
+ 
+
+ align:start position:0%
+important properties
+property one is that it's of a single
+
+ align:start position:0%
+property one is that it's of a single
+ 
+
+ align:start position:0%
+property one is that it's of a single
+polarity there aren't pluses and minuses
+
+ align:start position:0%
+polarity there aren't pluses and minuses
+ 
+
+ align:start position:0%
+polarity there aren't pluses and minuses
+there's just a single polarity
+
+ align:start position:0%
+there's just a single polarity
+ 
+
+ align:start position:0%
+there's just a single polarity
+um and it's a fixed size
+
+ align:start position:0%
+um and it's a fixed size
+ 
+
+ align:start position:0%
+um and it's a fixed size
+a more excited neuron does not produce
+
+ align:start position:0%
+a more excited neuron does not produce
+ 
+
+ align:start position:0%
+a more excited neuron does not produce
+bigger action potential so how's the
+
+ align:start position:0%
+bigger action potential so how's the
+ 
+
+ align:start position:0%
+bigger action potential so how's the
+neuron going to tell another neuron that
+
+ align:start position:0%
+neuron going to tell another neuron that
+ 
+
+ align:start position:0%
+neuron going to tell another neuron that
+it's more excited
+
+ align:start position:0%
+it's more excited
+ 
+
+ align:start position:0%
+it's more excited
+would you guess it's going to say make
+
+ align:start position:0%
+would you guess it's going to say make
+ 
+
+ align:start position:0%
+would you guess it's going to say make
+more more uh
+
+ align:start position:0%
+more more uh
+ 
+
+ align:start position:0%
+more more uh
+um action potential so it's frequency
+
+ align:start position:0%
+um action potential so it's frequency
+ 
+
+ align:start position:0%
+um action potential so it's frequency
+coding it's it's level of um excitement
+
+ align:start position:0%
+coding it's it's level of um excitement
+ 
+
+ align:start position:0%
+coding it's it's level of um excitement
+but Action potentials are fixed size and
+
+ align:start position:0%
+but Action potentials are fixed size and
+ 
+
+ align:start position:0%
+but Action potentials are fixed size and
+and fixed sign electrochemical signals
+
+ align:start position:0%
+and fixed sign electrochemical signals
+ 
+
+ align:start position:0%
+and fixed sign electrochemical signals
+powering their way down this uh axon
+
+ align:start position:0%
+powering their way down this uh axon
+ 
+
+ align:start position:0%
+powering their way down this uh axon
+these bumps
+
+ align:start position:0%
+these bumps
+ 
+
+ align:start position:0%
+these bumps
+wrapping
+
+ align:start position:0%
+wrapping
+ 
+
+ align:start position:0%
+wrapping
+um around the axon are actually another
+
+ align:start position:0%
+um around the axon are actually another
+ 
+
+ align:start position:0%
+um around the axon are actually another
+cell type they're a form oops they're a
+
+ align:start position:0%
+cell type they're a form oops they're a
+ 
+
+ align:start position:0%
+cell type they're a form oops they're a
+form of glia known as uh myelin
+
+ align:start position:0%
+form of glia known as uh myelin
+ 
+
+ align:start position:0%
+form of glia known as uh myelin
+they act as it acts as insulation
+
+ align:start position:0%
+they act as it acts as insulation
+ 
+
+ align:start position:0%
+they act as it acts as insulation
+keeping the signal in one neuron
+
+ align:start position:0%
+keeping the signal in one neuron
+ 
+
+ align:start position:0%
+keeping the signal in one neuron
+separate from the signal in others and
+
+ align:start position:0%
+separate from the signal in others and
+ 
+
+ align:start position:0%
+separate from the signal in others and
+it also acts to speed transmission there
+
+ align:start position:0%
+it also acts to speed transmission there
+ 
+
+ align:start position:0%
+it also acts to speed transmission there
+are a number of neurological diseases
+
+ align:start position:0%
+are a number of neurological diseases
+ 
+
+ align:start position:0%
+are a number of neurological diseases
+whose cause is not a problem with the
+
+ align:start position:0%
+whose cause is not a problem with the
+ 
+
+ align:start position:0%
+whose cause is not a problem with the
+neuron but a problem with the myelin
+
+ align:start position:0%
+neuron but a problem with the myelin
+ 
+
+ align:start position:0%
+neuron but a problem with the myelin
+demyelinating diseases like multiple
+
+ align:start position:0%
+demyelinating diseases like multiple
+ 
+
+ align:start position:0%
+demyelinating diseases like multiple
+sclerosis for example
+
+ align:start position:0%
+sclerosis for example
+ 
+
+ align:start position:0%
+sclerosis for example
+have their effect because the insulation
+
+ align:start position:0%
+have their effect because the insulation
+ 
+
+ align:start position:0%
+have their effect because the insulation
+is breaking down not because the the
+
+ align:start position:0%
+is breaking down not because the the
+ 
+
+ align:start position:0%
+is breaking down not because the the
+nerve cells themselves are breaking down
+
+ align:start position:0%
+nerve cells themselves are breaking down
+ 
+
+ align:start position:0%
+nerve cells themselves are breaking down
+um that signal reaches the uh the
+
+ align:start position:0%
+um that signal reaches the uh the
+ 
+
+ align:start position:0%
+um that signal reaches the uh the
+arborization of the axon it you know
+
+ align:start position:0%
+arborization of the axon it you know
+ 
+
+ align:start position:0%
+arborization of the axon it you know
+then goes off and talks to a bunch of
+
+ align:start position:0%
+then goes off and talks to a bunch of
+ 
+
+ align:start position:0%
+then goes off and talks to a bunch of
+other neurons or if this was a motor
+
+ align:start position:0%
+other neurons or if this was a motor
+ 
+
+ align:start position:0%
+other neurons or if this was a motor
+neuron it would be talking to muscle
+
+ align:start position:0%
+neuron it would be talking to muscle
+ 
+
+ align:start position:0%
+neuron it would be talking to muscle
+typically it does not make a direct
+
+ align:start position:0%
+typically it does not make a direct
+ 
+
+ align:start position:0%
+typically it does not make a direct
+electrical contact if you look at
+
+ align:start position:0%
+electrical contact if you look at
+ 
+
+ align:start position:0%
+electrical contact if you look at
+connections between stuff in your
+
+ align:start position:0%
+connections between stuff in your
+ 
+
+ align:start position:0%
+connections between stuff in your
+computer those are a direct electrical
+
+ align:start position:0%
+computer those are a direct electrical
+ 
+
+ align:start position:0%
+computer those are a direct electrical
+contacts not the way things work in the
+
+ align:start position:0%
+contacts not the way things work in the
+ 
+
+ align:start position:0%
+contacts not the way things work in the
+nervous system in the nervous system
+
+ align:start position:0%
+nervous system in the nervous system
+ 
+
+ align:start position:0%
+nervous system in the nervous system
+there's a small Gap called a synapse
+
+ align:start position:0%
+there's a small Gap called a synapse
+ 
+
+ align:start position:0%
+there's a small Gap called a synapse
+and to signal from one neuron to another
+
+ align:start position:0%
+and to signal from one neuron to another
+ 
+
+ align:start position:0%
+and to signal from one neuron to another
+an electrical signal coming down the
+
+ align:start position:0%
+an electrical signal coming down the
+ 
+
+ align:start position:0%
+an electrical signal coming down the
+Axon
+
+ align:start position:0%
+Axon
+ 
+
+ align:start position:0%
+Axon
+causes chemicals to be released into the
+
+ align:start position:0%
+causes chemicals to be released into the
+ 
+
+ align:start position:0%
+causes chemicals to be released into the
+Gap they diffuse across
+
+ align:start position:0%
+Gap they diffuse across
+ 
+
+ align:start position:0%
+Gap they diffuse across
+the Gap and bind to receptors on the
+
+ align:start position:0%
+the Gap and bind to receptors on the
+ 
+
+ align:start position:0%
+the Gap and bind to receptors on the
+other side and that binding either
+
+ align:start position:0%
+other side and that binding either
+ 
+
+ align:start position:0%
+other side and that binding either
+produces a little Plus or a little minus
+
+ align:start position:0%
+produces a little Plus or a little minus
+ 
+
+ align:start position:0%
+produces a little Plus or a little minus
+depending on the nature of the chemical
+
+ align:start position:0%
+depending on the nature of the chemical
+ 
+
+ align:start position:0%
+depending on the nature of the chemical
+the nature of the receptor and then the
+
+ align:start position:0%
+the nature of the receptor and then the
+ 
+
+ align:start position:0%
+the nature of the receptor and then the
+whole process starts again so you go
+
+ align:start position:0%
+whole process starts again so you go
+ 
+
+ align:start position:0%
+whole process starts again so you go
+from an essentially electrical signal to
+
+ align:start position:0%
+from an essentially electrical signal to
+ 
+
+ align:start position:0%
+from an essentially electrical signal to
+a chemical signal then back to and
+
+ align:start position:0%
+a chemical signal then back to and
+ 
+
+ align:start position:0%
+a chemical signal then back to and
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+um electrical signal these neurotrans
+
+ align:start position:0%
+um electrical signal these neurotrans
+ 
+
+ align:start position:0%
+um electrical signal these neurotrans
+so-called neurotransmitter chemicals are
+
+ align:start position:0%
+so-called neurotransmitter chemicals are
+ 
+
+ align:start position:0%
+so-called neurotransmitter chemicals are
+the targets of lots of the uh of the
+
+ align:start position:0%
+the targets of lots of the uh of the
+ 
+
+ align:start position:0%
+the targets of lots of the uh of the
+drugs that are used to modulate
+
+ align:start position:0%
+drugs that are used to modulate
+ 
+
+ align:start position:0%
+drugs that are used to modulate
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+mental States like anti-depressive drugs
+
+ align:start position:0%
+mental States like anti-depressive drugs
+ 
+
+ align:start position:0%
+mental States like anti-depressive drugs
+for example and not not just not just
+
+ align:start position:0%
+for example and not not just not just
+ 
+
+ align:start position:0%
+for example and not not just not just
+drugs over the counter uh not just
+
+ align:start position:0%
+drugs over the counter uh not just
+ 
+
+ align:start position:0%
+drugs over the counter uh not just
+prescription drugs let's see what are
+
+ align:start position:0%
+prescription drugs let's see what are
+ 
+
+ align:start position:0%
+prescription drugs let's see what are
+you drinking there oh that's just tea
+
+ align:start position:0%
+you drinking there oh that's just tea
+ 
+
+ align:start position:0%
+you drinking there oh that's just tea
+how boring
+
+ align:start position:0%
+how boring
+ 
+
+ align:start position:0%
+how boring
+um the uh well I wasn't actually
+
+ align:start position:0%
+um the uh well I wasn't actually
+ 
+
+ align:start position:0%
+um the uh well I wasn't actually
+thinking she was probably putting away a
+
+ align:start position:0%
+thinking she was probably putting away a
+ 
+
+ align:start position:0%
+thinking she was probably putting away a
+margarita but
+
+ align:start position:0%
+margarita but
+ 
+
+ align:start position:0%
+margarita but
+um that drug would be working on on a
+
+ align:start position:0%
+um that drug would be working on on a
+ 
+
+ align:start position:0%
+um that drug would be working on on a
+synapse the caffeine that you are
+
+ align:start position:0%
+synapse the caffeine that you are
+ 
+
+ align:start position:0%
+synapse the caffeine that you are
+pouring into your uh uh brain is is
+
+ align:start position:0%
+pouring into your uh uh brain is is
+ 
+
+ align:start position:0%
+pouring into your uh uh brain is is
+working on neurotransmitter and and
+
+ align:start position:0%
+working on neurotransmitter and and
+ 
+
+ align:start position:0%
+working on neurotransmitter and and
+synaptic uh properties that that's
+
+ align:start position:0%
+synaptic uh properties that that's
+ 
+
+ align:start position:0%
+synaptic uh properties that that's
+that's where you get your chance to
+
+ align:start position:0%
+that's where you get your chance to
+ 
+
+ align:start position:0%
+that's where you get your chance to
+affect large numbers of neurons at one
+
+ align:start position:0%
+affect large numbers of neurons at one
+ 
+
+ align:start position:0%
+affect large numbers of neurons at one
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+um we'll we'll talk more about that
+
+ align:start position:0%
+um we'll we'll talk more about that
+ 
+
+ align:start position:0%
+um we'll we'll talk more about that
+later now if I look at my cute little
+
+ align:start position:0%
+later now if I look at my cute little
+ 
+
+ align:start position:0%
+later now if I look at my cute little
+diagram yes you should have been able by
+
+ align:start position:0%
+diagram yes you should have been able by
+ 
+
+ align:start position:0%
+diagram yes you should have been able by
+now to fill in
+
+ align:start position:0%
+now to fill in
+ 
+
+ align:start position:0%
+now to fill in
+all the I wonder what that interesting
+
+ align:start position:0%
+all the I wonder what that interesting
+ 
+
+ align:start position:0%
+all the I wonder what that interesting
+thing is at the top actually the middle
+
+ align:start position:0%
+thing is at the top actually the middle
+ 
+
+ align:start position:0%
+thing is at the top actually the middle
+one at the top
+
+ align:start position:0%
+one at the top
+ 
+
+ align:start position:0%
+one at the top
+what do you figure sell
+
+ align:start position:0%
+what do you figure sell
+ 
+
+ align:start position:0%
+what do you figure sell
+it's not axon it's not myelin those are
+
+ align:start position:0%
+it's not axon it's not myelin those are
+ 
+
+ align:start position:0%
+it's not axon it's not myelin those are
+the two at the bottom right and Center
+
+ align:start position:0%
+the two at the bottom right and Center
+ 
+
+ align:start position:0%
+the two at the bottom right and Center
+the uh one on the top right is pointing
+
+ align:start position:0%
+the uh one on the top right is pointing
+ 
+
+ align:start position:0%
+the uh one on the top right is pointing
+to synapse the one at the top left is
+
+ align:start position:0%
+to synapse the one at the top left is
+ 
+
+ align:start position:0%
+to synapse the one at the top left is
+pointing to dendrites and the one at the
+
+ align:start position:0%
+pointing to dendrites and the one at the
+ 
+
+ align:start position:0%
+pointing to dendrites and the one at the
+top bottom left is pointing to the cell
+
+ align:start position:0%
+top bottom left is pointing to the cell
+ 
+
+ align:start position:0%
+top bottom left is pointing to the cell
+body
+
+ align:start position:0%
+body
+ 
+
+ align:start position:0%
+body
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+well that's the one the one on the
+
+ align:start position:0%
+well that's the one the one on the
+ 
+
+ align:start position:0%
+well that's the one the one on the
+bottom left I figure is pointing to the
+
+ align:start position:0%
+bottom left I figure is pointing to the
+ 
+
+ align:start position:0%
+bottom left I figure is pointing to the
+Soma or cell body
+
+ align:start position:0%
+Soma or cell body
+ 
+
+ align:start position:0%
+Soma or cell body
+um I think the one at the top middle is
+
+ align:start position:0%
+um I think the one at the top middle is
+ 
+
+ align:start position:0%
+um I think the one at the top middle is
+pointing to the whole thing neuron yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graduated oh maybe ah yes thank you oh
+
+ align:start position:0%
+graduated oh maybe ah yes thank you oh
+ 
+
+ align:start position:0%
+graduated oh maybe ah yes thank you oh
+somebody's been doing the reading
+
+ align:start position:0%
+somebody's been doing the reading
+ 
+
+ align:start position:0%
+somebody's been doing the reading
+um yes okay you you are correct so the
+
+ align:start position:0%
+um yes okay you you are correct so the
+ 
+
+ align:start position:0%
+um yes okay you you are correct so the
+top middle is almost undoubtedly
+
+ align:start position:0%
+top middle is almost undoubtedly
+ 
+
+ align:start position:0%
+top middle is almost undoubtedly
+pointing to the axon that whole long
+
+ align:start position:0%
+pointing to the axon that whole long
+ 
+
+ align:start position:0%
+pointing to the axon that whole long
+thing and the the bottom um what uh what
+
+ align:start position:0%
+thing and the the bottom um what uh what
+ 
+
+ align:start position:0%
+thing and the the bottom um what uh what
+she's pointing out is that that that uh
+
+ align:start position:0%
+she's pointing out is that that that uh
+ 
+
+ align:start position:0%
+she's pointing out is that that that uh
+bottom middle one is pointing to these
+
+ align:start position:0%
+bottom middle one is pointing to these
+ 
+
+ align:start position:0%
+bottom middle one is pointing to these
+the the the
+
+ align:start position:0%
+the the the
+ 
+
+ align:start position:0%
+the the the
+the The Valleys amongst the bumps and
+
+ align:start position:0%
+the The Valleys amongst the bumps and
+ 
+
+ align:start position:0%
+the The Valleys amongst the bumps and
+those are called the nodes
+
+ align:start position:0%
+those are called the nodes
+ 
+
+ align:start position:0%
+those are called the nodes
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+ranvier
+
+ align:start position:0%
+ranvier
+ 
+
+ align:start position:0%
+ranvier
+undoubtedly named after you know Joe
+
+ align:start position:0%
+undoubtedly named after you know Joe
+ 
+
+ align:start position:0%
+undoubtedly named after you know Joe
+ranvier
+
+ align:start position:0%
+ranvier
+ 
+
+ align:start position:0%
+ranvier
+um who I don't know anything about but
+
+ align:start position:0%
+um who I don't know anything about but
+ 
+
+ align:start position:0%
+um who I don't know anything about but
+um there what what the way that myelin
+
+ align:start position:0%
+um there what what the way that myelin
+ 
+
+ align:start position:0%
+um there what what the way that myelin
+speeds up transmission is it makes it
+
+ align:start position:0%
+speeds up transmission is it makes it
+ 
+
+ align:start position:0%
+speeds up transmission is it makes it
+possible for the action potential rather
+
+ align:start position:0%
+possible for the action potential rather
+ 
+
+ align:start position:0%
+possible for the action potential rather
+than just going down the axon in a nice
+
+ align:start position:0%
+than just going down the axon in a nice
+ 
+
+ align:start position:0%
+than just going down the axon in a nice
+smooth fashion it jumps from node to
+
+ align:start position:0%
+smooth fashion it jumps from node to
+ 
+
+ align:start position:0%
+smooth fashion it jumps from node to
+node
+
+ align:start position:0%
+node
+ 
+
+ align:start position:0%
+node
+um and uh and so that's why the nodes
+
+ align:start position:0%
+um and uh and so that's why the nodes
+ 
+
+ align:start position:0%
+um and uh and so that's why the nodes
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay I'm glad we've solved that you
+
+ align:start position:0%
+okay I'm glad we've solved that you
+ 
+
+ align:start position:0%
+okay I'm glad we've solved that you
+would have thought I would have thought
+
+ align:start position:0%
+would have thought I would have thought
+ 
+
+ align:start position:0%
+would have thought I would have thought
+about that before putting the thing on
+
+ align:start position:0%
+about that before putting the thing on
+ 
+
+ align:start position:0%
+about that before putting the thing on
+the handout
+
+ align:start position:0%
+the handout
+ 
+
+ align:start position:0%
+the handout
+um okay any other questions about
+
+ align:start position:0%
+um okay any other questions about
+ 
+
+ align:start position:0%
+um okay any other questions about
+neurons or things yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well it's boring cell stuff happening
+
+ align:start position:0%
+well it's boring cell stuff happening
+ 
+
+ align:start position:0%
+well it's boring cell stuff happening
+all over the place I mean we shouldn't
+
+ align:start position:0%
+all over the place I mean we shouldn't
+ 
+
+ align:start position:0%
+all over the place I mean we shouldn't
+of course call it boring cell stuff
+
+ align:start position:0%
+of course call it boring cell stuff
+ 
+
+ align:start position:0%
+of course call it boring cell stuff
+because then guys in like course seven
+
+ align:start position:0%
+because then guys in like course seven
+ 
+
+ align:start position:0%
+because then guys in like course seven
+coming you know put a hit on us and
+
+ align:start position:0%
+coming you know put a hit on us and
+ 
+
+ align:start position:0%
+coming you know put a hit on us and
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+um but uh but yeah that's it's neurons
+
+ align:start position:0%
+um but uh but yeah that's it's neurons
+ 
+
+ align:start position:0%
+um but uh but yeah that's it's neurons
+are cells like other cells and they have
+
+ align:start position:0%
+are cells like other cells and they have
+ 
+
+ align:start position:0%
+are cells like other cells and they have
+to do all the you know respiratory
+
+ align:start position:0%
+to do all the you know respiratory
+ 
+
+ align:start position:0%
+to do all the you know respiratory
+things that other cells have to do
+
+ align:start position:0%
+things that other cells have to do
+ 
+
+ align:start position:0%
+things that other cells have to do
+um but you know our interest in them of
+
+ align:start position:0%
+um but you know our interest in them of
+ 
+
+ align:start position:0%
+um but you know our interest in them of
+course is as as little communication and
+
+ align:start position:0%
+course is as as little communication and
+ 
+
+ align:start position:0%
+course is as as little communication and
+computational units yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wraps around the axon and and acts as as
+
+ align:start position:0%
+wraps around the axon and and acts as as
+ 
+
+ align:start position:0%
+wraps around the axon and and acts as as
+insulation and and uh speed bumps I
+
+ align:start position:0%
+insulation and and uh speed bumps I
+ 
+
+ align:start position:0%
+insulation and and uh speed bumps I
+guess you think of these as the speed
+
+ align:start position:0%
+guess you think of these as the speed
+ 
+
+ align:start position:0%
+guess you think of these as the speed
+bumps except they speed things up rather
+
+ align:start position:0%
+bumps except they speed things up rather
+ 
+
+ align:start position:0%
+bumps except they speed things up rather
+than slowing things down
+
+ align:start position:0%
+than slowing things down
+ 
+
+ align:start position:0%
+than slowing things down
+um boy I bet that just confused matters
+
+ align:start position:0%
+um boy I bet that just confused matters
+ 
+
+ align:start position:0%
+um boy I bet that just confused matters
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that said what I want to do today
+
+ align:start position:0%
+that said what I want to do today
+ 
+
+ align:start position:0%
+that said what I want to do today
+is to talk about
+
+ align:start position:0%
+is to talk about
+ 
+
+ align:start position:0%
+is to talk about
+why we do anything
+
+ align:start position:0%
+why we do anything
+ 
+
+ align:start position:0%
+why we do anything
+it's the general topic of motivation
+
+ align:start position:0%
+it's the general topic of motivation
+ 
+
+ align:start position:0%
+it's the general topic of motivation
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you might well you can ask ask a
+
+ align:start position:0%
+you might well you can ask ask a
+ 
+
+ align:start position:0%
+you might well you can ask ask a
+question like why do you eat
+
+ align:start position:0%
+question like why do you eat
+ 
+
+ align:start position:0%
+question like why do you eat
+and you say well you gotta eat cause you
+
+ align:start position:0%
+and you say well you gotta eat cause you
+ 
+
+ align:start position:0%
+and you say well you gotta eat cause you
+need if you don't eat you die
+
+ align:start position:0%
+need if you don't eat you die
+ 
+
+ align:start position:0%
+need if you don't eat you die
+prove it right that's not a stupid point
+
+ align:start position:0%
+prove it right that's not a stupid point
+ 
+
+ align:start position:0%
+prove it right that's not a stupid point
+he meant it as a stupid point but it's
+
+ align:start position:0%
+he meant it as a stupid point but it's
+ 
+
+ align:start position:0%
+he meant it as a stupid point but it's
+not a stupid point does a rat why does a
+
+ align:start position:0%
+not a stupid point does a rat why does a
+ 
+
+ align:start position:0%
+not a stupid point does a rat why does a
+rat eat does a rat know it's gonna die
+
+ align:start position:0%
+rat eat does a rat know it's gonna die
+ 
+
+ align:start position:0%
+rat eat does a rat know it's gonna die
+is a rat sitting there you know with
+
+ align:start position:0%
+is a rat sitting there you know with
+ 
+
+ align:start position:0%
+is a rat sitting there you know with
+sort of existential concerns about it's
+
+ align:start position:0%
+sort of existential concerns about it's
+ 
+
+ align:start position:0%
+sort of existential concerns about it's
+I don't think so particularly and even
+
+ align:start position:0%
+I don't think so particularly and even
+ 
+
+ align:start position:0%
+I don't think so particularly and even
+if it were the case
+
+ align:start position:0%
+if it were the case
+ 
+
+ align:start position:0%
+if it were the case
+you know if you don't eat you're gonna
+
+ align:start position:0%
+you know if you don't eat you're gonna
+ 
+
+ align:start position:0%
+you know if you don't eat you're gonna
+die well so what
+
+ align:start position:0%
+die well so what
+ 
+
+ align:start position:0%
+die well so what
+you gotta answer I mean is it why you do
+
+ align:start position:0%
+you gotta answer I mean is it why you do
+ 
+
+ align:start position:0%
+you gotta answer I mean is it why you do
+anything is a question that requires
+
+ align:start position:0%
+anything is a question that requires
+ 
+
+ align:start position:0%
+anything is a question that requires
+some sort of an answer and I will give
+
+ align:start position:0%
+some sort of an answer and I will give
+ 
+
+ align:start position:0%
+some sort of an answer and I will give
+um a three-part answer part one of the
+
+ align:start position:0%
+um a three-part answer part one of the
+ 
+
+ align:start position:0%
+um a three-part answer part one of the
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+um will be that you are a slave to you
+
+ align:start position:0%
+um will be that you are a slave to you
+ 
+
+ align:start position:0%
+um will be that you are a slave to you
+do things as a slave to the environment
+
+ align:start position:0%
+do things as a slave to the environment
+ 
+
+ align:start position:0%
+do things as a slave to the environment
+part two will be that you do things as a
+
+ align:start position:0%
+part two will be that you do things as a
+ 
+
+ align:start position:0%
+part two will be that you do things as a
+slave in fact to your own brain and part
+
+ align:start position:0%
+slave in fact to your own brain and part
+ 
+
+ align:start position:0%
+slave in fact to your own brain and part
+three will be to say well Parts one and
+
+ align:start position:0%
+three will be to say well Parts one and
+ 
+
+ align:start position:0%
+three will be to say well Parts one and
+two seemed a little simple-minded we'd
+
+ align:start position:0%
+two seemed a little simple-minded we'd
+ 
+
+ align:start position:0%
+two seemed a little simple-minded we'd
+better try and get to a somewhat richer
+
+ align:start position:0%
+better try and get to a somewhat richer
+ 
+
+ align:start position:0%
+better try and get to a somewhat richer
+explanation that might explain why
+
+ align:start position:0%
+explanation that might explain why
+ 
+
+ align:start position:0%
+explanation that might explain why
+um your your uh sitting here in a
+
+ align:start position:0%
+um your your uh sitting here in a
+ 
+
+ align:start position:0%
+um your your uh sitting here in a
+classroom doing this rather complicated
+
+ align:start position:0%
+classroom doing this rather complicated
+ 
+
+ align:start position:0%
+classroom doing this rather complicated
+activity since what we'll be talking
+
+ align:start position:0%
+activity since what we'll be talking
+ 
+
+ align:start position:0%
+activity since what we'll be talking
+about is well oh one of the things we'll
+
+ align:start position:0%
+about is well oh one of the things we'll
+ 
+
+ align:start position:0%
+about is well oh one of the things we'll
+be talking about is the reason that is
+
+ align:start position:0%
+be talking about is the reason that is
+ 
+
+ align:start position:0%
+be talking about is the reason that is
+the obvious fact that I am a psych
+
+ align:start position:0%
+the obvious fact that I am a psych
+ 
+
+ align:start position:0%
+the obvious fact that I am a psych
+professor and not an artist
+
+ align:start position:0%
+professor and not an artist
+ 
+
+ align:start position:0%
+professor and not an artist
+um so you will have to uh bear with the
+
+ align:start position:0%
+um so you will have to uh bear with the
+ 
+
+ align:start position:0%
+um so you will have to uh bear with the
+fact that uh for present purposes that
+
+ align:start position:0%
+fact that uh for present purposes that
+ 
+
+ align:start position:0%
+fact that uh for present purposes that
+is a cat
+
+ align:start position:0%
+is a cat
+ 
+
+ align:start position:0%
+is a cat
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and and that is a rat
+
+ align:start position:0%
+and and that is a rat
+ 
+
+ align:start position:0%
+and and that is a rat
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+you are neither and the third part of
+
+ align:start position:0%
+you are neither and the third part of
+ 
+
+ align:start position:0%
+you are neither and the third part of
+the lecture will be devoted to explain
+
+ align:start position:0%
+the lecture will be devoted to explain
+ 
+
+ align:start position:0%
+the lecture will be devoted to explain
+to to trying to talk about the uh the
+
+ align:start position:0%
+to to trying to talk about the uh the
+ 
+
+ align:start position:0%
+to to trying to talk about the uh the
+Richer set of motivations that you might
+
+ align:start position:0%
+Richer set of motivations that you might
+ 
+
+ align:start position:0%
+Richer set of motivations that you might
+have and that even animals
+
+ align:start position:0%
+have and that even animals
+ 
+
+ align:start position:0%
+have and that even animals
+um might have well a good starting place
+
+ align:start position:0%
+um might have well a good starting place
+ 
+
+ align:start position:0%
+um might have well a good starting place
+even if it's a bad bit of art
+
+ align:start position:0%
+even if it's a bad bit of art
+ 
+
+ align:start position:0%
+even if it's a bad bit of art
+um would be uh that this is an unusually
+
+ align:start position:0%
+um would be uh that this is an unusually
+ 
+
+ align:start position:0%
+um would be uh that this is an unusually
+pathetic cat even for me
+
+ align:start position:0%
+pathetic cat even for me
+ 
+
+ align:start position:0%
+pathetic cat even for me
+um the uh
+
+ align:start position:0%
+um the uh
+ 
+
+ align:start position:0%
+um the uh
+back in the uh
+
+ align:start position:0%
+back in the uh
+ 
+
+ align:start position:0%
+back in the uh
+shortly before the turn of the last
+
+ align:start position:0%
+shortly before the turn of the last
+ 
+
+ align:start position:0%
+shortly before the turn of the last
+century
+
+ align:start position:0%
+century
+ 
+
+ align:start position:0%
+century
+uh Thorndike Edward Thorndike up at
+
+ align:start position:0%
+uh Thorndike Edward Thorndike up at
+ 
+
+ align:start position:0%
+uh Thorndike Edward Thorndike up at
+Harvard was doing experiments of the
+
+ align:start position:0%
+Harvard was doing experiments of the
+ 
+
+ align:start position:0%
+Harvard was doing experiments of the
+following form he would take cats who
+
+ align:start position:0%
+following form he would take cats who
+ 
+
+ align:start position:0%
+following form he would take cats who
+were hungry cats
+
+ align:start position:0%
+were hungry cats
+ 
+
+ align:start position:0%
+were hungry cats
+um and he would throw them in a box that
+
+ align:start position:0%
+um and he would throw them in a box that
+ 
+
+ align:start position:0%
+um and he would throw them in a box that
+looked um sort of like a a packing crate
+
+ align:start position:0%
+looked um sort of like a a packing crate
+ 
+
+ align:start position:0%
+looked um sort of like a a packing crate
+kind of thing
+
+ align:start position:0%
+kind of thing
+ 
+
+ align:start position:0%
+kind of thing
+um and you know but it slats all over
+
+ align:start position:0%
+um and you know but it slats all over
+ 
+
+ align:start position:0%
+um and you know but it slats all over
+the place and and outside of the box is
+
+ align:start position:0%
+the place and and outside of the box is
+ 
+
+ align:start position:0%
+the place and and outside of the box is
+a a bit of fish I bet you know if I drew
+
+ align:start position:0%
+a a bit of fish I bet you know if I drew
+ 
+
+ align:start position:0%
+a a bit of fish I bet you know if I drew
+a bit of fish you'd never know what it
+
+ align:start position:0%
+a bit of fish you'd never know what it
+ 
+
+ align:start position:0%
+a bit of fish you'd never know what it
+was this at least looks sort of like a
+
+ align:start position:0%
+was this at least looks sort of like a
+ 
+
+ align:start position:0%
+was this at least looks sort of like a
+fish so there's a bit of fish you got a
+
+ align:start position:0%
+fish so there's a bit of fish you got a
+ 
+
+ align:start position:0%
+fish so there's a bit of fish you got a
+Hungry Cat you got the fish
+
+ align:start position:0%
+Hungry Cat you got the fish
+ 
+
+ align:start position:0%
+Hungry Cat you got the fish
+um cat wants fish
+
+ align:start position:0%
+um cat wants fish
+ 
+
+ align:start position:0%
+um cat wants fish
+um what's the cat gonna do well the cat
+
+ align:start position:0%
+um what's the cat gonna do well the cat
+ 
+
+ align:start position:0%
+um what's the cat gonna do well the cat
+is sort of bouncing off the walls
+
+ align:start position:0%
+is sort of bouncing off the walls
+ 
+
+ align:start position:0%
+is sort of bouncing off the walls
+um being uh annoyed and and and and
+
+ align:start position:0%
+um being uh annoyed and and and and
+ 
+
+ align:start position:0%
+um being uh annoyed and and and and
+agitated and
+
+ align:start position:0%
+agitated and
+ 
+
+ align:start position:0%
+agitated and
+um and the way this box is set up
+
+ align:start position:0%
+um and the way this box is set up
+ 
+
+ align:start position:0%
+um and the way this box is set up
+is what they're called puzzle boxes
+
+ align:start position:0%
+is what they're called puzzle boxes
+ 
+
+ align:start position:0%
+is what they're called puzzle boxes
+because there's a in effect a a a TR
+
+ align:start position:0%
+because there's a in effect a a a TR
+ 
+
+ align:start position:0%
+because there's a in effect a a a TR
+there's a trick to getting out it might
+
+ align:start position:0%
+there's a trick to getting out it might
+ 
+
+ align:start position:0%
+there's a trick to getting out it might
+be that there's a a lever back here
+
+ align:start position:0%
+be that there's a a lever back here
+ 
+
+ align:start position:0%
+be that there's a a lever back here
+that's attached to some string and
+
+ align:start position:0%
+that's attached to some string and
+ 
+
+ align:start position:0%
+that's attached to some string and
+pulley Arrangement that lifts a gate
+
+ align:start position:0%
+pulley Arrangement that lifts a gate
+ 
+
+ align:start position:0%
+pulley Arrangement that lifts a gate
+over here and
+
+ align:start position:0%
+over here and
+ 
+
+ align:start position:0%
+over here and
+um if the cat happens to bounce into
+
+ align:start position:0%
+um if the cat happens to bounce into
+ 
+
+ align:start position:0%
+um if the cat happens to bounce into
+this uh lever
+
+ align:start position:0%
+this uh lever
+ 
+
+ align:start position:0%
+this uh lever
+um the gate goes up cat goes out gets
+
+ align:start position:0%
+um the gate goes up cat goes out gets
+ 
+
+ align:start position:0%
+um the gate goes up cat goes out gets
+the fish great well it's a little piece
+
+ align:start position:0%
+the fish great well it's a little piece
+ 
+
+ align:start position:0%
+the fish great well it's a little piece
+of fish and he's a Hungry Cat and what
+
+ align:start position:0%
+of fish and he's a Hungry Cat and what
+ 
+
+ align:start position:0%
+of fish and he's a Hungry Cat and what
+happens to the cat immediately
+
+ align:start position:0%
+happens to the cat immediately
+ 
+
+ align:start position:0%
+happens to the cat immediately
+thereafter is Thorndike grabs the cat
+
+ align:start position:0%
+thereafter is Thorndike grabs the cat
+ 
+
+ align:start position:0%
+thereafter is Thorndike grabs the cat
+again throws him back in the box
+
+ align:start position:0%
+again throws him back in the box
+ 
+
+ align:start position:0%
+again throws him back in the box
+what's the cat do well what uh whatever
+
+ align:start position:0%
+what's the cat do well what uh whatever
+ 
+
+ align:start position:0%
+what's the cat do well what uh whatever
+the cat is doing
+
+ align:start position:0%
+the cat is doing
+ 
+
+ align:start position:0%
+the cat is doing
+what Thorndike is doing is measuring the
+
+ align:start position:0%
+what Thorndike is doing is measuring the
+ 
+
+ align:start position:0%
+what Thorndike is doing is measuring the
+amount of time that it takes for
+
+ align:start position:0%
+amount of time that it takes for
+ 
+
+ align:start position:0%
+amount of time that it takes for
+the cat to get out of the box
+
+ align:start position:0%
+the cat to get out of the box
+ 
+
+ align:start position:0%
+the cat to get out of the box
+as a function of the uh the number of
+
+ align:start position:0%
+as a function of the uh the number of
+ 
+
+ align:start position:0%
+as a function of the uh the number of
+times that the cat's been chucked back
+
+ align:start position:0%
+times that the cat's been chucked back
+ 
+
+ align:start position:0%
+times that the cat's been chucked back
+in the box so you've got time
+
+ align:start position:0%
+in the box so you've got time
+ 
+
+ align:start position:0%
+in the box so you've got time
+as a function of uh we can call them
+
+ align:start position:0%
+as a function of uh we can call them
+ 
+
+ align:start position:0%
+as a function of uh we can call them
+trials the number of times the cat's
+
+ align:start position:0%
+trials the number of times the cat's
+ 
+
+ align:start position:0%
+trials the number of times the cat's
+been in the Box initially takes the cat
+
+ align:start position:0%
+been in the Box initially takes the cat
+ 
+
+ align:start position:0%
+been in the Box initially takes the cat
+some amount of time the next time maybe
+
+ align:start position:0%
+some amount of time the next time maybe
+ 
+
+ align:start position:0%
+some amount of time the next time maybe
+he's a little quicker
+
+ align:start position:0%
+he's a little quicker
+ 
+
+ align:start position:0%
+he's a little quicker
+and you get some sort of a function that
+
+ align:start position:0%
+and you get some sort of a function that
+ 
+
+ align:start position:0%
+and you get some sort of a function that
+eventually gets to some sort of
+
+ align:start position:0%
+eventually gets to some sort of
+ 
+
+ align:start position:0%
+eventually gets to some sort of
+asymptote where you Chuck The Cat In The
+
+ align:start position:0%
+asymptote where you Chuck The Cat In The
+ 
+
+ align:start position:0%
+asymptote where you Chuck The Cat In The
+Box the cat looks at you in a disgusted
+
+ align:start position:0%
+Box the cat looks at you in a disgusted
+ 
+
+ align:start position:0%
+Box the cat looks at you in a disgusted
+kind of way goes over to the levers goes
+
+ align:start position:0%
+kind of way goes over to the levers goes
+ 
+
+ align:start position:0%
+kind of way goes over to the levers goes
+eats the fish says okay we got to do
+
+ align:start position:0%
+eats the fish says okay we got to do
+ 
+
+ align:start position:0%
+eats the fish says okay we got to do
+this again fine
+
+ align:start position:0%
+this again fine
+ 
+
+ align:start position:0%
+this again fine
+um this is a learning curve in fact this
+
+ align:start position:0%
+um this is a learning curve in fact this
+ 
+
+ align:start position:0%
+um this is a learning curve in fact this
+is the original use of the term learning
+
+ align:start position:0%
+is the original use of the term learning
+ 
+
+ align:start position:0%
+is the original use of the term learning
+curve when you talk about going up the
+
+ align:start position:0%
+curve when you talk about going up the
+ 
+
+ align:start position:0%
+curve when you talk about going up the
+learning curve and stuff like that you
+
+ align:start position:0%
+learning curve and stuff like that you
+ 
+
+ align:start position:0%
+learning curve and stuff like that you
+are invoking Thorndike
+
+ align:start position:0%
+are invoking Thorndike
+ 
+
+ align:start position:0%
+are invoking Thorndike
+um what is the cat learning
+
+ align:start position:0%
+um what is the cat learning
+ 
+
+ align:start position:0%
+um what is the cat learning
+um in the 19th century and even today if
+
+ align:start position:0%
+um in the 19th century and even today if
+ 
+
+ align:start position:0%
+um in the 19th century and even today if
+you go to uh you know the animal section
+
+ align:start position:0%
+you go to uh you know the animal section
+ 
+
+ align:start position:0%
+you go to uh you know the animal section
+of Borders or something like that there
+
+ align:start position:0%
+of Borders or something like that there
+ 
+
+ align:start position:0%
+of Borders or something like that there
+are lots of books that will tell you
+
+ align:start position:0%
+are lots of books that will tell you
+ 
+
+ align:start position:0%
+are lots of books that will tell you
+about the you know the the rich mental
+
+ align:start position:0%
+about the you know the the rich mental
+ 
+
+ align:start position:0%
+about the you know the the rich mental
+life of of your cat
+
+ align:start position:0%
+life of of your cat
+ 
+
+ align:start position:0%
+life of of your cat
+um and so on Thorndike wasn't buying it
+
+ align:start position:0%
+um and so on Thorndike wasn't buying it
+ 
+
+ align:start position:0%
+um and so on Thorndike wasn't buying it
+what Thorndike uh said
+
+ align:start position:0%
+what Thorndike uh said
+ 
+
+ align:start position:0%
+what Thorndike uh said
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+um that
+
+ align:start position:0%
+um that
+ 
+
+ align:start position:0%
+um that
+there are good things in the world we'll
+
+ align:start position:0%
+there are good things in the world we'll
+ 
+
+ align:start position:0%
+there are good things in the world we'll
+call those uh reinforcers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they come in two forms
+
+ align:start position:0%
+they come in two forms
+ 
+
+ align:start position:0%
+they come in two forms
+there are positive reinforcers
+
+ align:start position:0%
+there are positive reinforcers
+ 
+
+ align:start position:0%
+there are positive reinforcers
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well uh well here as an example if if
+
+ align:start position:0%
+well uh well here as an example if if
+ 
+
+ align:start position:0%
+well uh well here as an example if if
+you tell a joke
+
+ align:start position:0%
+you tell a joke
+ 
+
+ align:start position:0%
+you tell a joke
+and people laugh that's a positive
+
+ align:start position:0%
+and people laugh that's a positive
+ 
+
+ align:start position:0%
+and people laugh that's a positive
+reinforcer you did something something
+
+ align:start position:0%
+reinforcer you did something something
+ 
+
+ align:start position:0%
+reinforcer you did something something
+good happened
+
+ align:start position:0%
+good happened
+ 
+
+ align:start position:0%
+good happened
+there are also negative reinforcers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those are also good things the jargon is
+
+ align:start position:0%
+those are also good things the jargon is
+ 
+
+ align:start position:0%
+those are also good things the jargon is
+unfortunate but a negative reinforcer is
+
+ align:start position:0%
+unfortunate but a negative reinforcer is
+ 
+
+ align:start position:0%
+unfortunate but a negative reinforcer is
+a good thing focus on the reinforcement
+
+ align:start position:0%
+a good thing focus on the reinforcement
+ 
+
+ align:start position:0%
+a good thing focus on the reinforcement
+part not the negative part A negative
+
+ align:start position:0%
+part not the negative part A negative
+ 
+
+ align:start position:0%
+part not the negative part A negative
+reinforcer is
+
+ align:start position:0%
+reinforcer is
+ 
+
+ align:start position:0%
+reinforcer is
+um the car alarm is going off
+
+ align:start position:0%
+um the car alarm is going off
+ 
+
+ align:start position:0%
+um the car alarm is going off
+right you do something that makes that
+
+ align:start position:0%
+right you do something that makes that
+ 
+
+ align:start position:0%
+right you do something that makes that
+noise stop
+
+ align:start position:0%
+noise stop
+ 
+
+ align:start position:0%
+noise stop
+right that's a good thing the cessation
+
+ align:start position:0%
+right that's a good thing the cessation
+ 
+
+ align:start position:0%
+right that's a good thing the cessation
+of something unpleasant like hunger for
+
+ align:start position:0%
+of something unpleasant like hunger for
+ 
+
+ align:start position:0%
+of something unpleasant like hunger for
+example is a negative reinforcer it's
+
+ align:start position:0%
+example is a negative reinforcer it's
+ 
+
+ align:start position:0%
+example is a negative reinforcer it's
+also a good thing a bad thing in this
+
+ align:start position:0%
+also a good thing a bad thing in this
+ 
+
+ align:start position:0%
+also a good thing a bad thing in this
+jargon is punishment is called
+
+ align:start position:0%
+jargon is punishment is called
+ 
+
+ align:start position:0%
+jargon is punishment is called
+punishment
+
+ align:start position:0%
+punishment
+ 
+
+ align:start position:0%
+punishment
+right you tell a joke
+
+ align:start position:0%
+right you tell a joke
+ 
+
+ align:start position:0%
+right you tell a joke
+the person you're telling a joke the
+
+ align:start position:0%
+the person you're telling a joke the
+ 
+
+ align:start position:0%
+the person you're telling a joke the
+joke to takes offense and smacks you
+
+ align:start position:0%
+joke to takes offense and smacks you
+ 
+
+ align:start position:0%
+joke to takes offense and smacks you
+that's punishment
+
+ align:start position:0%
+that's punishment
+ 
+
+ align:start position:0%
+that's punishment
+what Thorndike said what Thorndike
+
+ align:start position:0%
+what Thorndike said what Thorndike
+ 
+
+ align:start position:0%
+what Thorndike said what Thorndike
+formulated which is undoubtedly on the
+
+ align:start position:0%
+formulated which is undoubtedly on the
+ 
+
+ align:start position:0%
+formulated which is undoubtedly on the
+handout somewhere is
+
+ align:start position:0%
+handout somewhere is
+ 
+
+ align:start position:0%
+handout somewhere is
+the law of effect
+
+ align:start position:0%
+the law of effect
+ 
+
+ align:start position:0%
+the law of effect
+yeah at the top of the second page he
+
+ align:start position:0%
+yeah at the top of the second page he
+ 
+
+ align:start position:0%
+yeah at the top of the second page he
+proposed what what he called the law of
+
+ align:start position:0%
+proposed what what he called the law of
+ 
+
+ align:start position:0%
+proposed what what he called the law of
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+and he said that
+
+ align:start position:0%
+and he said that
+ 
+
+ align:start position:0%
+and he said that
+something that's followed by a
+
+ align:start position:0%
+something that's followed by a
+ 
+
+ align:start position:0%
+something that's followed by a
+reinforcer a behavior that's followed by
+
+ align:start position:0%
+reinforcer a behavior that's followed by
+ 
+
+ align:start position:0%
+reinforcer a behavior that's followed by
+a reinforcer is more likely to recur
+
+ align:start position:0%
+a reinforcer is more likely to recur
+ 
+
+ align:start position:0%
+a reinforcer is more likely to recur
+take the joke example if you tell a joke
+
+ align:start position:0%
+take the joke example if you tell a joke
+ 
+
+ align:start position:0%
+take the joke example if you tell a joke
+and somebody and and people laugh the
+
+ align:start position:0%
+and somebody and and people laugh the
+ 
+
+ align:start position:0%
+and somebody and and people laugh the
+next time the opportunity presents
+
+ align:start position:0%
+next time the opportunity presents
+ 
+
+ align:start position:0%
+next time the opportunity presents
+itself you are more likely to tell that
+
+ align:start position:0%
+itself you are more likely to tell that
+ 
+
+ align:start position:0%
+itself you are more likely to tell that
+joke
+
+ align:start position:0%
+joke
+ 
+
+ align:start position:0%
+joke
+the negative law of effect
+
+ align:start position:0%
+the negative law of effect
+ 
+
+ align:start position:0%
+the negative law of effect
+um is uh is or is not on the handout
+
+ align:start position:0%
+um is uh is or is not on the handout
+ 
+
+ align:start position:0%
+um is uh is or is not on the handout
+somewhere well yes there it is a little
+
+ align:start position:0%
+somewhere well yes there it is a little
+ 
+
+ align:start position:0%
+somewhere well yes there it is a little
+further down under where it says
+
+ align:start position:0%
+further down under where it says
+ 
+
+ align:start position:0%
+further down under where it says
+punishment the negative law of effect
+
+ align:start position:0%
+punishment the negative law of effect
+ 
+
+ align:start position:0%
+punishment the negative law of effect
+says if you do something and something
+
+ align:start position:0%
+says if you do something and something
+ 
+
+ align:start position:0%
+says if you do something and something
+bad happens you're less likely to do it
+
+ align:start position:0%
+bad happens you're less likely to do it
+ 
+
+ align:start position:0%
+bad happens you're less likely to do it
+again you tell a joke somebody smacks
+
+ align:start position:0%
+again you tell a joke somebody smacks
+ 
+
+ align:start position:0%
+again you tell a joke somebody smacks
+you the next time the opportunity
+
+ align:start position:0%
+you the next time the opportunity
+ 
+
+ align:start position:0%
+you the next time the opportunity
+presents itself
+
+ align:start position:0%
+presents itself
+ 
+
+ align:start position:0%
+presents itself
+um unless you're a teenage male odds are
+
+ align:start position:0%
+um unless you're a teenage male odds are
+ 
+
+ align:start position:0%
+um unless you're a teenage male odds are
+that you won't tell that joke again the
+
+ align:start position:0%
+that you won't tell that joke again the
+ 
+
+ align:start position:0%
+that you won't tell that joke again the
+um well this is a hey this is a separate
+
+ align:start position:0%
+um well this is a hey this is a separate
+ 
+
+ align:start position:0%
+um well this is a hey this is a separate
+problem this is the the uh the burping
+
+ align:start position:0%
+problem this is the the uh the burping
+ 
+
+ align:start position:0%
+problem this is the the uh the burping
+problem right you you when you were
+
+ align:start position:0%
+problem right you you when you were
+ 
+
+ align:start position:0%
+problem right you you when you were
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+12 maybe you discovered you could burp
+
+ align:start position:0%
+12 maybe you discovered you could burp
+ 
+
+ align:start position:0%
+12 maybe you discovered you could burp
+the alphabet or something and your 12
+
+ align:start position:0%
+the alphabet or something and your 12
+ 
+
+ align:start position:0%
+the alphabet or something and your 12
+year old guy friends thought it was
+
+ align:start position:0%
+year old guy friends thought it was
+ 
+
+ align:start position:0%
+year old guy friends thought it was
+really great and you've never so the
+
+ align:start position:0%
+really great and you've never so the
+ 
+
+ align:start position:0%
+really great and you've never so the
+behavior got reinforced and
+
+ align:start position:0%
+behavior got reinforced and
+ 
+
+ align:start position:0%
+behavior got reinforced and
+unfortunately it takes a lot of smacks
+
+ align:start position:0%
+unfortunately it takes a lot of smacks
+ 
+
+ align:start position:0%
+unfortunately it takes a lot of smacks
+before you unlearn that but that's
+
+ align:start position:0%
+before you unlearn that but that's
+ 
+
+ align:start position:0%
+before you unlearn that but that's
+that's actually the next lecture we'll
+
+ align:start position:0%
+that's actually the next lecture we'll
+ 
+
+ align:start position:0%
+that's actually the next lecture we'll
+talk about that next week
+
+ align:start position:0%
+talk about that next week
+ 
+
+ align:start position:0%
+talk about that next week
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the uh I'm I'm looking at the handout
+
+ align:start position:0%
+the uh I'm I'm looking at the handout
+ 
+
+ align:start position:0%
+the uh I'm I'm looking at the handout
+and realizing that I failed to give you
+
+ align:start position:0%
+and realizing that I failed to give you
+ 
+
+ align:start position:0%
+and realizing that I failed to give you
+uh the great bunny example
+
+ align:start position:0%
+uh the great bunny example
+ 
+
+ align:start position:0%
+uh the great bunny example
+um and you're going to uh and you're
+
+ align:start position:0%
+um and you're going to uh and you're
+ 
+
+ align:start position:0%
+um and you're going to uh and you're
+going to look at your notes later and
+
+ align:start position:0%
+going to look at your notes later and
+ 
+
+ align:start position:0%
+going to look at your notes later and
+wonder what this is but I can use that
+
+ align:start position:0%
+wonder what this is but I can use that
+ 
+
+ align:start position:0%
+wonder what this is but I can use that
+to illustrate the uh the same point my
+
+ align:start position:0%
+to illustrate the uh the same point my
+ 
+
+ align:start position:0%
+to illustrate the uh the same point my
+my I I have a rabbit anybody want a
+
+ align:start position:0%
+my I I have a rabbit anybody want a
+ 
+
+ align:start position:0%
+my I I have a rabbit anybody want a
+rabbit we have a rabbit it's an accident
+
+ align:start position:0%
+rabbit we have a rabbit it's an accident
+ 
+
+ align:start position:0%
+rabbit we have a rabbit it's an accident
+you can have him
+
+ align:start position:0%
+you can have him
+ 
+
+ align:start position:0%
+you can have him
+um but anyway this rabbit when we walk
+
+ align:start position:0%
+um but anyway this rabbit when we walk
+ 
+
+ align:start position:0%
+um but anyway this rabbit when we walk
+when I go down into the kitchen in the
+
+ align:start position:0%
+when I go down into the kitchen in the
+ 
+
+ align:start position:0%
+when I go down into the kitchen in the
+morning goes berserk he's thumping up
+
+ align:start position:0%
+morning goes berserk he's thumping up
+ 
+
+ align:start position:0%
+morning goes berserk he's thumping up
+and down in his cage why is he what what
+
+ align:start position:0%
+and down in his cage why is he what what
+ 
+
+ align:start position:0%
+and down in his cage why is he what what
+what's he doing well basically
+
+ align:start position:0%
+what's he doing well basically
+ 
+
+ align:start position:0%
+what's he doing well basically
+um he's
+
+ align:start position:0%
+um he's
+ 
+
+ align:start position:0%
+um he's
+signaling that it's time for breakfast
+
+ align:start position:0%
+signaling that it's time for breakfast
+ 
+
+ align:start position:0%
+signaling that it's time for breakfast
+not just any breakfast you give him
+
+ align:start position:0%
+not just any breakfast you give him
+ 
+
+ align:start position:0%
+not just any breakfast you give him
+rabbit ciao he keeps thumping he's
+
+ align:start position:0%
+rabbit ciao he keeps thumping he's
+ 
+
+ align:start position:0%
+rabbit ciao he keeps thumping he's
+addicted to Reese's Pieces not Reese's
+
+ align:start position:0%
+addicted to Reese's Pieces not Reese's
+ 
+
+ align:start position:0%
+addicted to Reese's Pieces not Reese's
+Pieces the Reese's cereal it's very sad
+
+ align:start position:0%
+Pieces the Reese's cereal it's very sad
+ 
+
+ align:start position:0%
+Pieces the Reese's cereal it's very sad
+he's he's a he's a sugar sugar cereal
+
+ align:start position:0%
+he's he's a he's a sugar sugar cereal
+ 
+
+ align:start position:0%
+he's he's a he's a sugar sugar cereal
+junkie
+
+ align:start position:0%
+junkie
+ 
+
+ align:start position:0%
+junkie
+um and in these terms
+
+ align:start position:0%
+um and in these terms
+ 
+
+ align:start position:0%
+um and in these terms
+what's happened the way where his
+
+ align:start position:0%
+what's happened the way where his
+ 
+
+ align:start position:0%
+what's happened the way where his
+behavior is coming from what's driving
+
+ align:start position:0%
+behavior is coming from what's driving
+ 
+
+ align:start position:0%
+behavior is coming from what's driving
+his behavior is he was making some sort
+
+ align:start position:0%
+his behavior is he was making some sort
+ 
+
+ align:start position:0%
+his behavior is he was making some sort
+of arbitrary noise at some point when we
+
+ align:start position:0%
+of arbitrary noise at some point when we
+ 
+
+ align:start position:0%
+of arbitrary noise at some point when we
+fed him and perhaps when we fed him
+
+ align:start position:0%
+fed him and perhaps when we fed him
+ 
+
+ align:start position:0%
+fed him and perhaps when we fed him
+Reese's cereal the first time
+
+ align:start position:0%
+Reese's cereal the first time
+ 
+
+ align:start position:0%
+Reese's cereal the first time
+it was really good it was a positive
+
+ align:start position:0%
+it was really good it was a positive
+ 
+
+ align:start position:0%
+it was really good it was a positive
+reinforcer
+
+ align:start position:0%
+reinforcer
+ 
+
+ align:start position:0%
+reinforcer
+it made more likely the behavior that he
+
+ align:start position:0%
+it made more likely the behavior that he
+ 
+
+ align:start position:0%
+it made more likely the behavior that he
+had just been doing so the next time the
+
+ align:start position:0%
+had just been doing so the next time the
+ 
+
+ align:start position:0%
+had just been doing so the next time the
+opportunity presented himself he went
+
+ align:start position:0%
+opportunity presented himself he went
+ 
+
+ align:start position:0%
+opportunity presented himself he went
+Thump Thump Thump being the right time
+
+ align:start position:0%
+Thump Thump Thump being the right time
+ 
+
+ align:start position:0%
+Thump Thump Thump being the right time
+of day anyway he got more Reese's stuff
+
+ align:start position:0%
+of day anyway he got more Reese's stuff
+ 
+
+ align:start position:0%
+of day anyway he got more Reese's stuff
+and now by this law of effect kind of um
+
+ align:start position:0%
+and now by this law of effect kind of um
+ 
+
+ align:start position:0%
+and now by this law of effect kind of um
+training
+
+ align:start position:0%
+training
+ 
+
+ align:start position:0%
+training
+he has learned
+
+ align:start position:0%
+he has learned
+ 
+
+ align:start position:0%
+he has learned
+um that if he goes Thump Thump Thump
+
+ align:start position:0%
+um that if he goes Thump Thump Thump
+ 
+
+ align:start position:0%
+um that if he goes Thump Thump Thump
+we'll remember that it's time for the
+
+ align:start position:0%
+we'll remember that it's time for the
+ 
+
+ align:start position:0%
+we'll remember that it's time for the
+sweet cereal
+
+ align:start position:0%
+sweet cereal
+ 
+
+ align:start position:0%
+sweet cereal
+and and he gets very disappointed when
+
+ align:start position:0%
+and and he gets very disappointed when
+ 
+
+ align:start position:0%
+and and he gets very disappointed when
+it turns out that you know the the the
+
+ align:start position:0%
+it turns out that you know the the the
+ 
+
+ align:start position:0%
+it turns out that you know the the the
+sweet cereal Supply is run out we're
+
+ align:start position:0%
+sweet cereal Supply is run out we're
+ 
+
+ align:start position:0%
+sweet cereal Supply is run out we're
+trying to feed him like some health food
+
+ align:start position:0%
+trying to feed him like some health food
+ 
+
+ align:start position:0%
+trying to feed him like some health food
+stuff he's not not interested
+
+ align:start position:0%
+stuff he's not not interested
+ 
+
+ align:start position:0%
+stuff he's not not interested
+um carrots are okay but only barely so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why is it that animal why why how many
+
+ align:start position:0%
+why is it that animal why why how many
+ 
+
+ align:start position:0%
+why is it that animal why why how many
+of you have cats and dogs
+
+ align:start position:0%
+of you have cats and dogs
+ 
+
+ align:start position:0%
+of you have cats and dogs
+cats or dogs one or the other you don't
+
+ align:start position:0%
+cats or dogs one or the other you don't
+ 
+
+ align:start position:0%
+cats or dogs one or the other you don't
+have to have both almost all of you can
+
+ align:start position:0%
+have to have both almost all of you can
+ 
+
+ align:start position:0%
+have to have both almost all of you can
+probably tell me something about the
+
+ align:start position:0%
+probably tell me something about the
+ 
+
+ align:start position:0%
+probably tell me something about the
+brilliant intelligent behavior of this
+
+ align:start position:0%
+brilliant intelligent behavior of this
+ 
+
+ align:start position:0%
+brilliant intelligent behavior of this
+dog that doesn't or cat that doesn't
+
+ align:start position:0%
+dog that doesn't or cat that doesn't
+ 
+
+ align:start position:0%
+dog that doesn't or cat that doesn't
+sound like this sort of accidental
+
+ align:start position:0%
+sound like this sort of accidental
+ 
+
+ align:start position:0%
+sound like this sort of accidental
+learning of an association between a
+
+ align:start position:0%
+learning of an association between a
+ 
+
+ align:start position:0%
+learning of an association between a
+behavior and its consequences this sort
+
+ align:start position:0%
+behavior and its consequences this sort
+ 
+
+ align:start position:0%
+behavior and its consequences this sort
+of Association learning by the way is
+
+ align:start position:0%
+of Association learning by the way is
+ 
+
+ align:start position:0%
+of Association learning by the way is
+what I'll talk about the rules of it
+
+ align:start position:0%
+what I'll talk about the rules of it
+ 
+
+ align:start position:0%
+what I'll talk about the rules of it
+I'll talk about extensively next week
+
+ align:start position:0%
+I'll talk about extensively next week
+ 
+
+ align:start position:0%
+I'll talk about extensively next week
+but why is it that we're so convinced
+
+ align:start position:0%
+but why is it that we're so convinced
+ 
+
+ align:start position:0%
+but why is it that we're so convinced
+that animals have a much richer
+
+ align:start position:0%
+that animals have a much richer
+ 
+
+ align:start position:0%
+that animals have a much richer
+intellectual life well one possibility
+
+ align:start position:0%
+intellectual life well one possibility
+ 
+
+ align:start position:0%
+intellectual life well one possibility
+is that they do have a richer
+
+ align:start position:0%
+is that they do have a richer
+ 
+
+ align:start position:0%
+is that they do have a richer
+intellectual life than this the other
+
+ align:start position:0%
+intellectual life than this the other
+ 
+
+ align:start position:0%
+intellectual life than this the other
+the one that Thorndike
+
+ align:start position:0%
+the one that Thorndike
+ 
+
+ align:start position:0%
+the one that Thorndike
+thought he was seeing was what really
+
+ align:start position:0%
+thought he was seeing was what really
+ 
+
+ align:start position:0%
+thought he was seeing was what really
+boils down to uh selective reporting
+
+ align:start position:0%
+boils down to uh selective reporting
+ 
+
+ align:start position:0%
+boils down to uh selective reporting
+that I put the whole quote on the
+
+ align:start position:0%
+that I put the whole quote on the
+ 
+
+ align:start position:0%
+that I put the whole quote on the
+handout nah
+
+ align:start position:0%
+handout nah
+ 
+
+ align:start position:0%
+handout nah
+um what what Thorndike said
+
+ align:start position:0%
+um what what Thorndike said
+ 
+
+ align:start position:0%
+um what what Thorndike said
+is dogs get lost hundreds of times and
+
+ align:start position:0%
+is dogs get lost hundreds of times and
+ 
+
+ align:start position:0%
+is dogs get lost hundreds of times and
+nobody ever notices it or sends an
+
+ align:start position:0%
+nobody ever notices it or sends an
+ 
+
+ align:start position:0%
+nobody ever notices it or sends an
+account to a scientific magazine but let
+
+ align:start position:0%
+account to a scientific magazine but let
+ 
+
+ align:start position:0%
+account to a scientific magazine but let
+one dog find his way from Brooklyn to
+
+ align:start position:0%
+one dog find his way from Brooklyn to
+ 
+
+ align:start position:0%
+one dog find his way from Brooklyn to
+Yonkers and and that fact immediately
+
+ align:start position:0%
+Yonkers and and that fact immediately
+ 
+
+ align:start position:0%
+Yonkers and and that fact immediately
+becomes a circulating anecdote thousands
+
+ align:start position:0%
+becomes a circulating anecdote thousands
+ 
+
+ align:start position:0%
+becomes a circulating anecdote thousands
+of cats he says
+
+ align:start position:0%
+of cats he says
+ 
+
+ align:start position:0%
+of cats he says
+sit on thousands of occasions helplessly
+
+ align:start position:0%
+sit on thousands of occasions helplessly
+ 
+
+ align:start position:0%
+sit on thousands of occasions helplessly
+yelling
+
+ align:start position:0%
+yelling
+ 
+
+ align:start position:0%
+yelling
+and nobody ever writes to his friend the
+
+ align:start position:0%
+and nobody ever writes to his friend the
+ 
+
+ align:start position:0%
+and nobody ever writes to his friend the
+professor about it
+
+ align:start position:0%
+professor about it
+ 
+
+ align:start position:0%
+professor about it
+but let one cat claw at the knob
+
+ align:start position:0%
+but let one cat claw at the knob
+ 
+
+ align:start position:0%
+but let one cat claw at the knob
+seemingly in in uh
+
+ align:start position:0%
+seemingly in in uh
+ 
+
+ align:start position:0%
+seemingly in in uh
+um supposedly is a signal to be let out
+
+ align:start position:0%
+um supposedly is a signal to be let out
+ 
+
+ align:start position:0%
+um supposedly is a signal to be let out
+and straight away that cat becomes the
+
+ align:start position:0%
+and straight away that cat becomes the
+ 
+
+ align:start position:0%
+and straight away that cat becomes the
+representative of the cat mind what
+
+ align:start position:0%
+representative of the cat mind what
+ 
+
+ align:start position:0%
+representative of the cat mind what
+Thorndike thought was that you are that
+
+ align:start position:0%
+Thorndike thought was that you are that
+ 
+
+ align:start position:0%
+Thorndike thought was that you are that
+well at least the cat and perhaps by
+
+ align:start position:0%
+well at least the cat and perhaps by
+ 
+
+ align:start position:0%
+well at least the cat and perhaps by
+extension you are a slave to your
+
+ align:start position:0%
+extension you are a slave to your
+ 
+
+ align:start position:0%
+extension you are a slave to your
+environment you're the the contingencies
+
+ align:start position:0%
+environment you're the the contingencies
+ 
+
+ align:start position:0%
+environment you're the the contingencies
+in your environment shape what you do if
+
+ align:start position:0%
+in your environment shape what you do if
+ 
+
+ align:start position:0%
+in your environment shape what you do if
+the environment rewards you for pushing
+
+ align:start position:0%
+the environment rewards you for pushing
+ 
+
+ align:start position:0%
+the environment rewards you for pushing
+this lever you'll push this lever and
+
+ align:start position:0%
+this lever you'll push this lever and
+ 
+
+ align:start position:0%
+this lever you'll push this lever and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the cleverness the content of that is
+
+ align:start position:0%
+the cleverness the content of that is
+ 
+
+ align:start position:0%
+the cleverness the content of that is
+the seeming content of that is imposed
+
+ align:start position:0%
+the seeming content of that is imposed
+ 
+
+ align:start position:0%
+the seeming content of that is imposed
+from the outside it's not there it's not
+
+ align:start position:0%
+from the outside it's not there it's not
+ 
+
+ align:start position:0%
+from the outside it's not there it's not
+necessary you can explain it all you can
+
+ align:start position:0%
+necessary you can explain it all you can
+ 
+
+ align:start position:0%
+necessary you can explain it all you can
+explain why you do things purely in
+
+ align:start position:0%
+explain why you do things purely in
+ 
+
+ align:start position:0%
+explain why you do things purely in
+terms of um of these of this law of
+
+ align:start position:0%
+terms of um of these of this law of
+ 
+
+ align:start position:0%
+terms of um of these of this law of
+effect suitably elaborated and as I say
+
+ align:start position:0%
+effect suitably elaborated and as I say
+ 
+
+ align:start position:0%
+effect suitably elaborated and as I say
+the suitable elaboration
+
+ align:start position:0%
+the suitable elaboration
+ 
+
+ align:start position:0%
+the suitable elaboration
+um on that will come
+
+ align:start position:0%
+um on that will come
+ 
+
+ align:start position:0%
+um on that will come
+uh will come next week
+
+ align:start position:0%
+uh will come next week
+ 
+
+ align:start position:0%
+uh will come next week
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the elaboration by the way is known as
+
+ align:start position:0%
+the elaboration by the way is known as
+ 
+
+ align:start position:0%
+the elaboration by the way is known as
+behaviorism as a school of scientific of
+
+ align:start position:0%
+behaviorism as a school of scientific of
+ 
+
+ align:start position:0%
+behaviorism as a school of scientific of
+psychological thought that says that um
+
+ align:start position:0%
+psychological thought that says that um
+ 
+
+ align:start position:0%
+psychological thought that says that um
+that the explanation for your behavior
+
+ align:start position:0%
+that the explanation for your behavior
+ 
+
+ align:start position:0%
+that the explanation for your behavior
+can be found in the contingencies
+
+ align:start position:0%
+can be found in the contingencies
+ 
+
+ align:start position:0%
+can be found in the contingencies
+um that relate your actions to um to
+
+ align:start position:0%
+um that relate your actions to um to
+ 
+
+ align:start position:0%
+um that relate your actions to um to
+their consequences in the world and that
+
+ align:start position:0%
+their consequences in the world and that
+ 
+
+ align:start position:0%
+their consequences in the world and that
+relates to the relationships between
+
+ align:start position:0%
+relates to the relationships between
+ 
+
+ align:start position:0%
+relates to the relationships between
+stimuli
+
+ align:start position:0%
+stimuli
+ 
+
+ align:start position:0%
+stimuli
+um stimuli in the world that gets you
+
+ align:start position:0%
+um stimuli in the world that gets you
+ 
+
+ align:start position:0%
+um stimuli in the world that gets you
+some distance but what is it that
+
+ align:start position:0%
+some distance but what is it that
+ 
+
+ align:start position:0%
+some distance but what is it that
+actually makes something reinforcing why
+
+ align:start position:0%
+actually makes something reinforcing why
+ 
+
+ align:start position:0%
+actually makes something reinforcing why
+should something be reinforcing at all
+
+ align:start position:0%
+should something be reinforcing at all
+ 
+
+ align:start position:0%
+should something be reinforcing at all
+what is it about say food
+
+ align:start position:0%
+what is it about say food
+ 
+
+ align:start position:0%
+what is it about say food
+um that that you know why does the cat
+
+ align:start position:0%
+um that that you know why does the cat
+ 
+
+ align:start position:0%
+um that that you know why does the cat
+care that he gets out and and and
+
+ align:start position:0%
+care that he gets out and and and
+ 
+
+ align:start position:0%
+care that he gets out and and and
+satisfies his hunger for that you want
+
+ align:start position:0%
+satisfies his hunger for that you want
+ 
+
+ align:start position:0%
+satisfies his hunger for that you want
+to switch to uh the second form of
+
+ align:start position:0%
+to switch to uh the second form of
+ 
+
+ align:start position:0%
+to switch to uh the second form of
+slavery which is this notion that you
+
+ align:start position:0%
+slavery which is this notion that you
+ 
+
+ align:start position:0%
+slavery which is this notion that you
+are slave to your um to your own brain
+
+ align:start position:0%
+are slave to your um to your own brain
+ 
+
+ align:start position:0%
+are slave to your um to your own brain
+in a sense and uh the the the emblematic
+
+ align:start position:0%
+in a sense and uh the the the emblematic
+ 
+
+ align:start position:0%
+in a sense and uh the the the emblematic
+experiment for that uh is done some 50
+
+ align:start position:0%
+experiment for that uh is done some 50
+ 
+
+ align:start position:0%
+experiment for that uh is done some 50
+years after Thorndike is working with
+
+ align:start position:0%
+years after Thorndike is working with
+ 
+
+ align:start position:0%
+years after Thorndike is working with
+the with his puzzle box and that comes
+
+ align:start position:0%
+the with his puzzle box and that comes
+ 
+
+ align:start position:0%
+the with his puzzle box and that comes
+from an experiment done by Olton Milner
+
+ align:start position:0%
+from an experiment done by Olton Milner
+ 
+
+ align:start position:0%
+from an experiment done by Olton Milner
+it actually started as a mistake done by
+
+ align:start position:0%
+it actually started as a mistake done by
+ 
+
+ align:start position:0%
+it actually started as a mistake done by
+olds and Milner here's what they were
+
+ align:start position:0%
+olds and Milner here's what they were
+ 
+
+ align:start position:0%
+olds and Milner here's what they were
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+they were sticking electrodes into the
+
+ align:start position:0%
+they were sticking electrodes into the
+ 
+
+ align:start position:0%
+they were sticking electrodes into the
+brain of rats into the brains of rats
+
+ align:start position:0%
+brain of rats into the brains of rats
+ 
+
+ align:start position:0%
+brain of rats into the brains of rats
+um and down into the brain stem because
+
+ align:start position:0%
+um and down into the brain stem because
+ 
+
+ align:start position:0%
+um and down into the brain stem because
+what they wanted to do was to study
+
+ align:start position:0%
+what they wanted to do was to study
+ 
+
+ align:start position:0%
+what they wanted to do was to study
+arousal centers down in the brain stem I
+
+ align:start position:0%
+arousal centers down in the brain stem I
+ 
+
+ align:start position:0%
+arousal centers down in the brain stem I
+mentioned last time
+
+ align:start position:0%
+mentioned last time
+ 
+
+ align:start position:0%
+mentioned last time
+um are intimately involved in in things
+
+ align:start position:0%
+um are intimately involved in in things
+ 
+
+ align:start position:0%
+um are intimately involved in in things
+like sleep and wake it's a general level
+
+ align:start position:0%
+like sleep and wake it's a general level
+ 
+
+ align:start position:0%
+like sleep and wake it's a general level
+of arousal how do you know if a rat is
+
+ align:start position:0%
+of arousal how do you know if a rat is
+ 
+
+ align:start position:0%
+of arousal how do you know if a rat is
+aroused or not well one of the ways to
+
+ align:start position:0%
+aroused or not well one of the ways to
+ 
+
+ align:start position:0%
+aroused or not well one of the ways to
+measure arousal in a radius just to look
+
+ align:start position:0%
+measure arousal in a radius just to look
+ 
+
+ align:start position:0%
+measure arousal in a radius just to look
+at the amount of activity that that rat
+
+ align:start position:0%
+at the amount of activity that that rat
+ 
+
+ align:start position:0%
+at the amount of activity that that rat
+is emitting a rat that's just sort of
+
+ align:start position:0%
+is emitting a rat that's just sort of
+ 
+
+ align:start position:0%
+is emitting a rat that's just sort of
+sitting there is not very aroused now
+
+ align:start position:0%
+sitting there is not very aroused now
+ 
+
+ align:start position:0%
+sitting there is not very aroused now
+that that's running around is presumably
+
+ align:start position:0%
+that that's running around is presumably
+ 
+
+ align:start position:0%
+that that's running around is presumably
+aroused great so they're going to stick
+
+ align:start position:0%
+aroused great so they're going to stick
+ 
+
+ align:start position:0%
+aroused great so they're going to stick
+an electrode into the rat's brain and
+
+ align:start position:0%
+an electrode into the rat's brain and
+ 
+
+ align:start position:0%
+an electrode into the rat's brain and
+look at General levels
+
+ align:start position:0%
+look at General levels
+ 
+
+ align:start position:0%
+look at General levels
+of activity there's a problem that
+
+ align:start position:0%
+of activity there's a problem that
+ 
+
+ align:start position:0%
+of activity there's a problem that
+requires a control experiment first
+
+ align:start position:0%
+requires a control experiment first
+ 
+
+ align:start position:0%
+requires a control experiment first
+what other than sort of generalized
+
+ align:start position:0%
+what other than sort of generalized
+ 
+
+ align:start position:0%
+what other than sort of generalized
+arousal might get a rat to run around
+
+ align:start position:0%
+arousal might get a rat to run around
+ 
+
+ align:start position:0%
+arousal might get a rat to run around
+would you think
+
+ align:start position:0%
+would you think
+ 
+
+ align:start position:0%
+would you think
+sticking electrode in their brain
+
+ align:start position:0%
+sticking electrode in their brain
+ 
+
+ align:start position:0%
+sticking electrode in their brain
+um yeah well we've uh why why am I
+
+ align:start position:0%
+um yeah well we've uh why why am I
+ 
+
+ align:start position:0%
+um yeah well we've uh why why am I
+sticking an electrode in their brain
+
+ align:start position:0%
+sticking an electrode in their brain
+ 
+
+ align:start position:0%
+sticking an electrode in their brain
+make them run around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pain it might hurt right you know if so
+
+ align:start position:0%
+pain it might hurt right you know if so
+ 
+
+ align:start position:0%
+pain it might hurt right you know if so
+suppose all that happens when you uh
+
+ align:start position:0%
+suppose all that happens when you uh
+ 
+
+ align:start position:0%
+suppose all that happens when you uh
+um turn on the the electricity you know
+
+ align:start position:0%
+um turn on the the electricity you know
+ 
+
+ align:start position:0%
+um turn on the the electricity you know
+to stimulate the brain of the Rat is it
+
+ align:start position:0%
+to stimulate the brain of the Rat is it
+ 
+
+ align:start position:0%
+to stimulate the brain of the Rat is it
+hurts the rat's gonna run around but you
+
+ align:start position:0%
+hurts the rat's gonna run around but you
+ 
+
+ align:start position:0%
+hurts the rat's gonna run around but you
+wouldn't want to uh you wouldn't want to
+
+ align:start position:0%
+wouldn't want to uh you wouldn't want to
+ 
+
+ align:start position:0%
+wouldn't want to uh you wouldn't want to
+argue that this is a center for
+
+ align:start position:0%
+argue that this is a center for
+ 
+
+ align:start position:0%
+argue that this is a center for
+generalized arousal
+
+ align:start position:0%
+generalized arousal
+ 
+
+ align:start position:0%
+generalized arousal
+um plus you might not really want to be
+
+ align:start position:0%
+um plus you might not really want to be
+ 
+
+ align:start position:0%
+um plus you might not really want to be
+you know hurting your poor rat so anyway
+
+ align:start position:0%
+you know hurting your poor rat so anyway
+ 
+
+ align:start position:0%
+you know hurting your poor rat so anyway
+here's the experiment that they did
+
+ align:start position:0%
+here's the experiment that they did
+ 
+
+ align:start position:0%
+here's the experiment that they did
+what they did
+
+ align:start position:0%
+what they did
+ 
+
+ align:start position:0%
+what they did
+um was they watched the electrodes in
+
+ align:start position:0%
+um was they watched the electrodes in
+ 
+
+ align:start position:0%
+um was they watched the electrodes in
+the rat and they're looking at the rat
+
+ align:start position:0%
+the rat and they're looking at the rat
+ 
+
+ align:start position:0%
+the rat and they're looking at the rat
+and they only turn the the the
+
+ align:start position:0%
+and they only turn the the the
+ 
+
+ align:start position:0%
+and they only turn the the the
+electricity on when the rats over in
+
+ align:start position:0%
+electricity on when the rats over in
+ 
+
+ align:start position:0%
+electricity on when the rats over in
+this part of the cage
+
+ align:start position:0%
+this part of the cage
+ 
+
+ align:start position:0%
+this part of the cage
+so turn on the electricity if it hurts
+
+ align:start position:0%
+so turn on the electricity if it hurts
+ 
+
+ align:start position:0%
+so turn on the electricity if it hurts
+what does the rat do
+
+ align:start position:0%
+what does the rat do
+ 
+
+ align:start position:0%
+what does the rat do
+runs around but two to others
+
+ align:start position:0%
+runs around but two to others
+ 
+
+ align:start position:0%
+runs around but two to others
+oh hey oh it stopped yeah wander back
+
+ align:start position:0%
+oh hey oh it stopped yeah wander back
+ 
+
+ align:start position:0%
+oh hey oh it stopped yeah wander back
+over here
+
+ align:start position:0%
+over here
+ 
+
+ align:start position:0%
+over here
+okay right everybody knows rats learned
+
+ align:start position:0%
+okay right everybody knows rats learned
+ 
+
+ align:start position:0%
+okay right everybody knows rats learned
+this they knew that this very nobody had
+
+ align:start position:0%
+this they knew that this very nobody had
+ 
+
+ align:start position:0%
+this they knew that this very nobody had
+done this with with stimulation of the
+
+ align:start position:0%
+done this with with stimulation of the
+ 
+
+ align:start position:0%
+done this with with stimulation of the
+brain what what the this is a ver
+
+ align:start position:0%
+brain what what the this is a ver
+ 
+
+ align:start position:0%
+brain what what the this is a ver
+so-called aversive learning
+
+ align:start position:0%
+so-called aversive learning
+ 
+
+ align:start position:0%
+so-called aversive learning
+um that one of the typical ways of doing
+
+ align:start position:0%
+um that one of the typical ways of doing
+ 
+
+ align:start position:0%
+um that one of the typical ways of doing
+it is you Electrify the floor of the
+
+ align:start position:0%
+it is you Electrify the floor of the
+ 
+
+ align:start position:0%
+it is you Electrify the floor of the
+cage
+
+ align:start position:0%
+cage
+ 
+
+ align:start position:0%
+cage
+right so the rat goes over here
+
+ align:start position:0%
+right so the rat goes over here
+ 
+
+ align:start position:0%
+right so the rat goes over here
+discovers that um when he puts his
+
+ align:start position:0%
+discovers that um when he puts his
+ 
+
+ align:start position:0%
+discovers that um when he puts his
+little rat toes on the cage floor over
+
+ align:start position:0%
+little rat toes on the cage floor over
+ 
+
+ align:start position:0%
+little rat toes on the cage floor over
+here there's there's you know electric
+
+ align:start position:0%
+here there's there's you know electric
+ 
+
+ align:start position:0%
+here there's there's you know electric
+current running through it and you know
+
+ align:start position:0%
+current running through it and you know
+ 
+
+ align:start position:0%
+current running through it and you know
+and he's he's over here
+
+ align:start position:0%
+and he's he's over here
+ 
+
+ align:start position:0%
+and he's he's over here
+um okay so that's what they did and so
+
+ align:start position:0%
+um okay so that's what they did and so
+ 
+
+ align:start position:0%
+um okay so that's what they did and so
+the rat goes over here and
+
+ align:start position:0%
+the rat goes over here and
+ 
+
+ align:start position:0%
+the rat goes over here and
+on comes the juice for a little bit and
+
+ align:start position:0%
+on comes the juice for a little bit and
+ 
+
+ align:start position:0%
+on comes the juice for a little bit and
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the rat doesn't go anywhere and then the
+
+ align:start position:0%
+the rat doesn't go anywhere and then the
+ 
+
+ align:start position:0%
+the rat doesn't go anywhere and then the
+juice goes off and rats wandering around
+
+ align:start position:0%
+juice goes off and rats wandering around
+ 
+
+ align:start position:0%
+juice goes off and rats wandering around
+and and the rat comes back over here
+
+ align:start position:0%
+and and the rat comes back over here
+ 
+
+ align:start position:0%
+and and the rat comes back over here
+juice comes on for a little bit rat
+
+ align:start position:0%
+juice comes on for a little bit rat
+ 
+
+ align:start position:0%
+juice comes on for a little bit rat
+doesn't go anywhere in fact the rat
+
+ align:start position:0%
+doesn't go anywhere in fact the rat
+ 
+
+ align:start position:0%
+doesn't go anywhere in fact the rat
+comes back over here
+
+ align:start position:0%
+comes back over here
+ 
+
+ align:start position:0%
+comes back over here
+the rats sort of hanging around over
+
+ align:start position:0%
+the rats sort of hanging around over
+ 
+
+ align:start position:0%
+the rats sort of hanging around over
+here yeah
+
+ align:start position:0%
+here yeah
+ 
+
+ align:start position:0%
+here yeah
+let's do that again
+
+ align:start position:0%
+let's do that again
+ 
+
+ align:start position:0%
+let's do that again
+turns out that
+
+ align:start position:0%
+turns out that
+ 
+
+ align:start position:0%
+turns out that
+the rat was behaving
+
+ align:start position:0%
+the rat was behaving
+ 
+
+ align:start position:0%
+the rat was behaving
+as though it um
+
+ align:start position:0%
+as though it um
+ 
+
+ align:start position:0%
+as though it um
+as though the stimulation was
+
+ align:start position:0%
+as though the stimulation was
+ 
+
+ align:start position:0%
+as though the stimulation was
+reinforcing we could say as though he
+
+ align:start position:0%
+reinforcing we could say as though he
+ 
+
+ align:start position:0%
+reinforcing we could say as though he
+wanted to be
+
+ align:start position:0%
+wanted to be
+ 
+
+ align:start position:0%
+wanted to be
+um uh stimulated but it's a little dicey
+
+ align:start position:0%
+um uh stimulated but it's a little dicey
+ 
+
+ align:start position:0%
+um uh stimulated but it's a little dicey
+to talk about what a rat wants or
+
+ align:start position:0%
+to talk about what a rat wants or
+ 
+
+ align:start position:0%
+to talk about what a rat wants or
+doesn't want so you can use this more
+
+ align:start position:0%
+doesn't want so you can use this more
+ 
+
+ align:start position:0%
+doesn't want so you can use this more
+neutral language of reinforcement the
+
+ align:start position:0%
+neutral language of reinforcement the
+ 
+
+ align:start position:0%
+neutral language of reinforcement the
+rat was behaving as though
+
+ align:start position:0%
+rat was behaving as though
+ 
+
+ align:start position:0%
+rat was behaving as though
+um stimulation of the brain was
+
+ align:start position:0%
+um stimulation of the brain was
+ 
+
+ align:start position:0%
+um stimulation of the brain was
+reinforcing this was a surprise to uh
+
+ align:start position:0%
+reinforcing this was a surprise to uh
+ 
+
+ align:start position:0%
+reinforcing this was a surprise to uh
+Olson Milner uh the next surprise came
+
+ align:start position:0%
+Olson Milner uh the next surprise came
+ 
+
+ align:start position:0%
+Olson Milner uh the next surprise came
+when they actually uh looked at where
+
+ align:start position:0%
+when they actually uh looked at where
+ 
+
+ align:start position:0%
+when they actually uh looked at where
+the electro electrode had gone in this
+
+ align:start position:0%
+the electro electrode had gone in this
+ 
+
+ align:start position:0%
+the electro electrode had gone in this
+particular rat's brain that's the
+
+ align:start position:0%
+particular rat's brain that's the
+ 
+
+ align:start position:0%
+particular rat's brain that's the
+mistake part it turns out the electrode
+
+ align:start position:0%
+mistake part it turns out the electrode
+ 
+
+ align:start position:0%
+mistake part it turns out the electrode
+had bent
+
+ align:start position:0%
+had bent
+ 
+
+ align:start position:0%
+had bent
+and um instead of being where they
+
+ align:start position:0%
+and um instead of being where they
+ 
+
+ align:start position:0%
+and um instead of being where they
+wanted it in in the in the brain stem it
+
+ align:start position:0%
+wanted it in in the in the brain stem it
+ 
+
+ align:start position:0%
+wanted it in in the in the brain stem it
+was in a chunk of brain known as the
+
+ align:start position:0%
+was in a chunk of brain known as the
+ 
+
+ align:start position:0%
+was in a chunk of brain known as the
+lateral hypothalamus at least we think
+
+ align:start position:0%
+lateral hypothalamus at least we think
+ 
+
+ align:start position:0%
+lateral hypothalamus at least we think
+it was in the lateral hypothalamus don't
+
+ align:start position:0%
+it was in the lateral hypothalamus don't
+ 
+
+ align:start position:0%
+it was in the lateral hypothalamus don't
+actually know because not only did the
+
+ align:start position:0%
+actually know because not only did the
+ 
+
+ align:start position:0%
+actually know because not only did the
+electrode uh Bend but then they lost the
+
+ align:start position:0%
+electrode uh Bend but then they lost the
+ 
+
+ align:start position:0%
+electrode uh Bend but then they lost the
+brain
+
+ align:start position:0%
+brain
+ 
+
+ align:start position:0%
+brain
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+subsequently
+
+ align:start position:0%
+subsequently
+ 
+
+ align:start position:0%
+subsequently
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+they did very well for all the mistakes
+
+ align:start position:0%
+they did very well for all the mistakes
+ 
+
+ align:start position:0%
+they did very well for all the mistakes
+they made here uh hypothal uh
+
+ align:start position:0%
+they made here uh hypothal uh
+ 
+
+ align:start position:0%
+they made here uh hypothal uh
+um so
+
+ align:start position:0%
+um so
+ 
+
+ align:start position:0%
+um so
+what they did then was to deliberately
+
+ align:start position:0%
+what they did then was to deliberately
+ 
+
+ align:start position:0%
+what they did then was to deliberately
+uh stick electrodes into the lateral
+
+ align:start position:0%
+uh stick electrodes into the lateral
+ 
+
+ align:start position:0%
+uh stick electrodes into the lateral
+hypothalamus and to set the experiment
+
+ align:start position:0%
+hypothalamus and to set the experiment
+ 
+
+ align:start position:0%
+hypothalamus and to set the experiment
+up in a more formal fashion beautifully
+
+ align:start position:0%
+up in a more formal fashion beautifully
+ 
+
+ align:start position:0%
+up in a more formal fashion beautifully
+Illustrated here by my rat who's got
+
+ align:start position:0%
+Illustrated here by my rat who's got
+ 
+
+ align:start position:0%
+Illustrated here by my rat who's got
+electrode in his brain and that's a
+
+ align:start position:0%
+electrode in his brain and that's a
+ 
+
+ align:start position:0%
+electrode in his brain and that's a
+battery up there
+
+ align:start position:0%
+battery up there
+ 
+
+ align:start position:0%
+battery up there
+um and that's a lever now the rat can go
+
+ align:start position:0%
+um and that's a lever now the rat can go
+ 
+
+ align:start position:0%
+um and that's a lever now the rat can go
+off and uh self-stimulate he can go and
+
+ align:start position:0%
+off and uh self-stimulate he can go and
+ 
+
+ align:start position:0%
+off and uh self-stimulate he can go and
+choose uh if he pushes on this lever he
+
+ align:start position:0%
+choose uh if he pushes on this lever he
+ 
+
+ align:start position:0%
+choose uh if he pushes on this lever he
+gets a little pulse of electricity
+
+ align:start position:0%
+gets a little pulse of electricity
+ 
+
+ align:start position:0%
+gets a little pulse of electricity
+um to his brain and what's he do indeed
+
+ align:start position:0%
+um to his brain and what's he do indeed
+ 
+
+ align:start position:0%
+um to his brain and what's he do indeed
+rats with electrodes implanted in the
+
+ align:start position:0%
+rats with electrodes implanted in the
+ 
+
+ align:start position:0%
+rats with electrodes implanted in the
+right bits of the lateral hypothalamus
+
+ align:start position:0%
+right bits of the lateral hypothalamus
+ 
+
+ align:start position:0%
+right bits of the lateral hypothalamus
+will sit there and work for brain
+
+ align:start position:0%
+will sit there and work for brain
+ 
+
+ align:start position:0%
+will sit there and work for brain
+stimulation the way another rat might
+
+ align:start position:0%
+stimulation the way another rat might
+ 
+
+ align:start position:0%
+stimulation the way another rat might
+work to get rat pellets or water if it's
+
+ align:start position:0%
+work to get rat pellets or water if it's
+ 
+
+ align:start position:0%
+work to get rat pellets or water if it's
+thirsty or something like that
+
+ align:start position:0%
+thirsty or something like that
+ 
+
+ align:start position:0%
+thirsty or something like that
+um and they'll work hard in the uh uh
+
+ align:start position:0%
+um and they'll work hard in the uh uh
+ 
+
+ align:start position:0%
+um and they'll work hard in the uh uh
+the the the most dramatic version I can
+
+ align:start position:0%
+the the the most dramatic version I can
+ 
+
+ align:start position:0%
+the the the most dramatic version I can
+recall reading is a rat who our rats
+
+ align:start position:0%
+recall reading is a rat who our rats
+ 
+
+ align:start position:0%
+recall reading is a rat who our rats
+will work uh bar pressing 7 000 times an
+
+ align:start position:0%
+will work uh bar pressing 7 000 times an
+ 
+
+ align:start position:0%
+will work uh bar pressing 7 000 times an
+hour I think for uh uh um you know keep
+
+ align:start position:0%
+hour I think for uh uh um you know keep
+ 
+
+ align:start position:0%
+hour I think for uh uh um you know keep
+the brain stimulated there
+
+ align:start position:0%
+the brain stimulated there
+ 
+
+ align:start position:0%
+the brain stimulated there
+um so this this is this is apparently
+
+ align:start position:0%
+um so this this is this is apparently
+ 
+
+ align:start position:0%
+um so this this is this is apparently
+good stuff not everything is good stuff
+
+ align:start position:0%
+good stuff not everything is good stuff
+ 
+
+ align:start position:0%
+good stuff not everything is good stuff
+there are chunks of brain where the rat
+
+ align:start position:0%
+there are chunks of brain where the rat
+ 
+
+ align:start position:0%
+there are chunks of brain where the rat
+will work actively to turn off the
+
+ align:start position:0%
+will work actively to turn off the
+ 
+
+ align:start position:0%
+will work actively to turn off the
+stimulation so again and in this so
+
+ align:start position:0%
+stimulation so again and in this so
+ 
+
+ align:start position:0%
+stimulation so again and in this so
+turning on the stimulation would be a
+
+ align:start position:0%
+turning on the stimulation would be a
+ 
+
+ align:start position:0%
+turning on the stimulation would be a
+positive reinforcer turning off an
+
+ align:start position:0%
+positive reinforcer turning off an
+ 
+
+ align:start position:0%
+positive reinforcer turning off an
+aversive stimulation whether it's
+
+ align:start position:0%
+aversive stimulation whether it's
+ 
+
+ align:start position:0%
+aversive stimulation whether it's
+electricity to your feet or electricity
+
+ align:start position:0%
+electricity to your feet or electricity
+ 
+
+ align:start position:0%
+electricity to your feet or electricity
+to the wrong part of your brain that's a
+
+ align:start position:0%
+to the wrong part of your brain that's a
+ 
+
+ align:start position:0%
+to the wrong part of your brain that's a
+negative reinforcer
+
+ align:start position:0%
+negative reinforcer
+ 
+
+ align:start position:0%
+negative reinforcer
+um so you know there's there's current
+
+ align:start position:0%
+um so you know there's there's current
+ 
+
+ align:start position:0%
+um so you know there's there's current
+if you push the button the current stops
+
+ align:start position:0%
+if you push the button the current stops
+ 
+
+ align:start position:0%
+if you push the button the current stops
+um that's good from the rat's point of
+
+ align:start position:0%
+um that's good from the rat's point of
+ 
+
+ align:start position:0%
+um that's good from the rat's point of
+view
+
+ align:start position:0%
+view
+ 
+
+ align:start position:0%
+view
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in various surveys of rat brain it turns
+
+ align:start position:0%
+in various surveys of rat brain it turns
+ 
+
+ align:start position:0%
+in various surveys of rat brain it turns
+out that they're more positive locations
+
+ align:start position:0%
+out that they're more positive locations
+ 
+
+ align:start position:0%
+out that they're more positive locations
+than negative locations I don't know
+
+ align:start position:0%
+than negative locations I don't know
+ 
+
+ align:start position:0%
+than negative locations I don't know
+um you know we don't know if that's true
+
+ align:start position:0%
+um you know we don't know if that's true
+ 
+
+ align:start position:0%
+um you know we don't know if that's true
+of humans and we don't know if that
+
+ align:start position:0%
+of humans and we don't know if that
+ 
+
+ align:start position:0%
+of humans and we don't know if that
+means anything actually the study the
+
+ align:start position:0%
+means anything actually the study the
+ 
+
+ align:start position:0%
+means anything actually the study the
+the study that I noticed this morning
+
+ align:start position:0%
+the study that I noticed this morning
+ 
+
+ align:start position:0%
+the study that I noticed this morning
+um that I that I was thinking of here
+
+ align:start position:0%
+um that I that I was thinking of here
+ 
+
+ align:start position:0%
+um that I that I was thinking of here
+says that there are 60 in this one study
+
+ align:start position:0%
+says that there are 60 in this one study
+ 
+
+ align:start position:0%
+says that there are 60 in this one study
+60 neutral locations 30 percent
+
+ align:start position:0%
+60 neutral locations 30 percent
+ 
+
+ align:start position:0%
+60 neutral locations 30 percent
+rewarding locations and five percent
+
+ align:start position:0%
+rewarding locations and five percent
+ 
+
+ align:start position:0%
+rewarding locations and five percent
+aversive locations now the
+
+ align:start position:0%
+aversive locations now the
+ 
+
+ align:start position:0%
+aversive locations now the
+mathematically sophisticated among you
+
+ align:start position:0%
+mathematically sophisticated among you
+ 
+
+ align:start position:0%
+mathematically sophisticated among you
+will notice that adds up to 95 percent
+
+ align:start position:0%
+will notice that adds up to 95 percent
+ 
+
+ align:start position:0%
+will notice that adds up to 95 percent
+um and neutral rewarding and aversive
+
+ align:start position:0%
+um and neutral rewarding and aversive
+ 
+
+ align:start position:0%
+um and neutral rewarding and aversive
+would kind of seem to cover all the
+
+ align:start position:0%
+would kind of seem to cover all the
+ 
+
+ align:start position:0%
+would kind of seem to cover all the
+possibilities here so I have no idea
+
+ align:start position:0%
+possibilities here so I have no idea
+ 
+
+ align:start position:0%
+possibilities here so I have no idea
+what the other five percent of neurons
+
+ align:start position:0%
+what the other five percent of neurons
+ 
+
+ align:start position:0%
+what the other five percent of neurons
+were were doing that seems a lot for
+
+ align:start position:0%
+were were doing that seems a lot for
+ 
+
+ align:start position:0%
+were were doing that seems a lot for
+rounding error or something anyway
+
+ align:start position:0%
+rounding error or something anyway
+ 
+
+ align:start position:0%
+rounding error or something anyway
+more pleasant locations than um than
+
+ align:start position:0%
+more pleasant locations than um than
+ 
+
+ align:start position:0%
+more pleasant locations than um than
+unpleasant locations now around uh this
+
+ align:start position:0%
+unpleasant locations now around uh this
+ 
+
+ align:start position:0%
+unpleasant locations now around uh this
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+somebody who is a science fiction buff
+
+ align:start position:0%
+somebody who is a science fiction buff
+ 
+
+ align:start position:0%
+somebody who is a science fiction buff
+should say I've heard this before it
+
+ align:start position:0%
+should say I've heard this before it
+ 
+
+ align:start position:0%
+should say I've heard this before it
+shows up in in one of several uh classic
+
+ align:start position:0%
+shows up in in one of several uh classic
+ 
+
+ align:start position:0%
+shows up in in one of several uh classic
+science fiction stories the world is
+
+ align:start position:0%
+science fiction stories the world is
+ 
+
+ align:start position:0%
+science fiction stories the world is
+full of science fiction stories written
+
+ align:start position:0%
+full of science fiction stories written
+ 
+
+ align:start position:0%
+full of science fiction stories written
+by people just like you which is to say
+
+ align:start position:0%
+by people just like you which is to say
+ 
+
+ align:start position:0%
+by people just like you which is to say
+people who heard an introductory psych
+
+ align:start position:0%
+people who heard an introductory psych
+ 
+
+ align:start position:0%
+people who heard an introductory psych
+lecture and thought I can make a story
+
+ align:start position:0%
+lecture and thought I can make a story
+ 
+
+ align:start position:0%
+lecture and thought I can make a story
+out of this Memento is is perhaps the
+
+ align:start position:0%
+out of this Memento is is perhaps the
+ 
+
+ align:start position:0%
+out of this Memento is is perhaps the
+most recent movie example of that we'll
+
+ align:start position:0%
+most recent movie example of that we'll
+ 
+
+ align:start position:0%
+most recent movie example of that we'll
+get to that lecture later on in the uh
+
+ align:start position:0%
+get to that lecture later on in the uh
+ 
+
+ align:start position:0%
+get to that lecture later on in the uh
+um in the term anybody anybody familiar
+
+ align:start position:0%
+um in the term anybody anybody familiar
+ 
+
+ align:start position:0%
+um in the term anybody anybody familiar
+with the uh the the the Sci-Fi story uh
+
+ align:start position:0%
+with the uh the the the Sci-Fi story uh
+ 
+
+ align:start position:0%
+with the uh the the the Sci-Fi story uh
+that's related to to the rats here any
+
+ align:start position:0%
+that's related to to the rats here any
+ 
+
+ align:start position:0%
+that's related to to the rats here any
+of the various sci-fi stories
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mrs Frisbee and the Rats of nim what's
+
+ align:start position:0%
+Mrs Frisbee and the Rats of nim what's
+ 
+
+ align:start position:0%
+Mrs Frisbee and the Rats of nim what's
+what's
+
+ align:start position:0%
+what's
+ 
+
+ align:start position:0%
+what's
+no apart from the fact that that that
+
+ align:start position:0%
+no apart from the fact that that that
+ 
+
+ align:start position:0%
+no apart from the fact that that that
+Nim stand is is short for the National
+
+ align:start position:0%
+Nim stand is is short for the National
+ 
+
+ align:start position:0%
+Nim stand is is short for the National
+Institutes of mental health and and uh
+
+ align:start position:0%
+Institutes of mental health and and uh
+ 
+
+ align:start position:0%
+Institutes of mental health and and uh
+and and and
+
+ align:start position:0%
+and and and
+ 
+
+ align:start position:0%
+and and and
+they they don't much care for that uh
+
+ align:start position:0%
+they they don't much care for that uh
+ 
+
+ align:start position:0%
+they they don't much care for that uh
+but what what what are the Rats of nim
+
+ align:start position:0%
+but what what what are the Rats of nim
+ 
+
+ align:start position:0%
+but what what what are the Rats of nim
+doing oh no they're busy taking drugs
+
+ align:start position:0%
+doing oh no they're busy taking drugs
+ 
+
+ align:start position:0%
+doing oh no they're busy taking drugs
+and getting smart right no no no they're
+
+ align:start position:0%
+and getting smart right no no no they're
+ 
+
+ align:start position:0%
+and getting smart right no no no they're
+not sitting there stimulating their
+
+ align:start position:0%
+not sitting there stimulating their
+ 
+
+ align:start position:0%
+not sitting there stimulating their
+little selves yeah
+
+ align:start position:0%
+little selves yeah
+ 
+
+ align:start position:0%
+little selves yeah
+yeah okay yeah Terminal Man sounds right
+
+ align:start position:0%
+yeah okay yeah Terminal Man sounds right
+ 
+
+ align:start position:0%
+yeah okay yeah Terminal Man sounds right
+what's terminal man's issue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh yeah Dan it does give him pleasure
+
+ align:start position:0%
+oh yeah Dan it does give him pleasure
+ 
+
+ align:start position:0%
+oh yeah Dan it does give him pleasure
+yes okay that's that yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Flowers for Algernon no he's doing
+
+ align:start position:0%
+Flowers for Algernon no he's doing
+ 
+
+ align:start position:0%
+Flowers for Algernon no he's doing
+what's he doing is he being stimulated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+oh yeah no but he just becomes a super
+
+ align:start position:0%
+oh yeah no but he just becomes a super
+ 
+
+ align:start position:0%
+oh yeah no but he just becomes a super
+smart rat like the Rats of nim1
+
+ align:start position:0%
+smart rat like the Rats of nim1
+ 
+
+ align:start position:0%
+smart rat like the Rats of nim1
+he's got a different right I'm
+
+ align:start position:0%
+he's got a different right I'm
+ 
+
+ align:start position:0%
+he's got a different right I'm
+super smart rats we just know how to
+
+ align:start position:0%
+super smart rats we just know how to
+ 
+
+ align:start position:0%
+super smart rats we just know how to
+make rats who work hard on pushing
+
+ align:start position:0%
+make rats who work hard on pushing
+ 
+
+ align:start position:0%
+make rats who work hard on pushing
+leverage the um the terminal man one is
+
+ align:start position:0%
+leverage the um the terminal man one is
+ 
+
+ align:start position:0%
+leverage the um the terminal man one is
+is is is one of the one of the Sci-Fi
+
+ align:start position:0%
+is is is one of the one of the Sci-Fi
+ 
+
+ align:start position:0%
+is is is one of the one of the Sci-Fi
+examples that I I know about anyway look
+
+ align:start position:0%
+examples that I I know about anyway look
+ 
+
+ align:start position:0%
+examples that I I know about anyway look
+the critical issue that gets people
+
+ align:start position:0%
+the critical issue that gets people
+ 
+
+ align:start position:0%
+the critical issue that gets people
+writing science fiction stories is
+
+ align:start position:0%
+writing science fiction stories is
+ 
+
+ align:start position:0%
+writing science fiction stories is
+suppose we did this to a human would
+
+ align:start position:0%
+suppose we did this to a human would
+ 
+
+ align:start position:0%
+suppose we did this to a human would
+that human uh could you kill somebody
+
+ align:start position:0%
+that human uh could you kill somebody
+ 
+
+ align:start position:0%
+that human uh could you kill somebody
+by hooking them up to uh to
+
+ align:start position:0%
+by hooking them up to uh to
+ 
+
+ align:start position:0%
+by hooking them up to uh to
+self-stimulate their pleasure Center and
+
+ align:start position:0%
+self-stimulate their pleasure Center and
+ 
+
+ align:start position:0%
+self-stimulate their pleasure Center and
+they would kill themselves how would
+
+ align:start position:0%
+they would kill themselves how would
+ 
+
+ align:start position:0%
+they would kill themselves how would
+they kill themselves by you know sitting
+
+ align:start position:0%
+they kill themselves by you know sitting
+ 
+
+ align:start position:0%
+they kill themselves by you know sitting
+there and forgetting to eat
+
+ align:start position:0%
+there and forgetting to eat
+ 
+
+ align:start position:0%
+there and forgetting to eat
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+um well nobody's ever done this in
+
+ align:start position:0%
+um well nobody's ever done this in
+ 
+
+ align:start position:0%
+um well nobody's ever done this in
+humans of course it's been done in rats
+
+ align:start position:0%
+humans of course it's been done in rats
+ 
+
+ align:start position:0%
+humans of course it's been done in rats
+um and uh
+
+ align:start position:0%
+um and uh
+ 
+
+ align:start position:0%
+um and uh
+if you put
+
+ align:start position:0%
+if you put
+ 
+
+ align:start position:0%
+if you put
+uh if you if you put
+
+ align:start position:0%
+uh if you if you put
+ 
+
+ align:start position:0%
+uh if you if you put
+um a lever that gives food next to a
+
+ align:start position:0%
+um a lever that gives food next to a
+ 
+
+ align:start position:0%
+um a lever that gives food next to a
+lever that gives stimulation in in in a
+
+ align:start position:0%
+lever that gives stimulation in in in a
+ 
+
+ align:start position:0%
+lever that gives stimulation in in in a
+good spot in the rat's brain the rat
+
+ align:start position:0%
+good spot in the rat's brain the rat
+ 
+
+ align:start position:0%
+good spot in the rat's brain the rat
+will sit there and
+
+ align:start position:0%
+will sit there and
+ 
+
+ align:start position:0%
+will sit there and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh work away on the on on the
+
+ align:start position:0%
+uh work away on the on on the
+ 
+
+ align:start position:0%
+uh work away on the on on the
+self-stimulation lever
+
+ align:start position:0%
+self-stimulation lever
+ 
+
+ align:start position:0%
+self-stimulation lever
+um and uh at least in some of these
+
+ align:start position:0%
+um and uh at least in some of these
+ 
+
+ align:start position:0%
+um and uh at least in some of these
+studies well every now and then sort of
+
+ align:start position:0%
+studies well every now and then sort of
+ 
+
+ align:start position:0%
+studies well every now and then sort of
+say oh get a little food okay back over
+
+ align:start position:0%
+say oh get a little food okay back over
+ 
+
+ align:start position:0%
+say oh get a little food okay back over
+here to the video game stuff this is
+
+ align:start position:0%
+here to the video game stuff this is
+ 
+
+ align:start position:0%
+here to the video game stuff this is
+really good
+
+ align:start position:0%
+really good
+ 
+
+ align:start position:0%
+really good
+um right this is what this is what your
+
+ align:start position:0%
+um right this is what this is what your
+ 
+
+ align:start position:0%
+um right this is what this is what your
+parents thought you were doing right
+
+ align:start position:0%
+parents thought you were doing right
+ 
+
+ align:start position:0%
+parents thought you were doing right
+yeah come on down and eat dinner oh Mom
+
+ align:start position:0%
+yeah come on down and eat dinner oh Mom
+ 
+
+ align:start position:0%
+yeah come on down and eat dinner oh Mom
+I can't put it on pause yeah anyway the
+
+ align:start position:0%
+I can't put it on pause yeah anyway the
+ 
+
+ align:start position:0%
+I can't put it on pause yeah anyway the
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um would an animal actually kill itself
+
+ align:start position:0%
+um would an animal actually kill itself
+ 
+
+ align:start position:0%
+um would an animal actually kill itself
+uh gleitman says that hungry rats will
+
+ align:start position:0%
+uh gleitman says that hungry rats will
+ 
+
+ align:start position:0%
+uh gleitman says that hungry rats will
+opt for self-stimulation even though it
+
+ align:start position:0%
+opt for self-stimulation even though it
+ 
+
+ align:start position:0%
+opt for self-stimulation even though it
+literally brings starvation and then he
+
+ align:start position:0%
+literally brings starvation and then he
+ 
+
+ align:start position:0%
+literally brings starvation and then he
+cites an article that I went back and
+
+ align:start position:0%
+cites an article that I went back and
+ 
+
+ align:start position:0%
+cites an article that I went back and
+read
+
+ align:start position:0%
+read
+ 
+
+ align:start position:0%
+read
+um and and
+
+ align:start position:0%
+um and and
+ 
+
+ align:start position:0%
+um and and
+the rats in that study didn't starve
+
+ align:start position:0%
+the rats in that study didn't starve
+ 
+
+ align:start position:0%
+the rats in that study didn't starve
+themselves to death because the the
+
+ align:start position:0%
+themselves to death because the the
+ 
+
+ align:start position:0%
+themselves to death because the the
+researchers wouldn't do it um presumably
+
+ align:start position:0%
+researchers wouldn't do it um presumably
+ 
+
+ align:start position:0%
+researchers wouldn't do it um presumably
+because it seemed unethical to actually
+
+ align:start position:0%
+because it seemed unethical to actually
+ 
+
+ align:start position:0%
+because it seemed unethical to actually
+let a rat starve itself to death
+
+ align:start position:0%
+let a rat starve itself to death
+ 
+
+ align:start position:0%
+let a rat starve itself to death
+um but they will certainly reduce that
+
+ align:start position:0%
+um but they will certainly reduce that
+ 
+
+ align:start position:0%
+um but they will certainly reduce that
+you know they'll certainly get
+
+ align:start position:0%
+you know they'll certainly get
+ 
+
+ align:start position:0%
+you know they'll certainly get
+themselves pretty hungry
+
+ align:start position:0%
+themselves pretty hungry
+ 
+
+ align:start position:0%
+themselves pretty hungry
+um while amusing themselves with the uh
+
+ align:start position:0%
+um while amusing themselves with the uh
+ 
+
+ align:start position:0%
+um while amusing themselves with the uh
+uh by stimulating their brain there was
+
+ align:start position:0%
+uh by stimulating their brain there was
+ 
+
+ align:start position:0%
+uh by stimulating their brain there was
+a hand up oh there still is a hand up
+
+ align:start position:0%
+a hand up oh there still is a hand up
+ 
+
+ align:start position:0%
+a hand up oh there still is a hand up
+there look at that yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I I don't I don't know the truth or or
+
+ align:start position:0%
+I I don't I don't know the truth or or
+ 
+
+ align:start position:0%
+I I don't I don't know the truth or or
+falsity of so the story is a guy played
+
+ align:start position:0%
+falsity of so the story is a guy played
+ 
+
+ align:start position:0%
+falsity of so the story is a guy played
+video games for what was it 74 straight
+
+ align:start position:0%
+video games for what was it 74 straight
+ 
+
+ align:start position:0%
+video games for what was it 74 straight
+hours
+
+ align:start position:0%
+hours
+ 
+
+ align:start position:0%
+hours
+74 straight hours in Korea and then he
+
+ align:start position:0%
+74 straight hours in Korea and then he
+ 
+
+ align:start position:0%
+74 straight hours in Korea and then he
+died
+
+ align:start position:0%
+died
+ 
+
+ align:start position:0%
+died
+um actually the Korea part is is good
+
+ align:start position:0%
+um actually the Korea part is is good
+ 
+
+ align:start position:0%
+um actually the Korea part is is good
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+um because
+
+ align:start position:0%
+um because
+ 
+
+ align:start position:0%
+um because
+I have no idea whether this is true one
+
+ align:start position:0%
+I have no idea whether this is true one
+ 
+
+ align:start position:0%
+I have no idea whether this is true one
+way or the other it has all the
+
+ align:start position:0%
+way or the other it has all the
+ 
+
+ align:start position:0%
+way or the other it has all the
+Hallmarks of uh a so-called urban legend
+
+ align:start position:0%
+Hallmarks of uh a so-called urban legend
+ 
+
+ align:start position:0%
+Hallmarks of uh a so-called urban legend
+um it it has a grain of plausibility and
+
+ align:start position:0%
+um it it has a grain of plausibility and
+ 
+
+ align:start position:0%
+um it it has a grain of plausibility and
+is just sort of one step removed from
+
+ align:start position:0%
+is just sort of one step removed from
+ 
+
+ align:start position:0%
+is just sort of one step removed from
+from check ability right it's it's like
+
+ align:start position:0%
+from check ability right it's it's like
+ 
+
+ align:start position:0%
+from check ability right it's it's like
+the Kentucky fried breaded rat right
+
+ align:start position:0%
+the Kentucky fried breaded rat right
+ 
+
+ align:start position:0%
+the Kentucky fried breaded rat right
+everybody knows somebody else who knows
+
+ align:start position:0%
+everybody knows somebody else who knows
+ 
+
+ align:start position:0%
+everybody knows somebody else who knows
+that their cousin got a breaded rat once
+
+ align:start position:0%
+that their cousin got a breaded rat once
+ 
+
+ align:start position:0%
+that their cousin got a breaded rat once
+or uh yeah there's there's whole books
+
+ align:start position:0%
+or uh yeah there's there's whole books
+ 
+
+ align:start position:0%
+or uh yeah there's there's whole books
+of these things they're great I don't
+
+ align:start position:0%
+of these things they're great I don't
+ 
+
+ align:start position:0%
+of these things they're great I don't
+know maybe somebody did manage to play
+
+ align:start position:0%
+know maybe somebody did manage to play
+ 
+
+ align:start position:0%
+know maybe somebody did manage to play
+video games till they died people do all
+
+ align:start position:0%
+video games till they died people do all
+ 
+
+ align:start position:0%
+video games till they died people do all
+sorts of stupid things
+
+ align:start position:0%
+sorts of stupid things
+ 
+
+ align:start position:0%
+sorts of stupid things
+um I don't reckon recommend I don't
+
+ align:start position:0%
+um I don't reckon recommend I don't
+ 
+
+ align:start position:0%
+um I don't reckon recommend I don't
+recommend trying this your your yourself
+
+ align:start position:0%
+recommend trying this your your yourself
+ 
+
+ align:start position:0%
+recommend trying this your your yourself
+in any case rats will work very hard
+
+ align:start position:0%
+in any case rats will work very hard
+ 
+
+ align:start position:0%
+in any case rats will work very hard
+um in order to stimulate different parts
+
+ align:start position:0%
+um in order to stimulate different parts
+ 
+
+ align:start position:0%
+um in order to stimulate different parts
+of their brain what is it that they're
+
+ align:start position:0%
+of their brain what is it that they're
+ 
+
+ align:start position:0%
+of their brain what is it that they're
+um that they're working for
+
+ align:start position:0%
+um that they're working for
+ 
+
+ align:start position:0%
+um that they're working for
+um the evidence suggests that they're
+
+ align:start position:0%
+um the evidence suggests that they're
+ 
+
+ align:start position:0%
+um the evidence suggests that they're
+not just working for some sort of
+
+ align:start position:0%
+not just working for some sort of
+ 
+
+ align:start position:0%
+not just working for some sort of
+disembodied pleasure but that they're
+
+ align:start position:0%
+disembodied pleasure but that they're
+ 
+
+ align:start position:0%
+disembodied pleasure but that they're
+working for the reward associated with
+
+ align:start position:0%
+working for the reward associated with
+ 
+
+ align:start position:0%
+working for the reward associated with
+one or the other of
+
+ align:start position:0%
+one or the other of
+ 
+
+ align:start position:0%
+one or the other of
+um sort of basic hardwired
+
+ align:start position:0%
+um sort of basic hardwired
+ 
+
+ align:start position:0%
+um sort of basic hardwired
+um innate uh reward systems that you
+
+ align:start position:0%
+um innate uh reward systems that you
+ 
+
+ align:start position:0%
+um innate uh reward systems that you
+that the rap comes within that you come
+
+ align:start position:0%
+that the rap comes within that you come
+ 
+
+ align:start position:0%
+that the rap comes within that you come
+with too the reason that
+
+ align:start position:0%
+with too the reason that
+ 
+
+ align:start position:0%
+with too the reason that
+um uh in in this aspect of the slavery
+
+ align:start position:0%
+um uh in in this aspect of the slavery
+ 
+
+ align:start position:0%
+um uh in in this aspect of the slavery
+story that you'll work to get the fish
+
+ align:start position:0%
+story that you'll work to get the fish
+ 
+
+ align:start position:0%
+story that you'll work to get the fish
+if you're the cat
+
+ align:start position:0%
+if you're the cat
+ 
+
+ align:start position:0%
+if you're the cat
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+is that you came
+
+ align:start position:0%
+is that you came
+ 
+
+ align:start position:0%
+is that you came
+predisposed to think that hunger is bad
+
+ align:start position:0%
+predisposed to think that hunger is bad
+ 
+
+ align:start position:0%
+predisposed to think that hunger is bad
+and food is good this look it doesn't
+
+ align:start position:0%
+and food is good this look it doesn't
+ 
+
+ align:start position:0%
+and food is good this look it doesn't
+take very sophisticated evolutionary
+
+ align:start position:0%
+take very sophisticated evolutionary
+ 
+
+ align:start position:0%
+take very sophisticated evolutionary
+psychological theory to think this might
+
+ align:start position:0%
+psychological theory to think this might
+ 
+
+ align:start position:0%
+psychological theory to think this might
+be a good idea organisms that went into
+
+ align:start position:0%
+be a good idea organisms that went into
+ 
+
+ align:start position:0%
+be a good idea organisms that went into
+the world thinking that hunger is good
+
+ align:start position:0%
+the world thinking that hunger is good
+ 
+
+ align:start position:0%
+the world thinking that hunger is good
+and food is bad had many fewer progeny
+
+ align:start position:0%
+and food is bad had many fewer progeny
+ 
+
+ align:start position:0%
+and food is bad had many fewer progeny
+than the ones who thought that hunger
+
+ align:start position:0%
+than the ones who thought that hunger
+ 
+
+ align:start position:0%
+than the ones who thought that hunger
+was bad and food was good so it's not
+
+ align:start position:0%
+was bad and food was good so it's not
+ 
+
+ align:start position:0%
+was bad and food was good so it's not
+desperately surprising that you've got
+
+ align:start position:0%
+desperately surprising that you've got
+ 
+
+ align:start position:0%
+desperately surprising that you've got
+circuitry
+
+ align:start position:0%
+circuitry
+ 
+
+ align:start position:0%
+circuitry
+um that says if you're hungry you want
+
+ align:start position:0%
+um that says if you're hungry you want
+ 
+
+ align:start position:0%
+um that says if you're hungry you want
+to go and eat something and and the
+
+ align:start position:0%
+to go and eat something and and the
+ 
+
+ align:start position:0%
+to go and eat something and and the
+centers that are being stimulated are in
+
+ align:start position:0%
+centers that are being stimulated are in
+ 
+
+ align:start position:0%
+centers that are being stimulated are in
+chunks of brain that if you mess with
+
+ align:start position:0%
+chunks of brain that if you mess with
+ 
+
+ align:start position:0%
+chunks of brain that if you mess with
+them mess with the rat's ability to
+
+ align:start position:0%
+them mess with the rat's ability to
+ 
+
+ align:start position:0%
+them mess with the rat's ability to
+regulate its eating so it's a wonderful
+
+ align:start position:0%
+regulate its eating so it's a wonderful
+ 
+
+ align:start position:0%
+regulate its eating so it's a wonderful
+picture Enlightenment of a rat with a
+
+ align:start position:0%
+picture Enlightenment of a rat with a
+ 
+
+ align:start position:0%
+picture Enlightenment of a rat with a
+hypothalamic lesion a lesion in this
+
+ align:start position:0%
+hypothalamic lesion a lesion in this
+ 
+
+ align:start position:0%
+hypothalamic lesion a lesion in this
+sort of chunk of brain
+
+ align:start position:0%
+sort of chunk of brain
+ 
+
+ align:start position:0%
+sort of chunk of brain
+um the the specific lesion in this
+
+ align:start position:0%
+um the the specific lesion in this
+ 
+
+ align:start position:0%
+um the the specific lesion in this
+particular rat is in a chunk of brain
+
+ align:start position:0%
+particular rat is in a chunk of brain
+ 
+
+ align:start position:0%
+particular rat is in a chunk of brain
+that seems to be important in telling
+
+ align:start position:0%
+that seems to be important in telling
+ 
+
+ align:start position:0%
+that seems to be important in telling
+you when you're full so this rat never
+
+ align:start position:0%
+you when you're full so this rat never
+ 
+
+ align:start position:0%
+you when you're full so this rat never
+knows that he's full and with the result
+
+ align:start position:0%
+knows that he's full and with the result
+ 
+
+ align:start position:0%
+knows that he's full and with the result
+they keeps eating and so there's this
+
+ align:start position:0%
+they keeps eating and so there's this
+ 
+
+ align:start position:0%
+they keeps eating and so there's this
+picture in chapter three of a rat on a
+
+ align:start position:0%
+picture in chapter three of a rat on a
+ 
+
+ align:start position:0%
+picture in chapter three of a rat on a
+uh some of you may have already seen it
+
+ align:start position:0%
+uh some of you may have already seen it
+ 
+
+ align:start position:0%
+uh some of you may have already seen it
+on on a um one of those diet scales you
+
+ align:start position:0%
+on on a um one of those diet scales you
+ 
+
+ align:start position:0%
+on on a um one of those diet scales you
+know and this if he looks like a furry
+
+ align:start position:0%
+know and this if he looks like a furry
+ 
+
+ align:start position:0%
+know and this if he looks like a furry
+football he's just sort of overflowing
+
+ align:start position:0%
+football he's just sort of overflowing
+ 
+
+ align:start position:0%
+football he's just sort of overflowing
+that and and that's because he's got a a
+
+ align:start position:0%
+that and and that's because he's got a a
+ 
+
+ align:start position:0%
+that and and that's because he's got a a
+specific lesion in this little specific
+
+ align:start position:0%
+specific lesion in this little specific
+ 
+
+ align:start position:0%
+specific lesion in this little specific
+chunk of brain how do we know that
+
+ align:start position:0%
+chunk of brain how do we know that
+ 
+
+ align:start position:0%
+chunk of brain how do we know that
+that's what's going on here well you got
+
+ align:start position:0%
+that's what's going on here well you got
+ 
+
+ align:start position:0%
+that's what's going on here well you got
+a rat who's working a way to to be
+
+ align:start position:0%
+a rat who's working a way to to be
+ 
+
+ align:start position:0%
+a rat who's working a way to to be
+stimulated in this little particular
+
+ align:start position:0%
+stimulated in this little particular
+ 
+
+ align:start position:0%
+stimulated in this little particular
+chunk of brain
+
+ align:start position:0%
+chunk of brain
+ 
+
+ align:start position:0%
+chunk of brain
+um and if he so let's take this little
+
+ align:start position:0%
+um and if he so let's take this little
+ 
+
+ align:start position:0%
+um and if he so let's take this little
+chunk of brain
+
+ align:start position:0%
+chunk of brain
+ 
+
+ align:start position:0%
+chunk of brain
+if he's a full rat if you feed him up he
+
+ align:start position:0%
+if he's a full rat if you feed him up he
+ 
+
+ align:start position:0%
+if he's a full rat if you feed him up he
+doesn't work as hard it's just not as
+
+ align:start position:0%
+doesn't work as hard it's just not as
+ 
+
+ align:start position:0%
+doesn't work as hard it's just not as
+interesting you know this for in your
+
+ align:start position:0%
+interesting you know this for in your
+ 
+
+ align:start position:0%
+interesting you know this for in your
+own so
+
+ align:start position:0%
+own so
+ 
+
+ align:start position:0%
+own so
+you like Eminem's let's say you're
+
+ align:start position:0%
+you like Eminem's let's say you're
+ 
+
+ align:start position:0%
+you like Eminem's let's say you're
+willing to put you know you're willing
+
+ align:start position:0%
+willing to put you know you're willing
+ 
+
+ align:start position:0%
+willing to put you know you're willing
+to push the lever to get the M M's right
+
+ align:start position:0%
+to push the lever to get the M M's right
+ 
+
+ align:start position:0%
+to push the lever to get the M M's right
+you're willing to put the quarters in
+
+ align:start position:0%
+you're willing to put the quarters in
+ 
+
+ align:start position:0%
+you're willing to put the quarters in
+the machine will you do that forever no
+
+ align:start position:0%
+the machine will you do that forever no
+ 
+
+ align:start position:0%
+the machine will you do that forever no
+because eventually you get full and the
+
+ align:start position:0%
+because eventually you get full and the
+ 
+
+ align:start position:0%
+because eventually you get full and the
+M M's kind of look disgusting
+
+ align:start position:0%
+M M's kind of look disgusting
+ 
+
+ align:start position:0%
+M M's kind of look disgusting
+um so the same thing happens here if you
+
+ align:start position:0%
+um so the same thing happens here if you
+ 
+
+ align:start position:0%
+um so the same thing happens here if you
+the the pleasure that the rat is getting
+
+ align:start position:0%
+the the pleasure that the rat is getting
+ 
+
+ align:start position:0%
+the the pleasure that the rat is getting
+is modulated by
+
+ align:start position:0%
+is modulated by
+ 
+
+ align:start position:0%
+is modulated by
+um by satisfying the you know the the
+
+ align:start position:0%
+um by satisfying the you know the the
+ 
+
+ align:start position:0%
+um by satisfying the you know the the
+thing the thing about a direct
+
+ align:start position:0%
+thing the thing about a direct
+ 
+
+ align:start position:0%
+thing the thing about a direct
+electrical stimulation is it gives the
+
+ align:start position:0%
+electrical stimulation is it gives the
+ 
+
+ align:start position:0%
+electrical stimulation is it gives the
+sensation of of the satisfaction without
+
+ align:start position:0%
+sensation of of the satisfaction without
+ 
+
+ align:start position:0%
+sensation of of the satisfaction without
+actually satisfying anything so if
+
+ align:start position:0%
+actually satisfying anything so if
+ 
+
+ align:start position:0%
+actually satisfying anything so if
+you're getting the uh the m m is good
+
+ align:start position:0%
+you're getting the uh the m m is good
+ 
+
+ align:start position:0%
+you're getting the uh the m m is good
+thing without getting the m m you can
+
+ align:start position:0%
+thing without getting the m m you can
+ 
+
+ align:start position:0%
+thing without getting the m m you can
+sit there oh the m m is good forever and
+
+ align:start position:0%
+sit there oh the m m is good forever and
+ 
+
+ align:start position:0%
+sit there oh the m m is good forever and
+ever and and keep working at it okay so
+
+ align:start position:0%
+ever and and keep working at it okay so
+ 
+
+ align:start position:0%
+ever and and keep working at it okay so
+that's this little chunk of brain you go
+
+ align:start position:0%
+that's this little chunk of brain you go
+ 
+
+ align:start position:0%
+that's this little chunk of brain you go
+over to this other chunk of brain where
+
+ align:start position:0%
+over to this other chunk of brain where
+ 
+
+ align:start position:0%
+over to this other chunk of brain where
+the rat will also work hard and that rat
+
+ align:start position:0%
+the rat will also work hard and that rat
+ 
+
+ align:start position:0%
+the rat will also work hard and that rat
+um doesn't care if he's full that rat
+
+ align:start position:0%
+um doesn't care if he's full that rat
+ 
+
+ align:start position:0%
+um doesn't care if he's full that rat
+cares
+
+ align:start position:0%
+cares
+ 
+
+ align:start position:0%
+cares
+um whether he's mated recently
+
+ align:start position:0%
+um whether he's mated recently
+ 
+
+ align:start position:0%
+um whether he's mated recently
+so you know this one is is is part you
+
+ align:start position:0%
+so you know this one is is is part you
+ 
+
+ align:start position:0%
+so you know this one is is is part you
+know this little chunk of brain is
+
+ align:start position:0%
+know this little chunk of brain is
+ 
+
+ align:start position:0%
+know this little chunk of brain is
+presumably related to the reward uh
+
+ align:start position:0%
+presumably related to the reward uh
+ 
+
+ align:start position:0%
+presumably related to the reward uh
+systems having to do with sex and mating
+
+ align:start position:0%
+systems having to do with sex and mating
+ 
+
+ align:start position:0%
+systems having to do with sex and mating
+again it doesn't take an evolutionary
+
+ align:start position:0%
+again it doesn't take an evolutionary
+ 
+
+ align:start position:0%
+again it doesn't take an evolutionary
+psych genius to figure out that this
+
+ align:start position:0%
+psych genius to figure out that this
+ 
+
+ align:start position:0%
+psych genius to figure out that this
+would be sensible stuff for um for a
+
+ align:start position:0%
+would be sensible stuff for um for a
+ 
+
+ align:start position:0%
+would be sensible stuff for um for a
+brain to come with
+
+ align:start position:0%
+brain to come with
+ 
+
+ align:start position:0%
+brain to come with
+organisms that didn't find mating
+
+ align:start position:0%
+organisms that didn't find mating
+ 
+
+ align:start position:0%
+organisms that didn't find mating
+rewarding
+
+ align:start position:0%
+rewarding
+ 
+
+ align:start position:0%
+rewarding
+didn't leave many offspring you know it
+
+ align:start position:0%
+didn't leave many offspring you know it
+ 
+
+ align:start position:0%
+didn't leave many offspring you know it
+just didn't work out that well for them
+
+ align:start position:0%
+just didn't work out that well for them
+ 
+
+ align:start position:0%
+just didn't work out that well for them
+and so you know there's another reward
+
+ align:start position:0%
+and so you know there's another reward
+ 
+
+ align:start position:0%
+and so you know there's another reward
+system similarly for thirst
+
+ align:start position:0%
+system similarly for thirst
+ 
+
+ align:start position:0%
+system similarly for thirst
+um that there are separate reward
+
+ align:start position:0%
+um that there are separate reward
+ 
+
+ align:start position:0%
+um that there are separate reward
+systems okay so in some sense you end up
+
+ align:start position:0%
+systems okay so in some sense you end up
+ 
+
+ align:start position:0%
+systems okay so in some sense you end up
+doing stuff in order to light up little
+
+ align:start position:0%
+doing stuff in order to light up little
+ 
+
+ align:start position:0%
+doing stuff in order to light up little
+pieces of brain or to turn off little
+
+ align:start position:0%
+pieces of brain or to turn off little
+ 
+
+ align:start position:0%
+pieces of brain or to turn off little
+pieces of brain that's the sense in
+
+ align:start position:0%
+pieces of brain that's the sense in
+ 
+
+ align:start position:0%
+pieces of brain that's the sense in
+which you are a slave to
+
+ align:start position:0%
+which you are a slave to
+ 
+
+ align:start position:0%
+which you are a slave to
+um to your brain
+
+ align:start position:0%
+um to your brain
+ 
+
+ align:start position:0%
+um to your brain
+um now you know that only gets you so
+
+ align:start position:0%
+um now you know that only gets you so
+ 
+
+ align:start position:0%
+um now you know that only gets you so
+far because that's fairly simple you
+
+ align:start position:0%
+far because that's fairly simple you
+ 
+
+ align:start position:0%
+far because that's fairly simple you
+know eat food little hunk of brain says
+
+ align:start position:0%
+know eat food little hunk of brain says
+ 
+
+ align:start position:0%
+know eat food little hunk of brain says
+you're happy
+
+ align:start position:0%
+you're happy
+ 
+
+ align:start position:0%
+you're happy
+um your behavior is somewhat more
+
+ align:start position:0%
+um your behavior is somewhat more
+ 
+
+ align:start position:0%
+um your behavior is somewhat more
+complicated than that
+
+ align:start position:0%
+complicated than that
+ 
+
+ align:start position:0%
+complicated than that
+um how do we get to that more
+
+ align:start position:0%
+um how do we get to that more
+ 
+
+ align:start position:0%
+um how do we get to that more
+complicated Behavior well stick with the
+
+ align:start position:0%
+complicated Behavior well stick with the
+ 
+
+ align:start position:0%
+complicated Behavior well stick with the
+m m example how do you get the um uh get
+
+ align:start position:0%
+m m example how do you get the um uh get
+ 
+
+ align:start position:0%
+m m example how do you get the um uh get
+to the m Ms well you gotta go down to
+
+ align:start position:0%
+to the m Ms well you gotta go down to
+ 
+
+ align:start position:0%
+to the m Ms well you gotta go down to
+the vending machine and put the money in
+
+ align:start position:0%
+the vending machine and put the money in
+ 
+
+ align:start position:0%
+the vending machine and put the money in
+and how do you learn to do that well
+
+ align:start position:0%
+and how do you learn to do that well
+ 
+
+ align:start position:0%
+and how do you learn to do that well
+maybe you learn to do that by a chain of
+
+ align:start position:0%
+maybe you learn to do that by a chain of
+ 
+
+ align:start position:0%
+maybe you learn to do that by a chain of
+associations back to the m Ms Eminem's
+
+ align:start position:0%
+associations back to the m Ms Eminem's
+ 
+
+ align:start position:0%
+associations back to the m Ms Eminem's
+oh they're good
+
+ align:start position:0%
+oh they're good
+ 
+
+ align:start position:0%
+oh they're good
+um getting M M's becomes good in its own
+
+ align:start position:0%
+um getting M M's becomes good in its own
+ 
+
+ align:start position:0%
+um getting M M's becomes good in its own
+right somebody gives me m M's that's
+
+ align:start position:0%
+right somebody gives me m M's that's
+ 
+
+ align:start position:0%
+right somebody gives me m M's that's
+that becomes rewarding by association
+
+ align:start position:0%
+that becomes rewarding by association
+ 
+
+ align:start position:0%
+that becomes rewarding by association
+with the fact that I will now get to eat
+
+ align:start position:0%
+with the fact that I will now get to eat
+ 
+
+ align:start position:0%
+with the fact that I will now get to eat
+the M Ms this machine will give me m M's
+
+ align:start position:0%
+the M Ms this machine will give me m M's
+ 
+
+ align:start position:0%
+the M Ms this machine will give me m M's
+but only if I give it quarters so I
+
+ align:start position:0%
+but only if I give it quarters so I
+ 
+
+ align:start position:0%
+but only if I give it quarters so I
+learned to give it quarters
+
+ align:start position:0%
+learned to give it quarters
+ 
+
+ align:start position:0%
+learned to give it quarters
+that's an interesting ring it sounded
+
+ align:start position:0%
+that's an interesting ring it sounded
+ 
+
+ align:start position:0%
+that's an interesting ring it sounded
+like a regular old phone
+
+ align:start position:0%
+like a regular old phone
+ 
+
+ align:start position:0%
+like a regular old phone
+um put them on vibrate that's what I do
+
+ align:start position:0%
+um put them on vibrate that's what I do
+ 
+
+ align:start position:0%
+um put them on vibrate that's what I do
+because let's see oh yeah it's just
+
+ align:start position:0%
+because let's see oh yeah it's just
+ 
+
+ align:start position:0%
+because let's see oh yeah it's just
+about the right time I should be
+
+ align:start position:0%
+about the right time I should be
+ 
+
+ align:start position:0%
+about the right time I should be
+vibrating anytime oops not that one I um
+
+ align:start position:0%
+vibrating anytime oops not that one I um
+ 
+
+ align:start position:0%
+vibrating anytime oops not that one I um
+my uh my uh 10th grader tends to phone
+
+ align:start position:0%
+my uh my uh 10th grader tends to phone
+ 
+
+ align:start position:0%
+my uh my uh 10th grader tends to phone
+in after school which is great
+
+ align:start position:0%
+in after school which is great
+ 
+
+ align:start position:0%
+in after school which is great
+um the only thing is that after school
+
+ align:start position:0%
+um the only thing is that after school
+ 
+
+ align:start position:0%
+um the only thing is that after school
+two days a week turns out to be here
+
+ align:start position:0%
+two days a week turns out to be here
+ 
+
+ align:start position:0%
+two days a week turns out to be here
+um and it's just not a good time to take
+
+ align:start position:0%
+um and it's just not a good time to take
+ 
+
+ align:start position:0%
+um and it's just not a good time to take
+a call
+
+ align:start position:0%
+a call
+ 
+
+ align:start position:0%
+a call
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+anyway so oh well so the 10th grader he
+
+ align:start position:0%
+anyway so oh well so the 10th grader he
+ 
+
+ align:start position:0%
+anyway so oh well so the 10th grader he
+likes M M's he needs quarters
+
+ align:start position:0%
+likes M M's he needs quarters
+ 
+
+ align:start position:0%
+likes M M's he needs quarters
+so he's got a emit behavior that I like
+
+ align:start position:0%
+so he's got a emit behavior that I like
+ 
+
+ align:start position:0%
+so he's got a emit behavior that I like
+so I'll give him quarters
+
+ align:start position:0%
+so I'll give him quarters
+ 
+
+ align:start position:0%
+so I'll give him quarters
+right and so you can see how you could
+
+ align:start position:0%
+right and so you can see how you could
+ 
+
+ align:start position:0%
+right and so you can see how you could
+build back from a primary sort of
+
+ align:start position:0%
+build back from a primary sort of
+ 
+
+ align:start position:0%
+build back from a primary sort of
+reinforcer like food is good to
+
+ align:start position:0%
+reinforcer like food is good to
+ 
+
+ align:start position:0%
+reinforcer like food is good to
+something much more remote like cleaning
+
+ align:start position:0%
+something much more remote like cleaning
+ 
+
+ align:start position:0%
+something much more remote like cleaning
+my room is good why is cleaning my if I
+
+ align:start position:0%
+my room is good why is cleaning my if I
+ 
+
+ align:start position:0%
+my room is good why is cleaning my if I
+clean my room daddy gives me quarters if
+
+ align:start position:0%
+clean my room daddy gives me quarters if
+ 
+
+ align:start position:0%
+clean my room daddy gives me quarters if
+like if Daddy gives me quarters I take
+
+ align:start position:0%
+like if Daddy gives me quarters I take
+ 
+
+ align:start position:0%
+like if Daddy gives me quarters I take
+quarters I put them in machine machine
+
+ align:start position:0%
+quarters I put them in machine machine
+ 
+
+ align:start position:0%
+quarters I put them in machine machine
+gives me m M's I eat M M's and all is
+
+ align:start position:0%
+gives me m M's I eat M M's and all is
+ 
+
+ align:start position:0%
+gives me m M's I eat M M's and all is
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+um that's okay uh but it it it probably
+
+ align:start position:0%
+um that's okay uh but it it it probably
+ 
+
+ align:start position:0%
+um that's okay uh but it it it probably
+doesn't do quite well the the brain
+
+ align:start position:0%
+doesn't do quite well the the brain
+ 
+
+ align:start position:0%
+doesn't do quite well the the brain
+suggests to us that that isn't quite
+
+ align:start position:0%
+suggests to us that that isn't quite
+ 
+
+ align:start position:0%
+suggests to us that that isn't quite
+enough for organizing even the feeding
+
+ align:start position:0%
+enough for organizing even the feeding
+ 
+
+ align:start position:0%
+enough for organizing even the feeding
+behavior of of a complex organism like
+
+ align:start position:0%
+behavior of of a complex organism like
+ 
+
+ align:start position:0%
+behavior of of a complex organism like
+us suppose that you are
+
+ align:start position:0%
+us suppose that you are
+ 
+
+ align:start position:0%
+us suppose that you are
+um doing that that what gets you to do
+
+ align:start position:0%
+um doing that that what gets you to do
+ 
+
+ align:start position:0%
+um doing that that what gets you to do
+your complicated sort of behavior
+
+ align:start position:0%
+your complicated sort of behavior
+ 
+
+ align:start position:0%
+your complicated sort of behavior
+um around feeding is the fact that
+
+ align:start position:0%
+um around feeding is the fact that
+ 
+
+ align:start position:0%
+um around feeding is the fact that
+you're hungry oh chapter three will tell
+
+ align:start position:0%
+you're hungry oh chapter three will tell
+ 
+
+ align:start position:0%
+you're hungry oh chapter three will tell
+you all about how you know that you're
+
+ align:start position:0%
+you all about how you know that you're
+ 
+
+ align:start position:0%
+you all about how you know that you're
+hungry
+
+ align:start position:0%
+hungry
+ 
+
+ align:start position:0%
+hungry
+um it's lovely sort of engineering work
+
+ align:start position:0%
+um it's lovely sort of engineering work
+ 
+
+ align:start position:0%
+um it's lovely sort of engineering work
+you've got little uh detectors receptors
+
+ align:start position:0%
+you've got little uh detectors receptors
+ 
+
+ align:start position:0%
+you've got little uh detectors receptors
+in the blood they're doing things like
+
+ align:start position:0%
+in the blood they're doing things like
+ 
+
+ align:start position:0%
+in the blood they're doing things like
+keeping track of blood sugar levels when
+
+ align:start position:0%
+keeping track of blood sugar levels when
+ 
+
+ align:start position:0%
+keeping track of blood sugar levels when
+those levels drop chunks of brain become
+
+ align:start position:0%
+those levels drop chunks of brain become
+ 
+
+ align:start position:0%
+those levels drop chunks of brain become
+active activity there is uh is
+
+ align:start position:0%
+active activity there is uh is
+ 
+
+ align:start position:0%
+active activity there is uh is
+apparently aversive probably
+
+ align:start position:0%
+apparently aversive probably
+ 
+
+ align:start position:0%
+apparently aversive probably
+corresponding to what you and I think of
+
+ align:start position:0%
+corresponding to what you and I think of
+ 
+
+ align:start position:0%
+corresponding to what you and I think of
+as hunger
+
+ align:start position:0%
+as hunger
+ 
+
+ align:start position:0%
+as hunger
+um when you get sugar in activity there
+
+ align:start position:0%
+um when you get sugar in activity there
+ 
+
+ align:start position:0%
+um when you get sugar in activity there
+drops lovely beautiful sort of control
+
+ align:start position:0%
+drops lovely beautiful sort of control
+ 
+
+ align:start position:0%
+drops lovely beautiful sort of control
+systems uh stuff worked out in great
+
+ align:start position:0%
+systems uh stuff worked out in great
+ 
+
+ align:start position:0%
+systems uh stuff worked out in great
+detail and discussed terrible detail in
+
+ align:start position:0%
+detail and discussed terrible detail in
+ 
+
+ align:start position:0%
+detail and discussed terrible detail in
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+um in chapter three but
+
+ align:start position:0%
+um in chapter three but
+ 
+
+ align:start position:0%
+um in chapter three but
+suppose you're not living in your food
+
+ align:start position:0%
+suppose you're not living in your food
+ 
+
+ align:start position:0%
+suppose you're not living in your food
+um right suppose
+
+ align:start position:0%
+um right suppose
+ 
+
+ align:start position:0%
+um right suppose
+well suppose you're like out on the
+
+ align:start position:0%
+well suppose you're like out on the
+ 
+
+ align:start position:0%
+well suppose you're like out on the
+plains of Africa somewhere and the M Ms
+
+ align:start position:0%
+plains of Africa somewhere and the M Ms
+ 
+
+ align:start position:0%
+plains of Africa somewhere and the M Ms
+aren't just sitting over there in the
+
+ align:start position:0%
+aren't just sitting over there in the
+ 
+
+ align:start position:0%
+aren't just sitting over there in the
+vending machine they're running around
+
+ align:start position:0%
+vending machine they're running around
+ 
+
+ align:start position:0%
+vending machine they're running around
+and you're gonna have to hunt them down
+
+ align:start position:0%
+and you're gonna have to hunt them down
+ 
+
+ align:start position:0%
+and you're gonna have to hunt them down
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you are sitting around until the
+
+ align:start position:0%
+if you are sitting around until the
+ 
+
+ align:start position:0%
+if you are sitting around until the
+blood sugar level gets low enough for
+
+ align:start position:0%
+blood sugar level gets low enough for
+ 
+
+ align:start position:0%
+blood sugar level gets low enough for
+unpleasant things to happen in these
+
+ align:start position:0%
+unpleasant things to happen in these
+ 
+
+ align:start position:0%
+unpleasant things to happen in these
+hardwired chunks of brain
+
+ align:start position:0%
+hardwired chunks of brain
+ 
+
+ align:start position:0%
+hardwired chunks of brain
+um to make you think okay all right I
+
+ align:start position:0%
+um to make you think okay all right I
+ 
+
+ align:start position:0%
+um to make you think okay all right I
+remember this m M's or wildebeests
+
+ align:start position:0%
+remember this m M's or wildebeests
+ 
+
+ align:start position:0%
+remember this m M's or wildebeests
+whichever it was they they're good I can
+
+ align:start position:0%
+whichever it was they they're good I can
+ 
+
+ align:start position:0%
+whichever it was they they're good I can
+eat them
+
+ align:start position:0%
+eat them
+ 
+
+ align:start position:0%
+eat them
+to get the wildebeest I gotta go clean
+
+ align:start position:0%
+to get the wildebeest I gotta go clean
+ 
+
+ align:start position:0%
+to get the wildebeest I gotta go clean
+my room anyway there's some complicated
+
+ align:start position:0%
+my room anyway there's some complicated
+ 
+
+ align:start position:0%
+my room anyway there's some complicated
+thing that you got to do but if you wait
+
+ align:start position:0%
+thing that you got to do but if you wait
+ 
+
+ align:start position:0%
+thing that you got to do but if you wait
+long enough
+
+ align:start position:0%
+long enough
+ 
+
+ align:start position:0%
+long enough
+before starting you may not get it the
+
+ align:start position:0%
+before starting you may not get it the
+ 
+
+ align:start position:0%
+before starting you may not get it the
+job done in time right it's going to
+
+ align:start position:0%
+job done in time right it's going to
+ 
+
+ align:start position:0%
+job done in time right it's going to
+take you a while to hunt down the uh the
+
+ align:start position:0%
+take you a while to hunt down the uh the
+ 
+
+ align:start position:0%
+take you a while to hunt down the uh the
+wildebeest if you wait till the gas tank
+
+ align:start position:0%
+wildebeest if you wait till the gas tank
+ 
+
+ align:start position:0%
+wildebeest if you wait till the gas tank
+is almost empty you know you may find
+
+ align:start position:0%
+is almost empty you know you may find
+ 
+
+ align:start position:0%
+is almost empty you know you may find
+yourself flat out on the planes with
+
+ align:start position:0%
+yourself flat out on the planes with
+ 
+
+ align:start position:0%
+yourself flat out on the planes with
+within with you know no food
+
+ align:start position:0%
+within with you know no food
+ 
+
+ align:start position:0%
+within with you know no food
+um so it would be useful
+
+ align:start position:0%
+um so it would be useful
+ 
+
+ align:start position:0%
+um so it would be useful
+if something got you up and mobilized
+
+ align:start position:0%
+if something got you up and mobilized
+ 
+
+ align:start position:0%
+if something got you up and mobilized
+for activity before you were actually
+
+ align:start position:0%
+for activity before you were actually
+ 
+
+ align:start position:0%
+for activity before you were actually
+hungry
+
+ align:start position:0%
+hungry
+ 
+
+ align:start position:0%
+hungry
+um before you actually were in in some
+
+ align:start position:0%
+um before you actually were in in some
+ 
+
+ align:start position:0%
+um before you actually were in in some
+sort of desperate need and the
+
+ align:start position:0%
+sort of desperate need and the
+ 
+
+ align:start position:0%
+sort of desperate need and the
+distinction that gets made and I trust
+
+ align:start position:0%
+distinction that gets made and I trust
+ 
+
+ align:start position:0%
+distinction that gets made and I trust
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+um bolded on the yes it's down there at
+
+ align:start position:0%
+um bolded on the yes it's down there at
+ 
+
+ align:start position:0%
+um bolded on the yes it's down there at
+the bottom of page two
+
+ align:start position:0%
+the bottom of page two
+ 
+
+ align:start position:0%
+the bottom of page two
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+is the distinction between
+
+ align:start position:0%
+is the distinction between
+ 
+
+ align:start position:0%
+is the distinction between
+consummatory and repetitive
+
+ align:start position:0%
+consummatory and repetitive
+ 
+
+ align:start position:0%
+consummatory and repetitive
+um behaviors or consummatory and and
+
+ align:start position:0%
+um behaviors or consummatory and and
+ 
+
+ align:start position:0%
+um behaviors or consummatory and and
+repetitive motivations uh consummatory
+
+ align:start position:0%
+repetitive motivations uh consummatory
+ 
+
+ align:start position:0%
+repetitive motivations uh consummatory
+ones are the ones we've been talking
+
+ align:start position:0%
+ones are the ones we've been talking
+ 
+
+ align:start position:0%
+ones are the ones we've been talking
+about so far eating M M's that's good
+
+ align:start position:0%
+about so far eating M M's that's good
+ 
+
+ align:start position:0%
+about so far eating M M's that's good
+um competitive ones are ones where the
+
+ align:start position:0%
+um competitive ones are ones where the
+ 
+
+ align:start position:0%
+um competitive ones are ones where the
+uh where the act of looking if you like
+
+ align:start position:0%
+uh where the act of looking if you like
+ 
+
+ align:start position:0%
+uh where the act of looking if you like
+um or getting yourself in a position to
+
+ align:start position:0%
+um or getting yourself in a position to
+ 
+
+ align:start position:0%
+um or getting yourself in a position to
+consume is it self-rewarding in the case
+
+ align:start position:0%
+consume is it self-rewarding in the case
+ 
+
+ align:start position:0%
+consume is it self-rewarding in the case
+of of uh of food that might be the sort
+
+ align:start position:0%
+of of uh of food that might be the sort
+ 
+
+ align:start position:0%
+of of uh of food that might be the sort
+of Thrill of the hunt kind of thing uh
+
+ align:start position:0%
+of Thrill of the hunt kind of thing uh
+ 
+
+ align:start position:0%
+of Thrill of the hunt kind of thing uh
+think about your cat right your cat who
+
+ align:start position:0%
+think about your cat right your cat who
+ 
+
+ align:start position:0%
+think about your cat right your cat who
+likes to jump on anything that moves why
+
+ align:start position:0%
+likes to jump on anything that moves why
+ 
+
+ align:start position:0%
+likes to jump on anything that moves why
+is that it's because the cat is
+
+ align:start position:0%
+is that it's because the cat is
+ 
+
+ align:start position:0%
+is that it's because the cat is
+hardwired
+
+ align:start position:0%
+hardwired
+ 
+
+ align:start position:0%
+hardwired
+um to like hunting and stuff it's just
+
+ align:start position:0%
+um to like hunting and stuff it's just
+ 
+
+ align:start position:0%
+um to like hunting and stuff it's just
+fun to grab stuff and kill it
+
+ align:start position:0%
+fun to grab stuff and kill it
+ 
+
+ align:start position:0%
+fun to grab stuff and kill it
+um now that's a useful thing to do if
+
+ align:start position:0%
+um now that's a useful thing to do if
+ 
+
+ align:start position:0%
+um now that's a useful thing to do if
+you are a cat-like animal because then
+
+ align:start position:0%
+you are a cat-like animal because then
+ 
+
+ align:start position:0%
+you are a cat-like animal because then
+there's going to be something around to
+
+ align:start position:0%
+there's going to be something around to
+ 
+
+ align:start position:0%
+there's going to be something around to
+eat when those blood sugar levels drop
+
+ align:start position:0%
+eat when those blood sugar levels drop
+ 
+
+ align:start position:0%
+eat when those blood sugar levels drop
+and you need to you know chew on a
+
+ align:start position:0%
+and you need to you know chew on a
+ 
+
+ align:start position:0%
+and you need to you know chew on a
+wildebeest for a while and it's um it's
+
+ align:start position:0%
+wildebeest for a while and it's um it's
+ 
+
+ align:start position:0%
+wildebeest for a while and it's um it's
+pretty clear that we have similar
+
+ align:start position:0%
+pretty clear that we have similar
+ 
+
+ align:start position:0%
+pretty clear that we have similar
+actually it's pretty clear in
+
+ align:start position:0%
+actually it's pretty clear in
+ 
+
+ align:start position:0%
+actually it's pretty clear in
+yesterday's political news that we have
+
+ align:start position:0%
+yesterday's political news that we have
+ 
+
+ align:start position:0%
+yesterday's political news that we have
+similar sorts of um uh
+
+ align:start position:0%
+similar sorts of um uh
+ 
+
+ align:start position:0%
+similar sorts of um uh
+a circuitry in uh in in ourselves
+
+ align:start position:0%
+a circuitry in uh in in ourselves
+ 
+
+ align:start position:0%
+a circuitry in uh in in ourselves
+um yesterday the assault rifle uh the
+
+ align:start position:0%
+um yesterday the assault rifle uh the
+ 
+
+ align:start position:0%
+um yesterday the assault rifle uh the
+assault weapon ban expired
+
+ align:start position:0%
+assault weapon ban expired
+ 
+
+ align:start position:0%
+assault weapon ban expired
+um Bush spent a lot of time not talking
+
+ align:start position:0%
+um Bush spent a lot of time not talking
+ 
+
+ align:start position:0%
+um Bush spent a lot of time not talking
+about it Carrie spent a lot of time
+
+ align:start position:0%
+about it Carrie spent a lot of time
+ 
+
+ align:start position:0%
+about it Carrie spent a lot of time
+saying I'm a Hunter I love to hunt I
+
+ align:start position:0%
+saying I'm a Hunter I love to hunt I
+ 
+
+ align:start position:0%
+saying I'm a Hunter I love to hunt I
+love to jump on moving things and stuff
+
+ align:start position:0%
+love to jump on moving things and stuff
+ 
+
+ align:start position:0%
+love to jump on moving things and stuff
+like that but I've never done it with an
+
+ align:start position:0%
+like that but I've never done it with an
+ 
+
+ align:start position:0%
+like that but I've never done it with an
+assault weapon you don't need to use in
+
+ align:start position:0%
+assault weapon you don't need to use in
+ 
+
+ align:start position:0%
+assault weapon you don't need to use in
+this he was he was
+
+ align:start position:0%
+this he was he was
+ 
+
+ align:start position:0%
+this he was he was
+um on this but he was very big on
+
+ align:start position:0%
+um on this but he was very big on
+ 
+
+ align:start position:0%
+um on this but he was very big on
+pointing out that he loves to hunt
+
+ align:start position:0%
+pointing out that he loves to hunt
+ 
+
+ align:start position:0%
+pointing out that he loves to hunt
+because apparently there's lots of
+
+ align:start position:0%
+because apparently there's lots of
+ 
+
+ align:start position:0%
+because apparently there's lots of
+people who love to hunt and go out and
+
+ align:start position:0%
+people who love to hunt and go out and
+ 
+
+ align:start position:0%
+people who love to hunt and go out and
+and and and and you know shoot things
+
+ align:start position:0%
+and and and and you know shoot things
+ 
+
+ align:start position:0%
+and and and and you know shoot things
+and and sometimes eat things
+
+ align:start position:0%
+and and sometimes eat things
+ 
+
+ align:start position:0%
+and and sometimes eat things
+um this is presumably related to this is
+
+ align:start position:0%
+um this is presumably related to this is
+ 
+
+ align:start position:0%
+um this is presumably related to this is
+presumably a form of repetitive behavior
+
+ align:start position:0%
+presumably a form of repetitive behavior
+ 
+
+ align:start position:0%
+presumably a form of repetitive behavior
+in in humans if you don't happen to love
+
+ align:start position:0%
+in in humans if you don't happen to love
+ 
+
+ align:start position:0%
+in in humans if you don't happen to love
+to hunt it doesn't mean that you're
+
+ align:start position:0%
+to hunt it doesn't mean that you're
+ 
+
+ align:start position:0%
+to hunt it doesn't mean that you're
+missing a piece of your brain
+
+ align:start position:0%
+missing a piece of your brain
+ 
+
+ align:start position:0%
+missing a piece of your brain
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+another realm of uh where repetitive
+
+ align:start position:0%
+another realm of uh where repetitive
+ 
+
+ align:start position:0%
+another realm of uh where repetitive
+behavior is important is in um uh in in
+
+ align:start position:0%
+behavior is important is in um uh in in
+ 
+
+ align:start position:0%
+behavior is important is in um uh in in
+the sex and romance Department right the
+
+ align:start position:0%
+the sex and romance Department right the
+ 
+
+ align:start position:0%
+the sex and romance Department right the
+if it were not the case that
+
+ align:start position:0%
+if it were not the case that
+ 
+
+ align:start position:0%
+if it were not the case that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that the act of looking for a mate
+
+ align:start position:0%
+that the act of looking for a mate
+ 
+
+ align:start position:0%
+that the act of looking for a mate
+is motivating in its own right
+
+ align:start position:0%
+is motivating in its own right
+ 
+
+ align:start position:0%
+is motivating in its own right
+um well you know that you know what are
+
+ align:start position:0%
+um well you know that you know what are
+ 
+
+ align:start position:0%
+um well you know that you know what are
+you gonna do wait around and and until
+
+ align:start position:0%
+you gonna do wait around and and until
+ 
+
+ align:start position:0%
+you gonna do wait around and and until
+all of a sudden I don't know whatever
+
+ align:start position:0%
+all of a sudden I don't know whatever
+ 
+
+ align:start position:0%
+all of a sudden I don't know whatever
+levels it is drop slow enough oh it's
+
+ align:start position:0%
+levels it is drop slow enough oh it's
+ 
+
+ align:start position:0%
+levels it is drop slow enough oh it's
+time to mate and you know
+
+ align:start position:0%
+time to mate and you know
+ 
+
+ align:start position:0%
+time to mate and you know
+it's just not the way we organize our
+
+ align:start position:0%
+it's just not the way we organize our
+ 
+
+ align:start position:0%
+it's just not the way we organize our
+it's not the way we organize our
+
+ align:start position:0%
+it's not the way we organize our
+ 
+
+ align:start position:0%
+it's not the way we organize our
+Behavior
+
+ align:start position:0%
+Behavior
+ 
+
+ align:start position:0%
+Behavior
+social life suggest that we find a
+
+ align:start position:0%
+social life suggest that we find a
+ 
+
+ align:start position:0%
+social life suggest that we find a
+degree of pleasure in um in the
+
+ align:start position:0%
+degree of pleasure in um in the
+ 
+
+ align:start position:0%
+degree of pleasure in um in the
+competitive aspects of seeking a mate
+
+ align:start position:0%
+competitive aspects of seeking a mate
+ 
+
+ align:start position:0%
+competitive aspects of seeking a mate
+not merely in the uh in the consummatory
+
+ align:start position:0%
+not merely in the uh in the consummatory
+ 
+
+ align:start position:0%
+not merely in the uh in the consummatory
+parts of it so you come with a set of
+
+ align:start position:0%
+parts of it so you come with a set of
+ 
+
+ align:start position:0%
+parts of it so you come with a set of
+um of of motivations
+
+ align:start position:0%
+um of of motivations
+ 
+
+ align:start position:0%
+um of of motivations
+that get you motivations from the sense
+
+ align:start position:0%
+that get you motivations from the sense
+ 
+
+ align:start position:0%
+that get you motivations from the sense
+of getting you to move
+
+ align:start position:0%
+of getting you to move
+ 
+
+ align:start position:0%
+of getting you to move
+um that seem to uh to to come with the
+
+ align:start position:0%
+um that seem to uh to to come with the
+ 
+
+ align:start position:0%
+um that seem to uh to to come with the
+systems these can be quite specific
+
+ align:start position:0%
+systems these can be quite specific
+ 
+
+ align:start position:0%
+systems these can be quite specific
+um by uh by the way that's the notion of
+
+ align:start position:0%
+um by uh by the way that's the notion of
+ 
+
+ align:start position:0%
+um by uh by the way that's the notion of
+preparedness that I see or it's related
+
+ align:start position:0%
+preparedness that I see or it's related
+ 
+
+ align:start position:0%
+preparedness that I see or it's related
+to this notion of preparedness that I
+
+ align:start position:0%
+to this notion of preparedness that I
+ 
+
+ align:start position:0%
+to this notion of preparedness that I
+see is actually above where it says
+
+ align:start position:0%
+see is actually above where it says
+ 
+
+ align:start position:0%
+see is actually above where it says
+consummatory and repetitive
+
+ align:start position:0%
+consummatory and repetitive
+ 
+
+ align:start position:0%
+consummatory and repetitive
+um behaviors on on uh
+
+ align:start position:0%
+um behaviors on on uh
+ 
+
+ align:start position:0%
+um behaviors on on uh
+on the handout
+
+ align:start position:0%
+on the handout
+ 
+
+ align:start position:0%
+on the handout
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you are
+
+ align:start position:0%
+you are
+ 
+
+ align:start position:0%
+you are
+surprisingly fine-tuned
+
+ align:start position:0%
+surprisingly fine-tuned
+ 
+
+ align:start position:0%
+surprisingly fine-tuned
+um in uh
+
+ align:start position:0%
+um in uh
+ 
+
+ align:start position:0%
+um in uh
+by by presumably by the history of the
+
+ align:start position:0%
+by by presumably by the history of the
+ 
+
+ align:start position:0%
+by by presumably by the history of the
+species so for instance
+
+ align:start position:0%
+species so for instance
+ 
+
+ align:start position:0%
+species so for instance
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+you you're built to uh to get away from
+
+ align:start position:0%
+you you're built to uh to get away from
+ 
+
+ align:start position:0%
+you you're built to uh to get away from
+scary things that are going to hurt you
+
+ align:start position:0%
+scary things that are going to hurt you
+ 
+
+ align:start position:0%
+scary things that are going to hurt you
+and and and and and uh
+
+ align:start position:0%
+and and and and and uh
+ 
+
+ align:start position:0%
+and and and and and uh
+um that seems reasonable enough and that
+
+ align:start position:0%
+um that seems reasonable enough and that
+ 
+
+ align:start position:0%
+um that seems reasonable enough and that
+can be specific enough to the point that
+
+ align:start position:0%
+can be specific enough to the point that
+ 
+
+ align:start position:0%
+can be specific enough to the point that
+it's easier to get you to be scared of
+
+ align:start position:0%
+it's easier to get you to be scared of
+ 
+
+ align:start position:0%
+it's easier to get you to be scared of
+spiders and snakes than it is to get you
+
+ align:start position:0%
+spiders and snakes than it is to get you
+ 
+
+ align:start position:0%
+spiders and snakes than it is to get you
+to be scared of bunnies and chickens
+
+ align:start position:0%
+to be scared of bunnies and chickens
+ 
+
+ align:start position:0%
+to be scared of bunnies and chickens
+um that sounds kind of obvious but
+
+ align:start position:0%
+um that sounds kind of obvious but
+ 
+
+ align:start position:0%
+um that sounds kind of obvious but
+there's no obvious reason why in fact
+
+ align:start position:0%
+there's no obvious reason why in fact
+ 
+
+ align:start position:0%
+there's no obvious reason why in fact
+one of the famous experiments in this
+
+ align:start position:0%
+one of the famous experiments in this
+ 
+
+ align:start position:0%
+one of the famous experiments in this
+sort of behaviorist tradition has a
+
+ align:start position:0%
+sort of behaviorist tradition has a
+ 
+
+ align:start position:0%
+sort of behaviorist tradition has a
+little baby known to history as little
+
+ align:start position:0%
+little baby known to history as little
+ 
+
+ align:start position:0%
+little baby known to history as little
+Albert there's a great film from the 20s
+
+ align:start position:0%
+Albert there's a great film from the 20s
+ 
+
+ align:start position:0%
+Albert there's a great film from the 20s
+of this little Albert is sitting there
+
+ align:start position:0%
+of this little Albert is sitting there
+ 
+
+ align:start position:0%
+of this little Albert is sitting there
+he's playing with a little white bunny
+
+ align:start position:0%
+he's playing with a little white bunny
+ 
+
+ align:start position:0%
+he's playing with a little white bunny
+John Watson founder of American
+
+ align:start position:0%
+John Watson founder of American
+ 
+
+ align:start position:0%
+John Watson founder of American
+behaviors and sneaks up behind little
+
+ align:start position:0%
+behaviors and sneaks up behind little
+ 
+
+ align:start position:0%
+behaviors and sneaks up behind little
+Albert with a Gong and
+
+ align:start position:0%
+Albert with a Gong and
+ 
+
+ align:start position:0%
+Albert with a Gong and
+Rings The Gong little Albert Goes if it
+
+ align:start position:0%
+Rings The Gong little Albert Goes if it
+ 
+
+ align:start position:0%
+Rings The Gong little Albert Goes if it
+was a cartoon would go straight up in
+
+ align:start position:0%
+was a cartoon would go straight up in
+ 
+
+ align:start position:0%
+was a cartoon would go straight up in
+the air
+
+ align:start position:0%
+the air
+ 
+
+ align:start position:0%
+the air
+um and it's you know scared out of his
+
+ align:start position:0%
+um and it's you know scared out of his
+ 
+
+ align:start position:0%
+um and it's you know scared out of his
+little Albert gourd and and is you know
+
+ align:start position:0%
+little Albert gourd and and is you know
+ 
+
+ align:start position:0%
+little Albert gourd and and is you know
+screaming and crying and stuff like that
+
+ align:start position:0%
+screaming and crying and stuff like that
+ 
+
+ align:start position:0%
+screaming and crying and stuff like that
+and and
+
+ align:start position:0%
+and and
+ 
+
+ align:start position:0%
+and and
+um and you know it's kind of harsh for
+
+ align:start position:0%
+um and you know it's kind of harsh for
+ 
+
+ align:start position:0%
+um and you know it's kind of harsh for
+little Albert but then that you bring
+
+ align:start position:0%
+little Albert but then that you bring
+ 
+
+ align:start position:0%
+little Albert but then that you bring
+Albert back you show him the bunny again
+
+ align:start position:0%
+Albert back you show him the bunny again
+ 
+
+ align:start position:0%
+Albert back you show him the bunny again
+does he want to play with the bunny
+
+ align:start position:0%
+does he want to play with the bunny
+ 
+
+ align:start position:0%
+does he want to play with the bunny
+no does he want to play with anything
+
+ align:start position:0%
+no does he want to play with anything
+ 
+
+ align:start position:0%
+no does he want to play with anything
+that's white and furry including Santa
+
+ align:start position:0%
+that's white and furry including Santa
+ 
+
+ align:start position:0%
+that's white and furry including Santa
+Claus apparently I seem to recall guys
+
+ align:start position:0%
+Claus apparently I seem to recall guys
+ 
+
+ align:start position:0%
+Claus apparently I seem to recall guys
+with bushy white beards he he recovered
+
+ align:start position:0%
+with bushy white beards he he recovered
+ 
+
+ align:start position:0%
+with bushy white beards he he recovered
+by the way he didn't grow up to be a
+
+ align:start position:0%
+by the way he didn't grow up to be a
+ 
+
+ align:start position:0%
+by the way he didn't grow up to be a
+psycho or anything
+
+ align:start position:0%
+psycho or anything
+ 
+
+ align:start position:0%
+psycho or anything
+um but you can train so you can you can
+
+ align:start position:0%
+um but you can train so you can you can
+ 
+
+ align:start position:0%
+um but you can train so you can you can
+train somebody to be scared of rabbits
+
+ align:start position:0%
+train somebody to be scared of rabbits
+ 
+
+ align:start position:0%
+train somebody to be scared of rabbits
+um but it's easier to train them to be
+
+ align:start position:0%
+um but it's easier to train them to be
+ 
+
+ align:start position:0%
+um but it's easier to train them to be
+scared of uh of snakes as if they were
+
+ align:start position:0%
+scared of uh of snakes as if they were
+ 
+
+ align:start position:0%
+scared of uh of snakes as if they were
+prepared
+
+ align:start position:0%
+prepared
+ 
+
+ align:start position:0%
+prepared
+um by the history of the species to be
+
+ align:start position:0%
+um by the history of the species to be
+ 
+
+ align:start position:0%
+um by the history of the species to be
+um to be scared of
+
+ align:start position:0%
+um to be scared of
+ 
+
+ align:start position:0%
+um to be scared of
+of of things like snakes and uh and
+
+ align:start position:0%
+of of things like snakes and uh and
+ 
+
+ align:start position:0%
+of of things like snakes and uh and
+spiders
+
+ align:start position:0%
+spiders
+ 
+
+ align:start position:0%
+spiders
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+you're a slave to the environment
+
+ align:start position:0%
+you're a slave to the environment
+ 
+
+ align:start position:0%
+you're a slave to the environment
+because your brain responds in rather
+
+ align:start position:0%
+because your brain responds in rather
+ 
+
+ align:start position:0%
+because your brain responds in rather
+specific ways to the environment but you
+
+ align:start position:0%
+specific ways to the environment but you
+ 
+
+ align:start position:0%
+specific ways to the environment but you
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+um a lot more complicated than that
+
+ align:start position:0%
+um a lot more complicated than that
+ 
+
+ align:start position:0%
+um a lot more complicated than that
+um for you at least you feel like you're
+
+ align:start position:0%
+um for you at least you feel like you're
+ 
+
+ align:start position:0%
+um for you at least you feel like you're
+a lot more complicated than something
+
+ align:start position:0%
+a lot more complicated than something
+ 
+
+ align:start position:0%
+a lot more complicated than something
+that's just a bundle of sort of
+
+ align:start position:0%
+that's just a bundle of sort of
+ 
+
+ align:start position:0%
+that's just a bundle of sort of
+engineering responses to glucose level
+
+ align:start position:0%
+engineering responses to glucose level
+ 
+
+ align:start position:0%
+engineering responses to glucose level
+low must go find wildebeest
+
+ align:start position:0%
+low must go find wildebeest
+ 
+
+ align:start position:0%
+low must go find wildebeest
+um and I want to spend the remainder of
+
+ align:start position:0%
+um and I want to spend the remainder of
+ 
+
+ align:start position:0%
+um and I want to spend the remainder of
+the lecture talking about some of those
+
+ align:start position:0%
+the lecture talking about some of those
+ 
+
+ align:start position:0%
+the lecture talking about some of those
+complexities but uh but but first I I
+
+ align:start position:0%
+complexities but uh but but first I I
+ 
+
+ align:start position:0%
+complexities but uh but but first I I
+want to give everybody a chance at least
+
+ align:start position:0%
+want to give everybody a chance at least
+ 
+
+ align:start position:0%
+want to give everybody a chance at least
+to stand up and and uh and stretch a
+
+ align:start position:0%
+to stand up and and uh and stretch a
+ 
+
+ align:start position:0%
+to stand up and and uh and stretch a
+little bit and fan themselves because
+
+ align:start position:0%
+little bit and fan themselves because
+ 
+
+ align:start position:0%
+little bit and fan themselves because
+it's warm in here
+
+ align:start position:0%
+it's warm in here
+ 
+
+ align:start position:0%
+it's warm in here
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+send this form back and my I I trust
+
+ align:start position:0%
+send this form back and my I I trust
+ 
+
+ align:start position:0%
+send this form back and my I I trust
+that means that you can be here at like
+
+ align:start position:0%
+that means that you can be here at like
+ 
+
+ align:start position:0%
+that means that you can be here at like
+five of two and yeah yeah well it's not
+
+ align:start position:0%
+five of two and yeah yeah well it's not
+ 
+
+ align:start position:0%
+five of two and yeah yeah well it's not
+useful after class okay this is this is
+
+ align:start position:0%
+useful after class okay this is this is
+ 
+
+ align:start position:0%
+useful after class okay this is this is
+all the information I have if there's a
+
+ align:start position:0%
+all the information I have if there's a
+ 
+
+ align:start position:0%
+all the information I have if there's a
+problem let me know but I will your name
+
+ align:start position:0%
+problem let me know but I will your name
+ 
+
+ align:start position:0%
+problem let me know but I will your name
+is nice to meet you and I trust that
+
+ align:start position:0%
+is nice to meet you and I trust that
+ 
+
+ align:start position:0%
+is nice to meet you and I trust that
+you'll be happily erasing my boards
+
+ align:start position:0%
+you'll be happily erasing my boards
+ 
+
+ align:start position:0%
+you'll be happily erasing my boards
+I think out there
+
+ align:start position:0%
+I think out there
+ 
+
+ align:start position:0%
+I think out there
+okay let us reconvene here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here here's the deal
+
+ align:start position:0%
+here here's the deal
+ 
+
+ align:start position:0%
+here here's the deal
+um I will I will typically try to be
+
+ align:start position:0%
+um I will I will typically try to be
+ 
+
+ align:start position:0%
+um I will I will typically try to be
+good and and uh and remember to give you
+
+ align:start position:0%
+good and and uh and remember to give you
+ 
+
+ align:start position:0%
+good and and uh and remember to give you
+a a you know a chance to sort of stretch
+
+ align:start position:0%
+a a you know a chance to sort of stretch
+ 
+
+ align:start position:0%
+a a you know a chance to sort of stretch
+your limbs a little bit
+
+ align:start position:0%
+your limbs a little bit
+ 
+
+ align:start position:0%
+your limbs a little bit
+um and and but it'll be a short stretch
+
+ align:start position:0%
+um and and but it'll be a short stretch
+ 
+
+ align:start position:0%
+um and and but it'll be a short stretch
+so you know if it's actually why am I
+
+ align:start position:0%
+so you know if it's actually why am I
+ 
+
+ align:start position:0%
+so you know if it's actually why am I
+telling you this it's the guys who
+
+ align:start position:0%
+telling you this it's the guys who
+ 
+
+ align:start position:0%
+telling you this it's the guys who
+thought they were off for 10 minutes who
+
+ align:start position:0%
+thought they were off for 10 minutes who
+ 
+
+ align:start position:0%
+thought they were off for 10 minutes who
+are now halfway down the hall to get the
+
+ align:start position:0%
+are now halfway down the hall to get the
+ 
+
+ align:start position:0%
+are now halfway down the hall to get the
+M Ms who have the problem but anyway
+
+ align:start position:0%
+M Ms who have the problem but anyway
+ 
+
+ align:start position:0%
+M Ms who have the problem but anyway
+um or the you know the ones who are out
+
+ align:start position:0%
+um or the you know the ones who are out
+ 
+
+ align:start position:0%
+um or the you know the ones who are out
+looking for wildebeest are really in
+
+ align:start position:0%
+looking for wildebeest are really in
+ 
+
+ align:start position:0%
+looking for wildebeest are really in
+trouble
+
+ align:start position:0%
+trouble
+ 
+
+ align:start position:0%
+trouble
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you might wonder
+
+ align:start position:0%
+you might wonder
+ 
+
+ align:start position:0%
+you might wonder
+what the role of emotion is in all this
+
+ align:start position:0%
+what the role of emotion is in all this
+ 
+
+ align:start position:0%
+what the role of emotion is in all this
+clearly motivation and emotion are are
+
+ align:start position:0%
+clearly motivation and emotion are are
+ 
+
+ align:start position:0%
+clearly motivation and emotion are are
+closely related they both talk about
+
+ align:start position:0%
+closely related they both talk about
+ 
+
+ align:start position:0%
+closely related they both talk about
+feeling
+
+ align:start position:0%
+feeling
+ 
+
+ align:start position:0%
+feeling
+um a lot you know that you know there's
+
+ align:start position:0%
+um a lot you know that you know there's
+ 
+
+ align:start position:0%
+um a lot you know that you know there's
+this feeling of of hunger but but
+
+ align:start position:0%
+this feeling of of hunger but but
+ 
+
+ align:start position:0%
+this feeling of of hunger but but
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the emotion part is
+
+ align:start position:0%
+the emotion part is
+ 
+
+ align:start position:0%
+the emotion part is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh well one way to think of it would be
+
+ align:start position:0%
+uh well one way to think of it would be
+ 
+
+ align:start position:0%
+uh well one way to think of it would be
+as a sort of a language a symbol system
+
+ align:start position:0%
+as a sort of a language a symbol system
+ 
+
+ align:start position:0%
+as a sort of a language a symbol system
+um that's a shorthand that helps you
+
+ align:start position:0%
+um that's a shorthand that helps you
+ 
+
+ align:start position:0%
+um that's a shorthand that helps you
+mobilize
+
+ align:start position:0%
+mobilize
+ 
+
+ align:start position:0%
+mobilize
+um your the way of talking to yourself
+
+ align:start position:0%
+um your the way of talking to yourself
+ 
+
+ align:start position:0%
+um your the way of talking to yourself
+um about what resources you might want
+
+ align:start position:0%
+um about what resources you might want
+ 
+
+ align:start position:0%
+um about what resources you might want
+to mobilize oh I feel fear that means I
+
+ align:start position:0%
+to mobilize oh I feel fear that means I
+ 
+
+ align:start position:0%
+to mobilize oh I feel fear that means I
+should do the following sorts of things
+
+ align:start position:0%
+should do the following sorts of things
+ 
+
+ align:start position:0%
+should do the following sorts of things
+um and it helps you generalize from
+
+ align:start position:0%
+um and it helps you generalize from
+ 
+
+ align:start position:0%
+um and it helps you generalize from
+event to event I feel fear now I felt
+
+ align:start position:0%
+event to event I feel fear now I felt
+ 
+
+ align:start position:0%
+event to event I feel fear now I felt
+fear before you know maybe there's some
+
+ align:start position:0%
+fear before you know maybe there's some
+ 
+
+ align:start position:0%
+fear before you know maybe there's some
+sort of relationship that I ought to be
+
+ align:start position:0%
+sort of relationship that I ought to be
+ 
+
+ align:start position:0%
+sort of relationship that I ought to be
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh noticing and perhaps it's uh one of
+
+ align:start position:0%
+uh noticing and perhaps it's uh one of
+ 
+
+ align:start position:0%
+uh noticing and perhaps it's uh one of
+its most important uses is as a form of
+
+ align:start position:0%
+its most important uses is as a form of
+ 
+
+ align:start position:0%
+its most important uses is as a form of
+communication between people or between
+
+ align:start position:0%
+communication between people or between
+ 
+
+ align:start position:0%
+communication between people or between
+uh animals more generally I'm if I'm
+
+ align:start position:0%
+uh animals more generally I'm if I'm
+ 
+
+ align:start position:0%
+uh animals more generally I'm if I'm
+afraid let's go let's go back to the
+
+ align:start position:0%
+afraid let's go let's go back to the
+ 
+
+ align:start position:0%
+afraid let's go let's go back to the
+plains of Africa
+
+ align:start position:0%
+plains of Africa
+ 
+
+ align:start position:0%
+plains of Africa
+um and switch sides if I'm a wildebeest
+
+ align:start position:0%
+um and switch sides if I'm a wildebeest
+ 
+
+ align:start position:0%
+um and switch sides if I'm a wildebeest
+and I see the leopard over there
+
+ align:start position:0%
+and I see the leopard over there
+ 
+
+ align:start position:0%
+and I see the leopard over there
+stalking through the underbrush
+
+ align:start position:0%
+stalking through the underbrush
+ 
+
+ align:start position:0%
+stalking through the underbrush
+um I should be afraid if you're not
+
+ align:start position:0%
+um I should be afraid if you're not
+ 
+
+ align:start position:0%
+um I should be afraid if you're not
+seeing the leopard but you're seeing me
+
+ align:start position:0%
+seeing the leopard but you're seeing me
+ 
+
+ align:start position:0%
+seeing the leopard but you're seeing me
+and I look afraid and you're the rest of
+
+ align:start position:0%
+and I look afraid and you're the rest of
+ 
+
+ align:start position:0%
+and I look afraid and you're the rest of
+the Wilder beasts you should be afraid
+
+ align:start position:0%
+the Wilder beasts you should be afraid
+ 
+
+ align:start position:0%
+the Wilder beasts you should be afraid
+too it's a good idea if you pick up on
+
+ align:start position:0%
+too it's a good idea if you pick up on
+ 
+
+ align:start position:0%
+too it's a good idea if you pick up on
+on the uh on the way that I feel now we
+
+ align:start position:0%
+on the uh on the way that I feel now we
+ 
+
+ align:start position:0%
+on the uh on the way that I feel now we
+tend to devalue that a bit because
+
+ align:start position:0%
+tend to devalue that a bit because
+ 
+
+ align:start position:0%
+tend to devalue that a bit because
+um you know we we tend to use verbal
+
+ align:start position:0%
+um you know we we tend to use verbal
+ 
+
+ align:start position:0%
+um you know we we tend to use verbal
+communication a lot to uh to convey
+
+ align:start position:0%
+communication a lot to uh to convey
+ 
+
+ align:start position:0%
+communication a lot to uh to convey
+information back and forth and for some
+
+ align:start position:0%
+information back and forth and for some
+ 
+
+ align:start position:0%
+information back and forth and for some
+things it's obviously a much more useful
+
+ align:start position:0%
+things it's obviously a much more useful
+ 
+
+ align:start position:0%
+things it's obviously a much more useful
+uh technique
+
+ align:start position:0%
+uh technique
+ 
+
+ align:start position:0%
+uh technique
+um I mean trying to teach Psychology by
+
+ align:start position:0%
+um I mean trying to teach Psychology by
+ 
+
+ align:start position:0%
+um I mean trying to teach Psychology by
+a set of emotional Expressions would not
+
+ align:start position:0%
+a set of emotional Expressions would not
+ 
+
+ align:start position:0%
+a set of emotional Expressions would not
+I I can't even conceive of how I would
+
+ align:start position:0%
+I I can't even conceive of how I would
+ 
+
+ align:start position:0%
+I I can't even conceive of how I would
+go about doing that
+
+ align:start position:0%
+go about doing that
+ 
+
+ align:start position:0%
+go about doing that
+um however we probably overvalue this
+
+ align:start position:0%
+um however we probably overvalue this
+ 
+
+ align:start position:0%
+um however we probably overvalue this
+the the the straight uh this sort of
+
+ align:start position:0%
+the the the straight uh this sort of
+ 
+
+ align:start position:0%
+the the the straight uh this sort of
+straight verbal nature of communication
+
+ align:start position:0%
+straight verbal nature of communication
+ 
+
+ align:start position:0%
+straight verbal nature of communication
+even between humans obviously non-verbal
+
+ align:start position:0%
+even between humans obviously non-verbal
+ 
+
+ align:start position:0%
+even between humans obviously non-verbal
+animals are going to have to use some
+
+ align:start position:0%
+animals are going to have to use some
+ 
+
+ align:start position:0%
+animals are going to have to use some
+other form of community education but
+
+ align:start position:0%
+other form of community education but
+ 
+
+ align:start position:0%
+other form of community education but
+even among humans we under rate the
+
+ align:start position:0%
+even among humans we under rate the
+ 
+
+ align:start position:0%
+even among humans we under rate the
+value of this um
+
+ align:start position:0%
+value of this um
+ 
+
+ align:start position:0%
+value of this um
+current of emotional
+
+ align:start position:0%
+current of emotional
+ 
+
+ align:start position:0%
+current of emotional
+um information transmission uh perhaps
+
+ align:start position:0%
+um information transmission uh perhaps
+ 
+
+ align:start position:0%
+um information transmission uh perhaps
+the clearest example of this is uh is
+
+ align:start position:0%
+the clearest example of this is uh is
+ 
+
+ align:start position:0%
+the clearest example of this is uh is
+email where
+
+ align:start position:0%
+email where
+ 
+
+ align:start position:0%
+email where
+um uh how many of you at some point have
+
+ align:start position:0%
+um uh how many of you at some point have
+ 
+
+ align:start position:0%
+um uh how many of you at some point have
+gotten into trouble on email because
+
+ align:start position:0%
+gotten into trouble on email because
+ 
+
+ align:start position:0%
+gotten into trouble on email because
+email has the characteristics of
+
+ align:start position:0%
+email has the characteristics of
+ 
+
+ align:start position:0%
+email has the characteristics of
+conversation without
+
+ align:start position:0%
+conversation without
+ 
+
+ align:start position:0%
+conversation without
+um the tone of voice you see you said
+
+ align:start position:0%
+um the tone of voice you see you said
+ 
+
+ align:start position:0%
+um the tone of voice you see you said
+something that you thought that where
+
+ align:start position:0%
+something that you thought that where
+ 
+
+ align:start position:0%
+something that you thought that where
+that you meant sarcastically or you
+
+ align:start position:0%
+that you meant sarcastically or you
+ 
+
+ align:start position:0%
+that you meant sarcastically or you
+thought was funny then somebody else
+
+ align:start position:0%
+thought was funny then somebody else
+ 
+
+ align:start position:0%
+thought was funny then somebody else
+read it as flat pros and they was not
+
+ align:start position:0%
+read it as flat pros and they was not
+ 
+
+ align:start position:0%
+read it as flat pros and they was not
+amused at all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually that's the root of all these uh
+
+ align:start position:0%
+actually that's the root of all these uh
+ 
+
+ align:start position:0%
+actually that's the root of all these uh
+um the little smiley faces and all these
+
+ align:start position:0%
+um the little smiley faces and all these
+ 
+
+ align:start position:0%
+um the little smiley faces and all these
+symbols that I don't know from nothing
+
+ align:start position:0%
+symbols that I don't know from nothing
+ 
+
+ align:start position:0%
+symbols that I don't know from nothing
+um the whole you you all know this
+
+ align:start position:0%
+um the whole you you all know this
+ 
+
+ align:start position:0%
+um the whole you you all know this
+there's some very elaborate vocabulary
+
+ align:start position:0%
+there's some very elaborate vocabulary
+ 
+
+ align:start position:0%
+there's some very elaborate vocabulary
+of basically emotional tokens to uh for
+
+ align:start position:0%
+of basically emotional tokens to uh for
+ 
+
+ align:start position:0%
+of basically emotional tokens to uh for
+your for instant messaging messaging or
+
+ align:start position:0%
+your for instant messaging messaging or
+ 
+
+ align:start position:0%
+your for instant messaging messaging or
+for email because it lacks that
+
+ align:start position:0%
+for email because it lacks that
+ 
+
+ align:start position:0%
+for email because it lacks that
+emotional tone of voice and without that
+
+ align:start position:0%
+emotional tone of voice and without that
+ 
+
+ align:start position:0%
+emotional tone of voice and without that
+the the the quality of the uh
+
+ align:start position:0%
+the the the quality of the uh
+ 
+
+ align:start position:0%
+the the the quality of the uh
+um the communication
+
+ align:start position:0%
+um the communication
+ 
+
+ align:start position:0%
+um the communication
+goes down but
+
+ align:start position:0%
+goes down but
+ 
+
+ align:start position:0%
+goes down but
+so you've got you've got emotions that's
+
+ align:start position:0%
+so you've got you've got emotions that's
+ 
+
+ align:start position:0%
+so you've got you've got emotions that's
+sort of a a superordinate
+
+ align:start position:0%
+sort of a a superordinate
+ 
+
+ align:start position:0%
+sort of a a superordinate
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+language that allows you to talk about
+
+ align:start position:0%
+language that allows you to talk about
+ 
+
+ align:start position:0%
+language that allows you to talk about
+motivational States even in the absence
+
+ align:start position:0%
+motivational States even in the absence
+ 
+
+ align:start position:0%
+motivational States even in the absence
+of any sort of verbal language I think
+
+ align:start position:0%
+of any sort of verbal language I think
+ 
+
+ align:start position:0%
+of any sort of verbal language I think
+you could probably make a convincing
+
+ align:start position:0%
+you could probably make a convincing
+ 
+
+ align:start position:0%
+you could probably make a convincing
+argument that basic motivational States
+
+ align:start position:0%
+argument that basic motivational States
+ 
+
+ align:start position:0%
+argument that basic motivational States
+exist
+
+ align:start position:0%
+exist
+ 
+
+ align:start position:0%
+exist
+um in very very simple organisms I mean
+
+ align:start position:0%
+um in very very simple organisms I mean
+ 
+
+ align:start position:0%
+um in very very simple organisms I mean
+and any any organism has to figure out
+
+ align:start position:0%
+and any any organism has to figure out
+ 
+
+ align:start position:0%
+and any any organism has to figure out
+um it has to have in some sense the
+
+ align:start position:0%
+um it has to have in some sense the
+ 
+
+ align:start position:0%
+um it has to have in some sense the
+motivation to to to feed itself and to
+
+ align:start position:0%
+motivation to to to feed itself and to
+ 
+
+ align:start position:0%
+motivation to to to feed itself and to
+reproduce it's only when you get to more
+
+ align:start position:0%
+reproduce it's only when you get to more
+ 
+
+ align:start position:0%
+reproduce it's only when you get to more
+elaborate organisms do you get something
+
+ align:start position:0%
+elaborate organisms do you get something
+ 
+
+ align:start position:0%
+elaborate organisms do you get something
+that looks like the sort of emotional
+
+ align:start position:0%
+that looks like the sort of emotional
+ 
+
+ align:start position:0%
+that looks like the sort of emotional
+life that you and I might have where
+
+ align:start position:0%
+life that you and I might have where
+ 
+
+ align:start position:0%
+life that you and I might have where
+it's being used as a in a sense a form
+
+ align:start position:0%
+it's being used as a in a sense a form
+ 
+
+ align:start position:0%
+it's being used as a in a sense a form
+of of communication but look so far we
+
+ align:start position:0%
+of of communication but look so far we
+ 
+
+ align:start position:0%
+of of communication but look so far we
+we're
+
+ align:start position:0%
+we're
+ 
+
+ align:start position:0%
+we're
+um still dealing in pretty simple terms
+
+ align:start position:0%
+um still dealing in pretty simple terms
+ 
+
+ align:start position:0%
+um still dealing in pretty simple terms
+you know we we've got you know sex and
+
+ align:start position:0%
+you know we we've got you know sex and
+ 
+
+ align:start position:0%
+you know we we've got you know sex and
+reproduction is good getting eaten by
+
+ align:start position:0%
+reproduction is good getting eaten by
+ 
+
+ align:start position:0%
+reproduction is good getting eaten by
+the leopard that's bad and so on
+
+ align:start position:0%
+the leopard that's bad and so on
+ 
+
+ align:start position:0%
+the leopard that's bad and so on
+um where we want to get
+
+ align:start position:0%
+um where we want to get
+ 
+
+ align:start position:0%
+um where we want to get
+where we and and where the chapter on
+
+ align:start position:0%
+where we and and where the chapter on
+ 
+
+ align:start position:0%
+where we and and where the chapter on
+motivation for instance never gets is
+
+ align:start position:0%
+motivation for instance never gets is
+ 
+
+ align:start position:0%
+motivation for instance never gets is
+you know uh sex and reproduction good
+
+ align:start position:0%
+you know uh sex and reproduction good
+ 
+
+ align:start position:0%
+you know uh sex and reproduction good
+Eternal damnation bad
+
+ align:start position:0%
+Eternal damnation bad
+ 
+
+ align:start position:0%
+Eternal damnation bad
+um or something like that or or how do
+
+ align:start position:0%
+um or something like that or or how do
+ 
+
+ align:start position:0%
+um or something like that or or how do
+you get from um you know hunger drives
+
+ align:start position:0%
+you get from um you know hunger drives
+ 
+
+ align:start position:0%
+you get from um you know hunger drives
+and sex drives to Thou shalt not murder
+
+ align:start position:0%
+and sex drives to Thou shalt not murder
+ 
+
+ align:start position:0%
+and sex drives to Thou shalt not murder
+and uh you know I want to grow up to be
+
+ align:start position:0%
+and uh you know I want to grow up to be
+ 
+
+ align:start position:0%
+and uh you know I want to grow up to be
+a chemical engineer
+
+ align:start position:0%
+a chemical engineer
+ 
+
+ align:start position:0%
+a chemical engineer
+um or something like that
+
+ align:start position:0%
+um or something like that
+ 
+
+ align:start position:0%
+um or something like that
+um it's those rather more complicated
+
+ align:start position:0%
+um it's those rather more complicated
+ 
+
+ align:start position:0%
+um it's those rather more complicated
+motivations
+
+ align:start position:0%
+motivations
+ 
+
+ align:start position:0%
+motivations
+um that
+
+ align:start position:0%
+um that
+ 
+
+ align:start position:0%
+um that
+require
+
+ align:start position:0%
+require
+ 
+
+ align:start position:0%
+require
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+more than just uh the you know feedback
+
+ align:start position:0%
+more than just uh the you know feedback
+ 
+
+ align:start position:0%
+more than just uh the you know feedback
+loops in the lateral hypothalamus to to
+
+ align:start position:0%
+loops in the lateral hypothalamus to to
+ 
+
+ align:start position:0%
+loops in the lateral hypothalamus to to
+make a make a good story
+
+ align:start position:0%
+make a make a good story
+ 
+
+ align:start position:0%
+make a make a good story
+um now
+
+ align:start position:0%
+um now
+ 
+
+ align:start position:0%
+um now
+one step to a
+
+ align:start position:0%
+one step to a
+ 
+
+ align:start position:0%
+one step to a
+richer account of why we do anything is
+
+ align:start position:0%
+richer account of why we do anything is
+ 
+
+ align:start position:0%
+richer account of why we do anything is
+to broaden the set of motivations
+
+ align:start position:0%
+to broaden the set of motivations
+ 
+
+ align:start position:0%
+to broaden the set of motivations
+um I have pointed already in the
+
+ align:start position:0%
+um I have pointed already in the
+ 
+
+ align:start position:0%
+um I have pointed already in the
+direction of um
+
+ align:start position:0%
+direction of um
+ 
+
+ align:start position:0%
+direction of um
+uh of one act of broadening that set
+
+ align:start position:0%
+uh of one act of broadening that set
+ 
+
+ align:start position:0%
+uh of one act of broadening that set
+um and that is this notion that if I'm a
+
+ align:start position:0%
+um and that is this notion that if I'm a
+ 
+
+ align:start position:0%
+um and that is this notion that if I'm a
+frightened wilder beast you should be a
+
+ align:start position:0%
+frightened wilder beast you should be a
+ 
+
+ align:start position:0%
+frightened wilder beast you should be a
+frightened wilder beast this is the
+
+ align:start position:0%
+frightened wilder beast this is the
+ 
+
+ align:start position:0%
+frightened wilder beast this is the
+notion that emotions are catching across
+
+ align:start position:0%
+notion that emotions are catching across
+ 
+
+ align:start position:0%
+notion that emotions are catching across
+individuals we talk about that on the
+
+ align:start position:0%
+individuals we talk about that on the
+ 
+
+ align:start position:0%
+individuals we talk about that on the
+handout I I put it as as empathy and
+
+ align:start position:0%
+handout I I put it as as empathy and
+ 
+
+ align:start position:0%
+handout I I put it as as empathy and
+described it as a
+
+ align:start position:0%
+described it as a
+ 
+
+ align:start position:0%
+described it as a
+social emotion
+
+ align:start position:0%
+social emotion
+ 
+
+ align:start position:0%
+social emotion
+and it's a it's a social emotion
+
+ align:start position:0%
+and it's a it's a social emotion
+ 
+
+ align:start position:0%
+and it's a it's a social emotion
+in this in in the sense that it helps to
+
+ align:start position:0%
+in this in in the sense that it helps to
+ 
+
+ align:start position:0%
+in this in in the sense that it helps to
+organize
+
+ align:start position:0%
+organize
+ 
+
+ align:start position:0%
+organize
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+social behavior interactions between
+
+ align:start position:0%
+social behavior interactions between
+ 
+
+ align:start position:0%
+social behavior interactions between
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+so for example well let's start with
+
+ align:start position:0%
+so for example well let's start with
+ 
+
+ align:start position:0%
+so for example well let's start with
+let's start with a bit of evidence that
+
+ align:start position:0%
+let's start with a bit of evidence that
+ 
+
+ align:start position:0%
+let's start with a bit of evidence that
+this comes with the system that it's not
+
+ align:start position:0%
+this comes with the system that it's not
+ 
+
+ align:start position:0%
+this comes with the system that it's not
+something I mean you spend a fair amount
+
+ align:start position:0%
+something I mean you spend a fair amount
+ 
+
+ align:start position:0%
+something I mean you spend a fair amount
+of time trying to teach people to be
+
+ align:start position:0%
+of time trying to teach people to be
+ 
+
+ align:start position:0%
+of time trying to teach people to be
+more empathic but the core of it is
+
+ align:start position:0%
+more empathic but the core of it is
+ 
+
+ align:start position:0%
+more empathic but the core of it is
+there from the start so how do you know
+
+ align:start position:0%
+there from the start so how do you know
+ 
+
+ align:start position:0%
+there from the start so how do you know
+it's there from the start you take a
+
+ align:start position:0%
+it's there from the start you take a
+ 
+
+ align:start position:0%
+it's there from the start you take a
+baby here's a baby here's a bunch of
+
+ align:start position:0%
+baby here's a baby here's a bunch of
+ 
+
+ align:start position:0%
+baby here's a baby here's a bunch of
+other babies poke this baby what's this
+
+ align:start position:0%
+other babies poke this baby what's this
+ 
+
+ align:start position:0%
+other babies poke this baby what's this
+baby do cry what do these babies do they
+
+ align:start position:0%
+baby do cry what do these babies do they
+ 
+
+ align:start position:0%
+baby do cry what do these babies do they
+also cry
+
+ align:start position:0%
+also cry
+ 
+
+ align:start position:0%
+also cry
+um why you haven't hurt those babies but
+
+ align:start position:0%
+um why you haven't hurt those babies but
+ 
+
+ align:start position:0%
+um why you haven't hurt those babies but
+those babies have in a sense caught the
+
+ align:start position:0%
+those babies have in a sense caught the
+ 
+
+ align:start position:0%
+those babies have in a sense caught the
+emotional state of the uh of the
+
+ align:start position:0%
+emotional state of the uh of the
+ 
+
+ align:start position:0%
+emotional state of the uh of the
+um other baby not only do babies catch
+
+ align:start position:0%
+um other baby not only do babies catch
+ 
+
+ align:start position:0%
+um other baby not only do babies catch
+their emotional each other's emotional
+
+ align:start position:0%
+their emotional each other's emotional
+ 
+
+ align:start position:0%
+their emotional each other's emotional
+states but
+
+ align:start position:0%
+states but
+ 
+
+ align:start position:0%
+states but
+um you are all here today
+
+ align:start position:0%
+um you are all here today
+ 
+
+ align:start position:0%
+um you are all here today
+um because
+
+ align:start position:0%
+um because
+ 
+
+ align:start position:0%
+um because
+um because of the same sort of empathic
+
+ align:start position:0%
+um because of the same sort of empathic
+ 
+
+ align:start position:0%
+um because of the same sort of empathic
+reaction when you were a little
+
+ align:start position:0%
+reaction when you were a little
+ 
+
+ align:start position:0%
+reaction when you were a little
+pre-verbal slug
+
+ align:start position:0%
+pre-verbal slug
+ 
+
+ align:start position:0%
+pre-verbal slug
+and you were
+
+ align:start position:0%
+and you were
+ 
+
+ align:start position:0%
+and you were
+um hungry what did you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah right you cried right that's all
+
+ align:start position:0%
+yeah right you cried right that's all
+ 
+
+ align:start position:0%
+yeah right you cried right that's all
+you could do
+
+ align:start position:0%
+you could do
+ 
+
+ align:start position:0%
+you could do
+um and how did that make your parents
+
+ align:start position:0%
+um and how did that make your parents
+ 
+
+ align:start position:0%
+um and how did that make your parents
+feel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well some of you are here today because
+
+ align:start position:0%
+well some of you are here today because
+ 
+
+ align:start position:0%
+well some of you are here today because
+you were lucky because apparently it
+
+ align:start position:0%
+you were lucky because apparently it
+ 
+
+ align:start position:0%
+you were lucky because apparently it
+made your parents feel angry and then
+
+ align:start position:0%
+made your parents feel angry and then
+ 
+
+ align:start position:0%
+made your parents feel angry and then
+which it probably did particularly at at
+
+ align:start position:0%
+which it probably did particularly at at
+ 
+
+ align:start position:0%
+which it probably did particularly at at
+weird hours Mara's looking at me and
+
+ align:start position:0%
+weird hours Mara's looking at me and
+ 
+
+ align:start position:0%
+weird hours Mara's looking at me and
+how old is the kid four and a half
+
+ align:start position:0%
+how old is the kid four and a half
+ 
+
+ align:start position:0%
+how old is the kid four and a half
+months we can we can we can check out uh
+
+ align:start position:0%
+months we can we can we can check out uh
+ 
+
+ align:start position:0%
+months we can we can we can check out uh
+if you haven't met Mara she's the head
+
+ align:start position:0%
+if you haven't met Mara she's the head
+ 
+
+ align:start position:0%
+if you haven't met Mara she's the head
+ta so she she knows everything about the
+
+ align:start position:0%
+ta so she she knows everything about the
+ 
+
+ align:start position:0%
+ta so she she knows everything about the
+the course and what recitation you're in
+
+ align:start position:0%
+the course and what recitation you're in
+ 
+
+ align:start position:0%
+the course and what recitation you're in
+and we can also use her all term as the
+
+ align:start position:0%
+and we can also use her all term as the
+ 
+
+ align:start position:0%
+and we can also use her all term as the
+official parent person
+
+ align:start position:0%
+official parent person
+ 
+
+ align:start position:0%
+official parent person
+at least parent of young young child
+
+ align:start position:0%
+at least parent of young young child
+ 
+
+ align:start position:0%
+at least parent of young young child
+type person
+
+ align:start position:0%
+type person
+ 
+
+ align:start position:0%
+type person
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+she will she will confirm that when your
+
+ align:start position:0%
+she will she will confirm that when your
+ 
+
+ align:start position:0%
+she will she will confirm that when your
+baby cries you want to make that baby
+
+ align:start position:0%
+baby cries you want to make that baby
+ 
+
+ align:start position:0%
+baby cries you want to make that baby
+stop crying fortunately most parents the
+
+ align:start position:0%
+stop crying fortunately most parents the
+ 
+
+ align:start position:0%
+stop crying fortunately most parents the
+ones who want their genes to make it
+
+ align:start position:0%
+ones who want their genes to make it
+ 
+
+ align:start position:0%
+ones who want their genes to make it
+into the Next Generation make the baby
+
+ align:start position:0%
+into the Next Generation make the baby
+ 
+
+ align:start position:0%
+into the Next Generation make the baby
+stop crying by doing things like feeding
+
+ align:start position:0%
+stop crying by doing things like feeding
+ 
+
+ align:start position:0%
+stop crying by doing things like feeding
+it and changing it and stuff like that
+
+ align:start position:0%
+it and changing it and stuff like that
+ 
+
+ align:start position:0%
+it and changing it and stuff like that
+if it didn't make you feel bad
+
+ align:start position:0%
+if it didn't make you feel bad
+ 
+
+ align:start position:0%
+if it didn't make you feel bad
+if the crying baby wasn't the car alarm
+
+ align:start position:0%
+if the crying baby wasn't the car alarm
+ 
+
+ align:start position:0%
+if the crying baby wasn't the car alarm
+of the developmental world you know hey
+
+ align:start position:0%
+of the developmental world you know hey
+ 
+
+ align:start position:0%
+of the developmental world you know hey
+the baby's crying oh that's cool you
+
+ align:start position:0%
+the baby's crying oh that's cool you
+ 
+
+ align:start position:0%
+the baby's crying oh that's cool you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+neat didn't know the baby could make
+
+ align:start position:0%
+neat didn't know the baby could make
+ 
+
+ align:start position:0%
+neat didn't know the baby could make
+that noise wonder what happens in a
+
+ align:start position:0%
+that noise wonder what happens in a
+ 
+
+ align:start position:0%
+that noise wonder what happens in a
+little yeah the baby cries you feel bad
+
+ align:start position:0%
+little yeah the baby cries you feel bad
+ 
+
+ align:start position:0%
+little yeah the baby cries you feel bad
+you do something about it
+
+ align:start position:0%
+you do something about it
+ 
+
+ align:start position:0%
+you do something about it
+um and and and and and you know that's
+
+ align:start position:0%
+um and and and and and you know that's
+ 
+
+ align:start position:0%
+um and and and and and you know that's
+that's that's how you end up
+
+ align:start position:0%
+that's that's how you end up
+ 
+
+ align:start position:0%
+that's that's how you end up
+that's how you end up getting there
+
+ align:start position:0%
+that's how you end up getting there
+ 
+
+ align:start position:0%
+that's how you end up getting there
+getting you know getting to uh the point
+
+ align:start position:0%
+getting you know getting to uh the point
+ 
+
+ align:start position:0%
+getting you know getting to uh the point
+where you can take care of yourself
+
+ align:start position:0%
+where you can take care of yourself
+ 
+
+ align:start position:0%
+where you can take care of yourself
+because somebody else was willing to
+
+ align:start position:0%
+because somebody else was willing to
+ 
+
+ align:start position:0%
+because somebody else was willing to
+take care of you at at that point and
+
+ align:start position:0%
+take care of you at at that point and
+ 
+
+ align:start position:0%
+take care of you at at that point and
+and obviously again in non-verbal
+
+ align:start position:0%
+and obviously again in non-verbal
+ 
+
+ align:start position:0%
+and obviously again in non-verbal
+animals like the rest of them it's
+
+ align:start position:0%
+animals like the rest of them it's
+ 
+
+ align:start position:0%
+animals like the rest of them it's
+really useful
+
+ align:start position:0%
+really useful
+ 
+
+ align:start position:0%
+really useful
+um if when you know your infant animal
+
+ align:start position:0%
+um if when you know your infant animal
+ 
+
+ align:start position:0%
+um if when you know your infant animal
+is feeling uncomfortable you recognize
+
+ align:start position:0%
+is feeling uncomfortable you recognize
+ 
+
+ align:start position:0%
+is feeling uncomfortable you recognize
+the need in some fashion and and you um
+
+ align:start position:0%
+the need in some fashion and and you um
+ 
+
+ align:start position:0%
+the need in some fashion and and you um
+and you do something about it so in a
+
+ align:start position:0%
+and you do something about it so in a
+ 
+
+ align:start position:0%
+and you do something about it so in a
+sense empathy is a sort of a
+
+ align:start position:0%
+sense empathy is a sort of a
+ 
+
+ align:start position:0%
+sense empathy is a sort of a
+prerequisite for successful
+
+ align:start position:0%
+prerequisite for successful
+ 
+
+ align:start position:0%
+prerequisite for successful
+um successful parenting
+
+ align:start position:0%
+um successful parenting
+ 
+
+ align:start position:0%
+um successful parenting
+um and uh this empathic catching of fear
+
+ align:start position:0%
+um and uh this empathic catching of fear
+ 
+
+ align:start position:0%
+um and uh this empathic catching of fear
+is is a useful way to keep yourself
+
+ align:start position:0%
+is is a useful way to keep yourself
+ 
+
+ align:start position:0%
+is is a useful way to keep yourself
+alive if you don't see the danger but
+
+ align:start position:0%
+alive if you don't see the danger but
+ 
+
+ align:start position:0%
+alive if you don't see the danger but
+somebody else does
+
+ align:start position:0%
+somebody else does
+ 
+
+ align:start position:0%
+somebody else does
+um that's oh and and
+
+ align:start position:0%
+um that's oh and and
+ 
+
+ align:start position:0%
+um that's oh and and
+um it's it's a good uh it's good for
+
+ align:start position:0%
+um it's it's a good uh it's good for
+ 
+
+ align:start position:0%
+um it's it's a good uh it's good for
+keeping you alive in other ways too
+
+ align:start position:0%
+keeping you alive in other ways too
+ 
+
+ align:start position:0%
+keeping you alive in other ways too
+um I won't do it
+
+ align:start position:0%
+um I won't do it
+ 
+
+ align:start position:0%
+um I won't do it
+um but if I were to suddenly decide to
+
+ align:start position:0%
+um but if I were to suddenly decide to
+ 
+
+ align:start position:0%
+um but if I were to suddenly decide to
+make myself throw up
+
+ align:start position:0%
+make myself throw up
+ 
+
+ align:start position:0%
+make myself throw up
+a bunch of you would feel really lousy
+
+ align:start position:0%
+a bunch of you would feel really lousy
+ 
+
+ align:start position:0%
+a bunch of you would feel really lousy
+right you know this by the way this is
+
+ align:start position:0%
+right you know this by the way this is
+ 
+
+ align:start position:0%
+right you know this by the way this is
+one that goes away when you become a
+
+ align:start position:0%
+one that goes away when you become a
+ 
+
+ align:start position:0%
+one that goes away when you become a
+parent you can you can modulate these
+
+ align:start position:0%
+parent you can you can modulate these
+ 
+
+ align:start position:0%
+parent you can you can modulate these
+things over if you felt incapacitatingly
+
+ align:start position:0%
+things over if you felt incapacitatingly
+ 
+
+ align:start position:0%
+things over if you felt incapacitatingly
+nauseous every time your child threw up
+
+ align:start position:0%
+nauseous every time your child threw up
+ 
+
+ align:start position:0%
+nauseous every time your child threw up
+your child did never make it because you
+
+ align:start position:0%
+your child did never make it because you
+ 
+
+ align:start position:0%
+your child did never make it because you
+just got a deal and clean up but at this
+
+ align:start position:0%
+just got a deal and clean up but at this
+ 
+
+ align:start position:0%
+just got a deal and clean up but at this
+point if I throw up you're gonna feel
+
+ align:start position:0%
+point if I throw up you're gonna feel
+ 
+
+ align:start position:0%
+point if I throw up you're gonna feel
+sick some of you will throw up I
+
+ align:start position:0%
+sick some of you will throw up I
+ 
+
+ align:start position:0%
+sick some of you will throw up I
+shouldn't keep talking about it because
+
+ align:start position:0%
+shouldn't keep talking about it because
+ 
+
+ align:start position:0%
+shouldn't keep talking about it because
+some of you will start feeling gross
+
+ align:start position:0%
+some of you will start feeling gross
+ 
+
+ align:start position:0%
+some of you will start feeling gross
+just thinking about it
+
+ align:start position:0%
+just thinking about it
+ 
+
+ align:start position:0%
+just thinking about it
+um that's also useful why because if I
+
+ align:start position:0%
+um that's also useful why because if I
+ 
+
+ align:start position:0%
+um that's also useful why because if I
+ate the wildebeest and it was a bad
+
+ align:start position:0%
+ate the wildebeest and it was a bad
+ 
+
+ align:start position:0%
+ate the wildebeest and it was a bad
+wildebeest
+
+ align:start position:0%
+wildebeest
+ 
+
+ align:start position:0%
+wildebeest
+you know and we're all vultures on the
+
+ align:start position:0%
+you know and we're all vultures on the
+ 
+
+ align:start position:0%
+you know and we're all vultures on the
+same wildebeest here if I'm looking kind
+
+ align:start position:0%
+same wildebeest here if I'm looking kind
+ 
+
+ align:start position:0%
+same wildebeest here if I'm looking kind
+of sick you might as well get rid of the
+
+ align:start position:0%
+of sick you might as well get rid of the
+ 
+
+ align:start position:0%
+of sick you might as well get rid of the
+wildebeest now because it's just not
+
+ align:start position:0%
+wildebeest now because it's just not
+ 
+
+ align:start position:0%
+wildebeest now because it's just not
+going to be doing you any good
+
+ align:start position:0%
+going to be doing you any good
+ 
+
+ align:start position:0%
+going to be doing you any good
+um so this catching business is is
+
+ align:start position:0%
+um so this catching business is is
+ 
+
+ align:start position:0%
+um so this catching business is is
+has has its utility now it's not a
+
+ align:start position:0%
+has has its utility now it's not a
+ 
+
+ align:start position:0%
+has has its utility now it's not a
+uniformly good thing because you can
+
+ align:start position:0%
+uniformly good thing because you can
+ 
+
+ align:start position:0%
+uniformly good thing because you can
+catch anti-social emotions just the way
+
+ align:start position:0%
+catch anti-social emotions just the way
+ 
+
+ align:start position:0%
+catch anti-social emotions just the way
+you can catch pro-social emotions so
+
+ align:start position:0%
+you can catch pro-social emotions so
+ 
+
+ align:start position:0%
+you can catch pro-social emotions so
+when you see seemingly incomprehensible
+
+ align:start position:0%
+when you see seemingly incomprehensible
+ 
+
+ align:start position:0%
+when you see seemingly incomprehensible
+events like how in the world can you
+
+ align:start position:0%
+events like how in the world can you
+ 
+
+ align:start position:0%
+events like how in the world can you
+explain
+
+ align:start position:0%
+explain
+ 
+
+ align:start position:0%
+explain
+um something like gang rape or or a
+
+ align:start position:0%
+um something like gang rape or or a
+ 
+
+ align:start position:0%
+um something like gang rape or or a
+massacre um in uh in in a war zone
+
+ align:start position:0%
+massacre um in uh in in a war zone
+ 
+
+ align:start position:0%
+massacre um in uh in in a war zone
+part of what's going on there is
+
+ align:start position:0%
+part of what's going on there is
+ 
+
+ align:start position:0%
+part of what's going on there is
+um the same sort of emotional contagion
+
+ align:start position:0%
+um the same sort of emotional contagion
+ 
+
+ align:start position:0%
+um the same sort of emotional contagion
+if one person isn't in a murderous rage
+
+ align:start position:0%
+if one person isn't in a murderous rage
+ 
+
+ align:start position:0%
+if one person isn't in a murderous rage
+people around them around that person
+
+ align:start position:0%
+people around them around that person
+ 
+
+ align:start position:0%
+people around them around that person
+can catch the murderous rage just the
+
+ align:start position:0%
+can catch the murderous rage just the
+ 
+
+ align:start position:0%
+can catch the murderous rage just the
+way they can uh catch
+
+ align:start position:0%
+way they can uh catch
+ 
+
+ align:start position:0%
+way they can uh catch
+um the fear or catch the nausea it's not
+
+ align:start position:0%
+um the fear or catch the nausea it's not
+ 
+
+ align:start position:0%
+um the fear or catch the nausea it's not
+just a sort of a pro-social
+
+ align:start position:0%
+just a sort of a pro-social
+ 
+
+ align:start position:0%
+just a sort of a pro-social
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motivation but empathy does serve the
+
+ align:start position:0%
+motivation but empathy does serve the
+ 
+
+ align:start position:0%
+motivation but empathy does serve the
+function of organizing larger scale
+
+ align:start position:0%
+function of organizing larger scale
+ 
+
+ align:start position:0%
+function of organizing larger scale
+sorts of
+
+ align:start position:0%
+sorts of
+ 
+
+ align:start position:0%
+sorts of
+sorts of behavior oh now how does this
+
+ align:start position:0%
+sorts of behavior oh now how does this
+ 
+
+ align:start position:0%
+sorts of behavior oh now how does this
+contagion actually work how does
+
+ align:start position:0%
+contagion actually work how does
+ 
+
+ align:start position:0%
+contagion actually work how does
+emotional contagion actually work
+
+ align:start position:0%
+emotional contagion actually work
+ 
+
+ align:start position:0%
+emotional contagion actually work
+interestingly part of the sort of
+
+ align:start position:0%
+interestingly part of the sort of
+ 
+
+ align:start position:0%
+interestingly part of the sort of
+reflexive mechanism of it seems to be
+
+ align:start position:0%
+reflexive mechanism of it seems to be
+ 
+
+ align:start position:0%
+reflexive mechanism of it seems to be
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um when you read my emotion you also
+
+ align:start position:0%
+um when you read my emotion you also
+ 
+
+ align:start position:0%
+um when you read my emotion you also
+mimic my emotion
+
+ align:start position:0%
+mimic my emotion
+ 
+
+ align:start position:0%
+mimic my emotion
+um it most clearly seen with facial
+
+ align:start position:0%
+um it most clearly seen with facial
+ 
+
+ align:start position:0%
+um it most clearly seen with facial
+expression if I smile at you you will
+
+ align:start position:0%
+expression if I smile at you you will
+ 
+
+ align:start position:0%
+expression if I smile at you you will
+smile you may not smile much but I'd be
+
+ align:start position:0%
+smile you may not smile much but I'd be
+ 
+
+ align:start position:0%
+smile you may not smile much but I'd be
+able to pick up if I was recording from
+
+ align:start position:0%
+able to pick up if I was recording from
+ 
+
+ align:start position:0%
+able to pick up if I was recording from
+your facial muscles I would be able to
+
+ align:start position:0%
+your facial muscles I would be able to
+ 
+
+ align:start position:0%
+your facial muscles I would be able to
+pick up
+
+ align:start position:0%
+pick up
+ 
+
+ align:start position:0%
+pick up
+a transient smile flitting across your
+
+ align:start position:0%
+a transient smile flitting across your
+ 
+
+ align:start position:0%
+a transient smile flitting across your
+face why is that important well how do
+
+ align:start position:0%
+face why is that important well how do
+ 
+
+ align:start position:0%
+face why is that important well how do
+you know if you are happy
+
+ align:start position:0%
+you know if you are happy
+ 
+
+ align:start position:0%
+you know if you are happy
+well it turns out and this is one of the
+
+ align:start position:0%
+well it turns out and this is one of the
+ 
+
+ align:start position:0%
+well it turns out and this is one of the
+senses in which feelings emotions are
+
+ align:start position:0%
+senses in which feelings emotions are
+ 
+
+ align:start position:0%
+senses in which feelings emotions are
+feelings is that you go out and you feel
+
+ align:start position:0%
+feelings is that you go out and you feel
+ 
+
+ align:start position:0%
+feelings is that you go out and you feel
+yourself and ask yourself how do I feel
+
+ align:start position:0%
+yourself and ask yourself how do I feel
+ 
+
+ align:start position:0%
+yourself and ask yourself how do I feel
+part of that is to feel your face in
+
+ align:start position:0%
+part of that is to feel your face in
+ 
+
+ align:start position:0%
+part of that is to feel your face in
+effect you know how does my face feel
+
+ align:start position:0%
+effect you know how does my face feel
+ 
+
+ align:start position:0%
+effect you know how does my face feel
+well I seem to be smiling why would I be
+
+ align:start position:0%
+well I seem to be smiling why would I be
+ 
+
+ align:start position:0%
+well I seem to be smiling why would I be
+smiling I must be smiling because I feel
+
+ align:start position:0%
+smiling I must be smiling because I feel
+ 
+
+ align:start position:0%
+smiling I must be smiling because I feel
+good because only dumb people smile when
+
+ align:start position:0%
+good because only dumb people smile when
+ 
+
+ align:start position:0%
+good because only dumb people smile when
+they're miserable right you know that
+
+ align:start position:0%
+they're miserable right you know that
+ 
+
+ align:start position:0%
+they're miserable right you know that
+that's unlike say well there are various
+
+ align:start position:0%
+that's unlike say well there are various
+ 
+
+ align:start position:0%
+that's unlike say well there are various
+social circumstances when you might do
+
+ align:start position:0%
+social circumstances when you might do
+ 
+
+ align:start position:0%
+social circumstances when you might do
+that but anyway it's it's it's useful
+
+ align:start position:0%
+that but anyway it's it's it's useful
+ 
+
+ align:start position:0%
+that but anyway it's it's it's useful
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+um you can actually try to demonstrate
+
+ align:start position:0%
+um you can actually try to demonstrate
+ 
+
+ align:start position:0%
+um you can actually try to demonstrate
+this here's an exercise for the reader
+
+ align:start position:0%
+this here's an exercise for the reader
+ 
+
+ align:start position:0%
+this here's an exercise for the reader
+if you like
+
+ align:start position:0%
+if you like
+ 
+
+ align:start position:0%
+if you like
+um I've done it as a as one of the
+
+ align:start position:0%
+um I've done it as a as one of the
+ 
+
+ align:start position:0%
+um I've done it as a as one of the
+writing assignments for the course in in
+
+ align:start position:0%
+writing assignments for the course in in
+ 
+
+ align:start position:0%
+writing assignments for the course in in
+various years it's sort of fun take say
+
+ align:start position:0%
+various years it's sort of fun take say
+ 
+
+ align:start position:0%
+various years it's sort of fun take say
+10 events of about the same duration say
+
+ align:start position:0%
+10 events of about the same duration say
+ 
+
+ align:start position:0%
+10 events of about the same duration say
+an hour because that that works for uh a
+
+ align:start position:0%
+an hour because that that works for uh a
+ 
+
+ align:start position:0%
+an hour because that that works for uh a
+lecture for example you know you know
+
+ align:start position:0%
+lecture for example you know you know
+ 
+
+ align:start position:0%
+lecture for example you know you know
+lecture recitation dinner a few events
+
+ align:start position:0%
+lecture recitation dinner a few events
+ 
+
+ align:start position:0%
+lecture recitation dinner a few events
+um study break you know events that are
+
+ align:start position:0%
+um study break you know events that are
+ 
+
+ align:start position:0%
+um study break you know events that are
+going to take about an hour take 10 of
+
+ align:start position:0%
+going to take about an hour take 10 of
+ 
+
+ align:start position:0%
+going to take about an hour take 10 of
+them shuffle them around put five of
+
+ align:start position:0%
+them shuffle them around put five of
+ 
+
+ align:start position:0%
+them shuffle them around put five of
+them in one pile randomly five in the
+
+ align:start position:0%
+them in one pile randomly five in the
+ 
+
+ align:start position:0%
+them in one pile randomly five in the
+other pile
+
+ align:start position:0%
+other pile
+ 
+
+ align:start position:0%
+other pile
+um then deliberately either try to smile
+
+ align:start position:0%
+um then deliberately either try to smile
+ 
+
+ align:start position:0%
+um then deliberately either try to smile
+or frown through you know smile through
+
+ align:start position:0%
+or frown through you know smile through
+ 
+
+ align:start position:0%
+or frown through you know smile through
+pile A and frown through pile B
+
+ align:start position:0%
+pile A and frown through pile B
+ 
+
+ align:start position:0%
+pile A and frown through pile B
+and ask yourself you can ask yourself a
+
+ align:start position:0%
+and ask yourself you can ask yourself a
+ 
+
+ align:start position:0%
+and ask yourself you can ask yourself a
+variety of questions uh the most obvious
+
+ align:start position:0%
+variety of questions uh the most obvious
+ 
+
+ align:start position:0%
+variety of questions uh the most obvious
+being how do I feel and and what's the
+
+ align:start position:0%
+being how do I feel and and what's the
+ 
+
+ align:start position:0%
+being how do I feel and and what's the
+effect on people around me
+
+ align:start position:0%
+effect on people around me
+ 
+
+ align:start position:0%
+effect on people around me
+um I mean if you
+
+ align:start position:0%
+um I mean if you
+ 
+
+ align:start position:0%
+um I mean if you
+you know frown like an idiot the the
+
+ align:start position:0%
+you know frown like an idiot the the
+ 
+
+ align:start position:0%
+you know frown like an idiot the the
+effect may be to uh to make people smile
+
+ align:start position:0%
+effect may be to uh to make people smile
+ 
+
+ align:start position:0%
+effect may be to uh to make people smile
+but uh
+
+ align:start position:0%
+but uh
+ 
+
+ align:start position:0%
+but uh
+um but if you what you know you you've
+
+ align:start position:0%
+um but if you what you know you you've
+ 
+
+ align:start position:0%
+um but if you what you know you you've
+done the experiment you were doing it
+
+ align:start position:0%
+done the experiment you were doing it
+ 
+
+ align:start position:0%
+done the experiment you were doing it
+like when you were uh early adolescence
+
+ align:start position:0%
+like when you were uh early adolescence
+ 
+
+ align:start position:0%
+like when you were uh early adolescence
+is one of the best times to do this
+
+ align:start position:0%
+is one of the best times to do this
+ 
+
+ align:start position:0%
+is one of the best times to do this
+particular experiment you show up at at
+
+ align:start position:0%
+particular experiment you show up at at
+ 
+
+ align:start position:0%
+particular experiment you show up at at
+the dinner table everybody's in a pretty
+
+ align:start position:0%
+the dinner table everybody's in a pretty
+ 
+
+ align:start position:0%
+the dinner table everybody's in a pretty
+good mood but you're not
+
+ align:start position:0%
+good mood but you're not
+ 
+
+ align:start position:0%
+good mood but you're not
+by the end of the meal you know that
+
+ align:start position:0%
+by the end of the meal you know that
+ 
+
+ align:start position:0%
+by the end of the meal you know that
+nobody's in a good mood anymore
+
+ align:start position:0%
+nobody's in a good mood anymore
+ 
+
+ align:start position:0%
+nobody's in a good mood anymore
+right well you can still do this I mean
+
+ align:start position:0%
+right well you can still do this I mean
+ 
+
+ align:start position:0%
+right well you can still do this I mean
+I'm not sure how ethical it is as an
+
+ align:start position:0%
+I'm not sure how ethical it is as an
+ 
+
+ align:start position:0%
+I'm not sure how ethical it is as an
+experiment to try out on on on your
+
+ align:start position:0%
+experiment to try out on on on your
+ 
+
+ align:start position:0%
+experiment to try out on on on your
+friends at dinner tonight but if you go
+
+ align:start position:0%
+friends at dinner tonight but if you go
+ 
+
+ align:start position:0%
+friends at dinner tonight but if you go
+to dinner feeling like junk and acting
+
+ align:start position:0%
+to dinner feeling like junk and acting
+ 
+
+ align:start position:0%
+to dinner feeling like junk and acting
+that way
+
+ align:start position:0%
+that way
+ 
+
+ align:start position:0%
+that way
+um you can make everybody else miserable
+
+ align:start position:0%
+um you can make everybody else miserable
+ 
+
+ align:start position:0%
+um you can make everybody else miserable
+too and isn't that great
+
+ align:start position:0%
+too and isn't that great
+ 
+
+ align:start position:0%
+too and isn't that great
+um but more to the point for the present
+
+ align:start position:0%
+um but more to the point for the present
+ 
+
+ align:start position:0%
+um but more to the point for the present
+point you can make yours hold on all
+
+ align:start position:0%
+point you can make yours hold on all
+ 
+
+ align:start position:0%
+point you can make yours hold on all
+that sappy garbage about a smile is your
+
+ align:start position:0%
+that sappy garbage about a smile is your
+ 
+
+ align:start position:0%
+that sappy garbage about a smile is your
+umbrella turn out to be sort of true and
+
+ align:start position:0%
+umbrella turn out to be sort of true and
+ 
+
+ align:start position:0%
+umbrella turn out to be sort of true and
+it doesn't even have to be a real smile
+
+ align:start position:0%
+it doesn't even have to be a real smile
+ 
+
+ align:start position:0%
+it doesn't even have to be a real smile
+if you take no that's somebody else's
+
+ align:start position:0%
+if you take no that's somebody else's
+ 
+
+ align:start position:0%
+if you take no that's somebody else's
+pen I'm not going to do it with somebody
+
+ align:start position:0%
+pen I'm not going to do it with somebody
+ 
+
+ align:start position:0%
+pen I'm not going to do it with somebody
+else's name if you take a pen this is an
+
+ align:start position:0%
+else's name if you take a pen this is an
+ 
+
+ align:start position:0%
+else's name if you take a pen this is an
+experiment that was was published a few
+
+ align:start position:0%
+experiment that was was published a few
+ 
+
+ align:start position:0%
+experiment that was was published a few
+years ago take a pen and hold it like
+
+ align:start position:0%
+years ago take a pen and hold it like
+ 
+
+ align:start position:0%
+years ago take a pen and hold it like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+um that courses their face into a sort
+
+ align:start position:0%
+um that courses their face into a sort
+ 
+
+ align:start position:0%
+um that courses their face into a sort
+of an idiot smile
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um whereas holding
+
+ align:start position:0%
+um whereas holding
+ 
+
+ align:start position:0%
+um whereas holding
+a pen like this does not it force it
+
+ align:start position:0%
+a pen like this does not it force it
+ 
+
+ align:start position:0%
+a pen like this does not it force it
+actually forces into a bit of a frown
+
+ align:start position:0%
+actually forces into a bit of a frown
+ 
+
+ align:start position:0%
+actually forces into a bit of a frown
+um if you do this and don't I'm already
+
+ align:start position:0%
+um if you do this and don't I'm already
+ 
+
+ align:start position:0%
+um if you do this and don't I'm already
+spoiling the control aspect of the
+
+ align:start position:0%
+spoiling the control aspect of the
+ 
+
+ align:start position:0%
+spoiling the control aspect of the
+experiment you don't tell people
+
+ align:start position:0%
+experiment you don't tell people
+ 
+
+ align:start position:0%
+experiment you don't tell people
+um why they're doing this you just make
+
+ align:start position:0%
+um why they're doing this you just make
+ 
+
+ align:start position:0%
+um why they're doing this you just make
+them do it for a while the people who do
+
+ align:start position:0%
+them do it for a while the people who do
+ 
+
+ align:start position:0%
+them do it for a while the people who do
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+feel better than the people who Guru and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enough that they don't know he's smiling
+
+ align:start position:0%
+enough that they don't know he's smiling
+ 
+
+ align:start position:0%
+enough that they don't know he's smiling
+he must feel good the fact that he's
+
+ align:start position:0%
+he must feel good the fact that he's
+ 
+
+ align:start position:0%
+he must feel good the fact that he's
+smiling because he's got a pen in his
+
+ align:start position:0%
+smiling because he's got a pen in his
+ 
+
+ align:start position:0%
+smiling because he's got a pen in his
+mouth turns out God it matters but it
+
+ align:start position:0%
+mouth turns out God it matters but it
+ 
+
+ align:start position:0%
+mouth turns out God it matters but it
+doesn't matter that much so if you're
+
+ align:start position:0%
+doesn't matter that much so if you're
+ 
+
+ align:start position:0%
+doesn't matter that much so if you're
+feeling down bite on a pen you'll feel
+
+ align:start position:0%
+feeling down bite on a pen you'll feel
+ 
+
+ align:start position:0%
+feeling down bite on a pen you'll feel
+much better about it
+
+ align:start position:0%
+much better about it
+ 
+
+ align:start position:0%
+much better about it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the um okay well look
+
+ align:start position:0%
+the um okay well look
+ 
+
+ align:start position:0%
+the um okay well look
+so you can get a certain amount of work
+
+ align:start position:0%
+so you can get a certain amount of work
+ 
+
+ align:start position:0%
+so you can get a certain amount of work
+done by broadening the set of of
+
+ align:start position:0%
+done by broadening the set of of
+ 
+
+ align:start position:0%
+done by broadening the set of of
+available
+
+ align:start position:0%
+available
+ 
+
+ align:start position:0%
+available
+um emotions available motivations that
+
+ align:start position:0%
+um emotions available motivations that
+ 
+
+ align:start position:0%
+um emotions available motivations that
+you want to talk about
+
+ align:start position:0%
+you want to talk about
+ 
+
+ align:start position:0%
+you want to talk about
+um why isn't the world a better place if
+
+ align:start position:0%
+um why isn't the world a better place if
+ 
+
+ align:start position:0%
+um why isn't the world a better place if
+you've got this you know this empathy
+
+ align:start position:0%
+you've got this you know this empathy
+ 
+
+ align:start position:0%
+you've got this you know this empathy
+thing going on and you've got this
+
+ align:start position:0%
+thing going on and you've got this
+ 
+
+ align:start position:0%
+thing going on and you've got this
+beautifully wired up brain that you're a
+
+ align:start position:0%
+beautifully wired up brain that you're a
+ 
+
+ align:start position:0%
+beautifully wired up brain that you're a
+slave to that's designed to make you eat
+
+ align:start position:0%
+slave to that's designed to make you eat
+ 
+
+ align:start position:0%
+slave to that's designed to make you eat
+and mate and do all those sort of good
+
+ align:start position:0%
+and mate and do all those sort of good
+ 
+
+ align:start position:0%
+and mate and do all those sort of good
+things why isn't the world a better
+
+ align:start position:0%
+things why isn't the world a better
+ 
+
+ align:start position:0%
+things why isn't the world a better
+place why doesn't it work better
+
+ align:start position:0%
+place why doesn't it work better
+ 
+
+ align:start position:0%
+place why doesn't it work better
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I point I look I can't solve that in the
+
+ align:start position:0%
+I point I look I can't solve that in the
+ 
+
+ align:start position:0%
+I point I look I can't solve that in the
+remaining 12 minutes or so
+
+ align:start position:0%
+remaining 12 minutes or so
+ 
+
+ align:start position:0%
+remaining 12 minutes or so
+um I've pointed to part of the answer
+
+ align:start position:0%
+um I've pointed to part of the answer
+ 
+
+ align:start position:0%
+um I've pointed to part of the answer
+just because you catch emotions doesn't
+
+ align:start position:0%
+just because you catch emotions doesn't
+ 
+
+ align:start position:0%
+just because you catch emotions doesn't
+necessarily mean you catch good ones it
+
+ align:start position:0%
+necessarily mean you catch good ones it
+ 
+
+ align:start position:0%
+necessarily mean you catch good ones it
+is also the case that not all of your
+
+ align:start position:0%
+is also the case that not all of your
+ 
+
+ align:start position:0%
+is also the case that not all of your
+motivations may be entirely benign
+
+ align:start position:0%
+motivations may be entirely benign
+ 
+
+ align:start position:0%
+motivations may be entirely benign
+so for example what's it got on the
+
+ align:start position:0%
+so for example what's it got on the
+ 
+
+ align:start position:0%
+so for example what's it got on the
+handout it doesn't have on the handout
+
+ align:start position:0%
+handout it doesn't have on the handout
+ 
+
+ align:start position:0%
+handout it doesn't have on the handout
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+aggression
+
+ align:start position:0%
+aggression
+ 
+
+ align:start position:0%
+aggression
+seems to be
+
+ align:start position:0%
+seems to be
+ 
+
+ align:start position:0%
+seems to be
+um there seems to have deep biological
+
+ align:start position:0%
+um there seems to have deep biological
+ 
+
+ align:start position:0%
+um there seems to have deep biological
+roots to it
+
+ align:start position:0%
+roots to it
+ 
+
+ align:start position:0%
+roots to it
+um it is a
+
+ align:start position:0%
+um it is a
+ 
+
+ align:start position:0%
+um it is a
+um not unreasonable
+
+ align:start position:0%
+um not unreasonable
+ 
+
+ align:start position:0%
+um not unreasonable
+reaction to a world of limited resources
+
+ align:start position:0%
+reaction to a world of limited resources
+ 
+
+ align:start position:0%
+reaction to a world of limited resources
+it's not necessarily a nice reaction to
+
+ align:start position:0%
+it's not necessarily a nice reaction to
+ 
+
+ align:start position:0%
+it's not necessarily a nice reaction to
+a world of limited resources but
+
+ align:start position:0%
+a world of limited resources but
+ 
+
+ align:start position:0%
+a world of limited resources but
+um you know if if you are
+
+ align:start position:0%
+um you know if if you are
+ 
+
+ align:start position:0%
+um you know if if you are
+um if there's a limited number of mates
+
+ align:start position:0%
+um if there's a limited number of mates
+ 
+
+ align:start position:0%
+um if there's a limited number of mates
+out there
+
+ align:start position:0%
+out there
+ 
+
+ align:start position:0%
+out there
+and uh and you can punch out all the uh
+
+ align:start position:0%
+and uh and you can punch out all the uh
+ 
+
+ align:start position:0%
+and uh and you can punch out all the uh
+all the other guys and grab all
+
+ align:start position:0%
+all the other guys and grab all
+ 
+
+ align:start position:0%
+all the other guys and grab all
+um all the uh all the women
+
+ align:start position:0%
+um all the uh all the women
+ 
+
+ align:start position:0%
+um all the uh all the women
+um well you get to have more progeny
+
+ align:start position:0%
+um well you get to have more progeny
+ 
+
+ align:start position:0%
+um well you get to have more progeny
+than the the guys you punched out
+
+ align:start position:0%
+than the the guys you punched out
+ 
+
+ align:start position:0%
+than the the guys you punched out
+fortunately Human Society is not
+
+ align:start position:0%
+fortunately Human Society is not
+ 
+
+ align:start position:0%
+fortunately Human Society is not
+organized particularly that way but
+
+ align:start position:0%
+organized particularly that way but
+ 
+
+ align:start position:0%
+organized particularly that way but
+there are plenty of animal societies
+
+ align:start position:0%
+there are plenty of animal societies
+ 
+
+ align:start position:0%
+there are plenty of animal societies
+that seem to be
+
+ align:start position:0%
+that seem to be
+ 
+
+ align:start position:0%
+that seem to be
+um elephant seals you've seen the uh you
+
+ align:start position:0%
+um elephant seals you've seen the uh you
+ 
+
+ align:start position:0%
+um elephant seals you've seen the uh you
+seeing these guys on on you know your
+
+ align:start position:0%
+seeing these guys on on you know your
+ 
+
+ align:start position:0%
+seeing these guys on on you know your
+favorite cable channel right they they
+
+ align:start position:0%
+favorite cable channel right they they
+ 
+
+ align:start position:0%
+favorite cable channel right they they
+want they they come up in thousands on
+
+ align:start position:0%
+want they they come up in thousands on
+ 
+
+ align:start position:0%
+want they they come up in thousands on
+the beaches near Antarctica and stuff
+
+ align:start position:0%
+the beaches near Antarctica and stuff
+ 
+
+ align:start position:0%
+the beaches near Antarctica and stuff
+and and you know these huge male guy
+
+ align:start position:0%
+and and you know these huge male guy
+ 
+
+ align:start position:0%
+and and you know these huge male guy
+elephant seals have like a thousand
+
+ align:start position:0%
+elephant seals have like a thousand
+ 
+
+ align:start position:0%
+elephant seals have like a thousand
+women what is a woman elephant seal I
+
+ align:start position:0%
+women what is a woman elephant seal I
+ 
+
+ align:start position:0%
+women what is a woman elephant seal I
+don't know anyway a thousand female
+
+ align:start position:0%
+don't know anyway a thousand female
+ 
+
+ align:start position:0%
+don't know anyway a thousand female
+elephant seals in there in their Harem
+
+ align:start position:0%
+elephant seals in there in their Harem
+ 
+
+ align:start position:0%
+elephant seals in there in their Harem
+and they have these huge fights over who
+
+ align:start position:0%
+and they have these huge fights over who
+ 
+
+ align:start position:0%
+and they have these huge fights over who
+gets to have a you know they can't share
+
+ align:start position:0%
+gets to have a you know they can't share
+ 
+
+ align:start position:0%
+gets to have a you know they can't share
+they just never went to preschool and
+
+ align:start position:0%
+they just never went to preschool and
+ 
+
+ align:start position:0%
+they just never went to preschool and
+learned how to share properly but part
+
+ align:start position:0%
+learned how to share properly but part
+ 
+
+ align:start position:0%
+learned how to share properly but part
+of um there's certainly enough
+
+ align:start position:0%
+of um there's certainly enough
+ 
+
+ align:start position:0%
+of um there's certainly enough
+aggression in human behavior to make it
+
+ align:start position:0%
+aggression in human behavior to make it
+ 
+
+ align:start position:0%
+aggression in human behavior to make it
+clear that that that sort of a
+
+ align:start position:0%
+clear that that that sort of a
+ 
+
+ align:start position:0%
+clear that that that sort of a
+motivational system is going to lead to
+
+ align:start position:0%
+motivational system is going to lead to
+ 
+
+ align:start position:0%
+motivational system is going to lead to
+a certain amount of conflict in the
+
+ align:start position:0%
+a certain amount of conflict in the
+ 
+
+ align:start position:0%
+a certain amount of conflict in the
+world and it's not all going to work out
+
+ align:start position:0%
+world and it's not all going to work out
+ 
+
+ align:start position:0%
+world and it's not all going to work out
+as sweetness and light people like Freud
+
+ align:start position:0%
+as sweetness and light people like Freud
+ 
+
+ align:start position:0%
+as sweetness and light people like Freud
+proposed that there was actually a Death
+
+ align:start position:0%
+proposed that there was actually a Death
+ 
+
+ align:start position:0%
+proposed that there was actually a Death
+Wish motivation
+
+ align:start position:0%
+Wish motivation
+ 
+
+ align:start position:0%
+Wish motivation
+um out there my sonatos uh is is is
+
+ align:start position:0%
+um out there my sonatos uh is is is
+ 
+
+ align:start position:0%
+um out there my sonatos uh is is is
+Freud's term
+
+ align:start position:0%
+Freud's term
+ 
+
+ align:start position:0%
+Freud's term
+um I may talk about that more later in
+
+ align:start position:0%
+um I may talk about that more later in
+ 
+
+ align:start position:0%
+um I may talk about that more later in
+the term
+
+ align:start position:0%
+the term
+ 
+
+ align:start position:0%
+the term
+um so that that that's the possibility
+
+ align:start position:0%
+um so that that that's the possibility
+ 
+
+ align:start position:0%
+um so that that that's the possibility
+that there are motivations that
+
+ align:start position:0%
+that there are motivations that
+ 
+
+ align:start position:0%
+that there are motivations that
+themselves are not particularly nice if
+
+ align:start position:0%
+themselves are not particularly nice if
+ 
+
+ align:start position:0%
+themselves are not particularly nice if
+you like is one possible reason that the
+
+ align:start position:0%
+you like is one possible reason that the
+ 
+
+ align:start position:0%
+you like is one possible reason that the
+world is is not
+
+ align:start position:0%
+world is is not
+ 
+
+ align:start position:0%
+world is is not
+hey uh a perfect place but um
+
+ align:start position:0%
+hey uh a perfect place but um
+ 
+
+ align:start position:0%
+hey uh a perfect place but um
+perhaps the most useful way of
+
+ align:start position:0%
+perhaps the most useful way of
+ 
+
+ align:start position:0%
+perhaps the most useful way of
+understanding why the world doesn't work
+
+ align:start position:0%
+understanding why the world doesn't work
+ 
+
+ align:start position:0%
+understanding why the world doesn't work
+out so well necessarily given all this
+
+ align:start position:0%
+out so well necessarily given all this
+ 
+
+ align:start position:0%
+out so well necessarily given all this
+marvelous
+
+ align:start position:0%
+marvelous
+ 
+
+ align:start position:0%
+marvelous
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+motivational Hardware if you like that
+
+ align:start position:0%
+motivational Hardware if you like that
+ 
+
+ align:start position:0%
+motivational Hardware if you like that
+you've got is that
+
+ align:start position:0%
+you've got is that
+ 
+
+ align:start position:0%
+you've got is that
+um look most of the time when we study
+
+ align:start position:0%
+um look most of the time when we study
+ 
+
+ align:start position:0%
+um look most of the time when we study
+these things we're studying a motivation
+
+ align:start position:0%
+these things we're studying a motivation
+ 
+
+ align:start position:0%
+these things we're studying a motivation
+in isolation you want to study this
+
+ align:start position:0%
+in isolation you want to study this
+ 
+
+ align:start position:0%
+in isolation you want to study this
+cat's ability to learn about the puzzle
+
+ align:start position:0%
+cat's ability to learn about the puzzle
+ 
+
+ align:start position:0%
+cat's ability to learn about the puzzle
+box and and the relation to the
+
+ align:start position:0%
+box and and the relation to the
+ 
+
+ align:start position:0%
+box and and the relation to the
+motivation of hunger you take a Hungry
+
+ align:start position:0%
+motivation of hunger you take a Hungry
+ 
+
+ align:start position:0%
+motivation of hunger you take a Hungry
+Cat you put it in a box the only thing
+
+ align:start position:0%
+Cat you put it in a box the only thing
+ 
+
+ align:start position:0%
+Cat you put it in a box the only thing
+of any interest here is how to get out
+
+ align:start position:0%
+of any interest here is how to get out
+ 
+
+ align:start position:0%
+of any interest here is how to get out
+of the box and get to the fish
+
+ align:start position:0%
+of the box and get to the fish
+ 
+
+ align:start position:0%
+of the box and get to the fish
+um you know the only thing of Interest
+
+ align:start position:0%
+um you know the only thing of Interest
+ 
+
+ align:start position:0%
+um you know the only thing of Interest
+here is you know the the the there's a
+
+ align:start position:0%
+here is you know the the the there's a
+ 
+
+ align:start position:0%
+here is you know the the the there's a
+rat who's maybe a hungry rat in this
+
+ align:start position:0%
+rat who's maybe a hungry rat in this
+ 
+
+ align:start position:0%
+rat who's maybe a hungry rat in this
+case he's got an electrode now and in
+
+ align:start position:0%
+case he's got an electrode now and in
+ 
+
+ align:start position:0%
+case he's got an electrode now and in
+the feeding centers of his brain
+
+ align:start position:0%
+the feeding centers of his brain
+ 
+
+ align:start position:0%
+the feeding centers of his brain
+and all the other things that a rat
+
+ align:start position:0%
+and all the other things that a rat
+ 
+
+ align:start position:0%
+and all the other things that a rat
+might do are just not relevant here you
+
+ align:start position:0%
+might do are just not relevant here you
+ 
+
+ align:start position:0%
+might do are just not relevant here you
+don't operate in a world like that you
+
+ align:start position:0%
+don't operate in a world like that you
+ 
+
+ align:start position:0%
+don't operate in a world like that you
+operate in a much more complicated space
+
+ align:start position:0%
+operate in a much more complicated space
+ 
+
+ align:start position:0%
+operate in a much more complicated space
+I mean we can cartoon that here here's
+
+ align:start position:0%
+I mean we can cartoon that here here's
+ 
+
+ align:start position:0%
+I mean we can cartoon that here here's
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+um you know if we got in the lab maybe
+
+ align:start position:0%
+um you know if we got in the lab maybe
+ 
+
+ align:start position:0%
+um you know if we got in the lab maybe
+we can we can uh just do uh an
+
+ align:start position:0%
+we can we can uh just do uh an
+ 
+
+ align:start position:0%
+we can we can uh just do uh an
+experiment on when you do or do not eat
+
+ align:start position:0%
+experiment on when you do or do not eat
+ 
+
+ align:start position:0%
+experiment on when you do or do not eat
+but that's not what you're dealing
+
+ align:start position:0%
+but that's not what you're dealing
+ 
+
+ align:start position:0%
+but that's not what you're dealing
+without in in your well all right here
+
+ align:start position:0%
+without in in your well all right here
+ 
+
+ align:start position:0%
+without in in your well all right here
+let's just wait to get to this question
+
+ align:start position:0%
+let's just wait to get to this question
+ 
+
+ align:start position:0%
+let's just wait to get to this question
+how many of you have ever eaten
+
+ align:start position:0%
+how many of you have ever eaten
+ 
+
+ align:start position:0%
+how many of you have ever eaten
+something when you weren't hungry
+
+ align:start position:0%
+something when you weren't hungry
+ 
+
+ align:start position:0%
+something when you weren't hungry
+what's the matter with you right you
+
+ align:start position:0%
+what's the matter with you right you
+ 
+
+ align:start position:0%
+what's the matter with you right you
+know I just told you you got this
+
+ align:start position:0%
+know I just told you you got this
+ 
+
+ align:start position:0%
+know I just told you you got this
+elaborate stuff I've already erased the
+
+ align:start position:0%
+elaborate stuff I've already erased the
+ 
+
+ align:start position:0%
+elaborate stuff I've already erased the
+lateral hypothalamus yeah the brain full
+
+ align:start position:0%
+lateral hypothalamus yeah the brain full
+ 
+
+ align:start position:0%
+lateral hypothalamus yeah the brain full
+of circuitry designed to make you eat
+
+ align:start position:0%
+of circuitry designed to make you eat
+ 
+
+ align:start position:0%
+of circuitry designed to make you eat
+when you're hungry and not to eat when
+
+ align:start position:0%
+when you're hungry and not to eat when
+ 
+
+ align:start position:0%
+when you're hungry and not to eat when
+you're not hungry and and you don't look
+
+ align:start position:0%
+you're not hungry and and you don't look
+ 
+
+ align:start position:0%
+you're not hungry and and you don't look
+like though that that furry uh football
+
+ align:start position:0%
+like though that that furry uh football
+ 
+
+ align:start position:0%
+like though that that furry uh football
+with a lesion in your brain so what's
+
+ align:start position:0%
+with a lesion in your brain so what's
+ 
+
+ align:start position:0%
+with a lesion in your brain so what's
+your problem that you're you're eating
+
+ align:start position:0%
+your problem that you're you're eating
+ 
+
+ align:start position:0%
+your problem that you're you're eating
+when you're um when you're not hungry
+
+ align:start position:0%
+when you're um when you're not hungry
+ 
+
+ align:start position:0%
+when you're um when you're not hungry
+um well all right let's let's think
+
+ align:start position:0%
+um well all right let's let's think
+ 
+
+ align:start position:0%
+um well all right let's let's think
+about this in sort of metaphorical terms
+
+ align:start position:0%
+about this in sort of metaphorical terms
+ 
+
+ align:start position:0%
+about this in sort of metaphorical terms
+let's imagine a situation
+
+ align:start position:0%
+let's imagine a situation
+ 
+
+ align:start position:0%
+let's imagine a situation
+um where there are lots of different
+
+ align:start position:0%
+um where there are lots of different
+ 
+
+ align:start position:0%
+um where there are lots of different
+possibilities pulling on you suppose
+
+ align:start position:0%
+possibilities pulling on you suppose
+ 
+
+ align:start position:0%
+possibilities pulling on you suppose
+you're at some sort of a social
+
+ align:start position:0%
+you're at some sort of a social
+ 
+
+ align:start position:0%
+you're at some sort of a social
+Gathering of some sort there are lots of
+
+ align:start position:0%
+Gathering of some sort there are lots of
+ 
+
+ align:start position:0%
+Gathering of some sort there are lots of
+possible things lots of motivational
+
+ align:start position:0%
+possible things lots of motivational
+ 
+
+ align:start position:0%
+possible things lots of motivational
+systems at work at any one
+
+ align:start position:0%
+systems at work at any one
+ 
+
+ align:start position:0%
+systems at work at any one
+um one time I mean one of the things you
+
+ align:start position:0%
+um one time I mean one of the things you
+ 
+
+ align:start position:0%
+um one time I mean one of the things you
+could probably do is eat
+
+ align:start position:0%
+could probably do is eat
+ 
+
+ align:start position:0%
+could probably do is eat
+um maybe there's the possibility for
+
+ align:start position:0%
+um maybe there's the possibility for
+ 
+
+ align:start position:0%
+um maybe there's the possibility for
+fighting
+
+ align:start position:0%
+fighting
+ 
+
+ align:start position:0%
+fighting
+um you know mating whoops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh sleep
+
+ align:start position:0%
+uh sleep
+ 
+
+ align:start position:0%
+uh sleep
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+study
+
+ align:start position:0%
+study
+ 
+
+ align:start position:0%
+study
+you know you could you could do all all
+
+ align:start position:0%
+you know you could you could do all all
+ 
+
+ align:start position:0%
+you know you could you could do all all
+sorts of you know run
+
+ align:start position:0%
+sorts of you know run
+ 
+
+ align:start position:0%
+sorts of you know run
+you could do all sorts of stuff
+
+ align:start position:0%
+you could do all sorts of stuff
+ 
+
+ align:start position:0%
+you could do all sorts of stuff
+and all of these things Each of which
+
+ align:start position:0%
+and all of these things Each of which
+ 
+
+ align:start position:0%
+and all of these things Each of which
+may have its own beautiful
+
+ align:start position:0%
+may have its own beautiful
+ 
+
+ align:start position:0%
+may have its own beautiful
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+hardwired core and it's elaboration from
+
+ align:start position:0%
+hardwired core and it's elaboration from
+ 
+
+ align:start position:0%
+hardwired core and it's elaboration from
+a lifetime of learning all of these
+
+ align:start position:0%
+a lifetime of learning all of these
+ 
+
+ align:start position:0%
+a lifetime of learning all of these
+things are pulling on you at once
+
+ align:start position:0%
+things are pulling on you at once
+ 
+
+ align:start position:0%
+things are pulling on you at once
+and and and well you know all right so
+
+ align:start position:0%
+and and and well you know all right so
+ 
+
+ align:start position:0%
+and and and well you know all right so
+maybe the sleep motivation and the study
+
+ align:start position:0%
+maybe the sleep motivation and the study
+ 
+
+ align:start position:0%
+maybe the sleep motivation and the study
+motivation are are are pretty weak at
+
+ align:start position:0%
+motivation are are are pretty weak at
+ 
+
+ align:start position:0%
+motivation are are are pretty weak at
+any given moment but you know let's
+
+ align:start position:0%
+any given moment but you know let's
+ 
+
+ align:start position:0%
+any given moment but you know let's
+let's suppose that there's pretty strong
+
+ align:start position:0%
+let's suppose that there's pretty strong
+ 
+
+ align:start position:0%
+let's suppose that there's pretty strong
+drives in in in in this direction
+
+ align:start position:0%
+drives in in in in this direction
+ 
+
+ align:start position:0%
+drives in in in in this direction
+um okay so if you're sitting in this in
+
+ align:start position:0%
+um okay so if you're sitting in this in
+ 
+
+ align:start position:0%
+um okay so if you're sitting in this in
+this exciting Vector field whereas the
+
+ align:start position:0%
+this exciting Vector field whereas the
+ 
+
+ align:start position:0%
+this exciting Vector field whereas the
+resultant right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+I'm not proposing this as a serious
+
+ align:start position:0%
+I'm not proposing this as a serious
+ 
+
+ align:start position:0%
+I'm not proposing this as a serious
+model of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of why you might eat when well I am
+
+ align:start position:0%
+of why you might eat when well I am
+ 
+
+ align:start position:0%
+of why you might eat when well I am
+proposing it as I'm not supposing as as
+
+ align:start position:0%
+proposing it as I'm not supposing as as
+ 
+
+ align:start position:0%
+proposing it as I'm not supposing as as
+a serious mathematical model of why you
+
+ align:start position:0%
+a serious mathematical model of why you
+ 
+
+ align:start position:0%
+a serious mathematical model of why you
+might eat but I'm I'm proposing it as a
+
+ align:start position:0%
+might eat but I'm I'm proposing it as a
+ 
+
+ align:start position:0%
+might eat but I'm I'm proposing it as a
+serious metaphor that you might engage
+
+ align:start position:0%
+serious metaphor that you might engage
+ 
+
+ align:start position:0%
+serious metaphor that you might engage
+and it's going to be much more
+
+ align:start position:0%
+and it's going to be much more
+ 
+
+ align:start position:0%
+and it's going to be much more
+complicated than and than than this
+
+ align:start position:0%
+complicated than and than than this
+ 
+
+ align:start position:0%
+complicated than and than than this
+right I mean part of the reason it's not
+
+ align:start position:0%
+right I mean part of the reason it's not
+ 
+
+ align:start position:0%
+right I mean part of the reason it's not
+just that there's you know want to meet
+
+ align:start position:0%
+just that there's you know want to meet
+ 
+
+ align:start position:0%
+just that there's you know want to meet
+want to fight or think I'll go eat
+
+ align:start position:0%
+want to fight or think I'll go eat
+ 
+
+ align:start position:0%
+want to fight or think I'll go eat
+instead but
+
+ align:start position:0%
+instead but
+ 
+
+ align:start position:0%
+instead but
+want to mate you know
+
+ align:start position:0%
+want to mate you know
+ 
+
+ align:start position:0%
+want to mate you know
+here now can't do that but there's
+
+ align:start position:0%
+here now can't do that but there's
+ 
+
+ align:start position:0%
+here now can't do that but there's
+um but there you know there's those
+
+ align:start position:0%
+um but there you know there's those
+ 
+
+ align:start position:0%
+um but there you know there's those
+brain stem chunks of General arousal
+
+ align:start position:0%
+brain stem chunks of General arousal
+ 
+
+ align:start position:0%
+brain stem chunks of General arousal
+yeah well I've sort of got a lot of
+
+ align:start position:0%
+yeah well I've sort of got a lot of
+ 
+
+ align:start position:0%
+yeah well I've sort of got a lot of
+activity here that I I got to do
+
+ align:start position:0%
+activity here that I I got to do
+ 
+
+ align:start position:0%
+activity here that I I got to do
+something so you end up with sort of
+
+ align:start position:0%
+something so you end up with sort of
+ 
+
+ align:start position:0%
+something so you end up with sort of
+displacement activity the problem is
+
+ align:start position:0%
+displacement activity the problem is
+ 
+
+ align:start position:0%
+displacement activity the problem is
+that the world is a complicated place
+
+ align:start position:0%
+that the world is a complicated place
+ 
+
+ align:start position:0%
+that the world is a complicated place
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the if you were ever going to reduce
+
+ align:start position:0%
+the if you were ever going to reduce
+ 
+
+ align:start position:0%
+the if you were ever going to reduce
+this to math it's going to have a lot of
+
+ align:start position:0%
+this to math it's going to have a lot of
+ 
+
+ align:start position:0%
+this to math it's going to have a lot of
+variables in
+
+ align:start position:0%
+variables in
+ 
+
+ align:start position:0%
+variables in
+um uh it's going to end up with a lot of
+
+ align:start position:0%
+um uh it's going to end up with a lot of
+ 
+
+ align:start position:0%
+um uh it's going to end up with a lot of
+variables in the equation most of us
+
+ align:start position:0%
+variables in the equation most of us
+ 
+
+ align:start position:0%
+variables in the equation most of us
+managed to do okay we eat when uh uh
+
+ align:start position:0%
+managed to do okay we eat when uh uh
+ 
+
+ align:start position:0%
+managed to do okay we eat when uh uh
+when we don't want but that's all right
+
+ align:start position:0%
+when we don't want but that's all right
+ 
+
+ align:start position:0%
+when we don't want but that's all right
+later on in the course you end up
+
+ align:start position:0%
+later on in the course you end up
+ 
+
+ align:start position:0%
+later on in the course you end up
+talking about the you know perhaps the
+
+ align:start position:0%
+talking about the you know perhaps the
+ 
+
+ align:start position:0%
+talking about the you know perhaps the
+people where
+
+ align:start position:0%
+people where
+ 
+
+ align:start position:0%
+people where
+you find that they're fighting too much
+
+ align:start position:0%
+you find that they're fighting too much
+ 
+
+ align:start position:0%
+you find that they're fighting too much
+or something like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um no lecture Thursday just to reiterate
+
+ align:start position:0%
+um no lecture Thursday just to reiterate
+ 
+
+ align:start position:0%
+um no lecture Thursday just to reiterate
+I will sign all those lovely ad drop
+
+ align:start position:0%
+I will sign all those lovely ad drop
+ 
+
+ align:start position:0%
+I will sign all those lovely ad drop
+cards I'll see you next week
\ No newline at end of file
diff --git a/CazYO1ET4ic.txt b/CazYO1ET4ic.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d048fbd105083eb6f733165554a7005a5082aabd
--- /dev/null
+++ b/CazYO1ET4ic.txt
@@ -0,0 +1,1907 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eyelids and like a
+
+ align:start position:0%
+eyelids and like a
+ 
+
+ align:start position:0%
+eyelids and like a
+jewel eyes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soft
+
+ align:start position:0%
+soft
+ 
+
+ align:start position:0%
+soft
+when with glories what shall rest of the
+
+ align:start position:0%
+when with glories what shall rest of the
+ 
+
+ align:start position:0%
+when with glories what shall rest of the
+What
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Remain
+
+ align:start position:0%
+Remain
+ 
+
+ align:start position:0%
+Remain
+seven the priest the
+
+ align:start position:0%
+seven the priest the
+ 
+
+ align:start position:0%
+seven the priest the
+Virgin my 17 s Seven Ages to and then
+
+ align:start position:0%
+Virgin my 17 s Seven Ages to and then
+ 
+
+ align:start position:0%
+Virgin my 17 s Seven Ages to and then
+they would in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+heaven finishing mors and
+
+ align:start position:0%
+heaven finishing mors and
+ 
+
+ align:start position:0%
+heaven finishing mors and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+control all the joys of thees all the
+
+ align:start position:0%
+control all the joys of thees all the
+ 
+
+ align:start position:0%
+control all the joys of thees all the
+Sorrows that wear out the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soul
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yest rich and
+
+ align:start position:0%
+yest rich and
+ 
+
+ align:start position:0%
+yest rich and
+tomorrow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C there have been and shall
+
+ align:start position:0%
+C there have been and shall
+ 
+
+ align:start position:0%
+C there have been and shall
+be that SM not and bite not
+
+ align:start position:0%
+be that SM not and bite not
+ 
+
+ align:start position:0%
+be that SM not and bite not
+in the love of
+
+ align:start position:0%
+in the love of
+ 
+
+ align:start position:0%
+in the love of
+thees the us indeed and in
+
+ align:start position:0%
+thees the us indeed and in
+ 
+
+ align:start position:0%
+thees the us indeed and in
+V wise and women and
+
+ align:start position:0%
+V wise and women and
+ 
+
+ align:start position:0%
+V wise and women and
+Wiest the
+
+ align:start position:0%
+Wiest the
+ 
+
+ align:start position:0%
+Wiest the
+lady
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of that was a little more solid I made
+
+ align:start position:0%
+of that was a little more solid I made
+ 
+
+ align:start position:0%
+of that was a little more solid I made
+uh now this time I made uh some more
+
+ align:start position:0%
+uh now this time I made uh some more
+ 
+
+ align:start position:0%
+uh now this time I made uh some more
+errors in pitch and uh in words but in
+
+ align:start position:0%
+errors in pitch and uh in words but in
+ 
+
+ align:start position:0%
+errors in pitch and uh in words but in
+any event I think that was that gives us
+
+ align:start position:0%
+any event I think that was that gives us
+ 
+
+ align:start position:0%
+any event I think that was that gives us
+a a flavor of what's going on and I
+
+ align:start position:0%
+a a flavor of what's going on and I
+ 
+
+ align:start position:0%
+a a flavor of what's going on and I
+really dig the melody it's like so
+
+ align:start position:0%
+really dig the melody it's like so
+ 
+
+ align:start position:0%
+really dig the melody it's like so
+wonderful it totally sings itself it's
+
+ align:start position:0%
+wonderful it totally sings itself it's
+ 
+
+ align:start position:0%
+wonderful it totally sings itself it's
+very organic and it's very
+
+ align:start position:0%
+very organic and it's very
+ 
+
+ align:start position:0%
+very organic and it's very
+much uh it's exactly the kind of thing
+
+ align:start position:0%
+much uh it's exactly the kind of thing
+ 
+
+ align:start position:0%
+much uh it's exactly the kind of thing
+that singers like in as much as because
+
+ align:start position:0%
+that singers like in as much as because
+ 
+
+ align:start position:0%
+that singers like in as much as because
+it makes sense on the page it lets us it
+
+ align:start position:0%
+it makes sense on the page it lets us it
+ 
+
+ align:start position:0%
+it makes sense on the page it lets us it
+frees up our brain a little bit more to
+
+ align:start position:0%
+frees up our brain a little bit more to
+ 
+
+ align:start position:0%
+frees up our brain a little bit more to
+make music um now that's not to say that
+
+ align:start position:0%
+make music um now that's not to say that
+ 
+
+ align:start position:0%
+make music um now that's not to say that
+Melody is the only thing that frees up a
+
+ align:start position:0%
+Melody is the only thing that frees up a
+ 
+
+ align:start position:0%
+Melody is the only thing that frees up a
+person's brain anything that it's
+
+ align:start position:0%
+person's brain anything that it's
+ 
+
+ align:start position:0%
+person's brain anything that it's
+vocally well written I don't care if
+
+ align:start position:0%
+vocally well written I don't care if
+ 
+
+ align:start position:0%
+vocally well written I don't care if
+it's tonal or non uh has that effect and
+
+ align:start position:0%
+it's tonal or non uh has that effect and
+ 
+
+ align:start position:0%
+it's tonal or non uh has that effect and
+that's the sort of like magic of good
+
+ align:start position:0%
+that's the sort of like magic of good
+ 
+
+ align:start position:0%
+that's the sort of like magic of good
+vocal writing uh just achieving that
+
+ align:start position:0%
+vocal writing uh just achieving that
+ 
+
+ align:start position:0%
+vocal writing uh just achieving that
+balance um was there anything that you
+
+ align:start position:0%
+balance um was there anything that you
+ 
+
+ align:start position:0%
+balance um was there anything that you
+wanted to say about the piece uh before
+
+ align:start position:0%
+wanted to say about the piece uh before
+ 
+
+ align:start position:0%
+wanted to say about the piece uh before
+Daniel and I made our comments not
+
+ align:start position:0%
+Daniel and I made our comments not
+ 
+
+ align:start position:0%
+Daniel and I made our comments not
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+anything I want to I want to ask you
+
+ align:start position:0%
+anything I want to I want to ask you
+ 
+
+ align:start position:0%
+anything I want to I want to ask you
+what you thought about the quicker
+
+ align:start position:0%
+what you thought about the quicker
+ 
+
+ align:start position:0%
+what you thought about the quicker
+Tempo I think I actually liked it it
+
+ align:start position:0%
+Tempo I think I actually liked it it
+ 
+
+ align:start position:0%
+Tempo I think I actually liked it it
+wasn't what I had intended but I think
+
+ align:start position:0%
+wasn't what I had intended but I think
+ 
+
+ align:start position:0%
+wasn't what I had intended but I think
+it really
+
+ align:start position:0%
+it really
+ 
+
+ align:start position:0%
+it really
+worked I kind of think it did too I
+
+ align:start position:0%
+worked I kind of think it did too I
+ 
+
+ align:start position:0%
+worked I kind of think it did too I
+think it I think it works well at that
+
+ align:start position:0%
+think it I think it works well at that
+ 
+
+ align:start position:0%
+think it I think it works well at that
+sort of you know dance little bit
+
+ align:start position:0%
+sort of you know dance little bit
+ 
+
+ align:start position:0%
+sort of you know dance little bit
+dancier Tempo or it would work much
+
+ align:start position:0%
+dancier Tempo or it would work much
+ 
+
+ align:start position:0%
+dancier Tempo or it would work much
+better much I mean it would work better
+
+ align:start position:0%
+better much I mean it would work better
+ 
+
+ align:start position:0%
+better much I mean it would work better
+much slower as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like like a
+
+ align:start position:0%
+like like a
+ 
+
+ align:start position:0%
+like like a
+Jew it feels kind of like you know
+
+ align:start position:0%
+Jew it feels kind of like you know
+ 
+
+ align:start position:0%
+Jew it feels kind of like you know
+nightclub shanto standing around last
+
+ align:start position:0%
+nightclub shanto standing around last
+ 
+
+ align:start position:0%
+nightclub shanto standing around last
+call 4 in the morning cigarette hanging
+
+ align:start position:0%
+call 4 in the morning cigarette hanging
+ 
+
+ align:start position:0%
+call 4 in the morning cigarette hanging
+off lip that kind of whole thing um in
+
+ align:start position:0%
+off lip that kind of whole thing um in
+ 
+
+ align:start position:0%
+off lip that kind of whole thing um in
+the middle it kind of that the sort of
+
+ align:start position:0%
+the middle it kind of that the sort of
+ 
+
+ align:start position:0%
+the middle it kind of that the sort of
+middle Tempo that we did at the first
+
+ align:start position:0%
+middle Tempo that we did at the first
+ 
+
+ align:start position:0%
+middle Tempo that we did at the first
+time at it doesn't really uh strike a
+
+ align:start position:0%
+time at it doesn't really uh strike a
+ 
+
+ align:start position:0%
+time at it doesn't really uh strike a
+cord in one thing or the other but the
+
+ align:start position:0%
+cord in one thing or the other but the
+ 
+
+ align:start position:0%
+cord in one thing or the other but the
+quicker Tempo it has this kind of
+
+ align:start position:0%
+quicker Tempo it has this kind of
+ 
+
+ align:start position:0%
+quicker Tempo it has this kind of
+insence to it um but I don't know if the
+
+ align:start position:0%
+insence to it um but I don't know if the
+ 
+
+ align:start position:0%
+insence to it um but I don't know if the
+inscience is what the poem needs or
+
+ align:start position:0%
+inscience is what the poem needs or
+ 
+
+ align:start position:0%
+inscience is what the poem needs or
+wants so that's up to you all of which
+
+ align:start position:0%
+wants so that's up to you all of which
+ 
+
+ align:start position:0%
+wants so that's up to you all of which
+is to say if you even if you don't care
+
+ align:start position:0%
+is to say if you even if you don't care
+ 
+
+ align:start position:0%
+is to say if you even if you don't care
+particularly what dyn what uh range your
+
+ align:start position:0%
+particularly what dyn what uh range your
+ 
+
+ align:start position:0%
+particularly what dyn what uh range your
+Tempo is in at least Mark a range of
+
+ align:start position:0%
+Tempo is in at least Mark a range of
+ 
+
+ align:start position:0%
+Tempo is in at least Mark a range of
+things that would be appropriate and if
+
+ align:start position:0%
+things that would be appropriate and if
+ 
+
+ align:start position:0%
+things that would be appropriate and if
+you don't want to be specific uh with an
+
+ align:start position:0%
+you don't want to be specific uh with an
+ 
+
+ align:start position:0%
+you don't want to be specific uh with an
+actual metronome marking at least gives
+
+ align:start position:0%
+actual metronome marking at least gives
+ 
+
+ align:start position:0%
+actual metronome marking at least gives
+something evocative at the beginning
+
+ align:start position:0%
+something evocative at the beginning
+ 
+
+ align:start position:0%
+something evocative at the beginning
+like uh you know fresh with Vigor or you
+
+ align:start position:0%
+like uh you know fresh with Vigor or you
+ 
+
+ align:start position:0%
+like uh you know fresh with Vigor or you
+know Saucy or you know feel free to use
+
+ align:start position:0%
+know Saucy or you know feel free to use
+ 
+
+ align:start position:0%
+know Saucy or you know feel free to use
+the the adverb or adjective of your
+
+ align:start position:0%
+the the adverb or adjective of your
+ 
+
+ align:start position:0%
+the the adverb or adjective of your
+choice as long as it really
+
+ align:start position:0%
+choice as long as it really
+ 
+
+ align:start position:0%
+choice as long as it really
+captures uh an image that makes sense I
+
+ align:start position:0%
+captures uh an image that makes sense I
+ 
+
+ align:start position:0%
+captures uh an image that makes sense I
+actually love it when I get a piece of
+
+ align:start position:0%
+actually love it when I get a piece of
+ 
+
+ align:start position:0%
+actually love it when I get a piece of
+music that says something incredibly
+
+ align:start position:0%
+music that says something incredibly
+ 
+
+ align:start position:0%
+music that says something incredibly
+specific and and weird it's like oh as
+
+ align:start position:0%
+specific and and weird it's like oh as
+ 
+
+ align:start position:0%
+specific and and weird it's like oh as
+though with a limp like oh okay well I
+
+ align:start position:0%
+though with a limp like oh okay well I
+ 
+
+ align:start position:0%
+though with a limp like oh okay well I
+all right I'll go for it yeah but that
+
+ align:start position:0%
+all right I'll go for it yeah but that
+ 
+
+ align:start position:0%
+all right I'll go for it yeah but that
+gives that really gives you something to
+
+ align:start position:0%
+gives that really gives you something to
+ 
+
+ align:start position:0%
+gives that really gives you something to
+work with that's the thing if you know
+
+ align:start position:0%
+work with that's the thing if you know
+ 
+
+ align:start position:0%
+work with that's the thing if you know
+that the composer had that in mind then
+
+ align:start position:0%
+that the composer had that in mind then
+ 
+
+ align:start position:0%
+that the composer had that in mind then
+you're like oh I look at the entire
+
+ align:start position:0%
+you're like oh I look at the entire
+ 
+
+ align:start position:0%
+you're like oh I look at the entire
+thing differently so if you had written
+
+ align:start position:0%
+thing differently so if you had written
+ 
+
+ align:start position:0%
+thing differently so if you had written
+it like lugubrious like a mournful
+
+ align:start position:0%
+it like lugubrious like a mournful
+ 
+
+ align:start position:0%
+it like lugubrious like a mournful
+Cabaret tune that would completely
+
+ align:start position:0%
+Cabaret tune that would completely
+ 
+
+ align:start position:0%
+Cabaret tune that would completely
+change the way I interpret the poem or
+
+ align:start position:0%
+change the way I interpret the poem or
+ 
+
+ align:start position:0%
+change the way I interpret the poem or
+if you did you know uh spritely with
+
+ align:start position:0%
+if you did you know uh spritely with
+ 
+
+ align:start position:0%
+if you did you know uh spritely with
+fire or uh in the style of a tador song
+
+ align:start position:0%
+fire or uh in the style of a tador song
+ 
+
+ align:start position:0%
+fire or uh in the style of a tador song
+or something like that that also would
+
+ align:start position:0%
+or something like that that also would
+ 
+
+ align:start position:0%
+or something like that that also would
+work but whatever it is you it's it's
+
+ align:start position:0%
+work but whatever it is you it's it's
+ 
+
+ align:start position:0%
+work but whatever it is you it's it's
+very helpful upfront to give us that
+
+ align:start position:0%
+very helpful upfront to give us that
+ 
+
+ align:start position:0%
+very helpful upfront to give us that
+feeling
+
+ align:start position:0%
+feeling
+ 
+
+ align:start position:0%
+feeling
+um I'm going to make two a couple of
+
+ align:start position:0%
+um I'm going to make two a couple of
+ 
+
+ align:start position:0%
+um I'm going to make two a couple of
+suggestions uh and forgive me for having
+
+ align:start position:0%
+suggestions uh and forgive me for having
+ 
+
+ align:start position:0%
+suggestions uh and forgive me for having
+baring without asking you first um you
+
+ align:start position:0%
+baring without asking you first um you
+ 
+
+ align:start position:0%
+baring without asking you first um you
+set the song very well you set the text
+
+ align:start position:0%
+set the song very well you set the text
+ 
+
+ align:start position:0%
+set the song very well you set the text
+very well it go it sort of goes along at
+
+ align:start position:0%
+very well it go it sort of goes along at
+ 
+
+ align:start position:0%
+very well it go it sort of goes along at
+a clip and we get the sense of the
+
+ align:start position:0%
+a clip and we get the sense of the
+ 
+
+ align:start position:0%
+a clip and we get the sense of the
+stropes being there but it's not so fast
+
+ align:start position:0%
+stropes being there but it's not so fast
+ 
+
+ align:start position:0%
+stropes being there but it's not so fast
+that the text is unintelligible I'm
+
+ align:start position:0%
+that the text is unintelligible I'm
+ 
+
+ align:start position:0%
+that the text is unintelligible I'm
+going to suggest that just to keep a
+
+ align:start position:0%
+going to suggest that just to keep a
+ 
+
+ align:start position:0%
+going to suggest that just to keep a
+little spicier a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sparkierdust through um so it's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+always how about or just as a matter a
+
+ align:start position:0%
+always how about or just as a matter a
+ 
+
+ align:start position:0%
+always how about or just as a matter a
+point of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depart there's all kinds of little ways
+
+ align:start position:0%
+depart there's all kinds of little ways
+ 
+
+ align:start position:0%
+depart there's all kinds of little ways
+you can remain true to your s sense of
+
+ align:start position:0%
+you can remain true to your s sense of
+ 
+
+ align:start position:0%
+you can remain true to your s sense of
+how the melody needs to go if you're
+
+ align:start position:0%
+how the melody needs to go if you're
+ 
+
+ align:start position:0%
+how the melody needs to go if you're
+going to use a quick Rhythm like that
+
+ align:start position:0%
+going to use a quick Rhythm like that
+ 
+
+ align:start position:0%
+going to use a quick Rhythm like that
+though especially at a quick Tempo make
+
+ align:start position:0%
+though especially at a quick Tempo make
+ 
+
+ align:start position:0%
+though especially at a quick Tempo make
+sure that the word that you're uh
+
+ align:start position:0%
+sure that the word that you're uh
+ 
+
+ align:start position:0%
+sure that the word that you're uh
+relegating to the shortest of the notes
+
+ align:start position:0%
+relegating to the shortest of the notes
+ 
+
+ align:start position:0%
+relegating to the shortest of the notes
+is not a big crispy one with tons of
+
+ align:start position:0%
+is not a big crispy one with tons of
+ 
+
+ align:start position:0%
+is not a big crispy one with tons of
+weird consonant in it um better to put
+
+ align:start position:0%
+weird consonant in it um better to put
+ 
+
+ align:start position:0%
+weird consonant in it um better to put
+them on words we would naturally skip
+
+ align:start position:0%
+them on words we would naturally skip
+ 
+
+ align:start position:0%
+them on words we would naturally skip
+over a little bit when speaking the poem
+
+ align:start position:0%
+over a little bit when speaking the poem
+ 
+
+ align:start position:0%
+over a little bit when speaking the poem
+um conjunctions
+
+ align:start position:0%
+um conjunctions
+ 
+
+ align:start position:0%
+um conjunctions
+articles
+
+ align:start position:0%
+articles
+ 
+
+ align:start position:0%
+articles
+um nothing don't relegate anything to a
+
+ align:start position:0%
+um nothing don't relegate anything to a
+ 
+
+ align:start position:0%
+um nothing don't relegate anything to a
+short unaccented beat that is of vital
+
+ align:start position:0%
+short unaccented beat that is of vital
+ 
+
+ align:start position:0%
+short unaccented beat that is of vital
+importance to our understanding of the
+
+ align:start position:0%
+importance to our understanding of the
+ 
+
+ align:start position:0%
+importance to our understanding of the
+text um I would also suggest that you
+
+ align:start position:0%
+text um I would also suggest that you
+ 
+
+ align:start position:0%
+text um I would also suggest that you
+mix up the I'm I'm stepping into your
+
+ align:start position:0%
+mix up the I'm I'm stepping into your
+ 
+
+ align:start position:0%
+mix up the I'm I'm stepping into your
+realm here for a second but um mix it up
+
+ align:start position:0%
+realm here for a second but um mix it up
+ 
+
+ align:start position:0%
+realm here for a second but um mix it up
+a little bit more with the piano
+
+ align:start position:0%
+a little bit more with the piano
+ 
+
+ align:start position:0%
+a little bit more with the piano
+accompaniment you've got you've got a
+
+ align:start position:0%
+accompaniment you've got you've got a
+ 
+
+ align:start position:0%
+accompaniment you've got you've got a
+very specific uh rhythmic and harmonic
+
+ align:start position:0%
+very specific uh rhythmic and harmonic
+ 
+
+ align:start position:0%
+very specific uh rhythmic and harmonic
+language it's a very clear style that
+
+ align:start position:0%
+language it's a very clear style that
+ 
+
+ align:start position:0%
+language it's a very clear style that
+you establish in the first verse but
+
+ align:start position:0%
+you establish in the first verse but
+ 
+
+ align:start position:0%
+you establish in the first verse but
+there are all kinds of variance within
+
+ align:start position:0%
+there are all kinds of variance within
+ 
+
+ align:start position:0%
+there are all kinds of variance within
+that sort of vaguely Spanish sort of
+
+ align:start position:0%
+that sort of vaguely Spanish sort of
+ 
+
+ align:start position:0%
+that sort of vaguely Spanish sort of
+Latin St style of writing um maybe
+
+ align:start position:0%
+Latin St style of writing um maybe
+ 
+
+ align:start position:0%
+Latin St style of writing um maybe
+instead of doing always uh just straight
+
+ align:start position:0%
+instead of doing always uh just straight
+ 
+
+ align:start position:0%
+instead of doing always uh just straight
+up cordal writing in the right hand have
+
+ align:start position:0%
+up cordal writing in the right hand have
+ 
+
+ align:start position:0%
+up cordal writing in the right hand have
+one verse where they're sort of strum
+
+ align:start position:0%
+one verse where they're sort of strum
+ 
+
+ align:start position:0%
+one verse where they're sort of strum
+like a like a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guitar
+
+ align:start position:0%
+guitar
+ 
+
+ align:start position:0%
+guitar
+or maybe have sustained cords in the
+
+ align:start position:0%
+or maybe have sustained cords in the
+ 
+
+ align:start position:0%
+or maybe have sustained cords in the
+right hand and and do something melodic
+
+ align:start position:0%
+right hand and and do something melodic
+ 
+
+ align:start position:0%
+right hand and and do something melodic
+with the left hand but it gives when
+
+ align:start position:0%
+with the left hand but it gives when
+ 
+
+ align:start position:0%
+with the left hand but it gives when
+you're writing strophic pieces I mean
+
+ align:start position:0%
+you're writing strophic pieces I mean
+ 
+
+ align:start position:0%
+you're writing strophic pieces I mean
+we've all heard Schubert songs that have
+
+ align:start position:0%
+we've all heard Schubert songs that have
+ 
+
+ align:start position:0%
+we've all heard Schubert songs that have
+like 27 verses and there is nothing
+
+ align:start position:0%
+like 27 verses and there is nothing
+ 
+
+ align:start position:0%
+like 27 verses and there is nothing
+literally written differently about any
+
+ align:start position:0%
+literally written differently about any
+ 
+
+ align:start position:0%
+literally written differently about any
+one of them and it sort of begs the
+
+ align:start position:0%
+one of them and it sort of begs the
+ 
+
+ align:start position:0%
+one of them and it sort of begs the
+question was this trip really necessary
+
+ align:start position:0%
+question was this trip really necessary
+ 
+
+ align:start position:0%
+question was this trip really necessary
+um I think that that is certainly a
+
+ align:start position:0%
+um I think that that is certainly a
+ 
+
+ align:start position:0%
+um I think that that is certainly a
+valid choice and I uphold Shubert in any
+
+ align:start position:0%
+valid choice and I uphold Shubert in any
+ 
+
+ align:start position:0%
+valid choice and I uphold Shubert in any
+way I humanly can but I think if you are
+
+ align:start position:0%
+way I humanly can but I think if you are
+ 
+
+ align:start position:0%
+way I humanly can but I think if you are
+writing stopic
+
+ align:start position:0%
+writing stopic
+ 
+
+ align:start position:0%
+writing stopic
+pieces no no poem I can think of is
+
+ align:start position:0%
+pieces no no poem I can think of is
+ 
+
+ align:start position:0%
+pieces no no poem I can think of is
+meant to be
+
+ align:start position:0%
+meant to be
+ 
+
+ align:start position:0%
+meant to be
+delivered how am I trying to say this
+
+ align:start position:0%
+delivered how am I trying to say this
+ 
+
+ align:start position:0%
+delivered how am I trying to say this
+each stanza of any poem demands
+
+ align:start position:0%
+each stanza of any poem demands
+ 
+
+ align:start position:0%
+each stanza of any poem demands
+something different regardless of the
+
+ align:start position:0%
+something different regardless of the
+ 
+
+ align:start position:0%
+something different regardless of the
+subject matter and I think that should
+
+ align:start position:0%
+subject matter and I think that should
+ 
+
+ align:start position:0%
+subject matter and I think that should
+uh have utterance in and and the the
+
+ align:start position:0%
+uh have utterance in and and the the
+ 
+
+ align:start position:0%
+uh have utterance in and and the the
+musical choices you make as well um
+
+ align:start position:0%
+musical choices you make as well um
+ 
+
+ align:start position:0%
+musical choices you make as well um
+Danel you want to say something yeah
+
+ align:start position:0%
+Danel you want to say something yeah
+ 
+
+ align:start position:0%
+Danel you want to say something yeah
+just quickly first of all Dynamics would
+
+ align:start position:0%
+just quickly first of all Dynamics would
+ 
+
+ align:start position:0%
+just quickly first of all Dynamics would
+help um we were it was kind of fun
+
+ align:start position:0%
+help um we were it was kind of fun
+ 
+
+ align:start position:0%
+help um we were it was kind of fun
+actually to make them up on our own uh
+
+ align:start position:0%
+actually to make them up on our own uh
+ 
+
+ align:start position:0%
+actually to make them up on our own uh
+and you gave us that Liberty but it can
+
+ align:start position:0%
+and you gave us that Liberty but it can
+ 
+
+ align:start position:0%
+and you gave us that Liberty but it can
+be unsettling to
+
+ align:start position:0%
+be unsettling to
+ 
+
+ align:start position:0%
+be unsettling to
+performers uh to have to do that uh
+
+ align:start position:0%
+performers uh to have to do that uh
+ 
+
+ align:start position:0%
+performers uh to have to do that uh
+again we want to know what's going on in
+
+ align:start position:0%
+again we want to know what's going on in
+ 
+
+ align:start position:0%
+again we want to know what's going on in
+your head and everything you can write
+
+ align:start position:0%
+your head and everything you can write
+ 
+
+ align:start position:0%
+your head and everything you can write
+helps us do that in the same vein I
+
+ align:start position:0%
+helps us do that in the same vein I
+ 
+
+ align:start position:0%
+helps us do that in the same vein I
+think you could show me better the
+
+ align:start position:0%
+think you could show me better the
+ 
+
+ align:start position:0%
+think you could show me better the
+relationship of these notes in the piano
+
+ align:start position:0%
+relationship of these notes in the piano
+ 
+
+ align:start position:0%
+relationship of these notes in the piano
+part and I took some Liberties in doing
+
+ align:start position:0%
+part and I took some Liberties in doing
+ 
+
+ align:start position:0%
+part and I took some Liberties in doing
+a little slur
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+staccato but I could I could have played
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it you know so I think it's your choice
+
+ align:start position:0%
+it you know so I think it's your choice
+ 
+
+ align:start position:0%
+it you know so I think it's your choice
+to make and there are infinite
+
+ align:start position:0%
+to make and there are infinite
+ 
+
+ align:start position:0%
+to make and there are infinite
+possibilities but some slur staccato
+
+ align:start position:0%
+possibilities but some slur staccato
+ 
+
+ align:start position:0%
+possibilities but some slur staccato
+combination that tells me the gesture
+
+ align:start position:0%
+combination that tells me the gesture
+ 
+
+ align:start position:0%
+combination that tells me the gesture
+you're going for and then the only other
+
+ align:start position:0%
+you're going for and then the only other
+ 
+
+ align:start position:0%
+you're going for and then the only other
+thing I wanted to add besides um
+
+ align:start position:0%
+thing I wanted to add besides um
+ 
+
+ align:start position:0%
+thing I wanted to add besides um
+encouraging you to elaborate as the
+
+ align:start position:0%
+encouraging you to elaborate as the
+ 
+
+ align:start position:0%
+encouraging you to elaborate as the
+stropes as we get through uh different
+
+ align:start position:0%
+stropes as we get through uh different
+ 
+
+ align:start position:0%
+stropes as we get through uh different
+verses um be careful sometimes you only
+
+ align:start position:0%
+verses um be careful sometimes you only
+ 
+
+ align:start position:0%
+verses um be careful sometimes you only
+use one eighth note in the right hand so
+
+ align:start position:0%
+use one eighth note in the right hand so
+ 
+
+ align:start position:0%
+use one eighth note in the right hand so
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go and sometimes it's used like in in in
+
+ align:start position:0%
+go and sometimes it's used like in in in
+ 
+
+ align:start position:0%
+go and sometimes it's used like in in in
+that case it makes sense to me because
+
+ align:start position:0%
+that case it makes sense to me because
+ 
+
+ align:start position:0%
+that case it makes sense to me because
+that little we expect two eighth notes
+
+ align:start position:0%
+that little we expect two eighth notes
+ 
+
+ align:start position:0%
+that little we expect two eighth notes
+and we only get one it kind of sets us
+
+ align:start position:0%
+and we only get one it kind of sets us
+ 
+
+ align:start position:0%
+and we only get one it kind of sets us
+up for that Cadence there but at other
+
+ align:start position:0%
+up for that Cadence there but at other
+ 
+
+ align:start position:0%
+up for that Cadence there but at other
+times in the
+
+ align:start position:0%
+times in the
+ 
+
+ align:start position:0%
+times in the
+piece I was caught off guard when I only
+
+ align:start position:0%
+piece I was caught off guard when I only
+ 
+
+ align:start position:0%
+piece I was caught off guard when I only
+got 1 eigh note and I didn't feel like
+
+ align:start position:0%
+got 1 eigh note and I didn't feel like
+ 
+
+ align:start position:0%
+got 1 eigh note and I didn't feel like
+it was actually serving a specific
+
+ align:start position:0%
+it was actually serving a specific
+ 
+
+ align:start position:0%
+it was actually serving a specific
+purpose um so I just say if you if you
+
+ align:start position:0%
+purpose um so I just say if you if you
+ 
+
+ align:start position:0%
+purpose um so I just say if you if you
+change the Rhythm in in that way by only
+
+ align:start position:0%
+change the Rhythm in in that way by only
+ 
+
+ align:start position:0%
+change the Rhythm in in that way by only
+using 1/8 note it is a it's a bold
+
+ align:start position:0%
+using 1/8 note it is a it's a bold
+ 
+
+ align:start position:0%
+using 1/8 note it is a it's a bold
+choice and it should have some kind of
+
+ align:start position:0%
+choice and it should have some kind of
+ 
+
+ align:start position:0%
+choice and it should have some kind of
+meaning meaning behind it otherwise it
+
+ align:start position:0%
+meaning meaning behind it otherwise it
+ 
+
+ align:start position:0%
+meaning meaning behind it otherwise it
+might just throw throw off the eye to
+
+ align:start position:0%
+might just throw throw off the eye to
+ 
+
+ align:start position:0%
+might just throw throw off the eye to
+not see those two notes when we're when
+
+ align:start position:0%
+not see those two notes when we're when
+ 
+
+ align:start position:0%
+not see those two notes when we're when
+we're used to it yeah if you're going to
+
+ align:start position:0%
+we're used to it yeah if you're going to
+ 
+
+ align:start position:0%
+we're used to it yeah if you're going to
+do something to switch up the texture
+
+ align:start position:0%
+do something to switch up the texture
+ 
+
+ align:start position:0%
+do something to switch up the texture
+really underline it for us um with
+
+ align:start position:0%
+really underline it for us um with
+ 
+
+ align:start position:0%
+really underline it for us um with
+markings or or by repetition or sort of
+
+ align:start position:0%
+markings or or by repetition or sort of
+ 
+
+ align:start position:0%
+markings or or by repetition or sort of
+symmetrical use of the same rhythmic
+
+ align:start position:0%
+symmetrical use of the same rhythmic
+ 
+
+ align:start position:0%
+symmetrical use of the same rhythmic
+gesture elsewhere in the
+
+ align:start position:0%
+gesture elsewhere in the
+ 
+
+ align:start position:0%
+gesture elsewhere in the
+piece um sorry I'm sorry we have to go
+
+ align:start position:0%
+piece um sorry I'm sorry we have to go
+ 
+
+ align:start position:0%
+piece um sorry I'm sorry we have to go
+off I'm sorry yeah I one more suggestion
+
+ align:start position:0%
+off I'm sorry yeah I one more suggestion
+ 
+
+ align:start position:0%
+off I'm sorry yeah I one more suggestion
+be said one
+
+ align:start position:0%
+be said one
+ 
+
+ align:start position:0%
+be said one
+octaves in the left hand at least for
+
+ align:start position:0%
+octaves in the left hand at least for
+ 
+
+ align:start position:0%
+octaves in the left hand at least for
+part of it or maybe switch the entire
+
+ align:start position:0%
+part of it or maybe switch the entire
+ 
+
+ align:start position:0%
+part of it or maybe switch the entire
+accompaniment at for one verse into a
+
+ align:start position:0%
+accompaniment at for one verse into a
+ 
+
+ align:start position:0%
+accompaniment at for one verse into a
+different octave but fatten it up give
+
+ align:start position:0%
+different octave but fatten it up give
+ 
+
+ align:start position:0%
+different octave but fatten it up give
+us a little something a little more of a
+
+ align:start position:0%
+us a little something a little more of a
+ 
+
+ align:start position:0%
+us a little something a little more of a
+cushion to sit on um at least for part
+
+ align:start position:0%
+cushion to sit on um at least for part
+ 
+
+ align:start position:0%
+cushion to sit on um at least for part
+of it I think it'll I think the filling
+
+ align:start position:0%
+of it I think it'll I think the filling
+ 
+
+ align:start position:0%
+of it I think it'll I think the filling
+out of it will sort of lend a little bit
+
+ align:start position:0%
+out of it will sort of lend a little bit
+ 
+
+ align:start position:0%
+out of it will sort of lend a little bit
+more sweep uh to it a sweep that is
+
+ align:start position:0%
+more sweep uh to it a sweep that is
+ 
+
+ align:start position:0%
+more sweep uh to it a sweep that is
+already implied by your Melody it's a
+
+ align:start position:0%
+already implied by your Melody it's a
+ 
+
+ align:start position:0%
+already implied by your Melody it's a
+beautiful piece well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done
\ No newline at end of file
diff --git a/CbDsSQEvEkA.txt b/CbDsSQEvEkA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c13a85ec871684635b9c88f435c698234ff6afd1
--- /dev/null
+++ b/CbDsSQEvEkA.txt
@@ -0,0 +1,1475 @@
+align:start position:0%
+ 
+so hi I'm Alyssa thread by day I run the
+
+ align:start position:0%
+so hi I'm Alyssa thread by day I run the
+ 
+
+ align:start position:0%
+so hi I'm Alyssa thread by day I run the
+MIT k12 videos program in the office of
+
+ align:start position:0%
+MIT k12 videos program in the office of
+ 
+
+ align:start position:0%
+MIT k12 videos program in the office of
+digital learning at MIT and I was the
+
+ align:start position:0%
+digital learning at MIT and I was the
+ 
+
+ align:start position:0%
+digital learning at MIT and I was the
+lead instructor / creator for 22 19 hi
+
+ align:start position:0%
+lead instructor / creator for 22 19 hi
+ 
+
+ align:start position:0%
+lead instructor / creator for 22 19 hi
+I'm Joshua gun and I'm the founder co
+
+ align:start position:0%
+I'm Joshua gun and I'm the founder co
+ 
+
+ align:start position:0%
+I'm Joshua gun and I'm the founder co
+founder of Planet nutshell a cambridge
+
+ align:start position:0%
+founder of Planet nutshell a cambridge
+ 
+
+ align:start position:0%
+founder of Planet nutshell a cambridge
+massachusetts-based animation studio and
+
+ align:start position:0%
+massachusetts-based animation studio and
+ 
+
+ align:start position:0%
+massachusetts-based animation studio and
+my role in the course was simply to do a
+
+ align:start position:0%
+my role in the course was simply to do a
+ 
+
+ align:start position:0%
+my role in the course was simply to do a
+workshop on storyboarding as well as a
+
+ align:start position:0%
+workshop on storyboarding as well as a
+ 
+
+ align:start position:0%
+workshop on storyboarding as well as a
+little instruction on animation in the
+
+ align:start position:0%
+little instruction on animation in the
+ 
+
+ align:start position:0%
+little instruction on animation in the
+context of producing educational media
+
+ align:start position:0%
+context of producing educational media
+ 
+
+ align:start position:0%
+context of producing educational media
+my name is George Zaidan I am a
+
+ align:start position:0%
+my name is George Zaidan I am a
+ 
+
+ align:start position:0%
+my name is George Zaidan I am a
+freelance science video host and writer
+
+ align:start position:0%
+freelance science video host and writer
+ 
+
+ align:start position:0%
+freelance science video host and writer
+and producer and for 22 19 I did a
+
+ align:start position:0%
+and producer and for 22 19 I did a
+ 
+
+ align:start position:0%
+and producer and for 22 19 I did a
+workshop on writing and hosting I'm
+
+ align:start position:0%
+workshop on writing and hosting I'm
+ 
+
+ align:start position:0%
+workshop on writing and hosting I'm
+Chris Babel I'm mediate development
+
+ align:start position:0%
+Chris Babel I'm mediate development
+ 
+
+ align:start position:0%
+Chris Babel I'm mediate development
+director for MIT s office of digital
+
+ align:start position:0%
+director for MIT s office of digital
+ 
+
+ align:start position:0%
+director for MIT s office of digital
+learning and for the course site was
+
+ align:start position:0%
+learning and for the course site was
+ 
+
+ align:start position:0%
+learning and for the course site was
+basically a guest lecturer I came in for
+
+ align:start position:0%
+basically a guest lecturer I came in for
+ 
+
+ align:start position:0%
+basically a guest lecturer I came in for
+a day or two to talk about visual
+
+ align:start position:0%
+a day or two to talk about visual
+ 
+
+ align:start position:0%
+a day or two to talk about visual
+storytelling so the way this class
+
+ align:start position:0%
+storytelling so the way this class
+ 
+
+ align:start position:0%
+storytelling so the way this class
+started I would say is George and I were
+
+ align:start position:0%
+started I would say is George and I were
+ 
+
+ align:start position:0%
+started I would say is George and I were
+working on science out loud which is
+
+ align:start position:0%
+working on science out loud which is
+ 
+
+ align:start position:0%
+working on science out loud which is
+this educational web series that's
+
+ align:start position:0%
+this educational web series that's
+ 
+
+ align:start position:0%
+this educational web series that's
+hosted by MIT students and sort of
+
+ align:start position:0%
+hosted by MIT students and sort of
+ 
+
+ align:start position:0%
+hosted by MIT students and sort of
+noticed that there was this big need to
+
+ align:start position:0%
+noticed that there was this big need to
+ 
+
+ align:start position:0%
+noticed that there was this big need to
+help students not only know how to
+
+ align:start position:0%
+help students not only know how to
+ 
+
+ align:start position:0%
+help students not only know how to
+articulate themselves on camera
+
+ align:start position:0%
+articulate themselves on camera
+ 
+
+ align:start position:0%
+articulate themselves on camera
+articulate well on camera but just
+
+ align:start position:0%
+articulate well on camera but just
+ 
+
+ align:start position:0%
+articulate well on camera but just
+understand digital media in general and
+
+ align:start position:0%
+understand digital media in general and
+ 
+
+ align:start position:0%
+understand digital media in general and
+that's a conversation that Chris and I
+
+ align:start position:0%
+that's a conversation that Chris and I
+ 
+
+ align:start position:0%
+that's a conversation that Chris and I
+have had since since I was your student
+
+ align:start position:0%
+have had since since I was your student
+ 
+
+ align:start position:0%
+have had since since I was your student
+that's an undergrad basic thing yeah
+
+ align:start position:0%
+that's an undergrad basic thing yeah
+ 
+
+ align:start position:0%
+that's an undergrad basic thing yeah
+yeah so yeah actually not really but
+
+ align:start position:0%
+yeah so yeah actually not really but
+ 
+
+ align:start position:0%
+yeah so yeah actually not really but
+yeah with science out loud I mean we we
+
+ align:start position:0%
+yeah with science out loud I mean we we
+ 
+
+ align:start position:0%
+yeah with science out loud I mean we we
+would do these like crash courses on
+
+ align:start position:0%
+would do these like crash courses on
+ 
+
+ align:start position:0%
+would do these like crash courses on
+scripting and writing these short videos
+
+ align:start position:0%
+scripting and writing these short videos
+ 
+
+ align:start position:0%
+scripting and writing these short videos
+but at the end of the day like we would
+
+ align:start position:0%
+but at the end of the day like we would
+ 
+
+ align:start position:0%
+but at the end of the day like we would
+still intervene quite a bit to make the
+
+ align:start position:0%
+still intervene quite a bit to make the
+ 
+
+ align:start position:0%
+still intervene quite a bit to make the
+videos good and at the end of the day
+
+ align:start position:0%
+videos good and at the end of the day
+ 
+
+ align:start position:0%
+videos good and at the end of the day
+the priority was making a great video
+
+ align:start position:0%
+the priority was making a great video
+ 
+
+ align:start position:0%
+the priority was making a great video
+and not necessarily on the students
+
+ align:start position:0%
+and not necessarily on the students
+ 
+
+ align:start position:0%
+and not necessarily on the students
+learning experience so I mean this was a
+
+ align:start position:0%
+learning experience so I mean this was a
+ 
+
+ align:start position:0%
+learning experience so I mean this was a
+space for them to develop these skills
+
+ align:start position:0%
+space for them to develop these skills
+ 
+
+ align:start position:0%
+space for them to develop these skills
+sort of lower stakes you know and not
+
+ align:start position:0%
+sort of lower stakes you know and not
+ 
+
+ align:start position:0%
+sort of lower stakes you know and not
+have to worry about creating something
+
+ align:start position:0%
+have to worry about creating something
+ 
+
+ align:start position:0%
+have to worry about creating something
+that was like going to be on a web
+
+ align:start position:0%
+that was like going to be on a web
+ 
+
+ align:start position:0%
+that was like going to be on a web
+series of the
+
+ align:start position:0%
+series of the
+ 
+
+ align:start position:0%
+series of the
+the class was supposed to be lower
+
+ align:start position:0%
+the class was supposed to be lower
+ 
+
+ align:start position:0%
+the class was supposed to be lower
+stakes yeah yeah because we had the
+
+ align:start position:0%
+stakes yeah yeah because we had the
+ 
+
+ align:start position:0%
+stakes yeah yeah because we had the
+science out loud was a lot of pressure
+
+ align:start position:0%
+science out loud was a lot of pressure
+ 
+
+ align:start position:0%
+science out loud was a lot of pressure
+we were shooting long days if they did
+
+ align:start position:0%
+we were shooting long days if they did
+ 
+
+ align:start position:0%
+we were shooting long days if they did
+you know they were didn't I felt like if
+
+ align:start position:0%
+you know they were didn't I felt like if
+ 
+
+ align:start position:0%
+you know they were didn't I felt like if
+they didn't get the take right they were
+
+ align:start position:0%
+they didn't get the take right they were
+ 
+
+ align:start position:0%
+they didn't get the take right they were
+nervous yeah or like if the script just
+
+ align:start position:0%
+nervous yeah or like if the script just
+ 
+
+ align:start position:0%
+nervous yeah or like if the script just
+wasn't good by the time we had to shoot
+
+ align:start position:0%
+wasn't good by the time we had to shoot
+ 
+
+ align:start position:0%
+wasn't good by the time we had to shoot
+like we would just fix it you know yeah
+
+ align:start position:0%
+like we would just fix it you know yeah
+ 
+
+ align:start position:0%
+like we would just fix it you know yeah
+and one of the things you and I have
+
+ align:start position:0%
+and one of the things you and I have
+ 
+
+ align:start position:0%
+and one of the things you and I have
+talked about a ton over the last couple
+
+ align:start position:0%
+talked about a ton over the last couple
+ 
+
+ align:start position:0%
+talked about a ton over the last couple
+of years is that tension between
+
+ align:start position:0%
+of years is that tension between
+ 
+
+ align:start position:0%
+of years is that tension between
+creating a consistently good product and
+
+ align:start position:0%
+creating a consistently good product and
+ 
+
+ align:start position:0%
+creating a consistently good product and
+teaching because if you're in a teaching
+
+ align:start position:0%
+teaching because if you're in a teaching
+ 
+
+ align:start position:0%
+teaching because if you're in a teaching
+environment you know in ever you know
+
+ align:start position:0%
+environment you know in ever you know
+ 
+
+ align:start position:0%
+environment you know in ever you know
+you're going to fail over and over and
+
+ align:start position:0%
+you're going to fail over and over and
+ 
+
+ align:start position:0%
+you're going to fail over and over and
+over again which does not lead to a
+
+ align:start position:0%
+over again which does not lead to a
+ 
+
+ align:start position:0%
+over again which does not lead to a
+particularly you know consistently good
+
+ align:start position:0%
+particularly you know consistently good
+ 
+
+ align:start position:0%
+particularly you know consistently good
+product which is what you're going for
+
+ align:start position:0%
+product which is what you're going for
+ 
+
+ align:start position:0%
+product which is what you're going for
+with science out loud so this class is
+
+ align:start position:0%
+with science out loud so this class is
+ 
+
+ align:start position:0%
+with science out loud so this class is
+kind of a way I think to I find a space
+
+ align:start position:0%
+kind of a way I think to I find a space
+ 
+
+ align:start position:0%
+kind of a way I think to I find a space
+in between where you can actually have
+
+ align:start position:0%
+in between where you can actually have
+ 
+
+ align:start position:0%
+in between where you can actually have
+have a little bit of a chance to
+
+ align:start position:0%
+have a little bit of a chance to
+ 
+
+ align:start position:0%
+have a little bit of a chance to
+experiment and learn by doing and fail
+
+ align:start position:0%
+experiment and learn by doing and fail
+ 
+
+ align:start position:0%
+experiment and learn by doing and fail
+bluntly but also you know not actually
+
+ align:start position:0%
+bluntly but also you know not actually
+ 
+
+ align:start position:0%
+bluntly but also you know not actually
+impact your show which is it needs to be
+
+ align:start position:0%
+impact your show which is it needs to be
+ 
+
+ align:start position:0%
+impact your show which is it needs to be
+consistently good was there any desire
+
+ align:start position:0%
+consistently good was there any desire
+ 
+
+ align:start position:0%
+consistently good was there any desire
+to sort of create an awareness for
+
+ align:start position:0%
+to sort of create an awareness for
+ 
+
+ align:start position:0%
+to sort of create an awareness for
+students of like other sort of creative
+
+ align:start position:0%
+students of like other sort of creative
+ 
+
+ align:start position:0%
+students of like other sort of creative
+opportunities outside of the science and
+
+ align:start position:0%
+opportunities outside of the science and
+ 
+
+ align:start position:0%
+opportunities outside of the science and
+math are their current studies I mean
+
+ align:start position:0%
+math are their current studies I mean
+ 
+
+ align:start position:0%
+math are their current studies I mean
+like I think it's a really interesting
+
+ align:start position:0%
+like I think it's a really interesting
+ 
+
+ align:start position:0%
+like I think it's a really interesting
+way this course is sort of offered to
+
+ align:start position:0%
+way this course is sort of offered to
+ 
+
+ align:start position:0%
+way this course is sort of offered to
+students who are engaged in stuff that's
+
+ align:start position:0%
+students who are engaged in stuff that's
+ 
+
+ align:start position:0%
+students who are engaged in stuff that's
+really quite different yeah I mean it's
+
+ align:start position:0%
+really quite different yeah I mean it's
+ 
+
+ align:start position:0%
+really quite different yeah I mean it's
+interesting because MIT has this
+
+ align:start position:0%
+interesting because MIT has this
+ 
+
+ align:start position:0%
+interesting because MIT has this
+communication requirement it's not
+
+ align:start position:0%
+communication requirement it's not
+ 
+
+ align:start position:0%
+communication requirement it's not
+really taken seriously by students
+
+ align:start position:0%
+really taken seriously by students
+ 
+
+ align:start position:0%
+really taken seriously by students
+because it's it's like I need to take a
+
+ align:start position:0%
+because it's it's like I need to take a
+ 
+
+ align:start position:0%
+because it's it's like I need to take a
+classroom required to write 20 pages of
+
+ align:start position:0%
+classroom required to write 20 pages of
+ 
+
+ align:start position:0%
+classroom required to write 20 pages of
+the paper and you and I were talking
+
+ align:start position:0%
+the paper and you and I were talking
+ 
+
+ align:start position:0%
+the paper and you and I were talking
+about one of the bio engineering
+
+ align:start position:0%
+about one of the bio engineering
+ 
+
+ align:start position:0%
+about one of the bio engineering
+communication fellows and he said
+
+ align:start position:0%
+communication fellows and he said
+ 
+
+ align:start position:0%
+communication fellows and he said
+something like I'm doing this program
+
+ align:start position:0%
+something like I'm doing this program
+ 
+
+ align:start position:0%
+something like I'm doing this program
+because I don't see a difference between
+
+ align:start position:0%
+because I don't see a difference between
+ 
+
+ align:start position:0%
+because I don't see a difference between
+science and science communication which
+
+ align:start position:0%
+science and science communication which
+ 
+
+ align:start position:0%
+science and science communication which
+I really I think like that inadvertently
+
+ align:start position:0%
+I really I think like that inadvertently
+ 
+
+ align:start position:0%
+I really I think like that inadvertently
+was what this class was about because
+
+ align:start position:0%
+was what this class was about because
+ 
+
+ align:start position:0%
+was what this class was about because
+it's not really about like how to host a
+
+ align:start position:0%
+it's not really about like how to host a
+ 
+
+ align:start position:0%
+it's not really about like how to host a
+science show or how to write a five
+
+ align:start position:0%
+science show or how to write a five
+ 
+
+ align:start position:0%
+science show or how to write a five
+minute script like that i don't care if
+
+ align:start position:0%
+minute script like that i don't care if
+ 
+
+ align:start position:0%
+minute script like that i don't care if
+they never make a five minute video
+
+ align:start position:0%
+they never make a five minute video
+ 
+
+ align:start position:0%
+they never make a five minute video
+again but hopefully the skills that they
+
+ align:start position:0%
+again but hopefully the skills that they
+ 
+
+ align:start position:0%
+again but hopefully the skills that they
+learned and picked up were things that
+
+ align:start position:0%
+learned and picked up were things that
+ 
+
+ align:start position:0%
+learned and picked up were things that
+they need to have regardless of what
+
+ align:start position:0%
+they need to have regardless of what
+ 
+
+ align:start position:0%
+they need to have regardless of what
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+going into just the ability to
+
+ align:start position:0%
+going into just the ability to
+ 
+
+ align:start position:0%
+going into just the ability to
+articulate passionately and clearly some
+
+ align:start position:0%
+articulate passionately and clearly some
+ 
+
+ align:start position:0%
+articulate passionately and clearly some
+very technical topics is it not only
+
+ align:start position:0%
+very technical topics is it not only
+ 
+
+ align:start position:0%
+very technical topics is it not only
+that you can get tricky you get trained
+
+ align:start position:0%
+that you can get tricky you get trained
+ 
+
+ align:start position:0%
+that you can get tricky you get trained
+on enough at MIT yeah i think i think
+
+ align:start position:0%
+on enough at MIT yeah i think i think
+ 
+
+ align:start position:0%
+on enough at MIT yeah i think i think
+the MIT communication requirement is an
+
+ align:start position:0%
+the MIT communication requirement is an
+ 
+
+ align:start position:0%
+the MIT communication requirement is an
+interesting situation too because it is
+
+ align:start position:0%
+interesting situation too because it is
+ 
+
+ align:start position:0%
+interesting situation too because it is
+all focused on writing and you know
+
+ align:start position:0%
+all focused on writing and you know
+ 
+
+ align:start position:0%
+all focused on writing and you know
+writing papers not even just writing not
+
+ align:start position:0%
+writing papers not even just writing not
+ 
+
+ align:start position:0%
+writing papers not even just writing not
+even writing like writing scripts
+
+ align:start position:0%
+even writing like writing scripts
+ 
+
+ align:start position:0%
+even writing like writing scripts
+writing papers and for instance the
+
+ align:start position:0%
+writing papers and for instance the
+ 
+
+ align:start position:0%
+writing papers and for instance the
+course that I teach that you took we
+
+ align:start position:0%
+course that I teach that you took we
+ 
+
+ align:start position:0%
+course that I teach that you took we
+initially had trouble getting it listed
+
+ align:start position:0%
+initially had trouble getting it listed
+ 
+
+ align:start position:0%
+initially had trouble getting it listed
+as is fulfilling the communication
+
+ align:start position:0%
+as is fulfilling the communication
+ 
+
+ align:start position:0%
+as is fulfilling the communication
+requirement even though students
+
+ align:start position:0%
+requirement even though students
+ 
+
+ align:start position:0%
+requirement even though students
+consistently said well this is all this
+
+ align:start position:0%
+consistently said well this is all this
+ 
+
+ align:start position:0%
+consistently said well this is all this
+course is about you know communication
+
+ align:start position:0%
+course is about you know communication
+ 
+
+ align:start position:0%
+course is about you know communication
+because the writing requirement was just
+
+ align:start position:0%
+because the writing requirement was just
+ 
+
+ align:start position:0%
+because the writing requirement was just
+a little bit shy of the 20 page or
+
+ align:start position:0%
+a little bit shy of the 20 page or
+ 
+
+ align:start position:0%
+a little bit shy of the 20 page or
+whatever it is a requirement so it's
+
+ align:start position:0%
+whatever it is a requirement so it's
+ 
+
+ align:start position:0%
+whatever it is a requirement so it's
+there's a whole other kind of
+
+ align:start position:0%
+there's a whole other kind of
+ 
+
+ align:start position:0%
+there's a whole other kind of
+communication which is as you say you
+
+ align:start position:0%
+communication which is as you say you
+ 
+
+ align:start position:0%
+communication which is as you say you
+know clear clear conceptualization
+
+ align:start position:0%
+know clear clear conceptualization
+ 
+
+ align:start position:0%
+know clear clear conceptualization
+visualization organization which is
+
+ align:start position:0%
+visualization organization which is
+ 
+
+ align:start position:0%
+visualization organization which is
+related to writing and writing kind of
+
+ align:start position:0%
+related to writing and writing kind of
+ 
+
+ align:start position:0%
+related to writing and writing kind of
+traditional papers but but you know it's
+
+ align:start position:0%
+traditional papers but but you know it's
+ 
+
+ align:start position:0%
+traditional papers but but you know it's
+in 2015 it's not just writing journal
+
+ align:start position:0%
+in 2015 it's not just writing journal
+ 
+
+ align:start position:0%
+in 2015 it's not just writing journal
+papers or kind of really more
+
+ align:start position:0%
+papers or kind of really more
+ 
+
+ align:start position:0%
+papers or kind of really more
+traditional pieces of text actually
+
+ align:start position:0%
+traditional pieces of text actually
+ 
+
+ align:start position:0%
+traditional pieces of text actually
+before I put the class together the
+
+ align:start position:0%
+before I put the class together the
+ 
+
+ align:start position:0%
+before I put the class together the
+first thing I did was just survey all of
+
+ align:start position:0%
+first thing I did was just survey all of
+ 
+
+ align:start position:0%
+first thing I did was just survey all of
+the media making classes on campus so
+
+ align:start position:0%
+the media making classes on campus so
+ 
+
+ align:start position:0%
+the media making classes on campus so
+anything related to video production or
+
+ align:start position:0%
+anything related to video production or
+ 
+
+ align:start position:0%
+anything related to video production or
+like script production and there are
+
+ align:start position:0%
+like script production and there are
+ 
+
+ align:start position:0%
+like script production and there are
+actually a lot of classes on campus that
+
+ align:start position:0%
+actually a lot of classes on campus that
+ 
+
+ align:start position:0%
+actually a lot of classes on campus that
+are about you know how do you edit how
+
+ align:start position:0%
+are about you know how do you edit how
+ 
+
+ align:start position:0%
+are about you know how do you edit how
+do you produce video but there wasn't
+
+ align:start position:0%
+do you produce video but there wasn't
+ 
+
+ align:start position:0%
+do you produce video but there wasn't
+one on really hosting actually and being
+
+ align:start position:0%
+one on really hosting actually and being
+ 
+
+ align:start position:0%
+one on really hosting actually and being
+on camera and being comfortable talking
+
+ align:start position:0%
+on camera and being comfortable talking
+ 
+
+ align:start position:0%
+on camera and being comfortable talking
+in front of people was something that we
+
+ align:start position:0%
+in front of people was something that we
+ 
+
+ align:start position:0%
+in front of people was something that we
+found to be very important through
+
+ align:start position:0%
+found to be very important through
+ 
+
+ align:start position:0%
+found to be very important through
+science out loud and something that
+
+ align:start position:0%
+science out loud and something that
+ 
+
+ align:start position:0%
+science out loud and something that
+students were the most uncomfortable
+
+ align:start position:0%
+students were the most uncomfortable
+ 
+
+ align:start position:0%
+students were the most uncomfortable
+with would you say yeah I mean they were
+
+ align:start position:0%
+with would you say yeah I mean they were
+ 
+
+ align:start position:0%
+with would you say yeah I mean they were
+they didn't even know they were
+
+ align:start position:0%
+they didn't even know they were
+ 
+
+ align:start position:0%
+they didn't even know they were
+uncomfortable with it they would just
+
+ align:start position:0%
+uncomfortable with it they would just
+ 
+
+ align:start position:0%
+uncomfortable with it they would just
+get they'd be like I had no problem I
+
+ align:start position:0%
+get they'd be like I had no problem I
+ 
+
+ align:start position:0%
+get they'd be like I had no problem I
+just I'll just talk and and then get in
+
+ align:start position:0%
+just I'll just talk and and then get in
+ 
+
+ align:start position:0%
+just I'll just talk and and then get in
+front of a camera and it's like Jack
+
+ align:start position:0%
+front of a camera and it's like Jack
+ 
+
+ align:start position:0%
+front of a camera and it's like Jack
+Donaghy in that episode of 30 rock
+
+ align:start position:0%
+Donaghy in that episode of 30 rock
+ 
+
+ align:start position:0%
+Donaghy in that episode of 30 rock
+really like can't really can't you know
+
+ align:start position:0%
+really like can't really can't you know
+ 
+
+ align:start position:0%
+really like can't really can't you know
+you don't understand why your body
+
+ align:start position:0%
+you don't understand why your body
+ 
+
+ align:start position:0%
+you don't understand why your body
+doesn't quite work the way you thought
+
+ align:start position:0%
+doesn't quite work the way you thought
+ 
+
+ align:start position:0%
+doesn't quite work the way you thought
+it was your voice is a little too high
+
+ align:start position:0%
+it was your voice is a little too high
+ 
+
+ align:start position:0%
+it was your voice is a little too high
+and you get nervous and then you'd screw
+
+ align:start position:0%
+and you get nervous and then you'd screw
+ 
+
+ align:start position:0%
+and you get nervous and then you'd screw
+up and then you screw up again and then
+
+ align:start position:0%
+up and then you screw up again and then
+ 
+
+ align:start position:0%
+up and then you screw up again and then
+you know they get and then they then
+
+ align:start position:0%
+you know they get and then they then
+ 
+
+ align:start position:0%
+you know they get and then they then
+they realize how hard it actually is to
+
+ align:start position:0%
+they realize how hard it actually is to
+ 
+
+ align:start position:0%
+they realize how hard it actually is to
+stand in front of a camera and say
+
+ align:start position:0%
+stand in front of a camera and say
+ 
+
+ align:start position:0%
+stand in front of a camera and say
+things so yeah just about standing in
+
+ align:start position:0%
+things so yeah just about standing in
+ 
+
+ align:start position:0%
+things so yeah just about standing in
+front of a camera though like any
+
+ align:start position:0%
+front of a camera though like any
+ 
+
+ align:start position:0%
+front of a camera though like any
+audience ready I feel like it was like I
+
+ align:start position:0%
+audience ready I feel like it was like I
+ 
+
+ align:start position:0%
+audience ready I feel like it was like I
+wanted them to learn how to be self
+
+ align:start position:0%
+wanted them to learn how to be self
+ 
+
+ align:start position:0%
+wanted them to learn how to be self
+aware of who they were as a presenter
+
+ align:start position:0%
+aware of who they were as a presenter
+ 
+
+ align:start position:0%
+aware of who they were as a presenter
+you know because like we weren't trying
+
+ align:start position:0%
+you know because like we weren't trying
+ 
+
+ align:start position:0%
+you know because like we weren't trying
+to make them become a persona like we
+
+ align:start position:0%
+to make them become a persona like we
+ 
+
+ align:start position:0%
+to make them become a persona like we
+called it becoming the next bill nye but
+
+ align:start position:0%
+called it becoming the next bill nye but
+ 
+
+ align:start position:0%
+called it becoming the next bill nye but
+it really wasn't that was like the first
+
+ align:start position:0%
+it really wasn't that was like the first
+ 
+
+ align:start position:0%
+it really wasn't that was like the first
+thing I talked about was that we're not
+
+ align:start position:0%
+thing I talked about was that we're not
+ 
+
+ align:start position:0%
+thing I talked about was that we're not
+actually turning you into Bill Nye that
+
+ align:start position:0%
+actually turning you into Bill Nye that
+ 
+
+ align:start position:0%
+actually turning you into Bill Nye that
+wherever you go whether it's a job
+
+ align:start position:0%
+wherever you go whether it's a job
+ 
+
+ align:start position:0%
+wherever you go whether it's a job
+interview or are you giving a TED talk
+
+ align:start position:0%
+interview or are you giving a TED talk
+ 
+
+ align:start position:0%
+interview or are you giving a TED talk
+or formal presentation I mean you need
+
+ align:start position:0%
+or formal presentation I mean you need
+ 
+
+ align:start position:0%
+or formal presentation I mean you need
+all these skills and you you can't like
+
+ align:start position:0%
+all these skills and you you can't like
+ 
+
+ align:start position:0%
+all these skills and you you can't like
+assume some sort of platonic personality
+
+ align:start position:0%
+assume some sort of platonic personality
+ 
+
+ align:start position:0%
+assume some sort of platonic personality
+you know when you do these things it's
+
+ align:start position:0%
+you know when you do these things it's
+ 
+
+ align:start position:0%
+you know when you do these things it's
+not acting it's just being being
+
+ align:start position:0%
+not acting it's just being being
+ 
+
+ align:start position:0%
+not acting it's just being being
+yourself themselves yeah mm-hmm but just
+
+ align:start position:0%
+yourself themselves yeah mm-hmm but just
+ 
+
+ align:start position:0%
+yourself themselves yeah mm-hmm but just
+a clear polish oh yeah kind of close to
+
+ align:start position:0%
+a clear polish oh yeah kind of close to
+ 
+
+ align:start position:0%
+a clear polish oh yeah kind of close to
+what the real thing is but maybe not
+
+ align:start position:0%
+what the real thing is but maybe not
+ 
+
+ align:start position:0%
+what the real thing is but maybe not
+entirely there where it is yeah
\ No newline at end of file
diff --git a/CdhuVhWTSMI.txt b/CdhuVhWTSMI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..53af916cf18fc2c750b578010b60d8f579527827
--- /dev/null
+++ b/CdhuVhWTSMI.txt
@@ -0,0 +1,1435 @@
+align:start position:0%
+ 
+so now we'll look at a third kind of sum
+
+ align:start position:0%
+so now we'll look at a third kind of sum
+ 
+
+ align:start position:0%
+so now we'll look at a third kind of sum
+that comes up all the time called
+
+ align:start position:0%
+that comes up all the time called
+ 
+
+ align:start position:0%
+that comes up all the time called
+harmonic sums and we'll Begin by
+
+ align:start position:0%
+harmonic sums and we'll Begin by
+ 
+
+ align:start position:0%
+harmonic sums and we'll Begin by
+examining an example where they come up
+
+ align:start position:0%
+examining an example where they come up
+ 
+
+ align:start position:0%
+examining an example where they come up
+really directly so here's the puzzle
+
+ align:start position:0%
+really directly so here's the puzzle
+ 
+
+ align:start position:0%
+really directly so here's the puzzle
+suppose that I'm trying to stack a bunch
+
+ align:start position:0%
+suppose that I'm trying to stack a bunch
+ 
+
+ align:start position:0%
+suppose that I'm trying to stack a bunch
+of books on a table assume all the books
+
+ align:start position:0%
+of books on a table assume all the books
+ 
+
+ align:start position:0%
+of books on a table assume all the books
+are the same size and weight and uniform
+
+ align:start position:0%
+are the same size and weight and uniform
+ 
+
+ align:start position:0%
+are the same size and weight and uniform
+and I'd like to stack them up one on top
+
+ align:start position:0%
+and I'd like to stack them up one on top
+ 
+
+ align:start position:0%
+and I'd like to stack them up one on top
+of the other in some way and try to get
+
+ align:start position:0%
+of the other in some way and try to get
+ 
+
+ align:start position:0%
+of the other in some way and try to get
+them as far out past the end of the
+
+ align:start position:0%
+them as far out past the end of the
+ 
+
+ align:start position:0%
+them as far out past the end of the
+table as I can manage now notice in this
+
+ align:start position:0%
+table as I can manage now notice in this
+ 
+
+ align:start position:0%
+table as I can manage now notice in this
+picture it seems kind of paradoxical the
+
+ align:start position:0%
+picture it seems kind of paradoxical the
+ 
+
+ align:start position:0%
+picture it seems kind of paradoxical the
+top book The the back end of the top
+
+ align:start position:0%
+top book The the back end of the top
+ 
+
+ align:start position:0%
+top book The the back end of the top
+book is past the edge of the table is it
+
+ align:start position:0%
+book is past the edge of the table is it
+ 
+
+ align:start position:0%
+book is past the edge of the table is it
+possible to do that is it possible to
+
+ align:start position:0%
+possible to do that is it possible to
+ 
+
+ align:start position:0%
+possible to do that is it possible to
+get the top book The the back of the top
+
+ align:start position:0%
+get the top book The the back of the top
+ 
+
+ align:start position:0%
+get the top book The the back of the top
+book past the edge of the table and how
+
+ align:start position:0%
+book past the edge of the table and how
+ 
+
+ align:start position:0%
+book past the edge of the table and how
+far out can you get the furthermost book
+
+ align:start position:0%
+far out can you get the furthermost book
+ 
+
+ align:start position:0%
+far out can you get the furthermost book
+to the right that's the question we want
+
+ align:start position:0%
+to the right that's the question we want
+ 
+
+ align:start position:0%
+to the right that's the question we want
+to ask well let's go back and uh do it
+
+ align:start position:0%
+to ask well let's go back and uh do it
+ 
+
+ align:start position:0%
+to ask well let's go back and uh do it
+for the simplest case which is one book
+
+ align:start position:0%
+for the simplest case which is one book
+ 
+
+ align:start position:0%
+for the simplest case which is one book
+so this amount will be a function of how
+
+ align:start position:0%
+so this amount will be a function of how
+ 
+
+ align:start position:0%
+so this amount will be a function of how
+many books we have we're interested in
+
+ align:start position:0%
+many books we have we're interested in
+ 
+
+ align:start position:0%
+many books we have we're interested in
+the overhang using n books overhang is
+
+ align:start position:0%
+the overhang using n books overhang is
+ 
+
+ align:start position:0%
+the overhang using n books overhang is
+the amount past the edge of the table
+
+ align:start position:0%
+the amount past the edge of the table
+ 
+
+ align:start position:0%
+the amount past the edge of the table
+that the rightmost um end of any book
+
+ align:start position:0%
+that the rightmost um end of any book
+ 
+
+ align:start position:0%
+that the rightmost um end of any book
+can be okay what do you do with one book
+
+ align:start position:0%
+can be okay what do you do with one book
+ 
+
+ align:start position:0%
+can be okay what do you do with one book
+well with one book assuming that the
+
+ align:start position:0%
+well with one book assuming that the
+ 
+
+ align:start position:0%
+well with one book assuming that the
+thing is uniform the center of mass is
+
+ align:start position:0%
+thing is uniform the center of mass is
+ 
+
+ align:start position:0%
+thing is uniform the center of mass is
+in the middle let's assume the book is
+
+ align:start position:0%
+in the middle let's assume the book is
+ 
+
+ align:start position:0%
+in the middle let's assume the book is
+of length one um so the center of mass
+
+ align:start position:0%
+of length one um so the center of mass
+ 
+
+ align:start position:0%
+of length one um so the center of mass
+of the book is at halfway down the book
+
+ align:start position:0%
+of the book is at halfway down the book
+ 
+
+ align:start position:0%
+of the book is at halfway down the book
+and if that Center of mass is not over
+
+ align:start position:0%
+and if that Center of mass is not over
+ 
+
+ align:start position:0%
+and if that Center of mass is not over
+the table then you're going to have
+
+ align:start position:0%
+the table then you're going to have
+ 
+
+ align:start position:0%
+the table then you're going to have
+torque and the book is going to fall
+
+ align:start position:0%
+torque and the book is going to fall
+ 
+
+ align:start position:0%
+torque and the book is going to fall
+so you got to keep the center of mass
+
+ align:start position:0%
+so you got to keep the center of mass
+ 
+
+ align:start position:0%
+so you got to keep the center of mass
+supported and the way to get the largest
+
+ align:start position:0%
+supported and the way to get the largest
+ 
+
+ align:start position:0%
+supported and the way to get the largest
+overhang is to have the center of mass
+
+ align:start position:0%
+overhang is to have the center of mass
+ 
+
+ align:start position:0%
+overhang is to have the center of mass
+right at the edge of the table here and
+
+ align:start position:0%
+right at the edge of the table here and
+ 
+
+ align:start position:0%
+right at the edge of the table here and
+in that case you can get the book to
+
+ align:start position:0%
+in that case you can get the book to
+ 
+
+ align:start position:0%
+in that case you can get the book to
+stick out half a book length without
+
+ align:start position:0%
+stick out half a book length without
+ 
+
+ align:start position:0%
+stick out half a book length without
+falling and what that tells us is that
+
+ align:start position:0%
+falling and what that tells us is that
+ 
+
+ align:start position:0%
+falling and what that tells us is that
+the one book overhang is a half it'll
+
+ align:start position:0%
+the one book overhang is a half it'll
+ 
+
+ align:start position:0%
+the one book overhang is a half it'll
+balance uh with the furthest uh end out
+
+ align:start position:0%
+balance uh with the furthest uh end out
+ 
+
+ align:start position:0%
+balance uh with the furthest uh end out
+exactly if the center of mass is on the
+
+ align:start position:0%
+exactly if the center of mass is on the
+ 
+
+ align:start position:0%
+exactly if the center of mass is on the
+edge and I get a half a book length for
+
+ align:start position:0%
+edge and I get a half a book length for
+ 
+
+ align:start position:0%
+edge and I get a half a book length for
+unit overhang all right let's proceed
+
+ align:start position:0%
+unit overhang all right let's proceed
+ 
+
+ align:start position:0%
+unit overhang all right let's proceed
+recursively or inductively suppose I
+
+ align:start position:0%
+recursively or inductively suppose I
+ 
+
+ align:start position:0%
+recursively or inductively suppose I
+have n books how am I going to get them
+
+ align:start position:0%
+have n books how am I going to get them
+ 
+
+ align:start position:0%
+have n books how am I going to get them
+to balance well let's assume that I
+
+ align:start position:0%
+to balance well let's assume that I
+ 
+
+ align:start position:0%
+to balance well let's assume that I
+figured out how to get a so-called
+
+ align:start position:0%
+figured out how to get a so-called
+ 
+
+ align:start position:0%
+figured out how to get a so-called
+stable stack of end books which if I
+
+ align:start position:0%
+stable stack of end books which if I
+ 
+
+ align:start position:0%
+stable stack of end books which if I
+completely supported it flat on the
+
+ align:start position:0%
+completely supported it flat on the
+ 
+
+ align:start position:0%
+completely supported it flat on the
+table it wouldn't fall over and I'm
+
+ align:start position:0%
+table it wouldn't fall over and I'm
+ 
+
+ align:start position:0%
+table it wouldn't fall over and I'm
+going to show you how to go from n to n
+
+ align:start position:0%
+going to show you how to go from n to n
+ 
+
+ align:start position:0%
+going to show you how to go from n to n
+plus one which is how you construct an
+
+ align:start position:0%
+plus one which is how you construct an
+ 
+
+ align:start position:0%
+plus one which is how you construct an
+arbitrarily large stack of books that
+
+ align:start position:0%
+arbitrarily large stack of books that
+ 
+
+ align:start position:0%
+arbitrarily large stack of books that
+won't fall over well if the stack
+
+ align:start position:0%
+won't fall over well if the stack
+ 
+
+ align:start position:0%
+won't fall over well if the stack
+completely resting on the table won't
+
+ align:start position:0%
+completely resting on the table won't
+ 
+
+ align:start position:0%
+completely resting on the table won't
+fall over that means that if it if I
+
+ align:start position:0%
+fall over that means that if it if I
+ 
+
+ align:start position:0%
+fall over that means that if it if I
+have the center of mass of it past the
+
+ align:start position:0%
+have the center of mass of it past the
+ 
+
+ align:start position:0%
+have the center of mass of it past the
+edge of the table by definition of the
+
+ align:start position:0%
+edge of the table by definition of the
+ 
+
+ align:start position:0%
+edge of the table by definition of the
+center of mass there's going to be an
+
+ align:start position:0%
+center of mass there's going to be an
+ 
+
+ align:start position:0%
+center of mass there's going to be an
+equal amount of weight on both sides of
+
+ align:start position:0%
+equal amount of weight on both sides of
+ 
+
+ align:start position:0%
+equal amount of weight on both sides of
+the center of mass and the thing is
+
+ align:start position:0%
+the center of mass and the thing is
+ 
+
+ align:start position:0%
+the center of mass and the thing is
+going to fall off the edge of the table
+
+ align:start position:0%
+going to fall off the edge of the table
+ 
+
+ align:start position:0%
+going to fall off the edge of the table
+by the same reasoning as we did for one
+
+ align:start position:0%
+by the same reasoning as we did for one
+ 
+
+ align:start position:0%
+by the same reasoning as we did for one
+book so the the stable end stack stable
+
+ align:start position:0%
+book so the the stable end stack stable
+ 
+
+ align:start position:0%
+book so the the stable end stack stable
+in the sense that it'll it won't fall
+
+ align:start position:0%
+in the sense that it'll it won't fall
+ 
+
+ align:start position:0%
+in the sense that it'll it won't fall
+over of itself if it was lying
+
+ align:start position:0%
+over of itself if it was lying
+ 
+
+ align:start position:0%
+over of itself if it was lying
+completely over the table in fact it
+
+ align:start position:0%
+completely over the table in fact it
+ 
+
+ align:start position:0%
+completely over the table in fact it
+won't fall over as long as its Center of
+
+ align:start position:0%
+won't fall over as long as its Center of
+ 
+
+ align:start position:0%
+won't fall over as long as its Center of
+mass is over the table table and to get
+
+ align:start position:0%
+mass is over the table table and to get
+ 
+
+ align:start position:0%
+mass is over the table table and to get
+it out the furthest amount to the right
+
+ align:start position:0%
+it out the furthest amount to the right
+ 
+
+ align:start position:0%
+it out the furthest amount to the right
+what I'm going to do is put it at the
+
+ align:start position:0%
+what I'm going to do is put it at the
+ 
+
+ align:start position:0%
+what I'm going to do is put it at the
+edge of the table okay so now I know how
+
+ align:start position:0%
+edge of the table okay so now I know how
+ 
+
+ align:start position:0%
+edge of the table okay so now I know how
+to place uh a stable stack of n books to
+
+ align:start position:0%
+to place uh a stable stack of n books to
+ 
+
+ align:start position:0%
+to place uh a stable stack of n books to
+get the largest overhang out of it what
+
+ align:start position:0%
+get the largest overhang out of it what
+ 
+
+ align:start position:0%
+get the largest overhang out of it what
+next oh well let's consider n plus1
+
+ align:start position:0%
+next oh well let's consider n plus1
+ 
+
+ align:start position:0%
+next oh well let's consider n plus1
+books and what do I have to do so I'm
+
+ align:start position:0%
+books and what do I have to do so I'm
+ 
+
+ align:start position:0%
+books and what do I have to do so I'm
+trying to do the same deal suppose that
+
+ align:start position:0%
+trying to do the same deal suppose that
+ 
+
+ align:start position:0%
+trying to do the same deal suppose that
+I have a nice stack of end books and I
+
+ align:start position:0%
+I have a nice stack of end books and I
+ 
+
+ align:start position:0%
+I have a nice stack of end books and I
+know how to support it so it won't tip
+
+ align:start position:0%
+know how to support it so it won't tip
+ 
+
+ align:start position:0%
+know how to support it so it won't tip
+over um and I now have end books n plus1
+
+ align:start position:0%
+over um and I now have end books n plus1
+ 
+
+ align:start position:0%
+over um and I now have end books n plus1
+books and I want to get out further what
+
+ align:start position:0%
+books and I want to get out further what
+ 
+
+ align:start position:0%
+books and I want to get out further what
+do I have to do well by the basic
+
+ align:start position:0%
+do I have to do well by the basic
+ 
+
+ align:start position:0%
+do I have to do well by the basic
+reasoning that we just went through now
+
+ align:start position:0%
+reasoning that we just went through now
+ 
+
+ align:start position:0%
+reasoning that we just went through now
+the center of mass of the whole stack of
+
+ align:start position:0%
+the center of mass of the whole stack of
+ 
+
+ align:start position:0%
+the center of mass of the whole stack of
+n plus1 books has to be over the edge of
+
+ align:start position:0%
+n plus1 books has to be over the edge of
+ 
+
+ align:start position:0%
+n plus1 books has to be over the edge of
+the table that's the way I'm going to
+
+ align:start position:0%
+the table that's the way I'm going to
+ 
+
+ align:start position:0%
+the table that's the way I'm going to
+get out the furthest so I know where the
+
+ align:start position:0%
+get out the furthest so I know where the
+ 
+
+ align:start position:0%
+get out the furthest so I know where the
+center of mass of n plus books are going
+
+ align:start position:0%
+center of mass of n plus books are going
+ 
+
+ align:start position:0%
+center of mass of n plus books are going
+to be at the edge of the table okay what
+
+ align:start position:0%
+to be at the edge of the table okay what
+ 
+
+ align:start position:0%
+to be at the edge of the table okay what
+about the center of mass of the top end
+
+ align:start position:0%
+about the center of mass of the top end
+ 
+
+ align:start position:0%
+about the center of mass of the top end
+books well I need them to be supported I
+
+ align:start position:0%
+books well I need them to be supported I
+ 
+
+ align:start position:0%
+books well I need them to be supported I
+need their Center of Mass to be
+
+ align:start position:0%
+need their Center of Mass to be
+ 
+
+ align:start position:0%
+need their Center of Mass to be
+supported they'll be supported providing
+
+ align:start position:0%
+supported they'll be supported providing
+ 
+
+ align:start position:0%
+supported they'll be supported providing
+their Center of mass is over the bottom
+
+ align:start position:0%
+their Center of mass is over the bottom
+ 
+
+ align:start position:0%
+their Center of mass is over the bottom
+book somewhere and the way to get it out
+
+ align:start position:0%
+book somewhere and the way to get it out
+ 
+
+ align:start position:0%
+book somewhere and the way to get it out
+furthest is to have it over the right
+
+ align:start position:0%
+furthest is to have it over the right
+ 
+
+ align:start position:0%
+furthest is to have it over the right
+edge of the bottom book so I'm going to
+
+ align:start position:0%
+edge of the bottom book so I'm going to
+ 
+
+ align:start position:0%
+edge of the bottom book so I'm going to
+put the center of mass of the of top end
+
+ align:start position:0%
+put the center of mass of the of top end
+ 
+
+ align:start position:0%
+put the center of mass of the of top end
+books at the edge of the N plus first
+
+ align:start position:0%
+books at the edge of the N plus first
+ 
+
+ align:start position:0%
+books at the edge of the N plus first
+book here yeah and that means that the
+
+ align:start position:0%
+book here yeah and that means that the
+ 
+
+ align:start position:0%
+book here yeah and that means that the
+incremental overhang that I get the
+
+ align:start position:0%
+incremental overhang that I get the
+ 
+
+ align:start position:0%
+incremental overhang that I get the
+increase in overhang that I get by
+
+ align:start position:0%
+increase in overhang that I get by
+ 
+
+ align:start position:0%
+increase in overhang that I get by
+adding one more book we can call the
+
+ align:start position:0%
+adding one more book we can call the
+ 
+
+ align:start position:0%
+adding one more book we can call the
+Delta overhang and it's the distance
+
+ align:start position:0%
+Delta overhang and it's the distance
+ 
+
+ align:start position:0%
+Delta overhang and it's the distance
+between the center of mass of n plus1
+
+ align:start position:0%
+between the center of mass of n plus1
+ 
+
+ align:start position:0%
+between the center of mass of n plus1
+books and the center of mass of n books
+
+ align:start position:0%
+books and the center of mass of n books
+ 
+
+ align:start position:0%
+books and the center of mass of n books
+and N here and N plus one here well
+
+ align:start position:0%
+and N here and N plus one here well
+ 
+
+ align:start position:0%
+and N here and N plus one here well
+let's see what's going on the center of
+
+ align:start position:0%
+let's see what's going on the center of
+ 
+
+ align:start position:0%
+let's see what's going on the center of
+mass of the uh end books is at some
+
+ align:start position:0%
+mass of the uh end books is at some
+ 
+
+ align:start position:0%
+mass of the uh end books is at some
+location here and the center of mass of
+
+ align:start position:0%
+location here and the center of mass of
+ 
+
+ align:start position:0%
+location here and the center of mass of
+the bottom book is halfway away half a
+
+ align:start position:0%
+the bottom book is halfway away half a
+ 
+
+ align:start position:0%
+the bottom book is halfway away half a
+book length away from where the N books
+
+ align:start position:0%
+book length away from where the N books
+ 
+
+ align:start position:0%
+book length away from where the N books
+are balanced on the edge of the bottom
+
+ align:start position:0%
+are balanced on the edge of the bottom
+ 
+
+ align:start position:0%
+are balanced on the edge of the bottom
+book so the center of mass of the end
+
+ align:start position:0%
+book so the center of mass of the end
+ 
+
+ align:start position:0%
+book so the center of mass of the end
+books is here the center of mass of the
+
+ align:start position:0%
+books is here the center of mass of the
+ 
+
+ align:start position:0%
+books is here the center of mass of the
+bottom book is there the distance
+
+ align:start position:0%
+bottom book is there the distance
+ 
+
+ align:start position:0%
+bottom book is there the distance
+between them is 1/2
+
+ align:start position:0%
+between them is 1/2
+ 
+
+ align:start position:0%
+between them is 1/2
+and I need the table to be at the
+
+ align:start position:0%
+and I need the table to be at the
+ 
+
+ align:start position:0%
+and I need the table to be at the
+balance point between the N books and
+
+ align:start position:0%
+balance point between the N books and
+ 
+
+ align:start position:0%
+balance point between the N books and
+the one book that's where the center of
+
+ align:start position:0%
+the one book that's where the center of
+ 
+
+ align:start position:0%
+the one book that's where the center of
+mass of the N plus1 books will be so I
+
+ align:start position:0%
+mass of the N plus1 books will be so I
+ 
+
+ align:start position:0%
+mass of the N plus1 books will be so I
+need to calculate amount that's going to
+
+ align:start position:0%
+need to calculate amount that's going to
+ 
+
+ align:start position:0%
+need to calculate amount that's going to
+be the increase in overhang so let's
+
+ align:start position:0%
+be the increase in overhang so let's
+ 
+
+ align:start position:0%
+be the increase in overhang so let's
+abstract it a little bit the Delta
+
+ align:start position:0%
+abstract it a little bit the Delta
+ 
+
+ align:start position:0%
+abstract it a little bit the Delta
+overhang is the distance from the nbook
+
+ align:start position:0%
+overhang is the distance from the nbook
+ 
+
+ align:start position:0%
+overhang is the distance from the nbook
+to the N plus one book centers of mass
+
+ align:start position:0%
+to the N plus one book centers of mass
+ 
+
+ align:start position:0%
+to the N plus one book centers of mass
+and if we think of this as a balancing
+
+ align:start position:0%
+and if we think of this as a balancing
+ 
+
+ align:start position:0%
+and if we think of this as a balancing
+diagram there's the N books or at least
+
+ align:start position:0%
+diagram there's the N books or at least
+ 
+
+ align:start position:0%
+diagram there's the N books or at least
+there's the center of mass of the N
+
+ align:start position:0%
+there's the center of mass of the N
+ 
+
+ align:start position:0%
+there's the center of mass of the N
+books there's the center of mass of the
+
+ align:start position:0%
+books there's the center of mass of the
+ 
+
+ align:start position:0%
+books there's the center of mass of the
+one book their distance 1/2 apart which
+
+ align:start position:0%
+one book their distance 1/2 apart which
+ 
+
+ align:start position:0%
+one book their distance 1/2 apart which
+which we said and they have to balance
+
+ align:start position:0%
+which we said and they have to balance
+ 
+
+ align:start position:0%
+which we said and they have to balance
+at the edge of the table so think of the
+
+ align:start position:0%
+at the edge of the table so think of the
+ 
+
+ align:start position:0%
+at the edge of the table so think of the
+edge of the table as the Pivot Point um
+
+ align:start position:0%
+edge of the table as the Pivot Point um
+ 
+
+ align:start position:0%
+edge of the table as the Pivot Point um
+and it's there and I need to calculate
+
+ align:start position:0%
+and it's there and I need to calculate
+ 
+
+ align:start position:0%
+and it's there and I need to calculate
+where is that Pivot Point how do I get
+
+ align:start position:0%
+where is that Pivot Point how do I get
+ 
+
+ align:start position:0%
+where is that Pivot Point how do I get
+this uh fulcrum uh or this uh balance
+
+ align:start position:0%
+this uh fulcrum uh or this uh balance
+ 
+
+ align:start position:0%
+this uh fulcrum uh or this uh balance
+beam to balance with weight n here and
+
+ align:start position:0%
+beam to balance with weight n here and
+ 
+
+ align:start position:0%
+beam to balance with weight n here and
+weight one there when there total length
+
+ align:start position:0%
+weight one there when there total length
+ 
+
+ align:start position:0%
+weight one there when there total length
+apart is a half what's this distance
+
+ align:start position:0%
+apart is a half what's this distance
+ 
+
+ align:start position:0%
+apart is a half what's this distance
+that distance is the Delta that I'm
+
+ align:start position:0%
+that distance is the Delta that I'm
+ 
+
+ align:start position:0%
+that distance is the Delta that I'm
+trying to calculate well you just know
+
+ align:start position:0%
+trying to calculate well you just know
+ 
+
+ align:start position:0%
+trying to calculate well you just know
+from uh physics that the balance point
+
+ align:start position:0%
+from uh physics that the balance point
+ 
+
+ align:start position:0%
+from uh physics that the balance point
+is uh going to be um the distance a half
+
+ align:start position:0%
+is uh going to be um the distance a half
+ 
+
+ align:start position:0%
+is uh going to be um the distance a half
+divided by uh the sum of N and n+ one
+
+ align:start position:0%
+divided by uh the sum of N and n+ one
+ 
+
+ align:start position:0%
+divided by uh the sum of N and n+ one
+okay I need the n * this amount to equal
+
+ align:start position:0%
+okay I need the n * this amount to equal
+ 
+
+ align:start position:0%
+okay I need the n * this amount to equal
+1 time that amount and if you check that
+
+ align:start position:0%
+1 time that amount and if you check that
+ 
+
+ align:start position:0%
+1 time that amount and if you check that
+out it means that Delta is a half over n
+
+ align:start position:0%
+out it means that Delta is a half over n
+ 
+
+ align:start position:0%
+out it means that Delta is a half over n
++ one or simplifying 1 over tce n + 1
+
+ align:start position:0%
++ one or simplifying 1 over tce n + 1
+ 
+
+ align:start position:0%
++ one or simplifying 1 over tce n + 1
+now you should stare at that diagram a
+
+ align:start position:0%
+now you should stare at that diagram a
+ 
+
+ align:start position:0%
+now you should stare at that diagram a
+little bit and remember your Elementary
+
+ align:start position:0%
+little bit and remember your Elementary
+ 
+
+ align:start position:0%
+little bit and remember your Elementary
+physics to realize uh the reasoning
+
+ align:start position:0%
+physics to realize uh the reasoning
+ 
+
+ align:start position:0%
+physics to realize uh the reasoning
+behind the formula for Delta okay well
+
+ align:start position:0%
+behind the formula for Delta okay well
+ 
+
+ align:start position:0%
+behind the formula for Delta okay well
+now I'm done because basically I've just
+
+ align:start position:0%
+now I'm done because basically I've just
+ 
+
+ align:start position:0%
+now I'm done because basically I've just
+figured out that the increase is this
+
+ align:start position:0%
+figured out that the increase is this
+ 
+
+ align:start position:0%
+figured out that the increase is this
+Delta overhang and now I know what it is
+
+ align:start position:0%
+Delta overhang and now I know what it is
+ 
+
+ align:start position:0%
+Delta overhang and now I know what it is
+it's 1 / t n + 1 and so what I can
+
+ align:start position:0%
+it's 1 / t n + 1 and so what I can
+ 
+
+ align:start position:0%
+it's 1 / t n + 1 and so what I can
+conclude is that the overhang of n books
+
+ align:start position:0%
+conclude is that the overhang of n books
+ 
+
+ align:start position:0%
+conclude is that the overhang of n books
+B1 is a half and BN + one is BN + 1 / t
+
+ align:start position:0%
+B1 is a half and BN + one is BN + 1 / t
+ 
+
+ align:start position:0%
+B1 is a half and BN + one is BN + 1 / t
+n + 1 so this is a recursive definition
+
+ align:start position:0%
+n + 1 so this is a recursive definition
+ 
+
+ align:start position:0%
+n + 1 so this is a recursive definition
+of BN but it's easy to see how it
+
+ align:start position:0%
+of BN but it's easy to see how it
+ 
+
+ align:start position:0%
+of BN but it's easy to see how it
+unwinds it means that BN is a half plus
+
+ align:start position:0%
+unwinds it means that BN is a half plus
+ 
+
+ align:start position:0%
+unwinds it means that BN is a half plus
+um uh 1
+
+ align:start position:0%
+um uh 1
+ 
+
+ align:start position:0%
+um uh 1
+1/2 of 1 + 1 plus 1 12 of 2 + 1 plus 1
+
+ align:start position:0%
+1/2 of 1 + 1 plus 1 12 of 2 + 1 plus 1
+ 
+
+ align:start position:0%
+1/2 of 1 + 1 plus 1 12 of 2 + 1 plus 1
+12 of 3 + 1 and so on if I factor out
+
+ align:start position:0%
+12 of 3 + 1 and so on if I factor out
+ 
+
+ align:start position:0%
+12 of 3 + 1 and so on if I factor out
+the half BN is a half * 1 + a half plus
+
+ align:start position:0%
+the half BN is a half * 1 + a half plus
+ 
+
+ align:start position:0%
+the half BN is a half * 1 + a half plus
+A3 out through 1/
+
+ align:start position:0%
+A3 out through 1/
+ 
+
+ align:start position:0%
+A3 out through 1/
+n okay that sum is the harmonic sum the
+
+ align:start position:0%
+n okay that sum is the harmonic sum the
+ 
+
+ align:start position:0%
+n okay that sum is the harmonic sum the
+sum 1 plus a half up through 1 over n is
+
+ align:start position:0%
+sum 1 plus a half up through 1 over n is
+ 
+
+ align:start position:0%
+sum 1 plus a half up through 1 over n is
+called hn or the harmonic sum and what
+
+ align:start position:0%
+called hn or the harmonic sum and what
+ 
+
+ align:start position:0%
+called hn or the harmonic sum and what
+we figured out or really the harmonic
+
+ align:start position:0%
+we figured out or really the harmonic
+ 
+
+ align:start position:0%
+we figured out or really the harmonic
+number is the value of that sum and what
+
+ align:start position:0%
+number is the value of that sum and what
+ 
+
+ align:start position:0%
+number is the value of that sum and what
+we fig figured out is that BN the amount
+
+ align:start position:0%
+we fig figured out is that BN the amount
+ 
+
+ align:start position:0%
+we fig figured out is that BN the amount
+that I can get n books out uh past the
+
+ align:start position:0%
+that I can get n books out uh past the
+ 
+
+ align:start position:0%
+that I can get n books out uh past the
+edge of the table is hn over two
\ No newline at end of file
diff --git a/CxuZZcUKxWM.txt b/CxuZZcUKxWM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..acf3518894af136e0fc59c47c4cd2a5805021f80
--- /dev/null
+++ b/CxuZZcUKxWM.txt
@@ -0,0 +1,3884 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+JOHN DONG: All right, so I'm
+sure everybody's kind of
+
+curious about Project 2.2
+Beta, so here's the
+
+preliminary performance
+results.
+
+There's still a bit more work
+to do on finalizing these
+
+numbers, but here's
+how they look.
+
+But before I show you guys that,
+I'd like to yell at you
+
+guys for a little bit.
+
+So this is a timeline of the
+submission deadline and when
+
+people submitted things.
+
+So from this zone to this zone
+is an hour, and I see like 50%
+
+of the commits made during
+that period.
+
+So a little bit of background,
+the submission checking system
+
+automatically clones a
+repository up to the deadline
+
+and not a second after.
+
+So if you look at from this
+to this, some people took
+
+quite a jump back.
+
+So just as a warning, please try
+to submit things on time.
+
+11:59 means 11:59, and to drive
+that point further, this
+
+is an example of a commit
+that I saw in somebody's
+
+repository, who's name
+I blanked out.
+
+Obviously, it's seven seconds
+past the deadline, so the
+
+automatic repository cloner
+didn't grab it.
+
+And the previous commit to that
+was like 10 days ago when
+
+Reid pushed out pentominoes
+grades.
+
+So don't do that either.
+
+A little break down on how
+often people commit.
+
+About a quarter of the class
+only made one commit to their
+
+repository.
+
+Half of you guys did three
+to 10 commits, which
+
+seems to be an up.
+
+Under 21+, there was somebody
+who did 100 some commits,
+
+which was pretty impressive.
+
+Yeah, very smart dude.
+
+Committing often is a good idea,
+so that you don't run
+
+into a situation like before.
+
+And next time definitely, there
+is going to be next to
+
+zero tolerance for people who
+don't commit things on time
+
+for the deadlines.
+
+Now, the numbers that
+people want.
+
+So for rotate, just as an
+interesting data point, this
+
+is the 512 by 512 case.
+
+It seems like not everybody
+remembered to carry over their
+
+optimizations for the 512 case
+over to the final, otherwise
+
+you would expect the numbers
+to be a little bit more
+
+similar and not off by
+a factor of eight.
+
+And for rotate overall, that's
+the distribution.
+
+The speed up factor is
+normalized to some constant
+
+that gives everybody a
+reasonable number.
+
+And there were a lot
+of groups that had
+
+code that didn't build.
+
+Yes?
+
+AUDIENCE: Does the speedup
+only include
+
+the rotate dot 64.
+
+JOHN DONG: Yes.
+
+Performance was only tested on
+the rotate dot 64, which is
+
+what we said in the
+handout also.
+
+So there were a lot of groups
+that didn't build, which
+
+really surprised me, and I think
+it's probably because
+
+half of you guys pushed things
+after the deadline, and I
+
+presume those things contained
+important commits towards
+
+making your code
+actually work.
+
+But in this case, there was no
+header files, there was no
+
+cross-testing.
+
+All we did was run your make
+file on your code, and we
+
+replaced your test bed dot c,
+and your k timing, so I'm not
+
+quite sure why people have
+code that doesn't build.
+
+For sort, this was the maximum
+size input that we allowed you
+
+guys to run.
+
+One group did really well.
+
+So all of these are correct.
+
+The correctness test is built
+in, and I replaced that with a
+
+clean copy that contains
+a couple additional
+
+checks, by the way.
+
+So I tried the other extreme,
+a relatively small array.
+
+AUDIENCE: Is the top
+the same person?
+
+JOHN DONG: I'm not sure whether
+or not the top is the
+
+same person.
+
+But the distribution wise seems
+like people didn't quite
+
+remember to optimize for
+the smallest case.
+
+And this is the current overall
+speedup factors for
+
+sort averaging.
+
+We did about 10 to 15 cases
+for rotate and sort.
+
+And that's the overall
+speedup distribution.
+
+SAMAN AMARASINGHE: OK, so now
+you're done with individual
+
+project, so you already did the
+last project individually,
+
+and then we are moving into,
+again, a group project.
+
+So the first thing we have,
+setting up automated system
+
+for you to say who your
+group members are.
+
+So we will send you information,
+and with that,
+
+what you have to do is run a
+script saying who your group
+
+members are, both group members
+have to do it, and
+
+then we will basically clear
+that account in there.
+
+That said, a lot of you didn't
+know, in the first project,
+
+how to work and what's
+the right mode of
+
+operations with the group.
+
+OK if we gave you to write
+100,000 lines of code, it
+
+makes sense to say, OK, I'm
+going to divide the problem
+
+into half, one person do
+one, the other person
+
+do the other half.
+
+The reason for doing the group
+is to try to get you to do
+
+pair programming, because
+talking to a lot of you,
+
+getting a lot of feedback, it
+looks like most of you spent a
+
+huge amount of time debugging.
+
+And since you're only writing
+a little amount of code, it
+
+makes a lot more sense to sit
+with your partner next to the
+
+screen, one person types, other
+person looks over, and
+
+then you have a much faster
+way of getting through the
+
+debugging process.
+
+So the next one, don't try to
+divide the problem by half.
+
+Just try to find some time,
+sit with each other.
+
+Then the other really disturbing
+thing is there have
+
+been a couple of groups that
+were completely dysfunctional.
+
+We get emails saying, OK, my
+group member didn't talk to
+
+me, or they didn't do any
+work, or they were very
+
+condescending.
+
+And that's really sad, because
+from my experience with MIT
+
+students, when you guys go to
+company, you guys probably
+
+will be the best programmers
+there.
+
+There's no question about it.
+
+I have seen that.
+
+To the point that some people
+might even resent it, to have
+
+this best programmer.
+
+But what I have seen is the fact
+a lot of you cannot work
+
+in the group, if you haven't
+developed that skill, you will
+
+not be the most impactful
+person.
+
+I have seen that again and again
+in my experience with
+
+doing a start-up.
+
+Our MIT students, their way of
+impacting is put all night do
+
+the entire project
+by themselves.
+
+Doable when you're doing a
+small change to a large
+
+project, but if you want
+to have a big change,
+
+you can't do that.
+
+You have to work with the
+group, figure out how to
+
+impact, how to communicate.
+
+This is more important learning
+than, say, trying to
+
+figure out how you can
+optimize something.
+
+So being individual contributors
+and able to do
+
+amazing things is important,
+but the fact that you can't
+
+work with a group is going to
+really make the impact you can
+
+make much less.
+
+So please, please learn how to
+work with your group members.
+
+Some of them might not be as
+good as you are, and that will
+
+be probably true in real life,
+too, but that doesn't mean you
+
+can be condescending towards
+them, make them feel inferior.
+
+That doesn't cut it.
+
+You have to learn how to
+work with these people.
+
+So part of your learning is
+working with others, and
+
+that's a large part
+of your learning.
+
+Don't consider that to be this
+external thing, even though
+
+you might think you can
+do a better job.
+
+Just work with the other person,
+especially in pair
+
+programming, because where
+both of you are sticking
+
+together, it's much easier.
+
+Because there are four eyes on
+your project, they might see
+
+something you don't see, and
+see whether you can work
+
+together like that.
+
+And I don't want to hear any
+more stories saying, look, my
+
+partner was too dumb, or my
+partner didn't show up, he
+
+couldn't deal with that.
+
+Those are not great excuses.
+
+And so we wonder.
+
+Some of them, we will pay
+attention to it, because it
+
+might be one person's
+unilateral actions
+
+that lead to that.
+
+Still, please, try to figure
+out how we can
+
+work with your partners.
+
+And hope you have a good
+partner experience.
+
+Use pair programming.
+
+Use a lot of good debugging
+techniques, and the next
+
+project will be fine.
+
+CHARLES LEISERSON: Great.
+
+We're going to talk
+more about caches.
+
+Whoo-whoo!
+
+OK.
+
+So for those who weren't here
+last time, we talked about the
+
+ideal cache model.
+
+As you recall, it has a
+two-level hierarchy and a
+
+cache size M bytes, and a cache
+line length of B bytes.
+
+It's fully associative
+and is optimal
+
+omniscient replacement strategy.
+
+However, we also learned that
+LRU was a good substitute, and
+
+that any of the asymptotic
+results that you can get with
+
+optimal, you could also
+get with LRU.
+
+The two performance measures
+that we talked about were the
+
+work, which deals with what the
+processor ends up doing,
+
+and the cache misses, which is
+the transfers between cache
+
+and main memory.
+
+You only have to count one
+direction, because what goes
+
+in basically goes out, so more
+or less, it's the same number.
+
+OK, so I'd like to start today
+by talking about some very
+
+basic algorithms that you have
+seen in your algorithms and
+
+data structures class, but which
+may look new when we
+
+start taking caches
+into account.
+
+So the first one here
+is the problem of
+
+merging two sorted arrays.
+
+So as you recall, you
+can basically do
+
+this in linear time.
+
+The way that the algorithm works
+is that it looks at the
+
+first element of the two
+arrays to be sorted and
+
+whichever is smaller, it
+puts in the output.
+
+And then it advances the pointer
+to the next element,
+
+and then whichever is smaller,
+it puts in the output.
+
+And in every step, it's doing
+just a constant amount of
+
+work, there are n items, so by
+the time this process is done,
+
+we basically spent time
+proportional to the number of
+
+items in the output list.
+
+So this should be
+fairly familiar.
+
+So the time to emerge n
+elements is order n.
+
+Now, the reason merging is
+useful is because you can use
+
+it in a sorting algorithm, a
+merge sorting algorithm.
+
+The way merge sort works is it
+essentially does divide and
+
+conquer on the array.
+
+It divides the array into two
+pieces, and it divides those
+
+each into two pieces, and those
+into two, until it gets
+
+down to something
+of unit size.
+
+And then what it does
+is it merges the
+
+two pairs of arrays.
+
+So for example here, the 19 and
+3 got merged together to
+
+be 3 and 19.
+
+The 12 and 46 were already in
+order, but you still had to do
+
+work to get it there
+and so forth.
+
+So it puts everything in order
+in pairs, and then for each of
+
+those, it puts it together into
+fours, and for each of
+
+those, it puts it together
+into the final list.
+
+Now of course, the way it does
+this is not in the order I
+
+showed you.
+
+It actually goes down and does
+a walk of this tree.
+
+But conceptually, you can see
+that it essentially comes down
+
+to merging pairs, merging
+quadruples, emerging octuples,
+
+and so forth, all the way until
+the program is done.
+
+So to calculate the work of
+Merge Sort, this is something
+
+you've seen before because it's
+exactly what you do in
+
+your algorithms class.
+
+You get a recurrence that
+says that the work,
+
+in this case is--
+
+well, if you have only one
+element, it's a constant
+
+amount of work, and otherwise,
+I solve two problems of half
+
+the size doing order n work,
+which is the time to merge the
+
+two elements.
+
+So classic divide and conquer.
+
+And I'm sure you're familiar
+with what the solution to this
+
+recurrence is.
+
+What's the solution to
+this recurrence?
+
+n log n.
+
+I want to, though, step through
+it, just to get
+
+everybody warmed up to the
+way that I want to solve
+
+recurrences so that you are in
+a position, when we do the
+
+caching analysis--
+
+we have a common framework for
+understanding how the caching
+
+analysis will work.
+
+So we're going to solve this
+recurrence, and if the base
+
+case is constant, we
+usually omit it.
+
+It's assumed.
+
+So we start out with W of n, and
+what we do is we replace
+
+it by the right hand side, where
+we put the constant term
+
+on the top and then
+the two children.
+
+So here I've gotten rid of the
+theta, because conceptually
+
+when I'm done, I can put a big
+theta around the whole thing,
+
+around the whole tree, and it
+just makes the math a little
+
+bit easier and a little
+bit clearer to see
+
+what's going on.
+
+So then I take each of those
+and I split those, and this
+
+time I've got n over 4.
+
+Correct?
+
+I checked for that
+one this time.
+
+It's funny because it was still
+there, actually, just a
+
+few minutes before class
+as I was going through.
+
+And we keep doing that until
+we get down to something of
+
+size one, until the recurrence
+bottoms out.
+
+So when you look at a recursion
+tree of this nature,
+
+the first thing that you
+typically want to do is take a
+
+look at what the height
+of the tree is.
+
+In this case, we're taking a
+problem of size n, and we're
+
+halving it at every step.
+
+And so the number of times we
+have to halve the argument--
+
+which turns out to be also equal
+to the work, but that's
+
+just coincidence--
+
+is log n times.
+
+So the height is log
+base 2 of n.
+
+Now what we do typically is we
+add things up across the rows,
+
+across the levels.
+
+So on the top level,
+we have n.
+
+On the next level, we have n.
+
+The next level, hey, n.
+
+To add up the bottom, just to
+make sure, we have to count up
+
+how many leaves there are, and
+the number of leaves, since
+
+this is a binary tree, is
+just 2 to the height.
+
+So it's 2 to the log
+n, which is n.
+
+So then I add across all the
+leaves, and I get the order 1
+
+at the base times n,
+which is order n.
+
+And so now I'm in a position
+to add up the total work,
+
+which is basically log n
+levels of n is total
+
+of order n log n.
+
+So hopefully, this
+is all review.
+
+Hopefully this is all review.
+
+You haven't seen this before.
+
+It's really neat, isn't it?
+
+But you've missed something
+along the way.
+
+So now with caching.
+
+So the first thing to observe is
+that merge subroutine, the
+
+number of cache misses that it
+has is order n over B. So as
+
+you're going through, these
+arrays are laid out
+
+continuously in memory.
+
+The number of misses--
+
+you're just going through
+the data once--
+
+is order n data, all going
+through contiguously.
+
+And so every time you bring in
+data, you get full spatial
+
+locality, there are n elements,
+it costs n over B.
+
+So is that plain?
+
+Hopefully that part's plain,
+because you bring in things of
+
+each axis, you get the
+same factor of B.
+
+So now merge sort--
+
+and this is, once again, the
+hard part is coming up with a
+
+recurrence, and then the other
+hard part is solving it.
+
+So there's two hard parts
+to recurrences.
+
+OK, so the merge sort algorithm
+solves two problems
+
+of size n over 2, and
+then does a merge.
+
+So the second line here is
+pretty straightforward.
+
+I take the cache misses
+that I need to do,
+
+and I take a merge.
+
+I may have a few other accesses
+in there, but they're
+
+going to be dominated
+by the merge.
+
+OK, so it's still going
+to be theta n over B.
+
+Now the hard part, generally, of
+dealing with cache analysis
+
+is how to do the base case,
+because the base case is more
+
+complicated than when you just
+do running time, you get that
+
+to run down to a base case
+of constant size.
+
+Here, you don't get to
+run down to base
+
+case of constant size.
+
+So what it says here is that
+we're going to run down until
+
+I have a sorting problem that
+fits in cache, n is going to
+
+be less than some constant times
+n, for some sufficiently
+
+small constant c less than 1.
+
+When in finally fits in cache,
+how many cache misses does it
+
+take me to sort it?
+
+Well, I only need to have the
+cold misses to bring that
+
+array into memory, and so that's
+just proportional to n
+
+over B, because for all the rest
+of the levels of merging,
+
+you're inside the cache.
+
+That make sense?
+
+So that's where we get
+this recurrence.
+
+This is always a tricky thing
+to figure out how to write
+
+that recurrence for
+a given thing.
+
+Then, as I say, the other
+tricky thing is how
+
+do you solve it?
+
+But we're going to solve it
+essentially the same way as we
+
+did before.
+
+I'm not going to go through all
+the steps here, except to
+
+just elaborate.
+
+So what we're doing is we're
+taking, and we have n over B
+
+at the top, and then we divide
+it into two problems, and for
+
+each of those--
+
+whoops, there's a c there
+that doesn't belong.
+
+It should just be n over
+2B on both, and then n
+
+over 4B, and so forth.
+
+And we keep going down until
+we get to our base case.
+
+Now in our base case, what I
+claim is that when I hit this
+
+base case, it's going to be the
+case that n is, in fact, a
+
+constant factor times n, so that
+n over B is almost the
+
+same as m over B. And the reason
+is because before I hit
+
+the base case, when I was at
+size twice n, and that was
+
+bigger than m.
+
+So if twice n is
+bigger than m--
+
+than my constant times m--
+
+but n is smaller than m, then
+it's the case that n and m are
+
+essentially the same size to
+within a constant factor,
+
+within a factor of
+two, in fact.
+
+And so therefore, here I can say
+that it's order m over B.
+
+And now the question is, how
+many levels did I have to go
+
+down cutting things in half
+before I got to something of
+
+size m over B?
+
+Well, the way that I usually
+think about this is--
+
+you can do it by taking the
+difference as I did before.
+
+The height of the whole tree is
+going to be log base 2 of
+
+n, and the height of this
+is basically log of--
+
+what's the size of n?
+
+It's going to be log of the size
+of n when this occurs.
+
+Well, n at that point is
+something like cm.
+
+So it's basically log n minus
+log cm, which is basically log
+
+of n over cm.
+
+How about some questions.
+
+Yeah, question.
+
+AUDIENCE: --the reason for why
+you just substituted on the
+
+left, [INAUDIBLE] over B, but
+on the right [INAUDIBLE].
+
+CHARLES LEISERSON: Here?
+
+AUDIENCE: No.
+
+CHARLES LEISERSON:
+Or you mean here?
+
+AUDIENCE: [INAUDIBLE].
+
+CHARLES LEISERSON: On
+the right side.
+
+AUDIENCE: On the right-most
+leaf, it's n over B. Is that
+
+all of the leaves added up
+because [INAUDIBLE]?
+
+CHARLES LEISERSON: No, no, no,
+this is going to be all of the
+
+leaves added up here.
+
+This is the stack I have
+on the right hand side.
+
+So we'll get there.
+
+So the point is, the number of
+leaves is 2 to this-- so
+
+that's just n over cm--
+
+times m over B. Well, n over
+cm times m over B, the m's
+
+cancel, and I get essentially
+n over b with whatever that
+
+constant is here.
+
+And so now I have n over b
+across every level, and then
+
+when I add those up, I have to
+go log of n over cm levels,
+
+which is the same as
+log of n over m.
+
+So I have n over B times
+log of n over m.
+
+Yeah, question?
+
+AUDIENCE: Initial assumption
+that c is some sufficiently
+
+small number, so 1
+over c would be a
+
+rather large factor.
+
+CHARLES LEISERSON: It could
+potentially be a large factor,
+
+but it's a constant.
+
+In other words, it can't
+vary with n.
+
+So in fact, typically for
+something like merge sort, the
+
+constant is going to
+be very close to--
+
+for most things, the constant
+there is typically only a few.
+
+Because the question is, how
+many other things do you need
+
+in order to make sure
+it fits in?
+
+In this case, you have n.
+
+Well, you have both the input
+and the output, so here, it's
+
+going to be, you have to fit
+both the input and the output
+
+into cache in order not
+to have the cache it.
+
+So it's basically going
+to be like a factor
+
+of 2 for merge sort.
+
+For the matrix multiplication,
+it was like a factor of three.
+
+So generally a fairly
+small number.
+
+Question?
+
+AUDIENCE: I guess that
+makes sense.
+
+But I [INAUDIBLE].
+
+So on the order of the size of
+the leaves, can you assume
+
+that n is more than cm, so
+you can substitute--
+
+CHARLES LEISERSON: Yeah, because
+basically, when it
+
+hits this condition--
+
+AUDIENCE: Right.
+
+I understand that.
+
+Then you're also saying, why
+isn't there more or less just
+
+one B, because there's n over
+cm, n is the same as cm.
+
+That's [INAUDIBLE].
+
+At the bottom level,
+there should be--
+
+CHARLES LEISERSON: Oh, did I
+do something wrong here?
+
+Number of leaves is--
+
+AUDIENCE: [INAUDIBLE].
+
+CHARLES LEISERSON:
+Right, right.
+
+Sorry.
+
+This is the n at the top.
+
+You always have to
+be careful here.
+
+So this is the n in this case,
+so this is some n, little n.
+
+So this is not the same n.
+
+This is the n that we
+had at the top.
+
+This is the notion of
+recurrences, like the n keeps
+
+recurring, but you
+know which ones--
+
+so it can be confusing,
+because if you're--
+
+so yeah.
+
+So this is not the
+n that's here.
+
+This is the n that started
+out at the top.
+
+So we're analyzing it
+in terms of the n.
+
+Some people write these things
+where they would write this in
+
+terms of k, and then analyze it
+for n, and for some people,
+
+that can be helpful to do, to
+disambiguate the two things.
+
+I always find it wastes a
+variable, and you know, those
+
+variables are hard to come by.
+
+There's only a finite
+number of them.
+
+OK, so are we good for this?
+
+So here, we ended up with
+n over b, log of n
+
+over m cache misses.
+
+So how does that compare?
+
+Let's just do a little
+thinking about this.
+
+Here's the recurrence, and
+I solved it out to this.
+
+So let's just look to
+see what this means.
+
+If I have a really big n, much
+bigger than the size of my
+
+cache, then I'm going to do a
+factor of B log n less misses
+
+than work, because the work
+is n over B log n.
+
+So if n compared to m-- let's
+say n was m squared or
+
+something--
+
+then n over m would
+still be n, if n
+
+was as big as m squared.
+
+So if n was as big as m squared,
+this log of n over m
+
+would still be log n.
+
+And so I would basically have n
+over B log n for a factor of
+
+B log n less misses than work.
+
+If they're about the same--
+
+did I get this right?
+
+If they're about the same size,
+if n is approximately m,
+
+maybe it's just a little bit
+bigger, then the log here
+
+disappears completely, and
+so I basically just
+
+have n over B misses.
+
+AUDIENCE: [INAUDIBLE].
+
+CHARLES LEISERSON: Yeah,
+but if n is like--
+
+AUDIENCE: [INAUDIBLE].
+
+CHARLES LEISERSON: Yeah.
+
+In fact, for this, you have to
+be careful as you get to the
+
+base cases.
+
+Technically, for some of this,
+I should be saying 1 plus log
+
+of n over m, and in some of the
+things I do later, I will
+
+put in the ones.
+
+But if you're looking at it
+asymptotically and n gets big,
+
+you don't have to worry
+about those cases.
+
+That just handles the case
+whether you're looking at n
+
+getting large or whether you're
+trying to handle a
+
+formula for all n, even
+if and n is small.
+
+Question?
+
+AUDIENCE: [INAUDIBLE]?
+
+CHARLES LEISERSON: The work
+was n log n, yes.
+
+The work was n log n.
+
+So here we basically have n over
+B log n, so I'm saving a
+
+factor of B in the case where
+it's about the same.
+
+Did I get this right?
+
+I'm just looking at this, and
+now I'm trying to reverse
+
+engineer what my argument is.
+
+So we're looking at n log n
+versus n over B log n over m.
+
+AUDIENCE: [INAUDIBLE PHRASE].
+
+So that you get a factor of B
+less misses, because you would
+
+be getting n over B like log
+of n, that's the only way
+
+you're getting a factor
+of B less misses.
+
+So I don't understand how you're
+saying, for n more or
+
+less equal to m.
+
+You would want something
+more like, for n--
+
+CHARLES LEISERSON: Well, if n
+and m are about the same size,
+
+the number of cache misses is
+just n over B. And the number
+
+of cache misses is n over B,
+and the work is n log n.
+
+So I've saved a factor
+of B times log n, OK?
+
+What did I say?
+
+AUDIENCE: [INAUDIBLE].
+
+CHARLES LEISERSON: B log m?
+
+No, I was saying that's
+for the case when n is
+
+much bigger than m.
+
+So let's take a look
+at the case--
+
+let me just do it on
+the board here.
+
+Let's suppose that n is like m
+squared, just as an example,
+
+big number.
+
+So I'm going to look at,
+essentially, n over B times
+
+log of n over m.
+
+So log of n over m, so what is
+n over m is about m, which is
+
+about square root of n, right?
+
+So this basically ends up being
+approximately n over B
+
+log of square root of n, which
+is the same as log n, to
+
+within a constant factor.
+
+I'm going to leave out the
+constant factors here.
+
+Then I want to compare
+that with n log n.
+
+So I get a factor of
+B less misses.
+
+So the first one, yes, OK.
+
+So I get a factor of B less
+misses, you're right.
+
+Then I get a factor
+of B less misses.
+
+So I think I've got
+these switched.
+
+So this is the case I'm doing
+is for n much bigger than m.
+
+So let's do the other case.
+
+I think I've got the two
+things switched.
+
+I'll fix it in the notes.
+
+If n and m are approximately
+the same, then the log is a
+
+constant, right?
+
+So this ends up being
+approximately n over B. And
+
+now when I take a look at the
+difference between the number
+
+of things, I get B log n.
+
+So I've got the two
+things mixed.
+
+Yeah?
+
+AUDIENCE: As n approaches m,
+then the log would approach
+
+zero, but were you talking
+about how it technically
+
+should be--
+
+CHARLES LEISERSON:
+1 plus n, yes.
+
+AUDIENCE: So technically, that
+approaches one when the log
+
+approaches zero.
+
+CHARLES LEISERSON: Yeah.
+
+AUDIENCE: These things are
+really hard for me, because
+
+they are really arbitrary.
+
+And then you're like, oh
+yeah, you can just put
+
+a 1 on top of there.
+
+And for example, I always miss
+those, because I usually try
+
+to do the math as rigorously
+as I can, and those ones
+
+generally do not appear,
+and you're
+
+like, oh, sure whatever.
+
+So how am I supposed to know
+that the log is actually not
+
+going to be zero, and I'm going
+to be like, yeah, you're
+
+not going to do any caches.
+
+CHARLES LEISERSON: Because
+generally, what we're doing is
+
+we're looking at how things
+scale, so we're generally
+
+looking at n being big, in which
+case it doesn't matter.
+
+These things only matter if
+n's-- for example, notice here
+
+that if n goes less than m,
+we're in real trouble, right?
+
+Because now the log
+is negative.
+
+Wait, what does that mean?
+
+Well, the answer is the analysis
+was assuming that n
+
+was sufficiently large
+compared with m.
+
+AUDIENCE: Why can't you just
+be like, oh, when n is for
+
+less than one, you can assume,
+well, n is 2n.
+
+In that case, you get log
+of two, which is still
+
+something or other.
+
+CHARLES LEISERSON:
+Yeah, exactly.
+
+So what happens in these things
+is if you get right on
+
+the cusp of fitting in memory,
+then these analyses like,
+
+well, what exactly is the
+answer, is dicey.
+
+But if you assume that
+it doesn't fit in,
+
+what's going to happen?
+
+Or that does fit in, what
+is going to happen?
+
+And then the analysis
+right on the edge is
+
+somewhere between there.
+
+Good.
+
+So I switched these.
+
+I said this the other
+way around.
+
+That's funny.
+
+I went through this, and then
+in my notes, I had them
+
+switched, and I said, oh my
+gosh, I did this wrong.
+
+And I've just gone through it,
+and it turns out I was right
+
+in my notes.
+
+Now, one of the things, if you
+look at what's going on--
+
+let's just go back to
+this picture here.
+
+What's going on here is each one
+of the passes that we're
+
+doing to do a merge is basically
+taking n over B
+
+misses to do a binary merge.
+
+We're going through all the data
+to merge just two things,
+
+and traversing all the data.
+
+So you can imagine, what would
+happen if I did, say, a
+
+four-way merge?
+
+With a four-way merge, I could
+actually merge four things
+
+with only a little bit more
+than n over B misses.
+
+In fact, that's what we're going
+to analyze in general.
+
+So the idea is that we can
+improve our cache efficiency
+
+by doing multi-way merging.
+
+So the idea here is, let's merge
+R, which is, let's say,
+
+less than n subarrays
+with a tournament.
+
+So here are R subarrays, and
+here's they're each, let's
+
+say, is of size n over R. And
+what we're going to do is
+
+merge them with a tournament, so
+this is a tournament where
+
+we say, who's the winner of
+these two, who's the winner of
+
+these two, et cetera.
+
+And then whoever wins at the top
+here, we take them and put
+
+them in the output, and then
+we repeat the tournament.
+
+Now let's just look
+what happens.
+
+It takes order R work to produce
+the forced output.
+
+So we got R things here.
+
+To playoff this tournament,
+there are R nodes here.
+
+They each have to do a constant
+amount of comparing
+
+before I end up with a single
+value to put in the output.
+
+So it costs me R to get
+this thing warmed up.
+
+But once I find the winner,
+and I remove the winner
+
+whatever chain he might have
+come along, how quickly can I
+
+repopulate the tournament
+with the next guy?
+
+The next guy only has to play
+the tournament on the path
+
+that was there.
+
+All the other matches,
+we know who won.
+
+So the second guy only cost me
+log R to produce the next guy.
+
+And the next guy is log R, and
+so once we get going, to do an
+
+R-way merge only costs me
+log R work per element.
+
+So the total work in merging is
+R, to get started, plus n
+
+log R. Well, R is less than n,
+so that's just n log R total
+
+to do the merging.
+
+That's the work.
+
+Now, let's take a look at what
+happens if I now do merge sort
+
+with R-way merges.
+
+So what I do is if I have only
+one element, then it's going
+
+to cost me order one time to
+merge it, because there's
+
+nothing to do, just put
+it in the output.
+
+Otherwise, I've got R problems
+of size n over R that I'm
+
+going to merge, and my
+merge takes n log R
+
+time to do the merge.
+
+So if I look at the recursion
+tree, I have n log R here
+
+starting here, then I branch R
+ways, and then I have n over R
+
+log R to do the R-way branching
+at the next level, n
+
+over R squared log R at the
+next level, et cetera.
+
+AUDIENCE: You said that the
+cost of processing is R.
+
+CHARLES LEISERSON:
+--is n log R.
+
+AUDIENCE: But is--
+
+CHARLES LEISERSON: Upfront,
+there's an order R cost, but
+
+the order R cost is dominated
+by the n log R, so we don't
+
+have to count that separately.
+
+We just have to worry
+about this guy.
+
+So as I go through here, I
+basically end up having a tree
+
+which is only log base R of n
+tall, because I'm dividing
+
+things into R pieces
+each time, rather
+
+than into two pieces.
+
+So I only go log base R steps
+till I get to the base case.
+
+But I'm doing an R-way merge,
+so the number of
+
+leaves is still n.
+
+But now when I add across here,
+I get n times log R, and
+
+I go across here, I get n times
+log R, because I got R
+
+copies of the same thing.
+
+Now I've got R squared times
+n over R squared
+
+log R, and so forth.
+
+And so at every level, I have
+n log R. So I have n log R
+
+times the number of levels here,
+which is log base R of
+
+n, plus the order n work at
+the bottom, which we can
+
+ignore because it's going
+to be dominated.
+
+And so what you notice here is,
+what's log base R of n?
+
+That's just log n over log R.
+So the log Rs cancel, and I
+
+get n log n plus n, which
+is just n log n.
+
+So after all that work, we still
+do the same amount of
+
+work, whether I do binary
+merging or R-way merging, the
+
+work is the same.
+
+But there's kind of
+a big difference
+
+when it comes to caching.
+
+So it's the same work as
+binary merge sort.
+
+So let's take a look
+at the caching.
+
+So let's assume that my
+tournament fits in the cache.
+
+So I want to make sure that R is
+less than m over B for some
+
+constant R. So when I do
+constant way, when I consider
+
+the R-way merging of contiguous
+arrays of total
+
+size n, the entire tournament
+plus 1 block from each array
+
+can fit in cache.
+
+So the tournament is never going
+to be responsible for
+
+generating cache misses, because
+I'm going to leave the
+
+tournament in memory.
+
+So if I'm the optimal algorithm,
+it's going to say,
+
+let's just leave the tournament
+in memory and bring
+
+in all the other things as
+we do the operation.
+
+Question?
+
+AUDIENCE: [INAUDIBLE]
+
+CHARLES LEISERSON: Those circles
+that I had, the tree.
+
+AUDIENCE: Is that a cumulative
+list of the elements that
+
+you've merged in already?
+
+CHARLES LEISERSON: I'm sorry.
+
+Is the--
+
+AUDIENCE: Is it a cumulative
+list of the length arrays that
+
+you've merged already?
+
+CHARLES LEISERSON: No, no, no.
+
+You haven't merged them.
+
+Let's just go back
+and make sure we
+
+understand the algorithm.
+
+The algorithm says that what we
+do is we compare the head
+
+of this pair and we produce a
+single value here, for which
+
+whatever is-- because
+these are already
+
+sorted to do the merge.
+
+These are already sorted.
+
+So I just have the minimum of
+these two here, and the
+
+minimum of these two here,
+and the minimum of all
+
+four of them here.
+
+So it's repeated.
+
+When we get to the top, we have
+now the minimum of all of
+
+these guys, and that's the guy
+that's the minimum overall, we
+
+put him in the output array.
+
+And now we walk back down the
+path that he came from, and
+
+what we do is we say, oh, this
+guy had a-- let's walk down
+
+the path, let's say we
+get to this guy.
+
+Let's advance the pointer
+in here and
+
+bring out another element.
+
+And now we play off the
+tournament here, play off the
+
+guy here, and he advances, and
+he advances, whatever.
+
+And now some other path
+may be the minimum.
+
+But it only took
+me log n work.
+
+I'm only keeping copies of the
+element, if you will, or the
+
+results of the comparisons along
+this in the tree here.
+
+And that tree, we're saying,
+fits in the cache, plus 1
+
+block, the first block.
+
+Whatever cache block fits in
+each of these arrays, no
+
+matter how much we've gone
+down, one of those
+
+is fitting in memory.
+
+So then what happens here is the
+entire tournament plus one
+
+block from each memory can fit
+in cache, and so therefore the
+
+number of cache misses that I'm
+going to have when I do
+
+the merge it's just essentially
+the time to take
+
+faults on that one cache block
+whenever I exceed it in each
+
+array, plus the one for the
+output that's similar.
+
+And so the total number of cache
+misses that I'm going to
+
+have is going to be n over B,
+because I'm just striding
+
+straight through memory, and
+that tournament, I don't have
+
+to worry about, because
+it's sitting in cache.
+
+And there's enough sitting in
+cache that all the other
+
+stuff, I can just keep one block
+from each of them in
+
+memory and still expect
+to get it.
+
+In fact, you need the tall cache
+assumption to assume
+
+that they all fit in memory.
+
+So therefore, the R-way merge
+sort is then, if it's
+
+sufficiently small, once again,
+we have the case that
+
+it fits in memory so I only have
+the cold misses to get
+
+there, n over B, if
+n is less than cm.
+
+And otherwise, it's R copies of
+the number of cache misses
+
+for n over R, plus n over B.
+Because this is what it took
+
+us here to do the merge.
+
+We get only n over B faults when
+we merge, as long as the
+
+tournament fits in cache.
+
+If the tournament doesn't fit
+in cache, it's a more
+
+complicated analysis.
+
+AUDIENCE: --n over B,
+that's cold misses.
+
+You're getting the stuff--
+
+CHARLES LEISERSON: Yeah,
+basically, it's the cold
+
+misses on the data,
+yes, basically.
+
+Good.
+
+So now, let's do the recursion
+tree for this.
+
+So we basically have n over B
+that we're going to pay at
+
+every level, dividing by R, et
+cetera, down to the point
+
+where things fit in cache.
+
+And by the time it fits in
+cache, it's going to be m over
+
+B, because n will be
+approximately m, just as we
+
+had before when we were
+doing the binary case.
+
+As soon as the subarray
+completely fits in memory, I
+
+don't have to when I'm
+doing the sorting.
+
+So this is now analyzing not the
+merging, this is analyzing
+
+the sorting now.
+
+This is the sorting,
+not the merging.
+
+So we get down to m over B, and
+I've gone now log base R,
+
+not log base 2 as we
+did before, but log
+
+base R n over cm.
+
+The number of leaves is n over
+cm, and so when I multiply
+
+this out, I get the same n over
+B here, and I've got n
+
+over B at every level here.
+
+So where's the win?
+
+The win is that I have only
+log base R of n over cm,
+
+rather than log base 2 levels
+in the tree, because the
+
+amount that every level
+cost me was the same,
+
+asymptotically.
+
+So when I add it up, I get n
+over B log base R of n over m,
+
+instead of n over B log
+base 2 of n over m.
+
+So how do we tune R?
+
+Well if we just look at this
+formula here, if I want to
+
+tune R, what should I
+do to R to make this
+
+be as small as possible?
+
+Make it as big as possible.
+
+But I had to assume that R was
+less than some constant times
+
+m so that it fits in cache.
+
+So that's, in fact, what I do,
+is I say R is m over B. So it
+
+fits in cache, we have at least
+one block for each thing
+
+that we're merging.
+
+And then when we do the analysis
+now, I take log base
+
+m over B here, and that's
+compared to the binary one,
+
+which was log base 2, which is
+a factor of-- because this is
+
+just log 2 over log base--
+
+of log of m over B savings
+in cache misses.
+
+Now, is that a significant
+number?
+
+Let's take a look.
+
+So if your l one cache is 32
+kilobytes, and we have cache
+
+lines of 64 bytes, that is
+basically the difference in
+
+the exponents, 9x savings.
+
+For l two cache, we get
+about a 12x savings.
+
+For l three, we get about
+a 17x savings.
+
+Now of course, there are some
+other constants going on in
+
+here, so you can't be absolutely
+sure that it's
+
+exactly these numbers, but it's
+going to be proportional
+
+to these numbers.
+
+So that's pretty good savings
+to do multi-way merging.
+
+So generally when you merge,
+don't merge pairs.
+
+Not a very good way of doing
+it if you want to take good
+
+advantage of cache.
+
+May give you some ideas for how
+to improve some sorts that
+
+you might have looked at.
+
+Now it turns out that there's
+a cache oblivious sorting
+
+algorithm, where you don't
+actually have--
+
+that was a cache aware algorithm
+that knew the size
+
+of the cache, and we tune
+R to get there.
+
+There is an algorithm called
+funnelsort, which is based on
+
+recursively sorting and
+n to the 1/3 groups of
+
+n to the 2/3 items.
+
+And then you merge the sorted
+groups with a merging process
+
+called an n to the 1/3 funnel.
+
+So this is more for fun,
+although the sorting
+
+algorithm, in my experience,
+from what others have told me
+
+about implementing it and so
+forth, is probably about 30%
+
+slower than the best hand-tuned
+algorithm.
+
+Whereas with matrix
+multiplication, the cache
+
+oblivious algorithms are as
+good as any cache aware
+
+algorithm as a practical matter,
+here, they're off by
+
+about 20% or 30%.
+
+So interesting research topic
+is build one of these things
+
+and make it really efficient
+so that it can compete with
+
+real sorts.
+
+So the k funnel merges k cubed
+items in k sorted lists,
+
+incurring this many
+cache funnels.
+
+Here, I did put in the one, for
+people who are concerned
+
+about the ones.
+
+And so then, you get this
+recurrence for the cache
+
+misses, because you solve n to
+the 1/3 problems of size n to
+
+the 2/3 recursively, plus
+this amount for merging.
+
+And that ends up giving you this
+bound, which turns out to
+
+be asymptotically optimal.
+
+And the way it works is there's
+basically, a k funnel
+
+is constructed recursively.
+
+And the idea is that what we
+have is, we have recursive k
+
+funnels, so this is going to be
+a merging process, that is
+
+going to produce k cubed items
+by having k to the 3/2 buffers
+
+that each are taking the square
+root of k guys and
+
+producing k guys out.
+
+So each of these guys is going
+to produce k, and the square
+
+root of k of them for a total
+of k to the 3/2, but each of
+
+these is going to be length
+square root of k, so we end up
+
+with k cubed.
+
+and And they basically feed each
+other, and then they get
+
+merged with their own k thing,
+and each of these then
+
+recursively is constructed
+the same way.
+
+And the basic idea is that you
+keep filling the buffers, I
+
+think I say this here, so that
+all these buffers end up being
+
+in contiguous storage.
+
+And the idea is, rather than
+going and just getting one
+
+element out as you do in a
+typical tournament, as long as
+
+you're going to go merge, let's
+merge a lot of stuff and
+
+put it into our buffer
+so we don't have to
+
+go back here again.
+
+So you sort of batch your
+merging in local regions, and
+
+that ends up using the
+cache efficiently
+
+in the local regions.
+
+Enough of sorting.
+
+Let's go on to physics.
+
+So many of you are probably
+studying in your linear
+
+algebra class or elsewhere,
+the heat equation.
+
+So, people familiar with
+heat diffusion?
+
+So it's a common one to
+do, and these were--
+
+I have a former student,
+Matteo Frigo, who is a
+
+brilliant coder on anything
+cache oblivious.
+
+He's got the best
+code out there.
+
+So the 2D heat equation, what we
+do is let's let u(t, x, y)
+
+be the temperature at time
+t at point (x, y).
+
+And now you can go through the
+physics and come up with an
+
+equation that looks like this,
+which says that basically the
+
+partial of u with respect to t
+is proportional to the sum of
+
+the second partials with
+respect to x and
+
+with respect to y.
+
+So basically what that says is,
+the hotter the difference
+
+between two things, the quicker
+things are going to
+
+adjust, the quicker
+the temperature
+
+moves between them.
+
+And alpha is the thermal
+diffusivity, which has--
+
+different materials have
+different thermal
+
+diffusivities.
+
+Say that three times fast.
+
+So if we do a simulation, we
+can end up with heats, say,
+
+put like this, and after
+it looks like this.
+
+See if we can get this
+running here.
+
+So now, let me see.
+
+So I can move my cursor around
+and make things.
+
+You can just sort of see
+that it simulates.
+
+You can see the simulation
+is actually pretty slow.
+
+Now, on my slide, I have a
+thing here that says--
+
+let's see if this breaks
+when we do it again.
+
+There we go.
+
+So we're getting around 100
+frames per minute in doing
+
+this simulation.
+
+And so how does this
+simulation work?
+
+So let's take a look at that.
+
+It's kind of a neat problem.
+
+So this is what happened
+when I did 6.172
+
+for a little while.
+
+It basically gave me that after
+a while, because it just
+
+sort of averages things,
+smears it out.
+
+So what's going on?
+
+Let's look at it in one
+dimension, because it's easier
+
+to understand than if we
+take on two dimensions.
+
+So assuming that we have,
+say, a bar which has no
+
+differential in this direction,
+
+only in this direction.
+
+So then we get to drop the
+partials with respect to y.
+
+So if I take a look at that,
+what I can do is what's called
+
+a finite difference
+
+approximation, which you probably--
+
+who's studied finite
+differences?
+
+So a few people.
+
+It's OK if you haven't.
+
+That's OK if you haven't, I'll
+teach it to you now.
+
+And then you're free to forget
+it, because that's not the
+
+part that I want you to
+understand, but it is
+
+interesting.
+
+So what I can do is look at the
+partial, for example, with
+
+respect to t, and just do an
+approximation the says, well,
+
+let me perturb t
+a little bit--
+
+that's what it means.
+
+So I add delta t minus u of t
+divided by t plus delta t
+
+minus t, which gives
+me delta t.
+
+And I can use that as an
+
+approximation for this partial.
+
+Then on the right hand side--
+well first of all, let me get
+
+the first derivative
+with respect to x.
+
+And basically here what I'll do
+is I'll do an approximation
+
+where I take x plus delta x over
+2 minus x minus delta x
+
+over 2, and once again, the
+differences in the terms there
+
+ends up being delta x.
+
+And now I use that to
+take the next one.
+
+So basically, to take this
+one, I basically take the
+
+partial with respect to delta
+x over 2, minus the partial
+
+with x minus delta x over 2, and
+take the partial of that,
+
+do the approximation.
+
+And what happens is, if you
+look at it, when I take a
+
+partial here I'm adding delta
+x over 2 twice, so I end up
+
+getting just a delta x here,
+and then the two things on
+
+either side combined give me my
+original one, 2 times u(t,
+
+x), and then another one here,
+and now the whole thing over
+
+delta x squared.
+
+And so what I can do is to
+reduce this heat equation,
+
+which is continuous, to
+something that we can handle
+
+in a computer, which is
+discrete, by saying OK, let's
+
+just do this approximation that
+says that this term must
+
+be equal to that term.
+
+And if you've studied the linear
+algebra that said that
+
+there are all kinds of
+conditions on convergence, and
+
+stability, and stuff like that,
+that are actually quite
+
+interesting from a numerical
+point of view, but we're not
+
+going to get into it.
+
+But basically, I've just taken
+that equation here and said,
+
+OK, that's my approximation
+for this one.
+
+And now what do I have here?
+
+I've got u of t plus delta t,
+and u things u of t, and then
+
+over here, they're all with t,
+but now the deltas are in--
+
+whoops, that should have
+been a delta x there.
+
+I don't know how
+that got there.
+
+That should be a
+delta x there.
+
+They're all in spatial
+over here.
+
+So what I can do is take this,
+and do an iterative process to
+
+compute this.
+
+And so the idea is, let me take
+this and throw this term
+
+onto the right hand side, and
+look at u of t plus delta t as
+
+if it's t plus 1.
+
+Let me make my delta be
+one, essentially.
+
+Throw the delta t over here
+times the alpha over delta x1,
+
+and then I get basically u of
+tx is based on u of t of x
+
+plus 1 and of x and x minus 1.
+
+As I say, there's a typo here.
+
+That should be a delta t.
+
+So what that says is that if I
+look at my one-dimensional
+
+process proceeding through
+time, what I'm doing is
+
+updating every point here based
+on the three points
+
+below it, diagonally
+to the right, and
+
+diagonally to the left.
+
+So this guy can be updated
+because of those.
+
+These we're not going update,
+because they're the boundary.
+
+So these can be fixed.
+
+In a periodic stencil,
+they may even wrap
+
+around like a torus.
+
+So basically, I can go through
+and update all these with
+
+whatever that hairy
+equation is.
+
+And this is basically what
+the code is that I
+
+showed you is doing.
+
+It just keeps updating everyone
+based on three until
+
+I've gone through a bunch of
+time, and that's how the
+
+system evolves.
+
+So any questions about
+how I got to here?
+
+So we're going to now
+look at this purely
+
+computer sciencey now.
+
+We don't have to understand
+any of those equations.
+
+We just have to understand
+the structure.
+
+The structure is that we're
+updating t plus 1 based on
+
+stuff on three points with
+some function that some
+
+physicist oracle gave
+us out of the blue.
+
+And so here is a pretty simple
+algorithm to do it.
+
+I basically have what's called
+the kernel, which does this
+
+updating, basically updating
+each one based on things.
+
+And what I'm going to do for
+computer science is I don't
+
+need to keep all the
+intermediate values.
+
+And so what I'm going
+to do is do what's
+
+called an even-odd trick.
+
+Basically if I have one row,
+I compute the next row into
+
+another array, and then I'll
+reuse that first array-- it's
+
+all been used up--
+
+and go back to the first one.
+
+So basically here, I'm just
+going to update t plus 1 mod
+
+2, and just allocate two arrays
+of size n, and just do
+
+modding all the way up.
+
+Is that clear?
+
+And other than that, it's
+basically doing the same
+
+thing, and I'm doing a little
+bit of fancy arithmetic here
+
+by passing--
+
+see stuff, where I'm passing the
+pointer to where I am in
+
+the array, so I only
+have to update it
+
+locally within the array.
+
+So I don't have to double
+indexing once I'm in the
+
+array, because I'm already
+indexed into the part of the
+
+array that I'm going to use, and
+then I am doing flipping.
+
+So this is just a little
+bit of cleverness.
+
+You might want to study
+this later.
+
+So what's happening then is I
+have this double nested loop
+
+where I have a time loop on the
+outside, and a space loop
+
+on the inside, and I'm basically
+going through and
+
+using a stencil of this shape,
+this is called a three point
+
+stencil, because you're
+basically taking three points
+
+to update one point.
+
+And now if I imagine that this
+dimension is bigger, n here is
+
+bigger than my cache size,
+what's going to happen?
+
+I'm going to take a cache fault
+here, these are all cold
+
+misses, et cetera.
+
+But when I get back to the
+beginning here, if I use LRU,
+
+nothing is going to be in memory
+that I happened to
+
+update over here.
+
+So I have to go and I
+take a cache fault
+
+on every cache line.
+
+And so if I'm going t steps into
+the future from where I
+
+started, I basically have n
+times t updates, and I save a
+
+factor of B, because I get the
+spatial locality because the u
+
+of t minus 1, u of t, and u of t
+plus 1, are all generally on
+
+the same-- are nearby, and all
+within one cache line.
+
+Question?
+
+AUDIENCE: The x's, what
+are the x's for?
+
+CHARLES LEISERSON: Sorry.
+
+I should have put the
+legend on here.
+
+The x's are a miss.
+
+So I do a miss when I update
+these, and then these I don't
+
+miss on, because it
+was brought in
+
+when I accessed that.
+
+And then I do a miss,
+and I'll do it--
+
+so basically I do it, then I
+shift over the stencil by one,
+
+and then I won't get a miss.
+
+So I'm just looking at the
+misses on the reads, not
+
+misses on the writes.
+
+I should have made
+that clear, too.
+
+But the point is, the writes
+don't help you, because it's
+
+all out of memory by the
+time I get up here.
+
+To the second row, if this is
+longer than my cache size,
+
+none of that's there
+if I'm using LRU.
+
+AUDIENCE: You have also a miss,
+like you need to get two
+
+[INAUDIBLE].
+
+CHARLES LEISERSON: Yeah, but
+what I'm saying is I'm only
+
+looking at the read misses.
+
+Yes, there are write misses as
+well, but basically, I'm only
+
+doing the read misses.
+
+You can look at the write
+misses as well.
+
+It makes the picture messier.
+
+So we've basically
+have nt over b.
+
+However this, let me tell
+you, is the way that
+
+everybody codes it.
+
+and And if you have a machine
+where you have any bandwidth
+
+issues to memory, especially for
+these large problems, this
+
+is not a very good way to
+do it, as it turns out.
+
+So it turns out that what you
+want to do is, as we've seen,
+
+divide and conquer is a really
+good way to do it.
+
+But in this case, when we're
+doing divide and conquer,
+
+we're actually not going to use
+rectangles, we're going to
+
+use trapezoids.
+
+And the reason is that a
+trapezoid has the nice
+
+property that--
+
+notice that if I have all these
+points in memory, then
+
+notice that I can compute all
+the guys that are read on the
+
+next level, and then I can
+compute all the guys that are
+
+next on the next level.
+
+And so for example, if you
+imagine that this part here
+
+fit within cache, I could
+actually keep going.
+
+I didn't have to stop here, I
+could keep going right up to a
+
+triangle if I wanted to, and
+compute all the values without
+
+having any more cache misses
+than those needed to bring in,
+
+essentially, one row--
+
+two rows, actually, because
+I'm reusing the
+
+rows as I go up.
+
+So what we're going to do is
+traverse trapezoidal regions
+
+of space-time points such that
+the points are between an
+
+upper limit, T1, and a low one,
+T0, and between an x0 and
+
+an x1, where now I have slopes
+here that are going to be, in
+
+general, this is
+plus 1 minus 1.
+
+And in fact, sometimes it will
+be straight, in which case
+
+we'll call it 0.
+
+It's really the inverse of the
+slope, but we'll still call it
+
+zero rather than infinity.
+
+So it's 1 over the slope.
+
+There's a name for
+that, right?
+
+Is that called the
+run or something?
+
+I forget, I don't remember
+my calculus.
+
+So that's what we're
+going to do.
+
+And we're going to leave the
+upper and right borders undone
+
+and include, so it's going
+to be a sort of half open
+
+trapezoid on the left and
+bottom, closed on the left and
+
+bottom, and open on
+the top and right.
+
+So the width is basically the
+midpoint here, and the height
+
+is the height, because they're
+always going to have
+
+parallel axes here.
+
+So here's how are our recursion
+is going to work.
+
+If the height is 1, then we
+can compute all space-time
+
+points in any way we want.
+
+I can just go through them if
+I want, because they're all
+
+independent.
+
+None depends on anybody else.
+
+So that's going to
+be our base case.
+
+If the width is greater than
+twice the height, however,
+
+then what we're going to do
+is we're going to cut the
+
+trapezoid through the middle
+of the slope of minus 1.
+
+And that will produce two new
+trapezoids, which we then will
+
+recursively compute all
+the elements of.
+
+So I'll start out with
+a trapezoid.
+
+Basically, if it ends up that
+it's a long and wide one, I'm
+
+going to make what's called a
+space cut, and cut it this
+
+way, and then I'm going to
+recursively do this one and
+
+then this one.
+
+And notice that I can
+do that because--
+
+all these guys I can do, but
+then when I get to the border
+
+here, this will already have
+been done by the time I'm
+
+computing these guys.
+
+So the requirement is that
+I've got to do things
+
+according to that map of triples
+that I showed you
+
+before, but I don't have to
+do them in the same order.
+
+I don't have to do the whole
+bottom row first.
+
+In this case, I can compute the
+whole trapezoid here, and
+
+then I can compute this
+trapezoid here, and then all
+
+the values that I'll need will
+have already been computed
+
+over here, that are on the
+boundary of this trapezoid.
+
+The other type of cut I'll
+do is what happens when a
+
+trapezoid gets too
+tall for me.
+
+So if the trapezoid is too tall,
+then what we'll do is
+
+we'll slice it through the
+middle, but the other way.
+
+We call that a time cut.
+
+So we won't take it all the way
+through time, we'll only
+
+take it partially
+through time.
+
+Now you can show, and I'm not
+going to show this in detail,
+
+but you can show that if I do
+this, my trapezoids are always
+
+sort of medium sized.
+
+I never get long, long
+skinny ones.
+
+If I start with something that's
+sort of got a good
+
+aspect ratio, I maintain a good
+aspect ratio through the
+
+entire code.
+
+So here's the implementation.
+
+This is what Matteo Frigo wrote,
+and I've modified it a
+
+little bit.
+
+So basically, we pass in it
+the values that let us
+
+identify the trapezoid, t0, t1,
+x0, and then the slope on
+
+the left side, x1 in the slope
+on the right side, where the
+
+dx0 and the dx1s are all either
+0, 1, or minus 1.
+
+And then what I do is I look at
+what the height is that my
+
+trapezoid is going
+to operate on.
+
+And if the height is 1, well,
+then I just run through all
+
+the elements, and I just
+compute the kernel--
+
+that program that I showed
+you before, that kernel--
+
+on all the elements.
+
+Nothing really to be done there,
+just go through and
+
+compute them individually
+with a four loop.
+
+Otherwise, if I've got the
+situation where the trapezoid
+
+is big, then I do this
+comparison, which I promise
+
+you-- you can work out the
+math if you wish--
+
+which I promise you tells you
+whether or not it's more than
+
+twice the height, as I said
+before, whether the width is
+
+more than twice the height.
+
+And if so, I compute the middle
+point, and then I
+
+partition it into two
+trapezoids, and I
+
+recursively call them.
+
+And otherwise, I simply cut the
+time in half, and then I
+
+do the bottom half and
+then the upper half.
+
+So getting all those parameters
+exactly right takes
+
+a little bit of thinking,
+makes my brain hurt, but
+
+Matteo is brilliant at
+this kind of coding.
+
+So let's see how
+well this does.
+
+So I'm not going to do a
+detailed analysis that I did
+
+before, but basically what's
+going on is at this level, if
+
+I'm doing divide and conquering,
+I'm only doing a
+
+constant amount of work
+managing this stuff.
+
+So my caches that I'm taking
+in the internal part of the
+
+tree are all going
+to be order one.
+
+Now each leaf is going to
+represent a trapezoid, which
+
+is going to be approximately h
+times w, where h and w are
+
+approximately equal, because
+they're going to be shaped--
+
+This is assuming I start out
+with a number of iterations to
+
+do that is at least as large as
+the number of points that I
+
+have to go on.
+
+If I start out with something
+that's really thin and flat,
+
+then it's not going
+to be the case.
+
+But if I start out with
+something that's deep enough,
+
+then I'm going to be able
+to make progress in an
+
+unconventional order into
+time by moving the time
+
+non-uniformly through
+the space.
+
+So each leaf represents a fairly
+balanced trapezoid.
+
+Each leaf basically
+is going to--
+
+if you look that the direction
+of the trapezoid is in time,
+
+so this represents the spatial
+dimension, and if I have
+
+something of size w, I
+can access it with
+
+only w over B misses.
+
+And when that fits in cache,
+where w is some constant less
+
+than m, so w is order m.
+
+So each of these things that's
+a leaf is only going to occur
+
+w over B misses.
+
+Now, the total space number
+of points I have to go
+
+after is n times t.
+
+N is going to be the full
+dimension this way, t is the
+
+height that way.
+
+And so since each leaf
+has hw points, I
+
+have nt over hw leaves.
+
+And the number of internal nodes
+is just the leaves minus
+
+1, so they can't contribute
+substantially, because there's
+
+only order one misses I'm taking
+here, whereas I've got
+
+something on the order of w
+over B misses for this.
+
+So therefore, now I
+can do my math.
+
+The number of cache misses
+I'm going to take is--
+
+well, how many leaves
+do I have?
+
+nt over hw.
+
+And what does each
+one cost us?
+
+W over B.
+
+And so now, when I multiply that
+out, well, hw is about m
+
+squared, and w over B is about m
+over B. And so I get nt over
+
+MB as being the total
+number of savings.
+
+so whereas the original
+algorithm only got nt over B,
+
+we've got this factor of a
+memory cache size in there
+
+showing us that we have far
+fewer cache misses.
+
+So the cache misses end up not
+being an issue for this.
+
+Any questions about that?
+
+So I want to show you a
+simulation of this three point
+
+stencil and comparing
+the two things.
+
+So this is going to be the
+looping version, where the red
+
+dots are where the cache misses
+are, and this is going
+
+to be the trapezoidal one.
+
+And basically, I have an n of 95
+and a t of 87, and what I'm
+
+going to do is assume a fully
+associative LRU cache that
+
+fits four points on a cache
+line, where the cache size is
+
+32, two to the fifth as opposed
+to two to the 15th,
+
+it's really little.
+
+If I get a cache hit, I'm going
+to call it one cycle.
+
+If I get a cache miss, I'm going
+to call it 10 cycles.
+
+We're going to race them.
+
+So on the left is the
+current world
+
+champion, the looping algorithm.
+
+And on the right is the cache
+oblivious trapezoid algorithm.
+
+So let's go.
+
+So you can see that it's
+basically, it's made a space
+
+cut there, but it's made a time
+cut across the top there.
+
+It said, this is too tall, so
+let me cut it this way.
+
+And that guy's, meanwhile,
+taking all those-- you can see
+
+how many cache misses
+he's taking.
+
+Let's speed him up.
+
+That's one way you can do
+it, is make it think.
+
+So let's see what happens if I
+have a cache of size eight.
+
+So here we go.
+
+I think I'm just doing
+the same thing.
+
+I know I can show
+you the cuts.
+
+Can I show you the cuts?
+
+I know.
+
+I think it's because I'm not--
+
+OK, let's try it.
+
+There we go.
+
+Now I'm showing the cuts
+as they go on.
+
+Let's do that again.
+
+We'll go fast and do it again.
+
+So those are the cuts that it's
+making to begin with as
+
+it's doing the divide
+and conquer.
+
+So I think this is the
+same size cache.
+
+So now I think I'm doing
+a bigger cache.
+
+I think I did a bigger cache,
+but I'm not sure I gave the
+
+other guy a bigger cache.
+
+Yeah, because it doesn't matter
+for the guy on the
+
+left, right?
+
+As long as the cache line is the
+same length and as long as
+
+it's not big enough, he's going
+to do the same thing.
+
+He didn't get to take advantage
+of the fact that the
+
+cache was bigger, because it
+was still smaller than the
+
+array that he's striping
+out there.
+
+Anyway, we can play with
+these all day.
+
+So if you make the cache lines
+bigger, then of course it'll
+
+go faster, because he'll
+have fewer misses.
+
+He'll get to bring it in.
+
+So let's see here.
+
+So let's now do it for real.
+
+So this is a two-dimensional
+problem.
+
+You can use the same thing
+to do what end up being
+
+three-dimensional trapezoids.
+
+In fact, you can generalize
+this trapezoid method to
+
+multiple dimensions.
+
+So this is the looping one.
+
+So let's start that one out.
+
+So it's going about 104
+frames a minute.
+
+I think by resizing it, the
+calibration is off.
+
+But in any case, let's switch to
+the cash oblivious version.
+
+Anybody notice something?
+
+Slower.
+
+Why is that?
+
+I gave code exactly
+as I had up there.
+
+No, it's not because it's
+two dimensions.
+
+AUDIENCE: [INAUDIBLE].
+
+CHARLES LEISERSON: I'm sorry?
+
+[INTERPOSING VOICES]
+
+CHARLES LEISERSON: Yeah, so now
+it's the trapezoiding at
+
+only 86 frames.
+
+What do you suppose
+is going on there?
+
+AUDIENCE: You have
+[INAUDIBLE].
+
+CHARLES LEISERSON: Yeah.
+
+So this is a case where if you
+look at the code I wrote, I
+
+went down to a t, a delta t,
+of one in my recursion.
+
+I recursed all the way down.
+
+Let's see what happens if
+instead of going all the way
+
+down, playing the trapezoid
+game on little tiny
+
+trapezoids, suppose I go down
+only to, say, when t is 10,
+
+and then do essentially
+the row major ones.
+
+So I'm basically coarsening
+the leaves of the thing.
+
+So to do that, I do this.
+
+So now we go--
+
+ah.
+
+So I have to coarsen in
+order to overcome the
+
+procedure call overhead.
+
+It has nothing to do
+with the cache.
+
+It has to the fact that the
+way that you implement
+
+recursion, recursion
+and function calls
+
+have a cost to them.
+
+And if what you're going to do
+is do a little tiny update of
+
+those few floating point
+operations--
+
+let's go back to the looping
+just to see.
+
+The looping is going
+about 107, 108, and
+
+trapezoiding at 136.
+
+So unfortunately, you need a
+voodoo variable, but it's a
+
+voodoo variable not to overcome
+the cache, but rather
+
+to deal with what's the
+overhead in using the
+
+processor when you do
+function calls.
+
+So let's see.
+
+How coarse can we make it?
+
+Let's try five, a coarsening
+of five?
+
+That's still pretty good.
+
+That's still pretty good.
+
+How about four?
+
+Still doing 131 frames
+a minute.
+
+How about three?
+
+Oh, we lost something there.
+
+How about two?
+
+So at a coarsening of two, I
+go 138, whereas the looping
+
+goes at about the same.
+
+I can't do 20.
+
+I didn't program that in.
+
+I just programmed up to 10.
+
+So if I go down to one, however,
+then you see it's not
+
+that efficient.
+
+But if I pick any number that's
+even slightly larger,
+
+that gives me just enough that
+the function call overhead
+
+ends up not being a
+
+substantial cost of the things.
+
+So let me just wrap up now.
+
+So I just have a couple
+more things.
+
+So I'm not going to really talk
+about these, but there
+
+are lots of cash oblivious
+algorithms that have been
+
+discovered in the last 10 or 15
+years for doing things like
+
+matrix transposition, which is
+similar to rotating a matrix.
+
+You can do that in a cache
+oblivious fashion.
+
+Strassen's algorithm, which
+does matrix multiplication
+
+using fewer than n
+cubed operations.
+
+The FFT can be computed in a
+cache oblivious fashion.
+
+And LUD composition
+is a popular
+
+thing to solve systems.
+
+In addition, there are cache
+oblivious data structures, and
+
+here are just a few of them.
+
+There's cache oblivious B-Trees
+and priority queues,
+
+and doing things called
+ordered-file maintenance.
+
+There's a whole raft.
+
+There's probably now several
+hundred papers written on
+
+cache oblivious algorithms, so
+something you should be aware
+
+of and understand how it is that
+you go about designing an
+
+algorithm of this nature.
+
+Not all of them are
+straightforward.
+
+For example, the FFT one does
+divide and conquer but not by
+
+dividing it into two.
+
+It divides it into square root
+of n pieces of size square
+
+root of n each in order to get
+a good cache efficient
+
+algorithm that doesn't have
+any tuning parameters.
+
+But almost all of them, since
+they're recursive, do have
+
+this annoying thing that you
+have to still coarsen the base
+
+case in order to get really good
+performance if you're not
+
+doing a lot of work in the
+leaves of the recursion.
+
+So any questions?
\ No newline at end of file
diff --git a/DDUudxi9VVo.txt b/DDUudxi9VVo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7fa8f94c9e020359977c64f09a4c3a06f72db5c4
--- /dev/null
+++ b/DDUudxi9VVo.txt
@@ -0,0 +1,7515 @@
+align:start position:0%
+ 
+all right so good morning again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody what are we doing
+
+ align:start position:0%
+everybody what are we doing
+ 
+
+ align:start position:0%
+everybody what are we doing
+today what did we do last
+
+ align:start position:0%
+today what did we do last
+ 
+
+ align:start position:0%
+today what did we do last
+time we worked on solution models then
+
+ align:start position:0%
+time we worked on solution models then
+ 
+
+ align:start position:0%
+time we worked on solution models then
+we were working on on
+
+ align:start position:0%
+we were working on on
+ 
+
+ align:start position:0%
+we were working on on
+and things like that so we're continuing
+
+ align:start position:0%
+and things like that so we're continuing
+ 
+
+ align:start position:0%
+and things like that so we're continuing
+to sort of um gently dip our our first
+
+ align:start position:0%
+to sort of um gently dip our our first
+ 
+
+ align:start position:0%
+to sort of um gently dip our our first
+our toes and our ankles into the sort of
+
+ align:start position:0%
+our toes and our ankles into the sort of
+ 
+
+ align:start position:0%
+our toes and our ankles into the sort of
+the deep end of the pool of the class
+
+ align:start position:0%
+the deep end of the pool of the class
+ 
+
+ align:start position:0%
+the deep end of the pool of the class
+which is you know binary phase diagrams
+
+ align:start position:0%
+which is you know binary phase diagrams
+ 
+
+ align:start position:0%
+which is you know binary phase diagrams
+and free energy composition diagram so
+
+ align:start position:0%
+and free energy composition diagram so
+ 
+
+ align:start position:0%
+and free energy composition diagram so
+we're getting deeper into the pool now
+
+ align:start position:0%
+we're getting deeper into the pool now
+ 
+
+ align:start position:0%
+we're getting deeper into the pool now
+um so what I want to start with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is some basic results for the
+
+ align:start position:0%
+is some basic results for the
+ 
+
+ align:start position:0%
+is some basic results for the
+equilibrium condition for multi
+
+ align:start position:0%
+equilibrium condition for multi
+ 
+
+ align:start position:0%
+equilibrium condition for multi
+component heterogeneous systems
+
+ align:start position:0%
+component heterogeneous systems
+ 
+
+ align:start position:0%
+component heterogeneous systems
+including Gibbs phase Rule and then
+
+ align:start position:0%
+including Gibbs phase Rule and then
+ 
+
+ align:start position:0%
+including Gibbs phase Rule and then
+we'll walk through a number of slides
+
+ align:start position:0%
+we'll walk through a number of slides
+ 
+
+ align:start position:0%
+we'll walk through a number of slides
+showing you binary phase diagrams how
+
+ align:start position:0%
+showing you binary phase diagrams how
+ 
+
+ align:start position:0%
+showing you binary phase diagrams how
+they look some interpretation of them
+
+ align:start position:0%
+they look some interpretation of them
+ 
+
+ align:start position:0%
+they look some interpretation of them
+the reading for today includes uh
+
+ align:start position:0%
+the reading for today includes uh
+ 
+
+ align:start position:0%
+the reading for today includes uh
+reading in both the Hoff and Callister
+
+ align:start position:0%
+reading in both the Hoff and Callister
+ 
+
+ align:start position:0%
+reading in both the Hoff and Callister
+and I hope that people are able to do
+
+ align:start position:0%
+and I hope that people are able to do
+ 
+
+ align:start position:0%
+and I hope that people are able to do
+both because there's a lot of uh
+
+ align:start position:0%
+both because there's a lot of uh
+ 
+
+ align:start position:0%
+both because there's a lot of uh
+foundational uh sort of um context that
+
+ align:start position:0%
+foundational uh sort of um context that
+ 
+
+ align:start position:0%
+foundational uh sort of um context that
+isn't really appropriate for you know um
+
+ align:start position:0%
+isn't really appropriate for you know um
+ 
+
+ align:start position:0%
+isn't really appropriate for you know um
+a Blackboard or whiteboard lecture but
+
+ align:start position:0%
+a Blackboard or whiteboard lecture but
+ 
+
+ align:start position:0%
+a Blackboard or whiteboard lecture but
+you kind of have to be familiar with
+
+ align:start position:0%
+you kind of have to be familiar with
+ 
+
+ align:start position:0%
+you kind of have to be familiar with
+just you know how phase diagrams look
+
+ align:start position:0%
+just you know how phase diagrams look
+ 
+
+ align:start position:0%
+just you know how phase diagrams look
+and how they're presented differently in
+
+ align:start position:0%
+and how they're presented differently in
+ 
+
+ align:start position:0%
+and how they're presented differently in
+different resources and and how they're
+
+ align:start position:0%
+different resources and and how they're
+ 
+
+ align:start position:0%
+different resources and and how they're
+used so we'll try to give you some of
+
+ align:start position:0%
+used so we'll try to give you some of
+ 
+
+ align:start position:0%
+used so we'll try to give you some of
+that today as well but we'll start with
+
+ align:start position:0%
+that today as well but we'll start with
+ 
+
+ align:start position:0%
+that today as well but we'll start with
+something a little bit more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+specific equilibrium in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multicomponent heterogeneous systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we actually haven't done this
+
+ align:start position:0%
+okay so we actually haven't done this
+ 
+
+ align:start position:0%
+okay so we actually haven't done this
+yet we've done equilibrium in
+
+ align:start position:0%
+yet we've done equilibrium in
+ 
+
+ align:start position:0%
+yet we've done equilibrium in
+multicomponent homogeneous systems that
+
+ align:start position:0%
+multicomponent homogeneous systems that
+ 
+
+ align:start position:0%
+multicomponent homogeneous systems that
+was reacting gas systems and then we've
+
+ align:start position:0%
+was reacting gas systems and then we've
+ 
+
+ align:start position:0%
+was reacting gas systems and then we've
+studied solution models those are models
+
+ align:start position:0%
+studied solution models those are models
+ 
+
+ align:start position:0%
+studied solution models those are models
+of phases which have multiple components
+
+ align:start position:0%
+of phases which have multiple components
+ 
+
+ align:start position:0%
+of phases which have multiple components
+but um we've studied them in isolation
+
+ align:start position:0%
+but um we've studied them in isolation
+ 
+
+ align:start position:0%
+but um we've studied them in isolation
+that is a model of a single phase a
+
+ align:start position:0%
+that is a model of a single phase a
+ 
+
+ align:start position:0%
+that is a model of a single phase a
+given phase
+
+ align:start position:0%
+given phase
+ 
+
+ align:start position:0%
+given phase
+and so it hasn't been heterogeneous yet
+
+ align:start position:0%
+and so it hasn't been heterogeneous yet
+ 
+
+ align:start position:0%
+and so it hasn't been heterogeneous yet
+heterogeneous means more than one phase
+
+ align:start position:0%
+heterogeneous means more than one phase
+ 
+
+ align:start position:0%
+heterogeneous means more than one phase
+but now we're sort of going to start
+
+ align:start position:0%
+but now we're sort of going to start
+ 
+
+ align:start position:0%
+but now we're sort of going to start
+putting it all
+
+ align:start position:0%
+putting it all
+ 
+
+ align:start position:0%
+putting it all
+together so let's draw a general picture
+
+ align:start position:0%
+together so let's draw a general picture
+ 
+
+ align:start position:0%
+together so let's draw a general picture
+of this and derive the equilibrium
+
+ align:start position:0%
+of this and derive the equilibrium
+ 
+
+ align:start position:0%
+of this and derive the equilibrium
+condition for
+
+ align:start position:0%
+condition for
+ 
+
+ align:start position:0%
+condition for
+this I'm going to need new
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sharpies I add that to my shopping
+
+ align:start position:0%
+Sharpies I add that to my shopping
+ 
+
+ align:start position:0%
+Sharpies I add that to my shopping
+list maybe this one is a little better
+
+ align:start position:0%
+list maybe this one is a little better
+ 
+
+ align:start position:0%
+list maybe this one is a little better
+okay so we
+
+ align:start position:0%
+okay so we
+ 
+
+ align:start position:0%
+okay so we
+have let's phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in general it's have phase Alpha and it
+
+ align:start position:0%
+in general it's have phase Alpha and it
+ 
+
+ align:start position:0%
+in general it's have phase Alpha and it
+has temperature Alpha pressure
+
+ align:start position:0%
+has temperature Alpha pressure
+ 
+
+ align:start position:0%
+has temperature Alpha pressure
+Alpha and
+
+ align:start position:0%
+Alpha and
+ 
+
+ align:start position:0%
+Alpha and
+X1 Alpha
+
+ align:start position:0%
+X1 Alpha
+ 
+
+ align:start position:0%
+X1 Alpha
+X2 Alpha and although in this class
+
+ align:start position:0%
+X2 Alpha and although in this class
+ 
+
+ align:start position:0%
+X2 Alpha and although in this class
+we're only going to deal with binary
+
+ align:start position:0%
+we're only going to deal with binary
+ 
+
+ align:start position:0%
+we're only going to deal with binary
+systems that there two components right
+
+ align:start position:0%
+systems that there two components right
+ 
+
+ align:start position:0%
+systems that there two components right
+now what we'll derive is more General so
+
+ align:start position:0%
+now what we'll derive is more General so
+ 
+
+ align:start position:0%
+now what we'll derive is more General so
+you can imagine
+
+ align:start position:0%
+you can imagine
+ 
+
+ align:start position:0%
+you can imagine
+having more than two components and then
+
+ align:start position:0%
+having more than two components and then
+ 
+
+ align:start position:0%
+having more than two components and then
+we're going to have phase beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this in general is at some
+
+ align:start position:0%
+and this in general is at some
+ 
+
+ align:start position:0%
+and this in general is at some
+temperature some
+
+ align:start position:0%
+temperature some
+ 
+
+ align:start position:0%
+temperature some
+pressure and it has some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+composition which of these pens is
+
+ align:start position:0%
+composition which of these pens is
+ 
+
+ align:start position:0%
+composition which of these pens is
+better this pen is
+
+ align:start position:0%
+better this pen is
+ 
+
+ align:start position:0%
+better this pen is
+better life is too short to keep faded
+
+ align:start position:0%
+better life is too short to keep faded
+ 
+
+ align:start position:0%
+better life is too short to keep faded
+Sharpies on your desk okay so the
+
+ align:start position:0%
+Sharpies on your desk okay so the
+ 
+
+ align:start position:0%
+Sharpies on your desk okay so the
+overall system is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isolated overall system is isolated and
+
+ align:start position:0%
+isolated overall system is isolated and
+ 
+
+ align:start position:0%
+isolated overall system is isolated and
+um you know so so we're going to use our
+
+ align:start position:0%
+um you know so so we're going to use our
+ 
+
+ align:start position:0%
+um you know so so we're going to use our
+isolation conditions that we remember
+
+ align:start position:0%
+isolation conditions that we remember
+ 
+
+ align:start position:0%
+isolation conditions that we remember
+from some time ago and here's what we're
+
+ align:start position:0%
+from some time ago and here's what we're
+ 
+
+ align:start position:0%
+from some time ago and here's what we're
+going to ask ourselves what is condition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+Alpha and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beta if the phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boundary is
+
+ align:start position:0%
+boundary is
+ 
+
+ align:start position:0%
+boundary is
+open so material can flip back and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forth non- rigid
+
+ align:start position:0%
+forth non- rigid
+ 
+
+ align:start position:0%
+forth non- rigid
+so this phase can grow or Shrink and
+
+ align:start position:0%
+so this phase can grow or Shrink and
+ 
+
+ align:start position:0%
+so this phase can grow or Shrink and
+this phase can grow or Shrink
+
+ align:start position:0%
+this phase can grow or Shrink
+ 
+
+ align:start position:0%
+this phase can grow or Shrink
+right and thermally conductive or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they sometimes that's known as a thermal
+
+ align:start position:0%
+they sometimes that's known as a thermal
+ 
+
+ align:start position:0%
+they sometimes that's known as a thermal
+but with the a thermally conductive so
+
+ align:start position:0%
+but with the a thermally conductive so
+ 
+
+ align:start position:0%
+but with the a thermally conductive so
+what is our condition for
+
+ align:start position:0%
+what is our condition for
+ 
+
+ align:start position:0%
+what is our condition for
+equilibrium in this
+
+ align:start position:0%
+equilibrium in this
+ 
+
+ align:start position:0%
+equilibrium in this
+situation
+
+ align:start position:0%
+situation
+ 
+
+ align:start position:0%
+situation
+so we're going to do something like what
+
+ align:start position:0%
+so we're going to do something like what
+ 
+
+ align:start position:0%
+so we're going to do something like what
+we did couple weeks ago now for the
+
+ align:start position:0%
+we did couple weeks ago now for the
+ 
+
+ align:start position:0%
+we did couple weeks ago now for the
+total
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system for the system as a
+
+ align:start position:0%
+system for the system as a
+ 
+
+ align:start position:0%
+system for the system as a
+whole we can write the full differential
+
+ align:start position:0%
+whole we can write the full differential
+ 
+
+ align:start position:0%
+whole we can write the full differential
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+entropy so we're going to sum
+
+ align:start position:0%
+entropy so we're going to sum
+ 
+
+ align:start position:0%
+entropy so we're going to sum
+now over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phases some over
+
+ align:start position:0%
+phases some over
+ 
+
+ align:start position:0%
+phases some over
+phases and we know what this is this is
+
+ align:start position:0%
+phases and we know what this is this is
+ 
+
+ align:start position:0%
+phases and we know what this is this is
+just from the combined statement here so
+
+ align:start position:0%
+just from the combined statement here so
+ 
+
+ align:start position:0%
+just from the combined statement here so
+phase label
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J and of course each phase we have to
+
+ align:start position:0%
+J and of course each phase we have to
+ 
+
+ align:start position:0%
+J and of course each phase we have to
+sum over components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components mu k
+
+ align:start position:0%
+components mu k
+ 
+
+ align:start position:0%
+components mu k
+j t
+
+ align:start position:0%
+j t
+ 
+
+ align:start position:0%
+j t
+j d
+
+ align:start position:0%
+j d
+ 
+
+ align:start position:0%
+j d
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+j this is very similar to what we've
+
+ align:start position:0%
+j this is very similar to what we've
+ 
+
+ align:start position:0%
+j this is very similar to what we've
+done
+
+ align:start position:0%
+done
+ 
+
+ align:start position:0%
+done
+before DS equal
+
+ align:start position:0%
+before DS equal
+ 
+
+ align:start position:0%
+before DS equal
+Z at
+
+ align:start position:0%
+Z at
+ 
+
+ align:start position:0%
+Z at
+equilibrium Le
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to the equilibrium conditions and I'm
+
+ align:start position:0%
+to the equilibrium conditions and I'm
+ 
+
+ align:start position:0%
+to the equilibrium conditions and I'm
+not going to write this out because
+
+ align:start position:0%
+not going to write this out because
+ 
+
+ align:start position:0%
+not going to write this out because
+you've seen it before more or
+
+ align:start position:0%
+you've seen it before more or
+ 
+
+ align:start position:0%
+you've seen it before more or
+less that is thermal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium mechanical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium and chemical equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thermal
+
+ align:start position:0%
+thermal
+ 
+
+ align:start position:0%
+thermal
+chemical sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mechanical and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chemical all right so let's do a see
+
+ align:start position:0%
+chemical all right so let's do a see
+ 
+
+ align:start position:0%
+chemical all right so let's do a see
+what the implications of this are we're
+
+ align:start position:0%
+what the implications of this are we're
+ 
+
+ align:start position:0%
+what the implications of this are we're
+going to start with Gibs phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we done we did g phase Ru before we
+
+ align:start position:0%
+so we done we did g phase Ru before we
+ 
+
+ align:start position:0%
+so we done we did g phase Ru before we
+did it rather briefly for unary systems
+
+ align:start position:0%
+did it rather briefly for unary systems
+ 
+
+ align:start position:0%
+did it rather briefly for unary systems
+we're going to revise it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+revised for multicomponent systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and as before we're going to use
+
+ align:start position:0%
+right and as before we're going to use
+ 
+
+ align:start position:0%
+right and as before we're going to use
+this pH to mean
+
+ align:start position:0%
+this pH to mean
+ 
+
+ align:start position:0%
+this pH to mean
+phases so F phases and C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components as before I'm not using
+
+ align:start position:0%
+components as before I'm not using
+ 
+
+ align:start position:0%
+components as before I'm not using
+capital P for phases as the book does
+
+ align:start position:0%
+capital P for phases as the book does
+ 
+
+ align:start position:0%
+capital P for phases as the book does
+because capital p means pressure so this
+
+ align:start position:0%
+because capital p means pressure so this
+ 
+
+ align:start position:0%
+because capital p means pressure so this
+is a problem in linear algebra we count
+
+ align:start position:0%
+is a problem in linear algebra we count
+ 
+
+ align:start position:0%
+is a problem in linear algebra we count
+our number of variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the number of variables let's see for
+
+ align:start position:0%
+the number of variables let's see for
+ 
+
+ align:start position:0%
+the number of variables let's see for
+phase Alpha we have temperature of alpha
+
+ align:start position:0%
+phase Alpha we have temperature of alpha
+ 
+
+ align:start position:0%
+phase Alpha we have temperature of alpha
+pressure of
+
+ align:start position:0%
+pressure of
+ 
+
+ align:start position:0%
+pressure of
+alpha X1 of alpha X2 of
+
+ align:start position:0%
+alpha X1 of alpha X2 of
+ 
+
+ align:start position:0%
+alpha X1 of alpha X2 of
+Alpha and all the way up to x c
+
+ align:start position:0%
+Alpha and all the way up to x c
+ 
+
+ align:start position:0%
+Alpha and all the way up to x c
+minus1 of
+
+ align:start position:0%
+minus1 of
+ 
+
+ align:start position:0%
+minus1 of
+alpha I'm not
+
+ align:start position:0%
+alpha I'm not
+ 
+
+ align:start position:0%
+alpha I'm not
+including the mole fraction of component
+
+ align:start position:0%
+including the mole fraction of component
+ 
+
+ align:start position:0%
+including the mole fraction of component
+C because because it's determined by the
+
+ align:start position:0%
+C because because it's determined by the
+ 
+
+ align:start position:0%
+C because because it's determined by the
+mole fractions from 1 to C minus one
+
+ align:start position:0%
+mole fractions from 1 to C minus one
+ 
+
+ align:start position:0%
+mole fractions from 1 to C minus one
+right you don't have C independent mole
+
+ align:start position:0%
+right you don't have C independent mole
+ 
+
+ align:start position:0%
+right you don't have C independent mole
+fractions you have C minus one
+
+ align:start position:0%
+fractions you have C minus one
+ 
+
+ align:start position:0%
+fractions you have C minus one
+independent M fractions because they
+
+ align:start position:0%
+independent M fractions because they
+ 
+
+ align:start position:0%
+independent M fractions because they
+have to sum to one okay that's for phase
+
+ align:start position:0%
+have to sum to one okay that's for phase
+ 
+
+ align:start position:0%
+have to sum to one okay that's for phase
+Alpha here's for phase beta T beta P
+
+ align:start position:0%
+Alpha here's for phase beta T beta P
+ 
+
+ align:start position:0%
+Alpha here's for phase beta T beta P
+beta X1 beta X2
+
+ align:start position:0%
+beta X1 beta X2
+ 
+
+ align:start position:0%
+beta X1 beta X2
+beta so forth and so on X cus1 beta and
+
+ align:start position:0%
+beta so forth and so on X cus1 beta and
+ 
+
+ align:start position:0%
+beta so forth and so on X cus1 beta and
+we can repeat this for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+each of f phases so we have this many
+
+ align:start position:0%
+each of f phases so we have this many
+ 
+
+ align:start position:0%
+each of f phases so we have this many
+lines or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variables and for each phase we have 2 +
+
+ align:start position:0%
+variables and for each phase we have 2 +
+ 
+
+ align:start position:0%
+variables and for each phase we have 2 +
+C -1 variables per per
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phase see what we're doing is we're
+
+ align:start position:0%
+phase see what we're doing is we're
+ 
+
+ align:start position:0%
+phase see what we're doing is we're
+counting the intens of variables that
+
+ align:start position:0%
+counting the intens of variables that
+ 
+
+ align:start position:0%
+counting the intens of variables that
+control this that that describe the
+
+ align:start position:0%
+control this that that describe the
+ 
+
+ align:start position:0%
+control this that that describe the
+system so the number of
+
+ align:start position:0%
+system so the number of
+ 
+
+ align:start position:0%
+system so the number of
+vs
+
+ align:start position:0%
+vs
+ 
+
+ align:start position:0%
+vs
+equals number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phases
+
+ align:start position:0%
+phases
+ 
+
+ align:start position:0%
+phases
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+times uh 2 + C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+-1 right so that's
+
+ align:start position:0%
+-1 right so that's
+ 
+
+ align:start position:0%
+-1 right so that's
+just number of phases times C + 1
+
+ align:start position:0%
+just number of phases times C + 1
+ 
+
+ align:start position:0%
+just number of phases times C + 1
+so that's a number of variables that
+
+ align:start position:0%
+so that's a number of variables that
+ 
+
+ align:start position:0%
+so that's a number of variables that
+describe the
+
+ align:start position:0%
+describe the
+ 
+
+ align:start position:0%
+describe the
+system and now we're going to apply
+
+ align:start position:0%
+system and now we're going to apply
+ 
+
+ align:start position:0%
+system and now we're going to apply
+our number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constraints at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium number of constraints at
+
+ align:start position:0%
+equilibrium number of constraints at
+ 
+
+ align:start position:0%
+equilibrium number of constraints at
+equilibrium so the the equilibrium
+
+ align:start position:0%
+equilibrium so the the equilibrium
+ 
+
+ align:start position:0%
+equilibrium so the the equilibrium
+conditions we we found in two slides ago
+
+ align:start position:0%
+conditions we we found in two slides ago
+ 
+
+ align:start position:0%
+conditions we we found in two slides ago
+so there there as
+
+ align:start position:0%
+so there there as
+ 
+
+ align:start position:0%
+so there there as
+follows temperature of alpha equals
+
+ align:start position:0%
+follows temperature of alpha equals
+ 
+
+ align:start position:0%
+follows temperature of alpha equals
+temperature of beta
+
+ align:start position:0%
+temperature of beta
+ 
+
+ align:start position:0%
+temperature of beta
+equals right for as many phases as you
+
+ align:start position:0%
+equals right for as many phases as you
+ 
+
+ align:start position:0%
+equals right for as many phases as you
+have you keep
+
+ align:start position:0%
+have you keep
+ 
+
+ align:start position:0%
+have you keep
+going pressure of alpha equals pressure
+
+ align:start position:0%
+going pressure of alpha equals pressure
+ 
+
+ align:start position:0%
+going pressure of alpha equals pressure
+of beta equals you keep
+
+ align:start position:0%
+of beta equals you keep
+ 
+
+ align:start position:0%
+of beta equals you keep
+going then chemical potential of
+
+ align:start position:0%
+going then chemical potential of
+ 
+
+ align:start position:0%
+going then chemical potential of
+component one in Phase Alpha equals
+
+ align:start position:0%
+component one in Phase Alpha equals
+ 
+
+ align:start position:0%
+component one in Phase Alpha equals
+chemical potential of component one uh
+
+ align:start position:0%
+chemical potential of component one uh
+ 
+
+ align:start position:0%
+chemical potential of component one uh
+in phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beta equals so forth then of course
+
+ align:start position:0%
+beta equals so forth then of course
+ 
+
+ align:start position:0%
+beta equals so forth then of course
+chemical potential component 2 in Phase
+
+ align:start position:0%
+chemical potential component 2 in Phase
+ 
+
+ align:start position:0%
+chemical potential component 2 in Phase
+Alpha equals chemical potential
+
+ align:start position:0%
+Alpha equals chemical potential
+ 
+
+ align:start position:0%
+Alpha equals chemical potential
+component two in Phase
+
+ align:start position:0%
+component two in Phase
+ 
+
+ align:start position:0%
+component two in Phase
+beta and you have to carry this all the
+
+ align:start position:0%
+beta and you have to carry this all the
+ 
+
+ align:start position:0%
+beta and you have to carry this all the
+way down to the chemical potential of
+
+ align:start position:0%
+way down to the chemical potential of
+ 
+
+ align:start position:0%
+way down to the chemical potential of
+component C in Phase Alpha equals
+
+ align:start position:0%
+component C in Phase Alpha equals
+ 
+
+ align:start position:0%
+component C in Phase Alpha equals
+chemical potential of component C in
+
+ align:start position:0%
+chemical potential of component C in
+ 
+
+ align:start position:0%
+chemical potential of component C in
+Phase
+
+ align:start position:0%
+Phase
+ 
+
+ align:start position:0%
+Phase
+beta and so forth and so on
+
+ align:start position:0%
+beta and so forth and so on
+ 
+
+ align:start position:0%
+beta and so forth and so on
+so we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have C +
+
+ align:start position:0%
+have C +
+ 
+
+ align:start position:0%
+have C +
+2 rows of equations temperature pressure
+
+ align:start position:0%
+2 rows of equations temperature pressure
+ 
+
+ align:start position:0%
+2 rows of equations temperature pressure
+and all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components and how many independent
+
+ align:start position:0%
+components and how many independent
+ 
+
+ align:start position:0%
+components and how many independent
+equations per row do we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+giv so this is going from temperature
+
+ align:start position:0%
+giv so this is going from temperature
+ 
+
+ align:start position:0%
+giv so this is going from temperature
+Alpha equals temperature beta equals all
+
+ align:start position:0%
+Alpha equals temperature beta equals all
+ 
+
+ align:start position:0%
+Alpha equals temperature beta equals all
+the way up to the temperature of the
+
+ align:start position:0%
+the way up to the temperature of the
+ 
+
+ align:start position:0%
+the way up to the temperature of the
+Final
+
+ align:start position:0%
+Final
+ 
+
+ align:start position:0%
+Final
+Phase how many independent equations do
+
+ align:start position:0%
+Phase how many independent equations do
+ 
+
+ align:start position:0%
+Phase how many independent equations do
+we have let's say in this one row minus
+
+ align:start position:0%
+we have let's say in this one row minus
+ 
+
+ align:start position:0%
+we have let's say in this one row minus
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+yeah right this equals that that equals
+
+ align:start position:0%
+yeah right this equals that that equals
+ 
+
+ align:start position:0%
+yeah right this equals that that equals
+that that equals that that equals that
+
+ align:start position:0%
+that that equals that that equals that
+ 
+
+ align:start position:0%
+that that equals that that equals that
+and so forth and then the final one
+
+ align:start position:0%
+and so forth and then the final one
+ 
+
+ align:start position:0%
+and so forth and then the final one
+equals the first one and you know you
+
+ align:start position:0%
+equals the first one and you know you
+ 
+
+ align:start position:0%
+equals the first one and you know you
+could just count the equal signs right
+
+ align:start position:0%
+could just count the equal signs right
+ 
+
+ align:start position:0%
+could just count the equal signs right
+the number of equal signs you're going
+
+ align:start position:0%
+the number of equal signs you're going
+ 
+
+ align:start position:0%
+the number of equal signs you're going
+to have in is is going to be minus one
+
+ align:start position:0%
+to have in is is going to be minus one
+ 
+
+ align:start position:0%
+to have in is is going to be minus one
+right good so that means we we have our
+
+ align:start position:0%
+right good so that means we we have our
+ 
+
+ align:start position:0%
+right good so that means we we have our
+number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constraints
+
+ align:start position:0%
+constraints
+ 
+
+ align:start position:0%
+constraints
+equals C +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2times f
+
+ align:start position:0%
+2times f
+ 
+
+ align:start position:0%
+2times f
+minus one okay so now we have
+
+ align:start position:0%
+minus one okay so now we have
+ 
+
+ align:start position:0%
+minus one okay so now we have
+constraints and we have variables so
+
+ align:start position:0%
+constraints and we have variables so
+ 
+
+ align:start position:0%
+constraints and we have variables so
+again this is a a linear algebra thing
+
+ align:start position:0%
+again this is a a linear algebra thing
+ 
+
+ align:start position:0%
+again this is a a linear algebra thing
+the number of degrees of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+freedom
+
+ align:start position:0%
+freedom
+ 
+
+ align:start position:0%
+freedom
+dof
+
+ align:start position:0%
+dof
+ 
+
+ align:start position:0%
+dof
+equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variables minus constraints
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this comes out to be C plus
+
+ align:start position:0%
+and this comes out to be C plus
+ 
+
+ align:start position:0%
+and this comes out to be C plus
+to minus number of phases and this is um
+
+ align:start position:0%
+to minus number of phases and this is um
+ 
+
+ align:start position:0%
+to minus number of phases and this is um
+a rather
+
+ align:start position:0%
+a rather
+ 
+
+ align:start position:0%
+a rather
+well-known result this is Gibbs phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rule
+
+ align:start position:0%
+rule
+ 
+
+ align:start position:0%
+rule
+for multicomponent systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's giip phase rule for multic
+
+ align:start position:0%
+that's giip phase rule for multic
+ 
+
+ align:start position:0%
+that's giip phase rule for multic
+component systems and what is that in
+
+ align:start position:0%
+component systems and what is that in
+ 
+
+ align:start position:0%
+component systems and what is that in
+words somebody I this what are we doing
+
+ align:start position:0%
+words somebody I this what are we doing
+ 
+
+ align:start position:0%
+words somebody I this what are we doing
+here what does that tell us in words
+
+ align:start position:0%
+here what does that tell us in words
+ 
+
+ align:start position:0%
+here what does that tell us in words
+what does that
+
+ align:start position:0%
+what does that
+ 
+
+ align:start position:0%
+what does that
+mean degree of
+
+ align:start position:0%
+mean degree of
+ 
+
+ align:start position:0%
+mean degree of
+freedom is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thermodynamic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variables
+
+ align:start position:0%
+variables
+ 
+
+ align:start position:0%
+variables
+that can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independently varied
+
+ align:start position:0%
+independently varied
+ 
+
+ align:start position:0%
+independently varied
+while
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maintaining
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between F
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phases in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system of C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components so an example of your
+
+ align:start position:0%
+components so an example of your
+ 
+
+ align:start position:0%
+components so an example of your
+familiar with already was from unary
+
+ align:start position:0%
+familiar with already was from unary
+ 
+
+ align:start position:0%
+familiar with already was from unary
+systems we had temperature and we had
+
+ align:start position:0%
+systems we had temperature and we had
+ 
+
+ align:start position:0%
+systems we had temperature and we had
+pressure and we had sat saturation Vapor
+
+ align:start position:0%
+pressure and we had sat saturation Vapor
+ 
+
+ align:start position:0%
+pressure and we had sat saturation Vapor
+pressures for example which kind of look
+
+ align:start position:0%
+pressures for example which kind of look
+ 
+
+ align:start position:0%
+pressures for example which kind of look
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+Pat you remember that that was a
+
+ align:start position:0%
+Pat you remember that that was a
+ 
+
+ align:start position:0%
+Pat you remember that that was a
+coexistence curve between vapor and
+
+ align:start position:0%
+coexistence curve between vapor and
+ 
+
+ align:start position:0%
+coexistence curve between vapor and
+solid phases in a un system right this
+
+ align:start position:0%
+solid phases in a un system right this
+ 
+
+ align:start position:0%
+solid phases in a un system right this
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+UN how many degrees of freedom does a
+
+ align:start position:0%
+UN how many degrees of freedom does a
+ 
+
+ align:start position:0%
+UN how many degrees of freedom does a
+line have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one one you can move along T left or
+
+ align:start position:0%
+one one you can move along T left or
+ 
+
+ align:start position:0%
+one one you can move along T left or
+right but once you've decided how far to
+
+ align:start position:0%
+right but once you've decided how far to
+ 
+
+ align:start position:0%
+right but once you've decided how far to
+move along T you can't arbitrarily vary
+
+ align:start position:0%
+move along T you can't arbitrarily vary
+ 
+
+ align:start position:0%
+move along T you can't arbitrarily vary
+P you got to you got to tow the line so
+
+ align:start position:0%
+P you got to you got to tow the line so
+ 
+
+ align:start position:0%
+P you got to you got to tow the line so
+basically you can move along the line in
+
+ align:start position:0%
+basically you can move along the line in
+ 
+
+ align:start position:0%
+basically you can move along the line in
+this direction or that direction that's
+
+ align:start position:0%
+this direction or that direction that's
+ 
+
+ align:start position:0%
+this direction or that direction that's
+your degree of
+
+ align:start position:0%
+your degree of
+ 
+
+ align:start position:0%
+your degree of
+Freedom this is a condition for
+
+ align:start position:0%
+Freedom this is a condition for
+ 
+
+ align:start position:0%
+Freedom this is a condition for
+two-phase equilibrium right this was
+
+ align:start position:0%
+two-phase equilibrium right this was
+ 
+
+ align:start position:0%
+two-phase equilibrium right this was
+degree of Freedom equals how many
+
+ align:start position:0%
+degree of Freedom equals how many
+ 
+
+ align:start position:0%
+degree of Freedom equals how many
+components in un 1 + 2 - 2 two
+
+ align:start position:0%
+components in un 1 + 2 - 2 two
+ 
+
+ align:start position:0%
+components in un 1 + 2 - 2 two
+phases one component right so this is
+
+ align:start position:0%
+phases one component right so this is
+ 
+
+ align:start position:0%
+phases one component right so this is
+this is one right the
+
+ align:start position:0%
+this is one right the
+ 
+
+ align:start position:0%
+this is one right the
+equation the the line here has one
+
+ align:start position:0%
+equation the the line here has one
+ 
+
+ align:start position:0%
+equation the the line here has one
+degree Freedom so if you start here and
+
+ align:start position:0%
+degree Freedom so if you start here and
+ 
+
+ align:start position:0%
+degree Freedom so if you start here and
+you go over here right you vary
+
+ align:start position:0%
+you go over here right you vary
+ 
+
+ align:start position:0%
+you go over here right you vary
+temperature and pressure in some random
+
+ align:start position:0%
+temperature and pressure in some random
+ 
+
+ align:start position:0%
+temperature and pressure in some random
+way and you end up over here you no
+
+ align:start position:0%
+way and you end up over here you no
+ 
+
+ align:start position:0%
+way and you end up over here you no
+longer can maintain two-phase
+
+ align:start position:0%
+longer can maintain two-phase
+ 
+
+ align:start position:0%
+longer can maintain two-phase
+equilibrium right you'll be in a one
+
+ align:start position:0%
+equilibrium right you'll be in a one
+ 
+
+ align:start position:0%
+equilibrium right you'll be in a one
+phase region and the entire system will
+
+ align:start position:0%
+phase region and the entire system will
+ 
+
+ align:start position:0%
+phase region and the entire system will
+vaporize that's what that means um in
+
+ align:start position:0%
+vaporize that's what that means um in
+ 
+
+ align:start position:0%
+vaporize that's what that means um in
+the context you're more familiar with so
+
+ align:start position:0%
+the context you're more familiar with so
+ 
+
+ align:start position:0%
+the context you're more familiar with so
+now let's let's see what that means in
+
+ align:start position:0%
+now let's let's see what that means in
+ 
+
+ align:start position:0%
+now let's let's see what that means in
+this new
+
+ align:start position:0%
+this new
+ 
+
+ align:start position:0%
+this new
+context
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case of a binary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system binary system
+
+ align:start position:0%
+system binary system
+ 
+
+ align:start position:0%
+system binary system
+C equals
+
+ align:start position:0%
+C equals
+ 
+
+ align:start position:0%
+C equals
+2 so if we
+
+ align:start position:0%
+2 so if we
+ 
+
+ align:start position:0%
+2 so if we
+have one phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degree of Freedom equals three so for
+
+ align:start position:0%
+degree of Freedom equals three so for
+ 
+
+ align:start position:0%
+degree of Freedom equals three so for
+example what are what are three things
+
+ align:start position:0%
+example what are what are three things
+ 
+
+ align:start position:0%
+example what are what are three things
+which I can all independently vary while
+
+ align:start position:0%
+which I can all independently vary while
+ 
+
+ align:start position:0%
+which I can all independently vary while
+staying in the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phase what are I what are my three
+
+ align:start position:0%
+phase what are I what are my three
+ 
+
+ align:start position:0%
+phase what are I what are my three
+independent parameters um
+
+ align:start position:0%
+independent parameters um
+ 
+
+ align:start position:0%
+independent parameters um
+for Solutions at fixed temperature and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressure volume
+
+ align:start position:0%
+pressure volume
+ 
+
+ align:start position:0%
+pressure volume
+well no temperature and pressure right
+
+ align:start position:0%
+well no temperature and pressure right
+ 
+
+ align:start position:0%
+well no temperature and pressure right
+those are my independent parameters for
+
+ align:start position:0%
+those are my independent parameters for
+ 
+
+ align:start position:0%
+those are my independent parameters for
+a fixed temperature and pressure system
+
+ align:start position:0%
+a fixed temperature and pressure system
+ 
+
+ align:start position:0%
+a fixed temperature and pressure system
+so temperature and
+
+ align:start position:0%
+so temperature and
+ 
+
+ align:start position:0%
+so temperature and
+pressure and let's say composition of of
+
+ align:start position:0%
+pressure and let's say composition of of
+ 
+
+ align:start position:0%
+pressure and let's say composition of of
+component one right I can vary any of
+
+ align:start position:0%
+component one right I can vary any of
+ 
+
+ align:start position:0%
+component one right I can vary any of
+these and I can vary them all three and
+
+ align:start position:0%
+these and I can vary them all three and
+ 
+
+ align:start position:0%
+these and I can vary them all three and
+I can vary them at at random and I'll
+
+ align:start position:0%
+I can vary them at at random and I'll
+ 
+
+ align:start position:0%
+I can vary them at at random and I'll
+still be in a one-phase
+
+ align:start position:0%
+still be in a one-phase
+ 
+
+ align:start position:0%
+still be in a one-phase
+equilibrium that's what that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about two- faase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degree of Freedom equals
+
+ align:start position:0%
+degree of Freedom equals
+ 
+
+ align:start position:0%
+degree of Freedom equals
+2 so here I can vary two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parameters but
+
+ align:start position:0%
+parameters but
+ 
+
+ align:start position:0%
+parameters but
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+third will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coary deterministically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I'm to
+
+ align:start position:0%
+if I'm to
+ 
+
+ align:start position:0%
+if I'm to
+stay into two phase
+
+ align:start position:0%
+stay into two phase
+ 
+
+ align:start position:0%
+stay into two phase
+region and we're going to see this
+
+ align:start position:0%
+region and we're going to see this
+ 
+
+ align:start position:0%
+region and we're going to see this
+emerge in the next couple lectures with
+
+ align:start position:0%
+emerge in the next couple lectures with
+ 
+
+ align:start position:0%
+emerge in the next couple lectures with
+two-phase regions and TI lines and so
+
+ align:start position:0%
+two-phase regions and TI lines and so
+ 
+
+ align:start position:0%
+two-phase regions and TI lines and so
+forth all right right so for example
+
+ align:start position:0%
+forth all right right so for example
+ 
+
+ align:start position:0%
+forth all right right so for example
+right for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+free to
+
+ align:start position:0%
+free to
+ 
+
+ align:start position:0%
+free to
+vary
+
+ align:start position:0%
+vary
+ 
+
+ align:start position:0%
+vary
+T and
+
+ align:start position:0%
+T and
+ 
+
+ align:start position:0%
+T and
+P but
+
+ align:start position:0%
+P but
+ 
+
+ align:start position:0%
+P but
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+X1 X2 of course follows from X1 must
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+follow okay so that's that's an
+
+ align:start position:0%
+follow okay so that's that's an
+ 
+
+ align:start position:0%
+follow okay so that's that's an
+example three phase right degree of
+
+ align:start position:0%
+example three phase right degree of
+ 
+
+ align:start position:0%
+example three phase right degree of
+Freedom equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 and
+
+ align:start position:0%
+1 and
+ 
+
+ align:start position:0%
+1 and
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+phase degree of Freedom equals zero so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before before we we couldn't have
+
+ align:start position:0%
+before before we we couldn't have
+ 
+
+ align:start position:0%
+before before we we couldn't have
+four-phase equilibrium with unary
+
+ align:start position:0%
+four-phase equilibrium with unary
+ 
+
+ align:start position:0%
+four-phase equilibrium with unary
+systems that wasn't allowed now we
+
+ align:start position:0%
+systems that wasn't allowed now we
+ 
+
+ align:start position:0%
+systems that wasn't allowed now we
+can and we see that in
+
+ align:start position:0%
+can and we see that in
+ 
+
+ align:start position:0%
+can and we see that in
+nature and here before we had three
+
+ align:start position:0%
+nature and here before we had three
+ 
+
+ align:start position:0%
+nature and here before we had three
+phase regions those were called triple
+
+ align:start position:0%
+phase regions those were called triple
+ 
+
+ align:start position:0%
+phase regions those were called triple
+points and they were points in unary
+
+ align:start position:0%
+points and they were points in unary
+ 
+
+ align:start position:0%
+points and they were points in unary
+Phase diagrams they couldn't vary now
+
+ align:start position:0%
+Phase diagrams they couldn't vary now
+ 
+
+ align:start position:0%
+Phase diagrams they couldn't vary now
+three-phase regions
+
+ align:start position:0%
+three-phase regions
+ 
+
+ align:start position:0%
+three-phase regions
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+lines in temperature pressure
+
+ align:start position:0%
+lines in temperature pressure
+ 
+
+ align:start position:0%
+lines in temperature pressure
+composition space right in this
+
+ align:start position:0%
+composition space right in this
+ 
+
+ align:start position:0%
+composition space right in this
+threedimensional space these three phase
+
+ align:start position:0%
+threedimensional space these three phase
+ 
+
+ align:start position:0%
+threedimensional space these three phase
+three three phase regions are our our
+
+ align:start position:0%
+three three phase regions are our our
+ 
+
+ align:start position:0%
+three three phase regions are our our
+lines so I'm done on the board for now
+
+ align:start position:0%
+lines so I'm done on the board for now
+ 
+
+ align:start position:0%
+lines so I'm done on the board for now
+I'm going to switch to slides and walk
+
+ align:start position:0%
+I'm going to switch to slides and walk
+ 
+
+ align:start position:0%
+I'm going to switch to slides and walk
+through some examples of binary phase
+
+ align:start position:0%
+through some examples of binary phase
+ 
+
+ align:start position:0%
+through some examples of binary phase
+diagrams and hopefully illustrate some
+
+ align:start position:0%
+diagrams and hopefully illustrate some
+ 
+
+ align:start position:0%
+diagrams and hopefully illustrate some
+of this stuff so let's let's see some
+
+ align:start position:0%
+of this stuff so let's let's see some
+ 
+
+ align:start position:0%
+of this stuff so let's let's see some
+examples of binary phas diagrams um
+
+ align:start position:0%
+examples of binary phas diagrams um
+ 
+
+ align:start position:0%
+examples of binary phas diagrams um
+here's one that I think I pulled from
+
+ align:start position:0%
+here's one that I think I pulled from
+ 
+
+ align:start position:0%
+here's one that I think I pulled from
+Callister right um and we talked about
+
+ align:start position:0%
+Callister right um and we talked about
+ 
+
+ align:start position:0%
+Callister right um and we talked about
+sugar water before in the class and so
+
+ align:start position:0%
+sugar water before in the class and so
+ 
+
+ align:start position:0%
+sugar water before in the class and so
+this is you know this is a very uh
+
+ align:start position:0%
+this is you know this is a very uh
+ 
+
+ align:start position:0%
+this is you know this is a very uh
+simple binary phase diagram we have the
+
+ align:start position:0%
+simple binary phase diagram we have the
+ 
+
+ align:start position:0%
+simple binary phase diagram we have the
+x-axis being composition here in weight
+
+ align:start position:0%
+x-axis being composition here in weight
+ 
+
+ align:start position:0%
+x-axis being composition here in weight
+percent normally we like to stick with
+
+ align:start position:0%
+percent normally we like to stick with
+ 
+
+ align:start position:0%
+percent normally we like to stick with
+atomic percent but this is in weight
+
+ align:start position:0%
+atomic percent but this is in weight
+ 
+
+ align:start position:0%
+atomic percent but this is in weight
+percent and the y- axis here in
+
+ align:start position:0%
+percent and the y- axis here in
+ 
+
+ align:start position:0%
+percent and the y- axis here in
+temperature they even have
+
+ align:start position:0%
+temperature they even have
+ 
+
+ align:start position:0%
+temperature they even have
+Fahrenheit and we have this concept of a
+
+ align:start position:0%
+Fahrenheit and we have this concept of a
+ 
+
+ align:start position:0%
+Fahrenheit and we have this concept of a
+solub ility limit so if you start with
+
+ align:start position:0%
+solub ility limit so if you start with
+ 
+
+ align:start position:0%
+solub ility limit so if you start with
+pure water here on the left hand side
+
+ align:start position:0%
+pure water here on the left hand side
+ 
+
+ align:start position:0%
+pure water here on the left hand side
+and you start adding
+
+ align:start position:0%
+and you start adding
+ 
+
+ align:start position:0%
+and you start adding
+sugar at some point you reach saturation
+
+ align:start position:0%
+sugar at some point you reach saturation
+ 
+
+ align:start position:0%
+sugar at some point you reach saturation
+and if you add any more sugar that Sugar
+
+ align:start position:0%
+and if you add any more sugar that Sugar
+ 
+
+ align:start position:0%
+and if you add any more sugar that Sugar
+will precipitate as solid pure sugar at
+
+ align:start position:0%
+will precipitate as solid pure sugar at
+ 
+
+ align:start position:0%
+will precipitate as solid pure sugar at
+the bottom of the beaker so this over
+
+ align:start position:0%
+the bottom of the beaker so this over
+ 
+
+ align:start position:0%
+the bottom of the beaker so this over
+here is the two-phase region and we
+
+ align:start position:0%
+here is the two-phase region and we
+ 
+
+ align:start position:0%
+here is the two-phase region and we
+understand that you can't actually have
+
+ align:start position:0%
+understand that you can't actually have
+ 
+
+ align:start position:0%
+understand that you can't actually have
+a uniform material with any of these
+
+ align:start position:0%
+a uniform material with any of these
+ 
+
+ align:start position:0%
+a uniform material with any of these
+compositions what's actually happening
+
+ align:start position:0%
+compositions what's actually happening
+ 
+
+ align:start position:0%
+compositions what's actually happening
+when you have an overall system
+
+ align:start position:0%
+when you have an overall system
+ 
+
+ align:start position:0%
+when you have an overall system
+composition in this region is you have a
+
+ align:start position:0%
+composition in this region is you have a
+ 
+
+ align:start position:0%
+composition in this region is you have a
+coexistence of saturated sugar
+
+ align:start position:0%
+coexistence of saturated sugar
+ 
+
+ align:start position:0%
+coexistence of saturated sugar
+water and pure solid sugar so that's
+
+ align:start position:0%
+water and pure solid sugar so that's
+ 
+
+ align:start position:0%
+water and pure solid sugar so that's
+what we understand this to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean why does this Co why does this
+
+ align:start position:0%
+mean why does this Co why does this
+ 
+
+ align:start position:0%
+mean why does this Co why does this
+solubility limit curve go up and to the
+
+ align:start position:0%
+solubility limit curve go up and to the
+ 
+
+ align:start position:0%
+solubility limit curve go up and to the
+right why does it not go up into the
+
+ align:start position:0%
+right why does it not go up into the
+ 
+
+ align:start position:0%
+right why does it not go up into the
+lift does it relate to the density
+
+ align:start position:0%
+lift does it relate to the density
+ 
+
+ align:start position:0%
+lift does it relate to the density
+it actually doesn't relate to the
+
+ align:start position:0%
+it actually doesn't relate to the
+ 
+
+ align:start position:0%
+it actually doesn't relate to the
+density this means that let's say
+
+ align:start position:0%
+density this means that let's say
+ 
+
+ align:start position:0%
+density this means that let's say
+imagine this
+
+ align:start position:0%
+imagine this
+ 
+
+ align:start position:0%
+imagine this
+65% um weight perc composition which
+
+ align:start position:0%
+65% um weight perc composition which
+ 
+
+ align:start position:0%
+65% um weight perc composition which
+would uh which would be super saturated
+
+ align:start position:0%
+would uh which would be super saturated
+ 
+
+ align:start position:0%
+would uh which would be super saturated
+at um lower
+
+ align:start position:0%
+at um lower
+ 
+
+ align:start position:0%
+at um lower
+temperature if we raise the temperature
+
+ align:start position:0%
+temperature if we raise the temperature
+ 
+
+ align:start position:0%
+temperature if we raise the temperature
+now we can actually achieve that that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solubility why would the solution phase
+
+ align:start position:0%
+solubility why would the solution phase
+ 
+
+ align:start position:0%
+solubility why would the solution phase
+be more favorable at higher temperature
+
+ align:start position:0%
+be more favorable at higher temperature
+ 
+
+ align:start position:0%
+be more favorable at higher temperature
+than lower temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it has higher entropy so it's an
+
+ align:start position:0%
+because it has higher entropy so it's an
+ 
+
+ align:start position:0%
+because it has higher entropy so it's an
+entropy effect that's right we remember
+
+ align:start position:0%
+entropy effect that's right we remember
+ 
+
+ align:start position:0%
+entropy effect that's right we remember
+Gibbs is H minus TS so as we raise the
+
+ align:start position:0%
+Gibbs is H minus TS so as we raise the
+ 
+
+ align:start position:0%
+Gibbs is H minus TS so as we raise the
+temperature entropy becomes more and
+
+ align:start position:0%
+temperature entropy becomes more and
+ 
+
+ align:start position:0%
+temperature entropy becomes more and
+more important it becomes a stronger
+
+ align:start position:0%
+more important it becomes a stronger
+ 
+
+ align:start position:0%
+more important it becomes a stronger
+driving force so Solutions um are more
+
+ align:start position:0%
+driving force so Solutions um are more
+ 
+
+ align:start position:0%
+driving force so Solutions um are more
+mixed up they have higher entropy than
+
+ align:start position:0%
+mixed up they have higher entropy than
+ 
+
+ align:start position:0%
+mixed up they have higher entropy than
+two phase regions with a segregated pure
+
+ align:start position:0%
+two phase regions with a segregated pure
+ 
+
+ align:start position:0%
+two phase regions with a segregated pure
+solute and so that's why you see um
+
+ align:start position:0%
+solute and so that's why you see um
+ 
+
+ align:start position:0%
+solute and so that's why you see um
+solubility regions typically expanding
+
+ align:start position:0%
+solubility regions typically expanding
+ 
+
+ align:start position:0%
+solubility regions typically expanding
+getting wider as you raise the
+
+ align:start position:0%
+getting wider as you raise the
+ 
+
+ align:start position:0%
+getting wider as you raise the
+temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right so let's talk about some other
+
+ align:start position:0%
+right so let's talk about some other
+ 
+
+ align:start position:0%
+right so let's talk about some other
+systems some definition here isomorphous
+
+ align:start position:0%
+systems some definition here isomorphous
+ 
+
+ align:start position:0%
+systems some definition here isomorphous
+system so now we're getting away from
+
+ align:start position:0%
+system so now we're getting away from
+ 
+
+ align:start position:0%
+system so now we're getting away from
+sugar water we're going more towards
+
+ align:start position:0%
+sugar water we're going more towards
+ 
+
+ align:start position:0%
+sugar water we're going more towards
+solids that are more in line with the
+
+ align:start position:0%
+solids that are more in line with the
+ 
+
+ align:start position:0%
+solids that are more in line with the
+core of dmse isomorphous systems means
+
+ align:start position:0%
+core of dmse isomorphous systems means
+ 
+
+ align:start position:0%
+core of dmse isomorphous systems means
+systems for which both peer components
+
+ align:start position:0%
+systems for which both peer components
+ 
+
+ align:start position:0%
+systems for which both peer components
+have the same crystal structure so
+
+ align:start position:0%
+have the same crystal structure so
+ 
+
+ align:start position:0%
+have the same crystal structure so
+that's a definition so an example we
+
+ align:start position:0%
+that's a definition so an example we
+ 
+
+ align:start position:0%
+that's a definition so an example we
+like in dmse is silicon
+
+ align:start position:0%
+like in dmse is silicon
+ 
+
+ align:start position:0%
+like in dmse is silicon
+geranium because silicon geranium is an
+
+ align:start position:0%
+geranium because silicon geranium is an
+ 
+
+ align:start position:0%
+geranium because silicon geranium is an
+isomorphous system and it's one that
+
+ align:start position:0%
+isomorphous system and it's one that
+ 
+
+ align:start position:0%
+isomorphous system and it's one that
+dmse has played a major role in
+
+ align:start position:0%
+dmse has played a major role in
+ 
+
+ align:start position:0%
+dmse has played a major role in
+developing so silicon and geranium both
+
+ align:start position:0%
+developing so silicon and geranium both
+ 
+
+ align:start position:0%
+developing so silicon and geranium both
+have this diamond diamond cubic crystal
+
+ align:start position:0%
+have this diamond diamond cubic crystal
+ 
+
+ align:start position:0%
+have this diamond diamond cubic crystal
+structure silicon geranium Alloys have a
+
+ align:start position:0%
+structure silicon geranium Alloys have a
+ 
+
+ align:start position:0%
+structure silicon geranium Alloys have a
+pretty important role in
+
+ align:start position:0%
+pretty important role in
+ 
+
+ align:start position:0%
+pretty important role in
+microprocessors and let's see what the
+
+ align:start position:0%
+microprocessors and let's see what the
+ 
+
+ align:start position:0%
+microprocessors and let's see what the
+phase diagram looks
+
+ align:start position:0%
+phase diagram looks
+ 
+
+ align:start position:0%
+phase diagram looks
+like so this is a phase diagram of silic
+
+ align:start position:0%
+like so this is a phase diagram of silic
+ 
+
+ align:start position:0%
+like so this is a phase diagram of silic
+and Germania so now what do we see at
+
+ align:start position:0%
+and Germania so now what do we see at
+ 
+
+ align:start position:0%
+and Germania so now what do we see at
+low temperature that is watch the axis
+
+ align:start position:0%
+low temperature that is watch the axis
+ 
+
+ align:start position:0%
+low temperature that is watch the axis
+here low temperature means below roughly
+
+ align:start position:0%
+here low temperature means below roughly
+ 
+
+ align:start position:0%
+here low temperature means below roughly
+a th000 c you know below 940 C that that
+
+ align:start position:0%
+a th000 c you know below 940 C that that
+ 
+
+ align:start position:0%
+a th000 c you know below 940 C that that
+counts as low temperature when you're
+
+ align:start position:0%
+counts as low temperature when you're
+ 
+
+ align:start position:0%
+counts as low temperature when you're
+dealing with with cently bonded solids
+
+ align:start position:0%
+dealing with with cently bonded solids
+ 
+
+ align:start position:0%
+dealing with with cently bonded solids
+like Silicon and
+
+ align:start position:0%
+like Silicon and
+ 
+
+ align:start position:0%
+like Silicon and
+geranium um you have the diamond
+
+ align:start position:0%
+geranium um you have the diamond
+ 
+
+ align:start position:0%
+geranium um you have the diamond
+structure throughout so you have Diamond
+
+ align:start position:0%
+structure throughout so you have Diamond
+ 
+
+ align:start position:0%
+structure throughout so you have Diamond
+throughout this entire region it's fully
+
+ align:start position:0%
+throughout this entire region it's fully
+ 
+
+ align:start position:0%
+throughout this entire region it's fully
+missible right Germania is fully
+
+ align:start position:0%
+missible right Germania is fully
+ 
+
+ align:start position:0%
+missible right Germania is fully
+missible in Silicon silicon is fully
+
+ align:start position:0%
+missible in Silicon silicon is fully
+ 
+
+ align:start position:0%
+missible in Silicon silicon is fully
+missible in geranium and we have only
+
+ align:start position:0%
+missible in geranium and we have only
+ 
+
+ align:start position:0%
+missible in geranium and we have only
+one phase field labeled Alpha solid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at high temperature we have fully
+
+ align:start position:0%
+at high temperature we have fully
+ 
+
+ align:start position:0%
+at high temperature we have fully
+missable
+
+ align:start position:0%
+missable
+ 
+
+ align:start position:0%
+missable
+liquids that's maybe not too surprising
+
+ align:start position:0%
+liquids that's maybe not too surprising
+ 
+
+ align:start position:0%
+liquids that's maybe not too surprising
+although we saw even last lecture an
+
+ align:start position:0%
+although we saw even last lecture an
+ 
+
+ align:start position:0%
+although we saw even last lecture an
+example of liquids which did not mix but
+
+ align:start position:0%
+example of liquids which did not mix but
+ 
+
+ align:start position:0%
+example of liquids which did not mix but
+at high temperature we have fully
+
+ align:start position:0%
+at high temperature we have fully
+ 
+
+ align:start position:0%
+at high temperature we have fully
+missable liquids at low temperature we
+
+ align:start position:0%
+missable liquids at low temperature we
+ 
+
+ align:start position:0%
+missable liquids at low temperature we
+have fully missible solids and the
+
+ align:start position:0%
+have fully missible solids and the
+ 
+
+ align:start position:0%
+have fully missible solids and the
+intermediate region is is um gives us
+
+ align:start position:0%
+intermediate region is is um gives us
+ 
+
+ align:start position:0%
+intermediate region is is um gives us
+this lenslike shape so this is called
+
+ align:start position:0%
+this lenslike shape so this is called
+ 
+
+ align:start position:0%
+this lenslike shape so this is called
+the lens
+
+ align:start position:0%
+the lens
+ 
+
+ align:start position:0%
+the lens
+diagram in general any phase diagram
+
+ align:start position:0%
+diagram in general any phase diagram
+ 
+
+ align:start position:0%
+diagram in general any phase diagram
+that has this this this kind of
+
+ align:start position:0%
+that has this this this kind of
+ 
+
+ align:start position:0%
+that has this this this kind of
+appearance uh with a two-phase region
+
+ align:start position:0%
+appearance uh with a two-phase region
+ 
+
+ align:start position:0%
+appearance uh with a two-phase region
+separating two fully missible uh regions
+
+ align:start position:0%
+separating two fully missible uh regions
+ 
+
+ align:start position:0%
+separating two fully missible uh regions
+it can be called the lens
+
+ align:start position:0%
+it can be called the lens
+ 
+
+ align:start position:0%
+it can be called the lens
+diagram just because it looks like a
+
+ align:start position:0%
+diagram just because it looks like a
+ 
+
+ align:start position:0%
+diagram just because it looks like a
+lens so what happens if I prepare a
+
+ align:start position:0%
+lens so what happens if I prepare a
+ 
+
+ align:start position:0%
+lens so what happens if I prepare a
+system with 30 we% silicon at 1200 degre
+
+ align:start position:0%
+system with 30 we% silicon at 1200 degre
+ 
+
+ align:start position:0%
+system with 30 we% silicon at 1200 degre
+C what happens at equilibrium for that
+
+ align:start position:0%
+C what happens at equilibrium for that
+ 
+
+ align:start position:0%
+C what happens at equilibrium for that
+system does anybody
+
+ align:start position:0%
+system does anybody
+ 
+
+ align:start position:0%
+system does anybody
+know is it a phase
+
+ align:start position:0%
+know is it a phase
+ 
+
+ align:start position:0%
+know is it a phase
+transformation you're going to have um
+
+ align:start position:0%
+transformation you're going to have um
+ 
+
+ align:start position:0%
+transformation you're going to have um
+yeah you could call it a phase
+
+ align:start position:0%
+yeah you could call it a phase
+ 
+
+ align:start position:0%
+yeah you could call it a phase
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+if if you wait long enough what is your
+
+ align:start position:0%
+if if you wait long enough what is your
+ 
+
+ align:start position:0%
+if if you wait long enough what is your
+Final Phase composition going to be what
+
+ align:start position:0%
+Final Phase composition going to be what
+ 
+
+ align:start position:0%
+Final Phase composition going to be what
+will you find in your system if you wait
+
+ align:start position:0%
+will you find in your system if you wait
+ 
+
+ align:start position:0%
+will you find in your system if you wait
+long enough for the transformation or
+
+ align:start position:0%
+long enough for the transformation or
+ 
+
+ align:start position:0%
+long enough for the transformation or
+the spontaneous process
+
+ align:start position:0%
+the spontaneous process
+ 
+
+ align:start position:0%
+the spontaneous process
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complete I have an overall composition
+
+ align:start position:0%
+complete I have an overall composition
+ 
+
+ align:start position:0%
+complete I have an overall composition
+of 38% silicon and the temperature is
+
+ align:start position:0%
+of 38% silicon and the temperature is
+ 
+
+ align:start position:0%
+of 38% silicon and the temperature is
+1200° C is it a combination of the alpha
+
+ align:start position:0%
+1200° C is it a combination of the alpha
+ 
+
+ align:start position:0%
+1200° C is it a combination of the alpha
+and liquid phases like in that region
+
+ align:start position:0%
+and liquid phases like in that region
+ 
+
+ align:start position:0%
+and liquid phases like in that region
+right so the Shaded region you're going
+
+ align:start position:0%
+right so the Shaded region you're going
+ 
+
+ align:start position:0%
+right so the Shaded region you're going
+to is a two-phase region It's a
+
+ align:start position:0%
+to is a two-phase region It's a
+ 
+
+ align:start position:0%
+to is a two-phase region It's a
+combination of Alpha and liquid in fact
+
+ align:start position:0%
+combination of Alpha and liquid in fact
+ 
+
+ align:start position:0%
+combination of Alpha and liquid in fact
+it's written right there Alpha and
+
+ align:start position:0%
+it's written right there Alpha and
+ 
+
+ align:start position:0%
+it's written right there Alpha and
+liquid and to find out what compositions
+
+ align:start position:0%
+liquid and to find out what compositions
+ 
+
+ align:start position:0%
+liquid and to find out what compositions
+those phases have you use the lever Rule
+
+ align:start position:0%
+those phases have you use the lever Rule
+ 
+
+ align:start position:0%
+those phases have you use the lever Rule
+and you apply the concept of TI lines so
+
+ align:start position:0%
+and you apply the concept of TI lines so
+ 
+
+ align:start position:0%
+and you apply the concept of TI lines so
+we have a liquid solution at this
+
+ align:start position:0%
+we have a liquid solution at this
+ 
+
+ align:start position:0%
+we have a liquid solution at this
+composition it's about 16 weight per and
+
+ align:start position:0%
+composition it's about 16 weight per and
+ 
+
+ align:start position:0%
+composition it's about 16 weight per and
+a solid solution at this composition
+
+ align:start position:0%
+a solid solution at this composition
+ 
+
+ align:start position:0%
+a solid solution at this composition
+it's about
+
+ align:start position:0%
+it's about
+ 
+
+ align:start position:0%
+it's about
+45% so it's a two-phase system with a
+
+ align:start position:0%
+45% so it's a two-phase system with a
+ 
+
+ align:start position:0%
+45% so it's a two-phase system with a
+germanium Rich liquid and a silicon
+
+ align:start position:0%
+germanium Rich liquid and a silicon
+ 
+
+ align:start position:0%
+germanium Rich liquid and a silicon
+richer
+
+ align:start position:0%
+richer
+ 
+
+ align:start position:0%
+richer
+solid face SE SE separation phas
+
+ align:start position:0%
+solid face SE SE separation phas
+ 
+
+ align:start position:0%
+solid face SE SE separation phas
+segregation that's right you should be
+
+ align:start position:0%
+segregation that's right you should be
+ 
+
+ align:start position:0%
+segregation that's right you should be
+familiar with this because it it it
+
+ align:start position:0%
+familiar with this because it it it
+ 
+
+ align:start position:0%
+familiar with this because it it it
+takes just a little bit of um flipping
+
+ align:start position:0%
+takes just a little bit of um flipping
+ 
+
+ align:start position:0%
+takes just a little bit of um flipping
+through the textbooks and looking at
+
+ align:start position:0%
+through the textbooks and looking at
+ 
+
+ align:start position:0%
+through the textbooks and looking at
+different pictures which we're going to
+
+ align:start position:0%
+different pictures which we're going to
+ 
+
+ align:start position:0%
+different pictures which we're going to
+continue to do for the next 20 minutes
+
+ align:start position:0%
+continue to do for the next 20 minutes
+ 
+
+ align:start position:0%
+continue to do for the next 20 minutes
+but you know this is something which you
+
+ align:start position:0%
+but you know this is something which you
+ 
+
+ align:start position:0%
+but you know this is something which you
+just have to familiarize yourself with
+
+ align:start position:0%
+just have to familiarize yourself with
+ 
+
+ align:start position:0%
+just have to familiarize yourself with
+um how to read these binary phase
+
+ align:start position:0%
+um how to read these binary phase
+ 
+
+ align:start position:0%
+um how to read these binary phase
+diagrams here's another point the y axis
+
+ align:start position:0%
+diagrams here's another point the y axis
+ 
+
+ align:start position:0%
+diagrams here's another point the y axis
+here tells you something about pure
+
+ align:start position:0%
+here tells you something about pure
+ 
+
+ align:start position:0%
+here tells you something about pure
+geranium the y axis here tells you
+
+ align:start position:0%
+geranium the y axis here tells you
+ 
+
+ align:start position:0%
+geranium the y axis here tells you
+something about pure geranium because
+
+ align:start position:0%
+something about pure geranium because
+ 
+
+ align:start position:0%
+something about pure geranium because
+it's um zero weight per silicon all
+
+ align:start position:0%
+it's um zero weight per silicon all
+ 
+
+ align:start position:0%
+it's um zero weight per silicon all
+right so what does it tell you about
+
+ align:start position:0%
+right so what does it tell you about
+ 
+
+ align:start position:0%
+right so what does it tell you about
+pure germanium what can you learn about
+
+ align:start position:0%
+pure germanium what can you learn about
+ 
+
+ align:start position:0%
+pure germanium what can you learn about
+pure germanium from just this y- axis
+
+ align:start position:0%
+pure germanium from just this y- axis
+ 
+
+ align:start position:0%
+pure germanium from just this y- axis
+alone it has a melting temperature of
+
+ align:start position:0%
+alone it has a melting temperature of
+ 
+
+ align:start position:0%
+alone it has a melting temperature of
+about 940 right you learn it melting
+
+ align:start position:0%
+about 940 right you learn it melting
+ 
+
+ align:start position:0%
+about 940 right you learn it melting
+temperature because this is a this is a
+
+ align:start position:0%
+temperature because this is a this is a
+ 
+
+ align:start position:0%
+temperature because this is a this is a
+little slice of the pure geranium phase
+
+ align:start position:0%
+little slice of the pure geranium phase
+ 
+
+ align:start position:0%
+little slice of the pure geranium phase
+diagram what's unsaid here is the
+
+ align:start position:0%
+diagram what's unsaid here is the
+ 
+
+ align:start position:0%
+diagram what's unsaid here is the
+pressure pressure is almost never
+
+ align:start position:0%
+pressure pressure is almost never
+ 
+
+ align:start position:0%
+pressure pressure is almost never
+reported in binary phase
+
+ align:start position:0%
+reported in binary phase
+ 
+
+ align:start position:0%
+reported in binary phase
+diagrams and unless it's reported
+
+ align:start position:0%
+diagrams and unless it's reported
+ 
+
+ align:start position:0%
+diagrams and unless it's reported
+otherwise you can assume one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+atmosphere okay so at one atmosphere as
+
+ align:start position:0%
+atmosphere okay so at one atmosphere as
+ 
+
+ align:start position:0%
+atmosphere okay so at one atmosphere as
+you take pure geranium and you heat it
+
+ align:start position:0%
+you take pure geranium and you heat it
+ 
+
+ align:start position:0%
+you take pure geranium and you heat it
+up you're in the alpha alpha alpha alpha
+
+ align:start position:0%
+up you're in the alpha alpha alpha alpha
+ 
+
+ align:start position:0%
+up you're in the alpha alpha alpha alpha
+alpha
+
+ align:start position:0%
+alpha
+ 
+
+ align:start position:0%
+alpha
+liquid so in between it melted good
+
+ align:start position:0%
+liquid so in between it melted good
+ 
+
+ align:start position:0%
+liquid so in between it melted good
+what's the melting temperature of
+
+ align:start position:0%
+what's the melting temperature of
+ 
+
+ align:start position:0%
+what's the melting temperature of
+silicon maybe somebody who hasn't uh
+
+ align:start position:0%
+silicon maybe somebody who hasn't uh
+ 
+
+ align:start position:0%
+silicon maybe somebody who hasn't uh
+hasn't contributed yet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today 1,412 degrees CS thanks yeah 1412
+
+ align:start position:0%
+today 1,412 degrees CS thanks yeah 1412
+ 
+
+ align:start position:0%
+today 1,412 degrees CS thanks yeah 1412
+that's right so if you take pure silicon
+
+ align:start position:0%
+that's right so if you take pure silicon
+ 
+
+ align:start position:0%
+that's right so if you take pure silicon
+you can see it's in
+
+ align:start position:0%
+you can see it's in
+ 
+
+ align:start position:0%
+you can see it's in
+Alpha and now it's in liquid so it
+
+ align:start position:0%
+Alpha and now it's in liquid so it
+ 
+
+ align:start position:0%
+Alpha and now it's in liquid so it
+melted 1412 so these binary phase
+
+ align:start position:0%
+melted 1412 so these binary phase
+ 
+
+ align:start position:0%
+melted 1412 so these binary phase
+diagrams contain unary phase diagrams
+
+ align:start position:0%
+diagrams contain unary phase diagrams
+ 
+
+ align:start position:0%
+diagrams contain unary phase diagrams
+they they contain isobaric slices
+
+ align:start position:0%
+they they contain isobaric slices
+ 
+
+ align:start position:0%
+they they contain isobaric slices
+through unary phase
+
+ align:start position:0%
+through unary phase
+ 
+
+ align:start position:0%
+through unary phase
+diagrams along the y-
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axis if you like you can imagine the
+
+ align:start position:0%
+axis if you like you can imagine the
+ 
+
+ align:start position:0%
+axis if you like you can imagine the
+unary phase diagram just coming out of
+
+ align:start position:0%
+unary phase diagram just coming out of
+ 
+
+ align:start position:0%
+unary phase diagram just coming out of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+board okay let's see what else here's a
+
+ align:start position:0%
+board okay let's see what else here's a
+ 
+
+ align:start position:0%
+board okay let's see what else here's a
+binary phase diagram we've seen this one
+
+ align:start position:0%
+binary phase diagram we've seen this one
+ 
+
+ align:start position:0%
+binary phase diagram we've seen this one
+already so this is an isomorphous system
+
+ align:start position:0%
+already so this is an isomorphous system
+ 
+
+ align:start position:0%
+already so this is an isomorphous system
+but it has a Mis ability Gap this is not
+
+ align:start position:0%
+but it has a Mis ability Gap this is not
+ 
+
+ align:start position:0%
+but it has a Mis ability Gap this is not
+a system which is fully missible this is
+
+ align:start position:0%
+a system which is fully missible this is
+ 
+
+ align:start position:0%
+a system which is fully missible this is
+a system which is missible at high
+
+ align:start position:0%
+a system which is missible at high
+ 
+
+ align:start position:0%
+a system which is missible at high
+temperature but imiss at low
+
+ align:start position:0%
+temperature but imiss at low
+ 
+
+ align:start position:0%
+temperature but imiss at low
+temperature we've seen we we we've
+
+ align:start position:0%
+temperature we've seen we we we've
+ 
+
+ align:start position:0%
+temperature we've seen we we we've
+started to see that the last time this
+
+ align:start position:0%
+started to see that the last time this
+ 
+
+ align:start position:0%
+started to see that the last time this
+is called the spinodal
+
+ align:start position:0%
+is called the spinodal
+ 
+
+ align:start position:0%
+is called the spinodal
+system and as you start at high
+
+ align:start position:0%
+system and as you start at high
+ 
+
+ align:start position:0%
+system and as you start at high
+temperature and you start cooling down
+
+ align:start position:0%
+temperature and you start cooling down
+ 
+
+ align:start position:0%
+temperature and you start cooling down
+you have separation into an ethanol Rich
+
+ align:start position:0%
+you have separation into an ethanol Rich
+ 
+
+ align:start position:0%
+you have separation into an ethanol Rich
+phase and a d Deane Rich phase so for
+
+ align:start position:0%
+phase and a d Deane Rich phase so for
+ 
+
+ align:start position:0%
+phase and a d Deane Rich phase so for
+instance let's imagine that I am at 4
+
+ align:start position:0%
+instance let's imagine that I am at 4
+ 
+
+ align:start position:0%
+instance let's imagine that I am at 4
+degrees C I have an overall system
+
+ align:start position:0%
+degrees C I have an overall system
+ 
+
+ align:start position:0%
+degrees C I have an overall system
+composition of6 Mo fraction of
+
+ align:start position:0%
+composition of6 Mo fraction of
+ 
+
+ align:start position:0%
+composition of6 Mo fraction of
+ethanol what should you expect to find
+
+ align:start position:0%
+ethanol what should you expect to find
+ 
+
+ align:start position:0%
+ethanol what should you expect to find
+it equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ask this should you expect to find a
+
+ align:start position:0%
+ask this should you expect to find a
+ 
+
+ align:start position:0%
+ask this should you expect to find a
+uniform solution with 6 Mo fraction of
+
+ align:start position:0%
+uniform solution with 6 Mo fraction of
+ 
+
+ align:start position:0%
+uniform solution with 6 Mo fraction of
+ethanol classes un sure but somebody
+
+ align:start position:0%
+ethanol classes un sure but somebody
+ 
+
+ align:start position:0%
+ethanol classes un sure but somebody
+guess let's take a wild guess what what
+
+ align:start position:0%
+guess let's take a wild guess what what
+ 
+
+ align:start position:0%
+guess let's take a wild guess what what
+would I expect to find an
+
+ align:start position:0%
+would I expect to find an
+ 
+
+ align:start position:0%
+would I expect to find an
+equilibrium overall system composition
+
+ align:start position:0%
+equilibrium overall system composition
+ 
+
+ align:start position:0%
+equilibrium overall system composition
+this is what I prepare 6 mol fraction
+
+ align:start position:0%
+this is what I prepare 6 mol fraction
+ 
+
+ align:start position:0%
+this is what I prepare 6 mol fraction
+ethanol 4 degrees C I I shake up the
+
+ align:start position:0%
+ethanol 4 degrees C I I shake up the
+ 
+
+ align:start position:0%
+ethanol 4 degrees C I I shake up the
+beaker and then I wait for a long time
+
+ align:start position:0%
+beaker and then I wait for a long time
+ 
+
+ align:start position:0%
+beaker and then I wait for a long time
+what will I find at
+
+ align:start position:0%
+what will I find at
+ 
+
+ align:start position:0%
+what will I find at
+equilibrium they spontaneously unmix it
+
+ align:start position:0%
+equilibrium they spontaneously unmix it
+ 
+
+ align:start position:0%
+equilibrium they spontaneously unmix it
+would spontaneously unmix thank you and
+
+ align:start position:0%
+would spontaneously unmix thank you and
+ 
+
+ align:start position:0%
+would spontaneously unmix thank you and
+it would unmix into what what would I
+
+ align:start position:0%
+it would unmix into what what would I
+ 
+
+ align:start position:0%
+it would unmix into what what would I
+find at the end of this
+
+ align:start position:0%
+find at the end of this
+ 
+
+ align:start position:0%
+find at the end of this
+process I love that spontaneous unmixing
+
+ align:start position:0%
+process I love that spontaneous unmixing
+ 
+
+ align:start position:0%
+process I love that spontaneous unmixing
+that's exactly right what would be the
+
+ align:start position:0%
+that's exactly right what would be the
+ 
+
+ align:start position:0%
+that's exactly right what would be the
+final product when when when the changes
+
+ align:start position:0%
+final product when when when the changes
+ 
+
+ align:start position:0%
+final product when when when the changes
+stop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happening part of this is is is stuff
+
+ align:start position:0%
+happening part of this is is is stuff
+ 
+
+ align:start position:0%
+happening part of this is is is stuff
+that you're working on in this P set
+
+ align:start position:0%
+that you're working on in this P set
+ 
+
+ align:start position:0%
+that you're working on in this P set
+which is in due for 4 days so I'm sort
+
+ align:start position:0%
+which is in due for 4 days so I'm sort
+ 
+
+ align:start position:0%
+which is in due for 4 days so I'm sort
+of cing the class on the spot but you
+
+ align:start position:0%
+of cing the class on the spot but you
+ 
+
+ align:start position:0%
+of cing the class on the spot but you
+imagine a TI line drawn to connect the
+
+ align:start position:0%
+imagine a TI line drawn to connect the
+ 
+
+ align:start position:0%
+imagine a TI line drawn to connect the
+re the edges of the two-phase
+
+ align:start position:0%
+re the edges of the two-phase
+ 
+
+ align:start position:0%
+re the edges of the two-phase
+region so what you have is ethanol Rich
+
+ align:start position:0%
+region so what you have is ethanol Rich
+ 
+
+ align:start position:0%
+region so what you have is ethanol Rich
+phase with is 85%
+
+ align:start position:0%
+phase with is 85%
+ 
+
+ align:start position:0%
+phase with is 85%
+ethanol and a Deane Rich phase with
+
+ align:start position:0%
+ethanol and a Deane Rich phase with
+ 
+
+ align:start position:0%
+ethanol and a Deane Rich phase with
+whatever this is 33% of the can and
+
+ align:start position:0%
+whatever this is 33% of the can and
+ 
+
+ align:start position:0%
+whatever this is 33% of the can and
+those are the two phases that you'll
+
+ align:start position:0%
+those are the two phases that you'll
+ 
+
+ align:start position:0%
+those are the two phases that you'll
+find coexisting at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium here's a slightly more
+
+ align:start position:0%
+equilibrium here's a slightly more
+ 
+
+ align:start position:0%
+equilibrium here's a slightly more
+complicated spinodal system now instead
+
+ align:start position:0%
+complicated spinodal system now instead
+ 
+
+ align:start position:0%
+complicated spinodal system now instead
+of a a
+
+ align:start position:0%
+of a a
+ 
+
+ align:start position:0%
+of a a
+system with a liquid spinal phase we now
+
+ align:start position:0%
+system with a liquid spinal phase we now
+ 
+
+ align:start position:0%
+system with a liquid spinal phase we now
+have a solid so there's a little bit
+
+ align:start position:0%
+have a solid so there's a little bit
+ 
+
+ align:start position:0%
+have a solid so there's a little bit
+more going on
+
+ align:start position:0%
+more going on
+ 
+
+ align:start position:0%
+more going on
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+this purplish region is a solid solution
+
+ align:start position:0%
+this purplish region is a solid solution
+ 
+
+ align:start position:0%
+this purplish region is a solid solution
+between aluminum and
+
+ align:start position:0%
+between aluminum and
+ 
+
+ align:start position:0%
+between aluminum and
+zinc now often in phas
+
+ align:start position:0%
+zinc now often in phas
+ 
+
+ align:start position:0%
+zinc now often in phas
+diagrams the parent or the pure material
+
+ align:start position:0%
+diagrams the parent or the pure material
+ 
+
+ align:start position:0%
+diagrams the parent or the pure material
+will be indicated in
+
+ align:start position:0%
+will be indicated in
+ 
+
+ align:start position:0%
+will be indicated in
+parenthesis what that tells you is that
+
+ align:start position:0%
+parenthesis what that tells you is that
+ 
+
+ align:start position:0%
+parenthesis what that tells you is that
+this solution region has the structure
+
+ align:start position:0%
+this solution region has the structure
+ 
+
+ align:start position:0%
+this solution region has the structure
+of pure
+
+ align:start position:0%
+of pure
+ 
+
+ align:start position:0%
+of pure
+aluminum reading binary phase diagrams
+
+ align:start position:0%
+aluminum reading binary phase diagrams
+ 
+
+ align:start position:0%
+aluminum reading binary phase diagrams
+is often an exercise in being a little
+
+ align:start position:0%
+is often an exercise in being a little
+ 
+
+ align:start position:0%
+is often an exercise in being a little
+frustrated in how the people who made
+
+ align:start position:0%
+frustrated in how the people who made
+ 
+
+ align:start position:0%
+frustrated in how the people who made
+the diagrams are very
+
+ align:start position:0%
+the diagrams are very
+ 
+
+ align:start position:0%
+the diagrams are very
+concise in other words there's a lot of
+
+ align:start position:0%
+concise in other words there's a lot of
+ 
+
+ align:start position:0%
+concise in other words there's a lot of
+shorthand and you'll encounter binary
+
+ align:start position:0%
+shorthand and you'll encounter binary
+ 
+
+ align:start position:0%
+shorthand and you'll encounter binary
+phase diagrams drawn in many different
+
+ align:start position:0%
+phase diagrams drawn in many different
+ 
+
+ align:start position:0%
+phase diagrams drawn in many different
+ways and with many different types of
+
+ align:start position:0%
+ways and with many different types of
+ 
+
+ align:start position:0%
+ways and with many different types of
+shorthand um if I could wave a magic
+
+ align:start position:0%
+shorthand um if I could wave a magic
+ 
+
+ align:start position:0%
+shorthand um if I could wave a magic
+wand and change all B binary phase
+
+ align:start position:0%
+wand and change all B binary phase
+ 
+
+ align:start position:0%
+wand and change all B binary phase
+diagrams in the world into a uniform
+
+ align:start position:0%
+diagrams in the world into a uniform
+ 
+
+ align:start position:0%
+diagrams in the world into a uniform
+presentation I would do so but I don't
+
+ align:start position:0%
+presentation I would do so but I don't
+ 
+
+ align:start position:0%
+presentation I would do so but I don't
+have that magic wand and so instead my
+
+ align:start position:0%
+have that magic wand and so instead my
+ 
+
+ align:start position:0%
+have that magic wand and so instead my
+job is to get you familiar with being a
+
+ align:start position:0%
+job is to get you familiar with being a
+ 
+
+ align:start position:0%
+job is to get you familiar with being a
+little bit annoyed that you're not
+
+ align:start position:0%
+little bit annoyed that you're not
+ 
+
+ align:start position:0%
+little bit annoyed that you're not
+getting all the information you need
+
+ align:start position:0%
+getting all the information you need
+ 
+
+ align:start position:0%
+getting all the information you need
+because many of you will see this next
+
+ align:start position:0%
+because many of you will see this next
+ 
+
+ align:start position:0%
+because many of you will see this next
+in Industry you'll go straight from O2
+
+ align:start position:0%
+in Industry you'll go straight from O2
+ 
+
+ align:start position:0%
+in Industry you'll go straight from O2
+to actually needing to read these things
+
+ align:start position:0%
+to actually needing to read these things
+ 
+
+ align:start position:0%
+to actually needing to read these things
+on the Joba so that's why I'm showing
+
+ align:start position:0%
+on the Joba so that's why I'm showing
+ 
+
+ align:start position:0%
+on the Joba so that's why I'm showing
+you these different presentations
+
+ align:start position:0%
+you these different presentations
+ 
+
+ align:start position:0%
+you these different presentations
+because it's the sort of thing you're
+
+ align:start position:0%
+because it's the sort of thing you're
+ 
+
+ align:start position:0%
+because it's the sort of thing you're
+going to find out there so aluminum here
+
+ align:start position:0%
+going to find out there so aluminum here
+ 
+
+ align:start position:0%
+going to find out there so aluminum here
+uh doesn't mean that this whole region
+
+ align:start position:0%
+uh doesn't mean that this whole region
+ 
+
+ align:start position:0%
+uh doesn't mean that this whole region
+is pure aluminum it's obviously not
+
+ align:start position:0%
+is pure aluminum it's obviously not
+ 
+
+ align:start position:0%
+is pure aluminum it's obviously not
+because this is the binary phase diagram
+
+ align:start position:0%
+because this is the binary phase diagram
+ 
+
+ align:start position:0%
+because this is the binary phase diagram
+what it does mean is that this whole
+
+ align:start position:0%
+what it does mean is that this whole
+ 
+
+ align:start position:0%
+what it does mean is that this whole
+solution region here has the structure
+
+ align:start position:0%
+solution region here has the structure
+ 
+
+ align:start position:0%
+solution region here has the structure
+of aluminum which happens to be
+
+ align:start position:0%
+of aluminum which happens to be
+ 
+
+ align:start position:0%
+of aluminum which happens to be
+FCC so we have an aluminum Rich FCC
+
+ align:start position:0%
+FCC so we have an aluminum Rich FCC
+ 
+
+ align:start position:0%
+FCC so we have an aluminum Rich FCC
+solid solution here and here is a
+
+ align:start position:0%
+solid solution here and here is a
+ 
+
+ align:start position:0%
+solid solution here and here is a
+spinodal at below 3502 de C this
+
+ align:start position:0%
+spinodal at below 3502 de C this
+ 
+
+ align:start position:0%
+spinodal at below 3502 de C this
+solution will spontaneously unmix into a
+
+ align:start position:0%
+solution will spontaneously unmix into a
+ 
+
+ align:start position:0%
+solution will spontaneously unmix into a
+zinc Rich FCC and an aluminum
+
+ align:start position:0%
+zinc Rich FCC and an aluminum
+ 
+
+ align:start position:0%
+zinc Rich FCC and an aluminum
+FCC so this little Dome here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a spinodal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system there's more going on here of
+
+ align:start position:0%
+system there's more going on here of
+ 
+
+ align:start position:0%
+system there's more going on here of
+course we there's more to read we see
+
+ align:start position:0%
+course we there's more to read we see
+ 
+
+ align:start position:0%
+course we there's more to read we see
+that zinc over here zinc over here is
+
+ align:start position:0%
+that zinc over here zinc over here is
+ 
+
+ align:start position:0%
+that zinc over here zinc over here is
+hexagonal close packed you can dissolve
+
+ align:start position:0%
+hexagonal close packed you can dissolve
+ 
+
+ align:start position:0%
+hexagonal close packed you can dissolve
+a little bit of aluminum and hcp zinc
+
+ align:start position:0%
+a little bit of aluminum and hcp zinc
+ 
+
+ align:start position:0%
+a little bit of aluminum and hcp zinc
+but not too much before its phase
+
+ align:start position:0%
+but not too much before its phase
+ 
+
+ align:start position:0%
+but not too much before its phase
+segregates the liquids are fully
+
+ align:start position:0%
+segregates the liquids are fully
+ 
+
+ align:start position:0%
+segregates the liquids are fully
+missible if you go up above the melting
+
+ align:start position:0%
+missible if you go up above the melting
+ 
+
+ align:start position:0%
+missible if you go up above the melting
+point of aluminum which you can read
+
+ align:start position:0%
+point of aluminum which you can read
+ 
+
+ align:start position:0%
+point of aluminum which you can read
+here at 660 degrees C then zinc and
+
+ align:start position:0%
+here at 660 degrees C then zinc and
+ 
+
+ align:start position:0%
+here at 660 degrees C then zinc and
+aluminum uh mix
+
+ align:start position:0%
+aluminum uh mix
+ 
+
+ align:start position:0%
+aluminum uh mix
+completely on these phase diagrams which
+
+ align:start position:0%
+completely on these phase diagrams which
+ 
+
+ align:start position:0%
+completely on these phase diagrams which
+are this is as produced by ASM and this
+
+ align:start position:0%
+are this is as produced by ASM and this
+ 
+
+ align:start position:0%
+are this is as produced by ASM and this
+is Society for Metallurgy so you're
+
+ align:start position:0%
+is Society for Metallurgy so you're
+ 
+
+ align:start position:0%
+is Society for Metallurgy so you're
+going to see a lot of these phase
+
+ align:start position:0%
+going to see a lot of these phase
+ 
+
+ align:start position:0%
+going to see a lot of these phase
+diagrams in your careers because ASM is
+
+ align:start position:0%
+diagrams in your careers because ASM is
+ 
+
+ align:start position:0%
+diagrams in your careers because ASM is
+a major source of data um they indicate
+
+ align:start position:0%
+a major source of data um they indicate
+ 
+
+ align:start position:0%
+a major source of data um they indicate
+solution regions with this nice purplish
+
+ align:start position:0%
+solution regions with this nice purplish
+ 
+
+ align:start position:0%
+solution regions with this nice purplish
+color and they indicate two-phase
+
+ align:start position:0%
+color and they indicate two-phase
+ 
+
+ align:start position:0%
+color and they indicate two-phase
+regions with a white fill so they don't
+
+ align:start position:0%
+regions with a white fill so they don't
+ 
+
+ align:start position:0%
+regions with a white fill so they don't
+they don't say two-phase region they
+
+ align:start position:0%
+they don't say two-phase region they
+ 
+
+ align:start position:0%
+they don't say two-phase region they
+don't tell you what two phases are
+
+ align:start position:0%
+don't tell you what two phases are
+ 
+
+ align:start position:0%
+don't tell you what two phases are
+coexisting how do you how do you tell
+
+ align:start position:0%
+coexisting how do you how do you tell
+ 
+
+ align:start position:0%
+coexisting how do you how do you tell
+what coexists so look where my cursor is
+
+ align:start position:0%
+what coexists so look where my cursor is
+ 
+
+ align:start position:0%
+what coexists so look where my cursor is
+what two phases
+
+ align:start position:0%
+what two phases
+ 
+
+ align:start position:0%
+what two phases
+coexist for systems with this overall
+
+ align:start position:0%
+coexist for systems with this overall
+ 
+
+ align:start position:0%
+coexist for systems with this overall
+composition as my cursor
+
+ align:start position:0%
+composition as my cursor
+ 
+
+ align:start position:0%
+composition as my cursor
+is you want to draw a TI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line so what two phases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coexist at this overall system
+
+ align:start position:0%
+coexist at this overall system
+ 
+
+ align:start position:0%
+coexist at this overall system
+composition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aluminum Rich FCC and liquid aluminum
+
+ align:start position:0%
+aluminum Rich FCC and liquid aluminum
+ 
+
+ align:start position:0%
+aluminum Rich FCC and liquid aluminum
+Rich FCC and liquid great okay here's
+
+ align:start position:0%
+Rich FCC and liquid great okay here's
+ 
+
+ align:start position:0%
+Rich FCC and liquid great okay here's
+another example somebody who hasn't uh
+
+ align:start position:0%
+another example somebody who hasn't uh
+ 
+
+ align:start position:0%
+another example somebody who hasn't uh
+contributed yet today please what phases
+
+ align:start position:0%
+contributed yet today please what phases
+ 
+
+ align:start position:0%
+contributed yet today please what phases
+coexist when I have an overall system
+
+ align:start position:0%
+coexist when I have an overall system
+ 
+
+ align:start position:0%
+coexist when I have an overall system
+composition is indicated by the cursor
+
+ align:start position:0%
+composition is indicated by the cursor
+ 
+
+ align:start position:0%
+composition is indicated by the cursor
+there is it zrich FCC and hcp that's
+
+ align:start position:0%
+there is it zrich FCC and hcp that's
+ 
+
+ align:start position:0%
+there is it zrich FCC and hcp that's
+right you're going to have here I'll
+
+ align:start position:0%
+right you're going to have here I'll
+ 
+
+ align:start position:0%
+right you're going to have here I'll
+I'll indicate a little more you're going
+
+ align:start position:0%
+I'll indicate a little more you're going
+ 
+
+ align:start position:0%
+I'll indicate a little more you're going
+to have a zinc Rich FCC
+
+ align:start position:0%
+to have a zinc Rich FCC
+ 
+
+ align:start position:0%
+to have a zinc Rich FCC
+with this
+
+ align:start position:0%
+with this
+ 
+
+ align:start position:0%
+with this
+composition coexisting with
+
+ align:start position:0%
+composition coexisting with
+ 
+
+ align:start position:0%
+composition coexisting with
+hcp with a little bit of aluminum
+
+ align:start position:0%
+hcp with a little bit of aluminum
+ 
+
+ align:start position:0%
+hcp with a little bit of aluminum
+dissolved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in so you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+this composition
+
+ align:start position:0%
+this composition
+ 
+
+ align:start position:0%
+this composition
+coexisting with this composition right
+
+ align:start position:0%
+coexisting with this composition right
+ 
+
+ align:start position:0%
+coexisting with this composition right
+that's how you read those two phase
+
+ align:start position:0%
+that's how you read those two phase
+ 
+
+ align:start position:0%
+that's how you read those two phase
+regions good okay so you have here uh
+
+ align:start position:0%
+regions good okay so you have here uh
+ 
+
+ align:start position:0%
+regions good okay so you have here uh
+what this is kind of interesting because
+
+ align:start position:0%
+what this is kind of interesting because
+ 
+
+ align:start position:0%
+what this is kind of interesting because
+if you cool down just a little bit
+
+ align:start position:0%
+if you cool down just a little bit
+ 
+
+ align:start position:0%
+if you cool down just a little bit
+more let's imagine cooling
+
+ align:start position:0%
+more let's imagine cooling
+ 
+
+ align:start position:0%
+more let's imagine cooling
+down to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temperature so when I
+
+ align:start position:0%
+temperature so when I
+ 
+
+ align:start position:0%
+temperature so when I
+am at the slightly higher
+
+ align:start position:0%
+am at the slightly higher
+ 
+
+ align:start position:0%
+am at the slightly higher
+temperature my system at equilibrium is
+
+ align:start position:0%
+temperature my system at equilibrium is
+ 
+
+ align:start position:0%
+temperature my system at equilibrium is
+zinc Ridge
+
+ align:start position:0%
+zinc Ridge
+ 
+
+ align:start position:0%
+zinc Ridge
+FCC and the hcp with a little aluminum
+
+ align:start position:0%
+FCC and the hcp with a little aluminum
+ 
+
+ align:start position:0%
+FCC and the hcp with a little aluminum
+but if I cool
+
+ align:start position:0%
+but if I cool
+ 
+
+ align:start position:0%
+but if I cool
+down suddenly my system composition in
+
+ align:start position:0%
+down suddenly my system composition in
+ 
+
+ align:start position:0%
+down suddenly my system composition in
+equilibrium is
+
+ align:start position:0%
+equilibrium is
+ 
+
+ align:start position:0%
+equilibrium is
+now aluminum Rich
+
+ align:start position:0%
+now aluminum Rich
+ 
+
+ align:start position:0%
+now aluminum Rich
+FCC an hcp with a little
+
+ align:start position:0%
+FCC an hcp with a little
+ 
+
+ align:start position:0%
+FCC an hcp with a little
+aluminum these phase diagrams get very
+
+ align:start position:0%
+aluminum these phase diagrams get very
+ 
+
+ align:start position:0%
+aluminum these phase diagrams get very
+rich and complicated as you can imagine
+
+ align:start position:0%
+rich and complicated as you can imagine
+ 
+
+ align:start position:0%
+rich and complicated as you can imagine
+we're just learning the basics here of
+
+ align:start position:0%
+we're just learning the basics here of
+ 
+
+ align:start position:0%
+we're just learning the basics here of
+how to read them let's move on here's
+
+ align:start position:0%
+how to read them let's move on here's
+ 
+
+ align:start position:0%
+how to read them let's move on here's
+another example this has something
+
+ align:start position:0%
+another example this has something
+ 
+
+ align:start position:0%
+another example this has something
+called intermediate phases so we have
+
+ align:start position:0%
+called intermediate phases so we have
+ 
+
+ align:start position:0%
+called intermediate phases so we have
+this chromium titanium system the
+
+ align:start position:0%
+this chromium titanium system the
+ 
+
+ align:start position:0%
+this chromium titanium system the
+chromium titanium system contains a lot
+
+ align:start position:0%
+chromium titanium system contains a lot
+ 
+
+ align:start position:0%
+chromium titanium system contains a lot
+of things which we're going to learn
+
+ align:start position:0%
+of things which we're going to learn
+ 
+
+ align:start position:0%
+of things which we're going to learn
+about it contains a tic a spinodal
+
+ align:start position:0%
+about it contains a tic a spinodal
+ 
+
+ align:start position:0%
+about it contains a tic a spinodal
+looking thing right it's got this BCC
+
+ align:start position:0%
+looking thing right it's got this BCC
+ 
+
+ align:start position:0%
+looking thing right it's got this BCC
+region which is fully missable in this
+
+ align:start position:0%
+region which is fully missable in this
+ 
+
+ align:start position:0%
+region which is fully missable in this
+little narrow temperature range at 1400
+
+ align:start position:0%
+little narrow temperature range at 1400
+ 
+
+ align:start position:0%
+little narrow temperature range at 1400
+degrees C looks like this system is
+
+ align:start position:0%
+degrees C looks like this system is
+ 
+
+ align:start position:0%
+degrees C looks like this system is
+fully missable as a solid in the BCC
+
+ align:start position:0%
+fully missable as a solid in the BCC
+ 
+
+ align:start position:0%
+fully missable as a solid in the BCC
+structure and you see here they've
+
+ align:start position:0%
+structure and you see here they've
+ 
+
+ align:start position:0%
+structure and you see here they've
+indicated that with parenthesis Thai
+
+ align:start position:0%
+indicated that with parenthesis Thai
+ 
+
+ align:start position:0%
+indicated that with parenthesis Thai
+chromium fully missible as
+
+ align:start position:0%
+chromium fully missible as
+ 
+
+ align:start position:0%
+chromium fully missible as
+BCC but when I cool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down I have spontaneous unmixing and
+
+ align:start position:0%
+down I have spontaneous unmixing and
+ 
+
+ align:start position:0%
+down I have spontaneous unmixing and
+here I don't just have spontaneous
+
+ align:start position:0%
+here I don't just have spontaneous
+ 
+
+ align:start position:0%
+here I don't just have spontaneous
+unmixing into chromium Rich BCC and
+
+ align:start position:0%
+unmixing into chromium Rich BCC and
+ 
+
+ align:start position:0%
+unmixing into chromium Rich BCC and
+titanium Rich BCC this system gives me
+
+ align:start position:0%
+titanium Rich BCC this system gives me
+ 
+
+ align:start position:0%
+titanium Rich BCC this system gives me
+intermediate phases which we'll cover in
+
+ align:start position:0%
+intermediate phases which we'll cover in
+ 
+
+ align:start position:0%
+intermediate phases which we'll cover in
+a couple weeks so it gets a little bit
+
+ align:start position:0%
+a couple weeks so it gets a little bit
+ 
+
+ align:start position:0%
+a couple weeks so it gets a little bit
+complicated I noticed on my annotations
+
+ align:start position:0%
+complicated I noticed on my annotations
+ 
+
+ align:start position:0%
+complicated I noticed on my annotations
+haven't uh disappeared so let me clear
+
+ align:start position:0%
+haven't uh disappeared so let me clear
+ 
+
+ align:start position:0%
+haven't uh disappeared so let me clear
+those there we go
+
+ align:start position:0%
+those there we go
+ 
+
+ align:start position:0%
+those there we go
+okay this system also has an interesting
+
+ align:start position:0%
+okay this system also has an interesting
+ 
+
+ align:start position:0%
+okay this system also has an interesting
+phenomenon of liquid melting point
+
+ align:start position:0%
+phenomenon of liquid melting point
+ 
+
+ align:start position:0%
+phenomenon of liquid melting point
+suppression
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is this is indicative of tic
+
+ align:start position:0%
+so this is this is indicative of tic
+ 
+
+ align:start position:0%
+so this is this is indicative of tic
+like Behavior we haven't gotten there
+
+ align:start position:0%
+like Behavior we haven't gotten there
+ 
+
+ align:start position:0%
+like Behavior we haven't gotten there
+yet but you see the melting point of the
+
+ align:start position:0%
+yet but you see the melting point of the
+ 
+
+ align:start position:0%
+yet but you see the melting point of the
+solution is actually lower than the
+
+ align:start position:0%
+solution is actually lower than the
+ 
+
+ align:start position:0%
+solution is actually lower than the
+melting point of either of the pure
+
+ align:start position:0%
+melting point of either of the pure
+ 
+
+ align:start position:0%
+melting point of either of the pure
+components that's very common
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Behavior we could probably stare at this
+
+ align:start position:0%
+Behavior we could probably stare at this
+ 
+
+ align:start position:0%
+Behavior we could probably stare at this
+for another hour and continue to be
+
+ align:start position:0%
+for another hour and continue to be
+ 
+
+ align:start position:0%
+for another hour and continue to be
+learning let me move on um no let let me
+
+ align:start position:0%
+learning let me move on um no let let me
+ 
+
+ align:start position:0%
+learning let me move on um no let let me
+not move on let me sit here for another
+
+ align:start position:0%
+not move on let me sit here for another
+ 
+
+ align:start position:0%
+not move on let me sit here for another
+minute and collect any questions or
+
+ align:start position:0%
+minute and collect any questions or
+ 
+
+ align:start position:0%
+minute and collect any questions or
+Curiosities that that that come up is
+
+ align:start position:0%
+Curiosities that that that come up is
+ 
+
+ align:start position:0%
+Curiosities that that that come up is
+there anything about this that that
+
+ align:start position:0%
+there anything about this that that
+ 
+
+ align:start position:0%
+there anything about this that that
+you're just burning to have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answered understanding that that this is
+
+ align:start position:0%
+answered understanding that that this is
+ 
+
+ align:start position:0%
+answered understanding that that this is
+kind of complicated and and we'll be
+
+ align:start position:0%
+kind of complicated and and we'll be
+ 
+
+ align:start position:0%
+kind of complicated and and we'll be
+spending the next couple weeks on
+
+ align:start position:0%
+spending the next couple weeks on
+ 
+
+ align:start position:0%
+spending the next couple weeks on
+diagrams like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so what happens when there's like a
+
+ align:start position:0%
+this so what happens when there's like a
+ 
+
+ align:start position:0%
+this so what happens when there's like a
+TI line that goes through multiple
+
+ align:start position:0%
+TI line that goes through multiple
+ 
+
+ align:start position:0%
+TI line that goes through multiple
+phases is it just telling you about
+
+ align:start position:0%
+phases is it just telling you about
+ 
+
+ align:start position:0%
+phases is it just telling you about
+what's happening on the left and right
+
+ align:start position:0%
+what's happening on the left and right
+ 
+
+ align:start position:0%
+what's happening on the left and right
+or yeah they're complic
+
+ align:start position:0%
+or yeah they're complic
+ 
+
+ align:start position:0%
+or yeah they're complic
+so what on Earth is going on here this
+
+ align:start position:0%
+so what on Earth is going on here this
+ 
+
+ align:start position:0%
+so what on Earth is going on here this
+is what's going on are you talking about
+
+ align:start position:0%
+is what's going on are you talking about
+ 
+
+ align:start position:0%
+is what's going on are you talking about
+this TI line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here yeah let's look at all the ti lines
+
+ align:start position:0%
+here yeah let's look at all the ti lines
+ 
+
+ align:start position:0%
+here yeah let's look at all the ti lines
+in this diagram let's start there at 686
+
+ align:start position:0%
+in this diagram let's start there at 686
+ 
+
+ align:start position:0%
+in this diagram let's start there at 686
+degrees they've drawn a TI line in
+
+ align:start position:0%
+degrees they've drawn a TI line in
+ 
+
+ align:start position:0%
+degrees they've drawn a TI line in
+between titanium and its hcp phase which
+
+ align:start position:0%
+between titanium and its hcp phase which
+ 
+
+ align:start position:0%
+between titanium and its hcp phase which
+has a tiny little sliver of chromium
+
+ align:start position:0%
+has a tiny little sliver of chromium
+ 
+
+ align:start position:0%
+has a tiny little sliver of chromium
+solubility you can just see that little
+
+ align:start position:0%
+solubility you can just see that little
+ 
+
+ align:start position:0%
+solubility you can just see that little
+purple
+
+ align:start position:0%
+purple
+ 
+
+ align:start position:0%
+purple
+region and This Ti Chrome 2 room
+
+ align:start position:0%
+region and This Ti Chrome 2 room
+ 
+
+ align:start position:0%
+region and This Ti Chrome 2 room
+temperature polymorph RT room
+
+ align:start position:0%
+temperature polymorph RT room
+ 
+
+ align:start position:0%
+temperature polymorph RT room
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+polymorph and so this this two-phase
+
+ align:start position:0%
+polymorph and so this this two-phase
+ 
+
+ align:start position:0%
+polymorph and so this this two-phase
+region down
+
+ align:start position:0%
+region down
+ 
+
+ align:start position:0%
+region down
+here below the tie line that's drawn is
+
+ align:start position:0%
+here below the tie line that's drawn is
+ 
+
+ align:start position:0%
+here below the tie line that's drawn is
+a two-phase region between titanium room
+
+ align:start position:0%
+a two-phase region between titanium room
+ 
+
+ align:start position:0%
+a two-phase region between titanium room
+temperature polymorph and This Ti chrome
+
+ align:start position:0%
+temperature polymorph and This Ti chrome
+ 
+
+ align:start position:0%
+temperature polymorph and This Ti chrome
+room temperature
+
+ align:start position:0%
+room temperature
+ 
+
+ align:start position:0%
+room temperature
+polymorph now when I go
+
+ align:start position:0%
+polymorph now when I go
+ 
+
+ align:start position:0%
+polymorph now when I go
+above what happened I went above this
+
+ align:start position:0%
+above what happened I went above this
+ 
+
+ align:start position:0%
+above what happened I went above this
+kind of funny looking minimum now this
+
+ align:start position:0%
+kind of funny looking minimum now this
+ 
+
+ align:start position:0%
+kind of funny looking minimum now this
+two-phase region is between Ty Chrome in
+
+ align:start position:0%
+two-phase region is between Ty Chrome in
+ 
+
+ align:start position:0%
+two-phase region is between Ty Chrome in
+the BCC structure and this Ty chromium
+
+ align:start position:0%
+the BCC structure and this Ty chromium
+ 
+
+ align:start position:0%
+the BCC structure and this Ty chromium
+to room temperature polymorph whereas
+
+ align:start position:0%
+to room temperature polymorph whereas
+ 
+
+ align:start position:0%
+to room temperature polymorph whereas
+this two-phase region is in between
+
+ align:start position:0%
+this two-phase region is in between
+ 
+
+ align:start position:0%
+this two-phase region is in between
+titanium rich hcp and this Tome
+
+ align:start position:0%
+titanium rich hcp and this Tome
+ 
+
+ align:start position:0%
+titanium rich hcp and this Tome
+BCC you could identify similar sorts of
+
+ align:start position:0%
+BCC you could identify similar sorts of
+ 
+
+ align:start position:0%
+BCC you could identify similar sorts of
+funny business over here when you look
+
+ align:start position:0%
+funny business over here when you look
+ 
+
+ align:start position:0%
+funny business over here when you look
+at at this point which is the lowest
+
+ align:start position:0%
+at at this point which is the lowest
+ 
+
+ align:start position:0%
+at at this point which is the lowest
+temperature that the high temperature
+
+ align:start position:0%
+temperature that the high temperature
+ 
+
+ align:start position:0%
+temperature that the high temperature
+one polymorph is stable at so you have a
+
+ align:start position:0%
+one polymorph is stable at so you have a
+ 
+
+ align:start position:0%
+one polymorph is stable at so you have a
+a phase transformation here between a
+
+ align:start position:0%
+a phase transformation here between a
+ 
+
+ align:start position:0%
+a phase transformation here between a
+room temperature polymorph and a high
+
+ align:start position:0%
+room temperature polymorph and a high
+ 
+
+ align:start position:0%
+room temperature polymorph and a high
+temperature polymorph
+
+ align:start position:0%
+temperature polymorph
+ 
+
+ align:start position:0%
+temperature polymorph
+and looks like there's two high
+
+ align:start position:0%
+and looks like there's two high
+ 
+
+ align:start position:0%
+and looks like there's two high
+temperature polymorphs there's a Ty
+
+ align:start position:0%
+temperature polymorphs there's a Ty
+ 
+
+ align:start position:0%
+temperature polymorphs there's a Ty
+Chrome 2 ht2 so there's there's several
+
+ align:start position:0%
+Chrome 2 ht2 so there's there's several
+ 
+
+ align:start position:0%
+Chrome 2 ht2 so there's there's several
+solid state Transformations here Ty
+
+ align:start position:0%
+solid state Transformations here Ty
+ 
+
+ align:start position:0%
+solid state Transformations here Ty
+Chrome 2 room temperature if you heat up
+
+ align:start position:0%
+Chrome 2 room temperature if you heat up
+ 
+
+ align:start position:0%
+Chrome 2 room temperature if you heat up
+it transforms to Ty Chrome 2 high
+
+ align:start position:0%
+it transforms to Ty Chrome 2 high
+ 
+
+ align:start position:0%
+it transforms to Ty Chrome 2 high
+temperature one and it continues to
+
+ align:start position:0%
+temperature one and it continues to
+ 
+
+ align:start position:0%
+temperature one and it continues to
+transform to Ty Chrome to high
+
+ align:start position:0%
+transform to Ty Chrome to high
+ 
+
+ align:start position:0%
+transform to Ty Chrome to high
+temperature 2 I can't tell you what
+
+ align:start position:0%
+temperature 2 I can't tell you what
+ 
+
+ align:start position:0%
+temperature 2 I can't tell you what
+those Crystal structures are I don't
+
+ align:start position:0%
+those Crystal structures are I don't
+ 
+
+ align:start position:0%
+those Crystal structures are I don't
+know the titanium chromium system very
+
+ align:start position:0%
+know the titanium chromium system very
+ 
+
+ align:start position:0%
+know the titanium chromium system very
+well but we know how to find out we go
+
+ align:start position:0%
+well but we know how to find out we go
+ 
+
+ align:start position:0%
+well but we know how to find out we go
+look up at land Sal Borstein we' learn
+
+ align:start position:0%
+look up at land Sal Borstein we' learn
+ 
+
+ align:start position:0%
+look up at land Sal Borstein we' learn
+what they're all about and this is not
+
+ align:start position:0%
+what they're all about and this is not
+ 
+
+ align:start position:0%
+what they're all about and this is not
+purely academic because these are
+
+ align:start position:0%
+purely academic because these are
+ 
+
+ align:start position:0%
+purely academic because these are
+structural
+
+ align:start position:0%
+structural
+ 
+
+ align:start position:0%
+structural
+Alloys and different Crystal structures
+
+ align:start position:0%
+Alloys and different Crystal structures
+ 
+
+ align:start position:0%
+Alloys and different Crystal structures
+have different mechanical properties so
+
+ align:start position:0%
+have different mechanical properties so
+ 
+
+ align:start position:0%
+have different mechanical properties so
+you might care very much how much of
+
+ align:start position:0%
+you might care very much how much of
+ 
+
+ align:start position:0%
+you might care very much how much of
+your your finished part is Tyrome 2 high
+
+ align:start position:0%
+your your finished part is Tyrome 2 high
+ 
+
+ align:start position:0%
+your your finished part is Tyrome 2 high
+temperature 2 Tyrome 2 high temperature
+
+ align:start position:0%
+temperature 2 Tyrome 2 high temperature
+ 
+
+ align:start position:0%
+temperature 2 Tyrome 2 high temperature
+one and T to room temperature right that
+
+ align:start position:0%
+one and T to room temperature right that
+ 
+
+ align:start position:0%
+one and T to room temperature right that
+might be a really important thing for
+
+ align:start position:0%
+might be a really important thing for
+ 
+
+ align:start position:0%
+might be a really important thing for
+you um so there's this funny TI line
+
+ align:start position:0%
+you um so there's this funny TI line
+ 
+
+ align:start position:0%
+you um so there's this funny TI line
+here that starts off at 1271 jogs down a
+
+ align:start position:0%
+here that starts off at 1271 jogs down a
+ 
+
+ align:start position:0%
+here that starts off at 1271 jogs down a
+little bit to
+
+ align:start position:0%
+little bit to
+ 
+
+ align:start position:0%
+little bit to
+1269 that indicates the transformation
+
+ align:start position:0%
+1269 that indicates the transformation
+ 
+
+ align:start position:0%
+1269 that indicates the transformation
+between the high temperature one at high
+
+ align:start position:0%
+between the high temperature one at high
+ 
+
+ align:start position:0%
+between the high temperature one at high
+temperature two polymorphs or titanium
+
+ align:start position:0%
+temperature two polymorphs or titanium
+ 
+
+ align:start position:0%
+temperature two polymorphs or titanium
+chromium
+
+ align:start position:0%
+chromium
+ 
+
+ align:start position:0%
+chromium
+2 yeah it gets complicated it gets
+
+ align:start position:0%
+2 yeah it gets complicated it gets
+ 
+
+ align:start position:0%
+2 yeah it gets complicated it gets
+complicated in a hurry so these diagrams
+
+ align:start position:0%
+complicated in a hurry so these diagrams
+ 
+
+ align:start position:0%
+complicated in a hurry so these diagrams
+are drawn minimally because I think if
+
+ align:start position:0%
+are drawn minimally because I think if
+ 
+
+ align:start position:0%
+are drawn minimally because I think if
+they were drawn with all the features
+
+ align:start position:0%
+they were drawn with all the features
+ 
+
+ align:start position:0%
+they were drawn with all the features
+you would be it would be like
+
+ align:start position:0%
+you would be it would be like
+ 
+
+ align:start position:0%
+you would be it would be like
+unreadable um but you know you do need
+
+ align:start position:0%
+unreadable um but you know you do need
+ 
+
+ align:start position:0%
+unreadable um but you know you do need
+to learn how to read
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them let me move on show you some
+
+ align:start position:0%
+them let me move on show you some
+ 
+
+ align:start position:0%
+them let me move on show you some
+examples here's another example we have
+
+ align:start position:0%
+examples here's another example we have
+ 
+
+ align:start position:0%
+examples here's another example we have
+a lot of spinodal examples in polymer
+
+ align:start position:0%
+a lot of spinodal examples in polymer
+ 
+
+ align:start position:0%
+a lot of spinodal examples in polymer
+systems this is an example of a polymer
+
+ align:start position:0%
+systems this is an example of a polymer
+ 
+
+ align:start position:0%
+systems this is an example of a polymer
+blend pfb and f8bt this is a polymer
+
+ align:start position:0%
+blend pfb and f8bt this is a polymer
+ 
+
+ align:start position:0%
+blend pfb and f8bt this is a polymer
+blend that's used to make solar cells
+
+ align:start position:0%
+blend that's used to make solar cells
+ 
+
+ align:start position:0%
+blend that's used to make solar cells
+and this is I think AFM data Atomic
+
+ align:start position:0%
+and this is I think AFM data Atomic
+ 
+
+ align:start position:0%
+and this is I think AFM data Atomic
+Force microscopy showing you that when
+
+ align:start position:0%
+Force microscopy showing you that when
+ 
+
+ align:start position:0%
+Force microscopy showing you that when
+you prepare a mixed a fully mixed system
+
+ align:start position:0%
+you prepare a mixed a fully mixed system
+ 
+
+ align:start position:0%
+you prepare a mixed a fully mixed system
+in this case a thin film and you anal it
+
+ align:start position:0%
+in this case a thin film and you anal it
+ 
+
+ align:start position:0%
+in this case a thin film and you anal it
+that is you you try to drive it towards
+
+ align:start position:0%
+that is you you try to drive it towards
+ 
+
+ align:start position:0%
+that is you you try to drive it towards
+equilibrium with time and temperature
+
+ align:start position:0%
+equilibrium with time and temperature
+ 
+
+ align:start position:0%
+equilibrium with time and temperature
+you start to see pattern formation
+
+ align:start position:0%
+you start to see pattern formation
+ 
+
+ align:start position:0%
+you start to see pattern formation
+that's the word for this this is called
+
+ align:start position:0%
+that's the word for this this is called
+ 
+
+ align:start position:0%
+that's the word for this this is called
+pattern information what starts off
+
+ align:start position:0%
+pattern information what starts off
+ 
+
+ align:start position:0%
+pattern information what starts off
+featur less develops features
+
+ align:start position:0%
+featur less develops features
+ 
+
+ align:start position:0%
+featur less develops features
+and these patterns which happen over
+
+ align:start position:0%
+and these patterns which happen over
+ 
+
+ align:start position:0%
+and these patterns which happen over
+nanometer length scales often have real
+
+ align:start position:0%
+nanometer length scales often have real
+ 
+
+ align:start position:0%
+nanometer length scales often have real
+functional implications so for example
+
+ align:start position:0%
+functional implications so for example
+ 
+
+ align:start position:0%
+functional implications so for example
+this is a report of the efficiency of a
+
+ align:start position:0%
+this is a report of the efficiency of a
+ 
+
+ align:start position:0%
+this is a report of the efficiency of a
+solar cell based on this
+
+ align:start position:0%
+solar cell based on this
+ 
+
+ align:start position:0%
+solar cell based on this
+stuff the efficiency only gets out of
+
+ align:start position:0%
+stuff the efficiency only gets out of
+ 
+
+ align:start position:0%
+stuff the efficiency only gets out of
+the basement once I start getting the
+
+ align:start position:0%
+the basement once I start getting the
+ 
+
+ align:start position:0%
+the basement once I start getting the
+pattern formation and there are reasons
+
+ align:start position:0%
+pattern formation and there are reasons
+ 
+
+ align:start position:0%
+pattern formation and there are reasons
+for that which which are go beyond the
+
+ align:start position:0%
+for that which which are go beyond the
+ 
+
+ align:start position:0%
+for that which which are go beyond the
+scope of this class but the point is
+
+ align:start position:0%
+scope of this class but the point is
+ 
+
+ align:start position:0%
+scope of this class but the point is
+that by changing the morphology by
+
+ align:start position:0%
+that by changing the morphology by
+ 
+
+ align:start position:0%
+that by changing the morphology by
+changing the
+
+ align:start position:0%
+changing the
+ 
+
+ align:start position:0%
+changing the
+phase fraction and driving from this
+
+ align:start position:0%
+phase fraction and driving from this
+ 
+
+ align:start position:0%
+phase fraction and driving from this
+single phase to this two-phase situation
+
+ align:start position:0%
+single phase to this two-phase situation
+ 
+
+ align:start position:0%
+single phase to this two-phase situation
+you can affect the performance of
+
+ align:start position:0%
+you can affect the performance of
+ 
+
+ align:start position:0%
+you can affect the performance of
+something like a solar cell so this
+
+ align:start position:0%
+something like a solar cell so this
+ 
+
+ align:start position:0%
+something like a solar cell so this
+becomes important there are countless
+
+ align:start position:0%
+becomes important there are countless
+ 
+
+ align:start position:0%
+becomes important there are countless
+examples for why this pattern formation
+
+ align:start position:0%
+examples for why this pattern formation
+ 
+
+ align:start position:0%
+examples for why this pattern formation
+controlling it is UN important for
+
+ align:start position:0%
+controlling it is UN important for
+ 
+
+ align:start position:0%
+controlling it is UN important for
+technology um most of those examples
+
+ align:start position:0%
+technology um most of those examples
+ 
+
+ align:start position:0%
+technology um most of those examples
+more there are probably more examples in
+
+ align:start position:0%
+more there are probably more examples in
+ 
+
+ align:start position:0%
+more there are probably more examples in
+structural Metals than there are in
+
+ align:start position:0%
+structural Metals than there are in
+ 
+
+ align:start position:0%
+structural Metals than there are in
+other fields um but it as we saw in the
+
+ align:start position:0%
+other fields um but it as we saw in the
+ 
+
+ align:start position:0%
+other fields um but it as we saw in the
+last lecture it extends even to
+
+ align:start position:0%
+last lecture it extends even to
+ 
+
+ align:start position:0%
+last lecture it extends even to
+cosmology okay um it's 10:55 I'll walk
+
+ align:start position:0%
+cosmology okay um it's 10:55 I'll walk
+ 
+
+ align:start position:0%
+cosmology okay um it's 10:55 I'll walk
+Qui through quickly through uh um let's
+
+ align:start position:0%
+Qui through quickly through uh um let's
+ 
+
+ align:start position:0%
+Qui through quickly through uh um let's
+see brass brass is nice I like brass
+
+ align:start position:0%
+see brass brass is nice I like brass
+ 
+
+ align:start position:0%
+see brass brass is nice I like brass
+maybe because I used to play uh French
+
+ align:start position:0%
+maybe because I used to play uh French
+ 
+
+ align:start position:0%
+maybe because I used to play uh French
+horn when I was in Middle School so this
+
+ align:start position:0%
+horn when I was in Middle School so this
+ 
+
+ align:start position:0%
+horn when I was in Middle School so this
+is brass This is complicated we're going
+
+ align:start position:0%
+is brass This is complicated we're going
+ 
+
+ align:start position:0%
+is brass This is complicated we're going
+to start stepping through diagrams like
+
+ align:start position:0%
+to start stepping through diagrams like
+ 
+
+ align:start position:0%
+to start stepping through diagrams like
+this we're not ready for it yet not
+
+ align:start position:0%
+this we're not ready for it yet not
+ 
+
+ align:start position:0%
+this we're not ready for it yet not
+quite but here's brass it's copper zinc
+
+ align:start position:0%
+quite but here's brass it's copper zinc
+ 
+
+ align:start position:0%
+quite but here's brass it's copper zinc
+so copper Rich FCC is called brass over
+
+ align:start position:0%
+so copper Rich FCC is called brass over
+ 
+
+ align:start position:0%
+so copper Rich FCC is called brass over
+here zinc we've seen zinc already we saw
+
+ align:start position:0%
+here zinc we've seen zinc already we saw
+ 
+
+ align:start position:0%
+here zinc we've seen zinc already we saw
+it a couple slides ago it's hcp and in
+
+ align:start position:0%
+it a couple slides ago it's hcp and in
+ 
+
+ align:start position:0%
+it a couple slides ago it's hcp and in
+between you have all these intermediate
+
+ align:start position:0%
+between you have all these intermediate
+ 
+
+ align:start position:0%
+between you have all these intermediate
+phases let's look how here's a
+
+ align:start position:0%
+phases let's look how here's a
+ 
+
+ align:start position:0%
+phases let's look how here's a
+simplified view right copper in
+
+ align:start position:0%
+simplified view right copper in
+ 
+
+ align:start position:0%
+simplified view right copper in
+parenthesis meaning this is a solution
+
+ align:start position:0%
+parenthesis meaning this is a solution
+ 
+
+ align:start position:0%
+parenthesis meaning this is a solution
+with the crystal structure of pure
+
+ align:start position:0%
+with the crystal structure of pure
+ 
+
+ align:start position:0%
+with the crystal structure of pure
+copper this a here is an
+
+ align:start position:0%
+copper this a here is an
+ 
+
+ align:start position:0%
+copper this a here is an
+alpha right here's zinc here's the zinc
+
+ align:start position:0%
+alpha right here's zinc here's the zinc
+ 
+
+ align:start position:0%
+alpha right here's zinc here's the zinc
+solid
+
+ align:start position:0%
+solid
+ 
+
+ align:start position:0%
+solid
+solution coming back to Gibbs phase rule
+
+ align:start position:0%
+solution coming back to Gibbs phase rule
+ 
+
+ align:start position:0%
+solution coming back to Gibbs phase rule
+here is a singlephase region with three
+
+ align:start position:0%
+here is a singlephase region with three
+ 
+
+ align:start position:0%
+here is a singlephase region with three
+degrees of freedom I can vary pressure
+
+ align:start position:0%
+degrees of freedom I can vary pressure
+ 
+
+ align:start position:0%
+degrees of freedom I can vary pressure
+temperature and composition while still
+
+ align:start position:0%
+temperature and composition while still
+ 
+
+ align:start position:0%
+temperature and composition while still
+staying in this brass phase
+
+ align:start position:0%
+staying in this brass phase
+ 
+
+ align:start position:0%
+staying in this brass phase
+right temperature and composition are X
+
+ align:start position:0%
+right temperature and composition are X
+ 
+
+ align:start position:0%
+right temperature and composition are X
+and Y on the plot you have to imagine
+
+ align:start position:0%
+and Y on the plot you have to imagine
+ 
+
+ align:start position:0%
+and Y on the plot you have to imagine
+pressure coming out of the
+
+ align:start position:0%
+pressure coming out of the
+ 
+
+ align:start position:0%
+pressure coming out of the
+board okay three
+
+ align:start position:0%
+board okay three
+ 
+
+ align:start position:0%
+board okay three
+phases here's a two-phase region so this
+
+ align:start position:0%
+phases here's a two-phase region so this
+ 
+
+ align:start position:0%
+phases here's a two-phase region so this
+is a two-phase region this is a region
+
+ align:start position:0%
+is a two-phase region this is a region
+ 
+
+ align:start position:0%
+is a two-phase region this is a region
+of coexistence between Alpha and beta
+
+ align:start position:0%
+of coexistence between Alpha and beta
+ 
+
+ align:start position:0%
+of coexistence between Alpha and beta
+and they only have two degrees of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+freedom
+
+ align:start position:0%
+freedom
+ 
+
+ align:start position:0%
+freedom
+because the composition of the phases is
+
+ align:start position:0%
+because the composition of the phases is
+ 
+
+ align:start position:0%
+because the composition of the phases is
+fixed by the end points of the Tha line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're not going to fully take time to
+
+ align:start position:0%
+we're not going to fully take time to
+ 
+
+ align:start position:0%
+we're not going to fully take time to
+sort of think about that now but I
+
+ align:start position:0%
+sort of think about that now but I
+ 
+
+ align:start position:0%
+sort of think about that now but I
+wanted to point it out here's a
+
+ align:start position:0%
+wanted to point it out here's a
+ 
+
+ align:start position:0%
+wanted to point it out here's a
+three-phase region Alpha Beta and liquid
+
+ align:start position:0%
+three-phase region Alpha Beta and liquid
+ 
+
+ align:start position:0%
+three-phase region Alpha Beta and liquid
+only one degree of
+
+ align:start position:0%
+only one degree of
+ 
+
+ align:start position:0%
+only one degree of
+Freedom so this defines a line through
+
+ align:start position:0%
+Freedom so this defines a line through
+ 
+
+ align:start position:0%
+Freedom so this defines a line through
+the temperature pressure composition
+
+ align:start position:0%
+the temperature pressure composition
+ 
+
+ align:start position:0%
+the temperature pressure composition
+space I don't have a four-phase region
+
+ align:start position:0%
+space I don't have a four-phase region
+ 
+
+ align:start position:0%
+space I don't have a four-phase region
+here okay um I'm going to we're 2
+
+ align:start position:0%
+here okay um I'm going to we're 2
+ 
+
+ align:start position:0%
+here okay um I'm going to we're 2
+minutes over so I'm going to end before
+
+ align:start position:0%
+minutes over so I'm going to end before
+ 
+
+ align:start position:0%
+minutes over so I'm going to end before
+I entertain you with uh pressure dep
+
+ align:start position:0%
+I entertain you with uh pressure dep
+ 
+
+ align:start position:0%
+I entertain you with uh pressure dep
+penet trary phase diagrams which uh
+
+ align:start position:0%
+penet trary phase diagrams which uh
+ 
+
+ align:start position:0%
+penet trary phase diagrams which uh
+mercifully is not covered in 302
\ No newline at end of file
diff --git a/EBYsEEcMFmY.txt b/EBYsEEcMFmY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..916ca399a59f9cb3df7970d3ffa34ff42782ea28
--- /dev/null
+++ b/EBYsEEcMFmY.txt
@@ -0,0 +1,3 @@
+Hi, I'm Susan I'm class of 2021 and this is pi
+
+3.141592653589793238462643383279
\ No newline at end of file
diff --git a/EW2hjUFRWZ0.txt b/EW2hjUFRWZ0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..98881dad5abba084537fed0821462a46db646923
--- /dev/null
+++ b/EW2hjUFRWZ0.txt
@@ -0,0 +1,14165 @@
+align:start position:0%
+ 
+okay so good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+afternoon and uh
+
+ align:start position:0%
+afternoon and uh
+ 
+
+ align:start position:0%
+afternoon and uh
+uh we
+
+ align:start position:0%
+uh we
+ 
+
+ align:start position:0%
+uh we
+are hopefully we'll uh
+
+ align:start position:0%
+are hopefully we'll uh
+ 
+
+ align:start position:0%
+are hopefully we'll uh
+finish the topic on uh liquid VAP or
+
+ align:start position:0%
+finish the topic on uh liquid VAP or
+ 
+
+ align:start position:0%
+finish the topic on uh liquid VAP or
+equilibria
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we we have seen that everything is uh
+
+ align:start position:0%
+uh we we have seen that everything is uh
+ 
+
+ align:start position:0%
+uh we we have seen that everything is uh
+contained in mechanical
+
+ align:start position:0%
+contained in mechanical
+ 
+
+ align:start position:0%
+contained in mechanical
+potentials and uh so this U summarizes
+
+ align:start position:0%
+potentials and uh so this U summarizes
+ 
+
+ align:start position:0%
+potentials and uh so this U summarizes
+for example for a pure substance when
+
+ align:start position:0%
+for example for a pure substance when
+ 
+
+ align:start position:0%
+for example for a pure substance when
+you have the two phases in mutual
+
+ align:start position:0%
+you have the two phases in mutual
+ 
+
+ align:start position:0%
+you have the two phases in mutual
+equilibrium like liquid and
+
+ align:start position:0%
+equilibrium like liquid and
+ 
+
+ align:start position:0%
+equilibrium like liquid and
+Vapor the equality of chemical
+
+ align:start position:0%
+Vapor the equality of chemical
+ 
+
+ align:start position:0%
+Vapor the equality of chemical
+potentials uh for the pure liquid and
+
+ align:start position:0%
+potentials uh for the pure liquid and
+ 
+
+ align:start position:0%
+potentials uh for the pure liquid and
+the pure uh
+
+ align:start position:0%
+the pure uh
+ 
+
+ align:start position:0%
+the pure uh
+Vapor gives a relation between pressure
+
+ align:start position:0%
+Vapor gives a relation between pressure
+ 
+
+ align:start position:0%
+Vapor gives a relation between pressure
+and temperature which we call
+
+ align:start position:0%
+and temperature which we call
+ 
+
+ align:start position:0%
+and temperature which we call
+Pat or the inverse function is tat
+
+ align:start position:0%
+Pat or the inverse function is tat
+ 
+
+ align:start position:0%
+Pat or the inverse function is tat
+that's what you find in for example the
+
+ align:start position:0%
+that's what you find in for example the
+ 
+
+ align:start position:0%
+that's what you find in for example the
+steam tables for water or every other
+
+ align:start position:0%
+steam tables for water or every other
+ 
+
+ align:start position:0%
+steam tables for water or every other
+substance has
+
+ align:start position:0%
+substance has
+ 
+
+ align:start position:0%
+substance has
+this uh establishes the PO the boiling
+
+ align:start position:0%
+this uh establishes the PO the boiling
+ 
+
+ align:start position:0%
+this uh establishes the PO the boiling
+point at a given
+
+ align:start position:0%
+point at a given
+ 
+
+ align:start position:0%
+point at a given
+pressure so the equivalent for a binary
+
+ align:start position:0%
+pressure so the equivalent for a binary
+ 
+
+ align:start position:0%
+pressure so the equivalent for a binary
+mixture is that now we have if if both
+
+ align:start position:0%
+mixture is that now we have if if both
+ 
+
+ align:start position:0%
+mixture is that now we have if if both
+substances are volatile and
+
+ align:start position:0%
+substances are volatile and
+ 
+
+ align:start position:0%
+substances are volatile and
+condensible then you have two uh
+
+ align:start position:0%
+condensible then you have two uh
+ 
+
+ align:start position:0%
+condensible then you have two uh
+chemical
+
+ align:start position:0%
+chemical
+ 
+
+ align:start position:0%
+chemical
+equilibrium uh chemical potential
+
+ align:start position:0%
+equilibrium uh chemical potential
+ 
+
+ align:start position:0%
+equilibrium uh chemical potential
+equalities that are required for Mutual
+
+ align:start position:0%
+equalities that are required for Mutual
+ 
+
+ align:start position:0%
+equalities that are required for Mutual
+stable equilibrium between the two
+
+ align:start position:0%
+stable equilibrium between the two
+ 
+
+ align:start position:0%
+stable equilibrium between the two
+phases of course uh the chemical
+
+ align:start position:0%
+phases of course uh the chemical
+ 
+
+ align:start position:0%
+phases of course uh the chemical
+potential be is now not only a function
+
+ align:start position:0%
+potential be is now not only a function
+ 
+
+ align:start position:0%
+potential be is now not only a function
+of temperature and pressure but also of
+
+ align:start position:0%
+of temperature and pressure but also of
+ 
+
+ align:start position:0%
+of temperature and pressure but also of
+composition but because this the mole
+
+ align:start position:0%
+composition but because this the mole
+ 
+
+ align:start position:0%
+composition but because this the mole
+fractions add up to one uh you just need
+
+ align:start position:0%
+fractions add up to one uh you just need
+ 
+
+ align:start position:0%
+fractions add up to one uh you just need
+one uh in independent mole fraction to
+
+ align:start position:0%
+one uh in independent mole fraction to
+ 
+
+ align:start position:0%
+one uh in independent mole fraction to
+represent the
+
+ align:start position:0%
+represent the
+ 
+
+ align:start position:0%
+represent the
+composition but you need one mole
+
+ align:start position:0%
+composition but you need one mole
+ 
+
+ align:start position:0%
+composition but you need one mole
+fraction for the uh liquid phase and
+
+ align:start position:0%
+fraction for the uh liquid phase and
+ 
+
+ align:start position:0%
+fraction for the uh liquid phase and
+another mole fraction for the vapor
+
+ align:start position:0%
+another mole fraction for the vapor
+ 
+
+ align:start position:0%
+another mole fraction for the vapor
+phase because they are not necessarily
+
+ align:start position:0%
+phase because they are not necessarily
+ 
+
+ align:start position:0%
+phase because they are not necessarily
+equal so these two
+
+ align:start position:0%
+equal so these two
+ 
+
+ align:start position:0%
+equal so these two
+equalities in the uh four variables TP
+
+ align:start position:0%
+equalities in the uh four variables TP
+ 
+
+ align:start position:0%
+equalities in the uh four variables TP
+y1f and
+
+ align:start position:0%
+y1f and
+ 
+
+ align:start position:0%
+y1f and
+y1g can be solved to
+
+ align:start position:0%
+y1g can be solved to
+ 
+
+ align:start position:0%
+y1g can be solved to
+give uh this relation so you only have a
+
+ align:start position:0%
+give uh this relation so you only have a
+ 
+
+ align:start position:0%
+give uh this relation so you only have a
+variance of two GES a phase rule
+
+ align:start position:0%
+variance of two GES a phase rule
+ 
+
+ align:start position:0%
+variance of two GES a phase rule
+variance of two meaning that for example
+
+ align:start position:0%
+variance of two meaning that for example
+ 
+
+ align:start position:0%
+variance of two meaning that for example
+if you fix temperature and
+
+ align:start position:0%
+if you fix temperature and
+ 
+
+ align:start position:0%
+if you fix temperature and
+pressure that automatically fixes a
+
+ align:start position:0%
+pressure that automatically fixes a
+ 
+
+ align:start position:0%
+pressure that automatically fixes a
+unique composition for the liquid and a
+
+ align:start position:0%
+unique composition for the liquid and a
+ 
+
+ align:start position:0%
+unique composition for the liquid and a
+unique composition for the uh Vapor that
+
+ align:start position:0%
+unique composition for the uh Vapor that
+ 
+
+ align:start position:0%
+unique composition for the uh Vapor that
+are not equal and the Raul's law that we
+
+ align:start position:0%
+are not equal and the Raul's law that we
+ 
+
+ align:start position:0%
+are not equal and the Raul's law that we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+developed establishes the relation
+
+ align:start position:0%
+developed establishes the relation
+ 
+
+ align:start position:0%
+developed establishes the relation
+between the composition of the in vapor
+
+ align:start position:0%
+between the composition of the in vapor
+ 
+
+ align:start position:0%
+between the composition of the in vapor
+and the composition of the
+
+ align:start position:0%
+and the composition of the
+ 
+
+ align:start position:0%
+and the composition of the
+liquid
+
+ align:start position:0%
+liquid
+ 
+
+ align:start position:0%
+liquid
+uh you can also rewrite solve these
+
+ align:start position:0%
+uh you can also rewrite solve these
+ 
+
+ align:start position:0%
+uh you can also rewrite solve these
+equations for other inde independent
+
+ align:start position:0%
+equations for other inde independent
+ 
+
+ align:start position:0%
+equations for other inde independent
+variables for example you keep T and the
+
+ align:start position:0%
+variables for example you keep T and the
+ 
+
+ align:start position:0%
+variables for example you keep T and the
+mole fraction of the liquid and you get
+
+ align:start position:0%
+mole fraction of the liquid and you get
+ 
+
+ align:start position:0%
+mole fraction of the liquid and you get
+a from these relations a function which
+
+ align:start position:0%
+a from these relations a function which
+ 
+
+ align:start position:0%
+a from these relations a function which
+we called the B the bubble
+
+ align:start position:0%
+we called the B the bubble
+ 
+
+ align:start position:0%
+we called the B the bubble
+line or if you instead like to keep the
+
+ align:start position:0%
+line or if you instead like to keep the
+ 
+
+ align:start position:0%
+line or if you instead like to keep the
+temperature and the composition of the
+
+ align:start position:0%
+temperature and the composition of the
+ 
+
+ align:start position:0%
+temperature and the composition of the
+vapor you get the DU
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line which can be expressed as pressure
+
+ align:start position:0%
+line which can be expressed as pressure
+ 
+
+ align:start position:0%
+line which can be expressed as pressure
+is a function of temperature but also
+
+ align:start position:0%
+is a function of temperature but also
+ 
+
+ align:start position:0%
+is a function of temperature but also
+temperature is a function of
+
+ align:start position:0%
+temperature is a function of
+ 
+
+ align:start position:0%
+temperature is a function of
+pressure okay so these are all
+
+ align:start position:0%
+pressure okay so these are all
+ 
+
+ align:start position:0%
+pressure okay so these are all
+equivalent
+
+ align:start position:0%
+equivalent
+ 
+
+ align:start position:0%
+equivalent
+forms and here is a sort of a thre
+
+ align:start position:0%
+forms and here is a sort of a thre
+ 
+
+ align:start position:0%
+forms and here is a sort of a thre
+dimensional representation of how these
+
+ align:start position:0%
+dimensional representation of how these
+ 
+
+ align:start position:0%
+dimensional representation of how these
+uh things look of course in the limit of
+
+ align:start position:0%
+uh things look of course in the limit of
+ 
+
+ align:start position:0%
+uh things look of course in the limit of
+the pure substances you get the usual PT
+
+ align:start position:0%
+the pure substances you get the usual PT
+ 
+
+ align:start position:0%
+the pure substances you get the usual PT
+diagram for that
+
+ align:start position:0%
+diagram for that
+ 
+
+ align:start position:0%
+diagram for that
+substance this is for one this is for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two but uh halfway when the mole
+
+ align:start position:0%
+two but uh halfway when the mole
+ 
+
+ align:start position:0%
+two but uh halfway when the mole
+fractions go from between zero and one
+
+ align:start position:0%
+fractions go from between zero and one
+ 
+
+ align:start position:0%
+fractions go from between zero and one
+then you get uh uh these
+
+ align:start position:0%
+then you get uh uh these
+ 
+
+ align:start position:0%
+then you get uh uh these
+relations uh as we have seen gives rise
+
+ align:start position:0%
+relations uh as we have seen gives rise
+ 
+
+ align:start position:0%
+relations uh as we have seen gives rise
+to gaps so to Regions that are forbidden
+
+ align:start position:0%
+to gaps so to Regions that are forbidden
+ 
+
+ align:start position:0%
+to gaps so to Regions that are forbidden
+that cannot be uh
+
+ align:start position:0%
+that cannot be uh
+ 
+
+ align:start position:0%
+that cannot be uh
+obtained uh in in which the substance
+
+ align:start position:0%
+obtained uh in in which the substance
+ 
+
+ align:start position:0%
+obtained uh in in which the substance
+doesn't behave in doesn't exist in
+
+ align:start position:0%
+doesn't behave in doesn't exist in
+ 
+
+ align:start position:0%
+doesn't behave in doesn't exist in
+stable equilibrium it likes to
+
+ align:start position:0%
+stable equilibrium it likes to
+ 
+
+ align:start position:0%
+stable equilibrium it likes to
+separate so today uh to finish up we
+
+ align:start position:0%
+separate so today uh to finish up we
+ 
+
+ align:start position:0%
+separate so today uh to finish up we
+need to see a little more about about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so the first uh result that we can
+
+ align:start position:0%
+this so the first uh result that we can
+ 
+
+ align:start position:0%
+this so the first uh result that we can
+uh talk about is called enry
+
+ align:start position:0%
+uh talk about is called enry
+ 
+
+ align:start position:0%
+uh talk about is called enry
+law which is a byproduct of R's law so
+
+ align:start position:0%
+law which is a byproduct of R's law so
+ 
+
+ align:start position:0%
+law which is a byproduct of R's law so
+remember R slow was a relation here this
+
+ align:start position:0%
+remember R slow was a relation here this
+ 
+
+ align:start position:0%
+remember R slow was a relation here this
+one uh that gives us as we just said the
+
+ align:start position:0%
+one uh that gives us as we just said the
+ 
+
+ align:start position:0%
+one uh that gives us as we just said the
+Rel the composition of the vapor phase
+
+ align:start position:0%
+Rel the composition of the vapor phase
+ 
+
+ align:start position:0%
+Rel the composition of the vapor phase
+in equilibrium
+
+ align:start position:0%
+in equilibrium
+ 
+
+ align:start position:0%
+in equilibrium
+is a function of the uh composition of
+
+ align:start position:0%
+is a function of the uh composition of
+ 
+
+ align:start position:0%
+is a function of the uh composition of
+the liquid phase with which it is in
+
+ align:start position:0%
+the liquid phase with which it is in
+ 
+
+ align:start position:0%
+the liquid phase with which it is in
+mutual
+
+ align:start position:0%
+mutual
+ 
+
+ align:start position:0%
+mutual
+equilibrium and the saturation pressure
+
+ align:start position:0%
+equilibrium and the saturation pressure
+ 
+
+ align:start position:0%
+equilibrium and the saturation pressure
+of the pure substance enters in the RS
+
+ align:start position:0%
+of the pure substance enters in the RS
+ 
+
+ align:start position:0%
+of the pure substance enters in the RS
+equation we derive this by equating the
+
+ align:start position:0%
+equation we derive this by equating the
+ 
+
+ align:start position:0%
+equation we derive this by equating the
+chemical potentials of substance
+
+ align:start position:0%
+chemical potentials of substance
+ 
+
+ align:start position:0%
+chemical potentials of substance
+one and
+
+ align:start position:0%
+one and
+ 
+
+ align:start position:0%
+one and
+U of course if you have if your mixture
+
+ align:start position:0%
+U of course if you have if your mixture
+ 
+
+ align:start position:0%
+U of course if you have if your mixture
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+ideal uh at all
+
+ align:start position:0%
+ideal uh at all
+ 
+
+ align:start position:0%
+ideal uh at all
+compositions and both substances are um
+
+ align:start position:0%
+compositions and both substances are um
+ 
+
+ align:start position:0%
+compositions and both substances are um
+volatile and condensible you have also a
+
+ align:start position:0%
+volatile and condensible you have also a
+ 
+
+ align:start position:0%
+volatile and condensible you have also a
+r slow for the second second substance
+
+ align:start position:0%
+r slow for the second second substance
+ 
+
+ align:start position:0%
+r slow for the second second substance
+and so you have the same expression like
+
+ align:start position:0%
+and so you have the same expression like
+ 
+
+ align:start position:0%
+and so you have the same expression like
+here only with the subscript two instead
+
+ align:start position:0%
+here only with the subscript two instead
+ 
+
+ align:start position:0%
+here only with the subscript two instead
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+however very few
+
+ align:start position:0%
+however very few
+ 
+
+ align:start position:0%
+however very few
+mixtures uh in the liquid phase are
+
+ align:start position:0%
+mixtures uh in the liquid phase are
+ 
+
+ align:start position:0%
+mixtures uh in the liquid phase are
+really uh ideal
+
+ align:start position:0%
+really uh ideal
+ 
+
+ align:start position:0%
+really uh ideal
+at all
+
+ align:start position:0%
+at all
+ 
+
+ align:start position:0%
+at all
+compositions but we
+
+ align:start position:0%
+compositions but we
+ 
+
+ align:start position:0%
+compositions but we
+know that in a dilute limit so for a
+
+ align:start position:0%
+know that in a dilute limit so for a
+ 
+
+ align:start position:0%
+know that in a dilute limit so for a
+dilute
+
+ align:start position:0%
+dilute
+ 
+
+ align:start position:0%
+dilute
+solution uh we argued that every liquid
+
+ align:start position:0%
+solution uh we argued that every liquid
+ 
+
+ align:start position:0%
+solution uh we argued that every liquid
+solution is always uh in that limit
+
+ align:start position:0%
+solution is always uh in that limit
+ 
+
+ align:start position:0%
+solution is always uh in that limit
+behaving as
+
+ align:start position:0%
+behaving as
+ 
+
+ align:start position:0%
+behaving as
+ideal so that means let consider
+
+ align:start position:0%
+ideal so that means let consider
+ 
+
+ align:start position:0%
+ideal so that means let consider
+component one as the solvent for
+
+ align:start position:0%
+component one as the solvent for
+ 
+
+ align:start position:0%
+component one as the solvent for
+which uh this equation is
+
+ align:start position:0%
+which uh this equation is
+ 
+
+ align:start position:0%
+which uh this equation is
+valid in the limit
+
+ align:start position:0%
+valid in the limit
+ 
+
+ align:start position:0%
+valid in the limit
+of uh y1f that means uh the liquid
+
+ align:start position:0%
+of uh y1f that means uh the liquid
+ 
+
+ align:start position:0%
+of uh y1f that means uh the liquid
+composition is very close to the pure
+
+ align:start position:0%
+composition is very close to the pure
+ 
+
+ align:start position:0%
+composition is very close to the pure
+substance so that's a dilute solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit substance two does not behave a
+
+ align:start position:0%
+limit substance two does not behave a
+ 
+
+ align:start position:0%
+limit substance two does not behave a
+slope but we will see that now next
+
+ align:start position:0%
+slope but we will see that now next
+ 
+
+ align:start position:0%
+slope but we will see that now next
+lines are going we're going to need to
+
+ align:start position:0%
+lines are going we're going to need to
+ 
+
+ align:start position:0%
+lines are going we're going to need to
+prove this relation here which looks uh
+
+ align:start position:0%
+prove this relation here which looks uh
+ 
+
+ align:start position:0%
+prove this relation here which looks uh
+which is enry law which looks
+
+ align:start position:0%
+which is enry law which looks
+ 
+
+ align:start position:0%
+which is enry law which looks
+similar to R's law except that instead
+
+ align:start position:0%
+similar to R's law except that instead
+ 
+
+ align:start position:0%
+similar to R's law except that instead
+of the saturation pressure of the
+
+ align:start position:0%
+of the saturation pressure of the
+ 
+
+ align:start position:0%
+of the saturation pressure of the
+substance of the second
+
+ align:start position:0%
+substance of the second
+ 
+
+ align:start position:0%
+substance of the second
+substance you
+
+ align:start position:0%
+substance you
+ 
+
+ align:start position:0%
+substance you
+have uh another function of not just
+
+ align:start position:0%
+have uh another function of not just
+ 
+
+ align:start position:0%
+have uh another function of not just
+temperature but temperature and pressure
+
+ align:start position:0%
+temperature but temperature and pressure
+ 
+
+ align:start position:0%
+temperature but temperature and pressure
+which is called enris volatility
+
+ align:start position:0%
+which is called enris volatility
+ 
+
+ align:start position:0%
+which is called enris volatility
+constant and it's going to be given by
+
+ align:start position:0%
+constant and it's going to be given by
+ 
+
+ align:start position:0%
+constant and it's going to be given by
+this relation here so how do we how do
+
+ align:start position:0%
+this relation here so how do we how do
+ 
+
+ align:start position:0%
+this relation here so how do we how do
+we obtain this and this is
+
+ align:start position:0%
+we obtain this and this is
+ 
+
+ align:start position:0%
+we obtain this and this is
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+valid
+
+ align:start position:0%
+valid
+ 
+
+ align:start position:0%
+valid
+um for any uh mixture in the dilute
+
+ align:start position:0%
+um for any uh mixture in the dilute
+ 
+
+ align:start position:0%
+um for any uh mixture in the dilute
+solution limit there is a there is a a
+
+ align:start position:0%
+solution limit there is a there is a a
+ 
+
+ align:start position:0%
+solution limit there is a there is a a
+constant like that it's called Enis
+
+ align:start position:0%
+constant like that it's called Enis
+ 
+
+ align:start position:0%
+constant like that it's called Enis
+constant but it's really a something
+
+ align:start position:0%
+constant but it's really a something
+ 
+
+ align:start position:0%
+constant but it's really a something
+that is independent of composition and
+
+ align:start position:0%
+that is independent of composition and
+ 
+
+ align:start position:0%
+that is independent of composition and
+it's a function but it is a function of
+
+ align:start position:0%
+it's a function but it is a function of
+ 
+
+ align:start position:0%
+it's a function but it is a function of
+temperature and pressure so it's
+
+ align:start position:0%
+temperature and pressure so it's
+ 
+
+ align:start position:0%
+temperature and pressure so it's
+constant once you f F temperature and
+
+ align:start position:0%
+constant once you f F temperature and
+ 
+
+ align:start position:0%
+constant once you f F temperature and
+pressure so where does it come about
+
+ align:start position:0%
+pressure so where does it come about
+ 
+
+ align:start position:0%
+pressure so where does it come about
+come it comes about from the Gibs doem
+
+ align:start position:0%
+come it comes about from the Gibs doem
+ 
+
+ align:start position:0%
+come it comes about from the Gibs doem
+relations because they can they must
+
+ align:start position:0%
+relations because they can they must
+ 
+
+ align:start position:0%
+relations because they can they must
+always hold remember GBS do relations
+
+ align:start position:0%
+always hold remember GBS do relations
+ 
+
+ align:start position:0%
+always hold remember GBS do relations
+are the ones that we use also to derive
+
+ align:start position:0%
+are the ones that we use also to derive
+ 
+
+ align:start position:0%
+are the ones that we use also to derive
+the GI phace
+
+ align:start position:0%
+the GI phace
+ 
+
+ align:start position:0%
+the GI phace
+Rule and the clus claperon
+
+ align:start position:0%
+Rule and the clus claperon
+ 
+
+ align:start position:0%
+Rule and the clus claperon
+relations for the pure
+
+ align:start position:0%
+relations for the pure
+ 
+
+ align:start position:0%
+relations for the pure
+substances uh for a binary mixture
+
+ align:start position:0%
+substances uh for a binary mixture
+ 
+
+ align:start position:0%
+substances uh for a binary mixture
+uh the usual summation becomes just two
+
+ align:start position:0%
+uh the usual summation becomes just two
+ 
+
+ align:start position:0%
+uh the usual summation becomes just two
+uh contributions here so this is uh
+
+ align:start position:0%
+uh contributions here so this is uh
+ 
+
+ align:start position:0%
+uh contributions here so this is uh
+minus sdt plus
+
+ align:start position:0%
+minus sdt plus
+ 
+
+ align:start position:0%
+minus sdt plus
+VDP plus the summation minus the
+
+ align:start position:0%
+VDP plus the summation minus the
+ 
+
+ align:start position:0%
+VDP plus the summation minus the
+summation of the mole fractions times
+
+ align:start position:0%
+summation of the mole fractions times
+ 
+
+ align:start position:0%
+summation of the mole fractions times
+the D of the chemical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potentials now suppose we fixed
+
+ align:start position:0%
+potentials now suppose we fixed
+ 
+
+ align:start position:0%
+potentials now suppose we fixed
+temperature and pressure so we set DT
+
+ align:start position:0%
+temperature and pressure so we set DT
+ 
+
+ align:start position:0%
+temperature and pressure so we set DT
+and DP equals z then you see this gives
+
+ align:start position:0%
+and DP equals z then you see this gives
+ 
+
+ align:start position:0%
+and DP equals z then you see this gives
+a relation between how uh the chemical
+
+ align:start position:0%
+a relation between how uh the chemical
+ 
+
+ align:start position:0%
+a relation between how uh the chemical
+potential of uh the second substance so
+
+ align:start position:0%
+potential of uh the second substance so
+ 
+
+ align:start position:0%
+potential of uh the second substance so
+of the solute in the dilute solution uh
+
+ align:start position:0%
+of the solute in the dilute solution uh
+ 
+
+ align:start position:0%
+of the solute in the dilute solution uh
+changes as uh you have changes in the
+
+ align:start position:0%
+changes as uh you have changes in the
+ 
+
+ align:start position:0%
+changes as uh you have changes in the
+chemical potential of the solvent so
+
+ align:start position:0%
+chemical potential of the solvent so
+ 
+
+ align:start position:0%
+chemical potential of the solvent so
+they are not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent so if since this
+
+ align:start position:0%
+independent so if since this
+ 
+
+ align:start position:0%
+independent so if since this
+solvent uh behaves like like this it's
+
+ align:start position:0%
+solvent uh behaves like like this it's
+ 
+
+ align:start position:0%
+solvent uh behaves like like this it's
+ideal so it obeys this uh ideal relation
+
+ align:start position:0%
+ideal so it obeys this uh ideal relation
+ 
+
+ align:start position:0%
+ideal so it obeys this uh ideal relation
+for chemical potential if you do the
+
+ align:start position:0%
+for chemical potential if you do the
+ 
+
+ align:start position:0%
+for chemical potential if you do the
+differential of that uh at constant T
+
+ align:start position:0%
+differential of that uh at constant T
+ 
+
+ align:start position:0%
+differential of that uh at constant T
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+P you are left with just the the
+
+ align:start position:0%
+P you are left with just the the
+ 
+
+ align:start position:0%
+P you are left with just the the
+differential of log of Y which is the Y
+
+ align:start position:0%
+differential of log of Y which is the Y
+ 
+
+ align:start position:0%
+differential of log of Y which is the Y
+over y okay so that's the mu1 in the
+
+ align:start position:0%
+over y okay so that's the mu1 in the
+ 
+
+ align:start position:0%
+over y okay so that's the mu1 in the
+liquid phase so you can substitute in
+
+ align:start position:0%
+liquid phase so you can substitute in
+ 
+
+ align:start position:0%
+liquid phase so you can substitute in
+this relation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so see this relation it can be
+
+ align:start position:0%
+here so see this relation it can be
+ 
+
+ align:start position:0%
+here so see this relation it can be
+Rewritten this
+
+ align:start position:0%
+Rewritten this
+ 
+
+ align:start position:0%
+Rewritten this
+way and then here for this one you
+
+ align:start position:0%
+way and then here for this one you
+ 
+
+ align:start position:0%
+way and then here for this one you
+substitute what we obtain from the ideal
+
+ align:start position:0%
+substitute what we obtain from the ideal
+ 
+
+ align:start position:0%
+substitute what we obtain from the ideal
+solution and here is what you get you
+
+ align:start position:0%
+solution and here is what you get you
+ 
+
+ align:start position:0%
+solution and here is what you get you
+get a similar
+
+ align:start position:0%
+get a similar
+ 
+
+ align:start position:0%
+get a similar
+relation so you get that also chemical
+
+ align:start position:0%
+relation so you get that also chemical
+ 
+
+ align:start position:0%
+relation so you get that also chemical
+potential of the second substance in the
+
+ align:start position:0%
+potential of the second substance in the
+ 
+
+ align:start position:0%
+potential of the second substance in the
+liquid uh solution behaves
+
+ align:start position:0%
+liquid uh solution behaves
+ 
+
+ align:start position:0%
+liquid uh solution behaves
+logarithmically with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+composition so that means that
+
+ align:start position:0%
+composition so that means that
+ 
+
+ align:start position:0%
+composition so that means that
+if it is
+
+ align:start position:0%
+if it is
+ 
+
+ align:start position:0%
+if it is
+logarithm see this for the ideal
+
+ align:start position:0%
+logarithm see this for the ideal
+ 
+
+ align:start position:0%
+logarithm see this for the ideal
+solution this is a logarithmic
+
+ align:start position:0%
+solution this is a logarithmic
+ 
+
+ align:start position:0%
+solution this is a logarithmic
+dependence and here you have the pure
+
+ align:start position:0%
+dependence and here you have the pure
+ 
+
+ align:start position:0%
+dependence and here you have the pure
+substance so the the constant here is a
+
+ align:start position:0%
+substance so the the constant here is a
+ 
+
+ align:start position:0%
+substance so the the constant here is a
+pure substance whereas for a oops okay
+
+ align:start position:0%
+pure substance whereas for a oops okay
+ 
+
+ align:start position:0%
+pure substance whereas for a oops okay
+whereas for for this other case if you
+
+ align:start position:0%
+whereas for for this other case if you
+ 
+
+ align:start position:0%
+whereas for for this other case if you
+integrate this
+
+ align:start position:0%
+integrate this
+ 
+
+ align:start position:0%
+integrate this
+relation uh you get something similar to
+
+ align:start position:0%
+relation uh you get something similar to
+ 
+
+ align:start position:0%
+relation uh you get something similar to
+the one up there but uh with a different
+
+ align:start position:0%
+the one up there but uh with a different
+ 
+
+ align:start position:0%
+the one up there but uh with a different
+integration constant that is not NE
+
+ align:start position:0%
+integration constant that is not NE
+ 
+
+ align:start position:0%
+integration constant that is not NE
+necessarily equal to the pure component
+
+ align:start position:0%
+necessarily equal to the pure component
+ 
+
+ align:start position:0%
+necessarily equal to the pure component
+chemical
+
+ align:start position:0%
+chemical
+ 
+
+ align:start position:0%
+chemical
+potential it is equal to the pure
+
+ align:start position:0%
+potential it is equal to the pure
+ 
+
+ align:start position:0%
+potential it is equal to the pure
+component chemical potential in the
+
+ align:start position:0%
+component chemical potential in the
+ 
+
+ align:start position:0%
+component chemical potential in the
+limit of Ideal solution all at all
+
+ align:start position:0%
+limit of Ideal solution all at all
+ 
+
+ align:start position:0%
+limit of Ideal solution all at all
+compositions so but in general this is
+
+ align:start position:0%
+compositions so but in general this is
+ 
+
+ align:start position:0%
+compositions so but in general this is
+some other function of temperature and
+
+ align:start position:0%
+some other function of temperature and
+ 
+
+ align:start position:0%
+some other function of temperature and
+pressure which nevertheless can be
+
+ align:start position:0%
+pressure which nevertheless can be
+ 
+
+ align:start position:0%
+pressure which nevertheless can be
+measured and uh and therefore you uh if
+
+ align:start position:0%
+measured and uh and therefore you uh if
+ 
+
+ align:start position:0%
+measured and uh and therefore you uh if
+you use this relation to obtain like we
+
+ align:start position:0%
+you use this relation to obtain like we
+ 
+
+ align:start position:0%
+you use this relation to obtain like we
+did for a obtaining R's law you obtain
+
+ align:start position:0%
+did for a obtaining R's law you obtain
+ 
+
+ align:start position:0%
+did for a obtaining R's law you obtain
+enry
+
+ align:start position:0%
+enry
+ 
+
+ align:start position:0%
+enry
+law and here is the explicit expression
+
+ align:start position:0%
+law and here is the explicit expression
+ 
+
+ align:start position:0%
+law and here is the explicit expression
+that derives for theis constant in terms
+
+ align:start position:0%
+that derives for theis constant in terms
+ 
+
+ align:start position:0%
+that derives for theis constant in terms
+of the saturation pressure of the second
+
+ align:start position:0%
+of the saturation pressure of the second
+ 
+
+ align:start position:0%
+of the saturation pressure of the second
+substance there is this correction
+
+ align:start position:0%
+substance there is this correction
+ 
+
+ align:start position:0%
+substance there is this correction
+factor and this correction factor can be
+
+ align:start position:0%
+factor and this correction factor can be
+ 
+
+ align:start position:0%
+factor and this correction factor can be
+very uh large for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+um one one important example in in some
+
+ align:start position:0%
+um one one important example in in some
+ 
+
+ align:start position:0%
+um one one important example in in some
+practices is is the one for nitrogen so
+
+ align:start position:0%
+practices is is the one for nitrogen so
+ 
+
+ align:start position:0%
+practices is is the one for nitrogen so
+the AR is
+
+ align:start position:0%
+the AR is
+ 
+
+ align:start position:0%
+the AR is
+constant as a value which is
+
+ align:start position:0%
+constant as a value which is
+ 
+
+ align:start position:0%
+constant as a value which is
+85,000 atmospheres so very high
+
+ align:start position:0%
+85,000 atmospheres so very high
+ 
+
+ align:start position:0%
+85,000 atmospheres so very high
+pressure uh from the point of view of of
+
+ align:start position:0%
+pressure uh from the point of view of of
+ 
+
+ align:start position:0%
+pressure uh from the point of view of of
+graphic point of view um okay suppose
+
+ align:start position:0%
+graphic point of view um okay suppose
+ 
+
+ align:start position:0%
+graphic point of view um okay suppose
+this one is mole fraction of the solvent
+
+ align:start position:0%
+this one is mole fraction of the solvent
+ 
+
+ align:start position:0%
+this one is mole fraction of the solvent
+say that we are talking about uh water
+
+ align:start position:0%
+say that we are talking about uh water
+ 
+
+ align:start position:0%
+say that we are talking about uh water
+okay so this is the dilute limit is is
+
+ align:start position:0%
+okay so this is the dilute limit is is
+ 
+
+ align:start position:0%
+okay so this is the dilute limit is is
+is in this area
+
+ align:start position:0%
+is in this area
+ 
+
+ align:start position:0%
+is in this area
+so Mo fraction of water is very close to
+
+ align:start position:0%
+so Mo fraction of water is very close to
+ 
+
+ align:start position:0%
+so Mo fraction of water is very close to
+one and so what is missing to get to one
+
+ align:start position:0%
+one and so what is missing to get to one
+ 
+
+ align:start position:0%
+one and so what is missing to get to one
+is the mole fraction of the
+
+ align:start position:0%
+is the mole fraction of the
+ 
+
+ align:start position:0%
+is the mole fraction of the
+solute and supposed solute is
+
+ align:start position:0%
+solute and supposed solute is
+ 
+
+ align:start position:0%
+solute and supposed solute is
+nitrogen uh okay uh the
+
+ align:start position:0%
+nitrogen uh okay uh the
+ 
+
+ align:start position:0%
+nitrogen uh okay uh the
+N slope me if you had ideal ideal um
+
+ align:start position:0%
+N slope me if you had ideal ideal um
+ 
+
+ align:start position:0%
+N slope me if you had ideal ideal um
+Behavior
+
+ align:start position:0%
+Behavior
+ 
+
+ align:start position:0%
+Behavior
+H this line represents the the partial
+
+ align:start position:0%
+H this line represents the the partial
+ 
+
+ align:start position:0%
+H this line represents the the partial
+pressure so it's the product of uh mole
+
+ align:start position:0%
+pressure so it's the product of uh mole
+ 
+
+ align:start position:0%
+pressure so it's the product of uh mole
+fraction and
+
+ align:start position:0%
+fraction and
+ 
+
+ align:start position:0%
+fraction and
+pressure and it's a straight line
+
+ align:start position:0%
+pressure and it's a straight line
+ 
+
+ align:start position:0%
+pressure and it's a straight line
+because that's a linear relation that
+
+ align:start position:0%
+because that's a linear relation that
+ 
+
+ align:start position:0%
+because that's a linear relation that
+takes you to the um saturation pressure
+
+ align:start position:0%
+takes you to the um saturation pressure
+ 
+
+ align:start position:0%
+takes you to the um saturation pressure
+of uh
+
+ align:start position:0%
+of uh
+ 
+
+ align:start position:0%
+of uh
+nitrogen okay uh since this Conant is
+
+ align:start position:0%
+nitrogen okay uh since this Conant is
+ 
+
+ align:start position:0%
+nitrogen okay uh since this Conant is
+very high the en constant is very high
+
+ align:start position:0%
+very high the en constant is very high
+ 
+
+ align:start position:0%
+very high the en constant is very high
+the actual slope here is much
+
+ align:start position:0%
+the actual slope here is much
+ 
+
+ align:start position:0%
+the actual slope here is much
+steeper okay and that is sort of the
+
+ align:start position:0%
+steeper okay and that is sort of the
+ 
+
+ align:start position:0%
+steeper okay and that is sort of the
+tangent of this uh IDE non- ideal
+
+ align:start position:0%
+tangent of this uh IDE non- ideal
+ 
+
+ align:start position:0%
+tangent of this uh IDE non- ideal
+Behavior U
+
+ align:start position:0%
+Behavior U
+ 
+
+ align:start position:0%
+Behavior U
+um Bubble uh bubble
+
+ align:start position:0%
+um Bubble uh bubble
+ 
+
+ align:start position:0%
+um Bubble uh bubble
+line now it why nitrogen is
+
+ align:start position:0%
+line now it why nitrogen is
+ 
+
+ align:start position:0%
+line now it why nitrogen is
+important for example for uh
+
+ align:start position:0%
+important for example for uh
+ 
+
+ align:start position:0%
+important for example for uh
+divers you know that there is this um
+
+ align:start position:0%
+divers you know that there is this um
+ 
+
+ align:start position:0%
+divers you know that there is this um
+problem of the compression and if you if
+
+ align:start position:0%
+problem of the compression and if you if
+ 
+
+ align:start position:0%
+problem of the compression and if you if
+you dive and you stay for a long time uh
+
+ align:start position:0%
+you dive and you stay for a long time uh
+ 
+
+ align:start position:0%
+you dive and you stay for a long time uh
+at high
+
+ align:start position:0%
+at high
+ 
+
+ align:start position:0%
+at high
+pressures
+
+ align:start position:0%
+pressures
+ 
+
+ align:start position:0%
+pressures
+nitrogen uh uh you see here if if I
+
+ align:start position:0%
+nitrogen uh uh you see here if if I
+ 
+
+ align:start position:0%
+nitrogen uh uh you see here if if I
+increase uh the the
+
+ align:start position:0%
+increase uh the the
+ 
+
+ align:start position:0%
+increase uh the the
+pressure the the mole fraction uh that
+
+ align:start position:0%
+pressure the the mole fraction uh that
+ 
+
+ align:start position:0%
+pressure the the mole fraction uh that
+of nitrogen that can stay in uh in the
+
+ align:start position:0%
+of nitrogen that can stay in uh in the
+ 
+
+ align:start position:0%
+of nitrogen that can stay in uh in the
+liquid so let's say the let's call it
+
+ align:start position:0%
+liquid so let's say the let's call it
+ 
+
+ align:start position:0%
+liquid so let's say the let's call it
+the solubility of nitrogen in the
+
+ align:start position:0%
+the solubility of nitrogen in the
+ 
+
+ align:start position:0%
+the solubility of nitrogen in the
+blood uh gets
+
+ align:start position:0%
+blood uh gets
+ 
+
+ align:start position:0%
+blood uh gets
+higher so the longer you stay the more
+
+ align:start position:0%
+higher so the longer you stay the more
+ 
+
+ align:start position:0%
+higher so the longer you stay the more
+nitrogen goes into your
+
+ align:start position:0%
+nitrogen goes into your
+ 
+
+ align:start position:0%
+nitrogen goes into your
+blood and then uh and this happens in
+
+ align:start position:0%
+blood and then uh and this happens in
+ 
+
+ align:start position:0%
+blood and then uh and this happens in
+the lungs now if you uh come up to C
+
+ align:start position:0%
+the lungs now if you uh come up to C
+ 
+
+ align:start position:0%
+the lungs now if you uh come up to C
+Surface too quickly and you don't let uh
+
+ align:start position:0%
+Surface too quickly and you don't let uh
+ 
+
+ align:start position:0%
+Surface too quickly and you don't let uh
+uh the necessary time to adjust back uh
+
+ align:start position:0%
+uh the necessary time to adjust back uh
+ 
+
+ align:start position:0%
+uh the necessary time to adjust back uh
+through the
+
+ align:start position:0%
+through the
+ 
+
+ align:start position:0%
+through the
+lungs uh this nitrogen will um evaporate
+
+ align:start position:0%
+lungs uh this nitrogen will um evaporate
+ 
+
+ align:start position:0%
+lungs uh this nitrogen will um evaporate
+from your bloodstream and form bubbles
+
+ align:start position:0%
+from your bloodstream and form bubbles
+ 
+
+ align:start position:0%
+from your bloodstream and form bubbles
+all over and these
+
+ align:start position:0%
+all over and these
+ 
+
+ align:start position:0%
+all over and these
+bubbles uh typically collect in
+
+ align:start position:0%
+bubbles uh typically collect in
+ 
+
+ align:start position:0%
+bubbles uh typically collect in
+joints and gives you a lot of pain
+
+ align:start position:0%
+joints and gives you a lot of pain
+ 
+
+ align:start position:0%
+joints and gives you a lot of pain
+especially when you move the joints and
+
+ align:start position:0%
+especially when you move the joints and
+ 
+
+ align:start position:0%
+especially when you move the joints and
+that's why the disease is called also
+
+ align:start position:0%
+that's why the disease is called also
+ 
+
+ align:start position:0%
+that's why the disease is called also
+the bends when you bend you you suffer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh but of course the enris Conant has
+
+ align:start position:0%
+uh but of course the enris Conant has
+ 
+
+ align:start position:0%
+uh but of course the enris Conant has
+also some other applications that also
+
+ align:start position:0%
+also some other applications that also
+ 
+
+ align:start position:0%
+also some other applications that also
+have to do with uh atmospheric and ocean
+
+ align:start position:0%
+have to do with uh atmospheric and ocean
+ 
+
+ align:start position:0%
+have to do with uh atmospheric and ocean
+science and uh so this is
+
+ align:start position:0%
+science and uh so this is
+ 
+
+ align:start position:0%
+science and uh so this is
+um for example it determines
+
+ align:start position:0%
+um for example it determines
+ 
+
+ align:start position:0%
+um for example it determines
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh composition of clouds Cloud droplets
+
+ align:start position:0%
+uh composition of clouds Cloud droplets
+ 
+
+ align:start position:0%
+uh composition of clouds Cloud droplets
+and also it is important in how for
+
+ align:start position:0%
+and also it is important in how for
+ 
+
+ align:start position:0%
+and also it is important in how for
+example pollutant some pollutants are
+
+ align:start position:0%
+example pollutant some pollutants are
+ 
+
+ align:start position:0%
+example pollutant some pollutants are
+absorbed in Waste Water Management uh
+
+ align:start position:0%
+absorbed in Waste Water Management uh
+ 
+
+ align:start position:0%
+absorbed in Waste Water Management uh
+plans treatment
+
+ align:start position:0%
+plans treatment
+ 
+
+ align:start position:0%
+plans treatment
+plans okay so this was an example of
+
+ align:start position:0%
+plans okay so this was an example of
+ 
+
+ align:start position:0%
+plans okay so this was an example of
+application of the Gibbs DM
+
+ align:start position:0%
+application of the Gibbs DM
+ 
+
+ align:start position:0%
+application of the Gibbs DM
+relation which has some practical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+applications um okay before we go on I
+
+ align:start position:0%
+applications um okay before we go on I
+ 
+
+ align:start position:0%
+applications um okay before we go on I
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+to stress again something that we have
+
+ align:start position:0%
+to stress again something that we have
+ 
+
+ align:start position:0%
+to stress again something that we have
+already discussed so I'm not going to go
+
+ align:start position:0%
+already discussed so I'm not going to go
+ 
+
+ align:start position:0%
+already discussed so I'm not going to go
+into too many details here but I I leave
+
+ align:start position:0%
+into too many details here but I I leave
+ 
+
+ align:start position:0%
+into too many details here but I I leave
+it this slides for
+
+ align:start position:0%
+it this slides for
+ 
+
+ align:start position:0%
+it this slides for
+reference
+
+ align:start position:0%
+reference
+ 
+
+ align:start position:0%
+reference
+because when we like we're going to do
+
+ align:start position:0%
+because when we like we're going to do
+ 
+
+ align:start position:0%
+because when we like we're going to do
+next we deal with models of uh
+
+ align:start position:0%
+next we deal with models of uh
+ 
+
+ align:start position:0%
+next we deal with models of uh
+mixtures to describe U these nonideal
+
+ align:start position:0%
+mixtures to describe U these nonideal
+ 
+
+ align:start position:0%
+mixtures to describe U these nonideal
+behaviors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um we are going to have to be uh
+
+ align:start position:0%
+um we are going to have to be uh
+ 
+
+ align:start position:0%
+um we are going to have to be uh
+concerned with the stability or the
+
+ align:start position:0%
+concerned with the stability or the
+ 
+
+ align:start position:0%
+concerned with the stability or the
+solubility limits uh uh the stability
+
+ align:start position:0%
+solubility limits uh uh the stability
+ 
+
+ align:start position:0%
+solubility limits uh uh the stability
+conditions for these mixtures because
+
+ align:start position:0%
+conditions for these mixtures because
+ 
+
+ align:start position:0%
+conditions for these mixtures because
+sometimes uh for example liquids you
+
+ align:start position:0%
+sometimes uh for example liquids you
+ 
+
+ align:start position:0%
+sometimes uh for example liquids you
+know oil and water don't mix at least
+
+ align:start position:0%
+know oil and water don't mix at least
+ 
+
+ align:start position:0%
+know oil and water don't mix at least
+not at all
+
+ align:start position:0%
+not at all
+ 
+
+ align:start position:0%
+not at all
+compositions uh so that is an effect of
+
+ align:start position:0%
+compositions uh so that is an effect of
+ 
+
+ align:start position:0%
+compositions uh so that is an effect of
+the the fact that at certain
+
+ align:start position:0%
+the the fact that at certain
+ 
+
+ align:start position:0%
+the the fact that at certain
+compositions a a a
+
+ align:start position:0%
+compositions a a a
+ 
+
+ align:start position:0%
+compositions a a a
+homogeneous mixture of oil and water is
+
+ align:start position:0%
+homogeneous mixture of oil and water is
+ 
+
+ align:start position:0%
+homogeneous mixture of oil and water is
+unstable at most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compositions all right well so our
+
+ align:start position:0%
+compositions all right well so our
+ 
+
+ align:start position:0%
+compositions all right well so our
+models will will give uh expressions for
+
+ align:start position:0%
+models will will give uh expressions for
+ 
+
+ align:start position:0%
+models will will give uh expressions for
+the uh GBS free energy and you can
+
+ align:start position:0%
+the uh GBS free energy and you can
+ 
+
+ align:start position:0%
+the uh GBS free energy and you can
+express the G free energy as
+
+ align:start position:0%
+express the G free energy as
+ 
+
+ align:start position:0%
+express the G free energy as
+the total value or the specific value
+
+ align:start position:0%
+the total value or the specific value
+ 
+
+ align:start position:0%
+the total value or the specific value
+and of course if we we are we are
+
+ align:start position:0%
+and of course if we we are we are
+ 
+
+ align:start position:0%
+and of course if we we are we are
+talking
+
+ align:start position:0%
+talking
+ 
+
+ align:start position:0%
+talking
+about large systems with large numbers
+
+ align:start position:0%
+about large systems with large numbers
+ 
+
+ align:start position:0%
+about large systems with large numbers
+of particles so we uh the we can apply
+
+ align:start position:0%
+of particles so we uh the we can apply
+ 
+
+ align:start position:0%
+of particles so we uh the we can apply
+the oiler relation and this is uh the
+
+ align:start position:0%
+the oiler relation and this is uh the
+ 
+
+ align:start position:0%
+the oiler relation and this is uh the
+fact that the GS specific GS free energy
+
+ align:start position:0%
+fact that the GS specific GS free energy
+ 
+
+ align:start position:0%
+fact that the GS specific GS free energy
+is essentially you can write it as the
+
+ align:start position:0%
+is essentially you can write it as the
+ 
+
+ align:start position:0%
+is essentially you can write it as the
+weighted sum of the chemical Potentials
+
+ align:start position:0%
+weighted sum of the chemical Potentials
+ 
+
+ align:start position:0%
+weighted sum of the chemical Potentials
+in weighted by the mole fractions of the
+
+ align:start position:0%
+in weighted by the mole fractions of the
+ 
+
+ align:start position:0%
+in weighted by the mole fractions of the
+components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh but we have remember that see you
+
+ align:start position:0%
+uh but we have remember that see you
+ 
+
+ align:start position:0%
+uh but we have remember that see you
+might be tempted to say that the the
+
+ align:start position:0%
+might be tempted to say that the the
+ 
+
+ align:start position:0%
+might be tempted to say that the the
+chemical therefore the chemical
+
+ align:start position:0%
+chemical therefore the chemical
+ 
+
+ align:start position:0%
+chemical therefore the chemical
+potential is the derivative of little G
+
+ align:start position:0%
+potential is the derivative of little G
+ 
+
+ align:start position:0%
+potential is the derivative of little G
+with respect to
+
+ align:start position:0%
+with respect to
+ 
+
+ align:start position:0%
+with respect to
+Y but it is not that's why you have to
+
+ align:start position:0%
+Y but it is not that's why you have to
+ 
+
+ align:start position:0%
+Y but it is not that's why you have to
+be careful the chemical potential when
+
+ align:start position:0%
+be careful the chemical potential when
+ 
+
+ align:start position:0%
+be careful the chemical potential when
+you want to write it in terms of the G
+
+ align:start position:0%
+you want to write it in terms of the G
+ 
+
+ align:start position:0%
+you want to write it in terms of the G
+fre energy is the partial of the G three
+
+ align:start position:0%
+fre energy is the partial of the G three
+ 
+
+ align:start position:0%
+fre energy is the partial of the G three
+energy capital G with respect to
+
+ align:start position:0%
+energy capital G with respect to
+ 
+
+ align:start position:0%
+energy capital G with respect to
+n at constant TP and all the other ends
+
+ align:start position:0%
+n at constant TP and all the other ends
+ 
+
+ align:start position:0%
+n at constant TP and all the other ends
+okay and if you do all the correc
+
+ align:start position:0%
+okay and if you do all the correc
+ 
+
+ align:start position:0%
+okay and if you do all the correc
+steps here it is here is the expression
+
+ align:start position:0%
+steps here it is here is the expression
+ 
+
+ align:start position:0%
+steps here it is here is the expression
+in terms of the uh specific Gibs free
+
+ align:start position:0%
+in terms of the uh specific Gibs free
+ 
+
+ align:start position:0%
+in terms of the uh specific Gibs free
+energy there are lots of contributions
+
+ align:start position:0%
+energy there are lots of contributions
+ 
+
+ align:start position:0%
+energy there are lots of contributions
+it's not just the partial of G with
+
+ align:start position:0%
+it's not just the partial of G with
+ 
+
+ align:start position:0%
+it's not just the partial of G with
+respect to
+
+ align:start position:0%
+respect to
+ 
+
+ align:start position:0%
+respect to
+Y there are other
+
+ align:start position:0%
+Y there are other
+ 
+
+ align:start position:0%
+Y there are other
+stuff for example
+
+ align:start position:0%
+stuff for example
+ 
+
+ align:start position:0%
+stuff for example
+if you assume uh if you apply this to
+
+ align:start position:0%
+if you assume uh if you apply this to
+ 
+
+ align:start position:0%
+if you assume uh if you apply this to
+the GI free energy of the ideal
+
+ align:start position:0%
+the GI free energy of the ideal
+ 
+
+ align:start position:0%
+the GI free energy of the ideal
+solution which we discussed last time
+
+ align:start position:0%
+solution which we discussed last time
+ 
+
+ align:start position:0%
+solution which we discussed last time
+also which is given so by only by this
+
+ align:start position:0%
+also which is given so by only by this
+ 
+
+ align:start position:0%
+also which is given so by only by this
+term plus the mixing mixing entropy type
+
+ align:start position:0%
+term plus the mixing mixing entropy type
+ 
+
+ align:start position:0%
+term plus the mixing mixing entropy type
+term and you do this derivative
+
+ align:start position:0%
+term and you do this derivative
+ 
+
+ align:start position:0%
+term and you do this derivative
+here you so you see that this this
+
+ align:start position:0%
+here you so you see that this this
+ 
+
+ align:start position:0%
+here you so you see that this this
+derivative of of the um lowercase G with
+
+ align:start position:0%
+derivative of of the um lowercase G with
+ 
+
+ align:start position:0%
+derivative of of the um lowercase G with
+respect to the mole fraction is equal to
+
+ align:start position:0%
+respect to the mole fraction is equal to
+ 
+
+ align:start position:0%
+respect to the mole fraction is equal to
+the pure component plus something like
+
+ align:start position:0%
+the pure component plus something like
+ 
+
+ align:start position:0%
+the pure component plus something like
+that so there is an RT term uh uh too
+
+ align:start position:0%
+that so there is an RT term uh uh too
+ 
+
+ align:start position:0%
+that so there is an RT term uh uh too
+many which makes it different from the
+
+ align:start position:0%
+many which makes it different from the
+ 
+
+ align:start position:0%
+many which makes it different from the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+ideal chemical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential but if you put this expression
+
+ align:start position:0%
+potential but if you put this expression
+ 
+
+ align:start position:0%
+potential but if you put this expression
+into here then you get the
+
+ align:start position:0%
+into here then you get the
+ 
+
+ align:start position:0%
+into here then you get the
+proper expression for the clinical
+
+ align:start position:0%
+proper expression for the clinical
+ 
+
+ align:start position:0%
+proper expression for the clinical
+potential for a binary
+
+ align:start position:0%
+potential for a binary
+ 
+
+ align:start position:0%
+potential for a binary
+mixture which is something that so these
+
+ align:start position:0%
+mixture which is something that so these
+ 
+
+ align:start position:0%
+mixture which is something that so these
+are relations that we will need uh in a
+
+ align:start position:0%
+are relations that we will need uh in a
+ 
+
+ align:start position:0%
+are relations that we will need uh in a
+few moment
+
+ align:start position:0%
+few moment
+ 
+
+ align:start position:0%
+few moment
+moments the for a binary
+
+ align:start position:0%
+moments the for a binary
+ 
+
+ align:start position:0%
+moments the for a binary
+mixture uh the specific EX3 energ is
+
+ align:start position:0%
+mixture uh the specific EX3 energ is
+ 
+
+ align:start position:0%
+mixture uh the specific EX3 energ is
+function of only one mole fraction of
+
+ align:start position:0%
+function of only one mole fraction of
+ 
+
+ align:start position:0%
+function of only one mole fraction of
+course because the other is is one minus
+
+ align:start position:0%
+course because the other is is one minus
+ 
+
+ align:start position:0%
+course because the other is is one minus
+one my 1us
+
+ align:start position:0%
+one my 1us
+ 
+
+ align:start position:0%
+one my 1us
+y1 the chemical potential if you use
+
+ align:start position:0%
+y1 the chemical potential if you use
+ 
+
+ align:start position:0%
+y1 the chemical potential if you use
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+expression can be written this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for the second component can be
+
+ align:start position:0%
+and for the second component can be
+ 
+
+ align:start position:0%
+and for the second component can be
+written this
+
+ align:start position:0%
+written this
+ 
+
+ align:start position:0%
+written this
+way in terms of the derivative of little
+
+ align:start position:0%
+way in terms of the derivative of little
+ 
+
+ align:start position:0%
+way in terms of the derivative of little
+G with respect to
+
+ align:start position:0%
+G with respect to
+ 
+
+ align:start position:0%
+G with respect to
+Y and uh
+
+ align:start position:0%
+Y and uh
+ 
+
+ align:start position:0%
+Y and uh
+so why where where do we need these two
+
+ align:start position:0%
+so why where where do we need these two
+ 
+
+ align:start position:0%
+so why where where do we need these two
+expressions we need them when we want to
+
+ align:start position:0%
+expressions we need them when we want to
+ 
+
+ align:start position:0%
+expressions we need them when we want to
+apply the conditions for Mutual
+
+ align:start position:0%
+apply the conditions for Mutual
+ 
+
+ align:start position:0%
+apply the conditions for Mutual
+equilibrium between two
+
+ align:start position:0%
+equilibrium between two
+ 
+
+ align:start position:0%
+equilibrium between two
+phases because if we have the two phases
+
+ align:start position:0%
+phases because if we have the two phases
+ 
+
+ align:start position:0%
+phases because if we have the two phases
+in equilibrium component one must have
+
+ align:start position:0%
+in equilibrium component one must have
+ 
+
+ align:start position:0%
+in equilibrium component one must have
+the same chemical potential in both
+
+ align:start position:0%
+the same chemical potential in both
+ 
+
+ align:start position:0%
+the same chemical potential in both
+phases and component two also so this
+
+ align:start position:0%
+phases and component two also so this
+ 
+
+ align:start position:0%
+phases and component two also so this
+gives give two relations and these two
+
+ align:start position:0%
+gives give two relations and these two
+ 
+
+ align:start position:0%
+gives give two relations and these two
+relations can be
+
+ align:start position:0%
+relations can be
+ 
+
+ align:start position:0%
+relations can be
+written from these two relations you can
+
+ align:start position:0%
+written from these two relations you can
+ 
+
+ align:start position:0%
+written from these two relations you can
+obtain this by substituting the
+
+ align:start position:0%
+obtain this by substituting the
+ 
+
+ align:start position:0%
+obtain this by substituting the
+expression about these two expressions
+
+ align:start position:0%
+expression about these two expressions
+ 
+
+ align:start position:0%
+expression about these two expressions
+here so it tells you that uh uh the
+
+ align:start position:0%
+here so it tells you that uh uh the
+ 
+
+ align:start position:0%
+here so it tells you that uh uh the
+partial of G with respect to
+
+ align:start position:0%
+partial of G with respect to
+ 
+
+ align:start position:0%
+partial of G with respect to
+Y must be equal for the two phases even
+
+ align:start position:0%
+Y must be equal for the two phases even
+ 
+
+ align:start position:0%
+Y must be equal for the two phases even
+if this derivative doesn't represent the
+
+ align:start position:0%
+if this derivative doesn't represent the
+ 
+
+ align:start position:0%
+if this derivative doesn't represent the
+chemical potential but only a part of it
+
+ align:start position:0%
+chemical potential but only a part of it
+ 
+
+ align:start position:0%
+chemical potential but only a part of it
+still it has to be equal for the two
+
+ align:start position:0%
+still it has to be equal for the two
+ 
+
+ align:start position:0%
+still it has to be equal for the two
+phases and plus it represents a slope
+
+ align:start position:0%
+phases and plus it represents a slope
+ 
+
+ align:start position:0%
+phases and plus it represents a slope
+that of a geometrical construction that
+
+ align:start position:0%
+that of a geometrical construction that
+ 
+
+ align:start position:0%
+that of a geometrical construction that
+uh uh looks like this so if I have if I
+
+ align:start position:0%
+uh uh looks like this so if I have if I
+ 
+
+ align:start position:0%
+uh uh looks like this so if I have if I
+plot uh
+
+ align:start position:0%
+plot uh
+ 
+
+ align:start position:0%
+plot uh
+G with respect to uh mole fraction why
+
+ align:start position:0%
+G with respect to uh mole fraction why
+ 
+
+ align:start position:0%
+G with respect to uh mole fraction why
+sometimes we will see you get
+
+ align:start position:0%
+sometimes we will see you get
+ 
+
+ align:start position:0%
+sometimes we will see you get
+uh Expressions I mean plots like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and we will see that uh the
+
+ align:start position:0%
+this and we will see that uh the
+ 
+
+ align:start position:0%
+this and we will see that uh the
+condition for Mutual equilibrium the
+
+ align:start position:0%
+condition for Mutual equilibrium the
+ 
+
+ align:start position:0%
+condition for Mutual equilibrium the
+first one this
+
+ align:start position:0%
+first one this
+ 
+
+ align:start position:0%
+first one this
+one says that if there are going to be
+
+ align:start position:0%
+one says that if there are going to be
+ 
+
+ align:start position:0%
+one says that if there are going to be
+if if you find a line which is tangent
+
+ align:start position:0%
+if if you find a line which is tangent
+ 
+
+ align:start position:0%
+if if you find a line which is tangent
+both here and there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+almost okay so this slope is
+
+ align:start position:0%
+almost okay so this slope is
+ 
+
+ align:start position:0%
+almost okay so this slope is
+DG uh d
+
+ align:start position:0%
+DG uh d
+ 
+
+ align:start position:0%
+DG uh d
+y also there but here is evaluated at y
+
+ align:start position:0%
+y also there but here is evaluated at y
+ 
+
+ align:start position:0%
+y also there but here is evaluated at y
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+first uh phase one and here it is
+
+ align:start position:0%
+first uh phase one and here it is
+ 
+
+ align:start position:0%
+first uh phase one and here it is
+evaluated at y double
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime so that uh so finding this tangent
+
+ align:start position:0%
+Prime so that uh so finding this tangent
+ 
+
+ align:start position:0%
+Prime so that uh so finding this tangent
+line identifies those two mole
+
+ align:start position:0%
+line identifies those two mole
+ 
+
+ align:start position:0%
+line identifies those two mole
+fractions that are in neutal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium and also see this is G Prime
+
+ align:start position:0%
+equilibrium and also see this is G Prime
+ 
+
+ align:start position:0%
+equilibrium and also see this is G Prime
+and that's g double
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime and as you see the equation of
+
+ align:start position:0%
+Prime and as you see the equation of
+ 
+
+ align:start position:0%
+Prime and as you see the equation of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+line is precisely
+
+ align:start position:0%
+line is precisely
+ 
+
+ align:start position:0%
+line is precisely
+this equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay so that
+
+ align:start position:0%
+here okay so that
+ 
+
+ align:start position:0%
+here okay so that
+construction helps us identify for a
+
+ align:start position:0%
+construction helps us identify for a
+ 
+
+ align:start position:0%
+construction helps us identify for a
+given uh temperature because here we
+
+ align:start position:0%
+given uh temperature because here we
+ 
+
+ align:start position:0%
+given uh temperature because here we
+have fixed a given temperature and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressure it helps uh identify these two
+
+ align:start position:0%
+pressure it helps uh identify these two
+ 
+
+ align:start position:0%
+pressure it helps uh identify these two
+points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+again that means suppose I fix now the
+
+ align:start position:0%
+again that means suppose I fix now the
+ 
+
+ align:start position:0%
+again that means suppose I fix now the
+pressure and I take that
+
+ align:start position:0%
+pressure and I take that
+ 
+
+ align:start position:0%
+pressure and I take that
+temperature so at this temperature
+
+ align:start position:0%
+temperature so at this temperature
+ 
+
+ align:start position:0%
+temperature so at this temperature
+T I'm going to
+
+ align:start position:0%
+T I'm going to
+ 
+
+ align:start position:0%
+T I'm going to
+plot these two points that I have found
+
+ align:start position:0%
+plot these two points that I have found
+ 
+
+ align:start position:0%
+plot these two points that I have found
+y Prime and Y double
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prime those this represents
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the two phases in mutal
+
+ align:start position:0%
+uh the two phases in mutal
+ 
+
+ align:start position:0%
+uh the two phases in mutal
+equilibrium so this would be say y1 for
+
+ align:start position:0%
+equilibrium so this would be say y1 for
+ 
+
+ align:start position:0%
+equilibrium so this would be say y1 for
+example for the for the phase
+
+ align:start position:0%
+example for the for the phase
+ 
+
+ align:start position:0%
+example for the for the phase
+um this would be y1 F and this is y1 G
+
+ align:start position:0%
+um this would be y1 F and this is y1 G
+ 
+
+ align:start position:0%
+um this would be y1 F and this is y1 G
+if you're talking about liquid Vapor
+
+ align:start position:0%
+if you're talking about liquid Vapor
+ 
+
+ align:start position:0%
+if you're talking about liquid Vapor
+equilibrium now if I change the
+
+ align:start position:0%
+equilibrium now if I change the
+ 
+
+ align:start position:0%
+equilibrium now if I change the
+temperature and make another plot of the
+
+ align:start position:0%
+temperature and make another plot of the
+ 
+
+ align:start position:0%
+temperature and make another plot of the
+same kind I'm going to identify
+
+ align:start position:0%
+same kind I'm going to identify
+ 
+
+ align:start position:0%
+same kind I'm going to identify
+by the same
+
+ align:start position:0%
+by the same
+ 
+
+ align:start position:0%
+by the same
+way the two
+
+ align:start position:0%
+way the two
+ 
+
+ align:start position:0%
+way the two
+other uh compositions that are
+
+ align:start position:0%
+other uh compositions that are
+ 
+
+ align:start position:0%
+other uh compositions that are
+correspond to the mutual equilibrium and
+
+ align:start position:0%
+correspond to the mutual equilibrium and
+ 
+
+ align:start position:0%
+correspond to the mutual equilibrium and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+on until I get to a temperature in which
+
+ align:start position:0%
+on until I get to a temperature in which
+ 
+
+ align:start position:0%
+on until I get to a temperature in which
+these Point are going points are going
+
+ align:start position:0%
+these Point are going points are going
+ 
+
+ align:start position:0%
+these Point are going points are going
+to coincide so I'm going to
+
+ align:start position:0%
+to coincide so I'm going to
+ 
+
+ align:start position:0%
+to coincide so I'm going to
+obtain a curve like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that maybe it's a bit smoother for in
+
+ align:start position:0%
+that maybe it's a bit smoother for in
+ 
+
+ align:start position:0%
+that maybe it's a bit smoother for in
+practice
+
+ align:start position:0%
+practice
+ 
+
+ align:start position:0%
+practice
+uh this is called this is a critical
+
+ align:start position:0%
+uh this is called this is a critical
+ 
+
+ align:start position:0%
+uh this is called this is a critical
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+point uh it's critical in what sense
+
+ align:start position:0%
+point uh it's critical in what sense
+ 
+
+ align:start position:0%
+point uh it's critical in what sense
+it's critical in the sense that above
+
+ align:start position:0%
+it's critical in the sense that above
+ 
+
+ align:start position:0%
+it's critical in the sense that above
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+temperature you can see that all
+
+ align:start position:0%
+temperature you can see that all
+ 
+
+ align:start position:0%
+temperature you can see that all
+compositions are possible for
+
+ align:start position:0%
+compositions are possible for
+ 
+
+ align:start position:0%
+compositions are possible for
+equilibrium whereas below
+
+ align:start position:0%
+equilibrium whereas below
+ 
+
+ align:start position:0%
+equilibrium whereas below
+here there is a gap so this area
+
+ align:start position:0%
+here there is a gap so this area
+ 
+
+ align:start position:0%
+here there is a gap so this area
+here is
+
+ align:start position:0%
+here is
+ 
+
+ align:start position:0%
+here is
+forbidden and it's called the visibility
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Gap there are no stable situations
+
+ align:start position:0%
+Gap there are no stable situations
+ 
+
+ align:start position:0%
+Gap there are no stable situations
+inside
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here but as we have seen for the pure
+
+ align:start position:0%
+here but as we have seen for the pure
+ 
+
+ align:start position:0%
+here but as we have seen for the pure
+substance we may have a metastable
+
+ align:start position:0%
+substance we may have a metastable
+ 
+
+ align:start position:0%
+substance we may have a metastable
+situations which is
+
+ align:start position:0%
+situations which is
+ 
+
+ align:start position:0%
+situations which is
+now what we want to uh analyze
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's try to do that construction
+
+ align:start position:0%
+so let's try to do that construction
+ 
+
+ align:start position:0%
+so let's try to do that construction
+with one of the uh models that we have
+
+ align:start position:0%
+with one of the uh models that we have
+ 
+
+ align:start position:0%
+with one of the uh models that we have
+assumed the simplest the one parameter
+
+ align:start position:0%
+assumed the simplest the one parameter
+ 
+
+ align:start position:0%
+assumed the simplest the one parameter
+marulas model for the binary mixture so
+
+ align:start position:0%
+marulas model for the binary mixture so
+ 
+
+ align:start position:0%
+marulas model for the binary mixture so
+just parameter a so the Gibs free
+
+ align:start position:0%
+just parameter a so the Gibs free
+ 
+
+ align:start position:0%
+just parameter a so the Gibs free
+energy is a sum of an ideal part and
+
+ align:start position:0%
+energy is a sum of an ideal part and
+ 
+
+ align:start position:0%
+energy is a sum of an ideal part and
+excess part the ideal part is given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here something can be computed from the
+
+ align:start position:0%
+here something can be computed from the
+ 
+
+ align:start position:0%
+here something can be computed from the
+pure substance properties something is
+
+ align:start position:0%
+pure substance properties something is
+ 
+
+ align:start position:0%
+pure substance properties something is
+related to the entropy of
+
+ align:start position:0%
+related to the entropy of
+ 
+
+ align:start position:0%
+related to the entropy of
+mixing and then here the excess part is
+
+ align:start position:0%
+mixing and then here the excess part is
+ 
+
+ align:start position:0%
+mixing and then here the excess part is
+related to the composition and to this
+
+ align:start position:0%
+related to the composition and to this
+ 
+
+ align:start position:0%
+related to the composition and to this
+constant a which you remember is is is
+
+ align:start position:0%
+constant a which you remember is is is
+ 
+
+ align:start position:0%
+constant a which you remember is is is
+a essentially the uh mixing enthalpy
+
+ align:start position:0%
+a essentially the uh mixing enthalpy
+ 
+
+ align:start position:0%
+a essentially the uh mixing enthalpy
+of the two components which in this
+
+ align:start position:0%
+of the two components which in this
+ 
+
+ align:start position:0%
+of the two components which in this
+model are equal for the two
+
+ align:start position:0%
+model are equal for the two
+ 
+
+ align:start position:0%
+model are equal for the two
+components okay so that's the
+
+ align:start position:0%
+components okay so that's the
+ 
+
+ align:start position:0%
+components okay so that's the
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+now we
+
+ align:start position:0%
+now we
+ 
+
+ align:start position:0%
+now we
+apply uh the
+
+ align:start position:0%
+apply uh the
+ 
+
+ align:start position:0%
+apply uh the
+stability
+
+ align:start position:0%
+stability
+ 
+
+ align:start position:0%
+stability
+conditions because you remember that for
+
+ align:start position:0%
+conditions because you remember that for
+ 
+
+ align:start position:0%
+conditions because you remember that for
+Mutual I mean for stable equilibrium
+
+ align:start position:0%
+Mutual I mean for stable equilibrium
+ 
+
+ align:start position:0%
+Mutual I mean for stable equilibrium
+we've derived while ago U General
+
+ align:start position:0%
+we've derived while ago U General
+ 
+
+ align:start position:0%
+we've derived while ago U General
+conditions for stability that are not
+
+ align:start position:0%
+conditions for stability that are not
+ 
+
+ align:start position:0%
+conditions for stability that are not
+just yes they are the theoretical things
+
+ align:start position:0%
+just yes they are the theoretical things
+ 
+
+ align:start position:0%
+just yes they are the theoretical things
+but which have practical consequences
+
+ align:start position:0%
+but which have practical consequences
+ 
+
+ align:start position:0%
+but which have practical consequences
+consequences uh and that therefore allow
+
+ align:start position:0%
+consequences uh and that therefore allow
+ 
+
+ align:start position:0%
+consequences uh and that therefore allow
+to describe uh some physical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reality okay so the second differential
+
+ align:start position:0%
+reality okay so the second differential
+ 
+
+ align:start position:0%
+reality okay so the second differential
+of G um if I move out from a state in
+
+ align:start position:0%
+of G um if I move out from a state in
+ 
+
+ align:start position:0%
+of G um if I move out from a state in
+which the system is in equ mutual
+
+ align:start position:0%
+which the system is in equ mutual
+ 
+
+ align:start position:0%
+which the system is in equ mutual
+equilibrium with Reser at temperature T
+
+ align:start position:0%
+equilibrium with Reser at temperature T
+ 
+
+ align:start position:0%
+equilibrium with Reser at temperature T
+and P and uh and I move out uh by
+
+ align:start position:0%
+and P and uh and I move out uh by
+ 
+
+ align:start position:0%
+and P and uh and I move out uh by
+changing the
+
+ align:start position:0%
+changing the
+ 
+
+ align:start position:0%
+changing the
+composition while keeping T and P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant uh this differential must be
+
+ align:start position:0%
+constant uh this differential must be
+ 
+
+ align:start position:0%
+constant uh this differential must be
+greater than zero so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implies that if I uh keep also n among
+
+ align:start position:0%
+implies that if I uh keep also n among
+ 
+
+ align:start position:0%
+implies that if I uh keep also n among
+the various possibilities uh I can of
+
+ align:start position:0%
+the various possibilities uh I can of
+ 
+
+ align:start position:0%
+the various possibilities uh I can of
+changing the composition I'm taking the
+
+ align:start position:0%
+changing the composition I'm taking the
+ 
+
+ align:start position:0%
+changing the composition I'm taking the
+simplest so I take uh uh keep constant
+
+ align:start position:0%
+simplest so I take uh uh keep constant
+ 
+
+ align:start position:0%
+simplest so I take uh uh keep constant
+the total amount and just change the
+
+ align:start position:0%
+the total amount and just change the
+ 
+
+ align:start position:0%
+the total amount and just change the
+relative
+
+ align:start position:0%
+relative
+ 
+
+ align:start position:0%
+relative
+composition so I just change the mole
+
+ align:start position:0%
+composition so I just change the mole
+ 
+
+ align:start position:0%
+composition so I just change the mole
+fraction of component
+
+ align:start position:0%
+fraction of component
+ 
+
+ align:start position:0%
+fraction of component
+one and this second differential
+
+ align:start position:0%
+one and this second differential
+ 
+
+ align:start position:0%
+one and this second differential
+uh gives rise well maybe here more than
+
+ align:start position:0%
+uh gives rise well maybe here more than
+ 
+
+ align:start position:0%
+uh gives rise well maybe here more than
+an equal sign there should be an arrow
+
+ align:start position:0%
+an equal sign there should be an arrow
+ 
+
+ align:start position:0%
+an equal sign there should be an arrow
+because this is not an equality it's
+
+ align:start position:0%
+because this is not an equality it's
+ 
+
+ align:start position:0%
+because this is not an equality it's
+wrong mathematically but uh because here
+
+ align:start position:0%
+wrong mathematically but uh because here
+ 
+
+ align:start position:0%
+wrong mathematically but uh because here
+should we should have also a d uh
+
+ align:start position:0%
+should we should have also a d uh
+ 
+
+ align:start position:0%
+should we should have also a d uh
+y1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared which being squared as
+
+ align:start position:0%
+squared which being squared as
+ 
+
+ align:start position:0%
+squared which being squared as
+a positive sign so it doesn't that it's
+
+ align:start position:0%
+a positive sign so it doesn't that it's
+ 
+
+ align:start position:0%
+a positive sign so it doesn't that it's
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+positive so I have to correct that
+
+ align:start position:0%
+positive so I have to correct that
+ 
+
+ align:start position:0%
+positive so I have to correct that
+and so this uh is the second derivative
+
+ align:start position:0%
+and so this uh is the second derivative
+ 
+
+ align:start position:0%
+and so this uh is the second derivative
+and on this graph the second
+
+ align:start position:0%
+and on this graph the second
+ 
+
+ align:start position:0%
+and on this graph the second
+derivative is the convexity no of the
+
+ align:start position:0%
+derivative is the convexity no of the
+ 
+
+ align:start position:0%
+derivative is the convexity no of the
+curve it has to be
+
+ align:start position:0%
+curve it has to be
+ 
+
+ align:start position:0%
+curve it has to be
+positive so you we see here that uh it's
+
+ align:start position:0%
+positive so you we see here that uh it's
+ 
+
+ align:start position:0%
+positive so you we see here that uh it's
+positive here it's positive here it's
+
+ align:start position:0%
+positive here it's positive here it's
+ 
+
+ align:start position:0%
+positive here it's positive here it's
+positive up to a certain point here but
+
+ align:start position:0%
+positive up to a certain point here but
+ 
+
+ align:start position:0%
+positive up to a certain point here but
+then it becomes negative second
+
+ align:start position:0%
+then it becomes negative second
+ 
+
+ align:start position:0%
+then it becomes negative second
+derivative so from from where it becomes
+
+ align:start position:0%
+derivative so from from where it becomes
+ 
+
+ align:start position:0%
+derivative so from from where it becomes
+negative to where it comes back
+
+ align:start position:0%
+negative to where it comes back
+ 
+
+ align:start position:0%
+negative to where it comes back
+positive this is the region of
+
+ align:start position:0%
+positive this is the region of
+ 
+
+ align:start position:0%
+positive this is the region of
+instability and these two points here
+
+ align:start position:0%
+instability and these two points here
+ 
+
+ align:start position:0%
+instability and these two points here
+are going to
+
+ align:start position:0%
+are going to
+ 
+
+ align:start position:0%
+are going to
+Define so they're not they there are a
+
+ align:start position:0%
+Define so they're not they there are a
+ 
+
+ align:start position:0%
+Define so they're not they there are a
+different uh there are a different uh um
+
+ align:start position:0%
+different uh there are a different uh um
+ 
+
+ align:start position:0%
+different uh there are a different uh um
+mole
+
+ align:start position:0%
+mole
+ 
+
+ align:start position:0%
+mole
+fractions than the two phases in a
+
+ align:start position:0%
+fractions than the two phases in a
+ 
+
+ align:start position:0%
+fractions than the two phases in a
+mutual equilibrium so see this is a
+
+ align:start position:0%
+mutual equilibrium so see this is a
+ 
+
+ align:start position:0%
+mutual equilibrium so see this is a
+different mole fraction and a different
+
+ align:start position:0%
+different mole fraction and a different
+ 
+
+ align:start position:0%
+different mole fraction and a different
+mole fraction so this will identify
+
+ align:start position:0%
+mole fraction so this will identify
+ 
+
+ align:start position:0%
+mole fraction so this will identify
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+curve inside
+
+ align:start position:0%
+curve inside
+ 
+
+ align:start position:0%
+curve inside
+here so the locus of all these other
+
+ align:start position:0%
+here so the locus of all these other
+ 
+
+ align:start position:0%
+here so the locus of all these other
+points this other curve is what we will
+
+ align:start position:0%
+points this other curve is what we will
+ 
+
+ align:start position:0%
+points this other curve is what we will
+call uh this spine noal
+
+ align:start position:0%
+call uh this spine noal
+ 
+
+ align:start position:0%
+call uh this spine noal
+curve so usually one calls this one is
+
+ align:start position:0%
+curve so usually one calls this one is
+ 
+
+ align:start position:0%
+curve so usually one calls this one is
+called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bodal and the one inside that's the SP
+
+ align:start position:0%
+bodal and the one inside that's the SP
+ 
+
+ align:start position:0%
+bodal and the one inside that's the SP
+no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+SP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we have the expression for the G
+
+ align:start position:0%
+okay so we have the expression for the G
+ 
+
+ align:start position:0%
+okay so we have the expression for the G
+free energy we can take derivatives let
+
+ align:start position:0%
+free energy we can take derivatives let
+ 
+
+ align:start position:0%
+free energy we can take derivatives let
+me skip the steps and go to the uh
+
+ align:start position:0%
+me skip the steps and go to the uh
+ 
+
+ align:start position:0%
+me skip the steps and go to the uh
+result here this is the second
+
+ align:start position:0%
+result here this is the second
+ 
+
+ align:start position:0%
+result here this is the second
+derivative it's in terms of the mole
+
+ align:start position:0%
+derivative it's in terms of the mole
+ 
+
+ align:start position:0%
+derivative it's in terms of the mole
+fractions RT and a the constant
+
+ align:start position:0%
+fractions RT and a the constant
+ 
+
+ align:start position:0%
+fractions RT and a the constant
+a for this to be greater than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero I see this is subtract so you need
+
+ align:start position:0%
+zero I see this is subtract so you need
+ 
+
+ align:start position:0%
+zero I see this is subtract so you need
+that a should not be too too
+
+ align:start position:0%
+that a should not be too too
+ 
+
+ align:start position:0%
+that a should not be too too
+large the maximum value of this fraction
+
+ align:start position:0%
+large the maximum value of this fraction
+ 
+
+ align:start position:0%
+large the maximum value of this fraction
+is one is um is two no is four because
+
+ align:start position:0%
+is one is um is two no is four because
+ 
+
+ align:start position:0%
+is one is um is two no is four because
+half and half and therefore a equals 2
+
+ align:start position:0%
+half and half and therefore a equals 2
+ 
+
+ align:start position:0%
+half and half and therefore a equals 2
+is the maximum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+allowed value so the stability condition
+
+ align:start position:0%
+allowed value so the stability condition
+ 
+
+ align:start position:0%
+allowed value so the stability condition
+is satisfied is if a is less than
+
+ align:start position:0%
+is satisfied is if a is less than
+ 
+
+ align:start position:0%
+is satisfied is if a is less than
+two the critical situation is when a is
+
+ align:start position:0%
+two the critical situation is when a is
+ 
+
+ align:start position:0%
+two the critical situation is when a is
+equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two and if a is greater than two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh you can
+
+ align:start position:0%
+uh you can
+ 
+
+ align:start position:0%
+uh you can
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+satisfy this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condition but only in a certain range
+
+ align:start position:0%
+condition but only in a certain range
+ 
+
+ align:start position:0%
+condition but only in a certain range
+see this is the expression is a like um
+
+ align:start position:0%
+see this is the expression is a like um
+ 
+
+ align:start position:0%
+see this is the expression is a like um
+a second order equation so you can solve
+
+ align:start position:0%
+a second order equation so you can solve
+ 
+
+ align:start position:0%
+a second order equation so you can solve
+it and you find uh this range so this is
+
+ align:start position:0%
+it and you find uh this range so this is
+ 
+
+ align:start position:0%
+it and you find uh this range so this is
+the um this is these uh this mole
+
+ align:start position:0%
+the um this is these uh this mole
+ 
+
+ align:start position:0%
+the um this is these uh this mole
+fraction and that is this other mole
+
+ align:start position:0%
+fraction and that is this other mole
+ 
+
+ align:start position:0%
+fraction and that is this other mole
+fraction as a function of parameter
+
+ align:start position:0%
+fraction as a function of parameter
+ 
+
+ align:start position:0%
+fraction as a function of parameter
+a so this is one part of the condition
+
+ align:start position:0%
+a so this is one part of the condition
+ 
+
+ align:start position:0%
+a so this is one part of the condition
+for it's a necessary condition for
+
+ align:start position:0%
+for it's a necessary condition for
+ 
+
+ align:start position:0%
+for it's a necessary condition for
+stability but the other condition for is
+
+ align:start position:0%
+stability but the other condition for is
+ 
+
+ align:start position:0%
+stability but the other condition for is
+that the the two phases are in mutual
+
+ align:start position:0%
+that the the two phases are in mutual
+ 
+
+ align:start position:0%
+that the the two phases are in mutual
+stabil stable equilibrium and therefore
+
+ align:start position:0%
+stabil stable equilibrium and therefore
+ 
+
+ align:start position:0%
+stabil stable equilibrium and therefore
+you also have the conditions that the
+
+ align:start position:0%
+you also have the conditions that the
+ 
+
+ align:start position:0%
+you also have the conditions that the
+chemical potentials must be
+
+ align:start position:0%
+chemical potentials must be
+ 
+
+ align:start position:0%
+chemical potentials must be
+equal and this two conditions
+
+ align:start position:0%
+equal and this two conditions
+ 
+
+ align:start position:0%
+equal and this two conditions
+essentially are correspond to this
+
+ align:start position:0%
+essentially are correspond to this
+ 
+
+ align:start position:0%
+essentially are correspond to this
+construction of the tangent line that we
+
+ align:start position:0%
+construction of the tangent line that we
+ 
+
+ align:start position:0%
+construction of the tangent line that we
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+described so this equation here if you
+
+ align:start position:0%
+described so this equation here if you
+ 
+
+ align:start position:0%
+described so this equation here if you
+fix an a you
+
+ align:start position:0%
+fix an a you
+ 
+
+ align:start position:0%
+fix an a you
+find uh you find the mole fractions of
+
+ align:start position:0%
+find uh you find the mole fractions of
+ 
+
+ align:start position:0%
+find uh you find the mole fractions of
+the phases in mutual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium so this is easy enough that
+
+ align:start position:0%
+equilibrium so this is easy enough that
+ 
+
+ align:start position:0%
+equilibrium so this is easy enough that
+you can implement it for example in an
+
+ align:start position:0%
+you can implement it for example in an
+ 
+
+ align:start position:0%
+you can implement it for example in an
+Excel
+
+ align:start position:0%
+Excel
+ 
+
+ align:start position:0%
+Excel
+file H so you see the the Gibs free
+
+ align:start position:0%
+file H so you see the the Gibs free
+ 
+
+ align:start position:0%
+file H so you see the the Gibs free
+energy uh little G uh mol is given by
+
+ align:start position:0%
+energy uh little G uh mol is given by
+ 
+
+ align:start position:0%
+energy uh little G uh mol is given by
+this relation it's the sum of the two
+
+ align:start position:0%
+this relation it's the sum of the two
+ 
+
+ align:start position:0%
+this relation it's the sum of the two
+contributions the
+
+ align:start position:0%
+contributions the
+ 
+
+ align:start position:0%
+contributions the
+ideal which is
+
+ align:start position:0%
+ideal which is
+ 
+
+ align:start position:0%
+ideal which is
+this and the excess which is
+
+ align:start position:0%
+this and the excess which is
+ 
+
+ align:start position:0%
+this and the excess which is
+that okay in this case for a less than
+
+ align:start position:0%
+that okay in this case for a less than
+ 
+
+ align:start position:0%
+that okay in this case for a less than
+two at all
+
+ align:start position:0%
+two at all
+ 
+
+ align:start position:0%
+two at all
+compositions the second derivative of G
+
+ align:start position:0%
+compositions the second derivative of G
+ 
+
+ align:start position:0%
+compositions the second derivative of G
+is positive and we have
+
+ align:start position:0%
+is positive and we have
+ 
+
+ align:start position:0%
+is positive and we have
+stability so at
+
+ align:start position:0%
+stability so at
+ 
+
+ align:start position:0%
+stability so at
+this uh in general this a depends on
+
+ align:start position:0%
+this uh in general this a depends on
+ 
+
+ align:start position:0%
+this uh in general this a depends on
+temperature let's say these
+
+ align:start position:0%
+temperature let's say these
+ 
+
+ align:start position:0%
+temperature let's say these
+temperatures uh so um the two liquids
+
+ align:start position:0%
+temperatures uh so um the two liquids
+ 
+
+ align:start position:0%
+temperatures uh so um the two liquids
+are completely
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+missible as you decrease the temperature
+
+ align:start position:0%
+missible as you decrease the temperature
+ 
+
+ align:start position:0%
+missible as you decrease the temperature
+the Val the value of a changes and
+
+ align:start position:0%
+the Val the value of a changes and
+ 
+
+ align:start position:0%
+the Val the value of a changes and
+eventually you reach the critical value
+
+ align:start position:0%
+eventually you reach the critical value
+ 
+
+ align:start position:0%
+eventually you reach the critical value
+a equals
+
+ align:start position:0%
+a equals
+ 
+
+ align:start position:0%
+a equals
+2 at that
+
+ align:start position:0%
+2 at that
+ 
+
+ align:start position:0%
+2 at that
+moment you still are okay in terms of
+
+ align:start position:0%
+moment you still are okay in terms of
+ 
+
+ align:start position:0%
+moment you still are okay in terms of
+stability but there at the minimum here
+
+ align:start position:0%
+stability but there at the minimum here
+ 
+
+ align:start position:0%
+stability but there at the minimum here
+um you have a second order derivative
+
+ align:start position:0%
+um you have a second order derivative
+ 
+
+ align:start position:0%
+um you have a second order derivative
+equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero not a minimum at this at some point
+
+ align:start position:0%
+zero not a minimum at this at some point
+ 
+
+ align:start position:0%
+zero not a minimum at this at some point
+you get a second order second Dera equal
+
+ align:start position:0%
+you get a second order second Dera equal
+ 
+
+ align:start position:0%
+you get a second order second Dera equal
+to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of course this plot for these plots we
+
+ align:start position:0%
+of course this plot for these plots we
+ 
+
+ align:start position:0%
+of course this plot for these plots we
+had to assume something about the
+
+ align:start position:0%
+had to assume something about the
+ 
+
+ align:start position:0%
+had to assume something about the
+properties of the pure substances so I
+
+ align:start position:0%
+properties of the pure substances so I
+ 
+
+ align:start position:0%
+properties of the pure substances so I
+assume the these values 02 for one
+
+ align:start position:0%
+assume the these values 02 for one
+ 
+
+ align:start position:0%
+assume the these values 02 for one
+substance and point uh uh four for the
+
+ align:start position:0%
+substance and point uh uh four for the
+ 
+
+ align:start position:0%
+substance and point uh uh four for the
+other if you uh Set uh uh lower
+
+ align:start position:0%
+other if you uh Set uh uh lower
+ 
+
+ align:start position:0%
+other if you uh Set uh uh lower
+temperature so you go to a greater than
+
+ align:start position:0%
+temperature so you go to a greater than
+ 
+
+ align:start position:0%
+temperature so you go to a greater than
+two then you get uh partial Miss
+
+ align:start position:0%
+two then you get uh partial Miss
+ 
+
+ align:start position:0%
+two then you get uh partial Miss
+ability you get this uh
+
+ align:start position:0%
+ability you get this uh
+ 
+
+ align:start position:0%
+ability you get this uh
+uh mbil Gap so from the spinoid
+
+ align:start position:0%
+uh mbil Gap so from the spinoid
+ 
+
+ align:start position:0%
+uh mbil Gap so from the spinoid
+composition here to the spidal compos
+
+ align:start position:0%
+composition here to the spidal compos
+ 
+
+ align:start position:0%
+composition here to the spidal compos
+composition there for the liquid and the
+
+ align:start position:0%
+composition there for the liquid and the
+ 
+
+ align:start position:0%
+composition there for the liquid and the
+vapor there is the this entire uh range
+
+ align:start position:0%
+vapor there is the this entire uh range
+ 
+
+ align:start position:0%
+vapor there is the this entire uh range
+of compositions in which the mixture
+
+ align:start position:0%
+of compositions in which the mixture
+ 
+
+ align:start position:0%
+of compositions in which the mixture
+doesn't
+
+ align:start position:0%
+doesn't
+ 
+
+ align:start position:0%
+doesn't
+uh want to
+
+ align:start position:0%
+uh want to
+ 
+
+ align:start position:0%
+uh want to
+stay so if you find if you manage to
+
+ align:start position:0%
+stay so if you find if you manage to
+ 
+
+ align:start position:0%
+stay so if you find if you manage to
+produce a mixture with this composition
+
+ align:start position:0%
+produce a mixture with this composition
+ 
+
+ align:start position:0%
+produce a mixture with this composition
+at these conditions of temperature and
+
+ align:start position:0%
+at these conditions of temperature and
+ 
+
+ align:start position:0%
+at these conditions of temperature and
+pressure it will separate spontaneously
+
+ align:start position:0%
+pressure it will separate spontaneously
+ 
+
+ align:start position:0%
+pressure it will separate spontaneously
+in search for
+
+ align:start position:0%
+in search for
+ 
+
+ align:start position:0%
+in search for
+stability and it will
+
+ align:start position:0%
+stability and it will
+ 
+
+ align:start position:0%
+stability and it will
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+um two phases so it will form a phase in
+
+ align:start position:0%
+um two phases so it will form a phase in
+ 
+
+ align:start position:0%
+um two phases so it will form a phase in
+which uh uh which is rich in component
+
+ align:start position:0%
+which uh uh which is rich in component
+ 
+
+ align:start position:0%
+which uh uh which is rich in component
+one this one and a phase in which is
+
+ align:start position:0%
+one this one and a phase in which is
+ 
+
+ align:start position:0%
+one this one and a phase in which is
+lean in component one which is this and
+
+ align:start position:0%
+lean in component one which is this and
+ 
+
+ align:start position:0%
+lean in component one which is this and
+eventually it will reach Mutual
+
+ align:start position:0%
+eventually it will reach Mutual
+ 
+
+ align:start position:0%
+eventually it will reach Mutual
+equilibrium I mean it
+
+ align:start position:0%
+equilibrium I mean it
+ 
+
+ align:start position:0%
+equilibrium I mean it
+will will face
+
+ align:start position:0%
+will will face
+ 
+
+ align:start position:0%
+will will face
+separate uh to two phases that are in
+
+ align:start position:0%
+separate uh to two phases that are in
+ 
+
+ align:start position:0%
+separate uh to two phases that are in
+mutual equilibrium at these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compositions okay these equations are
+
+ align:start position:0%
+compositions okay these equations are
+ 
+
+ align:start position:0%
+compositions okay these equations are
+again that constructions that we'
+
+ align:start position:0%
+again that constructions that we'
+ 
+
+ align:start position:0%
+again that constructions that we'
+already
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+done so if you uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by some means for example one
+
+ align:start position:0%
+by some means for example one
+ 
+
+ align:start position:0%
+by some means for example one
+possibility is to start from a mixture
+
+ align:start position:0%
+possibility is to start from a mixture
+ 
+
+ align:start position:0%
+possibility is to start from a mixture
+at a temperature above
+
+ align:start position:0%
+at a temperature above
+ 
+
+ align:start position:0%
+at a temperature above
+critical uh say here and then you find a
+
+ align:start position:0%
+critical uh say here and then you find a
+ 
+
+ align:start position:0%
+critical uh say here and then you find a
+way to quench
+
+ align:start position:0%
+way to quench
+ 
+
+ align:start position:0%
+way to quench
+it much like what we discussed also for
+
+ align:start position:0%
+it much like what we discussed also for
+ 
+
+ align:start position:0%
+it much like what we discussed also for
+the Vander bals spinodal decomposition
+
+ align:start position:0%
+the Vander bals spinodal decomposition
+ 
+
+ align:start position:0%
+the Vander bals spinodal decomposition
+so you quench to this uh Point
+
+ align:start position:0%
+so you quench to this uh Point
+ 
+
+ align:start position:0%
+so you quench to this uh Point
+here uh
+
+ align:start position:0%
+here uh
+ 
+
+ align:start position:0%
+here uh
+and uh so you uce the temperature at
+
+ align:start position:0%
+and uh so you uce the temperature at
+ 
+
+ align:start position:0%
+and uh so you uce the temperature at
+this point the the
+
+ align:start position:0%
+this point the the
+ 
+
+ align:start position:0%
+this point the the
+instability uh
+
+ align:start position:0%
+instability uh
+ 
+
+ align:start position:0%
+instability uh
+triggers what you see uh here it
+
+ align:start position:0%
+triggers what you see uh here it
+ 
+
+ align:start position:0%
+triggers what you see uh here it
+triggers that the fact that from
+
+ align:start position:0%
+triggers that the fact that from
+ 
+
+ align:start position:0%
+triggers that the fact that from
+homogeneous the phases uh U begin to
+
+ align:start position:0%
+homogeneous the phases uh U begin to
+ 
+
+ align:start position:0%
+homogeneous the phases uh U begin to
+separate because substance one uh either
+
+ align:start position:0%
+separate because substance one uh either
+ 
+
+ align:start position:0%
+separate because substance one uh either
+wants to be close to uh a lot of
+
+ align:start position:0%
+wants to be close to uh a lot of
+ 
+
+ align:start position:0%
+wants to be close to uh a lot of
+substance ones one or or a little of sub
+
+ align:start position:0%
+substance ones one or or a little of sub
+ 
+
+ align:start position:0%
+substance ones one or or a little of sub
+substance on so it you get diffusion U
+
+ align:start position:0%
+substance on so it you get diffusion U
+ 
+
+ align:start position:0%
+substance on so it you get diffusion U
+uh process and this is
+
+ align:start position:0%
+uh process and this is
+ 
+
+ align:start position:0%
+uh process and this is
+fast because you have uh uh as we have
+
+ align:start position:0%
+fast because you have uh uh as we have
+ 
+
+ align:start position:0%
+fast because you have uh uh as we have
+seen for the Vander vals case we have a
+
+ align:start position:0%
+seen for the Vander vals case we have a
+ 
+
+ align:start position:0%
+seen for the Vander vals case we have a
+lot of free energy available to create
+
+ align:start position:0%
+lot of free energy available to create
+ 
+
+ align:start position:0%
+lot of free energy available to create
+uh the um the surface that separates the
+
+ align:start position:0%
+uh the um the surface that separates the
+ 
+
+ align:start position:0%
+uh the um the surface that separates the
+two phases
+
+ align:start position:0%
+two phases
+ 
+
+ align:start position:0%
+two phases
+and then once that
+
+ align:start position:0%
+and then once that
+ 
+
+ align:start position:0%
+and then once that
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+coalesence
+
+ align:start position:0%
+coalesence
+ 
+
+ align:start position:0%
+coalesence
+makes uh uses up that surface
+
+ align:start position:0%
+makes uh uses up that surface
+ 
+
+ align:start position:0%
+makes uh uses up that surface
+energy and tries to to find
+
+ align:start position:0%
+energy and tries to to find
+ 
+
+ align:start position:0%
+energy and tries to to find
+configurations of of lesser uh um free
+
+ align:start position:0%
+configurations of of lesser uh um free
+ 
+
+ align:start position:0%
+configurations of of lesser uh um free
+energy by um
+
+ align:start position:0%
+energy by um
+ 
+
+ align:start position:0%
+energy by um
+making drops or bubbles uh drops in this
+
+ align:start position:0%
+making drops or bubbles uh drops in this
+ 
+
+ align:start position:0%
+making drops or bubbles uh drops in this
+case uh uh bigger and
+
+ align:start position:0%
+case uh uh bigger and
+ 
+
+ align:start position:0%
+case uh uh bigger and
+bigger and also here if you do the
+
+ align:start position:0%
+bigger and also here if you do the
+ 
+
+ align:start position:0%
+bigger and also here if you do the
+separation uh if you do this quenching
+
+ align:start position:0%
+separation uh if you do this quenching
+ 
+
+ align:start position:0%
+separation uh if you do this quenching
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+exactly the critical comp uh
+
+ align:start position:0%
+exactly the critical comp uh
+ 
+
+ align:start position:0%
+exactly the critical comp uh
+composition then uh the mixture the
+
+ align:start position:0%
+composition then uh the mixture the
+ 
+
+ align:start position:0%
+composition then uh the mixture the
+separation as you see doesn't doesn't U
+
+ align:start position:0%
+separation as you see doesn't doesn't U
+ 
+
+ align:start position:0%
+separation as you see doesn't doesn't U
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+either neither do U uh drop drops nor I
+
+ align:start position:0%
+either neither do U uh drop drops nor I
+ 
+
+ align:start position:0%
+either neither do U uh drop drops nor I
+mean doesn't do yeah in the Vander vals
+
+ align:start position:0%
+mean doesn't do yeah in the Vander vals
+ 
+
+ align:start position:0%
+mean doesn't do yeah in the Vander vals
+it's neither drops nor bubbles here it's
+
+ align:start position:0%
+it's neither drops nor bubbles here it's
+ 
+
+ align:start position:0%
+it's neither drops nor bubbles here it's
+uh it's drops in in all cases but you
+
+ align:start position:0%
+uh it's drops in in all cases but you
+ 
+
+ align:start position:0%
+uh it's drops in in all cases but you
+see instead of drops it's continuous uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um continuous
+
+ align:start position:0%
+um continuous
+ 
+
+ align:start position:0%
+um continuous
+regions that become gross and
+
+ align:start position:0%
+regions that become gross and
+ 
+
+ align:start position:0%
+regions that become gross and
+grosser if you instead are
+
+ align:start position:0%
+grosser if you instead are
+ 
+
+ align:start position:0%
+grosser if you instead are
+off critical on either side uh you get
+
+ align:start position:0%
+off critical on either side uh you get
+ 
+
+ align:start position:0%
+off critical on either side uh you get
+drops of uh one into a
+
+ align:start position:0%
+drops of uh one into a
+ 
+
+ align:start position:0%
+drops of uh one into a
+continuous um region of the
+
+ align:start position:0%
+continuous um region of the
+ 
+
+ align:start position:0%
+continuous um region of the
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now there is also this uh region
+
+ align:start position:0%
+okay now there is also this uh region
+ 
+
+ align:start position:0%
+okay now there is also this uh region
+here of meta stable States between the
+
+ align:start position:0%
+here of meta stable States between the
+ 
+
+ align:start position:0%
+here of meta stable States between the
+spinodal and the binodal uh
+
+ align:start position:0%
+spinodal and the binodal uh
+ 
+
+ align:start position:0%
+spinodal and the binodal uh
+curve there is a a
+
+ align:start position:0%
+curve there is a a
+ 
+
+ align:start position:0%
+curve there is a a
+metastability and these metastable
+
+ align:start position:0%
+metastability and these metastable
+ 
+
+ align:start position:0%
+metastability and these metastable
+states are uh interesting because
+
+ align:start position:0%
+states are uh interesting because
+ 
+
+ align:start position:0%
+states are uh interesting because
+sometimes they uh can be used for
+
+ align:start position:0%
+sometimes they uh can be used for
+ 
+
+ align:start position:0%
+sometimes they uh can be used for
+applications for
+
+ align:start position:0%
+applications for
+ 
+
+ align:start position:0%
+applications for
+example this is uh
+
+ align:start position:0%
+example this is uh
+ 
+
+ align:start position:0%
+example this is uh
+you U I know that
+
+ align:start position:0%
+you U I know that
+ 
+
+ align:start position:0%
+you U I know that
+um one of you is Greek and so uh
+
+ align:start position:0%
+um one of you is Greek and so uh
+ 
+
+ align:start position:0%
+um one of you is Greek and so uh
+certainly knows uh this uzo effect but
+
+ align:start position:0%
+certainly knows uh this uzo effect but
+ 
+
+ align:start position:0%
+certainly knows uh this uzo effect but
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+um uh in the
+
+ align:start position:0%
+um uh in the
+ 
+
+ align:start position:0%
+um uh in the
+Mediterranean there is these liquers
+
+ align:start position:0%
+Mediterranean there is these liquers
+ 
+
+ align:start position:0%
+Mediterranean there is these liquers
+that uh have very different names so
+
+ align:start position:0%
+that uh have very different names so
+ 
+
+ align:start position:0%
+that uh have very different names so
+let's see I wrote them down because I
+
+ align:start position:0%
+let's see I wrote them down because I
+ 
+
+ align:start position:0%
+let's see I wrote them down because I
+forget like in France get Anette or ptis
+
+ align:start position:0%
+forget like in France get Anette or ptis
+ 
+
+ align:start position:0%
+forget like in France get Anette or ptis
+and uh in Italy sambuka that one I know
+
+ align:start position:0%
+and uh in Italy sambuka that one I know
+ 
+
+ align:start position:0%
+and uh in Italy sambuka that one I know
+uh turkey is
+
+ align:start position:0%
+uh turkey is
+ 
+
+ align:start position:0%
+uh turkey is
+raki in Colombia uh there is some kind
+
+ align:start position:0%
+raki in Colombia uh there is some kind
+ 
+
+ align:start position:0%
+raki in Colombia uh there is some kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+guent which is um flavored with with
+
+ align:start position:0%
+guent which is um flavored with with
+ 
+
+ align:start position:0%
+guent which is um flavored with with
+anet with
+
+ align:start position:0%
+anet with
+ 
+
+ align:start position:0%
+anet with
+Anis uh Mexico also has its own and also
+
+ align:start position:0%
+Anis uh Mexico also has its own and also
+ 
+
+ align:start position:0%
+Anis uh Mexico also has its own and also
+uh some of the
+
+ align:start position:0%
+uh some of the
+ 
+
+ align:start position:0%
+uh some of the
+uh Egypt
+
+ align:start position:0%
+uh Egypt
+ 
+
+ align:start position:0%
+uh Egypt
+and Israel have
+
+ align:start position:0%
+and Israel have
+ 
+
+ align:start position:0%
+and Israel have
+araq uh so essentially this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the the funny thing of these U
+
+ align:start position:0%
+uh the the funny thing of these U
+ 
+
+ align:start position:0%
+uh the the funny thing of these U
+liquers is that they they are
+
+ align:start position:0%
+liquers is that they they are
+ 
+
+ align:start position:0%
+liquers is that they they are
+transparent
+
+ align:start position:0%
+transparent
+ 
+
+ align:start position:0%
+transparent
+so and when you mix it with water which
+
+ align:start position:0%
+so and when you mix it with water which
+ 
+
+ align:start position:0%
+so and when you mix it with water which
+is another transparent
+
+ align:start position:0%
+is another transparent
+ 
+
+ align:start position:0%
+is another transparent
+liquid they become they give you a Milky
+
+ align:start position:0%
+liquid they become they give you a Milky
+ 
+
+ align:start position:0%
+liquid they become they give you a Milky
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+opaque um thing so that's um always a
+
+ align:start position:0%
+opaque um thing so that's um always a
+ 
+
+ align:start position:0%
+opaque um thing so that's um always a
+sort of a mysterious U effect if you see
+
+ align:start position:0%
+sort of a mysterious U effect if you see
+ 
+
+ align:start position:0%
+sort of a mysterious U effect if you see
+it the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time uh it turns out that this effect it
+
+ align:start position:0%
+time uh it turns out that this effect it
+ 
+
+ align:start position:0%
+time uh it turns out that this effect it
+has been named Uso effect only
+
+ align:start position:0%
+has been named Uso effect only
+ 
+
+ align:start position:0%
+has been named Uso effect only
+relatively recently maybe 20 years ago
+
+ align:start position:0%
+relatively recently maybe 20 years ago
+ 
+
+ align:start position:0%
+relatively recently maybe 20 years ago
+when somebody uh some real
+
+ align:start position:0%
+when somebody uh some real
+ 
+
+ align:start position:0%
+when somebody uh some real
+scientist uh visited the
+
+ align:start position:0%
+scientist uh visited the
+ 
+
+ align:start position:0%
+scientist uh visited the
+Mediterranean uh but
+
+ align:start position:0%
+Mediterranean uh but
+ 
+
+ align:start position:0%
+Mediterranean uh but
+um and it is not spinodal
+
+ align:start position:0%
+um and it is not spinodal
+ 
+
+ align:start position:0%
+um and it is not spinodal
+decomposition it is just the
+
+ align:start position:0%
+decomposition it is just the
+ 
+
+ align:start position:0%
+decomposition it is just the
+fact uh that you start you generate a
+
+ align:start position:0%
+fact uh that you start you generate a
+ 
+
+ align:start position:0%
+fact uh that you start you generate a
+mixture okay this has to do
+
+ align:start position:0%
+mixture okay this has to do
+ 
+
+ align:start position:0%
+mixture okay this has to do
+this is more complicated because it's
+
+ align:start position:0%
+this is more complicated because it's
+ 
+
+ align:start position:0%
+this is more complicated because it's
+not a binary mixture it is a three
+
+ align:start position:0%
+not a binary mixture it is a three
+ 
+
+ align:start position:0%
+not a binary mixture it is a three
+component mixture it has uh water it has
+
+ align:start position:0%
+component mixture it has uh water it has
+ 
+
+ align:start position:0%
+component mixture it has uh water it has
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+alcohol which is
+
+ align:start position:0%
+alcohol which is
+ 
+
+ align:start position:0%
+alcohol which is
+ethanol and it has a little amounts of
+
+ align:start position:0%
+ethanol and it has a little amounts of
+ 
+
+ align:start position:0%
+ethanol and it has a little amounts of
+this um oily thing that you extract from
+
+ align:start position:0%
+this um oily thing that you extract from
+ 
+
+ align:start position:0%
+this um oily thing that you extract from
+the seeds of uh the of a plant of of a
+
+ align:start position:0%
+the seeds of uh the of a plant of of a
+ 
+
+ align:start position:0%
+the seeds of uh the of a plant of of a
+flower that is called an amet or
+
+ align:start position:0%
+flower that is called an amet or
+ 
+
+ align:start position:0%
+flower that is called an amet or
+something like
+
+ align:start position:0%
+something like
+ 
+
+ align:start position:0%
+something like
+that no I don't have the name of
+
+ align:start position:0%
+that no I don't have the name of
+ 
+
+ align:start position:0%
+that no I don't have the name of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh I think the chemical uh the the
+
+ align:start position:0%
+uh I think the chemical uh the the
+ 
+
+ align:start position:0%
+uh I think the chemical uh the the
+chemical composition of this oily thing
+
+ align:start position:0%
+chemical composition of this oily thing
+ 
+
+ align:start position:0%
+chemical composition of this oily thing
+that gives the flavor is trans anol and
+
+ align:start position:0%
+that gives the flavor is trans anol and
+ 
+
+ align:start position:0%
+that gives the flavor is trans anol and
+it's like C10 h12
+
+ align:start position:0%
+it's like C10 h12
+ 
+
+ align:start position:0%
+it's like C10 h12
+o you find uh all these in in these um
+
+ align:start position:0%
+o you find uh all these in in these um
+ 
+
+ align:start position:0%
+o you find uh all these in in these um
+nice articles that give U the scientific
+
+ align:start position:0%
+nice articles that give U the scientific
+ 
+
+ align:start position:0%
+nice articles that give U the scientific
+explanation and from which I have
+
+ align:start position:0%
+explanation and from which I have
+ 
+
+ align:start position:0%
+explanation and from which I have
+extracted these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pictures so the idea here is that you
+
+ align:start position:0%
+pictures so the idea here is that you
+ 
+
+ align:start position:0%
+pictures so the idea here is that you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+uh uh three
+
+ align:start position:0%
+uh uh three
+ 
+
+ align:start position:0%
+uh uh three
+substances so let me just uh see uh they
+
+ align:start position:0%
+substances so let me just uh see uh they
+ 
+
+ align:start position:0%
+substances so let me just uh see uh they
+call it
+
+ align:start position:0%
+call it
+ 
+
+ align:start position:0%
+call it
+dvb in that uh graph that this plays the
+
+ align:start position:0%
+dvb in that uh graph that this plays the
+ 
+
+ align:start position:0%
+dvb in that uh graph that this plays the
+role of the an is uh an his
+
+ align:start position:0%
+role of the an is uh an his
+ 
+
+ align:start position:0%
+role of the an is uh an his
+um yeah
+
+ align:start position:0%
+um yeah
+ 
+
+ align:start position:0%
+um yeah
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+is oil but I don't think they prefer to
+
+ align:start position:0%
+is oil but I don't think they prefer to
+ 
+
+ align:start position:0%
+is oil but I don't think they prefer to
+do it with a polymer that has
+
+ align:start position:0%
+do it with a polymer that has
+ 
+
+ align:start position:0%
+do it with a polymer that has
+polymeric oil that uh so they used d d
+
+ align:start position:0%
+polymeric oil that uh so they used d d
+ 
+
+ align:start position:0%
+polymeric oil that uh so they used d d
+venil Benzene so this is
+
+ align:start position:0%
+venil Benzene so this is
+ 
+
+ align:start position:0%
+venil Benzene so this is
+D
+
+ align:start position:0%
+D
+ 
+
+ align:start position:0%
+D
+vile
+
+ align:start position:0%
+vile
+ 
+
+ align:start position:0%
+vile
+Benzene at least in their experiment so
+
+ align:start position:0%
+Benzene at least in their experiment so
+ 
+
+ align:start position:0%
+Benzene at least in their experiment so
+let's say this is a substance uh C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now it turns out that this
+
+ align:start position:0%
+okay now it turns out that this
+ 
+
+ align:start position:0%
+okay now it turns out that this
+substance is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+soluble in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alcohol is not soluble in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+water so let's call water B
+
+ align:start position:0%
+water so let's call water B
+ 
+
+ align:start position:0%
+water so let's call water B
+and alcohol a okay so
+
+ align:start position:0%
+and alcohol a okay so
+ 
+
+ align:start position:0%
+and alcohol a okay so
+essentially here we
+
+ align:start position:0%
+essentially here we
+ 
+
+ align:start position:0%
+essentially here we
+have the mole
+
+ align:start position:0%
+have the mole
+ 
+
+ align:start position:0%
+have the mole
+fraction of the organic oil that uh
+
+ align:start position:0%
+fraction of the organic oil that uh
+ 
+
+ align:start position:0%
+fraction of the organic oil that uh
+that's our
+
+ align:start position:0%
+that's our
+ 
+
+ align:start position:0%
+that's our
+C and this is the mole
+
+ align:start position:0%
+C and this is the mole
+ 
+
+ align:start position:0%
+C and this is the mole
+fraction of uh the uh ethanol which is
+
+ align:start position:0%
+fraction of uh the uh ethanol which is
+ 
+
+ align:start position:0%
+fraction of uh the uh ethanol which is
+our a
+
+ align:start position:0%
+our a
+ 
+
+ align:start position:0%
+our a
+okay this is how this the the the the
+
+ align:start position:0%
+okay this is how this the the the the
+ 
+
+ align:start position:0%
+okay this is how this the the the the
+equivalent of this diagram looks at a
+
+ align:start position:0%
+equivalent of this diagram looks at a
+ 
+
+ align:start position:0%
+equivalent of this diagram looks at a
+fixed
+
+ align:start position:0%
+fixed
+ 
+
+ align:start position:0%
+fixed
+temperature as function of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compositions of course the mole fraction
+
+ align:start position:0%
+compositions of course the mole fraction
+ 
+
+ align:start position:0%
+compositions of course the mole fraction
+of water is one minus the sum of these
+
+ align:start position:0%
+of water is one minus the sum of these
+ 
+
+ align:start position:0%
+of water is one minus the sum of these
+two hence the uh triangular uh line
+
+ align:start position:0%
+two hence the uh triangular uh line
+ 
+
+ align:start position:0%
+two hence the uh triangular uh line
+here so up up here we got just pure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+water uh if you plot this uh since is
+
+ align:start position:0%
+water uh if you plot this uh since is
+ 
+
+ align:start position:0%
+water uh if you plot this uh since is
+very skewed if you plot it in a
+
+ align:start position:0%
+very skewed if you plot it in a
+ 
+
+ align:start position:0%
+very skewed if you plot it in a
+logarithmic scale in the composition of
+
+ align:start position:0%
+logarithmic scale in the composition of
+ 
+
+ align:start position:0%
+logarithmic scale in the composition of
+the organic
+
+ align:start position:0%
+the organic
+ 
+
+ align:start position:0%
+the organic
+oil uh this is how it
+
+ align:start position:0%
+oil uh this is how it
+ 
+
+ align:start position:0%
+oil uh this is how it
+looks it opens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up so what you typically have is
+
+ align:start position:0%
+up so what you typically have is
+ 
+
+ align:start position:0%
+up so what you typically have is
+uh Uso is a is a is a 40% by volume
+
+ align:start position:0%
+uh Uso is a is a is a 40% by volume
+ 
+
+ align:start position:0%
+uh Uso is a is a is a 40% by volume
+meaning about 35 or 34 % by weight and
+
+ align:start position:0%
+meaning about 35 or 34 % by weight and
+ 
+
+ align:start position:0%
+meaning about 35 or 34 % by weight and
+here is by weight uh so this is the
+
+ align:start position:0%
+here is by weight uh so this is the
+ 
+
+ align:start position:0%
+here is by weight uh so this is the
+alcohol
+
+ align:start position:0%
+alcohol
+ 
+
+ align:start position:0%
+alcohol
+content and let's say the content of
+
+ align:start position:0%
+content and let's say the content of
+ 
+
+ align:start position:0%
+content and let's say the content of
+this oily um
+
+ align:start position:0%
+this oily um
+ 
+
+ align:start position:0%
+this oily um
+an organic oil uh extract from these
+
+ align:start position:0%
+an organic oil uh extract from these
+ 
+
+ align:start position:0%
+an organic oil uh extract from these
+flowers from these seeds suppose is this
+
+ align:start position:0%
+flowers from these seeds suppose is this
+ 
+
+ align:start position:0%
+flowers from these seeds suppose is this
+much okay what happens is when you add
+
+ align:start position:0%
+much okay what happens is when you add
+ 
+
+ align:start position:0%
+much okay what happens is when you add
+water you dilute the solution and so the
+
+ align:start position:0%
+water you dilute the solution and so the
+ 
+
+ align:start position:0%
+water you dilute the solution and so the
+the fraction of ethanol goes down from
+
+ align:start position:0%
+the fraction of ethanol goes down from
+ 
+
+ align:start position:0%
+the fraction of ethanol goes down from
+35 say to uh you cross this line and you
+
+ align:start position:0%
+35 say to uh you cross this line and you
+ 
+
+ align:start position:0%
+35 say to uh you cross this line and you
+get into the the metastable
+
+ align:start position:0%
+get into the the metastable
+ 
+
+ align:start position:0%
+get into the the metastable
+region in that metastable
+
+ align:start position:0%
+region in that metastable
+ 
+
+ align:start position:0%
+region in that metastable
+region you get an
+
+ align:start position:0%
+region you get an
+ 
+
+ align:start position:0%
+region you get an
+immediate U
+
+ align:start position:0%
+immediate U
+ 
+
+ align:start position:0%
+immediate U
+separation or formation of these minute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+droplets which then
+
+ align:start position:0%
+droplets which then
+ 
+
+ align:start position:0%
+droplets which then
+because you so you
+
+ align:start position:0%
+because you so you
+ 
+
+ align:start position:0%
+because you so you
+release the excess G gives free energy
+
+ align:start position:0%
+release the excess G gives free energy
+ 
+
+ align:start position:0%
+release the excess G gives free energy
+that forms those minute
+
+ align:start position:0%
+that forms those minute
+ 
+
+ align:start position:0%
+that forms those minute
+droplets those droplets are the the
+
+ align:start position:0%
+droplets those droplets are the the
+ 
+
+ align:start position:0%
+droplets those droplets are the the
+reason uh why then uh light does
+
+ align:start position:0%
+reason uh why then uh light does
+ 
+
+ align:start position:0%
+reason uh why then uh light does
+not get through gets diffused by these
+
+ align:start position:0%
+not get through gets diffused by these
+ 
+
+ align:start position:0%
+not get through gets diffused by these
+droplets so that's why the
+
+ align:start position:0%
+droplets so that's why the
+ 
+
+ align:start position:0%
+droplets so that's why the
+liquid uh loses the transpar to
+
+ align:start position:0%
+liquid uh loses the transpar to
+ 
+
+ align:start position:0%
+liquid uh loses the transpar to
+light it's the the reasons are these
+
+ align:start position:0%
+light it's the the reasons are these
+ 
+
+ align:start position:0%
+light it's the the reasons are these
+droplets but differently from spinodal
+
+ align:start position:0%
+droplets but differently from spinodal
+ 
+
+ align:start position:0%
+droplets but differently from spinodal
+De composition if you
+
+ align:start position:0%
+De composition if you
+ 
+
+ align:start position:0%
+De composition if you
+had generated this kind of situation
+
+ align:start position:0%
+had generated this kind of situation
+ 
+
+ align:start position:0%
+had generated this kind of situation
+from the unstable State H the separation
+
+ align:start position:0%
+from the unstable State H the separation
+ 
+
+ align:start position:0%
+from the unstable State H the separation
+would would have been uh much more
+
+ align:start position:0%
+would would have been uh much more
+ 
+
+ align:start position:0%
+would would have been uh much more
+vigorous and it would
+
+ align:start position:0%
+vigorous and it would
+ 
+
+ align:start position:0%
+vigorous and it would
+generate have more energy so generate
+
+ align:start position:0%
+generate have more energy so generate
+ 
+
+ align:start position:0%
+generate have more energy so generate
+bigger uh drops in the end and and
+
+ align:start position:0%
+bigger uh drops in the end and and
+ 
+
+ align:start position:0%
+bigger uh drops in the end and and
+eventually the mixture will uh will
+
+ align:start position:0%
+eventually the mixture will uh will
+ 
+
+ align:start position:0%
+eventually the mixture will uh will
+separate or maybe in any case it will
+
+ align:start position:0%
+separate or maybe in any case it will
+ 
+
+ align:start position:0%
+separate or maybe in any case it will
+form bigger drops whereas uh in the oo
+
+ align:start position:0%
+form bigger drops whereas uh in the oo
+ 
+
+ align:start position:0%
+form bigger drops whereas uh in the oo
+effect you generate you produce very
+
+ align:start position:0%
+effect you generate you produce very
+ 
+
+ align:start position:0%
+effect you generate you produce very
+small uh droplets they they remain in a
+
+ align:start position:0%
+small uh droplets they they remain in a
+ 
+
+ align:start position:0%
+small uh droplets they they remain in a
+sort of an Emulsion that is relatively
+
+ align:start position:0%
+sort of an Emulsion that is relatively
+ 
+
+ align:start position:0%
+sort of an Emulsion that is relatively
+stable in other words it survives uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hours and u
+
+ align:start position:0%
+hours and u
+ 
+
+ align:start position:0%
+hours and u
+and in some
+
+ align:start position:0%
+and in some
+ 
+
+ align:start position:0%
+and in some
+cases this kind of process is wanted
+
+ align:start position:0%
+cases this kind of process is wanted
+ 
+
+ align:start position:0%
+cases this kind of process is wanted
+because uh there are applications in
+
+ align:start position:0%
+because uh there are applications in
+ 
+
+ align:start position:0%
+because uh there are applications in
+which you want to generate
+
+ align:start position:0%
+which you want to generate
+ 
+
+ align:start position:0%
+which you want to generate
+emulsions uh which is precisely a
+
+ align:start position:0%
+emulsions uh which is precisely a
+ 
+
+ align:start position:0%
+emulsions uh which is precisely a
+mixture of of a solvent with a lot of
+
+ align:start position:0%
+mixture of of a solvent with a lot of
+ 
+
+ align:start position:0%
+mixture of of a solvent with a lot of
+small droplets in it uh like when you do
+
+ align:start position:0%
+small droplets in it uh like when you do
+ 
+
+ align:start position:0%
+small droplets in it uh like when you do
+vinegret that's an Emulsion and
+
+ align:start position:0%
+vinegret that's an Emulsion and
+ 
+
+ align:start position:0%
+vinegret that's an Emulsion and
+uh many times in order to uh produce
+
+ align:start position:0%
+uh many times in order to uh produce
+ 
+
+ align:start position:0%
+uh many times in order to uh produce
+emulsions you need uh surfactant but
+
+ align:start position:0%
+emulsions you need uh surfactant but
+ 
+
+ align:start position:0%
+emulsions you need uh surfactant but
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+instead a way to
+
+ align:start position:0%
+instead a way to
+ 
+
+ align:start position:0%
+instead a way to
+produce uh emulsions without
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surfactant and chemical industry is full
+
+ align:start position:0%
+surfactant and chemical industry is full
+ 
+
+ align:start position:0%
+surfactant and chemical industry is full
+of processes that go back and forth uh
+
+ align:start position:0%
+of processes that go back and forth uh
+ 
+
+ align:start position:0%
+of processes that go back and forth uh
+with with this kind of uh of of effects
+
+ align:start position:0%
+with with this kind of uh of of effects
+ 
+
+ align:start position:0%
+with with this kind of uh of of effects
+in know order to uh separate or mix and
+
+ align:start position:0%
+in know order to uh separate or mix and
+ 
+
+ align:start position:0%
+in know order to uh separate or mix and
+uh uh generate uh things
+
+ align:start position:0%
+uh uh generate uh things
+ 
+
+ align:start position:0%
+uh uh generate uh things
+also uh I think that this um this method
+
+ align:start position:0%
+also uh I think that this um this method
+ 
+
+ align:start position:0%
+also uh I think that this um this method
+has also been used in order to generate
+
+ align:start position:0%
+has also been used in order to generate
+ 
+
+ align:start position:0%
+has also been used in order to generate
+scuffles for biological applications for
+
+ align:start position:0%
+scuffles for biological applications for
+ 
+
+ align:start position:0%
+scuffles for biological applications for
+example uh because if you once you have
+
+ align:start position:0%
+example uh because if you once you have
+ 
+
+ align:start position:0%
+example uh because if you once you have
+this Emulsion you freeze
+
+ align:start position:0%
+this Emulsion you freeze
+ 
+
+ align:start position:0%
+this Emulsion you freeze
+it in such a way way
+
+ align:start position:0%
+it in such a way way
+ 
+
+ align:start position:0%
+it in such a way way
+that uh okay if you freeze it in such a
+
+ align:start position:0%
+that uh okay if you freeze it in such a
+ 
+
+ align:start position:0%
+that uh okay if you freeze it in such a
+way that the the the bul phase remains
+
+ align:start position:0%
+way that the the the bul phase remains
+ 
+
+ align:start position:0%
+way that the the the bul phase remains
+liquid and the uh the droplets be become
+
+ align:start position:0%
+liquid and the uh the droplets be become
+ 
+
+ align:start position:0%
+liquid and the uh the droplets be become
+solid then you've generated small
+
+ align:start position:0%
+solid then you've generated small
+ 
+
+ align:start position:0%
+solid then you've generated small
+spheres so in this this is a way in
+
+ align:start position:0%
+spheres so in this this is a way in
+ 
+
+ align:start position:0%
+spheres so in this this is a way in
+which you produce small
+
+ align:start position:0%
+which you produce small
+ 
+
+ align:start position:0%
+which you produce small
+feares or conversely if you uh perhaps
+
+ align:start position:0%
+feares or conversely if you uh perhaps
+ 
+
+ align:start position:0%
+feares or conversely if you uh perhaps
+not these ones because they are not
+
+ align:start position:0%
+not these ones because they are not
+ 
+
+ align:start position:0%
+not these ones because they are not
+connected and so if you freeze
+
+ align:start position:0%
+connected and so if you freeze
+ 
+
+ align:start position:0%
+connected and so if you freeze
+this and
+
+ align:start position:0%
+this and
+ 
+
+ align:start position:0%
+this and
+uh uh the the liquid droplets remain
+
+ align:start position:0%
+uh uh the the liquid droplets remain
+ 
+
+ align:start position:0%
+uh uh the the liquid droplets remain
+liquid you you still have droplets and
+
+ align:start position:0%
+liquid you you still have droplets and
+ 
+
+ align:start position:0%
+liquid you you still have droplets and
+you not there is no path for the liquid
+
+ align:start position:0%
+you not there is no path for the liquid
+ 
+
+ align:start position:0%
+you not there is no path for the liquid
+to go away but if you use a situation
+
+ align:start position:0%
+to go away but if you use a situation
+ 
+
+ align:start position:0%
+to go away but if you use a situation
+like this one generated by a spinodal
+
+ align:start position:0%
+like this one generated by a spinodal
+ 
+
+ align:start position:0%
+like this one generated by a spinodal
+decomposition and you freeze then uh uh
+
+ align:start position:0%
+decomposition and you freeze then uh uh
+ 
+
+ align:start position:0%
+decomposition and you freeze then uh uh
+you because there is a path in which the
+
+ align:start position:0%
+you because there is a path in which the
+ 
+
+ align:start position:0%
+you because there is a path in which the
+say the the the dark phase becomes soft
+
+ align:start position:0%
+say the the the dark phase becomes soft
+ 
+
+ align:start position:0%
+say the the the dark phase becomes soft
+solid and the liquid in the white phase
+
+ align:start position:0%
+solid and the liquid in the white phase
+ 
+
+ align:start position:0%
+solid and the liquid in the white phase
+can drain away and then you you produced
+
+ align:start position:0%
+can drain away and then you you produced
+ 
+
+ align:start position:0%
+can drain away and then you you produced
+a a a porous material which can be used
+
+ align:start position:0%
+a a a porous material which can be used
+ 
+
+ align:start position:0%
+a a a porous material which can be used
+with a high surface um material that can
+
+ align:start position:0%
+with a high surface um material that can
+ 
+
+ align:start position:0%
+with a high surface um material that can
+be used for uh enhancing or studying uh
+
+ align:start position:0%
+be used for uh enhancing or studying uh
+ 
+
+ align:start position:0%
+be used for uh enhancing or studying uh
+biological but also for other uh
+
+ align:start position:0%
+biological but also for other uh
+ 
+
+ align:start position:0%
+biological but also for other uh
+applications in which you need you need
+
+ align:start position:0%
+applications in which you need you need
+ 
+
+ align:start position:0%
+applications in which you need you need
+a lot of surface for things to happen
+
+ align:start position:0%
+a lot of surface for things to happen
+ 
+
+ align:start position:0%
+a lot of surface for things to happen
+like uh catalysts
+
+ align:start position:0%
+like uh catalysts
+ 
+
+ align:start position:0%
+like uh catalysts
+uh okay all right so with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I think we
+
+ align:start position:0%
+uh I think we
+ 
+
+ align:start position:0%
+uh I think we
+can terminate the mixture stuff at least
+
+ align:start position:0%
+can terminate the mixture stuff at least
+ 
+
+ align:start position:0%
+can terminate the mixture stuff at least
+uh uh of that kind but uh we start with
+
+ align:start position:0%
+uh uh of that kind but uh we start with
+ 
+
+ align:start position:0%
+uh uh of that kind but uh we start with
+mixtures that are subject also to
+
+ align:start position:0%
+mixtures that are subject also to
+ 
+
+ align:start position:0%
+mixtures that are subject also to
+chemical reactions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is uh the two main um situations
+
+ align:start position:0%
+so this is uh the two main um situations
+ 
+
+ align:start position:0%
+so this is uh the two main um situations
+that we will uh
+
+ align:start position:0%
+that we will uh
+ 
+
+ align:start position:0%
+that we will uh
+approach uh at the beginning
+
+ align:start position:0%
+approach uh at the beginning
+ 
+
+ align:start position:0%
+approach uh at the beginning
+here it's two kinds of
+
+ align:start position:0%
+here it's two kinds of
+ 
+
+ align:start position:0%
+here it's two kinds of
+systems in which we have chemical
+
+ align:start position:0%
+systems in which we have chemical
+ 
+
+ align:start position:0%
+systems in which we have chemical
+reactions one is a closed system and the
+
+ align:start position:0%
+reactions one is a closed system and the
+ 
+
+ align:start position:0%
+reactions one is a closed system and the
+other is a open system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a model for a batch process
+
+ align:start position:0%
+so this is a model for a batch process
+ 
+
+ align:start position:0%
+so this is a model for a batch process
+and this is a model for a uh steady
+
+ align:start position:0%
+and this is a model for a uh steady
+ 
+
+ align:start position:0%
+and this is a model for a uh steady
+state flow
+
+ align:start position:0%
+state flow
+ 
+
+ align:start position:0%
+state flow
+process or flow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reactor in the close syst situation you
+
+ align:start position:0%
+reactor in the close syst situation you
+ 
+
+ align:start position:0%
+reactor in the close syst situation you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+Box uh the the application that I uh I
+
+ align:start position:0%
+Box uh the the application that I uh I
+ 
+
+ align:start position:0%
+Box uh the the application that I uh I
+like to have in mind uh is the internal
+
+ align:start position:0%
+like to have in mind uh is the internal
+ 
+
+ align:start position:0%
+like to have in mind uh is the internal
+combustion engine so you imagine that
+
+ align:start position:0%
+combustion engine so you imagine that
+ 
+
+ align:start position:0%
+combustion engine so you imagine that
+this wall is the is the Piston of your
+
+ align:start position:0%
+this wall is the is the Piston of your
+ 
+
+ align:start position:0%
+this wall is the is the Piston of your
+uh uh the cylinder of your um internal
+
+ align:start position:0%
+uh uh the cylinder of your um internal
+ 
+
+ align:start position:0%
+uh uh the cylinder of your um internal
+combustion engine and uh so this wall
+
+ align:start position:0%
+combustion engine and uh so this wall
+ 
+
+ align:start position:0%
+combustion engine and uh so this wall
+goes up and down and uh at the top dead
+
+ align:start position:0%
+goes up and down and uh at the top dead
+ 
+
+ align:start position:0%
+goes up and down and uh at the top dead
+center it will be at a certain volume
+
+ align:start position:0%
+center it will be at a certain volume
+ 
+
+ align:start position:0%
+center it will be at a certain volume
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+suppose the Piston stops there for a
+
+ align:start position:0%
+suppose the Piston stops there for a
+ 
+
+ align:start position:0%
+suppose the Piston stops there for a
+while okay so uh at that moment uh you
+
+ align:start position:0%
+while okay so uh at that moment uh you
+ 
+
+ align:start position:0%
+while okay so uh at that moment uh you
+have a mixture inside your um combuster
+
+ align:start position:0%
+have a mixture inside your um combuster
+ 
+
+ align:start position:0%
+have a mixture inside your um combuster
+chamber which is a mixture of air and
+
+ align:start position:0%
+chamber which is a mixture of air and
+ 
+
+ align:start position:0%
+chamber which is a mixture of air and
+your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fuel and some water vapor sometimes
+
+ align:start position:0%
+fuel and some water vapor sometimes
+ 
+
+ align:start position:0%
+fuel and some water vapor sometimes
+because air air is humid so there is
+
+ align:start position:0%
+because air air is humid so there is
+ 
+
+ align:start position:0%
+because air air is humid so there is
+water vapor content also at the
+
+ align:start position:0%
+water vapor content also at the
+ 
+
+ align:start position:0%
+water vapor content also at the
+beginning of the combustion
+
+ align:start position:0%
+beginning of the combustion
+ 
+
+ align:start position:0%
+beginning of the combustion
+process um it has some temperature some
+
+ align:start position:0%
+process um it has some temperature some
+ 
+
+ align:start position:0%
+process um it has some temperature some
+pressure because the Piston has
+
+ align:start position:0%
+pressure because the Piston has
+ 
+
+ align:start position:0%
+pressure because the Piston has
+compressed that mixture of course since
+
+ align:start position:0%
+compressed that mixture of course since
+ 
+
+ align:start position:0%
+compressed that mixture of course since
+we are in a stable equilibrium state it
+
+ align:start position:0%
+we are in a stable equilibrium state it
+ 
+
+ align:start position:0%
+we are in a stable equilibrium state it
+also has chemical
+
+ align:start position:0%
+also has chemical
+ 
+
+ align:start position:0%
+also has chemical
+potentials and if we want to compute the
+
+ align:start position:0%
+potentials and if we want to compute the
+ 
+
+ align:start position:0%
+potentials and if we want to compute the
+energy and the entropy because they will
+
+ align:start position:0%
+energy and the entropy because they will
+ 
+
+ align:start position:0%
+energy and the entropy because they will
+enter in the
+
+ align:start position:0%
+enter in the
+ 
+
+ align:start position:0%
+enter in the
+uh energy and entropy
+
+ align:start position:0%
+uh energy and entropy
+ 
+
+ align:start position:0%
+uh energy and entropy
+balances we know how to do it because we
+
+ align:start position:0%
+balances we know how to do it because we
+ 
+
+ align:start position:0%
+balances we know how to do it because we
+we've deal we've dealt with mixtures for
+
+ align:start position:0%
+we've deal we've dealt with mixtures for
+ 
+
+ align:start position:0%
+we've deal we've dealt with mixtures for
+a long time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now so the energy in general is simply
+
+ align:start position:0%
+now so the energy in general is simply
+ 
+
+ align:start position:0%
+now so the energy in general is simply
+given well simply is given
+
+ align:start position:0%
+given well simply is given
+ 
+
+ align:start position:0%
+given well simply is given
+by uh the weighted sum weighted on the
+
+ align:start position:0%
+by uh the weighted sum weighted on the
+ 
+
+ align:start position:0%
+by uh the weighted sum weighted on the
+amount
+
+ align:start position:0%
+amount
+ 
+
+ align:start position:0%
+amount
+s of the partial
+
+ align:start position:0%
+s of the partial
+ 
+
+ align:start position:0%
+s of the partial
+properties and the partial properties
+
+ align:start position:0%
+properties and the partial properties
+ 
+
+ align:start position:0%
+properties and the partial properties
+depend on composition and we here we can
+
+ align:start position:0%
+depend on composition and we here we can
+ 
+
+ align:start position:0%
+depend on composition and we here we can
+apply all our theories about ideal
+
+ align:start position:0%
+apply all our theories about ideal
+ 
+
+ align:start position:0%
+apply all our theories about ideal
+mixtures or other models and so
+
+ align:start position:0%
+mixtures or other models and so
+ 
+
+ align:start position:0%
+mixtures or other models and so
+on and the same holds also for the other
+
+ align:start position:0%
+on and the same holds also for the other
+ 
+
+ align:start position:0%
+on and the same holds also for the other
+properties like entropy which is the
+
+ align:start position:0%
+properties like entropy which is the
+ 
+
+ align:start position:0%
+properties like entropy which is the
+other one that is needed for the entropy
+
+ align:start position:0%
+other one that is needed for the entropy
+ 
+
+ align:start position:0%
+other one that is needed for the entropy
+bance Okay now what's new here is that
+
+ align:start position:0%
+bance Okay now what's new here is that
+ 
+
+ align:start position:0%
+bance Okay now what's new here is that
+uh next
+
+ align:start position:0%
+uh next
+ 
+
+ align:start position:0%
+uh next
+you sort of turn on chemical
+
+ align:start position:0%
+you sort of turn on chemical
+ 
+
+ align:start position:0%
+you sort of turn on chemical
+reactions so the composition is allowed
+
+ align:start position:0%
+reactions so the composition is allowed
+ 
+
+ align:start position:0%
+reactions so the composition is allowed
+to change according to one or more uh
+
+ align:start position:0%
+to change according to one or more uh
+ 
+
+ align:start position:0%
+to change according to one or more uh
+chemical reaction
+
+ align:start position:0%
+chemical reaction
+ 
+
+ align:start position:0%
+chemical reaction
+mechanisms we will describe them um I'll
+
+ align:start position:0%
+mechanisms we will describe them um I'll
+ 
+
+ align:start position:0%
+mechanisms we will describe them um I'll
+go into detail of the of this
+
+ align:start position:0%
+go into detail of the of this
+ 
+
+ align:start position:0%
+go into detail of the of this
+description in the next slide but we
+
+ align:start position:0%
+description in the next slide but we
+ 
+
+ align:start position:0%
+description in the next slide but we
+will describe it by this General
+
+ align:start position:0%
+will describe it by this General
+ 
+
+ align:start position:0%
+will describe it by this General
+notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what will happen is that um the
+
+ align:start position:0%
+and what will happen is that um the
+ 
+
+ align:start position:0%
+and what will happen is that um the
+process the the the fact that you turn
+
+ align:start position:0%
+process the the the fact that you turn
+ 
+
+ align:start position:0%
+process the the the fact that you turn
+on the possibility of the chemical
+
+ align:start position:0%
+on the possibility of the chemical
+ 
+
+ align:start position:0%
+on the possibility of the chemical
+reaction makes the the the the state
+
+ align:start position:0%
+reaction makes the the the the state
+ 
+
+ align:start position:0%
+reaction makes the the the the state
+evolve towards uh
+
+ align:start position:0%
+evolve towards uh
+ 
+
+ align:start position:0%
+evolve towards uh
+equilibrium and the composition will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change so in the end you will have a
+
+ align:start position:0%
+change so in the end you will have a
+ 
+
+ align:start position:0%
+change so in the end you will have a
+composition that is different from the
+
+ align:start position:0%
+composition that is different from the
+ 
+
+ align:start position:0%
+composition that is different from the
+beginning so here you have the reactants
+
+ align:start position:0%
+beginning so here you have the reactants
+ 
+
+ align:start position:0%
+beginning so here you have the reactants
+so R stands for reactants here not for
+
+ align:start position:0%
+so R stands for reactants here not for
+ 
+
+ align:start position:0%
+so R stands for reactants here not for
+Reservoir and uh P stands for products
+
+ align:start position:0%
+Reservoir and uh P stands for products
+ 
+
+ align:start position:0%
+Reservoir and uh P stands for products
+see these are the products of combustion
+
+ align:start position:0%
+see these are the products of combustion
+ 
+
+ align:start position:0%
+see these are the products of combustion
+for example in which case you have a uh
+
+ align:start position:0%
+for example in which case you have a uh
+ 
+
+ align:start position:0%
+for example in which case you have a uh
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+air which you've consumed some of the
+
+ align:start position:0%
+air which you've consumed some of the
+ 
+
+ align:start position:0%
+air which you've consumed some of the
+oxygen
+
+ align:start position:0%
+oxygen
+ 
+
+ align:start position:0%
+oxygen
+um and then you have a carbon dioxide
+
+ align:start position:0%
+um and then you have a carbon dioxide
+ 
+
+ align:start position:0%
+um and then you have a carbon dioxide
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+vapor and maybe some and nitrogen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oxide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay they will be because the reaction
+
+ align:start position:0%
+okay they will be because the reaction
+ 
+
+ align:start position:0%
+okay they will be because the reaction
+occurs
+
+ align:start position:0%
+occurs
+ 
+
+ align:start position:0%
+occurs
+irreversibly uh spontaneously there will
+
+ align:start position:0%
+irreversibly uh spontaneously there will
+ 
+
+ align:start position:0%
+irreversibly uh spontaneously there will
+be some entropy produced by
+
+ align:start position:0%
+be some entropy produced by
+ 
+
+ align:start position:0%
+be some entropy produced by
+reversibility you can compute once you
+
+ align:start position:0%
+reversibility you can compute once you
+ 
+
+ align:start position:0%
+reversibility you can compute once you
+have or at at least in terms of the
+
+ align:start position:0%
+have or at at least in terms of the
+ 
+
+ align:start position:0%
+have or at at least in terms of the
+final composition and the final
+
+ align:start position:0%
+final composition and the final
+ 
+
+ align:start position:0%
+final composition and the final
+temperature and
+
+ align:start position:0%
+temperature and
+ 
+
+ align:start position:0%
+temperature and
+pressure um you can compute the energy
+
+ align:start position:0%
+pressure um you can compute the energy
+ 
+
+ align:start position:0%
+pressure um you can compute the energy
+and the entropy the same way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only of course relative to the new
+
+ align:start position:0%
+only of course relative to the new
+ 
+
+ align:start position:0%
+only of course relative to the new
+composition maybe the F not all the
+
+ align:start position:0%
+composition maybe the F not all the
+ 
+
+ align:start position:0%
+composition maybe the F not all the
+final things are
+
+ align:start position:0%
+final things are
+ 
+
+ align:start position:0%
+final things are
+known uh if you can uh use up only the
+
+ align:start position:0%
+known uh if you can uh use up only the
+ 
+
+ align:start position:0%
+known uh if you can uh use up only the
+energy and the entropy balance and
+
+ align:start position:0%
+energy and the entropy balance and
+ 
+
+ align:start position:0%
+energy and the entropy balance and
+perhaps also the volume balance if if
+
+ align:start position:0%
+perhaps also the volume balance if if
+ 
+
+ align:start position:0%
+perhaps also the volume balance if if
+you assume that this volume remains
+
+ align:start position:0%
+you assume that this volume remains
+ 
+
+ align:start position:0%
+you assume that this volume remains
+constant or relatively constant because
+
+ align:start position:0%
+constant or relatively constant because
+ 
+
+ align:start position:0%
+constant or relatively constant because
+that reaction at the top dead center uh
+
+ align:start position:0%
+that reaction at the top dead center uh
+ 
+
+ align:start position:0%
+that reaction at the top dead center uh
+occurs very quick quickly and so the
+
+ align:start position:0%
+occurs very quick quickly and so the
+ 
+
+ align:start position:0%
+occurs very quick quickly and so the
+Piston doesn't move a lot uh then you
+
+ align:start position:0%
+Piston doesn't move a lot uh then you
+ 
+
+ align:start position:0%
+Piston doesn't move a lot uh then you
+have three equations energy entropy and
+
+ align:start position:0%
+have three equations energy entropy and
+ 
+
+ align:start position:0%
+have three equations energy entropy and
+volume balance with which you can solve
+
+ align:start position:0%
+volume balance with which you can solve
+ 
+
+ align:start position:0%
+volume balance with which you can solve
+for three
+
+ align:start position:0%
+for three
+ 
+
+ align:start position:0%
+for three
+unknowns so the various possible
+
+ align:start position:0%
+unknowns so the various possible
+ 
+
+ align:start position:0%
+unknowns so the various possible
+problems that can be solved are
+
+ align:start position:0%
+problems that can be solved are
+ 
+
+ align:start position:0%
+problems that can be solved are
+variations of this this
+
+ align:start position:0%
+variations of this this
+ 
+
+ align:start position:0%
+variations of this this
+thing and of
+
+ align:start position:0%
+thing and of
+ 
+
+ align:start position:0%
+thing and of
+course even though that is uh happens
+
+ align:start position:0%
+course even though that is uh happens
+ 
+
+ align:start position:0%
+course even though that is uh happens
+quickly maybe there is some U exchange
+
+ align:start position:0%
+quickly maybe there is some U exchange
+ 
+
+ align:start position:0%
+quickly maybe there is some U exchange
+of uh heat
+
+ align:start position:0%
+of uh heat
+ 
+
+ align:start position:0%
+of uh heat
+between your
+
+ align:start position:0%
+between your
+ 
+
+ align:start position:0%
+between your
+mixture uh and the walls of the
+
+ align:start position:0%
+mixture uh and the walls of the
+ 
+
+ align:start position:0%
+mixture uh and the walls of the
+container like the cylinder because the
+
+ align:start position:0%
+container like the cylinder because the
+ 
+
+ align:start position:0%
+container like the cylinder because the
+internal combustion engines are cooled
+
+ align:start position:0%
+internal combustion engines are cooled
+ 
+
+ align:start position:0%
+internal combustion engines are cooled
+water cooled or air cooled and so uh
+
+ align:start position:0%
+water cooled or air cooled and so uh
+ 
+
+ align:start position:0%
+water cooled or air cooled and so uh
+some of the energy can be exchanged with
+
+ align:start position:0%
+some of the energy can be exchanged with
+ 
+
+ align:start position:0%
+some of the energy can be exchanged with
+heat to the wall
+
+ align:start position:0%
+heat to the wall
+ 
+
+ align:start position:0%
+heat to the wall
+temperature and also the if the Piston
+
+ align:start position:0%
+temperature and also the if the Piston
+ 
+
+ align:start position:0%
+temperature and also the if the Piston
+is moving while this is happening there
+
+ align:start position:0%
+is moving while this is happening there
+ 
+
+ align:start position:0%
+is moving while this is happening there
+may also be some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work due to the pressure times the
+
+ align:start position:0%
+work due to the pressure times the
+ 
+
+ align:start position:0%
+work due to the pressure times the
+volume uh
+
+ align:start position:0%
+volume uh
+ 
+
+ align:start position:0%
+volume uh
+change okay so that's the setup of the
+
+ align:start position:0%
+change okay so that's the setup of the
+ 
+
+ align:start position:0%
+change okay so that's the setup of the
+close system so internal combustion
+
+ align:start position:0%
+close system so internal combustion
+ 
+
+ align:start position:0%
+close system so internal combustion
+engine here instead is
+
+ align:start position:0%
+engine here instead is
+ 
+
+ align:start position:0%
+engine here instead is
+a steady state burner or reactor again
+
+ align:start position:0%
+a steady state burner or reactor again
+ 
+
+ align:start position:0%
+a steady state burner or reactor again
+if I have in mind a combustion of the
+
+ align:start position:0%
+if I have in mind a combustion of the
+ 
+
+ align:start position:0%
+if I have in mind a combustion of the
+hydrocarbons this is a State burner
+
+ align:start position:0%
+hydrocarbons this is a State burner
+ 
+
+ align:start position:0%
+hydrocarbons this is a State burner
+which is typically uh inside a power uh
+
+ align:start position:0%
+which is typically uh inside a power uh
+ 
+
+ align:start position:0%
+which is typically uh inside a power uh
+combustion fossil fuel power
+
+ align:start position:0%
+combustion fossil fuel power
+ 
+
+ align:start position:0%
+combustion fossil fuel power
+plant here the idea is that you have a
+
+ align:start position:0%
+plant here the idea is that you have a
+ 
+
+ align:start position:0%
+plant here the idea is that you have a
+flow bulk flow one if it's all the
+
+ align:start position:0%
+flow bulk flow one if it's all the
+ 
+
+ align:start position:0%
+flow bulk flow one if it's all the
+substances are premixed or maybe you
+
+ align:start position:0%
+substances are premixed or maybe you
+ 
+
+ align:start position:0%
+substances are premixed or maybe you
+have several if you have some of the um
+
+ align:start position:0%
+have several if you have some of the um
+ 
+
+ align:start position:0%
+have several if you have some of the um
+substances that are inject for example
+
+ align:start position:0%
+substances that are inject for example
+ 
+
+ align:start position:0%
+substances that are inject for example
+air in you have a injection of air
+
+ align:start position:0%
+air in you have a injection of air
+ 
+
+ align:start position:0%
+air in you have a injection of air
+through one stream Al so one blf flow
+
+ align:start position:0%
+through one stream Al so one blf flow
+ 
+
+ align:start position:0%
+through one stream Al so one blf flow
+interaction and then uh your fuel
+
+ align:start position:0%
+interaction and then uh your fuel
+ 
+
+ align:start position:0%
+interaction and then uh your fuel
+injected in from another pipe that goes
+
+ align:start position:0%
+injected in from another pipe that goes
+ 
+
+ align:start position:0%
+injected in from another pipe that goes
+in so I indicate here a simple single
+
+ align:start position:0%
+in so I indicate here a simple single
+ 
+
+ align:start position:0%
+in so I indicate here a simple single
+Arrow but uh and but of course you you
+
+ align:start position:0%
+Arrow but uh and but of course you you
+ 
+
+ align:start position:0%
+Arrow but uh and but of course you you
+may have many the properties of for bulk
+
+ align:start position:0%
+may have many the properties of for bulk
+ 
+
+ align:start position:0%
+may have many the properties of for bulk
+flow
+
+ align:start position:0%
+flow
+ 
+
+ align:start position:0%
+flow
+interactions what what enters in the
+
+ align:start position:0%
+interactions what what enters in the
+ 
+
+ align:start position:0%
+interactions what what enters in the
+energy balance as you remember is the
+
+ align:start position:0%
+energy balance as you remember is the
+ 
+
+ align:start position:0%
+energy balance as you remember is the
+enthalpy
+
+ align:start position:0%
+enthalpy
+ 
+
+ align:start position:0%
+enthalpy
+and so we need the enthalpy the rate of
+
+ align:start position:0%
+and so we need the enthalpy the rate of
+ 
+
+ align:start position:0%
+and so we need the enthalpy the rate of
+enthalpy uh brought in uh by this uh
+
+ align:start position:0%
+enthalpy uh brought in uh by this uh
+ 
+
+ align:start position:0%
+enthalpy uh brought in uh by this uh
+Inlet uh bulk flow interaction which has
+
+ align:start position:0%
+Inlet uh bulk flow interaction which has
+ 
+
+ align:start position:0%
+Inlet uh bulk flow interaction which has
+to do with the partial
+
+ align:start position:0%
+to do with the partial
+ 
+
+ align:start position:0%
+to do with the partial
+enthalpies of the components in the
+
+ align:start position:0%
+enthalpies of the components in the
+ 
+
+ align:start position:0%
+enthalpies of the components in the
+mixtures for those that are mixed and
+
+ align:start position:0%
+mixtures for those that are mixed and
+ 
+
+ align:start position:0%
+mixtures for those that are mixed and
+that would be the specific if they are
+
+ align:start position:0%
+that would be the specific if they are
+ 
+
+ align:start position:0%
+that would be the specific if they are
+injected as pure components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the same for the
+
+ align:start position:0%
+and the same for the
+ 
+
+ align:start position:0%
+and the same for the
+outlet so the outlet here would be the
+
+ align:start position:0%
+outlet so the outlet here would be the
+ 
+
+ align:start position:0%
+outlet so the outlet here would be the
+hot product for example the hot products
+
+ align:start position:0%
+hot product for example the hot products
+ 
+
+ align:start position:0%
+hot product for example the hot products
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+combustion uh but in other
+
+ align:start position:0%
+combustion uh but in other
+ 
+
+ align:start position:0%
+combustion uh but in other
+configurations they could
+
+ align:start position:0%
+configurations they could
+ 
+
+ align:start position:0%
+configurations they could
+be uh if this reactor contains not only
+
+ align:start position:0%
+be uh if this reactor contains not only
+ 
+
+ align:start position:0%
+be uh if this reactor contains not only
+um just is not a diabatic but it
+
+ align:start position:0%
+um just is not a diabatic but it
+ 
+
+ align:start position:0%
+um just is not a diabatic but it
+contains also the machinery and the
+
+ align:start position:0%
+contains also the machinery and the
+ 
+
+ align:start position:0%
+contains also the machinery and the
+thermal cycle that extracts the energy
+
+ align:start position:0%
+thermal cycle that extracts the energy
+ 
+
+ align:start position:0%
+thermal cycle that extracts the energy
+and so on these would be just the
+
+ align:start position:0%
+and so on these would be just the
+ 
+
+ align:start position:0%
+and so on these would be just the
+products that gets that get exhausted at
+
+ align:start position:0%
+products that gets that get exhausted at
+ 
+
+ align:start position:0%
+products that gets that get exhausted at
+the chiminy or the stack of your power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plant all
+
+ align:start position:0%
+plant all
+ 
+
+ align:start position:0%
+plant all
+right and so then u in that case we may
+
+ align:start position:0%
+right and so then u in that case we may
+ 
+
+ align:start position:0%
+right and so then u in that case we may
+have heat interactions and work
+
+ align:start position:0%
+have heat interactions and work
+ 
+
+ align:start position:0%
+have heat interactions and work
+interactions while while this uh complex
+
+ align:start position:0%
+interactions while while this uh complex
+ 
+
+ align:start position:0%
+interactions while while this uh complex
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+power plant is evolving there is of
+
+ align:start position:0%
+power plant is evolving there is of
+ 
+
+ align:start position:0%
+power plant is evolving there is of
+course entropy produced by
+
+ align:start position:0%
+course entropy produced by
+ 
+
+ align:start position:0%
+course entropy produced by
+irreversibility and again the new aspect
+
+ align:start position:0%
+irreversibility and again the new aspect
+ 
+
+ align:start position:0%
+irreversibility and again the new aspect
+of that we need to deal with is the fact
+
+ align:start position:0%
+of that we need to deal with is the fact
+ 
+
+ align:start position:0%
+of that we need to deal with is the fact
+that inside here chemical reaction or
+
+ align:start position:0%
+that inside here chemical reaction or
+ 
+
+ align:start position:0%
+that inside here chemical reaction or
+chemical reactions can occur changing
+
+ align:start position:0%
+chemical reactions can occur changing
+ 
+
+ align:start position:0%
+chemical reactions can occur changing
+the composition from the inlet to the
+
+ align:start position:0%
+the composition from the inlet to the
+ 
+
+ align:start position:0%
+the composition from the inlet to the
+outlet the energy balance equation for a
+
+ align:start position:0%
+outlet the energy balance equation for a
+ 
+
+ align:start position:0%
+outlet the energy balance equation for a
+steady state says that the rate of
+
+ align:start position:0%
+steady state says that the rate of
+ 
+
+ align:start position:0%
+steady state says that the rate of
+change of the energy is zero because
+
+ align:start position:0%
+change of the energy is zero because
+ 
+
+ align:start position:0%
+change of the energy is zero because
+it's steady
+
+ align:start position:0%
+it's steady
+ 
+
+ align:start position:0%
+it's steady
+state and therefore uh that must be so
+
+ align:start position:0%
+state and therefore uh that must be so
+ 
+
+ align:start position:0%
+state and therefore uh that must be so
+the the rate at which the energies are
+
+ align:start position:0%
+the the rate at which the energies are
+ 
+
+ align:start position:0%
+the the rate at which the energies are
+exchanged in and out must balance to
+
+ align:start position:0%
+exchanged in and out must balance to
+ 
+
+ align:start position:0%
+exchanged in and out must balance to
+zero so the
+
+ align:start position:0%
+zero so the
+ 
+
+ align:start position:0%
+zero so the
+enthalpy uh of the
+
+ align:start position:0%
+enthalpy uh of the
+ 
+
+ align:start position:0%
+enthalpy uh of the
+inflow is a positive inaly of the
+
+ align:start position:0%
+inflow is a positive inaly of the
+ 
+
+ align:start position:0%
+inflow is a positive inaly of the
+outflower and the uh heat uh flow
+
+ align:start position:0%
+outflower and the uh heat uh flow
+ 
+
+ align:start position:0%
+outflower and the uh heat uh flow
+positive if if if it has the arrow
+
+ align:start position:0%
+positive if if if it has the arrow
+ 
+
+ align:start position:0%
+positive if if if it has the arrow
+inside it means positive if
+
+ align:start position:0%
+inside it means positive if
+ 
+
+ align:start position:0%
+inside it means positive if
+received minus the work which is as the
+
+ align:start position:0%
+received minus the work which is as the
+ 
+
+ align:start position:0%
+received minus the work which is as the
+arrow outward and so it's positive if it
+
+ align:start position:0%
+arrow outward and so it's positive if it
+ 
+
+ align:start position:0%
+arrow outward and so it's positive if it
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+produced and similarly for the uh
+
+ align:start position:0%
+produced and similarly for the uh
+ 
+
+ align:start position:0%
+produced and similarly for the uh
+entropy
+
+ align:start position:0%
+entropy
+ 
+
+ align:start position:0%
+entropy
+balance the entropy the rate of change
+
+ align:start position:0%
+balance the entropy the rate of change
+ 
+
+ align:start position:0%
+balance the entropy the rate of change
+of the entropy of the reactor because we
+
+ align:start position:0%
+of the entropy of the reactor because we
+ 
+
+ align:start position:0%
+of the entropy of the reactor because we
+are making a balance equation for this
+
+ align:start position:0%
+are making a balance equation for this
+ 
+
+ align:start position:0%
+are making a balance equation for this
+reactor here
+
+ align:start position:0%
+reactor here
+ 
+
+ align:start position:0%
+reactor here
+uh if it is steady state the properties
+
+ align:start position:0%
+uh if it is steady state the properties
+ 
+
+ align:start position:0%
+uh if it is steady state the properties
+don't change so the rate of entropy
+
+ align:start position:0%
+don't change so the rate of entropy
+ 
+
+ align:start position:0%
+don't change so the rate of entropy
+change is
+
+ align:start position:0%
+change is
+ 
+
+ align:start position:0%
+change is
+zero and uh so then you have a balance
+
+ align:start position:0%
+zero and uh so then you have a balance
+ 
+
+ align:start position:0%
+zero and uh so then you have a balance
+between the net amount of entropy that
+
+ align:start position:0%
+between the net amount of entropy that
+ 
+
+ align:start position:0%
+between the net amount of entropy that
+uh comes
+
+ align:start position:0%
+uh comes
+ 
+
+ align:start position:0%
+uh comes
+uh in and out and the entropy that is
+
+ align:start position:0%
+uh in and out and the entropy that is
+ 
+
+ align:start position:0%
+uh in and out and the entropy that is
+produced by
+
+ align:start position:0%
+produced by
+ 
+
+ align:start position:0%
+produced by
+reversibility okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now if you look at these ones if you
+
+ align:start position:0%
+now if you look at these ones if you
+ 
+
+ align:start position:0%
+now if you look at these ones if you
+look at these equations uh and compare
+
+ align:start position:0%
+look at these equations uh and compare
+ 
+
+ align:start position:0%
+look at these equations uh and compare
+them you are often tempted
+
+ align:start position:0%
+them you are often tempted
+ 
+
+ align:start position:0%
+them you are often tempted
+to for example rewrite these ones with
+
+ align:start position:0%
+to for example rewrite these ones with
+ 
+
+ align:start position:0%
+to for example rewrite these ones with
+HP and minus HR on the left hand
+
+ align:start position:0%
+HP and minus HR on the left hand
+ 
+
+ align:start position:0%
+HP and minus HR on the left hand
+side which is
+
+ align:start position:0%
+side which is
+ 
+
+ align:start position:0%
+side which is
+okay just a legitimate mathematical
+
+ align:start position:0%
+okay just a legitimate mathematical
+ 
+
+ align:start position:0%
+okay just a legitimate mathematical
+step however
+
+ align:start position:0%
+step however
+ 
+
+ align:start position:0%
+step however
+you should be shouldn't be confused
+
+ align:start position:0%
+you should be shouldn't be confused
+ 
+
+ align:start position:0%
+you should be shouldn't be confused
+because otherwise say well why do I use
+
+ align:start position:0%
+because otherwise say well why do I use
+ 
+
+ align:start position:0%
+because otherwise say well why do I use
+enthalpy here why do I use energy there
+
+ align:start position:0%
+enthalpy here why do I use energy there
+ 
+
+ align:start position:0%
+enthalpy here why do I use energy there
+okay you're not using enthalpy here the
+
+ align:start position:0%
+okay you're not using enthalpy here the
+ 
+
+ align:start position:0%
+okay you're not using enthalpy here the
+same way it doesn't play the role of the
+
+ align:start position:0%
+same way it doesn't play the role of the
+ 
+
+ align:start position:0%
+same way it doesn't play the role of the
+energy the rate of energy change is this
+
+ align:start position:0%
+energy the rate of energy change is this
+ 
+
+ align:start position:0%
+energy the rate of energy change is this
+zero here that zero is important so if
+
+ align:start position:0%
+zero here that zero is important so if
+ 
+
+ align:start position:0%
+zero here that zero is important so if
+you if you do that mathematical step you
+
+ align:start position:0%
+you if you do that mathematical step you
+ 
+
+ align:start position:0%
+you if you do that mathematical step you
+sort of kill a zero that is important
+
+ align:start position:0%
+sort of kill a zero that is important
+ 
+
+ align:start position:0%
+sort of kill a zero that is important
+and giv you remind reminder that you're
+
+ align:start position:0%
+and giv you remind reminder that you're
+ 
+
+ align:start position:0%
+and giv you remind reminder that you're
+talking about steady state uh
+
+ align:start position:0%
+talking about steady state uh
+ 
+
+ align:start position:0%
+talking about steady state uh
+process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay how about
+
+ align:start position:0%
+okay how about
+ 
+
+ align:start position:0%
+okay how about
+notation so let's take an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example of the reaction in which you you
+
+ align:start position:0%
+example of the reaction in which you you
+ 
+
+ align:start position:0%
+example of the reaction in which you you
+have two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hydrogen
+
+ align:start position:0%
+hydrogen
+ 
+
+ align:start position:0%
+hydrogen
+molecules this and that and an oxygen
+
+ align:start position:0%
+molecules this and that and an oxygen
+ 
+
+ align:start position:0%
+molecules this and that and an oxygen
+molecule and they get uh
+
+ align:start position:0%
+molecule and they get uh
+ 
+
+ align:start position:0%
+molecule and they get uh
+reassembled by this mechanism into two
+
+ align:start position:0%
+reassembled by this mechanism into two
+ 
+
+ align:start position:0%
+reassembled by this mechanism into two
+molecules of
+
+ align:start position:0%
+molecules of
+ 
+
+ align:start position:0%
+molecules of
+water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so I use the equal sign
+
+ align:start position:0%
+so I use the equal sign
+ 
+
+ align:start position:0%
+so I use the equal sign
+here to say that this refers simply to
+
+ align:start position:0%
+here to say that this refers simply to
+ 
+
+ align:start position:0%
+here to say that this refers simply to
+the mechanism it doesn't say which
+
+ align:start position:0%
+the mechanism it doesn't say which
+ 
+
+ align:start position:0%
+the mechanism it doesn't say which
+direction uh it will
+
+ align:start position:0%
+direction uh it will
+ 
+
+ align:start position:0%
+direction uh it will
+go it simply defines the
+
+ align:start position:0%
+go it simply defines the
+ 
+
+ align:start position:0%
+go it simply defines the
+mechanism and therefore you can go in
+
+ align:start position:0%
+mechanism and therefore you can go in
+ 
+
+ align:start position:0%
+mechanism and therefore you can go in
+One Direction but also the
+
+ align:start position:0%
+One Direction but also the
+ 
+
+ align:start position:0%
+One Direction but also the
+opposite
+
+ align:start position:0%
+opposite
+ 
+
+ align:start position:0%
+opposite
+okay and there is therefore some
+
+ align:start position:0%
+okay and there is therefore some
+ 
+
+ align:start position:0%
+okay and there is therefore some
+arbitrary uh choice you could put on the
+
+ align:start position:0%
+arbitrary uh choice you could put on the
+ 
+
+ align:start position:0%
+arbitrary uh choice you could put on the
+left hand side hydrogen and oxygen or
+
+ align:start position:0%
+left hand side hydrogen and oxygen or
+ 
+
+ align:start position:0%
+left hand side hydrogen and oxygen or
+you could put on the left hand side the
+
+ align:start position:0%
+you could put on the left hand side the
+ 
+
+ align:start position:0%
+you could put on the left hand side the
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+the symbol for water it's either one is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you can also once you have written
+
+ align:start position:0%
+okay you can also once you have written
+ 
+
+ align:start position:0%
+okay you can also once you have written
+that written it this way you can also
+
+ align:start position:0%
+that written it this way you can also
+ 
+
+ align:start position:0%
+that written it this way you can also
+put them all on the left hand
+
+ align:start position:0%
+put them all on the left hand
+ 
+
+ align:start position:0%
+put them all on the left hand
+side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and with the stochiometric coefficients
+
+ align:start position:0%
+and with the stochiometric coefficients
+ 
+
+ align:start position:0%
+and with the stochiometric coefficients
+positive for what you will consider the
+
+ align:start position:0%
+positive for what you will consider the
+ 
+
+ align:start position:0%
+positive for what you will consider the
+products of the reaction and negative
+
+ align:start position:0%
+products of the reaction and negative
+ 
+
+ align:start position:0%
+products of the reaction and negative
+for those for those that you will
+
+ align:start position:0%
+for those for those that you will
+ 
+
+ align:start position:0%
+for those for those that you will
+consider consider the
+
+ align:start position:0%
+consider consider the
+ 
+
+ align:start position:0%
+consider consider the
+uh the the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reactant okay now the meaning of the
+
+ align:start position:0%
+reactant okay now the meaning of the
+ 
+
+ align:start position:0%
+reactant okay now the meaning of the
+stochiometric
+
+ align:start position:0%
+stochiometric
+ 
+
+ align:start position:0%
+stochiometric
+coefficients are that they
+
+ align:start position:0%
+coefficients are that they
+ 
+
+ align:start position:0%
+coefficients are that they
+determine the possible changes in
+
+ align:start position:0%
+determine the possible changes in
+ 
+
+ align:start position:0%
+determine the possible changes in
+composition so if I start with a
+
+ align:start position:0%
+composition so if I start with a
+ 
+
+ align:start position:0%
+composition so if I start with a
+composition which is given by these
+
+ align:start position:0%
+composition which is given by these
+ 
+
+ align:start position:0%
+composition which is given by these
+numbers any anything
+
+ align:start position:0%
+numbers any anything
+ 
+
+ align:start position:0%
+numbers any anything
+and then I want to see uh how the
+
+ align:start position:0%
+and then I want to see uh how the
+ 
+
+ align:start position:0%
+and then I want to see uh how the
+composition that composition can change
+
+ align:start position:0%
+composition that composition can change
+ 
+
+ align:start position:0%
+composition that composition can change
+according to this reaction mechanism and
+
+ align:start position:0%
+according to this reaction mechanism and
+ 
+
+ align:start position:0%
+according to this reaction mechanism and
+only this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one then you can write these changes are
+
+ align:start position:0%
+one then you can write these changes are
+ 
+
+ align:start position:0%
+one then you can write these changes are
+not uh completely uh
+
+ align:start position:0%
+not uh completely uh
+ 
+
+ align:start position:0%
+not uh completely uh
+arbitrary because you have to have the
+
+ align:start position:0%
+arbitrary because you have to have the
+ 
+
+ align:start position:0%
+arbitrary because you have to have the
+fact that the the ratio of the change of
+
+ align:start position:0%
+fact that the the ratio of the change of
+ 
+
+ align:start position:0%
+fact that the the ratio of the change of
+one component to the to the
+
+ align:start position:0%
+one component to the to the
+ 
+
+ align:start position:0%
+one component to the to the
+respective stochiometric coefficient
+
+ align:start position:0%
+respective stochiometric coefficient
+ 
+
+ align:start position:0%
+respective stochiometric coefficient
+must be equal to the same ratio for all
+
+ align:start position:0%
+must be equal to the same ratio for all
+ 
+
+ align:start position:0%
+must be equal to the same ratio for all
+the other components so this ratio we're
+
+ align:start position:0%
+the other components so this ratio we're
+ 
+
+ align:start position:0%
+the other components so this ratio we're
+going to call the reaction coordinate or
+
+ align:start position:0%
+going to call the reaction coordinate or
+ 
+
+ align:start position:0%
+going to call the reaction coordinate or
+change in reaction coordinates that
+
+ align:start position:0%
+change in reaction coordinates that
+ 
+
+ align:start position:0%
+change in reaction coordinates that
+defines the reaction coordinates the the
+
+ align:start position:0%
+defines the reaction coordinates the the
+ 
+
+ align:start position:0%
+defines the reaction coordinates the the
+change over the stochiometric
+
+ align:start position:0%
+change over the stochiometric
+ 
+
+ align:start position:0%
+change over the stochiometric
+coefficient notice that this
+
+ align:start position:0%
+coefficient notice that this
+ 
+
+ align:start position:0%
+coefficient notice that this
+stochiometric coefficient must be
+
+ align:start position:0%
+stochiometric coefficient must be
+ 
+
+ align:start position:0%
+stochiometric coefficient must be
+taken with the sign the proper sign so
+
+ align:start position:0%
+taken with the sign the proper sign so
+ 
+
+ align:start position:0%
+taken with the sign the proper sign so
+negative for the reactant and positive
+
+ align:start position:0%
+negative for the reactant and positive
+ 
+
+ align:start position:0%
+negative for the reactant and positive
+for the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+products okay so with that in
+
+ align:start position:0%
+products okay so with that in
+ 
+
+ align:start position:0%
+products okay so with that in
+mind
+
+ align:start position:0%
+mind
+ 
+
+ align:start position:0%
+mind
+then in order to introduce a notation
+
+ align:start position:0%
+then in order to introduce a notation
+ 
+
+ align:start position:0%
+then in order to introduce a notation
+that also uh that is typically used
+
+ align:start position:0%
+that also uh that is typically used
+ 
+
+ align:start position:0%
+that also uh that is typically used
+in software that deals with
+
+ align:start position:0%
+in software that deals with
+ 
+
+ align:start position:0%
+in software that deals with
+calculations uh of chemical equilibrium
+
+ align:start position:0%
+calculations uh of chemical equilibrium
+ 
+
+ align:start position:0%
+calculations uh of chemical equilibrium
+or chemical kinetics
+
+ align:start position:0%
+or chemical kinetics
+ 
+
+ align:start position:0%
+or chemical kinetics
+uh we can
+
+ align:start position:0%
+uh we can
+ 
+
+ align:start position:0%
+uh we can
+Define a symbol a sub I a sub 1 a sub 2
+
+ align:start position:0%
+Define a symbol a sub I a sub 1 a sub 2
+ 
+
+ align:start position:0%
+Define a symbol a sub I a sub 1 a sub 2
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+sub3 uh to represent the the chemical
+
+ align:start position:0%
+sub3 uh to represent the the chemical
+ 
+
+ align:start position:0%
+sub3 uh to represent the the chemical
+symbols in the list so for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+um we make we make a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+table one two three we decided to call
+
+ align:start position:0%
+table one two three we decided to call
+ 
+
+ align:start position:0%
+table one two three we decided to call
+uh the first component to make it H2 the
+
+ align:start position:0%
+uh the first component to make it H2 the
+ 
+
+ align:start position:0%
+uh the first component to make it H2 the
+second component is oxygen and the third
+
+ align:start position:0%
+second component is oxygen and the third
+ 
+
+ align:start position:0%
+second component is oxygen and the third
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+water okay so the stochiometric
+
+ align:start position:0%
+water okay so the stochiometric
+ 
+
+ align:start position:0%
+water okay so the stochiometric
+coefficient we use the symbol nuai for
+
+ align:start position:0%
+coefficient we use the symbol nuai for
+ 
+
+ align:start position:0%
+coefficient we use the symbol nuai for
+the stochiometric
+
+ align:start position:0%
+the stochiometric
+ 
+
+ align:start position:0%
+the stochiometric
+coefficient is
+
+ align:start position:0%
+coefficient is
+ 
+
+ align:start position:0%
+coefficient is
+min-2 for hydrogen minus one for oxygen
+
+ align:start position:0%
+min-2 for hydrogen minus one for oxygen
+ 
+
+ align:start position:0%
+min-2 for hydrogen minus one for oxygen
+and two for water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you you see that this equation here
+
+ align:start position:0%
+then you you see that this equation here
+ 
+
+ align:start position:0%
+then you you see that this equation here
+that presents the chemical reaction
+
+ align:start position:0%
+that presents the chemical reaction
+ 
+
+ align:start position:0%
+that presents the chemical reaction
+mechanism translates into this summation
+
+ align:start position:0%
+mechanism translates into this summation
+ 
+
+ align:start position:0%
+mechanism translates into this summation
+which we we can write in the summation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way the advantage of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is that so I have um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this for my first reaction but suppose I
+
+ align:start position:0%
+this for my first reaction but suppose I
+ 
+
+ align:start position:0%
+this for my first reaction but suppose I
+have because in general uh life is not
+
+ align:start position:0%
+have because in general uh life is not
+ 
+
+ align:start position:0%
+have because in general uh life is not
+simple and uh very few things can be
+
+ align:start position:0%
+simple and uh very few things can be
+ 
+
+ align:start position:0%
+simple and uh very few things can be
+described with just a single chemical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reaction for example even for that uh
+
+ align:start position:0%
+reaction for example even for that uh
+ 
+
+ align:start position:0%
+reaction for example even for that uh
+formation I mean water just for the
+
+ align:start position:0%
+formation I mean water just for the
+ 
+
+ align:start position:0%
+formation I mean water just for the
+combustion of
+
+ align:start position:0%
+combustion of
+ 
+
+ align:start position:0%
+combustion of
+hydrogen uh
+
+ align:start position:0%
+hydrogen uh
+ 
+
+ align:start position:0%
+hydrogen uh
+I think that
+
+ align:start position:0%
+I think that
+ 
+
+ align:start position:0%
+I think that
+the the mechanism you have to consider
+
+ align:start position:0%
+the the mechanism you have to consider
+ 
+
+ align:start position:0%
+the the mechanism you have to consider
+at least uh forget now probably eight
+
+ align:start position:0%
+at least uh forget now probably eight
+ 
+
+ align:start position:0%
+at least uh forget now probably eight
+mechanisms and uh for the combustion of
+
+ align:start position:0%
+mechanisms and uh for the combustion of
+ 
+
+ align:start position:0%
+mechanisms and uh for the combustion of
+methane it's probably 250 or
+
+ align:start position:0%
+methane it's probably 250 or
+ 
+
+ align:start position:0%
+methane it's probably 250 or
+more that play a role uh and determine
+
+ align:start position:0%
+more that play a role uh and determine
+ 
+
+ align:start position:0%
+more that play a role uh and determine
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+kinetics different thing is for
+
+ align:start position:0%
+kinetics different thing is for
+ 
+
+ align:start position:0%
+kinetics different thing is for
+equilibrium but for the kinetics you
+
+ align:start position:0%
+equilibrium but for the kinetics you
+ 
+
+ align:start position:0%
+equilibrium but for the kinetics you
+need many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mechanisms Okay so for example suppose
+
+ align:start position:0%
+mechanisms Okay so for example suppose
+ 
+
+ align:start position:0%
+mechanisms Okay so for example suppose
+we have also
+
+ align:start position:0%
+we have also
+ 
+
+ align:start position:0%
+we have also
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+important equation
+
+ align:start position:0%
+important equation
+ 
+
+ align:start position:0%
+important equation
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+for combustion which is the dissociation
+
+ align:start position:0%
+for combustion which is the dissociation
+ 
+
+ align:start position:0%
+for combustion which is the dissociation
+of CO2 in Co and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oxygen uh if together with my uh initial
+
+ align:start position:0%
+oxygen uh if together with my uh initial
+ 
+
+ align:start position:0%
+oxygen uh if together with my uh initial
+reaction which is 2
+
+ align:start position:0%
+reaction which is 2
+ 
+
+ align:start position:0%
+reaction which is 2
+h2+ O2 =
+
+ align:start position:0%
+h2+ O2 =
+ 
+
+ align:start position:0%
+h2+ O2 =
+H2O which we already represented in our
+
+ align:start position:0%
+H2O which we already represented in our
+ 
+
+ align:start position:0%
+H2O which we already represented in our
+list if we also have that one we can
+
+ align:start position:0%
+list if we also have that one we can
+ 
+
+ align:start position:0%
+list if we also have that one we can
+keep going in the in
+
+ align:start position:0%
+keep going in the in
+ 
+
+ align:start position:0%
+keep going in the in
+our um list of of uh chemical species
+
+ align:start position:0%
+our um list of of uh chemical species
+ 
+
+ align:start position:0%
+our um list of of uh chemical species
+that are relevant to our
+
+ align:start position:0%
+that are relevant to our
+ 
+
+ align:start position:0%
+that are relevant to our
+problem we add CO2 and
+
+ align:start position:0%
+problem we add CO2 and
+ 
+
+ align:start position:0%
+problem we add CO2 and
+Co of course they don't play a role in
+
+ align:start position:0%
+Co of course they don't play a role in
+ 
+
+ align:start position:0%
+Co of course they don't play a role in
+the first reaction so we'll have
+
+ align:start position:0%
+the first reaction so we'll have
+ 
+
+ align:start position:0%
+the first reaction so we'll have
+psychometric coefficients for reaction
+
+ align:start position:0%
+psychometric coefficients for reaction
+ 
+
+ align:start position:0%
+psychometric coefficients for reaction
+One let's say this is reaction one so
+
+ align:start position:0%
+One let's say this is reaction one so
+ 
+
+ align:start position:0%
+One let's say this is reaction one so
+I'm putting a superscript one for the
+
+ align:start position:0%
+I'm putting a superscript one for the
+ 
+
+ align:start position:0%
+I'm putting a superscript one for the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+reaction and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I put here the chemical
+
+ align:start position:0%
+then I put here the chemical
+ 
+
+ align:start position:0%
+then I put here the chemical
+uh sociometric coefficients for the
+
+ align:start position:0%
+uh sociometric coefficients for the
+ 
+
+ align:start position:0%
+uh sociometric coefficients for the
+second reaction so for the second
+
+ align:start position:0%
+second reaction so for the second
+ 
+
+ align:start position:0%
+second reaction so for the second
+reaction I have plus one since it's a
+
+ align:start position:0%
+reaction I have plus one since it's a
+ 
+
+ align:start position:0%
+reaction I have plus one since it's a
+product for Co So Co is one
+
+ align:start position:0%
+product for Co So Co is one
+ 
+
+ align:start position:0%
+product for Co So Co is one
+oxygen 1 12
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so5 positive and CO2 it's it's on the
+
+ align:start position:0%
+so5 positive and CO2 it's it's on the
+ 
+
+ align:start position:0%
+so5 positive and CO2 it's it's on the
+left hand side so it's negative it's
+
+ align:start position:0%
+left hand side so it's negative it's
+ 
+
+ align:start position:0%
+left hand side so it's negative it's
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+one of course the
+
+ align:start position:0%
+one of course the
+ 
+
+ align:start position:0%
+one of course the
+others are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero because in reaction one there is no
+
+ align:start position:0%
+zero because in reaction one there is no
+ 
+
+ align:start position:0%
+zero because in reaction one there is no
+play by CO2 and Co and in reaction two
+
+ align:start position:0%
+play by CO2 and Co and in reaction two
+ 
+
+ align:start position:0%
+play by CO2 and Co and in reaction two
+there's no play by water and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hydrogen and so you see I have just put
+
+ align:start position:0%
+hydrogen and so you see I have just put
+ 
+
+ align:start position:0%
+hydrogen and so you see I have just put
+a j there and I have a system of as many
+
+ align:start position:0%
+a j there and I have a system of as many
+ 
+
+ align:start position:0%
+a j there and I have a system of as many
+chemical reactions as we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+want now the proportionality
+
+ align:start position:0%
+want now the proportionality
+ 
+
+ align:start position:0%
+want now the proportionality
+relations namely these relations here
+
+ align:start position:0%
+relations namely these relations here
+ 
+
+ align:start position:0%
+relations namely these relations here
+that uh represent the role of chemical
+
+ align:start position:0%
+that uh represent the role of chemical
+ 
+
+ align:start position:0%
+that uh represent the role of chemical
+um I mean sociometric coefficients in
+
+ align:start position:0%
+um I mean sociometric coefficients in
+ 
+
+ align:start position:0%
+um I mean sociometric coefficients in
+order to uh represent what compositions
+
+ align:start position:0%
+order to uh represent what compositions
+ 
+
+ align:start position:0%
+order to uh represent what compositions
+are changes in composition are possible
+
+ align:start position:0%
+are changes in composition are possible
+ 
+
+ align:start position:0%
+are changes in composition are possible
+are written this way or
+
+ align:start position:0%
+are written this way or
+ 
+
+ align:start position:0%
+are written this way or
+also in generic terms like Delta n over
+
+ align:start position:0%
+also in generic terms like Delta n over
+ 
+
+ align:start position:0%
+also in generic terms like Delta n over
+new subi equals Delta Epsilon which
+
+ align:start position:0%
+new subi equals Delta Epsilon which
+ 
+
+ align:start position:0%
+new subi equals Delta Epsilon which
+which we
+
+ align:start position:0%
+which we
+ 
+
+ align:start position:0%
+which we
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+write uh more uh explicitly for example
+
+ align:start position:0%
+write uh more uh explicitly for example
+ 
+
+ align:start position:0%
+write uh more uh explicitly for example
+if we like in the previous uh uh
+
+ align:start position:0%
+if we like in the previous uh uh
+ 
+
+ align:start position:0%
+if we like in the previous uh uh
+examples with like in the batch process
+
+ align:start position:0%
+examples with like in the batch process
+ 
+
+ align:start position:0%
+examples with like in the batch process
+the composition goes to uh from the that
+
+ align:start position:0%
+the composition goes to uh from the that
+ 
+
+ align:start position:0%
+the composition goes to uh from the that
+of the reactants to that of uh the uh
+
+ align:start position:0%
+of the reactants to that of uh the uh
+ 
+
+ align:start position:0%
+of the reactants to that of uh the uh
+products so the change Delta n is equal
+
+ align:start position:0%
+products so the change Delta n is equal
+ 
+
+ align:start position:0%
+products so the change Delta n is equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+uh final minus initial so this is NP
+
+ align:start position:0%
+uh final minus initial so this is NP
+ 
+
+ align:start position:0%
+uh final minus initial so this is NP
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+NR is equal to U new sub Epsilon new new
+
+ align:start position:0%
+NR is equal to U new sub Epsilon new new
+ 
+
+ align:start position:0%
+NR is equal to U new sub Epsilon new new
+sorry new sub times
+
+ align:start position:0%
+sorry new sub times
+ 
+
+ align:start position:0%
+sorry new sub times
+Epsilon and this Epsilon here could
+
+ align:start position:0%
+Epsilon and this Epsilon here could
+ 
+
+ align:start position:0%
+Epsilon and this Epsilon here could
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+uh it's actually it's it's a Delta it's
+
+ align:start position:0%
+uh it's actually it's it's a Delta it's
+ 
+
+ align:start position:0%
+uh it's actually it's it's a Delta it's
+the difference between the value of the
+
+ align:start position:0%
+the difference between the value of the
+ 
+
+ align:start position:0%
+the difference between the value of the
+reaction coordinate that describes the
+
+ align:start position:0%
+reaction coordinate that describes the
+ 
+
+ align:start position:0%
+reaction coordinate that describes the
+products and the value of the reaction
+
+ align:start position:0%
+products and the value of the reaction
+ 
+
+ align:start position:0%
+products and the value of the reaction
+coordinate that describes the reactant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+composition if we have instead this
+
+ align:start position:0%
+composition if we have instead this
+ 
+
+ align:start position:0%
+composition if we have instead this
+steady state
+
+ align:start position:0%
+steady state
+ 
+
+ align:start position:0%
+steady state
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+uh um flow
+
+ align:start position:0%
+uh um flow
+ 
+
+ align:start position:0%
+uh um flow
+uh continuous
+
+ align:start position:0%
+uh continuous
+ 
+
+ align:start position:0%
+uh continuous
+reaction then we talk about the rate of
+
+ align:start position:0%
+reaction then we talk about the rate of
+ 
+
+ align:start position:0%
+reaction then we talk about the rate of
+change of uh the composition so we take
+
+ align:start position:0%
+change of uh the composition so we take
+ 
+
+ align:start position:0%
+change of uh the composition so we take
+we Define we divide this by DT so Delta
+
+ align:start position:0%
+we Define we divide this by DT so Delta
+ 
+
+ align:start position:0%
+we Define we divide this by DT so Delta
+n by delta T is the stric coefficient
+
+ align:start position:0%
+n by delta T is the stric coefficient
+ 
+
+ align:start position:0%
+n by delta T is the stric coefficient
+times Delta EP delta T let's call it
+
+ align:start position:0%
+times Delta EP delta T let's call it
+ 
+
+ align:start position:0%
+times Delta EP delta T let's call it
+Epsilon
+
+ align:start position:0%
+Epsilon
+ 
+
+ align:start position:0%
+Epsilon
+Dot and so you you find that the rate
+
+ align:start position:0%
+Dot and so you you find that the rate
+ 
+
+ align:start position:0%
+Dot and so you you find that the rate
+that which the the difference between
+
+ align:start position:0%
+that which the the difference between
+ 
+
+ align:start position:0%
+that which the the difference between
+the rate at which the products and the
+
+ align:start position:0%
+the rate at which the products and the
+ 
+
+ align:start position:0%
+the rate at which the products and the
+reactants come out and in is related to
+
+ align:start position:0%
+reactants come out and in is related to
+ 
+
+ align:start position:0%
+reactants come out and in is related to
+this rate of change of the reaction
+
+ align:start position:0%
+this rate of change of the reaction
+ 
+
+ align:start position:0%
+this rate of change of the reaction
+coordinate which uh somehow is related
+
+ align:start position:0%
+coordinate which uh somehow is related
+ 
+
+ align:start position:0%
+coordinate which uh somehow is related
+to the uh reaction rate or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rates in
+
+ align:start position:0%
+rates in
+ 
+
+ align:start position:0%
+rates in
+fact do I have it in the next slide no
+
+ align:start position:0%
+fact do I have it in the next slide no
+ 
+
+ align:start position:0%
+fact do I have it in the next slide no
+uh so in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fact so we have n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dot
+
+ align:start position:0%
+dot
+ 
+
+ align:start position:0%
+dot
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+p is equal to n do I
+
+ align:start position:0%
+p is equal to n do I
+ 
+
+ align:start position:0%
+p is equal to n do I
+plus uh okay so if you have only one
+
+ align:start position:0%
+plus uh okay so if you have only one
+ 
+
+ align:start position:0%
+plus uh okay so if you have only one
+reaction is uh the summation of uh
+
+ align:start position:0%
+reaction is uh the summation of uh
+ 
+
+ align:start position:0%
+reaction is uh the summation of uh
+Epsilon Dot
+
+ align:start position:0%
+Epsilon Dot
+ 
+
+ align:start position:0%
+Epsilon Dot
+times new I but if I have several
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reactions then each one has its own uh
+
+ align:start position:0%
+reactions then each one has its own uh
+ 
+
+ align:start position:0%
+reactions then each one has its own uh
+reaction coordinate and I have to sum
+
+ align:start position:0%
+reaction coordinate and I have to sum
+ 
+
+ align:start position:0%
+reaction coordinate and I have to sum
+up the
+
+ align:start position:0%
+up the
+ 
+
+ align:start position:0%
+up the
+contribution uh to the change of the
+
+ align:start position:0%
+contribution uh to the change of the
+ 
+
+ align:start position:0%
+contribution uh to the change of the
+various reactions in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+play
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now let's let's go back sorry
+
+ align:start position:0%
+okay so now let's let's go back sorry
+ 
+
+ align:start position:0%
+okay so now let's let's go back sorry
+let's go back here to the
+
+ align:start position:0%
+let's go back here to the
+ 
+
+ align:start position:0%
+let's go back here to the
+structure of the balance
+
+ align:start position:0%
+structure of the balance
+ 
+
+ align:start position:0%
+structure of the balance
+equations in the balance
+
+ align:start position:0%
+equations in the balance
+ 
+
+ align:start position:0%
+equations in the balance
+equations you have we have to deal with
+
+ align:start position:0%
+equations you have we have to deal with
+ 
+
+ align:start position:0%
+equations you have we have to deal with
+differen between the energy between
+
+ align:start position:0%
+differen between the energy between
+ 
+
+ align:start position:0%
+differen between the energy between
+products and reactants the entropy
+
+ align:start position:0%
+products and reactants the entropy
+ 
+
+ align:start position:0%
+products and reactants the entropy
+between products and reactants also here
+
+ align:start position:0%
+between products and reactants also here
+ 
+
+ align:start position:0%
+between products and reactants also here
+the enthalpy between reactants and
+
+ align:start position:0%
+the enthalpy between reactants and
+ 
+
+ align:start position:0%
+the enthalpy between reactants and
+products the entropy these differences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes it is true that uh we can um write
+
+ align:start position:0%
+yes it is true that uh we can um write
+ 
+
+ align:start position:0%
+yes it is true that uh we can um write
+them we know how to write them except
+
+ align:start position:0%
+them we know how to write them except
+ 
+
+ align:start position:0%
+them we know how to write them except
+that we have to learn a proper way to
+
+ align:start position:0%
+that we have to learn a proper way to
+ 
+
+ align:start position:0%
+that we have to learn a proper way to
+deal with the fact that uh the
+
+ align:start position:0%
+deal with the fact that uh the
+ 
+
+ align:start position:0%
+deal with the fact that uh the
+composition is changing here so some
+
+ align:start position:0%
+composition is changing here so some
+ 
+
+ align:start position:0%
+composition is changing here so some
+molecules are disappearing and some are
+
+ align:start position:0%
+molecules are disappearing and some are
+ 
+
+ align:start position:0%
+molecules are disappearing and some are
+appearing uh that have different
+
+ align:start position:0%
+appearing uh that have different
+ 
+
+ align:start position:0%
+appearing uh that have different
+properties and therefore we have to be
+
+ align:start position:0%
+properties and therefore we have to be
+ 
+
+ align:start position:0%
+properties and therefore we have to be
+careful in how we take uh
+
+ align:start position:0%
+careful in how we take uh
+ 
+
+ align:start position:0%
+careful in how we take uh
+reference
+
+ align:start position:0%
+reference
+ 
+
+ align:start position:0%
+reference
+value for these
+
+ align:start position:0%
+value for these
+ 
+
+ align:start position:0%
+value for these
+properties and this is done
+
+ align:start position:0%
+properties and this is done
+ 
+
+ align:start position:0%
+properties and this is done
+here for example U of those differences
+
+ align:start position:0%
+here for example U of those differences
+ 
+
+ align:start position:0%
+here for example U of those differences
+let's take uh one which is the
+
+ align:start position:0%
+let's take uh one which is the
+ 
+
+ align:start position:0%
+let's take uh one which is the
+energy so we write the
+
+ align:start position:0%
+energy so we write the
+ 
+
+ align:start position:0%
+energy so we write the
+energy difference between products and
+
+ align:start position:0%
+energy difference between products and
+ 
+
+ align:start position:0%
+energy difference between products and
+reactants as uh as we said okay so this
+
+ align:start position:0%
+reactants as uh as we said okay so this
+ 
+
+ align:start position:0%
+reactants as uh as we said okay so this
+is just the implementation of what we
+
+ align:start position:0%
+is just the implementation of what we
+ 
+
+ align:start position:0%
+is just the implementation of what we
+said
+
+ align:start position:0%
+said
+ 
+
+ align:start position:0%
+said
+in terms of partial
+
+ align:start position:0%
+in terms of partial
+ 
+
+ align:start position:0%
+in terms of partial
+properties
+
+ align:start position:0%
+properties
+ 
+
+ align:start position:0%
+properties
+now we let's add and
+
+ align:start position:0%
+now we let's add and
+ 
+
+ align:start position:0%
+now we let's add and
+subtract something which will not change
+
+ align:start position:0%
+subtract something which will not change
+ 
+
+ align:start position:0%
+subtract something which will not change
+therefore the result and which we select
+
+ align:start position:0%
+therefore the result and which we select
+ 
+
+ align:start position:0%
+therefore the result and which we select
+to added
+
+ align:start position:0%
+to added
+ 
+
+ align:start position:0%
+to added
+subtract for each um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constituent the specific property of
+
+ align:start position:0%
+constituent the specific property of
+ 
+
+ align:start position:0%
+constituent the specific property of
+pure component of that constituent at
+
+ align:start position:0%
+pure component of that constituent at
+ 
+
+ align:start position:0%
+pure component of that constituent at
+some reference and here let's say at
+
+ align:start position:0%
+some reference and here let's say at
+ 
+
+ align:start position:0%
+some reference and here let's say at
+some reference temperature and
+
+ align:start position:0%
+some reference temperature and
+ 
+
+ align:start position:0%
+some reference temperature and
+pressure I'm going to call the pressure
+
+ align:start position:0%
+pressure I'm going to call the pressure
+ 
+
+ align:start position:0%
+pressure I'm going to call the pressure
+p not because typically it's taken the
+
+ align:start position:0%
+p not because typically it's taken the
+ 
+
+ align:start position:0%
+p not because typically it's taken the
+standard pressure is the one
+
+ align:start position:0%
+standard pressure is the one
+ 
+
+ align:start position:0%
+standard pressure is the one
+atmosphere whereas here for temperature
+
+ align:start position:0%
+atmosphere whereas here for temperature
+ 
+
+ align:start position:0%
+atmosphere whereas here for temperature
+let's use the generic temperature for
+
+ align:start position:0%
+let's use the generic temperature for
+ 
+
+ align:start position:0%
+let's use the generic temperature for
+the moment if it will
+
+ align:start position:0%
+the moment if it will
+ 
+
+ align:start position:0%
+the moment if it will
+be the the standard temperature to to
+
+ align:start position:0%
+be the the standard temperature to to
+ 
+
+ align:start position:0%
+be the the standard temperature to to
+298.15 that we we will denote it by T
+
+ align:start position:0%
+298.15 that we we will denote it by T
+ 
+
+ align:start position:0%
+298.15 that we we will denote it by T
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+but for the moment this can be done at
+
+ align:start position:0%
+but for the moment this can be done at
+ 
+
+ align:start position:0%
+but for the moment this can be done at
+any temperature and this temperature is
+
+ align:start position:0%
+any temperature and this temperature is
+ 
+
+ align:start position:0%
+any temperature and this temperature is
+not necessarily equal to either TR or
+
+ align:start position:0%
+not necessarily equal to either TR or
+ 
+
+ align:start position:0%
+not necessarily equal to either TR or
+TP okay so we add and subtract so here
+
+ align:start position:0%
+TP okay so we add and subtract so here
+ 
+
+ align:start position:0%
+TP okay so we add and subtract so here
+is here it is so we uh we subtract from
+
+ align:start position:0%
+is here it is so we uh we subtract from
+ 
+
+ align:start position:0%
+is here it is so we uh we subtract from
+from this summation we subtract from
+
+ align:start position:0%
+from this summation we subtract from
+ 
+
+ align:start position:0%
+from this summation we subtract from
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+summation but then we realize that since
+
+ align:start position:0%
+summation but then we realize that since
+ 
+
+ align:start position:0%
+summation but then we realize that since
+we put it in this summation here it is
+
+ align:start position:0%
+we put it in this summation here it is
+ 
+
+ align:start position:0%
+we put it in this summation here it is
+um multiplied by
+
+ align:start position:0%
+um multiplied by
+ 
+
+ align:start position:0%
+um multiplied by
+NP and here it is multiplied by NR so we
+
+ align:start position:0%
+NP and here it is multiplied by NR so we
+ 
+
+ align:start position:0%
+NP and here it is multiplied by NR so we
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+to add up
+
+ align:start position:0%
+to add up
+ 
+
+ align:start position:0%
+to add up
+uh what we
+
+ align:start position:0%
+uh what we
+ 
+
+ align:start position:0%
+uh what we
+subtracted so
+
+ align:start position:0%
+subtracted so
+ 
+
+ align:start position:0%
+subtracted so
+this multiplied by the corresponding
+
+ align:start position:0%
+this multiplied by the corresponding
+ 
+
+ align:start position:0%
+this multiplied by the corresponding
+amounts
+
+ align:start position:0%
+amounts
+ 
+
+ align:start position:0%
+amounts
+here so in this summation that
+
+ align:start position:0%
+here so in this summation that
+ 
+
+ align:start position:0%
+here so in this summation that
+compensates for those subtractions is we
+
+ align:start position:0%
+compensates for those subtractions is we
+ 
+
+ align:start position:0%
+compensates for those subtractions is we
+we we recognize
+
+ align:start position:0%
+we we recognize
+ 
+
+ align:start position:0%
+we we recognize
+uh the difference between composition in
+
+ align:start position:0%
+uh the difference between composition in
+ 
+
+ align:start position:0%
+uh the difference between composition in
+between products and reactants and
+
+ align:start position:0%
+between products and reactants and
+ 
+
+ align:start position:0%
+between products and reactants and
+that's related to
+
+ align:start position:0%
+that's related to
+ 
+
+ align:start position:0%
+that's related to
+the uh reaction
+
+ align:start position:0%
+the uh reaction
+ 
+
+ align:start position:0%
+the uh reaction
+coordinate through the proportionality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relations so the Epsilon doesn't have a
+
+ align:start position:0%
+relations so the Epsilon doesn't have a
+ 
+
+ align:start position:0%
+relations so the Epsilon doesn't have a
+subscr it goes out of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+summation and here we are left with the
+
+ align:start position:0%
+summation and here we are left with the
+ 
+
+ align:start position:0%
+summation and here we are left with the
+summation of the stochiometric
+
+ align:start position:0%
+summation of the stochiometric
+ 
+
+ align:start position:0%
+summation of the stochiometric
+coefficients which multiply this
+
+ align:start position:0%
+coefficients which multiply this
+ 
+
+ align:start position:0%
+coefficients which multiply this
+reference with with the
+
+ align:start position:0%
+reference with with the
+ 
+
+ align:start position:0%
+reference with with the
+pure component
+
+ align:start position:0%
+pure component
+ 
+
+ align:start position:0%
+pure component
+properties uh specific properties at
+
+ align:start position:0%
+properties uh specific properties at
+ 
+
+ align:start position:0%
+properties uh specific properties at
+those reference temperature and
+
+ align:start position:0%
+those reference temperature and
+ 
+
+ align:start position:0%
+those reference temperature and
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+summation we call it the energy of the
+
+ align:start position:0%
+summation we call it the energy of the
+ 
+
+ align:start position:0%
+summation we call it the energy of the
+reaction at standard pressure and at
+
+ align:start position:0%
+reaction at standard pressure and at
+ 
+
+ align:start position:0%
+reaction at standard pressure and at
+that temperature and we denote it by
+
+ align:start position:0%
+that temperature and we denote it by
+ 
+
+ align:start position:0%
+that temperature and we denote it by
+this symbol here so that defines the
+
+ align:start position:0%
+this symbol here so that defines the
+ 
+
+ align:start position:0%
+this symbol here so that defines the
+energy of the
+
+ align:start position:0%
+energy of the
+ 
+
+ align:start position:0%
+energy of the
+reaction you can do that for for all the
+
+ align:start position:0%
+reaction you can do that for for all the
+ 
+
+ align:start position:0%
+reaction you can do that for for all the
+other uh for all the other um differen
+
+ align:start position:0%
+other uh for all the other um differen
+ 
+
+ align:start position:0%
+other uh for all the other um differen
+here for example this is for the
+
+ align:start position:0%
+here for example this is for the
+ 
+
+ align:start position:0%
+here for example this is for the
+enthalpy the rate of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enthalpies add and
+
+ align:start position:0%
+enthalpies add and
+ 
+
+ align:start position:0%
+enthalpies add and
+subtract uh the pure component specific
+
+ align:start position:0%
+subtract uh the pure component specific
+ 
+
+ align:start position:0%
+subtract uh the pure component specific
+enthalpy you get
+
+ align:start position:0%
+enthalpy you get
+ 
+
+ align:start position:0%
+enthalpy you get
+uh in this final term you get the
+
+ align:start position:0%
+uh in this final term you get the
+ 
+
+ align:start position:0%
+uh in this final term you get the
+proportionality relation for the
+
+ align:start position:0%
+proportionality relation for the
+ 
+
+ align:start position:0%
+proportionality relation for the
+continuous process Epsilon dot goes out
+
+ align:start position:0%
+continuous process Epsilon dot goes out
+ 
+
+ align:start position:0%
+continuous process Epsilon dot goes out
+of the summation the summ you also call
+
+ align:start position:0%
+of the summation the summ you also call
+ 
+
+ align:start position:0%
+of the summation the summ you also call
+it the enthalpy of the reaction uh at it
+
+ align:start position:0%
+it the enthalpy of the reaction uh at it
+ 
+
+ align:start position:0%
+it the enthalpy of the reaction uh at it
+is the enthalpy of the reaction because
+
+ align:start position:0%
+is the enthalpy of the reaction because
+ 
+
+ align:start position:0%
+is the enthalpy of the reaction because
+uh it has in it refers to a specific
+
+ align:start position:0%
+uh it has in it refers to a specific
+ 
+
+ align:start position:0%
+uh it has in it refers to a specific
+reaction because it depends on the
+
+ align:start position:0%
+reaction because it depends on the
+ 
+
+ align:start position:0%
+reaction because it depends on the
+stochiometric co efficients of that
+
+ align:start position:0%
+stochiometric co efficients of that
+ 
+
+ align:start position:0%
+stochiometric co efficients of that
+reaction okay so I'll have an enthalpy
+
+ align:start position:0%
+reaction okay so I'll have an enthalpy
+ 
+
+ align:start position:0%
+reaction okay so I'll have an enthalpy
+of this reaction another enthalpy for
+
+ align:start position:0%
+of this reaction another enthalpy for
+ 
+
+ align:start position:0%
+of this reaction another enthalpy for
+that reaction so each reaction has its
+
+ align:start position:0%
+that reaction so each reaction has its
+ 
+
+ align:start position:0%
+that reaction so each reaction has its
+own value for these properties of
+
+ align:start position:0%
+own value for these properties of
+ 
+
+ align:start position:0%
+own value for these properties of
+reaction we call them properties of
+
+ align:start position:0%
+reaction we call them properties of
+ 
+
+ align:start position:0%
+reaction we call them properties of
+reaction and here's the list you can do
+
+ align:start position:0%
+reaction and here's the list you can do
+ 
+
+ align:start position:0%
+reaction and here's the list you can do
+that for for all properties including
+
+ align:start position:0%
+that for for all properties including
+ 
+
+ align:start position:0%
+that for for all properties including
+energy entropy enpy gives fre energy and
+
+ align:start position:0%
+energy entropy enpy gives fre energy and
+ 
+
+ align:start position:0%
+energy entropy enpy gives fre energy and
+even
+
+ align:start position:0%
+even
+ 
+
+ align:start position:0%
+even
+volume and of course since they these
+
+ align:start position:0%
+volume and of course since they these
+ 
+
+ align:start position:0%
+volume and of course since they these
+are uh pure component uh uh
+
+ align:start position:0%
+are uh pure component uh uh
+ 
+
+ align:start position:0%
+are uh pure component uh uh
+properties
+
+ align:start position:0%
+properties
+ 
+
+ align:start position:0%
+properties
+um the relation that hold
+
+ align:start position:0%
+um the relation that hold
+ 
+
+ align:start position:0%
+um the relation that hold
+between properties also hold
+
+ align:start position:0%
+between properties also hold
+ 
+
+ align:start position:0%
+between properties also hold
+between uh the properties of reaction so
+
+ align:start position:0%
+between uh the properties of reaction so
+ 
+
+ align:start position:0%
+between uh the properties of reaction so
+since the Gibs free energy you can write
+
+ align:start position:0%
+since the Gibs free energy you can write
+ 
+
+ align:start position:0%
+since the Gibs free energy you can write
+it as H minus TS it turns out that the
+
+ align:start position:0%
+it as H minus TS it turns out that the
+ 
+
+ align:start position:0%
+it as H minus TS it turns out that the
+GI free energy of reaction is equal to
+
+ align:start position:0%
+GI free energy of reaction is equal to
+ 
+
+ align:start position:0%
+GI free energy of reaction is equal to
+the enthalpy of reactions minus t times
+
+ align:start position:0%
+the enthalpy of reactions minus t times
+ 
+
+ align:start position:0%
+the enthalpy of reactions minus t times
+the entropy of
+
+ align:start position:0%
+the entropy of
+ 
+
+ align:start position:0%
+the entropy of
+reaction or since the enthalpy uh is
+
+ align:start position:0%
+reaction or since the enthalpy uh is
+ 
+
+ align:start position:0%
+reaction or since the enthalpy uh is
+equal to energy plus PV U plus PV there
+
+ align:start position:0%
+equal to energy plus PV U plus PV there
+ 
+
+ align:start position:0%
+equal to energy plus PV U plus PV there
+there is a relation also between the
+
+ align:start position:0%
+there is a relation also between the
+ 
+
+ align:start position:0%
+there is a relation also between the
+enthalpy of reaction the energy of
+
+ align:start position:0%
+enthalpy of reaction the energy of
+ 
+
+ align:start position:0%
+enthalpy of reaction the energy of
+reaction and the uh volume of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reaction this is for a generic
+
+ align:start position:0%
+reaction this is for a generic
+ 
+
+ align:start position:0%
+reaction this is for a generic
+temperature T at standard temperature
+
+ align:start position:0%
+temperature T at standard temperature
+ 
+
+ align:start position:0%
+temperature T at standard temperature
+pressure also the temperature is fixed
+
+ align:start position:0%
+pressure also the temperature is fixed
+ 
+
+ align:start position:0%
+pressure also the temperature is fixed
+we we drop the symbol uh function of T
+
+ align:start position:0%
+we we drop the symbol uh function of T
+ 
+
+ align:start position:0%
+we we drop the symbol uh function of T
+and for for Simplicity we just uh by
+
+ align:start position:0%
+and for for Simplicity we just uh by
+ 
+
+ align:start position:0%
+and for for Simplicity we just uh by
+convention say well if if there is
+
+ align:start position:0%
+convention say well if if there is
+ 
+
+ align:start position:0%
+convention say well if if there is
+no dependence of of t means that we are
+
+ align:start position:0%
+no dependence of of t means that we are
+ 
+
+ align:start position:0%
+no dependence of of t means that we are
+at at T not so the KN here is uh has two
+
+ align:start position:0%
+at at T not so the KN here is uh has two
+ 
+
+ align:start position:0%
+at at T not so the KN here is uh has two
+meaning uh pressure and also temperature
+
+ align:start position:0%
+meaning uh pressure and also temperature
+ 
+
+ align:start position:0%
+meaning uh pressure and also temperature
+are at standard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values now it turns out that if you want
+
+ align:start position:0%
+values now it turns out that if you want
+ 
+
+ align:start position:0%
+values now it turns out that if you want
+to uh
+
+ align:start position:0%
+to uh
+ 
+
+ align:start position:0%
+to uh
+compute the properties
+
+ align:start position:0%
+compute the properties
+ 
+
+ align:start position:0%
+compute the properties
+of reaction you see as we've said every
+
+ align:start position:0%
+of reaction you see as we've said every
+ 
+
+ align:start position:0%
+of reaction you see as we've said every
+reaction has its own properties
+
+ align:start position:0%
+reaction has its own properties
+ 
+
+ align:start position:0%
+reaction has its own properties
+should then be uh all uh measured so if
+
+ align:start position:0%
+should then be uh all uh measured so if
+ 
+
+ align:start position:0%
+should then be uh all uh measured so if
+you have one
+
+ align:start position:0%
+you have one
+ 
+
+ align:start position:0%
+you have one
+uh interesting in one reaction you have
+
+ align:start position:0%
+uh interesting in one reaction you have
+ 
+
+ align:start position:0%
+uh interesting in one reaction you have
+to find the experimental values of
+
+ align:start position:0%
+to find the experimental values of
+ 
+
+ align:start position:0%
+to find the experimental values of
+somebody who measured these the
+
+ align:start position:0%
+somebody who measured these the
+ 
+
+ align:start position:0%
+somebody who measured these the
+properties for your reaction well the
+
+ align:start position:0%
+properties for your reaction well the
+ 
+
+ align:start position:0%
+properties for your reaction well the
+answer is no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fortunately because of the EST relation
+
+ align:start position:0%
+fortunately because of the EST relation
+ 
+
+ align:start position:0%
+fortunately because of the EST relation
+which we will prove in a
+
+ align:start position:0%
+which we will prove in a
+ 
+
+ align:start position:0%
+which we will prove in a
+moment uh whereby you you
+
+ align:start position:0%
+moment uh whereby you you
+ 
+
+ align:start position:0%
+moment uh whereby you you
+it turns out that uh there is a minimal
+
+ align:start position:0%
+it turns out that uh there is a minimal
+ 
+
+ align:start position:0%
+it turns out that uh there is a minimal
+set of uh measurements that you have to
+
+ align:start position:0%
+set of uh measurements that you have to
+ 
+
+ align:start position:0%
+set of uh measurements that you have to
+make which is um the measurement of the
+
+ align:start position:0%
+make which is um the measurement of the
+ 
+
+ align:start position:0%
+make which is um the measurement of the
+reactions of formations of the various
+
+ align:start position:0%
+reactions of formations of the various
+ 
+
+ align:start position:0%
+reactions of formations of the various
+component once you have those uh using
+
+ align:start position:0%
+component once you have those uh using
+ 
+
+ align:start position:0%
+component once you have those uh using
+these relations H
+
+ align:start position:0%
+these relations H
+ 
+
+ align:start position:0%
+these relations H
+relations uh you can find the
+
+ align:start position:0%
+relations uh you can find the
+ 
+
+ align:start position:0%
+relations uh you can find the
+um properties of reaction for any
+
+ align:start position:0%
+um properties of reaction for any
+ 
+
+ align:start position:0%
+um properties of reaction for any
+reaction by just taking the weighted sum
+
+ align:start position:0%
+reaction by just taking the weighted sum
+ 
+
+ align:start position:0%
+reaction by just taking the weighted sum
+with the
+
+ align:start position:0%
+with the
+ 
+
+ align:start position:0%
+with the
+stochiometric coefficients of your
+
+ align:start position:0%
+stochiometric coefficients of your
+ 
+
+ align:start position:0%
+stochiometric coefficients of your
+reaction of the reactions of formations
+
+ align:start position:0%
+reaction of the reactions of formations
+ 
+
+ align:start position:0%
+reaction of the reactions of formations
+of the various uh of the various
+
+ align:start position:0%
+of the various uh of the various
+ 
+
+ align:start position:0%
+of the various uh of the various
+molecules that play in your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reaction so essentially
+
+ align:start position:0%
+reaction so essentially
+ 
+
+ align:start position:0%
+reaction so essentially
+here I'm interested in
+
+ align:start position:0%
+here I'm interested in
+ 
+
+ align:start position:0%
+here I'm interested in
+energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh symbol yeah okay the F goes before f
+
+ align:start position:0%
+uh symbol yeah okay the F goes before f
+ 
+
+ align:start position:0%
+uh symbol yeah okay the F goes before f
+i not and then I'll have to list
+
+ align:start position:0%
+i not and then I'll have to list
+ 
+
+ align:start position:0%
+i not and then I'll have to list
+somewhere here the values of the en
+
+ align:start position:0%
+somewhere here the values of the en
+ 
+
+ align:start position:0%
+somewhere here the values of the en
+energies of formation for these various
+
+ align:start position:0%
+energies of formation for these various
+ 
+
+ align:start position:0%
+energies of formation for these various
+components and these ones I find
+
+ align:start position:0%
+components and these ones I find
+ 
+
+ align:start position:0%
+components and these ones I find
+tabulated in the handbooks of
+
+ align:start position:0%
+tabulated in the handbooks of
+ 
+
+ align:start position:0%
+tabulated in the handbooks of
+chemical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+physics now before before we prove this
+
+ align:start position:0%
+physics now before before we prove this
+ 
+
+ align:start position:0%
+physics now before before we prove this
+relation let's
+
+ align:start position:0%
+relation let's
+ 
+
+ align:start position:0%
+relation let's
+U uh
+
+ align:start position:0%
+U uh
+ 
+
+ align:start position:0%
+U uh
+see the meaning of this Delta
+
+ align:start position:0%
+see the meaning of this Delta
+ 
+
+ align:start position:0%
+see the meaning of this Delta
+U and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta actually this is for enthalpy and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+entropy and so let's consider one
+
+ align:start position:0%
+entropy and so let's consider one
+ 
+
+ align:start position:0%
+entropy and so let's consider one
+particular reaction like that of in
+
+ align:start position:0%
+particular reaction like that of in
+ 
+
+ align:start position:0%
+particular reaction like that of in
+which hydrogen molecule splits into uh
+
+ align:start position:0%
+which hydrogen molecule splits into uh
+ 
+
+ align:start position:0%
+which hydrogen molecule splits into uh
+two hydrogen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+atoms so here I'm drying I'm drawing the
+
+ align:start position:0%
+atoms so here I'm drying I'm drawing the
+ 
+
+ align:start position:0%
+atoms so here I'm drying I'm drawing the
+uh eus s or actually the enal versus S
+
+ align:start position:0%
+uh eus s or actually the enal versus S
+ 
+
+ align:start position:0%
+uh eus s or actually the enal versus S
+curve for the stable equilibrium
+
+ align:start position:0%
+curve for the stable equilibrium
+ 
+
+ align:start position:0%
+curve for the stable equilibrium
+states of atomic hydrogen this is atomic
+
+ align:start position:0%
+states of atomic hydrogen this is atomic
+ 
+
+ align:start position:0%
+states of atomic hydrogen this is atomic
+hydrogen in the amount of one fixed
+
+ align:start position:0%
+hydrogen in the amount of one fixed
+ 
+
+ align:start position:0%
+hydrogen in the amount of one fixed
+fixed amount one
+
+ align:start position:0%
+fixed amount one
+ 
+
+ align:start position:0%
+fixed amount one
+mole and at standard pressure one
+
+ align:start position:0%
+mole and at standard pressure one
+ 
+
+ align:start position:0%
+mole and at standard pressure one
+atmosphere this other curve represents
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+half a
+
+ align:start position:0%
+half a
+ 
+
+ align:start position:0%
+half a
+mole
+
+ align:start position:0%
+mole
+ 
+
+ align:start position:0%
+mole
+of molecular hydrogen
+
+ align:start position:0%
+of molecular hydrogen
+ 
+
+ align:start position:0%
+of molecular hydrogen
+H2 also at standard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressure then I take a
+
+ align:start position:0%
+pressure then I take a
+ 
+
+ align:start position:0%
+pressure then I take a
+slope equal to
+
+ align:start position:0%
+slope equal to
+ 
+
+ align:start position:0%
+slope equal to
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+Kelvin and search for the point on this
+
+ align:start position:0%
+Kelvin and search for the point on this
+ 
+
+ align:start position:0%
+Kelvin and search for the point on this
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+what I have that temperature turns out
+
+ align:start position:0%
+what I have that temperature turns out
+ 
+
+ align:start position:0%
+what I have that temperature turns out
+the derivative of the of H with respect
+
+ align:start position:0%
+the derivative of the of H with respect
+ 
+
+ align:start position:0%
+the derivative of the of H with respect
+to S constant p is uh equal to the
+
+ align:start position:0%
+to S constant p is uh equal to the
+ 
+
+ align:start position:0%
+to S constant p is uh equal to the
+temperature so also on this diagram uh
+
+ align:start position:0%
+temperature so also on this diagram uh
+ 
+
+ align:start position:0%
+temperature so also on this diagram uh
+the slope is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temperature and here I find it
+
+ align:start position:0%
+temperature and here I find it
+ 
+
+ align:start position:0%
+temperature and here I find it
+here and for this other substance I find
+
+ align:start position:0%
+here and for this other substance I find
+ 
+
+ align:start position:0%
+here and for this other substance I find
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there now these two curves
+
+ align:start position:0%
+there now these two curves
+ 
+
+ align:start position:0%
+there now these two curves
+uh until uh yesterday
+
+ align:start position:0%
+uh until uh yesterday
+ 
+
+ align:start position:0%
+uh until uh yesterday
+or until we didn't consider chemical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reactions we're sort of
+
+ align:start position:0%
+reactions we're sort of
+ 
+
+ align:start position:0%
+reactions we're sort of
+independent if we needed to describe the
+
+ align:start position:0%
+independent if we needed to describe the
+ 
+
+ align:start position:0%
+independent if we needed to describe the
+properties of this molecule we just draw
+
+ align:start position:0%
+properties of this molecule we just draw
+ 
+
+ align:start position:0%
+properties of this molecule we just draw
+this curve anywhere taking an
+
+ align:start position:0%
+this curve anywhere taking an
+ 
+
+ align:start position:0%
+this curve anywhere taking an
+arbitrary zero for the enthalpy I didn't
+
+ align:start position:0%
+arbitrary zero for the enthalpy I didn't
+ 
+
+ align:start position:0%
+arbitrary zero for the enthalpy I didn't
+matter but now instead what matters is
+
+ align:start position:0%
+matter but now instead what matters is
+ 
+
+ align:start position:0%
+matter but now instead what matters is
+the fact that you with a chemical
+
+ align:start position:0%
+the fact that you with a chemical
+ 
+
+ align:start position:0%
+the fact that you with a chemical
+reaction mechanism you can go from one
+
+ align:start position:0%
+reaction mechanism you can go from one
+ 
+
+ align:start position:0%
+reaction mechanism you can go from one
+substance to the
+
+ align:start position:0%
+substance to the
+ 
+
+ align:start position:0%
+substance to the
+other so they the you cannot arbitrarily
+
+ align:start position:0%
+other so they the you cannot arbitrarily
+ 
+
+ align:start position:0%
+other so they the you cannot arbitrarily
+choose reference values for the
+
+ align:start position:0%
+choose reference values for the
+ 
+
+ align:start position:0%
+choose reference values for the
+properties uh for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+both because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for example if you look at um suppose we
+
+ align:start position:0%
+for example if you look at um suppose we
+ 
+
+ align:start position:0%
+for example if you look at um suppose we
+were at zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh in order
+
+ align:start position:0%
+uh in order
+ 
+
+ align:start position:0%
+uh in order
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+split uh this molecule of atomic I mean
+
+ align:start position:0%
+split uh this molecule of atomic I mean
+ 
+
+ align:start position:0%
+split uh this molecule of atomic I mean
+molecular hydrogen into two hydrogen you
+
+ align:start position:0%
+molecular hydrogen into two hydrogen you
+ 
+
+ align:start position:0%
+molecular hydrogen into two hydrogen you
+have to break a bond chemical Bond and
+
+ align:start position:0%
+have to break a bond chemical Bond and
+ 
+
+ align:start position:0%
+have to break a bond chemical Bond and
+the strength of this chemical
+
+ align:start position:0%
+the strength of this chemical
+ 
+
+ align:start position:0%
+the strength of this chemical
+bond corresponds to an energy that you
+
+ align:start position:0%
+bond corresponds to an energy that you
+ 
+
+ align:start position:0%
+bond corresponds to an energy that you
+have to provide in order to uh
+
+ align:start position:0%
+have to provide in order to uh
+ 
+
+ align:start position:0%
+have to provide in order to uh
+detach these two atoms that compose the
+
+ align:start position:0%
+detach these two atoms that compose the
+ 
+
+ align:start position:0%
+detach these two atoms that compose the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+molecule this energy this bond
+
+ align:start position:0%
+molecule this energy this bond
+ 
+
+ align:start position:0%
+molecule this energy this bond
+energy is what you have to plot here so
+
+ align:start position:0%
+energy is what you have to plot here so
+ 
+
+ align:start position:0%
+energy is what you have to plot here so
+that is is uh the the number that allows
+
+ align:start position:0%
+that is is uh the the number that allows
+ 
+
+ align:start position:0%
+that is is uh the the number that allows
+you to place in relative position the
+
+ align:start position:0%
+you to place in relative position the
+ 
+
+ align:start position:0%
+you to place in relative position the
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+curves because this value you
+
+ align:start position:0%
+curves because this value you
+ 
+
+ align:start position:0%
+curves because this value you
+measure uh and
+
+ align:start position:0%
+measure uh and
+ 
+
+ align:start position:0%
+measure uh and
+therefore these two curves must be at
+
+ align:start position:0%
+therefore these two curves must be at
+ 
+
+ align:start position:0%
+therefore these two curves must be at
+this distance
+
+ align:start position:0%
+this distance
+ 
+
+ align:start position:0%
+this distance
+here then using the properties of the
+
+ align:start position:0%
+here then using the properties of the
+ 
+
+ align:start position:0%
+here then using the properties of the
+the substances of the pure substances
+
+ align:start position:0%
+the substances of the pure substances
+ 
+
+ align:start position:0%
+the substances of the pure substances
+here you can compute like using specific
+
+ align:start position:0%
+here you can compute like using specific
+ 
+
+ align:start position:0%
+here you can compute like using specific
+ke and so on you can compute what would
+
+ align:start position:0%
+ke and so on you can compute what would
+ 
+
+ align:start position:0%
+ke and so on you can compute what would
+be the value of the enthalpy at this
+
+ align:start position:0%
+be the value of the enthalpy at this
+ 
+
+ align:start position:0%
+be the value of the enthalpy at this
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+and then also using the specific Heats
+
+ align:start position:0%
+and then also using the specific Heats
+ 
+
+ align:start position:0%
+and then also using the specific Heats
+of this other substance you can uh
+
+ align:start position:0%
+of this other substance you can uh
+ 
+
+ align:start position:0%
+of this other substance you can uh
+integrate the equation this
+
+ align:start position:0%
+integrate the equation this
+ 
+
+ align:start position:0%
+integrate the equation this
+the the fundamental relation and get to
+
+ align:start position:0%
+the the fundamental relation and get to
+ 
+
+ align:start position:0%
+the the fundamental relation and get to
+this point okay these are correspond to
+
+ align:start position:0%
+this point okay these are correspond to
+ 
+
+ align:start position:0%
+this point okay these are correspond to
+the standard the
+
+ align:start position:0%
+the standard the
+ 
+
+ align:start position:0%
+the standard the
+conditions
+
+ align:start position:0%
+conditions
+ 
+
+ align:start position:0%
+conditions
+and the enthalpy of
+
+ align:start position:0%
+and the enthalpy of
+ 
+
+ align:start position:0%
+and the enthalpy of
+formation of uh Atomic hydrogen so of of
+
+ align:start position:0%
+formation of uh Atomic hydrogen so of of
+ 
+
+ align:start position:0%
+formation of uh Atomic hydrogen so of of
+this state here uh from from molecular
+
+ align:start position:0%
+this state here uh from from molecular
+ 
+
+ align:start position:0%
+this state here uh from from molecular
+hydrogen is is given by the difference
+
+ align:start position:0%
+hydrogen is is given by the difference
+ 
+
+ align:start position:0%
+hydrogen is is given by the difference
+in the inal between here and there this
+
+ align:start position:0%
+in the inal between here and there this
+ 
+
+ align:start position:0%
+in the inal between here and there this
+is the amount of energy that you have to
+
+ align:start position:0%
+is the amount of energy that you have to
+ 
+
+ align:start position:0%
+is the amount of energy that you have to
+provide in a steady state
+
+ align:start position:0%
+provide in a steady state
+ 
+
+ align:start position:0%
+provide in a steady state
+reactor uh where as input you have
+
+ align:start position:0%
+reactor uh where as input you have
+ 
+
+ align:start position:0%
+reactor uh where as input you have
+hydrogen at standard conditions and as
+
+ align:start position:0%
+hydrogen at standard conditions and as
+ 
+
+ align:start position:0%
+hydrogen at standard conditions and as
+output you have
+
+ align:start position:0%
+output you have
+ 
+
+ align:start position:0%
+output you have
+a atomic hydrogen at also standard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions all right
+
+ align:start position:0%
+conditions all right
+ 
+
+ align:start position:0%
+conditions all right
+and this also there is a difference in
+
+ align:start position:0%
+and this also there is a difference in
+ 
+
+ align:start position:0%
+and this also there is a difference in
+entropy this difference in entropy
+
+ align:start position:0%
+entropy this difference in entropy
+ 
+
+ align:start position:0%
+entropy this difference in entropy
+corresponds to the entropy of uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formation okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+this the strength of the bondes we will
+
+ align:start position:0%
+this the strength of the bondes we will
+ 
+
+ align:start position:0%
+this the strength of the bondes we will
+return on this graph but just to the
+
+ align:start position:0%
+return on this graph but just to the
+ 
+
+ align:start position:0%
+return on this graph but just to the
+strength of the of the bonds
+
+ align:start position:0%
+strength of the of the bonds
+ 
+
+ align:start position:0%
+strength of the of the bonds
+um is uh also um describable
+
+ align:start position:0%
+um is uh also um describable
+ 
+
+ align:start position:0%
+um is uh also um describable
+using for example Leonard Jones's
+
+ align:start position:0%
+using for example Leonard Jones's
+ 
+
+ align:start position:0%
+using for example Leonard Jones's
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+but the strength and the distances in
+
+ align:start position:0%
+but the strength and the distances in
+ 
+
+ align:start position:0%
+but the strength and the distances in
+play are very
+
+ align:start position:0%
+play are very
+ 
+
+ align:start position:0%
+play are very
+different for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example this would
+
+ align:start position:0%
+example this would
+ 
+
+ align:start position:0%
+example this would
+be uh the Leonard Jones potential that
+
+ align:start position:0%
+be uh the Leonard Jones potential that
+ 
+
+ align:start position:0%
+be uh the Leonard Jones potential that
+describes the calent
+
+ align:start position:0%
+describes the calent
+ 
+
+ align:start position:0%
+describes the calent
+bond uh which is what happens when um
+
+ align:start position:0%
+bond uh which is what happens when um
+ 
+
+ align:start position:0%
+bond uh which is what happens when um
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um hydrogen atom gets close to the
+
+ align:start position:0%
+um hydrogen atom gets close to the
+ 
+
+ align:start position:0%
+um hydrogen atom gets close to the
+oxygen
+
+ align:start position:0%
+oxygen
+ 
+
+ align:start position:0%
+oxygen
+and U gets to share
+
+ align:start position:0%
+and U gets to share
+ 
+
+ align:start position:0%
+and U gets to share
+U they get to share two
+
+ align:start position:0%
+U they get to share two
+ 
+
+ align:start position:0%
+U they get to share two
+electrons and these two electrons form a
+
+ align:start position:0%
+electrons and these two electrons form a
+ 
+
+ align:start position:0%
+electrons and these two electrons form a
+a negative charge enough
+
+ align:start position:0%
+a negative charge enough
+ 
+
+ align:start position:0%
+a negative charge enough
+to to cover up the repulsion between the
+
+ align:start position:0%
+to to cover up the repulsion between the
+ 
+
+ align:start position:0%
+to to cover up the repulsion between the
+positive charges of the
+
+ align:start position:0%
+positive charges of the
+ 
+
+ align:start position:0%
+positive charges of the
+nuclei okay so then this this is the
+
+ align:start position:0%
+nuclei okay so then this this is the
+ 
+
+ align:start position:0%
+nuclei okay so then this this is the
+repulsion of the nuclear this is the
+
+ align:start position:0%
+repulsion of the nuclear this is the
+ 
+
+ align:start position:0%
+repulsion of the nuclear this is the
+attraction and this is a very heavy um
+
+ align:start position:0%
+attraction and this is a very heavy um
+ 
+
+ align:start position:0%
+attraction and this is a very heavy um
+dip it is 459 KJ per
+
+ align:start position:0%
+dip it is 459 KJ per
+ 
+
+ align:start position:0%
+dip it is 459 KJ per
+mole if you compare it with the Vander
+
+ align:start position:0%
+mole if you compare it with the Vander
+ 
+
+ align:start position:0%
+mole if you compare it with the Vander
+vales forces between uh um that that are
+
+ align:start position:0%
+vales forces between uh um that that are
+ 
+
+ align:start position:0%
+vales forces between uh um that that are
+that you can calculate for water
+
+ align:start position:0%
+that you can calculate for water
+ 
+
+ align:start position:0%
+that you can calculate for water
+molecules
+
+ align:start position:0%
+molecules
+ 
+
+ align:start position:0%
+molecules
+in that describes the liquid and Vapor
+
+ align:start position:0%
+in that describes the liquid and Vapor
+ 
+
+ align:start position:0%
+in that describes the liquid and Vapor
+phase for water molecules using the
+
+ align:start position:0%
+phase for water molecules using the
+ 
+
+ align:start position:0%
+phase for water molecules using the
+lonard John's uh fluid model that we
+
+ align:start position:0%
+lonard John's uh fluid model that we
+ 
+
+ align:start position:0%
+lonard John's uh fluid model that we
+discussed the value of the
+
+ align:start position:0%
+discussed the value of the
+ 
+
+ align:start position:0%
+discussed the value of the
+Epsilon is uh you see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's what is it 4,000 times smaller
+
+ align:start position:0%
+it's what is it 4,000 times smaller
+ 
+
+ align:start position:0%
+it's what is it 4,000 times smaller
+5,000 time times
+
+ align:start position:0%
+5,000 time times
+ 
+
+ align:start position:0%
+5,000 time times
+smaller so much that in order to show it
+
+ align:start position:0%
+smaller so much that in order to show it
+ 
+
+ align:start position:0%
+smaller so much that in order to show it
+in the plot I have to multiply it here
+
+ align:start position:0%
+in the plot I have to multiply it here
+ 
+
+ align:start position:0%
+in the plot I have to multiply it here
+by a factor of a
+
+ align:start position:0%
+by a factor of a
+ 
+
+ align:start position:0%
+by a factor of a
+thousand and still it's smaller and also
+
+ align:start position:0%
+thousand and still it's smaller and also
+ 
+
+ align:start position:0%
+thousand and still it's smaller and also
+the minimum
+
+ align:start position:0%
+the minimum
+ 
+
+ align:start position:0%
+the minimum
+here for the Vander vales forces the
+
+ align:start position:0%
+here for the Vander vales forces the
+ 
+
+ align:start position:0%
+here for the Vander vales forces the
+attraction between
+
+ align:start position:0%
+attraction between
+ 
+
+ align:start position:0%
+attraction between
+molecules uh which are also of
+
+ align:start position:0%
+molecules uh which are also of
+ 
+
+ align:start position:0%
+molecules uh which are also of
+electrostatic nature but of from
+
+ align:start position:0%
+electrostatic nature but of from
+ 
+
+ align:start position:0%
+electrostatic nature but of from
+different source is
+
+ align:start position:0%
+different source is
+ 
+
+ align:start position:0%
+different source is
+uh makes
+
+ align:start position:0%
+uh makes
+ 
+
+ align:start position:0%
+uh makes
+the has very larger much larger
+
+ align:start position:0%
+the has very larger much larger
+ 
+
+ align:start position:0%
+the has very larger much larger
+characteristic uh distances so it's like
+
+ align:start position:0%
+characteristic uh distances so it's like
+ 
+
+ align:start position:0%
+characteristic uh distances so it's like
+uh uh three angstrom here or or 300
+
+ align:start position:0%
+uh uh three angstrom here or or 300
+ 
+
+ align:start position:0%
+uh uh three angstrom here or or 300
+picometers here and instead for the
+
+ align:start position:0%
+picometers here and instead for the
+ 
+
+ align:start position:0%
+picometers here and instead for the
+calent bond is of the order of
+
+ align:start position:0%
+calent bond is of the order of
+ 
+
+ align:start position:0%
+calent bond is of the order of
+74 so they have to get much closer in
+
+ align:start position:0%
+74 so they have to get much closer in
+ 
+
+ align:start position:0%
+74 so they have to get much closer in
+order to in order for these um much
+
+ align:start position:0%
+order to in order for these um much
+ 
+
+ align:start position:0%
+order to in order for these um much
+stronger forces to to to get in play and
+
+ align:start position:0%
+stronger forces to to to get in play and
+ 
+
+ align:start position:0%
+stronger forces to to to get in play and
+hold the molecule so this is
+
+ align:start position:0%
+hold the molecule so this is
+ 
+
+ align:start position:0%
+hold the molecule so this is
+a to to say that uh
+
+ align:start position:0%
+a to to say that uh
+ 
+
+ align:start position:0%
+a to to say that uh
+um yes you can use Leonard Jones
+
+ align:start position:0%
+um yes you can use Leonard Jones
+ 
+
+ align:start position:0%
+um yes you can use Leonard Jones
+although it's not really a great model
+
+ align:start position:0%
+although it's not really a great model
+ 
+
+ align:start position:0%
+although it's not really a great model
+for for this kind of of bonds but it it
+
+ align:start position:0%
+for for this kind of of bonds but it it
+ 
+
+ align:start position:0%
+for for this kind of of bonds but it it
+gives you the first order
+
+ align:start position:0%
+gives you the first order
+ 
+
+ align:start position:0%
+gives you the first order
+uh idea and
+
+ align:start position:0%
+uh idea and
+ 
+
+ align:start position:0%
+uh idea and
+but you have to realize also of the
+
+ align:start position:0%
+but you have to realize also of the
+ 
+
+ align:start position:0%
+but you have to realize also of the
+different order of magnitude of the
+
+ align:start position:0%
+different order of magnitude of the
+ 
+
+ align:start position:0%
+different order of magnitude of the
+strengths of the bonds with respect to
+
+ align:start position:0%
+strengths of the bonds with respect to
+ 
+
+ align:start position:0%
+strengths of the bonds with respect to
+the V vales
+
+ align:start position:0%
+the V vales
+ 
+
+ align:start position:0%
+the V vales
+forces okay so yeah let's stop here I
+
+ align:start position:0%
+forces okay so yeah let's stop here I
+ 
+
+ align:start position:0%
+forces okay so yeah let's stop here I
+guess yeah
\ No newline at end of file
diff --git a/Ea2YTXJrhkM.txt b/Ea2YTXJrhkM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..96fd596f960c6d9710362239d420dcd56da5b2a2
--- /dev/null
+++ b/Ea2YTXJrhkM.txt
@@ -0,0 +1,11731 @@
+align:start position:0%
+ 
+okay well i guess
+
+ align:start position:0%
+okay well i guess
+ 
+
+ align:start position:0%
+okay well i guess
+i'll get started and let people trickle
+
+ align:start position:0%
+i'll get started and let people trickle
+ 
+
+ align:start position:0%
+i'll get started and let people trickle
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+if anybody else is coming in so my name
+
+ align:start position:0%
+if anybody else is coming in so my name
+ 
+
+ align:start position:0%
+if anybody else is coming in so my name
+is john grimes
+
+ align:start position:0%
+is john grimes
+ 
+
+ align:start position:0%
+is john grimes
+and i work in the chemistry department's
+
+ align:start position:0%
+and i work in the chemistry department's
+ 
+
+ align:start position:0%
+and i work in the chemistry department's
+instrumentation facility
+
+ align:start position:0%
+instrumentation facility
+ 
+
+ align:start position:0%
+instrumentation facility
+and down there we've got a number of
+
+ align:start position:0%
+and down there we've got a number of
+ 
+
+ align:start position:0%
+and down there we've got a number of
+different instruments
+
+ align:start position:0%
+different instruments
+ 
+
+ align:start position:0%
+different instruments
+we have five mass spec instruments
+
+ align:start position:0%
+we have five mass spec instruments
+ 
+
+ align:start position:0%
+we have five mass spec instruments
+that is not my specialty so other than
+
+ align:start position:0%
+that is not my specialty so other than
+ 
+
+ align:start position:0%
+that is not my specialty so other than
+being able to point them out i can't
+
+ align:start position:0%
+being able to point them out i can't
+ 
+
+ align:start position:0%
+being able to point them out i can't
+really tell you that much about them
+
+ align:start position:0%
+really tell you that much about them
+ 
+
+ align:start position:0%
+really tell you that much about them
+i help run the nmrs and so
+
+ align:start position:0%
+i help run the nmrs and so
+ 
+
+ align:start position:0%
+i help run the nmrs and so
+what i do is i teach students how to use
+
+ align:start position:0%
+what i do is i teach students how to use
+ 
+
+ align:start position:0%
+what i do is i teach students how to use
+the nmrs
+
+ align:start position:0%
+the nmrs
+ 
+
+ align:start position:0%
+the nmrs
+i will help them select what experiments
+
+ align:start position:0%
+i will help them select what experiments
+ 
+
+ align:start position:0%
+i will help them select what experiments
+they possibly need to use in order to
+
+ align:start position:0%
+they possibly need to use in order to
+ 
+
+ align:start position:0%
+they possibly need to use in order to
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+give them the answer that they're
+
+ align:start position:0%
+give them the answer that they're
+ 
+
+ align:start position:0%
+give them the answer that they're
+looking for
+
+ align:start position:0%
+looking for
+ 
+
+ align:start position:0%
+looking for
+and i'll also help them interpret the
+
+ align:start position:0%
+and i'll also help them interpret the
+ 
+
+ align:start position:0%
+and i'll also help them interpret the
+data or at least
+
+ align:start position:0%
+data or at least
+ 
+
+ align:start position:0%
+data or at least
+get them started off on interpreting the
+
+ align:start position:0%
+get them started off on interpreting the
+ 
+
+ align:start position:0%
+get them started off on interpreting the
+data so that they can
+
+ align:start position:0%
+data so that they can
+ 
+
+ align:start position:0%
+data so that they can
+do that on their own when they're doing
+
+ align:start position:0%
+do that on their own when they're doing
+ 
+
+ align:start position:0%
+do that on their own when they're doing
+their own research
+
+ align:start position:0%
+their own research
+ 
+
+ align:start position:0%
+their own research
+so what i hope to talk to you about
+
+ align:start position:0%
+so what i hope to talk to you about
+ 
+
+ align:start position:0%
+so what i hope to talk to you about
+today is
+
+ align:start position:0%
+today is
+ 
+
+ align:start position:0%
+today is
+what an nmr instrument is
+
+ align:start position:0%
+what an nmr instrument is
+ 
+
+ align:start position:0%
+what an nmr instrument is
+what it actually consists of as far as
+
+ align:start position:0%
+what it actually consists of as far as
+ 
+
+ align:start position:0%
+what it actually consists of as far as
+the parts
+
+ align:start position:0%
+the parts
+ 
+
+ align:start position:0%
+the parts
+what the analytical technique of nmr
+
+ align:start position:0%
+what the analytical technique of nmr
+ 
+
+ align:start position:0%
+what the analytical technique of nmr
+is and how we measure the signal
+
+ align:start position:0%
+is and how we measure the signal
+ 
+
+ align:start position:0%
+is and how we measure the signal
+and then go into some examples of how to
+
+ align:start position:0%
+and then go into some examples of how to
+ 
+
+ align:start position:0%
+and then go into some examples of how to
+interpret the data
+
+ align:start position:0%
+interpret the data
+ 
+
+ align:start position:0%
+interpret the data
+so you know here's a picture of one of
+
+ align:start position:0%
+so you know here's a picture of one of
+ 
+
+ align:start position:0%
+so you know here's a picture of one of
+our instruments there and here's an
+
+ align:start position:0%
+our instruments there and here's an
+ 
+
+ align:start position:0%
+our instruments there and here's an
+example spectrum
+
+ align:start position:0%
+example spectrum
+ 
+
+ align:start position:0%
+example spectrum
+of adenosine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so nuclear magnetic resonance is what
+
+ align:start position:0%
+so nuclear magnetic resonance is what
+ 
+
+ align:start position:0%
+so nuclear magnetic resonance is what
+nmr stands for
+
+ align:start position:0%
+nmr stands for
+ 
+
+ align:start position:0%
+nmr stands for
+and it's the study of molecular
+
+ align:start position:0%
+and it's the study of molecular
+ 
+
+ align:start position:0%
+and it's the study of molecular
+structure by
+
+ align:start position:0%
+structure by
+ 
+
+ align:start position:0%
+structure by
+measuring the interaction of radio
+
+ align:start position:0%
+measuring the interaction of radio
+ 
+
+ align:start position:0%
+measuring the interaction of radio
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+energy with a collection of nuclei that
+
+ align:start position:0%
+energy with a collection of nuclei that
+ 
+
+ align:start position:0%
+energy with a collection of nuclei that
+you've taken
+
+ align:start position:0%
+you've taken
+ 
+
+ align:start position:0%
+you've taken
+and you've put into a strong magnetic
+
+ align:start position:0%
+and you've put into a strong magnetic
+ 
+
+ align:start position:0%
+and you've put into a strong magnetic
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+so it's an analytical technique that is
+
+ align:start position:0%
+so it's an analytical technique that is
+ 
+
+ align:start position:0%
+so it's an analytical technique that is
+based
+
+ align:start position:0%
+based
+ 
+
+ align:start position:0%
+based
+on nucleuses or nuclei
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intrinsic angular momentum
+
+ align:start position:0%
+intrinsic angular momentum
+ 
+
+ align:start position:0%
+intrinsic angular momentum
+it is a non-destructive analytical
+
+ align:start position:0%
+it is a non-destructive analytical
+ 
+
+ align:start position:0%
+it is a non-destructive analytical
+technique
+
+ align:start position:0%
+technique
+ 
+
+ align:start position:0%
+technique
+and that's important if you're a
+
+ align:start position:0%
+and that's important if you're a
+ 
+
+ align:start position:0%
+and that's important if you're a
+graduate student
+
+ align:start position:0%
+graduate student
+ 
+
+ align:start position:0%
+graduate student
+in the chemistry department wherever
+
+ align:start position:0%
+in the chemistry department wherever
+ 
+
+ align:start position:0%
+in the chemistry department wherever
+even an undergraduate
+
+ align:start position:0%
+even an undergraduate
+ 
+
+ align:start position:0%
+even an undergraduate
+and you have worked long and hard to
+
+ align:start position:0%
+and you have worked long and hard to
+ 
+
+ align:start position:0%
+and you have worked long and hard to
+synthesize
+
+ align:start position:0%
+synthesize
+ 
+
+ align:start position:0%
+synthesize
+some natural product that's you know 15
+
+ align:start position:0%
+some natural product that's you know 15
+ 
+
+ align:start position:0%
+some natural product that's you know 15
+steps into a synthesis
+
+ align:start position:0%
+steps into a synthesis
+ 
+
+ align:start position:0%
+steps into a synthesis
+you've only got a half milligram of that
+
+ align:start position:0%
+you've only got a half milligram of that
+ 
+
+ align:start position:0%
+you've only got a half milligram of that
+and it's
+
+ align:start position:0%
+and it's
+ 
+
+ align:start position:0%
+and it's
+a year's worth of your life's work you
+
+ align:start position:0%
+a year's worth of your life's work you
+ 
+
+ align:start position:0%
+a year's worth of your life's work you
+don't want
+
+ align:start position:0%
+don't want
+ 
+
+ align:start position:0%
+don't want
+to destroy that sample analyzing it so
+
+ align:start position:0%
+to destroy that sample analyzing it so
+ 
+
+ align:start position:0%
+to destroy that sample analyzing it so
+you can take that sample
+
+ align:start position:0%
+you can take that sample
+ 
+
+ align:start position:0%
+you can take that sample
+and you can put it in a small little
+
+ align:start position:0%
+and you can put it in a small little
+ 
+
+ align:start position:0%
+and you can put it in a small little
+cylindrical glass tube
+
+ align:start position:0%
+cylindrical glass tube
+ 
+
+ align:start position:0%
+cylindrical glass tube
+you can analyze it and then you can take
+
+ align:start position:0%
+you can analyze it and then you can take
+ 
+
+ align:start position:0%
+you can analyze it and then you can take
+that sample back out
+
+ align:start position:0%
+that sample back out
+ 
+
+ align:start position:0%
+that sample back out
+and use it for something else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the technique allows you
+
+ align:start position:0%
+so the technique allows you
+ 
+
+ align:start position:0%
+so the technique allows you
+to determine connectivity within a
+
+ align:start position:0%
+to determine connectivity within a
+ 
+
+ align:start position:0%
+to determine connectivity within a
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+so i've drawn this is something i'll
+
+ align:start position:0%
+so i've drawn this is something i'll
+ 
+
+ align:start position:0%
+so i've drawn this is something i'll
+bring up a spectrum of later it's just
+
+ align:start position:0%
+bring up a spectrum of later it's just
+ 
+
+ align:start position:0%
+bring up a spectrum of later it's just
+3-heptanone but it will allow you to see
+
+ align:start position:0%
+3-heptanone but it will allow you to see
+ 
+
+ align:start position:0%
+3-heptanone but it will allow you to see
+that protons on this terminal carbon
+
+ align:start position:0%
+that protons on this terminal carbon
+ 
+
+ align:start position:0%
+that protons on this terminal carbon
+are connected to that and next to a
+
+ align:start position:0%
+are connected to that and next to a
+ 
+
+ align:start position:0%
+are connected to that and next to a
+carbon here that has two protons on it
+
+ align:start position:0%
+carbon here that has two protons on it
+ 
+
+ align:start position:0%
+carbon here that has two protons on it
+so it looks
+
+ align:start position:0%
+so it looks
+ 
+
+ align:start position:0%
+so it looks
+through bond connectivity and it won't
+
+ align:start position:0%
+through bond connectivity and it won't
+ 
+
+ align:start position:0%
+through bond connectivity and it won't
+necessarily give you connectivity
+
+ align:start position:0%
+necessarily give you connectivity
+ 
+
+ align:start position:0%
+necessarily give you connectivity
+all the way through the molecule but you
+
+ align:start position:0%
+all the way through the molecule but you
+ 
+
+ align:start position:0%
+all the way through the molecule but you
+can build up say this chunk of the
+
+ align:start position:0%
+can build up say this chunk of the
+ 
+
+ align:start position:0%
+can build up say this chunk of the
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+and this chunk and then you can link it
+
+ align:start position:0%
+and this chunk and then you can link it
+ 
+
+ align:start position:0%
+and this chunk and then you can link it
+together picture linking together a
+
+ align:start position:0%
+together picture linking together a
+ 
+
+ align:start position:0%
+together picture linking together a
+chain
+
+ align:start position:0%
+chain
+ 
+
+ align:start position:0%
+chain
+that allows you to put together the
+
+ align:start position:0%
+that allows you to put together the
+ 
+
+ align:start position:0%
+that allows you to put together the
+whole molecule
+
+ align:start position:0%
+whole molecule
+ 
+
+ align:start position:0%
+whole molecule
+it will also show you interactions
+
+ align:start position:0%
+it will also show you interactions
+ 
+
+ align:start position:0%
+it will also show you interactions
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+space i'm not going to embarrass myself
+
+ align:start position:0%
+space i'm not going to embarrass myself
+ 
+
+ align:start position:0%
+space i'm not going to embarrass myself
+and try and draw
+
+ align:start position:0%
+and try and draw
+ 
+
+ align:start position:0%
+and try and draw
+a protein but there can be two parts of
+
+ align:start position:0%
+a protein but there can be two parts of
+ 
+
+ align:start position:0%
+a protein but there can be two parts of
+a molecule
+
+ align:start position:0%
+a molecule
+ 
+
+ align:start position:0%
+a molecule
+that are hundreds of atoms away from
+
+ align:start position:0%
+that are hundreds of atoms away from
+ 
+
+ align:start position:0%
+that are hundreds of atoms away from
+each other if you were to try and go
+
+ align:start position:0%
+each other if you were to try and go
+ 
+
+ align:start position:0%
+each other if you were to try and go
+through the chemical bonds yet they're
+
+ align:start position:0%
+through the chemical bonds yet they're
+ 
+
+ align:start position:0%
+through the chemical bonds yet they're
+held near each other in space
+
+ align:start position:0%
+held near each other in space
+ 
+
+ align:start position:0%
+held near each other in space
+and you can monitor how close they are
+
+ align:start position:0%
+and you can monitor how close they are
+ 
+
+ align:start position:0%
+and you can monitor how close they are
+and that helps determine the
+
+ align:start position:0%
+and that helps determine the
+ 
+
+ align:start position:0%
+and that helps determine the
+three-dimensional structure of molecules
+
+ align:start position:0%
+three-dimensional structure of molecules
+ 
+
+ align:start position:0%
+three-dimensional structure of molecules
+and so all the
+
+ align:start position:0%
+and so all the
+ 
+
+ align:start position:0%
+and so all the
+time protein structures are solved by
+
+ align:start position:0%
+time protein structures are solved by
+ 
+
+ align:start position:0%
+time protein structures are solved by
+nmr
+
+ align:start position:0%
+nmr
+ 
+
+ align:start position:0%
+nmr
+and you can use it to monitor other
+
+ align:start position:0%
+and you can use it to monitor other
+ 
+
+ align:start position:0%
+and you can use it to monitor other
+processes too
+
+ align:start position:0%
+processes too
+ 
+
+ align:start position:0%
+processes too
+such as whether a protein is bound a
+
+ align:start position:0%
+such as whether a protein is bound a
+ 
+
+ align:start position:0%
+such as whether a protein is bound a
+small molecule
+
+ align:start position:0%
+small molecule
+ 
+
+ align:start position:0%
+small molecule
+whether there's hindered rotation about
+
+ align:start position:0%
+whether there's hindered rotation about
+ 
+
+ align:start position:0%
+whether there's hindered rotation about
+a bond so something like where'd my
+
+ align:start position:0%
+a bond so something like where'd my
+ 
+
+ align:start position:0%
+a bond so something like where'd my
+chalk go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you take something like dimethyl
+
+ align:start position:0%
+if you take something like dimethyl
+ 
+
+ align:start position:0%
+if you take something like dimethyl
+mamid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this bond here has partial double bond
+
+ align:start position:0%
+this bond here has partial double bond
+ 
+
+ align:start position:0%
+this bond here has partial double bond
+character
+
+ align:start position:0%
+character
+ 
+
+ align:start position:0%
+character
+and you can see separate peaks for those
+
+ align:start position:0%
+and you can see separate peaks for those
+ 
+
+ align:start position:0%
+and you can see separate peaks for those
+methyl groups
+
+ align:start position:0%
+methyl groups
+ 
+
+ align:start position:0%
+methyl groups
+and you can rationalize it by the
+
+ align:start position:0%
+and you can rationalize it by the
+ 
+
+ align:start position:0%
+and you can rationalize it by the
+hindered rotation around that bond
+
+ align:start position:0%
+hindered rotation around that bond
+ 
+
+ align:start position:0%
+hindered rotation around that bond
+so and there are even other techniques
+
+ align:start position:0%
+so and there are even other techniques
+ 
+
+ align:start position:0%
+so and there are even other techniques
+and so everybody is going to be familiar
+
+ align:start position:0%
+and so everybody is going to be familiar
+ 
+
+ align:start position:0%
+and so everybody is going to be familiar
+with what nmr is and hopefully none of
+
+ align:start position:0%
+with what nmr is and hopefully none of
+ 
+
+ align:start position:0%
+with what nmr is and hopefully none of
+you have had to have one but it's the
+
+ align:start position:0%
+you have had to have one but it's the
+ 
+
+ align:start position:0%
+you have had to have one but it's the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+physical technique as an mri so
+
+ align:start position:0%
+physical technique as an mri so
+ 
+
+ align:start position:0%
+physical technique as an mri so
+here's an mri of unfortunately my
+
+ align:start position:0%
+here's an mri of unfortunately my
+ 
+
+ align:start position:0%
+here's an mri of unfortunately my
+daughter's head after she swam into the
+
+ align:start position:0%
+daughter's head after she swam into the
+ 
+
+ align:start position:0%
+daughter's head after she swam into the
+pool end in a swim match
+
+ align:start position:0%
+pool end in a swim match
+ 
+
+ align:start position:0%
+pool end in a swim match
+nothing happened to her but you can take
+
+ align:start position:0%
+nothing happened to her but you can take
+ 
+
+ align:start position:0%
+nothing happened to her but you can take
+pictures
+
+ align:start position:0%
+pictures
+ 
+
+ align:start position:0%
+pictures
+with nmr in the past i've used it to
+
+ align:start position:0%
+with nmr in the past i've used it to
+ 
+
+ align:start position:0%
+with nmr in the past i've used it to
+take pictures of
+
+ align:start position:0%
+take pictures of
+ 
+
+ align:start position:0%
+take pictures of
+insects you can also
+
+ align:start position:0%
+insects you can also
+ 
+
+ align:start position:0%
+insects you can also
+do analytical techniques in vitro
+
+ align:start position:0%
+do analytical techniques in vitro
+ 
+
+ align:start position:0%
+do analytical techniques in vitro
+diagnostics so
+
+ align:start position:0%
+diagnostics so
+ 
+
+ align:start position:0%
+diagnostics so
+there's a test out there called the nmr
+
+ align:start position:0%
+there's a test out there called the nmr
+ 
+
+ align:start position:0%
+there's a test out there called the nmr
+lipoprofile
+
+ align:start position:0%
+lipoprofile
+ 
+
+ align:start position:0%
+lipoprofile
+and it will analyze your cholesterol
+
+ align:start position:0%
+and it will analyze your cholesterol
+ 
+
+ align:start position:0%
+and it will analyze your cholesterol
+i.e the density or the concentration of
+
+ align:start position:0%
+i.e the density or the concentration of
+ 
+
+ align:start position:0%
+i.e the density or the concentration of
+lipoproteins that's circulating around
+
+ align:start position:0%
+lipoproteins that's circulating around
+ 
+
+ align:start position:0%
+lipoproteins that's circulating around
+in your blood
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what is an nmr instrument
+
+ align:start position:0%
+so what is an nmr instrument
+ 
+
+ align:start position:0%
+so what is an nmr instrument
+um nmr instruments come in
+
+ align:start position:0%
+um nmr instruments come in
+ 
+
+ align:start position:0%
+um nmr instruments come in
+two flavors or at least maybe they come
+
+ align:start position:0%
+two flavors or at least maybe they come
+ 
+
+ align:start position:0%
+two flavors or at least maybe they come
+in more flavors but here at mit we have
+
+ align:start position:0%
+in more flavors but here at mit we have
+ 
+
+ align:start position:0%
+in more flavors but here at mit we have
+two types of nmr instruments
+
+ align:start position:0%
+two types of nmr instruments
+ 
+
+ align:start position:0%
+two types of nmr instruments
+there are ones that are referred to as
+
+ align:start position:0%
+there are ones that are referred to as
+ 
+
+ align:start position:0%
+there are ones that are referred to as
+high resolution instruments which
+
+ align:start position:0%
+high resolution instruments which
+ 
+
+ align:start position:0%
+high resolution instruments which
+generally have a stronger
+
+ align:start position:0%
+generally have a stronger
+ 
+
+ align:start position:0%
+generally have a stronger
+magnet and they're bigger they're also
+
+ align:start position:0%
+magnet and they're bigger they're also
+ 
+
+ align:start position:0%
+magnet and they're bigger they're also
+dust they're not desktop but benchtop
+
+ align:start position:0%
+dust they're not desktop but benchtop
+ 
+
+ align:start position:0%
+dust they're not desktop but benchtop
+instruments which is what you're going
+
+ align:start position:0%
+instruments which is what you're going
+ 
+
+ align:start position:0%
+instruments which is what you're going
+to use
+
+ align:start position:0%
+to use
+ 
+
+ align:start position:0%
+to use
+in your lab so each of these has the
+
+ align:start position:0%
+in your lab so each of these has the
+ 
+
+ align:start position:0%
+in your lab so each of these has the
+exact
+
+ align:start position:0%
+exact
+ 
+
+ align:start position:0%
+exact
+same constituent parts
+
+ align:start position:0%
+same constituent parts
+ 
+
+ align:start position:0%
+same constituent parts
+i didn't go over and try and take your
+
+ align:start position:0%
+i didn't go over and try and take your
+ 
+
+ align:start position:0%
+i didn't go over and try and take your
+bench top instrument apart to get a
+
+ align:start position:0%
+bench top instrument apart to get a
+ 
+
+ align:start position:0%
+bench top instrument apart to get a
+picture of those parts because i
+
+ align:start position:0%
+picture of those parts because i
+ 
+
+ align:start position:0%
+picture of those parts because i
+wouldn't have gotten it back together
+
+ align:start position:0%
+wouldn't have gotten it back together
+ 
+
+ align:start position:0%
+wouldn't have gotten it back together
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it would have never worked so i'm going
+
+ align:start position:0%
+it would have never worked so i'm going
+ 
+
+ align:start position:0%
+it would have never worked so i'm going
+to go through one of our instruments and
+
+ align:start position:0%
+to go through one of our instruments and
+ 
+
+ align:start position:0%
+to go through one of our instruments and
+show you
+
+ align:start position:0%
+show you
+ 
+
+ align:start position:0%
+show you
+the individual parts but keep in mind
+
+ align:start position:0%
+the individual parts but keep in mind
+ 
+
+ align:start position:0%
+the individual parts but keep in mind
+it's the exact same thing
+
+ align:start position:0%
+it's the exact same thing
+ 
+
+ align:start position:0%
+it's the exact same thing
+that's in the instrument that you'll be
+
+ align:start position:0%
+that's in the instrument that you'll be
+ 
+
+ align:start position:0%
+that's in the instrument that you'll be
+using
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you got to have a strong magnetic
+
+ align:start position:0%
+so you got to have a strong magnetic
+ 
+
+ align:start position:0%
+so you got to have a strong magnetic
+field to immerse your sample
+
+ align:start position:0%
+field to immerse your sample
+ 
+
+ align:start position:0%
+field to immerse your sample
+in and obviously that's supplied by a
+
+ align:start position:0%
+in and obviously that's supplied by a
+ 
+
+ align:start position:0%
+in and obviously that's supplied by a
+strong magnet
+
+ align:start position:0%
+strong magnet
+ 
+
+ align:start position:0%
+strong magnet
+so magnets will come in two flavors
+
+ align:start position:0%
+so magnets will come in two flavors
+ 
+
+ align:start position:0%
+so magnets will come in two flavors
+in the benchtop instruments they are a
+
+ align:start position:0%
+in the benchtop instruments they are a
+ 
+
+ align:start position:0%
+in the benchtop instruments they are a
+permanent magnet has anybody ever taken
+
+ align:start position:0%
+permanent magnet has anybody ever taken
+ 
+
+ align:start position:0%
+permanent magnet has anybody ever taken
+apart
+
+ align:start position:0%
+apart
+ 
+
+ align:start position:0%
+apart
+old computers and you can get the hard
+
+ align:start position:0%
+old computers and you can get the hard
+ 
+
+ align:start position:0%
+old computers and you can get the hard
+drives and their
+
+ align:start position:0%
+drives and their
+ 
+
+ align:start position:0%
+drives and their
+strong magnets in there that are sort of
+
+ align:start position:0%
+strong magnets in there that are sort of
+ 
+
+ align:start position:0%
+strong magnets in there that are sort of
+silver colored
+
+ align:start position:0%
+silver colored
+ 
+
+ align:start position:0%
+silver colored
+those are made from a neodymium iron
+
+ align:start position:0%
+those are made from a neodymium iron
+ 
+
+ align:start position:0%
+those are made from a neodymium iron
+boron
+
+ align:start position:0%
+boron
+ 
+
+ align:start position:0%
+boron
+alloy and that is what they use for the
+
+ align:start position:0%
+alloy and that is what they use for the
+ 
+
+ align:start position:0%
+alloy and that is what they use for the
+permanent magnets that are in the
+
+ align:start position:0%
+permanent magnets that are in the
+ 
+
+ align:start position:0%
+permanent magnets that are in the
+benchtop systems
+
+ align:start position:0%
+benchtop systems
+ 
+
+ align:start position:0%
+benchtop systems
+there's been a great improvement in
+
+ align:start position:0%
+there's been a great improvement in
+ 
+
+ align:start position:0%
+there's been a great improvement in
+those in the past
+
+ align:start position:0%
+those in the past
+ 
+
+ align:start position:0%
+those in the past
+i guess 15 years or so there used not to
+
+ align:start position:0%
+i guess 15 years or so there used not to
+ 
+
+ align:start position:0%
+i guess 15 years or so there used not to
+be any bench top instruments it was
+
+ align:start position:0%
+be any bench top instruments it was
+ 
+
+ align:start position:0%
+be any bench top instruments it was
+difficult to engineer and machine
+
+ align:start position:0%
+difficult to engineer and machine
+ 
+
+ align:start position:0%
+difficult to engineer and machine
+permanent magnets that would give a
+
+ align:start position:0%
+permanent magnets that would give a
+ 
+
+ align:start position:0%
+permanent magnets that would give a
+uniform magnetic field
+
+ align:start position:0%
+uniform magnetic field
+ 
+
+ align:start position:0%
+uniform magnetic field
+but they've been able to do that and so
+
+ align:start position:0%
+but they've been able to do that and so
+ 
+
+ align:start position:0%
+but they've been able to do that and so
+there are a lot of bench top instruments
+
+ align:start position:0%
+there are a lot of bench top instruments
+ 
+
+ align:start position:0%
+there are a lot of bench top instruments
+that are out there now
+
+ align:start position:0%
+that are out there now
+ 
+
+ align:start position:0%
+that are out there now
+the standard nmr and they are for
+
+ align:start position:0%
+the standard nmr and they are for
+ 
+
+ align:start position:0%
+the standard nmr and they are for
+well they're termed high resolution nmrs
+
+ align:start position:0%
+well they're termed high resolution nmrs
+ 
+
+ align:start position:0%
+well they're termed high resolution nmrs
+because they have stronger magnetic
+
+ align:start position:0%
+because they have stronger magnetic
+ 
+
+ align:start position:0%
+because they have stronger magnetic
+fields that can be
+
+ align:start position:0%
+fields that can be
+ 
+
+ align:start position:0%
+fields that can be
+then can be generated from permanent
+
+ align:start position:0%
+then can be generated from permanent
+ 
+
+ align:start position:0%
+then can be generated from permanent
+magnets
+
+ align:start position:0%
+magnets
+ 
+
+ align:start position:0%
+magnets
+use what are called superconducting
+
+ align:start position:0%
+use what are called superconducting
+ 
+
+ align:start position:0%
+use what are called superconducting
+magnets so the magnetic field
+
+ align:start position:0%
+magnets so the magnetic field
+ 
+
+ align:start position:0%
+magnets so the magnetic field
+is generated by the circulation of
+
+ align:start position:0%
+is generated by the circulation of
+ 
+
+ align:start position:0%
+is generated by the circulation of
+electric
+
+ align:start position:0%
+electric
+ 
+
+ align:start position:0%
+electric
+charge in a superconductor
+
+ align:start position:0%
+charge in a superconductor
+ 
+
+ align:start position:0%
+charge in a superconductor
+and if you're familiar with
+
+ align:start position:0%
+and if you're familiar with
+ 
+
+ align:start position:0%
+and if you're familiar with
+superconductors
+
+ align:start position:0%
+superconductors
+ 
+
+ align:start position:0%
+superconductors
+usually they have to be below some
+
+ align:start position:0%
+usually they have to be below some
+ 
+
+ align:start position:0%
+usually they have to be below some
+specific temperature in order to
+
+ align:start position:0%
+specific temperature in order to
+ 
+
+ align:start position:0%
+specific temperature in order to
+maintain their conductivity
+
+ align:start position:0%
+maintain their conductivity
+ 
+
+ align:start position:0%
+maintain their conductivity
+while the temperature of the critical
+
+ align:start position:0%
+while the temperature of the critical
+ 
+
+ align:start position:0%
+while the temperature of the critical
+temperature has come
+
+ align:start position:0%
+temperature has come
+ 
+
+ align:start position:0%
+temperature has come
+up in recent years for superconductors
+
+ align:start position:0%
+up in recent years for superconductors
+ 
+
+ align:start position:0%
+up in recent years for superconductors
+as far as producing something that's
+
+ align:start position:0%
+as far as producing something that's
+ 
+
+ align:start position:0%
+as far as producing something that's
+easily machinable
+
+ align:start position:0%
+easily machinable
+ 
+
+ align:start position:0%
+easily machinable
+into wire that you can wrap into a coil
+
+ align:start position:0%
+into wire that you can wrap into a coil
+ 
+
+ align:start position:0%
+into wire that you can wrap into a coil
+they haven't
+
+ align:start position:0%
+they haven't
+ 
+
+ align:start position:0%
+they haven't
+the higher temperature higher critical
+
+ align:start position:0%
+the higher temperature higher critical
+ 
+
+ align:start position:0%
+the higher temperature higher critical
+temperature superconductors aren't
+
+ align:start position:0%
+temperature superconductors aren't
+ 
+
+ align:start position:0%
+temperature superconductors aren't
+easily
+
+ align:start position:0%
+easily
+ 
+
+ align:start position:0%
+easily
+malleable so you still have to use
+
+ align:start position:0%
+malleable so you still have to use
+ 
+
+ align:start position:0%
+malleable so you still have to use
+something that you've got to get really
+
+ align:start position:0%
+something that you've got to get really
+ 
+
+ align:start position:0%
+something that you've got to get really
+cold
+
+ align:start position:0%
+cold
+ 
+
+ align:start position:0%
+cold
+i.e down to liquid helium temperature
+
+ align:start position:0%
+i.e down to liquid helium temperature
+ 
+
+ align:start position:0%
+i.e down to liquid helium temperature
+so in a superconducting magnet you've
+
+ align:start position:0%
+so in a superconducting magnet you've
+ 
+
+ align:start position:0%
+so in a superconducting magnet you've
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+but think of it as a giant thermos which
+
+ align:start position:0%
+but think of it as a giant thermos which
+ 
+
+ align:start position:0%
+but think of it as a giant thermos which
+is what this can
+
+ align:start position:0%
+is what this can
+ 
+
+ align:start position:0%
+is what this can
+is you've got a hole through the center
+
+ align:start position:0%
+is you've got a hole through the center
+ 
+
+ align:start position:0%
+is you've got a hole through the center
+which is called the room temperature
+
+ align:start position:0%
+which is called the room temperature
+ 
+
+ align:start position:0%
+which is called the room temperature
+bore it's room temperature because it is
+
+ align:start position:0%
+bore it's room temperature because it is
+ 
+
+ align:start position:0%
+bore it's room temperature because it is
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+cold your sample
+
+ align:start position:0%
+cold your sample
+ 
+
+ align:start position:0%
+cold your sample
+which is in this little tube that i
+
+ align:start position:0%
+which is in this little tube that i
+ 
+
+ align:start position:0%
+which is in this little tube that i
+showed you
+
+ align:start position:0%
+showed you
+ 
+
+ align:start position:0%
+showed you
+generally will be held in
+
+ align:start position:0%
+generally will be held in
+ 
+
+ align:start position:0%
+generally will be held in
+what's called a spinner so this little
+
+ align:start position:0%
+what's called a spinner so this little
+ 
+
+ align:start position:0%
+what's called a spinner so this little
+blue thing you will put it in the top of
+
+ align:start position:0%
+blue thing you will put it in the top of
+ 
+
+ align:start position:0%
+blue thing you will put it in the top of
+the magnet
+
+ align:start position:0%
+the magnet
+ 
+
+ align:start position:0%
+the magnet
+and it will just ride down on a cushion
+
+ align:start position:0%
+and it will just ride down on a cushion
+ 
+
+ align:start position:0%
+and it will just ride down on a cushion
+of air
+
+ align:start position:0%
+of air
+ 
+
+ align:start position:0%
+of air
+somewhere to about there in the center
+
+ align:start position:0%
+somewhere to about there in the center
+ 
+
+ align:start position:0%
+somewhere to about there in the center
+of mag in the center of the magnet
+
+ align:start position:0%
+of mag in the center of the magnet
+ 
+
+ align:start position:0%
+of mag in the center of the magnet
+on the bench top instrument what's nice
+
+ align:start position:0%
+on the bench top instrument what's nice
+ 
+
+ align:start position:0%
+on the bench top instrument what's nice
+let's see if we can back up the slide
+
+ align:start position:0%
+let's see if we can back up the slide
+ 
+
+ align:start position:0%
+let's see if we can back up the slide
+um all you do you can see it and it'll
+
+ align:start position:0%
+um all you do you can see it and it'll
+ 
+
+ align:start position:0%
+um all you do you can see it and it'll
+be obvious when you run it in the lab
+
+ align:start position:0%
+be obvious when you run it in the lab
+ 
+
+ align:start position:0%
+be obvious when you run it in the lab
+for yourself you just put the tube right
+
+ align:start position:0%
+for yourself you just put the tube right
+ 
+
+ align:start position:0%
+for yourself you just put the tube right
+down in there you don't have to put it
+
+ align:start position:0%
+down in there you don't have to put it
+ 
+
+ align:start position:0%
+down in there you don't have to put it
+in any
+
+ align:start position:0%
+in any
+ 
+
+ align:start position:0%
+in any
+specific holder so
+
+ align:start position:0%
+specific holder so
+ 
+
+ align:start position:0%
+specific holder so
+your sample tube goes down that bore
+
+ align:start position:0%
+your sample tube goes down that bore
+ 
+
+ align:start position:0%
+your sample tube goes down that bore
+from underneath
+
+ align:start position:0%
+from underneath
+ 
+
+ align:start position:0%
+from underneath
+the instrument comes the nmr probe which
+
+ align:start position:0%
+the instrument comes the nmr probe which
+ 
+
+ align:start position:0%
+the instrument comes the nmr probe which
+i'll
+
+ align:start position:0%
+i'll
+ 
+
+ align:start position:0%
+i'll
+talk about in a second so that
+
+ align:start position:0%
+talk about in a second so that
+ 
+
+ align:start position:0%
+talk about in a second so that
+superconducting wire
+
+ align:start position:0%
+superconducting wire
+ 
+
+ align:start position:0%
+superconducting wire
+is wound in a coil around that room
+
+ align:start position:0%
+is wound in a coil around that room
+ 
+
+ align:start position:0%
+is wound in a coil around that room
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+bore this chamber here which if i can
+
+ align:start position:0%
+bore this chamber here which if i can
+ 
+
+ align:start position:0%
+bore this chamber here which if i can
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+is number six that is a chamber that is
+
+ align:start position:0%
+is number six that is a chamber that is
+ 
+
+ align:start position:0%
+is number six that is a chamber that is
+full of liquid helium so when you set up
+
+ align:start position:0%
+full of liquid helium so when you set up
+ 
+
+ align:start position:0%
+full of liquid helium so when you set up
+one of these magnets
+
+ align:start position:0%
+one of these magnets
+ 
+
+ align:start position:0%
+one of these magnets
+you cool it off you fill that with
+
+ align:start position:0%
+you cool it off you fill that with
+ 
+
+ align:start position:0%
+you cool it off you fill that with
+liquid helium
+
+ align:start position:0%
+liquid helium
+ 
+
+ align:start position:0%
+liquid helium
+and then you put a charge on this
+
+ align:start position:0%
+and then you put a charge on this
+ 
+
+ align:start position:0%
+and then you put a charge on this
+superconducting wire
+
+ align:start position:0%
+superconducting wire
+ 
+
+ align:start position:0%
+superconducting wire
+and the charge is about a hundred to two
+
+ align:start position:0%
+and the charge is about a hundred to two
+ 
+
+ align:start position:0%
+and the charge is about a hundred to two
+hundred amps
+
+ align:start position:0%
+hundred amps
+ 
+
+ align:start position:0%
+hundred amps
+and 200 amps is the amount of charge
+
+ align:start position:0%
+and 200 amps is the amount of charge
+ 
+
+ align:start position:0%
+and 200 amps is the amount of charge
+that goes through a medium-sized house
+
+ align:start position:0%
+that goes through a medium-sized house
+ 
+
+ align:start position:0%
+that goes through a medium-sized house
+so it's got a
+
+ align:start position:0%
+so it's got a
+ 
+
+ align:start position:0%
+so it's got a
+good amount of electricity on there
+
+ align:start position:0%
+good amount of electricity on there
+ 
+
+ align:start position:0%
+good amount of electricity on there
+that's circulating around
+
+ align:start position:0%
+that's circulating around
+ 
+
+ align:start position:0%
+that's circulating around
+as long as you keep it cold meaning as
+
+ align:start position:0%
+as long as you keep it cold meaning as
+ 
+
+ align:start position:0%
+as long as you keep it cold meaning as
+long as you top it off with liquid
+
+ align:start position:0%
+long as you top it off with liquid
+ 
+
+ align:start position:0%
+long as you top it off with liquid
+helium
+
+ align:start position:0%
+helium
+ 
+
+ align:start position:0%
+helium
+every few months it's going to remain a
+
+ align:start position:0%
+every few months it's going to remain a
+ 
+
+ align:start position:0%
+every few months it's going to remain a
+magnet
+
+ align:start position:0%
+magnet
+ 
+
+ align:start position:0%
+magnet
+and generate a powerful field so if you
+
+ align:start position:0%
+and generate a powerful field so if you
+ 
+
+ align:start position:0%
+and generate a powerful field so if you
+just had liquid helium touching metal
+
+ align:start position:0%
+just had liquid helium touching metal
+ 
+
+ align:start position:0%
+just had liquid helium touching metal
+the outside of that metal would be a big
+
+ align:start position:0%
+the outside of that metal would be a big
+ 
+
+ align:start position:0%
+the outside of that metal would be a big
+chunk of ice
+
+ align:start position:0%
+chunk of ice
+ 
+
+ align:start position:0%
+chunk of ice
+so this has an evacuated
+
+ align:start position:0%
+so this has an evacuated
+ 
+
+ align:start position:0%
+so this has an evacuated
+not layer but i guess you know a portion
+
+ align:start position:0%
+not layer but i guess you know a portion
+ 
+
+ align:start position:0%
+not layer but i guess you know a portion
+of it that's evacuated with a high
+
+ align:start position:0%
+of it that's evacuated with a high
+ 
+
+ align:start position:0%
+of it that's evacuated with a high
+vacuum to provide insulation
+
+ align:start position:0%
+vacuum to provide insulation
+ 
+
+ align:start position:0%
+vacuum to provide insulation
+outside of that is a layer of liquid
+
+ align:start position:0%
+outside of that is a layer of liquid
+ 
+
+ align:start position:0%
+outside of that is a layer of liquid
+nitrogen and we fill that weekly
+
+ align:start position:0%
+nitrogen and we fill that weekly
+ 
+
+ align:start position:0%
+nitrogen and we fill that weekly
+and that just cuts down on any thermal
+
+ align:start position:0%
+and that just cuts down on any thermal
+ 
+
+ align:start position:0%
+and that just cuts down on any thermal
+transmission even though you've got a
+
+ align:start position:0%
+transmission even though you've got a
+ 
+
+ align:start position:0%
+transmission even though you've got a
+high
+
+ align:start position:0%
+high
+ 
+
+ align:start position:0%
+high
+vacuum there and then outside of that is
+
+ align:start position:0%
+vacuum there and then outside of that is
+ 
+
+ align:start position:0%
+vacuum there and then outside of that is
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+high vacuum layer and then the room
+
+ align:start position:0%
+high vacuum layer and then the room
+ 
+
+ align:start position:0%
+high vacuum layer and then the room
+and so you can walk up to the can and
+
+ align:start position:0%
+and so you can walk up to the can and
+ 
+
+ align:start position:0%
+and so you can walk up to the can and
+you can touch it and it won't feel cold
+
+ align:start position:0%
+you can touch it and it won't feel cold
+ 
+
+ align:start position:0%
+you can touch it and it won't feel cold
+at all
+
+ align:start position:0%
+at all
+ 
+
+ align:start position:0%
+at all
+so that's what the magnet consists of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the nmr measurement
+
+ align:start position:0%
+um the nmr measurement
+ 
+
+ align:start position:0%
+um the nmr measurement
+is based on the strength of the magnet
+
+ align:start position:0%
+is based on the strength of the magnet
+ 
+
+ align:start position:0%
+is based on the strength of the magnet
+so b naught is what i'm calling that
+
+ align:start position:0%
+so b naught is what i'm calling that
+ 
+
+ align:start position:0%
+so b naught is what i'm calling that
+and the gyromagnetic ratio of the nuclei
+
+ align:start position:0%
+and the gyromagnetic ratio of the nuclei
+ 
+
+ align:start position:0%
+and the gyromagnetic ratio of the nuclei
+that you're looking at we're going to
+
+ align:start position:0%
+that you're looking at we're going to
+ 
+
+ align:start position:0%
+that you're looking at we're going to
+talk about hydrogen today
+
+ align:start position:0%
+talk about hydrogen today
+ 
+
+ align:start position:0%
+talk about hydrogen today
+and so you've got to be able to
+
+ align:start position:0%
+and so you've got to be able to
+ 
+
+ align:start position:0%
+and so you've got to be able to
+synthesize precise
+
+ align:start position:0%
+synthesize precise
+ 
+
+ align:start position:0%
+synthesize precise
+frequencies with precise
+
+ align:start position:0%
+frequencies with precise
+ 
+
+ align:start position:0%
+frequencies with precise
+durations and power levels in order to
+
+ align:start position:0%
+durations and power levels in order to
+ 
+
+ align:start position:0%
+durations and power levels in order to
+send those to your sample
+
+ align:start position:0%
+send those to your sample
+ 
+
+ align:start position:0%
+send those to your sample
+so you've got this console it's got
+
+ align:start position:0%
+so you've got this console it's got
+ 
+
+ align:start position:0%
+so you've got this console it's got
+amplifiers in there
+
+ align:start position:0%
+amplifiers in there
+ 
+
+ align:start position:0%
+amplifiers in there
+you know 100 watt amplifiers is pretty
+
+ align:start position:0%
+you know 100 watt amplifiers is pretty
+ 
+
+ align:start position:0%
+you know 100 watt amplifiers is pretty
+much the standard actually i shouldn't
+
+ align:start position:0%
+much the standard actually i shouldn't
+ 
+
+ align:start position:0%
+much the standard actually i shouldn't
+even say that's the standard i think
+
+ align:start position:0%
+even say that's the standard i think
+ 
+
+ align:start position:0%
+even say that's the standard i think
+ours have 500 watt amplifiers in there
+
+ align:start position:0%
+ours have 500 watt amplifiers in there
+ 
+
+ align:start position:0%
+ours have 500 watt amplifiers in there
+you've got different boards it used to
+
+ align:start position:0%
+you've got different boards it used to
+ 
+
+ align:start position:0%
+you've got different boards it used to
+be that these
+
+ align:start position:0%
+be that these
+ 
+
+ align:start position:0%
+be that these
+all were plugged into these you know
+
+ align:start position:0%
+all were plugged into these you know
+ 
+
+ align:start position:0%
+all were plugged into these you know
+long things with connections and it
+
+ align:start position:0%
+long things with connections and it
+ 
+
+ align:start position:0%
+long things with connections and it
+talked through what was called a
+
+ align:start position:0%
+talked through what was called a
+ 
+
+ align:start position:0%
+talked through what was called a
+backplane
+
+ align:start position:0%
+backplane
+ 
+
+ align:start position:0%
+backplane
+but now that these are modern digital
+
+ align:start position:0%
+but now that these are modern digital
+ 
+
+ align:start position:0%
+but now that these are modern digital
+consoles
+
+ align:start position:0%
+consoles
+ 
+
+ align:start position:0%
+consoles
+it all talks via ethernet so everything
+
+ align:start position:0%
+it all talks via ethernet so everything
+ 
+
+ align:start position:0%
+it all talks via ethernet so everything
+has an address
+
+ align:start position:0%
+has an address
+ 
+
+ align:start position:0%
+has an address
+and it talks to each other it routes the
+
+ align:start position:0%
+and it talks to each other it routes the
+ 
+
+ align:start position:0%
+and it talks to each other it routes the
+signal to where it needs to go
+
+ align:start position:0%
+signal to where it needs to go
+ 
+
+ align:start position:0%
+signal to where it needs to go
+you've also got some pre-amplifiers here
+
+ align:start position:0%
+you've also got some pre-amplifiers here
+ 
+
+ align:start position:0%
+you've also got some pre-amplifiers here
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+all this material or everything that's
+
+ align:start position:0%
+all this material or everything that's
+ 
+
+ align:start position:0%
+all this material or everything that's
+in the console will generate the signal
+
+ align:start position:0%
+in the console will generate the signal
+ 
+
+ align:start position:0%
+in the console will generate the signal
+that is sent to your sample in order to
+
+ align:start position:0%
+that is sent to your sample in order to
+ 
+
+ align:start position:0%
+that is sent to your sample in order to
+excite it the way
+
+ align:start position:0%
+excite it the way
+ 
+
+ align:start position:0%
+excite it the way
+that you need to in order to get the
+
+ align:start position:0%
+that you need to in order to get the
+ 
+
+ align:start position:0%
+that you need to in order to get the
+information out that you want to
+
+ align:start position:0%
+information out that you want to
+ 
+
+ align:start position:0%
+information out that you want to
+this also will take the signal that your
+
+ align:start position:0%
+this also will take the signal that your
+ 
+
+ align:start position:0%
+this also will take the signal that your
+sample gives
+
+ align:start position:0%
+sample gives
+ 
+
+ align:start position:0%
+sample gives
+off and it will amplify it
+
+ align:start position:0%
+off and it will amplify it
+ 
+
+ align:start position:0%
+off and it will amplify it
+and digitize it and send it to the
+
+ align:start position:0%
+and digitize it and send it to the
+ 
+
+ align:start position:0%
+and digitize it and send it to the
+computer
+
+ align:start position:0%
+computer
+ 
+
+ align:start position:0%
+computer
+so that it can be processed into
+
+ align:start position:0%
+so that it can be processed into
+ 
+
+ align:start position:0%
+so that it can be processed into
+something you can use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to send the sample so the console
+
+ align:start position:0%
+to send the sample so the console
+ 
+
+ align:start position:0%
+to send the sample so the console
+generates all that signal but it's got
+
+ align:start position:0%
+generates all that signal but it's got
+ 
+
+ align:start position:0%
+generates all that signal but it's got
+to be broadcast
+
+ align:start position:0%
+to be broadcast
+ 
+
+ align:start position:0%
+to be broadcast
+to your sample somehow and so we think
+
+ align:start position:0%
+to your sample somehow and so we think
+ 
+
+ align:start position:0%
+to your sample somehow and so we think
+of the probe
+
+ align:start position:0%
+of the probe
+ 
+
+ align:start position:0%
+of the probe
+as the nmr antenna so probes can come
+
+ align:start position:0%
+as the nmr antenna so probes can come
+ 
+
+ align:start position:0%
+as the nmr antenna so probes can come
+in a number of different formats there
+
+ align:start position:0%
+in a number of different formats there
+ 
+
+ align:start position:0%
+in a number of different formats there
+can be probes for looking at
+
+ align:start position:0%
+can be probes for looking at
+ 
+
+ align:start position:0%
+can be probes for looking at
+solids so you wouldn't even dissolve
+
+ align:start position:0%
+solids so you wouldn't even dissolve
+ 
+
+ align:start position:0%
+solids so you wouldn't even dissolve
+your sample
+
+ align:start position:0%
+your sample
+ 
+
+ align:start position:0%
+your sample
+in a liquid there can be what are called
+
+ align:start position:0%
+in a liquid there can be what are called
+ 
+
+ align:start position:0%
+in a liquid there can be what are called
+flow probes where you've got just
+
+ align:start position:0%
+flow probes where you've got just
+ 
+
+ align:start position:0%
+flow probes where you've got just
+we call it a cell but it's just a
+
+ align:start position:0%
+we call it a cell but it's just a
+ 
+
+ align:start position:0%
+we call it a cell but it's just a
+container that's a certain volume
+
+ align:start position:0%
+container that's a certain volume
+ 
+
+ align:start position:0%
+container that's a certain volume
+and you pump your sample up through a
+
+ align:start position:0%
+and you pump your sample up through a
+ 
+
+ align:start position:0%
+and you pump your sample up through a
+tube into that cell
+
+ align:start position:0%
+tube into that cell
+ 
+
+ align:start position:0%
+tube into that cell
+analyze it and then you pump it out
+
+ align:start position:0%
+analyze it and then you pump it out
+ 
+
+ align:start position:0%
+analyze it and then you pump it out
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+we call them microcoil probes which just
+
+ align:start position:0%
+we call them microcoil probes which just
+ 
+
+ align:start position:0%
+we call them microcoil probes which just
+has a small cell
+
+ align:start position:0%
+has a small cell
+ 
+
+ align:start position:0%
+has a small cell
+so i've used ones or had them in the
+
+ align:start position:0%
+so i've used ones or had them in the
+ 
+
+ align:start position:0%
+so i've used ones or had them in the
+past in other labs where it had a five
+
+ align:start position:0%
+past in other labs where it had a five
+ 
+
+ align:start position:0%
+past in other labs where it had a five
+microliter cell
+
+ align:start position:0%
+microliter cell
+ 
+
+ align:start position:0%
+microliter cell
+so you could look at just a very small
+
+ align:start position:0%
+so you could look at just a very small
+ 
+
+ align:start position:0%
+so you could look at just a very small
+amount of things there are also probes
+
+ align:start position:0%
+amount of things there are also probes
+ 
+
+ align:start position:0%
+amount of things there are also probes
+that are known as cryogenic probes
+
+ align:start position:0%
+that are known as cryogenic probes
+ 
+
+ align:start position:0%
+that are known as cryogenic probes
+those the electronics that are in the
+
+ align:start position:0%
+those the electronics that are in the
+ 
+
+ align:start position:0%
+those the electronics that are in the
+probe are held at liquid helium or
+
+ align:start position:0%
+probe are held at liquid helium or
+ 
+
+ align:start position:0%
+probe are held at liquid helium or
+liquid nitrogen temperature
+
+ align:start position:0%
+liquid nitrogen temperature
+ 
+
+ align:start position:0%
+liquid nitrogen temperature
+and by doing that it cuts down on the
+
+ align:start position:0%
+and by doing that it cuts down on the
+ 
+
+ align:start position:0%
+and by doing that it cuts down on the
+inherent electric noise that's present
+
+ align:start position:0%
+inherent electric noise that's present
+ 
+
+ align:start position:0%
+inherent electric noise that's present
+in the circuits and it makes them more
+
+ align:start position:0%
+in the circuits and it makes them more
+ 
+
+ align:start position:0%
+in the circuits and it makes them more
+sensitive
+
+ align:start position:0%
+sensitive
+ 
+
+ align:start position:0%
+sensitive
+so i've brought a probe here and you're
+
+ align:start position:0%
+so i've brought a probe here and you're
+ 
+
+ align:start position:0%
+so i've brought a probe here and you're
+not going to be able to see this from
+
+ align:start position:0%
+not going to be able to see this from
+ 
+
+ align:start position:0%
+not going to be able to see this from
+where you're sitting back there but you
+
+ align:start position:0%
+where you're sitting back there but you
+ 
+
+ align:start position:0%
+where you're sitting back there but you
+can come up and look at it later if you
+
+ align:start position:0%
+can come up and look at it later if you
+ 
+
+ align:start position:0%
+can come up and look at it later if you
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+your bench top instrument will have this
+
+ align:start position:0%
+your bench top instrument will have this
+ 
+
+ align:start position:0%
+your bench top instrument will have this
+same stuff in it
+
+ align:start position:0%
+same stuff in it
+ 
+
+ align:start position:0%
+same stuff in it
+it's just not going to look like this
+
+ align:start position:0%
+it's just not going to look like this
+ 
+
+ align:start position:0%
+it's just not going to look like this
+exactly so
+
+ align:start position:0%
+exactly so
+ 
+
+ align:start position:0%
+exactly so
+this is what gets inserted up from the
+
+ align:start position:0%
+this is what gets inserted up from the
+ 
+
+ align:start position:0%
+this is what gets inserted up from the
+bottom of the magnet and it's just
+
+ align:start position:0%
+bottom of the magnet and it's just
+ 
+
+ align:start position:0%
+bottom of the magnet and it's just
+it's screwed in and it stays in the
+
+ align:start position:0%
+it's screwed in and it stays in the
+ 
+
+ align:start position:0%
+it's screwed in and it stays in the
+bottom of the magnet there's only a
+
+ align:start position:0%
+bottom of the magnet there's only a
+ 
+
+ align:start position:0%
+bottom of the magnet there's only a
+couple of connections
+
+ align:start position:0%
+couple of connections
+ 
+
+ align:start position:0%
+couple of connections
+where the wires from the console are
+
+ align:start position:0%
+where the wires from the console are
+ 
+
+ align:start position:0%
+where the wires from the console are
+hooked up to this
+
+ align:start position:0%
+hooked up to this
+ 
+
+ align:start position:0%
+hooked up to this
+and so this one i can take the cover off
+
+ align:start position:0%
+and so this one i can take the cover off
+ 
+
+ align:start position:0%
+and so this one i can take the cover off
+of and you can look at this
+
+ align:start position:0%
+of and you can look at this
+ 
+
+ align:start position:0%
+of and you can look at this
+when you come up up in the very top
+
+ align:start position:0%
+when you come up up in the very top
+ 
+
+ align:start position:0%
+when you come up up in the very top
+of the probe is there's a little glass
+
+ align:start position:0%
+of the probe is there's a little glass
+ 
+
+ align:start position:0%
+of the probe is there's a little glass
+insert and there's some flat
+
+ align:start position:0%
+insert and there's some flat
+ 
+
+ align:start position:0%
+insert and there's some flat
+ribbons of wire that are wound around
+
+ align:start position:0%
+ribbons of wire that are wound around
+ 
+
+ align:start position:0%
+ribbons of wire that are wound around
+here and so i've got that pointed out in
+
+ align:start position:0%
+here and so i've got that pointed out in
+ 
+
+ align:start position:0%
+here and so i've got that pointed out in
+fact i think that's the same probe that
+
+ align:start position:0%
+fact i think that's the same probe that
+ 
+
+ align:start position:0%
+fact i think that's the same probe that
+i took a picture of
+
+ align:start position:0%
+i took a picture of
+ 
+
+ align:start position:0%
+i took a picture of
+and so your sample
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will go down and it will go right into
+
+ align:start position:0%
+will go down and it will go right into
+ 
+
+ align:start position:0%
+will go down and it will go right into
+where those coils of wire are and so the
+
+ align:start position:0%
+where those coils of wire are and so the
+ 
+
+ align:start position:0%
+where those coils of wire are and so the
+coils of wire will
+
+ align:start position:0%
+coils of wire will
+ 
+
+ align:start position:0%
+coils of wire will
+send the signal to your sample that's
+
+ align:start position:0%
+send the signal to your sample that's
+ 
+
+ align:start position:0%
+send the signal to your sample that's
+being generated in the console
+
+ align:start position:0%
+being generated in the console
+ 
+
+ align:start position:0%
+being generated in the console
+and then when that signal gets turned
+
+ align:start position:0%
+and then when that signal gets turned
+ 
+
+ align:start position:0%
+and then when that signal gets turned
+off your sample will relax back
+
+ align:start position:0%
+off your sample will relax back
+ 
+
+ align:start position:0%
+off your sample will relax back
+to its equilibrium state and it will
+
+ align:start position:0%
+to its equilibrium state and it will
+ 
+
+ align:start position:0%
+to its equilibrium state and it will
+induce
+
+ align:start position:0%
+induce
+ 
+
+ align:start position:0%
+induce
+a small voltage in these coils which
+
+ align:start position:0%
+a small voltage in these coils which
+ 
+
+ align:start position:0%
+a small voltage in these coils which
+gets picked up
+
+ align:start position:0%
+gets picked up
+ 
+
+ align:start position:0%
+gets picked up
+sent back through that console and off
+
+ align:start position:0%
+sent back through that console and off
+ 
+
+ align:start position:0%
+sent back through that console and off
+to the computer to generate your
+
+ align:start position:0%
+to the computer to generate your
+ 
+
+ align:start position:0%
+to the computer to generate your
+spectrum
+
+ align:start position:0%
+spectrum
+ 
+
+ align:start position:0%
+spectrum
+so i will leave this right here if you
+
+ align:start position:0%
+so i will leave this right here if you
+ 
+
+ align:start position:0%
+so i will leave this right here if you
+come up later to look at it
+
+ align:start position:0%
+come up later to look at it
+ 
+
+ align:start position:0%
+come up later to look at it
+feel free to pick it up just be very
+
+ align:start position:0%
+feel free to pick it up just be very
+ 
+
+ align:start position:0%
+feel free to pick it up just be very
+careful this is glass and you don't want
+
+ align:start position:0%
+careful this is glass and you don't want
+ 
+
+ align:start position:0%
+careful this is glass and you don't want
+to bang on it or bend it because it will
+
+ align:start position:0%
+to bang on it or bend it because it will
+ 
+
+ align:start position:0%
+to bang on it or bend it because it will
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you can break it not that it's working
+
+ align:start position:0%
+you can break it not that it's working
+ 
+
+ align:start position:0%
+you can break it not that it's working
+anyways anymore but
+
+ align:start position:0%
+anyways anymore but
+ 
+
+ align:start position:0%
+anyways anymore but
+we like to have it for demonstrations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the nmr signal itself
+
+ align:start position:0%
+okay so the nmr signal itself
+ 
+
+ align:start position:0%
+okay so the nmr signal itself
+it's generated when a collection of
+
+ align:start position:0%
+it's generated when a collection of
+ 
+
+ align:start position:0%
+it's generated when a collection of
+nuclei meaning your sample was placed
+
+ align:start position:0%
+nuclei meaning your sample was placed
+ 
+
+ align:start position:0%
+nuclei meaning your sample was placed
+in a strong magnetic field and
+
+ align:start position:0%
+in a strong magnetic field and
+ 
+
+ align:start position:0%
+in a strong magnetic field and
+irradiated with radio frequency energy
+
+ align:start position:0%
+irradiated with radio frequency energy
+ 
+
+ align:start position:0%
+irradiated with radio frequency energy
+of the appropriate frequency and we'll
+
+ align:start position:0%
+of the appropriate frequency and we'll
+ 
+
+ align:start position:0%
+of the appropriate frequency and we'll
+see what that is in a second
+
+ align:start position:0%
+see what that is in a second
+ 
+
+ align:start position:0%
+see what that is in a second
+the signal is a very small amount of
+
+ align:start position:0%
+the signal is a very small amount of
+ 
+
+ align:start position:0%
+the signal is a very small amount of
+energy that's given off
+
+ align:start position:0%
+energy that's given off
+ 
+
+ align:start position:0%
+energy that's given off
+as the nuclei in your sample transition
+
+ align:start position:0%
+as the nuclei in your sample transition
+ 
+
+ align:start position:0%
+as the nuclei in your sample transition
+back to their equilibrium state
+
+ align:start position:0%
+back to their equilibrium state
+ 
+
+ align:start position:0%
+back to their equilibrium state
+and it's really it's a time dependent
+
+ align:start position:0%
+and it's really it's a time dependent
+ 
+
+ align:start position:0%
+and it's really it's a time dependent
+current that's induced
+
+ align:start position:0%
+current that's induced
+ 
+
+ align:start position:0%
+current that's induced
+in the coil in the probe on the order of
+
+ align:start position:0%
+in the coil in the probe on the order of
+ 
+
+ align:start position:0%
+in the coil in the probe on the order of
+microvolts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it possesses four different
+
+ align:start position:0%
+so it possesses four different
+ 
+
+ align:start position:0%
+so it possesses four different
+four properties and only four properties
+
+ align:start position:0%
+four properties and only four properties
+ 
+
+ align:start position:0%
+four properties and only four properties
+that we make use of
+
+ align:start position:0%
+that we make use of
+ 
+
+ align:start position:0%
+that we make use of
+so pictured right here is an actual nmr
+
+ align:start position:0%
+so pictured right here is an actual nmr
+ 
+
+ align:start position:0%
+so pictured right here is an actual nmr
+signal
+
+ align:start position:0%
+signal
+ 
+
+ align:start position:0%
+signal
+it's what we call a free induction decay
+
+ align:start position:0%
+it's what we call a free induction decay
+ 
+
+ align:start position:0%
+it's what we call a free induction decay
+it's just a
+
+ align:start position:0%
+it's just a
+ 
+
+ align:start position:0%
+it's just a
+damped sinusoid and out of that you can
+
+ align:start position:0%
+damped sinusoid and out of that you can
+ 
+
+ align:start position:0%
+damped sinusoid and out of that you can
+get these four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four properties that you can make use of
+
+ align:start position:0%
+four properties that you can make use of
+ 
+
+ align:start position:0%
+four properties that you can make use of
+the one that we usually or make the most
+
+ align:start position:0%
+the one that we usually or make the most
+ 
+
+ align:start position:0%
+the one that we usually or make the most
+use of
+
+ align:start position:0%
+use of
+ 
+
+ align:start position:0%
+use of
+is the frequency and so i'll tell you
+
+ align:start position:0%
+is the frequency and so i'll tell you
+ 
+
+ align:start position:0%
+is the frequency and so i'll tell you
+how you can convert this to this
+
+ align:start position:0%
+how you can convert this to this
+ 
+
+ align:start position:0%
+how you can convert this to this
+in a few slides but where lines will
+
+ align:start position:0%
+in a few slides but where lines will
+ 
+
+ align:start position:0%
+in a few slides but where lines will
+appear
+
+ align:start position:0%
+appear
+ 
+
+ align:start position:0%
+appear
+on this graph tells us something about
+
+ align:start position:0%
+on this graph tells us something about
+ 
+
+ align:start position:0%
+on this graph tells us something about
+the molecular environment
+
+ align:start position:0%
+the molecular environment
+ 
+
+ align:start position:0%
+the molecular environment
+that whatever gave rise to that signal
+
+ align:start position:0%
+that whatever gave rise to that signal
+ 
+
+ align:start position:0%
+that whatever gave rise to that signal
+is in so that's when
+
+ align:start position:0%
+is in so that's when
+ 
+
+ align:start position:0%
+is in so that's when
+most of the time that's what you use the
+
+ align:start position:0%
+most of the time that's what you use the
+ 
+
+ align:start position:0%
+most of the time that's what you use the
+next most common
+
+ align:start position:0%
+next most common
+ 
+
+ align:start position:0%
+next most common
+piece of information used out of it is
+
+ align:start position:0%
+piece of information used out of it is
+ 
+
+ align:start position:0%
+piece of information used out of it is
+the intensity
+
+ align:start position:0%
+the intensity
+ 
+
+ align:start position:0%
+the intensity
+so the intensity of a resonance in the
+
+ align:start position:0%
+so the intensity of a resonance in the
+ 
+
+ align:start position:0%
+so the intensity of a resonance in the
+nmr spectrum
+
+ align:start position:0%
+nmr spectrum
+ 
+
+ align:start position:0%
+nmr spectrum
+is going to be directly proportional to
+
+ align:start position:0%
+is going to be directly proportional to
+ 
+
+ align:start position:0%
+is going to be directly proportional to
+the number of
+
+ align:start position:0%
+the number of
+ 
+
+ align:start position:0%
+the number of
+nuclei that give rise to that signal
+
+ align:start position:0%
+nuclei that give rise to that signal
+ 
+
+ align:start position:0%
+nuclei that give rise to that signal
+and that doesn't mean just well it also
+
+ align:start position:0%
+and that doesn't mean just well it also
+ 
+
+ align:start position:0%
+and that doesn't mean just well it also
+means you know just
+
+ align:start position:0%
+means you know just
+ 
+
+ align:start position:0%
+means you know just
+every nuclei that's in there but
+
+ align:start position:0%
+every nuclei that's in there but
+ 
+
+ align:start position:0%
+every nuclei that's in there but
+specifically for instance
+
+ align:start position:0%
+specifically for instance
+ 
+
+ align:start position:0%
+specifically for instance
+if you've got one signal from this group
+
+ align:start position:0%
+if you've got one signal from this group
+ 
+
+ align:start position:0%
+if you've got one signal from this group
+of protons and one signal from this
+
+ align:start position:0%
+of protons and one signal from this
+ 
+
+ align:start position:0%
+of protons and one signal from this
+group of protons
+
+ align:start position:0%
+group of protons
+ 
+
+ align:start position:0%
+group of protons
+their intensity is going to be equal
+
+ align:start position:0%
+their intensity is going to be equal
+ 
+
+ align:start position:0%
+their intensity is going to be equal
+because three protons gave rise to this
+
+ align:start position:0%
+because three protons gave rise to this
+ 
+
+ align:start position:0%
+because three protons gave rise to this
+signal
+
+ align:start position:0%
+signal
+ 
+
+ align:start position:0%
+signal
+and three protons gave rise to that
+
+ align:start position:0%
+and three protons gave rise to that
+ 
+
+ align:start position:0%
+and three protons gave rise to that
+signal
+
+ align:start position:0%
+signal
+ 
+
+ align:start position:0%
+signal
+so you can use that as an internal check
+
+ align:start position:0%
+so you can use that as an internal check
+ 
+
+ align:start position:0%
+so you can use that as an internal check
+in molecules to make sure that you're
+
+ align:start position:0%
+in molecules to make sure that you're
+ 
+
+ align:start position:0%
+in molecules to make sure that you're
+identifying
+
+ align:start position:0%
+identifying
+ 
+
+ align:start position:0%
+identifying
+peaks correctly you can also use it to
+
+ align:start position:0%
+peaks correctly you can also use it to
+ 
+
+ align:start position:0%
+peaks correctly you can also use it to
+quantify
+
+ align:start position:0%
+quantify
+ 
+
+ align:start position:0%
+quantify
+molecules you know different molecules
+
+ align:start position:0%
+molecules you know different molecules
+ 
+
+ align:start position:0%
+molecules you know different molecules
+that are present
+
+ align:start position:0%
+that are present
+ 
+
+ align:start position:0%
+that are present
+in a sample and you can even
+
+ align:start position:0%
+in a sample and you can even
+ 
+
+ align:start position:0%
+in a sample and you can even
+make a sample where you've spiked a
+
+ align:start position:0%
+make a sample where you've spiked a
+ 
+
+ align:start position:0%
+make a sample where you've spiked a
+known amount
+
+ align:start position:0%
+known amount
+ 
+
+ align:start position:0%
+known amount
+of something in there to serve as a
+
+ align:start position:0%
+of something in there to serve as a
+ 
+
+ align:start position:0%
+of something in there to serve as a
+standard and then
+
+ align:start position:0%
+standard and then
+ 
+
+ align:start position:0%
+standard and then
+quantify the amount of an unknown that
+
+ align:start position:0%
+quantify the amount of an unknown that
+ 
+
+ align:start position:0%
+quantify the amount of an unknown that
+you've put in there
+
+ align:start position:0%
+you've put in there
+ 
+
+ align:start position:0%
+you've put in there
+another property is the phase of the
+
+ align:start position:0%
+another property is the phase of the
+ 
+
+ align:start position:0%
+another property is the phase of the
+signal so
+
+ align:start position:0%
+signal so
+ 
+
+ align:start position:0%
+signal so
+what i'm showing here is not something
+
+ align:start position:0%
+what i'm showing here is not something
+ 
+
+ align:start position:0%
+what i'm showing here is not something
+you're going to acquire it's called a
+
+ align:start position:0%
+you're going to acquire it's called a
+ 
+
+ align:start position:0%
+you're going to acquire it's called a
+two-dimensional spectrum but what i'm
+
+ align:start position:0%
+two-dimensional spectrum but what i'm
+ 
+
+ align:start position:0%
+two-dimensional spectrum but what i'm
+trying to highlight is that
+
+ align:start position:0%
+trying to highlight is that
+ 
+
+ align:start position:0%
+trying to highlight is that
+each of these colors be it i called it
+
+ align:start position:0%
+each of these colors be it i called it
+ 
+
+ align:start position:0%
+each of these colors be it i called it
+red i think it might be
+
+ align:start position:0%
+red i think it might be
+ 
+
+ align:start position:0%
+red i think it might be
+you know something some blend of that or
+
+ align:start position:0%
+you know something some blend of that or
+ 
+
+ align:start position:0%
+you know something some blend of that or
+blue are a different
+
+ align:start position:0%
+blue are a different
+ 
+
+ align:start position:0%
+blue are a different
+phase specifically think of this does
+
+ align:start position:0%
+phase specifically think of this does
+ 
+
+ align:start position:0%
+phase specifically think of this does
+anybody know what a two-dimensional map
+
+ align:start position:0%
+anybody know what a two-dimensional map
+ 
+
+ align:start position:0%
+anybody know what a two-dimensional map
+is ever look at a topographic map where
+
+ align:start position:0%
+is ever look at a topographic map where
+ 
+
+ align:start position:0%
+is ever look at a topographic map where
+you've got mountains that are
+
+ align:start position:0%
+you've got mountains that are
+ 
+
+ align:start position:0%
+you've got mountains that are
+outlined by contours so you can think
+
+ align:start position:0%
+outlined by contours so you can think
+ 
+
+ align:start position:0%
+outlined by contours so you can think
+uh what do they call it so i said blue
+
+ align:start position:0%
+uh what do they call it so i said blue
+ 
+
+ align:start position:0%
+uh what do they call it so i said blue
+is negative so think of the negative
+
+ align:start position:0%
+is negative so think of the negative
+ 
+
+ align:start position:0%
+is negative so think of the negative
+think of the blue cross peaks as being
+
+ align:start position:0%
+think of the blue cross peaks as being
+ 
+
+ align:start position:0%
+think of the blue cross peaks as being
+holes or going down
+
+ align:start position:0%
+holes or going down
+ 
+
+ align:start position:0%
+holes or going down
+into the plane and think of the red ones
+
+ align:start position:0%
+into the plane and think of the red ones
+ 
+
+ align:start position:0%
+into the plane and think of the red ones
+as coming out of the plane
+
+ align:start position:0%
+as coming out of the plane
+ 
+
+ align:start position:0%
+as coming out of the plane
+so the way that this experiment
+
+ align:start position:0%
+so the way that this experiment
+ 
+
+ align:start position:0%
+so the way that this experiment
+is acquired it makes
+
+ align:start position:0%
+is acquired it makes
+ 
+
+ align:start position:0%
+is acquired it makes
+methylene groups have a negative phase
+
+ align:start position:0%
+methylene groups have a negative phase
+ 
+
+ align:start position:0%
+methylene groups have a negative phase
+and it makes methyl and methionine
+
+ align:start position:0%
+and it makes methyl and methionine
+ 
+
+ align:start position:0%
+and it makes methyl and methionine
+groups have a positive phase
+
+ align:start position:0%
+groups have a positive phase
+ 
+
+ align:start position:0%
+groups have a positive phase
+so that's really useful when you're
+
+ align:start position:0%
+so that's really useful when you're
+ 
+
+ align:start position:0%
+so that's really useful when you're
+looking at an unknown because right off
+
+ align:start position:0%
+looking at an unknown because right off
+ 
+
+ align:start position:0%
+looking at an unknown because right off
+the bat you can just say okay i know
+
+ align:start position:0%
+the bat you can just say okay i know
+ 
+
+ align:start position:0%
+the bat you can just say okay i know
+that this this this and this
+
+ align:start position:0%
+that this this this and this
+ 
+
+ align:start position:0%
+that this this this and this
+or from a methyl or methion and i know
+
+ align:start position:0%
+or from a methyl or methion and i know
+ 
+
+ align:start position:0%
+or from a methyl or methion and i know
+that these blue peaks
+
+ align:start position:0%
+that these blue peaks
+ 
+
+ align:start position:0%
+that these blue peaks
+are from methylenes and then
+
+ align:start position:0%
+are from methylenes and then
+ 
+
+ align:start position:0%
+are from methylenes and then
+specifically i can look at it and say
+
+ align:start position:0%
+specifically i can look at it and say
+ 
+
+ align:start position:0%
+specifically i can look at it and say
+okay since this one and this one are in
+
+ align:start position:0%
+okay since this one and this one are in
+ 
+
+ align:start position:0%
+okay since this one and this one are in
+a line
+
+ align:start position:0%
+a line
+ 
+
+ align:start position:0%
+a line
+next to each other i know that these are
+
+ align:start position:0%
+next to each other i know that these are
+ 
+
+ align:start position:0%
+next to each other i know that these are
+protons on the same
+
+ align:start position:0%
+protons on the same
+ 
+
+ align:start position:0%
+protons on the same
+carbon the last piece of information
+
+ align:start position:0%
+carbon the last piece of information
+ 
+
+ align:start position:0%
+carbon the last piece of information
+that comes out of an nmr
+
+ align:start position:0%
+that comes out of an nmr
+ 
+
+ align:start position:0%
+that comes out of an nmr
+signal is the duration of the decay so
+
+ align:start position:0%
+signal is the duration of the decay so
+ 
+
+ align:start position:0%
+signal is the duration of the decay so
+it can be longer it can be
+
+ align:start position:0%
+it can be longer it can be
+ 
+
+ align:start position:0%
+it can be longer it can be
+shorter you can use that like for things
+
+ align:start position:0%
+shorter you can use that like for things
+ 
+
+ align:start position:0%
+shorter you can use that like for things
+like i
+
+ align:start position:0%
+like i
+ 
+
+ align:start position:0%
+like i
+hinted at before where you have a small
+
+ align:start position:0%
+hinted at before where you have a small
+ 
+
+ align:start position:0%
+hinted at before where you have a small
+molecules usually have a long decay
+
+ align:start position:0%
+molecules usually have a long decay
+ 
+
+ align:start position:0%
+molecules usually have a long decay
+large molecules usually have a very
+
+ align:start position:0%
+large molecules usually have a very
+ 
+
+ align:start position:0%
+large molecules usually have a very
+short decay so if you have a protein
+
+ align:start position:0%
+short decay so if you have a protein
+ 
+
+ align:start position:0%
+short decay so if you have a protein
+that's binding a small molecule
+
+ align:start position:0%
+that's binding a small molecule
+ 
+
+ align:start position:0%
+that's binding a small molecule
+substrate
+
+ align:start position:0%
+substrate
+ 
+
+ align:start position:0%
+substrate
+its decay is going to transition from
+
+ align:start position:0%
+its decay is going to transition from
+ 
+
+ align:start position:0%
+its decay is going to transition from
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+long to something short and you can use
+
+ align:start position:0%
+long to something short and you can use
+ 
+
+ align:start position:0%
+long to something short and you can use
+that to tell
+
+ align:start position:0%
+that to tell
+ 
+
+ align:start position:0%
+that to tell
+that your molecule has been bound any
+
+ align:start position:0%
+that your molecule has been bound any
+ 
+
+ align:start position:0%
+that your molecule has been bound any
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so unfortunately not all
+
+ align:start position:0%
+all right so unfortunately not all
+ 
+
+ align:start position:0%
+all right so unfortunately not all
+nuclei can be measured
+
+ align:start position:0%
+nuclei can be measured
+ 
+
+ align:start position:0%
+nuclei can be measured
+by nmr any nucleus that possesses
+
+ align:start position:0%
+by nmr any nucleus that possesses
+ 
+
+ align:start position:0%
+by nmr any nucleus that possesses
+angular momentum will exhibit a magnetic
+
+ align:start position:0%
+angular momentum will exhibit a magnetic
+ 
+
+ align:start position:0%
+angular momentum will exhibit a magnetic
+moment that will interact
+
+ align:start position:0%
+moment that will interact
+ 
+
+ align:start position:0%
+moment that will interact
+with a magnetic field we taught just
+
+ align:start position:0%
+with a magnetic field we taught just
+ 
+
+ align:start position:0%
+with a magnetic field we taught just
+like electrons if you learned about in
+
+ align:start position:0%
+like electrons if you learned about in
+ 
+
+ align:start position:0%
+like electrons if you learned about in
+general chemistry where you've learned
+
+ align:start position:0%
+general chemistry where you've learned
+ 
+
+ align:start position:0%
+general chemistry where you've learned
+the quantum numbers and you learned
+
+ align:start position:0%
+the quantum numbers and you learned
+ 
+
+ align:start position:0%
+the quantum numbers and you learned
+about spin
+
+ align:start position:0%
+about spin
+ 
+
+ align:start position:0%
+about spin
+it's the same for nuclei so we say a
+
+ align:start position:0%
+it's the same for nuclei so we say a
+ 
+
+ align:start position:0%
+it's the same for nuclei so we say a
+nucleus possesses spin in reference to a
+
+ align:start position:0%
+nucleus possesses spin in reference to a
+ 
+
+ align:start position:0%
+nucleus possesses spin in reference to a
+spin quantum number
+
+ align:start position:0%
+spin quantum number
+ 
+
+ align:start position:0%
+spin quantum number
+which is labeled i it's
+
+ align:start position:0%
+which is labeled i it's
+ 
+
+ align:start position:0%
+which is labeled i it's
+easy to think of nuclei as cute little
+
+ align:start position:0%
+easy to think of nuclei as cute little
+ 
+
+ align:start position:0%
+easy to think of nuclei as cute little
+balls that are rotating around
+
+ align:start position:0%
+balls that are rotating around
+ 
+
+ align:start position:0%
+balls that are rotating around
+but remember they're not spinning it's
+
+ align:start position:0%
+but remember they're not spinning it's
+ 
+
+ align:start position:0%
+but remember they're not spinning it's
+just an inherent
+
+ align:start position:0%
+just an inherent
+ 
+
+ align:start position:0%
+just an inherent
+physical property that seems like
+
+ align:start position:0%
+physical property that seems like
+ 
+
+ align:start position:0%
+physical property that seems like
+they're little spinning balls when
+
+ align:start position:0%
+they're little spinning balls when
+ 
+
+ align:start position:0%
+they're little spinning balls when
+they're not
+
+ align:start position:0%
+they're not
+ 
+
+ align:start position:0%
+they're not
+so the rules for determining if a
+
+ align:start position:0%
+so the rules for determining if a
+ 
+
+ align:start position:0%
+so the rules for determining if a
+nucleus has spin or not
+
+ align:start position:0%
+nucleus has spin or not
+ 
+
+ align:start position:0%
+nucleus has spin or not
+it's present in either half integer or
+
+ align:start position:0%
+it's present in either half integer or
+ 
+
+ align:start position:0%
+it's present in either half integer or
+integer values
+
+ align:start position:0%
+integer values
+ 
+
+ align:start position:0%
+integer values
+you don't really have to worry about
+
+ align:start position:0%
+you don't really have to worry about
+ 
+
+ align:start position:0%
+you don't really have to worry about
+that for this class we're going to be
+
+ align:start position:0%
+that for this class we're going to be
+ 
+
+ align:start position:0%
+that for this class we're going to be
+looking
+
+ align:start position:0%
+looking
+ 
+
+ align:start position:0%
+looking
+at spin one-half nuclei protons which
+
+ align:start position:0%
+at spin one-half nuclei protons which
+ 
+
+ align:start position:0%
+at spin one-half nuclei protons which
+are the easiest to interpret and luckily
+
+ align:start position:0%
+are the easiest to interpret and luckily
+ 
+
+ align:start position:0%
+are the easiest to interpret and luckily
+protons have a 99.9 185 percent
+
+ align:start position:0%
+protons have a 99.9 185 percent
+ 
+
+ align:start position:0%
+protons have a 99.9 185 percent
+natural abundance so it's
+
+ align:start position:0%
+natural abundance so it's
+ 
+
+ align:start position:0%
+natural abundance so it's
+the most sensitive and strongest
+
+ align:start position:0%
+the most sensitive and strongest
+ 
+
+ align:start position:0%
+the most sensitive and strongest
+nmr signal that you can get out of any
+
+ align:start position:0%
+nmr signal that you can get out of any
+ 
+
+ align:start position:0%
+nmr signal that you can get out of any
+nucleus
+
+ align:start position:0%
+nucleus
+ 
+
+ align:start position:0%
+nucleus
+there are like i said the rules for
+
+ align:start position:0%
+there are like i said the rules for
+ 
+
+ align:start position:0%
+there are like i said the rules for
+determining whether something has
+
+ align:start position:0%
+determining whether something has
+ 
+
+ align:start position:0%
+determining whether something has
+spin nuclei with even proton an even
+
+ align:start position:0%
+spin nuclei with even proton an even
+ 
+
+ align:start position:0%
+spin nuclei with even proton an even
+number of protons and an even number of
+
+ align:start position:0%
+number of protons and an even number of
+ 
+
+ align:start position:0%
+number of protons and an even number of
+neutrons
+
+ align:start position:0%
+neutrons
+ 
+
+ align:start position:0%
+neutrons
+do not have nuclear spin and so they're
+
+ align:start position:0%
+do not have nuclear spin and so they're
+ 
+
+ align:start position:0%
+do not have nuclear spin and so they're
+nuclear or their nmr
+
+ align:start position:0%
+nuclear or their nmr
+ 
+
+ align:start position:0%
+nuclear or their nmr
+inactive unfortunately the next
+
+ align:start position:0%
+inactive unfortunately the next
+ 
+
+ align:start position:0%
+inactive unfortunately the next
+most common thing that we would love to
+
+ align:start position:0%
+most common thing that we would love to
+ 
+
+ align:start position:0%
+most common thing that we would love to
+look at is organic chemist
+
+ align:start position:0%
+look at is organic chemist
+ 
+
+ align:start position:0%
+look at is organic chemist
+is carbon and carbon has six protons and
+
+ align:start position:0%
+is carbon and carbon has six protons and
+ 
+
+ align:start position:0%
+is carbon and carbon has six protons and
+six neutrons
+
+ align:start position:0%
+six neutrons
+ 
+
+ align:start position:0%
+six neutrons
+for carbon 12 and so we can't it's
+
+ align:start position:0%
+for carbon 12 and so we can't it's
+ 
+
+ align:start position:0%
+for carbon 12 and so we can't it's
+nmr inactive luckily for us though
+
+ align:start position:0%
+nmr inactive luckily for us though
+ 
+
+ align:start position:0%
+nmr inactive luckily for us though
+carbon has an isotope that's 1.1 percent
+
+ align:start position:0%
+carbon has an isotope that's 1.1 percent
+ 
+
+ align:start position:0%
+carbon has an isotope that's 1.1 percent
+naturally abundant which is c13 and we
+
+ align:start position:0%
+naturally abundant which is c13 and we
+ 
+
+ align:start position:0%
+naturally abundant which is c13 and we
+can look at that
+
+ align:start position:0%
+can look at that
+ 
+
+ align:start position:0%
+can look at that
+and we take a hit on sensitivity but we
+
+ align:start position:0%
+and we take a hit on sensitivity but we
+ 
+
+ align:start position:0%
+and we take a hit on sensitivity but we
+can still get an nmr spectrum of that so
+
+ align:start position:0%
+can still get an nmr spectrum of that so
+ 
+
+ align:start position:0%
+can still get an nmr spectrum of that so
+that's good
+
+ align:start position:0%
+that's good
+ 
+
+ align:start position:0%
+that's good
+some nuclei have multiple nmr active
+
+ align:start position:0%
+some nuclei have multiple nmr active
+ 
+
+ align:start position:0%
+some nuclei have multiple nmr active
+isotopes
+
+ align:start position:0%
+isotopes
+ 
+
+ align:start position:0%
+isotopes
+that doesn't mean they always appear in
+
+ align:start position:0%
+that doesn't mean they always appear in
+ 
+
+ align:start position:0%
+that doesn't mean they always appear in
+the same spectrum
+
+ align:start position:0%
+the same spectrum
+ 
+
+ align:start position:0%
+the same spectrum
+they will have different gyromagnetic
+
+ align:start position:0%
+they will have different gyromagnetic
+ 
+
+ align:start position:0%
+they will have different gyromagnetic
+ratios
+
+ align:start position:0%
+ratios
+ 
+
+ align:start position:0%
+ratios
+so they will appear at different overall
+
+ align:start position:0%
+so they will appear at different overall
+ 
+
+ align:start position:0%
+so they will appear at different overall
+frequencies but you can
+
+ align:start position:0%
+frequencies but you can
+ 
+
+ align:start position:0%
+frequencies but you can
+look at sometimes you can use that to
+
+ align:start position:0%
+look at sometimes you can use that to
+ 
+
+ align:start position:0%
+look at sometimes you can use that to
+your advantage you could take a spectrum
+
+ align:start position:0%
+your advantage you could take a spectrum
+ 
+
+ align:start position:0%
+your advantage you could take a spectrum
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+10 boron and a separate spectrum of 11
+
+ align:start position:0%
+10 boron and a separate spectrum of 11
+ 
+
+ align:start position:0%
+10 boron and a separate spectrum of 11
+boron
+
+ align:start position:0%
+boron
+ 
+
+ align:start position:0%
+boron
+or proton we use the signal
+
+ align:start position:0%
+or proton we use the signal
+ 
+
+ align:start position:0%
+or proton we use the signal
+from deuterium as a
+
+ align:start position:0%
+from deuterium as a
+ 
+
+ align:start position:0%
+from deuterium as a
+lock signal for the magnet
+
+ align:start position:0%
+lock signal for the magnet
+ 
+
+ align:start position:0%
+lock signal for the magnet
+to focus on and counteract its inherent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drift
+
+ align:start position:0%
+drift
+ 
+
+ align:start position:0%
+drift
+so what's the physical basis of the nmr
+
+ align:start position:0%
+so what's the physical basis of the nmr
+ 
+
+ align:start position:0%
+so what's the physical basis of the nmr
+signal um in a magnetic field all those
+
+ align:start position:0%
+signal um in a magnetic field all those
+ 
+
+ align:start position:0%
+signal um in a magnetic field all those
+little magnetic moments are going to
+
+ align:start position:0%
+little magnetic moments are going to
+ 
+
+ align:start position:0%
+little magnetic moments are going to
+adopt an orientation relative to that
+
+ align:start position:0%
+adopt an orientation relative to that
+ 
+
+ align:start position:0%
+adopt an orientation relative to that
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+the allowed orientation of these moments
+
+ align:start position:0%
+the allowed orientation of these moments
+ 
+
+ align:start position:0%
+the allowed orientation of these moments
+is going to be explained by quantum
+
+ align:start position:0%
+is going to be explained by quantum
+ 
+
+ align:start position:0%
+is going to be explained by quantum
+mechanics
+
+ align:start position:0%
+mechanics
+ 
+
+ align:start position:0%
+mechanics
+luckily we don't have to really get into
+
+ align:start position:0%
+luckily we don't have to really get into
+ 
+
+ align:start position:0%
+luckily we don't have to really get into
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and the process that nuclei undergo
+
+ align:start position:0%
+and the process that nuclei undergo
+ 
+
+ align:start position:0%
+and the process that nuclei undergo
+during an experiment can be rationalized
+
+ align:start position:0%
+during an experiment can be rationalized
+ 
+
+ align:start position:0%
+during an experiment can be rationalized
+in two ways you can think of it in terms
+
+ align:start position:0%
+in two ways you can think of it in terms
+ 
+
+ align:start position:0%
+in two ways you can think of it in terms
+of vectors
+
+ align:start position:0%
+of vectors
+ 
+
+ align:start position:0%
+of vectors
+so which way those little magnetic
+
+ align:start position:0%
+so which way those little magnetic
+ 
+
+ align:start position:0%
+so which way those little magnetic
+fields are pointing or you can think of
+
+ align:start position:0%
+fields are pointing or you can think of
+ 
+
+ align:start position:0%
+fields are pointing or you can think of
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+in terms of the energy levels that the
+
+ align:start position:0%
+in terms of the energy levels that the
+ 
+
+ align:start position:0%
+in terms of the energy levels that the
+nuclei adopt
+
+ align:start position:0%
+nuclei adopt
+ 
+
+ align:start position:0%
+nuclei adopt
+when they're put in that magnetic field
+
+ align:start position:0%
+when they're put in that magnetic field
+ 
+
+ align:start position:0%
+when they're put in that magnetic field
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i tried to make a little cartoon here
+
+ align:start position:0%
+i tried to make a little cartoon here
+ 
+
+ align:start position:0%
+i tried to make a little cartoon here
+with no magnetic field these are
+
+ align:start position:0%
+with no magnetic field these are
+ 
+
+ align:start position:0%
+with no magnetic field these are
+supposed to just be all randomly
+
+ align:start position:0%
+supposed to just be all randomly
+ 
+
+ align:start position:0%
+supposed to just be all randomly
+oriented
+
+ align:start position:0%
+oriented
+ 
+
+ align:start position:0%
+oriented
+but when i immerse my collection of
+
+ align:start position:0%
+but when i immerse my collection of
+ 
+
+ align:start position:0%
+but when i immerse my collection of
+molecules
+
+ align:start position:0%
+molecules
+ 
+
+ align:start position:0%
+molecules
+you know that's in my sample in a
+
+ align:start position:0%
+you know that's in my sample in a
+ 
+
+ align:start position:0%
+you know that's in my sample in a
+magnetic field they will
+
+ align:start position:0%
+magnetic field they will
+ 
+
+ align:start position:0%
+magnetic field they will
+line up and be either with the field or
+
+ align:start position:0%
+line up and be either with the field or
+ 
+
+ align:start position:0%
+line up and be either with the field or
+against the field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so if we look at one nucleus when we
+
+ align:start position:0%
+and so if we look at one nucleus when we
+ 
+
+ align:start position:0%
+and so if we look at one nucleus when we
+place it in a magnetic field
+
+ align:start position:0%
+place it in a magnetic field
+ 
+
+ align:start position:0%
+place it in a magnetic field
+quantum mechanics tells us that it's not
+
+ align:start position:0%
+quantum mechanics tells us that it's not
+ 
+
+ align:start position:0%
+quantum mechanics tells us that it's not
+just going to point straight up
+
+ align:start position:0%
+just going to point straight up
+ 
+
+ align:start position:0%
+just going to point straight up
+it's there's got to be some uncertainty
+
+ align:start position:0%
+it's there's got to be some uncertainty
+ 
+
+ align:start position:0%
+it's there's got to be some uncertainty
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+where that nucleus is pointing and so
+
+ align:start position:0%
+where that nucleus is pointing and so
+ 
+
+ align:start position:0%
+where that nucleus is pointing and so
+it is going to precess meaning it's
+
+ align:start position:0%
+it is going to precess meaning it's
+ 
+
+ align:start position:0%
+it is going to precess meaning it's
+going to rotate around the direction
+
+ align:start position:0%
+going to rotate around the direction
+ 
+
+ align:start position:0%
+going to rotate around the direction
+of the magnetic field with the
+
+ align:start position:0%
+of the magnetic field with the
+ 
+
+ align:start position:0%
+of the magnetic field with the
+characteristic frequency
+
+ align:start position:0%
+characteristic frequency
+ 
+
+ align:start position:0%
+characteristic frequency
+which we call the larmor frequency it's
+
+ align:start position:0%
+which we call the larmor frequency it's
+ 
+
+ align:start position:0%
+which we call the larmor frequency it's
+named for what's the name joseph larmore
+
+ align:start position:0%
+named for what's the name joseph larmore
+ 
+
+ align:start position:0%
+named for what's the name joseph larmore
+who was a
+
+ align:start position:0%
+who was a
+ 
+
+ align:start position:0%
+who was a
+physicist back in the late 1800s early
+
+ align:start position:0%
+physicist back in the late 1800s early
+ 
+
+ align:start position:0%
+physicist back in the late 1800s early
+1900s
+
+ align:start position:0%
+1900s
+ 
+
+ align:start position:0%
+1900s
+that frequency is going to be directly
+
+ align:start position:0%
+that frequency is going to be directly
+ 
+
+ align:start position:0%
+that frequency is going to be directly
+proportional
+
+ align:start position:0%
+proportional
+ 
+
+ align:start position:0%
+proportional
+to the strength of the magnet that you
+
+ align:start position:0%
+to the strength of the magnet that you
+ 
+
+ align:start position:0%
+to the strength of the magnet that you
+put your sample
+
+ align:start position:0%
+put your sample
+ 
+
+ align:start position:0%
+put your sample
+in i've
+
+ align:start position:0%
+in i've
+ 
+
+ align:start position:0%
+in i've
+unfortunately so gyromagnetic ratio
+
+ align:start position:0%
+unfortunately so gyromagnetic ratio
+ 
+
+ align:start position:0%
+unfortunately so gyromagnetic ratio
+can be specified in either radians per
+
+ align:start position:0%
+can be specified in either radians per
+ 
+
+ align:start position:0%
+can be specified in either radians per
+second per tesla
+
+ align:start position:0%
+second per tesla
+ 
+
+ align:start position:0%
+second per tesla
+or in hertz per tesla i apologize for
+
+ align:start position:0%
+or in hertz per tesla i apologize for
+ 
+
+ align:start position:0%
+or in hertz per tesla i apologize for
+not being too careful
+
+ align:start position:0%
+not being too careful
+ 
+
+ align:start position:0%
+not being too careful
+and that i will jump back and forth
+
+ align:start position:0%
+and that i will jump back and forth
+ 
+
+ align:start position:0%
+and that i will jump back and forth
+between the two
+
+ align:start position:0%
+between the two
+ 
+
+ align:start position:0%
+between the two
+so for a proton if we take a magnet
+
+ align:start position:0%
+so for a proton if we take a magnet
+ 
+
+ align:start position:0%
+so for a proton if we take a magnet
+that's 11.75
+
+ align:start position:0%
+that's 11.75
+ 
+
+ align:start position:0%
+that's 11.75
+tesla and we put it our sample in there
+
+ align:start position:0%
+tesla and we put it our sample in there
+ 
+
+ align:start position:0%
+tesla and we put it our sample in there
+it's going to precess around the field
+
+ align:start position:0%
+it's going to precess around the field
+ 
+
+ align:start position:0%
+it's going to precess around the field
+at 500 megahertz
+
+ align:start position:0%
+at 500 megahertz
+ 
+
+ align:start position:0%
+at 500 megahertz
+and so when we talk about nmr
+
+ align:start position:0%
+and so when we talk about nmr
+ 
+
+ align:start position:0%
+and so when we talk about nmr
+instruments is just
+
+ align:start position:0%
+instruments is just
+ 
+
+ align:start position:0%
+instruments is just
+as far as what size they are they're
+
+ align:start position:0%
+as far as what size they are they're
+ 
+
+ align:start position:0%
+as far as what size they are they're
+not specified by the strength of their
+
+ align:start position:0%
+not specified by the strength of their
+ 
+
+ align:start position:0%
+not specified by the strength of their
+magnet
+
+ align:start position:0%
+magnet
+ 
+
+ align:start position:0%
+magnet
+they're specified by the frequency that
+
+ align:start position:0%
+they're specified by the frequency that
+ 
+
+ align:start position:0%
+they're specified by the frequency that
+a proton
+
+ align:start position:0%
+a proton
+ 
+
+ align:start position:0%
+a proton
+precesses in a field with a magnet of
+
+ align:start position:0%
+precesses in a field with a magnet of
+ 
+
+ align:start position:0%
+precesses in a field with a magnet of
+that strength so
+
+ align:start position:0%
+that strength so
+ 
+
+ align:start position:0%
+that strength so
+if you come down to the dcif i'll say i
+
+ align:start position:0%
+if you come down to the dcif i'll say i
+ 
+
+ align:start position:0%
+if you come down to the dcif i'll say i
+have a 500 or i have a 600 or i have a
+
+ align:start position:0%
+have a 500 or i have a 600 or i have a
+ 
+
+ align:start position:0%
+have a 500 or i have a 600 or i have a
+400.
+
+ align:start position:0%
+400.
+ 
+
+ align:start position:0%
+400.
+in the undergraduate teaching labs you
+
+ align:start position:0%
+in the undergraduate teaching labs you
+ 
+
+ align:start position:0%
+in the undergraduate teaching labs you
+have a 300 and i think the bench top is
+
+ align:start position:0%
+have a 300 and i think the bench top is
+ 
+
+ align:start position:0%
+have a 300 and i think the bench top is
+a 60 megahertz
+
+ align:start position:0%
+a 60 megahertz
+ 
+
+ align:start position:0%
+a 60 megahertz
+and you know i'd have to go look up in a
+
+ align:start position:0%
+and you know i'd have to go look up in a
+ 
+
+ align:start position:0%
+and you know i'd have to go look up in a
+table or do the calculation
+
+ align:start position:0%
+table or do the calculation
+ 
+
+ align:start position:0%
+table or do the calculation
+how strong in tesla a 60hz megahertz
+
+ align:start position:0%
+how strong in tesla a 60hz megahertz
+ 
+
+ align:start position:0%
+how strong in tesla a 60hz megahertz
+nmr magnet is but that's the way it's
+
+ align:start position:0%
+nmr magnet is but that's the way it's
+ 
+
+ align:start position:0%
+nmr magnet is but that's the way it's
+specified
+
+ align:start position:0%
+specified
+ 
+
+ align:start position:0%
+specified
+so that's for one nuclei when you put it
+
+ align:start position:0%
+so that's for one nuclei when you put it
+ 
+
+ align:start position:0%
+so that's for one nuclei when you put it
+in the magnetic field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but our sample is actually a bunch of
+
+ align:start position:0%
+but our sample is actually a bunch of
+ 
+
+ align:start position:0%
+but our sample is actually a bunch of
+different nuclei
+
+ align:start position:0%
+different nuclei
+ 
+
+ align:start position:0%
+different nuclei
+or not well yes it's a bunch of
+
+ align:start position:0%
+or not well yes it's a bunch of
+ 
+
+ align:start position:0%
+or not well yes it's a bunch of
+different nuclei so it's a collection of
+
+ align:start position:0%
+different nuclei so it's a collection of
+ 
+
+ align:start position:0%
+different nuclei so it's a collection of
+nuclei
+
+ align:start position:0%
+nuclei
+ 
+
+ align:start position:0%
+nuclei
+we don't have to keep track of every
+
+ align:start position:0%
+we don't have to keep track of every
+ 
+
+ align:start position:0%
+we don't have to keep track of every
+individual
+
+ align:start position:0%
+individual
+ 
+
+ align:start position:0%
+individual
+nucleus and deal with the quantum
+
+ align:start position:0%
+nucleus and deal with the quantum
+ 
+
+ align:start position:0%
+nucleus and deal with the quantum
+mechanics when we look at nmr
+
+ align:start position:0%
+mechanics when we look at nmr
+ 
+
+ align:start position:0%
+mechanics when we look at nmr
+experiments we can treat the whole
+
+ align:start position:0%
+experiments we can treat the whole
+ 
+
+ align:start position:0%
+experiments we can treat the whole
+sample as
+
+ align:start position:0%
+sample as
+ 
+
+ align:start position:0%
+sample as
+a collection of the nuclei so summing up
+
+ align:start position:0%
+a collection of the nuclei so summing up
+ 
+
+ align:start position:0%
+a collection of the nuclei so summing up
+all the individual
+
+ align:start position:0%
+all the individual
+ 
+
+ align:start position:0%
+all the individual
+magnetic moments and just look at the
+
+ align:start position:0%
+magnetic moments and just look at the
+ 
+
+ align:start position:0%
+magnetic moments and just look at the
+bulk magnetization
+
+ align:start position:0%
+bulk magnetization
+ 
+
+ align:start position:0%
+bulk magnetization
+and so we can use statistical mechanics
+
+ align:start position:0%
+and so we can use statistical mechanics
+ 
+
+ align:start position:0%
+and so we can use statistical mechanics
+in order to
+
+ align:start position:0%
+in order to
+ 
+
+ align:start position:0%
+in order to
+figure out what's going on so
+
+ align:start position:0%
+figure out what's going on so
+ 
+
+ align:start position:0%
+figure out what's going on so
+we put our nucleus you know here's our
+
+ align:start position:0%
+we put our nucleus you know here's our
+ 
+
+ align:start position:0%
+we put our nucleus you know here's our
+sample we've got
+
+ align:start position:0%
+sample we've got
+ 
+
+ align:start position:0%
+sample we've got
+say 10 milligrams of material we've got
+
+ align:start position:0%
+say 10 milligrams of material we've got
+ 
+
+ align:start position:0%
+say 10 milligrams of material we've got
+it dissolved in about 600 microliters of
+
+ align:start position:0%
+it dissolved in about 600 microliters of
+ 
+
+ align:start position:0%
+it dissolved in about 600 microliters of
+a deuterated solvent
+
+ align:start position:0%
+a deuterated solvent
+ 
+
+ align:start position:0%
+a deuterated solvent
+we drop it down so it goes in our probe
+
+ align:start position:0%
+we drop it down so it goes in our probe
+ 
+
+ align:start position:0%
+we drop it down so it goes in our probe
+in the magnet
+
+ align:start position:0%
+in the magnet
+ 
+
+ align:start position:0%
+in the magnet
+and our collection of nuclei will start
+
+ align:start position:0%
+and our collection of nuclei will start
+ 
+
+ align:start position:0%
+and our collection of nuclei will start
+precessing
+
+ align:start position:0%
+precessing
+ 
+
+ align:start position:0%
+precessing
+either aligned with the field or aligned
+
+ align:start position:0%
+either aligned with the field or aligned
+ 
+
+ align:start position:0%
+either aligned with the field or aligned
+opposite the field so there will be a
+
+ align:start position:0%
+opposite the field so there will be a
+ 
+
+ align:start position:0%
+opposite the field so there will be a
+slight
+
+ align:start position:0%
+slight
+ 
+
+ align:start position:0%
+slight
+energetic preference for those nucleis
+
+ align:start position:0%
+energetic preference for those nucleis
+ 
+
+ align:start position:0%
+energetic preference for those nucleis
+to have their magnetic moment aligned
+
+ align:start position:0%
+to have their magnetic moment aligned
+ 
+
+ align:start position:0%
+to have their magnetic moment aligned
+with the field
+
+ align:start position:0%
+with the field
+ 
+
+ align:start position:0%
+with the field
+and that population difference will
+
+ align:start position:0%
+and that population difference will
+ 
+
+ align:start position:0%
+and that population difference will
+result
+
+ align:start position:0%
+result
+ 
+
+ align:start position:0%
+result
+in this net magnetization that we call
+
+ align:start position:0%
+in this net magnetization that we call
+ 
+
+ align:start position:0%
+in this net magnetization that we call
+the bulk magnetization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+put that down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can jump from thinking of
+
+ align:start position:0%
+so we can jump from thinking of
+ 
+
+ align:start position:0%
+so we can jump from thinking of
+vectors to thinking of energy levels so
+
+ align:start position:0%
+vectors to thinking of energy levels so
+ 
+
+ align:start position:0%
+vectors to thinking of energy levels so
+everything that is aligned with the
+
+ align:start position:0%
+everything that is aligned with the
+ 
+
+ align:start position:0%
+everything that is aligned with the
+field is going to be
+
+ align:start position:0%
+field is going to be
+ 
+
+ align:start position:0%
+field is going to be
+at a lower energy level and we call that
+
+ align:start position:0%
+at a lower energy level and we call that
+ 
+
+ align:start position:0%
+at a lower energy level and we call that
+just the plus one half nuclei and
+
+ align:start position:0%
+just the plus one half nuclei and
+ 
+
+ align:start position:0%
+just the plus one half nuclei and
+everything that is aligned against the
+
+ align:start position:0%
+everything that is aligned against the
+ 
+
+ align:start position:0%
+everything that is aligned against the
+field is going to be at a higher energy
+
+ align:start position:0%
+field is going to be at a higher energy
+ 
+
+ align:start position:0%
+field is going to be at a higher energy
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+at negative one half and so the
+
+ align:start position:0%
+at negative one half and so the
+ 
+
+ align:start position:0%
+at negative one half and so the
+difference between these two levels is
+
+ align:start position:0%
+difference between these two levels is
+ 
+
+ align:start position:0%
+difference between these two levels is
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+increase as the strength of the magnetic
+
+ align:start position:0%
+increase as the strength of the magnetic
+ 
+
+ align:start position:0%
+increase as the strength of the magnetic
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+increases and so you know maybe
+
+ align:start position:0%
+increases and so you know maybe
+ 
+
+ align:start position:0%
+increases and so you know maybe
+over here on the 60 megahertz the
+
+ align:start position:0%
+over here on the 60 megahertz the
+ 
+
+ align:start position:0%
+over here on the 60 megahertz the
+difference is only that much but when
+
+ align:start position:0%
+difference is only that much but when
+ 
+
+ align:start position:0%
+difference is only that much but when
+you get to our 600
+
+ align:start position:0%
+you get to our 600
+ 
+
+ align:start position:0%
+you get to our 600
+it's a lot more here's where the
+
+ align:start position:0%
+it's a lot more here's where the
+ 
+
+ align:start position:0%
+it's a lot more here's where the
+measurement or the principle behind the
+
+ align:start position:0%
+measurement or the principle behind the
+ 
+
+ align:start position:0%
+measurement or the principle behind the
+nmr measurement comes in
+
+ align:start position:0%
+nmr measurement comes in
+ 
+
+ align:start position:0%
+nmr measurement comes in
+you're making nuclei transition from
+
+ align:start position:0%
+you're making nuclei transition from
+ 
+
+ align:start position:0%
+you're making nuclei transition from
+one energy level to the other energy
+
+ align:start position:0%
+one energy level to the other energy
+ 
+
+ align:start position:0%
+one energy level to the other energy
+level so you're perturbing their
+
+ align:start position:0%
+level so you're perturbing their
+ 
+
+ align:start position:0%
+level so you're perturbing their
+equilibrium distribution
+
+ align:start position:0%
+equilibrium distribution
+ 
+
+ align:start position:0%
+equilibrium distribution
+and then you're letting them relax back
+
+ align:start position:0%
+and then you're letting them relax back
+ 
+
+ align:start position:0%
+and then you're letting them relax back
+and that's what gives off the signal
+
+ align:start position:0%
+and that's what gives off the signal
+ 
+
+ align:start position:0%
+and that's what gives off the signal
+that we make use of in nmr
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i guess i jumped too far ahead and my
+
+ align:start position:0%
+so i guess i jumped too far ahead and my
+ 
+
+ align:start position:0%
+so i guess i jumped too far ahead and my
+verbiage so
+
+ align:start position:0%
+verbiage so
+ 
+
+ align:start position:0%
+verbiage so
+we have our have our sample in there
+
+ align:start position:0%
+we have our have our sample in there
+ 
+
+ align:start position:0%
+we have our have our sample in there
+it's lined up
+
+ align:start position:0%
+it's lined up
+ 
+
+ align:start position:0%
+it's lined up
+and we perturb it with an rf pulse so
+
+ align:start position:0%
+and we perturb it with an rf pulse so
+ 
+
+ align:start position:0%
+and we perturb it with an rf pulse so
+now i've jumped back to vectors
+
+ align:start position:0%
+now i've jumped back to vectors
+ 
+
+ align:start position:0%
+now i've jumped back to vectors
+if you think of it in terms of vectors
+
+ align:start position:0%
+if you think of it in terms of vectors
+ 
+
+ align:start position:0%
+if you think of it in terms of vectors
+when you
+
+ align:start position:0%
+when you
+ 
+
+ align:start position:0%
+when you
+when you generate that radio frequency
+
+ align:start position:0%
+when you generate that radio frequency
+ 
+
+ align:start position:0%
+when you generate that radio frequency
+pulse that has the frequency equal to
+
+ align:start position:0%
+pulse that has the frequency equal to
+ 
+
+ align:start position:0%
+pulse that has the frequency equal to
+the difference in those energy levels
+
+ align:start position:0%
+the difference in those energy levels
+ 
+
+ align:start position:0%
+the difference in those energy levels
+you are in essence generating a small
+
+ align:start position:0%
+you are in essence generating a small
+ 
+
+ align:start position:0%
+you are in essence generating a small
+magnetic field that is aligned
+
+ align:start position:0%
+magnetic field that is aligned
+ 
+
+ align:start position:0%
+magnetic field that is aligned
+in this case it's arbitrary but we'll
+
+ align:start position:0%
+in this case it's arbitrary but we'll
+ 
+
+ align:start position:0%
+in this case it's arbitrary but we'll
+say it's aligned along the x-axis
+
+ align:start position:0%
+say it's aligned along the x-axis
+ 
+
+ align:start position:0%
+say it's aligned along the x-axis
+that acts to topple or not topple
+
+ align:start position:0%
+that acts to topple or not topple
+ 
+
+ align:start position:0%
+that acts to topple or not topple
+tip this bulk magnetization vector off
+
+ align:start position:0%
+tip this bulk magnetization vector off
+ 
+
+ align:start position:0%
+tip this bulk magnetization vector off
+of being pointed
+
+ align:start position:0%
+of being pointed
+ 
+
+ align:start position:0%
+of being pointed
+with the main field over into the x y
+
+ align:start position:0%
+with the main field over into the x y
+ 
+
+ align:start position:0%
+with the main field over into the x y
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+it's still precessing around at
+
+ align:start position:0%
+it's still precessing around at
+ 
+
+ align:start position:0%
+it's still precessing around at
+that characteristic frequency
+
+ align:start position:0%
+that characteristic frequency
+ 
+
+ align:start position:0%
+that characteristic frequency
+and when it has a component in the xy
+
+ align:start position:0%
+and when it has a component in the xy
+ 
+
+ align:start position:0%
+and when it has a component in the xy
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+that will generate a current in these
+
+ align:start position:0%
+that will generate a current in these
+ 
+
+ align:start position:0%
+that will generate a current in these
+little coils in the probe
+
+ align:start position:0%
+little coils in the probe
+ 
+
+ align:start position:0%
+little coils in the probe
+which is then received back at the
+
+ align:start position:0%
+which is then received back at the
+ 
+
+ align:start position:0%
+which is then received back at the
+console and sent to the computer
+
+ align:start position:0%
+console and sent to the computer
+ 
+
+ align:start position:0%
+console and sent to the computer
+so we pulse our sample
+
+ align:start position:0%
+so we pulse our sample
+ 
+
+ align:start position:0%
+so we pulse our sample
+and depending on how long we turn on
+
+ align:start position:0%
+and depending on how long we turn on
+ 
+
+ align:start position:0%
+and depending on how long we turn on
+that pulse for and it's usually the
+
+ align:start position:0%
+that pulse for and it's usually the
+ 
+
+ align:start position:0%
+that pulse for and it's usually the
+order of microseconds i think our
+
+ align:start position:0%
+order of microseconds i think our
+ 
+
+ align:start position:0%
+order of microseconds i think our
+pulses are set up to be about 10
+
+ align:start position:0%
+pulses are set up to be about 10
+ 
+
+ align:start position:0%
+pulses are set up to be about 10
+microseconds we can tip
+
+ align:start position:0%
+microseconds we can tip
+ 
+
+ align:start position:0%
+microseconds we can tip
+this over to some varying degree
+
+ align:start position:0%
+this over to some varying degree
+ 
+
+ align:start position:0%
+this over to some varying degree
+and so usually we try and tip it over by
+
+ align:start position:0%
+and so usually we try and tip it over by
+ 
+
+ align:start position:0%
+and so usually we try and tip it over by
+a specific amount
+
+ align:start position:0%
+a specific amount
+ 
+
+ align:start position:0%
+a specific amount
+which is a 90 degree pulse because that
+
+ align:start position:0%
+which is a 90 degree pulse because that
+ 
+
+ align:start position:0%
+which is a 90 degree pulse because that
+will generate the maximum amount of
+
+ align:start position:0%
+will generate the maximum amount of
+ 
+
+ align:start position:0%
+will generate the maximum amount of
+signal
+
+ align:start position:0%
+signal
+ 
+
+ align:start position:0%
+signal
+that we can get out so we tip it over
+
+ align:start position:0%
+that we can get out so we tip it over
+ 
+
+ align:start position:0%
+that we can get out so we tip it over
+into the xy plane we turn off that
+
+ align:start position:0%
+into the xy plane we turn off that
+ 
+
+ align:start position:0%
+into the xy plane we turn off that
+pulse and then we let it relax and we
+
+ align:start position:0%
+pulse and then we let it relax and we
+ 
+
+ align:start position:0%
+pulse and then we let it relax and we
+collect our signal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our signals i think i said this before
+
+ align:start position:0%
+our signals i think i said this before
+ 
+
+ align:start position:0%
+our signals i think i said this before
+is called the free induction decay and
+
+ align:start position:0%
+is called the free induction decay and
+ 
+
+ align:start position:0%
+is called the free induction decay and
+so here's another diagram of it
+
+ align:start position:0%
+so here's another diagram of it
+ 
+
+ align:start position:0%
+so here's another diagram of it
+we've turned off that pulse the signal
+
+ align:start position:0%
+we've turned off that pulse the signal
+ 
+
+ align:start position:0%
+we've turned off that pulse the signal
+is precessing here but it relaxes back
+
+ align:start position:0%
+is precessing here but it relaxes back
+ 
+
+ align:start position:0%
+is precessing here but it relaxes back
+so that the component here gets shorter
+
+ align:start position:0%
+so that the component here gets shorter
+ 
+
+ align:start position:0%
+so that the component here gets shorter
+and shorter while we
+
+ align:start position:0%
+and shorter while we
+ 
+
+ align:start position:0%
+and shorter while we
+grow back the component in the z
+
+ align:start position:0%
+grow back the component in the z
+ 
+
+ align:start position:0%
+grow back the component in the z
+direction that gives us this voltage
+
+ align:start position:0%
+direction that gives us this voltage
+ 
+
+ align:start position:0%
+direction that gives us this voltage
+in my laser diet that gets picked up in
+
+ align:start position:0%
+in my laser diet that gets picked up in
+ 
+
+ align:start position:0%
+in my laser diet that gets picked up in
+the coil
+
+ align:start position:0%
+the coil
+ 
+
+ align:start position:0%
+the coil
+we can do that multiple times so
+
+ align:start position:0%
+we can do that multiple times so
+ 
+
+ align:start position:0%
+we can do that multiple times so
+if you've got a strong sample you can
+
+ align:start position:0%
+if you've got a strong sample you can
+ 
+
+ align:start position:0%
+if you've got a strong sample you can
+just take one scan but
+
+ align:start position:0%
+just take one scan but
+ 
+
+ align:start position:0%
+just take one scan but
+usually we'll take multiple scans
+
+ align:start position:0%
+usually we'll take multiple scans
+ 
+
+ align:start position:0%
+usually we'll take multiple scans
+because you can do what's called
+
+ align:start position:0%
+because you can do what's called
+ 
+
+ align:start position:0%
+because you can do what's called
+signal averaging which is add them
+
+ align:start position:0%
+signal averaging which is add them
+ 
+
+ align:start position:0%
+signal averaging which is add them
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+um you can and that can help you remove
+
+ align:start position:0%
+um you can and that can help you remove
+ 
+
+ align:start position:0%
+um you can and that can help you remove
+artifacts increase your
+
+ align:start position:0%
+artifacts increase your
+ 
+
+ align:start position:0%
+artifacts increase your
+signal to noise and other things
+
+ align:start position:0%
+signal to noise and other things
+ 
+
+ align:start position:0%
+signal to noise and other things
+so that's what the free induction decay
+
+ align:start position:0%
+so that's what the free induction decay
+ 
+
+ align:start position:0%
+so that's what the free induction decay
+is in the nmr signal
+
+ align:start position:0%
+is in the nmr signal
+ 
+
+ align:start position:0%
+is in the nmr signal
+i put this back in my slide pack
+
+ align:start position:0%
+i put this back in my slide pack
+ 
+
+ align:start position:0%
+i put this back in my slide pack
+after um i gave
+
+ align:start position:0%
+after um i gave
+ 
+
+ align:start position:0%
+after um i gave
+the slides to professor dolan to print
+
+ align:start position:0%
+the slides to professor dolan to print
+ 
+
+ align:start position:0%
+the slides to professor dolan to print
+so you don't have this in your handouts
+
+ align:start position:0%
+so you don't have this in your handouts
+ 
+
+ align:start position:0%
+so you don't have this in your handouts
+unfortunately
+
+ align:start position:0%
+unfortunately
+ 
+
+ align:start position:0%
+unfortunately
+this is just i was thinking this is
+
+ align:start position:0%
+this is just i was thinking this is
+ 
+
+ align:start position:0%
+this is just i was thinking this is
+still a good way to show about the nmr
+
+ align:start position:0%
+still a good way to show about the nmr
+ 
+
+ align:start position:0%
+still a good way to show about the nmr
+signal but in terms of the number of
+
+ align:start position:0%
+signal but in terms of the number of
+ 
+
+ align:start position:0%
+signal but in terms of the number of
+spins in the energy levels
+
+ align:start position:0%
+spins in the energy levels
+ 
+
+ align:start position:0%
+spins in the energy levels
+so here's your equilibrium you've got
+
+ align:start position:0%
+so here's your equilibrium you've got
+ 
+
+ align:start position:0%
+so here's your equilibrium you've got
+more spins
+
+ align:start position:0%
+more spins
+ 
+
+ align:start position:0%
+more spins
+pointing you know i'm saying they're
+
+ align:start position:0%
+pointing you know i'm saying they're
+ 
+
+ align:start position:0%
+pointing you know i'm saying they're
+pointing down in this lower energy level
+
+ align:start position:0%
+pointing down in this lower energy level
+ 
+
+ align:start position:0%
+pointing down in this lower energy level
+you pulse it and that equalizes the
+
+ align:start position:0%
+you pulse it and that equalizes the
+ 
+
+ align:start position:0%
+you pulse it and that equalizes the
+energy level so i
+
+ align:start position:0%
+energy level so i
+ 
+
+ align:start position:0%
+energy level so i
+will forget how many are in each but
+
+ align:start position:0%
+will forget how many are in each but
+ 
+
+ align:start position:0%
+will forget how many are in each but
+there's supposed to be an equal number
+
+ align:start position:0%
+there's supposed to be an equal number
+ 
+
+ align:start position:0%
+there's supposed to be an equal number
+of arrows
+
+ align:start position:0%
+of arrows
+ 
+
+ align:start position:0%
+of arrows
+then after you turn off that pulse the
+
+ align:start position:0%
+then after you turn off that pulse the
+ 
+
+ align:start position:0%
+then after you turn off that pulse the
+spins that got transitioned to the upper
+
+ align:start position:0%
+spins that got transitioned to the upper
+ 
+
+ align:start position:0%
+spins that got transitioned to the upper
+energy level will relax
+
+ align:start position:0%
+energy level will relax
+ 
+
+ align:start position:0%
+energy level will relax
+back down so there's a predominantly
+
+ align:start position:0%
+back down so there's a predominantly
+ 
+
+ align:start position:0%
+back down so there's a predominantly
+they're more predominantly in the lower
+
+ align:start position:0%
+they're more predominantly in the lower
+ 
+
+ align:start position:0%
+they're more predominantly in the lower
+energy than the upper energy
+
+ align:start position:0%
+energy than the upper energy
+ 
+
+ align:start position:0%
+energy than the upper energy
+as they do that they give off
+
+ align:start position:0%
+as they do that they give off
+ 
+
+ align:start position:0%
+as they do that they give off
+the free induction decay which is your
+
+ align:start position:0%
+the free induction decay which is your
+ 
+
+ align:start position:0%
+the free induction decay which is your
+nmr signal
+
+ align:start position:0%
+nmr signal
+ 
+
+ align:start position:0%
+nmr signal
+there any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what do we do with that fid
+
+ align:start position:0%
+okay so what do we do with that fid
+ 
+
+ align:start position:0%
+okay so what do we do with that fid
+you know i've been doing this i don't
+
+ align:start position:0%
+you know i've been doing this i don't
+ 
+
+ align:start position:0%
+you know i've been doing this i don't
+know since 1999
+
+ align:start position:0%
+know since 1999
+ 
+
+ align:start position:0%
+know since 1999
+i can look at an fid i can say well
+
+ align:start position:0%
+i can look at an fid i can say well
+ 
+
+ align:start position:0%
+i can look at an fid i can say well
+that's a long one i can look at an fid
+
+ align:start position:0%
+that's a long one i can look at an fid
+ 
+
+ align:start position:0%
+that's a long one i can look at an fid
+and say yeah that's got several
+
+ align:start position:0%
+and say yeah that's got several
+ 
+
+ align:start position:0%
+and say yeah that's got several
+different frequencies in there
+
+ align:start position:0%
+different frequencies in there
+ 
+
+ align:start position:0%
+different frequencies in there
+but as far as looking in an fid and
+
+ align:start position:0%
+but as far as looking in an fid and
+ 
+
+ align:start position:0%
+but as far as looking in an fid and
+saying oh that comes from dmf or oh that
+
+ align:start position:0%
+saying oh that comes from dmf or oh that
+ 
+
+ align:start position:0%
+saying oh that comes from dmf or oh that
+comes from ethyl acetate
+
+ align:start position:0%
+comes from ethyl acetate
+ 
+
+ align:start position:0%
+comes from ethyl acetate
+no i can't do that and i doubt that
+
+ align:start position:0%
+no i can't do that and i doubt that
+ 
+
+ align:start position:0%
+no i can't do that and i doubt that
+anybody else could
+
+ align:start position:0%
+anybody else could
+ 
+
+ align:start position:0%
+anybody else could
+so we have to transform that
+
+ align:start position:0%
+so we have to transform that
+ 
+
+ align:start position:0%
+so we have to transform that
+and somehow make sense of it and so that
+
+ align:start position:0%
+and somehow make sense of it and so that
+ 
+
+ align:start position:0%
+and somehow make sense of it and so that
+is done
+
+ align:start position:0%
+is done
+ 
+
+ align:start position:0%
+is done
+using a fourier transform and so a
+
+ align:start position:0%
+using a fourier transform and so a
+ 
+
+ align:start position:0%
+using a fourier transform and so a
+fourier transform
+
+ align:start position:0%
+fourier transform
+ 
+
+ align:start position:0%
+fourier transform
+takes something that is in the time
+
+ align:start position:0%
+takes something that is in the time
+ 
+
+ align:start position:0%
+takes something that is in the time
+domain
+
+ align:start position:0%
+domain
+ 
+
+ align:start position:0%
+domain
+and it transforms it to the frequency
+
+ align:start position:0%
+and it transforms it to the frequency
+ 
+
+ align:start position:0%
+and it transforms it to the frequency
+domain
+
+ align:start position:0%
+domain
+ 
+
+ align:start position:0%
+domain
+and a long time ago before the advent of
+
+ align:start position:0%
+and a long time ago before the advent of
+ 
+
+ align:start position:0%
+and a long time ago before the advent of
+computers
+
+ align:start position:0%
+computers
+ 
+
+ align:start position:0%
+computers
+nmr wasn't done using f fourier
+
+ align:start position:0%
+nmr wasn't done using f fourier
+ 
+
+ align:start position:0%
+nmr wasn't done using f fourier
+transforms because it was
+
+ align:start position:0%
+transforms because it was
+ 
+
+ align:start position:0%
+transforms because it was
+computationally
+
+ align:start position:0%
+computationally
+ 
+
+ align:start position:0%
+computationally
+too difficult and so someone
+
+ align:start position:0%
+too difficult and so someone
+ 
+
+ align:start position:0%
+too difficult and so someone
+back in the 60s actually someone famous
+
+ align:start position:0%
+back in the 60s actually someone famous
+ 
+
+ align:start position:0%
+back in the 60s actually someone famous
+at ibm developed a way
+
+ align:start position:0%
+at ibm developed a way
+ 
+
+ align:start position:0%
+at ibm developed a way
+to do this make it a little bit easier
+
+ align:start position:0%
+to do this make it a little bit easier
+ 
+
+ align:start position:0%
+to do this make it a little bit easier
+but they still had to print out little
+
+ align:start position:0%
+but they still had to print out little
+ 
+
+ align:start position:0%
+but they still had to print out little
+cards and you'd punch holes in them and
+
+ align:start position:0%
+cards and you'd punch holes in them and
+ 
+
+ align:start position:0%
+cards and you'd punch holes in them and
+it would take
+
+ align:start position:0%
+it would take
+ 
+
+ align:start position:0%
+it would take
+days and days to feed it into a machine
+
+ align:start position:0%
+days and days to feed it into a machine
+ 
+
+ align:start position:0%
+days and days to feed it into a machine
+and nowadays you know your
+
+ align:start position:0%
+and nowadays you know your
+ 
+
+ align:start position:0%
+and nowadays you know your
+phone can do it it's got more
+
+ align:start position:0%
+phone can do it it's got more
+ 
+
+ align:start position:0%
+phone can do it it's got more
+computational power than something that
+
+ align:start position:0%
+computational power than something that
+ 
+
+ align:start position:0%
+computational power than something that
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+old room so everything is done by
+
+ align:start position:0%
+old room so everything is done by
+ 
+
+ align:start position:0%
+old room so everything is done by
+fourier transform now
+
+ align:start position:0%
+fourier transform now
+ 
+
+ align:start position:0%
+fourier transform now
+that gives us our spectrum which
+
+ align:start position:0%
+that gives us our spectrum which
+ 
+
+ align:start position:0%
+that gives us our spectrum which
+consists of lines
+
+ align:start position:0%
+consists of lines
+ 
+
+ align:start position:0%
+consists of lines
+which we can look at and we can
+
+ align:start position:0%
+which we can look at and we can
+ 
+
+ align:start position:0%
+which we can look at and we can
+interpret and figure out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and no i couldn't do a fourier transform
+
+ align:start position:0%
+and no i couldn't do a fourier transform
+ 
+
+ align:start position:0%
+and no i couldn't do a fourier transform
+or solve one
+
+ align:start position:0%
+or solve one
+ 
+
+ align:start position:0%
+or solve one
+in my head or even on paper so it's just
+
+ align:start position:0%
+in my head or even on paper so it's just
+ 
+
+ align:start position:0%
+in my head or even on paper so it's just
+something the computer does
+
+ align:start position:0%
+something the computer does
+ 
+
+ align:start position:0%
+something the computer does
+so let's back up i've given away a lot
+
+ align:start position:0%
+so let's back up i've given away a lot
+ 
+
+ align:start position:0%
+so let's back up i've given away a lot
+of this because i've already showed you
+
+ align:start position:0%
+of this because i've already showed you
+ 
+
+ align:start position:0%
+of this because i've already showed you
+several spectra and you see that there
+
+ align:start position:0%
+several spectra and you see that there
+ 
+
+ align:start position:0%
+several spectra and you see that there
+are multiple lines
+
+ align:start position:0%
+are multiple lines
+ 
+
+ align:start position:0%
+are multiple lines
+but you know here's the free curve the
+
+ align:start position:0%
+but you know here's the free curve the
+ 
+
+ align:start position:0%
+but you know here's the free curve the
+equation for the frequency
+
+ align:start position:0%
+equation for the frequency
+ 
+
+ align:start position:0%
+equation for the frequency
+being proportional to the magnetic field
+
+ align:start position:0%
+being proportional to the magnetic field
+ 
+
+ align:start position:0%
+being proportional to the magnetic field
+strength and you might
+
+ align:start position:0%
+strength and you might
+ 
+
+ align:start position:0%
+strength and you might
+think okay i have protons
+
+ align:start position:0%
+think okay i have protons
+ 
+
+ align:start position:0%
+think okay i have protons
+why don't i just get one peak because i
+
+ align:start position:0%
+why don't i just get one peak because i
+ 
+
+ align:start position:0%
+why don't i just get one peak because i
+have protons
+
+ align:start position:0%
+have protons
+ 
+
+ align:start position:0%
+have protons
+and i would have one peak for protons
+
+ align:start position:0%
+and i would have one peak for protons
+ 
+
+ align:start position:0%
+and i would have one peak for protons
+and one peak for other nuclei
+
+ align:start position:0%
+and one peak for other nuclei
+ 
+
+ align:start position:0%
+and one peak for other nuclei
+if it did that i wouldn't be up here
+
+ align:start position:0%
+if it did that i wouldn't be up here
+ 
+
+ align:start position:0%
+if it did that i wouldn't be up here
+talking to you
+
+ align:start position:0%
+talking to you
+ 
+
+ align:start position:0%
+talking to you
+about this because while it might be a
+
+ align:start position:0%
+about this because while it might be a
+ 
+
+ align:start position:0%
+about this because while it might be a
+fine and dandy measurement for a
+
+ align:start position:0%
+fine and dandy measurement for a
+ 
+
+ align:start position:0%
+fine and dandy measurement for a
+physicist
+
+ align:start position:0%
+physicist
+ 
+
+ align:start position:0%
+physicist
+to use it'd be useless for us in
+
+ align:start position:0%
+to use it'd be useless for us in
+ 
+
+ align:start position:0%
+to use it'd be useless for us in
+chemistry because we'd only get one peak
+
+ align:start position:0%
+chemistry because we'd only get one peak
+ 
+
+ align:start position:0%
+chemistry because we'd only get one peak
+for all the different protons that are
+
+ align:start position:0%
+for all the different protons that are
+ 
+
+ align:start position:0%
+for all the different protons that are
+in our sample luckily
+
+ align:start position:0%
+in our sample luckily
+ 
+
+ align:start position:0%
+in our sample luckily
+when you put your sample in a magnet
+
+ align:start position:0%
+when you put your sample in a magnet
+ 
+
+ align:start position:0%
+when you put your sample in a magnet
+whatever the local magnetic
+
+ align:start position:0%
+whatever the local magnetic
+ 
+
+ align:start position:0%
+whatever the local magnetic
+environment is that the nuclei
+
+ align:start position:0%
+environment is that the nuclei
+ 
+
+ align:start position:0%
+environment is that the nuclei
+reside in that is going to
+
+ align:start position:0%
+reside in that is going to
+ 
+
+ align:start position:0%
+reside in that is going to
+modify the lar or the external field
+
+ align:start position:0%
+modify the lar or the external field
+ 
+
+ align:start position:0%
+modify the lar or the external field
+that those
+
+ align:start position:0%
+that those
+ 
+
+ align:start position:0%
+that those
+nuclei feel and so that's what spreads
+
+ align:start position:0%
+nuclei feel and so that's what spreads
+ 
+
+ align:start position:0%
+nuclei feel and so that's what spreads
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+our single signal from proton
+
+ align:start position:0%
+our single signal from proton
+ 
+
+ align:start position:0%
+our single signal from proton
+a proton into the different regions of
+
+ align:start position:0%
+a proton into the different regions of
+ 
+
+ align:start position:0%
+a proton into the different regions of
+the spectrum
+
+ align:start position:0%
+the spectrum
+ 
+
+ align:start position:0%
+the spectrum
+so this is supposed to be ethyl acetate
+
+ align:start position:0%
+so this is supposed to be ethyl acetate
+ 
+
+ align:start position:0%
+so this is supposed to be ethyl acetate
+i've got a doubly bound
+
+ align:start position:0%
+i've got a doubly bound
+ 
+
+ align:start position:0%
+i've got a doubly bound
+oxygen here i've got a single bound
+
+ align:start position:0%
+oxygen here i've got a single bound
+ 
+
+ align:start position:0%
+oxygen here i've got a single bound
+oxygen here methylene methyl
+
+ align:start position:0%
+oxygen here methylene methyl
+ 
+
+ align:start position:0%
+oxygen here methylene methyl
+and methyl so oxygen i think
+
+ align:start position:0%
+and methyl so oxygen i think
+ 
+
+ align:start position:0%
+and methyl so oxygen i think
+as everybody might know is
+
+ align:start position:0%
+as everybody might know is
+ 
+
+ align:start position:0%
+as everybody might know is
+electronegative it's really greedy it
+
+ align:start position:0%
+electronegative it's really greedy it
+ 
+
+ align:start position:0%
+electronegative it's really greedy it
+doesn't like to share its electrons
+
+ align:start position:0%
+doesn't like to share its electrons
+ 
+
+ align:start position:0%
+doesn't like to share its electrons
+so it pulls electron density away
+
+ align:start position:0%
+so it pulls electron density away
+ 
+
+ align:start position:0%
+so it pulls electron density away
+from things that are nearby and that's
+
+ align:start position:0%
+from things that are nearby and that's
+ 
+
+ align:start position:0%
+from things that are nearby and that's
+why i've got these little deltas up here
+
+ align:start position:0%
+why i've got these little deltas up here
+ 
+
+ align:start position:0%
+why i've got these little deltas up here
+indicating the partial negative charge
+
+ align:start position:0%
+indicating the partial negative charge
+ 
+
+ align:start position:0%
+indicating the partial negative charge
+the things that are bound closest to it
+
+ align:start position:0%
+the things that are bound closest to it
+ 
+
+ align:start position:0%
+the things that are bound closest to it
+and even further out they're going to be
+
+ align:start position:0%
+and even further out they're going to be
+ 
+
+ align:start position:0%
+and even further out they're going to be
+more positively charged or partial
+
+ align:start position:0%
+more positively charged or partial
+ 
+
+ align:start position:0%
+more positively charged or partial
+positively charged than they would have
+
+ align:start position:0%
+positively charged than they would have
+ 
+
+ align:start position:0%
+positively charged than they would have
+been because the electron density is
+
+ align:start position:0%
+been because the electron density is
+ 
+
+ align:start position:0%
+been because the electron density is
+being pulled away from it
+
+ align:start position:0%
+being pulled away from it
+ 
+
+ align:start position:0%
+being pulled away from it
+so that's what helps spread out those
+
+ align:start position:0%
+so that's what helps spread out those
+ 
+
+ align:start position:0%
+so that's what helps spread out those
+signals
+
+ align:start position:0%
+signals
+ 
+
+ align:start position:0%
+signals
+we call this chemical shift
+
+ align:start position:0%
+we call this chemical shift
+ 
+
+ align:start position:0%
+we call this chemical shift
+it's denoted on a spectrum as ppm and
+
+ align:start position:0%
+it's denoted on a spectrum as ppm and
+ 
+
+ align:start position:0%
+it's denoted on a spectrum as ppm and
+oftentimes it's denoted with delta not
+
+ align:start position:0%
+oftentimes it's denoted with delta not
+ 
+
+ align:start position:0%
+oftentimes it's denoted with delta not
+to be confused with the delta i've used
+
+ align:start position:0%
+to be confused with the delta i've used
+ 
+
+ align:start position:0%
+to be confused with the delta i've used
+for the small
+
+ align:start position:0%
+for the small
+ 
+
+ align:start position:0%
+for the small
+charges but you might see that on the
+
+ align:start position:0%
+charges but you might see that on the
+ 
+
+ align:start position:0%
+charges but you might see that on the
+axis
+
+ align:start position:0%
+axis
+ 
+
+ align:start position:0%
+axis
+of it so anything that can perturb
+
+ align:start position:0%
+of it so anything that can perturb
+ 
+
+ align:start position:0%
+of it so anything that can perturb
+electron density
+
+ align:start position:0%
+electron density
+ 
+
+ align:start position:0%
+electron density
+will affect we call it the shielding of
+
+ align:start position:0%
+will affect we call it the shielding of
+ 
+
+ align:start position:0%
+will affect we call it the shielding of
+the nucleus
+
+ align:start position:0%
+the nucleus
+ 
+
+ align:start position:0%
+the nucleus
+not only electronegative things where
+
+ align:start position:0%
+not only electronegative things where
+ 
+
+ align:start position:0%
+not only electronegative things where
+nuclei are oriented in relation to
+
+ align:start position:0%
+nuclei are oriented in relation to
+ 
+
+ align:start position:0%
+nuclei are oriented in relation to
+double bonds
+
+ align:start position:0%
+double bonds
+ 
+
+ align:start position:0%
+double bonds
+in a benzene ring you've got the clouds
+
+ align:start position:0%
+in a benzene ring you've got the clouds
+ 
+
+ align:start position:0%
+in a benzene ring you've got the clouds
+of electron density
+
+ align:start position:0%
+of electron density
+ 
+
+ align:start position:0%
+of electron density
+in those pi orbitals and
+
+ align:start position:0%
+in those pi orbitals and
+ 
+
+ align:start position:0%
+in those pi orbitals and
+things that get oriented directed into
+
+ align:start position:0%
+things that get oriented directed into
+ 
+
+ align:start position:0%
+things that get oriented directed into
+that will be more shielded
+
+ align:start position:0%
+that will be more shielded
+ 
+
+ align:start position:0%
+that will be more shielded
+things that are sticking off the ring
+
+ align:start position:0%
+things that are sticking off the ring
+ 
+
+ align:start position:0%
+things that are sticking off the ring
+equatorially or not equatorial
+
+ align:start position:0%
+equatorially or not equatorial
+ 
+
+ align:start position:0%
+equatorially or not equatorial
+but in the plane will be de-shielded so
+
+ align:start position:0%
+but in the plane will be de-shielded so
+ 
+
+ align:start position:0%
+but in the plane will be de-shielded so
+that has an effect
+
+ align:start position:0%
+that has an effect
+ 
+
+ align:start position:0%
+that has an effect
+so all these things will combine
+
+ align:start position:0%
+so all these things will combine
+ 
+
+ align:start position:0%
+so all these things will combine
+together to spread out what's in your
+
+ align:start position:0%
+together to spread out what's in your
+ 
+
+ align:start position:0%
+together to spread out what's in your
+spectrum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here is just a spectrum
+
+ align:start position:0%
+so here is just a spectrum
+ 
+
+ align:start position:0%
+so here is just a spectrum
+of my ethyl acetate and so notice i've
+
+ align:start position:0%
+of my ethyl acetate and so notice i've
+ 
+
+ align:start position:0%
+of my ethyl acetate and so notice i've
+spread it out well i haven't spread it
+
+ align:start position:0%
+spread it out well i haven't spread it
+ 
+
+ align:start position:0%
+spread it out well i haven't spread it
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+it is spread out into three separate
+
+ align:start position:0%
+it is spread out into three separate
+ 
+
+ align:start position:0%
+it is spread out into three separate
+signals
+
+ align:start position:0%
+signals
+ 
+
+ align:start position:0%
+signals
+you can use nmr solely as a fingerprint
+
+ align:start position:0%
+you can use nmr solely as a fingerprint
+ 
+
+ align:start position:0%
+you can use nmr solely as a fingerprint
+and tabulate i know that
+
+ align:start position:0%
+and tabulate i know that
+ 
+
+ align:start position:0%
+and tabulate i know that
+only such and such resonance is comet
+
+ align:start position:0%
+only such and such resonance is comet
+ 
+
+ align:start position:0%
+only such and such resonance is comet
+two-point i don't know we'll call that
+
+ align:start position:0%
+two-point i don't know we'll call that
+ 
+
+ align:start position:0%
+two-point i don't know we'll call that
+2.01 and so
+
+ align:start position:0%
+2.01 and so
+ 
+
+ align:start position:0%
+2.01 and so
+you can go look in a table and say oh
+
+ align:start position:0%
+you can go look in a table and say oh
+ 
+
+ align:start position:0%
+you can go look in a table and say oh
+well this must be from
+
+ align:start position:0%
+well this must be from
+ 
+
+ align:start position:0%
+well this must be from
+one of these small subset of molecules
+
+ align:start position:0%
+one of these small subset of molecules
+ 
+
+ align:start position:0%
+one of these small subset of molecules
+because they only have something at 2.01
+
+ align:start position:0%
+because they only have something at 2.01
+ 
+
+ align:start position:0%
+because they only have something at 2.01
+it's more important to be able to
+
+ align:start position:0%
+it's more important to be able to
+ 
+
+ align:start position:0%
+it's more important to be able to
+rationalize where things appear
+
+ align:start position:0%
+rationalize where things appear
+ 
+
+ align:start position:0%
+rationalize where things appear
+by or yeah where things appear on the
+
+ align:start position:0%
+by or yeah where things appear on the
+ 
+
+ align:start position:0%
+by or yeah where things appear on the
+spectrum by where they are in the
+
+ align:start position:0%
+spectrum by where they are in the
+ 
+
+ align:start position:0%
+spectrum by where they are in the
+molecule because that will help you
+
+ align:start position:0%
+molecule because that will help you
+ 
+
+ align:start position:0%
+molecule because that will help you
+analyze the spectrum better so if we
+
+ align:start position:0%
+analyze the spectrum better so if we
+ 
+
+ align:start position:0%
+analyze the spectrum better so if we
+look at this
+
+ align:start position:0%
+look at this
+ 
+
+ align:start position:0%
+look at this
+we've got three peaks now i talked about
+
+ align:start position:0%
+we've got three peaks now i talked about
+ 
+
+ align:start position:0%
+we've got three peaks now i talked about
+intensity being one of the properties of
+
+ align:start position:0%
+intensity being one of the properties of
+ 
+
+ align:start position:0%
+intensity being one of the properties of
+the signal earlier
+
+ align:start position:0%
+the signal earlier
+ 
+
+ align:start position:0%
+the signal earlier
+i don't know if you can see this but
+
+ align:start position:0%
+i don't know if you can see this but
+ 
+
+ align:start position:0%
+i don't know if you can see this but
+there's a
+
+ align:start position:0%
+there's a
+ 
+
+ align:start position:0%
+there's a
+3.10 under there
+
+ align:start position:0%
+3.10 under there
+ 
+
+ align:start position:0%
+3.10 under there
+3.10 under here and a 2
+
+ align:start position:0%
+3.10 under here and a 2
+ 
+
+ align:start position:0%
+3.10 under here and a 2
+under here so that's the relative
+
+ align:start position:0%
+under here so that's the relative
+ 
+
+ align:start position:0%
+under here so that's the relative
+intensity
+
+ align:start position:0%
+intensity
+ 
+
+ align:start position:0%
+intensity
+of those signals now
+
+ align:start position:0%
+of those signals now
+ 
+
+ align:start position:0%
+of those signals now
+one thing that is common when you're
+
+ align:start position:0%
+one thing that is common when you're
+ 
+
+ align:start position:0%
+one thing that is common when you're
+first learning nmr is to think
+
+ align:start position:0%
+first learning nmr is to think
+ 
+
+ align:start position:0%
+first learning nmr is to think
+that the integrals are dead on exact so
+
+ align:start position:0%
+that the integrals are dead on exact so
+ 
+
+ align:start position:0%
+that the integrals are dead on exact so
+that it should be 3.00
+
+ align:start position:0%
+that it should be 3.00
+ 
+
+ align:start position:0%
+that it should be 3.00
+no it's going to be close but it's not
+
+ align:start position:0%
+no it's going to be close but it's not
+ 
+
+ align:start position:0%
+no it's going to be close but it's not
+going to be exact you've got to take
+
+ align:start position:0%
+going to be exact you've got to take
+ 
+
+ align:start position:0%
+going to be exact you've got to take
+great care
+
+ align:start position:0%
+great care
+ 
+
+ align:start position:0%
+great care
+when you're acquiring the spectrum to
+
+ align:start position:0%
+when you're acquiring the spectrum to
+ 
+
+ align:start position:0%
+when you're acquiring the spectrum to
+get your integrals to be as you know
+
+ align:start position:0%
+get your integrals to be as you know
+ 
+
+ align:start position:0%
+get your integrals to be as you know
+close to perfect
+
+ align:start position:0%
+close to perfect
+ 
+
+ align:start position:0%
+close to perfect
+so we call 3.13 so
+
+ align:start position:0%
+so we call 3.13 so
+ 
+
+ align:start position:0%
+so we call 3.13 so
+we know we can look at our molecule
+
+ align:start position:0%
+we know we can look at our molecule
+ 
+
+ align:start position:0%
+we know we can look at our molecule
+we've got two methyl groups so we can
+
+ align:start position:0%
+we've got two methyl groups so we can
+ 
+
+ align:start position:0%
+we've got two methyl groups so we can
+guess that these are both from the
+
+ align:start position:0%
+guess that these are both from the
+ 
+
+ align:start position:0%
+guess that these are both from the
+methyl groups
+
+ align:start position:0%
+methyl groups
+ 
+
+ align:start position:0%
+methyl groups
+because they integrate to three and that
+
+ align:start position:0%
+because they integrate to three and that
+ 
+
+ align:start position:0%
+because they integrate to three and that
+this is from the methylene
+
+ align:start position:0%
+this is from the methylene
+ 
+
+ align:start position:0%
+this is from the methylene
+because it integrates to two so why is
+
+ align:start position:0%
+because it integrates to two so why is
+ 
+
+ align:start position:0%
+because it integrates to two so why is
+this methylene
+
+ align:start position:0%
+this methylene
+ 
+
+ align:start position:0%
+this methylene
+all the way down at four and these are
+
+ align:start position:0%
+all the way down at four and these are
+ 
+
+ align:start position:0%
+all the way down at four and these are
+up here
+
+ align:start position:0%
+up here
+ 
+
+ align:start position:0%
+up here
+well what's the methylene next to it's
+
+ align:start position:0%
+well what's the methylene next to it's
+ 
+
+ align:start position:0%
+well what's the methylene next to it's
+next it's bound straight to the oxygen
+
+ align:start position:0%
+next it's bound straight to the oxygen
+ 
+
+ align:start position:0%
+next it's bound straight to the oxygen
+so the oxygen
+
+ align:start position:0%
+so the oxygen
+ 
+
+ align:start position:0%
+so the oxygen
+is withdrawing the electron density away
+
+ align:start position:0%
+is withdrawing the electron density away
+ 
+
+ align:start position:0%
+is withdrawing the electron density away
+from that methylene
+
+ align:start position:0%
+from that methylene
+ 
+
+ align:start position:0%
+from that methylene
+and it is shifting the peak what we call
+
+ align:start position:0%
+and it is shifting the peak what we call
+ 
+
+ align:start position:0%
+and it is shifting the peak what we call
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+field which means to the left
+
+ align:start position:0%
+field which means to the left
+ 
+
+ align:start position:0%
+field which means to the left
+on an nmr spectrum that's a leftover
+
+ align:start position:0%
+on an nmr spectrum that's a leftover
+ 
+
+ align:start position:0%
+on an nmr spectrum that's a leftover
+term
+
+ align:start position:0%
+term
+ 
+
+ align:start position:0%
+term
+from in the old days when they would
+
+ align:start position:0%
+from in the old days when they would
+ 
+
+ align:start position:0%
+from in the old days when they would
+sweep you would actually adjust the
+
+ align:start position:0%
+sweep you would actually adjust the
+ 
+
+ align:start position:0%
+sweep you would actually adjust the
+frequency or not frequency you'd adjust
+
+ align:start position:0%
+frequency or not frequency you'd adjust
+ 
+
+ align:start position:0%
+frequency or not frequency you'd adjust
+the strength of the magnet so
+
+ align:start position:0%
+the strength of the magnet so
+ 
+
+ align:start position:0%
+the strength of the magnet so
+anything that was down in this direction
+
+ align:start position:0%
+anything that was down in this direction
+ 
+
+ align:start position:0%
+anything that was down in this direction
+used a weaker magnetic field strength
+
+ align:start position:0%
+used a weaker magnetic field strength
+ 
+
+ align:start position:0%
+used a weaker magnetic field strength
+anything that was up in this direction
+
+ align:start position:0%
+anything that was up in this direction
+ 
+
+ align:start position:0%
+anything that was up in this direction
+used a
+
+ align:start position:0%
+used a
+ 
+
+ align:start position:0%
+used a
+stronger magnetic field strength
+
+ align:start position:0%
+stronger magnetic field strength
+ 
+
+ align:start position:0%
+stronger magnetic field strength
+nowadays we don't do that the magnet's
+
+ align:start position:0%
+nowadays we don't do that the magnet's
+ 
+
+ align:start position:0%
+nowadays we don't do that the magnet's
+always just
+
+ align:start position:0%
+always just
+ 
+
+ align:start position:0%
+always just
+what the magnet is but those terms are
+
+ align:start position:0%
+what the magnet is but those terms are
+ 
+
+ align:start position:0%
+what the magnet is but those terms are
+still around so anything to the left is
+
+ align:start position:0%
+still around so anything to the left is
+ 
+
+ align:start position:0%
+still around so anything to the left is
+downfield anything to the right is up
+
+ align:start position:0%
+downfield anything to the right is up
+ 
+
+ align:start position:0%
+downfield anything to the right is up
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+so this one is de-shielded the most it
+
+ align:start position:0%
+so this one is de-shielded the most it
+ 
+
+ align:start position:0%
+so this one is de-shielded the most it
+is at 4.1
+
+ align:start position:0%
+is at 4.1
+ 
+
+ align:start position:0%
+is at 4.1
+the next peak is
+
+ align:start position:0%
+the next peak is
+ 
+
+ align:start position:0%
+the next peak is
+this one now we've got to choose is it
+
+ align:start position:0%
+this one now we've got to choose is it
+ 
+
+ align:start position:0%
+this one now we've got to choose is it
+from this methyl
+
+ align:start position:0%
+from this methyl
+ 
+
+ align:start position:0%
+from this methyl
+or is it from this methyl and so you
+
+ align:start position:0%
+or is it from this methyl and so you
+ 
+
+ align:start position:0%
+or is it from this methyl and so you
+would look and you say okay
+
+ align:start position:0%
+would look and you say okay
+ 
+
+ align:start position:0%
+would look and you say okay
+both of these are bound to carbon but
+
+ align:start position:0%
+both of these are bound to carbon but
+ 
+
+ align:start position:0%
+both of these are bound to carbon but
+the carbon that this one is bound to
+
+ align:start position:0%
+the carbon that this one is bound to
+ 
+
+ align:start position:0%
+the carbon that this one is bound to
+is a carbon that is doubly bound to an
+
+ align:start position:0%
+is a carbon that is doubly bound to an
+ 
+
+ align:start position:0%
+is a carbon that is doubly bound to an
+oxygen
+
+ align:start position:0%
+oxygen
+ 
+
+ align:start position:0%
+oxygen
+so electron density is being drawn away
+
+ align:start position:0%
+so electron density is being drawn away
+ 
+
+ align:start position:0%
+so electron density is being drawn away
+from that
+
+ align:start position:0%
+from that
+ 
+
+ align:start position:0%
+from that
+carbon by the oxygen so that's still
+
+ align:start position:0%
+carbon by the oxygen so that's still
+ 
+
+ align:start position:0%
+carbon by the oxygen so that's still
+going to also have electron density
+
+ align:start position:0%
+going to also have electron density
+ 
+
+ align:start position:0%
+going to also have electron density
+being pulled away
+
+ align:start position:0%
+being pulled away
+ 
+
+ align:start position:0%
+being pulled away
+from this methyl and so that's going to
+
+ align:start position:0%
+from this methyl and so that's going to
+ 
+
+ align:start position:0%
+from this methyl and so that's going to
+shift it down
+
+ align:start position:0%
+shift it down
+ 
+
+ align:start position:0%
+shift it down
+here this carbon is just bound to a
+
+ align:start position:0%
+here this carbon is just bound to a
+ 
+
+ align:start position:0%
+here this carbon is just bound to a
+plane carbon without
+
+ align:start position:0%
+plane carbon without
+ 
+
+ align:start position:0%
+plane carbon without
+a double bound oxygen on it and so
+
+ align:start position:0%
+a double bound oxygen on it and so
+ 
+
+ align:start position:0%
+a double bound oxygen on it and so
+it's not deshielded as much although
+
+ align:start position:0%
+it's not deshielded as much although
+ 
+
+ align:start position:0%
+it's not deshielded as much although
+if i took a spectrum that had so
+
+ align:start position:0%
+if i took a spectrum that had so
+ 
+
+ align:start position:0%
+if i took a spectrum that had so
+well that's if i just had an alkane like
+
+ align:start position:0%
+well that's if i just had an alkane like
+ 
+
+ align:start position:0%
+well that's if i just had an alkane like
+pentane
+
+ align:start position:0%
+pentane
+ 
+
+ align:start position:0%
+pentane
+and i looked at the terminal methyl on
+
+ align:start position:0%
+and i looked at the terminal methyl on
+ 
+
+ align:start position:0%
+and i looked at the terminal methyl on
+pentane it would be over here because it
+
+ align:start position:0%
+pentane it would be over here because it
+ 
+
+ align:start position:0%
+pentane it would be over here because it
+would not
+
+ align:start position:0%
+would not
+ 
+
+ align:start position:0%
+would not
+be de-shielded at all compared to this
+
+ align:start position:0%
+be de-shielded at all compared to this
+ 
+
+ align:start position:0%
+be de-shielded at all compared to this
+another thing you might be questioning
+
+ align:start position:0%
+another thing you might be questioning
+ 
+
+ align:start position:0%
+another thing you might be questioning
+is why
+
+ align:start position:0%
+is why
+ 
+
+ align:start position:0%
+is why
+are these ones split into multiple peaks
+
+ align:start position:0%
+are these ones split into multiple peaks
+ 
+
+ align:start position:0%
+are these ones split into multiple peaks
+but this one is only a single peak let
+
+ align:start position:0%
+but this one is only a single peak let
+ 
+
+ align:start position:0%
+but this one is only a single peak let
+me make sure i kept my slides in order
+
+ align:start position:0%
+me make sure i kept my slides in order
+ 
+
+ align:start position:0%
+me make sure i kept my slides in order
+okay i did
+
+ align:start position:0%
+okay i did
+ 
+
+ align:start position:0%
+okay i did
+that is due to what is called coupling
+
+ align:start position:0%
+that is due to what is called coupling
+ 
+
+ align:start position:0%
+that is due to what is called coupling
+so protons that are bound to a carbon
+
+ align:start position:0%
+so protons that are bound to a carbon
+ 
+
+ align:start position:0%
+so protons that are bound to a carbon
+will in essence talk to protons
+
+ align:start position:0%
+will in essence talk to protons
+ 
+
+ align:start position:0%
+will in essence talk to protons
+on neighboring carbons through the bonds
+
+ align:start position:0%
+on neighboring carbons through the bonds
+ 
+
+ align:start position:0%
+on neighboring carbons through the bonds
+and it's called
+
+ align:start position:0%
+and it's called
+ 
+
+ align:start position:0%
+and it's called
+spin spin coupling or scalar coupling
+
+ align:start position:0%
+spin spin coupling or scalar coupling
+ 
+
+ align:start position:0%
+spin spin coupling or scalar coupling
+and so you will have protons
+
+ align:start position:0%
+and so you will have protons
+ 
+
+ align:start position:0%
+and so you will have protons
+peaks split apart into characteristic
+
+ align:start position:0%
+peaks split apart into characteristic
+ 
+
+ align:start position:0%
+peaks split apart into characteristic
+patterns
+
+ align:start position:0%
+patterns
+ 
+
+ align:start position:0%
+patterns
+um what else of so
+
+ align:start position:0%
+um what else of so
+ 
+
+ align:start position:0%
+um what else of so
+this the splitting on those peaks
+
+ align:start position:0%
+this the splitting on those peaks
+ 
+
+ align:start position:0%
+this the splitting on those peaks
+is not dependent on the main field
+
+ align:start position:0%
+is not dependent on the main field
+ 
+
+ align:start position:0%
+is not dependent on the main field
+so that if i took that ethyl acetate
+
+ align:start position:0%
+so that if i took that ethyl acetate
+ 
+
+ align:start position:0%
+so that if i took that ethyl acetate
+spectrum and i forget what strength i
+
+ align:start position:0%
+spectrum and i forget what strength i
+ 
+
+ align:start position:0%
+spectrum and i forget what strength i
+maybe will say i acquired that at 500
+
+ align:start position:0%
+maybe will say i acquired that at 500
+ 
+
+ align:start position:0%
+maybe will say i acquired that at 500
+megahertz
+
+ align:start position:0%
+megahertz
+ 
+
+ align:start position:0%
+megahertz
+and i measure the difference between
+
+ align:start position:0%
+and i measure the difference between
+ 
+
+ align:start position:0%
+and i measure the difference between
+those peaks
+
+ align:start position:0%
+those peaks
+ 
+
+ align:start position:0%
+those peaks
+and we'll say it's 8 hertz if i take
+
+ align:start position:0%
+and we'll say it's 8 hertz if i take
+ 
+
+ align:start position:0%
+and we'll say it's 8 hertz if i take
+that molecule
+
+ align:start position:0%
+that molecule
+ 
+
+ align:start position:0%
+that molecule
+i put it in a gigahertz machine which is
+
+ align:start position:0%
+i put it in a gigahertz machine which is
+ 
+
+ align:start position:0%
+i put it in a gigahertz machine which is
+twice as strong
+
+ align:start position:0%
+twice as strong
+ 
+
+ align:start position:0%
+twice as strong
+and i measure the splitting it'll still
+
+ align:start position:0%
+and i measure the splitting it'll still
+ 
+
+ align:start position:0%
+and i measure the splitting it'll still
+be that same value
+
+ align:start position:0%
+be that same value
+ 
+
+ align:start position:0%
+be that same value
+so for simple spectra
+
+ align:start position:0%
+so for simple spectra
+ 
+
+ align:start position:0%
+so for simple spectra
+the splitting fall is what's called the
+
+ align:start position:0%
+the splitting fall is what's called the
+ 
+
+ align:start position:0%
+the splitting fall is what's called the
+n plus one rule
+
+ align:start position:0%
+n plus one rule
+ 
+
+ align:start position:0%
+n plus one rule
+and so you look at the number
+
+ align:start position:0%
+and so you look at the number
+ 
+
+ align:start position:0%
+and so you look at the number
+of protons on neighboring carbons
+
+ align:start position:0%
+of protons on neighboring carbons
+ 
+
+ align:start position:0%
+of protons on neighboring carbons
+and you add that up so i guess i should
+
+ align:start position:0%
+and you add that up so i guess i should
+ 
+
+ align:start position:0%
+and you add that up so i guess i should
+have drawn another molecule where my
+
+ align:start position:0%
+have drawn another molecule where my
+ 
+
+ align:start position:0%
+have drawn another molecule where my
+chalk go
+
+ align:start position:0%
+chalk go
+ 
+
+ align:start position:0%
+chalk go
+so for instance we'll take this one here
+
+ align:start position:0%
+so for instance we'll take this one here
+ 
+
+ align:start position:0%
+so for instance we'll take this one here
+so ch3 i've got two protons over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's going to give me a simple
+
+ align:start position:0%
+so it's going to give me a simple
+ 
+
+ align:start position:0%
+so it's going to give me a simple
+spectrum so it's going to be
+
+ align:start position:0%
+spectrum so it's going to be
+ 
+
+ align:start position:0%
+spectrum so it's going to be
+split by two plus one equals three
+
+ align:start position:0%
+split by two plus one equals three
+ 
+
+ align:start position:0%
+split by two plus one equals three
+and let's see i'm gonna
+
+ align:start position:0%
+and let's see i'm gonna
+ 
+
+ align:start position:0%
+and let's see i'm gonna
+close this and bring up
+
+ align:start position:0%
+close this and bring up
+ 
+
+ align:start position:0%
+close this and bring up
+my real spectrum so this
+
+ align:start position:0%
+my real spectrum so this
+ 
+
+ align:start position:0%
+my real spectrum so this
+spectrum is of three heptanone
+
+ align:start position:0%
+spectrum is of three heptanone
+ 
+
+ align:start position:0%
+spectrum is of three heptanone
+and the methyl here
+
+ align:start position:0%
+and the methyl here
+ 
+
+ align:start position:0%
+and the methyl here
+and the methyl here are these two
+
+ align:start position:0%
+and the methyl here are these two
+ 
+
+ align:start position:0%
+and the methyl here are these two
+resonances over there
+
+ align:start position:0%
+resonances over there
+ 
+
+ align:start position:0%
+resonances over there
+and so you can in fact see that those
+
+ align:start position:0%
+and so you can in fact see that those
+ 
+
+ align:start position:0%
+and so you can in fact see that those
+are split into three peaks because each
+
+ align:start position:0%
+are split into three peaks because each
+ 
+
+ align:start position:0%
+are split into three peaks because each
+of them has
+
+ align:start position:0%
+of them has
+ 
+
+ align:start position:0%
+of them has
+two protons next to it now not
+
+ align:start position:0%
+two protons next to it now not
+ 
+
+ align:start position:0%
+two protons next to it now not
+everything behaves that way when you get
+
+ align:start position:0%
+everything behaves that way when you get
+ 
+
+ align:start position:0%
+everything behaves that way when you get
+into more complicated molecules
+
+ align:start position:0%
+into more complicated molecules
+ 
+
+ align:start position:0%
+into more complicated molecules
+splitting can be completely
+
+ align:start position:0%
+splitting can be completely
+ 
+
+ align:start position:0%
+splitting can be completely
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+non-rationalizable in general so there
+
+ align:start position:0%
+non-rationalizable in general so there
+ 
+
+ align:start position:0%
+non-rationalizable in general so there
+are several ways that can happen
+
+ align:start position:0%
+are several ways that can happen
+ 
+
+ align:start position:0%
+are several ways that can happen
+the most common way is when the
+
+ align:start position:0%
+the most common way is when the
+ 
+
+ align:start position:0%
+the most common way is when the
+difference in chemical shifts
+
+ align:start position:0%
+difference in chemical shifts
+ 
+
+ align:start position:0%
+difference in chemical shifts
+between two nuclei is not much
+
+ align:start position:0%
+between two nuclei is not much
+ 
+
+ align:start position:0%
+between two nuclei is not much
+bigger than their coupling constant
+
+ align:start position:0%
+bigger than their coupling constant
+ 
+
+ align:start position:0%
+bigger than their coupling constant
+you'll just get a whole bunch of
+
+ align:start position:0%
+you'll just get a whole bunch of
+ 
+
+ align:start position:0%
+you'll just get a whole bunch of
+different peaks
+
+ align:start position:0%
+different peaks
+ 
+
+ align:start position:0%
+different peaks
+i can drag up an example of that in a
+
+ align:start position:0%
+i can drag up an example of that in a
+ 
+
+ align:start position:0%
+i can drag up an example of that in a
+second so let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops okay so that crashed oh well so i
+
+ align:start position:0%
+oops okay so that crashed oh well so i
+ 
+
+ align:start position:0%
+oops okay so that crashed oh well so i
+won't do that
+
+ align:start position:0%
+won't do that
+ 
+
+ align:start position:0%
+won't do that
+okay so i've given you a table in there
+
+ align:start position:0%
+okay so i've given you a table in there
+ 
+
+ align:start position:0%
+okay so i've given you a table in there
+that gives some of the common
+
+ align:start position:0%
+that gives some of the common
+ 
+
+ align:start position:0%
+that gives some of the common
+splitting patterns that you'll observe
+
+ align:start position:0%
+splitting patterns that you'll observe
+ 
+
+ align:start position:0%
+splitting patterns that you'll observe
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+a simple spectrum is where the splitting
+
+ align:start position:0%
+a simple spectrum is where the splitting
+ 
+
+ align:start position:0%
+a simple spectrum is where the splitting
+obeys this n plus one rule
+
+ align:start position:0%
+obeys this n plus one rule
+ 
+
+ align:start position:0%
+obeys this n plus one rule
+and so all the multiplets will be
+
+ align:start position:0%
+and so all the multiplets will be
+ 
+
+ align:start position:0%
+and so all the multiplets will be
+analyzable that way
+
+ align:start position:0%
+analyzable that way
+ 
+
+ align:start position:0%
+analyzable that way
+and you'll you'll know it if you look at
+
+ align:start position:0%
+and you'll you'll know it if you look at
+ 
+
+ align:start position:0%
+and you'll you'll know it if you look at
+something and you don't
+
+ align:start position:0%
+something and you don't
+ 
+
+ align:start position:0%
+something and you don't
+see these common patterns you can
+
+ align:start position:0%
+see these common patterns you can
+ 
+
+ align:start position:0%
+see these common patterns you can
+automatically say okay there's you know
+
+ align:start position:0%
+automatically say okay there's you know
+ 
+
+ align:start position:0%
+automatically say okay there's you know
+more complex splitting that's going
+
+ align:start position:0%
+more complex splitting that's going
+ 
+
+ align:start position:0%
+more complex splitting that's going
+on in there or non-first order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the intensities of those peaks in
+
+ align:start position:0%
+the intensities of those peaks in
+ 
+
+ align:start position:0%
+the intensities of those peaks in
+a first order multiplet will
+
+ align:start position:0%
+a first order multiplet will
+ 
+
+ align:start position:0%
+a first order multiplet will
+obey or agree with the coefficients of a
+
+ align:start position:0%
+obey or agree with the coefficients of a
+ 
+
+ align:start position:0%
+obey or agree with the coefficients of a
+binomial expansion i.e pascal's triangle
+
+ align:start position:0%
+binomial expansion i.e pascal's triangle
+ 
+
+ align:start position:0%
+binomial expansion i.e pascal's triangle
+so you know for n equals two you will
+
+ align:start position:0%
+so you know for n equals two you will
+ 
+
+ align:start position:0%
+so you know for n equals two you will
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+one to two to one and for three one to
+
+ align:start position:0%
+one to two to one and for three one to
+ 
+
+ align:start position:0%
+one to two to one and for three one to
+three to three to one so they will obey
+
+ align:start position:0%
+three to three to one so they will obey
+ 
+
+ align:start position:0%
+three to three to one so they will obey
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+if it was non-first order you might see
+
+ align:start position:0%
+if it was non-first order you might see
+ 
+
+ align:start position:0%
+if it was non-first order you might see
+four peaks
+
+ align:start position:0%
+four peaks
+ 
+
+ align:start position:0%
+four peaks
+but you wouldn't have that same
+
+ align:start position:0%
+but you wouldn't have that same
+ 
+
+ align:start position:0%
+but you wouldn't have that same
+intensity pattern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's some example other examples of
+
+ align:start position:0%
+so here's some example other examples of
+ 
+
+ align:start position:0%
+so here's some example other examples of
+nmr spectra
+
+ align:start position:0%
+nmr spectra
+ 
+
+ align:start position:0%
+nmr spectra
+here's a simple one ethanol we can look
+
+ align:start position:0%
+here's a simple one ethanol we can look
+ 
+
+ align:start position:0%
+here's a simple one ethanol we can look
+at this and we can rationalize
+
+ align:start position:0%
+at this and we can rationalize
+ 
+
+ align:start position:0%
+at this and we can rationalize
+where the peaks appear in the same
+
+ align:start position:0%
+where the peaks appear in the same
+ 
+
+ align:start position:0%
+where the peaks appear in the same
+fashion
+
+ align:start position:0%
+fashion
+ 
+
+ align:start position:0%
+fashion
+we've got a methyl group and a
+
+ align:start position:0%
+we've got a methyl group and a
+ 
+
+ align:start position:0%
+we've got a methyl group and a
+methionine
+
+ align:start position:0%
+methionine
+ 
+
+ align:start position:0%
+methionine
+so if we look at the methyl group we see
+
+ align:start position:0%
+so if we look at the methyl group we see
+ 
+
+ align:start position:0%
+so if we look at the methyl group we see
+that there's one
+
+ align:start position:0%
+that there's one
+ 
+
+ align:start position:0%
+that there's one
+two protons next to each other so we
+
+ align:start position:0%
+two protons next to each other so we
+ 
+
+ align:start position:0%
+two protons next to each other so we
+would expect
+
+ align:start position:0%
+would expect
+ 
+
+ align:start position:0%
+would expect
+the resonance for that to be split into
+
+ align:start position:0%
+the resonance for that to be split into
+ 
+
+ align:start position:0%
+the resonance for that to be split into
+three separate peaks
+
+ align:start position:0%
+three separate peaks
+ 
+
+ align:start position:0%
+three separate peaks
+and there in fact we see a triplet and
+
+ align:start position:0%
+and there in fact we see a triplet and
+ 
+
+ align:start position:0%
+and there in fact we see a triplet and
+then for the methylene not
+
+ align:start position:0%
+then for the methylene not
+ 
+
+ align:start position:0%
+then for the methylene not
+it's default now because there's nothing
+
+ align:start position:0%
+it's default now because there's nothing
+ 
+
+ align:start position:0%
+it's default now because there's nothing
+where that's the only other one
+
+ align:start position:0%
+where that's the only other one
+ 
+
+ align:start position:0%
+where that's the only other one
+you would expect one two three four
+
+ align:start position:0%
+you would expect one two three four
+ 
+
+ align:start position:0%
+you would expect one two three four
+peaks and you see that
+
+ align:start position:0%
+peaks and you see that
+ 
+
+ align:start position:0%
+peaks and you see that
+and now this is tricky why do you not
+
+ align:start position:0%
+and now this is tricky why do you not
+ 
+
+ align:start position:0%
+and now this is tricky why do you not
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+three peaks for the oh even though it's
+
+ align:start position:0%
+three peaks for the oh even though it's
+ 
+
+ align:start position:0%
+three peaks for the oh even though it's
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+two protons next to it oh
+
+ align:start position:0%
+two protons next to it oh
+ 
+
+ align:start position:0%
+two protons next to it oh
+and nh have exchangeable protons
+
+ align:start position:0%
+and nh have exchangeable protons
+ 
+
+ align:start position:0%
+and nh have exchangeable protons
+and so the proton is coming on and off
+
+ align:start position:0%
+and so the proton is coming on and off
+ 
+
+ align:start position:0%
+and so the proton is coming on and off
+that molecule in a faster time period
+
+ align:start position:0%
+that molecule in a faster time period
+ 
+
+ align:start position:0%
+that molecule in a faster time period
+than the nmr measurement
+
+ align:start position:0%
+than the nmr measurement
+ 
+
+ align:start position:0%
+than the nmr measurement
+so you just see an average of
+
+ align:start position:0%
+so you just see an average of
+ 
+
+ align:start position:0%
+so you just see an average of
+the chemical shifts meaning it gives you
+
+ align:start position:0%
+the chemical shifts meaning it gives you
+ 
+
+ align:start position:0%
+the chemical shifts meaning it gives you
+a single peak rather than splitting into
+
+ align:start position:0%
+a single peak rather than splitting into
+ 
+
+ align:start position:0%
+a single peak rather than splitting into
+a triplet
+
+ align:start position:0%
+a triplet
+ 
+
+ align:start position:0%
+a triplet
+uh these didn't come out very big but
+
+ align:start position:0%
+uh these didn't come out very big but
+ 
+
+ align:start position:0%
+uh these didn't come out very big but
+it's just so you know if you get
+
+ align:start position:0%
+it's just so you know if you get
+ 
+
+ align:start position:0%
+it's just so you know if you get
+with bigger molecules you get more peaks
+
+ align:start position:0%
+with bigger molecules you get more peaks
+ 
+
+ align:start position:0%
+with bigger molecules you get more peaks
+if you zoom in on these you'll see that
+
+ align:start position:0%
+if you zoom in on these you'll see that
+ 
+
+ align:start position:0%
+if you zoom in on these you'll see that
+a lot of these do not give
+
+ align:start position:0%
+a lot of these do not give
+ 
+
+ align:start position:0%
+a lot of these do not give
+simple triplets or quartets or doublets
+
+ align:start position:0%
+simple triplets or quartets or doublets
+ 
+
+ align:start position:0%
+simple triplets or quartets or doublets
+that you've got a lot of more complex
+
+ align:start position:0%
+that you've got a lot of more complex
+ 
+
+ align:start position:0%
+that you've got a lot of more complex
+splitting
+
+ align:start position:0%
+splitting
+ 
+
+ align:start position:0%
+splitting
+going on in the molecule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so here's an example of an ester i
+
+ align:start position:0%
+and so here's an example of an ester i
+ 
+
+ align:start position:0%
+and so here's an example of an ester i
+think that you all are going to be
+
+ align:start position:0%
+think that you all are going to be
+ 
+
+ align:start position:0%
+think that you all are going to be
+synthesizing esters so if we look at
+
+ align:start position:0%
+synthesizing esters so if we look at
+ 
+
+ align:start position:0%
+synthesizing esters so if we look at
+these two compounds
+
+ align:start position:0%
+these two compounds
+ 
+
+ align:start position:0%
+these two compounds
+and something i didn't point out well
+
+ align:start position:0%
+and something i didn't point out well
+ 
+
+ align:start position:0%
+and something i didn't point out well
+i'll show you this in another slide
+
+ align:start position:0%
+i'll show you this in another slide
+ 
+
+ align:start position:0%
+i'll show you this in another slide
+anything that appears in an aromatic
+
+ align:start position:0%
+anything that appears in an aromatic
+ 
+
+ align:start position:0%
+anything that appears in an aromatic
+ring
+
+ align:start position:0%
+ring
+ 
+
+ align:start position:0%
+ring
+is going to be de-shielded so it's going
+
+ align:start position:0%
+is going to be de-shielded so it's going
+ 
+
+ align:start position:0%
+is going to be de-shielded so it's going
+to be far downfield and i think i said
+
+ align:start position:0%
+to be far downfield and i think i said
+ 
+
+ align:start position:0%
+to be far downfield and i think i said
+that before you've got the electron
+
+ align:start position:0%
+that before you've got the electron
+ 
+
+ align:start position:0%
+that before you've got the electron
+density
+
+ align:start position:0%
+density
+ 
+
+ align:start position:0%
+density
+of the pi orbitals above and below
+
+ align:start position:0%
+of the pi orbitals above and below
+ 
+
+ align:start position:0%
+of the pi orbitals above and below
+the ring which would shield something
+
+ align:start position:0%
+the ring which would shield something
+ 
+
+ align:start position:0%
+the ring which would shield something
+but those protons are held not there but
+
+ align:start position:0%
+but those protons are held not there but
+ 
+
+ align:start position:0%
+but those protons are held not there but
+straight out from the ring so they're in
+
+ align:start position:0%
+straight out from the ring so they're in
+ 
+
+ align:start position:0%
+straight out from the ring so they're in
+a d
+
+ align:start position:0%
+a d
+ 
+
+ align:start position:0%
+a d
+shielded region so right off the bat we
+
+ align:start position:0%
+shielded region so right off the bat we
+ 
+
+ align:start position:0%
+shielded region so right off the bat we
+can look and we can say okay we know
+
+ align:start position:0%
+can look and we can say okay we know
+ 
+
+ align:start position:0%
+can look and we can say okay we know
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this must be or these peaks must be
+
+ align:start position:0%
+this must be or these peaks must be
+ 
+
+ align:start position:0%
+this must be or these peaks must be
+from the protons on the phenyl rings
+
+ align:start position:0%
+from the protons on the phenyl rings
+ 
+
+ align:start position:0%
+from the protons on the phenyl rings
+unfortunately there's no integration on
+
+ align:start position:0%
+unfortunately there's no integration on
+ 
+
+ align:start position:0%
+unfortunately there's no integration on
+here but you also if i had the
+
+ align:start position:0%
+here but you also if i had the
+ 
+
+ align:start position:0%
+here but you also if i had the
+integration values
+
+ align:start position:0%
+integration values
+ 
+
+ align:start position:0%
+integration values
+you would see that those both integrate
+
+ align:start position:0%
+you would see that those both integrate
+ 
+
+ align:start position:0%
+you would see that those both integrate
+the five and that would
+
+ align:start position:0%
+the five and that would
+ 
+
+ align:start position:0%
+the five and that would
+tell you something about it too so now
+
+ align:start position:0%
+tell you something about it too so now
+ 
+
+ align:start position:0%
+tell you something about it too so now
+the question
+
+ align:start position:0%
+the question
+ 
+
+ align:start position:0%
+the question
+becomes which splitting patterns in this
+
+ align:start position:0%
+becomes which splitting patterns in this
+ 
+
+ align:start position:0%
+becomes which splitting patterns in this
+region down here agree
+
+ align:start position:0%
+region down here agree
+ 
+
+ align:start position:0%
+region down here agree
+with what we see up here so if we look
+
+ align:start position:0%
+with what we see up here so if we look
+ 
+
+ align:start position:0%
+with what we see up here so if we look
+at our
+
+ align:start position:0%
+at our
+ 
+
+ align:start position:0%
+at our
+ester we see that on
+
+ align:start position:0%
+ester we see that on
+ 
+
+ align:start position:0%
+ester we see that on
+this ester over here we've got and we
+
+ align:start position:0%
+this ester over here we've got and we
+ 
+
+ align:start position:0%
+this ester over here we've got and we
+saw this with ethyl acetate we have the
+
+ align:start position:0%
+saw this with ethyl acetate we have the
+ 
+
+ align:start position:0%
+saw this with ethyl acetate we have the
+methyl
+
+ align:start position:0%
+methyl
+ 
+
+ align:start position:0%
+methyl
+and the methylene bound to the oxygen
+
+ align:start position:0%
+and the methylene bound to the oxygen
+ 
+
+ align:start position:0%
+and the methylene bound to the oxygen
+so we know that the methyl and the
+
+ align:start position:0%
+so we know that the methyl and the
+ 
+
+ align:start position:0%
+so we know that the methyl and the
+methylene
+
+ align:start position:0%
+methylene
+ 
+
+ align:start position:0%
+methylene
+are going to split into a triplet and a
+
+ align:start position:0%
+are going to split into a triplet and a
+ 
+
+ align:start position:0%
+are going to split into a triplet and a
+quartet
+
+ align:start position:0%
+quartet
+ 
+
+ align:start position:0%
+quartet
+and we know that that quartet is going
+
+ align:start position:0%
+and we know that that quartet is going
+ 
+
+ align:start position:0%
+and we know that that quartet is going
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+shifted downfield because it's bound to
+
+ align:start position:0%
+shifted downfield because it's bound to
+ 
+
+ align:start position:0%
+shifted downfield because it's bound to
+that oxygen
+
+ align:start position:0%
+that oxygen
+ 
+
+ align:start position:0%
+that oxygen
+now that's not to say that also in this
+
+ align:start position:0%
+now that's not to say that also in this
+ 
+
+ align:start position:0%
+now that's not to say that also in this
+one they're not going to be split into a
+
+ align:start position:0%
+one they're not going to be split into a
+ 
+
+ align:start position:0%
+one they're not going to be split into a
+triplet
+
+ align:start position:0%
+triplet
+ 
+
+ align:start position:0%
+triplet
+in a quartet but this carbonyl carbon
+
+ align:start position:0%
+in a quartet but this carbonyl carbon
+ 
+
+ align:start position:0%
+in a quartet but this carbonyl carbon
+is not going to drag the peak as far
+
+ align:start position:0%
+is not going to drag the peak as far
+ 
+
+ align:start position:0%
+is not going to drag the peak as far
+down field
+
+ align:start position:0%
+down field
+ 
+
+ align:start position:0%
+down field
+as it does over here so we can say
+
+ align:start position:0%
+as it does over here so we can say
+ 
+
+ align:start position:0%
+as it does over here so we can say
+that this compound here is from
+
+ align:start position:0%
+that this compound here is from
+ 
+
+ align:start position:0%
+that this compound here is from
+this one and this peak right here
+
+ align:start position:0%
+this one and this peak right here
+ 
+
+ align:start position:0%
+this one and this peak right here
+is my single methylene that doesn't have
+
+ align:start position:0%
+is my single methylene that doesn't have
+ 
+
+ align:start position:0%
+is my single methylene that doesn't have
+any protons next to it
+
+ align:start position:0%
+any protons next to it
+ 
+
+ align:start position:0%
+any protons next to it
+whereas this compound over here
+
+ align:start position:0%
+whereas this compound over here
+ 
+
+ align:start position:0%
+whereas this compound over here
+is this one here did i just do that no i
+
+ align:start position:0%
+is this one here did i just do that no i
+ 
+
+ align:start position:0%
+is this one here did i just do that no i
+just said that backwards
+
+ align:start position:0%
+just said that backwards
+ 
+
+ align:start position:0%
+just said that backwards
+this compound here is this one
+
+ align:start position:0%
+this compound here is this one
+ 
+
+ align:start position:0%
+this compound here is this one
+this compound here is this one so here's
+
+ align:start position:0%
+this compound here is this one so here's
+ 
+
+ align:start position:0%
+this compound here is this one so here's
+the single methylene
+
+ align:start position:0%
+the single methylene
+ 
+
+ align:start position:0%
+the single methylene
+and here it is here's the methylene that
+
+ align:start position:0%
+and here it is here's the methylene that
+ 
+
+ align:start position:0%
+and here it is here's the methylene that
+split into a quartet
+
+ align:start position:0%
+split into a quartet
+ 
+
+ align:start position:0%
+split into a quartet
+and it's right there whereas in this one
+
+ align:start position:0%
+and it's right there whereas in this one
+ 
+
+ align:start position:0%
+and it's right there whereas in this one
+this methylene is shifted a little
+
+ align:start position:0%
+this methylene is shifted a little
+ 
+
+ align:start position:0%
+this methylene is shifted a little
+farther downfield because now it's bound
+
+ align:start position:0%
+farther downfield because now it's bound
+ 
+
+ align:start position:0%
+farther downfield because now it's bound
+to the oxygen
+
+ align:start position:0%
+to the oxygen
+ 
+
+ align:start position:0%
+to the oxygen
+does that make sense to everybody
+
+ align:start position:0%
+does that make sense to everybody
+ 
+
+ align:start position:0%
+does that make sense to everybody
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm not going to go over this completely
+
+ align:start position:0%
+i'm not going to go over this completely
+ 
+
+ align:start position:0%
+i'm not going to go over this completely
+you can look at this you can also look
+
+ align:start position:0%
+you can look at this you can also look
+ 
+
+ align:start position:0%
+you can look at this you can also look
+up you can find
+
+ align:start position:0%
+up you can find
+ 
+
+ align:start position:0%
+up you can find
+stuff like this online everywhere this
+
+ align:start position:0%
+stuff like this online everywhere this
+ 
+
+ align:start position:0%
+stuff like this online everywhere this
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+fella over in england who puts out these
+
+ align:start position:0%
+fella over in england who puts out these
+ 
+
+ align:start position:0%
+fella over in england who puts out these
+graphics called compound kim
+
+ align:start position:0%
+graphics called compound kim
+ 
+
+ align:start position:0%
+graphics called compound kim
+i don't know if anybody follows him on
+
+ align:start position:0%
+i don't know if anybody follows him on
+ 
+
+ align:start position:0%
+i don't know if anybody follows him on
+twitter but he's got all sorts of great
+
+ align:start position:0%
+twitter but he's got all sorts of great
+ 
+
+ align:start position:0%
+twitter but he's got all sorts of great
+chemistry education graphics this is one
+
+ align:start position:0%
+chemistry education graphics this is one
+ 
+
+ align:start position:0%
+chemistry education graphics this is one
+that just gives an idea of the different
+
+ align:start position:0%
+that just gives an idea of the different
+ 
+
+ align:start position:0%
+that just gives an idea of the different
+chemical
+
+ align:start position:0%
+chemical
+ 
+
+ align:start position:0%
+chemical
+shift values and where things appear and
+
+ align:start position:0%
+shift values and where things appear and
+ 
+
+ align:start position:0%
+shift values and where things appear and
+so you can see you know an oh on a
+
+ align:start position:0%
+so you can see you know an oh on a
+ 
+
+ align:start position:0%
+so you can see you know an oh on a
+carboxylic acid is going to be very
+
+ align:start position:0%
+carboxylic acid is going to be very
+ 
+
+ align:start position:0%
+carboxylic acid is going to be very
+de-shielded
+
+ align:start position:0%
+de-shielded
+ 
+
+ align:start position:0%
+de-shielded
+amide protons are going to be in this
+
+ align:start position:0%
+amide protons are going to be in this
+ 
+
+ align:start position:0%
+amide protons are going to be in this
+region
+
+ align:start position:0%
+region
+ 
+
+ align:start position:0%
+region
+and etc so that can give you some idea
+
+ align:start position:0%
+and etc so that can give you some idea
+ 
+
+ align:start position:0%
+and etc so that can give you some idea
+of where to look for resonances
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i said that we can take spectra of
+
+ align:start position:0%
+i said that we can take spectra of
+ 
+
+ align:start position:0%
+i said that we can take spectra of
+carbon
+
+ align:start position:0%
+carbon
+ 
+
+ align:start position:0%
+carbon
+carbon is a lot less sensitive than
+
+ align:start position:0%
+carbon is a lot less sensitive than
+ 
+
+ align:start position:0%
+carbon is a lot less sensitive than
+proton in fact
+
+ align:start position:0%
+proton in fact
+ 
+
+ align:start position:0%
+proton in fact
+sensitivity wise if you just compare
+
+ align:start position:0%
+sensitivity wise if you just compare
+ 
+
+ align:start position:0%
+sensitivity wise if you just compare
+the gyromagnetic ratio of carbon to
+
+ align:start position:0%
+the gyromagnetic ratio of carbon to
+ 
+
+ align:start position:0%
+the gyromagnetic ratio of carbon to
+proton it's a fourth
+
+ align:start position:0%
+proton it's a fourth
+ 
+
+ align:start position:0%
+proton it's a fourth
+of proton so when like i said we specify
+
+ align:start position:0%
+of proton so when like i said we specify
+ 
+
+ align:start position:0%
+of proton so when like i said we specify
+our magnets by
+
+ align:start position:0%
+our magnets by
+ 
+
+ align:start position:0%
+our magnets by
+the precession frequency of protons so
+
+ align:start position:0%
+the precession frequency of protons so
+ 
+
+ align:start position:0%
+the precession frequency of protons so
+on a 500 megahertz instrument it would
+
+ align:start position:0%
+on a 500 megahertz instrument it would
+ 
+
+ align:start position:0%
+on a 500 megahertz instrument it would
+be a 125 megahertz
+
+ align:start position:0%
+be a 125 megahertz
+ 
+
+ align:start position:0%
+be a 125 megahertz
+carbon instrument so you take that
+
+ align:start position:0%
+carbon instrument so you take that
+ 
+
+ align:start position:0%
+carbon instrument so you take that
+one-fourth of a hit
+
+ align:start position:0%
+one-fourth of a hit
+ 
+
+ align:start position:0%
+one-fourth of a hit
+because of the gyromagnetic ratio but
+
+ align:start position:0%
+because of the gyromagnetic ratio but
+ 
+
+ align:start position:0%
+because of the gyromagnetic ratio but
+then you also take a big hit
+
+ align:start position:0%
+then you also take a big hit
+ 
+
+ align:start position:0%
+then you also take a big hit
+because only 1.1 percent of the carbon
+
+ align:start position:0%
+because only 1.1 percent of the carbon
+ 
+
+ align:start position:0%
+because only 1.1 percent of the carbon
+present
+
+ align:start position:0%
+present
+ 
+
+ align:start position:0%
+present
+in your sample is made of carbon 13
+
+ align:start position:0%
+in your sample is made of carbon 13
+ 
+
+ align:start position:0%
+in your sample is made of carbon 13
+which is the nmr active
+
+ align:start position:0%
+which is the nmr active
+ 
+
+ align:start position:0%
+which is the nmr active
+carbon the rest of its carbon-12 which
+
+ align:start position:0%
+carbon the rest of its carbon-12 which
+ 
+
+ align:start position:0%
+carbon the rest of its carbon-12 which
+is nmr
+
+ align:start position:0%
+is nmr
+ 
+
+ align:start position:0%
+is nmr
+inactive but you can still acquire
+
+ align:start position:0%
+inactive but you can still acquire
+ 
+
+ align:start position:0%
+inactive but you can still acquire
+carbon spectrum a carbon spectra has a
+
+ align:start position:0%
+carbon spectrum a carbon spectra has a
+ 
+
+ align:start position:0%
+carbon spectrum a carbon spectra has a
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+bigger frequency spread so you don't
+
+ align:start position:0%
+bigger frequency spread so you don't
+ 
+
+ align:start position:0%
+bigger frequency spread so you don't
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+overlap as much that can be very useful
+
+ align:start position:0%
+overlap as much that can be very useful
+ 
+
+ align:start position:0%
+overlap as much that can be very useful
+and this combined with a proton
+
+ align:start position:0%
+and this combined with a proton
+ 
+
+ align:start position:0%
+and this combined with a proton
+will can tell you a lot about your
+
+ align:start position:0%
+will can tell you a lot about your
+ 
+
+ align:start position:0%
+will can tell you a lot about your
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+you're not going to acquire these on the
+
+ align:start position:0%
+you're not going to acquire these on the
+ 
+
+ align:start position:0%
+you're not going to acquire these on the
+bench top instrument although i guess
+
+ align:start position:0%
+bench top instrument although i guess
+ 
+
+ align:start position:0%
+bench top instrument although i guess
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+they probably will if you have a very
+
+ align:start position:0%
+they probably will if you have a very
+ 
+
+ align:start position:0%
+they probably will if you have a very
+very concentrated sample
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is just to show an example you can
+
+ align:start position:0%
+this is just to show an example you can
+ 
+
+ align:start position:0%
+this is just to show an example you can
+do very complex
+
+ align:start position:0%
+do very complex
+ 
+
+ align:start position:0%
+do very complex
+samples or experiments this is a
+
+ align:start position:0%
+samples or experiments this is a
+ 
+
+ align:start position:0%
+samples or experiments this is a
+three-dimensional spectrum of a protein
+
+ align:start position:0%
+three-dimensional spectrum of a protein
+ 
+
+ align:start position:0%
+three-dimensional spectrum of a protein
+so this is something you would use in
+
+ align:start position:0%
+so this is something you would use in
+ 
+
+ align:start position:0%
+so this is something you would use in
+determining the protein structure
+
+ align:start position:0%
+determining the protein structure
+ 
+
+ align:start position:0%
+determining the protein structure
+i've never acquired one of these so all
+
+ align:start position:0%
+i've never acquired one of these so all
+ 
+
+ align:start position:0%
+i've never acquired one of these so all
+i can tell you
+
+ align:start position:0%
+i can tell you
+ 
+
+ align:start position:0%
+i can tell you
+is that you're looking both at
+
+ align:start position:0%
+is that you're looking both at
+ 
+
+ align:start position:0%
+is that you're looking both at
+carbon resonance what do we have up here
+
+ align:start position:0%
+carbon resonance what do we have up here
+ 
+
+ align:start position:0%
+carbon resonance what do we have up here
+for the so oh okay sorry
+
+ align:start position:0%
+for the so oh okay sorry
+ 
+
+ align:start position:0%
+for the so oh okay sorry
+so it's the protein was expressed by
+
+ align:start position:0%
+so it's the protein was expressed by
+ 
+
+ align:start position:0%
+so it's the protein was expressed by
+bacteria that were growing
+
+ align:start position:0%
+bacteria that were growing
+ 
+
+ align:start position:0%
+bacteria that were growing
+in food that was labeled with n15 and
+
+ align:start position:0%
+in food that was labeled with n15 and
+ 
+
+ align:start position:0%
+in food that was labeled with n15 and
+c13 so that
+
+ align:start position:0%
+c13 so that
+ 
+
+ align:start position:0%
+c13 so that
+there's incorporation of those nuclei
+
+ align:start position:0%
+there's incorporation of those nuclei
+ 
+
+ align:start position:0%
+there's incorporation of those nuclei
+in there and it will give you signal and
+
+ align:start position:0%
+in there and it will give you signal and
+ 
+
+ align:start position:0%
+in there and it will give you signal and
+you can use that
+
+ align:start position:0%
+you can use that
+ 
+
+ align:start position:0%
+you can use that
+uh let's see i'm almost finished i think
+
+ align:start position:0%
+uh let's see i'm almost finished i think
+ 
+
+ align:start position:0%
+uh let's see i'm almost finished i think
+we're about out of time whoop
+
+ align:start position:0%
+we're about out of time whoop
+ 
+
+ align:start position:0%
+we're about out of time whoop
+sample preparation when you're preparing
+
+ align:start position:0%
+sample preparation when you're preparing
+ 
+
+ align:start position:0%
+sample preparation when you're preparing
+your samples
+
+ align:start position:0%
+your samples
+ 
+
+ align:start position:0%
+your samples
+it is important to prepare
+
+ align:start position:0%
+it is important to prepare
+ 
+
+ align:start position:0%
+it is important to prepare
+clean samples there should not be
+
+ align:start position:0%
+clean samples there should not be
+ 
+
+ align:start position:0%
+clean samples there should not be
+particulate matter
+
+ align:start position:0%
+particulate matter
+ 
+
+ align:start position:0%
+particulate matter
+in your samples you should filter them
+
+ align:start position:0%
+in your samples you should filter them
+ 
+
+ align:start position:0%
+in your samples you should filter them
+if you do have particulate matter
+
+ align:start position:0%
+if you do have particulate matter
+ 
+
+ align:start position:0%
+if you do have particulate matter
+from your reaction because that will
+
+ align:start position:0%
+from your reaction because that will
+ 
+
+ align:start position:0%
+from your reaction because that will
+having particles in there
+
+ align:start position:0%
+having particles in there
+ 
+
+ align:start position:0%
+having particles in there
+will lead to poorer spectra that'll be
+
+ align:start position:0%
+will lead to poorer spectra that'll be
+ 
+
+ align:start position:0%
+will lead to poorer spectra that'll be
+difficult
+
+ align:start position:0%
+difficult
+ 
+
+ align:start position:0%
+difficult
+to interpret um nmr tubes are the very
+
+ align:start position:0%
+to interpret um nmr tubes are the very
+ 
+
+ align:start position:0%
+to interpret um nmr tubes are the very
+thin
+
+ align:start position:0%
+thin
+ 
+
+ align:start position:0%
+thin
+glass wall tubes so be careful with them
+
+ align:start position:0%
+glass wall tubes so be careful with them
+ 
+
+ align:start position:0%
+glass wall tubes so be careful with them
+you know you if you snap this
+
+ align:start position:0%
+you know you if you snap this
+ 
+
+ align:start position:0%
+you know you if you snap this
+you can easily stick it in your hand so
+
+ align:start position:0%
+you can easily stick it in your hand so
+ 
+
+ align:start position:0%
+you can easily stick it in your hand so
+be very careful with that
+
+ align:start position:0%
+be very careful with that
+ 
+
+ align:start position:0%
+be very careful with that
+use a deuterated solvent when you're
+
+ align:start position:0%
+use a deuterated solvent when you're
+ 
+
+ align:start position:0%
+use a deuterated solvent when you're
+preparing your samples i think you'll be
+
+ align:start position:0%
+preparing your samples i think you'll be
+ 
+
+ align:start position:0%
+preparing your samples i think you'll be
+giving that by your tas anyways
+
+ align:start position:0%
+giving that by your tas anyways
+ 
+
+ align:start position:0%
+giving that by your tas anyways
+and never put a dirty tube in the
+
+ align:start position:0%
+and never put a dirty tube in the
+ 
+
+ align:start position:0%
+and never put a dirty tube in the
+instrument you should always clean the
+
+ align:start position:0%
+instrument you should always clean the
+ 
+
+ align:start position:0%
+instrument you should always clean the
+tube off on the outside
+
+ align:start position:0%
+tube off on the outside
+ 
+
+ align:start position:0%
+tube off on the outside
+um and then i think the last slide that
+
+ align:start position:0%
+um and then i think the last slide that
+ 
+
+ align:start position:0%
+um and then i think the last slide that
+i have
+
+ align:start position:0%
+i have
+ 
+
+ align:start position:0%
+i have
+is about shimming shimming is adjusting
+
+ align:start position:0%
+is about shimming shimming is adjusting
+ 
+
+ align:start position:0%
+is about shimming shimming is adjusting
+the homogeneity of the magnetic field
+
+ align:start position:0%
+the homogeneity of the magnetic field
+ 
+
+ align:start position:0%
+the homogeneity of the magnetic field
+so if you remember from that equation
+
+ align:start position:0%
+so if you remember from that equation
+ 
+
+ align:start position:0%
+so if you remember from that equation
+and you don't even have to know how to
+
+ align:start position:0%
+and you don't even have to know how to
+ 
+
+ align:start position:0%
+and you don't even have to know how to
+sign
+
+ align:start position:0%
+sign
+ 
+
+ align:start position:0%
+sign
+or solve this so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your frequency is directly proportional
+
+ align:start position:0%
+your frequency is directly proportional
+ 
+
+ align:start position:0%
+your frequency is directly proportional
+to the magnetic field strength
+
+ align:start position:0%
+to the magnetic field strength
+ 
+
+ align:start position:0%
+to the magnetic field strength
+shimming means making your magnetic
+
+ align:start position:0%
+shimming means making your magnetic
+ 
+
+ align:start position:0%
+shimming means making your magnetic
+field homogeneous
+
+ align:start position:0%
+field homogeneous
+ 
+
+ align:start position:0%
+field homogeneous
+so that the top of your sample
+
+ align:start position:0%
+so that the top of your sample
+ 
+
+ align:start position:0%
+so that the top of your sample
+feels the same strength field as the
+
+ align:start position:0%
+feels the same strength field as the
+ 
+
+ align:start position:0%
+feels the same strength field as the
+bottom of your sample
+
+ align:start position:0%
+bottom of your sample
+ 
+
+ align:start position:0%
+bottom of your sample
+the machine will do it automatically but
+
+ align:start position:0%
+the machine will do it automatically but
+ 
+
+ align:start position:0%
+the machine will do it automatically but
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+the top of your sample feels a different
+
+ align:start position:0%
+the top of your sample feels a different
+ 
+
+ align:start position:0%
+the top of your sample feels a different
+magnetic field strength than the bottom
+
+ align:start position:0%
+magnetic field strength than the bottom
+ 
+
+ align:start position:0%
+magnetic field strength than the bottom
+then it's going to have two separate
+
+ align:start position:0%
+then it's going to have two separate
+ 
+
+ align:start position:0%
+then it's going to have two separate
+frequencies for where those protons
+
+ align:start position:0%
+frequencies for where those protons
+ 
+
+ align:start position:0%
+frequencies for where those protons
+precess which means the line broadens
+
+ align:start position:0%
+precess which means the line broadens
+ 
+
+ align:start position:0%
+precess which means the line broadens
+out and if that line broadens out it
+
+ align:start position:0%
+out and if that line broadens out it
+ 
+
+ align:start position:0%
+out and if that line broadens out it
+makes it harder
+
+ align:start position:0%
+makes it harder
+ 
+
+ align:start position:0%
+makes it harder
+to interpret and then
+
+ align:start position:0%
+to interpret and then
+ 
+
+ align:start position:0%
+to interpret and then
+i'll skip over this one the last thing i
+
+ align:start position:0%
+i'll skip over this one the last thing i
+ 
+
+ align:start position:0%
+i'll skip over this one the last thing i
+guess
+
+ align:start position:0%
+guess
+ 
+
+ align:start position:0%
+guess
+questions i put in some references in
+
+ align:start position:0%
+questions i put in some references in
+ 
+
+ align:start position:0%
+questions i put in some references in
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+this is a great thing to do with old
+
+ align:start position:0%
+this is a great thing to do with old
+ 
+
+ align:start position:0%
+this is a great thing to do with old
+magnets if you're artistic with cutting
+
+ align:start position:0%
+magnets if you're artistic with cutting
+ 
+
+ align:start position:0%
+magnets if you're artistic with cutting
+tools i would
+
+ align:start position:0%
+tools i would
+ 
+
+ align:start position:0%
+tools i would
+love to have my own pizza oven with an
+
+ align:start position:0%
+love to have my own pizza oven with an
+ 
+
+ align:start position:0%
+love to have my own pizza oven with an
+old magnet
+
+ align:start position:0%
+old magnet
+ 
+
+ align:start position:0%
+old magnet
+so if anybody has any questions please
+
+ align:start position:0%
+so if anybody has any questions please
+ 
+
+ align:start position:0%
+so if anybody has any questions please
+let me know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and no that's not a friend of mine's
+
+ align:start position:0%
+and no that's not a friend of mine's
+ 
+
+ align:start position:0%
+and no that's not a friend of mine's
+either i just snag that off the web
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything else thank you
+
+ align:start position:0%
+anything else thank you
+ 
+
+ align:start position:0%
+anything else thank you
+and if you want to look at this if you
+
+ align:start position:0%
+and if you want to look at this if you
+ 
+
+ align:start position:0%
+and if you want to look at this if you
+have time you can come up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/FE4d7BVFxoA.txt b/FE4d7BVFxoA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ba9caa3f7edb8ab1420571cf9c36119a209183a0
--- /dev/null
+++ b/FE4d7BVFxoA.txt
@@ -0,0 +1,467 @@
+align:start position:0%
+ 
+hi here we are in week four can you
+
+ align:start position:0%
+hi here we are in week four can you
+ 
+
+ align:start position:0%
+hi here we are in week four can you
+believe it we're going to be taking a
+
+ align:start position:0%
+believe it we're going to be taking a
+ 
+
+ align:start position:0%
+believe it we're going to be taking a
+quick look at using your mobile devices
+
+ align:start position:0%
+quick look at using your mobile devices
+ 
+
+ align:start position:0%
+quick look at using your mobile devices
+in your uh camera phones and we're also
+
+ align:start position:0%
+in your uh camera phones and we're also
+ 
+
+ align:start position:0%
+in your uh camera phones and we're also
+going to take a very superficial look at
+
+ align:start position:0%
+going to take a very superficial look at
+ 
+
+ align:start position:0%
+going to take a very superficial look at
+making videos superficial in the sense
+
+ align:start position:0%
+making videos superficial in the sense
+ 
+
+ align:start position:0%
+making videos superficial in the sense
+that we're not going to teach you step
+
+ align:start position:0%
+that we're not going to teach you step
+ 
+
+ align:start position:0%
+that we're not going to teach you step
+by step the idea is for you to use what
+
+ align:start position:0%
+by step the idea is for you to use what
+ 
+
+ align:start position:0%
+by step the idea is for you to use what
+you've already learned which is an
+
+ align:start position:0%
+you've already learned which is an
+ 
+
+ align:start position:0%
+you've already learned which is an
+extraordinary amount in terms of making
+
+ align:start position:0%
+extraordinary amount in terms of making
+ 
+
+ align:start position:0%
+extraordinary amount in terms of making
+your still pictures and applying it to
+
+ align:start position:0%
+your still pictures and applying it to
+ 
+
+ align:start position:0%
+your still pictures and applying it to
+making videos and we'll show you by
+
+ align:start position:0%
+making videos and we'll show you by
+ 
+
+ align:start position:0%
+making videos and we'll show you by
+example of of some very very interesting
+
+ align:start position:0%
+example of of some very very interesting
+ 
+
+ align:start position:0%
+example of of some very very interesting
+videos that people have made of Science
+
+ align:start position:0%
+videos that people have made of Science
+ 
+
+ align:start position:0%
+videos that people have made of Science
+and Engineering I'm going to take a look
+
+ align:start position:0%
+and Engineering I'm going to take a look
+ 
+
+ align:start position:0%
+and Engineering I'm going to take a look
+at my notes here so we'll uh take a
+
+ align:start position:0%
+at my notes here so we'll uh take a
+ 
+
+ align:start position:0%
+at my notes here so we'll uh take a
+quick look back uh Natasha has some
+
+ align:start position:0%
+quick look back uh Natasha has some
+ 
+
+ align:start position:0%
+quick look back uh Natasha has some
+comments and and takes that she saw in
+
+ align:start position:0%
+comments and and takes that she saw in
+ 
+
+ align:start position:0%
+comments and and takes that she saw in
+the week about life let me just quickly
+
+ align:start position:0%
+the week about life let me just quickly
+ 
+
+ align:start position:0%
+the week about life let me just quickly
+tell you who Natasha is Natasha is the
+
+ align:start position:0%
+tell you who Natasha is Natasha is the
+ 
+
+ align:start position:0%
+tell you who Natasha is Natasha is the
+one responsible for creating the videos
+
+ align:start position:0%
+one responsible for creating the videos
+ 
+
+ align:start position:0%
+one responsible for creating the videos
+in terms of fabricating them all of
+
+ align:start position:0%
+in terms of fabricating them all of
+ 
+
+ align:start position:0%
+in terms of fabricating them all of
+these tutorials the way we worked was
+
+ align:start position:0%
+these tutorials the way we worked was
+ 
+
+ align:start position:0%
+these tutorials the way we worked was
+the following I just did not want to
+
+ align:start position:0%
+the following I just did not want to
+ 
+
+ align:start position:0%
+the following I just did not want to
+make talking head tutorials it's not my
+
+ align:start position:0%
+make talking head tutorials it's not my
+ 
+
+ align:start position:0%
+make talking head tutorials it's not my
+style and this is of course all about
+
+ align:start position:0%
+style and this is of course all about
+ 
+
+ align:start position:0%
+style and this is of course all about
+pictures so the idea was for me to
+
+ align:start position:0%
+pictures so the idea was for me to
+ 
+
+ align:start position:0%
+pictures so the idea was for me to
+collect 20 years of images and some
+
+ align:start position:0%
+collect 20 years of images and some
+ 
+
+ align:start position:0%
+collect 20 years of images and some
+recent ones too of course and then what
+
+ align:start position:0%
+recent ones too of course and then what
+ 
+
+ align:start position:0%
+recent ones too of course and then what
+I did was created storyboards which then
+
+ align:start position:0%
+I did was created storyboards which then
+ 
+
+ align:start position:0%
+I did was created storyboards which then
+Natasha
+
+ align:start position:0%
+Natasha
+ 
+
+ align:start position:0%
+Natasha
+collected the the images I gave her and
+
+ align:start position:0%
+collected the the images I gave her and
+ 
+
+ align:start position:0%
+collected the the images I gave her and
+in over overlaid the uh voiceovers that
+
+ align:start position:0%
+in over overlaid the uh voiceovers that
+ 
+
+ align:start position:0%
+in over overlaid the uh voiceovers that
+I made and we went back and forth and we
+
+ align:start position:0%
+I made and we went back and forth and we
+ 
+
+ align:start position:0%
+I made and we went back and forth and we
+edited this and that and then she added
+
+ align:start position:0%
+edited this and that and then she added
+ 
+
+ align:start position:0%
+edited this and that and then she added
+some of her magic and that's how we got
+
+ align:start position:0%
+some of her magic and that's how we got
+ 
+
+ align:start position:0%
+some of her magic and that's how we got
+the videos that we got which I I think
+
+ align:start position:0%
+the videos that we got which I I think
+ 
+
+ align:start position:0%
+the videos that we got which I I think
+work I hope you think they're working I
+
+ align:start position:0%
+work I hope you think they're working I
+ 
+
+ align:start position:0%
+work I hope you think they're working I
+think that we're getting comments from
+
+ align:start position:0%
+think that we're getting comments from
+ 
+
+ align:start position:0%
+think that we're getting comments from
+you that you're enjoying the videos
+
+ align:start position:0%
+you that you're enjoying the videos
+ 
+
+ align:start position:0%
+you that you're enjoying the videos
+which is part of this it's not only
+
+ align:start position:0%
+which is part of this it's not only
+ 
+
+ align:start position:0%
+which is part of this it's not only
+learning but it's enjoying the stuff
+
+ align:start position:0%
+learning but it's enjoying the stuff
+ 
+
+ align:start position:0%
+learning but it's enjoying the stuff
+because otherwise why I bother so if you
+
+ align:start position:0%
+because otherwise why I bother so if you
+ 
+
+ align:start position:0%
+because otherwise why I bother so if you
+remember a while ago I said please uh
+
+ align:start position:0%
+remember a while ago I said please uh
+ 
+
+ align:start position:0%
+remember a while ago I said please uh
+read your manual and your manual will
+
+ align:start position:0%
+read your manual and your manual will
+ 
+
+ align:start position:0%
+read your manual and your manual will
+will talk about white balance some of
+
+ align:start position:0%
+will talk about white balance some of
+ 
+
+ align:start position:0%
+will talk about white balance some of
+you are not balancing your light
+
+ align:start position:0%
+you are not balancing your light
+ 
+
+ align:start position:0%
+you are not balancing your light
+properly and that we saw this more in
+
+ align:start position:0%
+properly and that we saw this more in
+ 
+
+ align:start position:0%
+properly and that we saw this more in
+this past week it's very simple it's
+
+ align:start position:0%
+this past week it's very simple it's
+ 
+
+ align:start position:0%
+this past week it's very simple it's
+just a means of telling the camera what
+
+ align:start position:0%
+just a means of telling the camera what
+ 
+
+ align:start position:0%
+just a means of telling the camera what
+temperature to adjust the images for and
+
+ align:start position:0%
+temperature to adjust the images for and
+ 
+
+ align:start position:0%
+temperature to adjust the images for and
+and you'll you'll find a better image i'
+
+ align:start position:0%
+and you'll you'll find a better image i'
+ 
+
+ align:start position:0%
+and you'll you'll find a better image i'
+we'd really rather you do that here in
+
+ align:start position:0%
+we'd really rather you do that here in
+ 
+
+ align:start position:0%
+we'd really rather you do that here in
+while you make the camera uh make the
+
+ align:start position:0%
+while you make the camera uh make the
+ 
+
+ align:start position:0%
+while you make the camera uh make the
+pictures and not do it in
+
+ align:start position:0%
+pictures and not do it in
+ 
+
+ align:start position:0%
+pictures and not do it in
+post-production uh it's it's something
+
+ align:start position:0%
+post-production uh it's it's something
+ 
+
+ align:start position:0%
+post-production uh it's it's something
+that you might want to look at okay so
+
+ align:start position:0%
+that you might want to look at okay so
+ 
+
+ align:start position:0%
+that you might want to look at okay so
+that's it here we go in week four have
+
+ align:start position:0%
+that's it here we go in week four have
+ 
+
+ align:start position:0%
+that's it here we go in week four have
+fun
\ No newline at end of file
diff --git a/FEsKwINx--I.txt b/FEsKwINx--I.txt
new file mode 100644
index 0000000000000000000000000000000000000000..84d2ab58d9e8e26a7eb115887961cfd7e857ef78
--- /dev/null
+++ b/FEsKwINx--I.txt
@@ -0,0 +1,1668 @@
+The following content is
+provided by MIT OpenCourseWare
+
+under a Creative Commons
+license.
+
+Additional information about
+our license, and MIT
+
+OpenCourseWare in general, is
+available at ocw.mit.edu.
+
+PROFESSOR: OK.
+
+Let's resume.
+
+I cut things off at a time when
+we had the final answer.
+
+And I left you hanging because
+we don't know what the final
+
+answer is telling us.
+
+This says that as we change the
+orientation of the normal
+
+to the plate, relative to x3
+and, secondarily, as we change
+
+the angle between the threefold
+axis and x2, we get
+
+this strange third-rank
+trigonometric function.
+
+Let's convert these cosines into
+the appropriate angles.
+
+This was the twofold axis.
+
+And this was x1.
+
+This was the direction of
+the threefold axis.
+
+This was x3.
+
+And this is the direction x2.
+
+And that comes out in between
+a pair of twofold axes.
+
+And we may want to look at this
+from up above, relative
+
+to these twofold axes
+that occur.
+
+This thing here looks like
+a trigonometric identity,
+
+doesn't it?
+
+Let's let this angle
+here be theta.
+
+And l1, then, is cosine
+of theta.
+
+And so our geometry is that this
+is l1 cosine of theta.
+
+This is l2, which is the cosine
+of the angle between
+
+our direction and x2.
+
+And that is the cosine of
+pi over 2, minus theta.
+
+And that, then, is equal
+to sine of theta.
+
+So this identity, as
+you all know--
+
+I'm not telling you anything
+that you don't already know--
+
+this is d is equal to
+d1,1 1, times the
+
+cosine of 3 theta, right?
+
+You knew that.
+
+Believe it or not, it is.
+
+It's one of these obscure
+trigonometric identities,
+
+which wouldn't occur to you in
+a million years unless you go
+
+digging through some
+handbooks.
+
+So this is rather astonishingly
+simple.
+
+It's simply a cosine function.
+
+But the interesting thing
+is it goes as a
+
+function of 3 theta.
+
+So this goes through one cycle
+between a pair of adjacent
+
+twofold axes.
+
+So it starts out as d1,1.
+
+And it finishes up at d1,1.
+
+And in between it
+is minus d1,1.
+
+And so it goes down.
+
+And now we come to something
+that I do differently than
+
+most people do.
+
+Most people will say it
+goes as minus d1,1.
+
+But minus d1,1 I like to show
+as a lobe going off in this
+
+direction, with a minus sign.
+
+AUDIENCE: How do you get
+that cosine of 3 theta?
+
+PROFESSOR: Hmm?
+
+AUDIENCE: How do you get d
+equals d1 cosine 3 theta?
+
+PROFESSOR: How do I get that?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: That is just a
+trigonometric identify,
+
+believe it or not, a well-known
+
+trigonometric identify.
+
+Actually, it's an exceedingly
+obscure
+
+trigonometric identity.
+
+So the way this is going to go
+from x1 is it's going to be a
+
+positive lobe around x1.
+
+There's going to be a negative
+lobe along x2 and then a
+
+positive lobe again about the
+twofold axis that's 120
+
+degrees away.
+
+And then a negative lobe, and
+then a positive lobe opposite
+
+this negative lobe, and a
+negative lobe opposite this
+
+positive lobe.
+
+So it's a six-membered--
+
+six lobes.
+
+There is always a positive lobe
+opposite a negative lobe.
+
+And what this means is that the
+charge is of opposite sign
+
+on opposite ends of
+the twofold axes.
+
+So the response peaks
+up on twofold axes.
+
+Now the thing that I don't like
+is that what Nye does is
+
+to say, OK, this is
+a negative value.
+
+So you should plot the radius
+in a negative direction.
+
+And that puts it over here,
+right on top of
+
+this positive lobe.
+
+So what Nye shows is the polar
+plot of this result, in the
+
+plane of the twofold axes,
+is simply this.
+
+This is x1.
+
+And he shows a lobe here.
+
+And he shows a lobe here.
+
+And he shows a lobe here.
+
+And if you interpret that as a
+polar plot you say, well, I
+
+know what the value
+is in here.
+
+It's decreasing.
+
+And there's nothing
+going on in here.
+
+So the response must be 0.
+
+And then it starts
+coming up again.
+
+And there's a response in
+different directions here.
+
+And then it goes
+back down to 0.
+
+And in this range, there's
+nothing going on.
+
+And that's not true.
+
+What's going on is a negative
+value of the modulus.
+
+And to me, that becomes
+abundantly clear if you just
+
+put a sign that labels the sign
+of the modulus within
+
+those lobes.
+
+Now I submit, that's pretty
+anisotropic, isn't it?
+
+Yes, Steve?
+
+AUDIENCE: Did you just
+arbitrarily choose where your
+
+positive and negatives
+go, is it [INAUDIBLE]
+
+out here?
+
+PROFESSOR: No.
+
+This comes out here.
+
+When l1 is 0, that's--
+
+excuse me.
+
+When the angle is
+0, l1 is plus 1.
+
+Remember that l1 is the
+cosine of this angle.
+
+When that angle is 0, then
+the value is plus 1.
+
+So I was careful to put
+the label x1 on this.
+
+Now the other thing that we
+should examine is how these
+
+lobes vary in a direction
+perpendicular to x, in a
+
+direction that includes x3.
+
+So let us look at how the
+function varies in a direction
+
+perpendicular to--
+
+that includes x1 and x3.
+
+OK.
+
+Call this angle phi.
+
+And in the x1, x3 plane, d1,1,1
+prime turns out to be
+
+l1 cubed d1,1.
+
+Before you go to our
+general expression.
+
+And l2 is cosine of 90.
+
+This thing drops out.
+
+We're left with simply
+d1,1 prime equals
+
+l cubed times d1,1.
+
+So this then goes as cosine
+cubed of phi, which is a lobe
+
+that starts out at plus 1.
+
+And then because it's cosine
+cubed, this dies out very,
+
+very rapidly.
+
+So these lobes are very flat in
+the x1, x2 plane, die out
+
+very rapidly as the cube of phi,
+where phi is the angle
+
+between the twofold
+axis and x3.
+
+So the interesting thing about
+this surface is that if you
+
+decided to pick up the random
+fragment of crystal and
+
+determine what its Piezoelectric
+Modulus is.
+
+One way of doing this,
+a poor man's test for
+
+piezoelectricity is to just
+clamp a fragment of crystal
+
+between two electrodes and
+then hook this up to a
+
+variable frequency generator
+that sweeps through a range of
+
+frequencies, changes the
+frequency of a voltage across
+
+these plates, and then comes
+back and sweeps again.
+
+Or alternatively, have
+a knob one on that
+
+lets you change frequency.
+
+Then put a pair of earphones
+across the crystal.
+
+And if we would do that, by
+having this variable frequency
+
+generator, as we turned it,
+when we hit a resonant
+
+frequency that set up either
+a full wavelength of a
+
+vibrational wave in
+the crystal--
+
+or half wavelength, or one
+wavelength, or 3/2
+
+wavelength--
+
+there'd be a resonance.
+
+And the capacitance does
+something crazy.
+
+It does like this as
+you go through
+
+the resonant frequency.
+
+And then your simple
+detector--
+
+a pair of earphones--
+
+as you tuned the frequency, you
+would hear static as you
+
+went through this discontinuity
+in capacitance.
+
+Or alternatively, you could put
+this on a cathode ray tube
+
+and just have a sweep frequency
+and put the voltage
+
+across the electrodes on the
+oscilloscope screen.
+
+And you would see something
+like this, and then this
+
+discontinuity, and then
+maybe second harmonic.
+
+And it would work just fine.
+
+This is a poor man's way of
+detecting piezoelectricity.
+
+But what if--
+
+what if--
+
+you happen to have your piece of
+quartz with the electrodes
+
+directly on the c-axis?
+
+The modulus would be 0, and you
+wouldn't detect anything.
+
+Or if you put on the probes
+such that they were in a
+
+direction that was in between
+these lobes where, again, the
+
+Piezoelectric Modulus
+has gone to 0.
+
+You wouldn't find anything.
+
+So measuring the Piezoelectric
+Modulus for a random chunk of
+
+material is dangerous, if you
+just look at one direction and
+
+say nothing's going on; it's
+not piezoelectric.
+
+The other thing is the
+material could have a
+
+piezoelectric response that's
+so weak you just
+
+can't measure it.
+
+Yeah, OK?
+
+AUDIENCE: This stuff's only for
+single crystals, right?
+
+Because if you [INAUDIBLE]
+polycrystal material, you're
+
+getting [INAUDIBLE] averaging.
+
+PROFESSOR: You're averaging
+over all directions.
+
+So this is for a
+single crystal.
+
+And that's the only time you
+get these exotic, very
+
+anisotropic surfaces.
+
+Another method that I've
+seen in a rather old
+
+book is really nice.
+
+What you do is you cut your
+crystal into a little plate.
+
+And then you drive the plate by
+means of putting electrodes
+
+on it and hook this up to
+a variable frequency.
+
+And if the material is
+transparent, you will set up--
+
+depending on the velocity of
+sound in the material--
+
+you will set up standing
+waves when you
+
+hit the right frequency.
+
+And these lines that I've drawn
+are places where the
+
+displacement is always 0.
+
+And these things that I've
+indicated at little squares is
+
+a region where the displacement
+goes up and down
+
+between its maximum and
+minimum extreme.
+
+Now if this crystal is
+transparent and you shine a
+
+light through it, these little
+regions bounded by lines of
+
+zero displacement act
+like little lenses.
+
+So if you pass a beam of light
+through it, you get a bunch of
+
+right maxima, little focused
+spots on the sheet.
+
+And you can determine for a
+particular frequency if this
+
+is the 1 and 1/2 wavelengths
+along a dimension that you
+
+know, you can again find the
+Piezoelectric Moduli.
+
+So there are lots of ways of
+detecting this effect.
+
+But when you have a single
+crystal, you've got to really
+
+look at this as a function
+of direction, to
+
+be absolutely sure.
+
+One other Piezoelectric Modulus
+is in the problem set.
+
+4 bar 3m, this is the structure
+of sphalerite and a
+
+lot of the compound
+semiconductors.
+
+This is not in the notes.
+
+But if you try the problem,
+what you find is, again, a
+
+highly, highly anisotropic
+behavior.
+
+And this is the direction of the
+unit cell of the crystal.
+
+You find that the piezoelectric
+response is a
+
+series of very sharp lobes,
+positive and negative, going
+
+along the directions of the body
+diagonal, namely the 1,
+
+1, 1 directions in
+the crystal.
+
+And then there's another
+lobe that goes like
+
+this, negative, positive.
+
+Another lobe that goes up here,
+positive and negative.
+
+So very sharp lobes along the
+body diagonal, alternately
+
+positive, negative, positive,
+negative as you go around 0,
+
+0, 1 plane.
+
+OK.
+
+That's what the longitudinal
+piezoelectric effect is like.
+
+You can invent single-crystal
+devices for weighing fish.
+
+And then you have an interesting
+question.
+
+If you hang the weight on the
+crystal, and it's a flat
+
+plate, how would you orient the
+crystal to get the optimum
+
+sensitivity?
+
+So you define a scalar modulus
+for the crystal in the
+
+particular direction you're
+exerting a uniaxial stress.
+
+And then you express this module
+in terms of theta, the
+
+angle of rotation, within
+the crystographic plane.
+
+In the case of the sup cell if
+you looked at that geometry,
+
+that is a flat plate subject
+to compression, where you
+
+measure the surface charge
+perpendicular to the direction
+
+of the uniaxial stress,
+not parallel to it
+
+as we've done here.
+
+And then there's a question if
+you rotate the plane of the
+
+crystal about the imposed
+stress, what orientation gives
+
+you optimum, maximum response?
+
+So there are fun things that
+you could do with that.
+
+We have a quiz next time.
+
+There's a lame-duck period after
+the quiz will be over.
+
+And I want to say a little bit
+about the tensor aspects of
+
+elastic moduli.
+
+Mechanical behavior is something
+that you have or
+
+will cover in great detail in
+a graduate-level class on
+
+mechanics, but I think very
+few people who deal with
+
+things other than cubic
+materials or with
+
+single-crystal materials where
+the elastic constants are
+
+functions of crystal symmetry
+and direction.
+
+So let me, at least at the
+time available, set up a
+
+definition of stress
+in terms of strain.
+
+Stress is a second-rank
+tensor.
+
+There are six unique
+components.
+
+So we could write an expression
+for sigma 1,1;
+
+sigma 2,2; sigma 3,3; sigma
+4,4; and sigma 5,5.
+
+And sigma--
+
+AUDIENCE: --1,2.
+
+PROFESSOR: No, I want to
+go down like this.
+
+So this would be sigma 2,3;
+sigma 1,3; and sigma 1,2;
+
+eventually to be known as sigma
+1, sigma 2, sigma 3,
+
+sigma 4, sigma 5,
+and sigma six.
+
+But actually, if we're writing
+out a full tensor relation, we
+
+should write down all
+six elements here.
+
+So let me do that and
+put in a 3,2.
+
+Put in all nine of them, because
+before we condense to
+
+matrix form, that is what
+we're going to have.
+
+So we'll have a sigma 2,3; we'll
+have a sigma 3,2; we'll
+
+have a sigma 1,3; a sigma 3,1;
+a sigma 1,2; and a sigma 2,1.
+
+And we can express each of the
+stresses in terms of the
+
+elements of strain.
+
+So I'll have an epsilon 1,1;
+an epsilon 1,2; an epsilon
+
+2,2; an epsilon 3,3; an epsilon
+2,3; an epsilon 3,2;
+
+an epsilon 1,3; an epsilon 3,1;
+an epsilon 1,2; and an
+
+epsilon 2,1.
+
+Nine terms, nine terms.
+
+And in between is going
+to be a tensor
+
+consisting of 9 by 9 elements.
+
+There will be 81 different
+coefficients in here.
+
+If we want to derive symmetry
+constraints, we're going to
+
+have to, for every one of
+those 81 elements, do a
+
+transformation.
+
+And each transformed element is
+going to be a sum of four
+
+direction cosines times one
+tensor element, repeated 81
+
+different times.
+
+Not something to be undertaken
+on a short afternoon.
+
+OK.
+
+What are the tensor
+elements in here?
+
+They are represented
+by the symbol c.
+
+This would be c1,1,1,1.
+
+This would be c1,1,2,2 times
+epsilon 2,2; a c1,1,3,3; a
+
+c1,1,2,3; and so on.
+
+And these c's, in one of the
+great perversions of
+
+scientific notation, are
+called stiffnesses.
+
+The other thing we could
+do is to write
+
+strain in terms of stress.
+
+And really, stress
+is something you
+
+can do to the crystal.
+
+So stress is an independent
+variable.
+
+And this is something that
+I feel more at home with.
+
+So I'll have an epsilon 1,1;
+2,2; 3,3; epsilon 3,2; 2,3;
+
+epsilon 1,3; epsilon
+3,1; epsilon 2,1;
+
+and an epsilon 1,2.
+
+Again, nine elements
+of strain.
+
+And these will be given by
+coefficients times each of the
+
+nine elements of stress, sigma
+1,1; sigma 2,2; sigma 3,3;
+
+sigma 2,3; sigma 3,2; and
+so on for nine different
+
+components.
+
+Andy the coefficients here are
+designated with the symbol s.
+
+These are the tensor elements.
+
+So this is s1,1,1.
+
+This is s1,1,2,2.
+
+And the s's stand
+for compliances.
+
+Now English is a very
+strange language.
+
+But to call compliance s and to
+call stiffness c is surely
+
+a perversion that can be
+designed for no other purpose
+
+than to confuse the introductory
+student and give
+
+the instructor some feeling
+of superiority.
+
+I don't feel superior, I feel
+embarrassed that I have to
+
+explain this.
+
+Stiffness, c; compliance, s.
+
+It's got be one of
+the atrocities
+
+of scientific notation.
+
+To remember which goes with
+which, I'll tell you what
+
+works for me.
+
+If it doesn't work for
+you, forget it.
+
+The s goes with sigma.
+
+And the little c goes
+with the epsilon.
+
+That's a c with a bar in it.
+
+That works for me.
+
+If it doesn't work for you, use
+your own mnemonic device.
+
+English does a lot of things
+strangely, but nothing is as
+
+perverse as this.
+
+Now what's some examples?
+
+Consider this.
+
+You park your car in your
+driveway, but you drive your
+
+car on a parkway.
+
+Why don't you drive your car
+on a driveway and park your
+
+car in a parkway?
+
+No, it's the other way around.
+
+It's almost as bad as this.
+
+What are some other ones?
+
+In my basement, I have something
+that's called a hot
+
+water heater.
+
+You don't heat hot water,
+you heat cold water.
+
+Why isn't it called a
+cold water heater?
+
+Even better, I once worked
+for a year and a half in
+
+Switzerland.
+
+And in the kitchen of my home
+I had, in German, an
+
+elektrowarmwasse
+rsheissungsapparat.
+
+That's one word that's
+11 syllables.
+
+The Germans have a knack with
+the language that we have
+
+never approached in English.
+
+But there's another one
+you've probably heard.
+
+You know what the prefix
+"pro" means.
+
+That means for, and "con"
+means against.
+
+And so progress is moving
+forward, and I leave it to you
+
+to decide what Congress means.
+
+OK.
+
+So I could go on and on.
+
+I probably shouldn't, unless
+you egg me on.
+
+No, I won't.
+
+But anyway, there are--
+
+OK, I'll give another one.
+
+Why is what a doctor does
+called "practice"?
+
+This is not reassuring at all.
+
+Let me invite you over
+to my practice.
+
+And why is it when you take an
+airplane your flight ends with
+
+a terminal?
+
+That's doesn't sound very
+encouraging either.
+
+So anyway, language is silly.
+
+And I guess if you want to
+call c stiffnesses and s
+
+compliances, it's OK.
+
+The verbal description of these
+terms means something.
+
+Because if the stiffness is very
+high, that says that a
+
+little bit of strain requires
+that you haven't posed a very
+
+large stress.
+
+So stiff is when the material
+is resistant to stress.
+
+So you have to have a very,
+very large strain to get
+
+yourself a given level
+of stress.
+
+Conversely, if the material is
+very compliant, a very small
+
+stress for a compliant
+material should
+
+give you a big strain.
+
+And that's exactly what a large
+value of s will do.
+
+It will give you a large
+strain for a
+
+relatively small stress.
+
+So the words describe
+what's going on.
+
+OK.
+
+There is great utility in
+reducing these equations to a
+
+matrix form, which is going to
+cut us down from a 9 by 9, or
+
+a tensor with 81 elements, to a
+smaller number of subscripts
+
+and a smaller number of matrix
+elements, so if we let sigma 1
+
+be sigma 1,1; if we let sigma
+2 be equal to sigma 2,2 and
+
+sigma 3 be equal to sigma 3.
+
+And then if we write the
+inequalities we've had before,
+
+and we let epsilon 1,1 to be
+replaced by epsilon 1, then we
+
+would have out in front here a
+term simply c1,1, a 1 for the
+
+sigma and a 1 for the epsilon.
+
+The next term would be c1,2
+times epsilon 2, where
+
+obviously epsilon 2 has replaced
+epsilon 2,2, and 1
+
+stands for the two
+indices, 1,1.
+
+So this will go c1,3;
+epsilon 3.
+
+And then you hit these
+messy factors of two.
+
+You'll have a pair of terms.
+
+You'll have c1,4.
+
+And that will stand for
+a term c1,1,2,3.
+
+And then there'll be another
+term c1,1,3,2.
+
+And if you want to write this
+as a matrix, c1,4 has to be
+
+equal to the sum of these two
+things, times epsilon 4.
+
+That's the only way you can
+write it as a matrix.
+
+And if you think it was bad
+worrying about a factor of 2
+
+in front of half of the terms on
+the right-hand side of the
+
+equation, we're going to be
+dealing with factors of 2 for
+
+terms in the upper
+3 by 3 array.
+
+We're going to be worrying about
+a factor of 4, somehow
+
+or other, down in the
+lower 3 by 3 array.
+
+So the way you handle the
+factor of 2 really is a
+
+nightmare for relations
+in elasticity.
+
+But continuing on with the first
+line, c1,5 times epsilon
+
+5 would be a combination of
+c1,1,3,1 plus 1,1,1,3.
+
+And then finally, when you get
+to c1,6 times epsilon 6, that
+
+would represent a combination
+of c1,1,2,1 plus c1,1,1,2.
+
+You have to make a decision
+where to swallow the 2.
+
+And probably the best thing
+I can do is to give you
+
+conventions for relabeling
+stress, strain, stiffness, and
+
+compliance, which I'll
+pass around to you.
+
+No big deal, except that this
+is a case where you can eat
+
+the 2's early on, but you
+can't even break even.
+
+So very, very briefly, what
+you do is you convert the
+
+tensor elements of stress to
+matrix elements in exactly the
+
+same way we did with
+piezoelectricity.
+
+For strains, we do exactly the
+same thing that we did with
+
+the converse piezoelectric
+effect.
+
+The factor of 2 that you
+swallowed in definition of
+
+stress pops up to haunt
+you when you
+
+deal with the strains.
+
+And you cannot write a nice
+matrix relation unless you
+
+divide the off-diagonal elements
+of strain by 1/2.
+
+And that was exactly the same
+thing we encountered with the
+
+converse piezoelectric effect,
+which related strain to an
+
+applied electric field.
+
+In defining the matrix
+stiffnesses, the c's, you
+
+forge straight ahead, and you
+let ci,j,k,l, which is
+
+identical to ci,j,l,k--
+
+that's the term that relates the
+two equal shear stresses--
+
+and you define that as a
+matrix term with two
+
+subscripts.
+
+No factors of 2 or
+4 are involved.
+
+Then when you hit the s's,
+there's a nightmare.
+
+si,j,k,l is sm,n if m and n
+are 1, 2, or 3; that is to
+
+say, not 4, 5, or 6.
+
+si,j,k,l, which is the same as
+s,i,j,l,k, has to be defined
+
+as one half of sm,n, where
+m or n is 4, 5, or 6.
+
+And then finally, you have to
+throw in a factor of 4 when
+
+both m and n are 4, 5, or six
+or, in other words, m and n
+
+are not 1, 2, or 3.
+
+So it is a mess.
+
+And these are rules that you
+have to bear in mind if you're
+
+ever going to go from matrix
+form, which works absolutely
+
+lovely in a fixed coordinate
+system.
+
+But if you have a single crystal
+and you want to refer
+
+it to different axes, you have
+to be prepared to resurrect
+
+the full tensor form.
+
+And then and only then can you
+work symmetry transformations.
+
+I don't want to go through the
+simple algebra of expanding
+
+and contracting these terms.
+
+So the next two sheets show
+you how you condense from
+
+tensor to matrix notation, and
+then go back from matrix
+
+notation to tensor notation.
+
+This is for the compliances
+si,j,k.
+
+And the next page does the same
+thing, if you care to
+
+write stress in terms
+of strain.
+
+And there are a lot
+more factors of
+
+2 that appear there.
+
+But again, it shows you how you
+go from tensor notation,
+
+for subscripts on the c's, down
+to matrix notation with 2
+
+subscripts, and then go back up
+again to tensor notation.
+
+So it's a tedious business.
+
+And you've got to keep careful
+tracks of your factors of 2
+
+and your factors of 4.
+
+How about symmetry
+restrictions?
+
+Holy mackerel.
+
+Transformation of 81
+different elements.
+
+Well, in order to do the tensor
+transformations, you
+
+have to go to the full-force
+subscript notation.
+
+Only then is a law of
+transformation defined.
+
+Fourth-rank properties
+are even tensors.
+
+So mercifully, there are
+not as many different
+
+possibilities.
+
+All point groups that differ
+by presence or absence of
+
+inversion have exactly the
+same form of the tensor.
+
+So symmetry 2, m, and
+2/m look alike.
+
+Symmetry 2, 2mm, and 2/m,
+2/m, 2/m look alike.
+
+So there's only one orthorhombic
+tensor, only one
+
+kind of monoclinic tensor, only
+one kind of triclinic
+
+tensor, and so on.
+
+And the only place that you have
+more than one form of the
+
+tensor for a particular set of
+point groups is looking at the
+
+point groups that are based
+on single-rotation axes,
+
+something like 4, 4 bar 4m, and
+those that are based on
+
+the axial arrangements
+4, 2, 2.
+
+So they're different, just as
+they were for second-rank
+
+tensor properties.
+
+For cubic, a rather
+remarkable result.
+
+There are three independent
+compliances.
+
+But cubic crystals are not
+elastically isotropic.
+
+They are anisotropic.
+
+And it's just the nature of the
+tensor that requires that.
+
+So rather than letting you hang
+by your thumbs wondering
+
+what's on these pages, let me
+pass around the summary of
+
+symmetry constraints.
+
+If you understood what we did
+for third-rank tensors or even
+
+second-rank tensors,
+you how to do this.
+
+And fortunately, the
+terms almost over.
+
+So I can't make you do it, which
+is probably an enormous
+
+relief to you.
+
+Some additional bits
+of information.
+
+The transformations for
+hexagonal crystals are
+
+complicated because threefold
+and sixfold axes do not change
+
+the reference axes x1, x2,
+x3 into one another.
+
+And the equations that relate
+the individual tensor elements
+
+are more complex.
+
+For the threefold axis, for
+example, 2 s1,1 minus 2 s1,2
+
+is equal to s4,4.
+
+So they're not simple relations
+between them.
+
+And that's simply because
+you're not changing one
+
+reference access into another.
+
+You're changing x1, for
+example, into a linear
+
+combination of x1 and x2.
+
+Two things down here
+of interest.
+
+I said that cubic crystals
+are not isotropic.
+
+What would have to be
+the case if the
+
+material were to be isotropic?
+
+Well, it turns out that if you
+do this for the compliances,
+
+s, if 1/2 of s4,4 is equal to
+s1,1 minus s1,2, then the
+
+material is elastically
+isotropic.
+
+If you do this in terms
+stiffnesses, the c's, then 2
+
+c4,4 is equal to c1,1 minus
+c1,2 if the material is
+
+supposed to be isotropic or
+going to be isotropic.
+
+Then there is one
+other inequality
+
+that depends on structure.
+
+And this is something known
+as the Cauchy relation.
+
+And it depends on the
+interatomic forces.
+
+The first condition that has to
+be met is that the forces
+
+between the atoms should
+be central forces.
+
+What is a central force?
+
+Well, this is a case where the
+attractive force between the
+
+atoms is directly along the line
+joining their centers.
+
+Isn't that always the case?
+
+Don't crystals hold together
+because there's an attractive
+
+force between atoms?
+
+Well actually, for metallic
+crystals and ionic crystals,
+
+maybe that's not a bad
+assumption, particularly for
+
+ionic crystals.
+
+But if you had a covalent
+material, where the bonding
+
+was due to overlap of orbitals
+like this, then the thing that
+
+holds the crystal together
+is overlap
+
+between these orbitals.
+
+And the force holding the atoms
+together is a force that
+
+goes through this shared
+electron pair.
+
+And that's not a
+central force.
+
+And so the Cauchy relation
+generally fails rather badly
+
+for covalently bonded
+materials.
+
+Second assumption is
+that each atom is
+
+at a center of symmetry.
+
+And the reason for that is so
+the force in the plus-x
+
+direction is the same
+as the force
+
+in the minus-x direction.
+
+And that is not true for any
+material that has tetrahedral
+
+coordination.
+
+So it's not true for any
+of the forms of SiO2.
+
+It's not true for any of the
+compound semiconductors that
+
+are based on tetrahedral
+units.
+
+So there, the atom inside of
+these tetrahedra is decidedly
+
+not at an inversion center.
+
+And finally, you assume that the
+crystal is under no state
+
+of initial stress.
+
+Because if it is under initial
+stress, you've squished it,
+
+you've stretched the bonds.
+
+And the forces--
+
+not to a major degree, to be
+sure, but-- the forces will
+
+not truly be perfect
+central forces.
+
+So if all three of these
+assumptions are satisfied,
+
+then you have an additional
+equality
+
+c1,2 is equal to c4,4.
+
+What I'll do next time is I'll
+bring in some examples of data
+
+for stiffnesses and compliances
+and, in
+
+particular, show you how some
+of these elastic tensor
+
+elements change with
+temperature.
+
+And we can examine them to see
+how well the Cauchy equality
+
+or the isotropy condition
+is satisfied.
+
+All right.
+
+That's about all that we'll
+do about the definition of
+
+fourth-rank tensor properties.
+
+On next Tuesday to wrap the
+term up, we'll look at the
+
+variation of some elastic
+moduli, such as Young's
+
+Modulus or the shear modulus,
+for different symmetries as a
+
+function of direction
+in the crystal, OK?
\ No newline at end of file
diff --git a/FRgckt9lDQ8.txt b/FRgckt9lDQ8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d29358e9ef589342239823c6bf13c78b37cf03fc
--- /dev/null
+++ b/FRgckt9lDQ8.txt
@@ -0,0 +1,2990 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation, or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK, OK.
+
+The weekend is over.
+
+One announcement.
+
+Last weekly test will be
+tomorrow, and it'll be based
+
+on homework 11, focused
+on polymers.
+
+And then the following week
+is the very last week of
+
+semester, and there's no
+testing, no work required of
+
+you, when the subject
+has a final exam.
+
+And this one has a big final
+exam, big celebration, so
+
+there will be no weekly
+test next Tuesday.
+
+So this is the last one,
+so get out the Kleenex.
+
+All right.
+
+So today we want to continue the
+treatment of biochemistry.
+
+Last day we started looking at
+proteins, and the building
+
+blocks of proteins
+are amino acids.
+
+And so we looked at the basic
+structure of amino acids,
+
+shown here, which is an sp3
+hybridized central carbon,
+
+which I've designated
+alpha carbon.
+
+And three of the four
+bonds are the same
+
+in every amino acid.
+
+Every amino acid has,
+off the central
+
+carbon, an amino group.
+
+This is the nitrogen
+with two hydrogens.
+
+It has a hydrogen, a lone
+hydrogen, and it has a
+
+carboxylic acid, which
+is this COOH.
+
+Double bond here, I'm looking at
+four sticks off the carbon.
+
+One, two, three, four.
+
+And this proton here is the one
+that can fall off and go
+
+over to the side.
+
+And when it does so, then
+we end up with the acid.
+
+It's a proton donor.
+
+And then the fourth bond
+is this designated R.
+
+R is the substituent, and
+it could be anything.
+
+We could put a cyanide
+up there, if we want.
+
+Anything that conforms to this
+architecture with whatever
+
+choice of R is still qualified
+as amino acid.
+
+There are only twenty
+choices of R that
+
+are found in protein.
+
+We also studied chirality,
+which is handedness.
+
+Some of these amino acid
+molecules are chiral.
+
+That is to say, if you put this
+carboxylic acid in the
+
+lower left, and the amino group
+in the lower right, you
+
+have molecules that are
+seemingly identical, but not
+
+superimposable.
+
+We call them chiral.
+
+And the two forms are
+called enantiomers.
+
+And only the L-enantiomer
+is found in proteins.
+
+And we saw that the L is
+determined on the basis of
+
+polarization rotation
+of light in an
+
+aqueous solution of this.
+
+Except for lycene.
+
+In the case of lycene,
+we have H up here.
+
+So we have an H above
+and an H below.
+
+That molecule is not chiral.
+
+So nineteen of the twenty amino
+acids that we find in
+
+proteins exhibit chirality.
+
+And later in the lecture we
+started looking at aqueous
+
+solution behavior of
+the amino acids.
+
+And what happens is, when they
+dissolve in aqueous solution,
+
+they form zwitterions.
+
+Zwitterions by proton
+transfer.
+
+So the proton goes off the
+carboxylic acid and joins the
+
+amino end, so you have a plus
+end and a minus end.
+
+And then we looked at what
+happens with the behavior in
+
+aqueous solution, and
+we came up with the
+
+Henderson-Hasselbalch
+equation.
+
+And here it is, plotted.
+
+This is the case for alanine.
+
+In the case of alanine, we have
+the methyl group here.
+
+So the R is CH3.
+
+Everything else is the same.
+
+So you can see that here's the
+neutral zwitterion, where the
+
+H off of the carboxylic acid,
+has transferred over
+
+to the amino end.
+
+We have charge neutrality.
+
+The molecule started off net
+neutral, and now the plus is
+
+over here, conferring a positive
+charge to this end,
+
+and leaving this end less
+a positive charge,
+
+and therefore minus.
+
+So it's globally neutral, but
+locally positive and negative.
+
+Hence the term zwitterion,
+because it's essentially dual
+
+gender, both positive
+and negative.
+
+And we looked at the aqueous
+solution behavior of the
+
+zwitterion, and we saw that
+zwitterion is responsive to
+
+its environment.
+
+And we reasoned that this is
+how you start to impart
+
+animation to something.
+
+How do you get something
+animated?
+
+You get something animated by
+having it respond to its
+
+environment.
+
+A rock sits there.
+
+You can talk to the rock,
+nothing happens to the rock.
+
+But animated objects, if they're
+endowed with hearing,
+
+if you talk to them, sometimes
+they respond.
+
+So what's going on there?
+
+It to do with the ability
+to respond chemically.
+
+And so what we saw
+here is, when we
+
+went into low pH regime--
+
+low pH means very, very high
+proton concentration.
+
+The zwitterion responds by the
+le Chatelier principle to try
+
+to minimize that acidity.
+
+So it gobbles up protons.
+
+And over here we see that
+it gobbles up protons by
+
+attaching to this carboxylic
+acid end.
+
+That's a proton attachment
+site.
+
+And in the extreme, all of the
+zwitterions have been capped
+
+by protons.
+
+So over here we have complete
+protonation, and that's what
+
+we're showing in this graph
+here, which is just basically
+
+the one that's up on the
+screen, but I'm using
+
+different-- see, this
+is taken from one
+
+of the biology readings.
+
+They say equivalence
+of hydroxyl.
+
+There's no hydroxyl here.
+
+I don't know how these--
+
+you know, the language of some
+of these branches of
+
+science puzzle me.
+
+That's equivalence
+of hydroxyl, but
+
+we don't have hydroxyl!
+
+It's all about protons.
+
+So here it is, in terms of the
+equivalence of H plus.
+
+So here's the neutral
+zwitterion.
+
+That's this thing here.
+
+And this H, if it falls off, it
+can then become the neutral
+
+zwitterion.
+
+And then what happens is, as
+we go to very, very low pH,
+
+what happens is that
+the zwitterion
+
+starts attaching protons.
+
+So this is a neutral zwitterion
+to which we've
+
+attached the H.
+
+So it's much--
+
+to me this is transparent.
+
+What this reads--
+
+I don't know.
+
+Equivalence of OH?
+
+There's no OH.
+
+That's a way of saying it's
+fully protonated.
+
+BUt to me that's sort
+of a backwards way.
+
+Don't tell me what it isn't.
+
+Tell me what it is.
+
+So this is fully protonated
+over here.
+
+And as the pH rises, the
+zwitterion feels less
+
+compelled to gobble up the
+protons, so it sheds protons.
+
+And finally the pH gets to a
+point that's high enough that
+
+the zwitterion plays no role,
+and it exists as the neutral
+
+zwitterion.
+
+That's the isoelectric point.
+
+We have a 100% concentration
+of zwitterion.
+
+Then we go to the
+other extreme.
+
+The other extreme is
+the high pH regime,
+
+where it's proton deficient.
+
+And so zwitterion
+responds by--
+
+what?
+
+Throwing out hydroxyls?
+
+No!
+
+In spite of what's written here,
+there are no hydroxyls.
+
+What zwitterion does, is it
+tries to shed protons to
+
+compensate for the proton
+deficiency.
+
+And so some of the HAs become
+just A minus, because the H's
+
+are being liberated.
+
+And over here at the extreme,
+all of the zwitterion has lost
+
+its H here.
+
+And so now you have something
+that's net negative.
+
+Over here you have something
+that's net positive.
+
+In the center it's
+net neutral.
+
+So this is the high pH regime,
+low pH regime, and this is the
+
+Henderson-Hasselbalch equation,
+which answers the
+
+question, what is the ratio of
+neutral zwitterion to either
+
+the deprotonated form or
+the protonated form as
+
+a function of pH?
+
+You tell me the pH, and I'll
+tell you what the ratio is.
+
+Last thing that's really cool
+about this, and shows you the
+
+power of this mechanism of
+attachment or detachment, is
+
+as follows.
+
+Look at here.
+
+This is not exactly to scale,
+but it's reasonable.
+
+You see the pK?
+
+This is pK1.
+
+This is for the protonating
+reaction.
+
+So over here I have neutral
+zwitterion, over here I have
+
+no neutral zwitterion, all
+the zwitterions are fully
+
+protonated.
+
+And in between, I've got--
+
+this is supposed to be sort
+of halfway across here.
+
+So this is 50-50.
+
+But look at what happens.
+
+For very, very large changes
+in ratio of zwitterion to
+
+protonated zwitterion, the pH
+doesn't change that much.
+
+The pH changes a lot here, and
+it changes a lot here.
+
+But over a vast expanse of
+protonation or deprotonation,
+
+the pH kind of hovers
+around pK1.
+
+So the zwitterion is really
+doing its job.
+
+It's trying to hold that
+solution from shifting pH
+
+dramatically.
+
+We say that zwitterion, by doing
+so, acts as a buffer.
+
+A buffer holds pH
+near constant.
+
+And the near constant value
+it's going to hold
+
+it to is its pK.
+
+So in the acidic regime, in the
+very low pH regime, over a
+
+broad range of protonation
+deprotonation, it's going to
+
+be roughly a pK1.
+
+And the same thing happens
+over here.
+
+You see?
+
+Over a broad range of A minus
+to HA, the pH kind of holds
+
+around pK2.
+
+And then finally, over here, the
+system gives up and then
+
+it shoots up to the
+100% deprotonated.
+
+So that's the story there, and
+you see the isoelectric point
+
+in the middle.
+
+Now, so far all we've done is
+we've said what happens when
+
+we have a simple amino acid that
+has just the one proton
+
+attachment point on the
+carboxylic acid
+
+and the amino acid.
+
+But it can get more
+complicated.
+
+And there is an example in the
+homework that you might want
+
+to look at before
+the final exam.
+
+And that's the case where the R
+group itself has the ability
+
+to protonate or deprotonate.
+
+Suppose this R group had
+a COOH ending here.
+
+Can you see that it could
+also participate?
+
+And so then the isoelectric
+point isn't simply going to be
+
+the average of the
+pK1 and the pK2.
+
+Because now there's a pK for
+this thing, as well.
+
+So this is the example
+of the tritratable--
+
+that's the term they use.
+
+If I could just spell it, I
+could convey the information.
+
+Titratable R group.
+
+That's what they're
+talking about.
+
+Otherwise, if the R group is a
+
+neutral, it's just a spectator.
+
+Doesn't doesn't participate
+any more than this.
+
+See, here's a hydrogen.
+
+Look at this one, people.
+
+You see this hydrogen?
+
+It doesn't participate at all.
+
+Please don't tell me at some
+point that the zwitterion
+
+says, I'm out of hydrogens
+from here, I'm out of
+
+hydrogens for here, I'm going
+to start shedding this.
+
+This is a really strong
+covalent bond.
+
+It's not going anywhere.
+
+If you want titration, you've
+got to put the titratable R
+
+group up here.
+
+OK?
+
+This is so cool.
+
+So now, I'm going to show you
+an application of this stuff
+
+that's used in biology.
+
+And I know, because one year
+they gave a crash course for
+
+engineering faculty in biology,
+and we did we
+
+actually did this experiment
+in the lab.
+
+So I'm going to show you how
+you can use the fact that
+
+zwitterion changes in response
+to its environment in the
+
+laboratory.
+
+So what we're going to
+do is I'm going to
+
+make a column here.
+
+This is a column, and it's an
+aqueous solution, a column of
+
+varying pH.
+
+So it starts at the top, and
+just for argument's sake, I'm
+
+going to put high pH here at
+the top, and low pH here.
+
+So it's an aqueous solution.
+
+You can say, wait a minute.
+
+He just taught us fixed laws.
+
+This is proton deficient
+this is proton rich.
+
+Aren't the protons going to go
+north and the hydroxyls are
+
+going to go south?
+
+Yes.
+
+So what are we going to do?
+
+We are going to slow
+down diffusion.
+
+We're going to change the
+diffusion coefficient, and
+
+what we're going to do is, we're
+going to fill this with
+
+a solid suspension and
+turn it into a gel.
+
+So what's the function
+of the gel?
+
+Don't say that Professor
+Sadoway said
+
+that he stopped diffusion.
+
+Diffusion goes on, but it
+goes on at a slow rate.
+
+So over the time duration of
+the experiment, for all
+
+intents and purposes, the pH
+changes imperceptibly in
+
+comparison to everything
+else that's going on.
+
+It's all about time scales.
+
+You realize, we are all aging.
+
+We've been aging ever since
+I started this lecture.
+
+But for all intents and
+purposes, we can view
+
+ourselves as being the
+age we were when we
+
+walked in the room.
+
+And even over the semester,
+chances are.
+
+All right?
+
+Now if we meet back here in ten
+years' time, expect to see
+
+some changes.
+
+Right?
+
+But over the time scale of the
+experiment, we can say we take
+
+diffusion out.
+
+So that means the high pH is
+here, the low pH is here.
+
+Now what I want to do, what is
+it I'm trying to accomplish?
+
+I want to separate an
+amino acid mix.
+
+And just for grins and chuckles,
+we're going to have
+
+A1, A2, and A3.
+
+Three different amino acids.
+
+Which means just three of
+these things, but three
+
+different R values.
+
+I'm going to pour
+them the top.
+
+I've got this aqueous
+solution, got
+
+all three amino acids.
+
+So what happens when
+they fall in here?
+
+When they fall in here, they
+start diffusing, too.
+
+Right?
+
+Well, first of all, they hit a
+very, very high pH regime.
+
+So what what's the immediate
+response to those amino acids
+
+in a high pH regime?
+
+They're all amino acids.
+
+They're all those rescuers.
+
+And they say, Hi, pH.
+
+It's proton deficient?
+
+I can help!
+
+And they all start
+shedding protons.
+
+And so within moments,
+all of those amino
+
+acids have been totally--
+
+as they say in California--
+
+totally deprotonated.
+
+And here it is.
+
+So they're all sitting there,
+in net negative.
+
+They're all sitting there in net
+negative, right up here.
+
+But I just told you, I shut off
+diffusion, slowed it down.
+
+But I want to get out of
+here before dinner.
+
+So I don't want the protons
+moving, but I do want the
+
+amino acids to get moving.
+
+So what do I do?
+
+I put on my elecrochemist's
+hat, because as you know,
+
+electrochemistry is the highest
+form of chemistry, the
+
+most noble form of chemistry.
+
+It happens to be the
+area that work in.
+
+And so what we do is we
+electrify the ends.
+
+And we'll polarize
+the top negative
+
+and the bottom positive.
+
+Well, I just poured in a bunch
+of amino acids that became net
+
+negative, and now they're next
+to the negative electrode.
+
+So what happens?
+
+Now they're in an electric
+field, and they start moving.
+
+They start moving in the
+electric field, and they're
+
+all net negative.
+
+But what happens, is they
+move down here.
+
+So this is medium pH.
+
+Can you see?
+
+I've established the
+pH gradient.
+
+And as they move from high pH
+to medium pH, the proton
+
+deficiency isn't as intense.
+
+So they're responding to
+their environments.
+
+They're saying, you know, back
+there I had to get rid of all
+
+my protons.
+
+But now, it doesn't feel so
+proton deficient, so I can
+
+start taking protons on.
+
+They respond to their
+environments.
+
+So here, they're
+all A minuses.
+
+And if they ever get down here,
+
+they'll all be HAA pluses.
+
+And so what are they in here?
+
+They're sort of on their
+way to becoming HAs.
+
+Because the pH is continuously
+variable.
+
+So as they become less negative,
+what happens to the
+
+driving force by the
+negative electrode?
+
+It's weaker.
+
+So the protons were, first
+of all, they're anions.
+
+They're net anions.
+
+They go, whoa!
+
+Negative!
+
+And they start moving, and then
+they get less and less
+
+negative, and the field gets
+weaker and weaker.
+
+And eventually, they take on
+enough protons that they
+
+become neutral zwitterions.
+
+And what is the response
+of a neutral ion
+
+in an electric field?
+
+Nothing.
+
+It stops.
+
+And so let's say, this happens
+to be the isoelectric point of
+
+amino acid number 1.
+
+So it gets to the isoelectric
+point, and it
+
+doesn't move anymore.
+
+And number 2 and number 3 keep
+going, and this might be the
+
+PI of have number 2, and this
+might be the PI of number 3.
+
+And now I want only amino acid
+number 1 from this mix, I can
+
+now go in-- this is a gel.
+
+It's put down on the
+glass plate, or you
+
+can put it in a column.
+
+Now you where they are.
+
+You come in--
+
+because you've got a pH meter,
+you know where this is.
+
+You know the PI.
+
+Bingo.
+
+That's where they are.
+
+And if I want number 2,
+they're right here.
+
+And number 3, they're
+right here.
+
+So this process is called
+gel electrophoresis.
+
+This is the term.
+
+It tells you nothing
+about the process.
+
+It tells you how
+to conduct it.
+
+You make a gel, and you
+polarize the ends.
+
+Electrophoresis is simply
+particles moving in an
+
+electric field.
+
+You can paint a car this way.
+
+Obviously the car, when the
+car is made of metal.
+
+If you have a fiberglass body,
+you can't use electrophoresis.
+
+The car is made of metal, you
+polarize the car, and the
+
+paint, the paint has
+got dipoles.
+
+And so the paint sticks
+to the car.
+
+And then you lift it out, let it
+drip, and then just get the
+
+right amount of paint
+proportional to the charge you
+
+put on the car by
+electrophoresis.
+
+What's that got to
+do with this?
+
+It doesn't talk about
+the focusing here.
+
+So the mechanism here is called
+isoelectric focusing.
+
+So isoelectric focusing is the
+principle by which we can
+
+separate the amino acids
+from one another.
+
+The gel electrophoresis column
+is a device in which we do so.
+
+And let's be modern, so we'll
+give it a three-letter
+
+initialization.
+
+IEF, isoelectric focusing.
+
+Isn't that cool?
+
+Yeah.
+
+I thought so.
+
+Anyway.
+
+OK.
+
+Everybody's still zoned out
+from turkey or something.
+
+No response.
+
+This is brilliant.
+
+It's beautiful, and it
+integrates all of this
+
+material, and deadpan.
+
+All of this withholding love.
+
+You've been with your families,
+I can tell.
+
+All of the old family
+dynamic, see?
+
+It's here.
+
+You brought it with you.
+
+Leave it!
+
+Leave it at the airport.
+
+OK.
+
+Now.
+
+So we've been talking about
+the amino acids.
+
+We said we're going
+to use these as
+
+building blocks for proteins.
+
+Let's build some proteins now.
+
+So protein synthesis.
+
+So we're going to make
+macromolecule.
+
+What are we making?
+
+We're making a macromolecule.
+
+Protein is a macromolecule.
+
+You notice I didn't say polymer,
+because a polymer
+
+going to have--
+
+every element along
+the backbone is
+
+going to be the same.
+
+But I'm telling you that we can
+change the choice of R at
+
+every station.
+
+So it's a macromolecule,
+but it's not
+
+necessarily a polymer.
+
+But we do know, if we're going
+back a macromolecule, we've
+
+got two choices.
+
+Addition or condensation
+polymerization.
+
+So I look at the basic
+structure--
+
+let's put it back the way we
+found it, so that people don't
+
+leave thinking that we have
+two carboxylic acids.
+
+So the most the most general
+form doesn't have a titratable
+
+R group, but it does
+have an R up here.
+
+So I want to take one of these
+and link it to another one.
+
+So how do I do it?
+
+Well, right off the
+bat, addition
+
+polymerization is no good.
+
+Because even if I had enough
+energy in my body to form a
+
+radical, what could
+I do with this?
+
+There are no double
+bonds here!
+
+There are no double
+bonds here.
+
+I can't break a double bond and
+then allow this to bond to
+
+its neighbor.
+
+So axiomatically, I have
+to go with condensation
+
+polymerization.
+
+OK?
+
+Macromolecule formation by
+condensation reaction.
+
+I don't even want to say the
+word polymerization.
+
+By condensation reaction.
+
+OK.
+
+So let's look at an
+example here.
+
+An example will be this.
+
+I'm going to write,
+here is the COO R.
+
+So I'm going to show this,
+and then over here--
+
+well, maybe I'd better show
+some fine structure.
+
+I'll give you a little
+more fine structure.
+
+So we'll put the double
+bond up here, O minus.
+
+And then over here, I'm
+going to put H3N plus.
+
+So here's the neutral
+zwitterion, agreed?
+
+And I've got some kind of
+an R group up here.
+
+And I'm going to put next to
+it a second one of these.
+
+So here's the alpha carbon,
+and we'll go COO.
+
+And then over here, I'm going
+to unpack this nitrogen.
+
+It's got one, two,
+three hydrogens,
+
+and it's net positive.
+
+So there's the neutral
+zwitterion.
+
+So now by condensation reaction,
+what we'll do is
+
+we'll take this oxygen off of
+the left amino acid, and we'll
+
+take two of the hydrogens off
+of this amino acid, and we
+
+will eject a water molecule.
+
+We'll eject the water
+molecule.
+
+And that's safe.
+
+It's compatible with the body.
+
+And now what's left?
+
+This carbon is naked.
+
+One, two, three.
+
+There's a bond sitting here that
+used to go to the oxygen.
+
+And this nitrogen, it's
+sitting naked too.
+
+And so now we can do, is we can
+make a link between this
+
+carbon and this nitrogen.
+
+And this bond is called
+the peptide bond.
+
+This is the peptide bond.
+
+OK?
+
+And we see that the atomic mass
+of the dipeptide is less
+
+than the sum of the masses of
+the individual components,
+
+because we've lost the water.
+
+So I think I've got
+some slides here.
+
+What's here?
+
+Oh.
+
+This is just the various,
+pK1 and pK2.
+
+And then this side chain here,
+this is the value of the pK
+
+should you have a titratable
+R group.
+
+That's why there's the
+third column here.
+
+So when you see this--
+
+you see, they're all roughly
+around two for the highly
+
+acidic regime, and all around
+high nines, low tens for the
+
+alkaline regime.
+
+Roughly the same.
+
+All right.
+
+Now connotation polymerization.
+
+This is the formation
+of nylons.
+
+You see how you bond this
+mer to the adjacent mer?
+
+Look at this.
+
+The nitrogen, that hydrogen
+is sticking up.
+
+There's the nitrogen bonding
+to the carbon.
+
+There's a long pair, and
+nitrogen-carbon.
+
+Amide bond, peptide
+bond, same thing.
+
+The same bond in the backbone
+of nylon is the same bond in
+
+the backbone of protein.
+
+Only, the biologists call this
+the peptide bond, the polymer
+
+scientists call this
+the amide bond.
+
+Think about that when, you know,
+the holidays are coming,
+
+you think you're really special,
+and you know, the
+
+proteins in your body are really
+bound the same way that
+
+nylon is, you know?
+
+All right.
+
+So now let's consider--
+
+and here's some examples.
+
+Here's a peptide.
+
+So it's a long chain here.
+
+So it starts, here's the
+amino group, H3N.
+
+It's got glycene, and then
+leucine, and valine,
+
+glutamine, et cetera.
+
+So there it goes, all the way
+around, around, around,
+
+around, around.
+
+And here's another one.
+
+There's the amino group, and
+then, boom, boom, boom.
+
+What's happening here?
+
+All of these click stops
+along here are this.
+
+H2NCHCOOH.
+
+And the only thing that's
+changing is the R group.
+
+If this were nylon, it
+would be the same
+
+thing, all the way down.
+
+That's how this differentiates
+itself.
+
+All polymers are
+macromolecules.
+
+All macromolecules
+are not polymers.
+
+These are not polymers, but
+they are macromolecules.
+
+And what else do you see here?
+
+Look at this.
+
+Cysteine happens to have
+a double bond.
+
+A residual double bond
+in its R group.
+
+Well, where you see a double
+bond, you go, I can break the
+
+double bond, and then I can
+make a another bond.
+
+And that's what happens.
+
+So we break the double bond with
+the sulfur, and now we
+
+make a disulfide linkage.
+
+What do you think the mechanical
+properties of this
+
+protein are?
+
+Mechanically, what do you
+think this one's like?
+
+It's rubbery.
+
+This is an elastomer, because
+you can move the top chain
+
+vis-a-vis the bottom chain until
+these disulfide linkages
+
+are flattened.
+
+And then if you let it
+go, it springs back.
+
+It's the mechanical properties
+of, in this
+
+case, this is insulin.
+
+Now I want to give you a sense
+of the variety here.
+
+How much information--
+
+because ultimately, it's all
+about reproduction, right?
+
+That's the number one function
+of any living
+
+organism, is to reproduce.
+
+That's what makes it life.
+
+Right?
+
+So it needs an instruction
+set.
+
+And the instruction set doesn't
+come in the box.
+
+It comes inside the organism.
+
+And this is the language.
+
+This is all we have
+to work with.
+
+So here's a simple example.
+
+This is, how many combinations
+do you have of dipeptides?
+
+So when you start with
+two amino acids.
+
+So this is phenylalanine
+and aspartic acid.
+
+So if I told you, you have
+A and B, and how many AB
+
+mixtures can you come up with?
+
+You'd say, well, you've
+got AA, you've got BB,
+
+and you've got AB.
+
+You know, it's sort of
+like calculus, right?
+
+If you square A plus B,
+you'd get A squared,
+
+plus 2AB, plus B squared.
+
+But because of chirality, AB
+is distinguishable from BA.
+
+This is cool.
+
+This is, again, math
+serving us, instead
+
+of we serving math.
+
+All right?
+
+So A plus B squared
+is A squared
+
+plus 2AB plus B squared.
+
+But no, no, not in biology.
+
+Because AB is chiral,
+and therefore
+
+distinguishable from BA.
+
+Now you understand chirality.
+
+So here's--
+
+you get four.
+
+Because see, in this case,
+phenylalanine peptide to
+
+aspartic acid is distinguishable
+from the one
+
+on the right.
+
+They're distinguishable.
+
+They're different.
+
+OK, so that let's
+roll with that.
+
+Let's say, so if I start with
+two amino acids, and I want to
+
+make dipeptides, well,
+that's trivial.
+
+That's 2 squared, is 4.
+
+So I got four different
+dipeptides, starting with two
+
+amino acids.
+
+Now, suppose I said, how many
+different dipeptides can we
+
+make, period?
+
+Well, I know I've got a library
+of 20 amino acids that
+
+are found in proteins.
+
+So that means the number of
+dipeptides would be then 20
+
+squared, which is 400.
+
+But that's hardly
+a macromolecule.
+
+So let's get into the
+macromolecule business.
+
+So suppose I took a library of
+twenty amino acids, and I
+
+said, how many kilopeptides
+could I make?
+
+What's a kilopeptide?
+
+A kilopeptide is something
+that's got 1000
+
+peptide bonds in it.
+
+So that's going to be 20 to the
+power of 1000, which is 10
+
+to the power of 1300.
+
+And this is small.
+
+n equals 1000.
+
+I'm not stretching the point
+by pulling something
+
+exceptional out.
+
+A polymer, if it were polymer,
+1000 units long, you'd say,
+
+that's sort of fair to
+middling length.
+
+I'm not pulling out the longest
+polymer ever known.
+
+I didn't go to the Guinness
+Book of Records for this.
+
+This is just plain vanilla
+mer length.
+
+So look.
+
+How much information
+can be contained?
+
+That's in a single element.
+
+OK.
+
+So later on we're going to
+return to this, and appreciate
+
+how we can get to such
+information density.
+
+And this I think I alluded
+to on Wednesday.
+
+These are the three-letter
+initializations, and I'll post
+
+this at the website.
+
+So these are the airports that
+correspond to the three-letter
+
+initialization.
+
+Then I showed you the one-letter
+abbreviation for
+
+each of the peptides.
+
+You know, it's kind of strange,
+because the amino
+
+acids are what they are.
+
+And most airports, they're
+not like the main ones.
+
+It's not like Boston
+or New York.
+
+It's weird places like Australia
+and Texas and stuff.
+
+You know?
+
+So--
+
+hey, you've got to have
+a sense of humor!
+
+Come on.
+
+All right.
+
+And there's glutamic acid.
+
+There's no airport that has
+GLU as its three-letter--
+
+OK.
+
+So here we are.
+
+So now we want to do
+is want to talk
+
+about protein structure.
+
+And so we're going to look at
+this as material scientists.
+
+We're not going to look at it
+the way chemists, capital
+
+C-chemists, do.
+
+And I think by looking at it
+from a structure perspective,
+
+you get some insights
+into what we can
+
+do with these things.
+
+So protein structure.
+
+And I'm going to use the
+terminology that the
+
+biologists use.
+
+So first of all, they have
+something they call the
+
+primary structure
+of the protein.
+
+And it speaks to composition,
+the composition.
+
+Well, what's the composition?
+
+We know that every protein is
+made of amino acids, and every
+
+amino acid is virtually
+identical,
+
+except for the R group.
+
+So when you say the composition,
+you're really
+
+saying, what is the
+R sequence?
+
+It's the amino acid sequence
+down the backbone.
+
+Because you've polymerized
+this thing, or
+
+macromolecularized it.
+
+Amino acid sequence, which
+along the backbone.
+
+Which is really the R groups.
+
+The sequence of R groups,
+which is going to be the
+
+sequence, OK?
+
+All right.
+
+So here you can see.
+
+There's an amino
+acid sequence.
+
+Number two is the--
+
+these are really--
+
+you know, like the polymer
+people had conformality.
+
+You know, they had nice,
+powerful words.
+
+The first order is the primary,
+and then the second
+
+one is the secondary.
+
+I'm trying to make fun of the
+biologists, and you're sitting
+
+there, you know, with that
+same Thanksgiving
+
+dinner table stoicism.
+
+OK.
+
+So what's the secondary?
+
+The secondary structure of
+proteins speaks to packing.
+
+And what's the gambit here?
+
+Why do they pack in
+different ways?
+
+Well, just as we saw,
+you can have a long
+
+chain, straight chain.
+
+Sometimes things full
+back on themselves.
+
+It's still a straight chain, but
+there's a curve, a bend in
+
+it, and so on.
+
+What proteins are going to do in
+order to pack, is to try to
+
+maximize hydrogen bonding.
+
+And this is not even
+between proteins.
+
+This is a protein forming
+on itself.
+
+And you could argue, why do you
+maximize hydrogen bonding?
+
+Because when you make more bonds
+per unit volume, you
+
+decrease the energy
+of a system.
+
+You've been taught that
+over and over again.
+
+So these are long chain
+molecules, but they still can
+
+loop back on one another.
+
+And if you've got a choice of
+forming a dipole-dipole
+
+interaction, a induced
+dipole-induced dipole
+
+interaction, or a hydrogen bond,
+which is going to give
+
+you the most decrease
+per unit bond?
+
+It's hydrogen.
+
+So if you can form hydrogen
+bonds, that gives you the most
+
+impact per bond.
+
+If you don't have hydrogen
+bonding capability, then you
+
+go for dipole-dipole.
+
+And if you don't have
+dipole-dipole, then it's just
+
+the weak van der Waals, or
+the London dispersion.
+
+So that's why this thing goes
+for hydrogen bonding.
+
+Because it wants to.
+
+It wants to decrease
+the energy.
+
+So I have to show you
+a few cartoons here.
+
+All right.
+
+So here's a sketch taken from
+one of the readings.
+
+So there's alpha carbon.
+
+This is the carboxylic
+acid, right here.
+
+And this is the peptide bond
+between one carbon and a
+
+nitrogen in an adjacent unit.
+
+All right?
+
+So there's the peptide bond.
+
+The interesting thing is that
+even though this is sp3
+
+hybridized, data show that all
+six atoms lie in a plane.
+
+So what happened last
+time when we came
+
+up with this conundrum?
+
+sp3 hybridized, but the data
+showed it all lies in a plane.
+
+That was benzene, remember?
+
+And how do we skate with
+the puck on benzene?
+
+Resonance.
+
+We said it resonates between two
+structures, and sometimes
+
+the nitrogen lies
+in the plane.
+
+Sometimes the alpha carbon
+lies in the plane.
+
+But thanks to resonance,
+all six of these
+
+can lie in the plane.
+
+OK.
+
+So now how do we get to
+hydrogen bonding?
+
+So there's the resonance.
+
+All right.
+
+Good.
+
+So you see, this is free
+to rotate, right?
+
+Once we accept that these six
+atoms line in a plane, and
+
+these six atoms line in a plane,
+and 109 degree angle is
+
+fixed, but there's that degree
+of rotation, which is what
+
+gave us the original C17H36
+folding back on itself, only
+
+we're going to fold back on
+ourselves in groups of six.
+
+So we've got a deck
+of cards here.
+
+I've got six here, six
+here, six here.
+
+So what am I going to do?
+
+I'm going to try to make this
+blue plane lie relative to the
+
+yellow plane in such a way as to
+maximize hydrogen bonding.
+
+Speaking of energy deficit,
+we need battery.
+
+All right, here we go.
+
+So now we're going
+to maximize.
+
+Look.
+
+You see, if I rotate this blue
+plane in just the right way, I
+
+can set up to have a hydrogen
+bond form between this
+
+hydrogen and this oxygen, and on
+the orange plane, an oxygen
+
+and a hydrogen.
+
+So now it becomes a matter
+of figuring out,
+
+what are these angles?
+
+You see, there's a phi
+and a psi here.
+
+What are the angles phi and
+psi to give the maximum
+
+hydrogen bonding between these
+two six-packs of atoms?
+
+And from that, you get
+secondary structure.
+
+It's all about maximizing
+hydrogen bonding.
+
+After that, if you understand
+what I just
+
+said, the rest is trivia.
+
+So here's what happens.
+
+Here's one structure.
+
+And this was first discovered,
+if you like, revealed, by
+
+Linus Pauling, 1951.
+
+Linus Pauling and Corey, 1951,
+came with the realization that
+
+if the protein spirals in a
+helix, it will line up the
+
+maximum number of
+hydrogen-oxygen hydrogen
+
+bonding opportunities, as
+opposed to going straight.
+
+So it doesn't go perfectly
+straight, it coils.
+
+And this is two different
+cartoons trying to show.
+
+So you can see peptide bonds,
+and then every so often you
+
+get a hydrogen-oxyge bond.
+
+Because it spins around, and
+the idea is, as the helix
+
+forms, you can think of it as--
+have you ever gone up a
+
+spiral staircase?
+
+And you think of each subsequent
+turn of the spiral
+
+as a new gallery.
+
+And what you've got is hydrogen
+
+bonds between the galleries.
+
+So you're going up, and there's
+a hydrogen bond here,
+
+and you keep turning, and
+there's a hydrogen bond here,
+
+and there's a hydrogen
+bond here.
+
+That's the way to get maximum
+hydrogen bonding.
+
+There it is.
+
+There's another example.
+
+Maybe this is a nicer one.
+
+And there's 3.6 residues
+per turn.
+
+That means, per turn is 3.6 R
+groups, which, it's called
+
+residues because historically,
+when people did the chemical
+
+analysis, the residue contained
+the substituent.
+
+That's how they determined
+what the identity of the
+
+protein is.
+
+They can't just look at it.
+
+And you can't use
+spectroscopy.
+
+Maybe now you can, but
+in the old days--
+
+I mean, these are all, look.
+
+Low mass.
+
+Hydrogen, oxygen, nitrogen.
+
+They're not distinguishable.
+
+They're all low-Z elements.
+
+So they had to do wet chemistry,
+and they would
+
+actually peel off the
+R groups, which
+
+were called the residuals.
+
+And so 3.6 residuals
+per turn give you
+
+this alpha helix structure.
+
+there's a second structure
+that works.
+
+The second structure is
+between two chains.
+
+So in this case, instead of
+going coiling by yourself, and
+
+forming the galleries, what you
+do is you take two chains
+
+side by side, and you pace them
+so that you get maximum
+
+amount of hydrogen bonding.
+
+I showed you this with nylon,
+how two strands
+
+of nylon bond together.
+
+They can form hydrogen bonds.
+
+Same thing here.
+
+And now, since these are jerking
+in a motion of six in
+
+a plane, six in a plane, six
+in a plane, six in a plane,
+
+what you end up with
+is this pleating.
+
+It's hard to see here.
+
+Maybe if your eye can follow
+along the top here.
+
+Here's sort of a cream-colored
+one, orangey-cream, and it's
+
+moving sort of southwest to
+northeast. And here's one
+
+that's sort of a grayish, and
+it's moving from northwest to
+
+southeast. And then
+up, and then down.
+
+And zig and then zag.
+
+And this is called the
+pleated sheet.
+
+This is the beta form.
+
+The alpha form is the helix,
+and the beta form is the
+
+pleated sheet.
+
+Same thing up here in a
+different kind of model.
+
+Which I look at that and I go,
+I don't get any information
+
+from this thing at all.
+
+But they put it in the books.
+
+Who cares.
+
+This is where you learn
+something, right here.
+
+Once you appreciate that those
+six atoms have to be in a
+
+plane, and how to maximize
+hydrogen bonding.
+
+So let's put that down.
+
+This is all Linus Pauling.
+
+So secondary.
+
+So you know that six
+atoms in plane,
+
+which leads to resonance.
+
+And now, from there, you just
+needs the genius of Linus
+
+Pauling, and then you conclude
+that to maximize hydrogen
+
+bonding, you form the alpha
+helix with hydrogen bonding
+
+between galleries.
+
+All right?
+
+And then the second one is the
+pleated sheet, or people just
+
+call it the sheet.
+
+But to me, the sheet
+means nothing!
+
+It's the fact that
+it's pleated.
+
+So I'm going to ignore
+what the books say.
+
+Pleated, pleated sheet.
+
+OK.
+
+So this is hydrogen
+bonds between
+
+galleries of the same protein.
+
+Whereas this is hydrogen
+bonding between
+
+macromolecules.
+
+So if they're both pleated,
+it's going to work.
+
+Or of course, that could be
+folding back on itself.
+
+Remember how I showed you the
+first day the chain, how the
+
+chain wanted to zig-zag,
+to crystallize?
+
+Do you think protein
+is liable to fold?
+
+You've heard of protein
+folding?
+
+Why does it fold?
+
+Because it wants to maximize
+hydrogen bonding!
+
+And when it folds, it's not
+going to maximize hydrogen
+
+bonding unless it is in
+the beta pleated sheet
+
+arrangement.
+
+Otherwise, what's the
+point of folding?
+
+Because you can't
+make the link.
+
+Because I'm the oxygen, the
+hydrogen's way over there.
+
+If that hydrogen were
+right over here, we
+
+could form the bond.
+
+And then the third
+one is random.
+
+So let's take a look.
+
+I think I've got some
+images here.
+
+Oh, here's another one,
+showing the-- yeah.
+
+I'm trying to, I'm really
+working hard.
+
+Here's six, here's six,
+here's six, and
+
+there's the common carbon.
+
+OK?
+
+And now you can see
+the hydrogen
+
+bonds forming between.
+
+So this could be one protein,
+this could be another protein,
+
+or this could be the same
+protein that's folding back on
+
+itself in a
+pseudo-crystallization ploy.
+
+Yeah.
+
+All right.
+
+So if you look in the biology
+literature, you'll see
+
+drawings like this.
+
+You've seen these, huh?
+
+You look at them and go, what
+are they talking about?
+
+Now you know!
+
+This is the secondary
+structure.
+
+Let's start over here
+at the amino end.
+
+So you're moving along, and it's
+just sort of random, and
+
+now, all of a sudden, look.
+
+Round and round and round.
+
+What are you looking at?
+
+For this run of length, it's
+in the alpha helix form!
+
+And then it kind of goes random
+for a little bit, and
+
+then it goes green.
+
+And this green area
+is pleated sheet.
+
+So if the pleated sheet goes
+this way, and then it goes
+
+random, and then the pleated
+sheet goes this way, what's
+
+going to happen? there's going
+to be hydrogen bonding here,
+
+hydrogen bonding here, hydrogen
+bonding here.
+
+And you know, how is it that
+this thing decides, oh,
+
+somewhere around
+here, I think.
+
+I think I'll just go into an
+alpha helix arrangement.
+
+Why is it alpha helix here,
+and not alpha helix here?
+
+Because of the instant
+choice of R groups!
+
+The instant choice of R groups
+will dictate whether it can
+
+turn around.
+
+Because if you've got glycene
+with its dinky little hydrogen
+
+on one side, you're compact
+and you can move around.
+
+But some of these other pendant
+groups are big, and
+
+you can't just shove them
+one into the other.
+
+They'll repel.
+
+They won't fit.
+
+So this dictates--
+
+so in essence, the secondary
+structure is set, the table is
+
+set by the primary structure,
+isn't it?
+
+This is so cool.
+
+Then there's the tertiary
+structure.
+
+Because random isn't, as they
+say in California, it's not
+
+totally random.
+
+There's some order to it.
+
+So let's look at the
+order that comes.
+
+See this?
+
+Look over here.
+
+You see up here?
+
+This is supposed to
+be random coil.
+
+But look at it.
+
+It's kind of dentate
+there, isn't it.
+
+See, it's sort of tooth-like.
+
+Do you think that the artist
+just did that?
+
+Why is it like that?
+
+Because of the molecular
+forces!
+
+So let's think on it.
+
+Oh!
+
+This is a little piece
+from Guys and Dolls.
+
+1951.
+
+The same your Pauling
+enunciated this.
+
+I bet you think that when
+people talk about the
+
+chemistry between folks, that
+it's a '60s phenomenon.
+
+You know, the hippies,
+drug culture.
+
+No.
+
+It goes way back.
+
+Goes to the '50s.
+
+Listen to this.
+
+This Sky Masterson, and he's
+going to tell Sarah-- she's
+
+the one that's the,
+she plays the--
+
+what do you call it--
+
+she works at the Salvation
+Army mission.
+
+And he's a gambler, which in
+those days was really, you
+
+know, like low-life.
+
+And he's flirting with her,
+and she, of course, has
+
+nothing to do with him,
+and eventually, they
+
+fall in love, of course.
+
+But anyway, so she's told him
+how she's going to meet the
+
+man of her life.
+
+And she's very linear.
+
+He's got all of these
+characteristics, and
+
+so on and so forth.
+
+Real linear.
+
+And this guy's a gambler, so
+he's going to tell her how
+
+he's going to find the
+love of his life.
+
+[BEGIN FILM PLAYBACK]
+
+Do you want to hear how a
+gambler feels about the big
+
+heart drop?
+
+No!
+
+Well, I'll tell you.
+
+Mine will come as a
+surprise to me.
+
+Mine, I leave to chance
+and chemistry?
+
+Chemistry?
+
+Yeah, chemistry.
+
+Suddenly I'll know when
+my love comes along.
+
+I'll know--
+
+[END FILM PLAYBACK]
+
+So there you have it.
+
+From 1951.
+
+Chemistry, again, chemistry!
+
+Chemistry is the central thing.
+
+OK.
+
+Now let's go forward.
+
+All right.
+
+So now let's figure out why--
+
+and now I want to answer the
+question, why is this forming
+
+a tooth-like structure?
+
+Why?
+
+There's a reason
+for everything.
+
+All right.
+
+So here we are, moving along
+a length of random coils.
+
+So we're in zone three
+here, random.
+
+But it's not completely
+random.
+
+So this is the tertiary
+structure, and it has to do
+
+with interactions between
+the R groups.
+
+So let's look at number
+one, zone one here.
+
+We've got two cysteines,
+and cysteine both
+
+have sulfur in them.
+
+It turns out that the sulfurs
+can form a covalent bond here.
+
+This is between two
+R groups along a
+
+certain length of chain.
+
+And once that covalent bond
+forms, this chain now can't
+
+just go flopping any which
+way, because it's
+
+being held in place.
+
+It's like you put
+a prop there.
+
+Over here, what do we
+have in zone two?
+
+We have one R group that's
+got a hydroxyl.
+
+Another one's got an oxygen.
+
+There's a hydrogen bond forming
+between side groups.
+
+And in order to form that
+hydrogen bond, can you see
+
+that this coil is
+actually bent?
+
+You see, there's a kink here.
+
+This coil should be
+much longer, if it
+
+were straight, distended.
+
+But it's actually compressed
+a little bit in order to
+
+facilitate the formation
+of this hydrogen bond.
+
+Which means now, this coil
+will stay in this
+
+configuration.
+
+And then over here,
+what do we have?
+
+Here we have a substituent group
+that's net positive,
+
+here we have a substituent group
+that's net negative, and
+
+we have an electrostatic
+force.
+
+This is coulombic.
+
+This is plus attracts minus.
+
+And they form.
+
+And over here, this is
+very interesting.
+
+What do we have here?
+
+We have a whole bunch of R
+groups that are all non-polar.
+
+And this thing's sitting
+in an aqueous solution.
+
+And what do you know about
+non-polar groups in water?
+
+They're hydrophobic!
+
+So I've got this one
+hydrophobic group
+
+sticking out over here.
+
+It's just going to
+have to take it.
+
+Because it's bound
+to the backbone.
+
+But I've got another
+one over here, and
+
+the backbone is flexible.
+
+And I've got another
+one over here.
+
+Can you see that if the backbone
+folds around, I can
+
+collect all the hydrophobic
+entities, and present to the
+
+water the hydrophilic opposite
+side of the backbone.
+
+Because if the R group here is
+hydrophobic, look what's on
+
+the other side.
+
+These guys.
+
+So if I can take all of these
+and cluster them, then I sort
+
+of minimize the energy.
+
+Because that there is a
+repulsive energy term, right?
+
+The water doesn't like the
+non-polar R group.
+
+So let's minimize their
+contact, you know?
+
+If you've got two siblings that
+are fighting, you put
+
+them at the other end
+of the table.
+
+You don't sit them next
+to one another.
+
+So here's what you do.
+
+You cluster all of this
+stuff, and that
+
+causes big hairpin turn.
+
+So this is called hydrophobic
+interactions.
+
+And that's the tertiary
+structure.
+
+So you see all of those.
+
+That's great.
+
+OK.
+
+I see we're getting close
+to the witching hour.
+
+So maybe I'll teach you how to
+do your laundry and send you
+
+on your way.
+
+So this interaction I'm just
+showing you right here is the
+
+same thing that's happening
+when you do your laundry.
+
+Now, what's a detergent?
+
+A detergent is this long
+molecule that's got-- you see
+
+this zig-zag here?
+
+That's the aliphatic.
+
+That's the hydrocarbons chain.
+
+And it is hydrophobic.
+
+The soil on your clothing is
+usually some dirt, but it's
+
+covered by some grease
+and oil.
+
+So if you just soak it in water,
+the water can't get at
+
+the grease and oil.
+
+So what you do, is you put these
+molecules in that are
+
+very long, and then they've got
+this COO ending, right?
+
+And now what happens?
+
+This can form hydrogen bonds
+to the water, whereas these
+
+long hydrophobic tails can bond
+to the grease and oil.
+
+And then you put this in the
+washing machine, and what's
+
+the washing machine do?
+
+Mechanically agitate.
+
+So you've got these tails,
+hydrophobic tails, stabbing
+
+the grease and oil, bonded to
+the water, shake the living
+
+daylights out of this, and
+release the grease and oil,
+
+which then will release the
+soil, rinse the whole thing,
+
+and you've got clean clothing.
+
+So it's the bonding here.
+
+What you've got is an
+amphipathic molecule with a
+
+hydrophobic tail and a
+hydrophilic head that allows
+
+you to do your laundry.
+
+All right.
+
+Get out of here.
+
+We'll see you on Wednesday.
\ No newline at end of file
diff --git a/GLFg2UBMAxc.txt b/GLFg2UBMAxc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..422ac9aa3d9e17bead063d473daab487506b6c43
--- /dev/null
+++ b/GLFg2UBMAxc.txt
@@ -0,0 +1,1419 @@
+align:start position:0%
+ 
+hi welcome to recitation my name is
+
+ align:start position:0%
+hi welcome to recitation my name is
+ 
+
+ align:start position:0%
+hi welcome to recitation my name is
+Martina and I'll be a recitation
+
+ align:start position:0%
+Martina and I'll be a recitation
+ 
+
+ align:start position:0%
+Martina and I'll be a recitation
+instructor for some of these linear
+
+ align:start position:0%
+instructor for some of these linear
+ 
+
+ align:start position:0%
+instructor for some of these linear
+algebra videos today's problem is a
+
+ align:start position:0%
+algebra videos today's problem is a
+ 
+
+ align:start position:0%
+algebra videos today's problem is a
+straightforward solved the following
+
+ align:start position:0%
+straightforward solved the following
+ 
+
+ align:start position:0%
+straightforward solved the following
+linear system with four equations and
+
+ align:start position:0%
+linear system with four equations and
+ 
+
+ align:start position:0%
+linear system with four equations and
+four unknowns using the method of
+
+ align:start position:0%
+four unknowns using the method of
+ 
+
+ align:start position:0%
+four unknowns using the method of
+elimination the system is X minus y
+
+ align:start position:0%
+elimination the system is X minus y
+ 
+
+ align:start position:0%
+elimination the system is X minus y
+minus Z plus U equals 0 2 X plus 2 Z
+
+ align:start position:0%
+minus Z plus U equals 0 2 X plus 2 Z
+ 
+
+ align:start position:0%
+minus Z plus U equals 0 2 X plus 2 Z
+equal 8 minus y minus 2 Z equals minus 8
+
+ align:start position:0%
+equal 8 minus y minus 2 Z equals minus 8
+ 
+
+ align:start position:0%
+equal 8 minus y minus 2 Z equals minus 8
+and 3x minus 3y minus 2z plus 4 u equals
+
+ align:start position:0%
+and 3x minus 3y minus 2z plus 4 u equals
+ 
+
+ align:start position:0%
+and 3x minus 3y minus 2z plus 4 u equals
+7 and although you might know different
+
+ align:start position:0%
+7 and although you might know different
+ 
+
+ align:start position:0%
+7 and although you might know different
+ways to solve this system at this point
+
+ align:start position:0%
+ways to solve this system at this point
+ 
+
+ align:start position:0%
+ways to solve this system at this point
+the method of elimination is going to
+
+ align:start position:0%
+the method of elimination is going to
+ 
+
+ align:start position:0%
+the method of elimination is going to
+show up million a million times during
+
+ align:start position:0%
+show up million a million times during
+ 
+
+ align:start position:0%
+show up million a million times during
+these videos so it's really important to
+
+ align:start position:0%
+these videos so it's really important to
+ 
+
+ align:start position:0%
+these videos so it's really important to
+get it right
+
+ align:start position:0%
+get it right
+ 
+
+ align:start position:0%
+get it right
+so I suggest you try solving this system
+
+ align:start position:0%
+so I suggest you try solving this system
+ 
+
+ align:start position:0%
+so I suggest you try solving this system
+now using the method of elimination as
+
+ align:start position:0%
+now using the method of elimination as
+ 
+
+ align:start position:0%
+now using the method of elimination as
+it was described in class I'm going to
+
+ align:start position:0%
+it was described in class I'm going to
+ 
+
+ align:start position:0%
+it was described in class I'm going to
+leave you alone with the problem you
+
+ align:start position:0%
+leave you alone with the problem you
+ 
+
+ align:start position:0%
+leave you alone with the problem you
+should pause the video solve it yourself
+
+ align:start position:0%
+should pause the video solve it yourself
+ 
+
+ align:start position:0%
+should pause the video solve it yourself
+and then come back and compare your
+
+ align:start position:0%
+and then come back and compare your
+ 
+
+ align:start position:0%
+and then come back and compare your
+solution with mine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're back so the method of
+
+ align:start position:0%
+and we're back so the method of
+ 
+
+ align:start position:0%
+and we're back so the method of
+elimination if you remember it from
+
+ align:start position:0%
+elimination if you remember it from
+ 
+
+ align:start position:0%
+elimination if you remember it from
+class consisted of replacing this system
+
+ align:start position:0%
+class consisted of replacing this system
+ 
+
+ align:start position:0%
+class consisted of replacing this system
+with an equivalent system equivalent
+
+ align:start position:0%
+with an equivalent system equivalent
+ 
+
+ align:start position:0%
+with an equivalent system equivalent
+meaning they have the same solution by a
+
+ align:start position:0%
+meaning they have the same solution by a
+ 
+
+ align:start position:0%
+meaning they have the same solution by a
+series of row operations row operations
+
+ align:start position:0%
+series of row operations row operations
+ 
+
+ align:start position:0%
+series of row operations row operations
+are not supposed to change the solution
+
+ align:start position:0%
+are not supposed to change the solution
+ 
+
+ align:start position:0%
+are not supposed to change the solution
+to the system and therefore example
+
+ align:start position:0%
+to the system and therefore example
+ 
+
+ align:start position:0%
+to the system and therefore example
+exchange the order of two equations
+
+ align:start position:0%
+exchange the order of two equations
+ 
+
+ align:start position:0%
+exchange the order of two equations
+multiplied an equation with another zero
+
+ align:start position:0%
+multiplied an equation with another zero
+ 
+
+ align:start position:0%
+multiplied an equation with another zero
+number and add a nonzero multiple of one
+
+ align:start position:0%
+number and add a nonzero multiple of one
+ 
+
+ align:start position:0%
+number and add a nonzero multiple of one
+equation to the other so let's do that
+
+ align:start position:0%
+equation to the other so let's do that
+ 
+
+ align:start position:0%
+equation to the other so let's do that
+as we're going to do this serious for
+
+ align:start position:0%
+as we're going to do this serious for
+ 
+
+ align:start position:0%
+as we're going to do this serious for
+automatic operation we don't really want
+
+ align:start position:0%
+automatic operation we don't really want
+ 
+
+ align:start position:0%
+automatic operation we don't really want
+to copy the names of the variables and
+
+ align:start position:0%
+to copy the names of the variables and
+ 
+
+ align:start position:0%
+to copy the names of the variables and
+the Equality signs every time so we're
+
+ align:start position:0%
+the Equality signs every time so we're
+ 
+
+ align:start position:0%
+the Equality signs every time so we're
+going to keep the important information
+
+ align:start position:0%
+going to keep the important information
+ 
+
+ align:start position:0%
+going to keep the important information
+which are these numbers these
+
+ align:start position:0%
+which are these numbers these
+ 
+
+ align:start position:0%
+which are these numbers these
+coefficients here we're going to keep
+
+ align:start position:0%
+coefficients here we're going to keep
+ 
+
+ align:start position:0%
+coefficients here we're going to keep
+that information in a matrix so let's
+
+ align:start position:0%
+that information in a matrix so let's
+ 
+
+ align:start position:0%
+that information in a matrix so let's
+write a matrix each row is going to
+
+ align:start position:0%
+write a matrix each row is going to
+ 
+
+ align:start position:0%
+write a matrix each row is going to
+correspond to an equation and each
+
+ align:start position:0%
+correspond to an equation and each
+ 
+
+ align:start position:0%
+correspond to an equation and each
+column is going to correspond to an
+
+ align:start position:0%
+column is going to correspond to an
+ 
+
+ align:start position:0%
+column is going to correspond to an
+unknown so the first row is 1 minus 1
+
+ align:start position:0%
+unknown so the first row is 1 minus 1
+ 
+
+ align:start position:0%
+unknown so the first row is 1 minus 1
+minus 1 1 the second row corresponding
+
+ align:start position:0%
+minus 1 1 the second row corresponding
+ 
+
+ align:start position:0%
+minus 1 1 the second row corresponding
+to the second equation is 2 0 to 0 and
+
+ align:start position:0%
+to the second equation is 2 0 to 0 and
+ 
+
+ align:start position:0%
+to the second equation is 2 0 to 0 and
+you want to be very careful to put zeros
+
+ align:start position:0%
+you want to be very careful to put zeros
+ 
+
+ align:start position:0%
+you want to be very careful to put zeros
+on the right spots here the third
+
+ align:start position:0%
+on the right spots here the third
+ 
+
+ align:start position:0%
+on the right spots here the third
+equation is 0 0 minus 1 minus 2 0 and
+
+ align:start position:0%
+equation is 0 0 minus 1 minus 2 0 and
+ 
+
+ align:start position:0%
+equation is 0 0 minus 1 minus 2 0 and
+the fourth equation
+
+ align:start position:0%
+the fourth equation
+ 
+
+ align:start position:0%
+the fourth equation
+fourth row corresponding to the fourth
+
+ align:start position:0%
+fourth row corresponding to the fourth
+ 
+
+ align:start position:0%
+fourth row corresponding to the fourth
+equation is 3 minus 3 minus 2 4 and as
+
+ align:start position:0%
+equation is 3 minus 3 minus 2 4 and as
+ 
+
+ align:start position:0%
+equation is 3 minus 3 minus 2 4 and as
+we care about the right-hand side as
+
+ align:start position:0%
+we care about the right-hand side as
+ 
+
+ align:start position:0%
+we care about the right-hand side as
+well we're going to copy this
+
+ align:start position:0%
+well we're going to copy this
+ 
+
+ align:start position:0%
+well we're going to copy this
+information as well and get the
+
+ align:start position:0%
+information as well and get the
+ 
+
+ align:start position:0%
+information as well and get the
+Augmented matrix of the system 0 8 minus
+
+ align:start position:0%
+Augmented matrix of the system 0 8 minus
+ 
+
+ align:start position:0%
+Augmented matrix of the system 0 8 minus
+8 so ok and now let's try reducing this
+
+ align:start position:0%
+8 so ok and now let's try reducing this
+ 
+
+ align:start position:0%
+8 so ok and now let's try reducing this
+matrix to an upper triangular one we
+
+ align:start position:0%
+matrix to an upper triangular one we
+ 
+
+ align:start position:0%
+matrix to an upper triangular one we
+start with the first column and we're
+
+ align:start position:0%
+start with the first column and we're
+ 
+
+ align:start position:0%
+start with the first column and we're
+going to use this number called the
+
+ align:start position:0%
+going to use this number called the
+ 
+
+ align:start position:0%
+going to use this number called the
+pivot to get rid of all the numbers
+
+ align:start position:0%
+pivot to get rid of all the numbers
+ 
+
+ align:start position:0%
+pivot to get rid of all the numbers
+under it so to get zeros here and here a
+
+ align:start position:0%
+under it so to get zeros here and here a
+ 
+
+ align:start position:0%
+under it so to get zeros here and here a
+way to do it
+
+ align:start position:0%
+way to do it
+ 
+
+ align:start position:0%
+way to do it
+is well to get rid of this - I have to
+
+ align:start position:0%
+is well to get rid of this - I have to
+ 
+
+ align:start position:0%
+is well to get rid of this - I have to
+multiply the first row by minus two and
+
+ align:start position:0%
+multiply the first row by minus two and
+ 
+
+ align:start position:0%
+multiply the first row by minus two and
+add it to the second one this is not
+
+ align:start position:0%
+add it to the second one this is not
+ 
+
+ align:start position:0%
+add it to the second one this is not
+straight writing this here is not
+
+ align:start position:0%
+straight writing this here is not
+ 
+
+ align:start position:0%
+straight writing this here is not
+strictly necessary but I like to do a
+
+ align:start position:0%
+strictly necessary but I like to do a
+ 
+
+ align:start position:0%
+strictly necessary but I like to do a
+bit of bookkeeping because I'm prone to
+
+ align:start position:0%
+bit of bookkeeping because I'm prone to
+ 
+
+ align:start position:0%
+bit of bookkeeping because I'm prone to
+make a lot of errors while doing this
+
+ align:start position:0%
+make a lot of errors while doing this
+ 
+
+ align:start position:0%
+make a lot of errors while doing this
+simple arithmetic operations and then if
+
+ align:start position:0%
+simple arithmetic operations and then if
+ 
+
+ align:start position:0%
+simple arithmetic operations and then if
+I get to the end figure out I made a
+
+ align:start position:0%
+I get to the end figure out I made a
+ 
+
+ align:start position:0%
+I get to the end figure out I made a
+mistake somewhere
+
+ align:start position:0%
+mistake somewhere
+ 
+
+ align:start position:0%
+mistake somewhere
+this bookkeeping makes it easier to
+
+ align:start position:0%
+this bookkeeping makes it easier to
+ 
+
+ align:start position:0%
+this bookkeeping makes it easier to
+backtrack and find find the place where
+
+ align:start position:0%
+backtrack and find find the place where
+ 
+
+ align:start position:0%
+backtrack and find find the place where
+I made this mistake so we replace this
+
+ align:start position:0%
+I made this mistake so we replace this
+ 
+
+ align:start position:0%
+I made this mistake so we replace this
+matrix with another matrix the first row
+
+ align:start position:0%
+matrix with another matrix the first row
+ 
+
+ align:start position:0%
+matrix with another matrix the first row
+stays the same 1 minus 1 minus 1 1 0 the
+
+ align:start position:0%
+stays the same 1 minus 1 minus 1 1 0 the
+ 
+
+ align:start position:0%
+stays the same 1 minus 1 minus 1 1 0 the
+second row gets replaced by a second row
+
+ align:start position:0%
+second row gets replaced by a second row
+ 
+
+ align:start position:0%
+second row gets replaced by a second row
+minus 2 times the first row the aim of
+
+ align:start position:0%
+minus 2 times the first row the aim of
+ 
+
+ align:start position:0%
+minus 2 times the first row the aim of
+that is to get a 0 here so that's good
+
+ align:start position:0%
+that is to get a 0 here so that's good
+ 
+
+ align:start position:0%
+that is to get a 0 here so that's good
+next on this position here we get minus
+
+ align:start position:0%
+next on this position here we get minus
+ 
+
+ align:start position:0%
+next on this position here we get minus
+2 times minus 1 which is 2 plus 0 which
+
+ align:start position:0%
+2 times minus 1 which is 2 plus 0 which
+ 
+
+ align:start position:0%
+2 times minus 1 which is 2 plus 0 which
+is 2 minus 1 times minus 2 which is 2
+
+ align:start position:0%
+is 2 minus 1 times minus 2 which is 2
+ 
+
+ align:start position:0%
+is 2 minus 1 times minus 2 which is 2
+plus 2 which is 4 minus 2 plus 0 which
+
+ align:start position:0%
+plus 2 which is 4 minus 2 plus 0 which
+ 
+
+ align:start position:0%
+plus 2 which is 4 minus 2 plus 0 which
+is minus 2 and 8 minus 2 times 0 which
+
+ align:start position:0%
+is minus 2 and 8 minus 2 times 0 which
+ 
+
+ align:start position:0%
+is minus 2 and 8 minus 2 times 0 which
+is 8 the third row already has a 0 here
+
+ align:start position:0%
+is 8 the third row already has a 0 here
+ 
+
+ align:start position:0%
+is 8 the third row already has a 0 here
+so I can just copy it over 0 minus 1
+
+ align:start position:0%
+so I can just copy it over 0 minus 1
+ 
+
+ align:start position:0%
+so I can just copy it over 0 minus 1
+minus 2 0 minus 8 and together 0 here
+
+ align:start position:0%
+minus 2 0 minus 8 and together 0 here
+ 
+
+ align:start position:0%
+minus 2 0 minus 8 and together 0 here
+I'm going to multiply the first row by
+
+ align:start position:0%
+I'm going to multiply the first row by
+ 
+
+ align:start position:0%
+I'm going to multiply the first row by
+minus 3 and add it to the fourth row and
+
+ align:start position:0%
+minus 3 and add it to the fourth row and
+ 
+
+ align:start position:0%
+minus 3 and add it to the fourth row and
+get 0 minus 3 times minus 1 is 3 minus 3
+
+ align:start position:0%
+get 0 minus 3 times minus 1 is 3 minus 3
+ 
+
+ align:start position:0%
+get 0 minus 3 times minus 1 is 3 minus 3
+is 0 minus 3 minus 1 oh sorry
+
+ align:start position:0%
+is 0 minus 3 minus 1 oh sorry
+ 
+
+ align:start position:0%
+is 0 minus 3 minus 1 oh sorry
+3 minus 2 is 1 and minus 3 plus 4 is 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there we go the first column looks
+
+ align:start position:0%
+and there we go the first column looks
+ 
+
+ align:start position:0%
+and there we go the first column looks
+like a first column of an upper
+
+ align:start position:0%
+like a first column of an upper
+ 
+
+ align:start position:0%
+like a first column of an upper
+triangular matrix now let's do the same
+
+ align:start position:0%
+triangular matrix now let's do the same
+ 
+
+ align:start position:0%
+triangular matrix now let's do the same
+to the second column this is going to be
+
+ align:start position:0%
+to the second column this is going to be
+ 
+
+ align:start position:0%
+to the second column this is going to be
+our pivot the number that we use to get
+
+ align:start position:0%
+our pivot the number that we use to get
+ 
+
+ align:start position:0%
+our pivot the number that we use to get
+rid of numbers under it and we see that
+
+ align:start position:0%
+rid of numbers under it and we see that
+ 
+
+ align:start position:0%
+rid of numbers under it and we see that
+to get rid of this number here we will
+
+ align:start position:0%
+to get rid of this number here we will
+ 
+
+ align:start position:0%
+to get rid of this number here we will
+need to multiply it with 1/2 so multiply
+
+ align:start position:0%
+need to multiply it with 1/2 so multiply
+ 
+
+ align:start position:0%
+need to multiply it with 1/2 so multiply
+the whole second row with 1/2 and edit
+
+ align:start position:0%
+the whole second row with 1/2 and edit
+ 
+
+ align:start position:0%
+the whole second row with 1/2 and edit
+to the third row the matrix that we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll have the first row the same stays
+
+ align:start position:0%
+we'll have the first row the same stays
+ 
+
+ align:start position:0%
+we'll have the first row the same stays
+the same 1 minus 1 minus 1 1 0 the
+
+ align:start position:0%
+the same 1 minus 1 minus 1 1 0 the
+ 
+
+ align:start position:0%
+the same 1 minus 1 minus 1 1 0 the
+second row stays the same 0 2 4 minus 2
+
+ align:start position:0%
+second row stays the same 0 2 4 minus 2
+ 
+
+ align:start position:0%
+second row stays the same 0 2 4 minus 2
+8 the third row gets replaced by the
+
+ align:start position:0%
+8 the third row gets replaced by the
+ 
+
+ align:start position:0%
+8 the third row gets replaced by the
+third row plus 1/2 times the second row
+
+ align:start position:0%
+third row plus 1/2 times the second row
+ 
+
+ align:start position:0%
+third row plus 1/2 times the second row
+and becomes 0 0 2 minus 2 which is 0
+
+ align:start position:0%
+and becomes 0 0 2 minus 2 which is 0
+ 
+
+ align:start position:0%
+and becomes 0 0 2 minus 2 which is 0
+minus 1 plus 0 which is minus 1 and 4
+
+ align:start position:0%
+minus 1 plus 0 which is minus 1 and 4
+ 
+
+ align:start position:0%
+minus 1 plus 0 which is minus 1 and 4
+minus 8 which is minus 4 in the third
+
+ align:start position:0%
+minus 8 which is minus 4 in the third
+ 
+
+ align:start position:0%
+minus 8 which is minus 4 in the third
+row the fourth row already has a 0 here
+
+ align:start position:0%
+row the fourth row already has a 0 here
+ 
+
+ align:start position:0%
+row the fourth row already has a 0 here
+so I just copy it over 0 0 1 1 7 and now
+
+ align:start position:0%
+so I just copy it over 0 0 1 1 7 and now
+ 
+
+ align:start position:0%
+so I just copy it over 0 0 1 1 7 and now
+let's look at this matrix it has the
+
+ align:start position:0%
+let's look at this matrix it has the
+ 
+
+ align:start position:0%
+let's look at this matrix it has the
+first 2 columns as they're supposed to
+
+ align:start position:0%
+first 2 columns as they're supposed to
+ 
+
+ align:start position:0%
+first 2 columns as they're supposed to
+be zeros under the day I don't know and
+
+ align:start position:0%
+be zeros under the day I don't know and
+ 
+
+ align:start position:0%
+be zeros under the day I don't know and
+now we want to get a 0 here normally
+
+ align:start position:0%
+now we want to get a 0 here normally
+ 
+
+ align:start position:0%
+now we want to get a 0 here normally
+what I would do is to circle this number
+
+ align:start position:0%
+what I would do is to circle this number
+ 
+
+ align:start position:0%
+what I would do is to circle this number
+here multiply it by something so that I
+
+ align:start position:0%
+here multiply it by something so that I
+ 
+
+ align:start position:0%
+here multiply it by something so that I
+get a minus 1 and edits to this row to
+
+ align:start position:0%
+get a minus 1 and edits to this row to
+ 
+
+ align:start position:0%
+get a minus 1 and edits to this row to
+get a 0 here but that's not going to
+
+ align:start position:0%
+get a 0 here but that's not going to
+ 
+
+ align:start position:0%
+get a 0 here but that's not going to
+work you might remember from lectures
+
+ align:start position:0%
+work you might remember from lectures
+ 
+
+ align:start position:0%
+work you might remember from lectures
+that zeros can never be pivots or you
+
+ align:start position:0%
+that zeros can never be pivots or you
+ 
+
+ align:start position:0%
+that zeros can never be pivots or you
+can just try finding a number such that
+
+ align:start position:0%
+can just try finding a number such that
+ 
+
+ align:start position:0%
+can just try finding a number such that
+0 times this number equals minus 1 and
+
+ align:start position:0%
+0 times this number equals minus 1 and
+ 
+
+ align:start position:0%
+0 times this number equals minus 1 and
+seeing that such a number doesn't exist
+
+ align:start position:0%
+seeing that such a number doesn't exist
+ 
+
+ align:start position:0%
+seeing that such a number doesn't exist
+because you're always going to get 0 so
+
+ align:start position:0%
+because you're always going to get 0 so
+ 
+
+ align:start position:0%
+because you're always going to get 0 so
+we cannot proceed as with it until now
+
+ align:start position:0%
+we cannot proceed as with it until now
+ 
+
+ align:start position:0%
+we cannot proceed as with it until now
+but is there another way to get a 0 here
+
+ align:start position:0%
+but is there another way to get a 0 here
+ 
+
+ align:start position:0%
+but is there another way to get a 0 here
+there is a very simple row operation
+
+ align:start position:0%
+there is a very simple row operation
+ 
+
+ align:start position:0%
+there is a very simple row operation
+which because it's just of switching the
+
+ align:start position:0%
+which because it's just of switching the
+ 
+
+ align:start position:0%
+which because it's just of switching the
+3rd and the 4th row it certainly doesn't
+
+ align:start position:0%
+3rd and the 4th row it certainly doesn't
+ 
+
+ align:start position:0%
+3rd and the 4th row it certainly doesn't
+change the solution of the system so
+
+ align:start position:0%
+change the solution of the system so
+ 
+
+ align:start position:0%
+change the solution of the system so
+let's do that let's get the next matrix
+
+ align:start position:0%
+let's do that let's get the next matrix
+ 
+
+ align:start position:0%
+let's do that let's get the next matrix
+which is 1 minus 1 minus 1 1 0 0 2 4
+
+ align:start position:0%
+which is 1 minus 1 minus 1 1 0 0 2 4
+ 
+
+ align:start position:0%
+which is 1 minus 1 minus 1 1 0 0 2 4
+minus 2 8 then we put the 4th row here 0
+
+ align:start position:0%
+minus 2 8 then we put the 4th row here 0
+ 
+
+ align:start position:0%
+minus 2 8 then we put the 4th row here 0
+0 1 1
+
+ align:start position:0%
+0 1 1
+ 
+
+ align:start position:0%
+0 1 1
+seven and we put the third row here 0 0
+
+ align:start position:0%
+seven and we put the third row here 0 0
+ 
+
+ align:start position:0%
+seven and we put the third row here 0 0
+0 minus 1 minus 4 and there it is this
+
+ align:start position:0%
+0 minus 1 minus 4 and there it is this
+ 
+
+ align:start position:0%
+0 minus 1 minus 4 and there it is this
+is an upper triangular matrix so in the
+
+ align:start position:0%
+is an upper triangular matrix so in the
+ 
+
+ align:start position:0%
+is an upper triangular matrix so in the
+same way as at the beginning we had the
+
+ align:start position:0%
+same way as at the beginning we had the
+ 
+
+ align:start position:0%
+same way as at the beginning we had the
+system and then wrote the matrix
+
+ align:start position:0%
+system and then wrote the matrix
+ 
+
+ align:start position:0%
+system and then wrote the matrix
+representing it this matrix also
+
+ align:start position:0%
+representing it this matrix also
+ 
+
+ align:start position:0%
+representing it this matrix also
+represents a system and this system has
+
+ align:start position:0%
+represents a system and this system has
+ 
+
+ align:start position:0%
+represents a system and this system has
+the same solutions as the initial system
+
+ align:start position:0%
+the same solutions as the initial system
+ 
+
+ align:start position:0%
+the same solutions as the initial system
+but is much easier to solve now let me
+
+ align:start position:0%
+but is much easier to solve now let me
+ 
+
+ align:start position:0%
+but is much easier to solve now let me
+write this back as a system and let me
+
+ align:start position:0%
+write this back as a system and let me
+ 
+
+ align:start position:0%
+write this back as a system and let me
+do that not starting from the first
+
+ align:start position:0%
+do that not starting from the first
+ 
+
+ align:start position:0%
+do that not starting from the first
+equation but starting from the last
+
+ align:start position:0%
+equation but starting from the last
+ 
+
+ align:start position:0%
+equation but starting from the last
+equation so the last equation here reads
+
+ align:start position:0%
+equation so the last equation here reads
+ 
+
+ align:start position:0%
+equation so the last equation here reads
+minus u equals minus 4 which is
+
+ align:start position:0%
+minus u equals minus 4 which is
+ 
+
+ align:start position:0%
+minus u equals minus 4 which is
+equations go pretty easy to a pretty
+
+ align:start position:0%
+equations go pretty easy to a pretty
+ 
+
+ align:start position:0%
+equations go pretty easy to a pretty
+easy one to solve the solution is U
+
+ align:start position:0%
+easy one to solve the solution is U
+ 
+
+ align:start position:0%
+easy one to solve the solution is U
+equals 4 now let's go back to the third
+
+ align:start position:0%
+equals 4 now let's go back to the third
+ 
+
+ align:start position:0%
+equals 4 now let's go back to the third
+equation the third equation reads Y oh
+
+ align:start position:0%
+equation the third equation reads Y oh
+ 
+
+ align:start position:0%
+equation the third equation reads Y oh
+no I'm sorry Z the third column
+
+ align:start position:0%
+no I'm sorry Z the third column
+ 
+
+ align:start position:0%
+no I'm sorry Z the third column
+corresponds to Z plus u equals 7 but we
+
+ align:start position:0%
+corresponds to Z plus u equals 7 but we
+ 
+
+ align:start position:0%
+corresponds to Z plus u equals 7 but we
+know what's u now so it reads Z plus 4
+
+ align:start position:0%
+know what's u now so it reads Z plus 4
+ 
+
+ align:start position:0%
+know what's u now so it reads Z plus 4
+equals 7 which just becomes Z equals 3
+
+ align:start position:0%
+equals 7 which just becomes Z equals 3
+ 
+
+ align:start position:0%
+equals 7 which just becomes Z equals 3
+the second equation is 2 times y plus 4
+
+ align:start position:0%
+the second equation is 2 times y plus 4
+ 
+
+ align:start position:0%
+the second equation is 2 times y plus 4
+times Z but Z is 3 minus 2 times U but U
+
+ align:start position:0%
+times Z but Z is 3 minus 2 times U but U
+ 
+
+ align:start position:0%
+times Z but Z is 3 minus 2 times U but U
+is 4 equals 8 and from this one can
+
+ align:start position:0%
+is 4 equals 8 and from this one can
+ 
+
+ align:start position:0%
+is 4 equals 8 and from this one can
+easily compute that Y is equal to 2 and
+
+ align:start position:0%
+easily compute that Y is equal to 2 and
+ 
+
+ align:start position:0%
+easily compute that Y is equal to 2 and
+finally the first equation reads X minus
+
+ align:start position:0%
+finally the first equation reads X minus
+ 
+
+ align:start position:0%
+finally the first equation reads X minus
+y minus Z plus u
+
+ align:start position:0%
+y minus Z plus u
+ 
+
+ align:start position:0%
+y minus Z plus u
+equals zero or x equals one and this is
+
+ align:start position:0%
+equals zero or x equals one and this is
+ 
+
+ align:start position:0%
+equals zero or x equals one and this is
+our solution X Y Z and u equal 1 2 3 & 4
+
+ align:start position:0%
+our solution X Y Z and u equal 1 2 3 & 4
+ 
+
+ align:start position:0%
+our solution X Y Z and u equal 1 2 3 & 4
+this finish is the problem but I would
+
+ align:start position:0%
+this finish is the problem but I would
+ 
+
+ align:start position:0%
+this finish is the problem but I would
+very strongly encourage you now to take
+
+ align:start position:0%
+very strongly encourage you now to take
+ 
+
+ align:start position:0%
+very strongly encourage you now to take
+this solution and plug it back into the
+
+ align:start position:0%
+this solution and plug it back into the
+ 
+
+ align:start position:0%
+this solution and plug it back into the
+original system and check if it's really
+
+ align:start position:0%
+original system and check if it's really
+ 
+
+ align:start position:0%
+original system and check if it's really
+a solution and that's all I want you to
+
+ align:start position:0%
+a solution and that's all I want you to
+ 
+
+ align:start position:0%
+a solution and that's all I want you to
+say today
\ No newline at end of file
diff --git a/GbuXLQ08n4A.txt b/GbuXLQ08n4A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0781ca2937843fb344d30c23d60a603ca298a55a
--- /dev/null
+++ b/GbuXLQ08n4A.txt
@@ -0,0 +1,7827 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu today we're going to talk
+
+ align:start position:0%
+ocw.mit.edu today we're going to talk
+ 
+
+ align:start position:0%
+ocw.mit.edu today we're going to talk
+about the borne Oppenheimer
+
+ align:start position:0%
+about the borne Oppenheimer
+ 
+
+ align:start position:0%
+about the borne Oppenheimer
+approximation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is the crucial tool that
+
+ align:start position:0%
+and this is the crucial tool that
+ 
+
+ align:start position:0%
+and this is the crucial tool that
+enables us to write the hamiltonian for
+
+ align:start position:0%
+enables us to write the hamiltonian for
+ 
+
+ align:start position:0%
+enables us to write the hamiltonian for
+molecules in a form that we can
+
+ align:start position:0%
+molecules in a form that we can
+ 
+
+ align:start position:0%
+molecules in a form that we can
+use and so uh many people are confused
+
+ align:start position:0%
+use and so uh many people are confused
+ 
+
+ align:start position:0%
+use and so uh many people are confused
+about the born Oppenheimer approximation
+
+ align:start position:0%
+about the born Oppenheimer approximation
+ 
+
+ align:start position:0%
+about the born Oppenheimer approximation
+in the sense that uh as soon as you
+
+ align:start position:0%
+in the sense that uh as soon as you
+ 
+
+ align:start position:0%
+in the sense that uh as soon as you
+start getting violations of it then it's
+
+ align:start position:0%
+start getting violations of it then it's
+ 
+
+ align:start position:0%
+start getting violations of it then it's
+no longer applicable but the borop hour
+
+ align:start position:0%
+no longer applicable but the borop hour
+ 
+
+ align:start position:0%
+no longer applicable but the borop hour
+approximation is a way for getting a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complete
+
+ align:start position:0%
+complete
+ 
+
+ align:start position:0%
+complete
+basis
+
+ align:start position:0%
+basis
+ 
+
+ align:start position:0%
+basis
+set with which you can describe anything
+
+ align:start position:0%
+set with which you can describe anything
+ 
+
+ align:start position:0%
+set with which you can describe anything
+and so you might as well make some kind
+
+ align:start position:0%
+and so you might as well make some kind
+ 
+
+ align:start position:0%
+and so you might as well make some kind
+of an approximation if it enables you to
+
+ align:start position:0%
+of an approximation if it enables you to
+ 
+
+ align:start position:0%
+of an approximation if it enables you to
+have a complete set of wave
+
+ align:start position:0%
+have a complete set of wave
+ 
+
+ align:start position:0%
+have a complete set of wave
+functions in which you can evaluate then
+
+ align:start position:0%
+functions in which you can evaluate then
+ 
+
+ align:start position:0%
+functions in which you can evaluate then
+any term in the
+
+ align:start position:0%
+any term in the
+ 
+
+ align:start position:0%
+any term in the
+hamiltonian now what we'd really like to
+
+ align:start position:0%
+hamiltonian now what we'd really like to
+ 
+
+ align:start position:0%
+hamiltonian now what we'd really like to
+do is to take the full wave function the
+
+ align:start position:0%
+do is to take the full wave function the
+ 
+
+ align:start position:0%
+do is to take the full wave function the
+exact wave function function and write
+
+ align:start position:0%
+exact wave function function and write
+ 
+
+ align:start position:0%
+exact wave function function and write
+it as a product of simpler things and
+
+ align:start position:0%
+it as a product of simpler things and
+ 
+
+ align:start position:0%
+it as a product of simpler things and
+for molecules we would like it to be an
+
+ align:start position:0%
+for molecules we would like it to be an
+ 
+
+ align:start position:0%
+for molecules we would like it to be an
+electronic
+
+ align:start position:0%
+electronic
+ 
+
+ align:start position:0%
+electronic
+factor a vibrational factor and a
+
+ align:start position:0%
+factor a vibrational factor and a
+ 
+
+ align:start position:0%
+factor a vibrational factor and a
+rotational Factor it may be spin orbit
+
+ align:start position:0%
+rotational Factor it may be spin orbit
+ 
+
+ align:start position:0%
+rotational Factor it may be spin orbit
+as well but we'd like to factor the wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function and the general way you factor
+
+ align:start position:0%
+function and the general way you factor
+ 
+
+ align:start position:0%
+function and the general way you factor
+a wave function is you write the
+
+ align:start position:0%
+a wave function is you write the
+ 
+
+ align:start position:0%
+a wave function is you write the
+hamiltonian as a sum of Parts say
+
+ align:start position:0%
+hamiltonian as a sum of Parts say
+ 
+
+ align:start position:0%
+hamiltonian as a sum of Parts say
+electronic plus vibration plus
+
+ align:start position:0%
+electronic plus vibration plus
+ 
+
+ align:start position:0%
+electronic plus vibration plus
+rotation and then it enables you to
+
+ align:start position:0%
+rotation and then it enables you to
+ 
+
+ align:start position:0%
+rotation and then it enables you to
+write the energy
+
+ align:start position:0%
+write the energy
+ 
+
+ align:start position:0%
+write the energy
+as I'll use correct notation here
+
+ align:start position:0%
+as I'll use correct notation here
+ 
+
+ align:start position:0%
+as I'll use correct notation here
+uh an electronic
+
+ align:start position:0%
+uh an electronic
+ 
+
+ align:start position:0%
+uh an electronic
+term and maybe we'd have an index for
+
+ align:start position:0%
+term and maybe we'd have an index for
+ 
+
+ align:start position:0%
+term and maybe we'd have an index for
+which one plus a vibrational term and
+
+ align:start position:0%
+which one plus a vibrational term and
+ 
+
+ align:start position:0%
+which one plus a vibrational term and
+that would be associated with a
+
+ align:start position:0%
+that would be associated with a
+ 
+
+ align:start position:0%
+that would be associated with a
+particular electronic
+
+ align:start position:0%
+particular electronic
+ 
+
+ align:start position:0%
+particular electronic
+State and then a rotational term
+
+ align:start position:0%
+State and then a rotational term
+ 
+
+ align:start position:0%
+State and then a rotational term
+which so this is what we'd like and this
+
+ align:start position:0%
+which so this is what we'd like and this
+ 
+
+ align:start position:0%
+which so this is what we'd like and this
+is the notation that is conventionally
+
+ align:start position:0%
+is the notation that is conventionally
+ 
+
+ align:start position:0%
+is the notation that is conventionally
+used in molecules t for electronic I
+
+ align:start position:0%
+used in molecules t for electronic I
+ 
+
+ align:start position:0%
+used in molecules t for electronic I
+don't know why G for vibration I don't
+
+ align:start position:0%
+don't know why G for vibration I don't
+ 
+
+ align:start position:0%
+don't know why G for vibration I don't
+know why and F for rotation I don't know
+
+ align:start position:0%
+know why and F for rotation I don't know
+ 
+
+ align:start position:0%
+know why and F for rotation I don't know
+why and it may be that in German those
+
+ align:start position:0%
+why and it may be that in German those
+ 
+
+ align:start position:0%
+why and it may be that in German those
+letters
+
+ align:start position:0%
+letters
+ 
+
+ align:start position:0%
+letters
+mean something but I I really think that
+
+ align:start position:0%
+mean something but I I really think that
+ 
+
+ align:start position:0%
+mean something but I I really think that
+they just their origin is
+
+ align:start position:0%
+they just their origin is
+ 
+
+ align:start position:0%
+they just their origin is
+random uh so this is what we'd like to
+
+ align:start position:0%
+random uh so this is what we'd like to
+ 
+
+ align:start position:0%
+random uh so this is what we'd like to
+do and it's not quite possible to do
+
+ align:start position:0%
+do and it's not quite possible to do
+ 
+
+ align:start position:0%
+do and it's not quite possible to do
+this without making some
+
+ align:start position:0%
+this without making some
+ 
+
+ align:start position:0%
+this without making some
+artistic or physically sensible
+
+ align:start position:0%
+artistic or physically sensible
+ 
+
+ align:start position:0%
+artistic or physically sensible
+approximations recall in our treatment
+
+ align:start position:0%
+approximations recall in our treatment
+ 
+
+ align:start position:0%
+approximations recall in our treatment
+of atoms what we like to do for atoms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is to think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orbitals and so what you'd really like
+
+ align:start position:0%
+orbitals and so what you'd really like
+ 
+
+ align:start position:0%
+orbitals and so what you'd really like
+to be able to do with atoms is to write
+
+ align:start position:0%
+to be able to do with atoms is to write
+ 
+
+ align:start position:0%
+to be able to do with atoms is to write
+the hamiltonian as a sum of individual
+
+ align:start position:0%
+the hamiltonian as a sum of individual
+ 
+
+ align:start position:0%
+the hamiltonian as a sum of individual
+orbital hamiltonians and we know we
+
+ align:start position:0%
+orbital hamiltonians and we know we
+ 
+
+ align:start position:0%
+orbital hamiltonians and we know we
+can't do that we know that there is a
+
+ align:start position:0%
+can't do that we know that there is a
+ 
+
+ align:start position:0%
+can't do that we know that there is a
+term one / RI J that spoils all
+
+ align:start position:0%
+term one / RI J that spoils all
+ 
+
+ align:start position:0%
+term one / RI J that spoils all
+such uh dreams and so we have to somehow
+
+ align:start position:0%
+such uh dreams and so we have to somehow
+ 
+
+ align:start position:0%
+such uh dreams and so we have to somehow
+work around the reality that orbitals
+
+ align:start position:0%
+work around the reality that orbitals
+ 
+
+ align:start position:0%
+work around the reality that orbitals
+are not a good representation of the
+
+ align:start position:0%
+are not a good representation of the
+ 
+
+ align:start position:0%
+are not a good representation of the
+hamiltonian but what we always do when
+
+ align:start position:0%
+hamiltonian but what we always do when
+ 
+
+ align:start position:0%
+hamiltonian but what we always do when
+we saw for atoms we still kept the
+
+ align:start position:0%
+we saw for atoms we still kept the
+ 
+
+ align:start position:0%
+we saw for atoms we still kept the
+orbital approximation and we wrote the
+
+ align:start position:0%
+orbital approximation and we wrote the
+ 
+
+ align:start position:0%
+orbital approximation and we wrote the
+hamiltonian as a function of Parts an
+
+ align:start position:0%
+hamiltonian as a function of Parts an
+ 
+
+ align:start position:0%
+hamiltonian as a function of Parts an
+orbital
+
+ align:start position:0%
+orbital
+ 
+
+ align:start position:0%
+orbital
+energy a spin orbit
+
+ align:start position:0%
+energy a spin orbit
+ 
+
+ align:start position:0%
+energy a spin orbit
+term and
+
+ align:start position:0%
+term and
+ 
+
+ align:start position:0%
+term and
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and
+
+ align:start position:0%
+uh and
+ 
+
+ align:start position:0%
+uh and
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electron terms
+
+ align:start position:0%
+electron terms
+ 
+
+ align:start position:0%
+electron terms
+so we couldn't use the simple
+
+ align:start position:0%
+so we couldn't use the simple
+ 
+
+ align:start position:0%
+so we couldn't use the simple
+approximation so instead uh we embedded
+
+ align:start position:0%
+approximation so instead uh we embedded
+ 
+
+ align:start position:0%
+approximation so instead uh we embedded
+the orbital Concept in individual things
+
+ align:start position:0%
+the orbital Concept in individual things
+ 
+
+ align:start position:0%
+the orbital Concept in individual things
+one electron one electron and two
+
+ align:start position:0%
+one electron one electron and two
+ 
+
+ align:start position:0%
+one electron one electron and two
+electron terms and that gave us a
+
+ align:start position:0%
+electron terms and that gave us a
+ 
+
+ align:start position:0%
+electron terms and that gave us a
+representation of the atomic
+
+ align:start position:0%
+representation of the atomic
+ 
+
+ align:start position:0%
+representation of the atomic
+spectrum so you can be sure that for
+
+ align:start position:0%
+spectrum so you can be sure that for
+ 
+
+ align:start position:0%
+spectrum so you can be sure that for
+molecules we're going to have to make
+
+ align:start position:0%
+molecules we're going to have to make
+ 
+
+ align:start position:0%
+molecules we're going to have to make
+some clever
+
+ align:start position:0%
+some clever
+ 
+
+ align:start position:0%
+some clever
+approximations analogous to what was
+
+ align:start position:0%
+approximations analogous to what was
+ 
+
+ align:start position:0%
+approximations analogous to what was
+happening what happened over here and
+
+ align:start position:0%
+happening what happened over here and
+ 
+
+ align:start position:0%
+happening what happened over here and
+the approximation is always going to be
+
+ align:start position:0%
+the approximation is always going to be
+ 
+
+ align:start position:0%
+the approximation is always going to be
+let us think about what we would like it
+
+ align:start position:0%
+let us think about what we would like it
+ 
+
+ align:start position:0%
+let us think about what we would like it
+to how we would like it to come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out ignore certain terms in the
+
+ align:start position:0%
+out ignore certain terms in the
+ 
+
+ align:start position:0%
+out ignore certain terms in the
+hamiltonian that are
+
+ align:start position:0%
+hamiltonian that are
+ 
+
+ align:start position:0%
+hamiltonian that are
+Troublesome that gives us an
+
+ align:start position:0%
+Troublesome that gives us an
+ 
+
+ align:start position:0%
+Troublesome that gives us an
+h0 with which we we for which it's easy
+
+ align:start position:0%
+h0 with which we we for which it's easy
+ 
+
+ align:start position:0%
+h0 with which we we for which it's easy
+to find igen
+
+ align:start position:0%
+to find igen
+ 
+
+ align:start position:0%
+to find igen
+functions and that's our those are our
+
+ align:start position:0%
+functions and that's our those are our
+ 
+
+ align:start position:0%
+functions and that's our those are our
+basis functions now these are real
+
+ align:start position:0%
+basis functions now these are real
+ 
+
+ align:start position:0%
+basis functions now these are real
+functions and they're a complete set of
+
+ align:start position:0%
+functions and they're a complete set of
+ 
+
+ align:start position:0%
+functions and they're a complete set of
+functions and using them we can then
+
+ align:start position:0%
+functions and using them we can then
+ 
+
+ align:start position:0%
+functions and using them we can then
+evaluate the effects of all of the terms
+
+ align:start position:0%
+evaluate the effects of all of the terms
+ 
+
+ align:start position:0%
+evaluate the effects of all of the terms
+we left
+
+ align:start position:0%
+we left
+ 
+
+ align:start position:0%
+we left
+out so this is a standard procedure and
+
+ align:start position:0%
+out so this is a standard procedure and
+ 
+
+ align:start position:0%
+out so this is a standard procedure and
+it's called the borop approximation or
+
+ align:start position:0%
+it's called the borop approximation or
+ 
+
+ align:start position:0%
+it's called the borop approximation or
+at least the way in which I'm going to
+
+ align:start position:0%
+at least the way in which I'm going to
+ 
+
+ align:start position:0%
+at least the way in which I'm going to
+do implement this analysis is called the
+
+ align:start position:0%
+do implement this analysis is called the
+ 
+
+ align:start position:0%
+do implement this analysis is called the
+borop approximation now in the notes you
+
+ align:start position:0%
+borop approximation now in the notes you
+ 
+
+ align:start position:0%
+borop approximation now in the notes you
+have or that you may have there are a
+
+ align:start position:0%
+have or that you may have there are a
+ 
+
+ align:start position:0%
+have or that you may have there are a
+lot of little typos and they're all
+
+ align:start position:0%
+lot of little typos and they're all
+ 
+
+ align:start position:0%
+lot of little typos and they're all
+going to get fixed later today but uh I
+
+ align:start position:0%
+going to get fixed later today but uh I
+ 
+
+ align:start position:0%
+going to get fixed later today but uh I
+can only find all of the typos when I'm
+
+ align:start position:0%
+can only find all of the typos when I'm
+ 
+
+ align:start position:0%
+can only find all of the typos when I'm
+actually loading the lecture which means
+
+ align:start position:0%
+actually loading the lecture which means
+ 
+
+ align:start position:0%
+actually loading the lecture which means
+about 5 minutes before I come down here
+
+ align:start position:0%
+about 5 minutes before I come down here
+ 
+
+ align:start position:0%
+about 5 minutes before I come down here
+I finished debugging the lecture notes
+
+ align:start position:0%
+I finished debugging the lecture notes
+ 
+
+ align:start position:0%
+I finished debugging the lecture notes
+so anyway okay
+
+ align:start position:0%
+so anyway okay
+ 
+
+ align:start position:0%
+so anyway okay
+so we
+
+ align:start position:0%
+so we
+ 
+
+ align:start position:0%
+so we
+have for a diatomic molecule we have a
+
+ align:start position:0%
+have for a diatomic molecule we have a
+ 
+
+ align:start position:0%
+have for a diatomic molecule we have a
+hamiltonian which is expressed in terms
+
+ align:start position:0%
+hamiltonian which is expressed in terms
+ 
+
+ align:start position:0%
+hamiltonian which is expressed in terms
+of electron
+
+ align:start position:0%
+of electron
+ 
+
+ align:start position:0%
+of electron
+coordinates the internuclear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+separation and the orientation of the
+
+ align:start position:0%
+separation and the orientation of the
+ 
+
+ align:start position:0%
+separation and the orientation of the
+internuclear axis relative to the
+
+ align:start position:0%
+internuclear axis relative to the
+ 
+
+ align:start position:0%
+internuclear axis relative to the
+laboratory so we need two angles to
+
+ align:start position:0%
+laboratory so we need two angles to
+ 
+
+ align:start position:0%
+laboratory so we need two angles to
+determine uh the orientation of a
+
+ align:start position:0%
+determine uh the orientation of a
+ 
+
+ align:start position:0%
+determine uh the orientation of a
+line and so the the for datomic
+
+ align:start position:0%
+line and so the the for datomic
+ 
+
+ align:start position:0%
+line and so the the for datomic
+molecules we have two angles that
+
+ align:start position:0%
+molecules we have two angles that
+ 
+
+ align:start position:0%
+molecules we have two angles that
+specify the orientation of the body
+
+ align:start position:0%
+specify the orientation of the body
+ 
+
+ align:start position:0%
+specify the orientation of the body
+fixed coordinate system relative to the
+
+ align:start position:0%
+fixed coordinate system relative to the
+ 
+
+ align:start position:0%
+fixed coordinate system relative to the
+laboratory fixed coordinate system you
+
+ align:start position:0%
+laboratory fixed coordinate system you
+ 
+
+ align:start position:0%
+laboratory fixed coordinate system you
+have two coordinate systems uh uh the
+
+ align:start position:0%
+have two coordinate systems uh uh the
+ 
+
+ align:start position:0%
+have two coordinate systems uh uh the
+origin is the center of mass in both but
+
+ align:start position:0%
+origin is the center of mass in both but
+ 
+
+ align:start position:0%
+origin is the center of mass in both but
+because of rotation the two coordinate
+
+ align:start position:0%
+because of rotation the two coordinate
+ 
+
+ align:start position:0%
+because of rotation the two coordinate
+systems uh are are not
+
+ align:start position:0%
+systems uh are are not
+ 
+
+ align:start position:0%
+systems uh are are not
+coincident and uh now normally when you
+
+ align:start position:0%
+coincident and uh now normally when you
+ 
+
+ align:start position:0%
+coincident and uh now normally when you
+have two coordinate systems body and
+
+ align:start position:0%
+have two coordinate systems body and
+ 
+
+ align:start position:0%
+have two coordinate systems body and
+laboratory you use three Oiler
+
+ align:start position:0%
+laboratory you use three Oiler
+ 
+
+ align:start position:0%
+laboratory you use three Oiler
+angles to to but if you have a diatomic
+
+ align:start position:0%
+angles to to but if you have a diatomic
+ 
+
+ align:start position:0%
+angles to to but if you have a diatomic
+molecule the rotation about the body
+
+ align:start position:0%
+molecule the rotation about the body
+ 
+
+ align:start position:0%
+molecule the rotation about the body
+axis is not
+
+ align:start position:0%
+axis is not
+ 
+
+ align:start position:0%
+axis is not
+defined and so we don't use three Oiler
+
+ align:start position:0%
+defined and so we don't use three Oiler
+ 
+
+ align:start position:0%
+defined and so we don't use three Oiler
+angles there is implicitly a third Oiler
+
+ align:start position:0%
+angles there is implicitly a third Oiler
+ 
+
+ align:start position:0%
+angles there is implicitly a third Oiler
+angle which appears in Phase conventions
+
+ align:start position:0%
+angle which appears in Phase conventions
+ 
+
+ align:start position:0%
+angle which appears in Phase conventions
+so if you
+
+ align:start position:0%
+so if you
+ 
+
+ align:start position:0%
+so if you
+have somebody's formal algebra for
+
+ align:start position:0%
+have somebody's formal algebra for
+ 
+
+ align:start position:0%
+have somebody's formal algebra for
+describing the
+
+ align:start position:0%
+describing the
+ 
+
+ align:start position:0%
+describing the
+relationship of um the body fix
+
+ align:start position:0%
+relationship of um the body fix
+ 
+
+ align:start position:0%
+relationship of um the body fix
+coordinate system to the laboratory
+
+ align:start position:0%
+coordinate system to the laboratory
+ 
+
+ align:start position:0%
+coordinate system to the laboratory
+there is implicit a phase Choice which
+
+ align:start position:0%
+there is implicit a phase Choice which
+ 
+
+ align:start position:0%
+there is implicit a phase Choice which
+is the definition of that third angle
+
+ align:start position:0%
+is the definition of that third angle
+ 
+
+ align:start position:0%
+is the definition of that third angle
+and Quantum chemists and spectroscopists
+
+ align:start position:0%
+and Quantum chemists and spectroscopists
+ 
+
+ align:start position:0%
+and Quantum chemists and spectroscopists
+almost always use different phase
+
+ align:start position:0%
+almost always use different phase
+ 
+
+ align:start position:0%
+almost always use different phase
+conventions and this appears as factors
+
+ align:start position:0%
+conventions and this appears as factors
+ 
+
+ align:start position:0%
+conventions and this appears as factors
+of minus one uh that pop up in random
+
+ align:start position:0%
+of minus one uh that pop up in random
+ 
+
+ align:start position:0%
+of minus one uh that pop up in random
+locations and that's an interesting
+
+ align:start position:0%
+locations and that's an interesting
+ 
+
+ align:start position:0%
+locations and that's an interesting
+thing okay so what we would like to be
+
+ align:start position:0%
+thing okay so what we would like to be
+ 
+
+ align:start position:0%
+thing okay so what we would like to be
+able to do is to write this hamiltonian
+
+ align:start position:0%
+able to do is to write this hamiltonian
+ 
+
+ align:start position:0%
+able to do is to write this hamiltonian
+in a way where we separate separated it
+
+ align:start position:0%
+in a way where we separate separated it
+ 
+
+ align:start position:0%
+in a way where we separate separated it
+out into terms corresponding to the
+
+ align:start position:0%
+out into terms corresponding to the
+ 
+
+ align:start position:0%
+out into terms corresponding to the
+individual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coordinates so in order to do this we
+
+ align:start position:0%
+coordinates so in order to do this we
+ 
+
+ align:start position:0%
+coordinates so in order to do this we
+invoke a a very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important approximation or we make a
+
+ align:start position:0%
+important approximation or we make a
+ 
+
+ align:start position:0%
+important approximation or we make a
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+important approximation we clamp the
+
+ align:start position:0%
+important approximation we clamp the
+ 
+
+ align:start position:0%
+important approximation we clamp the
+nuclei so if the nuclei are nailed to
+
+ align:start position:0%
+nuclei so if the nuclei are nailed to
+ 
+
+ align:start position:0%
+nuclei so if the nuclei are nailed to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Blackboard the molecule isn't going to
+
+ align:start position:0%
+Blackboard the molecule isn't going to
+ 
+
+ align:start position:0%
+Blackboard the molecule isn't going to
+rotate and it is isn't going to uh
+
+ align:start position:0%
+rotate and it is isn't going to uh
+ 
+
+ align:start position:0%
+rotate and it is isn't going to uh
+vibrate it's not going to do
+
+ align:start position:0%
+vibrate it's not going to do
+ 
+
+ align:start position:0%
+vibrate it's not going to do
+anything and so if we clamp the nuclei
+
+ align:start position:0%
+anything and so if we clamp the nuclei
+ 
+
+ align:start position:0%
+anything and so if we clamp the nuclei
+then we are in a position to solve the
+
+ align:start position:0%
+then we are in a position to solve the
+ 
+
+ align:start position:0%
+then we are in a position to solve the
+electronic shering
+
+ align:start position:0%
+electronic shering
+ 
+
+ align:start position:0%
+electronic shering
+equation and so it's certainly true that
+
+ align:start position:0%
+equation and so it's certainly true that
+ 
+
+ align:start position:0%
+equation and so it's certainly true that
+in solving the electronic Shoring
+
+ align:start position:0%
+in solving the electronic Shoring
+ 
+
+ align:start position:0%
+in solving the electronic Shoring
+equation we're going to have the same
+
+ align:start position:0%
+equation we're going to have the same
+ 
+
+ align:start position:0%
+equation we're going to have the same
+problems in molecules as we had in atoms
+
+ align:start position:0%
+problems in molecules as we had in atoms
+ 
+
+ align:start position:0%
+problems in molecules as we had in atoms
+it's not going to be possible to write
+
+ align:start position:0%
+it's not going to be possible to write
+ 
+
+ align:start position:0%
+it's not going to be possible to write
+this as a simple single
+
+ align:start position:0%
+this as a simple single
+ 
+
+ align:start position:0%
+this as a simple single
+configuration you're going to have to do
+
+ align:start position:0%
+configuration you're going to have to do
+ 
+
+ align:start position:0%
+configuration you're going to have to do
+all sorts of complicated things but the
+
+ align:start position:0%
+all sorts of complicated things but the
+ 
+
+ align:start position:0%
+all sorts of complicated things but the
+important thing is if you clamp the
+
+ align:start position:0%
+important thing is if you clamp the
+ 
+
+ align:start position:0%
+important thing is if you clamp the
+nuclei there is a an
+
+ align:start position:0%
+nuclei there is a an
+ 
+
+ align:start position:0%
+nuclei there is a an
+electronic wave function which you could
+
+ align:start position:0%
+electronic wave function which you could
+ 
+
+ align:start position:0%
+electronic wave function which you could
+in principle solve
+
+ align:start position:0%
+in principle solve
+ 
+
+ align:start position:0%
+in principle solve
+for and that's all we care about as
+
+ align:start position:0%
+for and that's all we care about as
+ 
+
+ align:start position:0%
+for and that's all we care about as
+spectroscopist that there is such a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+so we have an operator corresponding to
+
+ align:start position:0%
+so we have an operator corresponding to
+ 
+
+ align:start position:0%
+so we have an operator corresponding to
+the nuclear kinetic energy and that
+
+ align:start position:0%
+the nuclear kinetic energy and that
+ 
+
+ align:start position:0%
+the nuclear kinetic energy and that
+contains both vibration and rotation and
+
+ align:start position:0%
+contains both vibration and rotation and
+ 
+
+ align:start position:0%
+contains both vibration and rotation and
+when we do that we get a wave function
+
+ align:start position:0%
+when we do that we get a wave function
+ 
+
+ align:start position:0%
+when we do that we get a wave function
+electronic wave
+
+ align:start position:0%
+electronic wave
+ 
+
+ align:start position:0%
+electronic wave
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+or and that electronic wave function is
+
+ align:start position:0%
+or and that electronic wave function is
+ 
+
+ align:start position:0%
+or and that electronic wave function is
+a function of electron
+
+ align:start position:0%
+a function of electron
+ 
+
+ align:start position:0%
+a function of electron
+coordinates and it depends on what
+
+ align:start position:0%
+coordinates and it depends on what
+ 
+
+ align:start position:0%
+coordinates and it depends on what
+internuclear distance we chose when we
+
+ align:start position:0%
+internuclear distance we chose when we
+ 
+
+ align:start position:0%
+internuclear distance we chose when we
+nail the poor atoms to the
+
+ align:start position:0%
+nail the poor atoms to the
+ 
+
+ align:start position:0%
+nail the poor atoms to the
+Blackboard and so
+
+ align:start position:0%
+Blackboard and so
+ 
+
+ align:start position:0%
+Blackboard and so
+what we do is
+
+ align:start position:0%
+what we do is
+ 
+
+ align:start position:0%
+what we do is
+uh we choose a series of a grid of
+
+ align:start position:0%
+uh we choose a series of a grid of
+ 
+
+ align:start position:0%
+uh we choose a series of a grid of
+values of R and we get this thing
+
+ align:start position:0%
+values of R and we get this thing
+ 
+
+ align:start position:0%
+values of R and we get this thing
+parametrically dependent on
+
+ align:start position:0%
+parametrically dependent on
+ 
+
+ align:start position:0%
+parametrically dependent on
+R so we have a function of r little r
+
+ align:start position:0%
+R so we have a function of r little r
+ 
+
+ align:start position:0%
+R so we have a function of r little r
+and Big
+
+ align:start position:0%
+and Big
+ 
+
+ align:start position:0%
+and Big
+R and all that you need to do is to
+
+ align:start position:0%
+R and all that you need to do is to
+ 
+
+ align:start position:0%
+R and all that you need to do is to
+think yes it is possible to solve the
+
+ align:start position:0%
+think yes it is possible to solve the
+ 
+
+ align:start position:0%
+think yes it is possible to solve the
+electronic shorter equation at each
+
+ align:start position:0%
+electronic shorter equation at each
+ 
+
+ align:start position:0%
+electronic shorter equation at each
+value of Big
+
+ align:start position:0%
+value of Big
+ 
+
+ align:start position:0%
+value of Big
+R how you solve it doesn't matter that
+
+ align:start position:0%
+R how you solve it doesn't matter that
+ 
+
+ align:start position:0%
+R how you solve it doesn't matter that
+there is such a solution and so at the
+
+ align:start position:0%
+there is such a solution and so at the
+ 
+
+ align:start position:0%
+there is such a solution and so at the
+end you get something which is a
+
+ align:start position:0%
+end you get something which is a
+ 
+
+ align:start position:0%
+end you get something which is a
+function of little r and Big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R so the clamped nuclei shorter
+
+ align:start position:0%
+R so the clamped nuclei shorter
+ 
+
+ align:start position:0%
+R so the clamped nuclei shorter
+equation uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh gives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us electron
+
+ align:start position:0%
+us electron
+ 
+
+ align:start position:0%
+us electron
+energies as a function of Big R and
+
+ align:start position:0%
+energies as a function of Big R and
+ 
+
+ align:start position:0%
+energies as a function of Big R and
+these we call the potential energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve and for polyatomic molecules it's
+
+ align:start position:0%
+curve and for polyatomic molecules it's
+ 
+
+ align:start position:0%
+curve and for polyatomic molecules it's
+pretty much the same thing except now
+
+ align:start position:0%
+pretty much the same thing except now
+ 
+
+ align:start position:0%
+pretty much the same thing except now
+there's several different G geometric
+
+ align:start position:0%
+there's several different G geometric
+ 
+
+ align:start position:0%
+there's several different G geometric
+parameters and you get the potential
+
+ align:start position:0%
+parameters and you get the potential
+ 
+
+ align:start position:0%
+parameters and you get the potential
+energy surface
+
+ align:start position:0%
+energy surface
+ 
+
+ align:start position:0%
+energy surface
+there are a family of related
+
+ align:start position:0%
+there are a family of related
+ 
+
+ align:start position:0%
+there are a family of related
+approximations uh so the clamped nuclei
+
+ align:start position:0%
+approximations uh so the clamped nuclei
+ 
+
+ align:start position:0%
+approximations uh so the clamped nuclei
+approximation is easy to understand but
+
+ align:start position:0%
+approximation is easy to understand but
+ 
+
+ align:start position:0%
+approximation is easy to understand but
+when you approach polyatomic molecules
+
+ align:start position:0%
+when you approach polyatomic molecules
+ 
+
+ align:start position:0%
+when you approach polyatomic molecules
+there are variations on that but
+
+ align:start position:0%
+there are variations on that but
+ 
+
+ align:start position:0%
+there are variations on that but
+okay so when we solve the electronic
+
+ align:start position:0%
+okay so when we solve the electronic
+ 
+
+ align:start position:0%
+okay so when we solve the electronic
+Shing equation there are many different
+
+ align:start position:0%
+Shing equation there are many different
+ 
+
+ align:start position:0%
+Shing equation there are many different
+igen values at each R and so we say that
+
+ align:start position:0%
+igen values at each R and so we say that
+ 
+
+ align:start position:0%
+igen values at each R and so we say that
+there is a potential curve for each such
+
+ align:start position:0%
+there is a potential curve for each such
+ 
+
+ align:start position:0%
+there is a potential curve for each such
+igen value we connect the
+
+ align:start position:0%
+igen value we connect the
+ 
+
+ align:start position:0%
+igen value we connect the
+dots and so we put an i indicating which
+
+ align:start position:0%
+dots and so we put an i indicating which
+ 
+
+ align:start position:0%
+dots and so we put an i indicating which
+electronic State on the potential energy
+
+ align:start position:0%
+electronic State on the potential energy
+ 
+
+ align:start position:0%
+electronic State on the potential energy
+curve v i of R and on the wave
+
+ align:start position:0%
+curve v i of R and on the wave
+ 
+
+ align:start position:0%
+curve v i of R and on the wave
+function so that I says this is a
+
+ align:start position:0%
+function so that I says this is a
+ 
+
+ align:start position:0%
+function so that I says this is a
+particular electronic
+
+ align:start position:0%
+particular electronic
+ 
+
+ align:start position:0%
+particular electronic
+State nuclear not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moving for the I st
+
+ align:start position:0%
+moving for the I st
+ 
+
+ align:start position:0%
+moving for the I st
+uh we then have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so we've we' solved solved the
+
+ align:start position:0%
+um so we've we' solved solved the
+ 
+
+ align:start position:0%
+um so we've we' solved solved the
+electronic part of the problem we have
+
+ align:start position:0%
+electronic part of the problem we have
+ 
+
+ align:start position:0%
+electronic part of the problem we have
+a the I State and we have now a
+
+ align:start position:0%
+a the I State and we have now a
+ 
+
+ align:start position:0%
+a the I State and we have now a
+hamiltonian which is got everything that
+
+ align:start position:0%
+hamiltonian which is got everything that
+ 
+
+ align:start position:0%
+hamiltonian which is got everything that
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+didn't allow for
+
+ align:start position:0%
+didn't allow for
+ 
+
+ align:start position:0%
+didn't allow for
+before so it's the rotation vibration
+
+ align:start position:0%
+before so it's the rotation vibration
+ 
+
+ align:start position:0%
+before so it's the rotation vibration
+ham tonian
+
+ align:start position:0%
+ham tonian
+ 
+
+ align:start position:0%
+ham tonian
+and it's implicitly a function of
+
+ align:start position:0%
+and it's implicitly a function of
+ 
+
+ align:start position:0%
+and it's implicitly a function of
+internuclear distance Theta and F and
+
+ align:start position:0%
+internuclear distance Theta and F and
+ 
+
+ align:start position:0%
+internuclear distance Theta and F and
+what we'd like to do is we like to
+
+ align:start position:0%
+what we'd like to do is we like to
+ 
+
+ align:start position:0%
+what we'd like to do is we like to
+separate this into two parts a
+
+ align:start position:0%
+separate this into two parts a
+ 
+
+ align:start position:0%
+separate this into two parts a
+rotational
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part which depends on Theta and fi and a
+
+ align:start position:0%
+part which depends on Theta and fi and a
+ 
+
+ align:start position:0%
+part which depends on Theta and fi and a
+vibrational
+
+ align:start position:0%
+vibrational
+ 
+
+ align:start position:0%
+vibrational
+part which depends only on R we'd like
+
+ align:start position:0%
+part which depends only on R we'd like
+ 
+
+ align:start position:0%
+part which depends only on R we'd like
+to separ whenever we have a function of
+
+ align:start position:0%
+to separ whenever we have a function of
+ 
+
+ align:start position:0%
+to separ whenever we have a function of
+several variables we'd like to separate
+
+ align:start position:0%
+several variables we'd like to separate
+ 
+
+ align:start position:0%
+several variables we'd like to separate
+it now can we do that now uh um and so
+
+ align:start position:0%
+it now can we do that now uh um and so
+ 
+
+ align:start position:0%
+it now can we do that now uh um and so
+what we do is we say
+
+ align:start position:0%
+what we do is we say
+ 
+
+ align:start position:0%
+what we do is we say
+okay uh we're not going to allow the
+
+ align:start position:0%
+okay uh we're not going to allow the
+ 
+
+ align:start position:0%
+okay uh we're not going to allow the
+molecule to rotate but we are going to
+
+ align:start position:0%
+molecule to rotate but we are going to
+ 
+
+ align:start position:0%
+molecule to rotate but we are going to
+allow it to vibrate or we're not going
+
+ align:start position:0%
+allow it to vibrate or we're not going
+ 
+
+ align:start position:0%
+allow it to vibrate or we're not going
+to allow it to vibrate we're going to
+
+ align:start position:0%
+to allow it to vibrate we're going to
+ 
+
+ align:start position:0%
+to allow it to vibrate we're going to
+allow it to rotate and so we we relax
+
+ align:start position:0%
+allow it to rotate and so we we relax
+ 
+
+ align:start position:0%
+allow it to rotate and so we we relax
+you know we remove the pins but we say
+
+ align:start position:0%
+you know we remove the pins but we say
+ 
+
+ align:start position:0%
+you know we remove the pins but we say
+only one of you know you do only one of
+
+ align:start position:0%
+only one of you know you do only one of
+ 
+
+ align:start position:0%
+only one of you know you do only one of
+these two bad
+
+ align:start position:0%
+these two bad
+ 
+
+ align:start position:0%
+these two bad
+things and uh we then uh can Define
+
+ align:start position:0%
+things and uh we then uh can Define
+ 
+
+ align:start position:0%
+things and uh we then uh can Define
+basis sets and so we have a a set
+
+ align:start position:0%
+basis sets and so we have a a set
+ 
+
+ align:start position:0%
+basis sets and so we have a a set
+of basis
+
+ align:start position:0%
+of basis
+ 
+
+ align:start position:0%
+of basis
+functions which are igen functions
+
+ align:start position:0%
+functions which are igen functions
+ 
+
+ align:start position:0%
+functions which are igen functions
+of J little Z the projection of J on the
+
+ align:start position:0%
+of J little Z the projection of J on the
+ 
+
+ align:start position:0%
+of J little Z the projection of J on the
+body axis j s and J big Z which which is
+
+ align:start position:0%
+body axis j s and J big Z which which is
+ 
+
+ align:start position:0%
+body axis j s and J big Z which which is
+the projection of J in the laboratory
+
+ align:start position:0%
+the projection of J in the laboratory
+ 
+
+ align:start position:0%
+the projection of J in the laboratory
+and so these are this is I fun igen
+
+ align:start position:0%
+and so these are this is I fun igen
+ 
+
+ align:start position:0%
+and so these are this is I fun igen
+value of JZ this is J squared this is JZ
+
+ align:start position:0%
+value of JZ this is J squared this is JZ
+ 
+
+ align:start position:0%
+value of JZ this is J squared this is JZ
+okay so we have a set of
+
+ align:start position:0%
+okay so we have a set of
+ 
+
+ align:start position:0%
+okay so we have a set of
+functions and those are Universal
+
+ align:start position:0%
+functions and those are Universal
+ 
+
+ align:start position:0%
+functions and those are Universal
+functions these are angular momentum
+
+ align:start position:0%
+functions these are angular momentum
+ 
+
+ align:start position:0%
+functions these are angular momentum
+functions and so it these functions
+
+ align:start position:0%
+functions and so it these functions
+ 
+
+ align:start position:0%
+functions and so it these functions
+don't depend on anything except the isot
+
+ align:start position:0%
+don't depend on anything except the isot
+ 
+
+ align:start position:0%
+don't depend on anything except the isot
+isotropy of space so we have these these
+
+ align:start position:0%
+isotropy of space so we have these these
+ 
+
+ align:start position:0%
+isotropy of space so we have these these
+functions and we're going to use them to
+
+ align:start position:0%
+functions and we're going to use them to
+ 
+
+ align:start position:0%
+functions and we're going to use them to
+simplify the
+
+ align:start position:0%
+simplify the
+ 
+
+ align:start position:0%
+simplify the
+electronic uh
+
+ align:start position:0%
+electronic uh
+ 
+
+ align:start position:0%
+electronic uh
+the the separation of variables okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to say we have a
+
+ align:start position:0%
+so we're going to say we have a
+ 
+
+ align:start position:0%
+so we're going to say we have a
+rotational hamiltonian and somehow we're
+
+ align:start position:0%
+rotational hamiltonian and somehow we're
+ 
+
+ align:start position:0%
+rotational hamiltonian and somehow we're
+going to we're going to look at the
+
+ align:start position:0%
+going to we're going to look at the
+ 
+
+ align:start position:0%
+going to we're going to look at the
+rotational hamiltonian and we're going
+
+ align:start position:0%
+rotational hamiltonian and we're going
+ 
+
+ align:start position:0%
+rotational hamiltonian and we're going
+to use these things to evaluate Matrix
+
+ align:start position:0%
+to use these things to evaluate Matrix
+ 
+
+ align:start position:0%
+to use these things to evaluate Matrix
+elements of it
+
+ align:start position:0%
+elements of it
+ 
+
+ align:start position:0%
+elements of it
+now this thing has to be
+
+ align:start position:0%
+now this thing has to be
+ 
+
+ align:start position:0%
+now this thing has to be
+simplified we have we're going to throw
+
+ align:start position:0%
+simplified we have we're going to throw
+ 
+
+ align:start position:0%
+simplified we have we're going to throw
+away certain terms here and you'll see
+
+ align:start position:0%
+away certain terms here and you'll see
+ 
+
+ align:start position:0%
+away certain terms here and you'll see
+how this this works okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh we're going to define a
+
+ align:start position:0%
+so uh we're going to define a
+ 
+
+ align:start position:0%
+so uh we're going to define a
+function a potential energy curve which
+
+ align:start position:0%
+function a potential energy curve which
+ 
+
+ align:start position:0%
+function a potential energy curve which
+what we had before and but this
+
+ align:start position:0%
+what we had before and but this
+ 
+
+ align:start position:0%
+what we had before and but this
+potential energy curve is going to have
+
+ align:start position:0%
+potential energy curve is going to have
+ 
+
+ align:start position:0%
+potential energy curve is going to have
+two more uh indices on it
+
+ align:start position:0%
+two more uh indices on it
+ 
+
+ align:start position:0%
+two more uh indices on it
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh that will be VI I of R plus
+
+ align:start position:0%
+uh that will be VI I of R plus
+ 
+
+ align:start position:0%
+uh that will be VI I of R plus
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r j + 1 - Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 okay so here remember for atoms we had
+
+ align:start position:0%
+2 okay so here remember for atoms we had
+ 
+
+ align:start position:0%
+2 okay so here remember for atoms we had
+the bare potential
+
+ align:start position:0%
+the bare potential
+ 
+
+ align:start position:0%
+the bare potential
+and a centrifugal term and here we have
+
+ align:start position:0%
+and a centrifugal term and here we have
+ 
+
+ align:start position:0%
+and a centrifugal term and here we have
+a centrifugal an effective or uh
+
+ align:start position:0%
+a centrifugal an effective or uh
+ 
+
+ align:start position:0%
+a centrifugal an effective or uh
+potential which is the clamped uh
+
+ align:start position:0%
+potential which is the clamped uh
+ 
+
+ align:start position:0%
+potential which is the clamped uh
+nuclei potential energy curve something
+
+ align:start position:0%
+nuclei potential energy curve something
+ 
+
+ align:start position:0%
+nuclei potential energy curve something
+we got from solving the electronic shary
+
+ align:start position:0%
+we got from solving the electronic shary
+ 
+
+ align:start position:0%
+we got from solving the electronic shary
+equation at a series of points and then
+
+ align:start position:0%
+equation at a series of points and then
+ 
+
+ align:start position:0%
+equation at a series of points and then
+connecting them and then we have the
+
+ align:start position:0%
+connecting them and then we have the
+ 
+
+ align:start position:0%
+connecting them and then we have the
+rotational contribution to it which
+
+ align:start position:0%
+rotational contribution to it which
+ 
+
+ align:start position:0%
+rotational contribution to it which
+depends on some quantum numbers and so
+
+ align:start position:0%
+depends on some quantum numbers and so
+ 
+
+ align:start position:0%
+depends on some quantum numbers and so
+for each value of J and Omega we
+
+ align:start position:0%
+for each value of J and Omega we
+ 
+
+ align:start position:0%
+for each value of J and Omega we
+have a slightly
+
+ align:start position:0%
+have a slightly
+ 
+
+ align:start position:0%
+have a slightly
+different uh
+
+ align:start position:0%
+different uh
+ 
+
+ align:start position:0%
+different uh
+nuclear uh potential
+
+ align:start position:0%
+nuclear uh potential
+ 
+
+ align:start position:0%
+nuclear uh potential
+energy this is usually a a very minor
+
+ align:start position:0%
+energy this is usually a a very minor
+ 
+
+ align:start position:0%
+energy this is usually a a very minor
+thing but it's implicitly there and so
+
+ align:start position:0%
+thing but it's implicitly there and so
+ 
+
+ align:start position:0%
+thing but it's implicitly there and so
+we are going to get since this is the
+
+ align:start position:0%
+we are going to get since this is the
+ 
+
+ align:start position:0%
+we are going to get since this is the
+potential curve the potential curve and
+
+ align:start position:0%
+potential curve the potential curve and
+ 
+
+ align:start position:0%
+potential curve the potential curve and
+the kinetic energy is uh uh uh the
+
+ align:start position:0%
+the kinetic energy is uh uh uh the
+ 
+
+ align:start position:0%
+the kinetic energy is uh uh uh the
+nuclear kinetic energy we're going to
+
+ align:start position:0%
+nuclear kinetic energy we're going to
+ 
+
+ align:start position:0%
+nuclear kinetic energy we're going to
+get uh a set of basis functions for the
+
+ align:start position:0%
+get uh a set of basis functions for the
+ 
+
+ align:start position:0%
+get uh a set of basis functions for the
+vibration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which have this form so they are for
+
+ align:start position:0%
+which have this form so they are for
+ 
+
+ align:start position:0%
+which have this form so they are for
+each electronic State there's going to
+
+ align:start position:0%
+each electronic State there's going to
+ 
+
+ align:start position:0%
+each electronic State there's going to
+be a family of vibrational levels and
+
+ align:start position:0%
+be a family of vibrational levels and
+ 
+
+ align:start position:0%
+be a family of vibrational levels and
+unfortunately each vibrational level or
+
+ align:start position:0%
+unfortunately each vibrational level or
+ 
+
+ align:start position:0%
+unfortunately each vibrational level or
+state has a j and Omega dependence which
+
+ align:start position:0%
+state has a j and Omega dependence which
+ 
+
+ align:start position:0%
+state has a j and Omega dependence which
+we are going to ignore but it's there so
+
+ align:start position:0%
+we are going to ignore but it's there so
+ 
+
+ align:start position:0%
+we are going to ignore but it's there so
+we have to do something to make that go
+
+ align:start position:0%
+we have to do something to make that go
+ 
+
+ align:start position:0%
+we have to do something to make that go
+away or we have to at least be aware
+
+ align:start position:0%
+away or we have to at least be aware
+ 
+
+ align:start position:0%
+away or we have to at least be aware
+that they the the wave functions we
+
+ align:start position:0%
+that they the the wave functions we
+ 
+
+ align:start position:0%
+that they the the wave functions we
+Define are igen functions of this and
+
+ align:start position:0%
+Define are igen functions of this and
+ 
+
+ align:start position:0%
+Define are igen functions of this and
+they do depend on an operator some
+
+ align:start position:0%
+they do depend on an operator some
+ 
+
+ align:start position:0%
+they do depend on an operator some
+function of internuclear distance and
+
+ align:start position:0%
+function of internuclear distance and
+ 
+
+ align:start position:0%
+function of internuclear distance and
+quantum numbers here so to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be and then once we've done all this we
+
+ align:start position:0%
+be and then once we've done all this we
+ 
+
+ align:start position:0%
+be and then once we've done all this we
+uh want to get the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exact wave function and the exact wave
+
+ align:start position:0%
+exact wave function and the exact wave
+ 
+
+ align:start position:0%
+exact wave function and the exact wave
+function uh we use these basis functions
+
+ align:start position:0%
+function uh we use these basis functions
+ 
+
+ align:start position:0%
+function uh we use these basis functions
+the vibrational and uh rotational basis
+
+ align:start position:0%
+the vibrational and uh rotational basis
+ 
+
+ align:start position:0%
+the vibrational and uh rotational basis
+functions in order to calculate Matrix
+
+ align:start position:0%
+functions in order to calculate Matrix
+ 
+
+ align:start position:0%
+functions in order to calculate Matrix
+elements of all of the things that we've
+
+ align:start position:0%
+elements of all of the things that we've
+ 
+
+ align:start position:0%
+elements of all of the things that we've
+had to throw away along the
+
+ align:start position:0%
+had to throw away along the
+ 
+
+ align:start position:0%
+had to throw away along the
+way okay this is this is a very boring
+
+ align:start position:0%
+way okay this is this is a very boring
+ 
+
+ align:start position:0%
+way okay this is this is a very boring
+formal lecture uh and so you could chear
+
+ align:start position:0%
+formal lecture uh and so you could chear
+ 
+
+ align:start position:0%
+formal lecture uh and so you could chear
+me up and yourselves up by asking
+
+ align:start position:0%
+me up and yourselves up by asking
+ 
+
+ align:start position:0%
+me up and yourselves up by asking
+questions okay so let's uh let's begin
+
+ align:start position:0%
+questions okay so let's uh let's begin
+ 
+
+ align:start position:0%
+questions okay so let's uh let's begin
+this this uh analysis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the hamiltonian can be written as
+
+ align:start position:0%
+the hamiltonian can be written as
+ 
+
+ align:start position:0%
+the hamiltonian can be written as
+kinetic energy of the electrons plus
+
+ align:start position:0%
+kinetic energy of the electrons plus
+ 
+
+ align:start position:0%
+kinetic energy of the electrons plus
+kinetic energy of the nucle N neutrons
+
+ align:start position:0%
+kinetic energy of the nucle N neutrons
+ 
+
+ align:start position:0%
+kinetic energy of the nucle N neutrons
+plus the potential energy associated
+
+ align:start position:0%
+plus the potential energy associated
+ 
+
+ align:start position:0%
+plus the potential energy associated
+with the electron nuclear interactions
+
+ align:start position:0%
+with the electron nuclear interactions
+ 
+
+ align:start position:0%
+with the electron nuclear interactions
+potential energy of the interaction
+
+ align:start position:0%
+potential energy of the interaction
+ 
+
+ align:start position:0%
+potential energy of the interaction
+between nuclei and we have the inter
+
+ align:start position:0%
+between nuclei and we have the inter
+ 
+
+ align:start position:0%
+between nuclei and we have the inter
+electronic term so these are all the
+
+ align:start position:0%
+electronic term so these are all the
+ 
+
+ align:start position:0%
+electronic term so these are all the
+terms in the
+
+ align:start position:0%
+terms in the
+ 
+
+ align:start position:0%
+terms in the
+hamiltonian and the electronic
+
+ align:start position:0%
+hamiltonian and the electronic
+ 
+
+ align:start position:0%
+hamiltonian and the electronic
+term is written in the usual way p i s
+
+ align:start position:0%
+term is written in the usual way p i s
+ 
+
+ align:start position:0%
+term is written in the usual way p i s
+the electron kinetic momentum over uh
+
+ align:start position:0%
+the electron kinetic momentum over uh
+ 
+
+ align:start position:0%
+the electron kinetic momentum over uh
+two mass of the
+
+ align:start position:0%
+two mass of the
+ 
+
+ align:start position:0%
+two mass of the
+electron and uh uh that becomes
+
+ align:start position:0%
+electron and uh uh that becomes
+ 
+
+ align:start position:0%
+electron and uh uh that becomes
+minus d^
+
+ align:start position:0%
+minus d^
+ 
+
+ align:start position:0%
+minus d^
+s uh I some
+
+ align:start position:0%
+s uh I some
+ 
+
+ align:start position:0%
+s uh I some
+I and we have some H bar squared over to
+
+ align:start position:0%
+I and we have some H bar squared over to
+ 
+
+ align:start position:0%
+I and we have some H bar squared over to
+mass of the electron so we have a second
+
+ align:start position:0%
+mass of the electron so we have a second
+ 
+
+ align:start position:0%
+mass of the electron so we have a second
+derivative uh with respect to the
+
+ align:start position:0%
+derivative uh with respect to the
+ 
+
+ align:start position:0%
+derivative uh with respect to the
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+coordinate Carol I had a question about
+
+ align:start position:0%
+coordinate Carol I had a question about
+ 
+
+ align:start position:0%
+coordinate Carol I had a question about
+the formula yes that b constant which is
+
+ align:start position:0%
+the formula yes that b constant which is
+ 
+
+ align:start position:0%
+the formula yes that b constant which is
+not constant but sort of continuous
+
+ align:start position:0%
+not constant but sort of continuous
+ 
+
+ align:start position:0%
+not constant but sort of continuous
+function of r is it
+
+ align:start position:0%
+function of r is it
+ 
+
+ align:start position:0%
+function of r is it
+uh is there a principal difference uh in
+
+ align:start position:0%
+uh is there a principal difference uh in
+ 
+
+ align:start position:0%
+uh is there a principal difference uh in
+defining it as a continuous function of
+
+ align:start position:0%
+defining it as a continuous function of
+ 
+
+ align:start position:0%
+defining it as a continuous function of
+r versus defining it as a function of
+
+ align:start position:0%
+r versus defining it as a function of
+ 
+
+ align:start position:0%
+r versus defining it as a function of
+vibrational quantum number well
+
+ align:start position:0%
+vibrational quantum number well
+ 
+
+ align:start position:0%
+vibrational quantum number well
+uh any function of
+
+ align:start position:0%
+uh any function of
+ 
+
+ align:start position:0%
+uh any function of
+r i mean suppose you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this you just say okay we have a
+
+ align:start position:0%
+this you just say okay we have a
+ 
+
+ align:start position:0%
+this you just say okay we have a
+function of r we'd like to have it as a
+
+ align:start position:0%
+function of r we'd like to have it as a
+ 
+
+ align:start position:0%
+function of r we'd like to have it as a
+function of quantum number we just
+
+ align:start position:0%
+function of quantum number we just
+ 
+
+ align:start position:0%
+function of quantum number we just
+calculate the expectation value if if we
+
+ align:start position:0%
+calculate the expectation value if if we
+ 
+
+ align:start position:0%
+calculate the expectation value if if we
+know what the vibrational wave functions
+
+ align:start position:0%
+know what the vibrational wave functions
+ 
+
+ align:start position:0%
+know what the vibrational wave functions
+are and we know the r dependence of this
+
+ align:start position:0%
+are and we know the r dependence of this
+ 
+
+ align:start position:0%
+are and we know the r dependence of this
+thing well then it becomes a trivial
+
+ align:start position:0%
+thing well then it becomes a trivial
+ 
+
+ align:start position:0%
+thing well then it becomes a trivial
+matter to write the V dependence of it
+
+ align:start position:0%
+matter to write the V dependence of it
+ 
+
+ align:start position:0%
+matter to write the V dependence of it
+and so you know you you start out by
+
+ align:start position:0%
+and so you know you you start out by
+ 
+
+ align:start position:0%
+and so you know you you start out by
+writing things in operator form and then
+
+ align:start position:0%
+writing things in operator form and then
+ 
+
+ align:start position:0%
+writing things in operator form and then
+you you you do various integrals over
+
+ align:start position:0%
+you you you do various integrals over
+ 
+
+ align:start position:0%
+you you you do various integrals over
+them to simplify them or reduce them to
+
+ align:start position:0%
+them to simplify them or reduce them to
+ 
+
+ align:start position:0%
+them to simplify them or reduce them to
+things that operate in a particular
+
+ align:start position:0%
+things that operate in a particular
+ 
+
+ align:start position:0%
+things that operate in a particular
+Subspace other cases where it's not
+
+ align:start position:0%
+Subspace other cases where it's not
+ 
+
+ align:start position:0%
+Subspace other cases where it's not
+possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I I think the answer is
+
+ align:start position:0%
+uh I I think the answer is
+ 
+
+ align:start position:0%
+uh I I think the answer is
+no uh it may be that when you uh when
+
+ align:start position:0%
+no uh it may be that when you uh when
+ 
+
+ align:start position:0%
+no uh it may be that when you uh when
+you are dealing with a real problem
+
+ align:start position:0%
+you are dealing with a real problem
+ 
+
+ align:start position:0%
+you are dealing with a real problem
+there are many interactions between
+
+ align:start position:0%
+there are many interactions between
+ 
+
+ align:start position:0%
+there are many interactions between
+different electronic states which make
+
+ align:start position:0%
+different electronic states which make
+ 
+
+ align:start position:0%
+different electronic states which make
+this uh a part of an exceedingly
+
+ align:start position:0%
+this uh a part of an exceedingly
+ 
+
+ align:start position:0%
+this uh a part of an exceedingly
+complicated analysis but it's always
+
+ align:start position:0%
+complicated analysis but it's always
+ 
+
+ align:start position:0%
+complicated analysis but it's always
+possible you know to say we have a
+
+ align:start position:0%
+possible you know to say we have a
+ 
+
+ align:start position:0%
+possible you know to say we have a
+potential curve we Define that by doing
+
+ align:start position:0%
+potential curve we Define that by doing
+ 
+
+ align:start position:0%
+potential curve we Define that by doing
+this clamp nuclei approach and so from
+
+ align:start position:0%
+this clamp nuclei approach and so from
+ 
+
+ align:start position:0%
+this clamp nuclei approach and so from
+that potential curve we can get wave
+
+ align:start position:0%
+that potential curve we can get wave
+ 
+
+ align:start position:0%
+that potential curve we can get wave
+functions and so we can always do this
+
+ align:start position:0%
+functions and so we can always do this
+ 
+
+ align:start position:0%
+functions and so we can always do this
+but sometimes the potential curves you
+
+ align:start position:0%
+but sometimes the potential curves you
+ 
+
+ align:start position:0%
+but sometimes the potential curves you
+get by this clamped nuclei
+
+ align:start position:0%
+get by this clamped nuclei
+ 
+
+ align:start position:0%
+get by this clamped nuclei
+approximation are incredibly far from
+
+ align:start position:0%
+approximation are incredibly far from
+ 
+
+ align:start position:0%
+approximation are incredibly far from
+the truth they're the truth they they
+
+ align:start position:0%
+the truth they're the truth they they
+ 
+
+ align:start position:0%
+the truth they're the truth they they
+are they're right but you have to do a
+
+ align:start position:0%
+are they're right but you have to do a
+ 
+
+ align:start position:0%
+are they're right but you have to do a
+huge amount of calculations because uh
+
+ align:start position:0%
+huge amount of calculations because uh
+ 
+
+ align:start position:0%
+huge amount of calculations because uh
+the adiabetic approximation is grossly
+
+ align:start position:0%
+the adiabetic approximation is grossly
+ 
+
+ align:start position:0%
+the adiabetic approximation is grossly
+wrong due to a weakly avoided Crossing
+
+ align:start position:0%
+wrong due to a weakly avoided Crossing
+ 
+
+ align:start position:0%
+wrong due to a weakly avoided Crossing
+you know some but we'll get to that
+
+ align:start position:0%
+you know some but we'll get to that
+ 
+
+ align:start position:0%
+you know some but we'll get to that
+so it's always possible to do this but
+
+ align:start position:0%
+so it's always possible to do this but
+ 
+
+ align:start position:0%
+so it's always possible to do this but
+sometimes it's not very smart to do this
+
+ align:start position:0%
+sometimes it's not very smart to do this
+ 
+
+ align:start position:0%
+sometimes it's not very smart to do this
+or it's not smart to use the adiabatic
+
+ align:start position:0%
+or it's not smart to use the adiabatic
+ 
+
+ align:start position:0%
+or it's not smart to use the adiabatic
+approach uh and then you still do
+
+ align:start position:0%
+approach uh and then you still do
+ 
+
+ align:start position:0%
+approach uh and then you still do
+something like this but you're doing it
+
+ align:start position:0%
+something like this but you're doing it
+ 
+
+ align:start position:0%
+something like this but you're doing it
+for the diabetic
+
+ align:start position:0%
+for the diabetic
+ 
+
+ align:start position:0%
+for the diabetic
+potentials and so you know the thing
+
+ align:start position:0%
+potentials and so you know the thing
+ 
+
+ align:start position:0%
+potentials and so you know the thing
+that you want to come away from in this
+
+ align:start position:0%
+that you want to come away from in this
+ 
+
+ align:start position:0%
+that you want to come away from in this
+lecture is to understand what went into
+
+ align:start position:0%
+lecture is to understand what went into
+ 
+
+ align:start position:0%
+lecture is to understand what went into
+the adiabetic approximation and if I get
+
+ align:start position:0%
+the adiabetic approximation and if I get
+ 
+
+ align:start position:0%
+the adiabetic approximation and if I get
+to the end then I'll I'll I'll talk
+
+ align:start position:0%
+to the end then I'll I'll I'll talk
+ 
+
+ align:start position:0%
+to the end then I'll I'll I'll talk
+about okay well when is the adiabatic
+
+ align:start position:0%
+about okay well when is the adiabatic
+ 
+
+ align:start position:0%
+about okay well when is the adiabatic
+picture a bad picture and when do you
+
+ align:start position:0%
+picture a bad picture and when do you
+ 
+
+ align:start position:0%
+picture a bad picture and when do you
+how how do you go to the diabetic the
+
+ align:start position:0%
+how how do you go to the diabetic the
+ 
+
+ align:start position:0%
+how how do you go to the diabetic the
+opposite of adiabetic and why
+
+ align:start position:0%
+opposite of adiabetic and why
+ 
+
+ align:start position:0%
+opposite of adiabetic and why
+I'm sure I'm not going to get there
+
+ align:start position:0%
+I'm sure I'm not going to get there
+ 
+
+ align:start position:0%
+I'm sure I'm not going to get there
+because I'm going very
+
+ align:start position:0%
+because I'm going very
+ 
+
+ align:start position:0%
+because I'm going very
+slowly um so we have this hamoni
+
+ align:start position:0%
+slowly um so we have this hamoni
+ 
+
+ align:start position:0%
+slowly um so we have this hamoni
+consisting of many terms uh and uh this
+
+ align:start position:0%
+consisting of many terms uh and uh this
+ 
+
+ align:start position:0%
+consisting of many terms uh and uh this
+one is kind of trivial we have the
+
+ align:start position:0%
+one is kind of trivial we have the
+ 
+
+ align:start position:0%
+one is kind of trivial we have the
+nuclear uh kinetic energy term and so
+
+ align:start position:0%
+nuclear uh kinetic energy term and so
+ 
+
+ align:start position:0%
+nuclear uh kinetic energy term and so
+that uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we were talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diatomics and so that's the nuclear
+
+ align:start position:0%
+diatomics and so that's the nuclear
+ 
+
+ align:start position:0%
+diatomics and so that's the nuclear
+kinetic energy and uh but we often write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it as a function of r Theta and F and
+
+ align:start position:0%
+it as a function of r Theta and F and
+ 
+
+ align:start position:0%
+it as a function of r Theta and F and
+and what we end up getting is a nuclear
+
+ align:start position:0%
+and what we end up getting is a nuclear
+ 
+
+ align:start position:0%
+and what we end up getting is a nuclear
+term which depends on
+
+ align:start position:0%
+term which depends on
+ 
+
+ align:start position:0%
+term which depends on
+R and a rotational
+
+ align:start position:0%
+R and a rotational
+ 
+
+ align:start position:0%
+R and a rotational
+term which depends on R parametrically
+
+ align:start position:0%
+term which depends on R parametrically
+ 
+
+ align:start position:0%
+term which depends on R parametrically
+in Theta F just analogous to the borne
+
+ align:start position:0%
+in Theta F just analogous to the borne
+ 
+
+ align:start position:0%
+in Theta F just analogous to the borne
+Oppenheimer we pull out something and
+
+ align:start position:0%
+Oppenheimer we pull out something and
+ 
+
+ align:start position:0%
+Oppenheimer we pull out something and
+this is this is the radial kinetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy it corresponds
+
+ align:start position:0%
+energy it corresponds
+ 
+
+ align:start position:0%
+energy it corresponds
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+uh d s of this radial thing and this is
+
+ align:start position:0%
+uh d s of this radial thing and this is
+ 
+
+ align:start position:0%
+uh d s of this radial thing and this is
+where we get into trouble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and
+
+ align:start position:0%
+okay and
+ 
+
+ align:start position:0%
+okay and
+uh and so this rotational term it has
+
+ align:start position:0%
+uh and so this rotational term it has
+ 
+
+ align:start position:0%
+uh and so this rotational term it has
+the uh the Theta F dependence and the
+
+ align:start position:0%
+the uh the Theta F dependence and the
+ 
+
+ align:start position:0%
+the uh the Theta F dependence and the
+rotational uh hamiltonian can has to has
+
+ align:start position:0%
+rotational uh hamiltonian can has to has
+ 
+
+ align:start position:0%
+rotational uh hamiltonian can has to has
+to depend on inter nuclear
+
+ align:start position:0%
+to depend on inter nuclear
+ 
+
+ align:start position:0%
+to depend on inter nuclear
+distance okay so the rotational term so
+
+ align:start position:0%
+distance okay so the rotational term so
+ 
+
+ align:start position:0%
+distance okay so the rotational term so
+we already are starting to unclamp the
+
+ align:start position:0%
+we already are starting to unclamp the
+ 
+
+ align:start position:0%
+we already are starting to unclamp the
+nuclei and we're saying okay the there's
+
+ align:start position:0%
+nuclei and we're saying okay the there's
+ 
+
+ align:start position:0%
+nuclei and we're saying okay the there's
+two terms and initially we're going to
+
+ align:start position:0%
+two terms and initially we're going to
+ 
+
+ align:start position:0%
+two terms and initially we're going to
+suppress this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay but the rotational term has the
+
+ align:start position:0%
+one okay but the rotational term has the
+ 
+
+ align:start position:0%
+one okay but the rotational term has the
+form - h bar^ 2/ 2 mu R 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have a notational problem this is
+
+ align:start position:0%
+we have a notational problem this is
+ 
+
+ align:start position:0%
+we have a notational problem this is
+internuclear distance and this is
+
+ align:start position:0%
+internuclear distance and this is
+ 
+
+ align:start position:0%
+internuclear distance and this is
+nuclear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation
+
+ align:start position:0%
+rotation
+ 
+
+ align:start position:0%
+rotation
+unfortunately we call the rotational
+
+ align:start position:0%
+unfortunately we call the rotational
+ 
+
+ align:start position:0%
+unfortunately we call the rotational
+angular momentum of the bare nuclei
+
+ align:start position:0%
+angular momentum of the bare nuclei
+ 
+
+ align:start position:0%
+angular momentum of the bare nuclei
+are but we we we get rid of this really
+
+ align:start position:0%
+are but we we we get rid of this really
+ 
+
+ align:start position:0%
+are but we we we get rid of this really
+really fast because we always rewrite
+
+ align:start position:0%
+really fast because we always rewrite
+ 
+
+ align:start position:0%
+really fast because we always rewrite
+this thing and in terms of more familiar
+
+ align:start position:0%
+this thing and in terms of more familiar
+ 
+
+ align:start position:0%
+this thing and in terms of more familiar
+angular momenta
+
+ align:start position:0%
+angular momenta
+ 
+
+ align:start position:0%
+angular momenta
+but notationally that's what we're stuck
+
+ align:start position:0%
+but notationally that's what we're stuck
+ 
+
+ align:start position:0%
+but notationally that's what we're stuck
+with and so
+
+ align:start position:0%
+with and so
+ 
+
+ align:start position:0%
+with and so
+R is J - l -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s so this is the bare nuclei uh angular
+
+ align:start position:0%
+s so this is the bare nuclei uh angular
+ 
+
+ align:start position:0%
+s so this is the bare nuclei uh angular
+momentum this is the total angular
+
+ align:start position:0%
+momentum this is the total angular
+ 
+
+ align:start position:0%
+momentum this is the total angular
+momentum this is the electron orbital
+
+ align:start position:0%
+momentum this is the electron orbital
+ 
+
+ align:start position:0%
+momentum this is the electron orbital
+angular momentum this is a spin Orit
+
+ align:start position:0%
+angular momentum this is a spin Orit
+ 
+
+ align:start position:0%
+angular momentum this is a spin Orit
+spin angular momentum and this is a
+
+ align:start position:0%
+spin angular momentum and this is a
+ 
+
+ align:start position:0%
+spin angular momentum and this is a
+vector equation this is a correct
+
+ align:start position:0%
+vector equation this is a correct
+ 
+
+ align:start position:0%
+vector equation this is a correct
+equation um and uh
+
+ align:start position:0%
+equation um and uh
+ 
+
+ align:start position:0%
+equation um and uh
+there is one useful thing about this for
+
+ align:start position:0%
+there is one useful thing about this for
+ 
+
+ align:start position:0%
+there is one useful thing about this for
+diatomic molecules this guy is
+
+ align:start position:0%
+diatomic molecules this guy is
+ 
+
+ align:start position:0%
+diatomic molecules this guy is
+necessarily perpendicular to the
+
+ align:start position:0%
+necessarily perpendicular to the
+ 
+
+ align:start position:0%
+necessarily perpendicular to the
+internuclear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axis which is what leads to this
+
+ align:start position:0%
+axis which is what leads to this
+ 
+
+ align:start position:0%
+axis which is what leads to this
+ambiguity of uh
+
+ align:start position:0%
+ambiguity of uh
+ 
+
+ align:start position:0%
+ambiguity of uh
+um uh of that third Oiler angle because
+
+ align:start position:0%
+um uh of that third Oiler angle because
+ 
+
+ align:start position:0%
+um uh of that third Oiler angle because
+you don't need it but it's implicitly
+
+ align:start position:0%
+you don't need it but it's implicitly
+ 
+
+ align:start position:0%
+you don't need it but it's implicitly
+there and so uh there is no projection
+
+ align:start position:0%
+there and so uh there is no projection
+ 
+
+ align:start position:0%
+there and so uh there is no projection
+of this on the body frame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this does project into the laboratory
+
+ align:start position:0%
+this does project into the laboratory
+ 
+
+ align:start position:0%
+this does project into the laboratory
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so excuse
+
+ align:start position:0%
+so excuse
+ 
+
+ align:start position:0%
+so excuse
+me uh so anyway there this is an angular
+
+ align:start position:0%
+me uh so anyway there this is an angular
+ 
+
+ align:start position:0%
+me uh so anyway there this is an angular
+momentum we're going to be doing stuff
+
+ align:start position:0%
+momentum we're going to be doing stuff
+ 
+
+ align:start position:0%
+momentum we're going to be doing stuff
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+it and mu is the reduced Mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so there's a lot of stuff here that
+
+ align:start position:0%
+okay so there's a lot of stuff here that
+ 
+
+ align:start position:0%
+okay so there's a lot of stuff here that
+uh I'm going to skip over but we we have
+
+ align:start position:0%
+uh I'm going to skip over but we we have
+ 
+
+ align:start position:0%
+uh I'm going to skip over but we we have
+two coordinate systems that we're
+
+ align:start position:0%
+two coordinate systems that we're
+ 
+
+ align:start position:0%
+two coordinate systems that we're
+concerned
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with and we use capital letters for the
+
+ align:start position:0%
+with and we use capital letters for the
+ 
+
+ align:start position:0%
+with and we use capital letters for the
+laboratory projections and lowercase
+
+ align:start position:0%
+laboratory projections and lowercase
+ 
+
+ align:start position:0%
+laboratory projections and lowercase
+letters for body fix projections
+
+ align:start position:0%
+letters for body fix projections
+ 
+
+ align:start position:0%
+letters for body fix projections
+and uh we're going to see uh we're going
+
+ align:start position:0%
+and uh we're going to see uh we're going
+ 
+
+ align:start position:0%
+and uh we're going to see uh we're going
+to look at things like this now we want
+
+ align:start position:0%
+to look at things like this now we want
+ 
+
+ align:start position:0%
+to look at things like this now we want
+to write the hamiltonian now is a
+
+ align:start position:0%
+to write the hamiltonian now is a
+ 
+
+ align:start position:0%
+to write the hamiltonian now is a
+function of an electronic factor a
+
+ align:start position:0%
+function of an electronic factor a
+ 
+
+ align:start position:0%
+function of an electronic factor a
+vibrational factor and a rotational
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+factor and we're going to write the
+
+ align:start position:0%
+factor and we're going to write the
+ 
+
+ align:start position:0%
+factor and we're going to write the
+energies as
+
+ align:start position:0%
+energies as
+ 
+
+ align:start position:0%
+energies as
+uh the electronic vibration rotation and
+
+ align:start position:0%
+uh the electronic vibration rotation and
+ 
+
+ align:start position:0%
+uh the electronic vibration rotation and
+we could even even include spin in there
+
+ align:start position:0%
+we could even even include spin in there
+ 
+
+ align:start position:0%
+we could even even include spin in there
+we wanted to as
+
+ align:start position:0%
+we wanted to as
+ 
+
+ align:start position:0%
+we wanted to as
+ti+
+
+ align:start position:0%
+ti+
+ 
+
+ align:start position:0%
+ti+
+g v+ f i v j this is our goal and we're
+
+ align:start position:0%
+g v+ f i v j this is our goal and we're
+ 
+
+ align:start position:0%
+g v+ f i v j this is our goal and we're
+we're going to achieve this goal very
+
+ align:start position:0%
+we're going to achieve this goal very
+ 
+
+ align:start position:0%
+we're going to achieve this goal very
+soon and the wave function if we can
+
+ align:start position:0%
+soon and the wave function if we can
+ 
+
+ align:start position:0%
+soon and the wave function if we can
+write this hamiltonian in this way by
+
+ align:start position:0%
+write this hamiltonian in this way by
+ 
+
+ align:start position:0%
+write this hamiltonian in this way by
+making clever approximations then the
+
+ align:start position:0%
+making clever approximations then the
+ 
+
+ align:start position:0%
+making clever approximations then the
+wave function is going to be expressed
+
+ align:start position:0%
+wave function is going to be expressed
+ 
+
+ align:start position:0%
+wave function is going to be expressed
+as an electronic
+
+ align:start position:0%
+as an electronic
+ 
+
+ align:start position:0%
+as an electronic
+factor a vibrational Factor uh
+
+ align:start position:0%
+factor a vibrational Factor uh
+ 
+
+ align:start position:0%
+factor a vibrational Factor uh
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+uh and a rotational Factor so this is
+
+ align:start position:0%
+uh and a rotational Factor so this is
+ 
+
+ align:start position:0%
+uh and a rotational Factor so this is
+the kind of thing we're hoping to to do
+
+ align:start position:0%
+the kind of thing we're hoping to to do
+ 
+
+ align:start position:0%
+the kind of thing we're hoping to to do
+and we'll do anything anything at all in
+
+ align:start position:0%
+and we'll do anything anything at all in
+ 
+
+ align:start position:0%
+and we'll do anything anything at all in
+order to achieve this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goal including
+
+ align:start position:0%
+goal including
+ 
+
+ align:start position:0%
+goal including
+lying
+
+ align:start position:0%
+lying
+ 
+
+ align:start position:0%
+lying
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh the borop arm
+
+ align:start position:0%
+uh the borop arm
+ 
+
+ align:start position:0%
+uh the borop arm
+approximation allows us to say well
+
+ align:start position:0%
+approximation allows us to say well
+ 
+
+ align:start position:0%
+approximation allows us to say well
+since the electrons move fast relative
+
+ align:start position:0%
+since the electrons move fast relative
+ 
+
+ align:start position:0%
+since the electrons move fast relative
+to the nuclei it's probably a good idea
+
+ align:start position:0%
+to the nuclei it's probably a good idea
+ 
+
+ align:start position:0%
+to the nuclei it's probably a good idea
+to let the nuclear kinetic energy go to
+
+ align:start position:0%
+to let the nuclear kinetic energy go to
+ 
+
+ align:start position:0%
+to let the nuclear kinetic energy go to
+zero it it's not true that it's
+
+ align:start position:0%
+zero it it's not true that it's
+ 
+
+ align:start position:0%
+zero it it's not true that it's
+zero but it's it's a reasonable thing
+
+ align:start position:0%
+zero but it's it's a reasonable thing
+ 
+
+ align:start position:0%
+zero but it's it's a reasonable thing
+it's not going to cost you too much in
+
+ align:start position:0%
+it's not going to cost you too much in
+ 
+
+ align:start position:0%
+it's not going to cost you too much in
+neglecting this it will be a good basis
+
+ align:start position:0%
+neglecting this it will be a good basis
+ 
+
+ align:start position:0%
+neglecting this it will be a good basis
+set and the things that come from
+
+ align:start position:0%
+set and the things that come from
+ 
+
+ align:start position:0%
+set and the things that come from
+neglecting this can easily fixed after
+
+ align:start position:0%
+neglecting this can easily fixed after
+ 
+
+ align:start position:0%
+neglecting this can easily fixed after
+we've defined functions so the borop
+
+ align:start position:0%
+we've defined functions so the borop
+ 
+
+ align:start position:0%
+we've defined functions so the borop
+approximation is something it's an
+
+ align:start position:0%
+approximation is something it's an
+ 
+
+ align:start position:0%
+approximation is something it's an
+example of a fast slow separation that
+
+ align:start position:0%
+example of a fast slow separation that
+ 
+
+ align:start position:0%
+example of a fast slow separation that
+is really a good
+
+ align:start position:0%
+is really a good
+ 
+
+ align:start position:0%
+is really a good
+separation for separating vibration from
+
+ align:start position:0%
+separation for separating vibration from
+ 
+
+ align:start position:0%
+separation for separating vibration from
+rotation we also make fast slow
+
+ align:start position:0%
+rotation we also make fast slow
+ 
+
+ align:start position:0%
+rotation we also make fast slow
+approximations which is not good much
+
+ align:start position:0%
+approximations which is not good much
+ 
+
+ align:start position:0%
+approximations which is not good much
+worse and for uh so there are many times
+
+ align:start position:0%
+worse and for uh so there are many times
+ 
+
+ align:start position:0%
+worse and for uh so there are many times
+when we impose a a separation of
+
+ align:start position:0%
+when we impose a a separation of
+ 
+
+ align:start position:0%
+when we impose a a separation of
+coordinates by saying this is fast and
+
+ align:start position:0%
+coordinates by saying this is fast and
+ 
+
+ align:start position:0%
+coordinates by saying this is fast and
+this is slow and it's a born Oppenheimer
+
+ align:start position:0%
+this is slow and it's a born Oppenheimer
+ 
+
+ align:start position:0%
+this is slow and it's a born Oppenheimer
+La approximation but the approximation
+
+ align:start position:0%
+La approximation but the approximation
+ 
+
+ align:start position:0%
+La approximation but the approximation
+is much worse but this is a great
+
+ align:start position:0%
+is much worse but this is a great
+ 
+
+ align:start position:0%
+is much worse but this is a great
+example of seeing okay we do
+
+ align:start position:0%
+example of seeing okay we do
+ 
+
+ align:start position:0%
+example of seeing okay we do
+this uh we take something out it enables
+
+ align:start position:0%
+this uh we take something out it enables
+ 
+
+ align:start position:0%
+this uh we take something out it enables
+us to write the wave functions in a
+
+ align:start position:0%
+us to write the wave functions in a
+ 
+
+ align:start position:0%
+us to write the wave functions in a
+clever way and then we bring them back
+
+ align:start position:0%
+clever way and then we bring them back
+ 
+
+ align:start position:0%
+clever way and then we bring them back
+and we evaluate the uh consequences of
+
+ align:start position:0%
+and we evaluate the uh consequences of
+ 
+
+ align:start position:0%
+and we evaluate the uh consequences of
+our neglect and we put it in we have an
+
+ align:start position:0%
+our neglect and we put it in we have an
+ 
+
+ align:start position:0%
+our neglect and we put it in we have an
+exact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+result okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know I at the beginning I told
+
+ align:start position:0%
+so you know I at the beginning I told
+ 
+
+ align:start position:0%
+so you know I at the beginning I told
+you what we would do we would clamp the
+
+ align:start position:0%
+you what we would do we would clamp the
+ 
+
+ align:start position:0%
+you what we would do we would clamp the
+nuclei we'd solve the extraordinary
+
+ align:start position:0%
+nuclei we'd solve the extraordinary
+ 
+
+ align:start position:0%
+nuclei we'd solve the extraordinary
+equation we'd get the potential energy
+
+ align:start position:0%
+equation we'd get the potential energy
+ 
+
+ align:start position:0%
+equation we'd get the potential energy
+curves uh and U so uh I'm not going to
+
+ align:start position:0%
+curves uh and U so uh I'm not going to
+ 
+
+ align:start position:0%
+curves uh and U so uh I'm not going to
+repeat
+
+ align:start position:0%
+repeat
+ 
+
+ align:start position:0%
+repeat
+this but now so we've done that and
+
+ align:start position:0%
+this but now so we've done that and
+ 
+
+ align:start position:0%
+this but now so we've done that and
+we've got our uh We've clamped the
+
+ align:start position:0%
+we've got our uh We've clamped the
+ 
+
+ align:start position:0%
+we've got our uh We've clamped the
+nuclei we've got our potential curves
+
+ align:start position:0%
+nuclei we've got our potential curves
+ 
+
+ align:start position:0%
+nuclei we've got our potential curves
+that we defined
+
+ align:start position:0%
+that we defined
+ 
+
+ align:start position:0%
+that we defined
+pointwise uh and
+
+ align:start position:0%
+pointwise uh and
+ 
+
+ align:start position:0%
+pointwise uh and
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+and now we want to ask well we have a
+
+ align:start position:0%
+and now we want to ask well we have a
+ 
+
+ align:start position:0%
+and now we want to ask well we have a
+nuclear uh kinetic energy term Del
+
+ align:start position:0%
+nuclear uh kinetic energy term Del
+ 
+
+ align:start position:0%
+nuclear uh kinetic energy term Del
+squared and uh what are the consequences
+
+ align:start position:0%
+squared and uh what are the consequences
+ 
+
+ align:start position:0%
+squared and uh what are the consequences
+of ignoring it so what does this
+
+ align:start position:0%
+of ignoring it so what does this
+ 
+
+ align:start position:0%
+of ignoring it so what does this
+do and so suppose we have Dell squar
+
+ align:start position:0%
+do and so suppose we have Dell squar
+ 
+
+ align:start position:0%
+do and so suppose we have Dell squar
+operating on a product of two
+
+ align:start position:0%
+operating on a product of two
+ 
+
+ align:start position:0%
+operating on a product of two
+functions we use the chain Rule and so
+
+ align:start position:0%
+functions we use the chain Rule and so
+ 
+
+ align:start position:0%
+functions we use the chain Rule and so
+this is going to be equal to
+
+ align:start position:0%
+this is going to be equal to
+ 
+
+ align:start position:0%
+this is going to be equal to
+d d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+b plus
+
+ align:start position:0%
+b plus
+ 
+
+ align:start position:0%
+b plus
+d a d
+
+ align:start position:0%
+d a d
+ 
+
+ align:start position:0%
+d a d
+b plus now we bring the other guy in so
+
+ align:start position:0%
+b plus now we bring the other guy in so
+ 
+
+ align:start position:0%
+b plus now we bring the other guy in so
+we have uh um so we'll have
+
+ align:start position:0%
+we have uh um so we'll have
+ 
+
+ align:start position:0%
+we have uh um so we'll have
+a Del
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um okay now we rewrite this so now we
+
+ align:start position:0%
+um okay now we rewrite this so now we
+ 
+
+ align:start position:0%
+um okay now we rewrite this so now we
+get the from the first term we get a D
+
+ align:start position:0%
+get the from the first term we get a D
+ 
+
+ align:start position:0%
+get the from the first term we get a D
+Squared
+
+ align:start position:0%
+Squared
+ 
+
+ align:start position:0%
+Squared
+a B plus a d a d b and from this one we
+
+ align:start position:0%
+a B plus a d a d b and from this one we
+ 
+
+ align:start position:0%
+a B plus a d a d b and from this one we
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+Del
+
+ align:start position:0%
+Del
+ 
+
+ align:start position:0%
+Del
+a Del B and finally a d
+
+ align:start position:0%
+a Del B and finally a d
+ 
+
+ align:start position:0%
+a Del B and finally a d
+s
+
+ align:start position:0%
+s
+ 
+
+ align:start position:0%
+s
+b so we get d s a * B we get d a DB and
+
+ align:start position:0%
+b so we get d s a * B we get d a DB and
+ 
+
+ align:start position:0%
+b so we get d s a * B we get d a DB and
+two of those and an a d s
+
+ align:start position:0%
+two of those and an a d s
+ 
+
+ align:start position:0%
+two of those and an a d s
+b so the nuclear kinetic energy if we
+
+ align:start position:0%
+b so the nuclear kinetic energy if we
+ 
+
+ align:start position:0%
+b so the nuclear kinetic energy if we
+have uh a product of say
+
+ align:start position:0%
+have uh a product of say
+ 
+
+ align:start position:0%
+have uh a product of say
+f i
+
+ align:start position:0%
+f i
+ 
+
+ align:start position:0%
+f i
+r Kai I
+
+ align:start position:0%
+r Kai I
+ 
+
+ align:start position:0%
+r Kai I
+VJ
+
+ align:start position:0%
+VJ
+ 
+
+ align:start position:0%
+VJ
+Omega uh Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so we
+
+ align:start position:0%
+uh so we
+ 
+
+ align:start position:0%
+uh so we
+have this nuclear kinetic energy
+
+ align:start position:0%
+have this nuclear kinetic energy
+ 
+
+ align:start position:0%
+have this nuclear kinetic energy
+operating on the product of an
+
+ align:start position:0%
+operating on the product of an
+ 
+
+ align:start position:0%
+operating on the product of an
+electronic times a vibrational wave
+
+ align:start position:0%
+electronic times a vibrational wave
+ 
+
+ align:start position:0%
+electronic times a vibrational wave
+function they're both functions of Big R
+
+ align:start position:0%
+function they're both functions of Big R
+ 
+
+ align:start position:0%
+function they're both functions of Big R
+implicitly in this case explicitly in
+
+ align:start position:0%
+implicitly in this case explicitly in
+ 
+
+ align:start position:0%
+implicitly in this case explicitly in
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case so normally we think of wave
+
+ align:start position:0%
+case so normally we think of wave
+ 
+
+ align:start position:0%
+case so normally we think of wave
+functions electronic wave functions as
+
+ align:start position:0%
+functions electronic wave functions as
+ 
+
+ align:start position:0%
+functions electronic wave functions as
+not being strong functions of R we'd
+
+ align:start position:0%
+not being strong functions of R we'd
+ 
+
+ align:start position:0%
+not being strong functions of R we'd
+like to think that the electronic wave
+
+ align:start position:0%
+like to think that the electronic wave
+ 
+
+ align:start position:0%
+like to think that the electronic wave
+function doesn't change as we Mo stretch
+
+ align:start position:0%
+function doesn't change as we Mo stretch
+ 
+
+ align:start position:0%
+function doesn't change as we Mo stretch
+the molecule but we know it has to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+so we're going to be having uh
+
+ align:start position:0%
+so we're going to be having uh
+ 
+
+ align:start position:0%
+so we're going to be having uh
+derivatives with respect to our first
+
+ align:start position:0%
+derivatives with respect to our first
+ 
+
+ align:start position:0%
+derivatives with respect to our first
+and second derivatives with respect to
+
+ align:start position:0%
+and second derivatives with respect to
+ 
+
+ align:start position:0%
+and second derivatives with respect to
+our operating on the wave function the
+
+ align:start position:0%
+our operating on the wave function the
+ 
+
+ align:start position:0%
+our operating on the wave function the
+electronic wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function and our physical intuition is
+
+ align:start position:0%
+function and our physical intuition is
+ 
+
+ align:start position:0%
+function and our physical intuition is
+that these are going to be small
+
+ align:start position:0%
+that these are going to be small
+ 
+
+ align:start position:0%
+that these are going to be small
+effects but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose we uh we calculate the potential
+
+ align:start position:0%
+suppose we uh we calculate the potential
+ 
+
+ align:start position:0%
+suppose we uh we calculate the potential
+energy uh so suppose we solve the
+
+ align:start position:0%
+energy uh so suppose we solve the
+ 
+
+ align:start position:0%
+energy uh so suppose we solve the
+electronic shorting equation and we have
+
+ align:start position:0%
+electronic shorting equation and we have
+ 
+
+ align:start position:0%
+electronic shorting equation and we have
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+states and of the same Symmetry and
+
+ align:start position:0%
+states and of the same Symmetry and
+ 
+
+ align:start position:0%
+states and of the same Symmetry and
+normally what happens is the igen values
+
+ align:start position:0%
+normally what happens is the igen values
+ 
+
+ align:start position:0%
+normally what happens is the igen values
+of the electronic shorting equation will
+
+ align:start position:0%
+of the electronic shorting equation will
+ 
+
+ align:start position:0%
+of the electronic shorting equation will
+exhibit these avoided
+
+ align:start position:0%
+exhibit these avoided
+ 
+
+ align:start position:0%
+exhibit these avoided
+Crossings and and if the uh uh
+
+ align:start position:0%
+Crossings and and if the uh uh
+ 
+
+ align:start position:0%
+Crossings and and if the uh uh
+interaction between these two uh
+
+ align:start position:0%
+interaction between these two uh
+ 
+
+ align:start position:0%
+interaction between these two uh
+potential curves or two states is large
+
+ align:start position:0%
+potential curves or two states is large
+ 
+
+ align:start position:0%
+potential curves or two states is large
+then the avoided Crossings will be
+
+ align:start position:0%
+then the avoided Crossings will be
+ 
+
+ align:start position:0%
+then the avoided Crossings will be
+strongly
+
+ align:start position:0%
+strongly
+ 
+
+ align:start position:0%
+strongly
+avoided and the electronic wave function
+
+ align:start position:0%
+avoided and the electronic wave function
+ 
+
+ align:start position:0%
+avoided and the electronic wave function
+will be changing with internuclear
+
+ align:start position:0%
+will be changing with internuclear
+ 
+
+ align:start position:0%
+will be changing with internuclear
+distance in a slow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way and as a result of that these
+
+ align:start position:0%
+way and as a result of that these
+ 
+
+ align:start position:0%
+way and as a result of that these
+neglected terms of the nuclear kinetic
+
+ align:start position:0%
+neglected terms of the nuclear kinetic
+ 
+
+ align:start position:0%
+neglected terms of the nuclear kinetic
+energy operating on the electronic wave
+
+ align:start position:0%
+energy operating on the electronic wave
+ 
+
+ align:start position:0%
+energy operating on the electronic wave
+function are going to be small fixable
+
+ align:start position:0%
+function are going to be small fixable
+ 
+
+ align:start position:0%
+function are going to be small fixable
+treatable as small corrections to the
+
+ align:start position:0%
+treatable as small corrections to the
+ 
+
+ align:start position:0%
+treatable as small corrections to the
+problem but sometimes you get something
+
+ align:start position:0%
+problem but sometimes you get something
+ 
+
+ align:start position:0%
+problem but sometimes you get something
+that looks like this where you have a
+
+ align:start position:0%
+that looks like this where you have a
+ 
+
+ align:start position:0%
+that looks like this where you have a
+very weakly avoided
+
+ align:start position:0%
+very weakly avoided
+ 
+
+ align:start position:0%
+very weakly avoided
+Crossing two states of the same symmetry
+
+ align:start position:0%
+Crossing two states of the same symmetry
+ 
+
+ align:start position:0%
+Crossing two states of the same symmetry
+can never cross because uh
+
+ align:start position:0%
+can never cross because uh
+ 
+
+ align:start position:0%
+can never cross because uh
+uh the they uh
+
+ align:start position:0%
+uh the they uh
+ 
+
+ align:start position:0%
+uh the they uh
+if if they have the same symmetry there
+
+ align:start position:0%
+if if they have the same symmetry there
+ 
+
+ align:start position:0%
+if if they have the same symmetry there
+will be Matrix elements of the
+
+ align:start position:0%
+will be Matrix elements of the
+ 
+
+ align:start position:0%
+will be Matrix elements of the
+hamiltonian between them and sometimes
+
+ align:start position:0%
+hamiltonian between them and sometimes
+ 
+
+ align:start position:0%
+hamiltonian between them and sometimes
+those Matrix elements are so small that
+
+ align:start position:0%
+those Matrix elements are so small that
+ 
+
+ align:start position:0%
+those Matrix elements are so small that
+they get really really close and if that
+
+ align:start position:0%
+they get really really close and if that
+ 
+
+ align:start position:0%
+they get really really close and if that
+is true well then this will be a very
+
+ align:start position:0%
+is true well then this will be a very
+ 
+
+ align:start position:0%
+is true well then this will be a very
+sharp avoided Crossing and the these
+
+ align:start position:0%
+sharp avoided Crossing and the these
+ 
+
+ align:start position:0%
+sharp avoided Crossing and the these
+nuclear kinetic energy uh
+
+ align:start position:0%
+nuclear kinetic energy uh
+ 
+
+ align:start position:0%
+nuclear kinetic energy uh
+derivatives will become enormous at that
+
+ align:start position:0%
+derivatives will become enormous at that
+ 
+
+ align:start position:0%
+derivatives will become enormous at that
+point and when that occurs
+
+ align:start position:0%
+point and when that occurs
+ 
+
+ align:start position:0%
+point and when that occurs
+the diabet the adiabetic approximation
+
+ align:start position:0%
+the diabet the adiabetic approximation
+ 
+
+ align:start position:0%
+the diabet the adiabetic approximation
+is completely horrible because a
+
+ align:start position:0%
+is completely horrible because a
+ 
+
+ align:start position:0%
+is completely horrible because a
+neglected term gets big but you say well
+
+ align:start position:0%
+neglected term gets big but you say well
+ 
+
+ align:start position:0%
+neglected term gets big but you say well
+this thing you know all I have to do is
+
+ align:start position:0%
+this thing you know all I have to do is
+ 
+
+ align:start position:0%
+this thing you know all I have to do is
+close my eyes and pretend it's going to
+
+ align:start position:0%
+close my eyes and pretend it's going to
+ 
+
+ align:start position:0%
+close my eyes and pretend it's going to
+cross because there's something that's
+
+ align:start position:0%
+cross because there's something that's
+ 
+
+ align:start position:0%
+cross because there's something that's
+really small that's being
+
+ align:start position:0%
+really small that's being
+ 
+
+ align:start position:0%
+really small that's being
+neglected and that's called the diabetic
+
+ align:start position:0%
+neglected and that's called the diabetic
+ 
+
+ align:start position:0%
+neglected and that's called the diabetic
+approximation it's the approximation
+
+ align:start position:0%
+approximation it's the approximation
+ 
+
+ align:start position:0%
+approximation it's the approximation
+where in fact you do insist that the
+
+ align:start position:0%
+where in fact you do insist that the
+ 
+
+ align:start position:0%
+where in fact you do insist that the
+electronic wave function uh um
+
+ align:start position:0%
+electronic wave function uh um
+ 
+
+ align:start position:0%
+electronic wave function uh um
+uh doesn't change abruptly with r it
+
+ align:start position:0%
+uh doesn't change abruptly with r it
+ 
+
+ align:start position:0%
+uh doesn't change abruptly with r it
+changes in a trivial way with
+
+ align:start position:0%
+changes in a trivial way with
+ 
+
+ align:start position:0%
+changes in a trivial way with
+r and then this little avoided
+
+ align:start position:0%
+r and then this little avoided
+ 
+
+ align:start position:0%
+r and then this little avoided
+Crossing is a small
+
+ align:start position:0%
+Crossing is a small
+ 
+
+ align:start position:0%
+Crossing is a small
+perturbation it's an electronic
+
+ align:start position:0%
+perturbation it's an electronic
+ 
+
+ align:start position:0%
+perturbation it's an electronic
+interaction energy that uh uh connects
+
+ align:start position:0%
+interaction energy that uh uh connects
+ 
+
+ align:start position:0%
+interaction energy that uh uh connects
+states of the same Symmetry and so you
+
+ align:start position:0%
+states of the same Symmetry and so you
+ 
+
+ align:start position:0%
+states of the same Symmetry and so you
+go to a different representation the
+
+ align:start position:0%
+go to a different representation the
+ 
+
+ align:start position:0%
+go to a different representation the
+diabetic versus the adiabetic so this is
+
+ align:start position:0%
+diabetic versus the adiabetic so this is
+ 
+
+ align:start position:0%
+diabetic versus the adiabetic so this is
+something that puzzles people a lot how
+
+ align:start position:0%
+something that puzzles people a lot how
+ 
+
+ align:start position:0%
+something that puzzles people a lot how
+can the nuclear kinetic
+
+ align:start position:0%
+can the nuclear kinetic
+ 
+
+ align:start position:0%
+can the nuclear kinetic
+energy act on the electronic wave
+
+ align:start position:0%
+energy act on the electronic wave
+ 
+
+ align:start position:0%
+energy act on the electronic wave
+function it seems you know it seems
+
+ align:start position:0%
+function it seems you know it seems
+ 
+
+ align:start position:0%
+function it seems you know it seems
+mixing of metaphors nuclear electronic
+
+ align:start position:0%
+mixing of metaphors nuclear electronic
+ 
+
+ align:start position:0%
+mixing of metaphors nuclear electronic
+they're different things but the
+
+ align:start position:0%
+they're different things but the
+ 
+
+ align:start position:0%
+they're different things but the
+important thing is that the electronic
+
+ align:start position:0%
+important thing is that the electronic
+ 
+
+ align:start position:0%
+important thing is that the electronic
+wave function depends parametrically on
+
+ align:start position:0%
+wave function depends parametrically on
+ 
+
+ align:start position:0%
+wave function depends parametrically on
+internuclear distance and there's two
+
+ align:start position:0%
+internuclear distance and there's two
+ 
+
+ align:start position:0%
+internuclear distance and there's two
+terms there's the Dell squar operating
+
+ align:start position:0%
+terms there's the Dell squar operating
+ 
+
+ align:start position:0%
+terms there's the Dell squar operating
+on the electronic and there's the Dell
+
+ align:start position:0%
+on the electronic and there's the Dell
+ 
+
+ align:start position:0%
+on the electronic and there's the Dell
+operating on the electronic and another
+
+ align:start position:0%
+operating on the electronic and another
+ 
+
+ align:start position:0%
+operating on the electronic and another
+one on the so there's two uh two kinds
+
+ align:start position:0%
+one on the so there's two uh two kinds
+ 
+
+ align:start position:0%
+one on the so there's two uh two kinds
+of terms that get neglected and they're
+
+ align:start position:0%
+of terms that get neglected and they're
+ 
+
+ align:start position:0%
+of terms that get neglected and they're
+usually small they're usually not of any
+
+ align:start position:0%
+usually small they're usually not of any
+ 
+
+ align:start position:0%
+usually small they're usually not of any
+consequence and can be put in and uh uh
+
+ align:start position:0%
+consequence and can be put in and uh uh
+ 
+
+ align:start position:0%
+consequence and can be put in and uh uh
+often you know you don't put both of
+
+ align:start position:0%
+often you know you don't put both of
+ 
+
+ align:start position:0%
+often you know you don't put both of
+them in because one of them is easy to
+
+ align:start position:0%
+them in because one of them is easy to
+ 
+
+ align:start position:0%
+them in because one of them is easy to
+put in and the other one is complicated
+
+ align:start position:0%
+put in and the other one is complicated
+ 
+
+ align:start position:0%
+put in and the other one is complicated
+so this is easy this is not so easy and
+
+ align:start position:0%
+so this is easy this is not so easy and
+ 
+
+ align:start position:0%
+so this is easy this is not so easy and
+so there are different levels of the
+
+ align:start position:0%
+so there are different levels of the
+ 
+
+ align:start position:0%
+so there are different levels of the
+adiabetic diabetic approximation
+
+ align:start position:0%
+adiabetic diabetic approximation
+ 
+
+ align:start position:0%
+adiabetic diabetic approximation
+depending on whether you include both or
+
+ align:start position:0%
+depending on whether you include both or
+ 
+
+ align:start position:0%
+depending on whether you include both or
+not okay
+
+ align:start position:0%
+not okay
+ 
+
+ align:start position:0%
+not okay
+so that's the really essential piece
+
+ align:start position:0%
+so that's the really essential piece
+ 
+
+ align:start position:0%
+so that's the really essential piece
+here that's the trick uh that we're
+
+ align:start position:0%
+here that's the trick uh that we're
+ 
+
+ align:start position:0%
+here that's the trick uh that we're
+going to ignore
+
+ align:start position:0%
+going to ignore
+ 
+
+ align:start position:0%
+going to ignore
+these uh nuclear kinetic energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interactions okay
+
+ align:start position:0%
+interactions okay
+ 
+
+ align:start position:0%
+interactions okay
+so ask one sort of a uh backup question
+
+ align:start position:0%
+so ask one sort of a uh backup question
+ 
+
+ align:start position:0%
+so ask one sort of a uh backup question
+for a second absolutely
+
+ align:start position:0%
+for a second absolutely
+ 
+
+ align:start position:0%
+for a second absolutely
+so um vibration and rotation it's some
+
+ align:start position:0%
+so um vibration and rotation it's some
+ 
+
+ align:start position:0%
+so um vibration and rotation it's some
+vibrations are separable from some
+
+ align:start position:0%
+vibrations are separable from some
+ 
+
+ align:start position:0%
+vibrations are separable from some
+rotations quite well and some of them
+
+ align:start position:0%
+rotations quite well and some of them
+ 
+
+ align:start position:0%
+rotations quite well and some of them
+are not now are we talking about a
+
+ align:start position:0%
+are not now are we talking about a
+ 
+
+ align:start position:0%
+are not now are we talking about a
+diatomic molecule or we talking about
+
+ align:start position:0%
+diatomic molecule or we talking about
+ 
+
+ align:start position:0%
+diatomic molecule or we talking about
+polyatomic
+
+ align:start position:0%
+polyatomic
+ 
+
+ align:start position:0%
+polyatomic
+molecule up to you
+
+ align:start position:0%
+molecule up to you
+ 
+
+ align:start position:0%
+molecule up to you
+well for a diatomic molecule there's
+
+ align:start position:0%
+well for a diatomic molecule there's
+ 
+
+ align:start position:0%
+well for a diatomic molecule there's
+only one vibration one kind of vibration
+
+ align:start position:0%
+only one vibration one kind of vibration
+ 
+
+ align:start position:0%
+only one vibration one kind of vibration
+one rotation and one kind of rotation
+
+ align:start position:0%
+one rotation and one kind of rotation
+ 
+
+ align:start position:0%
+one rotation and one kind of rotation
+but some but some rotations I guess as
+
+ align:start position:0%
+but some but some rotations I guess as
+ 
+
+ align:start position:0%
+but some but some rotations I guess as
+you go higher rotation get faster so
+
+ align:start position:0%
+you go higher rotation get faster so
+ 
+
+ align:start position:0%
+you go higher rotation get faster so
+I mean what we're always doing is we're
+
+ align:start position:0%
+I mean what we're always doing is we're
+ 
+
+ align:start position:0%
+I mean what we're always doing is we're
+always saying we're going to write a set
+
+ align:start position:0%
+always saying we're going to write a set
+ 
+
+ align:start position:0%
+always saying we're going to write a set
+of a complete set of basis functions and
+
+ align:start position:0%
+of a complete set of basis functions and
+ 
+
+ align:start position:0%
+of a complete set of basis functions and
+each of the degrees of freedom is going
+
+ align:start position:0%
+each of the degrees of freedom is going
+ 
+
+ align:start position:0%
+each of the degrees of freedom is going
+to be handled in a special way that
+
+ align:start position:0%
+to be handled in a special way that
+ 
+
+ align:start position:0%
+to be handled in a special way that
+we've agreed is is the best way and and
+
+ align:start position:0%
+we've agreed is is the best way and and
+ 
+
+ align:start position:0%
+we've agreed is is the best way and and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um what we normally do is we say we're
+
+ align:start position:0%
+um what we normally do is we say we're
+ 
+
+ align:start position:0%
+um what we normally do is we say we're
+going to define the rotational wave
+
+ align:start position:0%
+going to define the rotational wave
+ 
+
+ align:start position:0%
+going to define the rotational wave
+functions by clamping the
+
+ align:start position:0%
+functions by clamping the
+ 
+
+ align:start position:0%
+functions by clamping the
+nuclei so we're still keeping part of
+
+ align:start position:0%
+nuclei so we're still keeping part of
+ 
+
+ align:start position:0%
+nuclei so we're still keeping part of
+the clamped nuclear we clamped the
+
+ align:start position:0%
+the clamped nuclear we clamped the
+ 
+
+ align:start position:0%
+the clamped nuclear we clamped the
+internuclear distance where we let the
+
+ align:start position:0%
+internuclear distance where we let the
+ 
+
+ align:start position:0%
+internuclear distance where we let the
+the four
+
+ align:start position:0%
+the four
+ 
+
+ align:start position:0%
+the four
+so and uh and then well as the molecule
+
+ align:start position:0%
+so and uh and then well as the molecule
+ 
+
+ align:start position:0%
+so and uh and then well as the molecule
+vibrates the rotational constant depends
+
+ align:start position:0%
+vibrates the rotational constant depends
+ 
+
+ align:start position:0%
+vibrates the rotational constant depends
+on R and so that affects the rotation
+
+ align:start position:0%
+on R and so that affects the rotation
+ 
+
+ align:start position:0%
+on R and so that affects the rotation
+and so then we say okay we're going to
+
+ align:start position:0%
+and so then we say okay we're going to
+ 
+
+ align:start position:0%
+and so then we say okay we're going to
+integrate over the vibrational
+
+ align:start position:0%
+integrate over the vibrational
+ 
+
+ align:start position:0%
+integrate over the vibrational
+coordinate to get the rotational
+
+ align:start position:0%
+coordinate to get the rotational
+ 
+
+ align:start position:0%
+coordinate to get the rotational
+constant as opposed to the rotational
+
+ align:start position:0%
+constant as opposed to the rotational
+ 
+
+ align:start position:0%
+constant as opposed to the rotational
+operator so the reason I was asking is I
+
+ align:start position:0%
+operator so the reason I was asking is I
+ 
+
+ align:start position:0%
+operator so the reason I was asking is I
+was wondering let's now think of a
+
+ align:start position:0%
+was wondering let's now think of a
+ 
+
+ align:start position:0%
+was wondering let's now think of a
+polyon molecule where there's some very
+
+ align:start position:0%
+polyon molecule where there's some very
+ 
+
+ align:start position:0%
+polyon molecule where there's some very
+very fast vibrations and very very slow
+
+ align:start position:0%
+very fast vibrations and very very slow
+ 
+
+ align:start position:0%
+very fast vibrations and very very slow
+pretations as well as others that you
+
+ align:start position:0%
+pretations as well as others that you
+ 
+
+ align:start position:0%
+pretations as well as others that you
+know it becomes worse and worse neglect
+
+ align:start position:0%
+know it becomes worse and worse neglect
+ 
+
+ align:start position:0%
+know it becomes worse and worse neglect
+them could you write three terms in a
+
+ align:start position:0%
+them could you write three terms in a
+ 
+
+ align:start position:0%
+them could you write three terms in a
+hamiltonian one for vibrations one for
+
+ align:start position:0%
+hamiltonian one for vibrations one for
+ 
+
+ align:start position:0%
+hamiltonian one for vibrations one for
+rotations and then another for things we
+
+ align:start position:0%
+rotations and then another for things we
+ 
+
+ align:start position:0%
+rotations and then another for things we
+don't want to make this fast slow
+
+ align:start position:0%
+don't want to make this fast slow
+ 
+
+ align:start position:0%
+don't want to make this fast slow
+approximation well there is yeah
+
+ align:start position:0%
+approximation well there is yeah
+ 
+
+ align:start position:0%
+approximation well there is yeah
+okay so rotation is generally slow
+
+ align:start position:0%
+okay so rotation is generally slow
+ 
+
+ align:start position:0%
+okay so rotation is generally slow
+compared to vibration but there are
+
+ align:start position:0%
+compared to vibration but there are
+ 
+
+ align:start position:0%
+compared to vibration but there are
+sometimes very large amplitude very slow
+
+ align:start position:0%
+sometimes very large amplitude very slow
+ 
+
+ align:start position:0%
+sometimes very large amplitude very slow
+vibrations and we just demote them into
+
+ align:start position:0%
+vibrations and we just demote them into
+ 
+
+ align:start position:0%
+vibrations and we just demote them into
+rotations and so we solve the the fast
+
+ align:start position:0%
+rotations and so we solve the the fast
+ 
+
+ align:start position:0%
+rotations and so we solve the the fast
+vibrational Hiltonia and then we have a
+
+ align:start position:0%
+vibrational Hiltonia and then we have a
+ 
+
+ align:start position:0%
+vibrational Hiltonia and then we have a
+rotation vibration large amplitude term
+
+ align:start position:0%
+rotation vibration large amplitude term
+ 
+
+ align:start position:0%
+rotation vibration large amplitude term
+and that's perfectly legitimate you can
+
+ align:start position:0%
+and that's perfectly legitimate you can
+ 
+
+ align:start position:0%
+and that's perfectly legitimate you can
+you make whatever partitioning of the
+
+ align:start position:0%
+you make whatever partitioning of the
+ 
+
+ align:start position:0%
+you make whatever partitioning of the
+Motions you want in order to Define
+
+ align:start position:0%
+Motions you want in order to Define
+ 
+
+ align:start position:0%
+Motions you want in order to Define
+complete sets of basis functions and
+
+ align:start position:0%
+complete sets of basis functions and
+ 
+
+ align:start position:0%
+complete sets of basis functions and
+people actually do that and this is a
+
+ align:start position:0%
+people actually do that and this is a
+ 
+
+ align:start position:0%
+people actually do that and this is a
+known you bet
+
+ align:start position:0%
+known you bet
+ 
+
+ align:start position:0%
+known you bet
+okay known to many people not well to me
+
+ align:start position:0%
+okay known to many people not well to me
+ 
+
+ align:start position:0%
+okay known to many people not well to me
+I know people do it but I cannot
+
+ align:start position:0%
+I know people do it but I cannot
+ 
+
+ align:start position:0%
+I know people do it but I cannot
+instruct you on how it's done at least
+
+ align:start position:0%
+instruct you on how it's done at least
+ 
+
+ align:start position:0%
+instruct you on how it's done at least
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+today okay
+
+ align:start position:0%
+today okay
+ 
+
+ align:start position:0%
+today okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so we have for an electronic State I
+
+ align:start position:0%
+uh so we have for an electronic State I
+ 
+
+ align:start position:0%
+uh so we have for an electronic State I
+don't want to do that that we have
+
+ align:start position:0%
+don't want to do that that we have
+ 
+
+ align:start position:0%
+don't want to do that that we have
+the uh the hamiltonian now we've
+
+ align:start position:0%
+the uh the hamiltonian now we've
+ 
+
+ align:start position:0%
+the uh the hamiltonian now we've
+explained what we're doing and we have a
+
+ align:start position:0%
+explained what we're doing and we have a
+ 
+
+ align:start position:0%
+explained what we're doing and we have a
+nuclear uh kinetic energy term we have
+
+ align:start position:0%
+nuclear uh kinetic energy term we have
+ 
+
+ align:start position:0%
+nuclear uh kinetic energy term we have
+h^ S over 2 mu R
+
+ align:start position:0%
+h^ S over 2 mu R
+ 
+
+ align:start position:0%
+h^ S over 2 mu R
+2 this is called the rotational
+
+ align:start position:0%
+2 this is called the rotational
+ 
+
+ align:start position:0%
+2 this is called the rotational
+operator and then we have hr^ 2 -
+
+ align:start position:0%
+operator and then we have hr^ 2 -
+ 
+
+ align:start position:0%
+operator and then we have hr^ 2 -
+2 R 2 I just put this in here here
+
+ align:start position:0%
+2 R 2 I just put this in here here
+ 
+
+ align:start position:0%
+2 R 2 I just put this in here here
+because when you apply a angular
+
+ align:start position:0%
+because when you apply a angular
+ 
+
+ align:start position:0%
+because when you apply a angular
+momentum function to a wave function you
+
+ align:start position:0%
+momentum function to a wave function you
+ 
+
+ align:start position:0%
+momentum function to a wave function you
+get always a number times H bar and so
+
+ align:start position:0%
+get always a number times H bar and so
+ 
+
+ align:start position:0%
+get always a number times H bar and so
+that's just
+
+ align:start position:0%
+that's just
+ 
+
+ align:start position:0%
+that's just
+cancelling that so that this that this
+
+ align:start position:0%
+cancelling that so that this that this
+ 
+
+ align:start position:0%
+cancelling that so that this that this
+is just numbers no units and this
+
+ align:start position:0%
+is just numbers no units and this
+ 
+
+ align:start position:0%
+is just numbers no units and this
+everything all the units are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so we have found
+
+ align:start position:0%
+here so we have found
+ 
+
+ align:start position:0%
+here so we have found
+a procedure to simplify the hamiltonian
+
+ align:start position:0%
+a procedure to simplify the hamiltonian
+ 
+
+ align:start position:0%
+a procedure to simplify the hamiltonian
+to write it as
+
+ align:start position:0%
+to write it as
+ 
+
+ align:start position:0%
+to write it as
+nuclear kinetic
+
+ align:start position:0%
+nuclear kinetic
+ 
+
+ align:start position:0%
+nuclear kinetic
+energy nuclear potential energy and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation this is not the truth this is
+
+ align:start position:0%
+rotation this is not the truth this is
+ 
+
+ align:start position:0%
+rotation this is not the truth this is
+just what we do this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h0 and uh uh we already know that since
+
+ align:start position:0%
+h0 and uh uh we already know that since
+ 
+
+ align:start position:0%
+h0 and uh uh we already know that since
+this involves motion of theeta fi and
+
+ align:start position:0%
+this involves motion of theeta fi and
+ 
+
+ align:start position:0%
+this involves motion of theeta fi and
+this involves R this couples the
+
+ align:start position:0%
+this involves R this couples the
+ 
+
+ align:start position:0%
+this involves R this couples the
+the vibration to the rotation this is
+
+ align:start position:0%
+the vibration to the rotation this is
+ 
+
+ align:start position:0%
+the vibration to the rotation this is
+this is a bad term but it's not a not a
+
+ align:start position:0%
+this is a bad term but it's not a not a
+ 
+
+ align:start position:0%
+this is a bad term but it's not a not a
+bad term in a in that it makes big
+
+ align:start position:0%
+bad term in a in that it makes big
+ 
+
+ align:start position:0%
+bad term in a in that it makes big
+problems it just says we have to do some
+
+ align:start position:0%
+problems it just says we have to do some
+ 
+
+ align:start position:0%
+problems it just says we have to do some
+algebra
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we have these functions
+
+ align:start position:0%
+so we have these functions
+ 
+
+ align:start position:0%
+so we have these functions
+again uh and they igen functions of
+
+ align:start position:0%
+again uh and they igen functions of
+ 
+
+ align:start position:0%
+again uh and they igen functions of
+angular momenta which are Universal
+
+ align:start position:0%
+angular momenta which are Universal
+ 
+
+ align:start position:0%
+angular momenta which are Universal
+things and we can use these
+
+ align:start position:0%
+things and we can use these
+ 
+
+ align:start position:0%
+things and we can use these
+functions uh to uh
+
+ align:start position:0%
+functions uh to uh
+ 
+
+ align:start position:0%
+functions uh to uh
+calculate uh the direction cosiness we
+
+ align:start position:0%
+calculate uh the direction cosiness we
+ 
+
+ align:start position:0%
+calculate uh the direction cosiness we
+can say okay here we would like to know
+
+ align:start position:0%
+can say okay here we would like to know
+ 
+
+ align:start position:0%
+can say okay here we would like to know
+the projection of J on the body
+
+ align:start position:0%
+the projection of J on the body
+ 
+
+ align:start position:0%
+the projection of J on the body
+Z and
+
+ align:start position:0%
+Z and
+ 
+
+ align:start position:0%
+Z and
+uh for these functions they have the
+
+ align:start position:0%
+uh for these functions they have the
+ 
+
+ align:start position:0%
+uh for these functions they have the
+property that that
+
+ align:start position:0%
+property that that
+ 
+
+ align:start position:0%
+property that that
+is given by JJ + one square
+
+ align:start position:0%
+is given by JJ + one square
+ 
+
+ align:start position:0%
+is given by JJ + one square
+root and the
+
+ align:start position:0%
+root and the
+ 
+
+ align:start position:0%
+root and the
+cosine of
+
+ align:start position:0%
+cosine of
+ 
+
+ align:start position:0%
+cosine of
+J
+
+ align:start position:0%
+J
+ 
+
+ align:start position:0%
+J
+on body
+
+ align:start position:0%
+on body
+ 
+
+ align:start position:0%
+on body
+Z is Omega over JJ +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 square
+
+ align:start position:0%
+1 square
+ 
+
+ align:start position:0%
+1 square
+root this is a very useful thing because
+
+ align:start position:0%
+root this is a very useful thing because
+ 
+
+ align:start position:0%
+root this is a very useful thing because
+it provides a way of interpreting a lot
+
+ align:start position:0%
+it provides a way of interpreting a lot
+ 
+
+ align:start position:0%
+it provides a way of interpreting a lot
+of stuff I mean suppose
+
+ align:start position:0%
+of stuff I mean suppose
+ 
+
+ align:start position:0%
+of stuff I mean suppose
+you have a particular
+
+ align:start position:0%
+you have a particular
+ 
+
+ align:start position:0%
+you have a particular
+State uh and uh so you have a molecule
+
+ align:start position:0%
+State uh and uh so you have a molecule
+ 
+
+ align:start position:0%
+State uh and uh so you have a molecule
+in a particular
+
+ align:start position:0%
+in a particular
+ 
+
+ align:start position:0%
+in a particular
+Omega and the molecule has a dipole
+
+ align:start position:0%
+Omega and the molecule has a dipole
+ 
+
+ align:start position:0%
+Omega and the molecule has a dipole
+moment say along the body axis you want
+
+ align:start position:0%
+moment say along the body axis you want
+ 
+
+ align:start position:0%
+moment say along the body axis you want
+to know the projection of that dipole
+
+ align:start position:0%
+to know the projection of that dipole
+ 
+
+ align:start position:0%
+to know the projection of that dipole
+moment on
+
+ align:start position:0%
+moment on
+ 
+
+ align:start position:0%
+moment on
+J use One Direction cosine and then you
+
+ align:start position:0%
+J use One Direction cosine and then you
+ 
+
+ align:start position:0%
+J use One Direction cosine and then you
+want to know the projection of J on the
+
+ align:start position:0%
+want to know the projection of J on the
+ 
+
+ align:start position:0%
+want to know the projection of J on the
+laboratory axis and that tells you how
+
+ align:start position:0%
+laboratory axis and that tells you how
+ 
+
+ align:start position:0%
+laboratory axis and that tells you how
+anything in the body is transferred into
+
+ align:start position:0%
+anything in the body is transferred into
+ 
+
+ align:start position:0%
+anything in the body is transferred into
+the laboratory and this has to do with
+
+ align:start position:0%
+the laboratory and this has to do with
+ 
+
+ align:start position:0%
+the laboratory and this has to do with
+the Stark effect it has to do with
+
+ align:start position:0%
+the Stark effect it has to do with
+ 
+
+ align:start position:0%
+the Stark effect it has to do with
+transition electronic Transitions and so
+
+ align:start position:0%
+transition electronic Transitions and so
+ 
+
+ align:start position:0%
+transition electronic Transitions and so
+these Direction
+
+ align:start position:0%
+these Direction
+ 
+
+ align:start position:0%
+these Direction
+cosiness which are properties of these
+
+ align:start position:0%
+cosiness which are properties of these
+ 
+
+ align:start position:0%
+cosiness which are properties of these
+wave functions these wave functions
+
+ align:start position:0%
+wave functions these wave functions
+ 
+
+ align:start position:0%
+wave functions these wave functions
+enable you to know this but often you
+
+ align:start position:0%
+enable you to know this but often you
+ 
+
+ align:start position:0%
+enable you to know this but often you
+want to make some kind of sort of
+
+ align:start position:0%
+want to make some kind of sort of
+ 
+
+ align:start position:0%
+want to make some kind of sort of
+classical uh uh statement about how do
+
+ align:start position:0%
+classical uh uh statement about how do
+ 
+
+ align:start position:0%
+classical uh uh statement about how do
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+I mean after all when a molecule
+
+ align:start position:0%
+I mean after all when a molecule
+ 
+
+ align:start position:0%
+I mean after all when a molecule
+rotates and there's something that
+
+ align:start position:0%
+rotates and there's something that
+ 
+
+ align:start position:0%
+rotates and there's something that
+that's a so a property of the molecule
+
+ align:start position:0%
+that's a so a property of the molecule
+ 
+
+ align:start position:0%
+that's a so a property of the molecule
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+rotating it's trying to average it out
+
+ align:start position:0%
+rotating it's trying to average it out
+ 
+
+ align:start position:0%
+rotating it's trying to average it out
+relative to the
+
+ align:start position:0%
+relative to the
+ 
+
+ align:start position:0%
+relative to the
+laboratory but some of that can be
+
+ align:start position:0%
+laboratory but some of that can be
+ 
+
+ align:start position:0%
+laboratory but some of that can be
+remembered because J isn't uh moving in
+
+ align:start position:0%
+remembered because J isn't uh moving in
+ 
+
+ align:start position:0%
+remembered because J isn't uh moving in
+the laboratory it has a definite
+
+ align:start position:0%
+the laboratory it has a definite
+ 
+
+ align:start position:0%
+the laboratory it has a definite
+projection on the Z quantization axis so
+
+ align:start position:0%
+projection on the Z quantization axis so
+ 
+
+ align:start position:0%
+projection on the Z quantization axis so
+there's a huge amount of physical
+
+ align:start position:0%
+there's a huge amount of physical
+ 
+
+ align:start position:0%
+there's a huge amount of physical
+Insight that comes from the functions
+
+ align:start position:0%
+Insight that comes from the functions
+ 
+
+ align:start position:0%
+Insight that comes from the functions
+and these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things and so I I really you know my
+
+ align:start position:0%
+things and so I I really you know my
+ 
+
+ align:start position:0%
+things and so I I really you know my
+understanding of molecules is very much
+
+ align:start position:0%
+understanding of molecules is very much
+ 
+
+ align:start position:0%
+understanding of molecules is very much
+based on the use of Direction cosiness
+
+ align:start position:0%
+based on the use of Direction cosiness
+ 
+
+ align:start position:0%
+based on the use of Direction cosiness
+they're the same thing as 3j
+
+ align:start position:0%
+they're the same thing as 3j
+ 
+
+ align:start position:0%
+they're the same thing as 3j
+coefficients or kpch Gordon
+
+ align:start position:0%
+coefficients or kpch Gordon
+ 
+
+ align:start position:0%
+coefficients or kpch Gordon
+coefficients uh but this is a uh a very
+
+ align:start position:0%
+coefficients uh but this is a uh a very
+ 
+
+ align:start position:0%
+coefficients uh but this is a uh a very
+simple
+
+ align:start position:0%
+simple
+ 
+
+ align:start position:0%
+simple
+semi-classical thing okay what time is
+
+ align:start position:0%
+semi-classical thing okay what time is
+ 
+
+ align:start position:0%
+semi-classical thing okay what time is
+it how much time do I have
+
+ align:start position:0%
+it how much time do I have
+ 
+
+ align:start position:0%
+it how much time do I have
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+much okay so we have these functions and
+
+ align:start position:0%
+much okay so we have these functions and
+ 
+
+ align:start position:0%
+much okay so we have these functions and
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+have this quantity R the angular
+
+ align:start position:0%
+have this quantity R the angular
+ 
+
+ align:start position:0%
+have this quantity R the angular
+momentum squared and we can write that
+
+ align:start position:0%
+momentum squared and we can write that
+ 
+
+ align:start position:0%
+momentum squared and we can write that
+as j^ 2 as J - l - San
+
+ align:start position:0%
+as j^ 2 as J - l - San
+ 
+
+ align:start position:0%
+as j^ 2 as J - l - San
+squared and then we manipulate that into
+
+ align:start position:0%
+squared and then we manipulate that into
+ 
+
+ align:start position:0%
+squared and then we manipulate that into
+a form and I'm going to stop almost
+
+ align:start position:0%
+a form and I'm going to stop almost
+ 
+
+ align:start position:0%
+a form and I'm going to stop almost
+immediately that is convenient for
+
+ align:start position:0%
+immediately that is convenient for
+ 
+
+ align:start position:0%
+immediately that is convenient for
+evaluating uh Matrix elements of these
+
+ align:start position:0%
+evaluating uh Matrix elements of these
+ 
+
+ align:start position:0%
+evaluating uh Matrix elements of these
+sorts of
+
+ align:start position:0%
+sorts of
+ 
+
+ align:start position:0%
+sorts of
+things we write we rewrite this as j^2
+
+ align:start position:0%
+things we write we rewrite this as j^2
+ 
+
+ align:start position:0%
+things we write we rewrite this as j^2
+minus J little
+
+ align:start position:0%
+minus J little
+ 
+
+ align:start position:0%
+minus J little
+z^2 plus l^2 - L z^
+
+ align:start position:0%
+z^2 plus l^2 - L z^
+ 
+
+ align:start position:0%
+z^2 plus l^2 - L z^
+2 plus S2 minus sz^ 2 these are all
+
+ align:start position:0%
+2 plus S2 minus sz^ 2 these are all
+ 
+
+ align:start position:0%
+2 plus S2 minus sz^ 2 these are all
+trivial things these are fully diagonal
+
+ align:start position:0%
+trivial things these are fully diagonal
+ 
+
+ align:start position:0%
+trivial things these are fully diagonal
+in the usual basis set and then there's
+
+ align:start position:0%
+in the usual basis set and then there's
+ 
+
+ align:start position:0%
+in the usual basis set and then there's
+the other stuff which involves J X l x +
+
+ align:start position:0%
+the other stuff which involves J X l x +
+ 
+
+ align:start position:0%
+the other stuff which involves J X l x +
+j y l
+
+ align:start position:0%
+j y l
+ 
+
+ align:start position:0%
+j y l
+y * 2 all of the Cross
+
+ align:start position:0%
+y * 2 all of the Cross
+ 
+
+ align:start position:0%
+y * 2 all of the Cross
+terms and those cross terms lead to
+
+ align:start position:0%
+terms and those cross terms lead to
+ 
+
+ align:start position:0%
+terms and those cross terms lead to
+these are the things that one neglects
+
+ align:start position:0%
+these are the things that one neglects
+ 
+
+ align:start position:0%
+these are the things that one neglects
+they lead to what the phenomena called l
+
+ align:start position:0%
+they lead to what the phenomena called l
+ 
+
+ align:start position:0%
+they lead to what the phenomena called l
+uncoupling s uncoupling and rotational
+
+ align:start position:0%
+uncoupling s uncoupling and rotational
+ 
+
+ align:start position:0%
+uncoupling s uncoupling and rotational
+electronic perturbations and so these
+
+ align:start position:0%
+electronic perturbations and so these
+ 
+
+ align:start position:0%
+electronic perturbations and so these
+are things you put in and they lead to
+
+ align:start position:0%
+are things you put in and they lead to
+ 
+
+ align:start position:0%
+are things you put in and they lead to
+extra stuff that you have to deal with
+
+ align:start position:0%
+extra stuff that you have to deal with
+ 
+
+ align:start position:0%
+extra stuff that you have to deal with
+but this is the simple part of the
+
+ align:start position:0%
+but this is the simple part of the
+ 
+
+ align:start position:0%
+but this is the simple part of the
+hamiltonian the rotational hamiltonian
+
+ align:start position:0%
+hamiltonian the rotational hamiltonian
+ 
+
+ align:start position:0%
+hamiltonian the rotational hamiltonian
+and generally one only looks at that
+
+ align:start position:0%
+and generally one only looks at that
+ 
+
+ align:start position:0%
+and generally one only looks at that
+part j^ s JJ + 1 minus Omega 2qu this
+
+ align:start position:0%
+part j^ s JJ + 1 minus Omega 2qu this
+ 
+
+ align:start position:0%
+part j^ s JJ + 1 minus Omega 2qu this
+other stuff is not important okay I'm
+
+ align:start position:0%
+other stuff is not important okay I'm
+ 
+
+ align:start position:0%
+other stuff is not important okay I'm
+not going to uh say anything more about
+
+ align:start position:0%
+not going to uh say anything more about
+ 
+
+ align:start position:0%
+not going to uh say anything more about
+the born op
+
+ align:start position:0%
+the born op
+ 
+
+ align:start position:0%
+the born op
+approximation uh I'm not sure what the
+
+ align:start position:0%
+approximation uh I'm not sure what the
+ 
+
+ align:start position:0%
+approximation uh I'm not sure what the
+next lecture is but I'm going to do that
+
+ align:start position:0%
+next lecture is but I'm going to do that
+ 
+
+ align:start position:0%
+next lecture is but I'm going to do that
+but and I'm going to issue corrections
+
+ align:start position:0%
+but and I'm going to issue corrections
+ 
+
+ align:start position:0%
+but and I'm going to issue corrections
+to this lecture online and right along
+
+ align:start position:0%
+to this lecture online and right along
+ 
+
+ align:start position:0%
+to this lecture online and right along
+but the important thing is we Define
+
+ align:start position:0%
+but the important thing is we Define
+ 
+
+ align:start position:0%
+but the important thing is we Define
+basis functions complete sets of basis
+
+ align:start position:0%
+basis functions complete sets of basis
+ 
+
+ align:start position:0%
+basis functions complete sets of basis
+functions by neglecting certain terms in
+
+ align:start position:0%
+functions by neglecting certain terms in
+ 
+
+ align:start position:0%
+functions by neglecting certain terms in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+hamiltonian sometimes we know exactly
+
+ align:start position:0%
+hamiltonian sometimes we know exactly
+ 
+
+ align:start position:0%
+hamiltonian sometimes we know exactly
+what the term is that we neglect and we
+
+ align:start position:0%
+what the term is that we neglect and we
+ 
+
+ align:start position:0%
+what the term is that we neglect and we
+neglect it because we know it ought to
+
+ align:start position:0%
+neglect it because we know it ought to
+ 
+
+ align:start position:0%
+neglect it because we know it ought to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+small sometimes we cannot Define what
+
+ align:start position:0%
+small sometimes we cannot Define what
+ 
+
+ align:start position:0%
+small sometimes we cannot Define what
+that term is that we're neglecting as in
+
+ align:start position:0%
+that term is that we're neglecting as in
+ 
+
+ align:start position:0%
+that term is that we're neglecting as in
+the case of defining diabetic functions
+
+ align:start position:0%
+the case of defining diabetic functions
+ 
+
+ align:start position:0%
+the case of defining diabetic functions
+there's some term in the interelectronic
+
+ align:start position:0%
+there's some term in the interelectronic
+ 
+
+ align:start position:0%
+there's some term in the interelectronic
+repulsion that results in an avoided
+
+ align:start position:0%
+repulsion that results in an avoided
+ 
+
+ align:start position:0%
+repulsion that results in an avoided
+Crossing we cannot specify what that is
+
+ align:start position:0%
+Crossing we cannot specify what that is
+ 
+
+ align:start position:0%
+Crossing we cannot specify what that is
+but we can get it by looking at the
+
+ align:start position:0%
+but we can get it by looking at the
+ 
+
+ align:start position:0%
+but we can get it by looking at the
+adiabatic functions in the region of the
+
+ align:start position:0%
+adiabatic functions in the region of the
+ 
+
+ align:start position:0%
+adiabatic functions in the region of the
+crossing and so there is a way of Def
+
+ align:start position:0%
+crossing and so there is a way of Def
+ 
+
+ align:start position:0%
+crossing and so there is a way of Def
+extracting a diabetic representation
+
+ align:start position:0%
+extracting a diabetic representation
+ 
+
+ align:start position:0%
+extracting a diabetic representation
+from the adiabatic one and then using
+
+ align:start position:0%
+from the adiabatic one and then using
+ 
+
+ align:start position:0%
+from the adiabatic one and then using
+the diabetic representation because
+
+ align:start position:0%
+the diabetic representation because
+ 
+
+ align:start position:0%
+the diabetic representation because
+that's benign in terms of the bad things
+
+ align:start position:0%
+that's benign in terms of the bad things
+ 
+
+ align:start position:0%
+that's benign in terms of the bad things
+that you're going to have to deal with I
+
+ align:start position:0%
+that you're going to have to deal with I
+ 
+
+ align:start position:0%
+that you're going to have to deal with I
+mean one of the things you don't want is
+
+ align:start position:0%
+mean one of the things you don't want is
+ 
+
+ align:start position:0%
+mean one of the things you don't want is
+off diagonal matrix elements that are
+
+ align:start position:0%
+off diagonal matrix elements that are
+ 
+
+ align:start position:0%
+off diagonal matrix elements that are
+large compared to the level spacings
+
+ align:start position:0%
+large compared to the level spacings
+ 
+
+ align:start position:0%
+large compared to the level spacings
+that you have in your zero order
+
+ align:start position:0%
+that you have in your zero order
+ 
+
+ align:start position:0%
+that you have in your zero order
+hamiltonian if they're large I mean if
+
+ align:start position:0%
+hamiltonian if they're large I mean if
+ 
+
+ align:start position:0%
+hamiltonian if they're large I mean if
+you have an interaction which is larger
+
+ align:start position:0%
+you have an interaction which is larger
+ 
+
+ align:start position:0%
+you have an interaction which is larger
+than the vibrational frequency in some
+
+ align:start position:0%
+than the vibrational frequency in some
+ 
+
+ align:start position:0%
+than the vibrational frequency in some
+State then you're going to be
+
+ align:start position:0%
+State then you're going to be
+ 
+
+ align:start position:0%
+State then you're going to be
+diagonalizing a
+
+ align:start position:0%
+diagonalizing a
+ 
+
+ align:start position:0%
+diagonalizing a
+matrix which is essentially infinite
+
+ align:start position:0%
+matrix which is essentially infinite
+ 
+
+ align:start position:0%
+matrix which is essentially infinite
+which is bad you really want to
+
+ align:start position:0%
+which is bad you really want to
+ 
+
+ align:start position:0%
+which is bad you really want to
+diagonalize 2 by two matrices because
+
+ align:start position:0%
+diagonalize 2 by two matrices because
+ 
+
+ align:start position:0%
+diagonalize 2 by two matrices because
+there's a small thing that you have to
+
+ align:start position:0%
+there's a small thing that you have to
+ 
+
+ align:start position:0%
+there's a small thing that you have to
+do to fix up the the neglected
+
+ align:start position:0%
+do to fix up the the neglected
+ 
+
+ align:start position:0%
+do to fix up the the neglected
+approximation the approximation you've
+
+ align:start position:0%
+approximation the approximation you've
+ 
+
+ align:start position:0%
+approximation the approximation you've
+made okay so that's it is
+
+ align:start position:0%
+made okay so that's it is
+ 
+
+ align:start position:0%
+made okay so that's it is
+everybody more comfortable with the born
+
+ align:start position:0%
+everybody more comfortable with the born
+ 
+
+ align:start position:0%
+everybody more comfortable with the born
+op approximation now than they were
+
+ align:start position:0%
+op approximation now than they were
+ 
+
+ align:start position:0%
+op approximation now than they were
+before this this class let's hope they
+
+ align:start position:0%
+before this this class let's hope they
+ 
+
+ align:start position:0%
+before this this class let's hope they
+are you are okay
\ No newline at end of file
diff --git a/HHwDX-3IPT0.txt b/HHwDX-3IPT0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7777c8c2291ff23d30c4b303784cbb445a52e3be
--- /dev/null
+++ b/HHwDX-3IPT0.txt
@@ -0,0 +1,7608 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu Way wave equation so the
+
+ align:start position:0%
+ocw.mit.edu Way wave equation so the
+ 
+
+ align:start position:0%
+ocw.mit.edu Way wave equation so the
+model for hyperbolic equations and that
+
+ align:start position:0%
+model for hyperbolic equations and that
+ 
+
+ align:start position:0%
+model for hyperbolic equations and that
+word hyperbolic tells me that that um
+
+ align:start position:0%
+word hyperbolic tells me that that um
+ 
+
+ align:start position:0%
+word hyperbolic tells me that that um
+signals are traveling with finite speed
+
+ align:start position:0%
+signals are traveling with finite speed
+ 
+
+ align:start position:0%
+signals are traveling with finite speed
+in this case the speed is C and in this
+
+ align:start position:0%
+in this case the speed is C and in this
+ 
+
+ align:start position:0%
+in this case the speed is C and in this
+case the signals are only going to the
+
+ align:start position:0%
+case the signals are only going to the
+ 
+
+ align:start position:0%
+case the signals are only going to the
+left the two-way wave equation will
+
+ align:start position:0%
+left the two-way wave equation will
+ 
+
+ align:start position:0%
+left the two-way wave equation will
+travel left and right but again finite
+
+ align:start position:0%
+travel left and right but again finite
+ 
+
+ align:start position:0%
+travel left and right but again finite
+speed the I I emphasize finite speed
+
+ align:start position:0%
+speed the I I emphasize finite speed
+ 
+
+ align:start position:0%
+speed the I I emphasize finite speed
+because for the heat
+
+ align:start position:0%
+because for the heat
+ 
+
+ align:start position:0%
+because for the heat
+equation that the speed is infinite you
+
+ align:start position:0%
+equation that the speed is infinite you
+ 
+
+ align:start position:0%
+equation that the speed is infinite you
+as soon as you change an initial
+
+ align:start position:0%
+as soon as you change an initial
+ 
+
+ align:start position:0%
+as soon as you change an initial
+condition at any later time you
+
+ align:start position:0%
+condition at any later time you
+ 
+
+ align:start position:0%
+condition at any later time you
+immediately feel the effect well
+
+ align:start position:0%
+immediately feel the effect well
+ 
+
+ align:start position:0%
+immediately feel the effect well
+probably small effect way way out so so
+
+ align:start position:0%
+probably small effect way way out so so
+ 
+
+ align:start position:0%
+probably small effect way way out so so
+diffusion travels with infinite speed
+
+ align:start position:0%
+diffusion travels with infinite speed
+ 
+
+ align:start position:0%
+diffusion travels with infinite speed
+waves travel with finite speed okay now
+
+ align:start position:0%
+waves travel with finite speed okay now
+ 
+
+ align:start position:0%
+waves travel with finite speed okay now
+and the difference sort of is that the
+
+ align:start position:0%
+and the difference sort of is that the
+ 
+
+ align:start position:0%
+and the difference sort of is that the
+uh true amplif the true growth factor G
+
+ align:start position:0%
+uh true amplif the true growth factor G
+ 
+
+ align:start position:0%
+uh true amplif the true growth factor G
+you remember the true growth factor was
+
+ align:start position:0%
+you remember the true growth factor was
+ 
+
+ align:start position:0%
+you remember the true growth factor was
+for the wave equation the for the for
+
+ align:start position:0%
+for the wave equation the for the for
+ 
+
+ align:start position:0%
+for the wave equation the for the for
+the this is the G for the that multip
+
+ align:start position:0%
+the this is the G for the that multip
+ 
+
+ align:start position:0%
+the this is the G for the that multip
+IES the exponential e to the I KX in the
+
+ align:start position:0%
+IES the exponential e to the I KX in the
+ 
+
+ align:start position:0%
+IES the exponential e to the I KX in the
+difference equation and G the true
+
+ align:start position:0%
+difference equation and G the true
+ 
+
+ align:start position:0%
+difference equation and G the true
+G is e to the i k
+
+ align:start position:0%
+G is e to the i k
+ 
+
+ align:start position:0%
+G is e to the i k
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+t so that what I was going to say is
+
+ align:start position:0%
+t so that what I was going to say is
+ 
+
+ align:start position:0%
+t so that what I was going to say is
+that that has absolute value
+
+ align:start position:0%
+that that has absolute value
+ 
+
+ align:start position:0%
+that that has absolute value
+one again a difference from the heat
+
+ align:start position:0%
+one again a difference from the heat
+ 
+
+ align:start position:0%
+one again a difference from the heat
+equation for the heat equation with the
+
+ align:start position:0%
+equation for the heat equation with the
+ 
+
+ align:start position:0%
+equation for the heat equation with the
+fusion G will be smaller than one you're
+
+ align:start position:0%
+fusion G will be smaller than one you're
+ 
+
+ align:start position:0%
+fusion G will be smaller than one you're
+losing energy for the wave equation the
+
+ align:start position:0%
+losing energy for the wave equation the
+ 
+
+ align:start position:0%
+losing energy for the wave equation the
+energy is constant and the wave is just
+
+ align:start position:0%
+energy is constant and the wave is just
+ 
+
+ align:start position:0%
+energy is constant and the wave is just
+moving okay so it's a little more
+
+ align:start position:0%
+moving okay so it's a little more
+ 
+
+ align:start position:0%
+moving okay so it's a little more
+delicate because we're trying to this G
+
+ align:start position:0%
+delicate because we're trying to this G
+ 
+
+ align:start position:0%
+delicate because we're trying to this G
+in the difference equation has to stay
+
+ align:start position:0%
+in the difference equation has to stay
+ 
+
+ align:start position:0%
+in the difference equation has to stay
+be somehow close to that one which is
+
+ align:start position:0%
+be somehow close to that one which is
+ 
+
+ align:start position:0%
+be somehow close to that one which is
+right on the unit circle and yet we got
+
+ align:start position:0%
+right on the unit circle and yet we got
+ 
+
+ align:start position:0%
+right on the unit circle and yet we got
+to stay we can't go outside the unit
+
+ align:start position:0%
+to stay we can't go outside the unit
+ 
+
+ align:start position:0%
+to stay we can't go outside the unit
+circle
+
+ align:start position:0%
+circle
+ 
+
+ align:start position:0%
+circle
+so here are two methods we had one
+
+ align:start position:0%
+so here are two methods we had one
+ 
+
+ align:start position:0%
+so here are two methods we had one
+method last time that
+
+ align:start position:0%
+method last time that
+ 
+
+ align:start position:0%
+method last time that
+worked that was one one-sided
+
+ align:start position:0%
+worked that was one one-sided
+ 
+
+ align:start position:0%
+worked that was one one-sided
+differences and of course you had to
+
+ align:start position:0%
+differences and of course you had to
+ 
+
+ align:start position:0%
+differences and of course you had to
+take the difference on the good side the
+
+ align:start position:0%
+take the difference on the good side the
+ 
+
+ align:start position:0%
+take the difference on the good side the
+upwind side and that was first order and
+
+ align:start position:0%
+upwind side and that was first order and
+ 
+
+ align:start position:0%
+upwind side and that was first order and
+the Cent Fredick Ley condition was the
+
+ align:start position:0%
+the Cent Fredick Ley condition was the
+ 
+
+ align:start position:0%
+the Cent Fredick Ley condition was the
+same as the vanoyan stability condition
+
+ align:start position:0%
+same as the vanoyan stability condition
+ 
+
+ align:start position:0%
+same as the vanoyan stability condition
+and it was R between zero and one R was
+
+ align:start position:0%
+and it was R between zero and one R was
+ 
+
+ align:start position:0%
+and it was R between zero and one R was
+this R is this ratio C delta T over
+
+ align:start position:0%
+this R is this ratio C delta T over
+ 
+
+ align:start position:0%
+this R is this ratio C delta T over
+Delta X that comes
+
+ align:start position:0%
+Delta X that comes
+ 
+
+ align:start position:0%
+Delta X that comes
+in for it comes into the wave equation
+
+ align:start position:0%
+in for it comes into the wave equation
+ 
+
+ align:start position:0%
+in for it comes into the wave equation
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+now we really have to think about better
+
+ align:start position:0%
+now we really have to think about better
+ 
+
+ align:start position:0%
+now we really have to think about better
+methods other methods and here are
+
+ align:start position:0%
+methods other methods and here are
+ 
+
+ align:start position:0%
+methods other methods and here are
+two LAX frieds which will only be first
+
+ align:start position:0%
+two LAX frieds which will only be first
+ 
+
+ align:start position:0%
+two LAX frieds which will only be first
+order so when I these are the questions
+
+ align:start position:0%
+order so when I these are the questions
+ 
+
+ align:start position:0%
+order so when I these are the questions
+I always ask and then finally experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean these are these answering these
+
+ align:start position:0%
+I mean these are these answering these
+ 
+
+ align:start position:0%
+I mean these are these answering these
+questions will certainly be a guide to
+
+ align:start position:0%
+questions will certainly be a guide to
+ 
+
+ align:start position:0%
+questions will certainly be a guide to
+what we'll see experimentally but it
+
+ align:start position:0%
+what we'll see experimentally but it
+ 
+
+ align:start position:0%
+what we'll see experimentally but it
+there's more to learn from actually
+
+ align:start position:0%
+there's more to learn from actually
+ 
+
+ align:start position:0%
+there's more to learn from actually
+doing the numbers okay the accuracy LAX
+
+ align:start position:0%
+doing the numbers okay the accuracy LAX
+ 
+
+ align:start position:0%
+doing the numbers okay the accuracy LAX
+friedr will be only first order whereas
+
+ align:start position:0%
+friedr will be only first order whereas
+ 
+
+ align:start position:0%
+friedr will be only first order whereas
+LAX
+
+ align:start position:0%
+LAX
+ 
+
+ align:start position:0%
+LAX
+wend will be second order so with
+
+ align:start position:0%
+wend will be second order so with
+ 
+
+ align:start position:0%
+wend will be second order so with
+respect to accuracy that's certainly
+
+ align:start position:0%
+respect to accuracy that's certainly
+ 
+
+ align:start position:0%
+respect to accuracy that's certainly
+better
+
+ align:start position:0%
+better
+ 
+
+ align:start position:0%
+better
+okay can we see that maybe without too
+
+ align:start position:0%
+okay can we see that maybe without too
+ 
+
+ align:start position:0%
+okay can we see that maybe without too
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+calculation the notes would have the
+
+ align:start position:0%
+calculation the notes would have the
+ 
+
+ align:start position:0%
+calculation the notes would have the
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+details the can you see here's LAX wend
+
+ align:start position:0%
+details the can you see here's LAX wend
+ 
+
+ align:start position:0%
+details the can you see here's LAX wend
+LAX
+
+ align:start position:0%
+LAX
+ 
+
+ align:start position:0%
+LAX
+frieds so what's the idea of LAX
+
+ align:start position:0%
+frieds so what's the idea of LAX
+ 
+
+ align:start position:0%
+frieds so what's the idea of LAX
+friedricks you you remember the total
+
+ align:start position:0%
+friedricks you you remember the total
+ 
+
+ align:start position:0%
+friedricks you you remember the total
+failure the complete and absolute
+
+ align:start position:0%
+failure the complete and absolute
+ 
+
+ align:start position:0%
+failure the complete and absolute
+failure when we used a time difference
+
+ align:start position:0%
+failure when we used a time difference
+ 
+
+ align:start position:0%
+failure when we used a time difference
+there and a space difference
+
+ align:start position:0%
+there and a space difference
+ 
+
+ align:start position:0%
+there and a space difference
+there you remember that that gave uh the
+
+ align:start position:0%
+there you remember that that gave uh the
+ 
+
+ align:start position:0%
+there you remember that that gave uh the
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+difference that produced a one in G and
+
+ align:start position:0%
+difference that produced a one in G and
+ 
+
+ align:start position:0%
+difference that produced a one in G and
+this space difference produced
+
+ align:start position:0%
+this space difference produced
+ 
+
+ align:start position:0%
+this space difference produced
+an imaginary part in G so we had G as
+
+ align:start position:0%
+an imaginary part in G so we had G as
+ 
+
+ align:start position:0%
+an imaginary part in G so we had G as
+one plus something imaginary when we
+
+ align:start position:0%
+one plus something imaginary when we
+ 
+
+ align:start position:0%
+one plus something imaginary when we
+were outside the circle automatically
+
+ align:start position:0%
+were outside the circle automatically
+ 
+
+ align:start position:0%
+were outside the circle automatically
+well fried's thought of a way to get
+
+ align:start position:0%
+well fried's thought of a way to get
+ 
+
+ align:start position:0%
+well fried's thought of a way to get
+around that instead of using ujn here
+
+ align:start position:0%
+around that instead of using ujn here
+ 
+
+ align:start position:0%
+around that instead of using ujn here
+instead of the backward difference he
+
+ align:start position:0%
+instead of the backward difference he
+ 
+
+ align:start position:0%
+instead of the backward difference he
+replaced ujn by the average of that
+
+ align:start position:0%
+replaced ujn by the average of that
+ 
+
+ align:start position:0%
+replaced ujn by the average of that
+value and that value so that so that
+
+ align:start position:0%
+value and that value so that so that
+ 
+
+ align:start position:0%
+value and that value so that so that
+both sides now involve just two numbers
+
+ align:start position:0%
+both sides now involve just two numbers
+ 
+
+ align:start position:0%
+both sides now involve just two numbers
+UJ and u u this one and this one this
+
+ align:start position:0%
+UJ and u u this one and this one this
+ 
+
+ align:start position:0%
+UJ and u u this one and this one this
+this one is not used
+
+ align:start position:0%
+this one is not used
+ 
+
+ align:start position:0%
+this one is not used
+now and again for still first order you
+
+ align:start position:0%
+now and again for still first order you
+ 
+
+ align:start position:0%
+now and again for still first order you
+won't be
+
+ align:start position:0%
+won't be
+ 
+
+ align:start position:0%
+won't be
+surprised that this approximation is has
+
+ align:start position:0%
+surprised that this approximation is has
+ 
+
+ align:start position:0%
+surprised that this approximation is has
+got first order
+
+ align:start position:0%
+got first order
+ 
+
+ align:start position:0%
+got first order
+error and but stability now is back with
+
+ align:start position:0%
+error and but stability now is back with
+ 
+
+ align:start position:0%
+error and but stability now is back with
+us and easy to check
+
+ align:start position:0%
+us and easy to check
+ 
+
+ align:start position:0%
+us and easy to check
+because now each new value depends on
+
+ align:start position:0%
+because now each new value depends on
+ 
+
+ align:start position:0%
+because now each new value depends on
+what old values just these two and with
+
+ align:start position:0%
+what old values just these two and with
+ 
+
+ align:start position:0%
+what old values just these two and with
+what coefficients so let's let let me
+
+ align:start position:0%
+what coefficients so let's let let me
+ 
+
+ align:start position:0%
+what coefficients so let's let let me
+just check stability for LAX frieds so
+
+ align:start position:0%
+just check stability for LAX frieds so
+ 
+
+ align:start position:0%
+just check stability for LAX frieds so
+UJ + 1 n the new value is some multiple
+
+ align:start position:0%
+UJ + 1 n the new value is some multiple
+ 
+
+ align:start position:0%
+UJ + 1 n the new value is some multiple
+of this guy the one on the left left and
+
+ align:start position:0%
+of this guy the one on the left left and
+ 
+
+ align:start position:0%
+of this guy the one on the left left and
+some multiple of this one the one on the
+
+ align:start position:0%
+some multiple of this one the one on the
+ 
+
+ align:start position:0%
+some multiple of this one the one on the
+right and what are those multiples let's
+
+ align:start position:0%
+right and what are those multiples let's
+ 
+
+ align:start position:0%
+right and what are those multiples let's
+see I'm going to move things over to the
+
+ align:start position:0%
+see I'm going to move things over to the
+ 
+
+ align:start position:0%
+see I'm going to move things over to the
+right hand side of the equation so I
+
+ align:start position:0%
+right hand side of the equation so I
+ 
+
+ align:start position:0%
+right hand side of the equation so I
+think there's a
+
+ align:start position:0%
+think there's a
+ 
+
+ align:start position:0%
+think there's a
+half and then I think there's an R over
+
+ align:start position:0%
+half and then I think there's an R over
+ 
+
+ align:start position:0%
+half and then I think there's an R over
+R minus I guess this is the one that
+
+ align:start position:0%
+R minus I guess this is the one that
+ 
+
+ align:start position:0%
+R minus I guess this is the one that
+comes in with a minus
+
+ align:start position:0%
+comes in with a minus
+ 
+
+ align:start position:0%
+comes in with a minus
+sign it's the one on the left and the
+
+ align:start position:0%
+sign it's the one on the left and the
+ 
+
+ align:start position:0%
+sign it's the one on the left and the
+one on the right UJ + 1 n there's a half
+
+ align:start position:0%
+one on the right UJ + 1 n there's a half
+ 
+
+ align:start position:0%
+one on the right UJ + 1 n there's a half
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+R2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay simple
+
+ align:start position:0%
+okay simple
+ 
+
+ align:start position:0%
+okay simple
+idea simple idea and it has one
+
+ align:start position:0%
+idea simple idea and it has one
+ 
+
+ align:start position:0%
+idea simple idea and it has one
+advantage important advantage over
+
+ align:start position:0%
+advantage important advantage over
+ 
+
+ align:start position:0%
+advantage important advantage over
+upwind one-sided that we saw last time
+
+ align:start position:0%
+upwind one-sided that we saw last time
+ 
+
+ align:start position:0%
+upwind one-sided that we saw last time
+it's not a great method it's only first
+
+ align:start position:0%
+it's not a great method it's only first
+ 
+
+ align:start position:0%
+it's not a great method it's only first
+first order here if
+
+ align:start position:0%
+first order here if
+ 
+
+ align:start position:0%
+first order here if
+I and you see what the you see when it's
+
+ align:start position:0%
+I and you see what the you see when it's
+ 
+
+ align:start position:0%
+I and you see what the you see when it's
+going to be stable
+
+ align:start position:0%
+going to be stable
+ 
+
+ align:start position:0%
+going to be stable
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+coefficients add to
+
+ align:start position:0%
+coefficients add to
+ 
+
+ align:start position:0%
+coefficients add to
+one our coefficients always add to one
+
+ align:start position:0%
+one our coefficients always add to one
+ 
+
+ align:start position:0%
+one our coefficients always add to one
+right because if we have a constant
+
+ align:start position:0%
+right because if we have a constant
+ 
+
+ align:start position:0%
+right because if we have a constant
+state this next step should be that same
+
+ align:start position:0%
+state this next step should be that same
+ 
+
+ align:start position:0%
+state this next step should be that same
+state it's not going to
+
+ align:start position:0%
+state it's not going to
+ 
+
+ align:start position:0%
+state it's not going to
+change but so uh but instead of having
+
+ align:start position:0%
+change but so uh but instead of having
+ 
+
+ align:start position:0%
+change but so uh but instead of having
+the typical one in the G I have it split
+
+ align:start position:0%
+the typical one in the G I have it split
+ 
+
+ align:start position:0%
+the typical one in the G I have it split
+into a half so what is g for this guy G
+
+ align:start position:0%
+into a half so what is g for this guy G
+ 
+
+ align:start position:0%
+into a half so what is g for this guy G
+for for this guy is this number 1 - R /2
+
+ align:start position:0%
+for for this guy is this number 1 - R /2
+ 
+
+ align:start position:0%
+for for this guy is this number 1 - R /2
+* e - i k Delta
+
+ align:start position:0%
+* e - i k Delta
+ 
+
+ align:start position:0%
+* e - i k Delta
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+plus this
+
+ align:start position:0%
+plus this
+ 
+
+ align:start position:0%
+plus this
+number time e the plus I Delta X are you
+
+ align:start position:0%
+number time e the plus I Delta X are you
+ 
+
+ align:start position:0%
+number time e the plus I Delta X are you
+you you're seeing now the
+
+ align:start position:0%
+you you're seeing now the
+ 
+
+ align:start position:0%
+you you're seeing now the
+pattern so I sort of
+
+ align:start position:0%
+pattern so I sort of
+ 
+
+ align:start position:0%
+pattern so I sort of
+jumped to G without plugging in the e
+
+ align:start position:0%
+jumped to G without plugging in the e
+ 
+
+ align:start position:0%
+jumped to G without plugging in the e
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+ikx taking a step and then factoring out
+
+ align:start position:0%
+ikx taking a step and then factoring out
+ 
+
+ align:start position:0%
+ikx taking a step and then factoring out
+e to the ikx I did it without without
+
+ align:start position:0%
+e to the ikx I did it without without
+ 
+
+ align:start position:0%
+e to the ikx I did it without without
+writing down the e to the IX this is
+
+ align:start position:0%
+writing down the e to the IX this is
+ 
+
+ align:start position:0%
+writing down the e to the IX this is
+what factors
+
+ align:start position:0%
+what factors
+ 
+
+ align:start position:0%
+what factors
+out and
+
+ align:start position:0%
+out and
+ 
+
+ align:start position:0%
+out and
+uh when oh maybe a one plus r would be
+
+ align:start position:0%
+uh when oh maybe a one plus r would be
+ 
+
+ align:start position:0%
+uh when oh maybe a one plus r would be
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+correct
+
+ align:start position:0%
+correct
+ 
+
+ align:start position:0%
+correct
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so stability requires this complex
+
+ align:start position:0%
+so stability requires this complex
+ 
+
+ align:start position:0%
+so stability requires this complex
+number which I could write in different
+
+ align:start position:0%
+number which I could write in different
+ 
+
+ align:start position:0%
+number which I could write in different
+ways
+
+ align:start position:0%
+ways
+ 
+
+ align:start position:0%
+ways
+I could the the real part there would be
+
+ align:start position:0%
+I could the the real part there would be
+ 
+
+ align:start position:0%
+I could the the real part there would be
+a cosine this this would actually be the
+
+ align:start position:0%
+a cosine this this would actually be the
+ 
+
+ align:start position:0%
+a cosine this this would actually be the
+cosine plus r time the S Plus I time the
+
+ align:start position:0%
+cosine plus r time the S Plus I time the
+ 
+
+ align:start position:0%
+cosine plus r time the S Plus I time the
+sign this is really I could rewrite that
+
+ align:start position:0%
+sign this is really I could rewrite that
+ 
+
+ align:start position:0%
+sign this is really I could rewrite that
+as cos K Delta
+
+ align:start position:0%
+as cos K Delta
+ 
+
+ align:start position:0%
+as cos K Delta
+X plus I sin K Delta
+
+ align:start position:0%
+X plus I sin K Delta
+ 
+
+ align:start position:0%
+X plus I sin K Delta
+X I don't know which way you let you
+
+ align:start position:0%
+X I don't know which way you let you
+ 
+
+ align:start position:0%
+X I don't know which way you let you
+hear this shows you the real and
+
+ align:start position:0%
+hear this shows you the real and
+ 
+
+ align:start position:0%
+hear this shows you the real and
+imaginary parts that makes it
+
+ align:start position:0%
+imaginary parts that makes it
+ 
+
+ align:start position:0%
+imaginary parts that makes it
+nice this shows you the two Co
+
+ align:start position:0%
+nice this shows you the two Co
+ 
+
+ align:start position:0%
+nice this shows you the two Co
+efficients that makes it
+
+ align:start position:0%
+efficients that makes it
+ 
+
+ align:start position:0%
+efficients that makes it
+nice and can you see stability so what
+
+ align:start position:0%
+nice and can you see stability so what
+ 
+
+ align:start position:0%
+nice and can you see stability so what
+is Kuran fried Levy the the the
+
+ align:start position:0%
+is Kuran fried Levy the the the
+ 
+
+ align:start position:0%
+is Kuran fried Levy the the the
+characteristic discussion the argument
+
+ align:start position:0%
+characteristic discussion the argument
+ 
+
+ align:start position:0%
+characteristic discussion the argument
+based on
+
+ align:start position:0%
+based on
+ 
+
+ align:start position:0%
+based on
+characteristics says what stability is
+
+ align:start position:0%
+characteristics says what stability is
+ 
+
+ align:start position:0%
+characteristics says what stability is
+going to mean that delta
+
+ align:start position:0%
+going to mean that delta
+ 
+
+ align:start position:0%
+going to mean that delta
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+has stability is going to happen when R
+
+ align:start position:0%
+has stability is going to happen when R
+ 
+
+ align:start position:0%
+has stability is going to happen when R
+is below one it's just like upwind
+
+ align:start position:0%
+is below one it's just like upwind
+ 
+
+ align:start position:0%
+is below one it's just like upwind
+except that R could also be coming C
+
+ align:start position:0%
+except that R could also be coming C
+ 
+
+ align:start position:0%
+except that R could also be coming C
+could have the opposite
+
+ align:start position:0%
+could have the opposite
+ 
+
+ align:start position:0%
+could have the opposite
+sign LAX frieds is prepared for C to be
+
+ align:start position:0%
+sign LAX frieds is prepared for C to be
+ 
+
+ align:start position:0%
+sign LAX frieds is prepared for C to be
+positive or negative because it's it's
+
+ align:start position:0%
+positive or negative because it's it's
+ 
+
+ align:start position:0%
+positive or negative because it's it's
+not purely up wind or purely downwind
+
+ align:start position:0%
+not purely up wind or purely downwind
+ 
+
+ align:start position:0%
+not purely up wind or purely downwind
+it's both winds okay so and do you see
+
+ align:start position:0%
+it's both winds okay so and do you see
+ 
+
+ align:start position:0%
+it's both winds okay so and do you see
+that if R is anywhere so this
+
+ align:start position:0%
+that if R is anywhere so this
+ 
+
+ align:start position:0%
+that if R is anywhere so this
+is the condition is going to be that
+
+ align:start position:0%
+is the condition is going to be that
+ 
+
+ align:start position:0%
+is the condition is going to be that
+minus1
+
+ align:start position:0%
+minus1
+ 
+
+ align:start position:0%
+minus1
+is R is between minus1 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and and see what's nice about
+
+ align:start position:0%
+one and and see what's nice about
+ 
+
+ align:start position:0%
+one and and see what's nice about
+Fredrick's in that
+
+ align:start position:0%
+Fredrick's in that
+ 
+
+ align:start position:0%
+Fredrick's in that
+case this number is positive this number
+
+ align:start position:0%
+case this number is positive this number
+ 
+
+ align:start position:0%
+case this number is positive this number
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+positive because the one is bigger than
+
+ align:start position:0%
+positive because the one is bigger than
+ 
+
+ align:start position:0%
+positive because the one is bigger than
+the R so uh so each
+
+ align:start position:0%
+the R so uh so each
+ 
+
+ align:start position:0%
+the R so uh so each
+step and they and they add to one so
+
+ align:start position:0%
+step and they and they add to one so
+ 
+
+ align:start position:0%
+step and they and they add to one so
+each step takes the new value as a
+
+ align:start position:0%
+each step takes the new value as a
+ 
+
+ align:start position:0%
+each step takes the new value as a
+combination of the two old values and of
+
+ align:start position:0%
+combination of the two old values and of
+ 
+
+ align:start position:0%
+combination of the two old values and of
+course the magnitude can't be bigger
+
+ align:start position:0%
+course the magnitude can't be bigger
+ 
+
+ align:start position:0%
+course the magnitude can't be bigger
+than one so so under this condition I
+
+ align:start position:0%
+than one so so under this condition I
+ 
+
+ align:start position:0%
+than one so so under this condition I
+have positive coefficients that's
+
+ align:start position:0%
+have positive coefficients that's
+ 
+
+ align:start position:0%
+have positive coefficients that's
+positive and that's
+
+ align:start position:0%
+positive and that's
+ 
+
+ align:start position:0%
+positive and that's
+positive they multiply things of
+
+ align:start position:0%
+positive they multiply things of
+ 
+
+ align:start position:0%
+positive they multiply things of
+absolute value one so
+
+ align:start position:0%
+absolute value one so
+ 
+
+ align:start position:0%
+absolute value one so
+they can't the sum can't get Beyond one
+
+ align:start position:0%
+they can't the sum can't get Beyond one
+ 
+
+ align:start position:0%
+they can't the sum can't get Beyond one
+or you might like it here the magnitude
+
+ align:start position:0%
+or you might like it here the magnitude
+ 
+
+ align:start position:0%
+or you might like it here the magnitude
+squ is cine 2 + r^ 2 sin 2 and if R is
+
+ align:start position:0%
+squ is cine 2 + r^ 2 sin 2 and if R is
+ 
+
+ align:start position:0%
+squ is cine 2 + r^ 2 sin 2 and if R is
+below 1 we're smaller than cosine squ
+
+ align:start position:0%
+below 1 we're smaller than cosine squ
+ 
+
+ align:start position:0%
+below 1 we're smaller than cosine squ
+plus sin squ which is one so if I draw
+
+ align:start position:0%
+plus sin squ which is one so if I draw
+ 
+
+ align:start position:0%
+plus sin squ which is one so if I draw
+the uh just for a moment if I draw the
+
+ align:start position:0%
+the uh just for a moment if I draw the
+ 
+
+ align:start position:0%
+the uh just for a moment if I draw the
+the G in the complex
+
+ align:start position:0%
+the G in the complex
+ 
+
+ align:start position:0%
+the G in the complex
+plane so there's the unit circle K
+
+ align:start position:0%
+plane so there's the unit circle K
+ 
+
+ align:start position:0%
+plane so there's the unit circle K
+equals 0 is always there that's at
+
+ align:start position:0%
+equals 0 is always there that's at
+ 
+
+ align:start position:0%
+equals 0 is always there that's at
+that's at one then these points
+
+ align:start position:0%
+that's at one then these points
+ 
+
+ align:start position:0%
+that's at one then these points
+I think probably those points fall on an
+
+ align:start position:0%
+I think probably those points fall on an
+ 
+
+ align:start position:0%
+I think probably those points fall on an
+ellipse here where we go up as high as
+
+ align:start position:0%
+ellipse here where we go up as high as
+ 
+
+ align:start position:0%
+ellipse here where we go up as high as
+r or magnitude of R and we go left right
+
+ align:start position:0%
+r or magnitude of R and we go left right
+ 
+
+ align:start position:0%
+r or magnitude of R and we go left right
+as far
+
+ align:start position:0%
+as far
+ 
+
+ align:start position:0%
+as far
+as uh this is K Delta xal pi as far as
+
+ align:start position:0%
+as uh this is K Delta xal pi as far as
+ 
+
+ align:start position:0%
+as uh this is K Delta xal pi as far as
+minus one so it's
+
+ align:start position:0%
+minus one so it's
+ 
+
+ align:start position:0%
+minus one so it's
+uh it's
+
+ align:start position:0%
+uh it's
+ 
+
+ align:start position:0%
+uh it's
+stable if this is less than one
+
+ align:start position:0%
+stable if this is less than one
+ 
+
+ align:start position:0%
+stable if this is less than one
+not not nothing hard in fact uh
+
+ align:start position:0%
+not not nothing hard in fact uh
+ 
+
+ align:start position:0%
+not not nothing hard in fact uh
+easy two positive numbers that add to
+
+ align:start position:0%
+easy two positive numbers that add to
+ 
+
+ align:start position:0%
+easy two positive numbers that add to
+one now just there's a I've added
+
+ align:start position:0%
+one now just there's a I've added
+ 
+
+ align:start position:0%
+one now just there's a I've added
+a problem in the problem
+
+ align:start position:0%
+a problem in the problem
+ 
+
+ align:start position:0%
+a problem in the problem
+set and not requiring it to be turned in
+
+ align:start position:0%
+set and not requiring it to be turned in
+ 
+
+ align:start position:0%
+set and not requiring it to be turned in
+but just to mention it
+
+ align:start position:0%
+but just to mention it
+ 
+
+ align:start position:0%
+but just to mention it
+here that uh whenever the coefficients
+
+ align:start position:0%
+here that uh whenever the coefficients
+ 
+
+ align:start position:0%
+here that uh whenever the coefficients
+are all
+
+ align:start position:0%
+are all
+ 
+
+ align:start position:0%
+are all
+positive the accuracy could only be
+
+ align:start position:0%
+positive the accuracy could only be
+ 
+
+ align:start position:0%
+positive the accuracy could only be
+first order so
+
+ align:start position:0%
+first order so
+ 
+
+ align:start position:0%
+first order so
+we we can't get too far with positive
+
+ align:start position:0%
+we we can't get too far with positive
+ 
+
+ align:start position:0%
+we we can't get too far with positive
+coefficients first order accuracy is the
+
+ align:start position:0%
+coefficients first order accuracy is the
+ 
+
+ align:start position:0%
+coefficients first order accuracy is the
+best
+
+ align:start position:0%
+best
+ 
+
+ align:start position:0%
+best
+possible except in the extreme case when
+
+ align:start position:0%
+possible except in the extreme case when
+ 
+
+ align:start position:0%
+possible except in the extreme case when
+we're right on the characteristic so if
+
+ align:start position:0%
+we're right on the characteristic so if
+ 
+
+ align:start position:0%
+we're right on the characteristic so if
+R was exactly one if R you remember that
+
+ align:start position:0%
+R was exactly one if R you remember that
+ 
+
+ align:start position:0%
+R was exactly one if R you remember that
+special case when R is exactly one and
+
+ align:start position:0%
+special case when R is exactly one and
+ 
+
+ align:start position:0%
+special case when R is exactly one and
+we're following exactly the line that
+
+ align:start position:0%
+we're following exactly the line that
+ 
+
+ align:start position:0%
+we're following exactly the line that
+carries the true information R is one
+
+ align:start position:0%
+carries the true information R is one
+ 
+
+ align:start position:0%
+carries the true information R is one
+that's gone and this is just so if R is
+
+ align:start position:0%
+that's gone and this is just so if R is
+ 
+
+ align:start position:0%
+that's gone and this is just so if R is
+one then UJ + 1 n is U is this is that
+
+ align:start position:0%
+one then UJ + 1 n is U is this is that
+ 
+
+ align:start position:0%
+one then UJ + 1 n is U is this is that
+number and we're just carrying that
+
+ align:start position:0%
+number and we're just carrying that
+ 
+
+ align:start position:0%
+number and we're just carrying that
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+exactly I have to say again that
+
+ align:start position:0%
+exactly I have to say again that
+ 
+
+ align:start position:0%
+exactly I have to say again that
+uh with that the idea of trying to
+
+ align:start position:0%
+uh with that the idea of trying to
+ 
+
+ align:start position:0%
+uh with that the idea of trying to
+follow that characteristic is a totally
+
+ align:start position:0%
+follow that characteristic is a totally
+ 
+
+ align:start position:0%
+follow that characteristic is a totally
+natural one and and I'm not uh writing
+
+ align:start position:0%
+natural one and and I'm not uh writing
+ 
+
+ align:start position:0%
+natural one and and I'm not uh writing
+down here a method that tries to do that
+
+ align:start position:0%
+down here a method that tries to do that
+ 
+
+ align:start position:0%
+down here a method that tries to do that
+but it wouldn't be a bad idea in one
+
+ align:start position:0%
+but it wouldn't be a bad idea in one
+ 
+
+ align:start position:0%
+but it wouldn't be a bad idea in one
+dimension you couldn't do it really well
+
+ align:start position:0%
+dimension you couldn't do it really well
+ 
+
+ align:start position:0%
+dimension you couldn't do it really well
+in higher Dimensions where these ideas
+
+ align:start position:0%
+in higher Dimensions where these ideas
+ 
+
+ align:start position:0%
+in higher Dimensions where these ideas
+uh do continue to apply okay so that's
+
+ align:start position:0%
+uh do continue to apply okay so that's
+ 
+
+ align:start position:0%
+uh do continue to apply okay so that's
+like freedrick that's like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Fredick
+
+ align:start position:0%
+Fredick
+ 
+
+ align:start position:0%
+Fredick
+okay so now let me turn to LAX
+
+ align:start position:0%
+okay so now let me turn to LAX
+ 
+
+ align:start position:0%
+okay so now let me turn to LAX
+wendu the these are natural
+
+ align:start position:0%
+wendu the these are natural
+ 
+
+ align:start position:0%
+wendu the these are natural
+ideas but
+
+ align:start position:0%
+ideas but
+ 
+
+ align:start position:0%
+ideas but
+LAX and wro did it first they said well
+
+ align:start position:0%
+LAX and wro did it first they said well
+ 
+
+ align:start position:0%
+LAX and wro did it first they said well
+if I use these three
+
+ align:start position:0%
+if I use these three
+ 
+
+ align:start position:0%
+if I use these three
+values all
+
+ align:start position:0%
+values all
+ 
+
+ align:start position:0%
+values all
+three then certainly I can get the
+
+ align:start position:0%
+three then certainly I can get the
+ 
+
+ align:start position:0%
+three then certainly I can get the
+accuracy up one more because I have one
+
+ align:start position:0%
+accuracy up one more because I have one
+ 
+
+ align:start position:0%
+accuracy up one more because I have one
+more coefficient to choose
+
+ align:start position:0%
+more coefficient to choose
+ 
+
+ align:start position:0%
+more coefficient to choose
+and to see what they
+
+ align:start position:0%
+and to see what they
+ 
+
+ align:start position:0%
+and to see what they
+did uh the easiest way is to write it as
+
+ align:start position:0%
+did uh the easiest way is to write it as
+ 
+
+ align:start position:0%
+did uh the easiest way is to write it as
+a time difference on the left to see how
+
+ align:start position:0%
+a time difference on the left to see how
+ 
+
+ align:start position:0%
+a time difference on the left to see how
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+matched all they want to do is match
+
+ align:start position:0%
+matched all they want to do is match
+ 
+
+ align:start position:0%
+matched all they want to do is match
+that second term that Delta x² term in
+
+ align:start position:0%
+that second term that Delta x² term in
+ 
+
+ align:start position:0%
+that second term that Delta x² term in
+the tailor
+
+ align:start position:0%
+the tailor
+ 
+
+ align:start position:0%
+the tailor
+series and because because this is going
+
+ align:start position:0%
+series and because because this is going
+ 
+
+ align:start position:0%
+series and because because this is going
+to this is gives us a d by
+
+ align:start position:0%
+to this is gives us a d by
+ 
+
+ align:start position:0%
+to this is gives us a d by
+DT this will give us a d by DX with uh
+
+ align:start position:0%
+DT this will give us a d by DX with uh
+ 
+
+ align:start position:0%
+DT this will give us a d by DX with uh
+centered so we get extra accuracy there
+
+ align:start position:0%
+centered so we get extra accuracy there
+ 
+
+ align:start position:0%
+centered so we get extra accuracy there
+and the matching that we need is this
+
+ align:start position:0%
+and the matching that we need is this
+ 
+
+ align:start position:0%
+and the matching that we need is this
+term and and do you recognize that what
+
+ align:start position:0%
+term and and do you recognize that what
+ 
+
+ align:start position:0%
+term and and do you recognize that what
+what does that term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximate uh and I hope I've got it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximates uxx right so this is
+
+ align:start position:0%
+approximates uxx right so this is
+ 
+
+ align:start position:0%
+approximates uxx right so this is
+they've thrown in a term that
+
+ align:start position:0%
+they've thrown in a term that
+ 
+
+ align:start position:0%
+they've thrown in a term that
+approximates
+
+ align:start position:0%
+approximates
+ 
+
+ align:start position:0%
+approximates
+uxx and its purpose is to catch the next
+
+ align:start position:0%
+uxx and its purpose is to catch the next
+ 
+
+ align:start position:0%
+uxx and its purpose is to catch the next
+order of
+
+ align:start position:0%
+order of
+ 
+
+ align:start position:0%
+order of
+accuracy and hopefully not lose
+
+ align:start position:0%
+accuracy and hopefully not lose
+ 
+
+ align:start position:0%
+accuracy and hopefully not lose
+stability hopefully remain stable so
+
+ align:start position:0%
+stability hopefully remain stable so
+ 
+
+ align:start position:0%
+stability hopefully remain stable so
+we're we're what we're doing now what
+
+ align:start position:0%
+we're we're what we're doing now what
+ 
+
+ align:start position:0%
+we're we're what we're doing now what
+Lex wend are doing is staying even
+
+ align:start position:0%
+Lex wend are doing is staying even
+ 
+
+ align:start position:0%
+Lex wend are doing is staying even
+closer to this
+
+ align:start position:0%
+closer to this
+ 
+
+ align:start position:0%
+closer to this
+curve and I guess I have forgotten
+
+ align:start position:0%
+curve and I guess I have forgotten
+ 
+
+ align:start position:0%
+curve and I guess I have forgotten
+exactly what their Curve will be if I
+
+ align:start position:0%
+exactly what their Curve will be if I
+ 
+
+ align:start position:0%
+exactly what their Curve will be if I
+write down G oh maybe you could ask mlap
+
+ align:start position:0%
+write down G oh maybe you could ask mlap
+ 
+
+ align:start position:0%
+write down G oh maybe you could ask mlap
+to do that write down the G for this for
+
+ align:start position:0%
+to do that write down the G for this for
+ 
+
+ align:start position:0%
+to do that write down the G for this for
+LA
+
+ align:start position:0%
+LA
+ 
+
+ align:start position:0%
+LA
+wend it's uh got that extra
+
+ align:start position:0%
+wend it's uh got that extra
+ 
+
+ align:start position:0%
+wend it's uh got that extra
+term and uh plot absolute value of G and
+
+ align:start position:0%
+term and uh plot absolute value of G and
+ 
+
+ align:start position:0%
+term and uh plot absolute value of G and
+I guess you might plot it along with
+
+ align:start position:0%
+I guess you might plot it along with
+ 
+
+ align:start position:0%
+I guess you might plot it along with
+the LAX Freed's value so what am I
+
+ align:start position:0%
+the LAX Freed's value so what am I
+ 
+
+ align:start position:0%
+the LAX Freed's value so what am I
+guessing well I'm pretty sure that the
+
+ align:start position:0%
+guessing well I'm pretty sure that the
+ 
+
+ align:start position:0%
+guessing well I'm pretty sure that the
+LAX wend one will hug the unit circle
+
+ align:start position:0%
+LAX wend one will hug the unit circle
+ 
+
+ align:start position:0%
+LAX wend one will hug the unit circle
+more closely but it'll stay inside
+
+ align:start position:0%
+more closely but it'll stay inside
+ 
+
+ align:start position:0%
+more closely but it'll stay inside
+so can I
+
+ align:start position:0%
+so can I
+ 
+
+ align:start position:0%
+so can I
+just LAX wend off is is G closer to
+
+ align:start position:0%
+just LAX wend off is is G closer to
+ 
+
+ align:start position:0%
+just LAX wend off is is G closer to
+one at least for small k at least for a
+
+ align:start position:0%
+one at least for small k at least for a
+ 
+
+ align:start position:0%
+one at least for small k at least for a
+small K that's where we that's really
+
+ align:start position:0%
+small K that's where we that's really
+ 
+
+ align:start position:0%
+small K that's where we that's really
+where the accuracy is checked is how
+
+ align:start position:0%
+where the accuracy is checked is how
+ 
+
+ align:start position:0%
+where the accuracy is checked is how
+close do these tailor series
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+match and uh LAX W off Match better
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they stay inside that takes a little
+
+ align:start position:0%
+and they stay inside that takes a little
+ 
+
+ align:start position:0%
+and they stay inside that takes a little
+calculation took me a while yesterday to
+
+ align:start position:0%
+calculation took me a while yesterday to
+ 
+
+ align:start position:0%
+calculation took me a while yesterday to
+rewrite the the write out the
+
+ align:start position:0%
+rewrite the the write out the
+ 
+
+ align:start position:0%
+rewrite the the write out the
+G Square the real part Square the
+
+ align:start position:0%
+G Square the real part Square the
+ 
+
+ align:start position:0%
+G Square the real part Square the
+imaginary part add them up and this is
+
+ align:start position:0%
+imaginary part add them up and this is
+ 
+
+ align:start position:0%
+imaginary part add them up and this is
+what I got so for LAX wend I got g^
+
+ align:start position:0%
+what I got so for LAX wend I got g^
+ 
+
+ align:start position:0%
+what I got so for LAX wend I got g^
+2 is
+
+ align:start position:0%
+2 is
+ 
+
+ align:start position:0%
+2 is
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+minus r 2 - R 4 * 1 - cine K Delta x^
+
+ align:start position:0%
+minus r 2 - R 4 * 1 - cine K Delta x^
+ 
+
+ align:start position:0%
+minus r 2 - R 4 * 1 - cine K Delta x^
+s and I put in the notes
+
+ align:start position:0%
+s and I put in the notes
+ 
+
+ align:start position:0%
+s and I put in the notes
+eventually much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algebra but it does the
+
+ align:start position:0%
+algebra but it does the
+ 
+
+ align:start position:0%
+algebra but it does the
+job because if R SAR so what's the
+
+ align:start position:0%
+job because if R SAR so what's the
+ 
+
+ align:start position:0%
+job because if R SAR so what's the
+stability Condition it's again this same
+
+ align:start position:0%
+stability Condition it's again this same
+ 
+
+ align:start position:0%
+stability Condition it's again this same
+guy the same condition R 2 below one
+
+ align:start position:0%
+guy the same condition R 2 below one
+ 
+
+ align:start position:0%
+guy the same condition R 2 below one
+and again we could be on we could have a
+
+ align:start position:0%
+and again we could be on we could have a
+ 
+
+ align:start position:0%
+and again we could be on we could have a
+left going wave and a right going wave
+
+ align:start position:0%
+left going wave and a right going wave
+ 
+
+ align:start position:0%
+left going wave and a right going wave
+now you'll say what's the good of that
+
+ align:start position:0%
+now you'll say what's the good of that
+ 
+
+ align:start position:0%
+now you'll say what's the good of that
+here we just have one wave but in the on
+
+ align:start position:0%
+here we just have one wave but in the on
+ 
+
+ align:start position:0%
+here we just have one wave but in the on
+Friday we'll have a wave going both ways
+
+ align:start position:0%
+Friday we'll have a wave going both ways
+ 
+
+ align:start position:0%
+Friday we'll have a wave going both ways
+so LAX
+
+ align:start position:0%
+so LAX
+ 
+
+ align:start position:0%
+so LAX
+friedricks and LAX wend can both deal
+
+ align:start position:0%
+friedricks and LAX wend can both deal
+ 
+
+ align:start position:0%
+friedricks and LAX wend can both deal
+with that in fact their stability
+
+ align:start position:0%
+with that in fact their stability
+ 
+
+ align:start position:0%
+with that in fact their stability
+conditions are the same in fact you may
+
+ align:start position:0%
+conditions are the same in fact you may
+ 
+
+ align:start position:0%
+conditions are the same in fact you may
+be wondering why would anybody use
+
+ align:start position:0%
+be wondering why would anybody use
+ 
+
+ align:start position:0%
+be wondering why would anybody use
+Fredick when LX wend gives higher
+
+ align:start position:0%
+Fredick when LX wend gives higher
+ 
+
+ align:start position:0%
+Fredick when LX wend gives higher
+accuracy at
+
+ align:start position:0%
+accuracy at
+ 
+
+ align:start position:0%
+accuracy at
+no real significant increase in cost so
+
+ align:start position:0%
+no real significant increase in cost so
+ 
+
+ align:start position:0%
+no real significant increase in cost so
+lik wend is a
+
+ align:start position:0%
+lik wend is a
+ 
+
+ align:start position:0%
+lik wend is a
+favorite uh but don't forget still
+
+ align:start position:0%
+favorite uh but don't forget still
+ 
+
+ align:start position:0%
+favorite uh but don't forget still
+experiment has to be done to see what it
+
+ align:start position:0%
+experiment has to be done to see what it
+ 
+
+ align:start position:0%
+experiment has to be done to see what it
+really does in practice
+
+ align:start position:0%
+really does in practice
+ 
+
+ align:start position:0%
+really does in practice
+because you know right now everything's
+
+ align:start position:0%
+because you know right now everything's
+ 
+
+ align:start position:0%
+because you know right now everything's
+looking in LAX W's favor with one an
+
+ align:start position:0%
+looking in LAX W's favor with one an
+ 
+
+ align:start position:0%
+looking in LAX W's favor with one an
+exception LAX
+
+ align:start position:0%
+exception LAX
+ 
+
+ align:start position:0%
+exception LAX
+frieds which only use these two
+
+ align:start position:0%
+frieds which only use these two
+ 
+
+ align:start position:0%
+frieds which only use these two
+coefficients had them positive this is
+
+ align:start position:0%
+coefficients had them positive this is
+ 
+
+ align:start position:0%
+coefficients had them positive this is
+positive this is
+
+ align:start position:0%
+positive this is
+ 
+
+ align:start position:0%
+positive this is
+positive where LAX wend is going to have
+
+ align:start position:0%
+positive where LAX wend is going to have
+ 
+
+ align:start position:0%
+positive where LAX wend is going to have
+a negative let's see where will a
+
+ align:start position:0%
+a negative let's see where will a
+ 
+
+ align:start position:0%
+a negative let's see where will a
+negative I think there'll be a
+
+ align:start position:0%
+negative I think there'll be a
+ 
+
+ align:start position:0%
+negative I think there'll be a
+negative uh coefficient in here
+
+ align:start position:0%
+negative uh coefficient in here
+ 
+
+ align:start position:0%
+negative uh coefficient in here
+somewhere yeah
+
+ align:start position:0%
+somewhere yeah
+ 
+
+ align:start position:0%
+somewhere yeah
+probably uh one of the three outside
+
+ align:start position:0%
+probably uh one of the three outside
+ 
+
+ align:start position:0%
+probably uh one of the three outside
+guys I I know that we couldn't have
+
+ align:start position:0%
+guys I I know that we couldn't have
+ 
+
+ align:start position:0%
+guys I I know that we couldn't have
+three positive coefficients and get up
+
+ align:start position:0%
+three positive coefficients and get up
+ 
+
+ align:start position:0%
+three positive coefficients and get up
+to second order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+accuracy and now where do we pay the
+
+ align:start position:0%
+accuracy and now where do we pay the
+ 
+
+ align:start position:0%
+accuracy and now where do we pay the
+price for that where do we pay the price
+
+ align:start position:0%
+price for that where do we pay the price
+ 
+
+ align:start position:0%
+price for that where do we pay the price
+oh I should finish here if suppose r s
+
+ align:start position:0%
+oh I should finish here if suppose r s
+ 
+
+ align:start position:0%
+oh I should finish here if suppose r s
+is bigger than one if I I if you accept
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this calculation which has a nice result
+
+ align:start position:0%
+this calculation which has a nice result
+ 
+
+ align:start position:0%
+this calculation which has a nice result
+but took a while if r s is below one
+
+ align:start position:0%
+but took a while if r s is below one
+ 
+
+ align:start position:0%
+but took a while if r s is below one
+then what do I know about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G suppose r s is bigger than
+
+ align:start position:0%
+G suppose r s is bigger than
+ 
+
+ align:start position:0%
+G suppose r s is bigger than
+one what can we say from this
+
+ align:start position:0%
+one what can we say from this
+ 
+
+ align:start position:0%
+one what can we say from this
+formula does that hit you right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+G if R square this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+certainly well absolute G yeah I i' I
+
+ align:start position:0%
+certainly well absolute G yeah I i' I
+ 
+
+ align:start position:0%
+certainly well absolute G yeah I i' I
+taken the actual G and squared its real
+
+ align:start position:0%
+taken the actual G and squared its real
+ 
+
+ align:start position:0%
+taken the actual G and squared its real
+part squared its imaginary
+
+ align:start position:0%
+part squared its imaginary
+ 
+
+ align:start position:0%
+part squared its imaginary
+part did all the algebra I could think
+
+ align:start position:0%
+part did all the algebra I could think
+ 
+
+ align:start position:0%
+part did all the algebra I could think
+of and got this
+
+ align:start position:0%
+of and got this
+ 
+
+ align:start position:0%
+of and got this
+answer and uh for the magnitude squared
+
+ align:start position:0%
+answer and uh for the magnitude squared
+ 
+
+ align:start position:0%
+answer and uh for the magnitude squared
+so the magnitude squared is never going
+
+ align:start position:0%
+so the magnitude squared is never going
+ 
+
+ align:start position:0%
+so the magnitude squared is never going
+to go below zero I don't have to think
+
+ align:start position:0%
+to go below zero I don't have to think
+ 
+
+ align:start position:0%
+to go below zero I don't have to think
+of that it's just I want to be sure it's
+
+ align:start position:0%
+of that it's just I want to be sure it's
+ 
+
+ align:start position:0%
+of that it's just I want to be sure it's
+below one and so all I really want to do
+
+ align:start position:0%
+below one and so all I really want to do
+ 
+
+ align:start position:0%
+below one and so all I really want to do
+is be sure that what I'm subt that I'm
+
+ align:start position:0%
+is be sure that what I'm subt that I'm
+ 
+
+ align:start position:0%
+is be sure that what I'm subt that I'm
+subtracting something positive
+
+ align:start position:0%
+subtracting something positive
+ 
+
+ align:start position:0%
+subtracting something positive
+there okay am I subtracting something
+
+ align:start position:0%
+there okay am I subtracting something
+ 
+
+ align:start position:0%
+there okay am I subtracting something
+positive well that's certainly positive
+
+ align:start position:0%
+positive well that's certainly positive
+ 
+
+ align:start position:0%
+positive well that's certainly positive
+and is this
+
+ align:start position:0%
+and is this
+ 
+
+ align:start position:0%
+and is this
+positive yeah r s will be bigger than R
+
+ align:start position:0%
+positive yeah r s will be bigger than R
+ 
+
+ align:start position:0%
+positive yeah r s will be bigger than R
+4th if r s is less than one then R the
+
+ align:start position:0%
+4th if r s is less than one then R the
+ 
+
+ align:start position:0%
+4th if r s is less than one then R the
+4th is even smaller so this is positive
+
+ align:start position:0%
+4th is even smaller so this is positive
+ 
+
+ align:start position:0%
+4th is even smaller so this is positive
+this is positive I'm subtracting
+
+ align:start position:0%
+this is positive I'm subtracting
+ 
+
+ align:start position:0%
+this is positive I'm subtracting
+something so G is certainly not bigger
+
+ align:start position:0%
+something so G is certainly not bigger
+ 
+
+ align:start position:0%
+something so G is certainly not bigger
+than one and that's good yeah yeah so
+
+ align:start position:0%
+than one and that's good yeah yeah so
+ 
+
+ align:start position:0%
+than one and that's good yeah yeah so
+that formula really makes it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evident and I guess also evident that
+
+ align:start position:0%
+evident and I guess also evident that
+ 
+
+ align:start position:0%
+evident and I guess also evident that
+we're getting some high accuracy do you
+
+ align:start position:0%
+we're getting some high accuracy do you
+ 
+
+ align:start position:0%
+we're getting some high accuracy do you
+see what's the
+
+ align:start position:0%
+see what's the
+ 
+
+ align:start position:0%
+see what's the
+uh what's the size of this when K is
+
+ align:start position:0%
+uh what's the size of this when K is
+ 
+
+ align:start position:0%
+uh what's the size of this when K is
+small when K is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+small if I'm taking the cosine of a
+
+ align:start position:0%
+small if I'm taking the cosine of a
+ 
+
+ align:start position:0%
+small if I'm taking the cosine of a
+small angle what am I looking at there
+
+ align:start position:0%
+small angle what am I looking at there
+ 
+
+ align:start position:0%
+small angle what am I looking at there
+if if this is a small angle Theta I'm
+
+ align:start position:0%
+if if this is a small angle Theta I'm
+ 
+
+ align:start position:0%
+if if this is a small angle Theta I'm
+looking at 1us cosine Theta that's of
+
+ align:start position:0%
+looking at 1us cosine Theta that's of
+ 
+
+ align:start position:0%
+looking at 1us cosine Theta that's of
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+order Theta squar Theta
+
+ align:start position:0%
+order Theta squar Theta
+ 
+
+ align:start position:0%
+order Theta squar Theta
+squared and that's and then that's
+
+ align:start position:0%
+squared and that's and then that's
+ 
+
+ align:start position:0%
+squared and that's and then that's
+squared again so that I'm up to Thea the
+
+ align:start position:0%
+squared again so that I'm up to Thea the
+ 
+
+ align:start position:0%
+squared again so that I'm up to Thea the
+4 that's why
+
+ align:start position:0%
+4 that's why
+ 
+
+ align:start position:0%
+4 that's why
+I'm getting off to a good start
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay so stability we've got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two-sided we've
+
+ align:start position:0%
+two-sided we've
+ 
+
+ align:start position:0%
+two-sided we've
+got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experiment can I just try to draw a
+
+ align:start position:0%
+experiment can I just try to draw a
+ 
+
+ align:start position:0%
+experiment can I just try to draw a
+little graph of what I think the the
+
+ align:start position:0%
+little graph of what I think the the
+ 
+
+ align:start position:0%
+little graph of what I think the the
+U the two methods will
+
+ align:start position:0%
+U the two methods will
+ 
+
+ align:start position:0%
+U the two methods will
+do for uh our model problem like this
+
+ align:start position:0%
+do for uh our model problem like this
+ 
+
+ align:start position:0%
+do for uh our model problem like this
+model problem
+
+ align:start position:0%
+model problem
+ 
+
+ align:start position:0%
+model problem
+of of a wave moving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+along I I want to try to draw
+
+ align:start position:0%
+along I I want to try to draw
+ 
+
+ align:start position:0%
+along I I want to try to draw
+at uh at uh let's say at uh tal 1 for
+
+ align:start position:0%
+at uh at uh let's say at uh tal 1 for
+ 
+
+ align:start position:0%
+at uh at uh let's say at uh tal 1 for
+example so at t equal one the wave
+
+ align:start position:0%
+example so at t equal one the wave
+ 
+
+ align:start position:0%
+example so at t equal one the wave
+should be along should be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and I'll draw I'll well you might
+
+ align:start position:0%
+here and I'll draw I'll well you might
+ 
+
+ align:start position:0%
+here and I'll draw I'll well you might
+say this is totally
+
+ align:start position:0%
+say this is totally
+ 
+
+ align:start position:0%
+say this is totally
+unsatisfactory and it and it is because
+
+ align:start position:0%
+unsatisfactory and it and it is because
+ 
+
+ align:start position:0%
+unsatisfactory and it and it is because
+I'm just drawing by hand what
+
+ align:start position:0%
+I'm just drawing by hand what
+ 
+
+ align:start position:0%
+I'm just drawing by hand what
+the what you can what you can see and
+
+ align:start position:0%
+the what you can what you can see and
+ 
+
+ align:start position:0%
+the what you can what you can see and
+maybe should this would be a perfect
+
+ align:start position:0%
+maybe should this would be a perfect
+ 
+
+ align:start position:0%
+maybe should this would be a perfect
+experiment and I really could use for
+
+ align:start position:0%
+experiment and I really could use for
+ 
+
+ align:start position:0%
+experiment and I really could use for
+the notes the notes could use a proper
+
+ align:start position:0%
+the notes the notes could use a proper
+ 
+
+ align:start position:0%
+the notes the notes could use a proper
+graph here okay I think what you
+
+ align:start position:0%
+graph here okay I think what you
+ 
+
+ align:start position:0%
+graph here okay I think what you
+see is well let's see at tal 1 both
+
+ align:start position:0%
+see is well let's see at tal 1 both
+ 
+
+ align:start position:0%
+see is well let's see at tal 1 both
+methods are going to be zero way out
+
+ align:start position:0%
+methods are going to be zero way out
+ 
+
+ align:start position:0%
+methods are going to be zero way out
+here and they'll be
+
+ align:start position:0%
+here and they'll be
+ 
+
+ align:start position:0%
+here and they'll be
+one way out here and why is that because
+
+ align:start position:0%
+one way out here and why is that because
+ 
+
+ align:start position:0%
+one way out here and why is that because
+the signal speed is
+
+ align:start position:0%
+the signal speed is
+ 
+
+ align:start position:0%
+the signal speed is
+finite right this way way out here it
+
+ align:start position:0%
+finite right this way way out here it
+ 
+
+ align:start position:0%
+finite right this way way out here it
+hasn't heard about this wave of water
+
+ align:start position:0%
+hasn't heard about this wave of water
+ 
+
+ align:start position:0%
+hasn't heard about this wave of water
+way out here it doesn't know that the
+
+ align:start position:0%
+way out here it doesn't know that the
+ 
+
+ align:start position:0%
+way out here it doesn't know that the
+that it's not a constant but the
+
+ align:start position:0%
+that it's not a constant but the
+ 
+
+ align:start position:0%
+that it's not a constant but the
+question is and I guess the thing has
+
+ align:start position:0%
+question is and I guess the thing has
+ 
+
+ align:start position:0%
+question is and I guess the thing has
+moved so maybe maybe maybe can I try
+
+ align:start position:0%
+moved so maybe maybe maybe can I try
+ 
+
+ align:start position:0%
+moved so maybe maybe maybe can I try
+roughly so the true wall of water would
+
+ align:start position:0%
+roughly so the true wall of water would
+ 
+
+ align:start position:0%
+roughly so the true wall of water would
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+that and I think that what Lex wendra
+
+ align:start position:0%
+that and I think that what Lex wendra
+ 
+
+ align:start position:0%
+that and I think that what Lex wendra
+Lex
+
+ align:start position:0%
+Lex
+ 
+
+ align:start position:0%
+Lex
+friedr so Lex friedr
+
+ align:start position:0%
+friedr so Lex friedr
+ 
+
+ align:start position:0%
+friedr so Lex friedr
+with positive
+
+ align:start position:0%
+with positive
+ 
+
+ align:start position:0%
+with positive
+coefficients
+
+ align:start position:0%
+coefficients
+ 
+
+ align:start position:0%
+coefficients
+will show a smooth
+
+ align:start position:0%
+will show a smooth
+ 
+
+ align:start position:0%
+will show a smooth
+profile but the perfect signal will get
+
+ align:start position:0%
+profile but the perfect signal will get
+ 
+
+ align:start position:0%
+profile but the perfect signal will get
+spread out the perfect signal will get
+
+ align:start position:0%
+spread out the perfect signal will get
+ 
+
+ align:start position:0%
+spread out the perfect signal will get
+spread out why is that let me draw just
+
+ align:start position:0%
+spread out why is that let me draw just
+ 
+
+ align:start position:0%
+spread out why is that let me draw just
+draw a spread out signal so apologies to
+
+ align:start position:0%
+draw a spread out signal so apologies to
+ 
+
+ align:start position:0%
+draw a spread out signal so apologies to
+do this by hand I think it's probably
+
+ align:start position:0%
+do this by hand I think it's probably
+ 
+
+ align:start position:0%
+do this by hand I think it's probably
+going to be pretty centered but it's
+
+ align:start position:0%
+going to be pretty centered but it's
+ 
+
+ align:start position:0%
+going to be pretty centered but it's
+going to be spread out so that I think
+
+ align:start position:0%
+going to be spread out so that I think
+ 
+
+ align:start position:0%
+going to be spread out so that I think
+would be LAX Free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bricks that's very rough right
+
+ align:start position:0%
+Bricks that's very rough right
+ 
+
+ align:start position:0%
+Bricks that's very rough right
+but I
+
+ align:start position:0%
+but I
+ 
+
+ align:start position:0%
+but I
+really hearty thanks for anybody who
+
+ align:start position:0%
+really hearty thanks for anybody who
+ 
+
+ align:start position:0%
+really hearty thanks for anybody who
+gives me a code that does it uh and
+
+ align:start position:0%
+gives me a code that does it uh and
+ 
+
+ align:start position:0%
+gives me a code that does it uh and
+graphs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it uh but the the main point is we have
+
+ align:start position:0%
+it uh but the the main point is we have
+ 
+
+ align:start position:0%
+it uh but the the main point is we have
+a lot of of smear ing here the the
+
+ align:start position:0%
+a lot of of smear ing here the the
+ 
+
+ align:start position:0%
+a lot of of smear ing here the the
+accuracy is not going to be terrific
+
+ align:start position:0%
+accuracy is not going to be terrific
+ 
+
+ align:start position:0%
+accuracy is not going to be terrific
+okay but the there isn't any
+
+ align:start position:0%
+okay but the there isn't any
+ 
+
+ align:start position:0%
+okay but the there isn't any
+bumpiness the reason there's no
+
+ align:start position:0%
+bumpiness the reason there's no
+ 
+
+ align:start position:0%
+bumpiness the reason there's no
+bumpiness is that we're LAX fried's
+
+ align:start position:0%
+bumpiness is that we're LAX fried's
+ 
+
+ align:start position:0%
+bumpiness is that we're LAX fried's
+with has these positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coefficients so that every value always
+
+ align:start position:0%
+coefficients so that every value always
+ 
+
+ align:start position:0%
+coefficients so that every value always
+has to stay between zero and one the
+
+ align:start position:0%
+has to stay between zero and one the
+ 
+
+ align:start position:0%
+has to stay between zero and one the
+starting values were between 0 and one
+
+ align:start position:0%
+starting values were between 0 and one
+ 
+
+ align:start position:0%
+starting values were between 0 and one
+at every step that the the the values
+
+ align:start position:0%
+at every step that the the the values
+ 
+
+ align:start position:0%
+at every step that the the the values
+are between Z and one because we're
+
+ align:start position:0%
+are between Z and one because we're
+ 
+
+ align:start position:0%
+are between Z and one because we're
+always taking a
+
+ align:start position:0%
+always taking a
+ 
+
+ align:start position:0%
+always taking a
+combination of uh a positive multiple of
+
+ align:start position:0%
+combination of uh a positive multiple of
+ 
+
+ align:start position:0%
+combination of uh a positive multiple of
+one value and another positive multiple
+
+ align:start position:0%
+one value and another positive multiple
+ 
+
+ align:start position:0%
+one value and another positive multiple
+of the other value and the two
+
+ align:start position:0%
+of the other value and the two
+ 
+
+ align:start position:0%
+of the other value and the two
+coefficients adding to one you know
+
+ align:start position:0%
+coefficients adding to one you know
+ 
+
+ align:start position:0%
+coefficients adding to one you know
+we're like taking 30% of one and 70% of
+
+ align:start position:0%
+we're like taking 30% of one and 70% of
+ 
+
+ align:start position:0%
+we're like taking 30% of one and 70% of
+another and we
+
+ align:start position:0%
+another and we
+ 
+
+ align:start position:0%
+another and we
+never we never we're always in between
+
+ align:start position:0%
+never we never we're always in between
+ 
+
+ align:start position:0%
+never we never we're always in between
+the zero and the one okay what about
+
+ align:start position:0%
+the zero and the one okay what about
+ 
+
+ align:start position:0%
+the zero and the one okay what about
+Lex
+
+ align:start position:0%
+Lex
+ 
+
+ align:start position:0%
+Lex
+wro what are you expecting for Lex
+
+ align:start position:0%
+wro what are you expecting for Lex
+ 
+
+ align:start position:0%
+wro what are you expecting for Lex
+wro expecting better accuracy
+
+ align:start position:0%
+wro expecting better accuracy
+ 
+
+ align:start position:0%
+wro expecting better accuracy
+expecting uh if I were on the bowl I'd
+
+ align:start position:0%
+expecting uh if I were on the bowl I'd
+ 
+
+ align:start position:0%
+expecting uh if I were on the bowl I'd
+have another color Okay LAX wend will be
+
+ align:start position:0%
+have another color Okay LAX wend will be
+ 
+
+ align:start position:0%
+have another color Okay LAX wend will be
+a much
+
+ align:start position:0%
+a much
+ 
+
+ align:start position:0%
+a much
+better
+
+ align:start position:0%
+better
+ 
+
+ align:start position:0%
+better
+uh profile sharper
+
+ align:start position:0%
+uh profile sharper
+ 
+
+ align:start position:0%
+uh profile sharper
+profile
+
+ align:start position:0%
+profile
+ 
+
+ align:start position:0%
+profile
+but you know what the price is going to
+
+ align:start position:0%
+but you know what the price is going to
+ 
+
+ align:start position:0%
+but you know what the price is going to
+be there'll be some oscillation
+
+ align:start position:0%
+be there'll be some oscillation
+ 
+
+ align:start position:0%
+be there'll be some oscillation
+there'll be some oscillations behind I
+
+ align:start position:0%
+there'll be some oscillations behind I
+ 
+
+ align:start position:0%
+there'll be some oscillations behind I
+think behind oh gosh I should know
+
+ align:start position:0%
+think behind oh gosh I should know
+ 
+
+ align:start position:0%
+think behind oh gosh I should know
+forgive me
+
+ align:start position:0%
+forgive me
+ 
+
+ align:start position:0%
+forgive me
+for I can fix these if you'll tell me
+
+ align:start position:0%
+for I can fix these if you'll tell me
+ 
+
+ align:start position:0%
+for I can fix these if you'll tell me
+how on the
+
+ align:start position:0%
+how on the
+ 
+
+ align:start position:0%
+how on the
+next because I'm not sure that I I
+
+ align:start position:0%
+next because I'm not sure that I I
+ 
+
+ align:start position:0%
+next because I'm not sure that I I
+should know whether they're at both
+
+ align:start position:0%
+should know whether they're at both
+ 
+
+ align:start position:0%
+should know whether they're at both
+whether the oscillation happens at both
+
+ align:start position:0%
+whether the oscillation happens at both
+ 
+
+ align:start position:0%
+whether the oscillation happens at both
+ends I doubt it ah no I doubt I don't
+
+ align:start position:0%
+ends I doubt it ah no I doubt I don't
+ 
+
+ align:start position:0%
+ends I doubt it ah no I doubt I don't
+think it will why do I not think it will
+
+ align:start position:0%
+think it will why do I not think it will
+ 
+
+ align:start position:0%
+think it will why do I not think it will
+because in LAX wend the three
+
+ align:start position:0%
+because in LAX wend the three
+ 
+
+ align:start position:0%
+because in LAX wend the three
+coefficients one of them will be
+
+ align:start position:0%
+coefficients one of them will be
+ 
+
+ align:start position:0%
+coefficients one of them will be
+negative and two will be positive
+
+ align:start position:0%
+negative and two will be positive
+ 
+
+ align:start position:0%
+negative and two will be positive
+they'll add to one of course and so the
+
+ align:start position:0%
+they'll add to one of course and so the
+ 
+
+ align:start position:0%
+they'll add to one of course and so the
+the oscillations which are coming from
+
+ align:start position:0%
+the oscillations which are coming from
+ 
+
+ align:start position:0%
+the oscillations which are coming from
+like sometimes a negative coefficient
+
+ align:start position:0%
+like sometimes a negative coefficient
+ 
+
+ align:start position:0%
+like sometimes a negative coefficient
+sometimes a positive will all be on one
+
+ align:start position:0%
+sometimes a positive will all be on one
+ 
+
+ align:start position:0%
+sometimes a positive will all be on one
+side so only one of those only one of
+
+ align:start position:0%
+side so only one of those only one of
+ 
+
+ align:start position:0%
+side so only one of those only one of
+those oscillations is in so this is my
+
+ align:start position:0%
+those oscillations is in so this is my
+ 
+
+ align:start position:0%
+those oscillations is in so this is my
+picture of can I of LAX
+
+ align:start position:0%
+picture of can I of LAX
+ 
+
+ align:start position:0%
+picture of can I of LAX
+wend with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oscillations behind
+
+ align:start position:0%
+oscillations behind
+ 
+
+ align:start position:0%
+oscillations behind
+the the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wavefront
+
+ align:start position:0%
+wavefront
+ 
+
+ align:start position:0%
+wavefront
+okay all
+
+ align:start position:0%
+okay all
+ 
+
+ align:start position:0%
+okay all
+right if you've done any Computing you
+
+ align:start position:0%
+right if you've done any Computing you
+ 
+
+ align:start position:0%
+right if you've done any Computing you
+when you see these oscillations you IMM
+
+ align:start position:0%
+when you see these oscillations you IMM
+ 
+
+ align:start position:0%
+when you see these oscillations you IMM
+immediately think of somebody's name
+
+ align:start position:0%
+immediately think of somebody's name
+ 
+
+ align:start position:0%
+immediately think of somebody's name
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+Gibbs and of course Gibbs you remember
+
+ align:start position:0%
+Gibbs and of course Gibbs you remember
+ 
+
+ align:start position:0%
+Gibbs and of course Gibbs you remember
+the Gibbs phenomenon that comes when
+
+ align:start position:0%
+the Gibbs phenomenon that comes when
+ 
+
+ align:start position:0%
+the Gibbs phenomenon that comes when
+you're approximating a square
+
+ align:start position:0%
+you're approximating a square
+ 
+
+ align:start position:0%
+you're approximating a square
+wave like
+
+ align:start position:0%
+wave like
+ 
+
+ align:start position:0%
+wave like
+these by pure 4A
+
+ align:start position:0%
+these by pure 4A
+ 
+
+ align:start position:0%
+these by pure 4A
+Series so the Gibb the classical Gibbs
+
+ align:start position:0%
+Series so the Gibb the classical Gibbs
+ 
+
+ align:start position:0%
+Series so the Gibb the classical Gibbs
+phenomenon is take the 4A series for a
+
+ align:start position:0%
+phenomenon is take the 4A series for a
+ 
+
+ align:start position:0%
+phenomenon is take the 4A series for a
+square wave while it's
+
+ align:start position:0%
+square wave while it's
+ 
+
+ align:start position:0%
+square wave while it's
+smooth but and and then truncate that
+
+ align:start position:0%
+smooth but and and then truncate that
+ 
+
+ align:start position:0%
+smooth but and and then truncate that
+series cut that series off at 100 terms
+
+ align:start position:0%
+series cut that series off at 100 terms
+ 
+
+ align:start position:0%
+series cut that series off at 100 terms
+or a thousand terms and Gibbs notice and
+
+ align:start position:0%
+or a thousand terms and Gibbs notice and
+ 
+
+ align:start position:0%
+or a thousand terms and Gibbs notice and
+it's always a problem that these
+
+ align:start position:0%
+it's always a problem that these
+ 
+
+ align:start position:0%
+it's always a problem that these
+oscillations appear uh right near the
+
+ align:start position:0%
+oscillations appear uh right near the
+ 
+
+ align:start position:0%
+oscillations appear uh right near the
+near the um the front so far away no
+
+ align:start position:0%
+near the um the front so far away no
+ 
+
+ align:start position:0%
+near the um the front so far away no
+problem but uh and and here we here we
+
+ align:start position:0%
+problem but uh and and here we here we
+ 
+
+ align:start position:0%
+problem but uh and and here we here we
+really see it only on one side because
+
+ align:start position:0%
+really see it only on one side because
+ 
+
+ align:start position:0%
+really see it only on one side because
+we're not doing Gibbs for a series
+
+ align:start position:0%
+we're not doing Gibbs for a series
+ 
+
+ align:start position:0%
+we're not doing Gibbs for a series
+experiment we're doing Lex wend wave
+
+ align:start position:0%
+experiment we're doing Lex wend wave
+ 
+
+ align:start position:0%
+experiment we're doing Lex wend wave
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+experiment when I say we I really hope
+
+ align:start position:0%
+experiment when I say we I really hope
+ 
+
+ align:start position:0%
+experiment when I say we I really hope
+you'll do it and and uh few lines of mat
+
+ align:start position:0%
+you'll do it and and uh few lines of mat
+ 
+
+ align:start position:0%
+you'll do it and and uh few lines of mat
+lab will be greatly
+
+ align:start position:0%
+lab will be greatly
+ 
+
+ align:start position:0%
+lab will be greatly
+appreciated maybe Mr Cho can uh
+
+ align:start position:0%
+appreciated maybe Mr Cho can uh
+ 
+
+ align:start position:0%
+appreciated maybe Mr Cho can uh
+um you could email to him for example uh
+
+ align:start position:0%
+um you could email to him for example uh
+ 
+
+ align:start position:0%
+um you could email to him for example uh
+uh a code and a and the plot okay so
+
+ align:start position:0%
+uh a code and a and the plot okay so
+ 
+
+ align:start position:0%
+uh a code and a and the plot okay so
+what is that that tell us tells us LAX
+
+ align:start position:0%
+what is that that tell us tells us LAX
+ 
+
+ align:start position:0%
+what is that that tell us tells us LAX
+wend has got a lot of
+
+ align:start position:0%
+wend has got a lot of
+ 
+
+ align:start position:0%
+wend has got a lot of
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+but uh this oscillation isn't good and
+
+ align:start position:0%
+but uh this oscillation isn't good and
+ 
+
+ align:start position:0%
+but uh this oscillation isn't good and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so and how are you going to get rid of
+
+ align:start position:0%
+so and how are you going to get rid of
+ 
+
+ align:start position:0%
+so and how are you going to get rid of
+it well how do you get rid of
+
+ align:start position:0%
+it well how do you get rid of
+ 
+
+ align:start position:0%
+it well how do you get rid of
+bumpiness you introduce diffusion so
+
+ align:start position:0%
+bumpiness you introduce diffusion so
+ 
+
+ align:start position:0%
+bumpiness you introduce diffusion so
+diffusion
+
+ align:start position:0%
+diffusion
+ 
+
+ align:start position:0%
+diffusion
+heat equation
+
+ align:start position:0%
+heat equation
+ 
+
+ align:start position:0%
+heat equation
+stuff smooth things out wave equations
+
+ align:start position:0%
+stuff smooth things out wave equations
+ 
+
+ align:start position:0%
+stuff smooth things out wave equations
+don't smooth things out this wall of
+
+ align:start position:0%
+don't smooth things out this wall of
+ 
+
+ align:start position:0%
+don't smooth things out this wall of
+water in the wave equation stayed a
+
+ align:start position:0%
+water in the wave equation stayed a
+ 
+
+ align:start position:0%
+water in the wave equation stayed a
+sharp wall but we'll see very soon in
+
+ align:start position:0%
+sharp wall but we'll see very soon in
+ 
+
+ align:start position:0%
+sharp wall but we'll see very soon in
+the heat equation
+
+ align:start position:0%
+the heat equation
+ 
+
+ align:start position:0%
+the heat equation
+diffusion viscosity all those those
+
+ align:start position:0%
+diffusion viscosity all those those
+ 
+
+ align:start position:0%
+diffusion viscosity all those those
+physical things connect numerically to a
+
+ align:start position:0%
+physical things connect numerically to a
+ 
+
+ align:start position:0%
+physical things connect numerically to a
+smoother solution smoother profile and
+
+ align:start position:0%
+smoother solution smoother profile and
+ 
+
+ align:start position:0%
+smoother solution smoother profile and
+so that that is really a key idea is and
+
+ align:start position:0%
+so that that is really a key idea is and
+ 
+
+ align:start position:0%
+so that that is really a key idea is and
+and we'll see it but it will make the
+
+ align:start position:0%
+and we'll see it but it will make the
+ 
+
+ align:start position:0%
+and we'll see it but it will make the
+problem not
+
+ align:start position:0%
+problem not
+ 
+
+ align:start position:0%
+problem not
+linear if we if we want to stay with a
+
+ align:start position:0%
+linear if we if we want to stay with a
+ 
+
+ align:start position:0%
+linear if we if we want to stay with a
+linear equation and increase the
+
+ align:start position:0%
+linear equation and increase the
+ 
+
+ align:start position:0%
+linear equation and increase the
+accuracy we're going to get oscillation
+
+ align:start position:0%
+accuracy we're going to get oscillation
+ 
+
+ align:start position:0%
+accuracy we're going to get oscillation
+but if
+
+ align:start position:0%
+but if
+ 
+
+ align:start position:0%
+but if
+we locate the oscillation introduce some
+
+ align:start position:0%
+we locate the oscillation introduce some
+ 
+
+ align:start position:0%
+we locate the oscillation introduce some
+diffusion in the right
+
+ align:start position:0%
+diffusion in the right
+ 
+
+ align:start position:0%
+diffusion in the right
+place we
+
+ align:start position:0%
+place we
+ 
+
+ align:start position:0%
+place we
+can reduce the oscillation so that's the
+
+ align:start position:0%
+can reduce the oscillation so that's the
+ 
+
+ align:start position:0%
+can reduce the oscillation so that's the
+you know that that's where I mean this
+
+ align:start position:0%
+you know that that's where I mean this
+ 
+
+ align:start position:0%
+you know that that's where I mean this
+is what you really have to do if you
+
+ align:start position:0%
+is what you really have to do if you
+ 
+
+ align:start position:0%
+is what you really have to do if you
+want good uh output from numerical
+
+ align:start position:0%
+want good uh output from numerical
+ 
+
+ align:start position:0%
+want good uh output from numerical
+methods even on that simple model
+
+ align:start position:0%
+methods even on that simple model
+ 
+
+ align:start position:0%
+methods even on that simple model
+problem you'll have to have this idea of
+
+ align:start position:0%
+problem you'll have to have this idea of
+ 
+
+ align:start position:0%
+problem you'll have to have this idea of
+numerical
+
+ align:start position:0%
+numerical
+ 
+
+ align:start position:0%
+numerical
+viscosity artificial viscosity numerical
+
+ align:start position:0%
+viscosity artificial viscosity numerical
+ 
+
+ align:start position:0%
+viscosity artificial viscosity numerical
+diffusion popped in at the right
+
+ align:start position:0%
+diffusion popped in at the right
+ 
+
+ align:start position:0%
+diffusion popped in at the right
+spot and uh so we'll see that maybe the
+
+ align:start position:0%
+spot and uh so we'll see that maybe the
+ 
+
+ align:start position:0%
+spot and uh so we'll see that maybe the
+right place to see it will be for when
+
+ align:start position:0%
+right place to see it will be for when
+ 
+
+ align:start position:0%
+right place to see it will be for when
+the equation itself is already
+
+ align:start position:0%
+the equation itself is already
+ 
+
+ align:start position:0%
+the equation itself is already
+nonlinear that's where it um has
+
+ align:start position:0%
+nonlinear that's where it um has
+ 
+
+ align:start position:0%
+nonlinear that's where it um has
+developed a lot so we'll when we get to
+
+ align:start position:0%
+developed a lot so we'll when we get to
+ 
+
+ align:start position:0%
+developed a lot so we'll when we get to
+nonlinear wave equations which isn't far
+
+ align:start position:0%
+nonlinear wave equations which isn't far
+ 
+
+ align:start position:0%
+nonlinear wave equations which isn't far
+off uh that's what we'll see okay so now
+
+ align:start position:0%
+off uh that's what we'll see okay so now
+ 
+
+ align:start position:0%
+off uh that's what we'll see okay so now
+I guess I have one more Topic in
+
+ align:start position:0%
+I guess I have one more Topic in
+ 
+
+ align:start position:0%
+I guess I have one more Topic in
+the in this um
+
+ align:start position:0%
+the in this um
+ 
+
+ align:start position:0%
+the in this um
+lecture and that is
+
+ align:start position:0%
+lecture and that is
+ 
+
+ align:start position:0%
+lecture and that is
+convergence how do you show that we know
+
+ align:start position:0%
+convergence how do you show that we know
+ 
+
+ align:start position:0%
+convergence how do you show that we know
+we sort of know that we need
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stability so I guess yeah I have to come
+
+ align:start position:0%
+stability so I guess yeah I have to come
+ 
+
+ align:start position:0%
+stability so I guess yeah I have to come
+to the question of convergence all right
+
+ align:start position:0%
+to the question of convergence all right
+ 
+
+ align:start position:0%
+to the question of convergence all right
+and of course I have to
+
+ align:start position:0%
+and of course I have to
+ 
+
+ align:start position:0%
+and of course I have to
+mention the more than mention the uh
+
+ align:start position:0%
+mention the more than mention the uh
+ 
+
+ align:start position:0%
+mention the more than mention the uh
+key result in the whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory it the connection so we have
+
+ align:start position:0%
+Theory it the connection so we have
+ 
+
+ align:start position:0%
+Theory it the connection so we have
+methods that are first order second
+
+ align:start position:0%
+methods that are first order second
+ 
+
+ align:start position:0%
+methods that are first order second
+order stable or unstable and then the
+
+ align:start position:0%
+order stable or unstable and then the
+ 
+
+ align:start position:0%
+order stable or unstable and then the
+key idea is this
+
+ align:start position:0%
+key idea is this
+ 
+
+ align:start position:0%
+key idea is this
+LAX again he enters lack equivalence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the so this is a little bit of pure math
+
+ align:start position:0%
+the so this is a little bit of pure math
+ 
+
+ align:start position:0%
+the so this is a little bit of pure math
+comes into this and it gives exactly the
+
+ align:start position:0%
+comes into this and it gives exactly the
+ 
+
+ align:start position:0%
+comes into this and it gives exactly the
+result we would expect stability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+implies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+convergence and convergence implies
+
+ align:start position:0%
+convergence and convergence implies
+ 
+
+ align:start position:0%
+convergence and convergence implies
+stability so that's the two ideas are
+
+ align:start position:0%
+stability so that's the two ideas are
+ 
+
+ align:start position:0%
+stability so that's the two ideas are
+equivalent for uh provided we're talking
+
+ align:start position:0%
+equivalent for uh provided we're talking
+ 
+
+ align:start position:0%
+equivalent for uh provided we're talking
+about a decent problem for uh for uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consistent approximation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well-posed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems okay well I've got four words
+
+ align:start position:0%
+problems okay well I've got four words
+ 
+
+ align:start position:0%
+problems okay well I've got four words
+on the board four key words here
+
+ align:start position:0%
+on the board four key words here
+ 
+
+ align:start position:0%
+on the board four key words here
+stability we kind of know what that
+
+ align:start position:0%
+stability we kind of know what that
+ 
+
+ align:start position:0%
+stability we kind of know what that
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+convergence these are the new words and
+
+ align:start position:0%
+convergence these are the new words and
+ 
+
+ align:start position:0%
+convergence these are the new words and
+I'll just um and actually so consistent
+
+ align:start position:0%
+I'll just um and actually so consistent
+ 
+
+ align:start position:0%
+I'll just um and actually so consistent
+means that the method is at least first
+
+ align:start position:0%
+means that the method is at least first
+ 
+
+ align:start position:0%
+means that the method is at least first
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+order that that the difference equation
+
+ align:start position:0%
+order that that the difference equation
+ 
+
+ align:start position:0%
+order that that the difference equation
+approaches the differential
+
+ align:start position:0%
+approaches the differential
+ 
+
+ align:start position:0%
+approaches the differential
+equation at a single
+
+ align:start position:0%
+equation at a single
+ 
+
+ align:start position:0%
+equation at a single
+step well posed means that the
+
+ align:start position:0%
+step well posed means that the
+ 
+
+ align:start position:0%
+step well posed means that the
+differential equation is
+
+ align:start position:0%
+differential equation is
+ 
+
+ align:start position:0%
+differential equation is
+okay so for example what would be a non
+
+ align:start position:0%
+okay so for example what would be a non
+ 
+
+ align:start position:0%
+okay so for example what would be a non
+well-posed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem uh well when we get to the heat
+
+ align:start position:0%
+problem uh well when we get to the heat
+ 
+
+ align:start position:0%
+problem uh well when we get to the heat
+equation if you ran the heat equation
+
+ align:start position:0%
+equation if you ran the heat equation
+ 
+
+ align:start position:0%
+equation if you ran the heat equation
+backward in time
+
+ align:start position:0%
+backward in time
+ 
+
+ align:start position:0%
+backward in time
+that would give us an equation DT is
+
+ align:start position:0%
+that would give us an equation DT is
+ 
+
+ align:start position:0%
+that would give us an equation DT is
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+uxx that would be not well
+
+ align:start position:0%
+uxx that would be not well
+ 
+
+ align:start position:0%
+uxx that would be not well
+posed that would be not well posed or if
+
+ align:start position:0%
+posed that would be not well posed or if
+ 
+
+ align:start position:0%
+posed that would be not well posed or if
+you triy to solve Lassa
+
+ align:start position:0%
+you triy to solve Lassa
+ 
+
+ align:start position:0%
+you triy to solve Lassa
+equation say utt plus uxx =
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0 uh from initial
+
+ align:start position:0%
+0 uh from initial
+ 
+
+ align:start position:0%
+0 uh from initial
+values that would not be well posted
+
+ align:start position:0%
+values that would not be well posted
+ 
+
+ align:start position:0%
+values that would not be well posted
+but we're so we're going to we're but
+
+ align:start position:0%
+but we're so we're going to we're but
+ 
+
+ align:start position:0%
+but we're so we're going to we're but
+we're dealing with well-posed problems
+
+ align:start position:0%
+we're dealing with well-posed problems
+ 
+
+ align:start position:0%
+we're dealing with well-posed problems
+the wave
+
+ align:start position:0%
+the wave
+ 
+
+ align:start position:0%
+the wave
+equation which has the right sign and
+
+ align:start position:0%
+equation which has the right sign and
+ 
+
+ align:start position:0%
+equation which has the right sign and
+the heat equation with the right sign so
+
+ align:start position:0%
+the heat equation with the right sign so
+ 
+
+ align:start position:0%
+the heat equation with the right sign so
+our problems are going to be well posed
+
+ align:start position:0%
+our problems are going to be well posed
+ 
+
+ align:start position:0%
+our problems are going to be well posed
+you you can like safely think okay we're
+
+ align:start position:0%
+you you can like safely think okay we're
+ 
+
+ align:start position:0%
+you you can like safely think okay we're
+only talking about consistent
+
+ align:start position:0%
+only talking about consistent
+ 
+
+ align:start position:0%
+only talking about consistent
+approximations to well-posed problems
+
+ align:start position:0%
+approximations to well-posed problems
+ 
+
+ align:start position:0%
+approximations to well-posed problems
+and and here's the main point okay that
+
+ align:start position:0%
+and and here's the main point okay that
+ 
+
+ align:start position:0%
+and and here's the main point okay that
+stability holds if and only if
+
+ align:start position:0%
+stability holds if and only if
+ 
+
+ align:start position:0%
+stability holds if and only if
+convergence holds okay so there's
+
+ align:start position:0%
+convergence holds okay so there's
+ 
+
+ align:start position:0%
+convergence holds okay so there's
+actually two things to show there
+
+ align:start position:0%
+actually two things to show there
+ 
+
+ align:start position:0%
+actually two things to show there
+how does stability give convergence and
+
+ align:start position:0%
+how does stability give convergence and
+ 
+
+ align:start position:0%
+how does stability give convergence and
+how and why does convergence require
+
+ align:start position:0%
+how and why does convergence require
+ 
+
+ align:start position:0%
+how and why does convergence require
+stability so that instability could not
+
+ align:start position:0%
+stability so that instability could not
+ 
+
+ align:start position:0%
+stability so that instability could not
+geted
+
+ align:start position:0%
+geted
+ 
+
+ align:start position:0%
+geted
+okay so that that's sort of like maybe
+
+ align:start position:0%
+okay so that that's sort of like maybe
+ 
+
+ align:start position:0%
+okay so that that's sort of like maybe
+the fundamental theorem of numerical
+
+ align:start position:0%
+the fundamental theorem of numerical
+ 
+
+ align:start position:0%
+the fundamental theorem of numerical
+analysis the the fact that stability a
+
+ align:start position:0%
+analysis the the fact that stability a
+ 
+
+ align:start position:0%
+analysis the the fact that stability a
+bound so what is we better say what
+
+ align:start position:0%
+bound so what is we better say what
+ 
+
+ align:start position:0%
+bound so what is we better say what
+stability is and and what is convergent
+
+ align:start position:0%
+stability is and and what is convergent
+ 
+
+ align:start position:0%
+stability is and and what is convergent
+so let me let me capture these
+
+ align:start position:0%
+so let me let me capture these
+ 
+
+ align:start position:0%
+so let me let me capture these
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+uh in uh
+
+ align:start position:0%
+uh in uh
+ 
+
+ align:start position:0%
+uh in uh
+inequalities in in in mathematical terms
+
+ align:start position:0%
+inequalities in in in mathematical terms
+ 
+
+ align:start position:0%
+inequalities in in in mathematical terms
+rather than just words okay so uh so
+
+ align:start position:0%
+rather than just words okay so uh so
+ 
+
+ align:start position:0%
+rather than just words okay so uh so
+those are the ideas maybe I'm going to
+
+ align:start position:0%
+those are the ideas maybe I'm going to
+ 
+
+ align:start position:0%
+those are the ideas maybe I'm going to
+have to write a little above here but so
+
+ align:start position:0%
+have to write a little above here but so
+ 
+
+ align:start position:0%
+have to write a little above here but so
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+does what's our method right okay okay
+
+ align:start position:0%
+does what's our method right okay okay
+ 
+
+ align:start position:0%
+does what's our method right okay okay
+so I need some notation and then I'll
+
+ align:start position:0%
+so I need some notation and then I'll
+ 
+
+ align:start position:0%
+so I need some notation and then I'll
+lift the board and we'll see what each
+
+ align:start position:0%
+lift the board and we'll see what each
+ 
+
+ align:start position:0%
+lift the board and we'll see what each
+thing means so our our our method we
+
+ align:start position:0%
+thing means so our our our method we
+ 
+
+ align:start position:0%
+thing means so our our our method we
+we're we're allowing
+
+ align:start position:0%
+we're we're allowing
+ 
+
+ align:start position:0%
+we're we're allowing
+any difference method that moves forward
+
+ align:start position:0%
+any difference method that moves forward
+ 
+
+ align:start position:0%
+any difference method that moves forward
+in time there's
+
+ align:start position:0%
+in time there's
+ 
+
+ align:start position:0%
+in time there's
+time let me use R for the
+
+ align:start position:0%
+time let me use R for the
+ 
+
+ align:start position:0%
+time let me use R for the
+true operator that takes the function
+
+ align:start position:0%
+true operator that takes the function
+ 
+
+ align:start position:0%
+true operator that takes the function
+follows the differential equation to the
+
+ align:start position:0%
+follows the differential equation to the
+ 
+
+ align:start position:0%
+follows the differential equation to the
+next time so I'm going to say that U the
+
+ align:start position:0%
+next time so I'm going to say that U the
+ 
+
+ align:start position:0%
+next time so I'm going to say that U the
+true U which is always a small U at
+
+ align:start position:0%
+true U which is always a small U at
+ 
+
+ align:start position:0%
+true U which is always a small U at
+delta T is some R some something R time
+
+ align:start position:0%
+delta T is some R some something R time
+ 
+
+ align:start position:0%
+delta T is some R some something R time
+U of T where the approximate
+
+ align:start position:0%
+U of T where the approximate
+ 
+
+ align:start position:0%
+U of T where the approximate
+guy is some s * U
+
+ align:start position:0%
+guy is some s * U
+ 
+
+ align:start position:0%
+guy is some s * U
+of okay so R
+
+ align:start position:0%
+of okay so R
+ 
+
+ align:start position:0%
+of okay so R
+is the true solution so well posed so of
+
+ align:start position:0%
+is the true solution so well posed so of
+ 
+
+ align:start position:0%
+is the true solution so well posed so of
+course to take if if this is n delta T
+
+ align:start position:0%
+course to take if if this is n delta T
+ 
+
+ align:start position:0%
+course to take if if this is n delta T
+then we've taken r n times so the the
+
+ align:start position:0%
+then we've taken r n times so the the
+ 
+
+ align:start position:0%
+then we've taken r n times so the the
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+solution is R to the N times the initial
+
+ align:start position:0%
+solution is R to the N times the initial
+ 
+
+ align:start position:0%
+solution is R to the N times the initial
+value and the approximate guy is s n
+
+ align:start position:0%
+value and the approximate guy is s n
+ 
+
+ align:start position:0%
+value and the approximate guy is s n
+times times the initial value and we'll
+
+ align:start position:0%
+times times the initial value and we'll
+ 
+
+ align:start position:0%
+times times the initial value and we'll
+we might as well start out with those
+
+ align:start position:0%
+we might as well start out with those
+ 
+
+ align:start position:0%
+we might as well start out with those
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+okay so that's what R and S
+
+ align:start position:0%
+okay so that's what R and S
+ 
+
+ align:start position:0%
+okay so that's what R and S
+are now we got three
+
+ align:start position:0%
+are now we got three
+ 
+
+ align:start position:0%
+are now we got three
+ideas here what does well pose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean well posed means that the
+
+ align:start position:0%
+mean well posed means that the
+ 
+
+ align:start position:0%
+mean well posed means that the
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+true thing is bounded that R to the n *
+
+ align:start position:0%
+true thing is bounded that R to the n *
+ 
+
+ align:start position:0%
+true thing is bounded that R to the n *
+U is less than some constant time U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these inequalities are sort of part of
+
+ align:start position:0%
+these inequalities are sort of part of
+ 
+
+ align:start position:0%
+these inequalities are sort of part of
+the mathematics of partial differential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equations I think you've got to to take
+
+ align:start position:0%
+equations I think you've got to to take
+ 
+
+ align:start position:0%
+equations I think you've got to to take
+them as not
+
+ align:start position:0%
+them as not
+ 
+
+ align:start position:0%
+them as not
+uh I
+
+ align:start position:0%
+uh I
+ 
+
+ align:start position:0%
+uh I
+mean take them as sort of a reasonable
+
+ align:start position:0%
+mean take them as sort of a reasonable
+ 
+
+ align:start position:0%
+mean take them as sort of a reasonable
+statement that the this is
+
+ align:start position:0%
+statement that the this is
+ 
+
+ align:start position:0%
+statement that the this is
+energy this you typically will measure
+
+ align:start position:0%
+energy this you typically will measure
+ 
+
+ align:start position:0%
+energy this you typically will measure
+the energy and in our wave equation C1
+
+ align:start position:0%
+the energy and in our wave equation C1
+ 
+
+ align:start position:0%
+the energy and in our wave equation C1
+the constant C1 will be
+
+ align:start position:0%
+the constant C1 will be
+ 
+
+ align:start position:0%
+the constant C1 will be
+one the energy doesn't
+
+ align:start position:0%
+one the energy doesn't
+ 
+
+ align:start position:0%
+one the energy doesn't
+change in another
+
+ align:start position:0%
+change in another
+ 
+
+ align:start position:0%
+change in another
+problem we could allow the possibility
+
+ align:start position:0%
+problem we could allow the possibility
+ 
+
+ align:start position:0%
+problem we could allow the possibility
+of C1 being a little bigger than one but
+
+ align:start position:0%
+of C1 being a little bigger than one but
+ 
+
+ align:start position:0%
+of C1 being a little bigger than one but
+think of C1 as
+
+ align:start position:0%
+think of C1 as
+ 
+
+ align:start position:0%
+think of C1 as
+one okay then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stability will be abound on S to the
+
+ align:start position:0%
+stability will be abound on S to the
+ 
+
+ align:start position:0%
+stability will be abound on S to the
+end say C2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and again in in our examples C2 has been
+
+ align:start position:0%
+and again in in our examples C2 has been
+ 
+
+ align:start position:0%
+and again in in our examples C2 has been
+one this is like C2 is
+
+ align:start position:0%
+one this is like C2 is
+ 
+
+ align:start position:0%
+one this is like C2 is
+like uh I mean the s to the n on each
+
+ align:start position:0%
+like uh I mean the s to the n on each
+ 
+
+ align:start position:0%
+like uh I mean the s to the n on each
+exponential is this G to the nth and G
+
+ align:start position:0%
+exponential is this G to the nth and G
+ 
+
+ align:start position:0%
+exponential is this G to the nth and G
+is below one so so often C1 and C2 will
+
+ align:start position:0%
+is below one so so often C1 and C2 will
+ 
+
+ align:start position:0%
+is below one so so often C1 and C2 will
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and then finally what is this idea
+
+ align:start position:0%
+one and then finally what is this idea
+ 
+
+ align:start position:0%
+one and then finally what is this idea
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consistency and this means consistent
+
+ align:start position:0%
+consistency and this means consistent
+ 
+
+ align:start position:0%
+consistency and this means consistent
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+that so what's
+
+ align:start position:0%
+that so what's
+ 
+
+ align:start position:0%
+that so what's
+consistent the consistent is
+
+ align:start position:0%
+consistent the consistent is
+ 
+
+ align:start position:0%
+consistent the consistent is
+comparing
+
+ align:start position:0%
+comparing
+ 
+
+ align:start position:0%
+comparing
+the diff differential equation with the
+
+ align:start position:0%
+the diff differential equation with the
+ 
+
+ align:start position:0%
+the diff differential equation with the
+difference equation it's comparing r
+
+ align:start position:0%
+difference equation it's comparing r
+ 
+
+ align:start position:0%
+difference equation it's comparing r
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+s and at a single
+
+ align:start position:0%
+s and at a single
+ 
+
+ align:start position:0%
+s and at a single
+step they should be close so single step
+
+ align:start position:0%
+step they should be close so single step
+ 
+
+ align:start position:0%
+step they should be close so single step
+R minus
+
+ align:start position:0%
+R minus
+ 
+
+ align:start position:0%
+R minus
+s u that's the starting with the same U
+
+ align:start position:0%
+s u that's the starting with the same U
+ 
+
+ align:start position:0%
+s u that's the starting with the same U
+I'm just taking one step in the
+
+ align:start position:0%
+I'm just taking one step in the
+ 
+
+ align:start position:0%
+I'm just taking one step in the
+differential equation and comparing it
+
+ align:start position:0%
+differential equation and comparing it
+ 
+
+ align:start position:0%
+differential equation and comparing it
+with one step in the differential in the
+
+ align:start position:0%
+with one step in the differential in the
+ 
+
+ align:start position:0%
+with one step in the differential in the
+difference equation and I would want
+
+ align:start position:0%
+difference equation and I would want
+ 
+
+ align:start position:0%
+difference equation and I would want
+that to be say say
+
+ align:start position:0%
+that to be say say
+ 
+
+ align:start position:0%
+that to be say say
+C3 maybe delta T to the p + 1 was that
+
+ align:start position:0%
+C3 maybe delta T to the p + 1 was that
+ 
+
+ align:start position:0%
+C3 maybe delta T to the p + 1 was that
+is that times some size of some of
+
+ align:start position:0%
+is that times some size of some of
+ 
+
+ align:start position:0%
+is that times some size of some of
+u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+order delta T to the p + one or like
+
+ align:start position:0%
+order delta T to the p + one or like
+ 
+
+ align:start position:0%
+order delta T to the p + one or like
+Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t^2 this would be this would be the
+
+ align:start position:0%
+t^2 this would be this would be the
+ 
+
+ align:start position:0%
+t^2 this would be this would be the
+usual
+
+ align:start position:0%
+usual
+ 
+
+ align:start position:0%
+usual
+situation that when it's
+
+ align:start position:0%
+situation that when it's
+ 
+
+ align:start position:0%
+situation that when it's
+stable so if so at the moment then I I
+
+ align:start position:0%
+stable so if so at the moment then I I
+ 
+
+ align:start position:0%
+stable so if so at the moment then I I
+want to say if these are all true then I
+
+ align:start position:0%
+want to say if these are all true then I
+ 
+
+ align:start position:0%
+want to say if these are all true then I
+get convergence cuz I'm going to I'm
+
+ align:start position:0%
+get convergence cuz I'm going to I'm
+ 
+
+ align:start position:0%
+get convergence cuz I'm going to I'm
+going to what I'm now going to do is
+
+ align:start position:0%
+going to what I'm now going to do is
+ 
+
+ align:start position:0%
+going to what I'm now going to do is
+show that stability implies
+
+ align:start position:0%
+show that stability implies
+ 
+
+ align:start position:0%
+show that stability implies
+convergence it it it's what we did
+
+ align:start position:0%
+convergence it it it's what we did
+ 
+
+ align:start position:0%
+convergence it it it's what we did
+for ordinary differential equations I
+
+ align:start position:0%
+for ordinary differential equations I
+ 
+
+ align:start position:0%
+for ordinary differential equations I
+had a this was the local error this is
+
+ align:start position:0%
+had a this was the local error this is
+ 
+
+ align:start position:0%
+had a this was the local error this is
+the local error that I called de the
+
+ align:start position:0%
+the local error that I called de the
+ 
+
+ align:start position:0%
+the local error that I called de the
+discreation
+
+ align:start position:0%
+discreation
+ 
+
+ align:start position:0%
+discreation
+error and these are saying so this is
+
+ align:start position:0%
+error and these are saying so this is
+ 
+
+ align:start position:0%
+error and these are saying so this is
+saying that the here's here's really
+
+ align:start position:0%
+saying that the here's here's really
+ 
+
+ align:start position:0%
+saying that the here's here's really
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+happens so I I would want to look at the
+
+ align:start position:0%
+happens so I I would want to look at the
+ 
+
+ align:start position:0%
+happens so I I would want to look at the
+error up here after end
+
+ align:start position:0%
+error up here after end
+ 
+
+ align:start position:0%
+error up here after end
+steps so the error after end steps
+
+ align:start position:0%
+steps so the error after end steps
+ 
+
+ align:start position:0%
+steps so the error after end steps
+typical term is I follow the
+
+ align:start position:0%
+typical term is I follow the
+ 
+
+ align:start position:0%
+typical term is I follow the
+differential equation that's
+
+ align:start position:0%
+differential equation that's
+ 
+
+ align:start position:0%
+differential equation that's
+U then I have this little error
+
+ align:start position:0%
+U then I have this little error
+ 
+
+ align:start position:0%
+U then I have this little error
+de which I make at that step the
+
+ align:start position:0%
+de which I make at that step the
+ 
+
+ align:start position:0%
+de which I make at that step the
+difference between R and S and then I
+
+ align:start position:0%
+difference between R and S and then I
+ 
+
+ align:start position:0%
+difference between R and S and then I
+follow the difference
+
+ align:start position:0%
+follow the difference
+ 
+
+ align:start position:0%
+follow the difference
+equation up to the remaining time
+
+ align:start position:0%
+equation up to the remaining time
+ 
+
+ align:start position:0%
+equation up to the remaining time
+what I want to show is
+
+ align:start position:0%
+what I want to show is
+ 
+
+ align:start position:0%
+what I want to show is
+that that that I can track the error and
+
+ align:start position:0%
+that that that I can track the error and
+ 
+
+ align:start position:0%
+that that that I can track the error and
+can and and and and bound
+
+ align:start position:0%
+can and and and and bound
+ 
+
+ align:start position:0%
+can and and and and bound
+it I don't know if you remember the
+
+ align:start position:0%
+it I don't know if you remember the
+ 
+
+ align:start position:0%
+it I don't know if you remember the
+discussion for ordinary differential
+
+ align:start position:0%
+discussion for ordinary differential
+ 
+
+ align:start position:0%
+discussion for ordinary differential
+equations but it went the same way we we
+
+ align:start position:0%
+equations but it went the same way we we
+ 
+
+ align:start position:0%
+equations but it went the same way we we
+had we we looked at the the new error de
+
+ align:start position:0%
+had we we looked at the the new error de
+ 
+
+ align:start position:0%
+had we we looked at the the new error de
+that was produced at each time step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K when we took K steps of when we were
+
+ align:start position:0%
+K when we took K steps of when we were
+ 
+
+ align:start position:0%
+K when we took K steps of when we were
+we got up to this point with the true
+
+ align:start position:0%
+we got up to this point with the true
+ 
+
+ align:start position:0%
+we got up to this point with the true
+solution we plugged the true solution
+
+ align:start position:0%
+solution we plugged the true solution
+ 
+
+ align:start position:0%
+solution we plugged the true solution
+into the difference equation it had a
+
+ align:start position:0%
+into the difference equation it had a
+ 
+
+ align:start position:0%
+into the difference equation it had a
+little error and whatever their error
+
+ align:start position:0%
+little error and whatever their error
+ 
+
+ align:start position:0%
+little error and whatever their error
+there was that got thrown in with other
+
+ align:start position:0%
+there was that got thrown in with other
+ 
+
+ align:start position:0%
+there was that got thrown in with other
+errors and propagated up
+
+ align:start position:0%
+errors and propagated up
+ 
+
+ align:start position:0%
+errors and propagated up
+to any later time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in is that am I bringing back what we
+
+ align:start position:0%
+in is that am I bringing back what we
+ 
+
+ align:start position:0%
+in is that am I bringing back what we
+did there or or just you can just see
+
+ align:start position:0%
+did there or or just you can just see
+ 
+
+ align:start position:0%
+did there or or just you can just see
+that's what we're going to have here and
+
+ align:start position:0%
+that's what we're going to have here and
+ 
+
+ align:start position:0%
+that's what we're going to have here and
+now how will I express
+
+ align:start position:0%
+now how will I express
+ 
+
+ align:start position:0%
+now how will I express
+that somehow I I have to estimate the
+
+ align:start position:0%
+that somehow I I have to estimate the
+ 
+
+ align:start position:0%
+that somehow I I have to estimate the
+difference between R to the n and S to
+
+ align:start position:0%
+difference between R to the n and S to
+ 
+
+ align:start position:0%
+difference between R to the n and S to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+N that's really my problem actually it's
+
+ align:start position:0%
+N that's really my problem actually it's
+ 
+
+ align:start position:0%
+N that's really my problem actually it's
+a nice
+
+ align:start position:0%
+a nice
+ 
+
+ align:start position:0%
+a nice
+problem suppose I have a control of of
+
+ align:start position:0%
+problem suppose I have a control of of
+ 
+
+ align:start position:0%
+problem suppose I have a control of of
+powers of R and S and I know that R
+
+ align:start position:0%
+powers of R and S and I know that R
+ 
+
+ align:start position:0%
+powers of R and S and I know that R
+minus s is small somehow how do I show
+
+ align:start position:0%
+minus s is small somehow how do I show
+ 
+
+ align:start position:0%
+minus s is small somehow how do I show
+that R to the nth minus s the N is small
+
+ align:start position:0%
+that R to the nth minus s the N is small
+ 
+
+ align:start position:0%
+that R to the nth minus s the N is small
+that that's my job that's this is the
+
+ align:start position:0%
+that that's my job that's this is the
+ 
+
+ align:start position:0%
+that that's my job that's this is the
+error when I apply it to a to a starting
+
+ align:start position:0%
+error when I apply it to a to a starting
+ 
+
+ align:start position:0%
+error when I apply it to a to a starting
+value U this is the difference between
+
+ align:start position:0%
+value U this is the difference between
+ 
+
+ align:start position:0%
+value U this is the difference between
+little U and big U so how do I what I
+
+ align:start position:0%
+little U and big U so how do I what I
+ 
+
+ align:start position:0%
+little U and big U so how do I what I
+want to do is split it out
+
+ align:start position:0%
+want to do is split it out
+ 
+
+ align:start position:0%
+want to do is split it out
+into this situation where I just have
+
+ align:start position:0%
+into this situation where I just have
+ 
+
+ align:start position:0%
+into this situation where I just have
+one R minus s so look look I think this
+
+ align:start position:0%
+one R minus s so look look I think this
+ 
+
+ align:start position:0%
+one R minus s so look look I think this
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+work so suppose I have I think I could
+
+ align:start position:0%
+work so suppose I have I think I could
+ 
+
+ align:start position:0%
+work so suppose I have I think I could
+start with R to the nus1 * r r -
+
+ align:start position:0%
+start with R to the nus1 * r r -
+ 
+
+ align:start position:0%
+start with R to the nus1 * r r -
+s and then an R to the N - 2 * an r - s
+
+ align:start position:0%
+s and then an R to the N - 2 * an r - s
+ 
+
+ align:start position:0%
+s and then an R to the N - 2 * an r - s
+times an
+
+ align:start position:0%
+times an
+ 
+
+ align:start position:0%
+times an
+S oh maybe I don't sorry this guy is
+
+ align:start position:0%
+S oh maybe I don't sorry this guy is
+ 
+
+ align:start position:0%
+S oh maybe I don't sorry this guy is
+going to carry me I'd rather do
+
+ align:start position:0%
+going to carry me I'd rather do
+ 
+
+ align:start position:0%
+going to carry me I'd rather do
+sorry got to do it right because I want
+
+ align:start position:0%
+sorry got to do it right because I want
+ 
+
+ align:start position:0%
+sorry got to do it right because I want
+the RS to come first I want
+
+ align:start position:0%
+the RS to come first I want
+ 
+
+ align:start position:0%
+the RS to come first I want
+maybe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um r - s * s the N
+
+ align:start position:0%
+um r - s * s the N
+ 
+
+ align:start position:0%
+um r - s * s the N
+-1 and
+
+ align:start position:0%
+-1 and
+ 
+
+ align:start position:0%
+-1 and
+then sorry I want RS on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right good finally got
+
+ align:start position:0%
+right good finally got
+ 
+
+ align:start position:0%
+right good finally got
+it so that gives me the r to the nth but
+
+ align:start position:0%
+it so that gives me the r to the nth but
+ 
+
+ align:start position:0%
+it so that gives me the r to the nth but
+I've subtracted off so I need an
+
+ align:start position:0%
+I've subtracted off so I need an
+ 
+
+ align:start position:0%
+I've subtracted off so I need an
+s r - s r to the N - 2
+
+ align:start position:0%
+s r - s r to the N - 2
+ 
+
+ align:start position:0%
+s r - s r to the N - 2
+and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on sorry for this bit of of algebra in
+
+ align:start position:0%
+on sorry for this bit of of algebra in
+ 
+
+ align:start position:0%
+on sorry for this bit of of algebra in
+the middle of practical things but uh do
+
+ align:start position:0%
+the middle of practical things but uh do
+ 
+
+ align:start position:0%
+the middle of practical things but uh do
+you see
+
+ align:start position:0%
+you see
+ 
+
+ align:start position:0%
+you see
+that this is this is the case where I
+
+ align:start position:0%
+that this is this is the case where I
+ 
+
+ align:start position:0%
+that this is this is the case where I
+followed the differential equation up
+
+ align:start position:0%
+followed the differential equation up
+ 
+
+ align:start position:0%
+followed the differential equation up
+and at the last step I made an
+
+ align:start position:0%
+and at the last step I made an
+ 
+
+ align:start position:0%
+and at the last step I made an
+error this is the case where I followed
+
+ align:start position:0%
+error this is the case where I followed
+ 
+
+ align:start position:0%
+error this is the case where I followed
+the differential equation almost to the
+
+ align:start position:0%
+the differential equation almost to the
+ 
+
+ align:start position:0%
+the differential equation almost to the
+top I made an error and then I had one
+
+ align:start position:0%
+top I made an error and then I had one
+ 
+
+ align:start position:0%
+top I made an error and then I had one
+more step to go with the difference
+
+ align:start position:0%
+more step to go with the difference
+ 
+
+ align:start position:0%
+more step to go with the difference
+method see the the S is doing this part
+
+ align:start position:0%
+method see the the S is doing this part
+ 
+
+ align:start position:0%
+method see the the S is doing this part
+so a typical term will be a power of s s
+
+ align:start position:0%
+so a typical term will be a power of s s
+ 
+
+ align:start position:0%
+so a typical term will be a power of s s
+to some power r - s r to some
+
+ align:start position:0%
+to some power r - s r to some
+ 
+
+ align:start position:0%
+to some power r - s r to some
+power I'm breaking the the error at n
+
+ align:start position:0%
+power I'm breaking the the error at n
+ 
+
+ align:start position:0%
+power I'm breaking the the error at n
+steps into n different terms each from
+
+ align:start position:0%
+steps into n different terms each from
+ 
+
+ align:start position:0%
+steps into n different terms each from
+the error at one step this is the error
+
+ align:start position:0%
+the error at one step this is the error
+ 
+
+ align:start position:0%
+the error at one step this is the error
+at the last step this is the error at
+
+ align:start position:0%
+at the last step this is the error at
+ 
+
+ align:start position:0%
+at the last step this is the error at
+the next to last step and so on okay
+
+ align:start position:0%
+the next to last step and so on okay
+ 
+
+ align:start position:0%
+the next to last step and so on okay
+okay we've got
+
+ align:start position:0%
+okay we've got
+ 
+
+ align:start position:0%
+okay we've got
+it because I just estimate every term
+
+ align:start position:0%
+it because I just estimate every term
+ 
+
+ align:start position:0%
+it because I just estimate every term
+every term has a power of R which gives
+
+ align:start position:0%
+every term has a power of R which gives
+ 
+
+ align:start position:0%
+every term has a power of R which gives
+me a C1 a power of s which gives me a C2
+
+ align:start position:0%
+me a C1 a power of s which gives me a C2
+ 
+
+ align:start position:0%
+me a C1 a power of s which gives me a C2
+and the discretization error the
+
+ align:start position:0%
+and the discretization error the
+ 
+
+ align:start position:0%
+and the discretization error the
+one-step actual error R minus s which
+
+ align:start position:0%
+one-step actual error R minus s which
+ 
+
+ align:start position:0%
+one-step actual error R minus s which
+gives me a C3 and this delta T to the p
+
+ align:start position:0%
+gives me a C3 and this delta T to the p
+ 
+
+ align:start position:0%
+gives me a C3 and this delta T to the p
++ 1 and you see
+
+ align:start position:0%
++ 1 and you see
+ 
+
+ align:start position:0%
++ 1 and you see
+that I'm just piling up
+
+ align:start position:0%
+that I'm just piling up
+ 
+
+ align:start position:0%
+that I'm just piling up
+n of these
+
+ align:start position:0%
+n of these
+ 
+
+ align:start position:0%
+n of these
+so I'm getting n of those delta T to the
+
+ align:start position:0%
+so I'm getting n of those delta T to the
+ 
+
+ align:start position:0%
+so I'm getting n of those delta T to the
+P +1 so the final result will be I'll
+
+ align:start position:0%
+P +1 so the final result will be I'll
+ 
+
+ align:start position:0%
+P +1 so the final result will be I'll
+have n of these delta T to the p + 1's
+
+ align:start position:0%
+have n of these delta T to the p + 1's
+ 
+
+ align:start position:0%
+have n of these delta T to the p + 1's
+and that will
+
+ align:start position:0%
+and that will
+ 
+
+ align:start position:0%
+and that will
+be T and delta T delta T to the P so
+
+ align:start position:0%
+be T and delta T delta T to the P so
+ 
+
+ align:start position:0%
+be T and delta T delta T to the P so
+that'll be the
+
+ align:start position:0%
+that'll be the
+ 
+
+ align:start position:0%
+that'll be the
+error
+
+ align:start position:0%
+error
+ 
+
+ align:start position:0%
+error
+well since I made went to all the
+
+ align:start position:0%
+well since I made went to all the
+ 
+
+ align:start position:0%
+well since I made went to all the
+trouble of defining a C1 C2 and C3 those
+
+ align:start position:0%
+trouble of defining a C1 C2 and C3 those
+ 
+
+ align:start position:0%
+trouble of defining a C1 C2 and C3 those
+those three numbers so the eror will
+
+ align:start position:0%
+those three numbers so the eror will
+ 
+
+ align:start position:0%
+those three numbers so the eror will
+there'll be a C1 * C2 * C3 constant
+
+ align:start position:0%
+there'll be a C1 * C2 * C3 constant
+ 
+
+ align:start position:0%
+there'll be a C1 * C2 * C3 constant
+there to to uh in the
+
+ align:start position:0%
+there to to uh in the
+ 
+
+ align:start position:0%
+there to to uh in the
+bound have a look at the notes for
+
+ align:start position:0%
+bound have a look at the notes for
+ 
+
+ align:start position:0%
+bound have a look at the notes for
+that and let me just conclude with
+
+ align:start position:0%
+that and let me just conclude with
+ 
+
+ align:start position:0%
+that and let me just conclude with
+lax's
+
+ align:start position:0%
+lax's
+ 
+
+ align:start position:0%
+lax's
+Insight on the other part the fact
+
+ align:start position:0%
+Insight on the other part the fact
+ 
+
+ align:start position:0%
+Insight on the other part the fact
+that convergence requires stability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that you see that what I've shown is
+
+ align:start position:0%
+so that you see that what I've shown is
+ 
+
+ align:start position:0%
+so that you see that what I've shown is
+that if we're stable if I bound these
+
+ align:start position:0%
+that if we're stable if I bound these
+ 
+
+ align:start position:0%
+that if we're stable if I bound these
+bound these bound these then I have a
+
+ align:start position:0%
+bound these bound these then I have a
+ 
+
+ align:start position:0%
+bound these bound these then I have a
+bound on the error and it's that's
+
+ align:start position:0%
+bound on the error and it's that's
+ 
+
+ align:start position:0%
+bound on the error and it's that's
+convergence the other way is why if it's
+
+ align:start position:0%
+convergence the other way is why if it's
+ 
+
+ align:start position:0%
+convergence the other way is why if it's
+unstable how do you know it couldn't
+
+ align:start position:0%
+unstable how do you know it couldn't
+ 
+
+ align:start position:0%
+unstable how do you know it couldn't
+convert how do we know that convergence
+
+ align:start position:0%
+convert how do we know that convergence
+ 
+
+ align:start position:0%
+convert how do we know that convergence
+requires
+
+ align:start position:0%
+requires
+ 
+
+ align:start position:0%
+requires
+stability and there it's a little
+
+ align:start position:0%
+stability and there it's a little
+ 
+
+ align:start position:0%
+stability and there it's a little
+delicate so I've just this is the last
+
+ align:start position:0%
+delicate so I've just this is the last
+ 
+
+ align:start position:0%
+delicate so I've just this is the last
+30 seconds of the lecture just to
+
+ align:start position:0%
+30 seconds of the lecture just to
+ 
+
+ align:start position:0%
+30 seconds of the lecture just to
+mention this
+
+ align:start position:0%
+mention this
+ 
+
+ align:start position:0%
+mention this
+Point uh CU it's easy to miss a key
+
+ align:start position:0%
+Point uh CU it's easy to miss a key
+ 
+
+ align:start position:0%
+Point uh CU it's easy to miss a key
+Point
+
+ align:start position:0%
+Point
+ 
+
+ align:start position:0%
+Point
+here we've tracked the different now now
+
+ align:start position:0%
+here we've tracked the different now now
+ 
+
+ align:start position:0%
+here we've tracked the different now now
+I'm supposing that the method is
+
+ align:start position:0%
+I'm supposing that the method is
+ 
+
+ align:start position:0%
+I'm supposing that the method is
+unstable and I want to show that it will
+
+ align:start position:0%
+unstable and I want to show that it will
+ 
+
+ align:start position:0%
+unstable and I want to show that it will
+fail right that's that's my job now
+
+ align:start position:0%
+fail right that's that's my job now
+ 
+
+ align:start position:0%
+fail right that's that's my job now
+that's lax's other half of lax's theorem
+
+ align:start position:0%
+that's lax's other half of lax's theorem
+ 
+
+ align:start position:0%
+that's lax's other half of lax's theorem
+if it's unstable the method will fail
+
+ align:start position:0%
+if it's unstable the method will fail
+ 
+
+ align:start position:0%
+if it's unstable the method will fail
+there'll be some initial value for which
+
+ align:start position:0%
+there'll be some initial value for which
+ 
+
+ align:start position:0%
+there'll be some initial value for which
+it blows up okay now you might say well
+
+ align:start position:0%
+it blows up okay now you might say well
+ 
+
+ align:start position:0%
+it blows up okay now you might say well
+that initial value is just e to the
+
+ align:start position:0%
+that initial value is just e to the
+ 
+
+ align:start position:0%
+that initial value is just e to the
+IX but we didn't follow this point but
+
+ align:start position:0%
+IX but we didn't follow this point but
+ 
+
+ align:start position:0%
+IX but we didn't follow this point but
+if I take an ed the I KX where G is
+
+ align:start position:0%
+if I take an ed the I KX where G is
+ 
+
+ align:start position:0%
+if I take an ed the I KX where G is
+bigger than
+
+ align:start position:0%
+bigger than
+ 
+
+ align:start position:0%
+bigger than
+one of course that is getting Amplified
+
+ align:start position:0%
+one of course that is getting Amplified
+ 
+
+ align:start position:0%
+one of course that is getting Amplified
+a bit but for that particular Eed of the
+
+ align:start position:0%
+a bit but for that particular Eed of the
+ 
+
+ align:start position:0%
+a bit but for that particular Eed of the
+IX when delta T decreases so if I have a
+
+ align:start position:0%
+IX when delta T decreases so if I have a
+ 
+
+ align:start position:0%
+IX when delta T decreases so if I have a
+you see this is a k Delta x what I'm
+
+ align:start position:0%
+you see this is a k Delta x what I'm
+ 
+
+ align:start position:0%
+you see this is a k Delta x what I'm
+trying to say is that for a fixed k even
+
+ align:start position:0%
+trying to say is that for a fixed k even
+ 
+
+ align:start position:0%
+trying to say is that for a fixed k even
+an unstable method can work for a fixed
+
+ align:start position:0%
+an unstable method can work for a fixed
+ 
+
+ align:start position:0%
+an unstable method can work for a fixed
+frequency K as delta T and Delta X get
+
+ align:start position:0%
+frequency K as delta T and Delta X get
+ 
+
+ align:start position:0%
+frequency K as delta T and Delta X get
+smaller these guys whether they're
+
+ align:start position:0%
+smaller these guys whether they're
+ 
+
+ align:start position:0%
+smaller these guys whether they're
+outside or inside will will be coming
+
+ align:start position:0%
+outside or inside will will be coming
+ 
+
+ align:start position:0%
+outside or inside will will be coming
+down toward one and if you're patient
+
+ align:start position:0%
+down toward one and if you're patient
+ 
+
+ align:start position:0%
+down toward one and if you're patient
+you could see it actually works so it's
+
+ align:start position:0%
+you could see it actually works so it's
+ 
+
+ align:start position:0%
+you could see it actually works so it's
+somehow the initial function that blow
+
+ align:start position:0%
+somehow the initial function that blow
+ 
+
+ align:start position:0%
+somehow the initial function that blow
+that doesn't work that blows up is a
+
+ align:start position:0%
+that doesn't work that blows up is a
+ 
+
+ align:start position:0%
+that doesn't work that blows up is a
+combination of frequencies a single
+
+ align:start position:0%
+combination of frequencies a single
+ 
+
+ align:start position:0%
+combination of frequencies a single
+frequency actually you move down here
+
+ align:start position:0%
+frequency actually you move down here
+ 
+
+ align:start position:0%
+frequency actually you move down here
+and it's not it it's not catastrophic in
+
+ align:start position:0%
+and it's not it it's not catastrophic in
+ 
+
+ align:start position:0%
+and it's not it it's not catastrophic in
+the end but a combination of frequency
+
+ align:start position:0%
+the end but a combination of frequency
+ 
+
+ align:start position:0%
+the end but a combination of frequency
+so that as one frequency moves down
+
+ align:start position:0%
+so that as one frequency moves down
+ 
+
+ align:start position:0%
+so that as one frequency moves down
+another one is moving into this position
+
+ align:start position:0%
+another one is moving into this position
+ 
+
+ align:start position:0%
+another one is moving into this position
+another one into this
+
+ align:start position:0%
+another one into this
+ 
+
+ align:start position:0%
+another one into this
+that there is a typical initial function
+
+ align:start position:0%
+that there is a typical initial function
+ 
+
+ align:start position:0%
+that there is a typical initial function
+and it is disastrous so that's what LAX
+
+ align:start position:0%
+and it is disastrous so that's what LAX
+ 
+
+ align:start position:0%
+and it is disastrous so that's what LAX
+had
+
+ align:start position:0%
+had
+ 
+
+ align:start position:0%
+had
+to catch the notes will use the single
+
+ align:start position:0%
+to catch the notes will use the single
+ 
+
+ align:start position:0%
+to catch the notes will use the single
+word unit uniform boundedness anyway the
+
+ align:start position:0%
+word unit uniform boundedness anyway the
+ 
+
+ align:start position:0%
+word unit uniform boundedness anyway the
+this is one point where pure
+
+ align:start position:0%
+this is one point where pure
+ 
+
+ align:start position:0%
+this is one point where pure
+MTH a kind of neat a neat result in pure
+
+ align:start position:0%
+MTH a kind of neat a neat result in pure
+ 
+
+ align:start position:0%
+MTH a kind of neat a neat result in pure
+Mass says that if stability
+
+ align:start position:0%
+Mass says that if stability
+ 
+
+ align:start position:0%
+Mass says that if stability
+fails then there is some
+
+ align:start position:0%
+fails then there is some
+ 
+
+ align:start position:0%
+fails then there is some
+single starting value on which it will
+
+ align:start position:0%
+single starting value on which it will
+ 
+
+ align:start position:0%
+single starting value on which it will
+fail that starting value won't be a pure
+
+ align:start position:0%
+fail that starting value won't be a pure
+ 
+
+ align:start position:0%
+fail that starting value won't be a pure
+e to the ikx because it as we said
+
+ align:start position:0%
+e to the ikx because it as we said
+ 
+
+ align:start position:0%
+e to the ikx because it as we said
+actually in the end
+
+ align:start position:0%
+actually in the end
+ 
+
+ align:start position:0%
+actually in the end
+gets to be okay but there will be a
+
+ align:start position:0%
+gets to be okay but there will be a
+ 
+
+ align:start position:0%
+gets to be okay but there will be a
+combination of frequencies that'll fail
+
+ align:start position:0%
+combination of frequencies that'll fail
+ 
+
+ align:start position:0%
+combination of frequencies that'll fail
+and so convergence will fail so that's
+
+ align:start position:0%
+and so convergence will fail so that's
+ 
+
+ align:start position:0%
+and so convergence will fail so that's
+the that's the key theorem and I'll
+
+ align:start position:0%
+the that's the key theorem and I'll
+ 
+
+ align:start position:0%
+the that's the key theorem and I'll
+probably won't use the word theorem
+
+ align:start position:0%
+probably won't use the word theorem
+ 
+
+ align:start position:0%
+probably won't use the word theorem
+again but this is one time when it's
+
+ align:start position:0%
+again but this is one time when it's
+ 
+
+ align:start position:0%
+again but this is one time when it's
+Justified and when a little a little uh
+
+ align:start position:0%
+Justified and when a little a little uh
+ 
+
+ align:start position:0%
+Justified and when a little a little uh
+Al sort of
+
+ align:start position:0%
+Al sort of
+ 
+
+ align:start position:0%
+Al sort of
+abstract functional analysis gives the
+
+ align:start position:0%
+abstract functional analysis gives the
+ 
+
+ align:start position:0%
+abstract functional analysis gives the
+conclusion that convergence requires
+
+ align:start position:0%
+conclusion that convergence requires
+ 
+
+ align:start position:0%
+conclusion that convergence requires
+stability okay so you'll see that in the
+
+ align:start position:0%
+stability okay so you'll see that in the
+ 
+
+ align:start position:0%
+stability okay so you'll see that in the
+notes and next time we move on to the
+
+ align:start position:0%
+notes and next time we move on to the
+ 
+
+ align:start position:0%
+notes and next time we move on to the
+true wave equation second order thanks
\ No newline at end of file
diff --git a/I2vEKf7L0Y4.txt b/I2vEKf7L0Y4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..64c5176b455fc17458c3d392c381736ab7c472cd
--- /dev/null
+++ b/I2vEKf7L0Y4.txt
@@ -0,0 +1,12571 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just clarify one question uh which was
+
+ align:start position:0%
+just clarify one question uh which was
+ 
+
+ align:start position:0%
+just clarify one question uh which was
+asked last time so so when we calculate
+
+ align:start position:0%
+asked last time so so when we calculate
+ 
+
+ align:start position:0%
+asked last time so so when we calculate
+the total cost action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the uh say for this e plus e minus
+
+ align:start position:0%
+for the uh say for this e plus e minus
+ 
+
+ align:start position:0%
+for the uh say for this e plus e minus
+to Mu plus u matters
+
+ align:start position:0%
+to Mu plus u matters
+ 
+
+ align:start position:0%
+to Mu plus u matters
+then we find that there's a funny
+
+ align:start position:0%
+then we find that there's a funny
+ 
+
+ align:start position:0%
+then we find that there's a funny
+perfect yeah and let me just write down
+
+ align:start position:0%
+perfect yeah and let me just write down
+ 
+
+ align:start position:0%
+perfect yeah and let me just write down
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+so then there's a factor like this
+
+ align:start position:0%
+so then there's a factor like this
+ 
+
+ align:start position:0%
+so then there's a factor like this
+and find square
+
+ align:start position:0%
+and find square
+ 
+
+ align:start position:0%
+and find square
+e squared divided by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M Square
+
+ align:start position:0%
+M Square
+ 
+
+ align:start position:0%
+M Square
+e square and then times something else
+
+ align:start position:0%
+e square and then times something else
+ 
+
+ align:start position:0%
+e square and then times something else
+okay so attempt something else
+
+ align:start position:0%
+okay so attempt something else
+ 
+
+ align:start position:0%
+okay so attempt something else
+and so there's funny feature that this
+
+ align:start position:0%
+and so there's funny feature that this
+ 
+
+ align:start position:0%
+and so there's funny feature that this
+Factor seems to to blow up when the E is
+
+ align:start position:0%
+Factor seems to to blow up when the E is
+ 
+
+ align:start position:0%
+Factor seems to to blow up when the E is
+equal to M okay so if you decrease e to
+
+ align:start position:0%
+equal to M okay so if you decrease e to
+ 
+
+ align:start position:0%
+equal to M okay so if you decrease e to
+the to the value of M and then and then
+
+ align:start position:0%
+the to the value of M and then and then
+ 
+
+ align:start position:0%
+the to the value of M and then and then
+this evening blows up
+
+ align:start position:0%
+this evening blows up
+ 
+
+ align:start position:0%
+this evening blows up
+but because this never happens in the
+
+ align:start position:0%
+but because this never happens in the
+ 
+
+ align:start position:0%
+but because this never happens in the
+real situation in the real situation
+
+ align:start position:0%
+real situation in the real situation
+ 
+
+ align:start position:0%
+real situation in the real situation
+because this Mass
+
+ align:start position:0%
+because this Mass
+ 
+
+ align:start position:0%
+because this Mass
+is much larger than this Mass so the
+
+ align:start position:0%
+is much larger than this Mass so the
+ 
+
+ align:start position:0%
+is much larger than this Mass so the
+upstairs will go to zero before this
+
+ align:start position:0%
+upstairs will go to zero before this
+ 
+
+ align:start position:0%
+upstairs will go to zero before this
+blows up so that's why people never
+
+ align:start position:0%
+blows up so that's why people never
+ 
+
+ align:start position:0%
+blows up so that's why people never
+cared about it okay including myself
+
+ align:start position:0%
+cared about it okay including myself
+ 
+
+ align:start position:0%
+cared about it okay including myself
+but you can ask the question supposed to
+
+ align:start position:0%
+but you can ask the question supposed to
+ 
+
+ align:start position:0%
+but you can ask the question supposed to
+the electron is more massive than the
+
+ align:start position:0%
+the electron is more massive than the
+ 
+
+ align:start position:0%
+the electron is more massive than the
+muon
+
+ align:start position:0%
+muon
+ 
+
+ align:start position:0%
+muon
+and then you will reach the zeros of
+
+ align:start position:0%
+and then you will reach the zeros of
+ 
+
+ align:start position:0%
+and then you will reach the zeros of
+this first before you reach the zero of
+
+ align:start position:0%
+this first before you reach the zero of
+ 
+
+ align:start position:0%
+this first before you reach the zero of
+this and then you will see something
+
+ align:start position:0%
+this and then you will see something
+ 
+
+ align:start position:0%
+this and then you will see something
+blows up okay then it's curious
+
+ align:start position:0%
+blows up okay then it's curious
+ 
+
+ align:start position:0%
+blows up okay then it's curious
+there's a very simple mathematical
+
+ align:start position:0%
+there's a very simple mathematical
+ 
+
+ align:start position:0%
+there's a very simple mathematical
+reason for this
+
+ align:start position:0%
+reason for this
+ 
+
+ align:start position:0%
+reason for this
+uh and the the reading is that
+
+ align:start position:0%
+uh and the the reading is that
+ 
+
+ align:start position:0%
+uh and the the reading is that
+cross-sacking is defined remember the
+
+ align:start position:0%
+cross-sacking is defined remember the
+ 
+
+ align:start position:0%
+cross-sacking is defined remember the
+cross-section is defined to be uh
+
+ align:start position:0%
+cross-section is defined to be uh
+ 
+
+ align:start position:0%
+cross-section is defined to be uh
+to be defined to be the divided bundle
+
+ align:start position:0%
+to be defined to be the divided bundle
+ 
+
+ align:start position:0%
+to be defined to be the divided bundle
+of the flux
+
+ align:start position:0%
+of the flux
+ 
+
+ align:start position:0%
+of the flux
+and the flux
+
+ align:start position:0%
+and the flux
+ 
+
+ align:start position:0%
+and the flux
+is proportional T1 is the density times
+
+ align:start position:0%
+is proportional T1 is the density times
+ 
+
+ align:start position:0%
+is proportional T1 is the density times
+the velocity
+
+ align:start position:0%
+the velocity
+ 
+
+ align:start position:0%
+the velocity
+and the density is the same it's just
+
+ align:start position:0%
+and the density is the same it's just
+ 
+
+ align:start position:0%
+and the density is the same it's just
+one particle a per volume and then then
+
+ align:start position:0%
+one particle a per volume and then then
+ 
+
+ align:start position:0%
+one particle a per volume and then then
+the velocity equals zero when this is
+
+ align:start position:0%
+the velocity equals zero when this is
+ 
+
+ align:start position:0%
+the velocity equals zero when this is
+precisely comes when the velocity equals
+
+ align:start position:0%
+precisely comes when the velocity equals
+ 
+
+ align:start position:0%
+precisely comes when the velocity equals
+zero okay because when the velocity
+
+ align:start position:0%
+zero okay because when the velocity
+ 
+
+ align:start position:0%
+zero okay because when the velocity
+becomes very very slow then you then
+
+ align:start position:0%
+becomes very very slow then you then
+ 
+
+ align:start position:0%
+becomes very very slow then you then
+your flux become very slow and smaller
+
+ align:start position:0%
+your flux become very slow and smaller
+ 
+
+ align:start position:0%
+your flux become very slow and smaller
+than this become big so mathematically
+
+ align:start position:0%
+than this become big so mathematically
+ 
+
+ align:start position:0%
+than this become big so mathematically
+that's the reason why this becomes very
+
+ align:start position:0%
+that's the reason why this becomes very
+ 
+
+ align:start position:0%
+that's the reason why this becomes very
+big okay uh uh when you take the
+
+ align:start position:0%
+big okay uh uh when you take the
+ 
+
+ align:start position:0%
+big okay uh uh when you take the
+velocity consider
+
+ align:start position:0%
+velocity consider
+ 
+
+ align:start position:0%
+velocity consider
+but still
+
+ align:start position:0%
+but still
+ 
+
+ align:start position:0%
+but still
+it is a little bit funny I should admit
+
+ align:start position:0%
+it is a little bit funny I should admit
+ 
+
+ align:start position:0%
+it is a little bit funny I should admit
+so when the velocity is equal to zero of
+
+ align:start position:0%
+so when the velocity is equal to zero of
+ 
+
+ align:start position:0%
+so when the velocity is equal to zero of
+course it's on physical because when
+
+ align:start position:0%
+course it's on physical because when
+ 
+
+ align:start position:0%
+course it's on physical because when
+velocity is zero they just never scatter
+
+ align:start position:0%
+velocity is zero they just never scatter
+ 
+
+ align:start position:0%
+velocity is zero they just never scatter
+okay so so this Divergence is never used
+
+ align:start position:0%
+okay so so this Divergence is never used
+ 
+
+ align:start position:0%
+okay so so this Divergence is never used
+but you can ask the question
+
+ align:start position:0%
+but you can ask the question
+ 
+
+ align:start position:0%
+but you can ask the question
+why why physically somehow when when you
+
+ align:start position:0%
+why why physically somehow when when you
+ 
+
+ align:start position:0%
+why why physically somehow when when you
+decrease the V and somehow the the cross
+
+ align:start position:0%
+decrease the V and somehow the the cross
+ 
+
+ align:start position:0%
+decrease the V and somehow the the cross
+action should become bigger and bigger
+
+ align:start position:0%
+action should become bigger and bigger
+ 
+
+ align:start position:0%
+action should become bigger and bigger
+and the mathematical is due to the flux
+
+ align:start position:0%
+and the mathematical is due to the flux
+ 
+
+ align:start position:0%
+and the mathematical is due to the flux
+just due to the way the cross-section is
+
+ align:start position:0%
+just due to the way the cross-section is
+ 
+
+ align:start position:0%
+just due to the way the cross-section is
+is defined but that's but I also
+
+ align:start position:0%
+is defined but that's but I also
+ 
+
+ align:start position:0%
+is defined but that's but I also
+mentioned before that the cross action
+
+ align:start position:0%
+mentioned before that the cross action
+ 
+
+ align:start position:0%
+mentioned before that the cross action
+is supposed to measure the effective
+
+ align:start position:0%
+is supposed to measure the effective
+ 
+
+ align:start position:0%
+is supposed to measure the effective
+area of the interaction and then why
+
+ align:start position:0%
+area of the interaction and then why
+ 
+
+ align:start position:0%
+area of the interaction and then why
+should that depend on the velocity okay
+
+ align:start position:0%
+should that depend on the velocity okay
+ 
+
+ align:start position:0%
+should that depend on the velocity okay
+and so this aspect that I don't have a
+
+ align:start position:0%
+and so this aspect that I don't have a
+ 
+
+ align:start position:0%
+and so this aspect that I don't have a
+very good explanation and and but this
+
+ align:start position:0%
+very good explanation and and but this
+ 
+
+ align:start position:0%
+very good explanation and and but this
+is the mathematical reason for it
+
+ align:start position:0%
+is the mathematical reason for it
+ 
+
+ align:start position:0%
+is the mathematical reason for it
+okay good yeah so this is just classify
+
+ align:start position:0%
+okay good yeah so this is just classify
+ 
+
+ align:start position:0%
+okay good yeah so this is just classify
+uh clarify the uh the question uh
+
+ align:start position:0%
+uh clarify the uh the question uh
+ 
+
+ align:start position:0%
+uh clarify the uh the question uh
+um over the last time
+
+ align:start position:0%
+um over the last time
+ 
+
+ align:start position:0%
+um over the last time
+okay so so then we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talk about Crossing symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's consider two process
+
+ align:start position:0%
+so let's consider two process
+ 
+
+ align:start position:0%
+so let's consider two process
+wine is the E plus e minus
+
+ align:start position:0%
+wine is the E plus e minus
+ 
+
+ align:start position:0%
+wine is the E plus e minus
+goes to Mu plus mu minus as we just
+
+ align:start position:0%
+goes to Mu plus mu minus as we just
+ 
+
+ align:start position:0%
+goes to Mu plus mu minus as we just
+discussed
+
+ align:start position:0%
+discussed
+ 
+
+ align:start position:0%
+discussed
+with the family diagram going like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is the e minus E plus
+
+ align:start position:0%
+okay so this is the e minus E plus
+ 
+
+ align:start position:0%
+okay so this is the e minus E plus
+this is a mu minus mu class okay
+
+ align:start position:0%
+this is a mu minus mu class okay
+ 
+
+ align:start position:0%
+this is a mu minus mu class okay
+and you
+
+ align:start position:0%
+and you
+ 
+
+ align:start position:0%
+and you
+so there's also another process
+
+ align:start position:0%
+so there's also another process
+ 
+
+ align:start position:0%
+so there's also another process
+let's considered a lot of process
+
+ align:start position:0%
+let's considered a lot of process
+ 
+
+ align:start position:0%
+let's considered a lot of process
+which is e minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mule minus going to e minus plus mu
+
+ align:start position:0%
+mule minus going to e minus plus mu
+ 
+
+ align:start position:0%
+mule minus going to e minus plus mu
+malice
+
+ align:start position:0%
+malice
+ 
+
+ align:start position:0%
+malice
+and the final diagram for this
+
+ align:start position:0%
+and the final diagram for this
+ 
+
+ align:start position:0%
+and the final diagram for this
+is given by this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is the E minus
+
+ align:start position:0%
+okay so this is the E minus
+ 
+
+ align:start position:0%
+okay so this is the E minus
+and real minus is the initial State now
+
+ align:start position:0%
+and real minus is the initial State now
+ 
+
+ align:start position:0%
+and real minus is the initial State now
+and this is a humanus and this is Mu
+
+ align:start position:0%
+and this is a humanus and this is Mu
+ 
+
+ align:start position:0%
+and this is a humanus and this is Mu
+matter okay again only one diagram
+
+ align:start position:0%
+matter okay again only one diagram
+ 
+
+ align:start position:0%
+matter okay again only one diagram
+contributes
+
+ align:start position:0%
+contributes
+ 
+
+ align:start position:0%
+contributes
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so if you compare a and b
+
+ align:start position:0%
+so if you compare a and b
+ 
+
+ align:start position:0%
+so if you compare a and b
+you can see that the B is the same the
+
+ align:start position:0%
+you can see that the B is the same the
+ 
+
+ align:start position:0%
+you can see that the B is the same the
+diagram for B is essentially the diagram
+
+ align:start position:0%
+diagram for B is essentially the diagram
+ 
+
+ align:start position:0%
+diagram for B is essentially the diagram
+for a
+
+ align:start position:0%
+for a
+ 
+
+ align:start position:0%
+for a
+if you view it sideway
+
+ align:start position:0%
+if you view it sideway
+ 
+
+ align:start position:0%
+if you view it sideway
+okay we will view it sideway and then
+
+ align:start position:0%
+okay we will view it sideway and then
+ 
+
+ align:start position:0%
+okay we will view it sideway and then
+you see this goes through that and then
+
+ align:start position:0%
+you see this goes through that and then
+ 
+
+ align:start position:0%
+you see this goes through that and then
+this becomes fellow State and the final
+
+ align:start position:0%
+this becomes fellow State and the final
+ 
+
+ align:start position:0%
+this becomes fellow State and the final
+State coming out the human e plus is
+
+ align:start position:0%
+State coming out the human e plus is
+ 
+
+ align:start position:0%
+State coming out the human e plus is
+going to become emanas and this is just
+
+ align:start position:0%
+going to become emanas and this is just
+ 
+
+ align:start position:0%
+going to become emanas and this is just
+become that okay
+
+ align:start position:0%
+become that okay
+ 
+
+ align:start position:0%
+become that okay
+so so the difference between these two
+
+ align:start position:0%
+so so the difference between these two
+ 
+
+ align:start position:0%
+so so the difference between these two
+is that the E plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so e plus
+
+ align:start position:0%
+so e plus
+ 
+
+ align:start position:0%
+so e plus
+in initial state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+then goes to e minus
+
+ align:start position:0%
+then goes to e minus
+ 
+
+ align:start position:0%
+then goes to e minus
+in final state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of B okay in federal states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and similarly
+
+ align:start position:0%
+and similarly
+ 
+
+ align:start position:0%
+and similarly
+the MU Plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+final state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+then become
+
+ align:start position:0%
+then become
+ 
+
+ align:start position:0%
+then become
+the the the MU minus
+
+ align:start position:0%
+the the the MU minus
+ 
+
+ align:start position:0%
+the the the MU minus
+in the initial state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so uh yeah so we essentially
+
+ align:start position:0%
+so uh yeah so we essentially
+ 
+
+ align:start position:0%
+so uh yeah so we essentially
+you see U plus essentially you take the
+
+ align:start position:0%
+you see U plus essentially you take the
+ 
+
+ align:start position:0%
+you see U plus essentially you take the
+E plus going to the other side become e
+
+ align:start position:0%
+E plus going to the other side become e
+ 
+
+ align:start position:0%
+E plus going to the other side become e
+minus and then take a mu plus going to
+
+ align:start position:0%
+minus and then take a mu plus going to
+ 
+
+ align:start position:0%
+minus and then take a mu plus going to
+this side become Humanity okay so
+
+ align:start position:0%
+this side become Humanity okay so
+ 
+
+ align:start position:0%
+this side become Humanity okay so
+essentially you just exchange that
+
+ align:start position:0%
+essentially you just exchange that
+ 
+
+ align:start position:0%
+essentially you just exchange that
+so uh so now let's label the uh the the
+
+ align:start position:0%
+so uh so now let's label the uh the the
+ 
+
+ align:start position:0%
+so uh so now let's label the uh the the
+the quantum numbers
+
+ align:start position:0%
+the quantum numbers
+ 
+
+ align:start position:0%
+the quantum numbers
+so suppose let's call this P1
+
+ align:start position:0%
+so suppose let's call this P1
+ 
+
+ align:start position:0%
+so suppose let's call this P1
+R1
+
+ align:start position:0%
+R1
+ 
+
+ align:start position:0%
+R1
+so so this is called
+
+ align:start position:0%
+so so this is called
+ 
+
+ align:start position:0%
+so so this is called
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+P2
+
+ align:start position:0%
+P2
+ 
+
+ align:start position:0%
+P2
+R2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the code this one
+
+ align:start position:0%
+and the code this one
+ 
+
+ align:start position:0%
+and the code this one
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+say code this one K1
+
+ align:start position:0%
+say code this one K1
+ 
+
+ align:start position:0%
+say code this one K1
+S1
+
+ align:start position:0%
+S1
+ 
+
+ align:start position:0%
+S1
+so these are the correlation and this is
+
+ align:start position:0%
+so these are the correlation and this is
+ 
+
+ align:start position:0%
+so these are the correlation and this is
+K2 S2
+
+ align:start position:0%
+K2 S2
+ 
+
+ align:start position:0%
+K2 S2
+and now similarly a label here by P1
+
+ align:start position:0%
+and now similarly a label here by P1
+ 
+
+ align:start position:0%
+and now similarly a label here by P1
+R1
+
+ align:start position:0%
+R1
+ 
+
+ align:start position:0%
+R1
+neighborhood this one by P2 R2 bar so
+
+ align:start position:0%
+neighborhood this one by P2 R2 bar so
+ 
+
+ align:start position:0%
+neighborhood this one by P2 R2 bar so
+this is for the anti-particle
+
+ align:start position:0%
+this is for the anti-particle
+ 
+
+ align:start position:0%
+this is for the anti-particle
+and so this one would be the um
+
+ align:start position:0%
+and so this one would be the um
+ 
+
+ align:start position:0%
+and so this one would be the um
+K1 S1
+
+ align:start position:0%
+K1 S1
+ 
+
+ align:start position:0%
+K1 S1
+and then this will be K2 S2 bar okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so now if we look at this map
+
+ align:start position:0%
+so so now if we look at this map
+ 
+
+ align:start position:0%
+so so now if we look at this map
+so it's like
+
+ align:start position:0%
+so it's like
+ 
+
+ align:start position:0%
+so it's like
+in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the process a
+
+ align:start position:0%
+in the process a
+ 
+
+ align:start position:0%
+in the process a
+we we take this to the initial State P2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R2
+
+ align:start position:0%
+R2
+ 
+
+ align:start position:0%
+R2
+if we replace it by minus K2
+
+ align:start position:0%
+if we replace it by minus K2
+ 
+
+ align:start position:0%
+if we replace it by minus K2
+S2
+
+ align:start position:0%
+S2
+ 
+
+ align:start position:0%
+S2
+okay minus K2 means that the uh yeah so
+
+ align:start position:0%
+okay minus K2 means that the uh yeah so
+ 
+
+ align:start position:0%
+okay minus K2 means that the uh yeah so
+this one e plus now become the final
+
+ align:start position:0%
+this one e plus now become the final
+ 
+
+ align:start position:0%
+this one e plus now become the final
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+so so this is the so from the momentum
+
+ align:start position:0%
+so so this is the so from the momentum
+ 
+
+ align:start position:0%
+so so this is the so from the momentum
+Direction this is going in and this will
+
+ align:start position:0%
+Direction this is going in and this will
+ 
+
+ align:start position:0%
+Direction this is going in and this will
+be going out so we need to change the
+
+ align:start position:0%
+be going out so we need to change the
+ 
+
+ align:start position:0%
+be going out so we need to change the
+sign okay we did change the sign
+
+ align:start position:0%
+sign okay we did change the sign
+ 
+
+ align:start position:0%
+sign okay we did change the sign
+and the or similarly the K2
+
+ align:start position:0%
+and the or similarly the K2
+ 
+
+ align:start position:0%
+and the or similarly the K2
+for S2
+
+ align:start position:0%
+for S2
+ 
+
+ align:start position:0%
+for S2
+for K2 S2 bar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then go to minus P2
+
+ align:start position:0%
+and then go to minus P2
+ 
+
+ align:start position:0%
+and then go to minus P2
+R2
+
+ align:start position:0%
+R2
+ 
+
+ align:start position:0%
+R2
+then we get
+
+ align:start position:0%
+then we get
+ 
+
+ align:start position:0%
+then we get
+if you make this placement we then we
+
+ align:start position:0%
+if you make this placement we then we
+ 
+
+ align:start position:0%
+if you make this placement we then we
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+the process B okay
+
+ align:start position:0%
+the process B okay
+ 
+
+ align:start position:0%
+the process B okay
+okay the process P so you just make the
+
+ align:start position:0%
+okay the process P so you just make the
+ 
+
+ align:start position:0%
+okay the process P so you just make the
+replacement and then another replacement
+
+ align:start position:0%
+replacement and then another replacement
+ 
+
+ align:start position:0%
+replacement and then another replacement
+then the processing a will go to those
+
+ align:start position:0%
+then the processing a will go to those
+ 
+
+ align:start position:0%
+then the processing a will go to those
+processing B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for scalar so suppose you forget
+
+ align:start position:0%
+so for scalar so suppose you forget
+ 
+
+ align:start position:0%
+so for scalar so suppose you forget
+about those validations
+
+ align:start position:0%
+about those validations
+ 
+
+ align:start position:0%
+about those validations
+if we can see the uh had to be talking
+
+ align:start position:0%
+if we can see the uh had to be talking
+ 
+
+ align:start position:0%
+if we can see the uh had to be talking
+about the uh uh uh scalar particles
+
+ align:start position:0%
+about the uh uh uh scalar particles
+ 
+
+ align:start position:0%
+about the uh uh uh scalar particles
+there's no correlation and then this
+
+ align:start position:0%
+there's no correlation and then this
+ 
+
+ align:start position:0%
+there's no correlation and then this
+just trivially
+
+ align:start position:0%
+just trivially
+ 
+
+ align:start position:0%
+just trivially
+so for scalar with them we just have
+
+ align:start position:0%
+so for scalar with them we just have
+ 
+
+ align:start position:0%
+so for scalar with them we just have
+triviality
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can just do the replacement you you
+
+ align:start position:0%
+we can just do the replacement you you
+ 
+
+ align:start position:0%
+we can just do the replacement you you
+can just um
+
+ align:start position:0%
+can just um
+ 
+
+ align:start position:0%
+can just um
+DC that the then the amplitude for the
+
+ align:start position:0%
+DC that the then the amplitude for the
+ 
+
+ align:start position:0%
+DC that the then the amplitude for the
+process a
+
+ align:start position:0%
+process a
+ 
+
+ align:start position:0%
+process a
+with P1 minus K2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the K1
+
+ align:start position:0%
+and the K1
+ 
+
+ align:start position:0%
+and the K1
+minus P2
+
+ align:start position:0%
+minus P2
+ 
+
+ align:start position:0%
+minus P2
+and then will be just equal to the
+
+ align:start position:0%
+and then will be just equal to the
+ 
+
+ align:start position:0%
+and then will be just equal to the
+amplitude for the process B with P1 P2
+
+ align:start position:0%
+amplitude for the process B with P1 P2
+ 
+
+ align:start position:0%
+amplitude for the process B with P1 P2
+K1 K2
+
+ align:start position:0%
+K1 K2
+ 
+
+ align:start position:0%
+K1 K2
+okay so we just remain
+
+ align:start position:0%
+okay so we just remain
+ 
+
+ align:start position:0%
+okay so we just remain
+rename your momentum of your process a
+
+ align:start position:0%
+rename your momentum of your process a
+ 
+
+ align:start position:0%
+rename your momentum of your process a
+and then you will just get the uh
+
+ align:start position:0%
+and then you will just get the uh
+ 
+
+ align:start position:0%
+and then you will just get the uh
+essentially the amplitude for two P
+
+ align:start position:0%
+essentially the amplitude for two P
+ 
+
+ align:start position:0%
+essentially the amplitude for two P
+because the only thing
+
+ align:start position:0%
+because the only thing
+ 
+
+ align:start position:0%
+because the only thing
+you need to do is just exchange the name
+
+ align:start position:0%
+you need to do is just exchange the name
+ 
+
+ align:start position:0%
+you need to do is just exchange the name
+of the momentum okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then we'll be truly the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but for fermions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we should we should worry about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the wave function
+
+ align:start position:0%
+the wave function
+ 
+
+ align:start position:0%
+the wave function
+associated with external X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so in a
+
+ align:start position:0%
+okay so so in a
+ 
+
+ align:start position:0%
+okay so so in a
+so let me just write down those wave
+
+ align:start position:0%
+so let me just write down those wave
+ 
+
+ align:start position:0%
+so let me just write down those wave
+function explicit three
+
+ align:start position:0%
+function explicit three
+ 
+
+ align:start position:0%
+function explicit three
+so in a
+
+ align:start position:0%
+so in a
+ 
+
+ align:start position:0%
+so in a
+so the P2 R2 bar
+
+ align:start position:0%
+so the P2 R2 bar
+ 
+
+ align:start position:0%
+so the P2 R2 bar
+I'll associate
+
+ align:start position:0%
+I'll associate
+ 
+
+ align:start position:0%
+I'll associate
+with the wave function
+
+ align:start position:0%
+with the wave function
+ 
+
+ align:start position:0%
+with the wave function
+is to be V bar R2
+
+ align:start position:0%
+is to be V bar R2
+ 
+
+ align:start position:0%
+is to be V bar R2
+P2 okay so this is for the E plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so the
+
+ align:start position:0%
+and so the
+ 
+
+ align:start position:0%
+and so the
+under the K2
+
+ align:start position:0%
+under the K2
+ 
+
+ align:start position:0%
+under the K2
+S2 bar
+
+ align:start position:0%
+S2 bar
+ 
+
+ align:start position:0%
+S2 bar
+are related to vs2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K2
+
+ align:start position:0%
+K2
+ 
+
+ align:start position:0%
+K2
+okay so this is related to the MU plus
+
+ align:start position:0%
+okay so this is related to the MU plus
+ 
+
+ align:start position:0%
+okay so this is related to the MU plus
+okay so according to our previous rule
+
+ align:start position:0%
+okay so according to our previous rule
+ 
+
+ align:start position:0%
+okay so according to our previous rule
+but in b
+
+ align:start position:0%
+but in b
+ 
+
+ align:start position:0%
+but in b
+the corresponding the wave function for
+
+ align:start position:0%
+the corresponding the wave function for
+ 
+
+ align:start position:0%
+the corresponding the wave function for
+these two
+
+ align:start position:0%
+these two
+ 
+
+ align:start position:0%
+these two
+so the K2 S2
+
+ align:start position:0%
+so the K2 S2
+ 
+
+ align:start position:0%
+so the K2 S2
+so the corresponding one
+
+ align:start position:0%
+so the corresponding one
+ 
+
+ align:start position:0%
+so the corresponding one
+uh uh uh is the one you want to exchange
+
+ align:start position:0%
+uh uh uh is the one you want to exchange
+ 
+
+ align:start position:0%
+uh uh uh is the one you want to exchange
+is us two bar
+
+ align:start position:0%
+is us two bar
+ 
+
+ align:start position:0%
+is us two bar
+K2
+
+ align:start position:0%
+K2
+ 
+
+ align:start position:0%
+K2
+so this is corresponding to e minus
+
+ align:start position:0%
+so this is corresponding to e minus
+ 
+
+ align:start position:0%
+so this is corresponding to e minus
+and the P2
+
+ align:start position:0%
+and the P2
+ 
+
+ align:start position:0%
+and the P2
+R2
+
+ align:start position:0%
+R2
+ 
+
+ align:start position:0%
+R2
+then that's corresponding to u r q
+
+ align:start position:0%
+then that's corresponding to u r q
+ 
+
+ align:start position:0%
+then that's corresponding to u r q
+p q
+
+ align:start position:0%
+p q
+ 
+
+ align:start position:0%
+p q
+mu magnets okay
+
+ align:start position:0%
+mu magnets okay
+ 
+
+ align:start position:0%
+mu magnets okay
+so now you see even when you make the
+
+ align:start position:0%
+so now you see even when you make the
+ 
+
+ align:start position:0%
+so now you see even when you make the
+label change
+
+ align:start position:0%
+label change
+ 
+
+ align:start position:0%
+label change
+suppose you make the label replacement
+
+ align:start position:0%
+suppose you make the label replacement
+ 
+
+ align:start position:0%
+suppose you make the label replacement
+from here to replace by that
+
+ align:start position:0%
+from here to replace by that
+ 
+
+ align:start position:0%
+from here to replace by that
+you're not going to change the wave
+
+ align:start position:0%
+you're not going to change the wave
+ 
+
+ align:start position:0%
+you're not going to change the wave
+function from V to U
+
+ align:start position:0%
+function from V to U
+ 
+
+ align:start position:0%
+function from V to U
+okay so the waveform here actually is
+
+ align:start position:0%
+okay so the waveform here actually is
+ 
+
+ align:start position:0%
+okay so the waveform here actually is
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+so so similarly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so similarly this does not uh so this
+
+ align:start position:0%
+so so similarly this does not uh so this
+ 
+
+ align:start position:0%
+so so similarly this does not uh so this
+does not work if you have formions okay
+
+ align:start position:0%
+does not work if you have formions okay
+ 
+
+ align:start position:0%
+does not work if you have formions okay
+if I put them in a big because the wave
+
+ align:start position:0%
+if I put them in a big because the wave
+ 
+
+ align:start position:0%
+if I put them in a big because the wave
+function changes it changes from V to U
+
+ align:start position:0%
+function changes it changes from V to U
+ 
+
+ align:start position:0%
+function changes it changes from V to U
+H in this case and here a case again
+
+ align:start position:0%
+H in this case and here a case again
+ 
+
+ align:start position:0%
+H in this case and here a case again
+also V to U okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but actually this is another problem if
+
+ align:start position:0%
+but actually this is another problem if
+ 
+
+ align:start position:0%
+but actually this is another problem if
+we can see the unpolarized spin sum
+
+ align:start position:0%
+we can see the unpolarized spin sum
+ 
+
+ align:start position:0%
+we can see the unpolarized spin sum
+actually still works okay for
+
+ align:start position:0%
+actually still works okay for
+ 
+
+ align:start position:0%
+actually still works okay for
+unpolarized
+
+ align:start position:0%
+unpolarized
+ 
+
+ align:start position:0%
+unpolarized
+so if you have an unpolarized situation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember we need to sum over all the
+
+ align:start position:0%
+remember we need to sum over all the
+ 
+
+ align:start position:0%
+remember we need to sum over all the
+spins
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and consider M Square sum of all the
+
+ align:start position:0%
+and consider M Square sum of all the
+ 
+
+ align:start position:0%
+and consider M Square sum of all the
+spins
+
+ align:start position:0%
+spins
+ 
+
+ align:start position:0%
+spins
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now let's
+
+ align:start position:0%
+so now let's
+ 
+
+ align:start position:0%
+so now let's
+so that we we are involved this one sum
+
+ align:start position:0%
+so that we we are involved this one sum
+ 
+
+ align:start position:0%
+so that we we are involved this one sum
+with itself for example uh uh when you
+
+ align:start position:0%
+with itself for example uh uh when you
+ 
+
+ align:start position:0%
+with itself for example uh uh when you
+sum of all the r2s then we will have
+
+ align:start position:0%
+sum of all the r2s then we will have
+ 
+
+ align:start position:0%
+sum of all the r2s then we will have
+something like this okay so
+
+ align:start position:0%
+something like this okay so
+ 
+
+ align:start position:0%
+something like this okay so
+so for example we need to sum over R2
+
+ align:start position:0%
+so for example we need to sum over R2
+ 
+
+ align:start position:0%
+so for example we need to sum over R2
+then we will have a combination like VR2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P2 right so the calculation we did
+
+ align:start position:0%
+P2 right so the calculation we did
+ 
+
+ align:start position:0%
+P2 right so the calculation we did
+before and v r 2 bar
+
+ align:start position:0%
+before and v r 2 bar
+ 
+
+ align:start position:0%
+before and v r 2 bar
+P2 okay
+
+ align:start position:0%
+P2 okay
+ 
+
+ align:start position:0%
+P2 okay
+and then this one will give you
+
+ align:start position:0%
+and then this one will give you
+ 
+
+ align:start position:0%
+and then this one will give you
+just minus
+
+ align:start position:0%
+just minus
+ 
+
+ align:start position:0%
+just minus
+minus ip2 slash
+
+ align:start position:0%
+minus ip2 slash
+ 
+
+ align:start position:0%
+minus ip2 slash
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+M of the electron
+
+ align:start position:0%
+M of the electron
+ 
+
+ align:start position:0%
+M of the electron
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and now
+
+ align:start position:0%
+and now
+ 
+
+ align:start position:0%
+and now
+you can just do the replacement let's
+
+ align:start position:0%
+you can just do the replacement let's
+ 
+
+ align:start position:0%
+you can just do the replacement let's
+just do the bridge and the P2 and
+
+ align:start position:0%
+just do the bridge and the P2 and
+ 
+
+ align:start position:0%
+just do the bridge and the P2 and
+basically by minus K2
+
+ align:start position:0%
+basically by minus K2
+ 
+
+ align:start position:0%
+basically by minus K2
+so if you do the replacement then that
+
+ align:start position:0%
+so if you do the replacement then that
+ 
+
+ align:start position:0%
+so if you do the replacement then that
+goes to
+
+ align:start position:0%
+goes to
+ 
+
+ align:start position:0%
+goes to
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+I slash K2 plus still electron Mass okay
+
+ align:start position:0%
+I slash K2 plus still electron Mass okay
+ 
+
+ align:start position:0%
+I slash K2 plus still electron Mass okay
+and then this is the same
+
+ align:start position:0%
+and then this is the same
+ 
+
+ align:start position:0%
+and then this is the same
+as the sum of S2
+
+ align:start position:0%
+as the sum of S2
+ 
+
+ align:start position:0%
+as the sum of S2
+us2 K2
+
+ align:start position:0%
+us2 K2
+ 
+
+ align:start position:0%
+us2 K2
+U S 2 R okay Q okay
+
+ align:start position:0%
+U S 2 R okay Q okay
+ 
+
+ align:start position:0%
+U S 2 R okay Q okay
+so despite that the wave function are
+
+ align:start position:0%
+so despite that the wave function are
+ 
+
+ align:start position:0%
+so despite that the wave function are
+the different
+
+ align:start position:0%
+the different
+ 
+
+ align:start position:0%
+the different
+okay so uh the wave from here but after
+
+ align:start position:0%
+okay so uh the wave from here but after
+ 
+
+ align:start position:0%
+okay so uh the wave from here but after
+you do the spin sum
+
+ align:start position:0%
+you do the spin sum
+ 
+
+ align:start position:0%
+you do the spin sum
+okay they actually get the same answer
+
+ align:start position:0%
+okay they actually get the same answer
+ 
+
+ align:start position:0%
+okay they actually get the same answer
+okay so so this is the same as the minus
+
+ align:start position:0%
+okay so so this is the same as the minus
+ 
+
+ align:start position:0%
+okay so so this is the same as the minus
+this one okay
+
+ align:start position:0%
+this one okay
+ 
+
+ align:start position:0%
+this one okay
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+so each so in this case after you do the
+
+ align:start position:0%
+so each so in this case after you do the
+ 
+
+ align:start position:0%
+so each so in this case after you do the
+string sound so each replacement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this case just give your
+
+ align:start position:0%
+so in this case just give your
+ 
+
+ align:start position:0%
+so in this case just give your
+give us a minus sign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+when you calculate this spin sum the M
+
+ align:start position:0%
+when you calculate this spin sum the M
+ 
+
+ align:start position:0%
+when you calculate this spin sum the M
+squared okay
+
+ align:start position:0%
+squared okay
+ 
+
+ align:start position:0%
+squared okay
+but now since we need to replace two of
+
+ align:start position:0%
+but now since we need to replace two of
+ 
+
+ align:start position:0%
+but now since we need to replace two of
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+okay so so two minus sign is a positive
+
+ align:start position:0%
+okay so so two minus sign is a positive
+ 
+
+ align:start position:0%
+okay so so two minus sign is a positive
+sign so we conclude
+
+ align:start position:0%
+sign so we conclude
+ 
+
+ align:start position:0%
+sign so we conclude
+so we conclude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we conclude
+
+ align:start position:0%
+so we conclude
+ 
+
+ align:start position:0%
+so we conclude
+that the sum of a spin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evaluated at P1 minus K2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and K1 minus P2
+
+ align:start position:0%
+and K1 minus P2
+ 
+
+ align:start position:0%
+and K1 minus P2
+is the same
+
+ align:start position:0%
+is the same
+ 
+
+ align:start position:0%
+is the same
+as the sum of a spin
+
+ align:start position:0%
+as the sum of a spin
+ 
+
+ align:start position:0%
+as the sum of a spin
+the amplitude for B squared divided as
+
+ align:start position:0%
+the amplitude for B squared divided as
+ 
+
+ align:start position:0%
+the amplitude for B squared divided as
+the P1
+
+ align:start position:0%
+the P1
+ 
+
+ align:start position:0%
+the P1
+2. okay one and two okay so there's a
+
+ align:start position:0%
+2. okay one and two okay so there's a
+ 
+
+ align:start position:0%
+2. okay one and two okay so there's a
+simple relation between the amplitude a
+
+ align:start position:0%
+simple relation between the amplitude a
+ 
+
+ align:start position:0%
+simple relation between the amplitude a
+square when you sus to the spin sum and
+
+ align:start position:0%
+square when you sus to the spin sum and
+ 
+
+ align:start position:0%
+square when you sus to the spin sum and
+we just need to rename at the momentum
+
+ align:start position:0%
+we just need to rename at the momentum
+ 
+
+ align:start position:0%
+we just need to rename at the momentum
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+we name the moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any questions on this
+
+ align:start position:0%
+any questions on this
+ 
+
+ align:start position:0%
+any questions on this
+so so for for unpolarized amplitude Okay
+
+ align:start position:0%
+so so for for unpolarized amplitude Okay
+ 
+
+ align:start position:0%
+so so for for unpolarized amplitude Okay
+so so so we still have this very nice
+
+ align:start position:0%
+so so so we still have this very nice
+ 
+
+ align:start position:0%
+so so so we still have this very nice
+relation
+
+ align:start position:0%
+relation
+ 
+
+ align:start position:0%
+relation
+between these two process okay if you
+
+ align:start position:0%
+between these two process okay if you
+ 
+
+ align:start position:0%
+between these two process okay if you
+calculate one of them then you don't
+
+ align:start position:0%
+calculate one of them then you don't
+ 
+
+ align:start position:0%
+calculate one of them then you don't
+need to calculate the other you can just
+
+ align:start position:0%
+need to calculate the other you can just
+ 
+
+ align:start position:0%
+need to calculate the other you can just
+immediately get the answer you just
+
+ align:start position:0%
+immediately get the answer you just
+ 
+
+ align:start position:0%
+immediately get the answer you just
+change your fuel momentum okay change
+
+ align:start position:0%
+change your fuel momentum okay change
+ 
+
+ align:start position:0%
+change your fuel momentum okay change
+your cover moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so but
+
+ align:start position:0%
+so but
+ 
+
+ align:start position:0%
+so but
+if you consider polarized amplitude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the story is now is much Sim now
+
+ align:start position:0%
+okay so the story is now is much Sim now
+ 
+
+ align:start position:0%
+okay so the story is now is much Sim now
+you do have a problem
+
+ align:start position:0%
+you do have a problem
+ 
+
+ align:start position:0%
+you do have a problem
+because now you have say another wave
+
+ align:start position:0%
+because now you have say another wave
+ 
+
+ align:start position:0%
+because now you have say another wave
+function different okay
+
+ align:start position:0%
+function different okay
+ 
+
+ align:start position:0%
+function different okay
+but nevertheless
+
+ align:start position:0%
+but nevertheless
+ 
+
+ align:start position:0%
+but nevertheless
+you can choose up
+
+ align:start position:0%
+you can choose up
+ 
+
+ align:start position:0%
+you can choose up
+choose a different basis okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by choosing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+appropriate basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can still
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+directly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relates
+
+ align:start position:0%
+relates
+ 
+
+ align:start position:0%
+relates
+equated amplitude Okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you can still recreate the
+
+ align:start position:0%
+okay you can still recreate the
+ 
+
+ align:start position:0%
+okay you can still recreate the
+amplitude
+
+ align:start position:0%
+amplitude
+ 
+
+ align:start position:0%
+amplitude
+okay so uh yeah we're not going to there
+
+ align:start position:0%
+okay so uh yeah we're not going to there
+ 
+
+ align:start position:0%
+okay so uh yeah we're not going to there
+okay but it's possible say you choose a
+
+ align:start position:0%
+okay but it's possible say you choose a
+ 
+
+ align:start position:0%
+okay but it's possible say you choose a
+basis
+
+ align:start position:0%
+basis
+ 
+
+ align:start position:0%
+basis
+of V2 and U2 and U and the and then and
+
+ align:start position:0%
+of V2 and U2 and U and the and then and
+ 
+
+ align:start position:0%
+of V2 and U2 and U and the and then and
+this and somehow you can relate them to
+
+ align:start position:0%
+this and somehow you can relate them to
+ 
+
+ align:start position:0%
+this and somehow you can relate them to
+each other okay
+
+ align:start position:0%
+each other okay
+ 
+
+ align:start position:0%
+each other okay
+so this relation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between the amplitude of a and b
+
+ align:start position:0%
+between the amplitude of a and b
+ 
+
+ align:start position:0%
+between the amplitude of a and b
+so this is called Crossing symmetry
+
+ align:start position:0%
+so this is called Crossing symmetry
+ 
+
+ align:start position:0%
+so this is called Crossing symmetry
+okay yeah let me just call this star so
+
+ align:start position:0%
+okay yeah let me just call this star so
+ 
+
+ align:start position:0%
+okay yeah let me just call this star so
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+is called
+
+ align:start position:0%
+is called
+ 
+
+ align:start position:0%
+is called
+Crossing symmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so calling us calling it The symmetry is
+
+ align:start position:0%
+so calling us calling it The symmetry is
+ 
+
+ align:start position:0%
+so calling us calling it The symmetry is
+actually a misnomer
+
+ align:start position:0%
+actually a misnomer
+ 
+
+ align:start position:0%
+actually a misnomer
+because this is not the Symmetry okay
+
+ align:start position:0%
+because this is not the Symmetry okay
+ 
+
+ align:start position:0%
+because this is not the Symmetry okay
+this is just a relation
+
+ align:start position:0%
+this is just a relation
+ 
+
+ align:start position:0%
+this is just a relation
+between the amplitudes of different
+
+ align:start position:0%
+between the amplitudes of different
+ 
+
+ align:start position:0%
+between the amplitudes of different
+process okay so so this is another
+
+ align:start position:0%
+process okay so so this is another
+ 
+
+ align:start position:0%
+process okay so so this is another
+symmetry so so the Symmetry should be
+
+ align:start position:0%
+symmetry so so the Symmetry should be
+ 
+
+ align:start position:0%
+symmetry so so the Symmetry should be
+put as codes okay so so this is just
+
+ align:start position:0%
+put as codes okay so so this is just
+ 
+
+ align:start position:0%
+put as codes okay so so this is just
+expressed regulation of one amplitude to
+
+ align:start position:0%
+expressed regulation of one amplitude to
+ 
+
+ align:start position:0%
+expressed regulation of one amplitude to
+the relation of a lot of amplitude
+
+ align:start position:0%
+the relation of a lot of amplitude
+ 
+
+ align:start position:0%
+the relation of a lot of amplitude
+ablation of yeah just relation between
+
+ align:start position:0%
+ablation of yeah just relation between
+ 
+
+ align:start position:0%
+ablation of yeah just relation between
+the amplitude of the one process to the
+
+ align:start position:0%
+the amplitude of the one process to the
+ 
+
+ align:start position:0%
+the amplitude of the one process to the
+amplitude of another process
+
+ align:start position:0%
+amplitude of another process
+ 
+
+ align:start position:0%
+amplitude of another process
+and this relation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the relation comes from a fundamental
+
+ align:start position:0%
+the relation comes from a fundamental
+ 
+
+ align:start position:0%
+the relation comes from a fundamental
+fact
+
+ align:start position:0%
+fact
+ 
+
+ align:start position:0%
+fact
+come from a very simple fact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if we consider this feminic
+
+ align:start position:0%
+okay so if we consider this feminic
+ 
+
+ align:start position:0%
+okay so if we consider this feminic
+field PSI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subsequent play two row
+
+ align:start position:0%
+subsequent play two row
+ 
+
+ align:start position:0%
+subsequent play two row
+it can either
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+allow it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember PSI is called a
+
+ align:start position:0%
+remember PSI is called a
+ 
+
+ align:start position:0%
+remember PSI is called a
+plus b dagger okay
+
+ align:start position:0%
+plus b dagger okay
+ 
+
+ align:start position:0%
+plus b dagger okay
+so it's called a plus b dagger
+
+ align:start position:0%
+so it's called a plus b dagger
+ 
+
+ align:start position:0%
+so it's called a plus b dagger
+so you can either violate
+
+ align:start position:0%
+so you can either violate
+ 
+
+ align:start position:0%
+so you can either violate
+an initial particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the a part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or can create
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an initial anti-particle
+
+ align:start position:0%
+an initial anti-particle
+ 
+
+ align:start position:0%
+an initial anti-particle
+or concrete so sorry a final
+
+ align:start position:0%
+or concrete so sorry a final
+ 
+
+ align:start position:0%
+or concrete so sorry a final
+sorry the antibiotic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so so let me just
+
+ align:start position:0%
+so so so let me just
+ 
+
+ align:start position:0%
+so so so let me just
+elaborate
+
+ align:start position:0%
+elaborate
+ 
+
+ align:start position:0%
+elaborate
+so so if we have a
+
+ align:start position:0%
+so so if we have a
+ 
+
+ align:start position:0%
+so so if we have a
+when you act on this side
+
+ align:start position:0%
+when you act on this side
+ 
+
+ align:start position:0%
+when you act on this side
+react on this side can uh you only have
+
+ align:start position:0%
+react on this side can uh you only have
+ 
+
+ align:start position:0%
+react on this side can uh you only have
+a a if you have a particle in initial
+
+ align:start position:0%
+a a if you have a particle in initial
+ 
+
+ align:start position:0%
+a a if you have a particle in initial
+State then a can can relate that
+
+ align:start position:0%
+State then a can can relate that
+ 
+
+ align:start position:0%
+State then a can can relate that
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+but if a acts on the left
+
+ align:start position:0%
+but if a acts on the left
+ 
+
+ align:start position:0%
+but if a acts on the left
+and X on the left a become a dagger
+
+ align:start position:0%
+and X on the left a become a dagger
+ 
+
+ align:start position:0%
+and X on the left a become a dagger
+and then and then create an Enterprise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uh so um
+
+ align:start position:0%
+yeah uh so um
+ 
+
+ align:start position:0%
+yeah uh so um
+so so in such a process X
+
+ align:start position:0%
+so so in such a process X
+ 
+
+ align:start position:0%
+so so in such a process X
+plus a goes to y
+
+ align:start position:0%
+plus a goes to y
+ 
+
+ align:start position:0%
+plus a goes to y
+and then you can just so this relates to
+
+ align:start position:0%
+and then you can just so this relates to
+ 
+
+ align:start position:0%
+and then you can just so this relates to
+so X and Y are some combination yeah
+
+ align:start position:0%
+so X and Y are some combination yeah
+ 
+
+ align:start position:0%
+so X and Y are some combination yeah
+some combination of particles and then
+
+ align:start position:0%
+some combination of particles and then
+ 
+
+ align:start position:0%
+some combination of particles and then
+this just relates to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+x equals two
+
+ align:start position:0%
+x equals two
+ 
+
+ align:start position:0%
+x equals two
+y plus a bar
+
+ align:start position:0%
+y plus a bar
+ 
+
+ align:start position:0%
+y plus a bar
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so so here just
+
+ align:start position:0%
+and so so here just
+ 
+
+ align:start position:0%
+and so so here just
+X and Y some collection particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah age is some particle okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so just confirm that okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah e minus all mu
+
+ align:start position:0%
+yeah e minus all mu
+ 
+
+ align:start position:0%
+yeah e minus all mu
+yeah just say you have the you have one
+
+ align:start position:0%
+yeah just say you have the you have one
+ 
+
+ align:start position:0%
+yeah just say you have the you have one
+field for for E you have one field from
+
+ align:start position:0%
+field for for E you have one field from
+ 
+
+ align:start position:0%
+field for for E you have one field from
+U yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+are you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say it again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+heuristically you may yeah yeah but it's
+
+ align:start position:0%
+heuristically you may yeah yeah but it's
+ 
+
+ align:start position:0%
+heuristically you may yeah yeah but it's
+simpler than that yeah it's simpler than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+just say that like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so so that's why you have to
+
+ align:start position:0%
+yeah yeah so so that's why you have to
+ 
+
+ align:start position:0%
+yeah yeah so so that's why you have to
+change the momentum uh so so it's some
+
+ align:start position:0%
+change the momentum uh so so it's some
+ 
+
+ align:start position:0%
+change the momentum uh so so it's some
+momentum for for this process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one into some momentum for that process
+
+ align:start position:0%
+one into some momentum for that process
+ 
+
+ align:start position:0%
+one into some momentum for that process
+yeah yeah it's already we have to switch
+
+ align:start position:0%
+yeah yeah it's already we have to switch
+ 
+
+ align:start position:0%
+yeah yeah it's already we have to switch
+the ignition value
+
+ align:start position:0%
+the ignition value
+ 
+
+ align:start position:0%
+the ignition value
+yeah yeah just uh it's not say these two
+
+ align:start position:0%
+yeah yeah just uh it's not say these two
+ 
+
+ align:start position:0%
+yeah yeah just uh it's not say these two
+process are the same it's just this
+
+ align:start position:0%
+process are the same it's just this
+ 
+
+ align:start position:0%
+process are the same it's just this
+process for one side of momentum uh have
+
+ align:start position:0%
+process for one side of momentum uh have
+ 
+
+ align:start position:0%
+process for one side of momentum uh have
+the same amplitude as the uh the other
+
+ align:start position:0%
+the same amplitude as the uh the other
+ 
+
+ align:start position:0%
+the same amplitude as the uh the other
+process for some other sets of movement
+
+ align:start position:0%
+process for some other sets of movement
+ 
+
+ align:start position:0%
+process for some other sets of movement
+yeah there's a relation between them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now let's consider another
+
+ align:start position:0%
+so now let's consider another
+ 
+
+ align:start position:0%
+so now let's consider another
+uh process important process called
+
+ align:start position:0%
+uh process important process called
+ 
+
+ align:start position:0%
+uh process important process called
+confidence guide right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so complex scattering plays a very
+
+ align:start position:0%
+so complex scattering plays a very
+ 
+
+ align:start position:0%
+so complex scattering plays a very
+important role
+
+ align:start position:0%
+important role
+ 
+
+ align:start position:0%
+important role
+in the early days of physics
+
+ align:start position:0%
+in the early days of physics
+ 
+
+ align:start position:0%
+in the early days of physics
+and in showing that actually
+
+ align:start position:0%
+and in showing that actually
+ 
+
+ align:start position:0%
+and in showing that actually
+yeah this is one of the early
+
+ align:start position:0%
+yeah this is one of the early
+ 
+
+ align:start position:0%
+yeah this is one of the early
+experiments to show that the microscopic
+
+ align:start position:0%
+experiments to show that the microscopic
+ 
+
+ align:start position:0%
+experiments to show that the microscopic
+world is governed by quantum mechanics
+
+ align:start position:0%
+world is governed by quantum mechanics
+ 
+
+ align:start position:0%
+world is governed by quantum mechanics
+rather than classical mechanics
+
+ align:start position:0%
+rather than classical mechanics
+ 
+
+ align:start position:0%
+rather than classical mechanics
+so so now let's consider uh uh how to uh
+
+ align:start position:0%
+so so now let's consider uh uh how to uh
+ 
+
+ align:start position:0%
+so so now let's consider uh uh how to uh
+calculate the uh the physics for this
+
+ align:start position:0%
+calculate the uh the physics for this
+ 
+
+ align:start position:0%
+calculate the uh the physics for this
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+so so content scattering is a process
+
+ align:start position:0%
+so so content scattering is a process
+ 
+
+ align:start position:0%
+so so content scattering is a process
+you have a photon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then the you get another Photon and
+
+ align:start position:0%
+and then the you get another Photon and
+ 
+
+ align:start position:0%
+and then the you get another Photon and
+then you get a lot of electron
+
+ align:start position:0%
+then you get a lot of electron
+ 
+
+ align:start position:0%
+then you get a lot of electron
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so we can show the family diagram
+
+ align:start position:0%
+and so we can show the family diagram
+ 
+
+ align:start position:0%
+and so we can show the family diagram
+for it
+
+ align:start position:0%
+for it
+ 
+
+ align:start position:0%
+for it
+so one family diagram is 40 in this just
+
+ align:start position:0%
+so one family diagram is 40 in this just
+ 
+
+ align:start position:0%
+so one family diagram is 40 in this just
+imagine you have a formionic trajectory
+
+ align:start position:0%
+imagine you have a formionic trajectory
+ 
+
+ align:start position:0%
+imagine you have a formionic trajectory
+so you can imagine at some point there's
+
+ align:start position:0%
+so you can imagine at some point there's
+ 
+
+ align:start position:0%
+so you can imagine at some point there's
+a photon come in
+
+ align:start position:0%
+a photon come in
+ 
+
+ align:start position:0%
+a photon come in
+okay so this is the electron line
+
+ align:start position:0%
+okay so this is the electron line
+ 
+
+ align:start position:0%
+okay so this is the electron line
+the electron line is the arrow is the
+
+ align:start position:0%
+the electron line is the arrow is the
+ 
+
+ align:start position:0%
+the electron line is the arrow is the
+charge line so so the photon line the
+
+ align:start position:0%
+charge line so so the photon line the
+ 
+
+ align:start position:0%
+charge line so so the photon line the
+arrow should be understood just as a
+
+ align:start position:0%
+arrow should be understood just as a
+ 
+
+ align:start position:0%
+arrow should be understood just as a
+momentum okay and then and then you emit
+
+ align:start position:0%
+momentum okay and then and then you emit
+ 
+
+ align:start position:0%
+momentum okay and then and then you emit
+another Photon okay as a final state
+
+ align:start position:0%
+another Photon okay as a final state
+ 
+
+ align:start position:0%
+another Photon okay as a final state
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is the uh the fireman the
+
+ align:start position:0%
+so this is the uh the fireman the
+ 
+
+ align:start position:0%
+so this is the uh the fireman the
+simplest format diagram
+
+ align:start position:0%
+simplest format diagram
+ 
+
+ align:start position:0%
+simplest format diagram
+for this process
+
+ align:start position:0%
+for this process
+ 
+
+ align:start position:0%
+for this process
+but actually there are two diagrams
+
+ align:start position:0%
+but actually there are two diagrams
+ 
+
+ align:start position:0%
+but actually there are two diagrams
+because you can also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for this deduction line
+
+ align:start position:0%
+for this deduction line
+ 
+
+ align:start position:0%
+for this deduction line
+you can also first emit
+
+ align:start position:0%
+you can also first emit
+ 
+
+ align:start position:0%
+you can also first emit
+the photon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then absorb a photon
+
+ align:start position:0%
+and then absorb a photon
+ 
+
+ align:start position:0%
+and then absorb a photon
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+you also have that okay so so you have
+
+ align:start position:0%
+you also have that okay so so you have
+ 
+
+ align:start position:0%
+you also have that okay so so you have
+two and these two process are
+
+ align:start position:0%
+two and these two process are
+ 
+
+ align:start position:0%
+two and these two process are
+independent uh uh uh another set okay
+
+ align:start position:0%
+independent uh uh uh another set okay
+ 
+
+ align:start position:0%
+independent uh uh uh another set okay
+so so now let me put some label on the
+
+ align:start position:0%
+so so now let me put some label on the
+ 
+
+ align:start position:0%
+so so now let me put some label on the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+on the uh on the diagram so again the uh
+
+ align:start position:0%
+on the uh on the diagram so again the uh
+ 
+
+ align:start position:0%
+on the uh on the diagram so again the uh
+the fermion is P1 R1 so electron initial
+
+ align:start position:0%
+the fermion is P1 R1 so electron initial
+ 
+
+ align:start position:0%
+the fermion is P1 R1 so electron initial
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+and let's put its final state to be K1
+
+ align:start position:0%
+and let's put its final state to be K1
+ 
+
+ align:start position:0%
+and let's put its final state to be K1
+S1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the photon let's put its initial state
+
+ align:start position:0%
+the photon let's put its initial state
+ 
+
+ align:start position:0%
+the photon let's put its initial state
+to be P2
+
+ align:start position:0%
+to be P2
+ 
+
+ align:start position:0%
+to be P2
+Alpha so Alpha now is supervisation
+
+ align:start position:0%
+Alpha so Alpha now is supervisation
+ 
+
+ align:start position:0%
+Alpha so Alpha now is supervisation
+for the photon
+
+ align:start position:0%
+for the photon
+ 
+
+ align:start position:0%
+for the photon
+and so so call it Alpha One
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then this one is called K2
+
+ align:start position:0%
+and then this one is called K2
+ 
+
+ align:start position:0%
+and then this one is called K2
+Alpha 2.
+
+ align:start position:0%
+Alpha 2.
+ 
+
+ align:start position:0%
+Alpha 2.
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then the next label this index to be
+
+ align:start position:0%
+and then the next label this index to be
+ 
+
+ align:start position:0%
+and then the next label this index to be
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+and this index to be mu okay
+
+ align:start position:0%
+and this index to be mu okay
+ 
+
+ align:start position:0%
+and this index to be mu okay
+because of the photon carry a vector
+
+ align:start position:0%
+because of the photon carry a vector
+ 
+
+ align:start position:0%
+because of the photon carry a vector
+index because the polarization carrier
+
+ align:start position:0%
+index because the polarization carrier
+ 
+
+ align:start position:0%
+index because the polarization carrier
+back to index so so this will heat
+
+ align:start position:0%
+back to index so so this will heat
+ 
+
+ align:start position:0%
+back to index so so this will heat
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+so I always imagine the momentum is
+
+ align:start position:0%
+so I always imagine the momentum is
+ 
+
+ align:start position:0%
+so I always imagine the momentum is
+coming in for the initial State and the
+
+ align:start position:0%
+coming in for the initial State and the
+ 
+
+ align:start position:0%
+coming in for the initial State and the
+momentum come out for the final States
+
+ align:start position:0%
+momentum come out for the final States
+ 
+
+ align:start position:0%
+momentum come out for the final States
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and for this diagram it's the same thing
+
+ align:start position:0%
+and for this diagram it's the same thing
+ 
+
+ align:start position:0%
+and for this diagram it's the same thing
+so I have P1 so I label the P1 R1
+
+ align:start position:0%
+so I have P1 so I label the P1 R1
+ 
+
+ align:start position:0%
+so I have P1 so I label the P1 R1
+so this is the P2
+
+ align:start position:0%
+so this is the P2
+ 
+
+ align:start position:0%
+so this is the P2
+Alpha 1.
+
+ align:start position:0%
+Alpha 1.
+ 
+
+ align:start position:0%
+Alpha 1.
+and so this is k1 S1
+
+ align:start position:0%
+and so this is k1 S1
+ 
+
+ align:start position:0%
+and so this is k1 S1
+and this is K2 Alpha Q
+
+ align:start position:0%
+and this is K2 Alpha Q
+ 
+
+ align:start position:0%
+and this is K2 Alpha Q
+the only difference
+
+ align:start position:0%
+the only difference
+ 
+
+ align:start position:0%
+the only difference
+is the row of mu and U it is Switched so
+
+ align:start position:0%
+is the row of mu and U it is Switched so
+ 
+
+ align:start position:0%
+is the row of mu and U it is Switched so
+for the outer neck it's mu so mu naught
+
+ align:start position:0%
+for the outer neck it's mu so mu naught
+ 
+
+ align:start position:0%
+for the outer neck it's mu so mu naught
+is here
+
+ align:start position:0%
+is here
+ 
+
+ align:start position:0%
+is here
+and for this one is new here okay so U
+
+ align:start position:0%
+and for this one is new here okay so U
+ 
+
+ align:start position:0%
+and for this one is new here okay so U
+is associated the prediction of the Ingo
+
+ align:start position:0%
+is associated the prediction of the Ingo
+ 
+
+ align:start position:0%
+is associated the prediction of the Ingo
+in photon and the MU is the polarization
+
+ align:start position:0%
+in photon and the MU is the polarization
+ 
+
+ align:start position:0%
+in photon and the MU is the polarization
+associated with the other going forward
+
+ align:start position:0%
+associated with the other going forward
+ 
+
+ align:start position:0%
+associated with the other going forward
+okay so this is my family diagram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so this process compared to the one we
+
+ align:start position:0%
+so this process compared to the one we
+ 
+
+ align:start position:0%
+so this process compared to the one we
+considered this e plus e minus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these have some new elements
+
+ align:start position:0%
+so these have some new elements
+ 
+
+ align:start position:0%
+so these have some new elements
+so that's why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a good example to look at
+
+ align:start position:0%
+this is a good example to look at
+ 
+
+ align:start position:0%
+this is a good example to look at
+so the do do element there are two do
+
+ align:start position:0%
+so the do do element there are two do
+ 
+
+ align:start position:0%
+so the do do element there are two do
+elements
+
+ align:start position:0%
+elements
+ 
+
+ align:start position:0%
+elements
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+in this example we have
+
+ align:start position:0%
+in this example we have
+ 
+
+ align:start position:0%
+in this example we have
+so this propagate is a feminic one so
+
+ align:start position:0%
+so this propagate is a feminic one so
+ 
+
+ align:start position:0%
+so this propagate is a feminic one so
+now we have an intermediate feminic
+
+ align:start position:0%
+now we have an intermediate feminic
+ 
+
+ align:start position:0%
+now we have an intermediate feminic
+propagator okay
+
+ align:start position:0%
+propagator okay
+ 
+
+ align:start position:0%
+propagator okay
+so and the momentum for this one
+
+ align:start position:0%
+so and the momentum for this one
+ 
+
+ align:start position:0%
+so and the momentum for this one
+so let's call it
+
+ align:start position:0%
+so let's call it
+ 
+
+ align:start position:0%
+so let's call it
+Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 equal to K1 plus K2
+
+ align:start position:0%
+1 equal to K1 plus K2
+ 
+
+ align:start position:0%
+1 equal to K1 plus K2
+so this is P1 plus P2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this one will have a different
+
+ align:start position:0%
+but this one will have a different
+ 
+
+ align:start position:0%
+but this one will have a different
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+so D here is called Q2
+
+ align:start position:0%
+so D here is called Q2
+ 
+
+ align:start position:0%
+so D here is called Q2
+will have so what's the momentum for
+
+ align:start position:0%
+will have so what's the momentum for
+ 
+
+ align:start position:0%
+will have so what's the momentum for
+this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I show the momentum going to to the
+
+ align:start position:0%
+if I show the momentum going to to the
+ 
+
+ align:start position:0%
+if I show the momentum going to to the
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+yeah so let me put it here
+
+ align:start position:0%
+yeah so let me put it here
+ 
+
+ align:start position:0%
+yeah so let me put it here
+so what would be the momentum of this
+
+ align:start position:0%
+so what would be the momentum of this
+ 
+
+ align:start position:0%
+so what would be the momentum of this
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+let's call it Q2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can you read the momentum of this
+
+ align:start position:0%
+can you read the momentum of this
+ 
+
+ align:start position:0%
+can you read the momentum of this
+intermediate line from the diagram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's P1 minus K2
+
+ align:start position:0%
+yeah it's P1 minus K2
+ 
+
+ align:start position:0%
+yeah it's P1 minus K2
+because we have P1 come in and then K2
+
+ align:start position:0%
+because we have P1 come in and then K2
+ 
+
+ align:start position:0%
+because we have P1 come in and then K2
+come out so so that's the momentum okay
+
+ align:start position:0%
+come out so so that's the momentum okay
+ 
+
+ align:start position:0%
+come out so so that's the momentum okay
+so in this one you have P1 and then you
+
+ align:start position:0%
+so in this one you have P1 and then you
+ 
+
+ align:start position:0%
+so in this one you have P1 and then you
+have the P2 coming and then this is P1
+
+ align:start position:0%
+have the P2 coming and then this is P1
+ 
+
+ align:start position:0%
+have the P2 coming and then this is P1
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+okay so so so so so so the new element
+
+ align:start position:0%
+okay so so so so so so the new element
+ 
+
+ align:start position:0%
+okay so so so so so so the new element
+is that now we have a premium propagator
+
+ align:start position:0%
+is that now we have a premium propagator
+ 
+
+ align:start position:0%
+is that now we have a premium propagator
+as in the media States
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the secondary element
+
+ align:start position:0%
+okay and the secondary element
+ 
+
+ align:start position:0%
+okay and the secondary element
+is now we have photons
+
+ align:start position:0%
+is now we have photons
+ 
+
+ align:start position:0%
+is now we have photons
+in the external state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is a new element compared
+
+ align:start position:0%
+okay so this is a new element compared
+ 
+
+ align:start position:0%
+okay so this is a new element compared
+to the to this e plus e minus example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now it's
+
+ align:start position:0%
+so now it's
+ 
+
+ align:start position:0%
+so now it's
+but still using our previous rule we can
+
+ align:start position:0%
+but still using our previous rule we can
+ 
+
+ align:start position:0%
+but still using our previous rule we can
+immediately divide down the amplitude
+
+ align:start position:0%
+immediately divide down the amplitude
+ 
+
+ align:start position:0%
+immediately divide down the amplitude
+okay I think I may not have enough space
+
+ align:start position:0%
+okay I think I may not have enough space
+ 
+
+ align:start position:0%
+okay I think I may not have enough space
+for this
+
+ align:start position:0%
+for this
+ 
+
+ align:start position:0%
+for this
+yeah let me try
+
+ align:start position:0%
+yeah let me try
+ 
+
+ align:start position:0%
+yeah let me try
+so let me start from here
+
+ align:start position:0%
+so let me start from here
+ 
+
+ align:start position:0%
+so let me start from here
+so so the so the amplitude
+
+ align:start position:0%
+so so the so the amplitude
+ 
+
+ align:start position:0%
+so so the so the amplitude
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+the I times the library yeah this I is
+
+ align:start position:0%
+the I times the library yeah this I is
+ 
+
+ align:start position:0%
+the I times the library yeah this I is
+not important
+
+ align:start position:0%
+not important
+ 
+
+ align:start position:0%
+not important
+but nevertheless let me just
+
+ align:start position:0%
+but nevertheless let me just
+ 
+
+ align:start position:0%
+but nevertheless let me just
+write it down
+
+ align:start position:0%
+write it down
+ 
+
+ align:start position:0%
+write it down
+so the amplitude is given by
+
+ align:start position:0%
+so the amplitude is given by
+ 
+
+ align:start position:0%
+so the amplitude is given by
+so let's so we follow
+
+ align:start position:0%
+so let's so we follow
+ 
+
+ align:start position:0%
+so let's so we follow
+you see we follow the formionic line so
+
+ align:start position:0%
+you see we follow the formionic line so
+ 
+
+ align:start position:0%
+you see we follow the formionic line so
+here there's one formionic line okay
+
+ align:start position:0%
+here there's one formionic line okay
+ 
+
+ align:start position:0%
+here there's one formionic line okay
+and so we should follow that formionic
+
+ align:start position:0%
+and so we should follow that formionic
+ 
+
+ align:start position:0%
+and so we should follow that formionic
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+and then and then we also have the uh
+
+ align:start position:0%
+and then and then we also have the uh
+ 
+
+ align:start position:0%
+and then and then we also have the uh
+the photon polarization okay so let's
+
+ align:start position:0%
+the photon polarization okay so let's
+ 
+
+ align:start position:0%
+the photon polarization okay so let's
+first write down the photon polarization
+
+ align:start position:0%
+first write down the photon polarization
+ 
+
+ align:start position:0%
+first write down the photon polarization
+so for this fourth and final stage then
+
+ align:start position:0%
+so for this fourth and final stage then
+ 
+
+ align:start position:0%
+so for this fourth and final stage then
+we just have Epsilon mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+so K2
+
+ align:start position:0%
+so K2
+ 
+
+ align:start position:0%
+so K2
+okay so remember for the photon in the
+
+ align:start position:0%
+okay so remember for the photon in the
+ 
+
+ align:start position:0%
+okay so remember for the photon in the
+fallow State we need to put the star
+
+ align:start position:0%
+fallow State we need to put the star
+ 
+
+ align:start position:0%
+fallow State we need to put the star
+and also remember the MU is associated
+
+ align:start position:0%
+and also remember the MU is associated
+ 
+
+ align:start position:0%
+and also remember the MU is associated
+with the photon in the final state
+
+ align:start position:0%
+with the photon in the final state
+ 
+
+ align:start position:0%
+with the photon in the final state
+and then we have Epsilon U for the
+
+ align:start position:0%
+and then we have Epsilon U for the
+ 
+
+ align:start position:0%
+and then we have Epsilon U for the
+initial state of the photon alpha 1
+
+ align:start position:0%
+initial state of the photon alpha 1
+ 
+
+ align:start position:0%
+initial state of the photon alpha 1
+then K1
+
+ align:start position:0%
+then K1
+ 
+
+ align:start position:0%
+then K1
+okay so this is the photon one okay
+
+ align:start position:0%
+okay so this is the photon one okay
+ 
+
+ align:start position:0%
+okay so this is the photon one okay
+Photon per addition Factor
+
+ align:start position:0%
+Photon per addition Factor
+ 
+
+ align:start position:0%
+Photon per addition Factor
+and now we need to write down the uh
+
+ align:start position:0%
+and now we need to write down the uh
+ 
+
+ align:start position:0%
+and now we need to write down the uh
+so these two facts are the same
+
+ align:start position:0%
+so these two facts are the same
+ 
+
+ align:start position:0%
+so these two facts are the same
+for both process okay for both process
+
+ align:start position:0%
+for both process okay for both process
+ 
+
+ align:start position:0%
+for both process okay for both process
+we are not changing the external Photon
+
+ align:start position:0%
+we are not changing the external Photon
+ 
+
+ align:start position:0%
+we are not changing the external Photon
+States okay so these two factors are the
+
+ align:start position:0%
+States okay so these two factors are the
+ 
+
+ align:start position:0%
+States okay so these two factors are the
+same okay
+
+ align:start position:0%
+same okay
+ 
+
+ align:start position:0%
+same okay
+so so now
+
+ align:start position:0%
+so so now
+ 
+
+ align:start position:0%
+so so now
+another rest
+
+ align:start position:0%
+another rest
+ 
+
+ align:start position:0%
+another rest
+so now let's look at this diagram and
+
+ align:start position:0%
+so now let's look at this diagram and
+ 
+
+ align:start position:0%
+so now let's look at this diagram and
+follow this formionic line okay
+
+ align:start position:0%
+follow this formionic line okay
+ 
+
+ align:start position:0%
+follow this formionic line okay
+so we start with here and then going
+
+ align:start position:0%
+so we start with here and then going
+ 
+
+ align:start position:0%
+so we start with here and then going
+backwards
+
+ align:start position:0%
+backwards
+ 
+
+ align:start position:0%
+backwards
+so so we just have U Bar
+
+ align:start position:0%
+so so we just have U Bar
+ 
+
+ align:start position:0%
+so so we just have U Bar
+S1 K1
+
+ align:start position:0%
+S1 K1
+ 
+
+ align:start position:0%
+S1 K1
+for this electron in the fellow state
+
+ align:start position:0%
+for this electron in the fellow state
+ 
+
+ align:start position:0%
+for this electron in the fellow state
+and then we have feminic propagate and
+
+ align:start position:0%
+and then we have feminic propagate and
+ 
+
+ align:start position:0%
+and then we have feminic propagate and
+then we have this vertex
+
+ align:start position:0%
+then we have this vertex
+ 
+
+ align:start position:0%
+then we have this vertex
+should be minus IE gamma Nu
+
+ align:start position:0%
+should be minus IE gamma Nu
+ 
+
+ align:start position:0%
+should be minus IE gamma Nu
+or this order is important because they
+
+ align:start position:0%
+or this order is important because they
+ 
+
+ align:start position:0%
+or this order is important because they
+are all matrices okay they all have
+
+ align:start position:0%
+are all matrices okay they all have
+ 
+
+ align:start position:0%
+are all matrices okay they all have
+spinal indices and so this is a matrix
+
+ align:start position:0%
+spinal indices and so this is a matrix
+ 
+
+ align:start position:0%
+spinal indices and so this is a matrix
+and then we have this famionic
+
+ align:start position:0%
+and then we have this famionic
+ 
+
+ align:start position:0%
+and then we have this famionic
+propagator
+
+ align:start position:0%
+propagator
+ 
+
+ align:start position:0%
+propagator
+which is the minus one
+
+ align:start position:0%
+which is the minus one
+ 
+
+ align:start position:0%
+which is the minus one
+IQ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one slash so here Q so I just write down
+
+ align:start position:0%
+one slash so here Q so I just write down
+ 
+
+ align:start position:0%
+one slash so here Q so I just write down
+the feminic propagator minus m
+
+ align:start position:0%
+the feminic propagator minus m
+ 
+
+ align:start position:0%
+the feminic propagator minus m
+plus I absolute
+
+ align:start position:0%
+plus I absolute
+ 
+
+ align:start position:0%
+plus I absolute
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so I did
+
+ align:start position:0%
+so I did
+ 
+
+ align:start position:0%
+so I did
+the final State intermediate propagator
+
+ align:start position:0%
+the final State intermediate propagator
+ 
+
+ align:start position:0%
+the final State intermediate propagator
+and then I have another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vertex
+
+ align:start position:0%
+vertex
+ 
+
+ align:start position:0%
+vertex
+and now it's new
+
+ align:start position:0%
+and now it's new
+ 
+
+ align:start position:0%
+and now it's new
+and then I have the final
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's the that's the that diagram
+
+ align:start position:0%
+so that's the that's the that diagram
+ 
+
+ align:start position:0%
+so that's the that's the that diagram
+okay that's a diagram and now for this
+
+ align:start position:0%
+okay that's a diagram and now for this
+ 
+
+ align:start position:0%
+okay that's a diagram and now for this
+diagram we do the same thing
+
+ align:start position:0%
+diagram we do the same thing
+ 
+
+ align:start position:0%
+diagram we do the same thing
+and then Plus
+
+ align:start position:0%
+and then Plus
+ 
+
+ align:start position:0%
+and then Plus
+so the final State again is the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the US1
+
+ align:start position:0%
+is the US1
+ 
+
+ align:start position:0%
+is the US1
+bar
+
+ align:start position:0%
+bar
+ 
+
+ align:start position:0%
+bar
+K1
+
+ align:start position:0%
+K1
+ 
+
+ align:start position:0%
+K1
+but now here you have IE gamma Nu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now the order changed
+
+ align:start position:0%
+so now the order changed
+ 
+
+ align:start position:0%
+so now the order changed
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then you have the photon then you
+
+ align:start position:0%
+and then you have the photon then you
+ 
+
+ align:start position:0%
+and then you have the photon then you
+have this feminic propagator
+
+ align:start position:0%
+have this feminic propagator
+ 
+
+ align:start position:0%
+have this feminic propagator
+which is iq2 Slash
+
+ align:start position:0%
+which is iq2 Slash
+ 
+
+ align:start position:0%
+which is iq2 Slash
+plus M minus Epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then you have then have my e-commer
+
+ align:start position:0%
+and then you have then have my e-commer
+ 
+
+ align:start position:0%
+and then you have then have my e-commer
+mu
+
+ align:start position:0%
+mu
+ 
+
+ align:start position:0%
+mu
+from here
+
+ align:start position:0%
+from here
+ 
+
+ align:start position:0%
+from here
+and then you have the final state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P1
+
+ align:start position:0%
+P1
+ 
+
+ align:start position:0%
+P1
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yeah
+
+ align:start position:0%
+yes yeah
+ 
+
+ align:start position:0%
+yes yeah
+if we're working with bosons it doesn't
+
+ align:start position:0%
+if we're working with bosons it doesn't
+ 
+
+ align:start position:0%
+if we're working with bosons it doesn't
+matter this seems like the the real
+
+ align:start position:0%
+matter this seems like the the real
+ 
+
+ align:start position:0%
+matter this seems like the the real
+difference is not like the kinematic
+
+ align:start position:0%
+difference is not like the kinematic
+ 
+
+ align:start position:0%
+difference is not like the kinematic
+difference of like which one gets so
+
+ align:start position:0%
+difference of like which one gets so
+ 
+
+ align:start position:0%
+difference of like which one gets so
+further and it's the fact that we have
+
+ align:start position:0%
+further and it's the fact that we have
+ 
+
+ align:start position:0%
+further and it's the fact that we have
+this uh Vector that describes the
+
+ align:start position:0%
+this uh Vector that describes the
+ 
+
+ align:start position:0%
+this uh Vector that describes the
+polarization of the book is right no
+
+ align:start position:0%
+polarization of the book is right no
+ 
+
+ align:start position:0%
+polarization of the book is right no
+just the uh these are just two
+
+ align:start position:0%
+just the uh these are just two
+ 
+
+ align:start position:0%
+just the uh these are just two
+equivalent assignment diagrams
+
+ align:start position:0%
+equivalent assignment diagrams
+ 
+
+ align:start position:0%
+equivalent assignment diagrams
+in equivalent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no no even even not for the uh even not
+
+ align:start position:0%
+no no even even not for the uh even not
+ 
+
+ align:start position:0%
+no no even even not for the uh even not
+for the even not for uh even they are
+
+ align:start position:0%
+for the even not for uh even they are
+ 
+
+ align:start position:0%
+for the even not for uh even they are
+not vectors still they're in equipment
+
+ align:start position:0%
+not vectors still they're in equipment
+ 
+
+ align:start position:0%
+not vectors still they're in equipment
+diagrams because the momentum here is
+
+ align:start position:0%
+diagrams because the momentum here is
+ 
+
+ align:start position:0%
+diagrams because the momentum here is
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+the momentum is different yeah so so
+
+ align:start position:0%
+the momentum is different yeah so so
+ 
+
+ align:start position:0%
+the momentum is different yeah so so
+they're still in equipment diagram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so these are the amplitude
+
+ align:start position:0%
+so so these are the amplitude
+ 
+
+ align:start position:0%
+so so these are the amplitude
+so again we look at
+
+ align:start position:0%
+so again we look at
+ 
+
+ align:start position:0%
+so again we look at
+unpolarized cross-action
+
+ align:start position:0%
+unpolarized cross-action
+ 
+
+ align:start position:0%
+unpolarized cross-action
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cross-action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's look at the unpolarized
+
+ align:start position:0%
+so let's look at the unpolarized
+ 
+
+ align:start position:0%
+so let's look at the unpolarized
+situation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so again we need to average over
+
+ align:start position:0%
+okay so again we need to average over
+ 
+
+ align:start position:0%
+okay so again we need to average over
+the initial Spin and sum over the final
+
+ align:start position:0%
+the initial Spin and sum over the final
+ 
+
+ align:start position:0%
+the initial Spin and sum over the final
+spin
+
+ align:start position:0%
+spin
+ 
+
+ align:start position:0%
+spin
+so here now the difference is how we
+
+ align:start position:0%
+so here now the difference is how we
+ 
+
+ align:start position:0%
+so here now the difference is how we
+lead to average also over sum over the
+
+ align:start position:0%
+lead to average also over sum over the
+ 
+
+ align:start position:0%
+lead to average also over sum over the
+index for Alpha and for Alpha One and
+
+ align:start position:0%
+index for Alpha and for Alpha One and
+ 
+
+ align:start position:0%
+index for Alpha and for Alpha One and
+Alpha two
+
+ align:start position:0%
+Alpha two
+ 
+
+ align:start position:0%
+Alpha two
+they only have two polarization
+
+ align:start position:0%
+they only have two polarization
+ 
+
+ align:start position:0%
+they only have two polarization
+so again you get when you average over
+
+ align:start position:0%
+so again you get when you average over
+ 
+
+ align:start position:0%
+so again you get when you average over
+the Alpha One you get the factor one
+
+ align:start position:0%
+the Alpha One you get the factor one
+ 
+
+ align:start position:0%
+the Alpha One you get the factor one
+half okay so still we get just factor of
+
+ align:start position:0%
+half okay so still we get just factor of
+ 
+
+ align:start position:0%
+half okay so still we get just factor of
+one quarter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some of all the spins
+
+ align:start position:0%
+some of all the spins
+ 
+
+ align:start position:0%
+some of all the spins
+of M Square
+
+ align:start position:0%
+of M Square
+ 
+
+ align:start position:0%
+of M Square
+so this is just the same
+
+ align:start position:0%
+so this is just the same
+ 
+
+ align:start position:0%
+so this is just the same
+I sum over
+
+ align:start position:0%
+I sum over
+ 
+
+ align:start position:0%
+I sum over
+say Alpha One
+
+ align:start position:0%
+say Alpha One
+ 
+
+ align:start position:0%
+say Alpha One
+Alpha 2 R1 R2
+
+ align:start position:0%
+Alpha 2 R1 R2
+ 
+
+ align:start position:0%
+Alpha 2 R1 R2
+okay M squared okay
+
+ align:start position:0%
+okay M squared okay
+ 
+
+ align:start position:0%
+okay M squared okay
+and each index
+
+ align:start position:0%
+and each index
+ 
+
+ align:start position:0%
+and each index
+take value one and two okay because the
+
+ align:start position:0%
+take value one and two okay because the
+ 
+
+ align:start position:0%
+take value one and two okay because the
+photon also only have two partitions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now I will not do a complete the
+
+ align:start position:0%
+so now I will not do a complete the
+ 
+
+ align:start position:0%
+so now I will not do a complete the
+calculation of this okay so so you just
+
+ align:start position:0%
+calculation of this okay so so you just
+ 
+
+ align:start position:0%
+calculation of this okay so so you just
+Square it
+
+ align:start position:0%
+Square it
+ 
+
+ align:start position:0%
+Square it
+so you use the trick and you use the uh
+
+ align:start position:0%
+so you use the trick and you use the uh
+ 
+
+ align:start position:0%
+so you use the trick and you use the uh
+it's just squared and then you just try
+
+ align:start position:0%
+it's just squared and then you just try
+ 
+
+ align:start position:0%
+it's just squared and then you just try
+to calculate it okay and now to
+
+ align:start position:0%
+to calculate it okay and now to
+ 
+
+ align:start position:0%
+to calculate it okay and now to
+calculate this guy now we need to use
+
+ align:start position:0%
+calculate this guy now we need to use
+ 
+
+ align:start position:0%
+calculate this guy now we need to use
+some more tricks okay so so I will just
+
+ align:start position:0%
+some more tricks okay so so I will just
+ 
+
+ align:start position:0%
+some more tricks okay so so I will just
+explain the what are the tricks needed
+
+ align:start position:0%
+explain the what are the tricks needed
+ 
+
+ align:start position:0%
+explain the what are the tricks needed
+to do tricks needed to compute this guy
+
+ align:start position:0%
+to do tricks needed to compute this guy
+ 
+
+ align:start position:0%
+to do tricks needed to compute this guy
+and we will not actually do a
+
+ align:start position:0%
+and we will not actually do a
+ 
+
+ align:start position:0%
+and we will not actually do a
+calculation okay let's do a genuine
+
+ align:start position:0%
+calculation okay let's do a genuine
+ 
+
+ align:start position:0%
+calculation okay let's do a genuine
+package
+
+ align:start position:0%
+package
+ 
+
+ align:start position:0%
+package
+so the so the new elements we need to
+
+ align:start position:0%
+so the so the new elements we need to
+ 
+
+ align:start position:0%
+so the so the new elements we need to
+use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this
+
+ align:start position:0%
+so so this
+ 
+
+ align:start position:0%
+so so this
+so a few new tricks
+
+ align:start position:0%
+so a few new tricks
+ 
+
+ align:start position:0%
+so a few new tricks
+in order to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to do the calculation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the first trick is how you treat this
+
+ align:start position:0%
+so the first trick is how you treat this
+ 
+
+ align:start position:0%
+so the first trick is how you treat this
+feminic propagator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so how you treat the feminic
+
+ align:start position:0%
+okay so how you treat the feminic
+ 
+
+ align:start position:0%
+okay so how you treat the feminic
+proposator
+
+ align:start position:0%
+proposator
+ 
+
+ align:start position:0%
+proposator
+so so so we can just rewrite
+
+ align:start position:0%
+so so so we can just rewrite
+ 
+
+ align:start position:0%
+so so so we can just rewrite
+yeah so so this is the inverse of a
+
+ align:start position:0%
+yeah so so this is the inverse of a
+ 
+
+ align:start position:0%
+yeah so so this is the inverse of a
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+okay so we uh we can just do the uh
+
+ align:start position:0%
+okay so we uh we can just do the uh
+ 
+
+ align:start position:0%
+okay so we uh we can just do the uh
+yeah say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe has a propagator like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay slash plus m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon because the at the downstairs
+
+ align:start position:0%
+Epsilon because the at the downstairs
+ 
+
+ align:start position:0%
+Epsilon because the at the downstairs
+level there also this is the same as i k
+
+ align:start position:0%
+level there also this is the same as i k
+ 
+
+ align:start position:0%
+level there also this is the same as i k
+slash plus m
+
+ align:start position:0%
+slash plus m
+ 
+
+ align:start position:0%
+slash plus m
+K squared plus M squared
+
+ align:start position:0%
+K squared plus M squared
+ 
+
+ align:start position:0%
+K squared plus M squared
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+it's just because the the the familiar
+
+ align:start position:0%
+it's just because the the the familiar
+ 
+
+ align:start position:0%
+it's just because the the the familiar
+relation we used before that a k slash
+
+ align:start position:0%
+relation we used before that a k slash
+ 
+
+ align:start position:0%
+relation we used before that a k slash
+plus m
+
+ align:start position:0%
+plus m
+ 
+
+ align:start position:0%
+plus m
+K slash minus m
+
+ align:start position:0%
+K slash minus m
+ 
+
+ align:start position:0%
+K slash minus m
+is equal to minus K squared
+
+ align:start position:0%
+is equal to minus K squared
+ 
+
+ align:start position:0%
+is equal to minus K squared
+minus M squared
+
+ align:start position:0%
+minus M squared
+ 
+
+ align:start position:0%
+minus M squared
+okay so you can just see and then the
+
+ align:start position:0%
+okay so you can just see and then the
+ 
+
+ align:start position:0%
+okay so you can just see and then the
+inverse of this Matrix is just given by
+
+ align:start position:0%
+inverse of this Matrix is just given by
+ 
+
+ align:start position:0%
+inverse of this Matrix is just given by
+this Matrix sorry
+
+ align:start position:0%
+this Matrix sorry
+ 
+
+ align:start position:0%
+this Matrix sorry
+missing guy
+
+ align:start position:0%
+missing guy
+ 
+
+ align:start position:0%
+missing guy
+here should be minus sign
+
+ align:start position:0%
+here should be minus sign
+ 
+
+ align:start position:0%
+here should be minus sign
+the inverse of this Matrix just given by
+
+ align:start position:0%
+the inverse of this Matrix just given by
+ 
+
+ align:start position:0%
+the inverse of this Matrix just given by
+that Matrix okay
+
+ align:start position:0%
+that Matrix okay
+ 
+
+ align:start position:0%
+that Matrix okay
+so and then you can use this to simplify
+
+ align:start position:0%
+so and then you can use this to simplify
+ 
+
+ align:start position:0%
+so and then you can use this to simplify
+then you can use to simplify that
+
+ align:start position:0%
+then you can use to simplify that
+ 
+
+ align:start position:0%
+then you can use to simplify that
+expression a little bit okay
+
+ align:start position:0%
+expression a little bit okay
+ 
+
+ align:start position:0%
+expression a little bit okay
+so this is first thing used
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the second thing used
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is when do the spin sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the performance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for Spinners we use the same trigger as
+
+ align:start position:0%
+for Spinners we use the same trigger as
+ 
+
+ align:start position:0%
+for Spinners we use the same trigger as
+before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the one we used for the last example
+
+ align:start position:0%
+as the one we used for the last example
+ 
+
+ align:start position:0%
+as the one we used for the last example
+but for photons there's some new
+
+ align:start position:0%
+but for photons there's some new
+ 
+
+ align:start position:0%
+but for photons there's some new
+elements okay
+
+ align:start position:0%
+elements okay
+ 
+
+ align:start position:0%
+elements okay
+so now let's discuss how we treat the
+
+ align:start position:0%
+so now let's discuss how we treat the
+ 
+
+ align:start position:0%
+so now let's discuss how we treat the
+photons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now I choose photons and the way to
+
+ align:start position:0%
+so now I choose photons and the way to
+ 
+
+ align:start position:0%
+so now I choose photons and the way to
+treat the photons actually involve some
+
+ align:start position:0%
+treat the photons actually involve some
+ 
+
+ align:start position:0%
+treat the photons actually involve some
+important physics
+
+ align:start position:0%
+important physics
+ 
+
+ align:start position:0%
+important physics
+so let me explain a a little bit how we
+
+ align:start position:0%
+so let me explain a a little bit how we
+ 
+
+ align:start position:0%
+so let me explain a a little bit how we
+do that okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's focus on one of the
+
+ align:start position:0%
+okay so let's focus on one of the
+ 
+
+ align:start position:0%
+okay so let's focus on one of the
+photons say let's look at this uh uh
+
+ align:start position:0%
+photons say let's look at this uh uh
+ 
+
+ align:start position:0%
+photons say let's look at this uh uh
+this the final Photon okay so so the
+
+ align:start position:0%
+this the final Photon okay so so the
+ 
+
+ align:start position:0%
+this the final Photon okay so so the
+polarization have the following form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it doesn't matter say say let's look at
+
+ align:start position:0%
+it doesn't matter say say let's look at
+ 
+
+ align:start position:0%
+it doesn't matter say say let's look at
+this one initial photo
+
+ align:start position:0%
+this one initial photo
+ 
+
+ align:start position:0%
+this one initial photo
+and then the amplitude then then you
+
+ align:start position:0%
+and then the amplitude then then you
+ 
+
+ align:start position:0%
+and then the amplitude then then you
+have this
+
+ align:start position:0%
+have this
+ 
+
+ align:start position:0%
+have this
+then the whole amplitude is a scalar
+
+ align:start position:0%
+then the whole amplitude is a scalar
+ 
+
+ align:start position:0%
+then the whole amplitude is a scalar
+okay so the amplitude then has the
+
+ align:start position:0%
+okay so the amplitude then has the
+ 
+
+ align:start position:0%
+okay so the amplitude then has the
+structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that they have Epsilon new star a u
+
+ align:start position:0%
+that they have Epsilon new star a u
+ 
+
+ align:start position:0%
+that they have Epsilon new star a u
+Alpha
+
+ align:start position:0%
+Alpha
+ 
+
+ align:start position:0%
+Alpha
+times m m Nu okay
+
+ align:start position:0%
+times m m Nu okay
+ 
+
+ align:start position:0%
+times m m Nu okay
+just say this is the polarization and
+
+ align:start position:0%
+just say this is the polarization and
+ 
+
+ align:start position:0%
+just say this is the polarization and
+the rest I just call them new B because
+
+ align:start position:0%
+the rest I just call them new B because
+ 
+
+ align:start position:0%
+the rest I just call them new B because
+the index has to be a contracted okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now I do the spin sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I now sum over U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to to the to the spin sum over the alpha
+
+ align:start position:0%
+to to the to the spin sum over the alpha
+ 
+
+ align:start position:0%
+to to the to the spin sum over the alpha
+and then I just have Alpha equal to 1 2
+
+ align:start position:0%
+and then I just have Alpha equal to 1 2
+ 
+
+ align:start position:0%
+and then I just have Alpha equal to 1 2
+the screen sum relevant for the alpha I
+
+ align:start position:0%
+the screen sum relevant for the alpha I
+ 
+
+ align:start position:0%
+the screen sum relevant for the alpha I
+just have alpha one two and then I have
+
+ align:start position:0%
+just have alpha one two and then I have
+ 
+
+ align:start position:0%
+just have alpha one two and then I have
+Epsilon
+
+ align:start position:0%
+Epsilon
+ 
+
+ align:start position:0%
+Epsilon
+news
+
+ align:start position:0%
+news
+ 
+
+ align:start position:0%
+news
+Alpha star
+
+ align:start position:0%
+Alpha star
+ 
+
+ align:start position:0%
+Alpha star
+of a new Alpha
+
+ align:start position:0%
+of a new Alpha
+ 
+
+ align:start position:0%
+of a new Alpha
+Alpha uh um yeah mu star
+
+ align:start position:0%
+Alpha uh um yeah mu star
+ 
+
+ align:start position:0%
+Alpha uh um yeah mu star
+of a new
+
+ align:start position:0%
+of a new
+ 
+
+ align:start position:0%
+of a new
+Alpha and then I have mu
+
+ align:start position:0%
+Alpha and then I have mu
+ 
+
+ align:start position:0%
+Alpha and then I have mu
+stop
+
+ align:start position:0%
+stop
+ 
+
+ align:start position:0%
+stop
+and have M view okay I just take the
+
+ align:start position:0%
+and have M view okay I just take the
+ 
+
+ align:start position:0%
+and have M view okay I just take the
+square of it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now to do the spin sum you know we
+
+ align:start position:0%
+so now to do the spin sum you know we
+ 
+
+ align:start position:0%
+so now to do the spin sum you know we
+look at this object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I need to look at this object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so remember
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so do you know do you remember what is
+
+ align:start position:0%
+so do you know do you remember what is
+ 
+
+ align:start position:0%
+so do you know do you remember what is
+the sum of this object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because of the the physical Photon
+
+ align:start position:0%
+because of the the physical Photon
+ 
+
+ align:start position:0%
+because of the the physical Photon
+polarization uh is projected to the
+
+ align:start position:0%
+polarization uh is projected to the
+ 
+
+ align:start position:0%
+polarization uh is projected to the
+transverse space okay
+
+ align:start position:0%
+transverse space okay
+ 
+
+ align:start position:0%
+transverse space okay
+so uh so this gives you the transverse
+
+ align:start position:0%
+so uh so this gives you the transverse
+ 
+
+ align:start position:0%
+so uh so this gives you the transverse
+project
+
+ align:start position:0%
+project
+ 
+
+ align:start position:0%
+project
+but now I claim
+
+ align:start position:0%
+but now I claim
+ 
+
+ align:start position:0%
+but now I claim
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+so if you do the uh the alpha
+
+ align:start position:0%
+so if you do the uh the alpha
+ 
+
+ align:start position:0%
+so if you do the uh the alpha
+1 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mu
+
+ align:start position:0%
+mu
+ 
+
+ align:start position:0%
+mu
+Alpha star
+
+ align:start position:0%
+Alpha star
+ 
+
+ align:start position:0%
+Alpha star
+new Alpha so this gives you the
+
+ align:start position:0%
+new Alpha so this gives you the
+ 
+
+ align:start position:0%
+new Alpha so this gives you the
+transverse projector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now the claim by transverse project
+
+ align:start position:0%
+but now the claim by transverse project
+ 
+
+ align:start position:0%
+but now the claim by transverse project
+project is a little bit awkward to work
+
+ align:start position:0%
+project is a little bit awkward to work
+ 
+
+ align:start position:0%
+project is a little bit awkward to work
+with Okay but the claim
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+claim
+
+ align:start position:0%
+claim
+ 
+
+ align:start position:0%
+claim
+he said actually I can replace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sum of alpha equal to one Q
+
+ align:start position:0%
+the sum of alpha equal to one Q
+ 
+
+ align:start position:0%
+the sum of alpha equal to one Q
+by actually sum over Alpha for all
+
+ align:start position:0%
+by actually sum over Alpha for all
+ 
+
+ align:start position:0%
+by actually sum over Alpha for all
+polarizations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we'll make some of all
+
+ align:start position:0%
+so now we'll make some of all
+ 
+
+ align:start position:0%
+so now we'll make some of all
+polarizations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I sum of O Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then now do you know what is this do you
+
+ align:start position:0%
+then now do you know what is this do you
+ 
+
+ align:start position:0%
+then now do you know what is this do you
+remember what is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you just get this menu
+
+ align:start position:0%
+you just get this menu
+ 
+
+ align:start position:0%
+you just get this menu
+okay and this one is much simpler
+
+ align:start position:0%
+okay and this one is much simpler
+ 
+
+ align:start position:0%
+okay and this one is much simpler
+okay so now the claim
+
+ align:start position:0%
+okay so now the claim
+ 
+
+ align:start position:0%
+okay so now the claim
+okay so now the claim
+
+ align:start position:0%
+okay so now the claim
+ 
+
+ align:start position:0%
+okay so now the claim
+he said we can just simply replace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we can replace this by intermittent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so the
+
+ align:start position:0%
+so so the
+ 
+
+ align:start position:0%
+so so the
+yeah so this is the claim
+
+ align:start position:0%
+yeah so this is the claim
+ 
+
+ align:start position:0%
+yeah so this is the claim
+okay so this amounts to the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is equivalent to the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you look at the difference between
+
+ align:start position:0%
+so if you look at the difference between
+ 
+
+ align:start position:0%
+so if you look at the difference between
+these two
+
+ align:start position:0%
+these two
+ 
+
+ align:start position:0%
+these two
+so now if you look at the difference
+
+ align:start position:0%
+so now if you look at the difference
+ 
+
+ align:start position:0%
+so now if you look at the difference
+between the alpha you could do sum over
+
+ align:start position:0%
+between the alpha you could do sum over
+ 
+
+ align:start position:0%
+between the alpha you could do sum over
+1 2 and the alpha sum of O here
+
+ align:start position:0%
+1 2 and the alpha sum of O here
+ 
+
+ align:start position:0%
+1 2 and the alpha sum of O here
+so the difference in other words
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we claim
+
+ align:start position:0%
+we claim
+ 
+
+ align:start position:0%
+we claim
+that sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha equal to 0 and 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon
+
+ align:start position:0%
+Epsilon
+ 
+
+ align:start position:0%
+Epsilon
+Alpha star mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and Alpha Nu
+
+ align:start position:0%
+and Alpha Nu
+ 
+
+ align:start position:0%
+and Alpha Nu
+Alpha
+
+ align:start position:0%
+Alpha
+ 
+
+ align:start position:0%
+Alpha
+and new
+
+ align:start position:0%
+and new
+ 
+
+ align:start position:0%
+and new
+M new to be zero okay
+
+ align:start position:0%
+M new to be zero okay
+ 
+
+ align:start position:0%
+M new to be zero okay
+so so the thing so the difference
+
+ align:start position:0%
+so so the thing so the difference
+ 
+
+ align:start position:0%
+so so the thing so the difference
+between the two is just from sum 0 to 3
+
+ align:start position:0%
+between the two is just from sum 0 to 3
+ 
+
+ align:start position:0%
+between the two is just from sum 0 to 3
+okay so in other words
+
+ align:start position:0%
+okay so in other words
+ 
+
+ align:start position:0%
+okay so in other words
+so if I write down this explicitly
+
+ align:start position:0%
+so if I write down this explicitly
+ 
+
+ align:start position:0%
+so if I write down this explicitly
+okay so this corresponding to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this goes one into
+
+ align:start position:0%
+so so this goes one into
+ 
+
+ align:start position:0%
+so so this goes one into
+zero Epsilon mu 0 and mu
+
+ align:start position:0%
+zero Epsilon mu 0 and mu
+ 
+
+ align:start position:0%
+zero Epsilon mu 0 and mu
+squared is equal to
+
+ align:start position:0%
+squared is equal to
+ 
+
+ align:start position:0%
+squared is equal to
+Epsilon mu 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and mu
+
+ align:start position:0%
+and mu
+ 
+
+ align:start position:0%
+and mu
+squared okay
+
+ align:start position:0%
+squared okay
+ 
+
+ align:start position:0%
+squared okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so this claim
+
+ align:start position:0%
+so this claim
+ 
+
+ align:start position:0%
+so this claim
+is equivalent to this claim okay so so
+
+ align:start position:0%
+is equivalent to this claim okay so so
+ 
+
+ align:start position:0%
+is equivalent to this claim okay so so
+these two uh will cancel each other yeah
+
+ align:start position:0%
+these two uh will cancel each other yeah
+ 
+
+ align:start position:0%
+these two uh will cancel each other yeah
+the reason uh the equal here is because
+
+ align:start position:0%
+the reason uh the equal here is because
+ 
+
+ align:start position:0%
+the reason uh the equal here is because
+the the signature the zeros component
+
+ align:start position:0%
+the the signature the zeros component
+ 
+
+ align:start position:0%
+the the signature the zeros component
+there's a minus sign okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so it tells you that the sum of these
+
+ align:start position:0%
+so so it tells you that the sum of these
+ 
+
+ align:start position:0%
+so so it tells you that the sum of these
+two actually will cancel each other
+
+ align:start position:0%
+two actually will cancel each other
+ 
+
+ align:start position:0%
+two actually will cancel each other
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now let me remind you how we choose
+
+ align:start position:0%
+so now let me remind you how we choose
+ 
+
+ align:start position:0%
+so now let me remind you how we choose
+the uh the price yeah yeah now let me
+
+ align:start position:0%
+the uh the price yeah yeah now let me
+ 
+
+ align:start position:0%
+the uh the price yeah yeah now let me
+try to prove this fact
+
+ align:start position:0%
+try to prove this fact
+ 
+
+ align:start position:0%
+try to prove this fact
+okay it turns out this fact is actually
+
+ align:start position:0%
+okay it turns out this fact is actually
+ 
+
+ align:start position:0%
+okay it turns out this fact is actually
+uh uh very uh important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contain very important physics here okay
+
+ align:start position:0%
+contain very important physics here okay
+ 
+
+ align:start position:0%
+contain very important physics here okay
+so do you have any questions before I do
+
+ align:start position:0%
+so do you have any questions before I do
+ 
+
+ align:start position:0%
+so do you have any questions before I do
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good
+
+ align:start position:0%
+okay good
+ 
+
+ align:start position:0%
+okay good
+so so so now let me try to try to show
+
+ align:start position:0%
+so so so now let me try to try to show
+ 
+
+ align:start position:0%
+so so so now let me try to try to show
+this is true okay
+
+ align:start position:0%
+this is true okay
+ 
+
+ align:start position:0%
+this is true okay
+so let me just remind you of a
+
+ align:start position:0%
+so let me just remind you of a
+ 
+
+ align:start position:0%
+so let me just remind you of a
+convention
+
+ align:start position:0%
+convention
+ 
+
+ align:start position:0%
+convention
+he said mu
+
+ align:start position:0%
+he said mu
+ 
+
+ align:start position:0%
+he said mu
+0 is equal to just zero just just one
+
+ align:start position:0%
+0 is equal to just zero just just one
+ 
+
+ align:start position:0%
+0 is equal to just zero just just one
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+and a mu 3
+
+ align:start position:0%
+and a mu 3
+ 
+
+ align:start position:0%
+and a mu 3
+is equal to zero and then in the
+
+ align:start position:0%
+is equal to zero and then in the
+ 
+
+ align:start position:0%
+is equal to zero and then in the
+direction of the k
+
+ align:start position:0%
+direction of the k
+ 
+
+ align:start position:0%
+direction of the k
+okay it's in the direction okay
+
+ align:start position:0%
+okay it's in the direction okay
+ 
+
+ align:start position:0%
+okay it's in the direction okay
+okay and the the the Epsilon view one
+
+ align:start position:0%
+okay and the the the Epsilon view one
+ 
+
+ align:start position:0%
+okay and the the the Epsilon view one
+two will be orthogonal to both of them
+
+ align:start position:0%
+two will be orthogonal to both of them
+ 
+
+ align:start position:0%
+two will be orthogonal to both of them
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yes I'm going to both of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now to see this equation let me call
+
+ align:start position:0%
+so now to see this equation let me call
+ 
+
+ align:start position:0%
+so now to see this equation let me call
+this equation star star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's consider just uh a general
+
+ align:start position:0%
+so let's consider just uh a general
+ 
+
+ align:start position:0%
+so let's consider just uh a general
+physical process
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can actually make a general statement
+
+ align:start position:0%
+we can actually make a general statement
+ 
+
+ align:start position:0%
+we can actually make a general statement
+okay not just restricted to to that
+
+ align:start position:0%
+okay not just restricted to to that
+ 
+
+ align:start position:0%
+okay not just restricted to to that
+particular example we have here so let's
+
+ align:start position:0%
+particular example we have here so let's
+ 
+
+ align:start position:0%
+particular example we have here so let's
+just consider some some general process
+
+ align:start position:0%
+just consider some some general process
+ 
+
+ align:start position:0%
+just consider some some general process
+so you have some advantage of initial
+
+ align:start position:0%
+so you have some advantage of initial
+ 
+
+ align:start position:0%
+so you have some advantage of initial
+States and go some parallel States
+
+ align:start position:0%
+States and go some parallel States
+ 
+
+ align:start position:0%
+States and go some parallel States
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but imagine one of the initial state is
+
+ align:start position:0%
+but imagine one of the initial state is
+ 
+
+ align:start position:0%
+but imagine one of the initial state is
+a photon
+
+ align:start position:0%
+a photon
+ 
+
+ align:start position:0%
+a photon
+is the one we are interested here with
+
+ align:start position:0%
+is the one we are interested here with
+ 
+
+ align:start position:0%
+is the one we are interested here with
+polarization K Alpha
+
+ align:start position:0%
+polarization K Alpha
+ 
+
+ align:start position:0%
+polarization K Alpha
+okay before it doesn't get off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+so now the uh the amplitude
+
+ align:start position:0%
+so now the uh the amplitude
+ 
+
+ align:start position:0%
+so now the uh the amplitude
+it just become
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mu and then this is the same
+
+ align:start position:0%
+mu and then this is the same
+ 
+
+ align:start position:0%
+mu and then this is the same
+okay as the
+
+ align:start position:0%
+okay as the
+ 
+
+ align:start position:0%
+okay as the
+you have some
+
+ align:start position:0%
+you have some
+ 
+
+ align:start position:0%
+you have some
+final stage
+
+ align:start position:0%
+final stage
+ 
+
+ align:start position:0%
+final stage
+and then you have some initial state
+
+ align:start position:0%
+and then you have some initial state
+ 
+
+ align:start position:0%
+and then you have some initial state
+but within the initial State there's a k
+
+ align:start position:0%
+but within the initial State there's a k
+ 
+
+ align:start position:0%
+but within the initial State there's a k
+Alpha state
+
+ align:start position:0%
+Alpha state
+ 
+
+ align:start position:0%
+Alpha state
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+the K of a state equals one into the
+
+ align:start position:0%
+the K of a state equals one into the
+ 
+
+ align:start position:0%
+the K of a state equals one into the
+photon
+
+ align:start position:0%
+photon
+ 
+
+ align:start position:0%
+photon
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now remember
+
+ align:start position:0%
+but now remember
+ 
+
+ align:start position:0%
+but now remember
+which we discussed in your homework okay
+
+ align:start position:0%
+which we discussed in your homework okay
+ 
+
+ align:start position:0%
+which we discussed in your homework okay
+so that's the purpose of to put it in
+
+ align:start position:0%
+so that's the purpose of to put it in
+ 
+
+ align:start position:0%
+so that's the purpose of to put it in
+your homework
+
+ align:start position:0%
+your homework
+ 
+
+ align:start position:0%
+your homework
+that the final States
+
+ align:start position:0%
+that the final States
+ 
+
+ align:start position:0%
+that the final States
+for K Alpha
+
+ align:start position:0%
+for K Alpha
+ 
+
+ align:start position:0%
+for K Alpha
+which defined by transverse polarization
+
+ align:start position:0%
+which defined by transverse polarization
+ 
+
+ align:start position:0%
+which defined by transverse polarization
+is only
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a representative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the equivalence class of states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and within the this equivalence class
+
+ align:start position:0%
+and within the this equivalence class
+ 
+
+ align:start position:0%
+and within the this equivalence class
+they are rated by this code now States
+
+ align:start position:0%
+they are rated by this code now States
+ 
+
+ align:start position:0%
+they are rated by this code now States
+okay so so so the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the um
+
+ align:start position:0%
+so the um
+ 
+
+ align:start position:0%
+so the um
+so we can shift it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by law states the physics will be the
+
+ align:start position:0%
+by law states the physics will be the
+ 
+
+ align:start position:0%
+by law states the physics will be the
+same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now remember the last state is like
+
+ align:start position:0%
+so now remember the last state is like
+ 
+
+ align:start position:0%
+so now remember the last state is like
+it's aggregate transformation
+
+ align:start position:0%
+it's aggregate transformation
+ 
+
+ align:start position:0%
+it's aggregate transformation
+so the last States corresponding to and
+
+ align:start position:0%
+so the last States corresponding to and
+ 
+
+ align:start position:0%
+so the last States corresponding to and
+this process because why don't you
+
+ align:start position:0%
+this process because why don't you
+ 
+
+ align:start position:0%
+this process because why don't you
+change your initial you change your
+
+ align:start position:0%
+change your initial you change your
+ 
+
+ align:start position:0%
+change your initial you change your
+polarization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+that corresponding to your last state
+
+ align:start position:0%
+that corresponding to your last state
+ 
+
+ align:start position:0%
+that corresponding to your last state
+and now State uh the feature is that
+
+ align:start position:0%
+and now State uh the feature is that
+ 
+
+ align:start position:0%
+and now State uh the feature is that
+it's a authorizations proportional to
+
+ align:start position:0%
+it's a authorizations proportional to
+ 
+
+ align:start position:0%
+it's a authorizations proportional to
+the momentum
+
+ align:start position:0%
+the momentum
+ 
+
+ align:start position:0%
+the momentum
+okay so that's how we are uh uh yeah
+
+ align:start position:0%
+okay so that's how we are uh uh yeah
+ 
+
+ align:start position:0%
+okay so that's how we are uh uh yeah
+remember we showed that yeah because
+
+ align:start position:0%
+remember we showed that yeah because
+ 
+
+ align:start position:0%
+remember we showed that yeah because
+this is like a gay transformation
+
+ align:start position:0%
+this is like a gay transformation
+ 
+
+ align:start position:0%
+this is like a gay transformation
+and this is aggregate transmission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the under the uh we also discussed
+
+ align:start position:0%
+and the under the uh we also discussed
+ 
+
+ align:start position:0%
+and the under the uh we also discussed
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+yeah the reason this is the equivalence
+
+ align:start position:0%
+yeah the reason this is the equivalence
+ 
+
+ align:start position:0%
+yeah the reason this is the equivalence
+class because when you shift parallel
+
+ align:start position:0%
+class because when you shift parallel
+ 
+
+ align:start position:0%
+class because when you shift parallel
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+the overlap between the last days to any
+
+ align:start position:0%
+the overlap between the last days to any
+ 
+
+ align:start position:0%
+the overlap between the last days to any
+to any state is zero okay to any state
+
+ align:start position:0%
+to any state is zero okay to any state
+ 
+
+ align:start position:0%
+to any state is zero okay to any state
+it's still and so you can uh shift by
+
+ align:start position:0%
+it's still and so you can uh shift by
+ 
+
+ align:start position:0%
+it's still and so you can uh shift by
+alarms state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the fact that you can shift this very
+
+ align:start position:0%
+so the fact that you can shift this very
+ 
+
+ align:start position:0%
+so the fact that you can shift this very
+last stage your physics is the same
+
+ align:start position:0%
+last stage your physics is the same
+ 
+
+ align:start position:0%
+last stage your physics is the same
+so now use this equation to here
+
+ align:start position:0%
+so now use this equation to here
+ 
+
+ align:start position:0%
+so now use this equation to here
+so this implies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this implies
+
+ align:start position:0%
+so this implies
+ 
+
+ align:start position:0%
+so this implies
+that M View
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K mu must be zero
+
+ align:start position:0%
+K mu must be zero
+ 
+
+ align:start position:0%
+K mu must be zero
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+the MB will KB must be zero
+
+ align:start position:0%
+the MB will KB must be zero
+ 
+
+ align:start position:0%
+the MB will KB must be zero
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and this is a very important identity
+
+ align:start position:0%
+and this is a very important identity
+ 
+
+ align:start position:0%
+and this is a very important identity
+this is called World identity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because this is a very important feature
+
+ align:start position:0%
+because this is a very important feature
+ 
+
+ align:start position:0%
+because this is a very important feature
+which are which can simplify your
+
+ align:start position:0%
+which are which can simplify your
+ 
+
+ align:start position:0%
+which are which can simplify your
+calculation a lot okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so the MU must satisfy the feature
+
+ align:start position:0%
+so so the MU must satisfy the feature
+ 
+
+ align:start position:0%
+so so the MU must satisfy the feature
+that when it contract with this K mu you
+
+ align:start position:0%
+that when it contract with this K mu you
+ 
+
+ align:start position:0%
+that when it contract with this K mu you
+get zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now remember the K mu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they just equal to
+
+ align:start position:0%
+they just equal to
+ 
+
+ align:start position:0%
+they just equal to
+so this is anxious external state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+or manners yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this is the answer external state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then this is just given by
+
+ align:start position:0%
+and then this is just given by
+ 
+
+ align:start position:0%
+and then this is just given by
+if I take a factor k out
+
+ align:start position:0%
+if I take a factor k out
+ 
+
+ align:start position:0%
+if I take a factor k out
+and this given by minus one and then K
+
+ align:start position:0%
+and this given by minus one and then K
+ 
+
+ align:start position:0%
+and this given by minus one and then K
+and the k
+
+ align:start position:0%
+and the k
+ 
+
+ align:start position:0%
+and the k
+and this is the fact that I think we
+
+ align:start position:0%
+and this is the fact that I think we
+ 
+
+ align:start position:0%
+and this is the fact that I think we
+also used in your P set and this is the
+
+ align:start position:0%
+also used in your P set and this is the
+ 
+
+ align:start position:0%
+also used in your P set and this is the
+say and this thing is just the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the difference
+
+ align:start position:0%
+as the difference
+ 
+
+ align:start position:0%
+as the difference
+between the zeros validation vector and
+
+ align:start position:0%
+between the zeros validation vector and
+ 
+
+ align:start position:0%
+between the zeros validation vector and
+the third one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay from what we wrote here
+
+ align:start position:0%
+okay from what we wrote here
+ 
+
+ align:start position:0%
+okay from what we wrote here
+well I think I I get the
+
+ align:start position:0%
+well I think I I get the
+ 
+
+ align:start position:0%
+well I think I I get the
+sign
+
+ align:start position:0%
+sign
+ 
+
+ align:start position:0%
+sign
+yeah the sign does not matter very much
+
+ align:start position:0%
+yeah the sign does not matter very much
+ 
+
+ align:start position:0%
+yeah the sign does not matter very much
+here let me just make sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah for my sign this would be yeah yeah
+
+ align:start position:0%
+yeah for my sign this would be yeah yeah
+ 
+
+ align:start position:0%
+yeah for my sign this would be yeah yeah
+yeah yeah yeah it's minus absolute
+
+ align:start position:0%
+yeah yeah yeah it's minus absolute
+ 
+
+ align:start position:0%
+yeah yeah yeah it's minus absolute
+that's right
+
+ align:start position:0%
+that's right
+ 
+
+ align:start position:0%
+that's right
+so so from here
+
+ align:start position:0%
+so so from here
+ 
+
+ align:start position:0%
+so so from here
+and then this equation then it just
+
+ align:start position:0%
+and then this equation then it just
+ 
+
+ align:start position:0%
+and then this equation then it just
+implies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the Epsilon mu zero
+
+ align:start position:0%
+that the Epsilon mu zero
+ 
+
+ align:start position:0%
+that the Epsilon mu zero
+mu is equal to Epsilon mu3
+
+ align:start position:0%
+mu is equal to Epsilon mu3
+ 
+
+ align:start position:0%
+mu is equal to Epsilon mu3
+and mu
+
+ align:start position:0%
+and mu
+ 
+
+ align:start position:0%
+and mu
+so that tells you that Epsom mu zero
+
+ align:start position:0%
+so that tells you that Epsom mu zero
+ 
+
+ align:start position:0%
+so that tells you that Epsom mu zero
+Square mu
+
+ align:start position:0%
+Square mu
+ 
+
+ align:start position:0%
+Square mu
+squared is equal to Epsilon mu 3 and mu
+
+ align:start position:0%
+squared is equal to Epsilon mu 3 and mu
+ 
+
+ align:start position:0%
+squared is equal to Epsilon mu 3 and mu
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+okay so this is the one we wanted to
+
+ align:start position:0%
+okay so this is the one we wanted to
+ 
+
+ align:start position:0%
+okay so this is the one we wanted to
+prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is the one we wanted to
+
+ align:start position:0%
+okay so this is the one we wanted to
+ 
+
+ align:start position:0%
+okay so this is the one we wanted to
+prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this simplifies life a lot
+
+ align:start position:0%
+so this simplifies life a lot
+ 
+
+ align:start position:0%
+so this simplifies life a lot
+okay and so so now we show that we can
+
+ align:start position:0%
+okay and so so now we show that we can
+ 
+
+ align:start position:0%
+okay and so so now we show that we can
+actually make this replacement
+
+ align:start position:0%
+actually make this replacement
+ 
+
+ align:start position:0%
+actually make this replacement
+okay because the zero and three
+
+ align:start position:0%
+okay because the zero and three
+ 
+
+ align:start position:0%
+okay because the zero and three
+components are together become actually
+
+ align:start position:0%
+components are together become actually
+ 
+
+ align:start position:0%
+components are together become actually
+a law vector and that's actually uh uh
+
+ align:start position:0%
+a law vector and that's actually uh uh
+ 
+
+ align:start position:0%
+a law vector and that's actually uh uh
+uh uh does not contribute
+
+ align:start position:0%
+uh uh does not contribute
+ 
+
+ align:start position:0%
+uh uh does not contribute
+so now now this amplitude we have two
+
+ align:start position:0%
+so now now this amplitude we have two
+ 
+
+ align:start position:0%
+so now now this amplitude we have two
+external photons
+
+ align:start position:0%
+external photons
+ 
+
+ align:start position:0%
+external photons
+so we can write it as okay so for
+
+ align:start position:0%
+so we can write it as okay so for
+ 
+
+ align:start position:0%
+so we can write it as okay so for
+Simplicity
+
+ align:start position:0%
+Simplicity
+ 
+
+ align:start position:0%
+Simplicity
+so so for our amplitude
+
+ align:start position:0%
+so so for our amplitude
+ 
+
+ align:start position:0%
+so so for our amplitude
+so back
+
+ align:start position:0%
+so back
+ 
+
+ align:start position:0%
+so back
+to competent case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to the competent story
+
+ align:start position:0%
+to the competent story
+ 
+
+ align:start position:0%
+to the competent story
+and then then the amplitude then have
+
+ align:start position:0%
+and then then the amplitude then have
+ 
+
+ align:start position:0%
+and then then the amplitude then have
+the form
+
+ align:start position:0%
+the form
+ 
+
+ align:start position:0%
+the form
+so we have two
+
+ align:start position:0%
+so we have two
+ 
+
+ align:start position:0%
+so we have two
+so I have Epsilon Mu Alpha 2
+
+ align:start position:0%
+so I have Epsilon Mu Alpha 2
+ 
+
+ align:start position:0%
+so I have Epsilon Mu Alpha 2
+star and Epsilon Nu alpha 1 and then
+
+ align:start position:0%
+star and Epsilon Nu alpha 1 and then
+ 
+
+ align:start position:0%
+star and Epsilon Nu alpha 1 and then
+this will multiply some team removed
+
+ align:start position:0%
+this will multiply some team removed
+ 
+
+ align:start position:0%
+this will multiply some team removed
+okay so I call the rest Timmy mu
+
+ align:start position:0%
+okay so I call the rest Timmy mu
+ 
+
+ align:start position:0%
+okay so I call the rest Timmy mu
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+when I do the spin sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I can just
+
+ align:start position:0%
+then I can just
+ 
+
+ align:start position:0%
+then I can just
+use this twice okay for for each Epsilon
+
+ align:start position:0%
+use this twice okay for for each Epsilon
+ 
+
+ align:start position:0%
+use this twice okay for for each Epsilon
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then I just get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+essentially I just get the uh uh so this
+
+ align:start position:0%
+essentially I just get the uh uh so this
+ 
+
+ align:start position:0%
+essentially I just get the uh uh so this
+I will yeah let me just write one more
+
+ align:start position:0%
+I will yeah let me just write one more
+ 
+
+ align:start position:0%
+I will yeah let me just write one more
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+I will get Alpha One
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha 2 equal to one to two
+
+ align:start position:0%
+Alpha 2 equal to one to two
+ 
+
+ align:start position:0%
+Alpha 2 equal to one to two
+then I have Epsilon
+
+ align:start position:0%
+then I have Epsilon
+ 
+
+ align:start position:0%
+then I have Epsilon
+Mu Alpha
+
+ align:start position:0%
+Mu Alpha
+ 
+
+ align:start position:0%
+Mu Alpha
+Q star
+
+ align:start position:0%
+Q star
+ 
+
+ align:start position:0%
+Q star
+Epsilon Lambda Alpha Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so epsilonu upper 1
+
+ align:start position:0%
+and so epsilonu upper 1
+ 
+
+ align:start position:0%
+and so epsilonu upper 1
+Epsilon rho
+
+ align:start position:0%
+Epsilon rho
+ 
+
+ align:start position:0%
+Epsilon rho
+of one star
+
+ align:start position:0%
+of one star
+ 
+
+ align:start position:0%
+of one star
+and then I have t mu Nu
+
+ align:start position:0%
+and then I have t mu Nu
+ 
+
+ align:start position:0%
+and then I have t mu Nu
+Chi Lambda row star
+
+ align:start position:0%
+Chi Lambda row star
+ 
+
+ align:start position:0%
+Chi Lambda row star
+okay I just Square this guy
+
+ align:start position:0%
+okay I just Square this guy
+ 
+
+ align:start position:0%
+okay I just Square this guy
+and now I can replace this where Lambda
+
+ align:start position:0%
+and now I can replace this where Lambda
+ 
+
+ align:start position:0%
+and now I can replace this where Lambda
+I can replace by Ether Mutual okay so
+
+ align:start position:0%
+I can replace by Ether Mutual okay so
+ 
+
+ align:start position:0%
+I can replace by Ether Mutual okay so
+and then this just become equal to
+
+ align:start position:0%
+and then this just become equal to
+ 
+
+ align:start position:0%
+and then this just become equal to
+Lambda
+
+ align:start position:0%
+Lambda
+ 
+
+ align:start position:0%
+Lambda
+row
+
+ align:start position:0%
+row
+ 
+
+ align:start position:0%
+row
+and T
+
+ align:start position:0%
+and T
+ 
+
+ align:start position:0%
+and T
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+row
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so
+
+ align:start position:0%
+so so
+ 
+
+ align:start position:0%
+so so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so this just makes a a life much easier
+
+ align:start position:0%
+so this just makes a a life much easier
+ 
+
+ align:start position:0%
+so this just makes a a life much easier
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+next life much easier
+
+ align:start position:0%
+next life much easier
+ 
+
+ align:start position:0%
+next life much easier
+so uh um yeah so
+
+ align:start position:0%
+so uh um yeah so
+ 
+
+ align:start position:0%
+so uh um yeah so
+essentially these are the two important
+
+ align:start position:0%
+essentially these are the two important
+ 
+
+ align:start position:0%
+essentially these are the two important
+tricks which one need to do in the
+
+ align:start position:0%
+tricks which one need to do in the
+ 
+
+ align:start position:0%
+tricks which one need to do in the
+photon in this competent case compared
+
+ align:start position:0%
+photon in this competent case compared
+ 
+
+ align:start position:0%
+photon in this competent case compared
+with this story
+
+ align:start position:0%
+with this story
+ 
+
+ align:start position:0%
+with this story
+and once you have this
+
+ align:start position:0%
+and once you have this
+ 
+
+ align:start position:0%
+and once you have this
+and this part will be just the spin
+
+ align:start position:0%
+and this part will be just the spin
+ 
+
+ align:start position:0%
+and this part will be just the spin
+sound
+
+ align:start position:0%
+sound
+ 
+
+ align:start position:0%
+sound
+for the for the uh for the formula and
+
+ align:start position:0%
+for the for the uh for the formula and
+ 
+
+ align:start position:0%
+for the for the uh for the formula and
+then that we can just use the same trick
+
+ align:start position:0%
+then that we can just use the same trick
+ 
+
+ align:start position:0%
+then that we can just use the same trick
+as we did last time okay so we will not
+
+ align:start position:0%
+as we did last time okay so we will not
+ 
+
+ align:start position:0%
+as we did last time okay so we will not
+repeat that
+
+ align:start position:0%
+repeat that
+ 
+
+ align:start position:0%
+repeat that
+so now let me just write down your final
+
+ align:start position:0%
+so now let me just write down your final
+ 
+
+ align:start position:0%
+so now let me just write down your final
+answer okay and now we can just write
+
+ align:start position:0%
+answer okay and now we can just write
+ 
+
+ align:start position:0%
+answer okay and now we can just write
+down the final answer
+
+ align:start position:0%
+down the final answer
+ 
+
+ align:start position:0%
+down the final answer
+so before writing down the final answer
+
+ align:start position:0%
+so before writing down the final answer
+ 
+
+ align:start position:0%
+so before writing down the final answer
+let me just uh Define the frame
+
+ align:start position:0%
+let me just uh Define the frame
+ 
+
+ align:start position:0%
+let me just uh Define the frame
+so for the component scattering it's
+
+ align:start position:0%
+so for the component scattering it's
+ 
+
+ align:start position:0%
+so for the component scattering it's
+often convenient
+
+ align:start position:0%
+often convenient
+ 
+
+ align:start position:0%
+often convenient
+you can see the the rest frame of the
+
+ align:start position:0%
+you can see the the rest frame of the
+ 
+
+ align:start position:0%
+you can see the the rest frame of the
+electron so we can see the photon
+
+ align:start position:0%
+electron so we can see the photon
+ 
+
+ align:start position:0%
+electron so we can see the photon
+because there's no rice frame for Photon
+
+ align:start position:0%
+because there's no rice frame for Photon
+ 
+
+ align:start position:0%
+because there's no rice frame for Photon
+okay so it's often convenient to
+
+ align:start position:0%
+okay so it's often convenient to
+ 
+
+ align:start position:0%
+okay so it's often convenient to
+consider the rest frame of the electron
+
+ align:start position:0%
+consider the rest frame of the electron
+ 
+
+ align:start position:0%
+consider the rest frame of the electron
+so let's just consider the picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is often uh the way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+roughly
+
+ align:start position:0%
+roughly
+ 
+
+ align:start position:0%
+roughly
+often also experiment is done
+
+ align:start position:0%
+often also experiment is done
+ 
+
+ align:start position:0%
+often also experiment is done
+okay so you can essentially consider the
+
+ align:start position:0%
+okay so you can essentially consider the
+ 
+
+ align:start position:0%
+okay so you can essentially consider the
+say electron in the matter and which
+
+ align:start position:0%
+say electron in the matter and which
+ 
+
+ align:start position:0%
+say electron in the matter and which
+they don't have much velocity and then
+
+ align:start position:0%
+they don't have much velocity and then
+ 
+
+ align:start position:0%
+they don't have much velocity and then
+you can have a photon coming yes imagine
+
+ align:start position:0%
+you can have a photon coming yes imagine
+ 
+
+ align:start position:0%
+you can have a photon coming yes imagine
+you have an electron here
+
+ align:start position:0%
+you have an electron here
+ 
+
+ align:start position:0%
+you have an electron here
+and you have a photon come in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if you have a photon come in so
+
+ align:start position:0%
+okay if you have a photon come in so
+ 
+
+ align:start position:0%
+okay if you have a photon come in so
+let's call this uh the incoming access
+
+ align:start position:0%
+let's call this uh the incoming access
+ 
+
+ align:start position:0%
+let's call this uh the incoming access
+to be the z-axis
+
+ align:start position:0%
+to be the z-axis
+ 
+
+ align:start position:0%
+to be the z-axis
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then then after the scatter in the
+
+ align:start position:0%
+and then then after the scatter in the
+ 
+
+ align:start position:0%
+and then then after the scatter in the
+photon
+
+ align:start position:0%
+photon
+ 
+
+ align:start position:0%
+photon
+say will be scattered into this
+
+ align:start position:0%
+say will be scattered into this
+ 
+
+ align:start position:0%
+say will be scattered into this
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+okay so let's call this device
+
+ align:start position:0%
+okay so let's call this device
+ 
+
+ align:start position:0%
+okay so let's call this device
+okay so yeah okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this setup
+
+ align:start position:0%
+so in this setup
+ 
+
+ align:start position:0%
+so in this setup
+so let's then the momentum of electron
+
+ align:start position:0%
+so let's then the momentum of electron
+ 
+
+ align:start position:0%
+so let's then the momentum of electron
+it's just the m0
+
+ align:start position:0%
+it's just the m0
+ 
+
+ align:start position:0%
+it's just the m0
+okay just the mass of the momentum or I
+
+ align:start position:0%
+okay just the mass of the momentum or I
+ 
+
+ align:start position:0%
+okay just the mass of the momentum or I
+erased the how I label the momentum
+
+ align:start position:0%
+erased the how I label the momentum
+ 
+
+ align:start position:0%
+erased the how I label the momentum
+and the momentum of the photon incoming
+
+ align:start position:0%
+and the momentum of the photon incoming
+ 
+
+ align:start position:0%
+and the momentum of the photon incoming
+Photon P2
+
+ align:start position:0%
+Photon P2
+ 
+
+ align:start position:0%
+Photon P2
+would be just Omega
+
+ align:start position:0%
+would be just Omega
+ 
+
+ align:start position:0%
+would be just Omega
+0 0
+
+ align:start position:0%
+0 0
+ 
+
+ align:start position:0%
+0 0
+Omega okay so only I have the momentum
+
+ align:start position:0%
+Omega okay so only I have the momentum
+ 
+
+ align:start position:0%
+Omega okay so only I have the momentum
+in the Z Direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then then
+
+ align:start position:0%
+and then then
+ 
+
+ align:start position:0%
+and then then
+the final momentum with the electron is
+
+ align:start position:0%
+the final momentum with the electron is
+ 
+
+ align:start position:0%
+the final momentum with the electron is
+K mu okay one
+
+ align:start position:0%
+K mu okay one
+ 
+
+ align:start position:0%
+K mu okay one
+so this can be something okay so let's
+
+ align:start position:0%
+so this can be something okay so let's
+ 
+
+ align:start position:0%
+so this can be something okay so let's
+not worry about it then for the for the
+
+ align:start position:0%
+not worry about it then for the for the
+ 
+
+ align:start position:0%
+not worry about it then for the for the
+photon
+
+ align:start position:0%
+photon
+ 
+
+ align:start position:0%
+photon
+the photon momentum final Photon
+
+ align:start position:0%
+the photon momentum final Photon
+ 
+
+ align:start position:0%
+the photon momentum final Photon
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+so let's call it yeah so this is K2
+
+ align:start position:0%
+so let's call it yeah so this is K2
+ 
+
+ align:start position:0%
+so let's call it yeah so this is K2
+okay so K2 we can parameterize it by
+
+ align:start position:0%
+okay so K2 we can parameterize it by
+ 
+
+ align:start position:0%
+okay so K2 we can parameterize it by
+Omega Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+Omega Prime
+
+ align:start position:0%
+Omega Prime
+ 
+
+ align:start position:0%
+Omega Prime
+then going into the uh the the spatial
+
+ align:start position:0%
+then going into the uh the the spatial
+ 
+
+ align:start position:0%
+then going into the uh the the spatial
+uh uh Direction the unit Vector in the
+
+ align:start position:0%
+uh uh Direction the unit Vector in the
+ 
+
+ align:start position:0%
+uh uh Direction the unit Vector in the
+spatial direction for K2 let's call it n
+
+ align:start position:0%
+spatial direction for K2 let's call it n
+ 
+
+ align:start position:0%
+spatial direction for K2 let's call it n
+okay so this is the direction of n which
+
+ align:start position:0%
+okay so this is the direction of n which
+ 
+
+ align:start position:0%
+okay so this is the direction of n which
+is the Theta angle with respect to the Z
+
+ align:start position:0%
+is the Theta angle with respect to the Z
+ 
+
+ align:start position:0%
+is the Theta angle with respect to the Z
+Direction okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then the k y and just can be
+
+ align:start position:0%
+and then the k y and just can be
+ 
+
+ align:start position:0%
+and then the k y and just can be
+obtained by by momentum connivation from
+
+ align:start position:0%
+obtained by by momentum connivation from
+ 
+
+ align:start position:0%
+obtained by by momentum connivation from
+these quantities okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so K1
+
+ align:start position:0%
+so so K1
+ 
+
+ align:start position:0%
+so so K1
+would be just P1 plus P2 minus K2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so from the fact that the electron have
+
+ align:start position:0%
+so from the fact that the electron have
+ 
+
+ align:start position:0%
+so from the fact that the electron have
+a static Mass
+
+ align:start position:0%
+a static Mass
+ 
+
+ align:start position:0%
+a static Mass
+minus M Square
+
+ align:start position:0%
+minus M Square
+ 
+
+ align:start position:0%
+minus M Square
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so so you can uh uh and then this
+
+ align:start position:0%
+so so so you can uh uh and then this
+ 
+
+ align:start position:0%
+so so so you can uh uh and then this
+relation
+
+ align:start position:0%
+relation
+ 
+
+ align:start position:0%
+relation
+then the P1 plus P2 minus K2 should
+
+ align:start position:0%
+then the P1 plus P2 minus K2 should
+ 
+
+ align:start position:0%
+then the P1 plus P2 minus K2 should
+satisfy the constraint that this should
+
+ align:start position:0%
+satisfy the constraint that this should
+ 
+
+ align:start position:0%
+satisfy the constraint that this should
+be equal to minus M squared
+
+ align:start position:0%
+be equal to minus M squared
+ 
+
+ align:start position:0%
+be equal to minus M squared
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should satisfy the exchange
+
+ align:start position:0%
+should satisfy the exchange
+ 
+
+ align:start position:0%
+should satisfy the exchange
+from this equation you can actually
+
+ align:start position:0%
+from this equation you can actually
+ 
+
+ align:start position:0%
+from this equation you can actually
+consol
+
+ align:start position:0%
+consol
+ 
+
+ align:start position:0%
+consol
+Omega Prime
+
+ align:start position:0%
+Omega Prime
+ 
+
+ align:start position:0%
+Omega Prime
+in terms of Omega okay so we are not
+
+ align:start position:0%
+in terms of Omega okay so we are not
+ 
+
+ align:start position:0%
+in terms of Omega okay so we are not
+write down this equation explicitly you
+
+ align:start position:0%
+write down this equation explicitly you
+ 
+
+ align:start position:0%
+write down this equation explicitly you
+can easily check yourself
+
+ align:start position:0%
+can easily check yourself
+ 
+
+ align:start position:0%
+can easily check yourself
+okay you can usually check yourself
+
+ align:start position:0%
+okay you can usually check yourself
+ 
+
+ align:start position:0%
+okay you can usually check yourself
+so you find the Omega Prime is equal to
+
+ align:start position:0%
+so you find the Omega Prime is equal to
+ 
+
+ align:start position:0%
+so you find the Omega Prime is equal to
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+divided by 1 plus
+
+ align:start position:0%
+divided by 1 plus
+ 
+
+ align:start position:0%
+divided by 1 plus
+Omega m
+
+ align:start position:0%
+Omega m
+ 
+
+ align:start position:0%
+Omega m
+and Y minus cosine Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+so this is the final frequency
+
+ align:start position:0%
+so this is the final frequency
+ 
+
+ align:start position:0%
+so this is the final frequency
+of the photon
+
+ align:start position:0%
+of the photon
+ 
+
+ align:start position:0%
+of the photon
+okay expressed
+
+ align:start position:0%
+okay expressed
+ 
+
+ align:start position:0%
+okay expressed
+in terms of the initial frequency of the
+
+ align:start position:0%
+in terms of the initial frequency of the
+ 
+
+ align:start position:0%
+in terms of the initial frequency of the
+photon and the mass of the electron and
+
+ align:start position:0%
+photon and the mass of the electron and
+ 
+
+ align:start position:0%
+photon and the mass of the electron and
+then this scattering angle Theta okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+let me just write down the final answer
+
+ align:start position:0%
+let me just write down the final answer
+ 
+
+ align:start position:0%
+let me just write down the final answer
+with this setup
+
+ align:start position:0%
+with this setup
+ 
+
+ align:start position:0%
+with this setup
+and then you find in the right in the
+
+ align:start position:0%
+and then you find in the right in the
+ 
+
+ align:start position:0%
+and then you find in the right in the
+rest frame of electron
+
+ align:start position:0%
+rest frame of electron
+ 
+
+ align:start position:0%
+rest frame of electron
+the differential cross-section can be
+
+ align:start position:0%
+the differential cross-section can be
+ 
+
+ align:start position:0%
+the differential cross-section can be
+written
+
+ align:start position:0%
+written
+ 
+
+ align:start position:0%
+written
+so so again the the Phi direction would
+
+ align:start position:0%
+so so again the the Phi direction would
+ 
+
+ align:start position:0%
+so so again the the Phi direction would
+be symmetric okay
+
+ align:start position:0%
+be symmetric okay
+ 
+
+ align:start position:0%
+be symmetric okay
+and so so let's only worry about the
+
+ align:start position:0%
+and so so let's only worry about the
+ 
+
+ align:start position:0%
+and so so let's only worry about the
+in the Theta Direction so this can be
+
+ align:start position:0%
+in the Theta Direction so this can be
+ 
+
+ align:start position:0%
+in the Theta Direction so this can be
+written as
+
+ align:start position:0%
+written as
+ 
+
+ align:start position:0%
+written as
+Pi Alpha Square so Alpha Square the
+
+ align:start position:0%
+Pi Alpha Square so Alpha Square the
+ 
+
+ align:start position:0%
+Pi Alpha Square so Alpha Square the
+alpha against fine structure constant
+
+ align:start position:0%
+alpha against fine structure constant
+ 
+
+ align:start position:0%
+alpha against fine structure constant
+divided by m Square
+
+ align:start position:0%
+divided by m Square
+ 
+
+ align:start position:0%
+divided by m Square
+and then given by Omega Prime
+
+ align:start position:0%
+and then given by Omega Prime
+ 
+
+ align:start position:0%
+and then given by Omega Prime
+the final momentum frequency
+
+ align:start position:0%
+the final momentum frequency
+ 
+
+ align:start position:0%
+the final momentum frequency
+for the photon divided by Omega Square
+
+ align:start position:0%
+for the photon divided by Omega Square
+ 
+
+ align:start position:0%
+for the photon divided by Omega Square
+and Omega Prime
+
+ align:start position:0%
+and Omega Prime
+ 
+
+ align:start position:0%
+and Omega Prime
+divided by Omega and Omega Omega Prime
+
+ align:start position:0%
+divided by Omega and Omega Omega Prime
+ 
+
+ align:start position:0%
+divided by Omega and Omega Omega Prime
+minus sine squares
+
+ align:start position:0%
+minus sine squares
+ 
+
+ align:start position:0%
+minus sine squares
+okay so this is the final answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is the final answer for the
+
+ align:start position:0%
+okay so this is the final answer for the
+ 
+
+ align:start position:0%
+okay so this is the final answer for the
+confidence question the cross section
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this formula actually contains
+
+ align:start position:0%
+okay so this formula actually contains
+ 
+
+ align:start position:0%
+okay so this formula actually contains
+lots of physics
+
+ align:start position:0%
+lots of physics
+ 
+
+ align:start position:0%
+lots of physics
+contains not the physics so let me just
+
+ align:start position:0%
+contains not the physics so let me just
+ 
+
+ align:start position:0%
+contains not the physics so let me just
+uh describe some of the physics here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the first
+
+ align:start position:0%
+so the first
+ 
+
+ align:start position:0%
+so the first
+so let's first consider the regime that
+
+ align:start position:0%
+so let's first consider the regime that
+ 
+
+ align:start position:0%
+so let's first consider the regime that
+the photons have very slow uh low energy
+
+ align:start position:0%
+the photons have very slow uh low energy
+ 
+
+ align:start position:0%
+the photons have very slow uh low energy
+okay it is known as the photon Shining
+
+ align:start position:0%
+okay it is known as the photon Shining
+ 
+
+ align:start position:0%
+okay it is known as the photon Shining
+some Knights shining on the uh uh uh
+
+ align:start position:0%
+some Knights shining on the uh uh uh
+ 
+
+ align:start position:0%
+some Knights shining on the uh uh uh
+so suppose the the photon have very low
+
+ align:start position:0%
+so suppose the the photon have very low
+ 
+
+ align:start position:0%
+so suppose the the photon have very low
+frequency much smaller than the electron
+
+ align:start position:0%
+frequency much smaller than the electron
+ 
+
+ align:start position:0%
+frequency much smaller than the electron
+Mass
+
+ align:start position:0%
+Mass
+ 
+
+ align:start position:0%
+Mass
+so now if you look at this formula
+
+ align:start position:0%
+so now if you look at this formula
+ 
+
+ align:start position:0%
+so now if you look at this formula
+so if the initial Photon have is much
+
+ align:start position:0%
+so if the initial Photon have is much
+ 
+
+ align:start position:0%
+so if the initial Photon have is much
+much smaller than the mass and then
+
+ align:start position:0%
+much smaller than the mass and then
+ 
+
+ align:start position:0%
+much smaller than the mass and then
+these factors are approximately zero
+
+ align:start position:0%
+these factors are approximately zero
+ 
+
+ align:start position:0%
+these factors are approximately zero
+then you find in this regime that Omega
+
+ align:start position:0%
+then you find in this regime that Omega
+ 
+
+ align:start position:0%
+then you find in this regime that Omega
+Prime is actually approximately equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+okay so you find in this regime
+
+ align:start position:0%
+okay so you find in this regime
+ 
+
+ align:start position:0%
+okay so you find in this regime
+the frequency actually does not change
+
+ align:start position:0%
+the frequency actually does not change
+ 
+
+ align:start position:0%
+the frequency actually does not change
+when the when when the photon scattered
+
+ align:start position:0%
+when the when when the photon scattered
+ 
+
+ align:start position:0%
+when the when when the photon scattered
+away from the electron
+
+ align:start position:0%
+away from the electron
+ 
+
+ align:start position:0%
+away from the electron
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then and then and then now Omega
+
+ align:start position:0%
+and then and then and then now Omega
+ 
+
+ align:start position:0%
+and then and then and then now Omega
+Prime equal to Omega so so this Factor
+
+ align:start position:0%
+Prime equal to Omega so so this Factor
+ 
+
+ align:start position:0%
+Prime equal to Omega so so this Factor
+become one this Factor becomes one and
+
+ align:start position:0%
+become one this Factor becomes one and
+ 
+
+ align:start position:0%
+become one this Factor becomes one and
+one minus sine Theta equal to cosine
+
+ align:start position:0%
+one minus sine Theta equal to cosine
+ 
+
+ align:start position:0%
+one minus sine Theta equal to cosine
+squared C there and this becomes one
+
+ align:start position:0%
+squared C there and this becomes one
+ 
+
+ align:start position:0%
+squared C there and this becomes one
+and then you find then the then the D
+
+ align:start position:0%
+and then you find then the then the D
+ 
+
+ align:start position:0%
+and then you find then the then the D
+Sigma the cosine Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just equal to Pi Alpha Square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divided by m Square
+
+ align:start position:0%
+divided by m Square
+ 
+
+ align:start position:0%
+divided by m Square
+then plus one cosine squared theta
+
+ align:start position:0%
+then plus one cosine squared theta
+ 
+
+ align:start position:0%
+then plus one cosine squared theta
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is a
+
+ align:start position:0%
+so this is a
+ 
+
+ align:start position:0%
+so this is a
+so this is a famous formula
+
+ align:start position:0%
+so this is a famous formula
+ 
+
+ align:start position:0%
+so this is a famous formula
+uh uh in in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah more than 100 years ago or even
+
+ align:start position:0%
+yeah more than 100 years ago or even
+ 
+
+ align:start position:0%
+yeah more than 100 years ago or even
+more so because this is the classical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is called the terms and
+
+ align:start position:0%
+so this is called the terms and
+ 
+
+ align:start position:0%
+so this is called the terms and
+cross-section
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so these are terms and
+
+ align:start position:0%
+okay so these are terms and
+ 
+
+ align:start position:0%
+okay so these are terms and
+cross-section derived
+
+ align:start position:0%
+cross-section derived
+ 
+
+ align:start position:0%
+cross-section derived
+from the classical electrodynamics
+
+ align:start position:0%
+from the classical electrodynamics
+ 
+
+ align:start position:0%
+from the classical electrodynamics
+okay and so this is a result already
+
+ align:start position:0%
+okay and so this is a result already
+ 
+
+ align:start position:0%
+okay and so this is a result already
+known okay in the 19th century from the
+
+ align:start position:0%
+known okay in the 19th century from the
+ 
+
+ align:start position:0%
+known okay in the 19th century from the
+classical electrodynamics
+
+ align:start position:0%
+classical electrodynamics
+ 
+
+ align:start position:0%
+classical electrodynamics
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so class how people derive this formula
+
+ align:start position:0%
+so class how people derive this formula
+ 
+
+ align:start position:0%
+so class how people derive this formula
+in the classical electrodynamics
+
+ align:start position:0%
+in the classical electrodynamics
+ 
+
+ align:start position:0%
+in the classical electrodynamics
+so so in classic retractable Dynamics
+
+ align:start position:0%
+so so in classic retractable Dynamics
+ 
+
+ align:start position:0%
+so so in classic retractable Dynamics
+you do this you do it this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So In classical electrodynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so light is believed to be a wave
+
+ align:start position:0%
+so light is believed to be a wave
+ 
+
+ align:start position:0%
+so light is believed to be a wave
+electromagnetic wave okay
+
+ align:start position:0%
+electromagnetic wave okay
+ 
+
+ align:start position:0%
+electromagnetic wave okay
+so essentially it's an electromagnetic
+
+ align:start position:0%
+so essentially it's an electromagnetic
+ 
+
+ align:start position:0%
+so essentially it's an electromagnetic
+wave so this electron or this electric
+
+ align:start position:0%
+wave so this electron or this electric
+ 
+
+ align:start position:0%
+wave so this electron or this electric
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+serviceation
+
+ align:start position:0%
+serviceation
+ 
+
+ align:start position:0%
+serviceation
+and then the magnitude
+
+ align:start position:0%
+and then the magnitude
+ 
+
+ align:start position:0%
+and then the magnitude
+and then it's a it's a wave okay it's a
+
+ align:start position:0%
+and then it's a it's a wave okay it's a
+ 
+
+ align:start position:0%
+and then it's a it's a wave okay it's a
+plane wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so from the class equalizer Dynamics the
+
+ align:start position:0%
+so from the class equalizer Dynamics the
+ 
+
+ align:start position:0%
+so from the class equalizer Dynamics the
+light is just wave okay when you shine
+
+ align:start position:0%
+light is just wave okay when you shine
+ 
+
+ align:start position:0%
+light is just wave okay when you shine
+the light on the material the light will
+
+ align:start position:0%
+the light on the material the light will
+ 
+
+ align:start position:0%
+the light on the material the light will
+scatter
+
+ align:start position:0%
+scatter
+ 
+
+ align:start position:0%
+scatter
+and the and the physical description of
+
+ align:start position:0%
+and the and the physical description of
+ 
+
+ align:start position:0%
+and the and the physical description of
+the light scatter is the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the uh
+
+ align:start position:0%
+so the uh
+ 
+
+ align:start position:0%
+so the uh
+so this is a so this is oscillating
+
+ align:start position:0%
+so this is a so this is oscillating
+ 
+
+ align:start position:0%
+so this is a so this is oscillating
+electric field
+
+ align:start position:0%
+electric field
+ 
+
+ align:start position:0%
+electric field
+so if you have a Charged particle like
+
+ align:start position:0%
+so if you have a Charged particle like
+ 
+
+ align:start position:0%
+so if you have a Charged particle like
+electron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we'll oscillate
+
+ align:start position:0%
+then we'll oscillate
+ 
+
+ align:start position:0%
+then we'll oscillate
+because it has a charge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+under such an e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+essentially the electron
+
+ align:start position:0%
+essentially the electron
+ 
+
+ align:start position:0%
+essentially the electron
+so you can approximate the electron in
+
+ align:start position:0%
+so you can approximate the electron in
+ 
+
+ align:start position:0%
+so you can approximate the electron in
+the matter just by by a forced harmonic
+
+ align:start position:0%
+the matter just by by a forced harmonic
+ 
+
+ align:start position:0%
+the matter just by by a forced harmonic
+oscillator okay the fourth oscillation
+
+ align:start position:0%
+oscillator okay the fourth oscillation
+ 
+
+ align:start position:0%
+oscillator okay the fourth oscillation
+it's the first oscillation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oscillation essentially
+
+ align:start position:0%
+oscillation essentially
+ 
+
+ align:start position:0%
+oscillation essentially
+the election velocity electron will have
+
+ align:start position:0%
+the election velocity electron will have
+ 
+
+ align:start position:0%
+the election velocity electron will have
+acceleration
+
+ align:start position:0%
+acceleration
+ 
+
+ align:start position:0%
+acceleration
+given by essentially given by the uh uh
+
+ align:start position:0%
+given by essentially given by the uh uh
+ 
+
+ align:start position:0%
+given by essentially given by the uh uh
+uh given by this yeah let me just
+
+ align:start position:0%
+uh given by this yeah let me just
+ 
+
+ align:start position:0%
+uh given by this yeah let me just
+proportional
+
+ align:start position:0%
+proportional
+ 
+
+ align:start position:0%
+proportional
+so the expansion I Omega t
+
+ align:start position:0%
+so the expansion I Omega t
+ 
+
+ align:start position:0%
+so the expansion I Omega t
+plus i k x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay essentially just the fourth
+
+ align:start position:0%
+okay essentially just the fourth
+ 
+
+ align:start position:0%
+okay essentially just the fourth
+organization will like this
+
+ align:start position:0%
+organization will like this
+ 
+
+ align:start position:0%
+organization will like this
+and then from classical electrodynamics
+
+ align:start position:0%
+and then from classical electrodynamics
+ 
+
+ align:start position:0%
+and then from classical electrodynamics
+because this is accelerated motion this
+
+ align:start position:0%
+because this is accelerated motion this
+ 
+
+ align:start position:0%
+because this is accelerated motion this
+is accelerated charge
+
+ align:start position:0%
+is accelerated charge
+ 
+
+ align:start position:0%
+is accelerated charge
+and accelerated oscillators in the
+
+ align:start position:0%
+and accelerated oscillators in the
+ 
+
+ align:start position:0%
+and accelerated oscillators in the
+classical electrodynamic will emits
+
+ align:start position:0%
+classical electrodynamic will emits
+ 
+
+ align:start position:0%
+classical electrodynamic will emits
+waves okay we're immediate actual
+
+ align:start position:0%
+waves okay we're immediate actual
+ 
+
+ align:start position:0%
+waves okay we're immediate actual
+magnetic wave
+
+ align:start position:0%
+magnetic wave
+ 
+
+ align:start position:0%
+magnetic wave
+so so this will radiate
+
+ align:start position:0%
+so so this will radiate
+ 
+
+ align:start position:0%
+so so this will radiate
+so this will lead to radiation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with frequency Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so essentially controlled by the uh by
+
+ align:start position:0%
+so essentially controlled by the uh by
+ 
+
+ align:start position:0%
+so essentially controlled by the uh by
+this acceleration okay
+
+ align:start position:0%
+this acceleration okay
+ 
+
+ align:start position:0%
+this acceleration okay
+so so this is the classical result in
+
+ align:start position:0%
+so so this is the classical result in
+ 
+
+ align:start position:0%
+so so this is the classical result in
+the classical electrodynamics that such
+
+ align:start position:0%
+the classical electrodynamics that such
+ 
+
+ align:start position:0%
+the classical electrodynamics that such
+oscillator emits the light with
+
+ align:start position:0%
+oscillator emits the light with
+ 
+
+ align:start position:0%
+oscillator emits the light with
+frequency Omega
+
+ align:start position:0%
+frequency Omega
+ 
+
+ align:start position:0%
+frequency Omega
+so that's the scattering process from
+
+ align:start position:0%
+so that's the scattering process from
+ 
+
+ align:start position:0%
+so that's the scattering process from
+the classical point of view
+
+ align:start position:0%
+the classical point of view
+ 
+
+ align:start position:0%
+the classical point of view
+okay uh from a classical Point of View
+
+ align:start position:0%
+okay uh from a classical Point of View
+ 
+
+ align:start position:0%
+okay uh from a classical Point of View
+Drive the oscillator the oscillator
+
+ align:start position:0%
+Drive the oscillator the oscillator
+ 
+
+ align:start position:0%
+Drive the oscillator the oscillator
+where you meet okay
+
+ align:start position:0%
+where you meet okay
+ 
+
+ align:start position:0%
+where you meet okay
+and if you go from this process
+
+ align:start position:0%
+and if you go from this process
+ 
+
+ align:start position:0%
+and if you go from this process
+then you precise find this formula okay
+
+ align:start position:0%
+then you precise find this formula okay
+ 
+
+ align:start position:0%
+then you precise find this formula okay
+you profess find this formula okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so regarding this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the value of Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+the Omega Prime the immediate Photon
+
+ align:start position:0%
+the Omega Prime the immediate Photon
+ 
+
+ align:start position:0%
+the Omega Prime the immediate Photon
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+so in this story Omega Prime always
+
+ align:start position:0%
+so in this story Omega Prime always
+ 
+
+ align:start position:0%
+so in this story Omega Prime always
+equal to Omega okay we could just
+
+ align:start position:0%
+equal to Omega okay we could just
+ 
+
+ align:start position:0%
+equal to Omega okay we could just
+retrieve a treatment oscillation okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so classically
+
+ align:start position:0%
+so so classically
+ 
+
+ align:start position:0%
+so so classically
+so classically or you always have this
+
+ align:start position:0%
+so classically or you always have this
+ 
+
+ align:start position:0%
+so classically or you always have this
+so you always have elastic scattering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the photon frequency does not change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then the uh and then the uh the
+
+ align:start position:0%
+okay and then the uh and then the uh the
+ 
+
+ align:start position:0%
+okay and then the uh and then the uh the
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+so let me call this equation one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and equation one holds
+
+ align:start position:0%
+and equation one holds
+ 
+
+ align:start position:0%
+and equation one holds
+okay yeah yeah the enemy code is a and b
+
+ align:start position:0%
+okay yeah yeah the enemy code is a and b
+ 
+
+ align:start position:0%
+okay yeah yeah the enemy code is a and b
+so not and equation one holds so the
+
+ align:start position:0%
+so not and equation one holds so the
+ 
+
+ align:start position:0%
+so not and equation one holds so the
+classical very robust prediction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that you always have elastic
+
+ align:start position:0%
+is that you always have elastic
+ 
+
+ align:start position:0%
+is that you always have elastic
+scattering when you shine Knight on the
+
+ align:start position:0%
+scattering when you shine Knight on the
+ 
+
+ align:start position:0%
+scattering when you shine Knight on the
+uh this competent and then the equation
+
+ align:start position:0%
+uh this competent and then the equation
+ 
+
+ align:start position:0%
+uh this competent and then the equation
+you have this Thompson called cross
+
+ align:start position:0%
+you have this Thompson called cross
+ 
+
+ align:start position:0%
+you have this Thompson called cross
+action
+
+ align:start position:0%
+action
+ 
+
+ align:start position:0%
+action
+but then now in the in the in the early
+
+ align:start position:0%
+but then now in the in the in the early
+ 
+
+ align:start position:0%
+but then now in the in the in the early
+part of the 20th century
+
+ align:start position:0%
+part of the 20th century
+ 
+
+ align:start position:0%
+part of the 20th century
+when competency this experiment
+
+ align:start position:0%
+when competency this experiment
+ 
+
+ align:start position:0%
+when competency this experiment
+and then he said when he observed
+
+ align:start position:0%
+and then he said when he observed
+ 
+
+ align:start position:0%
+and then he said when he observed
+actually the frequency can be smaller
+
+ align:start position:0%
+actually the frequency can be smaller
+ 
+
+ align:start position:0%
+actually the frequency can be smaller
+okay so so in this formula generally
+
+ align:start position:0%
+okay so so in this formula generally
+ 
+
+ align:start position:0%
+okay so so in this formula generally
+Omega Prime is smaller than Omega
+
+ align:start position:0%
+Omega Prime is smaller than Omega
+ 
+
+ align:start position:0%
+Omega Prime is smaller than Omega
+okay but in quantum mechanics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but but in general but in quantum
+
+ align:start position:0%
+but but in general but in quantum
+ 
+
+ align:start position:0%
+but but in general but in quantum
+mechanics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we see that Omega Prime is generic
+
+ align:start position:0%
+we see that Omega Prime is generic
+ 
+
+ align:start position:0%
+we see that Omega Prime is generic
+smaller
+
+ align:start position:0%
+smaller
+ 
+
+ align:start position:0%
+smaller
+the Omega B
+
+ align:start position:0%
+the Omega B
+ 
+
+ align:start position:0%
+the Omega B
+because this is one plus a factor which
+
+ align:start position:0%
+because this is one plus a factor which
+ 
+
+ align:start position:0%
+because this is one plus a factor which
+is greater than one
+
+ align:start position:0%
+is greater than one
+ 
+
+ align:start position:0%
+is greater than one
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in particular this deviation will
+
+ align:start position:0%
+and in particular this deviation will
+ 
+
+ align:start position:0%
+and in particular this deviation will
+become obvious when Omega become
+
+ align:start position:0%
+become obvious when Omega become
+ 
+
+ align:start position:0%
+become obvious when Omega become
+comparable to n
+
+ align:start position:0%
+comparable to n
+ 
+
+ align:start position:0%
+comparable to n
+okay but all we can become comparable to
+
+ align:start position:0%
+okay but all we can become comparable to
+ 
+
+ align:start position:0%
+okay but all we can become comparable to
+3M
+
+ align:start position:0%
+3M
+ 
+
+ align:start position:0%
+3M
+and also yeah so this is the uh um
+
+ align:start position:0%
+and also yeah so this is the uh um
+ 
+
+ align:start position:0%
+and also yeah so this is the uh um
+quantum mechanics so you will always
+
+ align:start position:0%
+quantum mechanics so you will always
+ 
+
+ align:start position:0%
+quantum mechanics so you will always
+have in inelastic scattering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this makes sense
+
+ align:start position:0%
+so this makes sense
+ 
+
+ align:start position:0%
+so this makes sense
+because because the just for momentum
+
+ align:start position:0%
+because because the just for momentum
+ 
+
+ align:start position:0%
+because because the just for momentum
+conversation
+
+ align:start position:0%
+conversation
+ 
+
+ align:start position:0%
+conversation
+electron uh
+
+ align:start position:0%
+electron uh
+ 
+
+ align:start position:0%
+electron uh
+if some Photon heat the electron
+
+ align:start position:0%
+if some Photon heat the electron
+ 
+
+ align:start position:0%
+if some Photon heat the electron
+electron needs to move
+
+ align:start position:0%
+electron needs to move
+ 
+
+ align:start position:0%
+electron needs to move
+we actually need to move then of course
+
+ align:start position:0%
+we actually need to move then of course
+ 
+
+ align:start position:0%
+we actually need to move then of course
+the energy will increase
+
+ align:start position:0%
+the energy will increase
+ 
+
+ align:start position:0%
+the energy will increase
+and then energy will increase in the
+
+ align:start position:0%
+and then energy will increase in the
+ 
+
+ align:start position:0%
+and then energy will increase in the
+Omega Prime of course have to be smaller
+
+ align:start position:0%
+Omega Prime of course have to be smaller
+ 
+
+ align:start position:0%
+Omega Prime of course have to be smaller
+than Omega okay so in the rest frame
+
+ align:start position:0%
+than Omega okay so in the rest frame
+ 
+
+ align:start position:0%
+than Omega okay so in the rest frame
+election always gain energy
+
+ align:start position:0%
+election always gain energy
+ 
+
+ align:start position:0%
+election always gain energy
+so that's why in the quantum mechanics
+
+ align:start position:0%
+so that's why in the quantum mechanics
+ 
+
+ align:start position:0%
+so that's why in the quantum mechanics
+always in elastic scattering okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then then the style no longer and
+
+ align:start position:0%
+and then then the style no longer and
+ 
+
+ align:start position:0%
+and then then the style no longer and
+this equation one no longer holds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the early days
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the early days
+
+ align:start position:0%
+so in the early days
+ 
+
+ align:start position:0%
+so in the early days
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+cannot be explained using classical
+
+ align:start position:0%
+cannot be explained using classical
+ 
+
+ align:start position:0%
+cannot be explained using classical
+actor Dynamics okay so so this is
+
+ align:start position:0%
+actor Dynamics okay so so this is
+ 
+
+ align:start position:0%
+actor Dynamics okay so so this is
+decisive
+
+ align:start position:0%
+decisive
+ 
+
+ align:start position:0%
+decisive
+evidence
+
+ align:start position:0%
+evidence
+ 
+
+ align:start position:0%
+evidence
+that actually Photon uh the light
+
+ align:start position:0%
+that actually Photon uh the light
+ 
+
+ align:start position:0%
+that actually Photon uh the light
+behaves very different uh Quantum
+
+ align:start position:0%
+behaves very different uh Quantum
+ 
+
+ align:start position:0%
+behaves very different uh Quantum
+mechanically from classical uh wave okay
+
+ align:start position:0%
+mechanically from classical uh wave okay
+ 
+
+ align:start position:0%
+mechanically from classical uh wave okay
+in fact
+
+ align:start position:0%
+in fact
+ 
+
+ align:start position:0%
+in fact
+this simple fact can be just explained
+
+ align:start position:0%
+this simple fact can be just explained
+ 
+
+ align:start position:0%
+this simple fact can be just explained
+by treating a photon as a particle okay
+
+ align:start position:0%
+by treating a photon as a particle okay
+ 
+
+ align:start position:0%
+by treating a photon as a particle okay
+so this is a decisive support the photo
+
+ align:start position:0%
+so this is a decisive support the photo
+ 
+
+ align:start position:0%
+so this is a decisive support the photo
+actually behave like particle okay a
+
+ align:start position:0%
+actually behave like particle okay a
+ 
+
+ align:start position:0%
+actually behave like particle okay a
+behavior like a particle
+
+ align:start position:0%
+behavior like a particle
+ 
+
+ align:start position:0%
+behavior like a particle
+so or or the so this to the particle
+
+ align:start position:0%
+so or or the so this to the particle
+ 
+
+ align:start position:0%
+so or or the so this to the particle
+feature of photon okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so we are out of time soon so
+
+ align:start position:0%
+okay so so we are out of time soon so
+ 
+
+ align:start position:0%
+okay so so we are out of time soon so
+let me just mention one simple
+
+ align:start position:0%
+let me just mention one simple
+ 
+
+ align:start position:0%
+let me just mention one simple
+uh application of this uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in particular let me just mention two
+
+ align:start position:0%
+so in particular let me just mention two
+ 
+
+ align:start position:0%
+so in particular let me just mention two
+two small things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one thing is that
+
+ align:start position:0%
+so one thing is that
+ 
+
+ align:start position:0%
+so one thing is that
+if Omega is much much greater than m
+
+ align:start position:0%
+if Omega is much much greater than m
+ 
+
+ align:start position:0%
+if Omega is much much greater than m
+then Omega Prime
+
+ align:start position:0%
+then Omega Prime
+ 
+
+ align:start position:0%
+then Omega Prime
+divided by n become very small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so these actually become a much
+
+ align:start position:0%
+okay so these actually become a much
+ 
+
+ align:start position:0%
+okay so these actually become a much
+much smaller than one so except
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+exactly equal to zero okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+so if you the initial Photon momentum is
+
+ align:start position:0%
+so if you the initial Photon momentum is
+ 
+
+ align:start position:0%
+so if you the initial Photon momentum is
+energy is very big then actually most of
+
+ align:start position:0%
+energy is very big then actually most of
+ 
+
+ align:start position:0%
+energy is very big then actually most of
+the energy will go to the electron okay
+
+ align:start position:0%
+the energy will go to the electron okay
+ 
+
+ align:start position:0%
+the energy will go to the electron okay
+uh and then the fallow frequencies
+
+ align:start position:0%
+uh and then the fallow frequencies
+ 
+
+ align:start position:0%
+uh and then the fallow frequencies
+actually become much much smaller than
+
+ align:start position:0%
+actually become much much smaller than
+ 
+
+ align:start position:0%
+actually become much much smaller than
+initial frequency
+
+ align:start position:0%
+initial frequency
+ 
+
+ align:start position:0%
+initial frequency
+so this is one remark
+
+ align:start position:0%
+so this is one remark
+ 
+
+ align:start position:0%
+so this is one remark
+and another remark
+
+ align:start position:0%
+and another remark
+ 
+
+ align:start position:0%
+and another remark
+so this is in the
+
+ align:start position:0%
+so this is in the
+ 
+
+ align:start position:0%
+so this is in the
+electron rest frame
+
+ align:start position:0%
+electron rest frame
+ 
+
+ align:start position:0%
+electron rest frame
+but in a different frame
+
+ align:start position:0%
+but in a different frame
+ 
+
+ align:start position:0%
+but in a different frame
+you will actually get very different
+
+ align:start position:0%
+you will actually get very different
+ 
+
+ align:start position:0%
+you will actually get very different
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+so now let's imagine we have a frame
+
+ align:start position:0%
+so now let's imagine we have a frame
+ 
+
+ align:start position:0%
+so now let's imagine we have a frame
+so so in this Frame the uh you left on
+
+ align:start position:0%
+so so in this Frame the uh you left on
+ 
+
+ align:start position:0%
+so so in this Frame the uh you left on
+your seats here the photon comes in okay
+
+ align:start position:0%
+your seats here the photon comes in okay
+ 
+
+ align:start position:0%
+your seats here the photon comes in okay
+in the Z Direction now imagine we boost
+
+ align:start position:0%
+in the Z Direction now imagine we boost
+ 
+
+ align:start position:0%
+in the Z Direction now imagine we boost
+the system in an active Z Direction
+
+ align:start position:0%
+the system in an active Z Direction
+ 
+
+ align:start position:0%
+the system in an active Z Direction
+okay in the active Z Direction so the
+
+ align:start position:0%
+okay in the active Z Direction so the
+ 
+
+ align:start position:0%
+okay in the active Z Direction so the
+result of this boost is that the photon
+
+ align:start position:0%
+result of this boost is that the photon
+ 
+
+ align:start position:0%
+result of this boost is that the photon
+energy becomes very small
+
+ align:start position:0%
+energy becomes very small
+ 
+
+ align:start position:0%
+energy becomes very small
+and the electron energy will become
+
+ align:start position:0%
+and the electron energy will become
+ 
+
+ align:start position:0%
+and the electron energy will become
+bigger and bigger when you increase the
+
+ align:start position:0%
+bigger and bigger when you increase the
+ 
+
+ align:start position:0%
+bigger and bigger when you increase the
+Boost okay because the Boost is opposite
+
+ align:start position:0%
+Boost okay because the Boost is opposite
+ 
+
+ align:start position:0%
+Boost okay because the Boost is opposite
+to the direction of the photon so the uh
+
+ align:start position:0%
+to the direction of the photon so the uh
+ 
+
+ align:start position:0%
+to the direction of the photon so the uh
+so so that you boost more and the force
+
+ align:start position:0%
+so so that you boost more and the force
+ 
+
+ align:start position:0%
+so so that you boost more and the force
+energy will become smaller and smaller
+
+ align:start position:0%
+energy will become smaller and smaller
+ 
+
+ align:start position:0%
+energy will become smaller and smaller
+okay so now imagine you go to a frame
+
+ align:start position:0%
+okay so now imagine you go to a frame
+ 
+
+ align:start position:0%
+okay so now imagine you go to a frame
+which first I have a very small energy
+
+ align:start position:0%
+which first I have a very small energy
+ 
+
+ align:start position:0%
+which first I have a very small energy
+compared to electron
+
+ align:start position:0%
+compared to electron
+ 
+
+ align:start position:0%
+compared to electron
+okay and then this is a very then next
+
+ align:start position:0%
+okay and then this is a very then next
+ 
+
+ align:start position:0%
+okay and then this is a very then next
+frame will be a very fast electron
+
+ align:start position:0%
+frame will be a very fast electron
+ 
+
+ align:start position:0%
+frame will be a very fast electron
+heat a very low energy photon
+
+ align:start position:0%
+heat a very low energy photon
+ 
+
+ align:start position:0%
+heat a very low energy photon
+okay so this is called the inverse
+
+ align:start position:0%
+okay so this is called the inverse
+ 
+
+ align:start position:0%
+okay so this is called the inverse
+competence guide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so in this case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the the energy in the the energy in
+
+ align:start position:0%
+then the the energy in the the energy in
+ 
+
+ align:start position:0%
+then the the energy in the the energy in
+the initial energy in the electron then
+
+ align:start position:0%
+the initial energy in the electron then
+ 
+
+ align:start position:0%
+the initial energy in the electron then
+can be transferred into the photon then
+
+ align:start position:0%
+can be transferred into the photon then
+ 
+
+ align:start position:0%
+can be transferred into the photon then
+then it yeah just you have a very fast
+
+ align:start position:0%
+then it yeah just you have a very fast
+ 
+
+ align:start position:0%
+then it yeah just you have a very fast
+part a very high energy electron heat a
+
+ align:start position:0%
+part a very high energy electron heat a
+ 
+
+ align:start position:0%
+part a very high energy electron heat a
+low energy Photon then just give a big
+
+ align:start position:0%
+low energy Photon then just give a big
+ 
+
+ align:start position:0%
+low energy Photon then just give a big
+kick to the photon and the photons have
+
+ align:start position:0%
+kick to the photon and the photons have
+ 
+
+ align:start position:0%
+kick to the photon and the photons have
+very high energy
+
+ align:start position:0%
+very high energy
+ 
+
+ align:start position:0%
+very high energy
+so this is a very simple effect
+
+ align:start position:0%
+so this is a very simple effect
+ 
+
+ align:start position:0%
+so this is a very simple effect
+but it can have very important a a
+
+ align:start position:0%
+but it can have very important a a
+ 
+
+ align:start position:0%
+but it can have very important a a
+astrophysical uh applications
+
+ align:start position:0%
+astrophysical uh applications
+ 
+
+ align:start position:0%
+astrophysical uh applications
+so so this is called the important
+
+ align:start position:0%
+so so this is called the important
+ 
+
+ align:start position:0%
+so so this is called the important
+application in this code
+
+ align:start position:0%
+application in this code
+ 
+
+ align:start position:0%
+application in this code
+is effect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so essentially they have the simple
+
+ align:start position:0%
+so essentially they have the simple
+ 
+
+ align:start position:0%
+so essentially they have the simple
+observation like this
+
+ align:start position:0%
+observation like this
+ 
+
+ align:start position:0%
+observation like this
+so so in the universe we have the uh the
+
+ align:start position:0%
+so so in the universe we have the uh the
+ 
+
+ align:start position:0%
+so so in the universe we have the uh the
+migrant microback
+
+ align:start position:0%
+migrant microback
+ 
+
+ align:start position:0%
+migrant microback
+we have a macro wave background
+
+ align:start position:0%
+we have a macro wave background
+ 
+
+ align:start position:0%
+we have a macro wave background
+radiation
+
+ align:start position:0%
+radiation
+ 
+
+ align:start position:0%
+radiation
+okay the microwave background radiation
+
+ align:start position:0%
+okay the microwave background radiation
+ 
+
+ align:start position:0%
+okay the microwave background radiation
+the the photon is very low energy
+
+ align:start position:0%
+the the photon is very low energy
+ 
+
+ align:start position:0%
+the the photon is very low energy
+because the temperature is very low
+
+ align:start position:0%
+because the temperature is very low
+ 
+
+ align:start position:0%
+because the temperature is very low
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but now if the uh but around a Galaxy
+
+ align:start position:0%
+but now if the uh but around a Galaxy
+ 
+
+ align:start position:0%
+but now if the uh but around a Galaxy
+so if you audio the Galaxy Center
+
+ align:start position:0%
+so if you audio the Galaxy Center
+ 
+
+ align:start position:0%
+so if you audio the Galaxy Center
+so near the Galaxy cluster and the
+
+ align:start position:0%
+so near the Galaxy cluster and the
+ 
+
+ align:start position:0%
+so near the Galaxy cluster and the
+grassy cluster some of the election
+
+ align:start position:0%
+grassy cluster some of the election
+ 
+
+ align:start position:0%
+grassy cluster some of the election
+there can have very high energy
+
+ align:start position:0%
+there can have very high energy
+ 
+
+ align:start position:0%
+there can have very high energy
+and when they scatter
+
+ align:start position:0%
+and when they scatter
+ 
+
+ align:start position:0%
+and when they scatter
+on the microwave background Photon and
+
+ align:start position:0%
+on the microwave background Photon and
+ 
+
+ align:start position:0%
+on the microwave background Photon and
+then they can give those microwave back
+
+ align:start position:0%
+then they can give those microwave back
+ 
+
+ align:start position:0%
+then they can give those microwave back
+a photon a big peak okay and then they
+
+ align:start position:0%
+a photon a big peak okay and then they
+ 
+
+ align:start position:0%
+a photon a big peak okay and then they
+will uh uh then the photon will get a
+
+ align:start position:0%
+will uh uh then the photon will get a
+ 
+
+ align:start position:0%
+will uh uh then the photon will get a
+very high energy
+
+ align:start position:0%
+very high energy
+ 
+
+ align:start position:0%
+very high energy
+so then by looking at the photon
+
+ align:start position:0%
+so then by looking at the photon
+ 
+
+ align:start position:0%
+so then by looking at the photon
+Spectrum in the sky
+
+ align:start position:0%
+Spectrum in the sky
+ 
+
+ align:start position:0%
+Spectrum in the sky
+look for this kind of a hot spot and
+
+ align:start position:0%
+look for this kind of a hot spot and
+ 
+
+ align:start position:0%
+look for this kind of a hot spot and
+then this is a way to detect the Galaxy
+
+ align:start position:0%
+then this is a way to detect the Galaxy
+ 
+
+ align:start position:0%
+then this is a way to detect the Galaxy
+cluster
+
+ align:start position:0%
+cluster
+ 
+
+ align:start position:0%
+cluster
+okay then you can just use this uh
+
+ align:start position:0%
+okay then you can just use this uh
+ 
+
+ align:start position:0%
+okay then you can just use this uh
+inverse counter scattering that detects
+
+ align:start position:0%
+inverse counter scattering that detects
+ 
+
+ align:start position:0%
+inverse counter scattering that detects
+the the location of the Galaxy cluster
+
+ align:start position:0%
+the the location of the Galaxy cluster
+ 
+
+ align:start position:0%
+the the location of the Galaxy cluster
+and so so it's a very it's very cool or
+
+ align:start position:0%
+and so so it's a very it's very cool or
+ 
+
+ align:start position:0%
+and so so it's a very it's very cool or
+or it's a very cool application
\ No newline at end of file
diff --git a/IEPuLyxRmJc.txt b/IEPuLyxRmJc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..195bb69a8ce4cb0d01c4dc50d15093230c3f1e95
--- /dev/null
+++ b/IEPuLyxRmJc.txt
@@ -0,0 +1,377 @@
+Have you ever wondered why the word Ambulance
+is printed as its mirror image on the front
+
+an Ambulance truck? The word is written this
+way so that drivers can read the word in their
+
+rearview mirror signaling them to pull over
+if necessary. In chemistry and biology, molecules
+
+can also be mirror image of each other and
+have very different functions.
+
+This video is part of the Structure-Function-Properties
+video series. The structure, function and
+
+properties of a system are related and depend
+on the processes that define or create the
+
+system.
+
+Hi, my name is Brad Pentelute, and I am a
+professor of chemistry at MIT. My research
+
+focuses on the biological properties of mirror-image
+proteins and how these macromolecules may
+
+be used in pharmaceutical applications and
+therapeutics.
+
+Before watching this video, you should be
+familiar with: Molecular Geometry, the structure
+
+of the 20 naturally occurring amino acids,
+as well as have an understanding of what a
+
+protein is and its three-dimensional structure
+
+After watching this video, you will be able
+to:
+
+Identify chiral objects and molecules
+Understand how chirality plays a role in the
+
+function of biological compounds.
+
+Let's begin by talking about chirality. In
+this video, you'll see that chirality is an
+
+important feature in biological molecules
+because molecular structure is often closely
+
+related to biological function.
+
+A molecule is chiral if it is not superimposable
+with its mirror image. But, before we talk
+
+about chirality in molecules, let's first
+look at a couple of ordinary objects to learn
+
+exactly what we mean by the term, chirality.
+
+Let's look at a common example of chirality
+in this left and right glove. Gloves are mirror
+
+images of one another. The gloves look identical
+but we know from experience that they are
+
+not the same. They have different shapes.
+One fits only your left hand and the other
+
+fits only your right hand. If we try to lay
+the right glove on top of the left glove and
+
+align their key features, we see that they
+are not superimposable at all. Because left
+
+and right gloves are non-superimposable mirror
+images, we can say that gloves are chiral.
+
+Are there other objects that you can think
+of that are chiral? Please pause the video
+
+here to think of a few examples.
+
+You may have suggested such objects as your
+left or right ears, a drinking fountain, or
+
+a screw.
+
+Let's look at this airplane. Is it chiral?
+If we take the airplane and compare it to
+
+its mirror image, we can see that the two
+images are identical and are superimposable.
+
+Therefore, the airplane is not chiral. Can
+you describe what characteristic of the airplane
+
+makes it achiral? Please pause the video and
+give a possible answer.
+
+There is a plane of symmetry through the center
+of the airplane itself. If one half of an
+
+object can be reflected onto its other half,
+then the object is never chiral. Can you think
+
+of another object with an internal plane of
+symmetry? Please pause the video and try to
+
+think of other achiral objects and where the
+internal plane of symmetry would be.
+
+Objects such as a chair, a drinking glass,
+and a fork have an internal plane of symmetry
+
+and hence are achiral. The planes of symmetry
+are here, here, and here.
+
+Notice that there is no way to divide a right-handed
+glove into two equal halves, which is why
+
+the glove is chiral.
+
+Finally, another everyday object that I want
+to show you is this fan. First, let's think.
+
+Do you think a fan is chiral? Please pause
+the video and discuss this with a friend.
+
+Is the fan chiral? Yes, it is. Each blade
+is hung with a tilt that makes the fan chiral!
+
+The function of the tilted blades pushes air
+forward to create a wind chill effect to cool
+
+you. However, the tilted blades also cause
+the fan to be non-superimposable with its
+
+mirror image. As you can see, the mirror image
+has blades that tilt in the opposite direction.
+
+All objects can be classified as chiral or
+achiral, including molecules.
+
+As with objects, a molecule is chiral if it
+is non-superimposable with its mirror image.
+
+The mirror image of a chiral molecule is called
+its enantiomer. Enantio is Greek for opposite
+
+and the term enantiomer describes the relationship
+between the two molecules.
+
+Enantiomers have identical molecular formulas
+and have the same chemical connectivity but
+
+differ in the three-dimensional spatial arrangement
+of the atoms in the molecule.
+
+Let's look at this model of the molecule,
+bromo-chloro-iodo methane. The green ball
+
+represents a chlorine atom, the orange ball
+represents a bromine atom, the purple ball
+
+represents an iodine atom and the white ball
+represents a hydrogen atom.
+
+If we take our molecule and hold it in front
+of a mirror, we see the molecule and its image
+
+in the mirror. But, now let's look at 3-D
+models of both our original molecule and its
+
+mirror image. We see that the two are not
+superimposable, regardless of how one rotates
+
+the molecules. Hence, this tells us that bromo-chloro-iodo
+methane is a chiral molecule.
+
+A quick way to know if a molecule is chiral
+is to check and see if it has a chiral center.
+
+A chiral center is a tetrahedral atom attached
+to four different atoms or groups. The tetrahedral
+
+atom is usually carbon.
+
+Let's make a model of the organic compound,
+2-chlorobutane. The number 2 in front of the
+
+compound name means that chlorine is on the
+second carbon atom. This carbon is attached
+
+to four different groups, chlorine, hydrogen,
+a -CH3 group and a -CH2CH3 group and that
+
+means that it's a chiral center.
+What would happen to the chirality of this
+
+compound if we substituted the hydrogen atom
+with a second chlorine atom? Would the resulting
+
+molecule be chiral? Please pause the video
+here.
+
+This new molecule, called 2, 2 di-chlorobutane
+is not chiral. The second carbon with two
+
+chlorine atoms no longer has four different
+groups attached. You can even see that this
+
+molecule has an internal plane of symmetry
+and therefore can be superimposable on its
+
+mirror image.
+When we do have a chiral molecule, sometimes
+
+its enantiomer has an entirely different function.
+For example, the enantiomers of Carvone are
+
+the flavors of caraway and spearmint. One
+enantiomer of Carvone fits into a specific
+
+receptor in your nose only in the way a left-handed
+glove fits your left hand. The other enantiomer
+
+of carvone fits into an entirely different
+receptor, resulting in the different odor.Many
+
+drugs such as the pain reliever, ibuprofen
+has biological activity while its enantiomer
+
+As with simple molecules, it is possible for
+proteins to exist that are mirror images of
+
+each other. However, this doesn't occur in
+nature. Naturally occurring proteins are composed
+
+of L-amino acids only. It is not clear why
+nature selected for this particular enantiomer.
+
+Selection of L-amino acids has structural
+consequences for a proteins three-dimensional
+
+shape.
+
+Pause the video here and discuss with a friend
+the general structure of amino acids. What
+
+are the groups attached to the central carbon?
+Which if any of the amino acids are achiral?
+
+An amino acid contains both an amino group
+and a carboxylic acid group. It also contains
+
+a hydrogen atom and a sidechain. The central
+atom is carbon. Of the 20 naturally occurring
+
+amino acids, glycine is the only achiral amino
+acid. Its sidechain is a second hydrogen atom.
+
+The remaining 19 amino acids have the L configuration.
+
+Let us recall that naturally occurring amino
+acids have an L-configuration and combine
+
+to form L-proteins. However, scientists can
+now chemically synthesize proteins made up
+
+entirely of D-amino acids. These synthetic
+macromolecules are also known as D-proteins.
+
+Interestingly, these proteins fold into three-
+dimensional structures, which mirror those
+
+of the naturally occurring L-protein counter-part.
+
+Snow fleas are a species of dark blue insect.
+They are often seen bouncing around on the
+
+snow in the winter. Ice fish live in the Antarctic.
+These fish live in the ocean at subzero temperatures.
+
+What do the snow flea and the arctic fish
+have in common? They can both survive in subfreezing
+
+temperatures. How do they do this? Both creatures
+make a class of proteins called Antifreeze
+
+proteins. These proteins protect these organisms
+and others, including moths, beetles, plants
+
+and even bacteria by binding to water and
+stopping the growth of ice crystals in their
+
+bodies.
+Is water chiral? Please pause the video here
+
+and try to answer this question.
+
+Here you can see the chemical structure of
+water. As you can see, it has two planes of
+
+symmetry, and water is superimposable with
+its own mirror image.
+
+The antifreeze protein is comprised of 81
+amino acids folded into six helices. Each
+
+helix is connected by amino acids that form
+a short connecting loop. The helices in the
+
+antifreeze protein are left-handed. Do you
+think the helices are chiral? Pause the video
+
+and discuss this with a friend.
+
+The helix winds up in the direction of your
+left thumb when your fingers are curled in
+
+to make a fist. These helices do not have
+an internal plane of symmetry, and are not
+
+superimposable with their mirror images. They
+are chiral.
+
+The antifreeze protein was the first protein
+whose mirror image was chemically synthesized.
+
+The mirror image protein is composed of entirely
+D-amino acids. The helices are right-handed,
+
+opposite to that of the naturally occurring
+protein. They wind up in the direction of
+
+your right thumb when your fingers are curled
+in to make a fist. In proteins, we see chirality
+
+in the amino acid units and in the secondary
+structure as well.
+
+Do you think the D-form of the antifreeze
+protein will have a function the same as or
+
+different from the natural L-form? Please
+pause the video here and discuss with a friend.
+
+Interestingly, the mirror image protein has
+the same antifreeze properties. This is because
+
+its binding partner, water is achiral. So
+the mirror image protein can still bind water.
+
+Hopefully by now you have the tools to recognize
+chiral objects and molecules, and the role
+
+that chirality can play in recognition and
+specificity between biological systems. In
+
+this video, we saw that an object or molecule
+is chiral if it cannot be superimposed onto
+
+its mirror image. Objects or molecules that
+have an internal plane of symmetry are never
+
+chiral. We also talked about enantiomers,
+which are the mirror image of a chiral molecule.
+
+Since the spatial orientation of the atoms
+in enantiomers are different, chiral compounds
+
+can and often do have distinct functions.
+But, as you saw with the antifreeze protein,
+
+sometimes there are exceptions to the rule!
\ No newline at end of file
diff --git a/IqmrNUoiy7g.txt b/IqmrNUoiy7g.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eaf39451a3414b329f0b5ec19ffaa5a31b328572
--- /dev/null
+++ b/IqmrNUoiy7g.txt
@@ -0,0 +1,2051 @@
+align:start position:0%
+ 
+one one of our challenges over the next
+
+ align:start position:0%
+one one of our challenges over the next
+ 
+
+ align:start position:0%
+one one of our challenges over the next
+couple of days is we we have people
+
+ align:start position:0%
+couple of days is we we have people
+ 
+
+ align:start position:0%
+couple of days is we we have people
+who've come here from all over the world
+
+ align:start position:0%
+who've come here from all over the world
+ 
+
+ align:start position:0%
+who've come here from all over the world
+thank you very much for for for being
+
+ align:start position:0%
+thank you very much for for for being
+ 
+
+ align:start position:0%
+thank you very much for for for being
+here uh with all the snow and weather
+
+ align:start position:0%
+here uh with all the snow and weather
+ 
+
+ align:start position:0%
+here uh with all the snow and weather
+that has beset us uh here at the last
+
+ align:start position:0%
+that has beset us uh here at the last
+ 
+
+ align:start position:0%
+that has beset us uh here at the last
+minute actually June morai from Japan
+
+ align:start position:0%
+minute actually June morai from Japan
+ 
+
+ align:start position:0%
+minute actually June morai from Japan
+was caught in a snowstorm at Narita
+
+ align:start position:0%
+was caught in a snowstorm at Narita
+ 
+
+ align:start position:0%
+was caught in a snowstorm at Narita
+Airport in Japan and so won't be able to
+
+ align:start position:0%
+Airport in Japan and so won't be able to
+ 
+
+ align:start position:0%
+Airport in Japan and so won't be able to
+join us till later today and I'm sure
+
+ align:start position:0%
+join us till later today and I'm sure
+ 
+
+ align:start position:0%
+join us till later today and I'm sure
+that there will be people trickling in
+
+ align:start position:0%
+that there will be people trickling in
+ 
+
+ align:start position:0%
+that there will be people trickling in
+as well we wanted to keep this uh this
+
+ align:start position:0%
+as well we wanted to keep this uh this
+ 
+
+ align:start position:0%
+as well we wanted to keep this uh this
+convocation as small and focused as
+
+ align:start position:0%
+convocation as small and focused as
+ 
+
+ align:start position:0%
+convocation as small and focused as
+possible uh to see if we could uh
+
+ align:start position:0%
+possible uh to see if we could uh
+ 
+
+ align:start position:0%
+possible uh to see if we could uh
+actually make some Headway and and to
+
+ align:start position:0%
+actually make some Headway and and to
+ 
+
+ align:start position:0%
+actually make some Headway and and to
+remind you of the uh of the objectives
+
+ align:start position:0%
+remind you of the uh of the objectives
+ 
+
+ align:start position:0%
+remind you of the uh of the objectives
+uh that were set forth by the conference
+
+ align:start position:0%
+uh that were set forth by the conference
+ 
+
+ align:start position:0%
+uh that were set forth by the conference
+committee uh we talked about wanting to
+
+ align:start position:0%
+committee uh we talked about wanting to
+ 
+
+ align:start position:0%
+committee uh we talked about wanting to
+identify opportunities for collaborative
+
+ align:start position:0%
+identify opportunities for collaborative
+ 
+
+ align:start position:0%
+identify opportunities for collaborative
+research to determine uh you know what
+
+ align:start position:0%
+research to determine uh you know what
+ 
+
+ align:start position:0%
+research to determine uh you know what
+the core core research components of
+
+ align:start position:0%
+the core core research components of
+ 
+
+ align:start position:0%
+the core core research components of
+some of these opportunities might be and
+
+ align:start position:0%
+some of these opportunities might be and
+ 
+
+ align:start position:0%
+some of these opportunities might be and
+uh uh use these sessions that we have
+
+ align:start position:0%
+uh uh use these sessions that we have
+ 
+
+ align:start position:0%
+uh uh use these sessions that we have
+today uh to begin a sort of a technology
+
+ align:start position:0%
+today uh to begin a sort of a technology
+ 
+
+ align:start position:0%
+today uh to begin a sort of a technology
+Road mapping process that we hope to
+
+ align:start position:0%
+Road mapping process that we hope to
+ 
+
+ align:start position:0%
+Road mapping process that we hope to
+follow on uh with subsequent events uh
+
+ align:start position:0%
+follow on uh with subsequent events uh
+ 
+
+ align:start position:0%
+follow on uh with subsequent events uh
+uh at uh uh leading out of here which
+
+ align:start position:0%
+uh at uh uh leading out of here which
+ 
+
+ align:start position:0%
+uh at uh uh leading out of here which
+we'll share with you uh more on tomorrow
+
+ align:start position:0%
+we'll share with you uh more on tomorrow
+ 
+
+ align:start position:0%
+we'll share with you uh more on tomorrow
+but so uh first I'd like to welcome you
+
+ align:start position:0%
+but so uh first I'd like to welcome you
+ 
+
+ align:start position:0%
+but so uh first I'd like to welcome you
+on behalf of MIT and the Auto ID Labs
+
+ align:start position:0%
+on behalf of MIT and the Auto ID Labs
+ 
+
+ align:start position:0%
+on behalf of MIT and the Auto ID Labs
+here at MIT who's the host for this
+
+ align:start position:0%
+here at MIT who's the host for this
+ 
+
+ align:start position:0%
+here at MIT who's the host for this
+event uh my name is Steve Miles I'm a
+
+ align:start position:0%
+event uh my name is Steve Miles I'm a
+ 
+
+ align:start position:0%
+event uh my name is Steve Miles I'm a
+research engineer here at the lab and am
+
+ align:start position:0%
+research engineer here at the lab and am
+ 
+
+ align:start position:0%
+research engineer here at the lab and am
+the uh conference committee chair for uh
+
+ align:start position:0%
+the uh conference committee chair for uh
+ 
+
+ align:start position:0%
+the uh conference committee chair for uh
+for this Gathering uh I'd like to just
+
+ align:start position:0%
+for this Gathering uh I'd like to just
+ 
+
+ align:start position:0%
+for this Gathering uh I'd like to just
+give you an overview of what's what's
+
+ align:start position:0%
+give you an overview of what's what's
+ 
+
+ align:start position:0%
+give you an overview of what's what's
+happening over the next couple of days
+
+ align:start position:0%
+happening over the next couple of days
+ 
+
+ align:start position:0%
+happening over the next couple of days
+so you can visualize the the agenda and
+
+ align:start position:0%
+so you can visualize the the agenda and
+ 
+
+ align:start position:0%
+so you can visualize the the agenda and
+and then also uh thank some of the
+
+ align:start position:0%
+and then also uh thank some of the
+ 
+
+ align:start position:0%
+and then also uh thank some of the
+people uh who are here with us today
+
+ align:start position:0%
+people uh who are here with us today
+ 
+
+ align:start position:0%
+people uh who are here with us today
+without whom uh this event uh couldn't
+
+ align:start position:0%
+without whom uh this event uh couldn't
+ 
+
+ align:start position:0%
+without whom uh this event uh couldn't
+have happened so um I guess first to
+
+ align:start position:0%
+have happened so um I guess first to
+ 
+
+ align:start position:0%
+have happened so um I guess first to
+start with the with the thank yous
+
+ align:start position:0%
+start with the with the thank yous
+ 
+
+ align:start position:0%
+start with the with the thank yous
+there's a conference committee that was
+
+ align:start position:0%
+there's a conference committee that was
+ 
+
+ align:start position:0%
+there's a conference committee that was
+very much created ad hoc people who knew
+
+ align:start position:0%
+very much created ad hoc people who knew
+ 
+
+ align:start position:0%
+very much created ad hoc people who knew
+people who were leading researchers in
+
+ align:start position:0%
+people who were leading researchers in
+ 
+
+ align:start position:0%
+people who were leading researchers in
+this area uh and uh out of that that
+
+ align:start position:0%
+this area uh and uh out of that that
+ 
+
+ align:start position:0%
+this area uh and uh out of that that
+conference committee there are half a do
+
+ align:start position:0%
+conference committee there are half a do
+ 
+
+ align:start position:0%
+conference committee there are half a do
+dozen key contributors who are here who
+
+ align:start position:0%
+dozen key contributors who are here who
+ 
+
+ align:start position:0%
+dozen key contributors who are here who
+I'd like to acknowledge and maybe ask
+
+ align:start position:0%
+I'd like to acknowledge and maybe ask
+ 
+
+ align:start position:0%
+I'd like to acknowledge and maybe ask
+you to stand as I uh as I say your name
+
+ align:start position:0%
+you to stand as I uh as I say your name
+ 
+
+ align:start position:0%
+you to stand as I uh as I say your name
+so that people can see who you are
+
+ align:start position:0%
+so that people can see who you are
+ 
+
+ align:start position:0%
+so that people can see who you are
+because again these are good
+
+ align:start position:0%
+because again these are good
+ 
+
+ align:start position:0%
+because again these are good
+collaborators these are people with whom
+
+ align:start position:0%
+collaborators these are people with whom
+ 
+
+ align:start position:0%
+collaborators these are people with whom
+we've established uh and begun begun to
+
+ align:start position:0%
+we've established uh and begun begun to
+ 
+
+ align:start position:0%
+we've established uh and begun begun to
+think of ways that we can work together
+
+ align:start position:0%
+think of ways that we can work together
+ 
+
+ align:start position:0%
+think of ways that we can work together
+so Dr Bill hardgrave from the University
+
+ align:start position:0%
+so Dr Bill hardgrave from the University
+ 
+
+ align:start position:0%
+so Dr Bill hardgrave from the University
+of Arkansas Bill are you here and Dr
+
+ align:start position:0%
+of Arkansas Bill are you here and Dr
+ 
+
+ align:start position:0%
+of Arkansas Bill are you here and Dr
+jizelle Bennett from Georgia Tech stay
+
+ align:start position:0%
+jizelle Bennett from Georgia Tech stay
+ 
+
+ align:start position:0%
+jizelle Bennett from Georgia Tech stay
+standing because I'm going to ask
+
+ align:start position:0%
+standing because I'm going to ask
+ 
+
+ align:start position:0%
+standing because I'm going to ask
+everybody to applaud when but so
+
+ align:start position:0%
+everybody to applaud when but so
+ 
+
+ align:start position:0%
+everybody to applaud when but so
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+jeanpierre okay uh Dr Rob Clark from
+
+ align:start position:0%
+jeanpierre okay uh Dr Rob Clark from
+ 
+
+ align:start position:0%
+jeanpierre okay uh Dr Rob Clark from
+MSU uh Dr Demitri
+
+ align:start position:0%
+MSU uh Dr Demitri
+ 
+
+ align:start position:0%
+MSU uh Dr Demitri
+kitis from epfl in Switzerland and and
+
+ align:start position:0%
+kitis from epfl in Switzerland and and
+ 
+
+ align:start position:0%
+kitis from epfl in Switzerland and and
+actually uh a non-academic but who was
+
+ align:start position:0%
+actually uh a non-academic but who was
+ 
+
+ align:start position:0%
+actually uh a non-academic but who was
+the person who gets the credit for for
+
+ align:start position:0%
+the person who gets the credit for for
+ 
+
+ align:start position:0%
+the person who gets the credit for for
+the idea of this convocation Mark Rob
+
+ align:start position:0%
+the idea of this convocation Mark Rob
+ 
+
+ align:start position:0%
+the idea of this convocation Mark Rob
+Roberty from uh RFID Journal so this
+
+ align:start position:0%
+Roberty from uh RFID Journal so this
+ 
+
+ align:start position:0%
+Roberty from uh RFID Journal so this
+group of people has been very
+
+ align:start position:0%
+group of people has been very
+ 
+
+ align:start position:0%
+group of people has been very
+instrumental in putting together the
+
+ align:start position:0%
+instrumental in putting together the
+ 
+
+ align:start position:0%
+instrumental in putting together the
+speakers please acknowledge them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then there's a second group that's
+
+ align:start position:0%
+and then there's a second group that's
+ 
+
+ align:start position:0%
+and then there's a second group that's
+really the core group of academic
+
+ align:start position:0%
+really the core group of academic
+ 
+
+ align:start position:0%
+really the core group of academic
+collaborators who had an equal share in
+
+ align:start position:0%
+collaborators who had an equal share in
+ 
+
+ align:start position:0%
+collaborators who had an equal share in
+putting this event together and who you
+
+ align:start position:0%
+putting this event together and who you
+ 
+
+ align:start position:0%
+putting this event together and who you
+will hear from today those of you who
+
+ align:start position:0%
+will hear from today those of you who
+ 
+
+ align:start position:0%
+will hear from today those of you who
+don't know them again we'd like to
+
+ align:start position:0%
+don't know them again we'd like to
+ 
+
+ align:start position:0%
+don't know them again we'd like to
+recognize them as a group so Dr elar F
+
+ align:start position:0%
+recognize them as a group so Dr elar F
+ 
+
+ align:start position:0%
+recognize them as a group so Dr elar F
+from the University of St
+
+ align:start position:0%
+from the University of St
+ 
+
+ align:start position:0%
+from the University of St
+gallon and uh Duncan ma McFarland from
+
+ align:start position:0%
+gallon and uh Duncan ma McFarland from
+ 
+
+ align:start position:0%
+gallon and uh Duncan ma McFarland from
+Cambridge University who's represented
+
+ align:start position:0%
+Cambridge University who's represented
+ 
+
+ align:start position:0%
+Cambridge University who's represented
+by Alan Thorne today is Alan here uh Dr
+
+ align:start position:0%
+by Alan Thorne today is Alan here uh Dr
+ 
+
+ align:start position:0%
+by Alan Thorne today is Alan here uh Dr
+Jun maray of Koo who is in a snowstorm
+
+ align:start position:0%
+Jun maray of Koo who is in a snowstorm
+ 
+
+ align:start position:0%
+Jun maray of Koo who is in a snowstorm
+but is represented by shagu su
+
+ align:start position:0%
+but is represented by shagu su
+ 
+
+ align:start position:0%
+but is represented by shagu su
+Suzuki uh uh Dr howman of Fudan
+
+ align:start position:0%
+Suzuki uh uh Dr howman of Fudan
+ 
+
+ align:start position:0%
+Suzuki uh uh Dr howman of Fudan
+University uh Dr Peter Cole from the
+
+ align:start position:0%
+University uh Dr Peter Cole from the
+ 
+
+ align:start position:0%
+University uh Dr Peter Cole from the
+University at Adelaide and Dr sanle of
+
+ align:start position:0%
+University at Adelaide and Dr sanle of
+ 
+
+ align:start position:0%
+University at Adelaide and Dr sanle of
+the information and Communications
+
+ align:start position:0%
+the information and Communications
+ 
+
+ align:start position:0%
+the information and Communications
+University uh in Korea the latest
+
+ align:start position:0%
+University uh in Korea the latest
+ 
+
+ align:start position:0%
+University uh in Korea the latest
+editions of the Auto ID Labs family
+
+ align:start position:0%
+editions of the Auto ID Labs family
+ 
+
+ align:start position:0%
+editions of the Auto ID Labs family
+together with John Williams who's the
+
+ align:start position:0%
+together with John Williams who's the
+ 
+
+ align:start position:0%
+together with John Williams who's the
+director of the Auto ID Labs here at MIT
+
+ align:start position:0%
+director of the Auto ID Labs here at MIT
+ 
+
+ align:start position:0%
+director of the Auto ID Labs here at MIT
+so a hand for uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this group has been working
+
+ align:start position:0%
+so so this group has been working
+ 
+
+ align:start position:0%
+so so this group has been working
+together now for several years uh
+
+ align:start position:0%
+together now for several years uh
+ 
+
+ align:start position:0%
+together now for several years uh
+looking at ways to collaborate to meet
+
+ align:start position:0%
+looking at ways to collaborate to meet
+ 
+
+ align:start position:0%
+looking at ways to collaborate to meet
+some of the uh some of the opportunities
+
+ align:start position:0%
+some of the uh some of the opportunities
+ 
+
+ align:start position:0%
+some of the uh some of the opportunities
+uh that result as a that come from the
+
+ align:start position:0%
+uh that result as a that come from the
+ 
+
+ align:start position:0%
+uh that result as a that come from the
+adoption of RFID and then finally we
+
+ align:start position:0%
+adoption of RFID and then finally we
+ 
+
+ align:start position:0%
+adoption of RFID and then finally we
+have uh uh graduate students here at MIT
+
+ align:start position:0%
+have uh uh graduate students here at MIT
+ 
+
+ align:start position:0%
+have uh uh graduate students here at MIT
+who've been instrumental in in putting
+
+ align:start position:0%
+who've been instrumental in in putting
+ 
+
+ align:start position:0%
+who've been instrumental in in putting
+this event together is Ali delois here
+
+ align:start position:0%
+this event together is Ali delois here
+ 
+
+ align:start position:0%
+this event together is Ali delois here
+Ali may be out front but she gets the
+
+ align:start position:0%
+Ali may be out front but she gets the
+ 
+
+ align:start position:0%
+Ali may be out front but she gets the
+credit for the logo for the the the
+
+ align:start position:0%
+credit for the logo for the the the
+ 
+
+ align:start position:0%
+credit for the logo for the the the
+posters out front and has organized a
+
+ align:start position:0%
+posters out front and has organized a
+ 
+
+ align:start position:0%
+posters out front and has organized a
+series of fun demonstrations uh of RFID
+
+ align:start position:0%
+series of fun demonstrations uh of RFID
+ 
+
+ align:start position:0%
+series of fun demonstrations uh of RFID
+technology at the MIT Museum tonight for
+
+ align:start position:0%
+technology at the MIT Museum tonight for
+ 
+
+ align:start position:0%
+technology at the MIT Museum tonight for
+the reception and Shri RAM krishnam on
+
+ align:start position:0%
+the reception and Shri RAM krishnam on
+ 
+
+ align:start position:0%
+the reception and Shri RAM krishnam on
+AV uh doctoral candidate in the program
+
+ align:start position:0%
+AV uh doctoral candidate in the program
+ 
+
+ align:start position:0%
+AV uh doctoral candidate in the program
+here together with
+
+ align:start position:0%
+here together with
+ 
+
+ align:start position:0%
+here together with
+seam whose last name I won't try to
+
+ align:start position:0%
+seam whose last name I won't try to
+ 
+
+ align:start position:0%
+seam whose last name I won't try to
+pronounce uh and he's been the volunteer
+
+ align:start position:0%
+pronounce uh and he's been the volunteer
+ 
+
+ align:start position:0%
+pronounce uh and he's been the volunteer
+coordinator so thank you very much to to
+
+ align:start position:0%
+coordinator so thank you very much to to
+ 
+
+ align:start position:0%
+coordinator so thank you very much to to
+that to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+group so so just briefly the outline for
+
+ align:start position:0%
+group so so just briefly the outline for
+ 
+
+ align:start position:0%
+group so so just briefly the outline for
+the day uh John Williams will introduce
+
+ align:start position:0%
+the day uh John Williams will introduce
+ 
+
+ align:start position:0%
+the day uh John Williams will introduce
+our keynote speaker uh following a break
+
+ align:start position:0%
+our keynote speaker uh following a break
+ 
+
+ align:start position:0%
+our keynote speaker uh following a break
+we will then go into sort of this
+
+ align:start position:0%
+we will then go into sort of this
+ 
+
+ align:start position:0%
+we will then go into sort of this
+morning the horizontal technology
+
+ align:start position:0%
+morning the horizontal technology
+ 
+
+ align:start position:0%
+morning the horizontal technology
+sessions so a session on the network
+
+ align:start position:0%
+sessions so a session on the network
+ 
+
+ align:start position:0%
+sessions so a session on the network
+technology related to RFID a session on
+
+ align:start position:0%
+technology related to RFID a session on
+ 
+
+ align:start position:0%
+technology related to RFID a session on
+the tag technology and a session on the
+
+ align:start position:0%
+the tag technology and a session on the
+ 
+
+ align:start position:0%
+the tag technology and a session on the
+RF and the utilization of RF as we look
+
+ align:start position:0%
+RF and the utilization of RF as we look
+ 
+
+ align:start position:0%
+RF and the utilization of RF as we look
+uh you know out in the in the 10 years
+
+ align:start position:0%
+uh you know out in the in the 10 years
+ 
+
+ align:start position:0%
+uh you know out in the in the 10 years
+to come and then in the afternoon we
+
+ align:start position:0%
+to come and then in the afternoon we
+ 
+
+ align:start position:0%
+to come and then in the afternoon we
+move right into sort of Industry
+
+ align:start position:0%
+move right into sort of Industry
+ 
+
+ align:start position:0%
+move right into sort of Industry
+applications for RFID focused around uh
+
+ align:start position:0%
+applications for RFID focused around uh
+ 
+
+ align:start position:0%
+applications for RFID focused around uh
+research areas that have been brought to
+
+ align:start position:0%
+research areas that have been brought to
+ 
+
+ align:start position:0%
+research areas that have been brought to
+the various labs around the world um so
+
+ align:start position:0%
+the various labs around the world um so
+ 
+
+ align:start position:0%
+the various labs around the world um so
+starting with anti-counterfeiting that
+
+ align:start position:0%
+starting with anti-counterfeiting that
+ 
+
+ align:start position:0%
+starting with anti-counterfeiting that
+is led by Dr Elgar FL which is the
+
+ align:start position:0%
+is led by Dr Elgar FL which is the
+ 
+
+ align:start position:0%
+is led by Dr Elgar FL which is the
+flagship product or project for the Auto
+
+ align:start position:0%
+flagship product or project for the Auto
+ 
+
+ align:start position:0%
+flagship product or project for the Auto
+ID Labs collaboration but then uh an
+
+ align:start position:0%
+ID Labs collaboration but then uh an
+ 
+
+ align:start position:0%
+ID Labs collaboration but then uh an
+initiative led by uh Allen at the
+
+ align:start position:0%
+initiative led by uh Allen at the
+ 
+
+ align:start position:0%
+initiative led by uh Allen at the
+University of C bridge in uh in
+
+ align:start position:0%
+University of C bridge in uh in
+ 
+
+ align:start position:0%
+University of C bridge in uh in
+Aeronautics uh for those of you who may
+
+ align:start position:0%
+Aeronautics uh for those of you who may
+ 
+
+ align:start position:0%
+Aeronautics uh for those of you who may
+not be familiar with this opportunity
+
+ align:start position:0%
+not be familiar with this opportunity
+ 
+
+ align:start position:0%
+not be familiar with this opportunity
+Boeing and Airbus have decided to to
+
+ align:start position:0%
+Boeing and Airbus have decided to to
+ 
+
+ align:start position:0%
+Boeing and Airbus have decided to to
+redesign their entire supply chain more
+
+ align:start position:0%
+redesign their entire supply chain more
+ 
+
+ align:start position:0%
+redesign their entire supply chain more
+on the order of the on the model of the
+
+ align:start position:0%
+on the order of the on the model of the
+ 
+
+ align:start position:0%
+on the order of the on the model of the
+automotive industry where they'll be
+
+ align:start position:0%
+automotive industry where they'll be
+ 
+
+ align:start position:0%
+automotive industry where they'll be
+able to to exchange subassemblies and
+
+ align:start position:0%
+able to to exchange subassemblies and
+ 
+
+ align:start position:0%
+able to to exchange subassemblies and
+there's a requirement for an active tag
+
+ align:start position:0%
+there's a requirement for an active tag
+ 
+
+ align:start position:0%
+there's a requirement for an active tag
+to go on those subassemblies so that a
+
+ align:start position:0%
+to go on those subassemblies so that a
+ 
+
+ align:start position:0%
+to go on those subassemblies so that a
+Boeing shop might might exchange a sub
+
+ align:start position:0%
+Boeing shop might might exchange a sub
+ 
+
+ align:start position:0%
+Boeing shop might might exchange a sub
+assembly with an Airbus customer and for
+
+ align:start position:0%
+assembly with an Airbus customer and for
+ 
+
+ align:start position:0%
+assembly with an Airbus customer and for
+that to occur will clearly involve uh
+
+ align:start position:0%
+that to occur will clearly involve uh
+ 
+
+ align:start position:0%
+that to occur will clearly involve uh
+University Research and aircraft Parts
+
+ align:start position:0%
+University Research and aircraft Parts
+ 
+
+ align:start position:0%
+University Research and aircraft Parts
+manufacturers throughout the world and
+
+ align:start position:0%
+manufacturers throughout the world and
+ 
+
+ align:start position:0%
+manufacturers throughout the world and
+will require a response from the
+
+ align:start position:0%
+will require a response from the
+ 
+
+ align:start position:0%
+will require a response from the
+academic Community that's far more
+
+ align:start position:0%
+academic Community that's far more
+ 
+
+ align:start position:0%
+academic Community that's far more
+coordinated than what we've done in the
+
+ align:start position:0%
+coordinated than what we've done in the
+ 
+
+ align:start position:0%
+coordinated than what we've done in the
+past and from from Aeronautics we go
+
+ align:start position:0%
+past and from from Aeronautics we go
+ 
+
+ align:start position:0%
+past and from from Aeronautics we go
+into automotive and then we're very
+
+ align:start position:0%
+into automotive and then we're very
+ 
+
+ align:start position:0%
+into automotive and then we're very
+privileged to have uh uh the vice
+
+ align:start position:0%
+privileged to have uh uh the vice
+ 
+
+ align:start position:0%
+privileged to have uh uh the vice
+president of Johnson and Johnson who's
+
+ align:start position:0%
+president of Johnson and Johnson who's
+ 
+
+ align:start position:0%
+president of Johnson and Johnson who's
+put together together with the EPC
+
+ align:start position:0%
+put together together with the EPC
+ 
+
+ align:start position:0%
+put together together with the EPC
+Global uh uh healthc care U uh life
+
+ align:start position:0%
+Global uh uh healthc care U uh life
+ 
+
+ align:start position:0%
+Global uh uh healthc care U uh life
+sciences coordinator a program on or a
+
+ align:start position:0%
+sciences coordinator a program on or a
+ 
+
+ align:start position:0%
+sciences coordinator a program on or a
+session on Healthcare to conclude the
+
+ align:start position:0%
+session on Healthcare to conclude the
+ 
+
+ align:start position:0%
+session on Healthcare to conclude the
+the the day and and then at at 5:00 we
+
+ align:start position:0%
+the the day and and then at at 5:00 we
+ 
+
+ align:start position:0%
+the the day and and then at at 5:00 we
+will um move up to the MIT Museum for
+
+ align:start position:0%
+will um move up to the MIT Museum for
+ 
+
+ align:start position:0%
+will um move up to the MIT Museum for
+reception and a time to meet one another
+
+ align:start position:0%
+reception and a time to meet one another
+ 
+
+ align:start position:0%
+reception and a time to meet one another
+and also please take a chance to see the
+
+ align:start position:0%
+and also please take a chance to see the
+ 
+
+ align:start position:0%
+and also please take a chance to see the
+half a dozen demos which are which are
+
+ align:start position:0%
+half a dozen demos which are which are
+ 
+
+ align:start position:0%
+half a dozen demos which are which are
+there uh showing uh different
+
+ align:start position:0%
+there uh showing uh different
+ 
+
+ align:start position:0%
+there uh showing uh different
+applications for RFID I believe one of
+
+ align:start position:0%
+applications for RFID I believe one of
+ 
+
+ align:start position:0%
+applications for RFID I believe one of
+which has a is an espresso machine which
+
+ align:start position:0%
+which has a is an espresso machine which
+ 
+
+ align:start position:0%
+which has a is an espresso machine which
+recognizes your taste in coffee by your
+
+ align:start position:0%
+recognizes your taste in coffee by your
+ 
+
+ align:start position:0%
+recognizes your taste in coffee by your
+by your cup as I understand
+
+ align:start position:0%
+by your cup as I understand
+ 
+
+ align:start position:0%
+by your cup as I understand
+it and then uh uh tomorrow we we have a
+
+ align:start position:0%
+it and then uh uh tomorrow we we have a
+ 
+
+ align:start position:0%
+it and then uh uh tomorrow we we have a
+a a very extensive session in uh in
+
+ align:start position:0%
+a a very extensive session in uh in
+ 
+
+ align:start position:0%
+a a very extensive session in uh in
+supply chain and then packaging and uh
+
+ align:start position:0%
+supply chain and then packaging and uh
+ 
+
+ align:start position:0%
+supply chain and then packaging and uh
+uh after a a light box L box lunch will
+
+ align:start position:0%
+uh after a a light box L box lunch will
+ 
+
+ align:start position:0%
+uh after a a light box L box lunch will
+reconvene for applications for RFID
+
+ align:start position:0%
+reconvene for applications for RFID
+ 
+
+ align:start position:0%
+reconvene for applications for RFID
+beyond the supply chain and then a
+
+ align:start position:0%
+beyond the supply chain and then a
+ 
+
+ align:start position:0%
+beyond the supply chain and then a
+concluding panel uh with some of the
+
+ align:start position:0%
+concluding panel uh with some of the
+ 
+
+ align:start position:0%
+concluding panel uh with some of the
+executives uh who are here and and part
+
+ align:start position:0%
+executives uh who are here and and part
+ 
+
+ align:start position:0%
+executives uh who are here and and part
+of the format of each of these sessions
+
+ align:start position:0%
+of the format of each of these sessions
+ 
+
+ align:start position:0%
+of the format of each of these sessions
+is to give academics no more academics
+
+ align:start position:0%
+is to give academics no more academics
+ 
+
+ align:start position:0%
+is to give academics no more academics
+no more than 10 minutes to talk about
+
+ align:start position:0%
+no more than 10 minutes to talk about
+ 
+
+ align:start position:0%
+no more than 10 minutes to talk about
+really what's key in our research and
+
+ align:start position:0%
+really what's key in our research and
+ 
+
+ align:start position:0%
+really what's key in our research and
+then to get some feedback in each of the
+
+ align:start position:0%
+then to get some feedback in each of the
+ 
+
+ align:start position:0%
+then to get some feedback in each of the
+sessions both from industry panelists
+
+ align:start position:0%
+sessions both from industry panelists
+ 
+
+ align:start position:0%
+sessions both from industry panelists
+and from the audience as to the
+
+ align:start position:0%
+and from the audience as to the
+ 
+
+ align:start position:0%
+and from the audience as to the
+applicability utility and possible
+
+ align:start position:0%
+applicability utility and possible
+ 
+
+ align:start position:0%
+applicability utility and possible
+Direction uh for for that uh that
+
+ align:start position:0%
+Direction uh for for that uh that
+ 
+
+ align:start position:0%
+Direction uh for for that uh that
+research so are there are there any
+
+ align:start position:0%
+research so are there are there any
+ 
+
+ align:start position:0%
+research so are there are there any
+questions about the logistics there was
+
+ align:start position:0%
+questions about the logistics there was
+ 
+
+ align:start position:0%
+questions about the logistics there was
+one question bathrooms are
+
+ align:start position:0%
+one question bathrooms are
+ 
+
+ align:start position:0%
+one question bathrooms are
+located that way uh for lunch we are
+
+ align:start position:0%
+located that way uh for lunch we are
+ 
+
+ align:start position:0%
+located that way uh for lunch we are
+going to walk to the other side of
+
+ align:start position:0%
+going to walk to the other side of
+ 
+
+ align:start position:0%
+going to walk to the other side of
+massab to the student center and so we
+
+ align:start position:0%
+massab to the student center and so we
+ 
+
+ align:start position:0%
+massab to the student center and so we
+might we might try to do this through
+
+ align:start position:0%
+might we might try to do this through
+ 
+
+ align:start position:0%
+might we might try to do this through
+the buildings to stay dry we'll see how
+
+ align:start position:0%
+the buildings to stay dry we'll see how
+ 
+
+ align:start position:0%
+the buildings to stay dry we'll see how
+how the weather holds up um but if there
+
+ align:start position:0%
+how the weather holds up um but if there
+ 
+
+ align:start position:0%
+how the weather holds up um but if there
+are no questions uh about logistics at
+
+ align:start position:0%
+are no questions uh about logistics at
+ 
+
+ align:start position:0%
+are no questions uh about logistics at
+this time I'd like to hand the uh
+
+ align:start position:0%
+this time I'd like to hand the uh
+ 
+
+ align:start position:0%
+this time I'd like to hand the uh
+convocation over to professor John
+
+ align:start position:0%
+convocation over to professor John
+ 
+
+ align:start position:0%
+convocation over to professor John
+Williams who's the director of the Auto
+
+ align:start position:0%
+Williams who's the director of the Auto
+ 
+
+ align:start position:0%
+Williams who's the director of the Auto
+ID Labs here at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+MIT uh thanks very much uh I want to
+
+ align:start position:0%
+MIT uh thanks very much uh I want to
+ 
+
+ align:start position:0%
+MIT uh thanks very much uh I want to
+welcome you all here to MIT on this kind
+
+ align:start position:0%
+welcome you all here to MIT on this kind
+ 
+
+ align:start position:0%
+welcome you all here to MIT on this kind
+of uh typical uh Boston day um I often
+
+ align:start position:0%
+of uh typical uh Boston day um I often
+ 
+
+ align:start position:0%
+of uh typical uh Boston day um I often
+wondered why MIT got so much research
+
+ align:start position:0%
+wondered why MIT got so much research
+ 
+
+ align:start position:0%
+wondered why MIT got so much research
+done and until I moved here and then I
+
+ align:start position:0%
+done and until I moved here and then I
+ 
+
+ align:start position:0%
+done and until I moved here and then I
+began to understand that in the winter
+
+ align:start position:0%
+began to understand that in the winter
+ 
+
+ align:start position:0%
+began to understand that in the winter
+you're basically locked in and there's
+
+ align:start position:0%
+you're basically locked in and there's
+ 
+
+ align:start position:0%
+you're basically locked in and there's
+nothing to do except research so that's
+
+ align:start position:0%
+nothing to do except research so that's
+ 
+
+ align:start position:0%
+nothing to do except research so that's
+the explanation uh why MIT uh is pretty
+
+ align:start position:0%
+the explanation uh why MIT uh is pretty
+ 
+
+ align:start position:0%
+the explanation uh why MIT uh is pretty
+Innovative I'd like to thank Steve uh
+
+ align:start position:0%
+Innovative I'd like to thank Steve uh
+ 
+
+ align:start position:0%
+Innovative I'd like to thank Steve uh
+miles especially for putting this on
+
+ align:start position:0%
+miles especially for putting this on
+ 
+
+ align:start position:0%
+miles especially for putting this on
+really it's been his effort uh along
+
+ align:start position:0%
+really it's been his effort uh along
+ 
+
+ align:start position:0%
+really it's been his effort uh along
+with the organizing committee um but
+
+ align:start position:0%
+with the organizing committee um but
+ 
+
+ align:start position:0%
+with the organizing committee um but
+he's done a tremendous amount so I'd
+
+ align:start position:0%
+he's done a tremendous amount so I'd
+ 
+
+ align:start position:0%
+he's done a tremendous amount so I'd
+like to give
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a uh before I well we uh I welcome uh
+
+ align:start position:0%
+a uh before I well we uh I welcome uh
+ 
+
+ align:start position:0%
+a uh before I well we uh I welcome uh
+our our first speaker um I'd like to
+
+ align:start position:0%
+our our first speaker um I'd like to
+ 
+
+ align:start position:0%
+our our first speaker um I'd like to
+just remind you I think how important
+
+ align:start position:0%
+just remind you I think how important
+ 
+
+ align:start position:0%
+just remind you I think how important
+this is that in the Auto ID Labs uh this
+
+ align:start position:0%
+this is that in the Auto ID Labs uh this
+ 
+
+ align:start position:0%
+this is that in the Auto ID Labs uh this
+uh Consortium of seven Labs we got
+
+ align:start position:0%
+uh Consortium of seven Labs we got
+ 
+
+ align:start position:0%
+uh Consortium of seven Labs we got
+together um as uh a Consortium with the
+
+ align:start position:0%
+together um as uh a Consortium with the
+ 
+
+ align:start position:0%
+together um as uh a Consortium with the
+goal of architecting the internet of
+
+ align:start position:0%
+goal of architecting the internet of
+ 
+
+ align:start position:0%
+goal of architecting the internet of
+things and when you talk about the
+
+ align:start position:0%
+things and when you talk about the
+ 
+
+ align:start position:0%
+things and when you talk about the
+internet of things it's really an
+
+ align:start position:0%
+internet of things it's really an
+ 
+
+ align:start position:0%
+internet of things it's really an
+infrastructure that's going to have to
+
+ align:start position:0%
+infrastructure that's going to have to
+ 
+
+ align:start position:0%
+infrastructure that's going to have to
+last 100 years if you think about the
+
+ align:start position:0%
+last 100 years if you think about the
+ 
+
+ align:start position:0%
+last 100 years if you think about the
+railway system the power
+
+ align:start position:0%
+railway system the power
+ 
+
+ align:start position:0%
+railway system the power
+system um our water supply systems these
+
+ align:start position:0%
+system um our water supply systems these
+ 
+
+ align:start position:0%
+system um our water supply systems these
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+infrastructures that uh support society
+
+ align:start position:0%
+infrastructures that uh support society
+ 
+
+ align:start position:0%
+infrastructures that uh support society
+and are going to have to last I worry
+
+ align:start position:0%
+and are going to have to last I worry
+ 
+
+ align:start position:0%
+and are going to have to last I worry
+that about this infrastructure that we
+
+ align:start position:0%
+that about this infrastructure that we
+ 
+
+ align:start position:0%
+that about this infrastructure that we
+need to think seriously about it that
+
+ align:start position:0%
+need to think seriously about it that
+ 
+
+ align:start position:0%
+need to think seriously about it that
+it's not just fast moving consumer goods
+
+ align:start position:0%
+it's not just fast moving consumer goods
+ 
+
+ align:start position:0%
+it's not just fast moving consumer goods
+it's it's going to be knowing what what
+
+ align:start position:0%
+it's it's going to be knowing what what
+ 
+
+ align:start position:0%
+it's it's going to be knowing what what
+something is where it is when it's the
+
+ align:start position:0%
+something is where it is when it's the
+ 
+
+ align:start position:0%
+something is where it is when it's the
+there and why it's there and this is
+
+ align:start position:0%
+there and why it's there and this is
+ 
+
+ align:start position:0%
+there and why it's there and this is
+going to be tremendously important that
+
+ align:start position:0%
+going to be tremendously important that
+ 
+
+ align:start position:0%
+going to be tremendously important that
+we future proof uh this architecture and
+
+ align:start position:0%
+we future proof uh this architecture and
+ 
+
+ align:start position:0%
+we future proof uh this architecture and
+I think that's the goal uh of this
+
+ align:start position:0%
+I think that's the goal uh of this
+ 
+
+ align:start position:0%
+I think that's the goal uh of this
+convocation is for us to identify the
+
+ align:start position:0%
+convocation is for us to identify the
+ 
+
+ align:start position:0%
+convocation is for us to identify the
+research that's
+
+ align:start position:0%
+research that's
+ 
+
+ align:start position:0%
+research that's
+necessary so that this infrastructure
+
+ align:start position:0%
+necessary so that this infrastructure
+ 
+
+ align:start position:0%
+necessary so that this infrastructure
+Will Survive so I think it's
+
+ align:start position:0%
+Will Survive so I think it's
+ 
+
+ align:start position:0%
+Will Survive so I think it's
+tremendously important that we think
+
+ align:start position:0%
+tremendously important that we think
+ 
+
+ align:start position:0%
+tremendously important that we think
+about that that this Glo it's a global
+
+ align:start position:0%
+about that that this Glo it's a global
+ 
+
+ align:start position:0%
+about that that this Glo it's a global
+infrastructure it's cross countries
+
+ align:start position:0%
+infrastructure it's cross countries
+ 
+
+ align:start position:0%
+infrastructure it's cross countries
+cross boundaries it's going to be
+
+ align:start position:0%
+cross boundaries it's going to be
+ 
+
+ align:start position:0%
+cross boundaries it's going to be
+incredibly difficult to do that so
+
+ align:start position:0%
+incredibly difficult to do that so
+ 
+
+ align:start position:0%
+incredibly difficult to do that so
+we're very fortunate today to have one
+
+ align:start position:0%
+we're very fortunate today to have one
+ 
+
+ align:start position:0%
+we're very fortunate today to have one
+of the founders of RFID Professor sanay
+
+ align:start position:0%
+of the founders of RFID Professor sanay
+ 
+
+ align:start position:0%
+of the founders of RFID Professor sanay
+Sharma here uh who's going to tell us um
+
+ align:start position:0%
+Sharma here uh who's going to tell us um
+ 
+
+ align:start position:0%
+Sharma here uh who's going to tell us um
+about research in
+
+ align:start position:0%
+about research in
+ 
+
+ align:start position:0%
+about research in
+RFID uh so I'd like to welcome him and
+
+ align:start position:0%
+RFID uh so I'd like to welcome him and
+ 
+
+ align:start position:0%
+RFID uh so I'd like to welcome him and
+welcome you all to
\ No newline at end of file
diff --git a/It2ggiEoIoI.txt b/It2ggiEoIoI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a534f25339a8bf93fc9db6dae8602a94059506e5
--- /dev/null
+++ b/It2ggiEoIoI.txt
@@ -0,0 +1,15371 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay welcome to the second
+
+ align:start position:0%
+ocw.mit.edu okay welcome to the second
+ 
+
+ align:start position:0%
+ocw.mit.edu okay welcome to the second
+uh lecture in the CDD spring Forum here
+
+ align:start position:0%
+uh lecture in the CDD spring Forum here
+ 
+
+ align:start position:0%
+uh lecture in the CDD spring Forum here
+at MIT Department of urban studies and
+
+ align:start position:0%
+at MIT Department of urban studies and
+ 
+
+ align:start position:0%
+at MIT Department of urban studies and
+planning uh sensing Place photography is
+
+ align:start position:0%
+planning uh sensing Place photography is
+ 
+
+ align:start position:0%
+planning uh sensing Place photography is
+inquiry
+
+ align:start position:0%
+inquiry
+ 
+
+ align:start position:0%
+inquiry
+and uh before I introduce our speaker
+
+ align:start position:0%
+and uh before I introduce our speaker
+ 
+
+ align:start position:0%
+and uh before I introduce our speaker
+for tonight Camilo varara I want to
+
+ align:start position:0%
+for tonight Camilo varara I want to
+ 
+
+ align:start position:0%
+for tonight Camilo varara I want to
+remind you all uh that Lou Watts will be
+
+ align:start position:0%
+remind you all uh that Lou Watts will be
+ 
+
+ align:start position:0%
+remind you all uh that Lou Watts will be
+speaking next week Lou is uh professor
+
+ align:start position:0%
+speaking next week Lou is uh professor
+ 
+
+ align:start position:0%
+speaking next week Lou is uh professor
+at the University of California Santa
+
+ align:start position:0%
+at the University of California Santa
+ 
+
+ align:start position:0%
+at the University of California Santa
+Cruz uh taught at Berkeley for many
+
+ align:start position:0%
+Cruz uh taught at Berkeley for many
+ 
+
+ align:start position:0%
+Cruz uh taught at Berkeley for many
+years and he will be speaking on
+
+ align:start position:0%
+years and he will be speaking on
+ 
+
+ align:start position:0%
+years and he will be speaking on
+communities of color traces of history
+
+ align:start position:0%
+communities of color traces of history
+ 
+
+ align:start position:0%
+communities of color traces of history
+and culture about his search tracing uh
+
+ align:start position:0%
+and culture about his search tracing uh
+ 
+
+ align:start position:0%
+and culture about his search tracing uh
+in both rural communities and urban
+
+ align:start position:0%
+in both rural communities and urban
+ 
+
+ align:start position:0%
+in both rural communities and urban
+commun ities um the roots of
+
+ align:start position:0%
+commun ities um the roots of
+ 
+
+ align:start position:0%
+commun ities um the roots of
+African-American uh history and
+
+ align:start position:0%
+African-American uh history and
+ 
+
+ align:start position:0%
+African-American uh history and
+culture I first uh I've known Camila
+
+ align:start position:0%
+culture I first uh I've known Camila
+ 
+
+ align:start position:0%
+culture I first uh I've known Camila
+agar's work for some time since his book
+
+ align:start position:0%
+agar's work for some time since his book
+ 
+
+ align:start position:0%
+agar's work for some time since his book
+uh the new American ghetto was published
+
+ align:start position:0%
+uh the new American ghetto was published
+ 
+
+ align:start position:0%
+uh the new American ghetto was published
+but I had the pleasure of meeting him
+
+ align:start position:0%
+but I had the pleasure of meeting him
+ 
+
+ align:start position:0%
+but I had the pleasure of meeting him
+just after American ruins had come out
+
+ align:start position:0%
+just after American ruins had come out
+ 
+
+ align:start position:0%
+just after American ruins had come out
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+1999 at a conference at the University
+
+ align:start position:0%
+1999 at a conference at the University
+ 
+
+ align:start position:0%
+1999 at a conference at the University
+of Michigan in an arbor and uh we poured
+
+ align:start position:0%
+of Michigan in an arbor and uh we poured
+ 
+
+ align:start position:0%
+of Michigan in an arbor and uh we poured
+over his book and um it turned out
+
+ align:start position:0%
+over his book and um it turned out
+ 
+
+ align:start position:0%
+over his book and um it turned out
+Camille had a rental car and was
+
+ align:start position:0%
+Camille had a rental car and was
+ 
+
+ align:start position:0%
+Camille had a rental car and was
+planning on going in shooting
+
+ align:start position:0%
+planning on going in shooting
+ 
+
+ align:start position:0%
+planning on going in shooting
+photographs in Detroit in Detroit uh at
+
+ align:start position:0%
+photographs in Detroit in Detroit uh at
+ 
+
+ align:start position:0%
+photographs in Detroit in Detroit uh at
+the end of the conference so um we
+
+ align:start position:0%
+the end of the conference so um we
+ 
+
+ align:start position:0%
+the end of the conference so um we
+hooked up and uh took a field trip into
+
+ align:start position:0%
+hooked up and uh took a field trip into
+ 
+
+ align:start position:0%
+hooked up and uh took a field trip into
+uh Detroit into the uh the train station
+
+ align:start position:0%
+uh Detroit into the uh the train station
+ 
+
+ align:start position:0%
+uh Detroit into the uh the train station
+and the old Packard plant and um really
+
+ align:start position:0%
+and the old Packard plant and um really
+ 
+
+ align:start position:0%
+and the old Packard plant and um really
+um uh some extraordinary uh places
+
+ align:start position:0%
+um uh some extraordinary uh places
+ 
+
+ align:start position:0%
+um uh some extraordinary uh places
+Camilo has been photographing
+
+ align:start position:0%
+Camilo has been photographing
+ 
+
+ align:start position:0%
+Camilo has been photographing
+many different American cities for uh
+
+ align:start position:0%
+many different American cities for uh
+ 
+
+ align:start position:0%
+many different American cities for uh
+decades uh in some cases from the same
+
+ align:start position:0%
+decades uh in some cases from the same
+ 
+
+ align:start position:0%
+decades uh in some cases from the same
+place coming back to the same street
+
+ align:start position:0%
+place coming back to the same street
+ 
+
+ align:start position:0%
+place coming back to the same street
+corner or to the same rooftop looking
+
+ align:start position:0%
+corner or to the same rooftop looking
+ 
+
+ align:start position:0%
+corner or to the same rooftop looking
+down uh on the same scene and
+
+ align:start position:0%
+down uh on the same scene and
+ 
+
+ align:start position:0%
+down uh on the same scene and
+photographing uh the changes over time
+
+ align:start position:0%
+photographing uh the changes over time
+ 
+
+ align:start position:0%
+photographing uh the changes over time
+in cam in New Jersey in Philadelphia in
+
+ align:start position:0%
+in cam in New Jersey in Philadelphia in
+ 
+
+ align:start position:0%
+in cam in New Jersey in Philadelphia in
+New York City in Chicago in
+
+ align:start position:0%
+New York City in Chicago in
+ 
+
+ align:start position:0%
+New York City in Chicago in
+Detroit um and uh numerous nous other
+
+ align:start position:0%
+Detroit um and uh numerous nous other
+ 
+
+ align:start position:0%
+Detroit um and uh numerous nous other
+cities across the country he's won um
+
+ align:start position:0%
+cities across the country he's won um
+ 
+
+ align:start position:0%
+cities across the country he's won um
+many awards most recently he's uh was
+
+ align:start position:0%
+many awards most recently he's uh was
+ 
+
+ align:start position:0%
+many awards most recently he's uh was
+appointed a MacArthur fellow and uh has
+
+ align:start position:0%
+appointed a MacArthur fellow and uh has
+ 
+
+ align:start position:0%
+appointed a MacArthur fellow and uh has
+many books so if you get intrigued and
+
+ align:start position:0%
+many books so if you get intrigued and
+ 
+
+ align:start position:0%
+many books so if you get intrigued and
+introduced to his photography here
+
+ align:start position:0%
+introduced to his photography here
+ 
+
+ align:start position:0%
+introduced to his photography here
+tonight um you can uh so we have a the
+
+ align:start position:0%
+tonight um you can uh so we have a the
+ 
+
+ align:start position:0%
+tonight um you can uh so we have a the
+new edition of American ruins up here on
+
+ align:start position:0%
+new edition of American ruins up here on
+ 
+
+ align:start position:0%
+new edition of American ruins up here on
+the table that you can take a look at
+
+ align:start position:0%
+the table that you can take a look at
+ 
+
+ align:start position:0%
+the table that you can take a look at
+afterwards um I won't go on and on
+
+ align:start position:0%
+afterwards um I won't go on and on
+ 
+
+ align:start position:0%
+afterwards um I won't go on and on
+anymore come lives in New York and he'll
+
+ align:start position:0%
+anymore come lives in New York and he'll
+ 
+
+ align:start position:0%
+anymore come lives in New York and he'll
+tell you more about what he does and how
+
+ align:start position:0%
+tell you more about what he does and how
+ 
+
+ align:start position:0%
+tell you more about what he does and how
+he goes about doing it and why uh his
+
+ align:start position:0%
+he goes about doing it and why uh his
+ 
+
+ align:start position:0%
+he goes about doing it and why uh his
+background by the way is as a
+
+ align:start position:0%
+background by the way is as a
+ 
+
+ align:start position:0%
+background by the way is as a
+sociologist well it's a great pleasure
+
+ align:start position:0%
+sociologist well it's a great pleasure
+ 
+
+ align:start position:0%
+sociologist well it's a great pleasure
+yeah well um very happy to be here this
+
+ align:start position:0%
+yeah well um very happy to be here this
+ 
+
+ align:start position:0%
+yeah well um very happy to be here this
+is my second time here I was invited uh
+
+ align:start position:0%
+is my second time here I was invited uh
+ 
+
+ align:start position:0%
+is my second time here I was invited uh
+about 15 years ago and uh I
+
+ align:start position:0%
+about 15 years ago and uh I
+ 
+
+ align:start position:0%
+about 15 years ago and uh I
+spoke there was somebody teaching Urban
+
+ align:start position:0%
+spoke there was somebody teaching Urban
+ 
+
+ align:start position:0%
+spoke there was somebody teaching Urban
+studies here that had run from mayor
+
+ align:start position:0%
+studies here that had run from mayor
+ 
+
+ align:start position:0%
+studies here that had run from mayor
+Boston a couple times name was Mel
+
+ align:start position:0%
+Boston a couple times name was Mel
+ 
+
+ align:start position:0%
+Boston a couple times name was Mel
+King and uh he he taught a course in
+
+ align:start position:0%
+King and uh he he taught a course in
+ 
+
+ align:start position:0%
+King and uh he he taught a course in
+urban history here or Urban
+
+ align:start position:0%
+urban history here or Urban
+ 
+
+ align:start position:0%
+urban history here or Urban
+studies and there were two students who
+
+ align:start position:0%
+studies and there were two students who
+ 
+
+ align:start position:0%
+studies and there were two students who
+I don't know where they had found out
+
+ align:start position:0%
+I don't know where they had found out
+ 
+
+ align:start position:0%
+I don't know where they had found out
+what I was doing I don't think my book
+
+ align:start position:0%
+what I was doing I don't think my book
+ 
+
+ align:start position:0%
+what I was doing I don't think my book
+was out at that time but I was doing
+
+ align:start position:0%
+was out at that time but I was doing
+ 
+
+ align:start position:0%
+was out at that time but I was doing
+some articles of different pieces and I
+
+ align:start position:0%
+some articles of different pieces and I
+ 
+
+ align:start position:0%
+some articles of different pieces and I
+think something had come out in the
+
+ align:start position:0%
+think something had come out in the
+ 
+
+ align:start position:0%
+think something had come out in the
+nation or something and one of the
+
+ align:start position:0%
+nation or something and one of the
+ 
+
+ align:start position:0%
+nation or something and one of the
+students called Berg call
+
+ align:start position:0%
+students called Berg call
+ 
+
+ align:start position:0%
+students called Berg call
+me and I spoke I will never forget
+
+ align:start position:0%
+me and I spoke I will never forget
+ 
+
+ align:start position:0%
+me and I spoke I will never forget
+because it was like an
+
+ align:start position:0%
+because it was like an
+ 
+
+ align:start position:0%
+because it was like an
+Amphitheater and it was all pack and
+
+ align:start position:0%
+Amphitheater and it was all pack and
+ 
+
+ align:start position:0%
+Amphitheater and it was all pack and
+there was students standing up in the
+
+ align:start position:0%
+there was students standing up in the
+ 
+
+ align:start position:0%
+there was students standing up in the
+back and and uh and it was you know
+
+ align:start position:0%
+back and and uh and it was you know
+ 
+
+ align:start position:0%
+back and and uh and it was you know
+almost
+
+ align:start position:0%
+almost
+ 
+
+ align:start position:0%
+almost
+like an operating room except that it
+
+ align:start position:0%
+like an operating room except that it
+ 
+
+ align:start position:0%
+like an operating room except that it
+didn't have a Cav there in front of
+
+ align:start position:0%
+didn't have a Cav there in front of
+ 
+
+ align:start position:0%
+didn't have a Cav there in front of
+me uh and it was a very exciting thing I
+
+ align:start position:0%
+me uh and it was a very exciting thing I
+ 
+
+ align:start position:0%
+me uh and it was a very exciting thing I
+just I was Tongue Tied more than I am
+
+ align:start position:0%
+just I was Tongue Tied more than I am
+ 
+
+ align:start position:0%
+just I was Tongue Tied more than I am
+now and uh but it was a receptive crowd
+
+ align:start position:0%
+now and uh but it was a receptive crowd
+ 
+
+ align:start position:0%
+now and uh but it was a receptive crowd
+and it was a it was a great moment for
+
+ align:start position:0%
+and it was a it was a great moment for
+ 
+
+ align:start position:0%
+and it was a it was a great moment for
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+so I have very fun memories and I'm
+
+ align:start position:0%
+so I have very fun memories and I'm
+ 
+
+ align:start position:0%
+so I have very fun memories and I'm
+happy to be here and I'm happy to be
+
+ align:start position:0%
+happy to be here and I'm happy to be
+ 
+
+ align:start position:0%
+happy to be here and I'm happy to be
+invited here uh I will briefly try to
+
+ align:start position:0%
+invited here uh I will briefly try to
+ 
+
+ align:start position:0%
+invited here uh I will briefly try to
+set up this this idea this website of
+
+ align:start position:0%
+set up this this idea this website of
+ 
+
+ align:start position:0%
+set up this this idea this website of
+mine and and what I'm trying to do uh I
+
+ align:start position:0%
+mine and and what I'm trying to do uh I
+ 
+
+ align:start position:0%
+mine and and what I'm trying to do uh I
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh what I was trying to do is what I
+
+ align:start position:0%
+uh what I was trying to do is what I
+ 
+
+ align:start position:0%
+uh what I was trying to do is what I
+used to see one of my professors at
+
+ align:start position:0%
+used to see one of my professors at
+ 
+
+ align:start position:0%
+used to see one of my professors at
+Columbia do he would take a hand like
+
+ align:start position:0%
+Columbia do he would take a hand like
+ 
+
+ align:start position:0%
+Columbia do he would take a hand like
+this and he says here put the two hands
+
+ align:start position:0%
+this and he says here put the two hands
+ 
+
+ align:start position:0%
+this and he says here put the two hands
+together then you make an image of it an
+
+ align:start position:0%
+together then you make an image of it an
+ 
+
+ align:start position:0%
+together then you make an image of it an
+impression so how do you take a city and
+
+ align:start position:0%
+impression so how do you take a city and
+ 
+
+ align:start position:0%
+impression so how do you take a city and
+you through pictures you make an
+
+ align:start position:0%
+you through pictures you make an
+ 
+
+ align:start position:0%
+you through pictures you make an
+impression so that that city is
+
+ align:start position:0%
+impression so that that city is
+ 
+
+ align:start position:0%
+impression so that that city is
+reflected in the images that you
+
+ align:start position:0%
+reflected in the images that you
+ 
+
+ align:start position:0%
+reflected in the images that you
+take uh you realize that most
+
+ align:start position:0%
+take uh you realize that most
+ 
+
+ align:start position:0%
+take uh you realize that most
+images that make it into the history
+
+ align:start position:0%
+images that make it into the history
+ 
+
+ align:start position:0%
+images that make it into the history
+books or make it into the planning books
+
+ align:start position:0%
+books or make it into the planning books
+ 
+
+ align:start position:0%
+books or make it into the planning books
+you know they they different sources
+
+ align:start position:0%
+you know they they different sources
+ 
+
+ align:start position:0%
+you know they they different sources
+that they come out they're either you
+
+ align:start position:0%
+that they come out they're either you
+ 
+
+ align:start position:0%
+that they come out they're either you
+know from the city archives they're
+
+ align:start position:0%
+know from the city archives they're
+ 
+
+ align:start position:0%
+know from the city archives they're
+either from Union archives they are from
+
+ align:start position:0%
+either from Union archives they are from
+ 
+
+ align:start position:0%
+either from Union archives they are from
+from the newspapers most use most often
+
+ align:start position:0%
+from the newspapers most use most often
+ 
+
+ align:start position:0%
+from the newspapers most use most often
+and they have to do with events so that
+
+ align:start position:0%
+and they have to do with events so that
+ 
+
+ align:start position:0%
+and they have to do with events so that
+they don't the the the city the way the
+
+ align:start position:0%
+they don't the the the city the way the
+ 
+
+ align:start position:0%
+they don't the the the city the way the
+way cities happen the way their ordinary
+
+ align:start position:0%
+way cities happen the way their ordinary
+ 
+
+ align:start position:0%
+way cities happen the way their ordinary
+life the way street lays down is not
+
+ align:start position:0%
+life the way street lays down is not
+ 
+
+ align:start position:0%
+life the way street lays down is not
+something of interest uh often times
+
+ align:start position:0%
+something of interest uh often times
+ 
+
+ align:start position:0%
+something of interest uh often times
+when it when it was of Interest was when
+
+ align:start position:0%
+when it when it was of Interest was when
+ 
+
+ align:start position:0%
+when it when it was of Interest was when
+the city was first built so you wanted
+
+ align:start position:0%
+the city was first built so you wanted
+ 
+
+ align:start position:0%
+the city was first built so you wanted
+to show
+
+ align:start position:0%
+to show
+ 
+
+ align:start position:0%
+to show
+how the main street was growing and
+
+ align:start position:0%
+how the main street was growing and
+ 
+
+ align:start position:0%
+how the main street was growing and
+often times you use time-lapse pictures
+
+ align:start position:0%
+often times you use time-lapse pictures
+ 
+
+ align:start position:0%
+often times you use time-lapse pictures
+I remember one time researching this and
+
+ align:start position:0%
+I remember one time researching this and
+ 
+
+ align:start position:0%
+I remember one time researching this and
+finding out Brazilian cities and I had
+
+ align:start position:0%
+finding out Brazilian cities and I had
+ 
+
+ align:start position:0%
+finding out Brazilian cities and I had
+time-lapse pictures of streets of
+
+ align:start position:0%
+time-lapse pictures of streets of
+ 
+
+ align:start position:0%
+time-lapse pictures of streets of
+Brazilian cities that showed you know
+
+ align:start position:0%
+Brazilian cities that showed you know
+ 
+
+ align:start position:0%
+Brazilian cities that showed you know
+how how the
+
+ align:start position:0%
+how how the
+ 
+
+ align:start position:0%
+how how the
+developers where uh how the city was
+
+ align:start position:0%
+developers where uh how the city was
+ 
+
+ align:start position:0%
+developers where uh how the city was
+growing and becoming in fact larger and
+
+ align:start position:0%
+growing and becoming in fact larger and
+ 
+
+ align:start position:0%
+growing and becoming in fact larger and
+larger and larger so photography was on
+
+ align:start position:0%
+larger and larger so photography was on
+ 
+
+ align:start position:0%
+larger and larger so photography was on
+the side of progress and
+
+ align:start position:0%
+the side of progress and
+ 
+
+ align:start position:0%
+the side of progress and
+growth and uh my interest has always
+
+ align:start position:0%
+growth and uh my interest has always
+ 
+
+ align:start position:0%
+growth and uh my interest has always
+been just this
+
+ align:start position:0%
+been just this
+ 
+
+ align:start position:0%
+been just this
+process of of of the decline of the
+
+ align:start position:0%
+process of of of the decline of the
+ 
+
+ align:start position:0%
+process of of of the decline of the
+American city is what happens to the to
+
+ align:start position:0%
+American city is what happens to the to
+ 
+
+ align:start position:0%
+American city is what happens to the to
+the physical uh
+
+ align:start position:0%
+the physical uh
+ 
+
+ align:start position:0%
+the physical uh
+city as capital gets pulled out as Jobs
+
+ align:start position:0%
+city as capital gets pulled out as Jobs
+ 
+
+ align:start position:0%
+city as capital gets pulled out as Jobs
+get pulled out as and and and not
+
+ align:start position:0%
+get pulled out as and and and not
+ 
+
+ align:start position:0%
+get pulled out as and and and not
+replaced at one
+
+ align:start position:0%
+replaced at one
+ 
+
+ align:start position:0%
+replaced at one
+time for number of years it was the
+
+ align:start position:0%
+time for number of years it was the
+ 
+
+ align:start position:0%
+time for number of years it was the
+government that would uh step in and
+
+ align:start position:0%
+government that would uh step in and
+ 
+
+ align:start position:0%
+government that would uh step in and
+then all kinds of programs would be
+
+ align:start position:0%
+then all kinds of programs would be
+ 
+
+ align:start position:0%
+then all kinds of programs would be
+created which then in turn would change
+
+ align:start position:0%
+created which then in turn would change
+ 
+
+ align:start position:0%
+created which then in turn would change
+the shape of the
+
+ align:start position:0%
+the shape of the
+ 
+
+ align:start position:0%
+the shape of the
+city but
+
+ align:start position:0%
+city but
+ 
+
+ align:start position:0%
+city but
+uh more recently the government has
+
+ align:start position:0%
+uh more recently the government has
+ 
+
+ align:start position:0%
+uh more recently the government has
+pulled out and one of the ways in which
+
+ align:start position:0%
+pulled out and one of the ways in which
+ 
+
+ align:start position:0%
+pulled out and one of the ways in which
+you can see it if you take some of the
+
+ align:start position:0%
+you can see it if you take some of the
+ 
+
+ align:start position:0%
+you can see it if you take some of the
+the most popular most famous or better
+
+ align:start position:0%
+the most popular most famous or better
+ 
+
+ align:start position:0%
+the most popular most famous or better
+if if if I could say so uh Urban uh
+
+ align:start position:0%
+if if if I could say so uh Urban uh
+ 
+
+ align:start position:0%
+if if if I could say so uh Urban uh
+history books and you look by times you
+
+ align:start position:0%
+history books and you look by times you
+ 
+
+ align:start position:0%
+history books and you look by times you
+know the times to which they go if the
+
+ align:start position:0%
+know the times to which they go if the
+ 
+
+ align:start position:0%
+know the times to which they go if the
+books are more recent if the books cover
+
+ align:start position:0%
+books are more recent if the books cover
+ 
+
+ align:start position:0%
+books are more recent if the books cover
+than last uh the last 10 years or so uh
+
+ align:start position:0%
+than last uh the last 10 years or so uh
+ 
+
+ align:start position:0%
+than last uh the last 10 years or so uh
+you look for the in the index for the
+
+ align:start position:0%
+you look for the in the index for the
+ 
+
+ align:start position:0%
+you look for the in the index for the
+number of times State and and and
+
+ align:start position:0%
+number of times State and and and
+ 
+
+ align:start position:0%
+number of times State and and and
+federal government shows up and you see
+
+ align:start position:0%
+federal government shows up and you see
+ 
+
+ align:start position:0%
+federal government shows up and you see
+that the number is much smaller than
+
+ align:start position:0%
+that the number is much smaller than
+ 
+
+ align:start position:0%
+that the number is much smaller than
+what it was for books that deal with an
+
+ align:start position:0%
+what it was for books that deal with an
+ 
+
+ align:start position:0%
+what it was for books that deal with an
+earlier
+
+ align:start position:0%
+earlier
+ 
+
+ align:start position:0%
+earlier
+period so with that said
+
+ align:start position:0%
+period so with that said
+ 
+
+ align:start position:0%
+period so with that said
+uh as a
+
+ align:start position:0%
+uh as a
+ 
+
+ align:start position:0%
+uh as a
+photographer um there are many
+
+ align:start position:0%
+photographer um there are many
+ 
+
+ align:start position:0%
+photographer um there are many
+photographers that have photographed
+
+ align:start position:0%
+photographers that have photographed
+ 
+
+ align:start position:0%
+photographers that have photographed
+poverty poverty being a separate thing
+
+ align:start position:0%
+poverty poverty being a separate thing
+ 
+
+ align:start position:0%
+poverty poverty being a separate thing
+that photographing a city poverty just
+
+ align:start position:0%
+that photographing a city poverty just
+ 
+
+ align:start position:0%
+that photographing a city poverty just
+tends the photography of poverty tends
+
+ align:start position:0%
+tends the photography of poverty tends
+ 
+
+ align:start position:0%
+tends the photography of poverty tends
+to concentrate on the idea of a person a
+
+ align:start position:0%
+to concentrate on the idea of a person a
+ 
+
+ align:start position:0%
+to concentrate on the idea of a person a
+person who happens to be
+
+ align:start position:0%
+person who happens to be
+ 
+
+ align:start position:0%
+person who happens to be
+destitute that never appealed to me
+
+ align:start position:0%
+destitute that never appealed to me
+ 
+
+ align:start position:0%
+destitute that never appealed to me
+because human beings don't change very
+
+ align:start position:0%
+because human beings don't change very
+ 
+
+ align:start position:0%
+because human beings don't change very
+much I mean they change into terms of
+
+ align:start position:0%
+much I mean they change into terms of
+ 
+
+ align:start position:0%
+much I mean they change into terms of
+the clothes that they wear but you know
+
+ align:start position:0%
+the clothes that they wear but you know
+ 
+
+ align:start position:0%
+the clothes that they wear but you know
+seeing a poor person from the 19th
+
+ align:start position:0%
+seeing a poor person from the 19th
+ 
+
+ align:start position:0%
+seeing a poor person from the 19th
+century and seeing a poor person from
+
+ align:start position:0%
+century and seeing a poor person from
+ 
+
+ align:start position:0%
+century and seeing a poor person from
+the 20th century something very similar
+
+ align:start position:0%
+the 20th century something very similar
+ 
+
+ align:start position:0%
+the 20th century something very similar
+what really interested me was the
+
+ align:start position:0%
+what really interested me was the
+ 
+
+ align:start position:0%
+what really interested me was the
+background of poverty what was behind
+
+ align:start position:0%
+background of poverty what was behind
+ 
+
+ align:start position:0%
+background of poverty what was behind
+this what was behind what was behind
+
+ align:start position:0%
+this what was behind what was behind
+ 
+
+ align:start position:0%
+this what was behind what was behind
+people and then the environment in which
+
+ align:start position:0%
+people and then the environment in which
+ 
+
+ align:start position:0%
+people and then the environment in which
+they live because that has changed that
+
+ align:start position:0%
+they live because that has changed that
+ 
+
+ align:start position:0%
+they live because that has changed that
+that goes
+
+ align:start position:0%
+that goes
+ 
+
+ align:start position:0%
+that goes
+from uh uh uh change very dramatic
+
+ align:start position:0%
+from uh uh uh change very dramatic
+ 
+
+ align:start position:0%
+from uh uh uh change very dramatic
+I mean for those of you who uh used to
+
+ align:start position:0%
+I mean for those of you who uh used to
+ 
+
+ align:start position:0%
+I mean for those of you who uh used to
+be familiar with the high-rise projects
+
+ align:start position:0%
+be familiar with the high-rise projects
+ 
+
+ align:start position:0%
+be familiar with the high-rise projects
+you know you can go to a city like
+
+ align:start position:0%
+you know you can go to a city like
+ 
+
+ align:start position:0%
+you know you can go to a city like
+Chicago today and look for those
+
+ align:start position:0%
+Chicago today and look for those
+ 
+
+ align:start position:0%
+Chicago today and look for those
+highrises that were stretch for in the
+
+ align:start position:0%
+highrises that were stretch for in the
+ 
+
+ align:start position:0%
+highrises that were stretch for in the
+case of the Taylor hommes for about 2
+
+ align:start position:0%
+case of the Taylor hommes for about 2
+ 
+
+ align:start position:0%
+case of the Taylor hommes for about 2
+miles and probably you find one or two
+
+ align:start position:0%
+miles and probably you find one or two
+ 
+
+ align:start position:0%
+miles and probably you find one or two
+examples left you know where there were
+
+ align:start position:0%
+examples left you know where there were
+ 
+
+ align:start position:0%
+examples left you know where there were
+40 or 50 big towers standing up so it's
+
+ align:start position:0%
+40 or 50 big towers standing up so it's
+ 
+
+ align:start position:0%
+40 or 50 big towers standing up so it's
+this landscape that I intend to I have
+
+ align:start position:0%
+this landscape that I intend to I have
+ 
+
+ align:start position:0%
+this landscape that I intend to I have
+docu mented and I intend to present to
+
+ align:start position:0%
+docu mented and I intend to present to
+ 
+
+ align:start position:0%
+docu mented and I intend to present to
+you today and what I have done uh what
+
+ align:start position:0%
+you today and what I have done uh what
+ 
+
+ align:start position:0%
+you today and what I have done uh what
+what the way the form I I'm trying to
+
+ align:start position:0%
+what the way the form I I'm trying to
+ 
+
+ align:start position:0%
+what the way the form I I'm trying to
+present it is by showing you photographs
+
+ align:start position:0%
+present it is by showing you photographs
+ 
+
+ align:start position:0%
+present it is by showing you photographs
+of the city of
+
+ align:start position:0%
+of the city of
+ 
+
+ align:start position:0%
+of the city of
+Camden which is a a city that I have
+
+ align:start position:0%
+Camden which is a a city that I have
+ 
+
+ align:start position:0%
+Camden which is a a city that I have
+photographed since the since
+
+ align:start position:0%
+photographed since the since
+ 
+
+ align:start position:0%
+photographed since the since
+1979 this has done with support with the
+
+ align:start position:0%
+1979 this has done with support with the
+ 
+
+ align:start position:0%
+1979 this has done with support with the
+Ford foundation and working together
+
+ align:start position:0%
+Ford foundation and working together
+ 
+
+ align:start position:0%
+Ford foundation and working together
+under the sponsorship of ruers
+
+ align:start position:0%
+under the sponsorship of ruers
+ 
+
+ align:start position:0%
+under the sponsorship of ruers
+University who Happ to have a c a campus
+
+ align:start position:0%
+University who Happ to have a c a campus
+ 
+
+ align:start position:0%
+University who Happ to have a c a campus
+in Camden in association with a
+
+ align:start position:0%
+in Camden in association with a
+ 
+
+ align:start position:0%
+in Camden in association with a
+historian of Camden whose name
+
+ align:start position:0%
+historian of Camden whose name
+ 
+
+ align:start position:0%
+historian of Camden whose name
+is how Gillette and he's just uh
+
+ align:start position:0%
+is how Gillette and he's just uh
+ 
+
+ align:start position:0%
+is how Gillette and he's just uh
+completed a book called Camden after the
+
+ align:start position:0%
+completed a book called Camden after the
+ 
+
+ align:start position:0%
+completed a book called Camden after the
+fall and he's done a very concise
+
+ align:start position:0%
+fall and he's done a very concise
+ 
+
+ align:start position:0%
+fall and he's done a very concise
+introduction to the website where you
+
+ align:start position:0%
+introduction to the website where you
+ 
+
+ align:start position:0%
+introduction to the website where you
+can you get the major figures and the
+
+ align:start position:0%
+can you get the major figures and the
+ 
+
+ align:start position:0%
+can you get the major figures and the
+major changes that Camden has gone
+
+ align:start position:0%
+major changes that Camden has gone
+ 
+
+ align:start position:0%
+major changes that Camden has gone
+through uh Camden uh the Camden website
+
+ align:start position:0%
+through uh Camden uh the Camden website
+ 
+
+ align:start position:0%
+through uh Camden uh the Camden website
+is invincible cities that come and the
+
+ align:start position:0%
+is invincible cities that come and the
+ 
+
+ align:start position:0%
+is invincible cities that come and the
+Invincible cities comes from the fact
+
+ align:start position:0%
+Invincible cities comes from the fact
+ 
+
+ align:start position:0%
+Invincible cities comes from the fact
+that Walt Whitman used to live in the
+
+ align:start position:0%
+that Walt Whitman used to live in the
+ 
+
+ align:start position:0%
+that Walt Whitman used to live in the
+city he died there in
+
+ align:start position:0%
+city he died there in
+ 
+
+ align:start position:0%
+city he died there in
+1880 and his house is still there and
+
+ align:start position:0%
+1880 and his house is still there and
+ 
+
+ align:start position:0%
+1880 and his house is still there and
+his great his his uh mousum is still
+
+ align:start position:0%
+his great his his uh mousum is still
+ 
+
+ align:start position:0%
+his great his his uh mousum is still
+there and you will see it in the
+
+ align:start position:0%
+there and you will see it in the
+ 
+
+ align:start position:0%
+there and you will see it in the
+pictures so what I like to do is to
+
+ align:start position:0%
+pictures so what I like to do is to
+ 
+
+ align:start position:0%
+pictures so what I like to do is to
+start with the picture with the
+
+ align:start position:0%
+start with the picture with the
+ 
+
+ align:start position:0%
+start with the picture with the
+photographs show you the photographs
+
+ align:start position:0%
+photographs show you the photographs
+ 
+
+ align:start position:0%
+photographs show you the photographs
+relatively quickly and then if possible
+
+ align:start position:0%
+relatively quickly and then if possible
+ 
+
+ align:start position:0%
+relatively quickly and then if possible
+to open up for question questions
+
+ align:start position:0%
+to open up for question questions
+ 
+
+ align:start position:0%
+to open up for question questions
+because I I found that in several places
+
+ align:start position:0%
+because I I found that in several places
+ 
+
+ align:start position:0%
+because I I found that in several places
+where I have given this presentation the
+
+ align:start position:0%
+where I have given this presentation the
+ 
+
+ align:start position:0%
+where I have given this presentation the
+questions at the end after the
+
+ align:start position:0%
+questions at the end after the
+ 
+
+ align:start position:0%
+questions at the end after the
+presentations
+
+ align:start position:0%
+presentations
+ 
+
+ align:start position:0%
+presentations
+become uh much more uh it be the whole
+
+ align:start position:0%
+become uh much more uh it be the whole
+ 
+
+ align:start position:0%
+become uh much more uh it be the whole
+thing becomes much much more interesting
+
+ align:start position:0%
+thing becomes much much more interesting
+ 
+
+ align:start position:0%
+thing becomes much much more interesting
+so we start with a photograph of the
+
+ align:start position:0%
+so we start with a photograph of the
+ 
+
+ align:start position:0%
+so we start with a photograph of the
+inside of a factory now what you will
+
+ align:start position:0%
+inside of a factory now what you will
+ 
+
+ align:start position:0%
+inside of a factory now what you will
+see four or five like this in the
+
+ align:start position:0%
+see four or five like this in the
+ 
+
+ align:start position:0%
+see four or five like this in the
+website and what was very interesting is
+
+ align:start position:0%
+website and what was very interesting is
+ 
+
+ align:start position:0%
+website and what was very interesting is
+that this was a chemical plant it's and
+
+ align:start position:0%
+that this was a chemical plant it's and
+ 
+
+ align:start position:0%
+that this was a chemical plant it's and
+this chemical plant called huling
+
+ align:start position:0%
+this chemical plant called huling
+ 
+
+ align:start position:0%
+this chemical plant called huling
+SC in
+
+ align:start position:0%
+SC in
+ 
+
+ align:start position:0%
+SC in
+Camden became for someone like a little
+
+ align:start position:0%
+Camden became for someone like a little
+ 
+
+ align:start position:0%
+Camden became for someone like a little
+art
+
+ align:start position:0%
+art
+ 
+
+ align:start position:0%
+art
+gallery and in this little Art Gallery I
+
+ align:start position:0%
+gallery and in this little Art Gallery I
+ 
+
+ align:start position:0%
+gallery and in this little Art Gallery I
+selected this eye to to open the website
+
+ align:start position:0%
+selected this eye to to open the website
+ 
+
+ align:start position:0%
+selected this eye to to open the website
+it's like the eye of the photographer
+
+ align:start position:0%
+it's like the eye of the photographer
+ 
+
+ align:start position:0%
+it's like the eye of the photographer
+but it's the eye of the photographer
+
+ align:start position:0%
+but it's the eye of the photographer
+ 
+
+ align:start position:0%
+but it's the eye of the photographer
+within a factory window and it the idea
+
+ align:start position:0%
+within a factory window and it the idea
+ 
+
+ align:start position:0%
+within a factory window and it the idea
+of deindustrialization and the
+
+ align:start position:0%
+of deindustrialization and the
+ 
+
+ align:start position:0%
+of deindustrialization and the
+post-industrial city sort of come
+
+ align:start position:0%
+post-industrial city sort of come
+ 
+
+ align:start position:0%
+post-industrial city sort of come
+together in some
+
+ align:start position:0%
+together in some
+ 
+
+ align:start position:0%
+together in some
+way let me just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see I
+
+ align:start position:0%
+see I
+ 
+
+ align:start position:0%
+see I
+started taking pictures of Camden and
+
+ align:start position:0%
+started taking pictures of Camden and
+ 
+
+ align:start position:0%
+started taking pictures of Camden and
+this has been my policy since the the
+
+ align:start position:0%
+this has been my policy since the the
+ 
+
+ align:start position:0%
+this has been my policy since the the
+very beginning of of uh of uh of this
+
+ align:start position:0%
+very beginning of of uh of uh of this
+ 
+
+ align:start position:0%
+very beginning of of uh of uh of this
+attempt at getting a replica of a city
+
+ align:start position:0%
+attempt at getting a replica of a city
+ 
+
+ align:start position:0%
+attempt at getting a replica of a city
+is is whenever there is an high point of
+
+ align:start position:0%
+is is whenever there is an high point of
+ 
+
+ align:start position:0%
+is is whenever there is an high point of
+view make a an effort to go to the roof
+
+ align:start position:0%
+view make a an effort to go to the roof
+ 
+
+ align:start position:0%
+view make a an effort to go to the roof
+every time I go to that City and this
+
+ align:start position:0%
+every time I go to that City and this
+ 
+
+ align:start position:0%
+every time I go to that City and this
+has been my Purge so year after year
+
+ align:start position:0%
+has been my Purge so year after year
+ 
+
+ align:start position:0%
+has been my Purge so year after year
+after year I would go to this building
+
+ align:start position:0%
+after year I would go to this building
+ 
+
+ align:start position:0%
+after year I would go to this building
+which was a building that was built in
+
+ align:start position:0%
+which was a building that was built in
+ 
+
+ align:start position:0%
+which was a building that was built in
+in North Camden for the purpose of
+
+ align:start position:0%
+in North Camden for the purpose of
+ 
+
+ align:start position:0%
+in North Camden for the purpose of
+providing a different type of Housing
+
+ align:start position:0%
+providing a different type of Housing
+ 
+
+ align:start position:0%
+providing a different type of Housing
+and a better type of Housing and a more
+
+ align:start position:0%
+and a better type of Housing and a more
+ 
+
+ align:start position:0%
+and a better type of Housing and a more
+secure type of housing to the people who
+
+ align:start position:0%
+secure type of housing to the people who
+ 
+
+ align:start position:0%
+secure type of housing to the people who
+lived in those raw houses that you see
+
+ align:start position:0%
+lived in those raw houses that you see
+ 
+
+ align:start position:0%
+lived in those raw houses that you see
+below so the idea was to keep the people
+
+ align:start position:0%
+below so the idea was to keep the people
+ 
+
+ align:start position:0%
+below so the idea was to keep the people
+incoming and to stop them from going out
+
+ align:start position:0%
+incoming and to stop them from going out
+ 
+
+ align:start position:0%
+incoming and to stop them from going out
+so I
+
+ align:start position:0%
+so I
+ 
+
+ align:start position:0%
+so I
+did that I went to that building to that
+
+ align:start position:0%
+did that I went to that building to that
+ 
+
+ align:start position:0%
+did that I went to that building to that
+same corner you see the largest grocery
+
+ align:start position:0%
+same corner you see the largest grocery
+ 
+
+ align:start position:0%
+same corner you see the largest grocery
+store in North Camden is right on the at
+
+ align:start position:0%
+store in North Camden is right on the at
+ 
+
+ align:start position:0%
+store in North Camden is right on the at
+is right
+
+ align:start position:0%
+is right
+ 
+
+ align:start position:0%
+is right
+here where I'm
+
+ align:start position:0%
+here where I'm
+ 
+
+ align:start position:0%
+here where I'm
+pointing
+
+ align:start position:0%
+pointing
+ 
+
+ align:start position:0%
+pointing
+uh it's still there the house has
+
+ align:start position:0%
+uh it's still there the house has
+ 
+
+ align:start position:0%
+uh it's still there the house has
+disappeared they built uh some new new
+
+ align:start position:0%
+disappeared they built uh some new new
+ 
+
+ align:start position:0%
+disappeared they built uh some new new
+housing was built by the river the river
+
+ align:start position:0%
+housing was built by the river the river
+ 
+
+ align:start position:0%
+housing was built by the river the river
+is the Delaware River and the
+
+ align:start position:0%
+is the Delaware River and the
+ 
+
+ align:start position:0%
+is the Delaware River and the
+center this center part of the
+
+ align:start position:0%
+center this center part of the
+ 
+
+ align:start position:0%
+center this center part of the
+photograph it's almost all
+
+ align:start position:0%
+photograph it's almost all
+ 
+
+ align:start position:0%
+photograph it's almost all
+disappeared Camden lost about 40,000
+
+ align:start position:0%
+disappeared Camden lost about 40,000
+ 
+
+ align:start position:0%
+disappeared Camden lost about 40,000
+inhabitants and now has a little under
+
+ align:start position:0%
+inhabitants and now has a little under
+ 
+
+ align:start position:0%
+inhabitants and now has a little under
+880,000 people living there North Camden
+
+ align:start position:0%
+880,000 people living there North Camden
+ 
+
+ align:start position:0%
+880,000 people living there North Camden
+was a very very uh densely populated
+
+ align:start position:0%
+was a very very uh densely populated
+ 
+
+ align:start position:0%
+was a very very uh densely populated
+area of Camden and there were factories
+
+ align:start position:0%
+area of Camden and there were factories
+ 
+
+ align:start position:0%
+area of Camden and there were factories
+all around the place you could walk from
+
+ align:start position:0%
+all around the place you could walk from
+ 
+
+ align:start position:0%
+all around the place you could walk from
+here and work in a place called RCA
+
+ align:start position:0%
+here and work in a place called RCA
+ 
+
+ align:start position:0%
+here and work in a place called RCA
+which during the work where during the
+
+ align:start position:0%
+which during the work where during the
+ 
+
+ align:start position:0%
+which during the work where during the
+war employed as many as 25,000 people in
+
+ align:start position:0%
+war employed as many as 25,000 people in
+ 
+
+ align:start position:0%
+war employed as many as 25,000 people in
+something like 20 buildings and you're
+
+ align:start position:0%
+something like 20 buildings and you're
+ 
+
+ align:start position:0%
+something like 20 buildings and you're
+going to see one of the buildings was
+
+ align:start position:0%
+going to see one of the buildings was
+ 
+
+ align:start position:0%
+going to see one of the buildings was
+saved and you'll see it at the end of
+
+ align:start position:0%
+saved and you'll see it at the end of
+ 
+
+ align:start position:0%
+saved and you'll see it at the end of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+presentation so you see that there is
+
+ align:start position:0%
+presentation so you see that there is
+ 
+
+ align:start position:0%
+presentation so you see that there is
+some new housing being built but much
+
+ align:start position:0%
+some new housing being built but much
+ 
+
+ align:start position:0%
+some new housing being built but much
+many more are disappearing from that
+
+ align:start position:0%
+many more are disappearing from that
+ 
+
+ align:start position:0%
+many more are disappearing from that
+Central Area up just see that's the last
+
+ align:start position:0%
+Central Area up just see that's the last
+ 
+
+ align:start position:0%
+Central Area up just see that's the last
+of the series The River in the back is a
+
+ align:start position:0%
+of the series The River in the back is a
+ 
+
+ align:start position:0%
+of the series The River in the back is a
+Delaware that's the one that Washington
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crossed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we talk about images as a source of
+
+ align:start position:0%
+and we talk about images as a source of
+ 
+
+ align:start position:0%
+and we talk about images as a source of
+Discovery this is the house that was
+
+ align:start position:0%
+Discovery this is the house that was
+ 
+
+ align:start position:0%
+Discovery this is the house that was
+standing right in the middle of the
+
+ align:start position:0%
+standing right in the middle of the
+ 
+
+ align:start position:0%
+standing right in the middle of the
+picture that we saw
+
+ align:start position:0%
+picture that we saw
+ 
+
+ align:start position:0%
+picture that we saw
+before and what you see there is
+
+ align:start position:0%
+before and what you see there is
+ 
+
+ align:start position:0%
+before and what you see there is
+something that uh that I had never seen
+
+ align:start position:0%
+something that uh that I had never seen
+ 
+
+ align:start position:0%
+something that uh that I had never seen
+before and that is that children would
+
+ align:start position:0%
+before and that is that children would
+ 
+
+ align:start position:0%
+before and that is that children would
+go out and I saw this more than once uh
+
+ align:start position:0%
+go out and I saw this more than once uh
+ 
+
+ align:start position:0%
+go out and I saw this more than once uh
+and there was an abandoned house and
+
+ align:start position:0%
+and there was an abandoned house and
+ 
+
+ align:start position:0%
+and there was an abandoned house and
+there's bricks that are falling so that
+
+ align:start position:0%
+there's bricks that are falling so that
+ 
+
+ align:start position:0%
+there's bricks that are falling so that
+you know maybe because there's there was
+
+ align:start position:0%
+you know maybe because there's there was
+ 
+
+ align:start position:0%
+you know maybe because there's there was
+no place to play maybe there was no gym
+
+ align:start position:0%
+no place to play maybe there was no gym
+ 
+
+ align:start position:0%
+no place to play maybe there was no gym
+no no other place so one of the sports
+
+ align:start position:0%
+no no other place so one of the sports
+ 
+
+ align:start position:0%
+no no other place so one of the sports
+one of the
+
+ align:start position:0%
+one of the
+ 
+
+ align:start position:0%
+one of the
+games that that that that was there was
+
+ align:start position:0%
+games that that that that was there was
+ 
+
+ align:start position:0%
+games that that that that was there was
+throwing uh bricks at a standing block
+
+ align:start position:0%
+throwing uh bricks at a standing block
+ 
+
+ align:start position:0%
+throwing uh bricks at a standing block
+as standing wall until the wall actually
+
+ align:start position:0%
+as standing wall until the wall actually
+ 
+
+ align:start position:0%
+as standing wall until the wall actually
+collapse and I thought this is part of
+
+ align:start position:0%
+collapse and I thought this is part of
+ 
+
+ align:start position:0%
+collapse and I thought this is part of
+my idea of the knowledge that you can
+
+ align:start position:0%
+my idea of the knowledge that you can
+ 
+
+ align:start position:0%
+my idea of the knowledge that you can
+acquire about the city that unless you
+
+ align:start position:0%
+acquire about the city that unless you
+ 
+
+ align:start position:0%
+acquire about the city that unless you
+live there for a long time and unless
+
+ align:start position:0%
+live there for a long time and unless
+ 
+
+ align:start position:0%
+live there for a long time and unless
+you take notes it will always elude you
+
+ align:start position:0%
+you take notes it will always elude you
+ 
+
+ align:start position:0%
+you take notes it will always elude you
+if you deal with secondary material it
+
+ align:start position:0%
+if you deal with secondary material it
+ 
+
+ align:start position:0%
+if you deal with secondary material it
+would never get recorded is that there
+
+ align:start position:0%
+would never get recorded is that there
+ 
+
+ align:start position:0%
+would never get recorded is that there
+is if if if you were to take the time
+
+ align:start position:0%
+is if if if you were to take the time
+ 
+
+ align:start position:0%
+is if if if you were to take the time
+and to look systematically you would
+
+ align:start position:0%
+and to look systematically you would
+ 
+
+ align:start position:0%
+and to look systematically you would
+find a whole series of of activities
+
+ align:start position:0%
+find a whole series of of activities
+ 
+
+ align:start position:0%
+find a whole series of of activities
+that you won't see anywhere else and
+
+ align:start position:0%
+that you won't see anywhere else and
+ 
+
+ align:start position:0%
+that you won't see anywhere else and
+this was one of
+
+ align:start position:0%
+this was one of
+ 
+
+ align:start position:0%
+this was one of
+them so how a a street many of this
+
+ align:start position:0%
+them so how a a street many of this
+ 
+
+ align:start position:0%
+them so how a a street many of this
+images I have taken them year after year
+
+ align:start position:0%
+images I have taken them year after year
+ 
+
+ align:start position:0%
+images I have taken them year after year
+after year I could show you this uh 15
+
+ align:start position:0%
+after year I could show you this uh 15
+ 
+
+ align:start position:0%
+after year I could show you this uh 15
+times taking over over 20 some year
+
+ align:start position:0%
+times taking over over 20 some year
+ 
+
+ align:start position:0%
+times taking over over 20 some year
+period the first picture is in
+
+ align:start position:0%
+period the first picture is in
+ 
+
+ align:start position:0%
+period the first picture is in
+1979 uh what I found you know sort of
+
+ align:start position:0%
+1979 uh what I found you know sort of
+ 
+
+ align:start position:0%
+1979 uh what I found you know sort of
+mesmerizing was the idea that a city
+
+ align:start position:0%
+mesmerizing was the idea that a city
+ 
+
+ align:start position:0%
+mesmerizing was the idea that a city
+could disappear you you know is that is
+
+ align:start position:0%
+could disappear you you know is that is
+ 
+
+ align:start position:0%
+could disappear you you know is that is
+that here the city is more or less
+
+ align:start position:0%
+that here the city is more or less
+ 
+
+ align:start position:0%
+that here the city is more or less
+complete some of the houses are boarded
+
+ align:start position:0%
+complete some of the houses are boarded
+ 
+
+ align:start position:0%
+complete some of the houses are boarded
+up and there the first picture is 79 the
+
+ align:start position:0%
+up and there the first picture is 79 the
+ 
+
+ align:start position:0%
+up and there the first picture is 79 the
+second picture is in
+
+ align:start position:0%
+second picture is in
+ 
+
+ align:start position:0%
+second picture is in
+88 uh and then what I found that I also
+
+ align:start position:0%
+88 uh and then what I found that I also
+ 
+
+ align:start position:0%
+88 uh and then what I found that I also
+very peculiar and interesting about
+
+ align:start position:0%
+very peculiar and interesting about
+ 
+
+ align:start position:0%
+very peculiar and interesting about
+Camden was I was that the the sign that
+
+ align:start position:0%
+Camden was I was that the the sign that
+ 
+
+ align:start position:0%
+Camden was I was that the the sign that
+you see that says danger hard grve demol
+
+ align:start position:0%
+you see that says danger hard grve demol
+ 
+
+ align:start position:0%
+you see that says danger hard grve demol
+uh that this uh sign was everywhere and
+
+ align:start position:0%
+uh that this uh sign was everywhere and
+ 
+
+ align:start position:0%
+uh that this uh sign was everywhere and
+then I found out that he had a
+
+ align:start position:0%
+then I found out that he had a
+ 
+
+ align:start position:0%
+then I found out that he had a
+website and on the website there was a
+
+ align:start position:0%
+website and on the website there was a
+ 
+
+ align:start position:0%
+website and on the website there was a
+claim to have demolish as many as 5,000
+
+ align:start position:0%
+claim to have demolish as many as 5,000
+ 
+
+ align:start position:0%
+claim to have demolish as many as 5,000
+buildings in Camden and then the
+
+ align:start position:0%
+buildings in Camden and then the
+ 
+
+ align:start position:0%
+buildings in Camden and then the
+the I came to the realization that
+
+ align:start position:0%
+the I came to the realization that
+ 
+
+ align:start position:0%
+the I came to the realization that
+instead in the city of Camden instead of
+
+ align:start position:0%
+instead in the city of Camden instead of
+ 
+
+ align:start position:0%
+instead in the city of Camden instead of
+having a master builder like we did have
+
+ align:start position:0%
+having a master builder like we did have
+ 
+
+ align:start position:0%
+having a master builder like we did have
+in New York with Robert Moses we had
+
+ align:start position:0%
+in New York with Robert Moses we had
+ 
+
+ align:start position:0%
+in New York with Robert Moses we had
+Master M Builders and maybe in the in
+
+ align:start position:0%
+Master M Builders and maybe in the in
+ 
+
+ align:start position:0%
+Master M Builders and maybe in the in
+other cities that have suffered and have
+
+ align:start position:0%
+other cities that have suffered and have
+ 
+
+ align:start position:0%
+other cities that have suffered and have
+been taken down so much as as as
+
+ align:start position:0%
+been taken down so much as as as
+ 
+
+ align:start position:0%
+been taken down so much as as as
+Camden uh I don't know if it was just
+
+ align:start position:0%
+Camden uh I don't know if it was just
+ 
+
+ align:start position:0%
+Camden uh I don't know if it was just
+one person or one company that that has
+
+ align:start position:0%
+one person or one company that that has
+ 
+
+ align:start position:0%
+one person or one company that that has
+done most of Detroit it's probably more
+
+ align:start position:0%
+done most of Detroit it's probably more
+ 
+
+ align:start position:0%
+done most of Detroit it's probably more
+than that but I think this whole process
+
+ align:start position:0%
+than that but I think this whole process
+ 
+
+ align:start position:0%
+than that but I think this whole process
+of taking a city down it's almost as
+
+ align:start position:0%
+of taking a city down it's almost as
+ 
+
+ align:start position:0%
+of taking a city down it's almost as
+interesting as a process of building a
+
+ align:start position:0%
+interesting as a process of building a
+ 
+
+ align:start position:0%
+interesting as a process of building a
+city and I think it's also a process
+
+ align:start position:0%
+city and I think it's also a process
+ 
+
+ align:start position:0%
+city and I think it's also a process
+that's worth studying
+
+ align:start position:0%
+that's worth studying
+ 
+
+ align:start position:0%
+that's worth studying
+because and here is something that
+
+ align:start position:0%
+because and here is something that
+ 
+
+ align:start position:0%
+because and here is something that
+impressed me very much and came to my
+
+ align:start position:0%
+impressed me very much and came to my
+ 
+
+ align:start position:0%
+impressed me very much and came to my
+attention a few months ago was a a
+
+ align:start position:0%
+attention a few months ago was a a
+ 
+
+ align:start position:0%
+attention a few months ago was a a
+report that that that came out of funny
+
+ align:start position:0%
+report that that that came out of funny
+ 
+
+ align:start position:0%
+report that that that came out of funny
+may I think and it was written up in one
+
+ align:start position:0%
+may I think and it was written up in one
+ 
+
+ align:start position:0%
+may I think and it was written up in one
+of their
+
+ align:start position:0%
+of their
+ 
+
+ align:start position:0%
+of their
+Publications about what were the 10 most
+
+ align:start position:0%
+Publications about what were the 10 most
+ 
+
+ align:start position:0%
+Publications about what were the 10 most
+important forces acting on the American
+
+ align:start position:0%
+important forces acting on the American
+ 
+
+ align:start position:0%
+important forces acting on the American
+city uh up to the year
+
+ align:start position:0%
+city uh up to the year
+ 
+
+ align:start position:0%
+city uh up to the year
+2000 and what were the most important
+
+ align:start position:0%
+2000 and what were the most important
+ 
+
+ align:start position:0%
+2000 and what were the most important
+factors that were going to be present in
+
+ align:start position:0%
+factors that were going to be present in
+ 
+
+ align:start position:0%
+factors that were going to be present in
+the American city uh for the next 50
+
+ align:start position:0%
+the American city uh for the next 50
+ 
+
+ align:start position:0%
+the American city uh for the next 50
+years and one of them in which a group
+
+ align:start position:0%
+years and one of them in which a group
+ 
+
+ align:start position:0%
+years and one of them in which a group
+of 150 historians and planners and so on
+
+ align:start position:0%
+of 150 historians and planners and so on
+ 
+
+ align:start position:0%
+of 150 historians and planners and so on
+uh agreed on overwhelmingly I mean it
+
+ align:start position:0%
+uh agreed on overwhelmingly I mean it
+ 
+
+ align:start position:0%
+uh agreed on overwhelmingly I mean it
+wasn't like 50/50 or divided it was that
+
+ align:start position:0%
+wasn't like 50/50 or divided it was that
+ 
+
+ align:start position:0%
+wasn't like 50/50 or divided it was that
+uh we were going to have a permanent
+
+ align:start position:0%
+uh we were going to have a permanent
+ 
+
+ align:start position:0%
+uh we were going to have a permanent
+underclass and they Ed the word
+
+ align:start position:0%
+underclass and they Ed the word
+ 
+
+ align:start position:0%
+underclass and they Ed the word
+permanent underclass well if we have a
+
+ align:start position:0%
+permanent underclass well if we have a
+ 
+
+ align:start position:0%
+permanent underclass well if we have a
+permanent underclass we're going to have
+
+ align:start position:0%
+permanent underclass we're going to have
+ 
+
+ align:start position:0%
+permanent underclass we're going to have
+permanent
+
+ align:start position:0%
+permanent
+ 
+
+ align:start position:0%
+permanent
+camons I'm just so it happens to me all
+
+ align:start position:0%
+camons I'm just so it happens to me all
+ 
+
+ align:start position:0%
+camons I'm just so it happens to me all
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+time and uh uh if we're going to have a
+
+ align:start position:0%
+time and uh uh if we're going to have a
+ 
+
+ align:start position:0%
+time and uh uh if we're going to have a
+a permanent campons we may as well get
+
+ align:start position:0%
+a permanent campons we may as well get
+ 
+
+ align:start position:0%
+a permanent campons we may as well get
+to know them because they are part of
+
+ align:start position:0%
+to know them because they are part of
+ 
+
+ align:start position:0%
+to know them because they are part of
+what the country is all about and they
+
+ align:start position:0%
+what the country is all about and they
+ 
+
+ align:start position:0%
+what the country is all about and they
+are part of uh of of the history of the
+
+ align:start position:0%
+are part of uh of of the history of the
+ 
+
+ align:start position:0%
+are part of uh of of the history of the
+country and uh and I also think
+
+ align:start position:0%
+country and uh and I also think
+ 
+
+ align:start position:0%
+country and uh and I also think
+uh in some way uh and in most of us
+
+ align:start position:0%
+uh in some way uh and in most of us
+ 
+
+ align:start position:0%
+uh in some way uh and in most of us
+although you know it's it's this this
+
+ align:start position:0%
+although you know it's it's this this
+ 
+
+ align:start position:0%
+although you know it's it's this this
+this sort of thought is very
+
+ align:start position:0%
+this sort of thought is very
+ 
+
+ align:start position:0%
+this sort of thought is very
+discouraging this idea of permanence I
+
+ align:start position:0%
+discouraging this idea of permanence I
+ 
+
+ align:start position:0%
+discouraging this idea of permanence I
+think in most of us there's still an
+
+ align:start position:0%
+think in most of us there's still an
+ 
+
+ align:start position:0%
+think in most of us there's still an
+idea that that these extremes of poverty
+
+ align:start position:0%
+idea that that these extremes of poverty
+ 
+
+ align:start position:0%
+idea that that these extremes of poverty
+don't need to
+
+ align:start position:0%
+don't need to
+ 
+
+ align:start position:0%
+don't need to
+exist most of all in a city in a country
+
+ align:start position:0%
+exist most of all in a city in a country
+ 
+
+ align:start position:0%
+exist most of all in a city in a country
+as rich as the United States but that
+
+ align:start position:0%
+as rich as the United States but that
+ 
+
+ align:start position:0%
+as rich as the United States but that
+has been said too
+
+ align:start position:0%
+has been said too
+ 
+
+ align:start position:0%
+has been said too
+much that picture was taking in 96 and
+
+ align:start position:0%
+much that picture was taking in 96 and
+ 
+
+ align:start position:0%
+much that picture was taking in 96 and
+that's what the block looks like right
+
+ align:start position:0%
+that's what the block looks like right
+ 
+
+ align:start position:0%
+that's what the block looks like right
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+uh The Pink House on the right was uh of
+
+ align:start position:0%
+uh The Pink House on the right was uh of
+ 
+
+ align:start position:0%
+uh The Pink House on the right was uh of
+a lady that you see here and she
+
+ align:start position:0%
+a lady that you see here and she
+ 
+
+ align:start position:0%
+a lady that you see here and she
+happened to be very secure and and she
+
+ align:start position:0%
+happened to be very secure and and she
+ 
+
+ align:start position:0%
+happened to be very secure and and she
+had this very nice apartment right there
+
+ align:start position:0%
+had this very nice apartment right there
+ 
+
+ align:start position:0%
+had this very nice apartment right there
+on that block where everything was
+
+ align:start position:0%
+on that block where everything was
+ 
+
+ align:start position:0%
+on that block where everything was
+collapsing and one time I asked her how
+
+ align:start position:0%
+collapsing and one time I asked her how
+ 
+
+ align:start position:0%
+collapsing and one time I asked her how
+and she said well there are four Latino
+
+ align:start position:0%
+and she said well there are four Latino
+ 
+
+ align:start position:0%
+and she said well there are four Latino
+policemen in the in the Camden police
+
+ align:start position:0%
+policemen in the in the Camden police
+ 
+
+ align:start position:0%
+policemen in the in the Camden police
+force and four of them and the four of
+
+ align:start position:0%
+force and four of them and the four of
+ 
+
+ align:start position:0%
+force and four of them and the four of
+them are nephews of mine so so they
+
+ align:start position:0%
+them are nephews of mine so so they
+ 
+
+ align:start position:0%
+them are nephews of mine so so they
+would take a break and come and have a
+
+ align:start position:0%
+would take a break and come and have a
+ 
+
+ align:start position:0%
+would take a break and come and have a
+cup of coffee with her and so everybody
+
+ align:start position:0%
+cup of coffee with her and so everybody
+ 
+
+ align:start position:0%
+cup of coffee with her and so everybody
+left her
+
+ align:start position:0%
+left her
+ 
+
+ align:start position:0%
+left her
+alone she died very
+
+ align:start position:0%
+alone she died very
+ 
+
+ align:start position:0%
+alone she died very
+recently that was one of the most
+
+ align:start position:0%
+recently that was one of the most
+ 
+
+ align:start position:0%
+recently that was one of the most
+important Corners in cam then the street
+
+ align:start position:0%
+important Corners in cam then the street
+ 
+
+ align:start position:0%
+important Corners in cam then the street
+was called Broadway there were big
+
+ align:start position:0%
+was called Broadway there were big
+ 
+
+ align:start position:0%
+was called Broadway there were big
+theaters right there across the street
+
+ align:start position:0%
+theaters right there across the street
+ 
+
+ align:start position:0%
+theaters right there across the street
+and uh uh this is this is in Decline the
+
+ align:start position:0%
+and uh uh this is this is in Decline the
+ 
+
+ align:start position:0%
+and uh uh this is this is in Decline the
+year was
+
+ align:start position:0%
+year was
+ 
+
+ align:start position:0%
+year was
+1981 the next uh uh photograph was just
+
+ align:start position:0%
+1981 the next uh uh photograph was just
+ 
+
+ align:start position:0%
+1981 the next uh uh photograph was just
+taken so this is the process the
+
+ align:start position:0%
+taken so this is the process the
+ 
+
+ align:start position:0%
+taken so this is the process the
+dismantling the the taking down of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+buildings and that's a view of the same
+
+ align:start position:0%
+buildings and that's a view of the same
+ 
+
+ align:start position:0%
+buildings and that's a view of the same
+building uh with a person that's waiting
+
+ align:start position:0%
+building uh with a person that's waiting
+ 
+
+ align:start position:0%
+building uh with a person that's waiting
+for the bus but it sort of reminded me
+
+ align:start position:0%
+for the bus but it sort of reminded me
+ 
+
+ align:start position:0%
+for the bus but it sort of reminded me
+of the views of ancient Rome where you
+
+ align:start position:0%
+of the views of ancient Rome where you
+ 
+
+ align:start position:0%
+of the views of ancient Rome where you
+had the the the Shepherds uh in front of
+
+ align:start position:0%
+had the the the Shepherds uh in front of
+ 
+
+ align:start position:0%
+had the the the Shepherds uh in front of
+a Coliseum or some of the classical
+
+ align:start position:0%
+a Coliseum or some of the classical
+ 
+
+ align:start position:0%
+a Coliseum or some of the classical
+buildings and and uh and was this that
+
+ align:start position:0%
+buildings and and uh and was this that
+ 
+
+ align:start position:0%
+buildings and and uh and was this that
+disparity of of uh of uh lives and and
+
+ align:start position:0%
+disparity of of uh of uh lives and and
+ 
+
+ align:start position:0%
+disparity of of uh of uh lives and and
+and you know the context in where they
+
+ align:start position:0%
+and you know the context in where they
+ 
+
+ align:start position:0%
+and you know the context in where they
+were
+
+ align:start position:0%
+were
+ 
+
+ align:start position:0%
+were
+placed uh over the years I've seen the
+
+ align:start position:0%
+placed uh over the years I've seen the
+ 
+
+ align:start position:0%
+placed uh over the years I've seen the
+effort this the bank is now a church and
+
+ align:start position:0%
+effort this the bank is now a church and
+ 
+
+ align:start position:0%
+effort this the bank is now a church and
+I have seen the effort that the church
+
+ align:start position:0%
+I have seen the effort that the church
+ 
+
+ align:start position:0%
+I have seen the effort that the church
+has had to go through to be able to
+
+ align:start position:0%
+has had to go through to be able to
+ 
+
+ align:start position:0%
+has had to go through to be able to
+paint that immense building so it took
+
+ align:start position:0%
+paint that immense building so it took
+ 
+
+ align:start position:0%
+paint that immense building so it took
+them like five years to do one side and
+
+ align:start position:0%
+them like five years to do one side and
+ 
+
+ align:start position:0%
+them like five years to do one side and
+then they try to do the other side that
+
+ align:start position:0%
+then they try to do the other side that
+ 
+
+ align:start position:0%
+then they try to do the other side that
+Main Street side and they still haven't
+
+ align:start position:0%
+Main Street side and they still haven't
+ 
+
+ align:start position:0%
+Main Street side and they still haven't
+gotten to the
+
+ align:start position:0%
+gotten to the
+ 
+
+ align:start position:0%
+gotten to the
+top the the buildings areas become
+
+ align:start position:0%
+top the the buildings areas become
+ 
+
+ align:start position:0%
+top the the buildings areas become
+adapted like this is the end of the sort
+
+ align:start position:0%
+adapted like this is the end of the sort
+ 
+
+ align:start position:0%
+adapted like this is the end of the sort
+of normal state of this corner of
+
+ align:start position:0%
+of normal state of this corner of
+ 
+
+ align:start position:0%
+of normal state of this corner of
+Broadway when it was before it's it's
+
+ align:start position:0%
+Broadway when it was before it's it's
+ 
+
+ align:start position:0%
+Broadway when it was before it's it's
+one of those Corners that typically got
+
+ align:start position:0%
+one of those Corners that typically got
+ 
+
+ align:start position:0%
+one of those Corners that typically got
+killed by the malls and there was a mall
+
+ align:start position:0%
+killed by the malls and there was a mall
+ 
+
+ align:start position:0%
+killed by the malls and there was a mall
+in Camden called the Cherry Hill Mall
+
+ align:start position:0%
+in Camden called the Cherry Hill Mall
+ 
+
+ align:start position:0%
+in Camden called the Cherry Hill Mall
+that attracted most of the businesses
+
+ align:start position:0%
+that attracted most of the businesses
+ 
+
+ align:start position:0%
+that attracted most of the businesses
+that were in on Broadway
+
+ align:start position:0%
+that were in on Broadway
+ 
+
+ align:start position:0%
+that were in on Broadway
+so that the appliances and television
+
+ align:start position:0%
+so that the appliances and television
+ 
+
+ align:start position:0%
+so that the appliances and television
+stores went over to the mall and the hat
+
+ align:start position:0%
+stores went over to the mall and the hat
+ 
+
+ align:start position:0%
+stores went over to the mall and the hat
+shop that's next door maybe they did
+
+ align:start position:0%
+shop that's next door maybe they did
+ 
+
+ align:start position:0%
+shop that's next door maybe they did
+there no hat chops anymore and the drugs
+
+ align:start position:0%
+there no hat chops anymore and the drugs
+ 
+
+ align:start position:0%
+there no hat chops anymore and the drugs
+and all of that uh went there and now
+
+ align:start position:0%
+and all of that uh went there and now
+ 
+
+ align:start position:0%
+and all of that uh went there and now
+the area became that's what it is today
+
+ align:start position:0%
+the area became that's what it is today
+ 
+
+ align:start position:0%
+the area became that's what it is today
+the first one was in 79 today it became
+
+ align:start position:0%
+the first one was in 79 today it became
+ 
+
+ align:start position:0%
+the first one was in 79 today it became
+more a sort of Center for people who are
+
+ align:start position:0%
+more a sort of Center for people who are
+ 
+
+ align:start position:0%
+more a sort of Center for people who are
+down and out so this has become the area
+
+ align:start position:0%
+down and out so this has become the area
+ 
+
+ align:start position:0%
+down and out so this has become the area
+where you find most of the shelters most
+
+ align:start position:0%
+where you find most of the shelters most
+ 
+
+ align:start position:0%
+where you find most of the shelters most
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+it's it could be compared to actually to
+
+ align:start position:0%
+it's it could be compared to actually to
+ 
+
+ align:start position:0%
+it's it could be compared to actually to
+a repair station for human beings in a
+
+ align:start position:0%
+a repair station for human beings in a
+ 
+
+ align:start position:0%
+a repair station for human beings in a
+place where you go uh when you don't
+
+ align:start position:0%
+place where you go uh when you don't
+ 
+
+ align:start position:0%
+place where you go uh when you don't
+have anywhere to stay a place where you
+
+ align:start position:0%
+have anywhere to stay a place where you
+ 
+
+ align:start position:0%
+have anywhere to stay a place where you
+go when you're battered battered or a
+
+ align:start position:0%
+go when you're battered battered or a
+ 
+
+ align:start position:0%
+go when you're battered battered or a
+place where you go when uh when you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+addictions again in uh in uh in a empty
+
+ align:start position:0%
+addictions again in uh in uh in a empty
+ 
+
+ align:start position:0%
+addictions again in uh in uh in a empty
+lots sometimes you see this Creations
+
+ align:start position:0%
+lots sometimes you see this Creations
+ 
+
+ align:start position:0%
+lots sometimes you see this Creations
+that develop sort of
+
+ align:start position:0%
+that develop sort of
+ 
+
+ align:start position:0%
+that develop sort of
+uh one piece at a time and what this is
+
+ align:start position:0%
+uh one piece at a time and what this is
+ 
+
+ align:start position:0%
+uh one piece at a time and what this is
+is a local Catholic Church that went to
+
+ align:start position:0%
+is a local Catholic Church that went to
+ 
+
+ align:start position:0%
+is a local Catholic Church that went to
+one of the empty lots and put a cross
+
+ align:start position:0%
+one of the empty lots and put a cross
+ 
+
+ align:start position:0%
+one of the empty lots and put a cross
+there you know
+
+ align:start position:0%
+there you know
+ 
+
+ align:start position:0%
+there you know
+as now that we don't have the state and
+
+ align:start position:0%
+as now that we don't have the state and
+ 
+
+ align:start position:0%
+as now that we don't have the state and
+the federal government to help us we
+
+ align:start position:0%
+the federal government to help us we
+ 
+
+ align:start position:0%
+the federal government to help us we
+have to go to a higher power and so they
+
+ align:start position:0%
+have to go to a higher power and so they
+ 
+
+ align:start position:0%
+have to go to a higher power and so they
+put this there and then other people
+
+ align:start position:0%
+put this there and then other people
+ 
+
+ align:start position:0%
+put this there and then other people
+begin to bring their their their benches
+
+ align:start position:0%
+begin to bring their their their benches
+ 
+
+ align:start position:0%
+begin to bring their their their benches
+and their Tire Planters and it becomes
+
+ align:start position:0%
+and their Tire Planters and it becomes
+ 
+
+ align:start position:0%
+and their Tire Planters and it becomes
+kind of a little uh sacred space that I
+
+ align:start position:0%
+kind of a little uh sacred space that I
+ 
+
+ align:start position:0%
+kind of a little uh sacred space that I
+continue to keep under
+
+ align:start position:0%
+continue to keep under
+ 
+
+ align:start position:0%
+continue to keep under
+observation uh that's a
+
+ align:start position:0%
+observation uh that's a
+ 
+
+ align:start position:0%
+observation uh that's a
+church it's of course the last of the
+
+ align:start position:0%
+church it's of course the last of the
+ 
+
+ align:start position:0%
+church it's of course the last of the
+rowhouses on this block and probably the
+
+ align:start position:0%
+rowhouses on this block and probably the
+ 
+
+ align:start position:0%
+rowhouses on this block and probably the
+only one and there you can see how it's
+
+ align:start position:0%
+only one and there you can see how it's
+ 
+
+ align:start position:0%
+only one and there you can see how it's
+this the stoop that leads to the the
+
+ align:start position:0%
+this the stoop that leads to the the
+ 
+
+ align:start position:0%
+this the stoop that leads to the the
+that leads up it's also used to lead to
+
+ align:start position:0%
+that leads up it's also used to lead to
+ 
+
+ align:start position:0%
+that leads up it's also used to lead to
+the house next to
+
+ align:start position:0%
+the house next to
+ 
+
+ align:start position:0%
+the house next to
+it again another church the the there's
+
+ align:start position:0%
+it again another church the the there's
+ 
+
+ align:start position:0%
+it again another church the the there's
+no shortage of churches in Camden they
+
+ align:start position:0%
+no shortage of churches in Camden they
+ 
+
+ align:start position:0%
+no shortage of churches in Camden they
+is very cheap to get a building that you
+
+ align:start position:0%
+is very cheap to get a building that you
+ 
+
+ align:start position:0%
+is very cheap to get a building that you
+can habilitate and put a church in it's
+
+ align:start position:0%
+can habilitate and put a church in it's
+ 
+
+ align:start position:0%
+can habilitate and put a church in it's
+also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the city is very insecure Camden has
+
+ align:start position:0%
+uh the city is very insecure Camden has
+ 
+
+ align:start position:0%
+uh the city is very insecure Camden has
+for two years in a row was declared to
+
+ align:start position:0%
+for two years in a row was declared to
+ 
+
+ align:start position:0%
+for two years in a row was declared to
+be the most dangerous city in
+
+ align:start position:0%
+be the most dangerous city in
+ 
+
+ align:start position:0%
+be the most dangerous city in
+America so you can see here that uh that
+
+ align:start position:0%
+America so you can see here that uh that
+ 
+
+ align:start position:0%
+America so you can see here that uh that
+people don't take chances with Windows
+
+ align:start position:0%
+people don't take chances with Windows
+ 
+
+ align:start position:0%
+people don't take chances with Windows
+and that sort of
+
+ align:start position:0%
+and that sort of
+ 
+
+ align:start position:0%
+and that sort of
+thing this is an old church this was
+
+ align:start position:0%
+thing this is an old church this was
+ 
+
+ align:start position:0%
+thing this is an old church this was
+back in ' 881 and it doesn't exist
+
+ align:start position:0%
+back in ' 881 and it doesn't exist
+ 
+
+ align:start position:0%
+back in ' 881 and it doesn't exist
+anymore and there was a garage and I
+
+ align:start position:0%
+anymore and there was a garage and I
+ 
+
+ align:start position:0%
+anymore and there was a garage and I
+went to service there you very very long
+
+ align:start position:0%
+went to service there you very very long
+ 
+
+ align:start position:0%
+went to service there you very very long
+building and you could see about 80
+
+ align:start position:0%
+building and you could see about 80
+ 
+
+ align:start position:0%
+building and you could see about 80
+people inside of
+
+ align:start position:0%
+people inside of
+ 
+
+ align:start position:0%
+people inside of
+there it's another
+
+ align:start position:0%
+there it's another
+ 
+
+ align:start position:0%
+there it's another
+one and that's the back of yet another
+
+ align:start position:0%
+one and that's the back of yet another
+ 
+
+ align:start position:0%
+one and that's the back of yet another
+church as you can see I mean the tragedy
+
+ align:start position:0%
+church as you can see I mean the tragedy
+ 
+
+ align:start position:0%
+church as you can see I mean the tragedy
+with buildings like this of course if
+
+ align:start position:0%
+with buildings like this of course if
+ 
+
+ align:start position:0%
+with buildings like this of course if
+there is a fire and people have to try
+
+ align:start position:0%
+there is a fire and people have to try
+ 
+
+ align:start position:0%
+there is a fire and people have to try
+to get out of
+
+ align:start position:0%
+to get out of
+ 
+
+ align:start position:0%
+to get out of
+it and that's the last of an industrial
+
+ align:start position:0%
+it and that's the last of an industrial
+ 
+
+ align:start position:0%
+it and that's the last of an industrial
+neighborhood that was very near near the
+
+ align:start position:0%
+neighborhood that was very near near the
+ 
+
+ align:start position:0%
+neighborhood that was very near near the
+New York Shipyard which was the the
+
+ align:start position:0%
+New York Shipyard which was the the
+ 
+
+ align:start position:0%
+New York Shipyard which was the the
+largest industry in in Camden
+
+ align:start position:0%
+largest industry in in Camden
+ 
+
+ align:start position:0%
+largest industry in in Camden
+particularly during the war when they
+
+ align:start position:0%
+particularly during the war when they
+ 
+
+ align:start position:0%
+particularly during the war when they
+made the ships this huge ship building
+
+ align:start position:0%
+made the ships this huge ship building
+ 
+
+ align:start position:0%
+made the ships this huge ship building
+complex uh the whole neighborhood left
+
+ align:start position:0%
+complex uh the whole neighborhood left
+ 
+
+ align:start position:0%
+complex uh the whole neighborhood left
+the church was kept the church was
+
+ align:start position:0%
+the church was kept the church was
+ 
+
+ align:start position:0%
+the church was kept the church was
+originally a Ukrainian Catholic Church
+
+ align:start position:0%
+originally a Ukrainian Catholic Church
+ 
+
+ align:start position:0%
+originally a Ukrainian Catholic Church
+is now about Baptist
+
+ align:start position:0%
+is now about Baptist
+ 
+
+ align:start position:0%
+is now about Baptist
+Church the sidewalks are all you know
+
+ align:start position:0%
+Church the sidewalks are all you know
+ 
+
+ align:start position:0%
+Church the sidewalks are all you know
+impossible you can't walk the sidewalk
+
+ align:start position:0%
+impossible you can't walk the sidewalk
+ 
+
+ align:start position:0%
+impossible you can't walk the sidewalk
+so people walk through the middle of the
+
+ align:start position:0%
+so people walk through the middle of the
+ 
+
+ align:start position:0%
+so people walk through the middle of the
+streets the churches that were built by
+
+ align:start position:0%
+streets the churches that were built by
+ 
+
+ align:start position:0%
+streets the churches that were built by
+the by the old imigrant communities are
+
+ align:start position:0%
+the by the old imigrant communities are
+ 
+
+ align:start position:0%
+the by the old imigrant communities are
+still standing like that one but that
+
+ align:start position:0%
+still standing like that one but that
+ 
+
+ align:start position:0%
+still standing like that one but that
+one just recently lost the cross one day
+
+ align:start position:0%
+one just recently lost the cross one day
+ 
+
+ align:start position:0%
+one just recently lost the cross one day
+the cross came tumbling down and it's a
+
+ align:start position:0%
+the cross came tumbling down and it's a
+ 
+
+ align:start position:0%
+the cross came tumbling down and it's a
+huge church you can imagine that that
+
+ align:start position:0%
+huge church you can imagine that that
+ 
+
+ align:start position:0%
+huge church you can imagine that that
+cross uh must have a some commotion when
+
+ align:start position:0%
+cross uh must have a some commotion when
+ 
+
+ align:start position:0%
+cross uh must have a some commotion when
+it came
+
+ align:start position:0%
+it came
+ 
+
+ align:start position:0%
+it came
+down areas like this are selected for a
+
+ align:start position:0%
+down areas like this are selected for a
+ 
+
+ align:start position:0%
+down areas like this are selected for a
+certain type of billboards that you see
+
+ align:start position:0%
+certain type of billboards that you see
+ 
+
+ align:start position:0%
+certain type of billboards that you see
+all over uh the neighborhood and
+
+ align:start position:0%
+all over uh the neighborhood and
+ 
+
+ align:start position:0%
+all over uh the neighborhood and
+billboards like this that you don't put
+
+ align:start position:0%
+billboards like this that you don't put
+ 
+
+ align:start position:0%
+billboards like this that you don't put
+in any other neighborhood except the
+
+ align:start position:0%
+in any other neighborhood except the
+ 
+
+ align:start position:0%
+in any other neighborhood except the
+poorest neighborhoods in America this I
+
+ align:start position:0%
+poorest neighborhoods in America this I
+ 
+
+ align:start position:0%
+poorest neighborhoods in America this I
+saw this billboard in nework too because
+
+ align:start position:0%
+saw this billboard in nework too because
+ 
+
+ align:start position:0%
+saw this billboard in nework too because
+it was in New Jersey
+
+ align:start position:0%
+it was in New Jersey
+ 
+
+ align:start position:0%
+it was in New Jersey
+billboard that one too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's the most recent one it's it's
+
+ align:start position:0%
+and that's the most recent one it's it's
+ 
+
+ align:start position:0%
+and that's the most recent one it's it's
+sort of ironic because you look at it
+
+ align:start position:0%
+sort of ironic because you look at it
+ 
+
+ align:start position:0%
+sort of ironic because you look at it
+and and it talks about paying and
+
+ align:start position:0%
+and and it talks about paying and
+ 
+
+ align:start position:0%
+and and it talks about paying and
+helping the children and and and it's
+
+ align:start position:0%
+helping the children and and and it's
+ 
+
+ align:start position:0%
+helping the children and and and it's
+literally in a place
+
+ align:start position:0%
+literally in a place
+ 
+
+ align:start position:0%
+literally in a place
+where you know the idea of money it's
+
+ align:start position:0%
+where you know the idea of money it's
+ 
+
+ align:start position:0%
+where you know the idea of money it's
+such it's such a rarity
+
+ align:start position:0%
+such it's such a rarity
+ 
+
+ align:start position:0%
+such it's such a rarity
+so again that's a police raid in a block
+
+ align:start position:0%
+so again that's a police raid in a block
+ 
+
+ align:start position:0%
+so again that's a police raid in a block
+it's what happens I remember
+
+ align:start position:0%
+it's what happens I remember
+ 
+
+ align:start position:0%
+it's what happens I remember
+in New York during the Heyday of the of
+
+ align:start position:0%
+in New York during the Heyday of the of
+ 
+
+ align:start position:0%
+in New York during the Heyday of the of
+crack you know back in 81 or
+
+ align:start position:0%
+crack you know back in 81 or
+ 
+
+ align:start position:0%
+crack you know back in 81 or
+82 uh people used to storm a building
+
+ align:start position:0%
+82 uh people used to storm a building
+ 
+
+ align:start position:0%
+82 uh people used to storm a building
+they would just uh the police and the
+
+ align:start position:0%
+they would just uh the police and the
+ 
+
+ align:start position:0%
+they would just uh the police and the
+state police and sometimes the FBI would
+
+ align:start position:0%
+state police and sometimes the FBI would
+ 
+
+ align:start position:0%
+state police and sometimes the FBI would
+come in and they would seal a building
+
+ align:start position:0%
+come in and they would seal a building
+ 
+
+ align:start position:0%
+come in and they would seal a building
+and then go like 200 at the time into
+
+ align:start position:0%
+and then go like 200 at the time into
+ 
+
+ align:start position:0%
+and then go like 200 at the time into
+the building and people compare them to
+
+ align:start position:0%
+the building and people compare them to
+ 
+
+ align:start position:0%
+the building and people compare them to
+a sort of an earthquake or something and
+
+ align:start position:0%
+a sort of an earthquake or something and
+ 
+
+ align:start position:0%
+a sort of an earthquake or something and
+this is in
+
+ align:start position:0%
+this is in
+ 
+
+ align:start position:0%
+this is in
+Camden uh where the they block is sealed
+
+ align:start position:0%
+Camden uh where the they block is sealed
+ 
+
+ align:start position:0%
+Camden uh where the they block is sealed
+the Vans are all lined up you see two or
+
+ align:start position:0%
+the Vans are all lined up you see two or
+ 
+
+ align:start position:0%
+the Vans are all lined up you see two or
+three lined UPS uh Vans lined up and
+
+ align:start position:0%
+three lined UPS uh Vans lined up and
+ 
+
+ align:start position:0%
+three lined UPS uh Vans lined up and
+then people who have uh
+
+ align:start position:0%
+then people who have uh
+ 
+
+ align:start position:0%
+then people who have uh
+uh an arrest warrant uh on their name
+
+ align:start position:0%
+uh an arrest warrant uh on their name
+ 
+
+ align:start position:0%
+uh an arrest warrant uh on their name
+are then taking on the Vans and then
+
+ align:start position:0%
+are then taking on the Vans and then
+ 
+
+ align:start position:0%
+are then taking on the Vans and then
+taking to prison from
+
+ align:start position:0%
+taking to prison from
+ 
+
+ align:start position:0%
+taking to prison from
+there that was a picture that I just
+
+ align:start position:0%
+there that was a picture that I just
+ 
+
+ align:start position:0%
+there that was a picture that I just
+happened to walk into looking for a
+
+ align:start position:0%
+happened to walk into looking for a
+ 
+
+ align:start position:0%
+happened to walk into looking for a
+higher point of view I went went into
+
+ align:start position:0%
+higher point of view I went went into
+ 
+
+ align:start position:0%
+higher point of view I went went into
+the second floor of an abandoned house
+
+ align:start position:0%
+the second floor of an abandoned house
+ 
+
+ align:start position:0%
+the second floor of an abandoned house
+and there she was uh my first impression
+
+ align:start position:0%
+and there she was uh my first impression
+ 
+
+ align:start position:0%
+and there she was uh my first impression
+was that she was dead and then I just
+
+ align:start position:0%
+was that she was dead and then I just
+ 
+
+ align:start position:0%
+was that she was dead and then I just
+went and get the cops and say and
+
+ align:start position:0%
+went and get the cops and say and
+ 
+
+ align:start position:0%
+went and get the cops and say and
+actually she wasn't
+
+ align:start position:0%
+actually she wasn't
+ 
+
+ align:start position:0%
+actually she wasn't
+there the memorials you know which had
+
+ align:start position:0%
+there the memorials you know which had
+ 
+
+ align:start position:0%
+there the memorials you know which had
+the reflection of this violence I mean
+
+ align:start position:0%
+the reflection of this violence I mean
+ 
+
+ align:start position:0%
+the reflection of this violence I mean
+there's always a new crop of memorials
+
+ align:start position:0%
+there's always a new crop of memorials
+ 
+
+ align:start position:0%
+there's always a new crop of memorials
+and in this case a stop sign becomes a
+
+ align:start position:0%
+and in this case a stop sign becomes a
+ 
+
+ align:start position:0%
+and in this case a stop sign becomes a
+memorial this on
+
+ align:start position:0%
+memorial this on
+ 
+
+ align:start position:0%
+memorial this on
+Broadway uh and here it's four of the
+
+ align:start position:0%
+Broadway uh and here it's four of the
+ 
+
+ align:start position:0%
+Broadway uh and here it's four of the
+local board that uh that uh you know
+
+ align:start position:0%
+local board that uh that uh you know
+ 
+
+ align:start position:0%
+local board that uh that uh you know
+they become sort of towering figures in
+
+ align:start position:0%
+they become sort of towering figures in
+ 
+
+ align:start position:0%
+they become sort of towering figures in
+the neighborhood and the fact that they
+
+ align:start position:0%
+the neighborhood and the fact that they
+ 
+
+ align:start position:0%
+the neighborhood and the fact that they
+were memorialized in this way so
+
+ align:start position:0%
+were memorialized in this way so
+ 
+
+ align:start position:0%
+were memorialized in this way so
+infuriated the local Catholic priest
+
+ align:start position:0%
+infuriated the local Catholic priest
+ 
+
+ align:start position:0%
+infuriated the local Catholic priest
+that he came with paint en roller and
+
+ align:start position:0%
+that he came with paint en roller and
+ 
+
+ align:start position:0%
+that he came with paint en roller and
+painted over this uh this uh figures and
+
+ align:start position:0%
+painted over this uh this uh figures and
+ 
+
+ align:start position:0%
+painted over this uh this uh figures and
+at the same time a whole group of drug
+
+ align:start position:0%
+at the same time a whole group of drug
+ 
+
+ align:start position:0%
+at the same time a whole group of drug
+dealers from North Camden came to scream
+
+ align:start position:0%
+dealers from North Camden came to scream
+ 
+
+ align:start position:0%
+dealers from North Camden came to scream
+at him while he was painting over this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a more recent one from uh East
+
+ align:start position:0%
+that's a more recent one from uh East
+ 
+
+ align:start position:0%
+that's a more recent one from uh East
+Camden and this is one that it's almost
+
+ align:start position:0%
+Camden and this is one that it's almost
+ 
+
+ align:start position:0%
+Camden and this is one that it's almost
+like the Masterpiece of the genre it was
+
+ align:start position:0%
+like the Masterpiece of the genre it was
+ 
+
+ align:start position:0%
+like the Masterpiece of the genre it was
+it was uh featur in the New York Times
+
+ align:start position:0%
+it was uh featur in the New York Times
+ 
+
+ align:start position:0%
+it was uh featur in the New York Times
+about a year ago and uh the reporter and
+
+ align:start position:0%
+about a year ago and uh the reporter and
+ 
+
+ align:start position:0%
+about a year ago and uh the reporter and
+the and the police and a policeman
+
+ align:start position:0%
+the and the police and a policeman
+ 
+
+ align:start position:0%
+the and the police and a policeman
+agreed that this was sort of a a gem of
+
+ align:start position:0%
+agreed that this was sort of a a gem of
+ 
+
+ align:start position:0%
+agreed that this was sort of a a gem of
+a mural but at the same time they said
+
+ align:start position:0%
+a mural but at the same time they said
+ 
+
+ align:start position:0%
+a mural but at the same time they said
+Well it has to go you know cuz it's
+
+ align:start position:0%
+Well it has to go you know cuz it's
+ 
+
+ align:start position:0%
+Well it has to go you know cuz it's
+glorifies the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trade that's another
+
+ align:start position:0%
+trade that's another
+ 
+
+ align:start position:0%
+trade that's another
+one and
+
+ align:start position:0%
+one and
+ 
+
+ align:start position:0%
+one and
+that then the city has all the signs
+
+ align:start position:0%
+that then the city has all the signs
+ 
+
+ align:start position:0%
+that then the city has all the signs
+that have been left you know from the
+
+ align:start position:0%
+that have been left you know from the
+ 
+
+ align:start position:0%
+that have been left you know from the
+times when when Camden was a city like
+
+ align:start position:0%
+times when when Camden was a city like
+ 
+
+ align:start position:0%
+times when when Camden was a city like
+any like most like many other cities in
+
+ align:start position:0%
+any like most like many other cities in
+ 
+
+ align:start position:0%
+any like most like many other cities in
+America and there are signs like this
+
+ align:start position:0%
+America and there are signs like this
+ 
+
+ align:start position:0%
+America and there are signs like this
+this is a store that for some reason
+
+ align:start position:0%
+this is a store that for some reason
+ 
+
+ align:start position:0%
+this is a store that for some reason
+still is functioning
+
+ align:start position:0%
+still is functioning
+ 
+
+ align:start position:0%
+still is functioning
+but many of the other ones are have
+
+ align:start position:0%
+but many of the other ones are have
+ 
+
+ align:start position:0%
+but many of the other ones are have
+disappeared and they have left their
+
+ align:start position:0%
+disappeared and they have left their
+ 
+
+ align:start position:0%
+disappeared and they have left their
+signs
+
+ align:start position:0%
+signs
+ 
+
+ align:start position:0%
+signs
+there some of the companies and some of
+
+ align:start position:0%
+there some of the companies and some of
+ 
+
+ align:start position:0%
+there some of the companies and some of
+the logos have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disappeared and that's Christopher
+
+ align:start position:0%
+disappeared and that's Christopher
+ 
+
+ align:start position:0%
+disappeared and that's Christopher
+Columbus that was put in a in a city
+
+ align:start position:0%
+Columbus that was put in a in a city
+ 
+
+ align:start position:0%
+Columbus that was put in a in a city
+park by the Italian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Community and then there are the signs
+
+ align:start position:0%
+Community and then there are the signs
+ 
+
+ align:start position:0%
+Community and then there are the signs
+of the old of of you know the
+
+ align:start position:0%
+of the old of of you know the
+ 
+
+ align:start position:0%
+of the old of of you know the
+that connect that tells you know were
+
+ align:start position:0%
+that connect that tells you know were
+ 
+
+ align:start position:0%
+that connect that tells you know were
+once a great City we were we had great
+
+ align:start position:0%
+once a great City we were we had great
+ 
+
+ align:start position:0%
+once a great City we were we had great
+Bridges we had great buildings and
+
+ align:start position:0%
+Bridges we had great buildings and
+ 
+
+ align:start position:0%
+Bridges we had great buildings and
+that's the uh Ben Franklin
+
+ align:start position:0%
+that's the uh Ben Franklin
+ 
+
+ align:start position:0%
+that's the uh Ben Franklin
+Bridge that's one of the peers of the B
+
+ align:start position:0%
+Bridge that's one of the peers of the B
+ 
+
+ align:start position:0%
+Bridge that's one of the peers of the B
+Ben Franklin Bridge that says
+
+ align:start position:0%
+Ben Franklin Bridge that says
+ 
+
+ align:start position:0%
+Ben Franklin Bridge that says
+Camin that's the house where Walt
+
+ align:start position:0%
+Camin that's the house where Walt
+ 
+
+ align:start position:0%
+Camin that's the house where Walt
+Whitman lived back in
+
+ align:start position:0%
+Whitman lived back in
+ 
+
+ align:start position:0%
+Whitman lived back in
+1984 you can see it had a abandoned
+
+ align:start position:0%
+1984 you can see it had a abandoned
+ 
+
+ align:start position:0%
+1984 you can see it had a abandoned
+house right next to it and it had a
+
+ align:start position:0%
+house right next to it and it had a
+ 
+
+ align:start position:0%
+house right next to it and it had a
+vacant one that was a crumbl crumbling
+
+ align:start position:0%
+vacant one that was a crumbl crumbling
+ 
+
+ align:start position:0%
+vacant one that was a crumbl crumbling
+ruin and another vacant house that was
+
+ align:start position:0%
+ruin and another vacant house that was
+ 
+
+ align:start position:0%
+ruin and another vacant house that was
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+fixed and later across the street from
+
+ align:start position:0%
+fixed and later across the street from
+ 
+
+ align:start position:0%
+fixed and later across the street from
+the Walt Whitman house they put the the
+
+ align:start position:0%
+the Walt Whitman house they put the the
+ 
+
+ align:start position:0%
+the Walt Whitman house they put the the
+S the Camden County
+
+ align:start position:0%
+S the Camden County
+ 
+
+ align:start position:0%
+S the Camden County
+jail so it's sort of it's It's one can't
+
+ align:start position:0%
+jail so it's sort of it's It's one can't
+ 
+
+ align:start position:0%
+jail so it's sort of it's It's one can't
+help thinking you know of what would
+
+ align:start position:0%
+help thinking you know of what would
+ 
+
+ align:start position:0%
+help thinking you know of what would
+Walt Woodman have written if he was
+
+ align:start position:0%
+Walt Woodman have written if he was
+ 
+
+ align:start position:0%
+Walt Woodman have written if he was
+still around that's where he's buried in
+
+ align:start position:0%
+still around that's where he's buried in
+ 
+
+ align:start position:0%
+still around that's where he's buried in
+the cemetery and surprising
+
+ align:start position:0%
+the cemetery and surprising
+ 
+
+ align:start position:0%
+the cemetery and surprising
+his mum is one of the buildings that has
+
+ align:start position:0%
+his mum is one of the buildings that has
+ 
+
+ align:start position:0%
+his mum is one of the buildings that has
+changed the least but his intention from
+
+ align:start position:0%
+changed the least but his intention from
+ 
+
+ align:start position:0%
+changed the least but his intention from
+the very beginning was to build build
+
+ align:start position:0%
+the very beginning was to build build
+ 
+
+ align:start position:0%
+the very beginning was to build build
+something really rugged and rough that
+
+ align:start position:0%
+something really rugged and rough that
+ 
+
+ align:start position:0%
+something really rugged and rough that
+would last for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forever in in n in
+
+ align:start position:0%
+forever in in n in
+ 
+
+ align:start position:0%
+forever in in n in
+1976 during the B sentennial there was a
+
+ align:start position:0%
+1976 during the B sentennial there was a
+ 
+
+ align:start position:0%
+1976 during the B sentennial there was a
+debate in
+
+ align:start position:0%
+debate in
+ 
+
+ align:start position:0%
+debate in
+Camden I'm the reporter of that debate
+
+ align:start position:0%
+Camden I'm the reporter of that debate
+ 
+
+ align:start position:0%
+Camden I'm the reporter of that debate
+the debate was should we join the
+
+ align:start position:0%
+the debate was should we join the
+ 
+
+ align:start position:0%
+the debate was should we join the
+Centennial and they it went back and
+
+ align:start position:0%
+Centennial and they it went back and
+ 
+
+ align:start position:0%
+Centennial and they it went back and
+forth between this the teenagers and and
+
+ align:start position:0%
+forth between this the teenagers and and
+ 
+
+ align:start position:0%
+forth between this the teenagers and and
+and and they said uh what what was there
+
+ align:start position:0%
+and and they said uh what what was there
+ 
+
+ align:start position:0%
+and and they said uh what what was there
+for us to what is there for us to cheer
+
+ align:start position:0%
+for us to what is there for us to cheer
+ 
+
+ align:start position:0%
+for us to what is there for us to cheer
+about the bicentennial we still were
+
+ align:start position:0%
+about the bicentennial we still were
+ 
+
+ align:start position:0%
+about the bicentennial we still were
+slaves for another 100
+
+ align:start position:0%
+slaves for another 100
+ 
+
+ align:start position:0%
+slaves for another 100
+years and then at the same time the city
+
+ align:start position:0%
+years and then at the same time the city
+ 
+
+ align:start position:0%
+years and then at the same time the city
+of Philadelphia Was preparing itself for
+
+ align:start position:0%
+of Philadelphia Was preparing itself for
+ 
+
+ align:start position:0%
+of Philadelphia Was preparing itself for
+a great uh celebration they had the Tall
+
+ align:start position:0%
+a great uh celebration they had the Tall
+ 
+
+ align:start position:0%
+a great uh celebration they had the Tall
+Ships coming and they had the the
+
+ align:start position:0%
+Ships coming and they had the the
+ 
+
+ align:start position:0%
+Ships coming and they had the the
+fireworks so that Spirit of Celebration
+
+ align:start position:0%
+fireworks so that Spirit of Celebration
+ 
+
+ align:start position:0%
+fireworks so that Spirit of Celebration
+got into the
+
+ align:start position:0%
+got into the
+ 
+
+ align:start position:0%
+got into the
+students uh the high the high school
+
+ align:start position:0%
+students uh the high the high school
+ 
+
+ align:start position:0%
+students uh the high the high school
+students and uh the city gave them some
+
+ align:start position:0%
+students and uh the city gave them some
+ 
+
+ align:start position:0%
+students and uh the city gave them some
+paint and they started putting a series
+
+ align:start position:0%
+paint and they started putting a series
+ 
+
+ align:start position:0%
+paint and they started putting a series
+of motives that are very crude but to me
+
+ align:start position:0%
+of motives that are very crude but to me
+ 
+
+ align:start position:0%
+of motives that are very crude but to me
+this is very revealing and very moving
+
+ align:start position:0%
+this is very revealing and very moving
+ 
+
+ align:start position:0%
+this is very revealing and very moving
+so you see some some the the date
+
+ align:start position:0%
+so you see some some the the date
+ 
+
+ align:start position:0%
+so you see some some the the date
+1776 the horses you know they some some
+
+ align:start position:0%
+1776 the horses you know they some some
+ 
+
+ align:start position:0%
+1776 the horses you know they some some
+pictures of Indian maidens
+
+ align:start position:0%
+pictures of Indian maidens
+ 
+
+ align:start position:0%
+pictures of Indian maidens
+there and then some africanamerican
+
+ align:start position:0%
+there and then some africanamerican
+ 
+
+ align:start position:0%
+there and then some africanamerican
+fighter is you know fighting during the
+
+ align:start position:0%
+fighter is you know fighting during the
+ 
+
+ align:start position:0%
+fighter is you know fighting during the
+Revolutionary War an eagle that got
+
+ align:start position:0%
+Revolutionary War an eagle that got
+ 
+
+ align:start position:0%
+Revolutionary War an eagle that got
+eroded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there and here you have
+
+ align:start position:0%
+there and here you have
+ 
+
+ align:start position:0%
+there and here you have
+the the the African-American worker and
+
+ align:start position:0%
+the the the African-American worker and
+ 
+
+ align:start position:0%
+the the the African-American worker and
+at the same time the CI famous Civil
+
+ align:start position:0%
+at the same time the CI famous Civil
+ 
+
+ align:start position:0%
+at the same time the CI famous Civil
+Rights photograph there uh that has been
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+superimposed and that's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+detail and that's all there is left of
+
+ align:start position:0%
+detail and that's all there is left of
+ 
+
+ align:start position:0%
+detail and that's all there is left of
+that it's h it's the old
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flag this is another one of the
+
+ align:start position:0%
+flag this is another one of the
+ 
+
+ align:start position:0%
+flag this is another one of the
+photographs that was found in the that
+
+ align:start position:0%
+photographs that was found in the that
+ 
+
+ align:start position:0%
+photographs that was found in the that
+was taken in the same Factory where the
+
+ align:start position:0%
+was taken in the same Factory where the
+ 
+
+ align:start position:0%
+was taken in the same Factory where the
+first picture was and I think it's a
+
+ align:start position:0%
+first picture was and I think it's a
+ 
+
+ align:start position:0%
+first picture was and I think it's a
+play with the with the Statue of
+
+ align:start position:0%
+play with the with the Statue of
+ 
+
+ align:start position:0%
+play with the with the Statue of
+Liberty some buildings stay and I I
+
+ align:start position:0%
+Liberty some buildings stay and I I
+ 
+
+ align:start position:0%
+Liberty some buildings stay and I I
+think this is what uh this one of the
+
+ align:start position:0%
+think this is what uh this one of the
+ 
+
+ align:start position:0%
+think this is what uh this one of the
+things that I find very interesting
+
+ align:start position:0%
+things that I find very interesting
+ 
+
+ align:start position:0%
+things that I find very interesting
+is it's a few people managed to make the
+
+ align:start position:0%
+is it's a few people managed to make the
+ 
+
+ align:start position:0%
+is it's a few people managed to make the
+transition as the city made the
+
+ align:start position:0%
+transition as the city made the
+ 
+
+ align:start position:0%
+transition as the city made the
+transition they stay there with their
+
+ align:start position:0%
+transition they stay there with their
+ 
+
+ align:start position:0%
+transition they stay there with their
+businesses in this case it was a couple
+
+ align:start position:0%
+businesses in this case it was a couple
+ 
+
+ align:start position:0%
+businesses in this case it was a couple
+that had that bar but they continue
+
+ align:start position:0%
+that had that bar but they continue
+ 
+
+ align:start position:0%
+that had that bar but they continue
+having that
+
+ align:start position:0%
+having that
+ 
+
+ align:start position:0%
+having that
+bar uh even though the neighborhood
+
+ align:start position:0%
+bar uh even though the neighborhood
+ 
+
+ align:start position:0%
+bar uh even though the neighborhood
+around them changed completely so even
+
+ align:start position:0%
+around them changed completely so even
+ 
+
+ align:start position:0%
+around them changed completely so even
+though it was a neighborhood of poles
+
+ align:start position:0%
+though it was a neighborhood of poles
+ 
+
+ align:start position:0%
+though it was a neighborhood of poles
+and ukrainians and and uh Irish it uh it
+
+ align:start position:0%
+and ukrainians and and uh Irish it uh it
+ 
+
+ align:start position:0%
+and ukrainians and and uh Irish it uh it
+changed into an African-American
+
+ align:start position:0%
+changed into an African-American
+ 
+
+ align:start position:0%
+changed into an African-American
+neighborhood but they were there and the
+
+ align:start position:0%
+neighborhood but they were there and the
+ 
+
+ align:start position:0%
+neighborhood but they were there and the
+business continued to thrive and
+
+ align:start position:0%
+business continued to thrive and
+ 
+
+ align:start position:0%
+business continued to thrive and
+everything around them sort of
+
+ align:start position:0%
+everything around them sort of
+ 
+
+ align:start position:0%
+everything around them sort of
+disappeared so here is this bar one of
+
+ align:start position:0%
+disappeared so here is this bar one of
+ 
+
+ align:start position:0%
+disappeared so here is this bar one of
+the strangest bars in America that is in
+
+ align:start position:0%
+the strangest bars in America that is in
+ 
+
+ align:start position:0%
+the strangest bars in America that is in
+the middle of nowhere and it has uh
+
+ align:start position:0%
+the middle of nowhere and it has uh
+ 
+
+ align:start position:0%
+the middle of nowhere and it has uh
+sometimes you find around it almost the
+
+ align:start position:0%
+sometimes you find around it almost the
+ 
+
+ align:start position:0%
+sometimes you find around it almost the
+whole lifestyle being built if you go a
+
+ align:start position:0%
+whole lifestyle being built if you go a
+ 
+
+ align:start position:0%
+whole lifestyle being built if you go a
+summer day you find people barbecuing
+
+ align:start position:0%
+summer day you find people barbecuing
+ 
+
+ align:start position:0%
+summer day you find people barbecuing
+all around there as if it was a city
+
+ align:start position:0%
+all around there as if it was a city
+ 
+
+ align:start position:0%
+all around there as if it was a city
+park if you go in the winter you find
+
+ align:start position:0%
+park if you go in the winter you find
+ 
+
+ align:start position:0%
+park if you go in the winter you find
+people selling such things as socks and
+
+ align:start position:0%
+people selling such things as socks and
+ 
+
+ align:start position:0%
+people selling such things as socks and
+and and cigarettes and so
+
+ align:start position:0%
+and and cigarettes and so
+ 
+
+ align:start position:0%
+and and cigarettes and so
+on another one of the things that it's
+
+ align:start position:0%
+on another one of the things that it's
+ 
+
+ align:start position:0%
+on another one of the things that it's
+left behind that stay there and uh and
+
+ align:start position:0%
+left behind that stay there and uh and
+ 
+
+ align:start position:0%
+left behind that stay there and uh and
+that's uh that's a store in Camden
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that is a place that sells religious
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+objects most to mostly to a Latino uh uh
+
+ align:start position:0%
+objects most to mostly to a Latino uh uh
+ 
+
+ align:start position:0%
+objects most to mostly to a Latino uh uh
+what you say to a Latino clientele
+
+ align:start position:0%
+what you say to a Latino clientele
+ 
+
+ align:start position:0%
+what you say to a Latino clientele
+that's part of the eroded ccape that's
+
+ align:start position:0%
+that's part of the eroded ccape that's
+ 
+
+ align:start position:0%
+that's part of the eroded ccape that's
+what you
+
+ align:start position:0%
+what you
+ 
+
+ align:start position:0%
+what you
+know some of the streets or many of the
+
+ align:start position:0%
+know some of the streets or many of the
+ 
+
+ align:start position:0%
+know some of the streets or many of the
+streets of the city look like
+
+ align:start position:0%
+streets of the city look like
+ 
+
+ align:start position:0%
+streets of the city look like
+today a a house that has been sealed
+
+ align:start position:0%
+today a a house that has been sealed
+ 
+
+ align:start position:0%
+today a a house that has been sealed
+there and sort of preserved
+
+ align:start position:0%
+there and sort of preserved
+ 
+
+ align:start position:0%
+there and sort of preserved
+standing uh
+
+ align:start position:0%
+standing uh
+ 
+
+ align:start position:0%
+standing uh
+almost
+
+ align:start position:0%
+almost
+ 
+
+ align:start position:0%
+almost
+blinded one house and here is something
+
+ align:start position:0%
+blinded one house and here is something
+ 
+
+ align:start position:0%
+blinded one house and here is something
+that uh that I I do want to do uh uh
+
+ align:start position:0%
+that uh that I I do want to do uh uh
+ 
+
+ align:start position:0%
+that uh that I I do want to do uh uh
+follow through this uh what happens when
+
+ align:start position:0%
+follow through this uh what happens when
+ 
+
+ align:start position:0%
+follow through this uh what happens when
+there is one house that is either
+
+ align:start position:0%
+there is one house that is either
+ 
+
+ align:start position:0%
+there is one house that is either
+attached to a house that is abandoned or
+
+ align:start position:0%
+attached to a house that is abandoned or
+ 
+
+ align:start position:0%
+attached to a house that is abandoned or
+where like in this case is attached to
+
+ align:start position:0%
+where like in this case is attached to
+ 
+
+ align:start position:0%
+where like in this case is attached to
+several houses that are abandoned does
+
+ align:start position:0%
+several houses that are abandoned does
+ 
+
+ align:start position:0%
+several houses that are abandoned does
+it how long does it continue what
+
+ align:start position:0%
+it how long does it continue what
+ 
+
+ align:start position:0%
+it how long does it continue what
+happens to the people inside how do they
+
+ align:start position:0%
+happens to the people inside how do they
+ 
+
+ align:start position:0%
+happens to the people inside how do they
+perceive their situation what what is uh
+
+ align:start position:0%
+perceive their situation what what is uh
+ 
+
+ align:start position:0%
+perceive their situation what what is uh
+uh you know if I go there next year if I
+
+ align:start position:0%
+uh you know if I go there next year if I
+ 
+
+ align:start position:0%
+uh you know if I go there next year if I
+go there the year after will will they
+
+ align:start position:0%
+go there the year after will will they
+ 
+
+ align:start position:0%
+go there the year after will will they
+still be there will they sell the house
+
+ align:start position:0%
+still be there will they sell the house
+ 
+
+ align:start position:0%
+still be there will they sell the house
+and give it you know to somebody else
+
+ align:start position:0%
+and give it you know to somebody else
+ 
+
+ align:start position:0%
+and give it you know to somebody else
+again here is one that is occupied and
+
+ align:start position:0%
+again here is one that is occupied and
+ 
+
+ align:start position:0%
+again here is one that is occupied and
+is tied up to all those other houses
+
+ align:start position:0%
+is tied up to all those other houses
+ 
+
+ align:start position:0%
+is tied up to all those other houses
+that are scheduled to be demolished you
+
+ align:start position:0%
+that are scheduled to be demolished you
+ 
+
+ align:start position:0%
+that are scheduled to be demolished you
+can see the sign there for demolition
+
+ align:start position:0%
+can see the sign there for demolition
+ 
+
+ align:start position:0%
+can see the sign there for demolition
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+houses that will go very soon part of
+
+ align:start position:0%
+houses that will go very soon part of
+ 
+
+ align:start position:0%
+houses that will go very soon part of
+the reason why so many houses in this
+
+ align:start position:0%
+the reason why so many houses in this
+ 
+
+ align:start position:0%
+the reason why so many houses in this
+particular area are going is because the
+
+ align:start position:0%
+particular area are going is because the
+ 
+
+ align:start position:0%
+particular area are going is because the
+land itself was polluted there much of
+
+ align:start position:0%
+land itself was polluted there much of
+ 
+
+ align:start position:0%
+land itself was polluted there much of
+that industrialization that the heavy
+
+ align:start position:0%
+that industrialization that the heavy
+ 
+
+ align:start position:0%
+that industrialization that the heavy
+industry that took place that was there
+
+ align:start position:0%
+industry that took place that was there
+ 
+
+ align:start position:0%
+industry that took place that was there
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+Thrive uh polluted the land and uh
+
+ align:start position:0%
+Thrive uh polluted the land and uh
+ 
+
+ align:start position:0%
+Thrive uh polluted the land and uh
+depending on what the pollutants are
+
+ align:start position:0%
+depending on what the pollutants are
+ 
+
+ align:start position:0%
+depending on what the pollutants are
+sometimes that can take seven years
+
+ align:start position:0%
+sometimes that can take seven years
+ 
+
+ align:start position:0%
+sometimes that can take seven years
+sometimes longer than seven years to
+
+ align:start position:0%
+sometimes longer than seven years to
+ 
+
+ align:start position:0%
+sometimes longer than seven years to
+clean uh and it's really a major
+
+ align:start position:0%
+clean uh and it's really a major
+ 
+
+ align:start position:0%
+clean uh and it's really a major
+undertaking so this area is all going to
+
+ align:start position:0%
+undertaking so this area is all going to
+ 
+
+ align:start position:0%
+undertaking so this area is all going to
+be cleared and I you know the cleanup
+
+ align:start position:0%
+be cleared and I you know the cleanup
+ 
+
+ align:start position:0%
+be cleared and I you know the cleanup
+period is going to
+
+ align:start position:0%
+period is going to
+ 
+
+ align:start position:0%
+period is going to
+start the houses start peeling you know
+
+ align:start position:0%
+start the houses start peeling you know
+ 
+
+ align:start position:0%
+start the houses start peeling you know
+so the different this is the sense you
+
+ align:start position:0%
+so the different this is the sense you
+ 
+
+ align:start position:0%
+so the different this is the sense you
+get the same sense in
+
+ align:start position:0%
+get the same sense in
+ 
+
+ align:start position:0%
+get the same sense in
+Detroit in many of the other American
+
+ align:start position:0%
+Detroit in many of the other American
+ 
+
+ align:start position:0%
+Detroit in many of the other American
+cities and then you start getting the
+
+ align:start position:0%
+cities and then you start getting the
+ 
+
+ align:start position:0%
+cities and then you start getting the
+older the older uh skins you know I
+
+ align:start position:0%
+older the older uh skins you know I
+ 
+
+ align:start position:0%
+older the older uh skins you know I
+think of this almost as you know having
+
+ align:start position:0%
+think of this almost as you know having
+ 
+
+ align:start position:0%
+think of this almost as you know having
+an x-ray of the of the house where you
+
+ align:start position:0%
+an x-ray of the of the house where you
+ 
+
+ align:start position:0%
+an x-ray of the of the house where you
+you almost can date you can date all
+
+ align:start position:0%
+you almost can date you can date all
+ 
+
+ align:start position:0%
+you almost can date you can date all
+those skins you know you know when
+
+ align:start position:0%
+those skins you know you know when
+ 
+
+ align:start position:0%
+those skins you know you know when
+aluminum siding came you know when when
+
+ align:start position:0%
+aluminum siding came you know when when
+ 
+
+ align:start position:0%
+aluminum siding came you know when when
+this this other asbest siding or you
+
+ align:start position:0%
+this this other asbest siding or you
+ 
+
+ align:start position:0%
+this this other asbest siding or you
+know all the different sidings that uh
+
+ align:start position:0%
+know all the different sidings that uh
+ 
+
+ align:start position:0%
+know all the different sidings that uh
+that were around in the 30s or the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+20s that is the case of a woman that had
+
+ align:start position:0%
+20s that is the case of a woman that had
+ 
+
+ align:start position:0%
+20s that is the case of a woman that had
+to live with a house with a vacant house
+
+ align:start position:0%
+to live with a house with a vacant house
+ 
+
+ align:start position:0%
+to live with a house with a vacant house
+next to
+
+ align:start position:0%
+next to
+ 
+
+ align:start position:0%
+next to
+her and she had done so for 7 years and
+
+ align:start position:0%
+her and she had done so for 7 years and
+ 
+
+ align:start position:0%
+her and she had done so for 7 years and
+in 7 years uh the house was still bacon
+
+ align:start position:0%
+in 7 years uh the house was still bacon
+ 
+
+ align:start position:0%
+in 7 years uh the house was still bacon
+that's a house the house next door had
+
+ align:start position:0%
+that's a house the house next door had
+ 
+
+ align:start position:0%
+that's a house the house next door had
+recently been vacated an elderly lady
+
+ align:start position:0%
+recently been vacated an elderly lady
+ 
+
+ align:start position:0%
+recently been vacated an elderly lady
+lived there and she got too old and she
+
+ align:start position:0%
+lived there and she got too old and she
+ 
+
+ align:start position:0%
+lived there and she got too old and she
+had to go to a hospice and uh of course
+
+ align:start position:0%
+had to go to a hospice and uh of course
+ 
+
+ align:start position:0%
+had to go to a hospice and uh of course
+the house was burnt and but the next
+
+ align:start position:0%
+the house was burnt and but the next
+ 
+
+ align:start position:0%
+the house was burnt and but the next
+door they continue to live there even
+
+ align:start position:0%
+door they continue to live there even
+ 
+
+ align:start position:0%
+door they continue to live there even
+though it's wide
+
+ align:start position:0%
+though it's wide
+ 
+
+ align:start position:0%
+though it's wide
+open it's similar situation
+
+ align:start position:0%
+open it's similar situation
+ 
+
+ align:start position:0%
+open it's similar situation
+here and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I I I don't have much to say about
+
+ align:start position:0%
+here I I I don't have much to say about
+ 
+
+ align:start position:0%
+here I I I don't have much to say about
+this I just I mean the man he has a job
+
+ align:start position:0%
+this I just I mean the man he has a job
+ 
+
+ align:start position:0%
+this I just I mean the man he has a job
+he goes out to the clean hotels in in in
+
+ align:start position:0%
+he goes out to the clean hotels in in in
+ 
+
+ align:start position:0%
+he goes out to the clean hotels in in in
+the surrounding areas of the city and
+
+ align:start position:0%
+the surrounding areas of the city and
+ 
+
+ align:start position:0%
+the surrounding areas of the city and
+then he comes home and this is his home
+
+ align:start position:0%
+then he comes home and this is his home
+ 
+
+ align:start position:0%
+then he comes home and this is his home
+and he's uh doing some clean up and some
+
+ align:start position:0%
+and he's uh doing some clean up and some
+ 
+
+ align:start position:0%
+and he's uh doing some clean up and some
+painting efforts that go just part of
+
+ align:start position:0%
+painting efforts that go just part of
+ 
+
+ align:start position:0%
+painting efforts that go just part of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+facade that's another
+
+ align:start position:0%
+facade that's another
+ 
+
+ align:start position:0%
+facade that's another
+example the institutions too pass a
+
+ align:start position:0%
+example the institutions too pass a
+ 
+
+ align:start position:0%
+example the institutions too pass a
+certain point uh up to a certain point
+
+ align:start position:0%
+certain point uh up to a certain point
+ 
+
+ align:start position:0%
+certain point uh up to a certain point
+they were like the institutions anywhere
+
+ align:start position:0%
+they were like the institutions anywhere
+ 
+
+ align:start position:0%
+they were like the institutions anywhere
+in America and then the in then they
+
+ align:start position:0%
+in America and then the in then they
+ 
+
+ align:start position:0%
+in America and then the in then they
+began to be built in a styles that were
+
+ align:start position:0%
+began to be built in a styles that were
+ 
+
+ align:start position:0%
+began to be built in a styles that were
+only adapted for the inner city and this
+
+ align:start position:0%
+only adapted for the inner city and this
+ 
+
+ align:start position:0%
+only adapted for the inner city and this
+is a case of a school uh you know I'm
+
+ align:start position:0%
+is a case of a school uh you know I'm
+ 
+
+ align:start position:0%
+is a case of a school uh you know I'm
+sure that that if you go to uh
+
+ align:start position:0%
+sure that that if you go to uh
+ 
+
+ align:start position:0%
+sure that that if you go to uh
+some other cities you know that are more
+
+ align:start position:0%
+some other cities you know that are more
+ 
+
+ align:start position:0%
+some other cities you know that are more
+of you won't see schools that look like
+
+ align:start position:0%
+of you won't see schools that look like
+ 
+
+ align:start position:0%
+of you won't see schools that look like
+this and the irony of course is that the
+
+ align:start position:0%
+this and the irony of course is that the
+ 
+
+ align:start position:0%
+this and the irony of course is that the
+schools put this
+
+ align:start position:0%
+schools put this
+ 
+
+ align:start position:0%
+schools put this
+big flag there that's another example of
+
+ align:start position:0%
+big flag there that's another example of
+ 
+
+ align:start position:0%
+big flag there that's another example of
+a school in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Camden some of them may have been
+
+ align:start position:0%
+Camden some of them may have been
+ 
+
+ align:start position:0%
+Camden some of them may have been
+adapted may have been that the style uh
+
+ align:start position:0%
+adapted may have been that the style uh
+ 
+
+ align:start position:0%
+adapted may have been that the style uh
+it's a style that was built in the 60s
+
+ align:start position:0%
+it's a style that was built in the 60s
+ 
+
+ align:start position:0%
+it's a style that was built in the 60s
+when they still thought that maybe this
+
+ align:start position:0%
+when they still thought that maybe this
+ 
+
+ align:start position:0%
+when they still thought that maybe this
+situation was not going to be permanent
+
+ align:start position:0%
+situation was not going to be permanent
+ 
+
+ align:start position:0%
+situation was not going to be permanent
+and then they put those metal cages on
+
+ align:start position:0%
+and then they put those metal cages on
+ 
+
+ align:start position:0%
+and then they put those metal cages on
+the Windows
+
+ align:start position:0%
+the Windows
+ 
+
+ align:start position:0%
+the Windows
+afterwards that's a sign from another
+
+ align:start position:0%
+afterwards that's a sign from another
+ 
+
+ align:start position:0%
+afterwards that's a sign from another
+one of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+schools that's a daycare center also
+
+ align:start position:0%
+schools that's a daycare center also
+ 
+
+ align:start position:0%
+schools that's a daycare center also
+from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Camin
+
+ align:start position:0%
+Camin
+ 
+
+ align:start position:0%
+Camin
+and that those are the leftovers of
+
+ align:start position:0%
+and that those are the leftovers of
+ 
+
+ align:start position:0%
+and that those are the leftovers of
+indust industrialism that was the Smoke
+
+ align:start position:0%
+indust industrialism that was the Smoke
+ 
+
+ align:start position:0%
+indust industrialism that was the Smoke
+Stack that was it's been demolished
+
+ align:start position:0%
+Stack that was it's been demolished
+ 
+
+ align:start position:0%
+Stack that was it's been demolished
+since then the house is not there it's a
+
+ align:start position:0%
+since then the house is not there it's a
+ 
+
+ align:start position:0%
+since then the house is not there it's a
+picture back in
+
+ align:start position:0%
+picture back in
+ 
+
+ align:start position:0%
+picture back in
+1982 the interior of a factory that's
+
+ align:start position:0%
+1982 the interior of a factory that's
+ 
+
+ align:start position:0%
+1982 the interior of a factory that's
+first used to it was a chemical plant
+
+ align:start position:0%
+first used to it was a chemical plant
+ 
+
+ align:start position:0%
+first used to it was a chemical plant
+and then later is used to store
+
+ align:start position:0%
+and then later is used to store
+ 
+
+ align:start position:0%
+and then later is used to store
+materials and then uh that that's taken
+
+ align:start position:0%
+materials and then uh that that's taken
+ 
+
+ align:start position:0%
+materials and then uh that that's taken
+down and and um what they do is they use
+
+ align:start position:0%
+down and and um what they do is they use
+ 
+
+ align:start position:0%
+down and and um what they do is they use
+it as for paper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recycling the top of buildings I use as
+
+ align:start position:0%
+recycling the top of buildings I use as
+ 
+
+ align:start position:0%
+recycling the top of buildings I use as
+antennas you know to keep cell phones
+
+ align:start position:0%
+antennas you know to keep cell phones
+ 
+
+ align:start position:0%
+antennas you know to keep cell phones
+going and and this was uh this drum
+
+ align:start position:0%
+going and and this was uh this drum
+ 
+
+ align:start position:0%
+going and and this was uh this drum
+antenna that are not use anymore not you
+
+ align:start position:0%
+antenna that are not use anymore not you
+ 
+
+ align:start position:0%
+antenna that are not use anymore not you
+not in use anymore but now you don't
+
+ align:start position:0%
+not in use anymore but now you don't
+ 
+
+ align:start position:0%
+not in use anymore but now you don't
+take them down so they stay there
+
+ align:start position:0%
+take them down so they stay there
+ 
+
+ align:start position:0%
+take them down so they stay there
+there's this sort of
+
+ align:start position:0%
+there's this sort of
+ 
+
+ align:start position:0%
+there's this sort of
+cumulative uh sense where you take
+
+ align:start position:0%
+cumulative uh sense where you take
+ 
+
+ align:start position:0%
+cumulative uh sense where you take
+layers of you take layers of antennas so
+
+ align:start position:0%
+layers of you take layers of antennas so
+ 
+
+ align:start position:0%
+layers of you take layers of antennas so
+you go into the different type of
+
+ align:start position:0%
+you go into the different type of
+ 
+
+ align:start position:0%
+you go into the different type of
+antennas
+
+ align:start position:0%
+antennas
+ 
+
+ align:start position:0%
+antennas
+today uh but the old is left
+
+ align:start position:0%
+today uh but the old is left
+ 
+
+ align:start position:0%
+today uh but the old is left
+there that's an extraordinary sign in so
+
+ align:start position:0%
+there that's an extraordinary sign in so
+ 
+
+ align:start position:0%
+there that's an extraordinary sign in so
+far as you're trying to sell some
+
+ align:start position:0%
+far as you're trying to sell some
+ 
+
+ align:start position:0%
+far as you're trying to sell some
+property and it's seems to me that is
+
+ align:start position:0%
+property and it's seems to me that is
+ 
+
+ align:start position:0%
+property and it's seems to me that is
+more to discourage people from buying it
+
+ align:start position:0%
+more to discourage people from buying it
+ 
+
+ align:start position:0%
+more to discourage people from buying it
+uh it's a it's in an area that is
+
+ align:start position:0%
+uh it's a it's in an area that is
+ 
+
+ align:start position:0%
+uh it's a it's in an area that is
+polluted and finally the homeowners had
+
+ align:start position:0%
+polluted and finally the homeowners had
+ 
+
+ align:start position:0%
+polluted and finally the homeowners had
+to had to make a deal with the city and
+
+ align:start position:0%
+to had to make a deal with the city and
+ 
+
+ align:start position:0%
+to had to make a deal with the city and
+sell and uh uh this is what the blocks
+
+ align:start position:0%
+sell and uh uh this is what the blocks
+ 
+
+ align:start position:0%
+sell and uh uh this is what the blocks
+were like that's a view of one of the
+
+ align:start position:0%
+were like that's a view of one of the
+ 
+
+ align:start position:0%
+were like that's a view of one of the
+houses not
+
+ align:start position:0%
+houses not
+ 
+
+ align:start position:0%
+houses not
+far and uh also in in this is uh
+
+ align:start position:0%
+far and uh also in in this is uh
+ 
+
+ align:start position:0%
+far and uh also in in this is uh
+combination between what it's left there
+
+ align:start position:0%
+combination between what it's left there
+ 
+
+ align:start position:0%
+combination between what it's left there
+and stays there you know like the drums
+
+ align:start position:0%
+and stays there you know like the drums
+ 
+
+ align:start position:0%
+and stays there you know like the drums
+in the building that we saw before the
+
+ align:start position:0%
+in the building that we saw before the
+ 
+
+ align:start position:0%
+in the building that we saw before the
+boat that gets there that somebody back
+
+ align:start position:0%
+boat that gets there that somebody back
+ 
+
+ align:start position:0%
+boat that gets there that somebody back
+20 years ago thought well I'll buy this
+
+ align:start position:0%
+20 years ago thought well I'll buy this
+ 
+
+ align:start position:0%
+20 years ago thought well I'll buy this
+boat it's cheap on my spare time I'll
+
+ align:start position:0%
+boat it's cheap on my spare time I'll
+ 
+
+ align:start position:0%
+boat it's cheap on my spare time I'll
+fix it and then it stays there because
+
+ align:start position:0%
+fix it and then it stays there because
+ 
+
+ align:start position:0%
+fix it and then it stays there because
+once he get it there it was vandalized
+
+ align:start position:0%
+once he get it there it was vandalized
+ 
+
+ align:start position:0%
+once he get it there it was vandalized
+and he realized that it was going to be
+
+ align:start position:0%
+and he realized that it was going to be
+ 
+
+ align:start position:0%
+and he realized that it was going to be
+much harder to fix it but yet stays
+
+ align:start position:0%
+much harder to fix it but yet stays
+ 
+
+ align:start position:0%
+much harder to fix it but yet stays
+there gas stations
+
+ align:start position:0%
+there gas stations
+ 
+
+ align:start position:0%
+there gas stations
+this is a whole street that was closed
+
+ align:start position:0%
+this is a whole street that was closed
+ 
+
+ align:start position:0%
+this is a whole street that was closed
+you know because the whole street was
+
+ align:start position:0%
+you know because the whole street was
+ 
+
+ align:start position:0%
+you know because the whole street was
+contaminated there just one house still
+
+ align:start position:0%
+contaminated there just one house still
+ 
+
+ align:start position:0%
+contaminated there just one house still
+occupy
+
+ align:start position:0%
+occupy
+ 
+
+ align:start position:0%
+occupy
+there and the trees too you begin to
+
+ align:start position:0%
+there and the trees too you begin to
+ 
+
+ align:start position:0%
+there and the trees too you begin to
+think this is probably the most uh
+
+ align:start position:0%
+think this is probably the most uh
+ 
+
+ align:start position:0%
+think this is probably the most uh
+beautiful these are probably the most
+
+ align:start position:0%
+beautiful these are probably the most
+ 
+
+ align:start position:0%
+beautiful these are probably the most
+beautiful trees in the street in the
+
+ align:start position:0%
+beautiful trees in the street in the
+ 
+
+ align:start position:0%
+beautiful trees in the street in the
+city they make a canopy over the street
+
+ align:start position:0%
+city they make a canopy over the street
+ 
+
+ align:start position:0%
+city they make a canopy over the street
+and uh uh the all the houses are going
+
+ align:start position:0%
+and uh uh the all the houses are going
+ 
+
+ align:start position:0%
+and uh uh the all the houses are going
+to be clear from there and I don't know
+
+ align:start position:0%
+to be clear from there and I don't know
+ 
+
+ align:start position:0%
+to be clear from there and I don't know
+if if the contamination affects the
+
+ align:start position:0%
+if if the contamination affects the
+ 
+
+ align:start position:0%
+if if the contamination affects the
+trees too so that the trees will
+
+ align:start position:0%
+trees too so that the trees will
+ 
+
+ align:start position:0%
+trees too so that the trees will
+be uh demolished too that was the
+
+ align:start position:0%
+be uh demolished too that was the
+ 
+
+ align:start position:0%
+be uh demolished too that was the
+old the old Carnegie Library the Camden
+
+ align:start position:0%
+old the old Carnegie Library the Camden
+ 
+
+ align:start position:0%
+old the old Carnegie Library the Camden
+free public library that was put there
+
+ align:start position:0%
+free public library that was put there
+ 
+
+ align:start position:0%
+free public library that was put there
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+1904 and then uh it was abandoned and it
+
+ align:start position:0%
+1904 and then uh it was abandoned and it
+ 
+
+ align:start position:0%
+1904 and then uh it was abandoned and it
+had trees growing
+
+ align:start position:0%
+had trees growing
+ 
+
+ align:start position:0%
+had trees growing
+inside and there you get a sense of the
+
+ align:start position:0%
+inside and there you get a sense of the
+ 
+
+ align:start position:0%
+inside and there you get a sense of the
+sort of Elegance that was there in the
+
+ align:start position:0%
+sort of Elegance that was there in the
+ 
+
+ align:start position:0%
+sort of Elegance that was there in the
+library that's what it looks like today
+
+ align:start position:0%
+library that's what it looks like today
+ 
+
+ align:start position:0%
+library that's what it looks like today
+as the there's a plan to refurbish the
+
+ align:start position:0%
+as the there's a plan to refurbish the
+ 
+
+ align:start position:0%
+as the there's a plan to refurbish the
+library and uh uh put it to use again
+
+ align:start position:0%
+library and uh uh put it to use again
+ 
+
+ align:start position:0%
+library and uh uh put it to use again
+you know if if if it doesn't crumble all
+
+ align:start position:0%
+you know if if if it doesn't crumble all
+ 
+
+ align:start position:0%
+you know if if if it doesn't crumble all
+together there are fields that are full
+
+ align:start position:0%
+together there are fields that are full
+ 
+
+ align:start position:0%
+together there are fields that are full
+of the Machinery that was used you know
+
+ align:start position:0%
+of the Machinery that was used you know
+ 
+
+ align:start position:0%
+of the Machinery that was used you know
+in the hey days of Camden can almost
+
+ align:start position:0%
+in the hey days of Camden can almost
+ 
+
+ align:start position:0%
+in the hey days of Camden can almost
+study a history of old Machinery just by
+
+ align:start position:0%
+study a history of old Machinery just by
+ 
+
+ align:start position:0%
+study a history of old Machinery just by
+going to the junkyards of Camden and
+
+ align:start position:0%
+going to the junkyards of Camden and
+ 
+
+ align:start position:0%
+going to the junkyards of Camden and
+this is uh this claws are part of of of
+
+ align:start position:0%
+this is uh this claws are part of of of
+ 
+
+ align:start position:0%
+this is uh this claws are part of of of
+I believe of a
+
+ align:start position:0%
+I believe of a
+ 
+
+ align:start position:0%
+I believe of a
+crane the city that used to make ships
+
+ align:start position:0%
+crane the city that used to make ships
+ 
+
+ align:start position:0%
+crane the city that used to make ships
+now takes them apart and then the metal
+
+ align:start position:0%
+now takes them apart and then the metal
+ 
+
+ align:start position:0%
+now takes them apart and then the metal
+from the ships is exported to China
+
+ align:start position:0%
+from the ships is exported to China
+ 
+
+ align:start position:0%
+from the ships is exported to China
+where is used to build new
+
+ align:start position:0%
+where is used to build new
+ 
+
+ align:start position:0%
+where is used to build new
+products that's another one Camden has
+
+ align:start position:0%
+products that's another one Camden has
+ 
+
+ align:start position:0%
+products that's another one Camden has
+this huge areas that were one industrial
+
+ align:start position:0%
+this huge areas that were one industrial
+ 
+
+ align:start position:0%
+this huge areas that were one industrial
+areas now they are full they're they're
+
+ align:start position:0%
+areas now they are full they're they're
+ 
+
+ align:start position:0%
+areas now they are full they're they're
+junkyards
+
+ align:start position:0%
+junkyards
+ 
+
+ align:start position:0%
+junkyards
+so the city has become not only uh the
+
+ align:start position:0%
+so the city has become not only uh the
+ 
+
+ align:start position:0%
+so the city has become not only uh the
+the transition has been from production
+
+ align:start position:0%
+the transition has been from production
+ 
+
+ align:start position:0%
+the transition has been from production
+to to this uh junkyards but
+
+ align:start position:0%
+to to this uh junkyards but
+ 
+
+ align:start position:0%
+to to this uh junkyards but
+uh also uh prisons have been built in
+
+ align:start position:0%
+uh also uh prisons have been built in
+ 
+
+ align:start position:0%
+uh also uh prisons have been built in
+Camden there have been two large prisons
+
+ align:start position:0%
+Camden there have been two large prisons
+ 
+
+ align:start position:0%
+Camden there have been two large prisons
+and in addition to that there's been
+
+ align:start position:0%
+and in addition to that there's been
+ 
+
+ align:start position:0%
+and in addition to that there's been
+uh Camden has become the place where the
+
+ align:start position:0%
+uh Camden has become the place where the
+ 
+
+ align:start position:0%
+uh Camden has become the place where the
+sew the sewage from the sub
+
+ align:start position:0%
+sew the sewage from the sub
+ 
+
+ align:start position:0%
+sew the sewage from the sub
+is treated so in some of these
+
+ align:start position:0%
+is treated so in some of these
+ 
+
+ align:start position:0%
+is treated so in some of these
+neighborhoods you know the particularly
+
+ align:start position:0%
+neighborhoods you know the particularly
+ 
+
+ align:start position:0%
+neighborhoods you know the particularly
+the one where you saw the sign
+
+ align:start position:0%
+the one where you saw the sign
+ 
+
+ align:start position:0%
+the one where you saw the sign
+before if you go around uh the smell is
+
+ align:start position:0%
+before if you go around uh the smell is
+ 
+
+ align:start position:0%
+before if you go around uh the smell is
+almost unbearable
+
+ align:start position:0%
+almost unbearable
+ 
+
+ align:start position:0%
+almost unbearable
+sometimes see this is a truck you know
+
+ align:start position:0%
+sometimes see this is a truck you know
+ 
+
+ align:start position:0%
+sometimes see this is a truck you know
+where the the all refrigerators and the
+
+ align:start position:0%
+where the the all refrigerators and the
+ 
+
+ align:start position:0%
+where the the all refrigerators and the
+like are being taken to one of the young
+
+ align:start position:0%
+like are being taken to one of the young
+ 
+
+ align:start position:0%
+like are being taken to one of the young
+yards that's the prison that's the the
+
+ align:start position:0%
+yards that's the prison that's the the
+ 
+
+ align:start position:0%
+yards that's the prison that's the the
+state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+prison not to say that there is
+
+ align:start position:0%
+prison not to say that there is
+ 
+
+ align:start position:0%
+prison not to say that there is
+not a still some some uh
+
+ align:start position:0%
+not a still some some uh
+ 
+
+ align:start position:0%
+not a still some some uh
+uh sort of everyday normal life I mean
+
+ align:start position:0%
+uh sort of everyday normal life I mean
+ 
+
+ align:start position:0%
+uh sort of everyday normal life I mean
+there is a Police Athletic League and
+
+ align:start position:0%
+there is a Police Athletic League and
+ 
+
+ align:start position:0%
+there is a Police Athletic League and
+the kids are uh play soccer there in the
+
+ align:start position:0%
+the kids are uh play soccer there in the
+ 
+
+ align:start position:0%
+the kids are uh play soccer there in the
+fields uh there are places like this
+
+ align:start position:0%
+fields uh there are places like this
+ 
+
+ align:start position:0%
+fields uh there are places like this
+trailer p park which to me was
+
+ align:start position:0%
+trailer p park which to me was
+ 
+
+ align:start position:0%
+trailer p park which to me was
+extraordinary because it was the only
+
+ align:start position:0%
+extraordinary because it was the only
+ 
+
+ align:start position:0%
+extraordinary because it was the only
+place where I saw probably 100 or more
+
+ align:start position:0%
+place where I saw probably 100 or more
+ 
+
+ align:start position:0%
+place where I saw probably 100 or more
+than 100 units none of which was
+
+ align:start position:0%
+than 100 units none of which was
+ 
+
+ align:start position:0%
+than 100 units none of which was
+abandoned so here the trailer park which
+
+ align:start position:0%
+abandoned so here the trailer park which
+ 
+
+ align:start position:0%
+abandoned so here the trailer park which
+usually is used to you know to despair a
+
+ align:start position:0%
+usually is used to you know to despair a
+ 
+
+ align:start position:0%
+usually is used to you know to despair a
+neighborhood say it's it it's somebody
+
+ align:start position:0%
+neighborhood say it's it it's somebody
+ 
+
+ align:start position:0%
+neighborhood say it's it it's somebody
+from a trailer park was the good
+
+ align:start position:0%
+from a trailer park was the good
+ 
+
+ align:start position:0%
+from a trailer park was the good
+neighborhood that's a hope six project
+
+ align:start position:0%
+neighborhood that's a hope six project
+ 
+
+ align:start position:0%
+neighborhood that's a hope six project
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cden you know the old projects that were
+
+ align:start position:0%
+cden you know the old projects that were
+ 
+
+ align:start position:0%
+cden you know the old projects that were
+demolish and near the Waterfront near
+
+ align:start position:0%
+demolish and near the Waterfront near
+ 
+
+ align:start position:0%
+demolish and near the Waterfront near
+the Delaware River and very close to
+
+ align:start position:0%
+the Delaware River and very close to
+ 
+
+ align:start position:0%
+the Delaware River and very close to
+downtown Philadelphia a number of
+
+ align:start position:0%
+downtown Philadelphia a number of
+ 
+
+ align:start position:0%
+downtown Philadelphia a number of
+buildings some of them historic
+
+ align:start position:0%
+buildings some of them historic
+ 
+
+ align:start position:0%
+buildings some of them historic
+buildings have being fixed uh through a
+
+ align:start position:0%
+buildings have being fixed uh through a
+ 
+
+ align:start position:0%
+buildings have being fixed uh through a
+recovery program that put something on
+
+ align:start position:0%
+recovery program that put something on
+ 
+
+ align:start position:0%
+recovery program that put something on
+the order of $170 million from the state
+
+ align:start position:0%
+the order of $170 million from the state
+ 
+
+ align:start position:0%
+the order of $170 million from the state
+to be used to do such things
+
+ align:start position:0%
+to be used to do such things
+ 
+
+ align:start position:0%
+to be used to do such things
+as an an aquarium an expansion of the
+
+ align:start position:0%
+as an an aquarium an expansion of the
+ 
+
+ align:start position:0%
+as an an aquarium an expansion of the
+aquarium some industrial parks a a
+
+ align:start position:0%
+aquarium some industrial parks a a
+ 
+
+ align:start position:0%
+aquarium some industrial parks a a
+center for performance pering arts and
+
+ align:start position:0%
+center for performance pering arts and
+ 
+
+ align:start position:0%
+center for performance pering arts and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+on and this building that was then fixed
+
+ align:start position:0%
+on and this building that was then fixed
+ 
+
+ align:start position:0%
+on and this building that was then fixed
+this was the headquarters of RCA for in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Camden a building famous because it had
+
+ align:start position:0%
+Camden a building famous because it had
+ 
+
+ align:start position:0%
+Camden a building famous because it had
+the logo of the company on the top of
+
+ align:start position:0%
+the logo of the company on the top of
+ 
+
+ align:start position:0%
+the logo of the company on the top of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+tower and then it was allowed to
+
+ align:start position:0%
+tower and then it was allowed to
+ 
+
+ align:start position:0%
+tower and then it was allowed to
+deteriorate but then it was fixed and
+
+ align:start position:0%
+deteriorate but then it was fixed and
+ 
+
+ align:start position:0%
+deteriorate but then it was fixed and
+they with $50 million of government help
+
+ align:start position:0%
+they with $50 million of government help
+ 
+
+ align:start position:0%
+they with $50 million of government help
+and now it's a
+
+ align:start position:0%
+and now it's a
+ 
+
+ align:start position:0%
+and now it's a
+success because the trip to
+
+ align:start position:0%
+success because the trip to
+ 
+
+ align:start position:0%
+success because the trip to
+Philadelphia takes 10 15 minutes to
+
+ align:start position:0%
+Philadelphia takes 10 15 minutes to
+ 
+
+ align:start position:0%
+Philadelphia takes 10 15 minutes to
+downtown
+
+ align:start position:0%
+downtown
+ 
+
+ align:start position:0%
+downtown
+Philadelphia and there's there's like a
+
+ align:start position:0%
+Philadelphia and there's there's like a
+ 
+
+ align:start position:0%
+Philadelphia and there's there's like a
+security Cordon
+
+ align:start position:0%
+security Cordon
+ 
+
+ align:start position:0%
+security Cordon
+around it's like
+
+ align:start position:0%
+around it's like
+ 
+
+ align:start position:0%
+around it's like
+recreating it's like creating a wall two
+
+ align:start position:0%
+recreating it's like creating a wall two
+ 
+
+ align:start position:0%
+recreating it's like creating a wall two
+cities separated by a
+
+ align:start position:0%
+cities separated by a
+ 
+
+ align:start position:0%
+cities separated by a
+wall That's the aquarium the entrance to
+
+ align:start position:0%
+wall That's the aquarium the entrance to
+ 
+
+ align:start position:0%
+wall That's the aquarium the entrance to
+the aquarium which is now run private
+
+ align:start position:0%
+the aquarium which is now run private
+ 
+
+ align:start position:0%
+the aquarium which is now run private
+was built and pay with public
+
+ align:start position:0%
+was built and pay with public
+ 
+
+ align:start position:0%
+was built and pay with public
+funds on the edges of Camden you see
+
+ align:start position:0%
+funds on the edges of Camden you see
+ 
+
+ align:start position:0%
+funds on the edges of Camden you see
+some immigrant an immigrant presence as
+
+ align:start position:0%
+some immigrant an immigrant presence as
+ 
+
+ align:start position:0%
+some immigrant an immigrant presence as
+you see uh in this case you see
+
+ align:start position:0%
+you see uh in this case you see
+ 
+
+ align:start position:0%
+you see uh in this case you see
+Vietnamese people and they have a couple
+
+ align:start position:0%
+Vietnamese people and they have a couple
+ 
+
+ align:start position:0%
+Vietnamese people and they have a couple
+of Vietnamese restaurants as well as uh
+
+ align:start position:0%
+of Vietnamese restaurants as well as uh
+ 
+
+ align:start position:0%
+of Vietnamese restaurants as well as uh
+p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pagod and several
+
+ align:start position:0%
+pagod and several
+ 
+
+ align:start position:0%
+pagod and several
+businesses also Mexicans are starting to
+
+ align:start position:0%
+businesses also Mexicans are starting to
+ 
+
+ align:start position:0%
+businesses also Mexicans are starting to
+come to Camden and this is also in the
+
+ align:start position:0%
+come to Camden and this is also in the
+ 
+
+ align:start position:0%
+come to Camden and this is also in the
+periphery and this is one of the
+
+ align:start position:0%
+periphery and this is one of the
+ 
+
+ align:start position:0%
+periphery and this is one of the
+restaurants and this is uh the so what
+
+ align:start position:0%
+restaurants and this is uh the so what
+ 
+
+ align:start position:0%
+restaurants and this is uh the so what
+I'm trying to show that some of the
+
+ align:start position:0%
+I'm trying to show that some of the
+ 
+
+ align:start position:0%
+I'm trying to show that some of the
+elements of recovery you know have to do
+
+ align:start position:0%
+elements of recovery you know have to do
+ 
+
+ align:start position:0%
+elements of recovery you know have to do
+with the presence of the immigrants that
+
+ align:start position:0%
+with the presence of the immigrants that
+ 
+
+ align:start position:0%
+with the presence of the immigrants that
+are coming in at the same time you have
+
+ align:start position:0%
+are coming in at the same time you have
+ 
+
+ align:start position:0%
+are coming in at the same time you have
+the other recovery which is the state
+
+ align:start position:0%
+the other recovery which is the state
+ 
+
+ align:start position:0%
+the other recovery which is the state
+sponsor recovery which is creating the
+
+ align:start position:0%
+sponsor recovery which is creating the
+ 
+
+ align:start position:0%
+sponsor recovery which is creating the
+separate section of Camden and which
+
+ align:start position:0%
+separate section of Camden and which
+ 
+
+ align:start position:0%
+separate section of Camden and which
+brought among other things the
+
+ align:start position:0%
+brought among other things the
+ 
+
+ align:start position:0%
+brought among other things the
+battleship New New Jersey which is there
+
+ align:start position:0%
+battleship New New Jersey which is there
+ 
+
+ align:start position:0%
+battleship New New Jersey which is there
+uh and uh the city of chemen bid for it
+
+ align:start position:0%
+uh and uh the city of chemen bid for it
+ 
+
+ align:start position:0%
+uh and uh the city of chemen bid for it
+and they finally got it and that it's
+
+ align:start position:0%
+and they finally got it and that it's
+ 
+
+ align:start position:0%
+and they finally got it and that it's
+the idea is that it attracts visitors
+
+ align:start position:0%
+the idea is that it attracts visitors
+ 
+
+ align:start position:0%
+the idea is that it attracts visitors
+and keeps the city you know the visitors
+
+ align:start position:0%
+and keeps the city you know the visitors
+ 
+
+ align:start position:0%
+and keeps the city you know the visitors
+will spend money there and that will
+
+ align:start position:0%
+will spend money there and that will
+ 
+
+ align:start position:0%
+will spend money there and that will
+keep the city
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alive so uh I'm very glad to have
+
+ align:start position:0%
+alive so uh I'm very glad to have
+ 
+
+ align:start position:0%
+alive so uh I'm very glad to have
+uh Spoken Here I hope that this was of
+
+ align:start position:0%
+uh Spoken Here I hope that this was of
+ 
+
+ align:start position:0%
+uh Spoken Here I hope that this was of
+interest to you and that you have many
+
+ align:start position:0%
+interest to you and that you have many
+ 
+
+ align:start position:0%
+interest to you and that you have many
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+questions and uh I hope I'm able to
+
+ align:start position:0%
+questions and uh I hope I'm able to
+ 
+
+ align:start position:0%
+questions and uh I hope I'm able to
+answer them I'm particularly happy to
+
+ align:start position:0%
+answer them I'm particularly happy to
+ 
+
+ align:start position:0%
+answer them I'm particularly happy to
+see my friend K Park here with whom we
+
+ align:start position:0%
+see my friend K Park here with whom we
+ 
+
+ align:start position:0%
+see my friend K Park here with whom we
+go a long way and uh we work together in
+
+ align:start position:0%
+go a long way and uh we work together in
+ 
+
+ align:start position:0%
+go a long way and uh we work together in
+Detroit and we did a show on storefront
+
+ align:start position:0%
+Detroit and we did a show on storefront
+ 
+
+ align:start position:0%
+Detroit and we did a show on storefront
+of art and architecture in New York
+
+ align:start position:0%
+of art and architecture in New York
+ 
+
+ align:start position:0%
+of art and architecture in New York
+which he used to
+
+ align:start position:0%
+which he used to
+ 
+
+ align:start position:0%
+which he used to
+run uh and uh I'm very happy that my
+
+ align:start position:0%
+run uh and uh I'm very happy that my
+ 
+
+ align:start position:0%
+run uh and uh I'm very happy that my
+friend an brought me here and be able to
+
+ align:start position:0%
+friend an brought me here and be able to
+ 
+
+ align:start position:0%
+friend an brought me here and be able to
+talk to you so let's uh let's see if if
+
+ align:start position:0%
+talk to you so let's uh let's see if if
+ 
+
+ align:start position:0%
+talk to you so let's uh let's see if if
+you have some questions and uh let's
+
+ align:start position:0%
+you have some questions and uh let's
+ 
+
+ align:start position:0%
+you have some questions and uh let's
+have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discussion go ahead
+
+ align:start position:0%
+discussion go ahead
+ 
+
+ align:start position:0%
+discussion go ahead
+L the power of your narrative on Camden
+
+ align:start position:0%
+L the power of your narrative on Camden
+ 
+
+ align:start position:0%
+L the power of your narrative on Camden
+is really quite immense and though what
+
+ align:start position:0%
+is really quite immense and though what
+ 
+
+ align:start position:0%
+is really quite immense and though what
+you presented tonight was in the end
+
+ align:start position:0%
+you presented tonight was in the end
+ 
+
+ align:start position:0%
+you presented tonight was in the end
+Balan by some of the more positive
+
+ align:start position:0%
+Balan by some of the more positive
+ 
+
+ align:start position:0%
+Balan by some of the more positive
+things it would have the overall effect
+
+ align:start position:0%
+things it would have the overall effect
+ 
+
+ align:start position:0%
+things it would have the overall effect
+of documenting decline of the city and
+
+ align:start position:0%
+of documenting decline of the city and
+ 
+
+ align:start position:0%
+of documenting decline of the city and
+my question is do you want your work to
+
+ align:start position:0%
+my question is do you want your work to
+ 
+
+ align:start position:0%
+my question is do you want your work to
+be perceived that way uh as opposed to
+
+ align:start position:0%
+be perceived that way uh as opposed to
+ 
+
+ align:start position:0%
+be perceived that way uh as opposed to
+uh photographing the city in terms of
+
+ align:start position:0%
+uh photographing the city in terms of
+ 
+
+ align:start position:0%
+uh photographing the city in terms of
+its coping mechanisms and the efforts
+
+ align:start position:0%
+its coping mechanisms and the efforts
+ 
+
+ align:start position:0%
+its coping mechanisms and the efforts
+that that people have um given that
+
+ align:start position:0%
+that that people have um given that
+ 
+
+ align:start position:0%
+that that people have um given that
+photography is is such an important way
+
+ align:start position:0%
+photography is is such an important way
+ 
+
+ align:start position:0%
+photography is is such an important way
+to image and reimage places to those who
+
+ align:start position:0%
+to image and reimage places to those who
+ 
+
+ align:start position:0%
+to image and reimage places to those who
+who don't visit yes um does it concern
+
+ align:start position:0%
+who don't visit yes um does it concern
+ 
+
+ align:start position:0%
+who don't visit yes um does it concern
+you that people would come away from
+
+ align:start position:0%
+you that people would come away from
+ 
+
+ align:start position:0%
+you that people would come away from
+your work uh feeling more despair about
+
+ align:start position:0%
+your work uh feeling more despair about
+ 
+
+ align:start position:0%
+your work uh feeling more despair about
+Camden uh rather than uh looking at
+
+ align:start position:0%
+Camden uh rather than uh looking at
+ 
+
+ align:start position:0%
+Camden uh rather than uh looking at
+those images that you saw towards the
+
+ align:start position:0%
+those images that you saw towards the
+ 
+
+ align:start position:0%
+those images that you saw towards the
+end and what what is the role of of a
+
+ align:start position:0%
+end and what what is the role of of a
+ 
+
+ align:start position:0%
+end and what what is the role of of a
+photographer uh in caring about the
+
+ align:start position:0%
+photographer uh in caring about the
+ 
+
+ align:start position:0%
+photographer uh in caring about the
+future of a place um when the story
+
+ align:start position:0%
+future of a place um when the story
+ 
+
+ align:start position:0%
+future of a place um when the story
+story is in part one of Destruction and
+
+ align:start position:0%
+story is in part one of Destruction and
+ 
+
+ align:start position:0%
+story is in part one of Destruction and
+decline well I think it's a fair
+
+ align:start position:0%
+decline well I think it's a fair
+ 
+
+ align:start position:0%
+decline well I think it's a fair
+question and it's a question that I've
+
+ align:start position:0%
+question and it's a question that I've
+ 
+
+ align:start position:0%
+question and it's a question that I've
+been thinking about for a long
+
+ align:start position:0%
+been thinking about for a long
+ 
+
+ align:start position:0%
+been thinking about for a long
+time and
+
+ align:start position:0%
+time and
+ 
+
+ align:start position:0%
+time and
+uh you know that's why I preceded my
+
+ align:start position:0%
+uh you know that's why I preceded my
+ 
+
+ align:start position:0%
+uh you know that's why I preceded my
+presentation by quoting that uh that uh
+
+ align:start position:0%
+presentation by quoting that uh that uh
+ 
+
+ align:start position:0%
+presentation by quoting that uh that uh
+survey of uh historians and planners and
+
+ align:start position:0%
+survey of uh historians and planners and
+ 
+
+ align:start position:0%
+survey of uh historians and planners and
+by quoting the the the
+
+ align:start position:0%
+by quoting the the the
+ 
+
+ align:start position:0%
+by quoting the the the
+by starting with the idea of the
+
+ align:start position:0%
+by starting with the idea of the
+ 
+
+ align:start position:0%
+by starting with the idea of the
+permanent condition I think I think that
+
+ align:start position:0%
+permanent condition I think I think that
+ 
+
+ align:start position:0%
+permanent condition I think I think that
+the main uh the main role of somebody
+
+ align:start position:0%
+the main uh the main role of somebody
+ 
+
+ align:start position:0%
+the main uh the main role of somebody
+that it's to see and
+
+ align:start position:0%
+that it's to see and
+ 
+
+ align:start position:0%
+that it's to see and
+Report uh has to be to do that in a form
+
+ align:start position:0%
+Report uh has to be to do that in a form
+ 
+
+ align:start position:0%
+Report uh has to be to do that in a form
+that is as complete as possible and if
+
+ align:start position:0%
+that is as complete as possible and if
+ 
+
+ align:start position:0%
+that is as complete as possible and if
+nobody else is going to report this
+
+ align:start position:0%
+nobody else is going to report this
+ 
+
+ align:start position:0%
+nobody else is going to report this
+mechanisms of survival of surviving
+
+ align:start position:0%
+mechanisms of survival of surviving
+ 
+
+ align:start position:0%
+mechanisms of survival of surviving
+which are often mechanism of decline
+
+ align:start position:0%
+which are often mechanism of decline
+ 
+
+ align:start position:0%
+which are often mechanism of decline
+because you know what if in the case of
+
+ align:start position:0%
+because you know what if in the case of
+ 
+
+ align:start position:0%
+because you know what if in the case of
+of the Packer plant that used to make
+
+ align:start position:0%
+of the Packer plant that used to make
+ 
+
+ align:start position:0%
+of the Packer plant that used to make
+automobile Automobiles and used to make
+
+ align:start position:0%
+automobile Automobiles and used to make
+ 
+
+ align:start position:0%
+automobile Automobiles and used to make
+uh engines for planes and so on you come
+
+ align:start position:0%
+uh engines for planes and so on you come
+ 
+
+ align:start position:0%
+uh engines for planes and so on you come
+one day and uh and they have 50 or 60
+
+ align:start position:0%
+one day and uh and they have 50 or 60
+ 
+
+ align:start position:0%
+one day and uh and they have 50 or 60
+different uh outfits one of which has
+
+ align:start position:0%
+different uh outfits one of which has
+ 
+
+ align:start position:0%
+different uh outfits one of which has
+old shoes to export to some to some
+
+ align:start position:0%
+old shoes to export to some to some
+ 
+
+ align:start position:0%
+old shoes to export to some to some
+place in the third world another one has
+
+ align:start position:0%
+place in the third world another one has
+ 
+
+ align:start position:0%
+place in the third world another one has
+cardboard I mean inition there's a a
+
+ align:start position:0%
+cardboard I mean inition there's a a
+ 
+
+ align:start position:0%
+cardboard I mean inition there's a a
+downgrading of function there and I it
+
+ align:start position:0%
+downgrading of function there and I it
+ 
+
+ align:start position:0%
+downgrading of function there and I it
+seems to me also that some of the ways
+
+ align:start position:0%
+seems to me also that some of the ways
+ 
+
+ align:start position:0%
+seems to me also that some of the ways
+in which we've going about uh you know
+
+ align:start position:0%
+in which we've going about uh you know
+ 
+
+ align:start position:0%
+in which we've going about uh you know
+trying to get the capital the force the
+
+ align:start position:0%
+trying to get the capital the force the
+ 
+
+ align:start position:0%
+trying to get the capital the force the
+Vitality back into the cities have not
+
+ align:start position:0%
+Vitality back into the cities have not
+ 
+
+ align:start position:0%
+Vitality back into the cities have not
+worked and are not working now and the
+
+ align:start position:0%
+worked and are not working now and the
+ 
+
+ align:start position:0%
+worked and are not working now and the
+people who keep on talking about the
+
+ align:start position:0%
+people who keep on talking about the
+ 
+
+ align:start position:0%
+people who keep on talking about the
+metropolitan area they should be a
+
+ align:start position:0%
+metropolitan area they should be a
+ 
+
+ align:start position:0%
+metropolitan area they should be a
+metropolitan I mean you know you don't
+
+ align:start position:0%
+metropolitan I mean you know you don't
+ 
+
+ align:start position:0%
+metropolitan I mean you know you don't
+see any any eagerness in the suburbs to
+
+ align:start position:0%
+see any any eagerness in the suburbs to
+ 
+
+ align:start position:0%
+see any any eagerness in the suburbs to
+say look I'm going to Cher my wealth
+
+ align:start position:0%
+say look I'm going to Cher my wealth
+ 
+
+ align:start position:0%
+say look I'm going to Cher my wealth
+with you you know sure taxes will help
+
+ align:start position:0%
+with you you know sure taxes will help
+ 
+
+ align:start position:0%
+with you you know sure taxes will help
+to pay something you know for will help
+
+ align:start position:0%
+to pay something you know for will help
+ 
+
+ align:start position:0%
+to pay something you know for will help
+to pay for better schools for Camden or
+
+ align:start position:0%
+to pay for better schools for Camden or
+ 
+
+ align:start position:0%
+to pay for better schools for Camden or
+something or other um you know because
+
+ align:start position:0%
+something or other um you know because
+ 
+
+ align:start position:0%
+something or other um you know because
+if you do the the the math you realize
+
+ align:start position:0%
+if you do the the the math you realize
+ 
+
+ align:start position:0%
+if you do the the the math you realize
+that the metropolitan areas and all of
+
+ align:start position:0%
+that the metropolitan areas and all of
+ 
+
+ align:start position:0%
+that the metropolitan areas and all of
+these areas is is they're very affluent
+
+ align:start position:0%
+these areas is is they're very affluent
+ 
+
+ align:start position:0%
+these areas is is they're very affluent
+and and it wouldn't take very much to to
+
+ align:start position:0%
+and and it wouldn't take very much to to
+ 
+
+ align:start position:0%
+and and it wouldn't take very much to to
+improve significantly the conditions of
+
+ align:start position:0%
+improve significantly the conditions of
+ 
+
+ align:start position:0%
+improve significantly the conditions of
+of of Camden yet the moment you start
+
+ align:start position:0%
+of of Camden yet the moment you start
+ 
+
+ align:start position:0%
+of of Camden yet the moment you start
+hearing the politic s there you know the
+
+ align:start position:0%
+hearing the politic s there you know the
+ 
+
+ align:start position:0%
+hearing the politic s there you know the
+way they defend their money their turfs
+
+ align:start position:0%
+way they defend their money their turfs
+ 
+
+ align:start position:0%
+way they defend their money their turfs
+the way they don't want higher taxes you
+
+ align:start position:0%
+the way they don't want higher taxes you
+ 
+
+ align:start position:0%
+the way they don't want higher taxes you
+don't imagine that that is ever going to
+
+ align:start position:0%
+don't imagine that that is ever going to
+ 
+
+ align:start position:0%
+don't imagine that that is ever going to
+happen so then what are you left with
+
+ align:start position:0%
+happen so then what are you left with
+ 
+
+ align:start position:0%
+happen so then what are you left with
+well what you're left with it's it's a
+
+ align:start position:0%
+well what you're left with it's it's a
+ 
+
+ align:start position:0%
+well what you're left with it's it's a
+powerful weapon which is the
+
+ align:start position:0%
+powerful weapon which is the
+ 
+
+ align:start position:0%
+powerful weapon which is the
+internet and then you sort of have to go
+
+ align:start position:0%
+internet and then you sort of have to go
+ 
+
+ align:start position:0%
+internet and then you sort of have to go
+into forums like this and say look you
+
+ align:start position:0%
+into forums like this and say look you
+ 
+
+ align:start position:0%
+into forums like this and say look you
+know look at my website you know and and
+
+ align:start position:0%
+know look at my website you know and and
+ 
+
+ align:start position:0%
+know look at my website you know and and
+the hope is that
+
+ align:start position:0%
+the hope is that
+ 
+
+ align:start position:0%
+the hope is that
+somehow uh you know it may not be to you
+
+ align:start position:0%
+somehow uh you know it may not be to you
+ 
+
+ align:start position:0%
+somehow uh you know it may not be to you
+it may move someone that it's not from
+
+ align:start position:0%
+it may move someone that it's not from
+ 
+
+ align:start position:0%
+it may move someone that it's not from
+the immediate area it's not from the
+
+ align:start position:0%
+the immediate area it's not from the
+ 
+
+ align:start position:0%
+the immediate area it's not from the
+metropolitan area it's not from across
+
+ align:start position:0%
+metropolitan area it's not from across
+ 
+
+ align:start position:0%
+metropolitan area it's not from across
+the the River from Camden but it may be
+
+ align:start position:0%
+the the River from Camden but it may be
+ 
+
+ align:start position:0%
+the the River from Camden but it may be
+from thousands of miles away and say
+
+ align:start position:0%
+from thousands of miles away and say
+ 
+
+ align:start position:0%
+from thousands of miles away and say
+look you know there may be something I
+
+ align:start position:0%
+look you know there may be something I
+ 
+
+ align:start position:0%
+look you know there may be something I
+can do in this city I mean uh in some
+
+ align:start position:0%
+can do in this city I mean uh in some
+ 
+
+ align:start position:0%
+can do in this city I mean uh in some
+ways you did it uh Kong you went to
+
+ align:start position:0%
+ways you did it uh Kong you went to
+ 
+
+ align:start position:0%
+ways you did it uh Kong you went to
+Detroit and you were there and you try
+
+ align:start position:0%
+Detroit and you were there and you try
+ 
+
+ align:start position:0%
+Detroit and you were there and you try
+to start something in Detroit and
+
+ align:start position:0%
+to start something in Detroit and
+ 
+
+ align:start position:0%
+to start something in Detroit and
+uh I I
+
+ align:start position:0%
+uh I I
+ 
+
+ align:start position:0%
+uh I I
+I don't know I mean I
+
+ align:start position:0%
+I don't know I mean I
+ 
+
+ align:start position:0%
+I don't know I mean I
+guess there's a new crop of human beings
+
+ align:start position:0%
+guess there's a new crop of human beings
+ 
+
+ align:start position:0%
+guess there's a new crop of human beings
+here you know they they're they're in
+
+ align:start position:0%
+here you know they they're they're in
+ 
+
+ align:start position:0%
+here you know they they're they're in
+their 20s and and they they're from all
+
+ align:start position:0%
+their 20s and and they they're from all
+ 
+
+ align:start position:0%
+their 20s and and they they're from all
+over and and they may some of them may
+
+ align:start position:0%
+over and and they may some of them may
+ 
+
+ align:start position:0%
+over and and they may some of them may
+see uh their future or part of their
+
+ align:start position:0%
+see uh their future or part of their
+ 
+
+ align:start position:0%
+see uh their future or part of their
+future involv in places like this for
+
+ align:start position:0%
+future involv in places like this for
+ 
+
+ align:start position:0%
+future involv in places like this for
+whatever reason I mean because you know
+
+ align:start position:0%
+whatever reason I mean because you know
+ 
+
+ align:start position:0%
+whatever reason I mean because you know
+one way to introduce them to to this
+
+ align:start position:0%
+one way to introduce them to to this
+ 
+
+ align:start position:0%
+one way to introduce them to to this
+places is through the
+
+ align:start position:0%
+places is through the
+ 
+
+ align:start position:0%
+places is through the
+images whether that's going to work or
+
+ align:start position:0%
+images whether that's going to work or
+ 
+
+ align:start position:0%
+images whether that's going to work or
+not you know I don't know I don't know I
+
+ align:start position:0%
+not you know I don't know I don't know I
+ 
+
+ align:start position:0%
+not you know I don't know I don't know I
+mean of course uh of course it's it's
+
+ align:start position:0%
+mean of course uh of course it's it's
+ 
+
+ align:start position:0%
+mean of course uh of course it's it's
+it's kind of a
+
+ align:start position:0%
+it's kind of a
+ 
+
+ align:start position:0%
+it's kind of a
+wild um uh statement you know to say to
+
+ align:start position:0%
+wild um uh statement you know to say to
+ 
+
+ align:start position:0%
+wild um uh statement you know to say to
+you know sort of not very realistic but
+
+ align:start position:0%
+you know sort of not very realistic but
+ 
+
+ align:start position:0%
+you know sort of not very realistic but
+then again what else is
+
+ align:start position:0%
+then again what else is
+ 
+
+ align:start position:0%
+then again what else is
+there what would you
+
+ align:start position:0%
+there what would you
+ 
+
+ align:start position:0%
+there what would you
+know what your view what do you see the
+
+ align:start position:0%
+know what your view what do you see the
+ 
+
+ align:start position:0%
+know what your view what do you see the
+future of this placees like you you
+
+ align:start position:0%
+future of this placees like you you
+ 
+
+ align:start position:0%
+future of this placees like you you
+think Gary's going to get any better in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Detroit within the next 5 years let's
+
+ align:start position:0%
+Detroit within the next 5 years let's
+ 
+
+ align:start position:0%
+Detroit within the next 5 years let's
+say or 10 years I guess the the only
+
+ align:start position:0%
+say or 10 years I guess the the only
+ 
+
+ align:start position:0%
+say or 10 years I guess the the only
+question is whether if if part of the
+
+ align:start position:0%
+question is whether if if part of the
+ 
+
+ align:start position:0%
+question is whether if if part of the
+goal is to attract people to care about
+
+ align:start position:0%
+goal is to attract people to care about
+ 
+
+ align:start position:0%
+goal is to attract people to care about
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+places how does one reconcile the most
+
+ align:start position:0%
+places how does one reconcile the most
+ 
+
+ align:start position:0%
+places how does one reconcile the most
+powerful and well disseminated images
+
+ align:start position:0%
+powerful and well disseminated images
+ 
+
+ align:start position:0%
+powerful and well disseminated images
+being more about the story of the
+
+ align:start position:0%
+being more about the story of the
+ 
+
+ align:start position:0%
+being more about the story of the
+decline Ali it with a fair amount of C
+
+ align:start position:0%
+decline Ali it with a fair amount of C
+ 
+
+ align:start position:0%
+decline Ali it with a fair amount of C
+mechanisms um versus the uh the attempts
+
+ align:start position:0%
+mechanisms um versus the uh the attempts
+ 
+
+ align:start position:0%
+mechanisms um versus the uh the attempts
+to focus on uh the the efforts by local
+
+ align:start position:0%
+to focus on uh the the efforts by local
+ 
+
+ align:start position:0%
+to focus on uh the the efforts by local
+community groups or other other efforts
+
+ align:start position:0%
+community groups or other other efforts
+ 
+
+ align:start position:0%
+community groups or other other efforts
+to uh reinvest in the places um do do
+
+ align:start position:0%
+to uh reinvest in the places um do do
+ 
+
+ align:start position:0%
+to uh reinvest in the places um do do
+you feel that that by becoming the
+
+ align:start position:0%
+you feel that that by becoming the
+ 
+
+ align:start position:0%
+you feel that that by becoming the
+self-appointed documentor of the city in
+
+ align:start position:0%
+self-appointed documentor of the city in
+ 
+
+ align:start position:0%
+self-appointed documentor of the city in
+a way that goes beyond what what others
+
+ align:start position:0%
+a way that goes beyond what what others
+ 
+
+ align:start position:0%
+a way that goes beyond what what others
+there are able to do by the of the
+
+ align:start position:0%
+there are able to do by the of the
+ 
+
+ align:start position:0%
+there are able to do by the of the
+quality and dissemination of your work
+
+ align:start position:0%
+quality and dissemination of your work
+ 
+
+ align:start position:0%
+quality and dissemination of your work
+um are you moving that City in the
+
+ align:start position:0%
+um are you moving that City in the
+ 
+
+ align:start position:0%
+um are you moving that City in the
+direction that you'd like it to be uh or
+
+ align:start position:0%
+direction that you'd like it to be uh or
+ 
+
+ align:start position:0%
+direction that you'd like it to be uh or
+or does it run the risk of scaring
+
+ align:start position:0%
+or does it run the risk of scaring
+ 
+
+ align:start position:0%
+or does it run the risk of scaring
+people off uh from investment in they
+
+ align:start position:0%
+people off uh from investment in they
+ 
+
+ align:start position:0%
+people off uh from investment in they
+already are Larry they already are
+
+ align:start position:0%
+already are Larry they already are
+ 
+
+ align:start position:0%
+already are Larry they already are
+they're out of it they are not the money
+
+ align:start position:0%
+they're out of it they are not the money
+ 
+
+ align:start position:0%
+they're out of it they are not the money
+that's coming in it's it's government
+
+ align:start position:0%
+that's coming in it's it's government
+ 
+
+ align:start position:0%
+that's coming in it's it's government
+money there is a company called sherokee
+
+ align:start position:0%
+money there is a company called sherokee
+ 
+
+ align:start position:0%
+money there is a company called sherokee
+that wants to tear down and and and uh
+
+ align:start position:0%
+that wants to tear down and and and uh
+ 
+
+ align:start position:0%
+that wants to tear down and and and uh
+and get a thousand people out of their
+
+ align:start position:0%
+and get a thousand people out of their
+ 
+
+ align:start position:0%
+and get a thousand people out of their
+homes and build 5,000 homes but it's a
+
+ align:start position:0%
+homes and build 5,000 homes but it's a
+ 
+
+ align:start position:0%
+homes and build 5,000 homes but it's a
+program you know I mean every every year
+
+ align:start position:0%
+program you know I mean every every year
+ 
+
+ align:start position:0%
+program you know I mean every every year
+it gets postponed one more year one more
+
+ align:start position:0%
+it gets postponed one more year one more
+ 
+
+ align:start position:0%
+it gets postponed one more year one more
+year and we don't know what the impact
+
+ align:start position:0%
+year and we don't know what the impact
+ 
+
+ align:start position:0%
+year and we don't know what the impact
+of that's going to be I mean to sort of
+
+ align:start position:0%
+of that's going to be I mean to sort of
+ 
+
+ align:start position:0%
+of that's going to be I mean to sort of
+create that ribbon by the Waterfront
+
+ align:start position:0%
+create that ribbon by the Waterfront
+ 
+
+ align:start position:0%
+create that ribbon by the Waterfront
+that is separated from the sort of core
+
+ align:start position:0%
+that is separated from the sort of core
+ 
+
+ align:start position:0%
+that is separated from the sort of core
+inner city
+
+ align:start position:0%
+inner city
+ 
+
+ align:start position:0%
+inner city
+place I realize it's a tough question
+
+ align:start position:0%
+place I realize it's a tough question
+ 
+
+ align:start position:0%
+place I realize it's a tough question
+and I don't have an answer for you but
+
+ align:start position:0%
+and I don't have an answer for you but
+ 
+
+ align:start position:0%
+and I don't have an answer for you but
+uh but uh but on the other hand I mean
+
+ align:start position:0%
+uh but uh but on the other hand I mean
+ 
+
+ align:start position:0%
+uh but uh but on the other hand I mean
+somebody has to tell the story of the
+
+ align:start position:0%
+somebody has to tell the story of the
+ 
+
+ align:start position:0%
+somebody has to tell the story of the
+sort of sort of Nitty Gritty of the
+
+ align:start position:0%
+sort of sort of Nitty Gritty of the
+ 
+
+ align:start position:0%
+sort of sort of Nitty Gritty of the
+client you know the story or what is
+
+ align:start position:0%
+client you know the story or what is
+ 
+
+ align:start position:0%
+client you know the story or what is
+like if you have your home if you clean
+
+ align:start position:0%
+like if you have your home if you clean
+ 
+
+ align:start position:0%
+like if you have your home if you clean
+your front yard if you put your plants
+
+ align:start position:0%
+your front yard if you put your plants
+ 
+
+ align:start position:0%
+your front yard if you put your plants
+there but you still have an abandoned
+
+ align:start position:0%
+there but you still have an abandoned
+ 
+
+ align:start position:0%
+there but you still have an abandoned
+house next door to it and you still live
+
+ align:start position:0%
+house next door to it and you still live
+ 
+
+ align:start position:0%
+house next door to it and you still live
+with the fear that that's going to catch
+
+ align:start position:0%
+with the fear that that's going to catch
+ 
+
+ align:start position:0%
+with the fear that that's going to catch
+on fire and burn your place and you
+
+ align:start position:0%
+on fire and burn your place and you
+ 
+
+ align:start position:0%
+on fire and burn your place and you
+probably can't stay can sleep very well
+
+ align:start position:0%
+probably can't stay can sleep very well
+ 
+
+ align:start position:0%
+probably can't stay can sleep very well
+at night I mean that's that you see
+
+ align:start position:0%
+at night I mean that's that you see
+ 
+
+ align:start position:0%
+at night I mean that's that you see
+whether it it's
+
+ align:start position:0%
+whether it it's
+ 
+
+ align:start position:0%
+whether it it's
+the the whole idea of being able to do
+
+ align:start position:0%
+the the whole idea of being able to do
+ 
+
+ align:start position:0%
+the the whole idea of being able to do
+something which is perfectly
+
+ align:start position:0%
+something which is perfectly
+ 
+
+ align:start position:0%
+something which is perfectly
+balanced is it's it's of course
+
+ align:start position:0%
+balanced is it's it's of course
+ 
+
+ align:start position:0%
+balanced is it's it's of course
+enrichable and and you know for one
+
+ align:start position:0%
+enrichable and and you know for one
+ 
+
+ align:start position:0%
+enrichable and and you know for one
+person is it's a very difficult one so
+
+ align:start position:0%
+person is it's a very difficult one so
+ 
+
+ align:start position:0%
+person is it's a very difficult one so
+in 30 years of photographing Hamden
+
+ align:start position:0%
+in 30 years of photographing Hamden
+ 
+
+ align:start position:0%
+in 30 years of photographing Hamden
+there's never been a case where that one
+
+ align:start position:0%
+there's never been a case where that one
+ 
+
+ align:start position:0%
+there's never been a case where that one
+inhabited house next to the abandoned
+
+ align:start position:0%
+inhabited house next to the abandoned
+ 
+
+ align:start position:0%
+inhabited house next to the abandoned
+one has been followed by a rehabitation
+
+ align:start position:0%
+one has been followed by a rehabitation
+ 
+
+ align:start position:0%
+one has been followed by a rehabitation
+of the one next door I'm sure that's
+
+ align:start position:0%
+of the one next door I'm sure that's
+ 
+
+ align:start position:0%
+of the one next door I'm sure that's
+happened I'm sure has happened but you
+
+ align:start position:0%
+happened I'm sure has happened but you
+ 
+
+ align:start position:0%
+happened I'm sure has happened but you
+see what happens and I think this is
+
+ align:start position:0%
+see what happens and I think this is
+ 
+
+ align:start position:0%
+see what happens and I think this is
+this is this is when you use images as a
+
+ align:start position:0%
+this is this is when you use images as a
+ 
+
+ align:start position:0%
+this is this is when you use images as a
+source of Discovery is that you dis
+
+ align:start position:0%
+source of Discovery is that you dis
+ 
+
+ align:start position:0%
+source of Discovery is that you dis
+discover the questions too and it I tell
+
+ align:start position:0%
+discover the questions too and it I tell
+ 
+
+ align:start position:0%
+discover the questions too and it I tell
+you it took me 29 years to realize that
+
+ align:start position:0%
+you it took me 29 years to realize that
+ 
+
+ align:start position:0%
+you it took me 29 years to realize that
+this is a way in which a problem was
+
+ align:start position:0%
+this is a way in which a problem was
+ 
+
+ align:start position:0%
+this is a way in which a problem was
+being posed in a very Stark way and that
+
+ align:start position:0%
+being posed in a very Stark way and that
+ 
+
+ align:start position:0%
+being posed in a very Stark way and that
+it could be it could it it it it it it
+
+ align:start position:0%
+it could be it could it it it it it it
+ 
+
+ align:start position:0%
+it could be it could it it it it it it
+can be done that someone can do a very
+
+ align:start position:0%
+can be done that someone can do a very
+ 
+
+ align:start position:0%
+can be done that someone can do a very
+beautiful piece of research because the
+
+ align:start position:0%
+beautiful piece of research because the
+ 
+
+ align:start position:0%
+beautiful piece of research because the
+places are there the addresses are there
+
+ align:start position:0%
+places are there the addresses are there
+ 
+
+ align:start position:0%
+places are there the addresses are there
+and then we would find out the answers
+
+ align:start position:0%
+and then we would find out the answers
+ 
+
+ align:start position:0%
+and then we would find out the answers
+to what you're saying my job is kind of
+
+ align:start position:0%
+to what you're saying my job is kind of
+ 
+
+ align:start position:0%
+to what you're saying my job is kind of
+put it in front you know here this is
+
+ align:start position:0%
+put it in front you know here this is
+ 
+
+ align:start position:0%
+put it in front you know here this is
+this is one one thing I think that also
+
+ align:start position:0%
+this is one one thing I think that also
+ 
+
+ align:start position:0%
+this is one one thing I think that also
+restores the dignity to the people who
+
+ align:start position:0%
+restores the dignity to the people who
+ 
+
+ align:start position:0%
+restores the dignity to the people who
+are still there and holding
+
+ align:start position:0%
+are still there and holding
+ 
+
+ align:start position:0%
+are still there and holding
+out you know I mean most of us would
+
+ align:start position:0%
+out you know I mean most of us would
+ 
+
+ align:start position:0%
+out you know I mean most of us would
+have lefted right but all I'm asking is
+
+ align:start position:0%
+have lefted right but all I'm asking is
+ 
+
+ align:start position:0%
+have lefted right but all I'm asking is
+whether you did ever find the case where
+
+ align:start position:0%
+whether you did ever find the case where
+ 
+
+ align:start position:0%
+whether you did ever find the case where
+those people are holding out were
+
+ align:start position:0%
+those people are holding out were
+ 
+
+ align:start position:0%
+those people are holding out were
+rewarded by
+
+ align:start position:0%
+rewarded by
+ 
+
+ align:start position:0%
+rewarded by
+by reinvestment next door as opposed to
+
+ align:start position:0%
+by reinvestment next door as opposed to
+ 
+
+ align:start position:0%
+by reinvestment next door as opposed to
+the building falling down well I guess
+
+ align:start position:0%
+the building falling down well I guess
+ 
+
+ align:start position:0%
+the building falling down well I guess
+my answer in a roundabout way is that
+
+ align:start position:0%
+my answer in a roundabout way is that
+ 
+
+ align:start position:0%
+my answer in a roundabout way is that
+I've been slowly trying to get to the
+
+ align:start position:0%
+I've been slowly trying to get to the
+ 
+
+ align:start position:0%
+I've been slowly trying to get to the
+usefulness of this approach you know
+
+ align:start position:0%
+usefulness of this approach you know
+ 
+
+ align:start position:0%
+usefulness of this approach you know
+rather than first you look for an
+
+ align:start position:0%
+rather than first you look for an
+ 
+
+ align:start position:0%
+rather than first you look for an
+impressionistic way and say look this
+
+ align:start position:0%
+impressionistic way and say look this
+ 
+
+ align:start position:0%
+impressionistic way and say look this
+gives you an impression of what this is
+
+ align:start position:0%
+gives you an impression of what this is
+ 
+
+ align:start position:0%
+gives you an impression of what this is
+and then you start doing the systematic
+
+ align:start position:0%
+and then you start doing the systematic
+ 
+
+ align:start position:0%
+and then you start doing the systematic
+way and now the this this this pairs
+
+ align:start position:0%
+way and now the this this this pairs
+ 
+
+ align:start position:0%
+way and now the this this this pairs
+stroke me as being something very
+
+ align:start position:0%
+stroke me as being something very
+ 
+
+ align:start position:0%
+stroke me as being something very
+powerful about a year and a half ago so
+
+ align:start position:0%
+powerful about a year and a half ago so
+ 
+
+ align:start position:0%
+powerful about a year and a half ago so
+I'm sure enough the next time I go to
+
+ align:start position:0%
+I'm sure enough the next time I go to
+ 
+
+ align:start position:0%
+I'm sure enough the next time I go to
+Camden I'm going back to all those
+
+ align:start position:0%
+Camden I'm going back to all those
+ 
+
+ align:start position:0%
+Camden I'm going back to all those
+addresses I have about 20 addresses or
+
+ align:start position:0%
+addresses I have about 20 addresses or
+ 
+
+ align:start position:0%
+addresses I have about 20 addresses or
+more than that and then I will know some
+
+ align:start position:0%
+more than that and then I will know some
+ 
+
+ align:start position:0%
+more than that and then I will know some
+of the story but you see this I'm trying
+
+ align:start position:0%
+of the story but you see this I'm trying
+ 
+
+ align:start position:0%
+of the story but you see this I'm trying
+to invent a research Tool uh all by
+
+ align:start position:0%
+to invent a research Tool uh all by
+ 
+
+ align:start position:0%
+to invent a research Tool uh all by
+myself and I'm not this is great ex of
+
+ align:start position:0%
+myself and I'm not this is great ex of
+ 
+
+ align:start position:0%
+myself and I'm not this is great ex of
+examples to work
+
+ align:start position:0%
+examples to work
+ 
+
+ align:start position:0%
+examples to work
+with gentle a question to him uh why are
+
+ align:start position:0%
+with gentle a question to him uh why are
+ 
+
+ align:start position:0%
+with gentle a question to him uh why are
+you uh uh I'm not quite sure whether try
+
+ align:start position:0%
+you uh uh I'm not quite sure whether try
+ 
+
+ align:start position:0%
+you uh uh I'm not quite sure whether try
+to get to but maybe I can ask the
+
+ align:start position:0%
+to get to but maybe I can ask the
+ 
+
+ align:start position:0%
+to get to but maybe I can ask the
+question turning it around the other way
+
+ align:start position:0%
+question turning it around the other way
+ 
+
+ align:start position:0%
+question turning it around the other way
+and say um what would do you think it's
+
+ align:start position:0%
+and say um what would do you think it's
+ 
+
+ align:start position:0%
+and say um what would do you think it's
+better not to photograph and Present oh
+
+ align:start position:0%
+better not to photograph and Present oh
+ 
+
+ align:start position:0%
+better not to photograph and Present oh
+no no no not not at all I just what I
+
+ align:start position:0%
+no no no not not at all I just what I
+ 
+
+ align:start position:0%
+no no no not not at all I just what I
+what I'm trying to understand is what is
+
+ align:start position:0%
+what I'm trying to understand is what is
+ 
+
+ align:start position:0%
+what I'm trying to understand is what is
+the the you know is the is it all in One
+
+ align:start position:0%
+the the you know is the is it all in One
+ 
+
+ align:start position:0%
+the the you know is the is it all in One
+Direction or is there a selection in
+
+ align:start position:0%
+Direction or is there a selection in
+ 
+
+ align:start position:0%
+Direction or is there a selection in
+what is what is documented that is meant
+
+ align:start position:0%
+what is what is documented that is meant
+ 
+
+ align:start position:0%
+what is what is documented that is meant
+to to uh tell the story of Decline and
+
+ align:start position:0%
+to to uh tell the story of Decline and
+ 
+
+ align:start position:0%
+to to uh tell the story of Decline and
+what happens to a photographer that is
+
+ align:start position:0%
+what happens to a photographer that is
+ 
+
+ align:start position:0%
+what happens to a photographer that is
+confronted with uh contradictory
+
+ align:start position:0%
+confronted with uh contradictory
+ 
+
+ align:start position:0%
+confronted with uh contradictory
+evidence uh about some things moving in
+
+ align:start position:0%
+evidence uh about some things moving in
+ 
+
+ align:start position:0%
+evidence uh about some things moving in
+One Direction and some things going the
+
+ align:start position:0%
+One Direction and some things going the
+ 
+
+ align:start position:0%
+One Direction and some things going the
+other it's no problem about the
+
+ align:start position:0%
+other it's no problem about the
+ 
+
+ align:start position:0%
+other it's no problem about the
+contradictory materal because it
+
+ align:start position:0%
+contradictory materal because it
+ 
+
+ align:start position:0%
+contradictory materal because it
+does and the other way yeah let me jump
+
+ align:start position:0%
+does and the other way yeah let me jump
+ 
+
+ align:start position:0%
+does and the other way yeah let me jump
+in on this I I think that to me um the
+
+ align:start position:0%
+in on this I I think that to me um the
+ 
+
+ align:start position:0%
+in on this I I think that to me um the
+most poignant images that among the most
+
+ align:start position:0%
+most poignant images that among the most
+ 
+
+ align:start position:0%
+most poignant images that among the most
+po images that showed are these recent
+
+ align:start position:0%
+po images that showed are these recent
+ 
+
+ align:start position:0%
+po images that showed are these recent
+ones of these pairs of
+
+ align:start position:0%
+ones of these pairs of
+ 
+
+ align:start position:0%
+ones of these pairs of
+houses uh where someone is caring for a
+
+ align:start position:0%
+houses uh where someone is caring for a
+ 
+
+ align:start position:0%
+houses uh where someone is caring for a
+place in the face of all this
+
+ align:start position:0%
+place in the face of all this
+ 
+
+ align:start position:0%
+place in the face of all this
+Devastation around them and this is
+
+ align:start position:0%
+Devastation around them and this is
+ 
+
+ align:start position:0%
+Devastation around them and this is
+these are recent photographs and
+
+ align:start position:0%
+these are recent photographs and
+ 
+
+ align:start position:0%
+these are recent photographs and
+essentially what the question that I
+
+ align:start position:0%
+essentially what the question that I
+ 
+
+ align:start position:0%
+essentially what the question that I
+want to ask
+
+ align:start position:0%
+want to ask
+ 
+
+ align:start position:0%
+want to ask
+is to describe a little bit about how
+
+ align:start position:0%
+is to describe a little bit about how
+ 
+
+ align:start position:0%
+is to describe a little bit about how
+you choose the places where you
+
+ align:start position:0%
+you choose the places where you
+ 
+
+ align:start position:0%
+you choose the places where you
+photograph because he I think you must
+
+ align:start position:0%
+photograph because he I think you must
+ 
+
+ align:start position:0%
+photograph because he I think you must
+think very deliberately from the
+
+ align:start position:0%
+think very deliberately from the
+ 
+
+ align:start position:0%
+think very deliberately from the
+beginning about where to go so don't
+
+ align:start position:0%
+beginning about where to go so don't
+ 
+
+ align:start position:0%
+beginning about where to go so don't
+forget he started 30 years 30 years ago
+
+ align:start position:0%
+forget he started 30 years 30 years ago
+ 
+
+ align:start position:0%
+forget he started 30 years 30 years ago
+started 30 years ago he had to make uh
+
+ align:start position:0%
+started 30 years ago he had to make uh
+ 
+
+ align:start position:0%
+started 30 years ago he had to make uh
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+decisions and so where how did you
+
+ align:start position:0%
+decisions and so where how did you
+ 
+
+ align:start position:0%
+decisions and so where how did you
+decide where to go and then how did you
+
+ align:start position:0%
+decide where to go and then how did you
+ 
+
+ align:start position:0%
+decide where to go and then how did you
+did you then Branch out after a while
+
+ align:start position:0%
+did you then Branch out after a while
+ 
+
+ align:start position:0%
+did you then Branch out after a while
+and start finding other things like
+
+ align:start position:0%
+and start finding other things like
+ 
+
+ align:start position:0%
+and start finding other things like
+these pairs of P yeah well you know you
+
+ align:start position:0%
+these pairs of P yeah well you know you
+ 
+
+ align:start position:0%
+these pairs of P yeah well you know you
+start because you want to show what
+
+ align:start position:0%
+start because you want to show what
+ 
+
+ align:start position:0%
+start because you want to show what
+extreme poverty and the environment of
+
+ align:start position:0%
+extreme poverty and the environment of
+ 
+
+ align:start position:0%
+extreme poverty and the environment of
+extreme poverty in the United States
+
+ align:start position:0%
+extreme poverty in the United States
+ 
+
+ align:start position:0%
+extreme poverty in the United States
+Urban poverty is like so you you figure
+
+ align:start position:0%
+Urban poverty is like so you you figure
+ 
+
+ align:start position:0%
+Urban poverty is like so you you figure
+it's like Jacob ree so Jacob ree goes
+
+ align:start position:0%
+it's like Jacob ree so Jacob ree goes
+ 
+
+ align:start position:0%
+it's like Jacob ree so Jacob ree goes
+and photographs the the lodging houses
+
+ align:start position:0%
+and photographs the the lodging houses
+ 
+
+ align:start position:0%
+and photographs the the lodging houses
+the apartments where people do peace
+
+ align:start position:0%
+the apartments where people do peace
+ 
+
+ align:start position:0%
+the apartments where people do peace
+work where entire fames live in one room
+
+ align:start position:0%
+work where entire fames live in one room
+ 
+
+ align:start position:0%
+work where entire fames live in one room
+the alleys where the bandits are the the
+
+ align:start position:0%
+the alleys where the bandits are the the
+ 
+
+ align:start position:0%
+the alleys where the bandits are the the
+child labor all of those things the
+
+ align:start position:0%
+child labor all of those things the
+ 
+
+ align:start position:0%
+child labor all of those things the
+difference is that Jacob Rees thought
+
+ align:start position:0%
+difference is that Jacob Rees thought
+ 
+
+ align:start position:0%
+difference is that Jacob Rees thought
+that he through his
+
+ align:start position:0%
+that he through his
+ 
+
+ align:start position:0%
+that he through his
+images could bring change and could
+
+ align:start position:0%
+images could bring change and could
+ 
+
+ align:start position:0%
+images could bring change and could
+bring the
+
+ align:start position:0%
+bring the
+ 
+
+ align:start position:0%
+bring the
+abolition of the of types of buildings
+
+ align:start position:0%
+abolition of the of types of buildings
+ 
+
+ align:start position:0%
+abolition of the of types of buildings
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+overcrowding uh create sanitary
+
+ align:start position:0%
+overcrowding uh create sanitary
+ 
+
+ align:start position:0%
+overcrowding uh create sanitary
+conditions create a healthy environment
+
+ align:start position:0%
+conditions create a healthy environment
+ 
+
+ align:start position:0%
+conditions create a healthy environment
+the the difference is that we've been
+
+ align:start position:0%
+the the difference is that we've been
+ 
+
+ align:start position:0%
+the the difference is that we've been
+we've seen the situations in some ways
+
+ align:start position:0%
+we've seen the situations in some ways
+ 
+
+ align:start position:0%
+we've seen the situations in some ways
+get worse over a period that by now I I
+
+ align:start position:0%
+get worse over a period that by now I I
+ 
+
+ align:start position:0%
+get worse over a period that by now I I
+take it to be about 50
+
+ align:start position:0%
+take it to be about 50
+ 
+
+ align:start position:0%
+take it to be about 50
+years so it seems to me that the
+
+ align:start position:0%
+years so it seems to me that the
+ 
+
+ align:start position:0%
+years so it seems to me that the
+strongest representation that you can
+
+ align:start position:0%
+strongest representation that you can
+ 
+
+ align:start position:0%
+strongest representation that you can
+make of this
+
+ align:start position:0%
+make of this
+ 
+
+ align:start position:0%
+make of this
+thing the the sense and I'm really you
+
+ align:start position:0%
+thing the the sense and I'm really you
+ 
+
+ align:start position:0%
+thing the the sense and I'm really you
+know I mean I think you and I are sort
+
+ align:start position:0%
+know I mean I think you and I are sort
+ 
+
+ align:start position:0%
+know I mean I think you and I are sort
+of passed you
+
+ align:start position:0%
+of passed you
+ 
+
+ align:start position:0%
+of passed you
+know the you know and I think I I'm
+
+ align:start position:0%
+know the you know and I think I I'm
+ 
+
+ align:start position:0%
+know the you know and I think I I'm
+addressing the 20 year olds I'm
+
+ align:start position:0%
+addressing the 20 year olds I'm
+ 
+
+ align:start position:0%
+addressing the 20 year olds I'm
+addressing the 15 year olds if I could I
+
+ align:start position:0%
+addressing the 15 year olds if I could I
+ 
+
+ align:start position:0%
+addressing the 15 year olds if I could I
+mean if I have to go I said look this is
+
+ align:start position:0%
+mean if I have to go I said look this is
+ 
+
+ align:start position:0%
+mean if I have to go I said look this is
+here they tell you this is your country
+
+ align:start position:0%
+here they tell you this is your country
+ 
+
+ align:start position:0%
+here they tell you this is your country
+they tell you this is going to be
+
+ align:start position:0%
+they tell you this is going to be
+ 
+
+ align:start position:0%
+they tell you this is going to be
+permanent that it's going to be here for
+
+ align:start position:0%
+permanent that it's going to be here for
+ 
+
+ align:start position:0%
+permanent that it's going to be here for
+the rest of the time you'll be you'll be
+
+ align:start position:0%
+the rest of the time you'll be you'll be
+ 
+
+ align:start position:0%
+the rest of the time you'll be you'll be
+alive do you think it's right I mean I
+
+ align:start position:0%
+alive do you think it's right I mean I
+ 
+
+ align:start position:0%
+alive do you think it's right I mean I
+don't say that thing I will never you'll
+
+ align:start position:0%
+don't say that thing I will never you'll
+ 
+
+ align:start position:0%
+don't say that thing I will never you'll
+never catch me saying it unless you kind
+
+ align:start position:0%
+never catch me saying it unless you kind
+ 
+
+ align:start position:0%
+never catch me saying it unless you kind
+of press me but I think that it's my
+
+ align:start position:0%
+of press me but I think that it's my
+ 
+
+ align:start position:0%
+of press me but I think that it's my
+hope that that is going to get some sort
+
+ align:start position:0%
+hope that that is going to get some sort
+ 
+
+ align:start position:0%
+hope that that is going to get some sort
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+response you know and maybe not you know
+
+ align:start position:0%
+response you know and maybe not you know
+ 
+
+ align:start position:0%
+response you know and maybe not you know
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+not I don't know let me just get one
+
+ align:start position:0%
+not I don't know let me just get one
+ 
+
+ align:start position:0%
+not I don't know let me just get one
+more and then you can go ahead there was
+
+ align:start position:0%
+more and then you can go ahead there was
+ 
+
+ align:start position:0%
+more and then you can go ahead there was
+an exhibit of last year in Berlin on
+
+ align:start position:0%
+an exhibit of last year in Berlin on
+ 
+
+ align:start position:0%
+an exhibit of last year in Berlin on
+shrinking cities yeah and they
+
+ align:start position:0%
+shrinking cities yeah and they
+ 
+
+ align:start position:0%
+shrinking cities yeah and they
+documented 500 cities that were in
+
+ align:start position:0%
+documented 500 cities that were in
+ 
+
+ align:start position:0%
+documented 500 cities that were in
+Decline post industrial cities so it
+
+ align:start position:0%
+Decline post industrial cities so it
+ 
+
+ align:start position:0%
+Decline post industrial cities so it
+seems to me that it's a Global
+
+ align:start position:0%
+seems to me that it's a Global
+ 
+
+ align:start position:0%
+seems to me that it's a Global
+phenomenon that it's part of advanced
+
+ align:start position:0%
+phenomenon that it's part of advanced
+ 
+
+ align:start position:0%
+phenomenon that it's part of advanced
+capitalism and something that's
+
+ align:start position:0%
+capitalism and something that's
+ 
+
+ align:start position:0%
+capitalism and something that's
+happening throughout the world and I
+
+ align:start position:0%
+happening throughout the world and I
+ 
+
+ align:start position:0%
+happening throughout the world and I
+don't know whether there's a clear
+
+ align:start position:0%
+don't know whether there's a clear
+ 
+
+ align:start position:0%
+don't know whether there's a clear
+analysis of that part of the exhibit
+
+ align:start position:0%
+analysis of that part of the exhibit
+ 
+
+ align:start position:0%
+analysis of that part of the exhibit
+though had similarities to what you've
+
+ align:start position:0%
+though had similarities to what you've
+ 
+
+ align:start position:0%
+though had similarities to what you've
+been doing and that it was it was almost
+
+ align:start position:0%
+been doing and that it was it was almost
+ 
+
+ align:start position:0%
+been doing and that it was it was almost
+like an archaeology of decline yes so
+
+ align:start position:0%
+like an archaeology of decline yes so
+ 
+
+ align:start position:0%
+like an archaeology of decline yes so
+you saw the effects you didn't see the
+
+ align:start position:0%
+you saw the effects you didn't see the
+ 
+
+ align:start position:0%
+you saw the effects you didn't see the
+response so it left you feeling you know
+
+ align:start position:0%
+response so it left you feeling you know
+ 
+
+ align:start position:0%
+response so it left you feeling you know
+not quite clear about the direction to
+
+ align:start position:0%
+not quite clear about the direction to
+ 
+
+ align:start position:0%
+not quite clear about the direction to
+take so I guess there's this issue which
+
+ align:start position:0%
+take so I guess there's this issue which
+ 
+
+ align:start position:0%
+take so I guess there's this issue which
+is what I guess Larry was Raising here
+
+ align:start position:0%
+is what I guess Larry was Raising here
+ 
+
+ align:start position:0%
+is what I guess Larry was Raising here
+of the the degree to which your images
+
+ align:start position:0%
+of the the degree to which your images
+ 
+
+ align:start position:0%
+of the the degree to which your images
+promote struggle and a sense that you
+
+ align:start position:0%
+promote struggle and a sense that you
+ 
+
+ align:start position:0%
+promote struggle and a sense that you
+can respond on different levels versus a
+
+ align:start position:0%
+can respond on different levels versus a
+ 
+
+ align:start position:0%
+can respond on different levels versus a
+sense that that that that this is
+
+ align:start position:0%
+sense that that that that this is
+ 
+
+ align:start position:0%
+sense that that that that this is
+something that's beyond you and you best
+
+ align:start position:0%
+something that's beyond you and you best
+ 
+
+ align:start position:0%
+something that's beyond you and you best
+Find Your Way outside of places like
+
+ align:start position:0%
+Find Your Way outside of places like
+ 
+
+ align:start position:0%
+Find Your Way outside of places like
+Campton because it's a very difficult
+
+ align:start position:0%
+Campton because it's a very difficult
+ 
+
+ align:start position:0%
+Campton because it's a very difficult
+struggle so that's one observation the
+
+ align:start position:0%
+struggle so that's one observation the
+ 
+
+ align:start position:0%
+struggle so that's one observation the
+other is that there really is this you
+
+ align:start position:0%
+other is that there really is this you
+ 
+
+ align:start position:0%
+other is that there really is this you
+know effort with the Ford foundation and
+
+ align:start position:0%
+know effort with the Ford foundation and
+ 
+
+ align:start position:0%
+know effort with the Ford foundation and
+the city and the state and the
+
+ align:start position:0%
+the city and the state and the
+ 
+
+ align:start position:0%
+the city and the state and the
+reinvestment fund and others to try and
+
+ align:start position:0%
+reinvestment fund and others to try and
+ 
+
+ align:start position:0%
+reinvestment fund and others to try and
+do something there but you don't really
+
+ align:start position:0%
+do something there but you don't really
+ 
+
+ align:start position:0%
+do something there but you don't really
+have an honest dialogue about the
+
+ align:start position:0%
+have an honest dialogue about the
+ 
+
+ align:start position:0%
+have an honest dialogue about the
+effects of th those kinds of efforts
+
+ align:start position:0%
+effects of th those kinds of efforts
+ 
+
+ align:start position:0%
+effects of th those kinds of efforts
+what's really working what isn't working
+
+ align:start position:0%
+what's really working what isn't working
+ 
+
+ align:start position:0%
+what's really working what isn't working
+what have you learned all of that so in
+
+ align:start position:0%
+what have you learned all of that so in
+ 
+
+ align:start position:0%
+what have you learned all of that so in
+the places like Camden and like I think
+
+ align:start position:0%
+the places like Camden and like I think
+ 
+
+ align:start position:0%
+the places like Camden and like I think
+there's sown Winchester and Baltimore
+
+ align:start position:0%
+there's sown Winchester and Baltimore
+ 
+
+ align:start position:0%
+there's sown Winchester and Baltimore
+where they where there's been this big
+
+ align:start position:0%
+where they where there's been this big
+ 
+
+ align:start position:0%
+where they where there's been this big
+effort to turn around a really
+
+ align:start position:0%
+effort to turn around a really
+ 
+
+ align:start position:0%
+effort to turn around a really
+distressed place you don't really see
+
+ align:start position:0%
+distressed place you don't really see
+ 
+
+ align:start position:0%
+distressed place you don't really see
+what exactly has worked um so that's a
+
+ align:start position:0%
+what exactly has worked um so that's a
+ 
+
+ align:start position:0%
+what exactly has worked um so that's a
+little bit you know in terms of those of
+
+ align:start position:0%
+little bit you know in terms of those of
+ 
+
+ align:start position:0%
+little bit you know in terms of those of
+us who want to do something about this
+
+ align:start position:0%
+us who want to do something about this
+ 
+
+ align:start position:0%
+us who want to do something about this
+are always kind of left feeling that
+
+ align:start position:0%
+are always kind of left feeling that
+ 
+
+ align:start position:0%
+are always kind of left feeling that
+there's a um that there's a big thing
+
+ align:start position:0%
+there's a um that there's a big thing
+ 
+
+ align:start position:0%
+there's a um that there's a big thing
+here to be dealt with but the Lessons
+
+ align:start position:0%
+here to be dealt with but the Lessons
+ 
+
+ align:start position:0%
+here to be dealt with but the Lessons
+Learned are not necessarily drawn out
+
+ align:start position:0%
+Learned are not necessarily drawn out
+ 
+
+ align:start position:0%
+Learned are not necessarily drawn out
+and I think you've documented What What
+
+ align:start position:0%
+and I think you've documented What What
+ 
+
+ align:start position:0%
+and I think you've documented What What
+In fact happens if nothing is done but
+
+ align:start position:0%
+In fact happens if nothing is done but
+ 
+
+ align:start position:0%
+In fact happens if nothing is done but
+you leave open whether or not anything
+
+ align:start position:0%
+you leave open whether or not anything
+ 
+
+ align:start position:0%
+you leave open whether or not anything
+can be
+
+ align:start position:0%
+can be
+ 
+
+ align:start position:0%
+can be
+done well I think that's fair and I I
+
+ align:start position:0%
+done well I think that's fair and I I
+ 
+
+ align:start position:0%
+done well I think that's fair and I I
+what I find what interest
+
+ align:start position:0%
+what I find what interest
+ 
+
+ align:start position:0%
+what I find what interest
+me is to try to the
+
+ align:start position:0%
+me is to try to the
+ 
+
+ align:start position:0%
+me is to try to the
+outmost to make the places understand
+
+ align:start position:0%
+outmost to make the places understand
+ 
+
+ align:start position:0%
+outmost to make the places understand
+able in other words I think what you say
+
+ align:start position:0%
+able in other words I think what you say
+ 
+
+ align:start position:0%
+able in other words I think what you say
+and Kong was involved with the Berlin
+
+ align:start position:0%
+and Kong was involved with the Berlin
+ 
+
+ align:start position:0%
+and Kong was involved with the Berlin
+project
+
+ align:start position:0%
+project
+ 
+
+ align:start position:0%
+project
+uh you know I think having an
+
+ align:start position:0%
+uh you know I think having an
+ 
+
+ align:start position:0%
+uh you know I think having an
+involvement with a place of 26 years
+
+ align:start position:0%
+involvement with a place of 26 years
+ 
+
+ align:start position:0%
+involvement with a place of 26 years
+allows you to be able to follow certain
+
+ align:start position:0%
+allows you to be able to follow certain
+ 
+
+ align:start position:0%
+allows you to be able to follow certain
+stories and those stories will make
+
+ align:start position:0%
+stories and those stories will make
+ 
+
+ align:start position:0%
+stories and those stories will make
+people relate to the place I mean the
+
+ align:start position:0%
+people relate to the place I mean the
+ 
+
+ align:start position:0%
+people relate to the place I mean the
+stories sometimes may not be uh stories
+
+ align:start position:0%
+stories sometimes may not be uh stories
+ 
+
+ align:start position:0%
+stories sometimes may not be uh stories
+of great achievement you know just
+
+ align:start position:0%
+of great achievement you know just
+ 
+
+ align:start position:0%
+of great achievement you know just
+putting a few paintings on on a on a
+
+ align:start position:0%
+putting a few paintings on on a on a
+ 
+
+ align:start position:0%
+putting a few paintings on on a on a
+block or two of Broadway in Camden may
+
+ align:start position:0%
+block or two of Broadway in Camden may
+ 
+
+ align:start position:0%
+block or two of Broadway in Camden may
+not amount to very much but it's
+
+ align:start position:0%
+not amount to very much but it's
+ 
+
+ align:start position:0%
+not amount to very much but it's
+certainly
+
+ align:start position:0%
+certainly
+ 
+
+ align:start position:0%
+certainly
+Illuminating in terms of what was like
+
+ align:start position:0%
+Illuminating in terms of what was like
+ 
+
+ align:start position:0%
+Illuminating in terms of what was like
+to be a teenager growing up in Camden
+
+ align:start position:0%
+to be a teenager growing up in Camden
+ 
+
+ align:start position:0%
+to be a teenager growing up in Camden
+and how do you respond to this situation
+
+ align:start position:0%
+and how do you respond to this situation
+ 
+
+ align:start position:0%
+and how do you respond to this situation
+of obviously living in a in conditions
+
+ align:start position:0%
+of obviously living in a in conditions
+ 
+
+ align:start position:0%
+of obviously living in a in conditions
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+extreme uh uh
+
+ align:start position:0%
+extreme uh uh
+ 
+
+ align:start position:0%
+extreme uh uh
+poverty across the river from what looks
+
+ align:start position:0%
+poverty across the river from what looks
+ 
+
+ align:start position:0%
+poverty across the river from what looks
+to you like a thriving Center
+
+ align:start position:0%
+to you like a thriving Center
+ 
+
+ align:start position:0%
+to you like a thriving Center
+City
+
+ align:start position:0%
+City
+ 
+
+ align:start position:0%
+City
+so it's it's
+
+ align:start position:0%
+so it's it's
+ 
+
+ align:start position:0%
+so it's it's
+it's how do you relate to it you see to
+
+ align:start position:0%
+it's how do you relate to it you see to
+ 
+
+ align:start position:0%
+it's how do you relate to it you see to
+me the great uh the great problem with
+
+ align:start position:0%
+me the great uh the great problem with
+ 
+
+ align:start position:0%
+me the great uh the great problem with
+this cities you know and I think it's
+
+ align:start position:0%
+this cities you know and I think it's
+ 
+
+ align:start position:0%
+this cities you know and I think it's
+just as true of Gary in the end I mean I
+
+ align:start position:0%
+just as true of Gary in the end I mean I
+ 
+
+ align:start position:0%
+just as true of Gary in the end I mean I
+think Detroit has gotten some interest
+
+ align:start position:0%
+think Detroit has gotten some interest
+ 
+
+ align:start position:0%
+think Detroit has gotten some interest
+uh but there are many other cities too
+
+ align:start position:0%
+uh but there are many other cities too
+ 
+
+ align:start position:0%
+uh but there are many other cities too
+that have like walls around them so that
+
+ align:start position:0%
+that have like walls around them so that
+ 
+
+ align:start position:0%
+that have like walls around them so that
+what happens there just doesn't count it
+
+ align:start position:0%
+what happens there just doesn't count it
+ 
+
+ align:start position:0%
+what happens there just doesn't count it
+doesn't make it it's not there it's not
+
+ align:start position:0%
+doesn't make it it's not there it's not
+ 
+
+ align:start position:0%
+doesn't make it it's not there it's not
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+books so so it's it's it's that vacuum
+
+ align:start position:0%
+books so so it's it's it's that vacuum
+ 
+
+ align:start position:0%
+books so so it's it's it's that vacuum
+that with whatever I can
+
+ align:start position:0%
+that with whatever I can
+ 
+
+ align:start position:0%
+that with whatever I can
+do that I want to fill up I want to say
+
+ align:start position:0%
+do that I want to fill up I want to say
+ 
+
+ align:start position:0%
+do that I want to fill up I want to say
+you know look you know this this this
+
+ align:start position:0%
+you know look you know this this this
+ 
+
+ align:start position:0%
+you know look you know this this this
+this building is from a time when Camden
+
+ align:start position:0%
+this building is from a time when Camden
+ 
+
+ align:start position:0%
+this building is from a time when Camden
+was like any other city in America you
+
+ align:start position:0%
+was like any other city in America you
+ 
+
+ align:start position:0%
+was like any other city in America you
+know when it was quote unquote
+
+ align:start position:0%
+know when it was quote unquote
+ 
+
+ align:start position:0%
+know when it was quote unquote
+normal you know but
+
+ align:start position:0%
+normal you know but
+ 
+
+ align:start position:0%
+normal you know but
+then things like this
+
+ align:start position:0%
+then things like this
+ 
+
+ align:start position:0%
+then things like this
+happen as the time progress and of
+
+ align:start position:0%
+happen as the time progress and of
+ 
+
+ align:start position:0%
+happen as the time progress and of
+course there are reasons for that and
+
+ align:start position:0%
+course there are reasons for that and
+ 
+
+ align:start position:0%
+course there are reasons for that and
+there's much more than what I can say
+
+ align:start position:0%
+there's much more than what I can say
+ 
+
+ align:start position:0%
+there's much more than what I can say
+that other people can say but I'm making
+
+ align:start position:0%
+that other people can say but I'm making
+ 
+
+ align:start position:0%
+that other people can say but I'm making
+a pitch I'm also saying and I'm glad to
+
+ align:start position:0%
+a pitch I'm also saying and I'm glad to
+ 
+
+ align:start position:0%
+a pitch I'm also saying and I'm glad to
+do it here that this is a legitimate
+
+ align:start position:0%
+do it here that this is a legitimate
+ 
+
+ align:start position:0%
+do it here that this is a legitimate
+course of study and I'm happy that for
+
+ align:start position:0%
+course of study and I'm happy that for
+ 
+
+ align:start position:0%
+course of study and I'm happy that for
+the first time people like Tom SRU and
+
+ align:start position:0%
+the first time people like Tom SRU and
+ 
+
+ align:start position:0%
+the first time people like Tom SRU and
+Howard Gillette and Robert self are
+
+ align:start position:0%
+Howard Gillette and Robert self are
+ 
+
+ align:start position:0%
+Howard Gillette and Robert self are
+taking this places and are writing
+
+ align:start position:0%
+taking this places and are writing
+ 
+
+ align:start position:0%
+taking this places and are writing
+monographs you know about Oakland about
+
+ align:start position:0%
+monographs you know about Oakland about
+ 
+
+ align:start position:0%
+monographs you know about Oakland about
+Detroit about the uh Camden New Jersey
+
+ align:start position:0%
+Detroit about the uh Camden New Jersey
+ 
+
+ align:start position:0%
+Detroit about the uh Camden New Jersey
+and they will be part there will be
+
+ align:start position:0%
+and they will be part there will be
+ 
+
+ align:start position:0%
+and they will be part there will be
+something that you cannot put a wall
+
+ align:start position:0%
+something that you cannot put a wall
+ 
+
+ align:start position:0%
+something that you cannot put a wall
+around because we're very good at
+
+ align:start position:0%
+around because we're very good at
+ 
+
+ align:start position:0%
+around because we're very good at
+putting walls around
+
+ align:start position:0%
+putting walls around
+ 
+
+ align:start position:0%
+putting walls around
+things I'm sorry you you like to let me
+
+ align:start position:0%
+things I'm sorry you you like to let me
+ 
+
+ align:start position:0%
+things I'm sorry you you like to let me
+just and I'm
+
+ align:start position:0%
+just and I'm
+ 
+
+ align:start position:0%
+just and I'm
+also and um I done several I see and um
+
+ align:start position:0%
+also and um I done several I see and um
+ 
+
+ align:start position:0%
+also and um I done several I see and um
+I definitely agre with you of the
+
+ align:start position:0%
+I definitely agre with you of the
+ 
+
+ align:start position:0%
+I definitely agre with you of the
+importance of being able to um see and
+
+ align:start position:0%
+importance of being able to um see and
+ 
+
+ align:start position:0%
+importance of being able to um see and
+feel the marks of the city over a period
+
+ align:start position:0%
+feel the marks of the city over a period
+ 
+
+ align:start position:0%
+feel the marks of the city over a period
+of time it's not something that can be
+
+ align:start position:0%
+of time it's not something that can be
+ 
+
+ align:start position:0%
+of time it's not something that can be
+done overnight people want to do it it's
+
+ align:start position:0%
+done overnight people want to do it it's
+ 
+
+ align:start position:0%
+done overnight people want to do it it's
+a complete dedication yeah took me 15
+
+ align:start position:0%
+a complete dedication yeah took me 15
+ 
+
+ align:start position:0%
+a complete dedication yeah took me 15
+I've done to City for 15 years I've done
+
+ align:start position:0%
+I've done to City for 15 years I've done
+ 
+
+ align:start position:0%
+I've done to City for 15 years I've done
+buin for 10
+
+ align:start position:0%
+buin for 10
+ 
+
+ align:start position:0%
+buin for 10
+years so um and and what's happening is
+
+ align:start position:0%
+years so um and and what's happening is
+ 
+
+ align:start position:0%
+years so um and and what's happening is
+not only that we're seeing the decain of
+
+ align:start position:0%
+not only that we're seeing the decain of
+ 
+
+ align:start position:0%
+not only that we're seeing the decain of
+cities but we're also seeing the booming
+
+ align:start position:0%
+cities but we're also seeing the booming
+ 
+
+ align:start position:0%
+cities but we're also seeing the booming
+of cities yes I we speak there's 14
+
+ align:start position:0%
+of cities yes I we speak there's 14
+ 
+
+ align:start position:0%
+of cities yes I we speak there's 14
+cities in born in China with 4 million
+
+ align:start position:0%
+cities in born in China with 4 million
+ 
+
+ align:start position:0%
+cities in born in China with 4 million
+people it is years and so it's it's the
+
+ align:start position:0%
+people it is years and so it's it's the
+ 
+
+ align:start position:0%
+people it is years and so it's it's the
+marks of immigration the marks of cultur
+
+ align:start position:0%
+marks of immigration the marks of cultur
+ 
+
+ align:start position:0%
+marks of immigration the marks of cultur
+the marks of and and and that's what
+
+ align:start position:0%
+the marks of and and and that's what
+ 
+
+ align:start position:0%
+the marks of and and and that's what
+we're photographing whether it's poor
+
+ align:start position:0%
+we're photographing whether it's poor
+ 
+
+ align:start position:0%
+we're photographing whether it's poor
+it's Rich who wealthy it's say aand or
+
+ align:start position:0%
+it's Rich who wealthy it's say aand or
+ 
+
+ align:start position:0%
+it's Rich who wealthy it's say aand or
+is an imploding neighborhood whatever it
+
+ align:start position:0%
+is an imploding neighborhood whatever it
+ 
+
+ align:start position:0%
+is an imploding neighborhood whatever it
+is it's just a mark and you should be
+
+ align:start position:0%
+is it's just a mark and you should be
+ 
+
+ align:start position:0%
+is it's just a mark and you should be
+photographed and be taking for what it
+
+ align:start position:0%
+photographed and be taking for what it
+ 
+
+ align:start position:0%
+photographed and be taking for what it
+is thank you thank you very much you
+
+ align:start position:0%
+is thank you thank you very much you
+ 
+
+ align:start position:0%
+is thank you thank you very much you
+want to say
+
+ align:start position:0%
+want to say
+ 
+
+ align:start position:0%
+want to say
+um during this period of time did you
+
+ align:start position:0%
+um during this period of time did you
+ 
+
+ align:start position:0%
+um during this period of time did you
+really uh sense that the Decay happened
+
+ align:start position:0%
+really uh sense that the Decay happened
+ 
+
+ align:start position:0%
+really uh sense that the Decay happened
+at different rates as it went along with
+
+ align:start position:0%
+at different rates as it went along with
+ 
+
+ align:start position:0%
+at different rates as it went along with
+it one where it just really hit and and
+
+ align:start position:0%
+it one where it just really hit and and
+ 
+
+ align:start position:0%
+it one where it just really hit and and
+also it's that coincided with other
+
+ align:start position:0%
+also it's that coincided with other
+ 
+
+ align:start position:0%
+also it's that coincided with other
+cities across the country so there was
+
+ align:start position:0%
+cities across the country so there was
+ 
+
+ align:start position:0%
+cities across the country so there was
+really a a moment in time where this
+
+ align:start position:0%
+really a a moment in time where this
+ 
+
+ align:start position:0%
+really a a moment in time where this
+really took off and do you feel like now
+
+ align:start position:0%
+really took off and do you feel like now
+ 
+
+ align:start position:0%
+really took off and do you feel like now
+that it's sort of uh in remission
+
+ align:start position:0%
+that it's sort of uh in remission
+ 
+
+ align:start position:0%
+that it's sort of uh in remission
+slowing down as far as
+
+ align:start position:0%
+slowing down as far as
+ 
+
+ align:start position:0%
+slowing down as far as
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+welcome sorry I haven't seen him for
+
+ align:start position:0%
+welcome sorry I haven't seen him for
+ 
+
+ align:start position:0%
+welcome sorry I haven't seen him for
+several
+
+ align:start position:0%
+several
+ 
+
+ align:start position:0%
+several
+years not another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes you know I think I think the period
+
+ align:start position:0%
+yes you know I think I think the period
+ 
+
+ align:start position:0%
+yes you know I think I think the period
+of the crack epidemic was one when you
+
+ align:start position:0%
+of the crack epidemic was one when you
+ 
+
+ align:start position:0%
+of the crack epidemic was one when you
+saw change happen very fast and
+
+ align:start position:0%
+saw change happen very fast and
+ 
+
+ align:start position:0%
+saw change happen very fast and
+buildings going up in flame and so on uh
+
+ align:start position:0%
+buildings going up in flame and so on uh
+ 
+
+ align:start position:0%
+buildings going up in flame and so on uh
+and so uh I don't know sometimes I get
+
+ align:start position:0%
+and so uh I don't know sometimes I get
+ 
+
+ align:start position:0%
+and so uh I don't know sometimes I get
+that sense you know like that block has
+
+ align:start position:0%
+that sense you know like that block has
+ 
+
+ align:start position:0%
+that sense you know like that block has
+gotten the form you know maybe the new
+
+ align:start position:0%
+gotten the form you know maybe the new
+ 
+
+ align:start position:0%
+gotten the form you know maybe the new
+form you know of the of the repair
+
+ align:start position:0%
+form you know of the of the repair
+ 
+
+ align:start position:0%
+form you know of the of the repair
+repair corner for for people you know
+
+ align:start position:0%
+repair corner for for people you know
+ 
+
+ align:start position:0%
+repair corner for for people you know
+with the pizza place and the and the
+
+ align:start position:0%
+with the pizza place and the and the
+ 
+
+ align:start position:0%
+with the pizza place and the and the
+shelter for better women and the shelter
+
+ align:start position:0%
+shelter for better women and the shelter
+ 
+
+ align:start position:0%
+shelter for better women and the shelter
+and the you know the methodone clinic
+
+ align:start position:0%
+and the you know the methodone clinic
+ 
+
+ align:start position:0%
+and the you know the methodone clinic
+and you know sort of the the new uh
+
+ align:start position:0%
+and you know sort of the the new uh
+ 
+
+ align:start position:0%
+and you know sort of the the new uh
+commercial block you know the new form
+
+ align:start position:0%
+commercial block you know the new form
+ 
+
+ align:start position:0%
+commercial block you know the new form
+of the commercial block you feel that at
+
+ align:start position:0%
+of the commercial block you feel that at
+ 
+
+ align:start position:0%
+of the commercial block you feel that at
+one at one point that that is maybe it's
+
+ align:start position:0%
+one at one point that that is maybe it's
+ 
+
+ align:start position:0%
+one at one point that that is maybe it's
+going to be like that for the next 10
+
+ align:start position:0%
+going to be like that for the next 10
+ 
+
+ align:start position:0%
+going to be like that for the next 10
+years now one thing that I didn't say at
+
+ align:start position:0%
+years now one thing that I didn't say at
+ 
+
+ align:start position:0%
+years now one thing that I didn't say at
+the beginning and I would I know that
+
+ align:start position:0%
+the beginning and I would I know that
+ 
+
+ align:start position:0%
+the beginning and I would I know that
+somebody asked a question how do I pick
+
+ align:start position:0%
+somebody asked a question how do I pick
+ 
+
+ align:start position:0%
+somebody asked a question how do I pick
+uh would I pi pick well I pick all toll
+
+ align:start position:0%
+uh would I pi pick well I pick all toll
+ 
+
+ align:start position:0%
+uh would I pi pick well I pick all toll
+points of view that I can get access to
+
+ align:start position:0%
+points of view that I can get access to
+ 
+
+ align:start position:0%
+points of view that I can get access to
+so if there is a bridge I go up the
+
+ align:start position:0%
+so if there is a bridge I go up the
+ 
+
+ align:start position:0%
+so if there is a bridge I go up the
+bridge and photograph from the bridge if
+
+ align:start position:0%
+bridge and photograph from the bridge if
+ 
+
+ align:start position:0%
+bridge and photograph from the bridge if
+there's a tall building I go up and
+
+ align:start position:0%
+there's a tall building I go up and
+ 
+
+ align:start position:0%
+there's a tall building I go up and
+photograph from the tall
+
+ align:start position:0%
+photograph from the tall
+ 
+
+ align:start position:0%
+photograph from the tall
+building I also do the major Commercial
+
+ align:start position:0%
+building I also do the major Commercial
+ 
+
+ align:start position:0%
+building I also do the major Commercial
+Street with a lot of care because I know
+
+ align:start position:0%
+Street with a lot of care because I know
+ 
+
+ align:start position:0%
+Street with a lot of care because I know
+the importance of those streets so I do
+
+ align:start position:0%
+the importance of those streets so I do
+ 
+
+ align:start position:0%
+the importance of those streets so I do
+it almost systematically you know every
+
+ align:start position:0%
+it almost systematically you know every
+ 
+
+ align:start position:0%
+it almost systematically you know every
+blog at least one picture two or three
+
+ align:start position:0%
+blog at least one picture two or three
+ 
+
+ align:start position:0%
+blog at least one picture two or three
+and try to stay with that
+
+ align:start position:0%
+and try to stay with that
+ 
+
+ align:start position:0%
+and try to stay with that
+in the case of Camden I did the street
+
+ align:start position:0%
+in the case of Camden I did the street
+ 
+
+ align:start position:0%
+in the case of Camden I did the street
+that had the and and and this and this
+
+ align:start position:0%
+that had the and and and this and this
+ 
+
+ align:start position:0%
+that had the and and and this and this
+was sort of insane when I think of it
+
+ align:start position:0%
+was sort of insane when I think of it
+ 
+
+ align:start position:0%
+was sort of insane when I think of it
+that the street where the drug trade was
+
+ align:start position:0%
+that the street where the drug trade was
+ 
+
+ align:start position:0%
+that the street where the drug trade was
+the the most intense and that was Bailey
+
+ align:start position:0%
+the the most intense and that was Bailey
+ 
+
+ align:start position:0%
+the the most intense and that was Bailey
+Street so you have a site if you click
+
+ align:start position:0%
+Street so you have a site if you click
+ 
+
+ align:start position:0%
+Street so you have a site if you click
+under the Bailey Street you see what a
+
+ align:start position:0%
+under the Bailey Street you see what a
+ 
+
+ align:start position:0%
+under the Bailey Street you see what a
+really a a street that had a very heavy
+
+ align:start position:0%
+really a a street that had a very heavy
+ 
+
+ align:start position:0%
+really a a street that had a very heavy
+drug traffic was
+
+ align:start position:0%
+drug traffic was
+ 
+
+ align:start position:0%
+drug traffic was
+like uh in addition to that I TR I try I
+
+ align:start position:0%
+like uh in addition to that I TR I try I
+ 
+
+ align:start position:0%
+like uh in addition to that I TR I try I
+I either drive around or walk
+
+ align:start position:0%
+I either drive around or walk
+ 
+
+ align:start position:0%
+I either drive around or walk
+around most blocks most neighborhoods
+
+ align:start position:0%
+around most blocks most neighborhoods
+ 
+
+ align:start position:0%
+around most blocks most neighborhoods
+most
+
+ align:start position:0%
+most
+ 
+
+ align:start position:0%
+most
+Alys uh go in try to go inside wherever
+
+ align:start position:0%
+Alys uh go in try to go inside wherever
+ 
+
+ align:start position:0%
+Alys uh go in try to go inside wherever
+I can go inside if I can go inside
+
+ align:start position:0%
+I can go inside if I can go inside
+ 
+
+ align:start position:0%
+I can go inside if I can go inside
+factories if the factories are open if
+
+ align:start position:0%
+factories if the factories are open if
+ 
+
+ align:start position:0%
+factories if the factories are open if
+they will let me go in I'll go in so uh
+
+ align:start position:0%
+they will let me go in I'll go in so uh
+ 
+
+ align:start position:0%
+they will let me go in I'll go in so uh
+once you start putting the dots on the
+
+ align:start position:0%
+once you start putting the dots on the
+ 
+
+ align:start position:0%
+once you start putting the dots on the
+map you know you get a sense right away
+
+ align:start position:0%
+map you know you get a sense right away
+ 
+
+ align:start position:0%
+map you know you get a sense right away
+of where where you you know what you're
+
+ align:start position:0%
+of where where you you know what you're
+ 
+
+ align:start position:0%
+of where where you you know what you're
+covering and what you're leaving
+
+ align:start position:0%
+covering and what you're leaving
+ 
+
+ align:start position:0%
+covering and what you're leaving
+out to me it's also very
+
+ align:start position:0%
+out to me it's also very
+ 
+
+ align:start position:0%
+out to me it's also very
+important the and and this I
+
+ align:start position:0%
+important the and and this I
+ 
+
+ align:start position:0%
+important the and and this I
+think it's a it's you see when you take
+
+ align:start position:0%
+think it's a it's you see when you take
+ 
+
+ align:start position:0%
+think it's a it's you see when you take
+the sort of pro pro
+
+ align:start position:0%
+the sort of pro pro
+ 
+
+ align:start position:0%
+the sort of pro pro
+propagandist uh photographer you know
+
+ align:start position:0%
+propagandist uh photographer you know
+ 
+
+ align:start position:0%
+propagandist uh photographer you know
+let's take and and I say it with
+
+ align:start position:0%
+let's take and and I say it with
+ 
+
+ align:start position:0%
+let's take and and I say it with
+admiration let's take LS hin that said
+
+ align:start position:0%
+admiration let's take LS hin that said
+ 
+
+ align:start position:0%
+admiration let's take LS hin that said
+let's abolish child labor you know and
+
+ align:start position:0%
+let's abolish child labor you know and
+ 
+
+ align:start position:0%
+let's abolish child labor you know and
+what do you need to abolish child labor
+
+ align:start position:0%
+what do you need to abolish child labor
+ 
+
+ align:start position:0%
+what do you need to abolish child labor
+well you show the Injustice of it you
+
+ align:start position:0%
+well you show the Injustice of it you
+ 
+
+ align:start position:0%
+well you show the Injustice of it you
+show children and the machines where
+
+ align:start position:0%
+show children and the machines where
+ 
+
+ align:start position:0%
+show children and the machines where
+they work you look at those pictures and
+
+ align:start position:0%
+they work you look at those pictures and
+ 
+
+ align:start position:0%
+they work you look at those pictures and
+you think this is terrible this should
+
+ align:start position:0%
+you think this is terrible this should
+ 
+
+ align:start position:0%
+you think this is terrible this should
+not happen we don't need this to happen
+
+ align:start position:0%
+not happen we don't need this to happen
+ 
+
+ align:start position:0%
+not happen we don't need this to happen
+we don't need these kids to be doing
+
+ align:start position:0%
+we don't need these kids to be doing
+ 
+
+ align:start position:0%
+we don't need these kids to be doing
+this we need them in school we need them
+
+ align:start position:0%
+this we need them in school we need them
+ 
+
+ align:start position:0%
+this we need them in school we need them
+you know getting a health healthy air
+
+ align:start position:0%
+you know getting a health healthy air
+ 
+
+ align:start position:0%
+you know getting a health healthy air
+and exercise and all of those
+
+ align:start position:0%
+and exercise and all of those
+ 
+
+ align:start position:0%
+and exercise and all of those
+things uh but on the other
+
+ align:start position:0%
+things uh but on the other
+ 
+
+ align:start position:0%
+things uh but on the other
+hand you don't see anything else that
+
+ align:start position:0%
+hand you don't see anything else that
+ 
+
+ align:start position:0%
+hand you don't see anything else that
+those kids did you don't see you don't
+
+ align:start position:0%
+those kids did you don't see you don't
+ 
+
+ align:start position:0%
+those kids did you don't see you don't
+you don't have any idea what they sang
+
+ align:start position:0%
+you don't have any idea what they sang
+ 
+
+ align:start position:0%
+you don't have any idea what they sang
+if they sang anything you don't have any
+
+ align:start position:0%
+if they sang anything you don't have any
+ 
+
+ align:start position:0%
+if they sang anything you don't have any
+idea what the homes look like you don't
+
+ align:start position:0%
+idea what the homes look like you don't
+ 
+
+ align:start position:0%
+idea what the homes look like you don't
+have any idea if they made any drawings
+
+ align:start position:0%
+have any idea if they made any drawings
+ 
+
+ align:start position:0%
+have any idea if they made any drawings
+or anything that's why the drawings the
+
+ align:start position:0%
+or anything that's why the drawings the
+ 
+
+ align:start position:0%
+or anything that's why the drawings the
+art the the forms that are created by
+
+ align:start position:0%
+art the the forms that are created by
+ 
+
+ align:start position:0%
+art the the forms that are created by
+the local residents are so important to
+
+ align:start position:0%
+the local residents are so important to
+ 
+
+ align:start position:0%
+the local residents are so important to
+me you know that's what the those
+
+ align:start position:0%
+me you know that's what the those
+ 
+
+ align:start position:0%
+me you know that's what the those
+Memorial walls that I show are so
+
+ align:start position:0%
+Memorial walls that I show are so
+ 
+
+ align:start position:0%
+Memorial walls that I show are so
+important to me because they are the
+
+ align:start position:0%
+important to me because they are the
+ 
+
+ align:start position:0%
+important to me because they are the
+product they they they you know they
+
+ align:start position:0%
+product they they they you know they
+ 
+
+ align:start position:0%
+product they they they you know they
+reflect the spirit of of of people who
+
+ align:start position:0%
+reflect the spirit of of of people who
+ 
+
+ align:start position:0%
+reflect the spirit of of of people who
+do live there and uh
+
+ align:start position:0%
+do live there and uh
+ 
+
+ align:start position:0%
+do live there and uh
+uh you know so that's that's that that
+
+ align:start position:0%
+uh you know so that's that's that that
+ 
+
+ align:start position:0%
+uh you know so that's that's that that
+that it's building over time take care
+
+ align:start position:0%
+that it's building over time take care
+ 
+
+ align:start position:0%
+that it's building over time take care
+have a good day and uh and uh you know
+
+ align:start position:0%
+have a good day and uh and uh you know
+ 
+
+ align:start position:0%
+have a good day and uh and uh you know
+those those are the basic things that I
+
+ align:start position:0%
+those those are the basic things that I
+ 
+
+ align:start position:0%
+those those are the basic things that I
+try to do when I when I photograph a
+
+ align:start position:0%
+try to do when I when I photograph a
+ 
+
+ align:start position:0%
+try to do when I when I photograph a
+city I'm sorry you go ahead I see you
+
+ align:start position:0%
+city I'm sorry you go ahead I see you
+ 
+
+ align:start position:0%
+city I'm sorry you go ahead I see you
+work very much as being a witness and a
+
+ align:start position:0%
+work very much as being a witness and a
+ 
+
+ align:start position:0%
+work very much as being a witness and a
+taxonomist of a certain class of cities
+
+ align:start position:0%
+taxonomist of a certain class of cities
+ 
+
+ align:start position:0%
+taxonomist of a certain class of cities
+in the US and and you've done this for
+
+ align:start position:0%
+in the US and and you've done this for
+ 
+
+ align:start position:0%
+in the US and and you've done this for
+you know about three decades yes leaving
+
+ align:start position:0%
+you know about three decades yes leaving
+ 
+
+ align:start position:0%
+you know about three decades yes leaving
+those two roles or side or or otherwise
+
+ align:start position:0%
+those two roles or side or or otherwise
+ 
+
+ align:start position:0%
+those two roles or side or or otherwise
+sort of collecting from your experience
+
+ align:start position:0%
+sort of collecting from your experience
+ 
+
+ align:start position:0%
+sort of collecting from your experience
+in those shoes what Insight can you give
+
+ align:start position:0%
+in those shoes what Insight can you give
+ 
+
+ align:start position:0%
+in those shoes what Insight can you give
+us or what have you learned about you
+
+ align:start position:0%
+us or what have you learned about you
+ 
+
+ align:start position:0%
+us or what have you learned about you
+know what cities are and what their
+
+ align:start position:0%
+know what cities are and what their
+ 
+
+ align:start position:0%
+know what cities are and what their
+Cycles are and where their resilience or
+
+ align:start position:0%
+Cycles are and where their resilience or
+ 
+
+ align:start position:0%
+Cycles are and where their resilience or
+lack thereof and and their hopes could
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+that's that's difficult one I mean you
+
+ align:start position:0%
+that's that's difficult one I mean you
+ 
+
+ align:start position:0%
+that's that's difficult one I mean you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+it's people think that the best thing to
+
+ align:start position:0%
+it's people think that the best thing to
+ 
+
+ align:start position:0%
+it's people think that the best thing to
+do I mean this I've heard from I'm sure
+
+ align:start position:0%
+do I mean this I've heard from I'm sure
+ 
+
+ align:start position:0%
+do I mean this I've heard from I'm sure
+you also have heard it you know that the
+
+ align:start position:0%
+you also have heard it you know that the
+ 
+
+ align:start position:0%
+you also have heard it you know that the
+best thing that people in Camden or in
+
+ align:start position:0%
+best thing that people in Camden or in
+ 
+
+ align:start position:0%
+best thing that people in Camden or in
+Gary could do is just pack up and go
+
+ align:start position:0%
+Gary could do is just pack up and go
+ 
+
+ align:start position:0%
+Gary could do is just pack up and go
+somewhere else you know it's now they're
+
+ align:start position:0%
+somewhere else you know it's now they're
+ 
+
+ align:start position:0%
+somewhere else you know it's now they're
+saying it about New
+
+ align:start position:0%
+saying it about New
+ 
+
+ align:start position:0%
+saying it about New
+Orleans of course they are
+
+ align:start position:0%
+Orleans of course they are
+ 
+
+ align:start position:0%
+Orleans of course they are
+out uh and uh
+
+ align:start position:0%
+out uh and uh
+ 
+
+ align:start position:0%
+out uh and uh
+you know is there a point where cities
+
+ align:start position:0%
+you know is there a point where cities
+ 
+
+ align:start position:0%
+you know is there a point where cities
+actually become a liability for the
+
+ align:start position:0%
+actually become a liability for the
+ 
+
+ align:start position:0%
+actually become a liability for the
+people who live there I mean it's a it's
+
+ align:start position:0%
+people who live there I mean it's a it's
+ 
+
+ align:start position:0%
+people who live there I mean it's a it's
+a heavy question you know we always
+
+ align:start position:0%
+a heavy question you know we always
+ 
+
+ align:start position:0%
+a heavy question you know we always
+thought that cities were such a positive
+
+ align:start position:0%
+thought that cities were such a positive
+ 
+
+ align:start position:0%
+thought that cities were such a positive
+thing you know that that that cities the
+
+ align:start position:0%
+thing you know that that that cities the
+ 
+
+ align:start position:0%
+thing you know that that that cities the
+crowning Glory of of of civilization
+
+ align:start position:0%
+crowning Glory of of of civilization
+ 
+
+ align:start position:0%
+crowning Glory of of of civilization
+it's it's the place where the mind can
+
+ align:start position:0%
+it's it's the place where the mind can
+ 
+
+ align:start position:0%
+it's it's the place where the mind can
+function you know most with most
+
+ align:start position:0%
+function you know most with most
+ 
+
+ align:start position:0%
+function you know most with most
+intensity with you know human beings
+
+ align:start position:0%
+intensity with you know human beings
+ 
+
+ align:start position:0%
+intensity with you know human beings
+become engaged and then see them
+
+ align:start position:0%
+become engaged and then see them
+ 
+
+ align:start position:0%
+become engaged and then see them
+you really as as dead places you know
+
+ align:start position:0%
+you really as as dead places you know
+ 
+
+ align:start position:0%
+you really as as dead places you know
+places
+
+ align:start position:0%
+places
+ 
+
+ align:start position:0%
+places
+where it should you should uh
+
+ align:start position:0%
+where it should you should uh
+ 
+
+ align:start position:0%
+where it should you should uh
+encourage but then you know the other
+
+ align:start position:0%
+encourage but then you know the other
+ 
+
+ align:start position:0%
+encourage but then you know the other
+problem really is it's it's it's uh is
+
+ align:start position:0%
+problem really is it's it's it's uh is
+ 
+
+ align:start position:0%
+problem really is it's it's it's uh is
+that we have no place for the people who
+
+ align:start position:0%
+that we have no place for the people who
+ 
+
+ align:start position:0%
+that we have no place for the people who
+live there even if they wanted to get
+
+ align:start position:0%
+live there even if they wanted to get
+ 
+
+ align:start position:0%
+live there even if they wanted to get
+out of there where would they go you
+
+ align:start position:0%
+out of there where would they go you
+ 
+
+ align:start position:0%
+out of there where would they go you
+know can you imagine the all the set of
+
+ align:start position:0%
+know can you imagine the all the set of
+ 
+
+ align:start position:0%
+know can you imagine the all the set of
+problems if they went to the more
+
+ align:start position:0%
+problems if they went to the more
+ 
+
+ align:start position:0%
+problems if they went to the more
+affluent South Jersey suburbs you know
+
+ align:start position:0%
+affluent South Jersey suburbs you know
+ 
+
+ align:start position:0%
+affluent South Jersey suburbs you know
+people who live in Camden and said look
+
+ align:start position:0%
+people who live in Camden and said look
+ 
+
+ align:start position:0%
+people who live in Camden and said look
+we're here we're willing to move out of
+
+ align:start position:0%
+we're here we're willing to move out of
+ 
+
+ align:start position:0%
+we're here we're willing to move out of
+Camden what uh what would happen uh I
+
+ align:start position:0%
+Camden what uh what would happen uh I
+ 
+
+ align:start position:0%
+Camden what uh what would happen uh I
+don't know if if this at all answers
+
+ align:start position:0%
+don't know if if this at all answers
+ 
+
+ align:start position:0%
+don't know if if this at all answers
+your question but but it's a it's an
+
+ align:start position:0%
+your question but but it's a it's an
+ 
+
+ align:start position:0%
+your question but but it's a it's an
+important it's an important question and
+
+ align:start position:0%
+important it's an important question and
+ 
+
+ align:start position:0%
+important it's an important question and
+it's important to think and I
+
+ align:start position:0%
+it's important to think and I
+ 
+
+ align:start position:0%
+it's important to think and I
+think to me I mean I think as long as
+
+ align:start position:0%
+think to me I mean I think as long as
+ 
+
+ align:start position:0%
+think to me I mean I think as long as
+you can keep your
+
+ align:start position:0%
+you can keep your
+ 
+
+ align:start position:0%
+you can keep your
+mind interested and focus into different
+
+ align:start position:0%
+mind interested and focus into different
+ 
+
+ align:start position:0%
+mind interested and focus into different
+aspects of this city as long as you can
+
+ align:start position:0%
+aspects of this city as long as you can
+ 
+
+ align:start position:0%
+aspects of this city as long as you can
+keep that this that the process that the
+
+ align:start position:0%
+keep that this that the process that the
+ 
+
+ align:start position:0%
+keep that this that the process that the
+changes engage you as as you know either
+
+ align:start position:0%
+changes engage you as as you know either
+ 
+
+ align:start position:0%
+changes engage you as as you know either
+by going to the website or by being able
+
+ align:start position:0%
+by going to the website or by being able
+ 
+
+ align:start position:0%
+by going to the website or by being able
+to read it in the city itself you know
+
+ align:start position:0%
+to read it in the city itself you know
+ 
+
+ align:start position:0%
+to read it in the city itself you know
+there is there is there is a possibility
+
+ align:start position:0%
+there is there is there is a possibility
+ 
+
+ align:start position:0%
+there is there is there is a possibility
+I think the the the really
+
+ align:start position:0%
+I think the the the really
+ 
+
+ align:start position:0%
+I think the the the really
+dark you know
+
+ align:start position:0%
+dark you know
+ 
+
+ align:start position:0%
+dark you know
+hopeless you know moment is when you say
+
+ align:start position:0%
+hopeless you know moment is when you say
+ 
+
+ align:start position:0%
+hopeless you know moment is when you say
+well there's there's nothing here
+
+ align:start position:0%
+well there's there's nothing here
+ 
+
+ align:start position:0%
+well there's there's nothing here
+there's nothing you know not even not
+
+ align:start position:0%
+there's nothing you know not even not
+ 
+
+ align:start position:0%
+there's nothing you know not even not
+even the stuff that may interest you
+
+ align:start position:0%
+even the stuff that may interest you
+ 
+
+ align:start position:0%
+even the stuff that may interest you
+because uh it's quirky or you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know I don't
+
+ align:start position:0%
+know I don't
+ 
+
+ align:start position:0%
+know I don't
+know any go ahead um I have a question
+
+ align:start position:0%
+know any go ahead um I have a question
+ 
+
+ align:start position:0%
+know any go ahead um I have a question
+about how you take pictures of places
+
+ align:start position:0%
+about how you take pictures of places
+ 
+
+ align:start position:0%
+about how you take pictures of places
+you take pictures of and one of the
+
+ align:start position:0%
+you take pictures of and one of the
+ 
+
+ align:start position:0%
+you take pictures of and one of the
+things that I noticed tonight was that
+
+ align:start position:0%
+things that I noticed tonight was that
+ 
+
+ align:start position:0%
+things that I noticed tonight was that
+um and in one of your one of your
+
+ align:start position:0%
+um and in one of your one of your
+ 
+
+ align:start position:0%
+um and in one of your one of your
+responses to the questions you mentioned
+
+ align:start position:0%
+responses to the questions you mentioned
+ 
+
+ align:start position:0%
+responses to the questions you mentioned
+it um
+
+ align:start position:0%
+it um
+ 
+
+ align:start position:0%
+it um
+and I I won't rephrase it exactly right
+
+ align:start position:0%
+and I I won't rephrase it exactly right
+ 
+
+ align:start position:0%
+and I I won't rephrase it exactly right
+but basically saying that you're are not
+
+ align:start position:0%
+but basically saying that you're are not
+ 
+
+ align:start position:0%
+but basically saying that you're are not
+interested in events per se but in
+
+ align:start position:0%
+interested in events per se but in
+ 
+
+ align:start position:0%
+interested in events per se but in
+longer term changes over time so I
+
+ align:start position:0%
+longer term changes over time so I
+ 
+
+ align:start position:0%
+longer term changes over time so I
+wonder and some but some of the stories
+
+ align:start position:0%
+wonder and some but some of the stories
+ 
+
+ align:start position:0%
+wonder and some but some of the stories
+that you told talk about things that
+
+ align:start position:0%
+that you told talk about things that
+ 
+
+ align:start position:0%
+that you told talk about things that
+happen in those places so I wonder when
+
+ align:start position:0%
+happen in those places so I wonder when
+ 
+
+ align:start position:0%
+happen in those places so I wonder when
+you when you're when you're in
+
+ align:start position:0%
+you when you're when you're in
+ 
+
+ align:start position:0%
+you when you're when you're in
+Camden um whether you take photos of
+
+ align:start position:0%
+Camden um whether you take photos of
+ 
+
+ align:start position:0%
+Camden um whether you take photos of
+political rallies or church services or
+
+ align:start position:0%
+political rallies or church services or
+ 
+
+ align:start position:0%
+political rallies or church services or
+parades or um the police resting someone
+
+ align:start position:0%
+parades or um the police resting someone
+ 
+
+ align:start position:0%
+parades or um the police resting someone
+or you know the kinds of images that we
+
+ align:start position:0%
+or you know the kinds of images that we
+ 
+
+ align:start position:0%
+or you know the kinds of images that we
+think of as like the photojournalist
+
+ align:start position:0%
+think of as like the photojournalist
+ 
+
+ align:start position:0%
+think of as like the photojournalist
+image that goes up on the the front page
+
+ align:start position:0%
+image that goes up on the the front page
+ 
+
+ align:start position:0%
+image that goes up on the the front page
+of the newspaper or shows up on the
+
+ align:start position:0%
+of the newspaper or shows up on the
+ 
+
+ align:start position:0%
+of the newspaper or shows up on the
+evening news or or the documents a story
+
+ align:start position:0%
+evening news or or the documents a story
+ 
+
+ align:start position:0%
+evening news or or the documents a story
+of a of a community of people you know a
+
+ align:start position:0%
+of a of a community of people you know a
+ 
+
+ align:start position:0%
+of a of a community of people you know a
+ethnic Pride Parade or the MLK Day
+
+ align:start position:0%
+ethnic Pride Parade or the MLK Day
+ 
+
+ align:start position:0%
+ethnic Pride Parade or the MLK Day
+Parade or things like that so my
+
+ align:start position:0%
+Parade or things like that so my
+ 
+
+ align:start position:0%
+Parade or things like that so my
+question is are those um events that you
+
+ align:start position:0%
+question is are those um events that you
+ 
+
+ align:start position:0%
+question is are those um events that you
+attend but you but you're interested in
+
+ align:start position:0%
+attend but you but you're interested in
+ 
+
+ align:start position:0%
+attend but you but you're interested in
+in showing other kinds of um views of
+
+ align:start position:0%
+in showing other kinds of um views of
+ 
+
+ align:start position:0%
+in showing other kinds of um views of
+the the built environment of the city um
+
+ align:start position:0%
+the the built environment of the city um
+ 
+
+ align:start position:0%
+the the built environment of the city um
+or are those images that you take but
+
+ align:start position:0%
+or are those images that you take but
+ 
+
+ align:start position:0%
+or are those images that you take but
+then when you edit and you decide the
+
+ align:start position:0%
+then when you edit and you decide the
+ 
+
+ align:start position:0%
+then when you edit and you decide the
+story that you want to tell those are
+
+ align:start position:0%
+story that you want to tell those are
+ 
+
+ align:start position:0%
+story that you want to tell those are
+ones that you tend to leave aside and
+
+ align:start position:0%
+ones that you tend to leave aside and
+ 
+
+ align:start position:0%
+ones that you tend to leave aside and
+instead focus on the slower PA of change
+
+ align:start position:0%
+instead focus on the slower PA of change
+ 
+
+ align:start position:0%
+instead focus on the slower PA of change
+in the build en well a a policy that I
+
+ align:start position:0%
+in the build en well a a policy that I
+ 
+
+ align:start position:0%
+in the build en well a a policy that I
+consciously took from the beginning of
+
+ align:start position:0%
+consciously took from the beginning of
+ 
+
+ align:start position:0%
+consciously took from the beginning of
+my documentation was to sort of Le to
+
+ align:start position:0%
+my documentation was to sort of Le to
+ 
+
+ align:start position:0%
+my documentation was to sort of Le to
+others what others were already doing so
+
+ align:start position:0%
+others what others were already doing so
+ 
+
+ align:start position:0%
+others what others were already doing so
+since I lived in New York the there was
+
+ align:start position:0%
+since I lived in New York the there was
+ 
+
+ align:start position:0%
+since I lived in New York the there was
+plenty of poverty in the lower side but
+
+ align:start position:0%
+plenty of poverty in the lower side but
+ 
+
+ align:start position:0%
+plenty of poverty in the lower side but
+there were plenty of photographers that
+
+ align:start position:0%
+there were plenty of photographers that
+ 
+
+ align:start position:0%
+there were plenty of photographers that
+were photographing the Lower Side why do
+
+ align:start position:0%
+were photographing the Lower Side why do
+ 
+
+ align:start position:0%
+were photographing the Lower Side why do
+you want another one you know so there
+
+ align:start position:0%
+you want another one you know so there
+ 
+
+ align:start position:0%
+you want another one you know so there
+are plenty of photographers that do
+
+ align:start position:0%
+are plenty of photographers that do
+ 
+
+ align:start position:0%
+are plenty of photographers that do
+those rallies that do those festivities
+
+ align:start position:0%
+those rallies that do those festivities
+ 
+
+ align:start position:0%
+those rallies that do those festivities
+and so on they don't do the you know
+
+ align:start position:0%
+and so on they don't do the you know
+ 
+
+ align:start position:0%
+and so on they don't do the you know
+that sort of drug or they may do it too
+
+ align:start position:0%
+that sort of drug or they may do it too
+ 
+
+ align:start position:0%
+that sort of drug or they may do it too
+you know they they they you know when
+
+ align:start position:0%
+you know they they they you know when
+ 
+
+ align:start position:0%
+you know they they they you know when
+they C off a block like the picture that
+
+ align:start position:0%
+they C off a block like the picture that
+ 
+
+ align:start position:0%
+they C off a block like the picture that
+I show you or the picture of a drug
+
+ align:start position:0%
+I show you or the picture of a drug
+ 
+
+ align:start position:0%
+I show you or the picture of a drug
+addict on the on the floor which you
+
+ align:start position:0%
+addict on the on the floor which you
+ 
+
+ align:start position:0%
+addict on the on the floor which you
+know I you could tell me that that's
+
+ align:start position:0%
+know I you could tell me that that's
+ 
+
+ align:start position:0%
+know I you could tell me that that's
+that was an extreme abuse of privacy
+
+ align:start position:0%
+that was an extreme abuse of privacy
+ 
+
+ align:start position:0%
+that was an extreme abuse of privacy
+which it was but uh but but uh I don't
+
+ align:start position:0%
+which it was but uh but but uh I don't
+ 
+
+ align:start position:0%
+which it was but uh but but uh I don't
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+um how can I say it it's
+
+ align:start position:0%
+um how can I say it it's
+ 
+
+ align:start position:0%
+um how can I say it it's
+uh there is a division of labor I mean
+
+ align:start position:0%
+uh there is a division of labor I mean
+ 
+
+ align:start position:0%
+uh there is a division of labor I mean
+those those newspapers do take those
+
+ align:start position:0%
+those those newspapers do take those
+ 
+
+ align:start position:0%
+those those newspapers do take those
+photographs constantly and they usually
+
+ align:start position:0%
+photographs constantly and they usually
+ 
+
+ align:start position:0%
+photographs constantly and they usually
+give them to the university so Roger
+
+ align:start position:0%
+give them to the university so Roger
+ 
+
+ align:start position:0%
+give them to the university so Roger
+scam at one time will get all the files
+
+ align:start position:0%
+scam at one time will get all the files
+ 
+
+ align:start position:0%
+scam at one time will get all the files
+from the career post and they will have
+
+ align:start position:0%
+from the career post and they will have
+ 
+
+ align:start position:0%
+from the career post and they will have
+the 880,000 pictures or 100,000 pictures
+
+ align:start position:0%
+the 880,000 pictures or 100,000 pictures
+ 
+
+ align:start position:0%
+the 880,000 pictures or 100,000 pictures
+and they will get a big write off for
+
+ align:start position:0%
+and they will get a big write off for
+ 
+
+ align:start position:0%
+and they will get a big write off for
+taxes and and they will have a huge
+
+ align:start position:0%
+taxes and and they will have a huge
+ 
+
+ align:start position:0%
+taxes and and they will have a huge
+number of photographs of precisely those
+
+ align:start position:0%
+number of photographs of precisely those
+ 
+
+ align:start position:0%
+number of photographs of precisely those
+things I don't know how
+
+ align:start position:0%
+things I don't know how
+ 
+
+ align:start position:0%
+things I don't know how
+well uh how can I say identify they will
+
+ align:start position:0%
+well uh how can I say identify they will
+ 
+
+ align:start position:0%
+well uh how can I say identify they will
+be I mean mine are you know I made sure
+
+ align:start position:0%
+be I mean mine are you know I made sure
+ 
+
+ align:start position:0%
+be I mean mine are you know I made sure
+that they are very well identified by
+
+ align:start position:0%
+that they are very well identified by
+ 
+
+ align:start position:0%
+that they are very well identified by
+place and
+
+ align:start position:0%
+place and
+ 
+
+ align:start position:0%
+place and
+time and if there is anything else else
+
+ align:start position:0%
+time and if there is anything else else
+ 
+
+ align:start position:0%
+time and if there is anything else else
+too to add there I I I put it there and
+
+ align:start position:0%
+too to add there I I I put it there and
+ 
+
+ align:start position:0%
+too to add there I I I put it there and
+if there's anyone to ask any question
+
+ align:start position:0%
+if there's anyone to ask any question
+ 
+
+ align:start position:0%
+if there's anyone to ask any question
+about what's happening I asked there but
+
+ align:start position:0%
+about what's happening I asked there but
+ 
+
+ align:start position:0%
+about what's happening I asked there but
+that's that's the reason why you don't
+
+ align:start position:0%
+that's that's the reason why you don't
+ 
+
+ align:start position:0%
+that's that's the reason why you don't
+have those uh those photographs there I
+
+ align:start position:0%
+have those uh those photographs there I
+ 
+
+ align:start position:0%
+have those uh those photographs there I
+figure if that's going on I mean I I you
+
+ align:start position:0%
+figure if that's going on I mean I I you
+ 
+
+ align:start position:0%
+figure if that's going on I mean I I you
+see it's there's a basic Idea Idea here
+
+ align:start position:0%
+see it's there's a basic Idea Idea here
+ 
+
+ align:start position:0%
+see it's there's a basic Idea Idea here
+the first time I spoke as a documentary
+
+ align:start position:0%
+the first time I spoke as a documentary
+ 
+
+ align:start position:0%
+the first time I spoke as a documentary
+photo
+
+ align:start position:0%
+photo
+ 
+
+ align:start position:0%
+photo
+photographer ever was at the City Museum
+
+ align:start position:0%
+photographer ever was at the City Museum
+ 
+
+ align:start position:0%
+photographer ever was at the City Museum
+of the city of New York
+
+ align:start position:0%
+of the city of New York
+ 
+
+ align:start position:0%
+of the city of New York
+and I show similar pictures of this
+
+ align:start position:0%
+and I show similar pictures of this
+ 
+
+ align:start position:0%
+and I show similar pictures of this
+mostly from the Bronx and somebody stood
+
+ align:start position:0%
+mostly from the Bronx and somebody stood
+ 
+
+ align:start position:0%
+mostly from the Bronx and somebody stood
+and said you call yourself a documentary
+
+ align:start position:0%
+and said you call yourself a documentary
+ 
+
+ align:start position:0%
+and said you call yourself a documentary
+photography you show us a bunch of
+
+ align:start position:0%
+photography you show us a bunch of
+ 
+
+ align:start position:0%
+photography you show us a bunch of
+pictures of buildings he says what what
+
+ align:start position:0%
+pictures of buildings he says what what
+ 
+
+ align:start position:0%
+pictures of buildings he says what what
+is this and uh uh well now the answer is
+
+ align:start position:0%
+is this and uh uh well now the answer is
+ 
+
+ align:start position:0%
+is this and uh uh well now the answer is
+uh the buildings speak for people you
+
+ align:start position:0%
+uh the buildings speak for people you
+ 
+
+ align:start position:0%
+uh the buildings speak for people you
+know you can see the hand of not just of
+
+ align:start position:0%
+know you can see the hand of not just of
+ 
+
+ align:start position:0%
+know you can see the hand of not just of
+time and but also the hand of people in
+
+ align:start position:0%
+time and but also the hand of people in
+ 
+
+ align:start position:0%
+time and but also the hand of people in
+the way the environment changes we just
+
+ align:start position:0%
+the way the environment changes we just
+ 
+
+ align:start position:0%
+the way the environment changes we just
+have to learn to read
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it go ahead I wanted to ask are there
+
+ align:start position:0%
+it go ahead I wanted to ask are there
+ 
+
+ align:start position:0%
+it go ahead I wanted to ask are there
+any other Northeastern cities that you
+
+ align:start position:0%
+any other Northeastern cities that you
+ 
+
+ align:start position:0%
+any other Northeastern cities that you
+might parallel can with and if so you
+
+ align:start position:0%
+might parallel can with and if so you
+ 
+
+ align:start position:0%
+might parallel can with and if so you
+know what cities are they and have you
+
+ align:start position:0%
+know what cities are they and have you
+ 
+
+ align:start position:0%
+know what cities are they and have you
+seen how many parallels have you seen
+
+ align:start position:0%
+seen how many parallels have you seen
+ 
+
+ align:start position:0%
+seen how many parallels have you seen
+because to me handon almost seems more
+
+ align:start position:0%
+because to me handon almost seems more
+ 
+
+ align:start position:0%
+because to me handon almost seems more
+like one of the midwestern cities like
+
+ align:start position:0%
+like one of the midwestern cities like
+ 
+
+ align:start position:0%
+like one of the midwestern cities like
+it's it's become isolated
+
+ align:start position:0%
+it's it's become isolated
+ 
+
+ align:start position:0%
+it's it's become isolated
+and it's you know if you look at
+
+ align:start position:0%
+and it's you know if you look at
+ 
+
+ align:start position:0%
+and it's you know if you look at
+Philadelphia and B more like in the
+
+ align:start position:0%
+Philadelphia and B more like in the
+ 
+
+ align:start position:0%
+Philadelphia and B more like in the
+early ' 80s when there just massive
+
+ align:start position:0%
+early ' 80s when there just massive
+ 
+
+ align:start position:0%
+early ' 80s when there just massive
+problems and such a huge part of the
+
+ align:start position:0%
+problems and such a huge part of the
+ 
+
+ align:start position:0%
+problems and such a huge part of the
+city was you know ghetto basically you
+
+ align:start position:0%
+city was you know ghetto basically you
+ 
+
+ align:start position:0%
+city was you know ghetto basically you
+know Camden's never Philadelphia and
+
+ align:start position:0%
+know Camden's never Philadelphia and
+ 
+
+ align:start position:0%
+know Camden's never Philadelphia and
+Baltimore have started to come back and
+
+ align:start position:0%
+Baltimore have started to come back and
+ 
+
+ align:start position:0%
+Baltimore have started to come back and
+Philadelphia has really come back but
+
+ align:start position:0%
+Philadelphia has really come back but
+ 
+
+ align:start position:0%
+Philadelphia has really come back but
+Camden is like this isolated place that
+
+ align:start position:0%
+Camden is like this isolated place that
+ 
+
+ align:start position:0%
+Camden is like this isolated place that
+it reminds me a lot more of
+
+ align:start position:0%
+it reminds me a lot more of
+ 
+
+ align:start position:0%
+it reminds me a lot more of
+Midwestern CI Lou trouble suffering and
+
+ align:start position:0%
+Midwestern CI Lou trouble suffering and
+ 
+
+ align:start position:0%
+Midwestern CI Lou trouble suffering and
+revitalizing well you know I I think
+
+ align:start position:0%
+revitalizing well you know I I think
+ 
+
+ align:start position:0%
+revitalizing well you know I I think
+there are parts of Philadelphia where I
+
+ align:start position:0%
+there are parts of Philadelphia where I
+ 
+
+ align:start position:0%
+there are parts of Philadelphia where I
+feel like I'm just en Camp than it was
+
+ align:start position:0%
+feel like I'm just en Camp than it was
+ 
+
+ align:start position:0%
+feel like I'm just en Camp than it was
+in North Philadelphia and parts of West
+
+ align:start position:0%
+in North Philadelphia and parts of West
+ 
+
+ align:start position:0%
+in North Philadelphia and parts of West
+Philadelphia like that uh I should have
+
+ align:start position:0%
+Philadelphia like that uh I should have
+ 
+
+ align:start position:0%
+Philadelphia like that uh I should have
+could have shown you some pictures of
+
+ align:start position:0%
+could have shown you some pictures of
+ 
+
+ align:start position:0%
+could have shown you some pictures of
+Philadelphia
+
+ align:start position:0%
+Philadelphia
+ 
+
+ align:start position:0%
+Philadelphia
+scenes
+
+ align:start position:0%
+scenes
+ 
+
+ align:start position:0%
+scenes
+um yeah Camden is Extreme and I think
+
+ align:start position:0%
+um yeah Camden is Extreme and I think
+ 
+
+ align:start position:0%
+um yeah Camden is Extreme and I think
+it's important because it's extreme and
+
+ align:start position:0%
+it's important because it's extreme and
+ 
+
+ align:start position:0%
+it's important because it's extreme and
+I think it should be shown you know with
+
+ align:start position:0%
+I think it should be shown you know with
+ 
+
+ align:start position:0%
+I think it should be shown you know with
+as much
+
+ align:start position:0%
+as much
+ 
+
+ align:start position:0%
+as much
+um how can I
+
+ align:start position:0%
+um how can I
+ 
+
+ align:start position:0%
+um how can I
+say you know
+
+ align:start position:0%
+say you know
+ 
+
+ align:start position:0%
+say you know
+they always told me not to use
+
+ align:start position:0%
+they always told me not to use
+ 
+
+ align:start position:0%
+they always told me not to use
+biological analogies or medical
+
+ align:start position:0%
+biological analogies or medical
+ 
+
+ align:start position:0%
+biological analogies or medical
+analogies but if you wanted to show the
+
+ align:start position:0%
+analogies but if you wanted to show the
+ 
+
+ align:start position:0%
+analogies but if you wanted to show the
+case of of of of something that's
+
+ align:start position:0%
+case of of of of something that's
+ 
+
+ align:start position:0%
+case of of of of something that's
+present in the body you know you want to
+
+ align:start position:0%
+present in the body you know you want to
+ 
+
+ align:start position:0%
+present in the body you know you want to
+show it in its maximum expression you
+
+ align:start position:0%
+show it in its maximum expression you
+ 
+
+ align:start position:0%
+show it in its maximum expression you
+know where it's strongest because there
+
+ align:start position:0%
+know where it's strongest because there
+ 
+
+ align:start position:0%
+know where it's strongest because there
+is what is where it's easier to
+
+ align:start position:0%
+is what is where it's easier to
+ 
+
+ align:start position:0%
+is what is where it's easier to
+understand uh if you can do that I mean
+
+ align:start position:0%
+understand uh if you can do that I mean
+ 
+
+ align:start position:0%
+understand uh if you can do that I mean
+and and and the United States doesn't
+
+ align:start position:0%
+and and and the United States doesn't
+ 
+
+ align:start position:0%
+and and and the United States doesn't
+have a lack of places like like like
+
+ align:start position:0%
+have a lack of places like like like
+ 
+
+ align:start position:0%
+have a lack of places like like like
+like I Benton harbors and other the big
+
+ align:start position:0%
+like I Benton harbors and other the big
+ 
+
+ align:start position:0%
+like I Benton harbors and other the big
+places big parts of Chicago and now
+
+ align:start position:0%
+places big parts of Chicago and now
+ 
+
+ align:start position:0%
+places big parts of Chicago and now
+there's a the number of suburbs in the
+
+ align:start position:0%
+there's a the number of suburbs in the
+ 
+
+ align:start position:0%
+there's a the number of suburbs in the
+south side of Chicago that they very
+
+ align:start position:0%
+south side of Chicago that they very
+ 
+
+ align:start position:0%
+south side of Chicago that they very
+much like this robins and and Harvey and
+
+ align:start position:0%
+much like this robins and and Harvey and
+ 
+
+ align:start position:0%
+much like this robins and and Harvey and
+so on and so forth I mean the list is is
+
+ align:start position:0%
+so on and so forth I mean the list is is
+ 
+
+ align:start position:0%
+so on and so forth I mean the list is is
+long so it's not it's not like I'm
+
+ align:start position:0%
+long so it's not it's not like I'm
+ 
+
+ align:start position:0%
+long so it's not it's not like I'm
+singling the
+
+ align:start position:0%
+singling the
+ 
+
+ align:start position:0%
+singling the
+one the one terrible place and certainly
+
+ align:start position:0%
+one the one terrible place and certainly
+ 
+
+ align:start position:0%
+one the one terrible place and certainly
+Detroit is it's another story so uh
+
+ align:start position:0%
+Detroit is it's another story so uh
+ 
+
+ align:start position:0%
+Detroit is it's another story so uh
+I don't know uh I don't know to what I
+
+ align:start position:0%
+I don't know uh I don't know to what I
+ 
+
+ align:start position:0%
+I don't know uh I don't know to what I
+don't think Camden is the exception
+
+ align:start position:0%
+don't think Camden is the exception
+ 
+
+ align:start position:0%
+don't think Camden is the exception
+Camden is it's it's it's a but I also
+
+ align:start position:0%
+Camden is it's it's it's a but I also
+ 
+
+ align:start position:0%
+Camden is it's it's it's a but I also
+think that through
+
+ align:start position:0%
+think that through
+ 
+
+ align:start position:0%
+think that through
+Camden you know the whole theme the
+
+ align:start position:0%
+Camden you know the whole theme the
+ 
+
+ align:start position:0%
+Camden you know the whole theme the
+whole this this story may become you
+
+ align:start position:0%
+whole this this story may become you
+ 
+
+ align:start position:0%
+whole this this story may become you
+know more poignant more you know may get
+
+ align:start position:0%
+know more poignant more you know may get
+ 
+
+ align:start position:0%
+know more poignant more you know may get
+May draw people
+
+ align:start position:0%
+May draw people
+ 
+
+ align:start position:0%
+May draw people
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+because it's extreme
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+ahead um your work essentially has to do
+
+ align:start position:0%
+ahead um your work essentially has to do
+ 
+
+ align:start position:0%
+ahead um your work essentially has to do
+with deep time and in that sense it's
+
+ align:start position:0%
+with deep time and in that sense it's
+ 
+
+ align:start position:0%
+with deep time and in that sense it's
+it's sort of different from the Instinct
+
+ align:start position:0%
+it's sort of different from the Instinct
+ 
+
+ align:start position:0%
+it's sort of different from the Instinct
+of Photography to capture a moment a
+
+ align:start position:0%
+of Photography to capture a moment a
+ 
+
+ align:start position:0%
+of Photography to capture a moment a
+great shot or something like that so my
+
+ align:start position:0%
+great shot or something like that so my
+ 
+
+ align:start position:0%
+great shot or something like that so my
+question is about when you choose to
+
+ align:start position:0%
+question is about when you choose to
+ 
+
+ align:start position:0%
+question is about when you choose to
+photograph really over over the last 26
+
+ align:start position:0%
+photograph really over over the last 26
+ 
+
+ align:start position:0%
+photograph really over over the last 26
+years of whether there is some
+
+ align:start position:0%
+years of whether there is some
+ 
+
+ align:start position:0%
+years of whether there is some
+significance to taking a picture in 79
+
+ align:start position:0%
+significance to taking a picture in 79
+ 
+
+ align:start position:0%
+significance to taking a picture in 79
+and then in it 8 if I'm correct and 96
+
+ align:start position:0%
+and then in it 8 if I'm correct and 96
+ 
+
+ align:start position:0%
+and then in it 8 if I'm correct and 96
+and so on do these points in time have
+
+ align:start position:0%
+and so on do these points in time have
+ 
+
+ align:start position:0%
+and so on do these points in time have
+some significance and also when you go
+
+ align:start position:0%
+some significance and also when you go
+ 
+
+ align:start position:0%
+some significance and also when you go
+to a place that you talked about what
+
+ align:start position:0%
+to a place that you talked about what
+ 
+
+ align:start position:0%
+to a place that you talked about what
+you choose to photograph but then is
+
+ align:start position:0%
+you choose to photograph but then is
+ 
+
+ align:start position:0%
+you choose to photograph but then is
+there a time of the month the year or
+
+ align:start position:0%
+there a time of the month the year or
+ 
+
+ align:start position:0%
+there a time of the month the year or
+even the time of day that you choose to
+
+ align:start position:0%
+even the time of day that you choose to
+ 
+
+ align:start position:0%
+even the time of day that you choose to
+photograph at as opposed to do you try
+
+ align:start position:0%
+photograph at as opposed to do you try
+ 
+
+ align:start position:0%
+photograph at as opposed to do you try
+to avoid something if you try to avoid
+
+ align:start position:0%
+to avoid something if you try to avoid
+ 
+
+ align:start position:0%
+to avoid something if you try to avoid
+events which you already talked about
+
+ align:start position:0%
+events which you already talked about
+ 
+
+ align:start position:0%
+events which you already talked about
+you may
+
+ align:start position:0%
+you may
+ 
+
+ align:start position:0%
+you may
+not well what
+
+ align:start position:0%
+not well what
+ 
+
+ align:start position:0%
+not well what
+I try to avoid the Chamber of
+
+ align:start position:0%
+I try to avoid the Chamber of
+ 
+
+ align:start position:0%
+I try to avoid the Chamber of
+Commerce I I I think you attribute too
+
+ align:start position:0%
+Commerce I I I think you attribute too
+ 
+
+ align:start position:0%
+Commerce I I I think you attribute too
+much to uh you know to sort
+
+ align:start position:0%
+much to uh you know to sort
+ 
+
+ align:start position:0%
+much to uh you know to sort
+of will you know I mean I'm I don't have
+
+ align:start position:0%
+of will you know I mean I'm I don't have
+ 
+
+ align:start position:0%
+of will you know I mean I'm I don't have
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+choices I started Camden because I had a
+
+ align:start position:0%
+choices I started Camden because I had a
+ 
+
+ align:start position:0%
+choices I started Camden because I had a
+chance to get a job for the state of New
+
+ align:start position:0%
+chance to get a job for the state of New
+ 
+
+ align:start position:0%
+chance to get a job for the state of New
+Jersey and I was working for the energy
+
+ align:start position:0%
+Jersey and I was working for the energy
+ 
+
+ align:start position:0%
+Jersey and I was working for the energy
+department and I managed to convince
+
+ align:start position:0%
+department and I managed to convince
+ 
+
+ align:start position:0%
+department and I managed to convince
+them that uh that to create a position
+
+ align:start position:0%
+them that uh that to create a position
+ 
+
+ align:start position:0%
+them that uh that to create a position
+for me that would involve getting me to
+
+ align:start position:0%
+for me that would involve getting me to
+ 
+
+ align:start position:0%
+for me that would involve getting me to
+the most depressed cities in New Jersey
+
+ align:start position:0%
+the most depressed cities in New Jersey
+ 
+
+ align:start position:0%
+the most depressed cities in New Jersey
+because I sort of said look we don't
+
+ align:start position:0%
+because I sort of said look we don't
+ 
+
+ align:start position:0%
+because I sort of said look we don't
+have a presence in cemin we don't have a
+
+ align:start position:0%
+have a presence in cemin we don't have a
+ 
+
+ align:start position:0%
+have a presence in cemin we don't have a
+presence in Patterson we don't have a
+
+ align:start position:0%
+presence in Patterson we don't have a
+ 
+
+ align:start position:0%
+presence in Patterson we don't have a
+presence in
+
+ align:start position:0%
+presence in
+ 
+
+ align:start position:0%
+presence in
+Trenton and so I had a state car and I
+
+ align:start position:0%
+Trenton and so I had a state car and I
+ 
+
+ align:start position:0%
+Trenton and so I had a state car and I
+had the possibility to organize meetings
+
+ align:start position:0%
+had the possibility to organize meetings
+ 
+
+ align:start position:0%
+had the possibility to organize meetings
+and so on in Camden so I had a chance to
+
+ align:start position:0%
+and so on in Camden so I had a chance to
+ 
+
+ align:start position:0%
+and so on in Camden so I had a chance to
+photograph there so I could only
+
+ align:start position:0%
+photograph there so I could only
+ 
+
+ align:start position:0%
+photograph there so I could only
+photograph when I had meetings there you
+
+ align:start position:0%
+photograph when I had meetings there you
+ 
+
+ align:start position:0%
+photograph when I had meetings there you
+know I couldn't just say look the
+
+ align:start position:0%
+know I couldn't just say look the
+ 
+
+ align:start position:0%
+know I couldn't just say look the
+weather looks perfect now I'm going to
+
+ align:start position:0%
+weather looks perfect now I'm going to
+ 
+
+ align:start position:0%
+weather looks perfect now I'm going to
+you know go and and and take these
+
+ align:start position:0%
+you know go and and and take these
+ 
+
+ align:start position:0%
+you know go and and and take these
+pictures and the years uh often times
+
+ align:start position:0%
+pictures and the years uh often times
+ 
+
+ align:start position:0%
+pictures and the years uh often times
+there are many more pictures than what
+
+ align:start position:0%
+there are many more pictures than what
+ 
+
+ align:start position:0%
+there are many more pictures than what
+you saw there but I just selected those
+
+ align:start position:0%
+you saw there but I just selected those
+ 
+
+ align:start position:0%
+you saw there but I just selected those
+because those shows change in a in a in
+
+ align:start position:0%
+because those shows change in a in a in
+ 
+
+ align:start position:0%
+because those shows change in a in a in
+a in a more clear way it's the the the
+
+ align:start position:0%
+a in a more clear way it's the the the
+ 
+
+ align:start position:0%
+a in a more clear way it's the the the
+choice choice becomes a problem you know
+
+ align:start position:0%
+choice choice becomes a problem you know
+ 
+
+ align:start position:0%
+choice choice becomes a problem you know
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+obviously the people people try to they
+
+ align:start position:0%
+obviously the people people try to they
+ 
+
+ align:start position:0%
+obviously the people people try to they
+tell you all the time you know I mean
+
+ align:start position:0%
+tell you all the time you know I mean
+ 
+
+ align:start position:0%
+tell you all the time you know I mean
+you're doing you're you're following
+
+ align:start position:0%
+you're doing you're you're following
+ 
+
+ align:start position:0%
+you're doing you're you're following
+your instincts you're you're expressing
+
+ align:start position:0%
+your instincts you're you're expressing
+ 
+
+ align:start position:0%
+your instincts you're you're expressing
+yourself you know you're you're you're
+
+ align:start position:0%
+yourself you know you're you're you're
+ 
+
+ align:start position:0%
+yourself you know you're you're you're
+doing you you're recreating your own
+
+ align:start position:0%
+doing you you're recreating your own
+ 
+
+ align:start position:0%
+doing you you're recreating your own
+private personal history and then you
+
+ align:start position:0%
+private personal history and then you
+ 
+
+ align:start position:0%
+private personal history and then you
+built the system to defeat that so that
+
+ align:start position:0%
+built the system to defeat that so that
+ 
+
+ align:start position:0%
+built the system to defeat that so that
+people can't say that because you know I
+
+ align:start position:0%
+people can't say that because you know I
+ 
+
+ align:start position:0%
+people can't say that because you know I
+don't put the allall buildings there
+
+ align:start position:0%
+don't put the allall buildings there
+ 
+
+ align:start position:0%
+don't put the allall buildings there
+somebody else put them there and I do I
+
+ align:start position:0%
+somebody else put them there and I do I
+ 
+
+ align:start position:0%
+somebody else put them there and I do I
+picked the light in a way which is not
+
+ align:start position:0%
+picked the light in a way which is not
+ 
+
+ align:start position:0%
+picked the light in a way which is not
+interesting light in terms of you know
+
+ align:start position:0%
+interesting light in terms of you know
+ 
+
+ align:start position:0%
+interesting light in terms of you know
+lights and shadows or angles that really
+
+ align:start position:0%
+lights and shadows or angles that really
+ 
+
+ align:start position:0%
+lights and shadows or angles that really
+fancy you know but I take I take
+
+ align:start position:0%
+fancy you know but I take I take
+ 
+
+ align:start position:0%
+fancy you know but I take I take
+pictures straight
+
+ align:start position:0%
+pictures straight
+ 
+
+ align:start position:0%
+pictures straight
+on because those are the ones that are
+
+ align:start position:0%
+on because those are the ones that are
+ 
+
+ align:start position:0%
+on because those are the ones that are
+easy make it easy to read the building
+
+ align:start position:0%
+easy make it easy to read the building
+ 
+
+ align:start position:0%
+easy make it easy to read the building
+to sort of duplicate the building to
+
+ align:start position:0%
+to sort of duplicate the building to
+ 
+
+ align:start position:0%
+to sort of duplicate the building to
+give you
+
+ align:start position:0%
+give you
+ 
+
+ align:start position:0%
+give you
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+another view of it uh as far as uh you
+
+ align:start position:0%
+another view of it uh as far as uh you
+ 
+
+ align:start position:0%
+another view of it uh as far as uh you
+know the using of time time lapse
+
+ align:start position:0%
+know the using of time time lapse
+ 
+
+ align:start position:0%
+know the using of time time lapse
+photographs I mean ever since the
+
+ align:start position:0%
+photographs I mean ever since the
+ 
+
+ align:start position:0%
+photographs I mean ever since the
+beginning I had the feeling that the
+
+ align:start position:0%
+beginning I had the feeling that the
+ 
+
+ align:start position:0%
+beginning I had the feeling that the
+best way to proceed was not to think
+
+ align:start position:0%
+best way to proceed was not to think
+ 
+
+ align:start position:0%
+best way to proceed was not to think
+that one picture would tell the whole
+
+ align:start position:0%
+that one picture would tell the whole
+ 
+
+ align:start position:0%
+that one picture would tell the whole
+story because it was absurd I knew that
+
+ align:start position:0%
+story because it was absurd I knew that
+ 
+
+ align:start position:0%
+story because it was absurd I knew that
+this was insane to try to take you know
+
+ align:start position:0%
+this was insane to try to take you know
+ 
+
+ align:start position:0%
+this was insane to try to take you know
+one picture of this building or one
+
+ align:start position:0%
+one picture of this building or one
+ 
+
+ align:start position:0%
+one picture of this building or one
+picture I I thought from the beginning
+
+ align:start position:0%
+picture I I thought from the beginning
+ 
+
+ align:start position:0%
+picture I I thought from the beginning
+that this pictures were like building
+
+ align:start position:0%
+that this pictures were like building
+ 
+
+ align:start position:0%
+that this pictures were like building
+blocks and if you wanted to build
+
+ align:start position:0%
+blocks and if you wanted to build
+ 
+
+ align:start position:0%
+blocks and if you wanted to build
+something you needed to take a whole lot
+
+ align:start position:0%
+something you needed to take a whole lot
+ 
+
+ align:start position:0%
+something you needed to take a whole lot
+of them and a whole lot of times and
+
+ align:start position:0%
+of them and a whole lot of times and
+ 
+
+ align:start position:0%
+of them and a whole lot of times and
+then you get a sense of of what was
+
+ align:start position:0%
+then you get a sense of of what was
+ 
+
+ align:start position:0%
+then you get a sense of of what was
+happening and and and could engage
+
+ align:start position:0%
+happening and and and could engage
+ 
+
+ align:start position:0%
+happening and and and could engage
+others in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that I think this is a good place to end
+
+ align:start position:0%
+that I think this is a good place to end
+ 
+
+ align:start position:0%
+that I think this is a good place to end
+and to thank you and also to remind
+
+ align:start position:0%
+and to thank you and also to remind
+ 
+
+ align:start position:0%
+and to thank you and also to remind
+folks to visit Camille agar's website
+
+ align:start position:0%
+folks to visit Camille agar's website
+ 
+
+ align:start position:0%
+folks to visit Camille agar's website
+Invincible cities.com it's really an
+
+ align:start position:0%
+Invincible cities.com it's really an
+ 
+
+ align:start position:0%
+Invincible cities.com it's really an
+extraordinary site in the way that it
+
+ align:start position:0%
+extraordinary site in the way that it
+ 
+
+ align:start position:0%
+extraordinary site in the way that it
+puts photographs and pres together and
+
+ align:start position:0%
+puts photographs and pres together and
+ 
+
+ align:start position:0%
+puts photographs and pres together and
+present them not only in terms of time
+
+ align:start position:0%
+present them not only in terms of time
+ 
+
+ align:start position:0%
+present them not only in terms of time
+but in terms of a fairly sophisticated
+
+ align:start position:0%
+but in terms of a fairly sophisticated
+ 
+
+ align:start position:0%
+but in terms of a fairly sophisticated
+mapping uh intera interactive mapping
+
+ align:start position:0%
+mapping uh intera interactive mapping
+ 
+
+ align:start position:0%
+mapping uh intera interactive mapping
+technique so you can zoom around find
+
+ align:start position:0%
+technique so you can zoom around find
+ 
+
+ align:start position:0%
+technique so you can zoom around find
+your way around cden and then go in and
+
+ align:start position:0%
+your way around cden and then go in and
+ 
+
+ align:start position:0%
+your way around cden and then go in and
+see a particular place at several
+
+ align:start position:0%
+see a particular place at several
+ 
+
+ align:start position:0%
+see a particular place at several
+different points in time so with that
+
+ align:start position:0%
+different points in time so with that
+ 
+
+ align:start position:0%
+different points in time so with that
+I'd like to thank you very much for
+
+ align:start position:0%
+I'd like to thank you very much for
+ 
+
+ align:start position:0%
+I'd like to thank you very much for
+coming and sharing not only your images
+
+ align:start position:0%
+coming and sharing not only your images
+ 
+
+ align:start position:0%
+coming and sharing not only your images
+with us but your generosity in the last
+
+ align:start position:0%
+with us but your generosity in the last
+ 
+
+ align:start position:0%
+with us but your generosity in the last
+uh hour answering questions
+
+ align:start position:0%
+uh hour answering questions
+ 
+
+ align:start position:0%
+uh hour answering questions
+I'm very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happy thank you
\ No newline at end of file
diff --git a/JCQnsPggTp8.txt b/JCQnsPggTp8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..943299e66d35502181c7c4da3fdedab71e10b332
--- /dev/null
+++ b/JCQnsPggTp8.txt
@@ -0,0 +1,627 @@
+align:start position:0%
+ 
+independence is one of the central
+
+ align:start position:0%
+independence is one of the central
+ 
+
+ align:start position:0%
+independence is one of the central
+concepts of probability theory because
+
+ align:start position:0%
+concepts of probability theory because
+ 
+
+ align:start position:0%
+concepts of probability theory because
+it allows us to build large models from
+
+ align:start position:0%
+it allows us to build large models from
+ 
+
+ align:start position:0%
+it allows us to build large models from
+simpler ones how should we define
+
+ align:start position:0%
+simpler ones how should we define
+ 
+
+ align:start position:0%
+simpler ones how should we define
+independence in the continuous case our
+
+ align:start position:0%
+independence in the continuous case our
+ 
+
+ align:start position:0%
+independence in the continuous case our
+guide comes from the discrete definition
+
+ align:start position:0%
+guide comes from the discrete definition
+ 
+
+ align:start position:0%
+guide comes from the discrete definition
+by analogy with the discrete case we
+
+ align:start position:0%
+by analogy with the discrete case we
+ 
+
+ align:start position:0%
+by analogy with the discrete case we
+will say that two jointly continuous
+
+ align:start position:0%
+will say that two jointly continuous
+ 
+
+ align:start position:0%
+will say that two jointly continuous
+random variables are independent if the
+
+ align:start position:0%
+random variables are independent if the
+ 
+
+ align:start position:0%
+random variables are independent if the
+joint PDF is equal to the product of the
+
+ align:start position:0%
+joint PDF is equal to the product of the
+ 
+
+ align:start position:0%
+joint PDF is equal to the product of the
+marginal PDFs we can now compare with
+
+ align:start position:0%
+marginal PDFs we can now compare with
+ 
+
+ align:start position:0%
+marginal PDFs we can now compare with
+the multiplication rule which is always
+
+ align:start position:0%
+the multiplication rule which is always
+ 
+
+ align:start position:0%
+the multiplication rule which is always
+true as long as the density of Y is
+
+ align:start position:0%
+true as long as the density of Y is
+ 
+
+ align:start position:0%
+true as long as the density of Y is
+positive so this is always true in the
+
+ align:start position:0%
+positive so this is always true in the
+ 
+
+ align:start position:0%
+positive so this is always true in the
+case of independence this is true so in
+
+ align:start position:0%
+case of independence this is true so in
+ 
+
+ align:start position:0%
+case of independence this is true so in
+the case of independence we must have
+
+ align:start position:0%
+the case of independence we must have
+ 
+
+ align:start position:0%
+the case of independence we must have
+that this term is equal to that term at
+
+ align:start position:0%
+that this term is equal to that term at
+ 
+
+ align:start position:0%
+that this term is equal to that term at
+least whenever this quantity the
+
+ align:start position:0%
+least whenever this quantity the
+ 
+
+ align:start position:0%
+least whenever this quantity the
+marginal of Y is positive so to restate
+
+ align:start position:0%
+marginal of Y is positive so to restate
+ 
+
+ align:start position:0%
+marginal of Y is positive so to restate
+it independence is equivalent to having
+
+ align:start position:0%
+it independence is equivalent to having
+ 
+
+ align:start position:0%
+it independence is equivalent to having
+the conditional given Y be the same as
+
+ align:start position:0%
+the conditional given Y be the same as
+ 
+
+ align:start position:0%
+the conditional given Y be the same as
+the unconditional PDF of X and this has
+
+ align:start position:0%
+the unconditional PDF of X and this has
+ 
+
+ align:start position:0%
+the unconditional PDF of X and this has
+to be true whenever Y has a positive
+
+ align:start position:0%
+to be true whenever Y has a positive
+ 
+
+ align:start position:0%
+to be true whenever Y has a positive
+density so that this quantity is
+
+ align:start position:0%
+density so that this quantity is
+ 
+
+ align:start position:0%
+density so that this quantity is
+well-defined and it also has to be true
+
+ align:start position:0%
+well-defined and it also has to be true
+ 
+
+ align:start position:0%
+well-defined and it also has to be true
+for all X's now what does this really
+
+ align:start position:0%
+for all X's now what does this really
+ 
+
+ align:start position:0%
+for all X's now what does this really
+mean the conditional PDF as we have
+
+ align:start position:0%
+mean the conditional PDF as we have
+ 
+
+ align:start position:0%
+mean the conditional PDF as we have
+discussed in terms of pictures is a
+
+ align:start position:0%
+discussed in terms of pictures is a
+ 
+
+ align:start position:0%
+discussed in terms of pictures is a
+slice of the joint PDF therefore
+
+ align:start position:0%
+slice of the joint PDF therefore
+ 
+
+ align:start position:0%
+slice of the joint PDF therefore
+independence is the same as requiring
+
+ align:start position:0%
+independence is the same as requiring
+ 
+
+ align:start position:0%
+independence is the same as requiring
+that all of the slices of the joint have
+
+ align:start position:0%
+that all of the slices of the joint have
+ 
+
+ align:start position:0%
+that all of the slices of the joint have
+the same shape and it is the shape of
+
+ align:start position:0%
+the same shape and it is the shape of
+ 
+
+ align:start position:0%
+the same shape and it is the shape of
+the marginal PDF for a more intuitive
+
+ align:start position:0%
+the marginal PDF for a more intuitive
+ 
+
+ align:start position:0%
+the marginal PDF for a more intuitive
+interpretation no matter what value of y
+
+ align:start position:0%
+interpretation no matter what value of y
+ 
+
+ align:start position:0%
+interpretation no matter what value of y
+you observe the distribution of X does
+
+ align:start position:0%
+you observe the distribution of X does
+ 
+
+ align:start position:0%
+you observe the distribution of X does
+not change in this sense why does not
+
+ align:start position:0%
+not change in this sense why does not
+ 
+
+ align:start position:0%
+not change in this sense why does not
+convey any information about X notice
+
+ align:start position:0%
+convey any information about X notice
+ 
+
+ align:start position:0%
+convey any information about X notice
+also that this definition is symmetric
+
+ align:start position:0%
+also that this definition is symmetric
+ 
+
+ align:start position:0%
+also that this definition is symmetric
+as far as x and y are concerned so by
+
+ align:start position:0%
+as far as x and y are concerned so by
+ 
+
+ align:start position:0%
+as far as x and y are concerned so by
+symmetry when we have independence it
+
+ align:start position:0%
+symmetry when we have independence it
+ 
+
+ align:start position:0%
+symmetry when we have independence it
+also means that X does not convey any
+
+ align:start position:0%
+also means that X does not convey any
+ 
+
+ align:start position:0%
+also means that X does not convey any
+information about Y and that the
+
+ align:start position:0%
+information about Y and that the
+ 
+
+ align:start position:0%
+information about Y and that the
+conditional density of Y given X has to
+
+ align:start position:0%
+conditional density of Y given X has to
+ 
+
+ align:start position:0%
+conditional density of Y given X has to
+be the same as
+
+ align:start position:0%
+be the same as
+ 
+
+ align:start position:0%
+be the same as
+the unconditional density of Y we can
+
+ align:start position:0%
+the unconditional density of Y we can
+ 
+
+ align:start position:0%
+the unconditional density of Y we can
+also define independence of multiple
+
+ align:start position:0%
+also define independence of multiple
+ 
+
+ align:start position:0%
+also define independence of multiple
+random variables the definition is the
+
+ align:start position:0%
+random variables the definition is the
+ 
+
+ align:start position:0%
+random variables the definition is the
+obvious one the joint PDF of all the
+
+ align:start position:0%
+obvious one the joint PDF of all the
+ 
+
+ align:start position:0%
+obvious one the joint PDF of all the
+random variables involved must be equal
+
+ align:start position:0%
+random variables involved must be equal
+ 
+
+ align:start position:0%
+random variables involved must be equal
+to the product of the marginal PDFs
+
+ align:start position:0%
+to the product of the marginal PDFs
+ 
+
+ align:start position:0%
+to the product of the marginal PDFs
+intuitively what that means is that
+
+ align:start position:0%
+intuitively what that means is that
+ 
+
+ align:start position:0%
+intuitively what that means is that
+knowing the values of some of the random
+
+ align:start position:0%
+knowing the values of some of the random
+ 
+
+ align:start position:0%
+knowing the values of some of the random
+variables does not affect our beliefs
+
+ align:start position:0%
+variables does not affect our beliefs
+ 
+
+ align:start position:0%
+variables does not affect our beliefs
+about the remaining random variables
+
+ align:start position:0%
+about the remaining random variables
+ 
+
+ align:start position:0%
+about the remaining random variables
+finally let us note some consequences of
+
+ align:start position:0%
+finally let us note some consequences of
+ 
+
+ align:start position:0%
+finally let us note some consequences of
+independent which are identical to the
+
+ align:start position:0%
+independent which are identical to the
+ 
+
+ align:start position:0%
+independent which are identical to the
+corresponding properties that we had in
+
+ align:start position:0%
+corresponding properties that we had in
+ 
+
+ align:start position:0%
+corresponding properties that we had in
+the discrete case and the proofs are
+
+ align:start position:0%
+the discrete case and the proofs are
+ 
+
+ align:start position:0%
+the discrete case and the proofs are
+also exactly the same so the expectation
+
+ align:start position:0%
+also exactly the same so the expectation
+ 
+
+ align:start position:0%
+also exactly the same so the expectation
+of the product of independent random
+
+ align:start position:0%
+of the product of independent random
+ 
+
+ align:start position:0%
+of the product of independent random
+variables is the product of the
+
+ align:start position:0%
+variables is the product of the
+ 
+
+ align:start position:0%
+variables is the product of the
+expectations the variance of the sum of
+
+ align:start position:0%
+expectations the variance of the sum of
+ 
+
+ align:start position:0%
+expectations the variance of the sum of
+independent random variables is the sum
+
+ align:start position:0%
+independent random variables is the sum
+ 
+
+ align:start position:0%
+independent random variables is the sum
+of the variances and functions of
+
+ align:start position:0%
+of the variances and functions of
+ 
+
+ align:start position:0%
+of the variances and functions of
+independent random variables are also
+
+ align:start position:0%
+independent random variables are also
+ 
+
+ align:start position:0%
+independent random variables are also
+independent which in particular implies
+
+ align:start position:0%
+independent which in particular implies
+ 
+
+ align:start position:0%
+independent which in particular implies
+using the previous rule that the
+
+ align:start position:0%
+using the previous rule that the
+ 
+
+ align:start position:0%
+using the previous rule that the
+expected value of a product of this kind
+
+ align:start position:0%
+expected value of a product of this kind
+ 
+
+ align:start position:0%
+expected value of a product of this kind
+is going to be the product of these
+
+ align:start position:0%
+is going to be the product of these
+ 
+
+ align:start position:0%
+is going to be the product of these
+expectations so independence of
+
+ align:start position:0%
+expectations so independence of
+ 
+
+ align:start position:0%
+expectations so independence of
+continuous random variables is pretty
+
+ align:start position:0%
+continuous random variables is pretty
+ 
+
+ align:start position:0%
+continuous random variables is pretty
+much the same as independence of
+
+ align:start position:0%
+much the same as independence of
+ 
+
+ align:start position:0%
+much the same as independence of
+discrete random variables as far as
+
+ align:start position:0%
+discrete random variables as far as
+ 
+
+ align:start position:0%
+discrete random variables as far as
+mathematics are concerned and the
+
+ align:start position:0%
+mathematics are concerned and the
+ 
+
+ align:start position:0%
+mathematics are concerned and the
+intuitive content of the independence
+
+ align:start position:0%
+intuitive content of the independence
+ 
+
+ align:start position:0%
+intuitive content of the independence
+assumption is the same as in the
+
+ align:start position:0%
+assumption is the same as in the
+ 
+
+ align:start position:0%
+assumption is the same as in the
+discrete case one random variable does
+
+ align:start position:0%
+discrete case one random variable does
+ 
+
+ align:start position:0%
+discrete case one random variable does
+not provide any information about the
+
+ align:start position:0%
+not provide any information about the
+ 
+
+ align:start position:0%
+not provide any information about the
+other
\ No newline at end of file
diff --git a/JrP0kUuZv20.txt b/JrP0kUuZv20.txt
new file mode 100644
index 0000000000000000000000000000000000000000..35ee2ab0782fa00fe071202aaf7f609204f18bcf
--- /dev/null
+++ b/JrP0kUuZv20.txt
@@ -0,0 +1,2891 @@
+align:start position:0%
+ 
+I thought at least these three questions
+
+ align:start position:0%
+I thought at least these three questions
+ 
+
+ align:start position:0%
+I thought at least these three questions
+could be part of our conversation later
+
+ align:start position:0%
+could be part of our conversation later
+ 
+
+ align:start position:0%
+could be part of our conversation later
+after we I want us to get up and
+
+ align:start position:0%
+after we I want us to get up and
+ 
+
+ align:start position:0%
+after we I want us to get up and
+actually create a public work but I've
+
+ align:start position:0%
+actually create a public work but I've
+ 
+
+ align:start position:0%
+actually create a public work but I've
+been thinking about how my contemporary
+
+ align:start position:0%
+been thinking about how my contemporary
+ 
+
+ align:start position:0%
+been thinking about how my contemporary
+art and social practice enable
+
+ align:start position:0%
+art and social practice enable
+ 
+
+ align:start position:0%
+art and social practice enable
+conversations about difficult subjects
+
+ align:start position:0%
+conversations about difficult subjects
+ 
+
+ align:start position:0%
+conversations about difficult subjects
+and that's part of what we're interested
+
+ align:start position:0%
+and that's part of what we're interested
+ 
+
+ align:start position:0%
+and that's part of what we're interested
+in couldn't that be the focus of a
+
+ align:start position:0%
+in couldn't that be the focus of a
+ 
+
+ align:start position:0%
+in couldn't that be the focus of a
+curriculum a multi-week a multi session
+
+ align:start position:0%
+curriculum a multi-week a multi session
+ 
+
+ align:start position:0%
+curriculum a multi-week a multi session
+unit of instruction with learners of
+
+ align:start position:0%
+unit of instruction with learners of
+ 
+
+ align:start position:0%
+unit of instruction with learners of
+many a range of Ages and in the range of
+
+ align:start position:0%
+many a range of Ages and in the range of
+ 
+
+ align:start position:0%
+many a range of Ages and in the range of
+spaces or why prepare teachers as agents
+
+ align:start position:0%
+spaces or why prepare teachers as agents
+ 
+
+ align:start position:0%
+spaces or why prepare teachers as agents
+of positive social change I mean some
+
+ align:start position:0%
+of positive social change I mean some
+ 
+
+ align:start position:0%
+of positive social change I mean some
+people say oh we have to prepare the
+
+ align:start position:0%
+people say oh we have to prepare the
+ 
+
+ align:start position:0%
+people say oh we have to prepare the
+fair but why what would come out of that
+
+ align:start position:0%
+fair but why what would come out of that
+ 
+
+ align:start position:0%
+fair but why what would come out of that
+or why not what does it mean maybe the
+
+ align:start position:0%
+or why not what does it mean maybe the
+ 
+
+ align:start position:0%
+or why not what does it mean maybe the
+question should be what what does it
+
+ align:start position:0%
+question should be what what does it
+ 
+
+ align:start position:0%
+question should be what what does it
+mean for teachers to be prepared as
+
+ align:start position:0%
+mean for teachers to be prepared as
+ 
+
+ align:start position:0%
+mean for teachers to be prepared as
+agents for social change some of you are
+
+ align:start position:0%
+agents for social change some of you are
+ 
+
+ align:start position:0%
+agents for social change some of you are
+studying in departments or programs
+
+ align:start position:0%
+studying in departments or programs
+ 
+
+ align:start position:0%
+studying in departments or programs
+where social change social activism
+
+ align:start position:0%
+where social change social activism
+ 
+
+ align:start position:0%
+where social change social activism
+positive social responsibility is
+
+ align:start position:0%
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+
+ align:start position:0%
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+essential to the mission what why do
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+essential to the mission what why do
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+
+ align:start position:0%
+that is that's such a good thing or how
+ 
+
+ align:start position:0%
+that is that's such a good thing or how
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+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+injustice interrupt conditions of
+
+ align:start position:0%
+injustice interrupt conditions of
+ 
+
+ align:start position:0%
+injustice interrupt conditions of
+inequality I might not be able to change
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
+inequality I might not be able to change
+them might not be able to stop them but
+
+ align:start position:0%
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+ 
+
+ align:start position:0%
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+maybe it interrupts it just long enough
+
+ align:start position:0%
+maybe it interrupts it just long enough
+ 
+
+ align:start position:0%
+maybe it interrupts it just long enough
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+
+ align:start position:0%
+to reposition or find other ways other
+ 
+
+ align:start position:0%
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+
+ align:start position:0%
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+ 
+
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+
+ align:start position:0%
+think this is a good time to stop and
+ 
+
+ align:start position:0%
+think this is a good time to stop and
+let's get up and let's make some public
+
+ align:start position:0%
+let's get up and let's make some public
+ 
+
+ align:start position:0%
+let's get up and let's make some public
+trouble I brought with me some
+
+ align:start position:0%
+trouble I brought with me some
+ 
+
+ align:start position:0%
+trouble I brought with me some
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+
+ align:start position:0%
+children's books and I also brought some
+ 
+
+ align:start position:0%
+children's books and I also brought some
+children's toys how many of you brought
+
+ align:start position:0%
+children's toys how many of you brought
+ 
+
+ align:start position:0%
+children's toys how many of you brought
+cell phones how many of those cell
+
+ align:start position:0%
+cell phones how many of those cell
+ 
+
+ align:start position:0%
+cell phones how many of those cell
+phones take pictures oh yeah now we can
+
+ align:start position:0%
+phones take pictures oh yeah now we can
+ 
+
+ align:start position:0%
+phones take pictures oh yeah now we can
+work is individuals we can work in pairs
+
+ align:start position:0%
+work is individuals we can work in pairs
+ 
+
+ align:start position:0%
+work is individuals we can work in pairs
+or trios if we want all right I have
+
+ align:start position:0%
+or trios if we want all right I have
+ 
+
+ align:start position:0%
+or trios if we want all right I have
+some children's books here I'll share
+
+ align:start position:0%
+some children's books here I'll share
+ 
+
+ align:start position:0%
+some children's books here I'll share
+them show these with you to you not all
+
+ align:start position:0%
+them show these with you to you not all
+ 
+
+ align:start position:0%
+them show these with you to you not all
+of them deal with uncomfortable stories
+
+ align:start position:0%
+of them deal with uncomfortable stories
+ 
+
+ align:start position:0%
+of them deal with uncomfortable stories
+some of them do there's a whole range of
+
+ align:start position:0%
+some of them do there's a whole range of
+ 
+
+ align:start position:0%
+some of them do there's a whole range of
+things like Flat Stanley on if you're
+
+ align:start position:0%
+things like Flat Stanley on if you're
+ 
+
+ align:start position:0%
+things like Flat Stanley on if you're
+snow the Flat Stanley to me there's a
+
+ align:start position:0%
+snow the Flat Stanley to me there's a
+ 
+
+ align:start position:0%
+snow the Flat Stanley to me there's a
+Henry box Brown deal here where you can
+
+ align:start position:0%
+Henry box Brown deal here where you can
+ 
+
+ align:start position:0%
+Henry box Brown deal here where you can
+mail individuals to different place here
+
+ align:start position:0%
+mail individuals to different place here
+ 
+
+ align:start position:0%
+mail individuals to different place here
+he's pretty happy about going to visit
+
+ align:start position:0%
+he's pretty happy about going to visit
+ 
+
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+he's pretty happy about going to visit
+his family but Henry couldn't do that or
+
+ align:start position:0%
+his family but Henry couldn't do that or
+ 
+
+ align:start position:0%
+his family but Henry couldn't do that or
+the big orange
+
+ align:start position:0%
+the big orange
+ 
+
+ align:start position:0%
+the big orange
+but this is about one house being
+
+ align:start position:0%
+but this is about one house being
+ 
+
+ align:start position:0%
+but this is about one house being
+different and then I won't ruin the
+
+ align:start position:0%
+different and then I won't ruin the
+ 
+
+ align:start position:0%
+different and then I won't ruin the
+story for you at the end but it's about
+
+ align:start position:0%
+story for you at the end but it's about
+ 
+
+ align:start position:0%
+story for you at the end but it's about
+finding your own way little blue and
+
+ align:start position:0%
+finding your own way little blue and
+ 
+
+ align:start position:0%
+finding your own way little blue and
+little yellow I don't know if about know
+
+ align:start position:0%
+little yellow I don't know if about know
+ 
+
+ align:start position:0%
+little yellow I don't know if about know
+if you know their story but when you mix
+
+ align:start position:0%
+if you know their story but when you mix
+ 
+
+ align:start position:0%
+if you know their story but when you mix
+blue and yellow you get green and what
+
+ align:start position:0%
+blue and yellow you get green and what
+ 
+
+ align:start position:0%
+blue and yellow you get green and what
+does it mean to be blue or yellow and
+
+ align:start position:0%
+does it mean to be blue or yellow and
+ 
+
+ align:start position:0%
+does it mean to be blue or yellow and
+how does mixing happen tar Beach about a
+
+ align:start position:0%
+how does mixing happen tar Beach about a
+ 
+
+ align:start position:0%
+how does mixing happen tar Beach about a
+little girl who she doesn't have
+
+ align:start position:0%
+little girl who she doesn't have
+ 
+
+ align:start position:0%
+little girl who she doesn't have
+something or can't go somewhere she just
+
+ align:start position:0%
+something or can't go somewhere she just
+ 
+
+ align:start position:0%
+something or can't go somewhere she just
+imagines that she can fly there and she
+
+ align:start position:0%
+imagines that she can fly there and she
+ 
+
+ align:start position:0%
+imagines that she can fly there and she
+can capture that experience bell hooks I
+
+ align:start position:0%
+can capture that experience bell hooks I
+ 
+
+ align:start position:0%
+can capture that experience bell hooks I
+don't know if you know her children's
+
+ align:start position:0%
+don't know if you know her children's
+ 
+
+ align:start position:0%
+don't know if you know her children's
+book skin again there's a wonderful book
+
+ align:start position:0%
+book skin again there's a wonderful book
+ 
+
+ align:start position:0%
+book skin again there's a wonderful book
+about distant learning disabilities
+
+ align:start position:0%
+about distant learning disabilities
+ 
+
+ align:start position:0%
+about distant learning disabilities
+reading in particular it's called the
+
+ align:start position:0%
+reading in particular it's called the
+ 
+
+ align:start position:0%
+reading in particular it's called the
+art of miss Chu where the art teacher
+
+ align:start position:0%
+art of miss Chu where the art teacher
+ 
+
+ align:start position:0%
+art of miss Chu where the art teacher
+her art teacher essentially figured out
+
+ align:start position:0%
+her art teacher essentially figured out
+ 
+
+ align:start position:0%
+her art teacher essentially figured out
+she was seeing the world differently her
+
+ align:start position:0%
+she was seeing the world differently her
+ 
+
+ align:start position:0%
+she was seeing the world differently her
+reading what issue is reading she was
+
+ align:start position:0%
+reading what issue is reading she was
+ 
+
+ align:start position:0%
+reading what issue is reading she was
+reading the spaces between the words not
+
+ align:start position:0%
+reading the spaces between the words not
+ 
+
+ align:start position:0%
+reading the spaces between the words not
+the words themselves just like an artist
+
+ align:start position:0%
+the words themselves just like an artist
+ 
+
+ align:start position:0%
+the words themselves just like an artist
+might try to render the negative space
+
+ align:start position:0%
+might try to render the negative space
+ 
+
+ align:start position:0%
+might try to render the negative space
+rather than the positive space or Maya
+
+ align:start position:0%
+rather than the positive space or Maya
+ 
+
+ align:start position:0%
+rather than the positive space or Maya
+Angelou poem and a jean-michel Basquiat
+
+ align:start position:0%
+Angelou poem and a jean-michel Basquiat
+ 
+
+ align:start position:0%
+Angelou poem and a jean-michel Basquiat
+poem put together jean-michel Basquiat
+
+ align:start position:0%
+poem put together jean-michel Basquiat
+ 
+
+ align:start position:0%
+poem put together jean-michel Basquiat
+images and Maya Angelou poem life
+
+ align:start position:0%
+images and Maya Angelou poem life
+ 
+
+ align:start position:0%
+images and Maya Angelou poem life
+doesn't frighten me anymore these are
+
+ align:start position:0%
+doesn't frighten me anymore these are
+ 
+
+ align:start position:0%
+doesn't frighten me anymore these are
+children's books that I found kids
+
+ align:start position:0%
+children's books that I found kids
+ 
+
+ align:start position:0%
+children's books that I found kids
+respond to in interesting ways so you
+
+ align:start position:0%
+respond to in interesting ways so you
+ 
+
+ align:start position:0%
+respond to in interesting ways so you
+might choose one of these books and find
+
+ align:start position:0%
+might choose one of these books and find
+ 
+
+ align:start position:0%
+might choose one of these books and find
+one of those unexpected public spaces
+
+ align:start position:0%
+one of those unexpected public spaces
+ 
+
+ align:start position:0%
+one of those unexpected public spaces
+where you don't think education or art
+
+ align:start position:0%
+where you don't think education or art
+ 
+
+ align:start position:0%
+where you don't think education or art
+making or art practice is supposed to
+
+ align:start position:0%
+making or art practice is supposed to
+ 
+
+ align:start position:0%
+making or art practice is supposed to
+happen you could take one of these books
+
+ align:start position:0%
+happen you could take one of these books
+ 
+
+ align:start position:0%
+happen you could take one of these books
+and go and read it there outloud and
+
+ align:start position:0%
+and go and read it there outloud and
+ 
+
+ align:start position:0%
+and go and read it there outloud and
+have somebody else or yourself videotape
+
+ align:start position:0%
+have somebody else or yourself videotape
+ 
+
+ align:start position:0%
+have somebody else or yourself videotape
+you or not videotape that's you can tell
+
+ align:start position:0%
+you or not videotape that's you can tell
+ 
+
+ align:start position:0%
+you or not videotape that's you can tell
+them make a video of mobile I sell a
+
+ align:start position:0%
+them make a video of mobile I sell a
+ 
+
+ align:start position:0%
+them make a video of mobile I sell a
+mobile video of you and you can put one
+
+ align:start position:0%
+mobile video of you and you can put one
+ 
+
+ align:start position:0%
+mobile video of you and you can put one
+of the hashtags where's where our
+
+ align:start position:0%
+of the hashtags where's where our
+ 
+
+ align:start position:0%
+of the hashtags where's where our
+hashtags Steve there's you can hashtag
+
+ align:start position:0%
+hashtags Steve there's you can hashtag
+ 
+
+ align:start position:0%
+hashtags Steve there's you can hashtag
+it and pop it up on social media if
+
+ align:start position:0%
+it and pop it up on social media if
+ 
+
+ align:start position:0%
+it and pop it up on social media if
+you'd like or you can take still photo
+
+ align:start position:0%
+you'd like or you can take still photo
+ 
+
+ align:start position:0%
+you'd like or you can take still photo
+of yourself or someone else reading out
+
+ align:start position:0%
+of yourself or someone else reading out
+ 
+
+ align:start position:0%
+of yourself or someone else reading out
+loud we can take several document that
+
+ align:start position:0%
+loud we can take several document that
+ 
+
+ align:start position:0%
+loud we can take several document that
+experience what would be interesting is
+
+ align:start position:0%
+experience what would be interesting is
+ 
+
+ align:start position:0%
+experience what would be interesting is
+is to see what kind of social
+
+ align:start position:0%
+is to see what kind of social
+ 
+
+ align:start position:0%
+is to see what kind of social
+interaction happens and think about the
+
+ align:start position:0%
+interaction happens and think about the
+ 
+
+ align:start position:0%
+interaction happens and think about the
+critique remember those little tiny
+
+ align:start position:0%
+critique remember those little tiny
+ 
+
+ align:start position:0%
+critique remember those little tiny
+townspeople and the tiny presidents the
+
+ align:start position:0%
+townspeople and the tiny presidents the
+ 
+
+ align:start position:0%
+townspeople and the tiny presidents the
+critiques of the store
+
+ align:start position:0%
+critiques of the store
+ 
+
+ align:start position:0%
+critiques of the store
+of the little people and the stories of
+
+ align:start position:0%
+of the little people and the stories of
+ 
+
+ align:start position:0%
+of the little people and the stories of
+those spaces there's a conversation that
+
+ align:start position:0%
+those spaces there's a conversation that
+ 
+
+ align:start position:0%
+those spaces there's a conversation that
+happens think about the story you might
+
+ align:start position:0%
+happens think about the story you might
+ 
+
+ align:start position:0%
+happens think about the story you might
+read in that space in relationship to
+
+ align:start position:0%
+read in that space in relationship to
+ 
+
+ align:start position:0%
+read in that space in relationship to
+that space or I have these little toys
+
+ align:start position:0%
+that space or I have these little toys
+ 
+
+ align:start position:0%
+that space or I have these little toys
+just three firefighters two of whom have
+
+ align:start position:0%
+just three firefighters two of whom have
+ 
+
+ align:start position:0%
+just three firefighters two of whom have
+razor stubble one has a mustache
+
+ align:start position:0%
+razor stubble one has a mustache
+ 
+
+ align:start position:0%
+razor stubble one has a mustache
+I wonder how gendered this is I'm just
+
+ align:start position:0%
+I wonder how gendered this is I'm just
+ 
+
+ align:start position:0%
+I wonder how gendered this is I'm just
+asking questions right now or little
+
+ align:start position:0%
+asking questions right now or little
+ 
+
+ align:start position:0%
+asking questions right now or little
+animals or I had little LEGO Minifigures
+
+ align:start position:0%
+animals or I had little LEGO Minifigures
+ 
+
+ align:start position:0%
+animals or I had little LEGO Minifigures
+they these have to be put together I
+
+ align:start position:0%
+they these have to be put together I
+ 
+
+ align:start position:0%
+they these have to be put together I
+mean you're welcome to take them and put
+
+ align:start position:0%
+mean you're welcome to take them and put
+ 
+
+ align:start position:0%
+mean you're welcome to take them and put
+them together and use them in the ways
+
+ align:start position:0%
+them together and use them in the ways
+ 
+
+ align:start position:0%
+them together and use them in the ways
+that you saw in the photographs
+
+ align:start position:0%
+that you saw in the photographs
+ 
+
+ align:start position:0%
+that you saw in the photographs
+critiquing having a conversation in a
+
+ align:start position:0%
+critiquing having a conversation in a
+ 
+
+ align:start position:0%
+critiquing having a conversation in a
+public space that story where's my
+
+ align:start position:0%
+public space that story where's my
+ 
+
+ align:start position:0%
+public space that story where's my
+Henry's freedombox I think I'm gonna
+
+ align:start position:0%
+Henry's freedombox I think I'm gonna
+ 
+
+ align:start position:0%
+Henry's freedombox I think I'm gonna
+take one of these pallets I can't take
+
+ align:start position:0%
+take one of these pallets I can't take
+ 
+
+ align:start position:0%
+take one of these pallets I can't take
+both of them I'm gonna take one of these
+
+ align:start position:0%
+both of them I'm gonna take one of these
+ 
+
+ align:start position:0%
+both of them I'm gonna take one of these
+and I'm going outside I'm gonna read
+
+ align:start position:0%
+and I'm going outside I'm gonna read
+ 
+
+ align:start position:0%
+and I'm going outside I'm gonna read
+this book I'm gonna perform that story
+
+ align:start position:0%
+this book I'm gonna perform that story
+ 
+
+ align:start position:0%
+this book I'm gonna perform that story
+outside
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Henry was lonely one day he met Nancy
+
+ align:start position:0%
+Henry was lonely one day he met Nancy
+ 
+
+ align:start position:0%
+Henry was lonely one day he met Nancy
+for the shopping for her mistress they
+
+ align:start position:0%
+for the shopping for her mistress they
+ 
+
+ align:start position:0%
+for the shopping for her mistress they
+walked and talked and agreed to meet
+
+ align:start position:0%
+walked and talked and agreed to meet
+ 
+
+ align:start position:0%
+walked and talked and agreed to meet
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+Henry felt like singing but slaves
+
+ align:start position:0%
+Henry felt like singing but slaves
+ 
+
+ align:start position:0%
+Henry felt like singing but slaves
+didn't dare sing in the streets instead
+
+ align:start position:0%
+didn't dare sing in the streets instead
+ 
+
+ align:start position:0%
+didn't dare sing in the streets instead
+he hummed all the way home Henry knew
+
+ align:start position:0%
+he hummed all the way home Henry knew
+ 
+
+ align:start position:0%
+he hummed all the way home Henry knew
+they were very lucky they live together
+
+ align:start position:0%
+they were very lucky they live together
+ 
+
+ align:start position:0%
+they were very lucky they live together
+even though they had different master
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can admit Oh
+
+ align:start position:0%
+I can admit Oh
+ 
+
+ align:start position:0%
+I can admit Oh
+I think beautiful
+
+ align:start position:0%
+I think beautiful
+ 
+
+ align:start position:0%
+I think beautiful
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does anyone want to talk about you want
+
+ align:start position:0%
+does anyone want to talk about you want
+ 
+
+ align:start position:0%
+does anyone want to talk about you want
+to talk about your own specific
+
+ align:start position:0%
+to talk about your own specific
+ 
+
+ align:start position:0%
+to talk about your own specific
+experience either reading a book out
+
+ align:start position:0%
+experience either reading a book out
+ 
+
+ align:start position:0%
+experience either reading a book out
+loud in public or reading a public space
+
+ align:start position:0%
+loud in public or reading a public space
+ 
+
+ align:start position:0%
+loud in public or reading a public space
+with a conversation with your figure
+
+ align:start position:0%
+with a conversation with your figure
+ 
+
+ align:start position:0%
+with a conversation with your figure
+mainly people ignored me some people
+
+ align:start position:0%
+mainly people ignored me some people
+ 
+
+ align:start position:0%
+mainly people ignored me some people
+like you said made it sort of a wide
+
+ align:start position:0%
+like you said made it sort of a wide
+ 
+
+ align:start position:0%
+like you said made it sort of a wide
+like somebody came realize they were
+
+ align:start position:0%
+like somebody came realize they were
+ 
+
+ align:start position:0%
+like somebody came realize they were
+sort of in the scope of the photograph
+
+ align:start position:0%
+sort of in the scope of the photograph
+ 
+
+ align:start position:0%
+sort of in the scope of the photograph
+and I'm so sorry oh and you were taking
+
+ align:start position:0%
+and I'm so sorry oh and you were taking
+ 
+
+ align:start position:0%
+and I'm so sorry oh and you were taking
+the photograph and you said never
+
+ align:start position:0%
+the photograph and you said never
+ 
+
+ align:start position:0%
+the photograph and you said never
+thought was okay you can go in no no no
+
+ align:start position:0%
+thought was okay you can go in no no no
+ 
+
+ align:start position:0%
+thought was okay you can go in no no no
+I am I to do
+
+ align:start position:0%
+I am I to do
+ 
+
+ align:start position:0%
+I am I to do
+so that was a I used to love to read
+
+ align:start position:0%
+so that was a I used to love to read
+ 
+
+ align:start position:0%
+so that was a I used to love to read
+children's books to my kids so it was so
+
+ align:start position:0%
+children's books to my kids so it was so
+ 
+
+ align:start position:0%
+children's books to my kids so it was so
+I mean you know it's just so much fun to
+
+ align:start position:0%
+I mean you know it's just so much fun to
+ 
+
+ align:start position:0%
+I mean you know it's just so much fun to
+be out there and showing everybody and
+
+ align:start position:0%
+be out there and showing everybody and
+ 
+
+ align:start position:0%
+be out there and showing everybody and
+and some people who looked into it and
+
+ align:start position:0%
+and some people who looked into it and
+ 
+
+ align:start position:0%
+and some people who looked into it and
+some people smiled and I saw people sort
+
+ align:start position:0%
+some people smiled and I saw people sort
+ 
+
+ align:start position:0%
+some people smiled and I saw people sort
+of taking pictures and then I was
+
+ align:start position:0%
+of taking pictures and then I was
+ 
+
+ align:start position:0%
+of taking pictures and then I was
+watching you and I saw somebody like
+
+ align:start position:0%
+watching you and I saw somebody like
+ 
+
+ align:start position:0%
+watching you and I saw somebody like
+doing posing walk to the side in front
+
+ align:start position:0%
+doing posing walk to the side in front
+ 
+
+ align:start position:0%
+doing posing walk to the side in front
+of you like wanting to have a picture
+
+ align:start position:0%
+of you like wanting to have a picture
+ 
+
+ align:start position:0%
+of you like wanting to have a picture
+like they figured this is some like
+
+ align:start position:0%
+like they figured this is some like
+ 
+
+ align:start position:0%
+like they figured this is some like
+thing and they wanted to be in it but
+
+ align:start position:0%
+thing and they wanted to be in it but
+ 
+
+ align:start position:0%
+thing and they wanted to be in it but
+not really in it so they were all on the
+
+ align:start position:0%
+not really in it so they were all on the
+ 
+
+ align:start position:0%
+not really in it so they were all on the
+side always they want you family though
+
+ align:start position:0%
+side always they want you family though
+ 
+
+ align:start position:0%
+side always they want you family though
+if you don't even know what ID is why
+
+ align:start position:0%
+if you don't even know what ID is why
+ 
+
+ align:start position:0%
+if you don't even know what ID is why
+I'm just so desperate to get a picture
+
+ align:start position:0%
+I'm just so desperate to get a picture
+ 
+
+ align:start position:0%
+I'm just so desperate to get a picture
+Nicolas MERS off visual culture scholar
+
+ align:start position:0%
+Nicolas MERS off visual culture scholar
+ 
+
+ align:start position:0%
+Nicolas MERS off visual culture scholar
+uses the word sublime to talk about
+
+ align:start position:0%
+uses the word sublime to talk about
+ 
+
+ align:start position:0%
+uses the word sublime to talk about
+those visual moments or those moments
+
+ align:start position:0%
+those visual moments or those moments
+ 
+
+ align:start position:0%
+those visual moments or those moments
+that are so repulsive you can't look
+
+ align:start position:0%
+that are so repulsive you can't look
+ 
+
+ align:start position:0%
+that are so repulsive you can't look
+away and so seductive you can't bear to
+
+ align:start position:0%
+away and so seductive you can't bear to
+ 
+
+ align:start position:0%
+away and so seductive you can't bear to
+look at it you know I mean it's that
+
+ align:start position:0%
+look at it you know I mean it's that
+ 
+
+ align:start position:0%
+look at it you know I mean it's that
+tension everybody calls that the sublime
+
+ align:start position:0%
+tension everybody calls that the sublime
+ 
+
+ align:start position:0%
+tension everybody calls that the sublime
+so maybe there's something sublime about
+
+ align:start position:0%
+so maybe there's something sublime about
+ 
+
+ align:start position:0%
+so maybe there's something sublime about
+that that they wanted to be part but
+
+ align:start position:0%
+that that they wanted to be part but
+ 
+
+ align:start position:0%
+that that they wanted to be part but
+knew something was going on but they
+
+ align:start position:0%
+knew something was going on but they
+ 
+
+ align:start position:0%
+knew something was going on but they
+weren't supposed to be part of it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+and maybe we see the little Lego
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goodness playing with a hatchet of
+
+ align:start position:0%
+goodness playing with a hatchet of
+ 
+
+ align:start position:0%
+goodness playing with a hatchet of
+course and so we were playing around
+
+ align:start position:0%
+course and so we were playing around
+ 
+
+ align:start position:0%
+course and so we were playing around
+with whether you had the hatchet or not
+
+ align:start position:0%
+with whether you had the hatchet or not
+ 
+
+ align:start position:0%
+with whether you had the hatchet or not
+have time today giving him like on
+
+ align:start position:0%
+have time today giving him like on
+ 
+
+ align:start position:0%
+have time today giving him like on
+different pictures from magazines or
+
+ align:start position:0%
+different pictures from magazines or
+ 
+
+ align:start position:0%
+different pictures from magazines or
+newspaper and he was in different
+
+ align:start position:0%
+newspaper and he was in different
+ 
+
+ align:start position:0%
+newspaper and he was in different
+contexts and they put him on the water
+
+ align:start position:0%
+contexts and they put him on the water
+ 
+
+ align:start position:0%
+contexts and they put him on the water
+bubbler and it's playing with him in the
+
+ align:start position:0%
+bubbler and it's playing with him in the
+ 
+
+ align:start position:0%
+bubbler and it's playing with him in the
+water bubbler but it was interesting and
+
+ align:start position:0%
+water bubbler but it was interesting and
+ 
+
+ align:start position:0%
+water bubbler but it was interesting and
+I did think about my kids that have a
+
+ align:start position:0%
+I did think about my kids that have a
+ 
+
+ align:start position:0%
+I did think about my kids that have a
+lot of fun my students a lot of fun of
+
+ align:start position:0%
+lot of fun my students a lot of fun of
+ 
+
+ align:start position:0%
+lot of fun my students a lot of fun of
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+so the hatchet tell me about why with
+
+ align:start position:0%
+so the hatchet tell me about why with
+ 
+
+ align:start position:0%
+so the hatchet tell me about why with
+and without the hatches is like
+
+ align:start position:0%
+and without the hatches is like
+ 
+
+ align:start position:0%
+and without the hatches is like
+accessorizing or I was like we had him
+
+ align:start position:0%
+accessorizing or I was like we had him
+ 
+
+ align:start position:0%
+accessorizing or I was like we had him
+in front of his headlights and according
+
+ align:start position:0%
+in front of his headlights and according
+ 
+
+ align:start position:0%
+in front of his headlights and according
+to the headline if you have a hatchet
+
+ align:start position:0%
+to the headline if you have a hatchet
+ 
+
+ align:start position:0%
+to the headline if you have a hatchet
+the headline meant one thing but if he
+
+ align:start position:0%
+the headline meant one thing but if he
+ 
+
+ align:start position:0%
+the headline meant one thing but if he
+didn't than a minute different things so
+
+ align:start position:0%
+didn't than a minute different things so
+ 
+
+ align:start position:0%
+didn't than a minute different things so
+that context changed once that weapon
+
+ align:start position:0%
+that context changed once that weapon
+ 
+
+ align:start position:0%
+that context changed once that weapon
+was introduced can you give us an
+
+ align:start position:0%
+was introduced can you give us an
+ 
+
+ align:start position:0%
+was introduced can you give us an
+example of one of those headlines
+
+ align:start position:0%
+example of one of those headlines
+ 
+
+ align:start position:0%
+example of one of those headlines
+someone won an award and we play in
+
+ align:start position:0%
+someone won an award and we play in
+ 
+
+ align:start position:0%
+someone won an award and we play in
+front of that with that with the hatchet
+
+ align:start position:0%
+front of that with that with the hatchet
+ 
+
+ align:start position:0%
+front of that with that with the hatchet
+which made it a little bit more ominous
+
+ align:start position:0%
+which made it a little bit more ominous
+ 
+
+ align:start position:0%
+which made it a little bit more ominous
+and then without the happiness like well
+
+ align:start position:0%
+and then without the happiness like well
+ 
+
+ align:start position:0%
+and then without the happiness like well
+you're playing with the various symbolic
+
+ align:start position:0%
+you're playing with the various symbolic
+ 
+
+ align:start position:0%
+you're playing with the various symbolic
+meanings that are referenced but not
+
+ align:start position:0%
+meanings that are referenced but not
+ 
+
+ align:start position:0%
+meanings that are referenced but not
+just the ninja but with that hatchet and
+
+ align:start position:0%
+just the ninja but with that hatchet and
+ 
+
+ align:start position:0%
+just the ninja but with that hatchet and
+the text so there's the layered readings
+
+ align:start position:0%
+the text so there's the layered readings
+ 
+
+ align:start position:0%
+the text so there's the layered readings
+and even that subtle seemingly innocuous
+
+ align:start position:0%
+and even that subtle seemingly innocuous
+ 
+
+ align:start position:0%
+and even that subtle seemingly innocuous
+change of hatchet or not hatchet shifts
+
+ align:start position:0%
+change of hatchet or not hatchet shifts
+ 
+
+ align:start position:0%
+change of hatchet or not hatchet shifts
+readings shifts shifts meaning there
+
+ align:start position:0%
+readings shifts shifts meaning there
+ 
+
+ align:start position:0%
+readings shifts shifts meaning there
+it's very powerful I hope some of what
+
+ align:start position:0%
+it's very powerful I hope some of what
+ 
+
+ align:start position:0%
+it's very powerful I hope some of what
+we've talked about gives you beginning
+
+ align:start position:0%
+we've talked about gives you beginning
+ 
+
+ align:start position:0%
+we've talked about gives you beginning
+points or places of departure for your
+
+ align:start position:0%
+points or places of departure for your
+ 
+
+ align:start position:0%
+points or places of departure for your
+own work as educators or artists
+
+ align:start position:0%
+own work as educators or artists
+ 
+
+ align:start position:0%
+own work as educators or artists
+continue this this work see what else
+
+ align:start position:0%
+continue this this work see what else
+ 
+
+ align:start position:0%
+continue this this work see what else
+you can trouble what other kinds of
+
+ align:start position:0%
+you can trouble what other kinds of
+ 
+
+ align:start position:0%
+you can trouble what other kinds of
+questions you can ask what other stories
+
+ align:start position:0%
+questions you can ask what other stories
+ 
+
+ align:start position:0%
+questions you can ask what other stories
+might be told maybe take the little
+
+ align:start position:0%
+might be told maybe take the little
+ 
+
+ align:start position:0%
+might be told maybe take the little
+figures and go make some more imagery
+
+ align:start position:0%
+figures and go make some more imagery
+ 
+
+ align:start position:0%
+figures and go make some more imagery
+maybe find them fire hose or attempt
+
+ align:start position:0%
+maybe find them fire hose or attempt
+ 
+
+ align:start position:0%
+maybe find them fire hose or attempt
+other performances maybe this is an
+
+ align:start position:0%
+other performances maybe this is an
+ 
+
+ align:start position:0%
+other performances maybe this is an
+assignment that would work for with your
+
+ align:start position:0%
+assignment that would work for with your
+ 
+
+ align:start position:0%
+assignment that would work for with your
+students and give it a shot and if it
+
+ align:start position:0%
+students and give it a shot and if it
+ 
+
+ align:start position:0%
+students and give it a shot and if it
+does or if it doesn't maybe sure social
+
+ align:start position:0%
+does or if it doesn't maybe sure social
+ 
+
+ align:start position:0%
+does or if it doesn't maybe sure social
+media drop me a line we'd love to hear
+
+ align:start position:0%
+media drop me a line we'd love to hear
+ 
+
+ align:start position:0%
+media drop me a line we'd love to hear
+what you're up to as a ripple from what
+
+ align:start position:0%
+what you're up to as a ripple from what
+ 
+
+ align:start position:0%
+what you're up to as a ripple from what
+we're doing here I said yesterday and
+
+ align:start position:0%
+we're doing here I said yesterday and
+ 
+
+ align:start position:0%
+we're doing here I said yesterday and
+last week as an artist as an educator as
+
+ align:start position:0%
+last week as an artist as an educator as
+ 
+
+ align:start position:0%
+last week as an artist as an educator as
+a researcher I have found that I'm more
+
+ align:start position:0%
+a researcher I have found that I'm more
+ 
+
+ align:start position:0%
+a researcher I have found that I'm more
+interested in
+
+ align:start position:0%
+interested in
+ 
+
+ align:start position:0%
+interested in
+changing the answers than I am in
+
+ align:start position:0%
+changing the answers than I am in
+ 
+
+ align:start position:0%
+changing the answers than I am in
+answering the questions for me the
+
+ align:start position:0%
+answering the questions for me the
+ 
+
+ align:start position:0%
+answering the questions for me the
+answers are the social constructs those
+
+ align:start position:0%
+answers are the social constructs those
+ 
+
+ align:start position:0%
+answers are the social constructs those
+practices those systems that people have
+
+ align:start position:0%
+practices those systems that people have
+ 
+
+ align:start position:0%
+practices those systems that people have
+put in place sometimes remaining
+
+ align:start position:0%
+put in place sometimes remaining
+ 
+
+ align:start position:0%
+put in place sometimes remaining
+unquestioned or under analyzed and maybe
+
+ align:start position:0%
+unquestioned or under analyzed and maybe
+ 
+
+ align:start position:0%
+unquestioned or under analyzed and maybe
+art-making through social engagement is
+
+ align:start position:0%
+art-making through social engagement is
+ 
+
+ align:start position:0%
+art-making through social engagement is
+one way to provoke reflection hoping to
+
+ align:start position:0%
+one way to provoke reflection hoping to
+ 
+
+ align:start position:0%
+one way to provoke reflection hoping to
+discover something in the process about
+
+ align:start position:0%
+discover something in the process about
+ 
+
+ align:start position:0%
+discover something in the process about
+those constructs I'll leave you with
+
+ align:start position:0%
+those constructs I'll leave you with
+ 
+
+ align:start position:0%
+those constructs I'll leave you with
+this the National Education Association
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a professional organization in the
+
+ align:start position:0%
+is a professional organization in the
+ 
+
+ align:start position:0%
+is a professional organization in the
+North America it's open internationally
+
+ align:start position:0%
+North America it's open internationally
+ 
+
+ align:start position:0%
+North America it's open internationally
+primarily made of k-12 art teachers but
+
+ align:start position:0%
+primarily made of k-12 art teachers but
+ 
+
+ align:start position:0%
+primarily made of k-12 art teachers but
+there are other educators aren't
+
+ align:start position:0%
+there are other educators aren't
+ 
+
+ align:start position:0%
+there are other educators aren't
+educators in the group higher education
+
+ align:start position:0%
+educators in the group higher education
+ 
+
+ align:start position:0%
+educators in the group higher education
+professionals museum educators there are
+
+ align:start position:0%
+professionals museum educators there are
+ 
+
+ align:start position:0%
+professionals museum educators there are
+two journals published studies in art
+
+ align:start position:0%
+two journals published studies in art
+ 
+
+ align:start position:0%
+two journals published studies in art
+education which is essentially the
+
+ align:start position:0%
+education which is essentially the
+ 
+
+ align:start position:0%
+education which is essentially the
+Journal of issues and research in our
+
+ align:start position:0%
+Journal of issues and research in our
+ 
+
+ align:start position:0%
+Journal of issues and research in our
+education and then art education which
+
+ align:start position:0%
+education and then art education which
+ 
+
+ align:start position:0%
+education and then art education which
+is essentially for primarily for k-12
+
+ align:start position:0%
+is essentially for primarily for k-12
+ 
+
+ align:start position:0%
+is essentially for primarily for k-12
+and museum educators and each issue they
+
+ align:start position:0%
+and museum educators and each issue they
+ 
+
+ align:start position:0%
+and museum educators and each issue they
+typically have six articles in here and
+
+ align:start position:0%
+typically have six articles in here and
+ 
+
+ align:start position:0%
+typically have six articles in here and
+then an instructional resource but this
+
+ align:start position:0%
+then an instructional resource but this
+ 
+
+ align:start position:0%
+then an instructional resource but this
+particular special issue that came out
+
+ align:start position:0%
+particular special issue that came out
+ 
+
+ align:start position:0%
+particular special issue that came out
+in July of 2017 it's a special issue and
+
+ align:start position:0%
+in July of 2017 it's a special issue and
+ 
+
+ align:start position:0%
+in July of 2017 it's a special issue and
+the theme the call for the theme was
+
+ align:start position:0%
+the theme the call for the theme was
+ 
+
+ align:start position:0%
+the theme the call for the theme was
+creative activity as a human right and
+
+ align:start position:0%
+creative activity as a human right and
+ 
+
+ align:start position:0%
+creative activity as a human right and
+the editor said you know instead of
+
+ align:start position:0%
+the editor said you know instead of
+ 
+
+ align:start position:0%
+the editor said you know instead of
+getting six all I see isn't how many I
+
+ align:start position:0%
+getting six all I see isn't how many I
+ 
+
+ align:start position:0%
+getting six all I see isn't how many I
+can get so he cut down the number length
+
+ align:start position:0%
+can get so he cut down the number length
+ 
+
+ align:start position:0%
+can get so he cut down the number length
+of the submission of these shorter
+
+ align:start position:0%
+of the submission of these shorter
+ 
+
+ align:start position:0%
+of the submission of these shorter
+pieces but they're really open to little
+
+ align:start position:0%
+pieces but they're really open to little
+ 
+
+ align:start position:0%
+pieces but they're really open to little
+pieces there's so many in here one of
+
+ align:start position:0%
+pieces there's so many in here one of
+ 
+
+ align:start position:0%
+pieces there's so many in here one of
+the articles in here is called socially
+
+ align:start position:0%
+the articles in here is called socially
+ 
+
+ align:start position:0%
+the articles in here is called socially
+engaged art education practices
+
+ align:start position:0%
+engaged art education practices
+ 
+
+ align:start position:0%
+engaged art education practices
+processes and possibilities and it's
+
+ align:start position:0%
+processes and possibilities and it's
+ 
+
+ align:start position:0%
+processes and possibilities and it's
+about ceramic water filters public
+
+ align:start position:0%
+about ceramic water filters public
+ 
+
+ align:start position:0%
+about ceramic water filters public
+performance socially engaged art and I
+
+ align:start position:0%
+performance socially engaged art and I
+ 
+
+ align:start position:0%
+performance socially engaged art and I
+co-authored this with two colleagues
+
+ align:start position:0%
+co-authored this with two colleagues
+ 
+
+ align:start position:0%
+co-authored this with two colleagues
+Ross Ross Schlemmer who is a professor
+
+ align:start position:0%
+Ross Ross Schlemmer who is a professor
+ 
+
+ align:start position:0%
+Ross Ross Schlemmer who is a professor
+of art education in southern Connecticut
+
+ align:start position:0%
+of art education in southern Connecticut
+ 
+
+ align:start position:0%
+of art education in southern Connecticut
+and Ericka Hitchcock who is a high
+
+ align:start position:0%
+and Ericka Hitchcock who is a high
+ 
+
+ align:start position:0%
+and Ericka Hitchcock who is a high
+school art teacher in Virginia Beach and
+
+ align:start position:0%
+school art teacher in Virginia Beach and
+ 
+
+ align:start position:0%
+school art teacher in Virginia Beach and
+so the three of us put our voices
+
+ align:start position:0%
+so the three of us put our voices
+ 
+
+ align:start position:0%
+so the three of us put our voices
+together to talk about our experiences
+
+ align:start position:0%
+together to talk about our experiences
+ 
+
+ align:start position:0%
+together to talk about our experiences
+here the other piece that I want to
+
+ align:start position:0%
+here the other piece that I want to
+ 
+
+ align:start position:0%
+here the other piece that I want to
+share with you it was was one that was
+
+ align:start position:0%
+share with you it was was one that was
+ 
+
+ align:start position:0%
+share with you it was was one that was
+written by
+
+ align:start position:0%
+written by
+ 
+
+ align:start position:0%
+written by
+three art educators at Maryland
+
+ align:start position:0%
+three art educators at Maryland
+ 
+
+ align:start position:0%
+three art educators at Maryland
+Institute College of Art in Baltimore
+
+ align:start position:0%
+Institute College of Art in Baltimore
+ 
+
+ align:start position:0%
+Institute College of Art in Baltimore
+you want to read the opening paragraph
+
+ align:start position:0%
+you want to read the opening paragraph
+ 
+
+ align:start position:0%
+you want to read the opening paragraph
+to you and then another excerpt in them
+
+ align:start position:0%
+to you and then another excerpt in them
+ 
+
+ align:start position:0%
+to you and then another excerpt in them
+we can have a final set of comments
+
+ align:start position:0%
+we can have a final set of comments
+ 
+
+ align:start position:0%
+we can have a final set of comments
+there article is called Baltimore
+
+ align:start position:0%
+there article is called Baltimore
+ 
+
+ align:start position:0%
+there article is called Baltimore
+uprising empowering pedagogy for change
+
+ align:start position:0%
+uprising empowering pedagogy for change
+ 
+
+ align:start position:0%
+uprising empowering pedagogy for change
+and was written by vanessa lopez adrian
+
+ align:start position:0%
+and was written by vanessa lopez adrian
+ 
+
+ align:start position:0%
+and was written by vanessa lopez adrian
+Pereira
+
+ align:start position:0%
+Pereira
+ 
+
+ align:start position:0%
+Pereira
+and Schuyler au the Baltimore uprising
+
+ align:start position:0%
+and Schuyler au the Baltimore uprising
+ 
+
+ align:start position:0%
+and Schuyler au the Baltimore uprising
+was in response to the death of Freddie
+
+ align:start position:0%
+was in response to the death of Freddie
+ 
+
+ align:start position:0%
+was in response to the death of Freddie
+gray
+
+ align:start position:0%
+gray
+ 
+
+ align:start position:0%
+gray
+who was fatally injured in April 2015
+
+ align:start position:0%
+who was fatally injured in April 2015
+ 
+
+ align:start position:0%
+who was fatally injured in April 2015
+while in police custody in Baltimore
+
+ align:start position:0%
+while in police custody in Baltimore
+ 
+
+ align:start position:0%
+while in police custody in Baltimore
+City the first evening of the uprising
+
+ align:start position:0%
+City the first evening of the uprising
+ 
+
+ align:start position:0%
+City the first evening of the uprising
+we were home glued to the television
+
+ align:start position:0%
+we were home glued to the television
+ 
+
+ align:start position:0%
+we were home glued to the television
+communicating with each other and our
+
+ align:start position:0%
+communicating with each other and our
+ 
+
+ align:start position:0%
+communicating with each other and our
+pre-service teachers worried about
+
+ align:start position:0%
+pre-service teachers worried about
+ 
+
+ align:start position:0%
+pre-service teachers worried about
+violent protests that were erupting in
+
+ align:start position:0%
+violent protests that were erupting in
+ 
+
+ align:start position:0%
+violent protests that were erupting in
+parts of the city that's one of those
+
+ align:start position:0%
+parts of the city that's one of those
+ 
+
+ align:start position:0%
+parts of the city that's one of those
+moments within your own community that
+
+ align:start position:0%
+moments within your own community that
+ 
+
+ align:start position:0%
+moments within your own community that
+changes the community certainly now
+
+ align:start position:0%
+changes the community certainly now
+ 
+
+ align:start position:0%
+changes the community certainly now
+Freddie Gray's name is is well known and
+
+ align:start position:0%
+Freddie Gray's name is is well known and
+ 
+
+ align:start position:0%
+Freddie Gray's name is is well known and
+so these three art education professors
+
+ align:start position:0%
+so these three art education professors
+ 
+
+ align:start position:0%
+so these three art education professors
+who were working with pre-service
+
+ align:start position:0%
+who were working with pre-service
+ 
+
+ align:start position:0%
+who were working with pre-service
+teachers we're faced with this real-life
+
+ align:start position:0%
+teachers we're faced with this real-life
+ 
+
+ align:start position:0%
+teachers we're faced with this real-life
+situation and what is our
+
+ align:start position:0%
+situation and what is our
+ 
+
+ align:start position:0%
+situation and what is our
+responsibilities aren't educators as
+
+ align:start position:0%
+responsibilities aren't educators as
+ 
+
+ align:start position:0%
+responsibilities aren't educators as
+artists as teachers as citizens within
+
+ align:start position:0%
+artists as teachers as citizens within
+ 
+
+ align:start position:0%
+artists as teachers as citizens within
+this community to prepare our teachers
+
+ align:start position:0%
+this community to prepare our teachers
+ 
+
+ align:start position:0%
+this community to prepare our teachers
+to to to face these issues in these
+
+ align:start position:0%
+to to to face these issues in these
+ 
+
+ align:start position:0%
+to to to face these issues in these
+situations and how do we do so
+
+ align:start position:0%
+situations and how do we do so
+ 
+
+ align:start position:0%
+situations and how do we do so
+responsibly not only as community
+
+ align:start position:0%
+responsibly not only as community
+ 
+
+ align:start position:0%
+responsibly not only as community
+members and related to them so these
+
+ align:start position:0%
+members and related to them so these
+ 
+
+ align:start position:0%
+members and related to them so these
+teachers as our students but knowing
+
+ align:start position:0%
+teachers as our students but knowing
+ 
+
+ align:start position:0%
+teachers as our students but knowing
+that these folks are going to become
+
+ align:start position:0%
+that these folks are going to become
+ 
+
+ align:start position:0%
+that these folks are going to become
+teachers who might face similar
+
+ align:start position:0%
+teachers who might face similar
+ 
+
+ align:start position:0%
+teachers who might face similar
+situations they constructed a pedagogy
+
+ align:start position:0%
+situations they constructed a pedagogy
+ 
+
+ align:start position:0%
+situations they constructed a pedagogy
+they call it a pedagogy for change
+
+ align:start position:0%
+they call it a pedagogy for change
+ 
+
+ align:start position:0%
+they call it a pedagogy for change
+framework I just want to read briefly
+
+ align:start position:0%
+framework I just want to read briefly
+ 
+
+ align:start position:0%
+framework I just want to read briefly
+what they wrote and then and then open
+
+ align:start position:0%
+what they wrote and then and then open
+ 
+
+ align:start position:0%
+what they wrote and then and then open
+up because I think this piece speak goes
+
+ align:start position:0%
+up because I think this piece speak goes
+ 
+
+ align:start position:0%
+up because I think this piece speak goes
+to the heart of what this theme for this
+
+ align:start position:0%
+to the heart of what this theme for this
+ 
+
+ align:start position:0%
+to the heart of what this theme for this
+week has been dealing with difficult
+
+ align:start position:0%
+week has been dealing with difficult
+ 
+
+ align:start position:0%
+week has been dealing with difficult
+situations and challenging social
+
+ align:start position:0%
+situations and challenging social
+ 
+
+ align:start position:0%
+situations and challenging social
+constructs primarily in this case police
+
+ align:start position:0%
+constructs primarily in this case police
+ 
+
+ align:start position:0%
+constructs primarily in this case police
+brutality there's elements of white
+
+ align:start position:0%
+brutality there's elements of white
+ 
+
+ align:start position:0%
+brutality there's elements of white
+supremacy and racism that flowed
+
+ align:start position:0%
+supremacy and racism that flowed
+ 
+
+ align:start position:0%
+supremacy and racism that flowed
+throughout as well they said we if we
+
+ align:start position:0%
+throughout as well they said we if we
+ 
+
+ align:start position:0%
+throughout as well they said we if we
+alongside our pre-service teachers
+
+ align:start position:0%
+alongside our pre-service teachers
+ 
+
+ align:start position:0%
+alongside our pre-service teachers
+engage with self as the
+
+ align:start position:0%
+engage with self as the
+ 
+
+ align:start position:0%
+engage with self as the
+first piece so there's four components
+
+ align:start position:0%
+first piece so there's four components
+ 
+
+ align:start position:0%
+first piece so there's four components
+ourself to understand the intersections
+
+ align:start position:0%
+ourself to understand the intersections
+ 
+
+ align:start position:0%
+ourself to understand the intersections
+of identities from our lived experiences
+
+ align:start position:0%
+of identities from our lived experiences
+ 
+
+ align:start position:0%
+of identities from our lived experiences
+examine through the lens of the
+
+ align:start position:0%
+examine through the lens of the
+ 
+
+ align:start position:0%
+examine through the lens of the
+historical context of established social
+
+ align:start position:0%
+historical context of established social
+ 
+
+ align:start position:0%
+historical context of established social
+injustice 'as in schools and communities
+
+ align:start position:0%
+injustice 'as in schools and communities
+ 
+
+ align:start position:0%
+injustice 'as in schools and communities
+context being the second then we have an
+
+ align:start position:0%
+context being the second then we have an
+ 
+
+ align:start position:0%
+context being the second then we have an
+informed understanding of these
+
+ align:start position:0%
+informed understanding of these
+ 
+
+ align:start position:0%
+informed understanding of these
+complexities that three students
+
+ align:start position:0%
+complexities that three students
+ 
+
+ align:start position:0%
+complexities that three students
+contribute to the cultural assets of
+
+ align:start position:0%
+contribute to the cultural assets of
+ 
+
+ align:start position:0%
+contribute to the cultural assets of
+every classroom with the goal of
+
+ align:start position:0%
+every classroom with the goal of
+ 
+
+ align:start position:0%
+every classroom with the goal of
+developing a critical for pedagogy for
+
+ align:start position:0%
+developing a critical for pedagogy for
+ 
+
+ align:start position:0%
+developing a critical for pedagogy for
+effecting change
+
+ align:start position:0%
+effecting change
+ 
+
+ align:start position:0%
+effecting change
+we're Dean necessary so the combination
+
+ align:start position:0%
+we're Dean necessary so the combination
+ 
+
+ align:start position:0%
+we're Dean necessary so the combination
+of self not only teachers but also the
+
+ align:start position:0%
+of self not only teachers but also the
+ 
+
+ align:start position:0%
+of self not only teachers but also the
+selves of the students we need to
+
+ align:start position:0%
+selves of the students we need to
+ 
+
+ align:start position:0%
+selves of the students we need to
+understanding of the context social
+
+ align:start position:0%
+understanding of the context social
+ 
+
+ align:start position:0%
+understanding of the context social
+cultural political locational and
+
+ align:start position:0%
+cultural political locational and
+ 
+
+ align:start position:0%
+cultural political locational and
+bringing the students in there as
+
+ align:start position:0%
+bringing the students in there as
+ 
+
+ align:start position:0%
+bringing the students in there as
+cultural assets within the conversation
+
+ align:start position:0%
+cultural assets within the conversation
+ 
+
+ align:start position:0%
+cultural assets within the conversation
+perhaps a formula the pedagogy emerges
+
+ align:start position:0%
+perhaps a formula the pedagogy emerges
+ 
+
+ align:start position:0%
+perhaps a formula the pedagogy emerges
+from that that formula I think it's a
+
+ align:start position:0%
+from that that formula I think it's a
+ 
+
+ align:start position:0%
+from that that formula I think it's a
+brilliant piece and then they walk
+
+ align:start position:0%
+brilliant piece and then they walk
+ 
+
+ align:start position:0%
+brilliant piece and then they walk
+through each of those components for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/KJheruCbwHU.txt b/KJheruCbwHU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..da2a3d4b65f2459b650f1c010f20282b6a70b7b4
--- /dev/null
+++ b/KJheruCbwHU.txt
@@ -0,0 +1,1630 @@
+PROFESSOR: Any questions about
+where we left off-- up to
+
+where we left off?
+
+OK, what I'll do then is give
+you a few more examples of the
+
+combinations in 22 to show which
+ones we have to retain
+
+as frameworks for
+crystallographic point groups
+
+and which ones exist as groups
+but which involve rotational
+
+symmetries that are not
+permitted to a lattice.
+
+So we've seen a combination of
+three orthogonal twofold axes
+
+and then projection that
+would look like this.
+
+And the international symbol for
+that point group is just a
+
+running list of the different
+axes that are present, 222.
+
+The next group in the sequence
+would be 3 2 2, where we took
+
+a 120 degree rotation.
+
+We combine that with a twofold
+axis perpendicular to it and
+
+the new twofold axis comes out
+and reminds you again of
+
+things that are quite clear but
+which are easy to forget--
+
+that this angle here is
+1/2 of 2 pi over 3.
+
+Don't forget that 1/2.
+
+So the neighboring twofold axis
+is 60 degrees away and
+
+then if we allow these axes to
+operate on each other, the net
+
+symmetry consistent set of
+axes looks like this.
+
+But let us look at a solid
+that has this symmetry.
+
+And such a solid would
+be a trigonal--
+
+triangular prism.
+
+And again we can use the corners
+of this polyhedron as
+
+the reference locations
+of our motifs.
+
+So let us put a first motif
+here, number 1.
+
+Let's rotate it by 120 degrees
+to get a second motif here.
+
+And then let us rotate that
+one down by a twofold axis
+
+coming out of one
+of the edges.
+
+That will give us number 3 that
+is down here or of the
+
+same chirality.
+
+And how do we get from 1 to
+3 directly in one shot?
+
+And the answer is about a
+twofold axis that comes out of
+
+the face of the prism.
+
+So again the prism that we've
+used as our reference is a
+
+prism that looks like this.
+
+We've got one twofold axis
+coming out of the face.
+
+The next twofold axis is the
+one that is equivalent to a
+
+threefold rotation followed
+by a twofold rotation.
+
+Now here we hit a situation in
+deciding on the name for the
+
+combination that is analogous
+to what we found in
+
+two-dimensional plane
+groups for 3mm.
+
+We saw that only one mirror
+plane was distinct.
+
+We look at this arrangement
+of axes--
+
+this was axis a, alpha,
+this was axis b, beta.
+
+But if I repeat one of these
+twofold axes by 120 degree
+
+rotations, this one is the
+opposite end of this one, this
+
+one is the opposite end of this
+one, and this one is the
+
+opposite end of this one.
+
+So there are only three kinds
+of-- there are three, twofold
+
+axes and they are related by
+the 120 degree rotation.
+
+Another way of saying that is
+that if we look at a trigonal
+
+prism, each of the twofold axes
+comes out of an edge and
+
+out of the opposite face.
+
+So there they all do the same
+thing in this regular prism--
+
+twofold axes extend between
+corners of the opposite face.
+
+So there are only--
+
+there's only one kind of twofold
+axis present in terms
+
+of being symmetry independent.
+
+So just as we called 3mm, 3m,
+and we call this one 3 2
+
+because all the twofold axes
+are symmetry equivalent.
+
+The next one that is
+crystallographic would be a
+
+combination of a 90 degree
+rotation with a pair of
+
+twofold axes that are normal to
+it and separated by 1/2 of
+
+pi over 2, the [? throw ?]
+of a fourfold axis.
+
+And the symbol for this one
+would be a fourfold and now
+
+there are two different
+kinds of twofold axes.
+
+And if we look at a regular
+square prism, we can again
+
+show that what we've been
+demonstrating for these other
+
+prisms is true.
+
+One twofold axis would come
+out of the face, the other
+
+twofold axis would come out of
+the midpoint of an edge, and
+
+the fourfold axis would
+come up here.
+
+And a 90 degree rotation, from
+here to here, followed by a
+
+twofold rotation about this
+axis, gives us as a net
+
+effect a 1, 2, 3.
+
+And that rotation from 1 to 3
+about this twofold axis gives
+
+us the combined mappings.
+
+Notice that the order in which
+we do them is unimportant.
+
+For example we could do the
+same thing but do two 180
+
+degree rotations about
+the twofold axes.
+
+Let's say we start by doing
+a rotation about
+
+this twofold axis.
+
+From here down to here.
+
+And then we do a twofold
+axis about the--
+
+twofold axis that comes out the
+face and that would take
+
+number 2, and rotate
+it up to number 3.
+
+And the way we get from 1 to 3
+directly is by a rotation of C
+
+pi over 2 about the square
+face of the prism.
+
+So do them in any
+order you like--
+
+two 180 degree rotations, or a
+90 degree rotation, one of the
+
+two full rotations with 90
+is the other twofold--
+
+the other type of
+twofold axis.
+
+The 90 degree rotation plus the
+second type of the twofold
+
+axis is the same as the first.
+
+So the result can be permuted
+and turns out to be the same
+
+combination.
+
+The next one that we would hit
+if we proceed systematically
+
+is non-crystallographic.
+
+And this would be
+a fivefold axis.
+
+And I'm foolhardy to even start
+trying to sketch this in
+
+three dimensions.
+
+Nevertheless, nothing ventured,
+nothing gained.
+
+Start with a twofold axis out of
+one of the edges and rotate
+
+from 1 down to 2.
+
+Follow that by a twofold
+rotation about the twofold
+
+axis that comes out
+of the face.
+
+And that gives us one number 3
+up here, and lo and behold,
+
+the way you get from 1 to 3
+directly is by a rotation
+
+through 1/5 of 2 pi.
+
+So this would be the
+non-crystallographic point
+
+group, 5- well it's not
+going to be 5 2 2.
+
+And that has a whole bunch
+of twofold axes separated
+
+by 1/10 of 2 pi.
+
+And just as in 3 2, twofold axes
+here all come out of the
+
+face and out of the
+opposite edge.
+
+So this would be called 522.
+
+A nice symmetry but not
+crystallographic, so we can
+
+promptly forget about.
+
+So what comes out of this is a
+family of groups that are all
+
+of the form n 2 2.
+
+The crystallographic ones are
+222, 32, 422 which we've
+
+looked at in detail, and one
+that I won't draw because
+
+there's so much symmetry
+it get's messy.
+
+This is 622.
+
+There is a Schoenflies
+notation.
+
+You remember the language that
+we encountered for our two
+
+dimensional point groups.
+
+We used m for mirror in the
+international notation.
+
+We used C standing for cyclic
+group, subscript s standing
+
+for Spiegel in the Schoenflies
+notation.
+
+The Schoenflies notation for all
+of this family of symmetry
+
+is Dn, and the D stands
+for dihedral.
+
+And the reason for that name is
+that the difference between
+
+all of these groups, besides the
+n-fold axis, is this angle
+
+between adjacent twofolds and
+this is a dihedral angle.
+
+I have a set of planes passing
+through a common axis; the
+
+angle between those planes is
+termed a dihedral angle.
+
+So this is called D for dihedral
+and then a subscript
+
+that gives the rank
+of the axis.
+
+So Dn generically.
+
+This is D2, this is D3, this
+is D4, and this is D6.
+
+Comments or debate?
+
+Yes, sir.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: [INAUDIBLE]
+
+--out of this face.
+
+So I got from here down to the
+diametrically opposed axis.
+
+And I rotate it about the
+adjacent one which comes out
+
+of an edge and--
+
+what did I do here.
+
+Here I did A pi over 2 from 1
+to 2, and then I did B pi,
+
+where this is B pi, and they
+turned out to be C pi, which
+
+is this one here.
+
+So going from here to here down
+to number 3 is the same
+
+as going from 1 to 3 in one
+shot about a twofold axis
+
+normal to the face.
+
+And actually I'm courageous
+to try to do this in three
+
+dimensions.
+
+We could do it in projection
+and then things are used--
+
+this for a point that's up,
+and use this for a point
+
+that's down.
+
+And then what we've done is to
+go from 1 that's up, to 2
+
+that's up, and then we rotate
+it about this twofold axis.
+
+That was 3, that's down.
+
+So when we get into complicated
+symmetries where
+
+you just can't do a proper
+job drawing them in an
+
+orthographic drawing, we'll do
+them in projection and use a
+
+solid dot for something that's
+up and an open circle for
+
+something that's down.
+
+Is there any other way we
+can combine things?
+
+Well what you would have to do
+is use these three relations,
+
+and plug and chug your way
+through all of the
+
+combinations which were
+enumerated in the handout.
+
+And I'll save ourselves a lot
+of work by saying that there
+
+are only two more
+combinations.
+
+And these are combinations of
+axes at angles that have
+
+relevance to directions
+in a cube.
+
+One of them is a twofold axis
+with a threefold axis with a
+
+threefold rotation.
+
+Again remember these are not
+
+equations in symmetry elements.
+
+This is really A pi, combined
+with B 2 pi over 3, combined
+
+with C 2 pi over 3.
+
+And the angles that fall out of
+this are all crazy things
+
+like 109 point something degrees
+and they make no sense
+
+whatsoever.
+
+They're not nice things like
+some multiples of 2 pi, 90
+
+degrees or 120 degrees.
+
+And they make no sense at all
+until you refer them to
+
+directions in a cube.
+
+And this one, 2 3 3, consists
+of a twofold axis coming out
+
+of the face of the cube, a 120
+degree rotation, so this is B
+
+2 pi over 3, this is A pi.
+
+And the other one, C2 pi over 3,
+corresponds to a threefold
+
+axis coming out of another
+body diagonal.
+
+I don't know if I want to be
+gutsy enough to try to
+
+illustrate that that
+really works.
+
+But one thing that we should do
+is to let these axes go to
+
+work on one another, and
+see what comes out.
+
+First thing we can say is that
+this threefold axis--
+
+if we extend it, it comes
+out of the bottom
+
+diagonal of the cube.
+
+This one, if we extend it, will
+come out of this diagonal
+
+of the cube.
+
+So there's a threefold here,
+and a threefold here.
+
+The twofold axis gives us a
+threefold axis that will come
+
+down this way.
+
+So there's a threefold axis
+here and a threefold axis
+
+coming out here.
+
+And then the twofold axis will
+rotate this threefold axis
+
+over to the remaining
+pair of corners.
+
+So we have created this by
+looking at a twofold rotation,
+
+combined with the threefold
+axis, combined with the
+
+rotation of another
+threefold axis.
+
+But in point of fact, if you let
+the twofold axis operate
+
+on the threefold axis coming out
+of one body diagonal, you
+
+get threefold axes
+automatically
+
+out of all body diagonals.
+
+So this is given the
+international symbol 2 3,
+
+because if you start with one
+twofold axis out of a face
+
+normal and one threefold
+axis out of--
+
+along a body diagonal, the
+twofold axis, acting on that
+
+threefold axis gives you one
+along every body diagonal.
+
+And the threefold axis--
+
+let me point out that a cube
+standing up on its body
+
+diagonal, with a threefold axis
+coming out here and these
+
+faces sloping down into
+the blackboard.
+
+If I have a twofold axis coming
+out of one face, the
+
+threefold axis puts a twofold
+axis on this face and rotates
+
+again 120 degrees and puts a
+twofold axis on this face.
+
+So the threefold axis relates
+all twofold axes coming out
+
+normal to the cubed face.
+
+And they were really just two
+independent axes in this
+
+combination.
+
+So 2 3 is the international
+symbol-- one kind of twofold
+
+axis, one kind of
+threefold axis--
+
+inclined at these crazy angles
+that are in a cube.
+
+The Schoenflies notation for
+this is T, and that stands for
+
+tetrahedron.
+
+And let me try to convince
+you that if I look at a
+
+tetrahedron, that that is the
+arrangement of pure rotation
+
+axes in a tetrahedron.
+
+And the way to show a
+tetrahedron is to
+
+inscribe it in a cube.
+
+So if I connect these two faces
+together and these two
+
+faces together, that will define
+for me a solid that has
+
+four triangular faces.
+
+Easier to recognize it when
+we put it up on one face.
+
+So this is a tetrahedron.
+
+Schoenflies symbol is T. And I
+love to get to this part of
+
+the semester and be at this
+point at the end of the hour,
+
+because if I draw a
+stereographic projection of
+
+the twofold axes, in this
+symmetry, I can take a couple
+
+of more twofold axes and add it
+to this combination which
+
+destroys the group.
+
+But lets me wish everybody a
+happy Halloween and exit to a
+
+stunned silence at the
+end of the hour.
+
+So this is a nice point
+group for October.
+
+There is one more and that is
+the highest symmetry of all.
+
+And this is a combination
+of a rotation--
+
+A pi over 2, a 90 degree
+rotation, with a rotation B 2
+
+pi over 3, rotation through one
+third of the circle, and
+
+the rotation C pi.
+
+And the directions between the
+axes that come out there don't
+
+come out some multiples
+of 2 pi.
+
+Again they are crazy angles
+that make no sense at all
+
+unless you refer them
+to directions
+
+that occur in a cube.
+
+The fourfold axis is in the
+direction that corresponds to
+
+the normal to a face.
+
+The twofold axis corresponds
+to a direction out
+
+of one of the edges.
+
+And the threefold axis
+corresponds to a direction
+
+that is a body diagonal.
+
+So again this is a mess.
+
+If we let those axes work on one
+another however, we will
+
+produce, more readily
+appreciated in a stereographic
+
+projection, fourfold axes along
+the directions that
+
+correspond to face normal.
+
+So the cube, threefold axes
+coming out of the body
+
+diagonals and twofold axes in
+between all of the fourfold
+
+axes in directions that
+correspond to the lines from
+
+the center of the cube out
+through the edges.
+
+So this is a group which
+would be called 4 3 2.
+
+There's one kind of fourfold
+axis related to all the others
+
+by the other rotation axes
+that are present.
+
+One kind of threefold axis that
+is related to all of the
+
+other threefold axes along the
+body diagonal by other
+
+rotation axes that
+are present.
+
+And twofold axes, one kind, all
+coming out of the edges.
+
+So this is the group that, in
+international tables, is
+
+called 4 3 2.
+
+And the Schoenflies notation,
+this is called O. And that is
+
+the general reaction when one
+sees this lovely combination.
+
+You go ooh and O is
+what it's called.
+
+But the O doesn't stand for
+a gasp, it stands for an
+
+octahedral.
+
+This is the symmetry
+of an octahedron--
+
+rotational symmetry
+of an octahedron.
+
+So that's it.
+
+That is the bestiary of ways
+in which you can combine
+
+crystallographic rotation axes
+in space about a fixed point
+
+of intersection.
+
+And there are eleven of them.
+
+There are the axes
+by themselves--
+
+1, 2, 3, 4, and 6.
+
+There are the dihedral groups,
+222, 32, 422, and 622..
+
+And then the two cubic groups,
+T and O. In the international
+
+notation, I'm mixing
+metaphors.
+
+These are 23 and 432.
+
+I call to your attention the
+insidious similarity of the
+
+two combinations of
+axes, 32 and 23.
+
+When the 3 comes first, this
+is a group of the form n22.
+
+When the 2 comes first, that
+is the tetrahedral group.
+
+So if you count them all up,
+there are 4, 2 is 6, and 5.
+
+There are eleven axial
+combinations.
+
+Quite a few more than the
+situation in two dimensions
+
+where we just had single
+rotation axes 1, 2, 3, 4, 6.
+
+Now we have those as in two
+dimensions but the dihedral
+
+groups and the two cubic
+arrangements of axes as well.
+
+So we don't have to stretch our
+vocabulary too much more
+
+to be all inclusive here.
+
+OK, comments?
+
+Takes your breath away,
+doesn't it?
+
+All right, let me indicate
+the next step in outline.
+
+What we will next do is
+introduce our remaining two
+
+symmetry operations
+into the picture.
+
+We have the eleven axial
+combinations.
+
+As I said, we can regard these
+as a framework that we can
+
+decorate with mirror planes and
+or the inversion center,
+
+which has not appeared until
+this point because inversion
+
+is inherently a three
+dimensional transformation.
+
+So what we're going to do
+is to take these axial
+
+combinations and add
+another symmetry
+
+operation to the group.
+
+And this as--
+
+we used the term earlier,
+this is an extender.
+
+We have something that
+constitutes a group by itself
+
+then we muck things up by adding
+another operation.
+
+Remember in all of this we are
+combining operations, not
+
+symmetry elements.
+
+So we'll take an axial
+combination and add the
+
+reflection sigma, a reflection
+operation sigma.
+
+Or take a rotation and combine
+it with the operation of
+
+inversion as an extender.
+
+So let's itemize the sorts of
+extenders we should consider.
+
+And the ground rules are that
+the extender should leave the
+
+arrangement of rotation
+axes invariant.
+
+Because if it doesn't, we are
+going to create a rotation
+
+operation that does not conform
+to the constraints
+
+that we used in Euler's
+construction.
+
+So for example, if we take
+222, which contains the
+
+operations A pi, B pi,
+C pi and identity,
+
+that's the group 222.
+
+If we would add to the
+arrangement 222 a mirror plane
+
+that snaked through some
+arbitrary fashion like this,
+
+that mirror plane is going to
+reproduce the twofold axis
+
+over to here.
+
+And that is either going to not
+constitute a group because
+
+this twofold, this twofold, and
+this twofold don't conform
+
+to Euler's construction.
+
+Or alternatively, if we put it
+in carefully at 45 degrees
+
+with this twofold axis, we're
+going to get twofold axes that
+
+are 45 degrees apart and that's
+going to change this
+
+into a fourfold axis.
+
+So if the addition of a mirror
+plane does not leave the
+
+arrangement of rotation axes--
+
+rotation operations--
+
+invariant, we're either going
+to get something that's
+
+impossible and does not
+constitute a group.
+
+Or else we're going to get
+a combination of rotation
+
+operations of higher symmetry
+which we've already found
+
+because we went through that
+process of combination using
+
+Euler's construction in
+an exhaustive fashion.
+
+So the rule then is that if we
+add the reflection operation
+
+sigma, then the arrangement of
+rotation operations must be
+
+left invariant.
+
+OK let's look at the
+single axes.
+
+If there's an n-fold axis, the
+ways we can add a reflection
+
+operation to that axis is to
+pass the reflection operation
+
+through the axis.
+
+And this is going to look very
+much like the two dimensional
+
+point groups of the form nmm
+except that rather than having
+
+a mirror line, imagine the
+whole works as extending
+
+upwards along the rotation
+axis and space.
+
+So this extender is called
+a vertical mirror plane.
+
+The other way we could add a
+mirror plane to an n-fold
+
+rotation axis is to put the
+mirror plane in an orientation
+
+that's perpendicular to
+the rotation axis.
+
+That didn't exist in two
+dimensions because that plane
+
+that's perpendicular
+to the axis is the
+
+plane of our paper.
+
+And unless we wanted to have a
+two-sided group that was on
+
+both the top of the paper and
+the bottom of the paper, and
+
+we make up the rules since
+it's our ball game.
+
+And that could be a group and
+these would be the two-sided
+
+plane groups, a plane
+point groups, but we
+
+didn't do that here.
+
+Adding the mirror plane, the
+reflection operation sigma, in
+
+a fashion that is normal to the
+rotation operation, A 2 pi
+
+over n, is another distinct
+combination.
+
+And this is called, very
+descriptively a horizontal
+
+mirror plane.
+
+That looks like about all you
+can do except for the cases
+
+where we have more than one kind
+of rotation axis present.
+
+So let me use 422
+as an example.
+
+We could add a horizontal mirror
+plane perpendicular to
+
+the principal axis of symmetry,
+and that would be
+
+the horizontal sigma.
+
+We could add a vertical
+mirror plane.
+
+And now there are two
+ways we can do it.
+
+We could put the mirror plane,
+the operation sigma, through
+
+the fourfold axis and in a
+fashion that was perpendicular
+
+to the twofold axis.
+
+And we will retain the
+term of vertical
+
+sigma for that addition.
+
+But the other thing that we
+could do would be to put the
+
+reflection operation interleaved
+between the
+
+twofold axes.
+
+That's going to take this one
+and flip it into this one,
+
+this one flip it into this
+one, flip these back and
+
+forth, and that doesn't create
+any new reflection.
+
+And this is referred to as a
+diagonal reflection plane.
+
+Diagonal to what?
+
+Diagonally interleaved between
+the twofold axes.
+
+And these are distinct additions
+and they will lead
+
+to different groups.
+
+In as far as addition of
+reflection operations is
+
+concerned, that's about all
+we can do that's distinct.
+
+And notice that this is
+for the groups Dn, and
+
+tetrahedral, and octahedral
+only.
+
+The distinction here
+is not defined for
+
+just a single axis.
+
+So there are three possible
+extenders here-- a vertical
+
+mirror plane, a horizontal
+mirror plane, a diagonal
+
+mirror plane, added to each of
+the eleven arrangements of
+
+rotation axes.
+
+And then the final extender
+that we could
+
+add is to add inversion.
+
+And the symbol for the inversion
+operation is 1 bar.
+
+And obviously if one point in
+space is going to be left
+
+invariant, you either add this
+on a single axis, and that is
+
+what you'd have to do for the
+groups Cn, or at the point of
+
+intersection.
+
+And that would be the case if
+more than one axis, and that's
+
+the groups of the form n22, T,
+
+and O. That's it.
+
+That's the job.
+
+So we should consider each of
+these possible additions of an
+
+extender systematically.
+
+I don't propose to do every
+single one independently.
+
+If we do a couple, you'll
+get the general idea.
+
+And I think because I have an
+honest face, and you've come
+
+to trust me, I can just describe
+the remaining results
+
+to you and we won't grind
+through every single one.
+
+Now the enormity of what I've
+proposed becomes apparent when
+
+I say that we now are going to
+have need of a number of
+
+different--
+
+what I call combination
+theorems, that let us complete
+
+the group multiplication
+table.
+
+And deduce, as a consequence,
+which symmetry operations must
+
+come into being because
+of these additions.
+
+So we'll want to know what
+happens when you add a
+
+vertical sigma to a rotation
+operation, A 2 pi over n.
+
+We'll want to know what
+happens when you add a
+
+horizontal sigma to a rotation
+operation, A 2 pi over n.
+
+And we're going to want to know
+what happens when you add
+
+a diagonal mirror plane, this
+really is a special case of
+
+the vertical mirror plane.
+
+And we'll want to know what
+happens when you add an
+
+inversion center to
+a rotation axis.
+
+So let me do a few of these
+and then next time we can
+
+start off and start driving
+the three dimensional
+
+symmetries.
+
+So let's just repeat the ones
+that we've already done.
+
+We said that if we have a
+rotation operation A alpha,
+
+and we put a reflection plane
+through it, that A alpha
+
+followed by a reflection plane
+passing through it-- let me
+
+call this sigma V-- because
+this is the so-called
+
+vertical, up orientation.
+
+We've already seen that
+in two dimensions.
+
+This is a vertical mirror plane,
+sigma prime, that is
+
+going to be alpha over 2
+away from the first.
+
+So that is something that we've
+already seen in it's
+
+entirety in the two dimensional
+point groups.
+
+There was m sigma, there was
+2mm, and that was C2V, 3m,
+
+that's C3V, 4mm, and that was
+C6V, and 6mm, and that's C4V,
+
+and that's C6V.
+
+So that is the result that we
+obtained for two dimensions.
+
+And you can see now the reason
+for distinguishing the mirror
+
+plane by saying it is a vertical
+mirror plane because
+
+this is in the three
+dimensional sense.
+
+It's vertical parallel to and
+passing through the rotation
+
+axis-- no longer a rotation
+point but a rotation axis.
+
+So we've got those theorems.
+
+What happens if we take a
+rotation operation, A pi, and
+
+put a horizontal reflection
+operation through it
+
+normal to that axis?
+
+So I'll call this sigma h,
+a horizontal operation.
+
+OK what we have to do is draw
+it out once and for all.
+
+Here's the first one, let's
+say it's right-handed.
+
+We'll rotate by A pi to get
+a second one which stays
+
+right-handed.
+
+And then we'll reflect it down
+in the horizontal mirror plane
+
+to get a third one which
+is left-handed.
+
+And now the question is, how
+is number one related to
+
+number three?
+
+Anybody want to hazard
+a guess?
+
+We've got to go from a
+right-handed one to a
+
+left-handed one.
+
+But these two guys are oriented
+
+anti-parallel to one another.
+
+So how do we relate the first
+one to the third one?
+
+I heard somebody mumble softly
+enough to remain anonymous.
+
+Inversion.
+
+Right.
+
+So as we go along making these
+combinations, if we had not
+
+been bright enough to think of
+the operation of inversion as
+
+a general transformation where
+the sense of all three
+
+coordinates is changed, we
+would have stumbled over
+
+headlong right here.
+
+Combine a rotation operation, A
+pi, with a mirror reflection
+
+that is perpendicular
+to the axis.
+
+The way you get from one to
+three in one shot is by
+
+inversion through a point that
+is at the intersection between
+
+the rotation axis and
+the mirror plane.
+
+So rotation followed by rotation
+in a vertical mirror
+
+plane that's perpendicular to
+the axis is the operation of
+
+inversion at the point
+of intersection.
+
+So again, if we had not been
+clever enough to invent it or
+
+tell you about in advance,
+there it is.
+
+When we start forming the group
+multiplication table, we
+
+would have had to have defined
+this operation to describe
+
+this relation.
+
+AUDIENCE: Is that sigma sub h?
+
+PROFESSOR: Ah yeah.
+
+Let me write that, sigma h.
+
+I thought that V didn't look
+like a V, so I changed it so
+
+it looked like a V but it
+shouldn't be a V. That's a
+
+horizontal mirror plane.
+
+OK this is a new combination and
+if we see what operations
+
+are going to be present in the
+group, we've got the two
+
+operations of the twofold
+axis, 1 and A pi.
+
+And what we have added is
+sigma h as an extender.
+
+So 1 and A pi, this little box
+here is the subgroup that we
+
+know and love as the
+twofold axis.
+
+And then we'll write sigma h
+here and now let's fill in the
+
+group multiplication table.
+
+Doing the identity operation
+twice is identity.
+
+Doing the identity operation
+followed by A pi is A pi.
+
+Identity followed by
+sigma h is sigma h.
+
+Identity followed by A
+pi, sigma h, lets me
+
+fill in those boxes.
+
+Do a rotation twice, that's
+the identity operation.
+
+Do a rotation of A pi and follow
+that by a reflection, A
+
+pi followed by reflection.
+
+This is the inversion
+operation.
+
+And so I should add inversion to
+my list of operations since
+
+it's come up.
+
+So 1 followed by inversion
+is inversion.
+
+A pi followed by inversion is
+the horizontal reflection.
+
+Horizontal reflection
+followed by A pi
+
+is the same as inversion.
+
+Horizontal reflection followed
+by horizontal reflection is
+
+the identity operation--
+
+brings me back to where
+I started from.
+
+And a horizontal reflection
+followed by inversion is the
+
+same as A pi.
+
+So I'll have another object
+down here to complete the
+
+three dimensional arrangement.
+
+And this is the group
+for operations--
+
+A pi, inversion, horizontal
+reflection, and
+
+the identity operation.
+
+So what do we call this one?
+
+The operation A pi plus a
+horizontal reflection
+
+operation gives rise to a group
+that is a twofold axis
+
+of its operations,
+
+perpendicular to a mirror plane.
+
+And this written as a fraction
+means that the 2 is
+
+perpendicular to the mirror
+plane rather than being
+
+parallel and in the plane
+of the mirror plane.
+
+So two codes for writing
+symbols.
+
+A 2 followed on the same line
+by the m means that the m is
+
+parallel to 2.
+
+We know that when we write them
+as a fraction, that will
+
+be our way of designating that
+this mirror plane is
+
+perpendicular to
+a twofold axis.
+
+OK it's the witching hour,
+4 o'clock exactly.
+
+That's when we ought to quit,
+so let's stop there.
\ No newline at end of file
diff --git a/KPF8owESMdo.txt b/KPF8owESMdo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2aa9809b27d3918605dc0b5226e23bd4d6b3a3a6
--- /dev/null
+++ b/KPF8owESMdo.txt
@@ -0,0 +1,923 @@
+align:start position:0%
+ 
+let us now illustrate the linear list
+
+ align:start position:0%
+let us now illustrate the linear list
+ 
+
+ align:start position:0%
+let us now illustrate the linear list
+mean square estimation methodology in
+
+ align:start position:0%
+mean square estimation methodology in
+ 
+
+ align:start position:0%
+mean square estimation methodology in
+the context of an example and we're
+
+ align:start position:0%
+the context of an example and we're
+ 
+
+ align:start position:0%
+the context of an example and we're
+going to revisit our familiar example
+
+ align:start position:0%
+going to revisit our familiar example
+ 
+
+ align:start position:0%
+going to revisit our familiar example
+that we considered earlier in the
+
+ align:start position:0%
+that we considered earlier in the
+ 
+
+ align:start position:0%
+that we considered earlier in the
+context of general least mean squares
+
+ align:start position:0%
+context of general least mean squares
+ 
+
+ align:start position:0%
+context of general least mean squares
+estimation let us remind ourselves what
+
+ align:start position:0%
+estimation let us remind ourselves what
+ 
+
+ align:start position:0%
+estimation let us remind ourselves what
+were the assumptions behind this example
+
+ align:start position:0%
+were the assumptions behind this example
+ 
+
+ align:start position:0%
+were the assumptions behind this example
+there is an unknown random variable that
+
+ align:start position:0%
+there is an unknown random variable that
+ 
+
+ align:start position:0%
+there is an unknown random variable that
+we wish to estimate and that random
+
+ align:start position:0%
+we wish to estimate and that random
+ 
+
+ align:start position:0%
+we wish to estimate and that random
+variable happens to be uniform on a
+
+ align:start position:0%
+variable happens to be uniform on a
+ 
+
+ align:start position:0%
+variable happens to be uniform on a
+range from 4 to 10 what we get to
+
+ align:start position:0%
+range from 4 to 10 what we get to
+ 
+
+ align:start position:0%
+range from 4 to 10 what we get to
+observe is a random variable X which is
+
+ align:start position:0%
+observe is a random variable X which is
+ 
+
+ align:start position:0%
+observe is a random variable X which is
+equal to theta plus or minus something
+
+ align:start position:0%
+equal to theta plus or minus something
+ 
+
+ align:start position:0%
+equal to theta plus or minus something
+so X is theta plus a noise term and that
+
+ align:start position:0%
+so X is theta plus a noise term and that
+ 
+
+ align:start position:0%
+so X is theta plus a noise term and that
+noise term can be anything in the range
+
+ align:start position:0%
+noise term can be anything in the range
+ 
+
+ align:start position:0%
+noise term can be anything in the range
+from minus 1 to plus 1 furthermore the
+
+ align:start position:0%
+from minus 1 to plus 1 furthermore the
+ 
+
+ align:start position:0%
+from minus 1 to plus 1 furthermore the
+distribution of U is this particular
+
+ align:start position:0%
+distribution of U is this particular
+ 
+
+ align:start position:0%
+distribution of U is this particular
+uniform no matter what theta is so theta
+
+ align:start position:0%
+uniform no matter what theta is so theta
+ 
+
+ align:start position:0%
+uniform no matter what theta is so theta
+and you are independent these modeling
+
+ align:start position:0%
+and you are independent these modeling
+ 
+
+ align:start position:0%
+and you are independent these modeling
+assumptions correspond to this picture
+
+ align:start position:0%
+assumptions correspond to this picture
+ 
+
+ align:start position:0%
+assumptions correspond to this picture
+this is the range of X and theta and the
+
+ align:start position:0%
+this is the range of X and theta and the
+ 
+
+ align:start position:0%
+this is the range of X and theta and the
+Joint Distribution of X and theta
+
+ align:start position:0%
+Joint Distribution of X and theta
+ 
+
+ align:start position:0%
+Joint Distribution of X and theta
+happens to be a uniform distribution on
+
+ align:start position:0%
+happens to be a uniform distribution on
+ 
+
+ align:start position:0%
+happens to be a uniform distribution on
+this particular shape however we're not
+
+ align:start position:0%
+this particular shape however we're not
+ 
+
+ align:start position:0%
+this particular shape however we're not
+really going to use this picture other
+
+ align:start position:0%
+really going to use this picture other
+ 
+
+ align:start position:0%
+really going to use this picture other
+than for illustration purposes you could
+
+ align:start position:0%
+than for illustration purposes you could
+ 
+
+ align:start position:0%
+than for illustration purposes you could
+take just this as the formulation of the
+
+ align:start position:0%
+take just this as the formulation of the
+ 
+
+ align:start position:0%
+take just this as the formulation of the
+problem that were interested in so now
+
+ align:start position:0%
+problem that were interested in so now
+ 
+
+ align:start position:0%
+problem that were interested in so now
+to develop the form of the optimal
+
+ align:start position:0%
+to develop the form of the optimal
+ 
+
+ align:start position:0%
+to develop the form of the optimal
+linear estimator all we need to do is to
+
+ align:start position:0%
+linear estimator all we need to do is to
+ 
+
+ align:start position:0%
+linear estimator all we need to do is to
+determine the various constants that
+
+ align:start position:0%
+determine the various constants that
+ 
+
+ align:start position:0%
+determine the various constants that
+show up so let's start with expectations
+
+ align:start position:0%
+show up so let's start with expectations
+ 
+
+ align:start position:0%
+show up so let's start with expectations
+theta is uniform from 4 to 10 therefore
+
+ align:start position:0%
+theta is uniform from 4 to 10 therefore
+ 
+
+ align:start position:0%
+theta is uniform from 4 to 10 therefore
+the expected value is the midpoint which
+
+ align:start position:0%
+the expected value is the midpoint which
+ 
+
+ align:start position:0%
+the expected value is the midpoint which
+is equal to 7 u has a symmetric
+
+ align:start position:0%
+is equal to 7 u has a symmetric
+ 
+
+ align:start position:0%
+is equal to 7 u has a symmetric
+distribution around 0 so it's expected
+
+ align:start position:0%
+distribution around 0 so it's expected
+ 
+
+ align:start position:0%
+distribution around 0 so it's expected
+value is it going to be equal to 0
+
+ align:start position:0%
+value is it going to be equal to 0
+ 
+
+ align:start position:0%
+value is it going to be equal to 0
+X is the sum of theta and u therefore
+
+ align:start position:0%
+X is the sum of theta and u therefore
+ 
+
+ align:start position:0%
+X is the sum of theta and u therefore
+its expected value is the sum of these
+
+ align:start position:0%
+its expected value is the sum of these
+ 
+
+ align:start position:0%
+its expected value is the sum of these
+two expected values and is equal to 7
+
+ align:start position:0%
+two expected values and is equal to 7
+ 
+
+ align:start position:0%
+two expected values and is equal to 7
+let us now look at variances the
+
+ align:start position:0%
+let us now look at variances the
+ 
+
+ align:start position:0%
+let us now look at variances the
+variance of a uniform is equal to the
+
+ align:start position:0%
+variance of a uniform is equal to the
+ 
+
+ align:start position:0%
+variance of a uniform is equal to the
+square of the length of the interval on
+
+ align:start position:0%
+square of the length of the interval on
+ 
+
+ align:start position:0%
+square of the length of the interval on
+which the uniform is distributed in this
+
+ align:start position:0%
+which the uniform is distributed in this
+ 
+
+ align:start position:0%
+which the uniform is distributed in this
+case it's 6 squared divided always by
+
+ align:start position:0%
+case it's 6 squared divided always by
+ 
+
+ align:start position:0%
+case it's 6 squared divided always by
+coefficient on 12 6 squared is 36 so we
+
+ align:start position:0%
+coefficient on 12 6 squared is 36 so we
+ 
+
+ align:start position:0%
+coefficient on 12 6 squared is 36 so we
+obtain 3 the variance of U is determined
+
+ align:start position:0%
+obtain 3 the variance of U is determined
+ 
+
+ align:start position:0%
+obtain 3 the variance of U is determined
+by a similar formula except that now we
+
+ align:start position:0%
+by a similar formula except that now we
+ 
+
+ align:start position:0%
+by a similar formula except that now we
+have an interval of length 2
+
+ align:start position:0%
+have an interval of length 2
+ 
+
+ align:start position:0%
+have an interval of length 2
+so we obtain 2 squared over 12 and this
+
+ align:start position:0%
+so we obtain 2 squared over 12 and this
+ 
+
+ align:start position:0%
+so we obtain 2 squared over 12 and this
+is 1/3 now let us look at the variance
+
+ align:start position:0%
+is 1/3 now let us look at the variance
+ 
+
+ align:start position:0%
+is 1/3 now let us look at the variance
+of X since X is the sum of theta and you
+
+ align:start position:0%
+of X since X is the sum of theta and you
+ 
+
+ align:start position:0%
+of X since X is the sum of theta and you
+and since the two of them are
+
+ align:start position:0%
+and since the two of them are
+ 
+
+ align:start position:0%
+and since the two of them are
+independent the variance of X is going
+
+ align:start position:0%
+independent the variance of X is going
+ 
+
+ align:start position:0%
+independent the variance of X is going
+to be the sum of these two variances
+
+ align:start position:0%
+to be the sum of these two variances
+ 
+
+ align:start position:0%
+to be the sum of these two variances
+which is 10 over 3 now let us try to
+
+ align:start position:0%
+which is 10 over 3 now let us try to
+ 
+
+ align:start position:0%
+which is 10 over 3 now let us try to
+calculate the covariance term the
+
+ align:start position:0%
+calculate the covariance term the
+ 
+
+ align:start position:0%
+calculate the covariance term the
+covariance of theta with X is this
+
+ align:start position:0%
+covariance of theta with X is this
+ 
+
+ align:start position:0%
+covariance of theta with X is this
+expression because X is Theta plus U and
+
+ align:start position:0%
+expression because X is Theta plus U and
+ 
+
+ align:start position:0%
+expression because X is Theta plus U and
+then using linearity properties of
+
+ align:start position:0%
+then using linearity properties of
+ 
+
+ align:start position:0%
+then using linearity properties of
+covariances this is the covariance of
+
+ align:start position:0%
+covariances this is the covariance of
+ 
+
+ align:start position:0%
+covariances this is the covariance of
+theta with itself plus the covariance of
+
+ align:start position:0%
+theta with itself plus the covariance of
+ 
+
+ align:start position:0%
+theta with itself plus the covariance of
+theta with you now theta and you are
+
+ align:start position:0%
+theta with you now theta and you are
+ 
+
+ align:start position:0%
+theta with you now theta and you are
+independent so this covariance is equal
+
+ align:start position:0%
+independent so this covariance is equal
+ 
+
+ align:start position:0%
+independent so this covariance is equal
+to 0 the covariance of theta with itself
+
+ align:start position:0%
+to 0 the covariance of theta with itself
+ 
+
+ align:start position:0%
+to 0 the covariance of theta with itself
+is just the same as the variance so here
+
+ align:start position:0%
+is just the same as the variance so here
+ 
+
+ align:start position:0%
+is just the same as the variance so here
+we obtain an answer of 3 and so now we
+
+ align:start position:0%
+we obtain an answer of 3 and so now we
+ 
+
+ align:start position:0%
+we obtain an answer of 3 and so now we
+have all the pieces of information that
+
+ align:start position:0%
+have all the pieces of information that
+ 
+
+ align:start position:0%
+have all the pieces of information that
+we need and we can proceed and write
+
+ align:start position:0%
+we need and we can proceed and write
+ 
+
+ align:start position:0%
+we need and we can proceed and write
+down the form of the linear estimator
+
+ align:start position:0%
+down the form of the linear estimator
+ 
+
+ align:start position:0%
+down the form of the linear estimator
+the expected value of theta is 7
+
+ align:start position:0%
+the expected value of theta is 7
+ 
+
+ align:start position:0%
+the expected value of theta is 7
+then the covariance of theta with X is
+
+ align:start position:0%
+then the covariance of theta with X is
+ 
+
+ align:start position:0%
+then the covariance of theta with X is
+three divided by the variance which is
+
+ align:start position:0%
+three divided by the variance which is
+ 
+
+ align:start position:0%
+three divided by the variance which is
+ten over three so this ratio becomes
+
+ align:start position:0%
+ten over three so this ratio becomes
+ 
+
+ align:start position:0%
+ten over three so this ratio becomes
+nine ten and then X minus the expected
+
+ align:start position:0%
+nine ten and then X minus the expected
+ 
+
+ align:start position:0%
+nine ten and then X minus the expected
+value of X gives us this term so this is
+
+ align:start position:0%
+value of X gives us this term so this is
+ 
+
+ align:start position:0%
+value of X gives us this term so this is
+the form of the optimal linear estimator
+
+ align:start position:0%
+the form of the optimal linear estimator
+ 
+
+ align:start position:0%
+the form of the optimal linear estimator
+and if you wish to plot it it is a curve
+
+ align:start position:0%
+and if you wish to plot it it is a curve
+ 
+
+ align:start position:0%
+and if you wish to plot it it is a curve
+of this kind it is actually interesting
+
+ align:start position:0%
+of this kind it is actually interesting
+ 
+
+ align:start position:0%
+of this kind it is actually interesting
+to contrast this solution to the shape
+
+ align:start position:0%
+to contrast this solution to the shape
+ 
+
+ align:start position:0%
+to contrast this solution to the shape
+of the optimal estimator the least mean
+
+ align:start position:0%
+of the optimal estimator the least mean
+ 
+
+ align:start position:0%
+of the optimal estimator the least mean
+squares estimator or the conditional
+
+ align:start position:0%
+squares estimator or the conditional
+ 
+
+ align:start position:0%
+squares estimator or the conditional
+expectation estimator which we had found
+
+ align:start position:0%
+expectation estimator which we had found
+ 
+
+ align:start position:0%
+expectation estimator which we had found
+earlier and which corresponds to this
+
+ align:start position:0%
+earlier and which corresponds to this
+ 
+
+ align:start position:0%
+earlier and which corresponds to this
+particular blue curve so in some sense
+
+ align:start position:0%
+particular blue curve so in some sense
+ 
+
+ align:start position:0%
+particular blue curve so in some sense
+the linear estimator is a pretty good
+
+ align:start position:0%
+the linear estimator is a pretty good
+ 
+
+ align:start position:0%
+the linear estimator is a pretty good
+approximation of the optimal nonlinear
+
+ align:start position:0%
+approximation of the optimal nonlinear
+ 
+
+ align:start position:0%
+approximation of the optimal nonlinear
+one it does the best job that it can do
+
+ align:start position:0%
+one it does the best job that it can do
+ 
+
+ align:start position:0%
+one it does the best job that it can do
+subject to the constraint that it has to
+
+ align:start position:0%
+subject to the constraint that it has to
+ 
+
+ align:start position:0%
+subject to the constraint that it has to
+be a linear function notice also that
+
+ align:start position:0%
+be a linear function notice also that
+ 
+
+ align:start position:0%
+be a linear function notice also that
+this coefficient here is of course
+
+ align:start position:0%
+this coefficient here is of course
+ 
+
+ align:start position:0%
+this coefficient here is of course
+positive this reflects the fact that two
+
+ align:start position:0%
+positive this reflects the fact that two
+ 
+
+ align:start position:0%
+positive this reflects the fact that two
+random variables X and theta are
+
+ align:start position:0%
+random variables X and theta are
+ 
+
+ align:start position:0%
+random variables X and theta are
+positively correlated this should be
+
+ align:start position:0%
+positively correlated this should be
+ 
+
+ align:start position:0%
+positively correlated this should be
+clear from this diagram when x increases
+
+ align:start position:0%
+clear from this diagram when x increases
+ 
+
+ align:start position:0%
+clear from this diagram when x increases
+theta tends to also increase and vice
+
+ align:start position:0%
+theta tends to also increase and vice
+ 
+
+ align:start position:0%
+theta tends to also increase and vice
+versa it's also reflected in the fact
+
+ align:start position:0%
+versa it's also reflected in the fact
+ 
+
+ align:start position:0%
+versa it's also reflected in the fact
+that the covariance is a positive number
+
+ align:start position:0%
+that the covariance is a positive number
+ 
+
+ align:start position:0%
+that the covariance is a positive number
+on the other hand because this
+
+ align:start position:0%
+on the other hand because this
+ 
+
+ align:start position:0%
+on the other hand because this
+coefficient is 9/10 and not equal to one
+
+ align:start position:0%
+coefficient is 9/10 and not equal to one
+ 
+
+ align:start position:0%
+coefficient is 9/10 and not equal to one
+this red line is somewhat slanted in
+
+ align:start position:0%
+this red line is somewhat slanted in
+ 
+
+ align:start position:0%
+this red line is somewhat slanted in
+comparison with the orientation of the
+
+ align:start position:0%
+comparison with the orientation of the
+ 
+
+ align:start position:0%
+comparison with the orientation of the
+diagram that we have the calculations
+
+ align:start position:0%
+diagram that we have the calculations
+ 
+
+ align:start position:0%
+diagram that we have the calculations
+that we went through in this particular
+
+ align:start position:0%
+that we went through in this particular
+ 
+
+ align:start position:0%
+that we went through in this particular
+example are pretty generic this is what
+
+ align:start position:0%
+example are pretty generic this is what
+ 
+
+ align:start position:0%
+example are pretty generic this is what
+you need to do in general you just look
+
+ align:start position:0%
+you need to do in general you just look
+ 
+
+ align:start position:0%
+you need to do in general you just look
+at the random variables involved you
+
+ align:start position:0%
+at the random variables involved you
+ 
+
+ align:start position:0%
+at the random variables involved you
+calculate their means you calculate
+
+ align:start position:0%
+calculate their means you calculate
+ 
+
+ align:start position:0%
+calculate their means you calculate
+their variances then you may have to do
+
+ align:start position:0%
+their variances then you may have to do
+ 
+
+ align:start position:0%
+their variances then you may have to do
+some extra work to calculate the
+
+ align:start position:0%
+some extra work to calculate the
+ 
+
+ align:start position:0%
+some extra work to calculate the
+covariance of interest and once you are
+
+ align:start position:0%
+covariance of interest and once you are
+ 
+
+ align:start position:0%
+covariance of interest and once you are
+done you
+
+ align:start position:0%
+done you
+ 
+
+ align:start position:0%
+done you
+again the numerical values that you have
+
+ align:start position:0%
+again the numerical values that you have
+ 
+
+ align:start position:0%
+again the numerical values that you have
+found and you obtained the form of the
+
+ align:start position:0%
+found and you obtained the form of the
+ 
+
+ align:start position:0%
+found and you obtained the form of the
+linear estimator
\ No newline at end of file
diff --git a/KkN_Dk3E2yw.txt b/KkN_Dk3E2yw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fc8aa3926b026f43595278fc02ff82d198ddfead
--- /dev/null
+++ b/KkN_Dk3E2yw.txt
@@ -0,0 +1,7067 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right about a ordinary differential
+
+ align:start position:0%
+all right about a ordinary differential
+ 
+
+ align:start position:0%
+all right about a ordinary differential
+equations initial value problems but
+
+ align:start position:0%
+equations initial value problems but
+ 
+
+ align:start position:0%
+equations initial value problems but
+before I start to talk about that I want
+
+ align:start position:0%
+before I start to talk about that I want
+ 
+
+ align:start position:0%
+before I start to talk about that I want
+to remind you next week's schedule is
+
+ align:start position:0%
+to remind you next week's schedule is
+ 
+
+ align:start position:0%
+to remind you next week's schedule is
+weird so there's no classes on Monday
+
+ align:start position:0%
+weird so there's no classes on Monday
+ 
+
+ align:start position:0%
+weird so there's no classes on Monday
+but instead we'll have Monday classes on
+
+ align:start position:0%
+but instead we'll have Monday classes on
+ 
+
+ align:start position:0%
+but instead we'll have Monday classes on
+Tuesday so I'll see you next on Tuesday
+
+ align:start position:0%
+Tuesday so I'll see you next on Tuesday
+ 
+
+ align:start position:0%
+Tuesday so I'll see you next on Tuesday
+morning and then we're not gonna have a
+
+ align:start position:0%
+morning and then we're not gonna have a
+ 
+
+ align:start position:0%
+morning and then we're not gonna have a
+class on Wednesday but we have the quiz
+
+ align:start position:0%
+class on Wednesday but we have the quiz
+ 
+
+ align:start position:0%
+class on Wednesday but we have the quiz
+and Wednesday night all right and then
+
+ align:start position:0%
+and Wednesday night all right and then
+ 
+
+ align:start position:0%
+and Wednesday night all right and then
+we'll get back to normal on Friday and I
+
+ align:start position:0%
+we'll get back to normal on Friday and I
+ 
+
+ align:start position:0%
+we'll get back to normal on Friday and I
+would expect that possibly the TAS might
+
+ align:start position:0%
+would expect that possibly the TAS might
+ 
+
+ align:start position:0%
+would expect that possibly the TAS might
+be interested in giving a help session a
+
+ align:start position:0%
+be interested in giving a help session a
+ 
+
+ align:start position:0%
+be interested in giving a help session a
+review on Wednesday at the class period
+
+ align:start position:0%
+review on Wednesday at the class period
+ 
+
+ align:start position:0%
+review on Wednesday at the class period
+is that they'll be here so if you want
+
+ align:start position:0%
+is that they'll be here so if you want
+ 
+
+ align:start position:0%
+is that they'll be here so if you want
+to come a class period it's ask
+
+ align:start position:0%
+to come a class period it's ask
+ 
+
+ align:start position:0%
+to come a class period it's ask
+questions and so all right got that
+
+ align:start position:0%
+questions and so all right got that
+ 
+
+ align:start position:0%
+questions and so all right got that
+piece that will be ready as well
+
+ align:start position:0%
+piece that will be ready as well
+ 
+
+ align:start position:0%
+piece that will be ready as well
+okay so I'll talk about today
+
+ align:start position:0%
+okay so I'll talk about today
+ 
+
+ align:start position:0%
+okay so I'll talk about today
+Oh Dei VP's can you guys hear this yes
+
+ align:start position:0%
+Oh Dei VP's can you guys hear this yes
+ 
+
+ align:start position:0%
+Oh Dei VP's can you guys hear this yes
+office hours like normal Monday all
+
+ align:start position:0%
+office hours like normal Monday all
+ 
+
+ align:start position:0%
+office hours like normal Monday all
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for those who you want to get your
+
+ align:start position:0%
+and for those who you want to get your
+ 
+
+ align:start position:0%
+and for those who you want to get your
+homework started earlier we might even
+
+ align:start position:0%
+homework started earlier we might even
+ 
+
+ align:start position:0%
+homework started earlier we might even
+post homework courses all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and evident
+
+ align:start position:0%
+and evident
+ 
+
+ align:start position:0%
+and evident
+I'm gonna focus exclusively on OD ibid
+
+ align:start position:0%
+I'm gonna focus exclusively on OD ibid
+ 
+
+ align:start position:0%
+I'm gonna focus exclusively on OD ibid
+as you can write this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright and I would just comment what do
+
+ align:start position:0%
+alright and I would just comment what do
+ 
+
+ align:start position:0%
+alright and I would just comment what do
+these things mean OTE means are very
+
+ align:start position:0%
+these things mean OTE means are very
+ 
+
+ align:start position:0%
+these things mean OTE means are very
+differential equation it means that the
+
+ align:start position:0%
+differential equation it means that the
+ 
+
+ align:start position:0%
+differential equation it means that the
+only differentials in the problem I'll
+
+ align:start position:0%
+only differentials in the problem I'll
+ 
+
+ align:start position:0%
+only differentials in the problem I'll
+respect to one variable so I'm gonna
+
+ align:start position:0%
+respect to one variable so I'm gonna
+ 
+
+ align:start position:0%
+respect to one variable so I'm gonna
+call that T it can be Z or X or whatever
+
+ align:start position:0%
+call that T it can be Z or X or whatever
+ 
+
+ align:start position:0%
+call that T it can be Z or X or whatever
+you want but it only call to you and so
+
+ align:start position:0%
+you want but it only call to you and so
+ 
+
+ align:start position:0%
+you want but it only call to you and so
+this is not partial differential
+
+ align:start position:0%
+this is not partial differential
+ 
+
+ align:start position:0%
+this is not partial differential
+equations where you get differentials
+
+ align:start position:0%
+equations where you get differentials
+ 
+
+ align:start position:0%
+equations where you get differentials
+respect to many variables initial value
+
+ align:start position:0%
+respect to many variables initial value
+ 
+
+ align:start position:0%
+respect to many variables initial value
+problems meaning that all the initial
+
+ align:start position:0%
+problems meaning that all the initial
+ 
+
+ align:start position:0%
+problems meaning that all the initial
+conditions are given in a single tea
+
+ align:start position:0%
+conditions are given in a single tea
+ 
+
+ align:start position:0%
+conditions are given in a single tea
+point where T is that the variable that
+
+ align:start position:0%
+point where T is that the variable that
+ 
+
+ align:start position:0%
+point where T is that the variable that
+appears in the differential alright so
+
+ align:start position:0%
+appears in the differential alright so
+ 
+
+ align:start position:0%
+appears in the differential alright so
+this is the form we're gonna do this is
+
+ align:start position:0%
+this is the form we're gonna do this is
+ 
+
+ align:start position:0%
+this is the form we're gonna do this is
+first order way of writing that they
+
+ align:start position:0%
+first order way of writing that they
+ 
+
+ align:start position:0%
+first order way of writing that they
+owed e's if you recall from homework 0
+
+ align:start position:0%
+owed e's if you recall from homework 0
+ 
+
+ align:start position:0%
+owed e's if you recall from homework 0
+problem number one we showed you there
+
+ align:start position:0%
+problem number one we showed you there
+ 
+
+ align:start position:0%
+problem number one we showed you there
+how you can write higher order
+
+ align:start position:0%
+how you can write higher order
+ 
+
+ align:start position:0%
+how you can write higher order
+differential equations as in to convert
+
+ align:start position:0%
+differential equations as in to convert
+ 
+
+ align:start position:0%
+differential equations as in to convert
+them into form of first order and I
+
+ align:start position:0%
+them into form of first order and I
+ 
+
+ align:start position:0%
+them into form of first order and I
+guess that's worthwhile to play down I
+
+ align:start position:0%
+guess that's worthwhile to play down I
+ 
+
+ align:start position:0%
+guess that's worthwhile to play down I
+could also comment that I'm going to
+
+ align:start position:0%
+could also comment that I'm going to
+ 
+
+ align:start position:0%
+could also comment that I'm going to
+just talk about F of Y however the OD e
+
+ align:start position:0%
+just talk about F of Y however the OD e
+ 
+
+ align:start position:0%
+just talk about F of Y however the OD e
+solvers in MATLAB expect F of T comma Y
+
+ align:start position:0%
+solvers in MATLAB expect F of T comma Y
+ 
+
+ align:start position:0%
+solvers in MATLAB expect F of T comma Y
+as therefore all right so let's just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explain little details about this so
+
+ align:start position:0%
+explain little details about this so
+ 
+
+ align:start position:0%
+explain little details about this so
+suppose I had a differential equation
+
+ align:start position:0%
+suppose I had a differential equation
+ 
+
+ align:start position:0%
+suppose I had a differential equation
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so this is like a differential
+
+ align:start position:0%
+all right so this is like a differential
+ 
+
+ align:start position:0%
+all right so this is like a differential
+equation you'd have for a body moving a
+
+ align:start position:0%
+equation you'd have for a body moving a
+ 
+
+ align:start position:0%
+equation you'd have for a body moving a
+particle moving with some friction force
+
+ align:start position:0%
+particle moving with some friction force
+ 
+
+ align:start position:0%
+particle moving with some friction force
+on it and some time varying force
+
+ align:start position:0%
+on it and some time varying force
+ 
+
+ align:start position:0%
+on it and some time varying force
+particle yeah no I don't mean no this is
+
+ align:start position:0%
+particle yeah no I don't mean no this is
+ 
+
+ align:start position:0%
+particle yeah no I don't mean no this is
+it all right so this is a different
+
+ align:start position:0%
+it all right so this is a different
+ 
+
+ align:start position:0%
+it all right so this is a different
+equation what you can do is to convert
+
+ align:start position:0%
+equation what you can do is to convert
+ 
+
+ align:start position:0%
+equation what you can do is to convert
+it into the form I have above is to
+
+ align:start position:0%
+it into the form I have above is to
+ 
+
+ align:start position:0%
+it into the form I have above is to
+write a new variable say V that's
+
+ align:start position:0%
+write a new variable say V that's
+ 
+
+ align:start position:0%
+write a new variable say V that's
+defined to be DX DT velocity and this
+
+ align:start position:0%
+defined to be DX DT velocity and this
+ 
+
+ align:start position:0%
+defined to be DX DT velocity and this
+has a time dependence but I told you I
+
+ align:start position:0%
+has a time dependence but I told you I
+ 
+
+ align:start position:0%
+has a time dependence but I told you I
+don't like time dependence so I'm gonna
+
+ align:start position:0%
+don't like time dependence so I'm gonna
+ 
+
+ align:start position:0%
+don't like time dependence so I'm gonna
+write it that way so we can also define
+
+ align:start position:0%
+write it that way so we can also define
+ 
+
+ align:start position:0%
+write it that way so we can also define
+another variable so we can define our
+
+ align:start position:0%
+another variable so we can define our
+ 
+
+ align:start position:0%
+another variable so we can define our
+new Y vector to be X B and T ok so this
+
+ align:start position:0%
+new Y vector to be X B and T ok so this
+ 
+
+ align:start position:0%
+new Y vector to be X B and T ok so this
+is why the first component of Y is the
+
+ align:start position:0%
+is why the first component of Y is the
+ 
+
+ align:start position:0%
+is why the first component of Y is the
+second component wise and second their
+
+ align:start position:0%
+second component wise and second their
+ 
+
+ align:start position:0%
+second component wise and second their
+commit of Y and then I can write down
+
+ align:start position:0%
+commit of Y and then I can write down
+ 
+
+ align:start position:0%
+commit of Y and then I can write down
+what F of Y is so the equation for D F
+
+ align:start position:0%
+what F of Y is so the equation for D F
+ 
+
+ align:start position:0%
+what F of Y is so the equation for D F
+DT is why - it's the second come out of
+
+ align:start position:0%
+DT is why - it's the second come out of
+ 
+
+ align:start position:0%
+DT is why - it's the second come out of
+y DF DT is equal to B the equation for
+
+ align:start position:0%
+y DF DT is equal to B the equation for
+ 
+
+ align:start position:0%
+y DF DT is equal to B the equation for
+the DV DT is given by this equation so
+
+ align:start position:0%
+the DV DT is given by this equation so
+ 
+
+ align:start position:0%
+the DV DT is given by this equation so
+that's F of Y 3 over m minus gamma Y 2
+
+ align:start position:0%
+that's F of Y 3 over m minus gamma Y 2
+ 
+
+ align:start position:0%
+that's F of Y 3 over m minus gamma Y 2
+and the equation D DT DT DT is just 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is my F of Y so this is f1 f2 f3
+
+ align:start position:0%
+so this is my F of Y so this is f1 f2 f3
+ 
+
+ align:start position:0%
+so this is my F of Y so this is f1 f2 f3
+said alright so this is just how you can
+
+ align:start position:0%
+said alright so this is just how you can
+ 
+
+ align:start position:0%
+said alright so this is just how you can
+convert if somebody writes the equation
+
+ align:start position:0%
+convert if somebody writes the equation
+ 
+
+ align:start position:0%
+convert if somebody writes the equation
+this way and you want to get it into the
+
+ align:start position:0%
+this way and you want to get it into the
+ 
+
+ align:start position:0%
+this way and you want to get it into the
+standard form that I'm gonna show you
+
+ align:start position:0%
+standard form that I'm gonna show you
+ 
+
+ align:start position:0%
+standard form that I'm gonna show you
+here dy DT goes F of Y this is how you
+
+ align:start position:0%
+here dy DT goes F of Y this is how you
+ 
+
+ align:start position:0%
+here dy DT goes F of Y this is how you
+convert all right
+
+ align:start position:0%
+convert all right
+ 
+
+ align:start position:0%
+convert all right
+and I just see a skill we haven't really
+
+ align:start position:0%
+and I just see a skill we haven't really
+ 
+
+ align:start position:0%
+and I just see a skill we haven't really
+emphasized so far in the course but I
+
+ align:start position:0%
+emphasized so far in the course but I
+ 
+
+ align:start position:0%
+emphasized so far in the course but I
+think a very important skill is to be
+
+ align:start position:0%
+think a very important skill is to be
+ 
+
+ align:start position:0%
+think a very important skill is to be
+able to get like a chemical engineering
+
+ align:start position:0%
+able to get like a chemical engineering
+ 
+
+ align:start position:0%
+able to get like a chemical engineering
+problem and rearrange it so it becomes a
+
+ align:start position:0%
+problem and rearrange it so it becomes a
+ 
+
+ align:start position:0%
+problem and rearrange it so it becomes a
+standard form that maps up to one of the
+
+ align:start position:0%
+standard form that maps up to one of the
+ 
+
+ align:start position:0%
+standard form that maps up to one of the
+solvers you know how to use so you know
+
+ align:start position:0%
+solvers you know how to use so you know
+ 
+
+ align:start position:0%
+solvers you know how to use so you know
+you get a problem has some differential
+
+ align:start position:0%
+you get a problem has some differential
+ 
+
+ align:start position:0%
+you get a problem has some differential
+in it right away you actually somehow
+
+ align:start position:0%
+in it right away you actually somehow
+ 
+
+ align:start position:0%
+in it right away you actually somehow
+rewrite it so it looks like this
+
+ align:start position:0%
+rewrite it so it looks like this
+ 
+
+ align:start position:0%
+rewrite it so it looks like this
+standard form or actually for matlab
+
+ align:start position:0%
+standard form or actually for matlab
+ 
+
+ align:start position:0%
+standard form or actually for matlab
+this form so MATLAB will say F of T Y if
+
+ align:start position:0%
+this form so MATLAB will say F of T Y if
+ 
+
+ align:start position:0%
+this form so MATLAB will say F of T Y if
+you can do that then you can go ahead
+
+ align:start position:0%
+you can do that then you can go ahead
+ 
+
+ align:start position:0%
+you can do that then you can go ahead
+and use those MATLAB solver to solve it
+
+ align:start position:0%
+and use those MATLAB solver to solve it
+ 
+
+ align:start position:0%
+and use those MATLAB solver to solve it
+but you know your variables may not have
+
+ align:start position:0%
+but you know your variables may not have
+ 
+
+ align:start position:0%
+but you know your variables may not have
+a letter Y appearing anywhere all right
+
+ align:start position:0%
+a letter Y appearing anywhere all right
+ 
+
+ align:start position:0%
+a letter Y appearing anywhere all right
+you have to figure out how to write it
+
+ align:start position:0%
+you have to figure out how to write it
+ 
+
+ align:start position:0%
+you have to figure out how to write it
+into the standard form and now once you
+
+ align:start position:0%
+into the standard form and now once you
+ 
+
+ align:start position:0%
+into the standard form and now once you
+can do that you can use it use this
+
+ align:start position:0%
+can do that you can use it use this
+ 
+
+ align:start position:0%
+can do that you can use it use this
+Alvers and the same thing with like the
+
+ align:start position:0%
+Alvers and the same thing with like the
+ 
+
+ align:start position:0%
+Alvers and the same thing with like the
+nonlinear equation solvers with the
+
+ align:start position:0%
+nonlinear equation solvers with the
+ 
+
+ align:start position:0%
+nonlinear equation solvers with the
+optimization software if you can rewrite
+
+ align:start position:0%
+optimization software if you can rewrite
+ 
+
+ align:start position:0%
+optimization software if you can rewrite
+it into the form that matches the
+
+ align:start position:0%
+it into the form that matches the
+ 
+
+ align:start position:0%
+it into the form that matches the
+standard form then once you're done
+
+ align:start position:0%
+standard form then once you're done
+ 
+
+ align:start position:0%
+standard form then once you're done
+you're done right you then you have you
+
+ align:start position:0%
+you're done right you then you have you
+ 
+
+ align:start position:0%
+you're done right you then you have you
+can just go in and call the can programs
+
+ align:start position:0%
+can just go in and call the can programs
+ 
+
+ align:start position:0%
+can just go in and call the can programs
+that work well for those forms all right
+
+ align:start position:0%
+that work well for those forms all right
+ 
+
+ align:start position:0%
+that work well for those forms all right
+now what do we want as the output so
+
+ align:start position:0%
+now what do we want as the output so
+ 
+
+ align:start position:0%
+now what do we want as the output so
+this is the problem this is the problem
+
+ align:start position:0%
+this is the problem this is the problem
+ 
+
+ align:start position:0%
+this is the problem this is the problem
+as opposed what do we really want out of
+
+ align:start position:0%
+as opposed what do we really want out of
+ 
+
+ align:start position:0%
+as opposed what do we really want out of
+this what we're gonna get out of it is a
+
+ align:start position:0%
+this what we're gonna get out of it is a
+ 
+
+ align:start position:0%
+this what we're gonna get out of it is a
+bunch of points Y actually matrix right
+
+ align:start position:0%
+bunch of points Y actually matrix right
+ 
+
+ align:start position:0%
+bunch of points Y actually matrix right
+it'll be a vector of Y value is
+
+ align:start position:0%
+it'll be a vector of Y value is
+ 
+
+ align:start position:0%
+it'll be a vector of Y value is
+typically wise a vector and we want to
+
+ align:start position:0%
+typically wise a vector and we want to
+ 
+
+ align:start position:0%
+typically wise a vector and we want to
+know it a bunch of time points okay and
+
+ align:start position:0%
+know it a bunch of time points okay and
+ 
+
+ align:start position:0%
+know it a bunch of time points okay and
+we want a lot of time points so we
+
+ align:start position:0%
+we want a lot of time points so we
+ 
+
+ align:start position:0%
+we want a lot of time points so we
+getting pretty plots of how the
+
+ align:start position:0%
+getting pretty plots of how the
+ 
+
+ align:start position:0%
+getting pretty plots of how the
+components of Y vary over time okay
+
+ align:start position:0%
+components of Y vary over time okay
+ 
+
+ align:start position:0%
+components of Y vary over time okay
+something that's what we usually want
+
+ align:start position:0%
+something that's what we usually want
+ 
+
+ align:start position:0%
+something that's what we usually want
+sometimes we just want like the final
+
+ align:start position:0%
+sometimes we just want like the final
+ 
+
+ align:start position:0%
+sometimes we just want like the final
+value y time value time some you know we
+
+ align:start position:0%
+value y time value time some you know we
+ 
+
+ align:start position:0%
+value y time value time some you know we
+integrate to some point in the stop and
+
+ align:start position:0%
+integrate to some point in the stop and
+ 
+
+ align:start position:0%
+integrate to some point in the stop and
+just one there the final value but a lot
+
+ align:start position:0%
+just one there the final value but a lot
+ 
+
+ align:start position:0%
+just one there the final value but a lot
+of times we actually make pretty
+
+ align:start position:0%
+of times we actually make pretty
+ 
+
+ align:start position:0%
+of times we actually make pretty
+lots so we probably want a lot of points
+
+ align:start position:0%
+lots so we probably want a lot of points
+ 
+
+ align:start position:0%
+lots so we probably want a lot of points
+here and making plots how many points do
+
+ align:start position:0%
+here and making plots how many points do
+ 
+
+ align:start position:0%
+here and making plots how many points do
+you need to make a nice plot maybe I
+
+ align:start position:0%
+you need to make a nice plot maybe I
+ 
+
+ align:start position:0%
+you need to make a nice plot maybe I
+don't know 100 points 50 points you can
+
+ align:start position:0%
+don't know 100 points 50 points you can
+ 
+
+ align:start position:0%
+don't know 100 points 50 points you can
+make a nice plot
+
+ align:start position:0%
+make a nice plot
+ 
+
+ align:start position:0%
+make a nice plot
+so that's the kind numbers you'd like
+
+ align:start position:0%
+so that's the kind numbers you'd like
+ 
+
+ align:start position:0%
+so that's the kind numbers you'd like
+and so the output of these programs is
+
+ align:start position:0%
+and so the output of these programs is
+ 
+
+ align:start position:0%
+and so the output of these programs is
+going to be something like a vector of
+
+ align:start position:0%
+going to be something like a vector of
+ 
+
+ align:start position:0%
+going to be something like a vector of
+the time points and then the matrix of
+
+ align:start position:0%
+the time points and then the matrix of
+ 
+
+ align:start position:0%
+the time points and then the matrix of
+the of the y-values for corresponding
+
+ align:start position:0%
+the of the y-values for corresponding
+ 
+
+ align:start position:0%
+the of the y-values for corresponding
+each time point and the way doesn't in
+
+ align:start position:0%
+each time point and the way doesn't in
+ 
+
+ align:start position:0%
+each time point and the way doesn't in
+MATLAB it's reasonable each row of y are
+
+ align:start position:0%
+MATLAB it's reasonable each row of y are
+ 
+
+ align:start position:0%
+MATLAB it's reasonable each row of y are
+the Y values that correspond to the same
+
+ align:start position:0%
+the Y values that correspond to the same
+ 
+
+ align:start position:0%
+the Y values that correspond to the same
+time point the first time point so the
+
+ align:start position:0%
+time point the first time point so the
+ 
+
+ align:start position:0%
+time point the first time point so the
+first row of Y corresponds to the first
+
+ align:start position:0%
+first row of Y corresponds to the first
+ 
+
+ align:start position:0%
+first row of Y corresponds to the first
+number and the time vector the second
+
+ align:start position:0%
+number and the time vector the second
+ 
+
+ align:start position:0%
+number and the time vector the second
+row in this little second the last one
+
+ align:start position:0%
+row in this little second the last one
+ 
+
+ align:start position:0%
+row in this little second the last one
+will be a time final okay and then you
+
+ align:start position:0%
+will be a time final okay and then you
+ 
+
+ align:start position:0%
+will be a time final okay and then you
+can plot okay so far okay
+
+ align:start position:0%
+can plot okay so far okay
+ 
+
+ align:start position:0%
+can plot okay so far okay
+and ideally ideally we would like these
+
+ align:start position:0%
+and ideally ideally we would like these
+ 
+
+ align:start position:0%
+and ideally ideally we would like these
+Y values that we compute these Y's we
+
+ align:start position:0%
+Y values that we compute these Y's we
+ 
+
+ align:start position:0%
+Y values that we compute these Y's we
+get out ideally we want them really
+
+ align:start position:0%
+get out ideally we want them really
+ 
+
+ align:start position:0%
+get out ideally we want them really
+close to what the true solution of the
+
+ align:start position:0%
+close to what the true solution of the
+ 
+
+ align:start position:0%
+close to what the true solution of the
+true differential equation is but we're
+
+ align:start position:0%
+true differential equation is but we're
+ 
+
+ align:start position:0%
+true differential equation is but we're
+doing numerical stuff so it's never
+
+ align:start position:0%
+doing numerical stuff so it's never
+ 
+
+ align:start position:0%
+doing numerical stuff so it's never
+going to be exactly the same and so a
+
+ align:start position:0%
+going to be exactly the same and so a
+ 
+
+ align:start position:0%
+going to be exactly the same and so a
+big part of the effort is trying to
+
+ align:start position:0%
+big part of the effort is trying to
+ 
+
+ align:start position:0%
+big part of the effort is trying to
+figure out how can we get the thing to
+
+ align:start position:0%
+figure out how can we get the thing to
+ 
+
+ align:start position:0%
+figure out how can we get the thing to
+compute Y calculated at each time point
+
+ align:start position:0%
+compute Y calculated at each time point
+ 
+
+ align:start position:0%
+compute Y calculated at each time point
+to be as close as possible to the truth
+
+ align:start position:0%
+to be as close as possible to the truth
+ 
+
+ align:start position:0%
+to be as close as possible to the truth
+and what the true solution of of the
+
+ align:start position:0%
+and what the true solution of of the
+ 
+
+ align:start position:0%
+and what the true solution of of the
+equations are and that just turns out to
+
+ align:start position:0%
+equations are and that just turns out to
+ 
+
+ align:start position:0%
+equations are and that just turns out to
+be difficult
+
+ align:start position:0%
+be difficult
+ 
+
+ align:start position:0%
+be difficult
+so that's a very important thing to
+
+ align:start position:0%
+so that's a very important thing to
+ 
+
+ align:start position:0%
+so that's a very important thing to
+worry about what else can I say about
+
+ align:start position:0%
+worry about what else can I say about
+ 
+
+ align:start position:0%
+worry about what else can I say about
+this we we specify this from T naught
+
+ align:start position:0%
+this we we specify this from T naught
+ 
+
+ align:start position:0%
+this we we specify this from T naught
+and you typically have to input your T
+
+ align:start position:0%
+and you typically have to input your T
+ 
+
+ align:start position:0%
+and you typically have to input your T
+final how far you want to go away from
+
+ align:start position:0%
+final how far you want to go away from
+ 
+
+ align:start position:0%
+final how far you want to go away from
+your T naught as another input normally
+
+ align:start position:0%
+your T naught as another input normally
+ 
+
+ align:start position:0%
+your T naught as another input normally
+people write it with T naught is like
+
+ align:start position:0%
+people write it with T naught is like
+ 
+
+ align:start position:0%
+people write it with T naught is like
+less than T final and so you're like
+
+ align:start position:0%
+less than T final and so you're like
+ 
+
+ align:start position:0%
+less than T final and so you're like
+integrating from left to right but you
+
+ align:start position:0%
+integrating from left to right but you
+ 
+
+ align:start position:0%
+integrating from left to right but you
+could actually write them put a negative
+
+ align:start position:0%
+could actually write them put a negative
+ 
+
+ align:start position:0%
+could actually write them put a negative
+sign in the equation corresponding of T
+
+ align:start position:0%
+sign in the equation corresponding of T
+ 
+
+ align:start position:0%
+sign in the equation corresponding of T
+change your variable sort of T prime
+
+ align:start position:0%
+change your variable sort of T prime
+ 
+
+ align:start position:0%
+change your variable sort of T prime
+that was equal to T final minus T if you
+
+ align:start position:0%
+that was equal to T final minus T if you
+ 
+
+ align:start position:0%
+that was equal to T final minus T if you
+wanted to and integrate the other
+
+ align:start position:0%
+wanted to and integrate the other
+ 
+
+ align:start position:0%
+wanted to and integrate the other
+direction and in fact in homework 0
+
+ align:start position:0%
+direction and in fact in homework 0
+ 
+
+ align:start position:0%
+direction and in fact in homework 0
+problem one we did that too
+
+ align:start position:0%
+problem one we did that too
+ 
+
+ align:start position:0%
+problem one we did that too
+okay so you can you can iterate
+
+ align:start position:0%
+okay so you can you can iterate
+ 
+
+ align:start position:0%
+okay so you can you can iterate
+frontward you get it backwards if
+
+ align:start position:0%
+frontward you get it backwards if
+ 
+
+ align:start position:0%
+frontward you get it backwards if
+somebody tells you the initial condition
+
+ align:start position:0%
+somebody tells you the initial condition
+ 
+
+ align:start position:0%
+somebody tells you the initial condition
+or condition in the center of the range
+
+ align:start position:0%
+or condition in the center of the range
+ 
+
+ align:start position:0%
+or condition in the center of the range
+you can integrate forward for part of
+
+ align:start position:0%
+you can integrate forward for part of
+ 
+
+ align:start position:0%
+you can integrate forward for part of
+the range and backwards the other way so
+
+ align:start position:0%
+the range and backwards the other way so
+ 
+
+ align:start position:0%
+the range and backwards the other way so
+anything like this so what's important
+
+ align:start position:0%
+anything like this so what's important
+ 
+
+ align:start position:0%
+anything like this so what's important
+for this to be what's called an initial
+
+ align:start position:0%
+for this to be what's called an initial
+ 
+
+ align:start position:0%
+for this to be what's called an initial
+value problem it's just that all of the
+
+ align:start position:0%
+value problem it's just that all of the
+ 
+
+ align:start position:0%
+value problem it's just that all of the
+specifications of Y are given at the
+
+ align:start position:0%
+specifications of Y are given at the
+ 
+
+ align:start position:0%
+specifications of Y are given at the
+same value of T it doesn't matter
+
+ align:start position:0%
+same value of T it doesn't matter
+ 
+
+ align:start position:0%
+same value of T it doesn't matter
+exactly what value of T it is later
+
+ align:start position:0%
+exactly what value of T it is later
+ 
+
+ align:start position:0%
+exactly what value of T it is later
+we'll talk about what happens if you
+
+ align:start position:0%
+we'll talk about what happens if you
+ 
+
+ align:start position:0%
+we'll talk about what happens if you
+don't know all the specifications of one
+
+ align:start position:0%
+don't know all the specifications of one
+ 
+
+ align:start position:0%
+don't know all the specifications of one
+value of time all right now how would
+
+ align:start position:0%
+value of time all right now how would
+ 
+
+ align:start position:0%
+value of time all right now how would
+you approach this probably a bunch of
+
+ align:start position:0%
+you approach this probably a bunch of
+ 
+
+ align:start position:0%
+you approach this probably a bunch of
+you if doing this already as
+
+ align:start position:0%
+you if doing this already as
+ 
+
+ align:start position:0%
+you if doing this already as
+undergraduate or maybe even high school
+
+ align:start position:0%
+undergraduate or maybe even high school
+ 
+
+ align:start position:0%
+undergraduate or maybe even high school
+you can write like a Taylor expansion y
+
+ align:start position:0%
+you can write like a Taylor expansion y
+ 
+
+ align:start position:0%
+you can write like a Taylor expansion y
+of T plus delta-t this Y of T right that
+
+ align:start position:0%
+of T plus delta-t this Y of T right that
+ 
+
+ align:start position:0%
+of T plus delta-t this Y of T right that
+and then I say wow I know do you why
+
+ align:start position:0%
+and then I say wow I know do you why
+ 
+
+ align:start position:0%
+and then I say wow I know do you why
+does he that's actually F alright so
+
+ align:start position:0%
+does he that's actually F alright so
+ 
+
+ align:start position:0%
+does he that's actually F alright so
+this is actually equal to right and then
+
+ align:start position:0%
+this is actually equal to right and then
+ 
+
+ align:start position:0%
+this is actually equal to right and then
+if I truncate the Taylor expansion now I
+
+ align:start position:0%
+if I truncate the Taylor expansion now I
+ 
+
+ align:start position:0%
+if I truncate the Taylor expansion now I
+have an update formula so I just forget
+
+ align:start position:0%
+have an update formula so I just forget
+ 
+
+ align:start position:0%
+have an update formula so I just forget
+this last bit I can put in my God my
+
+ align:start position:0%
+this last bit I can put in my God my
+ 
+
+ align:start position:0%
+this last bit I can put in my God my
+current value file at the initial
+
+ align:start position:0%
+current value file at the initial
+ 
+
+ align:start position:0%
+current value file at the initial
+condition the initial condition here
+
+ align:start position:0%
+condition the initial condition here
+ 
+
+ align:start position:0%
+condition the initial condition here
+evaluate F multiplied by delta T add
+
+ align:start position:0%
+evaluate F multiplied by delta T add
+ 
+
+ align:start position:0%
+evaluate F multiplied by delta T add
+them together and I'll get a new value
+
+ align:start position:0%
+them together and I'll get a new value
+ 
+
+ align:start position:0%
+them together and I'll get a new value
+of y and then I can repeat over and over
+
+ align:start position:0%
+of y and then I can repeat over and over
+ 
+
+ align:start position:0%
+of y and then I can repeat over and over
+again and in fact this is a very famous
+
+ align:start position:0%
+again and in fact this is a very famous
+ 
+
+ align:start position:0%
+again and in fact this is a very famous
+method it's called a forward Euler
+
+ align:start position:0%
+method it's called a forward Euler
+ 
+
+ align:start position:0%
+method it's called a forward Euler
+method where louis pretty smart guy so
+
+ align:start position:0%
+method where louis pretty smart guy so
+ 
+
+ align:start position:0%
+method where louis pretty smart guy so
+it's not completely ridiculous but it'll
+
+ align:start position:0%
+it's not completely ridiculous but it'll
+ 
+
+ align:start position:0%
+it's not completely ridiculous but it'll
+show you it has some problems so the
+
+ align:start position:0%
+show you it has some problems so the
+ 
+
+ align:start position:0%
+show you it has some problems so the
+forward Euler another way to write it is
+
+ align:start position:0%
+forward Euler another way to write it is
+ 
+
+ align:start position:0%
+forward Euler another way to write it is
+y nu is equal to Y old
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's called forward Euler and we
+
+ align:start position:0%
+okay that's called forward Euler and we
+ 
+
+ align:start position:0%
+okay that's called forward Euler and we
+can write a little implementation to
+
+ align:start position:0%
+can write a little implementation to
+ 
+
+ align:start position:0%
+can write a little implementation to
+this pretty easily so you can write y is
+
+ align:start position:0%
+this pretty easily so you can write y is
+ 
+
+ align:start position:0%
+this pretty easily so you can write y is
+equal to Y naught Y okay so there's your
+
+ align:start position:0%
+equal to Y naught Y okay so there's your
+ 
+
+ align:start position:0%
+equal to Y naught Y okay so there's your
+code for doing forward or Lex how many
+
+ align:start position:0%
+code for doing forward or Lex how many
+ 
+
+ align:start position:0%
+code for doing forward or Lex how many
+of you does paper
+
+ align:start position:0%
+of you does paper
+ 
+
+ align:start position:0%
+of you does paper
+okay so I can skip over this right now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many how many do this and it didn't
+
+ align:start position:0%
+how many how many do this and it didn't
+ 
+
+ align:start position:0%
+how many how many do this and it didn't
+work for problem okay so you're not
+
+ align:start position:0%
+work for problem okay so you're not
+ 
+
+ align:start position:0%
+work for problem okay so you're not
+doing harder problems
+
+ align:start position:0%
+doing harder problems
+ 
+
+ align:start position:0%
+doing harder problems
+all right well correct that all right
+
+ align:start position:0%
+all right well correct that all right
+ 
+
+ align:start position:0%
+all right well correct that all right
+so I noticed that this closely resembles
+
+ align:start position:0%
+so I noticed that this closely resembles
+ 
+
+ align:start position:0%
+so I noticed that this closely resembles
+the rectangle rule so the rectangle rule
+
+ align:start position:0%
+the rectangle rule so the rectangle rule
+ 
+
+ align:start position:0%
+the rectangle rule so the rectangle rule
+would look a lot the same instead of
+
+ align:start position:0%
+would look a lot the same instead of
+ 
+
+ align:start position:0%
+would look a lot the same instead of
+however if you're integrating a function
+
+ align:start position:0%
+however if you're integrating a function
+ 
+
+ align:start position:0%
+however if you're integrating a function
+so I have AI is equal to the integral of
+
+ align:start position:0%
+so I have AI is equal to the integral of
+ 
+
+ align:start position:0%
+so I have AI is equal to the integral of
+F of T DT then I can notice that the
+
+ align:start position:0%
+F of T DT then I can notice that the
+ 
+
+ align:start position:0%
+F of T DT then I can notice that the
+derivative of di DT is equal to f of T
+
+ align:start position:0%
+derivative of di DT is equal to f of T
+ 
+
+ align:start position:0%
+derivative of di DT is equal to f of T
+all right and so if I was going to do
+
+ align:start position:0%
+all right and so if I was going to do
+ 
+
+ align:start position:0%
+all right and so if I was going to do
+the rectangle
+
+ align:start position:0%
+the rectangle
+ 
+
+ align:start position:0%
+the rectangle
+roll it would look just the same as this
+
+ align:start position:0%
+roll it would look just the same as this
+ 
+
+ align:start position:0%
+roll it would look just the same as this
+except this would be a tea and maybe I
+
+ align:start position:0%
+except this would be a tea and maybe I
+ 
+
+ align:start position:0%
+except this would be a tea and maybe I
+would pick y 0 to be 0 and the final
+
+ align:start position:0%
+would pick y 0 to be 0 and the final
+ 
+
+ align:start position:0%
+would pick y 0 to be 0 and the final
+value of Y I would get 2 would be my
+
+ align:start position:0%
+value of Y I would get 2 would be my
+ 
+
+ align:start position:0%
+value of Y I would get 2 would be my
+integral my about you that I want okay
+
+ align:start position:0%
+integral my about you that I want okay
+ 
+
+ align:start position:0%
+integral my about you that I want okay
+so yeah how many of you done rectangle
+
+ align:start position:0%
+so yeah how many of you done rectangle
+ 
+
+ align:start position:0%
+so yeah how many of you done rectangle
+rule yes okay all right so you did this
+
+ align:start position:0%
+rule yes okay all right so you did this
+ 
+
+ align:start position:0%
+rule yes okay all right so you did this
+already
+
+ align:start position:0%
+already
+ 
+
+ align:start position:0%
+already
+now you remember in high school when
+
+ align:start position:0%
+now you remember in high school when
+ 
+
+ align:start position:0%
+now you remember in high school when
+they taught you the rectangle rule they
+
+ align:start position:0%
+they taught you the rectangle rule they
+ 
+
+ align:start position:0%
+they taught you the rectangle rule they
+probably mentioned that it's not very
+
+ align:start position:0%
+probably mentioned that it's not very
+ 
+
+ align:start position:0%
+probably mentioned that it's not very
+accurate and so then they also taught
+
+ align:start position:0%
+accurate and so then they also taught
+ 
+
+ align:start position:0%
+accurate and so then they also taught
+you some other ones right you guys how
+
+ align:start position:0%
+you some other ones right you guys how
+ 
+
+ align:start position:0%
+you some other ones right you guys how
+many of you learned the trapezoid rule
+
+ align:start position:0%
+many of you learned the trapezoid rule
+ 
+
+ align:start position:0%
+many of you learned the trapezoid rule
+how about the midpoint rule have a
+
+ align:start position:0%
+how about the midpoint rule have a
+ 
+
+ align:start position:0%
+how about the midpoint rule have a
+Simpsons rule all right so so at least
+
+ align:start position:0%
+Simpsons rule all right so so at least
+ 
+
+ align:start position:0%
+Simpsons rule all right so so at least
+the high school math teachers thought
+
+ align:start position:0%
+the high school math teachers thought
+ 
+
+ align:start position:0%
+the high school math teachers thought
+that this is inadequate to we're doing
+
+ align:start position:0%
+that this is inadequate to we're doing
+ 
+
+ align:start position:0%
+that this is inadequate to we're doing
+real work right so they tell you all
+
+ align:start position:0%
+real work right so they tell you all
+ 
+
+ align:start position:0%
+real work right so they tell you all
+these other things instead this was like
+
+ align:start position:0%
+these other things instead this was like
+ 
+
+ align:start position:0%
+these other things instead this was like
+your first baby thing right so let's
+
+ align:start position:0%
+your first baby thing right so let's
+ 
+
+ align:start position:0%
+your first baby thing right so let's
+talk about why it was that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's do the Taylor expansion a
+
+ align:start position:0%
+so let's do the Taylor expansion a
+ 
+
+ align:start position:0%
+so let's do the Taylor expansion a
+little bit further so let's do it for
+
+ align:start position:0%
+little bit further so let's do it for
+ 
+
+ align:start position:0%
+little bit further so let's do it for
+the for the numerical integration case
+
+ align:start position:0%
+the for the numerical integration case
+ 
+
+ align:start position:0%
+the for the numerical integration case
+so y plus del T is equal to Y of T plus
+
+ align:start position:0%
+so y plus del T is equal to Y of T plus
+ 
+
+ align:start position:0%
+so y plus del T is equal to Y of T plus
+delta T times f of T plus 1/2 delta T
+
+ align:start position:0%
+delta T times f of T plus 1/2 delta T
+ 
+
+ align:start position:0%
+delta T times f of T plus 1/2 delta T
+squared times all right and so when we
+
+ align:start position:0%
+squared times all right and so when we
+ 
+
+ align:start position:0%
+squared times all right and so when we
+made the approximation to do the
+
+ align:start position:0%
+made the approximation to do the
+ 
+
+ align:start position:0%
+made the approximation to do the
+rectangle rule we just threw this term
+
+ align:start position:0%
+rectangle rule we just threw this term
+ 
+
+ align:start position:0%
+rectangle rule we just threw this term
+away so that's the leading term that we
+
+ align:start position:0%
+away so that's the leading term that we
+ 
+
+ align:start position:0%
+away so that's the leading term that we
+throw away so we made in our order of
+
+ align:start position:0%
+throw away so we made in our order of
+ 
+
+ align:start position:0%
+throw away so we made in our order of
+delta T squared okay because normally a
+
+ align:start position:0%
+delta T squared okay because normally a
+ 
+
+ align:start position:0%
+delta T squared okay because normally a
+second rib is not exactly 0 so we have
+
+ align:start position:0%
+second rib is not exactly 0 so we have
+ 
+
+ align:start position:0%
+second rib is not exactly 0 so we have
+an error
+
+ align:start position:0%
+an error
+ 
+
+ align:start position:0%
+an error
+in each step that's a litter of delta T
+
+ align:start position:0%
+in each step that's a litter of delta T
+ 
+
+ align:start position:0%
+in each step that's a litter of delta T
+squared but how many steps do we make
+
+ align:start position:0%
+squared but how many steps do we make
+ 
+
+ align:start position:0%
+squared but how many steps do we make
+the number of steps is equal to T final
+
+ align:start position:0%
+the number of steps is equal to T final
+ 
+
+ align:start position:0%
+the number of steps is equal to T final
+minus T naught over delta T right so
+
+ align:start position:0%
+minus T naught over delta T right so
+ 
+
+ align:start position:0%
+minus T naught over delta T right so
+therefore we making 1 over delta T order
+
+ align:start position:0%
+therefore we making 1 over delta T order
+ 
+
+ align:start position:0%
+therefore we making 1 over delta T order
+steps so the total error is
+
+ align:start position:0%
+steps so the total error is
+ 
+
+ align:start position:0%
+steps so the total error is
+approximately number of steps times how
+
+ align:start position:0%
+approximately number of steps times how
+ 
+
+ align:start position:0%
+approximately number of steps times how
+much are you making each step so it's
+
+ align:start position:0%
+much are you making each step so it's
+ 
+
+ align:start position:0%
+much are you making each step so it's
+going to be a second something the
+
+ align:start position:0%
+going to be a second something the
+ 
+
+ align:start position:0%
+going to be a second something the
+second power and TT divided by something
+
+ align:start position:0%
+second power and TT divided by something
+ 
+
+ align:start position:0%
+second power and TT divided by something
+the first power delta T so it's the
+
+ align:start position:0%
+the first power delta T so it's the
+ 
+
+ align:start position:0%
+the first power delta T so it's the
+total error in the integral I it's going
+
+ align:start position:0%
+total error in the integral I it's going
+ 
+
+ align:start position:0%
+total error in the integral I it's going
+to be order of delta T have you doing
+
+ align:start position:0%
+to be order of delta T have you doing
+ 
+
+ align:start position:0%
+to be order of delta T have you doing
+the right angle rule and so what are
+
+ align:start position:0%
+the right angle rule and so what are
+ 
+
+ align:start position:0%
+the right angle rule and so what are
+delta T is not very good so if you want
+
+ align:start position:0%
+delta T is not very good so if you want
+ 
+
+ align:start position:0%
+delta T is not very good so if you want
+to increase your accuracy well be double
+
+ align:start position:0%
+to increase your accuracy well be double
+ 
+
+ align:start position:0%
+to increase your accuracy well be double
+if you cut your step size in half
+
+ align:start position:0%
+if you cut your step size in half
+ 
+
+ align:start position:0%
+if you cut your step size in half
+that means you double your CPU times to
+
+ align:start position:0%
+that means you double your CPU times to
+ 
+
+ align:start position:0%
+that means you double your CPU times to
+do twice as many function evaluations
+
+ align:start position:0%
+do twice as many function evaluations
+ 
+
+ align:start position:0%
+do twice as many function evaluations
+but you only gain you reduce your error
+
+ align:start position:0%
+but you only gain you reduce your error
+ 
+
+ align:start position:0%
+but you only gain you reduce your error
+by factor two so if you want to say gain
+
+ align:start position:0%
+by factor two so if you want to say gain
+ 
+
+ align:start position:0%
+by factor two so if you want to say gain
+three significant figures of accuracy in
+
+ align:start position:0%
+three significant figures of accuracy in
+ 
+
+ align:start position:0%
+three significant figures of accuracy in
+your number then you have to do a
+
+ align:start position:0%
+your number then you have to do a
+ 
+
+ align:start position:0%
+your number then you have to do a
+thousand a thousand more times bunch of
+
+ align:start position:0%
+thousand a thousand more times bunch of
+ 
+
+ align:start position:0%
+thousand a thousand more times bunch of
+work where as you did before all right
+
+ align:start position:0%
+work where as you did before all right
+ 
+
+ align:start position:0%
+work where as you did before all right
+so I have some amount of some precision
+
+ align:start position:0%
+so I have some amount of some precision
+ 
+
+ align:start position:0%
+so I have some amount of some precision
+with some number of steps
+
+ align:start position:0%
+with some number of steps
+ 
+
+ align:start position:0%
+with some number of steps
+I want to increase get three more
+
+ align:start position:0%
+I want to increase get three more
+ 
+
+ align:start position:0%
+I want to increase get three more
+significant figures to have to do
+
+ align:start position:0%
+significant figures to have to do
+ 
+
+ align:start position:0%
+significant figures to have to do
+thousand times as much work that's kind
+
+ align:start position:0%
+thousand times as much work that's kind
+ 
+
+ align:start position:0%
+thousand times as much work that's kind
+of bad scaling if I want to get six more
+
+ align:start position:0%
+of bad scaling if I want to get six more
+ 
+
+ align:start position:0%
+of bad scaling if I want to get six more
+significant figures I gonna do a million
+
+ align:start position:0%
+significant figures I gonna do a million
+ 
+
+ align:start position:0%
+significant figures I gonna do a million
+times more work and so at some point
+
+ align:start position:0%
+times more work and so at some point
+ 
+
+ align:start position:0%
+times more work and so at some point
+that's got to be kind of expensive so if
+
+ align:start position:0%
+that's got to be kind of expensive so if
+ 
+
+ align:start position:0%
+that's got to be kind of expensive so if
+you contrast it you can do things like
+
+ align:start position:0%
+you contrast it you can do things like
+ 
+
+ align:start position:0%
+you contrast it you can do things like
+the trapezoid rule and as you're
+
+ align:start position:0%
+the trapezoid rule and as you're
+ 
+
+ align:start position:0%
+the trapezoid rule and as you're
+probably well so the idea of this is you
+
+ align:start position:0%
+probably well so the idea of this is you
+ 
+
+ align:start position:0%
+probably well so the idea of this is you
+have your function you have some point T
+
+ align:start position:0%
+have your function you have some point T
+ 
+
+ align:start position:0%
+have your function you have some point T
+and T plus delta T you're trying to
+
+ align:start position:0%
+and T plus delta T you're trying to
+ 
+
+ align:start position:0%
+and T plus delta T you're trying to
+integrate between them let's say T no do
+
+ align:start position:0%
+integrate between them let's say T no do
+ 
+
+ align:start position:0%
+integrate between them let's say T no do
+you not that's all the T try to
+
+ align:start position:0%
+you not that's all the T try to
+ 
+
+ align:start position:0%
+you not that's all the T try to
+integrate here's the value of the
+
+ align:start position:0%
+integrate here's the value of the
+ 
+
+ align:start position:0%
+integrate here's the value of the
+function at T here's the function value
+
+ align:start position:0%
+function at T here's the function value
+ 
+
+ align:start position:0%
+function at T here's the function value
+the function in it T plus delta T if you
+
+ align:start position:0%
+the function in it T plus delta T if you
+ 
+
+ align:start position:0%
+the function in it T plus delta T if you
+do the rectangle rule what you say is I
+
+ align:start position:0%
+do the rectangle rule what you say is I
+ 
+
+ align:start position:0%
+do the rectangle rule what you say is I
+just draw a dry line here and integrate
+
+ align:start position:0%
+just draw a dry line here and integrate
+ 
+
+ align:start position:0%
+just draw a dry line here and integrate
+that rectangle let's say the real
+
+ align:start position:0%
+that rectangle let's say the real
+ 
+
+ align:start position:0%
+that rectangle let's say the real
+function really looks like this then I'm
+
+ align:start position:0%
+function really looks like this then I'm
+ 
+
+ align:start position:0%
+function really looks like this then I'm
+missing that area there so that's the
+
+ align:start position:0%
+missing that area there so that's the
+ 
+
+ align:start position:0%
+missing that area there so that's the
+error that's why the error cific if I do
+
+ align:start position:0%
+error that's why the error cific if I do
+ 
+
+ align:start position:0%
+error that's why the error cific if I do
+the trapezoid rule then the air is I
+
+ align:start position:0%
+the trapezoid rule then the air is I
+ 
+
+ align:start position:0%
+the trapezoid rule then the air is I
+actually overestimated the integral of
+
+ align:start position:0%
+actually overestimated the integral of
+ 
+
+ align:start position:0%
+actually overestimated the integral of
+the difference between this dotted line
+
+ align:start position:0%
+the difference between this dotted line
+ 
+
+ align:start position:0%
+the difference between this dotted line
+the solid line is less than the
+
+ align:start position:0%
+the solid line is less than the
+ 
+
+ align:start position:0%
+the solid line is less than the
+intervals between the solid line and
+
+ align:start position:0%
+intervals between the solid line and
+ 
+
+ align:start position:0%
+intervals between the solid line and
+that deadline so it's more accurate so
+
+ align:start position:0%
+that deadline so it's more accurate so
+ 
+
+ align:start position:0%
+that deadline so it's more accurate so
+that's why people like the trapezoid
+
+ align:start position:0%
+that's why people like the trapezoid
+ 
+
+ align:start position:0%
+that's why people like the trapezoid
+rule better then the rectangle we did
+
+ align:start position:0%
+rule better then the rectangle we did
+ 
+
+ align:start position:0%
+rule better then the rectangle we did
+the midpoint rule you'd evaluate this
+
+ align:start position:0%
+the midpoint rule you'd evaluate this
+ 
+
+ align:start position:0%
+the midpoint rule you'd evaluate this
+function halfway between these two
+
+ align:start position:0%
+function halfway between these two
+ 
+
+ align:start position:0%
+function halfway between these two
+points and then draw a dotted line here
+
+ align:start position:0%
+points and then draw a dotted line here
+ 
+
+ align:start position:0%
+points and then draw a dotted line here
+and there and integrate that guy and it
+
+ align:start position:0%
+and there and integrate that guy and it
+ 
+
+ align:start position:0%
+and there and integrate that guy and it
+would overestimate four part and
+
+ align:start position:0%
+would overestimate four part and
+ 
+
+ align:start position:0%
+would overestimate four part and
+underestimate four part and they would
+
+ align:start position:0%
+underestimate four part and they would
+ 
+
+ align:start position:0%
+underestimate four part and they would
+partially cancel each other out and so
+
+ align:start position:0%
+partially cancel each other out and so
+ 
+
+ align:start position:0%
+partially cancel each other out and so
+that's also would be more accurate than
+
+ align:start position:0%
+that's also would be more accurate than
+ 
+
+ align:start position:0%
+that's also would be more accurate than
+then doing the rectangle over straight
+
+ align:start position:0%
+then doing the rectangle over straight
+ 
+
+ align:start position:0%
+then doing the rectangle over straight
+okay so you did before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so what we're gonna try to do is
+
+ align:start position:0%
+and so what we're gonna try to do is
+ 
+
+ align:start position:0%
+and so what we're gonna try to do is
+instead of using this formula it did
+
+ align:start position:0%
+instead of using this formula it did
+ 
+
+ align:start position:0%
+instead of using this formula it did
+before we're gonna replace this with
+
+ align:start position:0%
+before we're gonna replace this with
+ 
+
+ align:start position:0%
+before we're gonna replace this with
+something else so I'm gonna call G & G
+
+ align:start position:0%
+something else so I'm gonna call G & G
+ 
+
+ align:start position:0%
+something else so I'm gonna call G & G
+is something that's supposed to be the
+
+ align:start position:0%
+is something that's supposed to be the
+ 
+
+ align:start position:0%
+is something that's supposed to be the
+average value of F over the rate over
+
+ align:start position:0%
+average value of F over the rate over
+ 
+
+ align:start position:0%
+average value of F over the rate over
+the step instead of just taking the
+
+ align:start position:0%
+the step instead of just taking the
+ 
+
+ align:start position:0%
+the step instead of just taking the
+value of F at the starting point I want
+
+ align:start position:0%
+value of F at the starting point I want
+ 
+
+ align:start position:0%
+value of F at the starting point I want
+to get sort of the average right because
+
+ align:start position:0%
+to get sort of the average right because
+ 
+
+ align:start position:0%
+to get sort of the average right because
+then integral related an average over
+
+ align:start position:0%
+then integral related an average over
+ 
+
+ align:start position:0%
+then integral related an average over
+the delta T so G is gonna be my way to
+
+ align:start position:0%
+the delta T so G is gonna be my way to
+ 
+
+ align:start position:0%
+the delta T so G is gonna be my way to
+estimate the average and there's going
+
+ align:start position:0%
+estimate the average and there's going
+ 
+
+ align:start position:0%
+estimate the average and there's going
+to be a zillion update formula is that
+
+ align:start position:0%
+to be a zillion update formula is that
+ 
+
+ align:start position:0%
+to be a zillion update formula is that
+different mathematicians have proposed
+
+ align:start position:0%
+different mathematicians have proposed
+ 
+
+ align:start position:0%
+different mathematicians have proposed
+over the years they give you different
+
+ align:start position:0%
+over the years they give you different
+ 
+
+ align:start position:0%
+over the years they give you different
+G's to tell you how to do the update
+
+ align:start position:0%
+G's to tell you how to do the update
+ 
+
+ align:start position:0%
+G's to tell you how to do the update
+okay and the key is trying to find a G
+
+ align:start position:0%
+okay and the key is trying to find a G
+ 
+
+ align:start position:0%
+okay and the key is trying to find a G
+that's really accurate you want to have
+
+ align:start position:0%
+that's really accurate you want to have
+ 
+
+ align:start position:0%
+that's really accurate you want to have
+one that's the most accurate you can
+
+ align:start position:0%
+one that's the most accurate you can
+ 
+
+ align:start position:0%
+one that's the most accurate you can
+because then your errors be less and if
+
+ align:start position:0%
+because then your errors be less and if
+ 
+
+ align:start position:0%
+because then your errors be less and if
+your R's or less then your delta T can
+
+ align:start position:0%
+your R's or less then your delta T can
+ 
+
+ align:start position:0%
+your R's or less then your delta T can
+be bigger which means your number of
+
+ align:start position:0%
+be bigger which means your number of
+ 
+
+ align:start position:0%
+be bigger which means your number of
+steps will be less which means your CPU
+
+ align:start position:0%
+steps will be less which means your CPU
+ 
+
+ align:start position:0%
+steps will be less which means your CPU
+time will be less so you can get you
+
+ align:start position:0%
+time will be less so you can get you
+ 
+
+ align:start position:0%
+time will be less so you can get you
+might be able to get more accuracy and
+
+ align:start position:0%
+might be able to get more accuracy and
+ 
+
+ align:start position:0%
+might be able to get more accuracy and
+let it use less CPU time both if you can
+
+ align:start position:0%
+let it use less CPU time both if you can
+ 
+
+ align:start position:0%
+let it use less CPU time both if you can
+find a really good formula for T for the
+
+ align:start position:0%
+find a really good formula for T for the
+ 
+
+ align:start position:0%
+find a really good formula for T for the
+update so what's the G for the trapezoid
+
+ align:start position:0%
+update so what's the G for the trapezoid
+ 
+
+ align:start position:0%
+update so what's the G for the trapezoid
+rule it's f of T plus F of T plus delta
+
+ align:start position:0%
+rule it's f of T plus F of T plus delta
+ 
+
+ align:start position:0%
+rule it's f of T plus F of T plus delta
+T over two right that's that that was
+
+ align:start position:0%
+T over two right that's that that was
+ 
+
+ align:start position:0%
+T over two right that's that that was
+the G you you just when you do the
+
+ align:start position:0%
+the G you you just when you do the
+ 
+
+ align:start position:0%
+the G you you just when you do the
+trapezoid rule when you're kids
+
+ align:start position:0%
+trapezoid rule when you're kids
+ 
+
+ align:start position:0%
+trapezoid rule when you're kids
+okay what's the G for the midpoint role
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's F of T plus delta-t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so the different genes are
+
+ align:start position:0%
+okay and so the different genes are
+ 
+
+ align:start position:0%
+okay and so the different genes are
+called different update formulas and
+
+ align:start position:0%
+called different update formulas and
+ 
+
+ align:start position:0%
+called different update formulas and
+these particular ones reduce the error
+
+ align:start position:0%
+these particular ones reduce the error
+ 
+
+ align:start position:0%
+these particular ones reduce the error
+from delta T delta T squared for a micro
+
+ align:start position:0%
+from delta T delta T squared for a micro
+ 
+
+ align:start position:0%
+from delta T delta T squared for a micro
+step to
+
+ align:start position:0%
+step to
+ 
+
+ align:start position:0%
+step to
+I think Delta T to the cubed power and
+
+ align:start position:0%
+I think Delta T to the cubed power and
+ 
+
+ align:start position:0%
+I think Delta T to the cubed power and
+then when you multiply by this one over
+
+ align:start position:0%
+then when you multiply by this one over
+ 
+
+ align:start position:0%
+then when you multiply by this one over
+delta T it turns out you go from being
+
+ align:start position:0%
+delta T it turns out you go from being
+ 
+
+ align:start position:0%
+delta T it turns out you go from being
+order of delta T to order of Delta T's
+
+ align:start position:0%
+order of delta T to order of Delta T's
+ 
+
+ align:start position:0%
+order of delta T to order of Delta T's
+and that's a really big change so now if
+
+ align:start position:0%
+and that's a really big change so now if
+ 
+
+ align:start position:0%
+and that's a really big change so now if
+I cut the step size by a factor of 10 I
+
+ align:start position:0%
+I cut the step size by a factor of 10 I
+ 
+
+ align:start position:0%
+I cut the step size by a factor of 10 I
+gain a factor of 100 in the accuracy if
+
+ align:start position:0%
+gain a factor of 100 in the accuracy if
+ 
+
+ align:start position:0%
+gain a factor of 100 in the accuracy if
+I want to get six more syndicate figures
+
+ align:start position:0%
+I want to get six more syndicate figures
+ 
+
+ align:start position:0%
+I want to get six more syndicate figures
+I do a thousand times more work not a
+
+ align:start position:0%
+I do a thousand times more work not a
+ 
+
+ align:start position:0%
+I do a thousand times more work not a
+million times more work so it's a pretty
+
+ align:start position:0%
+million times more work so it's a pretty
+ 
+
+ align:start position:0%
+million times more work so it's a pretty
+significant improvement and that people
+
+ align:start position:0%
+significant improvement and that people
+ 
+
+ align:start position:0%
+significant improvement and that people
+have pushed this one further and further
+
+ align:start position:0%
+have pushed this one further and further
+ 
+
+ align:start position:0%
+have pushed this one further and further
+and so actually the very common
+
+ align:start position:0%
+and so actually the very common
+ 
+
+ align:start position:0%
+and so actually the very common
+integrators that you might use nowadays
+
+ align:start position:0%
+integrators that you might use nowadays
+ 
+
+ align:start position:0%
+integrators that you might use nowadays
+would go out to fourth and fifth order
+
+ align:start position:0%
+would go out to fourth and fifth order
+ 
+
+ align:start position:0%
+would go out to fourth and fifth order
+methods and so they have complicated
+
+ align:start position:0%
+methods and so they have complicated
+ 
+
+ align:start position:0%
+methods and so they have complicated
+update formulas that are carefully
+
+ align:start position:0%
+update formulas that are carefully
+ 
+
+ align:start position:0%
+update formulas that are carefully
+designed to cancel out all the low order
+
+ align:start position:0%
+designed to cancel out all the low order
+ 
+
+ align:start position:0%
+designed to cancel out all the low order
+delta teague earths and just leave very
+
+ align:start position:0%
+delta teague earths and just leave very
+ 
+
+ align:start position:0%
+delta teague earths and just leave very
+high order ones and that's that's kind
+
+ align:start position:0%
+high order ones and that's that's kind
+ 
+
+ align:start position:0%
+high order ones and that's that's kind
+of the typical ones are like that and
+
+ align:start position:0%
+of the typical ones are like that and
+ 
+
+ align:start position:0%
+of the typical ones are like that and
+then some fancy ones might go even up to
+
+ align:start position:0%
+then some fancy ones might go even up to
+ 
+
+ align:start position:0%
+then some fancy ones might go even up to
+eighth order I've seen if you're really
+
+ align:start position:0%
+eighth order I've seen if you're really
+ 
+
+ align:start position:0%
+eighth order I've seen if you're really
+pushing it get really complicated G
+
+ align:start position:0%
+pushing it get really complicated G
+ 
+
+ align:start position:0%
+pushing it get really complicated G
+formulas then all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this is offered the integration but
+
+ align:start position:0%
+now this is offered the integration but
+ 
+
+ align:start position:0%
+now this is offered the integration but
+really our problem was the DoD's somme
+
+ align:start position:0%
+really our problem was the DoD's somme
+ 
+
+ align:start position:0%
+really our problem was the DoD's somme
+so instead of we have to do F of Y not F
+
+ align:start position:0%
+so instead of we have to do F of Y not F
+ 
+
+ align:start position:0%
+so instead of we have to do F of Y not F
+of T yeah so we did the rectangle rule
+
+ align:start position:0%
+of T yeah so we did the rectangle rule
+ 
+
+ align:start position:0%
+of T yeah so we did the rectangle rule
+we had F of T but the real problem is we
+
+ align:start position:0%
+we had F of T but the real problem is we
+ 
+
+ align:start position:0%
+we had F of T but the real problem is we
+have to do F of Y now the problem is we
+
+ align:start position:0%
+have to do F of Y now the problem is we
+ 
+
+ align:start position:0%
+have to do F of Y now the problem is we
+don't know what Y is y is our unknown so
+
+ align:start position:0%
+don't know what Y is y is our unknown so
+ 
+
+ align:start position:0%
+don't know what Y is y is our unknown so
+we generally have a problem here in the
+
+ align:start position:0%
+we generally have a problem here in the
+ 
+
+ align:start position:0%
+we generally have a problem here in the
+rect in the forward Euler we can get
+
+ align:start position:0%
+rect in the forward Euler we can get
+ 
+
+ align:start position:0%
+rect in the forward Euler we can get
+away with it because we just put the Y
+
+ align:start position:0%
+away with it because we just put the Y
+ 
+
+ align:start position:0%
+away with it because we just put the Y
+old value in but for example if we
+
+ align:start position:0%
+old value in but for example if we
+ 
+
+ align:start position:0%
+old value in but for example if we
+wanted to do midpoint here we have to
+
+ align:start position:0%
+wanted to do midpoint here we have to
+ 
+
+ align:start position:0%
+wanted to do midpoint here we have to
+know F at a different time point that we
+
+ align:start position:0%
+know F at a different time point that we
+ 
+
+ align:start position:0%
+know F at a different time point that we
+haven't computed yet because it's
+
+ align:start position:0%
+haven't computed yet because it's
+ 
+
+ align:start position:0%
+haven't computed yet because it's
+forward in time
+
+ align:start position:0%
+forward in time
+ 
+
+ align:start position:0%
+forward in time
+same thing with trapezoidal rule we have
+
+ align:start position:0%
+same thing with trapezoidal rule we have
+ 
+
+ align:start position:0%
+same thing with trapezoidal rule we have
+to know F at some future time point so
+
+ align:start position:0%
+to know F at some future time point so
+ 
+
+ align:start position:0%
+to know F at some future time point so
+it's not so easy actually to go directly
+
+ align:start position:0%
+it's not so easy actually to go directly
+ 
+
+ align:start position:0%
+it's not so easy actually to go directly
+from these formulas to something their
+
+ align:start position:0%
+from these formulas to something their
+ 
+
+ align:start position:0%
+from these formulas to something their
+explicit formula like this with a G in
+
+ align:start position:0%
+explicit formula like this with a G in
+ 
+
+ align:start position:0%
+explicit formula like this with a G in
+here where the things inside G the
+
+ align:start position:0%
+here where the things inside G the
+ 
+
+ align:start position:0%
+here where the things inside G the
+wisest idea are all Y values who
+
+ align:start position:0%
+wisest idea are all Y values who
+ 
+
+ align:start position:0%
+wisest idea are all Y values who
+actually know so this is a serious
+
+ align:start position:0%
+actually know so this is a serious
+ 
+
+ align:start position:0%
+actually know so this is a serious
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but just didn't stop people from doing
+
+ align:start position:0%
+but just didn't stop people from doing
+ 
+
+ align:start position:0%
+but just didn't stop people from doing
+it so so one idea is you could go back
+
+ align:start position:0%
+it so so one idea is you could go back
+ 
+
+ align:start position:0%
+it so so one idea is you could go back
+to the Taylor expansion and now do the
+
+ align:start position:0%
+to the Taylor expansion and now do the
+ 
+
+ align:start position:0%
+to the Taylor expansion and now do the
+Taylor expansion but in terms of F of Y
+
+ align:start position:0%
+Taylor expansion but in terms of F of Y
+ 
+
+ align:start position:0%
+Taylor expansion but in terms of F of Y
+so this is F of Y of T and then over
+
+ align:start position:0%
+so this is F of Y of T and then over
+ 
+
+ align:start position:0%
+so this is F of Y of T and then over
+here this is T squared Y DT squared but
+
+ align:start position:0%
+here this is T squared Y DT squared but
+ 
+
+ align:start position:0%
+here this is T squared Y DT squared but
+dy DT is AB so this is really DF DT but
+
+ align:start position:0%
+dy DT is AB so this is really DF DT but
+ 
+
+ align:start position:0%
+dy DT is AB so this is really DF DT but
+if it's actually not a function of T is
+
+ align:start position:0%
+if it's actually not a function of T is
+ 
+
+ align:start position:0%
+if it's actually not a function of T is
+a function of Y right but we can do
+
+ align:start position:0%
+a function of Y right but we can do
+ 
+
+ align:start position:0%
+a function of Y right but we can do
+chain rule so DF DT is equal to the sum
+
+ align:start position:0%
+chain rule so DF DT is equal to the sum
+ 
+
+ align:start position:0%
+chain rule so DF DT is equal to the sum
+DF do you why and do you IND to write
+
+ align:start position:0%
+DF do you why and do you IND to write
+ 
+
+ align:start position:0%
+DF do you why and do you IND to write
+but dy n DT is also is f and this is
+
+ align:start position:0%
+but dy n DT is also is f and this is
+ 
+
+ align:start position:0%
+but dy n DT is also is f and this is
+what we call the Jacobian of F so this
+
+ align:start position:0%
+what we call the Jacobian of F so this
+ 
+
+ align:start position:0%
+what we call the Jacobian of F so this
+is really saying this is equal to J
+
+ align:start position:0%
+is really saying this is equal to J
+ 
+
+ align:start position:0%
+is really saying this is equal to J
+times so that would be one possibility
+
+ align:start position:0%
+times so that would be one possibility
+ 
+
+ align:start position:0%
+times so that would be one possibility
+is you could go and write the Taylor
+
+ align:start position:0%
+is you could go and write the Taylor
+ 
+
+ align:start position:0%
+is you could go and write the Taylor
+expansion out to the next higher order
+
+ align:start position:0%
+expansion out to the next higher order
+ 
+
+ align:start position:0%
+expansion out to the next higher order
+explicitly putting in J times F here and
+
+ align:start position:0%
+explicitly putting in J times F here and
+ 
+
+ align:start position:0%
+explicitly putting in J times F here and
+then just being inner in the cubic terms
+
+ align:start position:0%
+then just being inner in the cubic terms
+ 
+
+ align:start position:0%
+then just being inner in the cubic terms
+now people don't do this usually they're
+
+ align:start position:0%
+now people don't do this usually they're
+ 
+
+ align:start position:0%
+now people don't do this usually they're
+what you know idea why this is not a
+
+ align:start position:0%
+what you know idea why this is not a
+ 
+
+ align:start position:0%
+what you know idea why this is not a
+popular thing to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah that's right that's right so how
+
+ align:start position:0%
+yeah that's right that's right so how
+ 
+
+ align:start position:0%
+yeah that's right that's right so how
+much how many function evaluations does
+
+ align:start position:0%
+much how many function evaluations does
+ 
+
+ align:start position:0%
+much how many function evaluations does
+it take to get the Jacobian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so each each function is F is in his end
+
+ align:start position:0%
+so each each function is F is in his end
+ 
+
+ align:start position:0%
+so each each function is F is in his end
+values right because it's a vector and
+
+ align:start position:0%
+values right because it's a vector and
+ 
+
+ align:start position:0%
+values right because it's a vector and
+then you have to do at least forward to
+
+ align:start position:0%
+then you have to do at least forward to
+ 
+
+ align:start position:0%
+then you have to do at least forward to
+say forward differences would be in
+
+ align:start position:0%
+say forward differences would be in
+ 
+
+ align:start position:0%
+say forward differences would be in
+function evaluations so instead of just
+
+ align:start position:0%
+function evaluations so instead of just
+ 
+
+ align:start position:0%
+function evaluations so instead of just
+doing one function evaluation like we
+
+ align:start position:0%
+doing one function evaluation like we
+ 
+
+ align:start position:0%
+doing one function evaluation like we
+were doing with the forward Euler now we
+
+ align:start position:0%
+were doing with the forward Euler now we
+ 
+
+ align:start position:0%
+were doing with the forward Euler now we
+have to do n plus one or something like
+
+ align:start position:0%
+have to do n plus one or something like
+ 
+
+ align:start position:0%
+have to do n plus one or something like
+that function evaluations and actually
+
+ align:start position:0%
+that function evaluations and actually
+ 
+
+ align:start position:0%
+that function evaluations and actually
+you probably need to send our
+
+ align:start position:0%
+you probably need to send our
+ 
+
+ align:start position:0%
+you probably need to send our
+differences so you need two times n plus
+
+ align:start position:0%
+differences so you need two times n plus
+ 
+
+ align:start position:0%
+differences so you need two times n plus
+1 say any of you do even you
+
+ align:start position:0%
+1 say any of you do even you
+ 
+
+ align:start position:0%
+1 say any of you do even you
+analytically and unless it's sparse it's
+
+ align:start position:0%
+analytically and unless it's sparse it's
+ 
+
+ align:start position:0%
+analytically and unless it's sparse it's
+still gonna be really expensive to
+
+ align:start position:0%
+still gonna be really expensive to
+ 
+
+ align:start position:0%
+still gonna be really expensive to
+compute it so it's a lot more effort to
+
+ align:start position:0%
+compute it so it's a lot more effort to
+ 
+
+ align:start position:0%
+compute it so it's a lot more effort to
+do it so they need to think well is it
+
+ align:start position:0%
+do it so they need to think well is it
+ 
+
+ align:start position:0%
+do it so they need to think well is it
+really worth it
+
+ align:start position:0%
+really worth it
+ 
+
+ align:start position:0%
+really worth it
+and so people have found other formulas
+
+ align:start position:0%
+and so people have found other formulas
+ 
+
+ align:start position:0%
+and so people have found other formulas
+that basically get rid of the delta T
+
+ align:start position:0%
+that basically get rid of the delta T
+ 
+
+ align:start position:0%
+that basically get rid of the delta T
+squared term that don't require so much
+
+ align:start position:0%
+squared term that don't require so much
+ 
+
+ align:start position:0%
+squared term that don't require so much
+effort and so that's that's what people
+
+ align:start position:0%
+effort and so that's that's what people
+ 
+
+ align:start position:0%
+effort and so that's that's what people
+do instead but this is an option you
+
+ align:start position:0%
+do instead but this is an option you
+ 
+
+ align:start position:0%
+do instead but this is an option you
+could do all right all right so instead
+
+ align:start position:0%
+could do all right all right so instead
+ 
+
+ align:start position:0%
+could do all right all right so instead
+what people do is they've decided to
+
+ align:start position:0%
+what people do is they've decided to
+ 
+
+ align:start position:0%
+what people do is they've decided to
+generalize the midpoint rule and try to
+
+ align:start position:0%
+generalize the midpoint rule and try to
+ 
+
+ align:start position:0%
+generalize the midpoint rule and try to
+figure out how can we get an estimate of
+
+ align:start position:0%
+figure out how can we get an estimate of
+ 
+
+ align:start position:0%
+figure out how can we get an estimate of
+the midpoint value that's cheap to
+
+ align:start position:0%
+the midpoint value that's cheap to
+ 
+
+ align:start position:0%
+the midpoint value that's cheap to
+evaluate and so what they say as well
+
+ align:start position:0%
+evaluate and so what they say as well
+ 
+
+ align:start position:0%
+evaluate and so what they say as well
+this is the G midpoint for numerical
+
+ align:start position:0%
+this is the G midpoint for numerical
+ 
+
+ align:start position:0%
+this is the G midpoint for numerical
+integration let's make a new G in point
+
+ align:start position:0%
+integration let's make a new G in point
+ 
+
+ align:start position:0%
+integration let's make a new G in point
+that works for when F is a function of Y
+
+ align:start position:0%
+that works for when F is a function of Y
+ 
+
+ align:start position:0%
+that works for when F is a function of Y
+so let's make it function y evaluated at
+
+ align:start position:0%
+so let's make it function y evaluated at
+ 
+
+ align:start position:0%
+so let's make it function y evaluated at
+T plus delta T over 2 okay so that's
+
+ align:start position:0%
+T plus delta T over 2 okay so that's
+ 
+
+ align:start position:0%
+T plus delta T over 2 okay so that's
+what the form looks like but then you
+
+ align:start position:0%
+what the form looks like but then you
+ 
+
+ align:start position:0%
+what the form looks like but then you
+say well I don't know what Y is at t
+
+ align:start position:0%
+say well I don't know what Y is at t
+ 
+
+ align:start position:0%
+say well I don't know what Y is at t
+plus delta T over 2 because I only know
+
+ align:start position:0%
+plus delta T over 2 because I only know
+ 
+
+ align:start position:0%
+plus delta T over 2 because I only know
+it at Y of T so then they say well let's
+
+ align:start position:0%
+it at Y of T so then they say well let's
+ 
+
+ align:start position:0%
+it at Y of T so then they say well let's
+do forward Euler for that so then they
+
+ align:start position:0%
+do forward Euler for that so then they
+ 
+
+ align:start position:0%
+do forward Euler for that so then they
+say well let's say it's approximately
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's what's the forward Euler formula
+
+ align:start position:0%
+that's what's the forward Euler formula
+ 
+
+ align:start position:0%
+that's what's the forward Euler formula
+it's Y of T plus delta T over 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is a formula that's is
+
+ align:start position:0%
+okay so this is a formula that's is
+ 
+
+ align:start position:0%
+okay so this is a formula that's is
+actually used in practice a lot and this
+
+ align:start position:0%
+actually used in practice a lot and this
+ 
+
+ align:start position:0%
+actually used in practice a lot and this
+one is called runge-kutta two second
+
+ align:start position:0%
+one is called runge-kutta two second
+ 
+
+ align:start position:0%
+one is called runge-kutta two second
+order runge-kutta formula and it's just
+
+ align:start position:0%
+order runge-kutta formula and it's just
+ 
+
+ align:start position:0%
+order runge-kutta formula and it's just
+the it's two it's the midpoint rule
+
+ align:start position:0%
+the it's two it's the midpoint rule
+ 
+
+ align:start position:0%
+the it's two it's the midpoint rule
+where we estimate the value of y of T
+
+ align:start position:0%
+where we estimate the value of y of T
+ 
+
+ align:start position:0%
+where we estimate the value of y of T
+plus Delta two using forward Euler and
+
+ align:start position:0%
+plus Delta two using forward Euler and
+ 
+
+ align:start position:0%
+plus Delta two using forward Euler and
+the Evangelist is very cheap I just
+
+ align:start position:0%
+the Evangelist is very cheap I just
+ 
+
+ align:start position:0%
+the Evangelist is very cheap I just
+devalue eight I just have to evaluate
+
+ align:start position:0%
+devalue eight I just have to evaluate
+ 
+
+ align:start position:0%
+devalue eight I just have to evaluate
+one function here one here is a two
+
+ align:start position:0%
+one function here one here is a two
+ 
+
+ align:start position:0%
+one function here one here is a two
+function calls in that way you get it
+
+ align:start position:0%
+function calls in that way you get it
+ 
+
+ align:start position:0%
+function calls in that way you get it
+update formula okay and this one turns
+
+ align:start position:0%
+update formula okay and this one turns
+ 
+
+ align:start position:0%
+update formula okay and this one turns
+out that it has the nice delta T scaling
+
+ align:start position:0%
+out that it has the nice delta T scaling
+ 
+
+ align:start position:0%
+out that it has the nice delta T scaling
+that you might like so that's the kind
+
+ align:start position:0%
+that you might like so that's the kind
+ 
+
+ align:start position:0%
+that you might like so that's the kind
+of thing people do and the runge-kutta
+
+ align:start position:0%
+of thing people do and the runge-kutta
+ 
+
+ align:start position:0%
+of thing people do and the runge-kutta
+guys went crazy and so one of the most
+
+ align:start position:0%
+guys went crazy and so one of the most
+ 
+
+ align:start position:0%
+guys went crazy and so one of the most
+popular solvers is called runge-kutta
+
+ align:start position:0%
+popular solvers is called runge-kutta
+ 
+
+ align:start position:0%
+popular solvers is called runge-kutta
+for five and that's the OD for five
+
+ align:start position:0%
+for five and that's the OD for five
+ 
+
+ align:start position:0%
+for five and that's the OD for five
+program in MATLAB and what that does is
+
+ align:start position:0%
+program in MATLAB and what that does is
+ 
+
+ align:start position:0%
+program in MATLAB and what that does is
+the fourth order extension of this and
+
+ align:start position:0%
+the fourth order extension of this and
+ 
+
+ align:start position:0%
+the fourth order extension of this and
+the fifth order extension of this and it
+
+ align:start position:0%
+the fifth order extension of this and it
+ 
+
+ align:start position:0%
+the fifth order extension of this and it
+uses them both and it compares them and
+
+ align:start position:0%
+uses them both and it compares them and
+ 
+
+ align:start position:0%
+uses them both and it compares them and
+uses the difference between them to
+
+ align:start position:0%
+uses the difference between them to
+ 
+
+ align:start position:0%
+uses the difference between them to
+estimate the error in the calculation
+
+ align:start position:0%
+estimate the error in the calculation
+ 
+
+ align:start position:0%
+estimate the error in the calculation
+and then use that to decide what what
+
+ align:start position:0%
+and then use that to decide what what
+ 
+
+ align:start position:0%
+and then use that to decide what what
+size delta T you need depending on what
+
+ align:start position:0%
+size delta T you need depending on what
+ 
+
+ align:start position:0%
+size delta T you need depending on what
+tolerances you demand right and the
+
+ align:start position:0%
+tolerances you demand right and the
+ 
+
+ align:start position:0%
+tolerances you demand right and the
+formulas for all those our own code
+
+ align:start position:0%
+formulas for all those our own code
+ 
+
+ align:start position:0%
+formulas for all those our own code
+formulas are given in the textbook now
+
+ align:start position:0%
+formulas are given in the textbook now
+ 
+
+ align:start position:0%
+formulas are given in the textbook now
+this starts to lead to the problem so we
+
+ align:start position:0%
+this starts to lead to the problem so we
+ 
+
+ align:start position:0%
+this starts to lead to the problem so we
+weren't able to actually evaluate the
+
+ align:start position:0%
+weren't able to actually evaluate the
+ 
+
+ align:start position:0%
+weren't able to actually evaluate the
+true G midpoint which we'd like to be
+
+ align:start position:0%
+true G midpoint which we'd like to be
+ 
+
+ align:start position:0%
+true G midpoint which we'd like to be
+here instead we had to use some
+
+ align:start position:0%
+here instead we had to use some
+ 
+
+ align:start position:0%
+here instead we had to use some
+approximation right in order to
+
+ align:start position:0%
+approximation right in order to
+ 
+
+ align:start position:0%
+approximation right in order to
+extrapolate forwards to the Y so this is
+
+ align:start position:0%
+extrapolate forwards to the Y so this is
+ 
+
+ align:start position:0%
+extrapolate forwards to the Y so this is
+hinting at the whole problem this whole
+
+ align:start position:0%
+hinting at the whole problem this whole
+ 
+
+ align:start position:0%
+hinting at the whole problem this whole
+problem is actually we're just
+
+ align:start position:0%
+problem is actually we're just
+ 
+
+ align:start position:0%
+problem is actually we're just
+extrapolating we know the the true value
+
+ align:start position:0%
+extrapolating we know the the true value
+ 
+
+ align:start position:0%
+extrapolating we know the the true value
+of y only 89 and all the rest were doing
+
+ align:start position:0%
+of y only 89 and all the rest were doing
+ 
+
+ align:start position:0%
+of y only 89 and all the rest were doing
+is extrapolating forwards and we're
+
+ align:start position:0%
+is extrapolating forwards and we're
+ 
+
+ align:start position:0%
+is extrapolating forwards and we're
+doing it over and over again so we're
+
+ align:start position:0%
+doing it over and over again so we're
+ 
+
+ align:start position:0%
+doing it over and over again so we're
+gonna do it for n steps maybe we'll do a
+
+ align:start position:0%
+gonna do it for n steps maybe we'll do a
+ 
+
+ align:start position:0%
+gonna do it for n steps maybe we'll do a
+thousand steps so if you're
+
+ align:start position:0%
+thousand steps so if you're
+ 
+
+ align:start position:0%
+thousand steps so if you're
+extrapolating and then based on that
+
+ align:start position:0%
+extrapolating and then based on that
+ 
+
+ align:start position:0%
+extrapolating and then based on that
+extrapolation you're gonna strap lead
+
+ align:start position:0%
+extrapolation you're gonna strap lead
+ 
+
+ align:start position:0%
+extrapolation you're gonna strap lead
+again and then based on that
+
+ align:start position:0%
+again and then based on that
+ 
+
+ align:start position:0%
+again and then based on that
+extrapolation you're gonna extrapolate
+
+ align:start position:0%
+extrapolation you're gonna extrapolate
+ 
+
+ align:start position:0%
+extrapolation you're gonna extrapolate
+and you can see that this is not really
+
+ align:start position:0%
+and you can see that this is not really
+ 
+
+ align:start position:0%
+and you can see that this is not really
+the most robust thing to do right
+
+ align:start position:0%
+the most robust thing to do right
+ 
+
+ align:start position:0%
+the most robust thing to do right
+because you know if you're have an
+
+ align:start position:0%
+because you know if you're have an
+ 
+
+ align:start position:0%
+because you know if you're have an
+experience you're not that exciting
+
+ align:start position:0%
+experience you're not that exciting
+ 
+
+ align:start position:0%
+experience you're not that exciting
+comfortable extrapolating at all and
+
+ align:start position:0%
+comfortable extrapolating at all and
+ 
+
+ align:start position:0%
+comfortable extrapolating at all and
+then you got to extrapolate you know a
+
+ align:start position:0%
+then you got to extrapolate you know a
+ 
+
+ align:start position:0%
+then you got to extrapolate you know a
+thousand times that's really it should
+
+ align:start position:0%
+thousand times that's really it should
+ 
+
+ align:start position:0%
+thousand times that's really it should
+be a little bit worried about what can
+
+ align:start position:0%
+be a little bit worried about what can
+ 
+
+ align:start position:0%
+be a little bit worried about what can
+happen so let's think about how the ER
+
+ align:start position:0%
+happen so let's think about how the ER
+ 
+
+ align:start position:0%
+happen so let's think about how the ER
+will propagate so we're going to have
+
+ align:start position:0%
+will propagate so we're going to have
+ 
+
+ align:start position:0%
+will propagate so we're going to have
+some errors when we do these
+
+ align:start position:0%
+some errors when we do these
+ 
+
+ align:start position:0%
+some errors when we do these
+extrapolations so we have here our T
+
+ align:start position:0%
+extrapolations so we have here our T
+ 
+
+ align:start position:0%
+extrapolations so we have here our T
+naught T note we're happy we know why
+
+ align:start position:0%
+naught T note we're happy we know why
+ 
+
+ align:start position:0%
+naught T note we're happy we know why
+not this is exactly like woohoo we go
+
+ align:start position:0%
+not this is exactly like woohoo we go
+ 
+
+ align:start position:0%
+not this is exactly like woohoo we go
+one value of y really good all right so
+
+ align:start position:0%
+one value of y really good all right so
+ 
+
+ align:start position:0%
+one value of y really good all right so
+now the question is the first the first
+
+ align:start position:0%
+now the question is the first the first
+ 
+
+ align:start position:0%
+now the question is the first the first
+step now we're gonna get a value y1 that
+
+ align:start position:0%
+step now we're gonna get a value y1 that
+ 
+
+ align:start position:0%
+step now we're gonna get a value y1 that
+we compute with one of these update
+
+ align:start position:0%
+we compute with one of these update
+ 
+
+ align:start position:0%
+we compute with one of these update
+formulas and it's gonna be good to some
+
+ align:start position:0%
+formulas and it's gonna be good to some
+ 
+
+ align:start position:0%
+formulas and it's gonna be good to some
+accuracy depending on how good or genius
+
+ align:start position:0%
+accuracy depending on how good or genius
+ 
+
+ align:start position:0%
+accuracy depending on how good or genius
+our update formula and no one's gonna
+
+ align:start position:0%
+our update formula and no one's gonna
+ 
+
+ align:start position:0%
+our update formula and no one's gonna
+have an R I should comment that this why
+
+ align:start position:0%
+have an R I should comment that this why
+ 
+
+ align:start position:0%
+have an R I should comment that this why
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+although we treat is exact it could have
+
+ align:start position:0%
+although we treat is exact it could have
+ 
+
+ align:start position:0%
+although we treat is exact it could have
+an hour or two but it'll probably be
+
+ align:start position:0%
+an hour or two but it'll probably be
+ 
+
+ align:start position:0%
+an hour or two but it'll probably be
+more like machine precision gonna hurt
+
+ align:start position:0%
+more like machine precision gonna hurt
+ 
+
+ align:start position:0%
+more like machine precision gonna hurt
+because we don't really know the initial
+
+ align:start position:0%
+because we don't really know the initial
+ 
+
+ align:start position:0%
+because we don't really know the initial
+conditions that well or it might be an
+
+ align:start position:0%
+conditions that well or it might be an
+ 
+
+ align:start position:0%
+conditions that well or it might be an
+experimental or about how well we know
+
+ align:start position:0%
+experimental or about how well we know
+ 
+
+ align:start position:0%
+experimental or about how well we know
+with the initial conditions are I'm not
+
+ align:start position:0%
+with the initial conditions are I'm not
+ 
+
+ align:start position:0%
+with the initial conditions are I'm not
+gonna worry about that one for now but
+
+ align:start position:0%
+gonna worry about that one for now but
+ 
+
+ align:start position:0%
+gonna worry about that one for now but
+be aware this is true it we don't really
+
+ align:start position:0%
+be aware this is true it we don't really
+ 
+
+ align:start position:0%
+be aware this is true it we don't really
+know the initial conditions perfectly
+
+ align:start position:0%
+know the initial conditions perfectly
+ 
+
+ align:start position:0%
+know the initial conditions perfectly
+either but certainly even if we treat
+
+ align:start position:0%
+either but certainly even if we treat
+ 
+
+ align:start position:0%
+either but certainly even if we treat
+this as being known perfectly we're not
+
+ align:start position:0%
+this as being known perfectly we're not
+ 
+
+ align:start position:0%
+this as being known perfectly we're not
+gonna have some error by the time we
+
+ align:start position:0%
+gonna have some error by the time we
+ 
+
+ align:start position:0%
+gonna have some error by the time we
+extrapolate to why would so now what
+
+ align:start position:0%
+extrapolate to why would so now what
+ 
+
+ align:start position:0%
+extrapolate to why would so now what
+happens at y2 so now we've added some
+
+ align:start position:0%
+happens at y2 so now we've added some
+ 
+
+ align:start position:0%
+happens at y2 so now we've added some
+worse they were t2 and we started from
+
+ align:start position:0%
+worse they were t2 and we started from
+ 
+
+ align:start position:0%
+worse they were t2 and we started from
+y1 y1 true plus I'm Aaron this is why
+
+ align:start position:0%
+y1 y1 true plus I'm Aaron this is why
+ 
+
+ align:start position:0%
+y1 y1 true plus I'm Aaron this is why
+why not was true we ther a second okay
+
+ align:start position:0%
+why not was true we ther a second okay
+ 
+
+ align:start position:0%
+why not was true we ther a second okay
+go ahead now we're starting from y1 true
+
+ align:start position:0%
+go ahead now we're starting from y1 true
+ 
+
+ align:start position:0%
+go ahead now we're starting from y1 true
+with somewhere in it because our mistake
+
+ align:start position:0%
+with somewhere in it because our mistake
+ 
+
+ align:start position:0%
+with somewhere in it because our mistake
+we made it the first step and then we
+
+ align:start position:0%
+we made it the first step and then we
+ 
+
+ align:start position:0%
+we made it the first step and then we
+see how that step propagates further so
+
+ align:start position:0%
+see how that step propagates further so
+ 
+
+ align:start position:0%
+see how that step propagates further so
+let's see what that's gonna say well say
+
+ align:start position:0%
+let's see what that's gonna say well say
+ 
+
+ align:start position:0%
+let's see what that's gonna say well say
+y 2 is going to equal Y 1 plus delta T
+
+ align:start position:0%
+y 2 is going to equal Y 1 plus delta T
+ 
+
+ align:start position:0%
+y 2 is going to equal Y 1 plus delta T
+times some update formula which will
+
+ align:start position:0%
+times some update formula which will
+ 
+
+ align:start position:0%
+times some update formula which will
+depend on line 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so but why one was not true
+
+ align:start position:0%
+right so but why one was not true
+ 
+
+ align:start position:0%
+right so but why one was not true
+anymore so this is actually equal to the
+
+ align:start position:0%
+anymore so this is actually equal to the
+ 
+
+ align:start position:0%
+anymore so this is actually equal to the
+what should have been the true value of
+
+ align:start position:0%
+what should have been the true value of
+ 
+
+ align:start position:0%
+what should have been the true value of
+y1 if we only knew what it was we don't
+
+ align:start position:0%
+y1 if we only knew what it was we don't
+ 
+
+ align:start position:0%
+y1 if we only knew what it was we don't
+know we have our error that we don't
+
+ align:start position:0%
+know we have our error that we don't
+ 
+
+ align:start position:0%
+know we have our error that we don't
+know exactly how big it is that we added
+
+ align:start position:0%
+know exactly how big it is that we added
+ 
+
+ align:start position:0%
+know exactly how big it is that we added
+one and then we have another term from
+
+ align:start position:0%
+one and then we have another term from
+ 
+
+ align:start position:0%
+one and then we have another term from
+this guy so it's going to be delta T
+
+ align:start position:0%
+this guy so it's going to be delta T
+ 
+
+ align:start position:0%
+this guy so it's going to be delta T
+times G of y1 true plus Delta 1 and then
+
+ align:start position:0%
+times G of y1 true plus Delta 1 and then
+ 
+
+ align:start position:0%
+times G of y1 true plus Delta 1 and then
+we know we're update for him was not
+
+ align:start position:0%
+we know we're update for him was not
+ 
+
+ align:start position:0%
+we know we're update for him was not
+right anyway so there's actually another
+
+ align:start position:0%
+right anyway so there's actually another
+ 
+
+ align:start position:0%
+right anyway so there's actually another
+sort of Delta 2 just because of they are
+
+ align:start position:0%
+sort of Delta 2 just because of they are
+ 
+
+ align:start position:0%
+sort of Delta 2 just because of they are
+in the update formula all right now if
+
+ align:start position:0%
+in the update formula all right now if
+ 
+
+ align:start position:0%
+in the update formula all right now if
+we had a great update formula these
+
+ align:start position:0%
+we had a great update formula these
+ 
+
+ align:start position:0%
+we had a great update formula these
+deltas are kind of small and if somehow
+
+ align:start position:0%
+deltas are kind of small and if somehow
+ 
+
+ align:start position:0%
+deltas are kind of small and if somehow
+by luck our Delta 1 was 0 then and we
+
+ align:start position:0%
+by luck our Delta 1 was 0 then and we
+ 
+
+ align:start position:0%
+by luck our Delta 1 was 0 then and we
+had a great update formula then we think
+
+ align:start position:0%
+had a great update formula then we think
+ 
+
+ align:start position:0%
+had a great update formula then we think
+that this error and y2 is gonna be
+
+ align:start position:0%
+that this error and y2 is gonna be
+ 
+
+ align:start position:0%
+that this error and y2 is gonna be
+pretty small okay but it's not true so
+
+ align:start position:0%
+pretty small okay but it's not true so
+ 
+
+ align:start position:0%
+pretty small okay but it's not true so
+really the errors are pretty big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's see if we can figure out do a
+
+ align:start position:0%
+so let's see if we can figure out do a
+ 
+
+ align:start position:0%
+so let's see if we can figure out do a
+Taylor expansion here so this will be G
+
+ align:start position:0%
+Taylor expansion here so this will be G
+ 
+
+ align:start position:0%
+Taylor expansion here so this will be G
+of y1 true Plus D DG y Jacobian of G
+
+ align:start position:0%
+of y1 true Plus D DG y Jacobian of G
+ 
+
+ align:start position:0%
+of y1 true Plus D DG y Jacobian of G
+respect to Y times Delta one and that's
+
+ align:start position:0%
+respect to Y times Delta one and that's
+ 
+
+ align:start position:0%
+respect to Y times Delta one and that's
+a first order Taylor expansion alright
+
+ align:start position:0%
+a first order Taylor expansion alright
+ 
+
+ align:start position:0%
+a first order Taylor expansion alright
+so now let's kind of group the terms so
+
+ align:start position:0%
+so now let's kind of group the terms so
+ 
+
+ align:start position:0%
+so now let's kind of group the terms so
+y2 is equal to y1 true plus the update
+
+ align:start position:0%
+y2 is equal to y1 true plus the update
+ 
+
+ align:start position:0%
+y2 is equal to y1 true plus the update
+formula of y1 true plus the iron in our
+
+ align:start position:0%
+formula of y1 true plus the iron in our
+ 
+
+ align:start position:0%
+formula of y1 true plus the iron in our
+update formula if we had started at Y at
+
+ align:start position:0%
+update formula if we had started at Y at
+ 
+
+ align:start position:0%
+update formula if we had started at Y at
+the true value so this is what we you
+
+ align:start position:0%
+the true value so this is what we you
+ 
+
+ align:start position:0%
+the true value so this is what we you
+know if somebody told us with the true
+
+ align:start position:0%
+know if somebody told us with the true
+ 
+
+ align:start position:0%
+know if somebody told us with the true
+value of y1 was this is a sizer we'd
+
+ align:start position:0%
+value of y1 was this is a sizer we'd
+ 
+
+ align:start position:0%
+value of y1 was this is a sizer we'd
+expect it's gonna be that little RI we
+
+ align:start position:0%
+expect it's gonna be that little RI we
+ 
+
+ align:start position:0%
+expect it's gonna be that little RI we
+calculated before but then on top of it
+
+ align:start position:0%
+calculated before but then on top of it
+ 
+
+ align:start position:0%
+calculated before but then on top of it
+we have these other terms we have a
+
+ align:start position:0%
+we have these other terms we have a
+ 
+
+ align:start position:0%
+we have these other terms we have a
+delta 1 because y1 was not the true
+
+ align:start position:0%
+delta 1 because y1 was not the true
+ 
+
+ align:start position:0%
+delta 1 because y1 was not the true
+value and sorry I lost it does it to you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we have delta T times DG d UI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times Delta 1 I'll emphasize these are
+
+ align:start position:0%
+times Delta 1 I'll emphasize these are
+ 
+
+ align:start position:0%
+times Delta 1 I'll emphasize these are
+all vectors I think that's it if we go
+
+ align:start position:0%
+all vectors I think that's it if we go
+ 
+
+ align:start position:0%
+all vectors I think that's it if we go
+and keep the first order so what is this
+
+ align:start position:0%
+and keep the first order so what is this
+ 
+
+ align:start position:0%
+and keep the first order so what is this
+thing this is a matrix right tgd Y so
+
+ align:start position:0%
+thing this is a matrix right tgd Y so
+ 
+
+ align:start position:0%
+thing this is a matrix right tgd Y so
+this is I can write it this way its
+
+ align:start position:0%
+this is I can write it this way its
+ 
+
+ align:start position:0%
+this is I can write it this way its
+identity matrix plus delta T times the
+
+ align:start position:0%
+identity matrix plus delta T times the
+ 
+
+ align:start position:0%
+identity matrix plus delta T times the
+Jacobian DG dy times the vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can see at every iteration when
+
+ align:start position:0%
+and you can see at every iteration when
+ 
+
+ align:start position:0%
+and you can see at every iteration when
+I do this I'm gonna get a similar factor
+
+ align:start position:0%
+I do this I'm gonna get a similar factor
+ 
+
+ align:start position:0%
+I do this I'm gonna get a similar factor
+like this and it's gonna again multiply
+
+ align:start position:0%
+like this and it's gonna again multiply
+ 
+
+ align:start position:0%
+like this and it's gonna again multiply
+Delta one I keep on multiplying the my
+
+ align:start position:0%
+Delta one I keep on multiplying the my
+ 
+
+ align:start position:0%
+Delta one I keep on multiplying the my
+urge from my previous step keep getting
+
+ align:start position:0%
+urge from my previous step keep getting
+ 
+
+ align:start position:0%
+urge from my previous step keep getting
+multiplied by this kind of factor so
+
+ align:start position:0%
+multiplied by this kind of factor so
+ 
+
+ align:start position:0%
+multiplied by this kind of factor so
+it's going to be really important to us
+
+ align:start position:0%
+it's going to be really important to us
+ 
+
+ align:start position:0%
+it's going to be really important to us
+I've got what the norm of this matrix is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right is what's gonna happen if the norm
+
+ align:start position:0%
+right is what's gonna happen if the norm
+ 
+
+ align:start position:0%
+right is what's gonna happen if the norm
+of this matrix is big what's happen
+
+ align:start position:0%
+of this matrix is big what's happen
+ 
+
+ align:start position:0%
+of this matrix is big what's happen
+that's right the errors gonna get
+
+ align:start position:0%
+that's right the errors gonna get
+ 
+
+ align:start position:0%
+that's right the errors gonna get
+multiplied by some factor say bigger
+
+ align:start position:0%
+multiplied by some factor say bigger
+ 
+
+ align:start position:0%
+multiplied by some factor say bigger
+than one every iteration and after we go
+
+ align:start position:0%
+than one every iteration and after we go
+ 
+
+ align:start position:0%
+than one every iteration and after we go
+a thousand iterations how big they are
+
+ align:start position:0%
+a thousand iterations how big they are
+ 
+
+ align:start position:0%
+a thousand iterations how big they are
+going to be really big right even if the
+
+ align:start position:0%
+going to be really big right even if the
+ 
+
+ align:start position:0%
+going to be really big right even if the
+thing is quite close to one one plus
+
+ align:start position:0%
+thing is quite close to one one plus
+ 
+
+ align:start position:0%
+thing is quite close to one one plus
+something to the one thousand powers
+
+ align:start position:0%
+something to the one thousand powers
+ 
+
+ align:start position:0%
+something to the one thousand powers
+gigantic so the what was originally a
+
+ align:start position:0%
+gigantic so the what was originally a
+ 
+
+ align:start position:0%
+gigantic so the what was originally a
+pretty small error because we chose a
+
+ align:start position:0%
+pretty small error because we chose a
+ 
+
+ align:start position:0%
+pretty small error because we chose a
+good G method is going to get multiplied
+
+ align:start position:0%
+good G method is going to get multiplied
+ 
+
+ align:start position:0%
+good G method is going to get multiplied
+by this huge amplification factor so the
+
+ align:start position:0%
+by this huge amplification factor so the
+ 
+
+ align:start position:0%
+by this huge amplification factor so the
+key thing for method to be what is
+
+ align:start position:0%
+key thing for method to be what is
+ 
+
+ align:start position:0%
+key thing for method to be what is
+called numerically stable is that this
+
+ align:start position:0%
+called numerically stable is that this
+ 
+
+ align:start position:0%
+called numerically stable is that this
+norm of this matrix has got to be less
+
+ align:start position:0%
+norm of this matrix has got to be less
+ 
+
+ align:start position:0%
+norm of this matrix has got to be less
+than one or maybe even equal equals one
+
+ align:start position:0%
+than one or maybe even equal equals one
+ 
+
+ align:start position:0%
+than one or maybe even equal equals one
+might be okay this is much bigger than
+
+ align:start position:0%
+might be okay this is much bigger than
+ 
+
+ align:start position:0%
+might be okay this is much bigger than
+one you're doomed your numerical R is
+
+ align:start position:0%
+one you're doomed your numerical R is
+ 
+
+ align:start position:0%
+one you're doomed your numerical R is
+just going to blow blow up from step to
+
+ align:start position:0%
+just going to blow blow up from step to
+ 
+
+ align:start position:0%
+just going to blow blow up from step to
+step to step and what's bad about it is
+
+ align:start position:0%
+step to step and what's bad about it is
+ 
+
+ align:start position:0%
+step to step and what's bad about it is
+actually sometimes you might not even be
+
+ align:start position:0%
+actually sometimes you might not even be
+ 
+
+ align:start position:0%
+actually sometimes you might not even be
+aware of this so you'll get some
+
+ align:start position:0%
+aware of this so you'll get some
+ 
+
+ align:start position:0%
+aware of this so you'll get some
+solution because it still calculate some
+
+ align:start position:0%
+solution because it still calculate some
+ 
+
+ align:start position:0%
+solution because it still calculate some
+numbers for the Y's at each step y1 y2
+
+ align:start position:0%
+numbers for the Y's at each step y1 y2
+ 
+
+ align:start position:0%
+numbers for the Y's at each step y1 y2
+y3 1/4 it's just running and running
+
+ align:start position:0%
+y3 1/4 it's just running and running
+ 
+
+ align:start position:0%
+y3 1/4 it's just running and running
+through the calculation but the numbers
+
+ align:start position:0%
+through the calculation but the numbers
+ 
+
+ align:start position:0%
+through the calculation but the numbers
+may become increasingly meaningless
+
+ align:start position:0%
+may become increasingly meaningless
+ 
+
+ align:start position:0%
+may become increasingly meaningless
+further away from the wide true as thing
+
+ align:start position:0%
+further away from the wide true as thing
+ 
+
+ align:start position:0%
+further away from the wide true as thing
+as time goes on it it's a steps go all
+
+ align:start position:0%
+as time goes on it it's a steps go all
+ 
+
+ align:start position:0%
+as time goes on it it's a steps go all
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yes it can yeah so that's what we
+
+ align:start position:0%
+yes yes it can yeah so that's what we
+ 
+
+ align:start position:0%
+yes yes it can yeah so that's what we
+call a stable a numerical method it's
+
+ align:start position:0%
+call a stable a numerical method it's
+ 
+
+ align:start position:0%
+call a stable a numerical method it's
+one that if you make an error an earlier
+
+ align:start position:0%
+one that if you make an error an earlier
+ 
+
+ align:start position:0%
+one that if you make an error an earlier
+step its impact diminishes as Tong steps
+
+ align:start position:0%
+step its impact diminishes as Tong steps
+ 
+
+ align:start position:0%
+step its impact diminishes as Tong steps
+go one that's what you want you can't
+
+ align:start position:0%
+go one that's what you want you can't
+ 
+
+ align:start position:0%
+go one that's what you want you can't
+always see this but if you can that's
+
+ align:start position:0%
+always see this but if you can that's
+ 
+
+ align:start position:0%
+always see this but if you can that's
+really great
+
+ align:start position:0%
+really great
+ 
+
+ align:start position:0%
+really great
+all right and that's what you really
+
+ align:start position:0%
+all right and that's what you really
+ 
+
+ align:start position:0%
+all right and that's what you really
+stable robust kind of method you know I
+
+ align:start position:0%
+stable robust kind of method you know I
+ 
+
+ align:start position:0%
+stable robust kind of method you know I
+give you something stupid stupidity
+
+ align:start position:0%
+give you something stupid stupidity
+ 
+
+ align:start position:0%
+give you something stupid stupidity
+early on my stupid evaporates away and
+
+ align:start position:0%
+early on my stupid evaporates away and
+ 
+
+ align:start position:0%
+early on my stupid evaporates away and
+it goes to the true solution that's what
+
+ align:start position:0%
+it goes to the true solution that's what
+ 
+
+ align:start position:0%
+it goes to the true solution that's what
+you want okay so let's think of cases
+
+ align:start position:0%
+you want okay so let's think of cases
+ 
+
+ align:start position:0%
+you want okay so let's think of cases
+where it's it's going to be problematic
+
+ align:start position:0%
+where it's it's going to be problematic
+ 
+
+ align:start position:0%
+where it's it's going to be problematic
+for sure so if dgv why save if all its
+
+ align:start position:0%
+for sure so if dgv why save if all its
+ 
+
+ align:start position:0%
+for sure so if dgv why save if all its
+eigenvalues are positive and you add it
+
+ align:start position:0%
+eigenvalues are positive and you add it
+ 
+
+ align:start position:0%
+eigenvalues are positive and you add it
+to identity matrix the thing is still
+
+ align:start position:0%
+to identity matrix the thing is still
+ 
+
+ align:start position:0%
+to identity matrix the thing is still
+gonna have identity make
+
+ align:start position:0%
+gonna have identity make
+ 
+
+ align:start position:0%
+gonna have identity make
+I give values bigger than one can you
+
+ align:start position:0%
+I give values bigger than one can you
+ 
+
+ align:start position:0%
+I give values bigger than one can you
+see that right and actually what do we
+
+ align:start position:0%
+see that right and actually what do we
+ 
+
+ align:start position:0%
+see that right and actually what do we
+say when dg2 y is positive has a
+
+ align:start position:0%
+say when dg2 y is positive has a
+ 
+
+ align:start position:0%
+say when dg2 y is positive has a
+positive eigenvalue you guys have a word
+
+ align:start position:0%
+positive eigenvalue you guys have a word
+ 
+
+ align:start position:0%
+positive eigenvalue you guys have a word
+for this already you learn in your
+
+ align:start position:0%
+for this already you learn in your
+ 
+
+ align:start position:0%
+for this already you learn in your
+differential equations class what do you
+
+ align:start position:0%
+differential equations class what do you
+ 
+
+ align:start position:0%
+differential equations class what do you
+call this kind of differential equations
+
+ align:start position:0%
+call this kind of differential equations
+ 
+
+ align:start position:0%
+call this kind of differential equations
+maybe not dg2 is back up to have a DF D
+
+ align:start position:0%
+maybe not dg2 is back up to have a DF D
+ 
+
+ align:start position:0%
+maybe not dg2 is back up to have a DF D
+Y if DF dy if that Jacobian has a
+
+ align:start position:0%
+Y if DF dy if that Jacobian has a
+ 
+
+ align:start position:0%
+Y if DF dy if that Jacobian has a
+positive eigen value what do you say yes
+
+ align:start position:0%
+positive eigen value what do you say yes
+ 
+
+ align:start position:0%
+positive eigen value what do you say yes
+remember this okay so this is probably
+
+ align:start position:0%
+remember this okay so this is probably
+ 
+
+ align:start position:0%
+remember this okay so this is probably
+called unstable differential equations
+
+ align:start position:0%
+called unstable differential equations
+ 
+
+ align:start position:0%
+called unstable differential equations
+right so if there's any positive eigen
+
+ align:start position:0%
+right so if there's any positive eigen
+ 
+
+ align:start position:0%
+right so if there's any positive eigen
+values then two initial conditions that
+
+ align:start position:0%
+values then two initial conditions that
+ 
+
+ align:start position:0%
+values then two initial conditions that
+differ by a little differential will
+
+ align:start position:0%
+differ by a little differential will
+ 
+
+ align:start position:0%
+differ by a little differential will
+exponentially separate as time goes on
+
+ align:start position:0%
+exponentially separate as time goes on
+ 
+
+ align:start position:0%
+exponentially separate as time goes on
+as long as the difference as any
+
+ align:start position:0%
+as long as the difference as any
+ 
+
+ align:start position:0%
+as long as the difference as any
+projection in the direction of the of
+
+ align:start position:0%
+projection in the direction of the of
+ 
+
+ align:start position:0%
+projection in the direction of the of
+the bad eigenvector right so those are
+
+ align:start position:0%
+the bad eigenvector right so those are
+ 
+
+ align:start position:0%
+the bad eigenvector right so those are
+called numerically unstable you know a
+
+ align:start position:0%
+called numerically unstable you know a
+ 
+
+ align:start position:0%
+called numerically unstable you know a
+lot of this actually existed in reality
+
+ align:start position:0%
+lot of this actually existed in reality
+ 
+
+ align:start position:0%
+lot of this actually existed in reality
+so explosions there's because you had
+
+ align:start position:0%
+so explosions there's because you had
+ 
+
+ align:start position:0%
+so explosions there's because you had
+some positive eigen value somewhere for
+
+ align:start position:0%
+some positive eigen value somewhere for
+ 
+
+ align:start position:0%
+some positive eigen value somewhere for
+example amplifiers like you buy an
+
+ align:start position:0%
+example amplifiers like you buy an
+ 
+
+ align:start position:0%
+example amplifiers like you buy an
+amplifier to crank up the music you get
+
+ align:start position:0%
+amplifier to crank up the music you get
+ 
+
+ align:start position:0%
+amplifier to crank up the music you get
+positive feedback when I remember first
+
+ align:start position:0%
+positive feedback when I remember first
+ 
+
+ align:start position:0%
+positive feedback when I remember first
+asjuan walk to some strange place and
+
+ align:start position:0%
+asjuan walk to some strange place and
+ 
+
+ align:start position:0%
+asjuan walk to some strange place and
+for some reason you got the feedback
+
+ align:start position:0%
+for some reason you got the feedback
+ 
+
+ align:start position:0%
+for some reason you got the feedback
+from the speakers so he had a positive
+
+ align:start position:0%
+from the speakers so he had a positive
+ 
+
+ align:start position:0%
+from the speakers so he had a positive
+eigenvalue to go there he little tiny
+
+ align:start position:0%
+eigenvalue to go there he little tiny
+ 
+
+ align:start position:0%
+eigenvalue to go there he little tiny
+noise and this microphone amplified to a
+
+ align:start position:0%
+noise and this microphone amplified to a
+ 
+
+ align:start position:0%
+noise and this microphone amplified to a
+big squeak
+
+ align:start position:0%
+big squeak
+ 
+
+ align:start position:0%
+big squeak
+so there are real systems like this that
+
+ align:start position:0%
+so there are real systems like this that
+ 
+
+ align:start position:0%
+so there are real systems like this that
+amplify and sometimes we want to model
+
+ align:start position:0%
+amplify and sometimes we want to model
+ 
+
+ align:start position:0%
+amplify and sometimes we want to model
+them like explosions for example is a
+
+ align:start position:0%
+them like explosions for example is a
+ 
+
+ align:start position:0%
+them like explosions for example is a
+pretty important word for chemical
+
+ align:start position:0%
+pretty important word for chemical
+ 
+
+ align:start position:0%
+pretty important word for chemical
+engineers but it's gonna be really tough
+
+ align:start position:0%
+engineers but it's gonna be really tough
+ 
+
+ align:start position:0%
+engineers but it's gonna be really tough
+because if you it's got positive
+
+ align:start position:0%
+because if you it's got positive
+ 
+
+ align:start position:0%
+because if you it's got positive
+eigenvalues then this is probably gonna
+
+ align:start position:0%
+eigenvalues then this is probably gonna
+ 
+
+ align:start position:0%
+eigenvalues then this is probably gonna
+have a norm bigger than one and then
+
+ align:start position:0%
+have a norm bigger than one and then
+ 
+
+ align:start position:0%
+have a norm bigger than one and then
+whatever little errors we make it any
+
+ align:start position:0%
+whatever little errors we make it any
+ 
+
+ align:start position:0%
+whatever little errors we make it any
+step in the whole calculation or we get
+
+ align:start position:0%
+step in the whole calculation or we get
+ 
+
+ align:start position:0%
+step in the whole calculation or we get
+amplified an amplified and amplified and
+
+ align:start position:0%
+amplified an amplified and amplified and
+ 
+
+ align:start position:0%
+amplified an amplified and amplified and
+who knows if we're gonna have any
+
+ align:start position:0%
+who knows if we're gonna have any
+ 
+
+ align:start position:0%
+who knows if we're gonna have any
+reality left in our solution by the time
+
+ align:start position:0%
+reality left in our solution by the time
+ 
+
+ align:start position:0%
+reality left in our solution by the time
+we get to the end okay all right so
+
+ align:start position:0%
+we get to the end okay all right so
+ 
+
+ align:start position:0%
+we get to the end okay all right so
+that's that's one kind of problem so how
+
+ align:start position:0%
+that's that's one kind of problem so how
+ 
+
+ align:start position:0%
+that's that's one kind of problem so how
+about we have a have a problem that's
+
+ align:start position:0%
+about we have a have a problem that's
+ 
+
+ align:start position:0%
+about we have a have a problem that's
+intrinsically stable that means that all
+
+ align:start position:0%
+intrinsically stable that means that all
+ 
+
+ align:start position:0%
+intrinsically stable that means that all
+the eigenvalues of the Jacobian of the
+
+ align:start position:0%
+the eigenvalues of the Jacobian of the
+ 
+
+ align:start position:0%
+the eigenvalues of the Jacobian of the
+original problem are negative so the
+
+ align:start position:0%
+original problem are negative so the
+ 
+
+ align:start position:0%
+original problem are negative so the
+things should be perfectly stable all
+
+ align:start position:0%
+things should be perfectly stable all
+ 
+
+ align:start position:0%
+things should be perfectly stable all
+from whatever initial kitchen they start
+
+ align:start position:0%
+from whatever initial kitchen they start
+ 
+
+ align:start position:0%
+from whatever initial kitchen they start
+to start it from the whole things are
+
+ align:start position:0%
+to start it from the whole things are
+ 
+
+ align:start position:0%
+to start it from the whole things are
+sure to come down to like an equilibrium
+
+ align:start position:0%
+sure to come down to like an equilibrium
+ 
+
+ align:start position:0%
+sure to come down to like an equilibrium
+point so that's a pretty common
+
+ align:start position:0%
+point so that's a pretty common
+ 
+
+ align:start position:0%
+point so that's a pretty common
+situation in chemical engineering - you
+
+ align:start position:0%
+situation in chemical engineering - you
+ 
+
+ align:start position:0%
+situation in chemical engineering - you
+start from some some state and it
+
+ align:start position:0%
+start from some some state and it
+ 
+
+ align:start position:0%
+start from some some state and it
+relaxes down to like an equilibrium
+
+ align:start position:0%
+relaxes down to like an equilibrium
+ 
+
+ align:start position:0%
+relaxes down to like an equilibrium
+state or a steady state well-behaved
+
+ align:start position:0%
+state or a steady state well-behaved
+ 
+
+ align:start position:0%
+state or a steady state well-behaved
+systems act like that so what I'm going
+
+ align:start position:0%
+systems act like that so what I'm going
+ 
+
+ align:start position:0%
+systems act like that so what I'm going
+to show you is that the despite the fact
+
+ align:start position:0%
+to show you is that the despite the fact
+ 
+
+ align:start position:0%
+to show you is that the despite the fact
+that the DF dy is well behaved it's
+
+ align:start position:0%
+that the DF dy is well behaved it's
+ 
+
+ align:start position:0%
+that the DF dy is well behaved it's
+possible that this some matrix might
+
+ align:start position:0%
+possible that this some matrix might
+ 
+
+ align:start position:0%
+possible that this some matrix might
+still be poorly behaved and still have a
+
+ align:start position:0%
+still be poorly behaved and still have a
+ 
+
+ align:start position:0%
+still be poorly behaved and still have a
+norm bigger than one and so that means
+
+ align:start position:0%
+norm bigger than one and so that means
+ 
+
+ align:start position:0%
+norm bigger than one and so that means
+you started from a problem that was
+
+ align:start position:0%
+you started from a problem that was
+ 
+
+ align:start position:0%
+you started from a problem that was
+perfectly well behaved and you broke it
+
+ align:start position:0%
+perfectly well behaved and you broke it
+ 
+
+ align:start position:0%
+perfectly well behaved and you broke it
+by your choice of numerical method so
+
+ align:start position:0%
+by your choice of numerical method so
+ 
+
+ align:start position:0%
+by your choice of numerical method so
+this is a very bad one this is the kind
+
+ align:start position:0%
+this is a very bad one this is the kind
+ 
+
+ align:start position:0%
+this is a very bad one this is the kind
+that could be really embarrassed if
+
+ align:start position:0%
+that could be really embarrassed if
+ 
+
+ align:start position:0%
+that could be really embarrassed if
+you're working in a company your boss
+
+ align:start position:0%
+you're working in a company your boss
+ 
+
+ align:start position:0%
+you're working in a company your boss
+gives you a problem he says please tell
+
+ align:start position:0%
+gives you a problem he says please tell
+ 
+
+ align:start position:0%
+gives you a problem he says please tell
+me the time it's gonna take the our
+
+ align:start position:0%
+me the time it's gonna take the our
+ 
+
+ align:start position:0%
+me the time it's gonna take the our
+reactor to relax after startup the
+
+ align:start position:0%
+reactor to relax after startup the
+ 
+
+ align:start position:0%
+reactor to relax after startup the
+system is perfectly well behaved it
+
+ align:start position:0%
+system is perfectly well behaved it
+ 
+
+ align:start position:0%
+system is perfectly well behaved it
+gives these beautiful equations that's
+
+ align:start position:0%
+gives these beautiful equations that's
+ 
+
+ align:start position:0%
+gives these beautiful equations that's
+your previous coworker worked out
+
+ align:start position:0%
+your previous coworker worked out
+ 
+
+ align:start position:0%
+your previous coworker worked out
+everything's fine you put it in there
+
+ align:start position:0%
+everything's fine you put it in there
+ 
+
+ align:start position:0%
+everything's fine you put it in there
+you use your stupid numerical solver and
+
+ align:start position:0%
+you use your stupid numerical solver and
+ 
+
+ align:start position:0%
+you use your stupid numerical solver and
+you get a wild oscillation and the thing
+
+ align:start position:0%
+you get a wild oscillation and the thing
+ 
+
+ align:start position:0%
+you get a wild oscillation and the thing
+blows up okay and that's going to be
+
+ align:start position:0%
+blows up okay and that's going to be
+ 
+
+ align:start position:0%
+blows up okay and that's going to be
+because of a poor choice of G so that it
+
+ align:start position:0%
+because of a poor choice of G so that it
+ 
+
+ align:start position:0%
+because of a poor choice of G so that it
+makes this normal this matrix bigger
+
+ align:start position:0%
+makes this normal this matrix bigger
+ 
+
+ align:start position:0%
+makes this normal this matrix bigger
+than one it's pretty easy for that to
+
+ align:start position:0%
+than one it's pretty easy for that to
+ 
+
+ align:start position:0%
+than one it's pretty easy for that to
+happen so you don't need a very
+
+ align:start position:0%
+happen so you don't need a very
+ 
+
+ align:start position:0%
+happen so you don't need a very
+complicated
+
+ align:start position:0%
+complicated
+ 
+
+ align:start position:0%
+complicated
+show it so let's just do a scalar case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe Y DT is equal to negative 2y y
+
+ align:start position:0%
+maybe Y DT is equal to negative 2y y
+ 
+
+ align:start position:0%
+maybe Y DT is equal to negative 2y y
+okay so this is a well-behaved
+
+ align:start position:0%
+okay so this is a well-behaved
+ 
+
+ align:start position:0%
+okay so this is a well-behaved
+differential equation what's the
+
+ align:start position:0%
+differential equation what's the
+ 
+
+ align:start position:0%
+differential equation what's the
+solution oh say why not why what's the
+
+ align:start position:0%
+solution oh say why not why what's the
+ 
+
+ align:start position:0%
+solution oh say why not why what's the
+solution yeah okay so it's perfectly
+
+ align:start position:0%
+solution yeah okay so it's perfectly
+ 
+
+ align:start position:0%
+solution yeah okay so it's perfectly
+well behaved function plot it here's one
+
+ align:start position:0%
+well behaved function plot it here's one
+ 
+
+ align:start position:0%
+well behaved function plot it here's one
+because okay so now let's solve this
+
+ align:start position:0%
+because okay so now let's solve this
+ 
+
+ align:start position:0%
+because okay so now let's solve this
+with a forward Euler method so you say
+
+ align:start position:0%
+with a forward Euler method so you say
+ 
+
+ align:start position:0%
+with a forward Euler method so you say
+that Y nu is equal to y plus delta T so
+
+ align:start position:0%
+that Y nu is equal to y plus delta T so
+ 
+
+ align:start position:0%
+that Y nu is equal to y plus delta T so
+in this case this is f okay negative 2y
+
+ align:start position:0%
+in this case this is f okay negative 2y
+ 
+
+ align:start position:0%
+in this case this is f okay negative 2y
+so perform or lower this is saying that
+
+ align:start position:0%
+so perform or lower this is saying that
+ 
+
+ align:start position:0%
+so perform or lower this is saying that
+this is negative 2y all right so let's
+
+ align:start position:0%
+this is negative 2y all right so let's
+ 
+
+ align:start position:0%
+this is negative 2y all right so let's
+choose a delta T so you don't equals one
+
+ align:start position:0%
+choose a delta T so you don't equals one
+ 
+
+ align:start position:0%
+choose a delta T so you don't equals one
+to start with so we're going to compute
+
+ align:start position:0%
+to start with so we're going to compute
+ 
+
+ align:start position:0%
+to start with so we're going to compute
+we started T equals zero we're computing
+
+ align:start position:0%
+we started T equals zero we're computing
+ 
+
+ align:start position:0%
+we started T equals zero we're computing
+out the T so we put one in here our
+
+ align:start position:0%
+out the T so we put one in here our
+ 
+
+ align:start position:0%
+out the T so we put one in here our
+initial condition was y equals one this
+
+ align:start position:0%
+initial condition was y equals one this
+ 
+
+ align:start position:0%
+initial condition was y equals one this
+one so this one times negative 2 times 1
+
+ align:start position:0%
+one so this one times negative 2 times 1
+ 
+
+ align:start position:0%
+one so this one times negative 2 times 1
+is negative 2 this is a 1 1 minus 2 is
+
+ align:start position:0%
+is negative 2 this is a 1 1 minus 2 is
+ 
+
+ align:start position:0%
+is negative 2 this is a 1 1 minus 2 is
+negative 1 so the first at the first
+
+ align:start position:0%
+negative 1 so the first at the first
+ 
+
+ align:start position:0%
+negative 1 so the first at the first
+step it goes from here under there okay
+
+ align:start position:0%
+step it goes from here under there okay
+ 
+
+ align:start position:0%
+step it goes from here under there okay
+this is not looking good
+
+ align:start position:0%
+this is not looking good
+ 
+
+ align:start position:0%
+this is not looking good
+all right this is a fifth man this is a
+
+ align:start position:0%
+all right this is a fifth man this is a
+ 
+
+ align:start position:0%
+all right this is a fifth man this is a
+physical variable especially gradually
+
+ align:start position:0%
+physical variable especially gradually
+ 
+
+ align:start position:0%
+physical variable especially gradually
+relaxing toward zero it going negative
+
+ align:start position:0%
+relaxing toward zero it going negative
+ 
+
+ align:start position:0%
+relaxing toward zero it going negative
+is not what you want all right and then
+
+ align:start position:0%
+is not what you want all right and then
+ 
+
+ align:start position:0%
+is not what you want all right and then
+I think we could go to the next step if
+
+ align:start position:0%
+I think we could go to the next step if
+ 
+
+ align:start position:0%
+I think we could go to the next step if
+you want so we can put in suppose Y is
+
+ align:start position:0%
+you want so we can put in suppose Y is
+ 
+
+ align:start position:0%
+you want so we can put in suppose Y is
+negative one and we're still doing a
+
+ align:start position:0%
+negative one and we're still doing a
+ 
+
+ align:start position:0%
+negative one and we're still doing a
+delta T of one step so negative 1 times
+
+ align:start position:0%
+delta T of one step so negative 1 times
+ 
+
+ align:start position:0%
+delta T of one step so negative 1 times
+negative 2 is positive 2 plus negative 1
+
+ align:start position:0%
+negative 2 is positive 2 plus negative 1
+ 
+
+ align:start position:0%
+negative 2 is positive 2 plus negative 1
+so this goes back to the starting point
+
+ align:start position:0%
+so this goes back to the starting point
+ 
+
+ align:start position:0%
+so this goes back to the starting point
+I'll get the sawtooth that's what you
+
+ align:start position:0%
+I'll get the sawtooth that's what you
+ 
+
+ align:start position:0%
+I'll get the sawtooth that's what you
+get and it turns out actually if you
+
+ align:start position:0%
+get and it turns out actually if you
+ 
+
+ align:start position:0%
+get and it turns out actually if you
+make delta T any larger than 1 then this
+
+ align:start position:0%
+make delta T any larger than 1 then this
+ 
+
+ align:start position:0%
+make delta T any larger than 1 then this
+thing this sawtooth amplifies so you
+
+ align:start position:0%
+thing this sawtooth amplifies so you
+ 
+
+ align:start position:0%
+thing this sawtooth amplifies so you
+have a oscillating solution that
+
+ align:start position:0%
+have a oscillating solution that
+ 
+
+ align:start position:0%
+have a oscillating solution that
+explodes which is a little bit different
+
+ align:start position:0%
+explodes which is a little bit different
+ 
+
+ align:start position:0%
+explodes which is a little bit different
+than the physical solution which gently
+
+ align:start position:0%
+than the physical solution which gently
+ 
+
+ align:start position:0%
+than the physical solution which gently
+relaxes okay and so this is just a
+
+ align:start position:0%
+relaxes okay and so this is just a
+ 
+
+ align:start position:0%
+relaxes okay and so this is just a
+scalar equation that you guys could have
+
+ align:start position:0%
+scalar equation that you guys could have
+ 
+
+ align:start position:0%
+scalar equation that you guys could have
+done in high school if your high school
+
+ align:start position:0%
+done in high school if your high school
+ 
+
+ align:start position:0%
+done in high school if your high school
+math teacher would be brave you would
+
+ align:start position:0%
+math teacher would be brave you would
+ 
+
+ align:start position:0%
+math teacher would be brave you would
+have show it to you but he did want to
+
+ align:start position:0%
+have show it to you but he did want to
+ 
+
+ align:start position:0%
+have show it to you but he did want to
+ruin your faith in the forward Euler
+
+ align:start position:0%
+ruin your faith in the forward Euler
+ 
+
+ align:start position:0%
+ruin your faith in the forward Euler
+method so he just showed you some nice
+
+ align:start position:0%
+method so he just showed you some nice
+ 
+
+ align:start position:0%
+method so he just showed you some nice
+simple one that worked out now you can
+
+ align:start position:0%
+simple one that worked out now you can
+ 
+
+ align:start position:0%
+simple one that worked out now you can
+make this work better by making the
+
+ align:start position:0%
+make this work better by making the
+ 
+
+ align:start position:0%
+make this work better by making the
+delta T smaller if you make the delta T
+
+ align:start position:0%
+delta T smaller if you make the delta T
+ 
+
+ align:start position:0%
+delta T smaller if you make the delta T
+small enough I think in this case I
+
+ align:start position:0%
+small enough I think in this case I
+ 
+
+ align:start position:0%
+small enough I think in this case I
+think is delta T is less than 1/2 then
+
+ align:start position:0%
+think is delta T is less than 1/2 then
+ 
+
+ align:start position:0%
+think is delta T is less than 1/2 then
+this actually behaves somewhat
+
+ align:start position:0%
+this actually behaves somewhat
+ 
+
+ align:start position:0%
+this actually behaves somewhat
+reasonably and so what's going on there
+
+ align:start position:0%
+reasonably and so what's going on there
+ 
+
+ align:start position:0%
+reasonably and so what's going on there
+is that I add any matrices like positive
+
+ align:start position:0%
+is that I add any matrices like positive
+ 
+
+ align:start position:0%
+is that I add any matrices like positive
+my Jacobian is negative and if I make
+
+ align:start position:0%
+my Jacobian is negative and if I make
+ 
+
+ align:start position:0%
+my Jacobian is negative and if I make
+delta T small enough this big positive
+
+ align:start position:0%
+delta T small enough this big positive
+ 
+
+ align:start position:0%
+delta T small enough this big positive
+number is bigger than this smaller
+
+ align:start position:0%
+number is bigger than this smaller
+ 
+
+ align:start position:0%
+number is bigger than this smaller
+negative number and the whole thing
+
+ align:start position:0%
+negative number and the whole thing
+ 
+
+ align:start position:0%
+negative number and the whole thing
+stays positive but less than 1 and so
+
+ align:start position:0%
+stays positive but less than 1 and so
+ 
+
+ align:start position:0%
+stays positive but less than 1 and so
+then the norm is good but if I make
+
+ align:start position:0%
+then the norm is good but if I make
+ 
+
+ align:start position:0%
+then the norm is good but if I make
+delta T 2 large I make this second term
+
+ align:start position:0%
+delta T 2 large I make this second term
+ 
+
+ align:start position:0%
+delta T 2 large I make this second term
+much larger if he gets much larger than
+
+ align:start position:0%
+much larger if he gets much larger than
+ 
+
+ align:start position:0%
+much larger if he gets much larger than
+1 it overwhelms the first term that
+
+ align:start position:0%
+1 it overwhelms the first term that
+ 
+
+ align:start position:0%
+1 it overwhelms the first term that
+thing's negative but when I do the norm
+
+ align:start position:0%
+thing's negative but when I do the norm
+ 
+
+ align:start position:0%
+thing's negative but when I do the norm
+it's positive and so it has an expansion
+
+ align:start position:0%
+it's positive and so it has an expansion
+ 
+
+ align:start position:0%
+it's positive and so it has an expansion
+and the negative 1 is why we get these
+
+ align:start position:0%
+and the negative 1 is why we get these
+ 
+
+ align:start position:0%
+and the negative 1 is why we get these
+oscillations so if you ever do numerical
+
+ align:start position:0%
+oscillations so if you ever do numerical
+ 
+
+ align:start position:0%
+oscillations so if you ever do numerical
+differential equation solution and you
+
+ align:start position:0%
+differential equation solution and you
+ 
+
+ align:start position:0%
+differential equation solution and you
+start seeing this kind of stuff it's
+
+ align:start position:0%
+start seeing this kind of stuff it's
+ 
+
+ align:start position:0%
+start seeing this kind of stuff it's
+almost certainly relate to this
+
+ align:start position:0%
+almost certainly relate to this
+ 
+
+ align:start position:0%
+almost certainly relate to this
+numerical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instability of the method and not really
+
+ align:start position:0%
+instability of the method and not really
+ 
+
+ align:start position:0%
+instability of the method and not really
+a physical thing I mean there are
+
+ align:start position:0%
+a physical thing I mean there are
+ 
+
+ align:start position:0%
+a physical thing I mean there are
+physical things that do this but not too
+
+ align:start position:0%
+physical things that do this but not too
+ 
+
+ align:start position:0%
+physical things that do this but not too
+often in chemical engineering
+
+ align:start position:0%
+often in chemical engineering
+ 
+
+ align:start position:0%
+often in chemical engineering
+fortunately
+
+ align:start position:0%
+fortunately
+ 
+
+ align:start position:0%
+fortunately
+all right questions the questions okay
+
+ align:start position:0%
+all right questions the questions okay
+ 
+
+ align:start position:0%
+all right questions the questions okay
+so in the textbook they have a big
+
+ align:start position:0%
+so in the textbook they have a big
+ 
+
+ align:start position:0%
+so in the textbook they have a big
+discussion about how to evaluate
+
+ align:start position:0%
+discussion about how to evaluate
+ 
+
+ align:start position:0%
+discussion about how to evaluate
+different fee methods in order to figure
+
+ align:start position:0%
+different fee methods in order to figure
+ 
+
+ align:start position:0%
+different fee methods in order to figure
+out if they're if they're guaranteed to
+
+ align:start position:0%
+out if they're if they're guaranteed to
+ 
+
+ align:start position:0%
+out if they're if they're guaranteed to
+be stable or under what conditions are
+
+ align:start position:0%
+be stable or under what conditions are
+ 
+
+ align:start position:0%
+be stable or under what conditions are
+stable and so that's that's worth a look
+
+ align:start position:0%
+stable and so that's that's worth a look
+ 
+
+ align:start position:0%
+stable and so that's that's worth a look
+to see and they are the detailed
+
+ align:start position:0%
+to see and they are the detailed
+ 
+
+ align:start position:0%
+to see and they are the detailed
+derivations for several questions
+
+ align:start position:0%
+derivations for several questions
+ 
+
+ align:start position:0%
+derivations for several questions
+alright so for the homework homework 4
+
+ align:start position:0%
+alright so for the homework homework 4
+ 
+
+ align:start position:0%
+alright so for the homework homework 4
+you're gonna have to write your own OD
+
+ align:start position:0%
+you're gonna have to write your own OD
+ 
+
+ align:start position:0%
+you're gonna have to write your own OD
+solver so you'll do update formulas and
+
+ align:start position:0%
+solver so you'll do update formulas and
+ 
+
+ align:start position:0%
+solver so you'll do update formulas and
+compare them when you come we come back
+
+ align:start position:0%
+compare them when you come we come back
+ 
+
+ align:start position:0%
+compare them when you come we come back
+on Tuesday I'll show you how this is
+
+ align:start position:0%
+on Tuesday I'll show you how this is
+ 
+
+ align:start position:0%
+on Tuesday I'll show you how this is
+usually dealt with by switching to
+
+ align:start position:0%
+usually dealt with by switching to
+ 
+
+ align:start position:0%
+usually dealt with by switching to
+implicit solvers and and talk about that
+
+ align:start position:0%
+implicit solvers and and talk about that
+ 
+
+ align:start position:0%
+implicit solvers and and talk about that
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+oh good weekend joy the three days off
\ No newline at end of file
diff --git a/Klw2POjgzVo.txt b/Klw2POjgzVo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fbd92ff0ec241d7af696d103e2d27c020407438b
--- /dev/null
+++ b/Klw2POjgzVo.txt
@@ -0,0 +1,6395 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by talking about clip X and then we're
+
+ align:start position:0%
+by talking about clip X and then we're
+ 
+
+ align:start position:0%
+by talking about clip X and then we're
+gonna move into module four which is the
+
+ align:start position:0%
+gonna move into module four which is the
+ 
+
+ align:start position:0%
+gonna move into module four which is the
+last module before spring break I'm
+
+ align:start position:0%
+last module before spring break I'm
+ 
+
+ align:start position:0%
+last module before spring break I'm
+synthesis and assembly line biosynthesis
+
+ align:start position:0%
+synthesis and assembly line biosynthesis
+ 
+
+ align:start position:0%
+synthesis and assembly line biosynthesis
+here so basically last time where we
+
+ align:start position:0%
+here so basically last time where we
+ 
+
+ align:start position:0%
+here so basically last time where we
+left off is we went over experiments
+
+ align:start position:0%
+left off is we went over experiments
+ 
+
+ align:start position:0%
+left off is we went over experiments
+that were done to look at denaturation
+
+ align:start position:0%
+that were done to look at denaturation
+ 
+
+ align:start position:0%
+that were done to look at denaturation
+translocation and degradation by clip XP
+
+ align:start position:0%
+translocation and degradation by clip XP
+ 
+
+ align:start position:0%
+translocation and degradation by clip XP
+and closed with a question about you
+
+ align:start position:0%
+and closed with a question about you
+ 
+
+ align:start position:0%
+and closed with a question about you
+know what actually is going on in clip X
+
+ align:start position:0%
+know what actually is going on in clip X
+ 
+
+ align:start position:0%
+know what actually is going on in clip X
+with this ATP binding and hydrolysis to
+
+ align:start position:0%
+with this ATP binding and hydrolysis to
+ 
+
+ align:start position:0%
+with this ATP binding and hydrolysis to
+allow for these condemned protein
+
+ align:start position:0%
+allow for these condemned protein
+ 
+
+ align:start position:0%
+allow for these condemned protein
+substrates to be unfolded and
+
+ align:start position:0%
+substrates to be unfolded and
+ 
+
+ align:start position:0%
+substrates to be unfolded and
+translocated into the degradation
+
+ align:start position:0%
+translocated into the degradation
+ 
+
+ align:start position:0%
+translocated into the degradation
+chamber and I left you just with this
+
+ align:start position:0%
+chamber and I left you just with this
+ 
+
+ align:start position:0%
+chamber and I left you just with this
+statement that you know although we
+
+ align:start position:0%
+statement that you know although we
+ 
+
+ align:start position:0%
+statement that you know although we
+think about clip X as this you know
+
+ align:start position:0%
+think about clip X as this you know
+ 
+
+ align:start position:0%
+think about clip X as this you know
+hexamer that has six identical subunits
+
+ align:start position:0%
+hexamer that has six identical subunits
+ 
+
+ align:start position:0%
+hexamer that has six identical subunits
+what studies have shown is that there's
+
+ align:start position:0%
+what studies have shown is that there's
+ 
+
+ align:start position:0%
+what studies have shown is that there's
+some inherent asymmetry within this
+
+ align:start position:0%
+some inherent asymmetry within this
+ 
+
+ align:start position:0%
+some inherent asymmetry within this
+Triple A plus ATPase and that's what
+
+ align:start position:0%
+Triple A plus ATPase and that's what
+ 
+
+ align:start position:0%
+Triple A plus ATPase and that's what
+we're going to talk about a little bit
+
+ align:start position:0%
+we're going to talk about a little bit
+ 
+
+ align:start position:0%
+we're going to talk about a little bit
+so this is just a slide from a few
+
+ align:start position:0%
+so this is just a slide from a few
+ 
+
+ align:start position:0%
+so this is just a slide from a few
+lectures ago that's showing the top view
+
+ align:start position:0%
+lectures ago that's showing the top view
+ 
+
+ align:start position:0%
+lectures ago that's showing the top view
+and side view of clip X and how we've
+
+ align:start position:0%
+and side view of clip X and how we've
+ 
+
+ align:start position:0%
+and side view of clip X and how we've
+thought about this and I think these
+
+ align:start position:0%
+thought about this and I think these
+ 
+
+ align:start position:0%
+thought about this and I think these
+studies just really highlight how
+
+ align:start position:0%
+studies just really highlight how
+ 
+
+ align:start position:0%
+studies just really highlight how
+complicated these machines are and that
+
+ align:start position:0%
+complicated these machines are and that
+ 
+
+ align:start position:0%
+complicated these machines are and that
+there's still a lot more we need to
+
+ align:start position:0%
+there's still a lot more we need to
+ 
+
+ align:start position:0%
+there's still a lot more we need to
+figure out here so as I said last time
+
+ align:start position:0%
+figure out here so as I said last time
+ 
+
+ align:start position:0%
+figure out here so as I said last time
+this asymmetry comes from whether or not
+
+ align:start position:0%
+this asymmetry comes from whether or not
+ 
+
+ align:start position:0%
+this asymmetry comes from whether or not
+each clip X subunit is bound to
+
+ align:start position:0%
+each clip X subunit is bound to
+ 
+
+ align:start position:0%
+each clip X subunit is bound to
+nucleotide and so basically from looking
+
+ align:start position:0%
+nucleotide and so basically from looking
+ 
+
+ align:start position:0%
+nucleotide and so basically from looking
+at many different crystal structures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what can be done is that the clip X
+
+ align:start position:0%
+okay what can be done is that the clip X
+ 
+
+ align:start position:0%
+okay what can be done is that the clip X
+subunits can be divided into two
+
+ align:start position:0%
+subunits can be divided into two
+ 
+
+ align:start position:0%
+subunits can be divided into two
+different types okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+based on conformation here okay and so
+
+ align:start position:0%
+based on conformation here okay and so
+ 
+
+ align:start position:0%
+based on conformation here okay and so
+in thinking about this we want to first
+
+ align:start position:0%
+in thinking about this we want to first
+ 
+
+ align:start position:0%
+in thinking about this we want to first
+think about the clip X domain
+
+ align:start position:0%
+think about the clip X domain
+ 
+
+ align:start position:0%
+think about the clip X domain
+organization okay and if we just think
+
+ align:start position:0%
+organization okay and if we just think
+ 
+
+ align:start position:0%
+organization okay and if we just think
+about this what clip X has is an N
+
+ align:start position:0%
+about this what clip X has is an N
+ 
+
+ align:start position:0%
+about this what clip X has is an N
+domain followed by a domain that's
+
+ align:start position:0%
+domain followed by a domain that's
+ 
+
+ align:start position:0%
+domain followed by a domain that's
+called the large domain and then
+
+ align:start position:0%
+called the large domain and then
+ 
+
+ align:start position:0%
+called the large domain and then
+followed by a small domain here okay so
+
+ align:start position:0%
+followed by a small domain here okay so
+ 
+
+ align:start position:0%
+followed by a small domain here okay so
+633 amino acids just to give you a sense
+
+ align:start position:0%
+633 amino acids just to give you a sense
+ 
+
+ align:start position:0%
+633 amino acids just to give you a sense
+of size and about 69 kilo daltons per
+
+ align:start position:0%
+of size and about 69 kilo daltons per
+ 
+
+ align:start position:0%
+of size and about 69 kilo daltons per
+subunit okay and so what we're gonna
+
+ align:start position:0%
+subunit okay and so what we're gonna
+ 
+
+ align:start position:0%
+subunit okay and so what we're gonna
+focus on are the large and the small
+
+ align:start position:0%
+focus on are the large and the small
+ 
+
+ align:start position:0%
+focus on are the large and the small
+subunits and what's observed from many
+
+ align:start position:0%
+subunits and what's observed from many
+ 
+
+ align:start position:0%
+subunits and what's observed from many
+different crystal structures and so
+
+ align:start position:0%
+different crystal structures and so
+ 
+
+ align:start position:0%
+different crystal structures and so
+these two different types of subunit
+
+ align:start position:0%
+these two different types of subunit
+ 
+
+ align:start position:0%
+these two different types of subunit
+have been described as loadable and
+
+ align:start position:0%
+have been described as loadable and
+ 
+
+ align:start position:0%
+have been described as loadable and
+unload a ball and that depends on
+
+ align:start position:0%
+unload a ball and that depends on
+ 
+
+ align:start position:0%
+unload a ball and that depends on
+whether or not nucleotide is bound okay
+
+ align:start position:0%
+whether or not nucleotide is bound okay
+ 
+
+ align:start position:0%
+whether or not nucleotide is bound okay
+so if we consider of these two types
+
+ align:start position:0%
+so if we consider of these two types
+ 
+
+ align:start position:0%
+so if we consider of these two types
+just thinking about the large and small
+
+ align:start position:0%
+just thinking about the large and small
+ 
+
+ align:start position:0%
+just thinking about the large and small
+domains we have this loadable
+
+ align:start position:0%
+domains we have this loadable
+ 
+
+ align:start position:0%
+domains we have this loadable
+arrangement okay which binds nucleotide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and in cartoon something like this
+
+ align:start position:0%
+okay and in cartoon something like this
+ 
+
+ align:start position:0%
+okay and in cartoon something like this
+so we have the large subunit we have the
+
+ align:start position:0%
+so we have the large subunit we have the
+ 
+
+ align:start position:0%
+so we have the large subunit we have the
+small subunit okay and we have this
+
+ align:start position:0%
+small subunit okay and we have this
+ 
+
+ align:start position:0%
+small subunit okay and we have this
+region that's called a hinge okay so
+
+ align:start position:0%
+region that's called a hinge okay so
+ 
+
+ align:start position:0%
+region that's called a hinge okay so
+this is one clip X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so ATP binds okay and so the other type
+
+ align:start position:0%
+so ATP binds okay and so the other type
+ 
+
+ align:start position:0%
+so ATP binds okay and so the other type
+is described as unload a ball okay and
+
+ align:start position:0%
+is described as unload a ball okay and
+ 
+
+ align:start position:0%
+is described as unload a ball okay and
+this type of subunit does not bind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nucleotide when in this unload Abul
+
+ align:start position:0%
+nucleotide when in this unload Abul
+ 
+
+ align:start position:0%
+nucleotide when in this unload Abul
+conformation okay and so we can draw
+
+ align:start position:0%
+conformation okay and so we can draw
+ 
+
+ align:start position:0%
+conformation okay and so we can draw
+this kind of like here again we have the
+
+ align:start position:0%
+this kind of like here again we have the
+ 
+
+ align:start position:0%
+this kind of like here again we have the
+large subunit okay and there's a change
+
+ align:start position:0%
+large subunit okay and there's a change
+ 
+
+ align:start position:0%
+large subunit okay and there's a change
+in conformation and here's the small
+
+ align:start position:0%
+in conformation and here's the small
+ 
+
+ align:start position:0%
+in conformation and here's the small
+subunit so what's been found from
+
+ align:start position:0%
+subunit so what's been found from
+ 
+
+ align:start position:0%
+subunit so what's been found from
+looking at many crystal structures is
+
+ align:start position:0%
+looking at many crystal structures is
+ 
+
+ align:start position:0%
+looking at many crystal structures is
+that within the clip acts hexamer
+
+ align:start position:0%
+that within the clip acts hexamer
+ 
+
+ align:start position:0%
+that within the clip acts hexamer
+there's an arrangement of these loadable
+
+ align:start position:0%
+there's an arrangement of these loadable
+ 
+
+ align:start position:0%
+there's an arrangement of these loadable
+and unload Abul subunits okay so in many
+
+ align:start position:0%
+and unload Abul subunits okay so in many
+ 
+
+ align:start position:0%
+and unload Abul subunits okay so in many
+crystals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what's fine found is that there's
+
+ align:start position:0%
+okay what's fine found is that there's
+ 
+
+ align:start position:0%
+okay what's fine found is that there's
+four loadable I'm just gonna do with l+
+
+ align:start position:0%
+four loadable I'm just gonna do with l+
+ 
+
+ align:start position:0%
+four loadable I'm just gonna do with l+
+to unload a ball subunits
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay arranged with about twofold
+
+ align:start position:0%
+okay arranged with about twofold
+ 
+
+ align:start position:0%
+okay arranged with about twofold
+symmetry so L you ll you L okay so
+
+ align:start position:0%
+symmetry so L you ll you L okay so
+ 
+
+ align:start position:0%
+symmetry so L you ll you L okay so
+there's some asymmetry in the subunits
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so also from these crystal
+
+ align:start position:0%
+okay and so also from these crystal
+ 
+
+ align:start position:0%
+okay and so also from these crystal
+structures there's some more
+
+ align:start position:0%
+structures there's some more
+ 
+
+ align:start position:0%
+structures there's some more
+observations that we don't see with just
+
+ align:start position:0%
+observations that we don't see with just
+ 
+
+ align:start position:0%
+observations that we don't see with just
+these cartoons of the six mer
+
+ align:start position:0%
+these cartoons of the six mer
+ 
+
+ align:start position:0%
+these cartoons of the six mer
+so we can learn about how subunits
+
+ align:start position:0%
+so we can learn about how subunits
+ 
+
+ align:start position:0%
+so we can learn about how subunits
+interactive course and this is what's
+
+ align:start position:0%
+interactive course and this is what's
+ 
+
+ align:start position:0%
+interactive course and this is what's
+shown so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we look at these structures and
+
+ align:start position:0%
+so if we look at these structures and
+ 
+
+ align:start position:0%
+so if we look at these structures and
+consider how these subunits interact
+
+ align:start position:0%
+consider how these subunits interact
+ 
+
+ align:start position:0%
+consider how these subunits interact
+what we find is that the small subunit
+
+ align:start position:0%
+what we find is that the small subunit
+ 
+
+ align:start position:0%
+what we find is that the small subunit
+of one clip X or sorry the small domain
+
+ align:start position:0%
+of one clip X or sorry the small domain
+ 
+
+ align:start position:0%
+of one clip X or sorry the small domain
+of one clip X subunit interacts with the
+
+ align:start position:0%
+of one clip X subunit interacts with the
+ 
+
+ align:start position:0%
+of one clip X subunit interacts with the
+large domain of the adjacent clip X
+
+ align:start position:0%
+large domain of the adjacent clip X
+ 
+
+ align:start position:0%
+large domain of the adjacent clip X
+subunit and so we can draw this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically if we consider a large domain
+
+ align:start position:0%
+basically if we consider a large domain
+ 
+
+ align:start position:0%
+basically if we consider a large domain
+and let's say this is subunit 2 then
+
+ align:start position:0%
+and let's say this is subunit 2 then
+ 
+
+ align:start position:0%
+and let's say this is subunit 2 then
+what we find is that there's the small
+
+ align:start position:0%
+what we find is that there's the small
+ 
+
+ align:start position:0%
+what we find is that there's the small
+domain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+a subunit next door so let's call this
+
+ align:start position:0%
+a subunit next door so let's call this
+ 
+
+ align:start position:0%
+a subunit next door so let's call this
+subunit one okay so here's our hinge of
+
+ align:start position:0%
+subunit one okay so here's our hinge of
+ 
+
+ align:start position:0%
+subunit one okay so here's our hinge of
+subunit one okay and atp-binding happens
+
+ align:start position:0%
+subunit one okay and atp-binding happens
+ 
+
+ align:start position:0%
+subunit one okay and atp-binding happens
+in here so we can think about this
+
+ align:start position:0%
+in here so we can think about this
+ 
+
+ align:start position:0%
+in here so we can think about this
+arrangement and then what's been defined
+
+ align:start position:0%
+arrangement and then what's been defined
+ 
+
+ align:start position:0%
+arrangement and then what's been defined
+is something called a rigid body okay
+
+ align:start position:0%
+is something called a rigid body okay
+ 
+
+ align:start position:0%
+is something called a rigid body okay
+and so this rigid body is comprised of
+
+ align:start position:0%
+and so this rigid body is comprised of
+ 
+
+ align:start position:0%
+and so this rigid body is comprised of
+the large domain of one subunit and the
+
+ align:start position:0%
+the large domain of one subunit and the
+ 
+
+ align:start position:0%
+the large domain of one subunit and the
+small domain of the next rigid body
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so large domain of one clip X I'm
+
+ align:start position:0%
+okay so large domain of one clip X I'm
+ 
+
+ align:start position:0%
+okay so large domain of one clip X I'm
+small domain of another subunit
+
+ align:start position:0%
+small domain of another subunit
+ 
+
+ align:start position:0%
+small domain of another subunit
+okay that's adjacent so in thinking
+
+ align:start position:0%
+okay that's adjacent so in thinking
+ 
+
+ align:start position:0%
+okay that's adjacent so in thinking
+about this we can consider the clip X
+
+ align:start position:0%
+about this we can consider the clip X
+ 
+
+ align:start position:0%
+about this we can consider the clip X
+hexamer in another way
+
+ align:start position:0%
+hexamer in another way
+ 
+
+ align:start position:0%
+hexamer in another way
+right so how I've initially presented it
+
+ align:start position:0%
+right so how I've initially presented it
+ 
+
+ align:start position:0%
+right so how I've initially presented it
+to you when we introduce these oligomers
+
+ align:start position:0%
+to you when we introduce these oligomers
+ 
+
+ align:start position:0%
+to you when we introduce these oligomers
+is just as a six more right six subunits
+
+ align:start position:0%
+is just as a six more right six subunits
+ 
+
+ align:start position:0%
+is just as a six more right six subunits
+but another way to think about clip X is
+
+ align:start position:0%
+but another way to think about clip X is
+ 
+
+ align:start position:0%
+but another way to think about clip X is
+that it's actually six rigid bodies that
+
+ align:start position:0%
+that it's actually six rigid bodies that
+ 
+
+ align:start position:0%
+that it's actually six rigid bodies that
+are connected by hinges where each rigid
+
+ align:start position:0%
+are connected by hinges where each rigid
+ 
+
+ align:start position:0%
+are connected by hinges where each rigid
+body has the component from two subunits
+
+ align:start position:0%
+body has the component from two subunits
+ 
+
+ align:start position:0%
+body has the component from two subunits
+a large domain from one and a small from
+
+ align:start position:0%
+a large domain from one and a small from
+ 
+
+ align:start position:0%
+a large domain from one and a small from
+another okay and so the hinges are
+
+ align:start position:0%
+another okay and so the hinges are
+ 
+
+ align:start position:0%
+another okay and so the hinges are
+within a single subunit right based on
+
+ align:start position:0%
+within a single subunit right based on
+ 
+
+ align:start position:0%
+within a single subunit right based on
+this cartoon where ATP binds and so the
+
+ align:start position:0%
+this cartoon where ATP binds and so the
+ 
+
+ align:start position:0%
+this cartoon where ATP binds and so the
+thinking is that ATP binding and
+
+ align:start position:0%
+thinking is that ATP binding and
+ 
+
+ align:start position:0%
+thinking is that ATP binding and
+hydrolysis result
+
+ align:start position:0%
+hydrolysis result
+ 
+
+ align:start position:0%
+hydrolysis result
+it's in changes in the hinged geometry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and that this change in
+
+ align:start position:0%
+okay and that this change in
+ 
+
+ align:start position:0%
+okay and that this change in
+conformation in the hinge with ATP
+
+ align:start position:0%
+conformation in the hinge with ATP
+ 
+
+ align:start position:0%
+conformation in the hinge with ATP
+binding and hydrolysis allows for
+
+ align:start position:0%
+binding and hydrolysis allows for
+ 
+
+ align:start position:0%
+binding and hydrolysis allows for
+conformational change in another subunit
+
+ align:start position:0%
+conformational change in another subunit
+ 
+
+ align:start position:0%
+conformational change in another subunit
+here okay there so six rigid body is
+
+ align:start position:0%
+here okay there so six rigid body is
+ 
+
+ align:start position:0%
+here okay there so six rigid body is
+connected by six hinges effectively as
+
+ align:start position:0%
+connected by six hinges effectively as
+ 
+
+ align:start position:0%
+connected by six hinges effectively as
+opposed to just six standalone subunits
+
+ align:start position:0%
+opposed to just six standalone subunits
+ 
+
+ align:start position:0%
+opposed to just six standalone subunits
+right each subunits communicating with
+
+ align:start position:0%
+right each subunits communicating with
+ 
+
+ align:start position:0%
+right each subunits communicating with
+one another here so this is pretty
+
+ align:start position:0%
+one another here so this is pretty
+ 
+
+ align:start position:0%
+one another here so this is pretty
+complicated right it's another level of
+
+ align:start position:0%
+complicated right it's another level of
+ 
+
+ align:start position:0%
+complicated right it's another level of
+sophistication within this hexamer here
+
+ align:start position:0%
+sophistication within this hexamer here
+ 
+
+ align:start position:0%
+sophistication within this hexamer here
+so what about these loadable and unload
+
+ align:start position:0%
+so what about these loadable and unload
+ 
+
+ align:start position:0%
+so what about these loadable and unload
+Abul confirmations right I've told you
+
+ align:start position:0%
+Abul confirmations right I've told you
+ 
+
+ align:start position:0%
+Abul confirmations right I've told you
+that in these crystal structures you
+
+ align:start position:0%
+that in these crystal structures you
+ 
+
+ align:start position:0%
+that in these crystal structures you
+know what seemed often are these four
+
+ align:start position:0%
+know what seemed often are these four
+ 
+
+ align:start position:0%
+know what seemed often are these four
+loadable and to unload able subunits
+
+ align:start position:0%
+loadable and to unload able subunits
+ 
+
+ align:start position:0%
+loadable and to unload able subunits
+with a particular arrangement so we can
+
+ align:start position:0%
+with a particular arrangement so we can
+ 
+
+ align:start position:0%
+with a particular arrangement so we can
+ask the question do these individual
+
+ align:start position:0%
+ask the question do these individual
+ 
+
+ align:start position:0%
+ask the question do these individual
+subunits maintain the same conformation
+
+ align:start position:0%
+subunits maintain the same conformation
+ 
+
+ align:start position:0%
+subunits maintain the same conformation
+during these attempts to denature and
+
+ align:start position:0%
+during these attempts to denature and
+ 
+
+ align:start position:0%
+during these attempts to denature and
+translocate polypeptides right so is one
+
+ align:start position:0%
+translocate polypeptides right so is one
+ 
+
+ align:start position:0%
+translocate polypeptides right so is one
+subunit just committed to being loadable
+
+ align:start position:0%
+subunit just committed to being loadable
+ 
+
+ align:start position:0%
+subunit just committed to being loadable
+and another subunit committed to being
+
+ align:start position:0%
+and another subunit committed to being
+ 
+
+ align:start position:0%
+and another subunit committed to being
+unloaded here or do they switch
+
+ align:start position:0%
+unloaded here or do they switch
+ 
+
+ align:start position:0%
+unloaded here or do they switch
+dynamically and so recently there are a
+
+ align:start position:0%
+dynamically and so recently there are a
+ 
+
+ align:start position:0%
+dynamically and so recently there are a
+number of studies looking at that and
+
+ align:start position:0%
+number of studies looking at that and
+ 
+
+ align:start position:0%
+number of studies looking at that and
+effectively as of a few years ago many
+
+ align:start position:0%
+effectively as of a few years ago many
+ 
+
+ align:start position:0%
+effectively as of a few years ago many
+studies suggest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or support switching okay by a given
+
+ align:start position:0%
+or support switching okay by a given
+ 
+
+ align:start position:0%
+or support switching okay by a given
+subunit okay and they also indicate that
+
+ align:start position:0%
+subunit okay and they also indicate that
+ 
+
+ align:start position:0%
+subunit okay and they also indicate that
+every clip X sub unit must bind to ATP
+
+ align:start position:0%
+every clip X sub unit must bind to ATP
+ 
+
+ align:start position:0%
+every clip X sub unit must bind to ATP
+at some point during these cycles for
+
+ align:start position:0%
+at some point during these cycles for
+ 
+
+ align:start position:0%
+at some point during these cycles for
+unfolding and translocation okay but
+
+ align:start position:0%
+unfolding and translocation okay but
+ 
+
+ align:start position:0%
+unfolding and translocation okay but
+they're not all doing it not all doing
+
+ align:start position:0%
+they're not all doing it not all doing
+ 
+
+ align:start position:0%
+they're not all doing it not all doing
+it at the same time so the way to think
+
+ align:start position:0%
+it at the same time so the way to think
+ 
+
+ align:start position:0%
+it at the same time so the way to think
+about this is that there's some dynamic
+
+ align:start position:0%
+about this is that there's some dynamic
+ 
+
+ align:start position:0%
+about this is that there's some dynamic
+inter conversion between these loadable
+
+ align:start position:0%
+inter conversion between these loadable
+ 
+
+ align:start position:0%
+inter conversion between these loadable
+and unload Abul subunits within the
+
+ align:start position:0%
+and unload Abul subunits within the
+ 
+
+ align:start position:0%
+and unload Abul subunits within the
+hexamer okay and somehow yep I don't
+
+ align:start position:0%
+hexamer okay and somehow yep I don't
+ 
+
+ align:start position:0%
+hexamer okay and somehow yep I don't
+know the answer to that because my GPA
+
+ align:start position:0%
+know the answer to that because my GPA
+ 
+
+ align:start position:0%
+know the answer to that because my GPA
+logs why you know a you guys have
+
+ align:start position:0%
+logs why you know a you guys have
+ 
+
+ align:start position:0%
+logs why you know a you guys have
+already seen 80
+
+ align:start position:0%
+already seen 80
+ 
+
+ align:start position:0%
+already seen 80
+or maybe yeah so the ch2 feet they
+
+ align:start position:0%
+or maybe yeah so the ch2 feet they
+ 
+
+ align:start position:0%
+or maybe yeah so the ch2 feet they
+really have very different properties
+
+ align:start position:0%
+really have very different properties
+ 
+
+ align:start position:0%
+really have very different properties
+when you study these but in keeping you
+
+ align:start position:0%
+when you study these but in keeping you
+ 
+
+ align:start position:0%
+when you study these but in keeping you
+know if these in probably they don't
+
+ align:start position:0%
+know if these in probably they don't
+ 
+
+ align:start position:0%
+know if these in probably they don't
+have a key because we present right they
+
+ align:start position:0%
+have a key because we present right they
+ 
+
+ align:start position:0%
+have a key because we present right they
+want to get us stable so anyhow that's
+
+ align:start position:0%
+want to get us stable so anyhow that's
+ 
+
+ align:start position:0%
+want to get us stable so anyhow that's
+something right so just is this this an
+
+ align:start position:0%
+something right so just is this this an
+ 
+
+ align:start position:0%
+something right so just is this this an
+artifact is what your am suggesting from
+
+ align:start position:0%
+artifact is what your am suggesting from
+ 
+
+ align:start position:0%
+artifact is what your am suggesting from
+use of a non-hydrolyzable ATP analog so
+
+ align:start position:0%
+use of a non-hydrolyzable ATP analog so
+ 
+
+ align:start position:0%
+use of a non-hydrolyzable ATP analog so
+next week someone should ask during
+
+ align:start position:0%
+next week someone should ask during
+ 
+
+ align:start position:0%
+next week someone should ask during
+recitation their earn that so what about
+
+ align:start position:0%
+recitation their earn that so what about
+ 
+
+ align:start position:0%
+recitation their earn that so what about
+the mechanical work how this is often
+
+ align:start position:0%
+the mechanical work how this is often
+ 
+
+ align:start position:0%
+the mechanical work how this is often
+depicted in terms of grabbing and
+
+ align:start position:0%
+depicted in terms of grabbing and
+ 
+
+ align:start position:0%
+depicted in terms of grabbing and
+pulling on a polypeptide substrate as
+
+ align:start position:0%
+pulling on a polypeptide substrate as
+ 
+
+ align:start position:0%
+pulling on a polypeptide substrate as
+via these rigid bodies so and we're not
+
+ align:start position:0%
+via these rigid bodies so and we're not
+ 
+
+ align:start position:0%
+via these rigid bodies so and we're not
+going to go into details about this but
+
+ align:start position:0%
+going to go into details about this but
+ 
+
+ align:start position:0%
+going to go into details about this but
+just to describe the typical cartoon
+
+ align:start position:0%
+just to describe the typical cartoon
+ 
+
+ align:start position:0%
+just to describe the typical cartoon
+picture effectively imagine we have some
+
+ align:start position:0%
+picture effectively imagine we have some
+ 
+
+ align:start position:0%
+picture effectively imagine we have some
+polypeptide that needs to enter the
+
+ align:start position:0%
+polypeptide that needs to enter the
+ 
+
+ align:start position:0%
+polypeptide that needs to enter the
+degradation chamber so those poor loops
+
+ align:start position:0%
+degradation chamber so those poor loops
+ 
+
+ align:start position:0%
+degradation chamber so those poor loops
+we heard about that are involved in
+
+ align:start position:0%
+we heard about that are involved in
+ 
+
+ align:start position:0%
+we heard about that are involved in
+substrate binding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are in the large domain of clip X so
+
+ align:start position:0%
+are in the large domain of clip X so
+ 
+
+ align:start position:0%
+are in the large domain of clip X so
+here we have one large domain and then
+
+ align:start position:0%
+here we have one large domain and then
+ 
+
+ align:start position:0%
+here we have one large domain and then
+we can have the small domain of the
+
+ align:start position:0%
+we can have the small domain of the
+ 
+
+ align:start position:0%
+we can have the small domain of the
+adjacent subunit here and just imagine
+
+ align:start position:0%
+adjacent subunit here and just imagine
+ 
+
+ align:start position:0%
+adjacent subunit here and just imagine
+here we have another large domain with
+
+ align:start position:0%
+here we have another large domain with
+ 
+
+ align:start position:0%
+here we have another large domain with
+its poor loop and then we'd have the
+
+ align:start position:0%
+its poor loop and then we'd have the
+ 
+
+ align:start position:0%
+its poor loop and then we'd have the
+adjacent subunit here okay so
+
+ align:start position:0%
+adjacent subunit here okay so
+ 
+
+ align:start position:0%
+adjacent subunit here okay so
+effectively it's thought that these poor
+
+ align:start position:0%
+effectively it's thought that these poor
+ 
+
+ align:start position:0%
+effectively it's thought that these poor
+loops and the large domains grip the
+
+ align:start position:0%
+loops and the large domains grip the
+ 
+
+ align:start position:0%
+loops and the large domains grip the
+substrate and help drag the substrate to
+
+ align:start position:0%
+substrate and help drag the substrate to
+ 
+
+ align:start position:0%
+substrate and help drag the substrate to
+allow for translocation into the
+
+ align:start position:0%
+allow for translocation into the
+ 
+
+ align:start position:0%
+allow for translocation into the
+degradation chamber okay so this would
+
+ align:start position:0%
+degradation chamber okay so this would
+ 
+
+ align:start position:0%
+degradation chamber okay so this would
+be going to the chamber that direction
+
+ align:start position:0%
+be going to the chamber that direction
+ 
+
+ align:start position:0%
+be going to the chamber that direction
+here for that so somehow the ATP binding
+
+ align:start position:0%
+here for that so somehow the ATP binding
+ 
+
+ align:start position:0%
+here for that so somehow the ATP binding
+and hydrolysis is allowing this to occur
+
+ align:start position:0%
+and hydrolysis is allowing this to occur
+ 
+
+ align:start position:0%
+and hydrolysis is allowing this to occur
+okay so to clip P here so next week in
+
+ align:start position:0%
+okay so to clip P here so next week in
+ 
+
+ align:start position:0%
+okay so to clip P here so next week in
+recitation you're gonna have a real
+
+ align:start position:0%
+recitation you're gonna have a real
+ 
+
+ align:start position:0%
+recitation you're gonna have a real
+treat because an expert Reuben will be
+
+ align:start position:0%
+treat because an expert Reuben will be
+ 
+
+ align:start position:0%
+treat because an expert Reuben will be
+discussing some single molecule methods
+
+ align:start position:0%
+discussing some single molecule methods
+ 
+
+ align:start position:0%
+discussing some single molecule methods
+that have been applied to studying this
+
+ align:start position:0%
+that have been applied to studying this
+ 
+
+ align:start position:0%
+that have been applied to studying this
+degradation chamber and so bring your
+
+ align:start position:0%
+degradation chamber and so bring your
+ 
+
+ align:start position:0%
+degradation chamber and so bring your
+questions to him because he really knows
+
+ align:start position:0%
+questions to him because he really knows
+ 
+
+ align:start position:0%
+questions to him because he really knows
+what is state of the field right now
+
+ align:start position:0%
+what is state of the field right now
+ 
+
+ align:start position:0%
+what is state of the field right now
+for this so we've talked a lot about how
+
+ align:start position:0%
+for this so we've talked a lot about how
+ 
+
+ align:start position:0%
+for this so we've talked a lot about how
+the substrate needs to get in right we
+
+ align:start position:0%
+the substrate needs to get in right we
+ 
+
+ align:start position:0%
+the substrate needs to get in right we
+have the SS are a tag we have all this
+
+ align:start position:0%
+have the SS are a tag we have all this
+ 
+
+ align:start position:0%
+have the SS are a tag we have all this
+ATP consumption unfolding translocation
+
+ align:start position:0%
+ATP consumption unfolding translocation
+ 
+
+ align:start position:0%
+ATP consumption unfolding translocation
+by clip X and then we talked about the
+
+ align:start position:0%
+by clip X and then we talked about the
+ 
+
+ align:start position:0%
+by clip X and then we talked about the
+serine protease mechanism in terms of
+
+ align:start position:0%
+serine protease mechanism in terms of
+ 
+
+ align:start position:0%
+serine protease mechanism in terms of
+how peptides are degraded in the chamber
+
+ align:start position:0%
+how peptides are degraded in the chamber
+ 
+
+ align:start position:0%
+how peptides are degraded in the chamber
+so then the final question just going to
+
+ align:start position:0%
+so then the final question just going to
+ 
+
+ align:start position:0%
+so then the final question just going to
+touch upon is how does the polypeptide
+
+ align:start position:0%
+touch upon is how does the polypeptide
+ 
+
+ align:start position:0%
+touch upon is how does the polypeptide
+that's been degraded get out of the
+
+ align:start position:0%
+that's been degraded get out of the
+ 
+
+ align:start position:0%
+that's been degraded get out of the
+chamber
+
+ align:start position:0%
+chamber
+ 
+
+ align:start position:0%
+chamber
+okay so clip X and P will give products
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that are seven to eight amino acids in
+
+ align:start position:0%
+that are seven to eight amino acids in
+ 
+
+ align:start position:0%
+that are seven to eight amino acids in
+length so short polypeptides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so how are they released and we can
+
+ align:start position:0%
+so how are they released and we can
+ 
+
+ align:start position:0%
+so how are they released and we can
+think about two possibilities for how
+
+ align:start position:0%
+think about two possibilities for how
+ 
+
+ align:start position:0%
+think about two possibilities for how
+these polypeptides are released you know
+
+ align:start position:0%
+these polypeptides are released you know
+ 
+
+ align:start position:0%
+these polypeptides are released you know
+one is that they're released through the
+
+ align:start position:0%
+one is that they're released through the
+ 
+
+ align:start position:0%
+one is that they're released through the
+axial force so somehow those pores that
+
+ align:start position:0%
+axial force so somehow those pores that
+ 
+
+ align:start position:0%
+axial force so somehow those pores that
+allow polypeptide substrate to go in
+
+ align:start position:0%
+allow polypeptide substrate to go in
+ 
+
+ align:start position:0%
+allow polypeptide substrate to go in
+also allow product fragments to go out
+
+ align:start position:0%
+also allow product fragments to go out
+ 
+
+ align:start position:0%
+also allow product fragments to go out
+and then the second option is that
+
+ align:start position:0%
+and then the second option is that
+ 
+
+ align:start position:0%
+and then the second option is that
+there's release through transient side
+
+ align:start position:0%
+there's release through transient side
+ 
+
+ align:start position:0%
+there's release through transient side
+pores okay between the clip p7 verse so
+
+ align:start position:0%
+pores okay between the clip p7 verse so
+ 
+
+ align:start position:0%
+pores okay between the clip p7 verse so
+effectively we imagine coming back to
+
+ align:start position:0%
+effectively we imagine coming back to
+ 
+
+ align:start position:0%
+effectively we imagine coming back to
+our clip P right we have a seven more
+
+ align:start position:0%
+our clip P right we have a seven more
+ 
+
+ align:start position:0%
+our clip P right we have a seven more
+back to back seven verse right do the
+
+ align:start position:0%
+back to back seven verse right do the
+ 
+
+ align:start position:0%
+back to back seven verse right do the
+fragments come out say of the hole or
+
+ align:start position:0%
+fragments come out say of the hole or
+ 
+
+ align:start position:0%
+fragments come out say of the hole or
+somehow do they come out from this
+
+ align:start position:0%
+somehow do they come out from this
+ 
+
+ align:start position:0%
+somehow do they come out from this
+region here to the best of my knowledge
+
+ align:start position:0%
+region here to the best of my knowledge
+ 
+
+ align:start position:0%
+region here to the best of my knowledge
+this is a bit unclear and I don't think
+
+ align:start position:0%
+this is a bit unclear and I don't think
+ 
+
+ align:start position:0%
+this is a bit unclear and I don't think
+they're mutually exclusive so you know
+
+ align:start position:0%
+they're mutually exclusive so you know
+ 
+
+ align:start position:0%
+they're mutually exclusive so you know
+questions have come up if they're to
+
+ align:start position:0%
+questions have come up if they're to
+ 
+
+ align:start position:0%
+questions have come up if they're to
+come out of an axial pore does that mean
+
+ align:start position:0%
+come out of an axial pore does that mean
+ 
+
+ align:start position:0%
+come out of an axial pore does that mean
+clip X has to be dissociated in terms of
+
+ align:start position:0%
+clip X has to be dissociated in terms of
+ 
+
+ align:start position:0%
+clip X has to be dissociated in terms of
+this equator region their structures
+
+ align:start position:0%
+this equator region their structures
+ 
+
+ align:start position:0%
+this equator region their structures
+showing that this degradation chamber
+
+ align:start position:0%
+showing that this degradation chamber
+ 
+
+ align:start position:0%
+showing that this degradation chamber
+can breathe and there's a picture of
+
+ align:start position:0%
+can breathe and there's a picture of
+ 
+
+ align:start position:0%
+can breathe and there's a picture of
+that in the posted notes from Friday
+
+ align:start position:0%
+that in the posted notes from Friday
+ 
+
+ align:start position:0%
+that in the posted notes from Friday
+where you can see opening here and there
+
+ align:start position:0%
+where you can see opening here and there
+ 
+
+ align:start position:0%
+where you can see opening here and there
+have been some experiments done where
+
+ align:start position:0%
+have been some experiments done where
+ 
+
+ align:start position:0%
+have been some experiments done where
+people have put systems in this region
+
+ align:start position:0%
+people have put systems in this region
+ 
+
+ align:start position:0%
+people have put systems in this region
+by site-directed mutagenesis so you can
+
+ align:start position:0%
+by site-directed mutagenesis so you can
+ 
+
+ align:start position:0%
+by site-directed mutagenesis so you can
+imagine for instance if you have
+
+ align:start position:0%
+imagine for instance if you have
+ 
+
+ align:start position:0%
+imagine for instance if you have
+Assisting here in a cysteine
+
+ align:start position:0%
+Assisting here in a cysteine
+ 
+
+ align:start position:0%
+Assisting here in a cysteine
+here and you oxidize to form a disulfide
+
+ align:start position:0%
+here and you oxidize to form a disulfide
+ 
+
+ align:start position:0%
+here and you oxidize to form a disulfide
+such that you know those two seven MERS
+
+ align:start position:0%
+such that you know those two seven MERS
+ 
+
+ align:start position:0%
+such that you know those two seven MERS
+are locked together you can ask if we
+
+ align:start position:0%
+are locked together you can ask if we
+ 
+
+ align:start position:0%
+are locked together you can ask if we
+load the chamber with small polypeptides
+
+ align:start position:0%
+load the chamber with small polypeptides
+ 
+
+ align:start position:0%
+load the chamber with small polypeptides
+and we have these effectively cross
+
+ align:start position:0%
+and we have these effectively cross
+ 
+
+ align:start position:0%
+and we have these effectively cross
+linked by disulphide scan the
+
+ align:start position:0%
+linked by disulphide scan the
+ 
+
+ align:start position:0%
+linked by disulphide scan the
+polypeptides get out and then if we
+
+ align:start position:0%
+polypeptides get out and then if we
+ 
+
+ align:start position:0%
+polypeptides get out and then if we
+reduce this write to have them no longer
+
+ align:start position:0%
+reduce this write to have them no longer
+ 
+
+ align:start position:0%
+reduce this write to have them no longer
+attached to one another
+
+ align:start position:0%
+attached to one another
+ 
+
+ align:start position:0%
+attached to one another
+do those polypeptide stay put or not
+
+ align:start position:0%
+do those polypeptide stay put or not
+ 
+
+ align:start position:0%
+do those polypeptide stay put or not
+there those experiments gave evidence
+
+ align:start position:0%
+there those experiments gave evidence
+ 
+
+ align:start position:0%
+there those experiments gave evidence
+and evidence for release of peptides
+
+ align:start position:0%
+and evidence for release of peptides
+ 
+
+ align:start position:0%
+and evidence for release of peptides
+through this region here but there's
+
+ align:start position:0%
+through this region here but there's
+ 
+
+ align:start position:0%
+through this region here but there's
+also evidence for release of peptides
+
+ align:start position:0%
+also evidence for release of peptides
+ 
+
+ align:start position:0%
+also evidence for release of peptides
+through the pore and in terms of cartoon
+
+ align:start position:0%
+through the pore and in terms of cartoon
+ 
+
+ align:start position:0%
+through the pore and in terms of cartoon
+depictions and the lecture notes if you
+
+ align:start position:0%
+depictions and the lecture notes if you
+ 
+
+ align:start position:0%
+depictions and the lecture notes if you
+take a close look you'll see that both
+
+ align:start position:0%
+take a close look you'll see that both
+ 
+
+ align:start position:0%
+take a close look you'll see that both
+both come out there so I'd say if you're
+
+ align:start position:0%
+both come out there so I'd say if you're
+ 
+
+ align:start position:0%
+both come out there so I'd say if you're
+curious about that you know you can read
+
+ align:start position:0%
+curious about that you know you can read
+ 
+
+ align:start position:0%
+curious about that you know you can read
+some some of the literature and come to
+
+ align:start position:0%
+some some of the literature and come to
+ 
+
+ align:start position:0%
+some some of the literature and come to
+some own conclusions one last point on
+
+ align:start position:0%
+some own conclusions one last point on
+ 
+
+ align:start position:0%
+some own conclusions one last point on
+the clip system before we move on to
+
+ align:start position:0%
+the clip system before we move on to
+ 
+
+ align:start position:0%
+the clip system before we move on to
+module four you should just be aware
+
+ align:start position:0%
+module four you should just be aware
+ 
+
+ align:start position:0%
+module four you should just be aware
+that there's other clip family members
+
+ align:start position:0%
+that there's other clip family members
+ 
+
+ align:start position:0%
+that there's other clip family members
+so not only clip xnp and so in the clip
+
+ align:start position:0%
+so not only clip xnp and so in the clip
+ 
+
+ align:start position:0%
+so not only clip xnp and so in the clip
+system actually I'm gonna make one other
+
+ align:start position:0%
+system actually I'm gonna make one other
+ 
+
+ align:start position:0%
+system actually I'm gonna make one other
+point after this - about degradation
+
+ align:start position:0%
+point after this - about degradation
+ 
+
+ align:start position:0%
+point after this - about degradation
+chambers but okay so their players clip
+
+ align:start position:0%
+chambers but okay so their players clip
+ 
+
+ align:start position:0%
+chambers but okay so their players clip
+a clip be in addition to clip X okay so
+
+ align:start position:0%
+a clip be in addition to clip X okay so
+ 
+
+ align:start position:0%
+a clip be in addition to clip X okay so
+these are all three different Triple A
+
+ align:start position:0%
+these are all three different Triple A
+ 
+
+ align:start position:0%
+these are all three different Triple A
+plus ATP ASE's okay and you've actually
+
+ align:start position:0%
+plus ATP ASE's okay and you've actually
+ 
+
+ align:start position:0%
+plus ATP ASE's okay and you've actually
+encountered clip B last week so this is
+
+ align:start position:0%
+encountered clip B last week so this is
+ 
+
+ align:start position:0%
+encountered clip B last week so this is
+HSP 100 which came up in question two on
+
+ align:start position:0%
+HSP 100 which came up in question two on
+ 
+
+ align:start position:0%
+HSP 100 which came up in question two on
+the exam they're by another name and
+
+ align:start position:0%
+the exam they're by another name and
+ 
+
+ align:start position:0%
+the exam they're by another name and
+then in addition to clip P there's also
+
+ align:start position:0%
+then in addition to clip P there's also
+ 
+
+ align:start position:0%
+then in addition to clip P there's also
+clip s and some other players here
+
+ align:start position:0%
+clip s and some other players here
+ 
+
+ align:start position:0%
+clip s and some other players here
+for that they each have their own
+
+ align:start position:0%
+for that they each have their own
+ 
+
+ align:start position:0%
+for that they each have their own
+personality within you know protein
+
+ align:start position:0%
+personality within you know protein
+ 
+
+ align:start position:0%
+personality within you know protein
+quality control here for that and then
+
+ align:start position:0%
+quality control here for that and then
+ 
+
+ align:start position:0%
+quality control here for that and then
+we've only looked at this degradation
+
+ align:start position:0%
+we've only looked at this degradation
+ 
+
+ align:start position:0%
+we've only looked at this degradation
+chamber from bacteria right you might
+
+ align:start position:0%
+chamber from bacteria right you might
+ 
+
+ align:start position:0%
+chamber from bacteria right you might
+want to ask the question what happens in
+
+ align:start position:0%
+want to ask the question what happens in
+ 
+
+ align:start position:0%
+want to ask the question what happens in
+other organisms right and the answer is
+
+ align:start position:0%
+other organisms right and the answer is
+ 
+
+ align:start position:0%
+other organisms right and the answer is
+that the complexity varies and systems
+
+ align:start position:0%
+that the complexity varies and systems
+ 
+
+ align:start position:0%
+that the complexity varies and systems
+become tremendously more complex as you
+
+ align:start position:0%
+become tremendously more complex as you
+ 
+
+ align:start position:0%
+become tremendously more complex as you
+move from bacteria into eukaryotes there
+
+ align:start position:0%
+move from bacteria into eukaryotes there
+ 
+
+ align:start position:0%
+move from bacteria into eukaryotes there
+and so if we consider the different
+
+ align:start position:0%
+and so if we consider the different
+ 
+
+ align:start position:0%
+and so if we consider the different
+degradation chambers what do we see so
+
+ align:start position:0%
+degradation chambers what do we see so
+ 
+
+ align:start position:0%
+degradation chambers what do we see so
+we find these proteasome x' and all
+
+ align:start position:0%
+we find these proteasome x' and all
+ 
+
+ align:start position:0%
+we find these proteasome x' and all
+forms of life and as I just said the
+
+ align:start position:0%
+forms of life and as I just said the
+ 
+
+ align:start position:0%
+forms of life and as I just said the
+level of complexity varies depending on
+
+ align:start position:0%
+level of complexity varies depending on
+ 
+
+ align:start position:0%
+level of complexity varies depending on
+the organism and so what we've seen
+
+ align:start position:0%
+the organism and so what we've seen
+ 
+
+ align:start position:0%
+the organism and so what we've seen
+right with flip p is the most simple
+
+ align:start position:0%
+right with flip p is the most simple
+ 
+
+ align:start position:0%
+right with flip p is the most simple
+system where we have two rings that have
+
+ align:start position:0%
+system where we have two rings that have
+ 
+
+ align:start position:0%
+system where we have two rings that have
+only one type of subunit so just say
+
+ align:start position:0%
+only one type of subunit so just say
+ 
+
+ align:start position:0%
+only one type of subunit so just say
+e.coli one type of subunit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what happens if we go to our key we
+
+ align:start position:0%
+okay what happens if we go to our key we
+ 
+
+ align:start position:0%
+okay what happens if we go to our key we
+find that we have four rings each of
+
+ align:start position:0%
+find that we have four rings each of
+ 
+
+ align:start position:0%
+find that we have four rings each of
+which is seven more and these four rings
+
+ align:start position:0%
+which is seven more and these four rings
+ 
+
+ align:start position:0%
+which is seven more and these four rings
+include two different types of subunits
+
+ align:start position:0%
+include two different types of subunits
+ 
+
+ align:start position:0%
+include two different types of subunits
+so I'll call these alpha and beta so
+
+ align:start position:0%
+so I'll call these alpha and beta so
+ 
+
+ align:start position:0%
+so I'll call these alpha and beta so
+what we find is that there's a seven mer
+
+ align:start position:0%
+what we find is that there's a seven mer
+ 
+
+ align:start position:0%
+what we find is that there's a seven mer
+of seven alpha subunits then seven
+
+ align:start position:0%
+of seven alpha subunits then seven
+ 
+
+ align:start position:0%
+of seven alpha subunits then seven
+births that have seven beta subunits and
+
+ align:start position:0%
+births that have seven beta subunits and
+ 
+
+ align:start position:0%
+births that have seven beta subunits and
+here a seven more with alpha okay so we
+
+ align:start position:0%
+here a seven more with alpha okay so we
+ 
+
+ align:start position:0%
+here a seven more with alpha okay so we
+see two types of subunit okay in four
+
+ align:start position:0%
+see two types of subunit okay in four
+ 
+
+ align:start position:0%
+see two types of subunit okay in four
+rings yeah
+
+ align:start position:0%
+rings yeah
+ 
+
+ align:start position:0%
+rings yeah
+so then what about yeast tremendously
+
+ align:start position:0%
+so then what about yeast tremendously
+ 
+
+ align:start position:0%
+so then what about yeast tremendously
+complex so we have this architecture
+
+ align:start position:0%
+complex so we have this architecture
+ 
+
+ align:start position:0%
+complex so we have this architecture
+again of four rings okay an organized
+
+ align:start position:0%
+again of four rings okay an organized
+ 
+
+ align:start position:0%
+again of four rings okay an organized
+Alpha Beta Beta Alpha but what we find
+
+ align:start position:0%
+Alpha Beta Beta Alpha but what we find
+ 
+
+ align:start position:0%
+Alpha Beta Beta Alpha but what we find
+in this case is that in each of these
+
+ align:start position:0%
+in this case is that in each of these
+ 
+
+ align:start position:0%
+in this case is that in each of these
+I'm not going to draw it like that but
+
+ align:start position:0%
+I'm not going to draw it like that but
+ 
+
+ align:start position:0%
+I'm not going to draw it like that but
+each of these have seven different
+
+ align:start position:0%
+each of these have seven different
+ 
+
+ align:start position:0%
+each of these have seven different
+subunits
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay there's a depiction of this in the
+
+ align:start position:0%
+okay there's a depiction of this in the
+ 
+
+ align:start position:0%
+okay there's a depiction of this in the
+notes so just imagine how does this get
+
+ align:start position:0%
+notes so just imagine how does this get
+ 
+
+ align:start position:0%
+notes so just imagine how does this get
+assembled I have no clue right but
+
+ align:start position:0%
+assembled I have no clue right but
+ 
+
+ align:start position:0%
+assembled I have no clue right but
+somehow each of these hep tumors has to
+
+ align:start position:0%
+somehow each of these hep tumors has to
+ 
+
+ align:start position:0%
+somehow each of these hep tumors has to
+be assembled with seven different
+
+ align:start position:0%
+be assembled with seven different
+ 
+
+ align:start position:0%
+be assembled with seven different
+subunits and then they're put together
+
+ align:start position:0%
+subunits and then they're put together
+ 
+
+ align:start position:0%
+subunits and then they're put together
+in this series of four rings and then as
+
+ align:start position:0%
+in this series of four rings and then as
+ 
+
+ align:start position:0%
+in this series of four rings and then as
+you'll see after Spring Break and
+
+ align:start position:0%
+you'll see after Spring Break and
+ 
+
+ align:start position:0%
+you'll see after Spring Break and
+Joanne's section the eukaryotic
+
+ align:start position:0%
+Joanne's section the eukaryotic
+ 
+
+ align:start position:0%
+Joanne's section the eukaryotic
+proteasome has this 19 s regulatory
+
+ align:start position:0%
+proteasome has this 19 s regulatory
+ 
+
+ align:start position:0%
+proteasome has this 19 s regulatory
+particle that's involved in recognizing
+
+ align:start position:0%
+particle that's involved in recognizing
+ 
+
+ align:start position:0%
+particle that's involved in recognizing
+condemn'd proteins that have poly
+
+ align:start position:0%
+condemn'd proteins that have poly
+ 
+
+ align:start position:0%
+condemn'd proteins that have poly
+ubiquitinated compared to the clip X
+
+ align:start position:0%
+ubiquitinated compared to the clip X
+ 
+
+ align:start position:0%
+ubiquitinated compared to the clip X
+ATPase it's much much more complex so
+
+ align:start position:0%
+ATPase it's much much more complex so
+ 
+
+ align:start position:0%
+ATPase it's much much more complex so
+there's many different proteins that
+
+ align:start position:0%
+there's many different proteins that
+ 
+
+ align:start position:0%
+there's many different proteins that
+constitute this necessary part of the
+
+ align:start position:0%
+constitute this necessary part of the
+ 
+
+ align:start position:0%
+constitute this necessary part of the
+machine but there is a hexamer ATPase
+
+ align:start position:0%
+machine but there is a hexamer ATPase
+ 
+
+ align:start position:0%
+machine but there is a hexamer ATPase
+hexamer within there to facilitate
+
+ align:start position:0%
+hexamer within there to facilitate
+ 
+
+ align:start position:0%
+hexamer within there to facilitate
+translocation of the polypeptide into
+
+ align:start position:0%
+translocation of the polypeptide into
+ 
+
+ align:start position:0%
+translocation of the polypeptide into
+the degradation chamber there so some of
+
+ align:start position:0%
+the degradation chamber there so some of
+ 
+
+ align:start position:0%
+the degradation chamber there so some of
+this will come come back again in the
+
+ align:start position:0%
+this will come come back again in the
+ 
+
+ align:start position:0%
+this will come come back again in the
+latter half of the class so with that
+
+ align:start position:0%
+latter half of the class so with that
+ 
+
+ align:start position:0%
+latter half of the class so with that
+we're gonna close on degradation and
+
+ align:start position:0%
+we're gonna close on degradation and
+ 
+
+ align:start position:0%
+we're gonna close on degradation and
+move into module four which is focused
+
+ align:start position:0%
+move into module four which is focused
+ 
+
+ align:start position:0%
+move into module four which is focused
+on macro molecular machines that are
+
+ align:start position:0%
+on macro molecular machines that are
+ 
+
+ align:start position:0%
+on macro molecular machines that are
+involved in the biosynthesis of natural
+
+ align:start position:0%
+involved in the biosynthesis of natural
+ 
+
+ align:start position:0%
+involved in the biosynthesis of natural
+products I'm specifically poly key tides
+
+ align:start position:0%
+products I'm specifically poly key tides
+ 
+
+ align:start position:0%
+products I'm specifically poly key tides
+and non-ribosomal peptide and so we're
+
+ align:start position:0%
+and non-ribosomal peptide and so we're
+ 
+
+ align:start position:0%
+and non-ribosomal peptide and so we're
+completely taking a loop back to
+
+ align:start position:0%
+completely taking a loop back to
+ 
+
+ align:start position:0%
+completely taking a loop back to
+thinking about a biological
+
+ align:start position:0%
+thinking about a biological
+ 
+
+ align:start position:0%
+thinking about a biological
+polymerization like what we were
+
+ align:start position:0%
+polymerization like what we were
+ 
+
+ align:start position:0%
+polymerization like what we were
+thinking with the ribosome from the
+
+ align:start position:0%
+thinking with the ribosome from the
+ 
+
+ align:start position:0%
+thinking with the ribosome from the
+process of breaking down a polypeptide
+
+ align:start position:0%
+process of breaking down a polypeptide
+ 
+
+ align:start position:0%
+process of breaking down a polypeptide
+and so where are we going we can think
+
+ align:start position:0%
+and so where are we going we can think
+ 
+
+ align:start position:0%
+and so where are we going we can think
+about assembly lines although this is a
+
+ align:start position:0%
+about assembly lines although this is a
+ 
+
+ align:start position:0%
+about assembly lines although this is a
+helpful way on the board to think about
+
+ align:start position:0%
+helpful way on the board to think about
+ 
+
+ align:start position:0%
+helpful way on the board to think about
+these systems but it's not really what
+
+ align:start position:0%
+these systems but it's not really what
+ 
+
+ align:start position:0%
+these systems but it's not really what
+they look like and you'll learn about
+
+ align:start position:0%
+they look like and you'll learn about
+ 
+
+ align:start position:0%
+they look like and you'll learn about
+that in recitation this week yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the ATP binding site is just
+
+ align:start position:0%
+okay so the ATP binding site is just
+ 
+
+ align:start position:0%
+okay so the ATP binding site is just
+rewinding here in that hinge region and
+
+ align:start position:0%
+rewinding here in that hinge region and
+ 
+
+ align:start position:0%
+rewinding here in that hinge region and
+there's going to be conformational
+
+ align:start position:0%
+there's going to be conformational
+ 
+
+ align:start position:0%
+there's going to be conformational
+change in the hinge with ATP binding and
+
+ align:start position:0%
+change in the hinge with ATP binding and
+ 
+
+ align:start position:0%
+change in the hinge with ATP binding and
+hydrolysis there okay and that that's
+
+ align:start position:0%
+hydrolysis there okay and that that's
+ 
+
+ align:start position:0%
+hydrolysis there okay and that that's
+sufficient in terms of the level of
+
+ align:start position:0%
+sufficient in terms of the level of
+ 
+
+ align:start position:0%
+sufficient in terms of the level of
+detail for this but the main thing to
+
+ align:start position:0%
+detail for this but the main thing to
+ 
+
+ align:start position:0%
+detail for this but the main thing to
+keep in mind right each subunit binds
+
+ align:start position:0%
+keep in mind right each subunit binds
+ 
+
+ align:start position:0%
+keep in mind right each subunit binds
+ATP but on the basis of the information
+
+ align:start position:0%
+ATP but on the basis of the information
+ 
+
+ align:start position:0%
+ATP but on the basis of the information
+gathered with the caveat Joanne brought
+
+ align:start position:0%
+gathered with the caveat Joanne brought
+ 
+
+ align:start position:0%
+gathered with the caveat Joanne brought
+up different subunits bind ATP at
+
+ align:start position:0%
+up different subunits bind ATP at
+ 
+
+ align:start position:0%
+up different subunits bind ATP at
+different times in the cycle okay there
+
+ align:start position:0%
+different times in the cycle okay there
+ 
+
+ align:start position:0%
+different times in the cycle okay there
+and changes in this subunit
+
+ align:start position:0%
+and changes in this subunit
+ 
+
+ align:start position:0%
+and changes in this subunit
+conformational changes that result from
+
+ align:start position:0%
+conformational changes that result from
+ 
+
+ align:start position:0%
+conformational changes that result from
+that can be translated right to the next
+
+ align:start position:0%
+that can be translated right to the next
+ 
+
+ align:start position:0%
+that can be translated right to the next
+door subunit okay so where are we going
+
+ align:start position:0%
+door subunit okay so where are we going
+ 
+
+ align:start position:0%
+door subunit okay so where are we going
+by a week from now you should have a
+
+ align:start position:0%
+by a week from now you should have a
+ 
+
+ align:start position:0%
+by a week from now you should have a
+good handle on how to think about the
+
+ align:start position:0%
+good handle on how to think about the
+ 
+
+ align:start position:0%
+good handle on how to think about the
+biosynthesis of structures like
+
+ align:start position:0%
+biosynthesis of structures like
+ 
+
+ align:start position:0%
+biosynthesis of structures like
+erythromycin those tennis Ilyn right
+
+ align:start position:0%
+erythromycin those tennis Ilyn right
+ 
+
+ align:start position:0%
+erythromycin those tennis Ilyn right
+these are products of assembly lines and
+
+ align:start position:0%
+these are products of assembly lines and
+ 
+
+ align:start position:0%
+these are products of assembly lines and
+so where will go is with a brief
+
+ align:start position:0%
+so where will go is with a brief
+ 
+
+ align:start position:0%
+so where will go is with a brief
+overview of fatty acid biosynthesis and
+
+ align:start position:0%
+overview of fatty acid biosynthesis and
+ 
+
+ align:start position:0%
+overview of fatty acid biosynthesis and
+then look into poly ki tight synthase
+
+ align:start position:0%
+then look into poly ki tight synthase
+ 
+
+ align:start position:0%
+then look into poly ki tight synthase
+and non-ribosomal peptide synthesis
+
+ align:start position:0%
+and non-ribosomal peptide synthesis
+ 
+
+ align:start position:0%
+and non-ribosomal peptide synthesis
+assembly lines here and then some case
+
+ align:start position:0%
+assembly lines here and then some case
+ 
+
+ align:start position:0%
+assembly lines here and then some case
+studies so on the topic of ATP where we
+
+ align:start position:0%
+studies so on the topic of ATP where we
+ 
+
+ align:start position:0%
+studies so on the topic of ATP where we
+just went back to with clip X just
+
+ align:start position:0%
+just went back to with clip X just
+ 
+
+ align:start position:0%
+just went back to with clip X just
+taking a look here what you know about
+
+ align:start position:0%
+taking a look here what you know about
+ 
+
+ align:start position:0%
+taking a look here what you know about
+these systems and ATP by the names this
+
+ align:start position:0%
+these systems and ATP by the names this
+ 
+
+ align:start position:0%
+these systems and ATP by the names this
+is just a little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+language use and definition so there's a
+
+ align:start position:0%
+language use and definition so there's a
+ 
+
+ align:start position:0%
+language use and definition so there's a
+subtle difference here what's what's the
+
+ align:start position:0%
+subtle difference here what's what's the
+ 
+
+ align:start position:0%
+subtle difference here what's what's the
+difference there's a sympathies yeah and
+
+ align:start position:0%
+difference there's a sympathies yeah and
+ 
+
+ align:start position:0%
+difference there's a sympathies yeah and
+what does that tell you right off the
+
+ align:start position:0%
+what does that tell you right off the
+ 
+
+ align:start position:0%
+what does that tell you right off the
+bat about ATP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's a subtlety right synthesis a
+
+ align:start position:0%
+so it's a subtlety right synthesis a
+ 
+
+ align:start position:0%
+so it's a subtlety right synthesis a
+general term since the taste indicates
+
+ align:start position:0%
+general term since the taste indicates
+ 
+
+ align:start position:0%
+general term since the taste indicates
+ATP is involved okay so as will see
+
+ align:start position:0%
+ATP is involved okay so as will see
+ 
+
+ align:start position:0%
+ATP is involved okay so as will see
+these non-ribosomal peptide synthesis
+
+ align:start position:0%
+these non-ribosomal peptide synthesis
+ 
+
+ align:start position:0%
+these non-ribosomal peptide synthesis
+employee ATP and we're going to see
+
+ align:start position:0%
+employee ATP and we're going to see
+ 
+
+ align:start position:0%
+employee ATP and we're going to see
+chemistry very similar to what you saw
+
+ align:start position:0%
+chemistry very similar to what you saw
+ 
+
+ align:start position:0%
+chemistry very similar to what you saw
+with the aminoacyl trna synthetases in
+
+ align:start position:0%
+with the aminoacyl trna synthetases in
+ 
+
+ align:start position:0%
+with the aminoacyl trna synthetases in
+terms of activating amino acid monomers
+
+ align:start position:0%
+terms of activating amino acid monomers
+ 
+
+ align:start position:0%
+terms of activating amino acid monomers
+but in this case the machine is forming
+
+ align:start position:0%
+but in this case the machine is forming
+ 
+
+ align:start position:0%
+but in this case the machine is forming
+a non-ribosomal peptide rather than a
+
+ align:start position:0%
+a non-ribosomal peptide rather than a
+ 
+
+ align:start position:0%
+a non-ribosomal peptide rather than a
+ribosomal peptide here if you are not
+
+ align:start position:0%
+ribosomal peptide here if you are not
+ 
+
+ align:start position:0%
+ribosomal peptide here if you are not
+familiar with fatty acid biosynthesis I
+
+ align:start position:0%
+familiar with fatty acid biosynthesis I
+ 
+
+ align:start position:0%
+familiar with fatty acid biosynthesis I
+highly encourage you to go do some
+
+ align:start position:0%
+highly encourage you to go do some
+ 
+
+ align:start position:0%
+highly encourage you to go do some
+review either from your 507 notes last
+
+ align:start position:0%
+review either from your 507 notes last
+ 
+
+ align:start position:0%
+review either from your 507 notes last
+term if you were in the class or from a
+
+ align:start position:0%
+term if you were in the class or from a
+ 
+
+ align:start position:0%
+term if you were in the class or from a
+biochemistry book and there'll be some
+
+ align:start position:0%
+biochemistry book and there'll be some
+ 
+
+ align:start position:0%
+biochemistry book and there'll be some
+additional slides of overview
+
+ align:start position:0%
+additional slides of overview
+ 
+
+ align:start position:0%
+additional slides of overview
+information posted online so we'll just
+
+ align:start position:0%
+information posted online so we'll just
+ 
+
+ align:start position:0%
+information posted online so we'll just
+touch upon it today but not go into a
+
+ align:start position:0%
+touch upon it today but not go into a
+ 
+
+ align:start position:0%
+touch upon it today but not go into a
+tremendous detail here so what are our
+
+ align:start position:0%
+tremendous detail here so what are our
+ 
+
+ align:start position:0%
+tremendous detail here so what are our
+questions for this module I think for
+
+ align:start position:0%
+questions for this module I think for
+ 
+
+ align:start position:0%
+questions for this module I think for
+most everyone in the room this module
+
+ align:start position:0%
+most everyone in the room this module
+ 
+
+ align:start position:0%
+most everyone in the room this module
+will contain the most new information
+
+ align:start position:0%
+will contain the most new information
+ 
+
+ align:start position:0%
+will contain the most new information
+from the standpoint of a new system
+
+ align:start position:0%
+from the standpoint of a new system
+ 
+
+ align:start position:0%
+from the standpoint of a new system
+compared to what we've talked about so
+
+ align:start position:0%
+compared to what we've talked about so
+ 
+
+ align:start position:0%
+compared to what we've talked about so
+far so what are poly key types and how
+
+ align:start position:0%
+far so what are poly key types and how
+ 
+
+ align:start position:0%
+far so what are poly key types and how
+are these molecules bio synthesized by
+
+ align:start position:0%
+are these molecules bio synthesized by
+ 
+
+ align:start position:0%
+are these molecules bio synthesized by
+polyketide synthases what are
+
+ align:start position:0%
+polyketide synthases what are
+ 
+
+ align:start position:0%
+polyketide synthases what are
+non-ribosomal peptide and how are they
+
+ align:start position:0%
+non-ribosomal peptide and how are they
+ 
+
+ align:start position:0%
+non-ribosomal peptide and how are they
+made by these machines called
+
+ align:start position:0%
+made by these machines called
+ 
+
+ align:start position:0%
+made by these machines called
+non-ribosomal peptide synthesis and what
+
+ align:start position:0%
+non-ribosomal peptide synthesis and what
+ 
+
+ align:start position:0%
+non-ribosomal peptide synthesis and what
+we're going to look at is the assembly
+
+ align:start position:0%
+we're going to look at is the assembly
+ 
+
+ align:start position:0%
+we're going to look at is the assembly
+line organization so effectively the
+
+ align:start position:0%
+line organization so effectively the
+ 
+
+ align:start position:0%
+line organization so effectively the
+organization of domains that provide
+
+ align:start position:0%
+organization of domains that provide
+ 
+
+ align:start position:0%
+organization of domains that provide
+these linear polymers so what is the
+
+ align:start position:0%
+these linear polymers so what is the
+ 
+
+ align:start position:0%
+these linear polymers so what is the
+assembly line organization and logic for
+
+ align:start position:0%
+assembly line organization and logic for
+ 
+
+ align:start position:0%
+assembly line organization and logic for
+PKS and likewise for n RP F and then we
+
+ align:start position:0%
+PKS and likewise for n RP F and then we
+ 
+
+ align:start position:0%
+PKS and likewise for n RP F and then we
+can ask how can a given assembly line
+
+ align:start position:0%
+can ask how can a given assembly line
+ 
+
+ align:start position:0%
+can ask how can a given assembly line
+for a given PKS or and RPS natural
+
+ align:start position:0%
+for a given PKS or and RPS natural
+ 
+
+ align:start position:0%
+for a given PKS or and RPS natural
+product be basically predicted from the
+
+ align:start position:0%
+product be basically predicted from the
+ 
+
+ align:start position:0%
+product be basically predicted from the
+structure of the natural product so you
+
+ align:start position:0%
+structure of the natural product so you
+ 
+
+ align:start position:0%
+structure of the natural product so you
+should be able to work back and forth in
+
+ align:start position:0%
+should be able to work back and forth in
+ 
+
+ align:start position:0%
+should be able to work back and forth in
+terms of looking at a structure and
+
+ align:start position:0%
+terms of looking at a structure and
+ 
+
+ align:start position:0%
+terms of looking at a structure and
+coming up with a bio synthetic
+
+ align:start position:0%
+coming up with a bio synthetic
+ 
+
+ align:start position:0%
+coming up with a bio synthetic
+prediction and also seeing bio synthetic
+
+ align:start position:0%
+prediction and also seeing bio synthetic
+ 
+
+ align:start position:0%
+prediction and also seeing bio synthetic
+machinery and getting a sense as to what
+
+ align:start position:0%
+machinery and getting a sense as to what
+ 
+
+ align:start position:0%
+machinery and getting a sense as to what
+that small molecule metabolite backbone
+
+ align:start position:0%
+that small molecule metabolite backbone
+ 
+
+ align:start position:0%
+that small molecule metabolite backbone
+might look like how are these studies
+
+ align:start position:0%
+might look like how are these studies
+ 
+
+ align:start position:0%
+might look like how are these studies
+experimentally and we'll look at the
+
+ align:start position:0%
+experimentally and we'll look at the
+ 
+
+ align:start position:0%
+experimentally and we'll look at the
+biosynthesis of a molecule called
+
+ align:start position:0%
+biosynthesis of a molecule called
+ 
+
+ align:start position:0%
+biosynthesis of a molecule called
+interrobang known as a case study and so
+
+ align:start position:0%
+interrobang known as a case study and so
+ 
+
+ align:start position:0%
+interrobang known as a case study and so
+one thing I'll just point out right now
+
+ align:start position:0%
+one thing I'll just point out right now
+ 
+
+ align:start position:0%
+one thing I'll just point out right now
+is that these synthesis and synthetases
+
+ align:start position:0%
+is that these synthesis and synthetases
+ 
+
+ align:start position:0%
+is that these synthesis and synthetases
+do not look like an assembly line and
+
+ align:start position:0%
+do not look like an assembly line and
+ 
+
+ align:start position:0%
+do not look like an assembly line and
+we'll draw domains in a linear order
+
+ align:start position:0%
+we'll draw domains in a linear order
+ 
+
+ align:start position:0%
+we'll draw domains in a linear order
+which really facilitates thinking about
+
+ align:start position:0%
+which really facilitates thinking about
+ 
+
+ align:start position:0%
+which really facilitates thinking about
+the chemistry but the structures are not
+
+ align:start position:0%
+the chemistry but the structures are not
+ 
+
+ align:start position:0%
+the chemistry but the structures are not
+just a line of you know domains or
+
+ align:start position:0%
+just a line of you know domains or
+ 
+
+ align:start position:0%
+just a line of you know domains or
+proteins next door to one another and
+
+ align:start position:0%
+proteins next door to one another and
+ 
+
+ align:start position:0%
+proteins next door to one another and
+this week in recitation you'll get to
+
+ align:start position:0%
+this week in recitation you'll get to
+ 
+
+ align:start position:0%
+this week in recitation you'll get to
+see some cryo-em studies on fatty acid
+
+ align:start position:0%
+see some cryo-em studies on fatty acid
+ 
+
+ align:start position:0%
+see some cryo-em studies on fatty acid
+synthase and related machines there
+
+ align:start position:0%
+synthase and related machines there
+ 
+
+ align:start position:0%
+synthase and related machines there
+which will give you a sense of their
+
+ align:start position:0%
+which will give you a sense of their
+ 
+
+ align:start position:0%
+which will give you a sense of their
+dynamics so just a review if we think
+
+ align:start position:0%
+dynamics so just a review if we think
+ 
+
+ align:start position:0%
+dynamics so just a review if we think
+about template driven or template
+
+ align:start position:0%
+about template driven or template
+ 
+
+ align:start position:0%
+about template driven or template
+dependent polymerizations in biology
+
+ align:start position:0%
+dependent polymerizations in biology
+ 
+
+ align:start position:0%
+dependent polymerizations in biology
+we're all familiar you know with DNA
+
+ align:start position:0%
+we're all familiar you know with DNA
+ 
+
+ align:start position:0%
+we're all familiar you know with DNA
+replication and transcription and
+
+ align:start position:0%
+replication and transcription and
+ 
+
+ align:start position:0%
+replication and transcription and
+translation and what you'll see in this
+
+ align:start position:0%
+translation and what you'll see in this
+ 
+
+ align:start position:0%
+translation and what you'll see in this
+unit is that these template driven
+
+ align:start position:0%
+unit is that these template driven
+ 
+
+ align:start position:0%
+unit is that these template driven
+polymerizations
+
+ align:start position:0%
+polymerizations
+ 
+
+ align:start position:0%
+polymerizations
+occur in the synthesis biosynthesis of
+
+ align:start position:0%
+occur in the synthesis biosynthesis of
+ 
+
+ align:start position:0%
+occur in the synthesis biosynthesis of
+natural products here and effectively
+
+ align:start position:0%
+natural products here and effectively
+ 
+
+ align:start position:0%
+natural products here and effectively
+these assembly lines in a way provide
+
+ align:start position:0%
+these assembly lines in a way provide
+ 
+
+ align:start position:0%
+these assembly lines in a way provide
+this template ok so they're small
+
+ align:start position:0%
+this template ok so they're small
+ 
+
+ align:start position:0%
+this template ok so they're small
+molecules being bio synthesized by
+
+ align:start position:0%
+molecules being bio synthesized by
+ 
+
+ align:start position:0%
+molecules being bio synthesized by
+microbes I'm using some pretty amazing
+
+ align:start position:0%
+microbes I'm using some pretty amazing
+ 
+
+ align:start position:0%
+microbes I'm using some pretty amazing
+machinery so when we think about
+
+ align:start position:0%
+machinery so when we think about
+ 
+
+ align:start position:0%
+machinery so when we think about
+template driven polymerizations right we
+
+ align:start position:0%
+template driven polymerizations right we
+ 
+
+ align:start position:0%
+template driven polymerizations right we
+think about an initiation process
+
+ align:start position:0%
+think about an initiation process
+ 
+
+ align:start position:0%
+think about an initiation process
+elongation process and termination we
+
+ align:start position:0%
+elongation process and termination we
+ 
+
+ align:start position:0%
+elongation process and termination we
+saw that with the translation cycle and
+
+ align:start position:0%
+saw that with the translation cycle and
+ 
+
+ align:start position:0%
+saw that with the translation cycle and
+we'll see the same type of systems here
+
+ align:start position:0%
+we'll see the same type of systems here
+ 
+
+ align:start position:0%
+we'll see the same type of systems here
+so what does some of these structures
+
+ align:start position:0%
+so what does some of these structures
+ 
+
+ align:start position:0%
+so what does some of these structures
+look like here are just some examples on
+
+ align:start position:0%
+look like here are just some examples on
+ 
+
+ align:start position:0%
+look like here are just some examples on
+the top of poly ki tights two examples
+
+ align:start position:0%
+the top of poly ki tights two examples
+ 
+
+ align:start position:0%
+the top of poly ki tights two examples
+right they look very different
+
+ align:start position:0%
+right they look very different
+ 
+
+ align:start position:0%
+right they look very different
+at first glance and they are so we have
+
+ align:start position:0%
+at first glance and they are so we have
+ 
+
+ align:start position:0%
+at first glance and they are so we have
+tetracycline right we have four fused
+
+ align:start position:0%
+tetracycline right we have four fused
+ 
+
+ align:start position:0%
+tetracycline right we have four fused
+six membered rings it's an aromatic
+
+ align:start position:0%
+six membered rings it's an aromatic
+ 
+
+ align:start position:0%
+six membered rings it's an aromatic
+polychaete ID and antibiotic we have
+
+ align:start position:0%
+polychaete ID and antibiotic we have
+ 
+
+ align:start position:0%
+polychaete ID and antibiotic we have
+this erythromycin here which is a
+
+ align:start position:0%
+this erythromycin here which is a
+ 
+
+ align:start position:0%
+this erythromycin here which is a
+macrolide right we encountered macro
+
+ align:start position:0%
+macrolide right we encountered macro
+ 
+
+ align:start position:0%
+macrolide right we encountered macro
+lines and the transfer
+
+ align:start position:0%
+lines and the transfer
+ 
+
+ align:start position:0%
+lines and the transfer
+in Section because they bind the
+
+ align:start position:0%
+in Section because they bind the
+ 
+
+ align:start position:0%
+in Section because they bind the
+ribosome another type of antibiotic if
+
+ align:start position:0%
+ribosome another type of antibiotic if
+ 
+
+ align:start position:0%
+ribosome another type of antibiotic if
+we look at some non-ribosomal peptide
+
+ align:start position:0%
+we look at some non-ribosomal peptide
+ 
+
+ align:start position:0%
+we look at some non-ribosomal peptide
+all that can be used like can be used
+
+ align:start position:0%
+all that can be used like can be used
+ 
+
+ align:start position:0%
+all that can be used like can be used
+clinically we see the penicillins so we
+
+ align:start position:0%
+clinically we see the penicillins so we
+ 
+
+ align:start position:0%
+clinically we see the penicillins so we
+have a four or five fused ring system
+
+ align:start position:0%
+have a four or five fused ring system
+ 
+
+ align:start position:0%
+have a four or five fused ring system
+here beta lactam this comes from three
+
+ align:start position:0%
+here beta lactam this comes from three
+ 
+
+ align:start position:0%
+here beta lactam this comes from three
+amino acid building blocks initially we
+
+ align:start position:0%
+amino acid building blocks initially we
+ 
+
+ align:start position:0%
+amino acid building blocks initially we
+have vancomycin this is an antibiotic of
+
+ align:start position:0%
+have vancomycin this is an antibiotic of
+ 
+
+ align:start position:0%
+have vancomycin this is an antibiotic of
+last resort and this structure looks
+
+ align:start position:0%
+last resort and this structure looks
+ 
+
+ align:start position:0%
+last resort and this structure looks
+really quite complicated but what we'll
+
+ align:start position:0%
+really quite complicated but what we'll
+ 
+
+ align:start position:0%
+really quite complicated but what we'll
+see is that it's based on seven non-pro
+
+ align:start position:0%
+see is that it's based on seven non-pro
+ 
+
+ align:start position:0%
+see is that it's based on seven non-pro
+do genetic protea genic amino acids so
+
+ align:start position:0%
+do genetic protea genic amino acids so
+ 
+
+ align:start position:0%
+do genetic protea genic amino acids so
+it's a seven more peptide backbone that
+
+ align:start position:0%
+it's a seven more peptide backbone that
+ 
+
+ align:start position:0%
+it's a seven more peptide backbone that
+gives rise to this structure here okay
+
+ align:start position:0%
+gives rise to this structure here okay
+ 
+
+ align:start position:0%
+gives rise to this structure here okay
+for that and then we see there's some
+
+ align:start position:0%
+for that and then we see there's some
+ 
+
+ align:start position:0%
+for that and then we see there's some
+sugars so these can be put on by other
+
+ align:start position:0%
+sugars so these can be put on by other
+ 
+
+ align:start position:0%
+sugars so these can be put on by other
+enzymes here so on top right we see a
+
+ align:start position:0%
+enzymes here so on top right we see a
+ 
+
+ align:start position:0%
+enzymes here so on top right we see a
+lot of ketones and OAH groups
+
+ align:start position:0%
+lot of ketones and OAH groups
+ 
+
+ align:start position:0%
+lot of ketones and OAH groups
+those are good hints that maybe
+
+ align:start position:0%
+those are good hints that maybe
+ 
+
+ align:start position:0%
+those are good hints that maybe
+polyketide logic is being used here we
+
+ align:start position:0%
+polyketide logic is being used here we
+ 
+
+ align:start position:0%
+polyketide logic is being used here we
+see a number of peptide bonds amide
+
+ align:start position:0%
+see a number of peptide bonds amide
+ 
+
+ align:start position:0%
+see a number of peptide bonds amide
+bonds a good indicator of an RPS at play
+
+ align:start position:0%
+bonds a good indicator of an RPS at play
+ 
+
+ align:start position:0%
+bonds a good indicator of an RPS at play
+and here just to point out if these
+
+ align:start position:0%
+and here just to point out if these
+ 
+
+ align:start position:0%
+and here just to point out if these
+systems get very complex and there's
+
+ align:start position:0%
+systems get very complex and there's
+ 
+
+ align:start position:0%
+systems get very complex and there's
+natural products out there that are bio
+
+ align:start position:0%
+natural products out there that are bio
+ 
+
+ align:start position:0%
+natural products out there that are bio
+synthesized from a combination of
+
+ align:start position:0%
+synthesized from a combination of
+ 
+
+ align:start position:0%
+synthesized from a combination of
+polyketide synthase logic and
+
+ align:start position:0%
+polyketide synthase logic and
+ 
+
+ align:start position:0%
+polyketide synthase logic and
+non-ribosomal peptide synthesis logic
+
+ align:start position:0%
+non-ribosomal peptide synthesis logic
+ 
+
+ align:start position:0%
+non-ribosomal peptide synthesis logic
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+these include molecules like your Sania
+
+ align:start position:0%
+these include molecules like your Sania
+ 
+
+ align:start position:0%
+these include molecules like your Sania
+baktun this is an iron key later
+
+ align:start position:0%
+baktun this is an iron key later
+ 
+
+ align:start position:0%
+baktun this is an iron key later
+produced by Yersinia pestis and some
+
+ align:start position:0%
+produced by Yersinia pestis and some
+ 
+
+ align:start position:0%
+produced by Yersinia pestis and some
+pathogenic e.coli on this
+
+ align:start position:0%
+pathogenic e.coli on this
+ 
+
+ align:start position:0%
+pathogenic e.coli on this
+immunosuppressant rapamycin as examples
+
+ align:start position:0%
+immunosuppressant rapamycin as examples
+ 
+
+ align:start position:0%
+immunosuppressant rapamycin as examples
+okay so as we move forward i put a lot
+
+ align:start position:0%
+okay so as we move forward i put a lot
+ 
+
+ align:start position:0%
+okay so as we move forward i put a lot
+of structures of small molecule
+
+ align:start position:0%
+of structures of small molecule
+ 
+
+ align:start position:0%
+of structures of small molecule
+metabolites and the slides you can go
+
+ align:start position:0%
+metabolites and the slides you can go
+ 
+
+ align:start position:0%
+metabolites and the slides you can go
+back and use them as a way to study and
+
+ align:start position:0%
+back and use them as a way to study and
+ 
+
+ align:start position:0%
+back and use them as a way to study and
+try to make predictions about what is
+
+ align:start position:0%
+try to make predictions about what is
+ 
+
+ align:start position:0%
+try to make predictions about what is
+the machinery at play for instance to
+
+ align:start position:0%
+the machinery at play for instance to
+ 
+
+ align:start position:0%
+the machinery at play for instance to
+give all of these hetero cycles how were
+
+ align:start position:0%
+give all of these hetero cycles how were
+ 
+
+ align:start position:0%
+give all of these hetero cycles how were
+those made we'll see the assembly line
+
+ align:start position:0%
+those made we'll see the assembly line
+ 
+
+ align:start position:0%
+those made we'll see the assembly line
+does that so what organisms produce
+
+ align:start position:0%
+does that so what organisms produce
+ 
+
+ align:start position:0%
+does that so what organisms produce
+these molecules largely bacteria and
+
+ align:start position:0%
+these molecules largely bacteria and
+ 
+
+ align:start position:0%
+these molecules largely bacteria and
+fungi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there are some correlations out
+
+ align:start position:0%
+and there are some correlations out
+ 
+
+ align:start position:0%
+and there are some correlations out
+there I'll just point out related to
+
+ align:start position:0%
+there I'll just point out related to
+ 
+
+ align:start position:0%
+there I'll just point out related to
+genome size and the number of
+
+ align:start position:0%
+genome size and the number of
+ 
+
+ align:start position:0%
+genome size and the number of
+metabolites being made so bioinformatics
+
+ align:start position:0%
+metabolites being made so bioinformatics
+ 
+
+ align:start position:0%
+metabolites being made so bioinformatics
+guides a lot of current studies of the
+
+ align:start position:0%
+guides a lot of current studies of the
+ 
+
+ align:start position:0%
+guides a lot of current studies of the
+biosynthesis of these types of molecules
+
+ align:start position:0%
+biosynthesis of these types of molecules
+ 
+
+ align:start position:0%
+biosynthesis of these types of molecules
+so you could imagine that you sequence a
+
+ align:start position:0%
+so you could imagine that you sequence a
+ 
+
+ align:start position:0%
+so you could imagine that you sequence a
+genome right you have some information
+
+ align:start position:0%
+genome right you have some information
+ 
+
+ align:start position:0%
+genome right you have some information
+about gene clusters so these are groups
+
+ align:start position:0%
+about gene clusters so these are groups
+ 
+
+ align:start position:0%
+about gene clusters so these are groups
+of genes where the proteins work
+
+ align:start position:0%
+of genes where the proteins work
+ 
+
+ align:start position:0%
+of genes where the proteins work
+together to biosynthesis ice the
+
+ align:start position:0%
+together to biosynthesis ice the
+ 
+
+ align:start position:0%
+together to biosynthesis ice the
+molecule and often the genes that encode
+
+ align:start position:0%
+molecule and often the genes that encode
+ 
+
+ align:start position:0%
+molecule and often the genes that encode
+proteins in these metabolites are
+
+ align:start position:0%
+proteins in these metabolites are
+ 
+
+ align:start position:0%
+proteins in these metabolites are
+clustered okay and so bioinformatics
+
+ align:start position:0%
+clustered okay and so bioinformatics
+ 
+
+ align:start position:0%
+clustered okay and so bioinformatics
+approaches can help find these what's
+
+ align:start position:0%
+approaches can help find these what's
+ 
+
+ align:start position:0%
+approaches can help find these what's
+found is that for bacteria some phyla
+
+ align:start position:0%
+found is that for bacteria some phyla
+ 
+
+ align:start position:0%
+found is that for bacteria some phyla
+are more prolific producers of these
+
+ align:start position:0%
+are more prolific producers of these
+ 
+
+ align:start position:0%
+are more prolific producers of these
+molecules than others and what's been
+
+ align:start position:0%
+molecules than others and what's been
+ 
+
+ align:start position:0%
+molecules than others and what's been
+shown in a general way is that organisms
+
+ align:start position:0%
+shown in a general way is that organisms
+ 
+
+ align:start position:0%
+shown in a general way is that organisms
+with small genomes so something like
+
+ align:start position:0%
+with small genomes so something like
+ 
+
+ align:start position:0%
+with small genomes so something like
+e.coli produce fewer of these
+
+ align:start position:0%
+e.coli produce fewer of these
+ 
+
+ align:start position:0%
+e.coli produce fewer of these
+metabolites that's not to say none so in
+
+ align:start position:0%
+metabolites that's not to say none so in
+ 
+
+ align:start position:0%
+metabolites that's not to say none so in
+tera bactin which we'll look at for a
+
+ align:start position:0%
+tera bactin which we'll look at for a
+ 
+
+ align:start position:0%
+tera bactin which we'll look at for a
+case study is made by E coli but they
+
+ align:start position:0%
+case study is made by E coli but they
+ 
+
+ align:start position:0%
+case study is made by E coli but they
+don't make as many and effectively
+
+ align:start position:0%
+don't make as many and effectively
+ 
+
+ align:start position:0%
+don't make as many and effectively
+organisms with larger genomes produce
+
+ align:start position:0%
+organisms with larger genomes produce
+ 
+
+ align:start position:0%
+organisms with larger genomes produce
+more and so here's just a correlation
+
+ align:start position:0%
+more and so here's just a correlation
+ 
+
+ align:start position:0%
+more and so here's just a correlation
+between the number of genes and the
+
+ align:start position:0%
+between the number of genes and the
+ 
+
+ align:start position:0%
+between the number of genes and the
+genome size of the organism where they
+
+ align:start position:0%
+genome size of the organism where they
+ 
+
+ align:start position:0%
+genome size of the organism where they
+see you know around 3 MB there's a
+
+ align:start position:0%
+see you know around 3 MB there's a
+ 
+
+ align:start position:0%
+see you know around 3 MB there's a
+switch here often these molecules
+
+ align:start position:0%
+switch here often these molecules
+ 
+
+ align:start position:0%
+switch here often these molecules
+hypotheses about like an evolutionary
+
+ align:start position:0%
+hypotheses about like an evolutionary
+ 
+
+ align:start position:0%
+hypotheses about like an evolutionary
+driving factor for the development of
+
+ align:start position:0%
+driving factor for the development of
+ 
+
+ align:start position:0%
+driving factor for the development of
+this machinery and why it correlates the
+
+ align:start position:0%
+this machinery and why it correlates the
+ 
+
+ align:start position:0%
+this machinery and why it correlates the
+genome size if there is I don't know I
+
+ align:start position:0%
+genome size if there is I don't know I
+ 
+
+ align:start position:0%
+genome size if there is I don't know I
+don't think about evolution very well
+
+ align:start position:0%
+don't think about evolution very well
+ 
+
+ align:start position:0%
+don't think about evolution very well
+quite frankly what is thought is that
+
+ align:start position:0%
+quite frankly what is thought is that
+ 
+
+ align:start position:0%
+quite frankly what is thought is that
+say many of these molecules are thought
+
+ align:start position:0%
+say many of these molecules are thought
+ 
+
+ align:start position:0%
+say many of these molecules are thought
+to be involved in defense and that say
+
+ align:start position:0%
+to be involved in defense and that say
+ 
+
+ align:start position:0%
+to be involved in defense and that say
+an organism with a smaller genome size
+
+ align:start position:0%
+an organism with a smaller genome size
+ 
+
+ align:start position:0%
+an organism with a smaller genome size
+uses other strategies and so I mean for
+
+ align:start position:0%
+uses other strategies and so I mean for
+ 
+
+ align:start position:0%
+uses other strategies and so I mean for
+instance ecoli which i cited as a small
+
+ align:start position:0%
+instance ecoli which i cited as a small
+ 
+
+ align:start position:0%
+instance ecoli which i cited as a small
+genome will use a number of ribosomal
+
+ align:start position:0%
+genome will use a number of ribosomal
+ 
+
+ align:start position:0%
+genome will use a number of ribosomal
+peptides as defense molecules you know
+
+ align:start position:0%
+peptides as defense molecules you know
+ 
+
+ align:start position:0%
+peptides as defense molecules you know
+they get post-translationally modified
+
+ align:start position:0%
+they get post-translationally modified
+ 
+
+ align:start position:0%
+they get post-translationally modified
+after the fact
+
+ align:start position:0%
+after the fact
+ 
+
+ align:start position:0%
+after the fact
+why that organism chooses to do that
+
+ align:start position:0%
+why that organism chooses to do that
+ 
+
+ align:start position:0%
+why that organism chooses to do that
+versus say something like streptomyces
+
+ align:start position:0%
+versus say something like streptomyces
+ 
+
+ align:start position:0%
+versus say something like streptomyces
+that produces many many different
+
+ align:start position:0%
+that produces many many different
+ 
+
+ align:start position:0%
+that produces many many different
+natural products I'm not sure about that
+
+ align:start position:0%
+natural products I'm not sure about that
+ 
+
+ align:start position:0%
+natural products I'm not sure about that
+there yeah okay so let's look at an
+
+ align:start position:0%
+there yeah okay so let's look at an
+ 
+
+ align:start position:0%
+there yeah okay so let's look at an
+example of a gene cluster just so you
+
+ align:start position:0%
+example of a gene cluster just so you
+ 
+
+ align:start position:0%
+example of a gene cluster just so you
+get a sense of how much machinery is
+
+ align:start position:0%
+get a sense of how much machinery is
+ 
+
+ align:start position:0%
+get a sense of how much machinery is
+required to do the full biosynthesis of
+
+ align:start position:0%
+required to do the full biosynthesis of
+ 
+
+ align:start position:0%
+required to do the full biosynthesis of
+a molecule so this is for a
+
+ align:start position:0%
+a molecule so this is for a
+ 
+
+ align:start position:0%
+a molecule so this is for a
+non-ribosomal peptide shown here and has
+
+ align:start position:0%
+non-ribosomal peptide shown here and has
+ 
+
+ align:start position:0%
+non-ribosomal peptide shown here and has
+some structural similarities to that
+
+ align:start position:0%
+some structural similarities to that
+ 
+
+ align:start position:0%
+some structural similarities to that
+angle niacin we saw on a prior slide and
+
+ align:start position:0%
+angle niacin we saw on a prior slide and
+ 
+
+ align:start position:0%
+angle niacin we saw on a prior slide and
+it was a member of the vancomycin family
+
+ align:start position:0%
+it was a member of the vancomycin family
+ 
+
+ align:start position:0%
+it was a member of the vancomycin family
+so this gene cluster for the
+
+ align:start position:0%
+so this gene cluster for the
+ 
+
+ align:start position:0%
+so this gene cluster for the
+biosynthesis of this metabolite contains
+
+ align:start position:0%
+biosynthesis of this metabolite contains
+ 
+
+ align:start position:0%
+biosynthesis of this metabolite contains
+30 different genes and it's depicted
+
+ align:start position:0%
+30 different genes and it's depicted
+ 
+
+ align:start position:0%
+30 different genes and it's depicted
+here so each one of these arrows
+
+ align:start position:0%
+here so each one of these arrows
+ 
+
+ align:start position:0%
+here so each one of these arrows
+indicates an open reading frame so each
+
+ align:start position:0%
+indicates an open reading frame so each
+ 
+
+ align:start position:0%
+indicates an open reading frame so each
+one begins with a start and with a stop
+
+ align:start position:0%
+one begins with a start and with a stop
+ 
+
+ align:start position:0%
+one begins with a start and with a stop
+codon and it's assumed to be the coding
+
+ align:start position:0%
+codon and it's assumed to be the coding
+ 
+
+ align:start position:0%
+codon and it's assumed to be the coding
+sequence of the gene and so what is
+
+ align:start position:0%
+sequence of the gene and so what is
+ 
+
+ align:start position:0%
+sequence of the gene and so what is
+encoded in these 30 genes well first
+
+ align:start position:0%
+encoded in these 30 genes well first
+ 
+
+ align:start position:0%
+encoded in these 30 genes well first
+there are the genes for what we call the
+
+ align:start position:0%
+there are the genes for what we call the
+ 
+
+ align:start position:0%
+there are the genes for what we call the
+assembly line okay and if it's isn't
+
+ align:start position:0%
+assembly line okay and if it's isn't
+ 
+
+ align:start position:0%
+assembly line okay and if it's isn't
+clear what assembly line means as we
+
+ align:start position:0%
+clear what assembly line means as we
+ 
+
+ align:start position:0%
+clear what assembly line means as we
+move forward through this week it will
+
+ align:start position:0%
+move forward through this week it will
+ 
+
+ align:start position:0%
+move forward through this week it will
+be so there's genes required to make the
+
+ align:start position:0%
+be so there's genes required to make the
+ 
+
+ align:start position:0%
+be so there's genes required to make the
+seven more polypeptide backbone
+
+ align:start position:0%
+seven more polypeptide backbone
+ 
+
+ align:start position:0%
+seven more polypeptide backbone
+there's genes required for modification
+
+ align:start position:0%
+there's genes required for modification
+ 
+
+ align:start position:0%
+there's genes required for modification
+of the backbone right so how do these
+
+ align:start position:0%
+of the backbone right so how do these
+ 
+
+ align:start position:0%
+of the backbone right so how do these
+sugars get attached for instance those
+
+ align:start position:0%
+sugars get attached for instance those
+ 
+
+ align:start position:0%
+sugars get attached for instance those
+are going to be some tailoring enzymes
+
+ align:start position:0%
+are going to be some tailoring enzymes
+ 
+
+ align:start position:0%
+are going to be some tailoring enzymes
+and then if you take a close look
+
+ align:start position:0%
+and then if you take a close look
+ 
+
+ align:start position:0%
+and then if you take a close look
+there's a number of non protein orogenic
+
+ align:start position:0%
+there's a number of non protein orogenic
+ 
+
+ align:start position:0%
+there's a number of non protein orogenic
+amino acids in this molecule and that
+
+ align:start position:0%
+amino acids in this molecule and that
+ 
+
+ align:start position:0%
+amino acids in this molecule and that
+means they have to come from somewhere
+
+ align:start position:0%
+means they have to come from somewhere
+ 
+
+ align:start position:0%
+means they have to come from somewhere
+and so this gene cluster also includes
+
+ align:start position:0%
+and so this gene cluster also includes
+ 
+
+ align:start position:0%
+and so this gene cluster also includes
+genes that are required for the
+
+ align:start position:0%
+genes that are required for the
+ 
+
+ align:start position:0%
+genes that are required for the
+biosynthesis of those monomers right so
+
+ align:start position:0%
+biosynthesis of those monomers right so
+ 
+
+ align:start position:0%
+biosynthesis of those monomers right so
+there's a lot of effort going into
+
+ align:start position:0%
+there's a lot of effort going into
+ 
+
+ align:start position:0%
+there's a lot of effort going into
+making this molecule by some organism
+
+ align:start position:0%
+making this molecule by some organism
+ 
+
+ align:start position:0%
+making this molecule by some organism
+I'm so presumably under some set of
+
+ align:start position:0%
+I'm so presumably under some set of
+ 
+
+ align:start position:0%
+I'm so presumably under some set of
+conditions is important so
+
+ align:start position:0%
+conditions is important so
+ 
+
+ align:start position:0%
+conditions is important so
+moving towards the chemistry with that
+
+ align:start position:0%
+moving towards the chemistry with that
+ 
+
+ align:start position:0%
+moving towards the chemistry with that
+background in hand what are some points
+
+ align:start position:0%
+background in hand what are some points
+ 
+
+ align:start position:0%
+background in hand what are some points
+to make so what we'll learn and see is
+
+ align:start position:0%
+to make so what we'll learn and see is
+ 
+
+ align:start position:0%
+to make so what we'll learn and see is
+that the assembly lines that produce the
+
+ align:start position:0%
+that the assembly lines that produce the
+ 
+
+ align:start position:0%
+that the assembly lines that produce the
+poly ki tides and non-ribosomal peptide
+
+ align:start position:0%
+poly ki tides and non-ribosomal peptide
+ 
+
+ align:start position:0%
+poly ki tides and non-ribosomal peptide
+are macro molecular machines
+
+ align:start position:0%
+are macro molecular machines
+ 
+
+ align:start position:0%
+are macro molecular machines
+so there's dedicated macro molecular
+
+ align:start position:0%
+so there's dedicated macro molecular
+ 
+
+ align:start position:0%
+so there's dedicated macro molecular
+machines for the biosynthesis of these
+
+ align:start position:0%
+machines for the biosynthesis of these
+ 
+
+ align:start position:0%
+machines for the biosynthesis of these
+secondary metabolites ok here and so
+
+ align:start position:0%
+secondary metabolites ok here and so
+ 
+
+ align:start position:0%
+secondary metabolites ok here and so
+what are secondary metabolites say
+
+ align:start position:0%
+what are secondary metabolites say
+ 
+
+ align:start position:0%
+what are secondary metabolites say
+versus a primary metabolite so what's
+
+ align:start position:0%
+versus a primary metabolite so what's
+ 
+
+ align:start position:0%
+versus a primary metabolite so what's
+the primary metabolite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the pathway like we have like what ghost
+
+ align:start position:0%
+the pathway like we have like what ghost
+ 
+
+ align:start position:0%
+the pathway like we have like what ghost
+ain't or like boy come down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so presumably the cell needs to get
+
+ align:start position:0%
+so presumably the cell needs to get
+ 
+
+ align:start position:0%
+so presumably the cell needs to get
+materials to biosynthesize the secondary
+
+ align:start position:0%
+materials to biosynthesize the secondary
+ 
+
+ align:start position:0%
+materials to biosynthesize the secondary
+metabolites to write somewhere these
+
+ align:start position:0%
+metabolites to write somewhere these
+ 
+
+ align:start position:0%
+metabolites to write somewhere these
+amino acid monomers or the monomers that
+
+ align:start position:0%
+amino acid monomers or the monomers that
+ 
+
+ align:start position:0%
+amino acid monomers or the monomers that
+are used for poly key types and that
+
+ align:start position:0%
+are used for poly key types and that
+ 
+
+ align:start position:0%
+are used for poly key types and that
+they need to they have to come from
+
+ align:start position:0%
+they need to they have to come from
+ 
+
+ align:start position:0%
+they need to they have to come from
+somewhere right so our primary
+
+ align:start position:0%
+somewhere right so our primary
+ 
+
+ align:start position:0%
+somewhere right so our primary
+metabolites important for growth yes
+
+ align:start position:0%
+metabolites important for growth yes
+ 
+
+ align:start position:0%
+metabolites important for growth yes
+development reproduction yeah right
+
+ align:start position:0%
+development reproduction yeah right
+ 
+
+ align:start position:0%
+development reproduction yeah right
+under normal conditions right we're in
+
+ align:start position:0%
+under normal conditions right we're in
+ 
+
+ align:start position:0%
+under normal conditions right we're in
+trouble if we don't have our primary
+
+ align:start position:0%
+trouble if we don't have our primary
+ 
+
+ align:start position:0%
+trouble if we don't have our primary
+metabolites there you know whether
+
+ align:start position:0%
+metabolites there you know whether
+ 
+
+ align:start position:0%
+metabolites there you know whether
+they're ingested or biosynthesized what
+
+ align:start position:0%
+they're ingested or biosynthesized what
+ 
+
+ align:start position:0%
+they're ingested or biosynthesized what
+about a secondary metabolite just taking
+
+ align:start position:0%
+about a secondary metabolite just taking
+ 
+
+ align:start position:0%
+about a secondary metabolite just taking
+that well you can write you can write so
+
+ align:start position:0%
+that well you can write you can write so
+ 
+
+ align:start position:0%
+that well you can write you can write so
+a secondary sorry yeah a secondary
+
+ align:start position:0%
+a secondary sorry yeah a secondary
+ 
+
+ align:start position:0%
+a secondary sorry yeah a secondary
+metabolite right is not like required
+
+ align:start position:0%
+metabolite right is not like required
+ 
+
+ align:start position:0%
+metabolite right is not like required
+for normal growth development
+
+ align:start position:0%
+for normal growth development
+ 
+
+ align:start position:0%
+for normal growth development
+reproduction right so for some reason
+
+ align:start position:0%
+reproduction right so for some reason
+ 
+
+ align:start position:0%
+reproduction right so for some reason
+under some circumstances of need these
+
+ align:start position:0%
+under some circumstances of need these
+ 
+
+ align:start position:0%
+under some circumstances of need these
+secondary metabolites get produced so
+
+ align:start position:0%
+secondary metabolites get produced so
+ 
+
+ align:start position:0%
+secondary metabolites get produced so
+for some of these antibiotic molecules
+
+ align:start position:0%
+for some of these antibiotic molecules
+ 
+
+ align:start position:0%
+for some of these antibiotic molecules
+maybe the organism needs to defend
+
+ align:start position:0%
+maybe the organism needs to defend
+ 
+
+ align:start position:0%
+maybe the organism needs to defend
+itself in the case of antara bactin or
+
+ align:start position:0%
+itself in the case of antara bactin or
+ 
+
+ align:start position:0%
+itself in the case of antara bactin or
+your semi of actin maybe that organism
+
+ align:start position:0%
+your semi of actin maybe that organism
+ 
+
+ align:start position:0%
+your semi of actin maybe that organism
+needs iron and so it's producing a
+
+ align:start position:0%
+needs iron and so it's producing a
+ 
+
+ align:start position:0%
+needs iron and so it's producing a
+molecule that will help it obtain that
+
+ align:start position:0%
+molecule that will help it obtain that
+ 
+
+ align:start position:0%
+molecule that will help it obtain that
+there okay so what is going on we've
+
+ align:start position:0%
+there okay so what is going on we've
+ 
+
+ align:start position:0%
+there okay so what is going on we've
+seen some pretty complex molecules what
+
+ align:start position:0%
+seen some pretty complex molecules what
+ 
+
+ align:start position:0%
+seen some pretty complex molecules what
+we're going to see is that these
+
+ align:start position:0%
+we're going to see is that these
+ 
+
+ align:start position:0%
+we're going to see is that these
+assembly lines convert simple acid
+
+ align:start position:0%
+assembly lines convert simple acid
+ 
+
+ align:start position:0%
+assembly lines convert simple acid
+monomers if it's a poly key type
+
+ align:start position:0%
+monomers if it's a poly key type
+ 
+
+ align:start position:0%
+monomers if it's a poly key type
+synthase or amino acid monomers for a
+
+ align:start position:0%
+synthase or amino acid monomers for a
+ 
+
+ align:start position:0%
+synthase or amino acid monomers for a
+non-ribosomal peptide synthesis tool in
+
+ align:start position:0%
+non-ribosomal peptide synthesis tool in
+ 
+
+ align:start position:0%
+non-ribosomal peptide synthesis tool in
+ear polymers okay so we're going to look
+
+ align:start position:0%
+ear polymers okay so we're going to look
+ 
+
+ align:start position:0%
+ear polymers okay so we're going to look
+at template driven polymerization that
+
+ align:start position:0%
+at template driven polymerization that
+ 
+
+ align:start position:0%
+at template driven polymerization that
+initially give linear polymers and in
+
+ align:start position:0%
+initially give linear polymers and in
+ 
+
+ align:start position:0%
+initially give linear polymers and in
+the case of PKS this is very similar to
+
+ align:start position:0%
+the case of PKS this is very similar to
+ 
+
+ align:start position:0%
+the case of PKS this is very similar to
+fatty acid biosynthesis what we see is
+
+ align:start position:0%
+fatty acid biosynthesis what we see is
+ 
+
+ align:start position:0%
+fatty acid biosynthesis what we see is
+that the assembly lines allow for
+
+ align:start position:0%
+that the assembly lines allow for
+ 
+
+ align:start position:0%
+that the assembly lines allow for
+iterative additions of melon eel and
+
+ align:start position:0%
+iterative additions of melon eel and
+ 
+
+ align:start position:0%
+iterative additions of melon eel and
+methylmalonyl units and they catalyze
+
+ align:start position:0%
+methylmalonyl units and they catalyze
+ 
+
+ align:start position:0%
+methylmalonyl units and they catalyze
+carbon carbon bond formations
+
+ align:start position:0%
+carbon carbon bond formations
+ 
+
+ align:start position:0%
+carbon carbon bond formations
+in the case of non-ribosomal peptide
+
+ align:start position:0%
+in the case of non-ribosomal peptide
+ 
+
+ align:start position:0%
+in the case of non-ribosomal peptide
+synthesis what we'll see is that these
+
+ align:start position:0%
+synthesis what we'll see is that these
+ 
+
+ align:start position:0%
+synthesis what we'll see is that these
+allow for condensations of amino acids
+
+ align:start position:0%
+allow for condensations of amino acids
+ 
+
+ align:start position:0%
+allow for condensations of amino acids
+to form peptide bonds and effectively
+
+ align:start position:0%
+to form peptide bonds and effectively
+ 
+
+ align:start position:0%
+to form peptide bonds and effectively
+form non-ribosomal polypeptides
+
+ align:start position:0%
+form non-ribosomal polypeptides
+ 
+
+ align:start position:0%
+form non-ribosomal polypeptides
+okay so polypeptide synthesis without
+
+ align:start position:0%
+okay so polypeptide synthesis without
+ 
+
+ align:start position:0%
+okay so polypeptide synthesis without
+the ribosome so even though the p KF and
+
+ align:start position:0%
+the ribosome so even though the p KF and
+ 
+
+ align:start position:0%
+the ribosome so even though the p KF and
+n RP s are forming a different type of
+
+ align:start position:0%
+n RP s are forming a different type of
+ 
+
+ align:start position:0%
+n RP s are forming a different type of
+bond and that requires different
+
+ align:start position:0%
+bond and that requires different
+ 
+
+ align:start position:0%
+bond and that requires different
+chemistry what we'll see is that they
+
+ align:start position:0%
+chemistry what we'll see is that they
+ 
+
+ align:start position:0%
+chemistry what we'll see is that they
+use very similar logic and just getting
+
+ align:start position:0%
+use very similar logic and just getting
+ 
+
+ align:start position:0%
+use very similar logic and just getting
+the logic sorted out initially makes
+
+ align:start position:0%
+the logic sorted out initially makes
+ 
+
+ align:start position:0%
+the logic sorted out initially makes
+life much easier down the road so take
+
+ align:start position:0%
+life much easier down the road so take
+ 
+
+ align:start position:0%
+life much easier down the road so take
+some time to look over the depictions in
+
+ align:start position:0%
+some time to look over the depictions in
+ 
+
+ align:start position:0%
+some time to look over the depictions in
+the notes outside of class as we go
+
+ align:start position:0%
+the notes outside of class as we go
+ 
+
+ align:start position:0%
+the notes outside of class as we go
+forward so these assembly lines use acyl
+
+ align:start position:0%
+forward so these assembly lines use acyl
+ 
+
+ align:start position:0%
+forward so these assembly lines use acyl
+or amino acyl thioester x' as the
+
+ align:start position:0%
+or amino acyl thioester x' as the
+ 
+
+ align:start position:0%
+or amino acyl thioester x' as the
+activated monomer units okay so then how
+
+ align:start position:0%
+activated monomer units okay so then how
+ 
+
+ align:start position:0%
+activated monomer units okay so then how
+do we get from this linear polypeptide
+
+ align:start position:0%
+do we get from this linear polypeptide
+ 
+
+ align:start position:0%
+do we get from this linear polypeptide
+to some more complex structure the short
+
+ align:start position:0%
+to some more complex structure the short
+ 
+
+ align:start position:0%
+to some more complex structure the short
+message on that is that you know the
+
+ align:start position:0%
+message on that is that you know the
+ 
+
+ align:start position:0%
+message on that is that you know the
+quote polymers that are produced and
+
+ align:start position:0%
+quote polymers that are produced and
+ 
+
+ align:start position:0%
+quote polymers that are produced and
+they may be short right we just saw some
+
+ align:start position:0%
+they may be short right we just saw some
+ 
+
+ align:start position:0%
+they may be short right we just saw some
+they are short seven amino acids for
+
+ align:start position:0%
+they are short seven amino acids for
+ 
+
+ align:start position:0%
+they are short seven amino acids for
+vancomycin they can go for undergo
+
+ align:start position:0%
+vancomycin they can go for undergo
+ 
+
+ align:start position:0%
+vancomycin they can go for undergo
+further elaboration to give these
+
+ align:start position:0%
+further elaboration to give these
+ 
+
+ align:start position:0%
+further elaboration to give these
+complex structures so there can be
+
+ align:start position:0%
+complex structures so there can be
+ 
+
+ align:start position:0%
+complex structures so there can be
+tailoring enzymes that work on the
+
+ align:start position:0%
+tailoring enzymes that work on the
+ 
+
+ align:start position:0%
+tailoring enzymes that work on the
+products of the assembly line or there
+
+ align:start position:0%
+products of the assembly line or there
+ 
+
+ align:start position:0%
+products of the assembly line or there
+can be domains in the assembly line that
+
+ align:start position:0%
+can be domains in the assembly line that
+ 
+
+ align:start position:0%
+can be domains in the assembly line that
+give additional activities that say
+
+ align:start position:0%
+give additional activities that say
+ 
+
+ align:start position:0%
+give additional activities that say
+allow for methylation or cyclization
+
+ align:start position:0%
+allow for methylation or cyclization
+ 
+
+ align:start position:0%
+allow for methylation or cyclization
+here so we can think about fatty acid
+
+ align:start position:0%
+here so we can think about fatty acid
+ 
+
+ align:start position:0%
+here so we can think about fatty acid
+synthase as a paradigm here and so if we
+
+ align:start position:0%
+synthase as a paradigm here and so if we
+ 
+
+ align:start position:0%
+synthase as a paradigm here and so if we
+think about fatty acid biosynthesis
+
+ align:start position:0%
+think about fatty acid biosynthesis
+ 
+
+ align:start position:0%
+think about fatty acid biosynthesis
+right making some molecule like this oil
+
+ align:start position:0%
+right making some molecule like this oil
+ 
+
+ align:start position:0%
+right making some molecule like this oil
+here just as brief overview in the last
+
+ align:start position:0%
+here just as brief overview in the last
+ 
+
+ align:start position:0%
+here just as brief overview in the last
+few minutes of class right fatty acids
+
+ align:start position:0%
+few minutes of class right fatty acids
+ 
+
+ align:start position:0%
+few minutes of class right fatty acids
+are synthesized by FAS and what happens
+
+ align:start position:0%
+are synthesized by FAS and what happens
+ 
+
+ align:start position:0%
+are synthesized by FAS and what happens
+is that there's elongation by one unit
+
+ align:start position:0%
+is that there's elongation by one unit
+ 
+
+ align:start position:0%
+is that there's elongation by one unit
+at a time okay and each unit it provides
+
+ align:start position:0%
+at a time okay and each unit it provides
+ 
+
+ align:start position:0%
+at a time okay and each unit it provides
+two carbons
+
+ align:start position:0%
+two carbons
+ 
+
+ align:start position:0%
+two carbons
+so there's two carbon atoms per D
+
+ align:start position:0%
+so there's two carbon atoms per D
+ 
+
+ align:start position:0%
+so there's two carbon atoms per D
+elongation and so hopefully you're all
+
+ align:start position:0%
+elongation and so hopefully you're all
+ 
+
+ align:start position:0%
+elongation and so hopefully you're all
+familiar with two ways to form a
+
+ align:start position:0%
+familiar with two ways to form a
+ 
+
+ align:start position:0%
+familiar with two ways to form a
+carbon-carbon bond at least related to
+
+ align:start position:0%
+carbon-carbon bond at least related to
+ 
+
+ align:start position:0%
+carbon-carbon bond at least related to
+biochemistry one of which is claisen
+
+ align:start position:0%
+biochemistry one of which is claisen
+ 
+
+ align:start position:0%
+biochemistry one of which is claisen
+condensations so claisen condensations
+
+ align:start position:0%
+condensations so claisen condensations
+ 
+
+ align:start position:0%
+condensations so claisen condensations
+allow for carbon-carbon bond formation
+
+ align:start position:0%
+allow for carbon-carbon bond formation
+ 
+
+ align:start position:0%
+allow for carbon-carbon bond formation
+and join the unit join the units to keep
+
+ align:start position:0%
+and join the unit join the units to keep
+ 
+
+ align:start position:0%
+and join the unit join the units to keep
+in mind the monomers are always bio
+
+ align:start position:0%
+in mind the monomers are always bio
+ 
+
+ align:start position:0%
+in mind the monomers are always bio
+esters non-toxic esters okay and for
+
+ align:start position:0%
+esters non-toxic esters okay and for
+ 
+
+ align:start position:0%
+esters non-toxic esters okay and for
+fatty acid biosynthesis the two monomer
+
+ align:start position:0%
+fatty acid biosynthesis the two monomer
+ 
+
+ align:start position:0%
+fatty acid biosynthesis the two monomer
+units are shown here so we have a
+
+ align:start position:0%
+units are shown here so we have a
+ 
+
+ align:start position:0%
+units are shown here so we have a
+starter and an extender acetyl co a or
+
+ align:start position:0%
+starter and an extender acetyl co a or
+ 
+
+ align:start position:0%
+starter and an extender acetyl co a or
+Millenial co a here okay and here we
+
+ align:start position:0%
+Millenial co a here okay and here we
+ 
+
+ align:start position:0%
+Millenial co a here okay and here we
+have coenzyme a so just as a brief
+
+ align:start position:0%
+have coenzyme a so just as a brief
+ 
+
+ align:start position:0%
+have coenzyme a so just as a brief
+review if we think about these monomer
+
+ align:start position:0%
+review if we think about these monomer
+ 
+
+ align:start position:0%
+review if we think about these monomer
+units
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so here we have seen Alcoa
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what can we say about this guy here
+
+ align:start position:0%
+so what can we say about this guy here
+ 
+
+ align:start position:0%
+so what can we say about this guy here
+in this dieter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so is this acidic or not compared
+
+ align:start position:0%
+right so is this acidic or not compared
+ 
+
+ align:start position:0%
+right so is this acidic or not compared
+to say an ox Oster
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many of you have heard about fatty
+
+ align:start position:0%
+how many of you have heard about fatty
+ 
+
+ align:start position:0%
+how many of you have heard about fatty
+acid biosynthesis like so why why are
+
+ align:start position:0%
+acid biosynthesis like so why why are
+ 
+
+ align:start position:0%
+acid biosynthesis like so why why are
+Theo esters used and not oxy Westers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we'll go into a little more
+
+ align:start position:0%
+okay so we'll go into a little more
+ 
+
+ align:start position:0%
+okay so we'll go into a little more
+detail on Friday there's no to make sure
+
+ align:start position:0%
+detail on Friday there's no to make sure
+ 
+
+ align:start position:0%
+detail on Friday there's no to make sure
+the chemistry is straight here because
+
+ align:start position:0%
+the chemistry is straight here because
+ 
+
+ align:start position:0%
+the chemistry is straight here because
+I'm not certain it is so okay so for
+
+ align:start position:0%
+I'm not certain it is so okay so for
+ 
+
+ align:start position:0%
+I'm not certain it is so okay so for
+Friday think about a bio ester versus an
+
+ align:start position:0%
+Friday think about a bio ester versus an
+ 
+
+ align:start position:0%
+Friday think about a bio ester versus an
+ox Wester okay and how do properties
+
+ align:start position:0%
+ox Wester okay and how do properties
+ 
+
+ align:start position:0%
+ox Wester okay and how do properties
+differ and why might we want to be using
+
+ align:start position:0%
+differ and why might we want to be using
+ 
+
+ align:start position:0%
+differ and why might we want to be using
+bio esters okay and also review the
+
+ align:start position:0%
+bio esters okay and also review the
+ 
+
+ align:start position:0%
+bio esters okay and also review the
+claisen condensation because that's the
+
+ align:start position:0%
+claisen condensation because that's the
+ 
+
+ align:start position:0%
+claisen condensation because that's the
+chemistry that's going to be happening
+
+ align:start position:0%
+chemistry that's going to be happening
+ 
+
+ align:start position:0%
+chemistry that's going to be happening
+to form the carbon-carbon bonds in the
+
+ align:start position:0%
+to form the carbon-carbon bonds in the
+ 
+
+ align:start position:0%
+to form the carbon-carbon bonds in the
+fatty acid synthase and in the
+
+ align:start position:0%
+fatty acid synthase and in the
+ 
+
+ align:start position:0%
+fatty acid synthase and in the
+polyketide synthases okay and what we're
+
+ align:start position:0%
+polyketide synthases okay and what we're
+ 
+
+ align:start position:0%
+polyketide synthases okay and what we're
+gonna see is that the monomers in each
+
+ align:start position:0%
+gonna see is that the monomers in each
+ 
+
+ align:start position:0%
+gonna see is that the monomers in each
+case they're tethered estai Oster so why
+
+ align:start position:0%
+case they're tethered estai Oster so why
+ 
+
+ align:start position:0%
+case they're tethered estai Oster so why
+why is that there okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I will turn around and point at
+
+ align:start position:0%
+and I will turn around and point at
+ 
+
+ align:start position:0%
+and I will turn around and point at
+somebody and you can let us know are you
+
+ align:start position:0%
+somebody and you can let us know are you
+ 
+
+ align:start position:0%
+somebody and you can let us know are you
+excited
+
+ align:start position:0%
+excited
+ 
+
+ align:start position:0%
+excited
+okay so you're off the hook for
+
+ align:start position:0%
+okay so you're off the hook for
+ 
+
+ align:start position:0%
+okay so you're off the hook for
+Wednesday I need to be out of town and
+
+ align:start position:0%
+Wednesday I need to be out of town and
+ 
+
+ align:start position:0%
+Wednesday I need to be out of town and
+I'll see you on Friday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/KyO8jcUR254.txt b/KyO8jcUR254.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5d64e17a5a4555e35ddc6bca595bf6e6dd36239b
--- /dev/null
+++ b/KyO8jcUR254.txt
@@ -0,0 +1,8317 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+hi today I'd like to look at the
+
+ align:start position:0%
+hi today I'd like to look at the
+ 
+
+ align:start position:0%
+hi today I'd like to look at the
+stability problem in a somewhat
+
+ align:start position:0%
+stability problem in a somewhat
+ 
+
+ align:start position:0%
+stability problem in a somewhat
+different way we've found to this point
+
+ align:start position:0%
+different way we've found to this point
+ 
+
+ align:start position:0%
+different way we've found to this point
+that we have two methods for evaluating
+
+ align:start position:0%
+that we have two methods for evaluating
+ 
+
+ align:start position:0%
+that we have two methods for evaluating
+the stability of a feedback system one
+
+ align:start position:0%
+the stability of a feedback system one
+ 
+
+ align:start position:0%
+the stability of a feedback system one
+of them we looked at very briefly or
+
+ align:start position:0%
+of them we looked at very briefly or
+ 
+
+ align:start position:0%
+of them we looked at very briefly or
+principally via homework problems in
+
+ align:start position:0%
+principally via homework problems in
+ 
+
+ align:start position:0%
+principally via homework problems in
+particular the rowth test and what the
+
+ align:start position:0%
+particular the rowth test and what the
+ 
+
+ align:start position:0%
+particular the rowth test and what the
+Ralph test does is simply give us a a
+
+ align:start position:0%
+Ralph test does is simply give us a a
+ 
+
+ align:start position:0%
+Ralph test does is simply give us a a
+straightforward numerical way of
+
+ align:start position:0%
+straightforward numerical way of
+ 
+
+ align:start position:0%
+straightforward numerical way of
+determining the number of poles of a
+
+ align:start position:0%
+determining the number of poles of a
+ 
+
+ align:start position:0%
+determining the number of poles of a
+closed loop transfer function that lie
+
+ align:start position:0%
+closed loop transfer function that lie
+ 
+
+ align:start position:0%
+closed loop transfer function that lie
+on the right half of the S plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi today I'd like to look at the
+
+ align:start position:0%
+hi today I'd like to look at the
+ 
+
+ align:start position:0%
+hi today I'd like to look at the
+stability problem in a somewhat
+
+ align:start position:0%
+stability problem in a somewhat
+ 
+
+ align:start position:0%
+stability problem in a somewhat
+different way we've found to this point
+
+ align:start position:0%
+different way we've found to this point
+ 
+
+ align:start position:0%
+different way we've found to this point
+that we have two methods for evaluating
+
+ align:start position:0%
+that we have two methods for evaluating
+ 
+
+ align:start position:0%
+that we have two methods for evaluating
+the stability of a feedback system one
+
+ align:start position:0%
+the stability of a feedback system one
+ 
+
+ align:start position:0%
+the stability of a feedback system one
+of them we looked at very briefly or
+
+ align:start position:0%
+of them we looked at very briefly or
+ 
+
+ align:start position:0%
+of them we looked at very briefly or
+principally via homework problems in
+
+ align:start position:0%
+principally via homework problems in
+ 
+
+ align:start position:0%
+principally via homework problems in
+particular the rowth test and what the
+
+ align:start position:0%
+particular the rowth test and what the
+ 
+
+ align:start position:0%
+particular the rowth test and what the
+rowth test does is simply give us a a
+
+ align:start position:0%
+rowth test does is simply give us a a
+ 
+
+ align:start position:0%
+rowth test does is simply give us a a
+straightforward numerical way of
+
+ align:start position:0%
+straightforward numerical way of
+ 
+
+ align:start position:0%
+straightforward numerical way of
+determining the number of poles of a
+
+ align:start position:0%
+determining the number of poles of a
+ 
+
+ align:start position:0%
+determining the number of poles of a
+closed loop transfer function
+
+ align:start position:0%
+closed loop transfer function
+ 
+
+ align:start position:0%
+closed loop transfer function
+that lie in the right half of the S
+
+ align:start position:0%
+that lie in the right half of the S
+ 
+
+ align:start position:0%
+that lie in the right half of the S
+plane and in that sense it simply gives
+
+ align:start position:0%
+plane and in that sense it simply gives
+ 
+
+ align:start position:0%
+plane and in that sense it simply gives
+us a binary answer to the stability
+
+ align:start position:0%
+us a binary answer to the stability
+ 
+
+ align:start position:0%
+us a binary answer to the stability
+problem in other words the system is
+
+ align:start position:0%
+problem in other words the system is
+ 
+
+ align:start position:0%
+problem in other words the system is
+either stable if if all of the poles of
+
+ align:start position:0%
+either stable if if all of the poles of
+ 
+
+ align:start position:0%
+either stable if if all of the poles of
+the closed loop transfer function lie in
+
+ align:start position:0%
+the closed loop transfer function lie in
+ 
+
+ align:start position:0%
+the closed loop transfer function lie in
+the left half of the S plane or it's not
+
+ align:start position:0%
+the left half of the S plane or it's not
+ 
+
+ align:start position:0%
+the left half of the S plane or it's not
+stable if one or more lie in the right
+
+ align:start position:0%
+stable if one or more lie in the right
+ 
+
+ align:start position:0%
+stable if one or more lie in the right
+half as an alternative to that sort of
+
+ align:start position:0%
+half as an alternative to that sort of
+ 
+
+ align:start position:0%
+half as an alternative to that sort of
+stability analysis we introduced the
+
+ align:start position:0%
+stability analysis we introduced the
+ 
+
+ align:start position:0%
+stability analysis we introduced the
+idea of a root Locust diagram and this
+
+ align:start position:0%
+idea of a root Locust diagram and this
+ 
+
+ align:start position:0%
+idea of a root Locust diagram and this
+gives us considerably more insight into
+
+ align:start position:0%
+gives us considerably more insight into
+ 
+
+ align:start position:0%
+gives us considerably more insight into
+the performance of the system we're able
+
+ align:start position:0%
+the performance of the system we're able
+ 
+
+ align:start position:0%
+the performance of the system we're able
+to determine relative stability in the
+
+ align:start position:0%
+to determine relative stability in the
+ 
+
+ align:start position:0%
+to determine relative stability in the
+case where system does have all of its
+
+ align:start position:0%
+case where system does have all of its
+ 
+
+ align:start position:0%
+case where system does have all of its
+closed loop poles in the left half of
+
+ align:start position:0%
+closed loop poles in the left half of
+ 
+
+ align:start position:0%
+closed loop poles in the left half of
+the S plane we're able to tell how close
+
+ align:start position:0%
+the S plane we're able to tell how close
+ 
+
+ align:start position:0%
+the S plane we're able to tell how close
+for example a dominant pole pair is to
+
+ align:start position:0%
+for example a dominant pole pair is to
+ 
+
+ align:start position:0%
+for example a dominant pole pair is to
+the right half plane and so this becomes
+
+ align:start position:0%
+the right half plane and so this becomes
+ 
+
+ align:start position:0%
+the right half plane and so this becomes
+a much more powerful tool for the design
+
+ align:start position:0%
+a much more powerful tool for the design
+ 
+
+ align:start position:0%
+a much more powerful tool for the design
+and feedback
+
+ align:start position:0%
+and feedback
+ 
+
+ align:start position:0%
+and feedback
+systems today we're going to look at
+
+ align:start position:0%
+systems today we're going to look at
+ 
+
+ align:start position:0%
+systems today we're going to look at
+another aspect of the stability problem
+
+ align:start position:0%
+another aspect of the stability problem
+ 
+
+ align:start position:0%
+another aspect of the stability problem
+in particular how can we determine the
+
+ align:start position:0%
+in particular how can we determine the
+ 
+
+ align:start position:0%
+in particular how can we determine the
+stability of a feedback system really
+
+ align:start position:0%
+stability of a feedback system really
+ 
+
+ align:start position:0%
+stability of a feedback system really
+based on frequency response measurements
+
+ align:start position:0%
+based on frequency response measurements
+ 
+
+ align:start position:0%
+based on frequency response measurements
+performed on the
+
+ align:start position:0%
+performed on the
+ 
+
+ align:start position:0%
+performed on the
+system and we'll see that this gives us
+
+ align:start position:0%
+system and we'll see that this gives us
+ 
+
+ align:start position:0%
+system and we'll see that this gives us
+yet another tool
+
+ align:start position:0%
+yet another tool
+ 
+
+ align:start position:0%
+yet another tool
+for looking at the stability of a
+
+ align:start position:0%
+for looking at the stability of a
+ 
+
+ align:start position:0%
+for looking at the stability of a
+feedback system and again a very
+
+ align:start position:0%
+feedback system and again a very
+ 
+
+ align:start position:0%
+feedback system and again a very
+powerful design tool why are we
+
+ align:start position:0%
+powerful design tool why are we
+ 
+
+ align:start position:0%
+powerful design tool why are we
+interested in an alternate technique
+
+ align:start position:0%
+interested in an alternate technique
+ 
+
+ align:start position:0%
+interested in an alternate technique
+root Locust certainly is a a fairly
+
+ align:start position:0%
+root Locust certainly is a a fairly
+ 
+
+ align:start position:0%
+root Locust certainly is a a fairly
+General way to look at the stability
+
+ align:start position:0%
+General way to look at the stability
+ 
+
+ align:start position:0%
+General way to look at the stability
+problem well one is just that there's
+
+ align:start position:0%
+problem well one is just that there's
+ 
+
+ align:start position:0%
+problem well one is just that there's
+certain systems which are more easily
+
+ align:start position:0%
+certain systems which are more easily
+ 
+
+ align:start position:0%
+certain systems which are more easily
+investigated by root Locus other systems
+
+ align:start position:0%
+investigated by root Locus other systems
+ 
+
+ align:start position:0%
+investigated by root Locus other systems
+are more readily investigated by
+
+ align:start position:0%
+are more readily investigated by
+ 
+
+ align:start position:0%
+are more readily investigated by
+frequency domain kinds of approaches and
+
+ align:start position:0%
+frequency domain kinds of approaches and
+ 
+
+ align:start position:0%
+frequency domain kinds of approaches and
+we can find different kinds of
+
+ align:start position:0%
+we can find different kinds of
+ 
+
+ align:start position:0%
+we can find different kinds of
+information via these two
+
+ align:start position:0%
+information via these two
+ 
+
+ align:start position:0%
+information via these two
+approaches uh but there's another reason
+
+ align:start position:0%
+approaches uh but there's another reason
+ 
+
+ align:start position:0%
+approaches uh but there's another reason
+and that is that uh there are certain
+
+ align:start position:0%
+and that is that uh there are certain
+ 
+
+ align:start position:0%
+and that is that uh there are certain
+sorts of systems that really don't lend
+
+ align:start position:0%
+sorts of systems that really don't lend
+ 
+
+ align:start position:0%
+sorts of systems that really don't lend
+themselves readily to analysis via root
+
+ align:start position:0%
+themselves readily to analysis via root
+ 
+
+ align:start position:0%
+themselves readily to analysis via root
+Locus techniques we realize that in
+
+ align:start position:0%
+Locus techniques we realize that in
+ 
+
+ align:start position:0%
+Locus techniques we realize that in
+order to perform a root Locus analysis
+
+ align:start position:0%
+order to perform a root Locus analysis
+ 
+
+ align:start position:0%
+order to perform a root Locus analysis
+we have to have the loop transmission of
+
+ align:start position:0%
+we have to have the loop transmission of
+ 
+
+ align:start position:0%
+we have to have the loop transmission of
+the feedback system expressed as a ratio
+
+ align:start position:0%
+the feedback system expressed as a ratio
+ 
+
+ align:start position:0%
+the feedback system expressed as a ratio
+of pols in s and in particular a finite
+
+ align:start position:0%
+of pols in s and in particular a finite
+ 
+
+ align:start position:0%
+of pols in s and in particular a finite
+ratio of polinomial in s a finite number
+
+ align:start position:0%
+ratio of polinomial in s a finite number
+ 
+
+ align:start position:0%
+ratio of polinomial in s a finite number
+of poles and zeros but not all transfer
+
+ align:start position:0%
+of poles and zeros but not all transfer
+ 
+
+ align:start position:0%
+of poles and zeros but not all transfer
+functions are expressable in that form
+
+ align:start position:0%
+functions are expressable in that form
+ 
+
+ align:start position:0%
+functions are expressable in that form
+for example a time delay has a transfer
+
+ align:start position:0%
+for example a time delay has a transfer
+ 
+
+ align:start position:0%
+for example a time delay has a transfer
+function e the minus s where to is the
+
+ align:start position:0%
+function e the minus s where to is the
+ 
+
+ align:start position:0%
+function e the minus s where to is the
+magnitude of the time
+
+ align:start position:0%
+magnitude of the time
+ 
+
+ align:start position:0%
+magnitude of the time
+delay and this transcendental function
+
+ align:start position:0%
+delay and this transcendental function
+ 
+
+ align:start position:0%
+delay and this transcendental function
+is not expressible as a ratio of
+
+ align:start position:0%
+is not expressible as a ratio of
+ 
+
+ align:start position:0%
+is not expressible as a ratio of
+polinomial where the polinomial
+
+ align:start position:0%
+polinomial where the polinomial
+ 
+
+ align:start position:0%
+polinomial where the polinomial
+polinomial themselves are finite so
+
+ align:start position:0%
+polinomial themselves are finite so
+ 
+
+ align:start position:0%
+polinomial themselves are finite so
+there's an example of a transfer
+
+ align:start position:0%
+there's an example of a transfer
+ 
+
+ align:start position:0%
+there's an example of a transfer
+function that really can't be used
+
+ align:start position:0%
+function that really can't be used
+ 
+
+ align:start position:0%
+function that really can't be used
+directly in our root Locus
+
+ align:start position:0%
+directly in our root Locus
+ 
+
+ align:start position:0%
+directly in our root Locus
+analysis another case of of major
+
+ align:start position:0%
+analysis another case of of major
+ 
+
+ align:start position:0%
+analysis another case of of major
+practical interest involves the case
+
+ align:start position:0%
+practical interest involves the case
+ 
+
+ align:start position:0%
+practical interest involves the case
+where the information concerning the
+
+ align:start position:0%
+where the information concerning the
+ 
+
+ align:start position:0%
+where the information concerning the
+loop transmission is available only in
+
+ align:start position:0%
+loop transmission is available only in
+ 
+
+ align:start position:0%
+loop transmission is available only in
+experimentally measured form in other
+
+ align:start position:0%
+experimentally measured form in other
+ 
+
+ align:start position:0%
+experimentally measured form in other
+words we may have measured the frequency
+
+ align:start position:0%
+words we may have measured the frequency
+ 
+
+ align:start position:0%
+words we may have measured the frequency
+response associated with Loop
+
+ align:start position:0%
+response associated with Loop
+ 
+
+ align:start position:0%
+response associated with Loop
+transmission we can if we want to curve
+
+ align:start position:0%
+transmission we can if we want to curve
+ 
+
+ align:start position:0%
+transmission we can if we want to curve
+fit and estimate that Loop transmission
+
+ align:start position:0%
+fit and estimate that Loop transmission
+ 
+
+ align:start position:0%
+fit and estimate that Loop transmission
+as a collection of poles and zeros but
+
+ align:start position:0%
+as a collection of poles and zeros but
+ 
+
+ align:start position:0%
+as a collection of poles and zeros but
+oftentimes that's a cumbersome operation
+
+ align:start position:0%
+oftentimes that's a cumbersome operation
+ 
+
+ align:start position:0%
+oftentimes that's a cumbersome operation
+and subject to inaccuracies so again
+
+ align:start position:0%
+and subject to inaccuracies so again
+ 
+
+ align:start position:0%
+and subject to inaccuracies so again
+it'd be helpful if we had a technique
+
+ align:start position:0%
+it'd be helpful if we had a technique
+ 
+
+ align:start position:0%
+it'd be helpful if we had a technique
+that could work directly with the
+
+ align:start position:0%
+that could work directly with the
+ 
+
+ align:start position:0%
+that could work directly with the
+measured frequency response of the loop
+
+ align:start position:0%
+measured frequency response of the loop
+ 
+
+ align:start position:0%
+measured frequency response of the loop
+transmission and would allow us to
+
+ align:start position:0%
+transmission and would allow us to
+ 
+
+ align:start position:0%
+transmission and would allow us to
+evaluate the stability of the system
+
+ align:start position:0%
+evaluate the stability of the system
+ 
+
+ align:start position:0%
+evaluate the stability of the system
+using that
+
+ align:start position:0%
+using that
+ 
+
+ align:start position:0%
+using that
+information we start again with a system
+
+ align:start position:0%
+information we start again with a system
+ 
+
+ align:start position:0%
+information we start again with a system
+in our standard form an input an output
+
+ align:start position:0%
+in our standard form an input an output
+ 
+
+ align:start position:0%
+in our standard form an input an output
+a forward path transmission small a of s
+
+ align:start position:0%
+a forward path transmission small a of s
+ 
+
+ align:start position:0%
+a forward path transmission small a of s
+and a feedback path transmission F
+
+ align:start position:0%
+and a feedback path transmission F
+ 
+
+ align:start position:0%
+and a feedback path transmission F
+ofs when we started looking at the
+
+ align:start position:0%
+ofs when we started looking at the
+ 
+
+ align:start position:0%
+ofs when we started looking at the
+stability problem we mentioned that we
+
+ align:start position:0%
+stability problem we mentioned that we
+ 
+
+ align:start position:0%
+stability problem we mentioned that we
+can give a physical idea of why we might
+
+ align:start position:0%
+can give a physical idea of why we might
+ 
+
+ align:start position:0%
+can give a physical idea of why we might
+have instability in some systems by
+
+ align:start position:0%
+have instability in some systems by
+ 
+
+ align:start position:0%
+have instability in some systems by
+considering what happens if we break the
+
+ align:start position:0%
+considering what happens if we break the
+ 
+
+ align:start position:0%
+considering what happens if we break the
+loop and look look at the Loop
+
+ align:start position:0%
+loop and look look at the Loop
+ 
+
+ align:start position:0%
+loop and look look at the Loop
+Transmission in other words we proposed
+
+ align:start position:0%
+Transmission in other words we proposed
+ 
+
+ align:start position:0%
+Transmission in other words we proposed
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+test where we apply a test generator to
+
+ align:start position:0%
+test where we apply a test generator to
+ 
+
+ align:start position:0%
+test where we apply a test generator to
+the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and look at the signal that the the
+
+ align:start position:0%
+here and look at the signal that the the
+ 
+
+ align:start position:0%
+here and look at the signal that the the
+loop returns possibly V
+
+ align:start position:0%
+loop returns possibly V
+ 
+
+ align:start position:0%
+loop returns possibly V
+subr and we found out that for certain
+
+ align:start position:0%
+subr and we found out that for certain
+ 
+
+ align:start position:0%
+subr and we found out that for certain
+systems in the absence of an input we'd
+
+ align:start position:0%
+systems in the absence of an input we'd
+ 
+
+ align:start position:0%
+systems in the absence of an input we'd
+be able to get V subr to be identically
+
+ align:start position:0%
+be able to get V subr to be identically
+ 
+
+ align:start position:0%
+be able to get V subr to be identically
+equal to V subt under sosal steady state
+
+ align:start position:0%
+equal to V subt under sosal steady state
+ 
+
+ align:start position:0%
+equal to V subt under sosal steady state
+conditions for some frequency of
+
+ align:start position:0%
+conditions for some frequency of
+ 
+
+ align:start position:0%
+conditions for some frequency of
+excitation when that happens we said
+
+ align:start position:0%
+excitation when that happens we said
+ 
+
+ align:start position:0%
+excitation when that happens we said
+well we could then imagine oscillation
+
+ align:start position:0%
+well we could then imagine oscillation
+ 
+
+ align:start position:0%
+well we could then imagine oscillation
+because we'd be able to
+
+ align:start position:0%
+because we'd be able to
+ 
+
+ align:start position:0%
+because we'd be able to
+reconnect the loop reclose the loop take
+
+ align:start position:0%
+reconnect the loop reclose the loop take
+ 
+
+ align:start position:0%
+reconnect the loop reclose the loop take
+away our generator and the system would
+
+ align:start position:0%
+away our generator and the system would
+ 
+
+ align:start position:0%
+away our generator and the system would
+continue to to oscillate forever in
+
+ align:start position:0%
+continue to to oscillate forever in
+ 
+
+ align:start position:0%
+continue to to oscillate forever in
+particular we looked at this situation
+
+ align:start position:0%
+particular we looked at this situation
+ 
+
+ align:start position:0%
+particular we looked at this situation
+uh for a system which had a loop
+
+ align:start position:0%
+uh for a system which had a loop
+ 
+
+ align:start position:0%
+uh for a system which had a loop
+transmission that included three
+
+ align:start position:0%
+transmission that included three
+ 
+
+ align:start position:0%
+transmission that included three
+coincident poles on the negative real
+
+ align:start position:0%
+coincident poles on the negative real
+ 
+
+ align:start position:0%
+coincident poles on the negative real
+axis and we found out that for that sort
+
+ align:start position:0%
+axis and we found out that for that sort
+ 
+
+ align:start position:0%
+axis and we found out that for that sort
+of a system if we had a low frequency
+
+ align:start position:0%
+of a system if we had a low frequency
+ 
+
+ align:start position:0%
+of a system if we had a low frequency
+Loop transmission magnitude a FN of 8
+
+ align:start position:0%
+Loop transmission magnitude a FN of 8
+ 
+
+ align:start position:0%
+Loop transmission magnitude a FN of 8
+the system in fact was capable of
+
+ align:start position:0%
+the system in fact was capable of
+ 
+
+ align:start position:0%
+the system in fact was capable of
+sustain constant amplitude
+
+ align:start position:0%
+sustain constant amplitude
+ 
+
+ align:start position:0%
+sustain constant amplitude
+oscillations I also mentioned that there
+
+ align:start position:0%
+oscillations I also mentioned that there
+ 
+
+ align:start position:0%
+oscillations I also mentioned that there
+were certain problems with that sort of
+
+ align:start position:0%
+were certain problems with that sort of
+ 
+
+ align:start position:0%
+were certain problems with that sort of
+analysis that it wasn't a completely
+
+ align:start position:0%
+analysis that it wasn't a completely
+ 
+
+ align:start position:0%
+analysis that it wasn't a completely
+General one and that it was possible
+
+ align:start position:0%
+General one and that it was possible
+ 
+
+ align:start position:0%
+General one and that it was possible
+that we could get into trouble with it
+
+ align:start position:0%
+that we could get into trouble with it
+ 
+
+ align:start position:0%
+that we could get into trouble with it
+and I'd like to go back and and look at
+
+ align:start position:0%
+and I'd like to go back and and look at
+ 
+
+ align:start position:0%
+and I'd like to go back and and look at
+another case of this and see where we
+
+ align:start position:0%
+another case of this and see where we
+ 
+
+ align:start position:0%
+another case of this and see where we
+might possibly get into trouble with
+
+ align:start position:0%
+might possibly get into trouble with
+ 
+
+ align:start position:0%
+might possibly get into trouble with
+that sort of simple-minded frequency
+
+ align:start position:0%
+that sort of simple-minded frequency
+ 
+
+ align:start position:0%
+that sort of simple-minded frequency
+response stability analysis again let's
+
+ align:start position:0%
+response stability analysis again let's
+ 
+
+ align:start position:0%
+response stability analysis again let's
+consider a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system where we're making Loop
+
+ align:start position:0%
+system where we're making Loop
+ 
+
+ align:start position:0%
+system where we're making Loop
+transmission measurements and suppose we
+
+ align:start position:0%
+transmission measurements and suppose we
+ 
+
+ align:start position:0%
+transmission measurements and suppose we
+had an a of
+
+ align:start position:0%
+had an a of
+ 
+
+ align:start position:0%
+had an a of
+minus1 and an F of one at some frequency
+
+ align:start position:0%
+minus1 and an F of one at some frequency
+ 
+
+ align:start position:0%
+minus1 and an F of one at some frequency
+in other words when we make sosal steady
+
+ align:start position:0%
+in other words when we make sosal steady
+ 
+
+ align:start position:0%
+in other words when we make sosal steady
+state measurements on the system we make
+
+ align:start position:0%
+state measurements on the system we make
+ 
+
+ align:start position:0%
+state measurements on the system we make
+the input zero we find that uh for some
+
+ align:start position:0%
+the input zero we find that uh for some
+ 
+
+ align:start position:0%
+the input zero we find that uh for some
+frequency of
+
+ align:start position:0%
+frequency of
+ 
+
+ align:start position:0%
+frequency of
+excitation a has a magnitude of 10 and
+
+ align:start position:0%
+excitation a has a magnitude of 10 and
+ 
+
+ align:start position:0%
+excitation a has a magnitude of 10 and
+provides a 180 Dee phase shift F has a
+
+ align:start position:0%
+provides a 180 Dee phase shift F has a
+ 
+
+ align:start position:0%
+provides a 180 Dee phase shift F has a
+magnitude of one with no phase shift
+
+ align:start position:0%
+magnitude of one with no phase shift
+ 
+
+ align:start position:0%
+magnitude of one with no phase shift
+consequently the loop transmission which
+
+ align:start position:0%
+consequently the loop transmission which
+ 
+
+ align:start position:0%
+consequently the loop transmission which
+includes one more inversion or one more
+
+ align:start position:0%
+includes one more inversion or one more
+ 
+
+ align:start position:0%
+includes one more inversion or one more
+180° phase shift at this point in the
+
+ align:start position:0%
+180° phase shift at this point in the
+ 
+
+ align:start position:0%
+180° phase shift at this point in the
+diagram has a magnitude of +
+
+ align:start position:0%
+diagram has a magnitude of +
+ 
+
+ align:start position:0%
+diagram has a magnitude of +
+10 and we suspect that that something
+
+ align:start position:0%
+10 and we suspect that that something
+ 
+
+ align:start position:0%
+10 and we suspect that that something
+might be wrong with that uh if we put in
+
+ align:start position:0%
+might be wrong with that uh if we put in
+ 
+
+ align:start position:0%
+might be wrong with that uh if we put in
+a test signal here get out a signal
+
+ align:start position:0%
+a test signal here get out a signal
+ 
+
+ align:start position:0%
+a test signal here get out a signal
+that's exactly in Phase with our test
+
+ align:start position:0%
+that's exactly in Phase with our test
+ 
+
+ align:start position:0%
+that's exactly in Phase with our test
+signal uh but 10 times as large we might
+
+ align:start position:0%
+signal uh but 10 times as large we might
+ 
+
+ align:start position:0%
+signal uh but 10 times as large we might
+suspect that there's potential
+
+ align:start position:0%
+suspect that there's potential
+ 
+
+ align:start position:0%
+suspect that there's potential
+difficulty with that sort of a
+
+ align:start position:0%
+difficulty with that sort of a
+ 
+
+ align:start position:0%
+difficulty with that sort of a
+system well there may or may not be as
+
+ align:start position:0%
+system well there may or may not be as
+ 
+
+ align:start position:0%
+system well there may or may not be as
+it happens we can't really tell about
+
+ align:start position:0%
+it happens we can't really tell about
+ 
+
+ align:start position:0%
+it happens we can't really tell about
+the stability of a feedback system by
+
+ align:start position:0%
+the stability of a feedback system by
+ 
+
+ align:start position:0%
+the stability of a feedback system by
+looking at its frequency response at
+
+ align:start position:0%
+looking at its frequency response at
+ 
+
+ align:start position:0%
+looking at its frequency response at
+only one frequency we really have to
+
+ align:start position:0%
+only one frequency we really have to
+ 
+
+ align:start position:0%
+only one frequency we really have to
+look at the frequency response of the
+
+ align:start position:0%
+look at the frequency response of the
+ 
+
+ align:start position:0%
+look at the frequency response of the
+system over all frequencies in order to
+
+ align:start position:0%
+system over all frequencies in order to
+ 
+
+ align:start position:0%
+system over all frequencies in order to
+say anything definite about the
+
+ align:start position:0%
+say anything definite about the
+ 
+
+ align:start position:0%
+say anything definite about the
+stability of the
+
+ align:start position:0%
+stability of the
+ 
+
+ align:start position:0%
+stability of the
+system let's
+
+ align:start position:0%
+system let's
+ 
+
+ align:start position:0%
+system let's
+consider the system that we mentioned
+
+ align:start position:0%
+consider the system that we mentioned
+ 
+
+ align:start position:0%
+consider the system that we mentioned
+earlier where a is equal to minus1 and F
+
+ align:start position:0%
+earlier where a is equal to minus1 and F
+ 
+
+ align:start position:0%
+earlier where a is equal to minus1 and F
+is equal to 1 we simply went blindly
+
+ align:start position:0%
+is equal to 1 we simply went blindly
+ 
+
+ align:start position:0%
+is equal to 1 we simply went blindly
+ahead we could write the Clos Loop
+
+ align:start position:0%
+ahead we could write the Clos Loop
+ 
+
+ align:start position:0%
+ahead we could write the Clos Loop
+transfer function of the system at the
+
+ align:start position:0%
+transfer function of the system at the
+ 
+
+ align:start position:0%
+transfer function of the system at the
+particular Omega which gives us the a of
+
+ align:start position:0%
+particular Omega which gives us the a of
+ 
+
+ align:start position:0%
+particular Omega which gives us the a of
+minus 10 and the F of one as simply the
+
+ align:start position:0%
+minus 10 and the F of one as simply the
+ 
+
+ align:start position:0%
+minus 10 and the F of one as simply the
+forward path over one minus the loop
+
+ align:start position:0%
+forward path over one minus the loop
+ 
+
+ align:start position:0%
+forward path over one minus the loop
+transmission
+
+ align:start position:0%
+transmission
+ 
+
+ align:start position:0%
+transmission
+but the forward path is now minus
+
+ align:start position:0%
+but the forward path is now minus
+ 
+
+ align:start position:0%
+but the forward path is now minus
+10 uh the loop transmission is itself +
+
+ align:start position:0%
+10 uh the loop transmission is itself +
+ 
+
+ align:start position:0%
+10 uh the loop transmission is itself +
+10 so we get 1 minus 10 in the
+
+ align:start position:0%
+10 so we get 1 minus 10 in the
+ 
+
+ align:start position:0%
+10 so we get 1 minus 10 in the
+denominator and we conclude that the
+
+ align:start position:0%
+denominator and we conclude that the
+ 
+
+ align:start position:0%
+denominator and we conclude that the
+input to Output transfer function at
+
+ align:start position:0%
+input to Output transfer function at
+ 
+
+ align:start position:0%
+input to Output transfer function at
+that frequency would have a magnitude of
+
+ align:start position:0%
+that frequency would have a magnitude of
+ 
+
+ align:start position:0%
+that frequency would have a magnitude of
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+9ths that's self-consistent let's
+
+ align:start position:0%
+9ths that's self-consistent let's
+ 
+
+ align:start position:0%
+9ths that's self-consistent let's
+consider what happens when we put in an
+
+ align:start position:0%
+consider what happens when we put in an
+ 
+
+ align:start position:0%
+consider what happens when we put in an
+input for example of one unit
+
+ align:start position:0%
+input for example of one unit
+ 
+
+ align:start position:0%
+input for example of one unit
+our equation if it's correct tells us
+
+ align:start position:0%
+our equation if it's correct tells us
+ 
+
+ align:start position:0%
+our equation if it's correct tells us
+that the output will then be 10
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+9ths and let's see when we subtract the
+
+ align:start position:0%
+9ths and let's see when we subtract the
+ 
+
+ align:start position:0%
+9ths and let's see when we subtract the
+10 9ths from the one unit we'll get
+
+ align:start position:0%
+10 9ths from the one unit we'll get
+ 
+
+ align:start position:0%
+10 9ths from the one unit we'll get
+minus 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+9th but at this particular frequency
+
+ align:start position:0%
+9th but at this particular frequency
+ 
+
+ align:start position:0%
+9th but at this particular frequency
+we've said that a of s is
+
+ align:start position:0%
+we've said that a of s is
+ 
+
+ align:start position:0%
+we've said that a of s is
+minus10 and when we multiply
+
+ align:start position:0%
+minus10 and when we multiply
+ 
+
+ align:start position:0%
+minus10 and when we multiply
+the - one 9th signal that exists at this
+
+ align:start position:0%
+the - one 9th signal that exists at this
+ 
+
+ align:start position:0%
+the - one 9th signal that exists at this
+point by minus1 we in fact get 10 9th so
+
+ align:start position:0%
+point by minus1 we in fact get 10 9th so
+ 
+
+ align:start position:0%
+point by minus1 we in fact get 10 9th so
+the arithmetic seems to be
+
+ align:start position:0%
+the arithmetic seems to be
+ 
+
+ align:start position:0%
+the arithmetic seems to be
+self-consistent and so it's at least
+
+ align:start position:0%
+self-consistent and so it's at least
+ 
+
+ align:start position:0%
+self-consistent and so it's at least
+superficially possible for this system
+
+ align:start position:0%
+superficially possible for this system
+ 
+
+ align:start position:0%
+superficially possible for this system
+to behave in the manner that I've
+
+ align:start position:0%
+to behave in the manner that I've
+ 
+
+ align:start position:0%
+to behave in the manner that I've
+described in other words behave in a
+
+ align:start position:0%
+described in other words behave in a
+ 
+
+ align:start position:0%
+described in other words behave in a
+stable manner even though at this
+
+ align:start position:0%
+stable manner even though at this
+ 
+
+ align:start position:0%
+stable manner even though at this
+particular frequency it has a loop
+
+ align:start position:0%
+particular frequency it has a loop
+ 
+
+ align:start position:0%
+particular frequency it has a loop
+transmission of +
+
+ align:start position:0%
+transmission of +
+ 
+
+ align:start position:0%
+transmission of +
+10 well as I say we have to look really
+
+ align:start position:0%
+10 well as I say we have to look really
+ 
+
+ align:start position:0%
+10 well as I say we have to look really
+at the characteristics of the loop
+
+ align:start position:0%
+at the characteristics of the loop
+ 
+
+ align:start position:0%
+at the characteristics of the loop
+transmission at all frequencies in order
+
+ align:start position:0%
+transmission at all frequencies in order
+ 
+
+ align:start position:0%
+transmission at all frequencies in order
+to determine stability this simple
+
+ align:start position:0%
+to determine stability this simple
+ 
+
+ align:start position:0%
+to determine stability this simple
+evaluation at one frequency isn't enough
+
+ align:start position:0%
+evaluation at one frequency isn't enough
+ 
+
+ align:start position:0%
+evaluation at one frequency isn't enough
+and in fact can can give us erroneous
+
+ align:start position:0%
+and in fact can can give us erroneous
+ 
+
+ align:start position:0%
+and in fact can can give us erroneous
+results the way we determine the
+
+ align:start position:0%
+results the way we determine the
+ 
+
+ align:start position:0%
+results the way we determine the
+stability of a feedback system based on
+
+ align:start position:0%
+stability of a feedback system based on
+ 
+
+ align:start position:0%
+stability of a feedback system based on
+frequency response measurements in
+
+ align:start position:0%
+frequency response measurements in
+ 
+
+ align:start position:0%
+frequency response measurements in
+particular the frequency response
+
+ align:start position:0%
+particular the frequency response
+ 
+
+ align:start position:0%
+particular the frequency response
+associated with Loop transmission is
+
+ align:start position:0%
+associated with Loop transmission is
+ 
+
+ align:start position:0%
+associated with Loop transmission is
+called the Nyquist
+
+ align:start position:0%
+called the Nyquist
+ 
+
+ align:start position:0%
+called the Nyquist
+test and here as we started with root
+
+ align:start position:0%
+test and here as we started with root
+ 
+
+ align:start position:0%
+test and here as we started with root
+Locus we look at the characteristic
+
+ align:start position:0%
+Locus we look at the characteristic
+ 
+
+ align:start position:0%
+Locus we look at the characteristic
+equation for the system which is simply
+
+ align:start position:0%
+equation for the system which is simply
+ 
+
+ align:start position:0%
+equation for the system which is simply
+one minus the loop transmission and in
+
+ align:start position:0%
+one minus the loop transmission and in
+ 
+
+ align:start position:0%
+one minus the loop transmission and in
+our standard notation that's 1 plus a of
+
+ align:start position:0%
+our standard notation that's 1 plus a of
+ 
+
+ align:start position:0%
+our standard notation that's 1 plus a of
+s f of s and again exactly as in the
+
+ align:start position:0%
+s f of s and again exactly as in the
+ 
+
+ align:start position:0%
+s f of s and again exactly as in the
+root Locus development we recognize that
+
+ align:start position:0%
+root Locus development we recognize that
+ 
+
+ align:start position:0%
+root Locus development we recognize that
+closed loop poles of the system will lie
+
+ align:start position:0%
+closed loop poles of the system will lie
+ 
+
+ align:start position:0%
+closed loop poles of the system will lie
+at values of s where this term goes to
+
+ align:start position:0%
+at values of s where this term goes to
+ 
+
+ align:start position:0%
+at values of s where this term goes to
+zero the characteristic equation is of
+
+ align:start position:0%
+zero the characteristic equation is of
+ 
+
+ align:start position:0%
+zero the characteristic equation is of
+course the denominator polinomial of any
+
+ align:start position:0%
+course the denominator polinomial of any
+ 
+
+ align:start position:0%
+course the denominator polinomial of any
+closed loop transfer function of the
+
+ align:start position:0%
+closed loop transfer function of the
+ 
+
+ align:start position:0%
+closed loop transfer function of the
+system and so the closed loop Pooles of
+
+ align:start position:0%
+system and so the closed loop Pooles of
+ 
+
+ align:start position:0%
+system and so the closed loop Pooles of
+the system lie at values of s where this
+
+ align:start position:0%
+the system lie at values of s where this
+ 
+
+ align:start position:0%
+the system lie at values of s where this
+quantity goes to
+
+ align:start position:0%
+quantity goes to
+ 
+
+ align:start position:0%
+quantity goes to
+zero or correspondingly uh at values of
+
+ align:start position:0%
+zero or correspondingly uh at values of
+ 
+
+ align:start position:0%
+zero or correspondingly uh at values of
+s where a of s f of s equals minus one
+
+ align:start position:0%
+s where a of s f of s equals minus one
+ 
+
+ align:start position:0%
+s where a of s f of s equals minus one
+that's those of course are the values of
+
+ align:start position:0%
+that's those of course are the values of
+ 
+
+ align:start position:0%
+that's those of course are the values of
+s for which this quantity goes to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero our system will be unstable if the
+
+ align:start position:0%
+zero our system will be unstable if the
+ 
+
+ align:start position:0%
+zero our system will be unstable if the
+closed loop Poes exist for values of s
+
+ align:start position:0%
+closed loop Poes exist for values of s
+ 
+
+ align:start position:0%
+closed loop Poes exist for values of s
+with positive real parts and other words
+
+ align:start position:0%
+with positive real parts and other words
+ 
+
+ align:start position:0%
+with positive real parts and other words
+if there's there if the system
+
+ align:start position:0%
+if there's there if the system
+ 
+
+ align:start position:0%
+if there's there if the system
+has closed loopholes lying in the right
+
+ align:start position:0%
+has closed loopholes lying in the right
+ 
+
+ align:start position:0%
+has closed loopholes lying in the right
+half of the S plane so our stability
+
+ align:start position:0%
+half of the S plane so our stability
+ 
+
+ align:start position:0%
+half of the S plane so our stability
+test is uh to determine if there are any
+
+ align:start position:0%
+test is uh to determine if there are any
+ 
+
+ align:start position:0%
+test is uh to determine if there are any
+values of s with positive real parts for
+
+ align:start position:0%
+values of s with positive real parts for
+ 
+
+ align:start position:0%
+values of s with positive real parts for
+which a of s f of s equals minus one
+
+ align:start position:0%
+which a of s f of s equals minus one
+ 
+
+ align:start position:0%
+which a of s f of s equals minus one
+that's the case if there's one or more
+
+ align:start position:0%
+that's the case if there's one or more
+ 
+
+ align:start position:0%
+that's the case if there's one or more
+than one value of s with a positive real
+
+ align:start position:0%
+than one value of s with a positive real
+ 
+
+ align:start position:0%
+than one value of s with a positive real
+part for which a of s f of s equals
+
+ align:start position:0%
+part for which a of s f of s equals
+ 
+
+ align:start position:0%
+part for which a of s f of s equals
+minus one the system is then
+
+ align:start position:0%
+minus one the system is then
+ 
+
+ align:start position:0%
+minus one the system is then
+unstable how do we make this
+
+ align:start position:0%
+unstable how do we make this
+ 
+
+ align:start position:0%
+unstable how do we make this
+determination well what Nyquist what the
+
+ align:start position:0%
+determination well what Nyquist what the
+ 
+
+ align:start position:0%
+determination well what Nyquist what the
+Nyquist test suggest that we do is the
+
+ align:start position:0%
+Nyquist test suggest that we do is the
+ 
+
+ align:start position:0%
+Nyquist test suggest that we do is the
+following we perform a mapping we
+
+ align:start position:0%
+following we perform a mapping we
+ 
+
+ align:start position:0%
+following we perform a mapping we
+evaluate our the negative of our Loop
+
+ align:start position:0%
+evaluate our the negative of our Loop
+ 
+
+ align:start position:0%
+evaluate our the negative of our Loop
+Transmission in particular the AF
+
+ align:start position:0%
+Transmission in particular the AF
+ 
+
+ align:start position:0%
+Transmission in particular the AF
+product for values of s so what we do is
+
+ align:start position:0%
+product for values of s so what we do is
+ 
+
+ align:start position:0%
+product for values of s so what we do is
+a mapping that takes values of s in the
+
+ align:start position:0%
+a mapping that takes values of s in the
+ 
+
+ align:start position:0%
+a mapping that takes values of s in the
+S
+
+ align:start position:0%
+S
+ 
+
+ align:start position:0%
+S
+plane and transfers them to an AF
+
+ align:start position:0%
+plane and transfers them to an AF
+ 
+
+ align:start position:0%
+plane and transfers them to an AF
+plane remember that AF of s is simply a
+
+ align:start position:0%
+plane remember that AF of s is simply a
+ 
+
+ align:start position:0%
+plane remember that AF of s is simply a
+function of S and S is a complex
+
+ align:start position:0%
+function of S and S is a complex
+ 
+
+ align:start position:0%
+function of S and S is a complex
+variable in general with a a real part
+
+ align:start position:0%
+variable in general with a a real part
+ 
+
+ align:start position:0%
+variable in general with a a real part
+and an imaginary part
+
+ align:start position:0%
+and an imaginary part
+ 
+
+ align:start position:0%
+and an imaginary part
+and so when we substitute substitute
+
+ align:start position:0%
+and so when we substitute substitute
+ 
+
+ align:start position:0%
+and so when we substitute substitute
+into AF some specific value of s
+
+ align:start position:0%
+into AF some specific value of s
+ 
+
+ align:start position:0%
+into AF some specific value of s
+corresponding to a point in the S plane
+
+ align:start position:0%
+corresponding to a point in the S plane
+ 
+
+ align:start position:0%
+corresponding to a point in the S plane
+we get a specific value for the AF
+
+ align:start position:0%
+we get a specific value for the AF
+ 
+
+ align:start position:0%
+we get a specific value for the AF
+product again a complex number and we
+
+ align:start position:0%
+product again a complex number and we
+ 
+
+ align:start position:0%
+product again a complex number and we
+choose to write that AF product in a
+
+ align:start position:0%
+choose to write that AF product in a
+ 
+
+ align:start position:0%
+choose to write that AF product in a
+particular form we choose to use a
+
+ align:start position:0%
+particular form we choose to use a
+ 
+
+ align:start position:0%
+particular form we choose to use a
+so-called gain phase representation for
+
+ align:start position:0%
+so-called gain phase representation for
+ 
+
+ align:start position:0%
+so-called gain phase representation for
+the AF product in other words here we
+
+ align:start position:0%
+the AF product in other words here we
+ 
+
+ align:start position:0%
+the AF product in other words here we
+have a gain phase plot in the AF plane
+
+ align:start position:0%
+have a gain phase plot in the AF plane
+ 
+
+ align:start position:0%
+have a gain phase plot in the AF plane
+if you will the this axis is magnitude
+
+ align:start position:0%
+if you will the this axis is magnitude
+ 
+
+ align:start position:0%
+if you will the this axis is magnitude
+or gain generally for the same reasons
+
+ align:start position:0%
+or gain generally for the same reasons
+ 
+
+ align:start position:0%
+or gain generally for the same reasons
+that we do with a bod plot why we use a
+
+ align:start position:0%
+that we do with a bod plot why we use a
+ 
+
+ align:start position:0%
+that we do with a bod plot why we use a
+logarithmic presentation so here we
+
+ align:start position:0%
+logarithmic presentation so here we
+ 
+
+ align:start position:0%
+logarithmic presentation so here we
+might have unit magnitude a magnitude of
+
+ align:start position:0%
+might have unit magnitude a magnitude of
+ 
+
+ align:start position:0%
+might have unit magnitude a magnitude of
+10 100 and so forth a tenth 1/ 100th
+
+ align:start position:0%
+10 100 and so forth a tenth 1/ 100th
+ 
+
+ align:start position:0%
+10 100 and so forth a tenth 1/ 100th
+again as I say a a logarithmic scale is
+
+ align:start position:0%
+again as I say a a logarithmic scale is
+ 
+
+ align:start position:0%
+again as I say a a logarithmic scale is
+usually most convenient because of the
+
+ align:start position:0%
+usually most convenient because of the
+ 
+
+ align:start position:0%
+usually most convenient because of the
+large dynamic range associated with the
+
+ align:start position:0%
+large dynamic range associated with the
+ 
+
+ align:start position:0%
+large dynamic range associated with the
+magnitude of the loop
+
+ align:start position:0%
+magnitude of the loop
+ 
+
+ align:start position:0%
+magnitude of the loop
+transmission and this axis is the angle
+
+ align:start position:0%
+transmission and this axis is the angle
+ 
+
+ align:start position:0%
+transmission and this axis is the angle
+associated with
+
+ align:start position:0%
+associated with
+ 
+
+ align:start position:0%
+associated with
+AF 0° in the middle plus 90° Plus
+
+ align:start position:0%
+AF 0° in the middle plus 90° Plus
+ 
+
+ align:start position:0%
+AF 0° in the middle plus 90° Plus
+180° and so forth and then negative
+
+ align:start position:0%
+180° and so forth and then negative
+ 
+
+ align:start position:0%
+180° and so forth and then negative
+angles to the left in this gain phase
+
+ align:start position:0%
+angles to the left in this gain phase
+ 
+
+ align:start position:0%
+angles to the left in this gain phase
+plane again we'll see many uses of a
+
+ align:start position:0%
+plane again we'll see many uses of a
+ 
+
+ align:start position:0%
+plane again we'll see many uses of a
+presentation of the loop transmission or
+
+ align:start position:0%
+presentation of the loop transmission or
+ 
+
+ align:start position:0%
+presentation of the loop transmission or
+the negative of the loop transmission
+
+ align:start position:0%
+the negative of the loop transmission
+ 
+
+ align:start position:0%
+the negative of the loop transmission
+the AF product in a gain phase plane but
+
+ align:start position:0%
+the AF product in a gain phase plane but
+ 
+
+ align:start position:0%
+the AF product in a gain phase plane but
+the important point is of course we can
+
+ align:start position:0%
+the important point is of course we can
+ 
+
+ align:start position:0%
+the important point is of course we can
+go from a point in the S plane
+
+ align:start position:0%
+go from a point in the S plane
+ 
+
+ align:start position:0%
+go from a point in the S plane
+substitute in that value of s to the
+
+ align:start position:0%
+substitute in that value of s to the
+ 
+
+ align:start position:0%
+substitute in that value of s to the
+expression for AF and determine a
+
+ align:start position:0%
+expression for AF and determine a
+ 
+
+ align:start position:0%
+expression for AF and determine a
+magnitude and angle which we then plot
+
+ align:start position:0%
+magnitude and angle which we then plot
+ 
+
+ align:start position:0%
+magnitude and angle which we then plot
+in the AF
+
+ align:start position:0%
+in the AF
+ 
+
+ align:start position:0%
+in the AF
+plane and there's certain properties of
+
+ align:start position:0%
+plane and there's certain properties of
+ 
+
+ align:start position:0%
+plane and there's certain properties of
+this mapping that are useful for our
+
+ align:start position:0%
+this mapping that are useful for our
+ 
+
+ align:start position:0%
+this mapping that are useful for our
+investigation of
+
+ align:start position:0%
+investigation of
+ 
+
+ align:start position:0%
+investigation of
+stability in particular if we evaluate
+
+ align:start position:0%
+stability in particular if we evaluate
+ 
+
+ align:start position:0%
+stability in particular if we evaluate
+the AF product as s takes on
+
+ align:start position:0%
+the AF product as s takes on
+ 
+
+ align:start position:0%
+the AF product as s takes on
+values lying on a small circle in the S
+
+ align:start position:0%
+values lying on a small circle in the S
+ 
+
+ align:start position:0%
+values lying on a small circle in the S
+plane we find that we get a small circle
+
+ align:start position:0%
+plane we find that we get a small circle
+ 
+
+ align:start position:0%
+plane we find that we get a small circle
+in the AF
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane we also find out that if we
+
+ align:start position:0%
+plane we also find out that if we
+ 
+
+ align:start position:0%
+plane we also find out that if we
+evaluate the AF product again for values
+
+ align:start position:0%
+evaluate the AF product again for values
+ 
+
+ align:start position:0%
+evaluate the AF product again for values
+of s that lie in a closed Contour in the
+
+ align:start position:0%
+of s that lie in a closed Contour in the
+ 
+
+ align:start position:0%
+of s that lie in a closed Contour in the
+S plane possibly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here when we evaluate the AF product as
+
+ align:start position:0%
+here when we evaluate the AF product as
+ 
+
+ align:start position:0%
+here when we evaluate the AF product as
+s takes on this sequence of values we
+
+ align:start position:0%
+s takes on this sequence of values we
+ 
+
+ align:start position:0%
+s takes on this sequence of values we
+again get a closed Contour in the AF
+
+ align:start position:0%
+again get a closed Contour in the AF
+ 
+
+ align:start position:0%
+again get a closed Contour in the AF
+plane possibly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this furthermore all values of s that
+
+ align:start position:0%
+this furthermore all values of s that
+ 
+
+ align:start position:0%
+this furthermore all values of s that
+lie to one side of this Contour in the S
+
+ align:start position:0%
+lie to one side of this Contour in the S
+ 
+
+ align:start position:0%
+lie to one side of this Contour in the S
+plane lie on one side of the Contour in
+
+ align:start position:0%
+plane lie on one side of the Contour in
+ 
+
+ align:start position:0%
+plane lie on one side of the Contour in
+the AF plane there's an issue of insided
+
+ align:start position:0%
+the AF plane there's an issue of insided
+ 
+
+ align:start position:0%
+the AF plane there's an issue of insided
+this outsid this here and we have to
+
+ align:start position:0%
+this outsid this here and we have to
+ 
+
+ align:start position:0%
+this outsid this here and we have to
+investigate that separately but for
+
+ align:start position:0%
+investigate that separately but for
+ 
+
+ align:start position:0%
+investigate that separately but for
+example if we found that a value of s
+
+ align:start position:0%
+example if we found that a value of s
+ 
+
+ align:start position:0%
+example if we found that a value of s
+here for example inside what we
+
+ align:start position:0%
+here for example inside what we
+ 
+
+ align:start position:0%
+here for example inside what we
+conventionally think of as being inside
+
+ align:start position:0%
+conventionally think of as being inside
+ 
+
+ align:start position:0%
+conventionally think of as being inside
+the Contour in the S plane uh for
+
+ align:start position:0%
+the Contour in the S plane uh for
+ 
+
+ align:start position:0%
+the Contour in the S plane uh for
+example lay here what appears to be
+
+ align:start position:0%
+example lay here what appears to be
+ 
+
+ align:start position:0%
+example lay here what appears to be
+outside the Contour in the AF plane then
+
+ align:start position:0%
+outside the Contour in the AF plane then
+ 
+
+ align:start position:0%
+outside the Contour in the AF plane then
+all value Val of s inside this Contour
+
+ align:start position:0%
+all value Val of s inside this Contour
+ 
+
+ align:start position:0%
+all value Val of s inside this Contour
+in the S plane would give rise to values
+
+ align:start position:0%
+in the S plane would give rise to values
+ 
+
+ align:start position:0%
+in the S plane would give rise to values
+of AF outside this Contour in the AF
+
+ align:start position:0%
+of AF outside this Contour in the AF
+ 
+
+ align:start position:0%
+of AF outside this Contour in the AF
+plane there's one additional property
+
+ align:start position:0%
+plane there's one additional property
+ 
+
+ align:start position:0%
+plane there's one additional property
+that we we'd like to use and that is
+
+ align:start position:0%
+that we we'd like to use and that is
+ 
+
+ align:start position:0%
+that we we'd like to use and that is
+that if we make a small right angle turn
+
+ align:start position:0%
+that if we make a small right angle turn
+ 
+
+ align:start position:0%
+that if we make a small right angle turn
+in other words we
+
+ align:start position:0%
+in other words we
+ 
+
+ align:start position:0%
+in other words we
+evaluate um AF four values of s that
+
+ align:start position:0%
+evaluate um AF four values of s that
+ 
+
+ align:start position:0%
+evaluate um AF four values of s that
+take on a right angle in the S plane uh
+
+ align:start position:0%
+take on a right angle in the S plane uh
+ 
+
+ align:start position:0%
+take on a right angle in the S plane uh
+we again get a right angle in the AF
+
+ align:start position:0%
+we again get a right angle in the AF
+ 
+
+ align:start position:0%
+we again get a right angle in the AF
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+possibly
+
+ align:start position:0%
+possibly
+ 
+
+ align:start position:0%
+possibly
+this uh as it happens there's a because
+
+ align:start position:0%
+this uh as it happens there's a because
+ 
+
+ align:start position:0%
+this uh as it happens there's a because
+of the choice of coordinates uh when we
+
+ align:start position:0%
+of the choice of coordinates uh when we
+ 
+
+ align:start position:0%
+of the choice of coordinates uh when we
+make a right hand turn in the S plane in
+
+ align:start position:0%
+make a right hand turn in the S plane in
+ 
+
+ align:start position:0%
+make a right hand turn in the S plane in
+other words if we evaluated AF along
+
+ align:start position:0%
+other words if we evaluated AF along
+ 
+
+ align:start position:0%
+other words if we evaluated AF along
+this path and that direction such that
+
+ align:start position:0%
+this path and that direction such that
+ 
+
+ align:start position:0%
+this path and that direction such that
+we took a rightand turn why we'd find
+
+ align:start position:0%
+we took a rightand turn why we'd find
+ 
+
+ align:start position:0%
+we took a rightand turn why we'd find
+that we actually take a leftand turn in
+
+ align:start position:0%
+that we actually take a leftand turn in
+ 
+
+ align:start position:0%
+that we actually take a leftand turn in
+the AF plane and that simply has to do
+
+ align:start position:0%
+the AF plane and that simply has to do
+ 
+
+ align:start position:0%
+the AF plane and that simply has to do
+with the choice of axes for the angle
+
+ align:start position:0%
+with the choice of axes for the angle
+ 
+
+ align:start position:0%
+with the choice of axes for the angle
+had we chosen to plot positive angles to
+
+ align:start position:0%
+had we chosen to plot positive angles to
+ 
+
+ align:start position:0%
+had we chosen to plot positive angles to
+the left rather than it's conventionally
+
+ align:start position:0%
+the left rather than it's conventionally
+ 
+
+ align:start position:0%
+the left rather than it's conventionally
+done why the the right hand turns would
+
+ align:start position:0%
+done why the the right hand turns would
+ 
+
+ align:start position:0%
+done why the the right hand turns would
+have been
+
+ align:start position:0%
+have been
+ 
+
+ align:start position:0%
+have been
+maintained well how do we use all of
+
+ align:start position:0%
+maintained well how do we use all of
+ 
+
+ align:start position:0%
+maintained well how do we use all of
+this to investigate the stability of a
+
+ align:start position:0%
+this to investigate the stability of a
+ 
+
+ align:start position:0%
+this to investigate the stability of a
+system the secret is to
+
+ align:start position:0%
+system the secret is to
+ 
+
+ align:start position:0%
+system the secret is to
+evaluate the AF
+
+ align:start position:0%
+evaluate the AF
+ 
+
+ align:start position:0%
+evaluate the AF
+quantity along a contour that concludes
+
+ align:start position:0%
+quantity along a contour that concludes
+ 
+
+ align:start position:0%
+quantity along a contour that concludes
+the region of Interest we're interested
+
+ align:start position:0%
+the region of Interest we're interested
+ 
+
+ align:start position:0%
+the region of Interest we're interested
+in whether there's any values of s with
+
+ align:start position:0%
+in whether there's any values of s with
+ 
+
+ align:start position:0%
+in whether there's any values of s with
+positive real parts that give rise to
+
+ align:start position:0%
+positive real parts that give rise to
+ 
+
+ align:start position:0%
+positive real parts that give rise to
+minus ones of the AF product and so what
+
+ align:start position:0%
+minus ones of the AF product and so what
+ 
+
+ align:start position:0%
+minus ones of the AF product and so what
+we do is evaluate the AF product along a
+
+ align:start position:0%
+we do is evaluate the AF product along a
+ 
+
+ align:start position:0%
+we do is evaluate the AF product along a
+contour that includes the entire region
+
+ align:start position:0%
+contour that includes the entire region
+ 
+
+ align:start position:0%
+contour that includes the entire region
+of interest in particular the entire
+
+ align:start position:0%
+of interest in particular the entire
+ 
+
+ align:start position:0%
+of interest in particular the entire
+right half of the S plane all values of
+
+ align:start position:0%
+right half of the S plane all values of
+ 
+
+ align:start position:0%
+right half of the S plane all values of
+s with positive real parts of course lie
+
+ align:start position:0%
+s with positive real parts of course lie
+ 
+
+ align:start position:0%
+s with positive real parts of course lie
+in the right half of the S plane so what
+
+ align:start position:0%
+in the right half of the S plane so what
+ 
+
+ align:start position:0%
+in the right half of the S plane so what
+we do is choose a contour in the S plane
+
+ align:start position:0%
+we do is choose a contour in the S plane
+ 
+
+ align:start position:0%
+we do is choose a contour in the S plane
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+includes the values of f s of interest
+
+ align:start position:0%
+includes the values of f s of interest
+ 
+
+ align:start position:0%
+includes the values of f s of interest
+and the one that does that is is one
+
+ align:start position:0%
+and the one that does that is is one
+ 
+
+ align:start position:0%
+and the one that does that is is one
+that includes the imaginary axis
+
+ align:start position:0%
+that includes the imaginary axis
+ 
+
+ align:start position:0%
+that includes the imaginary axis
+and then is eventually closed with a
+
+ align:start position:0%
+and then is eventually closed with a
+ 
+
+ align:start position:0%
+and then is eventually closed with a
+very large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+semicircle that includes the entire
+
+ align:start position:0%
+semicircle that includes the entire
+ 
+
+ align:start position:0%
+semicircle that includes the entire
+right half of the S
+
+ align:start position:0%
+right half of the S
+ 
+
+ align:start position:0%
+right half of the S
+plane so what we do is
+
+ align:start position:0%
+plane so what we do is
+ 
+
+ align:start position:0%
+plane so what we do is
+evaluate s on a contour like this that
+
+ align:start position:0%
+evaluate s on a contour like this that
+ 
+
+ align:start position:0%
+evaluate s on a contour like this that
+includes the region of interest and what
+
+ align:start position:0%
+includes the region of interest and what
+ 
+
+ align:start position:0%
+includes the region of interest and what
+we want to know is is whether there are
+
+ align:start position:0%
+we want to know is is whether there are
+ 
+
+ align:start position:0%
+we want to know is is whether there are
+any minus ones of the AF product that
+
+ align:start position:0%
+any minus ones of the AF product that
+ 
+
+ align:start position:0%
+any minus ones of the AF product that
+correspond to values of s in this region
+
+ align:start position:0%
+correspond to values of s in this region
+ 
+
+ align:start position:0%
+correspond to values of s in this region
+well the thing that gives us some
+
+ align:start position:0%
+well the thing that gives us some
+ 
+
+ align:start position:0%
+well the thing that gives us some
+Leverage is the fact that the minus ones
+
+ align:start position:0%
+Leverage is the fact that the minus ones
+ 
+
+ align:start position:0%
+Leverage is the fact that the minus ones
+are very clearly discernable in the AF
+
+ align:start position:0%
+are very clearly discernable in the AF
+ 
+
+ align:start position:0%
+are very clearly discernable in the AF
+plane if we look at the AF plane let's
+
+ align:start position:0%
+plane if we look at the AF plane let's
+ 
+
+ align:start position:0%
+plane if we look at the AF plane let's
+consider how we identify a minus one in
+
+ align:start position:0%
+consider how we identify a minus one in
+ 
+
+ align:start position:0%
+consider how we identify a minus one in
+the AF plane well a minus one of course
+
+ align:start position:0%
+the AF plane well a minus one of course
+ 
+
+ align:start position:0%
+the AF plane well a minus one of course
+is a magnitude of one and an angle of
+
+ align:start position:0%
+is a magnitude of one and an angle of
+ 
+
+ align:start position:0%
+is a magnitude of one and an angle of
+180° or minus
+
+ align:start position:0%
+180° or minus
+ 
+
+ align:start position:0%
+180° or minus
+180° or in general odd integral
+
+ align:start position:0%
+180° or in general odd integral
+ 
+
+ align:start position:0%
+180° or in general odd integral
+multiples of 180° so we have a minus1
+
+ align:start position:0%
+multiples of 180° so we have a minus1
+ 
+
+ align:start position:0%
+multiples of 180° so we have a minus1
+right here magnitude of one and angle of
+
+ align:start position:0%
+right here magnitude of one and angle of
+ 
+
+ align:start position:0%
+right here magnitude of one and angle of
+180° we have another minus1 in the AF
+
+ align:start position:0%
+180° we have another minus1 in the AF
+ 
+
+ align:start position:0%
+180° we have another minus1 in the AF
+plane minus 180° with a magnitude of one
+
+ align:start position:0%
+plane minus 180° with a magnitude of one
+ 
+
+ align:start position:0%
+plane minus 180° with a magnitude of one
+and we have more and more of these we
+
+ align:start position:0%
+and we have more and more of these we
+ 
+
+ align:start position:0%
+and we have more and more of these we
+have one another 360° displaced from
+
+ align:start position:0%
+have one another 360° displaced from
+ 
+
+ align:start position:0%
+have one another 360° displaced from
+this at Plus
+
+ align:start position:0%
+this at Plus
+ 
+
+ align:start position:0%
+this at Plus
+540° at minus 540 degre and so forth so
+
+ align:start position:0%
+540° at minus 540 degre and so forth so
+ 
+
+ align:start position:0%
+540° at minus 540 degre and so forth so
+the minus ones are very easily observed
+
+ align:start position:0%
+the minus ones are very easily observed
+ 
+
+ align:start position:0%
+the minus ones are very easily observed
+in the AF plane and that's the thing
+
+ align:start position:0%
+in the AF plane and that's the thing
+ 
+
+ align:start position:0%
+in the AF plane and that's the thing
+that that gives us leverage in or makes
+
+ align:start position:0%
+that that gives us leverage in or makes
+ 
+
+ align:start position:0%
+that that gives us leverage in or makes
+the Nyquist test a useful way of finding
+
+ align:start position:0%
+the Nyquist test a useful way of finding
+ 
+
+ align:start position:0%
+the Nyquist test a useful way of finding
+the stability of a system system let's
+
+ align:start position:0%
+the stability of a system system let's
+ 
+
+ align:start position:0%
+the stability of a system system let's
+look at how this might
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work here we show the Nyquist
+
+ align:start position:0%
+work here we show the Nyquist
+ 
+
+ align:start position:0%
+work here we show the Nyquist
+construction we again are looking in the
+
+ align:start position:0%
+construction we again are looking in the
+ 
+
+ align:start position:0%
+construction we again are looking in the
+S plane our usual axes the imaginary
+
+ align:start position:0%
+S plane our usual axes the imaginary
+ 
+
+ align:start position:0%
+S plane our usual axes the imaginary
+axis here J Omega the real axis and we
+
+ align:start position:0%
+axis here J Omega the real axis and we
+ 
+
+ align:start position:0%
+axis here J Omega the real axis and we
+choose a contour for our Nyquist test
+
+ align:start position:0%
+choose a contour for our Nyquist test
+ 
+
+ align:start position:0%
+choose a contour for our Nyquist test
+that includes the entire region of
+
+ align:start position:0%
+that includes the entire region of
+ 
+
+ align:start position:0%
+that includes the entire region of
+Interest usually we start at s equal 0
+
+ align:start position:0%
+Interest usually we start at s equal 0
+ 
+
+ align:start position:0%
+Interest usually we start at s equal 0
+plus just a small amount of J in other
+
+ align:start position:0%
+plus just a small amount of J in other
+ 
+
+ align:start position:0%
+plus just a small amount of J in other
+words at at this point in the S plane
+
+ align:start position:0%
+words at at this point in the S plane
+ 
+
+ align:start position:0%
+words at at this point in the S plane
+evaluate the AF product at s equals 0
+
+ align:start position:0%
+evaluate the AF product at s equals 0
+ 
+
+ align:start position:0%
+evaluate the AF product at s equals 0
+plus j0 plus if you will and then we
+
+ align:start position:0%
+plus j0 plus if you will and then we
+ 
+
+ align:start position:0%
+plus j0 plus if you will and then we
+continue evaluating the AF product as s
+
+ align:start position:0%
+continue evaluating the AF product as s
+ 
+
+ align:start position:0%
+continue evaluating the AF product as s
+takes on increasing values along this
+
+ align:start position:0%
+takes on increasing values along this
+ 
+
+ align:start position:0%
+takes on increasing values along this
+line an imaginary component but no real
+
+ align:start position:0%
+line an imaginary component but no real
+ 
+
+ align:start position:0%
+line an imaginary component but no real
+component we get magnitudes and angles
+
+ align:start position:0%
+component we get magnitudes and angles
+ 
+
+ align:start position:0%
+component we get magnitudes and angles
+for the AF product corresponding to the
+
+ align:start position:0%
+for the AF product corresponding to the
+ 
+
+ align:start position:0%
+for the AF product corresponding to the
+values of s along this line and of
+
+ align:start position:0%
+values of s along this line and of
+ 
+
+ align:start position:0%
+values of s along this line and of
+course those are simply uh the values
+
+ align:start position:0%
+course those are simply uh the values
+ 
+
+ align:start position:0%
+course those are simply uh the values
+that we'd get if we made frequency
+
+ align:start position:0%
+that we'd get if we made frequency
+ 
+
+ align:start position:0%
+that we'd get if we made frequency
+response measurements because evaluation
+
+ align:start position:0%
+response measurements because evaluation
+ 
+
+ align:start position:0%
+response measurements because evaluation
+of the AF product for S equals J Omega
+
+ align:start position:0%
+of the AF product for S equals J Omega
+ 
+
+ align:start position:0%
+of the AF product for S equals J Omega
+is exactly what we get when we evaluate
+
+ align:start position:0%
+is exactly what we get when we evaluate
+ 
+
+ align:start position:0%
+is exactly what we get when we evaluate
+the frequency response or measure the
+
+ align:start position:0%
+the frequency response or measure the
+ 
+
+ align:start position:0%
+the frequency response or measure the
+frequency response of our system so we
+
+ align:start position:0%
+frequency response of our system so we
+ 
+
+ align:start position:0%
+frequency response of our system so we
+can get the values of the AF product by
+
+ align:start position:0%
+can get the values of the AF product by
+ 
+
+ align:start position:0%
+can get the values of the AF product by
+experimental measurements and as I
+
+ align:start position:0%
+experimental measurements and as I
+ 
+
+ align:start position:0%
+experimental measurements and as I
+mentioned earlier that's one of the
+
+ align:start position:0%
+mentioned earlier that's one of the
+ 
+
+ align:start position:0%
+mentioned earlier that's one of the
+advantages of the nist test we can use
+
+ align:start position:0%
+advantages of the nist test we can use
+ 
+
+ align:start position:0%
+advantages of the nist test we can use
+experimentally determined data in order
+
+ align:start position:0%
+experimentally determined data in order
+ 
+
+ align:start position:0%
+experimentally determined data in order
+to look at the stability of a system
+
+ align:start position:0%
+to look at the stability of a system
+ 
+
+ align:start position:0%
+to look at the stability of a system
+uh we finally have reached a point in
+
+ align:start position:0%
+uh we finally have reached a point in
+ 
+
+ align:start position:0%
+uh we finally have reached a point in
+our construction where we have gone very
+
+ align:start position:0%
+our construction where we have gone very
+ 
+
+ align:start position:0%
+our construction where we have gone very
+very very far from the origin in the S
+
+ align:start position:0%
+very very far from the origin in the S
+ 
+
+ align:start position:0%
+very very far from the origin in the S
+plane in other words out to S equals
+
+ align:start position:0%
+plane in other words out to S equals
+ 
+
+ align:start position:0%
+plane in other words out to S equals
+still zero real part plus Jr where R is
+
+ align:start position:0%
+still zero real part plus Jr where R is
+ 
+
+ align:start position:0%
+still zero real part plus Jr where R is
+a large number we then continue the
+
+ align:start position:0%
+a large number we then continue the
+ 
+
+ align:start position:0%
+a large number we then continue the
+Contour into the region of
+
+ align:start position:0%
+Contour into the region of
+ 
+
+ align:start position:0%
+Contour into the region of
+interest uh along really almost any path
+
+ align:start position:0%
+interest uh along really almost any path
+ 
+
+ align:start position:0%
+interest uh along really almost any path
+but conventionally a large semicircle is
+
+ align:start position:0%
+but conventionally a large semicircle is
+ 
+
+ align:start position:0%
+but conventionally a large semicircle is
+chosen so we let s equal r e j
+
+ align:start position:0%
+chosen so we let s equal r e j
+ 
+
+ align:start position:0%
+chosen so we let s equal r e j
+Theta as Theta goes from plus 90° to -
+
+ align:start position:0%
+Theta as Theta goes from plus 90° to -
+ 
+
+ align:start position:0%
+Theta as Theta goes from plus 90° to -
+90° and then we continue our Contour
+
+ align:start position:0%
+90° and then we continue our Contour
+ 
+
+ align:start position:0%
+90° and then we continue our Contour
+here uh going from s = 0us Jr uh back to
+
+ align:start position:0%
+here uh going from s = 0us Jr uh back to
+ 
+
+ align:start position:0%
+here uh going from s = 0us Jr uh back to
+S = 0 + j 0 minus so this is the Contour
+
+ align:start position:0%
+S = 0 + j 0 minus so this is the Contour
+ 
+
+ align:start position:0%
+S = 0 + j 0 minus so this is the Contour
+that we use to evaluate the AF
+
+ align:start position:0%
+that we use to evaluate the AF
+ 
+
+ align:start position:0%
+that we use to evaluate the AF
+product and when we do
+
+ align:start position:0%
+product and when we do
+ 
+
+ align:start position:0%
+product and when we do
+that we get
+
+ align:start position:0%
+that we get
+ 
+
+ align:start position:0%
+that we get
+some cont tour in the AF plane and I've
+
+ align:start position:0%
+some cont tour in the AF plane and I've
+ 
+
+ align:start position:0%
+some cont tour in the AF plane and I've
+assumed this is the one that we've
+
+ align:start position:0%
+assumed this is the one that we've
+ 
+
+ align:start position:0%
+assumed this is the one that we've
+gotten here's the value of the AF
+
+ align:start position:0%
+gotten here's the value of the AF
+ 
+
+ align:start position:0%
+gotten here's the value of the AF
+product for S equal 0 + j0 plus as we
+
+ align:start position:0%
+product for S equal 0 + j0 plus as we
+ 
+
+ align:start position:0%
+product for S equal 0 + j0 plus as we
+increase Omega let s equal 0 plus J
+
+ align:start position:0%
+increase Omega let s equal 0 plus J
+ 
+
+ align:start position:0%
+increase Omega let s equal 0 plus J
+Omega only an imaginary component the
+
+ align:start position:0%
+Omega only an imaginary component the
+ 
+
+ align:start position:0%
+Omega only an imaginary component the
+real component being zero we assume uh
+
+ align:start position:0%
+real component being zero we assume uh
+ 
+
+ align:start position:0%
+real component being zero we assume uh
+for this particular illustration that
+
+ align:start position:0%
+for this particular illustration that
+ 
+
+ align:start position:0%
+for this particular illustration that
+the curve follows this path in other
+
+ align:start position:0%
+the curve follows this path in other
+ 
+
+ align:start position:0%
+the curve follows this path in other
+words its magnitude gets smaller here we
+
+ align:start position:0%
+words its magnitude gets smaller here we
+ 
+
+ align:start position:0%
+words its magnitude gets smaller here we
+have the magnitude in the gain phase AF
+
+ align:start position:0%
+have the magnitude in the gain phase AF
+ 
+
+ align:start position:0%
+have the magnitude in the gain phase AF
+plane the magnitude gets smaller in this
+
+ align:start position:0%
+plane the magnitude gets smaller in this
+ 
+
+ align:start position:0%
+plane the magnitude gets smaller in this
+direction the angle gets progressively
+
+ align:start position:0%
+direction the angle gets progressively
+ 
+
+ align:start position:0%
+direction the angle gets progressively
+more negative for increasing Omega and
+
+ align:start position:0%
+more negative for increasing Omega and
+ 
+
+ align:start position:0%
+more negative for increasing Omega and
+eventually we get down to some very
+
+ align:start position:0%
+eventually we get down to some very
+ 
+
+ align:start position:0%
+eventually we get down to some very
+small magnitude for S equal plus Jr we
+
+ align:start position:0%
+small magnitude for S equal plus Jr we
+ 
+
+ align:start position:0%
+small magnitude for S equal plus Jr we
+then have to look and we'll we'll do
+
+ align:start position:0%
+then have to look and we'll we'll do
+ 
+
+ align:start position:0%
+then have to look and we'll we'll do
+this in detail with a specific example
+
+ align:start position:0%
+this in detail with a specific example
+ 
+
+ align:start position:0%
+this in detail with a specific example
+but we then have to look at what happens
+
+ align:start position:0%
+but we then have to look at what happens
+ 
+
+ align:start position:0%
+but we then have to look at what happens
+uh as we continue into the right half of
+
+ align:start position:0%
+uh as we continue into the right half of
+ 
+
+ align:start position:0%
+uh as we continue into the right half of
+the S plane what happens to the AF
+
+ align:start position:0%
+the S plane what happens to the AF
+ 
+
+ align:start position:0%
+the S plane what happens to the AF
+product as we continue into the right
+
+ align:start position:0%
+product as we continue into the right
+ 
+
+ align:start position:0%
+product as we continue into the right
+half of the S plane along our large
+
+ align:start position:0%
+half of the S plane along our large
+ 
+
+ align:start position:0%
+half of the S plane along our large
+semicircle let say We'll look at the
+
+ align:start position:0%
+semicircle let say We'll look at the
+ 
+
+ align:start position:0%
+semicircle let say We'll look at the
+specifics of that for a numerical
+
+ align:start position:0%
+specifics of that for a numerical
+ 
+
+ align:start position:0%
+specifics of that for a numerical
+example uh and we find out of course
+
+ align:start position:0%
+example uh and we find out of course
+ 
+
+ align:start position:0%
+example uh and we find out of course
+that since AF uh has to be a a
+
+ align:start position:0%
+that since AF uh has to be a a
+ 
+
+ align:start position:0%
+that since AF uh has to be a a
+physically realizable transfer function
+
+ align:start position:0%
+physically realizable transfer function
+ 
+
+ align:start position:0%
+physically realizable transfer function
+or has to correspond to a physically
+
+ align:start position:0%
+or has to correspond to a physically
+ 
+
+ align:start position:0%
+or has to correspond to a physically
+realizable transfer function why there
+
+ align:start position:0%
+realizable transfer function why there
+ 
+
+ align:start position:0%
+realizable transfer function why there
+has to be symmetry in this AF plot and
+
+ align:start position:0%
+has to be symmetry in this AF plot and
+ 
+
+ align:start position:0%
+has to be symmetry in this AF plot and
+that symmetry is is shown in other words
+
+ align:start position:0%
+that symmetry is is shown in other words
+ 
+
+ align:start position:0%
+that symmetry is is shown in other words
+once we've plotted the first half of the
+
+ align:start position:0%
+once we've plotted the first half of the
+ 
+
+ align:start position:0%
+once we've plotted the first half of the
+curve starting at s equal j0 plus going
+
+ align:start position:0%
+curve starting at s equal j0 plus going
+ 
+
+ align:start position:0%
+curve starting at s equal j0 plus going
+out to S equal J are and then continuing
+
+ align:start position:0%
+out to S equal J are and then continuing
+ 
+
+ align:start position:0%
+out to S equal J are and then continuing
+along a large semicircle back to a point
+
+ align:start position:0%
+along a large semicircle back to a point
+ 
+
+ align:start position:0%
+along a large semicircle back to a point
+that corresponds to the positive real
+
+ align:start position:0%
+that corresponds to the positive real
+ 
+
+ align:start position:0%
+that corresponds to the positive real
+axis at at a radius R from the origin
+
+ align:start position:0%
+axis at at a radius R from the origin
+ 
+
+ align:start position:0%
+axis at at a radius R from the origin
+once we've drawn that much of the curve
+
+ align:start position:0%
+once we've drawn that much of the curve
+ 
+
+ align:start position:0%
+once we've drawn that much of the curve
+the rest of the curve has to be a mirror
+
+ align:start position:0%
+the rest of the curve has to be a mirror
+ 
+
+ align:start position:0%
+the rest of the curve has to be a mirror
+image of this leftand portion uh
+
+ align:start position:0%
+image of this leftand portion uh
+ 
+
+ align:start position:0%
+image of this leftand portion uh
+reflecting the fact that the poles and
+
+ align:start position:0%
+reflecting the fact that the poles and
+ 
+
+ align:start position:0%
+reflecting the fact that the poles and
+zeros associated with the AF product
+
+ align:start position:0%
+zeros associated with the AF product
+ 
+
+ align:start position:0%
+zeros associated with the AF product
+have to occur in complex conjugate
+
+ align:start position:0%
+have to occur in complex conjugate
+ 
+
+ align:start position:0%
+have to occur in complex conjugate
+pairs well here we see the minus one
+
+ align:start position:0%
+pairs well here we see the minus one
+ 
+
+ align:start position:0%
+pairs well here we see the minus one
+points there's two of them and our only
+
+ align:start position:0%
+points there's two of them and our only
+ 
+
+ align:start position:0%
+points there's two of them and our only
+remaining problem is the determination
+
+ align:start position:0%
+remaining problem is the determination
+ 
+
+ align:start position:0%
+remaining problem is the determination
+of insided outsid andness in other
+
+ align:start position:0%
+of insided outsid andness in other
+ 
+
+ align:start position:0%
+of insided outsid andness in other
+words we look at our original
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+construction and we readily identify
+
+ align:start position:0%
+construction and we readily identify
+ 
+
+ align:start position:0%
+construction and we readily identify
+this as the inside of of the Contour
+
+ align:start position:0%
+this as the inside of of the Contour
+ 
+
+ align:start position:0%
+this as the inside of of the Contour
+what appears to us to be the inside of
+
+ align:start position:0%
+what appears to us to be the inside of
+ 
+
+ align:start position:0%
+what appears to us to be the inside of
+the Contour in the S
+
+ align:start position:0%
+the Contour in the S
+ 
+
+ align:start position:0%
+the Contour in the S
+plane and if in fact we can find that
+
+ align:start position:0%
+plane and if in fact we can find that
+ 
+
+ align:start position:0%
+plane and if in fact we can find that
+there is one point in here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+plots in here in the AF plane then we
+
+ align:start position:0%
+plots in here in the AF plane then we
+ 
+
+ align:start position:0%
+plots in here in the AF plane then we
+conclude in this particular figure that
+
+ align:start position:0%
+conclude in this particular figure that
+ 
+
+ align:start position:0%
+conclude in this particular figure that
+there are two values of s with positive
+
+ align:start position:0%
+there are two values of s with positive
+ 
+
+ align:start position:0%
+there are two values of s with positive
+real parts that give us minus ones of
+
+ align:start position:0%
+real parts that give us minus ones of
+ 
+
+ align:start position:0%
+real parts that give us minus ones of
+the AF product that's clear because
+
+ align:start position:0%
+the AF product that's clear because
+ 
+
+ align:start position:0%
+the AF product that's clear because
+here's a minus1 here's another minus one
+
+ align:start position:0%
+here's a minus1 here's another minus one
+ 
+
+ align:start position:0%
+here's a minus1 here's another minus one
+inside our Contour in other words if
+
+ align:start position:0%
+inside our Contour in other words if
+ 
+
+ align:start position:0%
+inside our Contour in other words if
+this was the region that corresponded to
+
+ align:start position:0%
+this was the region that corresponded to
+ 
+
+ align:start position:0%
+this was the region that corresponded to
+the Shaded portion of of the Contour in
+
+ align:start position:0%
+the Shaded portion of of the Contour in
+ 
+
+ align:start position:0%
+the Shaded portion of of the Contour in
+the last figure uh then in fact we found
+
+ align:start position:0%
+the last figure uh then in fact we found
+ 
+
+ align:start position:0%
+the last figure uh then in fact we found
+two minus 1es of AF that correspond to
+
+ align:start position:0%
+two minus 1es of AF that correspond to
+ 
+
+ align:start position:0%
+two minus 1es of AF that correspond to
+values of s inside that shaded region in
+
+ align:start position:0%
+values of s inside that shaded region in
+ 
+
+ align:start position:0%
+values of s inside that shaded region in
+other words values of s with positive
+
+ align:start position:0%
+other words values of s with positive
+ 
+
+ align:start position:0%
+other words values of s with positive
+real parts so our system would then have
+
+ align:start position:0%
+real parts so our system would then have
+ 
+
+ align:start position:0%
+real parts so our system would then have
+two closed loop Poes lying in the right
+
+ align:start position:0%
+two closed loop Poes lying in the right
+ 
+
+ align:start position:0%
+two closed loop Poes lying in the right
+half of the S plane we'd conclude that
+
+ align:start position:0%
+half of the S plane we'd conclude that
+ 
+
+ align:start position:0%
+half of the S plane we'd conclude that
+it was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unstable let's apply this uh to a
+
+ align:start position:0%
+unstable let's apply this uh to a
+ 
+
+ align:start position:0%
+unstable let's apply this uh to a
+specific example where we assume that
+
+ align:start position:0%
+specific example where we assume that
+ 
+
+ align:start position:0%
+specific example where we assume that
+the transfer function is in fact
+
+ align:start position:0%
+the transfer function is in fact
+ 
+
+ align:start position:0%
+the transfer function is in fact
+expressable as a ratio of polinomial in
+
+ align:start position:0%
+expressable as a ratio of polinomial in
+ 
+
+ align:start position:0%
+expressable as a ratio of polinomial in
+s and let's see how that
+
+ align:start position:0%
+s and let's see how that
+ 
+
+ align:start position:0%
+s and let's see how that
+goes let's choose an AF product that's
+
+ align:start position:0%
+goes let's choose an AF product that's
+ 
+
+ align:start position:0%
+goes let's choose an AF product that's
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+3 uh over s + 1 * .1s +1 * 01 s +1 in
+
+ align:start position:0%
+3 uh over s + 1 * .1s +1 * 01 s +1 in
+ 
+
+ align:start position:0%
+3 uh over s + 1 * .1s +1 * 01 s +1 in
+other words we uh have an a FN a DC Loop
+
+ align:start position:0%
+other words we uh have an a FN a DC Loop
+ 
+
+ align:start position:0%
+other words we uh have an a FN a DC Loop
+transmission magnitude of 10 3 then we
+
+ align:start position:0%
+transmission magnitude of 10 3 then we
+ 
+
+ align:start position:0%
+transmission magnitude of 10 3 then we
+have three real axis poles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we show that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+situation uh in fact to Aid our
+
+ align:start position:0%
+situation uh in fact to Aid our
+ 
+
+ align:start position:0%
+situation uh in fact to Aid our
+Construction in the S plane why we show
+
+ align:start position:0%
+Construction in the S plane why we show
+ 
+
+ align:start position:0%
+Construction in the S plane why we show
+the three Loop transmission poles we'd
+
+ align:start position:0%
+the three Loop transmission poles we'd
+ 
+
+ align:start position:0%
+the three Loop transmission poles we'd
+also probably show zeros to help
+
+ align:start position:0%
+also probably show zeros to help
+ 
+
+ align:start position:0%
+also probably show zeros to help
+ourselves if any existed uh here we have
+
+ align:start position:0%
+ourselves if any existed uh here we have
+ 
+
+ align:start position:0%
+ourselves if any existed uh here we have
+a pole at
+
+ align:start position:0%
+a pole at
+ 
+
+ align:start position:0%
+a pole at
+minus1 a pole at Min
+
+ align:start position:0%
+minus1 a pole at Min
+ 
+
+ align:start position:0%
+minus1 a pole at Min
+-1 a third pole at s equal
+
+ align:start position:0%
+-1 a third pole at s equal
+ 
+
+ align:start position:0%
+-1 a third pole at s equal
+uh minus
+
+ align:start position:0%
+uh minus
+ 
+
+ align:start position:0%
+uh minus
+100 and here's the nyis Contour that
+
+ align:start position:0%
+100 and here's the nyis Contour that
+ 
+
+ align:start position:0%
+100 and here's the nyis Contour that
+we're interested in and we can see at
+
+ align:start position:0%
+we're interested in and we can see at
+ 
+
+ align:start position:0%
+we're interested in and we can see at
+least quickly what's happening the the
+
+ align:start position:0%
+least quickly what's happening the the
+ 
+
+ align:start position:0%
+least quickly what's happening the the
+the general nature of the plot in the AF
+
+ align:start position:0%
+the general nature of the plot in the AF
+ 
+
+ align:start position:0%
+the general nature of the plot in the AF
+plane by considering vectors drawn from
+
+ align:start position:0%
+plane by considering vectors drawn from
+ 
+
+ align:start position:0%
+plane by considering vectors drawn from
+these three poles to some point on the
+
+ align:start position:0%
+these three poles to some point on the
+ 
+
+ align:start position:0%
+these three poles to some point on the
+imaginary axis and we notice of course
+
+ align:start position:0%
+imaginary axis and we notice of course
+ 
+
+ align:start position:0%
+imaginary axis and we notice of course
+that this function would have a maximum
+
+ align:start position:0%
+that this function would have a maximum
+ 
+
+ align:start position:0%
+that this function would have a maximum
+magnitude at s equal zero and then since
+
+ align:start position:0%
+magnitude at s equal zero and then since
+ 
+
+ align:start position:0%
+magnitude at s equal zero and then since
+the length of these three vectors to a
+
+ align:start position:0%
+the length of these three vectors to a
+ 
+
+ align:start position:0%
+the length of these three vectors to a
+test point on the imaginary axis
+
+ align:start position:0%
+test point on the imaginary axis
+ 
+
+ align:start position:0%
+test point on the imaginary axis
+increases for increasing values of Omega
+
+ align:start position:0%
+increases for increasing values of Omega
+ 
+
+ align:start position:0%
+increases for increasing values of Omega
+why we' we'd find that the magnitude of
+
+ align:start position:0%
+why we' we'd find that the magnitude of
+ 
+
+ align:start position:0%
+why we' we'd find that the magnitude of
+the AF product would decrease we know
+
+ align:start position:0%
+the AF product would decrease we know
+ 
+
+ align:start position:0%
+the AF product would decrease we know
+it's DC value we know its value for S
+
+ align:start position:0%
+it's DC value we know its value for S
+ 
+
+ align:start position:0%
+it's DC value we know its value for S
+equals z and the magnitude will then
+
+ align:start position:0%
+equals z and the magnitude will then
+ 
+
+ align:start position:0%
+equals z and the magnitude will then
+decrease as Omega
+
+ align:start position:0%
+decrease as Omega
+ 
+
+ align:start position:0%
+decrease as Omega
+increases furthermore as we go to very
+
+ align:start position:0%
+increases furthermore as we go to very
+ 
+
+ align:start position:0%
+increases furthermore as we go to very
+large values of Omega way out up here in
+
+ align:start position:0%
+large values of Omega way out up here in
+ 
+
+ align:start position:0%
+large values of Omega way out up here in
+the top of the plane why the angle
+
+ align:start position:0%
+the top of the plane why the angle
+ 
+
+ align:start position:0%
+the top of the plane why the angle
+approaches minus 270° we eventually get-
+
+ align:start position:0%
+approaches minus 270° we eventually get-
+ 
+
+ align:start position:0%
+approaches minus 270° we eventually get-
+90 degrees of course from each of the
+
+ align:start position:0%
+90 degrees of course from each of the
+ 
+
+ align:start position:0%
+90 degrees of course from each of the
+three poles so the angle of the transfer
+
+ align:start position:0%
+three poles so the angle of the transfer
+ 
+
+ align:start position:0%
+three poles so the angle of the transfer
+function eventually approaches minus-
+
+ align:start position:0%
+function eventually approaches minus-
+ 
+
+ align:start position:0%
+function eventually approaches minus-
+270 degrees 3 times Theus
+
+ align:start position:0%
+270 degrees 3 times Theus
+ 
+
+ align:start position:0%
+270 degrees 3 times Theus
+90 once we're out to a very large radius
+
+ align:start position:0%
+90 once we're out to a very large radius
+ 
+
+ align:start position:0%
+90 once we're out to a very large radius
+and continue around why our magnitude
+
+ align:start position:0%
+and continue around why our magnitude
+ 
+
+ align:start position:0%
+and continue around why our magnitude
+stays fixed if R is very large compared
+
+ align:start position:0%
+stays fixed if R is very large compared
+ 
+
+ align:start position:0%
+stays fixed if R is very large compared
+to minus 100 then as we close the
+
+ align:start position:0%
+to minus 100 then as we close the
+ 
+
+ align:start position:0%
+to minus 100 then as we close the
+Contour why the lengths of these three
+
+ align:start position:0%
+Contour why the lengths of these three
+ 
+
+ align:start position:0%
+Contour why the lengths of these three
+vectors stay
+
+ align:start position:0%
+vectors stay
+ 
+
+ align:start position:0%
+vectors stay
+fixed uh as we go along a radius of
+
+ align:start position:0%
+fixed uh as we go along a radius of
+ 
+
+ align:start position:0%
+fixed uh as we go along a radius of
+capital r and we notice that the angle
+
+ align:start position:0%
+capital r and we notice that the angle
+ 
+
+ align:start position:0%
+capital r and we notice that the angle
+associated with the AF product must
+
+ align:start position:0%
+associated with the AF product must
+ 
+
+ align:start position:0%
+associated with the AF product must
+Return To Zero when our we're at this
+
+ align:start position:0%
+Return To Zero when our we're at this
+ 
+
+ align:start position:0%
+Return To Zero when our we're at this
+point on the Contour because again if we
+
+ align:start position:0%
+point on the Contour because again if we
+ 
+
+ align:start position:0%
+point on the Contour because again if we
+drew vectors from the three poles in
+
+ align:start position:0%
+drew vectors from the three poles in
+ 
+
+ align:start position:0%
+drew vectors from the three poles in
+question the angle associated with each
+
+ align:start position:0%
+question the angle associated with each
+ 
+
+ align:start position:0%
+question the angle associated with each
+of those vectors would be 0 deges they'd
+
+ align:start position:0%
+of those vectors would be 0 deges they'd
+ 
+
+ align:start position:0%
+of those vectors would be 0 deges they'd
+lie along the positive real axis and so
+
+ align:start position:0%
+lie along the positive real axis and so
+ 
+
+ align:start position:0%
+lie along the positive real axis and so
+that's sort of a an argument allows us
+
+ align:start position:0%
+that's sort of a an argument allows us
+ 
+
+ align:start position:0%
+that's sort of a an argument allows us
+to construct the corresponding plot in
+
+ align:start position:0%
+to construct the corresponding plot in
+ 
+
+ align:start position:0%
+to construct the corresponding plot in
+the AF plane and this is what happens
+
+ align:start position:0%
+the AF plane and this is what happens
+ 
+
+ align:start position:0%
+the AF plane and this is what happens
+when we do that here we start out at a
+
+ align:start position:0%
+when we do that here we start out at a
+ 
+
+ align:start position:0%
+when we do that here we start out at a
+value of a thand a magnitude of a thand
+
+ align:start position:0%
+value of a thand a magnitude of a thand
+ 
+
+ align:start position:0%
+value of a thand a magnitude of a thand
+1 10 100 a th000 a magnitude of a thand
+
+ align:start position:0%
+1 10 100 a th000 a magnitude of a thand
+ 
+
+ align:start position:0%
+1 10 100 a th000 a magnitude of a thand
+for S equal j0
+
+ align:start position:0%
+for S equal j0
+ 
+
+ align:start position:0%
+for S equal j0
+plus the as Omega increases the Ang Ang
+
+ align:start position:0%
+plus the as Omega increases the Ang Ang
+ 
+
+ align:start position:0%
+plus the as Omega increases the Ang Ang
+Le becomes negative ASM totically
+
+ align:start position:0%
+Le becomes negative ASM totically
+ 
+
+ align:start position:0%
+Le becomes negative ASM totically
+approaching -
+
+ align:start position:0%
+approaching -
+ 
+
+ align:start position:0%
+approaching -
+270° for S equal plus
+
+ align:start position:0%
+270° for S equal plus
+ 
+
+ align:start position:0%
+270° for S equal plus
+Jr uh the magnitude then stays fixed as
+
+ align:start position:0%
+Jr uh the magnitude then stays fixed as
+ 
+
+ align:start position:0%
+Jr uh the magnitude then stays fixed as
+we circle into the right half of the S
+
+ align:start position:0%
+we circle into the right half of the S
+ 
+
+ align:start position:0%
+we circle into the right half of the S
+plane for our evaluation and the plot is
+
+ align:start position:0%
+plane for our evaluation and the plot is
+ 
+
+ align:start position:0%
+plane for our evaluation and the plot is
+of course symmetric if we are careful in
+
+ align:start position:0%
+of course symmetric if we are careful in
+ 
+
+ align:start position:0%
+of course symmetric if we are careful in
+this construction uh we find out that
+
+ align:start position:0%
+this construction uh we find out that
+ 
+
+ align:start position:0%
+this construction uh we find out that
+the minus1
+
+ align:start position:0%
+the minus1
+ 
+
+ align:start position:0%
+the minus1
+points lie in the Shaded region for an a
+
+ align:start position:0%
+points lie in the Shaded region for an a
+ 
+
+ align:start position:0%
+points lie in the Shaded region for an a
+fnot of 1,000 and so our only final task
+
+ align:start position:0%
+fnot of 1,000 and so our only final task
+ 
+
+ align:start position:0%
+fnot of 1,000 and so our only final task
+is to determine whether this shaded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+region corresponds to this shaded region
+
+ align:start position:0%
+region corresponds to this shaded region
+ 
+
+ align:start position:0%
+region corresponds to this shaded region
+and the way to do that or at least one
+
+ align:start position:0%
+and the way to do that or at least one
+ 
+
+ align:start position:0%
+and the way to do that or at least one
+way to do it is to take a test
+
+ align:start position:0%
+way to do it is to take a test
+ 
+
+ align:start position:0%
+way to do it is to take a test
+detour uh incidentally we could do this
+
+ align:start position:0%
+detour uh incidentally we could do this
+ 
+
+ align:start position:0%
+detour uh incidentally we could do this
+by depending on the property that I
+
+ align:start position:0%
+by depending on the property that I
+ 
+
+ align:start position:0%
+by depending on the property that I
+mentioned earlier that when we take a
+
+ align:start position:0%
+mentioned earlier that when we take a
+ 
+
+ align:start position:0%
+mentioned earlier that when we take a
+right-and turn in the S plane we
+
+ align:start position:0%
+right-and turn in the S plane we
+ 
+
+ align:start position:0%
+right-and turn in the S plane we
+actually take a left left hand turn in
+
+ align:start position:0%
+actually take a left left hand turn in
+ 
+
+ align:start position:0%
+actually take a left left hand turn in
+the AF plane so here notice we've taken
+
+ align:start position:0%
+the AF plane so here notice we've taken
+ 
+
+ align:start position:0%
+the AF plane so here notice we've taken
+a right hand turn at this point in the S
+
+ align:start position:0%
+a right hand turn at this point in the S
+ 
+
+ align:start position:0%
+a right hand turn at this point in the S
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+and we find that we take a
+
+ align:start position:0%
+and we find that we take a
+ 
+
+ align:start position:0%
+and we find that we take a
+corresponding leftand turn in the AF
+
+ align:start position:0%
+corresponding leftand turn in the AF
+ 
+
+ align:start position:0%
+corresponding leftand turn in the AF
+plane like so and that in fact tells us
+
+ align:start position:0%
+plane like so and that in fact tells us
+ 
+
+ align:start position:0%
+plane like so and that in fact tells us
+that the Shaded regions correspond but
+
+ align:start position:0%
+that the Shaded regions correspond but
+ 
+
+ align:start position:0%
+that the Shaded regions correspond but
+another way to see that and one that I
+
+ align:start position:0%
+another way to see that and one that I
+ 
+
+ align:start position:0%
+another way to see that and one that I
+find physically more appealing is to
+
+ align:start position:0%
+find physically more appealing is to
+ 
+
+ align:start position:0%
+find physically more appealing is to
+take a little test detour let's look at
+
+ align:start position:0%
+take a little test detour let's look at
+ 
+
+ align:start position:0%
+take a little test detour let's look at
+a specific point inside this Contour in
+
+ align:start position:0%
+a specific point inside this Contour in
+ 
+
+ align:start position:0%
+a specific point inside this Contour in
+the right half of the S plane we can do
+
+ align:start position:0%
+the right half of the S plane we can do
+ 
+
+ align:start position:0%
+the right half of the S plane we can do
+that here we can assume we're at this
+
+ align:start position:0%
+that here we can assume we're at this
+ 
+
+ align:start position:0%
+that here we can assume we're at this
+point and then move in this direction a
+
+ align:start position:0%
+point and then move in this direction a
+ 
+
+ align:start position:0%
+point and then move in this direction a
+small amount when we do that the
+
+ align:start position:0%
+small amount when we do that the
+ 
+
+ align:start position:0%
+small amount when we do that the
+magnitude must drop since the vectors
+
+ align:start position:0%
+magnitude must drop since the vectors
+ 
+
+ align:start position:0%
+magnitude must drop since the vectors
+from the poles all increase in length so
+
+ align:start position:0%
+from the poles all increase in length so
+ 
+
+ align:start position:0%
+from the poles all increase in length so
+the magnitude of our function must drop
+
+ align:start position:0%
+the magnitude of our function must drop
+ 
+
+ align:start position:0%
+the magnitude of our function must drop
+the angle remains 0 de if we walk along
+
+ align:start position:0%
+the angle remains 0 de if we walk along
+ 
+
+ align:start position:0%
+the angle remains 0 de if we walk along
+the positive real axis so if we
+
+ align:start position:0%
+the positive real axis so if we
+ 
+
+ align:start position:0%
+the positive real axis so if we
+evaluated AF at a point in here its
+
+ align:start position:0%
+evaluated AF at a point in here its
+ 
+
+ align:start position:0%
+evaluated AF at a point in here its
+angle must be 0 degre but its magnitude
+
+ align:start position:0%
+angle must be 0 degre but its magnitude
+ 
+
+ align:start position:0%
+angle must be 0 degre but its magnitude
+must be smaller than the magnitude that
+
+ align:start position:0%
+must be smaller than the magnitude that
+ 
+
+ align:start position:0%
+must be smaller than the magnitude that
+corresponds to our evaluation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and so we conclude that as we move
+
+ align:start position:0%
+here and so we conclude that as we move
+ 
+
+ align:start position:0%
+here and so we conclude that as we move
+along the test D tour shown in the
+
+ align:start position:0%
+along the test D tour shown in the
+ 
+
+ align:start position:0%
+along the test D tour shown in the
+previous figure we move in this
+
+ align:start position:0%
+previous figure we move in this
+ 
+
+ align:start position:0%
+previous figure we move in this
+direction consequently the Shaded
+
+ align:start position:0%
+direction consequently the Shaded
+ 
+
+ align:start position:0%
+direction consequently the Shaded
+regions in the two figures
+
+ align:start position:0%
+regions in the two figures
+ 
+
+ align:start position:0%
+regions in the two figures
+correspond and that tells us in this
+
+ align:start position:0%
+correspond and that tells us in this
+ 
+
+ align:start position:0%
+correspond and that tells us in this
+particular example that there are two
+
+ align:start position:0%
+particular example that there are two
+ 
+
+ align:start position:0%
+particular example that there are two
+values of s with positive real parts
+
+ align:start position:0%
+values of s with positive real parts
+ 
+
+ align:start position:0%
+values of s with positive real parts
+that will lead to minus ones of the AF
+
+ align:start position:0%
+that will lead to minus ones of the AF
+ 
+
+ align:start position:0%
+that will lead to minus ones of the AF
+product here's a minus one here's a
+
+ align:start position:0%
+product here's a minus one here's a
+ 
+
+ align:start position:0%
+product here's a minus one here's a
+minus one there must be two values of s
+
+ align:start position:0%
+minus one there must be two values of s
+ 
+
+ align:start position:0%
+minus one there must be two values of s
+in the right half plane that give rise
+
+ align:start position:0%
+in the right half plane that give rise
+ 
+
+ align:start position:0%
+in the right half plane that give rise
+to those values of the AF product
+
+ align:start position:0%
+to those values of the AF product
+ 
+
+ align:start position:0%
+to those values of the AF product
+consequently we conclude that this
+
+ align:start position:0%
+consequently we conclude that this
+ 
+
+ align:start position:0%
+consequently we conclude that this
+particular system had two closed loop
+
+ align:start position:0%
+particular system had two closed loop
+ 
+
+ align:start position:0%
+particular system had two closed loop
+poles in the right half of the S plane
+
+ align:start position:0%
+poles in the right half of the S plane
+ 
+
+ align:start position:0%
+poles in the right half of the S plane
+it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unstable we of course suspected that
+
+ align:start position:0%
+unstable we of course suspected that
+ 
+
+ align:start position:0%
+unstable we of course suspected that
+already we can we can get this this same
+
+ align:start position:0%
+already we can we can get this this same
+ 
+
+ align:start position:0%
+already we can we can get this this same
+development by
+
+ align:start position:0%
+development by
+ 
+
+ align:start position:0%
+development by
+another technique that we know we can
+
+ align:start position:0%
+another technique that we know we can
+ 
+
+ align:start position:0%
+another technique that we know we can
+look at this from a root Locus point of
+
+ align:start position:0%
+look at this from a root Locus point of
+ 
+
+ align:start position:0%
+look at this from a root Locus point of
+view and here we draw a root Locus
+
+ align:start position:0%
+view and here we draw a root Locus
+ 
+
+ align:start position:0%
+view and here we draw a root Locus
+diagram for the same system uh we have a
+
+ align:start position:0%
+diagram for the same system uh we have a
+ 
+
+ align:start position:0%
+diagram for the same system uh we have a
+pole at minus1 a pole at minus10 a pole
+
+ align:start position:0%
+pole at minus1 a pole at minus10 a pole
+ 
+
+ align:start position:0%
+pole at minus1 a pole at minus10 a pole
+at minus 100 and we find out that if we
+
+ align:start position:0%
+at minus 100 and we find out that if we
+ 
+
+ align:start position:0%
+at minus 100 and we find out that if we
+do the root Locus construction this is a
+
+ align:start position:0%
+do the root Locus construction this is a
+ 
+
+ align:start position:0%
+do the root Locus construction this is a
+familiar pattern these two branches come
+
+ align:start position:0%
+familiar pattern these two branches come
+ 
+
+ align:start position:0%
+familiar pattern these two branches come
+together meet at about the arithmetic
+
+ align:start position:0%
+together meet at about the arithmetic
+ 
+
+ align:start position:0%
+together meet at about the arithmetic
+mean somewhere around minus 52 and then
+
+ align:start position:0%
+mean somewhere around minus 52 and then
+ 
+
+ align:start position:0%
+mean somewhere around minus 52 and then
+Branch off eventually reach asmp tootes
+
+ align:start position:0%
+Branch off eventually reach asmp tootes
+ 
+
+ align:start position:0%
+Branch off eventually reach asmp tootes
+that make angles of plus and minus
+
+ align:start position:0%
+that make angles of plus and minus
+ 
+
+ align:start position:0%
+that make angles of plus and minus
+60° and a third branch goes off into the
+
+ align:start position:0%
+60° and a third branch goes off into the
+ 
+
+ align:start position:0%
+60° and a third branch goes off into the
+left half plane and what that tells us
+
+ align:start position:0%
+left half plane and what that tells us
+ 
+
+ align:start position:0%
+left half plane and what that tells us
+is that for sufficiently large values of
+
+ align:start position:0%
+is that for sufficiently large values of
+ 
+
+ align:start position:0%
+is that for sufficiently large values of
+a fnot the system has two closed loop
+
+ align:start position:0%
+a fnot the system has two closed loop
+ 
+
+ align:start position:0%
+a fnot the system has two closed loop
+Poes with positive real parts here's one
+
+ align:start position:0%
+Poes with positive real parts here's one
+ 
+
+ align:start position:0%
+Poes with positive real parts here's one
+and here's one once the a fnot product
+
+ align:start position:0%
+and here's one once the a fnot product
+ 
+
+ align:start position:0%
+and here's one once the a fnot product
+gets large
+
+ align:start position:0%
+gets large
+ 
+
+ align:start position:0%
+gets large
+enough we see exactly that behavior in
+
+ align:start position:0%
+enough we see exactly that behavior in
+ 
+
+ align:start position:0%
+enough we see exactly that behavior in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+diagram this apparently is an a fnot
+
+ align:start position:0%
+diagram this apparently is an a fnot
+ 
+
+ align:start position:0%
+diagram this apparently is an a fnot
+product that's large enough for this
+
+ align:start position:0%
+product that's large enough for this
+ 
+
+ align:start position:0%
+product that's large enough for this
+particular location of the three real
+
+ align:start position:0%
+particular location of the three real
+ 
+
+ align:start position:0%
+particular location of the three real
+axis poles or the particular relative
+
+ align:start position:0%
+axis poles or the particular relative
+ 
+
+ align:start position:0%
+axis poles or the particular relative
+location we find out that an a fnot
+
+ align:start position:0%
+location we find out that an a fnot
+ 
+
+ align:start position:0%
+location we find out that an a fnot
+product of a thousand is enough we can
+
+ align:start position:0%
+product of a thousand is enough we can
+ 
+
+ align:start position:0%
+product of a thousand is enough we can
+convince ourselves of that for example
+
+ align:start position:0%
+convince ourselves of that for example
+ 
+
+ align:start position:0%
+convince ourselves of that for example
+via a ralth kind of
+
+ align:start position:0%
+via a ralth kind of
+ 
+
+ align:start position:0%
+via a ralth kind of
+development but uh that's shown in the
+
+ align:start position:0%
+development but uh that's shown in the
+ 
+
+ align:start position:0%
+development but uh that's shown in the
+Nyquist construction that we have two
+
+ align:start position:0%
+Nyquist construction that we have two
+ 
+
+ align:start position:0%
+Nyquist construction that we have two
+minus ones of the AF product uh that
+
+ align:start position:0%
+minus ones of the AF product uh that
+ 
+
+ align:start position:0%
+minus ones of the AF product uh that
+result four values of s with positive
+
+ align:start position:0%
+result four values of s with positive
+ 
+
+ align:start position:0%
+result four values of s with positive
+real Parts if we lowered the a f product
+
+ align:start position:0%
+real Parts if we lowered the a f product
+ 
+
+ align:start position:0%
+real Parts if we lowered the a f product
+that would correspond to Simply sliding
+
+ align:start position:0%
+that would correspond to Simply sliding
+ 
+
+ align:start position:0%
+that would correspond to Simply sliding
+the Shaded curve downward we lowered it
+
+ align:start position:0%
+the Shaded curve downward we lowered it
+ 
+
+ align:start position:0%
+the Shaded curve downward we lowered it
+enough we'd finally get it down when we
+
+ align:start position:0%
+enough we'd finally get it down when we
+ 
+
+ align:start position:0%
+enough we'd finally get it down when we
+lowered it about this much we'd finally
+
+ align:start position:0%
+lowered it about this much we'd finally
+ 
+
+ align:start position:0%
+lowered it about this much we'd finally
+get the curve down to the point where
+
+ align:start position:0%
+get the curve down to the point where
+ 
+
+ align:start position:0%
+get the curve down to the point where
+the minus ones were outside the Contour
+
+ align:start position:0%
+the minus ones were outside the Contour
+ 
+
+ align:start position:0%
+the minus ones were outside the Contour
+then the system would be stable and that
+
+ align:start position:0%
+then the system would be stable and that
+ 
+
+ align:start position:0%
+then the system would be stable and that
+corresponds to the
+
+ align:start position:0%
+corresponds to the
+ 
+
+ align:start position:0%
+corresponds to the
+condition where we've lowered we started
+
+ align:start position:0%
+condition where we've lowered we started
+ 
+
+ align:start position:0%
+condition where we've lowered we started
+a high Loop transmission magnitude a
+
+ align:start position:0%
+a high Loop transmission magnitude a
+ 
+
+ align:start position:0%
+a high Loop transmission magnitude a
+high aot fnot product we have two poles
+
+ align:start position:0%
+high aot fnot product we have two poles
+ 
+
+ align:start position:0%
+high aot fnot product we have two poles
+in the right half of the S plane we
+
+ align:start position:0%
+in the right half of the S plane we
+ 
+
+ align:start position:0%
+in the right half of the S plane we
+lower a FN and eventually the system
+
+ align:start position:0%
+lower a FN and eventually the system
+ 
+
+ align:start position:0%
+lower a FN and eventually the system
+becomes stable so we see exactly that
+
+ align:start position:0%
+becomes stable so we see exactly that
+ 
+
+ align:start position:0%
+becomes stable so we see exactly that
+same behavior as we must in the root
+
+ align:start position:0%
+same behavior as we must in the root
+ 
+
+ align:start position:0%
+same behavior as we must in the root
+Locus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+presentation well again as in the case
+
+ align:start position:0%
+presentation well again as in the case
+ 
+
+ align:start position:0%
+presentation well again as in the case
+of of the root Locus
+
+ align:start position:0%
+of of the root Locus
+ 
+
+ align:start position:0%
+of of the root Locus
+development we're interested in addition
+
+ align:start position:0%
+development we're interested in addition
+ 
+
+ align:start position:0%
+development we're interested in addition
+to a binary answer to the stability
+
+ align:start position:0%
+to a binary answer to the stability
+ 
+
+ align:start position:0%
+to a binary answer to the stability
+problem sort of a relative measure of
+
+ align:start position:0%
+problem sort of a relative measure of
+ 
+
+ align:start position:0%
+problem sort of a relative measure of
+stability usually we're able to fairly
+
+ align:start position:0%
+stability usually we're able to fairly
+ 
+
+ align:start position:0%
+stability usually we're able to fairly
+easily convince ourselves that the
+
+ align:start position:0%
+easily convince ourselves that the
+ 
+
+ align:start position:0%
+easily convince ourselves that the
+system is stable or fairly easily get
+
+ align:start position:0%
+system is stable or fairly easily get
+ 
+
+ align:start position:0%
+system is stable or fairly easily get
+the system to be stable in an absolute
+
+ align:start position:0%
+the system to be stable in an absolute
+ 
+
+ align:start position:0%
+the system to be stable in an absolute
+sense but the question is sort of how
+
+ align:start position:0%
+sense but the question is sort of how
+ 
+
+ align:start position:0%
+sense but the question is sort of how
+close to instability is it or some of
+
+ align:start position:0%
+close to instability is it or some of
+ 
+
+ align:start position:0%
+close to instability is it or some of
+the what are some of the useful measures
+
+ align:start position:0%
+the what are some of the useful measures
+ 
+
+ align:start position:0%
+the what are some of the useful measures
+of relative stability uh what are the
+
+ align:start position:0%
+of relative stability uh what are the
+ 
+
+ align:start position:0%
+of relative stability uh what are the
+values of some of the useful measures of
+
+ align:start position:0%
+values of some of the useful measures of
+ 
+
+ align:start position:0%
+values of some of the useful measures of
+relative stability really how close to
+
+ align:start position:0%
+relative stability really how close to
+ 
+
+ align:start position:0%
+relative stability really how close to
+instability are we and so forth and we
+
+ align:start position:0%
+instability are we and so forth and we
+ 
+
+ align:start position:0%
+instability are we and so forth and we
+we saw we could get that very easily in
+
+ align:start position:0%
+we saw we could get that very easily in
+ 
+
+ align:start position:0%
+we saw we could get that very easily in
+a root Locust construction but since we
+
+ align:start position:0%
+a root Locust construction but since we
+ 
+
+ align:start position:0%
+a root Locust construction but since we
+had the location of all of the closed
+
+ align:start position:0%
+had the location of all of the closed
+ 
+
+ align:start position:0%
+had the location of all of the closed
+loopholes of the system and we could
+
+ align:start position:0%
+loopholes of the system and we could
+ 
+
+ align:start position:0%
+loopholes of the system and we could
+tell for example the damping ratio
+
+ align:start position:0%
+tell for example the damping ratio
+ 
+
+ align:start position:0%
+tell for example the damping ratio
+associated with
+
+ align:start position:0%
+associated with
+ 
+
+ align:start position:0%
+associated with
+the dominant pole pair and and any other
+
+ align:start position:0%
+the dominant pole pair and and any other
+ 
+
+ align:start position:0%
+the dominant pole pair and and any other
+measure of relative stability that we'd
+
+ align:start position:0%
+measure of relative stability that we'd
+ 
+
+ align:start position:0%
+measure of relative stability that we'd
+like to have we have the information
+
+ align:start position:0%
+like to have we have the information
+ 
+
+ align:start position:0%
+like to have we have the information
+available what we do in this sort of a
+
+ align:start position:0%
+available what we do in this sort of a
+ 
+
+ align:start position:0%
+available what we do in this sort of a
+development in other words when we
+
+ align:start position:0%
+development in other words when we
+ 
+
+ align:start position:0%
+development in other words when we
+evaluate stability based on frequency
+
+ align:start position:0%
+evaluate stability based on frequency
+ 
+
+ align:start position:0%
+evaluate stability based on frequency
+response uh is to really look at
+
+ align:start position:0%
+response uh is to really look at
+ 
+
+ align:start position:0%
+response uh is to really look at
+features of the closed loop frequency
+
+ align:start position:0%
+features of the closed loop frequency
+ 
+
+ align:start position:0%
+features of the closed loop frequency
+response of the system and in particular
+
+ align:start position:0%
+response of the system and in particular
+ 
+
+ align:start position:0%
+response of the system and in particular
+look at things for example like the
+
+ align:start position:0%
+look at things for example like the
+ 
+
+ align:start position:0%
+look at things for example like the
+amount of peaking that we get when we
+
+ align:start position:0%
+amount of peaking that we get when we
+ 
+
+ align:start position:0%
+amount of peaking that we get when we
+look at the closed loop response of the
+
+ align:start position:0%
+look at the closed loop response of the
+ 
+
+ align:start position:0%
+look at the closed loop response of the
+system we excite the system
+
+ align:start position:0%
+system we excite the system
+ 
+
+ align:start position:0%
+system we excite the system
+look at sidal steady state response and
+
+ align:start position:0%
+look at sidal steady state response and
+ 
+
+ align:start position:0%
+look at sidal steady state response and
+we see for example the amount of
+
+ align:start position:0%
+we see for example the amount of
+ 
+
+ align:start position:0%
+we see for example the amount of
+resonant Peak we get we feel that that a
+
+ align:start position:0%
+resonant Peak we get we feel that that a
+ 
+
+ align:start position:0%
+resonant Peak we get we feel that that a
+larger resonant Peak indicates a
+
+ align:start position:0%
+larger resonant Peak indicates a
+ 
+
+ align:start position:0%
+larger resonant Peak indicates a
+relatively less stable
+
+ align:start position:0%
+relatively less stable
+ 
+
+ align:start position:0%
+relatively less stable
+system the evaluation is most easily
+
+ align:start position:0%
+system the evaluation is most easily
+ 
+
+ align:start position:0%
+system the evaluation is most easily
+made if we consider a system where the
+
+ align:start position:0%
+made if we consider a system where the
+ 
+
+ align:start position:0%
+made if we consider a system where the
+Dynamics are all in the forward path so
+
+ align:start position:0%
+Dynamics are all in the forward path so
+ 
+
+ align:start position:0%
+Dynamics are all in the forward path so
+I'll I'll assume a system uh input
+
+ align:start position:0%
+I'll I'll assume a system uh input
+ 
+
+ align:start position:0%
+I'll I'll assume a system uh input
+output and we assume that all of the
+
+ align:start position:0%
+output and we assume that all of the
+ 
+
+ align:start position:0%
+output and we assume that all of the
+Dynamics of the system are concentrated
+
+ align:start position:0%
+Dynamics of the system are concentrated
+ 
+
+ align:start position:0%
+Dynamics of the system are concentrated
+in the forward path and furthermore
+
+ align:start position:0%
+in the forward path and furthermore
+ 
+
+ align:start position:0%
+in the forward path and furthermore
+again just to normalize things we'll
+
+ align:start position:0%
+again just to normalize things we'll
+ 
+
+ align:start position:0%
+again just to normalize things we'll
+assume that we have Unity feedback and
+
+ align:start position:0%
+assume that we have Unity feedback and
+ 
+
+ align:start position:0%
+assume that we have Unity feedback and
+then what we're going to do is go ahead
+
+ align:start position:0%
+then what we're going to do is go ahead
+ 
+
+ align:start position:0%
+then what we're going to do is go ahead
+and look for basically resonances or
+
+ align:start position:0%
+and look for basically resonances or
+ 
+
+ align:start position:0%
+and look for basically resonances or
+peaking in the sidal steady state
+
+ align:start position:0%
+peaking in the sidal steady state
+ 
+
+ align:start position:0%
+peaking in the sidal steady state
+response that links V out to
+
+ align:start position:0%
+response that links V out to
+ 
+
+ align:start position:0%
+response that links V out to
+VI let me point out that this really
+
+ align:start position:0%
+VI let me point out that this really
+ 
+
+ align:start position:0%
+VI let me point out that this really
+isn't any any restriction suppose we had
+
+ align:start position:0%
+isn't any any restriction suppose we had
+ 
+
+ align:start position:0%
+isn't any any restriction suppose we had
+a general system where we were
+
+ align:start position:0%
+a general system where we were
+ 
+
+ align:start position:0%
+a general system where we were
+interested in the frequency response
+
+ align:start position:0%
+interested in the frequency response
+ 
+
+ align:start position:0%
+interested in the frequency response
+we'd like to determine uh V out over VI
+
+ align:start position:0%
+we'd like to determine uh V out over VI
+ 
+
+ align:start position:0%
+we'd like to determine uh V out over VI
+for some value of Omega uh and we had in
+
+ align:start position:0%
+for some value of Omega uh and we had in
+ 
+
+ align:start position:0%
+for some value of Omega uh and we had in
+general the Dynamics distributed between
+
+ align:start position:0%
+general the Dynamics distributed between
+ 
+
+ align:start position:0%
+general the Dynamics distributed between
+the forward path and the feedback path
+
+ align:start position:0%
+the forward path and the feedback path
+ 
+
+ align:start position:0%
+the forward path and the feedback path
+well we could manipulate the block
+
+ align:start position:0%
+well we could manipulate the block
+ 
+
+ align:start position:0%
+well we could manipulate the block
+diagram as follows this block diagram is
+
+ align:start position:0%
+diagram as follows this block diagram is
+ 
+
+ align:start position:0%
+diagram as follows this block diagram is
+identically equal to the lower one where
+
+ align:start position:0%
+identically equal to the lower one where
+ 
+
+ align:start position:0%
+identically equal to the lower one where
+we have the AF product in the forward
+
+ align:start position:0%
+we have the AF product in the forward
+ 
+
+ align:start position:0%
+we have the AF product in the forward
+path Unity feedback and then follow that
+
+ align:start position:0%
+path Unity feedback and then follow that
+ 
+
+ align:start position:0%
+path Unity feedback and then follow that
+by a block that's 1 over F of J Omega
+
+ align:start position:0%
+by a block that's 1 over F of J Omega
+ 
+
+ align:start position:0%
+by a block that's 1 over F of J Omega
+and we can really evaluate the relative
+
+ align:start position:0%
+and we can really evaluate the relative
+ 
+
+ align:start position:0%
+and we can really evaluate the relative
+stability of our system by considering
+
+ align:start position:0%
+stability of our system by considering
+ 
+
+ align:start position:0%
+stability of our system by considering
+just this part of the system so we
+
+ align:start position:0%
+just this part of the system so we
+ 
+
+ align:start position:0%
+just this part of the system so we
+really don't lose any generality when
+
+ align:start position:0%
+really don't lose any generality when
+ 
+
+ align:start position:0%
+really don't lose any generality when
+our interest is the evaluation of
+
+ align:start position:0%
+our interest is the evaluation of
+ 
+
+ align:start position:0%
+our interest is the evaluation of
+stability we found out in a root Locus
+
+ align:start position:0%
+stability we found out in a root Locus
+ 
+
+ align:start position:0%
+stability we found out in a root Locus
+sense that depends only on the AF
+
+ align:start position:0%
+sense that depends only on the AF
+ 
+
+ align:start position:0%
+sense that depends only on the AF
+product again when we look when we uh
+
+ align:start position:0%
+product again when we look when we uh
+ 
+
+ align:start position:0%
+product again when we look when we uh
+base our stability analysis on frequency
+
+ align:start position:0%
+base our stability analysis on frequency
+ 
+
+ align:start position:0%
+base our stability analysis on frequency
+measurements once again we're only
+
+ align:start position:0%
+measurements once again we're only
+ 
+
+ align:start position:0%
+measurements once again we're only
+really concerned in the about the AF
+
+ align:start position:0%
+really concerned in the about the AF
+ 
+
+ align:start position:0%
+really concerned in the about the AF
+product and we can determine our
+
+ align:start position:0%
+product and we can determine our
+ 
+
+ align:start position:0%
+product and we can determine our
+stability information from this portion
+
+ align:start position:0%
+stability information from this portion
+ 
+
+ align:start position:0%
+stability information from this portion
+of the block diagram corresponding
+
+ align:start position:0%
+of the block diagram corresponding
+ 
+
+ align:start position:0%
+of the block diagram corresponding
+correspondingly this one so what we'd
+
+ align:start position:0%
+correspondingly this one so what we'd
+ 
+
+ align:start position:0%
+correspondingly this one so what we'd
+like to do is look at the behavior of go
+
+ align:start position:0%
+like to do is look at the behavior of go
+ 
+
+ align:start position:0%
+like to do is look at the behavior of go
+over 1 + G where G is a function of J
+
+ align:start position:0%
+over 1 + G where G is a function of J
+ 
+
+ align:start position:0%
+over 1 + G where G is a function of J
+Omega we consider the closed loop gain a
+
+ align:start position:0%
+Omega we consider the closed loop gain a
+ 
+
+ align:start position:0%
+Omega we consider the closed loop gain a
+of J Omega being equal to G of J Omega
+
+ align:start position:0%
+of J Omega being equal to G of J Omega
+ 
+
+ align:start position:0%
+of J Omega being equal to G of J Omega
+over 1+ G of J Omega and we can very
+
+ align:start position:0%
+over 1+ G of J Omega and we can very
+ 
+
+ align:start position:0%
+over 1+ G of J Omega and we can very
+easily evaluate that for limiting cases
+
+ align:start position:0%
+easily evaluate that for limiting cases
+ 
+
+ align:start position:0%
+easily evaluate that for limiting cases
+because we recognize that this quantity
+
+ align:start position:0%
+because we recognize that this quantity
+ 
+
+ align:start position:0%
+because we recognize that this quantity
+is just about uh equal to one when the G
+
+ align:start position:0%
+is just about uh equal to one when the G
+ 
+
+ align:start position:0%
+is just about uh equal to one when the G
+of J Omega product uh is very very large
+
+ align:start position:0%
+of J Omega product uh is very very large
+ 
+
+ align:start position:0%
+of J Omega product uh is very very large
+in other words I should have an equals
+
+ align:start position:0%
+in other words I should have an equals
+ 
+
+ align:start position:0%
+in other words I should have an equals
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here when the G of J Omega product is
+
+ align:start position:0%
+here when the G of J Omega product is
+ 
+
+ align:start position:0%
+here when the G of J Omega product is
+very large under those conditions when G
+
+ align:start position:0%
+very large under those conditions when G
+ 
+
+ align:start position:0%
+very large under those conditions when G
+of J Omega is large compared to one uh
+
+ align:start position:0%
+of J Omega is large compared to one uh
+ 
+
+ align:start position:0%
+of J Omega is large compared to one uh
+the numerator denominator are just about
+
+ align:start position:0%
+the numerator denominator are just about
+ 
+
+ align:start position:0%
+the numerator denominator are just about
+equal and so the magnitude of this term
+
+ align:start position:0%
+equal and so the magnitude of this term
+ 
+
+ align:start position:0%
+equal and so the magnitude of this term
+is is just about one so we have one
+
+ align:start position:0%
+is is just about one so we have one
+ 
+
+ align:start position:0%
+is is just about one so we have one
+limit at the other end when G of J Omega
+
+ align:start position:0%
+limit at the other end when G of J Omega
+ 
+
+ align:start position:0%
+limit at the other end when G of J Omega
+is very small uh the denominator is
+
+ align:start position:0%
+is very small uh the denominator is
+ 
+
+ align:start position:0%
+is very small uh the denominator is
+dominated by the one term and under
+
+ align:start position:0%
+dominated by the one term and under
+ 
+
+ align:start position:0%
+dominated by the one term and under
+those conditions the ratio G over 1 + G
+
+ align:start position:0%
+those conditions the ratio G over 1 + G
+ 
+
+ align:start position:0%
+those conditions the ratio G over 1 + G
+is just about equal to G itself under
+
+ align:start position:0%
+is just about equal to G itself under
+ 
+
+ align:start position:0%
+is just about equal to G itself under
+those conditions G is not important in
+
+ align:start position:0%
+those conditions G is not important in
+ 
+
+ align:start position:0%
+those conditions G is not important in
+the denominator the difficulty in the
+
+ align:start position:0%
+the denominator the difficulty in the
+ 
+
+ align:start position:0%
+the denominator the difficulty in the
+evaluation comes when we're working at
+
+ align:start position:0%
+evaluation comes when we're working at
+ 
+
+ align:start position:0%
+evaluation comes when we're working at
+magnitudes of G of about one there the
+
+ align:start position:0%
+magnitudes of G of about one there the
+ 
+
+ align:start position:0%
+magnitudes of G of about one there the
+angle of G has a very profound effect on
+
+ align:start position:0%
+angle of G has a very profound effect on
+ 
+
+ align:start position:0%
+angle of G has a very profound effect on
+the quantity G over 1+ G for example if
+
+ align:start position:0%
+the quantity G over 1+ G for example if
+ 
+
+ align:start position:0%
+the quantity G over 1+ G for example if
+the magnitude of G is close to one but
+
+ align:start position:0%
+the magnitude of G is close to one but
+ 
+
+ align:start position:0%
+the magnitude of G is close to one but
+its angle is close to- 180° in other
+
+ align:start position:0%
+its angle is close to- 180° in other
+ 
+
+ align:start position:0%
+its angle is close to- 180° in other
+words G is about minus one we have a
+
+ align:start position:0%
+words G is about minus one we have a
+ 
+
+ align:start position:0%
+words G is about minus one we have a
+very very large magnitude for the G over
+
+ align:start position:0%
+very very large magnitude for the G over
+ 
+
+ align:start position:0%
+very very large magnitude for the G over
+1 plus G product conversely if the
+
+ align:start position:0%
+1 plus G product conversely if the
+ 
+
+ align:start position:0%
+1 plus G product conversely if the
+magnitude of G is about 1 and its angle
+
+ align:start position:0%
+magnitude of G is about 1 and its angle
+ 
+
+ align:start position:0%
+magnitude of G is about 1 and its angle
+is 0 degrees we have a magnitude of
+
+ align:start position:0%
+is 0 degrees we have a magnitude of
+ 
+
+ align:start position:0%
+is 0 degrees we have a magnitude of
+about a half uh for the G over 1+ G
+
+ align:start position:0%
+about a half uh for the G over 1+ G
+ 
+
+ align:start position:0%
+about a half uh for the G over 1+ G
+product so the difficulty is finding out
+
+ align:start position:0%
+product so the difficulty is finding out
+ 
+
+ align:start position:0%
+product so the difficulty is finding out
+or the place we have to focus on is what
+
+ align:start position:0%
+or the place we have to focus on is what
+ 
+
+ align:start position:0%
+or the place we have to focus on is what
+happens for magnitudes of G close to one
+
+ align:start position:0%
+happens for magnitudes of G close to one
+ 
+
+ align:start position:0%
+happens for magnitudes of G close to one
+uh at the extremes for large magnitudes
+
+ align:start position:0%
+uh at the extremes for large magnitudes
+ 
+
+ align:start position:0%
+uh at the extremes for large magnitudes
+of G or for small magnitudes of G uh
+
+ align:start position:0%
+of G or for small magnitudes of G uh
+ 
+
+ align:start position:0%
+of G or for small magnitudes of G uh
+it's fairly clear what the answer is
+
+ align:start position:0%
+it's fairly clear what the answer is
+ 
+
+ align:start position:0%
+it's fairly clear what the answer is
+well we'd be able to effectively make a
+
+ align:start position:0%
+well we'd be able to effectively make a
+ 
+
+ align:start position:0%
+well we'd be able to effectively make a
+dictionary that relates G uh over 1 plus
+
+ align:start position:0%
+dictionary that relates G uh over 1 plus
+ 
+
+ align:start position:0%
+dictionary that relates G uh over 1 plus
+g to g itself G is a complex number we
+
+ align:start position:0%
+g to g itself G is a complex number we
+ 
+
+ align:start position:0%
+g to g itself G is a complex number we
+could express it for example in gain
+
+ align:start position:0%
+could express it for example in gain
+ 
+
+ align:start position:0%
+could express it for example in gain
+phase terms as a magnitude and an angle
+
+ align:start position:0%
+phase terms as a magnitude and an angle
+ 
+
+ align:start position:0%
+phase terms as a magnitude and an angle
+and then there's some mapping from G as
+
+ align:start position:0%
+and then there's some mapping from G as
+ 
+
+ align:start position:0%
+and then there's some mapping from G as
+a a gain phase quantity a magnitude and
+
+ align:start position:0%
+a a gain phase quantity a magnitude and
+ 
+
+ align:start position:0%
+a a gain phase quantity a magnitude and
+angle to G over 1 plus G as a magnitude
+
+ align:start position:0%
+angle to G over 1 plus G as a magnitude
+ 
+
+ align:start position:0%
+angle to G over 1 plus G as a magnitude
+in angle and we could simply make up a
+
+ align:start position:0%
+in angle and we could simply make up a
+ 
+
+ align:start position:0%
+in angle and we could simply make up a
+dictionary that listed possible
+
+ align:start position:0%
+dictionary that listed possible
+ 
+
+ align:start position:0%
+dictionary that listed possible
+combinations for the magn itude and
+
+ align:start position:0%
+combinations for the magn itude and
+ 
+
+ align:start position:0%
+combinations for the magn itude and
+angle of G uh and the corresponding
+
+ align:start position:0%
+angle of G uh and the corresponding
+ 
+
+ align:start position:0%
+angle of G uh and the corresponding
+magnitudes and angles for G over 1 plus
+
+ align:start position:0%
+magnitudes and angles for G over 1 plus
+ 
+
+ align:start position:0%
+magnitudes and angles for G over 1 plus
+G it happens that a way that's a little
+
+ align:start position:0%
+G it happens that a way that's a little
+ 
+
+ align:start position:0%
+G it happens that a way that's a little
+bit more convenient for our purposes is
+
+ align:start position:0%
+bit more convenient for our purposes is
+ 
+
+ align:start position:0%
+bit more convenient for our purposes is
+to not make a dictionary but rather
+
+ align:start position:0%
+to not make a dictionary but rather
+ 
+
+ align:start position:0%
+to not make a dictionary but rather
+use a device called the Nickels
+
+ align:start position:0%
+use a device called the Nickels
+ 
+
+ align:start position:0%
+use a device called the Nickels
+chart and here's a nickels
+
+ align:start position:0%
+chart and here's a nickels
+ 
+
+ align:start position:0%
+chart and here's a nickels
+chart it's a little bit confusing uh but
+
+ align:start position:0%
+chart it's a little bit confusing uh but
+ 
+
+ align:start position:0%
+chart it's a little bit confusing uh but
+what there is is a
+
+ align:start position:0%
+what there is is a
+ 
+
+ align:start position:0%
+what there is is a
+grid in the background
+
+ align:start position:0%
+grid in the background
+ 
+
+ align:start position:0%
+grid in the background
+which are gain phase coordinates here's
+
+ align:start position:0%
+which are gain phase coordinates here's
+ 
+
+ align:start position:0%
+which are gain phase coordinates here's
+the magnitude of
+
+ align:start position:0%
+the magnitude of
+ 
+
+ align:start position:0%
+the magnitude of
+G uh the angle of G along here here we
+
+ align:start position:0%
+G uh the angle of G along here here we
+ 
+
+ align:start position:0%
+G uh the angle of G along here here we
+have a magnitude of G running from 10us
+
+ align:start position:0%
+have a magnitude of G running from 10us
+ 
+
+ align:start position:0%
+have a magnitude of G running from 10us
+3r up to 10 3 here we have an angle of G
+
+ align:start position:0%
+3r up to 10 3 here we have an angle of G
+ 
+
+ align:start position:0%
+3r up to 10 3 here we have an angle of G
+running from 0 degrees to minus 360° and
+
+ align:start position:0%
+running from 0 degrees to minus 360° and
+ 
+
+ align:start position:0%
+running from 0 degrees to minus 360° and
+this plane repeats every 360° so we we
+
+ align:start position:0%
+this plane repeats every 360° so we we
+ 
+
+ align:start position:0%
+this plane repeats every 360° so we we
+have all the information that we
+
+ align:start position:0%
+have all the information that we
+ 
+
+ align:start position:0%
+have all the information that we
+need and what we're able to do is go in
+
+ align:start position:0%
+need and what we're able to do is go in
+ 
+
+ align:start position:0%
+need and what we're able to do is go in
+uh for example we have a g of 10 and an
+
+ align:start position:0%
+uh for example we have a g of 10 and an
+ 
+
+ align:start position:0%
+uh for example we have a g of 10 and an
+angle of
+
+ align:start position:0%
+angle of
+ 
+
+ align:start position:0%
+angle of
+-60° that's a point in here somewhere
+
+ align:start position:0%
+-60° that's a point in here somewhere
+ 
+
+ align:start position:0%
+-60° that's a point in here somewhere
+and we can determine
+
+ align:start position:0%
+and we can determine
+ 
+
+ align:start position:0%
+and we can determine
+corresponding values for G over 1 + G
+
+ align:start position:0%
+corresponding values for G over 1 + G
+ 
+
+ align:start position:0%
+corresponding values for G over 1 + G
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+coordinates the the curved lines on the
+
+ align:start position:0%
+coordinates the the curved lines on the
+ 
+
+ align:start position:0%
+coordinates the the curved lines on the
+figure so if we went into our Point
+
+ align:start position:0%
+figure so if we went into our Point
+ 
+
+ align:start position:0%
+figure so if we went into our Point
+magnitude of g equals 10 uh angle of G
+
+ align:start position:0%
+magnitude of g equals 10 uh angle of G
+ 
+
+ align:start position:0%
+magnitude of g equals 10 uh angle of G
+is -60° that's somewhere in here well
+
+ align:start position:0%
+is -60° that's somewhere in here well
+ 
+
+ align:start position:0%
+is -60° that's somewhere in here well
+let's see we we'd be about on this
+
+ align:start position:0%
+let's see we we'd be about on this
+ 
+
+ align:start position:0%
+let's see we we'd be about on this
+magnitude curve for G over 1+ G that's a
+
+ align:start position:0%
+magnitude curve for G over 1+ G that's a
+ 
+
+ align:start position:0%
+magnitude curve for G over 1+ G that's a
+magnitude of about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.9 and we B if we cared on on about
+
+ align:start position:0%
+0.9 and we B if we cared on on about
+ 
+
+ align:start position:0%
+0.9 and we B if we cared on on about
+this angle contour for G over 1+ G uh
+
+ align:start position:0%
+this angle contour for G over 1+ G uh
+ 
+
+ align:start position:0%
+this angle contour for G over 1+ G uh
+the angle of G over 1 plus G would be
+
+ align:start position:0%
+the angle of G over 1 plus G would be
+ 
+
+ align:start position:0%
+the angle of G over 1 plus G would be
+about Min
+
+ align:start position:0%
+about Min
+ 
+
+ align:start position:0%
+about Min
+-10° in the Nickels chart the critical
+
+ align:start position:0%
+-10° in the Nickels chart the critical
+ 
+
+ align:start position:0%
+-10° in the Nickels chart the critical
+point is of course the minus one point a
+
+ align:start position:0%
+point is of course the minus one point a
+ 
+
+ align:start position:0%
+point is of course the minus one point a
+magnitude of one and an angle of- 180°
+
+ align:start position:0%
+magnitude of one and an angle of- 180°
+ 
+
+ align:start position:0%
+magnitude of one and an angle of- 180°
+and what happens uh as we approach that
+
+ align:start position:0%
+and what happens uh as we approach that
+ 
+
+ align:start position:0%
+and what happens uh as we approach that
+point here's a magnitude of one here's
+
+ align:start position:0%
+point here's a magnitude of one here's
+ 
+
+ align:start position:0%
+point here's a magnitude of one here's
+an angle of-
+
+ align:start position:0%
+an angle of-
+ 
+
+ align:start position:0%
+an angle of-
+180° and as we approach that point the
+
+ align:start position:0%
+180° and as we approach that point the
+ 
+
+ align:start position:0%
+180° and as we approach that point the
+magnitude Contours get larger and larger
+
+ align:start position:0%
+magnitude Contours get larger and larger
+ 
+
+ align:start position:0%
+magnitude Contours get larger and larger
+and larger here we're starting at a
+
+ align:start position:0%
+and larger here we're starting at a
+ 
+
+ align:start position:0%
+and larger here we're starting at a
+magnitude just slightly above 1 and now
+
+ align:start position:0%
+magnitude just slightly above 1 and now
+ 
+
+ align:start position:0%
+magnitude just slightly above 1 and now
+we're getting closer to G equal 1 here's
+
+ align:start position:0%
+we're getting closer to G equal 1 here's
+ 
+
+ align:start position:0%
+we're getting closer to G equal 1 here's
+G = 10 and an angle of minus
+
+ align:start position:0%
+G = 10 and an angle of minus
+ 
+
+ align:start position:0%
+G = 10 and an angle of minus
+180° and we have a magnitude of about uh
+
+ align:start position:0%
+180° and we have a magnitude of about uh
+ 
+
+ align:start position:0%
+180° and we have a magnitude of about uh
+1.1 or 1.2 at that point something like
+
+ align:start position:0%
+1.1 or 1.2 at that point something like
+ 
+
+ align:start position:0%
+1.1 or 1.2 at that point something like
+so about
+
+ align:start position:0%
+so about
+ 
+
+ align:start position:0%
+so about
+1.1 and now we're going down to a
+
+ align:start position:0%
+1.1 and now we're going down to a
+ 
+
+ align:start position:0%
+1.1 and now we're going down to a
+magnitude of the square root of 10 and
+
+ align:start position:0%
+magnitude of the square root of 10 and
+ 
+
+ align:start position:0%
+magnitude of the square root of 10 and
+we have a magnitude for G over 1 plus G
+
+ align:start position:0%
+we have a magnitude for G over 1 plus G
+ 
+
+ align:start position:0%
+we have a magnitude for G over 1 plus G
+of about
+
+ align:start position:0%
+of about
+ 
+
+ align:start position:0%
+of about
+1.5 and here as we approach the minus1
+
+ align:start position:0%
+1.5 and here as we approach the minus1
+ 
+
+ align:start position:0%
+1.5 and here as we approach the minus1
+point the magnitude gets larger and
+
+ align:start position:0%
+point the magnitude gets larger and
+ 
+
+ align:start position:0%
+point the magnitude gets larger and
+larger there'd be uh little ellipses in
+
+ align:start position:0%
+larger there'd be uh little ellipses in
+ 
+
+ align:start position:0%
+larger there'd be uh little ellipses in
+here with progressively larger
+
+ align:start position:0%
+here with progressively larger
+ 
+
+ align:start position:0%
+here with progressively larger
+magnitudes as we got closer and closer
+
+ align:start position:0%
+magnitudes as we got closer and closer
+ 
+
+ align:start position:0%
+magnitudes as we got closer and closer
+to the minus one
+
+ align:start position:0%
+to the minus one
+ 
+
+ align:start position:0%
+to the minus one
+point very nice way to look at this is
+
+ align:start position:0%
+point very nice way to look at this is
+ 
+
+ align:start position:0%
+point very nice way to look at this is
+to look at a three-dimensional Pres
+
+ align:start position:0%
+to look at a three-dimensional Pres
+ 
+
+ align:start position:0%
+to look at a three-dimensional Pres
+presentation of the Nickels chart
+
+ align:start position:0%
+presentation of the Nickels chart
+ 
+
+ align:start position:0%
+presentation of the Nickels chart
+something that we might call Mount
+
+ align:start position:0%
+something that we might call Mount
+ 
+
+ align:start position:0%
+something that we might call Mount
+nickels for example and here we have
+
+ align:start position:0%
+nickels for example and here we have
+ 
+
+ align:start position:0%
+nickels for example and here we have
+exactly that situation we are looking at
+
+ align:start position:0%
+exactly that situation we are looking at
+ 
+
+ align:start position:0%
+exactly that situation we are looking at
+precisely the diagram we have on the uh
+
+ align:start position:0%
+precisely the diagram we have on the uh
+ 
+
+ align:start position:0%
+precisely the diagram we have on the uh
+view graph uh where we have magnitude
+
+ align:start position:0%
+view graph uh where we have magnitude
+ 
+
+ align:start position:0%
+view graph uh where we have magnitude
+along this axis here we're at a
+
+ align:start position:0%
+along this axis here we're at a
+ 
+
+ align:start position:0%
+along this axis here we're at a
+magnitude of a tenth uh a magnitude of
+
+ align:start position:0%
+magnitude of a tenth uh a magnitude of
+ 
+
+ align:start position:0%
+magnitude of a tenth uh a magnitude of
+one in here and the magnitude increases
+
+ align:start position:0%
+one in here and the magnitude increases
+ 
+
+ align:start position:0%
+one in here and the magnitude increases
+in this direction for the magnitude of G
+
+ align:start position:0%
+in this direction for the magnitude of G
+ 
+
+ align:start position:0%
+in this direction for the magnitude of G
+and the angle of G runs along this axis
+
+ align:start position:0%
+and the angle of G runs along this axis
+ 
+
+ align:start position:0%
+and the angle of G runs along this axis
+uh here we have an angle of of 0 de and
+
+ align:start position:0%
+uh here we have an angle of of 0 de and
+ 
+
+ align:start position:0%
+uh here we have an angle of of 0 de and
+an angle ofus
+
+ align:start position:0%
+an angle ofus
+ 
+
+ align:start position:0%
+an angle ofus
+360° over at this
+
+ align:start position:0%
+360° over at this
+ 
+
+ align:start position:0%
+360° over at this
+Edge and now the magnitude of G over 1
+
+ align:start position:0%
+Edge and now the magnitude of G over 1
+ 
+
+ align:start position:0%
+Edge and now the magnitude of G over 1
+plus G is the height above the plane we
+
+ align:start position:0%
+plus G is the height above the plane we
+ 
+
+ align:start position:0%
+plus G is the height above the plane we
+have have sort of a contour map here
+
+ align:start position:0%
+have have sort of a contour map here
+ 
+
+ align:start position:0%
+have have sort of a contour map here
+actually a three-dimensional contour map
+
+ align:start position:0%
+actually a three-dimensional contour map
+ 
+
+ align:start position:0%
+actually a three-dimensional contour map
+and we get the value the magnitude of G
+
+ align:start position:0%
+and we get the value the magnitude of G
+ 
+
+ align:start position:0%
+and we get the value the magnitude of G
+over 1+ G as the height above this plane
+
+ align:start position:0%
+over 1+ G as the height above this plane
+ 
+
+ align:start position:0%
+over 1+ G as the height above this plane
+and so we can Envision uh uh for example
+
+ align:start position:0%
+and so we can Envision uh uh for example
+ 
+
+ align:start position:0%
+and so we can Envision uh uh for example
+drawing uh uh a series of values for the
+
+ align:start position:0%
+drawing uh uh a series of values for the
+ 
+
+ align:start position:0%
+drawing uh uh a series of values for the
+AF product as Omega changes evaluate AF
+
+ align:start position:0%
+AF product as Omega changes evaluate AF
+ 
+
+ align:start position:0%
+AF product as Omega changes evaluate AF
+of J Omega or G of J Omega for various
+
+ align:start position:0%
+of J Omega or G of J Omega for various
+ 
+
+ align:start position:0%
+of J Omega or G of J Omega for various
+values of Omega that'd be some Contour
+
+ align:start position:0%
+values of Omega that'd be some Contour
+ 
+
+ align:start position:0%
+values of Omega that'd be some Contour
+in the G plane it would have a magnitude
+
+ align:start position:0%
+in the G plane it would have a magnitude
+ 
+
+ align:start position:0%
+in the G plane it would have a magnitude
+and an angle for various values of of
+
+ align:start position:0%
+and an angle for various values of of
+ 
+
+ align:start position:0%
+and an angle for various values of of
+Omega and the
+
+ align:start position:0%
+Omega and the
+ 
+
+ align:start position:0%
+Omega and the
+height the magnitude of G over 1+ G
+
+ align:start position:0%
+height the magnitude of G over 1+ G
+ 
+
+ align:start position:0%
+height the magnitude of G over 1+ G
+would be the closed loop magnitude that
+
+ align:start position:0%
+would be the closed loop magnitude that
+ 
+
+ align:start position:0%
+would be the closed loop magnitude that
+corresponded at various frequencies when
+
+ align:start position:0%
+corresponded at various frequencies when
+ 
+
+ align:start position:0%
+corresponded at various frequencies when
+we had a a g at this point for example
+
+ align:start position:0%
+we had a a g at this point for example
+ 
+
+ align:start position:0%
+we had a a g at this point for example
+uh that's about a magnitude of one and
+
+ align:start position:0%
+uh that's about a magnitude of one and
+ 
+
+ align:start position:0%
+uh that's about a magnitude of one and
+and maybe an angle of
+
+ align:start position:0%
+and maybe an angle of
+ 
+
+ align:start position:0%
+and maybe an angle of
+U oh minus 150° or something like that
+
+ align:start position:0%
+U oh minus 150° or something like that
+ 
+
+ align:start position:0%
+U oh minus 150° or something like that
+why we'd find out that that we had a
+
+ align:start position:0%
+why we'd find out that that we had a
+ 
+
+ align:start position:0%
+why we'd find out that that we had a
+magnitude that was this much that's our
+
+ align:start position:0%
+magnitude that was this much that's our
+ 
+
+ align:start position:0%
+magnitude that was this much that's our
+relative elevation above the uh Unity
+
+ align:start position:0%
+relative elevation above the uh Unity
+ 
+
+ align:start position:0%
+relative elevation above the uh Unity
+Point and in particular the behavior
+
+ align:start position:0%
+Point and in particular the behavior
+ 
+
+ align:start position:0%
+Point and in particular the behavior
+that we
+
+ align:start position:0%
+that we
+ 
+
+ align:start position:0%
+that we
+see is that as we approach the minus1
+
+ align:start position:0%
+see is that as we approach the minus1
+ 
+
+ align:start position:0%
+see is that as we approach the minus1
+point as we approach a magnitude of one
+
+ align:start position:0%
+point as we approach a magnitude of one
+ 
+
+ align:start position:0%
+point as we approach a magnitude of one
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+here right
+
+ align:start position:0%
+here right
+ 
+
+ align:start position:0%
+here right
+here and an angle of minus 180° right
+
+ align:start position:0%
+here and an angle of minus 180° right
+ 
+
+ align:start position:0%
+here and an angle of minus 180° right
+here the magnitude gets progressively
+
+ align:start position:0%
+here the magnitude gets progressively
+ 
+
+ align:start position:0%
+here the magnitude gets progressively
+larger and precisely at the minus one
+
+ align:start position:0%
+larger and precisely at the minus one
+ 
+
+ align:start position:0%
+larger and precisely at the minus one
+point of course the magnitude goes to
+
+ align:start position:0%
+point of course the magnitude goes to
+ 
+
+ align:start position:0%
+point of course the magnitude goes to
+infinity and we can emphasize that I
+
+ align:start position:0%
+infinity and we can emphasize that I
+ 
+
+ align:start position:0%
+infinity and we can emphasize that I
+think in a in a somewhat graphic Way by
+
+ align:start position:0%
+think in a in a somewhat graphic Way by
+ 
+
+ align:start position:0%
+think in a in a somewhat graphic Way by
+putting a flag on top of Mount nickels
+
+ align:start position:0%
+putting a flag on top of Mount nickels
+ 
+
+ align:start position:0%
+putting a flag on top of Mount nickels
+right at the minus one point where the
+
+ align:start position:0%
+right at the minus one point where the
+ 
+
+ align:start position:0%
+right at the minus one point where the
+magnitude gets to be very very close to
+
+ align:start position:0%
+magnitude gets to be very very close to
+ 
+
+ align:start position:0%
+magnitude gets to be very very close to
+Infinity uh incidentally uh this is just
+
+ align:start position:0%
+Infinity uh incidentally uh this is just
+ 
+
+ align:start position:0%
+Infinity uh incidentally uh this is just
+really a pitch for the equivalent of
+
+ align:start position:0%
+really a pitch for the equivalent of
+ 
+
+ align:start position:0%
+really a pitch for the equivalent of
+this subject that I teach at MIT 6302 is
+
+ align:start position:0%
+this subject that I teach at MIT 6302 is
+ 
+
+ align:start position:0%
+this subject that I teach at MIT 6302 is
+the number of a feedback system subject
+
+ align:start position:0%
+the number of a feedback system subject
+ 
+
+ align:start position:0%
+the number of a feedback system subject
+that I teach at MIT and we didn't change
+
+ align:start position:0%
+that I teach at MIT and we didn't change
+ 
+
+ align:start position:0%
+that I teach at MIT and we didn't change
+the flag for this particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+presentation usually we don't need a
+
+ align:start position:0%
+presentation usually we don't need a
+ 
+
+ align:start position:0%
+presentation usually we don't need a
+nickels chart that extends over anywhere
+
+ align:start position:0%
+nickels chart that extends over anywhere
+ 
+
+ align:start position:0%
+nickels chart that extends over anywhere
+near as much area as the one that I've
+
+ align:start position:0%
+near as much area as the one that I've
+ 
+
+ align:start position:0%
+near as much area as the one that I've
+shown currently on The View graph we
+
+ align:start position:0%
+shown currently on The View graph we
+ 
+
+ align:start position:0%
+shown currently on The View graph we
+argued earlier that we were able to very
+
+ align:start position:0%
+argued earlier that we were able to very
+ 
+
+ align:start position:0%
+argued earlier that we were able to very
+easily estimate the behavior for large G
+
+ align:start position:0%
+easily estimate the behavior for large G
+ 
+
+ align:start position:0%
+easily estimate the behavior for large G
+magnitudes and for small G
+
+ align:start position:0%
+magnitudes and for small G
+ 
+
+ align:start position:0%
+magnitudes and for small G
+magnitudes so really we're only
+
+ align:start position:0%
+magnitudes so really we're only
+ 
+
+ align:start position:0%
+magnitudes so really we're only
+concerned with what goes on near a
+
+ align:start position:0%
+concerned with what goes on near a
+ 
+
+ align:start position:0%
+concerned with what goes on near a
+magnitude of g equals 1 and so normally
+
+ align:start position:0%
+magnitude of g equals 1 and so normally
+ 
+
+ align:start position:0%
+magnitude of g equals 1 and so normally
+when we're working with this Aid we use
+
+ align:start position:0%
+when we're working with this Aid we use
+ 
+
+ align:start position:0%
+when we're working with this Aid we use
+a an expanded nickels chart that focuses
+
+ align:start position:0%
+a an expanded nickels chart that focuses
+ 
+
+ align:start position:0%
+a an expanded nickels chart that focuses
+on the minus one point so here we have a
+
+ align:start position:0%
+on the minus one point so here we have a
+ 
+
+ align:start position:0%
+on the minus one point so here we have a
+nickels chart CH that covers only the
+
+ align:start position:0%
+nickels chart CH that covers only the
+ 
+
+ align:start position:0%
+nickels chart CH that covers only the
+range of angles from
+
+ align:start position:0%
+range of angles from
+ 
+
+ align:start position:0%
+range of angles from
+-60° uh down just slightly Beyond - 180
+
+ align:start position:0%
+-60° uh down just slightly Beyond - 180
+ 
+
+ align:start position:0%
+-60° uh down just slightly Beyond - 180
+degrees and magnitudes again that Center
+
+ align:start position:0%
+degrees and magnitudes again that Center
+ 
+
+ align:start position:0%
+degrees and magnitudes again that Center
+about the minus one or or the magnitude
+
+ align:start position:0%
+about the minus one or or the magnitude
+ 
+
+ align:start position:0%
+about the minus one or or the magnitude
+of one point here's one a
+
+ align:start position:0%
+of one point here's one a
+ 
+
+ align:start position:0%
+of one point here's one a
+tenth 100 10 and so we focus on the part
+
+ align:start position:0%
+tenth 100 10 and so we focus on the part
+ 
+
+ align:start position:0%
+tenth 100 10 and so we focus on the part
+of the gain phase plane that's of
+
+ align:start position:0%
+of the gain phase plane that's of
+ 
+
+ align:start position:0%
+of the gain phase plane that's of
+interest in particular the portion of
+
+ align:start position:0%
+interest in particular the portion of
+ 
+
+ align:start position:0%
+interest in particular the portion of
+the gain phase plane that uh corresponds
+
+ align:start position:0%
+the gain phase plane that uh corresponds
+ 
+
+ align:start position:0%
+the gain phase plane that uh corresponds
+to magnitudes close to one for the loop
+
+ align:start position:0%
+to magnitudes close to one for the loop
+ 
+
+ align:start position:0%
+to magnitudes close to one for the loop
+transmission and uh angles of the AF
+
+ align:start position:0%
+transmission and uh angles of the AF
+ 
+
+ align:start position:0%
+transmission and uh angles of the AF
+product ofus 180 degre corresponding to
+
+ align:start position:0%
+product ofus 180 degre corresponding to
+ 
+
+ align:start position:0%
+product ofus 180 degre corresponding to
+a positive Loop transmission with a
+
+ align:start position:0%
+a positive Loop transmission with a
+ 
+
+ align:start position:0%
+a positive Loop transmission with a
+magnitude of one so we focus on on this
+
+ align:start position:0%
+magnitude of one so we focus on on this
+ 
+
+ align:start position:0%
+magnitude of one so we focus on on this
+corner of the a of the Nickles chart
+
+ align:start position:0%
+corner of the a of the Nickles chart
+ 
+
+ align:start position:0%
+corner of the a of the Nickles chart
+this corner of the gain phase plane
+
+ align:start position:0%
+this corner of the gain phase plane
+ 
+
+ align:start position:0%
+this corner of the gain phase plane
+which is of greatest interest to us when
+
+ align:start position:0%
+which is of greatest interest to us when
+ 
+
+ align:start position:0%
+which is of greatest interest to us when
+we're evaluating the stability of a
+
+ align:start position:0%
+we're evaluating the stability of a
+ 
+
+ align:start position:0%
+we're evaluating the stability of a
+system and we use this is our measure
+
+ align:start position:0%
+system and we use this is our measure
+ 
+
+ align:start position:0%
+system and we use this is our measure
+really of relative stability we can
+
+ align:start position:0%
+really of relative stability we can
+ 
+
+ align:start position:0%
+really of relative stability we can
+imagine plotting
+
+ align:start position:0%
+imagine plotting
+ 
+
+ align:start position:0%
+imagine plotting
+a gain phase plot for a loop
+
+ align:start position:0%
+a gain phase plot for a loop
+ 
+
+ align:start position:0%
+a gain phase plot for a loop
+transmission we can plot an AF plot
+
+ align:start position:0%
+transmission we can plot an AF plot
+ 
+
+ align:start position:0%
+transmission we can plot an AF plot
+really just the leftand portion of the
+
+ align:start position:0%
+really just the leftand portion of the
+ 
+
+ align:start position:0%
+really just the leftand portion of the
+Nickels of the Nyquist construction we
+
+ align:start position:0%
+Nickels of the Nyquist construction we
+ 
+
+ align:start position:0%
+Nickels of the Nyquist construction we
+could plot that in this plane Omega
+
+ align:start position:0%
+could plot that in this plane Omega
+ 
+
+ align:start position:0%
+could plot that in this plane Omega
+would be a parameter running along that
+
+ align:start position:0%
+would be a parameter running along that
+ 
+
+ align:start position:0%
+would be a parameter running along that
+curve and what we'd do is find uh we'd
+
+ align:start position:0%
+curve and what we'd do is find uh we'd
+ 
+
+ align:start position:0%
+curve and what we'd do is find uh we'd
+be able to get the Clos Loop transfer
+
+ align:start position:0%
+be able to get the Clos Loop transfer
+ 
+
+ align:start position:0%
+be able to get the Clos Loop transfer
+function by simply evaluating the
+
+ align:start position:0%
+function by simply evaluating the
+ 
+
+ align:start position:0%
+function by simply evaluating the
+magnitude and if we cared to the angle
+
+ align:start position:0%
+magnitude and if we cared to the angle
+ 
+
+ align:start position:0%
+magnitude and if we cared to the angle
+of G over 1+ G uh as we progressed along
+
+ align:start position:0%
+of G over 1+ G uh as we progressed along
+ 
+
+ align:start position:0%
+of G over 1+ G uh as we progressed along
+the Contour in the a in the gain phase
+
+ align:start position:0%
+the Contour in the a in the gain phase
+ 
+
+ align:start position:0%
+the Contour in the a in the gain phase
+plane next time we'll look at an actual
+
+ align:start position:0%
+plane next time we'll look at an actual
+ 
+
+ align:start position:0%
+plane next time we'll look at an actual
+example of how we might do this
+
+ align:start position:0%
+example of how we might do this
+ 
+
+ align:start position:0%
+example of how we might do this
+construction and then continue with with
+
+ align:start position:0%
+construction and then continue with with
+ 
+
+ align:start position:0%
+construction and then continue with with
+our evaluation or our stability
+
+ align:start position:0%
+our evaluation or our stability
+ 
+
+ align:start position:0%
+our evaluation or our stability
+evaluation based on frequency domain
+
+ align:start position:0%
+evaluation based on frequency domain
+ 
+
+ align:start position:0%
+evaluation based on frequency domain
+Concepts thank you
\ No newline at end of file
diff --git a/LRcYRm5daCU.txt b/LRcYRm5daCU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..07b12939e75d88b4f8edefac98562683f800fe85
--- /dev/null
+++ b/LRcYRm5daCU.txt
@@ -0,0 +1,955 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hey dude how are you uh I'm not doing
+
+ align:start position:0%
+hey dude how are you uh I'm not doing
+ 
+
+ align:start position:0%
+hey dude how are you uh I'm not doing
+too well I'm trying to figure out which
+
+ align:start position:0%
+too well I'm trying to figure out which
+ 
+
+ align:start position:0%
+too well I'm trying to figure out which
+device to use to turn off the Goma
+
+ align:start position:0%
+device to use to turn off the Goma
+ 
+
+ align:start position:0%
+device to use to turn off the Goma
+module and stop buddy from growing too
+
+ align:start position:0%
+module and stop buddy from growing too
+ 
+
+ align:start position:0%
+module and stop buddy from growing too
+big but I don't know how to
+
+ align:start position:0%
+big but I don't know how to
+ 
+
+ align:start position:0%
+big but I don't know how to
+choose H well choosing the right device
+
+ align:start position:0%
+choose H well choosing the right device
+ 
+
+ align:start position:0%
+choose H well choosing the right device
+for your system can be pretty hard why
+
+ align:start position:0%
+for your system can be pretty hard why
+ 
+
+ align:start position:0%
+for your system can be pretty hard why
+don't we work on this together
+
+ align:start position:0%
+don't we work on this together
+ 
+
+ align:start position:0%
+don't we work on this together
+that would be great I am just going
+
+ align:start position:0%
+that would be great I am just going
+ 
+
+ align:start position:0%
+that would be great I am just going
+around in circles here well I'd suggest
+
+ align:start position:0%
+around in circles here well I'd suggest
+ 
+
+ align:start position:0%
+around in circles here well I'd suggest
+that you use a digital device to turn
+
+ align:start position:0%
+that you use a digital device to turn
+ 
+
+ align:start position:0%
+that you use a digital device to turn
+off the gtic module when buddy got to a
+
+ align:start position:0%
+off the gtic module when buddy got to a
+ 
+
+ align:start position:0%
+off the gtic module when buddy got to a
+certain size what's that well let's
+
+ align:start position:0%
+certain size what's that well let's
+ 
+
+ align:start position:0%
+certain size what's that well let's
+start with the basics All Digital
+
+ align:start position:0%
+start with the basics All Digital
+ 
+
+ align:start position:0%
+start with the basics All Digital
+devices have inputs and outputs that are
+
+ align:start position:0%
+devices have inputs and outputs that are
+ 
+
+ align:start position:0%
+devices have inputs and outputs that are
+always in one of two states either on or
+
+ align:start position:0%
+always in one of two states either on or
+ 
+
+ align:start position:0%
+always in one of two states either on or
+off people who work with electrical
+
+ align:start position:0%
+off people who work with electrical
+ 
+
+ align:start position:0%
+off people who work with electrical
+devices sometimes call the two states
+
+ align:start position:0%
+devices sometimes call the two states
+ 
+
+ align:start position:0%
+devices sometimes call the two states
+high and low because of the high or low
+
+ align:start position:0%
+high and low because of the high or low
+ 
+
+ align:start position:0%
+high and low because of the high or low
+voltages that the devices receive or
+
+ align:start position:0%
+voltages that the devices receive or
+ 
+
+ align:start position:0%
+voltages that the devices receive or
+produce other people think of the two
+
+ align:start position:0%
+produce other people think of the two
+ 
+
+ align:start position:0%
+produce other people think of the two
+states as true or false or as the
+
+ align:start position:0%
+states as true or false or as the
+ 
+
+ align:start position:0%
+states as true or false or as the
+numbers one and zero it really doesn't
+
+ align:start position:0%
+numbers one and zero it really doesn't
+ 
+
+ align:start position:0%
+numbers one and zero it really doesn't
+matter what's important for us is that
+
+ align:start position:0%
+matter what's important for us is that
+ 
+
+ align:start position:0%
+matter what's important for us is that
+if you hook up the output of a digital
+
+ align:start position:0%
+if you hook up the output of a digital
+ 
+
+ align:start position:0%
+if you hook up the output of a digital
+device to the gastic when the device
+
+ align:start position:0%
+device to the gastic when the device
+ 
+
+ align:start position:0%
+device to the gastic when the device
+produces a high signal buddy will
+
+ align:start position:0%
+produces a high signal buddy will
+ 
+
+ align:start position:0%
+produces a high signal buddy will
+inflate when the device produces a low
+
+ align:start position:0%
+inflate when the device produces a low
+ 
+
+ align:start position:0%
+inflate when the device produces a low
+signal buddy will stop inflating and
+
+ align:start position:0%
+signal buddy will stop inflating and
+ 
+
+ align:start position:0%
+signal buddy will stop inflating and
+he'll just stay the same size for a
+
+ align:start position:0%
+he'll just stay the same size for a
+ 
+
+ align:start position:0%
+he'll just stay the same size for a
+while that's cool but why make just two
+
+ align:start position:0%
+while that's cool but why make just two
+ 
+
+ align:start position:0%
+while that's cool but why make just two
+states wouldn't it be cooler to make
+
+ align:start position:0%
+states wouldn't it be cooler to make
+ 
+
+ align:start position:0%
+states wouldn't it be cooler to make
+budy get bigger really fast at first and
+
+ align:start position:0%
+budy get bigger really fast at first and
+ 
+
+ align:start position:0%
+budy get bigger really fast at first and
+then slow down when he's close to full
+
+ align:start position:0%
+then slow down when he's close to full
+ 
+
+ align:start position:0%
+then slow down when he's close to full
+size I really don't want to see him
+
+ align:start position:0%
+size I really don't want to see him
+ 
+
+ align:start position:0%
+size I really don't want to see him
+growing out of control like before
+
+ align:start position:0%
+growing out of control like before
+ 
+
+ align:start position:0%
+growing out of control like before
+couldn't we build an even more
+
+ align:start position:0%
+couldn't we build an even more
+ 
+
+ align:start position:0%
+couldn't we build an even more
+interesting system from devices with
+
+ align:start position:0%
+interesting system from devices with
+ 
+
+ align:start position:0%
+interesting system from devices with
+more States like three or even 10 those
+
+ align:start position:0%
+more States like three or even 10 those
+ 
+
+ align:start position:0%
+more States like three or even 10 those
+are all really interesting ideas but
+
+ align:start position:0%
+are all really interesting ideas but
+ 
+
+ align:start position:0%
+are all really interesting ideas but
+here's why two states makes the most
+
+ align:start position:0%
+here's why two states makes the most
+ 
+
+ align:start position:0%
+here's why two states makes the most
+sense let's imagine that you're
+
+ align:start position:0%
+sense let's imagine that you're
+ 
+
+ align:start position:0%
+sense let's imagine that you're
+measuring the output signal from your
+
+ align:start position:0%
+measuring the output signal from your
+ 
+
+ align:start position:0%
+measuring the output signal from your
+digital device over time depending on
+
+ align:start position:0%
+digital device over time depending on
+ 
+
+ align:start position:0%
+digital device over time depending on
+what the input to the digital device is
+
+ align:start position:0%
+what the input to the digital device is
+ 
+
+ align:start position:0%
+what the input to the digital device is
+the output will switch between its two
+
+ align:start position:0%
+the output will switch between its two
+ 
+
+ align:start position:0%
+the output will switch between its two
+ible States on and off but of course
+
+ align:start position:0%
+ible States on and off but of course
+ 
+
+ align:start position:0%
+ible States on and off but of course
+this drawing is actually a bit
+
+ align:start position:0%
+this drawing is actually a bit
+ 
+
+ align:start position:0%
+this drawing is actually a bit
+misleading see all digital devices
+
+ align:start position:0%
+misleading see all digital devices
+ 
+
+ align:start position:0%
+misleading see all digital devices
+whether they are genetic devices or
+
+ align:start position:0%
+whether they are genetic devices or
+ 
+
+ align:start position:0%
+whether they are genetic devices or
+electrical devices never produce a
+
+ align:start position:0%
+electrical devices never produce a
+ 
+
+ align:start position:0%
+electrical devices never produce a
+signal that is perfectly on or perfectly
+
+ align:start position:0%
+signal that is perfectly on or perfectly
+ 
+
+ align:start position:0%
+signal that is perfectly on or perfectly
+off like I've drawn here there are
+
+ align:start position:0%
+off like I've drawn here there are
+ 
+
+ align:start position:0%
+off like I've drawn here there are
+always some minor fluctuations in the
+
+ align:start position:0%
+always some minor fluctuations in the
+ 
+
+ align:start position:0%
+always some minor fluctuations in the
+signal these fluctuations aren't real
+
+ align:start position:0%
+signal these fluctuations aren't real
+ 
+
+ align:start position:0%
+signal these fluctuations aren't real
+changes in state of course but sometimes
+
+ align:start position:0%
+changes in state of course but sometimes
+ 
+
+ align:start position:0%
+changes in state of course but sometimes
+if the fluctuations are too big then
+
+ align:start position:0%
+if the fluctuations are too big then
+ 
+
+ align:start position:0%
+if the fluctuations are too big then
+they might tell the gematic to switch on
+
+ align:start position:0%
+they might tell the gematic to switch on
+ 
+
+ align:start position:0%
+they might tell the gematic to switch on
+when you really want it off oh no I
+
+ align:start position:0%
+when you really want it off oh no I
+ 
+
+ align:start position:0%
+when you really want it off oh no I
+definitely don't want that it took
+
+ align:start position:0%
+definitely don't want that it took
+ 
+
+ align:start position:0%
+definitely don't want that it took
+forever to clean up the lab last time
+
+ align:start position:0%
+forever to clean up the lab last time
+ 
+
+ align:start position:0%
+forever to clean up the lab last time
+that happened so the reason we limit the
+
+ align:start position:0%
+that happened so the reason we limit the
+ 
+
+ align:start position:0%
+that happened so the reason we limit the
+devices to two states is because they
+
+ align:start position:0%
+devices to two states is because they
+ 
+
+ align:start position:0%
+devices to two states is because they
+work better when there is noise
+
+ align:start position:0%
+work better when there is noise
+ 
+
+ align:start position:0%
+work better when there is noise
+exactly and you think Buddy's growth is
+
+ align:start position:0%
+exactly and you think Buddy's growth is
+ 
+
+ align:start position:0%
+exactly and you think Buddy's growth is
+noisy definitely he changes a little
+
+ align:start position:0%
+noisy definitely he changes a little
+ 
+
+ align:start position:0%
+noisy definitely he changes a little
+just when he breathes and he can grow
+
+ align:start position:0%
+just when he breathes and he can grow
+ 
+
+ align:start position:0%
+just when he breathes and he can grow
+and shrink a lot depending on how much
+
+ align:start position:0%
+and shrink a lot depending on how much
+ 
+
+ align:start position:0%
+and shrink a lot depending on how much
+food he has and what's around him and
+
+ align:start position:0%
+food he has and what's around him and
+ 
+
+ align:start position:0%
+food he has and what's around him and
+sometimes I think he changes size just
+
+ align:start position:0%
+sometimes I think he changes size just
+ 
+
+ align:start position:0%
+sometimes I think he changes size just
+to show off so it sounds like digital
+
+ align:start position:0%
+to show off so it sounds like digital
+ 
+
+ align:start position:0%
+to show off so it sounds like digital
+devices are the way to go it will tell
+
+ align:start position:0%
+devices are the way to go it will tell
+ 
+
+ align:start position:0%
+devices are the way to go it will tell
+the gas omatic device to turn on if
+
+ align:start position:0%
+the gas omatic device to turn on if
+ 
+
+ align:start position:0%
+the gas omatic device to turn on if
+Buddy's really growing and turn off if
+
+ align:start position:0%
+Buddy's really growing and turn off if
+ 
+
+ align:start position:0%
+Buddy's really growing and turn off if
+he's full size but ignore those in
+
+ align:start position:0%
+he's full size but ignore those in
+ 
+
+ align:start position:0%
+he's full size but ignore those in
+between size fluctuations he likes to
+
+ align:start position:0%
+between size fluctuations he likes to
+ 
+
+ align:start position:0%
+between size fluctuations he likes to
+make but how big are the fluctuations
+
+ align:start position:0%
+make but how big are the fluctuations
+ 
+
+ align:start position:0%
+make but how big are the fluctuations
+that the device will ignore how does it
+
+ align:start position:0%
+that the device will ignore how does it
+ 
+
+ align:start position:0%
+that the device will ignore how does it
+know well the device only knows what we
+
+ align:start position:0%
+know well the device only knows what we
+ 
+
+ align:start position:0%
+know well the device only knows what we
+tell it and we can split up on and off
+
+ align:start position:0%
+tell it and we can split up on and off
+ 
+
+ align:start position:0%
+tell it and we can split up on and off
+the way we choose okay then I'll put the
+
+ align:start position:0%
+the way we choose okay then I'll put the
+ 
+
+ align:start position:0%
+the way we choose okay then I'll put the
+onoff Border here dude where are you
+
+ align:start position:0%
+onoff Border here dude where are you
+ 
+
+ align:start position:0%
+onoff Border here dude where are you
+listening if the signal is somewhere
+
+ align:start position:0%
+listening if the signal is somewhere
+ 
+
+ align:start position:0%
+listening if the signal is somewhere
+near this boundary and noisy then the
+
+ align:start position:0%
+near this boundary and noisy then the
+ 
+
+ align:start position:0%
+near this boundary and noisy then the
+device will turn from on to off or off
+
+ align:start position:0%
+device will turn from on to off or off
+ 
+
+ align:start position:0%
+device will turn from on to off or off
+to on when you don't want it to here's
+
+ align:start position:0%
+to on when you don't want it to here's
+ 
+
+ align:start position:0%
+to on when you don't want it to here's
+what we can do let's just call this
+
+ align:start position:0%
+what we can do let's just call this
+ 
+
+ align:start position:0%
+what we can do let's just call this
+small part the valid signals and leave
+
+ align:start position:0%
+small part the valid signals and leave
+ 
+
+ align:start position:0%
+small part the valid signals and leave
+all this in between as invalid signals
+
+ align:start position:0%
+all this in between as invalid signals
+ 
+
+ align:start position:0%
+all this in between as invalid signals
+that way the device won't confuse on
+
+ align:start position:0%
+that way the device won't confuse on
+ 
+
+ align:start position:0%
+that way the device won't confuse on
+Signal values with off signal values so
+
+ align:start position:0%
+Signal values with off signal values so
+ 
+
+ align:start position:0%
+Signal values with off signal values so
+easily a Sally maybe I'm not getting
+
+ align:start position:0%
+easily a Sally maybe I'm not getting
+ 
+
+ align:start position:0%
+easily a Sally maybe I'm not getting
+this at all it looks like you just put
+
+ align:start position:0%
+this at all it looks like you just put
+ 
+
+ align:start position:0%
+this at all it looks like you just put
+in two boundaries and now you got twice
+
+ align:start position:0%
+in two boundaries and now you got twice
+ 
+
+ align:start position:0%
+in two boundaries and now you got twice
+as much trouble what's to stop the noise
+
+ align:start position:0%
+as much trouble what's to stop the noise
+ 
+
+ align:start position:0%
+as much trouble what's to stop the noise
+from switching between valid and invalid
+
+ align:start position:0%
+from switching between valid and invalid
+ 
+
+ align:start position:0%
+from switching between valid and invalid
+signals here and here dude I actually
+
+ align:start position:0%
+signals here and here dude I actually
+ 
+
+ align:start position:0%
+signals here and here dude I actually
+think you've got the hang of this here's
+
+ align:start position:0%
+think you've got the hang of this here's
+ 
+
+ align:start position:0%
+think you've got the hang of this here's
+the trick that Engineers use make the
+
+ align:start position:0%
+the trick that Engineers use make the
+ 
+
+ align:start position:0%
+the trick that Engineers use make the
+valid output ranges smaller than the
+
+ align:start position:0%
+valid output ranges smaller than the
+ 
+
+ align:start position:0%
+valid output ranges smaller than the
+input this way the quality of the output
+
+ align:start position:0%
+input this way the quality of the output
+ 
+
+ align:start position:0%
+input this way the quality of the output
+signal is always better than the quality
+
+ align:start position:0%
+signal is always better than the quality
+ 
+
+ align:start position:0%
+signal is always better than the quality
+of the input signal and even if there is
+
+ align:start position:0%
+of the input signal and even if there is
+ 
+
+ align:start position:0%
+of the input signal and even if there is
+noise on the input the digital device
+
+ align:start position:0%
+noise on the input the digital device
+ 
+
+ align:start position:0%
+noise on the input the digital device
+will get rid of it but producing a
+
+ align:start position:0%
+will get rid of it but producing a
+ 
+
+ align:start position:0%
+will get rid of it but producing a
+better output signal this trick even has
+
+ align:start position:0%
+better output signal this trick even has
+ 
+
+ align:start position:0%
+better output signal this trick even has
+a name
+
+ align:start position:0%
+a name
+ 
+
+ align:start position:0%
+a name
+Engineers call the difference between
+
+ align:start position:0%
+Engineers call the difference between
+ 
+
+ align:start position:0%
+Engineers call the difference between
+the valid input and output ranges the
+
+ align:start position:0%
+the valid input and output ranges the
+ 
+
+ align:start position:0%
+the valid input and output ranges the
+noise margin noise margins I like it
+
+ align:start position:0%
+noise margin noise margins I like it
+ 
+
+ align:start position:0%
+noise margin noise margins I like it
+digital devices sound Wicked useful but
+
+ align:start position:0%
+digital devices sound Wicked useful but
+ 
+
+ align:start position:0%
+digital devices sound Wicked useful but
+can we really build them out of DNA some
+
+ align:start position:0%
+can we really build them out of DNA some
+ 
+
+ align:start position:0%
+can we really build them out of DNA some
+have already been built I can show you
+
+ align:start position:0%
+have already been built I can show you
+ 
+
+ align:start position:0%
+have already been built I can show you
+how they work in some cells I've got
+
+ align:start position:0%
+how they work in some cells I've got
+ 
+
+ align:start position:0%
+how they work in some cells I've got
+growing in the lab the DNA device you
+
+ align:start position:0%
+growing in the lab the DNA device you
+ 
+
+ align:start position:0%
+growing in the lab the DNA device you
+want may be there already and ready to
+
+ align:start position:0%
+want may be there already and ready to
+ 
+
+ align:start position:0%
+want may be there already and ready to
+go do you have some time to come to the
+
+ align:start position:0%
+go do you have some time to come to the
+ 
+
+ align:start position:0%
+go do you have some time to come to the
+lab now can I answer in digital
\ No newline at end of file
diff --git a/LiO-HMhxAtY.txt b/LiO-HMhxAtY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8c8ed10a3747e6b3285a18532251b246b9143f4a
--- /dev/null
+++ b/LiO-HMhxAtY.txt
@@ -0,0 +1,228 @@
+We can use a 2-to-1 multiplexer to build a
+settable storage element.
+
+Recall that a MUX selects as its output value
+the value of one of its two data inputs.
+
+The output of the MUX serves as the state
+output of the memory component.
+
+Internally to the memory component we'll also
+connect the output of the MUX to its D0 data
+
+input.
+
+The MUX's D1 data input will become the data
+input of the memory component.
+
+And the select line of the MUX will become
+the memory component's load signal, here called
+
+the gate.
+
+When the gate input is LOW, the MUX's output
+is looped back through MUX through the D0
+
+data input,
+forming the bi-stable positive feedback loop
+
+discussed in the last section.
+
+Note our circuit now has a cycle, so it no
+longer qualifies as a combinational circuit.
+
+When the gate input is HIGH, the MUX's output
+is determined by the value of the D1 input,
+
+i.e., the data input of the memory component.
+
+To load new data into the memory component,
+we set the gate input HIGH for long enough
+
+for the Q output to become valid and stable.
+
+Looking at the truth table, we see that when
+G is 1, the Q output follows the D input.
+
+While the G input is HIGH, any changes in
+the D input will be reflected as changes in
+
+the Q output, the timing being determined
+by the tPD of the MUX.
+
+Then we can set the gate input LOW to switch
+the memory component into memory mode,
+
+where the stable Q value is maintained indefinitely
+by the positive feedback loop as shown in
+
+the first two rows of the truth table.
+
+Our memory device is a called a D latch, or
+just a latch for short, with the schematic
+
+symbol shown here.
+
+When the latch's gate is HIGH, the latch is
+open and information flows from the D input
+
+to the Q output.
+
+When the latch's gate is LOW, the latch is
+closed and in "memory mode", remembering whatever
+
+value was on the D input when the gate transitioned
+from HIGH to LOW.
+
+This is shown in the timing diagrams on the
+right.
+
+The waveforms show when a signal is stable,
+i.e., a constant signal that's either LOW
+
+or HIGH,
+and when a signal is changing, shown as one
+
+or more transitions between LOW and HIGH.
+
+When G is HIGH, we can see Q changing to a
+new stable output value no later than tPD
+
+after D reaches a new stable value.
+
+Our theory is that after G transitions to
+a LOW value, Q will stay stable at whatever
+
+value was on D when G made the HIGH to LOW
+transition.
+
+But, we know that in general, we can't assume
+anything about the output of a combinational
+
+device until tPD after the input transition.
+
+The device is allowed to do whatever it wants
+in the interval between tCD and tPD after
+
+the input transition.
+
+But how will our memory work if the 1-to-0
+transition on G causes the Q output to become
+
+invalid for a brief interval?
+
+After all it's the value on the Q output we're
+trying to remember!
+
+We're going to have ensure that a 1-to-0 transition
+on G doesn't affect the Q output.
+
+That's why we specified a lenient MUX for
+our memory component.
+
+The truth table for a lenient MUX is shown
+here.
+
+The output of a lenient MUX remains valid
+and stable even after an input transition
+
+under any of the following three conditions.
+
+(1) When we're loading the latch by setting
+G HIGH, once the D input has been valid and
+
+stable for tPD,
+we are guaranteed that the Q output will be
+
+stable and valid with the same value as the
+D input, independently of Q's initial value.
+
+Or (2) If both Q and D are valid and stable
+for tPD, the Q output will be unaffected by
+
+subsequent transitions on the G input.
+
+This is the situation that will allow us to
+have a 1-to-0 transition on G without contaminating
+
+the Q output.
+
+Or, finally, (3) if G is LOW and Q has been
+stable for at least tPD, the output will be
+
+unaffected by subsequent transitions on the
+D input.
+
+Does lenience guarantee a working latch?
+
+Well, only if we're careful about ensuring
+that signals are stable at the right times
+
+so we can leverage the lenient behavior of
+the MUX.
+
+Here are the steps we need to follow in order
+to ensure the latch will work as we want.
+
+First, while the G input is HIGH, set the
+D input to the value we wish store in the
+
+latch.
+
+Then, after tPD, we're guaranteed that value
+will be stable and valid on the Q output.
+
+This is condition (1) from the previous slide.
+
+Now we wait another tPD so that the information
+about the new value on the Q' input propagates
+
+through the internal circuitry of the latch.
+
+Now, both D *and* Q' have been stable for
+at least tPD, giving us condition (2) from
+
+the previous slide.
+
+So if D is stable for 2*tPD, transitions on
+G will not affect the Q output.
+
+This requirement on D is called the setup
+time of the latch: it's how long D must be
+
+stable and valid before the HIGH-to-LOW transition
+of G.
+
+Now we can set G to LOW, still holding D stable
+and valid.
+
+After another tPD to allow the new G value
+to propagate through the internal circuitry
+
+of the latch, we've satisfied condition (3)
+from the previous slide,
+
+and the Q output will be unaffected by subsequent
+transitions on D.
+
+This further requirement on D's stability
+is called the hold time of the latch:
+
+it's how long after the transition on G that
+D must stay stable and valid.
+
+Together the setup and hold time requirements
+are called the dynamic discipline, which must
+
+be followed if the latch is to operate correctly.
+
+In summary, the dynamic discipline requires
+that the D input be stable and valid both
+
+before and after a transition on G.
+
+If our circuit is designed to obey the dynamic
+discipline, we can guarantee that this memory
+
+component will reliably store the information
+on D when the gate makes a HIGH-to-LOW transition.
\ No newline at end of file
diff --git a/MBz0swcfztQ.txt b/MBz0swcfztQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c6730c33a28ed755b0f688c3dba8f20fc3ee0c31
--- /dev/null
+++ b/MBz0swcfztQ.txt
@@ -0,0 +1,2536 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: All right.
+
+As you're settling in, why don't
+you take 10 more seconds
+
+to answer the clicker
+question.
+
+This is the last question we'll
+see in class on the
+
+photoelectric effect, so
+hopefully we can have a very
+
+high success rate here to show
+we are all ready to move on
+
+with our lives here.
+
+OK, good.
+
+So, most of you did get
+the answer correct.
+
+For those of you that didn't,
+you, of course, can ask your
+
+TA's about this in recitation,
+they'll always have a copy of
+
+these slides.
+
+But just to point out the
+confusion can be we've
+
+actually switched what
+the question is here.
+
+What the information we gave was
+the work function, which
+
+is what we've been giving
+before, but now we gave you
+
+the kinetic energy of the
+ejected electron, so you just
+
+need to rearrange your equation
+so now you're solving
+
+for the incoming energy, which
+would mean that you need to
+
+add those two energies
+together.
+
+So, hopefully everyone that
+didn't get this right, can
+
+look at it again and think about
+asking it's just asking
+
+the question in a different
+kind of a way.
+
+All right.
+
+So, we can switch over
+to the class notes.
+
+So today, we're going to
+start talking about
+
+the hydrogen atom.
+
+Now that we have our Schrodinger
+equation for the
+
+hydrogen atom, we can talk about
+it very specifically in
+
+terms of binding energies and
+also in terms of orbitals.
+
+And we talked about on Wednesday
+the conditions that
+
+allowed us to use quantum
+mechanics, which then enable
+
+us to have the Schrodinger
+equation, which we can apply,
+
+and part of that is the
+wave particle duality
+
+of light and matter.
+
+So there was a good question in
+Wednesday's class about the
+
+de Broglie wavelength
+and if it can
+
+actually go to infinity.
+
+So I just wanted to address that
+quickly before we move
+
+on, and actually address another
+thing about dealing
+
+with wavelengths of particles
+that sometimes comes up.
+
+So, the question that we had in
+last class, was if we have
+
+actually a macroscopic particle,
+and the velocity
+
+let's say starts to approach
+zero, shouldn't we have the
+
+wavelength go to infinity, even
+if we have a magic board,
+
+and even if the mass
+is really large.
+
+So, in most cases, you would
+think that as the velocity
+
+gets very tiny, the mass is
+still going to be large enough
+
+to cancel it out and still
+make it such that the
+
+wavelength is going to be
+pretty small, right.
+
+Because if we think about the
+h, Planck's constant, here
+
+that's measured in 10 to the
+negative 34 joules per second.
+
+So, we would actually need a
+really, really, really tiny
+
+velocity here to actually
+overcome the size of the mass,
+
+if we're talking about
+macroscopic particles, to have
+
+a wavelength that's going
+to be on the order.
+
+So, let's say we're talking
+about the baseball, have a
+
+wavelength of the baseball
+that's on the
+
+order of the baseball.
+
+So, if we kind of think about
+the numbers we would need, we
+
+would actually need a velocity
+that approached something
+
+that's about 10 to the negative
+30 meters per second.
+
+So first of all, that's
+pretty slow here.
+
+It's going to be hard to measure
+anyway, and in fact,
+
+if we're talking about something
+going 10 to the
+
+negative 30, and we're going to
+observe it using our eyes,
+
+so you using visible light to
+observe something going this
+
+slow, we're actually not going
+to be able to do it because
+
+we're limited by the wavelength
+of light to see how
+
+precise we can measure where
+the actual position is.
+
+So let's say we have the
+wavelength of light somewhere
+
+on the order of 10 to the
+negative 5 meters, being the
+
+wavelength of light, we're
+only going to be able to
+
+measure the velocity because of
+the uncertainty principle
+
+to a certain degree.
+
+And it turns out it's three
+orders of magnitude that --
+
+the uncertainty is three orders
+of magnitude bigger
+
+than the velocity that we're
+actually trying to observe to
+
+get to a point where we could
+see the wavelength, for
+
+example, for even a baseball
+that is moving this slow?
+
+So that the more complete answer
+to the question is that
+
+no, we're never going to be able
+to observe that because
+
+of the uncertainty principle
+it's not possible to observe a
+
+velocity that's this slow for
+a macroscopic object.
+
+So, hopefully that kind of
+clears up that question.
+
+And, of course, when the
+velocity actually is zero,
+
+this equation that the de
+Broglie has put forth is valid
+
+for anything that has momentum,
+so if something does
+
+not have any velocity at all,
+it actually does not have
+
+momentum, so you can't apply
+that equation anyway.
+
+And another thing that came
+up, and it came up in
+
+remembering as I was writing
+your problem set for this
+
+week, which will be posted
+sometime this afternoon, your
+
+problem set 2, is when we're
+talking about wavelengths of
+
+particles, and for specifically
+for electrons
+
+sometimes, you're asked to
+calculate what the energy is.
+
+And I just want to remind
+everyone, so this is a
+
+separate thought here, that we
+often use the energy where
+
+energy is equal to h c divided
+by wavelength.
+
+So if we're talking about,
+for example, we know the
+
+wavelength of an electron and
+we're trying to find the
+
+energy or vice versa, is
+this an equation we
+
+can use to do that?
+
+What do you think?
+
+No.
+
+Hopefully you're going
+to say no.
+
+And the reason is, and this will
+come up on the problems
+
+and a lot of students end up
+using this equation, which is
+
+why I want to head it off and
+mention it ahead of time, we
+
+can't use an equation because
+this equation is very
+
+specific for light.
+
+We know it's very specific for
+light because in this equation
+
+is c, the speed of light.
+
+So any time you go to use this
+equation, if you're trying to
+
+use it for an electron, just
+ask yourself first, does an
+
+electron travel at the
+speed of light?
+
+And if your answer is no, your
+answer will be no, then you
+
+just know you can't use
+this equation here.
+
+So instead you'd have to maybe
+if you start with wavelength,
+
+go over there, and then figure
+out velocity and do something
+
+more like kinetic energy
+equals 1/2 n b
+
+squared to get there.
+
+So this is just a heads up
+for as you start your
+
+next problem set.
+
+All right.
+
+So jumping in to having
+established that, yes,
+
+particles have wave-like
+behavior, even though no,
+
+they're not actually photons,
+we can't use that equation.
+
+But we can use equations that
+describe waves to describe
+
+matter, and that's what we're
+going to be doing today.
+
+We're going to be looking
+at the solutions to the
+
+Schrodinger equation for
+a hydrogen atom, and
+
+specifically we'll be looking
+at the binding energy of the
+
+electron to the nucleus.
+
+So we'll be looking at the
+solution to this part of the
+
+Schrodinger equation where
+we're finding e.
+
+Then we'll go on, after we've
+made all of our predictions
+
+for what the energy should be,
+we can actually confirm
+
+whether or not we're correct,
+and we'll do this by looking
+
+at photon emission and photon
+absorption for hydrogen atoms,
+
+and we'll actually do a demo
+with that, too, so we can
+
+confirm it ourselves, as well
+as matching it with the
+
+observation of others.
+
+And if we have time, we'll move
+on also to talking about
+
+the other part of the solution
+to the Schrodinger equation,
+
+which is psi or this
+wave function here.
+
+And remember I said that
+wave function is just a
+
+representation of the particle,
+particularly when
+
+we're talking about electrons
+-- we're familiar with the
+
+term orbitals. psi is just a
+description of the orbital.
+
+So, we'll start with an
+introduction to that if we got
+
+to it at the end.
+
+So, to remind you, when we
+look at the Schrodinger
+
+equation here, we have two parts
+to it, so when we solve
+
+the Schrodinger equation, we're
+either finding psi,
+
+which as I said, is a wave
+function or an orbital.
+
+And in addition to finding psi,
+we can also solve to find
+
+e or to find the energy for any
+given psi, and these are
+
+the binding energies of the
+electron to the nucleus.
+
+And the most important thing
+about using the Schrodinger
+
+equation and getting out our
+solutions for potential
+
+orbitals and potential energies
+for an electron with
+
+the nucleus, is that what
+we find is that quantum
+
+mechanics, and quantum mechanics
+allowing us to get
+
+to the Schrodinger equation,
+allows us to correctly predict
+
+and confirm our observations
+for what we can actually
+
+measure are indeed the
+energy levels.
+
+Here we're talking about a
+hydrogen atom and that's what
+
+we'll focus on today.
+
+And it's incredibly precise
+and we're able to make the
+
+predictions and match them
+with experiment.
+
+Also, when we're looking at the
+Schrodinger equation, it
+
+allows us to explain a stable
+hydrogen atom, which is
+
+something that classical
+mechanics did
+
+not allow us to do.
+
+So here's the solution for a
+hydrogen atom, where we have
+
+the e term here is equal to
+everything written in green.
+
+We've got a lot of constants
+in this solution to the
+
+hydrogen atom, and we know
+what most of these mean.
+
+But remember that this whole
+term in green here is what is
+
+going to be equal to that
+binding energy between the
+
+nucleus of a hydrogen atom
+and the electron.
+
+So, let's go ahead and define
+our variables here, they
+
+should be familiar to us.
+
+We have the mass, first of all,
+m is equal to m e, so
+
+that's the electron mass.
+
+We also have e, which
+is going to be the
+
+charge on the electron.
+
+In addition to that, we have
+that epsilon nought value,
+
+remember that's the permittivity
+constant in a
+
+vacuum, and basically that is
+what we use as a conversion
+
+factor to get from units.
+
+We don't want namely coulombs
+to units, we want that will
+
+allow us to cancel out
+in this equation.
+
+And finally we have Planck's
+constant here, which we're all
+
+familiar with.
+
+So, what actually happens when
+people work with the solution
+
+to the Schrodinger equation for
+a hydrogen atom is that
+
+they don't always want to deal
+with all these constants here,
+
+so we can actually group them
+together and use them as a
+
+single new constant, and
+this new constant
+
+is the Rydberg constant.
+
+And the Rydberg constant is
+actually equal to 2 .
+
+1 8 times 10 to the negative
+18 joules.
+
+So when we pull out all of those
+constants and instead
+
+use the Rydberg constant, what
+it allows us to do is really
+
+simplify our energy equation.
+
+So now we have that energy is
+equal to the negative of the
+
+Rydberg constant divided
+by n squared.
+
+So, what we have left in our
+equation is only one part that
+
+we haven't explained yet, and
+that is that n value.
+
+And it turns out that when
+you solve the Schrodinger
+
+equation, you find that there
+are only certain allowed
+
+values of this integer n.
+
+And those allowed values range
+anywhere from n equals 1, you
+
+can have n equal that 2,
+3, and it goes all
+
+the way up to infinity.
+
+But the important part is that
+there are only certain allowed
+
+values, so for example,
+you can't have 1 .
+
+5 or 2 .
+
+3, there are only these
+interger numbers.
+
+And this n here is
+what we call the
+
+principle quantum number.
+
+And what we find is when we
+apply n and plug it in to our
+
+energy equation, is that what
+we see is now we don't just
+
+have one distinct answer, we
+don't just have one possible
+
+binding energy of the electron
+to the nucleus.
+
+We're going to find that we
+actually have a whole bunch of
+
+possible, in fact, an infinite
+number of possible energy
+
+levels, and that's easier
+to see on this
+
+energy diagram here.
+
+So, let's start with n equals
+1, since that's, of course,
+
+the simplest case.
+
+So, if we have n equals 1, we
+can plug it into our energy
+
+equation here, and find that the
+binding energy, the e sub
+
+n, for n equals 1, it's just
+going to be equal to the
+
+negative of the Rydberg
+constant, so we can actually
+
+graph that on an energy diagram
+here, and it's going
+
+to be down low at the bottom
+because that's going to be, in
+
+fact, the lowest or most
+negative energy
+
+when n equals 1.
+
+But we saw from our equation
+that there's more than just
+
+one possible value for n, so we
+could, for example, have n
+
+equals 2, n equals 3, all the
+way up to n equaling infinity.
+
+So what this tells us here is
+that this is not necessarily
+
+the binding energy of the
+electron in a hydrogen atom,
+
+it's also possible that it
+could, for example, have this
+
+energy, it could have this
+energy up here, it could have
+
+some energy way up here.
+
+So we have this infinite
+number of
+
+possible binding energies.
+
+But the really important
+point here is
+
+that they're quantized.
+
+So it's not a continuum of
+energy that we can have, it's
+
+only these punctuated points of
+energy that are possible.
+
+So as I tried to say on the
+board, we can have n equals 1,
+
+but since we can't have n equals
+1/2, we actually can't
+
+have a binding energy that's
+anywhere in between these
+
+levels that are indicated
+here.
+
+And that's a really important
+point for something that comes
+
+out of solving the Schrodinger
+equation is this quantization
+
+of energy levels.
+
+And thanks to our equation
+simplified here, it's very
+
+easy for us to figure out what
+actually the allowed energy
+
+levels are.
+
+So for n equals 2, what would
+the binding energy be?
+
+Someone shout it out.
+
+Yup.
+
+So, I think the compilation of
+the voices that I heard was
+
+negative r h over 2 squared.
+
+We can do the same thing for 3,
+negative r h over 3 squared
+
+is going to be our
+binding energy.
+
+For 4, we can go all the way up
+to infinity, and actually
+
+when we get to the point where
+it's infinity, what we find is
+
+the binding energy at that point
+is going to be zero.
+
+And when we get to infinity,
+what that means is that we now
+
+have a free electron, so now
+the electron has totally
+
+separated from the atom.
+
+And that makes sense because
+we're at the point where
+
+there's no binding energy
+keeping it stable.
+
+You'll also know that all of
+these binding energies here
+
+are negative, so the negative
+sign indicates that it's low.
+
+It's a more negative energy,
+it's a lower energy state.
+
+So whenever we're thinking
+about energy states, it's
+
+always more stable to be more
+low in an energy well, so
+
+that's why it makes sense that
+it's favorable, in fact, to
+
+have an electron interacting
+with the nucleus that
+
+stabilizes and lowers
+the energy of that
+
+electron by doing so.
+
+So, we actually term this n
+equals 1 state gets a special
+
+name, which we call the ground
+state, and it's called the
+
+ground state because it is, in
+fact, the lowest to the ground
+
+that we can get.
+
+It's the most negative and most
+stable energy level that
+
+we have. And when we think about
+kind of in a more out
+
+practical sense what we mean
+by all of these binding
+
+energies, another way that we
+can put it is to give it some
+
+physical significance, and the
+physical significance of
+
+binding energies is that they're
+equal to the negative
+
+of the ionization energies.
+
+So, for example, in a hydrogen
+atom, if you take the binding
+
+energy, the negative of that is
+going to be how much energy
+
+you have to put in to ionize
+the hydrogen atom.
+
+So, if, for example, we were
+looking at a hydrogen atom in
+
+the case where we have the
+n equals 1 state, so the
+
+electron is in that ground
+state, the ionization energy,
+
+it makes sense, is going to be
+the difference between the
+
+ground state and the energy it
+takes to be a free electron.
+
+When we graph that on our chart
+here, it becomes clear
+
+that yes, in fact, the
+ionization energy is just the
+
+negative of the binding energy,
+so we can just look
+
+over here and figure out what
+our ionization energy is.
+
+So when we're talking about the
+ground state of a hydrogen
+
+atom, our ionization energy is
+just the negative of the
+
+Rydberg constant, so
+that easy, it's 2 .
+
+1 8 times 10 to the negative
+18 joules.
+
+So, that should make a lot of
+sense intuitively, because it
+
+makes sense that if we need to
+ionize an atom, we need to put
+
+energy into the atom in order
+to eject that electron, and
+
+that energy we need to put in
+better be the difference
+
+between where we are now and
+where we have to be to be a
+
+free electron.
+
+So in most cases when we talk
+about ionization energy, if we
+
+don't say anything specific to
+the state we're talking about,
+
+you should always assume that we
+are, in fact, talking about
+
+the ground state.
+
+So, oftentimes you'll just be
+asked about ionization energy.
+
+If it doesn't say anything else
+we do mean n equals 1.
+
+But, in fact, we can also talk
+about the ionization energy of
+
+different states of the hydrogen
+atom or of any atom.
+
+So, for example, we could talk
+about the n equals 2 state, so
+
+that's this state here, and it's
+also what we could call
+
+the first excited state.
+
+So we have the ground state, and
+if we excite an electron
+
+into the next closest state,
+we're at the first excited
+
+state, or the n equals
+2 state.
+
+So, we can now calculate the
+ionization energy here. it's
+
+an easy calculation -- we're
+just taking the negative of
+
+the binding energy, again that
+makes sense, because it's this
+
+difference in energy here.
+
+So what we get is that the
+binding energy, when it's
+
+negative, the ionization
+energy is 5 .
+
+4 5 times 10 to the negative
+19 joules.
+
+So we should be able to think
+about these binding energies
+
+and figure out the ionization
+energy for any state that were
+
+asked about.
+
+So if we can switch over to a
+clicker question here and
+
+we'll let you do that.
+
+And what we're asking you to
+do is now tell us what the
+
+ionization energy is of a
+hydrogen atom that is in its
+
+third excited state.
+
+All right.
+
+Let's take 10 more
+seconds on that.
+
+OK.
+
+Interesting.
+
+Usually the majority is correct,
+but actually what you
+
+did was illustrate a point that
+I really wanted to stress
+
+and there's no better way to
+stress it then to get it
+
+incorrect, especially when
+it doesn't count, it
+
+doesn't hurt so bad.
+
+So, if you want to switch back
+over to the notes, we'll
+
+explain why, in fact, the
+correct answer is 4.
+
+So the key word here is that we
+asked you to identify the
+
+third excited state.
+
+So, what white is n equal to for
+the third excited state?
+
+4 OK.
+
+So that explains probably most
+of the confusion here and you
+
+just want to be careful when
+you're reading the problems
+
+that that's what you
+read correctly.
+
+I think everyone would now get
+the clicker question correct.
+
+So, the third excited state,
+is n equal to 4, because n
+
+equals 2 is first excited, 3 is
+second excited, 4 is third
+
+excited state.
+
+So now we can just take the
+negative of that binding
+
+energy here, and I've just
+rounded up here or 1 .
+
+4 times 10 to the negative
+19 joules.
+
+So, I noticed that a few, a
+very, very small proportion of
+
+you, did type in selections
+that were
+
+negative ionization energies.
+
+And I'll just say it right now
+you can absolutely never have
+
+a negative ionization energy,
+so that's good
+
+to remember as well.
+
+And intuitively, it should make
+sense, right, because
+
+ionization energy is the amount
+of energy you need to
+
+put in to eject an electron
+from an atom.
+
+So you don't want to put in a
+negative energy, that's not
+
+going to help you out, you need
+to put in positive energy
+
+to get an electron out
+of the system.
+
+So that's why you'll find
+binding energies are always
+
+negative, and ionization
+energies are always going to
+
+be positive, or you could look
+at the equation and see it
+
+from there as well.
+
+All right.
+
+So, using the equation we'd
+initially discussed, the
+
+negative r sub h over n squared,
+we could figure out
+
+all of the different ionization
+energies and
+
+binding energies for a hydrogen
+atom, and it turns
+
+out if we change the equation
+only slightly to add a
+
+negative z squared in there, so,
+negative z squared times
+
+the Rydberg constant over
+n squared, now let's us
+
+calculate energy levels for
+absolutely any atom as long as
+
+this one important stipulation,
+it only has 1
+
+electron in it.
+
+So basically we're dealing with
+hydrogen atoms and then
+
+we're going to be dealing
+with ions.
+
+So, for example, a helium
+plus 1 ion has 1
+
+electron at z equal 2.
+
+A lithium 2 plus ion has 1
+electron, it has z equals 3,
+
+so if we were to plug in, we
+would just do z squared up
+
+here, or 3 squared.
+
+Terbium 64 plus, another
+1 electron atom.
+
+What is z for that?
+
+Yup.
+
+65.
+
+So again, terbium 64 plus, not
+an ion we probably will run
+
+into, but if we did, we could,
+in fact, calculate all of the
+
+energy levels for it using
+this equation here.
+
+And the difference between the
+equation, the reason that that
+
+z squared comes in there is
+because if you go back to your
+
+notes from Wednesday, and you
+look at the long written out
+
+form of the Schrodinger equation
+for a hydrogen atom,
+
+or any 1 electron atom, you see
+the last term there is a
+
+coulomb potential energy
+between the
+
+electron and the nucleus.
+
+So, of course, when we have a
+charge on the nucleus equal to
+
+1, as we do in a hydrogen atom,
+the z is equal to 1, so
+
+it drops out there, but normally
+we would have to
+
+include the full charge on the
+nucleus, which is equal to z
+
+or the atomic number
+times the electron.
+
+So even if we strip an atom of
+all of its electrons, we still
+
+have that same amount
+of positive
+
+charge in the nucleus.
+
+So, this allows us to look at a
+bunch of different atoms, of
+
+course, limited to the fact
+that it has to be
+
+a 1 electron atom.
+
+So, now that we can calculate
+the binding energies, we can
+
+think about is this, in fact,
+what matches up with what's
+
+been observed, or, in fact,
+could we predict what we will
+
+observe in different kinds of
+situations now that we know
+
+how to use the binding
+energy, and hopefully
+
+we can and we will.
+
+So one thing we could do is we
+could look at the different
+
+wavelengths of light that are
+emitted by hydrogen atoms that
+
+are excited to a higher state.
+
+So what we'll do in a
+few minutes here is
+
+try this with hydrogen.
+
+So we'll take h 2 and we'll run
+-- or actually we'll have
+
+h 2 filled in an evacuated
+glass tube.
+
+When we increase the potential
+between the 2 electrodes that
+
+we have in the tube -- we
+actually split the h 2 into
+
+the individual hydrogen atoms,
+and not only do that, but also
+
+excite the atoms.
+
+So when you just run across an
+atom in the street, you can
+
+assume it's going to be in its
+most stable ground state,
+
+that's where the electron would
+be, but when we add
+
+energy to the system, we can
+actually excite it up into all
+
+different sorts of higher states
+-- n equals 6, n equals
+
+10, any of those
+higher states.
+
+But that only happens
+momentarily, because, of
+
+course, if you have an energy in
+a higher energy level, it's
+
+going to want to drop back down
+to that lower or more
+
+stable level.
+
+And when it does that it's going
+to give off some energy
+
+equal to the difference between
+those two levels.
+
+And that will be associated
+with a wavelength if it
+
+releases the energy in
+terms of a photon.
+
+So that's what we'll look
+at in a few minutes.
+
+There's some important things
+to point out about what is
+
+happening here.
+
+Just to visualize exactly what
+we're saying, what we're
+
+saying is when we have an energy
+in a higher energy
+
+level, so let's say energy
+level, this initial level high
+
+up here, and it drops down to
+a lower final level, what we
+
+find is that the photon that
+is going to be emitted is
+
+going to be emitted with the
+exact energy, and the
+
+important term here
+is the exact.
+
+That is the difference between
+these two energy states.
+
+That makes sense because we're
+losing energy, we're going to
+
+a level lower level, so we can
+give off that extra in the
+
+form of light.
+
+And we can actually write the
+equation for what we would
+
+expect the energy for
+the light to be.
+
+So this delta energy here is
+very simply the energy of the
+
+initial state minus the energy
+of the final state.
+
+This is a little bit generic,
+we're not actually specifying
+
+the states here, but we could,
+we know we can calculate the
+
+energy from any of the states.
+
+So, for example, let's say we
+excited the hydrogen atom such
+
+that the electron was starting
+in the n equals 6 state, so
+
+that's our n initial.
+
+And we drop down to the n equals
+2 state, or the first
+
+excited state.
+
+Then we would be able to change
+our equation to make it
+
+a little bit more specific and
+say that delta energy here is
+
+equal to energy of n equals 6,
+minus the energy of the n
+
+equals 2 state.
+
+When we talk about that
+frequency of light that's
+
+going to be emitted, it's not
+too commonly that we'll
+
+actually talk about it
+in terms of energy.
+
+A lot of times we talk about
+light in terms of its
+
+frequency or it's wavelength,
+but that's OK, because we know
+
+how to convert from energy to
+frequency, so we can do that
+
+here as well, where our
+frequency is just our energy
+
+divided by Planck's constant,
+and since here we're talking
+
+about a delta energy, we're
+going to talk about the
+
+frequency as being equal
+to delta energy over h.
+
+Or we can say the frequency is
+going to be equal to the
+
+energy initial minus the
+energy final all
+
+over Planck's constant.
+
+So this means that we can go
+directly from the energy
+
+between two levels to the
+frequency of the photon that's
+
+emitted when you go between
+those levels.
+
+What we can also do is say
+something about the wavelength
+
+as well because we know the
+relationship between energy
+
+and frequency and wavelength.
+
+So, in the first case here,
+let's say we go from a high
+
+level to a low level, let's say
+we go from five to one.
+
+If we have a large energy
+difference here, are we going
+
+to have a high or
+low frequency?
+
+Good.
+
+A high frequency.
+
+If we have a high frequency,
+what about the wavelength,
+
+long or short?
+
+All right.
+
+Good.
+
+So we should always be
+able to keep these
+
+relationships in mind.
+
+So, similarly in a case where
+instead we have a small energy
+
+difference, we're going to have
+a low frequency, which
+
+means that we're going to have
+a long wavelength here.
+
+So now we can go ahead
+and try observing
+
+some of this ourselves.
+
+So what we're actually going to
+do is this experiment that
+
+I explained here where we're
+going to excite hydrogen atoms
+
+such that they're electrons go
+into these higher energy
+
+levels, and then we're going to
+see if we can actually see
+
+individual wavelengths that
+come out of that that
+
+correspond with the
+energy difference.
+
+So, our detection devices are
+a little bit limited here
+
+today, we're actually only going
+to be using our eyes, so
+
+that means that we need to stick
+with the visible range
+
+of the electromagnetic
+spectrum.
+
+Actually that simplifies things,
+because that really
+
+cuts down on the number of
+wavelengths that we're going
+
+to be trying to observe here.
+
+So it turns out that in the
+visible range, when you figure
+
+out the differences between
+energy levels, in hydrogen
+
+atoms, there's only 4
+wavelengths that fall in the
+
+visible range of the spectrum.
+
+So hopefully, when we turn out
+the lights, we're going to
+
+turn on this lamp here, which
+has hydrogen in it and we're
+
+going to excite that hydrogen.
+
+You'll see light coming out, but
+it's, of course, going to
+
+be bulk light -- you're not
+going to be able to tell the
+
+individual wavelengths.
+
+So what our TAs, actually if
+they can come down now, are
+
+going to pass out to you is
+these either defraction
+
+goggles, or just a little plate,
+and you're going to be
+
+splitting that light into its
+individual wavelengths.
+
+And the glasses, there aren't
+enough to go around for all of
+
+you, so that's why
+there's plates.
+
+And though glasses do look way
+cooler, the plates work a
+
+little better, so either you or
+your neighbor should try to
+
+have one of the plates
+in case one of you
+
+can't see all the lines.
+
+So our TAs will pass these
+around for us.
+
+And I also want to point out,
+it's guaranteed pretty much
+
+you'll be able to see these
+three here in the visible
+
+range -- you may or may not be
+able to see, sometimes it's
+
+hard to see that one that's
+getting near the UV end of our
+
+visible spectrum.
+
+So we won't worry if
+we can't see that.
+
+I'll take one actually.
+
+Can you raise your hand if you
+if you still need one?
+
+All right, so TA's walk
+carefully now, I'm going to
+
+shut the lights down here.
+
+All right, so we do still have
+some little bits of ambient
+
+light, so you might
+see a slight
+
+amount of the full continuum.
+
+But if you look through your
+plate, and actually especially
+
+if you kind of look off to the
+side, hopefully you'll be able
+
+to see the individual lines
+of the spectrum.
+
+Is everyone seeing that?
+
+Yeah, pretty much.
+
+OK.
+
+Can anyone not see it?
+
+Does anyone need -- actually
+I can't even tell if
+
+you raise your hand.
+
+So ask your neighbor if you
+can't see it and get one of
+
+the plates if you're
+having trouble
+
+seeing with the glasses.
+
+So this should match up with
+the spectrum that we saw.
+
+And actually keep those
+glasses with you.
+
+We'll turn the light back
+on for a second here.
+
+And hydrogen atom is what
+we're learning about, so
+
+that's the most relevant here.
+
+But just to show you that each
+atom does have its own set of
+
+spectral lines, just for fun
+we'll look at neon also so you
+
+can have a comparison point.
+
+All right.
+
+So, this is probably a familiar
+color having seen
+
+many neon lights around
+everywhere.
+
+So you see with the neon is
+there's just a lot more lines
+
+in that orange part of the
+spectrum then compared to the
+
+hydrogen, and that's really what
+gives you that neon color
+
+in the neon signs.
+
+That's the true color of a neon
+being excited, sometimes
+
+neon signs are painted
+with other compounds.
+
+All right, does everyone
+have their fill of
+
+seeing the neon lines?
+
+STUDENT: No.
+
+PROFESSOR: All right, let's take
+two more seconds to look
+
+at neon then.
+
+All right.
+
+So our special effects portion
+of the class is over.
+
+And what you see when we see it
+with our eye, which is all
+
+the wavelengths, of course,
+mixed together, is whichever
+
+those wavelengths
+is most intense.
+
+So, when we looked at the
+individual neon lines, it was
+
+the orange colors that was most
+intense, which is why we
+
+were seeing kind of a general
+orange glow with the neon,
+
+which is different from what
+we see with the hydrogen.
+
+All right, so we can, in fact,
+observe individual lines.
+
+There's nothing more exciting
+to see with your glasses on,
+
+while you look nice.
+
+You can take those off if you
+wish to, or you can try to
+
+just be splitting the light in
+the room until the TAs grab
+
+your glasses, either is fine.
+
+It turns out that we are far
+from the first people,
+
+although it felt exciting, we
+did not discover this for the
+
+first time here today.
+
+In fact, J.J. Balmer, who was a
+school teacher in the 1800s,
+
+was the first to describe these
+lines that could be seen
+
+from hydrogen.
+
+And he saw the same lines that
+we saw here today, and
+
+although he could not explain,
+even start to explain why you
+
+saw only these specific
+lines and not a whole
+
+continuum of the light.
+
+Right, we already have an idea
+because we just talked about
+
+energy levels, we know there's
+only certain allowed energy
+
+levels, but at the time there's
+no reason J.J. Balmer
+
+should have known this, and in
+fact he didn't, but he still
+
+came up with a quantitative
+way to describe
+
+what was going on.
+
+He came up with this equation
+here where what he found was
+
+that he could explain the
+wavelengths of these different
+
+lines by multiplying 1 over 4
+minus 1 over some integer n,
+
+and multiplying it by
+this number, 3 .
+
+29 times 10 to the 15 Hertz,
+and he found that this was
+
+true where n was some
+integer value --
+
+3, 4, 5, or 6.
+
+So he could explain it
+quantitatively in terms of
+
+putting an equation with it, but
+he couldn't explain what
+
+was actually going on.
+
+But we, having learned about
+energy levels, having had the
+
+Schrodinger equation solved for
+us to understand what's
+
+going on, can, in fact, explain
+what happened when we
+
+saw these different colors.
+
+So, what we know is happening
+is that were having
+
+transitions from some excited
+states to a more relaxed
+
+lower, more stable state
+in the hydrogen atom.
+
+And it turns out what we can
+detect visibly with our eyes
+
+is in the visible range, and
+that means that the final
+
+state is n equals 2.
+
+Because you see how n equals 1
+is so much further away, and
+
+actually that's not to scale,
+it's actually much, much
+
+further down in the energy well,
+such that the energy of
+
+the light is so great that
+it's going to be in
+
+ultraviolet very high energy,
+high frequency range.
+
+So we can't actually see any of
+that, it's too high energy
+
+for us to see.
+
+So everything we see is going to
+be where we have the final
+
+energy state being n equals 2.
+
+So if we think about, for
+example, this red line here,
+
+which energy state or which
+principle quantum number do
+
+you think that our electron
+started in?
+
+STUDENT: Three.
+
+PROFESSOR: Good.
+
+So, it's going to be in 3,
+because that's the shortest
+
+energy difference we can have,
+and the red is the longest
+
+wavelength we can see -- those 2
+are inversely related, so it
+
+must be n equals 3.
+
+What about the kind of cyan-ish,
+blue-green one?
+
+Yup. so n equals
+4 for that one.
+
+Similarly we can go on,
+match up the others.
+
+So n equals 5 for the
+bluish-purple and the violet
+
+is n equals 6.
+
+And again, that matches up,
+because the violet, or getting
+
+really close to the UV range
+here has the longest energy,
+
+so the highest frequency, and
+that's going to be the
+
+shortest wavelength and we can
+see here it is, in fact, the
+
+shortest wavelength that
+we can actually see.
+
+So, we can see if we can come up
+with the same equation that
+
+J.J. Balmer came up with by
+actually starting with what we
+
+know and working our way that
+way instead of coming up from
+
+the other direction, which he
+did, which was just to explain
+
+what he saw.
+
+So, if we start instead with
+talking about the energy
+
+levels, we can relate these to
+frequency, because we already
+
+said that frequency is related
+to, or it's equal to the
+
+initial energy level here minus
+the final energy level
+
+there over Planck's constant
+to get us to frequency.
+
+And we also have the equation
+that comes out of Schrodinger
+
+equation that tell us exactly
+what that binding energy is,
+
+that binding energy is just
+equal to the negative of the
+
+Rydberg constant
+over n squared.
+
+So that means that our frequency
+is going to equal,
+
+if we plug in e n into the
+initial and final energy here,
+
+1 over Planck's constant times
+negative r h over n initial
+
+squared, minus negative r
+h over n final squared.
+
+So we have an equation that
+should relate how we can
+
+actually calculate
+the frequency to
+
+what J.J. Balmer observed.
+
+We can simplify this equation
+by pulling up the r h and
+
+getting rid of some of these
+negatives here by saying the
+
+frequency is going to be equal
+to the Rydberg constant
+
+divided by Planck's constant
+all times 1 over n final
+
+squared -- this is just to
+switch the signs around and
+
+get rid of some negatives
+-- minus 1
+
+over n initial squared.
+
+We can plug this in further when
+we're talking about the
+
+visible part of the light
+spectrum, because we know that
+
+for n final equals 2, then that
+would mean we plug in 2
+
+squared here, so what
+we get is 1 over 4.
+
+So this is our final equation,
+and this is actually called
+
+the Balmer series, which was
+named after Balmer, and this
+
+tells us the frequency of any
+of the lights where we start
+
+with an electron in some higher
+energy level and we
+
+drop down to an n final
+that's equal to 2.
+
+So it's a more specific version
+of the equation where
+
+we have the n final
+equal to 2.
+
+And it turns out that actually
+we find that this matches up
+
+perfectly with Balmer's
+equation, because the value of
+
+r h, the Rydberg constant
+divided by the Planck's
+
+constant is actually -- it's
+also another constant, so we
+
+can write it as this
+kind of strange
+
+looking cursive r here.
+
+Unfortunately, this is also call
+the Rydberg constant, so
+
+it's a little bit confusing.
+
+But really it means the Rydberg
+constant divided by h,
+
+and that's equal to 3 .
+
+29 times 10 to the
+15 per second.
+
+So if you remember what the
+equation Balmer found was this
+
+number multiplied
+by this here.
+
+So, we found the exact same
+equation, but just now
+
+starting from understanding
+the difference
+
+between energy levels.
+
+So, sometimes you'll find the
+Rydberg constant in different
+
+forms, but just make sure you
+pay attention to units because
+
+then you won't mess them up,
+because this is in inverse
+
+seconds here, the other Rydberg
+constant is in joules,
+
+so you'll be able to use what
+you need depending on how
+
+you're using that constant.
+
+So in talking about the hydrogen
+atom, they actually
+
+have different names for
+different series, which means
+
+in terms of different n
+values that we end in.
+
+So we talked about what we could
+see with visible light,
+
+we said that's actually
+the Balmer series.
+
+So anything that goes from a
+higher energy level to 2 is
+
+going to be falling within the
+Balmer series, which is in the
+
+visible range of the spectrum.
+
+We can think about the Lyman
+series, which is
+
+where n equals 1.
+
+We know that that's going to be
+a higher energy difference,
+
+so that means that we're going
+to be in the UV range.
+
+We can also go in the
+opposite direction.
+
+So, for example, when n equals
+3, that's called the Paschen
+
+series, and these are named
+after basically the people
+
+that first discovered these
+different lines and
+
+characterized them, and this
+is in the near IR range.
+
+And again, the n equals 4 is
+the Brackett series, and
+
+that's an IR range.
+
+I think there's names for even
+a few more levels up.
+
+You don't need to know those,
+but just because it's a
+
+special case with the hydrogen
+atom, they do tend to be named
+
+-- the most important, of
+course, tends to be the Balmer
+
+series because that's what we
+can actually see being emitted
+
+from the hydrogen atom.
+
+So, now we should be able to
+relate what we know about
+
+different frequencies and
+different wavelengths, so
+
+Darcy can you switch us over
+to a clicker question here?
+
+And we can also talk about the
+difference between what's
+
+happening when we have emission,
+and we're going to
+
+switch over to absorption.
+
+So, we just talked about
+emission, so before we head
+
+into absorption, if you can
+answer this clicker question
+
+in terms of what do you think
+absorption means having just
+
+discussed hydrogen
+emission here?
+
+So we have four choices in terms
+of initial and final
+
+energy levels, and also what
+it means in terms of the
+
+electron -- whether it's gaining
+energy or whether it's
+
+going to be emitting energy?
+
+So, why do you take 10 seconds
+on that, we'll
+
+make it a quick one.
+
+All right, great.
+
+So already just from knowing
+the emission part, we can
+
+figure out what absorption
+probably means.
+
+Absorption is just the opposite
+of emission, so
+
+instead of starting at a high
+energy level and dropping
+
+down, when we absorb light we
+start low and we absorb energy
+
+to bring ourselves up to an
+n final that's higher.
+
+And instead of having the
+electron giving off energy as
+
+a photon, instead now the
+electron is going to take in
+
+energy from light and move
+up to that higher level.
+
+So now we're going to be talking
+briefly about photon
+
+absorption here.
+
+So again, this is just stating
+the same thing, and it could
+
+take in a long wavelength light,
+which would give it
+
+just a little bit of energy,
+maybe just enough to head up
+
+one energy level or two, or we
+could take in a high energy
+
+photon, and that means that the
+electron is going to get
+
+to move up to an even
+higher energy level.
+
+And again, we can talk about the
+same relationship here, so
+
+it's a very similar equation to
+the Rydberg equation that
+
+we saw earlier, except now what
+you see is the n initial
+
+and the n final are
+swapped places.
+
+So instead now we have r h over
+Planck's constant times 1
+
+over n initial squared minus
+n final squared.
+
+And what you want to keep in
+mind is that whatever you're
+
+dealing with, whether it's
+absorption or emission, the
+
+frequency of the light is always
+going to be a positive
+
+number, so you always want to
+make sure what's inside these
+
+brackets here turns out
+to be positive.
+
+So that's just a little bit of
+a check for yourself, and it
+
+should make sense because what
+you're doing is you're
+
+calculating the difference
+between energy levels, so you
+
+just need to flip around which
+you put first to end up with a
+
+positive number here, and that's
+a little bit of a check
+
+that you can do what yourself.
+
+So let's do a sample calculation
+now using this
+
+Rydberg formula, and we'll
+switch back to emission, and
+
+the reason that we'll do that is
+because it would be nice to
+
+actually approve what we just
+saw here and calculate the
+
+frequency of one of our lines
+in the wavelength of one of
+
+the lines we saw.
+
+So what we'll do is this problem
+here, which is let's
+
+calculate out what the
+wavelength of radiation would
+
+be emitted from a hydrogen
+atom if we start at the n
+
+equals 3 level and we go down
+to the n equals 2 level.
+
+So what we need to do here is
+use the Rydberg formula, and
+
+actually you'll be given the
+Rydberg formulas in both
+
+forms, both or absorption and
+emission on the exams. if you
+
+don't want to use that, you can
+also derive it as we did
+
+every time, it should
+intuitively make
+
+sense how we got there.
+
+But the exams are pretty short,
+so we don't want you
+
+doing that every time, so we'll
+save the 2 minutes and
+
+give you the equations directly,
+but it's still
+
+important to know
+how to use them.
+
+So, we can get from these
+energy differences to
+
+frequency by frequency is equal
+to r sub h over Planck's
+
+constant times 1 over n
+final squared minus 1
+
+over n initial squared.
+
+So let's actually just simplify
+this to the other
+
+version of the Rydberg
+constant, since we
+
+can use that here.
+
+So kind of that strange cursive
+r, and our n final is
+
+2, so 1 over 2 squared minus n
+initial, so 1 over 3 squared.
+
+So, our frequency of light
+is going to be equal to r
+
+times 5 over 36.
+
+But when we were actually
+looking at our different
+
+wavelengths, what we associate
+mostly with color is the wave
+
+length of the light and not the
+frequency of the light, so
+
+let's look at wavelength
+instead.
+
+We know that wavelength
+is equal to c over nu.
+
+We can plug in what we have
+for nu, so we have 36 c
+
+divided by 5, and that cursivey
+Rydberg constant, and
+
+that gives us 36 times the
+speed of light, 2 .
+
+998 times 10 the 8 meters per
+second, all over 5 times 3 .
+
+29 times 10 to the
+15 per second.
+
+So, what we end up getting when
+we do this calculation is
+
+the wavelength of light,
+which is equal to 6 .
+
+57 times 10 to the negative 7
+meters, or if we convert that
+
+to nanometers, we have
+657 nanometers.
+
+So does anyone remember what
+range of light 657
+
+nanometers falls in?
+
+What color?
+
+STUDENT: Red.
+
+PROFESSOR: Yeah, it's
+in the red range.
+
+So that's promising.
+
+We did, in fact, see red in our
+spectrum, and it turns out
+
+that that's exactly the
+wavelength that we see is that
+
+we're at 657 nanometers.
+
+So it turns out that we can, in
+fact, use the energy levels
+
+to predict, and we could if we
+wanted to do them for all of
+
+the different wavelengths of
+light that we observed, and
+
+also all the different
+wavelengths of light that can
+
+be detected, even if we
+can't observe them.
+
+All right, so that's what we're
+going to cover in terms
+
+of the energy portion of the
+Schrodinger equation.
+
+I mentioned that we can also
+solve for psi here, which is
+
+the wave function, and we're
+running a little short on
+
+time, so we'll start on
+Monday with solving
+
+for the wave function.
\ No newline at end of file
diff --git a/MVJzzWfAwNY.txt b/MVJzzWfAwNY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..117ff7f0339a4ba9073ac6a58bb582e8c6678dc0
--- /dev/null
+++ b/MVJzzWfAwNY.txt
@@ -0,0 +1,1315 @@
+align:start position:0%
+ 
+welcome back to a20 special relativity
+
+ align:start position:0%
+welcome back to a20 special relativity
+ 
+
+ align:start position:0%
+welcome back to a20 special relativity
+so we're starting a new chapter in which
+
+ align:start position:0%
+so we're starting a new chapter in which
+ 
+
+ align:start position:0%
+so we're starting a new chapter in which
+we look at tests and implications of
+
+ align:start position:0%
+we look at tests and implications of
+ 
+
+ align:start position:0%
+we look at tests and implications of
+special relativity
+
+ align:start position:0%
+special relativity
+ 
+
+ align:start position:0%
+special relativity
+um we started the entire discussion
+
+ align:start position:0%
+um we started the entire discussion
+ 
+
+ align:start position:0%
+um we started the entire discussion
+um integration of neurons
+
+ align:start position:0%
+um integration of neurons
+ 
+
+ align:start position:0%
+um integration of neurons
+transformations and the description of
+
+ align:start position:0%
+transformations and the description of
+ 
+
+ align:start position:0%
+transformations and the description of
+the paradoxes
+
+ align:start position:0%
+the paradoxes
+ 
+
+ align:start position:0%
+the paradoxes
+based on einstein's postulates
+
+ align:start position:0%
+based on einstein's postulates
+ 
+
+ align:start position:0%
+based on einstein's postulates
+those are not axioms which means that we
+
+ align:start position:0%
+those are not axioms which means that we
+ 
+
+ align:start position:0%
+those are not axioms which means that we
+do actually have to verify um they are a
+
+ align:start position:0%
+do actually have to verify um they are a
+ 
+
+ align:start position:0%
+do actually have to verify um they are a
+prediction of how nature functions and
+
+ align:start position:0%
+prediction of how nature functions and
+ 
+
+ align:start position:0%
+prediction of how nature functions and
+experimental verification is needed to
+
+ align:start position:0%
+experimental verification is needed to
+ 
+
+ align:start position:0%
+experimental verification is needed to
+gain confidence
+
+ align:start position:0%
+gain confidence
+ 
+
+ align:start position:0%
+gain confidence
+that those
+
+ align:start position:0%
+that those
+ 
+
+ align:start position:0%
+that those
+postulates are actually correct or
+
+ align:start position:0%
+postulates are actually correct or
+ 
+
+ align:start position:0%
+postulates are actually correct or
+realized in nature
+
+ align:start position:0%
+realized in nature
+ 
+
+ align:start position:0%
+realized in nature
+and we have studied some of those tests
+
+ align:start position:0%
+and we have studied some of those tests
+ 
+
+ align:start position:0%
+and we have studied some of those tests
+already and this serves as a little bit
+
+ align:start position:0%
+already and this serves as a little bit
+ 
+
+ align:start position:0%
+already and this serves as a little bit
+of a review
+
+ align:start position:0%
+of a review
+ 
+
+ align:start position:0%
+of a review
+of the discussions we have this to this
+
+ align:start position:0%
+of the discussions we have this to this
+ 
+
+ align:start position:0%
+of the discussions we have this to this
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+one experimental test is stellar
+
+ align:start position:0%
+one experimental test is stellar
+ 
+
+ align:start position:0%
+one experimental test is stellar
+aberration which we discussed can be
+
+ align:start position:0%
+aberration which we discussed can be
+ 
+
+ align:start position:0%
+aberration which we discussed can be
+explained by special relativity and by
+
+ align:start position:0%
+explained by special relativity and by
+ 
+
+ align:start position:0%
+explained by special relativity and by
+velocity addition so this gives us some
+
+ align:start position:0%
+velocity addition so this gives us some
+ 
+
+ align:start position:0%
+velocity addition so this gives us some
+idea about what light is
+
+ align:start position:0%
+idea about what light is
+ 
+
+ align:start position:0%
+idea about what light is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+light
+
+ align:start position:0%
+light
+ 
+
+ align:start position:0%
+light
+is a trippy is being tested in a variety
+
+ align:start position:0%
+is a trippy is being tested in a variety
+ 
+
+ align:start position:0%
+is a trippy is being tested in a variety
+of different
+
+ align:start position:0%
+of different
+ 
+
+ align:start position:0%
+of different
+experiments starting from michaels and
+
+ align:start position:0%
+experiments starting from michaels and
+ 
+
+ align:start position:0%
+experiments starting from michaels and
+morley which basically tests that the
+
+ align:start position:0%
+morley which basically tests that the
+ 
+
+ align:start position:0%
+morley which basically tests that the
+speed of light is independent of the
+
+ align:start position:0%
+speed of light is independent of the
+ 
+
+ align:start position:0%
+speed of light is independent of the
+orientation of the apparatus
+
+ align:start position:0%
+orientation of the apparatus
+ 
+
+ align:start position:0%
+orientation of the apparatus
+we have not discussed in detail
+
+ align:start position:0%
+we have not discussed in detail
+ 
+
+ align:start position:0%
+we have not discussed in detail
+another experiment which is very similar
+
+ align:start position:0%
+another experiment which is very similar
+ 
+
+ align:start position:0%
+another experiment which is very similar
+is the canadian thorndike experiment
+
+ align:start position:0%
+is the canadian thorndike experiment
+ 
+
+ align:start position:0%
+is the canadian thorndike experiment
+which tests that the speed of light is
+
+ align:start position:0%
+which tests that the speed of light is
+ 
+
+ align:start position:0%
+which tests that the speed of light is
+also independent of the velocity of the
+
+ align:start position:0%
+also independent of the velocity of the
+ 
+
+ align:start position:0%
+also independent of the velocity of the
+apparatus itself
+
+ align:start position:0%
+apparatus itself
+ 
+
+ align:start position:0%
+apparatus itself
+as one of the homework assignments we
+
+ align:start position:0%
+as one of the homework assignments we
+ 
+
+ align:start position:0%
+as one of the homework assignments we
+looked at
+
+ align:start position:0%
+looked at
+ 
+
+ align:start position:0%
+looked at
+the sitter who tested that the speed of
+
+ align:start position:0%
+the sitter who tested that the speed of
+ 
+
+ align:start position:0%
+the sitter who tested that the speed of
+light is independent
+
+ align:start position:0%
+light is independent
+ 
+
+ align:start position:0%
+light is independent
+of the speed of the source
+
+ align:start position:0%
+of the speed of the source
+ 
+
+ align:start position:0%
+of the speed of the source
+and that has been tested for example
+
+ align:start position:0%
+and that has been tested for example
+ 
+
+ align:start position:0%
+and that has been tested for example
+with the motion of binary stars as we
+
+ align:start position:0%
+with the motion of binary stars as we
+ 
+
+ align:start position:0%
+with the motion of binary stars as we
+did in our pset in our homework
+
+ align:start position:0%
+did in our pset in our homework
+ 
+
+ align:start position:0%
+did in our pset in our homework
+assignment
+
+ align:start position:0%
+assignment
+ 
+
+ align:start position:0%
+assignment
+we can look in particle physics the
+
+ align:start position:0%
+we can look in particle physics the
+ 
+
+ align:start position:0%
+we can look in particle physics the
+decay of a pion into two photons and
+
+ align:start position:0%
+decay of a pion into two photons and
+ 
+
+ align:start position:0%
+decay of a pion into two photons and
+those pions they can have a lot of
+
+ align:start position:0%
+those pions they can have a lot of
+ 
+
+ align:start position:0%
+those pions they can have a lot of
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+for example with a better of 0.999 times
+
+ align:start position:0%
+for example with a better of 0.999 times
+ 
+
+ align:start position:0%
+for example with a better of 0.999 times
+speed of light and still the photons out
+
+ align:start position:0%
+speed of light and still the photons out
+ 
+
+ align:start position:0%
+speed of light and still the photons out
+of this decay they behave like any other
+
+ align:start position:0%
+of this decay they behave like any other
+ 
+
+ align:start position:0%
+of this decay they behave like any other
+photons they move with the speed of
+
+ align:start position:0%
+photons they move with the speed of
+ 
+
+ align:start position:0%
+photons they move with the speed of
+light
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then we discussed the doppler effect and
+
+ align:start position:0%
+then we discussed the doppler effect and
+ 
+
+ align:start position:0%
+then we discussed the doppler effect and
+relativistic doppler effect and
+
+ align:start position:0%
+relativistic doppler effect and
+ 
+
+ align:start position:0%
+relativistic doppler effect and
+analyzed
+
+ align:start position:0%
+analyzed
+ 
+
+ align:start position:0%
+analyzed
+light um with various frequencies
+
+ align:start position:0%
+light um with various frequencies
+ 
+
+ align:start position:0%
+light um with various frequencies
+and one of the hypotheses you could have
+
+ align:start position:0%
+and one of the hypotheses you could have
+ 
+
+ align:start position:0%
+and one of the hypotheses you could have
+is that the photon actually is a massive
+
+ align:start position:0%
+is that the photon actually is a massive
+ 
+
+ align:start position:0%
+is that the photon actually is a massive
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+this would directly modify coulomb's
+
+ align:start position:0%
+this would directly modify coulomb's
+ 
+
+ align:start position:0%
+this would directly modify coulomb's
+laws which are tested
+
+ align:start position:0%
+laws which are tested
+ 
+
+ align:start position:0%
+laws which are tested
+experimentally
+
+ align:start position:0%
+experimentally
+ 
+
+ align:start position:0%
+experimentally
+and those results would be dependent on
+
+ align:start position:0%
+and those results would be dependent on
+ 
+
+ align:start position:0%
+and those results would be dependent on
+the frequency um it is weird
+
+ align:start position:0%
+the frequency um it is weird
+ 
+
+ align:start position:0%
+the frequency um it is weird
+electromagnetic effect if you introduce
+
+ align:start position:0%
+electromagnetic effect if you introduce
+ 
+
+ align:start position:0%
+electromagnetic effect if you introduce
+a mass to the photons like torque on a
+
+ align:start position:0%
+a mass to the photons like torque on a
+ 
+
+ align:start position:0%
+a mass to the photons like torque on a
+magnetic ring
+
+ align:start position:0%
+magnetic ring
+ 
+
+ align:start position:0%
+magnetic ring
+again here precision measurements have
+
+ align:start position:0%
+again here precision measurements have
+ 
+
+ align:start position:0%
+again here precision measurements have
+been performed and they're all in
+
+ align:start position:0%
+been performed and they're all in
+ 
+
+ align:start position:0%
+been performed and they're all in
+agreement with the hypothesis that the
+
+ align:start position:0%
+agreement with the hypothesis that the
+ 
+
+ align:start position:0%
+agreement with the hypothesis that the
+photon is massless
+
+ align:start position:0%
+photon is massless
+ 
+
+ align:start position:0%
+photon is massless
+and we talked about the doppler shift in
+
+ align:start position:0%
+and we talked about the doppler shift in
+ 
+
+ align:start position:0%
+and we talked about the doppler shift in
+redshift
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for light
+
+ align:start position:0%
+for light
+ 
+
+ align:start position:0%
+for light
+another class of experiment is where we
+
+ align:start position:0%
+another class of experiment is where we
+ 
+
+ align:start position:0%
+another class of experiment is where we
+look directly at time
+
+ align:start position:0%
+look directly at time
+ 
+
+ align:start position:0%
+look directly at time
+dilation for example
+
+ align:start position:0%
+dilation for example
+ 
+
+ align:start position:0%
+dilation for example
+in the decay of the muon as we discussed
+
+ align:start position:0%
+in the decay of the muon as we discussed
+ 
+
+ align:start position:0%
+in the decay of the muon as we discussed
+we have cosmic neurons to study or we
+
+ align:start position:0%
+we have cosmic neurons to study or we
+ 
+
+ align:start position:0%
+we have cosmic neurons to study or we
+can produce neurons in the laboratory as
+
+ align:start position:0%
+can produce neurons in the laboratory as
+ 
+
+ align:start position:0%
+can produce neurons in the laboratory as
+well and study them or we can put very
+
+ align:start position:0%
+well and study them or we can put very
+ 
+
+ align:start position:0%
+well and study them or we can put very
+precise clocks on planes um fly them
+
+ align:start position:0%
+precise clocks on planes um fly them
+ 
+
+ align:start position:0%
+precise clocks on planes um fly them
+around the globe and compare them
+
+ align:start position:0%
+around the globe and compare them
+ 
+
+ align:start position:0%
+around the globe and compare them
+with stationary and and
+
+ align:start position:0%
+with stationary and and
+ 
+
+ align:start position:0%
+with stationary and and
+simply measure the effect of special
+
+ align:start position:0%
+simply measure the effect of special
+ 
+
+ align:start position:0%
+simply measure the effect of special
+relativity on those blocks
+
+ align:start position:0%
+relativity on those blocks
+ 
+
+ align:start position:0%
+relativity on those blocks
+in all of this experimentation and
+
+ align:start position:0%
+in all of this experimentation and
+ 
+
+ align:start position:0%
+in all of this experimentation and
+experimental verification it's important
+
+ align:start position:0%
+experimental verification it's important
+ 
+
+ align:start position:0%
+experimental verification it's important
+to understand the importance of
+
+ align:start position:0%
+to understand the importance of
+ 
+
+ align:start position:0%
+to understand the importance of
+uncertainties and the scientific process
+
+ align:start position:0%
+uncertainties and the scientific process
+ 
+
+ align:start position:0%
+uncertainties and the scientific process
+overall
+
+ align:start position:0%
+overall
+ 
+
+ align:start position:0%
+overall
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i think that you know in his women has a
+
+ align:start position:0%
+i think that you know in his women has a
+ 
+
+ align:start position:0%
+i think that you know in his women has a
+historic perspective on on science one
+
+ align:start position:0%
+historic perspective on on science one
+ 
+
+ align:start position:0%
+historic perspective on on science one
+often forgets
+
+ align:start position:0%
+often forgets
+ 
+
+ align:start position:0%
+often forgets
+that specific measurement comes with an
+
+ align:start position:0%
+that specific measurement comes with an
+ 
+
+ align:start position:0%
+that specific measurement comes with an
+uncertainty
+
+ align:start position:0%
+uncertainty
+ 
+
+ align:start position:0%
+uncertainty
+often the statistical uncertainty
+
+ align:start position:0%
+often the statistical uncertainty
+ 
+
+ align:start position:0%
+often the statistical uncertainty
+or systematic effects which are quite
+
+ align:start position:0%
+or systematic effects which are quite
+ 
+
+ align:start position:0%
+or systematic effects which are quite
+important to
+
+ align:start position:0%
+important to
+ 
+
+ align:start position:0%
+important to
+quantify the level of
+
+ align:start position:0%
+quantify the level of
+ 
+
+ align:start position:0%
+quantify the level of
+verification of the theoretical
+
+ align:start position:0%
+verification of the theoretical
+ 
+
+ align:start position:0%
+verification of the theoretical
+hypothesis
+
+ align:start position:0%
+hypothesis
+ 
+
+ align:start position:0%
+hypothesis
+one example here is and experiments can
+
+ align:start position:0%
+one example here is and experiments can
+ 
+
+ align:start position:0%
+one example here is and experiments can
+have biases as well and one example of a
+
+ align:start position:0%
+have biases as well and one example of a
+ 
+
+ align:start position:0%
+have biases as well and one example of a
+biased experiment is here one from by
+
+ align:start position:0%
+biased experiment is here one from by
+ 
+
+ align:start position:0%
+biased experiment is here one from by
+walter kaufman who tried to measure e
+
+ align:start position:0%
+walter kaufman who tried to measure e
+ 
+
+ align:start position:0%
+walter kaufman who tried to measure e
+over m the electric charge over the mass
+
+ align:start position:0%
+over m the electric charge over the mass
+ 
+
+ align:start position:0%
+over m the electric charge over the mass
+of the electron
+
+ align:start position:0%
+of the electron
+ 
+
+ align:start position:0%
+of the electron
+but he had a rather strong theoretical
+
+ align:start position:0%
+but he had a rather strong theoretical
+ 
+
+ align:start position:0%
+but he had a rather strong theoretical
+bias and he conducted the experiment at
+
+ align:start position:0%
+bias and he conducted the experiment at
+ 
+
+ align:start position:0%
+bias and he conducted the experiment at
+the time einstein was proposing his
+
+ align:start position:0%
+the time einstein was proposing his
+ 
+
+ align:start position:0%
+the time einstein was proposing his
+theory
+
+ align:start position:0%
+theory
+ 
+
+ align:start position:0%
+theory
+um you know
+
+ align:start position:0%
+um you know
+ 
+
+ align:start position:0%
+um you know
+the bias really came from the model of
+
+ align:start position:0%
+the bias really came from the model of
+ 
+
+ align:start position:0%
+the bias really came from the model of
+an electron at the time
+
+ align:start position:0%
+an electron at the time
+ 
+
+ align:start position:0%
+an electron at the time
+and his experiments
+
+ align:start position:0%
+and his experiments
+ 
+
+ align:start position:0%
+and his experiments
+were not inc were inconsistent with
+
+ align:start position:0%
+were not inc were inconsistent with
+ 
+
+ align:start position:0%
+were not inc were inconsistent with
+einstein so he said einstein is wrong
+
+ align:start position:0%
+einstein so he said einstein is wrong
+ 
+
+ align:start position:0%
+einstein so he said einstein is wrong
+einstein and lawrence are wrong um
+
+ align:start position:0%
+einstein and lawrence are wrong um
+ 
+
+ align:start position:0%
+einstein and lawrence are wrong um
+blanc looked at this and said maybe but
+
+ align:start position:0%
+blanc looked at this and said maybe but
+ 
+
+ align:start position:0%
+blanc looked at this and said maybe but
+einstein's conclusion immediately by
+
+ align:start position:0%
+einstein's conclusion immediately by
+ 
+
+ align:start position:0%
+einstein's conclusion immediately by
+looking at this was you know this cannot
+
+ align:start position:0%
+looking at this was you know this cannot
+ 
+
+ align:start position:0%
+looking at this was you know this cannot
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+and it took a little bit of of time to
+
+ align:start position:0%
+and it took a little bit of of time to
+ 
+
+ align:start position:0%
+and it took a little bit of of time to
+clear up those experiments until 1914.
+
+ align:start position:0%
+clear up those experiments until 1914.
+ 
+
+ align:start position:0%
+clear up those experiments until 1914.
+um you can read more about this in this
+
+ align:start position:0%
+um you can read more about this in this
+ 
+
+ align:start position:0%
+um you can read more about this in this
+wikipedia article about walter kaufman's
+
+ align:start position:0%
+wikipedia article about walter kaufman's
+ 
+
+ align:start position:0%
+wikipedia article about walter kaufman's
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+but let me just read this to you the
+
+ align:start position:0%
+but let me just read this to you the
+ 
+
+ align:start position:0%
+but let me just read this to you the
+prevalent results
+
+ align:start position:0%
+prevalent results
+ 
+
+ align:start position:0%
+prevalent results
+decide they speak against the
+
+ align:start position:0%
+decide they speak against the
+ 
+
+ align:start position:0%
+decide they speak against the
+correctness of lawrence assumptions as
+
+ align:start position:0%
+correctness of lawrence assumptions as
+ 
+
+ align:start position:0%
+correctness of lawrence assumptions as
+well as einstein's if an account
+
+ align:start position:0%
+well as einstein's if an account
+ 
+
+ align:start position:0%
+well as einstein's if an account
+of that one considers this basic
+
+ align:start position:0%
+of that one considers this basic
+ 
+
+ align:start position:0%
+of that one considers this basic
+assumption refuted so one would be
+
+ align:start position:0%
+assumption refuted so one would be
+ 
+
+ align:start position:0%
+assumption refuted so one would be
+forced to consider it a failure to
+
+ align:start position:0%
+forced to consider it a failure to
+ 
+
+ align:start position:0%
+forced to consider it a failure to
+attempt to base an entire field of
+
+ align:start position:0%
+attempt to base an entire field of
+ 
+
+ align:start position:0%
+attempt to base an entire field of
+physics including electrodynamics and
+
+ align:start position:0%
+physics including electrodynamics and
+ 
+
+ align:start position:0%
+physics including electrodynamics and
+optics upon the principle
+
+ align:start position:0%
+optics upon the principle
+ 
+
+ align:start position:0%
+optics upon the principle
+of relative movement
+
+ align:start position:0%
+of relative movement
+ 
+
+ align:start position:0%
+of relative movement
+we now know this was wrong but you know
+
+ align:start position:0%
+we now know this was wrong but you know
+ 
+
+ align:start position:0%
+we now know this was wrong but you know
+scientific process
+
+ align:start position:0%
+scientific process
+ 
+
+ align:start position:0%
+scientific process
+happens in
+
+ align:start position:0%
+happens in
+ 
+
+ align:start position:0%
+happens in
+uh in scientific environment and i
+
+ align:start position:0%
+uh in scientific environment and i
+ 
+
+ align:start position:0%
+uh in scientific environment and i
+started
+
+ align:start position:0%
+started
+ 
+
+ align:start position:0%
+started
+this class by explaining that one needs
+
+ align:start position:0%
+this class by explaining that one needs
+ 
+
+ align:start position:0%
+this class by explaining that one needs
+to be open-minded to uh to learn and to
+
+ align:start position:0%
+to be open-minded to uh to learn and to
+ 
+
+ align:start position:0%
+to be open-minded to uh to learn and to
+study and to grow
+
+ align:start position:0%
+study and to grow
+ 
+
+ align:start position:0%
+study and to grow
+scientifically and then have to question
+
+ align:start position:0%
+scientifically and then have to question
+ 
+
+ align:start position:0%
+scientifically and then have to question
+the assumptions understand assumptions
+
+ align:start position:0%
+the assumptions understand assumptions
+ 
+
+ align:start position:0%
+the assumptions understand assumptions
+when they go into measurements
+
+ align:start position:0%
+when they go into measurements
+ 
+
+ align:start position:0%
+when they go into measurements
+so this is the first part of this
+
+ align:start position:0%
+so this is the first part of this
+ 
+
+ align:start position:0%
+so this is the first part of this
+chapter where we talk about
+
+ align:start position:0%
+chapter where we talk about
+ 
+
+ align:start position:0%
+chapter where we talk about
+tests
+
+ align:start position:0%
+tests
+ 
+
+ align:start position:0%
+tests
+we will have a discussion of
+
+ align:start position:0%
+we will have a discussion of
+ 
+
+ align:start position:0%
+we will have a discussion of
+implications of special relativity as we
+
+ align:start position:0%
+implications of special relativity as we
+ 
+
+ align:start position:0%
+implications of special relativity as we
+move on from here
\ No newline at end of file
diff --git a/MvERdFp8mvI.txt b/MvERdFp8mvI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0a9b71a13e96cb3d1a5f9d3e0cc3f84c84309559
--- /dev/null
+++ b/MvERdFp8mvI.txt
@@ -0,0 +1,1211 @@
+align:start position:0%
+ 
+so far all of our output values and
+
+ align:start position:0%
+so far all of our output values and
+ 
+
+ align:start position:0%
+so far all of our output values and
+variables have been single numbers you
+
+ align:start position:0%
+variables have been single numbers you
+ 
+
+ align:start position:0%
+variables have been single numbers you
+can also create more advanced data
+
+ align:start position:0%
+can also create more advanced data
+ 
+
+ align:start position:0%
+can also create more advanced data
+structures in are like vectors and data
+
+ align:start position:0%
+structures in are like vectors and data
+ 
+
+ align:start position:0%
+structures in are like vectors and data
+frames a vector is a series of numbers
+
+ align:start position:0%
+frames a vector is a series of numbers
+ 
+
+ align:start position:0%
+frames a vector is a series of numbers
+or characters stored as the same object
+
+ align:start position:0%
+or characters stored as the same object
+ 
+
+ align:start position:0%
+or characters stored as the same object
+you can create a vector in R using the C
+
+ align:start position:0%
+you can create a vector in R using the C
+ 
+
+ align:start position:0%
+you can create a vector in R using the C
+function which stands for combined in
+
+ align:start position:0%
+function which stands for combined in
+ 
+
+ align:start position:0%
+function which stands for combined in
+your AR console type C and then in
+
+ align:start position:0%
+your AR console type C and then in
+ 
+
+ align:start position:0%
+your AR console type C and then in
+parentheses 2 comma 3 comma 5 comma 8
+
+ align:start position:0%
+parentheses 2 comma 3 comma 5 comma 8
+ 
+
+ align:start position:0%
+parentheses 2 comma 3 comma 5 comma 8
+comma 13 close the parentheses and hit
+
+ align:start position:0%
+comma 13 close the parentheses and hit
+ 
+
+ align:start position:0%
+comma 13 close the parentheses and hit
+enter this creates a vector of five
+
+ align:start position:0%
+enter this creates a vector of five
+ 
+
+ align:start position:0%
+enter this creates a vector of five
+numbers all stored as the same object to
+
+ align:start position:0%
+numbers all stored as the same object to
+ 
+
+ align:start position:0%
+numbers all stored as the same object to
+learn more about vectors in R let's
+
+ align:start position:0%
+learn more about vectors in R let's
+ 
+
+ align:start position:0%
+learn more about vectors in R let's
+enter some data into R about the life
+
+ align:start position:0%
+enter some data into R about the life
+ 
+
+ align:start position:0%
+enter some data into R about the life
+expectancies in different countries
+
+ align:start position:0%
+expectancies in different countries
+ 
+
+ align:start position:0%
+expectancies in different countries
+well first create a vector of country
+
+ align:start position:0%
+well first create a vector of country
+ 
+
+ align:start position:0%
+well first create a vector of country
+names called country using the C
+
+ align:start position:0%
+names called country using the C
+ 
+
+ align:start position:0%
+names called country using the C
+function will put each country name in
+
+ align:start position:0%
+function will put each country name in
+ 
+
+ align:start position:0%
+function will put each country name in
+quotes since we are typing characters
+
+ align:start position:0%
+quotes since we are typing characters
+ 
+
+ align:start position:0%
+quotes since we are typing characters
+not numbers so when your are a console
+
+ align:start position:0%
+not numbers so when your are a console
+ 
+
+ align:start position:0%
+not numbers so when your are a console
+type country equals and then C for the
+
+ align:start position:0%
+type country equals and then C for the
+ 
+
+ align:start position:0%
+type country equals and then C for the
+combine function parentheses and then
+
+ align:start position:0%
+combine function parentheses and then
+ 
+
+ align:start position:0%
+combine function parentheses and then
+Brazil in quotes comma China in quotes
+
+ align:start position:0%
+Brazil in quotes comma China in quotes
+ 
+
+ align:start position:0%
+Brazil in quotes comma China in quotes
+comma India in quotes comma Switzerland
+
+ align:start position:0%
+comma India in quotes comma Switzerland
+ 
+
+ align:start position:0%
+comma India in quotes comma Switzerland
+in quotes comma and then USA in quotes
+
+ align:start position:0%
+in quotes comma and then USA in quotes
+ 
+
+ align:start position:0%
+in quotes comma and then USA in quotes
+close the parentheses and hit enter now
+
+ align:start position:0%
+close the parentheses and hit enter now
+ 
+
+ align:start position:0%
+close the parentheses and hit enter now
+let's create a second vector this time
+
+ align:start position:0%
+let's create a second vector this time
+ 
+
+ align:start position:0%
+let's create a second vector this time
+with the life expectancies of these five
+
+ align:start position:0%
+with the life expectancies of these five
+ 
+
+ align:start position:0%
+with the life expectancies of these five
+countries in the same order that we
+
+ align:start position:0%
+countries in the same order that we
+ 
+
+ align:start position:0%
+countries in the same order that we
+entered the country names we'll call
+
+ align:start position:0%
+entered the country names we'll call
+ 
+
+ align:start position:0%
+entered the country names we'll call
+this one life expectancy equals C and
+
+ align:start position:0%
+this one life expectancy equals C and
+ 
+
+ align:start position:0%
+this one life expectancy equals C and
+then in parentheses 74 comma 76
+
+ align:start position:0%
+then in parentheses 74 comma 76
+ 
+
+ align:start position:0%
+then in parentheses 74 comma 76
+, 65 , 83 , 79 close the parentheses and
+
+ align:start position:0%
+, 65 , 83 , 79 close the parentheses and
+ 
+
+ align:start position:0%
+, 65 , 83 , 79 close the parentheses and
+hit enter now if you take a look at both
+
+ align:start position:0%
+hit enter now if you take a look at both
+ 
+
+ align:start position:0%
+hit enter now if you take a look at both
+country and life expectancy you can see
+
+ align:start position:0%
+country and life expectancy you can see
+ 
+
+ align:start position:0%
+country and life expectancy you can see
+that country has five character values
+
+ align:start position:0%
+that country has five character values
+ 
+
+ align:start position:0%
+that country has five character values
+and life expectancy has five numerical
+
+ align:start position:0%
+and life expectancy has five numerical
+ 
+
+ align:start position:0%
+and life expectancy has five numerical
+values a word of warning you shouldn't
+
+ align:start position:0%
+values a word of warning you shouldn't
+ 
+
+ align:start position:0%
+values a word of warning you shouldn't
+try to combine characters and numbers in
+
+ align:start position:0%
+try to combine characters and numbers in
+ 
+
+ align:start position:0%
+try to combine characters and numbers in
+the same vector are only allows one data
+
+ align:start position:0%
+the same vector are only allows one data
+ 
+
+ align:start position:0%
+the same vector are only allows one data
+type in each vector so all of the
+
+ align:start position:0%
+type in each vector so all of the
+ 
+
+ align:start position:0%
+type in each vector so all of the
+numbers will be converted to characters
+
+ align:start position:0%
+numbers will be converted to characters
+ 
+
+ align:start position:0%
+numbers will be converted to characters
+this is bad because it won't allow us to
+
+ align:start position:0%
+this is bad because it won't allow us to
+ 
+
+ align:start position:0%
+this is bad because it won't allow us to
+do any numerical calculations with the
+
+ align:start position:0%
+do any numerical calculations with the
+ 
+
+ align:start position:0%
+do any numerical calculations with the
+numbers like compute the mean if you
+
+ align:start position:0%
+numbers like compute the mean if you
+ 
+
+ align:start position:0%
+numbers like compute the mean if you
+want to display an element of a vector
+
+ align:start position:0%
+want to display an element of a vector
+ 
+
+ align:start position:0%
+want to display an element of a vector
+use square brackets for example we could
+
+ align:start position:0%
+use square brackets for example we could
+ 
+
+ align:start position:0%
+use square brackets for example we could
+type country and then a one in square
+
+ align:start position:0%
+type country and then a one in square
+ 
+
+ align:start position:0%
+type country and then a one in square
+brackets to get the first element of the
+
+ align:start position:0%
+brackets to get the first element of the
+ 
+
+ align:start position:0%
+brackets to get the first element of the
+country vector Brazil or we could type
+
+ align:start position:0%
+country vector Brazil or we could type
+ 
+
+ align:start position:0%
+country vector Brazil or we could type
+life expectancy and then a three in
+
+ align:start position:0%
+life expectancy and then a three in
+ 
+
+ align:start position:0%
+life expectancy and then a three in
+square brackets
+
+ align:start position:0%
+square brackets
+ 
+
+ align:start position:0%
+square brackets
+to get the third element of life
+
+ align:start position:0%
+to get the third element of life
+ 
+
+ align:start position:0%
+to get the third element of life
+expectancy 65 corresponding to India
+
+ align:start position:0%
+expectancy 65 corresponding to India
+ 
+
+ align:start position:0%
+expectancy 65 corresponding to India
+another nice function to create vectors
+
+ align:start position:0%
+another nice function to create vectors
+ 
+
+ align:start position:0%
+another nice function to create vectors
+in R is the seq function which creates a
+
+ align:start position:0%
+in R is the seq function which creates a
+ 
+
+ align:start position:0%
+in R is the seq function which creates a
+sequence of numbers try typing seq and
+
+ align:start position:0%
+sequence of numbers try typing seq and
+ 
+
+ align:start position:0%
+sequence of numbers try typing seq and
+then in parentheses 0 comma 100 comma 2
+
+ align:start position:0%
+then in parentheses 0 comma 100 comma 2
+ 
+
+ align:start position:0%
+then in parentheses 0 comma 100 comma 2
+close the parentheses and hit enter this
+
+ align:start position:0%
+close the parentheses and hit enter this
+ 
+
+ align:start position:0%
+close the parentheses and hit enter this
+gives a sequence of numbers from 0 to
+
+ align:start position:0%
+gives a sequence of numbers from 0 to
+ 
+
+ align:start position:0%
+gives a sequence of numbers from 0 to
+100 starting at 0 the first argument to
+
+ align:start position:0%
+100 starting at 0 the first argument to
+ 
+
+ align:start position:0%
+100 starting at 0 the first argument to
+the seq function ending at 100 the
+
+ align:start position:0%
+the seq function ending at 100 the
+ 
+
+ align:start position:0%
+the seq function ending at 100 the
+second argument the seq function and the
+
+ align:start position:0%
+second argument the seq function and the
+ 
+
+ align:start position:0%
+second argument the seq function and the
+numbers are in increments of 2 the third
+
+ align:start position:0%
+numbers are in increments of 2 the third
+ 
+
+ align:start position:0%
+numbers are in increments of 2 the third
+argument to the seq functions this can
+
+ align:start position:0%
+argument to the seq functions this can
+ 
+
+ align:start position:0%
+argument to the seq functions this can
+be useful if you want to create a unique
+
+ align:start position:0%
+be useful if you want to create a unique
+ 
+
+ align:start position:0%
+be useful if you want to create a unique
+identifier for observations now let's
+
+ align:start position:0%
+identifier for observations now let's
+ 
+
+ align:start position:0%
+identifier for observations now let's
+combine our vectors into what we call a
+
+ align:start position:0%
+combine our vectors into what we call a
+ 
+
+ align:start position:0%
+combine our vectors into what we call a
+data frame in R this will be an
+
+ align:start position:0%
+data frame in R this will be an
+ 
+
+ align:start position:0%
+data frame in R this will be an
+important data structure for us
+
+ align:start position:0%
+important data structure for us
+ 
+
+ align:start position:0%
+important data structure for us
+all of the data files we'll work with in
+
+ align:start position:0%
+all of the data files we'll work with in
+ 
+
+ align:start position:0%
+all of the data files we'll work with in
+this course will be loaded as data
+
+ align:start position:0%
+this course will be loaded as data
+ 
+
+ align:start position:0%
+this course will be loaded as data
+frames additionally many algorithms in R
+
+ align:start position:0%
+frames additionally many algorithms in R
+ 
+
+ align:start position:0%
+frames additionally many algorithms in R
+require all of the data to be in a
+
+ align:start position:0%
+require all of the data to be in a
+ 
+
+ align:start position:0%
+require all of the data to be in a
+single object like a data frame we'll
+
+ align:start position:0%
+single object like a data frame we'll
+ 
+
+ align:start position:0%
+single object like a data frame we'll
+call our data frame country data and
+
+ align:start position:0%
+call our data frame country data and
+ 
+
+ align:start position:0%
+call our data frame country data and
+then use the data frame function to
+
+ align:start position:0%
+then use the data frame function to
+ 
+
+ align:start position:0%
+then use the data frame function to
+combine country and life expectancy so
+
+ align:start position:0%
+combine country and life expectancy so
+ 
+
+ align:start position:0%
+combine country and life expectancy so
+after typing country data equals data
+
+ align:start position:0%
+after typing country data equals data
+ 
+
+ align:start position:0%
+after typing country data equals data
+frame in parentheses type country comma
+
+ align:start position:0%
+frame in parentheses type country comma
+ 
+
+ align:start position:0%
+frame in parentheses type country comma
+life expectancy then close the
+
+ align:start position:0%
+life expectancy then close the
+ 
+
+ align:start position:0%
+life expectancy then close the
+parentheses and hit enter let's take a
+
+ align:start position:0%
+parentheses and hit enter let's take a
+ 
+
+ align:start position:0%
+parentheses and hit enter let's take a
+look at country data by typing country
+
+ align:start position:0%
+look at country data by typing country
+ 
+
+ align:start position:0%
+look at country data by typing country
+data and hitting Enter it has two
+
+ align:start position:0%
+data and hitting Enter it has two
+ 
+
+ align:start position:0%
+data and hitting Enter it has two
+columns our variables and five rows
+
+ align:start position:0%
+columns our variables and five rows
+ 
+
+ align:start position:0%
+columns our variables and five rows
+our observations it's similar to how you
+
+ align:start position:0%
+our observations it's similar to how you
+ 
+
+ align:start position:0%
+our observations it's similar to how you
+might organize data in a spreadsheet
+
+ align:start position:0%
+might organize data in a spreadsheet
+ 
+
+ align:start position:0%
+might organize data in a spreadsheet
+software like Excel let's say we now
+
+ align:start position:0%
+software like Excel let's say we now
+ 
+
+ align:start position:0%
+software like Excel let's say we now
+want to add another variable to our data
+
+ align:start position:0%
+want to add another variable to our data
+ 
+
+ align:start position:0%
+want to add another variable to our data
+frame the population in thousands of
+
+ align:start position:0%
+frame the population in thousands of
+ 
+
+ align:start position:0%
+frame the population in thousands of
+each country we can do this by using a
+
+ align:start position:0%
+each country we can do this by using a
+ 
+
+ align:start position:0%
+each country we can do this by using a
+dollar sign to link the new data into
+
+ align:start position:0%
+dollar sign to link the new data into
+ 
+
+ align:start position:0%
+dollar sign to link the new data into
+the data frame so we'll type the name of
+
+ align:start position:0%
+the data frame so we'll type the name of
+ 
+
+ align:start position:0%
+the data frame so we'll type the name of
+our data frame country data and then a
+
+ align:start position:0%
+our data frame country data and then a
+ 
+
+ align:start position:0%
+our data frame country data and then a
+dollar sign followed by the name of the
+
+ align:start position:0%
+dollar sign followed by the name of the
+ 
+
+ align:start position:0%
+dollar sign followed by the name of the
+new variable we want to add population
+
+ align:start position:0%
+new variable we want to add population
+ 
+
+ align:start position:0%
+new variable we want to add population
+then we'll set this equal to C and in
+
+ align:start position:0%
+then we'll set this equal to C and in
+ 
+
+ align:start position:0%
+then we'll set this equal to C and in
+parentheses the population and thousands
+
+ align:start position:0%
+parentheses the population and thousands
+ 
+
+ align:start position:0%
+parentheses the population and thousands
+of each country so a hundred and ninety
+
+ align:start position:0%
+of each country so a hundred and ninety
+ 
+
+ align:start position:0%
+of each country so a hundred and ninety
+nine thousand comma 1 million three
+
+ align:start position:0%
+nine thousand comma 1 million three
+ 
+
+ align:start position:0%
+nine thousand comma 1 million three
+hundred and ninety thousand comma 1
+
+ align:start position:0%
+hundred and ninety thousand comma 1
+ 
+
+ align:start position:0%
+hundred and ninety thousand comma 1
+million two hundred and forty thousand
+
+ align:start position:0%
+million two hundred and forty thousand
+ 
+
+ align:start position:0%
+million two hundred and forty thousand
+comma seven thousand nine hundred and
+
+ align:start position:0%
+comma seven thousand nine hundred and
+ 
+
+ align:start position:0%
+comma seven thousand nine hundred and
+ninety-seven comma and 318,000 close the
+
+ align:start position:0%
+ninety-seven comma and 318,000 close the
+ 
+
+ align:start position:0%
+ninety-seven comma and 318,000 close the
+parentheses and hit enter now if you
+
+ align:start position:0%
+parentheses and hit enter now if you
+ 
+
+ align:start position:0%
+parentheses and hit enter now if you
+take a look at country data you should
+
+ align:start position:0%
+take a look at country data you should
+ 
+
+ align:start position:0%
+take a look at country data you should
+see that we have a third column
+
+ align:start position:0%
+see that we have a third column
+ 
+
+ align:start position:0%
+see that we have a third column
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+we'll use this dollar sign notation a
+
+ align:start position:0%
+we'll use this dollar sign notation a
+ 
+
+ align:start position:0%
+we'll use this dollar sign notation a
+lot and we'll talk about it more later
+
+ align:start position:0%
+lot and we'll talk about it more later
+ 
+
+ align:start position:0%
+lot and we'll talk about it more later
+in this lecture note that we had to give
+
+ align:start position:0%
+in this lecture note that we had to give
+ 
+
+ align:start position:0%
+in this lecture note that we had to give
+the population values in the correct
+
+ align:start position:0%
+the population values in the correct
+ 
+
+ align:start position:0%
+the population values in the correct
+order or we'll just combine the vectors
+
+ align:start position:0%
+order or we'll just combine the vectors
+ 
+
+ align:start position:0%
+order or we'll just combine the vectors
+in the order they're typed now suppose
+
+ align:start position:0%
+in the order they're typed now suppose
+ 
+
+ align:start position:0%
+in the order they're typed now suppose
+we want to add two new observations for
+
+ align:start position:0%
+we want to add two new observations for
+ 
+
+ align:start position:0%
+we want to add two new observations for
+Australia and Greece we first need to
+
+ align:start position:0%
+Australia and Greece we first need to
+ 
+
+ align:start position:0%
+Australia and Greece we first need to
+create new country life expectancy and
+
+ align:start position:0%
+create new country life expectancy and
+ 
+
+ align:start position:0%
+create new country life expectancy and
+population vectors so will now set
+
+ align:start position:0%
+population vectors so will now set
+ 
+
+ align:start position:0%
+population vectors so will now set
+country equal to the names of the new
+
+ align:start position:0%
+country equal to the names of the new
+ 
+
+ align:start position:0%
+country equal to the names of the new
+countries Australia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and Greece
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll set life expectancy equal to the
+
+ align:start position:0%
+we'll set life expectancy equal to the
+ 
+
+ align:start position:0%
+we'll set life expectancy equal to the
+new life expectancies 82 and 81 and
+
+ align:start position:0%
+new life expectancies 82 and 81 and
+ 
+
+ align:start position:0%
+new life expectancies 82 and 81 and
+we'll call population a vector of the
+
+ align:start position:0%
+we'll call population a vector of the
+ 
+
+ align:start position:0%
+we'll call population a vector of the
+populations of these countries
+
+ align:start position:0%
+populations of these countries
+ 
+
+ align:start position:0%
+populations of these countries
+twenty-three thousand and fifty and
+
+ align:start position:0%
+twenty-three thousand and fifty and
+ 
+
+ align:start position:0%
+twenty-three thousand and fifty and
+eleven thousand 125 then we can create a
+
+ align:start position:0%
+eleven thousand 125 then we can create a
+ 
+
+ align:start position:0%
+eleven thousand 125 then we can create a
+new data frame we'll call this one new
+
+ align:start position:0%
+new data frame we'll call this one new
+ 
+
+ align:start position:0%
+new data frame we'll call this one new
+country data and we'll set it equal to
+
+ align:start position:0%
+country data and we'll set it equal to
+ 
+
+ align:start position:0%
+country data and we'll set it equal to
+data dot frame and in parentheses
+
+ align:start position:0%
+data dot frame and in parentheses
+ 
+
+ align:start position:0%
+data dot frame and in parentheses
+country life expectancy and population
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+note that we combined three vectors here
+
+ align:start position:0%
+note that we combined three vectors here
+ 
+
+ align:start position:0%
+note that we combined three vectors here
+with the dataframe function if we take a
+
+ align:start position:0%
+with the dataframe function if we take a
+ 
+
+ align:start position:0%
+with the dataframe function if we take a
+look at new country data we can see that
+
+ align:start position:0%
+look at new country data we can see that
+ 
+
+ align:start position:0%
+look at new country data we can see that
+it's very similar to country data lastly
+
+ align:start position:0%
+it's very similar to country data lastly
+ 
+
+ align:start position:0%
+it's very similar to country data lastly
+let's combine country data and new
+
+ align:start position:0%
+let's combine country data and new
+ 
+
+ align:start position:0%
+let's combine country data and new
+country data with the R bind function
+
+ align:start position:0%
+country data with the R bind function
+ 
+
+ align:start position:0%
+country data with the R bind function
+which combines data frames by stacking
+
+ align:start position:0%
+which combines data frames by stacking
+ 
+
+ align:start position:0%
+which combines data frames by stacking
+the rows we'll call this new data frame
+
+ align:start position:0%
+the rows we'll call this new data frame
+ 
+
+ align:start position:0%
+the rows we'll call this new data frame
+all country data and we'll use the R
+
+ align:start position:0%
+all country data and we'll use the R
+ 
+
+ align:start position:0%
+all country data and we'll use the R
+bind function to combine country data
+
+ align:start position:0%
+bind function to combine country data
+ 
+
+ align:start position:0%
+bind function to combine country data
+and new country data if we take a look
+
+ align:start position:0%
+and new country data if we take a look
+ 
+
+ align:start position:0%
+and new country data if we take a look
+at all country data we can see that it
+
+ align:start position:0%
+at all country data we can see that it
+ 
+
+ align:start position:0%
+at all country data we can see that it
+has the three variables from before and
+
+ align:start position:0%
+has the three variables from before and
+ 
+
+ align:start position:0%
+has the three variables from before and
+all seven observations the functions
+
+ align:start position:0%
+all seven observations the functions
+ 
+
+ align:start position:0%
+all seven observations the functions
+we've used in this video have allowed us
+
+ align:start position:0%
+we've used in this video have allowed us
+ 
+
+ align:start position:0%
+we've used in this video have allowed us
+to create data structures and modify
+
+ align:start position:0%
+to create data structures and modify
+ 
+
+ align:start position:0%
+to create data structures and modify
+data structures in R but most of the
+
+ align:start position:0%
+data structures in R but most of the
+ 
+
+ align:start position:0%
+data structures in R but most of the
+time you'll be reading in data from an
+
+ align:start position:0%
+time you'll be reading in data from an
+ 
+
+ align:start position:0%
+time you'll be reading in data from an
+external file which we'll do in the next
+
+ align:start position:0%
+external file which we'll do in the next
+ 
+
+ align:start position:0%
+external file which we'll do in the next
+video
\ No newline at end of file
diff --git a/ND89SWpkWgw.txt b/ND89SWpkWgw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e846b3c7524c982d7d1ed6b41856071f3d3b4200
--- /dev/null
+++ b/ND89SWpkWgw.txt
@@ -0,0 +1,2827 @@
+align:start position:0%
+ 
+air is normally an insulator
+
+ align:start position:0%
+air is normally an insulator
+ 
+
+ align:start position:0%
+air is normally an insulator
+but under certain conditions it can
+
+ align:start position:0%
+but under certain conditions it can
+ 
+
+ align:start position:0%
+but under certain conditions it can
+suddenly and temporarily change into a
+
+ align:start position:0%
+suddenly and temporarily change into a
+ 
+
+ align:start position:0%
+suddenly and temporarily change into a
+conductor
+
+ align:start position:0%
+conductor
+ 
+
+ align:start position:0%
+conductor
+and we end up with a spark in this video
+
+ align:start position:0%
+and we end up with a spark in this video
+ 
+
+ align:start position:0%
+and we end up with a spark in this video
+we'll use the related concepts of
+
+ align:start position:0%
+we'll use the related concepts of
+ 
+
+ align:start position:0%
+we'll use the related concepts of
+electric fields and electric potential
+
+ align:start position:0%
+electric fields and electric potential
+ 
+
+ align:start position:0%
+electric fields and electric potential
+to explain how insulators can suddenly
+
+ align:start position:0%
+to explain how insulators can suddenly
+ 
+
+ align:start position:0%
+to explain how insulators can suddenly
+dramatically and temporarily
+
+ align:start position:0%
+dramatically and temporarily
+ 
+
+ align:start position:0%
+dramatically and temporarily
+become conductors this video is part of
+
+ align:start position:0%
+become conductors this video is part of
+ 
+
+ align:start position:0%
+become conductors this video is part of
+the derivatives and integrals video
+
+ align:start position:0%
+the derivatives and integrals video
+ 
+
+ align:start position:0%
+the derivatives and integrals video
+series
+
+ align:start position:0%
+series
+ 
+
+ align:start position:0%
+series
+derivatives and integrals are used to
+
+ align:start position:0%
+derivatives and integrals are used to
+ 
+
+ align:start position:0%
+derivatives and integrals are used to
+analyze the properties of a system
+
+ align:start position:0%
+analyze the properties of a system
+ 
+
+ align:start position:0%
+analyze the properties of a system
+derivatives describe local properties of
+
+ align:start position:0%
+derivatives describe local properties of
+ 
+
+ align:start position:0%
+derivatives describe local properties of
+systems and integrals quantify their
+
+ align:start position:0%
+systems and integrals quantify their
+ 
+
+ align:start position:0%
+systems and integrals quantify their
+cumulative properties
+
+ align:start position:0%
+cumulative properties
+ 
+
+ align:start position:0%
+cumulative properties
+hello my name is john mcgreevey i'm a
+
+ align:start position:0%
+hello my name is john mcgreevey i'm a
+ 
+
+ align:start position:0%
+hello my name is john mcgreevey i'm a
+professor in the physics department at
+
+ align:start position:0%
+professor in the physics department at
+ 
+
+ align:start position:0%
+professor in the physics department at
+mit
+
+ align:start position:0%
+mit
+ 
+
+ align:start position:0%
+mit
+and today i'll be talking with you about
+
+ align:start position:0%
+and today i'll be talking with you about
+ 
+
+ align:start position:0%
+and today i'll be talking with you about
+the electric field and electric
+
+ align:start position:0%
+the electric field and electric
+ 
+
+ align:start position:0%
+the electric field and electric
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+to get the most out of this video you
+
+ align:start position:0%
+to get the most out of this video you
+ 
+
+ align:start position:0%
+to get the most out of this video you
+should already have some exposure to the
+
+ align:start position:0%
+should already have some exposure to the
+ 
+
+ align:start position:0%
+should already have some exposure to the
+electric field and electric potential
+
+ align:start position:0%
+electric field and electric potential
+ 
+
+ align:start position:0%
+electric field and electric potential
+you should be able to take a
+
+ align:start position:0%
+you should be able to take a
+ 
+
+ align:start position:0%
+you should be able to take a
+mathematical expression for the field
+
+ align:start position:0%
+mathematical expression for the field
+ 
+
+ align:start position:0%
+mathematical expression for the field
+and obtain the potential and vice versa
+
+ align:start position:0%
+and obtain the potential and vice versa
+ 
+
+ align:start position:0%
+and obtain the potential and vice versa
+you should also know how to draw
+
+ align:start position:0%
+you should also know how to draw
+ 
+
+ align:start position:0%
+you should also know how to draw
+equipotential surfaces
+
+ align:start position:0%
+equipotential surfaces
+ 
+
+ align:start position:0%
+equipotential surfaces
+and electric field vectors throughout
+
+ align:start position:0%
+and electric field vectors throughout
+ 
+
+ align:start position:0%
+and electric field vectors throughout
+this video
+
+ align:start position:0%
+this video
+ 
+
+ align:start position:0%
+this video
+our goal is to help you gain a clearer
+
+ align:start position:0%
+our goal is to help you gain a clearer
+ 
+
+ align:start position:0%
+our goal is to help you gain a clearer
+picture of the electric field
+
+ align:start position:0%
+picture of the electric field
+ 
+
+ align:start position:0%
+picture of the electric field
+and the electric potential by the end of
+
+ align:start position:0%
+and the electric potential by the end of
+ 
+
+ align:start position:0%
+and the electric potential by the end of
+the video you should be able to describe
+
+ align:start position:0%
+the video you should be able to describe
+ 
+
+ align:start position:0%
+the video you should be able to describe
+the process of electrical breakdown
+
+ align:start position:0%
+the process of electrical breakdown
+ 
+
+ align:start position:0%
+the process of electrical breakdown
+by using either the field or the
+
+ align:start position:0%
+by using either the field or the
+ 
+
+ align:start position:0%
+by using either the field or the
+potential let's start with a review of
+
+ align:start position:0%
+potential let's start with a review of
+ 
+
+ align:start position:0%
+potential let's start with a review of
+electric field and electric potential
+
+ align:start position:0%
+electric field and electric potential
+ 
+
+ align:start position:0%
+electric field and electric potential
+first we'll describe them conceptually
+
+ align:start position:0%
+first we'll describe them conceptually
+ 
+
+ align:start position:0%
+first we'll describe them conceptually
+then we'll show the mathematical
+
+ align:start position:0%
+then we'll show the mathematical
+ 
+
+ align:start position:0%
+then we'll show the mathematical
+relationship between them and show some
+
+ align:start position:0%
+relationship between them and show some
+ 
+
+ align:start position:0%
+relationship between them and show some
+of their typical visual representations
+
+ align:start position:0%
+of their typical visual representations
+ 
+
+ align:start position:0%
+of their typical visual representations
+first let's see what you remember take
+
+ align:start position:0%
+first let's see what you remember take
+ 
+
+ align:start position:0%
+first let's see what you remember take
+out a piece of paper
+
+ align:start position:0%
+out a piece of paper
+ 
+
+ align:start position:0%
+out a piece of paper
+and write down everything you remember
+
+ align:start position:0%
+and write down everything you remember
+ 
+
+ align:start position:0%
+and write down everything you remember
+about the electric field in the electric
+
+ align:start position:0%
+about the electric field in the electric
+ 
+
+ align:start position:0%
+about the electric field in the electric
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+try to concentrate on their similarities
+
+ align:start position:0%
+try to concentrate on their similarities
+ 
+
+ align:start position:0%
+try to concentrate on their similarities
+and differences
+
+ align:start position:0%
+and differences
+ 
+
+ align:start position:0%
+and differences
+pause the video to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now you can compare the list you made to
+
+ align:start position:0%
+now you can compare the list you made to
+ 
+
+ align:start position:0%
+now you can compare the list you made to
+our list
+
+ align:start position:0%
+our list
+ 
+
+ align:start position:0%
+our list
+the electric field is generated by
+
+ align:start position:0%
+the electric field is generated by
+ 
+
+ align:start position:0%
+the electric field is generated by
+electric charges and extends an infinite
+
+ align:start position:0%
+electric charges and extends an infinite
+ 
+
+ align:start position:0%
+electric charges and extends an infinite
+distance from them
+
+ align:start position:0%
+distance from them
+ 
+
+ align:start position:0%
+distance from them
+if you bring a second electric charge
+
+ align:start position:0%
+if you bring a second electric charge
+ 
+
+ align:start position:0%
+if you bring a second electric charge
+into a region of electric field
+
+ align:start position:0%
+into a region of electric field
+ 
+
+ align:start position:0%
+into a region of electric field
+there will be a force exerted on it like
+
+ align:start position:0%
+there will be a force exerted on it like
+ 
+
+ align:start position:0%
+there will be a force exerted on it like
+all forces
+
+ align:start position:0%
+all forces
+ 
+
+ align:start position:0%
+all forces
+that force has a magnitude and a
+
+ align:start position:0%
+that force has a magnitude and a
+ 
+
+ align:start position:0%
+that force has a magnitude and a
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+the stronger the charge is the more
+
+ align:start position:0%
+the stronger the charge is the more
+ 
+
+ align:start position:0%
+the stronger the charge is the more
+force will be applied to it
+
+ align:start position:0%
+force will be applied to it
+ 
+
+ align:start position:0%
+force will be applied to it
+the electric field is a vector quantity
+
+ align:start position:0%
+the electric field is a vector quantity
+ 
+
+ align:start position:0%
+the electric field is a vector quantity
+it has a vector value at every point in
+
+ align:start position:0%
+it has a vector value at every point in
+ 
+
+ align:start position:0%
+it has a vector value at every point in
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+measured in newtons per coulomb or volts
+
+ align:start position:0%
+measured in newtons per coulomb or volts
+ 
+
+ align:start position:0%
+measured in newtons per coulomb or volts
+per meter
+
+ align:start position:0%
+per meter
+ 
+
+ align:start position:0%
+per meter
+much like the electric field electric
+
+ align:start position:0%
+much like the electric field electric
+ 
+
+ align:start position:0%
+much like the electric field electric
+potentials are created by charges
+
+ align:start position:0%
+potentials are created by charges
+ 
+
+ align:start position:0%
+potentials are created by charges
+and extend an infinite distance from
+
+ align:start position:0%
+and extend an infinite distance from
+ 
+
+ align:start position:0%
+and extend an infinite distance from
+them if you bring a second charge into a
+
+ align:start position:0%
+them if you bring a second charge into a
+ 
+
+ align:start position:0%
+them if you bring a second charge into a
+region of electrical potential
+
+ align:start position:0%
+region of electrical potential
+ 
+
+ align:start position:0%
+region of electrical potential
+that second charge will gain or lose
+
+ align:start position:0%
+that second charge will gain or lose
+ 
+
+ align:start position:0%
+that second charge will gain or lose
+potential energy
+
+ align:start position:0%
+potential energy
+ 
+
+ align:start position:0%
+potential energy
+the stronger that charge the more its
+
+ align:start position:0%
+the stronger that charge the more its
+ 
+
+ align:start position:0%
+the stronger that charge the more its
+potential energy will change
+
+ align:start position:0%
+potential energy will change
+ 
+
+ align:start position:0%
+potential energy will change
+unlike the electric field the electric
+
+ align:start position:0%
+unlike the electric field the electric
+ 
+
+ align:start position:0%
+unlike the electric field the electric
+potential is a scalar quantity
+
+ align:start position:0%
+potential is a scalar quantity
+ 
+
+ align:start position:0%
+potential is a scalar quantity
+which means that everywhere you look you
+
+ align:start position:0%
+which means that everywhere you look you
+ 
+
+ align:start position:0%
+which means that everywhere you look you
+can find one number that represents the
+
+ align:start position:0%
+can find one number that represents the
+ 
+
+ align:start position:0%
+can find one number that represents the
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+measured in joules per coulomb
+
+ align:start position:0%
+measured in joules per coulomb
+ 
+
+ align:start position:0%
+measured in joules per coulomb
+let's look at two ways to envision an
+
+ align:start position:0%
+let's look at two ways to envision an
+ 
+
+ align:start position:0%
+let's look at two ways to envision an
+electric potential for a positively
+
+ align:start position:0%
+electric potential for a positively
+ 
+
+ align:start position:0%
+electric potential for a positively
+charged line near the origin
+
+ align:start position:0%
+charged line near the origin
+ 
+
+ align:start position:0%
+charged line near the origin
+we're going to look at this in two
+
+ align:start position:0%
+we're going to look at this in two
+ 
+
+ align:start position:0%
+we're going to look at this in two
+dimensions to make things easier to see
+
+ align:start position:0%
+dimensions to make things easier to see
+ 
+
+ align:start position:0%
+dimensions to make things easier to see
+we can draw the level curves for the
+
+ align:start position:0%
+we can draw the level curves for the
+ 
+
+ align:start position:0%
+we can draw the level curves for the
+electric potential function
+
+ align:start position:0%
+electric potential function
+ 
+
+ align:start position:0%
+electric potential function
+these are called equipotential lines
+
+ align:start position:0%
+these are called equipotential lines
+ 
+
+ align:start position:0%
+these are called equipotential lines
+because the value of the potential
+
+ align:start position:0%
+because the value of the potential
+ 
+
+ align:start position:0%
+because the value of the potential
+is equal at every point on a given line
+
+ align:start position:0%
+is equal at every point on a given line
+ 
+
+ align:start position:0%
+is equal at every point on a given line
+for instance we might draw lines every
+
+ align:start position:0%
+for instance we might draw lines every
+ 
+
+ align:start position:0%
+for instance we might draw lines every
+10 volts
+
+ align:start position:0%
+10 volts
+ 
+
+ align:start position:0%
+10 volts
+if we plot the potential on the vertical
+
+ align:start position:0%
+if we plot the potential on the vertical
+ 
+
+ align:start position:0%
+if we plot the potential on the vertical
+axis we end up with this mountain-like
+
+ align:start position:0%
+axis we end up with this mountain-like
+ 
+
+ align:start position:0%
+axis we end up with this mountain-like
+shape
+
+ align:start position:0%
+shape
+ 
+
+ align:start position:0%
+shape
+we can imagine positive charges rolling
+
+ align:start position:0%
+we can imagine positive charges rolling
+ 
+
+ align:start position:0%
+we can imagine positive charges rolling
+down the mountain
+
+ align:start position:0%
+down the mountain
+ 
+
+ align:start position:0%
+down the mountain
+as they're pushed away from our line
+
+ align:start position:0%
+as they're pushed away from our line
+ 
+
+ align:start position:0%
+as they're pushed away from our line
+charge we can also sketch the electric
+
+ align:start position:0%
+charge we can also sketch the electric
+ 
+
+ align:start position:0%
+charge we can also sketch the electric
+field around a line charge
+
+ align:start position:0%
+field around a line charge
+ 
+
+ align:start position:0%
+field around a line charge
+if we pick regularly spaced points at
+
+ align:start position:0%
+if we pick regularly spaced points at
+ 
+
+ align:start position:0%
+if we pick regularly spaced points at
+which to draw our electric field vectors
+
+ align:start position:0%
+which to draw our electric field vectors
+ 
+
+ align:start position:0%
+which to draw our electric field vectors
+we end up with a picture like this one
+
+ align:start position:0%
+we end up with a picture like this one
+ 
+
+ align:start position:0%
+we end up with a picture like this one
+each vector shows the direction and
+
+ align:start position:0%
+each vector shows the direction and
+ 
+
+ align:start position:0%
+each vector shows the direction and
+strength of the electric field at that
+
+ align:start position:0%
+strength of the electric field at that
+ 
+
+ align:start position:0%
+strength of the electric field at that
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+the longer the arrow stronger the field
+
+ align:start position:0%
+the longer the arrow stronger the field
+ 
+
+ align:start position:0%
+the longer the arrow stronger the field
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+here you might imagine the arrow is
+
+ align:start position:0%
+here you might imagine the arrow is
+ 
+
+ align:start position:0%
+here you might imagine the arrow is
+pushing a positive charge away from our
+
+ align:start position:0%
+pushing a positive charge away from our
+ 
+
+ align:start position:0%
+pushing a positive charge away from our
+line charge
+
+ align:start position:0%
+line charge
+ 
+
+ align:start position:0%
+line charge
+displaying both the equipotential lines
+
+ align:start position:0%
+displaying both the equipotential lines
+ 
+
+ align:start position:0%
+displaying both the equipotential lines
+and the field vectors at once
+
+ align:start position:0%
+and the field vectors at once
+ 
+
+ align:start position:0%
+and the field vectors at once
+we get this picture you can see that the
+
+ align:start position:0%
+we get this picture you can see that the
+ 
+
+ align:start position:0%
+we get this picture you can see that the
+equipotential lines
+
+ align:start position:0%
+equipotential lines
+ 
+
+ align:start position:0%
+equipotential lines
+are always perpendicular to the field
+
+ align:start position:0%
+are always perpendicular to the field
+ 
+
+ align:start position:0%
+are always perpendicular to the field
+since charges create both fields and
+
+ align:start position:0%
+since charges create both fields and
+ 
+
+ align:start position:0%
+since charges create both fields and
+potentials both will be present
+
+ align:start position:0%
+potentials both will be present
+ 
+
+ align:start position:0%
+potentials both will be present
+all the time though we might only draw
+
+ align:start position:0%
+all the time though we might only draw
+ 
+
+ align:start position:0%
+all the time though we might only draw
+one or the other
+
+ align:start position:0%
+one or the other
+ 
+
+ align:start position:0%
+one or the other
+the field and potential are related
+
+ align:start position:0%
+the field and potential are related
+ 
+
+ align:start position:0%
+the field and potential are related
+mathematically through the gradient
+
+ align:start position:0%
+mathematically through the gradient
+ 
+
+ align:start position:0%
+mathematically through the gradient
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+as a vector operator the gradient turns
+
+ align:start position:0%
+as a vector operator the gradient turns
+ 
+
+ align:start position:0%
+as a vector operator the gradient turns
+the scalar potential
+
+ align:start position:0%
+the scalar potential
+ 
+
+ align:start position:0%
+the scalar potential
+into a vector field to go in the other
+
+ align:start position:0%
+into a vector field to go in the other
+ 
+
+ align:start position:0%
+into a vector field to go in the other
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+a line integral of the electric field
+
+ align:start position:0%
+a line integral of the electric field
+ 
+
+ align:start position:0%
+a line integral of the electric field
+turns that vector field into a scalar
+
+ align:start position:0%
+turns that vector field into a scalar
+ 
+
+ align:start position:0%
+turns that vector field into a scalar
+electric potential
+
+ align:start position:0%
+electric potential
+ 
+
+ align:start position:0%
+electric potential
+the negative sign that appears in both
+
+ align:start position:0%
+the negative sign that appears in both
+ 
+
+ align:start position:0%
+the negative sign that appears in both
+equations is important
+
+ align:start position:0%
+equations is important
+ 
+
+ align:start position:0%
+equations is important
+the electric field points in the
+
+ align:start position:0%
+the electric field points in the
+ 
+
+ align:start position:0%
+the electric field points in the
+opposite direction from any changes in
+
+ align:start position:0%
+opposite direction from any changes in
+ 
+
+ align:start position:0%
+opposite direction from any changes in
+the potential
+
+ align:start position:0%
+the potential
+ 
+
+ align:start position:0%
+the potential
+if the electric potential increases in a
+
+ align:start position:0%
+if the electric potential increases in a
+ 
+
+ align:start position:0%
+if the electric potential increases in a
+particular direction
+
+ align:start position:0%
+particular direction
+ 
+
+ align:start position:0%
+particular direction
+the electric field points in the
+
+ align:start position:0%
+the electric field points in the
+ 
+
+ align:start position:0%
+the electric field points in the
+opposite direction
+
+ align:start position:0%
+opposite direction
+ 
+
+ align:start position:0%
+opposite direction
+we're going to use something called
+
+ align:start position:0%
+we're going to use something called
+ 
+
+ align:start position:0%
+we're going to use something called
+electrical breakdown to illustrate our
+
+ align:start position:0%
+electrical breakdown to illustrate our
+ 
+
+ align:start position:0%
+electrical breakdown to illustrate our
+concepts today
+
+ align:start position:0%
+concepts today
+ 
+
+ align:start position:0%
+concepts today
+we'll start with an example give a
+
+ align:start position:0%
+we'll start with an example give a
+ 
+
+ align:start position:0%
+we'll start with an example give a
+definition
+
+ align:start position:0%
+definition
+ 
+
+ align:start position:0%
+definition
+then go into an explanation of the
+
+ align:start position:0%
+then go into an explanation of the
+ 
+
+ align:start position:0%
+then go into an explanation of the
+phenomenon
+
+ align:start position:0%
+phenomenon
+ 
+
+ align:start position:0%
+phenomenon
+here's a clip from the boston museum of
+
+ align:start position:0%
+here's a clip from the boston museum of
+ 
+
+ align:start position:0%
+here's a clip from the boston museum of
+science to demonstrate the phenomenon
+
+ align:start position:0%
+science to demonstrate the phenomenon
+ 
+
+ align:start position:0%
+science to demonstrate the phenomenon
+well my name is karen i'm one of the
+
+ align:start position:0%
+well my name is karen i'm one of the
+ 
+
+ align:start position:0%
+well my name is karen i'm one of the
+educators here at the museum of science
+
+ align:start position:0%
+educators here at the museum of science
+ 
+
+ align:start position:0%
+educators here at the museum of science
+the large machine that you see behind me
+
+ align:start position:0%
+the large machine that you see behind me
+ 
+
+ align:start position:0%
+the large machine that you see behind me
+with the two big balls on the top
+
+ align:start position:0%
+with the two big balls on the top
+ 
+
+ align:start position:0%
+with the two big balls on the top
+is called a van de graaff generator it
+
+ align:start position:0%
+is called a van de graaff generator it
+ 
+
+ align:start position:0%
+is called a van de graaff generator it
+is actually the world's
+
+ align:start position:0%
+is actually the world's
+ 
+
+ align:start position:0%
+is actually the world's
+largest air insulated van de graaff
+
+ align:start position:0%
+largest air insulated van de graaff
+ 
+
+ align:start position:0%
+largest air insulated van de graaff
+generator
+
+ align:start position:0%
+generator
+ 
+
+ align:start position:0%
+generator
+it was built by dr robert van der graal
+
+ align:start position:0%
+it was built by dr robert van der graal
+ 
+
+ align:start position:0%
+it was built by dr robert van der graal
+himself these days we do not use it as
+
+ align:start position:0%
+himself these days we do not use it as
+ 
+
+ align:start position:0%
+himself these days we do not use it as
+an atom smasher we use it as
+
+ align:start position:0%
+an atom smasher we use it as
+ 
+
+ align:start position:0%
+an atom smasher we use it as
+an example of lightning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and now we need to find out what
+
+ align:start position:0%
+here and now we need to find out what
+ 
+
+ align:start position:0%
+here and now we need to find out what
+happens if i strike this cave there were
+
+ align:start position:0%
+happens if i strike this cave there were
+ 
+
+ align:start position:0%
+happens if i strike this cave there were
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+million volts of electricity are you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ready
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so far so good here we go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's quite a dramatic demonstration
+
+ align:start position:0%
+that's quite a dramatic demonstration
+ 
+
+ align:start position:0%
+that's quite a dramatic demonstration
+let's look at this in a little more
+
+ align:start position:0%
+let's look at this in a little more
+ 
+
+ align:start position:0%
+let's look at this in a little more
+depth
+
+ align:start position:0%
+depth
+ 
+
+ align:start position:0%
+depth
+electrical breakdown is defined as the
+
+ align:start position:0%
+electrical breakdown is defined as the
+ 
+
+ align:start position:0%
+electrical breakdown is defined as the
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+by which an insulating material in a
+
+ align:start position:0%
+by which an insulating material in a
+ 
+
+ align:start position:0%
+by which an insulating material in a
+strong electric field
+
+ align:start position:0%
+strong electric field
+ 
+
+ align:start position:0%
+strong electric field
+becomes electrically conductive the
+
+ align:start position:0%
+becomes electrically conductive the
+ 
+
+ align:start position:0%
+becomes electrically conductive the
+material actually changes
+
+ align:start position:0%
+material actually changes
+ 
+
+ align:start position:0%
+material actually changes
+from being an insulator to being a
+
+ align:start position:0%
+from being an insulator to being a
+ 
+
+ align:start position:0%
+from being an insulator to being a
+conductor in the clip you saw
+
+ align:start position:0%
+conductor in the clip you saw
+ 
+
+ align:start position:0%
+conductor in the clip you saw
+this happened in the air near the van de
+
+ align:start position:0%
+this happened in the air near the van de
+ 
+
+ align:start position:0%
+this happened in the air near the van de
+graaff generator
+
+ align:start position:0%
+graaff generator
+ 
+
+ align:start position:0%
+graaff generator
+and a large electric spark resulted you
+
+ align:start position:0%
+and a large electric spark resulted you
+ 
+
+ align:start position:0%
+and a large electric spark resulted you
+may sometimes hear this referred to as
+
+ align:start position:0%
+may sometimes hear this referred to as
+ 
+
+ align:start position:0%
+may sometimes hear this referred to as
+breakdown potential
+
+ align:start position:0%
+breakdown potential
+ 
+
+ align:start position:0%
+breakdown potential
+or breakdown voltage which is the same
+
+ align:start position:0%
+or breakdown voltage which is the same
+ 
+
+ align:start position:0%
+or breakdown voltage which is the same
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+the exact value of the electric field
+
+ align:start position:0%
+the exact value of the electric field
+ 
+
+ align:start position:0%
+the exact value of the electric field
+needed depends on many factors
+
+ align:start position:0%
+needed depends on many factors
+ 
+
+ align:start position:0%
+needed depends on many factors
+including distance humidity temperature
+
+ align:start position:0%
+including distance humidity temperature
+ 
+
+ align:start position:0%
+including distance humidity temperature
+and the material itself
+
+ align:start position:0%
+and the material itself
+ 
+
+ align:start position:0%
+and the material itself
+here is a simplified explanation of how
+
+ align:start position:0%
+here is a simplified explanation of how
+ 
+
+ align:start position:0%
+here is a simplified explanation of how
+electrical breakdown works in air
+
+ align:start position:0%
+electrical breakdown works in air
+ 
+
+ align:start position:0%
+electrical breakdown works in air
+consider this house in a thunderstorm
+
+ align:start position:0%
+consider this house in a thunderstorm
+ 
+
+ align:start position:0%
+consider this house in a thunderstorm
+if we zoom in on the air above the house
+
+ align:start position:0%
+if we zoom in on the air above the house
+ 
+
+ align:start position:0%
+if we zoom in on the air above the house
+we can see the molecules of gas in the
+
+ align:start position:0%
+we can see the molecules of gas in the
+ 
+
+ align:start position:0%
+we can see the molecules of gas in the
+air
+
+ align:start position:0%
+air
+ 
+
+ align:start position:0%
+air
+thunderstorms involve strong electric
+
+ align:start position:0%
+thunderstorms involve strong electric
+ 
+
+ align:start position:0%
+thunderstorms involve strong electric
+fields and high
+
+ align:start position:0%
+fields and high
+ 
+
+ align:start position:0%
+fields and high
+electric potential differences we can
+
+ align:start position:0%
+electric potential differences we can
+ 
+
+ align:start position:0%
+electric potential differences we can
+represent those on our diagram
+
+ align:start position:0%
+represent those on our diagram
+ 
+
+ align:start position:0%
+represent those on our diagram
+imagine that one electron is pulled from
+
+ align:start position:0%
+imagine that one electron is pulled from
+ 
+
+ align:start position:0%
+imagine that one electron is pulled from
+its atom by the strong electric field
+
+ align:start position:0%
+its atom by the strong electric field
+ 
+
+ align:start position:0%
+its atom by the strong electric field
+because the electron is negatively
+
+ align:start position:0%
+because the electron is negatively
+ 
+
+ align:start position:0%
+because the electron is negatively
+charged it will accelerate against the
+
+ align:start position:0%
+charged it will accelerate against the
+ 
+
+ align:start position:0%
+charged it will accelerate against the
+electric field
+
+ align:start position:0%
+electric field
+ 
+
+ align:start position:0%
+electric field
+and will eventually collide with another
+
+ align:start position:0%
+and will eventually collide with another
+ 
+
+ align:start position:0%
+and will eventually collide with another
+atom that collision might knock another
+
+ align:start position:0%
+atom that collision might knock another
+ 
+
+ align:start position:0%
+atom that collision might knock another
+electron loose
+
+ align:start position:0%
+electron loose
+ 
+
+ align:start position:0%
+electron loose
+now there will be two electrons
+
+ align:start position:0%
+now there will be two electrons
+ 
+
+ align:start position:0%
+now there will be two electrons
+accelerating so a single electron
+
+ align:start position:0%
+accelerating so a single electron
+ 
+
+ align:start position:0%
+accelerating so a single electron
+can create a chain reaction where many
+
+ align:start position:0%
+can create a chain reaction where many
+ 
+
+ align:start position:0%
+can create a chain reaction where many
+atoms lose their electrons
+
+ align:start position:0%
+atoms lose their electrons
+ 
+
+ align:start position:0%
+atoms lose their electrons
+this creates a region of ionized air air
+
+ align:start position:0%
+this creates a region of ionized air air
+ 
+
+ align:start position:0%
+this creates a region of ionized air air
+is normally a good insulator
+
+ align:start position:0%
+is normally a good insulator
+ 
+
+ align:start position:0%
+is normally a good insulator
+but the presence of those ions allows it
+
+ align:start position:0%
+but the presence of those ions allows it
+ 
+
+ align:start position:0%
+but the presence of those ions allows it
+to conduct electricity
+
+ align:start position:0%
+to conduct electricity
+ 
+
+ align:start position:0%
+to conduct electricity
+resulting in a lightning bulb let's use
+
+ align:start position:0%
+resulting in a lightning bulb let's use
+ 
+
+ align:start position:0%
+resulting in a lightning bulb let's use
+the electric field and electric
+
+ align:start position:0%
+the electric field and electric
+ 
+
+ align:start position:0%
+the electric field and electric
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+to investigate the situation further
+
+ align:start position:0%
+to investigate the situation further
+ 
+
+ align:start position:0%
+to investigate the situation further
+here are the van de graaff generators
+
+ align:start position:0%
+here are the van de graaff generators
+ 
+
+ align:start position:0%
+here are the van de graaff generators
+from the video
+
+ align:start position:0%
+from the video
+ 
+
+ align:start position:0%
+from the video
+charged up with a metal ball as a target
+
+ align:start position:0%
+charged up with a metal ball as a target
+ 
+
+ align:start position:0%
+charged up with a metal ball as a target
+let's take a simplified version of the
+
+ align:start position:0%
+let's take a simplified version of the
+ 
+
+ align:start position:0%
+let's take a simplified version of the
+situation shown draw the equipotential
+
+ align:start position:0%
+situation shown draw the equipotential
+ 
+
+ align:start position:0%
+situation shown draw the equipotential
+surfaces around these two objects
+
+ align:start position:0%
+surfaces around these two objects
+ 
+
+ align:start position:0%
+surfaces around these two objects
+and then draw in the electric field
+
+ align:start position:0%
+and then draw in the electric field
+ 
+
+ align:start position:0%
+and then draw in the electric field
+arrows as well
+
+ align:start position:0%
+arrows as well
+ 
+
+ align:start position:0%
+arrows as well
+you can ignore the presence of the
+
+ align:start position:0%
+you can ignore the presence of the
+ 
+
+ align:start position:0%
+you can ignore the presence of the
+support pillars here are two hints
+
+ align:start position:0%
+support pillars here are two hints
+ 
+
+ align:start position:0%
+support pillars here are two hints
+first the small metal ball is grounded
+
+ align:start position:0%
+first the small metal ball is grounded
+ 
+
+ align:start position:0%
+first the small metal ball is grounded
+or earthed
+
+ align:start position:0%
+or earthed
+ 
+
+ align:start position:0%
+or earthed
+with an electrical potential of zero
+
+ align:start position:0%
+with an electrical potential of zero
+ 
+
+ align:start position:0%
+with an electrical potential of zero
+second the electrical charge on the
+
+ align:start position:0%
+second the electrical charge on the
+ 
+
+ align:start position:0%
+second the electrical charge on the
+generator
+
+ align:start position:0%
+generator
+ 
+
+ align:start position:0%
+generator
+will spread itself equally over the
+
+ align:start position:0%
+will spread itself equally over the
+ 
+
+ align:start position:0%
+will spread itself equally over the
+surface of the conducting spheres
+
+ align:start position:0%
+surface of the conducting spheres
+ 
+
+ align:start position:0%
+surface of the conducting spheres
+pause the video here to draw the
+
+ align:start position:0%
+pause the video here to draw the
+ 
+
+ align:start position:0%
+pause the video here to draw the
+equipotential lines and the field
+
+ align:start position:0%
+equipotential lines and the field
+ 
+
+ align:start position:0%
+equipotential lines and the field
+vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's another picture of the generator
+
+ align:start position:0%
+here's another picture of the generator
+ 
+
+ align:start position:0%
+here's another picture of the generator
+with the target ball nearby
+
+ align:start position:0%
+with the target ball nearby
+ 
+
+ align:start position:0%
+with the target ball nearby
+this picture is too complex let's create
+
+ align:start position:0%
+this picture is too complex let's create
+ 
+
+ align:start position:0%
+this picture is too complex let's create
+a simpler version of the picture
+
+ align:start position:0%
+a simpler version of the picture
+ 
+
+ align:start position:0%
+a simpler version of the picture
+that's better now we can draw in the
+
+ align:start position:0%
+that's better now we can draw in the
+ 
+
+ align:start position:0%
+that's better now we can draw in the
+lines
+
+ align:start position:0%
+lines
+ 
+
+ align:start position:0%
+lines
+our equipotential lines will hug the
+
+ align:start position:0%
+our equipotential lines will hug the
+ 
+
+ align:start position:0%
+our equipotential lines will hug the
+surface of the conductors
+
+ align:start position:0%
+surface of the conductors
+ 
+
+ align:start position:0%
+surface of the conductors
+when they're nearby because the charge
+
+ align:start position:0%
+when they're nearby because the charge
+ 
+
+ align:start position:0%
+when they're nearby because the charge
+is spread evenly across the surface of
+
+ align:start position:0%
+is spread evenly across the surface of
+ 
+
+ align:start position:0%
+is spread evenly across the surface of
+the conductor
+
+ align:start position:0%
+the conductor
+ 
+
+ align:start position:0%
+the conductor
+the whole surface will be at the same
+
+ align:start position:0%
+the whole surface will be at the same
+ 
+
+ align:start position:0%
+the whole surface will be at the same
+electric potential the echo potential
+
+ align:start position:0%
+electric potential the echo potential
+ 
+
+ align:start position:0%
+electric potential the echo potential
+lines will tend to be smoother when
+
+ align:start position:0%
+lines will tend to be smoother when
+ 
+
+ align:start position:0%
+lines will tend to be smoother when
+farther away from their conductors
+
+ align:start position:0%
+farther away from their conductors
+ 
+
+ align:start position:0%
+farther away from their conductors
+because the electric potential of the
+
+ align:start position:0%
+because the electric potential of the
+ 
+
+ align:start position:0%
+because the electric potential of the
+vendor graph generator gets up to about
+
+ align:start position:0%
+vendor graph generator gets up to about
+ 
+
+ align:start position:0%
+vendor graph generator gets up to about
+one million volts
+
+ align:start position:0%
+one million volts
+ 
+
+ align:start position:0%
+one million volts
+or a thousand kilovolts and we have
+
+ align:start position:0%
+or a thousand kilovolts and we have
+ 
+
+ align:start position:0%
+or a thousand kilovolts and we have
+drawn eight lines in the picture
+
+ align:start position:0%
+drawn eight lines in the picture
+ 
+
+ align:start position:0%
+drawn eight lines in the picture
+each line must represent a difference of
+
+ align:start position:0%
+each line must represent a difference of
+ 
+
+ align:start position:0%
+each line must represent a difference of
+about 125 kilovolts
+
+ align:start position:0%
+about 125 kilovolts
+ 
+
+ align:start position:0%
+about 125 kilovolts
+in this view we have colored in the
+
+ align:start position:0%
+in this view we have colored in the
+ 
+
+ align:start position:0%
+in this view we have colored in the
+regions where the equipotential lines
+
+ align:start position:0%
+regions where the equipotential lines
+ 
+
+ align:start position:0%
+regions where the equipotential lines
+are either more closely packed or less
+
+ align:start position:0%
+are either more closely packed or less
+ 
+
+ align:start position:0%
+are either more closely packed or less
+closely packed
+
+ align:start position:0%
+closely packed
+ 
+
+ align:start position:0%
+closely packed
+in the blue area with the close packed
+
+ align:start position:0%
+in the blue area with the close packed
+ 
+
+ align:start position:0%
+in the blue area with the close packed
+lines
+
+ align:start position:0%
+lines
+ 
+
+ align:start position:0%
+lines
+gradient of the potential is larger
+
+ align:start position:0%
+gradient of the potential is larger
+ 
+
+ align:start position:0%
+gradient of the potential is larger
+because the electric field is
+
+ align:start position:0%
+because the electric field is
+ 
+
+ align:start position:0%
+because the electric field is
+proportional to the gradient of the
+
+ align:start position:0%
+proportional to the gradient of the
+ 
+
+ align:start position:0%
+proportional to the gradient of the
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+the places where our lines are more
+
+ align:start position:0%
+the places where our lines are more
+ 
+
+ align:start position:0%
+the places where our lines are more
+closely packed will have a stronger
+
+ align:start position:0%
+closely packed will have a stronger
+ 
+
+ align:start position:0%
+closely packed will have a stronger
+electric field
+
+ align:start position:0%
+electric field
+ 
+
+ align:start position:0%
+electric field
+in the red areas where equipotential
+
+ align:start position:0%
+in the red areas where equipotential
+ 
+
+ align:start position:0%
+in the red areas where equipotential
+lines are far apart
+
+ align:start position:0%
+lines are far apart
+ 
+
+ align:start position:0%
+lines are far apart
+the gradient of the potential is smaller
+
+ align:start position:0%
+the gradient of the potential is smaller
+ 
+
+ align:start position:0%
+the gradient of the potential is smaller
+therefore the electric field will be
+
+ align:start position:0%
+therefore the electric field will be
+ 
+
+ align:start position:0%
+therefore the electric field will be
+weaker
+
+ align:start position:0%
+weaker
+ 
+
+ align:start position:0%
+weaker
+we can use this as a guide when drawing
+
+ align:start position:0%
+we can use this as a guide when drawing
+ 
+
+ align:start position:0%
+we can use this as a guide when drawing
+our field vectors
+
+ align:start position:0%
+our field vectors
+ 
+
+ align:start position:0%
+our field vectors
+let's draw in those electric field
+
+ align:start position:0%
+let's draw in those electric field
+ 
+
+ align:start position:0%
+let's draw in those electric field
+vectors now we have assumed here that
+
+ align:start position:0%
+vectors now we have assumed here that
+ 
+
+ align:start position:0%
+vectors now we have assumed here that
+the generator becomes positively charged
+
+ align:start position:0%
+the generator becomes positively charged
+ 
+
+ align:start position:0%
+the generator becomes positively charged
+but if it were negatively charged we
+
+ align:start position:0%
+but if it were negatively charged we
+ 
+
+ align:start position:0%
+but if it were negatively charged we
+could simply reverse the direction of
+
+ align:start position:0%
+could simply reverse the direction of
+ 
+
+ align:start position:0%
+could simply reverse the direction of
+our arrows
+
+ align:start position:0%
+our arrows
+ 
+
+ align:start position:0%
+our arrows
+look carefully our field arrows are
+
+ align:start position:0%
+look carefully our field arrows are
+ 
+
+ align:start position:0%
+look carefully our field arrows are
+perpendicular to the equipotential
+
+ align:start position:0%
+perpendicular to the equipotential
+ 
+
+ align:start position:0%
+perpendicular to the equipotential
+surfaces at all points
+
+ align:start position:0%
+surfaces at all points
+ 
+
+ align:start position:0%
+surfaces at all points
+check your own diagram is this true on
+
+ align:start position:0%
+check your own diagram is this true on
+ 
+
+ align:start position:0%
+check your own diagram is this true on
+yours as well
+
+ align:start position:0%
+yours as well
+ 
+
+ align:start position:0%
+yours as well
+our field arrows are longer where the
+
+ align:start position:0%
+our field arrows are longer where the
+ 
+
+ align:start position:0%
+our field arrows are longer where the
+equipotential lines are more closely
+
+ align:start position:0%
+equipotential lines are more closely
+ 
+
+ align:start position:0%
+equipotential lines are more closely
+packed
+
+ align:start position:0%
+packed
+ 
+
+ align:start position:0%
+packed
+is this true on your diagram if you need
+
+ align:start position:0%
+is this true on your diagram if you need
+ 
+
+ align:start position:0%
+is this true on your diagram if you need
+to revise your diagram or draw a new one
+
+ align:start position:0%
+to revise your diagram or draw a new one
+ 
+
+ align:start position:0%
+to revise your diagram or draw a new one
+do so now if you have questions for your
+
+ align:start position:0%
+do so now if you have questions for your
+ 
+
+ align:start position:0%
+do so now if you have questions for your
+teacher here's a chance to ask them
+
+ align:start position:0%
+teacher here's a chance to ask them
+ 
+
+ align:start position:0%
+teacher here's a chance to ask them
+pause the video here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some of you may be confused by the
+
+ align:start position:0%
+some of you may be confused by the
+ 
+
+ align:start position:0%
+some of you may be confused by the
+terminology that's used for this
+
+ align:start position:0%
+terminology that's used for this
+ 
+
+ align:start position:0%
+terminology that's used for this
+phenomenon
+
+ align:start position:0%
+phenomenon
+ 
+
+ align:start position:0%
+phenomenon
+many people refer to the breakdown
+
+ align:start position:0%
+many people refer to the breakdown
+ 
+
+ align:start position:0%
+many people refer to the breakdown
+potential required to create a spark
+
+ align:start position:0%
+potential required to create a spark
+ 
+
+ align:start position:0%
+potential required to create a spark
+however you may have noticed that the
+
+ align:start position:0%
+however you may have noticed that the
+ 
+
+ align:start position:0%
+however you may have noticed that the
+sparks in the video
+
+ align:start position:0%
+sparks in the video
+ 
+
+ align:start position:0%
+sparks in the video
+were produced where the electric field
+
+ align:start position:0%
+were produced where the electric field
+ 
+
+ align:start position:0%
+were produced where the electric field
+was the strongest
+
+ align:start position:0%
+was the strongest
+ 
+
+ align:start position:0%
+was the strongest
+not where the electric potential was the
+
+ align:start position:0%
+not where the electric potential was the
+ 
+
+ align:start position:0%
+not where the electric potential was the
+highest turn to a friend and discuss why
+
+ align:start position:0%
+highest turn to a friend and discuss why
+ 
+
+ align:start position:0%
+highest turn to a friend and discuss why
+this is the case
+
+ align:start position:0%
+this is the case
+ 
+
+ align:start position:0%
+this is the case
+pause the video here to discuss
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we return to the equations that
+
+ align:start position:0%
+if we return to the equations that
+ 
+
+ align:start position:0%
+if we return to the equations that
+relate the field and the potential we
+
+ align:start position:0%
+relate the field and the potential we
+ 
+
+ align:start position:0%
+relate the field and the potential we
+can improve our understanding
+
+ align:start position:0%
+can improve our understanding
+ 
+
+ align:start position:0%
+can improve our understanding
+you can see that we have a gradient term
+
+ align:start position:0%
+you can see that we have a gradient term
+ 
+
+ align:start position:0%
+you can see that we have a gradient term
+a derivative with respect to distance
+
+ align:start position:0%
+a derivative with respect to distance
+ 
+
+ align:start position:0%
+a derivative with respect to distance
+if our potential changes slowly over
+
+ align:start position:0%
+if our potential changes slowly over
+ 
+
+ align:start position:0%
+if our potential changes slowly over
+distance the field is weak
+
+ align:start position:0%
+distance the field is weak
+ 
+
+ align:start position:0%
+distance the field is weak
+and no spark is generated on the other
+
+ align:start position:0%
+and no spark is generated on the other
+ 
+
+ align:start position:0%
+and no spark is generated on the other
+hand
+
+ align:start position:0%
+hand
+ 
+
+ align:start position:0%
+hand
+if the potential changes quickly over
+
+ align:start position:0%
+if the potential changes quickly over
+ 
+
+ align:start position:0%
+if the potential changes quickly over
+distance the field is strong
+
+ align:start position:0%
+distance the field is strong
+ 
+
+ align:start position:0%
+distance the field is strong
+a stronger field is more likely to
+
+ align:start position:0%
+a stronger field is more likely to
+ 
+
+ align:start position:0%
+a stronger field is more likely to
+remove an electron from an atom
+
+ align:start position:0%
+remove an electron from an atom
+ 
+
+ align:start position:0%
+remove an electron from an atom
+in fact when numerical values are given
+
+ align:start position:0%
+in fact when numerical values are given
+ 
+
+ align:start position:0%
+in fact when numerical values are given
+for the breakdown potential
+
+ align:start position:0%
+for the breakdown potential
+ 
+
+ align:start position:0%
+for the breakdown potential
+they are often given in volts per meter
+
+ align:start position:0%
+they are often given in volts per meter
+ 
+
+ align:start position:0%
+they are often given in volts per meter
+which is actually a measurement of the
+
+ align:start position:0%
+which is actually a measurement of the
+ 
+
+ align:start position:0%
+which is actually a measurement of the
+electric field
+
+ align:start position:0%
+electric field
+ 
+
+ align:start position:0%
+electric field
+the term breakdown potential is a little
+
+ align:start position:0%
+the term breakdown potential is a little
+ 
+
+ align:start position:0%
+the term breakdown potential is a little
+misleading but it's still the standard
+
+ align:start position:0%
+misleading but it's still the standard
+ 
+
+ align:start position:0%
+misleading but it's still the standard
+terminology
+
+ align:start position:0%
+terminology
+ 
+
+ align:start position:0%
+terminology
+to review the gradient connects the
+
+ align:start position:0%
+to review the gradient connects the
+ 
+
+ align:start position:0%
+to review the gradient connects the
+electric field to the electric potential
+
+ align:start position:0%
+electric field to the electric potential
+ 
+
+ align:start position:0%
+electric field to the electric potential
+a steeper change in the potential
+
+ align:start position:0%
+a steeper change in the potential
+ 
+
+ align:start position:0%
+a steeper change in the potential
+results in a stronger electric field
+
+ align:start position:0%
+results in a stronger electric field
+ 
+
+ align:start position:0%
+results in a stronger electric field
+we also saw that electrical breakdowns
+
+ align:start position:0%
+we also saw that electrical breakdowns
+ 
+
+ align:start position:0%
+we also saw that electrical breakdowns
+happened in areas of strong electric
+
+ align:start position:0%
+happened in areas of strong electric
+ 
+
+ align:start position:0%
+happened in areas of strong electric
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+or a steep change in the electrical
+
+ align:start position:0%
+or a steep change in the electrical
+ 
+
+ align:start position:0%
+or a steep change in the electrical
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+we hope you enjoyed this clip from the
+
+ align:start position:0%
+we hope you enjoyed this clip from the
+ 
+
+ align:start position:0%
+we hope you enjoyed this clip from the
+theater of electricity at the boston
+
+ align:start position:0%
+theater of electricity at the boston
+ 
+
+ align:start position:0%
+theater of electricity at the boston
+museum of science
+
+ align:start position:0%
+museum of science
+ 
+
+ align:start position:0%
+museum of science
+good luck in your future studies of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electricity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/NOE2GDmSbDQ.txt b/NOE2GDmSbDQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5833e53f23181a4e4ea3ca86aac25a2e63895ded
--- /dev/null
+++ b/NOE2GDmSbDQ.txt
@@ -0,0 +1,3362 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: So over
+the last lecture,
+
+we have talked about
+coherence within an atom,
+
+coherence between two levels,
+coherence between three levels.
+
+And today, in the
+last class, we want
+
+to talk about coherence
+between atoms.
+
+So this is now, I think,
+for the first time
+
+in this course that we really
+have more than one atom.
+
+Well, maybe we discussed
+some collision or broadening,
+
+or we discussed [INAUDIBLE]
+interaction between two atoms.
+
+But usually, atomic physics
+is one atom at a time.
+
+But now we want to understand
+one important phenomenon which
+
+happens when we have many atoms.
+
+And the phenomenon is
+called superradiance.
+
+So I left something
+good for the end.
+
+And superradiance has
+in common the word
+
+super with superconductivity
+and superfluidity.
+
+And it really represents
+that the atom, many atoms
+
+act together.
+
+And the word super
+also means coherence
+
+among atoms-- superfluidity
+and superconductivity
+
+have macroscopic wave function
+where all the atoms, the meta
+
+waves are coherent.
+
+The phenomenon of
+superradiance, as we will see,
+
+has not so much to do
+with coherent atoms.
+
+It has more to do
+with coherent photons.
+
+So it's more-- some people
+regard superradiance as a laser
+
+without mirrors.
+
+But you'll see where
+the story leads us to.
+
+So just to set the
+stage-- for many atoms,
+
+we should first talk
+about single atoms.
+
+And all that is described
+in this landmark paper
+
+by [INAUDIBLE] in 1954, which
+is posted on our website.
+
+So if you have a single atom
+prepared in the excited state,
+
+it decays to the
+ground state, and we
+
+want to characterize the
+system by emission rate
+
+as a function of time.
+
+So the emission rate initially
+is gamma, the natural language
+
+of the excited state.
+
+And then, of course,
+the emission rate
+
+decays because we don't
+have any atoms left.
+
+Similarly, the probability
+to be in the ground state
+
+is zero initially, and then
+with an exponential approach,
+
+it eventually goes to
+unity after a while,
+
+after we have only atoms
+in the gamma state.
+
+So this is rather
+straightforward.
+
+But now we want to
+bring in a second atom.
+
+And I'm asking,
+what happens when
+
+we have not the one
+atom, but two atoms?
+
+One is in the ground state.
+
+One is excited.
+
+So pretty much what we have
+added to the original situation
+
+with one excited atom
+was we've brought in one
+
+ground state atom, which naively
+you would think does nothing.
+
+But that's not the case.
+
+What happens is-- and I
+assume just for review--
+
+we will drop the
+assumption later,
+
+but we assume for now
+that all the atoms
+
+are within one
+optical wavelength.
+
+What we then realize
+is for two atoms--
+
+and I will show you that
+in its full beauty--
+
+that the initial rate of light
+which comes out of the system
+
+is the same.
+
+So the extra ground
+state atom does not
+
+change the initial emission
+rate, but it goes down faster.
+
+And if we ask what is the
+probability that the atom is
+
+in the ground state, we find
+that it's only one half.
+
+So in other words, normalized
+[INAUDIBLE] system,
+
+we have a ground and excited
+state atom, and what comes out
+
+is only half a photon.
+
+Half of the atoms do not decay.
+
+So it's not the same
+rate and the same decay.
+
+Something profoundly
+has happened.
+
+And this is what you
+want to understand.
+
+So let me give you
+the correct answer.
+
+The rate of emission
+is a function
+
+of time for this situation.
+
+We start out with gamma, but
+then the emission decays, not
+
+with gamma but with 2 gamma.
+
+And the probability that both
+atoms are in the ground state--
+
+or that the second atom, so to
+speak, is in the ground state--
+
+will only asymptotically
+go to 1/2.
+
+And it does so
+exponentially-- but again,
+
+with the time constant,
+which is two times faster
+
+than for the single-atom system.
+
+So we have the same initial
+emission rate, but only
+
+probability of 1/2
+to emit at all.
+
+So in order to
+understand it, we have
+
+to look at an atom in the
+excited state and atom
+
+in the ground state.
+
+And we want to write
+down the wave function
+
+as a superposition of a
+symmetrized and antisymmetrized
+
+wave function.
+
+I should tell you, I'm going
+very slowly for two atoms.
+
+And then once I've introduced
+the concept for two atoms,
+
+with a few pen strokes, we can
+immediately discuss in atoms.
+
+So all the phsyics,
+all the understanding
+
+what goes on in
+superradiance is already
+
+displayed for two atoms.
+
+So we want to have
+a superposition
+
+of symmetric and
+antisymmetric wave function.
+
+The symmetric one is a
+normalized wave function
+
+which is ge plus eg.
+
+And we call that the
+superradiant wave function,
+
+for reasons which will
+become clear in a moment.
+
+And if you have a
+minus sign here,
+
+the antisymmetric
+combination, we
+
+call this subradiant
+wave function.
+
+Now, what happens is,
+we have to consider--
+
+so we have symmetrized
+the wave function.
+
+Well, I didn't
+really tell you why,
+
+but it's always
+good to symmetrize.
+
+Symmetry is, if you can
+use it, something good.
+
+And the reason why I
+symmetrized it is because I want
+
+look at the interaction
+Hamiltonian.
+
+And if I look at the interaction
+Hamiltonian-- the one
+
+we have seen many, many
+times but now for two atoms--
+
+we will immediately realize that
+this interaction Hamiltonian is
+
+symmetric.
+
+So therefore, if the
+Hamiltonian is symmetric,
+
+it's a really good
+starting point
+
+to have the wave function
+for the atoms expanded
+
+in a symmetric basis.
+
+And since I want to emphasize
+that the whole story I'm
+
+telling you today
+has nothing to do
+
+with the kind of
+second quantization--
+
+it is about
+spontaneous emission,
+
+but it's not
+involving any subtlety
+
+of spontaneous
+emission and field
+
+quantization-- I want to
+write down the interaction
+
+Hamiltonian both in a classical
+and a quantum mechanical way.
+
+In the classical way, we
+have the dipole moment d1.
+
+We have the dipole moment d2.
+
+And the atoms talk to the
+electric field at position RNT.
+
+And now you realize where
+some of the assumptions
+
+are important, since the
+atoms are localized to
+
+within a wavelength,
+they rarely talk
+
+to the same electric field.
+
+There are no phase factors.
+
+In about 55 minutes or so,
+we introduce phase factors
+
+for extended samples.
+
+But for now, we don't.
+
+And therefore, what
+the atoms couple with
+
+is with a dipole
+moment, which is
+
+a sum of the two dipole moments.
+
+So this is classical
+or semi-classical.
+
+So what enters in
+the Hamiltonian
+
+is only the sum of the
+operators for the two atoms.
+
+And the same happens
+in the QED Hamiltonian.
+
+And actually, I will get
+a little bit more mileage
+
+out of the QED Hamiltonian,
+as you will see in a moment.
+
+Because with the QED Hamiltonian
+we describe the atomic system--
+
+so at first atom
+one-- with the raising
+
+and lowering operator
+with the atoms interacting
+
+with a and a [INAUDIBLE].
+
+And then I have to add the term
+where the index one and two are
+
+exchanged.
+
+So we are introducing
+here-- that's
+
+convenient for two-level atom--
+the spin notation sigma plus
+
+and sigma minus are the
+raising and lowering operator
+
+which flip the atom from the
+ground to the excited state
+
+and vice versa.
+
+But the important
+part now is-- and this
+
+is where, actually, everything
+comes from in superradiance--
+
+that the coupling involves
+not the individual spins,
+
+little sigma plus,
+sigma 1 and sigma 2--
+
+it only involves the
+sum of the individuals.
+
+i equals 122, and later
+we extend the sum to n.
+
+So therefore, what matters
+for the interaction
+
+of the atoms with the
+electromagnetic field
+
+is the sum of all the
+atomic spin operators.
+
+And the sum is, of course,
+symmetric against exchange.
+
+So therefore, when
+we are asking what
+
+is the coupling of the
+state which I called
+
+the superradiant state, the
+one where we had symmetrized eg
+
+plus ge, or we ask,
+what is the coupling
+
+of the subradiant state
+to-- well, the state where
+
+both atoms are in
+the ground state.
+
+Well, now we can use symmetry.
+
+The left-hand side is symmetric.
+
+The operator is symmetric.
+
+And now only the symmetric
+state will couple.
+
+The antisymmetric
+state will not couple.
+
+So therefore, the subradiant
+state, eg minus ge,
+
+cannot decay.
+
+That's why we call
+it subradiant.
+
+I think a better word
+would be non-radiant,
+
+but non is definitely
+subradiant.
+
+And for the matrix
+element eg and ge,
+
+we find that we have actually
+an enhancement of the coupling
+
+by a factor of square root 2.
+
+So now we pretty much
+know what we have to do.
+
+You want to use the symmetry
+of-- let's assume we consider
+
+ground and excited state
+of each atom as spin 1/2.
+
+But now we want to look at the
+total spin, the total pseudo
+
+angular momentum
+of the two atoms,
+
+and later we extend
+it to n atoms.
+
+So we want to use now the
+power of the angular momentum
+
+description.
+
+And that goes like follows.
+
+We have four states
+of two atoms.
+
+And this is gg, ge, eg, and ee.
+
+And if I denote with
+ground state spin
+
+down, excited state spin
+up, I'm talking about 2
+
+spin 1/2 states.
+
+And 2 spin 1/2 states
+can couple to s
+
+equals 1, total s equals 1,
+and total spin s equals 0.
+
+And that's what I've done here.
+
+I've arranged the states ee, the
+symmetric superradiant state,
+
+the ground state, and
+the subradiant state.
+
+A variation energy
+level diagram--
+
+here we have 0
+excitation energy,
+
+here we have 1
+excitation energy,
+
+and here we have two excitations
+energies of the atom.
+
+But I've also labeled
+now the spin labels
+
+for the combined system.
+
+Those symmetrized states
+correspond to a spin equals 1.
+
+It's a triplet letter with
+three different magnetic quantum
+
+numbers.
+
+m equals plus 1 means
+everything is highly excited.
+
+m equals minus 1 means we are
+in the total ground state.
+
+And here we have
+the simulate state,
+
+which is the antisymmetric
+state or the subradiant state.
+
+And our interaction Hamiltonian
+is the total spin plus minus.
+
+It is the raising and
+the lowering operator.
+
+And you know that the
+raising and lowering
+
+operator for the spin is
+only making transitions
+
+within a manifold of total s.
+
+It just changes the end
+quantum number by plus minus 1.
+
+So the Hamiltonian cannot do
+anything to the simulate state,
+
+because there is no other
+simulate state to couple.
+
+But within the triplet
+manifold, the sigma plus sigma
+
+minus operator is
+creating transitions
+
+between the
+different end states.
+
+And the coupling constant,
+which for an individual atom
+
+was little g is now factor
+of square root 2 enhanced.
+
+And we will see in a few
+minutes, that for n atoms,
+
+it's square root n enhanced.
+
+And if any speak, that's where
+the word super in superradiance
+
+comes from.
+
+Yeah, actually let
+me just quickly add
+
+the diagram for the single atom.
+
+The single atom has only an
+excited state, a ground state.
+
+It corresponds to s equals 1/2.
+
+And we have magnetic
+quantum numbers off plus 1/2
+
+and minus 1/2.
+
+And the coupling due to
+the light atom interaction
+
+goes with the
+coupling constant g.
+
+So the key message
+we have learned here
+
+is that when we
+have several atoms
+
+within an optical
+wavelength, we should
+
+use for their
+description symmetrized
+
+and antisymmetrized states.
+
+Or when we generalize
+to more than two atoms,
+
+we should just add the
+total angular momenta
+
+by treating each atom
+as pseudo spin 1/2.
+
+And it is this
+angular classification
+
+which tells us how the
+radiation proceeds.
+
+Because the coupling to
+the electromagnetic field
+
+is only involving the
+lowering and raising
+
+operators for the total spin.
+
+And this only acts
+on a manifold where
+
+the total spin s is conserved.
+
+And what we get is transitions
+with delta in plus minus 1.
+
+So the question, have those
+effects been observed?
+
+Yes, they have, actually.
+
+And they're important
+for a lot of research.
+
+But just for two atoms,
+the simplest observation
+
+is when you take
+two atoms-- let's
+
+say two sodium atoms--
+bring them very close,
+
+and you form a
+sodium 2 molecule.
+
+And to some extent, in four
+states where the molecule are
+
+binding is not
+completely changing
+
+the electronic structure, we
+can regard the sodium 2 molecule
+
+as consisting of
+two sodium atoms.
+
+And indeed, if you do
+spectroscopy of the sodium 2
+
+molecule, you find
+some molecular states
+
+which are very long lived, like
+the subradiant states, which
+
+do not radiate at
+all, but then you
+
+find states which have a
+spontaneous emission rate which
+
+is about two times faster than
+the spontaneous emission rate.
+
+So you find that
+you can understand
+
+some radiative
+properties of molecules
+
+by assuming that they
+are related to the sub
+
+and superradiant
+state of the two atoms
+
+which form this molecule.
+
+So an example here
+is sodium 2 molecule.
+
+A state where the gamma molecule
+is approximately 2 times gamma
+
+sodium, or other states
+where it's very small.
+
+OK.
+
+Now we understand the basic four
+of superradiance in two atoms.
+
+And therefore, we can now
+generalize it to end particles.
+
+But before I use the
+spin algebra to describe
+
+end particles, I want to glean
+some intuition where we just
+
+consider-- and
+this takes us back
+
+to the beginning of the
+course-- where we consider
+
+end spins in a magnetic field.
+
+And I really invite you to think
+now completely classically.
+
+We'll describe it quantum
+mechanically in a moment.
+
+But I've often said
+in this course,
+
+if in doubt, if you have
+a classical description
+
+and a quantum mechanical
+and they seem to contradict,
+
+usually there is more truth
+in the classical description.
+
+It's so much easier
+to fool yourself
+
+with the formalism
+of quantum mechanics.
+
+So let's take end spins
+in a magnetic field
+
+and ask what happens.
+
+So we have end spins.
+
+So these are now real spins.
+
+They have a real
+magnetic moment.
+
+These are tiny
+little bar magnets.
+
+And we do pi over 2 pulse.
+
+And after we've done
+a pi over 2 products,
+
+the spins are aligned like this.
+
+Let's assume we had
+our magnetic field.
+
+And now what happens
+is these spins
+
+will precess at the
+line of frequency.
+
+So now you have your end spins.
+
+They precess together.
+
+And if you have a magnetic
+moment which oscillates,
+
+the classical equation
+of electromagnetism
+
+tells you that you have now
+a system which radiates.
+
+But compared to a single
+atom, the dipole moment
+
+is now n times the single
+atom dipole moment.
+
+So therefore, what do we
+expect for the radiated power?
+
+Well, if the
+electromagnetic radiation
+
+by an oscillating electric or
+an oscillating magnetic dipole
+
+moment scales with a
+dipole moment squared,
+
+therefore, we would expect
+that the power radiated
+
+is proportional to n squared.
+
+And that means I have to take
+the perfect of n [INAUDIBLE].
+
+This means this is n times
+higher than if you assume
+
+you have n individual
+particles, and each of them
+
+emits electromagnetic radiation.
+
+what I'm telling you
+is if you scatter
+
+n spins through your
+laboratory, you excite them.
+
+Pi over 2 pulse, they radiate.
+
+They radiate a power
+which is proportion to n.
+
+But if you put them all
+together, localize them better
+
+than the wavelengths,
+their radiated power
+
+is proportional to n
+square, which is an n times
+
+enhancement.
+
+So the way how I
+put it for n spins--
+
+and this is a situation of
+nuclear magnetic resonance--
+
+this is the completely
+natural picture.
+
+But if I would have asked
+you the question-- let's
+
+take n atoms which are excited
+and put them close together,
+
+you say, well, each atom
+does spontaneous emission,
+
+and if you have n atoms,
+we get n times c intensity
+
+you would have gotten
+a different result.
+
+So we are so accustomed
+to look at spins in NMR
+
+as a coherent system, look
+that all the spins add up
+
+to one giant antenna, to
+one giant oscillating dipole
+
+moment, whereas for
+atoms, we are so much used
+
+to saying each atom is
+its own particle and thus
+
+its own thing.
+
+So for n excited
+atoms, they are usually
+
+regarded as independent.
+
+However-- and this is
+the message of today--
+
+there shouldn't be a difference.
+
+All 2 level systems
+are equivalent.
+
+Side remark-- for NMR in
+spins, it is much, much easier
+
+to observe the effect,
+because the condition
+
+that all the spins are
+localized within one wavelength
+
+is always fulfilled
+if the wavelength is
+
+meter or kilometers.
+
+But if you have
+atoms which radiate
+
+at the optical wavelengths, this
+condition becomes nontrivial.
+
+That is partially responsible
+for the misconception
+
+that you treat the
+two-level system which
+
+is a spin in your
+head differently
+
+from the two-level
+system which is an atom.
+
+So the important
+difference here is lambda.
+
+And we have to compare
+it with a sample size.
+
+And usually, the sample
+size is much larger
+
+in the optical domain,
+and is much, much smaller
+
+in the NMR domain.
+
+However-- and that's
+what we'll see
+
+during the remainder
+of this class--
+
+some of the dramatic
+consequences of superradiance
+
+will even survive under
+suitable conditions
+
+in the extended samples.
+
+So when we have samples
+of excited atoms much,
+
+much larger than the
+optical wavelengths,
+
+we can still observe
+superradiance.
+
+So therefore, for
+pedagogical reasons,
+
+I first complete the
+focus on the case
+
+that everything is
+tightly localized.
+
+We derive some
+interesting equations,
+
+and then we see how
+they are modified
+
+when we go to extended samples.
+
+But I want to say, the
+intuition from spin systems,
+
+the intuition from
+classical precession
+
+and nuclear magnetic
+resonance, will help us
+
+what happens for
+electronically excited atoms.
+
+So we want to use
+this other spin 1/2
+
+system as a powerful
+analogy to guide us.
+
+So before I start with the
+angular momentum formalism,
+
+I want to emphasize that what
+are the ingredients here.
+
+Well, we're talking about
+coherence-- coherent radiation,
+
+coherence between atoms-- and
+we'll talk about radiation.
+
+And the important part
+here is the following.
+
+That when we talk
+about radiation,
+
+we have the situation
+that all atoms interact
+
+with a common radiation field.
+
+In other words, all the
+spins, all the atoms
+
+have to emit their
+photons into the same mode
+
+of the electromagnetic field.
+
+And therefore, you may
+be right in some limit
+
+that the atoms are independent,
+but not the photons they emit.
+
+They go into the same mode.
+
+And therefore, the emitted
+photons cannot be treated
+
+independently.
+
+And that's why the
+classical picture
+
+is so powerful for that.
+
+Because in the
+classic picture, we
+
+do a coherent summation
+of the field amplitudes.
+
+So we have constructive
+interference.
+
+The superposition principle
+of field amplitudes
+
+build into our equations and
+deeply engraved in our brains.
+
+And that's why when we
+use classical arguments,
+
+we automatically account for
+that the photons interfere,
+
+that the photons are
+emitted into the same mode
+
+of the electromagnetic field.
+
+And eventually, this
+leads to the phenomenon
+
+that we have coherence
+and enhancement when
+
+we look at spontaneous
+emission for n atoms
+
+which are sufficiently
+localized.
+
+So let me also discuss
+what we have assumed here.
+
+Number one is, we
+have assumed we
+
+have a localization
+of the sample
+
+smaller than the
+optical wavelengths.
+
+The other thing-- and
+this is really important--
+
+we are talking here about
+a collective phenomenon
+
+where n atoms act
+together and do something.
+
+They develop the phenomenon
+of superradiance.
+
+They decay much, much faster
+than any individual atom could
+
+do by itself.
+
+But nevertheless, we have not
+assumed-- or we have actually
+
+excluded in our
+description-- that there
+
+is any direct interaction
+between the atoms.
+
+The atoms have no
+[INAUDIBLE] interaction.
+
+They're not forming molecules.
+
+They're not part of a solid
+with shared electrons.
+
+The atoms are, in that
+sense, non-interacting.
+
+And therefore, in
+a way, as long as
+
+they are just
+atoms, independent.
+
+Finally-- and I want
+you to think about it--
+
+you can think about
+already for two atoms
+
+before we generalize
+it to n atoms.
+
+Think about it.
+
+What was really the
+assumption about the atoms?
+
+Do the atoms have to be bosons
+to be in this symmetric state?
+
+Can they be fermions?
+
+Or can they be even
+distinguishable particles?
+
+If the two atoms where
+one would be a sodium atom
+
+and one would be a rubidium
+atom-- but let's just
+
+say we live in a world where
+sodium and rubidium atoms emit
+
+exactly the same color of light.
+
+Would we have been sub
+and superradiant state
+
+for two atoms, one of which
+is sodium and one of which
+
+is rubidium?
+
+Yes?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Exactly.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yes.
+
+And that confuses many people.
+
+It is the indistinguishability
+of the photons
+
+they have emitted.
+
+It is the common mode where
+the photons are emitted.
+
+The atoms can be distinguished.
+
+Also, we've made the assumption
+that the atoms are localized to
+
+within an area which is
+much smaller than lambda.
+
+But you could imagine you
+have a solid state matrix
+
+and you have one atom
+here, one atom there,
+
+and you can go with a
+microscope and distinguish them.
+
+So therefore, the moment
+you can distinguish them
+
+because they are pinned
+down in a lattice--
+
+or if you don't like a lattice,
+take two microscopic ion traps
+
+a few nanometers
+apart, and you tightly
+
+hold onto two ions--
+it doesn't matter
+
+whether they are
+bosons or fermions.
+
+It only matters whether
+your bosons or fermions
+
+when the atomic wave
+functions overlap
+
+and you have to symmatrize it.
+
+As long as you have two atoms
+which are spatially separated,
+
+it doesn't matter whether
+they are bosons or fermions.
+
+And that also means they can
+be completely different atoms.
+
+You can already
+call the Boson A,
+
+Boson B. Now you can call
+it sodium and rubidium,
+
+and they can have different
+numbers of nucleus.
+
+They can be different numbers
+of neutrons in the nucleus.
+
+It could be different
+isotopes of the same atom.
+
+The whole collective
+phenomenon comes
+
+when they emit a photon
+into the same mode.
+
+OK.
+
+So now we want to
+treat to a formula
+
+treatment for end particles.
+
+So we have now the individual
+pseudo spins one half.
+
+We perform now with some
+overall end particles.
+
+We get the total spin s.
+
+The total spin s
+quantum number has
+
+to be smaller or
+equal to n over 2,
+
+because we have m
+spin 1/2 systems.
+
+The end quantum
+number is 1/2 times
+
+the difference of
+the atoms which
+
+are in the excited state
+minus the atoms which
+
+are in the ground state.
+
+And this is, of course, trivial.
+
+Trivially must be
+smaller than s.
+
+Because m is this
+z component of s.
+
+And we are now
+describing the system
+
+by the eigenstates s and
+n of the collective spin.
+
+So that means we have
+the following situation.
+
+We have a manifold-- we want to
+show now all the energy levels.
+
+We have a manifold which
+has a maximum spin n over 2.
+
+The next manifold
+has n over 2 minus 1.
+
+And the last one
+has-- let's assume
+
+we have an odd number of
+particles-- x equals 1/2.
+
+So here, we have
+now n energy levels.
+
+We can go from all
+the n atoms excited
+
+to all the n atoms
+being de-excited.
+
+In the following manifold,
+we have s is one less.
+
+And therefore, we have
+a letter of states
+
+which is a little bit shorter.
+
+And eventually,
+for s equals 1/2,
+
+we have only two components
+plus 1/2 and minus 1/2.
+
+So those levels interact with
+the electromagnetic field.
+
+The operator of the
+electromagnetic field,
+
+we have already
+derived that, involves
+
+the sum of all of the little
+sigma pluses, sigma i pluses,
+
+and we call the sum of all
+of them s plus and s minus.
+
+And the matrix element is
+now for spontaneous emission.
+
+You have a state with sm.
+
+s minus is the lowering operator
+for the n particle system,
+
+so it goes from a state
+with a certain number
+
+of atomic excitations
+to one excitation less,
+
+and that means this is the
+act of emitting spontaneously
+
+one photon.
+
+The operator s minus stays
+within the s manifold,
+
+so we state in the
+same letter, which
+
+is characterized by
+the quantum number s.
+
+But we lower the end
+quantum number by one.
+
+The end quantum
+number is a measure
+
+of the number of excitations.
+
+And we know from
+general spin algebra
+
+that this matrix element is s
+minus m plus 1 times s plus n.
+
+There are, of
+course, pre-factors
+
+like the dipole matrix
+element of a single atom.
+
+But I always want to normalize
+things to a single atom.
+
+And by just using
+the square root,
+
+if you have a single particle,
+which is in the s to m
+
+equals 1/2 state, then you
+see that it this square root
+
+is just 1.
+
+So therefore, for when I discuss
+now the relative strengths
+
+of the transitions
+between those eigenstates,
+
+I've always normalized
+to a single particle.
+
+For a single particle, the
+transition matrix element is 1.
+
+OK.
+
+So therefore, what we
+want to discuss now is,
+
+we want to discuss
+the rate, which
+
+is the matrix element
+squared, or the intensity
+
+of the observed radiation
+relative to a single particle.
+
+So the intensity-- and this
+is what we are talking about--
+
+is now the square root of the
+square root, or the square
+
+of the square root, which is s
+minus 1 plus m times s plus m.
+
+Pretty much, this is
+the complete description
+
+of superradiance for
+strongly localized atoms.
+
+It's all in this one formula.
+
+Once we learned how to
+classify the states,
+
+we can just borrow
+all the results
+
+from angular momentum, addition,
+and angular momentum operators.
+
+So I want to use this
+formula for the intensity
+
+and look at which is the most
+superradiant state, the state
+
+where all the particles
+are symmetric.
+
+And this is a
+state with s equals
+
+n where the spin is n over 2.
+
+So I'm looking now at
+the letter of m states,
+
+and I want to figure
+out what happens.
+
+So the maximum m
+state is m equals s,
+
+all the atoms are excited.
+
+And now the first
+photon gets emitted.
+
+So just put s equals m equals
+n half into the formula
+
+for the intensity, and you find
+that the intensity gives us
+
+this expression is just n.
+
+So we have n excited
+atoms, and they initially
+
+emit with an
+intensity which is n.
+
+And this is the same as for n
+completely independent atoms.
+
+So nothing really special
+to write home about.
+
+But now we should go
+further down the ladder,
+
+and let's look at the state
+which has m equals zero.
+
+Well, then the intensity
+of the matrix element
+
+squared for the transition,
+which goes to m equals zero,
+
+has an intensity
+which is n over 2.
+
+I will just look. s is
+n over 2, and m is zero.
+
+So we have the
+question whether we
+
+have odd or even
+number of particles,
+
+but it doesn't really matter.
+
+What dominates is always
+the big factor n over 2.
+
+So what we find
+out is that we have
+
+an enhancement, huge enhancement
+over independent atom,
+
+because this intensity
+goes with n squared,
+
+and this proportionality
+to n squared,
+
+this is a hallmark
+of superradiance.
+
+So this is what
+is characteristic
+
+for superradiance.
+
+We have an n times enhancement
+relative to the a singular
+
+atom.
+
+So this is one important aspect.
+
+Now, in the classical
+picture, that
+
+should come very naturally.
+
+If you have all
+the spins aligned
+
+and they start the
+[INAUDIBLE] procession,
+
+there is not a lot of
+oscillating dipole moment.
+
+But when half of the
+spins are de-excited,
+
+they are now in the XY plane.
+
+Now you have this giant antenna
+which oscillates and radiates.
+
+So it's clear that
+at the beginning,
+
+the effect is less pronounced,
+and if you're halfway
+
+down the Bloch sphere, then
+you would expect this n times
+
+enhancement.
+
+But now let's go
+further down the ladder
+
+and ask what happens when
+we arrive at the end.
+
+So I'm asking now, what
+is the intensity when
+
+the last photon gets emitted.
+
+There is only one
+excitation in the system.
+
+And the answer is, it's not
+one like an independent atom.
+
+If you inspect the square root
+expression, you find it's n.
+
+So we have one
+excitation in the system,
+
+but it's completely symmetrized.
+
+And therefore, we have
+an n times enhancement.
+
+And I want to show you
+where it comes about.
+
+So there's only one
+particle excited.
+
+And here, we have an
+n times enhancement.
+
+By the way, the states with
+the classification s and m
+
+are called the
+[INAUDIBLE] state.
+
+And this state here, which
+has a single excitation
+
+but it radiates n times
+faster than a single atom,
+
+is a very special
+[INAUDIBLE] state.
+
+And there is currently an effort
+in Professor [INAUDIBLE] lab
+
+to realize in a very
+well-controlled way
+
+this special [INAUDIBLE]
+state in the laboratory.
+
+There are non-classical
+states, because they're not
+
+behaving as you would
+maybe naturally assume
+
+a system with a single
+excitation to behave.
+
+So let's maybe try to
+shed some light on it.
+
+One way how you can intuitively
+understand superradiance
+
+is really with a
+classical antenna picture
+
+that you have n spins which
+form a microscopic dipole
+
+moment which oscillates.
+
+And this is a very nice picture
+to understand the n times
+
+enhancement when we
+have half of the atoms
+
+excited and the other
+half de-excited.
+
+Let me now give
+you a nice argument
+
+which explains why a single
+excitation in this system
+
+now leads to an n
+times enhanced decay.
+
+The situation is that
+the initial state
+
+for this last photon is,
+we have an excited atom,
+
+and all the atoms are
+in the ground state.
+
+However, we could also
+have in this nomenclature
+
+the second atom excited.
+
+Or we could have the third
+one excited, and so on.
+
+So therefore, what we
+have is-- because we
+
+are in the left-most [INAUDIBLE]
+which has the maximum s spin
+
+quantum number of n
+over 2, that means
+
+everything is fully symmetrized.
+
+So therefore, we have
+to fully symmetrize
+
+by summing over the
+n possibilities.
+
+And our final state is, of
+course, the fully symmetrized
+
+[INAUDIBLE] state.
+
+And now you realize
+that you have
+
+a coherent summation over--
+you have n contributions.
+
+So therefore, the matrix
+element has n contributions
+
+compared to single atom.
+
+The normalization is
+only square root n.
+
+So therefore, the matrix element
+is square root n times larger
+
+than for an individual atom.
+
+So by simply having
+one atom excited and n
+
+minus 1 atom not
+excited, but if you now
+
+have the fully
+symmetrized state,
+
+you don't know for fundamental
+reasons which atom is excited.
+
+You have a superposition
+state where the excitation
+
+can be with either of the atom.
+
+This state, which has a
+similar quantum of excitation,
+
+radiates n times faster
+than a single atom would.
+
+Let me make a side remark.
+
+Maybe some of you remember when
+we went to [INAUDIBLE] QED,
+
+we had just proudly quantized
+the electromagnetic field,
+
+and we discussed the
+vacuum Rabi splitting.
+
+And I told you that the
+vacuum Rabi splitting
+
+is if the cavity is not empty
+but is filled with n atoms,
+
+because of the matrix element
+of the a dagger operator,
+
+you get an enhancement of the
+vacuum Rabi splitting, which
+
+is square root n,
+then photon number.
+
+But then I showed you the
+important first observation,
+
+the pioneering research at Cal
+Tech by JF Kimball and Gerhard
+
+Rempe, and they didn't
+vary the photon number.
+
+They varied the atom number.
+
+And when they had more
+flux in the atomic beam,
+
+the Rabi splitting
+became larger and larger.
+
+Well, we've just
+learned that when
+
+we have n atoms, that the matrix
+element for emitting the photon
+
+is square root n times enhanced.
+
+So if you put n atoms in a
+cavity filled with little n
+
+photons, the Rabi splitting
+between the two modes
+
+has square root n plus
+1 in the photon number
+
+and square root big
+n in the atom number.
+
+So the effect I've shown you in
+the demonstration of the vacuum
+
+Rabi splitting is this
+scaling with the atom number.
+
+This actually can be understood
+as a superradiant effect.
+
+OK.
+
+So that's pretty
+much what I wanted
+
+to tell you about the basic
+phenomenon of superradiance.
+
+Now I want to discuss
+two more things.
+
+One is superradiance
+in an extended sample.
+
+Ad we have time for that.
+
+But I also want to discuss
+with you the question.
+
+Let's assume we have
+the same system,
+
+and we just convinced ourselves,
+yes, it's superradiant.
+
+Photons are emitted
+n times faster.
+
+Now, what would you think
+will happen when we are not
+
+looking for
+spontaneous emission,
+
+but we shine a
+laser light on it,
+
+and we are asking
+for induced emission?
+
+Or the other way
+around-- we ask--
+
+and you know that from
+Einstein's treatment,
+
+it's completely
+recipocal-- where
+
+we are asking the question,
+what happens to the absorption
+
+process?
+
+So is a stimulated emission
+process or an absorption
+
+process, are they
+also enhanced n times?
+
+I don't know.
+
+Do you have any
+opinions about that?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yes.
+
+It's a subtle way of counting.
+
+I've shown you that certain
+matrix element-- especially
+
+the matrix element when
+the spin is in the middle,
+
+is at 90 degrees-- that we
+have matrix elements which
+
+are n times enhanced.
+
+And of course, if you ask
+for absorption or stimulated
+
+emission, we are talking to
+a system which has an n times
+
+enhanced matrix element.
+
+And you would say,
+things go n times faster.
+
+Why don't you hold this
+thought for a moment?
+
+Now let me just wear
+another hat and let
+
+me say that we have assumed
+that we have n independent
+
+spins that are closely
+next to each other,
+
+but they're not interacting.
+
+And now I take these n spins,
+and for stimulated emission
+
+and absorption, we can just use
+a picture of Rabi oscillation.
+
+On the first Rabi
+cycle, we emit.
+
+On the next Rabi
+cycle, we absorb.
+
+So if I take now--
+and why don't you
+
+think not about these
+pseudo spins electronically,
+
+atoms with [INAUDIBLE]
+excitation--
+
+just think of real spins
+which have a magnetic moment,
+
+and you drive them to
+the magnetic field.
+
+So now you have
+your n little spins.
+
+You apply a magnetic
+field to them,
+
+time-dependent
+magnetic field, and
+
+the time-dependent
+magnetic field
+
+is now driving the spin
+in Rabi oscillations.
+
+And the external drive
+field talks to one spin,
+
+talks to the next,
+talks to all of them.
+
+But each of the
+spins does exactly
+
+the same Rabi oscillation it
+would do if all the other atoms
+
+where not present.
+
+So the picture is, you
+have an external field.
+
+All the atoms couple
+to the external field.
+
+But the coupling of each
+atom to this external field
+
+is exactly the same
+as of a single atom
+
+coupling to the external field.
+
+And the Rabi frequency
+for each atom
+
+is exactly the
+Rabi frequency you
+
+would get for a single atom.
+
+So therefore, based
+on this picture,
+
+I would expect that
+I have my end spins,
+
+and these can now be real
+spins with a magnetic moment,
+
+or can be atoms in the
+electronically excited state.
+
+I coherently drive them
+with a drive field,
+
+and they will do
+Rabi oscillations.
+
+But the frequency
+or Rabi oscillations
+
+will be the same as
+for a single atom.
+
+OK.
+
+We've just held the
+thought that their matrix
+
+elements in the Dickey
+states, which are square root
+
+n times larger, and
+the Dickey state
+
+seem to suggest
+something to us which
+
+would say there should
+be an enhancement,
+
+whereas the analysis
+in independent atoms,
+
+which are driven by an external
+field, also seems compelling.
+
+So now we have to reconcile
+the two approaches.
+
+Is the question clear?
+
+We want to figure out-- we have
+matrix elements in the Dickey
+
+state which suggest enhancement,
+but the simple picture
+
+of n independent atoms
+driven by an external field
+
+would say there
+is no enhancement.
+
+OK.
+
+So let me just write down more
+formally what I explained.
+
+When we have an initial
+state, which is all the atoms
+
+are in the ground
+state to the power n,
+
+and the state n
+would evolve when
+
+it is driven in
+a state phi of t,
+
+so now the exact wave
+function for our n particles
+
+is nothing else than the
+time-dependent solution
+
+of Schrodinger's equation
+for the single particle.
+
+So this is single
+particle to the power n.
+
+So therefore, this is pretty
+much a mathematical proof
+
+unless I've made a
+mistake, which I haven't.
+
+So it takes exactly half
+a single atom Rabi period
+
+to completely invert
+the population exactly
+
+s for a single atom.
+
+So that's the result.
+
+However, if you describe
+the system by Dickie states,
+
+you have matrix element which
+are matrix elements which
+
+are proportional to n.
+
+However, if you want to--
+I've described it just
+
+as a two-level system.
+
+Each atom does Rabi oscillation.
+
+I've said, OK, the
+system of n atoms
+
+is just n individual systems.
+
+But if you insist to describe
+it as a collective spin,
+
+then we have the Dickie states.
+
+Then we have the n
+times enhancement
+
+of the matrix element.
+
+But then we also have
+to go through n states.
+
+So we have n steps in
+the Dickie letter ladder.
+
+And one can say now-- and
+this is the exact argument--
+
+you have n steps.
+
+You take each step
+n times faster,
+
+but the total time is the same.
+
+So n times 1 over n is 1.
+
+OK.
+
+But now when we talk about
+spontaneous emission,
+
+we are not driving the system
+with an external field.
+
+It's really driven by the system
+itself, which emits photons
+
+into the empty mode.
+
+Spontaneous emission,
+each step is
+
+proportional to the
+matrix element squared,
+
+because we're talking
+about [INAUDIBLE]
+
+spontaneous emission.
+
+So this is proportional
+to n square.
+
+And if you say that
+we have n steps,
+
+well, then we have
+n squared over n.
+
+Then we have a speed up.
+
+Each step is n squared faster.
+
+We divide by n, and we
+get the superradiant speed
+
+of which is n.
+
+So superradiance is something
+that you observe in spontaneous
+
+emission, but you cannot
+absorb it in a driven system.
+
+Because in a driven
+system, you can
+
+say you have a classical
+external field.
+
+And this external
+talks to one atom,
+
+to n atoms exactly
+in the same way.
+
+It is really the interference
+of spontaneously emitted photons
+
+which is at the heart
+of superradiance.
+
+As a side remark,
+we are talking here
+
+about coherent effect,
+which is n times enhanced.
+
+And you can actually
+regard that as a kind
+
+of bosonic enhancement in
+the emission of photons,
+
+because the photons are bosons.
+
+When Bose-Einstein
+condensation was discovered
+
+and people were thinking about
+basic experiments, of course,
+
+one thing which
+was on our mind is,
+
+we wanted to show that
+there are processes
+
+in the Bose-Einstein condensate
+we are n times enhanced.
+
+For fermions, they
+would be suppressed.
+
+This is the flip side.
+
+Big enhancements for
+bosons, complete suppression
+
+for fermions.
+
+And we found that, for instance,
+the formation of the condensate
+
+had an n times enhancement.
+
+There was a stimulation factor.
+
+But we also thought you
+should actually-- there may
+
+be ways where you can observe
+suppression of light scattering
+
+or enhancement of
+light scattering.
+
+But we thought about it with
+two laser beam [INAUDIBLE]
+
+scattering, and the
+idea seemed compelling.
+
+And then we said,
+no, wait a moment.
+
+If you use laser beams,
+everything is stimulated.
+
+You can observe
+bosonic enhancement
+
+and fermeonic
+suppression only when
+
+you have spontaneous events.
+
+If you drive it in a
+unitary time evolution,
+
+you will not be able to see
+quantum statistical suppression
+
+or enhancement.
+
+And the same thing as
+we have seen here--
+
+when you have a
+stimulated system,
+
+everything is undergoing
+a unitary time evolution,
+
+and the unitary time
+evolution for n atoms
+
+is the same as
+for a single atom.
+
+You need the element of
+spontaneous emission.
+
+So I'm not proving it
+to you, but I'm just
+
+making as a remark--
+what we have seen here,
+
+that the superradiance
+only shows up
+
+in spontaneous emission
+and not when we drive
+
+the system-- a driven system
+is a unitary evolution.
+
+And the same conclusion which
+we just got for superradiance
+
+also applies if you want to
+observe fermionic suppression
+
+or pulsonic enhancement
+in quantum gases.
+
+It needs an element of
+spontaneous scattering
+
+or spontaneous emission.
+
+Yes?
+
+AUDIENCE: If we think of
+it in terms of interference
+
+of photons, how does
+that tie in here?
+
+Because if the stimulated
+[INAUDIBLE] photons are still
+
+interfering, then you can
+get emission [INAUDIBLE].
+
+PROFFESOR: The
+quick answer is, you
+
+have a classical field which
+you use for-- you have a laser
+
+field for stimulate
+emission for absorption.
+
+There are so many photons
+in the laser field
+
+that the few photons which your
+system emits do not matter.
+
+They are really talking
+to a classical field,
+
+and it doesn't matter whether
+the other n minus 1 atoms
+
+have emitted a photon, because
+you have zillions of photons
+
+in your laser field,
+and they determine
+
+the dynamics of the system.
+
+OK.
+
+Super radiance would
+not be as important
+
+as it is if it could not
+observed in extended samples.
+
+So now I want to use
+the last 10 minutes
+
+to show you what
+is kept and what
+
+has to be dropped when we
+talk about extended samples.
+
+So let's-- it doesn't
+really matter,
+
+but for pedagogical reasons,
+let's assume we have
+
+an extended sample
+which is much,
+
+much longer than the optical
+wavelengths along the long axis
+
+of the cigar and smaller
+along the short axis.
+
+The second condition
+that the cigar
+
+is smaller than along the long
+axis does not really matter.
+
+No, I'm not making
+this assumption.
+
+So it's a cigar, and
+let's just assume
+
+that everything is-- just saw
+a contradiction in my notes.
+
+So anyway, we have
+now a system which
+
+is-- let's have a Cuban
+cigar, a really thick cigar.
+
+And this is now our
+extended sample.
+
+And what I need is, I need the
+cross section of the sample A.
+
+And let's assume
+the length is l.
+
+This is diameter d.
+
+It's a cigar much,
+much larger than here.
+
+And yes, we are talking
+about superradiance,
+
+we are talking about
+spontaneous emission.
+
+But if you see a long
+cigar with excited atoms,
+
+you think immediately
+about lasing action.
+
+The photon is emitted is
+amplified along the path.
+
+And of course, the
+preferred direction
+
+where you would expect the
+maximum effect to happen
+
+is when the light is
+emitted along the long axis
+
+of the cigar.
+
+So you want to consider
+now preferential modes
+
+along the x-axis.
+
+So if you now assume
+that you have many atoms,
+
+and they emit light, if an atom
+here and here would emit light
+
+in this direction, it may
+constructively interfere.
+
+But in another direction, it
+will destructively interfere.
+
+But let us now consider what is
+the solid angle into which all
+
+of the atoms can
+coherently emit.
+
+Well, you know that from
+classical optics, the emission
+
+into a solid angle of lambda
+square over a can be coherent.
+
+Sort of similar to when
+you have a double slit
+
+and you ask, over what angle
+do the two slits emit inface.
+
+You get a bright fringe,
+and you get a dark fringe,
+
+you get the next bright fringe.
+
+The coherence, the angle
+over which the pass lengths
+
+differences do not add
+up to more than lambda.
+
+It's the deflection-limited
+angle which for a beam of size
+
+d is lambda over d.
+
+And if you take it to
+the second dimension,
+
+the solid angle is lambda
+squared over d squared.
+
+So that's what
+I'm talking about.
+
+So if you would give all
+the atoms in your assemble
+
+just the right
+phase that they are
+
+coherent to emit
+into the x-axis,
+
+they will also coherently emit
+into a small, solid angle,
+
+and the solid angle is
+given by this number.
+
+So the just of it is--
+and I will not completely
+
+prove it to you, but I just
+want to give you a taste--
+
+is that therefore, we still
+have a superradiant enhancement.
+
+We know the superradiant
+enhancement previously
+
+when we had the
+localized system was n.
+
+But now we have the
+n atoms act together,
+
+but they're not acting together
+for emission into 4 pi.
+
+They are acting together for
+emission into the solid angle.
+
+And if I write the
+big n as density
+
+n times l times a squared,
+the a squared cancels out
+
+and I get n lambda square l.
+
+And if you remember that
+the cross section of an atom
+
+was lambda square
+for absorption,
+
+if the atom is excited,
+the cross section
+
+for amplification of light
+for stimulated emission
+
+is also lambda squared.
+
+So lambda squared is
+the gain cross section.
+
+And what we find now as a
+superradiant enhancement factor
+
+is nothing else like
+something which reminds us
+
+of a laser, which reminds
+us of optical gain.
+
+And actually, the
+lasing phenomenon
+
+in superradiance in extended
+samples has a lot of analogies.
+
+In some limits,
+it's even identical.
+
+When we are talking about
+spontaneous emission,
+
+we are not talking about
+stimulated emission.
+
+But if you have a system
+which is in some excited state
+
+superradiant Dickey
+states, and we
+
+are asking what are the
+spontaneously emitted
+
+photons coming out,
+to say different atoms
+
+emit into the same
+mode, and now you
+
+have to add up the
+feeds coherently,
+
+this is a language
+we have used so far.
+
+Or if you use a language atom
+emits a photon and this photon
+
+gets amplified on its way out,
+those two language strongly
+
+overlap or in some limits
+are even identical.
+
+So the amplification
+of a photon on its way
+
+out, this is behind
+superradiance.
+
+But when the localize the atoms
+to lessen the wavelengths,
+
+well, the atoms pretty
+much emit as a whole
+
+and there is no pass
+lengths of the size
+
+of the optical wavelengths
+where you can say the photon
+
+propagates, gets amplified.
+
+So we have looked at just
+what comes out of it.
+
+But in extended
+sample, you could even
+
+address this situation.
+
+How do the photons get
+amplified, magnified,
+
+augmented when they travel
+from the center to the edge?
+
+So you could actually ask,
+what is the light intensity
+
+as a function of the
+position within the cigar?
+
+For localized
+samples, you can't.
+
+So let me just write that down.
+
+So this is analogous to
+optical amplification
+
+in an elongated,
+inverted medium.
+
+OK.
+
+So you can formally
+describe that.
+
+You can now define new
+Dickey states with respect
+
+to the preferred mode.
+
+And the preferred mode is
+the mode in the x direction.
+
+So what I've done is--
+remember, we have those atoms.
+
+Those atoms are now sitting at
+different positions, x1 and x2.
+
+And if I define
+Dickey states which
+
+have phase factors
+into the ik x1,
+
+into the ik x2, if now
+this atom emits a photon
+
+and this atom emits
+a photon, well,
+
+the second photon is x2
+minus x1 ahead of this photon
+
+if you think of those atoms
+sitting aligned in a string.
+
+But the phase vector is exactly
+canceling the propagation phase
+
+for the first atom in such
+a way that if you are now
+
+coupling these states to
+the electromagnetic field,
+
+the phase factors of the
+electromagnetic field
+
+in the mode cancel with
+those phase factors,
+
+and you again have the
+situation that each state here
+
+has an equal amplitude
+for emission.
+
+So now you have n
+possible contributions,
+
+and the normalization
+is 1 over square root n,
+
+and everything falls into place.
+
+And you can define that for two
+excited atoms with two phase
+
+factors and so on.
+
+So you can use immediately
+the same formalism.
+
+And what happens is those phase
+factors for the interaction
+
+Hamiltonian-- and
+our interaction
+
+Hamiltonian is now different.
+
+It is di.
+
+And now in an
+extended sample, we
+
+have to keep track of the
+precision of the atom.
+
+So for the coupling to the
+mode in the x direction,
+
+we have those phase factors.
+
+So all the phase factors cancel.
+
+And actually, I'm
+not telling you
+
+whether this is plus or
+minus in order to cancel.
+
+You pick the sign
+that they all cancel,
+
+and then you have superradiance.
+
+You have fully
+constructive interference.
+
+Yes.
+
+So all this looks now the
+same as superradiance,
+
+but there are also things
+which are different,
+
+and this is the following.
+
+If the atom would emit now
+photons, not in the preferred
+
+mode, then-- remember,
+we had the Dickey ladder.
+
+We had the most superradiant
+ladder, little bit
+
+less superradiant
+ladder, and eventually we
+
+had the subradiant
+ladder in order
+
+of smaller and smaller
+total quantum number s.
+
+Emission in the preferred
+mode stays in each letter,
+
+and we have the
+superradiant cascade.
+
+But emission into
+other modes is now
+
+coupling different s states.
+
+Because the operator or the
+phase factor into the IKR
+
+has broken to complete
+permutation symmetry
+
+between the sides.
+
+We have changed the symmetry.
+
+We have not the
+completely symmetric sum.
+
+We have a symmetric
+summation with phase factors.
+
+So therefore, the phenomenon
+is somewhat different.
+
+But we still have superradiant
+cascade for the preferred mode.
+
+And the result is that
+we have an enhancement
+
+for the most symmetric
+for the superradiant
+
+states, which is given by that.
+
+And this is nothing else than
+the resonant optical density
+
+of your center.
+
+So in experiments-- many of
+them go on in [INAUDIBLE] lab,
+
+where he uses collective
+spin and the storage
+
+of single photons in
+n atoms, the figure
+
+of [INAUDIBLE] of his samples
+is always the optical density,
+
+the number of atoms times lambda
+squared times the lengths.
+
+Finally-- and sorry for
+keeping you three more
+
+minutes-- the form
+of superradiance
+
+which is very important
+is Raman superradiance.
+
+We don't have an
+excited state where
+
+we put a lot of excitations on,
+because the excited state would
+
+be very short lived.
+
+So what we instead do is, we
+have Rabi frequency omega 1.
+
+We have a large
+[INAUDIBLE] delta.
+
+And then the
+spontaneous emission
+
+with the coupling
+constant g takes us down
+
+to the excited state.
+
+In the case that the Rabi
+frequency is much, much smaller
+
+than delta, we can
+eliminate the excited state
+
+from the description.
+
+And what we obtain
+is now a system
+
+which has an excited state.
+
+The widths of this
+excited state--
+
+this is pretty much the virtual
+state here-- is the scattering
+
+rate which is the probability
+to excite the atom
+
+is Rabi frequencied
+over detuning squared.
+
+That's just perturbation theory.
+
+And then we multiply with
+gamma or gamma over 2.
+
+So this is the rate of
+spontaneous emission out
+
+of the virtual state.
+
+And from this virtual state,
+we go now to the ground state.
+
+And the Rabi frequency,
+or the coupling
+
+for this virtual state,
+is the original coupling
+
+g between ground
+and excited state,
+
+but now pro-rated
+by the amplitude
+
+that we have mixed the excited
+state into the virtual state.
+
+So therefore, we have now
+obtained a superradiant system.
+
+And for instance,
+we did experiments
+
+which became classic now
+because they are conceptually so
+
+clear-- we took a
+Bose-Einstein condensate,
+
+we switched on one strong
+of resonant laser beam,
+
+and then we had a system
+which was 100% inverted,
+
+because we had no atoms
+into the final state.
+
+The final state is a
+Bose-Einstein condensate
+
+but with a recoil kick.
+
+So by just having a
+Bose-Einstein condensation
+
+and shining this laser light on
+it, we had now in this picture
+
+a 100% inverted system, which
+is the ideal realization
+
+of a fully inverted Dicky state.
+
+Everything is
+completely symmetric,
+
+and then we observed
+superradiant emission
+
+of light pulses.
+
+OK.
+
+So this has been the
+important realize--
+
+so important experiments have
+been done via BECs in my group
+
+and with cold atoms in
+with laser code samples
+
+in [INAUDIBLE].
+
+So why is superradiance
+so important?
+
+And this my last
+statement for this class
+
+and for the semester.
+
+So if you have extended
+sample superradiance,
+
+those samples are
+no longer coupling
+
+to the electromagnetic field
+with the coupling constant g.
+
+The coupling constant
+g is now multiplied
+
+by the optical density
+of your sample.
+
+And there is a lot of
+interest for current research
+
+for quantum computation,
+manipulation of photon states,
+
+and all that, to do cavity QED.
+
+And in cavity QED,
+we try to have
+
+very good mirrors,
+very small mode volume
+
+to have a very, very large g.
+
+But this large g which
+we achieve in a cavity,
+
+if you put many
+atoms in it, gets
+
+enhanced by the optical density.
+
+So the cavity enhancement and
+the superradiant enhancement
+
+is multiplicative.
+
+And often, it's very favorable
+for single photon manipulation
+
+if you do Bose.
+
+You getting enhancement form
+the cavity and enhancement
+
+due to superradiance.
+
+And the person who has
+really pioneered work
+
+along this direction is
+[INAUDIBLE] here at MIT.
+
+Anyway, yes, with
+five minutes delay,
+
+I finish the chapter
+on superradiance.
+
+Well, that's the
+end of this course.
+
+Let me thank you for your
+active participation.
+
+Sometimes as a lecturer, you
+learn as much as the students.
+
+And I think partially based on
+your questions and discussions,
+
+this is really true.
+
+I've learned a few new
+aspects of atomic physics.
+
+I hope you have
+learned something, too.
+
+And good luck in the future.
\ No newline at end of file
diff --git a/OQ-534Ovf4U.txt b/OQ-534Ovf4U.txt
new file mode 100644
index 0000000000000000000000000000000000000000..44386b44b9ce739c36f34937398dce86dc9fe8d6
--- /dev/null
+++ b/OQ-534Ovf4U.txt
@@ -0,0 +1,13579 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu uh last time we started uh
+
+ align:start position:0%
+ocw.mit.edu uh last time we started uh
+ 
+
+ align:start position:0%
+ocw.mit.edu uh last time we started uh
+looking in more detail at some of the
+
+ align:start position:0%
+looking in more detail at some of the
+ 
+
+ align:start position:0%
+looking in more detail at some of the
+statistical Basics uh these are the
+
+ align:start position:0%
+statistical Basics uh these are the
+ 
+
+ align:start position:0%
+statistical Basics uh these are the
+basis for a lot of the tools and
+
+ align:start position:0%
+basis for a lot of the tools and
+ 
+
+ align:start position:0%
+basis for a lot of the tools and
+techniques that we're going to be
+
+ align:start position:0%
+techniques that we're going to be
+ 
+
+ align:start position:0%
+techniques that we're going to be
+learning about throughout the term uh
+
+ align:start position:0%
+learning about throughout the term uh
+ 
+
+ align:start position:0%
+learning about throughout the term uh
+especially things like statistical
+
+ align:start position:0%
+especially things like statistical
+ 
+
+ align:start position:0%
+especially things like statistical
+process control statistical design of
+
+ align:start position:0%
+process control statistical design of
+ 
+
+ align:start position:0%
+process control statistical design of
+experiments uh robust optimization yield
+
+ align:start position:0%
+experiments uh robust optimization yield
+ 
+
+ align:start position:0%
+experiments uh robust optimization yield
+modeling uh and so on and so we're going
+
+ align:start position:0%
+modeling uh and so on and so we're going
+ 
+
+ align:start position:0%
+modeling uh and so on and so we're going
+to pick up more or less where we where
+
+ align:start position:0%
+to pick up more or less where we where
+ 
+
+ align:start position:0%
+to pick up more or less where we where
+we left off uh we talked a bit about the
+
+ align:start position:0%
+we left off uh we talked a bit about the
+ 
+
+ align:start position:0%
+we left off uh we talked a bit about the
+normal distribution and what I want to
+
+ align:start position:0%
+normal distribution and what I want to
+ 
+
+ align:start position:0%
+normal distribution and what I want to
+do is uh talk a little bit more about a
+
+ align:start position:0%
+do is uh talk a little bit more about a
+ 
+
+ align:start position:0%
+do is uh talk a little bit more about a
+few of the assumptions and and and why
+
+ align:start position:0%
+few of the assumptions and and and why
+ 
+
+ align:start position:0%
+few of the assumptions and and and why
+it's so common that we use it uh for
+
+ align:start position:0%
+it's so common that we use it uh for
+ 
+
+ align:start position:0%
+it's so common that we use it uh for
+describing some of the kinds of data
+
+ align:start position:0%
+describing some of the kinds of data
+ 
+
+ align:start position:0%
+describing some of the kinds of data
+that we looked at last time so we went
+
+ align:start position:0%
+that we looked at last time so we went
+ 
+
+ align:start position:0%
+that we looked at last time so we went
+through a fairly substantial number of
+
+ align:start position:0%
+through a fairly substantial number of
+ 
+
+ align:start position:0%
+through a fairly substantial number of
+different examples and saw um uh
+
+ align:start position:0%
+different examples and saw um uh
+ 
+
+ align:start position:0%
+different examples and saw um uh
+variation in time variation across uh
+
+ align:start position:0%
+variation in time variation across uh
+ 
+
+ align:start position:0%
+variation in time variation across uh
+different parameter sets and so on uh
+
+ align:start position:0%
+different parameter sets and so on uh
+ 
+
+ align:start position:0%
+different parameter sets and so on uh
+just to remind us here's the the
+
+ align:start position:0%
+just to remind us here's the the
+ 
+
+ align:start position:0%
+just to remind us here's the the
+standard normal is just a mean
+
+ align:start position:0%
+standard normal is just a mean
+ 
+
+ align:start position:0%
+standard normal is just a mean
+centered so if we have X as our data and
+
+ align:start position:0%
+centered so if we have X as our data and
+ 
+
+ align:start position:0%
+centered so if we have X as our data and
+we subtract off the mean and then
+
+ align:start position:0%
+we subtract off the mean and then
+ 
+
+ align:start position:0%
+we subtract off the mean and then
+normalize to the standard deviation we
+
+ align:start position:0%
+normalize to the standard deviation we
+ 
+
+ align:start position:0%
+normalize to the standard deviation we
+get a unit normal variable it's another
+
+ align:start position:0%
+get a unit normal variable it's another
+ 
+
+ align:start position:0%
+get a unit normal variable it's another
+random variable Z that uh has a
+
+ align:start position:0%
+random variable Z that uh has a
+ 
+
+ align:start position:0%
+random variable Z that uh has a
+distribution that is marked out in terms
+
+ align:start position:0%
+distribution that is marked out in terms
+ 
+
+ align:start position:0%
+distribution that is marked out in terms
+of numbers of standard deviation and so
+
+ align:start position:0%
+of numbers of standard deviation and so
+ 
+
+ align:start position:0%
+of numbers of standard deviation and so
+this is this is our our normal
+
+ align:start position:0%
+this is this is our our normal
+ 
+
+ align:start position:0%
+this is this is our our normal
+distribution some nice properties that
+
+ align:start position:0%
+distribution some nice properties that
+ 
+
+ align:start position:0%
+distribution some nice properties that
+we mentioned last time are that uh it
+
+ align:start position:0%
+we mentioned last time are that uh it
+ 
+
+ align:start position:0%
+we mentioned last time are that uh it
+only has two parameters so that
+
+ align:start position:0%
+only has two parameters so that
+ 
+
+ align:start position:0%
+only has two parameters so that
+completely describes the normal
+
+ align:start position:0%
+completely describes the normal
+ 
+
+ align:start position:0%
+completely describes the normal
+distribution uh the and the variance or
+
+ align:start position:0%
+distribution uh the and the variance or
+ 
+
+ align:start position:0%
+distribution uh the and the variance or
+standard deviation uh other properties
+
+ align:start position:0%
+standard deviation uh other properties
+ 
+
+ align:start position:0%
+standard deviation uh other properties
+are it's symmetric about the mean uh we
+
+ align:start position:0%
+are it's symmetric about the mean uh we
+ 
+
+ align:start position:0%
+are it's symmetric about the mean uh we
+actually will use that property quite a
+
+ align:start position:0%
+actually will use that property quite a
+ 
+
+ align:start position:0%
+actually will use that property quite a
+bit uh in terms of manipulating some of
+
+ align:start position:0%
+bit uh in terms of manipulating some of
+ 
+
+ align:start position:0%
+bit uh in terms of manipulating some of
+the uh table values that one would look
+
+ align:start position:0%
+the uh table values that one would look
+ 
+
+ align:start position:0%
+the uh table values that one would look
+up for the portion of the distribution
+
+ align:start position:0%
+up for the portion of the distribution
+ 
+
+ align:start position:0%
+up for the portion of the distribution
+that's out in in either of the tail so
+
+ align:start position:0%
+that's out in in either of the tail so
+ 
+
+ align:start position:0%
+that's out in in either of the tail so
+it's a perhaps obvious but we actually
+
+ align:start position:0%
+it's a perhaps obvious but we actually
+ 
+
+ align:start position:0%
+it's a perhaps obvious but we actually
+do use that so we'll come back to that a
+
+ align:start position:0%
+do use that so we'll come back to that a
+ 
+
+ align:start position:0%
+do use that so we'll come back to that a
+little bit later but what I wanted to to
+
+ align:start position:0%
+little bit later but what I wanted to to
+ 
+
+ align:start position:0%
+little bit later but what I wanted to to
+to start with a little bit is talking a
+
+ align:start position:0%
+to start with a little bit is talking a
+ 
+
+ align:start position:0%
+to start with a little bit is talking a
+little bit more about uh this assumption
+
+ align:start position:0%
+little bit more about uh this assumption
+ 
+
+ align:start position:0%
+little bit more about uh this assumption
+if you dive into it that that uh we are
+
+ align:start position:0%
+if you dive into it that that uh we are
+ 
+
+ align:start position:0%
+if you dive into it that that uh we are
+using a normal distribution very often
+
+ align:start position:0%
+using a normal distribution very often
+ 
+
+ align:start position:0%
+using a normal distribution very often
+and the questions are
+
+ align:start position:0%
+and the questions are
+ 
+
+ align:start position:0%
+and the questions are
+why um and how good of an approximation
+
+ align:start position:0%
+why um and how good of an approximation
+ 
+
+ align:start position:0%
+why um and how good of an approximation
+is that in most
+
+ align:start position:0%
+is that in most
+ 
+
+ align:start position:0%
+is that in most
+cases when can we use it when might we
+
+ align:start position:0%
+cases when can we use it when might we
+ 
+
+ align:start position:0%
+cases when can we use it when might we
+be motivated to use it and what we did
+
+ align:start position:0%
+be motivated to use it and what we did
+ 
+
+ align:start position:0%
+be motivated to use it and what we did
+last time is is we did a couple of
+
+ align:start position:0%
+last time is is we did a couple of
+ 
+
+ align:start position:0%
+last time is is we did a couple of
+things where we looked at at some of the
+
+ align:start position:0%
+things where we looked at at some of the
+ 
+
+ align:start position:0%
+things where we looked at at some of the
+data in particular we did histogram
+
+ align:start position:0%
+data in particular we did histogram
+ 
+
+ align:start position:0%
+data in particular we did histogram
+binning kinds of plots of uh
+
+ align:start position:0%
+binning kinds of plots of uh
+ 
+
+ align:start position:0%
+binning kinds of plots of uh
+variations and uh that would often
+
+ align:start position:0%
+variations and uh that would often
+ 
+
+ align:start position:0%
+variations and uh that would often
+motivate based on sort of the general
+
+ align:start position:0%
+motivate based on sort of the general
+ 
+
+ align:start position:0%
+motivate based on sort of the general
+shape that uh uh normal distribution
+
+ align:start position:0%
+shape that uh uh normal distribution
+ 
+
+ align:start position:0%
+shape that uh uh normal distribution
+looked looked
+
+ align:start position:0%
+looked looked
+ 
+
+ align:start position:0%
+looked looked
+appropriate um one can I guess do a
+
+ align:start position:0%
+appropriate um one can I guess do a
+ 
+
+ align:start position:0%
+appropriate um one can I guess do a
+curve fit to the histogram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would you ever try to do
+
+ align:start position:0%
+would you ever try to do
+ 
+
+ align:start position:0%
+would you ever try to do
+that so imagine that you actually had
+
+ align:start position:0%
+that so imagine that you actually had
+ 
+
+ align:start position:0%
+that so imagine that you actually had
+say the tops of the bins for uh a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution so maybe I had bins like
+
+ align:start position:0%
+distribution so maybe I had bins like
+ 
+
+ align:start position:0%
+distribution so maybe I had bins like
+this where some sense I
+
+ align:start position:0%
+this where some sense I
+ 
+
+ align:start position:0%
+this where some sense I
+had these as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values something like this
+
+ align:start position:0%
+values something like this
+ 
+
+ align:start position:0%
+values something like this
+would you actually try to do a normal
+
+ align:start position:0%
+would you actually try to do a normal
+ 
+
+ align:start position:0%
+would you actually try to do a normal
+distribution curve fit to that in other
+
+ align:start position:0%
+distribution curve fit to that in other
+ 
+
+ align:start position:0%
+distribution curve fit to that in other
+words if you said okay what I'm going to
+
+ align:start position:0%
+words if you said okay what I'm going to
+ 
+
+ align:start position:0%
+words if you said okay what I'm going to
+try to do is minimize the errors between
+
+ align:start position:0%
+try to do is minimize the errors between
+ 
+
+ align:start position:0%
+try to do is minimize the errors between
+these points and a normal
+
+ align:start position:0%
+these points and a normal
+ 
+
+ align:start position:0%
+these points and a normal
+distribution does that seem like a
+
+ align:start position:0%
+distribution does that seem like a
+ 
+
+ align:start position:0%
+distribution does that seem like a
+reasonable thing to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do yeah there are some gotes certainly
+
+ align:start position:0%
+do yeah there are some gotes certainly
+ 
+
+ align:start position:0%
+do yeah there are some gotes certainly
+uh with any histogram the the point was
+
+ align:start position:0%
+uh with any histogram the the point was
+ 
+
+ align:start position:0%
+uh with any histogram the the point was
+it's uh the shape of this distribution
+
+ align:start position:0%
+it's uh the shape of this distribution
+ 
+
+ align:start position:0%
+it's uh the shape of this distribution
+if you've everever played around
+
+ align:start position:0%
+if you've everever played around
+ 
+
+ align:start position:0%
+if you've everever played around
+especially with interactive tools where
+
+ align:start position:0%
+especially with interactive tools where
+ 
+
+ align:start position:0%
+especially with interactive tools where
+you can bend and plot up distributions
+
+ align:start position:0%
+you can bend and plot up distributions
+ 
+
+ align:start position:0%
+you can bend and plot up distributions
+if you were to change the the size of
+
+ align:start position:0%
+if you were to change the the size of
+ 
+
+ align:start position:0%
+if you were to change the the size of
+your bins you have this disturbing uh
+
+ align:start position:0%
+your bins you have this disturbing uh
+ 
+
+ align:start position:0%
+your bins you have this disturbing uh
+effect where the shape of your
+
+ align:start position:0%
+effect where the shape of your
+ 
+
+ align:start position:0%
+effect where the shape of your
+distribution sometimes changes a little
+
+ align:start position:0%
+distribution sometimes changes a little
+ 
+
+ align:start position:0%
+distribution sometimes changes a little
+bit out from under you so if you changed
+
+ align:start position:0%
+bit out from under you so if you changed
+ 
+
+ align:start position:0%
+bit out from under you so if you changed
+the bins you may well end up with
+
+ align:start position:0%
+the bins you may well end up with
+ 
+
+ align:start position:0%
+the bins you may well end up with
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+that that uh all of a sudden this one
+
+ align:start position:0%
+that that uh all of a sudden this one
+ 
+
+ align:start position:0%
+that that uh all of a sudden this one
+was low and now it's high and the next
+
+ align:start position:0%
+was low and now it's high and the next
+ 
+
+ align:start position:0%
+was low and now it's high and the next
+one is a little bit low and this one's
+
+ align:start position:0%
+one is a little bit low and this one's
+ 
+
+ align:start position:0%
+one is a little bit low and this one's
+up here you know if your bins are a
+
+ align:start position:0%
+up here you know if your bins are a
+ 
+
+ align:start position:0%
+up here you know if your bins are a
+little bit
+
+ align:start position:0%
+little bit
+ 
+
+ align:start position:0%
+little bit
+wider so that might be a concern but
+
+ align:start position:0%
+wider so that might be a concern but
+ 
+
+ align:start position:0%
+wider so that might be a concern but
+that's actually not the point that I'm
+
+ align:start position:0%
+that's actually not the point that I'm
+ 
+
+ align:start position:0%
+that's actually not the point that I'm
+after would you curve fit to a dist to
+
+ align:start position:0%
+after would you curve fit to a dist to
+ 
+
+ align:start position:0%
+after would you curve fit to a dist to
+this uh distribution to fit a normal to
+
+ align:start position:0%
+this uh distribution to fit a normal to
+ 
+
+ align:start position:0%
+this uh distribution to fit a normal to
+to your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data well you said that normal
+
+ align:start position:0%
+data well you said that normal
+ 
+
+ align:start position:0%
+data well you said that normal
+distribution is described by standard
+
+ align:start position:0%
+distribution is described by standard
+ 
+
+ align:start position:0%
+distribution is described by standard
+deviation and the mean so you might as
+
+ align:start position:0%
+deviation and the mean so you might as
+ 
+
+ align:start position:0%
+deviation and the mean so you might as
+well just take the mean and standard
+
+ align:start position:0%
+well just take the mean and standard
+ 
+
+ align:start position:0%
+well just take the mean and standard
+ation of your data beautiful and use
+
+ align:start position:0%
+ation of your data beautiful and use
+ 
+
+ align:start position:0%
+ation of your data beautiful and use
+that right right especially I guess the
+
+ align:start position:0%
+that right right especially I guess the
+ 
+
+ align:start position:0%
+that right right especially I guess the
+only circumstance I can imagine where it
+
+ align:start position:0%
+only circumstance I can imagine where it
+ 
+
+ align:start position:0%
+only circumstance I can imagine where it
+might make sense to curvefit is you
+
+ align:start position:0%
+might make sense to curvefit is you
+ 
+
+ align:start position:0%
+might make sense to curvefit is you
+didn't have the raw data you only had
+
+ align:start position:0%
+didn't have the raw data you only had
+ 
+
+ align:start position:0%
+didn't have the raw data you only had
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+bins that's kind of kind of strange I
+
+ align:start position:0%
+bins that's kind of kind of strange I
+ 
+
+ align:start position:0%
+bins that's kind of kind of strange I
+think in most cases you would in fact
+
+ align:start position:0%
+think in most cases you would in fact
+ 
+
+ align:start position:0%
+think in most cases you would in fact
+have the raw data and then you simply
+
+ align:start position:0%
+have the raw data and then you simply
+ 
+
+ align:start position:0%
+have the raw data and then you simply
+calculate uh the the the mean and the
+
+ align:start position:0%
+calculate uh the the the mean and the
+ 
+
+ align:start position:0%
+calculate uh the the the mean and the
+standard deviation now one thing we want
+
+ align:start position:0%
+standard deviation now one thing we want
+ 
+
+ align:start position:0%
+standard deviation now one thing we want
+to do and we'll get to a little bit
+
+ align:start position:0%
+to do and we'll get to a little bit
+ 
+
+ align:start position:0%
+to do and we'll get to a little bit
+today is why that's a reason able thing
+
+ align:start position:0%
+today is why that's a reason able thing
+ 
+
+ align:start position:0%
+today is why that's a reason able thing
+to do to actually go in and calculate
+
+ align:start position:0%
+to do to actually go in and calculate
+ 
+
+ align:start position:0%
+to do to actually go in and calculate
+the mean and standard deviation why is
+
+ align:start position:0%
+the mean and standard deviation why is
+ 
+
+ align:start position:0%
+the mean and standard deviation why is
+that a good estimator for the true mean
+
+ align:start position:0%
+that a good estimator for the true mean
+ 
+
+ align:start position:0%
+that a good estimator for the true mean
+and dis and and and uh uh underlying
+
+ align:start position:0%
+and dis and and and uh uh underlying
+ 
+
+ align:start position:0%
+and dis and and and uh uh underlying
+parameters for this distribution the
+
+ align:start position:0%
+parameters for this distribution the
+ 
+
+ align:start position:0%
+parameters for this distribution the
+true mean and the true
+
+ align:start position:0%
+true mean and the true
+ 
+
+ align:start position:0%
+true mean and the true
+variance um there's other things you can
+
+ align:start position:0%
+variance um there's other things you can
+ 
+
+ align:start position:0%
+variance um there's other things you can
+do certainly to to check and see if you
+
+ align:start position:0%
+do certainly to to check and see if you
+ 
+
+ align:start position:0%
+do certainly to to check and see if you
+had your data and you calculated the
+
+ align:start position:0%
+had your data and you calculated the
+ 
+
+ align:start position:0%
+had your data and you calculated the
+mean and standard deviation then you can
+
+ align:start position:0%
+mean and standard deviation then you can
+ 
+
+ align:start position:0%
+mean and standard deviation then you can
+plot perhaps your uh gaan on top of that
+
+ align:start position:0%
+plot perhaps your uh gaan on top of that
+ 
+
+ align:start position:0%
+plot perhaps your uh gaan on top of that
+distribution and that I think is a
+
+ align:start position:0%
+distribution and that I think is a
+ 
+
+ align:start position:0%
+distribution and that I think is a
+reasonable thing to do as a quick check
+
+ align:start position:0%
+reasonable thing to do as a quick check
+ 
+
+ align:start position:0%
+reasonable thing to do as a quick check
+visually to see how well it seems to map
+
+ align:start position:0%
+visually to see how well it seems to map
+ 
+
+ align:start position:0%
+visually to see how well it seems to map
+as well as a quick check that you had
+
+ align:start position:0%
+as well as a quick check that you had
+ 
+
+ align:start position:0%
+as well as a quick check that you had
+reasonable calculations not something
+
+ align:start position:0%
+reasonable calculations not something
+ 
+
+ align:start position:0%
+reasonable calculations not something
+strange uh go wrong uh just in in your
+
+ align:start position:0%
+strange uh go wrong uh just in in your
+ 
+
+ align:start position:0%
+strange uh go wrong uh just in in your
+numerical calculation of those
+
+ align:start position:0%
+numerical calculation of those
+ 
+
+ align:start position:0%
+numerical calculation of those
+parameters now there's a couple of other
+
+ align:start position:0%
+parameters now there's a couple of other
+ 
+
+ align:start position:0%
+parameters now there's a couple of other
+things that one can do to sort of check
+
+ align:start position:0%
+things that one can do to sort of check
+ 
+
+ align:start position:0%
+things that one can do to sort of check
+quickly visually uh the Assumption and
+
+ align:start position:0%
+quickly visually uh the Assumption and
+ 
+
+ align:start position:0%
+quickly visually uh the Assumption and
+then there's a couple of very nice uh
+
+ align:start position:0%
+then there's a couple of very nice uh
+ 
+
+ align:start position:0%
+then there's a couple of very nice uh
+additional tools uh that I'll I'll
+
+ align:start position:0%
+additional tools uh that I'll I'll
+ 
+
+ align:start position:0%
+additional tools uh that I'll I'll
+mention here for for either checking
+
+ align:start position:0%
+mention here for for either checking
+ 
+
+ align:start position:0%
+mention here for for either checking
+assumptions or visually
+
+ align:start position:0%
+assumptions or visually
+ 
+
+ align:start position:0%
+assumptions or visually
+um in a little bit more sophisticated
+
+ align:start position:0%
+um in a little bit more sophisticated
+ 
+
+ align:start position:0%
+um in a little bit more sophisticated
+way visually or numerically check uh a
+
+ align:start position:0%
+way visually or numerically check uh a
+ 
+
+ align:start position:0%
+way visually or numerically check uh a
+couple of those assumptions but one
+
+ align:start position:0%
+couple of those assumptions but one
+ 
+
+ align:start position:0%
+couple of those assumptions but one
+thing you can certainly do is look at uh
+
+ align:start position:0%
+thing you can certainly do is look at uh
+ 
+
+ align:start position:0%
+thing you can certainly do is look at uh
+the location of your data and just do a
+
+ align:start position:0%
+the location of your data and just do a
+ 
+
+ align:start position:0%
+the location of your data and just do a
+quick comparison between the percentage
+
+ align:start position:0%
+quick comparison between the percentage
+ 
+
+ align:start position:0%
+quick comparison between the percentage
+of data that you would expect in
+
+ align:start position:0%
+of data that you would expect in
+ 
+
+ align:start position:0%
+of data that you would expect in
+different bands of this data and and
+
+ align:start position:0%
+different bands of this data and and
+ 
+
+ align:start position:0%
+different bands of this data and and
+we'll we'll
+
+ align:start position:0%
+we'll we'll
+ 
+
+ align:start position:0%
+we'll we'll
+do some a little bit more uh examples
+
+ align:start position:0%
+do some a little bit more uh examples
+ 
+
+ align:start position:0%
+do some a little bit more uh examples
+there so that we know what percentage of
+
+ align:start position:0%
+there so that we know what percentage of
+ 
+
+ align:start position:0%
+there so that we know what percentage of
+the data we expect in the plus minus one
+
+ align:start position:0%
+the data we expect in the plus minus one
+ 
+
+ align:start position:0%
+the data we expect in the plus minus one
+Sigma band for example or what
+
+ align:start position:0%
+Sigma band for example or what
+ 
+
+ align:start position:0%
+Sigma band for example or what
+percentage of the data we would
+
+ align:start position:0%
+percentage of the data we would
+ 
+
+ align:start position:0%
+percentage of the data we would
+typically expect out in the three sigma
+
+ align:start position:0%
+typically expect out in the three sigma
+ 
+
+ align:start position:0%
+typically expect out in the three sigma
+taals of the data and so you can do a
+
+ align:start position:0%
+taals of the data and so you can do a
+ 
+
+ align:start position:0%
+taals of the data and so you can do a
+quick calculation and comparison of the
+
+ align:start position:0%
+quick calculation and comparison of the
+ 
+
+ align:start position:0%
+quick calculation and comparison of the
+percentage of data in each of these
+
+ align:start position:0%
+percentage of data in each of these
+ 
+
+ align:start position:0%
+percentage of data in each of these
+different bands and see you know is that
+
+ align:start position:0%
+different bands and see you know is that
+ 
+
+ align:start position:0%
+different bands and see you know is that
+matching up to what we would expect from
+
+ align:start position:0%
+matching up to what we would expect from
+ 
+
+ align:start position:0%
+matching up to what we would expect from
+a normal distribution um this actually
+
+ align:start position:0%
+a normal distribution um this actually
+ 
+
+ align:start position:0%
+a normal distribution um this actually
+gets very close to the idea of
+
+ align:start position:0%
+gets very close to the idea of
+ 
+
+ align:start position:0%
+gets very close to the idea of
+confidence
+
+ align:start position:0%
+confidence
+ 
+
+ align:start position:0%
+confidence
+intervals uh that that uh will formalize
+
+ align:start position:0%
+intervals uh that that uh will formalize
+ 
+
+ align:start position:0%
+intervals uh that that uh will formalize
+a little bit more now there's a couple
+
+ align:start position:0%
+a little bit more now there's a couple
+ 
+
+ align:start position:0%
+a little bit more now there's a couple
+of of additional things I've listed here
+
+ align:start position:0%
+of of additional things I've listed here
+ 
+
+ align:start position:0%
+of of additional things I've listed here
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+is you can look at the curtosis or do a
+
+ align:start position:0%
+is you can look at the curtosis or do a
+ 
+
+ align:start position:0%
+is you can look at the curtosis or do a
+quick calculation uh of cryosis which is
+
+ align:start position:0%
+quick calculation uh of cryosis which is
+ 
+
+ align:start position:0%
+quick calculation uh of cryosis which is
+a higher order statistical moment than
+
+ align:start position:0%
+a higher order statistical moment than
+ 
+
+ align:start position:0%
+a higher order statistical moment than
+the mean or the variance in fact if you
+
+ align:start position:0%
+the mean or the variance in fact if you
+ 
+
+ align:start position:0%
+the mean or the variance in fact if you
+look at the def def of the
+
+ align:start position:0%
+look at the def def of the
+ 
+
+ align:start position:0%
+look at the def def of the
+curtosis it's an expectation of the
+
+ align:start position:0%
+curtosis it's an expectation of the
+ 
+
+ align:start position:0%
+curtosis it's an expectation of the
+fourth
+
+ align:start position:0%
+fourth
+ 
+
+ align:start position:0%
+fourth
+moment or it is the a calculation a
+
+ align:start position:0%
+moment or it is the a calculation a
+ 
+
+ align:start position:0%
+moment or it is the a calculation a
+normalized version of the fourth moment
+
+ align:start position:0%
+normalized version of the fourth moment
+ 
+
+ align:start position:0%
+normalized version of the fourth moment
+and for a perfectly normal distribution
+
+ align:start position:0%
+and for a perfectly normal distribution
+ 
+
+ align:start position:0%
+and for a perfectly normal distribution
+uh this curosis value would be would be
+
+ align:start position:0%
+uh this curosis value would be would be
+ 
+
+ align:start position:0%
+uh this curosis value would be would be
+one and then as the distribution changes
+
+ align:start position:0%
+one and then as the distribution changes
+ 
+
+ align:start position:0%
+one and then as the distribution changes
+its shape either gets more peaked or
+
+ align:start position:0%
+its shape either gets more peaked or
+ 
+
+ align:start position:0%
+its shape either gets more peaked or
+less
+
+ align:start position:0%
+less
+ 
+
+ align:start position:0%
+less
+peaked go following other distributions
+
+ align:start position:0%
+peaked go following other distributions
+ 
+
+ align:start position:0%
+peaked go following other distributions
+other common distributions then it
+
+ align:start position:0%
+other common distributions then it
+ 
+
+ align:start position:0%
+other common distributions then it
+starts to deviate substantially from um
+
+ align:start position:0%
+starts to deviate substantially from um
+ 
+
+ align:start position:0%
+starts to deviate substantially from um
+from k equals 1 um and in fact this is a
+
+ align:start position:0%
+from k equals 1 um and in fact this is a
+ 
+
+ align:start position:0%
+from k equals 1 um and in fact this is a
+quick little tool to use sometimes if
+
+ align:start position:0%
+quick little tool to use sometimes if
+ 
+
+ align:start position:0%
+quick little tool to use sometimes if
+you're not
+
+ align:start position:0%
+you're not
+ 
+
+ align:start position:0%
+you're not
+sure well number one if it's normal and
+
+ align:start position:0%
+sure well number one if it's normal and
+ 
+
+ align:start position:0%
+sure well number one if it's normal and
+number two if it's not normal what
+
+ align:start position:0%
+number two if it's not normal what
+ 
+
+ align:start position:0%
+number two if it's not normal what
+distribution might it
+
+ align:start position:0%
+distribution might it
+ 
+
+ align:start position:0%
+distribution might it
+follow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um if you look here this is a nice plot
+
+ align:start position:0%
+um if you look here this is a nice plot
+ 
+
+ align:start position:0%
+um if you look here this is a nice plot
+although I didn't uh break out what all
+
+ align:start position:0%
+although I didn't uh break out what all
+ 
+
+ align:start position:0%
+although I didn't uh break out what all
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+these different
+
+ align:start position:0%
+these different
+ 
+
+ align:start position:0%
+these different
+uh distributions
+
+ align:start position:0%
+uh distributions
+ 
+
+ align:start position:0%
+uh distributions
+are this is just a plot normalized to to
+
+ align:start position:0%
+are this is just a plot normalized to to
+ 
+
+ align:start position:0%
+are this is just a plot normalized to to
+standard deviation of of the data of a
+
+ align:start position:0%
+standard deviation of of the data of a
+ 
+
+ align:start position:0%
+standard deviation of of the data of a
+diff a set of different
+
+ align:start position:0%
+diff a set of different
+ 
+
+ align:start position:0%
+diff a set of different
+distributions and the black one here is
+
+ align:start position:0%
+distributions and the black one here is
+ 
+
+ align:start position:0%
+distributions and the black one here is
+n so this is let me do the black one
+
+ align:start position:0%
+n so this is let me do the black one
+ 
+
+ align:start position:0%
+n so this is let me do the black one
+here right this is the end distribution
+
+ align:start position:0%
+here right this is the end distribution
+ 
+
+ align:start position:0%
+here right this is the end distribution
+that's our
+
+ align:start position:0%
+that's our
+ 
+
+ align:start position:0%
+that's our
+gaussian with a
+
+ align:start position:0%
+gaussian with a
+ 
+
+ align:start position:0%
+gaussian with a
+curtosis uh well I guess you got to look
+
+ align:start position:0%
+curtosis uh well I guess you got to look
+ 
+
+ align:start position:0%
+curtosis uh well I guess you got to look
+a little bit carefully at the defition
+
+ align:start position:0%
+a little bit carefully at the defition
+ 
+
+ align:start position:0%
+a little bit carefully at the defition
+actually I
+
+ align:start position:0%
+actually I
+ 
+
+ align:start position:0%
+actually I
+think if I go back to the previous page
+
+ align:start position:0%
+think if I go back to the previous page
+ 
+
+ align:start position:0%
+think if I go back to the previous page
+which is one uh that that Dave had this
+
+ align:start position:0%
+which is one uh that that Dave had this
+ 
+
+ align:start position:0%
+which is one uh that that Dave had this
+definition for sample data is
+
+ align:start position:0%
+definition for sample data is
+ 
+
+ align:start position:0%
+definition for sample data is
+essentially uh as n gets very large this
+
+ align:start position:0%
+essentially uh as n gets very large this
+ 
+
+ align:start position:0%
+essentially uh as n gets very large this
+subtracts off subtracts off three so
+
+ align:start position:0%
+subtracts off subtracts off three so
+ 
+
+ align:start position:0%
+subtracts off subtracts off three so
+that I believe then in this case this uh
+
+ align:start position:0%
+that I believe then in this case this uh
+ 
+
+ align:start position:0%
+that I believe then in this case this uh
+curtosis for a normal distribution is
+
+ align:start position:0%
+curtosis for a normal distribution is
+ 
+
+ align:start position:0%
+curtosis for a normal distribution is
+actually more like zero these two
+
+ align:start position:0%
+actually more like zero these two
+ 
+
+ align:start position:0%
+actually more like zero these two
+definitions you uh you might look up I'm
+
+ align:start position:0%
+definitions you uh you might look up I'm
+ 
+
+ align:start position:0%
+definitions you uh you might look up I'm
+not sure are exactly the same same
+
+ align:start position:0%
+not sure are exactly the same same
+ 
+
+ align:start position:0%
+not sure are exactly the same same
+rarely would you actually use this one
+
+ align:start position:0%
+rarely would you actually use this one
+ 
+
+ align:start position:0%
+rarely would you actually use this one
+you're going to actually use U use this
+
+ align:start position:0%
+you're going to actually use U use this
+ 
+
+ align:start position:0%
+you're going to actually use U use this
+definition which basically subtracts off
+
+ align:start position:0%
+definition which basically subtracts off
+ 
+
+ align:start position:0%
+definition which basically subtracts off
+a value this is this goes with the plot
+
+ align:start position:0%
+a value this is this goes with the plot
+ 
+
+ align:start position:0%
+a value this is this goes with the plot
+on the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+page so they are slightly different
+
+ align:start position:0%
+page so they are slightly different
+ 
+
+ align:start position:0%
+page so they are slightly different
+definitions I
+
+ align:start position:0%
+definitions I
+ 
+
+ align:start position:0%
+definitions I
+believe
+
+ align:start position:0%
+believe
+ 
+
+ align:start position:0%
+believe
+um so in that case that subtracting off
+
+ align:start position:0%
+um so in that case that subtracting off
+ 
+
+ align:start position:0%
+um so in that case that subtracting off
+the of of three for the normal
+
+ align:start position:0%
+the of of three for the normal
+ 
+
+ align:start position:0%
+the of of three for the normal
+distribution it ends up with a value of
+
+ align:start position:0%
+distribution it ends up with a value of
+ 
+
+ align:start position:0%
+distribution it ends up with a value of
+of of about zero now what's nice is as
+
+ align:start position:0%
+of of about zero now what's nice is as
+ 
+
+ align:start position:0%
+of of about zero now what's nice is as
+you get some of these distributions such
+
+ align:start position:0%
+you get some of these distributions such
+ 
+
+ align:start position:0%
+you get some of these distributions such
+as uh the lass distribution this very
+
+ align:start position:0%
+as uh the lass distribution this very
+ 
+
+ align:start position:0%
+as uh the lass distribution this very
+peaked one right
+
+ align:start position:0%
+peaked one right
+ 
+
+ align:start position:0%
+peaked one right
+here the cryosis value goes up it's an
+
+ align:start position:0%
+here the cryosis value goes up it's an
+ 
+
+ align:start position:0%
+here the cryosis value goes up it's an
+indication of a more Peak uh uh
+
+ align:start position:0%
+indication of a more Peak uh uh
+ 
+
+ align:start position:0%
+indication of a more Peak uh uh
+distribution uh the logistic
+
+ align:start position:0%
+distribution uh the logistic
+ 
+
+ align:start position:0%
+distribution uh the logistic
+distribution which we might talk about a
+
+ align:start position:0%
+distribution which we might talk about a
+ 
+
+ align:start position:0%
+distribution which we might talk about a
+little bit later uh it's one that comes
+
+ align:start position:0%
+little bit later uh it's one that comes
+ 
+
+ align:start position:0%
+little bit later uh it's one that comes
+up occasionally with uh uh
+
+ align:start position:0%
+up occasionally with uh uh
+ 
+
+ align:start position:0%
+up occasionally with uh uh
+some quality or discreet kinds of
+
+ align:start position:0%
+some quality or discreet kinds of
+ 
+
+ align:start position:0%
+some quality or discreet kinds of
+distributions has a curtosis of 1.2 and
+
+ align:start position:0%
+distributions has a curtosis of 1.2 and
+ 
+
+ align:start position:0%
+distributions has a curtosis of 1.2 and
+the interesting one here also is the
+
+ align:start position:0%
+the interesting one here also is the
+ 
+
+ align:start position:0%
+the interesting one here also is the
+uniform
+
+ align:start position:0%
+uniform
+ 
+
+ align:start position:0%
+uniform
+distribution Which is less sharply
+
+ align:start position:0%
+distribution Which is less sharply
+ 
+
+ align:start position:0%
+distribution Which is less sharply
+peaked than a gaussian and it actually
+
+ align:start position:0%
+peaked than a gaussian and it actually
+ 
+
+ align:start position:0%
+peaked than a gaussian and it actually
+has a negative kosis with that
+
+ align:start position:0%
+has a negative kosis with that
+ 
+
+ align:start position:0%
+has a negative kosis with that
+subtraction of the of the three off at
+
+ align:start position:0%
+subtraction of the of the three off at
+ 
+
+ align:start position:0%
+subtraction of the of the three off at
+at the end so you might find uh uh that
+
+ align:start position:0%
+at the end so you might find uh uh that
+ 
+
+ align:start position:0%
+at the end so you might find uh uh that
+as a useful tool I've rarely used
+
+ align:start position:0%
+as a useful tool I've rarely used
+ 
+
+ align:start position:0%
+as a useful tool I've rarely used
+curtosis actually as an indicator but I
+
+ align:start position:0%
+curtosis actually as an indicator but I
+ 
+
+ align:start position:0%
+curtosis actually as an indicator but I
+want it want to mention it to you
+
+ align:start position:0%
+want it want to mention it to you
+ 
+
+ align:start position:0%
+want it want to mention it to you
+because it uh it is it is out there as
+
+ align:start position:0%
+because it uh it is it is out there as
+ 
+
+ align:start position:0%
+because it uh it is it is out there as
+as a at least a hint at looking at some
+
+ align:start position:0%
+as a at least a hint at looking at some
+ 
+
+ align:start position:0%
+as a at least a hint at looking at some
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+distributions a more useful tool Yeah
+
+ align:start position:0%
+distributions a more useful tool Yeah
+ 
+
+ align:start position:0%
+distributions a more useful tool Yeah
+question so there's two different
+
+ align:start position:0%
+question so there's two different
+ 
+
+ align:start position:0%
+question so there's two different
+formulas is
+
+ align:start position:0%
+formulas is
+ 
+
+ align:start position:0%
+formulas is
+well yeah so this is for sample data and
+
+ align:start position:0%
+well yeah so this is for sample data and
+ 
+
+ align:start position:0%
+well yeah so this is for sample data and
+I think if you were to actually go
+
+ align:start position:0%
+I think if you were to actually go
+ 
+
+ align:start position:0%
+I think if you were to actually go
+in I mean essentially this I uh
+
+ align:start position:0%
+in I mean essentially this I uh
+ 
+
+ align:start position:0%
+in I mean essentially this I uh
+I I have not checked this this was uh
+
+ align:start position:0%
+I I have not checked this this was uh
+ 
+
+ align:start position:0%
+I I have not checked this this was uh
+some definitions
+
+ align:start position:0%
+some definitions
+ 
+
+ align:start position:0%
+some definitions
+from previous class notes uh I do
+
+ align:start position:0%
+from previous class notes uh I do
+ 
+
+ align:start position:0%
+from previous class notes uh I do
+believe when I did a a quick lookup on
+
+ align:start position:0%
+believe when I did a a quick lookup on
+ 
+
+ align:start position:0%
+believe when I did a a quick lookup on
+what kosis is I believe this is a
+
+ align:start position:0%
+what kosis is I believe this is a
+ 
+
+ align:start position:0%
+what kosis is I believe this is a
+better uh definition in terms of actual
+
+ align:start position:0%
+better uh definition in terms of actual
+ 
+
+ align:start position:0%
+better uh definition in terms of actual
+calculation formulas that you can use
+
+ align:start position:0%
+calculation formulas that you can use
+ 
+
+ align:start position:0%
+calculation formulas that you can use
+for calculating it um this is to give
+
+ align:start position:0%
+for calculating it um this is to give
+ 
+
+ align:start position:0%
+for calculating it um this is to give
+you the sense I mean it's sort of
+
+ align:start position:0%
+you the sense I mean it's sort of
+ 
+
+ align:start position:0%
+you the sense I mean it's sort of
+lurking in here you can see the
+
+ align:start position:0%
+lurking in here you can see the
+ 
+
+ align:start position:0%
+lurking in here you can see the
+expectation operation down in here um
+
+ align:start position:0%
+expectation operation down in here um
+ 
+
+ align:start position:0%
+expectation operation down in here um
+and then the normalization to the
+
+ align:start position:0%
+and then the normalization to the
+ 
+
+ align:start position:0%
+and then the normalization to the
+standard deviation in this case this is
+
+ align:start position:0%
+standard deviation in this case this is
+ 
+
+ align:start position:0%
+standard deviation in this case this is
+has to be your calculated standard
+
+ align:start position:0%
+has to be your calculated standard
+ 
+
+ align:start position:0%
+has to be your calculated standard
+deviation um this is kind of the
+
+ align:start position:0%
+deviation um this is kind of the
+ 
+
+ align:start position:0%
+deviation um this is kind of the
+abstracted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+uh so if you actually poke around you
+
+ align:start position:0%
+uh so if you actually poke around you
+ 
+
+ align:start position:0%
+uh so if you actually poke around you
+will find in the literature more than
+
+ align:start position:0%
+will find in the literature more than
+ 
+
+ align:start position:0%
+will find in the literature more than
+one definition of a
+
+ align:start position:0%
+one definition of a
+ 
+
+ align:start position:0%
+one definition of a
+curtosis uh my point was that this is
+
+ align:start position:0%
+curtosis uh my point was that this is
+ 
+
+ align:start position:0%
+curtosis uh my point was that this is
+what I would use if you want to use the
+
+ align:start position:0%
+what I would use if you want to use the
+ 
+
+ align:start position:0%
+what I would use if you want to use the
+plot on the next page in terms of coming
+
+ align:start position:0%
+plot on the next page in terms of coming
+ 
+
+ align:start position:0%
+plot on the next page in terms of coming
+up with a number that might also
+
+ align:start position:0%
+up with a number that might also
+ 
+
+ align:start position:0%
+up with a number that might also
+indicate if there's a different
+
+ align:start position:0%
+indicate if there's a different
+ 
+
+ align:start position:0%
+indicate if there's a different
+distribution that you might look
+
+ align:start position:0%
+distribution that you might look
+ 
+
+ align:start position:0%
+distribution that you might look
+at so it's related to the fourth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment a more useful tool and this is
+
+ align:start position:0%
+moment a more useful tool and this is
+ 
+
+ align:start position:0%
+moment a more useful tool and this is
+one that I actually do
+
+ align:start position:0%
+one that I actually do
+ 
+
+ align:start position:0%
+one that I actually do
+use is uh probability or or quantile
+
+ align:start position:0%
+use is uh probability or or quantile
+ 
+
+ align:start position:0%
+use is uh probability or or quantile
+quantile plots and there's a a
+
+ align:start position:0%
+quantile plots and there's a a
+ 
+
+ align:start position:0%
+quantile plots and there's a a
+section in Montgomery on that uh as well
+
+ align:start position:0%
+section in Montgomery on that uh as well
+ 
+
+ align:start position:0%
+section in Montgomery on that uh as well
+as different tool boxes will'll be able
+
+ align:start position:0%
+as different tool boxes will'll be able
+ 
+
+ align:start position:0%
+as different tool boxes will'll be able
+to generate these things and so here's
+
+ align:start position:0%
+to generate these things and so here's
+ 
+
+ align:start position:0%
+to generate these things and so here's
+an example for a quantile quantile
+
+ align:start position:0%
+an example for a quantile quantile
+ 
+
+ align:start position:0%
+an example for a quantile quantile
+plot by the by the way I did
+
+ align:start position:0%
+plot by the by the way I did
+ 
+
+ align:start position:0%
+plot by the by the way I did
+uh what I've started doing on the
+
+ align:start position:0%
+uh what I've started doing on the
+ 
+
+ align:start position:0%
+uh what I've started doing on the
+lecture notes on the web is put up an
+
+ align:start position:0%
+lecture notes on the web is put up an
+ 
+
+ align:start position:0%
+lecture notes on the web is put up an
+early draft as early as I can for uh the
+
+ align:start position:0%
+early draft as early as I can for uh the
+ 
+
+ align:start position:0%
+early draft as early as I can for uh the
+next couple of weeks of lecture notes
+
+ align:start position:0%
+next couple of weeks of lecture notes
+ 
+
+ align:start position:0%
+next couple of weeks of lecture notes
+but then as I'm editing and adding in uh
+
+ align:start position:0%
+but then as I'm editing and adding in uh
+ 
+
+ align:start position:0%
+but then as I'm editing and adding in uh
+you I'll I'll have the most up to-date
+
+ align:start position:0%
+you I'll I'll have the most up to-date
+ 
+
+ align:start position:0%
+you I'll I'll have the most up to-date
+one so if you've got slides you may be
+
+ align:start position:0%
+one so if you've got slides you may be
+ 
+
+ align:start position:0%
+one so if you've got slides you may be
+missing a couple of these if you printed
+
+ align:start position:0%
+missing a couple of these if you printed
+ 
+
+ align:start position:0%
+missing a couple of these if you printed
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+out before 9 or 10 p.m. last night I
+
+ align:start position:0%
+out before 9 or 10 p.m. last night I
+ 
+
+ align:start position:0%
+out before 9 or 10 p.m. last night I
+think these got updated about that time
+
+ align:start position:0%
+think these got updated about that time
+ 
+
+ align:start position:0%
+think these got updated about that time
+uh so this plot for example was not in
+
+ align:start position:0%
+uh so this plot for example was not in
+ 
+
+ align:start position:0%
+uh so this plot for example was not in
+the early draft of the slides and I'll
+
+ align:start position:0%
+the early draft of the slides and I'll
+ 
+
+ align:start position:0%
+the early draft of the slides and I'll
+try to indicate that with a little draft
+
+ align:start position:0%
+try to indicate that with a little draft
+ 
+
+ align:start position:0%
+try to indicate that with a little draft
+on the web page if if there's still
+
+ align:start position:0%
+on the web page if if there's still
+ 
+
+ align:start position:0%
+on the web page if if there's still
+early drafts of the
+
+ align:start position:0%
+early drafts of the
+ 
+
+ align:start position:0%
+early drafts of the
+slides so what are quantile quantile
+
+ align:start position:0%
+slides so what are quantile quantile
+ 
+
+ align:start position:0%
+slides so what are quantile quantile
+plots these are a little bit subtle in
+
+ align:start position:0%
+plots these are a little bit subtle in
+ 
+
+ align:start position:0%
+plots these are a little bit subtle in
+terms of uh uh explaining so so let me
+
+ align:start position:0%
+terms of uh uh explaining so so let me
+ 
+
+ align:start position:0%
+terms of uh uh explaining so so let me
+try to give it a shot at explaining and
+
+ align:start position:0%
+try to give it a shot at explaining and
+ 
+
+ align:start position:0%
+try to give it a shot at explaining and
+then if you have questions um uh let me
+
+ align:start position:0%
+then if you have questions um uh let me
+ 
+
+ align:start position:0%
+then if you have questions um uh let me
+know and then normally it's going to be
+
+ align:start position:0%
+know and then normally it's going to be
+ 
+
+ align:start position:0%
+know and then normally it's going to be
+generated by uh your statistics package
+
+ align:start position:0%
+generated by uh your statistics package
+ 
+
+ align:start position:0%
+generated by uh your statistics package
+there are hand ways to do it and I'll
+
+ align:start position:0%
+there are hand ways to do it and I'll
+ 
+
+ align:start position:0%
+there are hand ways to do it and I'll
+refer you to Montgomery for practice
+
+ align:start position:0%
+refer you to Montgomery for practice
+ 
+
+ align:start position:0%
+refer you to Montgomery for practice
+with actually trying to generate them if
+
+ align:start position:0%
+with actually trying to generate them if
+ 
+
+ align:start position:0%
+with actually trying to generate them if
+you had to by hand but here's the basic
+
+ align:start position:0%
+you had to by hand but here's the basic
+ 
+
+ align:start position:0%
+you had to by hand but here's the basic
+idea what we're plotting is uh
+
+ align:start position:0%
+idea what we're plotting is uh
+ 
+
+ align:start position:0%
+idea what we're plotting is uh
+the actual data that you've
+
+ align:start position:0%
+the actual data that you've
+ 
+
+ align:start position:0%
+the actual data that you've
+got and in the y axis you'll be plotting
+
+ align:start position:0%
+got and in the y axis you'll be plotting
+ 
+
+ align:start position:0%
+got and in the y axis you'll be plotting
+your data in terms of uh
+
+ align:start position:0%
+your data in terms of uh
+ 
+
+ align:start position:0%
+your data in terms of uh
+normalized distribution so you would
+
+ align:start position:0%
+normalized distribution so you would
+ 
+
+ align:start position:0%
+normalized distribution so you would
+normalize to the mean and then uh or
+
+ align:start position:0%
+normalize to the mean and then uh or
+ 
+
+ align:start position:0%
+normalize to the mean and then uh or
+Center to the mean and then scale it to
+
+ align:start position:0%
+Center to the mean and then scale it to
+ 
+
+ align:start position:0%
+Center to the mean and then scale it to
+your standard deviation so think of
+
+ align:start position:0%
+your standard deviation so think of
+ 
+
+ align:start position:0%
+your standard deviation so think of
+these as unit unit standard deviations
+
+ align:start position:0%
+these as unit unit standard deviations
+ 
+
+ align:start position:0%
+these as unit unit standard deviations
+so you simply find that as your sort of
+
+ align:start position:0%
+so you simply find that as your sort of
+ 
+
+ align:start position:0%
+so you simply find that as your sort of
+your Y location for your
+
+ align:start position:0%
+your Y location for your
+ 
+
+ align:start position:0%
+your Y location for your
+data okay then what you're plotting on
+
+ align:start position:0%
+data okay then what you're plotting on
+ 
+
+ align:start position:0%
+data okay then what you're plotting on
+the x axis is the normal theoretical I'm
+
+ align:start position:0%
+the x axis is the normal theoretical I'm
+ 
+
+ align:start position:0%
+the x axis is the normal theoretical I'm
+not sure I'd use quantiles here but the
+
+ align:start position:0%
+not sure I'd use quantiles here but the
+ 
+
+ align:start position:0%
+not sure I'd use quantiles here but the
+your normal theoretical standard
+
+ align:start position:0%
+your normal theoretical standard
+ 
+
+ align:start position:0%
+your normal theoretical standard
+deviation for that number of data points
+
+ align:start position:0%
+deviation for that number of data points
+ 
+
+ align:start position:0%
+deviation for that number of data points
+that you would have had and the location
+
+ align:start position:0%
+that you would have had and the location
+ 
+
+ align:start position:0%
+that you would have had and the location
+for each of those data points so imagine
+
+ align:start position:0%
+for each of those data points so imagine
+ 
+
+ align:start position:0%
+for each of those data points so imagine
+this is a 50 data points I'm not sure
+
+ align:start position:0%
+this is a 50 data points I'm not sure
+ 
+
+ align:start position:0%
+this is a 50 data points I'm not sure
+exactly how many data points this is if
+
+ align:start position:0%
+exactly how many data points this is if
+ 
+
+ align:start position:0%
+exactly how many data points this is if
+you were to take 50 data points and draw
+
+ align:start position:0%
+you were to take 50 data points and draw
+ 
+
+ align:start position:0%
+you were to take 50 data points and draw
+50 data points from a a normal
+
+ align:start position:0%
+50 data points from a a normal
+ 
+
+ align:start position:0%
+50 data points from a a normal
+distribution or order them and put them
+
+ align:start position:0%
+distribution or order them and put them
+ 
+
+ align:start position:0%
+distribution or order them and put them
+where you would expect uh on a normal
+
+ align:start position:0%
+where you would expect uh on a normal
+ 
+
+ align:start position:0%
+where you would expect uh on a normal
+distribution what you would have is many
+
+ align:start position:0%
+distribution what you would have is many
+ 
+
+ align:start position:0%
+distribution what you would have is many
+more data points near zero and as you
+
+ align:start position:0%
+more data points near zero and as you
+ 
+
+ align:start position:0%
+more data points near zero and as you
+get further and further out you know one
+
+ align:start position:0%
+get further and further out you know one
+ 
+
+ align:start position:0%
+get further and further out you know one
+out of 50 times or one out of 25 times
+
+ align:start position:0%
+out of 50 times or one out of 25 times
+ 
+
+ align:start position:0%
+out of 50 times or one out of 25 times
+you would expect to find a data point
+
+ align:start position:0%
+you would expect to find a data point
+ 
+
+ align:start position:0%
+you would expect to find a data point
+about whatever it is two 2 point one
+
+ align:start position:0%
+about whatever it is two 2 point one
+ 
+
+ align:start position:0%
+about whatever it is two 2 point one
+standard deviations away in other words
+
+ align:start position:0%
+standard deviations away in other words
+ 
+
+ align:start position:0%
+standard deviations away in other words
+if I were to compare the actual
+
+ align:start position:0%
+if I were to compare the actual
+ 
+
+ align:start position:0%
+if I were to compare the actual
+location of that data point in terms of
+
+ align:start position:0%
+location of that data point in terms of
+ 
+
+ align:start position:0%
+location of that data point in terms of
+its value within my sample distribution
+
+ align:start position:0%
+its value within my sample distribution
+ 
+
+ align:start position:0%
+its value within my sample distribution
+of 50 compared to if I just drew
+
+ align:start position:0%
+of 50 compared to if I just drew
+ 
+
+ align:start position:0%
+of 50 compared to if I just drew
+randomly 50 data points that would be
+
+ align:start position:0%
+randomly 50 data points that would be
+ 
+
+ align:start position:0%
+randomly 50 data points that would be
+its its
+
+ align:start position:0%
+its its
+ 
+
+ align:start position:0%
+its its
+location then what I can do is plot that
+
+ align:start position:0%
+location then what I can do is plot that
+ 
+
+ align:start position:0%
+location then what I can do is plot that
+coordinate for for that data so what you
+
+ align:start position:0%
+coordinate for for that data so what you
+ 
+
+ align:start position:0%
+coordinate for for that data so what you
+end up with is taking all of your data
+
+ align:start position:0%
+end up with is taking all of your data
+ 
+
+ align:start position:0%
+end up with is taking all of your data
+if you will you sort it from low to high
+
+ align:start position:0%
+if you will you sort it from low to high
+ 
+
+ align:start position:0%
+if you will you sort it from low to high
+and then starting
+
+ align:start position:0%
+and then starting
+ 
+
+ align:start position:0%
+and then starting
+at you know at the center in some sense
+
+ align:start position:0%
+at you know at the center in some sense
+ 
+
+ align:start position:0%
+at you know at the center in some sense
+you start working outward from the
+
+ align:start position:0%
+you start working outward from the
+ 
+
+ align:start position:0%
+you start working outward from the
+center ordering the data from the
+
+ align:start position:0%
+center ordering the data from the
+ 
+
+ align:start position:0%
+center ordering the data from the
+location of
+
+ align:start position:0%
+location of
+ 
+
+ align:start position:0%
+location of
+its uh index in your sorted data from
+
+ align:start position:0%
+its uh index in your sorted data from
+ 
+
+ align:start position:0%
+its uh index in your sorted data from
+number of standard deviations away from
+
+ align:start position:0%
+number of standard deviations away from
+ 
+
+ align:start position:0%
+number of standard deviations away from
+the from the mean that it would be
+
+ align:start position:0%
+the from the mean that it would be
+ 
+
+ align:start position:0%
+the from the mean that it would be
+compared to how far that data point
+
+ align:start position:0%
+compared to how far that data point
+ 
+
+ align:start position:0%
+compared to how far that data point
+actually was away from your sample mean
+
+ align:start position:0%
+actually was away from your sample mean
+ 
+
+ align:start position:0%
+actually was away from your sample mean
+and what that gives you if it were
+
+ align:start position:0%
+and what that gives you if it were
+ 
+
+ align:start position:0%
+and what that gives you if it were
+perfect and there was not you know any
+
+ align:start position:0%
+perfect and there was not you know any
+ 
+
+ align:start position:0%
+perfect and there was not you know any
+any sort of noise in your in your in
+
+ align:start position:0%
+any sort of noise in your in your in
+ 
+
+ align:start position:0%
+any sort of noise in your in your in
+your data that would give you this
+
+ align:start position:0%
+your data that would give you this
+ 
+
+ align:start position:0%
+your data that would give you this
+perfect matching line right every data
+
+ align:start position:0%
+perfect matching line right every data
+ 
+
+ align:start position:0%
+perfect matching line right every data
+point sort of Falls where you would
+
+ align:start position:0%
+point sort of Falls where you would
+ 
+
+ align:start position:0%
+point sort of Falls where you would
+expect it to now in your actual data
+
+ align:start position:0%
+expect it to now in your actual data
+ 
+
+ align:start position:0%
+expect it to now in your actual data
+you're going to see some deviations from
+
+ align:start position:0%
+you're going to see some deviations from
+ 
+
+ align:start position:0%
+you're going to see some deviations from
+that but what this is basically doing is
+
+ align:start position:0%
+that but what this is basically doing is
+ 
+
+ align:start position:0%
+that but what this is basically doing is
+kind of a a
+
+ align:start position:0%
+kind of a a
+ 
+
+ align:start position:0%
+kind of a a
+a compression of your data or an
+
+ align:start position:0%
+a compression of your data or an
+ 
+
+ align:start position:0%
+a compression of your data or an
+expansion of your data out in the Tails
+
+ align:start position:0%
+expansion of your data out in the Tails
+ 
+
+ align:start position:0%
+expansion of your data out in the Tails
+but a compression of your data near the
+
+ align:start position:0%
+but a compression of your data near the
+ 
+
+ align:start position:0%
+but a compression of your data near the
+center to be able to basically tell you
+
+ align:start position:0%
+center to be able to basically tell you
+ 
+
+ align:start position:0%
+center to be able to basically tell you
+how closely your data
+
+ align:start position:0%
+how closely your data
+ 
+
+ align:start position:0%
+how closely your data
+here is following the assumed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution and for this case here we
+
+ align:start position:0%
+distribution and for this case here we
+ 
+
+ align:start position:0%
+distribution and for this case here we
+plotted the location of 50 data points
+
+ align:start position:0%
+plotted the location of 50 data points
+ 
+
+ align:start position:0%
+plotted the location of 50 data points
+assuming was a normal distribution so
+
+ align:start position:0%
+assuming was a normal distribution so
+ 
+
+ align:start position:0%
+assuming was a normal distribution so
+that's where where my X values were
+
+ align:start position:0%
+that's where where my X values were
+ 
+
+ align:start position:0%
+that's where where my X values were
+coming from and as you can see here the
+
+ align:start position:0%
+coming from and as you can see here the
+ 
+
+ align:start position:0%
+coming from and as you can see here the
+data pretty much nicely follows follows
+
+ align:start position:0%
+data pretty much nicely follows follows
+ 
+
+ align:start position:0%
+data pretty much nicely follows follows
+this distribution you get a a few little
+
+ align:start position:0%
+this distribution you get a a few little
+ 
+
+ align:start position:0%
+this distribution you get a a few little
+things that look like it's uh you know
+
+ align:start position:0%
+things that look like it's uh you know
+ 
+
+ align:start position:0%
+things that look like it's uh you know
+kind of wandering or or or trailing off
+
+ align:start position:0%
+kind of wandering or or or trailing off
+ 
+
+ align:start position:0%
+kind of wandering or or or trailing off
+a little bit and then you also often
+
+ align:start position:0%
+a little bit and then you also often
+ 
+
+ align:start position:0%
+a little bit and then you also often
+look out here in the Tails and you find
+
+ align:start position:0%
+look out here in the Tails and you find
+ 
+
+ align:start position:0%
+look out here in the Tails and you find
+oh even out here for you know over two
+
+ align:start position:0%
+oh even out here for you know over two
+ 
+
+ align:start position:0%
+oh even out here for you know over two
+two standard deviations away it looks
+
+ align:start position:0%
+two standard deviations away it looks
+ 
+
+ align:start position:0%
+two standard deviations away it looks
+like I've got pretty good Fidelity to
+
+ align:start position:0%
+like I've got pretty good Fidelity to
+ 
+
+ align:start position:0%
+like I've got pretty good Fidelity to
+those Tails I might have that values
+
+ align:start position:0%
+those Tails I might have that values
+ 
+
+ align:start position:0%
+those Tails I might have that values
+that are a little bit further away from
+
+ align:start position:0%
+that are a little bit further away from
+ 
+
+ align:start position:0%
+that are a little bit further away from
+the mean than I might expect from a
+
+ align:start position:0%
+the mean than I might expect from a
+ 
+
+ align:start position:0%
+the mean than I might expect from a
+normal distribution but it's pretty
+
+ align:start position:0%
+normal distribution but it's pretty
+ 
+
+ align:start position:0%
+normal distribution but it's pretty
+close so this is the kind of plot that
+
+ align:start position:0%
+close so this is the kind of plot that
+ 
+
+ align:start position:0%
+close so this is the kind of plot that
+you would expect to see for data that in
+
+ align:start position:0%
+you would expect to see for data that in
+ 
+
+ align:start position:0%
+you would expect to see for data that in
+fact followed a normal
+
+ align:start position:0%
+fact followed a normal
+ 
+
+ align:start position:0%
+fact followed a normal
+distribution all right so I know that's
+
+ align:start position:0%
+distribution all right so I know that's
+ 
+
+ align:start position:0%
+distribution all right so I know that's
+confusing are there questions that that
+
+ align:start position:0%
+confusing are there questions that that
+ 
+
+ align:start position:0%
+confusing are there questions that that
+people have on what this yes yeah I have
+
+ align:start position:0%
+people have on what this yes yeah I have
+ 
+
+ align:start position:0%
+people have on what this yes yeah I have
+a question uh so so for each point um
+
+ align:start position:0%
+a question uh so so for each point um
+ 
+
+ align:start position:0%
+a question uh so so for each point um
+you you get the the y AIS by um the
+
+ align:start position:0%
+you you get the the y AIS by um the
+ 
+
+ align:start position:0%
+you you get the the y AIS by um the
+sampling value from your data right how
+
+ align:start position:0%
+sampling value from your data right how
+ 
+
+ align:start position:0%
+sampling value from your data right how
+do you get X do you do you get it based
+
+ align:start position:0%
+do you get X do you do you get it based
+ 
+
+ align:start position:0%
+do you get X do you do you get it based
+on the probability of that sampling
+
+ align:start position:0%
+on the probability of that sampling
+ 
+
+ align:start position:0%
+on the probability of that sampling
+point from your sampl distribution then
+
+ align:start position:0%
+point from your sampl distribution then
+ 
+
+ align:start position:0%
+point from your sampl distribution then
+you refer to the to the theoretical
+
+ align:start position:0%
+you refer to the to the theoretical
+ 
+
+ align:start position:0%
+you refer to the to the theoretical
+normal distribution with the same
+
+ align:start position:0%
+normal distribution with the same
+ 
+
+ align:start position:0%
+normal distribution with the same
+probability then you get a y
+
+ align:start position:0%
+probability then you get a y
+ 
+
+ align:start position:0%
+probability then you get a y
+x-axis uh yes very very close so for the
+
+ align:start position:0%
+x-axis uh yes very very close so for the
+ 
+
+ align:start position:0%
+x-axis uh yes very very close so for the
+for the y axis you've got it exactly
+
+ align:start position:0%
+for the y axis you've got it exactly
+ 
+
+ align:start position:0%
+for the y axis you've got it exactly
+right for the x axis what's interesting
+
+ align:start position:0%
+right for the x axis what's interesting
+ 
+
+ align:start position:0%
+right for the x axis what's interesting
+is you don't actually use the values of
+
+ align:start position:0%
+is you don't actually use the values of
+ 
+
+ align:start position:0%
+is you don't actually use the values of
+your of your data you just use its index
+
+ align:start position:0%
+your of your data you just use its index
+ 
+
+ align:start position:0%
+your of your data you just use its index
+location in a sample of the size that
+
+ align:start position:0%
+location in a sample of the size that
+ 
+
+ align:start position:0%
+location in a sample of the size that
+you've got in other words if I had if I
+
+ align:start position:0%
+you've got in other words if I had if I
+ 
+
+ align:start position:0%
+you've got in other words if I had if I
+had a a a a million points I would look
+
+ align:start position:0%
+had a a a a million points I would look
+ 
+
+ align:start position:0%
+had a a a a million points I would look
+at the lowest and I would expect that to
+
+ align:start position:0%
+at the lowest and I would expect that to
+ 
+
+ align:start position:0%
+at the lowest and I would expect that to
+be uh in a normal distribution I would
+
+ align:start position:0%
+be uh in a normal distribution I would
+ 
+
+ align:start position:0%
+be uh in a normal distribution I would
+EX look at where the probability the
+
+ align:start position:0%
+EX look at where the probability the
+ 
+
+ align:start position:0%
+EX look at where the probability the
+number of standard deviations where one
+
+ align:start position:0%
+number of standard deviations where one
+ 
+
+ align:start position:0%
+number of standard deviations where one
+out of 500,000 points is that far away
+
+ align:start position:0%
+out of 500,000 points is that far away
+ 
+
+ align:start position:0%
+out of 500,000 points is that far away
+from the mean so I would look up the
+
+ align:start position:0%
+from the mean so I would look up the
+ 
+
+ align:start position:0%
+from the mean so I would look up the
+inverse probability on a normal
+
+ align:start position:0%
+inverse probability on a normal
+ 
+
+ align:start position:0%
+inverse probability on a normal
+distribution of
+
+ align:start position:0%
+distribution of
+ 
+
+ align:start position:0%
+distribution of
+being uh of where one in five uh 500,000
+
+ align:start position:0%
+being uh of where one in five uh 500,000
+ 
+
+ align:start position:0%
+being uh of where one in five uh 500,000
+point what0 two to the whatever um um so
+
+ align:start position:0%
+point what0 two to the whatever um um so
+ 
+
+ align:start position:0%
+point what0 two to the whatever um um so
+I would basically look
+
+ align:start position:0%
+I would basically look
+ 
+
+ align:start position:0%
+I would basically look
+look uh on a tabulated normal
+
+ align:start position:0%
+look uh on a tabulated normal
+ 
+
+ align:start position:0%
+look uh on a tabulated normal
+probability plot going backwards from
+
+ align:start position:0%
+probability plot going backwards from
+ 
+
+ align:start position:0%
+probability plot going backwards from
+where uh that index
+
+ align:start position:0%
+where uh that index
+ 
+
+ align:start position:0%
+where uh that index
+my smallest point was and then I could
+
+ align:start position:0%
+my smallest point was and then I could
+ 
+
+ align:start position:0%
+my smallest point was and then I could
+do that for every point in my sample to
+
+ align:start position:0%
+do that for every point in my sample to
+ 
+
+ align:start position:0%
+do that for every point in my sample to
+figure out what the probability for its
+
+ align:start position:0%
+figure out what the probability for its
+ 
+
+ align:start position:0%
+figure out what the probability for its
+location should be on the on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x-axis so here's another example maybe
+
+ align:start position:0%
+x-axis so here's another example maybe
+ 
+
+ align:start position:0%
+x-axis so here's another example maybe
+this gives you a feel because these QQ
+
+ align:start position:0%
+this gives you a feel because these QQ
+ 
+
+ align:start position:0%
+this gives you a feel because these QQ
+plots the the quanti quanti plots can
+
+ align:start position:0%
+plots the the quanti quanti plots can
+ 
+
+ align:start position:0%
+plots the the quanti quanti plots can
+actually be used with other
+
+ align:start position:0%
+actually be used with other
+ 
+
+ align:start position:0%
+actually be used with other
+distributions as well they are not
+
+ align:start position:0%
+distributions as well they are not
+ 
+
+ align:start position:0%
+distributions as well they are not
+always QQ Norm plots they can be applied
+
+ align:start position:0%
+always QQ Norm plots they can be applied
+ 
+
+ align:start position:0%
+always QQ Norm plots they can be applied
+to whatever assumed probability
+
+ align:start position:0%
+to whatever assumed probability
+ 
+
+ align:start position:0%
+to whatever assumed probability
+distribution you might want to
+
+ align:start position:0%
+distribution you might want to
+ 
+
+ align:start position:0%
+distribution you might want to
+investigate
+
+ align:start position:0%
+investigate
+ 
+
+ align:start position:0%
+investigate
+um uh so here's an example where we
+
+ align:start position:0%
+um uh so here's an example where we
+ 
+
+ align:start position:0%
+um uh so here's an example where we
+again took the uh data but in this case
+
+ align:start position:0%
+again took the uh data but in this case
+ 
+
+ align:start position:0%
+again took the uh data but in this case
+the theoretical quantiles are actually
+
+ align:start position:0%
+the theoretical quantiles are actually
+ 
+
+ align:start position:0%
+the theoretical quantiles are actually
+lining
+
+ align:start position:0%
+lining
+ 
+
+ align:start position:0%
+lining
+up I'm assuming a normal distribution
+
+ align:start position:0%
+up I'm assuming a normal distribution
+ 
+
+ align:start position:0%
+up I'm assuming a normal distribution
+but in this example that I'm showing
+
+ align:start position:0%
+but in this example that I'm showing
+ 
+
+ align:start position:0%
+but in this example that I'm showing
+here the data actually came from let me
+
+ align:start position:0%
+here the data actually came from let me
+ 
+
+ align:start position:0%
+here the data actually came from let me
+erase me get rid of all this the data
+
+ align:start position:0%
+erase me get rid of all this the data
+ 
+
+ align:start position:0%
+erase me get rid of all this the data
+actually came from an exponential
+
+ align:start position:0%
+actually came from an exponential
+ 
+
+ align:start position:0%
+actually came from an exponential
+distribution okay so this is an example
+
+ align:start position:0%
+distribution okay so this is an example
+ 
+
+ align:start position:0%
+distribution okay so this is an example
+where I would have assumed things were
+
+ align:start position:0%
+where I would have assumed things were
+ 
+
+ align:start position:0%
+where I would have assumed things were
+coming uh from from a a
+
+ align:start position:0%
+coming uh from from a a
+ 
+
+ align:start position:0%
+coming uh from from a a
+gaussian so this is still for the normal
+
+ align:start position:0%
+gaussian so this is still for the normal
+ 
+
+ align:start position:0%
+gaussian so this is still for the normal
+quantiles but with an exponential an e
+
+ align:start position:0%
+quantiles but with an exponential an e
+ 
+
+ align:start position:0%
+quantiles but with an exponential an e
+to the you know e to the uh minus X or
+
+ align:start position:0%
+to the you know e to the uh minus X or
+ 
+
+ align:start position:0%
+to the you know e to the uh minus X or
+an e to the X kind of distribution what
+
+ align:start position:0%
+an e to the X kind of distribution what
+ 
+
+ align:start position:0%
+an e to the X kind of distribution what
+what you end up with are uh a lot of
+
+ align:start position:0%
+what you end up with are uh a lot of
+ 
+
+ align:start position:0%
+what you end up with are uh a lot of
+data values that are much larger much
+
+ align:start position:0%
+data values that are much larger much
+ 
+
+ align:start position:0%
+data values that are much larger much
+further away from the mean than you
+
+ align:start position:0%
+further away from the mean than you
+ 
+
+ align:start position:0%
+further away from the mean than you
+would expect from a gaussian and you
+
+ align:start position:0%
+would expect from a gaussian and you
+ 
+
+ align:start position:0%
+would expect from a gaussian and you
+also get a bunch of data that's
+
+ align:start position:0%
+also get a bunch of data that's
+ 
+
+ align:start position:0%
+also get a bunch of data that's
+much uh
+
+ align:start position:0%
+much uh
+ 
+
+ align:start position:0%
+much uh
+larger than you would expect from from a
+
+ align:start position:0%
+larger than you would expect from from a
+ 
+
+ align:start position:0%
+larger than you would expect from from a
+gaussian so this would be an example
+
+ align:start position:0%
+gaussian so this would be an example
+ 
+
+ align:start position:0%
+gaussian so this would be an example
+here where the normal QQ plot doesn't
+
+ align:start position:0%
+here where the normal QQ plot doesn't
+ 
+
+ align:start position:0%
+here where the normal QQ plot doesn't
+seem to match up it's sort of telling me
+
+ align:start position:0%
+seem to match up it's sort of telling me
+ 
+
+ align:start position:0%
+seem to match up it's sort of telling me
+my data really is not following along
+
+ align:start position:0%
+my data really is not following along
+ 
+
+ align:start position:0%
+my data really is not following along
+the normal distribution line now I
+
+ align:start position:0%
+the normal distribution line now I
+ 
+
+ align:start position:0%
+the normal distribution line now I
+didn't pull a plot but one could then
+
+ align:start position:0%
+didn't pull a plot but one could then
+ 
+
+ align:start position:0%
+didn't pull a plot but one could then
+ask the question maybe you look up
+
+ align:start position:0%
+ask the question maybe you look up
+ 
+
+ align:start position:0%
+ask the question maybe you look up
+curtosis or or maybe you uh look back at
+
+ align:start position:0%
+curtosis or or maybe you uh look back at
+ 
+
+ align:start position:0%
+curtosis or or maybe you uh look back at
+your data and say hm I think maybe an
+
+ align:start position:0%
+your data and say hm I think maybe an
+ 
+
+ align:start position:0%
+your data and say hm I think maybe an
+exponential distribution is really what
+
+ align:start position:0%
+exponential distribution is really what
+ 
+
+ align:start position:0%
+exponential distribution is really what
+this is following how would you plot
+
+ align:start position:0%
+this is following how would you plot
+ 
+
+ align:start position:0%
+this is following how would you plot
+that on a QQ Norm question doesn't the
+
+ align:start position:0%
+that on a QQ Norm question doesn't the
+ 
+
+ align:start position:0%
+that on a QQ Norm question doesn't the
+line go through
+
+ align:start position:0%
+line go through
+ 
+
+ align:start position:0%
+line go through
+z uh this is a good question these these
+
+ align:start position:0%
+z uh this is a good question these these
+ 
+
+ align:start position:0%
+z uh this is a good question these these
+don't appear to be mean centered uh to
+
+ align:start position:0%
+don't appear to be mean centered uh to
+ 
+
+ align:start position:0%
+don't appear to be mean centered uh to
+me so there's something weird on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plot yeah this does not I think what has
+
+ align:start position:0%
+plot yeah this does not I think what has
+ 
+
+ align:start position:0%
+plot yeah this does not I think what has
+happened here is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um these are not quite mean centered and
+
+ align:start position:0%
+um these are not quite mean centered and
+ 
+
+ align:start position:0%
+um these are not quite mean centered and
+normalized um so because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well so so in terms of z00 following on
+
+ align:start position:0%
+well so so in terms of z00 following on
+ 
+
+ align:start position:0%
+well so so in terms of z00 following on
+the plot that's not happening um so I'm
+
+ align:start position:0%
+the plot that's not happening um so I'm
+ 
+
+ align:start position:0%
+the plot that's not happening um so I'm
+a little I'm not sure exactly what
+
+ align:start position:0%
+a little I'm not sure exactly what
+ 
+
+ align:start position:0%
+a little I'm not sure exactly what
+what's going on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there conceptual normal on the on the
+
+ align:start position:0%
+there conceptual normal on the on the
+ 
+
+ align:start position:0%
+there conceptual normal on the on the
+data me yes it should and that's what
+
+ align:start position:0%
+data me yes it should and that's what
+ 
+
+ align:start position:0%
+data me yes it should and that's what
+I'm saying is this this
+
+ align:start position:0%
+I'm saying is this this
+ 
+
+ align:start position:0%
+I'm saying is this this
+plot I don't think is correctly mean
+
+ align:start position:0%
+plot I don't think is correctly mean
+ 
+
+ align:start position:0%
+plot I don't think is correctly mean
+centered because it should should then
+
+ align:start position:0%
+centered because it should should then
+ 
+
+ align:start position:0%
+centered because it should should then
+z0 kind of by definition has to has to
+
+ align:start position:0%
+z0 kind of by definition has to has to
+ 
+
+ align:start position:0%
+z0 kind of by definition has to has to
+fall oh oh that's what you're saying no
+
+ align:start position:0%
+fall oh oh that's what you're saying no
+ 
+
+ align:start position:0%
+fall oh oh that's what you're saying no
+see mean of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data right
+
+ align:start position:0%
+data right
+ 
+
+ align:start position:0%
+data right
+right but but I'm saying here's my Y
+
+ align:start position:0%
+right but but I'm saying here's my Y
+ 
+
+ align:start position:0%
+right but but I'm saying here's my Y
+data and my my zero mean is
+
+ align:start position:0%
+data and my my zero mean is
+ 
+
+ align:start position:0%
+data and my my zero mean is
+not I I don't have any negative I don't
+
+ align:start position:0%
+not I I don't have any negative I don't
+ 
+
+ align:start position:0%
+not I I don't have any negative I don't
+have any data lower than the mean and
+
+ align:start position:0%
+have any data lower than the mean and
+ 
+
+ align:start position:0%
+have any data lower than the mean and
+therefore that's that doesn't make any
+
+ align:start position:0%
+therefore that's that doesn't make any
+ 
+
+ align:start position:0%
+therefore that's that doesn't make any
+sense so this is not mean centered
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correctly looks to me looks the mean of
+
+ align:start position:0%
+correctly looks to me looks the mean of
+ 
+
+ align:start position:0%
+correctly looks to me looks the mean of
+the data
+
+ align:start position:0%
+the data
+ 
+
+ align:start position:0%
+the data
+slightly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that but if I mean Center and scale to
+
+ align:start position:0%
+that but if I mean Center and scale to
+ 
+
+ align:start position:0%
+that but if I mean Center and scale to
+to zero then the mean of my data
+
+ align:start position:0%
+to zero then the mean of my data
+ 
+
+ align:start position:0%
+to zero then the mean of my data
+H by definition that ought to be at zero
+
+ align:start position:0%
+H by definition that ought to be at zero
+ 
+
+ align:start position:0%
+H by definition that ought to be at zero
+right I do think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sh when you mean Center yeah you're
+
+ align:start position:0%
+sh when you mean Center yeah you're
+ 
+
+ align:start position:0%
+sh when you mean Center yeah you're
+shifting oh I think you're shifting like
+
+ align:start position:0%
+shifting oh I think you're shifting like
+ 
+
+ align:start position:0%
+shifting oh I think you're shifting like
+the conceptual you're not shifting the
+
+ align:start position:0%
+the conceptual you're not shifting the
+ 
+
+ align:start position:0%
+the conceptual you're not shifting the
+data you're shal you're saying might
+
+ align:start position:0%
+data you're shal you're saying might
+ 
+
+ align:start position:0%
+data you're shal you're saying might
+correspond to no in a in a normal in a
+
+ align:start position:0%
+correspond to no in a in a normal in a
+ 
+
+ align:start position:0%
+correspond to no in a in a normal in a
+in a in the the standard QQ Norm plot
+
+ align:start position:0%
+in a in the the standard QQ Norm plot
+ 
+
+ align:start position:0%
+in a in the the standard QQ Norm plot
+you mean Center you actually take your
+
+ align:start position:0%
+you mean Center you actually take your
+ 
+
+ align:start position:0%
+you mean Center you actually take your
+data you mean Center it you normalize it
+
+ align:start position:0%
+data you mean Center it you normalize it
+ 
+
+ align:start position:0%
+data you mean Center it you normalize it
+to the calculated sample standard
+
+ align:start position:0%
+to the calculated sample standard
+ 
+
+ align:start position:0%
+to the calculated sample standard
+deviation and plot that and that does
+
+ align:start position:0%
+deviation and plot that and that does
+ 
+
+ align:start position:0%
+deviation and plot that and that does
+not look like quite what they've done
+
+ align:start position:0%
+not look like quite what they've done
+ 
+
+ align:start position:0%
+not look like quite what they've done
+here I think these are still normalized
+
+ align:start position:0%
+here I think these are still normalized
+ 
+
+ align:start position:0%
+here I think these are still normalized
+a standard deviation but I think it's
+
+ align:start position:0%
+a standard deviation but I think it's
+ 
+
+ align:start position:0%
+a standard deviation but I think it's
+not quite mean centered but in some
+
+ align:start position:0%
+not quite mean centered but in some
+ 
+
+ align:start position:0%
+not quite mean centered but in some
+sense that doesn't actually matter in
+
+ align:start position:0%
+sense that doesn't actually matter in
+ 
+
+ align:start position:0%
+sense that doesn't actually matter in
+terms of the data following along
+
+ align:start position:0%
+terms of the data following along
+ 
+
+ align:start position:0%
+terms of the data following along
+following along the line it's still
+
+ align:start position:0%
+following along the line it's still
+ 
+
+ align:start position:0%
+following along the line it's still
+indicating that would just be a shift
+
+ align:start position:0%
+indicating that would just be a shift
+ 
+
+ align:start position:0%
+indicating that would just be a shift
+that would be a shift you said the data
+
+ align:start position:0%
+that would be a shift you said the data
+ 
+
+ align:start position:0%
+that would be a shift you said the data
+hasn't been normalized hasn't been mean
+
+ align:start position:0%
+hasn't been normalized hasn't been mean
+ 
+
+ align:start position:0%
+hasn't been normalized hasn't been mean
+centered but if it's an exponential
+
+ align:start position:0%
+centered but if it's an exponential
+ 
+
+ align:start position:0%
+centered but if it's an exponential
+distribution can you
+
+ align:start position:0%
+distribution can you
+ 
+
+ align:start position:0%
+distribution can you
+still normalize the
+
+ align:start position:0%
+still normalize the
+ 
+
+ align:start position:0%
+still normalize the
+data well in the in the in this first
+
+ align:start position:0%
+data well in the in the in this first
+ 
+
+ align:start position:0%
+data well in the in the in this first
+first use of such a
+
+ align:start position:0%
+first use of such a
+ 
+
+ align:start position:0%
+first use of such a
+plot um you would be testing the
+
+ align:start position:0%
+plot um you would be testing the
+ 
+
+ align:start position:0%
+plot um you would be testing the
+question did your data you don't know
+
+ align:start position:0%
+question did your data you don't know
+ 
+
+ align:start position:0%
+question did your data you don't know
+yet that it's it's exponential you just
+
+ align:start position:0%
+yet that it's it's exponential you just
+ 
+
+ align:start position:0%
+yet that it's it's exponential you just
+have data and you're testing does it
+
+ align:start position:0%
+have data and you're testing does it
+ 
+
+ align:start position:0%
+have data and you're testing does it
+fall on on the normal the normal line so
+
+ align:start position:0%
+fall on on the normal the normal line so
+ 
+
+ align:start position:0%
+fall on on the normal the normal line so
+you would still follow that procedure uh
+
+ align:start position:0%
+you would still follow that procedure uh
+ 
+
+ align:start position:0%
+you would still follow that procedure uh
+we'll look at an exponential
+
+ align:start position:0%
+we'll look at an exponential
+ 
+
+ align:start position:0%
+we'll look at an exponential
+distribution in a minute and of course
+
+ align:start position:0%
+distribution in a minute and of course
+ 
+
+ align:start position:0%
+distribution in a minute and of course
+every distribution has a mean so you can
+
+ align:start position:0%
+every distribution has a mean so you can
+ 
+
+ align:start position:0%
+every distribution has a mean so you can
+always mean Center um similarly every
+
+ align:start position:0%
+always mean Center um similarly every
+ 
+
+ align:start position:0%
+always mean Center um similarly every
+distribution has a a a variance that you
+
+ align:start position:0%
+distribution has a a a variance that you
+ 
+
+ align:start position:0%
+distribution has a a a variance that you
+can calculate uh the neat thing about
+
+ align:start position:0%
+can calculate uh the neat thing about
+ 
+
+ align:start position:0%
+can calculate uh the neat thing about
+the exponential is the mean and the
+
+ align:start position:0%
+the exponential is the mean and the
+ 
+
+ align:start position:0%
+the exponential is the mean and the
+variance are the same um but that's not
+
+ align:start position:0%
+variance are the same um but that's not
+ 
+
+ align:start position:0%
+variance are the same um but that's not
+entering in here there's something else
+
+ align:start position:0%
+entering in here there's something else
+ 
+
+ align:start position:0%
+entering in here there's something else
+weird so there's the risk of pulling a
+
+ align:start position:0%
+weird so there's the risk of pulling a
+ 
+
+ align:start position:0%
+weird so there's the risk of pulling a
+plot off at uh 950 at at at night I
+
+ align:start position:0%
+plot off at uh 950 at at at night I
+ 
+
+ align:start position:0%
+plot off at uh 950 at at at night I
+hadn't noticed that the uh it doesn't
+
+ align:start position:0%
+hadn't noticed that the uh it doesn't
+ 
+
+ align:start position:0%
+hadn't noticed that the uh it doesn't
+look correctly mean centered
+
+ align:start position:0%
+look correctly mean centered
+ 
+
+ align:start position:0%
+look correctly mean centered
+um but the additional point I wanted to
+
+ align:start position:0%
+um but the additional point I wanted to
+ 
+
+ align:start position:0%
+um but the additional point I wanted to
+make is I could actually take this same
+
+ align:start position:0%
+make is I could actually take this same
+ 
+
+ align:start position:0%
+make is I could actually take this same
+data I could produce a different plot
+
+ align:start position:0%
+data I could produce a different plot
+ 
+
+ align:start position:0%
+data I could produce a different plot
+not a normal QQ plot but an exponential
+
+ align:start position:0%
+not a normal QQ plot but an exponential
+ 
+
+ align:start position:0%
+not a normal QQ plot but an exponential
+QQ
+
+ align:start position:0%
+QQ
+ 
+
+ align:start position:0%
+QQ
+plot and if I were doing that in that
+
+ align:start position:0%
+plot and if I were doing that in that
+ 
+
+ align:start position:0%
+plot and if I were doing that in that
+case what I would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+is take my data still plot
+
+ align:start position:0%
+is take my data still plot
+ 
+
+ align:start position:0%
+is take my data still plot
+it hopefully mean
+
+ align:start position:0%
+it hopefully mean
+ 
+
+ align:start position:0%
+it hopefully mean
+centered and then number of standard
+
+ align:start position:0%
+centered and then number of standard
+ 
+
+ align:start position:0%
+centered and then number of standard
+deviations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+away but then along this axis I would
+
+ align:start position:0%
+away but then along this axis I would
+ 
+
+ align:start position:0%
+away but then along this axis I would
+calculate uh the the
+
+ align:start position:0%
+calculate uh the the
+ 
+
+ align:start position:0%
+calculate uh the the
+location in numbers of standard
+
+ align:start position:0%
+location in numbers of standard
+ 
+
+ align:start position:0%
+location in numbers of standard
+deviations based on the probability of
+
+ align:start position:0%
+deviations based on the probability of
+ 
+
+ align:start position:0%
+deviations based on the probability of
+an exponential distribution not based on
+
+ align:start position:0%
+an exponential distribution not based on
+ 
+
+ align:start position:0%
+an exponential distribution not based on
+the probability of that index location
+
+ align:start position:0%
+the probability of that index location
+ 
+
+ align:start position:0%
+the probability of that index location
+in a normal distribution so I would
+
+ align:start position:0%
+in a normal distribution so I would
+ 
+
+ align:start position:0%
+in a normal distribution so I would
+basically say for my 50 data points I
+
+ align:start position:0%
+basically say for my 50 data points I
+ 
+
+ align:start position:0%
+basically say for my 50 data points I
+expect uh the 25th data point larger
+
+ align:start position:0%
+expect uh the 25th data point larger
+ 
+
+ align:start position:0%
+expect uh the 25th data point larger
+than the mean to occur with uh uh in in
+
+ align:start position:0%
+than the mean to occur with uh uh in in
+ 
+
+ align:start position:0%
+than the mean to occur with uh uh in in
+that distribution I have to go you know
+
+ align:start position:0%
+that distribution I have to go you know
+ 
+
+ align:start position:0%
+that distribution I have to go you know
+2.1 dis uh uh normal normalized uh
+
+ align:start position:0%
+2.1 dis uh uh normal normalized uh
+ 
+
+ align:start position:0%
+2.1 dis uh uh normal normalized uh
+standard deviations away in order to get
+
+ align:start position:0%
+standard deviations away in order to get
+ 
+
+ align:start position:0%
+standard deviations away in order to get
+to that probability so that it takes my
+
+ align:start position:0%
+to that probability so that it takes my
+ 
+
+ align:start position:0%
+to that probability so that it takes my
+same Y data but then it plots
+
+ align:start position:0%
+same Y data but then it plots
+ 
+
+ align:start position:0%
+same Y data but then it plots
+along the line where if it really is
+
+ align:start position:0%
+along the line where if it really is
+ 
+
+ align:start position:0%
+along the line where if it really is
+exponential my data should fall
+
+ align:start position:0%
+exponential my data should fall
+ 
+
+ align:start position:0%
+exponential my data should fall
+along a one toone correspondence
+
+ align:start position:0%
+along a one toone correspondence
+ 
+
+ align:start position:0%
+along a one toone correspondence
+line okay so you don't often see the use
+
+ align:start position:0%
+line okay so you don't often see the use
+ 
+
+ align:start position:0%
+line okay so you don't often see the use
+of these QQ plots uh from the
+
+ align:start position:0%
+of these QQ plots uh from the
+ 
+
+ align:start position:0%
+of these QQ plots uh from the
+perspective of different distributions
+
+ align:start position:0%
+perspective of different distributions
+ 
+
+ align:start position:0%
+perspective of different distributions
+but you can use them what you often will
+
+ align:start position:0%
+but you can use them what you often will
+ 
+
+ align:start position:0%
+but you can use them what you often will
+see is is really this you'll see QQ Norm
+
+ align:start position:0%
+see is is really this you'll see QQ Norm
+ 
+
+ align:start position:0%
+see is is really this you'll see QQ Norm
+plots and they're lovely plots It's a
+
+ align:start position:0%
+plots and they're lovely plots It's a
+ 
+
+ align:start position:0%
+plots and they're lovely plots It's a
+Wonderful tool to do use because you're
+
+ align:start position:0%
+Wonderful tool to do use because you're
+ 
+
+ align:start position:0%
+Wonderful tool to do use because you're
+actually seeing all of your
+
+ align:start position:0%
+actually seeing all of your
+ 
+
+ align:start position:0%
+actually seeing all of your
+data okay it's got all of your actual
+
+ align:start position:0%
+data okay it's got all of your actual
+ 
+
+ align:start position:0%
+data okay it's got all of your actual
+data it's showing you that it
+
+ align:start position:0%
+data it's showing you that it
+ 
+
+ align:start position:0%
+data it's showing you that it
+corresponds roughly to a to a normal
+
+ align:start position:0%
+corresponds roughly to a to a normal
+ 
+
+ align:start position:0%
+corresponds roughly to a to a normal
+distribution it's also giving you very
+
+ align:start position:0%
+distribution it's also giving you very
+ 
+
+ align:start position:0%
+distribution it's also giving you very
+nice information about essentially your
+
+ align:start position:0%
+nice information about essentially your
+ 
+
+ align:start position:0%
+nice information about essentially your
+your um variance or standard
+
+ align:start position:0%
+your um variance or standard
+ 
+
+ align:start position:0%
+your um variance or standard
+deviation and there are variant of these
+
+ align:start position:0%
+deviation and there are variant of these
+ 
+
+ align:start position:0%
+deviation and there are variant of these
+plots that you will often see in the
+
+ align:start position:0%
+plots that you will often see in the
+ 
+
+ align:start position:0%
+plots that you will often see in the
+literature especially the semiconductor
+
+ align:start position:0%
+literature especially the semiconductor
+ 
+
+ align:start position:0%
+literature especially the semiconductor
+literature dealing with large numbers of
+
+ align:start position:0%
+literature dealing with large numbers of
+ 
+
+ align:start position:0%
+literature dealing with large numbers of
+of samples coming from uh different
+
+ align:start position:0%
+of samples coming from uh different
+ 
+
+ align:start position:0%
+of samples coming from uh different
+kinds of measurements so for example if
+
+ align:start position:0%
+kinds of measurements so for example if
+ 
+
+ align:start position:0%
+kinds of measurements so for example if
+you want to make contact resistance
+
+ align:start position:0%
+you want to make contact resistance
+ 
+
+ align:start position:0%
+you want to make contact resistance
+measurements for literally thousands of
+
+ align:start position:0%
+measurements for literally thousands of
+ 
+
+ align:start position:0%
+measurements for literally thousands of
+contacts and very succinctly present
+
+ align:start position:0%
+contacts and very succinctly present
+ 
+
+ align:start position:0%
+contacts and very succinctly present
+that data you will see families of QQ
+
+ align:start position:0%
+that data you will see families of QQ
+ 
+
+ align:start position:0%
+that data you will see families of QQ
+Norm plots so for example maybe you did
+
+ align:start position:0%
+Norm plots so for example maybe you did
+ 
+
+ align:start position:0%
+Norm plots so for example maybe you did
+a bunch of contacts at a particular size
+
+ align:start position:0%
+a bunch of contacts at a particular size
+ 
+
+ align:start position:0%
+a bunch of contacts at a particular size
+you would plot them like this and then
+
+ align:start position:0%
+you would plot them like this and then
+ 
+
+ align:start position:0%
+you would plot them like this and then
+maybe you had another data set where you
+
+ align:start position:0%
+maybe you had another data set where you
+ 
+
+ align:start position:0%
+maybe you had another data set where you
+had attempted to pattern those those uh
+
+ align:start position:0%
+had attempted to pattern those those uh
+ 
+
+ align:start position:0%
+had attempted to pattern those those uh
+contacts slightly larger slightly
+
+ align:start position:0%
+contacts slightly larger slightly
+ 
+
+ align:start position:0%
+contacts slightly larger slightly
+smaller and you would often see then
+
+ align:start position:0%
+smaller and you would often see then
+ 
+
+ align:start position:0%
+smaller and you would often see then
+another oops that's not very straight is
+
+ align:start position:0%
+another oops that's not very straight is
+ 
+
+ align:start position:0%
+another oops that's not very straight is
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+it's meant to be
+
+ align:start position:0%
+it's meant to be
+ 
+
+ align:start position:0%
+it's meant to be
+another underlying um set of data but
+
+ align:start position:0%
+another underlying um set of data but
+ 
+
+ align:start position:0%
+another underlying um set of data but
+you might find your data looking
+
+ align:start position:0%
+you might find your data looking
+ 
+
+ align:start position:0%
+you might find your data looking
+something like
+
+ align:start position:0%
+something like
+ 
+
+ align:start position:0%
+something like
+this and that kind of plot is really
+
+ align:start position:0%
+this and that kind of plot is really
+ 
+
+ align:start position:0%
+this and that kind of plot is really
+useful for showing that there is a a
+
+ align:start position:0%
+useful for showing that there is a a
+ 
+
+ align:start position:0%
+useful for showing that there is a a
+mean shift a mean difference between
+
+ align:start position:0%
+mean shift a mean difference between
+ 
+
+ align:start position:0%
+mean shift a mean difference between
+your data but also the variance is
+
+ align:start position:0%
+your data but also the variance is
+ 
+
+ align:start position:0%
+your data but also the variance is
+different in the two cases now exactly
+
+ align:start position:0%
+different in the two cases now exactly
+ 
+
+ align:start position:0%
+different in the two cases now exactly
+what you're plotting here might be a
+
+ align:start position:0%
+what you're plotting here might be a
+ 
+
+ align:start position:0%
+what you're plotting here might be a
+little bit different you might actually
+
+ align:start position:0%
+little bit different you might actually
+ 
+
+ align:start position:0%
+little bit different you might actually
+not plot uh quite normalized data you
+
+ align:start position:0%
+not plot uh quite normalized data you
+ 
+
+ align:start position:0%
+not plot uh quite normalized data you
+might actually use it in an
+
+ align:start position:0%
+might actually use it in an
+ 
+
+ align:start position:0%
+might actually use it in an
+unnormalized uh uh
+
+ align:start position:0%
+unnormalized uh uh
+ 
+
+ align:start position:0%
+unnormalized uh uh
+fashion and you here you might plot this
+
+ align:start position:0%
+fashion and you here you might plot this
+ 
+
+ align:start position:0%
+fashion and you here you might plot this
+not in terms of standard deviations but
+
+ align:start position:0%
+not in terms of standard deviations but
+ 
+
+ align:start position:0%
+not in terms of standard deviations but
+rather actual keep keep it in the
+
+ align:start position:0%
+rather actual keep keep it in the
+ 
+
+ align:start position:0%
+rather actual keep keep it in the
+quantiles or the probability of being
+
+ align:start position:0%
+quantiles or the probability of being
+ 
+
+ align:start position:0%
+quantiles or the probability of being
+that far
+
+ align:start position:0%
+that far
+ 
+
+ align:start position:0%
+that far
+away probability of that of that
+
+ align:start position:0%
+away probability of that of that
+ 
+
+ align:start position:0%
+away probability of that of that
+X it's weird the probability of that x
+
+ align:start position:0%
+X it's weird the probability of that x
+ 
+
+ align:start position:0%
+X it's weird the probability of that x
+value so for example you will often see
+
+ align:start position:0%
+value so for example you will often see
+ 
+
+ align:start position:0%
+value so for example you will often see
+these kinds of plots which would show
+
+ align:start position:0%
+these kinds of plots which would show
+ 
+
+ align:start position:0%
+these kinds of plots which would show
+things like
+
+ align:start position:0%
+things like
+ 
+
+ align:start position:0%
+things like
+um uh
+
+ align:start position:0%
+um uh
+ 
+
+ align:start position:0%
+um uh
+0.001
+
+ align:start position:0%
+0.001
+ 
+
+ align:start position:0%
+0.001
+0.01
+
+ align:start position:0%
+0.01
+ 
+
+ align:start position:0%
+0.01
+0.11 uh or or
+
+ align:start position:0%
+0.11 uh or or
+ 
+
+ align:start position:0%
+0.11 uh or or
+um something like that getting up to I
+
+ align:start position:0%
+um something like that getting up to I
+ 
+
+ align:start position:0%
+um something like that getting up to I
+guess 0.5 would be the equivalent for
+
+ align:start position:0%
+guess 0.5 would be the equivalent for
+ 
+
+ align:start position:0%
+guess 0.5 would be the equivalent for
+the the mean and then you start going
+
+ align:start position:0%
+the the mean and then you start going
+ 
+
+ align:start position:0%
+the the mean and then you start going
+larger uh 0.9 0.99 0.9
+
+ align:start position:0%
+larger uh 0.9 0.99 0.9
+ 
+
+ align:start position:0%
+larger uh 0.9 0.99 0.9
+999 in other words you might actually
+
+ align:start position:0%
+999 in other words you might actually
+ 
+
+ align:start position:0%
+999 in other words you might actually
+plot as I should have put these on the x
+
+ align:start position:0%
+plot as I should have put these on the x
+ 
+
+ align:start position:0%
+plot as I should have put these on the x
+value uh the probability that that you
+
+ align:start position:0%
+value uh the probability that that you
+ 
+
+ align:start position:0%
+value uh the probability that that you
+would find a data point that far away as
+
+ align:start position:0%
+would find a data point that far away as
+ 
+
+ align:start position:0%
+would find a data point that far away as
+opposed to implied probabilities
+
+ align:start position:0%
+opposed to implied probabilities
+ 
+
+ align:start position:0%
+opposed to implied probabilities
+uh uh in terms of number of standard
+
+ align:start position:0%
+uh uh in terms of number of standard
+ 
+
+ align:start position:0%
+uh uh in terms of number of standard
+deviations so there are some really cool
+
+ align:start position:0%
+deviations so there are some really cool
+ 
+
+ align:start position:0%
+deviations so there are some really cool
+variants of these plots that are very
+
+ align:start position:0%
+variants of these plots that are very
+ 
+
+ align:start position:0%
+variants of these plots that are very
+useful and I think we'll see some of
+
+ align:start position:0%
+useful and I think we'll see some of
+ 
+
+ align:start position:0%
+useful and I think we'll see some of
+these when we talk a little bit about
+
+ align:start position:0%
+these when we talk a little bit about
+ 
+
+ align:start position:0%
+these when we talk a little bit about
+yield and some other uh some other
+
+ align:start position:0%
+yield and some other uh some other
+ 
+
+ align:start position:0%
+yield and some other uh some other
+distributions a question
+
+ align:start position:0%
+distributions a question
+ 
+
+ align:start position:0%
+distributions a question
+yes yeah after I have the QQ plots how
+
+ align:start position:0%
+yes yeah after I have the QQ plots how
+ 
+
+ align:start position:0%
+yes yeah after I have the QQ plots how
+can I tell uh the confidence level that
+
+ align:start position:0%
+can I tell uh the confidence level that
+ 
+
+ align:start position:0%
+can I tell uh the confidence level that
+I have to say whether or not my data is
+
+ align:start position:0%
+I have to say whether or not my data is
+ 
+
+ align:start position:0%
+I have to say whether or not my data is
+normal distributed so the QQ plot does
+
+ align:start position:0%
+normal distributed so the QQ plot does
+ 
+
+ align:start position:0%
+normal distributed so the QQ plot does
+not actually tell you confidence
+
+ align:start position:0%
+not actually tell you confidence
+ 
+
+ align:start position:0%
+not actually tell you confidence
+intervals on either the hypothesis that
+
+ align:start position:0%
+intervals on either the hypothesis that
+ 
+
+ align:start position:0%
+intervals on either the hypothesis that
+it's normally distributed or confidence
+
+ align:start position:0%
+it's normally distributed or confidence
+ 
+
+ align:start position:0%
+it's normally distributed or confidence
+intervals on the uh parameter estimates
+
+ align:start position:0%
+intervals on the uh parameter estimates
+ 
+
+ align:start position:0%
+intervals on the uh parameter estimates
+there are some formal statistical tests
+
+ align:start position:0%
+there are some formal statistical tests
+ 
+
+ align:start position:0%
+there are some formal statistical tests
+where you can test that hypothesis of
+
+ align:start position:0%
+where you can test that hypothesis of
+ 
+
+ align:start position:0%
+where you can test that hypothesis of
+normality and essentially you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh can use those from your you're you're
+
+ align:start position:0%
+uh can use those from your you're you're
+ 
+
+ align:start position:0%
+uh can use those from your you're you're
+never going to hand calculate some of
+
+ align:start position:0%
+never going to hand calculate some of
+ 
+
+ align:start position:0%
+never going to hand calculate some of
+those uh statistics and then the
+
+ align:start position:0%
+those uh statistics and then the
+ 
+
+ align:start position:0%
+those uh statistics and then the
+probability associated with the derived
+
+ align:start position:0%
+probability associated with the derived
+ 
+
+ align:start position:0%
+probability associated with the derived
+statistic associated with normality
+
+ align:start position:0%
+statistic associated with normality
+ 
+
+ align:start position:0%
+statistic associated with normality
+you'll use your statistics package for
+
+ align:start position:0%
+you'll use your statistics package for
+ 
+
+ align:start position:0%
+you'll use your statistics package for
+that this gives you a good visual
+
+ align:start position:0%
+that this gives you a good visual
+ 
+
+ align:start position:0%
+that this gives you a good visual
+indication but to actually test is it
+
+ align:start position:0%
+indication but to actually test is it
+ 
+
+ align:start position:0%
+indication but to actually test is it
+normal or what is the probability that
+
+ align:start position:0%
+normal or what is the probability that
+ 
+
+ align:start position:0%
+normal or what is the probability that
+the data is non-normal that's a
+
+ align:start position:0%
+the data is non-normal that's a
+ 
+
+ align:start position:0%
+the data is non-normal that's a
+different question and then today we
+
+ align:start position:0%
+different question and then today we
+ 
+
+ align:start position:0%
+different question and then today we
+will start talking about confidence
+
+ align:start position:0%
+will start talking about confidence
+ 
+
+ align:start position:0%
+will start talking about confidence
+intervals on the mean and the variance
+
+ align:start position:0%
+intervals on the mean and the variance
+ 
+
+ align:start position:0%
+intervals on the mean and the variance
+which you also would not use the QQ Norm
+
+ align:start position:0%
+which you also would not use the QQ Norm
+ 
+
+ align:start position:0%
+which you also would not use the QQ Norm
+plot to generate okay so in fact let's
+
+ align:start position:0%
+plot to generate okay so in fact let's
+ 
+
+ align:start position:0%
+plot to generate okay so in fact let's
+get to that that that's
+
+ align:start position:0%
+get to that that that's
+ 
+
+ align:start position:0%
+get to that that that's
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regression
+
+ align:start position:0%
+regression
+ 
+
+ align:start position:0%
+regression
+uh well first
+
+ align:start position:0%
+uh well first
+ 
+
+ align:start position:0%
+uh well first
+off again if you were actually trying to
+
+ align:start position:0%
+off again if you were actually trying to
+ 
+
+ align:start position:0%
+off again if you were actually trying to
+estimate the parameters of normality you
+
+ align:start position:0%
+estimate the parameters of normality you
+ 
+
+ align:start position:0%
+estimate the parameters of normality you
+would you would just use the data and
+
+ align:start position:0%
+would you would just use the data and
+ 
+
+ align:start position:0%
+would you would just use the data and
+calculate the sample mean and Sample
+
+ align:start position:0%
+calculate the sample mean and Sample
+ 
+
+ align:start position:0%
+calculate the sample mean and Sample
+standard deviation I think if you are
+
+ align:start position:0%
+standard deviation I think if you are
+ 
+
+ align:start position:0%
+standard deviation I think if you are
+essentially what you are posing here is
+
+ align:start position:0%
+essentially what you are posing here is
+ 
+
+ align:start position:0%
+essentially what you are posing here is
+could I go in and look at these
+
+ align:start position:0%
+could I go in and look at these
+ 
+
+ align:start position:0%
+could I go in and look at these
+deviations and do some I don't know some
+
+ align:start position:0%
+deviations and do some I don't know some
+ 
+
+ align:start position:0%
+deviations and do some I don't know some
+of squared values of those deviations
+
+ align:start position:0%
+of squared values of those deviations
+ 
+
+ align:start position:0%
+of squared values of those deviations
+that's actually getting really close to
+
+ align:start position:0%
+that's actually getting really close to
+ 
+
+ align:start position:0%
+that's actually getting really close to
+calculating a statistic call it uh call
+
+ align:start position:0%
+calculating a statistic call it uh call
+ 
+
+ align:start position:0%
+calculating a statistic call it uh call
+it a w or some some some number A W
+
+ align:start position:0%
+it a w or some some some number A W
+ 
+
+ align:start position:0%
+it a w or some some some number A W
+statistic that I would form based on sum
+
+ align:start position:0%
+statistic that I would form based on sum
+ 
+
+ align:start position:0%
+statistic that I would form based on sum
+of squar deviations on one of these
+
+ align:start position:0%
+of squar deviations on one of these
+ 
+
+ align:start position:0%
+of squar deviations on one of these
+plots or some other maybe it's a Ab a
+
+ align:start position:0%
+plots or some other maybe it's a Ab a
+ 
+
+ align:start position:0%
+plots or some other maybe it's a Ab a
+sum of absolute uh distance
+
+ align:start position:0%
+sum of absolute uh distance
+ 
+
+ align:start position:0%
+sum of absolute uh distance
+deviations now I've got a statistic W
+
+ align:start position:0%
+deviations now I've got a statistic W
+ 
+
+ align:start position:0%
+deviations now I've got a statistic W
+and that's getting really close to the
+
+ align:start position:0%
+and that's getting really close to the
+ 
+
+ align:start position:0%
+and that's getting really close to the
+kinds of statistical test that one would
+
+ align:start position:0%
+kinds of statistical test that one would
+ 
+
+ align:start position:0%
+kinds of statistical test that one would
+run to ask the question of normality um
+
+ align:start position:0%
+run to ask the question of normality um
+ 
+
+ align:start position:0%
+run to ask the question of normality um
+I don't actually know what the formula
+
+ align:start position:0%
+I don't actually know what the formula
+ 
+
+ align:start position:0%
+I don't actually know what the formula
+is used in coming up with a W
+
+ align:start position:0%
+is used in coming up with a W
+ 
+
+ align:start position:0%
+is used in coming up with a W
+value uh and then uh uh you know what
+
+ align:start position:0%
+value uh and then uh uh you know what
+ 
+
+ align:start position:0%
+value uh and then uh uh you know what
+the normality tests are but that's the
+
+ align:start position:0%
+the normality tests are but that's the
+ 
+
+ align:start position:0%
+the normality tests are but that's the
+kernel of the idea is to actually look
+
+ align:start position:0%
+kernel of the idea is to actually look
+ 
+
+ align:start position:0%
+kernel of the idea is to actually look
+at your data form and
+
+ align:start position:0%
+at your data form and
+ 
+
+ align:start position:0%
+at your data form and
+aggregate value for that statistic that
+
+ align:start position:0%
+aggregate value for that statistic that
+ 
+
+ align:start position:0%
+aggregate value for that statistic that
+W statistic so for example if it was sum
+
+ align:start position:0%
+W statistic so for example if it was sum
+ 
+
+ align:start position:0%
+W statistic so for example if it was sum
+of absolute values and it for a sample
+
+ align:start position:0%
+of absolute values and it for a sample
+ 
+
+ align:start position:0%
+of absolute values and it for a sample
+of size 50 and that W is very near zero
+
+ align:start position:0%
+of size 50 and that W is very near zero
+ 
+
+ align:start position:0%
+of size 50 and that W is very near zero
+then you have high confidence that it's
+
+ align:start position:0%
+then you have high confidence that it's
+ 
+
+ align:start position:0%
+then you have high confidence that it's
+a normal distribution but as W gets
+
+ align:start position:0%
+a normal distribution but as W gets
+ 
+
+ align:start position:0%
+a normal distribution but as W gets
+bigger that would seem to indicate more
+
+ align:start position:0%
+bigger that would seem to indicate more
+ 
+
+ align:start position:0%
+bigger that would seem to indicate more
+and more likelihood that it's not normal
+
+ align:start position:0%
+and more likelihood that it's not normal
+ 
+
+ align:start position:0%
+and more likelihood that it's not normal
+and that's exactly the kind of thing
+
+ align:start position:0%
+and that's exactly the kind of thing
+ 
+
+ align:start position:0%
+and that's exactly the kind of thing
+that's going on in the formal
+
+ align:start position:0%
+that's going on in the formal
+ 
+
+ align:start position:0%
+that's going on in the formal
+statistical test for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normality okay so so here we've given
+
+ align:start position:0%
+normality okay so so here we've given
+ 
+
+ align:start position:0%
+normality okay so so here we've given
+you a few tools for being able to look
+
+ align:start position:0%
+you a few tools for being able to look
+ 
+
+ align:start position:0%
+you a few tools for being able to look
+at the data uh get a feel for is it
+
+ align:start position:0%
+at the data uh get a feel for is it
+ 
+
+ align:start position:0%
+at the data uh get a feel for is it
+normal or not but it hasn't sort of
+
+ align:start position:0%
+normal or not but it hasn't sort of
+ 
+
+ align:start position:0%
+normal or not but it hasn't sort of
+asked the answered the question how come
+
+ align:start position:0%
+asked the answered the question how come
+ 
+
+ align:start position:0%
+asked the answered the question how come
+so often we're using a normal
+
+ align:start position:0%
+so often we're using a normal
+ 
+
+ align:start position:0%
+so often we're using a normal
+distribution when we're uh actually
+
+ align:start position:0%
+distribution when we're uh actually
+ 
+
+ align:start position:0%
+distribution when we're uh actually
+looking at manufacturing data or other
+
+ align:start position:0%
+looking at manufacturing data or other
+ 
+
+ align:start position:0%
+looking at manufacturing data or other
+kinds of experimental data and a really
+
+ align:start position:0%
+kinds of experimental data and a really
+ 
+
+ align:start position:0%
+kinds of experimental data and a really
+important thing is the following
+
+ align:start position:0%
+important thing is the following
+ 
+
+ align:start position:0%
+important thing is the following
+observation the following fact that if
+
+ align:start position:0%
+observation the following fact that if
+ 
+
+ align:start position:0%
+observation the following fact that if
+we are forming
+
+ align:start position:0%
+we are forming
+ 
+
+ align:start position:0%
+we are forming
+a sum of independent observations of a
+
+ align:start position:0%
+a sum of independent observations of a
+ 
+
+ align:start position:0%
+a sum of independent observations of a
+random variable so X is uh
+
+ align:start position:0%
+random variable so X is uh
+ 
+
+ align:start position:0%
+random variable so X is uh
+uh has some underlying distribution and
+
+ align:start position:0%
+uh has some underlying distribution and
+ 
+
+ align:start position:0%
+uh has some underlying distribution and
+it doesn't actually matter what the
+
+ align:start position:0%
+it doesn't actually matter what the
+ 
+
+ align:start position:0%
+it doesn't actually matter what the
+underlying distribution
+
+ align:start position:0%
+underlying distribution
+ 
+
+ align:start position:0%
+underlying distribution
+is okay but I form in independent
+
+ align:start position:0%
+is okay but I form in independent
+ 
+
+ align:start position:0%
+is okay but I form in independent
+observations of that random variable and
+
+ align:start position:0%
+observations of that random variable and
+ 
+
+ align:start position:0%
+observations of that random variable and
+then I look at the distribution of the
+
+ align:start position:0%
+then I look at the distribution of the
+ 
+
+ align:start position:0%
+then I look at the distribution of the
+sum of X1 + X2 plus all uh in random
+
+ align:start position:0%
+sum of X1 + X2 plus all uh in random
+ 
+
+ align:start position:0%
+sum of X1 + X2 plus all uh in random
+variables the fascinating fact is that
+
+ align:start position:0%
+variables the fascinating fact is that
+ 
+
+ align:start position:0%
+variables the fascinating fact is that
+the sum of independent random variables
+
+ align:start position:0%
+the sum of independent random variables
+ 
+
+ align:start position:0%
+the sum of independent random variables
+tends towards a normal distribution this
+
+ align:start position:0%
+tends towards a normal distribution this
+ 
+
+ align:start position:0%
+tends towards a normal distribution this
+is the central limit theorem
+
+ align:start position:0%
+is the central limit theorem
+ 
+
+ align:start position:0%
+is the central limit theorem
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+so here's a neat little example if my
+
+ align:start position:0%
+so here's a neat little example if my
+ 
+
+ align:start position:0%
+so here's a neat little example if my
+underly distribution is in fact
+
+ align:start position:0%
+underly distribution is in fact
+ 
+
+ align:start position:0%
+underly distribution is in fact
+um something like a uniform distribution
+
+ align:start position:0%
+um something like a uniform distribution
+ 
+
+ align:start position:0%
+um something like a uniform distribution
+and I'm I'm s pulling off 20 samples of
+
+ align:start position:0%
+and I'm I'm s pulling off 20 samples of
+ 
+
+ align:start position:0%
+and I'm I'm s pulling off 20 samples of
+of X1 and 20 samples of X2 from a
+
+ align:start position:0%
+of X1 and 20 samples of X2 from a
+ 
+
+ align:start position:0%
+of X1 and 20 samples of X2 from a
+different uh uniform distribution I form
+
+ align:start position:0%
+different uh uniform distribution I form
+ 
+
+ align:start position:0%
+different uh uniform distribution I form
+say 100 samples of I guess 100 sets each
+
+ align:start position:0%
+say 100 samples of I guess 100 sets each
+ 
+
+ align:start position:0%
+say 100 samples of I guess 100 sets each
+one of these is I guess a a thousand
+
+ align:start position:0%
+one of these is I guess a a thousand
+ 
+
+ align:start position:0%
+one of these is I guess a a thousand
+points in in this example but I
+
+ align:start position:0%
+points in in this example but I
+ 
+
+ align:start position:0%
+points in in this example but I
+essentially take the sum of all of these
+
+ align:start position:0%
+essentially take the sum of all of these
+ 
+
+ align:start position:0%
+essentially take the sum of all of these
+random
+
+ align:start position:0%
+random
+ 
+
+ align:start position:0%
+random
+variables form a new random variable the
+
+ align:start position:0%
+variables form a new random variable the
+ 
+
+ align:start position:0%
+variables form a new random variable the
+new random variable is tends towards a a
+
+ align:start position:0%
+new random variable is tends towards a a
+ 
+
+ align:start position:0%
+new random variable is tends towards a a
+normal distribution with some some mean
+
+ align:start position:0%
+normal distribution with some some mean
+ 
+
+ align:start position:0%
+normal distribution with some some mean
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+variance um
+
+ align:start position:0%
+variance um
+ 
+
+ align:start position:0%
+variance um
+some of you I saw in uh 2853 and I had a
+
+ align:start position:0%
+some of you I saw in uh 2853 and I had a
+ 
+
+ align:start position:0%
+some of you I saw in uh 2853 and I had a
+nice link to a a website and I'll
+
+ align:start position:0%
+nice link to a a website and I'll
+ 
+
+ align:start position:0%
+nice link to a a website and I'll
+actually uh F dig that up and post it
+
+ align:start position:0%
+actually uh F dig that up and post it
+ 
+
+ align:start position:0%
+actually uh F dig that up and post it
+for for this class uh it's the sticky
+
+ align:start position:0%
+for for this class uh it's the sticky
+ 
+
+ align:start position:0%
+for for this class uh it's the sticky
+gooey uh U website it's a statistics uh
+
+ align:start position:0%
+gooey uh U website it's a statistics uh
+ 
+
+ align:start position:0%
+gooey uh U website it's a statistics uh
+interactive statistic package out of UC
+
+ align:start position:0%
+interactive statistic package out of UC
+ 
+
+ align:start position:0%
+interactive statistic package out of UC
+Berkeley it's really fun you can
+
+ align:start position:0%
+Berkeley it's really fun you can
+ 
+
+ align:start position:0%
+Berkeley it's really fun you can
+actually form these kinds of sums of
+
+ align:start position:0%
+actually form these kinds of sums of
+ 
+
+ align:start position:0%
+actually form these kinds of sums of
+random variables out of different
+
+ align:start position:0%
+random variables out of different
+ 
+
+ align:start position:0%
+random variables out of different
+underlying distributions and plot them
+
+ align:start position:0%
+underlying distributions and plot them
+ 
+
+ align:start position:0%
+underlying distributions and plot them
+and start to see how close the the sum
+
+ align:start position:0%
+and start to see how close the the sum
+ 
+
+ align:start position:0%
+and start to see how close the the sum
+or the normalized sum of these
+
+ align:start position:0%
+or the normalized sum of these
+ 
+
+ align:start position:0%
+or the normalized sum of these
+distributions are to to a normal uh so
+
+ align:start position:0%
+distributions are to to a normal uh so
+ 
+
+ align:start position:0%
+distributions are to to a normal uh so
+there's some very very nice uh uh
+
+ align:start position:0%
+there's some very very nice uh uh
+ 
+
+ align:start position:0%
+there's some very very nice uh uh
+interactive tools that you can sort of
+
+ align:start position:0%
+interactive tools that you can sort of
+ 
+
+ align:start position:0%
+interactive tools that you can sort of
+play with now an important Point here is
+
+ align:start position:0%
+play with now an important Point here is
+ 
+
+ align:start position:0%
+play with now an important Point here is
+if I'm calculating the
+
+ align:start position:0%
+if I'm calculating the
+ 
+
+ align:start position:0%
+if I'm calculating the
+mean so I'm calculating an xar across my
+
+ align:start position:0%
+mean so I'm calculating an xar across my
+ 
+
+ align:start position:0%
+mean so I'm calculating an xar across my
+data and I've got
+
+ align:start position:0%
+data and I've got
+ 
+
+ align:start position:0%
+data and I've got
+100 samples each drawn and I'm assuming
+
+ align:start position:0%
+100 samples each drawn and I'm assuming
+ 
+
+ align:start position:0%
+100 samples each drawn and I'm assuming
+I'm drawing it from the same underlying
+
+ align:start position:0%
+I'm drawing it from the same underlying
+ 
+
+ align:start position:0%
+I'm drawing it from the same underlying
+uh distribution whatever that may be
+
+ align:start position:0%
+uh distribution whatever that may be
+ 
+
+ align:start position:0%
+uh distribution whatever that may be
+what is the
+
+ align:start position:0%
+what is the
+ 
+
+ align:start position:0%
+what is the
+distribution of the sample
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean well if you you know look at the
+
+ align:start position:0%
+mean well if you you know look at the
+ 
+
+ align:start position:0%
+mean well if you you know look at the
+formula for the sample mean it's not
+
+ align:start position:0%
+formula for the sample mean it's not
+ 
+
+ align:start position:0%
+formula for the sample mean it's not
+exactly a sum of your data it's a sum of
+
+ align:start position:0%
+exactly a sum of your data it's a sum of
+ 
+
+ align:start position:0%
+exactly a sum of your data it's a sum of
+your data then divided by one right sum
+
+ align:start position:0%
+your data then divided by one right sum
+ 
+
+ align:start position:0%
+your data then divided by one right sum
+from IAL 1 to uh whatever n is of of of
+
+ align:start position:0%
+from IAL 1 to uh whatever n is of of of
+ 
+
+ align:start position:0%
+from IAL 1 to uh whatever n is of of of
+your individual samples so it is a sum
+
+ align:start position:0%
+your individual samples so it is a sum
+ 
+
+ align:start position:0%
+your individual samples so it is a sum
+and then with a constant out front but
+
+ align:start position:0%
+and then with a constant out front but
+ 
+
+ align:start position:0%
+and then with a constant out front but
+the point is by appealing to the central
+
+ align:start position:0%
+the point is by appealing to the central
+ 
+
+ align:start position:0%
+the point is by appealing to the central
+limit theorem the sample mean
+
+ align:start position:0%
+limit theorem the sample mean
+ 
+
+ align:start position:0%
+limit theorem the sample mean
+distribution the PDF associated with a
+
+ align:start position:0%
+distribution the PDF associated with a
+ 
+
+ align:start position:0%
+distribution the PDF associated with a
+sample
+
+ align:start position:0%
+sample
+ 
+
+ align:start position:0%
+sample
+mean always tends towards a normal
+
+ align:start position:0%
+mean always tends towards a normal
+ 
+
+ align:start position:0%
+mean always tends towards a normal
+distribution so we're going to come back
+
+ align:start position:0%
+distribution so we're going to come back
+ 
+
+ align:start position:0%
+distribution so we're going to come back
+to this idea of sampling and what the
+
+ align:start position:0%
+to this idea of sampling and what the
+ 
+
+ align:start position:0%
+to this idea of sampling and what the
+distribution is for sample statistics a
+
+ align:start position:0%
+distribution is for sample statistics a
+ 
+
+ align:start position:0%
+distribution is for sample statistics a
+little a little bit later but more
+
+ align:start position:0%
+little a little bit later but more
+ 
+
+ align:start position:0%
+little a little bit later but more
+generally very often what we're doing is
+
+ align:start position:0%
+generally very often what we're doing is
+ 
+
+ align:start position:0%
+generally very often what we're doing is
+pulling data out of a process that in in
+
+ align:start position:0%
+pulling data out of a process that in in
+ 
+
+ align:start position:0%
+pulling data out of a process that in in
+itself is already by the physics of the
+
+ align:start position:0%
+itself is already by the physics of the
+ 
+
+ align:start position:0%
+itself is already by the physics of the
+process highly
+
+ align:start position:0%
+process highly
+ 
+
+ align:start position:0%
+process highly
+averaged and therefore it's averaging
+
+ align:start position:0%
+averaged and therefore it's averaging
+ 
+
+ align:start position:0%
+averaged and therefore it's averaging
+lots of perhaps other underlying strange
+
+ align:start position:0%
+lots of perhaps other underlying strange
+ 
+
+ align:start position:0%
+lots of perhaps other underlying strange
+physics or or difficult
+
+ align:start position:0%
+physics or or difficult
+ 
+
+ align:start position:0%
+physics or or difficult
+physics uh but in aggregate um that
+
+ align:start position:0%
+physics uh but in aggregate um that
+ 
+
+ align:start position:0%
+physics uh but in aggregate um that
+averaging nature of the data itself not
+
+ align:start position:0%
+averaging nature of the data itself not
+ 
+
+ align:start position:0%
+averaging nature of the data itself not
+the operation that we perform but each
+
+ align:start position:0%
+the operation that we perform but each
+ 
+
+ align:start position:0%
+the operation that we perform but each
+an in individual underlying data point
+
+ align:start position:0%
+an in individual underlying data point
+ 
+
+ align:start position:0%
+an in individual underlying data point
+each individual xabi underneath of that
+
+ align:start position:0%
+each individual xabi underneath of that
+ 
+
+ align:start position:0%
+each individual xabi underneath of that
+may have some averaging by the physics
+
+ align:start position:0%
+may have some averaging by the physics
+ 
+
+ align:start position:0%
+may have some averaging by the physics
+going on that will help to drive it
+
+ align:start position:0%
+going on that will help to drive it
+ 
+
+ align:start position:0%
+going on that will help to drive it
+towards itself being a normal
+
+ align:start position:0%
+towards itself being a normal
+ 
+
+ align:start position:0%
+towards itself being a normal
+distribution okay so just to remind you
+
+ align:start position:0%
+distribution okay so just to remind you
+ 
+
+ align:start position:0%
+distribution okay so just to remind you
+the central limit theorem is probably
+
+ align:start position:0%
+the central limit theorem is probably
+ 
+
+ align:start position:0%
+the central limit theorem is probably
+the most used and perhaps often uh uh
+
+ align:start position:0%
+the most used and perhaps often uh uh
+ 
+
+ align:start position:0%
+the most used and perhaps often uh uh
+abused
+
+ align:start position:0%
+abused
+ 
+
+ align:start position:0%
+abused
+uh appeal to why we're using normal
+
+ align:start position:0%
+uh appeal to why we're using normal
+ 
+
+ align:start position:0%
+uh appeal to why we're using normal
+distrib tions very often it is still
+
+ align:start position:0%
+distrib tions very often it is still
+ 
+
+ align:start position:0%
+distrib tions very often it is still
+good to test it but but uh there is a
+
+ align:start position:0%
+good to test it but but uh there is a
+ 
+
+ align:start position:0%
+good to test it but but uh there is a
+good reason why very often our data uh
+
+ align:start position:0%
+good reason why very often our data uh
+ 
+
+ align:start position:0%
+good reason why very often our data uh
+does come up as normal
+
+ align:start position:0%
+does come up as normal
+ 
+
+ align:start position:0%
+does come up as normal
+distributions okay so I want to talk a
+
+ align:start position:0%
+distributions okay so I want to talk a
+ 
+
+ align:start position:0%
+distributions okay so I want to talk a
+little bit now about sampling because we
+
+ align:start position:0%
+little bit now about sampling because we
+ 
+
+ align:start position:0%
+little bit now about sampling because we
+are very often using actual measurements
+
+ align:start position:0%
+are very often using actual measurements
+ 
+
+ align:start position:0%
+are very often using actual measurements
+and data to try to get estimates for uh
+
+ align:start position:0%
+and data to try to get estimates for uh
+ 
+
+ align:start position:0%
+and data to try to get estimates for uh
+or more generally build a model of our
+
+ align:start position:0%
+or more generally build a model of our
+ 
+
+ align:start position:0%
+or more generally build a model of our
+random process our uh and estimate
+
+ align:start position:0%
+random process our uh and estimate
+ 
+
+ align:start position:0%
+random process our uh and estimate
+parameters of that random process and
+
+ align:start position:0%
+parameters of that random process and
+ 
+
+ align:start position:0%
+parameters of that random process and
+and we've said in general you know pie
+
+ align:start position:0%
+and we've said in general you know pie
+ 
+
+ align:start position:0%
+and we've said in general you know pie
+of X is unknown the data you always plot
+
+ align:start position:0%
+of X is unknown the data you always plot
+ 
+
+ align:start position:0%
+of X is unknown the data you always plot
+your raw data first and foremost and
+
+ align:start position:0%
+your raw data first and foremost and
+ 
+
+ align:start position:0%
+your raw data first and foremost and
+very often the raw data will suggest a
+
+ align:start position:0%
+very often the raw data will suggest a
+ 
+
+ align:start position:0%
+very often the raw data will suggest a
+distribution or then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+histograms uh May provide some insight
+
+ align:start position:0%
+histograms uh May provide some insight
+ 
+
+ align:start position:0%
+histograms uh May provide some insight
+so for
+
+ align:start position:0%
+so for
+ 
+
+ align:start position:0%
+so for
+example a very quick histogram will will
+
+ align:start position:0%
+example a very quick histogram will will
+ 
+
+ align:start position:0%
+example a very quick histogram will will
+very often give you the difference
+
+ align:start position:0%
+very often give you the difference
+ 
+
+ align:start position:0%
+very often give you the difference
+between a normal distribution and a
+
+ align:start position:0%
+between a normal distribution and a
+ 
+
+ align:start position:0%
+between a normal distribution and a
+uniform distribution right if it's if
+
+ align:start position:0%
+uniform distribution right if it's if
+ 
+
+ align:start position:0%
+uniform distribution right if it's if
+it's evenly falling and I don't have
+
+ align:start position:0%
+it's evenly falling and I don't have
+ 
+
+ align:start position:0%
+it's evenly falling and I don't have
+this fall off in the Tails that's a
+
+ align:start position:0%
+this fall off in the Tails that's a
+ 
+
+ align:start position:0%
+this fall off in the Tails that's a
+that's that's very important and then we
+
+ align:start position:0%
+that's that's very important and then we
+ 
+
+ align:start position:0%
+that's that's very important and then we
+can also use things like the QQ Norm
+
+ align:start position:0%
+can also use things like the QQ Norm
+ 
+
+ align:start position:0%
+can also use things like the QQ Norm
+plot to test some of those things so the
+
+ align:start position:0%
+plot to test some of those things so the
+ 
+
+ align:start position:0%
+plot to test some of those things so the
+first sort of job is to come up with
+
+ align:start position:0%
+first sort of job is to come up with
+ 
+
+ align:start position:0%
+first sort of job is to come up with
+what what uh what likely gener uh uh
+
+ align:start position:0%
+what what uh what likely gener uh uh
+ 
+
+ align:start position:0%
+what what uh what likely gener uh uh
+distribution you want to use you know
+
+ align:start position:0%
+distribution you want to use you know
+ 
+
+ align:start position:0%
+distribution you want to use you know
+nine times out of 10 U uh normal
+
+ align:start position:0%
+nine times out of 10 U uh normal
+ 
+
+ align:start position:0%
+nine times out of 10 U uh normal
+distribution will be appropriate and
+
+ align:start position:0%
+distribution will be appropriate and
+ 
+
+ align:start position:0%
+distribution will be appropriate and
+then the second thing is to estimate
+
+ align:start position:0%
+then the second thing is to estimate
+ 
+
+ align:start position:0%
+then the second thing is to estimate
+parameters of the
+
+ align:start position:0%
+parameters of the
+ 
+
+ align:start position:0%
+parameters of the
+distribution right and the normal
+
+ align:start position:0%
+distribution right and the normal
+ 
+
+ align:start position:0%
+distribution right and the normal
+distribution again to remind you just
+
+ align:start position:0%
+distribution again to remind you just
+ 
+
+ align:start position:0%
+distribution again to remind you just
+has these two parameters mean and
+
+ align:start position:0%
+has these two parameters mean and
+ 
+
+ align:start position:0%
+has these two parameters mean and
+variance and now what we want to do is
+
+ align:start position:0%
+variance and now what we want to do is
+ 
+
+ align:start position:0%
+variance and now what we want to do is
+is estimate them now everybody is used
+
+ align:start position:0%
+is estimate them now everybody is used
+ 
+
+ align:start position:0%
+is estimate them now everybody is used
+to the formulas we've got the formulas
+
+ align:start position:0%
+to the formulas we've got the formulas
+ 
+
+ align:start position:0%
+to the formulas we've got the formulas
+right here for calculating from your
+
+ align:start position:0%
+right here for calculating from your
+ 
+
+ align:start position:0%
+right here for calculating from your
+sample your limited number of pieces of
+
+ align:start position:0%
+sample your limited number of pieces of
+ 
+
+ align:start position:0%
+sample your limited number of pieces of
+data uh what things are
+
+ align:start position:0%
+data uh what things are
+ 
+
+ align:start position:0%
+data uh what things are
+uh what what a few important statistics
+
+ align:start position:0%
+uh what what a few important statistics
+ 
+
+ align:start position:0%
+uh what what a few important statistics
+are or or characteristics are of that
+
+ align:start position:0%
+are or or characteristics are of that
+ 
+
+ align:start position:0%
+are or or characteristics are of that
+data like the sample mean or the average
+
+ align:start position:0%
+data like the sample mean or the average
+ 
+
+ align:start position:0%
+data like the sample mean or the average
+and the sample variant
+
+ align:start position:0%
+and the sample variant
+ 
+
+ align:start position:0%
+and the sample variant
+uh but what I want to give you a feel
+
+ align:start position:0%
+uh but what I want to give you a feel
+ 
+
+ align:start position:0%
+uh but what I want to give you a feel
+for today perhaps the most subtle
+
+ align:start position:0%
+for today perhaps the most subtle
+ 
+
+ align:start position:0%
+for today perhaps the most subtle
+idea an important idea for interpret
+
+ align:start position:0%
+idea an important idea for interpret
+ 
+
+ align:start position:0%
+idea an important idea for interpret
+interpretation for establishment of
+
+ align:start position:0%
+interpretation for establishment of
+ 
+
+ align:start position:0%
+interpretation for establishment of
+confidence intervals for actually being
+
+ align:start position:0%
+confidence intervals for actually being
+ 
+
+ align:start position:0%
+confidence intervals for actually being
+able to say where you think the new
+
+ align:start position:0%
+able to say where you think the new
+ 
+
+ align:start position:0%
+able to say where you think the new
+values lie
+
+ align:start position:0%
+values lie
+ 
+
+ align:start position:0%
+values lie
+subtle idea is that these
+
+ align:start position:0%
+subtle idea is that these
+ 
+
+ align:start position:0%
+subtle idea is that these
+themselves are statistics that have
+
+ align:start position:0%
+themselves are statistics that have
+ 
+
+ align:start position:0%
+themselves are statistics that have
+their own PDF their own probability
+
+ align:start position:0%
+their own PDF their own probability
+ 
+
+ align:start position:0%
+their own PDF their own probability
+density function they have a sample
+
+ align:start position:0%
+density function they have a sample
+ 
+
+ align:start position:0%
+density function they have a sample
+statistics that fall that tell you the
+
+ align:start position:0%
+statistics that fall that tell you the
+ 
+
+ align:start position:0%
+statistics that fall that tell you the
+likelihood of observing particular
+
+ align:start position:0%
+likelihood of observing particular
+ 
+
+ align:start position:0%
+likelihood of observing particular
+values of them that
+
+ align:start position:0%
+values of them that
+ 
+
+ align:start position:0%
+values of them that
+establish bounds for where if I had a
+
+ align:start position:0%
+establish bounds for where if I had a
+ 
+
+ align:start position:0%
+establish bounds for where if I had a
+different sample how close you think the
+
+ align:start position:0%
+different sample how close you think the
+ 
+
+ align:start position:0%
+different sample how close you think the
+new sample still drawn from the under
+
+ align:start position:0%
+new sample still drawn from the under
+ 
+
+ align:start position:0%
+new sample still drawn from the under
+parent uh distribution would actually
+
+ align:start position:0%
+parent uh distribution would actually
+ 
+
+ align:start position:0%
+parent uh distribution would actually
+lie to the particular sample that I that
+
+ align:start position:0%
+lie to the particular sample that I that
+ 
+
+ align:start position:0%
+lie to the particular sample that I that
+I just drew so I'm going to explain that
+
+ align:start position:0%
+I just drew so I'm going to explain that
+ 
+
+ align:start position:0%
+I just drew so I'm going to explain that
+in a few more slides or several slides
+
+ align:start position:0%
+in a few more slides or several slides
+ 
+
+ align:start position:0%
+in a few more slides or several slides
+uh here but the key idea is it's really
+
+ align:start position:0%
+uh here but the key idea is it's really
+ 
+
+ align:start position:0%
+uh here but the key idea is it's really
+easy to uh calculate a couple of these
+
+ align:start position:0%
+easy to uh calculate a couple of these
+ 
+
+ align:start position:0%
+easy to uh calculate a couple of these
+moments the the the mean and the
+
+ align:start position:0%
+moments the the the mean and the
+ 
+
+ align:start position:0%
+moments the the the mean and the
+variance for the normal distribution
+
+ align:start position:0%
+variance for the normal distribution
+ 
+
+ align:start position:0%
+variance for the normal distribution
+that sort of tells you everything for an
+
+ align:start position:0%
+that sort of tells you everything for an
+ 
+
+ align:start position:0%
+that sort of tells you everything for an
+estimate of your raw data but then I
+
+ align:start position:0%
+estimate of your raw data but then I
+ 
+
+ align:start position:0%
+estimate of your raw data but then I
+want to get to the more subtle idea so
+
+ align:start position:0%
+want to get to the more subtle idea so
+ 
+
+ align:start position:0%
+want to get to the more subtle idea so
+that we can start talking about things
+
+ align:start position:0%
+that we can start talking about things
+ 
+
+ align:start position:0%
+that we can start talking about things
+like confidence
+
+ align:start position:0%
+like confidence
+ 
+
+ align:start position:0%
+like confidence
+intervals and a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simple a simple example uh to give you a
+
+ align:start position:0%
+simple a simple example uh to give you a
+ 
+
+ align:start position:0%
+simple a simple example uh to give you a
+little bit of a feel for this here is if
+
+ align:start position:0%
+little bit of a feel for this here is if
+ 
+
+ align:start position:0%
+little bit of a feel for this here is if
+I were to ask you kind of what
+
+ align:start position:0%
+I were to ask you kind of what
+ 
+
+ align:start position:0%
+I were to ask you kind of what
+distribution applies to the to the
+
+ align:start position:0%
+distribution applies to the to the
+ 
+
+ align:start position:0%
+distribution applies to the to the
+sample
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean where does that come from where
+
+ align:start position:0%
+mean where does that come from where
+ 
+
+ align:start position:0%
+mean where does that come from where
+does this notion of a distribution
+
+ align:start position:0%
+does this notion of a distribution
+ 
+
+ align:start position:0%
+does this notion of a distribution
+associated with the sample mean uh arise
+
+ align:start position:0%
+associated with the sample mean uh arise
+ 
+
+ align:start position:0%
+associated with the sample mean uh arise
+so if we look at the formula for the
+
+ align:start position:0%
+so if we look at the formula for the
+ 
+
+ align:start position:0%
+so if we look at the formula for the
+sample mean and expand it out in some
+
+ align:start position:0%
+sample mean and expand it out in some
+ 
+
+ align:start position:0%
+sample mean and expand it out in some
+sense we've got just a sum of
+
+ align:start position:0%
+sense we've got just a sum of
+ 
+
+ align:start position:0%
+sense we've got just a sum of
+independent random variables like we
+
+ align:start position:0%
+independent random variables like we
+ 
+
+ align:start position:0%
+independent random variables like we
+were talking about with the um Central
+
+ align:start position:0%
+were talking about with the um Central
+ 
+
+ align:start position:0%
+were talking about with the um Central
+limit theorem there are different
+
+ align:start position:0%
+limit theorem there are different
+ 
+
+ align:start position:0%
+limit theorem there are different
+constants in here and in this case for
+
+ align:start position:0%
+constants in here and in this case for
+ 
+
+ align:start position:0%
+constants in here and in this case for
+the sample mean statistic all of the
+
+ align:start position:0%
+the sample mean statistic all of the
+ 
+
+ align:start position:0%
+the sample mean statistic all of the
+constants are the same which is just uh
+
+ align:start position:0%
+constants are the same which is just uh
+ 
+
+ align:start position:0%
+constants are the same which is just uh
+you know one the total number of data
+
+ align:start position:0%
+you know one the total number of data
+ 
+
+ align:start position:0%
+you know one the total number of data
+points or sample points that I've got
+
+ align:start position:0%
+points or sample points that I've got
+ 
+
+ align:start position:0%
+points or sample points that I've got
+now you can go back to the definition of
+
+ align:start position:0%
+now you can go back to the definition of
+ 
+
+ align:start position:0%
+now you can go back to the definition of
+expectation that we talked about earlier
+
+ align:start position:0%
+expectation that we talked about earlier
+ 
+
+ align:start position:0%
+expectation that we talked about earlier
+and do the expectation operator across
+
+ align:start position:0%
+and do the expectation operator across
+ 
+
+ align:start position:0%
+and do the expectation operator across
+this and do expectation math so the
+
+ align:start position:0%
+this and do expectation math so the
+ 
+
+ align:start position:0%
+this and do expectation math so the
+expectation of
+
+ align:start position:0%
+expectation of
+ 
+
+ align:start position:0%
+expectation of
+ax is equal
+
+ align:start position:0%
+ax is equal
+ 
+
+ align:start position:0%
+ax is equal
+to just that constant times the
+
+ align:start position:0%
+to just that constant times the
+ 
+
+ align:start position:0%
+to just that constant times the
+expectation of uh the underlying random
+
+ align:start position:0%
+expectation of uh the underlying random
+ 
+
+ align:start position:0%
+expectation of uh the underlying random
+variable so the the the the 1 / n uh
+
+ align:start position:0%
+variable so the the the the 1 / n uh
+ 
+
+ align:start position:0%
+variable so the the the the 1 / n uh
+simply comes out to the to the left and
+
+ align:start position:0%
+simply comes out to the to the left and
+ 
+
+ align:start position:0%
+simply comes out to the to the left and
+and if I were to ask what is the mean of
+
+ align:start position:0%
+and if I were to ask what is the mean of
+ 
+
+ align:start position:0%
+and if I were to ask what is the mean of
+a uh the PDF associated with xbar it is
+
+ align:start position:0%
+a uh the PDF associated with xbar it is
+ 
+
+ align:start position:0%
+a uh the PDF associated with xbar it is
+going to be uh 1/n the the same the same
+
+ align:start position:0%
+going to be uh 1/n the the same the same
+ 
+
+ align:start position:0%
+going to be uh 1/n the the same the same
+mean now what else is going on here is
+
+ align:start position:0%
+mean now what else is going on here is
+ 
+
+ align:start position:0%
+mean now what else is going on here is
+if you look at the standard deviation of
+
+ align:start position:0%
+if you look at the standard deviation of
+ 
+
+ align:start position:0%
+if you look at the standard deviation of
+xbar hope you guys can see that there's
+
+ align:start position:0%
+xbar hope you guys can see that there's
+ 
+
+ align:start position:0%
+xbar hope you guys can see that there's
+a variance of xbar in here so that's an
+
+ align:start position:0%
+a variance of xbar in here so that's an
+ 
+
+ align:start position:0%
+a variance of xbar in here so that's an
+X and a bar which I
+
+ align:start position:0%
+X and a bar which I
+ 
+
+ align:start position:0%
+X and a bar which I
+just the pen doesn't line up exactly
+
+ align:start position:0%
+just the pen doesn't line up exactly
+ 
+
+ align:start position:0%
+just the pen doesn't line up exactly
+with the
+
+ align:start position:0%
+with the
+ 
+
+ align:start position:0%
+with the
+screen you can also do the expectation
+
+ align:start position:0%
+screen you can also do the expectation
+ 
+
+ align:start position:0%
+screen you can also do the expectation
+operator for uh oops not the expectation
+
+ align:start position:0%
+operator for uh oops not the expectation
+ 
+
+ align:start position:0%
+operator for uh oops not the expectation
+but the uh the variance
+
+ align:start position:0%
+but the uh the variance
+ 
+
+ align:start position:0%
+but the uh the variance
+operator and if you do the mathematics
+
+ align:start position:0%
+operator and if you do the mathematics
+ 
+
+ align:start position:0%
+operator and if you do the mathematics
+on variance of some ax that's equal to a
+
+ align:start position:0%
+on variance of some ax that's equal to a
+ 
+
+ align:start position:0%
+on variance of some ax that's equal to a
+s the variance of the
+
+ align:start position:0%
+s the variance of the
+ 
+
+ align:start position:0%
+s the variance of the
+underlying uh uh variable and if you
+
+ align:start position:0%
+underlying uh uh variable and if you
+ 
+
+ align:start position:0%
+underlying uh uh variable and if you
+follow that math through for the
+
+ align:start position:0%
+follow that math through for the
+ 
+
+ align:start position:0%
+follow that math through for the
+definition of xar and relate that to the
+
+ align:start position:0%
+definition of xar and relate that to the
+ 
+
+ align:start position:0%
+definition of xar and relate that to the
+variance of each of these x sub I what
+
+ align:start position:0%
+variance of each of these x sub I what
+ 
+
+ align:start position:0%
+variance of each of these x sub I what
+you find is that the variance I get an N
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times I'm I'm summing n of these random
+
+ align:start position:0%
+times I'm I'm summing n of these random
+ 
+
+ align:start position:0%
+times I'm I'm summing n of these random
+variables so I've got
+
+ align:start position:0%
+variables so I've got
+ 
+
+ align:start position:0%
+variables so I've got
+n times
+
+ align:start position:0%
+n times
+ 
+
+ align:start position:0%
+n times
+1/n is the constant in
+
+ align:start position:0%
+1/n is the constant in
+ 
+
+ align:start position:0%
+1/n is the constant in
+here so I get a 1 over n^ 2 times the
+
+ align:start position:0%
+here so I get a 1 over n^ 2 times the
+ 
+
+ align:start position:0%
+here so I get a 1 over n^ 2 times the
+underlying variance of my
+
+ align:start position:0%
+underlying variance of my
+ 
+
+ align:start position:0%
+underlying variance of my
+X so that I get a cancellation and the
+
+ align:start position:0%
+X so that I get a cancellation and the
+ 
+
+ align:start position:0%
+X so that I get a cancellation and the
+variance then of my
+
+ align:start position:0%
+variance then of my
+ 
+
+ align:start position:0%
+variance then of my
+xbar is is just equal to what I've what
+
+ align:start position:0%
+xbar is is just equal to what I've what
+ 
+
+ align:start position:0%
+xbar is is just equal to what I've what
+I've shown here a one over n of the
+
+ align:start position:0%
+I've shown here a one over n of the
+ 
+
+ align:start position:0%
+I've shown here a one over n of the
+variance of the underlying
+
+ align:start position:0%
+variance of the underlying
+ 
+
+ align:start position:0%
+variance of the underlying
+distribution so what's interesting here
+
+ align:start position:0%
+distribution so what's interesting here
+ 
+
+ align:start position:0%
+distribution so what's interesting here
+is if I start to ask about the
+
+ align:start position:0%
+is if I start to ask about the
+ 
+
+ align:start position:0%
+is if I start to ask about the
+distributions of associated with what
+
+ align:start position:0%
+distributions of associated with what
+ 
+
+ align:start position:0%
+distributions of associated with what
+are the mean and the variance of the
+
+ align:start position:0%
+are the mean and the variance of the
+ 
+
+ align:start position:0%
+are the mean and the variance of the
+normal distribution associated with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+xar right what is the mean of an xar
+
+ align:start position:0%
+xar right what is the mean of an xar
+ 
+
+ align:start position:0%
+xar right what is the mean of an xar
+that I would typically observe from lots
+
+ align:start position:0%
+that I would typically observe from lots
+ 
+
+ align:start position:0%
+that I would typically observe from lots
+of samples of my underlying distribution
+
+ align:start position:0%
+of samples of my underlying distribution
+ 
+
+ align:start position:0%
+of samples of my underlying distribution
+what is a variance I would observe it's
+
+ align:start position:0%
+what is a variance I would observe it's
+ 
+
+ align:start position:0%
+what is a variance I would observe it's
+related to the underlying
+
+ align:start position:0%
+related to the underlying
+ 
+
+ align:start position:0%
+related to the underlying
+distribution but it's not exactly the
+
+ align:start position:0%
+distribution but it's not exactly the
+ 
+
+ align:start position:0%
+distribution but it's not exactly the
+same I've got a new random variable an
+
+ align:start position:0%
+same I've got a new random variable an
+ 
+
+ align:start position:0%
+same I've got a new random variable an
+xbar that has a different mean and
+
+ align:start position:0%
+xbar that has a different mean and
+ 
+
+ align:start position:0%
+xbar that has a different mean and
+variance it's got the same
+
+ align:start position:0%
+variance it's got the same
+ 
+
+ align:start position:0%
+variance it's got the same
+mean in this case uh but the variance is
+
+ align:start position:0%
+mean in this case uh but the variance is
+ 
+
+ align:start position:0%
+mean in this case uh but the variance is
+actually scaled and this is extremely
+
+ align:start position:0%
+actually scaled and this is extremely
+ 
+
+ align:start position:0%
+actually scaled and this is extremely
+useful because the variance of my uh
+
+ align:start position:0%
+useful because the variance of my uh
+ 
+
+ align:start position:0%
+useful because the variance of my uh
+averaging means that I'm getting a
+
+ align:start position:0%
+averaging means that I'm getting a
+ 
+
+ align:start position:0%
+averaging means that I'm getting a
+tighter distribution a narrower or or
+
+ align:start position:0%
+tighter distribution a narrower or or
+ 
+
+ align:start position:0%
+tighter distribution a narrower or or
+smaller variance on the uh uh compared
+
+ align:start position:0%
+smaller variance on the uh uh compared
+ 
+
+ align:start position:0%
+smaller variance on the uh uh compared
+to the underlying distribution I'm going
+
+ align:start position:0%
+to the underlying distribution I'm going
+ 
+
+ align:start position:0%
+to the underlying distribution I'm going
+to show you that in a little bit more of
+
+ align:start position:0%
+to show you that in a little bit more of
+ 
+
+ align:start position:0%
+to show you that in a little bit more of
+a of a of a graphical
+
+ align:start position:0%
+a of a of a graphical
+ 
+
+ align:start position:0%
+a of a of a graphical
+fashion a little bit later because this
+
+ align:start position:0%
+fashion a little bit later because this
+ 
+
+ align:start position:0%
+fashion a little bit later because this
+is that's sort of a preview to this
+
+ align:start position:0%
+is that's sort of a preview to this
+ 
+
+ align:start position:0%
+is that's sort of a preview to this
+whole idea of sampling which is really
+
+ align:start position:0%
+whole idea of sampling which is really
+ 
+
+ align:start position:0%
+whole idea of sampling which is really
+critical okay we've already talked about
+
+ align:start position:0%
+critical okay we've already talked about
+ 
+
+ align:start position:0%
+critical okay we've already talked about
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+so the key thing here
+
+ align:start position:0%
+so the key thing here
+ 
+
+ align:start position:0%
+so the key thing here
+is uh to get to sort of this notion of
+
+ align:start position:0%
+is uh to get to sort of this notion of
+ 
+
+ align:start position:0%
+is uh to get to sort of this notion of
+sampling distributions what are the key
+
+ align:start position:0%
+sampling distributions what are the key
+ 
+
+ align:start position:0%
+sampling distributions what are the key
+distributions arising from the fact that
+
+ align:start position:0%
+distributions arising from the fact that
+ 
+
+ align:start position:0%
+distributions arising from the fact that
+I'm drawing multiple pieces of data from
+
+ align:start position:0%
+I'm drawing multiple pieces of data from
+ 
+
+ align:start position:0%
+I'm drawing multiple pieces of data from
+a parent distribution and then calculate
+
+ align:start position:0%
+a parent distribution and then calculate
+ 
+
+ align:start position:0%
+a parent distribution and then calculate
+things about that so we'll get to some
+
+ align:start position:0%
+things about that so we'll get to some
+ 
+
+ align:start position:0%
+things about that so we'll get to some
+of these key distributions besides the
+
+ align:start position:0%
+of these key distributions besides the
+ 
+
+ align:start position:0%
+of these key distributions besides the
+normal distribution we'll actually talk
+
+ align:start position:0%
+normal distribution we'll actually talk
+ 
+
+ align:start position:0%
+normal distribution we'll actually talk
+about these uh next class but what we
+
+ align:start position:0%
+about these uh next class but what we
+ 
+
+ align:start position:0%
+about these uh next class but what we
+want to do uh is go back and get a
+
+ align:start position:0%
+want to do uh is go back and get a
+ 
+
+ align:start position:0%
+want to do uh is go back and get a
+little bit more feel for not only the
+
+ align:start position:0%
+little bit more feel for not only the
+ 
+
+ align:start position:0%
+little bit more feel for not only the
+normal distribution but a few other
+
+ align:start position:0%
+normal distribution but a few other
+ 
+
+ align:start position:0%
+normal distribution but a few other
+distributions that often arise in
+
+ align:start position:0%
+distributions that often arise in
+ 
+
+ align:start position:0%
+distributions that often arise in
+manufacturing and then also start
+
+ align:start position:0%
+manufacturing and then also start
+ 
+
+ align:start position:0%
+manufacturing and then also start
+talking about these Notions of where the
+
+ align:start position:0%
+talking about these Notions of where the
+ 
+
+ align:start position:0%
+talking about these Notions of where the
+data actually lies what are the
+
+ align:start position:0%
+data actually lies what are the
+ 
+
+ align:start position:0%
+data actually lies what are the
+probabilities of data falling out in the
+
+ align:start position:0%
+probabilities of data falling out in the
+ 
+
+ align:start position:0%
+probabilities of data falling out in the
+Tails and using that then to start to
+
+ align:start position:0%
+Tails and using that then to start to
+ 
+
+ align:start position:0%
+Tails and using that then to start to
+get towards the idea of building
+
+ align:start position:0%
+get towards the idea of building
+ 
+
+ align:start position:0%
+get towards the idea of building
+confidence intervals on where we think
+
+ align:start position:0%
+confidence intervals on where we think
+ 
+
+ align:start position:0%
+confidence intervals on where we think
+the real mean of our underlying uh
+
+ align:start position:0%
+the real mean of our underlying uh
+ 
+
+ align:start position:0%
+the real mean of our underlying uh
+parent distribution sits next class
+
+ align:start position:0%
+parent distribution sits next class
+ 
+
+ align:start position:0%
+parent distribution sits next class
+we'll also get to hypothesis tests which
+
+ align:start position:0%
+we'll also get to hypothesis tests which
+ 
+
+ align:start position:0%
+we'll also get to hypothesis tests which
+arise naturally and actually start to
+
+ align:start position:0%
+arise naturally and actually start to
+ 
+
+ align:start position:0%
+arise naturally and actually start to
+get really close to statistical process
+
+ align:start position:0%
+get really close to statistical process
+ 
+
+ align:start position:0%
+get really close to statistical process
+control
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charting which is one of the fundamental
+
+ align:start position:0%
+charting which is one of the fundamental
+ 
+
+ align:start position:0%
+charting which is one of the fundamental
+tools of manufacturing control so what
+
+ align:start position:0%
+tools of manufacturing control so what
+ 
+
+ align:start position:0%
+tools of manufacturing control so what
+I'm going to do here is go back this is
+
+ align:start position:0%
+I'm going to do here is go back this is
+ 
+
+ align:start position:0%
+I'm going to do here is go back this is
+sort of the the plan for the next uh uh
+
+ align:start position:0%
+sort of the the plan for the next uh uh
+ 
+
+ align:start position:0%
+sort of the the plan for the next uh uh
+sort of the rest of today and starting
+
+ align:start position:0%
+sort of the rest of today and starting
+ 
+
+ align:start position:0%
+sort of the rest of today and starting
+into tomorrow we're going to go back
+
+ align:start position:0%
+into tomorrow we're going to go back
+ 
+
+ align:start position:0%
+into tomorrow we're going to go back
+just remind you of some of the discret
+
+ align:start position:0%
+just remind you of some of the discret
+ 
+
+ align:start position:0%
+just remind you of some of the discret
+variable distributions then talk about
+
+ align:start position:0%
+variable distributions then talk about
+ 
+
+ align:start position:0%
+variable distributions then talk about
+some of the uh which are are more
+
+ align:start position:0%
+some of the uh which are are more
+ 
+
+ align:start position:0%
+some of the uh which are are more
+applicable to sort of attribute modeling
+
+ align:start position:0%
+applicable to sort of attribute modeling
+ 
+
+ align:start position:0%
+applicable to sort of attribute modeling
+or yield modeling sort of discrete
+
+ align:start position:0%
+or yield modeling sort of discrete
+ 
+
+ align:start position:0%
+or yield modeling sort of discrete
+things then we'll come back and talk a
+
+ align:start position:0%
+things then we'll come back and talk a
+ 
+
+ align:start position:0%
+things then we'll come back and talk a
+little bit about uh The Continuous
+
+ align:start position:0%
+little bit about uh The Continuous
+ 
+
+ align:start position:0%
+little bit about uh The Continuous
+distributions and then also touch
+
+ align:start position:0%
+distributions and then also touch
+ 
+
+ align:start position:0%
+distributions and then also touch
+on how you manipulate um uh some of
+
+ align:start position:0%
+on how you manipulate um uh some of
+ 
+
+ align:start position:0%
+on how you manipulate um uh some of
+these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distributions okay discrete
+
+ align:start position:0%
+distributions okay discrete
+ 
+
+ align:start position:0%
+distributions okay discrete
+distributions people seen the beri
+
+ align:start position:0%
+distributions people seen the beri
+ 
+
+ align:start position:0%
+distributions people seen the beri
+distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before good this is like the simplest
+
+ align:start position:0%
+before good this is like the simplest
+ 
+
+ align:start position:0%
+before good this is like the simplest
+distribution the very simplest right you
+
+ align:start position:0%
+distribution the very simplest right you
+ 
+
+ align:start position:0%
+distribution the very simplest right you
+do a a trial you do an experiment can
+
+ align:start position:0%
+do a a trial you do an experiment can
+ 
+
+ align:start position:0%
+do a a trial you do an experiment can
+only have two
+
+ align:start position:0%
+only have two
+ 
+
+ align:start position:0%
+only have two
+outcomes success or failure you get to
+
+ align:start position:0%
+outcomes success or failure you get to
+ 
+
+ align:start position:0%
+outcomes success or failure you get to
+label what success is we'll label a
+
+ align:start position:0%
+label what success is we'll label a
+ 
+
+ align:start position:0%
+label what success is we'll label a
+success with the random variable taking
+
+ align:start position:0%
+success with the random variable taking
+ 
+
+ align:start position:0%
+success with the random variable taking
+on the value of one and failure taking
+
+ align:start position:0%
+on the value of one and failure taking
+ 
+
+ align:start position:0%
+on the value of one and failure taking
+on zero I could flip that you can start
+
+ align:start position:0%
+on zero I could flip that you can start
+ 
+
+ align:start position:0%
+on zero I could flip that you can start
+to see already a little bit of inkling
+
+ align:start position:0%
+to see already a little bit of inkling
+ 
+
+ align:start position:0%
+to see already a little bit of inkling
+of yield in here does the thing work or
+
+ align:start position:0%
+of yield in here does the thing work or
+ 
+
+ align:start position:0%
+of yield in here does the thing work or
+not the very simplest coarsest crudest
+
+ align:start position:0%
+not the very simplest coarsest crudest
+ 
+
+ align:start position:0%
+not the very simplest coarsest crudest
+uh kind of model for functionality and
+
+ align:start position:0%
+uh kind of model for functionality and
+ 
+
+ align:start position:0%
+uh kind of model for functionality and
+the probability or statistics associated
+
+ align:start position:0%
+the probability or statistics associated
+ 
+
+ align:start position:0%
+the probability or statistics associated
+with that is did the does the thing work
+
+ align:start position:0%
+with that is did the does the thing work
+ 
+
+ align:start position:0%
+with that is did the does the thing work
+or not and often we you know sort of
+
+ align:start position:0%
+or not and often we you know sort of
+ 
+
+ align:start position:0%
+or not and often we you know sort of
+talk about uh what is the probability
+
+ align:start position:0%
+talk about uh what is the probability
+ 
+
+ align:start position:0%
+talk about uh what is the probability
+that the thing is functioning at the end
+
+ align:start position:0%
+that the thing is functioning at the end
+ 
+
+ align:start position:0%
+that the thing is functioning at the end
+of the line maybe that's 0.95 so 95% of
+
+ align:start position:0%
+of the line maybe that's 0.95 so 95% of
+ 
+
+ align:start position:0%
+of the line maybe that's 0.95 so 95% of
+the time I think I've got yielding Parts
+
+ align:start position:0%
+the time I think I've got yielding Parts
+ 
+
+ align:start position:0%
+the time I think I've got yielding Parts
+out right for any
+
+ align:start position:0%
+out right for any
+ 
+
+ align:start position:0%
+out right for any
+one um experiment one outcome I've
+
+ align:start position:0%
+one um experiment one outcome I've
+ 
+
+ align:start position:0%
+one um experiment one outcome I've
+simply got a p and one minus P
+
+ align:start position:0%
+simply got a p and one minus P
+ 
+
+ align:start position:0%
+simply got a p and one minus P
+probability associated with that and the
+
+ align:start position:0%
+probability associated with that and the
+ 
+
+ align:start position:0%
+probability associated with that and the
+PDF can be expressed as as as shown here
+
+ align:start position:0%
+PDF can be expressed as as as shown here
+ 
+
+ align:start position:0%
+PDF can be expressed as as as shown here
+now we can go in and use our expectation
+
+ align:start position:0%
+now we can go in and use our expectation
+ 
+
+ align:start position:0%
+now we can go in and use our expectation
+operations for discret random Vari Ables
+
+ align:start position:0%
+operations for discret random Vari Ables
+ 
+
+ align:start position:0%
+operations for discret random Vari Ables
+uh and calculate what the mean and the
+
+ align:start position:0%
+uh and calculate what the mean and the
+ 
+
+ align:start position:0%
+uh and calculate what the mean and the
+variance are and those uh have nice
+
+ align:start position:0%
+variance are and those uh have nice
+ 
+
+ align:start position:0%
+variance are and those uh have nice
+close form uh functions for for those
+
+ align:start position:0%
+close form uh functions for for those
+ 
+
+ align:start position:0%
+close form uh functions for for those
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+outcomes okay so that's the Berle now
+
+ align:start position:0%
+outcomes okay so that's the Berle now
+ 
+
+ align:start position:0%
+outcomes okay so that's the Berle now
+the second easiest
+
+ align:start position:0%
+the second easiest
+ 
+
+ align:start position:0%
+the second easiest
+although it can actually look a little
+
+ align:start position:0%
+although it can actually look a little
+ 
+
+ align:start position:0%
+although it can actually look a little
+confusing at first glance but the second
+
+ align:start position:0%
+confusing at first glance but the second
+ 
+
+ align:start position:0%
+confusing at first glance but the second
+easiest distribution is a binomial
+
+ align:start position:0%
+easiest distribution is a binomial
+ 
+
+ align:start position:0%
+easiest distribution is a binomial
+distribution because it's saying that
+
+ align:start position:0%
+distribution because it's saying that
+ 
+
+ align:start position:0%
+distribution because it's saying that
+I'm simply taking that success or
+
+ align:start position:0%
+I'm simply taking that success or
+ 
+
+ align:start position:0%
+I'm simply taking that success or
+failure with a fixed probability p and
+
+ align:start position:0%
+failure with a fixed probability p and
+ 
+
+ align:start position:0%
+failure with a fixed probability p and
+running repeated trials of that so now
+
+ align:start position:0%
+running repeated trials of that so now
+ 
+
+ align:start position:0%
+running repeated trials of that so now
+I'm flipping my coin say with which has
+
+ align:start position:0%
+I'm flipping my coin say with which has
+ 
+
+ align:start position:0%
+I'm flipping my coin say with which has
+perhaps it's a weighted coin and it
+
+ align:start position:0%
+perhaps it's a weighted coin and it
+ 
+
+ align:start position:0%
+perhaps it's a weighted coin and it
+comes up heads with probability P that's
+
+ align:start position:0%
+comes up heads with probability P that's
+ 
+
+ align:start position:0%
+comes up heads with probability P that's
+not 0.5 maybe it's you know 0. n um but
+
+ align:start position:0%
+not 0.5 maybe it's you know 0. n um but
+ 
+
+ align:start position:0%
+not 0.5 maybe it's you know 0. n um but
+now I'm doing that repeated times I'm
+
+ align:start position:0%
+now I'm doing that repeated times I'm
+ 
+
+ align:start position:0%
+now I'm doing that repeated times I'm
+doing that n times now what's the
+
+ align:start position:0%
+doing that n times now what's the
+ 
+
+ align:start position:0%
+doing that n times now what's the
+probability of having n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+successes or I let me state that again
+
+ align:start position:0%
+successes or I let me state that again
+ 
+
+ align:start position:0%
+successes or I let me state that again
+what's the probability of having X
+
+ align:start position:0%
+what's the probability of having X
+ 
+
+ align:start position:0%
+what's the probability of having X
+successes when I ran in repeated trials
+
+ align:start position:0%
+successes when I ran in repeated trials
+ 
+
+ align:start position:0%
+successes when I ran in repeated trials
+so n is the number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Trials so if I ran 100 trials the
+
+ align:start position:0%
+Trials so if I ran 100 trials the
+ 
+
+ align:start position:0%
+Trials so if I ran 100 trials the
+probability that I had
+
+ align:start position:0%
+probability that I had
+ 
+
+ align:start position:0%
+probability that I had
+exactly x equals to 7 successes is given
+
+ align:start position:0%
+exactly x equals to 7 successes is given
+ 
+
+ align:start position:0%
+exactly x equals to 7 successes is given
+by this formula here and you can
+
+ align:start position:0%
+by this formula here and you can
+ 
+
+ align:start position:0%
+by this formula here and you can
+actually see this lurking in here how do
+
+ align:start position:0%
+actually see this lurking in here how do
+ 
+
+ align:start position:0%
+actually see this lurking in here how do
+I have seven successes well that mean p
+
+ align:start position:0%
+I have seven successes well that mean p
+ 
+
+ align:start position:0%
+I have seven successes well that mean p
+the probability of having a success had
+
+ align:start position:0%
+the probability of having a success had
+ 
+
+ align:start position:0%
+the probability of having a success had
+to come up exactly seven times and the
+
+ align:start position:0%
+to come up exactly seven times and the
+ 
+
+ align:start position:0%
+to come up exactly seven times and the
+rest of the times if I was running 100
+
+ align:start position:0%
+rest of the times if I was running 100
+ 
+
+ align:start position:0%
+rest of the times if I was running 100
+trials the other 93 tiles all had to be
+
+ align:start position:0%
+trials the other 93 tiles all had to be
+ 
+
+ align:start position:0%
+trials the other 93 tiles all had to be
+failures so I've simply got the product
+
+ align:start position:0%
+failures so I've simply got the product
+ 
+
+ align:start position:0%
+failures so I've simply got the product
+of all of those probabilities and then
+
+ align:start position:0%
+of all of those probabilities and then
+ 
+
+ align:start position:0%
+of all of those probabilities and then
+we've got the combinatorics the N choose
+
+ align:start position:0%
+we've got the combinatorics the N choose
+ 
+
+ align:start position:0%
+we've got the combinatorics the N choose
+X which tells me how many different
+
+ align:start position:0%
+X which tells me how many different
+ 
+
+ align:start position:0%
+X which tells me how many different
+orderings could have occurred by which I
+
+ align:start position:0%
+orderings could have occurred by which I
+ 
+
+ align:start position:0%
+orderings could have occurred by which I
+would get the seven successes and 93
+
+ align:start position:0%
+would get the seven successes and 93
+ 
+
+ align:start position:0%
+would get the seven successes and 93
+failures for n equal 100
+
+ align:start position:0%
+failures for n equal 100
+ 
+
+ align:start position:0%
+failures for n equal 100
+okay so that's that's simply the the the
+
+ align:start position:0%
+okay so that's that's simply the the the
+ 
+
+ align:start position:0%
+okay so that's that's simply the the the
+different uh numbers of combinations
+
+ align:start position:0%
+different uh numbers of combinations
+ 
+
+ align:start position:0%
+different uh numbers of combinations
+that can come up with that so the
+
+ align:start position:0%
+that can come up with that so the
+ 
+
+ align:start position:0%
+that can come up with that so the
+notation here by the way that we uh
+
+ align:start position:0%
+notation here by the way that we uh
+ 
+
+ align:start position:0%
+notation here by the way that we uh
+would often use I've already sort of
+
+ align:start position:0%
+would often use I've already sort of
+ 
+
+ align:start position:0%
+would often use I've already sort of
+snuck it in in some other places is this
+
+ align:start position:0%
+snuck it in in some other places is this
+ 
+
+ align:start position:0%
+snuck it in in some other places is this
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+TIY uh uh symbol here uh we're using to
+
+ align:start position:0%
+TIY uh uh symbol here uh we're using to
+ 
+
+ align:start position:0%
+TIY uh uh symbol here uh we're using to
+in to read as is distributed as some
+
+ align:start position:0%
+in to read as is distributed as some
+ 
+
+ align:start position:0%
+in to read as is distributed as some
+distribution and I'm using the the Big B
+
+ align:start position:0%
+distribution and I'm using the the Big B
+ 
+
+ align:start position:0%
+distribution and I'm using the the Big B
+to indicate indicate the binomial
+
+ align:start position:0%
+to indicate indicate the binomial
+ 
+
+ align:start position:0%
+to indicate indicate the binomial
+distribution which has associated with
+
+ align:start position:0%
+distribution which has associated with
+ 
+
+ align:start position:0%
+distribution which has associated with
+it the underlying uh beri probability
+
+ align:start position:0%
+it the underlying uh beri probability
+ 
+
+ align:start position:0%
+it the underlying uh beri probability
+success for any one trial and then and
+
+ align:start position:0%
+success for any one trial and then and
+ 
+
+ align:start position:0%
+success for any one trial and then and
+then the number of uh repeated
+
+ align:start position:0%
+then the number of uh repeated
+ 
+
+ align:start position:0%
+then the number of uh repeated
+trials okay so this is a discret
+
+ align:start position:0%
+trials okay so this is a discret
+ 
+
+ align:start position:0%
+trials okay so this is a discret
+probability what's the probability that
+
+ align:start position:0%
+probability what's the probability that
+ 
+
+ align:start position:0%
+probability what's the probability that
+X could take on
+
+ align:start position:0%
+X could take on
+ 
+
+ align:start position:0%
+X could take on
+0.7 zero right it's the number of
+
+ align:start position:0%
+0.7 zero right it's the number of
+ 
+
+ align:start position:0%
+0.7 zero right it's the number of
+successes uh uh out of this and here are
+
+ align:start position:0%
+successes uh uh out of this and here are
+ 
+
+ align:start position:0%
+successes uh uh out of this and here are
+some examples that just give you a
+
+ align:start position:0%
+some examples that just give you a
+ 
+
+ align:start position:0%
+some examples that just give you a
+little bit of a feel for what the bernui
+
+ align:start position:0%
+little bit of a feel for what the bernui
+ 
+
+ align:start position:0%
+little bit of a feel for what the bernui
+distribution U looks like this is the
+
+ align:start position:0%
+distribution U looks like this is the
+ 
+
+ align:start position:0%
+distribution U looks like this is the
+number of successes plotted as a
+
+ align:start position:0%
+number of successes plotted as a
+ 
+
+ align:start position:0%
+number of successes plotted as a
+histogram uh for some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values I think that this is if you try
+
+ align:start position:0%
+values I think that this is if you try
+ 
+
+ align:start position:0%
+values I think that this is if you try
+it uh I think this is a live spreadsheet
+
+ align:start position:0%
+it uh I think this is a live spreadsheet
+ 
+
+ align:start position:0%
+it uh I think this is a live spreadsheet
+so actually if you double click on this
+
+ align:start position:0%
+so actually if you double click on this
+ 
+
+ align:start position:0%
+so actually if you double click on this
+from your PowerPoint it may bring up the
+
+ align:start position:0%
+from your PowerPoint it may bring up the
+ 
+
+ align:start position:0%
+from your PowerPoint it may bring up the
+underlying uh Excel spreadsheet
+
+ align:start position:0%
+underlying uh Excel spreadsheet
+ 
+
+ align:start position:0%
+underlying uh Excel spreadsheet
+um so you can actually play with some of
+
+ align:start position:0%
+um so you can actually play with some of
+ 
+
+ align:start position:0%
+um so you can actually play with some of
+the parameters in this I don't remember
+
+ align:start position:0%
+the parameters in this I don't remember
+ 
+
+ align:start position:0%
+the parameters in this I don't remember
+what uh either P or n was for this but
+
+ align:start position:0%
+what uh either P or n was for this but
+ 
+
+ align:start position:0%
+what uh either P or n was for this but
+you can start to see it's really it does
+
+ align:start position:0%
+you can start to see it's really it does
+ 
+
+ align:start position:0%
+you can start to see it's really it does
+not look quite normal right
+
+ align:start position:0%
+not look quite normal right
+ 
+
+ align:start position:0%
+not look quite normal right
+because you can never have negative
+
+ align:start position:0%
+because you can never have negative
+ 
+
+ align:start position:0%
+because you can never have negative
+numbers of successes it's always
+
+ align:start position:0%
+numbers of successes it's always
+ 
+
+ align:start position:0%
+numbers of successes it's always
+truncated even if and and you you get
+
+ align:start position:0%
+truncated even if and and you you get
+ 
+
+ align:start position:0%
+truncated even if and and you you get
+sort of these these very non-normal uh
+
+ align:start position:0%
+sort of these these very non-normal uh
+ 
+
+ align:start position:0%
+sort of these these very non-normal uh
+kinds of distrib dist butions this is a
+
+ align:start position:0%
+kinds of distrib dist butions this is a
+ 
+
+ align:start position:0%
+kinds of distrib dist butions this is a
+binomial distribution but its location
+
+ align:start position:0%
+binomial distribution but its location
+ 
+
+ align:start position:0%
+binomial distribution but its location
+and its shape can change somewhat as you
+
+ align:start position:0%
+and its shape can change somewhat as you
+ 
+
+ align:start position:0%
+and its shape can change somewhat as you
+play with
+
+ align:start position:0%
+play with
+ 
+
+ align:start position:0%
+play with
+pnn by the way up here this is just the
+
+ align:start position:0%
+pnn by the way up here this is just the
+ 
+
+ align:start position:0%
+pnn by the way up here this is just the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+cumulative probability
+
+ align:start position:0%
+cumulative probability
+ 
+
+ align:start position:0%
+cumulative probability
+function just saying the probability
+
+ align:start position:0%
+function just saying the probability
+ 
+
+ align:start position:0%
+function just saying the probability
+that I've got X less than or equal to
+
+ align:start position:0%
+that I've got X less than or equal to
+ 
+
+ align:start position:0%
+that I've got X less than or equal to
+some value uh so that's also
+
+ align:start position:0%
+some value uh so that's also
+ 
+
+ align:start position:0%
+some value uh so that's also
+shown so then this is also in this
+
+ align:start position:0%
+shown so then this is also in this
+ 
+
+ align:start position:0%
+shown so then this is also in this
+histogram sort of normalized to the
+
+ align:start position:0%
+histogram sort of normalized to the
+ 
+
+ align:start position:0%
+histogram sort of normalized to the
+fraction
+
+ align:start position:0%
+fraction
+ 
+
+ align:start position:0%
+fraction
+uh of of of products and so now you can
+
+ align:start position:0%
+uh of of of products and so now you can
+ 
+
+ align:start position:0%
+uh of of of products and so now you can
+start to look
+
+ align:start position:0%
+start to look
+ 
+
+ align:start position:0%
+start to look
+at calculating If This Were my data and
+
+ align:start position:0%
+at calculating If This Were my data and
+ 
+
+ align:start position:0%
+at calculating If This Were my data and
+I simply it was actually coming from a
+
+ align:start position:0%
+I simply it was actually coming from a
+ 
+
+ align:start position:0%
+I simply it was actually coming from a
+line where I was looking at the
+
+ align:start position:0%
+line where I was looking at the
+ 
+
+ align:start position:0%
+line where I was looking at the
+probability of any one part uh um
+
+ align:start position:0%
+probability of any one part uh um
+ 
+
+ align:start position:0%
+probability of any one part uh um
+succeeding or not I could start to ask
+
+ align:start position:0%
+succeeding or not I could start to ask
+ 
+
+ align:start position:0%
+succeeding or not I could start to ask
+questions about the probability of
+
+ align:start position:0%
+questions about the probability of
+ 
+
+ align:start position:0%
+questions about the probability of
+seeing out of a thousand products coming
+
+ align:start position:0%
+seeing out of a thousand products coming
+ 
+
+ align:start position:0%
+seeing out of a thousand products coming
+off the line some number of defects or
+
+ align:start position:0%
+off the line some number of defects or
+ 
+
+ align:start position:0%
+off the line some number of defects or
+some number of failed products you can
+
+ align:start position:0%
+some number of failed products you can
+ 
+
+ align:start position:0%
+some number of failed products you can
+appeal to the binomial distribution for
+
+ align:start position:0%
+appeal to the binomial distribution for
+ 
+
+ align:start position:0%
+appeal to the binomial distribution for
+that now this is all still pretty coarse
+
+ align:start position:0%
+that now this is all still pretty coarse
+ 
+
+ align:start position:0%
+that now this is all still pretty coarse
+right it's just a very simplified model
+
+ align:start position:0%
+right it's just a very simplified model
+ 
+
+ align:start position:0%
+right it's just a very simplified model
+failure or success uh uh uh for yield
+
+ align:start position:0%
+failure or success uh uh uh for yield
+ 
+
+ align:start position:0%
+failure or success uh uh uh for yield
+now another discrete distribution is a
+
+ align:start position:0%
+now another discrete distribution is a
+ 
+
+ align:start position:0%
+now another discrete distribution is a
+Pon distribution
+
+ align:start position:0%
+Pon distribution
+ 
+
+ align:start position:0%
+Pon distribution
+um uh or uh also sometimes referred to
+
+ align:start position:0%
+um uh or uh also sometimes referred to
+ 
+
+ align:start position:0%
+um uh or uh also sometimes referred to
+as an exponential uh uh distribution
+
+ align:start position:0%
+as an exponential uh uh distribution
+ 
+
+ align:start position:0%
+as an exponential uh uh distribution
+although terminology there sometimes
+
+ align:start position:0%
+although terminology there sometimes
+ 
+
+ align:start position:0%
+although terminology there sometimes
+varies uh depending
+
+ align:start position:0%
+varies uh depending
+ 
+
+ align:start position:0%
+varies uh depending
+on uh whether uh people are including
+
+ align:start position:0%
+on uh whether uh people are including
+ 
+
+ align:start position:0%
+on uh whether uh people are including
+this component or not but the formal
+
+ align:start position:0%
+this component or not but the formal
+ 
+
+ align:start position:0%
+this component or not but the formal
+definition for the pon distribution um
+
+ align:start position:0%
+definition for the pon distribution um
+ 
+
+ align:start position:0%
+definition for the pon distribution um
+uh is shown here now it continues to be
+
+ align:start position:0%
+uh is shown here now it continues to be
+ 
+
+ align:start position:0%
+uh is shown here now it continues to be
+a discret distribution so I'm asking
+
+ align:start position:0%
+a discret distribution so I'm asking
+ 
+
+ align:start position:0%
+a discret distribution so I'm asking
+what is the probability associated with
+
+ align:start position:0%
+what is the probability associated with
+ 
+
+ align:start position:0%
+what is the probability associated with
+observing X taking on actual discret
+
+ align:start position:0%
+observing X taking on actual discret
+ 
+
+ align:start position:0%
+observing X taking on actual discret
+integer
+
+ align:start position:0%
+integer
+ 
+
+ align:start position:0%
+integer
+values but um this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a very nice distribution associated with
+
+ align:start position:0%
+a very nice distribution associated with
+ 
+
+ align:start position:0%
+a very nice distribution associated with
+uh kinds of uh operations that many of
+
+ align:start position:0%
+uh kinds of uh operations that many of
+ 
+
+ align:start position:0%
+uh kinds of uh operations that many of
+you saw in 2850 or 2.8 yeah
+
+ align:start position:0%
+you saw in 2850 or 2.8 yeah
+ 
+
+ align:start position:0%
+you saw in 2850 or 2.8 yeah
+2853 uh the arrival times uh in queing
+
+ align:start position:0%
+2853 uh the arrival times uh in queing
+ 
+
+ align:start position:0%
+2853 uh the arrival times uh in queing
+networks will often be uh pan dist
+
+ align:start position:0%
+networks will often be uh pan dist
+ 
+
+ align:start position:0%
+networks will often be uh pan dist
+distributed but it also can come up when
+
+ align:start position:0%
+distributed but it also can come up when
+ 
+
+ align:start position:0%
+distributed but it also can come up when
+we are dealing with very large numbers
+
+ align:start position:0%
+we are dealing with very large numbers
+ 
+
+ align:start position:0%
+we are dealing with very large numbers
+associated with the binomial
+
+ align:start position:0%
+associated with the binomial
+ 
+
+ align:start position:0%
+associated with the binomial
+distribution as a very good
+
+ align:start position:0%
+distribution as a very good
+ 
+
+ align:start position:0%
+distribution as a very good
+approximation to the
+
+ align:start position:0%
+approximation to the
+ 
+
+ align:start position:0%
+approximation to the
+binomial and this turns out to be really
+
+ align:start position:0%
+binomial and this turns out to be really
+ 
+
+ align:start position:0%
+binomial and this turns out to be really
+nice because if you actually go back to
+
+ align:start position:0%
+nice because if you actually go back to
+ 
+
+ align:start position:0%
+nice because if you actually go back to
+the binomial formula and try to
+
+ align:start position:0%
+the binomial formula and try to
+ 
+
+ align:start position:0%
+the binomial formula and try to
+calculate it for situations where where
+
+ align:start position:0%
+calculate it for situations where where
+ 
+
+ align:start position:0%
+calculate it for situations where where
+uh say n or X are very very large or P
+
+ align:start position:0%
+uh say n or X are very very large or P
+ 
+
+ align:start position:0%
+uh say n or X are very very large or P
+or one minus p is very very small or
+
+ align:start position:0%
+or one minus p is very very small or
+ 
+
+ align:start position:0%
+or one minus p is very very small or
+very large very close to either zero or
+
+ align:start position:0%
+very large very close to either zero or
+ 
+
+ align:start position:0%
+very large very close to either zero or
+one you end up with some problems some
+
+ align:start position:0%
+one you end up with some problems some
+ 
+
+ align:start position:0%
+one you end up with some problems some
+numerical problems
+
+ align:start position:0%
+numerical problems
+ 
+
+ align:start position:0%
+numerical problems
+right because if you actually try to
+
+ align:start position:0%
+right because if you actually try to
+ 
+
+ align:start position:0%
+right because if you actually try to
+calculate it for let's say p is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.00001 or maybe one minus p is equal to
+
+ align:start position:0%
+0.00001 or maybe one minus p is equal to
+ 
+
+ align:start position:0%
+0.00001 or maybe one minus p is equal to
+that let's say you have really really
+
+ align:start position:0%
+that let's say you have really really
+ 
+
+ align:start position:0%
+that let's say you have really really
+high
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yield um and I take that so if that's
+
+ align:start position:0%
+yield um and I take that so if that's
+ 
+
+ align:start position:0%
+yield um and I take that so if that's
+one minus p and I'm doing this for a
+
+ align:start position:0%
+one minus p and I'm doing this for a
+ 
+
+ align:start position:0%
+one minus p and I'm doing this for a
+sample of size a million I've got 01 to
+
+ align:start position:0%
+sample of size a million I've got 01 to
+ 
+
+ align:start position:0%
+sample of size a million I've got 01 to
+the 1 millionth power and numeric Ally
+
+ align:start position:0%
+the 1 millionth power and numeric Ally
+ 
+
+ align:start position:0%
+the 1 millionth power and numeric Ally
+you start losing the digits you can't
+
+ align:start position:0%
+you start losing the digits you can't
+ 
+
+ align:start position:0%
+you start losing the digits you can't
+hardly keep track of that but I might be
+
+ align:start position:0%
+hardly keep track of that but I might be
+ 
+
+ align:start position:0%
+hardly keep track of that but I might be
+asking what is the probability of some
+
+ align:start position:0%
+asking what is the probability of some
+ 
+
+ align:start position:0%
+asking what is the probability of some
+substantial number of failures and this
+
+ align:start position:0%
+substantial number of failures and this
+ 
+
+ align:start position:0%
+substantial number of failures and this
+the combinatorics end up being a really
+
+ align:start position:0%
+the combinatorics end up being a really
+ 
+
+ align:start position:0%
+the combinatorics end up being a really
+really large number so overall it's a
+
+ align:start position:0%
+really large number so overall it's a
+ 
+
+ align:start position:0%
+really large number so overall it's a
+the overall probability of asso seeing
+
+ align:start position:0%
+the overall probability of asso seeing
+ 
+
+ align:start position:0%
+the overall probability of asso seeing
+10 failures out of a Million Parts might
+
+ align:start position:0%
+10 failures out of a Million Parts might
+ 
+
+ align:start position:0%
+10 failures out of a Million Parts might
+be substantial but to calculate it you
+
+ align:start position:0%
+be substantial but to calculate it you
+ 
+
+ align:start position:0%
+be substantial but to calculate it you
+can't do it numerically because I've got
+
+ align:start position:0%
+can't do it numerically because I've got
+ 
+
+ align:start position:0%
+can't do it numerically because I've got
+a huge number times a really small
+
+ align:start position:0%
+a huge number times a really small
+ 
+
+ align:start position:0%
+a huge number times a really small
+number I get overflow or underflow and I
+
+ align:start position:0%
+number I get overflow or underflow and I
+ 
+
+ align:start position:0%
+number I get overflow or underflow and I
+can't actually uh uh calculate it what's
+
+ align:start position:0%
+can't actually uh uh calculate it what's
+ 
+
+ align:start position:0%
+can't actually uh uh calculate it what's
+useful is in those kinds of situations
+
+ align:start position:0%
+useful is in those kinds of situations
+ 
+
+ align:start position:0%
+useful is in those kinds of situations
+where um say n and
+
+ align:start position:0%
+where um say n and
+ 
+
+ align:start position:0%
+where um say n and
+p together the product of those things
+
+ align:start position:0%
+p together the product of those things
+ 
+
+ align:start position:0%
+p together the product of those things
+are reasonable sized numbers then the
+
+ align:start position:0%
+are reasonable sized numbers then the
+ 
+
+ align:start position:0%
+are reasonable sized numbers then the
+pan distribution is very very good
+
+ align:start position:0%
+pan distribution is very very good
+ 
+
+ align:start position:0%
+pan distribution is very very good
+approximation and this applies to things
+
+ align:start position:0%
+approximation and this applies to things
+ 
+
+ align:start position:0%
+approximation and this applies to things
+where you have very say low
+
+ align:start position:0%
+where you have very say low
+ 
+
+ align:start position:0%
+where you have very say low
+probability so so P might be very small
+
+ align:start position:0%
+probability so so P might be very small
+ 
+
+ align:start position:0%
+probability so so P might be very small
+but I'm asking or I have
+
+ align:start position:0%
+but I'm asking or I have
+ 
+
+ align:start position:0%
+but I'm asking or I have
+many many
+
+ align:start position:0%
+many many
+ 
+
+ align:start position:0%
+many many
+opportunities to
+
+ align:start position:0%
+opportunities to
+ 
+
+ align:start position:0%
+opportunities to
+observe that very low likelihood event
+
+ align:start position:0%
+observe that very low likelihood event
+ 
+
+ align:start position:0%
+observe that very low likelihood event
+so an example here that comes up in
+
+ align:start position:0%
+so an example here that comes up in
+ 
+
+ align:start position:0%
+so an example here that comes up in
+semiconductor manufacturing are things
+
+ align:start position:0%
+semiconductor manufacturing are things
+ 
+
+ align:start position:0%
+semiconductor manufacturing are things
+like the probability of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observing uh some number of defects on a
+
+ align:start position:0%
+observing uh some number of defects on a
+ 
+
+ align:start position:0%
+observing uh some number of defects on a
+wafer the likelihood of seeing a point
+
+ align:start position:0%
+wafer the likelihood of seeing a point
+ 
+
+ align:start position:0%
+wafer the likelihood of seeing a point
+defect on anyone location is very very
+
+ align:start position:0%
+defect on anyone location is very very
+ 
+
+ align:start position:0%
+defect on anyone location is very very
+very small but I've got lots and lots of
+
+ align:start position:0%
+very small but I've got lots and lots of
+ 
+
+ align:start position:0%
+very small but I've got lots and lots of
+area on the wafer lots and lots of
+
+ align:start position:0%
+area on the wafer lots and lots of
+ 
+
+ align:start position:0%
+area on the wafer lots and lots of
+opportunity for the appearance of that
+
+ align:start position:0%
+opportunity for the appearance of that
+ 
+
+ align:start position:0%
+opportunity for the appearance of that
+small defect and so you can start to
+
+ align:start position:0%
+small defect and so you can start to
+ 
+
+ align:start position:0%
+small defect and so you can start to
+talk about uh uh the product of those
+
+ align:start position:0%
+talk about uh uh the product of those
+ 
+
+ align:start position:0%
+talk about uh uh the product of those
+things or a rate per unit area that
+
+ align:start position:0%
+things or a rate per unit area that
+ 
+
+ align:start position:0%
+things or a rate per unit area that
+starts to become
+
+ align:start position:0%
+starts to become
+ 
+
+ align:start position:0%
+starts to become
+reasonable
+
+ align:start position:0%
+reasonable
+ 
+
+ align:start position:0%
+reasonable
+um another example is the number of
+
+ align:start position:0%
+um another example is the number of
+ 
+
+ align:start position:0%
+um another example is the number of
+misprints on a page of a book you don't
+
+ align:start position:0%
+misprints on a page of a book you don't
+ 
+
+ align:start position:0%
+misprints on a page of a book you don't
+expect for any one character on a book
+
+ align:start position:0%
+expect for any one character on a book
+ 
+
+ align:start position:0%
+expect for any one character on a book
+for that that uh uh to actually be a
+
+ align:start position:0%
+for that that uh uh to actually be a
+ 
+
+ align:start position:0%
+for that that uh uh to actually be a
+misprint but over the entire aggregate
+
+ align:start position:0%
+misprint but over the entire aggregate
+ 
+
+ align:start position:0%
+misprint but over the entire aggregate
+number of pages in your book you expect
+
+ align:start position:0%
+number of pages in your book you expect
+ 
+
+ align:start position:0%
+number of pages in your book you expect
+some number of misprints and the
+
+ align:start position:0%
+some number of misprints and the
+ 
+
+ align:start position:0%
+some number of misprints and the
+statistics that go with that are
+
+ align:start position:0%
+statistics that go with that are
+ 
+
+ align:start position:0%
+statistics that go with that are
+typically pan
+
+ align:start position:0%
+typically pan
+ 
+
+ align:start position:0%
+typically pan
+distributed and already mentioned that
+
+ align:start position:0%
+distributed and already mentioned that
+ 
+
+ align:start position:0%
+distributed and already mentioned that
+the mean and the variance if you
+
+ align:start position:0%
+the mean and the variance if you
+ 
+
+ align:start position:0%
+the mean and the variance if you
+actually apply those formulas to this
+
+ align:start position:0%
+actually apply those formulas to this
+ 
+
+ align:start position:0%
+actually apply those formulas to this
+distribution uh come out to the
+
+ align:start position:0%
+distribution uh come out to the
+ 
+
+ align:start position:0%
+distribution uh come out to the
+fascinating fact that they are
+
+ align:start position:0%
+fascinating fact that they are
+ 
+
+ align:start position:0%
+fascinating fact that they are
+numerically the same value by the way
+
+ align:start position:0%
+numerically the same value by the way
+ 
+
+ align:start position:0%
+numerically the same value by the way
+units wise they're not but uh X is an
+
+ align:start position:0%
+units wise they're not but uh X is an
+ 
+
+ align:start position:0%
+units wise they're not but uh X is an
+integer and and oops that should be X by
+
+ align:start position:0%
+integer and and oops that should be X by
+ 
+
+ align:start position:0%
+integer and and oops that should be X by
+the way come on cut that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out there we
+
+ align:start position:0%
+out there we
+ 
+
+ align:start position:0%
+out there we
+go okay so here's some example Pon
+
+ align:start position:0%
+go okay so here's some example Pon
+ 
+
+ align:start position:0%
+go okay so here's some example Pon
+distributions uh you can start to see
+
+ align:start position:0%
+distributions uh you can start to see
+ 
+
+ align:start position:0%
+distributions uh you can start to see
+one here for a mean of five that looks
+
+ align:start position:0%
+one here for a mean of five that looks
+ 
+
+ align:start position:0%
+one here for a mean of five that looks
+kind of close to the binomial
+
+ align:start position:0%
+kind of close to the binomial
+ 
+
+ align:start position:0%
+kind of close to the binomial
+distribution that I showed you earlier
+
+ align:start position:0%
+distribution that I showed you earlier
+ 
+
+ align:start position:0%
+distribution that I showed you earlier
+and then as the mean here is is
+
+ align:start position:0%
+and then as the mean here is is
+ 
+
+ align:start position:0%
+and then as the mean here is is
+increasing and the Lambda parameter you
+
+ align:start position:0%
+increasing and the Lambda parameter you
+ 
+
+ align:start position:0%
+increasing and the Lambda parameter you
+can start to see this distribution
+
+ align:start position:0%
+can start to see this distribution
+ 
+
+ align:start position:0%
+can start to see this distribution
+shifting uh to the right as we said
+
+ align:start position:0%
+shifting uh to the right as we said
+ 
+
+ align:start position:0%
+shifting uh to the right as we said
+Lambda is the mean it's also a
+
+ align:start position:0%
+Lambda is the mean it's also a
+ 
+
+ align:start position:0%
+Lambda is the mean it's also a
+characteristic of the variance right the
+
+ align:start position:0%
+characteristic of the variance right the
+ 
+
+ align:start position:0%
+characteristic of the variance right the
+variance is also equal
+
+ align:start position:0%
+variance is also equal
+ 
+
+ align:start position:0%
+variance is also equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+Lambda so that will also broaden out for
+
+ align:start position:0%
+Lambda so that will also broaden out for
+ 
+
+ align:start position:0%
+Lambda so that will also broaden out for
+larger numbers of
+
+ align:start position:0%
+larger numbers of
+ 
+
+ align:start position:0%
+larger numbers of
+uh of L or larger values of
+
+ align:start position:0%
+uh of L or larger values of
+ 
+
+ align:start position:0%
+uh of L or larger values of
+Lambda there's another observation in
+
+ align:start position:0%
+Lambda there's another observation in
+ 
+
+ align:start position:0%
+Lambda there's another observation in
+here which is
+
+ align:start position:0%
+here which is
+ 
+
+ align:start position:0%
+here which is
+useful what are these starting to look
+
+ align:start position:0%
+useful what are these starting to look
+ 
+
+ align:start position:0%
+useful what are these starting to look
+like for large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lambdas normal right if you looked at
+
+ align:start position:0%
+lambdas normal right if you looked at
+ 
+
+ align:start position:0%
+lambdas normal right if you looked at
+that it doesn't look very normal
+
+ align:start position:0%
+that it doesn't look very normal
+ 
+
+ align:start position:0%
+that it doesn't look very normal
+distributed it's truncated it's a little
+
+ align:start position:0%
+distributed it's truncated it's a little
+ 
+
+ align:start position:0%
+distributed it's truncated it's a little
+bit skewed but uh another approximation
+
+ align:start position:0%
+bit skewed but uh another approximation
+ 
+
+ align:start position:0%
+bit skewed but uh another approximation
+is for large for large Lambda that also
+
+ align:start position:0%
+is for large for large Lambda that also
+ 
+
+ align:start position:0%
+is for large for large Lambda that also
+tends towards a normal distribution so
+
+ align:start position:0%
+tends towards a normal distribution so
+ 
+
+ align:start position:0%
+tends towards a normal distribution so
+very very often you've got this success
+
+ align:start position:0%
+very very often you've got this success
+ 
+
+ align:start position:0%
+very very often you've got this success
+or succession of approximations where
+
+ align:start position:0%
+or succession of approximations where
+ 
+
+ align:start position:0%
+or succession of approximations where
+you might take a binomial approximate it
+
+ align:start position:0%
+you might take a binomial approximate it
+ 
+
+ align:start position:0%
+you might take a binomial approximate it
+as a bon but then for large numbers uh a
+
+ align:start position:0%
+as a bon but then for large numbers uh a
+ 
+
+ align:start position:0%
+as a bon but then for large numbers uh a
+normal distribution also uh can be a
+
+ align:start position:0%
+normal distribution also uh can be a
+ 
+
+ align:start position:0%
+normal distribution also uh can be a
+useful uh
+
+ align:start position:0%
+useful uh
+ 
+
+ align:start position:0%
+useful uh
+approximation so let's go back to uh The
+
+ align:start position:0%
+approximation so let's go back to uh The
+ 
+
+ align:start position:0%
+approximation so let's go back to uh The
+Continuous
+
+ align:start position:0%
+Continuous
+ 
+
+ align:start position:0%
+Continuous
+distributions uh the normal and the
+
+ align:start position:0%
+distributions uh the normal and the
+ 
+
+ align:start position:0%
+distributions uh the normal and the
+uniform and here I want to start getting
+
+ align:start position:0%
+uniform and here I want to start getting
+ 
+
+ align:start position:0%
+uniform and here I want to start getting
+to actually how you use or calculate
+
+ align:start position:0%
+to actually how you use or calculate
+ 
+
+ align:start position:0%
+to actually how you use or calculate
+probabilities of uh observations in
+
+ align:start position:0%
+probabilities of uh observations in
+ 
+
+ align:start position:0%
+probabilities of uh observations in
+certain ranges and in particular things
+
+ align:start position:0%
+certain ranges and in particular things
+ 
+
+ align:start position:0%
+certain ranges and in particular things
+like the probabilities of observing
+
+ align:start position:0%
+like the probabilities of observing
+ 
+
+ align:start position:0%
+like the probabilities of observing
+things out in the Tails so here's a
+
+ align:start position:0%
+things out in the Tails so here's a
+ 
+
+ align:start position:0%
+things out in the Tails so here's a
+continuous distribution that has a
+
+ align:start position:0%
+continuous distribution that has a
+ 
+
+ align:start position:0%
+continuous distribution that has a
+probability density function this is the
+
+ align:start position:0%
+probability density function this is the
+ 
+
+ align:start position:0%
+probability density function this is the
+normal uh excuse me the uniform
+
+ align:start position:0%
+normal uh excuse me the uniform
+ 
+
+ align:start position:0%
+normal uh excuse me the uniform
+distribution that has the same
+
+ align:start position:0%
+distribution that has the same
+ 
+
+ align:start position:0%
+distribution that has the same
+probability uh density for values in
+
+ align:start position:0%
+probability uh density for values in
+ 
+
+ align:start position:0%
+probability uh density for values in
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+range and then I've also indicated with
+
+ align:start position:0%
+range and then I've also indicated with
+ 
+
+ align:start position:0%
+range and then I've also indicated with
+the capital F our cumulative uh density
+
+ align:start position:0%
+the capital F our cumulative uh density
+ 
+
+ align:start position:0%
+the capital F our cumulative uh density
+function uh for that okay so this is
+
+ align:start position:0%
+function uh for that okay so this is
+ 
+
+ align:start position:0%
+function uh for that okay so this is
+just reminding you of a little bit of
+
+ align:start position:0%
+just reminding you of a little bit of
+ 
+
+ align:start position:0%
+just reminding you of a little bit of
+the terminology there but the I I'm
+
+ align:start position:0%
+the terminology there but the I I'm
+ 
+
+ align:start position:0%
+the terminology there but the I I'm
+highlighting the uniform distribution
+
+ align:start position:0%
+highlighting the uniform distribution
+ 
+
+ align:start position:0%
+highlighting the uniform distribution
+because there's a couple of very
+
+ align:start position:0%
+because there's a couple of very
+ 
+
+ align:start position:0%
+because there's a couple of very
+standard questions that if you have a
+
+ align:start position:0%
+standard questions that if you have a
+ 
+
+ align:start position:0%
+standard questions that if you have a
+known PDF or CDF these are the kinds of
+
+ align:start position:0%
+known PDF or CDF these are the kinds of
+ 
+
+ align:start position:0%
+known PDF or CDF these are the kinds of
+questions that you're going to be asking
+
+ align:start position:0%
+questions that you're going to be asking
+ 
+
+ align:start position:0%
+questions that you're going to be asking
+again and again and again and they're
+
+ align:start position:0%
+again and again and again and they're
+ 
+
+ align:start position:0%
+again and again and again and they're
+nice and intuitive off of the uniform
+
+ align:start position:0%
+nice and intuitive off of the uniform
+ 
+
+ align:start position:0%
+nice and intuitive off of the uniform
+distribution when we get to the normal
+
+ align:start position:0%
+distribution when we get to the normal
+ 
+
+ align:start position:0%
+distribution when we get to the normal
+and other distributions they're not
+
+ align:start position:0%
+and other distributions they're not
+ 
+
+ align:start position:0%
+and other distributions they're not
+quite as intuitive
+
+ align:start position:0%
+quite as intuitive
+ 
+
+ align:start position:0%
+quite as intuitive
+uh but but seeing them here for the for
+
+ align:start position:0%
+uh but but seeing them here for the for
+ 
+
+ align:start position:0%
+uh but but seeing them here for the for
+the uniform first I think helps one of
+
+ align:start position:0%
+the uniform first I think helps one of
+ 
+
+ align:start position:0%
+the uniform first I think helps one of
+the typical kinds of questions is I want
+
+ align:start position:0%
+the typical kinds of questions is I want
+ 
+
+ align:start position:0%
+the typical kinds of questions is I want
+to know what is the probability that
+
+ align:start position:0%
+to know what is the probability that
+ 
+
+ align:start position:0%
+to know what is the probability that
+some uh X is less than or equal to some
+
+ align:start position:0%
+some uh X is less than or equal to some
+ 
+
+ align:start position:0%
+some uh X is less than or equal to some
+value if I were to draw it
+
+ align:start position:0%
+value if I were to draw it
+ 
+
+ align:start position:0%
+value if I were to draw it
+from this underlying distribution from a
+
+ align:start position:0%
+from this underlying distribution from a
+ 
+
+ align:start position:0%
+from this underlying distribution from a
+normal distribution and so one could ask
+
+ align:start position:0%
+normal distribution and so one could ask
+ 
+
+ align:start position:0%
+normal distribution and so one could ask
+that using
+
+ align:start position:0%
+that using
+ 
+
+ align:start position:0%
+that using
+either the
+
+ align:start position:0%
+either the
+ 
+
+ align:start position:0%
+either the
+PDF or the cumulative density function
+
+ align:start position:0%
+PDF or the cumulative density function
+ 
+
+ align:start position:0%
+PDF or the cumulative density function
+function and sometimes one or the other
+
+ align:start position:0%
+function and sometimes one or the other
+ 
+
+ align:start position:0%
+function and sometimes one or the other
+if they're tabulated uh or available to
+
+ align:start position:0%
+if they're tabulated uh or available to
+ 
+
+ align:start position:0%
+if they're tabulated uh or available to
+you is easier to use clearly if this is
+
+ align:start position:0%
+you is easier to use clearly if this is
+ 
+
+ align:start position:0%
+you is easier to use clearly if this is
+the probability density function uh here
+
+ align:start position:0%
+the probability density function uh here
+ 
+
+ align:start position:0%
+the probability density function uh here
+I can ask it in terms of the interval
+
+ align:start position:0%
+I can ask it in terms of the interval
+ 
+
+ align:start position:0%
+I can ask it in terms of the interval
+question oops excuse me the interval
+
+ align:start position:0%
+question oops excuse me the interval
+ 
+
+ align:start position:0%
+question oops excuse me the interval
+question right here and say well the
+
+ align:start position:0%
+question right here and say well the
+ 
+
+ align:start position:0%
+question right here and say well the
+probability that X is less than or equal
+
+ align:start position:0%
+probability that X is less than or equal
+ 
+
+ align:start position:0%
+probability that X is less than or equal
+to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X1 is simply the integration up of that
+
+ align:start position:0%
+X1 is simply the integration up of that
+ 
+
+ align:start position:0%
+X1 is simply the integration up of that
+probability and you can do that
+
+ align:start position:0%
+probability and you can do that
+ 
+
+ align:start position:0%
+probability and you can do that
+numerically or you know just by hand on
+
+ align:start position:0%
+numerically or you know just by hand on
+ 
+
+ align:start position:0%
+numerically or you know just by hand on
+on such a simple distribution but the
+
+ align:start position:0%
+on such a simple distribution but the
+ 
+
+ align:start position:0%
+on such a simple distribution but the
+point is that is actually exactly the
+
+ align:start position:0%
+point is that is actually exactly the
+ 
+
+ align:start position:0%
+point is that is actually exactly the
+value that is tabulated on the
+
+ align:start position:0%
+value that is tabulated on the
+ 
+
+ align:start position:0%
+value that is tabulated on the
+cumulative density function that's the
+
+ align:start position:0%
+cumulative density function that's the
+ 
+
+ align:start position:0%
+cumulative density function that's the
+definition of the cumulative density
+
+ align:start position:0%
+definition of the cumulative density
+ 
+
+ align:start position:0%
+definition of the cumulative density
+function so if you've got the
+
+ align:start position:0%
+function so if you've got the
+ 
+
+ align:start position:0%
+function so if you've got the
+CDF you simply look it up and say what
+
+ align:start position:0%
+CDF you simply look it up and say what
+ 
+
+ align:start position:0%
+CDF you simply look it up and say what
+is f of X1 equal to whatever what
+
+ align:start position:0%
+is f of X1 equal to whatever what
+ 
+
+ align:start position:0%
+is f of X1 equal to whatever what
+whatever your value is for for that uh
+
+ align:start position:0%
+whatever your value is for for that uh
+ 
+
+ align:start position:0%
+whatever your value is for for that uh
+for that
+
+ align:start position:0%
+for that
+ 
+
+ align:start position:0%
+for that
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+function okay now similarly you can also
+
+ align:start position:0%
+function okay now similarly you can also
+ 
+
+ align:start position:0%
+function okay now similarly you can also
+ask the question what is the probability
+
+ align:start position:0%
+ask the question what is the probability
+ 
+
+ align:start position:0%
+ask the question what is the probability
+that X sits within some range say
+
+ align:start position:0%
+that X sits within some range say
+ 
+
+ align:start position:0%
+that X sits within some range say
+between X1 and
+
+ align:start position:0%
+between X1 and
+ 
+
+ align:start position:0%
+between X1 and
+X2 and again you can do that either off
+
+ align:start position:0%
+X2 and again you can do that either off
+ 
+
+ align:start position:0%
+X2 and again you can do that either off
+of the underlying density function just
+
+ align:start position:0%
+of the underlying density function just
+ 
+
+ align:start position:0%
+of the underlying density function just
+integrating and saying yes X has to lie
+
+ align:start position:0%
+integrating and saying yes X has to lie
+ 
+
+ align:start position:0%
+integrating and saying yes X has to lie
+between those values and integrate up
+
+ align:start position:0%
+between those values and integrate up
+ 
+
+ align:start position:0%
+between those values and integrate up
+the density or you can recognize that
+
+ align:start position:0%
+the density or you can recognize that
+ 
+
+ align:start position:0%
+the density or you can recognize that
+the probability
+
+ align:start position:0%
+the probability
+ 
+
+ align:start position:0%
+the probability
+that X is less than X2 is simply that
+
+ align:start position:0%
+that X is less than X2 is simply that
+ 
+
+ align:start position:0%
+that X is less than X2 is simply that
+value and subtract
+
+ align:start position:0%
+value and subtract
+ 
+
+ align:start position:0%
+value and subtract
+off that the probability that X was less
+
+ align:start position:0%
+off that the probability that X was less
+ 
+
+ align:start position:0%
+off that the probability that X was less
+than uh X1 is that and so therefore the
+
+ align:start position:0%
+than uh X1 is that and so therefore the
+ 
+
+ align:start position:0%
+than uh X1 is that and so therefore the
+difference between those two corresponds
+
+ align:start position:0%
+difference between those two corresponds
+ 
+
+ align:start position:0%
+difference between those two corresponds
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+integration um on the underlying
+
+ align:start position:0%
+integration um on the underlying
+ 
+
+ align:start position:0%
+integration um on the underlying
+probability density
+
+ align:start position:0%
+probability density
+ 
+
+ align:start position:0%
+probability density
+function okay so that's pretty easy that
+
+ align:start position:0%
+function okay so that's pretty easy that
+ 
+
+ align:start position:0%
+function okay so that's pretty easy that
+should be pretty clear let's talk about
+
+ align:start position:0%
+should be pretty clear let's talk about
+ 
+
+ align:start position:0%
+should be pretty clear let's talk about
+that also for the normal distribution
+
+ align:start position:0%
+that also for the normal distribution
+ 
+
+ align:start position:0%
+that also for the normal distribution
+because some of those values are not as
+
+ align:start position:0%
+because some of those values are not as
+ 
+
+ align:start position:0%
+because some of those values are not as
+easy to integrate up by hand in fact
+
+ align:start position:0%
+easy to integrate up by hand in fact
+ 
+
+ align:start position:0%
+easy to integrate up by hand in fact
+there exist no closed form uh formulas
+
+ align:start position:0%
+there exist no closed form uh formulas
+ 
+
+ align:start position:0%
+there exist no closed form uh formulas
+but they are tabulated for you and
+
+ align:start position:0%
+but they are tabulated for you and
+ 
+
+ align:start position:0%
+but they are tabulated for you and
+that's where going to the
+
+ align:start position:0%
+that's where going to the
+ 
+
+ align:start position:0%
+that's where going to the
+table on the normal distribution for
+
+ align:start position:0%
+table on the normal distribution for
+ 
+
+ align:start position:0%
+table on the normal distribution for
+things like f ofx are going to is is an
+
+ align:start position:0%
+things like f ofx are going to is is an
+ 
+
+ align:start position:0%
+things like f ofx are going to is is an
+operation that you will actually perform
+
+ align:start position:0%
+operation that you will actually perform
+ 
+
+ align:start position:0%
+operation that you will actually perform
+quite a bit when you're manipulating
+
+ align:start position:0%
+quite a bit when you're manipulating
+ 
+
+ align:start position:0%
+quite a bit when you're manipulating
+normal
+
+ align:start position:0%
+normal
+ 
+
+ align:start position:0%
+normal
+distributions so here's another plot uh
+
+ align:start position:0%
+distributions so here's another plot uh
+ 
+
+ align:start position:0%
+distributions so here's another plot uh
+we've already talked or I've shown uh
+
+ align:start position:0%
+we've already talked or I've shown uh
+ 
+
+ align:start position:0%
+we've already talked or I've shown uh
+other examples here of the normal
+
+ align:start position:0%
+other examples here of the normal
+ 
+
+ align:start position:0%
+other examples here of the normal
+distribution I've tagged off on this
+
+ align:start position:0%
+distribution I've tagged off on this
+ 
+
+ align:start position:0%
+distribution I've tagged off on this
+plot for us a few useful Little Numbers
+
+ align:start position:0%
+plot for us a few useful Little Numbers
+ 
+
+ align:start position:0%
+plot for us a few useful Little Numbers
+to have as rules of thumb this is
+
+ align:start position:0%
+to have as rules of thumb this is
+ 
+
+ align:start position:0%
+to have as rules of thumb this is
+actually I I think a moderately useful
+
+ align:start position:0%
+actually I I think a moderately useful
+ 
+
+ align:start position:0%
+actually I I think a moderately useful
+uh page to print out and sort of have
+
+ align:start position:0%
+uh page to print out and sort of have
+ 
+
+ align:start position:0%
+uh page to print out and sort of have
+off on the side for uh for your use in
+
+ align:start position:0%
+off on the side for uh for your use in
+ 
+
+ align:start position:0%
+off on the side for uh for your use in
+particular what I'm showing here is for
+
+ align:start position:0%
+particular what I'm showing here is for
+ 
+
+ align:start position:0%
+particular what I'm showing here is for
+the normal distribution you've got a
+
+ align:start position:0%
+the normal distribution you've got a
+ 
+
+ align:start position:0%
+the normal distribution you've got a
+formula you're hardly ever going to
+
+ align:start position:0%
+formula you're hardly ever going to
+ 
+
+ align:start position:0%
+formula you're hardly ever going to
+actually plug in values for the formula
+
+ align:start position:0%
+actually plug in values for the formula
+ 
+
+ align:start position:0%
+actually plug in values for the formula
+but if you look out plus one standard
+
+ align:start position:0%
+but if you look out plus one standard
+ 
+
+ align:start position:0%
+but if you look out plus one standard
+deviation plus two standard deviation on
+
+ align:start position:0%
+deviation plus two standard deviation on
+ 
+
+ align:start position:0%
+deviation plus two standard deviation on
+the PDF I've tried to indicate here how
+
+ align:start position:0%
+the PDF I've tried to indicate here how
+ 
+
+ align:start position:0%
+the PDF I've tried to indicate here how
+rapidly the the value of that
+
+ align:start position:0%
+rapidly the the value of that
+ 
+
+ align:start position:0%
+rapidly the the value of that
+probability density falls off so for
+
+ align:start position:0%
+probability density falls off so for
+ 
+
+ align:start position:0%
+probability density falls off so for
+example one standard deviation I'm about
+
+ align:start position:0%
+example one standard deviation I'm about
+ 
+
+ align:start position:0%
+example one standard deviation I'm about
+60% the peak two standard deviations I'm
+
+ align:start position:0%
+60% the peak two standard deviations I'm
+ 
+
+ align:start position:0%
+60% the peak two standard deviations I'm
+down to about 13.5% of the
+
+ align:start position:0%
+down to about 13.5% of the
+ 
+
+ align:start position:0%
+down to about 13.5% of the
+peak now more often than asking what is
+
+ align:start position:0%
+peak now more often than asking what is
+ 
+
+ align:start position:0%
+peak now more often than asking what is
+the relative probabilities of these
+
+ align:start position:0%
+the relative probabilities of these
+ 
+
+ align:start position:0%
+the relative probabilities of these
+things you're actually more often asking
+
+ align:start position:0%
+things you're actually more often asking
+ 
+
+ align:start position:0%
+things you're actually more often asking
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+is how much what is the integrated
+
+ align:start position:0%
+is how much what is the integrated
+ 
+
+ align:start position:0%
+is how much what is the integrated
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+density of the random variable out in
+
+ align:start position:0%
+density of the random variable out in
+ 
+
+ align:start position:0%
+density of the random variable out in
+some tail or in some central region and
+
+ align:start position:0%
+some tail or in some central region and
+ 
+
+ align:start position:0%
+some tail or in some central region and
+that's where the cumulative density
+
+ align:start position:0%
+that's where the cumulative density
+ 
+
+ align:start position:0%
+that's where the cumulative density
+function is really the one that you want
+
+ align:start position:0%
+function is really the one that you want
+ 
+
+ align:start position:0%
+function is really the one that you want
+to use and so what I'm showing here is
+
+ align:start position:0%
+to use and so what I'm showing here is
+ 
+
+ align:start position:0%
+to use and so what I'm showing here is
+out for some number of standard
+
+ align:start position:0%
+out for some number of standard
+ 
+
+ align:start position:0%
+out for some number of standard
+deviations this is muus 3 standard
+
+ align:start position:0%
+deviations this is muus 3 standard
+ 
+
+ align:start position:0%
+deviations this is muus 3 standard
+deviation this this is saying the
+
+ align:start position:0%
+deviation this this is saying the
+ 
+
+ align:start position:0%
+deviation this this is saying the
+probability that X is less than U mu - 3
+
+ align:start position:0%
+probability that X is less than U mu - 3
+ 
+
+ align:start position:0%
+probability that X is less than U mu - 3
+Sigma is exactly that value that equals
+
+ align:start position:0%
+Sigma is exactly that value that equals
+ 
+
+ align:start position:0%
+Sigma is exactly that value that equals
+F of mu
+
+ align:start position:0%
+F of mu
+ 
+
+ align:start position:0%
+F of mu
+minus 3 Sigma and I simply look that up
+
+ align:start position:0%
+minus 3 Sigma and I simply look that up
+ 
+
+ align:start position:0%
+minus 3 Sigma and I simply look that up
+and that's about
+
+ align:start position:0%
+and that's about
+ 
+
+ align:start position:0%
+and that's about
+0.135 or less than 0.1% of your data
+
+ align:start position:0%
+0.135 or less than 0.1% of your data
+ 
+
+ align:start position:0%
+0.135 or less than 0.1% of your data
+should fall Less Than 3 Sigma off the
+
+ align:start position:0%
+should fall Less Than 3 Sigma off the
+ 
+
+ align:start position:0%
+should fall Less Than 3 Sigma off the
+left side of your
+
+ align:start position:0%
+left side of your
+ 
+
+ align:start position:0%
+left side of your
+distribution and then I've tabulated
+
+ align:start position:0%
+distribution and then I've tabulated
+ 
+
+ align:start position:0%
+distribution and then I've tabulated
+that for two standard deviations one
+
+ align:start position:0%
+that for two standard deviations one
+ 
+
+ align:start position:0%
+that for two standard deviations one
+standard deviation by the way what's the
+
+ align:start position:0%
+standard deviation by the way what's the
+ 
+
+ align:start position:0%
+standard deviation by the way what's the
+probability now that I've marked it up
+
+ align:start position:0%
+probability now that I've marked it up
+ 
+
+ align:start position:0%
+probability now that I've marked it up
+that your
+
+ align:start position:0%
+that your
+ 
+
+ align:start position:0%
+that your
+data Falls less than your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean 50% it's a symmetric
+
+ align:start position:0%
+mean 50% it's a symmetric
+ 
+
+ align:start position:0%
+mean 50% it's a symmetric
+distribution and so in fact um you could
+
+ align:start position:0%
+distribution and so in fact um you could
+ 
+
+ align:start position:0%
+distribution and so in fact um you could
+then ask also the question you know
+
+ align:start position:0%
+then ask also the question you know
+ 
+
+ align:start position:0%
+then ask also the question you know
+what's what's the probability that my
+
+ align:start position:0%
+what's what's the probability that my
+ 
+
+ align:start position:0%
+what's what's the probability that my
+data is all the way from my left tail up
+
+ align:start position:0%
+data is all the way from my left tail up
+ 
+
+ align:start position:0%
+data is all the way from my left tail up
+to two standard deviations above the
+
+ align:start position:0%
+to two standard deviations above the
+ 
+
+ align:start position:0%
+to two standard deviations above the
+mean and that's
+
+ align:start position:0%
+mean and that's
+ 
+
+ align:start position:0%
+mean and that's
+97.7% but I want to also point out these
+
+ align:start position:0%
+97.7% but I want to also point out these
+ 
+
+ align:start position:0%
+97.7% but I want to also point out these
+this distribution itself is also sort of
+
+ align:start position:0%
+this distribution itself is also sort of
+ 
+
+ align:start position:0%
+this distribution itself is also sort of
+anti-symmetric um around the mean so
+
+ align:start position:0%
+anti-symmetric um around the mean so
+ 
+
+ align:start position:0%
+anti-symmetric um around the mean so
+this value and this value uh sum to
+
+ align:start position:0%
+this value and this value uh sum to
+ 
+
+ align:start position:0%
+this value and this value uh sum to
+one right so in other words one minus
+
+ align:start position:0%
+one right so in other words one minus
+ 
+
+ align:start position:0%
+one right so in other words one minus
+whatever is out in the upper tail
+
+ align:start position:0%
+whatever is out in the upper tail
+ 
+
+ align:start position:0%
+whatever is out in the upper tail
+is equal to the probability of being
+
+ align:start position:0%
+is equal to the probability of being
+ 
+
+ align:start position:0%
+is equal to the probability of being
+below the lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tail so what's tabulated is not mu minus
+
+ align:start position:0%
+tail so what's tabulated is not mu minus
+ 
+
+ align:start position:0%
+tail so what's tabulated is not mu minus
+numbers of standard deviations but what
+
+ align:start position:0%
+numbers of standard deviations but what
+ 
+
+ align:start position:0%
+numbers of standard deviations but what
+will often what is actually tabulated
+
+ align:start position:0%
+will often what is actually tabulated
+ 
+
+ align:start position:0%
+will often what is actually tabulated
+are the standardized or unit normal uh
+
+ align:start position:0%
+are the standardized or unit normal uh
+ 
+
+ align:start position:0%
+are the standardized or unit normal uh
+distribution again the mean centered
+
+ align:start position:0%
+distribution again the mean centered
+ 
+
+ align:start position:0%
+distribution again the mean centered
+version where I subtract off the mean
+
+ align:start position:0%
+version where I subtract off the mean
+ 
+
+ align:start position:0%
+version where I subtract off the mean
+and divide by uh the standard deviation
+
+ align:start position:0%
+and divide by uh the standard deviation
+ 
+
+ align:start position:0%
+and divide by uh the standard deviation
+and that gives
+
+ align:start position:0%
+and that gives
+ 
+
+ align:start position:0%
+and that gives
+a a PDF and a CDF that is universal
+
+ align:start position:0%
+a a PDF and a CDF that is universal
+ 
+
+ align:start position:0%
+a a PDF and a CDF that is universal
+right and that is what will often be
+
+ align:start position:0%
+right and that is what will often be
+ 
+
+ align:start position:0%
+right and that is what will often be
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+tabulated
+
+ align:start position:0%
+tabulated
+ 
+
+ align:start position:0%
+tabulated
+um as the unit normal cumulative density
+
+ align:start position:0%
+um as the unit normal cumulative density
+ 
+
+ align:start position:0%
+um as the unit normal cumulative density
+function and that's a in some sense
+
+ align:start position:0%
+function and that's a in some sense
+ 
+
+ align:start position:0%
+function and that's a in some sense
+that's what I actually showed on this
+
+ align:start position:0%
+that's what I actually showed on this
+ 
+
+ align:start position:0%
+that's what I actually showed on this
+plot by just labeling it as a function
+
+ align:start position:0%
+plot by just labeling it as a function
+ 
+
+ align:start position:0%
+plot by just labeling it as a function
+of mu and standard deviations but now
+
+ align:start position:0%
+of mu and standard deviations but now
+ 
+
+ align:start position:0%
+of mu and standard deviations but now
+when you normalize that becomes in units
+
+ align:start position:0%
+when you normalize that becomes in units
+ 
+
+ align:start position:0%
+when you normalize that becomes in units
+of Z as zero and then numbers of
+
+ align:start position:0%
+of Z as zero and then numbers of
+ 
+
+ align:start position:0%
+of Z as zero and then numbers of
+standard deviations off on the
+
+ align:start position:0%
+standard deviations off on the
+ 
+
+ align:start position:0%
+standard deviations off on the
+side now if you look at the back of
+
+ align:start position:0%
+side now if you look at the back of
+ 
+
+ align:start position:0%
+side now if you look at the back of
+Montgomery there's a whole bunch of
+
+ align:start position:0%
+Montgomery there's a whole bunch of
+ 
+
+ align:start position:0%
+Montgomery there's a whole bunch of
+these tables and you'll be using these
+
+ align:start position:0%
+these tables and you'll be using these
+ 
+
+ align:start position:0%
+these tables and you'll be using these
+tables in some of the problem sets and
+
+ align:start position:0%
+tables in some of the problem sets and
+ 
+
+ align:start position:0%
+tables in some of the problem sets and
+so on and there is a table for the unit
+
+ align:start position:0%
+so on and there is a table for the unit
+ 
+
+ align:start position:0%
+so on and there is a table for the unit
+normal and uh in particular there's
+
+ align:start position:0%
+normal and uh in particular there's
+ 
+
+ align:start position:0%
+normal and uh in particular there's
+a what's tabulated is this cumulative
+
+ align:start position:0%
+a what's tabulated is this cumulative
+ 
+
+ align:start position:0%
+a what's tabulated is this cumulative
+density function for the unit normal and
+
+ align:start position:0%
+density function for the unit normal and
+ 
+
+ align:start position:0%
+density function for the unit normal and
+we have a little bit of terminology here
+
+ align:start position:0%
+we have a little bit of terminology here
+ 
+
+ align:start position:0%
+we have a little bit of terminology here
+that I want to alert you to because we
+
+ align:start position:0%
+that I want to alert you to because we
+ 
+
+ align:start position:0%
+that I want to alert you to because we
+often talk about percentage points off
+
+ align:start position:0%
+often talk about percentage points off
+ 
+
+ align:start position:0%
+often talk about percentage points off
+of some distribution or percentage
+
+ align:start position:0%
+of some distribution or percentage
+ 
+
+ align:start position:0%
+of some distribution or percentage
+points of the uh the unit normal uh as
+
+ align:start position:0%
+points of the uh the unit normal uh as
+ 
+
+ align:start position:0%
+points of the uh the unit normal uh as
+pictured here and what we're talking
+
+ align:start position:0%
+pictured here and what we're talking
+ 
+
+ align:start position:0%
+pictured here and what we're talking
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+relating percentages of my distribution
+
+ align:start position:0%
+relating percentages of my distribution
+ 
+
+ align:start position:0%
+relating percentages of my distribution
+that are in some location usually the
+
+ align:start position:0%
+that are in some location usually the
+ 
+
+ align:start position:0%
+that are in some location usually the
+tails to numbers of standard deviations
+
+ align:start position:0%
+tails to numbers of standard deviations
+ 
+
+ align:start position:0%
+tails to numbers of standard deviations
+that I have to go in order to
+
+ align:start position:0%
+that I have to go in order to
+ 
+
+ align:start position:0%
+that I have to go in order to
+a portion that amount over in in the
+
+ align:start position:0%
+a portion that amount over in in the
+ 
+
+ align:start position:0%
+a portion that amount over in in the
+taals or in the central regions so a
+
+ align:start position:0%
+taals or in the central regions so a
+ 
+
+ align:start position:0%
+taals or in the central regions so a
+very typical question I might ask is how
+
+ align:start position:0%
+very typical question I might ask is how
+ 
+
+ align:start position:0%
+very typical question I might ask is how
+many Z's how many unit standard
+
+ align:start position:0%
+many Z's how many unit standard
+ 
+
+ align:start position:0%
+many Z's how many unit standard
+deviations how many
+
+ align:start position:0%
+deviations how many
+ 
+
+ align:start position:0%
+deviations how many
+Z's do I have to go away from the from
+
+ align:start position:0%
+Z's do I have to go away from the from
+ 
+
+ align:start position:0%
+Z's do I have to go away from the from
+the from the mean in order to get some
+
+ align:start position:0%
+the from the mean in order to get some
+ 
+
+ align:start position:0%
+the from the mean in order to get some
+alpha or some
+
+ align:start position:0%
+alpha or some
+ 
+
+ align:start position:0%
+alpha or some
+percentage of the distribution located
+
+ align:start position:0%
+percentage of the distribution located
+ 
+
+ align:start position:0%
+percentage of the distribution located
+out in that uh in in those Tails so for
+
+ align:start position:0%
+out in that uh in in those Tails so for
+ 
+
+ align:start position:0%
+out in that uh in in those Tails so for
+example I might say I want the
+
+ align:start position:0%
+example I might say I want the
+ 
+
+ align:start position:0%
+example I might say I want the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+20% uh 20th percentile percentage Point
+
+ align:start position:0%
+20% uh 20th percentile percentage Point
+ 
+
+ align:start position:0%
+20% uh 20th percentile percentage Point
+the0 2 uh probability that my data sits
+
+ align:start position:0%
+the0 2 uh probability that my data sits
+ 
+
+ align:start position:0%
+the0 2 uh probability that my data sits
+in the two
+
+ align:start position:0%
+in the two
+ 
+
+ align:start position:0%
+in the two
+tails right so for a total probability
+
+ align:start position:0%
+tails right so for a total probability
+ 
+
+ align:start position:0%
+tails right so for a total probability
+that all my data uh uh or the Remain the
+
+ align:start position:0%
+that all my data uh uh or the Remain the
+ 
+
+ align:start position:0%
+that all my data uh uh or the Remain the
+portion of my data is on either of the
+
+ align:start position:0%
+portion of my data is on either of the
+ 
+
+ align:start position:0%
+portion of my data is on either of the
+tail some uh further away than
+
+ align:start position:0%
+tail some uh further away than
+ 
+
+ align:start position:0%
+tail some uh further away than
+U some Z that means 10% is in each of
+
+ align:start position:0%
+U some Z that means 10% is in each of
+ 
+
+ align:start position:0%
+U some Z that means 10% is in each of
+the Tails and I'm asking the question
+
+ align:start position:0%
+the Tails and I'm asking the question
+ 
+
+ align:start position:0%
+the Tails and I'm asking the question
+what how far how many uh standard
+
+ align:start position:0%
+what how far how many uh standard
+ 
+
+ align:start position:0%
+what how far how many uh standard
+deviations do I have to go to get 10% in
+
+ align:start position:0%
+deviations do I have to go to get 10% in
+ 
+
+ align:start position:0%
+deviations do I have to go to get 10% in
+the left tail and 10% out in the right
+
+ align:start position:0%
+the left tail and 10% out in the right
+ 
+
+ align:start position:0%
+the left tail and 10% out in the right
+tail so I'm essentially asking the
+
+ align:start position:0%
+tail so I'm essentially asking the
+ 
+
+ align:start position:0%
+tail so I'm essentially asking the
+question what is the
+
+ align:start position:0%
+question what is the
+ 
+
+ align:start position:0%
+question what is the
+probability on the cumulative probab
+
+ align:start position:0%
+probability on the cumulative probab
+ 
+
+ align:start position:0%
+probability on the cumulative probab
+unit normal prob ility distribution
+
+ align:start position:0%
+unit normal prob ility distribution
+ 
+
+ align:start position:0%
+unit normal prob ility distribution
+function to get to how many Z's do I
+
+ align:start position:0%
+function to get to how many Z's do I
+ 
+
+ align:start position:0%
+function to get to how many Z's do I
+have to go to get to half of you know
+
+ align:start position:0%
+have to go to get to half of you know
+ 
+
+ align:start position:0%
+have to go to get to half of you know
+that Alpha probability being in in each
+
+ align:start position:0%
+that Alpha probability being in in each
+ 
+
+ align:start position:0%
+that Alpha probability being in in each
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+Tails one observation here is that these
+
+ align:start position:0%
+Tails one observation here is that these
+ 
+
+ align:start position:0%
+Tails one observation here is that these
+things are again uh uh anti-symmetric so
+
+ align:start position:0%
+things are again uh uh anti-symmetric so
+ 
+
+ align:start position:0%
+things are again uh uh anti-symmetric so
+I can also ask the question you know
+
+ align:start position:0%
+I can also ask the question you know
+ 
+
+ align:start position:0%
+I can also ask the question you know
+either looking just the right tail or
+
+ align:start position:0%
+either looking just the right tail or
+ 
+
+ align:start position:0%
+either looking just the right tail or
+the left
+
+ align:start position:0%
+the left
+ 
+
+ align:start position:0%
+the left
+tail and then you can do the inverse
+
+ align:start position:0%
+tail and then you can do the inverse
+ 
+
+ align:start position:0%
+tail and then you can do the inverse
+operation using the table so I'm
+
+ align:start position:0%
+operation using the table so I'm
+ 
+
+ align:start position:0%
+operation using the table so I'm
+actually asking the question what is the
+
+ align:start position:0%
+actually asking the question what is the
+ 
+
+ align:start position:0%
+actually asking the question what is the
+Z associated with that and I'm looking
+
+ align:start position:0%
+Z associated with that and I'm looking
+ 
+
+ align:start position:0%
+Z associated with that and I'm looking
+up on this plot so I might ask okay I
+
+ align:start position:0%
+up on this plot so I might ask okay I
+ 
+
+ align:start position:0%
+up on this plot so I might ask okay I
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+10% there in the tail how many Z's does
+
+ align:start position:0%
+10% there in the tail how many Z's does
+ 
+
+ align:start position:0%
+10% there in the tail how many Z's does
+that correspond to and to get 10% out in
+
+ align:start position:0%
+that correspond to and to get 10% out in
+ 
+
+ align:start position:0%
+that correspond to and to get 10% out in
+that left tail I got to go out 1.28
+
+ align:start position:0%
+that left tail I got to go out 1.28
+ 
+
+ align:start position:0%
+that left tail I got to go out 1.28
+standard deviations off to the left
+
+ align:start position:0%
+standard deviations off to the left
+ 
+
+ align:start position:0%
+standard deviations off to the left
+that's the operation that one would look
+
+ align:start position:0%
+that's the operation that one would look
+ 
+
+ align:start position:0%
+that's the operation that one would look
+up uh in the in the table so very often
+
+ align:start position:0%
+up uh in the in the table so very often
+ 
+
+ align:start position:0%
+up uh in the in the table so very often
+you would get to these kind kinds of of
+
+ align:start position:0%
+you would get to these kind kinds of of
+ 
+
+ align:start position:0%
+you would get to these kind kinds of of
+of uh
+
+ align:start position:0%
+of uh
+ 
+
+ align:start position:0%
+of uh
+lookups where you're you're
+
+ align:start position:0%
+lookups where you're you're
+ 
+
+ align:start position:0%
+lookups where you're you're
+relating the
+
+ align:start position:0%
+relating the
+ 
+
+ align:start position:0%
+relating the
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+Alpha of uh your data lying below
+
+ align:start position:0%
+Alpha of uh your data lying below
+ 
+
+ align:start position:0%
+Alpha of uh your data lying below
+that number of standard deviations and
+
+ align:start position:0%
+that number of standard deviations and
+ 
+
+ align:start position:0%
+that number of standard deviations and
+what that corresponding standard
+
+ align:start position:0%
+what that corresponding standard
+ 
+
+ align:start position:0%
+what that corresponding standard
+deviation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is okay so I didn't copy one of the uh
+
+ align:start position:0%
+is okay so I didn't copy one of the uh
+ 
+
+ align:start position:0%
+is okay so I didn't copy one of the uh
+the tables out of uh Montgomery but
+
+ align:start position:0%
+the tables out of uh Montgomery but
+ 
+
+ align:start position:0%
+the tables out of uh Montgomery but
+you'll get some practice with that uh on
+
+ align:start position:0%
+you'll get some practice with that uh on
+ 
+
+ align:start position:0%
+you'll get some practice with that uh on
+the problem
+
+ align:start position:0%
+the problem
+ 
+
+ align:start position:0%
+the problem
+sets now there's other related op
+
+ align:start position:0%
+sets now there's other related op
+ 
+
+ align:start position:0%
+sets now there's other related op
+operations you can do once you have that
+
+ align:start position:0%
+operations you can do once you have that
+ 
+
+ align:start position:0%
+operations you can do once you have that
+so for example now I can ask okay what
+
+ align:start position:0%
+so for example now I can ask okay what
+ 
+
+ align:start position:0%
+so for example now I can ask okay what
+is the probability not just that data
+
+ align:start position:0%
+is the probability not just that data
+ 
+
+ align:start position:0%
+is the probability not just that data
+lies out in the tail but what are the
+
+ align:start position:0%
+lies out in the tail but what are the
+ 
+
+ align:start position:0%
+lies out in the tail but what are the
+probabilities that it also or instead
+
+ align:start position:0%
+probabilities that it also or instead
+ 
+
+ align:start position:0%
+probabilities that it also or instead
+lies in the middle region they're all
+
+ align:start position:0%
+lies in the middle region they're all
+ 
+
+ align:start position:0%
+lies in the middle region they're all
+sort of the same the same kinds of
+
+ align:start position:0%
+sort of the same the same kinds of
+ 
+
+ align:start position:0%
+sort of the same the same kinds of
+operations and so for example here's a
+
+ align:start position:0%
+operations and so for example here's a
+ 
+
+ align:start position:0%
+operations and so for example here's a
+quick tabulation for three different
+
+ align:start position:0%
+quick tabulation for three different
+ 
+
+ align:start position:0%
+quick tabulation for three different
+kinds of uh examples where I'm asking
+
+ align:start position:0%
+kinds of uh examples where I'm asking
+ 
+
+ align:start position:0%
+kinds of uh examples where I'm asking
+not what is out in the Tails but I'm
+
+ align:start position:0%
+not what is out in the Tails but I'm
+ 
+
+ align:start position:0%
+not what is out in the Tails but I'm
+asking what is within the center plusus
+
+ align:start position:0%
+asking what is within the center plusus
+ 
+
+ align:start position:0%
+asking what is within the center plusus
+one Sigma region of the data and if you
+
+ align:start position:0%
+one Sigma region of the data and if you
+ 
+
+ align:start position:0%
+one Sigma region of the data and if you
+look very carefully I'm using exactly
+
+ align:start position:0%
+look very carefully I'm using exactly
+ 
+
+ align:start position:0%
+look very carefully I'm using exactly
+these uh cumulative probability density
+
+ align:start position:0%
+these uh cumulative probability density
+ 
+
+ align:start position:0%
+these uh cumulative probability density
+functions for the unit normal this is
+
+ align:start position:0%
+functions for the unit normal this is
+ 
+
+ align:start position:0%
+functions for the unit normal this is
+for a a unit
+
+ align:start position:0%
+for a a unit
+ 
+
+ align:start position:0%
+for a a unit
+normal um and looking out you know
+
+ align:start position:0%
+normal um and looking out you know
+ 
+
+ align:start position:0%
+normal um and looking out you know
+what's the cumulative probability over
+
+ align:start position:0%
+what's the cumulative probability over
+ 
+
+ align:start position:0%
+what's the cumulative probability over
+in the left tail the right right tail
+
+ align:start position:0%
+in the left tail the right right tail
+ 
+
+ align:start position:0%
+in the left tail the right right tail
+doing those observations but these are
+
+ align:start position:0%
+doing those observations but these are
+ 
+
+ align:start position:0%
+doing those observations but these are
+also very nice rules of thumb to have uh
+
+ align:start position:0%
+also very nice rules of thumb to have uh
+ 
+
+ align:start position:0%
+also very nice rules of thumb to have uh
+uh ready for you which is
+
+ align:start position:0%
+uh ready for you which is
+ 
+
+ align:start position:0%
+uh ready for you which is
+saying within plusus one standard
+
+ align:start position:0%
+saying within plusus one standard
+ 
+
+ align:start position:0%
+saying within plusus one standard
+deviation in a normal
+
+ align:start position:0%
+deviation in a normal
+ 
+
+ align:start position:0%
+deviation in a normal
+68 percent of your data is going to fall
+
+ align:start position:0%
+68 percent of your data is going to fall
+ 
+
+ align:start position:0%
+68 percent of your data is going to fall
+in that one Sigma
+
+ align:start position:0%
+in that one Sigma
+ 
+
+ align:start position:0%
+in that one Sigma
+region in the case of if I expand out to
+
+ align:start position:0%
+region in the case of if I expand out to
+ 
+
+ align:start position:0%
+region in the case of if I expand out to
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+Sigma now I've got 95% of my data should
+
+ align:start position:0%
+Sigma now I've got 95% of my data should
+ 
+
+ align:start position:0%
+Sigma now I've got 95% of my data should
+fall rough flate in there and if I
+
+ align:start position:0%
+fall rough flate in there and if I
+ 
+
+ align:start position:0%
+fall rough flate in there and if I
+expand out even further to the three
+
+ align:start position:0%
+expand out even further to the three
+ 
+
+ align:start position:0%
+expand out even further to the three
+sigma that's the 99.7% of your data
+
+ align:start position:0%
+sigma that's the 99.7% of your data
+ 
+
+ align:start position:0%
+sigma that's the 99.7% of your data
+would would be falling should fall uh
+
+ align:start position:0%
+would would be falling should fall uh
+ 
+
+ align:start position:0%
+would would be falling should fall uh
+within those those Center uh three uh
+
+ align:start position:0%
+within those those Center uh three uh
+ 
+
+ align:start position:0%
+within those those Center uh three uh
+standard
+
+ align:start position:0%
+standard
+ 
+
+ align:start position:0%
+standard
+deviations
+
+ align:start position:0%
+deviations
+ 
+
+ align:start position:0%
+deviations
+okay so the percentage points out there
+
+ align:start position:0%
+okay so the percentage points out there
+ 
+
+ align:start position:0%
+okay so the percentage points out there
+the the part that falls outside of that
+
+ align:start position:0%
+the the part that falls outside of that
+ 
+
+ align:start position:0%
+the the part that falls outside of that
+is is about three and a three and 1,000
+
+ align:start position:0%
+is is about three and a three and 1,000
+ 
+
+ align:start position:0%
+is is about three and a three and 1,000
+we'll come back to this when we see
+
+ align:start position:0%
+we'll come back to this when we see
+ 
+
+ align:start position:0%
+we'll come back to this when we see
+statistical process control and control
+
+ align:start position:0%
+statistical process control and control
+ 
+
+ align:start position:0%
+statistical process control and control
+charts because you may have run into
+
+ align:start position:0%
+charts because you may have run into
+ 
+
+ align:start position:0%
+charts because you may have run into
+these control charts we're often
+
+ align:start position:0%
+these control charts we're often
+ 
+
+ align:start position:0%
+these control charts we're often
+plotting the uh three sigma control
+
+ align:start position:0%
+plotting the uh three sigma control
+ 
+
+ align:start position:0%
+plotting the uh three sigma control
+limits and essentially what we're saying
+
+ align:start position:0%
+limits and essentially what we're saying
+ 
+
+ align:start position:0%
+limits and essentially what we're saying
+is only a very small fraction of my data
+
+ align:start position:0%
+is only a very small fraction of my data
+ 
+
+ align:start position:0%
+is only a very small fraction of my data
+three out of a th000 if I'm using plus
+
+ align:start position:0%
+three out of a th000 if I'm using plus
+ 
+
+ align:start position:0%
+three out of a th000 if I'm using plus
+minus three sigma control limits three
+
+ align:start position:0%
+minus three sigma control limits three
+ 
+
+ align:start position:0%
+minus three sigma control limits three
+out of a th points of my data by random
+
+ align:start position:0%
+out of a th points of my data by random
+ 
+
+ align:start position:0%
+out of a th points of my data by random
+chance alone should be falling outside
+
+ align:start position:0%
+chance alone should be falling outside
+ 
+
+ align:start position:0%
+chance alone should be falling outside
+of those three sigma bounds
+
+ align:start position:0%
+of those three sigma bounds
+ 
+
+ align:start position:0%
+of those three sigma bounds
+okay so that starts to get us close
+
+ align:start position:0%
+okay so that starts to get us close
+ 
+
+ align:start position:0%
+okay so that starts to get us close
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um statistical process control so what
+
+ align:start position:0%
+um statistical process control so what
+ 
+
+ align:start position:0%
+um statistical process control so what
+we're going to do uh next time is start
+
+ align:start position:0%
+we're going to do uh next time is start
+ 
+
+ align:start position:0%
+we're going to do uh next time is start
+to look a little bit more closely at
+
+ align:start position:0%
+to look a little bit more closely at
+ 
+
+ align:start position:0%
+to look a little bit more closely at
+statistics when I do form again things
+
+ align:start position:0%
+statistics when I do form again things
+ 
+
+ align:start position:0%
+statistics when I do form again things
+like uh the
+
+ align:start position:0%
+like uh the
+ 
+
+ align:start position:0%
+like uh the
+sample uh mean or I form oops the
+
+ align:start position:0%
+sample uh mean or I form oops the
+ 
+
+ align:start position:0%
+sample uh mean or I form oops the
+sample standard deviation or sample
+
+ align:start position:0%
+sample standard deviation or sample
+ 
+
+ align:start position:0%
+sample standard deviation or sample
+variance
+
+ align:start position:0%
+variance
+ 
+
+ align:start position:0%
+variance
+from my data those themselves have these
+
+ align:start position:0%
+from my data those themselves have these
+ 
+
+ align:start position:0%
+from my data those themselves have these
+probability densities associated with
+
+ align:start position:0%
+probability densities associated with
+ 
+
+ align:start position:0%
+probability densities associated with
+them and from that we're going to be
+
+ align:start position:0%
+them and from that we're going to be
+ 
+
+ align:start position:0%
+them and from that we're going to be
+able to go backwards and essentially
+
+ align:start position:0%
+able to go backwards and essentially
+ 
+
+ align:start position:0%
+able to go backwards and essentially
+work to try to understand
+
+ align:start position:0%
+work to try to understand
+ 
+
+ align:start position:0%
+work to try to understand
+oops um things about the underlying
+
+ align:start position:0%
+oops um things about the underlying
+ 
+
+ align:start position:0%
+oops um things about the underlying
+process distribution the parent
+
+ align:start position:0%
+process distribution the parent
+ 
+
+ align:start position:0%
+process distribution the parent
+probability distribution function uh
+
+ align:start position:0%
+probability distribution function uh
+ 
+
+ align:start position:0%
+probability distribution function uh
+associated with that so we're going to
+
+ align:start position:0%
+associated with that so we're going to
+ 
+
+ align:start position:0%
+associated with that so we're going to
+have to understand more complicated PDF
+
+ align:start position:0%
+have to understand more complicated PDF
+ 
+
+ align:start position:0%
+have to understand more complicated PDF
+FS than the normal
+
+ align:start position:0%
+FS than the normal
+ 
+
+ align:start position:0%
+FS than the normal
+distribution uh because things like the
+
+ align:start position:0%
+distribution uh because things like the
+ 
+
+ align:start position:0%
+distribution uh because things like the
+sample variance is not going to be
+
+ align:start position:0%
+sample variance is not going to be
+ 
+
+ align:start position:0%
+sample variance is not going to be
+normal normally distributed it's going
+
+ align:start position:0%
+normal normally distributed it's going
+ 
+
+ align:start position:0%
+normal normally distributed it's going
+to have its own bizarre distribution uh
+
+ align:start position:0%
+to have its own bizarre distribution uh
+ 
+
+ align:start position:0%
+to have its own bizarre distribution uh
+uh in this case the Ki Square
+
+ align:start position:0%
+uh in this case the Ki Square
+ 
+
+ align:start position:0%
+uh in this case the Ki Square
+distribution so we'll return to looking
+
+ align:start position:0%
+distribution so we'll return to looking
+ 
+
+ align:start position:0%
+distribution so we'll return to looking
+at some additional distributions but
+
+ align:start position:0%
+at some additional distributions but
+ 
+
+ align:start position:0%
+at some additional distributions but
+these same manipulations uh will come up
+
+ align:start position:0%
+these same manipulations uh will come up
+ 
+
+ align:start position:0%
+these same manipulations uh will come up
+again and what we're ultimately going to
+
+ align:start position:0%
+again and what we're ultimately going to
+ 
+
+ align:start position:0%
+again and what we're ultimately going to
+want to be able to do is make inferences
+
+ align:start position:0%
+want to be able to do is make inferences
+ 
+
+ align:start position:0%
+want to be able to do is make inferences
+about the underlying distribution the
+
+ align:start position:0%
+about the underlying distribution the
+ 
+
+ align:start position:0%
+about the underlying distribution the
+parent process what its mean is what its
+
+ align:start position:0%
+parent process what its mean is what its
+ 
+
+ align:start position:0%
+parent process what its mean is what its
+variance is based on the calculated
+
+ align:start position:0%
+variance is based on the calculated
+ 
+
+ align:start position:0%
+variance is based on the calculated
+sample mean and Sample variants that we
+
+ align:start position:0%
+sample mean and Sample variants that we
+ 
+
+ align:start position:0%
+sample mean and Sample variants that we
+might be used using and then also make
+
+ align:start position:0%
+might be used using and then also make
+ 
+
+ align:start position:0%
+might be used using and then also make
+inferences about the likelihood that the
+
+ align:start position:0%
+inferences about the likelihood that the
+ 
+
+ align:start position:0%
+inferences about the likelihood that the
+true mean lies in certain ranges or to
+
+ align:start position:0%
+true mean lies in certain ranges or to
+ 
+
+ align:start position:0%
+true mean lies in certain ranges or to
+put it another way next time we'll also
+
+ align:start position:0%
+put it another way next time we'll also
+ 
+
+ align:start position:0%
+put it another way next time we'll also
+be talking about confidence
+
+ align:start position:0%
+be talking about confidence
+ 
+
+ align:start position:0%
+be talking about confidence
+intervals okay so we'll see you on
+
+ align:start position:0%
+intervals okay so we'll see you on
+ 
+
+ align:start position:0%
+intervals okay so we'll see you on
+Thursday watch for the message from
+
+ align:start position:0%
+Thursday watch for the message from
+ 
+
+ align:start position:0%
+Thursday watch for the message from
+uh from Hayden about uh tours and uh
+
+ align:start position:0%
+uh from Hayden about uh tours and uh
+ 
+
+ align:start position:0%
+uh from Hayden about uh tours and uh
+enjoy
\ No newline at end of file
diff --git a/Od21y3eAwUo.txt b/Od21y3eAwUo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..154952fb358939b0a23444d8b68810018a6c0f7d
--- /dev/null
+++ b/Od21y3eAwUo.txt
@@ -0,0 +1,1979 @@
+align:start position:0%
+ 
+all right uh so my name is Lauren marman
+
+ align:start position:0%
+all right uh so my name is Lauren marman
+ 
+
+ align:start position:0%
+all right uh so my name is Lauren marman
+um I'm a senior right now I'm actually
+
+ align:start position:0%
+um I'm a senior right now I'm actually
+ 
+
+ align:start position:0%
+um I'm a senior right now I'm actually
+graduating in February I took this class
+
+ align:start position:0%
+graduating in February I took this class
+ 
+
+ align:start position:0%
+graduating in February I took this class
+because I decided I really wanted to
+
+ align:start position:0%
+because I decided I really wanted to
+ 
+
+ align:start position:0%
+because I decided I really wanted to
+make video games and this is a good
+
+ align:start position:0%
+make video games and this is a good
+ 
+
+ align:start position:0%
+make video games and this is a good
+class to take uh my team is seven people
+
+ align:start position:0%
+class to take uh my team is seven people
+ 
+
+ align:start position:0%
+class to take uh my team is seven people
+and we are mostly seniors um we made a
+
+ align:start position:0%
+and we are mostly seniors um we made a
+ 
+
+ align:start position:0%
+and we are mostly seniors um we made a
+game about CER the other team focused on
+
+ align:start position:0%
+game about CER the other team focused on
+ 
+
+ align:start position:0%
+game about CER the other team focused on
+the the younger 8 to 13 and we focused
+
+ align:start position:0%
+the the younger 8 to 13 and we focused
+ 
+
+ align:start position:0%
+the the younger 8 to 13 and we focused
+on a little bit older about 13 and above
+
+ align:start position:0%
+on a little bit older about 13 and above
+ 
+
+ align:start position:0%
+on a little bit older about 13 and above
+so we could have a little bit
+
+ align:start position:0%
+so we could have a little bit
+ 
+
+ align:start position:0%
+so we could have a little bit
+complicated more complicated mechanics
+
+ align:start position:0%
+complicated more complicated mechanics
+ 
+
+ align:start position:0%
+complicated more complicated mechanics
+and uh texts where we needed it so that
+
+ align:start position:0%
+and uh texts where we needed it so that
+ 
+
+ align:start position:0%
+and uh texts where we needed it so that
+we didn't really have to rely on
+
+ align:start position:0%
+we didn't really have to rely on
+ 
+
+ align:start position:0%
+we didn't really have to rely on
+figuring out how to make everything
+
+ align:start position:0%
+figuring out how to make everything
+ 
+
+ align:start position:0%
+figuring out how to make everything
+really easy to read so you know it uses
+
+ align:start position:0%
+really easy to read so you know it uses
+ 
+
+ align:start position:0%
+really easy to read so you know it uses
+English that assume someone who speaks
+
+ align:start position:0%
+English that assume someone who speaks
+ 
+
+ align:start position:0%
+English that assume someone who speaks
+English could read and understand very
+
+ align:start position:0%
+English could read and understand very
+ 
+
+ align:start position:0%
+English could read and understand very
+easily um and our game's a strategy game
+
+ align:start position:0%
+easily um and our game's a strategy game
+ 
+
+ align:start position:0%
+easily um and our game's a strategy game
+it's it's real time where you know the
+
+ align:start position:0%
+it's it's real time where you know the
+ 
+
+ align:start position:0%
+it's it's real time where you know the
+days are like you have to survive a year
+
+ align:start position:0%
+days are like you have to survive a year
+ 
+
+ align:start position:0%
+days are like you have to survive a year
+and the days are automatic so you have
+
+ align:start position:0%
+and the days are automatic so you have
+ 
+
+ align:start position:0%
+and the days are automatic so you have
+to go and uh take care of four different
+
+ align:start position:0%
+to go and uh take care of four different
+ 
+
+ align:start position:0%
+to go and uh take care of four different
+localities and give them either soap or
+
+ align:start position:0%
+localities and give them either soap or
+ 
+
+ align:start position:0%
+localities and give them either soap or
+water containers or electrolytes to help
+
+ align:start position:0%
+water containers or electrolytes to help
+ 
+
+ align:start position:0%
+water containers or electrolytes to help
+heal them and later on you get boiling
+
+ align:start position:0%
+heal them and later on you get boiling
+ 
+
+ align:start position:0%
+heal them and later on you get boiling
+water and you just have to you know take
+
+ align:start position:0%
+water and you just have to you know take
+ 
+
+ align:start position:0%
+water and you just have to you know take
+care of these four localities for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+year so we learned you know early on in
+
+ align:start position:0%
+year so we learned you know early on in
+ 
+
+ align:start position:0%
+year so we learned you know early on in
+the class you start by your first
+
+ align:start position:0%
+the class you start by your first
+ 
+
+ align:start position:0%
+the class you start by your first
+project is just a paper prototype and
+
+ align:start position:0%
+project is just a paper prototype and
+ 
+
+ align:start position:0%
+project is just a paper prototype and
+then after you have to make digital
+
+ align:start position:0%
+then after you have to make digital
+ 
+
+ align:start position:0%
+then after you have to make digital
+prototypes but they usually expect you
+
+ align:start position:0%
+prototypes but they usually expect you
+ 
+
+ align:start position:0%
+prototypes but they usually expect you
+to have a paper prototype and for this
+
+ align:start position:0%
+to have a paper prototype and for this
+ 
+
+ align:start position:0%
+to have a paper prototype and for this
+one they expected you to do you know
+
+ align:start position:0%
+one they expected you to do you know
+ 
+
+ align:start position:0%
+one they expected you to do you know
+however you wanted to and so we started
+
+ align:start position:0%
+however you wanted to and so we started
+ 
+
+ align:start position:0%
+however you wanted to and so we started
+off with a paper prototype and we sort
+
+ align:start position:0%
+off with a paper prototype and we sort
+ 
+
+ align:start position:0%
+off with a paper prototype and we sort
+of then quickly implemented it digitally
+
+ align:start position:0%
+of then quickly implemented it digitally
+ 
+
+ align:start position:0%
+of then quickly implemented it digitally
+because there were certain things that
+
+ align:start position:0%
+because there were certain things that
+ 
+
+ align:start position:0%
+because there were certain things that
+doing it with paper would take a long
+
+ align:start position:0%
+doing it with paper would take a long
+ 
+
+ align:start position:0%
+doing it with paper would take a long
+time to sort of make a calculation but
+
+ align:start position:0%
+time to sort of make a calculation but
+ 
+
+ align:start position:0%
+time to sort of make a calculation but
+uh we originally had like part of it was
+
+ align:start position:0%
+uh we originally had like part of it was
+ 
+
+ align:start position:0%
+uh we originally had like part of it was
+you could see on the screen what the
+
+ align:start position:0%
+you could see on the screen what the
+ 
+
+ align:start position:0%
+you could see on the screen what the
+localities where they were and then you
+
+ align:start position:0%
+localities where they were and then you
+ 
+
+ align:start position:0%
+localities where they were and then you
+would try to implement things but we
+
+ align:start position:0%
+would try to implement things but we
+ 
+
+ align:start position:0%
+would try to implement things but we
+didn't like have a screen to help you
+
+ align:start position:0%
+didn't like have a screen to help you
+ 
+
+ align:start position:0%
+didn't like have a screen to help you
+select that and so we would sort of like
+
+ align:start position:0%
+select that and so we would sort of like
+ 
+
+ align:start position:0%
+select that and so we would sort of like
+you tell us what you pick and then we
+
+ align:start position:0%
+you tell us what you pick and then we
+ 
+
+ align:start position:0%
+you tell us what you pick and then we
+quickly put it in the game and said it
+
+ align:start position:0%
+quickly put it in the game and said it
+ 
+
+ align:start position:0%
+quickly put it in the game and said it
+and so that's what we originally did and
+
+ align:start position:0%
+and so that's what we originally did and
+ 
+
+ align:start position:0%
+and so that's what we originally did and
+it was really hard to do it that way
+
+ align:start position:0%
+it was really hard to do it that way
+ 
+
+ align:start position:0%
+it was really hard to do it that way
+because people like going from the
+
+ align:start position:0%
+because people like going from the
+ 
+
+ align:start position:0%
+because people like going from the
+screen to a paper prototype they were
+
+ align:start position:0%
+screen to a paper prototype they were
+ 
+
+ align:start position:0%
+screen to a paper prototype they were
+confused and they didn't really see how
+
+ align:start position:0%
+confused and they didn't really see how
+ 
+
+ align:start position:0%
+confused and they didn't really see how
+things interacted so then we sort of our
+
+ align:start position:0%
+things interacted so then we sort of our
+ 
+
+ align:start position:0%
+things interacted so then we sort of our
+next big thing was make it all
+
+ align:start position:0%
+next big thing was make it all
+ 
+
+ align:start position:0%
+next big thing was make it all
+digital and in the presentation that you
+
+ align:start position:0%
+digital and in the presentation that you
+ 
+
+ align:start position:0%
+digital and in the presentation that you
+saw you know we had that original shot
+
+ align:start position:0%
+saw you know we had that original shot
+ 
+
+ align:start position:0%
+saw you know we had that original shot
+of the what the game looked like when we
+
+ align:start position:0%
+of the what the game looked like when we
+ 
+
+ align:start position:0%
+of the what the game looked like when we
+had it all digital and it was just like
+
+ align:start position:0%
+had it all digital and it was just like
+ 
+
+ align:start position:0%
+had it all digital and it was just like
+a really poorly designed gooey and it
+
+ align:start position:0%
+a really poorly designed gooey and it
+ 
+
+ align:start position:0%
+a really poorly designed gooey and it
+was hard to read and hard to understand
+
+ align:start position:0%
+was hard to read and hard to understand
+ 
+
+ align:start position:0%
+was hard to read and hard to understand
+and people were really struggling with
+
+ align:start position:0%
+and people were really struggling with
+ 
+
+ align:start position:0%
+and people were really struggling with
+it so I actually was the one who
+
+ align:start position:0%
+it so I actually was the one who
+ 
+
+ align:start position:0%
+it so I actually was the one who
+redesigned the guey and then it went
+
+ align:start position:0%
+redesigned the guey and then it went
+ 
+
+ align:start position:0%
+redesigned the guey and then it went
+through a couple iterations with the new
+
+ align:start position:0%
+through a couple iterations with the new
+ 
+
+ align:start position:0%
+through a couple iterations with the new
+guy so we decided how to make it the
+
+ align:start position:0%
+guy so we decided how to make it the
+ 
+
+ align:start position:0%
+guy so we decided how to make it the
+most clear and I mostly um I sat down
+
+ align:start position:0%
+most clear and I mostly um I sat down
+ 
+
+ align:start position:0%
+most clear and I mostly um I sat down
+and I looked at other strategy games
+
+ align:start position:0%
+and I looked at other strategy games
+ 
+
+ align:start position:0%
+and I looked at other strategy games
+mostly civilization um because I'm
+
+ align:start position:0%
+mostly civilization um because I'm
+ 
+
+ align:start position:0%
+mostly civilization um because I'm
+actually not a big strategy like game
+
+ align:start position:0%
+actually not a big strategy like game
+ 
+
+ align:start position:0%
+actually not a big strategy like game
+player so I actually had to go like look
+
+ align:start position:0%
+player so I actually had to go like look
+ 
+
+ align:start position:0%
+player so I actually had to go like look
+around see what other places do and I
+
+ align:start position:0%
+around see what other places do and I
+ 
+
+ align:start position:0%
+around see what other places do and I
+stole a little bit from civilization and
+
+ align:start position:0%
+stole a little bit from civilization and
+ 
+
+ align:start position:0%
+stole a little bit from civilization and
+a few other games that just had good
+
+ align:start position:0%
+a few other games that just had good
+ 
+
+ align:start position:0%
+a few other games that just had good
+elements of design that look clear and
+
+ align:start position:0%
+elements of design that look clear and
+ 
+
+ align:start position:0%
+elements of design that look clear and
+understandable even to someone who's
+
+ align:start position:0%
+understandable even to someone who's
+ 
+
+ align:start position:0%
+understandable even to someone who's
+never touched the game before and so
+
+ align:start position:0%
+never touched the game before and so
+ 
+
+ align:start position:0%
+never touched the game before and so
+that's what I wanted in our game so
+
+ align:start position:0%
+that's what I wanted in our game so
+ 
+
+ align:start position:0%
+that's what I wanted in our game so
+that's why we implemented it the way we
+
+ align:start position:0%
+that's why we implemented it the way we
+ 
+
+ align:start position:0%
+that's why we implemented it the way we
+did and yeah and then the game kind of
+
+ align:start position:0%
+did and yeah and then the game kind of
+ 
+
+ align:start position:0%
+did and yeah and then the game kind of
+turned into the way it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now so one of the biggest things is I'm
+
+ align:start position:0%
+now so one of the biggest things is I'm
+ 
+
+ align:start position:0%
+now so one of the biggest things is I'm
+not a programmer so I was doing either
+
+ align:start position:0%
+not a programmer so I was doing either
+ 
+
+ align:start position:0%
+not a programmer so I was doing either
+design or product management or you know
+
+ align:start position:0%
+design or product management or you know
+ 
+
+ align:start position:0%
+design or product management or you know
+this scrum Master is what they call it
+
+ align:start position:0%
+this scrum Master is what they call it
+ 
+
+ align:start position:0%
+this scrum Master is what they call it
+which is someone who sort of has to like
+
+ align:start position:0%
+which is someone who sort of has to like
+ 
+
+ align:start position:0%
+which is someone who sort of has to like
+take care of the team and make
+
+ align:start position:0%
+take care of the team and make
+ 
+
+ align:start position:0%
+take care of the team and make
+everything fit together whether it's
+
+ align:start position:0%
+everything fit together whether it's
+ 
+
+ align:start position:0%
+everything fit together whether it's
+with like including art and music and
+
+ align:start position:0%
+with like including art and music and
+ 
+
+ align:start position:0%
+with like including art and music and
+you coding making sure all those
+
+ align:start position:0%
+you coding making sure all those
+ 
+
+ align:start position:0%
+you coding making sure all those
+elements fit together into one cohesive
+
+ align:start position:0%
+elements fit together into one cohesive
+ 
+
+ align:start position:0%
+elements fit together into one cohesive
+hole and so that's sort of the role that
+
+ align:start position:0%
+hole and so that's sort of the role that
+ 
+
+ align:start position:0%
+hole and so that's sort of the role that
+I started to do and then really liked
+
+ align:start position:0%
+I started to do and then really liked
+ 
+
+ align:start position:0%
+I started to do and then really liked
+doing at first I thought you know oh and
+
+ align:start position:0%
+doing at first I thought you know oh and
+ 
+
+ align:start position:0%
+doing at first I thought you know oh and
+some of these projects I should take on
+
+ align:start position:0%
+some of these projects I should take on
+ 
+
+ align:start position:0%
+some of these projects I should take on
+a coding role to try to force myself to
+
+ align:start position:0%
+a coding role to try to force myself to
+ 
+
+ align:start position:0%
+a coding role to try to force myself to
+learn but I felt like I realized I
+
+ align:start position:0%
+learn but I felt like I realized I
+ 
+
+ align:start position:0%
+learn but I felt like I realized I
+didn't really want to I really liked
+
+ align:start position:0%
+didn't really want to I really liked
+ 
+
+ align:start position:0%
+didn't really want to I really liked
+doing this Ro instead but you learn that
+
+ align:start position:0%
+doing this Ro instead but you learn that
+ 
+
+ align:start position:0%
+doing this Ro instead but you learn that
+it's really hard especially in a class
+
+ align:start position:0%
+it's really hard especially in a class
+ 
+
+ align:start position:0%
+it's really hard especially in a class
+setting where people aren't really tied
+
+ align:start position:0%
+setting where people aren't really tied
+ 
+
+ align:start position:0%
+setting where people aren't really tied
+like monetarily to this class you can't
+
+ align:start position:0%
+like monetarily to this class you can't
+ 
+
+ align:start position:0%
+like monetarily to this class you can't
+lose your job if you don't do your job
+
+ align:start position:0%
+lose your job if you don't do your job
+ 
+
+ align:start position:0%
+lose your job if you don't do your job
+you can do poorly in the class but
+
+ align:start position:0%
+you can do poorly in the class but
+ 
+
+ align:start position:0%
+you can do poorly in the class but
+because it's the group thing you know
+
+ align:start position:0%
+because it's the group thing you know
+ 
+
+ align:start position:0%
+because it's the group thing you know
+you might not do that poorly because the
+
+ align:start position:0%
+you might not do that poorly because the
+ 
+
+ align:start position:0%
+you might not do that poorly because the
+group presented like this is our game
+
+ align:start position:0%
+group presented like this is our game
+ 
+
+ align:start position:0%
+group presented like this is our game
+and so unless you specifically call out
+
+ align:start position:0%
+and so unless you specifically call out
+ 
+
+ align:start position:0%
+and so unless you specifically call out
+that person they're still going to get
+
+ align:start position:0%
+that person they're still going to get
+ 
+
+ align:start position:0%
+that person they're still going to get
+credit for it and so it was really
+
+ align:start position:0%
+credit for it and so it was really
+ 
+
+ align:start position:0%
+credit for it and so it was really
+difficult as the product manager to get
+
+ align:start position:0%
+difficult as the product manager to get
+ 
+
+ align:start position:0%
+difficult as the product manager to get
+people to do what they said they were
+
+ align:start position:0%
+people to do what they said they were
+ 
+
+ align:start position:0%
+people to do what they said they were
+going to do in a timely manner and get
+
+ align:start position:0%
+going to do in a timely manner and get
+ 
+
+ align:start position:0%
+going to do in a timely manner and get
+people to respond to my emails and so it
+
+ align:start position:0%
+people to respond to my emails and so it
+ 
+
+ align:start position:0%
+people to respond to my emails and so it
+was really something that you have to
+
+ align:start position:0%
+was really something that you have to
+ 
+
+ align:start position:0%
+was really something that you have to
+get people to understand especially
+
+ align:start position:0%
+get people to understand especially
+ 
+
+ align:start position:0%
+get people to understand especially
+towards the end where we didn't have a
+
+ align:start position:0%
+towards the end where we didn't have a
+ 
+
+ align:start position:0%
+towards the end where we didn't have a
+lot done and we needed to change a lot
+
+ align:start position:0%
+lot done and we needed to change a lot
+ 
+
+ align:start position:0%
+lot done and we needed to change a lot
+that you know there's not a lot of time
+
+ align:start position:0%
+that you know there's not a lot of time
+ 
+
+ align:start position:0%
+that you know there's not a lot of time
+and there's still a lot to do and and
+
+ align:start position:0%
+and there's still a lot to do and and
+ 
+
+ align:start position:0%
+and there's still a lot to do and and
+then when I finally got everyone in a
+
+ align:start position:0%
+then when I finally got everyone in a
+ 
+
+ align:start position:0%
+then when I finally got everyone in a
+meeting and they all sat down and we
+
+ align:start position:0%
+meeting and they all sat down and we
+ 
+
+ align:start position:0%
+meeting and they all sat down and we
+talked about this like everyone you just
+
+ align:start position:0%
+talked about this like everyone you just
+ 
+
+ align:start position:0%
+talked about this like everyone you just
+heard it like oh that's when that's due
+
+ align:start position:0%
+heard it like oh that's when that's due
+ 
+
+ align:start position:0%
+heard it like oh that's when that's due
+so you know I finally got people in gear
+
+ align:start position:0%
+so you know I finally got people in gear
+ 
+
+ align:start position:0%
+so you know I finally got people in gear
+and so I wish I could have done this
+
+ align:start position:0%
+and so I wish I could have done this
+ 
+
+ align:start position:0%
+and so I wish I could have done this
+earlier in the semester um with just
+
+ align:start position:0%
+earlier in the semester um with just
+ 
+
+ align:start position:0%
+earlier in the semester um with just
+this project with the other project it
+
+ align:start position:0%
+this project with the other project it
+ 
+
+ align:start position:0%
+this project with the other project it
+was it people didn't usually fall into
+
+ align:start position:0%
+was it people didn't usually fall into
+ 
+
+ align:start position:0%
+was it people didn't usually fall into
+that trap as much because it was only
+
+ align:start position:0%
+that trap as much because it was only
+ 
+
+ align:start position:0%
+that trap as much because it was only
+two weeks so you know two weeks doesn't
+
+ align:start position:0%
+two weeks so you know two weeks doesn't
+ 
+
+ align:start position:0%
+two weeks so you know two weeks doesn't
+give you a lot of time to fail you got
+
+ align:start position:0%
+give you a lot of time to fail you got
+ 
+
+ align:start position:0%
+give you a lot of time to fail you got
+to do it quickly and but when it was 8
+
+ align:start position:0%
+to do it quickly and but when it was 8
+ 
+
+ align:start position:0%
+to do it quickly and but when it was 8
+weeks it was a lot of time and so people
+
+ align:start position:0%
+weeks it was a lot of time and so people
+ 
+
+ align:start position:0%
+weeks it was a lot of time and so people
+are like oh we can push this off a
+
+ align:start position:0%
+are like oh we can push this off a
+ 
+
+ align:start position:0%
+are like oh we can push this off a
+little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+further like it was really hard I
+
+ align:start position:0%
+further like it was really hard I
+ 
+
+ align:start position:0%
+further like it was really hard I
+actually ended up having um I talked to
+
+ align:start position:0%
+actually ended up having um I talked to
+ 
+
+ align:start position:0%
+actually ended up having um I talked to
+the professors to try to figure out a
+
+ align:start position:0%
+the professors to try to figure out a
+ 
+
+ align:start position:0%
+the professors to try to figure out a
+way to get my team to listen to me and
+
+ align:start position:0%
+way to get my team to listen to me and
+ 
+
+ align:start position:0%
+way to get my team to listen to me and
+it was still really hard but once you
+
+ align:start position:0%
+it was still really hard but once you
+ 
+
+ align:start position:0%
+it was still really hard but once you
+finally get everyone together and really
+
+ align:start position:0%
+finally get everyone together and really
+ 
+
+ align:start position:0%
+finally get everyone together and really
+lay it out very clearly I like the
+
+ align:start position:0%
+lay it out very clearly I like the
+ 
+
+ align:start position:0%
+lay it out very clearly I like the
+clarity is what I was missing I thought
+
+ align:start position:0%
+clarity is what I was missing I thought
+ 
+
+ align:start position:0%
+clarity is what I was missing I thought
+I was being very like clear and like
+
+ align:start position:0%
+I was being very like clear and like
+ 
+
+ align:start position:0%
+I was being very like clear and like
+this is how things would do and even
+
+ align:start position:0%
+this is how things would do and even
+ 
+
+ align:start position:0%
+this is how things would do and even
+with the way I was assigning tasks I
+
+ align:start position:0%
+with the way I was assigning tasks I
+ 
+
+ align:start position:0%
+with the way I was assigning tasks I
+thought I was being very clear and I
+
+ align:start position:0%
+thought I was being very clear and I
+ 
+
+ align:start position:0%
+thought I was being very clear and I
+wasn't I was
+
+ align:start position:0%
+wasn't I was
+ 
+
+ align:start position:0%
+wasn't I was
+really missing concrete details I said
+
+ align:start position:0%
+really missing concrete details I said
+ 
+
+ align:start position:0%
+really missing concrete details I said
+You know guys like uh implement this
+
+ align:start position:0%
+You know guys like uh implement this
+ 
+
+ align:start position:0%
+You know guys like uh implement this
+idea like Implement that you can like
+
+ align:start position:0%
+idea like Implement that you can like
+ 
+
+ align:start position:0%
+idea like Implement that you can like
+take the actions but I didn't tell them
+
+ align:start position:0%
+take the actions but I didn't tell them
+ 
+
+ align:start position:0%
+take the actions but I didn't tell them
+this is how it should look this is how
+
+ align:start position:0%
+this is how it should look this is how
+ 
+
+ align:start position:0%
+this is how it should look this is how
+it should feel and so when it got
+
+ align:start position:0%
+it should feel and so when it got
+ 
+
+ align:start position:0%
+it should feel and so when it got
+implemented it wasn't what I thought it
+
+ align:start position:0%
+implemented it wasn't what I thought it
+ 
+
+ align:start position:0%
+implemented it wasn't what I thought it
+was I'm like this is really
+
+ align:start position:0%
+was I'm like this is really
+ 
+
+ align:start position:0%
+was I'm like this is really
+disappointing this is really ugly and so
+
+ align:start position:0%
+disappointing this is really ugly and so
+ 
+
+ align:start position:0%
+disappointing this is really ugly and so
+when I sat down and redid it and then
+
+ align:start position:0%
+when I sat down and redid it and then
+ 
+
+ align:start position:0%
+when I sat down and redid it and then
+told them exactly what I expected things
+
+ align:start position:0%
+told them exactly what I expected things
+ 
+
+ align:start position:0%
+told them exactly what I expected things
+got done faster because it Le like like
+
+ align:start position:0%
+got done faster because it Le like like
+ 
+
+ align:start position:0%
+got done faster because it Le like like
+we said in our presentation people
+
+ align:start position:0%
+we said in our presentation people
+ 
+
+ align:start position:0%
+we said in our presentation people
+weren't really motivated for this game
+
+ align:start position:0%
+weren't really motivated for this game
+ 
+
+ align:start position:0%
+weren't really motivated for this game
+and so having the motivation and really
+
+ align:start position:0%
+and so having the motivation and really
+ 
+
+ align:start position:0%
+and so having the motivation and really
+vague instructions made it that people
+
+ align:start position:0%
+vague instructions made it that people
+ 
+
+ align:start position:0%
+vague instructions made it that people
+wouldn't do it until like you know you
+
+ align:start position:0%
+wouldn't do it until like you know you
+ 
+
+ align:start position:0%
+wouldn't do it until like you know you
+put that off like that's a really hard
+
+ align:start position:0%
+put that off like that's a really hard
+ 
+
+ align:start position:0%
+put that off like that's a really hard
+task I need to figure out what she
+
+ align:start position:0%
+task I need to figure out what she
+ 
+
+ align:start position:0%
+task I need to figure out what she
+expects and then I need to do it and I
+
+ align:start position:0%
+expects and then I need to do it and I
+ 
+
+ align:start position:0%
+expects and then I need to do it and I
+don't really want to so that's something
+
+ align:start position:0%
+don't really want to so that's something
+ 
+
+ align:start position:0%
+don't really want to so that's something
+you put off to the end and so when you
+
+ align:start position:0%
+you put off to the end and so when you
+ 
+
+ align:start position:0%
+you put off to the end and so when you
+give people clearer
+
+ align:start position:0%
+give people clearer
+ 
+
+ align:start position:0%
+give people clearer
+instructions it makes it easier just to
+
+ align:start position:0%
+instructions it makes it easier just to
+ 
+
+ align:start position:0%
+instructions it makes it easier just to
+do it because they're like oh like
+
+ align:start position:0%
+do it because they're like oh like
+ 
+
+ align:start position:0%
+do it because they're like oh like
+that's simple I can do that really
+
+ align:start position:0%
+that's simple I can do that really
+ 
+
+ align:start position:0%
+that's simple I can do that really
+quickly and so I think that was the
+
+ align:start position:0%
+quickly and so I think that was the
+ 
+
+ align:start position:0%
+quickly and so I think that was the
+easiest way is when you really set clear
+
+ align:start position:0%
+easiest way is when you really set clear
+ 
+
+ align:start position:0%
+easiest way is when you really set clear
+instructions clear
+
+ align:start position:0%
+instructions clear
+ 
+
+ align:start position:0%
+instructions clear
+deadlines and
+
+ align:start position:0%
+deadlines and
+ 
+
+ align:start position:0%
+deadlines and
+you can't really punish people there's
+
+ align:start position:0%
+you can't really punish people there's
+ 
+
+ align:start position:0%
+you can't really punish people there's
+no way of slapping them on the wrist
+
+ align:start position:0%
+no way of slapping them on the wrist
+ 
+
+ align:start position:0%
+no way of slapping them on the wrist
+when they don't do it but you can just
+
+ align:start position:0%
+when they don't do it but you can just
+ 
+
+ align:start position:0%
+when they don't do it but you can just
+not assign them work and you move it to
+
+ align:start position:0%
+not assign them work and you move it to
+ 
+
+ align:start position:0%
+not assign them work and you move it to
+somebody else and eventually people
+
+ align:start position:0%
+somebody else and eventually people
+ 
+
+ align:start position:0%
+somebody else and eventually people
+realize that they weren't getting
+
+ align:start position:0%
+realize that they weren't getting
+ 
+
+ align:start position:0%
+realize that they weren't getting
+assigned any work and they realized like
+
+ align:start position:0%
+assigned any work and they realized like
+ 
+
+ align:start position:0%
+assigned any work and they realized like
+hey I'm not actually doing anything for
+
+ align:start position:0%
+hey I'm not actually doing anything for
+ 
+
+ align:start position:0%
+hey I'm not actually doing anything for
+this can I have work and they said you
+
+ align:start position:0%
+this can I have work and they said you
+ 
+
+ align:start position:0%
+this can I have work and they said you
+know you have to do it by this time and
+
+ align:start position:0%
+know you have to do it by this time and
+ 
+
+ align:start position:0%
+know you have to do it by this time and
+if you don't then you know we're pretty
+
+ align:start position:0%
+if you don't then you know we're pretty
+ 
+
+ align:start position:0%
+if you don't then you know we're pretty
+screwed so uh really doing that really
+
+ align:start position:0%
+screwed so uh really doing that really
+ 
+
+ align:start position:0%
+screwed so uh really doing that really
+making sure you've cleared deadlines and
+
+ align:start position:0%
+making sure you've cleared deadlines and
+ 
+
+ align:start position:0%
+making sure you've cleared deadlines and
+Shifting the work around so that people
+
+ align:start position:0%
+Shifting the work around so that people
+ 
+
+ align:start position:0%
+Shifting the work around so that people
+who will do the work and can do the work
+
+ align:start position:0%
+who will do the work and can do the work
+ 
+
+ align:start position:0%
+who will do the work and can do the work
+and have the time to do work are getting
+
+ align:start position:0%
+and have the time to do work are getting
+ 
+
+ align:start position:0%
+and have the time to do work are getting
+the work and the people who either just
+
+ align:start position:0%
+the work and the people who either just
+ 
+
+ align:start position:0%
+the work and the people who either just
+aren't doing the work or maybe don't
+
+ align:start position:0%
+aren't doing the work or maybe don't
+ 
+
+ align:start position:0%
+aren't doing the work or maybe don't
+have the time that week cuz that also
+
+ align:start position:0%
+have the time that week cuz that also
+ 
+
+ align:start position:0%
+have the time that week cuz that also
+happens where like one week will be
+
+ align:start position:0%
+happens where like one week will be
+ 
+
+ align:start position:0%
+happens where like one week will be
+really tough so you shift the work away
+
+ align:start position:0%
+really tough so you shift the work away
+ 
+
+ align:start position:0%
+really tough so you shift the work away
+from them so you have to be better about
+
+ align:start position:0%
+from them so you have to be better about
+ 
+
+ align:start position:0%
+from them so you have to be better about
+I I think I if if I started being better
+
+ align:start position:0%
+I I think I if if I started being better
+ 
+
+ align:start position:0%
+I I think I if if I started being better
+about how I gave assigned work rather
+
+ align:start position:0%
+about how I gave assigned work rather
+ 
+
+ align:start position:0%
+about how I gave assigned work rather
+than just you know evenly dividing it uh
+
+ align:start position:0%
+than just you know evenly dividing it uh
+ 
+
+ align:start position:0%
+than just you know evenly dividing it uh
+that really would help with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+project so working with the client was
+
+ align:start position:0%
+project so working with the client was
+ 
+
+ align:start position:0%
+project so working with the client was
+hard cuz he was unavailable a lot and
+
+ align:start position:0%
+hard cuz he was unavailable a lot and
+ 
+
+ align:start position:0%
+hard cuz he was unavailable a lot and
+you know his he he the times he did come
+
+ align:start position:0%
+you know his he he the times he did come
+ 
+
+ align:start position:0%
+you know his he he the times he did come
+to class he said uh you know if you have
+
+ align:start position:0%
+to class he said uh you know if you have
+ 
+
+ align:start position:0%
+to class he said uh you know if you have
+to email me a question it better be
+
+ align:start position:0%
+to email me a question it better be
+ 
+
+ align:start position:0%
+to email me a question it better be
+really clear concise or like we're not
+
+ align:start position:0%
+really clear concise or like we're not
+ 
+
+ align:start position:0%
+really clear concise or like we're not
+going to answer it and so luckily in the
+
+ align:start position:0%
+going to answer it and so luckily in the
+ 
+
+ align:start position:0%
+going to answer it and so luckily in the
+beginning we kind of knew what we wanted
+
+ align:start position:0%
+beginning we kind of knew what we wanted
+ 
+
+ align:start position:0%
+beginning we kind of knew what we wanted
+to do with our game and so we just kind
+
+ align:start position:0%
+to do with our game and so we just kind
+ 
+
+ align:start position:0%
+to do with our game and so we just kind
+of went in that direction and then
+
+ align:start position:0%
+of went in that direction and then
+ 
+
+ align:start position:0%
+of went in that direction and then
+whenever Pablo came into class Pablo was
+
+ align:start position:0%
+whenever Pablo came into class Pablo was
+ 
+
+ align:start position:0%
+whenever Pablo came into class Pablo was
+our main client we also had Ellie but
+
+ align:start position:0%
+our main client we also had Ellie but
+ 
+
+ align:start position:0%
+our main client we also had Ellie but
+she was only in class A couple times and
+
+ align:start position:0%
+she was only in class A couple times and
+ 
+
+ align:start position:0%
+she was only in class A couple times and
+so we didn't get as much feedback from
+
+ align:start position:0%
+so we didn't get as much feedback from
+ 
+
+ align:start position:0%
+so we didn't get as much feedback from
+her so uh whenever Pablo came into class
+
+ align:start position:0%
+her so uh whenever Pablo came into class
+ 
+
+ align:start position:0%
+her so uh whenever Pablo came into class
+he told us what we needed to fix and
+
+ align:start position:0%
+he told us what we needed to fix and
+ 
+
+ align:start position:0%
+he told us what we needed to fix and
+that was the big biggest uh the biggest
+
+ align:start position:0%
+that was the big biggest uh the biggest
+ 
+
+ align:start position:0%
+that was the big biggest uh the biggest
+interaction with him that we had uh it
+
+ align:start position:0%
+interaction with him that we had uh it
+ 
+
+ align:start position:0%
+interaction with him that we had uh it
+was really at first we didn't really
+
+ align:start position:0%
+was really at first we didn't really
+ 
+
+ align:start position:0%
+was really at first we didn't really
+know who to design it for because they
+
+ align:start position:0%
+know who to design it for because they
+ 
+
+ align:start position:0%
+know who to design it for because they
+said you know we need a caller we need
+
+ align:start position:0%
+said you know we need a caller we need
+ 
+
+ align:start position:0%
+said you know we need a caller we need
+two caller games for everybody and so we
+
+ align:start position:0%
+two caller games for everybody and so we
+ 
+
+ align:start position:0%
+two caller games for everybody and so we
+were really unsure and so finally like
+
+ align:start position:0%
+were really unsure and so finally like
+ 
+
+ align:start position:0%
+were really unsure and so finally like
+three or four weeks into the project we
+
+ align:start position:0%
+three or four weeks into the project we
+ 
+
+ align:start position:0%
+three or four weeks into the project we
+sat down like we talked to the other
+
+ align:start position:0%
+sat down like we talked to the other
+ 
+
+ align:start position:0%
+sat down like we talked to the other
+caller team and said what are you doing
+
+ align:start position:0%
+caller team and said what are you doing
+ 
+
+ align:start position:0%
+caller team and said what are you doing
+cuz we're going to do the opposite so
+
+ align:start position:0%
+cuz we're going to do the opposite so
+ 
+
+ align:start position:0%
+cuz we're going to do the opposite so
+because they wanted two games that would
+
+ align:start position:0%
+because they wanted two games that would
+ 
+
+ align:start position:0%
+because they wanted two games that would
+be for different groups and so then we
+
+ align:start position:0%
+be for different groups and so then we
+ 
+
+ align:start position:0%
+be for different groups and so then we
+did that we talked to Pablo the next
+
+ align:start position:0%
+did that we talked to Pablo the next
+ 
+
+ align:start position:0%
+did that we talked to Pablo the next
+time he came in and he said yes this is
+
+ align:start position:0%
+time he came in and he said yes this is
+ 
+
+ align:start position:0%
+time he came in and he said yes this is
+what I want so luckily we managed to
+
+ align:start position:0%
+what I want so luckily we managed to
+ 
+
+ align:start position:0%
+what I want so luckily we managed to
+guess what he wanted it could have gone
+
+ align:start position:0%
+guess what he wanted it could have gone
+ 
+
+ align:start position:0%
+guess what he wanted it could have gone
+worse if we did something that he didn't
+
+ align:start position:0%
+worse if we did something that he didn't
+ 
+
+ align:start position:0%
+worse if we did something that he didn't
+wanted so if that had happened and he
+
+ align:start position:0%
+wanted so if that had happened and he
+ 
+
+ align:start position:0%
+wanted so if that had happened and he
+said you know you guys are really going
+
+ align:start position:0%
+said you know you guys are really going
+ 
+
+ align:start position:0%
+said you know you guys are really going
+in the wrong direction I think we would
+
+ align:start position:0%
+in the wrong direction I think we would
+ 
+
+ align:start position:0%
+in the wrong direction I think we would
+have like made sure to email him more
+
+ align:start position:0%
+have like made sure to email him more
+ 
+
+ align:start position:0%
+have like made sure to email him more
+but most of the time he's like I like
+
+ align:start position:0%
+but most of the time he's like I like
+ 
+
+ align:start position:0%
+but most of the time he's like I like
+the direction you're going you just need
+
+ align:start position:0%
+the direction you're going you just need
+ 
+
+ align:start position:0%
+the direction you're going you just need
+to fix these sorts of things so that's
+
+ align:start position:0%
+to fix these sorts of things so that's
+ 
+
+ align:start position:0%
+to fix these sorts of things so that's
+so that's what we did
\ No newline at end of file
diff --git a/OjhZYx1FbhI.txt b/OjhZYx1FbhI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3478d592543ba4d51672245c5050db768f06b0a1
--- /dev/null
+++ b/OjhZYx1FbhI.txt
@@ -0,0 +1,4955 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right so now we're going
+
+ align:start position:0%
+ocw.mit.edu all right so now we're going
+ 
+
+ align:start position:0%
+ocw.mit.edu all right so now we're going
+to move on to talk about um spontaneous
+
+ align:start position:0%
+to move on to talk about um spontaneous
+ 
+
+ align:start position:0%
+to move on to talk about um spontaneous
+change and so this is today's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+handout so spontaneous reaction is a
+
+ align:start position:0%
+handout so spontaneous reaction is a
+ 
+
+ align:start position:0%
+handout so spontaneous reaction is a
+reaction that proceeds in the forward
+
+ align:start position:0%
+reaction that proceeds in the forward
+ 
+
+ align:start position:0%
+reaction that proceeds in the forward
+Direction without any kind of outside
+
+ align:start position:0%
+Direction without any kind of outside
+ 
+
+ align:start position:0%
+Direction without any kind of outside
+intervention like heat being added for
+
+ align:start position:0%
+intervention like heat being added for
+ 
+
+ align:start position:0%
+intervention like heat being added for
+example it just it just
+
+ align:start position:0%
+example it just it just
+ 
+
+ align:start position:0%
+example it just it just
+goes in that in that in that
+
+ align:start position:0%
+goes in that in that in that
+ 
+
+ align:start position:0%
+goes in that in that in that
+Direction okay so um so we can talk
+
+ align:start position:0%
+Direction okay so um so we can talk
+ 
+
+ align:start position:0%
+Direction okay so um so we can talk
+about reactions following reactions are
+
+ align:start position:0%
+about reactions following reactions are
+ 
+
+ align:start position:0%
+about reactions following reactions are
+spontaneous at constant
+
+ align:start position:0%
+spontaneous at constant
+ 
+
+ align:start position:0%
+spontaneous at constant
+pressure and we'll see later that
+
+ align:start position:0%
+pressure and we'll see later that
+ 
+
+ align:start position:0%
+pressure and we'll see later that
+temperature can make a difference
+
+ align:start position:0%
+temperature can make a difference
+ 
+
+ align:start position:0%
+temperature can make a difference
+between whether something spontaneous or
+
+ align:start position:0%
+between whether something spontaneous or
+ 
+
+ align:start position:0%
+between whether something spontaneous or
+not but constant pressure here is an
+
+ align:start position:0%
+not but constant pressure here is an
+ 
+
+ align:start position:0%
+not but constant pressure here is an
+example iron plus oxygen and uh what is
+
+ align:start position:0%
+example iron plus oxygen and uh what is
+ 
+
+ align:start position:0%
+example iron plus oxygen and uh what is
+this in layman's term an example
+
+ align:start position:0%
+this in layman's term an example
+ 
+
+ align:start position:0%
+this in layman's term an example
+of rust yes and many of you are probably
+
+ align:start position:0%
+of rust yes and many of you are probably
+ 
+
+ align:start position:0%
+of rust yes and many of you are probably
+aware of this rust is a spontaneous
+
+ align:start position:0%
+aware of this rust is a spontaneous
+ 
+
+ align:start position:0%
+aware of this rust is a spontaneous
+process it's something that people try
+
+ align:start position:0%
+process it's something that people try
+ 
+
+ align:start position:0%
+process it's something that people try
+to do something about you don't want
+
+ align:start position:0%
+to do something about you don't want
+ 
+
+ align:start position:0%
+to do something about you don't want
+your car to rust if you're new to New
+
+ align:start position:0%
+your car to rust if you're new to New
+ 
+
+ align:start position:0%
+your car to rust if you're new to New
+England um and you're from a part of uh
+
+ align:start position:0%
+England um and you're from a part of uh
+ 
+
+ align:start position:0%
+England um and you're from a part of uh
+of the country that doesn't get so cold
+
+ align:start position:0%
+of the country that doesn't get so cold
+ 
+
+ align:start position:0%
+of the country that doesn't get so cold
+um you may not have you look at people's
+
+ align:start position:0%
+um you may not have you look at people's
+ 
+
+ align:start position:0%
+um you may not have you look at people's
+cars and you're like wow look at all
+
+ align:start position:0%
+cars and you're like wow look at all
+ 
+
+ align:start position:0%
+cars and you're like wow look at all
+that rust all over them yes rust happens
+
+ align:start position:0%
+that rust all over them yes rust happens
+ 
+
+ align:start position:0%
+that rust all over them yes rust happens
+especially in New England um and the
+
+ align:start position:0%
+especially in New England um and the
+ 
+
+ align:start position:0%
+especially in New England um and the
+Delta H here is negative is this
+
+ align:start position:0%
+Delta H here is negative is this
+ 
+
+ align:start position:0%
+Delta H here is negative is this
+endothermic or
+
+ align:start position:0%
+endothermic or
+ 
+
+ align:start position:0%
+endothermic or
+exothermic exothermic minus
+
+ align:start position:0%
+exothermic exothermic minus
+ 
+
+ align:start position:0%
+exothermic exothermic minus
+824 okay here is another uh spontaneous
+
+ align:start position:0%
+824 okay here is another uh spontaneous
+ 
+
+ align:start position:0%
+824 okay here is another uh spontaneous
+process this is molecule is
+
+ align:start position:0%
+process this is molecule is
+ 
+
+ align:start position:0%
+process this is molecule is
+ATP and it will hydroly which means
+
+ align:start position:0%
+ATP and it will hydroly which means
+ 
+
+ align:start position:0%
+ATP and it will hydroly which means
+react with water forming ADP so ATP is
+
+ align:start position:0%
+react with water forming ADP so ATP is
+ 
+
+ align:start position:0%
+react with water forming ADP so ATP is
+triphosphate ADP is diphosphate so one
+
+ align:start position:0%
+triphosphate ADP is diphosphate so one
+ 
+
+ align:start position:0%
+triphosphate ADP is diphosphate so one
+of the phosphates and here's the other
+
+ align:start position:0%
+of the phosphates and here's the other
+ 
+
+ align:start position:0%
+of the phosphates and here's the other
+phosphate comes off it hydrolyzes off
+
+ align:start position:0%
+phosphate comes off it hydrolyzes off
+ 
+
+ align:start position:0%
+phosphate comes off it hydrolyzes off
+and uh this is a spontaneous process we
+
+ align:start position:0%
+and uh this is a spontaneous process we
+ 
+
+ align:start position:0%
+and uh this is a spontaneous process we
+have a h we also have a Delta H knot of
+
+ align:start position:0%
+have a h we also have a Delta H knot of
+ 
+
+ align:start position:0%
+have a h we also have a Delta H knot of
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+24 kog per mole and remember when we
+
+ align:start position:0%
+24 kog per mole and remember when we
+ 
+
+ align:start position:0%
+24 kog per mole and remember when we
+oxidize glucose in our body we store
+
+ align:start position:0%
+oxidize glucose in our body we store
+ 
+
+ align:start position:0%
+oxidize glucose in our body we store
+that energy in ATP and we want that ATP
+
+ align:start position:0%
+that energy in ATP and we want that ATP
+ 
+
+ align:start position:0%
+that energy in ATP and we want that ATP
+to uh to be around and then when we uh
+
+ align:start position:0%
+to uh to be around and then when we uh
+ 
+
+ align:start position:0%
+to uh to be around and then when we uh
+break ATP apart it releases the energy
+
+ align:start position:0%
+break ATP apart it releases the energy
+ 
+
+ align:start position:0%
+break ATP apart it releases the energy
+so this is a very important biological
+
+ align:start position:0%
+so this is a very important biological
+ 
+
+ align:start position:0%
+so this is a very important biological
+process and you have a negative value
+
+ align:start position:0%
+process and you have a negative value
+ 
+
+ align:start position:0%
+process and you have a negative value
+exothermic reaction but but there's a
+
+ align:start position:0%
+exothermic reaction but but there's a
+ 
+
+ align:start position:0%
+exothermic reaction but but there's a
+few other examples of spontaneous
+
+ align:start position:0%
+few other examples of spontaneous
+ 
+
+ align:start position:0%
+few other examples of spontaneous
+reactions one of them is this one and
+
+ align:start position:0%
+reactions one of them is this one and
+ 
+
+ align:start position:0%
+reactions one of them is this one and
+we've probably all experien this if
+
+ align:start position:0%
+we've probably all experien this if
+ 
+
+ align:start position:0%
+we've probably all experien this if
+you're from New England you've seen uh
+
+ align:start position:0%
+you're from New England you've seen uh
+ 
+
+ align:start position:0%
+you're from New England you've seen uh
+snow melt so you've seen or ice melt uh
+
+ align:start position:0%
+snow melt so you've seen or ice melt uh
+ 
+
+ align:start position:0%
+snow melt so you've seen or ice melt uh
+solid to liquid if you're from a hot
+
+ align:start position:0%
+solid to liquid if you're from a hot
+ 
+
+ align:start position:0%
+solid to liquid if you're from a hot
+part of the world you probably had ice
+
+ align:start position:0%
+part of the world you probably had ice
+ 
+
+ align:start position:0%
+part of the world you probably had ice
+cubes in your nice refreshing drink with
+
+ align:start position:0%
+cubes in your nice refreshing drink with
+ 
+
+ align:start position:0%
+cubes in your nice refreshing drink with
+maybe a little umbrella on the top
+
+ align:start position:0%
+maybe a little umbrella on the top
+ 
+
+ align:start position:0%
+maybe a little umbrella on the top
+anyway you everyone I think has seen ice
+
+ align:start position:0%
+anyway you everyone I think has seen ice
+ 
+
+ align:start position:0%
+anyway you everyone I think has seen ice
+melt um but here Delta H9 is a positive
+
+ align:start position:0%
+melt um but here Delta H9 is a positive
+ 
+
+ align:start position:0%
+melt um but here Delta H9 is a positive
+value it's
+
+ align:start position:0%
+value it's
+ 
+
+ align:start position:0%
+value it's
+endothermic also if you have ammonium
+
+ align:start position:0%
+endothermic also if you have ammonium
+ 
+
+ align:start position:0%
+endothermic also if you have ammonium
+nitrate this will just come apart in a
+
+ align:start position:0%
+nitrate this will just come apart in a
+ 
+
+ align:start position:0%
+nitrate this will just come apart in a
+spontaneous reaction Delta H here is
+
+ align:start position:0%
+spontaneous reaction Delta H here is
+ 
+
+ align:start position:0%
+spontaneous reaction Delta H here is
+plus 28 K per mole
+
+ align:start position:0%
+plus 28 K per mole
+ 
+
+ align:start position:0%
+plus 28 K per mole
+so is Delta H the key to
+
+ align:start position:0%
+so is Delta H the key to
+ 
+
+ align:start position:0%
+so is Delta H the key to
+spontaneity it is
+
+ align:start position:0%
+spontaneity it is
+ 
+
+ align:start position:0%
+spontaneity it is
+not plays into it but it is not the
+
+ align:start position:0%
+not plays into it but it is not the
+ 
+
+ align:start position:0%
+not plays into it but it is not the
+determining Factor
+
+ align:start position:0%
+determining Factor
+ 
+
+ align:start position:0%
+determining Factor
+so if Delta H KN is not the key to
+
+ align:start position:0%
+so if Delta H KN is not the key to
+ 
+
+ align:start position:0%
+so if Delta H KN is not the key to
+spontaneity what
+
+ align:start position:0%
+spontaneity what
+ 
+
+ align:start position:0%
+spontaneity what
+is it is free energy yes particularly
+
+ align:start position:0%
+is it is free energy yes particularly
+ 
+
+ align:start position:0%
+is it is free energy yes particularly
+gives free energy or Delta
+
+ align:start position:0%
+gives free energy or Delta
+ 
+
+ align:start position:0%
+gives free energy or Delta
+G and you know I I uh I'm really happy
+
+ align:start position:0%
+G and you know I I uh I'm really happy
+ 
+
+ align:start position:0%
+G and you know I I uh I'm really happy
+they decided to add the Gibbs free
+
+ align:start position:0%
+they decided to add the Gibbs free
+ 
+
+ align:start position:0%
+they decided to add the Gibbs free
+energy because another thing of energy
+
+ align:start position:0%
+energy because another thing of energy
+ 
+
+ align:start position:0%
+energy because another thing of energy
+would be a lot so uh so having this free
+
+ align:start position:0%
+would be a lot so uh so having this free
+ 
+
+ align:start position:0%
+would be a lot so uh so having this free
+energy have an abbreviation of g i I
+
+ align:start position:0%
+energy have an abbreviation of g i I
+ 
+
+ align:start position:0%
+energy have an abbreviation of g i I
+think is a good thing so Gibbs free
+
+ align:start position:0%
+think is a good thing so Gibbs free
+ 
+
+ align:start position:0%
+think is a good thing so Gibbs free
+energy so Gibbs free energy depends on
+
+ align:start position:0%
+energy so Gibbs free energy depends on
+ 
+
+ align:start position:0%
+energy so Gibbs free energy depends on
+Delta H but it also depends on another
+
+ align:start position:0%
+Delta H but it also depends on another
+ 
+
+ align:start position:0%
+Delta H but it also depends on another
+term which is T Delta s temperature and
+
+ align:start position:0%
+term which is T Delta s temperature and
+ 
+
+ align:start position:0%
+term which is T Delta s temperature and
+Delta s change in enthropy
+
+ align:start position:0%
+Delta s change in enthropy
+ 
+
+ align:start position:0%
+Delta s change in enthropy
+so Delta G is the predictor of whether a
+
+ align:start position:0%
+so Delta G is the predictor of whether a
+ 
+
+ align:start position:0%
+so Delta G is the predictor of whether a
+reaction will go forward in a
+
+ align:start position:0%
+reaction will go forward in a
+ 
+
+ align:start position:0%
+reaction will go forward in a
+spontaneous in the for direction in a
+
+ align:start position:0%
+spontaneous in the for direction in a
+ 
+
+ align:start position:0%
+spontaneous in the for direction in a
+spontaneous fashion or not so let's just
+
+ align:start position:0%
+spontaneous fashion or not so let's just
+ 
+
+ align:start position:0%
+spontaneous fashion or not so let's just
+think about the sign of Delta G and what
+
+ align:start position:0%
+think about the sign of Delta G and what
+ 
+
+ align:start position:0%
+think about the sign of Delta G and what
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+means so again at constant temperature
+
+ align:start position:0%
+means so again at constant temperature
+ 
+
+ align:start position:0%
+means so again at constant temperature
+and pressure here Delta G less than zero
+
+ align:start position:0%
+and pressure here Delta G less than zero
+ 
+
+ align:start position:0%
+and pressure here Delta G less than zero
+negative Delta G is that spontaneous or
+
+ align:start position:0%
+negative Delta G is that spontaneous or
+ 
+
+ align:start position:0%
+negative Delta G is that spontaneous or
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+spontaneous positive Delta G it's not
+
+ align:start position:0%
+spontaneous positive Delta G it's not
+ 
+
+ align:start position:0%
+spontaneous positive Delta G it's not
+spontaneous non-spontaneous
+
+ align:start position:0%
+spontaneous non-spontaneous
+ 
+
+ align:start position:0%
+spontaneous non-spontaneous
+and Delta g equals z is one of the other
+
+ align:start position:0%
+and Delta g equals z is one of the other
+ 
+
+ align:start position:0%
+and Delta g equals z is one of the other
+things that I am very fond of which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium so Delta G indicates whether
+
+ align:start position:0%
+equilibrium so Delta G indicates whether
+ 
+
+ align:start position:0%
+equilibrium so Delta G indicates whether
+something is spontaneous or not negative
+
+ align:start position:0%
+something is spontaneous or not negative
+ 
+
+ align:start position:0%
+something is spontaneous or not negative
+value spontaneous in the forward
+
+ align:start position:0%
+value spontaneous in the forward
+ 
+
+ align:start position:0%
+value spontaneous in the forward
+Direction positive value not spontaneous
+
+ align:start position:0%
+Direction positive value not spontaneous
+ 
+
+ align:start position:0%
+Direction positive value not spontaneous
+in the forward Direction and equilibrium
+
+ align:start position:0%
+in the forward Direction and equilibrium
+ 
+
+ align:start position:0%
+in the forward Direction and equilibrium
+the thing we all try to reach in our
+
+ align:start position:0%
+the thing we all try to reach in our
+ 
+
+ align:start position:0%
+the thing we all try to reach in our
+lives okay so let's look at an example
+
+ align:start position:0%
+lives okay so let's look at an example
+ 
+
+ align:start position:0%
+lives okay so let's look at an example
+and calculate what Delta G is going to
+
+ align:start position:0%
+and calculate what Delta G is going to
+ 
+
+ align:start position:0%
+and calculate what Delta G is going to
+be so we saw this this equation already
+
+ align:start position:0%
+be so we saw this this equation already
+ 
+
+ align:start position:0%
+be so we saw this this equation already
+we have a positive Delta H knot and now
+
+ align:start position:0%
+we have a positive Delta H knot and now
+ 
+
+ align:start position:0%
+we have a positive Delta H knot and now
+I'm telling you that Delta s knot is
+
+ align:start position:0%
+I'm telling you that Delta s knot is
+ 
+
+ align:start position:0%
+I'm telling you that Delta s knot is
+also a positive value so we can use this
+
+ align:start position:0%
+also a positive value so we can use this
+ 
+
+ align:start position:0%
+also a positive value so we can use this
+equation and this is really one of the
+
+ align:start position:0%
+equation and this is really one of the
+ 
+
+ align:start position:0%
+equation and this is really one of the
+most important equations um in chemistry
+
+ align:start position:0%
+most important equations um in chemistry
+ 
+
+ align:start position:0%
+most important equations um in chemistry
+um figuring out this equation was really
+
+ align:start position:0%
+um figuring out this equation was really
+ 
+
+ align:start position:0%
+um figuring out this equation was really
+a crowning achievement um and uh you'll
+
+ align:start position:0%
+a crowning achievement um and uh you'll
+ 
+
+ align:start position:0%
+a crowning achievement um and uh you'll
+be using it a lot not just in this unit
+
+ align:start position:0%
+be using it a lot not just in this unit
+ 
+
+ align:start position:0%
+be using it a lot not just in this unit
+but pretty much in every unit from now
+
+ align:start position:0%
+but pretty much in every unit from now
+ 
+
+ align:start position:0%
+but pretty much in every unit from now
+on um you will be using this equation
+
+ align:start position:0%
+on um you will be using this equation
+ 
+
+ align:start position:0%
+on um you will be using this equation
+all right so room temperature pretty
+
+ align:start position:0%
+all right so room temperature pretty
+ 
+
+ align:start position:0%
+all right so room temperature pretty
+much we're not doing occasionally we'll
+
+ align:start position:0%
+much we're not doing occasionally we'll
+ 
+
+ align:start position:0%
+much we're not doing occasionally we'll
+do something not at room temperature but
+
+ align:start position:0%
+do something not at room temperature but
+ 
+
+ align:start position:0%
+do something not at room temperature but
+we like room temperature um so and we
+
+ align:start position:0%
+we like room temperature um so and we
+ 
+
+ align:start position:0%
+we like room temperature um so and we
+like it in kelvin um so Delta G KN so we
+
+ align:start position:0%
+like it in kelvin um so Delta G KN so we
+ 
+
+ align:start position:0%
+like it in kelvin um so Delta G KN so we
+plug in our Delta H value so it's going
+
+ align:start position:0%
+plug in our Delta H value so it's going
+ 
+
+ align:start position:0%
+plug in our Delta H value so it's going
+to equal Delta H minus the temperature
+
+ align:start position:0%
+to equal Delta H minus the temperature
+ 
+
+ align:start position:0%
+to equal Delta H minus the temperature
+and if a temperature isn't given in a
+
+ align:start position:0%
+and if a temperature isn't given in a
+ 
+
+ align:start position:0%
+and if a temperature isn't given in a
+problem you can assume that it's
+
+ align:start position:0%
+problem you can assume that it's
+ 
+
+ align:start position:0%
+problem you can assume that it's
+298 um and now we need to plug in Delta
+
+ align:start position:0%
+298 um and now we need to plug in Delta
+ 
+
+ align:start position:0%
+298 um and now we need to plug in Delta
+s but I left a blank here to make a
+
+ align:start position:0%
+s but I left a blank here to make a
+ 
+
+ align:start position:0%
+s but I left a blank here to make a
+point which is that Delta s's are almost
+
+ align:start position:0%
+point which is that Delta s's are almost
+ 
+
+ align:start position:0%
+point which is that Delta s's are almost
+always given in Jewels per Kelvin per
+
+ align:start position:0%
+always given in Jewels per Kelvin per
+ 
+
+ align:start position:0%
+always given in Jewels per Kelvin per
+mole but everything else is given in
+
+ align:start position:0%
+mole but everything else is given in
+ 
+
+ align:start position:0%
+mole but everything else is given in
+kles so you want to make sure you
+
+ align:start position:0%
+kles so you want to make sure you
+ 
+
+ align:start position:0%
+kles so you want to make sure you
+convert your units or you're going to
+
+ align:start position:0%
+convert your units or you're going to
+ 
+
+ align:start position:0%
+convert your units or you're going to
+come up with very funky answers at the
+
+ align:start position:0%
+come up with very funky answers at the
+ 
+
+ align:start position:0%
+come up with very funky answers at the
+end so from jewels to kilog so now plus
+
+ align:start position:0%
+end so from jewels to kilog so now plus
+ 
+
+ align:start position:0%
+end so from jewels to kilog so now plus
+0.109 K per Kelvin per
+
+ align:start position:0%
+0.109 K per Kelvin per
+ 
+
+ align:start position:0%
+0.109 K per Kelvin per
+mole and we can do this out now so we
+
+ align:start position:0%
+mole and we can do this out now so we
+ 
+
+ align:start position:0%
+mole and we can do this out now so we
+have plus 28 Minus 32.482947
+
+ align:start position:0%
+have plus 28 Minus 32.482947
+ 
+
+ align:start position:0%
+have plus 28 Minus 32.482947
+and why don't you tell me how many
+
+ align:start position:0%
+and why don't you tell me how many
+ 
+
+ align:start position:0%
+and why don't you tell me how many
+significant figures this answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has okay 10 more seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so uh at least uh at least some
+
+ align:start position:0%
+okay so uh at least uh at least some
+ 
+
+ align:start position:0%
+okay so uh at least uh at least some
+people got it right we've identified
+
+ align:start position:0%
+people got it right we've identified
+ 
+
+ align:start position:0%
+people got it right we've identified
+once again a
+
+ align:start position:0%
+once again a
+ 
+
+ align:start position:0%
+once again a
+weakness um so rules of adding and
+
+ align:start position:0%
+weakness um so rules of adding and
+ 
+
+ align:start position:0%
+weakness um so rules of adding and
+subtracting so we have 28 here minus 32
+
+ align:start position:0%
+subtracting so we have 28 here minus 32
+ 
+
+ align:start position:0%
+subtracting so we have 28 here minus 32
+there are no significant figures after
+
+ align:start position:0%
+there are no significant figures after
+ 
+
+ align:start position:0%
+there are no significant figures after
+the decimal point here so we're just
+
+ align:start position:0%
+the decimal point here so we're just
+ 
+
+ align:start position:0%
+the decimal point here so we're just
+left with
+
+ align:start position:0%
+left with
+ 
+
+ align:start position:0%
+left with
+four so when we're doing multiplication
+
+ align:start position:0%
+four so when we're doing multiplication
+ 
+
+ align:start position:0%
+four so when we're doing multiplication
+or division we consider the total number
+
+ align:start position:0%
+or division we consider the total number
+ 
+
+ align:start position:0%
+or division we consider the total number
+of significant figures but with addition
+
+ align:start position:0%
+of significant figures but with addition
+ 
+
+ align:start position:0%
+of significant figures but with addition
+and subtraction you got to pay attention
+
+ align:start position:0%
+and subtraction you got to pay attention
+ 
+
+ align:start position:0%
+and subtraction you got to pay attention
+to where the decimal point
+
+ align:start position:0%
+to where the decimal point
+ 
+
+ align:start position:0%
+to where the decimal point
+is and we get into the next unit there
+
+ align:start position:0%
+is and we get into the next unit there
+ 
+
+ align:start position:0%
+is and we get into the next unit there
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+logs and those have special rules of
+
+ align:start position:0%
+logs and those have special rules of
+ 
+
+ align:start position:0%
+logs and those have special rules of
+significant
+
+ align:start position:0%
+significant
+ 
+
+ align:start position:0%
+significant
+figures yes very exciting all right
+
+ align:start position:0%
+figures yes very exciting all right
+ 
+
+ align:start position:0%
+figures yes very exciting all right
+right so Delta G KN is negative here
+
+ align:start position:0%
+right so Delta G KN is negative here
+ 
+
+ align:start position:0%
+right so Delta G KN is negative here
+although Delta H is positive so this
+
+ align:start position:0%
+although Delta H is positive so this
+ 
+
+ align:start position:0%
+although Delta H is positive so this
+reaction is
+
+ align:start position:0%
+reaction is
+ 
+
+ align:start position:0%
+reaction is
+spontaneous it's not hugely it's a
+
+ align:start position:0%
+spontaneous it's not hugely it's a
+ 
+
+ align:start position:0%
+spontaneous it's not hugely it's a
+pretty small number but still it's
+
+ align:start position:0%
+pretty small number but still it's
+ 
+
+ align:start position:0%
+pretty small number but still it's
+spontaneous all right so let's consider
+
+ align:start position:0%
+spontaneous all right so let's consider
+ 
+
+ align:start position:0%
+spontaneous all right so let's consider
+our friend over here that we've been
+
+ align:start position:0%
+our friend over here that we've been
+ 
+
+ align:start position:0%
+our friend over here that we've been
+talking about glucose being oxidized to
+
+ align:start position:0%
+talking about glucose being oxidized to
+ 
+
+ align:start position:0%
+talking about glucose being oxidized to
+CO2 in water you practically should have
+
+ align:start position:0%
+CO2 in water you practically should have
+ 
+
+ align:start position:0%
+CO2 in water you practically should have
+the Delta H memorized for that at this
+
+ align:start position:0%
+the Delta H memorized for that at this
+ 
+
+ align:start position:0%
+the Delta H memorized for that at this
+point now I'm telling you what the Delta
+
+ align:start position:0%
+point now I'm telling you what the Delta
+ 
+
+ align:start position:0%
+point now I'm telling you what the Delta
+s knot is and it's positive
+
+ align:start position:0%
+s knot is and it's positive
+ 
+
+ align:start position:0%
+s knot is and it's positive
+233 Jew per Kelvin per mole and we can
+
+ align:start position:0%
+233 Jew per Kelvin per mole and we can
+ 
+
+ align:start position:0%
+233 Jew per Kelvin per mole and we can
+plug this into our equation to calculate
+
+ align:start position:0%
+plug this into our equation to calculate
+ 
+
+ align:start position:0%
+plug this into our equation to calculate
+a Delta G KN again remembering to
+
+ align:start position:0%
+a Delta G KN again remembering to
+ 
+
+ align:start position:0%
+a Delta G KN again remembering to
+convert jewels to
+
+ align:start position:0%
+convert jewels to
+ 
+
+ align:start position:0%
+convert jewels to
+kilog uh to do this and so now we see
+
+ align:start position:0%
+kilog uh to do this and so now we see
+ 
+
+ align:start position:0%
+kilog uh to do this and so now we see
+that it is a very uh has a very negative
+
+ align:start position:0%
+that it is a very uh has a very negative
+ 
+
+ align:start position:0%
+that it is a very uh has a very negative
+Delta G KN here minus 2, uh minus
+
+ align:start position:0%
+Delta G KN here minus 2, uh minus
+ 
+
+ align:start position:0%
+Delta G KN here minus 2, uh minus
+2885 K per mole um at room
+
+ align:start position:0%
+2885 K per mole um at room
+ 
+
+ align:start position:0%
+2885 K per mole um at room
+temperature so at room temperature this
+
+ align:start position:0%
+temperature so at room temperature this
+ 
+
+ align:start position:0%
+temperature so at room temperature this
+reaction is spontaneous but slow we saw
+
+ align:start position:0%
+reaction is spontaneous but slow we saw
+ 
+
+ align:start position:0%
+reaction is spontaneous but slow we saw
+that with the uh the the candies that
+
+ align:start position:0%
+that with the uh the the candies that
+ 
+
+ align:start position:0%
+that with the uh the the candies that
+had glucose in it we opened them up and
+
+ align:start position:0%
+had glucose in it we opened them up and
+ 
+
+ align:start position:0%
+had glucose in it we opened them up and
+no water or CO2 um were obviously being
+
+ align:start position:0%
+no water or CO2 um were obviously being
+ 
+
+ align:start position:0%
+no water or CO2 um were obviously being
+liberated in this um reaction because it
+
+ align:start position:0%
+liberated in this um reaction because it
+ 
+
+ align:start position:0%
+liberated in this um reaction because it
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+slow and now a clicker question I want
+
+ align:start position:0%
+slow and now a clicker question I want
+ 
+
+ align:start position:0%
+slow and now a clicker question I want
+you to tell me whether it would be
+
+ align:start position:0%
+you to tell me whether it would be
+ 
+
+ align:start position:0%
+you to tell me whether it would be
+spontaneous at different temperatures or
+
+ align:start position:0%
+spontaneous at different temperatures or
+ 
+
+ align:start position:0%
+spontaneous at different temperatures or
+not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay 10 more seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep so it is spontaneous at all
+
+ align:start position:0%
+yep so it is spontaneous at all
+ 
+
+ align:start position:0%
+yep so it is spontaneous at all
+temperatures not all reactions are but
+
+ align:start position:0%
+temperatures not all reactions are but
+ 
+
+ align:start position:0%
+temperatures not all reactions are but
+this one is so if we go back here the
+
+ align:start position:0%
+this one is so if we go back here the
+ 
+
+ align:start position:0%
+this one is so if we go back here the
+reaction spontaneous at all temperatures
+
+ align:start position:0%
+reaction spontaneous at all temperatures
+ 
+
+ align:start position:0%
+reaction spontaneous at all temperatures
+and that's because to be spontaneous you
+
+ align:start position:0%
+and that's because to be spontaneous you
+ 
+
+ align:start position:0%
+and that's because to be spontaneous you
+want a Delta G that's negative if Delta
+
+ align:start position:0%
+want a Delta G that's negative if Delta
+ 
+
+ align:start position:0%
+want a Delta G that's negative if Delta
+H is negative and Delta s is positive
+
+ align:start position:0%
+H is negative and Delta s is positive
+ 
+
+ align:start position:0%
+H is negative and Delta s is positive
+then you'll have a negative minus a
+
+ align:start position:0%
+then you'll have a negative minus a
+ 
+
+ align:start position:0%
+then you'll have a negative minus a
+negative so it doesn't matter what
+
+ align:start position:0%
+negative so it doesn't matter what
+ 
+
+ align:start position:0%
+negative so it doesn't matter what
+temperature is
+
+ align:start position:0%
+temperature is
+ 
+
+ align:start position:0%
+temperature is
+this will always yield a negative Delta
+
+ align:start position:0%
+this will always yield a negative Delta
+ 
+
+ align:start position:0%
+this will always yield a negative Delta
+G knot so other reactions that might not
+
+ align:start position:0%
+G knot so other reactions that might not
+ 
+
+ align:start position:0%
+G knot so other reactions that might not
+be the case but if you have negative
+
+ align:start position:0%
+be the case but if you have negative
+ 
+
+ align:start position:0%
+be the case but if you have negative
+Delta h and a positive um Delta s it
+
+ align:start position:0%
+Delta h and a positive um Delta s it
+ 
+
+ align:start position:0%
+Delta h and a positive um Delta s it
+will be spontaneous so negative Delta H
+
+ align:start position:0%
+will be spontaneous so negative Delta H
+ 
+
+ align:start position:0%
+will be spontaneous so negative Delta H
+again exothermic heat release and a
+
+ align:start position:0%
+again exothermic heat release and a
+ 
+
+ align:start position:0%
+again exothermic heat release and a
+positive entropy is a favorable thing
+
+ align:start position:0%
+positive entropy is a favorable thing
+ 
+
+ align:start position:0%
+positive entropy is a favorable thing
+entropy is always increasing so if this
+
+ align:start position:0%
+entropy is always increasing so if this
+ 
+
+ align:start position:0%
+entropy is always increasing so if this
+reaction has increase in entropy it'll
+
+ align:start position:0%
+reaction has increase in entropy it'll
+ 
+
+ align:start position:0%
+reaction has increase in entropy it'll
+be much more likely to be spontaneous
+
+ align:start position:0%
+be much more likely to be spontaneous
+ 
+
+ align:start position:0%
+be much more likely to be spontaneous
+all right so let's talk about
+
+ align:start position:0%
+all right so let's talk about
+ 
+
+ align:start position:0%
+all right so let's talk about
+entropy so entropy is a measure of
+
+ align:start position:0%
+entropy so entropy is a measure of
+ 
+
+ align:start position:0%
+entropy so entropy is a measure of
+disorder of a system Delta s is the
+
+ align:start position:0%
+disorder of a system Delta s is the
+ 
+
+ align:start position:0%
+disorder of a system Delta s is the
+change in
+
+ align:start position:0%
+change in
+ 
+
+ align:start position:0%
+change in
+entropy and Delta s again is a state
+
+ align:start position:0%
+entropy and Delta s again is a state
+ 
+
+ align:start position:0%
+entropy and Delta s again is a state
+function so one example of entropy in
+
+ align:start position:0%
+function so one example of entropy in
+ 
+
+ align:start position:0%
+function so one example of entropy in
+New England um are these uh stone walls
+
+ align:start position:0%
+New England um are these uh stone walls
+ 
+
+ align:start position:0%
+New England um are these uh stone walls
+that do not look absolutely beautiful um
+
+ align:start position:0%
+that do not look absolutely beautiful um
+ 
+
+ align:start position:0%
+that do not look absolutely beautiful um
+they often uh Stones falling everywhere
+
+ align:start position:0%
+they often uh Stones falling everywhere
+ 
+
+ align:start position:0%
+they often uh Stones falling everywhere
+and it doesn't matter if these the stone
+
+ align:start position:0%
+and it doesn't matter if these the stone
+ 
+
+ align:start position:0%
+and it doesn't matter if these the stone
+walls were probably built in 1600s or
+
+ align:start position:0%
+walls were probably built in 1600s or
+ 
+
+ align:start position:0%
+walls were probably built in 1600s or
+1700s in New England were fell totally
+
+ align:start position:0%
+1700s in New England were fell totally
+ 
+
+ align:start position:0%
+1700s in New England were fell totally
+apart and we rebuilt now we just care
+
+ align:start position:0%
+apart and we rebuilt now we just care
+ 
+
+ align:start position:0%
+apart and we rebuilt now we just care
+about um how the wall is compared to the
+
+ align:start position:0%
+about um how the wall is compared to the
+ 
+
+ align:start position:0%
+about um how the wall is compared to the
+way it started so Delta s again is a
+
+ align:start position:0%
+way it started so Delta s again is a
+ 
+
+ align:start position:0%
+way it started so Delta s again is a
+state function it doesn't depend on path
+
+ align:start position:0%
+state function it doesn't depend on path
+ 
+
+ align:start position:0%
+state function it doesn't depend on path
+and so if you get out and walk around
+
+ align:start position:0%
+and so if you get out and walk around
+ 
+
+ align:start position:0%
+and so if you get out and walk around
+and go like on the Minuteman Trail and
+
+ align:start position:0%
+and go like on the Minuteman Trail and
+ 
+
+ align:start position:0%
+and go like on the Minuteman Trail and
+see some of the historical sites um
+
+ align:start position:0%
+see some of the historical sites um
+ 
+
+ align:start position:0%
+see some of the historical sites um
+where Paul Riv rode his horse along a
+
+ align:start position:0%
+where Paul Riv rode his horse along a
+ 
+
+ align:start position:0%
+where Paul Riv rode his horse along a
+lot of stone walls there's a New England
+
+ align:start position:0%
+lot of stone walls there's a New England
+ 
+
+ align:start position:0%
+lot of stone walls there's a New England
+poet who write who writes about this
+
+ align:start position:0%
+poet who write who writes about this
+ 
+
+ align:start position:0%
+poet who write who writes about this
+Robert Frost and he said something there
+
+ align:start position:0%
+Robert Frost and he said something there
+ 
+
+ align:start position:0%
+Robert Frost and he said something there
+is that doesn't love a wall and that
+
+ align:start position:0%
+is that doesn't love a wall and that
+ 
+
+ align:start position:0%
+is that doesn't love a wall and that
+something is entropy entropy does not
+
+ align:start position:0%
+something is entropy entropy does not
+ 
+
+ align:start position:0%
+something is entropy entropy does not
+love a wall entropy does not like order
+
+ align:start position:0%
+love a wall entropy does not like order
+ 
+
+ align:start position:0%
+love a wall entropy does not like order
+um another example those of you uh who
+
+ align:start position:0%
+um another example those of you uh who
+ 
+
+ align:start position:0%
+um another example those of you uh who
+are learning more about me as a person
+
+ align:start position:0%
+are learning more about me as a person
+ 
+
+ align:start position:0%
+are learning more about me as a person
+uh know that uh that I am a fan of dogs
+
+ align:start position:0%
+uh know that uh that I am a fan of dogs
+ 
+
+ align:start position:0%
+uh know that uh that I am a fan of dogs
+this is my dog Shep um Shep does not
+
+ align:start position:0%
+this is my dog Shep um Shep does not
+ 
+
+ align:start position:0%
+this is my dog Shep um Shep does not
+like going to the groomers does not like
+
+ align:start position:0%
+like going to the groomers does not like
+ 
+
+ align:start position:0%
+like going to the groomers does not like
+it and I think that this is because he's
+
+ align:start position:0%
+it and I think that this is because he's
+ 
+
+ align:start position:0%
+it and I think that this is because he's
+been at my office hours and he knows
+
+ align:start position:0%
+been at my office hours and he knows
+ 
+
+ align:start position:0%
+been at my office hours and he knows
+that increasing entropy is favorable
+
+ align:start position:0%
+that increasing entropy is favorable
+ 
+
+ align:start position:0%
+that increasing entropy is favorable
+decreasing entropy is not and he says
+
+ align:start position:0%
+decreasing entropy is not and he says
+ 
+
+ align:start position:0%
+decreasing entropy is not and he says
+you know really this violates the laws
+
+ align:start position:0%
+you know really this violates the laws
+ 
+
+ align:start position:0%
+you know really this violates the laws
+of thermodynamics what you're doing to
+
+ align:start position:0%
+of thermodynamics what you're doing to
+ 
+
+ align:start position:0%
+of thermodynamics what you're doing to
+me and you should cease and desist um
+
+ align:start position:0%
+me and you should cease and desist um
+ 
+
+ align:start position:0%
+me and you should cease and desist um
+but anyway he still gets haircuts all
+
+ align:start position:0%
+but anyway he still gets haircuts all
+ 
+
+ align:start position:0%
+but anyway he still gets haircuts all
+right so entropy again is this measure
+
+ align:start position:0%
+right so entropy again is this measure
+ 
+
+ align:start position:0%
+right so entropy again is this measure
+of disorder of a system you have a
+
+ align:start position:0%
+of disorder of a system you have a
+ 
+
+ align:start position:0%
+of disorder of a system you have a
+positive Delta s which is going to be an
+
+ align:start position:0%
+positive Delta s which is going to be an
+ 
+
+ align:start position:0%
+positive Delta s which is going to be an
+increase in disorder and a negative
+
+ align:start position:0%
+increase in disorder and a negative
+ 
+
+ align:start position:0%
+increase in disorder and a negative
+Delta s is going to be a decrease in
+
+ align:start position:0%
+Delta s is going to be a decrease in
+ 
+
+ align:start position:0%
+Delta s is going to be a decrease in
+disorder and it a disorder can be you
+
+ align:start position:0%
+disorder and it a disorder can be you
+ 
+
+ align:start position:0%
+disorder and it a disorder can be you
+can be thinking about this is internal
+
+ align:start position:0%
+can be thinking about this is internal
+ 
+
+ align:start position:0%
+can be thinking about this is internal
+degrees of freedom in your molecule it
+
+ align:start position:0%
+degrees of freedom in your molecule it
+ 
+
+ align:start position:0%
+degrees of freedom in your molecule it
+can be thinking about this as vibrations
+
+ align:start position:0%
+can be thinking about this as vibrations
+ 
+
+ align:start position:0%
+can be thinking about this as vibrations
+all sorts of different things can lead
+
+ align:start position:0%
+all sorts of different things can lead
+ 
+
+ align:start position:0%
+all sorts of different things can lead
+to lead to uh to increase or decrease in
+
+ align:start position:0%
+to lead to uh to increase or decrease in
+ 
+
+ align:start position:0%
+to lead to uh to increase or decrease in
+entropy um but we often think about
+
+ align:start position:0%
+entropy um but we often think about
+ 
+
+ align:start position:0%
+entropy um but we often think about
+changes in entropy depending on if the
+
+ align:start position:0%
+changes in entropy depending on if the
+ 
+
+ align:start position:0%
+changes in entropy depending on if the
+reaction is changing in Phase SO gas
+
+ align:start position:0%
+reaction is changing in Phase SO gas
+ 
+
+ align:start position:0%
+reaction is changing in Phase SO gas
+molecules have greater disorder than
+
+ align:start position:0%
+molecules have greater disorder than
+ 
+
+ align:start position:0%
+molecules have greater disorder than
+liquid and liquid has greater disorder
+
+ align:start position:0%
+liquid and liquid has greater disorder
+ 
+
+ align:start position:0%
+liquid and liquid has greater disorder
+than uh solids and so a solid has all
+
+ align:start position:0%
+than uh solids and so a solid has all
+ 
+
+ align:start position:0%
+than uh solids and so a solid has all
+its molecules lined up um and liquid can
+
+ align:start position:0%
+its molecules lined up um and liquid can
+ 
+
+ align:start position:0%
+its molecules lined up um and liquid can
+move around a little bit more but gas
+
+ align:start position:0%
+move around a little bit more but gas
+ 
+
+ align:start position:0%
+move around a little bit more but gas
+really can spread all out so in terms of
+
+ align:start position:0%
+really can spread all out so in terms of
+ 
+
+ align:start position:0%
+really can spread all out so in terms of
+entropy and changes in entropy we can
+
+ align:start position:0%
+entropy and changes in entropy we can
+ 
+
+ align:start position:0%
+entropy and changes in entropy we can
+think about the phase change that's
+
+ align:start position:0%
+think about the phase change that's
+ 
+
+ align:start position:0%
+think about the phase change that's
+happening and even predict if
+
+ align:start position:0%
+happening and even predict if
+ 
+
+ align:start position:0%
+happening and even predict if
+something's going to be an increase in
+
+ align:start position:0%
+something's going to be an increase in
+ 
+
+ align:start position:0%
+something's going to be an increase in
+entropy or not so let's just look at one
+
+ align:start position:0%
+entropy or not so let's just look at one
+ 
+
+ align:start position:0%
+entropy or not so let's just look at one
+example so without a calculation predict
+
+ align:start position:0%
+example so without a calculation predict
+ 
+
+ align:start position:0%
+example so without a calculation predict
+the sign of Delta s and this is a
+
+ align:start position:0%
+the sign of Delta s and this is a
+ 
+
+ align:start position:0%
+the sign of Delta s and this is a
+clicker question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right um let's just take 10 more
+
+ align:start position:0%
+all right um let's just take 10 more
+ 
+
+ align:start position:0%
+all right um let's just take 10 more
+seconds and can our demo Tas come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+yep good so you predicted positive which
+
+ align:start position:0%
+yep good so you predicted positive which
+ 
+
+ align:start position:0%
+yep good so you predicted positive which
+is the correct answer and so here we're
+
+ align:start position:0%
+is the correct answer and so here we're
+ 
+
+ align:start position:0%
+is the correct answer and so here we're
+going from a liquid to a liquid and a
+
+ align:start position:0%
+going from a liquid to a liquid and a
+ 
+
+ align:start position:0%
+going from a liquid to a liquid and a
+gas um and so going to the gas that'll
+
+ align:start position:0%
+gas um and so going to the gas that'll
+ 
+
+ align:start position:0%
+gas um and so going to the gas that'll
+increase the disorder of the system so
+
+ align:start position:0%
+increase the disorder of the system so
+ 
+
+ align:start position:0%
+increase the disorder of the system so
+Delta s be positive so now we're
+
+ align:start position:0%
+Delta s be positive so now we're
+ 
+
+ align:start position:0%
+Delta s be positive so now we're
+actually going to do a demo of this
+
+ align:start position:0%
+actually going to do a demo of this
+ 
+
+ align:start position:0%
+actually going to do a demo of this
+particular reaction and so we have
+
+ align:start position:0%
+particular reaction and so we have
+ 
+
+ align:start position:0%
+particular reaction and so we have
+hydrogen peroxide um which can just be B
+
+ align:start position:0%
+hydrogen peroxide um which can just be B
+ 
+
+ align:start position:0%
+hydrogen peroxide um which can just be B
+bought at a CVS or local uh drugstore
+
+ align:start position:0%
+bought at a CVS or local uh drugstore
+ 
+
+ align:start position:0%
+bought at a CVS or local uh drugstore
+and it will uh go to liquid water and
+
+ align:start position:0%
+and it will uh go to liquid water and
+ 
+
+ align:start position:0%
+and it will uh go to liquid water and
+also oxygen gas and so how do you see a
+
+ align:start position:0%
+also oxygen gas and so how do you see a
+ 
+
+ align:start position:0%
+also oxygen gas and so how do you see a
+gas and you can see it by putting it in
+
+ align:start position:0%
+gas and you can see it by putting it in
+ 
+
+ align:start position:0%
+gas and you can see it by putting it in
+with soap bubbles so as bubbles of
+
+ align:start position:0%
+with soap bubbles so as bubbles of
+ 
+
+ align:start position:0%
+with soap bubbles so as bubbles of
+oxygen form the soap bubbles will uh
+
+ align:start position:0%
+oxygen form the soap bubbles will uh
+ 
+
+ align:start position:0%
+oxygen form the soap bubbles will uh
+bubble out and so you can see it and you
+
+ align:start position:0%
+bubble out and so you can see it and you
+ 
+
+ align:start position:0%
+bubble out and so you can see it and you
+can also add uh some kind of food color
+
+ align:start position:0%
+can also add uh some kind of food color
+ 
+
+ align:start position:0%
+can also add uh some kind of food color
+um and we have yeast as a catalyst to
+
+ align:start position:0%
+um and we have yeast as a catalyst to
+ 
+
+ align:start position:0%
+um and we have yeast as a catalyst to
+make it go a little bit faster so let's
+
+ align:start position:0%
+make it go a little bit faster so let's
+ 
+
+ align:start position:0%
+make it go a little bit faster so let's
+see if we can actually see disorder
+
+ align:start position:0%
+see if we can actually see disorder
+ 
+
+ align:start position:0%
+see if we can actually see disorder
+incase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know want the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mic if you want to just say if you want
+
+ align:start position:0%
+mic if you want to just say if you want
+ 
+
+ align:start position:0%
+mic if you want to just say if you want
+to talk at the same time here's a mic
+
+ align:start position:0%
+to talk at the same time here's a mic
+ 
+
+ align:start position:0%
+to talk at the same time here's a mic
+you're not gonna do that okay oh you do
+
+ align:start position:0%
+you're not gonna do that okay oh you do
+ 
+
+ align:start position:0%
+you're not gonna do that okay oh you do
+okay this on yes it is okay great so
+
+ align:start position:0%
+okay this on yes it is okay great so
+ 
+
+ align:start position:0%
+okay this on yes it is okay great so
+what we have going on here is we've got
+
+ align:start position:0%
+what we have going on here is we've got
+ 
+
+ align:start position:0%
+what we have going on here is we've got
+this container it's filled with water
+
+ align:start position:0%
+this container it's filled with water
+ 
+
+ align:start position:0%
+this container it's filled with water
+and what I did was I added about four
+
+ align:start position:0%
+and what I did was I added about four
+ 
+
+ align:start position:0%
+and what I did was I added about four
+teaspoons of yeast um the yeast as Kathy
+
+ align:start position:0%
+teaspoons of yeast um the yeast as Kathy
+ 
+
+ align:start position:0%
+teaspoons of yeast um the yeast as Kathy
+said is going to act as a catalyst um
+
+ align:start position:0%
+said is going to act as a catalyst um
+ 
+
+ align:start position:0%
+said is going to act as a catalyst um
+it's actually uh um a
+
+ align:start position:0%
+it's actually uh um a
+ 
+
+ align:start position:0%
+it's actually uh um a
+biological uh species it's actually
+
+ align:start position:0%
+biological uh species it's actually
+ 
+
+ align:start position:0%
+biological uh species it's actually
+going to it's a living species that's
+
+ align:start position:0%
+going to it's a living species that's
+ 
+
+ align:start position:0%
+going to it's a living species that's
+actually going to catalyze this reaction
+
+ align:start position:0%
+actually going to catalyze this reaction
+ 
+
+ align:start position:0%
+actually going to catalyze this reaction
+uh what Eric is doing is Eric is pouring
+
+ align:start position:0%
+uh what Eric is doing is Eric is pouring
+ 
+
+ align:start position:0%
+uh what Eric is doing is Eric is pouring
+some hydrogen peroxide he added some
+
+ align:start position:0%
+some hydrogen peroxide he added some
+ 
+
+ align:start position:0%
+some hydrogen peroxide he added some
+soap uh so as you see in the reaction
+
+ align:start position:0%
+soap uh so as you see in the reaction
+ 
+
+ align:start position:0%
+soap uh so as you see in the reaction
+the H2O2 is going to break down into
+
+ align:start position:0%
+the H2O2 is going to break down into
+ 
+
+ align:start position:0%
+the H2O2 is going to break down into
+water and gas uh the gas being oxygen
+
+ align:start position:0%
+water and gas uh the gas being oxygen
+ 
+
+ align:start position:0%
+water and gas uh the gas being oxygen
+and what we don't want to happen is we
+
+ align:start position:0%
+and what we don't want to happen is we
+ 
+
+ align:start position:0%
+and what we don't want to happen is we
+don't want just the gas to escape
+
+ align:start position:0%
+don't want just the gas to escape
+ 
+
+ align:start position:0%
+don't want just the gas to escape
+because then you guys can't see it so
+
+ align:start position:0%
+because then you guys can't see it so
+ 
+
+ align:start position:0%
+because then you guys can't see it so
+what Eric is doing right now is he's
+
+ align:start position:0%
+what Eric is doing right now is he's
+ 
+
+ align:start position:0%
+what Eric is doing right now is he's
+adding some soap the soap is actually
+
+ align:start position:0%
+adding some soap the soap is actually
+ 
+
+ align:start position:0%
+adding some soap the soap is actually
+going to catch if you will the uh
+
+ align:start position:0%
+going to catch if you will the uh
+ 
+
+ align:start position:0%
+going to catch if you will the uh
+escaping gas and turn it into a uh a
+
+ align:start position:0%
+escaping gas and turn it into a uh a
+ 
+
+ align:start position:0%
+escaping gas and turn it into a uh a
+foam and what we should be able to see
+
+ align:start position:0%
+foam and what we should be able to see
+ 
+
+ align:start position:0%
+foam and what we should be able to see
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+foam uh kind of escape from this
+
+ align:start position:0%
+foam uh kind of escape from this
+ 
+
+ align:start position:0%
+foam uh kind of escape from this
+container you ready okay so hopefully
+
+ align:start position:0%
+container you ready okay so hopefully
+ 
+
+ align:start position:0%
+container you ready okay so hopefully
+this will work we should put on our
+
+ align:start position:0%
+this will work we should put on our
+ 
+
+ align:start position:0%
+this will work we should put on our
+goggles smells really bad okay ready all
+
+ align:start position:0%
+goggles smells really bad okay ready all
+ 
+
+ align:start position:0%
+goggles smells really bad okay ready all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and get out of there look at that hey y
+
+ align:start position:0%
+and get out of there look at that hey y
+ 
+
+ align:start position:0%
+and get out of there look at that hey y
+wow that worked a lot better than we
+
+ align:start position:0%
+wow that worked a lot better than we
+ 
+
+ align:start position:0%
+wow that worked a lot better than we
+thought it was going to
+
+ align:start position:0%
+thought it was going to
+ 
+
+ align:start position:0%
+thought it was going to
+work and so this is something called the
+
+ align:start position:0%
+work and so this is something called the
+ 
+
+ align:start position:0%
+work and so this is something called the
+elephant toothpaste uh demo because that
+
+ align:start position:0%
+elephant toothpaste uh demo because that
+ 
+
+ align:start position:0%
+elephant toothpaste uh demo because that
+is sort of what if you were an elephant
+
+ align:start position:0%
+is sort of what if you were an elephant
+ 
+
+ align:start position:0%
+is sort of what if you were an elephant
+what you would probably be brushing your
+
+ align:start position:0%
+what you would probably be brushing your
+ 
+
+ align:start position:0%
+what you would probably be brushing your
+teeth with I don't know um yes so uh so
+
+ align:start position:0%
+teeth with I don't know um yes so uh so
+ 
+
+ align:start position:0%
+teeth with I don't know um yes so uh so
+this is uh entropy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+increasing okay so let's just see if we
+
+ align:start position:0%
+increasing okay so let's just see if we
+ 
+
+ align:start position:0%
+increasing okay so let's just see if we
+can uh quickly talk about a little more
+
+ align:start position:0%
+can uh quickly talk about a little more
+ 
+
+ align:start position:0%
+can uh quickly talk about a little more
+about entropy and then we'll end so
+
+ align:start position:0%
+about entropy and then we'll end so
+ 
+
+ align:start position:0%
+about entropy and then we'll end so
+entropy of reactions can be calculated
+
+ align:start position:0%
+entropy of reactions can be calculated
+ 
+
+ align:start position:0%
+entropy of reactions can be calculated
+from absolute values and again we can
+
+ align:start position:0%
+from absolute values and again we can
+ 
+
+ align:start position:0%
+from absolute values and again we can
+use this um this equation here so we
+
+ align:start position:0%
+use this um this equation here so we
+ 
+
+ align:start position:0%
+use this um this equation here so we
+have the Delta s of for of um a Delta s
+
+ align:start position:0%
+have the Delta s of for of um a Delta s
+ 
+
+ align:start position:0%
+have the Delta s of for of um a Delta s
+for a particular reaction is this can be
+
+ align:start position:0%
+for a particular reaction is this can be
+ 
+
+ align:start position:0%
+for a particular reaction is this can be
+calculated from the Delta s's of the
+
+ align:start position:0%
+calculated from the Delta s's of the
+ 
+
+ align:start position:0%
+calculated from the Delta s's of the
+products minus reactants so again we
+
+ align:start position:0%
+products minus reactants so again we
+ 
+
+ align:start position:0%
+products minus reactants so again we
+have products minus reactants the
+
+ align:start position:0%
+have products minus reactants the
+ 
+
+ align:start position:0%
+have products minus reactants the
+absolute value
+
+ align:start position:0%
+absolute value
+ 
+
+ align:start position:0%
+absolute value
+or an absolute Delta s um s equals or S
+
+ align:start position:0%
+or an absolute Delta s um s equals or S
+ 
+
+ align:start position:0%
+or an absolute Delta s um s equals or S
+equals zero for a perfect Crystal at a
+
+ align:start position:0%
+equals zero for a perfect Crystal at a
+ 
+
+ align:start position:0%
+equals zero for a perfect Crystal at a
+temperature of zero Kelvin you never
+
+ align:start position:0%
+temperature of zero Kelvin you never
+ 
+
+ align:start position:0%
+temperature of zero Kelvin you never
+really talk about s by itself it's
+
+ align:start position:0%
+really talk about s by itself it's
+ 
+
+ align:start position:0%
+really talk about s by itself it's
+always really Delta s um um and S of
+
+ align:start position:0%
+always really Delta s um um and S of
+ 
+
+ align:start position:0%
+always really Delta s um um and S of
+zero this is like the saddest thing for
+
+ align:start position:0%
+zero this is like the saddest thing for
+ 
+
+ align:start position:0%
+zero this is like the saddest thing for
+a crystallographer because you know
+
+ align:start position:0%
+a crystallographer because you know
+ 
+
+ align:start position:0%
+a crystallographer because you know
+you're never going to have a perfect
+
+ align:start position:0%
+you're never going to have a perfect
+ 
+
+ align:start position:0%
+you're never going to have a perfect
+Crystal um even if you go to zero Kelvin
+
+ align:start position:0%
+Crystal um even if you go to zero Kelvin
+ 
+
+ align:start position:0%
+Crystal um even if you go to zero Kelvin
+I feel like um at least experimentally
+
+ align:start position:0%
+I feel like um at least experimentally
+ 
+
+ align:start position:0%
+I feel like um at least experimentally
+so s equals z to me that's kind of sad
+
+ align:start position:0%
+so s equals z to me that's kind of sad
+ 
+
+ align:start position:0%
+so s equals z to me that's kind of sad
+okay um so if we just um put in for this
+
+ align:start position:0%
+okay um so if we just um put in for this
+ 
+
+ align:start position:0%
+okay um so if we just um put in for this
+reaction that we just uh just did we can
+
+ align:start position:0%
+reaction that we just uh just did we can
+ 
+
+ align:start position:0%
+reaction that we just uh just did we can
+put in our values here and we can put in
+
+ align:start position:0%
+put in our values here and we can put in
+ 
+
+ align:start position:0%
+put in our values here and we can put in
+we're forming liquid uh liquid water and
+
+ align:start position:0%
+we're forming liquid uh liquid water and
+ 
+
+ align:start position:0%
+we're forming liquid uh liquid water and
+we're forming O2 gas and um we are using
+
+ align:start position:0%
+we're forming O2 gas and um we are using
+ 
+
+ align:start position:0%
+we're forming O2 gas and um we are using
+two molecules of hydrogen peroxide H2O2
+
+ align:start position:0%
+two molecules of hydrogen peroxide H2O2
+ 
+
+ align:start position:0%
+two molecules of hydrogen peroxide H2O2
+here and so now we can calculate what
+
+ align:start position:0%
+here and so now we can calculate what
+ 
+
+ align:start position:0%
+here and so now we can calculate what
+that Delta s knot is
+
+ align:start position:0%
+that Delta s knot is
+ 
+
+ align:start position:0%
+that Delta s knot is
+um and it's a value of
+
+ align:start position:0%
+um and it's a value of
+ 
+
+ align:start position:0%
+um and it's a value of
+125 jewles per Kelvin per mole so again
+
+ align:start position:0%
+125 jewles per Kelvin per mole so again
+ 
+
+ align:start position:0%
+125 jewles per Kelvin per mole so again
+products water and gas minus reactants
+
+ align:start position:0%
+products water and gas minus reactants
+ 
+
+ align:start position:0%
+products water and gas minus reactants
+pay attention to the stochiometry and
+
+ align:start position:0%
+pay attention to the stochiometry and
+ 
+
+ align:start position:0%
+pay attention to the stochiometry and
+you can get your Delta s
+
+ align:start position:0%
+you can get your Delta s
+ 
+
+ align:start position:0%
+you can get your Delta s
+value and why is it positive again we
+
+ align:start position:0%
+value and why is it positive again we
+ 
+
+ align:start position:0%
+value and why is it positive again we
+already talked about this it's from
+
+ align:start position:0%
+already talked about this it's from
+ 
+
+ align:start position:0%
+already talked about this it's from
+because it's going from liquid to a
+
+ align:start position:0%
+because it's going from liquid to a
+ 
+
+ align:start position:0%
+because it's going from liquid to a
+liquid plus a
+
+ align:start position:0%
+liquid plus a
+ 
+
+ align:start position:0%
+liquid plus a
+gas and then if we plug these values in
+
+ align:start position:0%
+gas and then if we plug these values in
+ 
+
+ align:start position:0%
+gas and then if we plug these values in
+again to see see if it's spontaneous we
+
+ align:start position:0%
+again to see see if it's spontaneous we
+ 
+
+ align:start position:0%
+again to see see if it's spontaneous we
+can use this equation and plug in our
+
+ align:start position:0%
+can use this equation and plug in our
+ 
+
+ align:start position:0%
+can use this equation and plug in our
+values making sure we change our units
+
+ align:start position:0%
+values making sure we change our units
+ 
+
+ align:start position:0%
+values making sure we change our units
+and we can see that in fact this is a
+
+ align:start position:0%
+and we can see that in fact this is a
+ 
+
+ align:start position:0%
+and we can see that in fact this is a
+spontaneous reaction because it's
+
+ align:start position:0%
+spontaneous reaction because it's
+ 
+
+ align:start position:0%
+spontaneous reaction because it's
+negative here but you already knew that
+
+ align:start position:0%
+negative here but you already knew that
+ 
+
+ align:start position:0%
+negative here but you already knew that
+because you watched it Go
+
+ align:start position:0%
+because you watched it Go
+ 
+
+ align:start position:0%
+because you watched it Go
+spontaneously so most of the time you
+
+ align:start position:0%
+spontaneously so most of the time you
+ 
+
+ align:start position:0%
+spontaneously so most of the time you
+can't do the demo so then you can use
+
+ align:start position:0%
+can't do the demo so then you can use
+ 
+
+ align:start position:0%
+can't do the demo so then you can use
+this awesome equation right here okay so
+
+ align:start position:0%
+this awesome equation right here okay so
+ 
+
+ align:start position:0%
+this awesome equation right here okay so
+that's where we're stopping for today um
+
+ align:start position:0%
+that's where we're stopping for today um
+ 
+
+ align:start position:0%
+that's where we're stopping for today um
+and we'll see you all on
+
+ align:start position:0%
+and we'll see you all on
+ 
+
+ align:start position:0%
+and we'll see you all on
+Friday all right so if you take out your
+
+ align:start position:0%
+Friday all right so if you take out your
+ 
+
+ align:start position:0%
+Friday all right so if you take out your
+uh lecture 16 notes um the bottom of
+
+ align:start position:0%
+uh lecture 16 notes um the bottom of
+ 
+
+ align:start position:0%
+uh lecture 16 notes um the bottom of
+page three we had an example about the
+
+ align:start position:0%
+page three we had an example about the
+ 
+
+ align:start position:0%
+page three we had an example about the
+melting of ice um at room
+
+ align:start position:0%
+melting of ice um at room
+ 
+
+ align:start position:0%
+melting of ice um at room
+temperature so we had did a little demo
+
+ align:start position:0%
+temperature so we had did a little demo
+ 
+
+ align:start position:0%
+temperature so we had did a little demo
+for you at the end of class last time
+
+ align:start position:0%
+for you at the end of class last time
+ 
+
+ align:start position:0%
+for you at the end of class last time
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+calculated um a that the reaction was
+
+ align:start position:0%
+calculated um a that the reaction was
+ 
+
+ align:start position:0%
+calculated um a that the reaction was
+spontaneous uh for hydrogen uh hydrogen
+
+ align:start position:0%
+spontaneous uh for hydrogen uh hydrogen
+ 
+
+ align:start position:0%
+spontaneous uh for hydrogen uh hydrogen
+peroxide is is pretty reactive and we
+
+ align:start position:0%
+peroxide is is pretty reactive and we
+ 
+
+ align:start position:0%
+peroxide is is pretty reactive and we
+watched uh the O2 bubbles go and we did
+
+ align:start position:0%
+watched uh the O2 bubbles go and we did
+ 
+
+ align:start position:0%
+watched uh the O2 bubbles go and we did
+that calculation so we're thinking about
+
+ align:start position:0%
+that calculation so we're thinking about
+ 
+
+ align:start position:0%
+that calculation so we're thinking about
+not just Delta H but we're thinking
+
+ align:start position:0%
+not just Delta H but we're thinking
+ 
+
+ align:start position:0%
+not just Delta H but we're thinking
+about Delta s and we're now thinking
+
+ align:start position:0%
+about Delta s and we're now thinking
+ 
+
+ align:start position:0%
+about Delta s and we're now thinking
+about Delta G as well and how they all
+
+ align:start position:0%
+about Delta G as well and how they all
+ 
+
+ align:start position:0%
+about Delta G as well and how they all
+play together so when we started last
+
+ align:start position:0%
+play together so when we started last
+ 
+
+ align:start position:0%
+play together so when we started last
+lecture we had talked about the fact of
+
+ align:start position:0%
+lecture we had talked about the fact of
+ 
+
+ align:start position:0%
+lecture we had talked about the fact of
+some reactions that were spontaneous
+
+ align:start position:0%
+some reactions that were spontaneous
+ 
+
+ align:start position:0%
+some reactions that were spontaneous
+where Delta H was negative where it was
+
+ align:start position:0%
+where Delta H was negative where it was
+ 
+
+ align:start position:0%
+where Delta H was negative where it was
+exothermic where heat was released but
+
+ align:start position:0%
+exothermic where heat was released but
+ 
+
+ align:start position:0%
+exothermic where heat was released but
+then we also gave some examples where
+
+ align:start position:0%
+then we also gave some examples where
+ 
+
+ align:start position:0%
+then we also gave some examples where
+Delta H was positive and said but these
+
+ align:start position:0%
+Delta H was positive and said but these
+ 
+
+ align:start position:0%
+Delta H was positive and said but these
+are also spontaneous reac reactions we
+
+ align:start position:0%
+are also spontaneous reac reactions we
+ 
+
+ align:start position:0%
+are also spontaneous reac reactions we
+all know that at room temperature ice
+
+ align:start position:0%
+all know that at room temperature ice
+ 
+
+ align:start position:0%
+all know that at room temperature ice
+will melt we know that that's a
+
+ align:start position:0%
+will melt we know that that's a
+ 
+
+ align:start position:0%
+will melt we know that that's a
+spontaneous reaction but the Delta H for
+
+ align:start position:0%
+spontaneous reaction but the Delta H for
+ 
+
+ align:start position:0%
+spontaneous reaction but the Delta H for
+that reaction is actually a positive
+
+ align:start position:0%
+that reaction is actually a positive
+ 
+
+ align:start position:0%
+that reaction is actually a positive
+value it's an endothermic reaction so
+
+ align:start position:0%
+value it's an endothermic reaction so
+ 
+
+ align:start position:0%
+value it's an endothermic reaction so
+when we're thinking about these
+
+ align:start position:0%
+when we're thinking about these
+ 
+
+ align:start position:0%
+when we're thinking about these
+reactions in spontaneity we have to be
+
+ align:start position:0%
+reactions in spontaneity we have to be
+ 
+
+ align:start position:0%
+reactions in spontaneity we have to be
+thinking about Delta G not just Delta H
+
+ align:start position:0%
+thinking about Delta G not just Delta H
+ 
+
+ align:start position:0%
+thinking about Delta G not just Delta H
+and Delta G has to do with Delta H and
+
+ align:start position:0%
+and Delta G has to do with Delta H and
+ 
+
+ align:start position:0%
+and Delta G has to do with Delta H and
+Delta s so sometimes Delta s is the
+
+ align:start position:0%
+Delta s so sometimes Delta s is the
+ 
+
+ align:start position:0%
+Delta s so sometimes Delta s is the
+driving force behind whether a reaction
+
+ align:start position:0%
+driving force behind whether a reaction
+ 
+
+ align:start position:0%
+driving force behind whether a reaction
+is going to be spontaneous whether the
+
+ align:start position:0%
+is going to be spontaneous whether the
+ 
+
+ align:start position:0%
+is going to be spontaneous whether the
+Delta G will be negative or positive
+
+ align:start position:0%
+Delta G will be negative or positive
+ 
+
+ align:start position:0%
+Delta G will be negative or positive
+Delta s is making that determination so
+
+ align:start position:0%
+Delta s is making that determination so
+ 
+
+ align:start position:0%
+Delta s is making that determination so
+we can calculate what a Delta s for a
+
+ align:start position:0%
+we can calculate what a Delta s for a
+ 
+
+ align:start position:0%
+we can calculate what a Delta s for a
+reaction is if we know um the entropy
+
+ align:start position:0%
+reaction is if we know um the entropy
+ 
+
+ align:start position:0%
+reaction is if we know um the entropy
+values for the products and it's the sum
+
+ align:start position:0%
+values for the products and it's the sum
+ 
+
+ align:start position:0%
+values for the products and it's the sum
+of the entropy values for the products
+
+ align:start position:0%
+of the entropy values for the products
+ 
+
+ align:start position:0%
+of the entropy values for the products
+minus the sum for the reactants so when
+
+ align:start position:0%
+minus the sum for the reactants so when
+ 
+
+ align:start position:0%
+minus the sum for the reactants so when
+we are doing um Heats of formation we
+
+ align:start position:0%
+we are doing um Heats of formation we
+ 
+
+ align:start position:0%
+we are doing um Heats of formation we
+also had products minus reactants but we
+
+ align:start position:0%
+also had products minus reactants but we
+ 
+
+ align:start position:0%
+also had products minus reactants but we
+have one exception to this products
+
+ align:start position:0%
+have one exception to this products
+ 
+
+ align:start position:0%
+have one exception to this products
+minus reactant rules and that's when
+
+ align:start position:0%
+minus reactant rules and that's when
+ 
+
+ align:start position:0%
+minus reactant rules and that's when
+we're using what what things are we
+
+ align:start position:0%
+we're using what what things are we
+ 
+
+ align:start position:0%
+we're using what what things are we
+going to do reactants minus
+
+ align:start position:0%
+going to do reactants minus
+ 
+
+ align:start position:0%
+going to do reactants minus
+products
+
+ align:start position:0%
+products
+ 
+
+ align:start position:0%
+products
+Bond enthalpies right okay but here
+
+ align:start position:0%
+Bond enthalpies right okay but here
+ 
+
+ align:start position:0%
+Bond enthalpies right okay but here
+we're products minus reactants so we can
+
+ align:start position:0%
+we're products minus reactants so we can
+ 
+
+ align:start position:0%
+we're products minus reactants so we can
+uh plug those numbers in our product is
+
+ align:start position:0%
+uh plug those numbers in our product is
+ 
+
+ align:start position:0%
+uh plug those numbers in our product is
+our liquid water um our reactant is our
+
+ align:start position:0%
+our liquid water um our reactant is our
+ 
+
+ align:start position:0%
+our liquid water um our reactant is our
+solid water or our
+
+ align:start position:0%
+solid water or our
+ 
+
+ align:start position:0%
+solid water or our
+ice and we can calculate what the Delta
+
+ align:start position:0%
+ice and we can calculate what the Delta
+ 
+
+ align:start position:0%
+ice and we can calculate what the Delta
+s not is for this reaction we can put in
+
+ align:start position:0%
+s not is for this reaction we can put in
+ 
+
+ align:start position:0%
+s not is for this reaction we can put in
+our values and we get a posit positive
+
+ align:start position:0%
+our values and we get a posit positive
+ 
+
+ align:start position:0%
+our values and we get a posit positive
+value positive
+
+ align:start position:0%
+value positive
+ 
+
+ align:start position:0%
+value positive
+2859 jewles per Kelvin per mole and
+
+ align:start position:0%
+2859 jewles per Kelvin per mole and
+ 
+
+ align:start position:0%
+2859 jewles per Kelvin per mole and
+Delta s's tend to be in Jewels
+
+ align:start position:0%
+Delta s's tend to be in Jewels
+ 
+
+ align:start position:0%
+Delta s's tend to be in Jewels
+everything else is in
+
+ align:start position:0%
+everything else is in
+ 
+
+ align:start position:0%
+everything else is in
+kles so keep that in mind um and why why
+
+ align:start position:0%
+kles so keep that in mind um and why why
+ 
+
+ align:start position:0%
+kles so keep that in mind um and why why
+is why do you think this reaction it has
+
+ align:start position:0%
+is why do you think this reaction it has
+ 
+
+ align:start position:0%
+is why do you think this reaction it has
+a positive value why is Delta s greater
+
+ align:start position:0%
+a positive value why is Delta s greater
+ 
+
+ align:start position:0%
+a positive value why is Delta s greater
+than zero what would be your guess for
+
+ align:start position:0%
+than zero what would be your guess for
+ 
+
+ align:start position:0%
+than zero what would be your guess for
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happening yeah so we're going from a
+
+ align:start position:0%
+happening yeah so we're going from a
+ 
+
+ align:start position:0%
+happening yeah so we're going from a
+solid to a liquid so we're increasing
+
+ align:start position:0%
+solid to a liquid so we're increasing
+ 
+
+ align:start position:0%
+solid to a liquid so we're increasing
+the internal degrees of freedom the
+
+ align:start position:0%
+the internal degrees of freedom the
+ 
+
+ align:start position:0%
+the internal degrees of freedom the
+molecules of water can move around more
+
+ align:start position:0%
+molecules of water can move around more
+ 
+
+ align:start position:0%
+molecules of water can move around more
+in a liquid than they can in a solid so
+
+ align:start position:0%
+in a liquid than they can in a solid so
+ 
+
+ align:start position:0%
+in a liquid than they can in a solid so
+this is increasing the disorder of the
+
+ align:start position:0%
+this is increasing the disorder of the
+ 
+
+ align:start position:0%
+this is increasing the disorder of the
+system increasing um it you're
+
+ align:start position:0%
+system increasing um it you're
+ 
+
+ align:start position:0%
+system increasing um it you're
+increasing entropy here because the
+
+ align:start position:0%
+increasing entropy here because the
+ 
+
+ align:start position:0%
+increasing entropy here because the
+water molecules can move around more
+
+ align:start position:0%
+water molecules can move around more
+ 
+
+ align:start position:0%
+water molecules can move around more
+there's more freedom of motion so Delta
+
+ align:start position:0%
+there's more freedom of motion so Delta
+ 
+
+ align:start position:0%
+there's more freedom of motion so Delta
+s is POS positive it's
+
+ align:start position:0%
+s is POS positive it's
+ 
+
+ align:start position:0%
+s is POS positive it's
+increasing and then we can use that to
+
+ align:start position:0%
+increasing and then we can use that to
+ 
+
+ align:start position:0%
+increasing and then we can use that to
+calculate Delta G KN gives free energy
+
+ align:start position:0%
+calculate Delta G KN gives free energy
+ 
+
+ align:start position:0%
+calculate Delta G KN gives free energy
+we can plug in our Delta H value minus t
+
+ align:start position:0%
+we can plug in our Delta H value minus t
+ 
+
+ align:start position:0%
+we can plug in our Delta H value minus t
+room temperature times Delta s which we
+
+ align:start position:0%
+room temperature times Delta s which we
+ 
+
+ align:start position:0%
+room temperature times Delta s which we
+just calculated making sure that we
+
+ align:start position:0%
+just calculated making sure that we
+ 
+
+ align:start position:0%
+just calculated making sure that we
+convert from jewels to kogs and then our
+
+ align:start position:0%
+convert from jewels to kogs and then our
+ 
+
+ align:start position:0%
+convert from jewels to kogs and then our
+um units will be kogs per mole and here
+
+ align:start position:0%
+um units will be kogs per mole and here
+ 
+
+ align:start position:0%
+um units will be kogs per mole and here
+Delta G is a negative value so it is
+
+ align:start position:0%
+Delta G is a negative value so it is
+ 
+
+ align:start position:0%
+Delta G is a negative value so it is
+spontaneous we all know it's spontaneous
+
+ align:start position:0%
+spontaneous we all know it's spontaneous
+ 
+
+ align:start position:0%
+spontaneous we all know it's spontaneous
+we've observed this happening um so even
+
+ align:start position:0%
+we've observed this happening um so even
+ 
+
+ align:start position:0%
+we've observed this happening um so even
+though Delta H KN is positive it's an
+
+ align:start position:0%
+though Delta H KN is positive it's an
+ 
+
+ align:start position:0%
+though Delta H KN is positive it's an
+endothermic reaction ice melts at room
+
+ align:start position:0%
+endothermic reaction ice melts at room
+ 
+
+ align:start position:0%
+endothermic reaction ice melts at room
+temperature because the Delta G is
+
+ align:start position:0%
+temperature because the Delta G is
+ 
+
+ align:start position:0%
+temperature because the Delta G is
+negative all right so let's talk a
+
+ align:start position:0%
+negative all right so let's talk a
+ 
+
+ align:start position:0%
+negative all right so let's talk a
+little more about Delta G so let's talk
+
+ align:start position:0%
+little more about Delta G so let's talk
+ 
+
+ align:start position:0%
+little more about Delta G so let's talk
+about free energy of
+
+ align:start position:0%
+about free energy of
+ 
+
+ align:start position:0%
+about free energy of
+formation and the last page of this
+
+ align:start position:0%
+formation and the last page of this
+ 
+
+ align:start position:0%
+formation and the last page of this
+handout so free energy of formation um
+
+ align:start position:0%
+handout so free energy of formation um
+ 
+
+ align:start position:0%
+handout so free energy of formation um
+Delta G
+
+ align:start position:0%
+Delta G
+ 
+
+ align:start position:0%
+Delta G
+subf and so this is analogous to Delta h
+
+ align:start position:0%
+subf and so this is analogous to Delta h
+ 
+
+ align:start position:0%
+subf and so this is analogous to Delta h
+of formation so the en change in
+
+ align:start position:0%
+of formation so the en change in
+ 
+
+ align:start position:0%
+of formation so the en change in
+enthalpy of
+
+ align:start position:0%
+enthalpy of
+ 
+
+ align:start position:0%
+enthalpy of
+formation so again when you have the
+
+ align:start position:0%
+formation so again when you have the
+ 
+
+ align:start position:0%
+formation so again when you have the
+little uh little value here the standard
+
+ align:start position:0%
+little uh little value here the standard
+ 
+
+ align:start position:0%
+little uh little value here the standard
+gives free energy of formation for the F
+
+ align:start position:0%
+gives free energy of formation for the F
+ 
+
+ align:start position:0%
+gives free energy of formation for the F
+here and that's the formation of one
+
+ align:start position:0%
+here and that's the formation of one
+ 
+
+ align:start position:0%
+here and that's the formation of one
+mole of a molecule from its elements in
+
+ align:start position:0%
+mole of a molecule from its elements in
+ 
+
+ align:start position:0%
+mole of a molecule from its elements in
+the most uh stable State and in their
+
+ align:start position:0%
+the most uh stable State and in their
+ 
+
+ align:start position:0%
+the most uh stable State and in their
+standard
+
+ align:start position:0%
+standard
+ 
+
+ align:start position:0%
+standard
+States so we can have tables in your
+
+ align:start position:0%
+States so we can have tables in your
+ 
+
+ align:start position:0%
+States so we can have tables in your
+book of these values so your book in the
+
+ align:start position:0%
+book of these values so your book in the
+ 
+
+ align:start position:0%
+book of these values so your book in the
+back if you haven't explored the back of
+
+ align:start position:0%
+back if you haven't explored the back of
+ 
+
+ align:start position:0%
+back if you haven't explored the back of
+your book is lots of tables of things um
+
+ align:start position:0%
+your book is lots of tables of things um
+ 
+
+ align:start position:0%
+your book is lots of tables of things um
+including uh um information about Delta
+
+ align:start position:0%
+including uh um information about Delta
+ 
+
+ align:start position:0%
+including uh um information about Delta
+G's and Delta H's and bond enthalpies
+
+ align:start position:0%
+G's and Delta H's and bond enthalpies
+ 
+
+ align:start position:0%
+G's and Delta H's and bond enthalpies
+and all sorts of other things Redux
+
+ align:start position:0%
+and all sorts of other things Redux
+ 
+
+ align:start position:0%
+and all sorts of other things Redux
+potentials we haven't talked about yet
+
+ align:start position:0%
+potentials we haven't talked about yet
+ 
+
+ align:start position:0%
+potentials we haven't talked about yet
+lots of tables so you can look this up
+
+ align:start position:0%
+lots of tables so you can look this up
+ 
+
+ align:start position:0%
+lots of tables so you can look this up
+um or if you have already say looked up
+
+ align:start position:0%
+um or if you have already say looked up
+ 
+
+ align:start position:0%
+um or if you have already say looked up
+your Delta h of formation you can use
+
+ align:start position:0%
+your Delta h of formation you can use
+ 
+
+ align:start position:0%
+your Delta h of formation you can use
+this handy equation Delta G equal Delta
+
+ align:start position:0%
+this handy equation Delta G equal Delta
+ 
+
+ align:start position:0%
+this handy equation Delta G equal Delta
+H minus t Delta Delta s but if we plug
+
+ align:start position:0%
+H minus t Delta Delta s but if we plug
+ 
+
+ align:start position:0%
+H minus t Delta Delta s but if we plug
+in our Delta H's of formation we can get
+
+ align:start position:0%
+in our Delta H's of formation we can get
+ 
+
+ align:start position:0%
+in our Delta H's of formation we can get
+our Delta G's of formation so how you're
+
+ align:start position:0%
+our Delta G's of formation so how you're
+ 
+
+ align:start position:0%
+our Delta G's of formation so how you're
+going to calculate Dental Delta G of
+
+ align:start position:0%
+going to calculate Dental Delta G of
+ 
+
+ align:start position:0%
+going to calculate Dental Delta G of
+formation depends on what information
+
+ align:start position:0%
+formation depends on what information
+ 
+
+ align:start position:0%
+formation depends on what information
+you are given so let's think a little
+
+ align:start position:0%
+you are given so let's think a little
+ 
+
+ align:start position:0%
+you are given so let's think a little
+bit about what it means for particular
+
+ align:start position:0%
+bit about what it means for particular
+ 
+
+ align:start position:0%
+bit about what it means for particular
+Delta G's of formation if they're
+
+ align:start position:0%
+Delta G's of formation if they're
+ 
+
+ align:start position:0%
+Delta G's of formation if they're
+positive or if they're
+
+ align:start position:0%
+positive or if they're
+ 
+
+ align:start position:0%
+positive or if they're
+negative so let's look at an example and
+
+ align:start position:0%
+negative so let's look at an example and
+ 
+
+ align:start position:0%
+negative so let's look at an example and
+we saw this before this is the formation
+
+ align:start position:0%
+we saw this before this is the formation
+ 
+
+ align:start position:0%
+we saw this before this is the formation
+of carbon dioxide from elements in its
+
+ align:start position:0%
+of carbon dioxide from elements in its
+ 
+
+ align:start position:0%
+of carbon dioxide from elements in its
+most stable state which is uh graphite
+
+ align:start position:0%
+most stable state which is uh graphite
+ 
+
+ align:start position:0%
+most stable state which is uh graphite
+carbon and O2 gas so these are the
+
+ align:start position:0%
+carbon and O2 gas so these are the
+ 
+
+ align:start position:0%
+carbon and O2 gas so these are the
+elements in their most stable State
+
+ align:start position:0%
+elements in their most stable State
+ 
+
+ align:start position:0%
+elements in their most stable State
+forming CO2 now I'm telling you that the
+
+ align:start position:0%
+forming CO2 now I'm telling you that the
+ 
+
+ align:start position:0%
+forming CO2 now I'm telling you that the
+Delta G KN is minus
+
+ align:start position:0%
+Delta G KN is minus
+ 
+
+ align:start position:0%
+Delta G KN is minus
+39436 K per mole and we can think about
+
+ align:start position:0%
+39436 K per mole and we can think about
+ 
+
+ align:start position:0%
+39436 K per mole and we can think about
+why this what this information tells us
+
+ align:start position:0%
+why this what this information tells us
+ 
+
+ align:start position:0%
+why this what this information tells us
+that this is a fairly large negative
+
+ align:start position:0%
+that this is a fairly large negative
+ 
+
+ align:start position:0%
+that this is a fairly large negative
+number so if Delta um Delta G of form
+
+ align:start position:0%
+number so if Delta um Delta G of form
+ 
+
+ align:start position:0%
+number so if Delta um Delta G of form
+is less than zero What's going to be
+
+ align:start position:0%
+is less than zero What's going to be
+ 
+
+ align:start position:0%
+is less than zero What's going to be
+true thermodynamically and this is a
+
+ align:start position:0%
+true thermodynamically and this is a
+ 
+
+ align:start position:0%
+true thermodynamically and this is a
+clicker
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question all right let's just just take
+
+ align:start position:0%
+question all right let's just just take
+ 
+
+ align:start position:0%
+question all right let's just just take
+10 more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds interesting okay so let's think
+
+ align:start position:0%
+seconds interesting okay so let's think
+ 
+
+ align:start position:0%
+seconds interesting okay so let's think
+about why this is true this might be the
+
+ align:start position:0%
+about why this is true this might be the
+ 
+
+ align:start position:0%
+about why this is true this might be the
+deciding uh a deciding clicker question
+
+ align:start position:0%
+deciding uh a deciding clicker question
+ 
+
+ align:start position:0%
+deciding uh a deciding clicker question
+we'll see um so if it is negative
+
+ align:start position:0%
+we'll see um so if it is negative
+ 
+
+ align:start position:0%
+we'll see um so if it is negative
+value for Delta g a negative value for
+
+ align:start position:0%
+value for Delta g a negative value for
+ 
+
+ align:start position:0%
+value for Delta g a negative value for
+Delta g means that it's spontaneous in
+
+ align:start position:0%
+Delta g means that it's spontaneous in
+ 
+
+ align:start position:0%
+Delta g means that it's spontaneous in
+its forward Direction so here the
+
+ align:start position:0%
+its forward Direction so here the
+ 
+
+ align:start position:0%
+its forward Direction so here the
+formation from the elements in their
+
+ align:start position:0%
+formation from the elements in their
+ 
+
+ align:start position:0%
+formation from the elements in their
+most stable state if this is spontaneous
+
+ align:start position:0%
+most stable state if this is spontaneous
+ 
+
+ align:start position:0%
+most stable state if this is spontaneous
+in the forward Direction it also means
+
+ align:start position:0%
+in the forward Direction it also means
+ 
+
+ align:start position:0%
+in the forward Direction it also means
+that it's non-spontaneous in the reverse
+
+ align:start position:0%
+that it's non-spontaneous in the reverse
+ 
+
+ align:start position:0%
+that it's non-spontaneous in the reverse
+direction that means once CO2 forms it's
+
+ align:start position:0%
+direction that means once CO2 forms it's
+ 
+
+ align:start position:0%
+direction that means once CO2 forms it's
+going to be stable compared to the
+
+ align:start position:0%
+going to be stable compared to the
+ 
+
+ align:start position:0%
+going to be stable compared to the
+elements from which it came because it's
+
+ align:start position:0%
+elements from which it came because it's
+ 
+
+ align:start position:0%
+elements from which it came because it's
+non-spontaneous
+
+ align:start position:0%
+non-spontaneous
+ 
+
+ align:start position:0%
+non-spontaneous
+going in the reverse direction or at
+
+ align:start position:0%
+going in the reverse direction or at
+ 
+
+ align:start position:0%
+going in the reverse direction or at
+least that's the way that I like to
+
+ align:start position:0%
+least that's the way that I like to
+ 
+
+ align:start position:0%
+least that's the way that I like to
+think about it so relative to its
+
+ align:start position:0%
+think about it so relative to its
+ 
+
+ align:start position:0%
+think about it so relative to its
+elements it's stable spontaneous forward
+
+ align:start position:0%
+elements it's stable spontaneous forward
+ 
+
+ align:start position:0%
+elements it's stable spontaneous forward
+non-spontaneous in
+
+ align:start position:0%
+non-spontaneous in
+ 
+
+ align:start position:0%
+non-spontaneous in
+Reverse so this is kind of bad news for
+
+ align:start position:0%
+Reverse so this is kind of bad news for
+ 
+
+ align:start position:0%
+Reverse so this is kind of bad news for
+us because there's too much CO2 in our
+
+ align:start position:0%
+us because there's too much CO2 in our
+ 
+
+ align:start position:0%
+us because there's too much CO2 in our
+environment right now it's a greenhouse
+
+ align:start position:0%
+environment right now it's a greenhouse
+ 
+
+ align:start position:0%
+environment right now it's a greenhouse
+gas and wouldn't it be awesome if we
+
+ align:start position:0%
+gas and wouldn't it be awesome if we
+ 
+
+ align:start position:0%
+gas and wouldn't it be awesome if we
+could just uh encourage it all to uh go
+
+ align:start position:0%
+could just uh encourage it all to uh go
+ 
+
+ align:start position:0%
+could just uh encourage it all to uh go
+back to its elements for more oxygen
+
+ align:start position:0%
+back to its elements for more oxygen
+ 
+
+ align:start position:0%
+back to its elements for more oxygen
+which we could breathe how lovely make
+
+ align:start position:0%
+which we could breathe how lovely make
+ 
+
+ align:start position:0%
+which we could breathe how lovely make
+some nice graphite maybe compress it
+
+ align:start position:0%
+some nice graphite maybe compress it
+ 
+
+ align:start position:0%
+some nice graphite maybe compress it
+make some diamonds but no um it is uh
+
+ align:start position:0%
+make some diamonds but no um it is uh
+ 
+
+ align:start position:0%
+make some diamonds but no um it is uh
+quite stable compared to its elements so
+
+ align:start position:0%
+quite stable compared to its elements so
+ 
+
+ align:start position:0%
+quite stable compared to its elements so
+CO2 is in our environment causing global
+
+ align:start position:0%
+CO2 is in our environment causing global
+ 
+
+ align:start position:0%
+CO2 is in our environment causing global
+warming and uh it's going to be hard to
+
+ align:start position:0%
+warming and uh it's going to be hard to
+ 
+
+ align:start position:0%
+warming and uh it's going to be hard to
+solve that problem not easy to solve
+
+ align:start position:0%
+solve that problem not easy to solve
+ 
+
+ align:start position:0%
+solve that problem not easy to solve
+that problem so this is unfortunate news
+
+ align:start position:0%
+that problem so this is unfortunate news
+ 
+
+ align:start position:0%
+that problem so this is unfortunate news
+that thermodynamics gives us all right
+
+ align:start position:0%
+that thermodynamics gives us all right
+ 
+
+ align:start position:0%
+that thermodynamics gives us all right
+so then we can look at the other if you
+
+ align:start position:0%
+so then we can look at the other if you
+ 
+
+ align:start position:0%
+so then we can look at the other if you
+have a positive value for Delta um Delta
+
+ align:start position:0%
+have a positive value for Delta um Delta
+ 
+
+ align:start position:0%
+have a positive value for Delta um Delta
+G of formation then it's thermodynamic
+
+ align:start position:0%
+G of formation then it's thermodynamic
+ 
+
+ align:start position:0%
+G of formation then it's thermodynamic
+ially unstable compared to its elements
+
+ align:start position:0%
+ially unstable compared to its elements
+ 
+
+ align:start position:0%
+ially unstable compared to its elements
+so it's spontaneous going in the reverse
+
+ align:start position:0%
+so it's spontaneous going in the reverse
+ 
+
+ align:start position:0%
+so it's spontaneous going in the reverse
+Direction so it's
+
+ align:start position:0%
+Direction so it's
+ 
+
+ align:start position:0%
+Direction so it's
+unstable so thermodynamics tells us
+
+ align:start position:0%
+unstable so thermodynamics tells us
+ 
+
+ align:start position:0%
+unstable so thermodynamics tells us
+whether something is stable or
+
+ align:start position:0%
+whether something is stable or
+ 
+
+ align:start position:0%
+whether something is stable or
+unstable and kinetics tells us about
+
+ align:start position:0%
+unstable and kinetics tells us about
+ 
+
+ align:start position:0%
+unstable and kinetics tells us about
+whether things will react quickly or not
+
+ align:start position:0%
+whether things will react quickly or not
+ 
+
+ align:start position:0%
+whether things will react quickly or not
+so something can be kinetically inert it
+
+ align:start position:0%
+so something can be kinetically inert it
+ 
+
+ align:start position:0%
+so something can be kinetically inert it
+might take a long time to react but
+
+ align:start position:0%
+might take a long time to react but
+ 
+
+ align:start position:0%
+might take a long time to react but
+thermodynamics tell us us stable
+
+ align:start position:0%
+thermodynamics tell us us stable
+ 
+
+ align:start position:0%
+thermodynamics tell us us stable
+unstable so thermodynamics is great um
+
+ align:start position:0%
+unstable so thermodynamics is great um
+ 
+
+ align:start position:0%
+unstable so thermodynamics is great um
+but it doesn't tell us anything about
+
+ align:start position:0%
+but it doesn't tell us anything about
+ 
+
+ align:start position:0%
+but it doesn't tell us anything about
+the rates of reactions so nothing about
+
+ align:start position:0%
+the rates of reactions so nothing about
+ 
+
+ align:start position:0%
+the rates of reactions so nothing about
+the rates and that's kinetics so really
+
+ align:start position:0%
+the rates and that's kinetics so really
+ 
+
+ align:start position:0%
+the rates and that's kinetics so really
+thermodynamics and kinetics are very
+
+ align:start position:0%
+thermodynamics and kinetics are very
+ 
+
+ align:start position:0%
+thermodynamics and kinetics are very
+important for explaining reactions and
+
+ align:start position:0%
+important for explaining reactions and
+ 
+
+ align:start position:0%
+important for explaining reactions and
+we'll talk about more kinetics at the
+
+ align:start position:0%
+we'll talk about more kinetics at the
+ 
+
+ align:start position:0%
+we'll talk about more kinetics at the
+end so to calculate a Delta G for a
+
+ align:start position:0%
+end so to calculate a Delta G for a
+ 
+
+ align:start position:0%
+end so to calculate a Delta G for a
+reaction um it depends again what you're
+
+ align:start position:0%
+reaction um it depends again what you're
+ 
+
+ align:start position:0%
+reaction um it depends again what you're
+given you can sum up uh the Delta G um
+
+ align:start position:0%
+given you can sum up uh the Delta G um
+ 
+
+ align:start position:0%
+given you can sum up uh the Delta G um
+of formation of your products minus your
+
+ align:start position:0%
+of formation of your products minus your
+ 
+
+ align:start position:0%
+of formation of your products minus your
+reactants or you might use this you'll
+
+ align:start position:0%
+reactants or you might use this you'll
+ 
+
+ align:start position:0%
+reactants or you might use this you'll
+find yourself using this equation a lot
+
+ align:start position:0%
+find yourself using this equation a lot
+ 
+
+ align:start position:0%
+find yourself using this equation a lot
+this again is really uh was a crowning
+
+ align:start position:0%
+this again is really uh was a crowning
+ 
+
+ align:start position:0%
+this again is really uh was a crowning
+achievement of thermodynamics that Delta
+
+ align:start position:0%
+achievement of thermodynamics that Delta
+ 
+
+ align:start position:0%
+achievement of thermodynamics that Delta
+g equals Delta H minus t Delta s so
+
+ align:start position:0%
+g equals Delta H minus t Delta s so
+ 
+
+ align:start position:0%
+g equals Delta H minus t Delta s so
+again whatever information you're given
+
+ align:start position:0%
+again whatever information you're given
+ 
+
+ align:start position:0%
+again whatever information you're given
+you can use that to find these
+
+ align:start position:0%
+you can use that to find these
+ 
+
+ align:start position:0%
+you can use that to find these
+values okay so we're not done with this
+
+ align:start position:0%
+values okay so we're not done with this
+ 
+
+ align:start position:0%
+values okay so we're not done with this
+equation we're going to switch handouts
+
+ align:start position:0%
+equation we're going to switch handouts
+ 
+
+ align:start position:0%
+equation we're going to switch handouts
+but we're going to continue with that
+
+ align:start position:0%
+but we're going to continue with that
+ 
+
+ align:start position:0%
+but we're going to continue with that
+exact same equation
\ No newline at end of file
diff --git a/Oxk2nnuC130.txt b/Oxk2nnuC130.txt
new file mode 100644
index 0000000000000000000000000000000000000000..28e8118a83480c51a209646e21a5ebcf1cad3ab8
--- /dev/null
+++ b/Oxk2nnuC130.txt
@@ -0,0 +1,7571 @@
+align:start position:0%
+ 
+in the previous lecture I began
+
+ align:start position:0%
+in the previous lecture I began
+ 
+
+ align:start position:0%
+in the previous lecture I began
+the Einstein field equations in the most
+
+ align:start position:0%
+the Einstein field equations in the most
+ 
+
+ align:start position:0%
+the Einstein field equations in the most
+general form and then I specialized to
+
+ align:start position:0%
+general form and then I specialized to
+ 
+
+ align:start position:0%
+general form and then I specialized to
+linearize gravity taking the space-time
+
+ align:start position:0%
+linearize gravity taking the space-time
+ 
+
+ align:start position:0%
+linearize gravity taking the space-time
+metric assuming that I can find a
+
+ align:start position:0%
+metric assuming that I can find a
+ 
+
+ align:start position:0%
+metric assuming that I can find a
+coordinate system in which it is close
+
+ align:start position:0%
+coordinate system in which it is close
+ 
+
+ align:start position:0%
+coordinate system in which it is close
+to the ADA alpha beta form that we use
+
+ align:start position:0%
+to the ADA alpha beta form that we use
+ 
+
+ align:start position:0%
+to the ADA alpha beta form that we use
+for flat space-time plus a small
+
+ align:start position:0%
+for flat space-time plus a small
+ 
+
+ align:start position:0%
+for flat space-time plus a small
+perturbation something that's defined
+
+ align:start position:0%
+perturbation something that's defined
+ 
+
+ align:start position:0%
+perturbation something that's defined
+such that whenever I have that h
+
+ align:start position:0%
+such that whenever I have that h
+ 
+
+ align:start position:0%
+such that whenever I have that h
+multiplied by itself I can neglect it
+
+ align:start position:0%
+multiplied by itself I can neglect it
+ 
+
+ align:start position:0%
+multiplied by itself I can neglect it
+doing so I was able to recast the
+
+ align:start position:0%
+doing so I was able to recast the
+ 
+
+ align:start position:0%
+doing so I was able to recast the
+Einstein field equations as a simple
+
+ align:start position:0%
+Einstein field equations as a simple
+ 
+
+ align:start position:0%
+Einstein field equations as a simple
+linear equation which is the wave
+
+ align:start position:0%
+linear equation which is the wave
+ 
+
+ align:start position:0%
+linear equation which is the wave
+operator acting on a variant of that
+
+ align:start position:0%
+operator acting on a variant of that
+ 
+
+ align:start position:0%
+operator acting on a variant of that
+perturbation the trace reverse versions
+
+ align:start position:0%
+perturbation the trace reverse versions
+ 
+
+ align:start position:0%
+perturbation the trace reverse versions
+of that perturbation it is minus 16 pi G
+
+ align:start position:0%
+of that perturbation it is minus 16 pi G
+ 
+
+ align:start position:0%
+of that perturbation it is minus 16 pi G
+times the stress energy tensor so in
+
+ align:start position:0%
+times the stress energy tensor so in
+ 
+
+ align:start position:0%
+times the stress energy tensor so in
+doing this recasting I have essentially
+
+ align:start position:0%
+doing this recasting I have essentially
+ 
+
+ align:start position:0%
+doing this recasting I have essentially
+just a trick of reorganizing the
+
+ align:start position:0%
+just a trick of reorganizing the
+ 
+
+ align:start position:0%
+just a trick of reorganizing the
+variables I have taken my H alpha beta
+
+ align:start position:0%
+variables I have taken my H alpha beta
+ 
+
+ align:start position:0%
+variables I have taken my H alpha beta
+which describes the way in which
+
+ align:start position:0%
+which describes the way in which
+ 
+
+ align:start position:0%
+which describes the way in which
+space-time is shifted away from that of
+
+ align:start position:0%
+space-time is shifted away from that of
+ 
+
+ align:start position:0%
+space-time is shifted away from that of
+flat space-time the perturbation of flat
+
+ align:start position:0%
+flat space-time the perturbation of flat
+ 
+
+ align:start position:0%
+flat space-time the perturbation of flat
+space-time and I've just rearranged that
+
+ align:start position:0%
+space-time and I've just rearranged that
+ 
+
+ align:start position:0%
+space-time and I've just rearranged that
+to give it the trace with the opposite
+
+ align:start position:0%
+to give it the trace with the opposite
+ 
+
+ align:start position:0%
+to give it the trace with the opposite
+sign and I have chosen a gauge such as
+
+ align:start position:0%
+sign and I have chosen a gauge such as
+ 
+
+ align:start position:0%
+sign and I have chosen a gauge such as
+the divergence of that trace reverse
+
+ align:start position:0%
+the divergence of that trace reverse
+ 
+
+ align:start position:0%
+the divergence of that trace reverse
+metric perturbation is zero if we take
+
+ align:start position:0%
+metric perturbation is zero if we take
+ 
+
+ align:start position:0%
+metric perturbation is zero if we take
+this equation which is completely
+
+ align:start position:0%
+this equation which is completely
+ 
+
+ align:start position:0%
+this equation which is completely
+general for linearized space-time only
+
+ align:start position:0%
+general for linearized space-time only
+ 
+
+ align:start position:0%
+general for linearized space-time only
+thing which I had to do is choose a
+
+ align:start position:0%
+thing which I had to do is choose a
+ 
+
+ align:start position:0%
+thing which I had to do is choose a
+particular gauge and there's no physics
+
+ align:start position:0%
+particular gauge and there's no physics
+ 
+
+ align:start position:0%
+particular gauge and there's no physics
+than that that's essentially a
+
+ align:start position:0%
+than that that's essentially a
+ 
+
+ align:start position:0%
+than that that's essentially a
+coordinate choice if I then imagined
+
+ align:start position:0%
+coordinate choice if I then imagined
+ 
+
+ align:start position:0%
+coordinate choice if I then imagined
+that my source is static I will have
+
+ align:start position:0%
+that my source is static I will have
+ 
+
+ align:start position:0%
+that my source is static I will have
+static fields and so my wave operator
+
+ align:start position:0%
+static fields and so my wave operator
+ 
+
+ align:start position:0%
+static fields and so my wave operator
+goes over to a simple applause operator
+
+ align:start position:0%
+goes over to a simple applause operator
+ 
+
+ align:start position:0%
+goes over to a simple applause operator
+and then it's not too hard to show that
+
+ align:start position:0%
+and then it's not too hard to show that
+ 
+
+ align:start position:0%
+and then it's not too hard to show that
+the solution that emerges from this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+looks like this where Phi n is Newtonian
+
+ align:start position:0%
+looks like this where Phi n is Newtonian
+ 
+
+ align:start position:0%
+looks like this where Phi n is Newtonian
+gravitational potential which arises
+
+ align:start position:0%
+gravitational potential which arises
+ 
+
+ align:start position:0%
+gravitational potential which arises
+from a distribution of mass like some so
+
+ align:start position:0%
+from a distribution of mass like some so
+ 
+
+ align:start position:0%
+from a distribution of mass like some so
+this is the leading solution and it's
+
+ align:start position:0%
+this is the leading solution and it's
+ 
+
+ align:start position:0%
+this is the leading solution and it's
+one that is very powerful and very
+
+ align:start position:0%
+one that is very powerful and very
+ 
+
+ align:start position:0%
+one that is very powerful and very
+useful and it's actually using
+
+ align:start position:0%
+useful and it's actually using
+ 
+
+ align:start position:0%
+useful and it's actually using
+tremendous number of physics and
+
+ align:start position:0%
+tremendous number of physics and
+ 
+
+ align:start position:0%
+tremendous number of physics and
+astronomical applications this
+
+ align:start position:0%
+astronomical applications this
+ 
+
+ align:start position:0%
+astronomical applications this
+restriction to a static source though is
+
+ align:start position:0%
+restriction to a static source though is
+ 
+
+ align:start position:0%
+restriction to a static source though is
+well it's restrictive what if I do not
+
+ align:start position:0%
+well it's restrictive what if I do not
+ 
+
+ align:start position:0%
+well it's restrictive what if I do not
+want to simply consider a static source
+
+ align:start position:0%
+want to simply consider a static source
+ 
+
+ align:start position:0%
+want to simply consider a static source
+what if I'm interested in sources of the
+
+ align:start position:0%
+what if I'm interested in sources of the
+ 
+
+ align:start position:0%
+what if I'm interested in sources of the
+gravitational interaction that are
+
+ align:start position:0%
+gravitational interaction that are
+ 
+
+ align:start position:0%
+gravitational interaction that are
+themselves dynamical and so I emphasized
+
+ align:start position:0%
+themselves dynamical and so I emphasized
+ 
+
+ align:start position:0%
+themselves dynamical and so I emphasized
+last time that this wave equation my box
+
+ align:start position:0%
+last time that this wave equation my box
+ 
+
+ align:start position:0%
+last time that this wave equation my box
+H bar alpha beta equals -16 Pi GT alpha
+
+ align:start position:0%
+H bar alpha beta equals -16 Pi GT alpha
+ 
+
+ align:start position:0%
+H bar alpha beta equals -16 Pi GT alpha
+beta this is something that I hope you
+
+ align:start position:0%
+beta this is something that I hope you
+ 
+
+ align:start position:0%
+beta this is something that I hope you
+have already seen in the context of
+
+ align:start position:0%
+have already seen in the context of
+ 
+
+ align:start position:0%
+have already seen in the context of
+electrodynamics in particular whenever
+
+ align:start position:0%
+electrodynamics in particular whenever
+ 
+
+ align:start position:0%
+electrodynamics in particular whenever
+we have a wave equation whose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not even a wave equation but any
+
+ align:start position:0%
+not even a wave equation but any
+ 
+
+ align:start position:0%
+not even a wave equation but any
+differential equation that is of the
+
+ align:start position:0%
+differential equation that is of the
+ 
+
+ align:start position:0%
+differential equation that is of the
+form linear differential operator on
+
+ align:start position:0%
+form linear differential operator on
+ 
+
+ align:start position:0%
+form linear differential operator on
+field is equal to a source okay so I'm
+
+ align:start position:0%
+field is equal to a source okay so I'm
+ 
+
+ align:start position:0%
+field is equal to a source okay so I'm
+separately I'm separating out time and
+
+ align:start position:0%
+separately I'm separating out time and
+ 
+
+ align:start position:0%
+separately I'm separating out time and
+spatial behavior here whenever I have a
+
+ align:start position:0%
+spatial behavior here whenever I have a
+ 
+
+ align:start position:0%
+spatial behavior here whenever I have a
+situation which I'm interested in the
+
+ align:start position:0%
+situation which I'm interested in the
+ 
+
+ align:start position:0%
+situation which I'm interested in the
+studying a field that in which some
+
+ align:start position:0%
+studying a field that in which some
+ 
+
+ align:start position:0%
+studying a field that in which some
+differential operator operator acting on
+
+ align:start position:0%
+differential operator operator acting on
+ 
+
+ align:start position:0%
+differential operator operator acting on
+that field is equal to a source we can
+
+ align:start position:0%
+that field is equal to a source we can
+ 
+
+ align:start position:0%
+that field is equal to a source we can
+solve this using the technique of greens
+
+ align:start position:0%
+solve this using the technique of greens
+ 
+
+ align:start position:0%
+solve this using the technique of greens
+functions I am NOT going to be able to
+
+ align:start position:0%
+functions I am NOT going to be able to
+ 
+
+ align:start position:0%
+functions I am NOT going to be able to
+go through the technique of greens
+
+ align:start position:0%
+go through the technique of greens
+ 
+
+ align:start position:0%
+go through the technique of greens
+functions in detail I will quickly give
+
+ align:start position:0%
+functions in detail I will quickly give
+ 
+
+ align:start position:0%
+functions in detail I will quickly give
+you a synopsis of how it works and then
+
+ align:start position:0%
+you a synopsis of how it works and then
+ 
+
+ align:start position:0%
+you a synopsis of how it works and then
+I will look at particular greens
+
+ align:start position:0%
+I will look at particular greens
+ 
+
+ align:start position:0%
+I will look at particular greens
+function that applies to the wave
+
+ align:start position:0%
+function that applies to the wave
+ 
+
+ align:start position:0%
+function that applies to the wave
+operator students would like to read
+
+ align:start position:0%
+operator students would like to read
+ 
+
+ align:start position:0%
+operator students would like to read
+more about this I would point you to the
+
+ align:start position:0%
+more about this I would point you to the
+ 
+
+ align:start position:0%
+more about this I would point you to the
+textbook by Arkin I believe it isn't it
+
+ align:start position:0%
+textbook by Arkin I believe it isn't it
+ 
+
+ align:start position:0%
+textbook by Arkin I believe it isn't it
+it's called mathematical methods for
+
+ align:start position:0%
+it's called mathematical methods for
+ 
+
+ align:start position:0%
+it's called mathematical methods for
+physicists and in the third edition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+greens functions are described in
+
+ align:start position:0%
+greens functions are described in
+ 
+
+ align:start position:0%
+greens functions are described in
+section sixteen point five to sixteen
+
+ align:start position:0%
+section sixteen point five to sixteen
+ 
+
+ align:start position:0%
+section sixteen point five to sixteen
+point six so in a nutshell let me just
+
+ align:start position:0%
+point six so in a nutshell let me just
+ 
+
+ align:start position:0%
+point six so in a nutshell let me just
+give you a very brief synopsis of how
+
+ align:start position:0%
+give you a very brief synopsis of how
+ 
+
+ align:start position:0%
+give you a very brief synopsis of how
+this technique works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose we take our source which may be
+
+ align:start position:0%
+suppose we take our source which may be
+ 
+
+ align:start position:0%
+suppose we take our source which may be
+some complicated very ornate entity what
+
+ align:start position:0%
+some complicated very ornate entity what
+ 
+
+ align:start position:0%
+some complicated very ornate entity what
+we're going to do is replace that source
+
+ align:start position:0%
+we're going to do is replace that source
+ 
+
+ align:start position:0%
+we're going to do is replace that source
+with a delta function so imagine that I
+
+ align:start position:0%
+with a delta function so imagine that I
+ 
+
+ align:start position:0%
+with a delta function so imagine that I
+take s of T and X over to a delta at
+
+ align:start position:0%
+take s of T and X over to a delta at
+ 
+
+ align:start position:0%
+take s of T and X over to a delta at
+some time T prime and a 3-dimensional at
+
+ align:start position:0%
+some time T prime and a 3-dimensional at
+ 
+
+ align:start position:0%
+some time T prime and a 3-dimensional at
+Delta in some location X prime what I'm
+
+ align:start position:0%
+Delta in some location X prime what I'm
+ 
+
+ align:start position:0%
+Delta in some location X prime what I'm
+basically saying here is I'm imagining I
+
+ align:start position:0%
+basically saying here is I'm imagining I
+ 
+
+ align:start position:0%
+basically saying here is I'm imagining I
+a might have some source that's extended
+
+ align:start position:0%
+a might have some source that's extended
+ 
+
+ align:start position:0%
+a might have some source that's extended
+in time and extended in space and I'm
+
+ align:start position:0%
+in time and extended in space and I'm
+ 
+
+ align:start position:0%
+in time and extended in space and I'm
+just going to look at the little blip at
+
+ align:start position:0%
+just going to look at the little blip at
+ 
+
+ align:start position:0%
+just going to look at the little blip at
+one particular event that and see if you
+
+ align:start position:0%
+one particular event that and see if you
+ 
+
+ align:start position:0%
+one particular event that and see if you
+know I replace my source with this one
+
+ align:start position:0%
+know I replace my source with this one
+ 
+
+ align:start position:0%
+know I replace my source with this one
+single blip what does my what what field
+
+ align:start position:0%
+single blip what does my what what field
+ 
+
+ align:start position:0%
+single blip what does my what what field
+emerges from that what we're going to do
+
+ align:start position:0%
+emerges from that what we're going to do
+ 
+
+ align:start position:0%
+emerges from that what we're going to do
+is assert that a solution exists and we
+
+ align:start position:0%
+is assert that a solution exists and we
+ 
+
+ align:start position:0%
+is assert that a solution exists and we
+will call the field that arises when my
+
+ align:start position:0%
+will call the field that arises when my
+ 
+
+ align:start position:0%
+will call the field that arises when my
+source is replaced with a delta function
+
+ align:start position:0%
+source is replaced with a delta function
+ 
+
+ align:start position:0%
+source is replaced with a delta function
+we'll call it capital G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this notation means that this is
+
+ align:start position:0%
+okay this notation means that this is
+ 
+
+ align:start position:0%
+okay this notation means that this is
+the amount of field @tx arising from my
+
+ align:start position:0%
+the amount of field @tx arising from my
+ 
+
+ align:start position:0%
+the amount of field @tx arising from my
+source at t prime x prime okay so my
+
+ align:start position:0%
+source at t prime x prime okay so my
+ 
+
+ align:start position:0%
+source at t prime x prime okay so my
+differential equation for this equation
+
+ align:start position:0%
+differential equation for this equation
+ 
+
+ align:start position:0%
+differential equation for this equation
+for this solution G now looks like so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so whatever my linear operator is
+
+ align:start position:0%
+okay so whatever my linear operator is
+ 
+
+ align:start position:0%
+okay so whatever my linear operator is
+when an axial on this J it gives me the
+
+ align:start position:0%
+when an axial on this J it gives me the
+ 
+
+ align:start position:0%
+when an axial on this J it gives me the
+source which is now the Delta function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me just introduce a little bit of
+
+ align:start position:0%
+let me just introduce a little bit of
+ 
+
+ align:start position:0%
+let me just introduce a little bit of
+notation here so T and X I call this the
+
+ align:start position:0%
+notation here so T and X I call this the
+ 
+
+ align:start position:0%
+notation here so T and X I call this the
+field point this is the point at which
+
+ align:start position:0%
+field point this is the point at which
+ 
+
+ align:start position:0%
+field point this is the point at which
+the field G is being measured T prime X
+
+ align:start position:0%
+the field G is being measured T prime X
+ 
+
+ align:start position:0%
+the field G is being measured T prime X
+prime is my source point this is the
+
+ align:start position:0%
+prime is my source point this is the
+ 
+
+ align:start position:0%
+prime is my source point this is the
+point at which the the source is nonzero
+
+ align:start position:0%
+point at which the the source is nonzero
+ 
+
+ align:start position:0%
+point at which the the source is nonzero
+in a particular case it's actually a
+
+ align:start position:0%
+in a particular case it's actually a
+ 
+
+ align:start position:0%
+in a particular case it's actually a
+little Delta function spike the reason
+
+ align:start position:0%
+little Delta function spike the reason
+ 
+
+ align:start position:0%
+little Delta function spike the reason
+why we do this is pretty much by
+
+ align:start position:0%
+why we do this is pretty much by
+ 
+
+ align:start position:0%
+why we do this is pretty much by
+definition one second yes pretty much by
+
+ align:start position:0%
+definition one second yes pretty much by
+ 
+
+ align:start position:0%
+definition one second yes pretty much by
+definition if I take the source and I
+
+ align:start position:0%
+definition if I take the source and I
+ 
+
+ align:start position:0%
+definition if I take the source and I
+integrated against the Delta function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integrate over all time integrate over
+
+ align:start position:0%
+integrate over all time integrate over
+ 
+
+ align:start position:0%
+integrate over all time integrate over
+all space I must get the source back ok
+
+ align:start position:0%
+all space I must get the source back ok
+ 
+
+ align:start position:0%
+all space I must get the source back ok
+this is a tautology all I'm doing here
+
+ align:start position:0%
+this is a tautology all I'm doing here
+ 
+
+ align:start position:0%
+this is a tautology all I'm doing here
+is really saying this is the the
+
+ align:start position:0%
+is really saying this is the the
+ 
+
+ align:start position:0%
+is really saying this is the the
+properties of Delta functions however
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's sort of remarkable is if instead of
+
+ align:start position:0%
+it's sort of remarkable is if instead of
+ 
+
+ align:start position:0%
+it's sort of remarkable is if instead of
+integrating the source against the Delta
+
+ align:start position:0%
+integrating the source against the Delta
+ 
+
+ align:start position:0%
+integrating the source against the Delta
+functions if instead of the main grating
+
+ align:start position:0%
+functions if instead of the main grating
+ 
+
+ align:start position:0%
+functions if instead of the main grating
+the source against the Delta functions I
+
+ align:start position:0%
+the source against the Delta functions I
+ 
+
+ align:start position:0%
+the source against the Delta functions I
+integrate this source against the greens
+
+ align:start position:0%
+integrate this source against the greens
+ 
+
+ align:start position:0%
+integrate this source against the greens
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I do this then what I must get out of
+
+ align:start position:0%
+if I do this then what I must get out of
+ 
+
+ align:start position:0%
+if I do this then what I must get out of
+it this is a solution F this is actually
+
+ align:start position:0%
+it this is a solution F this is actually
+ 
+
+ align:start position:0%
+it this is a solution F this is actually
+very easy to prove simply take this
+
+ align:start position:0%
+very easy to prove simply take this
+ 
+
+ align:start position:0%
+very easy to prove simply take this
+equation let's call this equation a if
+
+ align:start position:0%
+equation let's call this equation a if
+ 
+
+ align:start position:0%
+equation let's call this equation a if
+you take equation a and operate on it
+
+ align:start position:0%
+you take equation a and operate on it
+ 
+
+ align:start position:0%
+you take equation a and operate on it
+with your differential operator G so if
+
+ align:start position:0%
+with your differential operator G so if
+ 
+
+ align:start position:0%
+with your differential operator G so if
+I hit equation a with D remember D it's
+
+ align:start position:0%
+I hit equation a with D remember D it's
+ 
+
+ align:start position:0%
+I hit equation a with D remember D it's
+a differential operator that acts on
+
+ align:start position:0%
+a differential operator that acts on
+ 
+
+ align:start position:0%
+a differential operator that acts on
+only the unprimed coordinates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know what let's just go and write
+
+ align:start position:0%
+you know what let's just go and write
+ 
+
+ align:start position:0%
+you know what let's just go and write
+this out so D on this integral when I
+
+ align:start position:0%
+this out so D on this integral when I
+ 
+
+ align:start position:0%
+this out so D on this integral when I
+hit D on this it goes straight through
+
+ align:start position:0%
+hit D on this it goes straight through
+ 
+
+ align:start position:0%
+hit D on this it goes straight through
+the integral this only axle on the
+
+ align:start position:0%
+the integral this only axle on the
+ 
+
+ align:start position:0%
+the integral this only axle on the
+unprimed coordinate so it ignores the
+
+ align:start position:0%
+unprimed coordinate so it ignores the
+ 
+
+ align:start position:0%
+unprimed coordinate so it ignores the
+integrals it ignores the S the only
+
+ align:start position:0%
+integrals it ignores the S the only
+ 
+
+ align:start position:0%
+integrals it ignores the S the only
+thing that that operator hits when I act
+
+ align:start position:0%
+thing that that operator hits when I act
+ 
+
+ align:start position:0%
+thing that that operator hits when I act
+on the integral is the greens function
+
+ align:start position:0%
+on the integral is the greens function
+ 
+
+ align:start position:0%
+on the integral is the greens function
+itself but I have asserted that the
+
+ align:start position:0%
+itself but I have asserted that the
+ 
+
+ align:start position:0%
+itself but I have asserted that the
+greens function is such that when D acts
+
+ align:start position:0%
+greens function is such that when D acts
+ 
+
+ align:start position:0%
+greens function is such that when D acts
+on it I get the Delta functions out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and by the definition of Delta functions
+
+ align:start position:0%
+and by the definition of Delta functions
+ 
+
+ align:start position:0%
+and by the definition of Delta functions
+this just gives me my source back so
+
+ align:start position:0%
+this just gives me my source back so
+ 
+
+ align:start position:0%
+this just gives me my source back so
+what this means is that if we can find
+
+ align:start position:0%
+what this means is that if we can find
+ 
+
+ align:start position:0%
+what this means is that if we can find
+the greens function for our differential
+
+ align:start position:0%
+the greens function for our differential
+ 
+
+ align:start position:0%
+the greens function for our differential
+operator all we need to do is integrate
+
+ align:start position:0%
+operator all we need to do is integrate
+ 
+
+ align:start position:0%
+operator all we need to do is integrate
+it against our source and the result
+
+ align:start position:0%
+it against our source and the result
+ 
+
+ align:start position:0%
+it against our source and the result
+must be the solution to our field
+
+ align:start position:0%
+must be the solution to our field
+ 
+
+ align:start position:0%
+must be the solution to our field
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+it's a beautiful technique so if you
+
+ align:start position:0%
+it's a beautiful technique so if you
+ 
+
+ align:start position:0%
+it's a beautiful technique so if you
+haven't seen this before
+
+ align:start position:0%
+haven't seen this before
+ 
+
+ align:start position:0%
+haven't seen this before
+I highly recommend that you turn to that
+
+ align:start position:0%
+I highly recommend that you turn to that
+ 
+
+ align:start position:0%
+I highly recommend that you turn to that
+reading in in arkin I'm going to just
+
+ align:start position:0%
+reading in in arkin I'm going to just
+ 
+
+ align:start position:0%
+reading in in arkin I'm going to just
+take advantage of this I'm gonna use
+
+ align:start position:0%
+take advantage of this I'm gonna use
+ 
+
+ align:start position:0%
+take advantage of this I'm gonna use
+this technique now particular I'm gonna
+
+ align:start position:0%
+this technique now particular I'm gonna
+ 
+
+ align:start position:0%
+this technique now particular I'm gonna
+take advantage of the fact that if my
+
+ align:start position:0%
+take advantage of the fact that if my
+ 
+
+ align:start position:0%
+take advantage of the fact that if my
+differential operator is in fact the
+
+ align:start position:0%
+differential operator is in fact the
+ 
+
+ align:start position:0%
+differential operator is in fact the
+flat space-time wave operator there is a
+
+ align:start position:0%
+flat space-time wave operator there is a
+ 
+
+ align:start position:0%
+flat space-time wave operator there is a
+very well-known solution for it's for
+
+ align:start position:0%
+very well-known solution for it's for
+ 
+
+ align:start position:0%
+very well-known solution for it's for
+the greens function it's called the
+
+ align:start position:0%
+the greens function it's called the
+ 
+
+ align:start position:0%
+the greens function it's called the
+radiative greens function in this case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm just going to write down what the
+
+ align:start position:0%
+I'm just going to write down what the
+ 
+
+ align:start position:0%
+I'm just going to write down what the
+solution is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I'm going to talk about the
+
+ align:start position:0%
+okay so I'm going to talk about the
+ 
+
+ align:start position:0%
+okay so I'm going to talk about the
+properties of this in just a moment
+
+ align:start position:0%
+properties of this in just a moment
+ 
+
+ align:start position:0%
+properties of this in just a moment
+well this comment that had this is
+
+ align:start position:0%
+well this comment that had this is
+ 
+
+ align:start position:0%
+well this comment that had this is
+something that you should be able to
+
+ align:start position:0%
+something that you should be able to
+ 
+
+ align:start position:0%
+something that you should be able to
+find developed in any good quality
+
+ align:start position:0%
+find developed in any good quality
+ 
+
+ align:start position:0%
+find developed in any good quality
+advanced electrodynamics textbook in my
+
+ align:start position:0%
+advanced electrodynamics textbook in my
+ 
+
+ align:start position:0%
+advanced electrodynamics textbook in my
+notes here I suggest looking at this
+
+ align:start position:0%
+notes here I suggest looking at this
+ 
+
+ align:start position:0%
+notes here I suggest looking at this
+place where I originally went through
+
+ align:start position:0%
+place where I originally went through
+ 
+
+ align:start position:0%
+place where I originally went through
+this carefully was in the second edition
+
+ align:start position:0%
+this carefully was in the second edition
+ 
+
+ align:start position:0%
+this carefully was in the second edition
+of Jackson it's presumably also present
+
+ align:start position:0%
+of Jackson it's presumably also present
+ 
+
+ align:start position:0%
+of Jackson it's presumably also present
+in the latest edition but it might be in
+
+ align:start position:0%
+in the latest edition but it might be in
+ 
+
+ align:start position:0%
+in the latest edition but it might be in
+a slightly different place in the second
+
+ align:start position:0%
+a slightly different place in the second
+ 
+
+ align:start position:0%
+a slightly different place in the second
+edition you can find this discussed in
+
+ align:start position:0%
+edition you can find this discussed in
+ 
+
+ align:start position:0%
+edition you can find this discussed in
+section 6.6 when I have taught mi t--'s
+
+ align:start position:0%
+section 6.6 when I have taught mi t--'s
+ 
+
+ align:start position:0%
+section 6.6 when I have taught mi t--'s
+jr. level electrodynamics course
+
+ align:start position:0%
+jr. level electrodynamics course
+ 
+
+ align:start position:0%
+jr. level electrodynamics course
+actually go through this and by
+
+ align:start position:0%
+actually go through this and by
+ 
+
+ align:start position:0%
+actually go through this and by
+essentially introducing a Fourier
+
+ align:start position:0%
+essentially introducing a Fourier
+ 
+
+ align:start position:0%
+essentially introducing a Fourier
+transform a Fourier decomposition D
+
+ align:start position:0%
+transform a Fourier decomposition D
+ 
+
+ align:start position:0%
+transform a Fourier decomposition D
+coming the wave operator into an
+
+ align:start position:0%
+coming the wave operator into an
+ 
+
+ align:start position:0%
+coming the wave operator into an
+algebraic operator just rearranged a
+
+ align:start position:0%
+algebraic operator just rearranged a
+ 
+
+ align:start position:0%
+algebraic operator just rearranged a
+bunch of terms then invert the Fourier
+
+ align:start position:0%
+bunch of terms then invert the Fourier
+ 
+
+ align:start position:0%
+bunch of terms then invert the Fourier
+transform it's not too hard to show that
+
+ align:start position:0%
+transform it's not too hard to show that
+ 
+
+ align:start position:0%
+transform it's not too hard to show that
+this is the result that comes out of
+
+ align:start position:0%
+this is the result that comes out of
+ 
+
+ align:start position:0%
+this is the result that comes out of
+that notice the argument of that Delta
+
+ align:start position:0%
+that notice the argument of that Delta
+ 
+
+ align:start position:0%
+that notice the argument of that Delta
+function and please bear in mind we are
+
+ align:start position:0%
+function and please bear in mind we are
+ 
+
+ align:start position:0%
+function and please bear in mind we are
+working in units in which we have set
+
+ align:start position:0%
+working in units in which we have set
+ 
+
+ align:start position:0%
+working in units in which we have set
+the speed of light equal to one so the
+
+ align:start position:0%
+the speed of light equal to one so the
+ 
+
+ align:start position:0%
+the speed of light equal to one so the
+Delta function it has support only at so
+
+ align:start position:0%
+Delta function it has support only at so
+ 
+
+ align:start position:0%
+Delta function it has support only at so
+it was going on here is this is taking
+
+ align:start position:0%
+it was going on here is this is taking
+ 
+
+ align:start position:0%
+it was going on here is this is taking
+into account the amount of time it takes
+
+ align:start position:0%
+into account the amount of time it takes
+ 
+
+ align:start position:0%
+into account the amount of time it takes
+for information to travel from the
+
+ align:start position:0%
+for information to travel from the
+ 
+
+ align:start position:0%
+for information to travel from the
+source point to the field point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if I can illustrate this with a
+
+ align:start position:0%
+okay if I can illustrate this with a
+ 
+
+ align:start position:0%
+okay if I can illustrate this with a
+little cartoon imagine I have some
+
+ align:start position:0%
+little cartoon imagine I have some
+ 
+
+ align:start position:0%
+little cartoon imagine I have some
+dynamical source of mass and energy
+
+ align:start position:0%
+dynamical source of mass and energy
+ 
+
+ align:start position:0%
+dynamical source of mass and energy
+that's down here wiggling away here is
+
+ align:start position:0%
+that's down here wiggling away here is
+ 
+
+ align:start position:0%
+that's down here wiggling away here is
+my one example of a source point that is
+
+ align:start position:0%
+my one example of a source point that is
+ 
+
+ align:start position:0%
+my one example of a source point that is
+going to end up inside the integral when
+
+ align:start position:0%
+going to end up inside the integral when
+ 
+
+ align:start position:0%
+going to end up inside the integral when
+I integrate up this green's function
+
+ align:start position:0%
+I integrate up this green's function
+ 
+
+ align:start position:0%
+I integrate up this green's function
+against my source here i am i'm an
+
+ align:start position:0%
+against my source here i am i'm an
+ 
+
+ align:start position:0%
+against my source here i am i'm an
+observer
+
+ align:start position:0%
+observer
+ 
+
+ align:start position:0%
+observer
+making my measurement out here at
+
+ align:start position:0%
+making my measurement out here at
+ 
+
+ align:start position:0%
+making my measurement out here at
+position x whatever is happening at x
+
+ align:start position:0%
+position x whatever is happening at x
+ 
+
+ align:start position:0%
+position x whatever is happening at x
+prime
+
+ align:start position:0%
+prime
+ 
+
+ align:start position:0%
+prime
+takes time to be communicated to me
+
+ align:start position:0%
+takes time to be communicated to me
+ 
+
+ align:start position:0%
+takes time to be communicated to me
+making my measurements out here at
+
+ align:start position:0%
+making my measurements out here at
+ 
+
+ align:start position:0%
+making my measurements out here at
+distance X the time lag is the distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that has to be traveled X minus X Prime
+
+ align:start position:0%
+that has to be traveled X minus X Prime
+ 
+
+ align:start position:0%
+that has to be traveled X minus X Prime
+and again I'll remind you we're working
+
+ align:start position:0%
+and again I'll remind you we're working
+ 
+
+ align:start position:0%
+and again I'll remind you we're working
+in units with a speed of light is equal
+
+ align:start position:0%
+in units with a speed of light is equal
+ 
+
+ align:start position:0%
+in units with a speed of light is equal
+to one we would divide by C if we are
+
+ align:start position:0%
+to one we would divide by C if we are
+ 
+
+ align:start position:0%
+to one we would divide by C if we are
+working in normal SI units okay so this
+
+ align:start position:0%
+working in normal SI units okay so this
+ 
+
+ align:start position:0%
+working in normal SI units okay so this
+factor in the greens function is
+
+ align:start position:0%
+factor in the greens function is
+ 
+
+ align:start position:0%
+factor in the greens function is
+building in I'm gonna do the integral in
+
+ align:start position:0%
+building in I'm gonna do the integral in
+ 
+
+ align:start position:0%
+building in I'm gonna do the integral in
+just a moment it is building in the fact
+
+ align:start position:0%
+just a moment it is building in the fact
+ 
+
+ align:start position:0%
+just a moment it is building in the fact
+that we need to account for the amount
+
+ align:start position:0%
+that we need to account for the amount
+ 
+
+ align:start position:0%
+that we need to account for the amount
+of time it takes for information about
+
+ align:start position:0%
+of time it takes for information about
+ 
+
+ align:start position:0%
+of time it takes for information about
+the sources dynamics to be radiatively
+
+ align:start position:0%
+the sources dynamics to be radiatively
+ 
+
+ align:start position:0%
+the sources dynamics to be radiatively
+communicated to observers far away from
+
+ align:start position:0%
+communicated to observers far away from
+ 
+
+ align:start position:0%
+communicated to observers far away from
+that source
+
+ align:start position:0%
+that source
+ 
+
+ align:start position:0%
+that source
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we are now going to apply
+
+ align:start position:0%
+all right so we are now going to apply
+ 
+
+ align:start position:0%
+all right so we are now going to apply
+this to the linearized the the Einstein
+
+ align:start position:0%
+this to the linearized the the Einstein
+ 
+
+ align:start position:0%
+this to the linearized the the Einstein
+field equation for linearized gravity so
+
+ align:start position:0%
+field equation for linearized gravity so
+ 
+
+ align:start position:0%
+field equation for linearized gravity so
+here is our field equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sadly the letter capital G is doing
+
+ align:start position:0%
+sadly the letter capital G is doing
+ 
+
+ align:start position:0%
+sadly the letter capital G is doing
+multiple duties in this lecture so when
+
+ align:start position:0%
+multiple duties in this lecture so when
+ 
+
+ align:start position:0%
+multiple duties in this lecture so when
+we solve this what we need to do is
+
+ align:start position:0%
+we solve this what we need to do is
+ 
+
+ align:start position:0%
+we solve this what we need to do is
+integrate t alpha beta regarded as a
+
+ align:start position:0%
+integrate t alpha beta regarded as a
+ 
+
+ align:start position:0%
+integrate t alpha beta regarded as a
+function of prime time T prime position
+
+ align:start position:0%
+function of prime time T prime position
+ 
+
+ align:start position:0%
+function of prime time T prime position
+X prime against the radiative greens
+
+ align:start position:0%
+X prime against the radiative greens
+ 
+
+ align:start position:0%
+X prime against the radiative greens
+function plug in the radiative green's
+
+ align:start position:0%
+function plug in the radiative green's
+ 
+
+ align:start position:0%
+function plug in the radiative green's
+function which we use okay this is the
+
+ align:start position:0%
+function which we use okay this is the
+ 
+
+ align:start position:0%
+function which we use okay this is the
+greens function that corresponds to that
+
+ align:start position:0%
+greens function that corresponds to that
+ 
+
+ align:start position:0%
+greens function that corresponds to that
+wave operator we have a minus 1 over 4
+
+ align:start position:0%
+wave operator we have a minus 1 over 4
+ 
+
+ align:start position:0%
+wave operator we have a minus 1 over 4
+pi hitting our minus 16 pi out front
+
+ align:start position:0%
+pi hitting our minus 16 pi out front
+ 
+
+ align:start position:0%
+pi hitting our minus 16 pi out front
+there we're gonna do the integral over
+
+ align:start position:0%
+there we're gonna do the integral over
+ 
+
+ align:start position:0%
+there we're gonna do the integral over
+the time variable and we're gonna leave
+
+ align:start position:0%
+the time variable and we're gonna leave
+ 
+
+ align:start position:0%
+the time variable and we're gonna leave
+our result expressed as an integral over
+
+ align:start position:0%
+our result expressed as an integral over
+ 
+
+ align:start position:0%
+our result expressed as an integral over
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is an exact solution of the
+
+ align:start position:0%
+this is an exact solution of the
+ 
+
+ align:start position:0%
+this is an exact solution of the
+linearised field equations of general
+
+ align:start position:0%
+linearised field equations of general
+ 
+
+ align:start position:0%
+linearised field equations of general
+relativity this is telling me that what
+
+ align:start position:0%
+relativity this is telling me that what
+ 
+
+ align:start position:0%
+relativity this is telling me that what
+happens the the field that is measured
+
+ align:start position:0%
+happens the the field that is measured
+ 
+
+ align:start position:0%
+happens the the field that is measured
+the trace reverse perturbation that is
+
+ align:start position:0%
+the trace reverse perturbation that is
+ 
+
+ align:start position:0%
+the trace reverse perturbation that is
+measured at time T and position X prime
+
+ align:start position:0%
+measured at time T and position X prime
+ 
+
+ align:start position:0%
+measured at time T and position X prime
+is given by integrating over my source
+
+ align:start position:0%
+is given by integrating over my source
+ 
+
+ align:start position:0%
+is given by integrating over my source
+all the dynamics that happened earlier
+
+ align:start position:0%
+all the dynamics that happened earlier
+ 
+
+ align:start position:0%
+all the dynamics that happened earlier
+than that time T right what I need to do
+
+ align:start position:0%
+than that time T right what I need to do
+ 
+
+ align:start position:0%
+than that time T right what I need to do
+is take into account that over this
+
+ align:start position:0%
+is take into account that over this
+ 
+
+ align:start position:0%
+is take into account that over this
+source I have to fold in the amount of
+
+ align:start position:0%
+source I have to fold in the amount of
+ 
+
+ align:start position:0%
+source I have to fold in the amount of
+time it takes for information from
+
+ align:start position:0%
+time it takes for information from
+ 
+
+ align:start position:0%
+time it takes for information from
+source point X prime to go out to X I
+
+ align:start position:0%
+source point X prime to go out to X I
+ 
+
+ align:start position:0%
+source point X prime to go out to X I
+integrate over the source at every point
+
+ align:start position:0%
+integrate over the source at every point
+ 
+
+ align:start position:0%
+integrate over the source at every point
+in the integrand I divide by the
+
+ align:start position:0%
+in the integrand I divide by the
+ 
+
+ align:start position:0%
+in the integrand I divide by the
+distance between the field point and the
+
+ align:start position:0%
+distance between the field point and the
+ 
+
+ align:start position:0%
+distance between the field point and the
+source point do that integral x for J
+
+ align:start position:0%
+source point do that integral x for J
+ 
+
+ align:start position:0%
+source point do that integral x for J
+there's my solution this is wonderful
+
+ align:start position:0%
+there's my solution this is wonderful
+ 
+
+ align:start position:0%
+there's my solution this is wonderful
+it's actually an exact solution like
+
+ align:start position:0%
+it's actually an exact solution like
+ 
+
+ align:start position:0%
+it's actually an exact solution like
+most exact solutions it's not always the
+
+ align:start position:0%
+most exact solutions it's not always the
+ 
+
+ align:start position:0%
+most exact solutions it's not always the
+most useful thing in the world okay
+
+ align:start position:0%
+most useful thing in the world okay
+ 
+
+ align:start position:0%
+most useful thing in the world okay
+there's one problem which we need to
+
+ align:start position:0%
+there's one problem which we need to
+ 
+
+ align:start position:0%
+there's one problem which we need to
+diagnose which is that in the way that
+
+ align:start position:0%
+diagnose which is that in the way that
+ 
+
+ align:start position:0%
+diagnose which is that in the way that
+this has been formulated it looks like
+
+ align:start position:0%
+this has been formulated it looks like
+ 
+
+ align:start position:0%
+this has been formulated it looks like
+every component of this trace reverse
+
+ align:start position:0%
+every component of this trace reverse
+ 
+
+ align:start position:0%
+every component of this trace reverse
+metric looks radiative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do I mean by it looks radiative
+
+ align:start position:0%
+what do I mean by it looks radiative
+ 
+
+ align:start position:0%
+what do I mean by it looks radiative
+well it came from a wave equation they
+
+ align:start position:0%
+well it came from a wave equation they
+ 
+
+ align:start position:0%
+well it came from a wave equation they
+all depend on information that traveled
+
+ align:start position:0%
+all depend on information that traveled
+ 
+
+ align:start position:0%
+all depend on information that traveled
+out at the speed of light with a time
+
+ align:start position:0%
+out at the speed of light with a time
+ 
+
+ align:start position:0%
+out at the speed of light with a time
+lag appropriate to the speed with which
+
+ align:start position:0%
+lag appropriate to the speed with which
+ 
+
+ align:start position:0%
+lag appropriate to the speed with which
+radiation moves in flat space-time you
+
+ align:start position:0%
+radiation moves in flat space-time you
+ 
+
+ align:start position:0%
+radiation moves in flat space-time you
+know you look at that you sort of say
+
+ align:start position:0%
+know you look at that you sort of say
+ 
+
+ align:start position:0%
+know you look at that you sort of say
+wow the entire metric has this sort of
+
+ align:start position:0%
+wow the entire metric has this sort of
+ 
+
+ align:start position:0%
+wow the entire metric has this sort of
+character that we associate with a
+
+ align:start position:0%
+character that we associate with a
+ 
+
+ align:start position:0%
+character that we associate with a
+propagating wave all of space-time is
+
+ align:start position:0%
+propagating wave all of space-time is
+ 
+
+ align:start position:0%
+propagating wave all of space-time is
+radiative we need to be careful about
+
+ align:start position:0%
+radiative we need to be careful about
+ 
+
+ align:start position:0%
+radiative we need to be careful about
+that because here is where we need to
+
+ align:start position:0%
+that because here is where we need to
+ 
+
+ align:start position:0%
+that because here is where we need to
+revisit and think carefully about what
+
+ align:start position:0%
+revisit and think carefully about what
+ 
+
+ align:start position:0%
+revisit and think carefully about what
+happens when we choose our gauge what
+
+ align:start position:0%
+happens when we choose our gauge what
+ 
+
+ align:start position:0%
+happens when we choose our gauge what
+I'm going to show you is a little
+
+ align:start position:0%
+I'm going to show you is a little
+ 
+
+ align:start position:0%
+I'm going to show you is a little
+demonstration that in this case the
+
+ align:start position:0%
+demonstration that in this case the
+ 
+
+ align:start position:0%
+demonstration that in this case the
+gauge we chose let me emphasize that was
+
+ align:start position:0%
+gauge we chose let me emphasize that was
+ 
+
+ align:start position:0%
+gauge we chose let me emphasize that was
+a wonderful gauge for putting the you
+
+ align:start position:0%
+a wonderful gauge for putting the you
+ 
+
+ align:start position:0%
+a wonderful gauge for putting the you
+know horribly messy field equation into
+
+ align:start position:0%
+know horribly messy field equation into
+ 
+
+ align:start position:0%
+know horribly messy field equation into
+a formal we could actually solve it but
+
+ align:start position:0%
+a formal we could actually solve it but
+ 
+
+ align:start position:0%
+a formal we could actually solve it but
+the gauge we chose is unfortunately
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+masking some of the physical character
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the space-time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this Lorentz gauge this Lorentz gauge
+
+ align:start position:0%
+so this Lorentz gauge this Lorentz gauge
+ 
+
+ align:start position:0%
+so this Lorentz gauge this Lorentz gauge
+was great for producing a set of field
+
+ align:start position:0%
+was great for producing a set of field
+ 
+
+ align:start position:0%
+was great for producing a set of field
+equations that you know we could bring
+
+ align:start position:0%
+equations that you know we could bring
+ 
+
+ align:start position:0%
+equations that you know we could bring
+to bear powerful mathematical techniques
+
+ align:start position:0%
+to bear powerful mathematical techniques
+ 
+
+ align:start position:0%
+to bear powerful mathematical techniques
+and get a closed form actually exact was
+
+ align:start position:0%
+and get a closed form actually exact was
+ 
+
+ align:start position:0%
+and get a closed form actually exact was
+in the context of linearized theory and
+
+ align:start position:0%
+in the context of linearized theory and
+ 
+
+ align:start position:0%
+in the context of linearized theory and
+exact solution but it might be
+
+ align:start position:0%
+exact solution but it might be
+ 
+
+ align:start position:0%
+exact solution but it might be
+misleading us as to what the resulting
+
+ align:start position:0%
+misleading us as to what the resulting
+ 
+
+ align:start position:0%
+misleading us as to what the resulting
+solution means let me illustrate this
+
+ align:start position:0%
+solution means let me illustrate this
+ 
+
+ align:start position:0%
+solution means let me illustrate this
+with an example from electrodynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose I gave you a vector potential it
+
+ align:start position:0%
+suppose I gave you a vector potential it
+ 
+
+ align:start position:0%
+suppose I gave you a vector potential it
+was of the form at a time like component
+
+ align:start position:0%
+was of the form at a time like component
+ 
+
+ align:start position:0%
+was of the form at a time like component
+that was Q over R minus Q Omega sine Q
+
+ align:start position:0%
+that was Q over R minus Q Omega sine Q
+ 
+
+ align:start position:0%
+that was Q over R minus Q Omega sine Q
+dot R minus Omega T over R little R is
+
+ align:start position:0%
+dot R minus Omega T over R little R is
+ 
+
+ align:start position:0%
+dot R minus Omega T over R little R is
+square root of x squared plus y squared
+
+ align:start position:0%
+square root of x squared plus y squared
+ 
+
+ align:start position:0%
+square root of x squared plus y squared
+plus Z squared and capital R is some
+
+ align:start position:0%
+plus Z squared and capital R is some
+ 
+
+ align:start position:0%
+plus Z squared and capital R is some
+parameter with the dimensions of length
+
+ align:start position:0%
+parameter with the dimensions of length
+ 
+
+ align:start position:0%
+parameter with the dimensions of length
+and my three spatial components of this
+
+ align:start position:0%
+and my three spatial components of this
+ 
+
+ align:start position:0%
+and my three spatial components of this
+thing I'm going to write them as KQ I
+
+ align:start position:0%
+thing I'm going to write them as KQ I
+ 
+
+ align:start position:0%
+thing I'm going to write them as KQ I
+sine K dot R minus Omega T capital R
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this is a potential that has a form
+
+ align:start position:0%
+okay this is a potential that has a form
+ 
+
+ align:start position:0%
+okay this is a potential that has a form
+that kind of looks like if you were if I
+
+ align:start position:0%
+that kind of looks like if you were if I
+ 
+
+ align:start position:0%
+that kind of looks like if you were if I
+were to sort of give this to you on an
+
+ align:start position:0%
+were to sort of give this to you on an
+ 
+
+ align:start position:0%
+were to sort of give this to you on an
+oral exam and say without doing any
+
+ align:start position:0%
+oral exam and say without doing any
+ 
+
+ align:start position:0%
+oral exam and say without doing any
+calculation what would you guess this is
+
+ align:start position:0%
+calculation what would you guess this is
+ 
+
+ align:start position:0%
+calculation what would you guess this is
+and that would actually be as you'll see
+
+ align:start position:0%
+and that would actually be as you'll see
+ 
+
+ align:start position:0%
+and that would actually be as you'll see
+in a moment they'll be a very unfair
+
+ align:start position:0%
+in a moment they'll be a very unfair
+ 
+
+ align:start position:0%
+in a moment they'll be a very unfair
+question of me to ask I look at this and
+
+ align:start position:0%
+question of me to ask I look at this and
+ 
+
+ align:start position:0%
+question of me to ask I look at this and
+I say you know what looks kind of like a
+
+ align:start position:0%
+I say you know what looks kind of like a
+ 
+
+ align:start position:0%
+I say you know what looks kind of like a
+Coulomb field and then there is
+
+ align:start position:0%
+Coulomb field and then there is
+ 
+
+ align:start position:0%
+Coulomb field and then there is
+something radiative that it's embedded
+
+ align:start position:0%
+something radiative that it's embedded
+ 
+
+ align:start position:0%
+something radiative that it's embedded
+in kind of a funny amplitude associate
+
+ align:start position:0%
+in kind of a funny amplitude associate
+ 
+
+ align:start position:0%
+in kind of a funny amplitude associate
+at that radiation but maybe this is sort
+
+ align:start position:0%
+at that radiation but maybe this is sort
+ 
+
+ align:start position:0%
+at that radiation but maybe this is sort
+of like a dipole radiator with a net
+
+ align:start position:0%
+of like a dipole radiator with a net
+ 
+
+ align:start position:0%
+of like a dipole radiator with a net
+monopole moments going on it you know
+
+ align:start position:0%
+monopole moments going on it you know
+ 
+
+ align:start position:0%
+monopole moments going on it you know
+we've got things that involve fields
+
+ align:start position:0%
+we've got things that involve fields
+ 
+
+ align:start position:0%
+we've got things that involve fields
+that oscillate in space and time they
+
+ align:start position:0%
+that oscillate in space and time they
+ 
+
+ align:start position:0%
+that oscillate in space and time they
+fall off as one of ours a complement
+
+ align:start position:0%
+fall off as one of ours a complement
+ 
+
+ align:start position:0%
+fall off as one of ours a complement
+falls off as one over R cubed yeah that
+
+ align:start position:0%
+falls off as one over R cubed yeah that
+ 
+
+ align:start position:0%
+falls off as one over R cubed yeah that
+would be my guess a point charge with
+
+ align:start position:0%
+would be my guess a point charge with
+ 
+
+ align:start position:0%
+would be my guess a point charge with
+radiation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so your oral examiner the next thing
+
+ align:start position:0%
+so your oral examiner the next thing
+ 
+
+ align:start position:0%
+so your oral examiner the next thing
+they say is great workout the
+
+ align:start position:0%
+they say is great workout the
+ 
+
+ align:start position:0%
+they say is great workout the
+electromagnetic field tensor
+
+ align:start position:0%
+electromagnetic field tensor
+ 
+
+ align:start position:0%
+electromagnetic field tensor
+corresponding to this so you do this by
+
+ align:start position:0%
+corresponding to this so you do this by
+ 
+
+ align:start position:0%
+corresponding to this so you do this by
+taking some derivatives and what results
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this this is the electromagnetic
+
+ align:start position:0%
+is this this is the electromagnetic
+ 
+
+ align:start position:0%
+is this this is the electromagnetic
+field tensor corresponding to a Coulomb
+
+ align:start position:0%
+field tensor corresponding to a Coulomb
+ 
+
+ align:start position:0%
+field tensor corresponding to a Coulomb
+electric field with no magnetic field
+
+ align:start position:0%
+electric field with no magnetic field
+ 
+
+ align:start position:0%
+electric field with no magnetic field
+this potential is nothing more than a
+
+ align:start position:0%
+this potential is nothing more than a
+ 
+
+ align:start position:0%
+this potential is nothing more than a
+Coulomb point charge in a really dumb
+
+ align:start position:0%
+Coulomb point charge in a really dumb
+ 
+
+ align:start position:0%
+Coulomb point charge in a really dumb
+gauge okay the way I actually generated
+
+ align:start position:0%
+gauge okay the way I actually generated
+ 
+
+ align:start position:0%
+gauge okay the way I actually generated
+this was I started with the Q over R
+
+ align:start position:0%
+this was I started with the Q over R
+ 
+
+ align:start position:0%
+this was I started with the Q over R
+potential of a Coulomb point charge I
+
+ align:start position:0%
+potential of a Coulomb point charge I
+ 
+
+ align:start position:0%
+potential of a Coulomb point charge I
+just applied some crazy gauge generator
+
+ align:start position:0%
+just applied some crazy gauge generator
+ 
+
+ align:start position:0%
+just applied some crazy gauge generator
+to it to see what happened so the
+
+ align:start position:0%
+to it to see what happened so the
+ 
+
+ align:start position:0%
+to it to see what happened so the
+parable of this story is whenever you
+
+ align:start position:0%
+parable of this story is whenever you
+ 
+
+ align:start position:0%
+parable of this story is whenever you
+are working with quantities that are
+
+ align:start position:0%
+are working with quantities that are
+ 
+
+ align:start position:0%
+are working with quantities that are
+subject to gauge transformations you
+
+ align:start position:0%
+subject to gauge transformations you
+ 
+
+ align:start position:0%
+subject to gauge transformations you
+have to be careful about drawing
+
+ align:start position:0%
+have to be careful about drawing
+ 
+
+ align:start position:0%
+have to be careful about drawing
+conclusions about what those quantities
+
+ align:start position:0%
+conclusions about what those quantities
+ 
+
+ align:start position:0%
+conclusions about what those quantities
+mean in terms of the physics you want to
+
+ align:start position:0%
+mean in terms of the physics you want to
+ 
+
+ align:start position:0%
+mean in terms of the physics you want to
+get out of it gauge can obscure the
+
+ align:start position:0%
+get out of it gauge can obscure the
+ 
+
+ align:start position:0%
+get out of it gauge can obscure the
+physics if we are not careful in
+
+ align:start position:0%
+physics if we are not careful in
+ 
+
+ align:start position:0%
+physics if we are not careful in
+particular there's almost like a
+
+ align:start position:0%
+particular there's almost like a
+ 
+
+ align:start position:0%
+particular there's almost like a
+conservation of pain principle here it
+
+ align:start position:0%
+conservation of pain principle here it
+ 
+
+ align:start position:0%
+conservation of pain principle here it
+is often the case that the best gauge
+
+ align:start position:0%
+is often the case that the best gauge
+ 
+
+ align:start position:0%
+is often the case that the best gauge
+for formulating tractable tractable
+
+ align:start position:0%
+for formulating tractable tractable
+ 
+
+ align:start position:0%
+for formulating tractable tractable
+equations for solving your problem turn
+
+ align:start position:0%
+equations for solving your problem turn
+ 
+
+ align:start position:0%
+equations for solving your problem turn
+out to be gauges that give you just
+
+ align:start position:0%
+out to be gauges that give you just
+ 
+
+ align:start position:0%
+out to be gauges that give you just
+crappy results if you want to interpret
+
+ align:start position:0%
+crappy results if you want to interpret
+ 
+
+ align:start position:0%
+crappy results if you want to interpret
+what's going on physically the remainder
+
+ align:start position:0%
+what's going on physically the remainder
+ 
+
+ align:start position:0%
+what's going on physically the remainder
+of this lab
+
+ align:start position:0%
+of this lab
+ 
+
+ align:start position:0%
+of this lab
+I am going to introduce something that's
+
+ align:start position:0%
+I am going to introduce something that's
+ 
+
+ align:start position:0%
+I am going to introduce something that's
+a slightly advanced topic um and I
+
+ align:start position:0%
+a slightly advanced topic um and I
+ 
+
+ align:start position:0%
+a slightly advanced topic um and I
+pretty shamelessly stole this from a
+
+ align:start position:0%
+pretty shamelessly stole this from a
+ 
+
+ align:start position:0%
+pretty shamelessly stole this from a
+paper hood I broke something that I did
+
+ align:start position:0%
+paper hood I broke something that I did
+ 
+
+ align:start position:0%
+paper hood I broke something that I did
+with a colleague of mine and a Flanagan
+
+ align:start position:0%
+with a colleague of mine and a Flanagan
+ 
+
+ align:start position:0%
+with a colleague of mine and a Flanagan
+and it's based on an idea that was
+
+ align:start position:0%
+and it's based on an idea that was
+ 
+
+ align:start position:0%
+and it's based on an idea that was
+developed in a different context by my
+
+ align:start position:0%
+developed in a different context by my
+ 
+
+ align:start position:0%
+developed in a different context by my
+MIT colleague Egbert Edie Bertrand so
+
+ align:start position:0%
+MIT colleague Egbert Edie Bertrand so
+ 
+
+ align:start position:0%
+MIT colleague Egbert Edie Bertrand so
+here's what we're going to do in the
+
+ align:start position:0%
+here's what we're going to do in the
+ 
+
+ align:start position:0%
+here's what we're going to do in the
+remainder of today's remainder of this
+
+ align:start position:0%
+remainder of today's remainder of this
+ 
+
+ align:start position:0%
+remainder of today's remainder of this
+this lecture what we're going to do is
+
+ align:start position:0%
+this lecture what we're going to do is
+ 
+
+ align:start position:0%
+this lecture what we're going to do is
+recast the metric and the source in a
+
+ align:start position:0%
+recast the metric and the source in a
+ 
+
+ align:start position:0%
+recast the metric and the source in a
+form which allows us to categorize the
+
+ align:start position:0%
+form which allows us to categorize the
+ 
+
+ align:start position:0%
+form which allows us to categorize the
+radiative and non-radiative degrees of
+
+ align:start position:0%
+radiative and non-radiative degrees of
+ 
+
+ align:start position:0%
+radiative and non-radiative degrees of
+freedom of the space-time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this will in fact we're going to do
+
+ align:start position:0%
+okay this will in fact we're going to do
+ 
+
+ align:start position:0%
+okay this will in fact we're going to do
+this in a way where the results are in
+
+ align:start position:0%
+this in a way where the results are in
+ 
+
+ align:start position:0%
+this in a way where the results are in
+fact completely generic provided we
+
+ align:start position:0%
+fact completely generic provided we
+ 
+
+ align:start position:0%
+fact completely generic provided we
+stick to linearized gravity gravity
+
+ align:start position:0%
+stick to linearized gravity gravity
+ 
+
+ align:start position:0%
+stick to linearized gravity gravity
+linearized around flat space-time which
+
+ align:start position:0%
+linearized around flat space-time which
+ 
+
+ align:start position:0%
+linearized around flat space-time which
+will be sufficient for our discussion
+
+ align:start position:0%
+will be sufficient for our discussion
+ 
+
+ align:start position:0%
+will be sufficient for our discussion
+right now I will give you the punchline
+
+ align:start position:0%
+right now I will give you the punchline
+ 
+
+ align:start position:0%
+right now I will give you the punchline
+upfront what we will discover is that
+
+ align:start position:0%
+upfront what we will discover is that
+ 
+
+ align:start position:0%
+upfront what we will discover is that
+space-time has for physical degrees of
+
+ align:start position:0%
+space-time has for physical degrees of
+ 
+
+ align:start position:0%
+space-time has for physical degrees of
+freedom that are non radiative in the
+
+ align:start position:0%
+freedom that are non radiative in the
+ 
+
+ align:start position:0%
+freedom that are non radiative in the
+hallmark of this is that they are going
+
+ align:start position:0%
+hallmark of this is that they are going
+ 
+
+ align:start position:0%
+hallmark of this is that they are going
+to be governed by differential equations
+
+ align:start position:0%
+to be governed by differential equations
+ 
+
+ align:start position:0%
+to be governed by differential equations
+that look like the Poisson equation they
+
+ align:start position:0%
+that look like the Poisson equation they
+ 
+
+ align:start position:0%
+that look like the Poisson equation they
+will look like the Laplace operator on
+
+ align:start position:0%
+will look like the Laplace operator on
+ 
+
+ align:start position:0%
+will look like the Laplace operator on
+some potential is equal to a source let
+
+ align:start position:0%
+some potential is equal to a source let
+ 
+
+ align:start position:0%
+some potential is equal to a source let
+me rewrite that this handwriting is
+
+ align:start position:0%
+me rewrite that this handwriting is
+ 
+
+ align:start position:0%
+me rewrite that this handwriting is
+terrible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spacetime has two more degrees of
+
+ align:start position:0%
+spacetime has two more degrees of
+ 
+
+ align:start position:0%
+spacetime has two more degrees of
+freedom that are radiative these are
+
+ align:start position:0%
+freedom that are radiative these are
+ 
+
+ align:start position:0%
+freedom that are radiative these are
+governed by wave equations the metric
+
+ align:start position:0%
+governed by wave equations the metric
+ 
+
+ align:start position:0%
+governed by wave equations the metric
+tensor of space-time has ten ten
+
+ align:start position:0%
+tensor of space-time has ten ten
+ 
+
+ align:start position:0%
+tensor of space-time has ten ten
+components ten unique components it's a
+
+ align:start position:0%
+components ten unique components it's a
+ 
+
+ align:start position:0%
+components ten unique components it's a
+four by four it's represented by before
+
+ align:start position:0%
+four by four it's represented by before
+ 
+
+ align:start position:0%
+four by four it's represented by before
+by four symmetric matrix okay so it has
+
+ align:start position:0%
+by four symmetric matrix okay so it has
+ 
+
+ align:start position:0%
+by four symmetric matrix okay so it has
+ten components in it four plus two does
+
+ align:start position:0%
+ten components in it four plus two does
+ 
+
+ align:start position:0%
+ten components in it four plus two does
+not equal ten you might look at this and
+
+ align:start position:0%
+not equal ten you might look at this and
+ 
+
+ align:start position:0%
+not equal ten you might look at this and
+think what about the other four
+
+ align:start position:0%
+think what about the other four
+ 
+
+ align:start position:0%
+think what about the other four
+components of this thing I've got four
+
+ align:start position:0%
+components of this thing I've got four
+ 
+
+ align:start position:0%
+components of this thing I've got four
+degrees of freedom that much correspond
+
+ align:start position:0%
+degrees of freedom that much correspond
+ 
+
+ align:start position:0%
+degrees of freedom that much correspond
+in some sense to four of those
+
+ align:start position:0%
+in some sense to four of those
+ 
+
+ align:start position:0%
+in some sense to four of those
+components I've got another two degrees
+
+ align:start position:0%
+components I've got another two degrees
+ 
+
+ align:start position:0%
+components I've got another two degrees
+of freedom that most cars belong to two
+
+ align:start position:0%
+of freedom that most cars belong to two
+ 
+
+ align:start position:0%
+of freedom that most cars belong to two
+of those components
+
+ align:start position:0%
+of those components
+ 
+
+ align:start position:0%
+of those components
+what's going on at the other four well
+
+ align:start position:0%
+what's going on at the other four well
+ 
+
+ align:start position:0%
+what's going on at the other four well
+the other four degrees of freedom are
+
+ align:start position:0%
+the other four degrees of freedom are
+ 
+
+ align:start position:0%
+the other four degrees of freedom are
+essentially eaten up by our gauged
+
+ align:start position:0%
+essentially eaten up by our gauged
+ 
+
+ align:start position:0%
+essentially eaten up by our gauged
+freedom okay we are free to specify our
+
+ align:start position:0%
+freedom okay we are free to specify our
+ 
+
+ align:start position:0%
+freedom okay we are free to specify our
+coordinates via an infinitesimal
+
+ align:start position:0%
+coordinates via an infinitesimal
+ 
+
+ align:start position:0%
+coordinates via an infinitesimal
+coordinate shift and so we have four
+
+ align:start position:0%
+coordinate shift and so we have four
+ 
+
+ align:start position:0%
+coordinate shift and so we have four
+degrees of freedom under our control
+
+ align:start position:0%
+degrees of freedom under our control
+ 
+
+ align:start position:0%
+degrees of freedom under our control
+general relativity insists on giving
+
+ align:start position:0%
+general relativity insists on giving
+ 
+
+ align:start position:0%
+general relativity insists on giving
+physics to the other six these four non
+
+ align:start position:0%
+physics to the other six these four non
+ 
+
+ align:start position:0%
+physics to the other six these four non
+radio degrees of freedom the two
+
+ align:start position:0%
+radio degrees of freedom the two
+ 
+
+ align:start position:0%
+radio degrees of freedom the two
+radiative ones and the four gauge
+
+ align:start position:0%
+radiative ones and the four gauge
+ 
+
+ align:start position:0%
+radiative ones and the four gauge
+degrees of freedom completely describe
+
+ align:start position:0%
+degrees of freedom completely describe
+ 
+
+ align:start position:0%
+degrees of freedom completely describe
+the space-time metric and just to use an
+
+ align:start position:0%
+the space-time metric and just to use an
+ 
+
+ align:start position:0%
+the space-time metric and just to use an
+analogy these non-radiative degrees of
+
+ align:start position:0%
+analogy these non-radiative degrees of
+ 
+
+ align:start position:0%
+analogy these non-radiative degrees of
+freedom are kind of like the non
+
+ align:start position:0%
+freedom are kind of like the non
+ 
+
+ align:start position:0%
+freedom are kind of like the non
+radiative electric and magnetic fields
+
+ align:start position:0%
+radiative electric and magnetic fields
+ 
+
+ align:start position:0%
+radiative electric and magnetic fields
+that you get in electrodynamics your two
+
+ align:start position:0%
+that you get in electrodynamics your two
+ 
+
+ align:start position:0%
+that you get in electrodynamics your two
+radio degrees of freedom are going to
+
+ align:start position:0%
+radio degrees of freedom are going to
+ 
+
+ align:start position:0%
+radio degrees of freedom are going to
+turn out to two polarization states
+
+ align:start position:0%
+turn out to two polarization states
+ 
+
+ align:start position:0%
+turn out to two polarization states
+associated with waves in the
+
+ align:start position:0%
+associated with waves in the
+ 
+
+ align:start position:0%
+associated with waves in the
+gravitational field in the same way that
+
+ align:start position:0%
+gravitational field in the same way that
+ 
+
+ align:start position:0%
+gravitational field in the same way that
+the electrodynamics in electrodynamics
+
+ align:start position:0%
+the electrodynamics in electrodynamics
+ 
+
+ align:start position:0%
+the electrodynamics in electrodynamics
+the electric magnetic
+
+ align:start position:0%
+the electric magnetic
+ 
+
+ align:start position:0%
+the electric magnetic
+you also have two polarizations
+
+ align:start position:0%
+you also have two polarizations
+ 
+
+ align:start position:0%
+you also have two polarizations
+associated with them so this is all
+
+ align:start position:0%
+associated with them so this is all
+ 
+
+ align:start position:0%
+associated with them so this is all
+worked out in great detail in a paper
+
+ align:start position:0%
+worked out in great detail in a paper
+ 
+
+ align:start position:0%
+worked out in great detail in a paper
+that Anna Flanagan of Cornell University
+
+ align:start position:0%
+that Anna Flanagan of Cornell University
+ 
+
+ align:start position:0%
+that Anna Flanagan of Cornell University
+and I wrote about sixteen years ago and
+
+ align:start position:0%
+and I wrote about sixteen years ago and
+ 
+
+ align:start position:0%
+and I wrote about sixteen years ago and
+so I will make available through the
+
+ align:start position:0%
+so I will make available through the
+ 
+
+ align:start position:0%
+so I will make available through the
+89-62 website a copy of that paper and
+
+ align:start position:0%
+89-62 website a copy of that paper and
+ 
+
+ align:start position:0%
+89-62 website a copy of that paper and
+it was Flanagan who sort of got this
+
+ align:start position:0%
+it was Flanagan who sort of got this
+ 
+
+ align:start position:0%
+it was Flanagan who sort of got this
+started and he and I then figured out
+
+ align:start position:0%
+started and he and I then figured out
+ 
+
+ align:start position:0%
+started and he and I then figured out
+all the details together
+
+ align:start position:0%
+all the details together
+ 
+
+ align:start position:0%
+all the details together
+Edie birching er is sort of the
+
+ align:start position:0%
+Edie birching er is sort of the
+ 
+
+ align:start position:0%
+Edie birching er is sort of the
+grandfather of this idea since he did
+
+ align:start position:0%
+grandfather of this idea since he did
+ 
+
+ align:start position:0%
+grandfather of this idea since he did
+something very similar in an analysis
+
+ align:start position:0%
+something very similar in an analysis
+ 
+
+ align:start position:0%
+something very similar in an analysis
+that characterized perturbations to
+
+ align:start position:0%
+that characterized perturbations to
+ 
+
+ align:start position:0%
+that characterized perturbations to
+cosmological spacetimes alright so
+
+ align:start position:0%
+cosmological spacetimes alright so
+ 
+
+ align:start position:0%
+cosmological spacetimes alright so
+here's how we proceed let's consider HM
+
+ align:start position:0%
+here's how we proceed let's consider HM
+ 
+
+ align:start position:0%
+here's how we proceed let's consider HM
+you know as a tensor field on a flat
+
+ align:start position:0%
+you know as a tensor field on a flat
+ 
+
+ align:start position:0%
+you know as a tensor field on a flat
+background in my in the previous lecture
+
+ align:start position:0%
+background in my in the previous lecture
+ 
+
+ align:start position:0%
+background in my in the previous lecture
+that I recorded I described how when I
+
+ align:start position:0%
+that I recorded I described how when I
+ 
+
+ align:start position:0%
+that I recorded I described how when I
+am working in linearized theory it's a
+
+ align:start position:0%
+am working in linearized theory it's a
+ 
+
+ align:start position:0%
+am working in linearized theory it's a
+useful fiction to think of HP new even
+
+ align:start position:0%
+useful fiction to think of HP new even
+ 
+
+ align:start position:0%
+useful fiction to think of HP new even
+then we know it's actually telling us
+
+ align:start position:0%
+then we know it's actually telling us
+ 
+
+ align:start position:0%
+then we know it's actually telling us
+about the curvature of space-time it's a
+
+ align:start position:0%
+about the curvature of space-time it's a
+ 
+
+ align:start position:0%
+about the curvature of space-time it's a
+useful fiction to think of it as a
+
+ align:start position:0%
+useful fiction to think of it as a
+ 
+
+ align:start position:0%
+useful fiction to think of it as a
+tensor field in a flat background and
+
+ align:start position:0%
+tensor field in a flat background and
+ 
+
+ align:start position:0%
+tensor field in a flat background and
+we're going to take advantage of that we
+
+ align:start position:0%
+we're going to take advantage of that we
+ 
+
+ align:start position:0%
+we're going to take advantage of that we
+are going to choose time and space
+
+ align:start position:0%
+are going to choose time and space
+ 
+
+ align:start position:0%
+are going to choose time and space
+coordinates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once I have chosen time and space
+
+ align:start position:0%
+once I have chosen time and space
+ 
+
+ align:start position:0%
+once I have chosen time and space
+coordinates I then think about how this
+
+ align:start position:0%
+coordinates I then think about how this
+ 
+
+ align:start position:0%
+coordinates I then think about how this
+4x4 tensor how its different components
+
+ align:start position:0%
+4x4 tensor how its different components
+ 
+
+ align:start position:0%
+4x4 tensor how its different components
+break up and how they behave with
+
+ align:start position:0%
+break up and how they behave with
+ 
+
+ align:start position:0%
+break up and how they behave with
+respect to rotations in the spatial
+
+ align:start position:0%
+respect to rotations in the spatial
+ 
+
+ align:start position:0%
+respect to rotations in the spatial
+coordinates I can you know imagine going
+
+ align:start position:0%
+coordinates I can you know imagine going
+ 
+
+ align:start position:0%
+coordinates I can you know imagine going
+in and tweak my spatial coordinate
+
+ align:start position:0%
+in and tweak my spatial coordinate
+ 
+
+ align:start position:0%
+in and tweak my spatial coordinate
+system and what I want to do is examine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how the components break up into
+
+ align:start position:0%
+how the components break up into
+ 
+
+ align:start position:0%
+how the components break up into
+subgroups with respect to spatial only
+
+ align:start position:0%
+subgroups with respect to spatial only
+ 
+
+ align:start position:0%
+subgroups with respect to spatial only
+coordinate transformations what we'll
+
+ align:start position:0%
+coordinate transformations what we'll
+ 
+
+ align:start position:0%
+coordinate transformations what we'll
+see is H mu nu is going to break up into
+
+ align:start position:0%
+see is H mu nu is going to break up into
+ 
+
+ align:start position:0%
+see is H mu nu is going to break up into
+you're gonna get one piece it's your
+
+ align:start position:0%
+you're gonna get one piece it's your
+ 
+
+ align:start position:0%
+you're gonna get one piece it's your
+time time piece okay if I have chosen my
+
+ align:start position:0%
+time time piece okay if I have chosen my
+ 
+
+ align:start position:0%
+time time piece okay if I have chosen my
+time in my space coordinates and I
+
+ align:start position:0%
+time in my space coordinates and I
+ 
+
+ align:start position:0%
+time in my space coordinates and I
+imagine messing around with my spatial
+
+ align:start position:0%
+imagine messing around with my spatial
+ 
+
+ align:start position:0%
+imagine messing around with my spatial
+coordinate system HTT is unchanged and
+
+ align:start position:0%
+coordinate system HTT is unchanged and
+ 
+
+ align:start position:0%
+coordinate system HTT is unchanged and
+so this I'm gonna actually give it a
+
+ align:start position:0%
+so this I'm gonna actually give it a
+ 
+
+ align:start position:0%
+so this I'm gonna actually give it a
+name I'm gonna call it minus 2 Phi this
+
+ align:start position:0%
+name I'm gonna call it minus 2 Phi this
+ 
+
+ align:start position:0%
+name I'm gonna call it minus 2 Phi this
+behaves as a scalar my space time piece
+
+ align:start position:0%
+behaves as a scalar my space time piece
+ 
+
+ align:start position:0%
+behaves as a scalar my space time piece
+so components of this of the forum h TI
+
+ align:start position:0%
+so components of this of the forum h TI
+ 
+
+ align:start position:0%
+so components of this of the forum h TI
+I'm gonna characterize this in more
+
+ align:start position:0%
+I'm gonna characterize this in more
+ 
+
+ align:start position:0%
+I'm gonna characterize this in more
+detail a little bit later but this these
+
+ align:start position:0%
+detail a little bit later but this these
+ 
+
+ align:start position:0%
+detail a little bit later but this these
+three numbers are going to behave with
+
+ align:start position:0%
+three numbers are going to behave with
+ 
+
+ align:start position:0%
+three numbers are going to behave with
+respect to spatial only coordinate
+
+ align:start position:0%
+respect to spatial only coordinate
+ 
+
+ align:start position:0%
+respect to spatial only coordinate
+transformations like a vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+likewise hij is going to behave like a
+
+ align:start position:0%
+likewise hij is going to behave like a
+ 
+
+ align:start position:0%
+likewise hij is going to behave like a
+3x3 tensor so let's break this down a
+
+ align:start position:0%
+3x3 tensor so let's break this down a
+ 
+
+ align:start position:0%
+3x3 tensor so let's break this down a
+little bit further whenever I am dealing
+
+ align:start position:0%
+little bit further whenever I am dealing
+ 
+
+ align:start position:0%
+little bit further whenever I am dealing
+with a function that is vector in nature
+
+ align:start position:0%
+with a function that is vector in nature
+ 
+
+ align:start position:0%
+with a function that is vector in nature
+and bear mine is a field so I'm dealing
+
+ align:start position:0%
+and bear mine is a field so I'm dealing
+ 
+
+ align:start position:0%
+and bear mine is a field so I'm dealing
+with a vector field I'm going to write
+
+ align:start position:0%
+with a vector field I'm going to write
+ 
+
+ align:start position:0%
+with a vector field I'm going to write
+this as a divergence free function plus
+
+ align:start position:0%
+this as a divergence free function plus
+ 
+
+ align:start position:0%
+this as a divergence free function plus
+the gradient of some scalar so what I'm
+
+ align:start position:0%
+the gradient of some scalar so what I'm
+ 
+
+ align:start position:0%
+the gradient of some scalar so what I'm
+going to do is say H CI is equal to beta
+
+ align:start position:0%
+going to do is say H CI is equal to beta
+ 
+
+ align:start position:0%
+going to do is say H CI is equal to beta
+I plus the gradient of some gamma and
+
+ align:start position:0%
+I plus the gradient of some gamma and
+ 
+
+ align:start position:0%
+I plus the gradient of some gamma and
+I'm going to require that the divergence
+
+ align:start position:0%
+I'm going to require that the divergence
+ 
+
+ align:start position:0%
+I'm going to require that the divergence
+of that beta be equal to zero notice
+
+ align:start position:0%
+of that beta be equal to zero notice
+ 
+
+ align:start position:0%
+of that beta be equal to zero notice
+since all of my indices are spatial
+
+ align:start position:0%
+since all of my indices are spatial
+ 
+
+ align:start position:0%
+since all of my indices are spatial
+indices and I am working in nearly
+
+ align:start position:0%
+indices and I am working in nearly
+ 
+
+ align:start position:0%
+indices and I am working in nearly
+Lorentz coordinates the placement of the
+
+ align:start position:0%
+Lorentz coordinates the placement of the
+ 
+
+ align:start position:0%
+Lorentz coordinates the placement of the
+indices whether it's upstairs or
+
+ align:start position:0%
+indices whether it's upstairs or
+ 
+
+ align:start position:0%
+indices whether it's upstairs or
+downstairs is immaterial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I will tend to write them all in the
+
+ align:start position:0%
+I will tend to write them all in the
+ 
+
+ align:start position:0%
+I will tend to write them all in the
+downstairs position and so repeated
+
+ align:start position:0%
+downstairs position and so repeated
+ 
+
+ align:start position:0%
+downstairs position and so repeated
+indices we're gonna sort of abuse the
+
+ align:start position:0%
+indices we're gonna sort of abuse the
+ 
+
+ align:start position:0%
+indices we're gonna sort of abuse the
+Einstein notation a little bit repeated
+
+ align:start position:0%
+Einstein notation a little bit repeated
+ 
+
+ align:start position:0%
+Einstein notation a little bit repeated
+indices will be summed over let's extend
+
+ align:start position:0%
+indices will be summed over let's extend
+ 
+
+ align:start position:0%
+indices will be summed over let's extend
+this logic to the tensor piece to hij
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this takes a little bit of thought so
+
+ align:start position:0%
+this takes a little bit of thought so
+ 
+
+ align:start position:0%
+this takes a little bit of thought so
+let me just write out the answer and
+
+ align:start position:0%
+let me just write out the answer and
+ 
+
+ align:start position:0%
+let me just write out the answer and
+then describe the character of every
+
+ align:start position:0%
+then describe the character of every
+ 
+
+ align:start position:0%
+then describe the character of every
+piece that goes into this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so hij can be written as h i j TT i will
+
+ align:start position:0%
+so hij can be written as h i j TT i will
+ 
+
+ align:start position:0%
+so hij can be written as h i j TT i will
+define that in a moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one-third H Delta IJ plus D sort of a
+
+ align:start position:0%
+one-third H Delta IJ plus D sort of a
+ 
+
+ align:start position:0%
+one-third H Delta IJ plus D sort of a
+symmetrize gradient of a vector epsilon
+
+ align:start position:0%
+symmetrize gradient of a vector epsilon
+ 
+
+ align:start position:0%
+symmetrize gradient of a vector epsilon
+plus Delta I Delta J minus one-third
+
+ align:start position:0%
+plus Delta I Delta J minus one-third
+ 
+
+ align:start position:0%
+plus Delta I Delta J minus one-third
+Delta IJ plus operator on some function
+
+ align:start position:0%
+Delta IJ plus operator on some function
+ 
+
+ align:start position:0%
+Delta IJ plus operator on some function
+lambda so let me go through and describe
+
+ align:start position:0%
+lambda so let me go through and describe
+ 
+
+ align:start position:0%
+lambda so let me go through and describe
+what each of these things mean and while
+
+ align:start position:0%
+what each of these things mean and while
+ 
+
+ align:start position:0%
+what each of these things mean and while
+I'm at it let me count up the number of
+
+ align:start position:0%
+I'm at it let me count up the number of
+ 
+
+ align:start position:0%
+I'm at it let me count up the number of
+degrees of freedom associate with them
+
+ align:start position:0%
+degrees of freedom associate with them
+ 
+
+ align:start position:0%
+degrees of freedom associate with them
+let's back up for just a second and do
+
+ align:start position:0%
+let's back up for just a second and do
+ 
+
+ align:start position:0%
+let's back up for just a second and do
+that over here gamma is a scalar so
+
+ align:start position:0%
+that over here gamma is a scalar so
+ 
+
+ align:start position:0%
+that over here gamma is a scalar so
+there's one degree of freedom associated
+
+ align:start position:0%
+there's one degree of freedom associated
+ 
+
+ align:start position:0%
+there's one degree of freedom associated
+with gamma let me move this over to here
+
+ align:start position:0%
+with gamma let me move this over to here
+ 
+
+ align:start position:0%
+with gamma let me move this over to here
+that's one degree of freedom beta is a
+
+ align:start position:0%
+that's one degree of freedom beta is a
+ 
+
+ align:start position:0%
+that's one degree of freedom beta is a
+vector but it's divergence less
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it's a vector I have three
+
+ align:start position:0%
+because it's a vector I have three
+ 
+
+ align:start position:0%
+because it's a vector I have three
+components but being divergence free
+
+ align:start position:0%
+components but being divergence free
+ 
+
+ align:start position:0%
+components but being divergence free
+those three components obey a constraint
+
+ align:start position:0%
+those three components obey a constraint
+ 
+
+ align:start position:0%
+those three components obey a constraint
+so that's 3 minus 1 so this scalar and
+
+ align:start position:0%
+so that's 3 minus 1 so this scalar and
+ 
+
+ align:start position:0%
+so that's 3 minus 1 so this scalar and
+this divergence free vector give me the
+
+ align:start position:0%
+this divergence free vector give me the
+ 
+
+ align:start position:0%
+this divergence free vector give me the
+three degrees of freedom I need to
+
+ align:start position:0%
+three degrees of freedom I need to
+ 
+
+ align:start position:0%
+three degrees of freedom I need to
+specify the three independent components
+
+ align:start position:0%
+specify the three independent components
+ 
+
+ align:start position:0%
+specify the three independent components
+of HTI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over here as I look through all of these
+
+ align:start position:0%
+over here as I look through all of these
+ 
+
+ align:start position:0%
+over here as I look through all of these
+different functions H is a scalar I have
+
+ align:start position:0%
+different functions H is a scalar I have
+ 
+
+ align:start position:0%
+different functions H is a scalar I have
+to find it in such a way hold on just
+
+ align:start position:0%
+to find it in such a way hold on just
+ 
+
+ align:start position:0%
+to find it in such a way hold on just
+one second I'm going to come back to
+
+ align:start position:0%
+one second I'm going to come back to
+ 
+
+ align:start position:0%
+one second I'm going to come back to
+that point in just a moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+epsilon J is a vector it is defined such
+
+ align:start position:0%
+epsilon J is a vector it is defined such
+ 
+
+ align:start position:0%
+epsilon J is a vector it is defined such
+that its divergence is zero okay so what
+
+ align:start position:0%
+that its divergence is zero okay so what
+ 
+
+ align:start position:0%
+that its divergence is zero okay so what
+is going on here is this contribution to
+
+ align:start position:0%
+is going on here is this contribution to
+ 
+
+ align:start position:0%
+is going on here is this contribution to
+H I J it gives me a piece of this thing
+
+ align:start position:0%
+H I J it gives me a piece of this thing
+ 
+
+ align:start position:0%
+H I J it gives me a piece of this thing
+that looks like the gradient of a vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this has three degrees of freedom minus
+
+ align:start position:0%
+this has three degrees of freedom minus
+ 
+
+ align:start position:0%
+this has three degrees of freedom minus
+one constraint this is a scalar it only
+
+ align:start position:0%
+one constraint this is a scalar it only
+ 
+
+ align:start position:0%
+one constraint this is a scalar it only
+has one degree of freedom associated
+
+ align:start position:0%
+has one degree of freedom associated
+ 
+
+ align:start position:0%
+has one degree of freedom associated
+with it lambda is another scalar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notice where as H feeds directly into
+
+ align:start position:0%
+notice where as H feeds directly into
+ 
+
+ align:start position:0%
+notice where as H feeds directly into
+hij its derivatives of lambda that feed
+
+ align:start position:0%
+hij its derivatives of lambda that feed
+ 
+
+ align:start position:0%
+hij its derivatives of lambda that feed
+into this so this has one degree of
+
+ align:start position:0%
+into this so this has one degree of
+ 
+
+ align:start position:0%
+into this so this has one degree of
+freedom but this is defined in such a
+
+ align:start position:0%
+freedom but this is defined in such a
+ 
+
+ align:start position:0%
+freedom but this is defined in such a
+way that if I take the trace of H I J
+
+ align:start position:0%
+way that if I take the trace of H I J
+ 
+
+ align:start position:0%
+way that if I take the trace of H I J
+this operator gives me zero right so the
+
+ align:start position:0%
+this operator gives me zero right so the
+ 
+
+ align:start position:0%
+this operator gives me zero right so the
+trace what the trace will do is sum over
+
+ align:start position:0%
+trace what the trace will do is sum over
+ 
+
+ align:start position:0%
+trace what the trace will do is sum over
+sum over elements when I and J are equal
+
+ align:start position:0%
+sum over elements when I and J are equal
+ 
+
+ align:start position:0%
+sum over elements when I and J are equal
+so this will give me essentially the
+
+ align:start position:0%
+so this will give me essentially the
+ 
+
+ align:start position:0%
+so this will give me essentially the
+Laplace operator but the trace of Delta
+
+ align:start position:0%
+Laplace operator but the trace of Delta
+ 
+
+ align:start position:0%
+Laplace operator but the trace of Delta
+IJ is 3 so I get Laplace operator
+
+ align:start position:0%
+IJ is 3 so I get Laplace operator
+ 
+
+ align:start position:0%
+IJ is 3 so I get Laplace operator
+- Laplace operator I get the 0 operator
+
+ align:start position:0%
+- Laplace operator I get the 0 operator
+ 
+
+ align:start position:0%
+- Laplace operator I get the 0 operator
+acting on lambda so this gives me 1
+
+ align:start position:0%
+acting on lambda so this gives me 1
+ 
+
+ align:start position:0%
+acting on lambda so this gives me 1
+degree of freedom this gave me one
+
+ align:start position:0%
+degree of freedom this gave me one
+ 
+
+ align:start position:0%
+degree of freedom this gave me one
+degree of freedom H I J TT and you know
+
+ align:start position:0%
+degree of freedom H I J TT and you know
+ 
+
+ align:start position:0%
+degree of freedom H I J TT and you know
+what I'm gonna go to a separate board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a tensor T T stands for
+
+ align:start position:0%
+this is a tensor T T stands for
+ 
+
+ align:start position:0%
+this is a tensor T T stands for
+transverse and traceless this is defined
+
+ align:start position:0%
+transverse and traceless this is defined
+ 
+
+ align:start position:0%
+transverse and traceless this is defined
+so that if I take its trace if I
+
+ align:start position:0%
+so that if I take its trace if I
+ 
+
+ align:start position:0%
+so that if I take its trace if I
+evaluate this I get zero okay so
+
+ align:start position:0%
+evaluate this I get zero okay so
+ 
+
+ align:start position:0%
+evaluate this I get zero okay so
+hij is a tensor but with no trace and
+
+ align:start position:0%
+hij is a tensor but with no trace and
+ 
+
+ align:start position:0%
+hij is a tensor but with no trace and
+it's defined so that if I take us to
+
+ align:start position:0%
+it's defined so that if I take us to
+ 
+
+ align:start position:0%
+it's defined so that if I take us to
+vergence I get zero so this guy has six
+
+ align:start position:0%
+vergence I get zero so this guy has six
+ 
+
+ align:start position:0%
+vergence I get zero so this guy has six
+independent components this is one
+
+ align:start position:0%
+independent components this is one
+ 
+
+ align:start position:0%
+independent components this is one
+constraint this is three constraints
+
+ align:start position:0%
+constraint this is three constraints
+ 
+
+ align:start position:0%
+constraint this is three constraints
+right because it holds for every value
+
+ align:start position:0%
+right because it holds for every value
+ 
+
+ align:start position:0%
+right because it holds for every value
+of Jack so this ends up giving me two
+
+ align:start position:0%
+of Jack so this ends up giving me two
+ 
+
+ align:start position:0%
+of Jack so this ends up giving me two
+free functions
+
+ align:start position:0%
+free functions
+ 
+
+ align:start position:0%
+free functions
+so as we sum all these up I miss anyone
+
+ align:start position:0%
+so as we sum all these up I miss anyone
+ 
+
+ align:start position:0%
+so as we sum all these up I miss anyone
+here right so I have I had totally
+
+ align:start position:0%
+here right so I have I had totally
+ 
+
+ align:start position:0%
+here right so I have I had totally
+characterized HP anew by a set of scalar
+
+ align:start position:0%
+characterized HP anew by a set of scalar
+ 
+
+ align:start position:0%
+characterized HP anew by a set of scalar
+vector and tensor functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I have a scalar Phi which I have over
+
+ align:start position:0%
+I have a scalar Phi which I have over
+ 
+
+ align:start position:0%
+I have a scalar Phi which I have over
+here to my time timepiece I have a
+
+ align:start position:0%
+here to my time timepiece I have a
+ 
+
+ align:start position:0%
+here to my time timepiece I have a
+scalar gamma I have a vector beta I I
+
+ align:start position:0%
+scalar gamma I have a vector beta I I
+ 
+
+ align:start position:0%
+scalar gamma I have a vector beta I I
+have a scalar H a scalar lambda a vector
+
+ align:start position:0%
+have a scalar H a scalar lambda a vector
+ 
+
+ align:start position:0%
+have a scalar H a scalar lambda a vector
+epsilon I and finally a tensor H I J
+
+ align:start position:0%
+epsilon I and finally a tensor H I J
+ 
+
+ align:start position:0%
+epsilon I and finally a tensor H I J
+tt ok so what I've done is let me just
+
+ align:start position:0%
+tt ok so what I've done is let me just
+ 
+
+ align:start position:0%
+tt ok so what I've done is let me just
+step back for a second what I've been
+
+ align:start position:0%
+step back for a second what I've been
+ 
+
+ align:start position:0%
+step back for a second what I've been
+doing in this exercise is trying to
+
+ align:start position:0%
+doing in this exercise is trying to
+ 
+
+ align:start position:0%
+doing in this exercise is trying to
+figure out with respect to its behavior
+
+ align:start position:0%
+figure out with respect to its behavior
+ 
+
+ align:start position:0%
+figure out with respect to its behavior
+under rotations and then just because
+
+ align:start position:0%
+under rotations and then just because
+ 
+
+ align:start position:0%
+under rotations and then just because
+it'll prove to be convenient in a moment
+
+ align:start position:0%
+it'll prove to be convenient in a moment
+ 
+
+ align:start position:0%
+it'll prove to be convenient in a moment
+its behavior when I sort of look at
+
+ align:start position:0%
+its behavior when I sort of look at
+ 
+
+ align:start position:0%
+its behavior when I sort of look at
+casting quantities in this irreducible
+
+ align:start position:0%
+casting quantities in this irreducible
+ 
+
+ align:start position:0%
+casting quantities in this irreducible
+form that involves divergence free
+
+ align:start position:0%
+form that involves divergence free
+ 
+
+ align:start position:0%
+form that involves divergence free
+vectors and gradients of scalars this is
+
+ align:start position:0%
+vectors and gradients of scalars this is
+ 
+
+ align:start position:0%
+vectors and gradients of scalars this is
+sort of the equivalent of doing that for
+
+ align:start position:0%
+sort of the equivalent of doing that for
+ 
+
+ align:start position:0%
+sort of the equivalent of doing that for
+a tensor function the ten degrees of the
+
+ align:start position:0%
+a tensor function the ten degrees of the
+ 
+
+ align:start position:0%
+a tensor function the ten degrees of the
+ten independent components in H mu nu
+
+ align:start position:0%
+ten independent components in H mu nu
+ 
+
+ align:start position:0%
+ten independent components in H mu nu
+have now been encapsulated by I've got
+
+ align:start position:0%
+have now been encapsulated by I've got
+ 
+
+ align:start position:0%
+have now been encapsulated by I've got
+one function here one here two here one
+
+ align:start position:0%
+one function here one here two here one
+ 
+
+ align:start position:0%
+one function here one here two here one
+here one here two here two here one two
+
+ align:start position:0%
+here one here two here two here one two
+ 
+
+ align:start position:0%
+here one here two here two here one two
+four five six eight and ten so all I've
+
+ align:start position:0%
+four five six eight and ten so all I've
+ 
+
+ align:start position:0%
+four five six eight and ten so all I've
+done is rewrite those ten independent
+
+ align:start position:0%
+done is rewrite those ten independent
+ 
+
+ align:start position:0%
+done is rewrite those ten independent
+components of H mu nu into a form that
+
+ align:start position:0%
+components of H mu nu into a form that
+ 
+
+ align:start position:0%
+components of H mu nu into a form that
+as we're going to see is particularly
+
+ align:start position:0%
+as we're going to see is particularly
+ 
+
+ align:start position:0%
+as we're going to see is particularly
+convenient for allowing us to understand
+
+ align:start position:0%
+convenient for allowing us to understand
+ 
+
+ align:start position:0%
+convenient for allowing us to understand
+what the gauge invariant degrees of
+
+ align:start position:0%
+what the gauge invariant degrees of
+ 
+
+ align:start position:0%
+what the gauge invariant degrees of
+freedom in space-time are at least in
+
+ align:start position:0%
+freedom in space-time are at least in
+ 
+
+ align:start position:0%
+freedom in space-time are at least in
+linearized theory all right so so far
+
+ align:start position:0%
+linearized theory all right so so far
+ 
+
+ align:start position:0%
+linearized theory all right so so far
+all I've really done is rewrite rewrite
+
+ align:start position:0%
+all I've really done is rewrite rewrite
+ 
+
+ align:start position:0%
+all I've really done is rewrite rewrite
+my metric using a set of auxiliary
+
+ align:start position:0%
+my metric using a set of auxiliary
+ 
+
+ align:start position:0%
+my metric using a set of auxiliary
+variables that might look a little bit
+
+ align:start position:0%
+variables that might look a little bit
+ 
+
+ align:start position:0%
+variables that might look a little bit
+crazy what we would like to do is
+
+ align:start position:0%
+crazy what we would like to do is
+ 
+
+ align:start position:0%
+crazy what we would like to do is
+examine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what my linearized Einstein field
+
+ align:start position:0%
+what my linearized Einstein field
+ 
+
+ align:start position:0%
+what my linearized Einstein field
+equations look like in terms of all of
+
+ align:start position:0%
+equations look like in terms of all of
+ 
+
+ align:start position:0%
+equations look like in terms of all of
+these new fields so in terms of the Phi
+
+ align:start position:0%
+these new fields so in terms of the Phi
+ 
+
+ align:start position:0%
+these new fields so in terms of the Phi
+Gamma beta H lambda epsilon h i j TT i
+
+ align:start position:0%
+Gamma beta H lambda epsilon h i j TT i
+ 
+
+ align:start position:0%
+Gamma beta H lambda epsilon h i j TT i
+would like to run this through the
+
+ align:start position:0%
+would like to run this through the
+ 
+
+ align:start position:0%
+would like to run this through the
+mechanism make my Einstein field
+
+ align:start position:0%
+mechanism make my Einstein field
+ 
+
+ align:start position:0%
+mechanism make my Einstein field
+equations but express it in terms of
+
+ align:start position:0%
+equations but express it in terms of
+ 
+
+ align:start position:0%
+equations but express it in terms of
+these things we'll see why that is in
+
+ align:start position:0%
+these things we'll see why that is in
+ 
+
+ align:start position:0%
+these things we'll see why that is in
+just a moment before I do this we have
+
+ align:start position:0%
+just a moment before I do this we have
+ 
+
+ align:start position:0%
+just a moment before I do this we have
+to be a little bit careful okay we have
+
+ align:start position:0%
+to be a little bit careful okay we have
+ 
+
+ align:start position:0%
+to be a little bit careful okay we have
+ten functions here we have four gauge
+
+ align:start position:0%
+ten functions here we have four gauge
+ 
+
+ align:start position:0%
+ten functions here we have four gauge
+degrees of freedom and the whole point
+
+ align:start position:0%
+degrees of freedom and the whole point
+ 
+
+ align:start position:0%
+degrees of freedom and the whole point
+of this exercise is to try to understand
+
+ align:start position:0%
+of this exercise is to try to understand
+ 
+
+ align:start position:0%
+of this exercise is to try to understand
+how to deal with the fact that a gauge
+
+ align:start position:0%
+how to deal with the fact that a gauge
+ 
+
+ align:start position:0%
+how to deal with the fact that a gauge
+that is convenient for doing my
+
+ align:start position:0%
+that is convenient for doing my
+ 
+
+ align:start position:0%
+that is convenient for doing my
+calculation may leave me with a result
+
+ align:start position:0%
+calculation may leave me with a result
+ 
+
+ align:start position:0%
+calculation may leave me with a result
+that is confusing in terms of the
+
+ align:start position:0%
+that is confusing in terms of the
+ 
+
+ align:start position:0%
+that is confusing in terms of the
+physics I'm trying to understand so what
+
+ align:start position:0%
+physics I'm trying to understand so what
+ 
+
+ align:start position:0%
+physics I'm trying to understand so what
+we are going to do is say that I can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take my generator of a gauge
+
+ align:start position:0%
+take my generator of a gauge
+ 
+
+ align:start position:0%
+take my generator of a gauge
+transformation C alpha I can write this
+
+ align:start position:0%
+transformation C alpha I can write this
+ 
+
+ align:start position:0%
+transformation C alpha I can write this
+since I have chosen time and space
+
+ align:start position:0%
+since I have chosen time and space
+ 
+
+ align:start position:0%
+since I have chosen time and space
+coordinates I can break it into a time
+
+ align:start position:0%
+coordinates I can break it into a time
+ 
+
+ align:start position:0%
+coordinates I can break it into a time
+like piece and a spatial piece I'm going
+
+ align:start position:0%
+like piece and a spatial piece I'm going
+ 
+
+ align:start position:0%
+like piece and a spatial piece I'm going
+to say the time like piece is some
+
+ align:start position:0%
+to say the time like piece is some
+ 
+
+ align:start position:0%
+to say the time like piece is some
+scalar field a and the spatial piece
+
+ align:start position:0%
+scalar field a and the spatial piece
+ 
+
+ align:start position:0%
+scalar field a and the spatial piece
+looks like a vector field B sub I plus
+
+ align:start position:0%
+looks like a vector field B sub I plus
+ 
+
+ align:start position:0%
+looks like a vector field B sub I plus
+the gradient of some scalar C and I'm
+
+ align:start position:0%
+the gradient of some scalar C and I'm
+ 
+
+ align:start position:0%
+the gradient of some scalar C and I'm
+going to require dibi to equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reason why I'm doing this is these
+
+ align:start position:0%
+reason why I'm doing this is these
+ 
+
+ align:start position:0%
+reason why I'm doing this is these
+functions that I came up with my thighs
+
+ align:start position:0%
+functions that I came up with my thighs
+ 
+
+ align:start position:0%
+functions that I came up with my thighs
+and gammas and betas and epsilon is
+
+ align:start position:0%
+and gammas and betas and epsilon is
+ 
+
+ align:start position:0%
+and gammas and betas and epsilon is
+whatever they are going to change if I
+
+ align:start position:0%
+whatever they are going to change if I
+ 
+
+ align:start position:0%
+whatever they are going to change if I
+introduce a gauge transformation so
+
+ align:start position:0%
+introduce a gauge transformation so
+ 
+
+ align:start position:0%
+introduce a gauge transformation so
+suppose I change gauge as we learn how
+
+ align:start position:0%
+suppose I change gauge as we learn how
+ 
+
+ align:start position:0%
+suppose I change gauge as we learn how
+to do in the previous lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you do this what you discover is
+
+ align:start position:0%
+when you do this what you discover is
+ 
+
+ align:start position:0%
+when you do this what you discover is
+the function Phi changes to the original
+
+ align:start position:0%
+the function Phi changes to the original
+ 
+
+ align:start position:0%
+the function Phi changes to the original
+Phi listen it looks like the time
+
+ align:start position:0%
+Phi listen it looks like the time
+ 
+
+ align:start position:0%
+Phi listen it looks like the time
+derivative of that scaler egg the beta
+
+ align:start position:0%
+derivative of that scaler egg the beta
+ 
+
+ align:start position:0%
+derivative of that scaler egg the beta
+picks up a term that looks like the time
+
+ align:start position:0%
+picks up a term that looks like the time
+ 
+
+ align:start position:0%
+picks up a term that looks like the time
+derivative of the Sumi the time
+
+ align:start position:0%
+derivative of the Sumi the time
+ 
+
+ align:start position:0%
+derivative of the Sumi the time
+derivative of the vector field B gamma
+
+ align:start position:0%
+derivative of the vector field B gamma
+ 
+
+ align:start position:0%
+derivative of the vector field B gamma
+goes to gamma minus a minus time
+
+ align:start position:0%
+goes to gamma minus a minus time
+ 
+
+ align:start position:0%
+goes to gamma minus a minus time
+derivative of C H goes to H minus to
+
+ align:start position:0%
+derivative of C H goes to H minus to
+ 
+
+ align:start position:0%
+derivative of C H goes to H minus to
+nobble squared of C so all of these
+
+ align:start position:0%
+nobble squared of C so all of these
+ 
+
+ align:start position:0%
+nobble squared of C so all of these
+functions that we sort of cleverly
+
+ align:start position:0%
+functions that we sort of cleverly
+ 
+
+ align:start position:0%
+functions that we sort of cleverly
+introduced trying to write these
+
+ align:start position:0%
+introduced trying to write these
+ 
+
+ align:start position:0%
+introduced trying to write these
+different pieces of the metric of
+
+ align:start position:0%
+different pieces of the metric of
+ 
+
+ align:start position:0%
+different pieces of the metric of
+space-time in an irreducible form when
+
+ align:start position:0%
+space-time in an irreducible form when
+ 
+
+ align:start position:0%
+space-time in an irreducible form when
+we change gauge they change in this way
+
+ align:start position:0%
+we change gauge they change in this way
+ 
+
+ align:start position:0%
+we change gauge they change in this way
+I left one out it turns out when you
+
+ align:start position:0%
+I left one out it turns out when you
+ 
+
+ align:start position:0%
+I left one out it turns out when you
+change gauge h i j TT goes to h i j TT
+
+ align:start position:0%
+change gauge h i j TT goes to h i j TT
+ 
+
+ align:start position:0%
+change gauge h i j TT goes to h i j TT
+this piece is actually gauge invariant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's really interesting because that
+
+ align:start position:0%
+that's really interesting because that
+ 
+
+ align:start position:0%
+that's really interesting because that
+tells me that once I have once I have
+
+ align:start position:0%
+tells me that once I have once I have
+ 
+
+ align:start position:0%
+tells me that once I have once I have
+worked out my field equations the piece
+
+ align:start position:0%
+worked out my field equations the piece
+ 
+
+ align:start position:0%
+worked out my field equations the piece
+of it that describes this transverse and
+
+ align:start position:0%
+of it that describes this transverse and
+ 
+
+ align:start position:0%
+of it that describes this transverse and
+traceless piece of the metric
+
+ align:start position:0%
+traceless piece of the metric
+ 
+
+ align:start position:0%
+traceless piece of the metric
+perturbation it has meaning in any
+
+ align:start position:0%
+perturbation it has meaning in any
+ 
+
+ align:start position:0%
+perturbation it has meaning in any
+representation that I write down so the
+
+ align:start position:0%
+representation that I write down so the
+ 
+
+ align:start position:0%
+representation that I write down so the
+piece that looks radiative in one
+
+ align:start position:0%
+piece that looks radiative in one
+ 
+
+ align:start position:0%
+piece that looks radiative in one
+representation in fact is radiative in
+
+ align:start position:0%
+representation in fact is radiative in
+ 
+
+ align:start position:0%
+representation in fact is radiative in
+all representations we still have to
+
+ align:start position:0%
+all representations we still have to
+ 
+
+ align:start position:0%
+all representations we still have to
+figure out what's going on with all this
+
+ align:start position:0%
+figure out what's going on with all this
+ 
+
+ align:start position:0%
+figure out what's going on with all this
+stuff okay so we have a little bit more
+
+ align:start position:0%
+stuff okay so we have a little bit more
+ 
+
+ align:start position:0%
+stuff okay so we have a little bit more
+work to do but we've just learned
+
+ align:start position:0%
+work to do but we've just learned
+ 
+
+ align:start position:0%
+work to do but we've just learned
+something very interesting about this so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at this point there's really no simple
+
+ align:start position:0%
+at this point there's really no simple
+ 
+
+ align:start position:0%
+at this point there's really no simple
+way to describe what you do next honest
+
+ align:start position:0%
+way to describe what you do next honest
+ 
+
+ align:start position:0%
+way to describe what you do next honest
+to god what you essentially do is you
+
+ align:start position:0%
+to god what you essentially do is you
+ 
+
+ align:start position:0%
+to god what you essentially do is you
+just stare at these things for a while
+
+ align:start position:0%
+just stare at these things for a while
+ 
+
+ align:start position:0%
+just stare at these things for a while
+and you start to notice that there are
+
+ align:start position:0%
+and you start to notice that there are
+ 
+
+ align:start position:0%
+and you start to notice that there are
+certain combinations of these different
+
+ align:start position:0%
+certain combinations of these different
+ 
+
+ align:start position:0%
+certain combinations of these different
+functions that like h IJ t t certain
+
+ align:start position:0%
+functions that like h IJ t t certain
+ 
+
+ align:start position:0%
+functions that like h IJ t t certain
+combinations of them are gauge invariant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I define capital Phi to be little
+
+ align:start position:0%
+so if I define capital Phi to be little
+ 
+
+ align:start position:0%
+so if I define capital Phi to be little
+Phi plus the time derivative of my gamma
+
+ align:start position:0%
+Phi plus the time derivative of my gamma
+ 
+
+ align:start position:0%
+Phi plus the time derivative of my gamma
+minus 1/2 to dine derivatives of lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I define theta 1/2 H - loss operator
+
+ align:start position:0%
+if I define theta 1/2 H - loss operator
+ 
+
+ align:start position:0%
+if I define theta 1/2 H - loss operator
+on lambda I define the vector field CI
+
+ align:start position:0%
+on lambda I define the vector field CI
+ 
+
+ align:start position:0%
+on lambda I define the vector field CI
+to be beta I minus one-half epsilon I
+
+ align:start position:0%
+to be beta I minus one-half epsilon I
+ 
+
+ align:start position:0%
+to be beta I minus one-half epsilon I
+note this vector field is divergence
+
+ align:start position:0%
+note this vector field is divergence
+ 
+
+ align:start position:0%
+note this vector field is divergence
+free and of course H I J
+
+ align:start position:0%
+free and of course H I J
+ 
+
+ align:start position:0%
+free and of course H I J
+tt
+
+ align:start position:0%
+tt
+ 
+
+ align:start position:0%
+tt
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+every one of these combinations is
+
+ align:start position:0%
+every one of these combinations is
+ 
+
+ align:start position:0%
+every one of these combinations is
+unchanged under a gauge transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but let's note something okay
+
+ align:start position:0%
+but let's note something okay
+ 
+
+ align:start position:0%
+but let's note something okay
+Phi is a scalar field theta is a scalar
+
+ align:start position:0%
+Phi is a scalar field theta is a scalar
+ 
+
+ align:start position:0%
+Phi is a scalar field theta is a scalar
+field so I have one plus one functions
+
+ align:start position:0%
+field so I have one plus one functions
+ 
+
+ align:start position:0%
+field so I have one plus one functions
+associated with them this is a
+
+ align:start position:0%
+associated with them this is a
+ 
+
+ align:start position:0%
+associated with them this is a
+divergence free vector so it has three
+
+ align:start position:0%
+divergence free vector so it has three
+ 
+
+ align:start position:0%
+divergence free vector so it has three
+minus one degrees of freedom associated
+
+ align:start position:0%
+minus one degrees of freedom associated
+ 
+
+ align:start position:0%
+minus one degrees of freedom associated
+with it and H I J this is traceless and
+
+ align:start position:0%
+with it and H I J this is traceless and
+ 
+
+ align:start position:0%
+with it and H I J this is traceless and
+divergence free and as I already counted
+
+ align:start position:0%
+divergence free and as I already counted
+ 
+
+ align:start position:0%
+divergence free and as I already counted
+up this guy has six minus one minus
+
+ align:start position:0%
+up this guy has six minus one minus
+ 
+
+ align:start position:0%
+up this guy has six minus one minus
+three degrees of freedom in it also till
+
+ align:start position:0%
+three degrees of freedom in it also till
+ 
+
+ align:start position:0%
+three degrees of freedom in it also till
+so when I characterize the gauge
+
+ align:start position:0%
+so when I characterize the gauge
+ 
+
+ align:start position:0%
+so when I characterize the gauge
+invariant degrees of freedom in the
+
+ align:start position:0%
+invariant degrees of freedom in the
+ 
+
+ align:start position:0%
+invariant degrees of freedom in the
+space-time I've only got six functions
+
+ align:start position:0%
+space-time I've only got six functions
+ 
+
+ align:start position:0%
+space-time I've only got six functions
+left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this is good right my original ten
+
+ align:start position:0%
+but this is good right my original ten
+ 
+
+ align:start position:0%
+but this is good right my original ten
+degrees of freedom in the space-time
+
+ align:start position:0%
+degrees of freedom in the space-time
+ 
+
+ align:start position:0%
+degrees of freedom in the space-time
+metric are characterized by these sort
+
+ align:start position:0%
+metric are characterized by these sort
+ 
+
+ align:start position:0%
+metric are characterized by these sort
+of six fundamental degrees of freedom in
+
+ align:start position:0%
+of six fundamental degrees of freedom in
+ 
+
+ align:start position:0%
+of six fundamental degrees of freedom in
+the gravitational field plus 4 gauge
+
+ align:start position:0%
+the gravitational field plus 4 gauge
+ 
+
+ align:start position:0%
+the gravitational field plus 4 gauge
+degrees of freedom that are bound up in
+
+ align:start position:0%
+degrees of freedom that are bound up in
+ 
+
+ align:start position:0%
+degrees of freedom that are bound up in
+my my gauge generators so what I would
+
+ align:start position:0%
+my my gauge generators so what I would
+ 
+
+ align:start position:0%
+my my gauge generators so what I would
+like to do is see if I can write the
+
+ align:start position:0%
+like to do is see if I can write the
+ 
+
+ align:start position:0%
+like to do is see if I can write the
+Einstein field equations in terms of
+
+ align:start position:0%
+Einstein field equations in terms of
+ 
+
+ align:start position:0%
+Einstein field equations in terms of
+these gauge invariant degrees of freedom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you know what I'm gonna write it in
+
+ align:start position:0%
+and you know what I'm gonna write it in
+ 
+
+ align:start position:0%
+and you know what I'm gonna write it in
+its full form ok we're of course gonna
+
+ align:start position:0%
+its full form ok we're of course gonna
+ 
+
+ align:start position:0%
+its full form ok we're of course gonna
+linearize this but what I'm going to do
+
+ align:start position:0%
+linearize this but what I'm going to do
+ 
+
+ align:start position:0%
+linearize this but what I'm going to do
+is take this thing write it in linearize
+
+ align:start position:0%
+is take this thing write it in linearize
+ 
+
+ align:start position:0%
+is take this thing write it in linearize
+gravity using my gauge invariant
+
+ align:start position:0%
+gravity using my gauge invariant
+ 
+
+ align:start position:0%
+gravity using my gauge invariant
+variables before I do this it's really
+
+ align:start position:0%
+variables before I do this it's really
+ 
+
+ align:start position:0%
+variables before I do this it's really
+helpful to first decompose the
+
+ align:start position:0%
+helpful to first decompose the
+ 
+
+ align:start position:0%
+helpful to first decompose the
+stress-energy tensor in a manner similar
+
+ align:start position:0%
+stress-energy tensor in a manner similar
+ 
+
+ align:start position:0%
+stress-energy tensor in a manner similar
+to how we decomposed our metric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what I'm going to do is I've chosen
+
+ align:start position:0%
+so what I'm going to do is I've chosen
+ 
+
+ align:start position:0%
+so what I'm going to do is I've chosen
+time and space directions so I'm gonna
+
+ align:start position:0%
+time and space directions so I'm gonna
+ 
+
+ align:start position:0%
+time and space directions so I'm gonna
+call it a time time piece row and energy
+
+ align:start position:0%
+call it a time time piece row and energy
+ 
+
+ align:start position:0%
+call it a time time piece row and energy
+density the time space piece we know
+
+ align:start position:0%
+density the time space piece we know
+ 
+
+ align:start position:0%
+density the time space piece we know
+that this tells me something about the
+
+ align:start position:0%
+that this tells me something about the
+ 
+
+ align:start position:0%
+that this tells me something about the
+flow of energy or the density of
+
+ align:start position:0%
+flow of energy or the density of
+ 
+
+ align:start position:0%
+flow of energy or the density of
+momentum and I'm gonna write this as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divergence free vector plus the gradient
+
+ align:start position:0%
+divergence free vector plus the gradient
+ 
+
+ align:start position:0%
+divergence free vector plus the gradient
+of some scalar and I am going to
+
+ align:start position:0%
+of some scalar and I am going to
+ 
+
+ align:start position:0%
+of some scalar and I am going to
+describe the space base piece as an
+
+ align:start position:0%
+describe the space base piece as an
+ 
+
+ align:start position:0%
+describe the space base piece as an
+isotropic pressure and anisotropic term
+
+ align:start position:0%
+isotropic pressure and anisotropic term
+ 
+
+ align:start position:0%
+isotropic pressure and anisotropic term
+I'm going to give you a constraint on
+
+ align:start position:0%
+I'm going to give you a constraint on
+ 
+
+ align:start position:0%
+I'm going to give you a constraint on
+this in just a moment some kind of a
+
+ align:start position:0%
+this in just a moment some kind of a
+ 
+
+ align:start position:0%
+this in just a moment some kind of a
+gradient of a CV some kind of a gradient
+
+ align:start position:0%
+gradient of a CV some kind of a gradient
+ 
+
+ align:start position:0%
+gradient of a CV some kind of a gradient
+of a vector field and then a
+
+ align:start position:0%
+of a vector field and then a
+ 
+
+ align:start position:0%
+of a vector field and then a
+second-order Trace free operator acting
+
+ align:start position:0%
+second-order Trace free operator acting
+ 
+
+ align:start position:0%
+second-order Trace free operator acting
+on a scalar okay so yeah I'm gonna want
+
+ align:start position:0%
+on a scalar okay so yeah I'm gonna want
+ 
+
+ align:start position:0%
+on a scalar okay so yeah I'm gonna want
+to introduce a couple of constraints
+
+ align:start position:0%
+to introduce a couple of constraints
+ 
+
+ align:start position:0%
+to introduce a couple of constraints
+here I'm going to require now the D is
+
+ align:start position:0%
+here I'm going to require now the D is
+ 
+
+ align:start position:0%
+here I'm going to require now the D is
+is zero I'm also going to require that
+
+ align:start position:0%
+is zero I'm also going to require that
+ 
+
+ align:start position:0%
+is zero I'm also going to require that
+the divergence of Sigma equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the divergence of this Sigma IJ be equal
+
+ align:start position:0%
+the divergence of this Sigma IJ be equal
+ 
+
+ align:start position:0%
+the divergence of this Sigma IJ be equal
+to zero and I'm going to require the
+
+ align:start position:0%
+to zero and I'm going to require the
+ 
+
+ align:start position:0%
+to zero and I'm going to require the
+trace of this guy be equal to zero let
+
+ align:start position:0%
+trace of this guy be equal to zero let
+ 
+
+ align:start position:0%
+trace of this guy be equal to zero let
+me strongly emphasize that really all
+
+ align:start position:0%
+me strongly emphasize that really all
+ 
+
+ align:start position:0%
+me strongly emphasize that really all
+I'm doing is rearranging terms I'm just
+
+ align:start position:0%
+I'm doing is rearranging terms I'm just
+ 
+
+ align:start position:0%
+I'm doing is rearranging terms I'm just
+trying to rewrite the compliments of my
+
+ align:start position:0%
+trying to rewrite the compliments of my
+ 
+
+ align:start position:0%
+trying to rewrite the compliments of my
+stress energy tensor using this
+
+ align:start position:0%
+stress energy tensor using this
+ 
+
+ align:start position:0%
+stress energy tensor using this
+decomposition under rotations and then
+
+ align:start position:0%
+decomposition under rotations and then
+ 
+
+ align:start position:0%
+decomposition under rotations and then
+looking at fields that can be written as
+
+ align:start position:0%
+looking at fields that can be written as
+ 
+
+ align:start position:0%
+looking at fields that can be written as
+divergence free vectors plus gradients
+
+ align:start position:0%
+divergence free vectors plus gradients
+ 
+
+ align:start position:0%
+divergence free vectors plus gradients
+of scalar
+
+ align:start position:0%
+of scalar
+ 
+
+ align:start position:0%
+of scalar
+and I have a typo I'm just trying to do
+
+ align:start position:0%
+and I have a typo I'm just trying to do
+ 
+
+ align:start position:0%
+and I have a typo I'm just trying to do
+this in a way that parallels what I did
+
+ align:start position:0%
+this in a way that parallels what I did
+ 
+
+ align:start position:0%
+this in a way that parallels what I did
+for the metric okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before I do this don't forget that I am
+
+ align:start position:0%
+before I do this don't forget that I am
+ 
+
+ align:start position:0%
+before I do this don't forget that I am
+required to make sure that my stress
+
+ align:start position:0%
+required to make sure that my stress
+ 
+
+ align:start position:0%
+required to make sure that my stress
+energy tensor satisfies the law of local
+
+ align:start position:0%
+energy tensor satisfies the law of local
+ 
+
+ align:start position:0%
+energy tensor satisfies the law of local
+conservation of energy and momentum when
+
+ align:start position:0%
+conservation of energy and momentum when
+ 
+
+ align:start position:0%
+conservation of energy and momentum when
+we do this what we find is that these
+
+ align:start position:0%
+we do this what we find is that these
+ 
+
+ align:start position:0%
+we do this what we find is that these
+various things that I introduced here
+
+ align:start position:0%
+various things that I introduced here
+ 
+
+ align:start position:0%
+various things that I introduced here
+some of them are related to each other
+
+ align:start position:0%
+some of them are related to each other
+ 
+
+ align:start position:0%
+some of them are related to each other
+so in particular what you find is the
+
+ align:start position:0%
+so in particular what you find is the
+ 
+
+ align:start position:0%
+so in particular what you find is the
+Laplace operator on s is equal to the
+
+ align:start position:0%
+Laplace operator on s is equal to the
+ 
+
+ align:start position:0%
+Laplace operator on s is equal to the
+time derivative of the density the
+
+ align:start position:0%
+time derivative of the density the
+ 
+
+ align:start position:0%
+time derivative of the density the
+energy density the plus operator on the
+
+ align:start position:0%
+energy density the plus operator on the
+ 
+
+ align:start position:0%
+energy density the plus operator on the
+scale or Sigma is related to the
+
+ align:start position:0%
+scale or Sigma is related to the
+ 
+
+ align:start position:0%
+scale or Sigma is related to the
+pressure and the time derivative
+
+ align:start position:0%
+pressure and the time derivative
+ 
+
+ align:start position:0%
+pressure and the time derivative
+derivative of this s finally the plus
+
+ align:start position:0%
+derivative of this s finally the plus
+ 
+
+ align:start position:0%
+derivative of this s finally the plus
+operator on that Sigma I is related to
+
+ align:start position:0%
+operator on that Sigma I is related to
+ 
+
+ align:start position:0%
+operator on that Sigma I is related to
+also the time derivative of this whoops
+
+ align:start position:0%
+also the time derivative of this whoops
+ 
+
+ align:start position:0%
+also the time derivative of this whoops
+time derivative si what this tells us is
+
+ align:start position:0%
+time derivative si what this tells us is
+ 
+
+ align:start position:0%
+time derivative si what this tells us is
+that so I really want to make sure
+
+ align:start position:0%
+that so I really want to make sure
+ 
+
+ align:start position:0%
+that so I really want to make sure
+people don't get too hung up on this
+
+ align:start position:0%
+people don't get too hung up on this
+ 
+
+ align:start position:0%
+people don't get too hung up on this
+this is really just sort of a convenient
+
+ align:start position:0%
+this is really just sort of a convenient
+ 
+
+ align:start position:0%
+this is really just sort of a convenient
+way of reorganizing the information in
+
+ align:start position:0%
+way of reorganizing the information in
+ 
+
+ align:start position:0%
+way of reorganizing the information in
+those terms but if you do want to think
+
+ align:start position:0%
+those terms but if you do want to think
+ 
+
+ align:start position:0%
+those terms but if you do want to think
+about this this is telling us that only
+
+ align:start position:0%
+about this this is telling us that only
+ 
+
+ align:start position:0%
+about this this is telling us that only
+Rho P si and Sigma IJ are freely
+
+ align:start position:0%
+Rho P si and Sigma IJ are freely
+ 
+
+ align:start position:0%
+Rho P si and Sigma IJ are freely
+specifiable if you know these there's a
+
+ align:start position:0%
+specifiable if you know these there's a
+ 
+
+ align:start position:0%
+specifiable if you know these there's a
+total of six functions here one scalar
+
+ align:start position:0%
+total of six functions here one scalar
+ 
+
+ align:start position:0%
+total of six functions here one scalar
+one scalar three vectors minus one can
+
+ align:start position:0%
+one scalar three vectors minus one can
+ 
+
+ align:start position:0%
+one scalar three vectors minus one can
+constraint six tensors minus four
+
+ align:start position:0%
+constraint six tensors minus four
+ 
+
+ align:start position:0%
+constraint six tensors minus four
+constraints cuz this is divergence less
+
+ align:start position:0%
+constraints cuz this is divergence less
+ 
+
+ align:start position:0%
+constraints cuz this is divergence less
+and trace free these are the only ones
+
+ align:start position:0%
+and trace free these are the only ones
+ 
+
+ align:start position:0%
+and trace free these are the only ones
+that are freely specified viable they
+
+ align:start position:0%
+that are freely specified viable they
+ 
+
+ align:start position:0%
+that are freely specified viable they
+determine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the other four fields okay
+
+ align:start position:0%
+the other four fields okay
+ 
+
+ align:start position:0%
+the other four fields okay
+so density pressure kind of an energy
+
+ align:start position:0%
+so density pressure kind of an energy
+ 
+
+ align:start position:0%
+so density pressure kind of an energy
+flow and anisotropic stresses okay
+
+ align:start position:0%
+flow and anisotropic stresses okay
+ 
+
+ align:start position:0%
+flow and anisotropic stresses okay
+redemption is at hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take all of the framework that we
+
+ align:start position:0%
+take all of the framework that we
+ 
+
+ align:start position:0%
+take all of the framework that we
+developed and that we discussed in the
+
+ align:start position:0%
+developed and that we discussed in the
+ 
+
+ align:start position:0%
+developed and that we discussed in the
+previous lecture and let's grind out the
+
+ align:start position:0%
+previous lecture and let's grind out the
+ 
+
+ align:start position:0%
+previous lecture and let's grind out the
+components of the Einstein tensors doing
+
+ align:start position:0%
+components of the Einstein tensors doing
+ 
+
+ align:start position:0%
+components of the Einstein tensors doing
+so to linear order in H which is
+
+ align:start position:0%
+so to linear order in H which is
+ 
+
+ align:start position:0%
+so to linear order in H which is
+equivalent to saying linear order in all
+
+ align:start position:0%
+equivalent to saying linear order in all
+ 
+
+ align:start position:0%
+equivalent to saying linear order in all
+of these fields that we've introduced
+
+ align:start position:0%
+of these fields that we've introduced
+ 
+
+ align:start position:0%
+of these fields that we've introduced
+what you find is GTT and is - Laplace
+
+ align:start position:0%
+what you find is GTT and is - Laplace
+ 
+
+ align:start position:0%
+what you find is GTT and is - Laplace
+operator times this fields theta GTI is
+
+ align:start position:0%
+operator times this fields theta GTI is
+ 
+
+ align:start position:0%
+operator times this fields theta GTI is
+minus 1/2 Laplace operator on this
+
+ align:start position:0%
+minus 1/2 Laplace operator on this
+ 
+
+ align:start position:0%
+minus 1/2 Laplace operator on this
+vector field sy - the time derivative
+
+ align:start position:0%
+vector field sy - the time derivative
+ 
+
+ align:start position:0%
+vector field sy - the time derivative
+the gradient of the time derivative of
+
+ align:start position:0%
+the gradient of the time derivative of
+ 
+
+ align:start position:0%
+the gradient of the time derivative of
+your Santa and gij
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's like a wave a wave operator on the
+
+ align:start position:0%
+it's like a wave a wave operator on the
+ 
+
+ align:start position:0%
+it's like a wave a wave operator on the
+TT piece of your metric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's a lot let's equate them to
+
+ align:start position:0%
+okay that's a lot let's equate them to
+ 
+
+ align:start position:0%
+okay that's a lot let's equate them to
+the source
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll take advantage of the fact
+
+ align:start position:0%
+and we'll take advantage of the fact
+ 
+
+ align:start position:0%
+and we'll take advantage of the fact
+that when you do this you're always
+
+ align:start position:0%
+that when you do this you're always
+ 
+
+ align:start position:0%
+that when you do this you're always
+going to associate like with like okay
+
+ align:start position:0%
+going to associate like with like okay
+ 
+
+ align:start position:0%
+going to associate like with like okay
+terms that are divergence free you're
+
+ align:start position:0%
+terms that are divergence free you're
+ 
+
+ align:start position:0%
+terms that are divergence free you're
+going to equate to a source that is
+
+ align:start position:0%
+going to equate to a source that is
+ 
+
+ align:start position:0%
+going to equate to a source that is
+divergence free things like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this completely characterizes the
+
+ align:start position:0%
+this completely characterizes the
+ 
+
+ align:start position:0%
+this completely characterizes the
+Einstein field equations solutions the
+
+ align:start position:0%
+Einstein field equations solutions the
+ 
+
+ align:start position:0%
+Einstein field equations solutions the
+Einstein field equations in linearized
+
+ align:start position:0%
+Einstein field equations in linearized
+ 
+
+ align:start position:0%
+Einstein field equations in linearized
+gravity now I want to make a couple of
+
+ align:start position:0%
+gravity now I want to make a couple of
+ 
+
+ align:start position:0%
+gravity now I want to make a couple of
+remarks about this when part of what was
+
+ align:start position:0%
+remarks about this when part of what was
+ 
+
+ align:start position:0%
+remarks about this when part of what was
+the motivation for this entire lecture
+
+ align:start position:0%
+the motivation for this entire lecture
+ 
+
+ align:start position:0%
+the motivation for this entire lecture
+was this observation that when we solve
+
+ align:start position:0%
+was this observation that when we solve
+ 
+
+ align:start position:0%
+was this observation that when we solve
+the field equations using the radiative
+
+ align:start position:0%
+the field equations using the radiative
+ 
+
+ align:start position:0%
+the field equations using the radiative
+green's function by construction the
+
+ align:start position:0%
+green's function by construction the
+ 
+
+ align:start position:0%
+green's function by construction the
+entire space-time solution had this
+
+ align:start position:0%
+entire space-time solution had this
+ 
+
+ align:start position:0%
+entire space-time solution had this
+radiative character associated with it
+
+ align:start position:0%
+radiative character associated with it
+ 
+
+ align:start position:0%
+radiative character associated with it
+everything sort of fell off as 1 over R
+
+ align:start position:0%
+everything sort of fell off as 1 over R
+ 
+
+ align:start position:0%
+everything sort of fell off as 1 over R
+and had a time dependence that reflected
+
+ align:start position:0%
+and had a time dependence that reflected
+ 
+
+ align:start position:0%
+and had a time dependence that reflected
+a time delay time it takes for radiation
+
+ align:start position:0%
+a time delay time it takes for radiation
+ 
+
+ align:start position:0%
+a time delay time it takes for radiation
+to travel from the source to the point
+
+ align:start position:0%
+to travel from the source to the point
+ 
+
+ align:start position:0%
+to travel from the source to the point
+at which the field is being measured
+
+ align:start position:0%
+at which the field is being measured
+ 
+
+ align:start position:0%
+at which the field is being measured
+but we saw via this electrodynamic
+
+ align:start position:0%
+but we saw via this electrodynamic
+ 
+
+ align:start position:0%
+but we saw via this electrodynamic
+example that we put up just for
+
+ align:start position:0%
+example that we put up just for
+ 
+
+ align:start position:0%
+example that we put up just for
+intuitions sake that it's entirely
+
+ align:start position:0%
+intuitions sake that it's entirely
+ 
+
+ align:start position:0%
+intuitions sake that it's entirely
+possible to have a totally non radiative
+
+ align:start position:0%
+possible to have a totally non radiative
+ 
+
+ align:start position:0%
+possible to have a totally non radiative
+field that looks rated of basically
+
+ align:start position:0%
+field that looks rated of basically
+ 
+
+ align:start position:0%
+field that looks rated of basically
+because we chose a gauge that masked its
+
+ align:start position:0%
+because we chose a gauge that masked its
+ 
+
+ align:start position:0%
+because we chose a gauge that masked its
+physical character this was a lengthy
+
+ align:start position:0%
+physical character this was a lengthy
+ 
+
+ align:start position:0%
+physical character this was a lengthy
+and I'll be blunt a somewhat advanced
+
+ align:start position:0%
+and I'll be blunt a somewhat advanced
+ 
+
+ align:start position:0%
+and I'll be blunt a somewhat advanced
+calculation okay I do not expect
+
+ align:start position:0%
+calculation okay I do not expect
+ 
+
+ align:start position:0%
+calculation okay I do not expect
+everyone to be able to follow this in
+
+ align:start position:0%
+everyone to be able to follow this in
+ 
+
+ align:start position:0%
+everyone to be able to follow this in
+great detail but I want you to
+
+ align:start position:0%
+great detail but I want you to
+ 
+
+ align:start position:0%
+great detail but I want you to
+understand how we got to this final end
+
+ align:start position:0%
+understand how we got to this final end
+ 
+
+ align:start position:0%
+understand how we got to this final end
+result here by decomposing the
+
+ align:start position:0%
+result here by decomposing the
+ 
+
+ align:start position:0%
+result here by decomposing the
+space-time the the perturbation to
+
+ align:start position:0%
+space-time the the perturbation to
+ 
+
+ align:start position:0%
+space-time the the perturbation to
+space-time in linearized theory into
+
+ align:start position:0%
+space-time in linearized theory into
+ 
+
+ align:start position:0%
+space-time in linearized theory into
+sort of as irreducible as possible a set
+
+ align:start position:0%
+sort of as irreducible as possible a set
+ 
+
+ align:start position:0%
+sort of as irreducible as possible a set
+of functions we found that there are
+
+ align:start position:0%
+of functions we found that there are
+ 
+
+ align:start position:0%
+of functions we found that there are
+exactly six degrees of freedom in that
+
+ align:start position:0%
+exactly six degrees of freedom in that
+ 
+
+ align:start position:0%
+exactly six degrees of freedom in that
+space-time that are completely gauge
+
+ align:start position:0%
+space-time that are completely gauge
+ 
+
+ align:start position:0%
+space-time that are completely gauge
+invariant
+
+ align:start position:0%
+invariant
+ 
+
+ align:start position:0%
+invariant
+these functions will be they will have
+
+ align:start position:0%
+these functions will be they will have
+ 
+
+ align:start position:0%
+these functions will be they will have
+this form they will obey these equations
+
+ align:start position:0%
+this form they will obey these equations
+ 
+
+ align:start position:0%
+this form they will obey these equations
+you can in principle you can solve these
+
+ align:start position:0%
+you can in principle you can solve these
+ 
+
+ align:start position:0%
+you can in principle you can solve these
+things and understand how these fields
+
+ align:start position:0%
+things and understand how these fields
+ 
+
+ align:start position:0%
+things and understand how these fields
+behave no matter what gauge you are
+
+ align:start position:0%
+behave no matter what gauge you are
+ 
+
+ align:start position:0%
+behave no matter what gauge you are
+working in and what we see is two
+
+ align:start position:0%
+working in and what we see is two
+ 
+
+ align:start position:0%
+working in and what we see is two
+degrees of freedom remember hij TT is a
+
+ align:start position:0%
+degrees of freedom remember hij TT is a
+ 
+
+ align:start position:0%
+degrees of freedom remember hij TT is a
+three by three tensor but it is
+
+ align:start position:0%
+three by three tensor but it is
+ 
+
+ align:start position:0%
+three by three tensor but it is
+traceless and its divergence less so
+
+ align:start position:0%
+traceless and its divergence less so
+ 
+
+ align:start position:0%
+traceless and its divergence less so
+there's actually only two degrees of
+
+ align:start position:0%
+there's actually only two degrees of
+ 
+
+ align:start position:0%
+there's actually only two degrees of
+freedom here it is indeed a wave
+
+ align:start position:0%
+freedom here it is indeed a wave
+ 
+
+ align:start position:0%
+freedom here it is indeed a wave
+equation it is the only piece of the
+
+ align:start position:0%
+equation it is the only piece of the
+ 
+
+ align:start position:0%
+equation it is the only piece of the
+metric that is a wave equation in every
+
+ align:start position:0%
+metric that is a wave equation in every
+ 
+
+ align:start position:0%
+metric that is a wave equation in every
+gauge in an every representation all
+
+ align:start position:0%
+gauge in an every representation all
+ 
+
+ align:start position:0%
+gauge in an every representation all
+other gravitational degrees of freedom
+
+ align:start position:0%
+other gravitational degrees of freedom
+ 
+
+ align:start position:0%
+other gravitational degrees of freedom
+obey something more like a place on
+
+ align:start position:0%
+obey something more like a place on
+ 
+
+ align:start position:0%
+obey something more like a place on
+equation these are non radiative this is
+
+ align:start position:0%
+equation these are non radiative this is
+ 
+
+ align:start position:0%
+equation these are non radiative this is
+radiative the way that we are going to
+
+ align:start position:0%
+radiative the way that we are going to
+ 
+
+ align:start position:0%
+radiative the way that we are going to
+use this the next thing which I want to
+
+ align:start position:0%
+use this the next thing which I want to
+ 
+
+ align:start position:0%
+use this the next thing which I want to
+talk about is gravitational radiation
+
+ align:start position:0%
+talk about is gravitational radiation
+ 
+
+ align:start position:0%
+talk about is gravitational radiation
+and what this calculation told you is
+
+ align:start position:0%
+and what this calculation told you is
+ 
+
+ align:start position:0%
+and what this calculation told you is
+that if you are interested in
+
+ align:start position:0%
+that if you are interested in
+ 
+
+ align:start position:0%
+that if you are interested in
+gravitational radiation this is the only
+
+ align:start position:0%
+gravitational radiation this is the only
+ 
+
+ align:start position:0%
+gravitational radiation this is the only
+piece of the space-time and the source
+
+ align:start position:0%
+piece of the space-time and the source
+ 
+
+ align:start position:0%
+piece of the space-time and the source
+that you need to be concerned about it
+
+ align:start position:0%
+that you need to be concerned about it
+ 
+
+ align:start position:0%
+that you need to be concerned about it
+will be it will give you if you solve
+
+ align:start position:0%
+will be it will give you if you solve
+ 
+
+ align:start position:0%
+will be it will give you if you solve
+that equation it will give you the gauge
+
+ align:start position:0%
+that equation it will give you the gauge
+ 
+
+ align:start position:0%
+that equation it will give you the gauge
+invariant radiative degrees of freedom
+
+ align:start position:0%
+invariant radiative degrees of freedom
+ 
+
+ align:start position:0%
+invariant radiative degrees of freedom
+in a spacetime no matter what
+
+ align:start position:0%
+in a spacetime no matter what
+ 
+
+ align:start position:0%
+in a spacetime no matter what
+representation you use so we are going
+
+ align:start position:0%
+representation you use so we are going
+ 
+
+ align:start position:0%
+representation you use so we are going
+to for the next couple of lectures we
+
+ align:start position:0%
+to for the next couple of lectures we
+ 
+
+ align:start position:0%
+to for the next couple of lectures we
+are going to focus on this we're going
+
+ align:start position:0%
+are going to focus on this we're going
+ 
+
+ align:start position:0%
+are going to focus on this we're going
+to show how we can sort of solve the
+
+ align:start position:0%
+to show how we can sort of solve the
+ 
+
+ align:start position:0%
+to show how we can sort of solve the
+Einstein field equations in a
+
+ align:start position:0%
+Einstein field equations in a
+ 
+
+ align:start position:0%
+Einstein field equations in a
+particularly convenient gauge and then
+
+ align:start position:0%
+particularly convenient gauge and then
+ 
+
+ align:start position:0%
+particularly convenient gauge and then
+say alright I know you know I've now got
+
+ align:start position:0%
+say alright I know you know I've now got
+ 
+
+ align:start position:0%
+say alright I know you know I've now got
+these ten functions for them are just
+
+ align:start position:0%
+these ten functions for them are just
+ 
+
+ align:start position:0%
+these ten functions for them are just
+purely things I can get rid of by
+
+ align:start position:0%
+purely things I can get rid of by
+ 
+
+ align:start position:0%
+purely things I can get rid of by
+choosing my gauge there's only six that
+
+ align:start position:0%
+choosing my gauge there's only six that
+ 
+
+ align:start position:0%
+choosing my gauge there's only six that
+are sort of truly physical of those six
+
+ align:start position:0%
+are sort of truly physical of those six
+ 
+
+ align:start position:0%
+are sort of truly physical of those six
+four of them don't constitute true radio
+
+ align:start position:0%
+four of them don't constitute true radio
+ 
+
+ align:start position:0%
+four of them don't constitute true radio
+degrees of freedom there's only two
+
+ align:start position:0%
+degrees of freedom there's only two
+ 
+
+ align:start position:0%
+degrees of freedom there's only two
+degrees of freedom of my solution to
+
+ align:start position:0%
+degrees of freedom of my solution to
+ 
+
+ align:start position:0%
+degrees of freedom of my solution to
+describe radiation we're going to talk
+
+ align:start position:0%
+describe radiation we're going to talk
+ 
+
+ align:start position:0%
+describe radiation we're going to talk
+about how to pull them out how to
+
+ align:start position:0%
+about how to pull them out how to
+ 
+
+ align:start position:0%
+about how to pull them out how to
+characterize them and the important
+
+ align:start position:0%
+characterize them and the important
+ 
+
+ align:start position:0%
+characterize them and the important
+physical content that this gravitational
+
+ align:start position:0%
+physical content that this gravitational
+ 
+
+ align:start position:0%
+physical content that this gravitational
+radiation carries so in a nutshell you
+
+ align:start position:0%
+radiation carries so in a nutshell you
+ 
+
+ align:start position:0%
+radiation carries so in a nutshell you
+should take this lecture as
+
+ align:start position:0%
+should take this lecture as
+ 
+
+ align:start position:0%
+should take this lecture as
+demonstrating that in a
+
+ align:start position:0%
+demonstrating that in a
+ 
+
+ align:start position:0%
+demonstrating that in a
+very very deep way spacetime always has
+
+ align:start position:0%
+very very deep way spacetime always has
+ 
+
+ align:start position:0%
+very very deep way spacetime always has
+some kind of a radiative component
+
+ align:start position:0%
+some kind of a radiative component
+ 
+
+ align:start position:0%
+some kind of a radiative component
+associated with it but it's really only
+
+ align:start position:0%
+associated with it but it's really only
+ 
+
+ align:start position:0%
+associated with it but it's really only
+encapsulated in two degrees of freedom
+
+ align:start position:0%
+encapsulated in two degrees of freedom
+ 
+
+ align:start position:0%
+encapsulated in two degrees of freedom
+in the space-time
+
+ align:start position:0%
+in the space-time
+ 
+
+ align:start position:0%
+in the space-time
+it may look otherwise but just be
+
+ align:start position:0%
+it may look otherwise but just be
+ 
+
+ align:start position:0%
+it may look otherwise but just be
+careful that's because your gauge has
+
+ align:start position:0%
+careful that's because your gauge has
+ 
+
+ align:start position:0%
+careful that's because your gauge has
+confused you essentially and with that I
+
+ align:start position:0%
+confused you essentially and with that I
+ 
+
+ align:start position:0%
+confused you essentially and with that I
+will stop this lecture here
\ No newline at end of file
diff --git a/PBMyBVPRtKA.txt b/PBMyBVPRtKA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3427541824eee31929244f8513ca6b4659bfa955
--- /dev/null
+++ b/PBMyBVPRtKA.txt
@@ -0,0 +1,15147 @@
+align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+name of the game today is compactness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so last time i recalled that the
+
+ align:start position:0%
+so last time i recalled that the
+ 
+
+ align:start position:0%
+so last time i recalled that the
+definition of
+
+ align:start position:0%
+definition of
+ 
+
+ align:start position:0%
+definition of
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subset of a metric space x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+every sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+xn
+
+ align:start position:0%
+xn
+ 
+
+ align:start position:0%
+xn
+and k so every sequence of elements in k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converging in k has a subsequence which
+
+ align:start position:0%
+converging in k has a subsequence which
+ 
+
+ align:start position:0%
+converging in k has a subsequence which
+converges to an element in k
+
+ align:start position:0%
+converges to an element in k
+ 
+
+ align:start position:0%
+converges to an element in k
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+so uh for example by the heiner burrell
+
+ align:start position:0%
+so uh for example by the heiner burrell
+ 
+
+ align:start position:0%
+so uh for example by the heiner burrell
+theorem closed and bounded subsets of rn
+
+ align:start position:0%
+theorem closed and bounded subsets of rn
+ 
+
+ align:start position:0%
+theorem closed and bounded subsets of rn
+or cn
+
+ align:start position:0%
+or cn
+ 
+
+ align:start position:0%
+or cn
+are compact this is from 18 100
+
+ align:start position:0%
+are compact this is from 18 100
+ 
+
+ align:start position:0%
+are compact this is from 18 100
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and general
+
+ align:start position:0%
+and general
+ 
+
+ align:start position:0%
+and general
+closed and bounded subsets of a hilbert
+
+ align:start position:0%
+closed and bounded subsets of a hilbert
+ 
+
+ align:start position:0%
+closed and bounded subsets of a hilbert
+space are not necessarily compact last
+
+ align:start position:0%
+space are not necessarily compact last
+ 
+
+ align:start position:0%
+space are not necessarily compact last
+time we looked at
+
+ align:start position:0%
+time we looked at
+ 
+
+ align:start position:0%
+time we looked at
+the closed unit ball um
+
+ align:start position:0%
+the closed unit ball um
+ 
+
+ align:start position:0%
+the closed unit ball um
+uh in a hilbert space or or
+
+ align:start position:0%
+uh in a hilbert space or or
+ 
+
+ align:start position:0%
+uh in a hilbert space or or
+let's say in little l2 this is not
+
+ align:start position:0%
+let's say in little l2 this is not
+ 
+
+ align:start position:0%
+let's say in little l2 this is not
+compact because you can take the
+
+ align:start position:0%
+compact because you can take the
+ 
+
+ align:start position:0%
+compact because you can take the
+orthonormal basis vectors you know which
+
+ align:start position:0%
+orthonormal basis vectors you know which
+ 
+
+ align:start position:0%
+orthonormal basis vectors you know which
+consists of uh which are the sequences
+
+ align:start position:0%
+consists of uh which are the sequences
+ 
+
+ align:start position:0%
+consists of uh which are the sequences
+that have zero except for one and say
+
+ align:start position:0%
+that have zero except for one and say
+ 
+
+ align:start position:0%
+that have zero except for one and say
+the n spot
+
+ align:start position:0%
+the n spot
+ 
+
+ align:start position:0%
+the n spot
+these are all of unit length and
+
+ align:start position:0%
+these are all of unit length and
+ 
+
+ align:start position:0%
+these are all of unit length and
+the sequence consisting of these
+
+ align:start position:0%
+the sequence consisting of these
+ 
+
+ align:start position:0%
+the sequence consisting of these
+basis vectors which are sequences so
+
+ align:start position:0%
+basis vectors which are sequences so
+ 
+
+ align:start position:0%
+basis vectors which are sequences so
+this sequence of sequences does not
+
+ align:start position:0%
+this sequence of sequences does not
+ 
+
+ align:start position:0%
+this sequence of sequences does not
+converge in little l two or have a
+
+ align:start position:0%
+converge in little l two or have a
+ 
+
+ align:start position:0%
+converge in little l two or have a
+subsequence which converges in little l
+
+ align:start position:0%
+subsequence which converges in little l
+ 
+
+ align:start position:0%
+subsequence which converges in little l
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+so we were looking for an additional
+
+ align:start position:0%
+so we were looking for an additional
+ 
+
+ align:start position:0%
+so we were looking for an additional
+condition that would ensure compactness
+
+ align:start position:0%
+condition that would ensure compactness
+ 
+
+ align:start position:0%
+condition that would ensure compactness
+and as a warm-up to this last time we
+
+ align:start position:0%
+and as a warm-up to this last time we
+ 
+
+ align:start position:0%
+and as a warm-up to this last time we
+proved the following that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're always working in a hilbert
+
+ align:start position:0%
+so we're always working in a hilbert
+ 
+
+ align:start position:0%
+so we're always working in a hilbert
+space it may be separable or not
+
+ align:start position:0%
+space it may be separable or not
+ 
+
+ align:start position:0%
+space it may be separable or not
+depending on if i say it is or not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if we take a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a convergent sequence in
+
+ align:start position:0%
+a convergent sequence in
+ 
+
+ align:start position:0%
+a convergent sequence in
+h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the conclusion is
+
+ align:start position:0%
+then the conclusion is
+ 
+
+ align:start position:0%
+then the conclusion is
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+that the set k consisting of all the
+
+ align:start position:0%
+that the set k consisting of all the
+ 
+
+ align:start position:0%
+that the set k consisting of all the
+elements of the sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the limit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the set k has what are called equi small
+
+ align:start position:0%
+the set k has what are called equi small
+ 
+
+ align:start position:0%
+the set k has what are called equi small
+tails with respect to any
+
+ align:start position:0%
+tails with respect to any
+ 
+
+ align:start position:0%
+tails with respect to any
+orthonormal subset of h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+e sub
+
+ align:start position:0%
+e sub
+ 
+
+ align:start position:0%
+e sub
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+is a countable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or the normal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subset of h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the following holds this condition we
+
+ align:start position:0%
+the following holds this condition we
+ 
+
+ align:start position:0%
+the following holds this condition we
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+k having equi small tails
+
+ align:start position:0%
+k having equi small tails
+ 
+
+ align:start position:0%
+k having equi small tails
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+for every epsilon positive
+
+ align:start position:0%
+for every epsilon positive
+ 
+
+ align:start position:0%
+for every epsilon positive
+there exists a natural number in
+
+ align:start position:0%
+there exists a natural number in
+ 
+
+ align:start position:0%
+there exists a natural number in
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+for all uh let's call it
+
+ align:start position:0%
+for all uh let's call it
+ 
+
+ align:start position:0%
+for all uh let's call it
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me use a different
+
+ align:start position:0%
+let me use a different
+ 
+
+ align:start position:0%
+let me use a different
+letter v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tilde and k so either an element of the
+
+ align:start position:0%
+tilde and k so either an element of the
+ 
+
+ align:start position:0%
+tilde and k so either an element of the
+sequence or v
+
+ align:start position:0%
+sequence or v
+ 
+
+ align:start position:0%
+sequence or v
+have that the sum
+
+ align:start position:0%
+have that the sum
+ 
+
+ align:start position:0%
+have that the sum
+over k bigger than n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared is less than
+
+ align:start position:0%
+squared is less than
+ 
+
+ align:start position:0%
+squared is less than
+epsilon squared so what this says in
+
+ align:start position:0%
+epsilon squared so what this says in
+ 
+
+ align:start position:0%
+epsilon squared so what this says in
+this condition we called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k has
+
+ align:start position:0%
+k has
+ 
+
+ align:start position:0%
+k has
+equi
+
+ align:start position:0%
+equi
+ 
+
+ align:start position:0%
+equi
+small tails
+
+ align:start position:0%
+small tails
+ 
+
+ align:start position:0%
+small tails
+with respect to this orthonormal subset
+
+ align:start position:0%
+with respect to this orthonormal subset
+ 
+
+ align:start position:0%
+with respect to this orthonormal subset
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+of course for any fixed v
+
+ align:start position:0%
+of course for any fixed v
+ 
+
+ align:start position:0%
+of course for any fixed v
+because uh this entire sum forget just k
+
+ align:start position:0%
+because uh this entire sum forget just k
+ 
+
+ align:start position:0%
+because uh this entire sum forget just k
+over n is bounded by
+
+ align:start position:0%
+over n is bounded by
+ 
+
+ align:start position:0%
+over n is bounded by
+uh the norm of this v tilde squared by
+
+ align:start position:0%
+uh the norm of this v tilde squared by
+ 
+
+ align:start position:0%
+uh the norm of this v tilde squared by
+bessel's inequality we can always choose
+
+ align:start position:0%
+bessel's inequality we can always choose
+ 
+
+ align:start position:0%
+bessel's inequality we can always choose
+an n for any individual
+
+ align:start position:0%
+an n for any individual
+ 
+
+ align:start position:0%
+an n for any individual
+v tilde
+
+ align:start position:0%
+v tilde
+ 
+
+ align:start position:0%
+v tilde
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+equi small tails means that i can choose
+
+ align:start position:0%
+equi small tails means that i can choose
+ 
+
+ align:start position:0%
+equi small tails means that i can choose
+this in
+
+ align:start position:0%
+this in
+ 
+
+ align:start position:0%
+this in
+uh independent of the element in k all
+
+ align:start position:0%
+uh independent of the element in k all
+ 
+
+ align:start position:0%
+uh independent of the element in k all
+right so if you like uniformly small
+
+ align:start position:0%
+right so if you like uniformly small
+ 
+
+ align:start position:0%
+right so if you like uniformly small
+tails is another way you could think
+
+ align:start position:0%
+tails is another way you could think
+ 
+
+ align:start position:0%
+tails is another way you could think
+about it okay
+
+ align:start position:0%
+about it okay
+ 
+
+ align:start position:0%
+about it okay
+but the terminology equi has has
+
+ align:start position:0%
+but the terminology equi has has
+ 
+
+ align:start position:0%
+but the terminology equi has has
+been used uh instead but another way is
+
+ align:start position:0%
+been used uh instead but another way is
+ 
+
+ align:start position:0%
+been used uh instead but another way is
+to think we can uniformly make the tails
+
+ align:start position:0%
+to think we can uniformly make the tails
+ 
+
+ align:start position:0%
+to think we can uniformly make the tails
+uh with respect to an orthonormal
+
+ align:start position:0%
+uh with respect to an orthonormal
+ 
+
+ align:start position:0%
+uh with respect to an orthonormal
+sequence or orthonormal subset of h
+
+ align:start position:0%
+sequence or orthonormal subset of h
+ 
+
+ align:start position:0%
+sequence or orthonormal subset of h
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+what we're going to prove is that in
+
+ align:start position:0%
+what we're going to prove is that in
+ 
+
+ align:start position:0%
+what we're going to prove is that in
+fact
+
+ align:start position:0%
+fact
+ 
+
+ align:start position:0%
+fact
+this condition here of having equi small
+
+ align:start position:0%
+this condition here of having equi small
+ 
+
+ align:start position:0%
+this condition here of having equi small
+tails with respect to an orthonormal
+
+ align:start position:0%
+tails with respect to an orthonormal
+ 
+
+ align:start position:0%
+tails with respect to an orthonormal
+basis on top of the set being closed and
+
+ align:start position:0%
+basis on top of the set being closed and
+ 
+
+ align:start position:0%
+basis on top of the set being closed and
+bounded suffice to prove um
+
+ align:start position:0%
+bounded suffice to prove um
+ 
+
+ align:start position:0%
+bounded suffice to prove um
+that the subset is compact and that's
+
+ align:start position:0%
+that the subset is compact and that's
+ 
+
+ align:start position:0%
+that the subset is compact and that's
+the following
+
+ align:start position:0%
+the following
+ 
+
+ align:start position:0%
+the following
+theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a separable
+
+ align:start position:0%
+a separable
+ 
+
+ align:start position:0%
+a separable
+hilbert space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let
+
+ align:start position:0%
+and let
+ 
+
+ align:start position:0%
+and let
+e k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an orthonormal basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i said suffice but not justifies it's
+
+ align:start position:0%
+so i said suffice but not justifies it's
+ 
+
+ align:start position:0%
+so i said suffice but not justifies it's
+also necessary as we'll show then k
+
+ align:start position:0%
+also necessary as we'll show then k
+ 
+
+ align:start position:0%
+also necessary as we'll show then k
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subset of h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if and only if
+
+ align:start position:0%
+if and only if
+ 
+
+ align:start position:0%
+if and only if
+k is
+
+ align:start position:0%
+k is
+ 
+
+ align:start position:0%
+k is
+closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+captioning not available
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+with respect to
+
+ align:start position:0%
+with respect to
+ 
+
+ align:start position:0%
+with respect to
+this orthonormal basis that's
+
+ align:start position:0%
+this orthonormal basis that's
+ 
+
+ align:start position:0%
+this orthonormal basis that's
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so in particular for any orthonormal
+
+ align:start position:0%
+so in particular for any orthonormal
+ 
+
+ align:start position:0%
+so in particular for any orthonormal
+basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so this um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+you know a complete description of
+
+ align:start position:0%
+you know a complete description of
+ 
+
+ align:start position:0%
+you know a complete description of
+compact set subsets of a hilbert space
+
+ align:start position:0%
+compact set subsets of a hilbert space
+ 
+
+ align:start position:0%
+compact set subsets of a hilbert space
+it's those subsets which are closed
+
+ align:start position:0%
+it's those subsets which are closed
+ 
+
+ align:start position:0%
+it's those subsets which are closed
+bounded and have equi small tails
+
+ align:start position:0%
+bounded and have equi small tails
+ 
+
+ align:start position:0%
+bounded and have equi small tails
+with respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+orthonormal basis and what this theorem
+
+ align:start position:0%
+orthonormal basis and what this theorem
+ 
+
+ align:start position:0%
+orthonormal basis and what this theorem
+also says is that if it has
+
+ align:start position:0%
+also says is that if it has
+ 
+
+ align:start position:0%
+also says is that if it has
+equi small tails with respect to one
+
+ align:start position:0%
+equi small tails with respect to one
+ 
+
+ align:start position:0%
+equi small tails with respect to one
+orthonormal basis uh and is closed and
+
+ align:start position:0%
+orthonormal basis uh and is closed and
+ 
+
+ align:start position:0%
+orthonormal basis uh and is closed and
+bounded then the same holds with respect
+
+ align:start position:0%
+bounded then the same holds with respect
+ 
+
+ align:start position:0%
+bounded then the same holds with respect
+to any orthonormal basis okay
+
+ align:start position:0%
+to any orthonormal basis okay
+ 
+
+ align:start position:0%
+to any orthonormal basis okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so let's prove uh so it's a two-way
+
+ align:start position:0%
+okay so let's prove uh so it's a two-way
+ 
+
+ align:start position:0%
+okay so let's prove uh so it's a two-way
+street
+
+ align:start position:0%
+street
+ 
+
+ align:start position:0%
+street
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+i doesn't make sense to say one street
+
+ align:start position:0%
+i doesn't make sense to say one street
+ 
+
+ align:start position:0%
+i doesn't make sense to say one street
+is shorter one side of the street is
+
+ align:start position:0%
+is shorter one side of the street is
+ 
+
+ align:start position:0%
+is shorter one side of the street is
+shorter
+
+ align:start position:0%
+shorter
+ 
+
+ align:start position:0%
+shorter
+uh maybe wider easier to use um
+
+ align:start position:0%
+uh maybe wider easier to use um
+ 
+
+ align:start position:0%
+uh maybe wider easier to use um
+but let's prove that if k is compact
+
+ align:start position:0%
+but let's prove that if k is compact
+ 
+
+ align:start position:0%
+but let's prove that if k is compact
+then it implies all of this so suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k is compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and k is closed
+
+ align:start position:0%
+and k is closed
+ 
+
+ align:start position:0%
+and k is closed
+and bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by general metric space theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+look this up in the 18 100s material
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay or intro to analysis material
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's
+
+ align:start position:0%
+so let's
+ 
+
+ align:start position:0%
+so let's
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this also gives us a
+
+ align:start position:0%
+this also gives us a
+ 
+
+ align:start position:0%
+this also gives us a
+opportunity to understand
+
+ align:start position:0%
+opportunity to understand
+ 
+
+ align:start position:0%
+opportunity to understand
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this equi-small tail condition as well
+
+ align:start position:0%
+this equi-small tail condition as well
+ 
+
+ align:start position:0%
+this equi-small tail condition as well
+by having to negate it so we're also
+
+ align:start position:0%
+by having to negate it so we're also
+ 
+
+ align:start position:0%
+by having to negate it so we're also
+going to prove that k has equi small
+
+ align:start position:0%
+going to prove that k has equi small
+ 
+
+ align:start position:0%
+going to prove that k has equi small
+tails by contradiction
+
+ align:start position:0%
+tails by contradiction
+ 
+
+ align:start position:0%
+tails by contradiction
+so suppose k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does not have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equi-small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tails
+
+ align:start position:0%
+tails
+ 
+
+ align:start position:0%
+tails
+with respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this basis or this orthonormal basis
+
+ align:start position:0%
+this basis or this orthonormal basis
+ 
+
+ align:start position:0%
+this basis or this orthonormal basis
+then what's that mean
+
+ align:start position:0%
+then what's that mean
+ 
+
+ align:start position:0%
+then what's that mean
+so this is a for all there exists in a
+
+ align:start position:0%
+so this is a for all there exists in a
+ 
+
+ align:start position:0%
+so this is a for all there exists in a
+statement
+
+ align:start position:0%
+statement
+ 
+
+ align:start position:0%
+statement
+so then there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some bad epsilon
+
+ align:start position:0%
+some bad epsilon
+ 
+
+ align:start position:0%
+some bad epsilon
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+we're all in natural number
+
+ align:start position:0%
+we're all in natural number
+ 
+
+ align:start position:0%
+we're all in natural number
+there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a u n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+so these ends are increasing
+
+ align:start position:0%
+so these ends are increasing
+ 
+
+ align:start position:0%
+so these ends are increasing
+such that u
+
+ align:start position:0%
+such that u
+ 
+
+ align:start position:0%
+such that u
+so we have the
+
+ align:start position:0%
+so we have the
+ 
+
+ align:start position:0%
+so we have the
+negation of the condition that's
+
+ align:start position:0%
+negation of the condition that's
+ 
+
+ align:start position:0%
+negation of the condition that's
+satisfied k bigger than n
+
+ align:start position:0%
+satisfied k bigger than n
+ 
+
+ align:start position:0%
+satisfied k bigger than n
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+u n
+
+ align:start position:0%
+u n
+ 
+
+ align:start position:0%
+u n
+e k
+
+ align:start position:0%
+e k
+ 
+
+ align:start position:0%
+e k
+squared is bigger than or equal to this
+
+ align:start position:0%
+squared is bigger than or equal to this
+ 
+
+ align:start position:0%
+squared is bigger than or equal to this
+epsilon not squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now this uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+note that
+
+ align:start position:0%
+note that
+ 
+
+ align:start position:0%
+note that
+this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequence in this compact set k and so by
+
+ align:start position:0%
+sequence in this compact set k and so by
+ 
+
+ align:start position:0%
+sequence in this compact set k and so by
+the defining property of a of a compact
+
+ align:start position:0%
+the defining property of a of a compact
+ 
+
+ align:start position:0%
+the defining property of a of a compact
+set it must have a convergent
+
+ align:start position:0%
+set it must have a convergent
+ 
+
+ align:start position:0%
+set it must have a convergent
+subsequence right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which implies
+
+ align:start position:0%
+which implies
+ 
+
+ align:start position:0%
+which implies
+there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a subsequence
+
+ align:start position:0%
+a subsequence
+ 
+
+ align:start position:0%
+a subsequence
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+uh which you know you usually denote use
+
+ align:start position:0%
+uh which you know you usually denote use
+ 
+
+ align:start position:0%
+uh which you know you usually denote use
+of n capital n sub
+
+ align:start position:0%
+of n capital n sub
+ 
+
+ align:start position:0%
+of n capital n sub
+m some other uh letter but i'll just
+
+ align:start position:0%
+m some other uh letter but i'll just
+ 
+
+ align:start position:0%
+m some other uh letter but i'll just
+call it
+
+ align:start position:0%
+call it
+ 
+
+ align:start position:0%
+call it
+to make it
+
+ align:start position:0%
+to make it
+ 
+
+ align:start position:0%
+to make it
+a little uh connection back to what we
+
+ align:start position:0%
+a little uh connection back to what we
+ 
+
+ align:start position:0%
+a little uh connection back to what we
+wrote a minute ago v sub n so this is a
+
+ align:start position:0%
+wrote a minute ago v sub n so this is a
+ 
+
+ align:start position:0%
+wrote a minute ago v sub n so this is a
+subsequence of u sub capital n
+
+ align:start position:0%
+subsequence of u sub capital n
+ 
+
+ align:start position:0%
+subsequence of u sub capital n
+and v in k
+
+ align:start position:0%
+and v in k
+ 
+
+ align:start position:0%
+and v in k
+such that b sub n converges to v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+we're all in
+
+ align:start position:0%
+we're all in
+ 
+
+ align:start position:0%
+we're all in
+natural number
+
+ align:start position:0%
+natural number
+ 
+
+ align:start position:0%
+natural number
+we have that sum over k bigger than n
+
+ align:start position:0%
+we have that sum over k bigger than n
+ 
+
+ align:start position:0%
+we have that sum over k bigger than n
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+v n
+
+ align:start position:0%
+v n
+ 
+
+ align:start position:0%
+v n
+e k
+
+ align:start position:0%
+e k
+ 
+
+ align:start position:0%
+e k
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+bigger than epsilon not squared right
+
+ align:start position:0%
+bigger than epsilon not squared right
+ 
+
+ align:start position:0%
+bigger than epsilon not squared right
+because this is a subsequence of the
+
+ align:start position:0%
+because this is a subsequence of the
+ 
+
+ align:start position:0%
+because this is a subsequence of the
+original sequence which that which
+
+ align:start position:0%
+original sequence which that which
+ 
+
+ align:start position:0%
+original sequence which that which
+satisfied this condition
+
+ align:start position:0%
+satisfied this condition
+ 
+
+ align:start position:0%
+satisfied this condition
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right now this would actually be
+
+ align:start position:0%
+all right now this would actually be
+ 
+
+ align:start position:0%
+all right now this would actually be
+capital n sub n but if i throw in some
+
+ align:start position:0%
+capital n sub n but if i throw in some
+ 
+
+ align:start position:0%
+capital n sub n but if i throw in some
+more capital n sub n would be
+
+ align:start position:0%
+more capital n sub n would be
+ 
+
+ align:start position:0%
+more capital n sub n would be
+uh you know increasing
+
+ align:start position:0%
+uh you know increasing
+ 
+
+ align:start position:0%
+uh you know increasing
+sequence of numbers and it's always
+
+ align:start position:0%
+sequence of numbers and it's always
+ 
+
+ align:start position:0%
+sequence of numbers and it's always
+bigger than n so i can replace that
+
+ align:start position:0%
+bigger than n so i can replace that
+ 
+
+ align:start position:0%
+bigger than n so i can replace that
+capital n sub n with this all right so
+
+ align:start position:0%
+capital n sub n with this all right so
+ 
+
+ align:start position:0%
+capital n sub n with this all right so
+this is this is fine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+that says the
+
+ align:start position:0%
+that says the
+ 
+
+ align:start position:0%
+that says the
+subset uh consisting of the elements v
+
+ align:start position:0%
+subset uh consisting of the elements v
+ 
+
+ align:start position:0%
+subset uh consisting of the elements v
+sub n
+
+ align:start position:0%
+sub n
+ 
+
+ align:start position:0%
+sub n
+and the natural number
+
+ align:start position:0%
+and the natural number
+ 
+
+ align:start position:0%
+and the natural number
+union v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does not have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equi-small tails which is a
+
+ align:start position:0%
+equi-small tails which is a
+ 
+
+ align:start position:0%
+equi-small tails which is a
+contradiction to
+
+ align:start position:0%
+contradiction to
+ 
+
+ align:start position:0%
+contradiction to
+the theorem we proved last time
+
+ align:start position:0%
+the theorem we proved last time
+ 
+
+ align:start position:0%
+the theorem we proved last time
+this contradicts the previous theorem
+
+ align:start position:0%
+this contradicts the previous theorem
+ 
+
+ align:start position:0%
+this contradicts the previous theorem
+that i stated and we proved last time
+
+ align:start position:0%
+that i stated and we proved last time
+ 
+
+ align:start position:0%
+that i stated and we proved last time
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so any convergent sequence along with
+
+ align:start position:0%
+so any convergent sequence along with
+ 
+
+ align:start position:0%
+so any convergent sequence along with
+its limit is a compact set
+
+ align:start position:0%
+its limit is a compact set
+ 
+
+ align:start position:0%
+its limit is a compact set
+and has equi small tails
+
+ align:start position:0%
+and has equi small tails
+ 
+
+ align:start position:0%
+and has equi small tails
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh that's a contradiction
+
+ align:start position:0%
+uh that's a contradiction
+ 
+
+ align:start position:0%
+uh that's a contradiction
+and what was the assumption that brought
+
+ align:start position:0%
+and what was the assumption that brought
+ 
+
+ align:start position:0%
+and what was the assumption that brought
+us to
+
+ align:start position:0%
+us to
+ 
+
+ align:start position:0%
+us to
+um this road forking itself is
+
+ align:start position:0%
+um this road forking itself is
+ 
+
+ align:start position:0%
+um this road forking itself is
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the assumption that k is not compact so
+
+ align:start position:0%
+the assumption that k is not compact so
+ 
+
+ align:start position:0%
+the assumption that k is not compact so
+therefore k i mean not k is compact k
+
+ align:start position:0%
+therefore k i mean not k is compact k
+ 
+
+ align:start position:0%
+therefore k i mean not k is compact k
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+equally small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tails
+
+ align:start position:0%
+tails
+ 
+
+ align:start position:0%
+tails
+with respect to
+
+ align:start position:0%
+with respect to
+ 
+
+ align:start position:0%
+with respect to
+this orthonormal basis
+
+ align:start position:0%
+this orthonormal basis
+ 
+
+ align:start position:0%
+this orthonormal basis
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's one direction
+
+ align:start position:0%
+so that's one direction
+ 
+
+ align:start position:0%
+so that's one direction
+that if k is compact then it has to have
+
+ align:start position:0%
+that if k is compact then it has to have
+ 
+
+ align:start position:0%
+that if k is compact then it has to have
+equi small tails with respect to the
+
+ align:start position:0%
+equi small tails with respect to the
+ 
+
+ align:start position:0%
+equi small tails with respect to the
+orthonormal basis all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know we didn't use anything about it
+
+ align:start position:0%
+you know we didn't use anything about it
+ 
+
+ align:start position:0%
+you know we didn't use anything about it
+being a basis so this also says that if
+
+ align:start position:0%
+being a basis so this also says that if
+ 
+
+ align:start position:0%
+being a basis so this also says that if
+you have a compact set then
+
+ align:start position:0%
+you have a compact set then
+ 
+
+ align:start position:0%
+you have a compact set then
+with respect to any orthonormal subset
+
+ align:start position:0%
+with respect to any orthonormal subset
+ 
+
+ align:start position:0%
+with respect to any orthonormal subset
+it has equity small tails with respect
+
+ align:start position:0%
+it has equity small tails with respect
+ 
+
+ align:start position:0%
+it has equity small tails with respect
+to that orthonormal subset
+
+ align:start position:0%
+to that orthonormal subset
+ 
+
+ align:start position:0%
+to that orthonormal subset
+okay so now let's use this condition
+
+ align:start position:0%
+okay so now let's use this condition
+ 
+
+ align:start position:0%
+okay so now let's use this condition
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that k is closed and bounded and has
+
+ align:start position:0%
+that k is closed and bounded and has
+ 
+
+ align:start position:0%
+that k is closed and bounded and has
+equi small tails to prove that k is
+
+ align:start position:0%
+equi small tails to prove that k is
+ 
+
+ align:start position:0%
+equi small tails to prove that k is
+compact
+
+ align:start position:0%
+compact
+ 
+
+ align:start position:0%
+compact
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+suppose k
+
+ align:start position:0%
+suppose k
+ 
+
+ align:start position:0%
+suppose k
+is closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and has equi small tails
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with respect to this orthonormal basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u n
+
+ align:start position:0%
+u n
+ 
+
+ align:start position:0%
+u n
+be a sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in k so we want to show that it has a
+
+ align:start position:0%
+in k so we want to show that it has a
+ 
+
+ align:start position:0%
+in k so we want to show that it has a
+subsequence
+
+ align:start position:0%
+subsequence
+ 
+
+ align:start position:0%
+subsequence
+which converges to an element in k now k
+
+ align:start position:0%
+which converges to an element in k now k
+ 
+
+ align:start position:0%
+which converges to an element in k now k
+is closed
+
+ align:start position:0%
+is closed
+ 
+
+ align:start position:0%
+is closed
+all right which means that if i take any
+
+ align:start position:0%
+all right which means that if i take any
+ 
+
+ align:start position:0%
+all right which means that if i take any
+sequence which converges in k
+
+ align:start position:0%
+sequence which converges in k
+ 
+
+ align:start position:0%
+sequence which converges in k
+or which any sequence of elements in k
+
+ align:start position:0%
+or which any sequence of elements in k
+ 
+
+ align:start position:0%
+or which any sequence of elements in k
+that converges the limit has to be in k
+
+ align:start position:0%
+that converges the limit has to be in k
+ 
+
+ align:start position:0%
+that converges the limit has to be in k
+that's that's the definition of a set
+
+ align:start position:0%
+that's that's the definition of a set
+ 
+
+ align:start position:0%
+that's that's the definition of a set
+being closed so i just need to show that
+
+ align:start position:0%
+being closed so i just need to show that
+ 
+
+ align:start position:0%
+being closed so i just need to show that
+this sequence
+
+ align:start position:0%
+this sequence
+ 
+
+ align:start position:0%
+this sequence
+in fact has a convergent subsequence all
+
+ align:start position:0%
+in fact has a convergent subsequence all
+ 
+
+ align:start position:0%
+in fact has a convergent subsequence all
+right that's all i have to show so since
+
+ align:start position:0%
+right that's all i have to show so since
+ 
+
+ align:start position:0%
+right that's all i have to show so since
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k is closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we just need to show
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as a convergent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the idea is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to use
+
+ align:start position:0%
+to use
+ 
+
+ align:start position:0%
+to use
+what we know about bounded subsets of
+
+ align:start position:0%
+what we know about bounded subsets of
+ 
+
+ align:start position:0%
+what we know about bounded subsets of
+complex numbers so we know about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounded subsets of complex numbers
+
+ align:start position:0%
+bounded subsets of complex numbers
+ 
+
+ align:start position:0%
+bounded subsets of complex numbers
+uh if i have a bounded sequence i
+
+ align:start position:0%
+uh if i have a bounded sequence i
+ 
+
+ align:start position:0%
+uh if i have a bounded sequence i
+shouldn't say subsets but um if i have a
+
+ align:start position:0%
+shouldn't say subsets but um if i have a
+ 
+
+ align:start position:0%
+shouldn't say subsets but um if i have a
+bounded sequence of complex numbers it
+
+ align:start position:0%
+bounded sequence of complex numbers it
+ 
+
+ align:start position:0%
+bounded sequence of complex numbers it
+has a convergent subsequence this is a
+
+ align:start position:0%
+has a convergent subsequence this is a
+ 
+
+ align:start position:0%
+has a convergent subsequence this is a
+balzonov balzano virustras usually it's
+
+ align:start position:0%
+balzonov balzano virustras usually it's
+ 
+
+ align:start position:0%
+balzonov balzano virustras usually it's
+stated in terms of subsets of r
+
+ align:start position:0%
+stated in terms of subsets of r
+ 
+
+ align:start position:0%
+stated in terms of subsets of r
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+sequences of complex numbers converge if
+
+ align:start position:0%
+sequences of complex numbers converge if
+ 
+
+ align:start position:0%
+sequences of complex numbers converge if
+and only if the real and imaginary part
+
+ align:start position:0%
+and only if the real and imaginary part
+ 
+
+ align:start position:0%
+and only if the real and imaginary part
+uh converge and are bounded if and only
+
+ align:start position:0%
+uh converge and are bounded if and only
+ 
+
+ align:start position:0%
+uh converge and are bounded if and only
+if the real and imaginary part which are
+
+ align:start position:0%
+if the real and imaginary part which are
+ 
+
+ align:start position:0%
+if the real and imaginary part which are
+sequences of real numbers are bounded
+
+ align:start position:0%
+sequences of real numbers are bounded
+ 
+
+ align:start position:0%
+sequences of real numbers are bounded
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+balzanovirusdross immediately implies a
+
+ align:start position:0%
+balzanovirusdross immediately implies a
+ 
+
+ align:start position:0%
+balzanovirusdross immediately implies a
+similar statement for complex numbers
+
+ align:start position:0%
+similar statement for complex numbers
+ 
+
+ align:start position:0%
+similar statement for complex numbers
+that every bounded
+
+ align:start position:0%
+that every bounded
+ 
+
+ align:start position:0%
+that every bounded
+sequence of complex numbers has a
+
+ align:start position:0%
+sequence of complex numbers has a
+ 
+
+ align:start position:0%
+sequence of complex numbers has a
+convergent
+
+ align:start position:0%
+convergent
+ 
+
+ align:start position:0%
+convergent
+subsequence okay so how would we use
+
+ align:start position:0%
+subsequence okay so how would we use
+ 
+
+ align:start position:0%
+subsequence okay so how would we use
+that what we're going to do is we're
+
+ align:start position:0%
+that what we're going to do is we're
+ 
+
+ align:start position:0%
+that what we're going to do is we're
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+you know expand u n's and this is where
+
+ align:start position:0%
+you know expand u n's and this is where
+ 
+
+ align:start position:0%
+you know expand u n's and this is where
+we'll use that this is an orthonormal
+
+ align:start position:0%
+we'll use that this is an orthonormal
+ 
+
+ align:start position:0%
+we'll use that this is an orthonormal
+basis
+
+ align:start position:0%
+basis
+ 
+
+ align:start position:0%
+basis
+in terms of this orthonormal basis so
+
+ align:start position:0%
+in terms of this orthonormal basis so
+ 
+
+ align:start position:0%
+in terms of this orthonormal basis so
+for each k
+
+ align:start position:0%
+for each k
+ 
+
+ align:start position:0%
+for each k
+we'll have
+
+ align:start position:0%
+we'll have
+ 
+
+ align:start position:0%
+we'll have
+a sequence of complex numbers given by
+
+ align:start position:0%
+a sequence of complex numbers given by
+ 
+
+ align:start position:0%
+a sequence of complex numbers given by
+the entry the kth entry
+
+ align:start position:0%
+the entry the kth entry
+ 
+
+ align:start position:0%
+the entry the kth entry
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+of course
+
+ align:start position:0%
+of course
+ 
+
+ align:start position:0%
+of course
+the case entry of this sequence okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that will be a bounded sequence of
+
+ align:start position:0%
+and that will be a bounded sequence of
+ 
+
+ align:start position:0%
+and that will be a bounded sequence of
+complex numbers because we're assuming
+
+ align:start position:0%
+complex numbers because we're assuming
+ 
+
+ align:start position:0%
+complex numbers because we're assuming
+um k is bounded and therefore this
+
+ align:start position:0%
+um k is bounded and therefore this
+ 
+
+ align:start position:0%
+um k is bounded and therefore this
+sequence is bounded in k all right
+
+ align:start position:0%
+sequence is bounded in k all right
+ 
+
+ align:start position:0%
+sequence is bounded in k all right
+so what we're going to end up having is
+
+ align:start position:0%
+so what we're going to end up having is
+ 
+
+ align:start position:0%
+so what we're going to end up having is
+entry by entry
+
+ align:start position:0%
+entry by entry
+ 
+
+ align:start position:0%
+entry by entry
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+bounded sequence of complex numbers
+
+ align:start position:0%
+bounded sequence of complex numbers
+ 
+
+ align:start position:0%
+bounded sequence of complex numbers
+where these complex numbers represent
+
+ align:start position:0%
+where these complex numbers represent
+ 
+
+ align:start position:0%
+where these complex numbers represent
+the kth entry
+
+ align:start position:0%
+the kth entry
+ 
+
+ align:start position:0%
+the kth entry
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the sequence of vectors
+
+ align:start position:0%
+the sequence of vectors
+ 
+
+ align:start position:0%
+the sequence of vectors
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we're going to then take a subsequence
+
+ align:start position:0%
+we're going to then take a subsequence
+ 
+
+ align:start position:0%
+we're going to then take a subsequence
+that converges
+
+ align:start position:0%
+that converges
+ 
+
+ align:start position:0%
+that converges
+for the first entry we're going to take
+
+ align:start position:0%
+for the first entry we're going to take
+ 
+
+ align:start position:0%
+for the first entry we're going to take
+a subsequence of that subsequence to get
+
+ align:start position:0%
+a subsequence of that subsequence to get
+ 
+
+ align:start position:0%
+a subsequence of that subsequence to get
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+a subsequence which can which converges
+
+ align:start position:0%
+a subsequence which can which converges
+ 
+
+ align:start position:0%
+a subsequence which can which converges
+for the first and second entry and then
+
+ align:start position:0%
+for the first and second entry and then
+ 
+
+ align:start position:0%
+for the first and second entry and then
+so on and so on um a diagonalization
+
+ align:start position:0%
+so on and so on um a diagonalization
+ 
+
+ align:start position:0%
+so on and so on um a diagonalization
+argument okay
+
+ align:start position:0%
+argument okay
+ 
+
+ align:start position:0%
+argument okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that subsequence will show um converges
+
+ align:start position:0%
+that subsequence will show um converges
+ 
+
+ align:start position:0%
+that subsequence will show um converges
+now it's not that simple because if you
+
+ align:start position:0%
+now it's not that simple because if you
+ 
+
+ align:start position:0%
+now it's not that simple because if you
+can do something 10 times it doesn't
+
+ align:start position:0%
+can do something 10 times it doesn't
+ 
+
+ align:start position:0%
+can do something 10 times it doesn't
+mean you can
+
+ align:start position:0%
+mean you can
+ 
+
+ align:start position:0%
+mean you can
+get some sort of uniform control we just
+
+ align:start position:0%
+get some sort of uniform control we just
+ 
+
+ align:start position:0%
+get some sort of uniform control we just
+have kind of control for any finite
+
+ align:start position:0%
+have kind of control for any finite
+ 
+
+ align:start position:0%
+have kind of control for any finite
+number of entries what saves us in the
+
+ align:start position:0%
+number of entries what saves us in the
+ 
+
+ align:start position:0%
+number of entries what saves us in the
+end is this equi-small tail
+
+ align:start position:0%
+end is this equi-small tail
+ 
+
+ align:start position:0%
+end is this equi-small tail
+condition which allows us to basically
+
+ align:start position:0%
+condition which allows us to basically
+ 
+
+ align:start position:0%
+condition which allows us to basically
+throw away
+
+ align:start position:0%
+throw away
+ 
+
+ align:start position:0%
+throw away
+you know kind of
+
+ align:start position:0%
+you know kind of
+ 
+
+ align:start position:0%
+you know kind of
+infinitely many entries
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what this says is that you know you can
+
+ align:start position:0%
+what this says is that you know you can
+ 
+
+ align:start position:0%
+what this says is that you know you can
+always choose an end so that
+
+ align:start position:0%
+always choose an end so that
+ 
+
+ align:start position:0%
+always choose an end so that
+kind of the tail end of the entries
+
+ align:start position:0%
+kind of the tail end of the entries
+ 
+
+ align:start position:0%
+kind of the tail end of the entries
+don't matter
+
+ align:start position:0%
+don't matter
+ 
+
+ align:start position:0%
+don't matter
+and so that with having control over the
+
+ align:start position:0%
+and so that with having control over the
+ 
+
+ align:start position:0%
+and so that with having control over the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+large block of entries will be enough to
+
+ align:start position:0%
+large block of entries will be enough to
+ 
+
+ align:start position:0%
+large block of entries will be enough to
+to conclude
+
+ align:start position:0%
+to conclude
+ 
+
+ align:start position:0%
+to conclude
+so that was uh the road map if you
+
+ align:start position:0%
+so that was uh the road map if you
+ 
+
+ align:start position:0%
+so that was uh the road map if you
+didn't follow the road map fine
+
+ align:start position:0%
+didn't follow the road map fine
+ 
+
+ align:start position:0%
+didn't follow the road map fine
+hopefully you follow the proof
+
+ align:start position:0%
+hopefully you follow the proof
+ 
+
+ align:start position:0%
+hopefully you follow the proof
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's a
+
+ align:start position:0%
+but it's a
+ 
+
+ align:start position:0%
+but it's a
+diagonal argument and
+
+ align:start position:0%
+diagonal argument and
+ 
+
+ align:start position:0%
+diagonal argument and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+those are easy to unders relatively easy
+
+ align:start position:0%
+those are easy to unders relatively easy
+ 
+
+ align:start position:0%
+those are easy to unders relatively easy
+to understand
+
+ align:start position:0%
+to understand
+ 
+
+ align:start position:0%
+to understand
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+somewhat difficult to write down so i
+
+ align:start position:0%
+somewhat difficult to write down so i
+ 
+
+ align:start position:0%
+somewhat difficult to write down so i
+will do my best but
+
+ align:start position:0%
+will do my best but
+ 
+
+ align:start position:0%
+will do my best but
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since k is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that implies there exists
+
+ align:start position:0%
+that implies there exists
+ 
+
+ align:start position:0%
+that implies there exists
+a c non-negative
+
+ align:start position:0%
+a c non-negative
+ 
+
+ align:start position:0%
+a c non-negative
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+we're all in
+
+ align:start position:0%
+we're all in
+ 
+
+ align:start position:0%
+we're all in
+norm of u sub n
+
+ align:start position:0%
+norm of u sub n
+ 
+
+ align:start position:0%
+norm of u sub n
+is less than or equal to c all right the
+
+ align:start position:0%
+is less than or equal to c all right the
+ 
+
+ align:start position:0%
+is less than or equal to c all right the
+c is independent of
+
+ align:start position:0%
+c is independent of
+ 
+
+ align:start position:0%
+c is independent of
+n it just depends on the the set k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and therefore
+
+ align:start position:0%
+all right and therefore
+ 
+
+ align:start position:0%
+all right and therefore
+this says for all
+
+ align:start position:0%
+this says for all
+ 
+
+ align:start position:0%
+this says for all
+k and n
+
+ align:start position:0%
+k and n
+ 
+
+ align:start position:0%
+k and n
+i should
+
+ align:start position:0%
+i should
+ 
+
+ align:start position:0%
+i should
+say uh for all k
+
+ align:start position:0%
+say uh for all k
+ 
+
+ align:start position:0%
+say uh for all k
+we're all in
+
+ align:start position:0%
+we're all in
+ 
+
+ align:start position:0%
+we're all in
+if i look at
+
+ align:start position:0%
+if i look at
+ 
+
+ align:start position:0%
+if i look at
+the kth
+
+ align:start position:0%
+the kth
+ 
+
+ align:start position:0%
+the kth
+uh if you let me call this the the
+
+ align:start position:0%
+uh if you let me call this the the
+ 
+
+ align:start position:0%
+uh if you let me call this the the
+fourier coefficient in this basis
+
+ align:start position:0%
+fourier coefficient in this basis
+ 
+
+ align:start position:0%
+fourier coefficient in this basis
+of these vector in this orthonormal
+
+ align:start position:0%
+of these vector in this orthonormal
+ 
+
+ align:start position:0%
+of these vector in this orthonormal
+basis of e k if i look at the kate's
+
+ align:start position:0%
+basis of e k if i look at the kate's
+ 
+
+ align:start position:0%
+basis of e k if i look at the kate's
+fourier coefficient
+
+ align:start position:0%
+fourier coefficient
+ 
+
+ align:start position:0%
+fourier coefficient
+uh this is bounded by
+
+ align:start position:0%
+uh this is bounded by
+ 
+
+ align:start position:0%
+uh this is bounded by
+um by koshi schwartz u n
+
+ align:start position:0%
+um by koshi schwartz u n
+ 
+
+ align:start position:0%
+um by koshi schwartz u n
+e k and these are orthonormal so this
+
+ align:start position:0%
+e k and these are orthonormal so this
+ 
+
+ align:start position:0%
+e k and these are orthonormal so this
+has unit length this is bounded by c
+
+ align:start position:0%
+has unit length this is bounded by c
+ 
+
+ align:start position:0%
+has unit length this is bounded by c
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so for each fixed k
+
+ align:start position:0%
+so for each fixed k
+ 
+
+ align:start position:0%
+so for each fixed k
+this is a sequence in n of complex
+
+ align:start position:0%
+this is a sequence in n of complex
+ 
+
+ align:start position:0%
+this is a sequence in n of complex
+numbers which is bounded
+
+ align:start position:0%
+numbers which is bounded
+ 
+
+ align:start position:0%
+numbers which is bounded
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sequence consisting of
+
+ align:start position:0%
+the sequence consisting of
+ 
+
+ align:start position:0%
+the sequence consisting of
+the k fourier coefficient of
+
+ align:start position:0%
+the k fourier coefficient of
+ 
+
+ align:start position:0%
+the k fourier coefficient of
+uh the elements u sub n so n is the
+
+ align:start position:0%
+uh the elements u sub n so n is the
+ 
+
+ align:start position:0%
+uh the elements u sub n so n is the
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+that's changing
+
+ align:start position:0%
+that's changing
+ 
+
+ align:start position:0%
+that's changing
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a bounded sequence of complex numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now this is where we're going to
+
+ align:start position:0%
+so now this is where we're going to
+ 
+
+ align:start position:0%
+so now this is where we're going to
+start
+
+ align:start position:0%
+start
+ 
+
+ align:start position:0%
+start
+choosing subsequences of subsequences so
+
+ align:start position:0%
+choosing subsequences of subsequences so
+ 
+
+ align:start position:0%
+choosing subsequences of subsequences so
+that we get convergence along the
+
+ align:start position:0%
+that we get convergence along the
+ 
+
+ align:start position:0%
+that we get convergence along the
+entries
+
+ align:start position:0%
+entries
+ 
+
+ align:start position:0%
+entries
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so since
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u sub
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is bounded
+
+ align:start position:0%
+is bounded
+ 
+
+ align:start position:0%
+is bounded
+this implies that there exists
+
+ align:start position:0%
+this implies that there exists
+ 
+
+ align:start position:0%
+this implies that there exists
+by bolzano virustras a subsequence
+
+ align:start position:0%
+by bolzano virustras a subsequence
+ 
+
+ align:start position:0%
+by bolzano virustras a subsequence
+which i'll denote u sub n sub 1 of k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let me not use k let's use
+
+ align:start position:0%
+uh let me not use k let's use
+ 
+
+ align:start position:0%
+uh let me not use k let's use
+um what do i use here j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e1 so one one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges
+
+ align:start position:0%
+converges
+ 
+
+ align:start position:0%
+converges
+in c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+um okay so i now have a subsequence of
+
+ align:start position:0%
+um okay so i now have a subsequence of
+ 
+
+ align:start position:0%
+um okay so i now have a subsequence of
+the original uh sequence uh
+
+ align:start position:0%
+the original uh sequence uh
+ 
+
+ align:start position:0%
+the original uh sequence uh
+of the uns so that the first entry
+
+ align:start position:0%
+of the uns so that the first entry
+ 
+
+ align:start position:0%
+of the uns so that the first entry
+converges
+
+ align:start position:0%
+converges
+ 
+
+ align:start position:0%
+converges
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh or
+
+ align:start position:0%
+uh or
+ 
+
+ align:start position:0%
+uh or
+this sequence converges now i'm gonna
+
+ align:start position:0%
+this sequence converges now i'm gonna
+ 
+
+ align:start position:0%
+this sequence converges now i'm gonna
+take
+
+ align:start position:0%
+take
+ 
+
+ align:start position:0%
+take
+okay so since
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you uh
+
+ align:start position:0%
+you uh
+ 
+
+ align:start position:0%
+you uh
+and one of j
+
+ align:start position:0%
+and one of j
+ 
+
+ align:start position:0%
+and one of j
+e2
+
+ align:start position:0%
+e2
+ 
+
+ align:start position:0%
+e2
+this is still
+
+ align:start position:0%
+this is still
+ 
+
+ align:start position:0%
+this is still
+a bounded sequence
+
+ align:start position:0%
+a bounded sequence
+ 
+
+ align:start position:0%
+a bounded sequence
+okay by what i showed here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounded sequence
+
+ align:start position:0%
+bounded sequence
+ 
+
+ align:start position:0%
+bounded sequence
+this implies
+
+ align:start position:0%
+this implies
+ 
+
+ align:start position:0%
+this implies
+there exists a
+
+ align:start position:0%
+there exists a
+ 
+
+ align:start position:0%
+there exists a
+subsequence now i'll call this
+
+ align:start position:0%
+subsequence now i'll call this
+ 
+
+ align:start position:0%
+subsequence now i'll call this
+subsequence
+
+ align:start position:0%
+subsequence
+ 
+
+ align:start position:0%
+subsequence
+u n
+
+ align:start position:0%
+u n
+ 
+
+ align:start position:0%
+u n
+2 of j
+
+ align:start position:0%
+2 of j
+ 
+
+ align:start position:0%
+2 of j
+e2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+so in two of j this is a sequence of
+
+ align:start position:0%
+so in two of j this is a sequence of
+ 
+
+ align:start position:0%
+so in two of j this is a sequence of
+integers that is a subset of these guys
+
+ align:start position:0%
+integers that is a subset of these guys
+ 
+
+ align:start position:0%
+integers that is a subset of these guys
+that's increasing
+
+ align:start position:0%
+that's increasing
+ 
+
+ align:start position:0%
+that's increasing
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+u n one of j
+
+ align:start position:0%
+u n one of j
+ 
+
+ align:start position:0%
+u n one of j
+e
+
+ align:start position:0%
+e
+ 
+
+ align:start position:0%
+e
+so i should say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which converges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now uh note
+
+ align:start position:0%
+so now uh note
+ 
+
+ align:start position:0%
+so now uh note
+this sequence converges
+
+ align:start position:0%
+this sequence converges
+ 
+
+ align:start position:0%
+this sequence converges
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but the in
+
+ align:start position:0%
+but the in
+ 
+
+ align:start position:0%
+but the in
+two of j so this is a
+
+ align:start position:0%
+two of j so this is a
+ 
+
+ align:start position:0%
+two of j so this is a
+you know a subsequence of integers
+
+ align:start position:0%
+you know a subsequence of integers
+ 
+
+ align:start position:0%
+you know a subsequence of integers
+that's a
+
+ align:start position:0%
+that's a
+ 
+
+ align:start position:0%
+that's a
+so this is a subsequence of integers of
+
+ align:start position:0%
+so this is a subsequence of integers of
+ 
+
+ align:start position:0%
+so this is a subsequence of integers of
+the n1 of js okay
+
+ align:start position:0%
+the n1 of js okay
+ 
+
+ align:start position:0%
+the n1 of js okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since the n2 of js are a subsequence of
+
+ align:start position:0%
+since the n2 of js are a subsequence of
+ 
+
+ align:start position:0%
+since the n2 of js are a subsequence of
+the n1 of js
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we get that
+
+ align:start position:0%
+we get that
+ 
+
+ align:start position:0%
+we get that
+limit
+
+ align:start position:0%
+limit
+ 
+
+ align:start position:0%
+limit
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+goes to infinity
+
+ align:start position:0%
+goes to infinity
+ 
+
+ align:start position:0%
+goes to infinity
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+u in one of j
+
+ align:start position:0%
+u in one of j
+ 
+
+ align:start position:0%
+u in one of j
+i should say n2 of j
+
+ align:start position:0%
+i should say n2 of j
+ 
+
+ align:start position:0%
+i should say n2 of j
+e1 so this is a subsequence
+
+ align:start position:0%
+e1 so this is a subsequence
+ 
+
+ align:start position:0%
+e1 so this is a subsequence
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+sequence so the n2 of js is just a
+
+ align:start position:0%
+sequence so the n2 of js is just a
+ 
+
+ align:start position:0%
+sequence so the n2 of js is just a
+subsequence of the n1 of js
+
+ align:start position:0%
+subsequence of the n1 of js
+ 
+
+ align:start position:0%
+subsequence of the n1 of js
+so since this
+
+ align:start position:0%
+so since this
+ 
+
+ align:start position:0%
+so since this
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+in j converges
+
+ align:start position:0%
+in j converges
+ 
+
+ align:start position:0%
+in j converges
+this subsequence also converges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now we've chosen the two so that we
+
+ align:start position:0%
+but now we've chosen the two so that we
+ 
+
+ align:start position:0%
+but now we've chosen the two so that we
+also have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not just
+
+ align:start position:0%
+not just
+ 
+
+ align:start position:0%
+not just
+convergence along the first entry but
+
+ align:start position:0%
+convergence along the first entry but
+ 
+
+ align:start position:0%
+convergence along the first entry but
+convergence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+along the second entry
+
+ align:start position:0%
+along the second entry
+ 
+
+ align:start position:0%
+along the second entry
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now you see what uh so this is how
+
+ align:start position:0%
+but now you see what uh so this is how
+ 
+
+ align:start position:0%
+but now you see what uh so this is how
+the argument goes
+
+ align:start position:0%
+the argument goes
+ 
+
+ align:start position:0%
+the argument goes
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+now i will take a subsequence of the n2
+
+ align:start position:0%
+now i will take a subsequence of the n2
+ 
+
+ align:start position:0%
+now i will take a subsequence of the n2
+of j so that uh the subsequence
+
+ align:start position:0%
+of j so that uh the subsequence
+ 
+
+ align:start position:0%
+of j so that uh the subsequence
+converges with
+
+ align:start position:0%
+converges with
+ 
+
+ align:start position:0%
+converges with
+uh when i pair it with e3
+
+ align:start position:0%
+uh when i pair it with e3
+ 
+
+ align:start position:0%
+uh when i pair it with e3
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then i take a subsequence of that
+
+ align:start position:0%
+and then i take a subsequence of that
+ 
+
+ align:start position:0%
+and then i take a subsequence of that
+subsequence uh
+
+ align:start position:0%
+subsequence uh
+ 
+
+ align:start position:0%
+subsequence uh
+so that i get e4 and so on and so on and
+
+ align:start position:0%
+so that i get e4 and so on and so on and
+ 
+
+ align:start position:0%
+so that i get e4 and so on and so on and
+all of these uh subsequences are
+
+ align:start position:0%
+all of these uh subsequences are
+ 
+
+ align:start position:0%
+all of these uh subsequences are
+subsequences of or the subsequences of
+
+ align:start position:0%
+subsequences of or the subsequences of
+ 
+
+ align:start position:0%
+subsequences of or the subsequences of
+integers are subsequences of the
+
+ align:start position:0%
+integers are subsequences of the
+ 
+
+ align:start position:0%
+integers are subsequences of the
+previous set of integers which are again
+
+ align:start position:0%
+previous set of integers which are again
+ 
+
+ align:start position:0%
+previous set of integers which are again
+a subsequence of the original integers n
+
+ align:start position:0%
+a subsequence of the original integers n
+ 
+
+ align:start position:0%
+a subsequence of the original integers n
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ok
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then ah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all
+
+ align:start position:0%
+for all
+ 
+
+ align:start position:0%
+for all
+l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists a subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of integers in
+
+ align:start position:0%
+of integers in
+ 
+
+ align:start position:0%
+of integers in
+l of j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the previous set of integers and
+
+ align:start position:0%
+of the previous set of integers and
+ 
+
+ align:start position:0%
+of the previous set of integers and
+let's say l minus 1 of j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+between 1 and l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit as j goes to infinity of u in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l of j
+
+ align:start position:0%
+l of j
+ 
+
+ align:start position:0%
+l of j
+e k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exists okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i hope this is uh
+
+ align:start position:0%
+so i hope this is uh
+ 
+
+ align:start position:0%
+so i hope this is uh
+i hope this is clear
+
+ align:start position:0%
+i hope this is clear
+ 
+
+ align:start position:0%
+i hope this is clear
+so you just take a subsequence of the
+
+ align:start position:0%
+so you just take a subsequence of the
+ 
+
+ align:start position:0%
+so you just take a subsequence of the
+original sequence so that the first
+
+ align:start position:0%
+original sequence so that the first
+ 
+
+ align:start position:0%
+original sequence so that the first
+entry converges take a subsequence of
+
+ align:start position:0%
+entry converges take a subsequence of
+ 
+
+ align:start position:0%
+entry converges take a subsequence of
+that so that the second entry converges
+
+ align:start position:0%
+that so that the second entry converges
+ 
+
+ align:start position:0%
+that so that the second entry converges
+and so on and so on so then you have
+
+ align:start position:0%
+and so on and so on so then you have
+ 
+
+ align:start position:0%
+and so on and so on so then you have
+this uh
+
+ align:start position:0%
+this uh
+ 
+
+ align:start position:0%
+this uh
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+nested uh
+
+ align:start position:0%
+nested uh
+ 
+
+ align:start position:0%
+nested uh
+subsequences so that at each
+
+ align:start position:0%
+subsequences so that at each
+ 
+
+ align:start position:0%
+subsequences so that at each
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+fixed l you have convergence of the
+
+ align:start position:0%
+fixed l you have convergence of the
+ 
+
+ align:start position:0%
+fixed l you have convergence of the
+first l entries
+
+ align:start position:0%
+first l entries
+ 
+
+ align:start position:0%
+first l entries
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so what you now do is that you pick
+
+ align:start position:0%
+and so what you now do is that you pick
+ 
+
+ align:start position:0%
+and so what you now do is that you pick
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me write
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or pick vl
+
+ align:start position:0%
+or pick vl
+ 
+
+ align:start position:0%
+or pick vl
+to be the diagonal along
+
+ align:start position:0%
+to be the diagonal along
+ 
+
+ align:start position:0%
+to be the diagonal along
+this sequence so
+
+ align:start position:0%
+this sequence so
+ 
+
+ align:start position:0%
+this sequence so
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+in l
+
+ align:start position:0%
+in l
+ 
+
+ align:start position:0%
+in l
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for l equals
+
+ align:start position:0%
+for l equals
+ 
+
+ align:start position:0%
+for l equals
+one two
+
+ align:start position:0%
+one two
+ 
+
+ align:start position:0%
+one two
+three and so on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+what we get is since
+
+ align:start position:0%
+what we get is since
+ 
+
+ align:start position:0%
+what we get is since
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you know the elf subsequence converges
+
+ align:start position:0%
+you know the elf subsequence converges
+ 
+
+ align:start position:0%
+you know the elf subsequence converges
+uh or the elf
+
+ align:start position:0%
+uh or the elf
+ 
+
+ align:start position:0%
+uh or the elf
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+kth entry
+
+ align:start position:0%
+kth entry
+ 
+
+ align:start position:0%
+kth entry
+for one betw
+
+ align:start position:0%
+for one betw
+ 
+
+ align:start position:0%
+for one betw
+okay so let me
+
+ align:start position:0%
+okay so let me
+ 
+
+ align:start position:0%
+okay so let me
+back up and say this one more time since
+
+ align:start position:0%
+back up and say this one more time since
+ 
+
+ align:start position:0%
+back up and say this one more time since
+for fixed l here
+
+ align:start position:0%
+for fixed l here
+ 
+
+ align:start position:0%
+for fixed l here
+i have convergence of the first l
+
+ align:start position:0%
+i have convergence of the first l
+ 
+
+ align:start position:0%
+i have convergence of the first l
+entries
+
+ align:start position:0%
+entries
+ 
+
+ align:start position:0%
+entries
+by picking along the diagonal i get a
+
+ align:start position:0%
+by picking along the diagonal i get a
+ 
+
+ align:start position:0%
+by picking along the diagonal i get a
+subsequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of u n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i have convergence
+
+ align:start position:0%
+i have convergence
+ 
+
+ align:start position:0%
+i have convergence
+uh for the kth entry
+
+ align:start position:0%
+uh for the kth entry
+ 
+
+ align:start position:0%
+uh for the kth entry
+as l goes to infinity
+
+ align:start position:0%
+as l goes to infinity
+ 
+
+ align:start position:0%
+as l goes to infinity
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+converges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i can take subsequences of subsequences
+
+ align:start position:0%
+i can take subsequences of subsequences
+ 
+
+ align:start position:0%
+i can take subsequences of subsequences
+and obtain a subsequence in the end so
+
+ align:start position:0%
+and obtain a subsequence in the end so
+ 
+
+ align:start position:0%
+and obtain a subsequence in the end so
+that uh for this subsequence of the
+
+ align:start position:0%
+that uh for this subsequence of the
+ 
+
+ align:start position:0%
+that uh for this subsequence of the
+original sequence u n's i have a
+
+ align:start position:0%
+original sequence u n's i have a
+ 
+
+ align:start position:0%
+original sequence u n's i have a
+convergence of the entries okay entry by
+
+ align:start position:0%
+convergence of the entries okay entry by
+ 
+
+ align:start position:0%
+convergence of the entries okay entry by
+entry or i have convergence of the
+
+ align:start position:0%
+entry or i have convergence of the
+ 
+
+ align:start position:0%
+entry or i have convergence of the
+fourier coefficients as l goes to
+
+ align:start position:0%
+fourier coefficients as l goes to
+ 
+
+ align:start position:0%
+fourier coefficients as l goes to
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+okay and now we're going to use um
+
+ align:start position:0%
+okay and now we're going to use um
+ 
+
+ align:start position:0%
+okay and now we're going to use um
+this equi small tails to prove that
+
+ align:start position:0%
+this equi small tails to prove that
+ 
+
+ align:start position:0%
+this equi small tails to prove that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the sequence v sub l converges we're
+
+ align:start position:0%
+the sequence v sub l converges we're
+ 
+
+ align:start position:0%
+the sequence v sub l converges we're
+just actually going to show it's koshi
+
+ align:start position:0%
+just actually going to show it's koshi
+ 
+
+ align:start position:0%
+just actually going to show it's koshi
+since h is a hilbert space we then
+
+ align:start position:0%
+since h is a hilbert space we then
+ 
+
+ align:start position:0%
+since h is a hilbert space we then
+conclude that
+
+ align:start position:0%
+conclude that
+ 
+
+ align:start position:0%
+conclude that
+it must
+
+ align:start position:0%
+it must
+ 
+
+ align:start position:0%
+it must
+converge
+
+ align:start position:0%
+converge
+ 
+
+ align:start position:0%
+converge
+so claim
+
+ align:start position:0%
+so claim
+ 
+
+ align:start position:0%
+so claim
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bl is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+koshi and then that will conclude the
+
+ align:start position:0%
+koshi and then that will conclude the
+ 
+
+ align:start position:0%
+koshi and then that will conclude the
+proof because then it has it must
+
+ align:start position:0%
+proof because then it has it must
+ 
+
+ align:start position:0%
+proof because then it has it must
+converge in h and by what i said at the
+
+ align:start position:0%
+converge in h and by what i said at the
+ 
+
+ align:start position:0%
+converge in h and by what i said at the
+beginning any
+
+ align:start position:0%
+beginning any
+ 
+
+ align:start position:0%
+beginning any
+uh since this is a subsequent this is a
+
+ align:start position:0%
+uh since this is a subsequent this is a
+ 
+
+ align:start position:0%
+uh since this is a subsequent this is a
+sequence of elements in k which is a
+
+ align:start position:0%
+sequence of elements in k which is a
+ 
+
+ align:start position:0%
+sequence of elements in k which is a
+closed set the limit has to be in k
+
+ align:start position:0%
+closed set the limit has to be in k
+ 
+
+ align:start position:0%
+closed set the limit has to be in k
+right so we just need to show it's koshi
+
+ align:start position:0%
+right so we just need to show it's koshi
+ 
+
+ align:start position:0%
+right so we just need to show it's koshi
+and then the proof is done
+
+ align:start position:0%
+and then the proof is done
+ 
+
+ align:start position:0%
+and then the proof is done
+so let epsilon be positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so since k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+equi-small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tails
+
+ align:start position:0%
+tails
+ 
+
+ align:start position:0%
+tails
+let's go over here
+
+ align:start position:0%
+let's go over here
+ 
+
+ align:start position:0%
+let's go over here
+there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+natural number capital n
+
+ align:start position:0%
+natural number capital n
+ 
+
+ align:start position:0%
+natural number capital n
+so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all l
+
+ align:start position:0%
+for all l
+ 
+
+ align:start position:0%
+for all l
+we have that the sum of
+
+ align:start position:0%
+we have that the sum of
+ 
+
+ align:start position:0%
+we have that the sum of
+squares k bigger than n
+
+ align:start position:0%
+squares k bigger than n
+ 
+
+ align:start position:0%
+squares k bigger than n
+of the tails v l
+
+ align:start position:0%
+of the tails v l
+ 
+
+ align:start position:0%
+of the tails v l
+e k
+
+ align:start position:0%
+e k
+ 
+
+ align:start position:0%
+e k
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+is less than
+
+ align:start position:0%
+is less than
+ 
+
+ align:start position:0%
+is less than
+epsilon squared over 16 y 16 because
+
+ align:start position:0%
+epsilon squared over 16 y 16 because
+ 
+
+ align:start position:0%
+epsilon squared over 16 y 16 because
+i want everything to come out correct in
+
+ align:start position:0%
+i want everything to come out correct in
+ 
+
+ align:start position:0%
+i want everything to come out correct in
+the end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since the in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sequences given by the first first in
+
+ align:start position:0%
+sequences given by the first first in
+ 
+
+ align:start position:0%
+sequences given by the first first in
+uh entries
+
+ align:start position:0%
+uh entries
+ 
+
+ align:start position:0%
+uh entries
+of the sequence vl so since the n
+
+ align:start position:0%
+of the sequence vl so since the n
+ 
+
+ align:start position:0%
+of the sequence vl so since the n
+sequences vl
+
+ align:start position:0%
+sequences vl
+ 
+
+ align:start position:0%
+sequences vl
+e1
+
+ align:start position:0%
+e1
+ 
+
+ align:start position:0%
+e1
+l
+
+ align:start position:0%
+l
+ 
+
+ align:start position:0%
+l
+up to
+
+ align:start position:0%
+up to
+ 
+
+ align:start position:0%
+up to
+vl
+
+ align:start position:0%
+vl
+ 
+
+ align:start position:0%
+vl
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+l so these are only so this is the bit
+
+ align:start position:0%
+l so these are only so this is the bit
+ 
+
+ align:start position:0%
+l so these are only so this is the bit
+where i said um
+
+ align:start position:0%
+where i said um
+ 
+
+ align:start position:0%
+where i said um
+you know equi small tails allows us to
+
+ align:start position:0%
+you know equi small tails allows us to
+ 
+
+ align:start position:0%
+you know equi small tails allows us to
+throw away
+
+ align:start position:0%
+throw away
+ 
+
+ align:start position:0%
+throw away
+uh kind of
+
+ align:start position:0%
+uh kind of
+ 
+
+ align:start position:0%
+uh kind of
+a large or
+
+ align:start position:0%
+a large or
+ 
+
+ align:start position:0%
+a large or
+the tail end of these entries and just
+
+ align:start position:0%
+the tail end of these entries and just
+ 
+
+ align:start position:0%
+the tail end of these entries and just
+control over the first finitely many
+
+ align:start position:0%
+control over the first finitely many
+ 
+
+ align:start position:0%
+control over the first finitely many
+uh entries gives us the the condition or
+
+ align:start position:0%
+uh entries gives us the the condition or
+ 
+
+ align:start position:0%
+uh entries gives us the the condition or
+the convergence that we want this is
+
+ align:start position:0%
+the convergence that we want this is
+ 
+
+ align:start position:0%
+the convergence that we want this is
+where that's happening
+
+ align:start position:0%
+where that's happening
+ 
+
+ align:start position:0%
+where that's happening
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so since these converge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exists
+
+ align:start position:0%
+there exists
+ 
+
+ align:start position:0%
+there exists
+a natural number m
+
+ align:start position:0%
+a natural number m
+ 
+
+ align:start position:0%
+a natural number m
+so that for all
+
+ align:start position:0%
+so that for all
+ 
+
+ align:start position:0%
+so that for all
+l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+bigger than
+
+ align:start position:0%
+bigger than
+ 
+
+ align:start position:0%
+bigger than
+uh capital m
+
+ align:start position:0%
+uh capital m
+ 
+
+ align:start position:0%
+uh capital m
+i have that the sum
+
+ align:start position:0%
+i have that the sum
+ 
+
+ align:start position:0%
+i have that the sum
+n equals 1 to capital n
+
+ align:start position:0%
+n equals 1 to capital n
+ 
+
+ align:start position:0%
+n equals 1 to capital n
+of v
+
+ align:start position:0%
+of v
+ 
+
+ align:start position:0%
+of v
+l
+
+ align:start position:0%
+l
+ 
+
+ align:start position:0%
+l
+e k
+
+ align:start position:0%
+e k
+ 
+
+ align:start position:0%
+e k
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+v
+
+ align:start position:0%
+v
+ 
+
+ align:start position:0%
+v
+m e k
+
+ align:start position:0%
+m e k
+ 
+
+ align:start position:0%
+m e k
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+is less than
+
+ align:start position:0%
+is less than
+ 
+
+ align:start position:0%
+is less than
+epsilon squared over four
+
+ align:start position:0%
+epsilon squared over four
+ 
+
+ align:start position:0%
+epsilon squared over four
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+each of these are convergent sequences
+
+ align:start position:0%
+each of these are convergent sequences
+ 
+
+ align:start position:0%
+each of these are convergent sequences
+so each of these are koshi sequences so
+
+ align:start position:0%
+so each of these are koshi sequences so
+ 
+
+ align:start position:0%
+so each of these are koshi sequences so
+for each one i can find uh capital m sub
+
+ align:start position:0%
+for each one i can find uh capital m sub
+ 
+
+ align:start position:0%
+for each one i can find uh capital m sub
+1 so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know just one of these entries is
+
+ align:start position:0%
+you know just one of these entries is
+ 
+
+ align:start position:0%
+you know just one of these entries is
+very small for l and m bigger than that
+
+ align:start position:0%
+very small for l and m bigger than that
+ 
+
+ align:start position:0%
+very small for l and m bigger than that
+capital m sub 1. and then i can do
+
+ align:start position:0%
+capital m sub 1. and then i can do
+ 
+
+ align:start position:0%
+capital m sub 1. and then i can do
+uh the next one so that for so this
+
+ align:start position:0%
+uh the next one so that for so this
+ 
+
+ align:start position:0%
+uh the next one so that for so this
+should be k i don't know what that looks
+
+ align:start position:0%
+should be k i don't know what that looks
+ 
+
+ align:start position:0%
+should be k i don't know what that looks
+like but k
+
+ align:start position:0%
+like but k
+ 
+
+ align:start position:0%
+like but k
+so that for k equals 2 it's very small
+
+ align:start position:0%
+so that for k equals 2 it's very small
+ 
+
+ align:start position:0%
+so that for k equals 2 it's very small
+and then up to k equals n and then i
+
+ align:start position:0%
+and then up to k equals n and then i
+ 
+
+ align:start position:0%
+and then up to k equals n and then i
+choose capital m to be the maximum over
+
+ align:start position:0%
+choose capital m to be the maximum over
+ 
+
+ align:start position:0%
+choose capital m to be the maximum over
+all those uh
+
+ align:start position:0%
+all those uh
+ 
+
+ align:start position:0%
+all those uh
+all those m sub uh
+
+ align:start position:0%
+all those m sub uh
+ 
+
+ align:start position:0%
+all those m sub uh
+m sub n's
+
+ align:start position:0%
+m sub n's
+ 
+
+ align:start position:0%
+m sub n's
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+i can always choose this because again
+
+ align:start position:0%
+i can always choose this because again
+ 
+
+ align:start position:0%
+i can always choose this because again
+there's only finitely many conditions i
+
+ align:start position:0%
+there's only finitely many conditions i
+ 
+
+ align:start position:0%
+there's only finitely many conditions i
+have to to verify
+
+ align:start position:0%
+have to to verify
+ 
+
+ align:start position:0%
+have to to verify
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now i claim this capital m
+
+ align:start position:0%
+now i claim this capital m
+ 
+
+ align:start position:0%
+now i claim this capital m
+works then for all l
+
+ align:start position:0%
+works then for all l
+ 
+
+ align:start position:0%
+works then for all l
+m bigger than or equal to m
+
+ align:start position:0%
+m bigger than or equal to m
+ 
+
+ align:start position:0%
+m bigger than or equal to m
+if we look at the norm of v l
+
+ align:start position:0%
+if we look at the norm of v l
+ 
+
+ align:start position:0%
+if we look at the norm of v l
+minus v m
+
+ align:start position:0%
+minus v m
+ 
+
+ align:start position:0%
+minus v m
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+i should say
+
+ align:start position:0%
+i should say
+ 
+
+ align:start position:0%
+i should say
+k equals 1 to n
+
+ align:start position:0%
+k equals 1 to n
+ 
+
+ align:start position:0%
+k equals 1 to n
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+v l minus v
+
+ align:start position:0%
+v l minus v
+ 
+
+ align:start position:0%
+v l minus v
+m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k equals
+
+ align:start position:0%
+k equals
+ 
+
+ align:start position:0%
+k equals
+k bigger than n
+
+ align:start position:0%
+k bigger than n
+ 
+
+ align:start position:0%
+k bigger than n
+v l minus v
+
+ align:start position:0%
+v l minus v
+ 
+
+ align:start position:0%
+v l minus v
+m e k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one half
+
+ align:start position:0%
+one half
+ 
+
+ align:start position:0%
+one half
+so um here i'm using the fact that uh we
+
+ align:start position:0%
+so um here i'm using the fact that uh we
+ 
+
+ align:start position:0%
+so um here i'm using the fact that uh we
+have an orthonormal basis right then
+
+ align:start position:0%
+have an orthonormal basis right then
+ 
+
+ align:start position:0%
+have an orthonormal basis right then
+in that case the norm is equal to the
+
+ align:start position:0%
+in that case the norm is equal to the
+ 
+
+ align:start position:0%
+in that case the norm is equal to the
+sum of the squares of
+
+ align:start position:0%
+sum of the squares of
+ 
+
+ align:start position:0%
+sum of the squares of
+of the uh of the fourier coefficients
+
+ align:start position:0%
+of the uh of the fourier coefficients
+ 
+
+ align:start position:0%
+of the uh of the fourier coefficients
+right bessel's inequality would say this
+
+ align:start position:0%
+right bessel's inequality would say this
+ 
+
+ align:start position:0%
+right bessel's inequality would say this
+is less than or equal to this side and
+
+ align:start position:0%
+is less than or equal to this side and
+ 
+
+ align:start position:0%
+is less than or equal to this side and
+wouldn't give us any control we want
+
+ align:start position:0%
+wouldn't give us any control we want
+ 
+
+ align:start position:0%
+wouldn't give us any control we want
+over the actual norm but because we're
+
+ align:start position:0%
+over the actual norm but because we're
+ 
+
+ align:start position:0%
+over the actual norm but because we're
+working in an orthonormal basis the norm
+
+ align:start position:0%
+working in an orthonormal basis the norm
+ 
+
+ align:start position:0%
+working in an orthonormal basis the norm
+of that is equal to the sum of squares
+
+ align:start position:0%
+of that is equal to the sum of squares
+ 
+
+ align:start position:0%
+of that is equal to the sum of squares
+take the square root
+
+ align:start position:0%
+take the square root
+ 
+
+ align:start position:0%
+take the square root
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+now the square root of a plus b that's
+
+ align:start position:0%
+now the square root of a plus b that's
+ 
+
+ align:start position:0%
+now the square root of a plus b that's
+always less than or equal to the square
+
+ align:start position:0%
+always less than or equal to the square
+ 
+
+ align:start position:0%
+always less than or equal to the square
+root of a plus the square root of b so
+
+ align:start position:0%
+root of a plus the square root of b so
+ 
+
+ align:start position:0%
+root of a plus the square root of b so
+that's less than uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a equals 1 to n of
+
+ align:start position:0%
+a equals 1 to n of
+ 
+
+ align:start position:0%
+a equals 1 to n of
+b l minus v m
+
+ align:start position:0%
+b l minus v m
+ 
+
+ align:start position:0%
+b l minus v m
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+one half plus
+
+ align:start position:0%
+one half plus
+ 
+
+ align:start position:0%
+one half plus
+k bigger than n
+
+ align:start position:0%
+k bigger than n
+ 
+
+ align:start position:0%
+k bigger than n
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v
+
+ align:start position:0%
+v
+ 
+
+ align:start position:0%
+v
+l
+
+ align:start position:0%
+l
+ 
+
+ align:start position:0%
+l
+e k so i'm just going to write this out
+
+ align:start position:0%
+e k so i'm just going to write this out
+ 
+
+ align:start position:0%
+e k so i'm just going to write this out
+a little differently
+
+ align:start position:0%
+a little differently
+ 
+
+ align:start position:0%
+a little differently
+v
+
+ align:start position:0%
+v
+ 
+
+ align:start position:0%
+v
+m e k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+half now this part we know is less than
+
+ align:start position:0%
+half now this part we know is less than
+ 
+
+ align:start position:0%
+half now this part we know is less than
+by how we've chosen capital m this
+
+ align:start position:0%
+by how we've chosen capital m this
+ 
+
+ align:start position:0%
+by how we've chosen capital m this
+finite part is small it's less than
+
+ align:start position:0%
+finite part is small it's less than
+ 
+
+ align:start position:0%
+finite part is small it's less than
+epsilon
+
+ align:start position:0%
+epsilon
+ 
+
+ align:start position:0%
+epsilon
+over two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's less than
+
+ align:start position:0%
+so that's less than
+ 
+
+ align:start position:0%
+so that's less than
+epsilon over 2 plus now we use um the
+
+ align:start position:0%
+epsilon over 2 plus now we use um the
+ 
+
+ align:start position:0%
+epsilon over 2 plus now we use um the
+triangle inequality
+
+ align:start position:0%
+triangle inequality
+ 
+
+ align:start position:0%
+triangle inequality
+now for little l2 right i can think of
+
+ align:start position:0%
+now for little l2 right i can think of
+ 
+
+ align:start position:0%
+now for little l2 right i can think of
+this as the sum in little l2 of
+
+ align:start position:0%
+this as the sum in little l2 of
+ 
+
+ align:start position:0%
+this as the sum in little l2 of
+or i can think of this as
+
+ align:start position:0%
+or i can think of this as
+ 
+
+ align:start position:0%
+or i can think of this as
+the norm in little l2 of
+
+ align:start position:0%
+the norm in little l2 of
+ 
+
+ align:start position:0%
+the norm in little l2 of
+this sequence in k
+
+ align:start position:0%
+this sequence in k
+ 
+
+ align:start position:0%
+this sequence in k
+minus this sequence in k right so this
+
+ align:start position:0%
+minus this sequence in k right so this
+ 
+
+ align:start position:0%
+minus this sequence in k right so this
+is less than or equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+k bigger than n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+l e k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one half plus
+
+ align:start position:0%
+one half plus
+ 
+
+ align:start position:0%
+one half plus
+some k bigger than
+
+ align:start position:0%
+some k bigger than
+ 
+
+ align:start position:0%
+some k bigger than
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah b
+
+ align:start position:0%
+yeah b
+ 
+
+ align:start position:0%
+yeah b
+m
+
+ align:start position:0%
+m
+ 
+
+ align:start position:0%
+m
+e k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one half
+
+ align:start position:0%
+one half
+ 
+
+ align:start position:0%
+one half
+all right we're almost done so this is
+
+ align:start position:0%
+all right we're almost done so this is
+ 
+
+ align:start position:0%
+all right we're almost done so this is
+less than uh the square part is less
+
+ align:start position:0%
+less than uh the square part is less
+ 
+
+ align:start position:0%
+less than uh the square part is less
+than epsilon squared over 16. so taking
+
+ align:start position:0%
+than epsilon squared over 16. so taking
+ 
+
+ align:start position:0%
+than epsilon squared over 16. so taking
+the square root of that i get epsilon
+
+ align:start position:0%
+the square root of that i get epsilon
+ 
+
+ align:start position:0%
+the square root of that i get epsilon
+over four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by how we chose n so this is based on
+
+ align:start position:0%
+by how we chose n so this is based on
+ 
+
+ align:start position:0%
+by how we chose n so this is based on
+how we chose n
+
+ align:start position:0%
+how we chose n
+ 
+
+ align:start position:0%
+how we chose n
+plus which came from the aqueous small
+
+ align:start position:0%
+plus which came from the aqueous small
+ 
+
+ align:start position:0%
+plus which came from the aqueous small
+tails part and this part also
+
+ align:start position:0%
+tails part and this part also
+ 
+
+ align:start position:0%
+tails part and this part also
+because of n is less than epsilon over
+
+ align:start position:0%
+because of n is less than epsilon over
+ 
+
+ align:start position:0%
+because of n is less than epsilon over
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+equals epsilon so we've now shown uh the
+
+ align:start position:0%
+equals epsilon so we've now shown uh the
+ 
+
+ align:start position:0%
+equals epsilon so we've now shown uh the
+claim that the subsequence v sub l is
+
+ align:start position:0%
+claim that the subsequence v sub l is
+ 
+
+ align:start position:0%
+claim that the subsequence v sub l is
+cochi and therefore it converges
+
+ align:start position:0%
+cochi and therefore it converges
+ 
+
+ align:start position:0%
+cochi and therefore it converges
+since h is complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one can readily verify now that the
+
+ align:start position:0%
+one can readily verify now that the
+ 
+
+ align:start position:0%
+one can readily verify now that the
+following subset
+
+ align:start position:0%
+following subset
+ 
+
+ align:start position:0%
+following subset
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+let k be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set of all sequences in little l2 with
+
+ align:start position:0%
+set of all sequences in little l2 with
+ 
+
+ align:start position:0%
+set of all sequences in little l2 with
+the property that
+
+ align:start position:0%
+the property that
+ 
+
+ align:start position:0%
+the property that
+ak
+
+ align:start position:0%
+ak
+ 
+
+ align:start position:0%
+ak
+is less than or equal to
+
+ align:start position:0%
+is less than or equal to
+ 
+
+ align:start position:0%
+is less than or equal to
+2 to the minus k so this is not a
+
+ align:start position:0%
+2 to the minus k so this is not a
+ 
+
+ align:start position:0%
+2 to the minus k so this is not a
+subspace it's a subset um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is compact
+
+ align:start position:0%
+is compact
+ 
+
+ align:start position:0%
+is compact
+okay this subset is known as the hilbert
+
+ align:start position:0%
+okay this subset is known as the hilbert
+ 
+
+ align:start position:0%
+okay this subset is known as the hilbert
+cube
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um you know maybe it's a bit unwieldy
+
+ align:start position:0%
+um you know maybe it's a bit unwieldy
+ 
+
+ align:start position:0%
+um you know maybe it's a bit unwieldy
+that our
+
+ align:start position:0%
+that our
+ 
+
+ align:start position:0%
+that our
+uh condition for being
+
+ align:start position:0%
+uh condition for being
+ 
+
+ align:start position:0%
+uh condition for being
+uh compact is is
+
+ align:start position:0%
+uh compact is is
+ 
+
+ align:start position:0%
+uh compact is is
+you know phrased in terms of an
+
+ align:start position:0%
+you know phrased in terms of an
+ 
+
+ align:start position:0%
+you know phrased in terms of an
+orthonormal basis
+
+ align:start position:0%
+orthonormal basis
+ 
+
+ align:start position:0%
+orthonormal basis
+right maybe that's not so simple to to
+
+ align:start position:0%
+right maybe that's not so simple to to
+ 
+
+ align:start position:0%
+right maybe that's not so simple to to
+verify or or
+
+ align:start position:0%
+verify or or
+ 
+
+ align:start position:0%
+verify or or
+you know definitely not necessarily kind
+
+ align:start position:0%
+you know definitely not necessarily kind
+ 
+
+ align:start position:0%
+you know definitely not necessarily kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what's the word i'm looking for
+
+ align:start position:0%
+what's the word i'm looking for
+ 
+
+ align:start position:0%
+what's the word i'm looking for
+canonical i guess that's a word i'm
+
+ align:start position:0%
+canonical i guess that's a word i'm
+ 
+
+ align:start position:0%
+canonical i guess that's a word i'm
+looking for
+
+ align:start position:0%
+looking for
+ 
+
+ align:start position:0%
+looking for
+in the sense that we have to make a
+
+ align:start position:0%
+in the sense that we have to make a
+ 
+
+ align:start position:0%
+in the sense that we have to make a
+choice to verify compactness but a
+
+ align:start position:0%
+choice to verify compactness but a
+ 
+
+ align:start position:0%
+choice to verify compactness but a
+different way of characterizing compact
+
+ align:start position:0%
+different way of characterizing compact
+ 
+
+ align:start position:0%
+different way of characterizing compact
+subsets of a hilbert space is the
+
+ align:start position:0%
+subsets of a hilbert space is the
+ 
+
+ align:start position:0%
+subsets of a hilbert space is the
+following now i'm not going to give the
+
+ align:start position:0%
+following now i'm not going to give the
+ 
+
+ align:start position:0%
+following now i'm not going to give the
+proof of this you can look it up in in
+
+ align:start position:0%
+proof of this you can look it up in in
+ 
+
+ align:start position:0%
+proof of this you can look it up in in
+melrose's notes um maybe i'll say a word
+
+ align:start position:0%
+melrose's notes um maybe i'll say a word
+ 
+
+ align:start position:0%
+melrose's notes um maybe i'll say a word
+about why it you should believe or think
+
+ align:start position:0%
+about why it you should believe or think
+ 
+
+ align:start position:0%
+about why it you should believe or think
+it's true um but again it evol involves
+
+ align:start position:0%
+it's true um but again it evol involves
+ 
+
+ align:start position:0%
+it's true um but again it evol involves
+a diagonal argument which that was tough
+
+ align:start position:0%
+a diagonal argument which that was tough
+ 
+
+ align:start position:0%
+a diagonal argument which that was tough
+enough to to do here
+
+ align:start position:0%
+enough to to do here
+ 
+
+ align:start position:0%
+enough to to do here
+or at least painful enough to write out
+
+ align:start position:0%
+or at least painful enough to write out
+ 
+
+ align:start position:0%
+or at least painful enough to write out
+um and so i don't want to do it again so
+
+ align:start position:0%
+um and so i don't want to do it again so
+ 
+
+ align:start position:0%
+um and so i don't want to do it again so
+we have the following that uh and this
+
+ align:start position:0%
+we have the following that uh and this
+ 
+
+ align:start position:0%
+we have the following that uh and this
+theorem also holds in a non-separable
+
+ align:start position:0%
+theorem also holds in a non-separable
+ 
+
+ align:start position:0%
+theorem also holds in a non-separable
+hilbert space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically by a trick
+
+ align:start position:0%
+basically by a trick
+ 
+
+ align:start position:0%
+basically by a trick
+of reducing it to a hill to a separable
+
+ align:start position:0%
+of reducing it to a hill to a separable
+ 
+
+ align:start position:0%
+of reducing it to a hill to a separable
+hilbert space but that's okay a subset k
+
+ align:start position:0%
+hilbert space but that's okay a subset k
+ 
+
+ align:start position:0%
+hilbert space but that's okay a subset k
+of a hilbert space h
+
+ align:start position:0%
+of a hilbert space h
+ 
+
+ align:start position:0%
+of a hilbert space h
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compact
+
+ align:start position:0%
+compact
+ 
+
+ align:start position:0%
+compact
+if and only if
+
+ align:start position:0%
+if and only if
+ 
+
+ align:start position:0%
+if and only if
+k is closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounded
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the following condition holds which
+
+ align:start position:0%
+and the following condition holds which
+ 
+
+ align:start position:0%
+and the following condition holds which
+you can think of as
+
+ align:start position:0%
+you can think of as
+ 
+
+ align:start position:0%
+you can think of as
+k can be approximated uh by
+
+ align:start position:0%
+k can be approximated uh by
+ 
+
+ align:start position:0%
+k can be approximated uh by
+finite dimensional
+
+ align:start position:0%
+finite dimensional
+ 
+
+ align:start position:0%
+finite dimensional
+subspaces
+
+ align:start position:0%
+subspaces
+ 
+
+ align:start position:0%
+subspaces
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all epsilon positive
+
+ align:start position:0%
+for all epsilon positive
+ 
+
+ align:start position:0%
+for all epsilon positive
+there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a finite
+
+ align:start position:0%
+a finite
+ 
+
+ align:start position:0%
+a finite
+dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subspace w
+
+ align:start position:0%
+subspace w
+ 
+
+ align:start position:0%
+subspace w
+in k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all u and k if i look at the
+
+ align:start position:0%
+for all u and k if i look at the
+ 
+
+ align:start position:0%
+for all u and k if i look at the
+distance from u to this finite
+
+ align:start position:0%
+distance from u to this finite
+ 
+
+ align:start position:0%
+distance from u to this finite
+dimensional subspace which
+
+ align:start position:0%
+dimensional subspace which
+ 
+
+ align:start position:0%
+dimensional subspace which
+uh i think i said at one point maybe i
+
+ align:start position:0%
+uh i think i said at one point maybe i
+ 
+
+ align:start position:0%
+uh i think i said at one point maybe i
+didn't but a finite dimensional subspace
+
+ align:start position:0%
+didn't but a finite dimensional subspace
+ 
+
+ align:start position:0%
+didn't but a finite dimensional subspace
+is always a closed uh subset
+
+ align:start position:0%
+is always a closed uh subset
+ 
+
+ align:start position:0%
+is always a closed uh subset
+subspace in h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a finite dimensional subspace is always
+
+ align:start position:0%
+a finite dimensional subspace is always
+ 
+
+ align:start position:0%
+a finite dimensional subspace is always
+closed but if i look at the distance
+
+ align:start position:0%
+closed but if i look at the distance
+ 
+
+ align:start position:0%
+closed but if i look at the distance
+from this point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to this subspace this finite dimensional
+
+ align:start position:0%
+to this subspace this finite dimensional
+ 
+
+ align:start position:0%
+to this subspace this finite dimensional
+subspace
+
+ align:start position:0%
+subspace
+ 
+
+ align:start position:0%
+subspace
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+less than epsilon okay so a subset in
+
+ align:start position:0%
+less than epsilon okay so a subset in
+ 
+
+ align:start position:0%
+less than epsilon okay so a subset in
+the hilbert space uh is compact if and
+
+ align:start position:0%
+the hilbert space uh is compact if and
+ 
+
+ align:start position:0%
+the hilbert space uh is compact if and
+only if it's closed bounded and if you
+
+ align:start position:0%
+only if it's closed bounded and if you
+ 
+
+ align:start position:0%
+only if it's closed bounded and if you
+like can be approximated by
+
+ align:start position:0%
+like can be approximated by
+ 
+
+ align:start position:0%
+like can be approximated by
+uh compact subsets of finite dimensional
+
+ align:start position:0%
+uh compact subsets of finite dimensional
+ 
+
+ align:start position:0%
+uh compact subsets of finite dimensional
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+subspaces okay another way to think
+
+ align:start position:0%
+subspaces okay another way to think
+ 
+
+ align:start position:0%
+subspaces okay another way to think
+about it
+
+ align:start position:0%
+about it
+ 
+
+ align:start position:0%
+about it
+now why is this kind of believable uh in
+
+ align:start position:0%
+now why is this kind of believable uh in
+ 
+
+ align:start position:0%
+now why is this kind of believable uh in
+the first place
+
+ align:start position:0%
+the first place
+ 
+
+ align:start position:0%
+the first place
+well what this uh
+
+ align:start position:0%
+well what this uh
+ 
+
+ align:start position:0%
+well what this uh
+where is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what the equi-small tail condition
+
+ align:start position:0%
+what the equi-small tail condition
+ 
+
+ align:start position:0%
+what the equi-small tail condition
+says
+
+ align:start position:0%
+says
+ 
+
+ align:start position:0%
+says
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+is basically that uh
+
+ align:start position:0%
+is basically that uh
+ 
+
+ align:start position:0%
+is basically that uh
+all elements in k
+
+ align:start position:0%
+all elements in k
+ 
+
+ align:start position:0%
+all elements in k
+can be approximated by
+
+ align:start position:0%
+can be approximated by
+ 
+
+ align:start position:0%
+can be approximated by
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+let epsilon be positive can be
+
+ align:start position:0%
+let epsilon be positive can be
+ 
+
+ align:start position:0%
+let epsilon be positive can be
+approximated by the subspace consisting
+
+ align:start position:0%
+approximated by the subspace consisting
+ 
+
+ align:start position:0%
+approximated by the subspace consisting
+of the span of the first one up to
+
+ align:start position:0%
+of the span of the first one up to
+ 
+
+ align:start position:0%
+of the span of the first one up to
+n uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basis vectors or orthonormal basis
+
+ align:start position:0%
+basis vectors or orthonormal basis
+ 
+
+ align:start position:0%
+basis vectors or orthonormal basis
+vectors right that's what this says
+
+ align:start position:0%
+vectors right that's what this says
+ 
+
+ align:start position:0%
+vectors right that's what this says
+for all epsilon the tails are small
+
+ align:start position:0%
+for all epsilon the tails are small
+ 
+
+ align:start position:0%
+for all epsilon the tails are small
+another way of saying that is that
+
+ align:start position:0%
+another way of saying that is that
+ 
+
+ align:start position:0%
+another way of saying that is that
+for all epsilon you can approximate any
+
+ align:start position:0%
+for all epsilon you can approximate any
+ 
+
+ align:start position:0%
+for all epsilon you can approximate any
+element in the set k
+
+ align:start position:0%
+element in the set k
+ 
+
+ align:start position:0%
+element in the set k
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+in the span of the first n
+
+ align:start position:0%
+in the span of the first n
+ 
+
+ align:start position:0%
+in the span of the first n
+uh basis vectors okay so k has to be
+
+ align:start position:0%
+uh basis vectors okay so k has to be
+ 
+
+ align:start position:0%
+uh basis vectors okay so k has to be
+close to
+
+ align:start position:0%
+close to
+ 
+
+ align:start position:0%
+close to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finite dimensional subspace
+
+ align:start position:0%
+finite dimensional subspace
+ 
+
+ align:start position:0%
+finite dimensional subspace
+but one can go the opposite direction as
+
+ align:start position:0%
+but one can go the opposite direction as
+ 
+
+ align:start position:0%
+but one can go the opposite direction as
+as well showing that
+
+ align:start position:0%
+as well showing that
+ 
+
+ align:start position:0%
+as well showing that
+um finite dimensional
+
+ align:start position:0%
+um finite dimensional
+ 
+
+ align:start position:0%
+um finite dimensional
+subspace uh
+
+ align:start position:0%
+subspace uh
+ 
+
+ align:start position:0%
+subspace uh
+being able to be approximated by those
+
+ align:start position:0%
+being able to be approximated by those
+ 
+
+ align:start position:0%
+being able to be approximated by those
+guys implies that k is compact and it's
+
+ align:start position:0%
+guys implies that k is compact and it's
+ 
+
+ align:start position:0%
+guys implies that k is compact and it's
+another kind of diagonal argument that i
+
+ align:start position:0%
+another kind of diagonal argument that i
+ 
+
+ align:start position:0%
+another kind of diagonal argument that i
+just don't want to write out and rather
+
+ align:start position:0%
+just don't want to write out and rather
+ 
+
+ align:start position:0%
+just don't want to write out and rather
+just start using these conditions
+
+ align:start position:0%
+just start using these conditions
+ 
+
+ align:start position:0%
+just start using these conditions
+instead to start saying things about
+
+ align:start position:0%
+instead to start saying things about
+ 
+
+ align:start position:0%
+instead to start saying things about
+when we can solve certain equations and
+
+ align:start position:0%
+when we can solve certain equations and
+ 
+
+ align:start position:0%
+when we can solve certain equations and
+certain interesting operators that uh
+
+ align:start position:0%
+certain interesting operators that uh
+ 
+
+ align:start position:0%
+certain interesting operators that uh
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+arise quite naturally okay
+
+ align:start position:0%
+arise quite naturally okay
+ 
+
+ align:start position:0%
+arise quite naturally okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so let's start talking about uh
+
+ align:start position:0%
+so let's start talking about uh
+ 
+
+ align:start position:0%
+so let's start talking about uh
+certain classes of operators
+
+ align:start position:0%
+certain classes of operators
+ 
+
+ align:start position:0%
+certain classes of operators
+and we should start with the simplest
+
+ align:start position:0%
+and we should start with the simplest
+ 
+
+ align:start position:0%
+and we should start with the simplest
+which are finite rank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operators so
+
+ align:start position:0%
+operators so
+ 
+
+ align:start position:0%
+operators so
+kind of the only uh
+
+ align:start position:0%
+kind of the only uh
+ 
+
+ align:start position:0%
+kind of the only uh
+linear operators you came into this
+
+ align:start position:0%
+linear operators you came into this
+ 
+
+ align:start position:0%
+linear operators you came into this
+class knowing probably
+
+ align:start position:0%
+class knowing probably
+ 
+
+ align:start position:0%
+class knowing probably
+if you didn't and
+
+ align:start position:0%
+if you didn't and
+ 
+
+ align:start position:0%
+if you didn't and
+you know you were more sophisticated
+
+ align:start position:0%
+you know you were more sophisticated
+ 
+
+ align:start position:0%
+you know you were more sophisticated
+that's good
+
+ align:start position:0%
+that's good
+ 
+
+ align:start position:0%
+that's good
+but um
+
+ align:start position:0%
+but um
+ 
+
+ align:start position:0%
+but um
+were you know matrices right
+
+ align:start position:0%
+were you know matrices right
+ 
+
+ align:start position:0%
+were you know matrices right
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+a matrix is just a linear transformation
+
+ align:start position:0%
+a matrix is just a linear transformation
+ 
+
+ align:start position:0%
+a matrix is just a linear transformation
+defined in terms of
+
+ align:start position:0%
+defined in terms of
+ 
+
+ align:start position:0%
+defined in terms of
+an orthonormal or not orthonormal basis
+
+ align:start position:0%
+an orthonormal or not orthonormal basis
+ 
+
+ align:start position:0%
+an orthonormal or not orthonormal basis
+but a basis in both the domain and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+target if we pick the target to be the
+
+ align:start position:0%
+target if we pick the target to be the
+ 
+
+ align:start position:0%
+target if we pick the target to be the
+domain we just fix the basis and then we
+
+ align:start position:0%
+domain we just fix the basis and then we
+ 
+
+ align:start position:0%
+domain we just fix the basis and then we
+can express a linear transformation as
+
+ align:start position:0%
+can express a linear transformation as
+ 
+
+ align:start position:0%
+can express a linear transformation as
+an array of numbers right
+
+ align:start position:0%
+an array of numbers right
+ 
+
+ align:start position:0%
+an array of numbers right
+um finite rank operators
+
+ align:start position:0%
+um finite rank operators
+ 
+
+ align:start position:0%
+um finite rank operators
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+the generalization of kind of what you
+
+ align:start position:0%
+the generalization of kind of what you
+ 
+
+ align:start position:0%
+the generalization of kind of what you
+think of matrices now for
+
+ align:start position:0%
+think of matrices now for
+ 
+
+ align:start position:0%
+think of matrices now for
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+to hilbert spaces okay and we'll see
+
+ align:start position:0%
+to hilbert spaces okay and we'll see
+ 
+
+ align:start position:0%
+to hilbert spaces okay and we'll see
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in just a minute so
+
+ align:start position:0%
+in just a minute so
+ 
+
+ align:start position:0%
+in just a minute so
+uh and what follows h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+hilbert space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+instead of writing the space of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bounded linear operators bhh i'm just
+
+ align:start position:0%
+bounded linear operators bhh i'm just
+ 
+
+ align:start position:0%
+bounded linear operators bhh i'm just
+going to concatenate this
+
+ align:start position:0%
+going to concatenate this
+ 
+
+ align:start position:0%
+going to concatenate this
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+by dropping one of those h's so the
+
+ align:start position:0%
+by dropping one of those h's so the
+ 
+
+ align:start position:0%
+by dropping one of those h's so the
+space of bounded linear operators from h
+
+ align:start position:0%
+space of bounded linear operators from h
+ 
+
+ align:start position:0%
+space of bounded linear operators from h
+to itself will be denoted by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b of h
+
+ align:start position:0%
+b of h
+ 
+
+ align:start position:0%
+b of h
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so uh finite rank operators
+
+ align:start position:0%
+so uh finite rank operators
+ 
+
+ align:start position:0%
+so uh finite rank operators
+these are
+
+ align:start position:0%
+these are
+ 
+
+ align:start position:0%
+these are
+like i said these will be the analog of
+
+ align:start position:0%
+like i said these will be the analog of
+ 
+
+ align:start position:0%
+like i said these will be the analog of
+matrices
+
+ align:start position:0%
+matrices
+ 
+
+ align:start position:0%
+matrices
+um but
+
+ align:start position:0%
+um but
+ 
+
+ align:start position:0%
+um but
+let me give a
+
+ align:start position:0%
+let me give a
+ 
+
+ align:start position:0%
+let me give a
+sort of invariant definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first so
+
+ align:start position:0%
+first so
+ 
+
+ align:start position:0%
+first so
+a bounded linear operator is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finite rank operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the range of t which is a subspace of h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is finite dimensional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me give you the sim maybe a simple
+
+ align:start position:0%
+let me give you the sim maybe a simple
+ 
+
+ align:start position:0%
+let me give you the sim maybe a simple
+of course you know the zero operator is
+
+ align:start position:0%
+of course you know the zero operator is
+ 
+
+ align:start position:0%
+of course you know the zero operator is
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+simple one any
+
+ align:start position:0%
+simple one any
+ 
+
+ align:start position:0%
+simple one any
+if h is a finite dimensional hilbert
+
+ align:start position:0%
+if h is a finite dimensional hilbert
+ 
+
+ align:start position:0%
+if h is a finite dimensional hilbert
+space iec in then every
+
+ align:start position:0%
+space iec in then every
+ 
+
+ align:start position:0%
+space iec in then every
+bounded linear operator is a finite rank
+
+ align:start position:0%
+bounded linear operator is a finite rank
+ 
+
+ align:start position:0%
+bounded linear operator is a finite rank
+operator because the range is always
+
+ align:start position:0%
+operator because the range is always
+ 
+
+ align:start position:0%
+operator because the range is always
+contained in in c n which is finite
+
+ align:start position:0%
+contained in in c n which is finite
+ 
+
+ align:start position:0%
+contained in in c n which is finite
+dimensional
+
+ align:start position:0%
+dimensional
+ 
+
+ align:start position:0%
+dimensional
+for example
+
+ align:start position:0%
+for example
+ 
+
+ align:start position:0%
+for example
+on little l two if i define t a
+
+ align:start position:0%
+on little l two if i define t a
+ 
+
+ align:start position:0%
+on little l two if i define t a
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to be now the sequence
+
+ align:start position:0%
+to be now the sequence
+ 
+
+ align:start position:0%
+to be now the sequence
+given by uh
+
+ align:start position:0%
+given by uh
+ 
+
+ align:start position:0%
+given by uh
+a one over one
+
+ align:start position:0%
+a one over one
+ 
+
+ align:start position:0%
+a one over one
+a two over two
+
+ align:start position:0%
+a two over two
+ 
+
+ align:start position:0%
+a two over two
+up to a
+
+ align:start position:0%
+up to a
+ 
+
+ align:start position:0%
+up to a
+n over n for some n and then 0
+
+ align:start position:0%
+n over n for some n and then 0
+ 
+
+ align:start position:0%
+n over n for some n and then 0
+afterwards
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is uh
+
+ align:start position:0%
+and this is uh
+ 
+
+ align:start position:0%
+and this is uh
+for a equals
+
+ align:start position:0%
+for a equals
+ 
+
+ align:start position:0%
+for a equals
+sequence in little l2
+
+ align:start position:0%
+sequence in little l2
+ 
+
+ align:start position:0%
+sequence in little l2
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+t is
+
+ align:start position:0%
+t is
+ 
+
+ align:start position:0%
+t is
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+a finite rank operator because the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+range of this operator so here n is a
+
+ align:start position:0%
+range of this operator so here n is a
+ 
+
+ align:start position:0%
+range of this operator so here n is a
+fixed number okay
+
+ align:start position:0%
+fixed number okay
+ 
+
+ align:start position:0%
+fixed number okay
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+acting on sequences and little l2 just
+
+ align:start position:0%
+acting on sequences and little l2 just
+ 
+
+ align:start position:0%
+acting on sequences and little l2 just
+spits out the first
+
+ align:start position:0%
+spits out the first
+ 
+
+ align:start position:0%
+spits out the first
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you know let's make this uh let's make
+
+ align:start position:0%
+you know let's make this uh let's make
+ 
+
+ align:start position:0%
+you know let's make this uh let's make
+this even more explicit let's say that's
+
+ align:start position:0%
+this even more explicit let's say that's
+ 
+
+ align:start position:0%
+this even more explicit let's say that's
+five
+
+ align:start position:0%
+five
+ 
+
+ align:start position:0%
+five
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+this is a finite rank operator because
+
+ align:start position:0%
+this is a finite rank operator because
+ 
+
+ align:start position:0%
+this is a finite rank operator because
+it's contained in the subspace
+
+ align:start position:0%
+it's contained in the subspace
+ 
+
+ align:start position:0%
+it's contained in the subspace
+consisting of uh
+
+ align:start position:0%
+consisting of uh
+ 
+
+ align:start position:0%
+consisting of uh
+those sequences which are zero after the
+
+ align:start position:0%
+those sequences which are zero after the
+ 
+
+ align:start position:0%
+those sequences which are zero after the
+fifth entry okay and that's finite
+
+ align:start position:0%
+fifth entry okay and that's finite
+ 
+
+ align:start position:0%
+fifth entry okay and that's finite
+dimensional a basis is given by the
+
+ align:start position:0%
+dimensional a basis is given by the
+ 
+
+ align:start position:0%
+dimensional a basis is given by the
+sequence consisting of zeros with a one
+
+ align:start position:0%
+sequence consisting of zeros with a one
+ 
+
+ align:start position:0%
+sequence consisting of zeros with a one
+here zeros with a one here zeros with a
+
+ align:start position:0%
+here zeros with a one here zeros with a
+ 
+
+ align:start position:0%
+here zeros with a one here zeros with a
+one here and so on okay so this is a
+
+ align:start position:0%
+one here and so on okay so this is a
+ 
+
+ align:start position:0%
+one here and so on okay so this is a
+finite rank operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so let me just uh put over here that as
+
+ align:start position:0%
+so let me just uh put over here that as
+ 
+
+ align:start position:0%
+so let me just uh put over here that as
+far as notation goes we write t is in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+r h
+
+ align:start position:0%
+r h
+ 
+
+ align:start position:0%
+r h
+r for rank finite rank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+r of h this is the set of all finite
+
+ align:start position:0%
+r of h this is the set of all finite
+ 
+
+ align:start position:0%
+r of h this is the set of all finite
+rank operators now it's not just a set
+
+ align:start position:0%
+rank operators now it's not just a set
+ 
+
+ align:start position:0%
+rank operators now it's not just a set
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's easy to see that this is a subspace
+
+ align:start position:0%
+it's easy to see that this is a subspace
+ 
+
+ align:start position:0%
+it's easy to see that this is a subspace
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bonax space consisting of all
+
+ align:start position:0%
+bonax space consisting of all
+ 
+
+ align:start position:0%
+bonax space consisting of all
+bounded linear operators from h to
+
+ align:start position:0%
+bounded linear operators from h to
+ 
+
+ align:start position:0%
+bounded linear operators from h to
+itself why is that well okay so if i
+
+ align:start position:0%
+itself why is that well okay so if i
+ 
+
+ align:start position:0%
+itself why is that well okay so if i
+take a
+
+ align:start position:0%
+take a
+ 
+
+ align:start position:0%
+take a
+operator that has
+
+ align:start position:0%
+operator that has
+ 
+
+ align:start position:0%
+operator that has
+finite dimensional range and multiply it
+
+ align:start position:0%
+finite dimensional range and multiply it
+ 
+
+ align:start position:0%
+finite dimensional range and multiply it
+by a scalar then the range of the scalar
+
+ align:start position:0%
+by a scalar then the range of the scalar
+ 
+
+ align:start position:0%
+by a scalar then the range of the scalar
+multiple of that operator is
+
+ align:start position:0%
+multiple of that operator is
+ 
+
+ align:start position:0%
+multiple of that operator is
+equal to the range of the original
+
+ align:start position:0%
+equal to the range of the original
+ 
+
+ align:start position:0%
+equal to the range of the original
+operator unless it's the scalar 0. so
+
+ align:start position:0%
+operator unless it's the scalar 0. so
+ 
+
+ align:start position:0%
+operator unless it's the scalar 0. so
+that will be finite dimensional on the
+
+ align:start position:0%
+that will be finite dimensional on the
+ 
+
+ align:start position:0%
+that will be finite dimensional on the
+other hand if i take two finite rank
+
+ align:start position:0%
+other hand if i take two finite rank
+ 
+
+ align:start position:0%
+other hand if i take two finite rank
+operators and i consider their sum
+
+ align:start position:0%
+operators and i consider their sum
+ 
+
+ align:start position:0%
+operators and i consider their sum
+the range of the sum is going to be
+
+ align:start position:0%
+the range of the sum is going to be
+ 
+
+ align:start position:0%
+the range of the sum is going to be
+contained in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direct sum of the ranges okay
+
+ align:start position:0%
+direct sum of the ranges okay
+ 
+
+ align:start position:0%
+direct sum of the ranges okay
+and the direct sum of two finite
+
+ align:start position:0%
+and the direct sum of two finite
+ 
+
+ align:start position:0%
+and the direct sum of two finite
+dimensional um
+
+ align:start position:0%
+dimensional um
+ 
+
+ align:start position:0%
+dimensional um
+spaces uh subspaces is again finite
+
+ align:start position:0%
+spaces uh subspaces is again finite
+ 
+
+ align:start position:0%
+spaces uh subspaces is again finite
+dimensional okay
+
+ align:start position:0%
+dimensional okay
+ 
+
+ align:start position:0%
+dimensional okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if one has dimension five and the other
+
+ align:start position:0%
+if one has dimension five and the other
+ 
+
+ align:start position:0%
+if one has dimension five and the other
+has dimension six then uh the
+
+ align:start position:0%
+has dimension six then uh the
+ 
+
+ align:start position:0%
+has dimension six then uh the
+direct sum of these two will be of
+
+ align:start position:0%
+direct sum of these two will be of
+ 
+
+ align:start position:0%
+direct sum of these two will be of
+dimension 11. so
+
+ align:start position:0%
+dimension 11. so
+ 
+
+ align:start position:0%
+dimension 11. so
+that is me talking you through the proof
+
+ align:start position:0%
+that is me talking you through the proof
+ 
+
+ align:start position:0%
+that is me talking you through the proof
+that this is a subspace so you know take
+
+ align:start position:0%
+that this is a subspace so you know take
+ 
+
+ align:start position:0%
+that this is a subspace so you know take
+a minute to
+
+ align:start position:0%
+a minute to
+ 
+
+ align:start position:0%
+a minute to
+to write it down
+
+ align:start position:0%
+to write it down
+ 
+
+ align:start position:0%
+to write it down
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but now let me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proved that these finite rank operators
+
+ align:start position:0%
+proved that these finite rank operators
+ 
+
+ align:start position:0%
+proved that these finite rank operators
+really are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+essentially matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have the following theorem
+
+ align:start position:0%
+we have the following theorem
+ 
+
+ align:start position:0%
+we have the following theorem
+characterizing a finite rank operators
+
+ align:start position:0%
+characterizing a finite rank operators
+ 
+
+ align:start position:0%
+characterizing a finite rank operators
+so t
+
+ align:start position:0%
+so t
+ 
+
+ align:start position:0%
+so t
+is a finite rank operator if and only if
+
+ align:start position:0%
+is a finite rank operator if and only if
+ 
+
+ align:start position:0%
+is a finite rank operator if and only if
+there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an orthonormal
+
+ align:start position:0%
+an orthonormal
+ 
+
+ align:start position:0%
+an orthonormal
+finite orthonormal subset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e k k equals 1 to some integer l
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+complex numbers
+
+ align:start position:0%
+complex numbers
+ 
+
+ align:start position:0%
+complex numbers
+c i j i j equals 1 to l
+
+ align:start position:0%
+c i j i j equals 1 to l
+ 
+
+ align:start position:0%
+c i j i j equals 1 to l
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+a subsequence or a subset of complex
+
+ align:start position:0%
+a subsequence or a subset of complex
+ 
+
+ align:start position:0%
+a subsequence or a subset of complex
+numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+if i want to compute what t apply to u
+
+ align:start position:0%
+if i want to compute what t apply to u
+ 
+
+ align:start position:0%
+if i want to compute what t apply to u
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+it's just going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sum i equals j
+
+ align:start position:0%
+sum i equals j
+ 
+
+ align:start position:0%
+sum i equals j
+i j goes from one to l of these numbers
+
+ align:start position:0%
+i j goes from one to l of these numbers
+ 
+
+ align:start position:0%
+i j goes from one to l of these numbers
+c i j times
+
+ align:start position:0%
+c i j times
+ 
+
+ align:start position:0%
+c i j times
+uh the
+
+ align:start position:0%
+uh the
+ 
+
+ align:start position:0%
+uh the
+j entry
+
+ align:start position:0%
+j entry
+ 
+
+ align:start position:0%
+j entry
+uh of u
+
+ align:start position:0%
+uh of u
+ 
+
+ align:start position:0%
+uh of u
+times e i
+
+ align:start position:0%
+times e i
+ 
+
+ align:start position:0%
+times e i
+okay so in other words uh t corresponds
+
+ align:start position:0%
+okay so in other words uh t corresponds
+ 
+
+ align:start position:0%
+okay so in other words uh t corresponds
+to a matrix
+
+ align:start position:0%
+to a matrix
+ 
+
+ align:start position:0%
+to a matrix
+where the coefficients are these c's
+
+ align:start position:0%
+where the coefficients are these c's
+ 
+
+ align:start position:0%
+where the coefficients are these c's
+basically acting on this finite
+
+ align:start position:0%
+basically acting on this finite
+ 
+
+ align:start position:0%
+basically acting on this finite
+dimensional
+
+ align:start position:0%
+dimensional
+ 
+
+ align:start position:0%
+dimensional
+subspace of eks
+
+ align:start position:0%
+subspace of eks
+ 
+
+ align:start position:0%
+subspace of eks
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+so let's
+
+ align:start position:0%
+so let's
+ 
+
+ align:start position:0%
+so let's
+give the proof of this
+
+ align:start position:0%
+give the proof of this
+ 
+
+ align:start position:0%
+give the proof of this
+one direction
+
+ align:start position:0%
+one direction
+ 
+
+ align:start position:0%
+one direction
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+immediate if t
+
+ align:start position:0%
+immediate if t
+ 
+
+ align:start position:0%
+immediate if t
+has such a representation then it has
+
+ align:start position:0%
+has such a representation then it has
+ 
+
+ align:start position:0%
+has such a representation then it has
+finite rank because then the image is
+
+ align:start position:0%
+finite rank because then the image is
+ 
+
+ align:start position:0%
+finite rank because then the image is
+contained in the span of the e i's for i
+
+ align:start position:0%
+contained in the span of the e i's for i
+ 
+
+ align:start position:0%
+contained in the span of the e i's for i
+going from one to l
+
+ align:start position:0%
+going from one to l
+ 
+
+ align:start position:0%
+going from one to l
+and that's a finite dimensional subspace
+
+ align:start position:0%
+and that's a finite dimensional subspace
+ 
+
+ align:start position:0%
+and that's a finite dimensional subspace
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is clear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this condition implies that t is a
+
+ align:start position:0%
+that this condition implies that t is a
+ 
+
+ align:start position:0%
+that this condition implies that t is a
+finite rank operator so let's go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the opposite direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since the range of t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's finite dimensional
+
+ align:start position:0%
+it's finite dimensional
+ 
+
+ align:start position:0%
+it's finite dimensional
+we can find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an orthonormal
+
+ align:start position:0%
+an orthonormal
+ 
+
+ align:start position:0%
+an orthonormal
+basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+call it e k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k equals 1 to
+
+ align:start position:0%
+k equals 1 to
+ 
+
+ align:start position:0%
+k equals 1 to
+n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+t applied to u
+
+ align:start position:0%
+t applied to u
+ 
+
+ align:start position:0%
+t applied to u
+is equal to uh so it's an element in the
+
+ align:start position:0%
+is equal to uh so it's an element in the
+ 
+
+ align:start position:0%
+is equal to uh so it's an element in the
+span of uh
+
+ align:start position:0%
+span of uh
+ 
+
+ align:start position:0%
+span of uh
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this spans the range so i can write this
+
+ align:start position:0%
+this spans the range so i can write this
+ 
+
+ align:start position:0%
+this spans the range so i can write this
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+some numbers
+
+ align:start position:0%
+some numbers
+ 
+
+ align:start position:0%
+some numbers
+times the
+
+ align:start position:0%
+times the
+ 
+
+ align:start position:0%
+times the
+eks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what are these numbers well these
+
+ align:start position:0%
+and what are these numbers well these
+ 
+
+ align:start position:0%
+and what are these numbers well these
+numbers since these are orthonormal have
+
+ align:start position:0%
+numbers since these are orthonormal have
+ 
+
+ align:start position:0%
+numbers since these are orthonormal have
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+t applied to u inner product
+
+ align:start position:0%
+t applied to u inner product
+ 
+
+ align:start position:0%
+t applied to u inner product
+e k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so t u
+
+ align:start position:0%
+all right so t u
+ 
+
+ align:start position:0%
+all right so t u
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so the range is spanned by these
+
+ align:start position:0%
+so the range is spanned by these
+ 
+
+ align:start position:0%
+so the range is spanned by these
+orthonormal uh
+
+ align:start position:0%
+orthonormal uh
+ 
+
+ align:start position:0%
+orthonormal uh
+vectors
+
+ align:start position:0%
+vectors
+ 
+
+ align:start position:0%
+vectors
+and anything in the span of this
+
+ align:start position:0%
+and anything in the span of this
+ 
+
+ align:start position:0%
+and anything in the span of this
+orthonormal vectors has to be written as
+
+ align:start position:0%
+orthonormal vectors has to be written as
+ 
+
+ align:start position:0%
+orthonormal vectors has to be written as
+that thing inner product e k times e k
+
+ align:start position:0%
+that thing inner product e k times e k
+ 
+
+ align:start position:0%
+that thing inner product e k times e k
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but let me now make an observation that
+
+ align:start position:0%
+but let me now make an observation that
+ 
+
+ align:start position:0%
+but let me now make an observation that
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+thing right
+
+ align:start position:0%
+thing right
+ 
+
+ align:start position:0%
+thing right
+here um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can write as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+the adjoint as
+
+ align:start position:0%
+the adjoint as
+ 
+
+ align:start position:0%
+the adjoint as
+u inner product
+
+ align:start position:0%
+u inner product
+ 
+
+ align:start position:0%
+u inner product
+t star
+
+ align:start position:0%
+t star
+ 
+
+ align:start position:0%
+t star
+ek
+
+ align:start position:0%
+ek
+ 
+
+ align:start position:0%
+ek
+ek
+
+ align:start position:0%
+ek
+ 
+
+ align:start position:0%
+ek
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+right the adjoint operator so
+
+ align:start position:0%
+right the adjoint operator so
+ 
+
+ align:start position:0%
+right the adjoint operator so
+t star which goes from h to h remember
+
+ align:start position:0%
+t star which goes from h to h remember
+ 
+
+ align:start position:0%
+t star which goes from h to h remember
+satisfies this property that given any
+
+ align:start position:0%
+satisfies this property that given any
+ 
+
+ align:start position:0%
+satisfies this property that given any
+two vectors uh a or u and v t applied to
+
+ align:start position:0%
+two vectors uh a or u and v t applied to
+ 
+
+ align:start position:0%
+two vectors uh a or u and v t applied to
+u inner product v is equal to u inner
+
+ align:start position:0%
+u inner product v is equal to u inner
+ 
+
+ align:start position:0%
+u inner product v is equal to u inner
+product t star v right that's the the
+
+ align:start position:0%
+product t star v right that's the the
+ 
+
+ align:start position:0%
+product t star v right that's the the
+uh defining property of the adjoint
+
+ align:start position:0%
+uh defining property of the adjoint
+ 
+
+ align:start position:0%
+uh defining property of the adjoint
+so i can write it like this and
+
+ align:start position:0%
+so i can write it like this and
+ 
+
+ align:start position:0%
+so i can write it like this and
+which is k equals 1 to n of u inner
+
+ align:start position:0%
+which is k equals 1 to n of u inner
+ 
+
+ align:start position:0%
+which is k equals 1 to n of u inner
+product called this v k
+
+ align:start position:0%
+product called this v k
+ 
+
+ align:start position:0%
+product called this v k
+e k bar e k bar where here
+
+ align:start position:0%
+e k bar e k bar where here
+ 
+
+ align:start position:0%
+e k bar e k bar where here
+v k is simply defined to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t star e k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let e 1 up to e l
+
+ align:start position:0%
+let e 1 up to e l
+ 
+
+ align:start position:0%
+let e 1 up to e l
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the orthonormal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subset of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+h
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+obtained by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+applying the gram schmidt
+
+ align:start position:0%
+applying the gram schmidt
+ 
+
+ align:start position:0%
+applying the gram schmidt
+process to vectors e1
+
+ align:start position:0%
+process to vectors e1
+ 
+
+ align:start position:0%
+process to vectors e1
+e2
+
+ align:start position:0%
+e2
+ 
+
+ align:start position:0%
+e2
+up to el
+
+ align:start position:0%
+up to el
+ 
+
+ align:start position:0%
+up to el
+v1
+
+ align:start position:0%
+v1
+ 
+
+ align:start position:0%
+v1
+up to vl
+
+ align:start position:0%
+up to vl
+ 
+
+ align:start position:0%
+up to vl
+okay so you know
+
+ align:start position:0%
+okay so you know
+ 
+
+ align:start position:0%
+okay so you know
+applying it to this subset i keep the e
+
+ align:start position:0%
+applying it to this subset i keep the e
+ 
+
+ align:start position:0%
+applying it to this subset i keep the e
+1 up to e l's and then i might pick up
+
+ align:start position:0%
+1 up to e l's and then i might pick up
+ 
+
+ align:start position:0%
+1 up to e l's and then i might pick up
+some more from the some more orthonormal
+
+ align:start position:0%
+some more from the some more orthonormal
+ 
+
+ align:start position:0%
+some more from the some more orthonormal
+vectors that are orthonormal to
+
+ align:start position:0%
+vectors that are orthonormal to
+ 
+
+ align:start position:0%
+vectors that are orthonormal to
+these guys
+
+ align:start position:0%
+these guys
+ 
+
+ align:start position:0%
+these guys
+when i hit the v1s up to vl
+
+ align:start position:0%
+when i hit the v1s up to vl
+ 
+
+ align:start position:0%
+when i hit the v1s up to vl
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+or i should should have gone to n i'm
+
+ align:start position:0%
+or i should should have gone to n i'm
+ 
+
+ align:start position:0%
+or i should should have gone to n i'm
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+not not l here but n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i obtain a um orthonormal subset
+
+ align:start position:0%
+so i obtain a um orthonormal subset
+ 
+
+ align:start position:0%
+so i obtain a um orthonormal subset
+that spans the same span of these guys
+
+ align:start position:0%
+that spans the same span of these guys
+ 
+
+ align:start position:0%
+that spans the same span of these guys
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so what does that mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there exists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers akj
+
+ align:start position:0%
+numbers akj
+ 
+
+ align:start position:0%
+numbers akj
+bkj
+
+ align:start position:0%
+bkj
+ 
+
+ align:start position:0%
+bkj
+let's call it i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ekbar is in the span of these
+
+ align:start position:0%
+ekbar is in the span of these
+ 
+
+ align:start position:0%
+ekbar is in the span of these
+orthonormal vectors so i can write it as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aki
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e i uh
+
+ align:start position:0%
+e i uh
+ 
+
+ align:start position:0%
+e i uh
+k equals 1 to
+
+ align:start position:0%
+k equals 1 to
+ 
+
+ align:start position:0%
+k equals 1 to
+l no no no
+
+ align:start position:0%
+l no no no
+ 
+
+ align:start position:0%
+l no no no
+sum is going the wrong way i equals 1 to
+
+ align:start position:0%
+sum is going the wrong way i equals 1 to
+ 
+
+ align:start position:0%
+sum is going the wrong way i equals 1 to
+l
+
+ align:start position:0%
+l
+ 
+
+ align:start position:0%
+l
+and also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the same for the v's
+
+ align:start position:0%
+the same for the v's
+ 
+
+ align:start position:0%
+the same for the v's
+some uh
+
+ align:start position:0%
+some uh
+ 
+
+ align:start position:0%
+some uh
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+v k equals
+
+ align:start position:0%
+v k equals
+ 
+
+ align:start position:0%
+v k equals
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+j equals one to l
+
+ align:start position:0%
+j equals one to l
+ 
+
+ align:start position:0%
+j equals one to l
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+uh ej
+
+ align:start position:0%
+uh ej
+ 
+
+ align:start position:0%
+uh ej
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um these are obtained by the gram
+
+ align:start position:0%
+so um these are obtained by the gram
+ 
+
+ align:start position:0%
+so um these are obtained by the gram
+schmidt process applied to this
+
+ align:start position:0%
+schmidt process applied to this
+ 
+
+ align:start position:0%
+schmidt process applied to this
+collection of vectors and therefore i
+
+ align:start position:0%
+collection of vectors and therefore i
+ 
+
+ align:start position:0%
+collection of vectors and therefore i
+can write each one of these vectors as a
+
+ align:start position:0%
+can write each one of these vectors as a
+ 
+
+ align:start position:0%
+can write each one of these vectors as a
+linear combination of these orthonormal
+
+ align:start position:0%
+linear combination of these orthonormal
+ 
+
+ align:start position:0%
+linear combination of these orthonormal
+vectors okay so that's all i'm saying
+
+ align:start position:0%
+vectors okay so that's all i'm saying
+ 
+
+ align:start position:0%
+vectors okay so that's all i'm saying
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we just plug this in to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this computation
+
+ align:start position:0%
+this computation
+ 
+
+ align:start position:0%
+this computation
+and we have t u which we computed was
+
+ align:start position:0%
+and we have t u which we computed was
+ 
+
+ align:start position:0%
+and we have t u which we computed was
+equal to sum from k equals 1 to n
+
+ align:start position:0%
+equal to sum from k equals 1 to n
+ 
+
+ align:start position:0%
+equal to sum from k equals 1 to n
+of u
+
+ align:start position:0%
+of u
+ 
+
+ align:start position:0%
+of u
+inner product v k
+
+ align:start position:0%
+inner product v k
+ 
+
+ align:start position:0%
+inner product v k
+e k bar this is equal to now if i stick
+
+ align:start position:0%
+e k bar this is equal to now if i stick
+ 
+
+ align:start position:0%
+e k bar this is equal to now if i stick
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+these sums here i get some
+
+ align:start position:0%
+these sums here i get some
+ 
+
+ align:start position:0%
+these sums here i get some
+i j equals 1 to l
+
+ align:start position:0%
+i j equals 1 to l
+ 
+
+ align:start position:0%
+i j equals 1 to l
+of sum
+
+ align:start position:0%
+of sum
+ 
+
+ align:start position:0%
+of sum
+k equals
+
+ align:start position:0%
+k equals
+ 
+
+ align:start position:0%
+k equals
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+1 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n of
+
+ align:start position:0%
+n of
+ 
+
+ align:start position:0%
+n of
+a k i
+
+ align:start position:0%
+a k i
+ 
+
+ align:start position:0%
+a k i
+b k
+
+ align:start position:0%
+b k
+ 
+
+ align:start position:0%
+b k
+j a complex conjugate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now u inner product e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+this is coming from when i stick in the
+
+ align:start position:0%
+this is coming from when i stick in the
+ 
+
+ align:start position:0%
+this is coming from when i stick in the
+vks
+
+ align:start position:0%
+vks
+ 
+
+ align:start position:0%
+vks
+uh e i okay and this is coming from when
+
+ align:start position:0%
+uh e i okay and this is coming from when
+ 
+
+ align:start position:0%
+uh e i okay and this is coming from when
+i stick in uh what i have for the e uh k
+
+ align:start position:0%
+i stick in uh what i have for the e uh k
+ 
+
+ align:start position:0%
+i stick in uh what i have for the e uh k
+bar all right
+
+ align:start position:0%
+bar all right
+ 
+
+ align:start position:0%
+bar all right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this number right here is my number cij
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and that's the that's the end so finite
+
+ align:start position:0%
+and that's the that's the end so finite
+ 
+
+ align:start position:0%
+and that's the that's the end so finite
+rank operators are
+
+ align:start position:0%
+rank operators are
+ 
+
+ align:start position:0%
+rank operators are
+you know really just matrices okay they
+
+ align:start position:0%
+you know really just matrices okay they
+ 
+
+ align:start position:0%
+you know really just matrices okay they
+you can just compute these numbers and
+
+ align:start position:0%
+you can just compute these numbers and
+ 
+
+ align:start position:0%
+you can just compute these numbers and
+they completely characterize uh the
+
+ align:start position:0%
+they completely characterize uh the
+ 
+
+ align:start position:0%
+they completely characterize uh the
+linear operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in particular the the kernel
+
+ align:start position:0%
+so in particular the the kernel
+ 
+
+ align:start position:0%
+so in particular the the kernel
+the null space of t is the subspace
+
+ align:start position:0%
+the null space of t is the subspace
+ 
+
+ align:start position:0%
+the null space of t is the subspace
+that's orthogonal to the
+
+ align:start position:0%
+that's orthogonal to the
+ 
+
+ align:start position:0%
+that's orthogonal to the
+e1 up to e
+
+ align:start position:0%
+e1 up to e
+ 
+
+ align:start position:0%
+e1 up to e
+l
+
+ align:start position:0%
+l
+ 
+
+ align:start position:0%
+l
+or at least includes that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+now from this we can
+
+ align:start position:0%
+now from this we can
+ 
+
+ align:start position:0%
+now from this we can
+include
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a nice property about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finite rank operators namely the first
+
+ align:start position:0%
+finite rank operators namely the first
+ 
+
+ align:start position:0%
+finite rank operators namely the first
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+if t is a finite rank operator then its
+
+ align:start position:0%
+if t is a finite rank operator then its
+ 
+
+ align:start position:0%
+if t is a finite rank operator then its
+adjoint is also a finite rank operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if t is a finite rank operator
+
+ align:start position:0%
+if t is a finite rank operator
+ 
+
+ align:start position:0%
+if t is a finite rank operator
+and a and b are just bounded
+
+ align:start position:0%
+and a and b are just bounded
+ 
+
+ align:start position:0%
+and a and b are just bounded
+linear operators on h
+
+ align:start position:0%
+linear operators on h
+ 
+
+ align:start position:0%
+linear operators on h
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+a times t times b
+
+ align:start position:0%
+a times t times b
+ 
+
+ align:start position:0%
+a times t times b
+this is also a finite rank operator
+
+ align:start position:0%
+this is also a finite rank operator
+ 
+
+ align:start position:0%
+this is also a finite rank operator
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+in fancy uh or in short form uh you
+
+ align:start position:0%
+in fancy uh or in short form uh you
+ 
+
+ align:start position:0%
+in fancy uh or in short form uh you
+would say that this is a
+
+ align:start position:0%
+would say that this is a
+ 
+
+ align:start position:0%
+would say that this is a
+star-closed two-sided ideal in
+
+ align:start position:0%
+star-closed two-sided ideal in
+ 
+
+ align:start position:0%
+star-closed two-sided ideal in
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the space of bounded linear operators
+
+ align:start position:0%
+the space of bounded linear operators
+ 
+
+ align:start position:0%
+the space of bounded linear operators
+or it's closed under taking adjoints and
+
+ align:start position:0%
+or it's closed under taking adjoints and
+ 
+
+ align:start position:0%
+or it's closed under taking adjoints and
+close undertaking the two-sided
+
+ align:start position:0%
+close undertaking the two-sided
+ 
+
+ align:start position:0%
+close undertaking the two-sided
+multiplication by bounded linear
+
+ align:start position:0%
+multiplication by bounded linear
+ 
+
+ align:start position:0%
+multiplication by bounded linear
+operators
+
+ align:start position:0%
+operators
+ 
+
+ align:start position:0%
+operators
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+two i'll leave as an exercise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know what's the point
+
+ align:start position:0%
+you know what's the point
+ 
+
+ align:start position:0%
+you know what's the point
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+t has finite dimensional range
+
+ align:start position:0%
+t has finite dimensional range
+ 
+
+ align:start position:0%
+t has finite dimensional range
+a then acts on that finite dimensional
+
+ align:start position:0%
+a then acts on that finite dimensional
+ 
+
+ align:start position:0%
+a then acts on that finite dimensional
+range and therefore its range uh
+
+ align:start position:0%
+range and therefore its range uh
+ 
+
+ align:start position:0%
+range and therefore its range uh
+the range of a hitting t must then be
+
+ align:start position:0%
+the range of a hitting t must then be
+ 
+
+ align:start position:0%
+the range of a hitting t must then be
+finite dimensional and what you do with
+
+ align:start position:0%
+finite dimensional and what you do with
+ 
+
+ align:start position:0%
+finite dimensional and what you do with
+b really doesn't matter okay
+
+ align:start position:0%
+b really doesn't matter okay
+ 
+
+ align:start position:0%
+b really doesn't matter okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+two is an exercise so let's prove one
+
+ align:start position:0%
+two is an exercise so let's prove one
+ 
+
+ align:start position:0%
+two is an exercise so let's prove one
+one will prove using this
+
+ align:start position:0%
+one will prove using this
+ 
+
+ align:start position:0%
+one will prove using this
+characterization of finite rank
+
+ align:start position:0%
+characterization of finite rank
+ 
+
+ align:start position:0%
+characterization of finite rank
+operators
+
+ align:start position:0%
+operators
+ 
+
+ align:start position:0%
+operators
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're assuming t is finite rank so we
+
+ align:start position:0%
+we're assuming t is finite rank so we
+ 
+
+ align:start position:0%
+we're assuming t is finite rank so we
+can write t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at some constant c i j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u and a product e
+
+ align:start position:0%
+u and a product e
+ 
+
+ align:start position:0%
+u and a product e
+j e i
+
+ align:start position:0%
+j e i
+ 
+
+ align:start position:0%
+j e i
+u and h so we can express it in that way
+
+ align:start position:0%
+u and h so we can express it in that way
+ 
+
+ align:start position:0%
+u and h so we can express it in that way
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+where these are just some fixed
+
+ align:start position:0%
+where these are just some fixed
+ 
+
+ align:start position:0%
+where these are just some fixed
+constants not depending on you
+
+ align:start position:0%
+constants not depending on you
+ 
+
+ align:start position:0%
+constants not depending on you
+and now let's compute how t star acts on
+
+ align:start position:0%
+and now let's compute how t star acts on
+ 
+
+ align:start position:0%
+and now let's compute how t star acts on
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+vectors by using this this defining
+
+ align:start position:0%
+vectors by using this this defining
+ 
+
+ align:start position:0%
+vectors by using this this defining
+property of the adjoint okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+t star v
+
+ align:start position:0%
+t star v
+ 
+
+ align:start position:0%
+t star v
+what we're going to do is we're going to
+
+ align:start position:0%
+what we're going to do is we're going to
+ 
+
+ align:start position:0%
+what we're going to do is we're going to
+come up with
+
+ align:start position:0%
+come up with
+ 
+
+ align:start position:0%
+come up with
+an expression for this as u inner
+
+ align:start position:0%
+an expression for this as u inner
+ 
+
+ align:start position:0%
+an expression for this as u inner
+product something
+
+ align:start position:0%
+product something
+ 
+
+ align:start position:0%
+product something
+and from which we can conclude that t
+
+ align:start position:0%
+and from which we can conclude that t
+ 
+
+ align:start position:0%
+and from which we can conclude that t
+star v has to equal that something for
+
+ align:start position:0%
+star v has to equal that something for
+ 
+
+ align:start position:0%
+star v has to equal that something for
+all v
+
+ align:start position:0%
+all v
+ 
+
+ align:start position:0%
+all v
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this is equal to
+
+ align:start position:0%
+now this is equal to
+ 
+
+ align:start position:0%
+now this is equal to
+by the defining property of the adjoint
+
+ align:start position:0%
+by the defining property of the adjoint
+ 
+
+ align:start position:0%
+by the defining property of the adjoint
+t applied to u
+
+ align:start position:0%
+t applied to u
+ 
+
+ align:start position:0%
+t applied to u
+v
+
+ align:start position:0%
+v
+ 
+
+ align:start position:0%
+v
+so this is equal to
+
+ align:start position:0%
+so this is equal to
+ 
+
+ align:start position:0%
+so this is equal to
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i and j will be understood to go from 1
+
+ align:start position:0%
+i and j will be understood to go from 1
+ 
+
+ align:start position:0%
+i and j will be understood to go from 1
+to l so this is just finite a finite sum
+
+ align:start position:0%
+to l so this is just finite a finite sum
+ 
+
+ align:start position:0%
+to l so this is just finite a finite sum
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+c i j
+
+ align:start position:0%
+c i j
+ 
+
+ align:start position:0%
+c i j
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+e i
+
+ align:start position:0%
+e i
+ 
+
+ align:start position:0%
+e i
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+or e j sorry
+
+ align:start position:0%
+or e j sorry
+ 
+
+ align:start position:0%
+or e j sorry
+e i
+
+ align:start position:0%
+e i
+ 
+
+ align:start position:0%
+e i
+inner product v
+
+ align:start position:0%
+inner product v
+ 
+
+ align:start position:0%
+inner product v
+now uh taking
+
+ align:start position:0%
+now uh taking
+ 
+
+ align:start position:0%
+now uh taking
+the inner product is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linear in the first entry so this is
+
+ align:start position:0%
+linear in the first entry so this is
+ 
+
+ align:start position:0%
+linear in the first entry so this is
+equal to sum i j again this is a finite
+
+ align:start position:0%
+equal to sum i j again this is a finite
+ 
+
+ align:start position:0%
+equal to sum i j again this is a finite
+sum i j
+
+ align:start position:0%
+sum i j
+ 
+
+ align:start position:0%
+sum i j
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+e j
+
+ align:start position:0%
+e j
+ 
+
+ align:start position:0%
+e j
+inner product e i b
+
+ align:start position:0%
+inner product e i b
+ 
+
+ align:start position:0%
+inner product e i b
+and now i'm just going to switch
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+kind of what i'm summing
+
+ align:start position:0%
+kind of what i'm summing
+ 
+
+ align:start position:0%
+kind of what i'm summing
+this i can write as
+
+ align:start position:0%
+this i can write as
+ 
+
+ align:start position:0%
+this i can write as
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u inner product
+
+ align:start position:0%
+u inner product
+ 
+
+ align:start position:0%
+u inner product
+sum i
+
+ align:start position:0%
+sum i
+ 
+
+ align:start position:0%
+sum i
+j
+
+ align:start position:0%
+j
+ 
+
+ align:start position:0%
+j
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+c i j
+
+ align:start position:0%
+c i j
+ 
+
+ align:start position:0%
+c i j
+bar so if i want to
+
+ align:start position:0%
+bar so if i want to
+ 
+
+ align:start position:0%
+bar so if i want to
+this i can write as you know bar bar but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e i
+
+ align:start position:0%
+e i
+ 
+
+ align:start position:0%
+e i
+b complex conjugate
+
+ align:start position:0%
+b complex conjugate
+ 
+
+ align:start position:0%
+b complex conjugate
+e j
+
+ align:start position:0%
+e j
+ 
+
+ align:start position:0%
+e j
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can check this is correct because
+
+ align:start position:0%
+we can check this is correct because
+ 
+
+ align:start position:0%
+we can check this is correct because
+okay so u will then inner product with
+
+ align:start position:0%
+okay so u will then inner product with
+ 
+
+ align:start position:0%
+okay so u will then inner product with
+each of the ejs and these constants when
+
+ align:start position:0%
+each of the ejs and these constants when
+ 
+
+ align:start position:0%
+each of the ejs and these constants when
+they come out of the inner product get
+
+ align:start position:0%
+they come out of the inner product get
+ 
+
+ align:start position:0%
+they come out of the inner product get
+hit by a complex conjugate which turns
+
+ align:start position:0%
+hit by a complex conjugate which turns
+ 
+
+ align:start position:0%
+hit by a complex conjugate which turns
+them back into cij and eiv
+
+ align:start position:0%
+them back into cij and eiv
+ 
+
+ align:start position:0%
+them back into cij and eiv
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the complex conjugate of the inner
+
+ align:start position:0%
+the complex conjugate of the inner
+ 
+
+ align:start position:0%
+the complex conjugate of the inner
+product is just the same as if i flip
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the entry so this is equal to
+
+ align:start position:0%
+the entry so this is equal to
+ 
+
+ align:start position:0%
+the entry so this is equal to
+c i j times
+
+ align:start position:0%
+c i j times
+ 
+
+ align:start position:0%
+c i j times
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+e i
+
+ align:start position:0%
+e i
+ 
+
+ align:start position:0%
+e i
+e j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this holds for all u and v so what
+
+ align:start position:0%
+now this holds for all u and v so what
+ 
+
+ align:start position:0%
+now this holds for all u and v so what
+have i shown i've shown that u
+
+ align:start position:0%
+have i shown i've shown that u
+ 
+
+ align:start position:0%
+have i shown i've shown that u
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+t star v
+
+ align:start position:0%
+t star v
+ 
+
+ align:start position:0%
+t star v
+minus this finite sum so i'll actually
+
+ align:start position:0%
+minus this finite sum so i'll actually
+ 
+
+ align:start position:0%
+minus this finite sum so i'll actually
+put it in here c i j
+
+ align:start position:0%
+put it in here c i j
+ 
+
+ align:start position:0%
+put it in here c i j
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+e i
+
+ align:start position:0%
+e i
+ 
+
+ align:start position:0%
+e i
+e j
+
+ align:start position:0%
+e j
+ 
+
+ align:start position:0%
+e j
+this equals 0 for all u
+
+ align:start position:0%
+this equals 0 for all u
+ 
+
+ align:start position:0%
+this equals 0 for all u
+for all v
+
+ align:start position:0%
+for all v
+ 
+
+ align:start position:0%
+for all v
+okay now for a fixed v this quantity
+
+ align:start position:0%
+okay now for a fixed v this quantity
+ 
+
+ align:start position:0%
+okay now for a fixed v this quantity
+here is orthogonal to everything in h
+
+ align:start position:0%
+here is orthogonal to everything in h
+ 
+
+ align:start position:0%
+here is orthogonal to everything in h
+so it has to be zero and therefore i
+
+ align:start position:0%
+so it has to be zero and therefore i
+ 
+
+ align:start position:0%
+so it has to be zero and therefore i
+conclude that t star v has to equal
+
+ align:start position:0%
+conclude that t star v has to equal
+ 
+
+ align:start position:0%
+conclude that t star v has to equal
+sum from i j equals one to l
+
+ align:start position:0%
+sum from i j equals one to l
+ 
+
+ align:start position:0%
+sum from i j equals one to l
+the complex conjugates of c i j
+
+ align:start position:0%
+the complex conjugates of c i j
+ 
+
+ align:start position:0%
+the complex conjugates of c i j
+v inner product e i
+
+ align:start position:0%
+v inner product e i
+ 
+
+ align:start position:0%
+v inner product e i
+e j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all v and h and that proves that t
+
+ align:start position:0%
+for all v and h and that proves that t
+ 
+
+ align:start position:0%
+for all v and h and that proves that t
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finite rank and also gives you the
+
+ align:start position:0%
+finite rank and also gives you the
+ 
+
+ align:start position:0%
+finite rank and also gives you the
+expression for
+
+ align:start position:0%
+expression for
+ 
+
+ align:start position:0%
+expression for
+the coefficients in terms of the old
+
+ align:start position:0%
+the coefficients in terms of the old
+ 
+
+ align:start position:0%
+the coefficients in terms of the old
+ones right i could write this um
+
+ align:start position:0%
+ones right i could write this um
+ 
+
+ align:start position:0%
+ones right i could write this um
+now if i wanted to write it in terms of
+
+ align:start position:0%
+now if i wanted to write it in terms of
+ 
+
+ align:start position:0%
+now if i wanted to write it in terms of
+you know the i being in front of the
+
+ align:start position:0%
+you know the i being in front of the
+ 
+
+ align:start position:0%
+you know the i being in front of the
+basis vector that i'm having here i
+
+ align:start position:0%
+basis vector that i'm having here i
+ 
+
+ align:start position:0%
+basis vector that i'm having here i
+write it as sum i j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we see that the matrix
+
+ align:start position:0%
+okay so we see that the matrix
+ 
+
+ align:start position:0%
+okay so we see that the matrix
+corresponding to the adjoint is you know
+
+ align:start position:0%
+corresponding to the adjoint is you know
+ 
+
+ align:start position:0%
+corresponding to the adjoint is you know
+what we computed last class basically
+
+ align:start position:0%
+what we computed last class basically
+ 
+
+ align:start position:0%
+what we computed last class basically
+is the complex conjugate of the
+
+ align:start position:0%
+is the complex conjugate of the
+ 
+
+ align:start position:0%
+is the complex conjugate of the
+transpose of this matrix
+
+ align:start position:0%
+transpose of this matrix
+ 
+
+ align:start position:0%
+transpose of this matrix
+okay of the original matrix c i j's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so that proves adjoints are
+
+ align:start position:0%
+all right so that proves adjoints are
+ 
+
+ align:start position:0%
+all right so that proves adjoints are
+also finite rank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+taking
+
+ align:start position:0%
+taking
+ 
+
+ align:start position:0%
+taking
+the adjoint of a finite rank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+leaves you in the space of finite rank
+
+ align:start position:0%
+leaves you in the space of finite rank
+ 
+
+ align:start position:0%
+leaves you in the space of finite rank
+operators
+
+ align:start position:0%
+operators
+ 
+
+ align:start position:0%
+operators
+if you take
+
+ align:start position:0%
+if you take
+ 
+
+ align:start position:0%
+if you take
+finite rank operators and compose them
+
+ align:start position:0%
+finite rank operators and compose them
+ 
+
+ align:start position:0%
+finite rank operators and compose them
+on the left and on the right with
+
+ align:start position:0%
+on the left and on the right with
+ 
+
+ align:start position:0%
+on the left and on the right with
+bounded operators
+
+ align:start position:0%
+bounded operators
+ 
+
+ align:start position:0%
+bounded operators
+uh you remain finite rank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+the subset of finite rank operators also
+
+ align:start position:0%
+the subset of finite rank operators also
+ 
+
+ align:start position:0%
+the subset of finite rank operators also
+form a subspace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the bonus space of bounded linear
+
+ align:start position:0%
+in the bonus space of bounded linear
+ 
+
+ align:start position:0%
+in the bonus space of bounded linear
+operators on a hilbert space
+
+ align:start position:0%
+operators on a hilbert space
+ 
+
+ align:start position:0%
+operators on a hilbert space
+so the space of bounded linear operators
+
+ align:start position:0%
+so the space of bounded linear operators
+ 
+
+ align:start position:0%
+so the space of bounded linear operators
+on a hilbert space naturally
+
+ align:start position:0%
+on a hilbert space naturally
+ 
+
+ align:start position:0%
+on a hilbert space naturally
+come with a norm as well the operator
+
+ align:start position:0%
+come with a norm as well the operator
+ 
+
+ align:start position:0%
+come with a norm as well the operator
+norm
+
+ align:start position:0%
+norm
+ 
+
+ align:start position:0%
+norm
+so the next obvious question is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the subspace of comp of
+
+ align:start position:0%
+is the subspace of comp of
+ 
+
+ align:start position:0%
+is the subspace of comp of
+finite rank operators is this closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+close not meaning not as it closed under
+
+ align:start position:0%
+close not meaning not as it closed under
+ 
+
+ align:start position:0%
+close not meaning not as it closed under
+taking linear combinations of course
+
+ align:start position:0%
+taking linear combinations of course
+ 
+
+ align:start position:0%
+taking linear combinations of course
+that holds for every subspace but if i
+
+ align:start position:0%
+that holds for every subspace but if i
+ 
+
+ align:start position:0%
+that holds for every subspace but if i
+take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh if i take
+
+ align:start position:0%
+uh if i take
+ 
+
+ align:start position:0%
+uh if i take
+a sequence of finite rank operators that
+
+ align:start position:0%
+a sequence of finite rank operators that
+ 
+
+ align:start position:0%
+a sequence of finite rank operators that
+are converging in operator norm
+
+ align:start position:0%
+are converging in operator norm
+ 
+
+ align:start position:0%
+are converging in operator norm
+to something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then is the
+
+ align:start position:0%
+then is the
+ 
+
+ align:start position:0%
+then is the
+limit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also a finite rank operator right so
+
+ align:start position:0%
+also a finite rank operator right so
+ 
+
+ align:start position:0%
+also a finite rank operator right so
+that's the the
+
+ align:start position:0%
+that's the the
+ 
+
+ align:start position:0%
+that's the the
+definition of being a closed uh
+
+ align:start position:0%
+definition of being a closed uh
+ 
+
+ align:start position:0%
+definition of being a closed uh
+subspace or let me say subset so that
+
+ align:start position:0%
+subspace or let me say subset so that
+ 
+
+ align:start position:0%
+subspace or let me say subset so that
+we're now
+
+ align:start position:0%
+we're now
+ 
+
+ align:start position:0%
+we're now
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+asking about this in in a metric sense
+
+ align:start position:0%
+asking about this in in a metric sense
+ 
+
+ align:start position:0%
+asking about this in in a metric sense
+all right is it a a closed
+
+ align:start position:0%
+all right is it a a closed
+ 
+
+ align:start position:0%
+all right is it a a closed
+subset
+
+ align:start position:0%
+subset
+ 
+
+ align:start position:0%
+subset
+in the space of bounded linear operators
+
+ align:start position:0%
+in the space of bounded linear operators
+ 
+
+ align:start position:0%
+in the space of bounded linear operators
+now the answer to this is no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why
+
+ align:start position:0%
+why
+ 
+
+ align:start position:0%
+why
+um let's for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take
+
+ align:start position:0%
+take
+ 
+
+ align:start position:0%
+take
+t n
+
+ align:start position:0%
+t n
+ 
+
+ align:start position:0%
+t n
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this will be
+
+ align:start position:0%
+this will be
+ 
+
+ align:start position:0%
+this will be
+a sequence of operators from little l
+
+ align:start position:0%
+a sequence of operators from little l
+ 
+
+ align:start position:0%
+a sequence of operators from little l
+two to little l two
+
+ align:start position:0%
+two to little l two
+ 
+
+ align:start position:0%
+two to little l two
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an element
+
+ align:start position:0%
+an element
+ 
+
+ align:start position:0%
+an element
+a and little l2
+
+ align:start position:0%
+a and little l2
+ 
+
+ align:start position:0%
+a and little l2
+this should give me another sequence in
+
+ align:start position:0%
+this should give me another sequence in
+ 
+
+ align:start position:0%
+this should give me another sequence in
+little l2 and it'll be the sequence
+
+ align:start position:0%
+little l2 and it'll be the sequence
+ 
+
+ align:start position:0%
+little l2 and it'll be the sequence
+given by a one over one
+
+ align:start position:0%
+given by a one over one
+ 
+
+ align:start position:0%
+given by a one over one
+a two over two
+
+ align:start position:0%
+a two over two
+ 
+
+ align:start position:0%
+a two over two
+up to
+
+ align:start position:0%
+up to
+ 
+
+ align:start position:0%
+up to
+a n over n
+
+ align:start position:0%
+a n over n
+ 
+
+ align:start position:0%
+a n over n
+and then zeros after that
+
+ align:start position:0%
+and then zeros after that
+ 
+
+ align:start position:0%
+and then zeros after that
+all right so t one the operator t one
+
+ align:start position:0%
+all right so t one the operator t one
+ 
+
+ align:start position:0%
+all right so t one the operator t one
+takes a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+takes the sequence in little l2 and just
+
+ align:start position:0%
+takes the sequence in little l2 and just
+ 
+
+ align:start position:0%
+takes the sequence in little l2 and just
+spits out the sequence that has the
+
+ align:start position:0%
+spits out the sequence that has the
+ 
+
+ align:start position:0%
+spits out the sequence that has the
+first entry divided by one and zero's
+
+ align:start position:0%
+first entry divided by one and zero's
+ 
+
+ align:start position:0%
+first entry divided by one and zero's
+followed after that okay that's the
+
+ align:start position:0%
+followed after that okay that's the
+ 
+
+ align:start position:0%
+followed after that okay that's the
+operator t1 t2 takes the sequence in
+
+ align:start position:0%
+operator t1 t2 takes the sequence in
+ 
+
+ align:start position:0%
+operator t1 t2 takes the sequence in
+little l2 and spits out
+
+ align:start position:0%
+little l2 and spits out
+ 
+
+ align:start position:0%
+little l2 and spits out
+the first entry divided by one the
+
+ align:start position:0%
+the first entry divided by one the
+ 
+
+ align:start position:0%
+the first entry divided by one the
+second entry divided by two uh and
+
+ align:start position:0%
+second entry divided by two uh and
+ 
+
+ align:start position:0%
+second entry divided by two uh and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and zero's after that t3 so on okay now
+
+ align:start position:0%
+and zero's after that t3 so on okay now
+ 
+
+ align:start position:0%
+and zero's after that t3 so on okay now
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is just a picture this is formal
+
+ align:start position:0%
+this is just a picture this is formal
+ 
+
+ align:start position:0%
+this is just a picture this is formal
+this is not meant to mean anything
+
+ align:start position:0%
+this is not meant to mean anything
+ 
+
+ align:start position:0%
+this is not meant to mean anything
+if i were to express this as you know an
+
+ align:start position:0%
+if i were to express this as you know an
+ 
+
+ align:start position:0%
+if i were to express this as you know an
+infinite matrix times an infinite vector
+
+ align:start position:0%
+infinite matrix times an infinite vector
+ 
+
+ align:start position:0%
+infinite matrix times an infinite vector
+or infinite length vector where the
+
+ align:start position:0%
+or infinite length vector where the
+ 
+
+ align:start position:0%
+or infinite length vector where the
+infinite length is you know the sequence
+
+ align:start position:0%
+infinite length is you know the sequence
+ 
+
+ align:start position:0%
+infinite length is you know the sequence
+aks
+
+ align:start position:0%
+aks
+ 
+
+ align:start position:0%
+aks
+this is one
+
+ align:start position:0%
+this is one
+ 
+
+ align:start position:0%
+this is one
+one-half
+
+ align:start position:0%
+one-half
+ 
+
+ align:start position:0%
+one-half
+3 1 over n
+
+ align:start position:0%
+3 1 over n
+ 
+
+ align:start position:0%
+3 1 over n
+0 0
+
+ align:start position:0%
+0 0
+ 
+
+ align:start position:0%
+0 0
+0 0
+
+ align:start position:0%
+0 0
+ 
+
+ align:start position:0%
+0 0
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+infinite matrix times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a1
+
+ align:start position:0%
+a1
+ 
+
+ align:start position:0%
+a1
+a2
+
+ align:start position:0%
+a2
+ 
+
+ align:start position:0%
+a2
+a3
+
+ align:start position:0%
+a3
+ 
+
+ align:start position:0%
+a3
+and so on okay so i'm just
+
+ align:start position:0%
+and so on okay so i'm just
+ 
+
+ align:start position:0%
+and so on okay so i'm just
+uh multiplying a one by one a two by
+
+ align:start position:0%
+uh multiplying a one by one a two by
+ 
+
+ align:start position:0%
+uh multiplying a one by one a two by
+half a three by a third and then
+
+ align:start position:0%
+half a three by a third and then
+ 
+
+ align:start position:0%
+half a three by a third and then
+you know up to a n over n uh multiplying
+
+ align:start position:0%
+you know up to a n over n uh multiplying
+ 
+
+ align:start position:0%
+you know up to a n over n uh multiplying
+a n by one over n and then the rest of
+
+ align:start position:0%
+a n by one over n and then the rest of
+ 
+
+ align:start position:0%
+a n by one over n and then the rest of
+the entries get spat out to give me zero
+
+ align:start position:0%
+the entries get spat out to give me zero
+ 
+
+ align:start position:0%
+the entries get spat out to give me zero
+so these are the finite rank operators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you can check
+
+ align:start position:0%
+and you can check
+ 
+
+ align:start position:0%
+and you can check
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that tn minus t and operator norm goes
+
+ align:start position:0%
+that tn minus t and operator norm goes
+ 
+
+ align:start position:0%
+that tn minus t and operator norm goes
+to zero where
+
+ align:start position:0%
+to zero where
+ 
+
+ align:start position:0%
+to zero where
+what is t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t is the operator that takes a and spits
+
+ align:start position:0%
+t is the operator that takes a and spits
+ 
+
+ align:start position:0%
+t is the operator that takes a and spits
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+so a will be an element in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+little l2
+
+ align:start position:0%
+little l2
+ 
+
+ align:start position:0%
+little l2
+now as n goes to infinity you know you
+
+ align:start position:0%
+now as n goes to infinity you know you
+ 
+
+ align:start position:0%
+now as n goes to infinity you know you
+can kind of guess what's going to happen
+
+ align:start position:0%
+can kind of guess what's going to happen
+ 
+
+ align:start position:0%
+can kind of guess what's going to happen
+is i end up multiplying everything by
+
+ align:start position:0%
+is i end up multiplying everything by
+ 
+
+ align:start position:0%
+is i end up multiplying everything by
+uh one over wherever entry i'm at a one
+
+ align:start position:0%
+uh one over wherever entry i'm at a one
+ 
+
+ align:start position:0%
+uh one over wherever entry i'm at a one
+over one
+
+ align:start position:0%
+over one
+ 
+
+ align:start position:0%
+over one
+a two over two
+
+ align:start position:0%
+a two over two
+ 
+
+ align:start position:0%
+a two over two
+a three over three
+
+ align:start position:0%
+a three over three
+ 
+
+ align:start position:0%
+a three over three
+a four over four
+
+ align:start position:0%
+a four over four
+ 
+
+ align:start position:0%
+a four over four
+and so on and on
+
+ align:start position:0%
+and so on and on
+ 
+
+ align:start position:0%
+and so on and on
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+as an exercise
+
+ align:start position:0%
+as an exercise
+ 
+
+ align:start position:0%
+as an exercise
+you can show that the operator norm of t
+
+ align:start position:0%
+you can show that the operator norm of t
+ 
+
+ align:start position:0%
+you can show that the operator norm of t
+minus t n this is less than or equal to
+
+ align:start position:0%
+minus t n this is less than or equal to
+ 
+
+ align:start position:0%
+minus t n this is less than or equal to
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+be one over
+
+ align:start position:0%
+be one over
+ 
+
+ align:start position:0%
+be one over
+n plus one something like that
+
+ align:start position:0%
+n plus one something like that
+ 
+
+ align:start position:0%
+n plus one something like that
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+now this operator here does not have
+
+ align:start position:0%
+now this operator here does not have
+ 
+
+ align:start position:0%
+now this operator here does not have
+finite rank
+
+ align:start position:0%
+finite rank
+ 
+
+ align:start position:0%
+finite rank
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+i can find
+
+ align:start position:0%
+i can find
+ 
+
+ align:start position:0%
+i can find
+you know infinitely many
+
+ align:start position:0%
+you know infinitely many
+ 
+
+ align:start position:0%
+you know infinitely many
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+linearly independent vectors in the
+
+ align:start position:0%
+linearly independent vectors in the
+ 
+
+ align:start position:0%
+linearly independent vectors in the
+range for example t of
+
+ align:start position:0%
+range for example t of
+ 
+
+ align:start position:0%
+range for example t of
+e
+
+ align:start position:0%
+e
+ 
+
+ align:start position:0%
+e
+1 where this here is the basis vector
+
+ align:start position:0%
+1 where this here is the basis vector
+ 
+
+ align:start position:0%
+1 where this here is the basis vector
+gives me the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+this is the first basis vector in little
+
+ align:start position:0%
+this is the first basis vector in little
+ 
+
+ align:start position:0%
+this is the first basis vector in little
+l two if this is the second basis vector
+
+ align:start position:0%
+l two if this is the second basis vector
+ 
+
+ align:start position:0%
+l two if this is the second basis vector
+in little l two
+
+ align:start position:0%
+in little l two
+ 
+
+ align:start position:0%
+in little l two
+this is just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so on if i applied t to e n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is one over n 0 0 and so on this is
+
+ align:start position:0%
+this is one over n 0 0 and so on this is
+ 
+
+ align:start position:0%
+this is one over n 0 0 and so on this is
+in the n spot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it just takes each basis vector
+
+ align:start position:0%
+so it just takes each basis vector
+ 
+
+ align:start position:0%
+so it just takes each basis vector
+and so if you'd like this is e1 this is
+
+ align:start position:0%
+and so if you'd like this is e1 this is
+ 
+
+ align:start position:0%
+and so if you'd like this is e1 this is
+one-half e2 this is one over n
+
+ align:start position:0%
+one-half e2 this is one over n
+ 
+
+ align:start position:0%
+one-half e2 this is one over n
+en and multiplies each of these basis
+
+ align:start position:0%
+en and multiplies each of these basis
+ 
+
+ align:start position:0%
+en and multiplies each of these basis
+vectors by
+
+ align:start position:0%
+vectors by
+ 
+
+ align:start position:0%
+vectors by
+one over uh
+
+ align:start position:0%
+one over uh
+ 
+
+ align:start position:0%
+one over uh
+you know the the
+
+ align:start position:0%
+you know the the
+ 
+
+ align:start position:0%
+you know the the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+integer that's
+
+ align:start position:0%
+integer that's
+ 
+
+ align:start position:0%
+integer that's
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not delineating with
+
+ align:start position:0%
+not delineating with
+ 
+
+ align:start position:0%
+not delineating with
+denoting them sorry
+
+ align:start position:0%
+denoting them sorry
+ 
+
+ align:start position:0%
+denoting them sorry
+all right it's the end of a day so
+
+ align:start position:0%
+all right it's the end of a day so
+ 
+
+ align:start position:0%
+all right it's the end of a day so
+some of uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some of my thinking has slowed down
+
+ align:start position:0%
+some of my thinking has slowed down
+ 
+
+ align:start position:0%
+some of my thinking has slowed down
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+finite rank operators are not closed uh
+
+ align:start position:0%
+finite rank operators are not closed uh
+ 
+
+ align:start position:0%
+finite rank operators are not closed uh
+is not a closed subset of
+
+ align:start position:0%
+is not a closed subset of
+ 
+
+ align:start position:0%
+is not a closed subset of
+of uh the space of bounded linear
+
+ align:start position:0%
+of uh the space of bounded linear
+ 
+
+ align:start position:0%
+of uh the space of bounded linear
+operators so what is
+
+ align:start position:0%
+operators so what is
+ 
+
+ align:start position:0%
+operators so what is
+what's the closure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you know finite rank operators we
+
+ align:start position:0%
+and you know finite rank operators we
+ 
+
+ align:start position:0%
+and you know finite rank operators we
+like to think we know how to solve
+
+ align:start position:0%
+like to think we know how to solve
+ 
+
+ align:start position:0%
+like to think we know how to solve
+equations for right i mean you know just
+
+ align:start position:0%
+equations for right i mean you know just
+ 
+
+ align:start position:0%
+equations for right i mean you know just
+based on this expression
+
+ align:start position:0%
+based on this expression
+ 
+
+ align:start position:0%
+based on this expression
+for a finite rank operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well if we want to solve t u equals say
+
+ align:start position:0%
+well if we want to solve t u equals say
+ 
+
+ align:start position:0%
+well if we want to solve t u equals say
+v well first we know v has to be in the
+
+ align:start position:0%
+v well first we know v has to be in the
+ 
+
+ align:start position:0%
+v well first we know v has to be in the
+range of
+
+ align:start position:0%
+range of
+ 
+
+ align:start position:0%
+range of
+has to be in the range of or in the span
+
+ align:start position:0%
+has to be in the range of or in the span
+ 
+
+ align:start position:0%
+has to be in the range of or in the span
+of these basis vectors that appear here
+
+ align:start position:0%
+of these basis vectors that appear here
+ 
+
+ align:start position:0%
+of these basis vectors that appear here
+and now once we've restricted to that
+
+ align:start position:0%
+and now once we've restricted to that
+ 
+
+ align:start position:0%
+and now once we've restricted to that
+then we can solve the the equation by
+
+ align:start position:0%
+then we can solve the the equation by
+ 
+
+ align:start position:0%
+then we can solve the the equation by
+you know looking at the properties of
+
+ align:start position:0%
+you know looking at the properties of
+ 
+
+ align:start position:0%
+you know looking at the properties of
+this matrix and
+
+ align:start position:0%
+this matrix and
+ 
+
+ align:start position:0%
+this matrix and
+you know the null space will be not only
+
+ align:start position:0%
+you know the null space will be not only
+ 
+
+ align:start position:0%
+you know the null space will be not only
+the null space that sits inside the span
+
+ align:start position:0%
+the null space that sits inside the span
+ 
+
+ align:start position:0%
+the null space that sits inside the span
+of these uh basis vectors but it will
+
+ align:start position:0%
+of these uh basis vectors but it will
+ 
+
+ align:start position:0%
+of these uh basis vectors but it will
+also include
+
+ align:start position:0%
+also include
+ 
+
+ align:start position:0%
+also include
+um the orthogonal complement in h of
+
+ align:start position:0%
+um the orthogonal complement in h of
+ 
+
+ align:start position:0%
+um the orthogonal complement in h of
+these basis vectors so you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solving equations involving finite rank
+
+ align:start position:0%
+solving equations involving finite rank
+ 
+
+ align:start position:0%
+solving equations involving finite rank
+operators ought to be
+
+ align:start position:0%
+operators ought to be
+ 
+
+ align:start position:0%
+operators ought to be
+you know fairly straightforward if we
+
+ align:start position:0%
+you know fairly straightforward if we
+ 
+
+ align:start position:0%
+you know fairly straightforward if we
+remember linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algebra unfortunately they're not closed
+
+ align:start position:0%
+algebra unfortunately they're not closed
+ 
+
+ align:start position:0%
+algebra unfortunately they're not closed
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+upon taking subsequent limits but
+
+ align:start position:0%
+upon taking subsequent limits but
+ 
+
+ align:start position:0%
+upon taking subsequent limits but
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we can identify the closure of
+
+ align:start position:0%
+we can identify the closure of
+ 
+
+ align:start position:0%
+we can identify the closure of
+so now the question is
+
+ align:start position:0%
+so now the question is
+ 
+
+ align:start position:0%
+so now the question is
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the closure of finite rank operators
+
+ align:start position:0%
+the closure of finite rank operators
+ 
+
+ align:start position:0%
+the closure of finite rank operators
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+the space of bounded linear operators on
+
+ align:start position:0%
+the space of bounded linear operators on
+ 
+
+ align:start position:0%
+the space of bounded linear operators on
+h so something in the closure has to be
+
+ align:start position:0%
+h so something in the closure has to be
+ 
+
+ align:start position:0%
+h so something in the closure has to be
+a limit of finite rank operators and
+
+ align:start position:0%
+a limit of finite rank operators and
+ 
+
+ align:start position:0%
+a limit of finite rank operators and
+since we know how to solve finite
+
+ align:start position:0%
+since we know how to solve finite
+ 
+
+ align:start position:0%
+since we know how to solve finite
+for f
+
+ align:start position:0%
+for f
+ 
+
+ align:start position:0%
+for f
+equations involving finite rank
+
+ align:start position:0%
+equations involving finite rank
+ 
+
+ align:start position:0%
+equations involving finite rank
+operators hopefully we know how to solve
+
+ align:start position:0%
+operators hopefully we know how to solve
+ 
+
+ align:start position:0%
+operators hopefully we know how to solve
+equations use you know with these
+
+ align:start position:0%
+equations use you know with these
+ 
+
+ align:start position:0%
+equations use you know with these
+operators
+
+ align:start position:0%
+operators
+ 
+
+ align:start position:0%
+operators
+as well is there a simple way we can
+
+ align:start position:0%
+as well is there a simple way we can
+ 
+
+ align:start position:0%
+as well is there a simple way we can
+characterize or not simple but at least
+
+ align:start position:0%
+characterize or not simple but at least
+ 
+
+ align:start position:0%
+characterize or not simple but at least
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+more useful uh way to characterize them
+
+ align:start position:0%
+more useful uh way to characterize them
+ 
+
+ align:start position:0%
+more useful uh way to characterize them
+than you know just being the limit of
+
+ align:start position:0%
+than you know just being the limit of
+ 
+
+ align:start position:0%
+than you know just being the limit of
+finite rank operators
+
+ align:start position:0%
+finite rank operators
+ 
+
+ align:start position:0%
+finite rank operators
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+so the answer to this question is so i
+
+ align:start position:0%
+so the answer to this question is so i
+ 
+
+ align:start position:0%
+so the answer to this question is so i
+won't even write okay all right answer
+
+ align:start position:0%
+won't even write okay all right answer
+ 
+
+ align:start position:0%
+won't even write okay all right answer
+is what are called
+
+ align:start position:0%
+is what are called
+ 
+
+ align:start position:0%
+is what are called
+comp compact operators
+
+ align:start position:0%
+comp compact operators
+ 
+
+ align:start position:0%
+comp compact operators
+so the subspace of compact operators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let me make a definition so k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a bounded linear operator is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compact operator
+
+ align:start position:0%
+compact operator
+ 
+
+ align:start position:0%
+compact operator
+if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the closure
+
+ align:start position:0%
+the closure
+ 
+
+ align:start position:0%
+the closure
+of the image of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the closed unit ball
+
+ align:start position:0%
+the closed unit ball
+ 
+
+ align:start position:0%
+the closed unit ball
+in h
+
+ align:start position:0%
+in h
+ 
+
+ align:start position:0%
+in h
+so the closure of the image by k
+
+ align:start position:0%
+so the closure of the image by k
+ 
+
+ align:start position:0%
+so the closure of the image by k
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+or the closure of the image of the
+
+ align:start position:0%
+or the closure of the image of the
+ 
+
+ align:start position:0%
+or the closure of the image of the
+closed unit ball is compact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know i can also write this as a
+
+ align:start position:0%
+you know i can also write this as a
+ 
+
+ align:start position:0%
+you know i can also write this as a
+closure of the subset
+
+ align:start position:0%
+closure of the subset
+ 
+
+ align:start position:0%
+closure of the subset
+k u
+
+ align:start position:0%
+k u
+ 
+
+ align:start position:0%
+k u
+norm of u less than or equal to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um i won't have time to prove this uh
+
+ align:start position:0%
+so um i won't have time to prove this uh
+ 
+
+ align:start position:0%
+so um i won't have time to prove this uh
+theorem in this class but we'll do it uh
+
+ align:start position:0%
+theorem in this class but we'll do it uh
+ 
+
+ align:start position:0%
+theorem in this class but we'll do it uh
+next time
+
+ align:start position:0%
+next time
+ 
+
+ align:start position:0%
+next time
+and we'll actually show that in fact
+
+ align:start position:0%
+and we'll actually show that in fact
+ 
+
+ align:start position:0%
+and we'll actually show that in fact
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+class of compact operators which are
+
+ align:start position:0%
+class of compact operators which are
+ 
+
+ align:start position:0%
+class of compact operators which are
+defined in this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a compact
+
+ align:start position:0%
+this is a compact
+ 
+
+ align:start position:0%
+this is a compact
+operator in this
+
+ align:start position:0%
+operator in this
+ 
+
+ align:start position:0%
+operator in this
+according to this definition if and only
+
+ align:start position:0%
+according to this definition if and only
+ 
+
+ align:start position:0%
+according to this definition if and only
+if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k is
+
+ align:start position:0%
+k is
+ 
+
+ align:start position:0%
+k is
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the closure of finite rank operators
+
+ align:start position:0%
+in the closure of finite rank operators
+ 
+
+ align:start position:0%
+in the closure of finite rank operators
+meaning there exists a sequence of
+
+ align:start position:0%
+meaning there exists a sequence of
+ 
+
+ align:start position:0%
+meaning there exists a sequence of
+finite rank operators converging in
+
+ align:start position:0%
+finite rank operators converging in
+ 
+
+ align:start position:0%
+finite rank operators converging in
+operator norm to k
+
+ align:start position:0%
+operator norm to k
+ 
+
+ align:start position:0%
+operator norm to k
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+again why are we interested in
+
+ align:start position:0%
+again why are we interested in
+ 
+
+ align:start position:0%
+again why are we interested in
+compact operators
+
+ align:start position:0%
+compact operators
+ 
+
+ align:start position:0%
+compact operators
+well we know how to solve finite rank or
+
+ align:start position:0%
+well we know how to solve finite rank or
+ 
+
+ align:start position:0%
+well we know how to solve finite rank or
+equations involving finite rank
+
+ align:start position:0%
+equations involving finite rank
+ 
+
+ align:start position:0%
+equations involving finite rank
+operators we just look at the
+
+ align:start position:0%
+operators we just look at the
+ 
+
+ align:start position:0%
+operators we just look at the
+you know at the subspace which is a
+
+ align:start position:0%
+you know at the subspace which is a
+ 
+
+ align:start position:0%
+you know at the subspace which is a
+that contains the range
+
+ align:start position:0%
+that contains the range
+ 
+
+ align:start position:0%
+that contains the range
+and then we look at the matrix
+
+ align:start position:0%
+and then we look at the matrix
+ 
+
+ align:start position:0%
+and then we look at the matrix
+that appears there in that decomposition
+
+ align:start position:0%
+that appears there in that decomposition
+ 
+
+ align:start position:0%
+that appears there in that decomposition
+comp compact operators there are
+
+ align:start position:0%
+comp compact operators there are
+ 
+
+ align:start position:0%
+comp compact operators there are
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+something completely
+
+ align:start position:0%
+something completely
+ 
+
+ align:start position:0%
+something completely
+you know new uh
+
+ align:start position:0%
+you know new uh
+ 
+
+ align:start position:0%
+you know new uh
+when we move to
+
+ align:start position:0%
+when we move to
+ 
+
+ align:start position:0%
+when we move to
+from finite dimensional uh linear
+
+ align:start position:0%
+from finite dimensional uh linear
+ 
+
+ align:start position:0%
+from finite dimensional uh linear
+algebra now to
+
+ align:start position:0%
+algebra now to
+ 
+
+ align:start position:0%
+algebra now to
+functional analysis because
+
+ align:start position:0%
+functional analysis because
+ 
+
+ align:start position:0%
+functional analysis because
+you know these are not exactly
+
+ align:start position:0%
+you know these are not exactly
+ 
+
+ align:start position:0%
+you know these are not exactly
+necessarily equal to
+
+ align:start position:0%
+necessarily equal to
+ 
+
+ align:start position:0%
+necessarily equal to
+finite rank operators i mean we just did
+
+ align:start position:0%
+finite rank operators i mean we just did
+ 
+
+ align:start position:0%
+finite rank operators i mean we just did
+this example a minute ago
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of this operator given here by where i
+
+ align:start position:0%
+of this operator given here by where i
+ 
+
+ align:start position:0%
+of this operator given here by where i
+take uh
+
+ align:start position:0%
+take uh
+ 
+
+ align:start position:0%
+take uh
+the entry of the sequence and divide it
+
+ align:start position:0%
+the entry of the sequence and divide it
+ 
+
+ align:start position:0%
+the entry of the sequence and divide it
+by the place that it occurred in the
+
+ align:start position:0%
+by the place that it occurred in the
+ 
+
+ align:start position:0%
+by the place that it occurred in the
+sequence uh for a sequence given in l2
+
+ align:start position:0%
+sequence uh for a sequence given in l2
+ 
+
+ align:start position:0%
+sequence uh for a sequence given in l2
+so if you believe the theorem this is a
+
+ align:start position:0%
+so if you believe the theorem this is a
+ 
+
+ align:start position:0%
+so if you believe the theorem this is a
+finite rank i mean not fine this is a
+
+ align:start position:0%
+finite rank i mean not fine this is a
+ 
+
+ align:start position:0%
+finite rank i mean not fine this is a
+compact operator it's the limit of
+
+ align:start position:0%
+compact operator it's the limit of
+ 
+
+ align:start position:0%
+compact operator it's the limit of
+the the sequence of finite rank
+
+ align:start position:0%
+the the sequence of finite rank
+ 
+
+ align:start position:0%
+the the sequence of finite rank
+operators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perhaps you want to
+
+ align:start position:0%
+perhaps you want to
+ 
+
+ align:start position:0%
+perhaps you want to
+take a try at trying to prove this is
+
+ align:start position:0%
+take a try at trying to prove this is
+ 
+
+ align:start position:0%
+take a try at trying to prove this is
+com a compact operator directly from the
+
+ align:start position:0%
+com a compact operator directly from the
+ 
+
+ align:start position:0%
+com a compact operator directly from the
+definition
+
+ align:start position:0%
+definition
+ 
+
+ align:start position:0%
+definition
+but um
+
+ align:start position:0%
+but um
+ 
+
+ align:start position:0%
+but um
+or not you can wait till next time and
+
+ align:start position:0%
+or not you can wait till next time and
+ 
+
+ align:start position:0%
+or not you can wait till next time and
+just use this theorem
+
+ align:start position:0%
+just use this theorem
+ 
+
+ align:start position:0%
+just use this theorem
+but many other operators
+
+ align:start position:0%
+but many other operators
+ 
+
+ align:start position:0%
+but many other operators
+interesting operators for example
+
+ align:start position:0%
+interesting operators for example
+ 
+
+ align:start position:0%
+interesting operators for example
+inverses of differential operators
+
+ align:start position:0%
+inverses of differential operators
+ 
+
+ align:start position:0%
+inverses of differential operators
+in fact turn out to be compact operators
+
+ align:start position:0%
+in fact turn out to be compact operators
+ 
+
+ align:start position:0%
+in fact turn out to be compact operators
+okay that's also why we're interested in
+
+ align:start position:0%
+okay that's also why we're interested in
+ 
+
+ align:start position:0%
+okay that's also why we're interested in
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+we got these by taking the closure of
+
+ align:start position:0%
+we got these by taking the closure of
+ 
+
+ align:start position:0%
+we got these by taking the closure of
+finite rank operators and then after so
+
+ align:start position:0%
+finite rank operators and then after so
+ 
+
+ align:start position:0%
+finite rank operators and then after so
+now we have this kind of interesting uh
+
+ align:start position:0%
+now we have this kind of interesting uh
+ 
+
+ align:start position:0%
+now we have this kind of interesting uh
+subspace of operators that we hope to be
+
+ align:start position:0%
+subspace of operators that we hope to be
+ 
+
+ align:start position:0%
+subspace of operators that we hope to be
+able to solve equations
+
+ align:start position:0%
+able to solve equations
+ 
+
+ align:start position:0%
+able to solve equations
+uh involving
+
+ align:start position:0%
+uh involving
+ 
+
+ align:start position:0%
+uh involving
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know that'll be
+
+ align:start position:0%
+you know that'll be
+ 
+
+ align:start position:0%
+you know that'll be
+basically what takes up uh the remainder
+
+ align:start position:0%
+basically what takes up uh the remainder
+ 
+
+ align:start position:0%
+basically what takes up uh the remainder
+of the our time in this course um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you know just staring at this definition
+
+ align:start position:0%
+you know just staring at this definition
+ 
+
+ align:start position:0%
+you know just staring at this definition
+you can kind of see that all right well
+
+ align:start position:0%
+you can kind of see that all right well
+ 
+
+ align:start position:0%
+you can kind of see that all right well
+you can see that if k is a finite rank
+
+ align:start position:0%
+you can see that if k is a finite rank
+ 
+
+ align:start position:0%
+you can see that if k is a finite rank
+operator then it's a compact operator
+
+ align:start position:0%
+operator then it's a compact operator
+ 
+
+ align:start position:0%
+operator then it's a compact operator
+right so just uh we're not going to
+
+ align:start position:0%
+right so just uh we're not going to
+ 
+
+ align:start position:0%
+right so just uh we're not going to
+prove this theorem like i said but just
+
+ align:start position:0%
+prove this theorem like i said but just
+ 
+
+ align:start position:0%
+prove this theorem like i said but just
+to see
+
+ align:start position:0%
+to see
+ 
+
+ align:start position:0%
+to see
+you know or or
+
+ align:start position:0%
+you know or or
+ 
+
+ align:start position:0%
+you know or or
+do a sanity check that
+
+ align:start position:0%
+do a sanity check that
+ 
+
+ align:start position:0%
+do a sanity check that
+finite rank operators ought to be
+
+ align:start position:0%
+finite rank operators ought to be
+ 
+
+ align:start position:0%
+finite rank operators ought to be
+compact operators well a finite rank
+
+ align:start position:0%
+compact operators well a finite rank
+ 
+
+ align:start position:0%
+compact operators well a finite rank
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+the image of
+
+ align:start position:0%
+the image of
+ 
+
+ align:start position:0%
+the image of
+this closed unit ball
+
+ align:start position:0%
+this closed unit ball
+ 
+
+ align:start position:0%
+this closed unit ball
+of a finite by a finite rank operator
+
+ align:start position:0%
+of a finite by a finite rank operator
+ 
+
+ align:start position:0%
+of a finite by a finite rank operator
+that's going to be
+
+ align:start position:0%
+that's going to be
+ 
+
+ align:start position:0%
+that's going to be
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+bounded subset
+
+ align:start position:0%
+bounded subset
+ 
+
+ align:start position:0%
+bounded subset
+of a finite dimensional subspace
+
+ align:start position:0%
+of a finite dimensional subspace
+ 
+
+ align:start position:0%
+of a finite dimensional subspace
+right any bounded operator takes bounded
+
+ align:start position:0%
+right any bounded operator takes bounded
+ 
+
+ align:start position:0%
+right any bounded operator takes bounded
+sets to bounded sets so
+
+ align:start position:0%
+sets to bounded sets so
+ 
+
+ align:start position:0%
+sets to bounded sets so
+if it's finite rank it takes this
+
+ align:start position:0%
+if it's finite rank it takes this
+ 
+
+ align:start position:0%
+if it's finite rank it takes this
+bounded set
+
+ align:start position:0%
+bounded set
+ 
+
+ align:start position:0%
+bounded set
+to a bounded subset of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a finite dimensional subspace of h
+
+ align:start position:0%
+of a finite dimensional subspace of h
+ 
+
+ align:start position:0%
+of a finite dimensional subspace of h
+and then i take the closure i get a
+
+ align:start position:0%
+and then i take the closure i get a
+ 
+
+ align:start position:0%
+and then i take the closure i get a
+bounded enclosed subset of a finite
+
+ align:start position:0%
+bounded enclosed subset of a finite
+ 
+
+ align:start position:0%
+bounded enclosed subset of a finite
+dimensional subspace and we know by hana
+
+ align:start position:0%
+dimensional subspace and we know by hana
+ 
+
+ align:start position:0%
+dimensional subspace and we know by hana
+burrell
+
+ align:start position:0%
+burrell
+ 
+
+ align:start position:0%
+burrell
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+closed and bounded subsets of finite
+
+ align:start position:0%
+closed and bounded subsets of finite
+ 
+
+ align:start position:0%
+closed and bounded subsets of finite
+dimensional subspaces
+
+ align:start position:0%
+dimensional subspaces
+ 
+
+ align:start position:0%
+dimensional subspaces
+are compact so you know that shows why
+
+ align:start position:0%
+are compact so you know that shows why
+ 
+
+ align:start position:0%
+are compact so you know that shows why
+at the very minimum you should believe
+
+ align:start position:0%
+at the very minimum you should believe
+ 
+
+ align:start position:0%
+at the very minimum you should believe
+that finite rank operators are compact
+
+ align:start position:0%
+that finite rank operators are compact
+ 
+
+ align:start position:0%
+that finite rank operators are compact
+okay so we'll stop there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/RIeeEJglO10.txt b/RIeeEJglO10.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8e7bbabfa77f1ef2eee17a590e94cbda8198c0ca
--- /dev/null
+++ b/RIeeEJglO10.txt
@@ -0,0 +1,12832 @@
+align:start position:0%
+ 
+okay so here we
+
+ align:start position:0%
+okay so here we
+ 
+
+ align:start position:0%
+okay so here we
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+hi we're just starting yeah we are a bit
+
+ align:start position:0%
+hi we're just starting yeah we are a bit
+ 
+
+ align:start position:0%
+hi we're just starting yeah we are a bit
+late
+
+ align:start position:0%
+late
+ 
+
+ align:start position:0%
+late
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+so today we um talk about liquid Vapor
+
+ align:start position:0%
+so today we um talk about liquid Vapor
+ 
+
+ align:start position:0%
+so today we um talk about liquid Vapor
+uh equilibrium in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mixtures you we have seen something
+
+ align:start position:0%
+mixtures you we have seen something
+ 
+
+ align:start position:0%
+mixtures you we have seen something
+already when we did the the Gibbs phase
+
+ align:start position:0%
+already when we did the the Gibbs phase
+ 
+
+ align:start position:0%
+already when we did the the Gibbs phase
+Rule and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you remember that um if we have U
+
+ align:start position:0%
+you remember that um if we have U
+ 
+
+ align:start position:0%
+you remember that um if we have U
+if we consider the list
+
+ align:start position:0%
+if we consider the list
+ 
+
+ align:start position:0%
+if we consider the list
+of properties of these properties like
+
+ align:start position:0%
+of properties of these properties like
+ 
+
+ align:start position:0%
+of properties of these properties like
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+pressure uh the
+
+ align:start position:0%
+pressure uh the
+ 
+
+ align:start position:0%
+pressure uh the
+compositions of say two phases for
+
+ align:start position:0%
+compositions of say two phases for
+ 
+
+ align:start position:0%
+compositions of say two phases for
+example a
+
+ align:start position:0%
+example a
+ 
+
+ align:start position:0%
+example a
+liquid and a
+
+ align:start position:0%
+liquid and a
+ 
+
+ align:start position:0%
+liquid and a
+gas
+
+ align:start position:0%
+gas
+ 
+
+ align:start position:0%
+gas
+phase um depending on how many
+
+ align:start position:0%
+phase um depending on how many
+ 
+
+ align:start position:0%
+phase um depending on how many
+components you
+
+ align:start position:0%
+components you
+ 
+
+ align:start position:0%
+components you
+have uh R is the number of
+
+ align:start position:0%
+have uh R is the number of
+ 
+
+ align:start position:0%
+have uh R is the number of
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+two uh minus the number of
+
+ align:start position:0%
+two uh minus the number of
+ 
+
+ align:start position:0%
+two uh minus the number of
+phases this was called the variance
+
+ align:start position:0%
+phases this was called the variance
+ 
+
+ align:start position:0%
+phases this was called the variance
+namely the number of these variables
+
+ align:start position:0%
+namely the number of these variables
+ 
+
+ align:start position:0%
+namely the number of these variables
+that are uh independently
+
+ align:start position:0%
+that are uh independently
+ 
+
+ align:start position:0%
+that are uh independently
+changeable uh so that you remain in the
+
+ align:start position:0%
+changeable uh so that you remain in the
+ 
+
+ align:start position:0%
+changeable uh so that you remain in the
+same kind of uh
+
+ align:start position:0%
+same kind of uh
+ 
+
+ align:start position:0%
+same kind of uh
+equilibrium like in this case we talking
+
+ align:start position:0%
+equilibrium like in this case we talking
+ 
+
+ align:start position:0%
+equilibrium like in this case we talking
+about liquid Vapor but you could also we
+
+ align:start position:0%
+about liquid Vapor but you could also we
+ 
+
+ align:start position:0%
+about liquid Vapor but you could also we
+also talk a little bit about solid
+
+ align:start position:0%
+also talk a little bit about solid
+ 
+
+ align:start position:0%
+also talk a little bit about solid
+liquid and and you could also do it for
+
+ align:start position:0%
+liquid and and you could also do it for
+ 
+
+ align:start position:0%
+liquid and and you could also do it for
+solid vapor and so
+
+ align:start position:0%
+solid vapor and so
+ 
+
+ align:start position:0%
+solid vapor and so
+on um
+
+ align:start position:0%
+on um
+ 
+
+ align:start position:0%
+on um
+okay of
+
+ align:start position:0%
+okay of
+ 
+
+ align:start position:0%
+okay of
+course the chemical
+
+ align:start position:0%
+course the chemical
+ 
+
+ align:start position:0%
+course the chemical
+potentials as usual will play major
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+role as they did in order to derive the
+
+ align:start position:0%
+role as they did in order to derive the
+ 
+
+ align:start position:0%
+role as they did in order to derive the
+Gib space rule
+
+ align:start position:0%
+Gib space rule
+ 
+
+ align:start position:0%
+Gib space rule
+so the first uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh result that we want to derive is the
+
+ align:start position:0%
+uh result that we want to derive is the
+ 
+
+ align:start position:0%
+uh result that we want to derive is the
+R's
+
+ align:start position:0%
+R's
+ 
+
+ align:start position:0%
+R's
+law R's law has to do with uh and we'll
+
+ align:start position:0%
+law R's law has to do with uh and we'll
+ 
+
+ align:start position:0%
+law R's law has to do with uh and we'll
+do it for the simplest situation so the
+
+ align:start position:0%
+do it for the simplest situation so the
+ 
+
+ align:start position:0%
+do it for the simplest situation so the
+simplest situation will be one uh
+
+ align:start position:0%
+simplest situation will be one uh
+ 
+
+ align:start position:0%
+simplest situation will be one uh
+like one of these two
+
+ align:start position:0%
+like one of these two
+ 
+
+ align:start position:0%
+like one of these two
+cases uh this one is a liquid a liquid
+
+ align:start position:0%
+cases uh this one is a liquid a liquid
+ 
+
+ align:start position:0%
+cases uh this one is a liquid a liquid
+solution with compon components one and
+
+ align:start position:0%
+solution with compon components one and
+ 
+
+ align:start position:0%
+solution with compon components one and
+two for example you can think of water
+
+ align:start position:0%
+two for example you can think of water
+ 
+
+ align:start position:0%
+two for example you can think of water
+as being component one and two could be
+
+ align:start position:0%
+as being component one and two could be
+ 
+
+ align:start position:0%
+as being component one and two could be
+salt so this is salt
+
+ align:start position:0%
+salt so this is salt
+ 
+
+ align:start position:0%
+salt so this is salt
+water and it is in mutual
+
+ align:start position:0%
+water and it is in mutual
+ 
+
+ align:start position:0%
+water and it is in mutual
+equilibrium with a a gaseous
+
+ align:start position:0%
+equilibrium with a a gaseous
+ 
+
+ align:start position:0%
+equilibrium with a a gaseous
+phase in which there is also water so
+
+ align:start position:0%
+phase in which there is also water so
+ 
+
+ align:start position:0%
+phase in which there is also water so
+one and there is another component three
+
+ align:start position:0%
+one and there is another component three
+ 
+
+ align:start position:0%
+one and there is another component three
+for example it could be
+
+ align:start position:0%
+for example it could be
+ 
+
+ align:start position:0%
+for example it could be
+air because humid air air has some
+
+ align:start position:0%
+air because humid air air has some
+ 
+
+ align:start position:0%
+air because humid air air has some
+humidity and humidity is water
+
+ align:start position:0%
+humidity and humidity is water
+ 
+
+ align:start position:0%
+humidity and humidity is water
+vapor so this is for example salt
+
+ align:start position:0%
+vapor so this is for example salt
+ 
+
+ align:start position:0%
+vapor so this is for example salt
+water uh and humidair moist air in uh
+
+ align:start position:0%
+water uh and humidair moist air in uh
+ 
+
+ align:start position:0%
+water uh and humidair moist air in uh
+Mutual
+
+ align:start position:0%
+Mutual
+ 
+
+ align:start position:0%
+Mutual
+equilibrium we are considering the case
+
+ align:start position:0%
+equilibrium we are considering the case
+ 
+
+ align:start position:0%
+equilibrium we are considering the case
+that um we will do this as a major
+
+ align:start position:0%
+that um we will do this as a major
+ 
+
+ align:start position:0%
+that um we will do this as a major
+example in which
+
+ align:start position:0%
+example in which
+ 
+
+ align:start position:0%
+example in which
+the uh other
+
+ align:start position:0%
+the uh other
+ 
+
+ align:start position:0%
+the uh other
+component in this case air so the
+
+ align:start position:0%
+component in this case air so the
+ 
+
+ align:start position:0%
+component in this case air so the
+molecules of oxygen and nitrogen in air
+
+ align:start position:0%
+molecules of oxygen and nitrogen in air
+ 
+
+ align:start position:0%
+molecules of oxygen and nitrogen in air
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+noncondensible so you do not find them
+
+ align:start position:0%
+noncondensible so you do not find them
+ 
+
+ align:start position:0%
+noncondensible so you do not find them
+in the liquid
+
+ align:start position:0%
+in the liquid
+ 
+
+ align:start position:0%
+in the liquid
+phase and
+
+ align:start position:0%
+phase and
+ 
+
+ align:start position:0%
+phase and
+conversely the other component in the
+
+ align:start position:0%
+conversely the other component in the
+ 
+
+ align:start position:0%
+conversely the other component in the
+liquid phase salt is nonvolatile so you
+
+ align:start position:0%
+liquid phase salt is nonvolatile so you
+ 
+
+ align:start position:0%
+liquid phase salt is nonvolatile so you
+don't find it in the vapor f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means that for Mutual
+
+ align:start position:0%
+that means that for Mutual
+ 
+
+ align:start position:0%
+that means that for Mutual
+equilibrium it is required only that the
+
+ align:start position:0%
+equilibrium it is required only that the
+ 
+
+ align:start position:0%
+equilibrium it is required only that the
+chemical potential of the component that
+
+ align:start position:0%
+chemical potential of the component that
+ 
+
+ align:start position:0%
+chemical potential of the component that
+can be exchanged between the two phases
+
+ align:start position:0%
+can be exchanged between the two phases
+ 
+
+ align:start position:0%
+can be exchanged between the two phases
+be equal so it means that the chemical
+
+ align:start position:0%
+be equal so it means that the chemical
+ 
+
+ align:start position:0%
+be equal so it means that the chemical
+potential of water in the liquid must be
+
+ align:start position:0%
+potential of water in the liquid must be
+ 
+
+ align:start position:0%
+potential of water in the liquid must be
+equal to the chemical potential of water
+
+ align:start position:0%
+equal to the chemical potential of water
+ 
+
+ align:start position:0%
+equal to the chemical potential of water
+vapor in uh the gases
+
+ align:start position:0%
+vapor in uh the gases
+ 
+
+ align:start position:0%
+vapor in uh the gases
+phas and this is one
+
+ align:start position:0%
+phas and this is one
+ 
+
+ align:start position:0%
+phas and this is one
+example the
+
+ align:start position:0%
+example the
+ 
+
+ align:start position:0%
+example the
+other is
+
+ align:start position:0%
+other is
+ 
+
+ align:start position:0%
+other is
+uh liquid over a solid so again think of
+
+ align:start position:0%
+uh liquid over a solid so again think of
+ 
+
+ align:start position:0%
+uh liquid over a solid so again think of
+water and
+
+ align:start position:0%
+water and
+ 
+
+ align:start position:0%
+water and
+salt and this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ice okay so again salt uh we assume is
+
+ align:start position:0%
+ice okay so again salt uh we assume is
+ 
+
+ align:start position:0%
+ice okay so again salt uh we assume is
+not um
+
+ align:start position:0%
+not um
+ 
+
+ align:start position:0%
+not um
+freezing so it's it's a solute of the
+
+ align:start position:0%
+freezing so it's it's a solute of the
+ 
+
+ align:start position:0%
+freezing so it's it's a solute of the
+liquid solution but it doesn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+freeze and
+
+ align:start position:0%
+freeze and
+ 
+
+ align:start position:0%
+freeze and
+uh and therefore we need only equality
+
+ align:start position:0%
+uh and therefore we need only equality
+ 
+
+ align:start position:0%
+uh and therefore we need only equality
+of chemical potential of component one
+
+ align:start position:0%
+of chemical potential of component one
+ 
+
+ align:start position:0%
+of chemical potential of component one
+between this and this and this actually
+
+ align:start position:0%
+between this and this and this actually
+ 
+
+ align:start position:0%
+between this and this and this actually
+is not a mixture it's just a pure
+
+ align:start position:0%
+is not a mixture it's just a pure
+ 
+
+ align:start position:0%
+is not a mixture it's just a pure
+component I mean this is just pure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eyes and of course the example
+
+ align:start position:0%
+eyes and of course the example
+ 
+
+ align:start position:0%
+eyes and of course the example
+this example is
+
+ align:start position:0%
+this example is
+ 
+
+ align:start position:0%
+this example is
+the is very practical for example when
+
+ align:start position:0%
+the is very practical for example when
+ 
+
+ align:start position:0%
+the is very practical for example when
+you put salt in on
+
+ align:start position:0%
+you put salt in on
+ 
+
+ align:start position:0%
+you put salt in on
+the uh side
+
+ align:start position:0%
+the uh side
+ 
+
+ align:start position:0%
+the uh side
+walks um for avoiding freezing uh for
+
+ align:start position:0%
+walks um for avoiding freezing uh for
+ 
+
+ align:start position:0%
+walks um for avoiding freezing uh for
+for changing the temperature at which
+
+ align:start position:0%
+for changing the temperature at which
+ 
+
+ align:start position:0%
+for changing the temperature at which
+freezing
+
+ align:start position:0%
+freezing
+ 
+
+ align:start position:0%
+freezing
+occurs and this is also uh you put salt
+
+ align:start position:0%
+occurs and this is also uh you put salt
+ 
+
+ align:start position:0%
+occurs and this is also uh you put salt
+in water and that will change the
+
+ align:start position:0%
+in water and that will change the
+ 
+
+ align:start position:0%
+in water and that will change the
+boiling pond point of this of the
+
+ align:start position:0%
+boiling pond point of this of the
+ 
+
+ align:start position:0%
+boiling pond point of this of the
+solution so when you
+
+ align:start position:0%
+solution so when you
+ 
+
+ align:start position:0%
+solution so when you
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+pasta uh you and you have salted your
+
+ align:start position:0%
+pasta uh you and you have salted your
+ 
+
+ align:start position:0%
+pasta uh you and you have salted your
+water the boiling point is not 100
+
+ align:start position:0%
+water the boiling point is not 100
+ 
+
+ align:start position:0%
+water the boiling point is not 100
+degrees celus is just a little bit more
+
+ align:start position:0%
+degrees celus is just a little bit more
+ 
+
+ align:start position:0%
+degrees celus is just a little bit more
+depending on how much salt you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+put okay
+
+ align:start position:0%
+put okay
+ 
+
+ align:start position:0%
+put okay
+so so how do we derive R's law
+
+ align:start position:0%
+so so how do we derive R's law
+ 
+
+ align:start position:0%
+so so how do we derive R's law
+as usual we only need to apply the
+
+ align:start position:0%
+as usual we only need to apply the
+ 
+
+ align:start position:0%
+as usual we only need to apply the
+equality of chemical potentials and then
+
+ align:start position:0%
+equality of chemical potentials and then
+ 
+
+ align:start position:0%
+equality of chemical potentials and then
+uh manipulate the equations
+
+ align:start position:0%
+uh manipulate the equations
+ 
+
+ align:start position:0%
+uh manipulate the equations
+somehow so uh let's say that we have two
+
+ align:start position:0%
+somehow so uh let's say that we have two
+ 
+
+ align:start position:0%
+somehow so uh let's say that we have two
+phases that for the moment we call A and
+
+ align:start position:0%
+phases that for the moment we call A and
+ 
+
+ align:start position:0%
+phases that for the moment we call A and
+B just generic fa two
+
+ align:start position:0%
+B just generic fa two
+ 
+
+ align:start position:0%
+B just generic fa two
+phases so the chemical potential of
+
+ align:start position:0%
+phases so the chemical potential of
+ 
+
+ align:start position:0%
+phases so the chemical potential of
+component one in Phase
+
+ align:start position:0%
+component one in Phase
+ 
+
+ align:start position:0%
+component one in Phase
+a we going to uh
+
+ align:start position:0%
+a we going to uh
+ 
+
+ align:start position:0%
+a we going to uh
+assume uh to derive R's slw ideal
+
+ align:start position:0%
+assume uh to derive R's slw ideal
+ 
+
+ align:start position:0%
+assume uh to derive R's slw ideal
+mixture or solution behavior for all
+
+ align:start position:0%
+mixture or solution behavior for all
+ 
+
+ align:start position:0%
+mixture or solution behavior for all
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+uh or actually for this component not
+
+ align:start position:0%
+uh or actually for this component not
+ 
+
+ align:start position:0%
+uh or actually for this component not
+for all components for this component
+
+ align:start position:0%
+for all components for this component
+ 
+
+ align:start position:0%
+for all components for this component
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um so this is the
+
+ align:start position:0%
+um so this is the
+ 
+
+ align:start position:0%
+um so this is the
+pure uh phase a pure component one plus
+
+ align:start position:0%
+pure uh phase a pure component one plus
+ 
+
+ align:start position:0%
+pure uh phase a pure component one plus
+the RT the log of the mole fraction of
+
+ align:start position:0%
+the RT the log of the mole fraction of
+ 
+
+ align:start position:0%
+the RT the log of the mole fraction of
+component one in in in the phase and
+
+ align:start position:0%
+component one in in in the phase and
+ 
+
+ align:start position:0%
+component one in in in the phase and
+then we rewrite the chemical potential
+
+ align:start position:0%
+then we rewrite the chemical potential
+ 
+
+ align:start position:0%
+then we rewrite the chemical potential
+at pressure
+
+ align:start position:0%
+at pressure
+ 
+
+ align:start position:0%
+at pressure
+p we rewrite it by integrating the
+
+ align:start position:0%
+p we rewrite it by integrating the
+ 
+
+ align:start position:0%
+p we rewrite it by integrating the
+derivative of the chemical potential
+
+ align:start position:0%
+derivative of the chemical potential
+ 
+
+ align:start position:0%
+derivative of the chemical potential
+with respect to P from P to P
+
+ align:start position:0%
+with respect to P from P to P
+ 
+
+ align:start position:0%
+with respect to P from P to P
+sat Pat being the saturation temperature
+
+ align:start position:0%
+sat Pat being the saturation temperature
+ 
+
+ align:start position:0%
+sat Pat being the saturation temperature
+at which the pure substance at that
+
+ align:start position:0%
+at which the pure substance at that
+ 
+
+ align:start position:0%
+at which the pure substance at that
+temperature changes or boils or
+
+ align:start position:0%
+temperature changes or boils or
+ 
+
+ align:start position:0%
+temperature changes or boils or
+freezes okay so this uh we
+
+ align:start position:0%
+freezes okay so this uh we
+ 
+
+ align:start position:0%
+freezes okay so this uh we
+so we rewrite this
+
+ align:start position:0%
+so we rewrite this
+ 
+
+ align:start position:0%
+so we rewrite this
+as chemical potential at another
+
+ align:start position:0%
+as chemical potential at another
+ 
+
+ align:start position:0%
+as chemical potential at another
+pressure and we pick the saturation
+
+ align:start position:0%
+pressure and we pick the saturation
+ 
+
+ align:start position:0%
+pressure and we pick the saturation
+pressure and then we integrate the
+
+ align:start position:0%
+pressure and then we integrate the
+ 
+
+ align:start position:0%
+pressure and then we integrate the
+derivative and remember that the
+
+ align:start position:0%
+derivative and remember that the
+ 
+
+ align:start position:0%
+derivative and remember that the
+derivative is just a specific
+
+ align:start position:0%
+derivative is just a specific
+ 
+
+ align:start position:0%
+derivative is just a specific
+volume and then we do exactly the same
+
+ align:start position:0%
+volume and then we do exactly the same
+ 
+
+ align:start position:0%
+volume and then we do exactly the same
+also for the other uh phase
+
+ align:start position:0%
+also for the other uh phase
+ 
+
+ align:start position:0%
+also for the other uh phase
+B just change the A's in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B's then we recall that when we have a
+
+ align:start position:0%
+B's then we recall that when we have a
+ 
+
+ align:start position:0%
+B's then we recall that when we have a
+pure substance this is the reason why we
+
+ align:start position:0%
+pure substance this is the reason why we
+ 
+
+ align:start position:0%
+pure substance this is the reason why we
+decided to use the the saturated
+
+ align:start position:0%
+decided to use the the saturated
+ 
+
+ align:start position:0%
+decided to use the the saturated
+saturation pressures when we have a pure
+
+ align:start position:0%
+saturation pressures when we have a pure
+ 
+
+ align:start position:0%
+saturation pressures when we have a pure
+substance the saturation pressure is
+
+ align:start position:0%
+substance the saturation pressure is
+ 
+
+ align:start position:0%
+substance the saturation pressure is
+defined precisely by that pressure at
+
+ align:start position:0%
+defined precisely by that pressure at
+ 
+
+ align:start position:0%
+defined precisely by that pressure at
+which at the given temperature the two
+
+ align:start position:0%
+which at the given temperature the two
+ 
+
+ align:start position:0%
+which at the given temperature the two
+chemical potentials of the two phases
+
+ align:start position:0%
+chemical potentials of the two phases
+ 
+
+ align:start position:0%
+chemical potentials of the two phases
+are equal so they are in mutual
+
+ align:start position:0%
+are equal so they are in mutual
+ 
+
+ align:start position:0%
+are equal so they are in mutual
+equilibrium so liquid and Vapor for
+
+ align:start position:0%
+equilibrium so liquid and Vapor for
+ 
+
+ align:start position:0%
+equilibrium so liquid and Vapor for
+example uh at the boiling point uh have
+
+ align:start position:0%
+example uh at the boiling point uh have
+ 
+
+ align:start position:0%
+example uh at the boiling point uh have
+uh equal temperature equal pressure and
+
+ align:start position:0%
+uh equal temperature equal pressure and
+ 
+
+ align:start position:0%
+uh equal temperature equal pressure and
+equal chemical potential but the three
+
+ align:start position:0%
+equal chemical potential but the three
+ 
+
+ align:start position:0%
+equal chemical potential but the three
+are not independent and uh the equality
+
+ align:start position:0%
+are not independent and uh the equality
+ 
+
+ align:start position:0%
+are not independent and uh the equality
+of chemical potential defines the
+
+ align:start position:0%
+of chemical potential defines the
+ 
+
+ align:start position:0%
+of chemical potential defines the
+saturation uh pressure at that
+
+ align:start position:0%
+saturation uh pressure at that
+ 
+
+ align:start position:0%
+saturation uh pressure at that
+temperature so that means that this and
+
+ align:start position:0%
+temperature so that means that this and
+ 
+
+ align:start position:0%
+temperature so that means that this and
+that cancel because they are equal the
+
+ align:start position:0%
+that cancel because they are equal the
+ 
+
+ align:start position:0%
+that cancel because they are equal the
+moment we equate the two chemical
+
+ align:start position:0%
+moment we equate the two chemical
+ 
+
+ align:start position:0%
+moment we equate the two chemical
+potentials these two will cancel and we
+
+ align:start position:0%
+potentials these two will cancel and we
+ 
+
+ align:start position:0%
+potentials these two will cancel and we
+are left with just the remaining terms
+
+ align:start position:0%
+are left with just the remaining terms
+ 
+
+ align:start position:0%
+are left with just the remaining terms
+and so these remaining terms apart with
+
+ align:start position:0%
+and so these remaining terms apart with
+ 
+
+ align:start position:0%
+and so these remaining terms apart with
+the logarithms that be put together the
+
+ align:start position:0%
+the logarithms that be put together the
+ 
+
+ align:start position:0%
+the logarithms that be put together the
+logarithm of becomes the logarith of the
+
+ align:start position:0%
+logarithm of becomes the logarith of the
+ 
+
+ align:start position:0%
+logarithm of becomes the logarith of the
+ratio of the mo
+
+ align:start position:0%
+ratio of the mo
+ 
+
+ align:start position:0%
+ratio of the mo
+fractions and the integral you can put
+
+ align:start position:0%
+fractions and the integral you can put
+ 
+
+ align:start position:0%
+fractions and the integral you can put
+it in this form is the integral of the
+
+ align:start position:0%
+it in this form is the integral of the
+ 
+
+ align:start position:0%
+it in this form is the integral of the
+difference between the
+
+ align:start position:0%
+difference between the
+ 
+
+ align:start position:0%
+difference between the
+specific volumes of the pure phases pure
+
+ align:start position:0%
+specific volumes of the pure phases pure
+ 
+
+ align:start position:0%
+specific volumes of the pure phases pure
+substance in in the two different
+
+ align:start position:0%
+substance in in the two different
+ 
+
+ align:start position:0%
+substance in in the two different
+phases so this is uh what you would call
+
+ align:start position:0%
+phases so this is uh what you would call
+ 
+
+ align:start position:0%
+phases so this is uh what you would call
+vfg for example or
+
+ align:start position:0%
+vfg for example or
+ 
+
+ align:start position:0%
+vfg for example or
+vjf it's the
+
+ align:start position:0%
+vjf it's the
+ 
+
+ align:start position:0%
+vjf it's the
+volume of vaporization or freezing and
+
+ align:start position:0%
+volume of vaporization or freezing and
+ 
+
+ align:start position:0%
+volume of vaporization or freezing and
+so on of the pure
+
+ align:start position:0%
+so on of the pure
+ 
+
+ align:start position:0%
+so on of the pure
+substance so this
+
+ align:start position:0%
+substance so this
+ 
+
+ align:start position:0%
+substance so this
+connects the
+
+ align:start position:0%
+connects the
+ 
+
+ align:start position:0%
+connects the
+compositions of these
+
+ align:start position:0%
+compositions of these
+ 
+
+ align:start position:0%
+compositions of these
+mixtures to
+
+ align:start position:0%
+mixtures to
+ 
+
+ align:start position:0%
+mixtures to
+properties of pure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+substance for example if we take uh uh
+
+ align:start position:0%
+substance for example if we take uh uh
+ 
+
+ align:start position:0%
+substance for example if we take uh uh
+this case
+
+ align:start position:0%
+this case
+ 
+
+ align:start position:0%
+this case
+where we have a air
+
+ align:start position:0%
+where we have a air
+ 
+
+ align:start position:0%
+where we have a air
+on moist air on on on salted water then
+
+ align:start position:0%
+on moist air on on on salted water then
+ 
+
+ align:start position:0%
+on moist air on on on salted water then
+for air we can assume the uh for the
+
+ align:start position:0%
+for air we can assume the uh for the
+ 
+
+ align:start position:0%
+for air we can assume the uh for the
+specific volume we can assume the ideal
+
+ align:start position:0%
+specific volume we can assume the ideal
+ 
+
+ align:start position:0%
+specific volume we can assume the ideal
+gas
+
+ align:start position:0%
+gas
+ 
+
+ align:start position:0%
+gas
+law for the liquid we can assume liquid
+
+ align:start position:0%
+law for the liquid we can assume liquid
+ 
+
+ align:start position:0%
+law for the liquid we can assume liquid
+water assume Inc compressible fluid
+
+ align:start position:0%
+water assume Inc compressible fluid
+ 
+
+ align:start position:0%
+water assume Inc compressible fluid
+model so that the volume is constant
+
+ align:start position:0%
+model so that the volume is constant
+ 
+
+ align:start position:0%
+model so that the volume is constant
+specific volume is constant
+
+ align:start position:0%
+specific volume is constant
+ 
+
+ align:start position:0%
+specific volume is constant
+remember these are molar specific
+
+ align:start position:0%
+remember these are molar specific
+ 
+
+ align:start position:0%
+remember these are molar specific
+volumes and then you do the integral
+
+ align:start position:0%
+volumes and then you do the integral
+ 
+
+ align:start position:0%
+volumes and then you do the integral
+here so do the integral for for
+
+ align:start position:0%
+here so do the integral for for
+ 
+
+ align:start position:0%
+here so do the integral for for
+the this is the part that contributed by
+
+ align:start position:0%
+the this is the part that contributed by
+ 
+
+ align:start position:0%
+the this is the part that contributed by
+the fact that the volume is constant so
+
+ align:start position:0%
+the fact that the volume is constant so
+ 
+
+ align:start position:0%
+the fact that the volume is constant so
+it's just a difference in the limits of
+
+ align:start position:0%
+it's just a difference in the limits of
+ 
+
+ align:start position:0%
+it's just a difference in the limits of
+integration and the other is you
+
+ align:start position:0%
+integration and the other is you
+ 
+
+ align:start position:0%
+integration and the other is you
+integrate DP over P so you get the
+
+ align:start position:0%
+integrate DP over P so you get the
+ 
+
+ align:start position:0%
+integrate DP over P so you get the
+logarithm of
+
+ align:start position:0%
+logarithm of
+ 
+
+ align:start position:0%
+logarithm of
+P so
+
+ align:start position:0%
+P so
+ 
+
+ align:start position:0%
+P so
+this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+result now it turns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+that this term
+
+ align:start position:0%
+that this term
+ 
+
+ align:start position:0%
+that this term
+here is much smaller than uh than one
+
+ align:start position:0%
+here is much smaller than uh than one
+ 
+
+ align:start position:0%
+here is much smaller than uh than one
+and therefore much smaller than this
+
+ align:start position:0%
+and therefore much smaller than this
+ 
+
+ align:start position:0%
+and therefore much smaller than this
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+uh value which is the logarithm of RT *
+
+ align:start position:0%
+uh value which is the logarithm of RT *
+ 
+
+ align:start position:0%
+uh value which is the logarithm of RT *
+the logarithm so
+
+ align:start position:0%
+the logarithm so
+ 
+
+ align:start position:0%
+the logarithm so
+U if you neglect
+
+ align:start position:0%
+U if you neglect
+ 
+
+ align:start position:0%
+U if you neglect
+that and you can compute it and and find
+
+ align:start position:0%
+that and you can compute it and and find
+ 
+
+ align:start position:0%
+that and you can compute it and and find
+that for example even for very high
+
+ align:start position:0%
+that for example even for very high
+ 
+
+ align:start position:0%
+that for example even for very high
+pressures and uh uh normal temperatures
+
+ align:start position:0%
+pressures and uh uh normal temperatures
+ 
+
+ align:start position:0%
+pressures and uh uh normal temperatures
+uh for liquid water and typical
+
+ align:start position:0%
+uh for liquid water and typical
+ 
+
+ align:start position:0%
+uh for liquid water and typical
+temperatures you this is of the order of
+
+ align:start position:0%
+temperatures you this is of the order of
+ 
+
+ align:start position:0%
+temperatures you this is of the order of
+less than one
+
+ align:start position:0%
+less than one
+ 
+
+ align:start position:0%
+less than one
+100 which is definitely enough lower
+
+ align:start position:0%
+100 which is definitely enough lower
+ 
+
+ align:start position:0%
+100 which is definitely enough lower
+than one to be neglect
+
+ align:start position:0%
+than one to be neglect
+ 
+
+ align:start position:0%
+than one to be neglect
+negligible and and so you neglect that
+
+ align:start position:0%
+negligible and and so you neglect that
+ 
+
+ align:start position:0%
+negligible and and so you neglect that
+if you consider it it would be called
+
+ align:start position:0%
+if you consider it it would be called
+ 
+
+ align:start position:0%
+if you consider it it would be called
+what is called the
+
+ align:start position:0%
+what is called the
+ 
+
+ align:start position:0%
+what is called the
+pointing pointing effect the pointing
+
+ align:start position:0%
+pointing pointing effect the pointing
+ 
+
+ align:start position:0%
+pointing pointing effect the pointing
+contribution so what we are doing is
+
+ align:start position:0%
+contribution so what we are doing is
+ 
+
+ align:start position:0%
+contribution so what we are doing is
+currently is um um normally described as
+
+ align:start position:0%
+currently is um um normally described as
+ 
+
+ align:start position:0%
+currently is um um normally described as
+neglecting the pointing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correction and pointing is a is the name
+
+ align:start position:0%
+correction and pointing is a is the name
+ 
+
+ align:start position:0%
+correction and pointing is a is the name
+of a person
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the the end result yeah this is a
+
+ align:start position:0%
+so the the end result yeah this is a
+ 
+
+ align:start position:0%
+so the the end result yeah this is a
+square bracket to
+
+ align:start position:0%
+square bracket to
+ 
+
+ align:start position:0%
+square bracket to
+many uh we find that log and log can go
+
+ align:start position:0%
+many uh we find that log and log can go
+ 
+
+ align:start position:0%
+many uh we find that log and log can go
+away and you get the ratio of the mole
+
+ align:start position:0%
+away and you get the ratio of the mole
+ 
+
+ align:start position:0%
+away and you get the ratio of the mole
+fraction of water uh in the air so
+
+ align:start position:0%
+fraction of water uh in the air so
+ 
+
+ align:start position:0%
+fraction of water uh in the air so
+that's the moist
+
+ align:start position:0%
+that's the moist
+ 
+
+ align:start position:0%
+that's the moist
+content over the the more
+
+ align:start position:0%
+content over the the more
+ 
+
+ align:start position:0%
+content over the the more
+fraction of water in the
+
+ align:start position:0%
+fraction of water in the
+ 
+
+ align:start position:0%
+fraction of water in the
+solution and here it is a solvent so
+
+ align:start position:0%
+solution and here it is a solvent so
+ 
+
+ align:start position:0%
+solution and here it is a solvent so
+it's the predominant uh
+
+ align:start position:0%
+it's the predominant uh
+ 
+
+ align:start position:0%
+it's the predominant uh
+uh you you could also apply it for for
+
+ align:start position:0%
+uh you you could also apply it for for
+ 
+
+ align:start position:0%
+uh you you could also apply it for for
+pure water in this case y1f is equal to
+
+ align:start position:0%
+pure water in this case y1f is equal to
+ 
+
+ align:start position:0%
+pure water in this case y1f is equal to
+one then that is equal and this is R's
+
+ align:start position:0%
+one then that is equal and this is R's
+ 
+
+ align:start position:0%
+one then that is equal and this is R's
+law to the ratio of the pressure over
+
+ align:start position:0%
+law to the ratio of the pressure over
+ 
+
+ align:start position:0%
+law to the ratio of the pressure over
+the saturation pressure of pure
+
+ align:start position:0%
+the saturation pressure of pure
+ 
+
+ align:start position:0%
+the saturation pressure of pure
+water this is the formula you can also
+
+ align:start position:0%
+water this is the formula you can also
+ 
+
+ align:start position:0%
+water this is the formula you can also
+remember then that the since the for an
+
+ align:start position:0%
+remember then that the since the for an
+ 
+
+ align:start position:0%
+remember then that the since the for an
+ideal
+
+ align:start position:0%
+ideal
+ 
+
+ align:start position:0%
+ideal
+gas uh mixture um ideal Gibs Delton
+
+ align:start position:0%
+gas uh mixture um ideal Gibs Delton
+ 
+
+ align:start position:0%
+gas uh mixture um ideal Gibs Delton
+mixture of ideal gas is the partial
+
+ align:start position:0%
+mixture of ideal gas is the partial
+ 
+
+ align:start position:0%
+mixture of ideal gas is the partial
+pressure uh of the component is equal to
+
+ align:start position:0%
+pressure uh of the component is equal to
+ 
+
+ align:start position:0%
+pressure uh of the component is equal to
+the mole fraction times the pressure of
+
+ align:start position:0%
+the mole fraction times the pressure of
+ 
+
+ align:start position:0%
+the mole fraction times the pressure of
+the mixture this can also be written as
+
+ align:start position:0%
+the mixture this can also be written as
+ 
+
+ align:start position:0%
+the mixture this can also be written as
+the partial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressure and so the partial pressure of
+
+ align:start position:0%
+pressure and so the partial pressure of
+ 
+
+ align:start position:0%
+pressure and so the partial pressure of
+the uh component one in the mixture is
+
+ align:start position:0%
+the uh component one in the mixture is
+ 
+
+ align:start position:0%
+the uh component one in the mixture is
+equal to the mole fraction in the liquid
+
+ align:start position:0%
+equal to the mole fraction in the liquid
+ 
+
+ align:start position:0%
+equal to the mole fraction in the liquid
+times the saturation pressure
+
+ align:start position:0%
+times the saturation pressure
+ 
+
+ align:start position:0%
+times the saturation pressure
+of component
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one if you apply the same formula here
+
+ align:start position:0%
+one if you apply the same formula here
+ 
+
+ align:start position:0%
+one if you apply the same formula here
+equation one for the case of liquid and
+
+ align:start position:0%
+equation one for the case of liquid and
+ 
+
+ align:start position:0%
+equation one for the case of liquid and
+solid F and J for
+
+ align:start position:0%
+solid F and J for
+ 
+
+ align:start position:0%
+solid F and J for
+solid so that means
+
+ align:start position:0%
+solid so that means
+ 
+
+ align:start position:0%
+solid so that means
+eyes both the volumes can be considered
+
+ align:start position:0%
+eyes both the volumes can be considered
+ 
+
+ align:start position:0%
+eyes both the volumes can be considered
+constant so they get out of the
+
+ align:start position:0%
+constant so they get out of the
+ 
+
+ align:start position:0%
+constant so they get out of the
+integral and so you have the difference
+
+ align:start position:0%
+integral and so you have the difference
+ 
+
+ align:start position:0%
+integral and so you have the difference
+so the volume of freezing the change
+
+ align:start position:0%
+so the volume of freezing the change
+ 
+
+ align:start position:0%
+so the volume of freezing the change
+that little change in uh density between
+
+ align:start position:0%
+that little change in uh density between
+ 
+
+ align:start position:0%
+that little change in uh density between
+pure water and the ice that make so that
+
+ align:start position:0%
+pure water and the ice that make so that
+ 
+
+ align:start position:0%
+pure water and the ice that make so that
+the ice floats on water that's the uh
+
+ align:start position:0%
+the ice floats on water that's the uh
+ 
+
+ align:start position:0%
+the ice floats on water that's the uh
+volume of
+
+ align:start position:0%
+volume of
+ 
+
+ align:start position:0%
+volume of
+freezing and
+
+ align:start position:0%
+freezing and
+ 
+
+ align:start position:0%
+freezing and
+um and so R slw become takes this other
+
+ align:start position:0%
+um and so R slw become takes this other
+ 
+
+ align:start position:0%
+um and so R slw become takes this other
+form so it gives
+
+ align:start position:0%
+form so it gives
+ 
+
+ align:start position:0%
+form so it gives
+you um the mole
+
+ align:start position:0%
+you um the mole
+ 
+
+ align:start position:0%
+you um the mole
+fraction of water in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution in terms of the difference in
+
+ align:start position:0%
+solution in terms of the difference in
+ 
+
+ align:start position:0%
+solution in terms of the difference in
+pressure saturation pressure this time
+
+ align:start position:0%
+pressure saturation pressure this time
+ 
+
+ align:start position:0%
+pressure saturation pressure this time
+this is the saturation pressure of
+
+ align:start position:0%
+this is the saturation pressure of
+ 
+
+ align:start position:0%
+this is the saturation pressure of
+course of the liquid ice
+
+ align:start position:0%
+course of the liquid ice
+ 
+
+ align:start position:0%
+course of the liquid ice
+transition times that volume of freezing
+
+ align:start position:0%
+transition times that volume of freezing
+ 
+
+ align:start position:0%
+transition times that volume of freezing
+ided by
+
+ align:start position:0%
+ided by
+ 
+
+ align:start position:0%
+ided by
+RT so with this you can
+
+ align:start position:0%
+RT so with this you can
+ 
+
+ align:start position:0%
+RT so with this you can
+compute uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these relations and these have to
+
+ align:start position:0%
+these relations and these have to
+ 
+
+ align:start position:0%
+these relations and these have to
+do with the phase
+
+ align:start position:0%
+do with the phase
+ 
+
+ align:start position:0%
+do with the phase
+rule so for example in this
+
+ align:start position:0%
+rule so for example in this
+ 
+
+ align:start position:0%
+rule so for example in this
+case we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U since it is a binary
+
+ align:start position:0%
+U since it is a binary
+ 
+
+ align:start position:0%
+U since it is a binary
+mixture it has uh just two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components okay
+
+ align:start position:0%
+components okay
+ 
+
+ align:start position:0%
+components okay
+but of
+
+ align:start position:0%
+but of
+ 
+
+ align:start position:0%
+but of
+course of course uh
+
+ align:start position:0%
+course of course uh
+ 
+
+ align:start position:0%
+course of course uh
+the second Mo fraction is is one minus
+
+ align:start position:0%
+the second Mo fraction is is one minus
+ 
+
+ align:start position:0%
+the second Mo fraction is is one minus
+the the the first and so you have one
+
+ align:start position:0%
+the the the first and so you have one
+ 
+
+ align:start position:0%
+the the the first and so you have one
+relation between these two and the same
+
+ align:start position:0%
+relation between these two and the same
+ 
+
+ align:start position:0%
+relation between these two and the same
+another relation between these and then
+
+ align:start position:0%
+another relation between these and then
+ 
+
+ align:start position:0%
+another relation between these and then
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+have the relations between the chemical
+
+ align:start position:0%
+have the relations between the chemical
+ 
+
+ align:start position:0%
+have the relations between the chemical
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+potentials that uh remove two other
+
+ align:start position:0%
+potentials that uh remove two other
+ 
+
+ align:start position:0%
+potentials that uh remove two other
+relations and so you are left with the
+
+ align:start position:0%
+relations and so you are left with the
+ 
+
+ align:start position:0%
+relations and so you are left with the
+fact that the moment you fix uh
+
+ align:start position:0%
+fact that the moment you fix uh
+ 
+
+ align:start position:0%
+fact that the moment you fix uh
+temperature and the
+
+ align:start position:0%
+temperature and the
+ 
+
+ align:start position:0%
+temperature and the
+pressure uh everything is
+
+ align:start position:0%
+pressure uh everything is
+ 
+
+ align:start position:0%
+pressure uh everything is
+set so the mole
+
+ align:start position:0%
+set so the mole
+ 
+
+ align:start position:0%
+set so the mole
+fractions are fixed like here you cannot
+
+ align:start position:0%
+fractions are fixed like here you cannot
+ 
+
+ align:start position:0%
+fractions are fixed like here you cannot
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+arbitrarily the mole fraction and still
+
+ align:start position:0%
+arbitrarily the mole fraction and still
+ 
+
+ align:start position:0%
+arbitrarily the mole fraction and still
+uh stay in mutual
+
+ align:start position:0%
+uh stay in mutual
+ 
+
+ align:start position:0%
+uh stay in mutual
+equili and here also you
+
+ align:start position:0%
+equili and here also you
+ 
+
+ align:start position:0%
+equili and here also you
+cannot the ratio of the mole fraction of
+
+ align:start position:0%
+cannot the ratio of the mole fraction of
+ 
+
+ align:start position:0%
+cannot the ratio of the mole fraction of
+the the of the liquid and the vapor is
+
+ align:start position:0%
+the the of the liquid and the vapor is
+ 
+
+ align:start position:0%
+the the of the liquid and the vapor is
+is fixed by the given temperature and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressure um you can
+
+ align:start position:0%
+pressure um you can
+ 
+
+ align:start position:0%
+pressure um you can
+U interpret
+
+ align:start position:0%
+U interpret
+ 
+
+ align:start position:0%
+U interpret
+u in a molecular
+
+ align:start position:0%
+u in a molecular
+ 
+
+ align:start position:0%
+u in a molecular
+way uh the r law
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see R's law says uh for
+
+ align:start position:0%
+see R's law says uh for
+ 
+
+ align:start position:0%
+see R's law says uh for
+example here we are considering a a
+
+ align:start position:0%
+example here we are considering a a
+ 
+
+ align:start position:0%
+example here we are considering a a
+different situation than the one before
+
+ align:start position:0%
+different situation than the one before
+ 
+
+ align:start position:0%
+different situation than the one before
+in which um not
+
+ align:start position:0%
+in which um not
+ 
+
+ align:start position:0%
+in which um not
+only component one but also component
+
+ align:start position:0%
+only component one but also component
+ 
+
+ align:start position:0%
+only component one but also component
+two can go um um Can can cross
+
+ align:start position:0%
+two can go um um Can can cross
+ 
+
+ align:start position:0%
+two can go um um Can can cross
+phase so it it can be for example the FG
+
+ align:start position:0%
+phase so it it can be for example the FG
+ 
+
+ align:start position:0%
+phase so it it can be for example the FG
+case it can be both volatile and
+
+ align:start position:0%
+case it can be both volatile and
+ 
+
+ align:start position:0%
+case it can be both volatile and
+condensable as this would be for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example wine wine is a solution of uh of
+
+ align:start position:0%
+example wine wine is a solution of uh of
+ 
+
+ align:start position:0%
+example wine wine is a solution of uh of
+alcohol and and um and water and when
+
+ align:start position:0%
+alcohol and and um and water and when
+ 
+
+ align:start position:0%
+alcohol and and um and water and when
+you boil that you'll get a vapor in
+
+ align:start position:0%
+you boil that you'll get a vapor in
+ 
+
+ align:start position:0%
+you boil that you'll get a vapor in
+which you have both alcohol and water
+
+ align:start position:0%
+which you have both alcohol and water
+ 
+
+ align:start position:0%
+which you have both alcohol and water
+but they are in different
+
+ align:start position:0%
+but they are in different
+ 
+
+ align:start position:0%
+but they are in different
+uh compositions so the mo when the are
+
+ align:start position:0%
+uh compositions so the mo when the are
+ 
+
+ align:start position:0%
+uh compositions so the mo when the are
+in mutual equilibrium the mole fraction
+
+ align:start position:0%
+in mutual equilibrium the mole fraction
+ 
+
+ align:start position:0%
+in mutual equilibrium the mole fraction
+uh of alcohol in in the liquid phase is
+
+ align:start position:0%
+uh of alcohol in in the liquid phase is
+ 
+
+ align:start position:0%
+uh of alcohol in in the liquid phase is
+different from the mole fraction of
+
+ align:start position:0%
+different from the mole fraction of
+ 
+
+ align:start position:0%
+different from the mole fraction of
+alcohol in the vapor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phase so R's law gives you which is
+
+ align:start position:0%
+phase so R's law gives you which is
+ 
+
+ align:start position:0%
+phase so R's law gives you which is
+written here
+
+ align:start position:0%
+written here
+ 
+
+ align:start position:0%
+written here
+again partial
+
+ align:start position:0%
+again partial
+ 
+
+ align:start position:0%
+again partial
+pressure of say water is equal to the
+
+ align:start position:0%
+pressure of say water is equal to the
+ 
+
+ align:start position:0%
+pressure of say water is equal to the
+mole fraction times the saturation
+
+ align:start position:0%
+mole fraction times the saturation
+ 
+
+ align:start position:0%
+mole fraction times the saturation
+pressure and if you have two components
+
+ align:start position:0%
+pressure and if you have two components
+ 
+
+ align:start position:0%
+pressure and if you have two components
+you have two RS slw one also for the
+
+ align:start position:0%
+you have two RS slw one also for the
+ 
+
+ align:start position:0%
+you have two RS slw one also for the
+second component because now that also
+
+ align:start position:0%
+second component because now that also
+ 
+
+ align:start position:0%
+second component because now that also
+component two can be exchanged you
+
+ align:start position:0%
+component two can be exchanged you
+ 
+
+ align:start position:0%
+component two can be exchanged you
+should write also the CH equality of
+
+ align:start position:0%
+should write also the CH equality of
+ 
+
+ align:start position:0%
+should write also the CH equality of
+chemical potential for that
+
+ align:start position:0%
+chemical potential for that
+ 
+
+ align:start position:0%
+chemical potential for that
+component so you get a second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+and you see uh here
+
+ align:start position:0%
+and you see uh here
+ 
+
+ align:start position:0%
+and you see uh here
+the the the the idea
+
+ align:start position:0%
+the the the the idea
+ 
+
+ align:start position:0%
+the the the the idea
+the molecular interpretation is this if
+
+ align:start position:0%
+the molecular interpretation is this if
+ 
+
+ align:start position:0%
+the molecular interpretation is this if
+you have a pure
+
+ align:start position:0%
+you have a pure
+ 
+
+ align:start position:0%
+you have a pure
+substance at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium um there is somehow
+
+ align:start position:0%
+equilibrium um there is somehow
+ 
+
+ align:start position:0%
+equilibrium um there is somehow
+uh an
+
+ align:start position:0%
+uh an
+ 
+
+ align:start position:0%
+uh an
+exchange
+
+ align:start position:0%
+exchange
+ 
+
+ align:start position:0%
+exchange
+um an equilibrated balanced exchange of
+
+ align:start position:0%
+um an equilibrated balanced exchange of
+ 
+
+ align:start position:0%
+um an equilibrated balanced exchange of
+molecules that are in the vapor phas
+
+ align:start position:0%
+molecules that are in the vapor phas
+ 
+
+ align:start position:0%
+molecules that are in the vapor phas
+that go down in the liquid and some and
+
+ align:start position:0%
+that go down in the liquid and some and
+ 
+
+ align:start position:0%
+that go down in the liquid and some and
+an equal amount of molecules that from
+
+ align:start position:0%
+an equal amount of molecules that from
+ 
+
+ align:start position:0%
+an equal amount of molecules that from
+the surface surf of the liquid go up in
+
+ align:start position:0%
+the surface surf of the liquid go up in
+ 
+
+ align:start position:0%
+the surface surf of the liquid go up in
+the vapor phase and this is for
+
+ align:start position:0%
+the vapor phase and this is for
+ 
+
+ align:start position:0%
+the vapor phase and this is for
+component one and this is for component
+
+ align:start position:0%
+component one and this is for component
+ 
+
+ align:start position:0%
+component one and this is for component
+two now when you have a
+
+ align:start position:0%
+two now when you have a
+ 
+
+ align:start position:0%
+two now when you have a
+mixture uh you see that on the surface
+
+ align:start position:0%
+mixture uh you see that on the surface
+ 
+
+ align:start position:0%
+mixture uh you see that on the surface
+you have some dark and some gray uh
+
+ align:start position:0%
+you have some dark and some gray uh
+ 
+
+ align:start position:0%
+you have some dark and some gray uh
+particles so the this Dynamic exchange
+
+ align:start position:0%
+particles so the this Dynamic exchange
+ 
+
+ align:start position:0%
+particles so the this Dynamic exchange
+that occurs between the the liquid and
+
+ align:start position:0%
+that occurs between the the liquid and
+ 
+
+ align:start position:0%
+that occurs between the the liquid and
+occurs
+
+ align:start position:0%
+occurs
+ 
+
+ align:start position:0%
+occurs
+only proportional to the amount of of of
+
+ align:start position:0%
+only proportional to the amount of of of
+ 
+
+ align:start position:0%
+only proportional to the amount of of of
+dark particles for the dark ones that
+
+ align:start position:0%
+dark particles for the dark ones that
+ 
+
+ align:start position:0%
+dark particles for the dark ones that
+are on on the
+
+ align:start position:0%
+are on on the
+ 
+
+ align:start position:0%
+are on on the
+surface so if you assume that the
+
+ align:start position:0%
+surface so if you assume that the
+ 
+
+ align:start position:0%
+surface so if you assume that the
+fraction of particles that are on the
+
+ align:start position:0%
+fraction of particles that are on the
+ 
+
+ align:start position:0%
+fraction of particles that are on the
+surface is equal to the mole fraction in
+
+ align:start position:0%
+surface is equal to the mole fraction in
+ 
+
+ align:start position:0%
+surface is equal to the mole fraction in
+the liquid
+
+ align:start position:0%
+the liquid
+ 
+
+ align:start position:0%
+the liquid
+phase then you see that the the partial
+
+ align:start position:0%
+phase then you see that the the partial
+ 
+
+ align:start position:0%
+phase then you see that the the partial
+uh pressure which is driving which is
+
+ align:start position:0%
+uh pressure which is driving which is
+ 
+
+ align:start position:0%
+uh pressure which is driving which is
+sort of driving this exchange with the
+
+ align:start position:0%
+sort of driving this exchange with the
+ 
+
+ align:start position:0%
+sort of driving this exchange with the
+black
+
+ align:start position:0%
+black
+ 
+
+ align:start position:0%
+black
+particles
+
+ align:start position:0%
+particles
+ 
+
+ align:start position:0%
+particles
+uh is only limited by the by a fraction
+
+ align:start position:0%
+uh is only limited by the by a fraction
+ 
+
+ align:start position:0%
+uh is only limited by the by a fraction
+which is the mole fraction by the
+
+ align:start position:0%
+which is the mole fraction by the
+ 
+
+ align:start position:0%
+which is the mole fraction by the
+fraction with which they occupy the
+
+ align:start position:0%
+fraction with which they occupy the
+ 
+
+ align:start position:0%
+fraction with which they occupy the
+surface and equally the other ones and
+
+ align:start position:0%
+surface and equally the other ones and
+ 
+
+ align:start position:0%
+surface and equally the other ones and
+therefore uh since the pressures add up
+
+ align:start position:0%
+therefore uh since the pressures add up
+ 
+
+ align:start position:0%
+therefore uh since the pressures add up
+um that's the uh that's the relation
+
+ align:start position:0%
+um that's the uh that's the relation
+ 
+
+ align:start position:0%
+um that's the uh that's the relation
+that is one way of interpreting
+
+ align:start position:0%
+that is one way of interpreting
+ 
+
+ align:start position:0%
+that is one way of interpreting
+this in any case when we have the two RS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equations we can usefully combine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+them by using the obvious fact that the
+
+ align:start position:0%
+them by using the obvious fact that the
+ 
+
+ align:start position:0%
+them by using the obvious fact that the
+mo fractions add up to
+
+ align:start position:0%
+mo fractions add up to
+ 
+
+ align:start position:0%
+mo fractions add up to
+one so for example I could add this and
+
+ align:start position:0%
+one so for example I could add this and
+ 
+
+ align:start position:0%
+one so for example I could add this and
+that if I add these two you see y1g +
+
+ align:start position:0%
+that if I add these two you see y1g +
+ 
+
+ align:start position:0%
+that if I add these two you see y1g +
+y2g is one so I remaining I'm remaining
+
+ align:start position:0%
+y2g is one so I remaining I'm remaining
+ 
+
+ align:start position:0%
+y2g is one so I remaining I'm remaining
+with P so so I obtain this pressure this
+
+ align:start position:0%
+with P so so I obtain this pressure this
+ 
+
+ align:start position:0%
+with P so so I obtain this pressure this
+expression that the pressure is equal to
+
+ align:start position:0%
+expression that the pressure is equal to
+ 
+
+ align:start position:0%
+expression that the pressure is equal to
+this plus that and of course instead of
+
+ align:start position:0%
+this plus that and of course instead of
+ 
+
+ align:start position:0%
+this plus that and of course instead of
+Y2 I write 1 minus YF this is called the
+
+ align:start position:0%
+Y2 I write 1 minus YF this is called the
+ 
+
+ align:start position:0%
+Y2 I write 1 minus YF this is called the
+bubble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line it expresses for a given uh
+
+ align:start position:0%
+line it expresses for a given uh
+ 
+
+ align:start position:0%
+line it expresses for a given uh
+pressure and temperature the composition
+
+ align:start position:0%
+pressure and temperature the composition
+ 
+
+ align:start position:0%
+pressure and temperature the composition
+of the liquid
+
+ align:start position:0%
+of the liquid
+ 
+
+ align:start position:0%
+of the liquid
+phase so if I give you the temperature
+
+ align:start position:0%
+phase so if I give you the temperature
+ 
+
+ align:start position:0%
+phase so if I give you the temperature
+and the pressure you can compute the
+
+ align:start position:0%
+and the pressure you can compute the
+ 
+
+ align:start position:0%
+and the pressure you can compute the
+mole fraction
+
+ align:start position:0%
+mole fraction
+ 
+
+ align:start position:0%
+mole fraction
+y1f uh because you can go on the tables
+
+ align:start position:0%
+y1f uh because you can go on the tables
+ 
+
+ align:start position:0%
+y1f uh because you can go on the tables
+of the pure substances for the
+
+ align:start position:0%
+of the pure substances for the
+ 
+
+ align:start position:0%
+of the pure substances for the
+pat of the two substances and then with
+
+ align:start position:0%
+pat of the two substances and then with
+ 
+
+ align:start position:0%
+pat of the two substances and then with
+this equation you you solve for YF
+
+ align:start position:0%
+this equation you you solve for YF
+ 
+
+ align:start position:0%
+this equation you you solve for YF
+y1f
+
+ align:start position:0%
+y1f
+ 
+
+ align:start position:0%
+y1f
+or if you would
+
+ align:start position:0%
+or if you would
+ 
+
+ align:start position:0%
+or if you would
+um you if you
+
+ align:start position:0%
+um you if you
+ 
+
+ align:start position:0%
+um you if you
+sum if you solve this equation for y1f
+
+ align:start position:0%
+sum if you solve this equation for y1f
+ 
+
+ align:start position:0%
+sum if you solve this equation for y1f
+and y2f and then sum up so that it's
+
+ align:start position:0%
+and y2f and then sum up so that it's
+ 
+
+ align:start position:0%
+and y2f and then sum up so that it's
+equal to one this is the other
+
+ align:start position:0%
+equal to one this is the other
+ 
+
+ align:start position:0%
+equal to one this is the other
+expression that you
+
+ align:start position:0%
+expression that you
+ 
+
+ align:start position:0%
+expression that you
+obtain this is a du line it contains uh
+
+ align:start position:0%
+obtain this is a du line it contains uh
+ 
+
+ align:start position:0%
+obtain this is a du line it contains uh
+the relation that gives you uh that
+
+ align:start position:0%
+the relation that gives you uh that
+ 
+
+ align:start position:0%
+the relation that gives you uh that
+allows you to solve for the uh mole
+
+ align:start position:0%
+allows you to solve for the uh mole
+ 
+
+ align:start position:0%
+allows you to solve for the uh mole
+fraction of component one in so the
+
+ align:start position:0%
+fraction of component one in so the
+ 
+
+ align:start position:0%
+fraction of component one in so the
+composition of the
+
+ align:start position:0%
+composition of the
+ 
+
+ align:start position:0%
+composition of the
+vapor at
+
+ align:start position:0%
+vapor at
+ 
+
+ align:start position:0%
+vapor at
+uh in the two-phase stage
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and of course once you have the the
+
+ align:start position:0%
+okay and of course once you have the the
+ 
+
+ align:start position:0%
+okay and of course once you have the the
+B the bubble Line This is really an
+
+ align:start position:0%
+B the bubble Line This is really an
+ 
+
+ align:start position:0%
+B the bubble Line This is really an
+equation of a line so you see that if
+
+ align:start position:0%
+equation of a line so you see that if
+ 
+
+ align:start position:0%
+equation of a line so you see that if
+you plot pressure versus mole
+
+ align:start position:0%
+you plot pressure versus mole
+ 
+
+ align:start position:0%
+you plot pressure versus mole
+fraction and in this case we're talking
+
+ align:start position:0%
+fraction and in this case we're talking
+ 
+
+ align:start position:0%
+fraction and in this case we're talking
+about if you're doing this equation here
+
+ align:start position:0%
+about if you're doing this equation here
+ 
+
+ align:start position:0%
+about if you're doing this equation here
+it's the mole fraction of the
+
+ align:start position:0%
+it's the mole fraction of the
+ 
+
+ align:start position:0%
+it's the mole fraction of the
+liquid uh you get you get a straight
+
+ align:start position:0%
+liquid uh you get you get a straight
+ 
+
+ align:start position:0%
+liquid uh you get you get a straight
+line that we call the bubble line and so
+
+ align:start position:0%
+line that we call the bubble line and so
+ 
+
+ align:start position:0%
+line that we call the bubble line and so
+for a given temperature and a given
+
+ align:start position:0%
+for a given temperature and a given
+ 
+
+ align:start position:0%
+for a given temperature and a given
+pressure you go here and read the mole
+
+ align:start position:0%
+pressure you go here and read the mole
+ 
+
+ align:start position:0%
+pressure you go here and read the mole
+fraction of the
+
+ align:start position:0%
+fraction of the
+ 
+
+ align:start position:0%
+fraction of the
+liquid the DU
+
+ align:start position:0%
+liquid the DU
+ 
+
+ align:start position:0%
+liquid the DU
+line is not a straight line because it's
+
+ align:start position:0%
+line is not a straight line because it's
+ 
+
+ align:start position:0%
+line is not a straight line because it's
+one / P that is linear in
+
+ align:start position:0%
+one / P that is linear in
+ 
+
+ align:start position:0%
+one / P that is linear in
+y so it has this shape and so for a
+
+ align:start position:0%
+y so it has this shape and so for a
+ 
+
+ align:start position:0%
+y so it has this shape and so for a
+given uh for that temperature and the
+
+ align:start position:0%
+given uh for that temperature and the
+ 
+
+ align:start position:0%
+given uh for that temperature and the
+given pressure you go down here and read
+
+ align:start position:0%
+given pressure you go down here and read
+ 
+
+ align:start position:0%
+given pressure you go down here and read
+the mole fraction of the vapor of course
+
+ align:start position:0%
+the mole fraction of the vapor of course
+ 
+
+ align:start position:0%
+the mole fraction of the vapor of course
+you you can eliminate pressure from the
+
+ align:start position:0%
+you you can eliminate pressure from the
+ 
+
+ align:start position:0%
+you you can eliminate pressure from the
+system of these two equations and then
+
+ align:start position:0%
+system of these two equations and then
+ 
+
+ align:start position:0%
+system of these two equations and then
+you get a direct relation between the
+
+ align:start position:0%
+you get a direct relation between the
+ 
+
+ align:start position:0%
+you get a direct relation between the
+composition of the vapor phase and the
+
+ align:start position:0%
+composition of the vapor phase and the
+ 
+
+ align:start position:0%
+composition of the vapor phase and the
+composition of the uh liquid
+
+ align:start position:0%
+composition of the uh liquid
+ 
+
+ align:start position:0%
+composition of the uh liquid
+phase where
+
+ align:start position:0%
+phase where
+ 
+
+ align:start position:0%
+phase where
+the where what counts is the ratio
+
+ align:start position:0%
+the where what counts is the ratio
+ 
+
+ align:start position:0%
+the where what counts is the ratio
+between the saturation pressures of the
+
+ align:start position:0%
+between the saturation pressures of the
+ 
+
+ align:start position:0%
+between the saturation pressures of the
+two substances which is called the
+
+ align:start position:0%
+two substances which is called the
+ 
+
+ align:start position:0%
+two substances which is called the
+relative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volatility and here is a plot so this is
+
+ align:start position:0%
+volatility and here is a plot so this is
+ 
+
+ align:start position:0%
+volatility and here is a plot so this is
+y f y1f this is y1
+
+ align:start position:0%
+y f y1f this is y1
+ 
+
+ align:start position:0%
+y f y1f this is y1
+G and this is how that equation
+
+ align:start position:0%
+G and this is how that equation
+ 
+
+ align:start position:0%
+G and this is how that equation
+looks of course remember that here if
+
+ align:start position:0%
+looks of course remember that here if
+ 
+
+ align:start position:0%
+looks of course remember that here if
+you have if we have written
+
+ align:start position:0%
+you have if we have written
+ 
+
+ align:start position:0%
+you have if we have written
+this for both substance one and
+
+ align:start position:0%
+this for both substance one and
+ 
+
+ align:start position:0%
+this for both substance one and
+substance
+
+ align:start position:0%
+substance
+ 
+
+ align:start position:0%
+substance
+two uh it it means that we have assumed
+
+ align:start position:0%
+two uh it it means that we have assumed
+ 
+
+ align:start position:0%
+two uh it it means that we have assumed
+that at all
+
+ align:start position:0%
+that at all
+ 
+
+ align:start position:0%
+that at all
+compositions the liquid behaves as an
+
+ align:start position:0%
+compositions the liquid behaves as an
+ 
+
+ align:start position:0%
+compositions the liquid behaves as an
+ideal uh solution
+
+ align:start position:0%
+ideal uh solution
+ 
+
+ align:start position:0%
+ideal uh solution
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+ideal solution yes and
+
+ align:start position:0%
+ideal solution yes and
+ 
+
+ align:start position:0%
+ideal solution yes and
+so this is a very strong assumption
+
+ align:start position:0%
+so this is a very strong assumption
+ 
+
+ align:start position:0%
+so this is a very strong assumption
+because most uh liquids do not uh behave
+
+ align:start position:0%
+because most uh liquids do not uh behave
+ 
+
+ align:start position:0%
+because most uh liquids do not uh behave
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+that but still this is a sort the
+
+ align:start position:0%
+that but still this is a sort the
+ 
+
+ align:start position:0%
+that but still this is a sort the
+starting point so that's how the bubble
+
+ align:start position:0%
+starting point so that's how the bubble
+ 
+
+ align:start position:0%
+starting point so that's how the bubble
+line and the D line uh look for uh an
+
+ align:start position:0%
+line and the D line uh look for uh an
+ 
+
+ align:start position:0%
+line and the D line uh look for uh an
+ideal model completely ideal model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that is enough to give an idea
+
+ align:start position:0%
+and that is enough to give an idea
+ 
+
+ align:start position:0%
+and that is enough to give an idea
+what what is done when we when we do
+
+ align:start position:0%
+what what is done when we when we do
+ 
+
+ align:start position:0%
+what what is done when we when we do
+distillation um you see this plot is
+
+ align:start position:0%
+distillation um you see this plot is
+ 
+
+ align:start position:0%
+distillation um you see this plot is
+done at constant
+
+ align:start position:0%
+done at constant
+ 
+
+ align:start position:0%
+done at constant
+temperature because it's easy because
+
+ align:start position:0%
+temperature because it's easy because
+ 
+
+ align:start position:0%
+temperature because it's easy because
+you fix the temperature you go and read
+
+ align:start position:0%
+you fix the temperature you go and read
+ 
+
+ align:start position:0%
+you fix the temperature you go and read
+the saturation pressures from these
+
+ align:start position:0%
+the saturation pressures from these
+ 
+
+ align:start position:0%
+the saturation pressures from these
+lines of course I can do also
+
+ align:start position:0%
+lines of course I can do also
+ 
+
+ align:start position:0%
+lines of course I can do also
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numerically a plot in which I fix the
+
+ align:start position:0%
+numerically a plot in which I fix the
+ 
+
+ align:start position:0%
+numerically a plot in which I fix the
+pressure and then for each temperature
+
+ align:start position:0%
+pressure and then for each temperature
+ 
+
+ align:start position:0%
+pressure and then for each temperature
+so if I fix the
+
+ align:start position:0%
+so if I fix the
+ 
+
+ align:start position:0%
+so if I fix the
+pressure for each temperature there uh I
+
+ align:start position:0%
+pressure for each temperature there uh I
+ 
+
+ align:start position:0%
+pressure for each temperature there uh I
+have to go and read the values that will
+
+ align:start position:0%
+have to go and read the values that will
+ 
+
+ align:start position:0%
+have to go and read the values that will
+give me the mole fractions and I do a
+
+ align:start position:0%
+give me the mole fractions and I do a
+ 
+
+ align:start position:0%
+give me the mole fractions and I do a
+plot and a plot will generally not
+
+ align:start position:0%
+plot and a plot will generally not
+ 
+
+ align:start position:0%
+plot and a plot will generally not
+produce uh straight lines any any longer
+
+ align:start position:0%
+produce uh straight lines any any longer
+ 
+
+ align:start position:0%
+produce uh straight lines any any longer
+if it is a plot at fixed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressure this is more useful because um
+
+ align:start position:0%
+pressure this is more useful because um
+ 
+
+ align:start position:0%
+pressure this is more useful because um
+mostly uh you you boil things at at a
+
+ align:start position:0%
+mostly uh you you boil things at at a
+ 
+
+ align:start position:0%
+mostly uh you you boil things at at a
+fixed
+
+ align:start position:0%
+fixed
+ 
+
+ align:start position:0%
+fixed
+pressure so here's the uh
+
+ align:start position:0%
+pressure so here's the uh
+ 
+
+ align:start position:0%
+pressure so here's the uh
+idea so we got the the bubble
+
+ align:start position:0%
+idea so we got the the bubble
+ 
+
+ align:start position:0%
+idea so we got the the bubble
+line um in the D the D line sorry um
+
+ align:start position:0%
+line um in the D the D line sorry um
+ 
+
+ align:start position:0%
+line um in the D the D line sorry um
+the D line here and the bubble line here
+
+ align:start position:0%
+the D line here and the bubble line here
+ 
+
+ align:start position:0%
+the D line here and the bubble line here
+so uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we suppose you start with a mixture in a
+
+ align:start position:0%
+we suppose you start with a mixture in a
+ 
+
+ align:start position:0%
+we suppose you start with a mixture in a
+liquid phase at this composition say
+
+ align:start position:0%
+liquid phase at this composition say
+ 
+
+ align:start position:0%
+liquid phase at this composition say
+50/50 and uh I hit it up at certain
+
+ align:start position:0%
+50/50 and uh I hit it up at certain
+ 
+
+ align:start position:0%
+50/50 and uh I hit it up at certain
+point I reach the bubble line and uh the
+
+ align:start position:0%
+point I reach the bubble line and uh the
+ 
+
+ align:start position:0%
+point I reach the bubble line and uh the
+first bubble gets
+
+ align:start position:0%
+first bubble gets
+ 
+
+ align:start position:0%
+first bubble gets
+uh boiled
+
+ align:start position:0%
+uh boiled
+ 
+
+ align:start position:0%
+uh boiled
+off that bubble is in equilibrium with
+
+ align:start position:0%
+off that bubble is in equilibrium with
+ 
+
+ align:start position:0%
+off that bubble is in equilibrium with
+my saturated liquid and has a
+
+ align:start position:0%
+my saturated liquid and has a
+ 
+
+ align:start position:0%
+my saturated liquid and has a
+composition which is
+
+ align:start position:0%
+composition which is
+ 
+
+ align:start position:0%
+composition which is
+here it has a different composition and
+
+ align:start position:0%
+here it has a different composition and
+ 
+
+ align:start position:0%
+here it has a different composition and
+we computed by that formula that we have
+
+ align:start position:0%
+we computed by that formula that we have
+ 
+
+ align:start position:0%
+we computed by that formula that we have
+uh derived based on the
+
+ align:start position:0%
+uh derived based on the
+ 
+
+ align:start position:0%
+uh derived based on the
+relative
+
+ align:start position:0%
+relative
+ 
+
+ align:start position:0%
+relative
+volatility of course you can express the
+
+ align:start position:0%
+volatility of course you can express the
+ 
+
+ align:start position:0%
+volatility of course you can express the
+relative volatility as ratio of
+
+ align:start position:0%
+relative volatility as ratio of
+ 
+
+ align:start position:0%
+relative volatility as ratio of
+pressures but it's it's also related to
+
+ align:start position:0%
+pressures but it's it's also related to
+ 
+
+ align:start position:0%
+pressures but it's it's also related to
+the ratio of the saturation temperatures
+
+ align:start position:0%
+the ratio of the saturation temperatures
+ 
+
+ align:start position:0%
+the ratio of the saturation temperatures
+because this T sat of p is the inverse
+
+ align:start position:0%
+because this T sat of p is the inverse
+ 
+
+ align:start position:0%
+because this T sat of p is the inverse
+function of P sat of
+
+ align:start position:0%
+function of P sat of
+ 
+
+ align:start position:0%
+function of P sat of
+T okay if I keep U uh heating
+
+ align:start position:0%
+T okay if I keep U uh heating
+ 
+
+ align:start position:0%
+T okay if I keep U uh heating
+up for example I have an equilibrium at
+
+ align:start position:0%
+up for example I have an equilibrium at
+ 
+
+ align:start position:0%
+up for example I have an equilibrium at
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+temperature and for an equilibrium at
+
+ align:start position:0%
+temperature and for an equilibrium at
+ 
+
+ align:start position:0%
+temperature and for an equilibrium at
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+temperature the the bubble line gives me
+
+ align:start position:0%
+temperature the the bubble line gives me
+ 
+
+ align:start position:0%
+temperature the the bubble line gives me
+the mole fraction of the liquid and the
+
+ align:start position:0%
+the mole fraction of the liquid and the
+ 
+
+ align:start position:0%
+the mole fraction of the liquid and the
+the due line gives me the mole fraction
+
+ align:start position:0%
+the due line gives me the mole fraction
+ 
+
+ align:start position:0%
+the due line gives me the mole fraction
+of the vapor again for following this
+
+ align:start position:0%
+of the vapor again for following this
+ 
+
+ align:start position:0%
+of the vapor again for following this
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+expression if the temperature goes
+
+ align:start position:0%
+expression if the temperature goes
+ 
+
+ align:start position:0%
+expression if the temperature goes
+up up to here I have saturated
+
+ align:start position:0%
+up up to here I have saturated
+ 
+
+ align:start position:0%
+up up to here I have saturated
+Vapor which is in equilibrium with the
+
+ align:start position:0%
+Vapor which is in equilibrium with the
+ 
+
+ align:start position:0%
+Vapor which is in equilibrium with the
+first or say last drop of uh liquid so
+
+ align:start position:0%
+first or say last drop of uh liquid so
+ 
+
+ align:start position:0%
+first or say last drop of uh liquid so
+this saturated Vapor then if I still hit
+
+ align:start position:0%
+this saturated Vapor then if I still hit
+ 
+
+ align:start position:0%
+this saturated Vapor then if I still hit
+it up it will go up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the idea is this if
+
+ align:start position:0%
+okay so the idea is this if
+ 
+
+ align:start position:0%
+okay so the idea is this if
+I if I start with a composition like
+
+ align:start position:0%
+I if I start with a composition like
+ 
+
+ align:start position:0%
+I if I start with a composition like
+50/50 and I want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+separate what I could do is to go up to
+
+ align:start position:0%
+separate what I could do is to go up to
+ 
+
+ align:start position:0%
+separate what I could do is to go up to
+this temperature here like an
+
+ align:start position:0%
+this temperature here like an
+ 
+
+ align:start position:0%
+this temperature here like an
+intermediate temperature between the
+
+ align:start position:0%
+intermediate temperature between the
+ 
+
+ align:start position:0%
+intermediate temperature between the
+temperature the saturation uh liquid
+
+ align:start position:0%
+temperature the saturation uh liquid
+ 
+
+ align:start position:0%
+temperature the saturation uh liquid
+temperature and the uh saturation Vapor
+
+ align:start position:0%
+temperature and the uh saturation Vapor
+ 
+
+ align:start position:0%
+temperature and the uh saturation Vapor
+temperature and notice
+
+ align:start position:0%
+temperature and notice
+ 
+
+ align:start position:0%
+temperature and notice
+that where as for a pure
+
+ align:start position:0%
+that where as for a pure
+ 
+
+ align:start position:0%
+that where as for a pure
+substance
+
+ align:start position:0%
+substance
+ 
+
+ align:start position:0%
+substance
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the the DU line and the bubble line
+
+ align:start position:0%
+the the DU line and the bubble line
+ 
+
+ align:start position:0%
+the the DU line and the bubble line
+coincide and there is only one
+
+ align:start position:0%
+coincide and there is only one
+ 
+
+ align:start position:0%
+coincide and there is only one
+temperature at which uh the pure
+
+ align:start position:0%
+temperature at which uh the pure
+ 
+
+ align:start position:0%
+temperature at which uh the pure
+substance becomes liquid and is also uh
+
+ align:start position:0%
+substance becomes liquid and is also uh
+ 
+
+ align:start position:0%
+substance becomes liquid and is also uh
+saturated so if you so this uh lens
+
+ align:start position:0%
+saturated so if you so this uh lens
+ 
+
+ align:start position:0%
+saturated so if you so this uh lens
+shaped thing will reduce to
+
+ align:start position:0%
+shaped thing will reduce to
+ 
+
+ align:start position:0%
+shaped thing will reduce to
+just a line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+here uh the boiling occurs over a range
+
+ align:start position:0%
+here uh the boiling occurs over a range
+ 
+
+ align:start position:0%
+here uh the boiling occurs over a range
+of temperatures between this and
+
+ align:start position:0%
+of temperatures between this and
+ 
+
+ align:start position:0%
+of temperatures between this and
+that this is not only for liquid and
+
+ align:start position:0%
+that this is not only for liquid and
+ 
+
+ align:start position:0%
+that this is not only for liquid and
+solid for example in also uh Metals if
+
+ align:start position:0%
+solid for example in also uh Metals if
+ 
+
+ align:start position:0%
+solid for example in also uh Metals if
+you go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+metalurgy this would be solid this would
+
+ align:start position:0%
+metalurgy this would be solid this would
+ 
+
+ align:start position:0%
+metalurgy this would be solid this would
+be liquid and this would be the
+
+ align:start position:0%
+be liquid and this would be the
+ 
+
+ align:start position:0%
+be liquid and this would be the
+solidus uh temperature and that's the
+
+ align:start position:0%
+solidus uh temperature and that's the
+ 
+
+ align:start position:0%
+solidus uh temperature and that's the
+liquidous temperature and this Gap uh
+
+ align:start position:0%
+liquidous temperature and this Gap uh
+ 
+
+ align:start position:0%
+liquidous temperature and this Gap uh
+is is like
+
+ align:start position:0%
+is is like
+ 
+
+ align:start position:0%
+is is like
+here okay so let's say we we we we put
+
+ align:start position:0%
+here okay so let's say we we we we put
+ 
+
+ align:start position:0%
+here okay so let's say we we we we put
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+temperature we are at the temperature
+
+ align:start position:0%
+temperature we are at the temperature
+ 
+
+ align:start position:0%
+temperature we are at the temperature
+intermediate between the liquidus and
+
+ align:start position:0%
+intermediate between the liquidus and
+ 
+
+ align:start position:0%
+intermediate between the liquidus and
+the vaporous so to speak temperature
+
+ align:start position:0%
+the vaporous so to speak temperature
+ 
+
+ align:start position:0%
+the vaporous so to speak temperature
+then you see that the two phases are
+
+ align:start position:0%
+then you see that the two phases are
+ 
+
+ align:start position:0%
+then you see that the two phases are
+one uh enriched in component two and the
+
+ align:start position:0%
+one uh enriched in component two and the
+ 
+
+ align:start position:0%
+one uh enriched in component two and the
+other en reached in component one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is what happens in one stage of
+
+ align:start position:0%
+so this is what happens in one stage of
+ 
+
+ align:start position:0%
+so this is what happens in one stage of
+a distillation
+
+ align:start position:0%
+a distillation
+ 
+
+ align:start position:0%
+a distillation
+column then what you do is you take the
+
+ align:start position:0%
+column then what you do is you take the
+ 
+
+ align:start position:0%
+column then what you do is you take the
+liquid and you set it you send it down
+
+ align:start position:0%
+liquid and you set it you send it down
+ 
+
+ align:start position:0%
+liquid and you set it you send it down
+to another
+
+ align:start position:0%
+to another
+ 
+
+ align:start position:0%
+to another
+stage which works at a different
+
+ align:start position:0%
+stage which works at a different
+ 
+
+ align:start position:0%
+stage which works at a different
+temperature and then you you take uh the
+
+ align:start position:0%
+temperature and then you you take uh the
+ 
+
+ align:start position:0%
+temperature and then you you take uh the
+the vapor and you send it up to uh
+
+ align:start position:0%
+the vapor and you send it up to uh
+ 
+
+ align:start position:0%
+the vapor and you send it up to uh
+condense into the
+
+ align:start position:0%
+condense into the
+ 
+
+ align:start position:0%
+condense into the
+uh uh upper
+
+ align:start position:0%
+uh uh upper
+ 
+
+ align:start position:0%
+uh uh upper
+stage and so on so that uh
+
+ align:start position:0%
+stage and so on so that uh
+ 
+
+ align:start position:0%
+stage and so on so that uh
+eventually you can
+
+ align:start position:0%
+eventually you can
+ 
+
+ align:start position:0%
+eventually you can
+um you see since you in the upper level
+
+ align:start position:0%
+um you see since you in the upper level
+ 
+
+ align:start position:0%
+um you see since you in the upper level
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+collected a mixture which is more rich
+
+ align:start position:0%
+collected a mixture which is more rich
+ 
+
+ align:start position:0%
+collected a mixture which is more rich
+in in
+
+ align:start position:0%
+in in
+ 
+
+ align:start position:0%
+in in
+in in um in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alcohol then
+
+ align:start position:0%
+alcohol then
+ 
+
+ align:start position:0%
+alcohol then
+you could uh play the same game go to an
+
+ align:start position:0%
+you could uh play the same game go to an
+ 
+
+ align:start position:0%
+you could uh play the same game go to an
+intermediate temperature like this one
+
+ align:start position:0%
+intermediate temperature like this one
+ 
+
+ align:start position:0%
+intermediate temperature like this one
+and then you generate an even more
+
+ align:start position:0%
+and then you generate an even more
+ 
+
+ align:start position:0%
+and then you generate an even more
+enriched um vapor and so on you can
+
+ align:start position:0%
+enriched um vapor and so on you can
+ 
+
+ align:start position:0%
+enriched um vapor and so on you can
+continue as much as you need in order to
+
+ align:start position:0%
+continue as much as you need in order to
+ 
+
+ align:start position:0%
+continue as much as you need in order to
+obtain um up to
+
+ align:start position:0%
+obtain um up to
+ 
+
+ align:start position:0%
+obtain um up to
+99% uh for example this is how they get
+
+ align:start position:0%
+99% uh for example this is how they get
+ 
+
+ align:start position:0%
+99% uh for example this is how they get
+96 uh
+
+ align:start position:0%
+96 uh
+ 
+
+ align:start position:0%
+96 uh
+volume percent alcohol that is used to
+
+ align:start position:0%
+volume percent alcohol that is used to
+ 
+
+ align:start position:0%
+volume percent alcohol that is used to
+make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+liquers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right so this is for
+
+ align:start position:0%
+okay all right so this is for
+ 
+
+ align:start position:0%
+okay all right so this is for
+distillation
+
+ align:start position:0%
+distillation
+ 
+
+ align:start position:0%
+distillation
+principle now
+
+ align:start position:0%
+principle now
+ 
+
+ align:start position:0%
+principle now
+another thing that can be explained by
+
+ align:start position:0%
+another thing that can be explained by
+ 
+
+ align:start position:0%
+another thing that can be explained by
+ral's
+
+ align:start position:0%
+ral's
+ 
+
+ align:start position:0%
+ral's
+law is as I mentioned this idea that uh
+
+ align:start position:0%
+law is as I mentioned this idea that uh
+ 
+
+ align:start position:0%
+law is as I mentioned this idea that uh
+this fact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that when you add salt on water that
+
+ align:start position:0%
+that when you add salt on water that
+ 
+
+ align:start position:0%
+that when you add salt on water that
+water will freeze at a lower temperature
+
+ align:start position:0%
+water will freeze at a lower temperature
+ 
+
+ align:start position:0%
+water will freeze at a lower temperature
+than zero
+
+ align:start position:0%
+than zero
+ 
+
+ align:start position:0%
+than zero
+Celsius or when you add salt in water
+
+ align:start position:0%
+Celsius or when you add salt in water
+ 
+
+ align:start position:0%
+Celsius or when you add salt in water
+that water will boil at a higher
+
+ align:start position:0%
+that water will boil at a higher
+ 
+
+ align:start position:0%
+that water will boil at a higher
+temperature than 100 degrees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+celsus how do we derive that okay okay
+
+ align:start position:0%
+celsus how do we derive that okay okay
+ 
+
+ align:start position:0%
+celsus how do we derive that okay okay
+we start from the routs law for the
+
+ align:start position:0%
+we start from the routs law for the
+ 
+
+ align:start position:0%
+we start from the routs law for the
+specific case so this is the the routs
+
+ align:start position:0%
+specific case so this is the the routs
+ 
+
+ align:start position:0%
+specific case so this is the the routs
+law for the uh liquid eyes case that we
+
+ align:start position:0%
+law for the uh liquid eyes case that we
+ 
+
+ align:start position:0%
+law for the uh liquid eyes case that we
+have seen couple of slides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ago and we
+
+ align:start position:0%
+ago and we
+ 
+
+ align:start position:0%
+ago and we
+take the differential of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and
+
+ align:start position:0%
+this and
+ 
+
+ align:start position:0%
+this and
+then realize that uh when we take uh the
+
+ align:start position:0%
+then realize that uh when we take uh the
+ 
+
+ align:start position:0%
+then realize that uh when we take uh the
+different itial of
+
+ align:start position:0%
+different itial of
+ 
+
+ align:start position:0%
+different itial of
+Pat we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually this is a pat of the pure
+
+ align:start position:0%
+actually this is a pat of the pure
+ 
+
+ align:start position:0%
+actually this is a pat of the pure
+substance so for the pure substance we
+
+ align:start position:0%
+substance so for the pure substance we
+ 
+
+ align:start position:0%
+substance so for the pure substance we
+can remember the Claus claperon relation
+
+ align:start position:0%
+can remember the Claus claperon relation
+ 
+
+ align:start position:0%
+can remember the Claus claperon relation
+that gives you the slope of this curve
+
+ align:start position:0%
+that gives you the slope of this curve
+ 
+
+ align:start position:0%
+that gives you the slope of this curve
+on the PT diagram this this is the the
+
+ align:start position:0%
+on the PT diagram this this is the the
+ 
+
+ align:start position:0%
+on the PT diagram this this is the the
+saturation pressure curve and the slope
+
+ align:start position:0%
+saturation pressure curve and the slope
+ 
+
+ align:start position:0%
+saturation pressure curve and the slope
+of that curve is the is given by the
+
+ align:start position:0%
+of that curve is the is given by the
+ 
+
+ align:start position:0%
+of that curve is the is given by the
+closes claperon relation and it is
+
+ align:start position:0%
+closes claperon relation and it is
+ 
+
+ align:start position:0%
+closes claperon relation and it is
+related to the enthalpy of a change of
+
+ align:start position:0%
+related to the enthalpy of a change of
+ 
+
+ align:start position:0%
+related to the enthalpy of a change of
+phase divided by the volume of the
+
+ align:start position:0%
+phase divided by the volume of the
+ 
+
+ align:start position:0%
+phase divided by the volume of the
+change of phase it's it's actually it
+
+ align:start position:0%
+change of phase it's it's actually it
+ 
+
+ align:start position:0%
+change of phase it's it's actually it
+should be the entropy of the changes of
+
+ align:start position:0%
+should be the entropy of the changes of
+ 
+
+ align:start position:0%
+should be the entropy of the changes of
+phase divided by the volume but the
+
+ align:start position:0%
+phase divided by the volume but the
+ 
+
+ align:start position:0%
+phase divided by the volume but the
+entropy of the change of phase is equal
+
+ align:start position:0%
+entropy of the change of phase is equal
+ 
+
+ align:start position:0%
+entropy of the change of phase is equal
+to the enthalpy over the temperature of
+
+ align:start position:0%
+to the enthalpy over the temperature of
+ 
+
+ align:start position:0%
+to the enthalpy over the temperature of
+the change of
+
+ align:start position:0%
+the change of
+ 
+
+ align:start position:0%
+the change of
+phase so you use this in this
+
+ align:start position:0%
+phase so you use this in this
+ 
+
+ align:start position:0%
+phase so you use this in this
+relation
+
+ align:start position:0%
+relation
+ 
+
+ align:start position:0%
+relation
+neglect
+
+ align:start position:0%
+neglect
+ 
+
+ align:start position:0%
+neglect
+um this term
+
+ align:start position:0%
+um this term
+ 
+
+ align:start position:0%
+um this term
+here if which is good if if you have a
+
+ align:start position:0%
+here if which is good if if you have a
+ 
+
+ align:start position:0%
+here if which is good if if you have a
+dilute solution therefore the mole
+
+ align:start position:0%
+dilute solution therefore the mole
+ 
+
+ align:start position:0%
+dilute solution therefore the mole
+fraction is close to one and therefore
+
+ align:start position:0%
+fraction is close to one and therefore
+ 
+
+ align:start position:0%
+fraction is close to one and therefore
+the logarith is close to
+
+ align:start position:0%
+the logarith is close to
+ 
+
+ align:start position:0%
+the logarith is close to
+zero and you're left with these three
+
+ align:start position:0%
+zero and you're left with these three
+ 
+
+ align:start position:0%
+zero and you're left with these three
+terms then if you consider that you're
+
+ align:start position:0%
+terms then if you consider that you're
+ 
+
+ align:start position:0%
+terms then if you consider that you're
+not changing the
+
+ align:start position:0%
+not changing the
+ 
+
+ align:start position:0%
+not changing the
+pressure so if you remain at constant
+
+ align:start position:0%
+pressure so if you remain at constant
+ 
+
+ align:start position:0%
+pressure so if you remain at constant
+pressure and change the
+
+ align:start position:0%
+pressure and change the
+ 
+
+ align:start position:0%
+pressure and change the
+composition of uh of the
+
+ align:start position:0%
+composition of uh of the
+ 
+
+ align:start position:0%
+composition of uh of the
+solution this relates this tells you how
+
+ align:start position:0%
+solution this relates this tells you how
+ 
+
+ align:start position:0%
+solution this relates this tells you how
+the temperature will change so
+
+ align:start position:0%
+the temperature will change so
+ 
+
+ align:start position:0%
+the temperature will change so
+essentially from this equation DP you
+
+ align:start position:0%
+essentially from this equation DP you
+ 
+
+ align:start position:0%
+essentially from this equation DP you
+can compute the derivative of t with
+
+ align:start position:0%
+can compute the derivative of t with
+ 
+
+ align:start position:0%
+can compute the derivative of t with
+respect to a change of mole fraction of
+
+ align:start position:0%
+respect to a change of mole fraction of
+ 
+
+ align:start position:0%
+respect to a change of mole fraction of
+constituent one but the change of mole
+
+ align:start position:0%
+constituent one but the change of mole
+ 
+
+ align:start position:0%
+constituent one but the change of mole
+fraction of constituent one is also
+
+ align:start position:0%
+fraction of constituent one is also
+ 
+
+ align:start position:0%
+fraction of constituent one is also
+equal to the negative of the change of
+
+ align:start position:0%
+equal to the negative of the change of
+ 
+
+ align:start position:0%
+equal to the negative of the change of
+the constituent two this case the
+
+ align:start position:0%
+the constituent two this case the
+ 
+
+ align:start position:0%
+the constituent two this case the
+salt and uh and and then you have a
+
+ align:start position:0%
+salt and uh and and then you have a
+ 
+
+ align:start position:0%
+salt and uh and and then you have a
+H and
+
+ align:start position:0%
+H and
+ 
+
+ align:start position:0%
+H and
+RT so in the end you
+
+ align:start position:0%
+RT so in the end you
+ 
+
+ align:start position:0%
+RT so in the end you
+find that
+
+ align:start position:0%
+find that
+ 
+
+ align:start position:0%
+find that
+the if you add a little bit of salt to
+
+ align:start position:0%
+the if you add a little bit of salt to
+ 
+
+ align:start position:0%
+the if you add a little bit of salt to
+the liquid
+
+ align:start position:0%
+the liquid
+ 
+
+ align:start position:0%
+the liquid
+solution the temperature at which you
+
+ align:start position:0%
+solution the temperature at which you
+ 
+
+ align:start position:0%
+solution the temperature at which you
+have equilibrium therefore the freezing
+
+ align:start position:0%
+have equilibrium therefore the freezing
+ 
+
+ align:start position:0%
+have equilibrium therefore the freezing
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temperature is
+
+ align:start position:0%
+temperature is
+ 
+
+ align:start position:0%
+temperature is
+changes from before by an amount that is
+
+ align:start position:0%
+changes from before by an amount that is
+ 
+
+ align:start position:0%
+changes from before by an amount that is
+related by these things RT squ the
+
+ align:start position:0%
+related by these things RT squ the
+ 
+
+ align:start position:0%
+related by these things RT squ the
+enthalpy so all properties that you can
+
+ align:start position:0%
+enthalpy so all properties that you can
+ 
+
+ align:start position:0%
+enthalpy so all properties that you can
+look up for the pure substance with a
+
+ align:start position:0%
+look up for the pure substance with a
+ 
+
+ align:start position:0%
+look up for the pure substance with a
+minus sign so this is the uh freezing
+
+ align:start position:0%
+minus sign so this is the uh freezing
+ 
+
+ align:start position:0%
+minus sign so this is the uh freezing
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+depression uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case and you can you can also plot it on
+
+ align:start position:0%
+case and you can you can also plot it on
+ 
+
+ align:start position:0%
+case and you can you can also plot it on
+this diagram so if you have a
+
+ align:start position:0%
+this diagram so if you have a
+ 
+
+ align:start position:0%
+this diagram so if you have a
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+U here I enlarge this area so the black
+
+ align:start position:0%
+U here I enlarge this area so the black
+ 
+
+ align:start position:0%
+U here I enlarge this area so the black
+curves are the pure substance if you add
+
+ align:start position:0%
+curves are the pure substance if you add
+ 
+
+ align:start position:0%
+curves are the pure substance if you add
+a little bit of salt in the solution
+
+ align:start position:0%
+a little bit of salt in the solution
+ 
+
+ align:start position:0%
+a little bit of salt in the solution
+then this black curve shifts to the blue
+
+ align:start position:0%
+then this black curve shifts to the blue
+ 
+
+ align:start position:0%
+then this black curve shifts to the blue
+curve at lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temperature and then also the same for
+
+ align:start position:0%
+temperature and then also the same for
+ 
+
+ align:start position:0%
+temperature and then also the same for
+the other side for the
+
+ align:start position:0%
+the other side for the
+ 
+
+ align:start position:0%
+the other side for the
+uh for the other case liquid over Vapor
+
+ align:start position:0%
+uh for the other case liquid over Vapor
+ 
+
+ align:start position:0%
+uh for the other case liquid over Vapor
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+boiling of a uh salted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution here we have to start from the
+
+ align:start position:0%
+solution here we have to start from the
+ 
+
+ align:start position:0%
+solution here we have to start from the
+rout law written for these two phases f
+
+ align:start position:0%
+rout law written for these two phases f
+ 
+
+ align:start position:0%
+rout law written for these two phases f
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+g which is this one again we do the
+
+ align:start position:0%
+g which is this one again we do the
+ 
+
+ align:start position:0%
+g which is this one again we do the
+differential again we use the clus clap
+
+ align:start position:0%
+differential again we use the clus clap
+ 
+
+ align:start position:0%
+differential again we use the clus clap
+relation and again we obtain uh a
+
+ align:start position:0%
+relation and again we obtain uh a
+ 
+
+ align:start position:0%
+relation and again we obtain uh a
+partial derivative of T at constant
+
+ align:start position:0%
+partial derivative of T at constant
+ 
+
+ align:start position:0%
+partial derivative of T at constant
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+uh how that boiling temperature changes
+
+ align:start position:0%
+uh how that boiling temperature changes
+ 
+
+ align:start position:0%
+uh how that boiling temperature changes
+when you add a little amount
+
+ align:start position:0%
+when you add a little amount
+ 
+
+ align:start position:0%
+when you add a little amount
+of component two which is the salt this
+
+ align:start position:0%
+of component two which is the salt this
+ 
+
+ align:start position:0%
+of component two which is the salt this
+time you have a plus sign the
+
+ align:start position:0%
+time you have a plus sign the
+ 
+
+ align:start position:0%
+time you have a plus sign the
+ingredients on the left hand side that
+
+ align:start position:0%
+ingredients on the left hand side that
+ 
+
+ align:start position:0%
+ingredients on the left hand side that
+look similar except that of course you
+
+ align:start position:0%
+look similar except that of course you
+ 
+
+ align:start position:0%
+look similar except that of course you
+have to put
+
+ align:start position:0%
+have to put
+ 
+
+ align:start position:0%
+have to put
+here the enthalpy of vaporization
+
+ align:start position:0%
+here the enthalpy of vaporization
+ 
+
+ align:start position:0%
+here the enthalpy of vaporization
+whereas here you have the enthalpy
+
+ align:start position:0%
+whereas here you have the enthalpy
+ 
+
+ align:start position:0%
+whereas here you have the enthalpy
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+melting and the plus sign so the curve
+
+ align:start position:0%
+melting and the plus sign so the curve
+ 
+
+ align:start position:0%
+melting and the plus sign so the curve
+the shift is on the right so the boiling
+
+ align:start position:0%
+the shift is on the right so the boiling
+ 
+
+ align:start position:0%
+the shift is on the right so the boiling
+temperature is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+higher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+boiling and freezing
+
+ align:start position:0%
+boiling and freezing
+ 
+
+ align:start position:0%
+boiling and freezing
+effects can also be
+
+ align:start position:0%
+effects can also be
+ 
+
+ align:start position:0%
+effects can also be
+used as means to measure and are
+
+ align:start position:0%
+used as means to measure and are
+ 
+
+ align:start position:0%
+used as means to measure and are
+actually used as means to measure the
+
+ align:start position:0%
+actually used as means to measure the
+ 
+
+ align:start position:0%
+actually used as means to measure the
+Sal content for example you take sea
+
+ align:start position:0%
+Sal content for example you take sea
+ 
+
+ align:start position:0%
+Sal content for example you take sea
+water and if you want to measure the
+
+ align:start position:0%
+water and if you want to measure the
+ 
+
+ align:start position:0%
+water and if you want to measure the
+salt content you run the experiment of
+
+ align:start position:0%
+salt content you run the experiment of
+ 
+
+ align:start position:0%
+salt content you run the experiment of
+freezing it and boiling it and then uh
+
+ align:start position:0%
+freezing it and boiling it and then uh
+ 
+
+ align:start position:0%
+freezing it and boiling it and then uh
+with that you can compute uh you see
+
+ align:start position:0%
+with that you can compute uh you see
+ 
+
+ align:start position:0%
+with that you can compute uh you see
+here by measuring the delta T and
+
+ align:start position:0%
+here by measuring the delta T and
+ 
+
+ align:start position:0%
+here by measuring the delta T and
+uh that is related to the amount of uh
+
+ align:start position:0%
+uh that is related to the amount of uh
+ 
+
+ align:start position:0%
+uh that is related to the amount of uh
+of um of salt that is salt content and
+
+ align:start position:0%
+of um of salt that is salt content and
+ 
+
+ align:start position:0%
+of um of salt that is salt content and
+therefore you you infer from that
+
+ align:start position:0%
+therefore you you infer from that
+ 
+
+ align:start position:0%
+therefore you you infer from that
+measurements those measurements
+
+ align:start position:0%
+measurements those measurements
+ 
+
+ align:start position:0%
+measurements those measurements
+these composition and salt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+content
+
+ align:start position:0%
+content
+ 
+
+ align:start position:0%
+content
+okay okay the problem is that of
+
+ align:start position:0%
+okay okay the problem is that of
+ 
+
+ align:start position:0%
+okay okay the problem is that of
+course ideal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mixtures are good
+
+ align:start position:0%
+mixtures are good
+ 
+
+ align:start position:0%
+mixtures are good
+models for the gasos
+
+ align:start position:0%
+models for the gasos
+ 
+
+ align:start position:0%
+models for the gasos
+phases not so good for the liquid
+
+ align:start position:0%
+phases not so good for the liquid
+ 
+
+ align:start position:0%
+phases not so good for the liquid
+phases and therefore not so good for the
+
+ align:start position:0%
+phases and therefore not so good for the
+ 
+
+ align:start position:0%
+phases and therefore not so good for the
+liquid equilibrium cases we are
+
+ align:start position:0%
+liquid equilibrium cases we are
+ 
+
+ align:start position:0%
+liquid equilibrium cases we are
+interested in because uh the reality is
+
+ align:start position:0%
+interested in because uh the reality is
+ 
+
+ align:start position:0%
+interested in because uh the reality is
+more complex than the ideal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+models so we remind ourselves of some
+
+ align:start position:0%
+models so we remind ourselves of some
+ 
+
+ align:start position:0%
+models so we remind ourselves of some
+results that are useful uh any in any
+
+ align:start position:0%
+results that are useful uh any in any
+ 
+
+ align:start position:0%
+results that are useful uh any in any
+problem with mixtures it's going to be
+
+ align:start position:0%
+problem with mixtures it's going to be
+ 
+
+ align:start position:0%
+problem with mixtures it's going to be
+useful here
+
+ align:start position:0%
+useful here
+ 
+
+ align:start position:0%
+useful here
+and they are going to be useful also
+
+ align:start position:0%
+and they are going to be useful also
+ 
+
+ align:start position:0%
+and they are going to be useful also
+from I think the next time we will start
+
+ align:start position:0%
+from I think the next time we will start
+ 
+
+ align:start position:0%
+from I think the next time we will start
+the systems with chemical
+
+ align:start position:0%
+the systems with chemical
+ 
+
+ align:start position:0%
+the systems with chemical
+reactions and these and these
+
+ align:start position:0%
+reactions and these and these
+ 
+
+ align:start position:0%
+reactions and these and these
+expressions are uh important namely that
+
+ align:start position:0%
+expressions are uh important namely that
+ 
+
+ align:start position:0%
+expressions are uh important namely that
+the the properties are given by the
+
+ align:start position:0%
+the the properties are given by the
+ 
+
+ align:start position:0%
+the the properties are given by the
+weighted sum weighted on the amounts of
+
+ align:start position:0%
+weighted sum weighted on the amounts of
+ 
+
+ align:start position:0%
+weighted sum weighted on the amounts of
+the partial
+
+ align:start position:0%
+the partial
+ 
+
+ align:start position:0%
+the partial
+properties the lower case with this with
+
+ align:start position:0%
+properties the lower case with this with
+ 
+
+ align:start position:0%
+properties the lower case with this with
+with a single subscript
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then these partial properties can be
+
+ align:start position:0%
+and then these partial properties can be
+ 
+
+ align:start position:0%
+and then these partial properties can be
+related to
+
+ align:start position:0%
+related to
+ 
+
+ align:start position:0%
+related to
+the specific properties of pure
+
+ align:start position:0%
+the specific properties of pure
+ 
+
+ align:start position:0%
+the specific properties of pure
+substances if you add what we called the
+
+ align:start position:0%
+substances if you add what we called the
+ 
+
+ align:start position:0%
+substances if you add what we called the
+um the mixing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+property but uh now what I want
+
+ align:start position:0%
+property but uh now what I want
+ 
+
+ align:start position:0%
+property but uh now what I want
+to uh go back to is this result that we
+
+ align:start position:0%
+to uh go back to is this result that we
+ 
+
+ align:start position:0%
+to uh go back to is this result that we
+haven't uh um used yet it's the D
+
+ align:start position:0%
+haven't uh um used yet it's the D
+ 
+
+ align:start position:0%
+haven't uh um used yet it's the D
+margules
+
+ align:start position:0%
+margules
+ 
+
+ align:start position:0%
+margules
+relation that we obtained when we did
+
+ align:start position:0%
+relation that we obtained when we did
+ 
+
+ align:start position:0%
+relation that we obtained when we did
+this for the simple for the simple
+
+ align:start position:0%
+this for the simple for the simple
+ 
+
+ align:start position:0%
+this for the simple for the simple
+system it was one of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+various say byproduct of this
+
+ align:start position:0%
+various say byproduct of this
+ 
+
+ align:start position:0%
+various say byproduct of this
+derivation so the do margus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relation can is is this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and is important when you try to uh
+
+ align:start position:0%
+and is important when you try to uh
+ 
+
+ align:start position:0%
+and is important when you try to uh
+develop uh models for non ideal behavior
+
+ align:start position:0%
+develop uh models for non ideal behavior
+ 
+
+ align:start position:0%
+develop uh models for non ideal behavior
+of the stable equilibrium State
+
+ align:start position:0%
+of the stable equilibrium State
+ 
+
+ align:start position:0%
+of the stable equilibrium State
+properties of
+
+ align:start position:0%
+properties of
+ 
+
+ align:start position:0%
+properties of
+mixes why is it important because it
+
+ align:start position:0%
+mixes why is it important because it
+ 
+
+ align:start position:0%
+mixes why is it important because it
+imposes
+
+ align:start position:0%
+imposes
+ 
+
+ align:start position:0%
+imposes
+um uh in rules about the interrelations
+
+ align:start position:0%
+um uh in rules about the interrelations
+ 
+
+ align:start position:0%
+um uh in rules about the interrelations
+that must
+
+ align:start position:0%
+that must
+ 
+
+ align:start position:0%
+that must
+exist you see this is a system of
+
+ align:start position:0%
+exist you see this is a system of
+ 
+
+ align:start position:0%
+exist you see this is a system of
+equations it's not just one
+
+ align:start position:0%
+equations it's not just one
+ 
+
+ align:start position:0%
+equations it's not just one
+there is one for every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+component and so it's not that
+
+ align:start position:0%
+component and so it's not that
+ 
+
+ align:start position:0%
+component and so it's not that
+you you see when you want to uh model
+
+ align:start position:0%
+you you see when you want to uh model
+ 
+
+ align:start position:0%
+you you see when you want to uh model
+properties of substances you have to uh
+
+ align:start position:0%
+properties of substances you have to uh
+ 
+
+ align:start position:0%
+properties of substances you have to uh
+come up with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correlations for these functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you might be tempted to use any sort
+
+ align:start position:0%
+and you might be tempted to use any sort
+ 
+
+ align:start position:0%
+and you might be tempted to use any sort
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+analytical uh form of these inter
+
+ align:start position:0%
+analytical uh form of these inter
+ 
+
+ align:start position:0%
+analytical uh form of these inter
+relations but do margules says no or at
+
+ align:start position:0%
+relations but do margules says no or at
+ 
+
+ align:start position:0%
+relations but do margules says no or at
+least you you may try but you should
+
+ align:start position:0%
+least you you may try but you should
+ 
+
+ align:start position:0%
+least you you may try but you should
+check the consistency with this relation
+
+ align:start position:0%
+check the consistency with this relation
+ 
+
+ align:start position:0%
+check the consistency with this relation
+because not all relations are good for
+
+ align:start position:0%
+because not all relations are good for
+ 
+
+ align:start position:0%
+because not all relations are good for
+that purpose because some
+
+ align:start position:0%
+that purpose because some
+ 
+
+ align:start position:0%
+that purpose because some
+violate this
+
+ align:start position:0%
+violate this
+ 
+
+ align:start position:0%
+violate this
+condition actually this condition
+
+ align:start position:0%
+condition actually this condition
+ 
+
+ align:start position:0%
+condition actually this condition
+remember that mu I comma J is the
+
+ align:start position:0%
+remember that mu I comma J is the
+ 
+
+ align:start position:0%
+remember that mu I comma J is the
+derivative of the chemical potential of
+
+ align:start position:0%
+derivative of the chemical potential of
+ 
+
+ align:start position:0%
+derivative of the chemical potential of
+component I with respect to the amount
+
+ align:start position:0%
+component I with respect to the amount
+ 
+
+ align:start position:0%
+component I with respect to the amount
+of component
+
+ align:start position:0%
+of component
+ 
+
+ align:start position:0%
+of component
+J and so it is a second derivative of
+
+ align:start position:0%
+J and so it is a second derivative of
+ 
+
+ align:start position:0%
+J and so it is a second derivative of
+the Gibs free energy with respect to two
+
+ align:start position:0%
+the Gibs free energy with respect to two
+ 
+
+ align:start position:0%
+the Gibs free energy with respect to two
+different uh um
+
+ align:start position:0%
+different uh um
+ 
+
+ align:start position:0%
+different uh um
+components or also equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components now you can view this uh
+
+ align:start position:0%
+components now you can view this uh
+ 
+
+ align:start position:0%
+components now you can view this uh
+system of this system of equations as a
+
+ align:start position:0%
+system of this system of equations as a
+ 
+
+ align:start position:0%
+system of this system of equations as a
+homogeneous uh system of linear
+
+ align:start position:0%
+homogeneous uh system of linear
+ 
+
+ align:start position:0%
+homogeneous uh system of linear
+equations in the unknowns
+
+ align:start position:0%
+equations in the unknowns
+ 
+
+ align:start position:0%
+equations in the unknowns
+n where uh mu i j is the Matrix of uh
+
+ align:start position:0%
+n where uh mu i j is the Matrix of uh
+ 
+
+ align:start position:0%
+n where uh mu i j is the Matrix of uh
+the linear
+
+ align:start position:0%
+the linear
+ 
+
+ align:start position:0%
+the linear
+coefficients and if you if you go back
+
+ align:start position:0%
+coefficients and if you if you go back
+ 
+
+ align:start position:0%
+coefficients and if you if you go back
+into your math courses you will find
+
+ align:start position:0%
+into your math courses you will find
+ 
+
+ align:start position:0%
+into your math courses you will find
+that the system of homogeneous equations
+
+ align:start position:0%
+that the system of homogeneous equations
+ 
+
+ align:start position:0%
+that the system of homogeneous equations
+has a solution only if the
+
+ align:start position:0%
+has a solution only if the
+ 
+
+ align:start position:0%
+has a solution only if the
+determinant of the Matrix of the
+
+ align:start position:0%
+determinant of the Matrix of the
+ 
+
+ align:start position:0%
+determinant of the Matrix of the
+coefficients is equal to
+
+ align:start position:0%
+coefficients is equal to
+ 
+
+ align:start position:0%
+coefficients is equal to
+zero so but this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determinant in this Matrix is the Matrix
+
+ align:start position:0%
+determinant in this Matrix is the Matrix
+ 
+
+ align:start position:0%
+determinant in this Matrix is the Matrix
+that is that we called the uh H because
+
+ align:start position:0%
+that is that we called the uh H because
+ 
+
+ align:start position:0%
+that is that we called the uh H because
+you see it's the Matrix of the second
+
+ align:start position:0%
+you see it's the Matrix of the second
+ 
+
+ align:start position:0%
+you see it's the Matrix of the second
+derivatives and its
+
+ align:start position:0%
+derivatives and its
+ 
+
+ align:start position:0%
+derivatives and its
+determinant is also something that we
+
+ align:start position:0%
+determinant is also something that we
+ 
+
+ align:start position:0%
+determinant is also something that we
+have encountered it's the
+
+ align:start position:0%
+have encountered it's the
+ 
+
+ align:start position:0%
+have encountered it's the
+Jacobian of the chemical
+
+ align:start position:0%
+Jacobian of the chemical
+ 
+
+ align:start position:0%
+Jacobian of the chemical
+potentials with respect to the
+
+ align:start position:0%
+potentials with respect to the
+ 
+
+ align:start position:0%
+potentials with respect to the
+compositions of course done at constant
+
+ align:start position:0%
+compositions of course done at constant
+ 
+
+ align:start position:0%
+compositions of course done at constant
+T and
+
+ align:start position:0%
+T and
+ 
+
+ align:start position:0%
+T and
+P so you need that Jacobian to be equal
+
+ align:start position:0%
+P so you need that Jacobian to be equal
+ 
+
+ align:start position:0%
+P so you need that Jacobian to be equal
+to zero so that is the condition so you
+
+ align:start position:0%
+to zero so that is the condition so you
+ 
+
+ align:start position:0%
+to zero so that is the condition so you
+cannot arbitrarily select these
+
+ align:start position:0%
+cannot arbitrarily select these
+ 
+
+ align:start position:0%
+cannot arbitrarily select these
+functions you have to check that that
+
+ align:start position:0%
+functions you have to check that that
+ 
+
+ align:start position:0%
+functions you have to check that that
+Jacobian be equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as you
+
+ align:start position:0%
+as you
+ 
+
+ align:start position:0%
+as you
+know we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decided to call this functional
+
+ align:start position:0%
+decided to call this functional
+ 
+
+ align:start position:0%
+decided to call this functional
+relation uh the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ideal so and in fact we're going to call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+uh new I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea of t p and Y this is a particular
+
+ align:start position:0%
+idea of t p and Y this is a particular
+ 
+
+ align:start position:0%
+idea of t p and Y this is a particular
+functional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relation so we have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check that um it
+
+ align:start position:0%
+check that um it
+ 
+
+ align:start position:0%
+check that um it
+satisfies the do
+
+ align:start position:0%
+satisfies the do
+ 
+
+ align:start position:0%
+satisfies the do
+marulas theor or
+
+ align:start position:0%
+marulas theor or
+ 
+
+ align:start position:0%
+marulas theor or
+relation so here is the ideal
+
+ align:start position:0%
+relation so here is the ideal
+ 
+
+ align:start position:0%
+relation so here is the ideal
+mixture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assumption uh so in order to do this uh
+
+ align:start position:0%
+assumption uh so in order to do this uh
+ 
+
+ align:start position:0%
+assumption uh so in order to do this uh
+this derivative Computing this
+
+ align:start position:0%
+this derivative Computing this
+ 
+
+ align:start position:0%
+this derivative Computing this
+derivative you have to
+
+ align:start position:0%
+derivative you have to
+ 
+
+ align:start position:0%
+derivative you have to
+be a bit careful in do in doing those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivatives
+
+ align:start position:0%
+derivatives
+ 
+
+ align:start position:0%
+derivatives
+uh I think I forget now if we have done
+
+ align:start position:0%
+uh I think I forget now if we have done
+ 
+
+ align:start position:0%
+uh I think I forget now if we have done
+this already but uh um the the key Point
+
+ align:start position:0%
+this already but uh um the the key Point
+ 
+
+ align:start position:0%
+this already but uh um the the key Point
+here is that you have to take the
+
+ align:start position:0%
+here is that you have to take the
+ 
+
+ align:start position:0%
+here is that you have to take the
+derivative of mu with respect at fixed
+
+ align:start position:0%
+derivative of mu with respect at fixed
+ 
+
+ align:start position:0%
+derivative of mu with respect at fixed
+temperature and pressure so this doesn't
+
+ align:start position:0%
+temperature and pressure so this doesn't
+ 
+
+ align:start position:0%
+temperature and pressure so this doesn't
+contribute it's only the logarithm of
+
+ align:start position:0%
+contribute it's only the logarithm of
+ 
+
+ align:start position:0%
+contribute it's only the logarithm of
+the mole
+
+ align:start position:0%
+the mole
+ 
+
+ align:start position:0%
+the mole
+fraction so the logarithm of the mole
+
+ align:start position:0%
+fraction so the logarithm of the mole
+ 
+
+ align:start position:0%
+fraction so the logarithm of the mole
+fraction you have to take its
+
+ align:start position:0%
+fraction you have to take its
+ 
+
+ align:start position:0%
+fraction you have to take its
+derivative with respect to the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+njs okay so NJ now NJ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's easier to write it this way so I'm
+
+ align:start position:0%
+it's easier to write it this way so I'm
+ 
+
+ align:start position:0%
+it's easier to write it this way so I'm
+taking the derivative with respect to
+
+ align:start position:0%
+taking the derivative with respect to
+ 
+
+ align:start position:0%
+taking the derivative with respect to
+NJ of the logarithm of the mole fraction
+
+ align:start position:0%
+NJ of the logarithm of the mole fraction
+ 
+
+ align:start position:0%
+NJ of the logarithm of the mole fraction
+the mole fraction of component I is n
+
+ align:start position:0%
+the mole fraction of component I is n
+ 
+
+ align:start position:0%
+the mole fraction of component I is n
+i divided by the
+
+ align:start position:0%
+i divided by the
+ 
+
+ align:start position:0%
+i divided by the
+sum of all the NS
+
+ align:start position:0%
+sum of all the NS
+ 
+
+ align:start position:0%
+sum of all the NS
+let's use another subscript
+
+ align:start position:0%
+let's use another subscript
+ 
+
+ align:start position:0%
+let's use another subscript
+K all right so that
+
+ align:start position:0%
+K all right so that
+ 
+
+ align:start position:0%
+K all right so that
+means that sometimes you find uh you
+
+ align:start position:0%
+means that sometimes you find uh you
+ 
+
+ align:start position:0%
+means that sometimes you find uh you
+have a contribution
+
+ align:start position:0%
+have a contribution
+ 
+
+ align:start position:0%
+have a contribution
+ution of the numerator When J is equal
+
+ align:start position:0%
+ution of the numerator When J is equal
+ 
+
+ align:start position:0%
+ution of the numerator When J is equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+I and that's why I use the chroner Delta
+
+ align:start position:0%
+I and that's why I use the chroner Delta
+ 
+
+ align:start position:0%
+I and that's why I use the chroner Delta
+and then uh that contribution is simply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh what one over the mole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fraction okay something like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and sorry not uh correct it's and
+
+ align:start position:0%
+and sorry not uh correct it's and
+ 
+
+ align:start position:0%
+and sorry not uh correct it's and
+subai because it's the
+
+ align:start position:0%
+subai because it's the
+ 
+
+ align:start position:0%
+subai because it's the
+logarithm the derivative of the
+
+ align:start position:0%
+logarithm the derivative of the
+ 
+
+ align:start position:0%
+logarithm the derivative of the
+logarithm is one
+
+ align:start position:0%
+logarithm is one
+ 
+
+ align:start position:0%
+logarithm is one
+over the the
+
+ align:start position:0%
+over the the
+ 
+
+ align:start position:0%
+over the the
+argument and then
+
+ align:start position:0%
+argument and then
+ 
+
+ align:start position:0%
+argument and then
+uh sometimes
+
+ align:start position:0%
+uh sometimes
+ 
+
+ align:start position:0%
+uh sometimes
+the derivative picks up something from
+
+ align:start position:0%
+the derivative picks up something from
+ 
+
+ align:start position:0%
+the derivative picks up something from
+the denominator the denominator this
+
+ align:start position:0%
+the denominator the denominator this
+ 
+
+ align:start position:0%
+the denominator the denominator this
+could be viewed as that is a constant so
+
+ align:start position:0%
+could be viewed as that is a constant so
+ 
+
+ align:start position:0%
+could be viewed as that is a constant so
+that is a log minus log of the of of
+
+ align:start position:0%
+that is a log minus log of the of of
+ 
+
+ align:start position:0%
+that is a log minus log of the of of
+this so it would be minus
+
+ align:start position:0%
+this so it would be minus
+ 
+
+ align:start position:0%
+this so it would be minus
+one over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n yeah so that's written here now that
+
+ align:start position:0%
+n yeah so that's written here now that
+ 
+
+ align:start position:0%
+n yeah so that's written here now that
+you've taken this this
+
+ align:start position:0%
+you've taken this this
+ 
+
+ align:start position:0%
+you've taken this this
+derivative you can substitute itute into
+
+ align:start position:0%
+derivative you can substitute itute into
+ 
+
+ align:start position:0%
+derivative you can substitute itute into
+here so you sum over
+
+ align:start position:0%
+here so you sum over
+ 
+
+ align:start position:0%
+here so you sum over
+n and verify that indeed that is equal
+
+ align:start position:0%
+n and verify that indeed that is equal
+ 
+
+ align:start position:0%
+n and verify that indeed that is equal
+to zero
+
+ align:start position:0%
+to zero
+ 
+
+ align:start position:0%
+to zero
+identically so
+
+ align:start position:0%
+identically so
+ 
+
+ align:start position:0%
+identically so
+obviously people have been careful in uh
+
+ align:start position:0%
+obviously people have been careful in uh
+ 
+
+ align:start position:0%
+obviously people have been careful in uh
+uh D people and also ourselves when we
+
+ align:start position:0%
+uh D people and also ourselves when we
+ 
+
+ align:start position:0%
+uh D people and also ourselves when we
+derive this we did it using the rules of
+
+ align:start position:0%
+derive this we did it using the rules of
+ 
+
+ align:start position:0%
+derive this we did it using the rules of
+the game and therefore it does uh obey
+
+ align:start position:0%
+the game and therefore it does uh obey
+ 
+
+ align:start position:0%
+the game and therefore it does uh obey
+the uh the marulas D marulas relation
+
+ align:start position:0%
+the uh the marulas D marulas relation
+ 
+
+ align:start position:0%
+the uh the marulas D marulas relation
+but when you when you start uh uh
+
+ align:start position:0%
+but when you when you start uh uh
+ 
+
+ align:start position:0%
+but when you when you start uh uh
+correlating experimental data for non-
+
+ align:start position:0%
+correlating experimental data for non-
+ 
+
+ align:start position:0%
+correlating experimental data for non-
+ideal
+
+ align:start position:0%
+ideal
+ 
+
+ align:start position:0%
+ideal
+Behavior you have to be uh careful in U
+
+ align:start position:0%
+Behavior you have to be uh careful in U
+ 
+
+ align:start position:0%
+Behavior you have to be uh careful in U
+cooking up uh functional relations that
+
+ align:start position:0%
+cooking up uh functional relations that
+ 
+
+ align:start position:0%
+cooking up uh functional relations that
+are U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compatible and this uh if you remember
+
+ align:start position:0%
+compatible and this uh if you remember
+ 
+
+ align:start position:0%
+compatible and this uh if you remember
+now that so
+
+ align:start position:0%
+now that so
+ 
+
+ align:start position:0%
+now that so
+um here it is so if we write we're going
+
+ align:start position:0%
+um here it is so if we write we're going
+ 
+
+ align:start position:0%
+um here it is so if we write we're going
+to decide to write uh the
+
+ align:start position:0%
+to decide to write uh the
+ 
+
+ align:start position:0%
+to decide to write uh the
+actual chemical potential as a sum of
+
+ align:start position:0%
+actual chemical potential as a sum of
+ 
+
+ align:start position:0%
+actual chemical potential as a sum of
+the ideal
+
+ align:start position:0%
+the ideal
+ 
+
+ align:start position:0%
+the ideal
+plus excess so in other words we we are
+
+ align:start position:0%
+plus excess so in other words we we are
+ 
+
+ align:start position:0%
+plus excess so in other words we we are
+going to call excess chemical potential
+
+ align:start position:0%
+going to call excess chemical potential
+ 
+
+ align:start position:0%
+going to call excess chemical potential
+the difference between the actual
+
+ align:start position:0%
+the difference between the actual
+ 
+
+ align:start position:0%
+the difference between the actual
+chemical potential and what uh uh and
+
+ align:start position:0%
+chemical potential and what uh uh and
+ 
+
+ align:start position:0%
+chemical potential and what uh uh and
+this ideal
+
+ align:start position:0%
+this ideal
+ 
+
+ align:start position:0%
+this ideal
+one so essentially we're going to
+
+ align:start position:0%
+one so essentially we're going to
+ 
+
+ align:start position:0%
+one so essentially we're going to
+say for the real
+
+ align:start position:0%
+say for the real
+ 
+
+ align:start position:0%
+say for the real
+uh substance for for the real
+
+ align:start position:0%
+uh substance for for the real
+ 
+
+ align:start position:0%
+uh substance for for the real
+mixture we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+need to Define how the behavior departs
+
+ align:start position:0%
+need to Define how the behavior departs
+ 
+
+ align:start position:0%
+need to Define how the behavior departs
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+ideal and this is called excess chemical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential or remember also
+
+ align:start position:0%
+potential or remember also
+ 
+
+ align:start position:0%
+potential or remember also
+this more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+chemical potentials of the pure
+
+ align:start position:0%
+chemical potentials of the pure
+ 
+
+ align:start position:0%
+chemical potentials of the pure
+substance are
+
+ align:start position:0%
+substance are
+ 
+
+ align:start position:0%
+substance are
+equal to the Gibs free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy so the to the specific GS free
+
+ align:start position:0%
+energy so the to the specific GS free
+ 
+
+ align:start position:0%
+energy so the to the specific GS free
+energy this will come
+
+ align:start position:0%
+energy this will come
+ 
+
+ align:start position:0%
+energy this will come
+up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also uh
+
+ align:start position:0%
+also uh
+ 
+
+ align:start position:0%
+also uh
+since we have defined uh these
+
+ align:start position:0%
+since we have defined uh these
+ 
+
+ align:start position:0%
+since we have defined uh these
+properties of uh of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mixing by the way we Define them it
+
+ align:start position:0%
+mixing by the way we Define them it
+ 
+
+ align:start position:0%
+mixing by the way we Define them it
+turns out that what we decided to call
+
+ align:start position:0%
+turns out that what we decided to call
+ 
+
+ align:start position:0%
+turns out that what we decided to call
+the excess chemical potential is equal
+
+ align:start position:0%
+the excess chemical potential is equal
+ 
+
+ align:start position:0%
+the excess chemical potential is equal
+to the difference between the enthalpy
+
+ align:start position:0%
+to the difference between the enthalpy
+ 
+
+ align:start position:0%
+to the difference between the enthalpy
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+mixing and the entropy of mixing
+
+ align:start position:0%
+mixing and the entropy of mixing
+ 
+
+ align:start position:0%
+mixing and the entropy of mixing
+multiplied by the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temperature not quite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only that part of the entropy of mixing
+
+ align:start position:0%
+only that part of the entropy of mixing
+ 
+
+ align:start position:0%
+only that part of the entropy of mixing
+that is not already included in the RT
+
+ align:start position:0%
+that is not already included in the RT
+ 
+
+ align:start position:0%
+that is not already included in the RT
+log of
+
+ align:start position:0%
+log of
+ 
+
+ align:start position:0%
+log of
+Y so you see here we call that the Delta
+
+ align:start position:0%
+Y so you see here we call that the Delta
+ 
+
+ align:start position:0%
+Y so you see here we call that the Delta
+s x so it it is an
+
+ align:start position:0%
+s x so it it is an
+ 
+
+ align:start position:0%
+s x so it it is an
+excess entropy of mixing because in the
+
+ align:start position:0%
+excess entropy of mixing because in the
+ 
+
+ align:start position:0%
+excess entropy of mixing because in the
+ideal solution there is a mixing effect
+
+ align:start position:0%
+ideal solution there is a mixing effect
+ 
+
+ align:start position:0%
+ideal solution there is a mixing effect
+that counts for that remember the
+
+ align:start position:0%
+that counts for that remember the
+ 
+
+ align:start position:0%
+that counts for that remember the
+surprise discussion uh counts with that
+
+ align:start position:0%
+surprise discussion uh counts with that
+ 
+
+ align:start position:0%
+surprise discussion uh counts with that
+R log of of Y this is the surprise and
+
+ align:start position:0%
+R log of of Y this is the surprise and
+ 
+
+ align:start position:0%
+R log of of Y this is the surprise and
+this is an
+
+ align:start position:0%
+this is an
+ 
+
+ align:start position:0%
+this is an
+entropy a part of the
+
+ align:start position:0%
+entropy a part of the
+ 
+
+ align:start position:0%
+entropy a part of the
+entropy of of the mixing entropy it's
+
+ align:start position:0%
+entropy of of the mixing entropy it's
+ 
+
+ align:start position:0%
+entropy of of the mixing entropy it's
+the only mixing entropy that we
+
+ align:start position:0%
+the only mixing entropy that we
+ 
+
+ align:start position:0%
+the only mixing entropy that we
+have uh under ideal behavior and you may
+
+ align:start position:0%
+have uh under ideal behavior and you may
+ 
+
+ align:start position:0%
+have uh under ideal behavior and you may
+have some extra some excess one
+
+ align:start position:0%
+have some extra some excess one
+ 
+
+ align:start position:0%
+have some extra some excess one
+so that's why we call we say here
+
+ align:start position:0%
+so that's why we call we say here
+ 
+
+ align:start position:0%
+so that's why we call we say here
+chemical potential
+
+ align:start position:0%
+chemical potential
+ 
+
+ align:start position:0%
+chemical potential
+excess is equal to the entire enthalpy
+
+ align:start position:0%
+excess is equal to the entire enthalpy
+ 
+
+ align:start position:0%
+excess is equal to the entire enthalpy
+of mixing because for the ideal mixture
+
+ align:start position:0%
+of mixing because for the ideal mixture
+ 
+
+ align:start position:0%
+of mixing because for the ideal mixture
+there is no enthalpy of
+
+ align:start position:0%
+there is no enthalpy of
+ 
+
+ align:start position:0%
+there is no enthalpy of
+mixing and only this uh excess part of
+
+ align:start position:0%
+mixing and only this uh excess part of
+ 
+
+ align:start position:0%
+mixing and only this uh excess part of
+the entropy of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mixing
+
+ align:start position:0%
+mixing
+ 
+
+ align:start position:0%
+mixing
+Okay so with that in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mind of course the another thing that we
+
+ align:start position:0%
+mind of course the another thing that we
+ 
+
+ align:start position:0%
+mind of course the another thing that we
+should remember is that the Gibs free
+
+ align:start position:0%
+should remember is that the Gibs free
+ 
+
+ align:start position:0%
+should remember is that the Gibs free
+energy if we are interested in the Gibs
+
+ align:start position:0%
+energy if we are interested in the Gibs
+ 
+
+ align:start position:0%
+energy if we are interested in the Gibs
+free energy of our entire mixture that
+
+ align:start position:0%
+free energy of our entire mixture that
+ 
+
+ align:start position:0%
+free energy of our entire mixture that
+is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and so if you want you can also
+
+ align:start position:0%
+this and so if you want you can also
+ 
+
+ align:start position:0%
+this and so if you want you can also
+Define parallel with the fact that we
+
+ align:start position:0%
+Define parallel with the fact that we
+ 
+
+ align:start position:0%
+Define parallel with the fact that we
+decided to write the chemical potential
+
+ align:start position:0%
+decided to write the chemical potential
+ 
+
+ align:start position:0%
+decided to write the chemical potential
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+mui ideal plus mui excess you can also
+
+ align:start position:0%
+mui ideal plus mui excess you can also
+ 
+
+ align:start position:0%
+mui ideal plus mui excess you can also
+plug that into here and obtain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a overall mixture uh gives free energy
+
+ align:start position:0%
+a overall mixture uh gives free energy
+ 
+
+ align:start position:0%
+a overall mixture uh gives free energy
+as a sum of an ideal part and an excess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part with that in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mind here is for example for a binary
+
+ align:start position:0%
+mind here is for example for a binary
+ 
+
+ align:start position:0%
+mind here is for example for a binary
+mixture let's
+
+ align:start position:0%
+mixture let's
+ 
+
+ align:start position:0%
+mixture let's
+fix this limit for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ourselves binary
+
+ align:start position:0%
+ourselves binary
+ 
+
+ align:start position:0%
+ourselves binary
+mixture uh here is the expression for
+
+ align:start position:0%
+mixture uh here is the expression for
+ 
+
+ align:start position:0%
+mixture uh here is the expression for
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+specific gives free energy so now if I
+
+ align:start position:0%
+specific gives free energy so now if I
+ 
+
+ align:start position:0%
+specific gives free energy so now if I
+take this
+
+ align:start position:0%
+take this
+ 
+
+ align:start position:0%
+take this
+G and divide by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n that gives me G Over N
+
+ align:start position:0%
+n that gives me G Over N
+ 
+
+ align:start position:0%
+n that gives me G Over N
+okay of course that summation becomes
+
+ align:start position:0%
+okay of course that summation becomes
+ 
+
+ align:start position:0%
+okay of course that summation becomes
+the mole fractions weighted chemical
+
+ align:start position:0%
+the mole fractions weighted chemical
+ 
+
+ align:start position:0%
+the mole fractions weighted chemical
+potentials and this becomes
+
+ align:start position:0%
+potentials and this becomes
+ 
+
+ align:start position:0%
+potentials and this becomes
+G Plus g x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G is therefore the weighted sum of the
+
+ align:start position:0%
+G is therefore the weighted sum of the
+ 
+
+ align:start position:0%
+G is therefore the weighted sum of the
+ideal chemical potentials weighted on
+
+ align:start position:0%
+ideal chemical potentials weighted on
+ 
+
+ align:start position:0%
+ideal chemical potentials weighted on
+the mole fractions and the ideal
+
+ align:start position:0%
+the mole fractions and the ideal
+ 
+
+ align:start position:0%
+the mole fractions and the ideal
+chemical potentials are these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ones so if I take that let's see if I
+
+ align:start position:0%
+ones so if I take that let's see if I
+ 
+
+ align:start position:0%
+ones so if I take that let's see if I
+can do this game like this take the
+
+ align:start position:0%
+can do this game like this take the
+ 
+
+ align:start position:0%
+can do this game like this take the
+weighted sum of these
+
+ align:start position:0%
+weighted sum of these
+ 
+
+ align:start position:0%
+weighted sum of these
+ones that gives me
+
+ align:start position:0%
+ones that gives me
+ 
+
+ align:start position:0%
+ones that gives me
+G small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ID okay so you see that in
+
+ align:start position:0%
+ID okay so you see that in
+ 
+
+ align:start position:0%
+ID okay so you see that in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+summation I have two contributions one
+
+ align:start position:0%
+summation I have two contributions one
+ 
+
+ align:start position:0%
+summation I have two contributions one
+is the weighted sum on the mo fractions
+
+ align:start position:0%
+is the weighted sum on the mo fractions
+ 
+
+ align:start position:0%
+is the weighted sum on the mo fractions
+of the pure component chemical
+
+ align:start position:0%
+of the pure component chemical
+ 
+
+ align:start position:0%
+of the pure component chemical
+potentials which are equal to the pure
+
+ align:start position:0%
+potentials which are equal to the pure
+ 
+
+ align:start position:0%
+potentials which are equal to the pure
+component gives three energies and that
+
+ align:start position:0%
+component gives three energies and that
+ 
+
+ align:start position:0%
+component gives three energies and that
+is this plus
+
+ align:start position:0%
+is this plus
+ 
+
+ align:start position:0%
+is this plus
+this because in this case binary mixture
+
+ align:start position:0%
+this because in this case binary mixture
+ 
+
+ align:start position:0%
+this because in this case binary mixture
+the sum is just limited to two
+
+ align:start position:0%
+the sum is just limited to two
+ 
+
+ align:start position:0%
+the sum is just limited to two
+components okay and then I have this
+
+ align:start position:0%
+components okay and then I have this
+ 
+
+ align:start position:0%
+components okay and then I have this
+this other summation that is here it's
+
+ align:start position:0%
+this other summation that is here it's
+ 
+
+ align:start position:0%
+this other summation that is here it's
+RT times the sum of Y log y That's the
+
+ align:start position:0%
+RT times the sum of Y log y That's the
+ 
+
+ align:start position:0%
+RT times the sum of Y log y That's the
+entropy of
+
+ align:start position:0%
+entropy of
+ 
+
+ align:start position:0%
+entropy of
+mixing isobaric
+
+ align:start position:0%
+mixing isobaric
+ 
+
+ align:start position:0%
+mixing isobaric
+mixing okay so that's the G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and these are the ideal chemical
+
+ align:start position:0%
+and these are the ideal chemical
+ 
+
+ align:start position:0%
+and these are the ideal chemical
+potentials and then we recall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that now below here I have listed some
+
+ align:start position:0%
+that now below here I have listed some
+ 
+
+ align:start position:0%
+that now below here I have listed some
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+historical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um guesses or sort of um
+
+ align:start position:0%
+um guesses or sort of um
+ 
+
+ align:start position:0%
+um guesses or sort of um
+semiempirical uh theories that have been
+
+ align:start position:0%
+semiempirical uh theories that have been
+ 
+
+ align:start position:0%
+semiempirical uh theories that have been
+developed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in order to come
+
+ align:start position:0%
+in order to come
+ 
+
+ align:start position:0%
+in order to come
+up uh with ways of representing the
+
+ align:start position:0%
+up uh with ways of representing the
+ 
+
+ align:start position:0%
+up uh with ways of representing the
+excess part so the the non ideal part of
+
+ align:start position:0%
+excess part so the the non ideal part of
+ 
+
+ align:start position:0%
+excess part so the the non ideal part of
+the behavior of
+
+ align:start position:0%
+the behavior of
+ 
+
+ align:start position:0%
+the behavior of
+mixtures the simplest
+
+ align:start position:0%
+mixtures the simplest
+ 
+
+ align:start position:0%
+mixtures the simplest
+one by
+
+ align:start position:0%
+one by
+ 
+
+ align:start position:0%
+one by
+margules see this is 19 18
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+yeah my grand father was 1889
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so he was six years
+
+ align:start position:0%
+so he was six years
+ 
+
+ align:start position:0%
+so he was six years
+old uh
+
+ align:start position:0%
+old uh
+ 
+
+ align:start position:0%
+old uh
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+GX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh is so it's so it's assumed to be like
+
+ align:start position:0%
+uh is so it's so it's assumed to be like
+ 
+
+ align:start position:0%
+uh is so it's so it's assumed to be like
+like symmetric a single parameter which
+
+ align:start position:0%
+like symmetric a single parameter which
+ 
+
+ align:start position:0%
+like symmetric a single parameter which
+may depend on temperature and
+
+ align:start position:0%
+may depend on temperature and
+ 
+
+ align:start position:0%
+may depend on temperature and
+pressure but the dependence composition
+
+ align:start position:0%
+pressure but the dependence composition
+ 
+
+ align:start position:0%
+pressure but the dependence composition
+is just the product of the two more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fractions and if you do
+
+ align:start position:0%
+fractions and if you do
+ 
+
+ align:start position:0%
+fractions and if you do
+the uh the proper derivatives in order
+
+ align:start position:0%
+the uh the proper derivatives in order
+ 
+
+ align:start position:0%
+the uh the proper derivatives in order
+to to obtain the the the excess chemical
+
+ align:start position:0%
+to to obtain the the the excess chemical
+ 
+
+ align:start position:0%
+to to obtain the the the excess chemical
+potential that derives from
+
+ align:start position:0%
+potential that derives from
+ 
+
+ align:start position:0%
+potential that derives from
+that you find that the chemical potent
+
+ align:start position:0%
+that you find that the chemical potent
+ 
+
+ align:start position:0%
+that you find that the chemical potent
+the excess chemical potential of
+
+ align:start position:0%
+the excess chemical potential of
+ 
+
+ align:start position:0%
+the excess chemical potential of
+component one is equal to that function
+
+ align:start position:0%
+component one is equal to that function
+ 
+
+ align:start position:0%
+component one is equal to that function
+to that let's call it Con Conant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a constant in terms that it doesn't
+
+ align:start position:0%
+a constant in terms that it doesn't
+ 
+
+ align:start position:0%
+a constant in terms that it doesn't
+depend on composition times the square
+
+ align:start position:0%
+depend on composition times the square
+ 
+
+ align:start position:0%
+depend on composition times the square
+of the mole fraction of the other
+
+ align:start position:0%
+of the mole fraction of the other
+ 
+
+ align:start position:0%
+of the mole fraction of the other
+component and the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here if you go down below here uh I have
+
+ align:start position:0%
+here if you go down below here uh I have
+ 
+
+ align:start position:0%
+here if you go down below here uh I have
+written an expression that um we
+
+ align:start position:0%
+written an expression that um we
+ 
+
+ align:start position:0%
+written an expression that um we
+have derived y
+
+ align:start position:0%
+have derived y
+ 
+
+ align:start position:0%
+have derived y
+ago that
+
+ align:start position:0%
+ago that
+ 
+
+ align:start position:0%
+ago that
+relates
+
+ align:start position:0%
+relates
+ 
+
+ align:start position:0%
+relates
+the uh enthalpy of mixing to the
+
+ align:start position:0%
+the uh enthalpy of mixing to the
+ 
+
+ align:start position:0%
+the uh enthalpy of mixing to the
+chemical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually since for the ideal uh chemical
+
+ align:start position:0%
+actually since for the ideal uh chemical
+ 
+
+ align:start position:0%
+actually since for the ideal uh chemical
+potential there is no enthalpy of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mixing and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if I if I take this expression here
+
+ align:start position:0%
+okay if I if I take this expression here
+ 
+
+ align:start position:0%
+okay if I if I take this expression here
+and uh uh do this
+
+ align:start position:0%
+and uh uh do this
+ 
+
+ align:start position:0%
+and uh uh do this
+derivative I obtain let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see uh so that's
+
+ align:start position:0%
+see uh so that's
+ 
+
+ align:start position:0%
+see uh so that's
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Y2 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t with
+
+ align:start position:0%
+t with
+ 
+
+ align:start position:0%
+t with
+respect to one over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's so it's a so it's it's equal to the
+
+ align:start position:0%
+it's so it's a so it's it's equal to the
+ 
+
+ align:start position:0%
+it's so it's a so it's it's equal to the
+chemical potential itself yeah there it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is because you divide by T div and take
+
+ align:start position:0%
+is because you divide by T div and take
+ 
+
+ align:start position:0%
+is because you divide by T div and take
+the derivative with respect to one / T
+
+ align:start position:0%
+the derivative with respect to one / T
+ 
+
+ align:start position:0%
+the derivative with respect to one / T
+that's just the one / T So derivative
+
+ align:start position:0%
+that's just the one / T So derivative
+ 
+
+ align:start position:0%
+that's just the one / T So derivative
+some simply
+
+ align:start position:0%
+some simply
+ 
+
+ align:start position:0%
+some simply
+one okay so
+
+ align:start position:0%
+one okay so
+ 
+
+ align:start position:0%
+one okay so
+it means that this so the the chemical
+
+ align:start position:0%
+it means that this so the the chemical
+ 
+
+ align:start position:0%
+it means that this so the the chemical
+the enthalpy of mixing is a Y2 so in the
+
+ align:start position:0%
+the enthalpy of mixing is a Y2 so in the
+ 
+
+ align:start position:0%
+the enthalpy of mixing is a Y2 so in the
+limit when Y2 is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 it means that the constant a
+
+ align:start position:0%
+1 it means that the constant a
+ 
+
+ align:start position:0%
+1 it means that the constant a
+represents the the enthalpy of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mixing and remember the
+
+ align:start position:0%
+mixing and remember the
+ 
+
+ align:start position:0%
+mixing and remember the
+enthalpy the mixing yeah the enthalpy of
+
+ align:start position:0%
+enthalpy the mixing yeah the enthalpy of
+ 
+
+ align:start position:0%
+enthalpy the mixing yeah the enthalpy of
+mixing is u
+
+ align:start position:0%
+mixing is u
+ 
+
+ align:start position:0%
+mixing is u
+um is the change in in enthalpy when you
+
+ align:start position:0%
+um is the change in in enthalpy when you
+ 
+
+ align:start position:0%
+um is the change in in enthalpy when you
+add a little bit of of that of substance
+
+ align:start position:0%
+add a little bit of of that of substance
+ 
+
+ align:start position:0%
+add a little bit of of that of substance
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+a a a mixture when in which uh the
+
+ align:start position:0%
+a a a mixture when in which uh the
+ 
+
+ align:start position:0%
+a a a mixture when in which uh the
+predominant component is
+
+ align:start position:0%
+predominant component is
+ 
+
+ align:start position:0%
+predominant component is
+two that's why we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evaluate we evaluate it at uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um at Y2 Y2 equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 but you can also find the same for the
+
+ align:start position:0%
+1 but you can also find the same for the
+ 
+
+ align:start position:0%
+1 but you can also find the same for the
+component one so it turns out that
+
+ align:start position:0%
+component one so it turns out that
+ 
+
+ align:start position:0%
+component one so it turns out that
+constant a is also equal to the to the
+
+ align:start position:0%
+constant a is also equal to the to the
+ 
+
+ align:start position:0%
+constant a is also equal to the to the
+mixing enthalpy of component two in in
+
+ align:start position:0%
+mixing enthalpy of component two in in
+ 
+
+ align:start position:0%
+mixing enthalpy of component two in in
+pure so essentially this says that the
+
+ align:start position:0%
+pure so essentially this says that the
+ 
+
+ align:start position:0%
+pure so essentially this says that the
+marulas one parameter model is able to
+
+ align:start position:0%
+marulas one parameter model is able to
+ 
+
+ align:start position:0%
+marulas one parameter model is able to
+modeling only liquid mixtures in which
+
+ align:start position:0%
+modeling only liquid mixtures in which
+ 
+
+ align:start position:0%
+modeling only liquid mixtures in which
+the effect of adding component one to
+
+ align:start position:0%
+the effect of adding component one to
+ 
+
+ align:start position:0%
+the effect of adding component one to
+Pure two is equal to the effect of
+
+ align:start position:0%
+Pure two is equal to the effect of
+ 
+
+ align:start position:0%
+Pure two is equal to the effect of
+adding component two to Pure one so in
+
+ align:start position:0%
+adding component two to Pure one so in
+ 
+
+ align:start position:0%
+adding component two to Pure one so in
+other words this
+
+ align:start position:0%
+other words this
+ 
+
+ align:start position:0%
+other words this
+mixture uh is very symmetric molecules
+
+ align:start position:0%
+mixture uh is very symmetric molecules
+ 
+
+ align:start position:0%
+mixture uh is very symmetric molecules
+are very uh similar to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another so he developed a two parameter
+
+ align:start position:0%
+another so he developed a two parameter
+ 
+
+ align:start position:0%
+another so he developed a two parameter
+model is slightly more complicated but
+
+ align:start position:0%
+model is slightly more complicated but
+ 
+
+ align:start position:0%
+model is slightly more complicated but
+at least I have two parameters and these
+
+ align:start position:0%
+at least I have two parameters and these
+ 
+
+ align:start position:0%
+at least I have two parameters and these
+two parameters turn out to
+
+ align:start position:0%
+two parameters turn out to
+ 
+
+ align:start position:0%
+two parameters turn out to
+be related to The Mixing enthalpies of
+
+ align:start position:0%
+be related to The Mixing enthalpies of
+ 
+
+ align:start position:0%
+be related to The Mixing enthalpies of
+the two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components which makes more sense
+
+ align:start position:0%
+components which makes more sense
+ 
+
+ align:start position:0%
+components which makes more sense
+because uh if I have a bunch of water
+
+ align:start position:0%
+because uh if I have a bunch of water
+ 
+
+ align:start position:0%
+because uh if I have a bunch of water
+and put some alcohol in it I obtain a
+
+ align:start position:0%
+and put some alcohol in it I obtain a
+ 
+
+ align:start position:0%
+and put some alcohol in it I obtain a
+different effect than if I had a bunch
+
+ align:start position:0%
+different effect than if I had a bunch
+ 
+
+ align:start position:0%
+different effect than if I had a bunch
+of alcohol and I put some water in it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so this is margul two parameters van
+
+ align:start position:0%
+and so this is margul two parameters van
+ 
+
+ align:start position:0%
+and so this is margul two parameters van
+lar also is a two parameter some sort of
+
+ align:start position:0%
+lar also is a two parameter some sort of
+ 
+
+ align:start position:0%
+lar also is a two parameter some sort of
+an inverse of marus 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parameter it
+
+ align:start position:0%
+parameter it
+ 
+
+ align:start position:0%
+parameter it
+also of course
+
+ align:start position:0%
+also of course
+ 
+
+ align:start position:0%
+also of course
+satisfies the do and
+
+ align:start position:0%
+satisfies the do and
+ 
+
+ align:start position:0%
+satisfies the do and
+margus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condition and again these A and B are
+
+ align:start position:0%
+condition and again these A and B are
+ 
+
+ align:start position:0%
+condition and again these A and B are
+related to the delta when you write it
+
+ align:start position:0%
+related to the delta when you write it
+ 
+
+ align:start position:0%
+related to the delta when you write it
+this way are related to The Mixing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enthalpies but two
+
+ align:start position:0%
+enthalpies but two
+ 
+
+ align:start position:0%
+enthalpies but two
+parameters for many many mixtures are
+
+ align:start position:0%
+parameters for many many mixtures are
+ 
+
+ align:start position:0%
+parameters for many many mixtures are
+not enough
+
+ align:start position:0%
+not enough
+ 
+
+ align:start position:0%
+not enough
+because molecules may be very different
+
+ align:start position:0%
+because molecules may be very different
+ 
+
+ align:start position:0%
+because molecules may be very different
+you may have long molecules small
+
+ align:start position:0%
+you may have long molecules small
+ 
+
+ align:start position:0%
+you may have long molecules small
+molecules you have to account for the
+
+ align:start position:0%
+molecules you have to account for the
+ 
+
+ align:start position:0%
+molecules you have to account for the
+fact that maybe a long molec is
+
+ align:start position:0%
+fact that maybe a long molec is
+ 
+
+ align:start position:0%
+fact that maybe a long molec is
+surrounded by many small molecules and
+
+ align:start position:0%
+surrounded by many small molecules and
+ 
+
+ align:start position:0%
+surrounded by many small molecules and
+so you need more parameters for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reality and people over and over have
+
+ align:start position:0%
+reality and people over and over have
+ 
+
+ align:start position:0%
+reality and people over and over have
+developed models with more parameters
+
+ align:start position:0%
+developed models with more parameters
+ 
+
+ align:start position:0%
+developed models with more parameters
+they all satisfy the D margus relation
+
+ align:start position:0%
+they all satisfy the D margus relation
+ 
+
+ align:start position:0%
+they all satisfy the D margus relation
+for example this
+
+ align:start position:0%
+for example this
+ 
+
+ align:start position:0%
+for example this
+one was considered by gugenheim and then
+
+ align:start position:0%
+one was considered by gugenheim and then
+ 
+
+ align:start position:0%
+one was considered by gugenheim and then
+became famous under the name of redlick
+
+ align:start position:0%
+became famous under the name of redlick
+ 
+
+ align:start position:0%
+became famous under the name of redlick
+ker uh this other
+
+ align:start position:0%
+ker uh this other
+ 
+
+ align:start position:0%
+ker uh this other
+one was developed by Wilson it's not the
+
+ align:start position:0%
+one was developed by Wilson it's not the
+ 
+
+ align:start position:0%
+one was developed by Wilson it's not the
+same Wilson as the uh Cloud
+
+ align:start position:0%
+same Wilson as the uh Cloud
+ 
+
+ align:start position:0%
+same Wilson as the uh Cloud
+chamber and based on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model uh developments and improvements
+
+ align:start position:0%
+model uh developments and improvements
+ 
+
+ align:start position:0%
+model uh developments and improvements
+of the Wilson model by prits and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+co-workers you have uh the models that
+
+ align:start position:0%
+co-workers you have uh the models that
+ 
+
+ align:start position:0%
+co-workers you have uh the models that
+you found you find now in your softwares
+
+ align:start position:0%
+you found you find now in your softwares
+ 
+
+ align:start position:0%
+you found you find now in your softwares
+that do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+modeling which have which have several
+
+ align:start position:0%
+modeling which have which have several
+ 
+
+ align:start position:0%
+modeling which have which have several
+uh par parameters which are
+
+ align:start position:0%
+uh par parameters which are
+ 
+
+ align:start position:0%
+uh par parameters which are
+related these epsilons are related to
+
+ align:start position:0%
+related these epsilons are related to
+ 
+
+ align:start position:0%
+related these epsilons are related to
+the Leonard
+
+ align:start position:0%
+the Leonard
+ 
+
+ align:start position:0%
+the Leonard
+jnes potential so to to the strength
+
+ align:start position:0%
+jnes potential so to to the strength
+ 
+
+ align:start position:0%
+jnes potential so to to the strength
+with which molecule one is attracted Ed
+
+ align:start position:0%
+with which molecule one is attracted Ed
+ 
+
+ align:start position:0%
+with which molecule one is attracted Ed
+by molecule
+
+ align:start position:0%
+by molecule
+ 
+
+ align:start position:0%
+by molecule
+one and this is molecule one attracted
+
+ align:start position:0%
+one and this is molecule one attracted
+ 
+
+ align:start position:0%
+one and this is molecule one attracted
+by molecules
+
+ align:start position:0%
+by molecules
+ 
+
+ align:start position:0%
+by molecules
+two and two by
+
+ align:start position:0%
+two and two by
+ 
+
+ align:start position:0%
+two and two by
+two and so you see there is some uh the
+
+ align:start position:0%
+two and so you see there is some uh the
+ 
+
+ align:start position:0%
+two and so you see there is some uh the
+physics the the physics behind this
+
+ align:start position:0%
+physics the the physics behind this
+ 
+
+ align:start position:0%
+physics the the physics behind this
+model uh is
+
+ align:start position:0%
+model uh is
+ 
+
+ align:start position:0%
+model uh is
+still related to the fact that we're
+
+ align:start position:0%
+still related to the fact that we're
+ 
+
+ align:start position:0%
+still related to the fact that we're
+trying to describe intermolecular forces
+
+ align:start position:0%
+trying to describe intermolecular forces
+ 
+
+ align:start position:0%
+trying to describe intermolecular forces
+and their
+
+ align:start position:0%
+and their
+ 
+
+ align:start position:0%
+and their
+effects and these are the specific
+
+ align:start position:0%
+effects and these are the specific
+ 
+
+ align:start position:0%
+effects and these are the specific
+volume over the pure uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in practice you
+
+ align:start position:0%
+so in practice you
+ 
+
+ align:start position:0%
+so in practice you
+describe chemical potentials and
+
+ align:start position:0%
+describe chemical potentials and
+ 
+
+ align:start position:0%
+describe chemical potentials and
+therefore it GS free energy uh of a
+
+ align:start position:0%
+therefore it GS free energy uh of a
+ 
+
+ align:start position:0%
+therefore it GS free energy uh of a
+mixture in this uh Way by adding up
+
+ align:start position:0%
+mixture in this uh Way by adding up
+ 
+
+ align:start position:0%
+mixture in this uh Way by adding up
+contributions so here are some examples
+
+ align:start position:0%
+contributions so here are some examples
+ 
+
+ align:start position:0%
+contributions so here are some examples
+I mean examples of uh how these
+
+ align:start position:0%
+I mean examples of uh how these
+ 
+
+ align:start position:0%
+I mean examples of uh how these
+contributions look as function for a
+
+ align:start position:0%
+contributions look as function for a
+ 
+
+ align:start position:0%
+contributions look as function for a
+binary mixture as function of U uh the
+
+ align:start position:0%
+binary mixture as function of U uh the
+ 
+
+ align:start position:0%
+binary mixture as function of U uh the
+mole fraction or of component
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one for
+
+ align:start position:0%
+one for
+ 
+
+ align:start position:0%
+one for
+example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um just the term y log y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this pinkish curve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here if you
+
+ align:start position:0%
+here if you
+ 
+
+ align:start position:0%
+here if you
+add also this other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term and of course it depends on on what
+
+ align:start position:0%
+term and of course it depends on on what
+ 
+
+ align:start position:0%
+term and of course it depends on on what
+assumptions you take for
+
+ align:start position:0%
+assumptions you take for
+ 
+
+ align:start position:0%
+assumptions you take for
+the for the GI free energies of the pure
+
+ align:start position:0%
+the for the GI free energies of the pure
+ 
+
+ align:start position:0%
+the for the GI free energies of the pure
+component here I assumed zero for
+
+ align:start position:0%
+component here I assumed zero for
+ 
+
+ align:start position:0%
+component here I assumed zero for
+component two and
+
+ align:start position:0%
+component two and
+ 
+
+ align:start position:0%
+component two and
+uh is this number here maybe 0
+
+ align:start position:0%
+uh is this number here maybe 0
+ 
+
+ align:start position:0%
+uh is this number here maybe 0
+point five or or or
+
+ align:start position:0%
+point five or or or
+ 
+
+ align:start position:0%
+point five or or or
+six for component one just to make this
+
+ align:start position:0%
+six for component one just to make this
+ 
+
+ align:start position:0%
+six for component one just to make this
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this this is the linear part the first
+
+ align:start position:0%
+this this is the linear part the first
+ 
+
+ align:start position:0%
+this this is the linear part the first
+two terms are linear in in the mole
+
+ align:start position:0%
+two terms are linear in in the mole
+ 
+
+ align:start position:0%
+two terms are linear in in the mole
+fraction and that's the blue
+
+ align:start position:0%
+fraction and that's the blue
+ 
+
+ align:start position:0%
+fraction and that's the blue
+curve so you add up the blue curve and
+
+ align:start position:0%
+curve so you add up the blue curve and
+ 
+
+ align:start position:0%
+curve so you add up the blue curve and
+the pinkish one and you get the red
+
+ align:start position:0%
+the pinkish one and you get the red
+ 
+
+ align:start position:0%
+the pinkish one and you get the red
+curve that is g
+
+ align:start position:0%
+curve that is g
+ 
+
+ align:start position:0%
+curve that is g
+ideal just like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and then here I
+
+ align:start position:0%
+that and then here I
+ 
+
+ align:start position:0%
+that and then here I
+plotted the marulas one parameter that's
+
+ align:start position:0%
+plotted the marulas one parameter that's
+ 
+
+ align:start position:0%
+plotted the marulas one parameter that's
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+green margul has two parameters the
+
+ align:start position:0%
+green margul has two parameters the
+ 
+
+ align:start position:0%
+green margul has two parameters the
+black and Van the orange
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now when you add
+
+ align:start position:0%
+now when you add
+ 
+
+ align:start position:0%
+now when you add
+up the ideal and the excess gives three
+
+ align:start position:0%
+up the ideal and the excess gives three
+ 
+
+ align:start position:0%
+up the ideal and the excess gives three
+energy see this is negative this is
+
+ align:start position:0%
+energy see this is negative this is
+ 
+
+ align:start position:0%
+energy see this is negative this is
+positive they add up and here is what
+
+ align:start position:0%
+positive they add up and here is what
+ 
+
+ align:start position:0%
+positive they add up and here is what
+you take you you
+
+ align:start position:0%
+you take you you
+ 
+
+ align:start position:0%
+you take you you
+obtain these are for the three cases
+
+ align:start position:0%
+obtain these are for the three cases
+ 
+
+ align:start position:0%
+obtain these are for the three cases
+marulas one parameter two parameters one
+
+ align:start position:0%
+marulas one parameter two parameters one
+ 
+
+ align:start position:0%
+marulas one parameter two parameters one
+lar you obtain shapes that are
+
+ align:start position:0%
+lar you obtain shapes that are
+ 
+
+ align:start position:0%
+lar you obtain shapes that are
+non-trivial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually in some cases that also they're
+
+ align:start position:0%
+actually in some cases that also they're
+ 
+
+ align:start position:0%
+actually in some cases that also they're
+also no good in the sense that they
+
+ align:start position:0%
+also no good in the sense that they
+ 
+
+ align:start position:0%
+also no good in the sense that they
+violate the stability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because the second derivative of uh
+
+ align:start position:0%
+because the second derivative of uh
+ 
+
+ align:start position:0%
+because the second derivative of uh
+G must always be
+
+ align:start position:0%
+G must always be
+ 
+
+ align:start position:0%
+G must always be
+positive we we'll come back to this
+
+ align:start position:0%
+positive we we'll come back to this
+ 
+
+ align:start position:0%
+positive we we'll come back to this
+uh in in a short
+
+ align:start position:0%
+uh in in a short
+ 
+
+ align:start position:0%
+uh in in a short
+while um so here we will find that there
+
+ align:start position:0%
+while um so here we will find that there
+ 
+
+ align:start position:0%
+while um so here we will find that there
+is where where the the convexity is uh
+
+ align:start position:0%
+is where where the the convexity is uh
+ 
+
+ align:start position:0%
+is where where the the convexity is uh
+second derivative is negative this will
+
+ align:start position:0%
+second derivative is negative this will
+ 
+
+ align:start position:0%
+second derivative is negative this will
+have unstable
+
+ align:start position:0%
+have unstable
+ 
+
+ align:start position:0%
+have unstable
+States and uh this will drive us to
+
+ align:start position:0%
+States and uh this will drive us to
+ 
+
+ align:start position:0%
+States and uh this will drive us to
+exactly the same uh ideas that we have
+
+ align:start position:0%
+exactly the same uh ideas that we have
+ 
+
+ align:start position:0%
+exactly the same uh ideas that we have
+seen for the Vander valal case for the
+
+ align:start position:0%
+seen for the Vander valal case for the
+ 
+
+ align:start position:0%
+seen for the Vander valal case for the
+pure substance un unstable States and
+
+ align:start position:0%
+pure substance un unstable States and
+ 
+
+ align:start position:0%
+pure substance un unstable States and
+also stable states are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possible but we postpone that for for a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+while when we are in the business of um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mixtures there are other terms that I
+
+ align:start position:0%
+mixtures there are other terms that I
+ 
+
+ align:start position:0%
+mixtures there are other terms that I
+only want to mention because they are
+
+ align:start position:0%
+only want to mention because they are
+ 
+
+ align:start position:0%
+only want to mention because they are
+used in the by the practitioners
+
+ align:start position:0%
+used in the by the practitioners
+ 
+
+ align:start position:0%
+used in the by the practitioners
+and that might be confusing so I want to
+
+ align:start position:0%
+and that might be confusing so I want to
+ 
+
+ align:start position:0%
+and that might be confusing so I want to
+link to what uh we're
+
+ align:start position:0%
+link to what uh we're
+ 
+
+ align:start position:0%
+link to what uh we're
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+doing these are called for the
+
+ align:start position:0%
+doing these are called for the
+ 
+
+ align:start position:0%
+doing these are called for the
+condensed
+
+ align:start position:0%
+condensed
+ 
+
+ align:start position:0%
+condensed
+phases we use activities and activity
+
+ align:start position:0%
+phases we use activities and activity
+ 
+
+ align:start position:0%
+phases we use activities and activity
+coefficients it's just another way of
+
+ align:start position:0%
+coefficients it's just another way of
+ 
+
+ align:start position:0%
+coefficients it's just another way of
+writing of of of of of writing the
+
+ align:start position:0%
+writing of of of of of writing the
+ 
+
+ align:start position:0%
+writing of of of of of writing the
+chemical potential so to
+
+ align:start position:0%
+chemical potential so to
+ 
+
+ align:start position:0%
+chemical potential so to
+speak you could Define the activity this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way so you take uh the chemical
+
+ align:start position:0%
+way so you take uh the chemical
+ 
+
+ align:start position:0%
+way so you take uh the chemical
+potential this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one you
+
+ align:start position:0%
+one you
+ 
+
+ align:start position:0%
+one you
+subtract the same at some reference
+
+ align:start position:0%
+subtract the same at some reference
+ 
+
+ align:start position:0%
+subtract the same at some reference
+conditions of pressure and
+
+ align:start position:0%
+conditions of pressure and
+ 
+
+ align:start position:0%
+conditions of pressure and
+composition so not necessarily the pure
+
+ align:start position:0%
+composition so not necessarily the pure
+ 
+
+ align:start position:0%
+composition so not necessarily the pure
+uh the pure
+
+ align:start position:0%
+uh the pure
+ 
+
+ align:start position:0%
+uh the pure
+substance divided by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+13 that
+
+ align:start position:0%
+13 that
+ 
+
+ align:start position:0%
+13 that
+means that essentially you rewriting
+
+ align:start position:0%
+means that essentially you rewriting
+ 
+
+ align:start position:0%
+means that essentially you rewriting
+your chemical potential as a term
+
+ align:start position:0%
+your chemical potential as a term
+ 
+
+ align:start position:0%
+your chemical potential as a term
+evaluated at those reference
+
+ align:start position:0%
+evaluated at those reference
+ 
+
+ align:start position:0%
+evaluated at those reference
+conditions plus RT log of the activity
+
+ align:start position:0%
+conditions plus RT log of the activity
+ 
+
+ align:start position:0%
+conditions plus RT log of the activity
+so that you have an an equation that
+
+ align:start position:0%
+so that you have an an equation that
+ 
+
+ align:start position:0%
+so that you have an an equation that
+resembles this
+
+ align:start position:0%
+resembles this
+ 
+
+ align:start position:0%
+resembles this
+one except that here you have the
+
+ align:start position:0%
+one except that here you have the
+ 
+
+ align:start position:0%
+one except that here you have the
+activity and here you have taken uh a
+
+ align:start position:0%
+activity and here you have taken uh a
+ 
+
+ align:start position:0%
+activity and here you have taken uh a
+reference
+
+ align:start position:0%
+reference
+ 
+
+ align:start position:0%
+reference
+chemical potential not for the pure
+
+ align:start position:0%
+chemical potential not for the pure
+ 
+
+ align:start position:0%
+chemical potential not for the pure
+substance but for the mixture at
+
+ align:start position:0%
+substance but for the mixture at
+ 
+
+ align:start position:0%
+substance but for the mixture at
+some uh uh conditions that you decide to
+
+ align:start position:0%
+some uh uh conditions that you decide to
+ 
+
+ align:start position:0%
+some uh uh conditions that you decide to
+be reference useful as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reference and you can also Define the
+
+ align:start position:0%
+reference and you can also Define the
+ 
+
+ align:start position:0%
+reference and you can also Define the
+activity coefficient which is the ratio
+
+ align:start position:0%
+activity coefficient which is the ratio
+ 
+
+ align:start position:0%
+activity coefficient which is the ratio
+of the activity to the mole
+
+ align:start position:0%
+of the activity to the mole
+ 
+
+ align:start position:0%
+of the activity to the mole
+fraction so that here you
+
+ align:start position:0%
+fraction so that here you
+ 
+
+ align:start position:0%
+fraction so that here you
+have uh the logarithm of Y
+
+ align:start position:0%
+have uh the logarithm of Y
+ 
+
+ align:start position:0%
+have uh the logarithm of Y
+which represents the ideal
+
+ align:start position:0%
+which represents the ideal
+ 
+
+ align:start position:0%
+which represents the ideal
+part of the contribution and the non-
+
+ align:start position:0%
+part of the contribution and the non-
+ 
+
+ align:start position:0%
+part of the contribution and the non-
+ideal or the
+
+ align:start position:0%
+ideal or the
+ 
+
+ align:start position:0%
+ideal or the
+excess is sort of all contained in this
+
+ align:start position:0%
+excess is sort of all contained in this
+ 
+
+ align:start position:0%
+excess is sort of all contained in this
+activity
+
+ align:start position:0%
+activity
+ 
+
+ align:start position:0%
+activity
+coefficient so that's just changing
+
+ align:start position:0%
+coefficient so that's just changing
+ 
+
+ align:start position:0%
+coefficient so that's just changing
+names defining variables but the
+
+ align:start position:0%
+names defining variables but the
+ 
+
+ align:start position:0%
+names defining variables but the
+substance of the matter is what we've
+
+ align:start position:0%
+substance of the matter is what we've
+ 
+
+ align:start position:0%
+substance of the matter is what we've
+done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh in in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same way people have uh sometimes used
+
+ align:start position:0%
+same way people have uh sometimes used
+ 
+
+ align:start position:0%
+same way people have uh sometimes used
+fasi this is used for for uh the gaseous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phases so Fugi
+
+ align:start position:0%
+phases so Fugi
+ 
+
+ align:start position:0%
+phases so Fugi
+is um play the
+
+ align:start position:0%
+is um play the
+ 
+
+ align:start position:0%
+is um play the
+role
+
+ align:start position:0%
+role
+ 
+
+ align:start position:0%
+role
+uh of sort of a general
+
+ align:start position:0%
+uh of sort of a general
+ 
+
+ align:start position:0%
+uh of sort of a general
+the partial pressures
+
+ align:start position:0%
+the partial pressures
+ 
+
+ align:start position:0%
+the partial pressures
+but the idea is that
+
+ align:start position:0%
+but the idea is that
+ 
+
+ align:start position:0%
+but the idea is that
+here you
+
+ align:start position:0%
+here you
+ 
+
+ align:start position:0%
+here you
+you so you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+define you see this relations let start
+
+ align:start position:0%
+define you see this relations let start
+ 
+
+ align:start position:0%
+define you see this relations let start
+from this relation here uh the chemical
+
+ align:start position:0%
+from this relation here uh the chemical
+ 
+
+ align:start position:0%
+from this relation here uh the chemical
+potential you write it again as usual
+
+ align:start position:0%
+potential you write it again as usual
+ 
+
+ align:start position:0%
+potential you write it again as usual
+like we did we do we
+
+ align:start position:0%
+like we did we do we
+ 
+
+ align:start position:0%
+like we did we do we
+did uh
+
+ align:start position:0%
+did uh
+ 
+
+ align:start position:0%
+did uh
+as we take as reference the pure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+substance then you you have rt log of
+
+ align:start position:0%
+substance then you you have rt log of
+ 
+
+ align:start position:0%
+substance then you you have rt log of
+Y okay and then you have plus RT log of
+
+ align:start position:0%
+Y okay and then you have plus RT log of
+ 
+
+ align:start position:0%
+Y okay and then you have plus RT log of
+p over p 0 plus RT log of so essentially
+
+ align:start position:0%
+p over p 0 plus RT log of so essentially
+ 
+
+ align:start position:0%
+p over p 0 plus RT log of so essentially
+you you you rename uh the
+
+ align:start position:0%
+you you you rename uh the
+ 
+
+ align:start position:0%
+you you you rename uh the
+excess chemical potential in terms of
+
+ align:start position:0%
+excess chemical potential in terms of
+ 
+
+ align:start position:0%
+excess chemical potential in terms of
+this uh fugacity uh coefficient
+
+ align:start position:0%
+this uh fugacity uh coefficient
+ 
+
+ align:start position:0%
+this uh fugacity uh coefficient
+or if you uh want to start from the
+
+ align:start position:0%
+or if you uh want to start from the
+ 
+
+ align:start position:0%
+or if you uh want to start from the
+chemical potential you define the
+
+ align:start position:0%
+chemical potential you define the
+ 
+
+ align:start position:0%
+chemical potential you define the
+fugacity by selecting again a reference
+
+ align:start position:0%
+fugacity by selecting again a reference
+ 
+
+ align:start position:0%
+fugacity by selecting again a reference
+uh uh condition for your mixture not
+
+ align:start position:0%
+uh uh condition for your mixture not
+ 
+
+ align:start position:0%
+uh uh condition for your mixture not
+necessarily like we do here the pure
+
+ align:start position:0%
+necessarily like we do here the pure
+ 
+
+ align:start position:0%
+necessarily like we do here the pure
+substance by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+selecting uh you select this coefficient
+
+ align:start position:0%
+selecting uh you select this coefficient
+ 
+
+ align:start position:0%
+selecting uh you select this coefficient
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+this this this this prefactor here has
+
+ align:start position:0%
+this this this this prefactor here has
+ 
+
+ align:start position:0%
+this this this this prefactor here has
+a something that in the limit of ideal
+
+ align:start position:0%
+a something that in the limit of ideal
+ 
+
+ align:start position:0%
+a something that in the limit of ideal
+gas behavior reduces to the partial
+
+ align:start position:0%
+gas behavior reduces to the partial
+ 
+
+ align:start position:0%
+gas behavior reduces to the partial
+pressure so the
+
+ align:start position:0%
+pressure so the
+ 
+
+ align:start position:0%
+pressure so the
+fugacity in those limit is the partial
+
+ align:start position:0%
+fugacity in those limit is the partial
+ 
+
+ align:start position:0%
+fugacity in those limit is the partial
+pressure times the exponent of
+
+ align:start position:0%
+pressure times the exponent of
+ 
+
+ align:start position:0%
+pressure times the exponent of
+this okay so again just this is just
+
+ align:start position:0%
+this okay so again just this is just
+ 
+
+ align:start position:0%
+this okay so again just this is just
+because I wanted to mention it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for example if you compute the
+
+ align:start position:0%
+for example if you compute the
+ 
+
+ align:start position:0%
+for example if you compute the
+activities for the marulas van and
+
+ align:start position:0%
+activities for the marulas van and
+ 
+
+ align:start position:0%
+activities for the marulas van and
+marulas 2 parameters here are the
+
+ align:start position:0%
+marulas 2 parameters here are the
+ 
+
+ align:start position:0%
+marulas 2 parameters here are the
+expressions and here are
+
+ align:start position:0%
+expressions and here are
+ 
+
+ align:start position:0%
+expressions and here are
+their for the van L this is I think this
+
+ align:start position:0%
+their for the van L this is I think this
+ 
+
+ align:start position:0%
+their for the van L this is I think this
+is for the one L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um how the activity depends on mole
+
+ align:start position:0%
+um how the activity depends on mole
+ 
+
+ align:start position:0%
+um how the activity depends on mole
+fraction and on that parameter that
+
+ align:start position:0%
+fraction and on that parameter that
+ 
+
+ align:start position:0%
+fraction and on that parameter that
+characterizes the model or the
+
+ align:start position:0%
+characterizes the model or the
+ 
+
+ align:start position:0%
+characterizes the model or the
+parameters A and B that
+
+ align:start position:0%
+parameters A and B that
+ 
+
+ align:start position:0%
+parameters A and B that
+characterize the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model and that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means that when we talk about liquid
+
+ align:start position:0%
+means that when we talk about liquid
+ 
+
+ align:start position:0%
+means that when we talk about liquid
+Vapor
+
+ align:start position:0%
+Vapor
+ 
+
+ align:start position:0%
+Vapor
+equilibrium for example let's suppose we
+
+ align:start position:0%
+equilibrium for example let's suppose we
+ 
+
+ align:start position:0%
+equilibrium for example let's suppose we
+use the vanar
+
+ align:start position:0%
+use the vanar
+ 
+
+ align:start position:0%
+use the vanar
+model and you remember that we have to
+
+ align:start position:0%
+model and you remember that we have to
+ 
+
+ align:start position:0%
+model and you remember that we have to
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+apply uh if we have two substances that
+
+ align:start position:0%
+apply uh if we have two substances that
+ 
+
+ align:start position:0%
+apply uh if we have two substances that
+are both volatile and uh
+
+ align:start position:0%
+are both volatile and uh
+ 
+
+ align:start position:0%
+are both volatile and uh
+condensable we have to apply twice the
+
+ align:start position:0%
+condensable we have to apply twice the
+ 
+
+ align:start position:0%
+condensable we have to apply twice the
+routes law now routs law rites for for a
+
+ align:start position:0%
+routes law now routs law rites for for a
+ 
+
+ align:start position:0%
+routes law now routs law rites for for a
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+a an non ideal
+
+ align:start position:0%
+a an non ideal
+ 
+
+ align:start position:0%
+a an non ideal
+mixture where you substitute the mole
+
+ align:start position:0%
+mixture where you substitute the mole
+ 
+
+ align:start position:0%
+mixture where you substitute the mole
+fraction with the activity the mole
+
+ align:start position:0%
+fraction with the activity the mole
+ 
+
+ align:start position:0%
+fraction with the activity the mole
+fraction of the for for the components
+
+ align:start position:0%
+fraction of the for for the components
+ 
+
+ align:start position:0%
+fraction of the for for the components
+in the liquid with their activities and
+
+ align:start position:0%
+in the liquid with their activities and
+ 
+
+ align:start position:0%
+in the liquid with their activities and
+we've given the expressions for the
+
+ align:start position:0%
+we've given the expressions for the
+ 
+
+ align:start position:0%
+we've given the expressions for the
+activities in the previous slide also
+
+ align:start position:0%
+activities in the previous slide also
+ 
+
+ align:start position:0%
+activities in the previous slide also
+for the vanar so if
+
+ align:start position:0%
+for the vanar so if
+ 
+
+ align:start position:0%
+for the vanar so if
+you if you do that
+
+ align:start position:0%
+you if you do that
+ 
+
+ align:start position:0%
+you if you do that
+substitution here is what uh the
+
+ align:start position:0%
+substitution here is what uh the
+ 
+
+ align:start position:0%
+substitution here is what uh the
+equations of the
+
+ align:start position:0%
+equations of the
+ 
+
+ align:start position:0%
+equations of the
+um Bubble line is and this is for the DU
+
+ align:start position:0%
+um Bubble line is and this is for the DU
+ 
+
+ align:start position:0%
+um Bubble line is and this is for the DU
+line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they used to be uh one of them used to
+
+ align:start position:0%
+they used to be uh one of them used to
+ 
+
+ align:start position:0%
+they used to be uh one of them used to
+be a straight
+
+ align:start position:0%
+be a straight
+ 
+
+ align:start position:0%
+be a straight
+line but with this uh non ideal
+
+ align:start position:0%
+line but with this uh non ideal
+ 
+
+ align:start position:0%
+line but with this uh non ideal
+model uh it
+
+ align:start position:0%
+model uh it
+ 
+
+ align:start position:0%
+model uh it
+becomes very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different and the DU line also becomes
+
+ align:start position:0%
+different and the DU line also becomes
+ 
+
+ align:start position:0%
+different and the DU line also becomes
+sort of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interesting so just two parameters
+
+ align:start position:0%
+interesting so just two parameters
+ 
+
+ align:start position:0%
+interesting so just two parameters
+introdu use a lot of structure and the
+
+ align:start position:0%
+introdu use a lot of structure and the
+ 
+
+ align:start position:0%
+introdu use a lot of structure and the
+behavior of your
+
+ align:start position:0%
+behavior of your
+ 
+
+ align:start position:0%
+behavior of your
+mixture including the possibility of
+
+ align:start position:0%
+mixture including the possibility of
+ 
+
+ align:start position:0%
+mixture including the possibility of
+this which is um called the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aotop the aotop is a a condition in
+
+ align:start position:0%
+aotop the aotop is a a condition in
+ 
+
+ align:start position:0%
+aotop the aotop is a a condition in
+which you go from
+
+ align:start position:0%
+which you go from
+ 
+
+ align:start position:0%
+which you go from
+liquid to uh vapor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and that change is not across a
+
+ align:start position:0%
+uh and that change is not across a
+ 
+
+ align:start position:0%
+uh and that change is not across a
+finite temperature
+
+ align:start position:0%
+finite temperature
+ 
+
+ align:start position:0%
+finite temperature
+difference but at a single temperature
+
+ align:start position:0%
+difference but at a single temperature
+ 
+
+ align:start position:0%
+difference but at a single temperature
+so it behaves as if it were a pure
+
+ align:start position:0%
+so it behaves as if it were a pure
+ 
+
+ align:start position:0%
+so it behaves as if it were a pure
+substance like few substance boils and
+
+ align:start position:0%
+substance like few substance boils and
+ 
+
+ align:start position:0%
+substance like few substance boils and
+condenses at the same unique
+
+ align:start position:0%
+condenses at the same unique
+ 
+
+ align:start position:0%
+condenses at the same unique
+temperature but this occurs only at that
+
+ align:start position:0%
+temperature but this occurs only at that
+ 
+
+ align:start position:0%
+temperature but this occurs only at that
+particular composition at other
+
+ align:start position:0%
+particular composition at other
+ 
+
+ align:start position:0%
+particular composition at other
+compositions instead you have a range of
+
+ align:start position:0%
+compositions instead you have a range of
+ 
+
+ align:start position:0%
+compositions instead you have a range of
+temperatures so the temperatures the
+
+ align:start position:0%
+temperatures so the temperatures the
+ 
+
+ align:start position:0%
+temperatures so the temperatures the
+temperature of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U liquidus is is
+
+ align:start position:0%
+U liquidus is is
+ 
+
+ align:start position:0%
+U liquidus is is
+is is different than than of the uh of
+
+ align:start position:0%
+is is different than than of the uh of
+ 
+
+ align:start position:0%
+is is different than than of the uh of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+vaporus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh this is
+
+ align:start position:0%
+okay uh this is
+ 
+
+ align:start position:0%
+okay uh this is
+done by combining these two you can
+
+ align:start position:0%
+done by combining these two you can
+ 
+
+ align:start position:0%
+done by combining these two you can
+construct a plot at a constant temp
+
+ align:start position:0%
+construct a plot at a constant temp
+ 
+
+ align:start position:0%
+construct a plot at a constant temp
+temperature but you can also the same
+
+ align:start position:0%
+temperature but you can also the same
+ 
+
+ align:start position:0%
+temperature but you can also the same
+equations construct the plot at constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+okay and of course you can eliminate the
+
+ align:start position:0%
+okay and of course you can eliminate the
+ 
+
+ align:start position:0%
+okay and of course you can eliminate the
+pressure between the two and
+
+ align:start position:0%
+pressure between the two and
+ 
+
+ align:start position:0%
+pressure between the two and
+construct for a given temperature or for
+
+ align:start position:0%
+construct for a given temperature or for
+ 
+
+ align:start position:0%
+construct for a given temperature or for
+a given pressure the relation that you
+
+ align:start position:0%
+a given pressure the relation that you
+ 
+
+ align:start position:0%
+a given pressure the relation that you
+have between the composition of the
+
+ align:start position:0%
+have between the composition of the
+ 
+
+ align:start position:0%
+have between the composition of the
+vapor phase and the composition of the
+
+ align:start position:0%
+vapor phase and the composition of the
+ 
+
+ align:start position:0%
+vapor phase and the composition of the
+liquid phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these are all things that you can
+
+ align:start position:0%
+so these are all things that you can
+ 
+
+ align:start position:0%
+so these are all things that you can
+Implement in an Excel file and so on and
+
+ align:start position:0%
+Implement in an Excel file and so on and
+ 
+
+ align:start position:0%
+Implement in an Excel file and so on and
+very easy if you have few
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parameters uh there is
+
+ align:start position:0%
+parameters uh there is
+ 
+
+ align:start position:0%
+parameters uh there is
+also a Lenard John model
+
+ align:start position:0%
+also a Lenard John model
+ 
+
+ align:start position:0%
+also a Lenard John model
+of the mixture of the binary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mixture so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here this model is
+
+ align:start position:0%
+here this model is
+ 
+
+ align:start position:0%
+here this model is
+taken again this article on Wikipedia
+
+ align:start position:0%
+taken again this article on Wikipedia
+ 
+
+ align:start position:0%
+taken again this article on Wikipedia
+from which I take these plots very
+
+ align:start position:0%
+from which I take these plots very
+ 
+
+ align:start position:0%
+from which I take these plots very
+nicely uh
+
+ align:start position:0%
+nicely uh
+ 
+
+ align:start position:0%
+nicely uh
+done it explains that you can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assume for the sigma you remember that
+
+ align:start position:0%
+assume for the sigma you remember that
+ 
+
+ align:start position:0%
+assume for the sigma you remember that
+the model of in the Leonard mod model
+
+ align:start position:0%
+the model of in the Leonard mod model
+ 
+
+ align:start position:0%
+the model of in the Leonard mod model
+lard Jones model Sigma is a
+
+ align:start position:0%
+lard Jones model Sigma is a
+ 
+
+ align:start position:0%
+lard Jones model Sigma is a
+representation of the
+
+ align:start position:0%
+representation of the
+ 
+
+ align:start position:0%
+representation of the
+the the diameter essentially of the two
+
+ align:start position:0%
+the the diameter essentially of the two
+ 
+
+ align:start position:0%
+the the diameter essentially of the two
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+particle so when they Collide the two
+
+ align:start position:0%
+particle so when they Collide the two
+ 
+
+ align:start position:0%
+particle so when they Collide the two
+centers of the two spheres are at a
+
+ align:start position:0%
+centers of the two spheres are at a
+ 
+
+ align:start position:0%
+centers of the two spheres are at a
+distance which is equal to the their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diameter if you have uh spheres of
+
+ align:start position:0%
+diameter if you have uh spheres of
+ 
+
+ align:start position:0%
+diameter if you have uh spheres of
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+sizes the
+
+ align:start position:0%
+sizes the
+ 
+
+ align:start position:0%
+sizes the
+diameter at which they Collide is sort
+
+ align:start position:0%
+diameter at which they Collide is sort
+ 
+
+ align:start position:0%
+diameter at which they Collide is sort
+of the the sum of the
+
+ align:start position:0%
+of the the sum of the
+ 
+
+ align:start position:0%
+of the the sum of the
+radi so the radi is a half of the
+
+ align:start position:0%
+radi so the radi is a half of the
+ 
+
+ align:start position:0%
+radi so the radi is a half of the
+diameter so the sum of the halfs is just
+
+ align:start position:0%
+diameter so the sum of the halfs is just
+ 
+
+ align:start position:0%
+diameter so the sum of the halfs is just
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+average diameter of the of the two
+
+ align:start position:0%
+average diameter of the of the two
+ 
+
+ align:start position:0%
+average diameter of the of the two
+proper
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diameters so you assume
+
+ align:start position:0%
+diameters so you assume
+ 
+
+ align:start position:0%
+diameters so you assume
+a ler John's
+
+ align:start position:0%
+a ler John's
+ 
+
+ align:start position:0%
+a ler John's
+curve uh or
+
+ align:start position:0%
+curve uh or
+ 
+
+ align:start position:0%
+curve uh or
+potential characterized by a sigma one2
+
+ align:start position:0%
+potential characterized by a sigma one2
+ 
+
+ align:start position:0%
+potential characterized by a sigma one2
+for the for the uh interaction between
+
+ align:start position:0%
+for the for the uh interaction between
+ 
+
+ align:start position:0%
+for the for the uh interaction between
+two unlike
+
+ align:start position:0%
+two unlike
+ 
+
+ align:start position:0%
+two unlike
+particles that is equal to this
+
+ align:start position:0%
+particles that is equal to this
+ 
+
+ align:start position:0%
+particles that is equal to this
+mean
+
+ align:start position:0%
+mean
+ 
+
+ align:start position:0%
+mean
+value and then for the depth of the
+
+ align:start position:0%
+value and then for the depth of the
+ 
+
+ align:start position:0%
+value and then for the depth of the
+Leonard John's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+valy you use um
+
+ align:start position:0%
+valy you use um
+ 
+
+ align:start position:0%
+valy you use um
+the geometric
+
+ align:start position:0%
+the geometric
+ 
+
+ align:start position:0%
+the geometric
+mean of the S of the pure component
+
+ align:start position:0%
+mean of the S of the pure component
+ 
+
+ align:start position:0%
+mean of the S of the pure component
+ones but then you also use an adjustable
+
+ align:start position:0%
+ones but then you also use an adjustable
+ 
+
+ align:start position:0%
+ones but then you also use an adjustable
+parameter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C now the
+
+ align:start position:0%
+C now the
+ 
+
+ align:start position:0%
+C now the
+geometric if assume if if C is equal to
+
+ align:start position:0%
+geometric if assume if if C is equal to
+ 
+
+ align:start position:0%
+geometric if assume if if C is equal to
+one this geometric uh uh
+
+ align:start position:0%
+one this geometric uh uh
+ 
+
+ align:start position:0%
+one this geometric uh uh
+mean uh gives you the equivalent of the
+
+ align:start position:0%
+mean uh gives you the equivalent of the
+ 
+
+ align:start position:0%
+mean uh gives you the equivalent of the
+ideal uh solution
+
+ align:start position:0%
+ideal uh solution
+ 
+
+ align:start position:0%
+ideal uh solution
+model and in fact you
+
+ align:start position:0%
+model and in fact you
+ 
+
+ align:start position:0%
+model and in fact you
+get that the bubble line is straight is
+
+ align:start position:0%
+get that the bubble line is straight is
+ 
+
+ align:start position:0%
+get that the bubble line is straight is
+a straight
+
+ align:start position:0%
+a straight
+ 
+
+ align:start position:0%
+a straight
+line and this is with C is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one uh if you change instead
+
+ align:start position:0%
+one uh if you change instead
+ 
+
+ align:start position:0%
+one uh if you change instead
+C to like greater than
+
+ align:start position:0%
+C to like greater than
+ 
+
+ align:start position:0%
+C to like greater than
+one you
+
+ align:start position:0%
+one you
+ 
+
+ align:start position:0%
+one you
+get real a non ideal mixture Behavior
+
+ align:start position:0%
+get real a non ideal mixture Behavior
+ 
+
+ align:start position:0%
+get real a non ideal mixture Behavior
+with an aotop at this
+
+ align:start position:0%
+with an aotop at this
+ 
+
+ align:start position:0%
+with an aotop at this
+composition if you change C from 1.2
+
+ align:start position:0%
+composition if you change C from 1.2
+ 
+
+ align:start position:0%
+composition if you change C from 1.2
+to 85 it goes on the other side so it's
+
+ align:start position:0%
+to 85 it goes on the other side so it's
+ 
+
+ align:start position:0%
+to 85 it goes on the other side so it's
+an isotrope uh upper isotrope lower
+
+ align:start position:0%
+an isotrope uh upper isotrope lower
+ 
+
+ align:start position:0%
+an isotrope uh upper isotrope lower
+isotrope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+also if
+
+ align:start position:0%
+also if
+ 
+
+ align:start position:0%
+also if
+you play with the ratio this is wrong
+
+ align:start position:0%
+you play with the ratio this is wrong
+ 
+
+ align:start position:0%
+you play with the ratio this is wrong
+this should be a Epsilon 2 over Epsilon
+
+ align:start position:0%
+this should be a Epsilon 2 over Epsilon
+ 
+
+ align:start position:0%
+this should be a Epsilon 2 over Epsilon
+one of course I need to correct that so
+
+ align:start position:0%
+one of course I need to correct that so
+ 
+
+ align:start position:0%
+one of course I need to correct that so
+if you change that from this one to very
+
+ align:start position:0%
+if you change that from this one to very
+ 
+
+ align:start position:0%
+if you change that from this one to very
+different you may find a
+
+ align:start position:0%
+different you may find a
+ 
+
+ align:start position:0%
+different you may find a
+critical region in other words that you
+
+ align:start position:0%
+critical region in other words that you
+ 
+
+ align:start position:0%
+critical region in other words that you
+could allow you to go from
+
+ align:start position:0%
+could allow you to go from
+ 
+
+ align:start position:0%
+could allow you to go from
+liquid to Vapor without a phase change
+
+ align:start position:0%
+liquid to Vapor without a phase change
+ 
+
+ align:start position:0%
+liquid to Vapor without a phase change
+similarly to what happens in a pure
+
+ align:start position:0%
+similarly to what happens in a pure
+ 
+
+ align:start position:0%
+similarly to what happens in a pure
+substance or if you have if you go above
+
+ align:start position:0%
+substance or if you have if you go above
+ 
+
+ align:start position:0%
+substance or if you have if you go above
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+critical uh point you can you can take a
+
+ align:start position:0%
+critical uh point you can you can take a
+ 
+
+ align:start position:0%
+critical uh point you can you can take a
+liquid to very and vice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+versa
+
+ align:start position:0%
+versa
+ 
+
+ align:start position:0%
+versa
+so this case is
+
+ align:start position:0%
+so this case is
+ 
+
+ align:start position:0%
+so this case is
+one see for example
+
+ align:start position:0%
+one see for example
+ 
+
+ align:start position:0%
+one see for example
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um in which you have a
+
+ align:start position:0%
+um in which you have a
+ 
+
+ align:start position:0%
+um in which you have a
+um well if you were in liquid liquid
+
+ align:start position:0%
+um well if you were in liquid liquid
+ 
+
+ align:start position:0%
+um well if you were in liquid liquid
+this would give you partial visibility
+
+ align:start position:0%
+this would give you partial visibility
+ 
+
+ align:start position:0%
+this would give you partial visibility
+but we'll do that in another in
+
+ align:start position:0%
+but we'll do that in another in
+ 
+
+ align:start position:0%
+but we'll do that in another in
+another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+occasion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now let's talk about a bit of
+
+ align:start position:0%
+okay so now let's talk about a bit of
+ 
+
+ align:start position:0%
+okay so now let's talk about a bit of
+the uh stability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conditions so I as you uh as we have
+
+ align:start position:0%
+conditions so I as you uh as we have
+ 
+
+ align:start position:0%
+conditions so I as you uh as we have
+seen we can go see the business here is
+
+ align:start position:0%
+seen we can go see the business here is
+ 
+
+ align:start position:0%
+seen we can go see the business here is
+to go from the properties of a pure
+
+ align:start position:0%
+to go from the properties of a pure
+ 
+
+ align:start position:0%
+to go from the properties of a pure
+substance to the properties of the other
+
+ align:start position:0%
+substance to the properties of the other
+ 
+
+ align:start position:0%
+substance to the properties of the other
+substance and all the way to all the
+
+ align:start position:0%
+substance and all the way to all the
+ 
+
+ align:start position:0%
+substance and all the way to all the
+compositions in
+
+ align:start position:0%
+compositions in
+ 
+
+ align:start position:0%
+compositions in
+between and when we uh when we do these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh diagrams
+
+ align:start position:0%
+uh diagrams
+ 
+
+ align:start position:0%
+uh diagrams
+here everything is
+
+ align:start position:0%
+here everything is
+ 
+
+ align:start position:0%
+here everything is
+fixed by the condition this is a binary
+
+ align:start position:0%
+fixed by the condition this is a binary
+ 
+
+ align:start position:0%
+fixed by the condition this is a binary
+composition so is fixed by the fact
+
+ align:start position:0%
+composition so is fixed by the fact
+ 
+
+ align:start position:0%
+composition so is fixed by the fact
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+mu1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F uh must be at
+
+ align:start position:0%
+F uh must be at
+ 
+
+ align:start position:0%
+F uh must be at
+TP y let's say one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+YF so for component one in the phase
+
+ align:start position:0%
+YF so for component one in the phase
+ 
+
+ align:start position:0%
+YF so for component one in the phase
+F I have to have the same chemical
+
+ align:start position:0%
+F I have to have the same chemical
+ 
+
+ align:start position:0%
+F I have to have the same chemical
+potential of the of that component in
+
+ align:start position:0%
+potential of the of that component in
+ 
+
+ align:start position:0%
+potential of the of that component in
+the phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G
+
+ align:start position:0%
+G
+ 
+
+ align:start position:0%
+G
+okay and that's one condition of of
+
+ align:start position:0%
+okay and that's one condition of of
+ 
+
+ align:start position:0%
+okay and that's one condition of of
+chemical of um Mutual stable equilibrium
+
+ align:start position:0%
+chemical of um Mutual stable equilibrium
+ 
+
+ align:start position:0%
+chemical of um Mutual stable equilibrium
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+m2f um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah well let's let's call it again one
+
+ align:start position:0%
+yeah well let's let's call it again one
+ 
+
+ align:start position:0%
+yeah well let's let's call it again one
+one F in the let's choose the for
+
+ align:start position:0%
+one F in the let's choose the for
+ 
+
+ align:start position:0%
+one F in the let's choose the for
+variables the mole fraction of one of
+
+ align:start position:0%
+variables the mole fraction of one of
+ 
+
+ align:start position:0%
+variables the mole fraction of one of
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+otherwise but I need to impose the
+
+ align:start position:0%
+otherwise but I need to impose the
+ 
+
+ align:start position:0%
+otherwise but I need to impose the
+condition for uh equality of the
+
+ align:start position:0%
+condition for uh equality of the
+ 
+
+ align:start position:0%
+condition for uh equality of the
+chemical potential also of the other
+
+ align:start position:0%
+chemical potential also of the other
+ 
+
+ align:start position:0%
+chemical potential also of the other
+component so mu2 must be equal to
+
+ align:start position:0%
+component so mu2 must be equal to
+ 
+
+ align:start position:0%
+component so mu2 must be equal to
+mu2 okay so I have a system of two
+
+ align:start position:0%
+mu2 okay so I have a system of two
+ 
+
+ align:start position:0%
+mu2 okay so I have a system of two
+equations
+
+ align:start position:0%
+equations
+ 
+
+ align:start position:0%
+equations
+here and that system of two
+
+ align:start position:0%
+here and that system of two
+ 
+
+ align:start position:0%
+here and that system of two
+equations can be
+
+ align:start position:0%
+equations can be
+ 
+
+ align:start position:0%
+equations can be
+solved in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+general to give
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this to give me the comp for a given
+
+ align:start position:0%
+this to give me the comp for a given
+ 
+
+ align:start position:0%
+this to give me the comp for a given
+temperature and pressure I can solve
+
+ align:start position:0%
+temperature and pressure I can solve
+ 
+
+ align:start position:0%
+temperature and pressure I can solve
+this system for the unknowns that are
+
+ align:start position:0%
+this system for the unknowns that are
+ 
+
+ align:start position:0%
+this system for the unknowns that are
+the mole
+
+ align:start position:0%
+the mole
+ 
+
+ align:start position:0%
+the mole
+fractions of component one in the gasius
+
+ align:start position:0%
+fractions of component one in the gasius
+ 
+
+ align:start position:0%
+fractions of component one in the gasius
+and in the vapor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phase so here I have pressure and
+
+ align:start position:0%
+phase so here I have pressure and
+ 
+
+ align:start position:0%
+phase so here I have pressure and
+temperature I fixed the pressure and the
+
+ align:start position:0%
+temperature I fixed the pressure and the
+ 
+
+ align:start position:0%
+temperature I fixed the pressure and the
+temperature and then that system of
+
+ align:start position:0%
+temperature and then that system of
+ 
+
+ align:start position:0%
+temperature and then that system of
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+gives me the mole fraction of the liquid
+
+ align:start position:0%
+gives me the mole fraction of the liquid
+ 
+
+ align:start position:0%
+gives me the mole fraction of the liquid
+and the mole fraction of the vapor so I
+
+ align:start position:0%
+and the mole fraction of the vapor so I
+ 
+
+ align:start position:0%
+and the mole fraction of the vapor so I
+have this surface so that equation here
+
+ align:start position:0%
+have this surface so that equation here
+ 
+
+ align:start position:0%
+have this surface so that equation here
+gives me is an equation
+
+ align:start position:0%
+gives me is an equation
+ 
+
+ align:start position:0%
+gives me is an equation
+of of this surface here actually this is
+
+ align:start position:0%
+of of this surface here actually this is
+ 
+
+ align:start position:0%
+of of this surface here actually this is
+on the liquid and on the vapor so it's
+
+ align:start position:0%
+on the liquid and on the vapor so it's
+ 
+
+ align:start position:0%
+on the liquid and on the vapor so it's
+on the other side but you can do it for
+
+ align:start position:0%
+on the other side but you can do it for
+ 
+
+ align:start position:0%
+on the other side but you can do it for
+all the
+
+ align:start position:0%
+all the
+ 
+
+ align:start position:0%
+all the
+phases and you have these gaps here
+
+ align:start position:0%
+phases and you have these gaps here
+ 
+
+ align:start position:0%
+phases and you have these gaps here
+these empty spaces between these
+
+ align:start position:0%
+these empty spaces between these
+ 
+
+ align:start position:0%
+these empty spaces between these
+surfaces which doesn't represent any uh
+
+ align:start position:0%
+surfaces which doesn't represent any uh
+ 
+
+ align:start position:0%
+surfaces which doesn't represent any uh
+um State because any stable State
+
+ align:start position:0%
+um State because any stable State
+ 
+
+ align:start position:0%
+um State because any stable State
+because if you are there this system
+
+ align:start position:0%
+because if you are there this system
+ 
+
+ align:start position:0%
+because if you are there this system
+likes to find stable equilibrium by
+
+ align:start position:0%
+likes to find stable equilibrium by
+ 
+
+ align:start position:0%
+likes to find stable equilibrium by
+separating and generating the two uh
+
+ align:start position:0%
+separating and generating the two uh
+ 
+
+ align:start position:0%
+separating and generating the two uh
+phases so that's uh the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea and uh yeah I think we we stop here
+
+ align:start position:0%
+idea and uh yeah I think we we stop here
+ 
+
+ align:start position:0%
+idea and uh yeah I think we we stop here
+because there's not enough time to do
+
+ align:start position:0%
+because there's not enough time to do
+ 
+
+ align:start position:0%
+because there's not enough time to do
+hry law uh but we can um yeah we so next
+
+ align:start position:0%
+hry law uh but we can um yeah we so next
+ 
+
+ align:start position:0%
+hry law uh but we can um yeah we so next
+time we will finish up this part and we
+
+ align:start position:0%
+time we will finish up this part and we
+ 
+
+ align:start position:0%
+time we will finish up this part and we
+start the systems with chemical
+
+ align:start position:0%
+start the systems with chemical
+ 
+
+ align:start position:0%
+start the systems with chemical
+reactions
\ No newline at end of file
diff --git a/RgGFvOpcQXY.txt b/RgGFvOpcQXY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bc60d14e67882a47884d9dffad6d445e8db1e985
--- /dev/null
+++ b/RgGFvOpcQXY.txt
@@ -0,0 +1,1059 @@
+align:start position:0%
+ 
+in this lecture sequence we will do a
+
+ align:start position:0%
+in this lecture sequence we will do a
+ 
+
+ align:start position:0%
+in this lecture sequence we will do a
+lot with normal random variables and for
+
+ align:start position:0%
+lot with normal random variables and for
+ 
+
+ align:start position:0%
+lot with normal random variables and for
+this reason it is useful to start with a
+
+ align:start position:0%
+this reason it is useful to start with a
+ 
+
+ align:start position:0%
+this reason it is useful to start with a
+simple observation that will allow us
+
+ align:start position:0%
+simple observation that will allow us
+ 
+
+ align:start position:0%
+simple observation that will allow us
+later on to move much faster
+
+ align:start position:0%
+later on to move much faster
+ 
+
+ align:start position:0%
+later on to move much faster
+recall that normal random variable with
+
+ align:start position:0%
+recall that normal random variable with
+ 
+
+ align:start position:0%
+recall that normal random variable with
+a certain mean and variance has a PDF of
+
+ align:start position:0%
+a certain mean and variance has a PDF of
+ 
+
+ align:start position:0%
+a certain mean and variance has a PDF of
+this particular form
+
+ align:start position:0%
+this particular form
+ 
+
+ align:start position:0%
+this particular form
+what if somebody gives you a PDF of this
+
+ align:start position:0%
+what if somebody gives you a PDF of this
+ 
+
+ align:start position:0%
+what if somebody gives you a PDF of this
+form and asks you what it corresponds to
+
+ align:start position:0%
+form and asks you what it corresponds to
+ 
+
+ align:start position:0%
+form and asks you what it corresponds to
+you can answer that this is exactly of
+
+ align:start position:0%
+you can answer that this is exactly of
+ 
+
+ align:start position:0%
+you can answer that this is exactly of
+this form provided that you make the
+
+ align:start position:0%
+this form provided that you make the
+ 
+
+ align:start position:0%
+this form provided that you make the
+identification that 3 is equal to mu so
+
+ align:start position:0%
+identification that 3 is equal to mu so
+ 
+
+ align:start position:0%
+identification that 3 is equal to mu so
+this is a normal PDF with a mean equal
+
+ align:start position:0%
+this is a normal PDF with a mean equal
+ 
+
+ align:start position:0%
+this is a normal PDF with a mean equal
+to 3 and whose variance can also be
+
+ align:start position:0%
+to 3 and whose variance can also be
+ 
+
+ align:start position:0%
+to 3 and whose variance can also be
+found by matching this constant that
+
+ align:start position:0%
+found by matching this constant that
+ 
+
+ align:start position:0%
+found by matching this constant that
+appears here with a number 8 this
+
+ align:start position:0%
+appears here with a number 8 this
+ 
+
+ align:start position:0%
+appears here with a number 8 this
+constant here is in the denominator so
+
+ align:start position:0%
+constant here is in the denominator so
+ 
+
+ align:start position:0%
+constant here is in the denominator so
+we have a term 1 over 2 Sigma squared
+
+ align:start position:0%
+we have a term 1 over 2 Sigma squared
+ 
+
+ align:start position:0%
+we have a term 1 over 2 Sigma squared
+this must be equal to 8 and from this we
+
+ align:start position:0%
+this must be equal to 8 and from this we
+ 
+
+ align:start position:0%
+this must be equal to 8 and from this we
+can infer that the variance of this
+
+ align:start position:0%
+can infer that the variance of this
+ 
+
+ align:start position:0%
+can infer that the variance of this
+random variable is equal to 1 over 16
+
+ align:start position:0%
+random variable is equal to 1 over 16
+ 
+
+ align:start position:0%
+random variable is equal to 1 over 16
+and if you also want to find out the
+
+ align:start position:0%
+and if you also want to find out the
+ 
+
+ align:start position:0%
+and if you also want to find out the
+value of this constant C you check the
+
+ align:start position:0%
+value of this constant C you check the
+ 
+
+ align:start position:0%
+value of this constant C you check the
+formula for normal PDFs the constant C
+
+ align:start position:0%
+formula for normal PDFs the constant C
+ 
+
+ align:start position:0%
+formula for normal PDFs the constant C
+is 1 over the standard deviation which
+
+ align:start position:0%
+is 1 over the standard deviation which
+ 
+
+ align:start position:0%
+is 1 over the standard deviation which
+is 1/4 in our case the square root of
+
+ align:start position:0%
+is 1/4 in our case the square root of
+ 
+
+ align:start position:0%
+is 1/4 in our case the square root of
+this number times the square root of 2
+
+ align:start position:0%
+this number times the square root of 2
+ 
+
+ align:start position:0%
+this number times the square root of 2
+pi now suppose that somebody gives you a
+
+ align:start position:0%
+pi now suppose that somebody gives you a
+ 
+
+ align:start position:0%
+pi now suppose that somebody gives you a
+PDF of this form it's a constant times
+
+ align:start position:0%
+PDF of this form it's a constant times
+ 
+
+ align:start position:0%
+PDF of this form it's a constant times
+the negative exponential of a quadratic
+
+ align:start position:0%
+the negative exponential of a quadratic
+ 
+
+ align:start position:0%
+the negative exponential of a quadratic
+function in X we will argue that this
+
+ align:start position:0%
+function in X we will argue that this
+ 
+
+ align:start position:0%
+function in X we will argue that this
+PDF is also a normal PDF and identify
+
+ align:start position:0%
+PDF is also a normal PDF and identify
+ 
+
+ align:start position:0%
+PDF is also a normal PDF and identify
+the parameters of that normal first
+
+ align:start position:0%
+the parameters of that normal first
+ 
+
+ align:start position:0%
+the parameters of that normal first
+let's start with a certain observation a
+
+ align:start position:0%
+let's start with a certain observation a
+ 
+
+ align:start position:0%
+let's start with a certain observation a
+PDF must integrate to 1 so it cannot
+
+ align:start position:0%
+PDF must integrate to 1 so it cannot
+ 
+
+ align:start position:0%
+PDF must integrate to 1 so it cannot
+blow up as X goes to infinity which
+
+ align:start position:0%
+blow up as X goes to infinity which
+ 
+
+ align:start position:0%
+blow up as X goes to infinity which
+means that this exponential needs to die
+
+ align:start position:0%
+means that this exponential needs to die
+ 
+
+ align:start position:0%
+means that this exponential needs to die
+out as X goes to infinity and that will
+
+ align:start position:0%
+out as X goes to infinity and that will
+ 
+
+ align:start position:0%
+out as X goes to infinity and that will
+only happen if this coefficient alpha
+
+ align:start position:0%
+only happen if this coefficient alpha
+ 
+
+ align:start position:0%
+only happen if this coefficient alpha
+here is positive so that we have e to
+
+ align:start position:0%
+here is positive so that we have e to
+ 
+
+ align:start position:0%
+here is positive so that we have e to
+the minus something positive and large
+
+ align:start position:0%
+the minus something positive and large
+ 
+
+ align:start position:0%
+the minus something positive and large
+which is going to die out therefore we
+
+ align:start position:0%
+which is going to die out therefore we
+ 
+
+ align:start position:0%
+which is going to die out therefore we
+must have alpha being a positive
+
+ align:start position:0%
+must have alpha being a positive
+ 
+
+ align:start position:0%
+must have alpha being a positive
+constant and let us assume from now on
+
+ align:start position:0%
+constant and let us assume from now on
+ 
+
+ align:start position:0%
+constant and let us assume from now on
+that this is the case what we will do
+
+ align:start position:0%
+that this is the case what we will do
+ 
+
+ align:start position:0%
+that this is the case what we will do
+next is we will try to
+
+ align:start position:0%
+next is we will try to
+ 
+
+ align:start position:0%
+next is we will try to
+right this PDF in this form and the
+
+ align:start position:0%
+right this PDF in this form and the
+ 
+
+ align:start position:0%
+right this PDF in this form and the
+trick that we're going to use is the
+
+ align:start position:0%
+trick that we're going to use is the
+ 
+
+ align:start position:0%
+trick that we're going to use is the
+following we will focus on the term in
+
+ align:start position:0%
+following we will focus on the term in
+ 
+
+ align:start position:0%
+following we will focus on the term in
+the exponent which we rewrite this way
+
+ align:start position:0%
+the exponent which we rewrite this way
+ 
+
+ align:start position:0%
+the exponent which we rewrite this way
+we take out a factor of alpha and then
+
+ align:start position:0%
+we take out a factor of alpha and then
+ 
+
+ align:start position:0%
+we take out a factor of alpha and then
+we will try to make this expression here
+
+ align:start position:0%
+we will try to make this expression here
+ 
+
+ align:start position:0%
+we will try to make this expression here
+appear like a square of this kind like a
+
+ align:start position:0%
+appear like a square of this kind like a
+ 
+
+ align:start position:0%
+appear like a square of this kind like a
+perfect square so what is involved is a
+
+ align:start position:0%
+perfect square so what is involved is a
+ 
+
+ align:start position:0%
+perfect square so what is involved is a
+certain method a certain trick called
+
+ align:start position:0%
+certain method a certain trick called
+ 
+
+ align:start position:0%
+certain method a certain trick called
+completing the square that is we write
+
+ align:start position:0%
+completing the square that is we write
+ 
+
+ align:start position:0%
+completing the square that is we write
+this term here in the form X plus
+
+ align:start position:0%
+this term here in the form X plus
+ 
+
+ align:start position:0%
+this term here in the form X plus
+something squared and then we may need
+
+ align:start position:0%
+something squared and then we may need
+ 
+
+ align:start position:0%
+something squared and then we may need
+some additional terms what should that
+
+ align:start position:0%
+some additional terms what should that
+ 
+
+ align:start position:0%
+some additional terms what should that
+something be we would like that
+
+ align:start position:0%
+something be we would like that
+ 
+
+ align:start position:0%
+something be we would like that
+something be such that when we expand
+
+ align:start position:0%
+something be such that when we expand
+ 
+
+ align:start position:0%
+something be such that when we expand
+this quadratic we get this term and that
+
+ align:start position:0%
+this quadratic we get this term and that
+ 
+
+ align:start position:0%
+this quadratic we get this term and that
+term well we get an x squared and then
+
+ align:start position:0%
+term well we get an x squared and then
+ 
+
+ align:start position:0%
+term well we get an x squared and then
+there's going to be a cross term what do
+
+ align:start position:0%
+there's going to be a cross term what do
+ 
+
+ align:start position:0%
+there's going to be a cross term what do
+we need here so that the cross term is
+
+ align:start position:0%
+we need here so that the cross term is
+ 
+
+ align:start position:0%
+we need here so that the cross term is
+equal to this what we need is a term
+
+ align:start position:0%
+equal to this what we need is a term
+ 
+
+ align:start position:0%
+equal to this what we need is a term
+equal to beta over 2 alpha because in
+
+ align:start position:0%
+equal to beta over 2 alpha because in
+ 
+
+ align:start position:0%
+equal to beta over 2 alpha because in
+that case the cross term is going to be
+
+ align:start position:0%
+that case the cross term is going to be
+ 
+
+ align:start position:0%
+that case the cross term is going to be
+2 times X times beta divided by 2 alpha
+
+ align:start position:0%
+2 times X times beta divided by 2 alpha
+ 
+
+ align:start position:0%
+2 times X times beta divided by 2 alpha
+the 2 in the beginning and that to
+
+ align:start position:0%
+the 2 in the beginning and that to
+ 
+
+ align:start position:0%
+the 2 in the beginning and that to
+cancel out so we're left with X beta
+
+ align:start position:0%
+cancel out so we're left with X beta
+ 
+
+ align:start position:0%
+cancel out so we're left with X beta
+over alpha which is exactly what we got
+
+ align:start position:0%
+over alpha which is exactly what we got
+ 
+
+ align:start position:0%
+over alpha which is exactly what we got
+here however this quadratic is going to
+
+ align:start position:0%
+here however this quadratic is going to
+ 
+
+ align:start position:0%
+here however this quadratic is going to
+have an additional term which is going
+
+ align:start position:0%
+have an additional term which is going
+ 
+
+ align:start position:0%
+have an additional term which is going
+to be the square of this which is not
+
+ align:start position:0%
+to be the square of this which is not
+ 
+
+ align:start position:0%
+to be the square of this which is not
+present here so to keep the two sides
+
+ align:start position:0%
+present here so to keep the two sides
+ 
+
+ align:start position:0%
+present here so to keep the two sides
+equal we need to subtract that term and
+
+ align:start position:0%
+equal we need to subtract that term and
+ 
+
+ align:start position:0%
+equal we need to subtract that term and
+finally we have the last term involving
+
+ align:start position:0%
+finally we have the last term involving
+ 
+
+ align:start position:0%
+finally we have the last term involving
+gamma therefore the PDF of X is of the
+
+ align:start position:0%
+gamma therefore the PDF of X is of the
+ 
+
+ align:start position:0%
+gamma therefore the PDF of X is of the
+form we have a certain constant from
+
+ align:start position:0%
+form we have a certain constant from
+ 
+
+ align:start position:0%
+form we have a certain constant from
+here then we have the negative
+
+ align:start position:0%
+here then we have the negative
+ 
+
+ align:start position:0%
+here then we have the negative
+exponential of this term e to the minus
+
+ align:start position:0%
+exponential of this term e to the minus
+ 
+
+ align:start position:0%
+exponential of this term e to the minus
+alpha
+
+ align:start position:0%
+alpha
+ 
+
+ align:start position:0%
+alpha
+X plus beta over 2 alpha squared and
+
+ align:start position:0%
+X plus beta over 2 alpha squared and
+ 
+
+ align:start position:0%
+X plus beta over 2 alpha squared and
+then there's the negative exponential of
+
+ align:start position:0%
+then there's the negative exponential of
+ 
+
+ align:start position:0%
+then there's the negative exponential of
+the rest which is going to be a term of
+
+ align:start position:0%
+the rest which is going to be a term of
+ 
+
+ align:start position:0%
+the rest which is going to be a term of
+the form e to the minus alpha times beta
+
+ align:start position:0%
+the form e to the minus alpha times beta
+ 
+
+ align:start position:0%
+the form e to the minus alpha times beta
+squared over 4 alpha squared plus gamma
+
+ align:start position:0%
+squared over 4 alpha squared plus gamma
+ 
+
+ align:start position:0%
+squared over 4 alpha squared plus gamma
+over alpha now this term here does not
+
+ align:start position:0%
+over alpha now this term here does not
+ 
+
+ align:start position:0%
+over alpha now this term here does not
+involve any X's so it can be absorbed
+
+ align:start position:0%
+involve any X's so it can be absorbed
+ 
+
+ align:start position:0%
+involve any X's so it can be absorbed
+into the constant C the dependence on X
+
+ align:start position:0%
+into the constant C the dependence on X
+ 
+
+ align:start position:0%
+into the constant C the dependence on X
+is only through this term and now this
+
+ align:start position:0%
+is only through this term and now this
+ 
+
+ align:start position:0%
+is only through this term and now this
+term looks exactly like what we've got
+
+ align:start position:0%
+term looks exactly like what we've got
+ 
+
+ align:start position:0%
+term looks exactly like what we've got
+up here provided that you make the
+
+ align:start position:0%
+up here provided that you make the
+ 
+
+ align:start position:0%
+up here provided that you make the
+following identifications mu has to be
+
+ align:start position:0%
+following identifications mu has to be
+ 
+
+ align:start position:0%
+following identifications mu has to be
+equal to what we have here but here's
+
+ align:start position:0%
+equal to what we have here but here's
+ 
+
+ align:start position:0%
+equal to what we have here but here's
+there's a man who signs you there's no
+
+ align:start position:0%
+there's a man who signs you there's no
+ 
+
+ align:start position:0%
+there's a man who signs you there's no
+minus sign and so mu is going to be the
+
+ align:start position:0%
+minus sign and so mu is going to be the
+ 
+
+ align:start position:0%
+minus sign and so mu is going to be the
+negative of what we have up here it's
+
+ align:start position:0%
+negative of what we have up here it's
+ 
+
+ align:start position:0%
+negative of what we have up here it's
+minus beta over 2 alpha and as for Sigma
+
+ align:start position:0%
+minus beta over 2 alpha and as for Sigma
+ 
+
+ align:start position:0%
+minus beta over 2 alpha and as for Sigma
+squared we match and say that 1 over 2
+
+ align:start position:0%
+squared we match and say that 1 over 2
+ 
+
+ align:start position:0%
+squared we match and say that 1 over 2
+Sigma squared must be equal to the
+
+ align:start position:0%
+Sigma squared must be equal to the
+ 
+
+ align:start position:0%
+Sigma squared must be equal to the
+constant that we have up here which is
+
+ align:start position:0%
+constant that we have up here which is
+ 
+
+ align:start position:0%
+constant that we have up here which is
+alpha and from this we conclude that
+
+ align:start position:0%
+alpha and from this we conclude that
+ 
+
+ align:start position:0%
+alpha and from this we conclude that
+Sigma squared is equal to 1 over 2 alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have concluded that a PDF of this
+
+ align:start position:0%
+so we have concluded that a PDF of this
+ 
+
+ align:start position:0%
+so we have concluded that a PDF of this
+type is indeed a normal PDF it has a
+
+ align:start position:0%
+type is indeed a normal PDF it has a
+ 
+
+ align:start position:0%
+type is indeed a normal PDF it has a
+mean equal to that value and the
+
+ align:start position:0%
+mean equal to that value and the
+ 
+
+ align:start position:0%
+mean equal to that value and the
+variance equal to that value actually to
+
+ align:start position:0%
+variance equal to that value actually to
+ 
+
+ align:start position:0%
+variance equal to that value actually to
+figure out what the mean of this PDF is
+
+ align:start position:0%
+figure out what the mean of this PDF is
+ 
+
+ align:start position:0%
+figure out what the mean of this PDF is
+we do not need to go through this whole
+
+ align:start position:0%
+we do not need to go through this whole
+ 
+
+ align:start position:0%
+we do not need to go through this whole
+exercise once we're convinced that this
+
+ align:start position:0%
+exercise once we're convinced that this
+ 
+
+ align:start position:0%
+exercise once we're convinced that this
+is a normal PDF then we know that the
+
+ align:start position:0%
+is a normal PDF then we know that the
+ 
+
+ align:start position:0%
+is a normal PDF then we know that the
+mean is equal to the peak of the PDF to
+
+ align:start position:0%
+mean is equal to the peak of the PDF to
+ 
+
+ align:start position:0%
+mean is equal to the peak of the PDF to
+find the peak we want to maximize this
+
+ align:start position:0%
+find the peak we want to maximize this
+ 
+
+ align:start position:0%
+find the peak we want to maximize this
+over all X's which is the same as
+
+ align:start position:0%
+over all X's which is the same as
+ 
+
+ align:start position:0%
+over all X's which is the same as
+minimizing this quadratic function over
+
+ align:start position:0%
+minimizing this quadratic function over
+ 
+
+ align:start position:0%
+minimizing this quadratic function over
+all X's where is this quadratic function
+
+ align:start position:0%
+all X's where is this quadratic function
+ 
+
+ align:start position:0%
+all X's where is this quadratic function
+minimized to find that place we can look
+
+ align:start position:0%
+minimized to find that place we can look
+ 
+
+ align:start position:0%
+minimized to find that place we can look
+at the exponent take its derivative and
+
+ align:start position:0%
+at the exponent take its derivative and
+ 
+
+ align:start position:0%
+at the exponent take its derivative and
+set it to 0
+
+ align:start position:0%
+set it to 0
+ 
+
+ align:start position:0%
+set it to 0
+so setting the derivative of the
+
+ align:start position:0%
+so setting the derivative of the
+ 
+
+ align:start position:0%
+so setting the derivative of the
+exponent to zero gives us the equation
+
+ align:start position:0%
+exponent to zero gives us the equation
+ 
+
+ align:start position:0%
+exponent to zero gives us the equation
+two Alpha X plus beta equal to zero and
+
+ align:start position:0%
+two Alpha X plus beta equal to zero and
+ 
+
+ align:start position:0%
+two Alpha X plus beta equal to zero and
+from this we solve for X and we can tell
+
+ align:start position:0%
+from this we solve for X and we can tell
+ 
+
+ align:start position:0%
+from this we solve for X and we can tell
+that the peak of the distribution is
+
+ align:start position:0%
+that the peak of the distribution is
+ 
+
+ align:start position:0%
+that the peak of the distribution is
+going to be when X takes this particular
+
+ align:start position:0%
+going to be when X takes this particular
+ 
+
+ align:start position:0%
+going to be when X takes this particular
+value this value must also be equal to
+
+ align:start position:0%
+value this value must also be equal to
+ 
+
+ align:start position:0%
+value this value must also be equal to
+the mean so this is a very useful fact
+
+ align:start position:0%
+the mean so this is a very useful fact
+ 
+
+ align:start position:0%
+the mean so this is a very useful fact
+to know and we will use it over and over
+
+ align:start position:0%
+to know and we will use it over and over
+ 
+
+ align:start position:0%
+to know and we will use it over and over
+negative exponential of a quadratic
+
+ align:start position:0%
+negative exponential of a quadratic
+ 
+
+ align:start position:0%
+negative exponential of a quadratic
+function of X is always a normal PDF
\ No newline at end of file
diff --git a/SLcZXbyGC3E.txt b/SLcZXbyGC3E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..93ab3b8edb9271e870ea5d4430a42bc1db4c62eb
--- /dev/null
+++ b/SLcZXbyGC3E.txt
@@ -0,0 +1,3328 @@
+PROFESSOR: Well, I hope you
+appreciate that we have
+
+inducted you into some real
+magic, the magic of building
+
+languages, really building
+new languages.
+
+What have we looked at?
+
+We've looked at an Escher
+picture language: this
+
+language invented by
+Peter Henderson.
+
+We looked at digital
+logic language.
+
+Let's see.
+
+We've looked at the
+query language.
+
+And the thing you should realize
+is, even though these
+
+were toy examples, they really
+are the kernels of really
+
+useful things.
+
+So, for instance, the Escher
+picture language was taken by
+
+Henry Wu, who's a student at
+MIT, and developed into a real
+
+language for laying out PC
+boards based just on extending
+
+those structures.
+
+And the digital logic language,
+Jerry mentioned when
+
+he showed it to you, was really
+extended to be used as
+
+the basis for a simulator
+that was used to
+
+design a real computer.
+
+And the query language,
+of course, is kind
+
+of the germ of prologue.
+
+So we built all of these
+languages, they're
+
+all based on LISP.
+
+A lot of people ask what
+particular problems is LISP
+
+good for solving for?
+
+The answer is LISP is not good
+for solving any particular
+
+problems. What LISP is good for
+is constructing within it
+
+the right language to solve
+the problems you want to
+
+solve, and that's how you
+should think about it.
+
+So all of these languages
+were based on LISP.
+
+Now, what's LISP based on?
+
+Where's that come from?
+
+Well, we looked at that too.
+
+We looked at the meta-circular
+evaluator and said well, LISP
+
+is based on LISP.
+
+And when we start looking at
+that, we've got to do some
+
+real magic, right?
+
+So what does that mean, right?
+
+Why operators, and fixed points,
+and the idea that what
+
+this means is that LISP is
+somehow the fixed-point
+
+equation for this funny set of
+things which are defined in
+
+terms of themselves.
+
+Now, it's real magic.
+
+Well, today, for a final piece
+of magic, we're going to make
+
+all the magic go away.
+
+We already know how
+to do that.
+
+The idea is, we're going to
+take the register machine
+
+architecture and show
+how to implement
+
+LISP on terms of that.
+
+And, remember, the idea of the
+register machine is that
+
+there's a fixed and finite
+part of the machine.
+
+There's a finite-state
+controller, which does some
+
+particular thing with a
+particular amount of hardware.
+
+There are particular data
+paths: the operation the
+
+machine does.
+
+And then, in order to implement
+recursion and
+
+sustain the illusion of
+infinity, there's some large
+
+amount of memory, which
+is the stack.
+
+So, if we implement LISP in
+terms of a register machine,
+
+then everything ought to
+become, at this point,
+
+completely concrete.
+
+All the magic should go away.
+
+And, by the end of this talk,
+I want you get the feeling
+
+that, as opposed to this very
+mysterious meta-circular
+
+evaluator, that a LISP evaluator
+really is something
+
+that's concrete enough that
+you can hold in the
+
+palm of your hand.
+
+You should be able to
+imagine holding a
+
+LISP interpreter there.
+
+All right, how are we
+going to do this?
+
+We already have all
+the ingredients.
+
+See, what you learned last time
+from Jerry is how to take
+
+any particular couple of LISP
+procedures and hand-translate
+
+them into something that runs
+on a register machine.
+
+So, to implement all of LISP on
+a register machine, all we
+
+have to do is take the
+particular procedures that are
+
+the meta-circular evaluator and
+hand-translate them for a
+
+register machine.
+
+And that does all
+of LISP, right?
+
+So, in principle, we already
+know how to do this.
+
+And, indeed, it's going to be
+no different, in kind, from
+
+translating, say, recursive
+factorial
+
+or recursive Fibonacci.
+
+It's just bigger and
+there's more of it.
+
+So it'd just be more details,
+but nothing really
+
+conceptually new.
+
+All right, also, when we've done
+that, and the thing is
+
+completely explicit, and we see
+how to implement LISP in
+
+terms of the actual sequential
+register operations, that's
+
+going to be our final most
+explicit model of
+
+LISP in this course.
+
+And, remember, that's
+a progression
+
+through this course.
+
+We started out with
+substitution, which is sort of
+
+like algebra.
+
+And then we went to the
+environment model, which
+
+talked about the actual
+frames and how
+
+they got linked together.
+
+And then we made that
+more concrete in the
+
+meta-circular evaluator.
+
+There are things the
+meta-circular evaluator
+
+doesn't tell us.
+
+You should realize that.
+
+For instance, it left unanswered
+the question of how
+
+a procedure, like recursive
+factorial here , somehow takes
+
+space that grows.
+
+On the other hand, a procedure
+which also looks syntactically
+
+recursive, called fact-iter,
+somehow doesn't take space.
+
+We justify that it doesn't need
+to take space by showing
+
+the substitution model.
+
+But we didn't really say how
+it happens that the machine
+
+manages to do that, that that
+has to do with the details of
+
+how arguments are passed
+to procedures.
+
+And that's the thing we didn't
+see in the meta-circular
+
+evaluator precisely because the
+way arguments got passed
+
+to procedures in this LISP
+depended on the way arguments
+
+got passed to procedures
+in this LISP.
+
+But, now, that's going to become
+extremely explicit.
+
+OK.
+
+Well, before going on to the
+evaluator, let me just give
+
+you a sense of what a whole LISP
+system looks like so you
+
+can see the parts we're going
+to talk about and the parts
+
+we're not going to talk about.
+
+Let's see, over here is a happy
+LISP user, and the LISP
+
+user is talking to something
+called the reader.
+
+The reader's job in life is to
+take characters from the user
+
+and turn them into data
+structures in something called
+
+a list structure memory.
+
+All right, so the reader is
+going to take symbols,
+
+parentheses, and A's and B's,
+and ones and threes that you
+
+type in, and turn these into
+actual list structure: pairs,
+
+and pointers, and things.
+
+And so, by the time evaluator
+is going, there are no
+
+characters in the world.
+
+And, of course, in more modern
+list systems, there's sort of
+
+a big morass here that might sit
+between the user and the
+
+reader: Windows systems, and top
+levels, and mice, and all
+
+kinds of things.
+
+But conceptually, characters
+are coming in.
+
+All right, the reader transforms
+these into pointers
+
+to stuff in this memory,
+and that's what the
+
+evaluator sees, OK?
+
+The evaluator has a
+bunch of helpers.
+
+It has all possible primitive
+operators you might want.
+
+So there's a completely separate
+box, a floating point
+
+unit, or all sorts of
+things, which do
+
+the primitive operators.
+
+And, if you want more special
+primitives, you build more
+
+primitive operators,
+but they're
+
+separate from the evaluator.
+
+The evaluator finally gets an
+answer and communicates that
+
+to the printer.
+
+And now, the printer's job in
+life is to take this list
+
+structure coming from the
+evaluator, and turn it back
+
+into characters, and communicate
+them to the user
+
+through whatever interface
+there is.
+
+OK.
+
+Well, today, what we're
+going to talk
+
+about is this evaluator.
+
+The primitive operators have
+nothing particular to do with
+
+LISP, they're however you like
+to implement primitive
+
+operations.
+
+The reader and printer are
+actually complicated, but
+
+we're not going to
+talk about them.
+
+They sort of have to do with
+details of how you might build
+
+up list structure
+from characters.
+
+So that is a long story,
+but we're not going
+
+to talk about it.
+
+The list structure memory, we'll
+talk about next time.
+
+So, pretty much, except for
+the details of reading and
+
+printing, the only mystery
+that's going to be left after
+
+you see the evaluator is how
+you build list structure on
+
+conventional memories.
+
+But we'll worry about
+that next time too.
+
+OK.
+
+Well, let's start talking
+about the evaluator.
+
+The one that we're going to show
+you, of course, is not, I
+
+think, nothing special
+about it.
+
+It's just a particular register
+
+machine that runs LISP.
+
+And it has seven registers,
+and here
+
+are the seven registers.
+
+There's a register, called EXP,
+and its job is to hold
+
+the expression to
+be evaluated.
+
+And by that, I mean it's going
+to hold a pointer to someplace
+
+in list structure memory
+that holds the
+
+expression to be evaluated.
+
+There's a register, called
+ENV, which holds the
+
+environment in which this
+expression is to be evaluated.
+
+And, again, I made a pointer.
+
+The environment is some
+data structure.
+
+There's a register, called
+FUN, which will hold the
+
+procedure to be applied when you
+go to apply a procedure.
+
+A register, called ARGL,
+which wants the list
+
+of evaluated arguments.
+
+What you can start seeing
+here is the basic
+
+structure of the evaluator.
+
+Remember how evaluators work.
+
+There's a piece that takes
+expressions and environments,
+
+and there's a piece that
+takes functions, or
+
+procedures and arguments.
+
+And going back and forth
+around here is
+
+the eval/apply loop.
+
+So those are the basic pieces
+of the eval and apply.
+
+Then there's some other things,
+there's continue.
+
+You just saw before how the
+continue register is used to
+
+implement recursion and
+stack discipline.
+
+There's a register that's going
+to hold the result of
+
+some evaluation.
+
+And then, besides that,
+there's one temporary
+
+register, called UNEV, which
+typically, in the evaluator,
+
+is going to be used to hold
+temporary pieces of the
+
+expression you're working on,
+which you haven't gotten
+
+around to evaluate yet, right?
+
+So there's my machine: a
+seven-register machine.
+
+And, of course, you might want
+to make a machine with a lot
+
+more registers to get better
+performance, but this is just
+
+a tiny, minimal one.
+
+Well, how about the
+data paths?
+
+This machine has a lot of
+special operations for LISP.
+
+So, here are some typical
+data paths.
+
+A typical one might be, oh,
+assign to the VAL register the
+
+contents of the EXP register.
+
+In terms of those diagrams you
+saw, that's a little button on
+
+some arrow.
+
+Here's a more complicated one.
+
+It says branch, if the thing in
+the expression register is
+
+a conditional to some label
+here, called the
+
+ev-conditional.
+
+And you can imagine this
+implemented in a lot of
+
+different ways.
+
+You might imagine this
+conditional test as a special
+
+purpose sub-routine, and
+conditional might be
+
+represented as some data
+abstraction that you don't
+
+care about at this
+level of detail.
+
+So that might be done
+as a sub-routine.
+
+This might be a machine with
+hardware-types, and
+
+conditional might be testing
+some bits for
+
+a particular code.
+
+There are all sorts of ways
+that's beneath the level of
+
+abstraction we're looking at.
+
+Another kind of operation, and
+there are a lot of different
+
+operations assigned to
+EXP, the first clause
+
+of what's in EXP.
+
+This might be part of processing
+a conditional.
+
+And, again, first clause is some
+selector whose details we
+
+don't care about.
+
+And you can, again, imagine that
+as a sub-routine which'll
+
+do some list operations, or
+you can imagine that as
+
+something that's built directly
+into hardware.
+
+The reason I keep saying you can
+imagine it built directly
+
+into hardware is even though
+there are a lot of operations,
+
+there are still a fixed
+number of them.
+
+I forget how many, maybe 150.
+
+So, it's plausible to think
+of building these
+
+directly into hardware.
+
+Here's a more complicated one.
+
+You can see this has to
+do with looking up
+
+the values of variables.
+
+It says assign to the VAL
+register the result of looking
+
+up the variable value of some
+particular expression, which,
+
+in this case, is supposed
+to be a variable in some
+
+environment.
+
+And this'll be some operation
+that searches through the
+
+environment structure, however
+it is represented, and goes
+
+and looks up that variable.
+
+And, again, that's below the
+level of detail that we're
+
+thinking about.
+
+This has to do with the details
+of the data structures
+
+for representing environments.
+
+But, anyway, there is this fixed
+and finite number of
+
+operations in the register
+machine.
+
+Well, what's its overall
+structure?
+
+Those are some typical
+operations.
+
+Remember what we have to
+do, we have to take the
+
+meta-circular evaluator--
+
+and here's a piece of the
+meta-circular evaluator.
+
+This is the one using abstract
+syntax that's in the book.
+
+It's a little bit different
+from the one
+
+that Jerry shows you.
+
+And the main thing to remember
+about the evaluator is that
+
+it's doing some sort of case
+analysis on the kinds of
+
+expressions: so if it's either
+self-evaluated, or quoted, or
+
+whatever else.
+
+And then, in the general case
+where the expression it's
+
+looking at is an application,
+there's some tricky
+
+recursions going on.
+
+First of all, eval has to call
+itself both to evaluate the
+
+operator and to evaluate
+all the operands.
+
+So there's this sort of red
+recursion of values walking
+
+down the tree that's really
+the easy recursion.
+
+That's just a val walking down
+this tree of expressions.
+
+Then, in the evaluator, there's
+a hard recursion.
+
+There's the red to green.
+
+Eval calls apply.
+
+That's the case where evaluating
+a procedure or
+
+argument reduces to applying
+the procedure
+
+to the list of arguments.
+
+And then, apply comes
+over here.
+
+Apply takes a procedure and
+arguments and, in the general
+
+case where there's a compound
+procedure, apply goes around
+
+and green calls red.
+
+Apply comes around and
+calls eval again.
+
+Eval's the body of the procedure
+in the result of
+
+extending the environment with
+the parameters of the
+
+procedure by binding
+the arguments.
+
+Except in the primitive case,
+where it just calls something
+
+else primitive-apply, which
+is not really the
+
+business of the evaluator.
+
+So this sort of red to green,
+to red to green, that's the
+
+eval/apply loop, and that's the
+thing that we're going to
+
+want to see in the evaluator.
+
+All right.
+
+Well, it won't surprise you at
+all that the two big pieces of
+
+this evaluator correspond
+to eval and apply.
+
+There's a piece called
+eval-dispatch, and a piece
+
+called apply-dispatch.
+
+And, before we get into the
+details of the code, the way
+
+to understand this is to think,
+again, in terms of
+
+these pieces of the evaluator
+having contracts with the rest
+
+of the world.
+
+What do they do from the outside
+before getting into
+
+the grungy details?
+
+Well, the contract for
+eval-dispatch--
+
+remember, it corresponds
+to eval.
+
+It's got to evaluate an
+expression in an environment.
+
+So, in particular, what this
+one is going to do,
+
+eval-dispatch will assume that,
+when you call it, that
+
+the expression you
+want to evaluate
+
+is in the EXP register.
+
+The environment in which you
+want the evaluation to take
+
+place is in the ENV register.
+
+And continue tells you the place
+where the machine should
+
+go next when the evaluation
+is done.
+
+Eval-dispatch's contract is that
+it'll actually perform
+
+that evaluation, and, at the end
+of which, it'll end up at
+
+the place specified
+by continue.
+
+The result of the evaluation
+will be in the VAL register.
+
+And it just warns you, it makes
+no promises about what
+
+happens to the registers.
+
+All other registers might
+be destroyed.
+
+So, there's one piece, OK?
+
+Together, the pieces,
+apply-dispatch that
+
+corresponds to apply, it's got
+to apply a procedure to some
+
+arguments, so it assumes that
+this register, ARGL, contains
+
+a list of the evaluated
+arguments.
+
+FUN contains the procedure.
+
+Those correspond to the
+arguments to the apply
+
+procedure in the meta-circular
+evaluator.
+
+And apply, in this particular
+evaluator, we're going to use
+
+a discipline which says the
+place the machine should go to
+
+next when apply is done is, at
+the moment apply-dispatch is
+
+called at the top of the stack,
+that's just discipline
+
+for the way this particular
+machine's organized.
+
+And now apply's contract
+is given all that.
+
+It'll perform the application.
+
+The result of that application
+will end up in VAL.
+
+The stack will be popped.
+
+And, again, the contents of all
+the other registers may be
+
+destroyed, all right?
+
+So that's the basic organization
+of this machine.
+
+Let's break for a little bit
+and see if there are any
+
+questions, and then we'll
+do a real example.
+
+Well, let's take the register
+machine now, and actually step
+
+through, and really, in real
+detail, so you see completely
+
+concrete how some expressions
+are evaluated, all right?
+
+So, let's start with a very
+simple expression.
+
+Let's evaluate the
+expression 1.
+
+And we need an environment, so
+let's imagine that somewhere
+
+there's an environment,
+we'll call it E,0.
+
+And just, since we'll use these
+later, we obviously
+
+don't really need anything
+to evaluate 1.
+
+But, just for reference later,
+let's assume that E,0 has in
+
+it an X that's bound to 3 and
+a Y that's bound to 4, OK?
+
+And now what we're going to do
+is we're going to evaluate 1
+
+in this environment, and so the
+ENV register has a pointer
+
+to this environment,
+E,0, all right?
+
+So let's watch that thing go.
+
+What I'm going to do is
+step through the code.
+
+And, let's see, I'll
+be the controller.
+
+And now what I need, since this
+gets rather complicated,
+
+is a very little
+execution unit.
+
+So here's the execution
+unit, OK?
+
+OK.
+
+OK.
+
+All right, now we're
+going to start.
+
+We're going to start
+the machine at
+
+eval-dispatch, right?
+
+That's the beginning of this.
+
+Eval-dispatch is going to look
+at the expression in dispatch,
+
+just like eval where we look
+at the very first thing.
+
+We branch on whether or
+not this expression is
+
+self-evaluating.
+
+Self-evaluating is some
+abstraction we
+
+put into the machine--
+
+it's going to be true
+for numbers--
+
+to a place called ev-self-eval,
+right?
+
+So me, being the controller,
+looks at ev-self-eval, so
+
+we'll go over to there.
+
+Ev-self-eval says fine, assign
+to val whatever is in the
+
+expression unit, OK?
+
+And I have a bug because what I
+didn't do when I initialized
+
+this machine is also say what's
+supposed to happen when
+
+it's done, so I should have
+started out the machine with
+
+done being in the continue
+register, OK?
+
+So we assign to VAL.
+
+And now go to fetch
+of continue, and
+
+[? the value changed. ?]
+
+OK.
+
+OK, let's try something
+harder.
+
+Let's reset the machine here,
+and we'll put in the
+
+expression register, X, OK?
+
+Start again at eval-dispatch.
+
+Check, is it self-evaluating?
+
+No.
+
+Is it a variable?
+
+Yes.
+
+We go off to ev-variable.
+
+It says assign to VAL, look up
+the variable value in the
+
+expression register, OK?
+
+Go to fetch of continue.
+
+PROFESSOR: Done.
+
+PROFESSOR: OK.
+
+All right.
+
+Well, that's the basic idea.
+
+That's a simple operation
+of the machine.
+
+Now, let's actually do something
+a little bit more
+
+interesting.
+
+Let's look at the expression
+the sum of x and y.
+
+OK.
+
+And now we'll see how you
+start unrolling these
+
+expression trees, OK?
+
+Well, start again at
+eval-dispatch, all right?
+
+Self-evaluating?
+
+No.
+
+Variable?
+
+No.
+
+All the other special forms
+which I didn't write down,
+
+like quote, and lambda,
+and set, and whatever,
+
+it's none of those.
+
+It turns out to be an
+application, so we go off to
+
+ev-application, OK?
+
+Ev-application, remember what
+it's going to do overall.
+
+It is going to evaluate
+the operator.
+
+It's going to evaluate the
+arguments, and then it's going
+
+to go apply them.
+
+So, before we start, since we're
+being very literal, we'd
+
+better remember that, somewhere
+in this environment,
+
+it's linked to another
+environment in which plus is
+
+bound to the primitive procedure
+plus before we get
+
+an unknown variable
+in our machine.
+
+OK, so we're at ev-application.
+
+OK, assign to UNEV the operands
+of what's in the
+
+expression register, OK?
+
+Those are the operands.
+
+UNEV's a temporary register
+where we're
+
+going to save them.
+
+PROFESSOR: I'm assigning.
+
+PROFESSOR: Assign to
+x the operator.
+
+Now, notice we've destroyed that
+expression in x, but the
+
+piece that we need is
+now in UNEV. OK.
+
+Now, we're going to get
+set up to recursively
+
+evaluate the operator.
+
+Save the continue register
+on the stack.
+
+Save the environment.
+
+Save UNEV. OK, assign
+to continue a
+
+label called eval-args.
+
+Now, what have we done?
+
+We've set up for a
+recursive call.
+
+We're about to go to
+eval-dispatch.
+
+We've set up for a recursive
+call to eval-dispatch.
+
+What did we do?
+
+We took the things we're going
+to need later, those operands
+
+that were in UNEV; the
+environment in which we're
+
+going to eventually have to,
+maybe, evaluate those
+
+operands; the place we
+eventually want to go to,
+
+which, in this case, was done;
+we've saved them on the stack.
+
+The reason we saved them
+on the stack is because
+
+eval-dispatch makes no promises
+about what registers
+
+it may destroy.
+
+So all that stuff is
+saved on the stack.
+
+Now, we've set up
+eval-dispatch's contract.
+
+There's a new expression, which
+is the operator plus; a
+
+new environment, although, in
+this case, it's the same one;
+
+and a new place to
+go to when you're
+
+done, which is eval-args.
+
+So that's set up.
+
+Now, we're going to go
+off to eval-dispatch.
+
+Here we are back at
+eval-dispatch.
+
+It's not self-evaluating.
+
+Oh, it's a variable, so
+we'd better go off to
+
+ev-variable, right?
+
+Ev-variable is assigned
+to VAL.
+
+Look up the variable value
+of the expression, OK?
+
+So VAL is the primitive
+procedure plus, OK?
+
+And go to fetch of continue.
+
+PROFESSOR: Eval-args.
+
+PROFESSOR: Right, which is
+now eval-args not done.
+
+So we come back here at
+eval-args, and what do we do?
+
+We're going to restore the stuff
+that we saved, so we
+
+restore UNEV. And notice, there,
+it wasn't necessary,
+
+although, in general,
+it would be.
+
+It might be some arbitrary
+evaluation that happened.
+
+We restore ENV. OK, we assign
+to FUN fetch of VAL.
+
+OK, now, we're going
+to go off and start
+
+evaluating some arguments.
+
+Well, first thing we'd better
+do is save FUN because some
+
+arbitrary stuff might happen
+in that evaluation.
+
+We initialize the argument list.
+Assign to argl an empty
+
+argument list, and go to
+eval-arg-loop, OK?
+
+At eval-arg-loop, the idea
+of this is we're going to
+
+evaluate the pieces of the
+expressions that are in UNEV,
+
+one by one, and move them from
+unevaluated in UNEV to
+
+evaluated in the arg list, OK?
+
+So we save argl.
+
+We assign to x the first operand
+of the stuff in UNEV.
+
+Now, we check and see if that
+was the last operand.
+
+In this case, it is
+not, all right?
+
+So we save the environment.
+
+We save UNEV because those
+are all things
+
+we might need later.
+
+We're going to need the
+environment to do some more
+
+evaluations.
+
+We're going to need UNEV to look
+at what the rest of those
+
+arguments were.
+
+We're going to assign continue
+a place called
+
+accumulate-args, or
+accumulate-arg.
+
+OK, now, we've set up
+for another call to
+
+eval-dispatch, OK?
+
+All right, now, let me
+short-circuit this so we don't
+
+go through the details
+of eval-dispatch.
+
+Eval-dispatch's contract says
+I'm going to end up, the world
+
+will end up, with the value of
+evaluating this expression in
+
+this environment in
+the VAL register,
+
+and I'll end up there.
+
+So we short-circuit all of this,
+and a 3 ends up in VAL.
+
+And, when we return from
+eval-dispatch, we're going to
+
+return to accumulate-arg.
+
+PROFESSOR: Accumulate-arg.
+
+PROFESSOR: With 3 in the
+VAL register, OK?
+
+So that short-circuited
+that evaluation.
+
+Now, what do we do?
+
+We're going to go back and
+look at the rest of the
+
+arguments, so we restore
+UNEV. We restore
+
+ENV. We restore argl.
+
+One thing.
+
+PROFESSOR: Oops!
+
+Parity error.
+
+[LAUGHTER]
+
+PROFESSOR: Restore argl.
+
+PROFESSOR: OK.
+
+OK, we assign to argl consing on
+fetch of the value register
+
+to what's in argl.
+
+OK, we assign to UNEV the rest
+of the operands in fetch of
+
+UNEV, and we go back
+to eval-arg-loop.
+
+PROFESSOR: Eval-arg-loop.
+
+PROFESSOR: OK.
+
+Now, we're about to do the next
+argument, so the first
+
+thing we do is save argl.
+
+OK, we assign to x the first
+operand of fetch of UNEV. OK,
+
+we test and see if that's
+the last operand.
+
+In this case, it is, so we're
+going to go to a special place
+
+that says evaluate the last
+argument because, notice,
+
+after evaluating the argument,
+we don't need the
+
+environment any more.
+
+That's going to be
+the difference.
+
+So here, at eval-last-arg,
+which is assigned to
+
+accumulate-last-arg, now,
+we're set up again for
+
+eval-dispatch.
+
+We've got a place to go
+to when we're done.
+
+We've got an expression.
+
+We've got an environment.
+
+OK, so we'll short-circuit the
+call to eval-dispatch.
+
+And what'll happen is there's
+a y there, it's 4 in that
+
+environment, so VAL will
+end up with 4 in it.
+
+And, then, we're going to end up
+at accumulate-last-arg, OK?
+
+So, at accumulate-last-arg,
+we restore argl.
+
+We assign to argl cons of fetch
+of the new value onto
+
+it, so we cons a 4 onto that.
+
+We restore what was saved in
+the function register.
+
+And notice, in this case, it had
+not been destroyed, but,
+
+in general, it will be.
+
+And now, we're ready to go off
+to apply-dispatch, all right?
+
+So we've just gone
+through the eval.
+
+We evaluated the argument, the
+operator, and the arguments,
+
+and now, we're about
+to apply them.
+
+So we come off to apply-dispatch
+here, OK?
+
+We come off to apply-dispatch,
+and we're going to check
+
+whether it's a primitive or
+a compound procedure.
+
+PROFESSOR: Yes.
+
+PROFESSOR: All right.
+
+So, in this case, it's a
+primitive procedure, and we go
+
+off to primitive-apply.
+
+So we go off to primitive-apply,
+and it says
+
+assign to VAL the result of
+applying primitive procedure
+
+of the function to the
+argument list.
+
+PROFESSOR: I don't
+know how to add.
+
+I'm just an execution unit.
+
+PROFESSOR: Well, I don't
+know how to add either.
+
+I'm just the evaluator, so we
+need a primitive operator.
+
+Let's see, so the primitive
+operator, what's the
+
+sum of 3 and 4?
+
+AUDIENCE: 7.
+
+PROFESSOR: OK, 7.
+
+PROFESSOR: Thank you.
+
+PROFESSOR: Now, we restore
+continue, and we go to fetch
+
+of continue.
+
+PROFESSOR: Done.
+
+PROFESSOR: OK.
+
+Well, that was in as much detail
+as you will ever see.
+
+We'll never do it in as
+much detail again.
+
+One very important thing to
+notice is that we just
+
+executed a recursive
+procedure, right?
+
+This whole thing, we used
+a stack and the
+
+evaluator was recursive.
+
+A lot of people think the reason
+that you need a stack
+
+and recursion in an evaluator
+is because you might be
+
+evaluating recursive
+procedures like
+
+factorial or Fibonacci.
+
+It's not true.
+
+So you notice we did recursion
+here, and all we evaluated was
+
+plus X, Y, all right?
+
+The reason that you need
+recursion in the evaluator is
+
+because the evaluation
+process, itself, is
+
+recursive, all right?
+
+It's not because the procedure
+that you might be evaluating
+
+in LISP is a recursive
+procedure.
+
+So that's an important
+thing that people get
+
+confused about a lot.
+
+The other thing to notice is
+that, when we're done here,
+
+we're really done.
+
+Not only are we at done, but
+there's no accumulated stuff
+
+on the stack, right?
+
+The machine is back to its
+initial state, all right?
+
+So that's part of what
+it means to be done.
+
+Another way to say that is the
+evaluation process has reduced
+
+the expression, plus X, Y,
+to the value here, 7.
+
+And by reduced, I mean a
+very particular thing.
+
+It means that there's nothing
+left on the stack.
+
+The machine is now in the same
+state, except there's
+
+something in the
+value register.
+
+It's not part of a sub-problem
+of anything.
+
+There's nothing to go back to.
+
+OK.
+
+Let's break.
+
+Question?
+
+AUDIENCE: The question here, in
+the stack, is because the
+
+data may be recursive.
+
+You may have embedded
+expressions, for instance.
+
+PROFESSOR: Yes, because you
+might have embedded
+
+expressions.
+
+But, again, don't confuse that
+with what people sometimes
+
+mean by the data may be
+recursive, which is to say you
+
+have these list-structured,
+recursive data list
+
+operations.
+
+That has nothing
+to do with it.
+
+It's simply that the
+expressions contain
+
+sub-expressions.
+
+Yeah?
+
+AUDIENCE: Why is it that the
+order of the arguments in the
+
+arg list got reversed?
+
+PROFESSOR: Ah!
+
+Yes, I should've
+mentioned that.
+
+Here, the reason the
+order is reversed--
+
+it's a question of what
+you mean by reversed.
+
+I believe it was Newton.
+
+In the very early part of
+optics, people realized that,
+
+when you look through the lens
+of your eye, the image was
+
+up-side down.
+
+And there was a lot of argument
+about why that didn't
+
+mean you saw things
+up-side down.
+
+So it's sort of the
+same issue.
+
+Reversed from what?
+
+So we just need some
+convention.
+
+The reason that they're coming
+at 4, 3 is because we're
+
+taking UNEV and consing
+the result onto argl.
+
+So you have to realize you've
+made that convention.
+
+The place that you have
+to realize that--
+
+well, there's actually
+two places.
+
+One is in
+apply-primitive-operator,
+
+which has to realize that the
+arguments to primitives go in,
+
+in the opposite order from the
+way you're writing them down.
+
+And the other one is, we'll see
+later when you actually go
+
+to bind a function's parameters,
+you should realize
+
+the arguments are going to
+come in from the opposite
+
+order of the variables to which
+you're binding them.
+
+So, if you just keep track of
+that, there's no problem.
+
+Also, this is completely
+arbitrary because, if we'd
+
+done, say, an iteration through
+a vector assigning
+
+them, they might come out
+in the other order, OK?
+
+So it's just a convention of
+the way this particular
+
+evaluator works.
+
+All right, let's take a break.
+
+We just saw evaluating an
+expression and, of course,
+
+that was very simple one.
+
+But, in essence, it would be
+no different if it was some
+
+big nested expression, so there
+would just be deeper
+
+recursion on the stack.
+
+But what I want to do now is
+show you the last piece.
+
+I want to walk you around this
+eval and apply loop, right?
+
+That's the thing we haven't
+seen, really.
+
+We haven't seen any compound
+procedures where applying a
+
+procedure reduces to evaluating
+the body of the
+
+procedure, so let's just
+suppose we had this.
+
+Suppose we were looking at the
+procedure define F of A and B
+
+to be the sum of A and B. So, as
+we typed in that procedure
+
+previously, and now we're going
+to evaluate F of X and
+
+Y, again, in this environment,
+E,0, where X is bound to 3 and
+
+Y is bound to 4.
+
+When the defined is executed,
+remember, there's a lambda
+
+here, and lambdas create
+procedures.
+
+And, basically, what will happen
+is, in E,0, we'll end
+
+up with a binding for F, which
+will say F is a procedure, and
+
+its args are A and B, and
+its body is plus a,b.
+
+So that's what the environment
+would have looked like had we
+
+made that definition.
+
+Then, when we go to evaluate F
+of X and Y, we'll go through
+
+exactly the same process
+that we did before.
+
+It's even the same expression.
+
+The only difference is that F,
+instead of having primitive
+
+plus in it, will have
+this thing.
+
+And so we'll go through exactly
+the same process,
+
+except this time, when we end
+up at apply-dispatch, the
+
+function register, instead of
+having primitive plus, will
+
+have a thing that will represent
+it saying procedure,
+
+where the args are A and B,
+and the body is plus A, B.
+
+And, again, what I mean, by
+its ENV, I mean there's a
+
+pointer to it, so don't worry
+that I'm writing a lot of
+
+stuff there.
+
+There's a pointer to this
+procedure data structure.
+
+OK, so, we're in exactly
+the same situation.
+
+We get to apply-dispatch,
+so, here, we come to
+
+apply-dispatch.
+
+Last time, we branched off
+to a primitive procedure.
+
+Here, it says oh, we now have a
+compound procedure, so we're
+
+going to go off to
+compound-apply.
+
+Now, what's compound-apply?
+
+Well, remember what the
+meta-circular evaluator did?
+
+Compound-apply said we're going
+to evaluate the body of
+
+the procedure in some
+new environment.
+
+Where does that new environment
+come from?
+
+We take the environment that
+was packaged with the
+
+procedure, we bind the
+parameters of the procedure to
+
+the arguments that we're passing
+in, and use that as a
+
+new frame to extend the
+procedure environment.
+
+And that's the environment
+in which we evaluate the
+
+procedure body, right?
+
+That's going around the
+apply/eval loop.
+
+That's apply coming back to
+call eval, all right?
+
+OK.
+
+So, now, that's all we have
+to do in compound-apply.
+
+What are we going to do?
+
+We're going to manufacture
+a new environment.
+
+And we're going to manufacture
+a new environment, let's see,
+
+that we'll call E,1.
+
+E,1 is going to be some
+environment where the
+
+parameters of the procedure,
+where A is bound to 3 and B is
+
+bound to 4, and it's linked
+to E,0 because
+
+that's where f is defined.
+
+And, in this environment, we're
+going to evaluate the
+
+body of the procedure.
+
+So let's look at that,
+all right?
+
+All right, here we are at
+compound-apply, which says
+
+assign to the expression
+register the body of the
+
+procedure that's in the
+function register.
+
+So I assign to the expression
+register the
+
+procedure body, OK?
+
+That's going to be evaluated
+in an environment which is
+
+formed by making some bindings
+using information determined
+
+by the procedure--
+
+that's what's in FUN--
+
+and the argument list.
+
+And let's not worry about
+exactly what that does, but
+
+you can see the information's
+there.
+
+So make bindings will say oh,
+the procedure, itself, had an
+
+environment attached to it.
+
+I didn't write that
+quite here.
+
+I should've said in environment
+because every
+
+procedure gets built with
+an environment.
+
+So, from that environment, it
+knows what the procedure's
+
+definition environment is.
+
+It knows what the
+arguments are.
+
+It looks at argl, and
+then you see a
+
+reversal convention here.
+
+It just has to know that argl
+is reversed, and it builds
+
+this frame, E,1.
+
+All right, so, let's assume that
+that's what make bindings
+
+returns, so it assigns to
+ENV this thing, E,1.
+
+All right, the next thing it
+says is restore continue.
+
+Remember what continue
+was here?
+
+It got put up in the
+last segment.
+
+Continue got stored.
+
+That was the original done,
+which said what are you going
+
+to do after you're done with
+this particular application?
+
+It was one of the very first
+things that happened when we
+
+evaluated the application.
+
+And now, finally, we're going
+to restore continue.
+
+Remember apply-dispatch's
+contract.
+
+It assumes that where it should
+go to next was on the
+
+stack, and there it
+was on the stack.
+
+Continue has done, and now
+we're going to go back to
+
+eval-dispatch.
+
+We're set up again.
+
+We have an expression,
+an environment, and
+
+a place to go to.
+
+We're not going to go through
+that because it's sort of the
+
+same expression.
+
+OK, but the thing, again, to
+notice is, at this point, we
+
+have reduced the original
+expression, F,X,Y, right?
+
+We've reduced evaluating F,X,Y
+in environment E,0 to evaluate
+
+plus A, B in E,1.
+
+And notice, nothing's
+on the stack, right?
+
+It's a reduction.
+
+At this point, the machine does
+not contain, as part of
+
+its state, the fact that it's
+in the middle of evaluating
+
+some procedure called f,
+that's gone, right?
+
+There's no accumulated
+state, OK?
+
+Again, that's a very
+important idea.
+
+That's the meaning of, when
+we used to write in the
+
+substitution model, this
+expression reduces to that
+
+expression.
+
+And you don't have to
+remember anything.
+
+And here, you see the meaning
+of reduction.
+
+At this point, there is
+nothing on the stack.
+
+See, that has very important
+consequences.
+
+Let's go back and look
+at iterative
+
+factorial, all right?
+
+Remember, this was some sort
+of loop and doing iter.
+
+And we kept saying that's an
+iterative procedure, right?
+
+And what we wrote, remember,
+are things like, we said,
+
+fact-iter of 5.
+
+We wrote things like reduces
+to iter of 1, and 1, and 5,
+
+which reduces to iter of 1, and
+2, and 5, and so on, and
+
+so on, and so on.
+
+And we kept saying well, look,
+you don't have to build up any
+
+storage to do that.
+
+And we waved our hands, and said
+in principle, there's no
+
+storage needed.
+
+Now, you see no storage
+needed.
+
+Each of these is a real
+reduction, right?
+
+As you walk through these
+expressions, what you'll see
+
+are these expressions on the
+stack in some particular
+
+environment, and then these
+expressions in the EXP
+
+register in some particular
+environment.
+
+And, at each point, there'll be
+no accumulated stuff on the
+
+stack because each one's
+a real reduction, OK?
+
+All right, so, for example,
+just to go through it in a
+
+little bit more care, if I start
+out with an expression
+
+that says something like, oh,
+say, fact-iter of 5 in some
+
+environment that will, at some
+point, create an environment
+
+in which n is down to 5.
+
+Let's call that--
+
+And, at some point, the machine
+will reduce this whole
+
+thing to a thing that says
+that's really iter of 1, and
+
+1, and n, evaluated in this
+environment, E,1 with nothing
+
+on the stack.
+
+See, at this moment, the machine
+is not remembering
+
+that evaluating this
+expression, iter--
+
+which is the loop-- is
+part of this thing
+
+called iterative factorial.
+
+It's not remembering that.
+
+It's just reducing the
+expression to that, right?
+
+If we look again at the body of
+iterative factorial, this
+
+expression has reduced
+to that expression.
+
+Oh, I shouldn't have
+the n there.
+
+It's a slightly different
+convention from the slide to
+
+the program, OK?
+
+And, then, what's the
+body of iter?
+
+Well, iter's going to be an it,
+and I won't go through the
+
+details of if.
+
+It'll evaluate the predicate.
+
+In this case, it'll be false.
+
+And this iter will now reduce
+to the expression iter of
+
+whatever it says, star,
+counter product, and--
+
+what does it say--
+
+plus counter 1 in some other
+environment, by this time,
+
+E,2, where E,2 will be set up
+having bindings for product
+
+and counter, right?
+
+And it'll reduce
+to that, right?
+
+It won't be remembering that
+it's part of something that it
+
+has to return to.
+
+And when iter calls iter again,
+it'll reduce to another
+
+thing that looks like this in
+some environment, E,3, which
+
+has new bindings for product
+and counter.
+
+So, if you're wondering, see,
+if you've always been queasy
+
+about how it is we've been
+saying those procedures, that
+
+look syntactically recursive,
+are, in fact, iterative, run
+
+in constant space, well, I don't
+know if this makes you
+
+less queasy, but at least it
+shows you what's happening.
+
+There really isn't any
+buildup there.
+
+Now, you might ask well, is
+there buildup in principle in
+
+these environment frames?
+
+And the answer is yeah, you
+have to make these new
+
+environment frames, but you
+don't have to hang onto them
+
+when you're done.
+
+They can be garbage collected,
+or the space can be reused
+
+automatically.
+
+But you see the control
+structure of the evaluator is
+
+really using this idea that you
+actually have a reduction,
+
+so these procedures really
+are iterative procedures.
+
+All right, let's stop
+for questions.
+
+All right, let's break.
+
+Let me contrast the iterative
+procedure just so you'll see
+
+where space does build up with
+a recursive procedure, so you
+
+can see the difference.
+
+Let's look at the evaluation
+of recursive
+
+factorial, all right?
+
+So, here's fact-recursive, or
+standard factorial definition.
+
+We said this one is still a
+recursive procedure, but this
+
+is actually a recursive
+process.
+
+And then, just to link it back
+to the way we started, we said
+
+oh, you can see that it's going
+to be recursive process
+
+by the substitution model
+because, if I say recursive
+
+factorial of 5, that turns
+into 5 times--
+
+what is it, fact-rec,
+or record fact--
+
+5 times recursive factorial of
+4, which turns into 5 times 4
+
+times fact-rec of 3, which
+returns into 5 times 4 times 3
+
+times, and so on, right?
+
+The idea is there was this chain
+of stuff building up,
+
+which justified, in the
+substitution model, the fact
+
+that it's recursive.
+
+And now, let's actually see that
+chain of stuff build up
+
+and where it is in
+the machine, OK?
+
+All right, well, let's
+imagine we're going
+
+to start out again.
+
+We'll tell it to evaluate
+recursive factorial of 5 in
+
+some environment, again, E,0
+where recursive factorial is
+
+defined, OK?
+
+Well, now we know what's
+eventually going to happen.
+
+This is going to come along,
+it'll evaluate those things,
+
+figure out it's a procedure,
+build somewhere over here an
+
+environment, E,1, which has n
+bound to 5, which hangs off of
+
+E,0, which would be, presumably,
+the definition
+
+environment of recursive
+factorial, OK?
+
+And, in this environment,
+it's going to go off and
+
+evaluate the body.
+
+So, again, the evaluation here
+will reduce to evaluating the
+
+body in E,1.
+
+That's going to look at an if,
+and I won't go through the
+
+details of if.
+
+It'll look at the predicate.
+
+It'll decide it eventually has
+to evaluate the alternative.
+
+So this whole thing, again, will
+reduce to the alternative
+
+of recursive factorial, the
+alternative clause, which says
+
+that this whole thing reduces
+to times n of recursive
+
+factorial of n minus 1 in
+the environment E,1, OK?
+
+So the original expression,
+now, is going to reduce to
+
+evaluating that expression,
+all right?
+
+Now we have an application.
+
+We did an application before.
+
+Remember what happens
+in an application?
+
+The first thing you do is you go
+off and you save the value
+
+of the continue register
+on the stack.
+
+So the stack here is going
+to have done in it.
+
+And then you're going to
+set up to evaluate
+
+the sub-parts, OK?
+
+So here we go off to evaluate
+the sub-parts.
+
+First thing we're going to do
+is evaluate the operator.
+
+What happens when we evaluate
+an operator?
+
+Well, we arrange things so that
+the operator ends up in
+
+the expression register.
+
+The environments in the ENV
+register continue someplace
+
+where we're going to go evaluate
+the arguments.
+
+And, on the stack, we've saved
+the original continue, which
+
+is where we wanted to be
+when we're all done.
+
+And then the things we needed
+when we're going to get done
+
+evaluating the operator, the
+things we'll need to evaluate
+
+the arguments, namely, the
+environment and those
+
+arguments, those unevaluated
+arguments, so there they are
+
+sitting on the stack.
+
+And we're about to go off to
+evaluate the operator.
+
+Well, when we return from
+this particular call--
+
+so we're about to call
+eval-dispatch here--
+
+when we return from this call,
+the value of that operator,
+
+which, in this case, is going to
+be the primitive multiplier
+
+procedure, will end up in the
+FUN register, all right?
+
+We're going to evaluate
+some arguments.
+
+They will evaluate in here.
+
+That'll give us 5,
+in this case.
+
+We're going to put that in the
+argl register, and then we'll
+
+go off to evaluate the
+second operand.
+
+So, at the point where we go
+off to evaluate the second
+
+operand-- and I'll skip details
+like computing, and
+
+minus 1, and all of that--
+but, when we go off to
+
+evaluate the second operand,
+that will eventually reduce to
+
+another call to fact-recursive.
+
+And, what we've got on the stack
+here is the operator
+
+from that combination that we're
+going to use it in and
+
+the other argument, OK?
+
+So, now, we're set up
+for another call
+
+to recursive factorial.
+
+And, when we're done with this
+one, we're going to go to
+
+accumulate the last arg.
+
+And remember what that'll do?
+
+That'll say oh, whatever the
+result of this has to get
+
+combined with that, and we're
+going to multiply them.
+
+But, notice now, we're at
+another recursive factorial.
+
+We're about to call
+eval-dispatch again, except we
+
+haven't really reduced it
+because there's stuff
+
+on the stack now.
+
+The stuff on the stack says oh,
+when you get back, you'd
+
+better multiply it by the
+5 you had hanging there.
+
+So, when we go off to make
+another call, we
+
+evaluate the n minus 1.
+
+That gives us another
+environment in which the new
+
+n's going to be down to 4.
+
+And we're about to call
+eval-dispatch again, right?
+
+We get another call.
+
+That 4 is going to end up
+in the same situation.
+
+We'll end up with another call
+to fact-recursive n.
+
+And sitting on the stack will be
+the stuff from the original
+
+one and, now, the subsidiary
+one we're doing.
+
+And both of them are waiting
+for the same thing.
+
+They're going to go to
+accumulate a last argument.
+
+And then, of course, when we
+go to the fourth call, the
+
+same thing happens, right?
+
+And this goes on,
+and on, and on.
+
+And what you see here on the
+stack, exactly what's sitting
+
+here on the stack, the thing
+that says times and 5.
+
+And what you're going to do with
+that is accumulate that
+
+into a last argument.
+
+That's exactly this, right?
+
+This is exactly where that
+stuff is hanging.
+
+Effectively, the operator you're
+going to apply, the
+
+other argument that it's got to
+be multiplied by when you
+
+get back and the parentheses,
+which says yeah, what you
+
+wanted to do was accumulate
+them.
+
+So, you see, the substitution
+model is not such a lie.
+
+That really is, in some
+sense, what's sitting
+
+right on the stack.
+
+OK.
+
+All right, so that, in some
+sense, should explain for you,
+
+or at least convince you, that,
+somehow, this evaluator
+
+is managing to take these
+procedures and execute some of
+
+them iteratively and some of
+them recursively, even though,
+
+as syntactically, they look
+like recursive procedures.
+
+How's it managing to do that?
+
+Well, the basic reason it's
+managing to do that is the
+
+evaluator is set up to save
+only what it needs later.
+
+So, for example, at the point
+where you've reduced
+
+evaluating an expression and an
+environment to applying a
+
+procedure to some arguments, it
+doesn't need that original
+
+environment anymore because any
+environment stuff will be
+
+packaged inside the procedures
+where the
+
+application's going to happen.
+
+All right, similarly, when
+you're going along evaluating
+
+an argument list, when you've
+finished evaluating the list,
+
+when you're finished evaluating
+the last argument,
+
+you don't need that argument
+list any more, right?
+
+And you don't need the
+environment where those
+
+arguments would be
+evaluated, OK?
+
+So the basic reason that this
+interpreter is being so smart
+
+is that it's not being smart
+at all, it's being stupid.
+
+It's just saying I'm
+only going to save
+
+what I really need.
+
+Well, let me show you here.
+
+Here's the actual thing that's
+making a tail recursive.
+
+Remember, it's the restore
+of continue.
+
+It's saying when I go off to
+evaluate the procedure body, I
+
+should tell eval to come back
+to the place where that
+
+original evaluation was supposed
+to come back to.
+
+So, in some sense, you want to
+say what's the actual line
+
+that makes a tail recursive?
+
+It's that one.
+
+If I wanted to build a non-tail
+recursive evaluator,
+
+for some strange reason, all I
+would need to do is, instead
+
+of restoring continue at this
+point, I'd set up a label down
+
+here called, "Where to come
+back after you've finished
+
+applying the procedure."
+Instead, I'd
+
+set continue to that.
+
+I'd go to eval-dispatch,
+and then eval-dispatch
+
+would come back here.
+
+At that point, I would restore
+continue and go to the
+
+original one.
+
+So here, the only consequence
+of that would be to make it
+
+non-tail recursive.
+
+It would give you exactly the
+same answers, except, if you
+
+did that iterative factorial
+and all those iterative
+
+procedures, it would execute
+recursively.
+
+Well, I lied to you a little
+bit, but just a little bit,
+
+because I showed you a slightly
+over-simplified
+
+evaluator where it assumes that
+each procedure body has
+
+only one expression.
+
+Remember, in general, a
+procedure has a sequence of
+
+expressions in it.
+
+So there's nothing really
+conceptually new.
+
+Let me just show you the actual
+evaluator that handles
+
+sequences of expressions.
+
+This is compound-apply now, and
+the only difference from
+
+the old one is that, instead of
+going off to eval directly,
+
+it takes the whole body of the
+procedure, which, in this
+
+case, is a sequence of
+expressions, and goes off to
+
+eval-sequence.
+
+And eval-sequence is a little
+loop that, basically, does
+
+these evaluations
+one at a time.
+
+So it does an evaluation.
+
+Says oh, when I come back, I'd
+better come back here to do
+
+the next one.
+
+And, when I'm all done, when
+I want to get the last
+
+expression, I just restore
+my continue and go off to
+
+eval-dispatch.
+
+And, again, if you wanted for
+some reason to break tail
+
+recursion in this evaluator,
+all you need to do is not
+
+handle the last expression,
+especially.
+
+Just say, after you've done the
+last expression, come back
+
+to some other place after which
+you restore continue.
+
+And, for some reason, a lot
+of LISP evaluators tended
+
+to work that way.
+
+And the only consequence of
+that is that iterative
+
+procedures built up stack.
+
+And it's not clear why
+that happened.
+
+All right.
+
+Well, let me just sort of
+summarize, since this is a lot
+
+of details in a big program.
+
+But the main point is that
+it's no different,
+
+conceptually, from translating
+any other program.
+
+And the main idea is that we
+have this universal evaluator
+
+program, the meta-circular
+evaluator.
+
+If we translate that
+into LISP, then
+
+we have all of LISP.
+
+And that's all we did, OK?
+
+The second point is that
+the magic's gone away.
+
+There should be no more magic
+in this whole system, right?
+
+In principle, it should all be
+very clear except, maybe, for
+
+how list structured
+memory works, and
+
+we'll see that later.
+
+But that's not very hard.
+
+The third point is that all this
+tail recursion came from
+
+the discipline of eval being
+very careful to save only what
+
+it needs next time.
+
+It's not some arbitrary thing
+where we're saying well,
+
+whenever we call a sub-routine,
+we'll save all
+
+the registers in the world
+and come back, right?
+
+See, sometimes it pays to really
+worry about efficiency.
+
+And, when you're down in the
+guts of your evaluator
+
+machine, it really pays to think
+about things like that
+
+because it makes big
+consequences.
+
+Well, I hope what this has
+done is really made the
+
+evaluator seem concrete,
+right?
+
+I hope you really believe that
+somebody could hold a LISP
+
+evaluator in the palm
+of their hand.
+
+Maybe to help you believe that,
+here's a LISP evaluator
+
+that I'm holding the palm
+of my hand, right?
+
+And this is a chip which is
+actually quite a bit more
+
+complicated than the evaluator
+I showed you.
+
+Maybe, here's a better
+picture of it.
+
+What there is, is you can see
+the same overall structure.
+
+This is a register array.
+
+These are the data paths.
+
+Here's a finite state
+controller.
+
+And again, finite state,
+that's all there is.
+
+And somewhere there's
+external memory
+
+that'll worry about things.
+
+And this particular one is very
+complicated because it's
+
+trying to run LISP fast. And
+it has some very, very fast
+
+parallel operations in there
+like, if you want to index
+
+into an array, simultaneously
+check that the index is an
+
+integer, check that it doesn't
+exceed the array bands, and go
+
+off and do the memory access,
+and do all those things
+
+simultaneously.
+
+And then, later, if they're
+all OK, actually
+
+get the value there.
+
+So there are a lot of
+complicated operations in
+
+these data paths for making
+LISP run in parallel.
+
+It's a completely non-risk
+philosophy of evaluating LISP.
+
+And then, this microcode
+is pretty complicated.
+
+Let's see, there's what?
+
+There's about 389 instructions
+of 220-bit microcode sitting
+
+here because these are very
+complicated data paths.
+
+And the whole thing has about
+89,000 transistors, OK?
+
+OK.
+
+Well, I hope that that takes
+away a lot of the mystery.
+
+Maybe somebody wants
+to look at this.
+
+Yeah.
+
+OK.
+
+Let's stop.
+
+Questions?
+
+AUDIENCE: OK, now, it sounds
+like what you're saying is
+
+that, with the restore continue
+put in the proper
+
+place, that procedures that
+would invoke a recursive
+
+process now invoke an integer
+process just by the way that
+
+the eval signature is?
+
+PROFESSOR: I think the way I'd
+prefer to put it is that, with
+
+restore continue put in the
+wrong place, you can cause any
+
+syntactically-looking recursive
+procedure, in fact,
+
+to build up stack as it runs.
+
+But there's no reason for that,
+so you might want to
+
+play around with it.
+
+You can just switch around two
+or three instructions in the
+
+way compound-apply comes back,
+and you'll get something which
+
+isn't tail recursive.
+
+But the thing I wanted to
+emphasize is there's no magic.
+
+It's not as if there's some
+very clever pre-processing
+
+program that's looking at this
+procedure, factorial iter, and
+
+say oh, gee, I really notice
+that I don't have to push
+
+stack in order to do this.
+
+Some people think that that's
+what's going on.
+
+It's something much, much more
+dumb than that, it's this one
+
+place you're putting the
+restore instruction.
+
+It's just automatic.
+
+AUDIENCE: OK.
+
+AUDIENCE: But that's not
+affecting the time
+
+complexity is it?
+
+PROFESSOR: No.
+
+AUDIENCE: It's just that it's
+handling it recursively
+
+instead of iteratively.
+
+But, in terms of the order of
+time it takes to finish the
+
+operation, it's the same one
+way or the other, right?
+
+PROFESSOR: Yes.
+
+Tail recursion is not going to
+change the time complexity of
+
+anything because, in some sense,
+it's the same algorithm
+
+that's going on.
+
+What it's doing is really making
+this thing run as an
+
+iteration, right?
+
+Not going to run out of memory
+counting up to a giant number
+
+simply because the stack
+would get pushed.
+
+See, the thing you really
+have to believe is
+
+that, when we write--
+
+see, we've been writing all
+these things called
+
+iterations, infinite loops,
+define loop to be called loop.
+
+That's is as much an iteration
+as if we wrote do forever
+
+loop, right?
+
+It's just syntactic sugar
+as the difference.
+
+These things are real, honest
+to god, iterations, right?
+
+They don't change the time
+complexity, but they turn them
+
+into real iterations.
+
+All right, thank you.
\ No newline at end of file
diff --git a/So6MK_FcP4E.txt b/So6MK_FcP4E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..13437a19ba6c38eb04c74d6aa49bbe5ae1e34af5
--- /dev/null
+++ b/So6MK_FcP4E.txt
@@ -0,0 +1,5356 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: So you'll
+recall last time
+
+we were working on
+protein-protein interactions.
+
+We're going to do a little
+bit to finish that up,
+
+with a topic that will be a
+good transition to the study
+
+of the gene regulatory networks.
+
+And the precise things we're
+going to discuss today,
+
+we're going to start off
+with Bayesian networks
+
+of protein-protein
+interaction prediction.
+
+And then we're going to get
+into gene expression data,
+
+at several different levels.
+
+We'll talk about
+some basic questions,
+
+of how to compare
+the two expression
+
+vectors for a gene,
+distance metrics.
+
+We'll talk about how to
+cluster gene expression data.
+
+The idea of
+identifying signatures
+
+of sets of genes, that
+might be predictive
+
+of some biological property.
+
+For example, a
+susceptibility to a disease.
+
+And then we'll talk about
+a number of different ways
+
+that people have
+developed to try
+
+to identify gene
+regulatory networks.
+
+That often goes by
+the name of modules.
+
+I don't particularly
+like that name.
+
+But that's what you'll
+find in the literature.
+
+And we're going to
+focus on a few of these,
+
+that have recently been
+compared head to head, using
+
+both synthetic and real data.
+
+And we'll see some
+of the results
+
+from that head to
+head comparison.
+
+So let's just launch into it.
+
+Remember last time we had
+started this unit looking
+
+at the structural
+predictions for proteins.
+
+And we started talking
+about how to predict
+
+protein-protein interactions.
+
+Last time we talked about
+both computational methods,
+
+and also experimental
+data, that could give us
+
+information about
+protein-protein interactions.
+
+Ostensibly measuring
+direct interactions,
+
+but we saw that there were
+possibly very, very high error
+
+rates.
+
+So we needed ways of integrating
+lots of different kinds of data
+
+in a probabilistic framework so
+we could predict for any pair
+
+proteins what's the
+probability that they interact.
+
+Not just the fact that
+they were detected
+
+in one assay or the other.
+
+And we started to talk
+about Bayesian networks
+
+in this context.
+
+Both useful as we'll see
+today, for predicting
+
+protein-protein
+interactions, and also
+
+for the gene regulatory
+network problem.
+
+So the Bayesian
+networks are a tool
+
+for reasoning probabilistically.
+
+That's the fundamental purpose.
+
+And we saw that they consisted
+of a graph, the network.
+
+And then the probabilities
+that represent the probability
+
+for each edge, the conditional
+probability tables.
+
+And that we can learn
+these from the data,
+
+either in a completely
+objective way, where
+
+we learn both the structure
+and the probability.
+
+Or where we impose the
+structure initially,
+
+and then we simply learn
+the probability tables.
+
+And we had nodes that
+represented the variables.
+
+They could be
+hidden nodes, where
+
+we don't know what the true
+answer is, and observed
+
+nodes, where we do.
+
+So in our case, we're
+trying to predict
+
+protein-protein interactions.
+
+There's some hidden
+variable that
+
+represents weather protein
+A and B truly interact.
+
+We don't know that answer.
+
+But we do know whether
+that interaction was
+
+detected in an experiment
+one, two, three or 4.
+
+Those are the
+effects, the observed.
+
+And so we want to
+reason backwards
+
+from the observations,
+to the hidden causes.
+
+So last time we talked about
+the high throughput experiments,
+
+that directly
+we're measuring out
+
+protein-protein interactions.
+
+We talked about yeast two
+hybrid and affinity capture
+
+mass spec-- here
+listed as pull-downs.
+
+And those could
+be used to predict
+
+protein-protein
+directions, by themselves.
+
+But we want to find out
+what other kinds of data
+
+we can use to amplify
+these results, to give us
+
+independent information about
+whether two proteins interact.
+
+And one thing you
+could look at is
+
+whether the expression
+of the two genes that you
+
+think might interact
+are similar.
+
+So if you look over many,
+many different conditions,
+
+you might expect
+the two proteins
+
+that interact with
+each other, would
+
+be expressed under
+similar conditions.
+
+Certainly if you saw
+two proteins that
+
+had exactly opposite
+expression patterns,
+
+you would be very unlikely to
+believe that they interacted.
+
+So the question is, how much
+is true at the other end
+
+of the spectrum?
+
+If things are very
+highly correlated,
+
+do they have a high
+probability of interaction?
+
+So this graph is a
+histogram for proteins
+
+that are known to
+interact, proteins
+
+that were shown in these
+high throughput experiments
+
+to interact, and proteins that
+are known not to interact,
+
+of how similar
+the expression is.
+
+On the far right
+are things that have
+
+extremely different expression
+patterns, a high distance.
+
+And we'll talk
+specifically about what
+
+distance is in just a minute.
+
+But these are very dissimilar
+expression patterns.
+
+These are very similar ones.
+
+So what do you
+see from this plot
+
+we looked at the last time?
+
+We saw that the
+interacting proteins
+
+are shifted a bit to the left.
+
+So the interacting ones
+have a higher probability
+
+of having similar
+expression patterns
+
+than the ones don't interact.
+
+But we couldn't
+draw any cut off,
+
+and say everything with this
+level expression similarity
+
+is guaranteed to interact.
+
+There's no way to divide these.
+
+So this will be useful in
+a probabilistic setting.
+
+But by itself, it would
+not be highly predictive.
+
+We also talked about
+evolutionary patterns,
+
+and we discussed whether the
+red or the green patterns
+
+here, would be more predictive.
+
+And which one was
+it, anyone remember?
+
+How many people thought the
+red was more predictive?
+
+How many the green?
+
+Right, the greens win.
+
+And we talked about the
+coevolution in other ways.
+
+So the paper that, I
+think, was one of the first
+
+to do this really
+nicely, try to predict
+
+protein-protein
+interaction patterns using
+
+Bayesian networks, is this
+one from Mark Gerstein's lab.
+
+And they start off as we
+talked about previously,
+
+we need some gold
+standard interactions,
+
+where we know two proteins
+really do interact or don't.
+
+They built their gold
+standard data set.
+
+The positive trending
+data, they took
+
+from a database
+called MIPS, which
+
+is a hand-curated database
+that digs into the literature
+
+quite deeply, to find out
+whether two proteins interact
+
+or not.
+
+And then the negative
+data they took
+
+were proteins that
+were identified
+
+as being localized to
+different parts of the cell.
+
+And this was done
+in yeast, to where
+
+there is pretty good data
+for a lot of proteins,
+
+to subcellular localization.
+
+So these are the data that
+went into their prediction.
+
+These were the experiments
+we've already talked about,
+
+the affinity capture mass
+spec and the yeast two hybrid.
+
+And then the other
+kinds of data they used
+
+were expression correlation,
+one just talked about.
+
+They also looked at
+annotations, whether proteins
+
+had the same annotation
+for function.
+
+And essentiality.
+
+So in yeast, it's
+pretty easy to go
+
+through every gene
+in the genome,
+
+knock it out, and determine
+whether that kills the cell
+
+or not.
+
+So they can label
+every gene in yeast, as
+
+to whether it's essential
+for survival or not.
+
+And you can see here, the
+number of interactions
+
+that were involved.
+
+And they decided
+to break this down
+
+into two separate
+prediction problems.
+
+So one was an
+experimental problem,
+
+using the four
+different large scale
+
+data sets in yeast from
+protein-protein interactions,
+
+to predict expression.
+
+The other one wore
+these other kinds
+
+of data, that were less direct.
+
+And they used slightly different
+kinds of Bayesian networks.
+
+So for this one, they
+used a naive Bayes.
+
+And what's the underlying
+assumption of the naive Bayes?
+
+The underlying assumption
+is that all the data
+
+are independent.
+
+So we looked at this previously.
+
+We discussed how
+you could, if you're
+
+trying to identify
+the likelihood ratio,
+
+and use it to rank things.
+
+You primarily need to
+focus on this term.
+
+Because this term will be the
+same for every pair of proteins
+
+that you're examining.
+
+Yes?
+
+AUDIENCE: Could you state
+again whether in a naive Bayes,
+
+all data are dependent
+or independent?
+
+PROFESSOR: Independent.
+
+AUDIENCE: OK.
+
+PROFESSOR: OK.
+
+So let's actually look
+at some of their data.
+
+So in this table, they're
+looking at the likelihood ratio
+
+that two proteins
+interact, based
+
+on whether the two
+proteins are essential.
+
+One is essential, and
+one is a nonessential.
+
+Both are nonessential.
+
+So that's what these
+two codes here mean.
+
+EE, both essential.
+
+NN, both nonessential,
+and any one and the other.
+
+And so they've computed
+for all those protein
+
+pairs, how many in
+their gold standard,
+
+are EE, how many are
+EN, how many are NN?
+
+So here are the
+numbers for the EE.
+
+There are just over 1,000, out
+of the 2,000, roughly 2,000
+
+that are EE.
+
+So that comes up with a
+probability of being essential,
+
+given that I know
+that you're positive.
+
+You're in the gold standard
+of roughly 50%, right?
+
+And you can assume something
+similar for the negatives.
+
+So these are the ones that
+definitely don't interact.
+
+So the probability of
+both being essential,
+
+given that it's negative,
+is about 15%, 14%.
+
+And so then the likelihood ratio
+comes out to just under four.
+
+So there's a fourfold
+increase in probability
+
+that something is interacting,
+given that it's essential,
+
+then not.
+
+And this is the table
+for all of the terms,
+
+for all of the different things
+that they were considering,
+
+that were not
+direct experiments.
+
+So this is the sensuality.
+
+This is expression correlation,
+with various values
+
+for the threshold, how similar
+the expression had to be.
+
+And these are the terms from
+the databases for annotation.
+
+And then for each
+of these, then we
+
+get a likelihood ratio
+of how predictive it is.
+
+So it's kind of informative to
+look at some of these numbers.
+
+We already saw that
+essentiality is
+
+pretty weak, predicted the fact
+that two genes are essential.
+
+It only gives you a
+slightly increased chance
+
+that they're
+interacting than not.
+
+But if two things, two genes
+have extremely high expression
+
+correlation, then they're
+more than a hundredfold more
+
+likely to interact than not.
+
+And the numbers
+for the annotations
+
+are significantly
+less than that.
+
+So this is a naive Bayes.
+
+We're going to multiply all
+those probabilities together.
+
+Now for the
+experimental data, they
+
+said, well, these are
+probably not all independent.
+
+The probably that you pick
+something up in one two
+
+hybrid experiment,
+is probably highly
+
+correlated with the
+probability that you pick it up
+
+in another two
+hybrid experiment.
+
+And one would hope that there's
+some correlation between things
+
+are identifying in two hybrid
+and affinity caption mass spec.
+
+Although we'll see whether
+or not that's the case.
+
+So they used what they refer
+to as a fully connected Bayes.
+
+And what do we mean by that?
+
+Remember, this was
+the naive Bayes,
+
+where everything is independent.
+
+So the probability
+of some observation
+
+is the product of all the
+individual probabilities.
+
+But in a fully
+connected Bayes, we
+
+don't have that
+independence assumption.
+
+So you need to actually
+explicitly compute
+
+what the probability
+is for an interaction,
+
+based on all the possible
+outcomes in those experiments.
+
+So that's not that much harder.
+
+We simply have a table now,
+where these columns represent
+
+each of the experimental
+data types--
+
+the affinity capture mass
+spec and the two hybrids.
+
+Ones indicate that
+it was detected,
+
+Zero is that it's not.
+
+And then we simply look
+again in our gold standard,
+
+and see how often a protein that
+had been detected in whatever
+
+the setting is here, in all
+of them except Ito, how often
+
+was it, how many of the
+gold positives do we get?
+
+And how many of
+the gold negatives?
+
+And then we can compute
+the probabilities.
+
+Now it's important
+to look at some
+
+of the numbers in these
+tables and dig in.
+
+Because you'll see the numbers
+here are really, really small.
+
+So they have to be
+interpreted with caution.
+
+So some of the
+things that might not
+
+hold up with much
+larger data sets.
+
+You might imagine the things
+that are experimentally
+
+detected in all of the
+high-throughput assays
+
+would be the most confident.
+
+That doesn't turn
+out to be the case.
+
+So these are sorted by the
+law of likelihood ratio,
+
+and the best one is not 1, 1, 1.
+
+It's up there.
+
+But it's not the
+top of the pack.
+
+And that's probably just the
+statistics of small numbers.
+
+If the databases were larger,
+experiments were larger,
+
+it probably would
+work out that way.
+
+So any question about how
+they formulated this problem,
+
+as a Bayesian network, or
+how they implemented it?
+
+OK.
+
+So the results then-- so once
+we have these likelihood ratios,
+
+we can try to choose a threshold
+for deciding what we're
+
+going to consider to be a
+true interaction and not.
+
+So here they've plotted for
+different likelihood ratio
+
+thresholds.
+
+On the x-axis, how many of the
+true positives you get right,
+
+versus how many you get wrong.
+
+So the true positive
+over the false positive.
+
+And you can
+arbitrarily decide, OK,
+
+well I want to be more-- I want
+to get more right than wrong.
+
+Not a bad way to decide things.
+
+So your passing
+grade here is 50%.
+
+So if I draw a line,
+a horizontal line,
+
+and wanted to get
+more right than wrong,
+
+you'll see that any
+of the individual
+
+signals that they were
+using, essentiality,
+
+database sanitation, and so on--
+all of those fall below that.
+
+So individually, they predict
+more wrongs than rights.
+
+But if you combine the data
+using this Bayesian network,
+
+then you can choose a
+likelihood threshold,
+
+where you do get more
+right than wrong.
+
+And you can set your
+threshold wherever you want.
+
+Similarly for the direct
+experimental data,
+
+you do better by combining--
+these are light pink lines,
+
+than you would with any of
+the individual data sets.
+
+So this shows the utility
+of combining the data,
+
+and reasoning from the
+data probabilistically.
+
+Any questions?
+
+So we'll return to
+Bayesian networks
+
+in a bit in the
+context of discovering
+
+gene regulatory networks.
+
+So we now want to move
+to gene expression data.
+
+And the primary reason to be so
+interested in gene expression
+
+data is simply that there's a
+huge amount of it out there.
+
+So just a short time ago
+we passed the million mark,
+
+with a number of
+expression data sets
+
+that had been collected
+in the databases.
+
+There's much less of any other
+kind of high throughput data.
+
+So if you look at proteomics
+or high-throughput genetic
+
+screens, there are
+tiny numbers, compared
+
+to gene expression data.
+
+So obviously techniques for
+analyzing gene expression data
+
+are going to play a very
+important role for a long time
+
+to come.
+
+Some of what I'm
+going to discuss today
+
+is covered in your textbooks.
+
+I encourage you to look
+at text section 16.2.
+
+The fundamental thing that
+we're interested in doing,
+
+is seeing how much
+biological knowledge
+
+we can infer from the
+gene expression data.
+
+So we might imagine
+that genes that
+
+are coexpressed under
+particular sets and conditions,
+
+have functional
+similarity, reflect
+
+common regulatory mechanisms,
+and our goal then,
+
+is to discover those mechanisms.
+
+So fundamental to this then, any
+time we have a pair of genes--
+
+and we look at their
+gene expression data--
+
+we want to decide
+how similar they are.
+
+So let's imagine that we had
+these data for four genes.
+
+And it's a time
+series experiment.
+
+And we're looking at the
+different expression levels.
+
+And we want some
+quantitative measure
+
+to decide which two
+genes are most similar.
+
+Well, it turns out
+it's a lot more
+
+subtle than we might think.
+
+So at first glance,
+oh, it's pretty obvious
+
+that these two are
+the most similar.
+
+But it really depends on
+what kind of similarity
+
+you're asking about.
+
+So we can describe
+any expression data
+
+set for any gene, is simply
+a multi-dimensional vector.
+
+Where this is the set
+of expression values
+
+we detected for the
+first gene, across all
+
+the different experimental
+conditions and so on,
+
+for the second.
+
+And what would be the
+most intuitive way
+
+of describing the
+distance between two
+
+multi-dimensional vectors?
+
+It would simply be
+Euclidean distance, right?
+
+So that's perfectly reasonable.
+
+So we can decide that the
+distance between two gene
+
+expression data sets, is
+simply the square root
+
+of the sum of the
+squares of the distances.
+
+So we'll take the sum over all
+the experimental conditions
+
+that we've looked at.
+
+Maybe it's a time series.
+
+Maybe it's different
+perturbations.
+
+And look at the difference in
+expression of gene A and gene
+
+B in that condition, K.
+And then evaluating this
+
+will tell us how similar two
+genes are in their expression
+
+profiles.
+
+Well, that's a specific
+example of a distance metric.
+
+It turns out that there's
+a formal definition
+
+for a distance metric.
+
+Distances have the
+following properties.
+
+They're always
+greater than zero.
+
+We never have
+negative distances.
+
+They are equal to zero under
+exactly one condition-- the two
+
+data points are the same.
+
+And they're symmetric.
+
+So the distance from
+A to B is the same
+
+as the distance from B to A.
+
+Now, to be a true
+distance, then you also
+
+have to satisfy the
+triangle inequality,
+
+that the distance from
+x to z is less than
+
+or equal to the sum
+of the distances
+
+through a third point.
+
+But we will find out
+that we don't actually
+
+need that for
+similarity measures.
+
+So we can have either
+a true distance
+
+metric for comparing gene
+expression data sets,
+
+or similarity measures as well.
+
+So let's go back to
+the simple example.
+
+So we decided that the
+red and the blue genes
+
+were nearly identical, in terms
+of their distance metrics.
+
+But that's not always
+exactly what we care about.
+
+So in biological settings,
+frequently the absolute level
+
+of gene expression is
+on some arbitrary scale.
+
+Certainly with
+expression arrays,
+
+it was completely arbitrary.
+
+It had to do with
+fluorescence properties,
+
+and how well probes
+hybridize to each other.
+
+But even with mRNA,
+how do we really
+
+know that 1,000 copies
+is fundamentally
+
+different from 1,200 copies
+of an RNA in the cell?
+
+We don't.
+
+So we might be more interested
+in distance metrics that
+
+capture not just the
+similarity of these two.
+
+But the fact that these
+two are also quite similar,
+
+in terms of the trajectory
+of the plot to this one.
+
+So can we come up with measures
+that capture this one as well?
+
+A very common one for this
+is Pearson correlation.
+
+So in Pearson correlation,
+we're gonna look at not just
+
+the expression of a
+gene across conditions.
+
+But we're gonna look at
+the z-score of that gene.
+
+So we'll take all
+of the data for all
+
+of the genes in a
+particular condition.
+
+And we'll compute the
+z-score by looking
+
+at the difference
+between the expression
+
+of a particular gene, in
+the average expression
+
+across the whole data set.
+
+And we're going to normalize
+it by the standard deviation.
+
+Yes?
+
+AUDIENCE: [INAUDIBLE]
+square there?
+
+PROFESSOR: Yes, you're right.
+
+There should be a square there.
+
+Thank you.
+
+So then to compute the
+Pearson correlation,
+
+we're going between
+two genes, A and B,
+
+we're going to take the
+sum over all experiments,
+
+that the z-score for A
+and the z-score for B,
+
+the product of that, summed
+over all the experiments.
+
+And these values as
+we'll see in a second,
+
+are going to range
+from plus 1, which
+
+would be a perfect
+correlation, to minus 1,
+
+which would be a perfect
+anti-correlation.
+
+And then we're going to find the
+distance is 1 minus this value.
+
+So things that are
+perfectly correlated then,
+
+would have an r of zero.
+
+And things that
+are anti-correlated
+
+would have a large one.
+
+So if we take a
+look at these two
+
+obviously by Euclidean
+distance, they'd
+
+be quite different
+from each other.
+
+But the z-scores have
+converted the expression values
+
+into z-scores over
+here, you can see
+
+that the z-scores
+obviously, this one
+
+is the most negative
+of all of the ones.
+
+And this as the lowest
+one in all of these.
+
+This one's the highest.
+
+And similarly for the red
+one, lowest to the highest.
+
+So the z-scores track very well.
+
+And when I take the
+product of this,
+
+the signs of the z-score for
+A and B are always the same.
+
+So I summed the product of the
+z-scores, I get a large number.
+
+And then the
+normalization guarantees
+
+that it comes out to one.
+
+And so the red
+and blue here will
+
+have a very high
+correlation coefficient.
+
+In this case, it's going
+to be an r correlation
+
+coefficient of 1.
+
+Whereas compared to this one,
+which is relatively flat,
+
+the correlation coefficient
+will be approximately zero.
+
+Any questions on that?
+
+So what about, say
+the blue and the red?
+
+Well, their z-scores
+are going to have
+
+almost the opposite
+sign every single time.
+
+And so that's going to add
+up to a large negative value.
+
+So for these, they'll be
+highly anti-correlated.
+
+So A, the blue and the red,
+have a correlation coefficient
+
+of minus 1.
+
+OK.
+
+So we have these
+two different ways
+
+of computing distance measures.
+
+We can compute the
+Euclidean distance,
+
+which would make the
+red and blue the same,
+
+but treat the green one as
+being completely different.
+
+Or we have the
+correlation, which
+
+would group all of these
+together, as being similar.
+
+What you want to do is going
+to depend on your setting.
+
+If you look in your
+textbook, you'll
+
+see a lot of other definitions
+of distance as well.
+
+Now what if you're missing
+a particular data point?
+
+This used to be a lot more
+of a problem with arrays
+
+than it is with [? RNAC. ?]
+With arrays, you'd often
+
+have dirt on the array, that
+it actually would literally
+
+cover up spots.
+
+But you have a bunch of choices.
+
+The most extreme would
+just be to ignore
+
+that row or column of your
+matrix across old data sets.
+
+That's usually not
+what we want to do.
+
+You could put in some
+arbitrary small value.
+
+But frequently we will do what's
+called imputing, where we'll
+
+try to identify the
+genes that have the most
+
+similar expression, and replace
+the value for the missing
+
+one with a value from
+the ones that we do know.
+
+Distance metrics,
+pretty straightforward.
+
+Now we want to
+use these distance
+
+metrics to actually
+cluster the data.
+
+And what's the idea here?
+
+That if we look across
+enough data sets,
+
+we might find certain groups of
+genes that function similarly
+
+across all those
+data sets, that might
+
+be revealing as to their
+biological function.
+
+So this is an example of an
+unsupervised learning problem.
+
+We don't know what the
+classes are, before we go in.
+
+We don't even know
+how many there are.
+
+We want to learn from the data.
+
+This is a very large
+area of machine learning.
+
+We're just gonna
+scrape the surface.
+
+Some of you may be
+familiar with the fact
+
+that these kinds of
+machine learning algorithms
+
+are used widely
+outside of biology.
+
+They're used by
+Netflix to tell you
+
+what would movie to choose next.
+
+Or Amazon, to try to
+sell you new products.
+
+And all the advertisers who send
+pop-up ads on your computer.
+
+But in our biological
+setting then, we
+
+have our gene expression
+data, collected possibly
+
+over very large
+numbers of conditions.
+
+And we want to find
+groups of genes
+
+that have some similarity.
+
+This is a figure from one of
+these very early papers, that
+
+sort of establish how
+people present these datas.
+
+So you'll almost always see
+the same kind of presentation.
+
+Typically you'll get a heat
+map, where genes are rows.
+
+And the different
+experiments here time,
+
+but it could be different
+perturbations, are the columns.
+
+And genes that go up
+in expression are red,
+
+and genes ago down in
+expression are green.
+
+And apologies to anyone
+who's colorblind.
+
+But that's just what the
+convention has become.
+
+OK, so then why cluster?
+
+So if we cluster
+across the rows, then
+
+we'll get sets of genes
+that potentially behave--
+
+that hopefully if
+we do this properly,
+
+behave similarly across
+different subsets
+
+of the experiments.
+
+And those might represent
+similar functions.
+
+And if we cluster
+the columns, then we
+
+get different experiments
+that show similar responses.
+
+So that might be in this
+case, different times that
+
+are similar.
+
+Hopefully those are ones
+that are close to each other.
+
+But if we have lots
+of different patients,
+
+as we'll see in a
+second, they might
+
+represent patients who have a
+similar version of a disease.
+
+And in fact, the clustering
+of genes does work.
+
+So even in this
+very early paper,
+
+they were able to identify a
+bunch of subsets of genes that
+
+showed similar expression
+at different time points,
+
+and turned out to be enriched
+in different categories.
+
+These ones were enriched in
+cholesterol biosynthesis,
+
+whereas these were enriched
+in wound healing, and so on.
+
+So how do you actually
+do clustering?
+
+This kind of clustering
+is called hierarchical.
+
+That's pretty straightforward.
+
+There are two versions of
+hierarchical clustering.
+
+There's what's called
+agglomerative and divisive.
+
+In agglomerative, you start
+off with each data point
+
+in its own cluster.
+
+And then you search for the
+most similar data point to it,
+
+and you group those together.
+
+And you keep doing
+that iteratively,
+
+building up larger
+and larger clusters.
+
+So we've discussed how to
+compare our individual genes.
+
+But you should be
+able to, right now,
+
+to find, if I gave you
+the vector of expression
+
+for a single gene, to find
+the other genes in the data
+
+set that's most similar,
+by either say, Euclidean
+
+or Pearson correlation,
+or what have you.
+
+But once you've grouped
+two genes together,
+
+how do you decide
+whether a third gene is
+
+similar to those two?
+
+So now we have to
+make some choices.
+
+And so there are number
+of different choices
+
+that are commonly made.
+
+So let's say these are our data.
+
+We've got these two
+clusters, Y and Z.
+
+And each circle represents a
+data point in those clusters.
+
+So we've got four
+genes in each cluster.
+
+Now we want to decide
+on a distance measure
+
+to compare cluster Y to
+cluster Z. So what could we do?
+
+So what are some possibilities?
+
+What might you do?
+
+AUDIENCE: We could take
+the average of all points.
+
+PROFESSOR: You could take the
+average of all points, right.
+
+What else could you do?
+
+Only a limited number
+of possibilities.
+
+AUDIENCE: Centroid?
+
+PROFESSOR: Yeah,
+so centroid, you
+
+could take some sort
+of average, right.
+
+Any other possibilities?
+
+AUDIENCE: You can
+pick a representative
+
+from each set [INAUDIBLE].
+
+PROFESSOR: So you could pick
+a representative, right?
+
+How would you decide in advance
+what that would be though?
+
+So maybe you have
+a way, maybe not.
+
+And what other
+possibilities are there?
+
+Yeah?
+
+AUDIENCE: Measure all
+the distances [INAUDIBLE]
+
+to all the nodes in the other.
+
+PROFESSOR: Right.
+
+So you could do all to all.
+
+What else could you do?
+
+You can take the minimum
+of all those values.
+
+You can take the maximum
+of all those values.
+
+And we'll see that all those
+are things that people do.
+
+So this clustering,
+there are already
+
+rather uninformative
+terms for some
+
+of these kinds of decisions.
+
+So it's called
+single linkage, is
+
+you decide that the distance
+between two clusters
+
+is based on the minimum distance
+between any member of cluster Y
+
+and any member of cluster Z.
+
+Complete linkage takes
+the maximum distance.
+
+And then the extremely
+unfortunately named
+
+Unweighted Pair Group Method
+using Centroids-- UPGMC,
+
+I won't try to say
+that very often-- takes
+
+the centroid, which was an
+early suggestion from the class.
+
+And then the UPGMA,
+Unweighted Pair Group Method
+
+with Arithmetic Mean,
+takes the average
+
+of all the distances,
+all suggestions
+
+that people have made.
+
+So when would you use
+one versus the other?
+
+Well, a priori, you
+don't necessarily know.
+
+But it's good to know
+how they'll behave.
+
+So what do you imagine
+is going to happen
+
+if you use single linkage,
+versus complete linkage.
+
+Remember, single linkage
+is the minimum distance.
+
+And complete linkage is
+the maximum distance.
+
+So what's going to
+happen in this case,
+
+if I use the minimum distance.
+
+Which two groups will I combine?
+
+AUDIENCE: The blue and the red.
+
+PROFESSOR: The blue
+and the red, right?
+
+Whereas if I use the
+maximum distance,
+
+then I'll combine the
+green and the red.
+
+So it's important
+to recognize, then,
+
+that the single linkage has this
+property of chaining together
+
+clusters, based on points
+that are near each other.
+
+Whereas the complete linkage
+is resistant to grouping things
+
+together, if they have outliers.
+
+So they'll behave differently.
+
+Now, if your data are
+compact, and you really
+
+do have tight clusters,
+it's not going
+
+to matter too much
+would you use.
+
+But in most biological settings,
+we're dealing with much noise,
+
+there's data.
+
+So you actually will
+get different results
+
+based on this.
+
+And as far as I know, there's
+no really principal way
+
+to figure out if you have no
+prior knowledge, which to use.
+
+Now all of these
+hierarchical clustering
+
+come with what's
+called a dendogram.
+
+And you'll see these at the
+top of all the clustering.
+
+And this represents
+the process by which
+
+the data were clustered.
+
+So the things that
+are most similar
+
+are most tightly connected
+in this dendogram.
+
+So these two data
+points, one and two, you
+
+have to go up very little in the
+y-axis, to get from one to two.
+
+Whereas if you want
+to go from one to 16,
+
+you have to traverse
+the entire dendogram.
+
+So the distance
+between two samples
+
+is how far vertically you have
+to go to connect between them.
+
+Now the good things
+are that the dendogram
+
+is, you can then understand
+the clustering of the data.
+
+So I can cut this dendogram
+at any particular distance,
+
+and get clearly divisions
+among my data sets.
+
+So if I cut here at
+this distance level,
+
+then I have two groups.
+
+One small, one
+consisting of these data.
+
+And one large, one
+consisting of these.
+
+Whereas if I cut down here, I
+have more groups of my data.
+
+So it doesn't require me in
+advance to know how many groups
+
+I have.
+
+I can look at the
+dendogram and infer it.
+
+The one risk is that you
+always get a dendogram that's
+
+hierarchical, regardless of
+if the data were hierarchical
+
+or not.
+
+So it's more a reflection of
+how you did your clustering
+
+than any fundamental
+structure of the data.
+
+So the fact that you get
+a hierarchical dendogram
+
+means really nothing
+about your data.
+
+It's simply a tool
+that you can use
+
+to try to divide it up
+into different groups.
+
+Any questions on the
+hierarchical clustering?
+
+Yes?
+
+AUDIENCE: If each data
+point is its own cluster,
+
+then won't that be consistent
+across, like, single linkage,
+
+complete linkage-- like,
+why would you cluster?
+
+Does that question make sense?
+
+Like if you cut it down below,
+then haven't you minimized--
+
+don't you successively
+minimize the variance, I guess,
+
+up to your clusters, by--
+
+PROFESSOR: So if I cut
+it at the lowest level,
+
+everybody is their own cluster.
+
+That's true.
+
+Right.
+
+I'm interested in
+finding out whether there
+
+are genes that behave
+similarly across the data sets.
+
+Or--
+
+AUDIENCE: My question
+is, how would you
+
+go about determining how
+many clusters your want?
+
+PROFESSOR: Oh, OK.
+
+So we'll come to
+that in a second.
+
+So hierarchical clustering,
+you don't actually
+
+have any objective
+way of doing that.
+
+But we'll talk about
+other means right now,
+
+where it's a little bit clearer.
+
+But actually
+fundamentally, there
+
+aren't a lot of good ways
+of knowing a priori what
+
+the right number of clusters is.
+
+But we'll look at some
+measures in a second that help.
+
+So hierarchical clustering,
+as your question implies,
+
+doesn't really tell you how
+many clusters there are.
+
+Another approach is
+to decide in advance
+
+how many clusters you expect.
+
+And then see whether you can
+get the data of the group
+
+into that number or not.
+
+And an example of
+that is something
+
+called k-means clustering.
+
+So the nice thing
+about it, is it
+
+does give you the
+sharp divisions.
+
+But again if you
+chose k incorrectly,
+
+we'll see in a
+second, you will get--
+
+you'll never less
+still get K-clusters.
+
+So K refers the
+number of clusters
+
+that you tell the algorithm
+you expect to get.
+
+So you specify that in advance.
+
+And then you try to
+find a set of clusters
+
+that minimizes the distance.
+
+So everybody's assigned
+to a particular cluster,
+
+and the center of that cluster.
+
+Is that clear?
+
+So that's what these
+equations represent.
+
+So the center of the
+cluster, the centroid,
+
+is just the average coordinates,
+over all the components
+
+of that cluster.
+
+And we're trying to find
+this set of clusters, C,
+
+that minimizes the sum of
+the square of the distances
+
+between each member of that
+cluster and the centroid.
+
+Any questions on how
+we're doing this?
+
+OK.
+
+All right.
+
+So what's the actual algorithm?
+
+That's remarkably simple.
+
+I'm choosing that initial
+set of random positions.
+
+And then I have the simple loop,
+I repeat until convergence.
+
+For every point, I assign
+it to the nearest centroid.
+
+So if my starting
+centroids would be circles,
+
+I look at every data
+point, and I ask,
+
+how close is it to
+any one of these?
+
+That's what the boundaries
+are, defined by these lines.
+
+So everything above this
+line belongs to the centroid.
+
+Everything over here
+belongs to this centroid.
+
+So I divide the data up by which
+centroid you are closest to.
+
+And I assign you
+to that centroid.
+
+That's step one.
+
+And step two, I
+compute new centroids.
+
+And that's what these
+triangles represent.
+
+So after I did
+that partitioning,
+
+it turns out that most
+of the things that
+
+were assigned to the triangular
+cluster live over here.
+
+So the centroid moves
+from being here to here.
+
+And I iterate this process.
+
+That's the entire K-means
+clustering algorithm.
+
+So here's an example
+where I generated data
+
+from three [? calcines. ?]
+I chose initial data
+
+points, which are the circles.
+
+I follow that protocol.
+
+Here's the first step.
+
+It computes new triangles.
+
+Second step, and
+then it converges.
+
+The distance stops changing.
+
+Now this question's
+already come up.
+
+So what happens if you
+choose the wrong K?
+
+So I believe there
+are three clusters.
+
+And really that's not the case.
+
+So what's going to happen?
+
+So in this data set,
+there really were.
+
+How many, there really
+were five clusters.
+
+Here, they're
+clustered correctly.
+
+What if I told the
+algorithm to do
+
+K-means clustering
+with a K of three?
+
+It would still find a way to
+come up with three clusters.
+
+So now it's grouped these
+two things, which are clearly
+
+generated from different
+[? calcines ?] scenes together.
+
+It's grouped these two,
+which were generated
+
+from different [? calcines ?]
+together, and so on.
+
+All right.
+
+So K-means clustering
+will do what
+
+you tell it to do, regardless of
+whether that's the right answer
+
+or not.
+
+And if you tell it there are
+more clusters than you expect--
+
+than really are
+there, then it'll
+
+start chopping up well-defined
+clusters into sub-clusters.
+
+So here it split this elongated
+one into two sub-clusters.
+
+It split this one
+arbitrarily into two.
+
+Just so it gets the final
+number that we asked for.
+
+Then how do you know what to do?
+
+Well, as I said, you don't--
+there's no guarantee to know.
+
+But one thing you can
+do is make this kind
+
+of plot, which shows for
+different values of K
+
+on the x-axis, the sum of the
+distances within the cluster.
+
+So the distance to the
+centroid within each cluster
+
+on the y-axis.
+
+And as I increase the number
+of K's, when I'm correctly
+
+[? purchasing ?] my
+data, when there really
+
+are more subgroups than
+I've already defined,
+
+then I'll see big drops.
+
+So I go from saying there are
+two to three in that case.
+
+I get a big drop in the distance
+between members of the cluster.
+
+Because I'm no longer including
+a data point over here.
+
+And in this cluster, with a
+data point in that cluster.
+
+But once I go beyond the
+correct number, which was five,
+
+you see that the benefits
+really start to trail off.
+
+So there's an
+inflection point here.
+
+There's an elbow-- sometimes
+it's called an elbow plot.
+
+After I go past
+the right number,
+
+I get less and less benefit
+from each additional clustering.
+
+So this gives us
+an empirical way
+
+of choosing approximately
+a correct value for K.
+
+Any questions on K-means?
+
+Yes?
+
+AUDIENCE: Does K-means
+recapitulate the clusters
+
+that you would
+get if you cut off
+
+your dendogram from hierarchical
+clustering at a certain level?
+
+PROFESSOR: Not necessarily.
+
+AUDIENCE: OK.
+
+But maybe.
+
+I don't know.
+
+It sort of seems to me
+as if you picked a level
+
+where you have a certain
+number of clusters,
+
+that that's similar, at least by
+centroid, by using the center?
+
+PROFESSOR: Yeah, I think because
+of the way that you do it,
+
+you're not even guaranteed
+to have a level, where
+
+you have exactly the
+right-- other questions?
+
+Yes?
+
+AUDIENCE: Could you
+just very quickly
+
+go over how you
+initialized where
+
+the starting points
+are, and the break ups?
+
+PROFESSOR: All right,
+so the question
+
+is how do you initialize
+the starting points?
+
+In fact, you have to make some
+arbitrary decisions about how
+
+the initialize the
+starting points.
+
+So they're usually
+chose in a random.
+
+And you will get
+different results,
+
+depending on how you do that.
+
+So that's another--
+so when you do it,
+
+it's non-deterministic
+in that sense.
+
+And you often want to
+initialize multiple times.
+
+And make sure you
+get similar results.
+
+Very good question.
+
+And in fact, that
+was not a set up.
+
+But what happens if you
+choose pathologically bad
+
+initial conditions?
+
+So you have the potential to
+converge to the right answer.
+
+But you're not guaranteed to
+converge to the right answer.
+
+So here's an example where
+I had-- I guess there really
+
+are three clusters in the data.
+
+I chose [INAUDIBLE]
+three, but I stuck
+
+all my initial coordinates down
+in the lower right-hand corner.
+
+And then when I do the
+clustering, if things go well,
+
+I get the right answer.
+
+But we're not guaranteed.
+
+But one thing we are guaranteed,
+is we always get convergence.
+
+So the algorithm will converge.
+
+Because at each
+step, it's either
+
+reducing the objective function,
+or it's leaving it the same.
+
+So we're guaranteed convergence.
+
+But it may be as we've seen
+previously in other settings,
+
+we may end up with local
+minimum, rather than
+
+the global optimum.
+
+And the way to fix
+that then would
+
+be to initialize again,
+with new starting positions.
+
+Other questions?
+
+What about a setting like this?
+
+Where we've got two
+well-defined clusters,
+
+and somebody who lives
+straight in the middle.
+
+So what's the
+algorithm going to do?
+
+Well, sometimes it'll put it
+in one side, of one cluster.
+
+And sometimes it'll end
+up in the other side.
+
+So an alternative to
+K-means clustering,
+
+which has to make one or the
+other arbitrary decision,
+
+is something that's called
+fuzzy K-means, which
+
+can put something
+actually literally,
+
+membership into both clusters.
+
+And it's very similar in
+structure to the K-means,
+
+with one important
+difference, which
+
+is a membership variable,
+that tells you for every data
+
+point, how much it belongs
+to the cluster one, cluster
+
+two, cluster three, and so on.
+
+So in both algorithms,
+we start off
+
+by choosing initial
+points as a cluster means,
+
+and looping through
+each of them.
+
+Now previously, we would make
+a hard assignment of each data
+
+point x sub i to
+a single cluster.
+
+And here we're going to
+calculate the probability
+
+that each data point
+belongs to a cluster.
+
+And that's where you
+get the fuzziness,
+
+because you could have a non
+unit, or a nonzero probability,
+
+belonging to any
+of the clusters.
+
+And now we're going, K-means,
+we recalculated the mean value,
+
+by just looking at the average
+of everybody in that cluster.
+
+Now in fuzzy K-means, we don't
+have everybody in the cluster.
+
+Because everybody belongs
+partially to the cluster.
+
+So we're going to take
+a weighted average.
+
+So here are the details
+of how you do that.
+
+In K-means, we are
+minimizing this function.
+
+We were trying to decide the
+class structure, the class
+
+memberships, that would minimize
+the distance of every member
+
+of that cluster, to the defined
+centroid of that cluster.
+
+Here it looks almost the same.
+
+Except we now have
+this new variable, mu,
+
+which is the membership.
+
+It's the membership of
+point j, in cluster i.
+
+So I'm trying to minimize
+a very similar function.
+
+But now if mu is one--
+if all my mus are one,
+
+then what do I get?
+
+K-means, right?
+
+But as soon as the mus are
+allowed to vary from one,
+
+they can be between
+zero and one,
+
+then points can
+contribute more or less.
+
+So that point there was stuck in
+the middle of the two clusters,
+
+if it had a mu of
+0.5 for each, it
+
+would contribute half to each.
+
+And then both the
+centroids would
+
+move a little bit
+towards the middle.
+
+So what's the
+result of K-means--
+
+I'm sorry, fuzzy
+K-means clustering?
+
+We still get K clusters.
+
+But now every gene or every
+object that we're clustering
+
+has a partial membership.
+
+So here's an example
+of that, where
+
+they did K-means
+clustering, with these six
+
+different clusters.
+
+But now every
+profile, every gene,
+
+has a color associated with it,
+that represents this mu value.
+
+Whether it goes from zero to
+one, with these rainbow colors,
+
+to the things that
+are reddish, or pink--
+
+those are the high
+confidence things
+
+that are very strongly,
+only in that cluster.
+
+Whereas the things that are
+more towards the yellow end
+
+of the spectrum are
+partially in this cluster
+
+and partially in other clusters.
+
+Questions?
+
+Any questions?
+
+So K-means, we've defined in
+terms of Euclidean distance.
+
+And that has clear advantages,
+in terms of computing things
+
+very easily.
+
+But it has some
+disadvantages as well.
+
+So one of the disadvantages
+is because we're
+
+using the squared
+distance, then outliers
+
+have a very big effect.
+
+Because I'm squaring the
+difference between vectors.
+
+That may not be the worst thing.
+
+But they also
+restrict us to things
+
+for which we can
+compute a centroid.
+
+We have to have data
+that are-- four or more,
+
+you can actually
+compute the mean value
+
+of all members of the cluster.
+
+Sometimes you want
+to cluster things
+
+that we only have
+qualitative data.
+
+Where instead of having
+a distance measure,
+
+we have similarity.
+
+This doesn't come up
+quite as often in-- well,
+
+it certainly doesn't come
+up in gene expression data
+
+or [? RNAC. ?] But you can
+imagine more qualitative data,
+
+where you ask people
+about similarity
+
+between different things
+or behavioral features,
+
+where you know the similarity
+between two objects.
+
+But you have no way of
+calculating the average object.
+
+One setting that you might
+[INAUDIBLE] have looked
+
+at-- if you're trying to
+cluster say, sequence motifs
+
+that you've computed
+with the EM algorithm.
+
+So what's the average
+sequence motif?
+
+That doesn't necessarily
+represent any true object,
+
+right?
+
+You might be better off--
+you can calculate it.
+
+But it doesn't mean anything.
+
+You might be better
+off calculating
+
+using rather than the
+average motif, the most
+
+central of the motifs that
+you actually observed.
+
+So that would be called
+a medoid, or an exemplar.
+
+It's a member of your cluster
+that's closest to the middle,
+
+even if it it's not
+smack dab in the middle.
+
+So instead of K-means, we can
+just think, well, K-medoids.
+
+So in K-means, we actually
+computed a centroid.
+
+And in medoids, we'll
+choose the existing data
+
+point that's most central.
+
+So what does that mean?
+
+If these are my data, the true
+mean is somewhere over here.
+
+But this one is the medoid.
+
+It's an exemplar that's
+close to the central point.
+
+But if there actually
+isn't anything here,
+
+then there isn't.
+
+So we're going to use
+the thing that's closest.
+
+So if these were
+all sequence motifs,
+
+rather than using some
+sequence motif that
+
+doesn't exist as the
+center of your cluster,
+
+you would use a sequence motif
+that actually does exist,
+
+and it's close to the center.
+
+So it's a simple
+variation on the K-means.
+
+Instead choosing K
+points in arbitrary space
+
+as our starting
+positions, we're going
+
+to choose K examples from the
+data as our starting medoids.
+
+And then we're going to place
+each point in the cluster that
+
+has the closest medoid,
+rather than median.
+
+And then when we
+do the update step,
+
+instead of choosing the
+average position to represent
+
+the cluster, we'll
+choose the medoid.
+
+The exemplar that's
+closest to the middle.
+
+Any questions on this?
+
+Yes?
+
+AUDIENCE: So if
+you use the medoid,
+
+do you lose the
+guaranteed convergence?
+
+Because I can
+picture a situation
+
+where you're sort of
+oscillating because now
+
+you have a discrete stack.
+
+PROFESSOR: That's
+a good question.
+
+That's probably right.
+
+Actually, I should
+think about that.
+
+I"m not sure.
+
+Yeah, that's probably right.
+
+Other questions?
+
+OK.
+
+There are a lot of other
+techniques for clustering.
+
+Your textbook talks about
+self organizing maps,
+
+which were popular at
+one point quite a lot.
+
+And there's also
+a nice technique
+
+called affinity
+propagation, which
+
+is a little bit outside
+the scope of this course,
+
+but has proved quite
+useful for clustering.
+
+OK.
+
+So why bother to do
+all this clustering?
+
+Our goal is to try to find
+some biological information,
+
+not just to find
+groups of genes.
+
+So what can you do
+with these things?
+
+Well, one thing that
+was identified early on,
+
+is if I could find sets of genes
+that behave similarly, maybe
+
+those could be used
+in a predictive way,
+
+to predict outcomes
+for patients,
+
+or some biological function.
+
+So we're going to
+look at that first.
+
+So one of the early
+papers in this field
+
+did clustering of
+microarrays for patients
+
+who had B-cell lymphoma.
+
+The patients had different
+kinds of B-cell lymphomas.
+
+And so they took their
+data, they clustered it.
+
+Again, each row
+represents a gene.
+
+And each column
+represents a patient here.
+
+And with this projector, it's
+a little bit hard to see.
+
+But when you look at
+the notes separately,
+
+you'll be able see
+that in the dendogram,
+
+there's a nice, sharp
+division between two
+
+large groups of patients.
+
+And it turns out that when
+you look at the pathologist's
+
+annotations for these
+patients, which was completely
+
+independent of the
+gene expression data,
+
+all of patients in
+the left hand group--
+
+almost all the patients
+in the left hand group,
+
+had one kind of lymphoma.
+
+And all the patients
+in the right hand group
+
+had a different
+kind of lymphoma.
+
+And this got people
+very excited.
+
+Because it suggested that
+the pure molecular features
+
+might be at least as good
+as pathological studies.
+
+So maybe you could completely
+automate the identification
+
+of different tumor types.
+
+Now the next thing that got
+people even more excited,
+
+was the idea that maybe
+you could actually
+
+use these patterns not
+just to recapitulate
+
+what a pathologist would
+find, but go beyond it,
+
+and actually make predictions
+from the patients.
+
+So in these plots--
+I don't know if we've
+
+seen these before
+yet in the class.
+
+But on the x-axis is survival.
+
+In the y-axis are the
+fraction of patients
+
+in a particular group,
+who survived that long.
+
+So as the patient's
+die, obviously
+
+the curve is dropping down.
+
+Each one of these
+drops represents
+
+the death of a patient,
+or the loss of the patient
+
+to the study for other reasons.
+
+And so in the middle,
+let's start with this one.
+
+This is what the clinicians
+would have decided.
+
+There are here, patients
+that they defined
+
+by clinical standards as
+being likely to do well,
+
+versus patients whom they
+defined by clinical standards,
+
+as likely to do poorly.
+
+And you could see there
+is a big difference
+
+in the plots for the
+low clinical risk
+
+patients at the top, and
+the high clinical risk
+
+patients at the bottom.
+
+On the left hand
+side, or what you
+
+get when you use purely
+gene expression data
+
+to cluster the patients into
+groups that you turn out
+
+to be high risk or low risk.
+
+And you can see that
+it's a little bit more
+
+statistically significant
+for the clinical risk.
+
+But it's pretty
+good over here, too.
+
+Now the really
+impressive thing is,
+
+what if you take the
+patients that the clinicians
+
+define as low clinical risk?
+
+And then you look at their
+gene expression data.
+
+Could you separate
+out the patients
+
+in that allegedly
+low clinical risk
+
+who are actually at high risk?
+
+And maybe then they
+would be diverted
+
+to have more aggressive
+therapy than patients
+
+who really and truly
+are low risk patients.
+
+And what they will
+show with just barely
+
+statistical significance,
+is that even
+
+among the clinically
+defined low risk patients,
+
+there is-- based on
+these gene signatures--
+
+the ability to
+distinguish patients
+
+who are going to do
+better, and patients
+
+who are going to do worse.
+
+So this was over a decade ago.
+
+And it really set off a
+frenzy of people looking
+
+for gene signatures for
+all sorts of things,
+
+that might be highly predictive.
+
+Now the fact that
+something is correlated,
+
+doesn't of course
+prove any causality.
+
+So one of the questions is, if
+I find a gene signature that
+
+is predictive of an outcome
+in one of the studies,
+
+can I use it then to go
+backwards, and actually
+
+define a therapy?
+
+In the ideal setting, I would
+have these gene signatures.
+
+I'd discover that
+they are clinically
+
+associated with outcome.
+
+I could dig in and
+discover what makes
+
+the patients to do worse, worse.
+
+And go and treat that.
+
+So is that the case or not?
+
+So let me show you some data
+from a breast cancer data set.
+
+Here's a breast cancer data set.
+
+Again the same kind of plot,
+where we've got the survival
+
+statistic on the y-axis, the
+number of years on the x-axis.
+
+And based on a gene
+signature, this group
+
+has defined a group
+that does better,
+
+and a group that does worse,
+the p value is significant.
+
+And it has a ratio, the
+death rate versus control
+
+is approximately two.
+
+OK.
+
+So does this lead us to
+any mechanistic insight
+
+into breast cancer.
+
+Well, it turns out in this
+case, the gene signature
+
+was defined based on
+postprandial laughter.
+
+So after dinner humor.
+
+Here's a gene set
+that defined something
+
+that has absolutely nothing
+to do with breast cancer,
+
+and it's predicting the outcome
+of breast cancer patients.
+
+Which leads to
+somewhat more of a joke
+
+that the testing
+whether laughter
+
+really is the best medicine.
+
+OK.
+
+So they went on-- they
+tried other genes sets.
+
+Here's the data
+set-- gene set that's
+
+not even defined in humans.
+
+It's the homologs of
+genes that are associated
+
+with social defeat in mice.
+
+And once again, you get a
+statistically significant
+
+p-value, and good hazard ratios.
+
+So what's going on?
+
+Well, these are not from
+a study that's actually
+
+trying to predict an
+outcome in breast cancer.
+
+It's a study that shows
+that most gene expression--
+
+most randomly selected
+sets of genes in the genome
+
+will give an outcome that's
+correlated-- a result that's
+
+correlated with a patient
+outcome in breast cancer.
+
+Yes?
+
+AUDIENCE: I'm a little confused.
+
+In the previous graph, could you
+just explain what is the black
+
+and what is the red?
+
+Is that individuals or groups?
+
+PROFESSOR: So the
+black are people
+
+that have the genes
+set signature, who
+
+have high levels
+of the genes that
+
+are defined in this gene set.
+
+And the red are ones have
+low, or the other way around.
+
+But it's defining all patients
+into two groups, based
+
+on whether they have a
+particular level of expression
+
+in this gene set,
+and then following
+
+those patients over time.
+
+Do they do better or worse?
+
+And similarly for
+all these plots.
+
+And he had another one which is
+a little less amusing, location
+
+of skin fibroblasts.
+
+The real critical point is this.
+
+Here, they compared
+the probability
+
+based on expectation
+an that all genes are
+
+independent of each
+other, the probability
+
+that that gene signatures
+correlated with outcome,
+
+for genes there were chosen
+at random or genes that
+
+were chosen from a database
+of gene signatures,
+
+that people have identified as
+being associated with pathways.
+
+And you get a very,
+very large fraction.
+
+So this is the p-value.
+
+So negative log of
+p-value, so negative values
+
+are more significant.
+
+A huge fraction
+of all genes sets
+
+that you pull at
+random from the genome,
+
+or that you pull from a
+compendium of known pathways,
+
+are going to be
+associated with outcome,
+
+in this breast cancer data set.
+
+So it's not just well
+annotated cancer pathways,
+
+that are associated.
+
+Its gene sets
+associated as we've
+
+seen, with laughter or
+social defeat in mice,
+
+and so on-- all sorts
+of crazy things,
+
+that have no mechanistic
+link to breast cancer.
+
+Let's take a second
+for that to sink in.
+
+I pull genes at random
+from the genome.
+
+I define patients
+based on whether they
+
+have high levels of expression
+of a random set of genes,
+
+or low levels of expression
+of that random set of genes.
+
+And I'm extremely likely
+to be able to predict
+
+the outcome in breast cancer.
+
+So that should be rather
+disturbing, right?
+
+So it turns out-- before
+we get to the answer
+
+then-- so this is not
+unique to breast cancer.
+
+They went through a whole bunch
+of data sets in the literature.
+
+Each row is a different
+previously published study,
+
+where someone had claimed
+to identify a signature
+
+for a particular kind
+of disease or outcome.
+
+And they took their
+random gene sets and asked
+
+how well the random
+genes sets did
+
+in predicting the outcome
+in these patients?
+
+And so these yellow
+plots represent
+
+the probability distribution
+for the random gene
+
+sets-- again on
+this projector, it's
+
+hard to see-- but there's a
+highlight in the left hand
+
+side at where the 5%, the best
+5% of the random gene sets are.
+
+This blue line is
+the near measure
+
+of statistical significance.
+
+It turns out that a
+few of these studies
+
+didn't even reach a normal level
+of statistical significance,
+
+let alone comparing
+to random gene sets.
+
+But for most of
+these, you don't do
+
+better than a good fraction
+of the randomly selected gene
+
+sets.
+
+So how could this be?
+
+So it turns out there is an
+answer to why this happens.
+
+And it's really
+quite fascinating.
+
+So here, we're using
+the hazard ratio,
+
+which is the death rate
+for the patients who
+
+have the signature,
+over the control group.
+
+So high hazard ratio means
+it's a very, very dissociative
+
+outcome.
+
+And they've plotted that against
+the correlation of the genes
+
+in the gene signature, with
+the expression of a gene called
+
+PCNA, Proliferating
+Cell Nuclear Antigen
+
+And it turns out a very, very
+large fraction of the genome
+
+is coexpressed.
+
+So genes are not expressed like
+random, completely independent
+
+random variables.
+
+There are lots of genes that
+show very similar expression
+
+levels, across
+all the data sets.
+
+Now PCNA is a gene that's
+been known by pathologists
+
+for a long time,
+as having higher
+
+levels than most
+digressive tumors.
+
+So a very, very large
+fraction of the genome
+
+is coexpressed with PCNA.
+
+Then high levels of
+randomly selected genes
+
+are going to be a very good
+predictor of tumor outcome.
+
+Because high levels of
+randomly expressed genes
+
+also means a very
+high probability
+
+of having a high level PCNA,
+which is a tumor marker.
+
+So we have to proceed
+with a lot of caution.
+
+We can find things that are
+highly correlated with outcome,
+
+that could have good value in
+terms of prognostic indicators.
+
+But there are going to
+be a lot of possibilities
+
+for sets of genes that
+have that property,
+
+they're good
+predictors of outcome.
+
+And many of them will
+have absolutely nothing
+
+to causally, with the
+process of the disease.
+
+So at the very least, it means
+don't start a drug company
+
+over every set of genes,
+if you identify this
+
+as associated with outcome.
+
+But the worst case
+scenario, it also
+
+means that those predictions
+will break down under settings
+
+that we haven't yet examined.
+
+And so that's the
+real fear, that you
+
+have a gene set
+signature that you think
+
+has a highly predictive outcome.
+
+It's only because you looked at
+a particular set of patients.
+
+But you look at a
+different set of patients,
+
+and that correlation
+will break down.
+
+So this is an area of research
+that's still quite in flux,
+
+in terms of how
+much utility there
+
+will be in identifying
+genes set signatures,
+
+in this completely
+objective way.
+
+And what we'll see in the
+course of this lecture
+
+and the next one,
+is it's probably
+
+going to be much more
+useful to incorporate
+
+other kinds of information
+that will constrain
+
+us to be more mechanistic.
+
+Any questions?
+
+All right.
+
+So now we're going to
+really get into the meat
+
+of the identification
+of gene modules.
+
+And we're going to try to
+see how much we can learn
+
+about regulatory structure
+from the gene expression data.
+
+So we're going to move up from
+just the pure expression data--
+
+say these genes at the
+bottom, to try to figure out
+
+what set of transcription
+factors we're driving,
+
+and maybe what signaling
+pathways lived upstream
+
+in those transcription
+factors, and turn them on.
+
+And the fundamental difference
+then between clustering-- which
+
+is what we've been looking in
+until now, and these modules,
+
+as people like to call
+them-- is that you
+
+can have a whole bunch
+of genes, and we've just
+
+seen that, that are
+correlated with each other,
+
+without being causally
+linked to each other.
+
+So we like to figure out which
+ones are actually functionally
+
+related, and not just
+statistically related.
+
+And the paper that's going
+to serve as our organizing
+
+principle in the
+rest of this lecture,
+
+maybe bleeding into
+the next lecture,
+
+is this paper,
+recently published
+
+that's called The
+DREAM5 Challenge.
+
+And this, like some of these
+other challenges that we've
+
+seen before, is the case where
+the organizers have data sets,
+
+where are they know
+the answer to what
+
+the regulatory structure is.
+
+They send out the data.
+
+People try to make the
+best predictions they can.
+
+And then they unseal
+the data, to let
+
+people know how well they did.
+
+And so you can get a
+relatively objective view
+
+of how well different
+kinds of approaches work.
+
+So this is the overall
+structure of this challenge.
+
+They had four different
+kinds of data.
+
+Three are real data sets from
+different organisms, E. coli,
+
+yeast, and
+Staphylococcus aureus.
+
+And then the fourth one,
+the one at the top here,
+
+is completely synthetic
+data that they generated it.
+
+And you get a sense of the
+scale of the data sets.
+
+So how many genes are involved,
+how many potential regulators.
+
+In some cases, they've given
+you specific information
+
+on knockouts, antibiotics,
+toxins, that are perturbing.
+
+And again here, the
+number of conditions that
+
+are being looked at,
+the number of arrays.
+
+So then they provide
+this data in a way
+
+that's very hard
+for the groups that
+
+are analyzing to trace it
+back to particular genes.
+
+Because you don't want people to
+use external data necessarily,
+
+to make their predictions.
+
+So every makes
+their predictions.
+
+They also, as part
+of this challenge,
+
+they actually they made
+their own metapredictions,
+
+based on the
+individual predictions
+
+by different groups.
+
+And we'll take a look
+at that in a second.
+
+And then they score
+how well they did.
+
+Now we'll get into the details
+of the scoring a little bit
+
+later.
+
+But what they found
+at the highest levels,
+
+that different kinds of
+methods behaved similarly.
+
+So the main groups
+that they found
+
+were these regression-based
+techniques.
+
+We'll talk about
+those in a second.
+
+Bayesian networks,
+which we've already
+
+discussed in a
+different context.
+
+A hodgepodge of different
+kinds of things.
+
+And then mutual information
+and correlation.
+
+So we're going to look in
+each of these main categories
+
+of prediction methods.
+
+So we're going to start with
+the Bayesian networks, which
+
+we just finished talking
+about in a completely
+
+different context.
+
+Here, instead of trying to
+predict whether interaction
+
+is true, based on the
+experimental data,
+
+we're going to try to predict
+whether a particular protein is
+
+involved in regulating a set of
+genes, based on the expression
+
+data.
+
+So in this context-- let's
+say I have cancer data sets,
+
+and I wanted to decide
+whether p53 is activated
+
+in those tumors, So this
+is a known pathway for p53.
+
+So if I told you
+the pathway, how
+
+might you figure out if p53
+is active from gene expression
+
+data?
+
+I tell you this pathway, give
+you this expression data--
+
+what's kind of a simple
+thing that you could do right
+
+away, to decide whether you
+think p53 is active or not?
+
+p53 is a transcriptional
+activator,
+
+but it should be turning
+on the genes of its targets
+
+when its on.
+
+So what's an
+obvious thing to do?
+
+AUDIENCE: Check the expression
+levels from the targets.
+
+PROFESSOR: Thank you.
+
+Right, so we could check
+the expression levels.
+
+The targets compute some
+simple statistics, right?
+
+OK.
+
+Well, that could work.
+
+But of course there could
+be other transcriptional
+
+regulators that regulate
+a similar set of genes.
+
+So that's not a
+guarantee that p53 is on.
+
+It might be some other
+transcriptional regulator.
+
+We could look for the
+pathways that activate p53.
+
+We could ask whether
+those genes are on.
+
+So we've got in this
+pathway, a bunch of kinases,
+
+an ATM, CHK1, and so
+on, that activate p53.
+
+Now if we had proteomic
+data, we could actually
+
+look whether those proteins
+are phosphorylated.
+
+But we have much, much
+less proteomic data.
+
+And most of these settings
+only have gene expression data.
+
+But you look at, is
+that gene expressed?
+
+Has the expression of one
+of these activating proteins
+
+gone up?
+
+And you can try to
+make an inference then.
+
+From whether there's more of
+these activating proteins,
+
+then maybe p53 is active.
+
+And therefore it's
+turning on it's targets.
+
+That's one step removed.
+
+So just the fact that there's
+a lot of ATM mRNA around
+
+doesn't mean that there's a
+lot of the ATM protein, which
+
+certainly doesn't mean that
+the ATM is phosphorylated
+
+and turning on its target.
+
+So again, we don't
+have a guarantee there.
+
+We could look more specifically
+whether the genes are
+
+differentially expressed.
+
+So the fact that they're on
+may not be as informative
+
+as if they were uniquely
+on in this tumor,
+
+and not on in control cells
+from the same patient.
+
+So that can be informative.
+
+But again changes
+in gene expression
+
+are not uniquely related to
+changes in protein level.
+
+So we're going to have to
+behave with a bit of caution.
+
+So the first step we're going
+to take in this direction,
+
+is try to build a
+Bayesian network.
+
+That's going to give us a way
+to reason probabilistically
+
+over all of these kinds of data,
+which by themselves are not
+
+great guarantees that we're
+getting the right answer.
+
+Just like in the protein
+prediction interaction problem,
+
+where individually coexpression
+wasn't all that great,
+
+essentiality wasn't
+all that great.
+
+But taken together, they
+could be quite helpful.
+
+So we want to compute
+the probability
+
+that the p53 pathway is
+active, given the data.
+
+And the only data we're
+going to have in the setting
+
+is gene expression data.
+
+So we're going to assume
+that for the targets
+
+of a transcription
+factor to be active,
+
+the transcription
+factor itself has
+
+to be expressed
+at a higher level.
+
+That's a restriction
+of analyzing
+
+these kinds of data
+that's very commonly used.
+
+So we're going to try to
+compute the probability that p53
+
+is activated, given the data.
+
+So how would I compute
+the probability,
+
+that given that some
+transcription factors on,
+
+that I see expression
+from target genes?
+
+How would I do this?
+
+I would just go into the data,
+and just count in the same way
+
+that we did in our
+previous setting.
+
+We could just look over
+all the experiments
+
+and tabulate whether one of the
+targets is up in expression,
+
+how often is the transcription
+factor that's potentially
+
+activating it up?
+
+And how often are all the
+possible combinations the case?
+
+And then we can use
+Bayesian statistics
+
+to try to compute
+the probability
+
+that a transcription
+factor is up, activated,
+
+given that I've seen the
+gene expression data.
+
+Is that clear?
+
+Good.
+
+So we want to try to not include
+just the down stream factors.
+
+Because that leads
+possibly, maybe there
+
+are multiple
+transcription factors
+
+that are equally
+likely to be driving
+
+expressions instead of genes.
+
+We want to include the
+upstream regulators as well.
+
+And so here, we're going
+to take advantage of one
+
+of the properties
+of Bayesian nets
+
+at where we looked
+at, explaining a way.
+
+And you'll remember
+this example, where
+
+we decided that if see
+that the grass is wet,
+
+and I know that
+it's raining, then
+
+I can consider less likely
+that the sprinklers were on.
+
+Even though there's no causal
+relationship between them.
+
+So if I see that a set of
+targets of transcription factor
+
+A are on, and I have evidence
+that the pathway upstream of A
+
+is on, that reduces my
+inferred probability
+
+that the transcription
+factor B is responsible.
+
+So that's of the nice things
+about Bayesian networks
+
+that gives us a way of
+reasoning automatically,
+
+over all the data, and not
+just the down stream targets.
+
+And the Bayesian networks
+can have multiple layers.
+
+So we can have one
+transcription factor
+
+turning another one,
+turns on other one,
+
+turns on another one.
+
+Again, we can have as
+many layers as necessary.
+
+But one thing we
+can't have are cycles.
+
+So we can't have a
+transcription factor
+
+that's at the bottom of this,
+going back and activating
+
+things that are at the top.
+
+And that's a
+fundamental limitation
+
+of Bayesian networks.
+
+We've already talked
+about the fact
+
+that in Bayesian networks,
+with these two problems that we
+
+to have to solve, we have to be
+able to define the structure.
+
+If we don't know any a priori.
+
+Here, we don't
+know what a priori.
+
+So we're going to have to learn
+the structure of the network.
+
+And then with the
+structure of the network,
+
+we're going to have to
+learn all the probabilities.
+
+So the conditional
+probability tables
+
+that relate to each
+variable to every other one.
+
+And then just two more
+small points about it.
+
+So if I just give
+you expression data,
+
+without any interventions--
+just the observations,
+
+then I can't decide what is a
+cause and what is an effect.
+
+So here this was done in
+the context of proteomics,
+
+but the same is true for
+gene expression data.
+
+If I have two variables, x and
+y, that are highly correlated,
+
+it could be that x activates y.
+
+It could be that y activates x.
+
+But if I perturb the system,
+and I block the activity of one
+
+of these two genes
+or proteins, then I
+
+can start to tell
+the difference.
+
+In this case, if
+you inhibit x, you
+
+don't see any activation of y.
+
+That's the yellow,
+all down here.
+
+But if you inhibit y,
+you see the full range
+
+of activity of x.
+
+So that implies that x
+is the activator of y.
+
+And so in these settings, if
+you want to learn a Bayesian
+
+network from data, you need
+more than just a compendium
+
+of gene expression data.
+
+If you want to get the
+directions correct,
+
+you need perturbations
+where someone has actually
+
+inhibited particular
+genes or proteins.
+
+Now, in a lot of these
+Bayesian networks,
+
+we're not going
+to try to include
+
+every possible gene and
+every possible protein.
+
+Either because we don't
+have measurements of it,
+
+or because we need
+a compact network.
+
+So there will often
+be cases where
+
+the true regulator
+in some causal chain,
+
+is missing from our data.
+
+So imagine this is the true
+causal chain-- x activates
+
+y, which then activates z and w.
+
+But either because we
+don't have the data on y,
+
+or because we left it out to
+make our models more compact,
+
+it's not in the model.
+
+We can still pick up the
+relationships between x and z,
+
+and x and w.
+
+But the data will
+be much noisier.
+
+Because we're missing
+that information.
+
+In the conditional
+probability tables,
+
+relating x to y, and then
+y because it's too targets.
+
+So Bayesian networks, we've
+already seen quite a lot.
+
+We now have some idea of how to
+transfer them from one domain
+
+to the domain of
+gene expression data.
+
+The next approach
+we want to look at
+
+is a regression-based approach.
+
+So the regression-based
+approaches
+
+are founded on a
+simple idea, which
+
+is that the expression
+gene is going
+
+to be some function
+of the expression
+
+levels of the regulator.
+
+We're going to
+actually try to come up
+
+with a formula that
+relates the activity
+
+levels of the
+transcription factors,
+
+and the activity
+level of the target.
+
+In this cartoon, I've
+got a gene that's
+
+on under one
+condition, that's off
+
+under some other conditions.
+
+What transforms it
+from being off to on,
+
+is the introduction of
+more of these transcription
+
+factors, that are
+binding to the promoter.
+
+So in general, I have
+some predicted level
+
+of expression for the gene.
+
+It's called the
+predicted level y.
+
+And it's some function,
+unspecified at this point, f
+
+of g, of all the expression
+levels of the transcription
+
+factors that regulate that gene.
+
+So just again,
+nomenclature is straight,
+
+x sub g is going to be
+the expression of gene x--
+
+I'm sorry, expression of gene g.
+
+This capital X, sub t of g
+is the set of transcription
+
+factors, that I believe
+are regulating that gene.
+
+And then f is an
+arbitrary function.
+
+We're going to have
+a noise term as well.
+
+Because this is the
+observed gene expression,
+
+not some sort of platonic view
+of the true gene expression.
+
+Now frequently, we'll
+have a specific function.
+
+So the simplest one
+you can imagine,
+
+which is a linear function.
+
+So the expression of
+any particular gene
+
+is going to be a
+linear function, a sum,
+
+of the expression of
+all of it's regulators,
+
+where each one has associated
+with it a coefficient beta.
+
+And that beta
+coefficient tells us
+
+how much particular a
+regulator influences that gene.
+
+So say, p53 might have
+a very large value.
+
+Some other
+transcriptional regulator
+
+might have a small
+value, representing
+
+their relative influence.
+
+Now, I don't know the
+beta values in advance.
+
+So that's one of the things
+that I need to learn.
+
+So I want to be able to
+find a setting that tells me
+
+what the beta values are for
+every possible transcription
+
+factor.
+
+If the algorithm sets
+the beta value to zero,
+
+what does that tell me?
+
+If a beta value
+is zero here, what
+
+does that tell me about that
+transcriptional regulator?
+
+No influence, right.
+
+And the higher the value, then
+the greater the influence.
+
+OK.
+
+So how do we discover these?
+
+So the tip of the
+approach then is
+
+to come up with some
+objective function
+
+that we're going
+to try to optimize.
+
+And an obvious
+objective function
+
+is the difference between
+the observed expression
+
+value for each gene,
+and the expected one,
+
+based on that linear function.
+
+And we're going to choose
+a set of data parameters
+
+that minimize the difference
+between the observed
+
+and the expected, minimize
+the sum of the squares.
+
+So the residual sum
+of the squares error,
+
+between the predicted
+and the observed.
+
+So this is a relatively
+standard regression problem,
+
+just in different setting.
+
+Now one of the problems with
+a standard regression problem,
+
+is that we'll
+typically get a lot
+
+of very small values of beta.
+
+So we won't get all
+zeros or all ones,
+
+meaning the algorithm is
+100% certain that these
+
+are the drivers
+and these are not.
+
+We'll get a lot of small values
+for many, many transcription
+
+factors.
+
+And OK, that could
+represent the reality.
+
+But the bad thing is
+that those data values
+
+are going to be unstable.
+
+So small changes in
+the training data
+
+will give you big changes, in
+which transcription factors
+
+have which values.
+
+So that not a desirable setting.
+
+There's a whole field
+built up around trying
+
+to come up with
+better solutions.
+
+I've given you some
+references here.
+
+One of them is to a
+paper that did well
+
+in the DREAM challenge.
+
+The other one is to
+a very good textbook,
+
+Elements of
+Statistical Learning.
+
+And there are various
+techniques that
+
+allow you to try to
+limit the number of betas
+
+that are non-zero.
+
+And by doing that, you get
+more robust predictions.
+
+At a cost, right, because there
+could be a lot of transcription
+
+factors that really do
+have small influences.
+
+But we'll trade
+that off, by getting
+
+more accurate predictions
+from the ones that
+
+have the big influences.
+
+Are there any questions
+on regression?
+
+So the last of the methods
+that we're examining-- this
+
+is a mutual information.
+
+We've already seen mutual
+information in the course.
+
+So information
+content is related
+
+to the probability of observing
+some variable in an alphabet.
+
+So in most languages,
+the probability
+
+of observing letters
+is quite variable.
+
+So Es are very common
+in the English language.
+
+Other letters are less common.
+
+As anyone who plays Hangman or
+watches Wheel of fortune knows.
+
+And we defined the
+entropy as the sum
+
+over all possible outcomes.
+
+The probability of
+observing some variable,
+
+and the information
+on to that variable,
+
+we can define the discrete
+case, or in the continuous case.
+
+And the critical
+thing is to have
+
+mutual information
+between two variables.
+
+So that's the difference between
+the entropy of those variables
+
+independently, and
+then the joint entropy.
+
+So things with a high
+mutual information,
+
+means that one variable gives
+the significant knowledge
+
+of what the other
+variable is doing.
+
+It reduces my uncertainty.
+
+That's the critical idea.
+
+OK.
+
+So we looked at
+correlation before.
+
+There could be
+settings where you
+
+have very low correlation
+between two variables,
+
+but have high
+mutual information.
+
+So consider these two genes,
+protein A and protein b,
+
+and the blue dots are the
+relationship between them.
+
+You can see that there's
+a lot of information
+
+content in these two variables.
+
+Knowing the value of A
+gives me a high confidence
+
+in the value of B. But
+there's no linear relationship
+
+that describes these.
+
+So if I use mutual
+information, I
+
+can capture
+situations like this,
+
+that I can't capture
+with correlation.
+
+And these kinds of
+situations actually occur.
+
+So for example in a
+feed-forward loop--
+
+say we've got a regulator
+A, and it directly
+
+activates B. It also directly
+activates C. But C inhibits B.
+
+So you've got the path on
+the left-hand sides that
+
+are pressing the accelerator.
+
+And the path on the right hand
+side pressing the stop pedal.
+
+That's called an incoherent
+feed-forward loop.
+
+And you can get under different
+settings, different kinds
+
+of results, where this
+is one of those examples.
+
+You can get much
+more complicated
+
+behavior. [INAUDIBLE] are papers
+that have really mapped out
+
+these behaviors across
+many parameters settings.
+
+You can get switches
+in the behavior.
+
+But in a lot of
+these settings, you
+
+will have high
+mutual information
+
+between two
+variables, even if you
+
+don't have any correlation,
+linear correlation
+
+between them.
+
+A well-publicized algorithm
+that uses mutual information
+
+to infer gene regulatory
+networks is called ARACNe.
+
+They go through and they
+compute the mutual information
+
+between all pairs of
+genes in their data set.
+
+And now one question you have
+with mutual information is,
+
+what defines a significant
+level of mutual information?
+
+So an obvious way to do
+this, to try to figure out
+
+what's significant, is
+to do randomizations.
+
+And so that's what they did.
+
+They shuffled the
+expression data,
+
+to compute mutual information
+among pairs of genes,
+
+where there isn't
+actually a need--
+
+there shouldn't be
+any relationships.
+
+Because the data
+had been shuffled.
+
+And then you can decide whether
+the observed mutual information
+
+is significantly
+greater than when
+
+you get from the
+randomized data.
+
+Now, the other thing that
+happens with mutual information
+
+is that indirect
+effects still apply
+
+to degrees of
+mutual information.
+
+So let's consider the set of
+genes that are shown on this.
+
+So you've got G2,
+which is actually
+
+a regulator of G1 and G3.
+
+So G2 is going to have
+high mutual information
+
+with G1, and with G3.
+
+Now, what's it going
+to be about G1 and G3?
+
+They're going to behave
+very similarly, as well.
+
+So it'll be a high degree
+of mutual information
+
+between G1 and G3.
+
+So if I just rely on
+mutual information,
+
+I can't tell what's a
+regulator and what's
+
+a fellow at the same
+level of regulation.
+
+They're both being affected
+by something above them.
+
+I can't tell the difference
+between those two.
+
+So they use what's called the
+data processing inequality,
+
+where they say, well, these
+regulatory interactions
+
+should have higher
+mutual information,
+
+than this, which is just
+between two common targets
+
+in the same parent.
+
+And so they drop from their
+network, those things which
+
+are the lower of the
+three in a triangle.
+
+So that was the original
+ARACNe algorithm,
+
+and then they modified
+it a little bit,
+
+to try to be more specific in
+terms of the regulators that
+
+were being picked up.
+
+And so they called
+this approach MINDy.
+
+And the core idea here,
+is that in addition
+
+to the transcription
+factors, you
+
+might have another protein that
+turns a transcription factor on
+
+or off.
+
+So if I look over
+different concentrations
+
+of the transcription factor,
+different levels of expression
+
+between transcription
+factors, I might
+
+find that there are some cases
+where this other protein turns
+
+it on, and other cases
+where it turns it off.
+
+So here, consider
+these two data sets.
+
+Looking at different
+concentrations
+
+of particular transcription
+factor and different expression
+
+levels, and in one
+case-- the blue ones,
+
+the modulator isn't
+present at all,
+
+or present at it's
+lowest possible level.
+
+And in the red case, it's
+present as a high level.
+
+And you can see that when
+the modulator is present only
+
+in low levels, there's no
+relationship between a target
+
+and it's transcription factor.
+
+Or when the modulator is
+present at a high level,
+
+then there's this
+linear response
+
+of the target to it's
+transcription factor.
+
+So this modulator seems to
+be a necessary component.
+
+So they went through and
+defined a whole bunch
+
+of settings like this.
+
+And then systematically search
+the data for these modulators.
+
+So they started off with the
+expression data set, genes
+
+in rows, experiments in columns.
+
+They do a set of
+filtering to remove things
+
+that are going to be
+problematic for the analysis.
+
+They look, for
+example, for settings
+
+where you have-- they had to
+start with a list of modulators
+
+and transcription factors,
+and they moved the ones
+
+where there isn't enough
+variation, and so on.
+
+And then they examine, for every
+modulator and transcription
+
+factor pair, cases
+where the modulator is
+
+present at its highest
+level, and where
+
+it's present at
+it's lowest level.
+
+So when the modulator is present
+at a high level-- let's say,
+
+when the modulator is
+present at a high level,
+
+there's a high
+mutual information
+
+between the transcription
+factor and the target.
+
+When the modulator is absent,
+there's no mutual information.
+
+That's a setting we
+looked at before.
+
+That would suggest that the
+modulator is an activator.
+
+It's a positive modulator.
+
+You can have the
+opposite situation,
+
+where when the modulator
+is present at low levels,
+
+there's mutual information
+between a transcription factor
+
+and it's target.
+
+When the modulator is
+present at a high level,
+
+you don't see anything.
+
+That would suggest
+that the modulator
+
+is a negative regulator.
+
+And then there are scenarios
+where there's either
+
+uniformly high
+information content
+
+between transcription factor
+target, or uniformly low.
+
+So the modulator doesn't
+seem to be doing anything.
+
+So we break it down
+into these categories.
+
+And you can look at all
+the different categories,
+
+in their supplemental tables.
+
+One thing that's
+kind of interesting
+
+is they assume that regardless
+of how high the transcription
+
+factor goes, you'll
+always see an increase
+
+in the expression of the target.
+
+So there is no
+saturation, which is
+
+an unnatural assumption
+in these data sets.
+
+OK.
+
+So I think I'll close with this
+example, from their experiment.
+
+And then in the
+next lecture, we'll
+
+look at how these
+different methods fare
+
+against each other in
+the DREAM challenge.
+
+So they specifically wanted
+to find regulators of MYC.
+
+So here's data for a
+particular regulator, SDK 38.
+
+Here's the set of
+expression of tumors
+
+where SDK 38
+expression is lowest.
+
+And a set of tumors where
+SDK 38 expression is highest.
+
+And they're sorted by the
+expression level of MYC.
+
+So on the left hand
+side, you'll see
+
+there's no particular
+relationship
+
+between the expression level
+of MYC and the targets.
+
+In the right hand side,
+there is a relationship
+
+between the expression
+level of MYC and targets.
+
+So having, apparently--
+at least at this level
+
+of mutual information, having
+higher levels of SDK 38,
+
+cause a relationship to occur.
+
+That would be example
+of an activator.
+
+OK.
+
+So this technique has
+a lot of advantages,
+
+and allows you to search rapidly
+over very large data sets,
+
+to find potential target
+transcription factor
+
+relationships, and also
+potential modulators.
+
+It has some limitations.
+
+Where the key limitations
+is that the signal has
+
+to be present in the
+expression data set.
+
+So in the case of
+a protein like p53,
+
+where we know it's activated
+by all sort of other processes,
+
+phosphorylation or NF-kappaB,
+where it's regulated
+
+by phosphorylation, you
+might not get any signal.
+
+So there has to be a case
+where the transcription
+
+factor itself, is
+changing expression.
+
+It also won't work if
+the modulator is always
+
+highly correlated
+with its target,
+
+for some other
+biological reason.
+
+So the modulator has to be
+on, for other reasons, when
+
+the target is, then
+you'll never be
+
+able to divide the
+data in this way.
+
+One of the other
+things I think that is
+
+problematic with
+these networks is
+
+that you get such
+large networks,
+
+and they're very
+hard to interpret.
+
+So in this case, this
+is the nearest neighbors
+
+of just one node in ARACNe.
+
+This is the mutual information
+network of microRNA modulators
+
+that has a quarter of
+a million interactions.
+
+And in these data
+sets, often you
+
+end up selecting a very,
+very large fraction
+
+of all the potential modulators.
+
+So of all the candidate
+transcription factors
+
+in modulators, it
+comes up with an answer
+
+that's roughly 10% to 20%
+of them are regulating
+
+any particular gene,
+which seems awfully high.
+
+OK.
+
+So any questions on the
+methods we've seen so far?
+
+OK.
+
+So when we come
+back on Thursday,
+
+we'll take a look
+at head to head
+
+of how these different methods
+perform on both the synthetic
+
+and the real data sets.
\ No newline at end of file
diff --git a/StbJIv49Aco.txt b/StbJIv49Aco.txt
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--- /dev/null
+++ b/StbJIv49Aco.txt
@@ -0,0 +1,587 @@
+align:start position:0%
+ 
+I love teaching this course and I tell
+
+ align:start position:0%
+I love teaching this course and I tell
+ 
+
+ align:start position:0%
+I love teaching this course and I tell
+the class that the first day um partly
+
+ align:start position:0%
+the class that the first day um partly
+ 
+
+ align:start position:0%
+the class that the first day um partly
+because of them I've learned that they
+
+ align:start position:0%
+because of them I've learned that they
+ 
+
+ align:start position:0%
+because of them I've learned that they
+are really serious and and and I have
+
+ align:start position:0%
+are really serious and and and I have
+ 
+
+ align:start position:0%
+are really serious and and and I have
+something that I hope they get which is
+
+ align:start position:0%
+something that I hope they get which is
+ 
+
+ align:start position:0%
+something that I hope they get which is
+the idea many of them took calculus
+
+ align:start position:0%
+the idea many of them took calculus
+ 
+
+ align:start position:0%
+the idea many of them took calculus
+differential equations survived it
+
+ align:start position:0%
+differential equations survived it
+ 
+
+ align:start position:0%
+differential equations survived it
+didn't especially enjoy it and I I'm
+
+ align:start position:0%
+didn't especially enjoy it and I I'm
+ 
+
+ align:start position:0%
+didn't especially enjoy it and I I'm
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+hoping uh that they think this they see
+
+ align:start position:0%
+hoping uh that they think this they see
+ 
+
+ align:start position:0%
+hoping uh that they think this they see
+math what math is about and uh how it
+
+ align:start position:0%
+math what math is about and uh how it
+ 
+
+ align:start position:0%
+math what math is about and uh how it
+looks for the pattern in a whole lot of
+
+ align:start position:0%
+looks for the pattern in a whole lot of
+ 
+
+ align:start position:0%
+looks for the pattern in a whole lot of
+different applications often engineering
+
+ align:start position:0%
+different applications often engineering
+ 
+
+ align:start position:0%
+different applications often engineering
+but many others too science economics
+
+ align:start position:0%
+but many others too science economics
+ 
+
+ align:start position:0%
+but many others too science economics
+biology wherever um and uh if they if
+
+ align:start position:0%
+biology wherever um and uh if they if
+ 
+
+ align:start position:0%
+biology wherever um and uh if they if
+they see the pattern then they're really
+
+ align:start position:0%
+they see the pattern then they're really
+ 
+
+ align:start position:0%
+they see the pattern then they're really
+seeing what what mathematics brings
+
+ align:start position:0%
+seeing what what mathematics brings
+ 
+
+ align:start position:0%
+seeing what what mathematics brings
+Beyond just formulas which is not what
+
+ align:start position:0%
+Beyond just formulas which is not what
+ 
+
+ align:start position:0%
+Beyond just formulas which is not what
+the subject's about and and uh and but
+
+ align:start position:0%
+the subject's about and and uh and but
+ 
+
+ align:start position:0%
+the subject's about and and uh and but
+getting getting answers and
+
+ align:start position:0%
+getting getting answers and
+ 
+
+ align:start position:0%
+getting getting answers and
+understanding so one part of the course
+
+ align:start position:0%
+understanding so one part of the course
+ 
+
+ align:start position:0%
+understanding so one part of the course
+is the modeling getting the equations
+
+ align:start position:0%
+is the modeling getting the equations
+ 
+
+ align:start position:0%
+is the modeling getting the equations
+what what's the structure and the second
+
+ align:start position:0%
+what what's the structure and the second
+ 
+
+ align:start position:0%
+what what's the structure and the second
+part of the course is how do you solve
+
+ align:start position:0%
+part of the course is how do you solve
+ 
+
+ align:start position:0%
+part of the course is how do you solve
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+equations uh sometimes Analytics Ally
+
+ align:start position:0%
+equations uh sometimes Analytics Ally
+ 
+
+ align:start position:0%
+equations uh sometimes Analytics Ally
+sometimes
+
+ align:start position:0%
+sometimes
+ 
+
+ align:start position:0%
+sometimes
+numerically and that's of course the
+
+ align:start position:0%
+numerically and that's of course the
+ 
+
+ align:start position:0%
+numerically and that's of course the
+reality of being a scientist or engineer
+
+ align:start position:0%
+reality of being a scientist or engineer
+ 
+
+ align:start position:0%
+reality of being a scientist or engineer
+now uh so I this course is three times a
+
+ align:start position:0%
+now uh so I this course is three times a
+ 
+
+ align:start position:0%
+now uh so I this course is three times a
+week very typical uh hours lecture and
+
+ align:start position:0%
+week very typical uh hours lecture and
+ 
+
+ align:start position:0%
+week very typical uh hours lecture and
+um fair amount of homework including
+
+ align:start position:0%
+um fair amount of homework including
+ 
+
+ align:start position:0%
+um fair amount of homework including
+some mat lab homework because that's the
+
+ align:start position:0%
+some mat lab homework because that's the
+ 
+
+ align:start position:0%
+some mat lab homework because that's the
+reality of
+
+ align:start position:0%
+reality of
+ 
+
+ align:start position:0%
+reality of
+how people get answers and also of
+
+ align:start position:0%
+how people get answers and also of
+ 
+
+ align:start position:0%
+how people get answers and also of
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+analytical pencil and paper homework to
+
+ align:start position:0%
+analytical pencil and paper homework to
+ 
+
+ align:start position:0%
+analytical pencil and paper homework to
+see the central ideas in use um and
+
+ align:start position:0%
+see the central ideas in use um and
+ 
+
+ align:start position:0%
+see the central ideas in use um and
+office hours from Tas because a lot of
+
+ align:start position:0%
+office hours from Tas because a lot of
+ 
+
+ align:start position:0%
+office hours from Tas because a lot of
+people haven't had linear algebra they
+
+ align:start position:0%
+people haven't had linear algebra they
+ 
+
+ align:start position:0%
+people haven't had linear algebra they
+haven't had
+
+ align:start position:0%
+haven't had
+ 
+
+ align:start position:0%
+haven't had
+1806 when they take this course and uh
+
+ align:start position:0%
+1806 when they take this course and uh
+ 
+
+ align:start position:0%
+1806 when they take this course and uh
+so they ask do I have to know linear
+
+ align:start position:0%
+so they ask do I have to know linear
+ 
+
+ align:start position:0%
+so they ask do I have to know linear
+algebra and I say well maybe not but you
+
+ align:start position:0%
+algebra and I say well maybe not but you
+ 
+
+ align:start position:0%
+algebra and I say well maybe not but you
+soon will well you know I think it's so
+
+ align:start position:0%
+soon will well you know I think it's so
+ 
+
+ align:start position:0%
+soon will well you know I think it's so
+fantastic to be able to have open
+
+ align:start position:0%
+fantastic to be able to have open
+ 
+
+ align:start position:0%
+fantastic to be able to have open
+courseware and and try to do something
+
+ align:start position:0%
+courseware and and try to do something
+ 
+
+ align:start position:0%
+courseware and and try to do something
+Beyond MIT and so what am I trying to do
+
+ align:start position:0%
+Beyond MIT and so what am I trying to do
+ 
+
+ align:start position:0%
+Beyond MIT and so what am I trying to do
+I guess I think that the teaching of
+
+ align:start position:0%
+I guess I think that the teaching of
+ 
+
+ align:start position:0%
+I guess I think that the teaching of
+Applied
+
+ align:start position:0%
+Applied
+ 
+
+ align:start position:0%
+Applied
+math uh has a has a big step forward
+
+ align:start position:0%
+math uh has a has a big step forward
+ 
+
+ align:start position:0%
+math uh has a has a big step forward
+still to take that that we in many
+
+ align:start position:0%
+still to take that that we in many
+ 
+
+ align:start position:0%
+still to take that that we in many
+situations we're doing what we did uh a
+
+ align:start position:0%
+situations we're doing what we did uh a
+ 
+
+ align:start position:0%
+situations we're doing what we did uh a
+while ago and uh not
+
+ align:start position:0%
+while ago and uh not
+ 
+
+ align:start position:0%
+while ago and uh not
+really uh bringing it home making the
+
+ align:start position:0%
+really uh bringing it home making the
+ 
+
+ align:start position:0%
+really uh bringing it home making the
+subject what it can be um and and part
+
+ align:start position:0%
+subject what it can be um and and part
+ 
+
+ align:start position:0%
+subject what it can be um and and part
+of that has got to be uh
+
+ align:start position:0%
+of that has got to be uh
+ 
+
+ align:start position:0%
+of that has got to be uh
+numerically numerical solution of of of
+
+ align:start position:0%
+numerically numerical solution of of of
+ 
+
+ align:start position:0%
+numerically numerical solution of of of
+the equations and also new applications
+
+ align:start position:0%
+the equations and also new applications
+ 
+
+ align:start position:0%
+the equations and also new applications
+well 18085 or really
+
+ align:start position:0%
+well 18085 or really
+ 
+
+ align:start position:0%
+well 18085 or really
+18075 has been an MIT course for a long
+
+ align:start position:0%
+18075 has been an MIT course for a long
+ 
+
+ align:start position:0%
+18075 has been an MIT course for a long
+time and uh Professor hilderbrand's
+
+ align:start position:0%
+time and uh Professor hilderbrand's
+ 
+
+ align:start position:0%
+time and uh Professor hilderbrand's
+textbooks were the were used he was a
+
+ align:start position:0%
+textbooks were the were used he was a
+ 
+
+ align:start position:0%
+textbooks were the were used he was a
+good exceptionally good
+
+ align:start position:0%
+good exceptionally good
+ 
+
+ align:start position:0%
+good exceptionally good
+teacher but there wasn't Computing
+
+ align:start position:0%
+teacher but there wasn't Computing
+ 
+
+ align:start position:0%
+teacher but there wasn't Computing
+wasn't part of it really and it has
+
+ align:start position:0%
+wasn't part of it really and it has
+ 
+
+ align:start position:0%
+wasn't part of it really and it has
+become part of what all
+
+ align:start position:0%
+become part of what all
+ 
+
+ align:start position:0%
+become part of what all
+users uh do to get answers so the course
+
+ align:start position:0%
+users uh do to get answers so the course
+ 
+
+ align:start position:0%
+users uh do to get answers so the course
+had to move forward and the first step
+
+ align:start position:0%
+had to move forward and the first step
+ 
+
+ align:start position:0%
+had to move forward and the first step
+was about 20 years ago with a new
+
+ align:start position:0%
+was about 20 years ago with a new
+ 
+
+ align:start position:0%
+was about 20 years ago with a new
+textbook different approach and and
+
+ align:start position:0%
+textbook different approach and and
+ 
+
+ align:start position:0%
+textbook different approach and and
+uh I have had a wonderful time teaching
+
+ align:start position:0%
+uh I have had a wonderful time teaching
+ 
+
+ align:start position:0%
+uh I have had a wonderful time teaching
+classes over those years and now it's
+
+ align:start position:0%
+classes over those years and now it's
+ 
+
+ align:start position:0%
+classes over those years and now it's
+ready for the next generation
\ No newline at end of file
diff --git a/SvjeCxVu2dI.txt b/SvjeCxVu2dI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4cf51475ec66d730fd7cba26a3ad882f69d72446
--- /dev/null
+++ b/SvjeCxVu2dI.txt
@@ -0,0 +1,234 @@
+PROFESSOR: Hello, and welcome
+to another help session on
+
+recombinant DNA.
+
+Today we're going to
+discuss genomic
+
+libraries and cDNA libraries.
+
+So what is a genomic library?
+
+Well, with most organisms
+the genome is really too
+
+large to deal with.
+
+It's too large to work
+with or to examine.
+
+So oftentimes it's more useful
+to cut it down into smaller
+
+pieces that you can
+then examine.
+
+How do we make a genomic
+library?
+
+Well, we start off with
+our cell of interest.
+
+And the first thing that we're
+going to do is we're going to
+
+isolate all the DNA
+from the cell.
+
+Once we have the DNA, we're
+going to use restriction
+
+enzymes to cut it into
+smaller sections.
+
+Now, we have to be very careful
+when we choose which
+
+restriction enzyme
+we want to use.
+
+We want to use an enzyme that
+has enough restriction sites
+
+in the genome so that we'll get
+small enough pieces to put
+
+in the vector, but not
+so small that all the
+
+genes get cut up.
+
+Usually what we we'll use for
+the vector is a plasmid.
+
+A plasmid is a very standard
+and easy way to get foreign
+
+DNA into a bacteria.
+
+So we're going to cut up our DNA
+and the plasmid with our
+
+restriction enzyme.
+
+Sometimes we might want to
+even make two different
+
+libraries using two different
+restriction enzymes so that
+
+we'll have the cuts in
+different places.
+
+Once we have our cut up DNA and
+our plasmids, now we need
+
+to ligate them together
+using DNA ligase.
+
+Once the cDNA is pasted into the
+plasmid, now we're ready
+
+to actually transform
+them into bacteria.
+
+It's very easy to transform
+plasmids into bacteria.
+
+There are multiple different
+ways to do it.
+
+One common one is to use heat
+shock, whereby you heat the
+
+bacteria up and then cool it
+down rapidly, which causes
+
+little holes to open
+up that allows the
+
+plasmids to be taken up.
+
+What we end up with are
+thousands of different
+
+bacteria cells, all with
+different sections of the DNA.
+
+So combined, all these different
+sections form the
+
+genome, the original genome that
+we have, but they're in
+
+much smaller sections.
+
+They're much easier
+to work with.
+
+And this combination of all
+these different cells forms
+
+our genomic library.
+
+So that's one type of library.
+
+Another type of library
+is a cDNA library.
+
+So the way that the cDNA library
+is different from a
+
+genomic library is that while
+the genomic library
+
+encompasses the entire genome of
+the cell, the cDNA library
+
+just looks at what genes are
+being expressed in the cell.
+
+So let's go over how we would
+make a cDNA library.
+
+What we're going to start off
+with is we're going to start
+
+off by isolating the mRNA.
+
+So the mRNA, clearly, is
+the RNA that's being
+
+expressed in the cell.
+
+This is what's ultimately-- the
+proteins are going to be
+
+produced by the cell.
+
+We're then going to use reverse
+transcription to
+
+create the DNA version
+of the RNA.
+
+This is what we're referring
+to, again, as the cDNA.
+
+Once we have the cDNA, we then
+need to add restriction sites
+
+to the ends of them.
+
+Remember, before we were just
+able to use innate restriction
+
+sites in the genomes.
+
+But for the cDNA library,
+we really want to
+
+keep the cDNA intact.
+
+We don't want to cut it up.
+
+So we just want to add
+restriction sites to the ends
+
+of the cDNA.
+
+Then we can treat the cDNA
+and the plasmids
+
+with restriction enzymes.
+
+Once again, once they've been
+cut up we can use DNA ligase
+
+to combine the cut up plasmids
+and the cut up cDNA to the
+
+complete plasmid plus cDNA.
+
+And finally, once again, we can
+transform our bacteria,
+
+and then the combination of
+all these cells, all with
+
+different types of cDNA,
+form our cDNA library.
+
+And cDNA libraries are very
+useful if you want to compare
+
+the difference in protein
+expressions between two
+
+different cells.
+
+Thank you very much.
+
+This has been another help
+session for recombinant DNA.
\ No newline at end of file
diff --git a/T1KLrKvCGbA.txt b/T1KLrKvCGbA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..87a13e329851e7166c1593143d3a8542cc63ffb8
--- /dev/null
+++ b/T1KLrKvCGbA.txt
@@ -0,0 +1,3185 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Back to
+master equations
+
+an optical Bloch equations.
+
+I hope you remember
+that on Monday we
+
+derived, under very
+general conditions,
+
+how dissipation, relaxation
+comes about in a quantum
+
+system, namely because we
+have a quantum system which
+
+interacts with a reservoir.
+
+The total system evolves, as
+quantum mechanics tells us,
+
+with a unitary time evolution.
+
+When we derive life what
+happens with the small system,
+
+due to the coupling
+with a bigger system,
+
+there are now suddenly-- the
+time evolution of the density
+
+matrix has relaxation
+terms, and we derived that.
+
+And the special equation
+we are interested
+
+in for two level
+system interacting
+
+with the vacuum--
+interacting with a vacuum
+
+for spontaneous emission
+are optical Bloch equations.
+
+Today I want to discuss with you
+some characteristic solutions
+
+of the optical Bloch equations.
+
+But before I do that, let
+me first discuss with you
+
+the assumptions we made to
+derive a master equation.
+
+And I hope you remember the Born
+approximation and the Markov
+
+approximation.
+
+The Born approximation says
+that the reservoir will never
+
+change.
+
+The reservoir is always, for
+instance, in the vacuum state.
+
+And the Markov
+approximation said
+
+that the correlations
+in the reservoir
+
+are delta function related.
+
+It can absorb photons
+instantaneously.
+
+The vacuum has no memory time.
+
+It's like a black hole.
+
+It sucks up everything.
+
+But it's always what it was
+initially, namely the vacuum.
+
+Do you know examples where those
+assumptions are not fulfilled?
+
+I make it so natural.
+
+These are the most
+natural assumptions,
+
+but what are systems which
+cannot be described with this
+
+approach.
+
+AUDIENCE: I was thinking maybe
+like an atom in a cavity.
+
+If you change the
+vacuum somehow.
+
+PROFESSOR: An atom in a cavity.
+
+Very good.
+
+If an atom emits--
+now it depends.
+
+We talk today about the master
+equation for photons and atoms
+
+in the cavity,
+but we will assume
+
+that the cavity
+is rapidly damped.
+
+If it's a high Q cavity,
+the atom emits a photon,
+
+but the cavity has memory.
+
+It stores the photon, and after
+one period of the vacuum Rabi
+
+oscillation, the photon
+goes back to the atom.
+
+So the vacuum has memory time.
+
+The vacuum has now
+a time constant,
+
+which is the same as the
+time constant for the atom,
+
+namely the period of
+the Rabi oscillation.
+
+Big violation of the
+Markov approximation.
+
+We do not have the very short
+correlation time of the system.
+
+We just integrate over in
+the much longer time scale,
+
+during which we are interested
+in the dynamics of the system.
+
+Maybe another example.
+
+Actually, this example violates
+both the Markov approximation,
+
+also the Born approximation,
+because the vacuum
+
+has changed when
+it has a photon.
+
+Do you know an example
+where maybe only
+
+the Born approximation
+is violated,
+
+namely the reservoir is
+changing due to interaction
+
+with the system?
+
+Well?
+
+Before we talked about the
+system in a big reservoir.
+
+What happens when you make
+the reservoir smaller?
+
+Well then when it
+absorbs energy.
+
+It will heat up and such.
+
+It will change.
+
+The Born approximation
+is actually,
+
+when it would come to energy
+transfer, the assumption
+
+that the reservoir has an
+infinite heat capacity.
+
+It can just take
+whatever the system wants
+
+to deliver without changing,
+for instance, it's temperature.
+
+OK, so at least
+you know now there
+
+are systems for which
+the treatment has
+
+to be generalized, and you
+understand maybe better
+
+the nature of
+approximations we have made.
+
+[INAUDIBLE]
+
+AUDIENCE: Just a question.
+
+For the last case which is where
+the Born approximation is not
+
+violated, is there
+any example of that?
+
+PROFESSOR: Well for instance,
+spontaneous emission
+
+into the vacuum, but
+the speed of light
+
+is so slow that it takes forever
+for the photon to escape.
+
+The Markov approximation
+is more about the time
+
+scale for the
+reservoir to react.
+
+And the Born approximation
+is if the reservoir is really
+
+big enough to simply absorb
+everything without changing.
+
+I don't know.
+
+You could maybe think about
+you have some reservoir,
+
+but it has very bad heat
+conduction or something.
+
+The transport is just very
+slow, and therefore you
+
+do not have the hierarchy
+of the two time scales.
+
+OK, any other questions
+about the master equation?
+
+Optical Bloch equations?
+
+Well, then we can
+learn more about
+
+the characteristic features
+of the optical Bloch equations
+
+by looking at solutions.
+
+And I would like to discuss
+three aspects of solution.
+
+I want to discuss the spectrum
+and the intensity of light
+
+emitted by the atoms.
+
+Secondly, we want to talk about
+transient and steady state
+
+solutions.
+
+And finally, actually I put it
+in the chapter of optical Bloch
+
+equations, but I
+will use a cavity
+
+for that example,
+which will actually
+
+go beyond optical
+Bloch equations.
+
+It's also nice for
+you to see that there
+
+is more than the
+optical Bloch equation,
+
+but it's the same formalism.
+
+And this is when we discuss the
+damping of the damped vacuum
+
+Rabi oscillations.
+
+I also picked this
+one example sort
+
+of as an appetizer,
+because I can introduce
+
+two concepts for you
+in this last example.
+
+One is the quantum Zeno effect.
+
+And the other one is the
+adiabatic elimination
+
+of coherences, which
+plays a major role
+
+in many, many
+theoretical treatments.
+
+But let's start with the first
+part, namely the spectrum
+
+and intensity of emitted light.
+
+And I want to start off this
+discussion with a clicker
+
+question.
+
+Do everybody take a
+clicker out of the box?
+
+So the situation is that
+we have an atom which
+
+is excited by laser light
+of frequency omega L.
+
+The atom has frequency omega 0.
+
+I'm discussing the limit
+of very low intensity.
+
+And the question
+for you is what is
+
+the spectrum of the
+emitted radiation?
+
+So in other words,
+we have our atom.
+
+We have the laser
+beam which comes here.
+
+And now the atom emits
+in all directions.
+
+And you collect and
+frequency analyze the light.
+
+And I want to give you
+four possibilities how
+
+the spectrum of the emitted
+light may look like.
+
+Let's assume that on
+the frequency axis
+
+this is the laser frequency.
+
+And this is the
+frequency of the atom.
+
+And the first possibility
+is that we observed
+
+a spectrum which is centered
+at the atomic frequency where
+
+the line meets gamma.
+
+The second option is that
+we observe a delta function,
+
+a very sharp peak at
+the frequency omega 0.
+
+The third possibility is
+the we observe a sharp peak
+
+at the laser frequency.
+
+And the fourth option is that
+we observe radiation centered
+
+at the laser frequency,
+but with gamma.
+
+So I would ask
+you for your vote.
+
+A, B, C, or D.
+
+Was there any questions
+about the choices?
+
+40 for in spectra.
+
+The low intensity limit
+of light scattered
+
+emitted by an atom which is
+excited with a laser beam.
+
+We can assume close
+to resonance, but not
+
+on resonance, so we can
+distinguish between the laser
+
+frequency and the
+atomic frequency.
+
+Anybody had a chance?
+
+OK.
+
+OK, good.
+
+A, B, C, D.
+
+Yes, let's discuss it.
+
+I want to draw your attention
+to one thing I said,
+
+namely low intensity.
+
+At low intensity, you can assume
+that there's only one photon
+
+scattered at a time, because
+the intensity-- we work
+
+in the limit of
+infinitesimal intensity.
+
+So I want to as you
+now, why don't you
+
+consider energy conservation and
+think about the problem again?
+
+OK, maybe I'm indicating I'm
+not happy with the answer.
+
+Maybe an obvious question
+which sometimes people
+
+get confused about, what
+about Doppler shifts?
+
+We assume the atom is infinitely
+heavy and cannot move.
+
+Or we trap it in an ion trap.
+
+It's in the ground
+state of the ion trap,
+
+and no kinetic
+energy is exchanged.
+
+So don't get confused,
+and I think none of you
+
+got confused about Doppler
+shifts in kinetic energy here.
+
+We eliminate that.
+
+OK.
+
+Well it's moving in
+the right direction.
+
+Now the two most frequent
+answers are those two.
+
+OK, I've asked you to take
+energy conservation really
+
+seriously.
+
+If you start with an
+atom in the ground state,
+
+and the monochromatic photon at
+the laser frequency, and you've
+
+done a wonderful job,
+which many labs can do.
+
+You've stabilized your laser
+with a precision of 1 hertz.
+
+And 1 Hertz, this is sort of
+what I do as a delta function.
+
+So if you take energy
+conservation absolutely
+
+seriously, the
+photon, which can--
+
+the atom is in the ground state
+after it has scattered light,
+
+so the energy of the
+atom has not changed.
+
+And you can only fulfill
+energy conservation
+
+if there is no change in
+the spectrum of the light.
+
+And that means delta function
+in, delta function out.
+
+Now I know I say it as if
+it would be the simplest
+
+thing in the world, but
+maybe you have questions.
+
+Does anybody want to
+maybe argue or defend
+
+why the light
+should be broadened?
+
+And actually discuss
+very soon other examples.
+
+We go to higher intensity,
+and at higher intensity
+
+other things end and
+other things are possible.
+
+But at the low
+intensity limit, do
+
+you have any
+suggestion what could
+
+cause the broadening of light?
+
+AUDIENCE: I guess this is more
+if [INAUDIBLE] but then look
+
+at it as pinned down,
+but you're going
+
+to see a Doppler shift from the
+recoil as the light comes out.
+
+So it accepts the light,
+and then it moves something,
+
+so then it has some velocity.
+
+And then when it
+emits, it's going
+
+to be emitting in
+a random direction.
+
+And so its final
+velocity is going
+
+to be in some basically
+arbitrary direction,
+
+because the two
+[INAUDIBLE] boosts
+
+that you get from
+accepting and emitting.
+
+PROFESSOR: OK now first of
+all, I wanted for this problem
+
+to assume that the mass
+of the atom is infinite.
+
+And at that point,
+the recoil energy
+
+has 1 over the mass term.
+
+The recoil energy is 0
+and we can neglect it.
+
+So the limit I'm
+talking about is sound.
+
+But you're right.
+
+If you want to bring in the
+recoil energy, what would then
+
+happen is if an atom
+absorbs a photon
+
+and emits it pretty much
+in the same direction,
+
+there is no momentum exchange.
+
+Then it will be close
+to the laser frequency.
+
+But then you will find,
+depending on the angle now,
+
+there is a shift between
+0 and 2 recoil energies.
+
+If you would, however, measure
+the light at a specific angle,
+
+you would still find
+a delta function,
+
+but you would find it shifted.
+
+But this is really
+a complication
+
+which involves now the
+mechanical effect of light
+
+and the recoil of a photon.
+
+It doesn't change the result.
+
+Energy conservation requires
+the spectrum to be, so to speak,
+
+a delta function
+in total energy.
+
+And what we have
+just discussed is
+
+that, depending on the
+scattering angle, maybe
+
+there's a kinetic
+energy to consider.
+
+So what else can
+broaden the light?
+
+Yes?
+
+AUDIENCE: Finite pulse time?
+
+PROFESSOR: Yes.
+
+So things are very different
+if I use a pulse laser.
+
+But here I said the incident
+light is monochromatic,
+
+just one frequency.
+
+And therefore you don't
+have any time resolution
+
+in the experiment.
+
+The moment you have
+time resolution,
+
+you would introduce into
+the whole discussion
+
+Fourier [INAUDIBLE] and such.
+
+But frankly, I ask this question
+every time I teach the course.
+
+And every time the vast
+majority of the class
+
+gives the wrong answer.
+
+Let me ask you
+something else which
+
+is maybe a little bit simpler,
+and that's the following.
+
+You have a harmonic
+oscillator which
+
+has an eigen frequency omega 0.
+
+You drive the
+harmonic oscillator
+
+at frequency omega L.
+What is the oscillation
+
+of the oscillator?
+
+Is it omega 0, the harmonic
+oscillator frequency?
+
+Or omega L, the drive frequency?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Of course,
+the drive frequency.
+
+There may be a short
+transient, but if we do not
+
+switch on the drive suddenly,
+we avoid the transient.
+
+The steady state solution is
+the harmonic oscillator always
+
+oscillates at the
+drive frequency.
+
+Now, isn't the atom a
+harmonic oscillator?
+
+In 8421 we discuss the
+oscillator strings.
+
+We discuss that
+the polarizability
+
+of the atom, the dipole
+moment, the AC stock shift
+
+can really be regarded as an
+oscillating dipole moment.
+
+So the atom for that
+purpose is nothing else
+
+than a driven
+harmonic oscillator.
+
+And when you drive the
+atom at a laser frequency,
+
+the dipole moment oscillates
+at which frequency?
+
+The laser frequency.
+
+Not the resonant frequency.
+
+And therefore, the light
+which is scattered--
+
+think about it semi classically.
+
+This is like an antenna.
+
+It's an electron.
+
+It's a charge.
+
+It's a dipole moment
+which oscillates
+
+at the drive frequency.
+
+And the light, which is emitted
+by this accelerated charge
+
+is at the drive frequency.
+
+The atom is, for that
+purpose, nothing else
+
+than a driven
+harmonic oscillator.
+
+And I'm saying that
+probably several times
+
+in that course, when you
+have a semi classical picture
+
+and a fully quantum picture,
+and they do not fully agree.
+
+I've never gone wrong with
+the semi classical picture.
+
+But myself and
+many of my students
+
+have come to very wrong answers
+by somehow holding on just
+
+to the quantum
+picture, and now seeing
+
+what the semi
+classical limit is.
+
+You may think too
+much here in the atom
+
+not as a harmonic oscillator,
+but a two level system.
+
+The two level
+system gets excited,
+
+and then after it is excited, it
+emits at the natural frequency.
+
+But you've taken something
+to seriously here.
+
+It's a two level system, but you
+cannot read the system that you
+
+first populate a level,
+and then you emit,
+
+because the energy of the
+laser is not exactly the energy
+
+needed to populate the level.
+
+So therefore you shouldn't do
+first order perturbation theory
+
+where you populate a level
+and then you wait and wait
+
+for the emitted photon.
+
+This is light scattering.
+
+It's a second order problem.
+
+One photon in, one photon out.
+
+And you have to conserve energy.
+
+Sorry for hammering
+on it, but it's
+
+really an example
+where you can maybe
+
+realize certain
+misconceptions, and I really
+
+want to make sure that
+you fully understand
+
+what's going on
+in this situation.
+
+Questions?
+
+Well, then let's make
+it more interesting.
+
+Let's introduce
+higher intensity.
+
+So let me first maybe
+show you-- we've
+
+talked a lot about
+diagrams-- what
+
+the diagram for this process is.
+
+So we have the laser
+frequency, and then we
+
+have the photon emitted.
+
+And of course, the length of
+this vector, this frequency
+
+is the same as the
+laser frequency.
+
+So let's move on now and
+talk about higher intensity.
+
+The high intensity
+case we discuss
+
+in great detail in 8421,
+but you pretty much I think
+
+know also from basic
+quantum physics
+
+what happens if you
+take a two level system
+
+and drive it strongly.
+
+If you drive it
+strongly, stronger
+
+than spontaneous
+emission, that means
+
+there is a limit
+where you can just
+
+forget about spontaneous
+emission in leading order,
+
+and the system is nothing else
+than a two level system coupled
+
+by a strong monochromatic drive.
+
+So I assume you've all
+heard about this solution?
+
+Get the Rabi oscillation between
+ground and excited state.
+
+So the high intensity
+limit are Rabi oscillations
+
+at the Rabi frequency.
+
+So what happens now to the
+spectrum of the emitted light
+
+if you are in the
+limit that you have
+
+Rabi oscillation of
+the atomic system?
+
+And I want you to think
+classically or semi
+
+classically.
+
+AUDIENCE: Three peaks.
+
+PROFESSOR: Three peaks
+you generate side bends.
+
+Classically, you have an
+emitter, an oscillating charge.
+
+But now you want to throw
+in that the atom goes
+
+from the ground to
+the excited state,
+
+from the excited to
+the ground state.
+
+So, so to speak, when
+it's in the ground state,
+
+it cannot emit.
+
+When it's in the excited
+state, it can emit and such.
+
+So you should think about
+an oscillating dipole
+
+which is now
+intensity modulated.
+
+And you know when you take
+a classic light source which
+
+is monochromatic, but put on top
+of it an intensity modulation
+
+at frequency omega Rabi,
+the solution of that
+
+are three peaks.
+
+The carrier, which is the
+laser frequency, plus two side
+
+bends at omega Rabi.
+
+So therefore, what we now
+expect for the spectrum is we
+
+have the laser
+frequency, and this
+
+is sort of our result
+for low intensity.
+
+However, when we-- in the
+limit of strong drive,
+
+and you will see in
+a moment where strong
+
+drive clearly comes in.
+
+So if you have this modulation
+at the Rabi frequency,
+
+you obtain side bends
+at the Rabi frequency.
+
+And the fact that there is
+a structure with three peaks
+
+is actually the
+famous Mollow triplet.
+
+I know when I was
+a graduate student
+
+there was big excitement
+because people measured
+
+for the first time
+the Mollow triplet.
+
+You need high resolution
+lasers and such,
+
+and people were just
+ready to measure that.
+
+Now it seems something which we
+just mention in basic courses
+
+because it's such
+a basic phenomenon.
+
+OK, but let's work a
+little bit more on that,
+
+namely the Rabi frequency is
+the Rabi frequency of the drive,
+
+or you can say the
+coupling matrix element.
+
+But when we have a
+detuning-- and this
+
+is what you want
+to discuss now--
+
+you have to add the
+detuning in quadrature.
+
+So this is a frequency at
+which the atomic population
+
+oscillates, and it is
+just semi classically
+
+the modulation of the
+atomic population which
+
+creates the side bends.
+
+Now if you take that to the
+limit of large detuning,
+
+or small drive, small Rabi
+frequency, this becomes delta.
+
+So that actually means if you
+go to our stick diagram here,
+
+the laser frequency is, of
+course, detuned by delta
+
+from the atomic frequency.
+
+But the Rabi frequency is delta,
+and this is the Rabi frequency.
+
+Maybe some people who pressed
+A and B feel now vindicated,
+
+because now you have a component
+of the emission spectrum, which
+
+is at the atomic
+resonance frequency.
+
+And you have a
+second peak, which
+
+is omega 0 minus 2
+delta or 2 omega Rabi.
+
+Question.
+
+How would you give
+a simple answer
+
+if I would ask you but what
+about energy conservation?
+
+I was hammering so much
+on energy conservation.
+
+How can we conserve energy
+by have a laser photon
+
+and emitting one at a
+different frequency?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: It's
+compensated with that.
+
+And now let me ask
+you another question.
+
+If you would scatter n photons
+and you do an experiment,
+
+you would expect that, due to
+Poisson fluctuation and such--
+
+we've talked about fluctuations
+of intensity and squeezed light
+
+and all that.
+
+But unless you do
+something special,
+
+you would expect if you excite
+an atom it emits n photons.
+
+You experiment.
+
+You measure plus
+minus square root
+
+and you measure
+Poisson in statistics.
+
+But now let's
+expect you observe n
+
+plus photons on the
+upper side bend.
+
+And you measure and you observe
+n minus photons on the lower
+
+side bend.
+
+Would you expect that
+n plus and n minus both
+
+have now Poisson
+fluctuations, or would you
+
+expect something else?
+
+In other words, let
+me be very specific,
+
+if you count n plus-- we can
+make it a clicker question.
+
+So you have a
+counting experiment,
+
+and you have n plus photons
+in the upper side bend and n
+
+minus in the lower side bend.
+
+And if you simply look
+at the variance, which
+
+is the square of the standard
+deviation from n plus,
+
+you find that it is
+Poisson distributed.
+
+So the question
+which I have now is
+
+what is the variance between
+n plus minus n minus.
+
+Is it simply the variance
+of n plus plus the variance
+
+of n minus?
+
+The second answer I
+want to give you is 0.
+
+And the third answer
+is something else.
+
+So this is A. This
+is B. And this is C.
+
+Yes.
+
+Energy conservation.
+
+So there shouldn't
+be any fluctuation.
+
+The emission of the upper side
+bend and the lower side bend
+
+have to be correlated.
+
+And you would immediately
+verify that if I
+
+show you what is the diagram.
+
+We have ground
+and excited state.
+
+We excite with a laser
+which has detuning.
+
+But then we emit a photon
+on the lower side bend.
+
+The second laser photon
+can now resonantly reach
+
+the excited state.
+
+And so you see we have absorbed
+two photons from the laser
+
+beam.
+
+And what we have
+emitted in this diagram
+
+is one lower and
+one upper side bend.
+
+This is what happens
+in second order-- well,
+
+second order in the laser
+beam, but fourth order
+
+in the diagram.
+
+We emit four photons.
+
+And each time the
+system does it,
+
+goes through that,
+it fulfills energy.
+
+Or if I call the upper side
+bend click and the lower side
+
+bend clack.
+
+The atom only makes click
+clack click clack clack click
+
+clack clack click clack.
+
+It never does click
+click clack clack.
+
+It cannot do two clicks because
+it has to fulfill this diagram,
+
+and they always come in pair.
+
+The two photons always
+come correlated.
+
+OK, so we understand
+now the spectrum.
+
+We understand when the
+resonant photons emerge.
+
+They emerge in
+the high intensity
+
+limit due to Rabi oscillations.
+
+The question is now what is
+the widths of those peaks?
+
+And I'm want to short you
+that too, because no you
+
+realize some things are easy,
+but other things are harder.
+
+In order to get that, you have
+to solve the optical Bloch
+
+equations, but I want to show
+you in the next half hour
+
+how we can at least get the
+salient features of this.
+
+Colin, you have a question?
+
+AUDIENCE: The picture you just
+offered about the [INAUDIBLE].
+
+That's assuming that
+we're not depleting
+
+the carrier [INAUDIBLE].
+
+Because if we're
+depleting the carrier,
+
+wouldn't we expect
+to see sort of
+
+like a high order, almost
+like a Bessel function.
+
+PROFESSOR: All right.
+
+OK, yes.
+
+AUDIENCE: First order on
+to the second [INAUDIBLE].
+
+PROFESSOR: Yes, thanks for
+bringing that to our attention.
+
+There is an assumption.
+
+When I said we
+have a laser beam,
+
+I assume we have
+a laser beam which
+
+delivers zillions of
+photons in such a way
+
+that depletion
+doesn't play a role.
+
+What that means technically
+we replace a laser beam by a c
+
+number, and a c
+number never changes,
+
+therefore cannot be depleted.
+
+But if you would use a
+very weak laser beam,
+
+we have to modify the answer.
+
+The extreme case would be if
+we use single photon sources,
+
+then of course we can
+never scatter two photons
+
+because there's only one
+photon in the source.
+
+But already if you would
+have hundreds or photons
+
+in your cavity and you
+put in a single atom,
+
+the scheduling of
+single photons would not
+
+cause major depletion effects.
+
+[INAUDIBLE]?
+
+AUDIENCE: In regards to the semi
+classical [? fabrication ?],
+
+we said we have
+a Rabi frequency,
+
+and when it's excited
+it's likely to emit,
+
+and when it's in the ground
+state it's not likely to emit.
+
+So whatever frequency you
+emit should be modulated
+
+by your Rabi frequency,
+but aren't you
+
+most likely to emit when
+you have a dipole moment?
+
+Which would be in the
+intermediate states between e
+
+and g, in which case those
+occur at twice the Rabi
+
+frequencies I think.
+
+PROFESSOR: OK, now
+you go to subtleties
+
+of a semi classical picture.
+
+Number one is-- I just want
+to say we're a little bit
+
+dangerous, on
+slippery slope here.
+
+One is I really discuss
+the spectrum here.
+
+When I discuss the
+spectrum, I don't
+
+know when the photon is emitted.
+
+So when I said we have
+a Rabi oscillation,
+
+I told you that the
+system is modulated,
+
+and this gives
+rise to side bends.
+
+But I can only spectrally
+solve the side bends
+
+if I fundamentally do not have
+the time resolution to measure
+
+when in the Rabi cycle
+is the photon emitted.
+
+The moment I would localize
+when the photon is emitted,
+
+whether the atom is in the
+ground or in the excited state,
+
+if I have a time resolution
+better than the Rabi
+
+oscillation, I do not have
+the spectral resolution
+
+to resolve the side bends.
+
+So therefore the question
+when the photon is emitted
+
+is not compatible with
+observing the spectrum.
+
+The second question, I
+think, can be addressed.
+
+And that's the following.
+
+I will show you in
+the next 45 minutes
+
+during this class
+that the steady states
+
+solution of the
+optical Bloch equations
+
+give us a rate of
+photon scattering
+
+which is simply gamma times
+the excited state fraction.
+
+So I think from that I would
+say the more you have atoms
+
+in the excited state, the
+larger is the scattering rate.
+
+So therefore, the
+semi classical picture
+
+that you have only a dipole
+moment when you are halfway
+
+between ground and excited
+state is overly simplistic here.
+
+Also, I just want to give
+you one word of warning.
+
+It's really an
+important comment.
+
+And this is the following.
+
+The oscillating dipole
+moment is a picture
+
+which uses sort of the
+analogy with the atom
+
+and the harmonic oscillator.
+
+And I mean yeah,
+I really sort of
+
+was a bit provocative
+a few minutes ago when
+
+I said just regard the atom
+as a harmonic oscillator.
+
+But you have to be careful.
+
+There is one fundamental
+limit between-- one
+
+fundamental difference between
+the harmonic oscillator
+
+and a two level atom.
+
+And the fact is the following.
+
+This is a two level atom, and
+this is a harmonic oscillator.
+
+So the difference
+is the following.
+
+An harmonic oscillator
+can be excited.
+
+You can pump more and
+more energy in it.
+
+You can go to larger
+amplitude coherent states,
+
+and there is no non linearity.
+
+The atom saturates.
+
+And this is the difference.
+
+Saturation.
+
+When saturation comes, when you
+put more than a few percent,
+
+let's say 50%, into
+the excited state,
+
+you have to be very,
+very, very careful
+
+with analogies with the
+harmonic oscillator.
+
+So if you have most of the
+population in the ground
+
+state, a little bit here,
+and almost nothing here,
+
+then we can describe the atom
+as an harmonic oscillator.
+
+And everything you glean
+from the model of an electron
+
+tethered with a spring is
+not only qualitatively,
+
+it's quantitatively
+correct if you
+
+throw in the oscillator
+strength of the atom.
+
+But the moment you pile
+up more population here,
+
+and you just ask
+about 50-50, at least
+
+I would say
+immediately be careful.
+
+Do not take the harmonic
+oscillator fully seriously
+
+at this point, because there's
+a fundamental difference.
+
+In the harmonic oscillator,
+when you're 50% here,
+
+you would have
+things over there.
+
+The harmonic oscillator
+stays linear.
+
+But the two level system
+starts to saturate.
+
+Good.
+
+So the question is now we
+understand the stick diagram
+
+of the Mollow
+triplet that we have
+
+always a line at the carrier.
+
+Let me just put marks here.
+
+We have the carrier and
+the resonance frequency,
+
+but the question is now what
+is the width of the spectrum.
+
+The general answer
+is rather difficult,
+
+but let me give it to you.
+
+And I will derive it from
+the optical Bloch equation.
+
+Let me discuss that one
+limit where the detuning is
+
+larger than anything else.
+
+And the other case
+is the resonant case.
+
+In general we
+started out by saying
+
+we have a delta function
+at low intensity.
+
+If you now go to higher
+and higher intensity,
+
+you still sort of have the delta
+function from the lowest order
+
+diagram, but the higher order
+diagram become more important.
+
+And the spectrum is in
+general a superposition
+
+of three broadened peaks
+and the delta function.
+
+At low intensity, you only
+have the delta function.
+
+At high intensity, the
+weight of the elastic scatter
+
+the delta function goes to 0.
+
+And now let's
+discuss the widths.
+
+And that shows you that even
+light scattering by a two level
+
+system, those very, very
+simple Jaynes Cummings model
+
+has interesting and maybe
+non intuitive aspect.
+
+The side bends have
+a width of gamma.
+
+The carrier has a
+width of 2 gamma.
+
+But when you are on resonance,
+the situation changes.
+
+The carrier has now a width
+of gamma and side bends
+
+have a width of 3/2 gamma.
+
+But if you look at it, the
+sum of the three widths
+
+is always 4 gamma.
+
+And you will understand
+that in a few minutes.
+
+OK, so this was more
+qualitative discussion.
+
+Let's now work
+more quantitatively
+
+and describe the Mollow triplet.
+
+The Hamiltonian for our system
+is the atomic Hamiltonian
+
+times the the z Pauli matrix.
+
+The z Pauli matrix
+is excited excited
+
+minus ground ground state.
+
+And because of the
+conservation of probability,
+
+it's 2 times the excited.
+
+Also just mathematically
+it's just that.
+
+We have the three
+Hamiltonian of the radiation
+
+field, which is a dagger a.
+
+And then we have the coupling
+of a two level system, which
+
+is the product of the
+atomic dipole moment written
+
+as sigma plus plus sigma minus
+raising and lowering operator.
+
+Just to remind us,
+sigma plus is e g.
+
+And sigma minus is g e.
+
+And then we have to multiply
+with a plus a dagger.
+
+If you want, the atomic
+part is the dipole moment,
+
+and this is the electric field
+both written as operators.
+
+So this is the electric field.
+
+And if you look at
+the coupling term--
+
+we've discussed it before.
+
+You have four terms.
+
+But in the rotating
+wave approximation,
+
+which we want to use
+here, we keep only
+
+the two resonant
+terms, which is when
+
+we raise an excitation
+in the atom,
+
+we lose an excitation
+in the light field.
+
+Or if you go from the
+excited to the ground state,
+
+we emit a photon.
+
+So we have two terms which
+form the rotating wave
+
+approximation.
+
+The other two terms
+are highly of resonant
+
+and can often be neglected.
+
+So this rotating
+wave approximation
+
+becomes of course the
+better, the more we
+
+go in resonant, because in
+one term is fully resonant
+
+and the other one is
+very off resonant.
+
+And in this case, we can
+simplify the Hamiltonian
+
+because the number of
+excitations is conserved.
+
+The number of
+excitations is the number
+
+of excitations in
+the photon field
+
+plus the number
+of excited atoms.
+
+So this is the
+operator which measures
+
+the number of excitations.
+
+If in a [INAUDIBLE]
+counter rotating term,
+
+this operator is conserved.
+
+So if I introduce as
+usual the detuning--
+
+this is what my notes say.
+
+It seems to have
+the opposite sign.
+
+I'm not sure if I made a
+sign error here or later,
+
+or if I changed the definition.
+
+Let's just move on and
+see how it works out.
+
+So if you now do the
+rotating wave approximation,
+
+our Hamiltonian has now-- by
+introducing the operator N,
+
+the number of [INAUDIBLE]
+times h bar omega.
+
+However, we have
+multiplied the N operator
+
+with the photon energy.
+
+If the energy is in
+the atom, we have
+
+made a mistake, which is
+delta, and we correct that
+
+by using the z Pauli matrix.
+
+And then our interaction
+term is a dagger times sigma
+
+minus plus a times sigma plus.
+
+Let's now discuss
+what are the eigen
+
+states of this Hamiltonian
+In the simple case
+
+when the detuning is 0.
+
+And we have sort of two
+levels of eigen state.
+
+One is the ground
+state with n photons.
+
+And one is the excited
+state with n photons.
+
+0, 1, 2.
+
+So we can label this
+by the photon number.
+
+And the excited state
+of course starts
+
+with a higher
+energy for 0 photon.
+
+This is the energy
+with one photon.
+
+And in the case of 0 detuning,
+the two letters are degenerate.
+
+And if we introduce the
+interaction, if g is now non 0,
+
+the levels split.
+
+And the splitting is given by g.
+
+There's a factor of two.
+
+But now if you have
+photons in the field,
+
+a dagger acting on the photon
+field gives n plus one.
+
+So therefore for one photon
+we have square root 2.
+
+In general, we get an expression
+which is square root n plus 1.
+
+Or to write it
+mathematically, if we
+
+have strong mixing
+between an excited
+
+state with n atoms--
+with n photons.
+
+And a ground state with n plus
+1 photons, for the case of delta
+
+equals 0, it's just plus minus.
+
+You metric as a metric
+contribution times 1
+
+over square root 2.
+
+And these are now with the
+states we label plus minus.
+
+The upper and lower
+state of each manifold.
+
+And n is the photon number
+in the excited state.
+
+n plus 1 is the photon
+number in the ground state.
+
+And the energy of those states
+is the number of [INAUDIBLE] n
+
+plus 1.
+
+But then we have the
+resonant splitting g.
+
+And because of the matrix
+element of a and a dagger,
+
+we get square root n plus 1.
+
+Now if you use
+very strong drive--
+
+and this addresses Colin's
+question about depletion--
+
+we use a laser beam, which is
+described by a Rabi frequency.
+
+This is proportional
+to the electric field.
+
+So be introduce
+the Rabi frequency,
+
+which is given by that.
+
+And the laser beam
+has so many photons
+
+that we don't care about n plus
+1 or scattering a few photons,
+
+so we simply replace n n plus 1
+n minus 1, whatever contains n,
+
+by the z number, which is the
+Rabi frequency of the laser
+
+beam.
+
+So this eventually means
+that we have too many folds.
+
+Plus, minus.
+
+Plus, minus.
+
+So we have two
+states plus minus,
+
+and they are periodic when we
+add one photon to the field.
+
+Periodic in n.
+
+The splitting is the Rabi
+frequency defined above.
+
+And now we realize that when
+we have spontaneous emission
+
+between the manifold for n
+minus 1 and the manifold n,
+
+we have two possibilities.
+
+To emit light on resonance.
+
+And we have then one possibility
+to emit an upper side bend.
+
+And one possibility to
+emit the lower side bend.
+
+So what is called
+the dressed atom
+
+picture is nothing else than
+the solution of an atom driven
+
+by a strong monochromatic field.
+
+The atom is dressed
+with photons,
+
+and the eigen states are
+no longer just atomic eigen
+
+states.
+
+These are dressed eigenstates
+of the combined atomic system
+
+plus laser field.
+
+So this dressed atom picture
+explains the Mollow triplet.
+
+And you can immediately
+generalize it
+
+if you want to
+arbitrarily tuning
+
+when the superposition
+states plus minus do not
+
+have equal weight.
+
+But it's what you've
+seen a million times,
+
+the diagonalization of
+a two by two matrix.
+
+Colin?
+
+AUDIENCE: How does this
+explain the [INAUDIBLE]?
+
+PROFESSOR: It does not.
+
+This is what I
+just wanted to say.
+
+It explains the Mollow triplet,
+but not the line widths.
+
+The line widths cannot be
+obtained perturbatively.
+
+So for that we have to discuss
+now the Bloch vector, which
+
+is a solution of the
+optical Bloch equation.
+
+So now I'm going to explain
+you not all glorious details,
+
+but the salient feature
+of the line bits.
+
+So the density matrix
+for two level atom
+
+can be written as-- let
+me back up a moment.
+
+The density matrix has
+four matrix elements.
+
+But if the sum of the
+diagonal matrix element
+
+is one conservation
+of probability,
+
+we have actually three
+independent matrix elements.
+
+And those three
+independent matrix elements
+
+can be parametrized by what
+is called the Bloch vector.
+
+A lot of you have seen it.
+
+We also discuss it in
+great detail in 8421.
+
+But I'm giving you
+the definition.
+
+And sigma is the vector
+of Pauli matrices.
+
+To be specific, the three
+components of the Bloch vector
+
+are as follows.
+
+The z comportment
+measures, you can say,
+
+the population inversion.
+
+The difference between ground
+and excited state population.
+
+And the x and y component
+measure the coherencies.
+
+Either the sum of
+the coherencies
+
+or the difference
+of the coherencies.
+
+And here is minus
+imaginary unit.
+
+If you replace the density
+matrix or the matrix elements
+
+sigma ee, or ee,
+or gg by definition
+
+the optical Bloch equation
+turns into differential
+
+equation for r.
+
+It's now a differential
+equation for r.
+
+And let me just write it down.
+
+Let me just write down
+the Hamiltonian part.
+
+This is the equation of
+motion for the density matrix.
+
+I will add on in a minute
+the relaxation part
+
+which comes from
+the master equation.
+
+This is just the
+Hamiltonian part.
+
+And this would result
+into an equation
+
+of motion for the
+Bloch vector, which
+
+has delta here minus
+delta here minus g.
+
+g and the rest of the
+matrix elements is 0.
+
+The Hamiltonian, using
+rotation matrices,
+
+can be written by
+a z rotation matrix
+
+plus g times the x rotation.
+
+And if you actually look at the
+solution-- it's not a finite.
+
+It's an infinitesimal rotation.
+
+This matrix tells you that the
+detuning does a z rotation,
+
+and the drive is responsible
+for an x rotation.
+
+Let me tell you what happens.
+
+You have seen the Bloch
+vector many cases.
+
+If you don't drive the
+system, the Bloch vector
+
+in the ground state is down.
+
+In the upper state it's up.
+
+If it's in between-- that's
+where Timo's dipole moment
+
+comes in-- we have
+a superposition
+
+of ground and excited state.
+
+And it rotates at the
+atomic frequency omega 0.
+
+But we are in the rotating
+frame of the laser at omega,
+
+so in the rotating frame, when
+the frame rotates with omega.
+
+And omega 0 rotation becomes
+the rotation with delta.
+
+So therefore, the free
+evolution of the atom
+
+is based on this Hamiltonian
+that the Bloch vector rotates
+
+with delta in the rotating
+frame of the laser.
+
+And it's a rotation
+around the z-axis.
+
+If you drive the system now,
+we take the Bloch vector
+
+from ground to excited,
+there are Rabi oscillations.
+
+And this is now a rotation
+around the x-axis.
+
+Well, whether it's x or y
+is a convention of notation,
+
+and I've defined it such
+that the driven system is
+
+an x rotation.
+
+The free evolution
+is a z rotation.
+
+And that's all you have to know.
+
+This is the most
+general solution
+
+of two level system
+without dissipation
+
+that we have two
+rotation angles.
+
+One is the free rotation,
+which is the detuning.
+
+It is the z-axis.
+
+And the driven system
+rotates around the x-axis.
+
+But now this is well known.
+
+This is boring.
+
+But now we want to add what
+the master equation gives us.
+
+And the master equation uses
+as its [? limb ?] platform
+
+where we have the sigma
+plus jump operator.
+
+And I told you that we have
+to use the following form.
+
+We'll hear more about
+it, probably not today,
+
+but on Friday.
+
+You know that this gives
+simply the optical--
+
+this gives us simply the
+optical Bloch equations.
+
+We discussed it on Monday that
+we have now a damping gamma
+
+term for the population.
+
+An excited state population
+decays with a rate of gamma.
+
+And the coherences, the off
+diagonal matrix elements,
+
+decay with a rate
+of gamma over 2,
+
+and we spent a long time
+discussing this vector of 2.
+
+So this would mean now that the
+equation for the Bloch vector
+
+has gamma 2 terms, which
+comes from the dampening
+
+of the coherences.
+
+And it has gamma, which is
+the damping of the population.
+
+Well if that would be all,
+everything is damped to 0,
+
+but everything is in the end
+leads to the ground state
+
+population.
+
+So we have to add this term.
+
+It's just a different way of
+the optical Bloch equations.
+
+We have discussed
+in great lengths
+
+this form of the
+optical Bloch equations.
+
+And the sigma plus sigma minus
+is because these are just
+
+simple matrices with
+one matrix element.
+
+You've seen the optical
+Bloch equation, I think.
+
+We did also that
+in 8421 21 that you
+
+have the derivative
+of the density matrix
+
+includes now damping of the
+off diagonal matrix elements
+
+by gamma over 2 damping by
+the diagonal matrix elements
+
+by gamma.
+
+If you simply substitute the r
+vector for the matrix element,
+
+you get this
+equation in one step.
+
+These are now the
+optical Bloch equations
+
+written as a differential
+equation for the Bloch vector.
+
+OK, sorry if that was confusing,
+but it's simple definition
+
+substitution no brainer.
+
+These are the optical
+Bloch equations
+
+written in terms
+of the Bloch vector
+
+and no longer in terms
+of the density matrix.
+
+And questions about that?
+
+OK, because now I want
+to draw conclusions.
+
+Our goal is to understand
+the spectrum and the line
+
+widths of the Mollow triplet
+of the emitted light.
+
+So I have to make
+the connection.
+
+How do I make the connection
+from the Bloch vector
+
+to emitted light?
+
+Well, it's done by
+the dipole moment,
+
+because it is the
+oscillating dipole which
+
+is responsible for emitting
+and scattering light.
+
+The dipole moment
+can of course be
+
+obtained from the solution
+of the optical Bloch
+
+equation for the density matrix.
+
+It is the trace of
+the density matrix
+
+times the operator
+we are interested in.
+
+And this involves the
+matrix element dge.
+
+The dipole moment has
+only matrix elements
+
+between excited
+and ground state.
+
+And ground and excited state.
+
+Trace rho other parentheses.
+
+So this is the matrix element.
+
+Let me now write down
+the density matrix
+
+in its matrix element
+rho ge plus rho eg.
+
+But now we want to
+go from the rotating
+
+frame back to the lab frame.
+
+And the rotating frame
+rotates at omega.
+
+So now I have to put back
+e to the i omega t and e
+
+to the minus i omega t.
+
+This is sort of going back from
+the rotating frame to the lab
+
+frame.
+
+And the picture
+of we want to use
+
+is-- the intuitive picture
+is to use the Bloch vector.
+
+So I'm expressing now
+those matrix elements
+
+by the component x and
+y of the Bloch vector.
+
+And since the x and y component
+was the sum or difference
+
+of diagram matrix element of
+the density the coherences.
+
+I get now cosine omega
+t and sine omega t.
+
+So that tells us that one
+component is in phase--
+
+well in phase means with respect
+to the driving field we assume
+
+that the system is
+driven by classical field
+
+e0 cosine omega t.
+
+And now we find that the
+oscillating dipole moment,
+
+it's a driven
+harmonic oscillator.
+
+And there is a part which is
+driven in phase with the drive
+
+field, and one which
+is in quadrature.
+
+So we have those two components.
+
+And the fact is
+now the following.
+
+If you have an
+oscillating dipole,
+
+this gives rise to immediate--
+or more accurately,
+
+I should say scattered light.
+
+Remember, if you assume there
+is photon first emitted and then
+
+a resonant photon absorbed,
+this picture is wrong.
+
+You should rather think
+of scattering light,
+
+but the light scattering is
+induced by the oscillating
+
+dipole.
+
+And what happens
+now is-- and this
+
+is why the Bloch vector
+and the Bloch sphere
+
+is such a wonderful picture.
+
+The dipole moment are
+the transverse component
+
+of the Bloch vector.
+
+So therefore, you can
+say that if you're
+
+interested in the spectrum of
+the emitted light, what you
+
+should find out is what
+is the spectrum of r.
+
+Let me back up one step.
+
+If you want to get the
+spectrum of the emitted light
+
+from first principles-- I'm
+cheating a little bit here.
+
+I'm saying let's get it
+from the dipole moment.
+
+You should actually get it
+from the correlation function
+
+of the dipole moment.
+
+It's sort of the two time
+correlation function.
+
+But you can show-- and this
+takes another 10, 20, 30
+
+pages in API.
+
+The temporal correlation
+function of the dipole moment
+
+fulfils the same differential
+equation as the Bloch vector.
+
+So I've given you here
+sort of the intuitive link
+
+that would oscillates is the
+Bloch vector it emits it.
+
+But technically,
+because you may not
+
+control the phase of each
+atom, you should rather
+
+say the spectrum
+is a correlation
+
+function of the
+dipole, and we should
+
+look at the spectrum of
+the correlation function.
+
+But instead, I'm looking
+now at the spectrum
+
+of the optical Bloch vector.
+
+And you can show mathematically
+exactly that they
+
+obey the same
+differential equation,
+
+but it's a little bit
+tedious to do that.
+
+OK, so therefore if you take
+this little inaccuracy--
+
+forgive me this inaccuracy.
+
+Once we know what
+the optical Bloch
+
+vector is doing spectrally,
+we know the spectrum
+
+of the emitted light.
+
+And for that, for the
+optical Bloch vector,
+
+we simply look at
+this matrix, and we
+
+ask what are the
+eigenvalues of this matrix?
+
+This matrix has three by three
+matrices, three eigenvalues.
+
+The real part of
+those eigenvalues
+
+gives us the position
+of the Mollow triplet.
+
+And the imaginary part gives
+us the widths of those peaks.
+
+So if you look at
+this matrix-- and I'm
+
+not doing the
+complicated cases here.
+
+If you look at this matrix for
+delta equals 0 and g equals 0.
+
+Well it is already
+in diagonal form,
+
+so it has three
+imaginary eigenvalues
+
+minus gamma over 2 minus
+gamma 2 minus gamma.
+
+So this matrix has three
+complex eigenvalues.
+
+And I want to discuss two cases.
+
+For this case we have
+minus gamma over 2
+
+for the x and y component
+of the optical Bloch vector.
+
+And the z component
+is minus gamma.
+
+And this is the situation.
+
+Apart from a factor
+of two that we
+
+have gamma, 2 gamma, and gamma.
+
+The fact of 2 comes of course.
+
+Are you asking what is the
+spectrum of the electric field
+
+or what is the
+spectrum of the power?
+
+If you go from e
+to e squared, then
+
+if you have an exponential
+decay with gamma of e,
+
+e squared decays with two gamma.
+
+So that's where
+factors of 2 come from.
+
+AUDIENCE: Can you label the top
+of the diagram with [INAUDIBLE]
+
+just the delta equals 0.
+
+PROFESSOR: Yes.
+
+Give me a second.
+
+AUDIENCE: [INAUDIBLE]
+g equals 0, right?
+
+PROFESSOR: The
+fact is here we're
+
+looking at limiting cases.
+
+And the more important
+thing is that this
+
+is the case of weak drive.
+
+So what is more important is
+that the drive frequency is 0.
+
+I'm not giving you
+the full picture here.
+
+The full glorious
+derivation is in API.
+
+And just tried to
+sort of entertain
+
+you by giving you
+a few appetizers.
+
+If you want, read it up there.
+
+But what I want to show you
+is they're two simple cases,
+
+but it looks already
+intriguing because here this
+
+is wider than the side bends,
+and here it's the opposite.
+
+And I want to give
+you a taste of it.
+
+And I'm not doing it
+rigorously, and you're right,
+
+I have to think about it.
+
+But the important part is
+that the drive frequency is 0.
+
+We are not driving, we
+are not rotating in x.
+
+The system is mainly
+rotating around the z-axis.
+
+And at that moment, the matrix
+for the differential equation
+
+for the optical Bloch vector
+has three imaginary parts.
+
+It's gamma, 2 gamma,
+and gamma or half of it
+
+if you look at the amplitude.
+
+And now I want to just
+show you in a second how
+
+we can get the second part.
+
+But yeah, I'm guilty as charged.
+
+There are small
+gaps in my argument.
+
+But all I want to
+show you is how
+
+you find-- I want to
+just sort of convince you
+
+that the optical Bloch
+equations with this matrix
+
+have all the ingredients
+to explain it.
+
+OK, so what I've done
+here is I've shown you
+
+that we have those
+three ingredients.
+
+And actually the moment--
+I should have said it
+
+before answering your question.
+
+When we now crank up delta,
+what we're physically doing
+
+is we're doing a rapid
+rotation of the Bloch vector
+
+around the z-axis.
+
+So when we rapidly
+around the z-axis,
+
+we're not doing anything
+to the z component,
+
+but we're strongly mixing
+the x and y component,
+
+but since [? half ?]
+the imaginary part--
+
+I'm waving my hands now.
+
+We're not changing the
+imaginary part for x and y.
+
+And we still have two imaginary
+parts, which are gamma over 2.
+
+One imaginary part
+which is gamma.
+
+I know I'm running out
+of time, but I only
+
+need a few more minutes.
+
+So if you do a rapid
+rotation around the z-axis,
+
+we obtain three eigenvalues.
+
+Since we rotate around the
+z-axis, we have minus gamma.
+
+Sorry, my notes are better
+than what I remember.
+
+I looked through the notes.
+
+But what I wanted to
+say was the following.
+
+I first show you what
+are the eigenvalues
+
+of this matrix in one case,
+which is just a warm up.
+
+I'm telling you there
+are those three values.
+
+And now I'm saying
+we are interested
+
+in the physical situation
+of rapid rotation.
+
+The rapid rotation modifies
+the three eigenvalues.
+
+The three eigenvalues
+are no longer real.
+
+The rapid rotation
+around the z-axis
+
+adds an imaginary i delta
+to the x and y-axis.
+
+Because now we are rotating,
+x and y are getting mixed.
+
+And this means now that
+we have three peaks.
+
+They are located in the
+rotating frame at 0.
+
+This is the carrier
+at plus minus delta.
+
+These are the two side bends.
+
+And this part are
+the widths of it.
+
+This is how you have to
+interpret the result.
+
+So we have to know three peaks.
+
+And the full widths
+of half maximum
+
+for the intensity, which
+is the amplitude squared
+
+is gamma, 2 gamma, and gamma.
+
+And we can now immediately
+proceed to the next case.
+
+If we are on resonance, and
+we drive The system strongly,
+
+now we are driving the
+system strongly around,
+
+not the z-axis,
+around the x-axis.
+
+So now if we add the strong
+drive around the x-axis,
+
+we have now eigenvalues
+which is plus minus ig.
+
+This is the rotation
+we add, and this
+
+gives e to the
+i-- in rotation ge
+
+to the i omega t gives an ig.
+
+And what happens
+is the following.
+
+The rapid rotation
+around the x-axis-- well,
+
+if you rotate around the
+x-axis, you're not touching x.
+
+And without any rotation,
+we had an eigenvalue
+
+for x which was
+minus gamma over 2.
+
+And if you take the matrix
+of whatever the system
+
+and rotate it around the
+x-axis, this is preserved.
+
+AUDIENCE: Excuse me.
+
+PROFESSOR: Yep, I
+need one more minute.
+
+Sorry.
+
+But the rotation around
+x strongly mixes y and z.
+
+So therefore the two
+other eigenvalues
+
+appear at rotation ig.
+
+And it is now the average
+of gamma and gamma over 2,
+
+which is 3/4 gamma.
+
+And if you go to the
+amplitude squared, it is 3/2.
+
+So therefore we
+have the situation
+
+that we have those
+three eigenvalues.
+
+And this is responsible
+for the three peaks
+
+at plus minus g and 0.
+
+And the widths of it
+is I have to multiply
+
+by a factor of 2
+gamma and 3/2 gamma.
+
+And this explains the
+two limiting cases
+
+I presented to you earlier.
+
+No time for question, the
+other people are waiting.
+
+Reminder we have
+class on Friday.
\ No newline at end of file
diff --git a/TCkLSYxx21c.txt b/TCkLSYxx21c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e7f5433c892b5a231201fb013f019fd1c57a45cf
--- /dev/null
+++ b/TCkLSYxx21c.txt
@@ -0,0 +1,1835 @@
+align:start position:0%
+ 
+okay now finally a nonlinear
+
+ align:start position:0%
+okay now finally a nonlinear
+ 
+
+ align:start position:0%
+okay now finally a nonlinear
+equation growth but it's the growth is
+
+ align:start position:0%
+equation growth but it's the growth is
+ 
+
+ align:start position:0%
+equation growth but it's the growth is
+cut off by competition slowed down by
+
+ align:start position:0%
+cut off by competition slowed down by
+ 
+
+ align:start position:0%
+cut off by competition slowed down by
+competition let me show you the equation
+
+ align:start position:0%
+competition let me show you the equation
+ 
+
+ align:start position:0%
+competition let me show you the equation
+it's in a way it's the simplest
+
+ align:start position:0%
+it's in a way it's the simplest
+ 
+
+ align:start position:0%
+it's in a way it's the simplest
+nonlinear equation I could think of we
+
+ align:start position:0%
+nonlinear equation I could think of we
+ 
+
+ align:start position:0%
+nonlinear equation I could think of we
+have the usual dydt equal a y that would
+
+ align:start position:0%
+have the usual dydt equal a y that would
+ 
+
+ align:start position:0%
+have the usual dydt equal a y that would
+give exponential growth the growth would
+
+ align:start position:0%
+give exponential growth the growth would
+ 
+
+ align:start position:0%
+give exponential growth the growth would
+go on forever but then as y gets large
+
+ align:start position:0%
+go on forever but then as y gets large
+ 
+
+ align:start position:0%
+go on forever but then as y gets large
+if you if we think of Y as the
+
+ align:start position:0%
+if you if we think of Y as the
+ 
+
+ align:start position:0%
+if you if we think of Y as the
+population so the growth is exponential
+
+ align:start position:0%
+population so the growth is exponential
+ 
+
+ align:start position:0%
+population so the growth is exponential
+when the birth rate higher than the
+
+ align:start position:0%
+when the birth rate higher than the
+ 
+
+ align:start position:0%
+when the birth rate higher than the
+death rate and we grow we have and and
+
+ align:start position:0%
+death rate and we grow we have and and
+ 
+
+ align:start position:0%
+death rate and we grow we have and and
+that's what's happening but our world
+
+ align:start position:0%
+that's what's happening but our world
+ 
+
+ align:start position:0%
+that's what's happening but our world
+population is not growing pure
+
+ align:start position:0%
+population is not growing pure
+ 
+
+ align:start position:0%
+population is not growing pure
+exponentially
+
+ align:start position:0%
+exponentially
+ 
+
+ align:start position:0%
+exponentially
+forever and this is a simple term a
+
+ align:start position:0%
+forever and this is a simple term a
+ 
+
+ align:start position:0%
+forever and this is a simple term a
+simple model not very accurate but it's
+
+ align:start position:0%
+simple model not very accurate but it's
+ 
+
+ align:start position:0%
+simple model not very accurate but it's
+the right place to start for
+
+ align:start position:0%
+the right place to start for
+ 
+
+ align:start position:0%
+the right place to start for
+compettition
+
+ align:start position:0%
+compettition
+ 
+
+ align:start position:0%
+compettition
+when you have too many people somehow
+
+ align:start position:0%
+when you have too many people somehow
+ 
+
+ align:start position:0%
+when you have too many people somehow
+the multiplying y * y gives you a a
+
+ align:start position:0%
+the multiplying y * y gives you a a
+ 
+
+ align:start position:0%
+the multiplying y * y gives you a a
+number of interactions of all the Y
+
+ align:start position:0%
+number of interactions of all the Y
+ 
+
+ align:start position:0%
+number of interactions of all the Y
+people with with themselves and those
+
+ align:start position:0%
+people with with themselves and those
+ 
+
+ align:start position:0%
+people with with themselves and those
+interactions that competition slows down
+
+ align:start position:0%
+interactions that competition slows down
+ 
+
+ align:start position:0%
+interactions that competition slows down
+the growth and so the coefficient there
+
+ align:start position:0%
+the growth and so the coefficient there
+ 
+
+ align:start position:0%
+the growth and so the coefficient there
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+negative we want to solve that nonlinear
+
+ align:start position:0%
+negative we want to solve that nonlinear
+ 
+
+ align:start position:0%
+negative we want to solve that nonlinear
+equation and learn from it
+
+ align:start position:0%
+equation and learn from it
+ 
+
+ align:start position:0%
+equation and learn from it
+and uh it's called the logistic
+
+ align:start position:0%
+and uh it's called the logistic
+ 
+
+ align:start position:0%
+and uh it's called the logistic
+equation that's it's got to be a famous
+
+ align:start position:0%
+equation that's it's got to be a famous
+ 
+
+ align:start position:0%
+equation that's it's got to be a famous
+example and it has a neat trick that
+
+ align:start position:0%
+example and it has a neat trick that
+ 
+
+ align:start position:0%
+example and it has a neat trick that
+allows you to solve it
+
+ align:start position:0%
+allows you to solve it
+ 
+
+ align:start position:0%
+allows you to solve it
+easily let me show you that trick the
+
+ align:start position:0%
+easily let me show you that trick the
+ 
+
+ align:start position:0%
+easily let me show you that trick the
+trick is to let Z bring in a new Z as 1
+
+ align:start position:0%
+trick is to let Z bring in a new Z as 1
+ 
+
+ align:start position:0%
+trick is to let Z bring in a new Z as 1
+over y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then if I write the equation for Z it
+
+ align:start position:0%
+then if I write the equation for Z it
+ 
+
+ align:start position:0%
+then if I write the equation for Z it
+will turn out to be linear so you see
+
+ align:start position:0%
+will turn out to be linear so you see
+ 
+
+ align:start position:0%
+will turn out to be linear so you see
+I'm always hoping and here succeeding to
+
+ align:start position:0%
+I'm always hoping and here succeeding to
+ 
+
+ align:start position:0%
+I'm always hoping and here succeeding to
+get back to a
+
+ align:start position:0%
+get back to a
+ 
+
+ align:start position:0%
+get back to a
+simple linear equation and
+
+ align:start position:0%
+simple linear equation and
+ 
+
+ align:start position:0%
+simple linear equation and
+this device happens to work for this
+
+ align:start position:0%
+this device happens to work for this
+ 
+
+ align:start position:0%
+this device happens to work for this
+problem we need in the end a more
+
+ align:start position:0%
+problem we need in the end a more
+ 
+
+ align:start position:0%
+problem we need in the end a more
+systematic way that would work for other
+
+ align:start position:0%
+systematic way that would work for other
+ 
+
+ align:start position:0%
+systematic way that would work for other
+problems like there could be some
+
+ align:start position:0%
+problems like there could be some
+ 
+
+ align:start position:0%
+problems like there could be some
+constant term
+
+ align:start position:0%
+constant term
+ 
+
+ align:start position:0%
+constant term
+from harvesting from from from uh
+
+ align:start position:0%
+from harvesting from from from uh
+ 
+
+ align:start position:0%
+from harvesting from from from uh
+changing the
+
+ align:start position:0%
+changing the
+ 
+
+ align:start position:0%
+changing the
+equation let me go with this one so
+
+ align:start position:0%
+equation let me go with this one so
+ 
+
+ align:start position:0%
+equation let me go with this one so
+what's the equation for Z then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dzdt the derivative of that that's y the
+
+ align:start position:0%
+dzdt the derivative of that that's y the
+ 
+
+ align:start position:0%
+dzdt the derivative of that that's y the
+-1 is
+
+ align:start position:0%
+-1 is
+ 
+
+ align:start position:0%
+-1 is
+-1 y to the-
+
+ align:start position:0%
+-1 y to the-
+ 
+
+ align:start position:0%
+-1 y to the-
+2times dydt right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the derivative of y-1 is -1 y - 2 * the
+
+ align:start position:0%
+the derivative of y-1 is -1 y - 2 * the
+ 
+
+ align:start position:0%
+the derivative of y-1 is -1 y - 2 * the
+derivative of of dydt but now dydt is a
+
+ align:start position:0%
+derivative of of dydt but now dydt is a
+ 
+
+ align:start position:0%
+derivative of of dydt but now dydt is a
+y - b y^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 and what do I
+
+ align:start position:0%
+2 and what do I
+ 
+
+ align:start position:0%
+2 and what do I
+have I've
+
+ align:start position:0%
+have I've
+ 
+
+ align:start position:0%
+have I've
+got a with a minus a y over y^
+
+ align:start position:0%
+got a with a minus a y over y^
+ 
+
+ align:start position:0%
+got a with a minus a y over y^
+2 that will be Z so that's minus a
+
+ align:start position:0%
+2 that will be Z so that's minus a
+ 
+
+ align:start position:0%
+2 that will be Z so that's minus a
+z minus minus giving me a plus b y^2
+
+ align:start position:0%
+z minus minus giving me a plus b y^2
+ 
+
+ align:start position:0%
+z minus minus giving me a plus b y^2
+over y^2 is just a
+
+ align:start position:0%
+over y^2 is just a
+ 
+
+ align:start position:0%
+over y^2 is just a
+constant look at the equation for z now
+
+ align:start position:0%
+constant look at the equation for z now
+ 
+
+ align:start position:0%
+constant look at the equation for z now
+couldn't be better
+
+ align:start position:0%
+couldn't be better
+ 
+
+ align:start position:0%
+couldn't be better
+dzdt is minus a
+
+ align:start position:0%
+dzdt is minus a
+ 
+
+ align:start position:0%
+dzdt is minus a
+z and plus a constant and we know the
+
+ align:start position:0%
+z and plus a constant and we know the
+ 
+
+ align:start position:0%
+z and plus a constant and we know the
+solution to that equation so I can write
+
+ align:start position:0%
+solution to that equation so I can write
+ 
+
+ align:start position:0%
+solution to that equation so I can write
+down the solution to that equation and I
+
+ align:start position:0%
+down the solution to that equation and I
+ 
+
+ align:start position:0%
+down the solution to that equation and I
+will then I just
+
+ align:start position:0%
+will then I just
+ 
+
+ align:start position:0%
+will then I just
+take y to be one over that solution
+
+ align:start position:0%
+take y to be one over that solution
+ 
+
+ align:start position:0%
+take y to be one over that solution
+maybe I'll just write y straight ahead
+
+ align:start position:0%
+maybe I'll just write y straight ahead
+ 
+
+ align:start position:0%
+maybe I'll just write y straight ahead
+I'll just write the the the the answer Y
+
+ align:start position:0%
+I'll just write the the the the answer Y
+ 
+
+ align:start position:0%
+I'll just write the the the the answer Y
+which is 1/ z and Z is the solution to
+
+ align:start position:0%
+which is 1/ z and Z is the solution to
+ 
+
+ align:start position:0%
+which is 1/ z and Z is the solution to
+this equation and let me see so I'm
+
+ align:start position:0%
+this equation and let me see so I'm
+ 
+
+ align:start position:0%
+this equation and let me see so I'm
+going to have an exponential but it's
+
+ align:start position:0%
+going to have an exponential but it's
+ 
+
+ align:start position:0%
+going to have an exponential but it's
+going to be the exponential e the minus
+
+ align:start position:0%
+going to be the exponential e the minus
+ 
+
+ align:start position:0%
+going to be the exponential e the minus
+a t is going to show up in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Z and there'll be more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there will will show up in Z and then
+
+ align:start position:0%
+there will will show up in Z and then
+ 
+
+ align:start position:0%
+there will will show up in Z and then
+when I do one over Z to get back to Y
+
+ align:start position:0%
+when I do one over Z to get back to Y
+ 
+
+ align:start position:0%
+when I do one over Z to get back to Y
+that exponential is going into the
+
+ align:start position:0%
+that exponential is going into the
+ 
+
+ align:start position:0%
+that exponential is going into the
+denominator that's what's new that's
+
+ align:start position:0%
+denominator that's what's new that's
+ 
+
+ align:start position:0%
+denominator that's what's new that's
+what's new let me let me get the whole
+
+ align:start position:0%
+what's new let me let me get the whole
+ 
+
+ align:start position:0%
+what's new let me let me get the whole
+thing correct I have a
+
+ align:start position:0%
+thing correct I have a
+ 
+
+ align:start position:0%
+thing correct I have a
+a otherwise these are constants D here
+
+ align:start position:0%
+a otherwise these are constants D here
+ 
+
+ align:start position:0%
+a otherwise these are constants D here
+and B goes there and I just have to tell
+
+ align:start position:0%
+and B goes there and I just have to tell
+ 
+
+ align:start position:0%
+and B goes there and I just have to tell
+you what the what the D is
+
+ align:start position:0%
+you what the what the D is
+ 
+
+ align:start position:0%
+you what the what the D is
+there D is going to involve the initial
+
+ align:start position:0%
+there D is going to involve the initial
+ 
+
+ align:start position:0%
+there D is going to involve the initial
+value y of 0 at time Z we start
+
+ align:start position:0%
+value y of 0 at time Z we start
+ 
+
+ align:start position:0%
+value y of 0 at time Z we start
+somewhere y of
+
+ align:start position:0%
+somewhere y of
+ 
+
+ align:start position:0%
+somewhere y of
+zero and we begin to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grow we'll
+
+ align:start position:0%
+grow we'll
+ 
+
+ align:start position:0%
+grow we'll
+grow but with the slowing down down term
+
+ align:start position:0%
+grow but with the slowing down down term
+ 
+
+ align:start position:0%
+grow but with the slowing down down term
+keeping us back and in the end it can't
+
+ align:start position:0%
+keeping us back and in the end it can't
+ 
+
+ align:start position:0%
+keeping us back and in the end it can't
+grow forever because that term becomes
+
+ align:start position:0%
+grow forever because that term becomes
+ 
+
+ align:start position:0%
+grow forever because that term becomes
+bigger than that
+
+ align:start position:0%
+bigger than that
+ 
+
+ align:start position:0%
+bigger than that
+one if if y went on and on increasing
+
+ align:start position:0%
+one if if y went on and on increasing
+ 
+
+ align:start position:0%
+one if if y went on and on increasing
+that can't happen so it it will in it
+
+ align:start position:0%
+that can't happen so it it will in it
+ 
+
+ align:start position:0%
+that can't happen so it it will in it
+can only increase while this is positive
+
+ align:start position:0%
+can only increase while this is positive
+ 
+
+ align:start position:0%
+can only increase while this is positive
+and that's only positive below that line
+
+ align:start position:0%
+and that's only positive below that line
+ 
+
+ align:start position:0%
+and that's only positive below that line
+here's what the curve does it goes
+
+ align:start position:0%
+here's what the curve does it goes
+ 
+
+ align:start position:0%
+here's what the curve does it goes
+upward but then it has to it can't cross
+
+ align:start position:0%
+upward but then it has to it can't cross
+ 
+
+ align:start position:0%
+upward but then it has to it can't cross
+that line
+
+ align:start position:0%
+that line
+ 
+
+ align:start position:0%
+that line
+because above that line for Big Y above
+
+ align:start position:0%
+because above that line for Big Y above
+ 
+
+ align:start position:0%
+because above that line for Big Y above
+that line for Big Y this negative term
+
+ align:start position:0%
+that line for Big Y this negative term
+ 
+
+ align:start position:0%
+that line for Big Y this negative term
+is means that the slope is negative if
+
+ align:start position:0%
+is means that the slope is negative if
+ 
+
+ align:start position:0%
+is means that the slope is negative if
+if I started with
+
+ align:start position:0%
+if I started with
+ 
+
+ align:start position:0%
+if I started with
+a with a big number I'd have to come
+
+ align:start position:0%
+a with a big number I'd have to come
+ 
+
+ align:start position:0%
+a with a big number I'd have to come
+down can I just draw that picture but
+
+ align:start position:0%
+down can I just draw that picture but
+ 
+
+ align:start position:0%
+down can I just draw that picture but
+it's really between here between these
+
+ align:start position:0%
+it's really between here between these
+ 
+
+ align:start position:0%
+it's really between here between these
+lines
+
+ align:start position:0%
+lines
+ 
+
+ align:start position:0%
+lines
+that I'm thinking the world population
+
+ align:start position:0%
+that I'm thinking the world population
+ 
+
+ align:start position:0%
+that I'm thinking the world population
+is so it started way back at sometime
+
+ align:start position:0%
+is so it started way back at sometime
+ 
+
+ align:start position:0%
+is so it started way back at sometime
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+infinity and
+
+ align:start position:0%
+infinity and
+ 
+
+ align:start position:0%
+infinity and
+it whatever it came up to time zero this
+
+ align:start position:0%
+it whatever it came up to time zero this
+ 
+
+ align:start position:0%
+it whatever it came up to time zero this
+is t equal
+
+ align:start position:0%
+is t equal
+ 
+
+ align:start position:0%
+is t equal
+0 starting population and of course T
+
+ align:start position:0%
+0 starting population and of course T
+ 
+
+ align:start position:0%
+0 starting population and of course T
+equals 0 could be the year
+
+ align:start position:0%
+equals 0 could be the year
+ 
+
+ align:start position:0%
+equals 0 could be the year
+2000 we can move the time axis as we
+
+ align:start position:0%
+2000 we can move the time axis as we
+ 
+
+ align:start position:0%
+2000 we can move the time axis as we
+want so t0 might be the year 2000 our
+
+ align:start position:0%
+want so t0 might be the year 2000 our
+ 
+
+ align:start position:0%
+want so t0 might be the year 2000 our
+population is still increasing but it
+
+ align:start position:0%
+population is still increasing but it
+ 
+
+ align:start position:0%
+population is still increasing but it
+won't go on forever it it will slow down
+
+ align:start position:0%
+won't go on forever it it will slow down
+ 
+
+ align:start position:0%
+won't go on forever it it will slow down
+and approach this limit A over B
+
+ align:start position:0%
+and approach this limit A over B
+ 
+
+ align:start position:0%
+and approach this limit A over B
+approaches A over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B so that number A over B is totally
+
+ align:start position:0%
+B so that number A over B is totally
+ 
+
+ align:start position:0%
+B so that number A over B is totally
+special for this
+
+ align:start position:0%
+special for this
+ 
+
+ align:start position:0%
+special for this
+equation and let me think about that
+
+ align:start position:0%
+equation and let me think about that
+ 
+
+ align:start position:0%
+equation and let me think about that
+part I let me give a name to this curve
+
+ align:start position:0%
+part I let me give a name to this curve
+ 
+
+ align:start position:0%
+part I let me give a name to this curve
+it's often called an a logistic curve
+
+ align:start position:0%
+it's often called an a logistic curve
+ 
+
+ align:start position:0%
+it's often called an a logistic curve
+that's okay but I like the name S curve
+
+ align:start position:0%
+that's okay but I like the name S curve
+ 
+
+ align:start position:0%
+that's okay but I like the name S curve
+it's an S
+
+ align:start position:0%
+it's an S
+ 
+
+ align:start position:0%
+it's an S
+curve in some way it or a sigmoidal
+
+ align:start position:0%
+curve in some way it or a sigmoidal
+ 
+
+ align:start position:0%
+curve in some way it or a sigmoidal
+curve in some way it looks a bit like an
+
+ align:start position:0%
+curve in some way it looks a bit like an
+ 
+
+ align:start position:0%
+curve in some way it looks a bit like an
+s a sort of very stretched out
+
+ align:start position:0%
+s a sort of very stretched out
+ 
+
+ align:start position:0%
+s a sort of very stretched out
+s okay so that and you see why do do it
+
+ align:start position:0%
+s okay so that and you see why do do it
+ 
+
+ align:start position:0%
+s okay so that and you see why do do it
+just takes a look here has as T goes to
+
+ align:start position:0%
+just takes a look here has as T goes to
+ 
+
+ align:start position:0%
+just takes a look here has as T goes to
+Infinity this becomes zero when T gets
+
+ align:start position:0%
+Infinity this becomes zero when T gets
+ 
+
+ align:start position:0%
+Infinity this becomes zero when T gets
+this exponential is gone and I just have
+
+ align:start position:0%
+this exponential is gone and I just have
+ 
+
+ align:start position:0%
+this exponential is gone and I just have
+a over B at the limit when T is minus
+
+ align:start position:0%
+a over B at the limit when T is minus
+ 
+
+ align:start position:0%
+a over B at the limit when T is minus
+infinity way it back at starting
+
+ align:start position:0%
+infinity way it back at starting
+ 
+
+ align:start position:0%
+infinity way it back at starting
+time when T is minus infinity that's a
+
+ align:start position:0%
+time when T is minus infinity that's a
+ 
+
+ align:start position:0%
+time when T is minus infinity that's a
+giant number this is I'm dividing by a
+
+ align:start position:0%
+giant number this is I'm dividing by a
+ 
+
+ align:start position:0%
+giant number this is I'm dividing by a
+giant number I'm at zero so way back at
+
+ align:start position:0%
+giant number I'm at zero so way back at
+ 
+
+ align:start position:0%
+giant number I'm at zero so way back at
+time minus infinity it started from zero
+
+ align:start position:0%
+time minus infinity it started from zero
+ 
+
+ align:start position:0%
+time minus infinity it started from zero
+there's those two possibilities yal 0
+
+ align:start position:0%
+there's those two possibilities yal 0
+ 
+
+ align:start position:0%
+there's those two possibilities yal 0
+and Y = A over B are the key things to
+
+ align:start position:0%
+and Y = A over B are the key things to
+ 
+
+ align:start position:0%
+and Y = A over B are the key things to
+see for this
+
+ align:start position:0%
+see for this
+ 
+
+ align:start position:0%
+see for this
+equation so I'm going to take a few
+
+ align:start position:0%
+equation so I'm going to take a few
+ 
+
+ align:start position:0%
+equation so I'm going to take a few
+minutes to see where do those come in
+
+ align:start position:0%
+minutes to see where do those come in
+ 
+
+ align:start position:0%
+minutes to see where do those come in
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+are steady States let me let me use that
+
+ align:start position:0%
+are steady States let me let me use that
+ 
+
+ align:start position:0%
+are steady States let me let me use that
+word and and show you what I mean steady
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+States critical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points for my equation dydt let me write
+
+ align:start position:0%
+points for my equation dydt let me write
+ 
+
+ align:start position:0%
+points for my equation dydt let me write
+the logistic equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again a steady state is a value of Y
+
+ align:start position:0%
+again a steady state is a value of Y
+ 
+
+ align:start position:0%
+again a steady state is a value of Y
+where the derivative is zero nothing
+
+ align:start position:0%
+where the derivative is zero nothing
+ 
+
+ align:start position:0%
+where the derivative is zero nothing
+happens it just sits there so if that is
+
+ align:start position:0%
+happens it just sits there so if that is
+ 
+
+ align:start position:0%
+happens it just sits there so if that is
+zero so a steady state let me use those
+
+ align:start position:0%
+zero so a steady state let me use those
+ 
+
+ align:start position:0%
+zero so a steady state let me use those
+capital Y for steady state those are
+
+ align:start position:0%
+capital Y for steady state those are
+ 
+
+ align:start position:0%
+capital Y for steady state those are
+just numbers there're the numbers where
+
+ align:start position:0%
+just numbers there're the numbers where
+ 
+
+ align:start position:0%
+just numbers there're the numbers where
+this is zero A1 y - b y^ 2 is 0 you see
+
+ align:start position:0%
+this is zero A1 y - b y^ 2 is 0 you see
+ 
+
+ align:start position:0%
+this is zero A1 y - b y^ 2 is 0 you see
+that if I start
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out at Y at Capital y a steady state
+
+ align:start position:0%
+out at Y at Capital y a steady state
+ 
+
+ align:start position:0%
+out at Y at Capital y a steady state
+that is zero the derivative is zero I
+
+ align:start position:0%
+that is zero the derivative is zero I
+ 
+
+ align:start position:0%
+that is zero the derivative is zero I
+stay there and there are two
+
+ align:start position:0%
+stay there and there are two
+ 
+
+ align:start position:0%
+stay there and there are two
+possibilities if I start this gives me
+
+ align:start position:0%
+possibilities if I start this gives me
+ 
+
+ align:start position:0%
+possibilities if I start this gives me
+two possibilities right what are the
+
+ align:start position:0%
+two possibilities right what are the
+ 
+
+ align:start position:0%
+two possibilities right what are the
+solutions to this equation this gives me
+
+ align:start position:0%
+solutions to this equation this gives me
+ 
+
+ align:start position:0%
+solutions to this equation this gives me
+y = zero is one solution clearly
+
+ align:start position:0%
+y = zero is one solution clearly
+ 
+
+ align:start position:0%
+y = zero is one solution clearly
+or y
+
+ align:start position:0%
+or y
+ 
+
+ align:start position:0%
+or y
+equals let's see if this equal that I
+
+ align:start position:0%
+equals let's see if this equal that I
+ 
+
+ align:start position:0%
+equals let's see if this equal that I
+could cancel the y y would be A over
+
+ align:start position:0%
+could cancel the y y would be A over
+ 
+
+ align:start position:0%
+could cancel the y y would be A over
+B exactly the two in the
+
+ align:start position:0%
+B exactly the two in the
+ 
+
+ align:start position:0%
+B exactly the two in the
+picture if I start at zero I stay at
+
+ align:start position:0%
+picture if I start at zero I stay at
+ 
+
+ align:start position:0%
+picture if I start at zero I stay at
+zero no population nothing can happen
+
+ align:start position:0%
+zero no population nothing can happen
+ 
+
+ align:start position:0%
+zero no population nothing can happen
+but if I move a little away if I get two
+
+ align:start position:0%
+but if I move a little away if I get two
+ 
+
+ align:start position:0%
+but if I move a little away if I get two
+people we grow
+
+ align:start position:0%
+people we grow
+ 
+
+ align:start position:0%
+people we grow
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+grow exponentially for a while but then
+
+ align:start position:0%
+grow exponentially for a while but then
+ 
+
+ align:start position:0%
+grow exponentially for a while but then
+the b y^ 2 term takes it gets in there
+
+ align:start position:0%
+the b y^ 2 term takes it gets in there
+ 
+
+ align:start position:0%
+the b y^ 2 term takes it gets in there
+slows us down and we slow down and we
+
+ align:start position:0%
+slows us down and we slow down and we
+ 
+
+ align:start position:0%
+slows us down and we slow down and we
+reach this a overb if we had started at
+
+ align:start position:0%
+reach this a overb if we had started at
+ 
+
+ align:start position:0%
+reach this a overb if we had started at
+A over B we would have stayed at A over
+
+ align:start position:0%
+A over B we would have stayed at A over
+ 
+
+ align:start position:0%
+A over B we would have stayed at A over
+B so that that s-curve picture is really
+
+ align:start position:0%
+B so that that s-curve picture is really
+ 
+
+ align:start position:0%
+B so that that s-curve picture is really
+uh a nice graph of the solution here's
+
+ align:start position:0%
+uh a nice graph of the solution here's
+ 
+
+ align:start position:0%
+uh a nice graph of the solution here's
+the solution at steady state going
+
+ align:start position:0%
+the solution at steady state going
+ 
+
+ align:start position:0%
+the solution at steady state going
+nowhere there's a solution at steady
+
+ align:start position:0%
+nowhere there's a solution at steady
+ 
+
+ align:start position:0%
+nowhere there's a solution at steady
+state with population competition and
+
+ align:start position:0%
+state with population competition and
+ 
+
+ align:start position:0%
+state with population competition and
+cooperation are balanced and nothing
+
+ align:start position:0%
+cooperation are balanced and nothing
+ 
+
+ align:start position:0%
+cooperation are balanced and nothing
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+otherwise whatever we we have S curves
+
+ align:start position:0%
+otherwise whatever we we have S curves
+ 
+
+ align:start position:0%
+otherwise whatever we we have S curves
+then they don't
+
+ align:start position:0%
+then they don't
+ 
+
+ align:start position:0%
+then they don't
+cross depending where where depending on
+
+ align:start position:0%
+cross depending where where depending on
+ 
+
+ align:start position:0%
+cross depending where where depending on
+the initial value we'll get be on one or
+
+ align:start position:0%
+the initial value we'll get be on one or
+ 
+
+ align:start position:0%
+the initial value we'll get be on one or
+other of these curves and they all go up
+
+ align:start position:0%
+other of these curves and they all go up
+ 
+
+ align:start position:0%
+other of these curves and they all go up
+to that carrying capacity that limiting
+
+ align:start position:0%
+to that carrying capacity that limiting
+ 
+
+ align:start position:0%
+to that carrying capacity that limiting
+population A over B right so the
+
+ align:start position:0%
+population A over B right so the
+ 
+
+ align:start position:0%
+population A over B right so the
+final take-home message about this
+
+ align:start position:0%
+final take-home message about this
+ 
+
+ align:start position:0%
+final take-home message about this
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+is as an example of equations with
+
+ align:start position:0%
+is as an example of equations with
+ 
+
+ align:start position:0%
+is as an example of equations with
+steady States this steady state is
+
+ align:start position:0%
+steady States this steady state is
+ 
+
+ align:start position:0%
+steady States this steady state is
+called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unstable because if we start near y
+
+ align:start position:0%
+unstable because if we start near y
+ 
+
+ align:start position:0%
+unstable because if we start near y
+equals 0 we take
+
+ align:start position:0%
+equals 0 we take
+ 
+
+ align:start position:0%
+equals 0 we take
+off if we start near y equals 0 we start
+
+ align:start position:0%
+off if we start near y equals 0 we start
+ 
+
+ align:start position:0%
+off if we start near y equals 0 we start
+growing we leave that Cady State this
+
+ align:start position:0%
+growing we leave that Cady State this
+ 
+
+ align:start position:0%
+growing we leave that Cady State this
+steady state is called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stable because if we're near A over B we
+
+ align:start position:0%
+stable because if we're near A over B we
+ 
+
+ align:start position:0%
+stable because if we're near A over B we
+get closer and closer to A over
+
+ align:start position:0%
+get closer and closer to A over
+ 
+
+ align:start position:0%
+get closer and closer to A over
+B I I'll do the example
+
+ align:start position:0%
+B I I'll do the example
+ 
+
+ align:start position:0%
+B I I'll do the example
+uh this this will be one example of a
+
+ align:start position:0%
+uh this this will be one example of a
+ 
+
+ align:start position:0%
+uh this this will be one example of a
+general problem dydt is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some function of Y some right hand side
+
+ align:start position:0%
+some function of Y some right hand side
+ 
+
+ align:start position:0%
+some function of Y some right hand side
+that depends on y that will be our next
+
+ align:start position:0%
+that depends on y that will be our next
+ 
+
+ align:start position:0%
+that depends on y that will be our next
+video to understand those equations dydt
+
+ align:start position:0%
+video to understand those equations dydt
+ 
+
+ align:start position:0%
+video to understand those equations dydt
+is f of Y notice that they are not
+
+ align:start position:0%
+is f of Y notice that they are not
+ 
+
+ align:start position:0%
+is f of Y notice that they are not
+linear but we can solve for steady
+
+ align:start position:0%
+linear but we can solve for steady
+ 
+
+ align:start position:0%
+linear but we can solve for steady
+States a steady state will be when F at
+
+ align:start position:0%
+States a steady state will be when F at
+ 
+
+ align:start position:0%
+States a steady state will be when F at
+y is zero then nothing happens but is
+
+ align:start position:0%
+y is zero then nothing happens but is
+ 
+
+ align:start position:0%
+y is zero then nothing happens but is
+that steady state stable or is it
+
+ align:start position:0%
+that steady state stable or is it
+ 
+
+ align:start position:0%
+that steady state stable or is it
+unstable that's the crucial thing for
+
+ align:start position:0%
+unstable that's the crucial thing for
+ 
+
+ align:start position:0%
+unstable that's the crucial thing for
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+applications are
+
+ align:start position:0%
+applications are
+ 
+
+ align:start position:0%
+applications are
+we settling down to something acceptable
+
+ align:start position:0%
+we settling down to something acceptable
+ 
+
+ align:start position:0%
+we settling down to something acceptable
+or are we blowing up to something
+
+ align:start position:0%
+or are we blowing up to something
+ 
+
+ align:start position:0%
+or are we blowing up to something
+impossible that's the next video thank
+
+ align:start position:0%
+impossible that's the next video thank
+ 
+
+ align:start position:0%
+impossible that's the next video thank
+you
\ No newline at end of file
diff --git a/TSdXJw83kyA.txt b/TSdXJw83kyA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3e202da8983f77f1d8858f8efaab304e23077103
--- /dev/null
+++ b/TSdXJw83kyA.txt
@@ -0,0 +1,5744 @@
+align:start position:0%
+ 
+okay this lecture is mostly about the
+
+ align:start position:0%
+okay this lecture is mostly about the
+ 
+
+ align:start position:0%
+okay this lecture is mostly about the
+idea of similar matrices I'm going to
+
+ align:start position:0%
+idea of similar matrices I'm going to
+ 
+
+ align:start position:0%
+idea of similar matrices I'm going to
+tell you what that word similar means
+
+ align:start position:0%
+tell you what that word similar means
+ 
+
+ align:start position:0%
+tell you what that word similar means
+and in what way two matrices are called
+
+ align:start position:0%
+and in what way two matrices are called
+ 
+
+ align:start position:0%
+and in what way two matrices are called
+similar but before I do that I have a
+
+ align:start position:0%
+similar but before I do that I have a
+ 
+
+ align:start position:0%
+similar but before I do that I have a
+little more to say about positive
+
+ align:start position:0%
+little more to say about positive
+ 
+
+ align:start position:0%
+little more to say about positive
+definite matrices you can tell this is a
+
+ align:start position:0%
+definite matrices you can tell this is a
+ 
+
+ align:start position:0%
+definite matrices you can tell this is a
+subject I think is really important and
+
+ align:start position:0%
+subject I think is really important and
+ 
+
+ align:start position:0%
+subject I think is really important and
+I told you what positive definite meant
+
+ align:start position:0%
+I told you what positive definite meant
+ 
+
+ align:start position:0%
+I told you what positive definite meant
+it means that this this expression this
+
+ align:start position:0%
+it means that this this expression this
+ 
+
+ align:start position:0%
+it means that this this expression this
+quadratic form X transpose ax is always
+
+ align:start position:0%
+quadratic form X transpose ax is always
+ 
+
+ align:start position:0%
+quadratic form X transpose ax is always
+positive but the direct way to test it
+
+ align:start position:0%
+positive but the direct way to test it
+ 
+
+ align:start position:0%
+positive but the direct way to test it
+was with eigenvalues or pivots or
+
+ align:start position:0%
+was with eigenvalues or pivots or
+ 
+
+ align:start position:0%
+was with eigenvalues or pivots or
+determinants so we know what it means we
+
+ align:start position:0%
+determinants so we know what it means we
+ 
+
+ align:start position:0%
+determinants so we know what it means we
+know how to test it but I didn't really
+
+ align:start position:0%
+know how to test it but I didn't really
+ 
+
+ align:start position:0%
+know how to test it but I didn't really
+say where positive definite matrices
+
+ align:start position:0%
+say where positive definite matrices
+ 
+
+ align:start position:0%
+say where positive definite matrices
+come from and so one thing I want to say
+
+ align:start position:0%
+come from and so one thing I want to say
+ 
+
+ align:start position:0%
+come from and so one thing I want to say
+is that they come from least squares in
+
+ align:start position:0%
+is that they come from least squares in
+ 
+
+ align:start position:0%
+is that they come from least squares in
+and all sorts of physical problems start
+
+ align:start position:0%
+and all sorts of physical problems start
+ 
+
+ align:start position:0%
+and all sorts of physical problems start
+with a rectangular matrix you remember
+
+ align:start position:0%
+with a rectangular matrix you remember
+ 
+
+ align:start position:0%
+with a rectangular matrix you remember
+in these squares that the crucial
+
+ align:start position:0%
+in these squares that the crucial
+ 
+
+ align:start position:0%
+in these squares that the crucial
+combination was a transpose a so I want
+
+ align:start position:0%
+combination was a transpose a so I want
+ 
+
+ align:start position:0%
+combination was a transpose a so I want
+to show that that's a positive definite
+
+ align:start position:0%
+to show that that's a positive definite
+ 
+
+ align:start position:0%
+to show that that's a positive definite
+matrix okay so I'm going to speak a
+
+ align:start position:0%
+matrix okay so I'm going to speak a
+ 
+
+ align:start position:0%
+matrix okay so I'm going to speak a
+little more about positive definite
+
+ align:start position:0%
+little more about positive definite
+ 
+
+ align:start position:0%
+little more about positive definite
+matrices just recapping so let me ask a
+
+ align:start position:0%
+matrices just recapping so let me ask a
+ 
+
+ align:start position:0%
+matrices just recapping so let me ask a
+question it may be on the homework
+
+ align:start position:0%
+question it may be on the homework
+ 
+
+ align:start position:0%
+question it may be on the homework
+suppose a matrix a is positive definite
+
+ align:start position:0%
+suppose a matrix a is positive definite
+ 
+
+ align:start position:0%
+suppose a matrix a is positive definite
+I mean by that it's all I'm assuming
+
+ align:start position:0%
+I mean by that it's all I'm assuming
+ 
+
+ align:start position:0%
+I mean by that it's all I'm assuming
+it's symmetric that's always built into
+
+ align:start position:0%
+it's symmetric that's always built into
+ 
+
+ align:start position:0%
+it's symmetric that's always built into
+the definition so we have a symmetric
+
+ align:start position:0%
+the definition so we have a symmetric
+ 
+
+ align:start position:0%
+the definition so we have a symmetric
+positive definite matrix what about its
+
+ align:start position:0%
+positive definite matrix what about its
+ 
+
+ align:start position:0%
+positive definite matrix what about its
+inverse is the inverse of a symmetric
+
+ align:start position:0%
+inverse is the inverse of a symmetric
+ 
+
+ align:start position:0%
+inverse is the inverse of a symmetric
+positive definite matrix also symmetric
+
+ align:start position:0%
+positive definite matrix also symmetric
+ 
+
+ align:start position:0%
+positive definite matrix also symmetric
+positive definite so you quickly think
+
+ align:start position:0%
+positive definite so you quickly think
+ 
+
+ align:start position:0%
+positive definite so you quickly think
+okay what do I know about the pivots
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the inverse matrix not much what do I
+
+ align:start position:0%
+of the inverse matrix not much what do I
+ 
+
+ align:start position:0%
+of the inverse matrix not much what do I
+know about the eigenvalues of the
+
+ align:start position:0%
+know about the eigenvalues of the
+ 
+
+ align:start position:0%
+know about the eigenvalues of the
+inverse matrix everything right the
+
+ align:start position:0%
+inverse matrix everything right the
+ 
+
+ align:start position:0%
+inverse matrix everything right the
+eigenvalues of the inverse are one over
+
+ align:start position:0%
+eigenvalues of the inverse are one over
+ 
+
+ align:start position:0%
+eigenvalues of the inverse are one over
+the eigenvalues of the matrix so if my
+
+ align:start position:0%
+the eigenvalues of the matrix so if my
+ 
+
+ align:start position:0%
+the eigenvalues of the matrix so if my
+matrix starts out positive definite then
+
+ align:start position:0%
+matrix starts out positive definite then
+ 
+
+ align:start position:0%
+matrix starts out positive definite then
+right away I know that its inverse is
+
+ align:start position:0%
+right away I know that its inverse is
+ 
+
+ align:start position:0%
+right away I know that its inverse is
+positive definite because those positive
+
+ align:start position:0%
+positive definite because those positive
+ 
+
+ align:start position:0%
+positive definite because those positive
+eigenvalues then one over the eigenvalue
+
+ align:start position:0%
+eigenvalues then one over the eigenvalue
+ 
+
+ align:start position:0%
+eigenvalues then one over the eigenvalue
+is also positive what if I know that a a
+
+ align:start position:0%
+is also positive what if I know that a a
+ 
+
+ align:start position:0%
+is also positive what if I know that a a
+matrix a and a matrix B are both
+
+ align:start position:0%
+matrix a and a matrix B are both
+ 
+
+ align:start position:0%
+matrix a and a matrix B are both
+positive definite let me ask you this
+
+ align:start position:0%
+positive definite let me ask you this
+ 
+
+ align:start position:0%
+positive definite let me ask you this
+suppose if a and B are positive definite
+
+ align:start position:0%
+suppose if a and B are positive definite
+ 
+
+ align:start position:0%
+suppose if a and B are positive definite
+what about what about a plus B in some
+
+ align:start position:0%
+what about what about a plus B in some
+ 
+
+ align:start position:0%
+what about what about a plus B in some
+way you hope that that would be true
+
+ align:start position:0%
+way you hope that that would be true
+ 
+
+ align:start position:0%
+way you hope that that would be true
+it's positive definite for a matrix is
+
+ align:start position:0%
+it's positive definite for a matrix is
+ 
+
+ align:start position:0%
+it's positive definite for a matrix is
+kind of like positive for a real number
+
+ align:start position:0%
+kind of like positive for a real number
+ 
+
+ align:start position:0%
+kind of like positive for a real number
+but we don't know the eigenvalues of a
+
+ align:start position:0%
+but we don't know the eigenvalues of a
+ 
+
+ align:start position:0%
+but we don't know the eigenvalues of a
+plus B we don't know the pivots of a
+
+ align:start position:0%
+plus B we don't know the pivots of a
+ 
+
+ align:start position:0%
+plus B we don't know the pivots of a
+plus B so we just like have to go down
+
+ align:start position:0%
+plus B so we just like have to go down
+ 
+
+ align:start position:0%
+plus B so we just like have to go down
+this list of all right which approach to
+
+ align:start position:0%
+this list of all right which approach to
+ 
+
+ align:start position:0%
+this list of all right which approach to
+positive definite can we get a handle on
+
+ align:start position:0%
+positive definite can we get a handle on
+ 
+
+ align:start position:0%
+positive definite can we get a handle on
+and this is a good one this is a good
+
+ align:start position:0%
+and this is a good one this is a good
+ 
+
+ align:start position:0%
+and this is a good one this is a good
+one can we how would we decide that if a
+
+ align:start position:0%
+one can we how would we decide that if a
+ 
+
+ align:start position:0%
+one can we how would we decide that if a
+was like this and if B was like this
+
+ align:start position:0%
+was like this and if B was like this
+ 
+
+ align:start position:0%
+was like this and if B was like this
+then we would look at X transpose a plus
+
+ align:start position:0%
+then we would look at X transpose a plus
+ 
+
+ align:start position:0%
+then we would look at X transpose a plus
+BX I'm sure this is in the homework now
+
+ align:start position:0%
+BX I'm sure this is in the homework now
+ 
+
+ align:start position:0%
+BX I'm sure this is in the homework now
+so we have X transpose ax but bigger
+
+ align:start position:0%
+so we have X transpose ax but bigger
+ 
+
+ align:start position:0%
+so we have X transpose ax but bigger
+than 0
+
+ align:start position:0%
+than 0
+ 
+
+ align:start position:0%
+than 0
+X transpose BX positive for all for all
+
+ align:start position:0%
+X transpose BX positive for all for all
+ 
+
+ align:start position:0%
+X transpose BX positive for all for all
+X so now I ask you about this guy and of
+
+ align:start position:0%
+X so now I ask you about this guy and of
+ 
+
+ align:start position:0%
+X so now I ask you about this guy and of
+course you just add that and that and we
+
+ align:start position:0%
+course you just add that and that and we
+ 
+
+ align:start position:0%
+course you just add that and that and we
+get what we want if a and B are positive
+
+ align:start position:0%
+get what we want if a and B are positive
+ 
+
+ align:start position:0%
+get what we want if a and B are positive
+definite so is a plus B so that's what
+
+ align:start position:0%
+definite so is a plus B so that's what
+ 
+
+ align:start position:0%
+definite so is a plus B so that's what
+I've shown so is a plus B just just
+
+ align:start position:0%
+I've shown so is a plus B just just
+ 
+
+ align:start position:0%
+I've shown so is a plus B just just
+be sort of ready for all the approaches
+
+ align:start position:0%
+be sort of ready for all the approaches
+ 
+
+ align:start position:0%
+be sort of ready for all the approaches
+through eigenvalues and through this
+
+ align:start position:0%
+through eigenvalues and through this
+ 
+
+ align:start position:0%
+through eigenvalues and through this
+expression and now finally one more
+
+ align:start position:0%
+expression and now finally one more
+ 
+
+ align:start position:0%
+expression and now finally one more
+thought about positive definite is this
+
+ align:start position:0%
+thought about positive definite is this
+ 
+
+ align:start position:0%
+thought about positive definite is this
+combination that came up in these
+
+ align:start position:0%
+combination that came up in these
+ 
+
+ align:start position:0%
+combination that came up in these
+squares can I do that so now now suppose
+
+ align:start position:0%
+squares can I do that so now now suppose
+ 
+
+ align:start position:0%
+squares can I do that so now now suppose
+a is rectangular M by n so I'm sorry
+
+ align:start position:0%
+a is rectangular M by n so I'm sorry
+ 
+
+ align:start position:0%
+a is rectangular M by n so I'm sorry
+that I've used the same letter a for the
+
+ align:start position:0%
+that I've used the same letter a for the
+ 
+
+ align:start position:0%
+that I've used the same letter a for the
+positive definite matrices for the and
+
+ align:start position:0%
+positive definite matrices for the and
+ 
+
+ align:start position:0%
+positive definite matrices for the and
+the eigenvalue chapter that i used way
+
+ align:start position:0%
+the eigenvalue chapter that i used way
+ 
+
+ align:start position:0%
+the eigenvalue chapter that i used way
+back in earlier chapters when the matrix
+
+ align:start position:0%
+back in earlier chapters when the matrix
+ 
+
+ align:start position:0%
+back in earlier chapters when the matrix
+was rectangular now that matrix a
+
+ align:start position:0%
+was rectangular now that matrix a
+ 
+
+ align:start position:0%
+was rectangular now that matrix a
+rectangular matrix no way it's positive
+
+ align:start position:0%
+rectangular matrix no way it's positive
+ 
+
+ align:start position:0%
+rectangular matrix no way it's positive
+definite it's not symmetric
+
+ align:start position:0%
+definite it's not symmetric
+ 
+
+ align:start position:0%
+definite it's not symmetric
+it's not even square in general but you
+
+ align:start position:0%
+it's not even square in general but you
+ 
+
+ align:start position:0%
+it's not even square in general but you
+remember that the key for these
+
+ align:start position:0%
+remember that the key for these
+ 
+
+ align:start position:0%
+remember that the key for these
+rectangular ones was a transpose a
+
+ align:start position:0%
+rectangular ones was a transpose a
+ 
+
+ align:start position:0%
+rectangular ones was a transpose a
+that's square that's symmetric those are
+
+ align:start position:0%
+that's square that's symmetric those are
+ 
+
+ align:start position:0%
+that's square that's symmetric those are
+things we knew it's a we knew back when
+
+ align:start position:0%
+things we knew it's a we knew back when
+ 
+
+ align:start position:0%
+things we knew it's a we knew back when
+we met this thing in in the least
+
+ align:start position:0%
+we met this thing in in the least
+ 
+
+ align:start position:0%
+we met this thing in in the least
+squares stuff in the projection stuff
+
+ align:start position:0%
+squares stuff in the projection stuff
+ 
+
+ align:start position:0%
+squares stuff in the projection stuff
+but now we know something more we can
+
+ align:start position:0%
+but now we know something more we can
+ 
+
+ align:start position:0%
+but now we know something more we can
+ask more important question a deeper
+
+ align:start position:0%
+ask more important question a deeper
+ 
+
+ align:start position:0%
+ask more important question a deeper
+question is it positive definite and we
+
+ align:start position:0%
+question is it positive definite and we
+ 
+
+ align:start position:0%
+question is it positive definite and we
+sort of hope so like we might in analogy
+
+ align:start position:0%
+sort of hope so like we might in analogy
+ 
+
+ align:start position:0%
+sort of hope so like we might in analogy
+with numbers this is like sort of like
+
+ align:start position:0%
+with numbers this is like sort of like
+ 
+
+ align:start position:0%
+with numbers this is like sort of like
+the square of a number and that's
+
+ align:start position:0%
+the square of a number and that's
+ 
+
+ align:start position:0%
+the square of a number and that's
+positive so now I want to ask the matrix
+
+ align:start position:0%
+positive so now I want to ask the matrix
+ 
+
+ align:start position:0%
+positive so now I want to ask the matrix
+question it is a transpose a positive
+
+ align:start position:0%
+question it is a transpose a positive
+ 
+
+ align:start position:0%
+question it is a transpose a positive
+definite okay now it's so again it's a
+
+ align:start position:0%
+definite okay now it's so again it's a
+ 
+
+ align:start position:0%
+definite okay now it's so again it's a
+rectangular a that I'm starting with but
+
+ align:start position:0%
+rectangular a that I'm starting with but
+ 
+
+ align:start position:0%
+rectangular a that I'm starting with but
+it's the combination a transpose a
+
+ align:start position:0%
+it's the combination a transpose a
+ 
+
+ align:start position:0%
+it's the combination a transpose a
+that's the square symmetric and
+
+ align:start position:0%
+that's the square symmetric and
+ 
+
+ align:start position:0%
+that's the square symmetric and
+hopefully
+
+ align:start position:0%
+hopefully
+ 
+
+ align:start position:0%
+hopefully
+- they've definite matrix so how do I
+
+ align:start position:0%
+- they've definite matrix so how do I
+ 
+
+ align:start position:0%
+- they've definite matrix so how do I
+see that it is positive definite or at
+
+ align:start position:0%
+see that it is positive definite or at
+ 
+
+ align:start position:0%
+see that it is positive definite or at
+least positive semi-definite you'll see
+
+ align:start position:0%
+least positive semi-definite you'll see
+ 
+
+ align:start position:0%
+least positive semi-definite you'll see
+that well I don't know the eigenvalues
+
+ align:start position:0%
+that well I don't know the eigenvalues
+ 
+
+ align:start position:0%
+that well I don't know the eigenvalues
+of this come of this product I don't
+
+ align:start position:0%
+of this come of this product I don't
+ 
+
+ align:start position:0%
+of this come of this product I don't
+want to work with the pivots the right
+
+ align:start position:0%
+want to work with the pivots the right
+ 
+
+ align:start position:0%
+want to work with the pivots the right
+thing the right quantity to look at is
+
+ align:start position:0%
+thing the right quantity to look at is
+ 
+
+ align:start position:0%
+thing the right quantity to look at is
+this X transpose ax eight X transpose
+
+ align:start position:0%
+this X transpose ax eight X transpose
+ 
+
+ align:start position:0%
+this X transpose ax eight X transpose
+times my matrix times X I'd like to see
+
+ align:start position:0%
+times my matrix times X I'd like to see
+ 
+
+ align:start position:0%
+times my matrix times X I'd like to see
+that this thing that that expression is
+
+ align:start position:0%
+that this thing that that expression is
+ 
+
+ align:start position:0%
+that this thing that that expression is
+always positive I'm not doing it with
+
+ align:start position:0%
+always positive I'm not doing it with
+ 
+
+ align:start position:0%
+always positive I'm not doing it with
+numbers I'm doing with symbols do you
+
+ align:start position:0%
+numbers I'm doing with symbols do you
+ 
+
+ align:start position:0%
+numbers I'm doing with symbols do you
+see how do I see that that expression
+
+ align:start position:0%
+see how do I see that that expression
+ 
+
+ align:start position:0%
+see how do I see that that expression
+comes out positive I'm taking a
+
+ align:start position:0%
+comes out positive I'm taking a
+ 
+
+ align:start position:0%
+comes out positive I'm taking a
+rectangular matrix a and an a transpose
+
+ align:start position:0%
+rectangular matrix a and an a transpose
+ 
+
+ align:start position:0%
+rectangular matrix a and an a transpose
+that gives me something square symmetric
+
+ align:start position:0%
+that gives me something square symmetric
+ 
+
+ align:start position:0%
+that gives me something square symmetric
+but now I want to see that if I multiply
+
+ align:start position:0%
+but now I want to see that if I multiply
+ 
+
+ align:start position:0%
+but now I want to see that if I multiply
+that if I do this I form this quadratic
+
+ align:start position:0%
+that if I do this I form this quadratic
+ 
+
+ align:start position:0%
+that if I do this I form this quadratic
+expression that I get this positive
+
+ align:start position:0%
+expression that I get this positive
+ 
+
+ align:start position:0%
+expression that I get this positive
+thing that goes upwards when i graph it
+
+ align:start position:0%
+thing that goes upwards when i graph it
+ 
+
+ align:start position:0%
+thing that goes upwards when i graph it
+how do I see that that's positive or
+
+ align:start position:0%
+how do I see that that's positive or
+ 
+
+ align:start position:0%
+how do I see that that's positive or
+absolutely it isn't negative anyway we
+
+ align:start position:0%
+absolutely it isn't negative anyway we
+ 
+
+ align:start position:0%
+absolutely it isn't negative anyway we
+will have to like to spend a minute on
+
+ align:start position:0%
+will have to like to spend a minute on
+ 
+
+ align:start position:0%
+will have to like to spend a minute on
+the question could it be zero but it
+
+ align:start position:0%
+the question could it be zero but it
+ 
+
+ align:start position:0%
+the question could it be zero but it
+can't be negative why can this never be
+
+ align:start position:0%
+can't be negative why can this never be
+ 
+
+ align:start position:0%
+can't be negative why can this never be
+negative the argument is like the one
+
+ align:start position:0%
+negative the argument is like the one
+ 
+
+ align:start position:0%
+negative the argument is like the one
+key idea in so many steps in linear
+
+ align:start position:0%
+key idea in so many steps in linear
+ 
+
+ align:start position:0%
+key idea in so many steps in linear
+algebra put those parentheses in a good
+
+ align:start position:0%
+algebra put those parentheses in a good
+ 
+
+ align:start position:0%
+algebra put those parentheses in a good
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+put the parentheses around a X and
+
+ align:start position:0%
+put the parentheses around a X and
+ 
+
+ align:start position:0%
+put the parentheses around a X and
+what's the what's the first part what's
+
+ align:start position:0%
+what's the what's the first part what's
+ 
+
+ align:start position:0%
+what's the what's the first part what's
+this X transpose a transpose that is ax
+
+ align:start position:0%
+this X transpose a transpose that is ax
+ 
+
+ align:start position:0%
+this X transpose a transpose that is ax
+transpose so what do we have we have the
+
+ align:start position:0%
+transpose so what do we have we have the
+ 
+
+ align:start position:0%
+transpose so what do we have we have the
+length squared of a X we have that's the
+
+ align:start position:0%
+length squared of a X we have that's the
+ 
+
+ align:start position:0%
+length squared of a X we have that's the
+column vector ax that's its row that's
+
+ align:start position:0%
+column vector ax that's its row that's
+ 
+
+ align:start position:0%
+column vector ax that's its row that's
+the row vector ax its length squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+length squared certainly greater than
+
+ align:start position:0%
+length squared certainly greater than
+ 
+
+ align:start position:0%
+length squared certainly greater than
+or possibly equal to zero so we have to
+
+ align:start position:0%
+or possibly equal to zero so we have to
+ 
+
+ align:start position:0%
+or possibly equal to zero so we have to
+deal with this little possibility could
+
+ align:start position:0%
+deal with this little possibility could
+ 
+
+ align:start position:0%
+deal with this little possibility could
+it be equal well when when could the
+
+ align:start position:0%
+it be equal well when when could the
+ 
+
+ align:start position:0%
+it be equal well when when could the
+length squared be zero only if the
+
+ align:start position:0%
+length squared be zero only if the
+ 
+
+ align:start position:0%
+length squared be zero only if the
+vector is zero right that's the only
+
+ align:start position:0%
+vector is zero right that's the only
+ 
+
+ align:start position:0%
+vector is zero right that's the only
+vector that has length squared zero so
+
+ align:start position:0%
+vector that has length squared zero so
+ 
+
+ align:start position:0%
+vector that has length squared zero so
+we have we would like to I would like to
+
+ align:start position:0%
+we have we would like to I would like to
+ 
+
+ align:start position:0%
+we have we would like to I would like to
+get that possibility out of there so I
+
+ align:start position:0%
+get that possibility out of there so I
+ 
+
+ align:start position:0%
+get that possibility out of there so I
+want to have ax not never never be zero
+
+ align:start position:0%
+want to have ax not never never be zero
+ 
+
+ align:start position:0%
+want to have ax not never never be zero
+except of course for the zero vector how
+
+ align:start position:0%
+except of course for the zero vector how
+ 
+
+ align:start position:0%
+except of course for the zero vector how
+do I assure that ax is never zero that
+
+ align:start position:0%
+do I assure that ax is never zero that
+ 
+
+ align:start position:0%
+do I assure that ax is never zero that
+in other words how do I sure that
+
+ align:start position:0%
+in other words how do I sure that
+ 
+
+ align:start position:0%
+in other words how do I sure that
+there's no null space of a the rank
+
+ align:start position:0%
+there's no null space of a the rank
+ 
+
+ align:start position:0%
+there's no null space of a the rank
+should be so now remember what's the
+
+ align:start position:0%
+should be so now remember what's the
+ 
+
+ align:start position:0%
+should be so now remember what's the
+rank when there's no null space by no
+
+ align:start position:0%
+rank when there's no null space by no
+ 
+
+ align:start position:0%
+rank when there's no null space by no
+null space you know what I mean only the
+
+ align:start position:0%
+null space you know what I mean only the
+ 
+
+ align:start position:0%
+null space you know what I mean only the
+zero vector in the null space so if I
+
+ align:start position:0%
+zero vector in the null space so if I
+ 
+
+ align:start position:0%
+zero vector in the null space so if I
+have a if I have an 11 by five matrix so
+
+ align:start position:0%
+have a if I have an 11 by five matrix so
+ 
+
+ align:start position:0%
+have a if I have an 11 by five matrix so
+it's got 11 rows 5 columns when is there
+
+ align:start position:0%
+it's got 11 rows 5 columns when is there
+ 
+
+ align:start position:0%
+it's got 11 rows 5 columns when is there
+no null space so the columns should be
+
+ align:start position:0%
+no null space so the columns should be
+ 
+
+ align:start position:0%
+no null space so the columns should be
+independent what's the rank and 5 rank
+
+ align:start position:0%
+independent what's the rank and 5 rank
+ 
+
+ align:start position:0%
+independent what's the rank and 5 rank
+and independent columns when so so if
+
+ align:start position:0%
+and independent columns when so so if
+ 
+
+ align:start position:0%
+and independent columns when so so if
+then I conclude yes positive definite
+
+ align:start position:0%
+then I conclude yes positive definite
+ 
+
+ align:start position:0%
+then I conclude yes positive definite
+and this was the assumption then a
+
+ align:start position:0%
+and this was the assumption then a
+ 
+
+ align:start position:0%
+and this was the assumption then a
+transpose a is invertible the the the
+
+ align:start position:0%
+transpose a is invertible the the the
+ 
+
+ align:start position:0%
+transpose a is invertible the the the
+least squares equations all work fine
+
+ align:start position:0%
+least squares equations all work fine
+ 
+
+ align:start position:0%
+least squares equations all work fine
+and more than that the the the matrix is
+
+ align:start position:0%
+and more than that the the the matrix is
+ 
+
+ align:start position:0%
+and more than that the the the matrix is
+even positive definite and I just just
+
+ align:start position:0%
+even positive definite and I just just
+ 
+
+ align:start position:0%
+even positive definite and I just just
+to say one comment about numerical
+
+ align:start position:0%
+to say one comment about numerical
+ 
+
+ align:start position:0%
+to say one comment about numerical
+things with a positive definite matrix
+
+ align:start position:0%
+things with a positive definite matrix
+ 
+
+ align:start position:0%
+things with a positive definite matrix
+you never have to do row exchanges you
+
+ align:start position:0%
+you never have to do row exchanges you
+ 
+
+ align:start position:0%
+you never have to do row exchanges you
+never run into unsuitably small numbers
+
+ align:start position:0%
+never run into unsuitably small numbers
+ 
+
+ align:start position:0%
+never run into unsuitably small numbers
+or zeros in the pivot position they're
+
+ align:start position:0%
+or zeros in the pivot position they're
+ 
+
+ align:start position:0%
+or zeros in the pivot position they're
+the right they're the great matrices to
+
+ align:start position:0%
+the right they're the great matrices to
+ 
+
+ align:start position:0%
+the right they're the great matrices to
+compute with and they're the great
+
+ align:start position:0%
+compute with and they're the great
+ 
+
+ align:start position:0%
+compute with and they're the great
+matrices to study so that's I wanted to
+
+ align:start position:0%
+matrices to study so that's I wanted to
+ 
+
+ align:start position:0%
+matrices to study so that's I wanted to
+take this first 10 min
+
+ align:start position:0%
+take this first 10 min
+ 
+
+ align:start position:0%
+take this first 10 min
+of grab the first 10 minutes away from
+
+ align:start position:0%
+of grab the first 10 minutes away from
+ 
+
+ align:start position:0%
+of grab the first 10 minutes away from
+similar matrices and continue with this
+
+ align:start position:0%
+similar matrices and continue with this
+ 
+
+ align:start position:0%
+similar matrices and continue with this
+much more with positive definite I'm
+
+ align:start position:0%
+much more with positive definite I'm
+ 
+
+ align:start position:0%
+much more with positive definite I'm
+really at this point now coming close to
+
+ align:start position:0%
+really at this point now coming close to
+ 
+
+ align:start position:0%
+really at this point now coming close to
+the end of the heart of linear algebra
+
+ align:start position:0%
+the end of the heart of linear algebra
+ 
+
+ align:start position:0%
+the end of the heart of linear algebra
+positive definiteness brought everything
+
+ align:start position:0%
+positive definiteness brought everything
+ 
+
+ align:start position:0%
+positive definiteness brought everything
+together similar matrices which is
+
+ align:start position:0%
+together similar matrices which is
+ 
+
+ align:start position:0%
+together similar matrices which is
+coming the rest of this hour is a key
+
+ align:start position:0%
+coming the rest of this hour is a key
+ 
+
+ align:start position:0%
+coming the rest of this hour is a key
+topic and please come on Monday Monday
+
+ align:start position:0%
+topic and please come on Monday Monday
+ 
+
+ align:start position:0%
+topic and please come on Monday Monday
+is about what's called the SVD singular
+
+ align:start position:0%
+is about what's called the SVD singular
+ 
+
+ align:start position:0%
+is about what's called the SVD singular
+values
+
+ align:start position:0%
+values
+ 
+
+ align:start position:0%
+values
+it's the has become a central fact in a
+
+ align:start position:0%
+it's the has become a central fact in a
+ 
+
+ align:start position:0%
+it's the has become a central fact in a
+central part of linear algebra I mean
+
+ align:start position:0%
+central part of linear algebra I mean
+ 
+
+ align:start position:0%
+central part of linear algebra I mean
+you could come after Monday also but
+
+ align:start position:0%
+you could come after Monday also but
+ 
+
+ align:start position:0%
+you could come after Monday also but
+Monday is that singular value thing is
+
+ align:start position:0%
+Monday is that singular value thing is
+ 
+
+ align:start position:0%
+Monday is that singular value thing is
+is has made it into this course ten
+
+ align:start position:0%
+is has made it into this course ten
+ 
+
+ align:start position:0%
+is has made it into this course ten
+years ago five years ago it wasn't in
+
+ align:start position:0%
+years ago five years ago it wasn't in
+ 
+
+ align:start position:0%
+years ago five years ago it wasn't in
+the course now it has to be okay so can
+
+ align:start position:0%
+the course now it has to be okay so can
+ 
+
+ align:start position:0%
+the course now it has to be okay so can
+I begin today's lecture proper with this
+
+ align:start position:0%
+I begin today's lecture proper with this
+ 
+
+ align:start position:0%
+I begin today's lecture proper with this
+idea of similar matrices this is what
+
+ align:start position:0%
+idea of similar matrices this is what
+ 
+
+ align:start position:0%
+idea of similar matrices this is what
+similar matrices mean so here let's
+
+ align:start position:0%
+similar matrices mean so here let's
+ 
+
+ align:start position:0%
+similar matrices mean so here let's
+start again I'll write it again so a and
+
+ align:start position:0%
+start again I'll write it again so a and
+ 
+
+ align:start position:0%
+start again I'll write it again so a and
+B are similar and B are now I'm these
+
+ align:start position:0%
+B are similar and B are now I'm these
+ 
+
+ align:start position:0%
+B are similar and B are now I'm these
+matrices I'm no longer talking about
+
+ align:start position:0%
+matrices I'm no longer talking about
+ 
+
+ align:start position:0%
+matrices I'm no longer talking about
+symmetric matrices in at least no longer
+
+ align:start position:0%
+symmetric matrices in at least no longer
+ 
+
+ align:start position:0%
+symmetric matrices in at least no longer
+expecting symmetric matrices I'm talking
+
+ align:start position:0%
+expecting symmetric matrices I'm talking
+ 
+
+ align:start position:0%
+expecting symmetric matrices I'm talking
+about two square matrices n by n a and B
+
+ align:start position:0%
+about two square matrices n by n a and B
+ 
+
+ align:start position:0%
+about two square matrices n by n a and B
+they're there n by n n by n matrices and
+
+ align:start position:0%
+they're there n by n n by n matrices and
+ 
+
+ align:start position:0%
+they're there n by n n by n matrices and
+I'm introducing this word similar so I'm
+
+ align:start position:0%
+I'm introducing this word similar so I'm
+ 
+
+ align:start position:0%
+I'm introducing this word similar so I'm
+gonna say what does it mean it means
+
+ align:start position:0%
+gonna say what does it mean it means
+ 
+
+ align:start position:0%
+gonna say what does it mean it means
+that they're connected in the way well
+
+ align:start position:0%
+that they're connected in the way well
+ 
+
+ align:start position:0%
+that they're connected in the way well
+in the way I've written here so let me
+
+ align:start position:0%
+in the way I've written here so let me
+ 
+
+ align:start position:0%
+in the way I've written here so let me
+rewrite it that means that means means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that for some matrix M which has to be
+
+ align:start position:0%
+that for some matrix M which has to be
+ 
+
+ align:start position:0%
+that for some matrix M which has to be
+invertible because you'll see that this
+
+ align:start position:0%
+invertible because you'll see that this
+ 
+
+ align:start position:0%
+invertible because you'll see that this
+one matrix is take the other matrix
+
+ align:start position:0%
+one matrix is take the other matrix
+ 
+
+ align:start position:0%
+one matrix is take the other matrix
+multiply on the right by M and on the
+
+ align:start position:0%
+multiply on the right by M and on the
+ 
+
+ align:start position:0%
+multiply on the right by M and on the
+left by M inverse so the question is why
+
+ align:start position:0%
+left by M inverse so the question is why
+ 
+
+ align:start position:0%
+left by M inverse so the question is why
+that combination what part of the answer
+
+ align:start position:0%
+that combination what part of the answer
+ 
+
+ align:start position:0%
+that combination what part of the answer
+you know already you remember we've done
+
+ align:start position:0%
+you know already you remember we've done
+ 
+
+ align:start position:0%
+you know already you remember we've done
+this we've taken a matrix a so let's do
+
+ align:start position:0%
+this we've taken a matrix a so let's do
+ 
+
+ align:start position:0%
+this we've taken a matrix a so let's do
+an example of similar suppose suppose a
+
+ align:start position:0%
+an example of similar suppose suppose a
+ 
+
+ align:start position:0%
+an example of similar suppose suppose a
+the matrix a suppose it has a full set
+
+ align:start position:0%
+the matrix a suppose it has a full set
+ 
+
+ align:start position:0%
+the matrix a suppose it has a full set
+of eigenvectors they go in this
+
+ align:start position:0%
+of eigenvectors they go in this
+ 
+
+ align:start position:0%
+of eigenvectors they go in this
+eigenvector matrix s then what was the
+
+ align:start position:0%
+eigenvector matrix s then what was the
+ 
+
+ align:start position:0%
+eigenvector matrix s then what was the
+main point of the whole the main
+
+ align:start position:0%
+main point of the whole the main
+ 
+
+ align:start position:0%
+main point of the whole the main
+calculation of the whole chapter was is
+
+ align:start position:0%
+calculation of the whole chapter was is
+ 
+
+ align:start position:0%
+calculation of the whole chapter was is
+use that eigenvector matrix s and it's
+
+ align:start position:0%
+use that eigenvector matrix s and it's
+ 
+
+ align:start position:0%
+use that eigenvector matrix s and it's
+inverse comes over there to produce the
+
+ align:start position:0%
+inverse comes over there to produce the
+ 
+
+ align:start position:0%
+inverse comes over there to produce the
+nicest possible matrix lambda nice as
+
+ align:start position:0%
+nicest possible matrix lambda nice as
+ 
+
+ align:start position:0%
+nicest possible matrix lambda nice as
+possible because it's diagonal so in our
+
+ align:start position:0%
+possible because it's diagonal so in our
+ 
+
+ align:start position:0%
+possible because it's diagonal so in our
+new language this is saying a is similar
+
+ align:start position:0%
+new language this is saying a is similar
+ 
+
+ align:start position:0%
+new language this is saying a is similar
+to lambda a is similar to lambda because
+
+ align:start position:0%
+to lambda a is similar to lambda because
+ 
+
+ align:start position:0%
+to lambda a is similar to lambda because
+there is a matrix and this particular
+
+ align:start position:0%
+there is a matrix and this particular
+ 
+
+ align:start position:0%
+there is a matrix and this particular
+there is an M and this particular M is
+
+ align:start position:0%
+there is an M and this particular M is
+ 
+
+ align:start position:0%
+there is an M and this particular M is
+this important guy this eigenvector
+
+ align:start position:0%
+this important guy this eigenvector
+ 
+
+ align:start position:0%
+this important guy this eigenvector
+matrix but if I take a different matrix
+
+ align:start position:0%
+matrix but if I take a different matrix
+ 
+
+ align:start position:0%
+matrix but if I take a different matrix
+M and I look at M inverse am the result
+
+ align:start position:0%
+M and I look at M inverse am the result
+ 
+
+ align:start position:0%
+M and I look at M inverse am the result
+won't come out diagonal but it'll come
+
+ align:start position:0%
+won't come out diagonal but it'll come
+ 
+
+ align:start position:0%
+won't come out diagonal but it'll come
+out a matrix B that's similar to a do
+
+ align:start position:0%
+out a matrix B that's similar to a do
+ 
+
+ align:start position:0%
+out a matrix B that's similar to a do
+you see that I'm what I'm doing is like
+
+ align:start position:0%
+you see that I'm what I'm doing is like
+ 
+
+ align:start position:0%
+you see that I'm what I'm doing is like
+I'm putting
+
+ align:start position:0%
+I'm putting
+ 
+
+ align:start position:0%
+I'm putting
+these matrices into families all of
+
+ align:start position:0%
+these matrices into families all of
+ 
+
+ align:start position:0%
+these matrices into families all of
+matrices in one in the in the family are
+
+ align:start position:0%
+matrices in one in the in the family are
+ 
+
+ align:start position:0%
+matrices in one in the in the family are
+similar to each other they're all each
+
+ align:start position:0%
+similar to each other they're all each
+ 
+
+ align:start position:0%
+similar to each other they're all each
+one in this family is connected to each
+
+ align:start position:0%
+one in this family is connected to each
+ 
+
+ align:start position:0%
+one in this family is connected to each
+other one by some matrix M and the like
+
+ align:start position:0%
+other one by some matrix M and the like
+ 
+
+ align:start position:0%
+other one by some matrix M and the like
+the outstanding member of the family is
+
+ align:start position:0%
+the outstanding member of the family is
+ 
+
+ align:start position:0%
+the outstanding member of the family is
+the diagonal guy I mean that's the
+
+ align:start position:0%
+the diagonal guy I mean that's the
+ 
+
+ align:start position:0%
+the diagonal guy I mean that's the
+simplest neatest matrix in this family
+
+ align:start position:0%
+simplest neatest matrix in this family
+ 
+
+ align:start position:0%
+simplest neatest matrix in this family
+of all the matrices that are similar to
+
+ align:start position:0%
+of all the matrices that are similar to
+ 
+
+ align:start position:0%
+of all the matrices that are similar to
+a the best one is lambda but there are
+
+ align:start position:0%
+a the best one is lambda but there are
+ 
+
+ align:start position:0%
+a the best one is lambda but there are
+lots of others because I can take
+
+ align:start position:0%
+lots of others because I can take
+ 
+
+ align:start position:0%
+lots of others because I can take
+different instead of s I can take any
+
+ align:start position:0%
+different instead of s I can take any
+ 
+
+ align:start position:0%
+different instead of s I can take any
+old matrix m and the old invertible
+
+ align:start position:0%
+old matrix m and the old invertible
+ 
+
+ align:start position:0%
+old matrix m and the old invertible
+matrix and and do it I better do an
+
+ align:start position:0%
+matrix and and do it I better do an
+ 
+
+ align:start position:0%
+matrix and and do it I better do an
+example ok suppose I take a as the
+
+ align:start position:0%
+example ok suppose I take a as the
+ 
+
+ align:start position:0%
+example ok suppose I take a as the
+matrix 2 1 1 2 okay do you know the
+
+ align:start position:0%
+matrix 2 1 1 2 okay do you know the
+ 
+
+ align:start position:0%
+matrix 2 1 1 2 okay do you know the
+eigenvalue matrix for that the
+
+ align:start position:0%
+eigenvalue matrix for that the
+ 
+
+ align:start position:0%
+eigenvalue matrix for that the
+eigenvalues of that matrix are well
+
+ align:start position:0%
+eigenvalues of that matrix are well
+ 
+
+ align:start position:0%
+eigenvalues of that matrix are well
+three and one so that and and the
+
+ align:start position:0%
+three and one so that and and the
+ 
+
+ align:start position:0%
+three and one so that and and the
+eigenvectors would be easy to find so
+
+ align:start position:0%
+eigenvectors would be easy to find so
+ 
+
+ align:start position:0%
+eigenvectors would be easy to find so
+this matrix is similar to this one but
+
+ align:start position:0%
+this matrix is similar to this one but
+ 
+
+ align:start position:0%
+this matrix is similar to this one but
+my point is like but also I can also
+
+ align:start position:0%
+my point is like but also I can also
+ 
+
+ align:start position:0%
+my point is like but also I can also
+take my matrix 2 1 1 2 I could multiply
+
+ align:start position:0%
+take my matrix 2 1 1 2 I could multiply
+ 
+
+ align:start position:0%
+take my matrix 2 1 1 2 I could multiply
+it by let's see what I'm just gonna cook
+
+ align:start position:0%
+it by let's see what I'm just gonna cook
+ 
+
+ align:start position:0%
+it by let's see what I'm just gonna cook
+up a matrix M here let me just invent 1
+
+ align:start position:0%
+up a matrix M here let me just invent 1
+ 
+
+ align:start position:0%
+up a matrix M here let me just invent 1
+4 1 0 and over here I'll put M inverse
+
+ align:start position:0%
+4 1 0 and over here I'll put M inverse
+ 
+
+ align:start position:0%
+4 1 0 and over here I'll put M inverse
+and because I happen to make that
+
+ align:start position:0%
+and because I happen to make that
+ 
+
+ align:start position:0%
+and because I happen to make that
+triangular I know that its inverse is
+
+ align:start position:0%
+triangular I know that its inverse is
+ 
+
+ align:start position:0%
+triangular I know that its inverse is
+that right so there's MN verse am that's
+
+ align:start position:0%
+that right so there's MN verse am that's
+ 
+
+ align:start position:0%
+that right so there's MN verse am that's
+going to produce some matrix oh well
+
+ align:start position:0%
+going to produce some matrix oh well
+ 
+
+ align:start position:0%
+going to produce some matrix oh well
+I've got to do the multiplication so
+
+ align:start position:0%
+I've got to do the multiplication so
+ 
+
+ align:start position:0%
+I've got to do the multiplication so
+hang on a second I'll just copy that 1
+
+ align:start position:0%
+hang on a second I'll just copy that 1
+ 
+
+ align:start position:0%
+hang on a second I'll just copy that 1
+minus 4 0 1 and multiply these guys so
+
+ align:start position:0%
+minus 4 0 1 and multiply these guys so
+ 
+
+ align:start position:0%
+minus 4 0 1 and multiply these guys so
+I'm getting 2 9 1
+
+ align:start position:0%
+I'm getting 2 9 1
+ 
+
+ align:start position:0%
+I'm getting 2 9 1
+six I think can you check it as I go
+
+ align:start position:0%
+six I think can you check it as I go
+ 
+
+ align:start position:0%
+six I think can you check it as I go
+because you you see I'm just so that's
+
+ align:start position:0%
+because you you see I'm just so that's
+ 
+
+ align:start position:0%
+because you you see I'm just so that's
+2-4 I'm getting a minus to 9 minus 24 is
+
+ align:start position:0%
+2-4 I'm getting a minus to 9 minus 24 is
+ 
+
+ align:start position:0%
+2-4 I'm getting a minus to 9 minus 24 is
+a minus 15 my god how did I get this and
+
+ align:start position:0%
+a minus 15 my god how did I get this and
+ 
+
+ align:start position:0%
+a minus 15 my god how did I get this and
+that's probably one and six so there's
+
+ align:start position:0%
+that's probably one and six so there's
+ 
+
+ align:start position:0%
+that's probably one and six so there's
+my matrix B and there is my matrix
+
+ align:start position:0%
+my matrix B and there is my matrix
+ 
+
+ align:start position:0%
+my matrix B and there is my matrix
+lambda there's my matrix a and my point
+
+ align:start position:0%
+lambda there's my matrix a and my point
+ 
+
+ align:start position:0%
+lambda there's my matrix a and my point
+is these are all similar matrices they
+
+ align:start position:0%
+is these are all similar matrices they
+ 
+
+ align:start position:0%
+is these are all similar matrices they
+all have something in common besides
+
+ align:start position:0%
+all have something in common besides
+ 
+
+ align:start position:0%
+all have something in common besides
+being just two by two they have
+
+ align:start position:0%
+being just two by two they have
+ 
+
+ align:start position:0%
+being just two by two they have
+something in common and that and what is
+
+ align:start position:0%
+something in common and that and what is
+ 
+
+ align:start position:0%
+something in common and that and what is
+it what's the point about two matrices
+
+ align:start position:0%
+it what's the point about two matrices
+ 
+
+ align:start position:0%
+it what's the point about two matrices
+that are built out of the B is built out
+
+ align:start position:0%
+that are built out of the B is built out
+ 
+
+ align:start position:0%
+that are built out of the B is built out
+of M inverse am what is it that a and B
+
+ align:start position:0%
+of M inverse am what is it that a and B
+ 
+
+ align:start position:0%
+of M inverse am what is it that a and B
+have in common that's the main tonight
+
+ align:start position:0%
+have in common that's the main tonight
+ 
+
+ align:start position:0%
+have in common that's the main tonight
+races they have the same eigenvalues
+
+ align:start position:0%
+races they have the same eigenvalues
+ 
+
+ align:start position:0%
+races they have the same eigenvalues
+this is this chapter is about
+
+ align:start position:0%
+this is this chapter is about
+ 
+
+ align:start position:0%
+this is this chapter is about
+eigenvalues and that's why we're
+
+ align:start position:0%
+eigenvalues and that's why we're
+ 
+
+ align:start position:0%
+eigenvalues and that's why we're
+interested in this family of matrices
+
+ align:start position:0%
+interested in this family of matrices
+ 
+
+ align:start position:0%
+interested in this family of matrices
+that have the same eigenvalues what are
+
+ align:start position:0%
+that have the same eigenvalues what are
+ 
+
+ align:start position:0%
+that have the same eigenvalues what are
+the eigenvalues in this example lambda
+
+ align:start position:0%
+the eigenvalues in this example lambda
+ 
+
+ align:start position:0%
+the eigenvalues in this example lambda
+the eigenvalues of that I could compute
+
+ align:start position:0%
+the eigenvalues of that I could compute
+ 
+
+ align:start position:0%
+the eigenvalues of that I could compute
+the eigenvalues of that I can compute
+
+ align:start position:0%
+the eigenvalues of that I can compute
+ 
+
+ align:start position:0%
+the eigenvalues of that I can compute
+really fast so the eigenvalues are 3 & 1
+
+ align:start position:0%
+really fast so the eigenvalues are 3 & 1
+ 
+
+ align:start position:0%
+really fast so the eigenvalues are 3 & 1
+for this for sure now did we do you see
+
+ align:start position:0%
+for this for sure now did we do you see
+ 
+
+ align:start position:0%
+for this for sure now did we do you see
+why the all you guys are 3 & 1 for that
+
+ align:start position:0%
+why the all you guys are 3 & 1 for that
+ 
+
+ align:start position:0%
+why the all you guys are 3 & 1 for that
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+if I click if I tell you the eigenvalues
+
+ align:start position:0%
+if I click if I tell you the eigenvalues
+ 
+
+ align:start position:0%
+if I click if I tell you the eigenvalues
+are 3 & 1
+
+ align:start position:0%
+are 3 & 1
+ 
+
+ align:start position:0%
+are 3 & 1
+you you you quickly process the trace
+
+ align:start position:0%
+you you you quickly process the trace
+ 
+
+ align:start position:0%
+you you you quickly process the trace
+which is then for quick agrees with 4
+
+ align:start position:0%
+which is then for quick agrees with 4
+ 
+
+ align:start position:0%
+which is then for quick agrees with 4
+and you process the determinant 3 times
+
+ align:start position:0%
+and you process the determinant 3 times
+ 
+
+ align:start position:0%
+and you process the determinant 3 times
+1 the determinant is 3 and you say yes
+
+ align:start position:0%
+1 the determinant is 3 and you say yes
+ 
+
+ align:start position:0%
+1 the determinant is 3 and you say yes
+it's right now I'm hoping that the
+
+ align:start position:0%
+it's right now I'm hoping that the
+ 
+
+ align:start position:0%
+it's right now I'm hoping that the
+eigenvalues of this thing are 3 & 1
+
+ align:start position:0%
+eigenvalues of this thing are 3 & 1
+ 
+
+ align:start position:0%
+eigenvalues of this thing are 3 & 1
+may I process the trace and the
+
+ align:start position:0%
+may I process the trace and the
+ 
+
+ align:start position:0%
+may I process the trace and the
+determinant for that one
+
+ align:start position:0%
+determinant for that one
+ 
+
+ align:start position:0%
+determinant for that one
+what's the trace here
+
+ align:start position:0%
+what's the trace here
+ 
+
+ align:start position:0%
+what's the trace here
+the trace of this matrix is 4 minus 2
+
+ align:start position:0%
+the trace of this matrix is 4 minus 2
+ 
+
+ align:start position:0%
+the trace of this matrix is 4 minus 2
+and 6 and that's what it should be
+
+ align:start position:0%
+and 6 and that's what it should be
+ 
+
+ align:start position:0%
+and 6 and that's what it should be
+what's the determinant minus 12 plus 15
+
+ align:start position:0%
+what's the determinant minus 12 plus 15
+ 
+
+ align:start position:0%
+what's the determinant minus 12 plus 15
+is 3 the determinant is 3 the
+
+ align:start position:0%
+is 3 the determinant is 3 the
+ 
+
+ align:start position:0%
+is 3 the determinant is 3 the
+eigenvalues of that matrix are also 3
+
+ align:start position:0%
+eigenvalues of that matrix are also 3
+ 
+
+ align:start position:0%
+eigenvalues of that matrix are also 3
+and 1 and you see I created this matrix
+
+ align:start position:0%
+and 1 and you see I created this matrix
+ 
+
+ align:start position:0%
+and 1 and you see I created this matrix
+just like I just took any M like one
+
+ align:start position:0%
+just like I just took any M like one
+ 
+
+ align:start position:0%
+just like I just took any M like one
+that popped into my head and computed M
+
+ align:start position:0%
+that popped into my head and computed M
+ 
+
+ align:start position:0%
+that popped into my head and computed M
+inverse am got that matrix it didn't
+
+ align:start position:0%
+inverse am got that matrix it didn't
+ 
+
+ align:start position:0%
+inverse am got that matrix it didn't
+look anything special but it's it's like
+
+ align:start position:0%
+look anything special but it's it's like
+ 
+
+ align:start position:0%
+look anything special but it's it's like
+a itself it has those eigenvalues 3 & 1
+
+ align:start position:0%
+a itself it has those eigenvalues 3 & 1
+ 
+
+ align:start position:0%
+a itself it has those eigenvalues 3 & 1
+so that's the main fact and let me write
+
+ align:start position:0%
+so that's the main fact and let me write
+ 
+
+ align:start position:0%
+so that's the main fact and let me write
+it down similar matrices have the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eigen values so I'll just put that as a
+
+ align:start position:0%
+eigen values so I'll just put that as a
+ 
+
+ align:start position:0%
+eigen values so I'll just put that as a
+as an important point and think why why
+
+ align:start position:0%
+as an important point and think why why
+ 
+
+ align:start position:0%
+as an important point and think why why
+is that so so that's what that family of
+
+ align:start position:0%
+is that so so that's what that family of
+ 
+
+ align:start position:0%
+is that so so that's what that family of
+matrices is the matrices that are
+
+ align:start position:0%
+matrices is the matrices that are
+ 
+
+ align:start position:0%
+matrices is the matrices that are
+similar to this a here are all the
+
+ align:start position:0%
+similar to this a here are all the
+ 
+
+ align:start position:0%
+similar to this a here are all the
+matrices with eigenvalues 3 and 1 every
+
+ align:start position:0%
+matrices with eigenvalues 3 and 1 every
+ 
+
+ align:start position:0%
+matrices with eigenvalues 3 and 1 every
+matrix with eigenvalues 3 & 1 there's
+
+ align:start position:0%
+matrix with eigenvalues 3 & 1 there's
+ 
+
+ align:start position:0%
+matrix with eigenvalues 3 & 1 there's
+some M that connects this guy 2 to the
+
+ align:start position:0%
+some M that connects this guy 2 to the
+ 
+
+ align:start position:0%
+some M that connects this guy 2 to the
+one you think of and then of course the
+
+ align:start position:0%
+one you think of and then of course the
+ 
+
+ align:start position:0%
+one you think of and then of course the
+most special guy in the whole family is
+
+ align:start position:0%
+most special guy in the whole family is
+ 
+
+ align:start position:0%
+most special guy in the whole family is
+the diagonal one with eigenvalues three
+
+ align:start position:0%
+the diagonal one with eigenvalues three
+ 
+
+ align:start position:0%
+the diagonal one with eigenvalues three
+and one sitting there on the diagonal
+
+ align:start position:0%
+and one sitting there on the diagonal
+ 
+
+ align:start position:0%
+and one sitting there on the diagonal
+but also I could find me tell me just a
+
+ align:start position:0%
+but also I could find me tell me just a
+ 
+
+ align:start position:0%
+but also I could find me tell me just a
+couple more members of the family
+
+ align:start position:0%
+couple more members of the family
+ 
+
+ align:start position:0%
+couple more members of the family
+another another tell me another matrix
+
+ align:start position:0%
+another another tell me another matrix
+ 
+
+ align:start position:0%
+another another tell me another matrix
+that has eigenvalues three and one well
+
+ align:start position:0%
+that has eigenvalues three and one well
+ 
+
+ align:start position:0%
+that has eigenvalues three and one well
+let's see I oh I'll just make it
+
+ align:start position:0%
+let's see I oh I'll just make it
+ 
+
+ align:start position:0%
+let's see I oh I'll just make it
+triangular that's in the family there is
+
+ align:start position:0%
+triangular that's in the family there is
+ 
+
+ align:start position:0%
+triangular that's in the family there is
+some M that that connects to this one
+
+ align:start position:0%
+some M that that connects to this one
+ 
+
+ align:start position:0%
+some M that that connects to this one
+and and and also this there's some
+
+ align:start position:0%
+and and and also this there's some
+ 
+
+ align:start position:0%
+and and and also this there's some
+matrix M
+
+ align:start position:0%
+matrix M
+ 
+
+ align:start position:0%
+matrix M
+so that M inverse a.m. comes out to be
+
+ align:start position:0%
+so that M inverse a.m. comes out to be
+ 
+
+ align:start position:0%
+so that M inverse a.m. comes out to be
+that there's a whole family here and
+
+ align:start position:0%
+that there's a whole family here and
+ 
+
+ align:start position:0%
+that there's a whole family here and
+they all share the same eigenvalues so
+
+ align:start position:0%
+they all share the same eigenvalues so
+ 
+
+ align:start position:0%
+they all share the same eigenvalues so
+why is that okay I'm gonna start the
+
+ align:start position:0%
+why is that okay I'm gonna start the
+ 
+
+ align:start position:0%
+why is that okay I'm gonna start the
+only possibility is to start with ax
+
+ align:start position:0%
+only possibility is to start with ax
+ 
+
+ align:start position:0%
+only possibility is to start with ax
+equal lambda X okay so suppose a has the
+
+ align:start position:0%
+equal lambda X okay so suppose a has the
+ 
+
+ align:start position:0%
+equal lambda X okay so suppose a has the
+eigenvalue lambda now I want to get B in
+
+ align:start position:0%
+eigenvalue lambda now I want to get B in
+ 
+
+ align:start position:0%
+eigenvalue lambda now I want to get B in
+the picture here somehow
+
+ align:start position:0%
+the picture here somehow
+ 
+
+ align:start position:0%
+the picture here somehow
+you remember B is M inverse am let's
+
+ align:start position:0%
+you remember B is M inverse am let's
+ 
+
+ align:start position:0%
+you remember B is M inverse am let's
+just remember that over here B is M
+
+ align:start position:0%
+just remember that over here B is M
+ 
+
+ align:start position:0%
+just remember that over here B is M
+inverse am and I want to see its
+
+ align:start position:0%
+inverse am and I want to see its
+ 
+
+ align:start position:0%
+inverse am and I want to see its
+eigenvalues how am I going to get M
+
+ align:start position:0%
+eigenvalues how am I going to get M
+ 
+
+ align:start position:0%
+eigenvalues how am I going to get M
+inverse a.m. into this equation let me
+
+ align:start position:0%
+inverse a.m. into this equation let me
+ 
+
+ align:start position:0%
+inverse a.m. into this equation let me
+that may just sort of do it I'll put in
+
+ align:start position:0%
+that may just sort of do it I'll put in
+ 
+
+ align:start position:0%
+that may just sort of do it I'll put in
+M times an M inverse in there right that
+
+ align:start position:0%
+M times an M inverse in there right that
+ 
+
+ align:start position:0%
+M times an M inverse in there right that
+was I haven't changed the left-hand side
+
+ align:start position:0%
+was I haven't changed the left-hand side
+ 
+
+ align:start position:0%
+was I haven't changed the left-hand side
+so I better not change the right-hand
+
+ align:start position:0%
+so I better not change the right-hand
+ 
+
+ align:start position:0%
+so I better not change the right-hand
+side so everybody's okay so far I just
+
+ align:start position:0%
+side so everybody's okay so far I just
+ 
+
+ align:start position:0%
+side so everybody's okay so far I just
+put in there see I want to get it so now
+
+ align:start position:0%
+put in there see I want to get it so now
+ 
+
+ align:start position:0%
+put in there see I want to get it so now
+I'll multiply on the left by M inverse I
+
+ align:start position:0%
+I'll multiply on the left by M inverse I
+ 
+
+ align:start position:0%
+I'll multiply on the left by M inverse I
+have to do the same to this side and
+
+ align:start position:0%
+have to do the same to this side and
+ 
+
+ align:start position:0%
+have to do the same to this side and
+that number lambda is just a number so
+
+ align:start position:0%
+that number lambda is just a number so
+ 
+
+ align:start position:0%
+that number lambda is just a number so
+it factors out in the front so what I
+
+ align:start position:0%
+it factors out in the front so what I
+ 
+
+ align:start position:0%
+it factors out in the front so what I
+had here is that this was safe I did the
+
+ align:start position:0%
+had here is that this was safe I did the
+ 
+
+ align:start position:0%
+had here is that this was safe I did the
+same thing to both sides and now I've
+
+ align:start position:0%
+same thing to both sides and now I've
+ 
+
+ align:start position:0%
+same thing to both sides and now I've
+got B there's B that's B times this
+
+ align:start position:0%
+got B there's B that's B times this
+ 
+
+ align:start position:0%
+got B there's B that's B times this
+vector M inverse X is equal to lambda
+
+ align:start position:0%
+vector M inverse X is equal to lambda
+ 
+
+ align:start position:0%
+vector M inverse X is equal to lambda
+times this vector M inverse X so what
+
+ align:start position:0%
+times this vector M inverse X so what
+ 
+
+ align:start position:0%
+times this vector M inverse X so what
+have I learned I've learned that B times
+
+ align:start position:0%
+have I learned I've learned that B times
+ 
+
+ align:start position:0%
+have I learned I've learned that B times
+some vector is lambda times that vector
+
+ align:start position:0%
+some vector is lambda times that vector
+ 
+
+ align:start position:0%
+some vector is lambda times that vector
+I've learned that lambda is an
+
+ align:start position:0%
+I've learned that lambda is an
+ 
+
+ align:start position:0%
+I've learned that lambda is an
+eigenvalue of B also so this is if so
+
+ align:start position:0%
+eigenvalue of B also so this is if so
+ 
+
+ align:start position:0%
+eigenvalue of B also so this is if so
+this is if lambda is an eigen value of a
+
+ align:start position:0%
+this is if lambda is an eigen value of a
+ 
+
+ align:start position:0%
+this is if lambda is an eigen value of a
+then I can write it this way and I
+
+ align:start position:0%
+then I can write it this way and I
+ 
+
+ align:start position:0%
+then I can write it this way and I
+discover that lambda is an eigen value
+
+ align:start position:0%
+discover that lambda is an eigen value
+ 
+
+ align:start position:0%
+discover that lambda is an eigen value
+of B that's the end of the proof the
+
+ align:start position:0%
+of B that's the end of the proof the
+ 
+
+ align:start position:0%
+of B that's the end of the proof the
+eigenvector
+
+ align:start position:0%
+eigenvector
+ 
+
+ align:start position:0%
+eigenvector
+didn't stay to say of course I don't
+
+ align:start position:0%
+didn't stay to say of course I don't
+ 
+
+ align:start position:0%
+didn't stay to say of course I don't
+expect the eigenvectors to say the same
+
+ align:start position:0%
+expect the eigenvectors to say the same
+ 
+
+ align:start position:0%
+expect the eigenvectors to say the same
+if all the eigenvalues are the same and
+
+ align:start position:0%
+if all the eigenvalues are the same and
+ 
+
+ align:start position:0%
+if all the eigenvalues are the same and
+all the eigenvectors are the same then
+
+ align:start position:0%
+all the eigenvectors are the same then
+ 
+
+ align:start position:0%
+all the eigenvectors are the same then
+probably the matrix is to say here the
+
+ align:start position:0%
+probably the matrix is to say here the
+ 
+
+ align:start position:0%
+probably the matrix is to say here the
+eigenvector changes so the eigenvector
+
+ align:start position:0%
+eigenvector changes so the eigenvector
+ 
+
+ align:start position:0%
+eigenvector changes so the eigenvector
+so the point is then the eigen vector of
+
+ align:start position:0%
+so the point is then the eigen vector of
+ 
+
+ align:start position:0%
+so the point is then the eigen vector of
+V of B is M inverse times the
+
+ align:start position:0%
+V of B is M inverse times the
+ 
+
+ align:start position:0%
+V of B is M inverse times the
+eigenvector of a okay
+
+ align:start position:0%
+eigenvector of a okay
+ 
+
+ align:start position:0%
+eigenvector of a okay
+that's all that this says here the
+
+ align:start position:0%
+that's all that this says here the
+ 
+
+ align:start position:0%
+that's all that this says here the
+eigenvector of a was X and so the M
+
+ align:start position:0%
+eigenvector of a was X and so the M
+ 
+
+ align:start position:0%
+eigenvector of a was X and so the M
+inverse similar matrices then have the
+
+ align:start position:0%
+inverse similar matrices then have the
+ 
+
+ align:start position:0%
+inverse similar matrices then have the
+same eigen values and their eigenvectors
+
+ align:start position:0%
+same eigen values and their eigenvectors
+ 
+
+ align:start position:0%
+same eigen values and their eigenvectors
+are just moved around of course that's
+
+ align:start position:0%
+are just moved around of course that's
+ 
+
+ align:start position:0%
+are just moved around of course that's
+what we that's what happened way back in
+
+ align:start position:0%
+what we that's what happened way back in
+ 
+
+ align:start position:0%
+what we that's what happened way back in
+the most important similar matrices are
+
+ align:start position:0%
+the most important similar matrices are
+ 
+
+ align:start position:0%
+the most important similar matrices are
+to diagonalize so what was the point
+
+ align:start position:0%
+to diagonalize so what was the point
+ 
+
+ align:start position:0%
+to diagonalize so what was the point
+when we diagonalized the eigenvalues
+
+ align:start position:0%
+when we diagonalized the eigenvalues
+ 
+
+ align:start position:0%
+when we diagonalized the eigenvalues
+stayed the same of course three and one
+
+ align:start position:0%
+stayed the same of course three and one
+ 
+
+ align:start position:0%
+stayed the same of course three and one
+what about the eigenvectors the
+
+ align:start position:0%
+what about the eigenvectors the
+ 
+
+ align:start position:0%
+what about the eigenvectors the
+eigenvectors were whatever they were for
+
+ align:start position:0%
+eigenvectors were whatever they were for
+ 
+
+ align:start position:0%
+eigenvectors were whatever they were for
+the matrix a but then what were the
+
+ align:start position:0%
+the matrix a but then what were the
+ 
+
+ align:start position:0%
+the matrix a but then what were the
+eigenvectors for the diagonal matrix
+
+ align:start position:0%
+eigenvectors for the diagonal matrix
+ 
+
+ align:start position:0%
+eigenvectors for the diagonal matrix
+they're just what are the eigenvectors
+
+ align:start position:0%
+they're just what are the eigenvectors
+ 
+
+ align:start position:0%
+they're just what are the eigenvectors
+of a diagonal matrix they're just 1 0
+
+ align:start position:0%
+of a diagonal matrix they're just 1 0
+ 
+
+ align:start position:0%
+of a diagonal matrix they're just 1 0
+and 0 1 so this step made the
+
+ align:start position:0%
+and 0 1 so this step made the
+ 
+
+ align:start position:0%
+and 0 1 so this step made the
+eigenvectors nice didn't change the
+
+ align:start position:0%
+eigenvectors nice didn't change the
+ 
+
+ align:start position:0%
+eigenvectors nice didn't change the
+eigen values and every time we don't
+
+ align:start position:0%
+eigen values and every time we don't
+ 
+
+ align:start position:0%
+eigen values and every time we don't
+change the eigen values same eigenvalues
+
+ align:start position:0%
+change the eigen values same eigenvalues
+ 
+
+ align:start position:0%
+change the eigen values same eigenvalues
+ok now so I've got all these matrices in
+
+ align:start position:0%
+ok now so I've got all these matrices in
+ 
+
+ align:start position:0%
+ok now so I've got all these matrices in
+I've got this family of matrices with
+
+ align:start position:0%
+I've got this family of matrices with
+ 
+
+ align:start position:0%
+I've got this family of matrices with
+eigenvalues 3 and 1 fine
+
+ align:start position:0%
+eigenvalues 3 and 1 fine
+ 
+
+ align:start position:0%
+eigenvalues 3 and 1 fine
+that's a nice family it's it's nice
+
+ align:start position:0%
+that's a nice family it's it's nice
+ 
+
+ align:start position:0%
+that's a nice family it's it's nice
+because those two eigenvalues are
+
+ align:start position:0%
+because those two eigenvalues are
+ 
+
+ align:start position:0%
+because those two eigenvalues are
+different I now have to to get into that
+
+ align:start position:0%
+different I now have to to get into that
+ 
+
+ align:start position:0%
+different I now have to to get into that
+into the less happy possibility that the
+
+ align:start position:0%
+into the less happy possibility that the
+ 
+
+ align:start position:0%
+into the less happy possibility that the
+two eigenvalues could be
+
+ align:start position:0%
+two eigenvalues could be
+ 
+
+ align:start position:0%
+two eigenvalues could be
+same and then it's a little trickier
+
+ align:start position:0%
+same and then it's a little trickier
+ 
+
+ align:start position:0%
+same and then it's a little trickier
+because you remember when two
+
+ align:start position:0%
+because you remember when two
+ 
+
+ align:start position:0%
+because you remember when two
+eigenvalues are the same what's the bad
+
+ align:start position:0%
+eigenvalues are the same what's the bad
+ 
+
+ align:start position:0%
+eigenvalues are the same what's the bad
+possibility that there might not be
+
+ align:start position:0%
+possibility that there might not be
+ 
+
+ align:start position:0%
+possibility that there might not be
+enough a full set of eigenvectors and we
+
+ align:start position:0%
+enough a full set of eigenvectors and we
+ 
+
+ align:start position:0%
+enough a full set of eigenvectors and we
+might not be able to diagonalize so i
+
+ align:start position:0%
+might not be able to diagonalize so i
+ 
+
+ align:start position:0%
+might not be able to diagonalize so i
+need to discuss
+
+ align:start position:0%
+need to discuss
+ 
+
+ align:start position:0%
+need to discuss
+the bad case so the bad can I just say
+
+ align:start position:0%
+the bad case so the bad can I just say
+ 
+
+ align:start position:0%
+the bad case so the bad can I just say
+bad if lambda 1 equals lambda 2 then the
+
+ align:start position:0%
+bad if lambda 1 equals lambda 2 then the
+ 
+
+ align:start position:0%
+bad if lambda 1 equals lambda 2 then the
+matrix might not be diagonalizable
+
+ align:start position:0%
+matrix might not be diagonalizable
+ 
+
+ align:start position:0%
+matrix might not be diagonalizable
+suppose lambda 1 equals lambda 2 equals
+
+ align:start position:0%
+suppose lambda 1 equals lambda 2 equals
+ 
+
+ align:start position:0%
+suppose lambda 1 equals lambda 2 equals
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+say now if I look at the family of
+
+ align:start position:0%
+say now if I look at the family of
+ 
+
+ align:start position:0%
+say now if I look at the family of
+matrices with eigenvalues 4 and 4 well
+
+ align:start position:0%
+matrices with eigenvalues 4 and 4 well
+ 
+
+ align:start position:0%
+matrices with eigenvalues 4 and 4 well
+one possibility occurs to me one family
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with eigenvalues 4 and 4 has this matrix
+
+ align:start position:0%
+with eigenvalues 4 and 4 has this matrix
+ 
+
+ align:start position:0%
+with eigenvalues 4 and 4 has this matrix
+in it 4 times the identity then another
+
+ align:start position:0%
+in it 4 times the identity then another
+ 
+
+ align:start position:0%
+in it 4 times the identity then another
+but now I want to ask also about the
+
+ align:start position:0%
+but now I want to ask also about the
+ 
+
+ align:start position:0%
+but now I want to ask also about the
+matrix 4 4 1 0 and my point here here's
+
+ align:start position:0%
+matrix 4 4 1 0 and my point here here's
+ 
+
+ align:start position:0%
+matrix 4 4 1 0 and my point here here's
+the whole point of this of this bad
+
+ align:start position:0%
+the whole point of this of this bad
+ 
+
+ align:start position:0%
+the whole point of this of this bad
+stuff is that this guy is not in the
+
+ align:start position:0%
+stuff is that this guy is not in the
+ 
+
+ align:start position:0%
+stuff is that this guy is not in the
+same family with that one the family of
+
+ align:start position:0%
+same family with that one the family of
+ 
+
+ align:start position:0%
+same family with that one the family of
+matrices that have eigenvalues 4 & 4 is
+
+ align:start position:0%
+matrices that have eigenvalues 4 & 4 is
+ 
+
+ align:start position:0%
+matrices that have eigenvalues 4 & 4 is
+two families there's this total loner
+
+ align:start position:0%
+two families there's this total loner
+ 
+
+ align:start position:0%
+two families there's this total loner
+here who's in a family off right just by
+
+ align:start position:0%
+here who's in a family off right just by
+ 
+
+ align:start position:0%
+here who's in a family off right just by
+himself and all the others are in with
+
+ align:start position:0%
+himself and all the others are in with
+ 
+
+ align:start position:0%
+himself and all the others are in with
+this guy so the the big family includes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one
+
+ align:start position:0%
+this one
+ 
+
+ align:start position:0%
+this one
+includes a whole lot of other matrices
+
+ align:start position:0%
+includes a whole lot of other matrices
+ 
+
+ align:start position:0%
+includes a whole lot of other matrices
+all in fact in this 2x2 case it you see
+
+ align:start position:0%
+all in fact in this 2x2 case it you see
+ 
+
+ align:start position:0%
+all in fact in this 2x2 case it you see
+where what do I mean what's the what am
+
+ align:start position:0%
+where what do I mean what's the what am
+ 
+
+ align:start position:0%
+where what do I mean what's the what am
+I using this word family by in in a
+
+ align:start position:0%
+I using this word family by in in a
+ 
+
+ align:start position:0%
+I using this word family by in in a
+family I mean they're similar so my
+
+ align:start position:0%
+family I mean they're similar so my
+ 
+
+ align:start position:0%
+family I mean they're similar so my
+point is that the only matrix that's
+
+ align:start position:0%
+point is that the only matrix that's
+ 
+
+ align:start position:0%
+point is that the only matrix that's
+similar to this is itself the only
+
+ align:start position:0%
+similar to this is itself the only
+ 
+
+ align:start position:0%
+similar to this is itself the only
+matrix that's similar to four times the
+
+ align:start position:0%
+matrix that's similar to four times the
+ 
+
+ align:start position:0%
+matrix that's similar to four times the
+identity is four times the identity it's
+
+ align:start position:0%
+identity is four times the identity it's
+ 
+
+ align:start position:0%
+identity is four times the identity it's
+off by itself what why is that the if
+
+ align:start position:0%
+off by itself what why is that the if
+ 
+
+ align:start position:0%
+off by itself what why is that the if
+this is my matrix four times the
+
+ align:start position:0%
+this is my matrix four times the
+ 
+
+ align:start position:0%
+this is my matrix four times the
+identity and I take it I multiply on the
+
+ align:start position:0%
+identity and I take it I multiply on the
+ 
+
+ align:start position:0%
+identity and I take it I multiply on the
+right by any matrix M I multiply on the
+
+ align:start position:0%
+right by any matrix M I multiply on the
+ 
+
+ align:start position:0%
+right by any matrix M I multiply on the
+left by M inverse what do I get this is
+
+ align:start position:0%
+left by M inverse what do I get this is
+ 
+
+ align:start position:0%
+left by M inverse what do I get this is
+any M but what's the result
+
+ align:start position:0%
+any M but what's the result
+ 
+
+ align:start position:0%
+any M but what's the result
+well factoring out a four that's just
+
+ align:start position:0%
+well factoring out a four that's just
+ 
+
+ align:start position:0%
+well factoring out a four that's just
+the identity matrix in there so then the
+
+ align:start position:0%
+the identity matrix in there so then the
+ 
+
+ align:start position:0%
+the identity matrix in there so then the
+M inverse cancels the M so I've just got
+
+ align:start position:0%
+M inverse cancels the M so I've just got
+ 
+
+ align:start position:0%
+M inverse cancels the M so I've just got
+this matrix back again so whatever the M
+
+ align:start position:0%
+this matrix back again so whatever the M
+ 
+
+ align:start position:0%
+this matrix back again so whatever the M
+is I'm not getting any more members of
+
+ align:start position:0%
+is I'm not getting any more members of
+ 
+
+ align:start position:0%
+is I'm not getting any more members of
+the family so this is one small family
+
+ align:start position:0%
+the family so this is one small family
+ 
+
+ align:start position:0%
+the family so this is one small family
+because it only has one person one
+
+ align:start position:0%
+because it only has one person one
+ 
+
+ align:start position:0%
+because it only has one person one
+matrix excuse me I think of these
+
+ align:start position:0%
+matrix excuse me I think of these
+ 
+
+ align:start position:0%
+matrix excuse me I think of these
+matrices as people by this point in 1806
+
+ align:start position:0%
+matrices as people by this point in 1806
+ 
+
+ align:start position:0%
+matrices as people by this point in 1806
+okay the other the other family includes
+
+ align:start position:0%
+okay the other the other family includes
+ 
+
+ align:start position:0%
+okay the other the other family includes
+all the rest all other matrices that
+
+ align:start position:0%
+all the rest all other matrices that
+ 
+
+ align:start position:0%
+all the rest all other matrices that
+have eigenvalues 4 & 4 this is somehow
+
+ align:start position:0%
+have eigenvalues 4 & 4 this is somehow
+ 
+
+ align:start position:0%
+have eigenvalues 4 & 4 this is somehow
+the best one in that family see I can't
+
+ align:start position:0%
+the best one in that family see I can't
+ 
+
+ align:start position:0%
+the best one in that family see I can't
+make it diagonal if it's diagonal it's
+
+ align:start position:0%
+make it diagonal if it's diagonal it's
+ 
+
+ align:start position:0%
+make it diagonal if it's diagonal it's
+this one it sits in its own by itself so
+
+ align:start position:0%
+this one it sits in its own by itself so
+ 
+
+ align:start position:0%
+this one it sits in its own by itself so
+I have to think okay what's the nearest
+
+ align:start position:0%
+I have to think okay what's the nearest
+ 
+
+ align:start position:0%
+I have to think okay what's the nearest
+I can get to diagonal but but it will
+
+ align:start position:0%
+I can get to diagonal but but it will
+ 
+
+ align:start position:0%
+I can get to diagonal but but it will
+not be diagonalizable that do you know
+
+ align:start position:0%
+not be diagonalizable that do you know
+ 
+
+ align:start position:0%
+not be diagonalizable that do you know
+that that matrix is not diagonalizable
+
+ align:start position:0%
+that that matrix is not diagonalizable
+ 
+
+ align:start position:0%
+that that matrix is not diagonalizable
+of course because if it was
+
+ align:start position:0%
+of course because if it was
+ 
+
+ align:start position:0%
+of course because if it was
+diagonalizable it would be similar to
+
+ align:start position:0%
+diagonalizable it would be similar to
+ 
+
+ align:start position:0%
+diagonalizable it would be similar to
+that which it isn't the eigenvalues of
+
+ align:start position:0%
+that which it isn't the eigenvalues of
+ 
+
+ align:start position:0%
+that which it isn't the eigenvalues of
+this are 4 & 4 but
+
+ align:start position:0%
+this are 4 & 4 but
+ 
+
+ align:start position:0%
+this are 4 & 4 but
+what's the what's the catch with that
+
+ align:start position:0%
+what's the what's the catch with that
+ 
+
+ align:start position:0%
+what's the what's the catch with that
+matrix it's only got one eigenvector
+
+ align:start position:0%
+matrix it's only got one eigenvector
+ 
+
+ align:start position:0%
+matrix it's only got one eigenvector
+that's a non diagonalizable matrix only
+
+ align:start position:0%
+that's a non diagonalizable matrix only
+ 
+
+ align:start position:0%
+that's a non diagonalizable matrix only
+one eigenvector and somehow if I made
+
+ align:start position:0%
+one eigenvector and somehow if I made
+ 
+
+ align:start position:0%
+one eigenvector and somehow if I made
+that one into a 10 or into a million I
+
+ align:start position:0%
+that one into a 10 or into a million I
+ 
+
+ align:start position:0%
+that one into a 10 or into a million I
+could find an M it's in the family it's
+
+ align:start position:0%
+could find an M it's in the family it's
+ 
+
+ align:start position:0%
+could find an M it's in the family it's
+similar but the best so the best guy in
+
+ align:start position:0%
+similar but the best so the best guy in
+ 
+
+ align:start position:0%
+similar but the best so the best guy in
+this family is this one and this is
+
+ align:start position:0%
+this family is this one and this is
+ 
+
+ align:start position:0%
+this family is this one and this is
+called the Jordan so this guy Jordan
+
+ align:start position:0%
+called the Jordan so this guy Jordan
+ 
+
+ align:start position:0%
+called the Jordan so this guy Jordan
+picked out so he like studied these
+
+ align:start position:0%
+picked out so he like studied these
+ 
+
+ align:start position:0%
+picked out so he like studied these
+families of matrices and in each family
+
+ align:start position:0%
+families of matrices and in each family
+ 
+
+ align:start position:0%
+families of matrices and in each family
+he picked out the nicest most diagonal
+
+ align:start position:0%
+he picked out the nicest most diagonal
+ 
+
+ align:start position:0%
+he picked out the nicest most diagonal
+one but not completely diagonal because
+
+ align:start position:0%
+one but not completely diagonal because
+ 
+
+ align:start position:0%
+one but not completely diagonal because
+there's nobody there isn't a diagonal
+
+ align:start position:0%
+there's nobody there isn't a diagonal
+ 
+
+ align:start position:0%
+there's nobody there isn't a diagonal
+matrix in this family so there's a one
+
+ align:start position:0%
+matrix in this family so there's a one
+ 
+
+ align:start position:0%
+matrix in this family so there's a one
+up there in the Jordan form okay yeah I
+
+ align:start position:0%
+up there in the Jordan form okay yeah I
+ 
+
+ align:start position:0%
+up there in the Jordan form okay yeah I
+think we've got to see some more
+
+ align:start position:0%
+think we've got to see some more
+ 
+
+ align:start position:0%
+think we've got to see some more
+matrices in that family let me let's
+
+ align:start position:0%
+matrices in that family let me let's
+ 
+
+ align:start position:0%
+matrices in that family let me let's
+just think of some other matrices whose
+
+ align:start position:0%
+just think of some other matrices whose
+ 
+
+ align:start position:0%
+just think of some other matrices whose
+eigenvalues are 4 & 4 but they're not 4
+
+ align:start position:0%
+eigenvalues are 4 & 4 but they're not 4
+ 
+
+ align:start position:0%
+eigenvalues are 4 & 4 but they're not 4
+times the identity so and I believe that
+
+ align:start position:0%
+times the identity so and I believe that
+ 
+
+ align:start position:0%
+times the identity so and I believe that
+that this that all the examples we pick
+
+ align:start position:0%
+that this that all the examples we pick
+ 
+
+ align:start position:0%
+that this that all the examples we pick
+up will be similar to each other and do
+
+ align:start position:0%
+up will be similar to each other and do
+ 
+
+ align:start position:0%
+up will be similar to each other and do
+you see why so so with in in in this
+
+ align:start position:0%
+you see why so so with in in in this
+ 
+
+ align:start position:0%
+you see why so so with in in in this
+topic of similar matrices the climax is
+
+ align:start position:0%
+topic of similar matrices the climax is
+ 
+
+ align:start position:0%
+topic of similar matrices the climax is
+the Jordan form so it says that every
+
+ align:start position:0%
+the Jordan form so it says that every
+ 
+
+ align:start position:0%
+the Jordan form so it says that every
+matrix I'll write down what the Jordan
+
+ align:start position:0%
+matrix I'll write down what the Jordan
+ 
+
+ align:start position:0%
+matrix I'll write down what the Jordan
+form what Jordan discovered he found the
+
+ align:start position:0%
+form what Jordan discovered he found the
+ 
+
+ align:start position:0%
+form what Jordan discovered he found the
+best looking matrix in each family and
+
+ align:start position:0%
+best looking matrix in each family and
+ 
+
+ align:start position:0%
+best looking matrix in each family and
+that's then we've got well then we've
+
+ align:start position:0%
+that's then we've got well then we've
+ 
+
+ align:start position:0%
+that's then we've got well then we've
+covered all matrices including the non
+
+ align:start position:0%
+covered all matrices including the non
+ 
+
+ align:start position:0%
+covered all matrices including the non
+diagonalizable one that's the point that
+
+ align:start position:0%
+diagonalizable one that's the point that
+ 
+
+ align:start position:0%
+diagonalizable one that's the point that
+that in some way Jordan completed the
+
+ align:start position:0%
+that in some way Jordan completed the
+ 
+
+ align:start position:0%
+that in some way Jordan completed the
+diagonalization by coming as near as he
+
+ align:start position:0%
+diagonalization by coming as near as he
+ 
+
+ align:start position:0%
+diagonalization by coming as near as he
+could which is his Jordan form and
+
+ align:start position:0%
+could which is his Jordan form and
+ 
+
+ align:start position:0%
+could which is his Jordan form and
+therefore if you want to cover all
+
+ align:start position:0%
+therefore if you want to cover all
+ 
+
+ align:start position:0%
+therefore if you want to cover all
+matrices you've got to get him in the
+
+ align:start position:0%
+matrices you've got to get him in the
+ 
+
+ align:start position:0%
+matrices you've got to get him in the
+picture it used to be when I took 18 Oh
+
+ align:start position:0%
+picture it used to be when I took 18 Oh
+ 
+
+ align:start position:0%
+picture it used to be when I took 18 Oh
+six that was the climax of the course
+
+ align:start position:0%
+six that was the climax of the course
+ 
+
+ align:start position:0%
+six that was the climax of the course
+this Jordan form stuff I think it's not
+
+ align:start position:0%
+this Jordan form stuff I think it's not
+ 
+
+ align:start position:0%
+this Jordan form stuff I think it's not
+the climax of linear algebra anymore
+
+ align:start position:0%
+the climax of linear algebra anymore
+ 
+
+ align:start position:0%
+the climax of linear algebra anymore
+because it's it's it's not easy to find
+
+ align:start position:0%
+because it's it's it's not easy to find
+ 
+
+ align:start position:0%
+because it's it's it's not easy to find
+this Jordan form for a general matrix
+
+ align:start position:0%
+this Jordan form for a general matrix
+ 
+
+ align:start position:0%
+this Jordan form for a general matrix
+because it depends on these eigen values
+
+ align:start position:0%
+because it depends on these eigen values
+ 
+
+ align:start position:0%
+because it depends on these eigen values
+being exactly the same you'd have to
+
+ align:start position:0%
+being exactly the same you'd have to
+ 
+
+ align:start position:0%
+being exactly the same you'd have to
+know exactly the eigen values and again
+
+ align:start position:0%
+know exactly the eigen values and again
+ 
+
+ align:start position:0%
+know exactly the eigen values and again
+you'd have to know exactly the rank and
+
+ align:start position:0%
+you'd have to know exactly the rank and
+ 
+
+ align:start position:0%
+you'd have to know exactly the rank and
+the slightest change in numbers will
+
+ align:start position:0%
+the slightest change in numbers will
+ 
+
+ align:start position:0%
+the slightest change in numbers will
+change those eigen values change the
+
+ align:start position:0%
+change those eigen values change the
+ 
+
+ align:start position:0%
+change those eigen values change the
+rank and therefore the whole thing is
+
+ align:start position:0%
+rank and therefore the whole thing is
+ 
+
+ align:start position:0%
+rank and therefore the whole thing is
+numerically not good thing but for
+
+ align:start position:0%
+numerically not good thing but for
+ 
+
+ align:start position:0%
+numerically not good thing but for
+algebra it's the right thing to
+
+ align:start position:0%
+algebra it's the right thing to
+ 
+
+ align:start position:0%
+algebra it's the right thing to
+understand this family so just tell me
+
+ align:start position:0%
+understand this family so just tell me
+ 
+
+ align:start position:0%
+understand this family so just tell me
+another matrix a few more matrices so
+
+ align:start position:0%
+another matrix a few more matrices so
+ 
+
+ align:start position:0%
+another matrix a few more matrices so
+more members of of their family let me
+
+ align:start position:0%
+more members of of their family let me
+ 
+
+ align:start position:0%
+more members of of their family let me
+put down again what what the best one is
+
+ align:start position:0%
+put down again what what the best one is
+ 
+
+ align:start position:0%
+put down again what what the best one is
+okay all right some more matrices let's
+
+ align:start position:0%
+okay all right some more matrices let's
+ 
+
+ align:start position:0%
+okay all right some more matrices let's
+see what what am I looking for
+
+ align:start position:0%
+see what what am I looking for
+ 
+
+ align:start position:0%
+see what what am I looking for
+I'm looking for matrices whose trace is
+
+ align:start position:0%
+I'm looking for matrices whose trace is
+ 
+
+ align:start position:0%
+I'm looking for matrices whose trace is
+what so if I'm looking for more matrices
+
+ align:start position:0%
+what so if I'm looking for more matrices
+ 
+
+ align:start position:0%
+what so if I'm looking for more matrices
+in the family they'll all have the same
+
+ align:start position:0%
+in the family they'll all have the same
+ 
+
+ align:start position:0%
+in the family they'll all have the same
+eigenvalues four and four so they're
+
+ align:start position:0%
+eigenvalues four and four so they're
+ 
+
+ align:start position:0%
+eigenvalues four and four so they're
+Trace will be eight so what why don't I
+
+ align:start position:0%
+Trace will be eight so what why don't I
+ 
+
+ align:start position:0%
+Trace will be eight so what why don't I
+just take like five and three I've got
+
+ align:start position:0%
+just take like five and three I've got
+ 
+
+ align:start position:0%
+just take like five and three I've got
+the trace right now the determinant
+
+ align:start position:0%
+the trace right now the determinant
+ 
+
+ align:start position:0%
+the trace right now the determinant
+should be what sixteen so I just fix
+
+ align:start position:0%
+should be what sixteen so I just fix
+ 
+
+ align:start position:0%
+should be what sixteen so I just fix
+this up so I put maybe a one and a minus
+
+ align:start position:0%
+this up so I put maybe a one and a minus
+ 
+
+ align:start position:0%
+this up so I put maybe a one and a minus
+one there okay there's a matrix with
+
+ align:start position:0%
+one there okay there's a matrix with
+ 
+
+ align:start position:0%
+one there okay there's a matrix with
+eigenvalues four and four because the
+
+ align:start position:0%
+eigenvalues four and four because the
+ 
+
+ align:start position:0%
+eigenvalues four and four because the
+trace is eight and the determinant is
+
+ align:start position:0%
+trace is eight and the determinant is
+ 
+
+ align:start position:0%
+trace is eight and the determinant is
+sixteen and I don't think it's
+
+ align:start position:0%
+sixteen and I don't think it's
+ 
+
+ align:start position:0%
+sixteen and I don't think it's
+diagonalizable do you know why it's not
+
+ align:start position:0%
+diagonalizable do you know why it's not
+ 
+
+ align:start position:0%
+diagonalizable do you know why it's not
+diagonalizable because if it was
+
+ align:start position:0%
+diagonalizable because if it was
+ 
+
+ align:start position:0%
+diagonalizable because if it was
+diagonalizable the diagonal form would
+
+ align:start position:0%
+diagonalizable the diagonal form would
+ 
+
+ align:start position:0%
+diagonalizable the diagonal form would
+have to be this but I can't
+
+ align:start position:0%
+have to be this but I can't
+ 
+
+ align:start position:0%
+have to be this but I can't
+get to that forum because whatever I do
+
+ align:start position:0%
+get to that forum because whatever I do
+ 
+
+ align:start position:0%
+get to that forum because whatever I do
+with any MN verse and a my stay with
+
+ align:start position:0%
+with any MN verse and a my stay with
+ 
+
+ align:start position:0%
+with any MN verse and a my stay with
+that forum I could never get connect
+
+ align:start position:0%
+that forum I could never get connect
+ 
+
+ align:start position:0%
+that forum I could never get connect
+those so I can put down more members
+
+ align:start position:0%
+those so I can put down more members
+ 
+
+ align:start position:0%
+those so I can put down more members
+here's another easy one I could put the
+
+ align:start position:0%
+here's another easy one I could put the
+ 
+
+ align:start position:0%
+here's another easy one I could put the
+four in the four in the and a seventeen
+
+ align:start position:0%
+four in the four in the and a seventeen
+ 
+
+ align:start position:0%
+four in the four in the and a seventeen
+down there all these matrices are
+
+ align:start position:0%
+down there all these matrices are
+ 
+
+ align:start position:0%
+down there all these matrices are
+similar if I could find an M that would
+
+ align:start position:0%
+similar if I could find an M that would
+ 
+
+ align:start position:0%
+similar if I could find an M that would
+show that that one is similar to that
+
+ align:start position:0%
+show that that one is similar to that
+ 
+
+ align:start position:0%
+show that that one is similar to that
+one and you can see the general picture
+
+ align:start position:0%
+one and you can see the general picture
+ 
+
+ align:start position:0%
+one and you can see the general picture
+is I can take any a and any eight minus
+
+ align:start position:0%
+is I can take any a and any eight minus
+ 
+
+ align:start position:0%
+is I can take any a and any eight minus
+a here and any oh I don't know whatever
+
+ align:start position:0%
+a here and any oh I don't know whatever
+ 
+
+ align:start position:0%
+a here and any oh I don't know whatever
+you put it B anyways you can see I can
+
+ align:start position:0%
+you put it B anyways you can see I can
+ 
+
+ align:start position:0%
+you put it B anyways you can see I can
+fill this in fill this in to make the
+
+ align:start position:0%
+fill this in fill this in to make the
+ 
+
+ align:start position:0%
+fill this in fill this in to make the
+trace equal eight the determinant equals
+
+ align:start position:0%
+trace equal eight the determinant equals
+ 
+
+ align:start position:0%
+trace equal eight the determinant equals
+sixteen I get all that family of
+
+ align:start position:0%
+sixteen I get all that family of
+ 
+
+ align:start position:0%
+sixteen I get all that family of
+matrices and they're all similar
+
+ align:start position:0%
+matrices and they're all similar
+ 
+
+ align:start position:0%
+matrices and they're all similar
+so we've seeing what eigenvalues do they
+
+ align:start position:0%
+so we've seeing what eigenvalues do they
+ 
+
+ align:start position:0%
+so we've seeing what eigenvalues do they
+all they're all similar and they all
+
+ align:start position:0%
+all they're all similar and they all
+ 
+
+ align:start position:0%
+all they're all similar and they all
+have only one eigenvector so if I'm if
+
+ align:start position:0%
+have only one eigenvector so if I'm if
+ 
+
+ align:start position:0%
+have only one eigenvector so if I'm if
+you allow me to add to this picture they
+
+ align:start position:0%
+you allow me to add to this picture they
+ 
+
+ align:start position:0%
+you allow me to add to this picture they
+have the same lambdas and they also have
+
+ align:start position:0%
+have the same lambdas and they also have
+ 
+
+ align:start position:0%
+have the same lambdas and they also have
+the same number of independent
+
+ align:start position:0%
+the same number of independent
+ 
+
+ align:start position:0%
+the same number of independent
+eigenvectors because if I get an
+
+ align:start position:0%
+eigenvectors because if I get an
+ 
+
+ align:start position:0%
+eigenvectors because if I get an
+eigenvector for X I get one for for a I
+
+ align:start position:0%
+eigenvector for X I get one for for a I
+ 
+
+ align:start position:0%
+eigenvector for X I get one for for a I
+get one for B also
+
+ align:start position:0%
+get one for B also
+ 
+
+ align:start position:0%
+get one for B also
+so and same number of eigenvectors but
+
+ align:start position:0%
+so and same number of eigenvectors but
+ 
+
+ align:start position:0%
+so and same number of eigenvectors but
+even more than that
+
+ align:start position:0%
+even more than that
+ 
+
+ align:start position:0%
+even more than that
+even more than that I mean it's not
+
+ align:start position:0%
+even more than that I mean it's not
+ 
+
+ align:start position:0%
+even more than that I mean it's not
+enough just to count like in vectors
+
+ align:start position:0%
+enough just to count like in vectors
+ 
+
+ align:start position:0%
+enough just to count like in vectors
+yeah let me give you an example why it's
+
+ align:start position:0%
+yeah let me give you an example why it's
+ 
+
+ align:start position:0%
+yeah let me give you an example why it's
+not even enough to count eigenvectors so
+
+ align:start position:0%
+not even enough to count eigenvectors so
+ 
+
+ align:start position:0%
+not even enough to count eigenvectors so
+another example so here are some
+
+ align:start position:0%
+another example so here are some
+ 
+
+ align:start position:0%
+another example so here are some
+matrices oh let me make them four by
+
+ align:start position:0%
+matrices oh let me make them four by
+ 
+
+ align:start position:0%
+matrices oh let me make them four by
+four okay here's a matrix I mean like if
+
+ align:start position:0%
+four okay here's a matrix I mean like if
+ 
+
+ align:start position:0%
+four okay here's a matrix I mean like if
+you want nightmares think about matrices
+
+ align:start position:0%
+you want nightmares think about matrices
+ 
+
+ align:start position:0%
+you want nightmares think about matrices
+like these so a1 off the diagonal say a1
+
+ align:start position:0%
+like these so a1 off the diagonal say a1
+ 
+
+ align:start position:0%
+like these so a1 off the diagonal say a1
+there how many what are the eigenvalues
+
+ align:start position:0%
+there how many what are the eigenvalues
+ 
+
+ align:start position:0%
+there how many what are the eigenvalues
+of that matrix Oh
+
+ align:start position:0%
+of that matrix Oh
+ 
+
+ align:start position:0%
+of that matrix Oh
+I mean okay what are the eigenvalues of
+
+ align:start position:0%
+I mean okay what are the eigenvalues of
+ 
+
+ align:start position:0%
+I mean okay what are the eigenvalues of
+that matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+please four zeros right so we're really
+
+ align:start position:0%
+please four zeros right so we're really
+ 
+
+ align:start position:0%
+please four zeros right so we're really
+getting bad matrices now so I mean this
+
+ align:start position:0%
+getting bad matrices now so I mean this
+ 
+
+ align:start position:0%
+getting bad matrices now so I mean this
+is like Jordan was a good guy but he he
+
+ align:start position:0%
+is like Jordan was a good guy but he he
+ 
+
+ align:start position:0%
+is like Jordan was a good guy but he he
+had to think about matrices that all
+
+ align:start position:0%
+had to think about matrices that all
+ 
+
+ align:start position:0%
+had to think about matrices that all
+that had like an eigenvalue repeated
+
+ align:start position:0%
+that had like an eigenvalue repeated
+ 
+
+ align:start position:0%
+that had like an eigenvalue repeated
+four times how many eigenvectors does
+
+ align:start position:0%
+four times how many eigenvectors does
+ 
+
+ align:start position:0%
+four times how many eigenvectors does
+that matrix have well I'm I can vet I
+
+ align:start position:0%
+that matrix have well I'm I can vet I
+ 
+
+ align:start position:0%
+that matrix have well I'm I can vet I
+can vectors will be since the eigen
+
+ align:start position:0%
+can vectors will be since the eigen
+ 
+
+ align:start position:0%
+can vectors will be since the eigen
+value is zero eigen vectors are be in
+
+ align:start position:0%
+value is zero eigen vectors are be in
+ 
+
+ align:start position:0%
+value is zero eigen vectors are be in
+the null space right I'm like in vectors
+
+ align:start position:0%
+the null space right I'm like in vectors
+ 
+
+ align:start position:0%
+the null space right I'm like in vectors
+are got to be ax equals zero X so what's
+
+ align:start position:0%
+are got to be ax equals zero X so what's
+ 
+
+ align:start position:0%
+are got to be ax equals zero X so what's
+the dimension of the null space -
+
+ align:start position:0%
+the dimension of the null space -
+ 
+
+ align:start position:0%
+the dimension of the null space -
+somebody said - and that's right why
+
+ align:start position:0%
+somebody said - and that's right why
+ 
+
+ align:start position:0%
+somebody said - and that's right why
+because you asked what's the rank of
+
+ align:start position:0%
+because you asked what's the rank of
+ 
+
+ align:start position:0%
+because you asked what's the rank of
+that matrix the rank is obviously to the
+
+ align:start position:0%
+that matrix the rank is obviously to the
+ 
+
+ align:start position:0%
+that matrix the rank is obviously to the
+number of independent rows is to the
+
+ align:start position:0%
+number of independent rows is to the
+ 
+
+ align:start position:0%
+number of independent rows is to the
+number of independent columns as to the
+
+ align:start position:0%
+number of independent columns as to the
+ 
+
+ align:start position:0%
+number of independent columns as to the
+rank is - so their null the dimension of
+
+ align:start position:0%
+rank is - so their null the dimension of
+ 
+
+ align:start position:0%
+rank is - so their null the dimension of
+the null space is 4 minus 2 so it's got
+
+ align:start position:0%
+the null space is 4 minus 2 so it's got
+ 
+
+ align:start position:0%
+the null space is 4 minus 2 so it's got
+two eigenvectors - eigenvectors -
+
+ align:start position:0%
+two eigenvectors - eigenvectors -
+ 
+
+ align:start position:0%
+two eigenvectors - eigenvectors -
+independent eigenvectors all right the
+
+ align:start position:0%
+independent eigenvectors all right the
+ 
+
+ align:start position:0%
+independent eigenvectors all right the
+dimension of the null space is 2 now
+
+ align:start position:0%
+dimension of the null space is 2 now
+ 
+
+ align:start position:0%
+dimension of the null space is 2 now
+suppose I change this 0 to a 7 the eigen
+
+ align:start position:0%
+suppose I change this 0 to a 7 the eigen
+ 
+
+ align:start position:0%
+suppose I change this 0 to a 7 the eigen
+values are all still 0 how what about
+
+ align:start position:0%
+values are all still 0 how what about
+ 
+
+ align:start position:0%
+values are all still 0 how what about
+how many eigen vectors what's the
+
+ align:start position:0%
+how many eigen vectors what's the
+ 
+
+ align:start position:0%
+how many eigen vectors what's the
+dimension of them what's the rank of
+
+ align:start position:0%
+dimension of them what's the rank of
+ 
+
+ align:start position:0%
+dimension of them what's the rank of
+this matrix now still - right so it's ok
+
+ align:start position:0%
+this matrix now still - right so it's ok
+ 
+
+ align:start position:0%
+this matrix now still - right so it's ok
+and actually this would be similar to
+
+ align:start position:0%
+and actually this would be similar to
+ 
+
+ align:start position:0%
+and actually this would be similar to
+the one that had a zero in there but
+
+ align:start position:0%
+the one that had a zero in there but
+ 
+
+ align:start position:0%
+the one that had a zero in there but
+it's not as beautiful Jordan picked this
+
+ align:start position:0%
+it's not as beautiful Jordan picked this
+ 
+
+ align:start position:0%
+it's not as beautiful Jordan picked this
+one he picked he put ones we have a 1 on
+
+ align:start position:0%
+one he picked he put ones we have a 1 on
+ 
+
+ align:start position:0%
+one he picked he put ones we have a 1 on
+the above the diagonal for every missing
+
+ align:start position:0%
+the above the diagonal for every missing
+ 
+
+ align:start position:0%
+the above the diagonal for every missing
+i convector and here we're missing two
+
+ align:start position:0%
+i convector and here we're missing two
+ 
+
+ align:start position:0%
+i convector and here we're missing two
+because we've got two so we've got two
+
+ align:start position:0%
+because we've got two so we've got two
+ 
+
+ align:start position:0%
+because we've got two so we've got two
+eigenvectors and two were missing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it's a four by four matrix okay
+
+ align:start position:0%
+because it's a four by four matrix okay
+ 
+
+ align:start position:0%
+because it's a four by four matrix okay
+now but I was going to give you this
+
+ align:start position:0%
+now but I was going to give you this
+ 
+
+ align:start position:0%
+now but I was going to give you this
+second example zero one zero zero let me
+
+ align:start position:0%
+second example zero one zero zero let me
+ 
+
+ align:start position:0%
+second example zero one zero zero let me
+just move the one oh not there off the
+
+ align:start position:0%
+just move the one oh not there off the
+ 
+
+ align:start position:0%
+just move the one oh not there off the
+diagonal and zero zero zero zero okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now tell me about this matrix its
+
+ align:start position:0%
+now tell me about this matrix its
+ 
+
+ align:start position:0%
+now tell me about this matrix its
+eigenvalues are four zeros again its
+
+ align:start position:0%
+eigenvalues are four zeros again its
+ 
+
+ align:start position:0%
+eigenvalues are four zeros again its
+rank is 2 again so it has two
+
+ align:start position:0%
+rank is 2 again so it has two
+ 
+
+ align:start position:0%
+rank is 2 again so it has two
+eigenvectors and two missing but the
+
+ align:start position:0%
+eigenvectors and two missing but the
+ 
+
+ align:start position:0%
+eigenvectors and two missing but the
+darn thing is not similar to that one
+
+ align:start position:0%
+darn thing is not similar to that one
+ 
+
+ align:start position:0%
+darn thing is not similar to that one
+account of eigenvectors looks like these
+
+ align:start position:0%
+account of eigenvectors looks like these
+ 
+
+ align:start position:0%
+account of eigenvectors looks like these
+could be similar but they're not Jordan
+
+ align:start position:0%
+could be similar but they're not Jordan
+ 
+
+ align:start position:0%
+could be similar but they're not Jordan
+see this is like a little little 3x3
+
+ align:start position:0%
+see this is like a little little 3x3
+ 
+
+ align:start position:0%
+see this is like a little little 3x3
+block and a little one by one block and
+
+ align:start position:0%
+block and a little one by one block and
+ 
+
+ align:start position:0%
+block and a little one by one block and
+this one is like a 2 by 2 block and a 2
+
+ align:start position:0%
+this one is like a 2 by 2 block and a 2
+ 
+
+ align:start position:0%
+this one is like a 2 by 2 block and a 2
+by 2 block and those blocks are called
+
+ align:start position:0%
+by 2 block and those blocks are called
+ 
+
+ align:start position:0%
+by 2 block and those blocks are called
+Jordan blocks so let me say what is a
+
+ align:start position:0%
+Jordan blocks so let me say what is a
+ 
+
+ align:start position:0%
+Jordan blocks so let me say what is a
+Jordan block
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+jay-j block number I has so a Jordan
+
+ align:start position:0%
+jay-j block number I has so a Jordan
+ 
+
+ align:start position:0%
+jay-j block number I has so a Jordan
+block has a repeated eigenvalue lambda I
+
+ align:start position:0%
+block has a repeated eigenvalue lambda I
+ 
+
+ align:start position:0%
+block has a repeated eigenvalue lambda I
+lambda I on the diagonal zeros below and
+
+ align:start position:0%
+lambda I on the diagonal zeros below and
+ 
+
+ align:start position:0%
+lambda I on the diagonal zeros below and
+ones above so there's a block with this
+
+ align:start position:0%
+ones above so there's a block with this
+ 
+
+ align:start position:0%
+ones above so there's a block with this
+guy repeated but it only has one
+
+ align:start position:0%
+guy repeated but it only has one
+ 
+
+ align:start position:0%
+guy repeated but it only has one
+eigenvector so why Jordan block has one
+
+ align:start position:0%
+eigenvector so why Jordan block has one
+ 
+
+ align:start position:0%
+eigenvector so why Jordan block has one
+eigenvector only this one has one
+
+ align:start position:0%
+eigenvector only this one has one
+ 
+
+ align:start position:0%
+eigenvector only this one has one
+eigenvector this block has one
+
+ align:start position:0%
+eigenvector this block has one
+ 
+
+ align:start position:0%
+eigenvector this block has one
+eigenvector and we get to this block has
+
+ align:start position:0%
+eigenvector and we get to this block has
+ 
+
+ align:start position:0%
+eigenvector and we get to this block has
+one eigenvector and that block has one
+
+ align:start position:0%
+one eigenvector and that block has one
+ 
+
+ align:start position:0%
+one eigenvector and that block has one
+eye
+
+ align:start position:0%
+eye
+ 
+
+ align:start position:0%
+eye
+vector and we get to so but the blocks
+
+ align:start position:0%
+vector and we get to so but the blocks
+ 
+
+ align:start position:0%
+vector and we get to so but the blocks
+are different sizes and that it turns
+
+ align:start position:0%
+are different sizes and that it turns
+ 
+
+ align:start position:0%
+are different sizes and that it turns
+out Jordan worked out then this is not
+
+ align:start position:0%
+out Jordan worked out then this is not
+ 
+
+ align:start position:0%
+out Jordan worked out then this is not
+similar not similar to this one so so
+
+ align:start position:0%
+similar not similar to this one so so
+ 
+
+ align:start position:0%
+similar not similar to this one so so
+I'm like giving you the whole story well
+
+ align:start position:0%
+I'm like giving you the whole story well
+ 
+
+ align:start position:0%
+I'm like giving you the whole story well
+not the whole story but the main themes
+
+ align:start position:0%
+not the whole story but the main themes
+ 
+
+ align:start position:0%
+not the whole story but the main themes
+of this story is is here is Jordan's
+
+ align:start position:0%
+of this story is is here is Jordan's
+ 
+
+ align:start position:0%
+of this story is is here is Jordan's
+theorem every square matrix a is similar
+
+ align:start position:0%
+theorem every square matrix a is similar
+ 
+
+ align:start position:0%
+theorem every square matrix a is similar
+to a Jordan matrix J and what's the
+
+ align:start position:0%
+to a Jordan matrix J and what's the
+ 
+
+ align:start position:0%
+to a Jordan matrix J and what's the
+Jordan matrix J it's a matrix with these
+
+ align:start position:0%
+Jordan matrix J it's a matrix with these
+ 
+
+ align:start position:0%
+Jordan matrix J it's a matrix with these
+blocks block Jordan block number one
+
+ align:start position:0%
+blocks block Jordan block number one
+ 
+
+ align:start position:0%
+blocks block Jordan block number one
+Jordan block number two and so on and
+
+ align:start position:0%
+Jordan block number two and so on and
+ 
+
+ align:start position:0%
+Jordan block number two and so on and
+let's say Jordan block number D and that
+
+ align:start position:0%
+let's say Jordan block number D and that
+ 
+
+ align:start position:0%
+let's say Jordan block number D and that
+was Jordan blocks look like that so the
+
+ align:start position:0%
+was Jordan blocks look like that so the
+ 
+
+ align:start position:0%
+was Jordan blocks look like that so the
+eigenvalues are sitting on the diagonal
+
+ align:start position:0%
+eigenvalues are sitting on the diagonal
+ 
+
+ align:start position:0%
+eigenvalues are sitting on the diagonal
+but we've got some of these ones above
+
+ align:start position:0%
+but we've got some of these ones above
+ 
+
+ align:start position:0%
+but we've got some of these ones above
+the diagonal we've got the number of so
+
+ align:start position:0%
+the diagonal we've got the number of so
+ 
+
+ align:start position:0%
+the diagonal we've got the number of so
+the number of blocks the number of
+
+ align:start position:0%
+the number of blocks the number of
+ 
+
+ align:start position:0%
+the number of blocks the number of
+blocks is the number of eigenvectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because we at one eigenvector per block
+
+ align:start position:0%
+because we at one eigenvector per block
+ 
+
+ align:start position:0%
+because we at one eigenvector per block
+so what i'm so if i summarize jordan's
+
+ align:start position:0%
+so what i'm so if i summarize jordan's
+ 
+
+ align:start position:0%
+so what i'm so if i summarize jordan's
+idea start with any a if its eigenvalues
+
+ align:start position:0%
+idea start with any a if its eigenvalues
+ 
+
+ align:start position:0%
+idea start with any a if its eigenvalues
+are distinct then what's it similar to
+
+ align:start position:0%
+are distinct then what's it similar to
+ 
+
+ align:start position:0%
+are distinct then what's it similar to
+this is the good case if I start with a
+
+ align:start position:0%
+this is the good case if I start with a
+ 
+
+ align:start position:0%
+this is the good case if I start with a
+matrix a and it has different
+
+ align:start position:0%
+matrix a and it has different
+ 
+
+ align:start position:0%
+matrix a and it has different
+eigenvalues it's n eigenvalues none of
+
+ align:start position:0%
+eigenvalues it's n eigenvalues none of
+ 
+
+ align:start position:0%
+eigenvalues it's n eigenvalues none of
+them are repeated then that's a diagonal
+
+ align:start position:0%
+them are repeated then that's a diagonal
+ 
+
+ align:start position:0%
+them are repeated then that's a diagonal
+diagonalizable matrix the Jordan block
+
+ align:start position:0%
+diagonalizable matrix the Jordan block
+ 
+
+ align:start position:0%
+diagonalizable matrix the Jordan block
+is has the Jordan matrix is diagonal its
+
+ align:start position:0%
+is has the Jordan matrix is diagonal its
+ 
+
+ align:start position:0%
+is has the Jordan matrix is diagonal its
+lambda so the good case the good case J
+
+ align:start position:0%
+lambda so the good case the good case J
+ 
+
+ align:start position:0%
+lambda so the good case the good case J
+is lambda all there are D equals n there
+
+ align:start position:0%
+is lambda all there are D equals n there
+ 
+
+ align:start position:0%
+is lambda all there are D equals n there
+are n eigenvectors and blocks
+
+ align:start position:0%
+are n eigenvectors and blocks
+ 
+
+ align:start position:0%
+are n eigenvectors and blocks
+diagonal everything great but Jordan
+
+ align:start position:0%
+diagonal everything great but Jordan
+ 
+
+ align:start position:0%
+diagonal everything great but Jordan
+covered all cases by including these
+
+ align:start position:0%
+covered all cases by including these
+ 
+
+ align:start position:0%
+covered all cases by including these
+cases of repeated eigenvalues and
+
+ align:start position:0%
+cases of repeated eigenvalues and
+ 
+
+ align:start position:0%
+cases of repeated eigenvalues and
+missing eigenvectors okay that's a
+
+ align:start position:0%
+missing eigenvectors okay that's a
+ 
+
+ align:start position:0%
+missing eigenvectors okay that's a
+description of Jordan that that's I
+
+ align:start position:0%
+description of Jordan that that's I
+ 
+
+ align:start position:0%
+description of Jordan that that's I
+haven't told you how to compute this
+
+ align:start position:0%
+haven't told you how to compute this
+ 
+
+ align:start position:0%
+haven't told you how to compute this
+thing and it isn't easy whereas the good
+
+ align:start position:0%
+thing and it isn't easy whereas the good
+ 
+
+ align:start position:0%
+thing and it isn't easy whereas the good
+case is the good case is what 1806 about
+
+ align:start position:0%
+case is the good case is what 1806 about
+ 
+
+ align:start position:0%
+case is the good case is what 1806 about
+isn't about the this case is what 1806
+
+ align:start position:0%
+isn't about the this case is what 1806
+ 
+
+ align:start position:0%
+isn't about the this case is what 1806
+was about 20 years ago so you can see
+
+ align:start position:0%
+was about 20 years ago so you can see
+ 
+
+ align:start position:0%
+was about 20 years ago so you can see
+you probably won't have on the final
+
+ align:start position:0%
+you probably won't have on the final
+ 
+
+ align:start position:0%
+you probably won't have on the final
+exam the computation of a Jordan matrix
+
+ align:start position:0%
+exam the computation of a Jordan matrix
+ 
+
+ align:start position:0%
+exam the computation of a Jordan matrix
+for some horrible thing with 4 repeated
+
+ align:start position:0%
+for some horrible thing with 4 repeated
+ 
+
+ align:start position:0%
+for some horrible thing with 4 repeated
+eigenvalues I'm I'm not that crazy about
+
+ align:start position:0%
+eigenvalues I'm I'm not that crazy about
+ 
+
+ align:start position:0%
+eigenvalues I'm I'm not that crazy about
+the Jordan form but I'm very positive
+
+ align:start position:0%
+the Jordan form but I'm very positive
+ 
+
+ align:start position:0%
+the Jordan form but I'm very positive
+about positive definite matrices and
+
+ align:start position:0%
+about positive definite matrices and
+ 
+
+ align:start position:0%
+about positive definite matrices and
+about them the idea that's coming Monday
+
+ align:start position:0%
+about them the idea that's coming Monday
+ 
+
+ align:start position:0%
+about them the idea that's coming Monday
+the singular value decomposition so I'll
+
+ align:start position:0%
+the singular value decomposition so I'll
+ 
+
+ align:start position:0%
+the singular value decomposition so I'll
+see you on Monday and have a great
+
+ align:start position:0%
+see you on Monday and have a great
+ 
+
+ align:start position:0%
+see you on Monday and have a great
+weekend bye
\ No newline at end of file
diff --git a/TdOuHUabbJs.txt b/TdOuHUabbJs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8595b8665d3d8da69b00453d12f37f06661fbd54
--- /dev/null
+++ b/TdOuHUabbJs.txt
@@ -0,0 +1,2827 @@
+align:start position:0%
+ 
+Um the session one is framing the
+
+ align:start position:0%
+Um the session one is framing the
+ 
+
+ align:start position:0%
+Um the session one is framing the
+challenge and we're going to go as high
+
+ align:start position:0%
+challenge and we're going to go as high
+ 
+
+ align:start position:0%
+challenge and we're going to go as high
+level as we can looking at the whole
+
+ align:start position:0%
+level as we can looking at the whole
+ 
+
+ align:start position:0%
+level as we can looking at the whole
+world and all of humanity.
+
+ align:start position:0%
+world and all of humanity.
+ 
+
+ align:start position:0%
+world and all of humanity.
+And um I I couldn't be more excited
+
+ align:start position:0%
+And um I I couldn't be more excited
+ 
+
+ align:start position:0%
+And um I I couldn't be more excited
+about the three speakers. Um I
+
+ align:start position:0%
+about the three speakers. Um I
+ 
+
+ align:start position:0%
+about the three speakers. Um I
+I will not do them justice by
+
+ align:start position:0%
+I will not do them justice by
+ 
+
+ align:start position:0%
+I will not do them justice by
+introducing. So I'm asking each of them
+
+ align:start position:0%
+introducing. So I'm asking each of them
+ 
+
+ align:start position:0%
+introducing. So I'm asking each of them
+to take a moment to introduce
+
+ align:start position:0%
+to take a moment to introduce
+ 
+
+ align:start position:0%
+to take a moment to introduce
+themselves. And uh we're going to start
+
+ align:start position:0%
+themselves. And uh we're going to start
+ 
+
+ align:start position:0%
+themselves. And uh we're going to start
+with Jason J from here at MIT Sloan
+
+ align:start position:0%
+with Jason J from here at MIT Sloan
+ 
+
+ align:start position:0%
+with Jason J from here at MIT Sloan
+School. Um who has I will just add one
+
+ align:start position:0%
+School. Um who has I will just add one
+ 
+
+ align:start position:0%
+School. Um who has I will just add one
+one piece of introduction. He has the uh
+
+ align:start position:0%
+one piece of introduction. He has the uh
+ 
+
+ align:start position:0%
+one piece of introduction. He has the uh
+incredible distinction which I I don't
+
+ align:start position:0%
+incredible distinction which I I don't
+ 
+
+ align:start position:0%
+incredible distinction which I I don't
+know if it's on on your LinkedIn but of
+
+ align:start position:0%
+know if it's on on your LinkedIn but of
+ 
+
+ align:start position:0%
+know if it's on on your LinkedIn but of
+being a early heat volunteer for an
+
+ align:start position:0%
+being a early heat volunteer for an
+ 
+
+ align:start position:0%
+being a early heat volunteer for an
+energy efficiency barn raising.
+
+ align:start position:0%
+energy efficiency barn raising.
+ 
+
+ align:start position:0%
+energy efficiency barn raising.
+>> That's right. I learned how to use a
+
+ align:start position:0%
+>> That's right. I learned how to use a
+ 
+
+ align:start position:0%
+>> That's right. I learned how to use a
+cocking gun from Zanb. Um
+
+ align:start position:0%
+cocking gun from Zanb. Um
+ 
+
+ align:start position:0%
+cocking gun from Zanb. Um
+um good morning everybody.
+
+ align:start position:0%
+um good morning everybody.
+ 
+
+ align:start position:0%
+um good morning everybody.
+>> Good morning everybody.
+
+ align:start position:0%
+>> Good morning everybody.
+ 
+
+ align:start position:0%
+>> Good morning everybody.
+>> All right. Um so I'm Jason Jay. I teach
+
+ align:start position:0%
+>> All right. Um so I'm Jason Jay. I teach
+ 
+
+ align:start position:0%
+>> All right. Um so I'm Jason Jay. I teach
+at the MIT Sloan School of Management.
+
+ align:start position:0%
+at the MIT Sloan School of Management.
+ 
+
+ align:start position:0%
+at the MIT Sloan School of Management.
+I'm the director of the sustainability
+
+ align:start position:0%
+I'm the director of the sustainability
+ 
+
+ align:start position:0%
+I'm the director of the sustainability
+initiative there. Um, I've had the great
+
+ align:start position:0%
+initiative there. Um, I've had the great
+ 
+
+ align:start position:0%
+initiative there. Um, I've had the great
+pleasure to be part of this heat journey
+
+ align:start position:0%
+pleasure to be part of this heat journey
+ 
+
+ align:start position:0%
+pleasure to be part of this heat journey
+from the beginning. As Zanab was saying,
+
+ align:start position:0%
+from the beginning. As Zanab was saying,
+ 
+
+ align:start position:0%
+from the beginning. As Zanab was saying,
+I when I did my PhD here, I was studying
+
+ align:start position:0%
+I when I did my PhD here, I was studying
+ 
+
+ align:start position:0%
+I when I did my PhD here, I was studying
+something called the Cambridge Energy
+
+ align:start position:0%
+something called the Cambridge Energy
+ 
+
+ align:start position:0%
+something called the Cambridge Energy
+Alliance. Um, and I was looking at the
+
+ align:start position:0%
+Alliance. Um, and I was looking at the
+ 
+
+ align:start position:0%
+Alliance. Um, and I was looking at the
+sort of multistakeholder collaborations
+
+ align:start position:0%
+sort of multistakeholder collaborations
+ 
+
+ align:start position:0%
+sort of multistakeholder collaborations
+that were occurring here um, around our
+
+ align:start position:0%
+that were occurring here um, around our
+ 
+
+ align:start position:0%
+that were occurring here um, around our
+our our city of Cambridge advancing
+
+ align:start position:0%
+our our city of Cambridge advancing
+ 
+
+ align:start position:0%
+our our city of Cambridge advancing
+energy efficiency topics. And part of
+
+ align:start position:0%
+energy efficiency topics. And part of
+ 
+
+ align:start position:0%
+energy efficiency topics. And part of
+that included participating in HEAT's
+
+ align:start position:0%
+that included participating in HEAT's
+ 
+
+ align:start position:0%
+that included participating in HEAT's
+early barn raisings. And I did in fact
+
+ align:start position:0%
+early barn raisings. And I did in fact
+ 
+
+ align:start position:0%
+early barn raisings. And I did in fact
+learn to use a cocking gun from Zanab
+
+ align:start position:0%
+learn to use a cocking gun from Zanab
+ 
+
+ align:start position:0%
+learn to use a cocking gun from Zanab
+um, as we were weatherizing people's
+
+ align:start position:0%
+um, as we were weatherizing people's
+ 
+
+ align:start position:0%
+um, as we were weatherizing people's
+homes. Um and then and then have gotten
+
+ align:start position:0%
+homes. Um and then and then have gotten
+ 
+
+ align:start position:0%
+homes. Um and then and then have gotten
+to watch as this whole thing has evolved
+
+ align:start position:0%
+to watch as this whole thing has evolved
+ 
+
+ align:start position:0%
+to watch as this whole thing has evolved
+um going to the gas leaks effort, the
+
+ align:start position:0%
+um going to the gas leaks effort, the
+ 
+
+ align:start position:0%
+um going to the gas leaks effort, the
+collaboration with um Eversource and
+
+ align:start position:0%
+collaboration with um Eversource and
+ 
+
+ align:start position:0%
+collaboration with um Eversource and
+other utility companies um the
+
+ align:start position:0%
+other utility companies um the
+ 
+
+ align:start position:0%
+other utility companies um the
+advancement of the legal policy
+
+ align:start position:0%
+advancement of the legal policy
+ 
+
+ align:start position:0%
+advancement of the legal policy
+framework around better measurement of
+
+ align:start position:0%
+framework around better measurement of
+ 
+
+ align:start position:0%
+framework around better measurement of
+gas leaks and then towards this this
+
+ align:start position:0%
+gas leaks and then towards this this
+ 
+
+ align:start position:0%
+gas leaks and then towards this this
+transformational idea of geothermal
+
+ align:start position:0%
+transformational idea of geothermal
+ 
+
+ align:start position:0%
+transformational idea of geothermal
+energy networks where now there's enough
+
+ align:start position:0%
+energy networks where now there's enough
+ 
+
+ align:start position:0%
+energy networks where now there's enough
+trust between the advocates and the
+
+ align:start position:0%
+trust between the advocates and the
+ 
+
+ align:start position:0%
+trust between the advocates and the
+utilities to actually say, "Hey, could
+
+ align:start position:0%
+utilities to actually say, "Hey, could
+ 
+
+ align:start position:0%
+utilities to actually say, "Hey, could
+we just not have you be a gas utility
+
+ align:start position:0%
+we just not have you be a gas utility
+ 
+
+ align:start position:0%
+we just not have you be a gas utility
+anymore?" which is kind of an audacious
+
+ align:start position:0%
+anymore?" which is kind of an audacious
+ 
+
+ align:start position:0%
+anymore?" which is kind of an audacious
+thing and is the reason we bring in Zanb
+
+ align:start position:0%
+thing and is the reason we bring in Zanb
+ 
+
+ align:start position:0%
+thing and is the reason we bring in Zanb
+as a guest speaker into our courses uh
+
+ align:start position:0%
+as a guest speaker into our courses uh
+ 
+
+ align:start position:0%
+as a guest speaker into our courses uh
+every year. Um what she asked me to do
+
+ align:start position:0%
+every year. Um what she asked me to do
+ 
+
+ align:start position:0%
+every year. Um what she asked me to do
+is to um as she said go to the level of
+
+ align:start position:0%
+is to um as she said go to the level of
+ 
+
+ align:start position:0%
+is to um as she said go to the level of
+the of all of the whole planet and all
+
+ align:start position:0%
+the of all of the whole planet and all
+ 
+
+ align:start position:0%
+the of all of the whole planet and all
+of humanity. Um and the way I'm going to
+
+ align:start position:0%
+of humanity. Um and the way I'm going to
+ 
+
+ align:start position:0%
+of humanity. Um and the way I'm going to
+do that is using an interactive
+
+ align:start position:0%
+do that is using an interactive
+ 
+
+ align:start position:0%
+do that is using an interactive
+simulation tool called NROSS. Um just
+
+ align:start position:0%
+simulation tool called NROSS. Um just
+ 
+
+ align:start position:0%
+simulation tool called NROSS. Um just
+quick show of hands, how many of you
+
+ align:start position:0%
+quick show of hands, how many of you
+ 
+
+ align:start position:0%
+quick show of hands, how many of you
+have seen NROs before? Okay. Uh about
+
+ align:start position:0%
+have seen NROs before? Okay. Uh about
+ 
+
+ align:start position:0%
+have seen NROs before? Okay. Uh about
+half the room. Okay. So um this is the
+
+ align:start position:0%
+half the room. Okay. So um this is the
+ 
+
+ align:start position:0%
+half the room. Okay. So um this is the
+the result of a collaboration between
+
+ align:start position:0%
+the result of a collaboration between
+ 
+
+ align:start position:0%
+the result of a collaboration between
+the MIT Sloan Sustainability Initiative
+
+ align:start position:0%
+the MIT Sloan Sustainability Initiative
+ 
+
+ align:start position:0%
+the MIT Sloan Sustainability Initiative
+and uh Climate Interactive which is a
+
+ align:start position:0%
+and uh Climate Interactive which is a
+ 
+
+ align:start position:0%
+and uh Climate Interactive which is a
+independent uh nonpartisan nonprofit
+
+ align:start position:0%
+independent uh nonpartisan nonprofit
+ 
+
+ align:start position:0%
+independent uh nonpartisan nonprofit
+made of mostly MIT grads um who um who
+
+ align:start position:0%
+made of mostly MIT grads um who um who
+ 
+
+ align:start position:0%
+made of mostly MIT grads um who um who
+do a simulation tool that behaves the
+
+ align:start position:0%
+do a simulation tool that behaves the
+ 
+
+ align:start position:0%
+do a simulation tool that behaves the
+same as the big supercomputer integrated
+
+ align:start position:0%
+same as the big supercomputer integrated
+ 
+
+ align:start position:0%
+same as the big supercomputer integrated
+assessment models but runs instantly on
+
+ align:start position:0%
+assessment models but runs instantly on
+ 
+
+ align:start position:0%
+assessment models but runs instantly on
+any laptop and is freely available and
+
+ align:start position:0%
+any laptop and is freely available and
+ 
+
+ align:start position:0%
+any laptop and is freely available and
+open source to anybody with a web
+
+ align:start position:0%
+open source to anybody with a web
+ 
+
+ align:start position:0%
+open source to anybody with a web
+browser. So, um you can't open it up on
+
+ align:start position:0%
+browser. So, um you can't open it up on
+ 
+
+ align:start position:0%
+browser. So, um you can't open it up on
+your phones, but on any laptop or iPad,
+
+ align:start position:0%
+your phones, but on any laptop or iPad,
+ 
+
+ align:start position:0%
+your phones, but on any laptop or iPad,
+um you can pull this up and experiment
+
+ align:start position:0%
+um you can pull this up and experiment
+ 
+
+ align:start position:0%
+um you can pull this up and experiment
+it with it yourself. And um I am not on
+
+ align:start position:0%
+it with it yourself. And um I am not on
+ 
+
+ align:start position:0%
+it with it yourself. And um I am not on
+the modeling team. I'm not a climate
+
+ align:start position:0%
+the modeling team. I'm not a climate
+ 
+
+ align:start position:0%
+the modeling team. I'm not a climate
+scientist. I'm not an energy scientist.
+
+ align:start position:0%
+scientist. I'm not an energy scientist.
+ 
+
+ align:start position:0%
+scientist. I'm not an energy scientist.
+I'm an organizations person, but I've
+
+ align:start position:0%
+I'm an organizations person, but I've
+ 
+
+ align:start position:0%
+I'm an organizations person, but I've
+been facilitating probably hundreds of
+
+ align:start position:0%
+been facilitating probably hundreds of
+ 
+
+ align:start position:0%
+been facilitating probably hundreds of
+workshops at this point using this tool.
+
+ align:start position:0%
+workshops at this point using this tool.
+ 
+
+ align:start position:0%
+workshops at this point using this tool.
+And that means that any of you can do
+
+ align:start position:0%
+And that means that any of you can do
+ 
+
+ align:start position:0%
+And that means that any of you can do
+that as well. Um which which I would
+
+ align:start position:0%
+that as well. Um which which I would
+ 
+
+ align:start position:0%
+that as well. Um which which I would
+certainly recommend. What I'm going to
+
+ align:start position:0%
+certainly recommend. What I'm going to
+ 
+
+ align:start position:0%
+certainly recommend. What I'm going to
+try to do is just use this to expose a
+
+ align:start position:0%
+try to do is just use this to expose a
+ 
+
+ align:start position:0%
+try to do is just use this to expose a
+little bit about the climate challenge
+
+ align:start position:0%
+little bit about the climate challenge
+ 
+
+ align:start position:0%
+little bit about the climate challenge
+um and how the things that we're talking
+
+ align:start position:0%
+um and how the things that we're talking
+ 
+
+ align:start position:0%
+um and how the things that we're talking
+about here today sort of fit within that
+
+ align:start position:0%
+about here today sort of fit within that
+ 
+
+ align:start position:0%
+about here today sort of fit within that
+bigger picture and what some of the
+
+ align:start position:0%
+bigger picture and what some of the
+ 
+
+ align:start position:0%
+bigger picture and what some of the
+system interactions are because this is
+
+ align:start position:0%
+system interactions are because this is
+ 
+
+ align:start position:0%
+system interactions are because this is
+a system dynamics model right this is
+
+ align:start position:0%
+a system dynamics model right this is
+ 
+
+ align:start position:0%
+a system dynamics model right this is
+the interdependence of um you know
+
+ align:start position:0%
+the interdependence of um you know
+ 
+
+ align:start position:0%
+the interdependence of um you know
+thousands of variables to produce the
+
+ align:start position:0%
+thousands of variables to produce the
+ 
+
+ align:start position:0%
+thousands of variables to produce the
+outcomes that we are facing. So here you
+
+ align:start position:0%
+outcomes that we are facing. So here you
+ 
+
+ align:start position:0%
+outcomes that we are facing. So here you
+can see on the left this is the stack of
+
+ align:start position:0%
+can see on the left this is the stack of
+ 
+
+ align:start position:0%
+can see on the left this is the stack of
+global energy. Um so she talked about a
+
+ align:start position:0%
+global energy. Um so she talked about a
+ 
+
+ align:start position:0%
+global energy. Um so she talked about a
+zeta jewel that humanity is using about
+
+ align:start position:0%
+zeta jewel that humanity is using about
+ 
+
+ align:start position:0%
+zeta jewel that humanity is using about
+half of a zeta jewel. So 500 exogles. Um
+
+ align:start position:0%
+half of a zeta jewel. So 500 exogles. Um
+ 
+
+ align:start position:0%
+half of a zeta jewel. So 500 exogles. Um
+you can see that here on this picture
+
+ align:start position:0%
+you can see that here on this picture
+ 
+
+ align:start position:0%
+you can see that here on this picture
+and that is made up of coal, oil, gas,
+
+ align:start position:0%
+and that is made up of coal, oil, gas,
+ 
+
+ align:start position:0%
+and that is made up of coal, oil, gas,
+renewables, biomass and nuclear. Um uh
+
+ align:start position:0%
+renewables, biomass and nuclear. Um uh
+ 
+
+ align:start position:0%
+renewables, biomass and nuclear. Um uh
+if we were to invent nuclear fusion or
+
+ align:start position:0%
+if we were to invent nuclear fusion or
+ 
+
+ align:start position:0%
+if we were to invent nuclear fusion or
+some other new zerocarbon, we could add
+
+ align:start position:0%
+some other new zerocarbon, we could add
+ 
+
+ align:start position:0%
+some other new zerocarbon, we could add
+that to the mix. We're not going to talk
+
+ align:start position:0%
+that to the mix. We're not going to talk
+ 
+
+ align:start position:0%
+that to the mix. We're not going to talk
+about that today. On the right we have
+
+ align:start position:0%
+about that today. On the right we have
+ 
+
+ align:start position:0%
+about that today. On the right we have
+the stack of greenhouse gas emissions
+
+ align:start position:0%
+the stack of greenhouse gas emissions
+ 
+
+ align:start position:0%
+the stack of greenhouse gas emissions
+that are partly related to that. So the
+
+ align:start position:0%
+that are partly related to that. So the
+ 
+
+ align:start position:0%
+that are partly related to that. So the
+largest source of human anthropogenic
+
+ align:start position:0%
+largest source of human anthropogenic
+ 
+
+ align:start position:0%
+largest source of human anthropogenic
+greenhouse gas emissions is uh CO2 from
+
+ align:start position:0%
+greenhouse gas emissions is uh CO2 from
+ 
+
+ align:start position:0%
+greenhouse gas emissions is uh CO2 from
+energy. That's about 35 gigatons uh a
+
+ align:start position:0%
+energy. That's about 35 gigatons uh a
+ 
+
+ align:start position:0%
+energy. That's about 35 gigatons uh a
+year right now. The second highest
+
+ align:start position:0%
+year right now. The second highest
+ 
+
+ align:start position:0%
+year right now. The second highest
+source is methane. So this is put on a
+
+ align:start position:0%
+source is methane. So this is put on a
+ 
+
+ align:start position:0%
+source is methane. So this is put on a
+100redyear uh CO2 equivalent units on
+
+ align:start position:0%
+100redyear uh CO2 equivalent units on
+ 
+
+ align:start position:0%
+100redyear uh CO2 equivalent units on
+this graph. So 10 gigatons of CO2
+
+ align:start position:0%
+this graph. So 10 gigatons of CO2
+ 
+
+ align:start position:0%
+this graph. So 10 gigatons of CO2
+equivalent from methane emissions. The
+
+ align:start position:0%
+equivalent from methane emissions. The
+ 
+
+ align:start position:0%
+equivalent from methane emissions. The
+third highest is land use change from
+
+ align:start position:0%
+third highest is land use change from
+ 
+
+ align:start position:0%
+third highest is land use change from
+deforestation and petlands and so on.
+
+ align:start position:0%
+deforestation and petlands and so on.
+ 
+
+ align:start position:0%
+deforestation and petlands and so on.
+And then you have nitrous oxide and F
+
+ align:start position:0%
+And then you have nitrous oxide and F
+ 
+
+ align:start position:0%
+And then you have nitrous oxide and F
+gases. So this gives you a picture of
+
+ align:start position:0%
+gases. So this gives you a picture of
+ 
+
+ align:start position:0%
+gases. So this gives you a picture of
+the faucet into the bathtub of the
+
+ align:start position:0%
+the faucet into the bathtub of the
+ 
+
+ align:start position:0%
+the faucet into the bathtub of the
+atmosphere. How much greenhouse gas we
+
+ align:start position:0%
+atmosphere. How much greenhouse gas we
+ 
+
+ align:start position:0%
+atmosphere. How much greenhouse gas we
+are putting into the atmosphere every
+
+ align:start position:0%
+are putting into the atmosphere every
+ 
+
+ align:start position:0%
+are putting into the atmosphere every
+year. And the result of that faucet
+
+ align:start position:0%
+year. And the result of that faucet
+ 
+
+ align:start position:0%
+year. And the result of that faucet
+being on stronger and stronger every
+
+ align:start position:0%
+being on stronger and stronger every
+ 
+
+ align:start position:0%
+being on stronger and stronger every
+year as we grow the global industrial
+
+ align:start position:0%
+year as we grow the global industrial
+ 
+
+ align:start position:0%
+year as we grow the global industrial
+economy is that the concentration of CO2
+
+ align:start position:0%
+economy is that the concentration of CO2
+ 
+
+ align:start position:0%
+economy is that the concentration of CO2
+in the atmosphere is increasing. Um
+
+ align:start position:0%
+in the atmosphere is increasing. Um
+ 
+
+ align:start position:0%
+in the atmosphere is increasing. Um
+right, we you've heard 350.org or
+
+ align:start position:0%
+right, we you've heard 350.org or
+ 
+
+ align:start position:0%
+right, we you've heard 350.org or
+wanting to get that back down to 350
+
+ align:start position:0%
+wanting to get that back down to 350
+ 
+
+ align:start position:0%
+wanting to get that back down to 350
+closer to pre-industrial levels. um
+
+ align:start position:0%
+closer to pre-industrial levels. um
+ 
+
+ align:start position:0%
+closer to pre-industrial levels. um
+we're now at about 424 and that
+
+ align:start position:0%
+we're now at about 424 and that
+ 
+
+ align:start position:0%
+we're now at about 424 and that
+increasing greenhouse gas as Zanv said
+
+ align:start position:0%
+increasing greenhouse gas as Zanv said
+ 
+
+ align:start position:0%
+increasing greenhouse gas as Zanv said
+creates this thermal regulation problem
+
+ align:start position:0%
+creates this thermal regulation problem
+ 
+
+ align:start position:0%
+creates this thermal regulation problem
+which is that we're heating the planet
+
+ align:start position:0%
+which is that we're heating the planet
+ 
+
+ align:start position:0%
+which is that we're heating the planet
+and so the temperature um is increasing
+
+ align:start position:0%
+and so the temperature um is increasing
+ 
+
+ align:start position:0%
+and so the temperature um is increasing
+um in 2024
+
+ align:start position:0%
+um in 2024
+ 
+
+ align:start position:0%
+um in 2024
+um you know the data is still coming in
+
+ align:start position:0%
+um you know the data is still coming in
+ 
+
+ align:start position:0%
+um you know the data is still coming in
+but we're really pushing close to that
+
+ align:start position:0%
+but we're really pushing close to that
+ 
+
+ align:start position:0%
+but we're really pushing close to that
+1.5 mark um and you can see in our
+
+ align:start position:0%
+1.5 mark um and you can see in our
+ 
+
+ align:start position:0%
+1.5 mark um and you can see in our
+business as usual projections um inroads
+
+ align:start position:0%
+business as usual projections um inroads
+ 
+
+ align:start position:0%
+business as usual projections um inroads
+we passed the 1.5 degree goal we passed
+
+ align:start position:0%
+we passed the 1.5 degree goal we passed
+ 
+
+ align:start position:0%
+we passed the 1.5 degree goal we passed
+the twoderee goal we at the end of the
+
+ align:start position:0%
+the twoderee goal we at the end of the
+ 
+
+ align:start position:0%
+the twoderee goal we at the end of the
+century hit 3.3° C, which is what this
+
+ align:start position:0%
+century hit 3.3° C, which is what this
+ 
+
+ align:start position:0%
+century hit 3.3° C, which is what this
+big number is. And unfortunately, the
+
+ align:start position:0%
+big number is. And unfortunately, the
+ 
+
+ align:start position:0%
+big number is. And unfortunately, the
+slope of this line is positive, which
+
+ align:start position:0%
+slope of this line is positive, which
+ 
+
+ align:start position:0%
+slope of this line is positive, which
+means that we're continuing to warm the
+
+ align:start position:0%
+means that we're continuing to warm the
+ 
+
+ align:start position:0%
+means that we're continuing to warm the
+planet into the 22nd century. Um, not
+
+ align:start position:0%
+planet into the 22nd century. Um, not
+ 
+
+ align:start position:0%
+planet into the 22nd century. Um, not
+everybody has a visceral sense of what
+
+ align:start position:0%
+everybody has a visceral sense of what
+ 
+
+ align:start position:0%
+everybody has a visceral sense of what
+3.3 degrees Celsius means. Um, and so
+
+ align:start position:0%
+3.3 degrees Celsius means. Um, and so
+ 
+
+ align:start position:0%
+3.3 degrees Celsius means. Um, and so
+one thing you can do is you can use the
+
+ align:start position:0%
+one thing you can do is you can use the
+ 
+
+ align:start position:0%
+one thing you can do is you can use the
+impact graphs in NROS to explore some of
+
+ align:start position:0%
+impact graphs in NROS to explore some of
+ 
+
+ align:start position:0%
+impact graphs in NROS to explore some of
+that. So for example, we can think about
+
+ align:start position:0%
+that. So for example, we can think about
+ 
+
+ align:start position:0%
+that. So for example, we can think about
+you know how much sea level rise might
+
+ align:start position:0%
+you know how much sea level rise might
+ 
+
+ align:start position:0%
+you know how much sea level rise might
+we see as a result of that warming or we
+
+ align:start position:0%
+we see as a result of that warming or we
+ 
+
+ align:start position:0%
+we see as a result of that warming or we
+can think about um you know other graphs
+
+ align:start position:0%
+can think about um you know other graphs
+ 
+
+ align:start position:0%
+can think about um you know other graphs
+like um the extinction risk from animal
+
+ align:start position:0%
+like um the extinction risk from animal
+ 
+
+ align:start position:0%
+like um the extinction risk from animal
+species. So the effects on biodiversity.
+
+ align:start position:0%
+species. So the effects on biodiversity.
+ 
+
+ align:start position:0%
+species. So the effects on biodiversity.
+Um, one of the things that if you
+
+ align:start position:0%
+Um, one of the things that if you
+ 
+
+ align:start position:0%
+Um, one of the things that if you
+haven't played with Androids in a little
+
+ align:start position:0%
+haven't played with Androids in a little
+ 
+
+ align:start position:0%
+haven't played with Androids in a little
+while, we've now added is that we
+
+ align:start position:0%
+while, we've now added is that we
+ 
+
+ align:start position:0%
+while, we've now added is that we
+interface with maps that are from the
+
+ align:start position:0%
+interface with maps that are from the
+ 
+
+ align:start position:0%
+interface with maps that are from the
+um, probable futures site, which allows
+
+ align:start position:0%
+um, probable futures site, which allows
+ 
+
+ align:start position:0%
+um, probable futures site, which allows
+you to see what happens kind of on a
+
+ align:start position:0%
+you to see what happens kind of on a
+ 
+
+ align:start position:0%
+you to see what happens kind of on a
+more regional or geographic basis to the
+
+ align:start position:0%
+more regional or geographic basis to the
+ 
+
+ align:start position:0%
+more regional or geographic basis to the
+places that we care about. So, for
+
+ align:start position:0%
+places that we care about. So, for
+ 
+
+ align:start position:0%
+places that we care about. So, for
+example, this is a picture of the number
+
+ align:start position:0%
+example, this is a picture of the number
+ 
+
+ align:start position:0%
+example, this is a picture of the number
+of extreme humidity and heat days. So,
+
+ align:start position:0%
+of extreme humidity and heat days. So,
+ 
+
+ align:start position:0%
+of extreme humidity and heat days. So,
+um, how many days per year do we have
+
+ align:start position:0%
+um, how many days per year do we have
+ 
+
+ align:start position:0%
+um, how many days per year do we have
+with wet bulb temperatures, um, above 26
+
+ align:start position:0%
+with wet bulb temperatures, um, above 26
+ 
+
+ align:start position:0%
+with wet bulb temperatures, um, above 26
+degrees C, which is where you start to
+
+ align:start position:0%
+degrees C, which is where you start to
+ 
+
+ align:start position:0%
+degrees C, which is where you start to
+have really serious health consequences
+
+ align:start position:0%
+have really serious health consequences
+ 
+
+ align:start position:0%
+have really serious health consequences
+of outdoor work, outdoor sports, um, and
+
+ align:start position:0%
+of outdoor work, outdoor sports, um, and
+ 
+
+ align:start position:0%
+of outdoor work, outdoor sports, um, and
+if you don't have cooling in your home,
+
+ align:start position:0%
+if you don't have cooling in your home,
+ 
+
+ align:start position:0%
+if you don't have cooling in your home,
+um, just even sleeping at night. So, um,
+
+ align:start position:0%
+um, just even sleeping at night. So, um,
+ 
+
+ align:start position:0%
+um, just even sleeping at night. So, um,
+you can see that the southeast of the
+
+ align:start position:0%
+you can see that the southeast of the
+ 
+
+ align:start position:0%
+you can see that the southeast of the
+United States starts to have really dire
+
+ align:start position:0%
+United States starts to have really dire
+ 
+
+ align:start position:0%
+United States starts to have really dire
+conditions. Um, but and and you can back
+
+ align:start position:0%
+conditions. Um, but and and you can back
+ 
+
+ align:start position:0%
+conditions. Um, but and and you can back
+this off by year and sort of see how
+
+ align:start position:0%
+this off by year and sort of see how
+ 
+
+ align:start position:0%
+this off by year and sort of see how
+this evolves. So here's where we were in
+
+ align:start position:0%
+this evolves. So here's where we were in
+ 
+
+ align:start position:0%
+this evolves. So here's where we were in
+2000 um in terms of the frequency of
+
+ align:start position:0%
+2000 um in terms of the frequency of
+ 
+
+ align:start position:0%
+2000 um in terms of the frequency of
+those ultra high heat days and you can
+
+ align:start position:0%
+those ultra high heat days and you can
+ 
+
+ align:start position:0%
+those ultra high heat days and you can
+see that um that's all uh increasing um
+
+ align:start position:0%
+see that um that's all uh increasing um
+ 
+
+ align:start position:0%
+see that um that's all uh increasing um
+you know throughout the throughout North
+
+ align:start position:0%
+you know throughout the throughout North
+ 
+
+ align:start position:0%
+you know throughout the throughout North
+America and of course if we look at
+
+ align:start position:0%
+America and of course if we look at
+ 
+
+ align:start position:0%
+America and of course if we look at
+other geographies in the world in
+
+ align:start position:0%
+other geographies in the world in
+ 
+
+ align:start position:0%
+other geographies in the world in
+subsaharan Africa um where my wife's
+
+ align:start position:0%
+subsaharan Africa um where my wife's
+ 
+
+ align:start position:0%
+subsaharan Africa um where my wife's
+family is in India um in in uh in uh in
+
+ align:start position:0%
+family is in India um in in uh in uh in
+ 
+
+ align:start position:0%
+family is in India um in in uh in uh in
+uh the eastern part in West Bengal you
+
+ align:start position:0%
+uh the eastern part in West Bengal you
+ 
+
+ align:start position:0%
+uh the eastern part in West Bengal you
+can see that there's very serious
+
+ align:start position:0%
+can see that there's very serious
+ 
+
+ align:start position:0%
+can see that there's very serious
+consequences and so what this means is
+
+ align:start position:0%
+consequences and so what this means is
+ 
+
+ align:start position:0%
+consequences and so what this means is
+that we have to learn how to cool our
+
+ align:start position:0%
+that we have to learn how to cool our
+ 
+
+ align:start position:0%
+that we have to learn how to cool our
+buildings things fast and quickly and
+
+ align:start position:0%
+buildings things fast and quickly and
+ 
+
+ align:start position:0%
+buildings things fast and quickly and
+cheaply and low carbon. Um, and so that
+
+ align:start position:0%
+cheaply and low carbon. Um, and so that
+ 
+
+ align:start position:0%
+cheaply and low carbon. Um, and so that
+demand for cooling is a big piece of the
+
+ align:start position:0%
+demand for cooling is a big piece of the
+ 
+
+ align:start position:0%
+demand for cooling is a big piece of the
+the puzzle of what we're going to be
+
+ align:start position:0%
+the puzzle of what we're going to be
+ 
+
+ align:start position:0%
+the puzzle of what we're going to be
+grappling with. So that's one thing just
+
+ align:start position:0%
+grappling with. So that's one thing just
+ 
+
+ align:start position:0%
+grappling with. So that's one thing just
+to kind of be oriented to what is the
+
+ align:start position:0%
+to kind of be oriented to what is the
+ 
+
+ align:start position:0%
+to kind of be oriented to what is the
+challenge and why are we trying to solve
+
+ align:start position:0%
+challenge and why are we trying to solve
+ 
+
+ align:start position:0%
+challenge and why are we trying to solve
+for more efficient lowcarbon um methods
+
+ align:start position:0%
+for more efficient lowcarbon um methods
+ 
+
+ align:start position:0%
+for more efficient lowcarbon um methods
+for doing um uh heating and cooling. Um
+
+ align:start position:0%
+for doing um uh heating and cooling. Um
+ 
+
+ align:start position:0%
+for doing um uh heating and cooling. Um
+now the um the other thing couple other
+
+ align:start position:0%
+now the um the other thing couple other
+ 
+
+ align:start position:0%
+now the um the other thing couple other
+things I wanted to just kind of
+
+ align:start position:0%
+things I wanted to just kind of
+ 
+
+ align:start position:0%
+things I wanted to just kind of
+illuminate here. Um so one is that um
+
+ align:start position:0%
+illuminate here. Um so one is that um
+ 
+
+ align:start position:0%
+illuminate here. Um so one is that um
+you know the methane as a significant
+
+ align:start position:0%
+you know the methane as a significant
+ 
+
+ align:start position:0%
+you know the methane as a significant
+source of greenhouse gases this lever
+
+ align:start position:0%
+source of greenhouse gases this lever
+ 
+
+ align:start position:0%
+source of greenhouse gases this lever
+here which is about the waste um oop
+
+ align:start position:0%
+here which is about the waste um oop
+ 
+
+ align:start position:0%
+here which is about the waste um oop
+sorry I'm not used to windows um can I
+
+ align:start position:0%
+sorry I'm not used to windows um can I
+ 
+
+ align:start position:0%
+sorry I'm not used to windows um can I
+make that go away? Okay good um this
+
+ align:start position:0%
+make that go away? Okay good um this
+ 
+
+ align:start position:0%
+make that go away? Okay good um this
+lever over here which is about the waste
+
+ align:start position:0%
+lever over here which is about the waste
+ 
+
+ align:start position:0%
+lever over here which is about the waste
+and leakage of um non CO2 greenhouse
+
+ align:start position:0%
+and leakage of um non CO2 greenhouse
+ 
+
+ align:start position:0%
+and leakage of um non CO2 greenhouse
+gases. So if we look at methane in
+
+ align:start position:0%
+gases. So if we look at methane in
+ 
+
+ align:start position:0%
+gases. So if we look at methane in
+particular um what you can see here is
+
+ align:start position:0%
+particular um what you can see here is
+ 
+
+ align:start position:0%
+particular um what you can see here is
+that people talk about methane a when we
+
+ align:start position:0%
+that people talk about methane a when we
+ 
+
+ align:start position:0%
+that people talk about methane a when we
+talk about methane oftentimes we talk
+
+ align:start position:0%
+talk about methane oftentimes we talk
+ 
+
+ align:start position:0%
+talk about methane oftentimes we talk
+about cows and agricultural sources and
+
+ align:start position:0%
+about cows and agricultural sources and
+ 
+
+ align:start position:0%
+about cows and agricultural sources and
+that is very important. You can see the
+
+ align:start position:0%
+that is very important. You can see the
+ 
+
+ align:start position:0%
+that is very important. You can see the
+agricultural methane emissions but what
+
+ align:start position:0%
+agricultural methane emissions but what
+ 
+
+ align:start position:0%
+agricultural methane emissions but what
+a lot of people don't think about is the
+
+ align:start position:0%
+a lot of people don't think about is the
+ 
+
+ align:start position:0%
+a lot of people don't think about is the
+fact that a very significant part of our
+
+ align:start position:0%
+fact that a very significant part of our
+ 
+
+ align:start position:0%
+fact that a very significant part of our
+methane emissions um you know this is
+
+ align:start position:0%
+methane emissions um you know this is
+ 
+
+ align:start position:0%
+methane emissions um you know this is
+you know depending on the time horizon
+
+ align:start position:0%
+you know depending on the time horizon
+ 
+
+ align:start position:0%
+you know depending on the time horizon
+you know 50 60 times stronger than CO2
+
+ align:start position:0%
+you know 50 60 times stronger than CO2
+ 
+
+ align:start position:0%
+you know 50 60 times stronger than CO2
+um do significantly come from energy
+
+ align:start position:0%
+um do significantly come from energy
+ 
+
+ align:start position:0%
+um do significantly come from energy
+production. So when we can move away
+
+ align:start position:0%
+production. So when we can move away
+ 
+
+ align:start position:0%
+production. So when we can move away
+from coal which leaks methane out of the
+
+ align:start position:0%
+from coal which leaks methane out of the
+ 
+
+ align:start position:0%
+from coal which leaks methane out of the
+mines, gas which leaks methane across
+
+ align:start position:0%
+mines, gas which leaks methane across
+ 
+
+ align:start position:0%
+mines, gas which leaks methane across
+the value chain and oil which leaks
+
+ align:start position:0%
+the value chain and oil which leaks
+ 
+
+ align:start position:0%
+the value chain and oil which leaks
+methane at the drilling sites um and in
+
+ align:start position:0%
+methane at the drilling sites um and in
+ 
+
+ align:start position:0%
+methane at the drilling sites um and in
+the refineries um we can work on this
+
+ align:start position:0%
+the refineries um we can work on this
+ 
+
+ align:start position:0%
+the refineries um we can work on this
+chunk right. So if we if we can if we
+
+ align:start position:0%
+chunk right. So if we if we can if we
+ 
+
+ align:start position:0%
+chunk right. So if we if we can if we
+can decrease methane leakage from the
+
+ align:start position:0%
+can decrease methane leakage from the
+ 
+
+ align:start position:0%
+can decrease methane leakage from the
+energy systems which was you know heat's
+
+ align:start position:0%
+energy systems which was you know heat's
+ 
+
+ align:start position:0%
+energy systems which was you know heat's
+first major effort. Yeah. Okay. So you
+
+ align:start position:0%
+first major effort. Yeah. Okay. So you
+ 
+
+ align:start position:0%
+first major effort. Yeah. Okay. So you
+can see this this bent the curve a
+
+ align:start position:0%
+can see this this bent the curve a
+ 
+
+ align:start position:0%
+can see this this bent the curve a
+little bit here. And if I just do a
+
+ align:start position:0%
+little bit here. And if I just do a
+ 
+
+ align:start position:0%
+little bit here. And if I just do a
+little um replay, you can see the
+
+ align:start position:0%
+little um replay, you can see the
+ 
+
+ align:start position:0%
+little um replay, you can see the
+change. So that um that bending of that
+
+ align:start position:0%
+change. So that um that bending of that
+ 
+
+ align:start position:0%
+change. So that um that bending of that
+curve of of energy leakage is one
+
+ align:start position:0%
+curve of of energy leakage is one
+ 
+
+ align:start position:0%
+curve of of energy leakage is one
+opportunity. But if we can get off of
+
+ align:start position:0%
+opportunity. But if we can get off of
+ 
+
+ align:start position:0%
+opportunity. But if we can get off of
+those of fossil fuels entirely, for
+
+ align:start position:0%
+those of fossil fuels entirely, for
+ 
+
+ align:start position:0%
+those of fossil fuels entirely, for
+example, by um you know, pricing CO2 um
+
+ align:start position:0%
+example, by um you know, pricing CO2 um
+ 
+
+ align:start position:0%
+example, by um you know, pricing CO2 um
+and doing things that are that that
+
+ align:start position:0%
+and doing things that are that that
+ 
+
+ align:start position:0%
+and doing things that are that that
+allow us to decarbonize energy supply,
+
+ align:start position:0%
+allow us to decarbonize energy supply,
+ 
+
+ align:start position:0%
+allow us to decarbonize energy supply,
+what you'll see is that those um those
+
+ align:start position:0%
+what you'll see is that those um those
+ 
+
+ align:start position:0%
+what you'll see is that those um those
+methane uh emissions from energy go down
+
+ align:start position:0%
+methane uh emissions from energy go down
+ 
+
+ align:start position:0%
+methane uh emissions from energy go down
+even further. So there's sort of a
+
+ align:start position:0%
+even further. So there's sort of a
+ 
+
+ align:start position:0%
+even further. So there's sort of a
+two-prong approach here, which is to
+
+ align:start position:0%
+two-prong approach here, which is to
+ 
+
+ align:start position:0%
+two-prong approach here, which is to
+reduce the leakage from the system that
+
+ align:start position:0%
+reduce the leakage from the system that
+ 
+
+ align:start position:0%
+reduce the leakage from the system that
+we have, which is the original gas leaks
+
+ align:start position:0%
+we have, which is the original gas leaks
+ 
+
+ align:start position:0%
+we have, which is the original gas leaks
+idea. And then there's the question of
+
+ align:start position:0%
+idea. And then there's the question of
+ 
+
+ align:start position:0%
+idea. And then there's the question of
+how do we transition away from these um
+
+ align:start position:0%
+how do we transition away from these um
+ 
+
+ align:start position:0%
+how do we transition away from these um
+highcarbon sources of energy? Um I'm
+
+ align:start position:0%
+highcarbon sources of energy? Um I'm
+ 
+
+ align:start position:0%
+highcarbon sources of energy? Um I'm
+just going to revert back without those
+
+ align:start position:0%
+just going to revert back without those
+ 
+
+ align:start position:0%
+just going to revert back without those
+changes and just say that. So then the
+
+ align:start position:0%
+changes and just say that. So then the
+ 
+
+ align:start position:0%
+changes and just say that. So then the
+question is, well, how might we simulate
+
+ align:start position:0%
+question is, well, how might we simulate
+ 
+
+ align:start position:0%
+question is, well, how might we simulate
+the effects of doing district geothermal
+
+ align:start position:0%
+the effects of doing district geothermal
+ 
+
+ align:start position:0%
+the effects of doing district geothermal
+like we're going to be talking about the
+
+ align:start position:0%
+like we're going to be talking about the
+ 
+
+ align:start position:0%
+like we're going to be talking about the
+next couple of days? And what I'll say
+
+ align:start position:0%
+next couple of days? And what I'll say
+ 
+
+ align:start position:0%
+next couple of days? And what I'll say
+is that that's a blind spot in tools
+
+ align:start position:0%
+is that that's a blind spot in tools
+ 
+
+ align:start position:0%
+is that that's a blind spot in tools
+like this because um as the first thing
+
+ align:start position:0%
+like this because um as the first thing
+ 
+
+ align:start position:0%
+like this because um as the first thing
+as Adam said today was that so much of
+
+ align:start position:0%
+as Adam said today was that so much of
+ 
+
+ align:start position:0%
+as Adam said today was that so much of
+our attention has been on electricity
+
+ align:start position:0%
+our attention has been on electricity
+ 
+
+ align:start position:0%
+our attention has been on electricity
+and light. We don't tend to think about
+
+ align:start position:0%
+and light. We don't tend to think about
+ 
+
+ align:start position:0%
+and light. We don't tend to think about
+thermal energy and I'll say that that's
+
+ align:start position:0%
+thermal energy and I'll say that that's
+ 
+
+ align:start position:0%
+thermal energy and I'll say that that's
+also the case for nodes. There is
+
+ align:start position:0%
+also the case for nodes. There is
+ 
+
+ align:start position:0%
+also the case for nodes. There is
+geothermal built into what we define as
+
+ align:start position:0%
+geothermal built into what we define as
+ 
+
+ align:start position:0%
+geothermal built into what we define as
+renewables. Um so that when you're you
+
+ align:start position:0%
+renewables. Um so that when you're you
+ 
+
+ align:start position:0%
+renewables. Um so that when you're you
+know you know subsidizing renewables or
+
+ align:start position:0%
+know you know subsidizing renewables or
+ 
+
+ align:start position:0%
+know you know subsidizing renewables or
+you're doing other moves like uh carbon
+
+ align:start position:0%
+you're doing other moves like uh carbon
+ 
+
+ align:start position:0%
+you're doing other moves like uh carbon
+pricing that do transition toward a
+
+ align:start position:0%
+pricing that do transition toward a
+ 
+
+ align:start position:0%
+pricing that do transition toward a
+renewable world that does include if you
+
+ align:start position:0%
+renewable world that does include if you
+ 
+
+ align:start position:0%
+renewable world that does include if you
+look at the details geothermal but it's
+
+ align:start position:0%
+look at the details geothermal but it's
+ 
+
+ align:start position:0%
+look at the details geothermal but it's
+largely thinking about that first bucket
+
+ align:start position:0%
+largely thinking about that first bucket
+ 
+
+ align:start position:0%
+largely thinking about that first bucket
+in her um in her graph of the um using
+
+ align:start position:0%
+in her um in her graph of the um using
+ 
+
+ align:start position:0%
+in her um in her graph of the um using
+geo using like the super high
+
+ align:start position:0%
+geo using like the super high
+ 
+
+ align:start position:0%
+geo using like the super high
+temperature geothermal to generate
+
+ align:start position:0%
+temperature geothermal to generate
+ 
+
+ align:start position:0%
+temperature geothermal to generate
+electricity. We're not really dealing
+
+ align:start position:0%
+electricity. We're not really dealing
+ 
+
+ align:start position:0%
+electricity. We're not really dealing
+with it um from a heat standpoint. The
+
+ align:start position:0%
+with it um from a heat standpoint. The
+ 
+
+ align:start position:0%
+with it um from a heat standpoint. The
+best way for us to represent that is for
+
+ align:start position:0%
+best way for us to represent that is for
+ 
+
+ align:start position:0%
+best way for us to represent that is for
+us to think about electrifying the
+
+ align:start position:0%
+us to think about electrifying the
+ 
+
+ align:start position:0%
+us to think about electrifying the
+building and industry space because what
+
+ align:start position:0%
+building and industry space because what
+ 
+
+ align:start position:0%
+building and industry space because what
+you're doing is you're often moving to
+
+ align:start position:0%
+you're doing is you're often moving to
+ 
+
+ align:start position:0%
+you're doing is you're often moving to
+some kind of a heat pump, a geothermal
+
+ align:start position:0%
+some kind of a heat pump, a geothermal
+ 
+
+ align:start position:0%
+some kind of a heat pump, a geothermal
+heat pump um in lie of a um but you're
+
+ align:start position:0%
+heat pump um in lie of a um but you're
+ 
+
+ align:start position:0%
+heat pump um in lie of a um but you're
+also doing that in a far more energy
+
+ align:start position:0%
+also doing that in a far more energy
+ 
+
+ align:start position:0%
+also doing that in a far more energy
+efficient way than um than you'd be
+
+ align:start position:0%
+efficient way than um than you'd be
+ 
+
+ align:start position:0%
+efficient way than um than you'd be
+doing otherwise with fossil fuels. So
+
+ align:start position:0%
+doing otherwise with fossil fuels. So
+ 
+
+ align:start position:0%
+doing otherwise with fossil fuels. So
+this is a this is a kind of an energy
+
+ align:start position:0%
+this is a this is a kind of an energy
+ 
+
+ align:start position:0%
+this is a this is a kind of an energy
+efficiency and electrification play
+
+ align:start position:0%
+efficiency and electrification play
+ 
+
+ align:start position:0%
+efficiency and electrification play
+which are you know important pieces of
+
+ align:start position:0%
+which are you know important pieces of
+ 
+
+ align:start position:0%
+which are you know important pieces of
+the puzzle. Um, the last thing I'll just
+
+ align:start position:0%
+the puzzle. Um, the last thing I'll just
+ 
+
+ align:start position:0%
+the puzzle. Um, the last thing I'll just
+say is that when you're anytime you're
+
+ align:start position:0%
+say is that when you're anytime you're
+ 
+
+ align:start position:0%
+say is that when you're anytime you're
+electrifying something, of course you'll
+
+ align:start position:0%
+electrifying something, of course you'll
+ 
+
+ align:start position:0%
+electrifying something, of course you'll
+have to and and you'll notice if you
+
+ align:start position:0%
+have to and and you'll notice if you
+ 
+
+ align:start position:0%
+have to and and you'll notice if you
+play with NROs that electrifying
+
+ align:start position:0%
+play with NROs that electrifying
+ 
+
+ align:start position:0%
+play with NROs that electrifying
+transport doesn't have a huge effect on
+
+ align:start position:0%
+transport doesn't have a huge effect on
+ 
+
+ align:start position:0%
+transport doesn't have a huge effect on
+the climate. Electrifying building an
+
+ align:start position:0%
+the climate. Electrifying building an
+ 
+
+ align:start position:0%
+the climate. Electrifying building an
+industry by itself doesn't have a huge
+
+ align:start position:0%
+industry by itself doesn't have a huge
+ 
+
+ align:start position:0%
+industry by itself doesn't have a huge
+effect on the climate. And part of that
+
+ align:start position:0%
+effect on the climate. And part of that
+ 
+
+ align:start position:0%
+effect on the climate. And part of that
+is because you're not decarbonizing the
+
+ align:start position:0%
+is because you're not decarbonizing the
+ 
+
+ align:start position:0%
+is because you're not decarbonizing the
+energy, the electricity supply. So you
+
+ align:start position:0%
+energy, the electricity supply. So you
+ 
+
+ align:start position:0%
+energy, the electricity supply. So you
+have to make sure that if you're running
+
+ align:start position:0%
+have to make sure that if you're running
+ 
+
+ align:start position:0%
+have to make sure that if you're running
+those heat pumps, you're running them
+
+ align:start position:0%
+those heat pumps, you're running them
+ 
+
+ align:start position:0%
+those heat pumps, you're running them
+off of lowcarbon electricity. And that's
+
+ align:start position:0%
+off of lowcarbon electricity. And that's
+ 
+
+ align:start position:0%
+off of lowcarbon electricity. And that's
+another system interaction. So if you
+
+ align:start position:0%
+another system interaction. So if you
+ 
+
+ align:start position:0%
+another system interaction. So if you
+can do things like uh you know stop
+
+ align:start position:0%
+can do things like uh you know stop
+ 
+
+ align:start position:0%
+can do things like uh you know stop
+building new coal plants and therefore
+
+ align:start position:0%
+building new coal plants and therefore
+ 
+
+ align:start position:0%
+building new coal plants and therefore
+um you know work toward kind of that
+
+ align:start position:0%
+um you know work toward kind of that
+ 
+
+ align:start position:0%
+um you know work toward kind of that
+decarbonization of the electricity
+
+ align:start position:0%
+decarbonization of the electricity
+ 
+
+ align:start position:0%
+decarbonization of the electricity
+system. If you you know do some really
+
+ align:start position:0%
+system. If you you know do some really
+ 
+
+ align:start position:0%
+system. If you you know do some really
+heavily heavy kind of um reductions
+
+ align:start position:0%
+heavily heavy kind of um reductions
+ 
+
+ align:start position:0%
+heavily heavy kind of um reductions
+either technologically or uh or through
+
+ align:start position:0%
+either technologically or uh or through
+ 
+
+ align:start position:0%
+either technologically or uh or through
+policy to reduce natural gas and so on
+
+ align:start position:0%
+policy to reduce natural gas and so on
+ 
+
+ align:start position:0%
+policy to reduce natural gas and so on
+then you're decarbonizing electricity
+
+ align:start position:0%
+then you're decarbonizing electricity
+ 
+
+ align:start position:0%
+then you're decarbonizing electricity
+supply then the electrifification
+
+ align:start position:0%
+supply then the electrifification
+ 
+
+ align:start position:0%
+supply then the electrifification
+actually has more of an impact on the
+
+ align:start position:0%
+actually has more of an impact on the
+ 
+
+ align:start position:0%
+actually has more of an impact on the
+climate. So just to say that these
+
+ align:start position:0%
+climate. So just to say that these
+ 
+
+ align:start position:0%
+climate. So just to say that these
+systems are interactive and we want to
+
+ align:start position:0%
+systems are interactive and we want to
+ 
+
+ align:start position:0%
+systems are interactive and we want to
+think about um as we are going and
+
+ align:start position:0%
+think about um as we are going and
+ 
+
+ align:start position:0%
+think about um as we are going and
+trying to solve these thermal heating
+
+ align:start position:0%
+trying to solve these thermal heating
+ 
+
+ align:start position:0%
+trying to solve these thermal heating
+problems that we do it in as renewably
+
+ align:start position:0%
+problems that we do it in as renewably
+ 
+
+ align:start position:0%
+problems that we do it in as renewably
+powered a way as possible. But also just
+
+ align:start position:0%
+powered a way as possible. But also just
+ 
+
+ align:start position:0%
+powered a way as possible. But also just
+that there are blind spots in so many of
+
+ align:start position:0%
+that there are blind spots in so many of
+ 
+
+ align:start position:0%
+that there are blind spots in so many of
+these modeling tools and so many of
+
+ align:start position:0%
+these modeling tools and so many of
+ 
+
+ align:start position:0%
+these modeling tools and so many of
+these policy discussions given the
+
+ align:start position:0%
+these policy discussions given the
+ 
+
+ align:start position:0%
+these policy discussions given the
+general tendency to focus very heavily
+
+ align:start position:0%
+general tendency to focus very heavily
+ 
+
+ align:start position:0%
+general tendency to focus very heavily
+on uh electricity.
+
+ align:start position:0%
+on uh electricity.
+ 
+
+ align:start position:0%
+on uh electricity.
+Is that what you want me to cover?
+
+ align:start position:0%
+Is that what you want me to cover?
+ 
+
+ align:start position:0%
+Is that what you want me to cover?
+Um, oh and I'll just say one one more
+
+ align:start position:0%
+Um, oh and I'll just say one one more
+ 
+
+ align:start position:0%
+Um, oh and I'll just say one one more
+thing which is that of course AI and it
+
+ align:start position:0%
+thing which is that of course AI and it
+ 
+
+ align:start position:0%
+thing which is that of course AI and it
+data center growth is driving you know
+
+ align:start position:0%
+data center growth is driving you know
+ 
+
+ align:start position:0%
+data center growth is driving you know
+increase in all of these parameters in
+
+ align:start position:0%
+increase in all of these parameters in
+ 
+
+ align:start position:0%
+increase in all of these parameters in
+terms of energy usage. So we have to do
+
+ align:start position:0%
+terms of energy usage. So we have to do
+ 
+
+ align:start position:0%
+terms of energy usage. So we have to do
+everything that much harder and that
+
+ align:start position:0%
+everything that much harder and that
+ 
+
+ align:start position:0%
+everything that much harder and that
+much faster. Um now hopefully the AI and
+
+ align:start position:0%
+much faster. Um now hopefully the AI and
+ 
+
+ align:start position:0%
+much faster. Um now hopefully the AI and
+the machine learning can help us and
+
+ align:start position:0%
+the machine learning can help us and
+ 
+
+ align:start position:0%
+the machine learning can help us and
+we're going to talk about the ways that
+
+ align:start position:0%
+we're going to talk about the ways that
+ 
+
+ align:start position:0%
+we're going to talk about the ways that
+advanced analytics can help us identify
+
+ align:start position:0%
+advanced analytics can help us identify
+ 
+
+ align:start position:0%
+advanced analytics can help us identify
+geothermal opportunities and optimize
+
+ align:start position:0%
+geothermal opportunities and optimize
+ 
+
+ align:start position:0%
+geothermal opportunities and optimize
+for them. But just notice just
+
+ align:start position:0%
+for them. But just notice just
+ 
+
+ align:start position:0%
+for them. But just notice just
+remembering whenever we talk about those
+
+ align:start position:0%
+remembering whenever we talk about those
+ 
+
+ align:start position:0%
+remembering whenever we talk about those
+types of computational things, we always
+
+ align:start position:0%
+types of computational things, we always
+ 
+
+ align:start position:0%
+types of computational things, we always
+want to think about the foot the
+
+ align:start position:0%
+want to think about the foot the
+ 
+
+ align:start position:0%
+want to think about the foot the
+handprint and the footprint of those
+
+ align:start position:0%
+handprint and the footprint of those
+ 
+
+ align:start position:0%
+handprint and the footprint of those
+technologies.
+
+ align:start position:0%
+technologies.
+ 
+
+ align:start position:0%
+technologies.
+>> Okay,
+
+ align:start position:0%
+>> Okay,
+ 
+
+ align:start position:0%
+>> Okay,
+>> thank you so much.
+
+ align:start position:0%
+>> thank you so much.
+ 
+
+ align:start position:0%
+>> thank you so much.
+>> Oh my gosh, that was amazing. And
+
+ align:start position:0%
+>> Oh my gosh, that was amazing. And
+ 
+
+ align:start position:0%
+>> Oh my gosh, that was amazing. And
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+>> all right, that that was amazing. And
+
+ align:start position:0%
+>> all right, that that was amazing. And
+ 
+
+ align:start position:0%
+>> all right, that that was amazing. And
+now And now we have to talk afterwards
+
+ align:start position:0%
+now And now we have to talk afterwards
+ 
+
+ align:start position:0%
+now And now we have to talk afterwards
+about getting geothermal in there with a
+
+ align:start position:0%
+about getting geothermal in there with a
+ 
+
+ align:start position:0%
+about getting geothermal in there with a
+little toggle switch. Yeah.
\ No newline at end of file
diff --git a/TkMsVwzd1C0.txt b/TkMsVwzd1C0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3e474f1d9f2ff5ba397adce2c8010fe96e265198
--- /dev/null
+++ b/TkMsVwzd1C0.txt
@@ -0,0 +1,2088 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation, or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+[MUSIC PLAYING]
+
+PROFESSOR: Over the last several
+lectures, we developed
+
+the Fourier representation for
+continuous-time signals.
+
+What I'd now like to do
+is develop a similar
+
+representation for
+discrete-time.
+
+And let me begin the discussion
+by reminding you of
+
+what our basic motivation was.
+
+The idea is that what we wanted
+to do was exploit the
+
+properties of linearity and
+time invariance for linear
+
+time-invariant systems.
+
+So in the case of linear
+time-invariant systems, the
+
+basic idea was to consider
+decomposing the input as a
+
+linear combination
+of basic inputs.
+
+And then, because of linearity,
+the output could be
+
+expressed as a linear
+combination of corresponding
+
+outputs where psi sub i is the
+output due to phi sub i.
+
+So basically, what we attempted
+to do was decompose
+
+the input, and then reconstruct
+the output through
+
+a linear combination of the
+outputs to those basic inputs.
+
+We then focused on the notion
+of choosing the basic inputs
+
+with two criteria in mind.
+
+One was to choose them so that a
+broad class of signals could
+
+be constructed out of
+those basic inputs.
+
+And the second was to choose the
+basic inputs, so that the
+
+response to those was
+easy to compute.
+
+And as you recall, one
+representation that we ended
+
+up with, with those basic
+criteria in mind, was the
+
+representation through
+convolution.
+
+And then in beginning the
+discussion of the Fourier
+
+representation of
+continuous-time signals, we
+
+chose as another set of basic
+inputs complex exponentials.
+
+So for continuous-time, we chose
+a set of basic inputs
+
+which were complex
+exponentials.
+
+The motivation there was the
+fact that the complex
+
+exponentials have what
+we refer to as the
+
+eigenfunction property.
+
+Namely, if we put complex
+exponentials into our
+
+continuous-time systems, then
+the output is a complex
+
+exponential of the same
+form with only a
+
+change in complex amplitude.
+
+And that change in complex
+amplitude is what we referred
+
+to as the frequency response
+of the system.
+
+And also, by the way, as it
+developed later, that
+
+frequency response, as you
+should now recognize from this
+
+expression, is in fact the
+Fourier transform, the
+
+continuous-time Fourier
+transform of the system
+
+impulse response.
+
+And the notion of decomposing
+a signal as a linear
+
+combination of these complex
+exponentials is what, first
+
+the Fourier series
+representation, and then later
+
+the Fourier transform
+representation
+
+corresponded to.
+
+And finally, to remind you of
+one additional point, the fact
+
+is that because of
+the eigenfunction
+
+property, the response--
+
+once we have decomposed the
+input as a linear combination
+
+of complex exponentials, the
+response to that linear
+
+combination is straightforward
+to compute once we know the
+
+frequency response because of
+the eigenfunction property.
+
+Now, basically the same strategy
+and many of the same
+
+ideas work in discrete-time,
+paralleling almost exactly
+
+what happened in
+continuous-time.
+
+So the similarities between
+discrete-time and
+
+continuous-time are
+very strong.
+
+Although as we'll see, there are
+a number of differences.
+
+And it's important as we go
+through the discussion to
+
+illuminate not only the
+similarities, but obviously
+
+also the differences.
+
+Well, let's begin with the
+eigenfunction property, and
+
+let me just state that just as
+in continuous-time, if we
+
+consider a set of basic signals,
+which are complex
+
+exponential rules, then
+discrete-time linear time-m
+
+invariant systems have the
+eigenfunction property.
+
+Namely, if we put a complex
+exponential into the system,
+
+the response is a complex
+exponential at the same
+
+complex frequency, and simply
+multiplied by an appropriate
+
+complex factor, or constant.
+
+And just as we did in
+continuous-time, we will be
+
+referring to this complex
+constant, which is a function,
+
+of course, the frequency of the
+complex exponential input.
+
+We'll be referring to this as
+the frequency response.
+
+And although it's not
+particularly evident at this
+
+point, as the discussion
+develops through this lecture,
+
+what in fact will happen is
+very much paralleling
+
+continuous-time.
+
+This particular expression, in
+fact, will correspond to what
+
+we'll refer to as the Fourier
+transform, the discrete-time
+
+Fourier transform of the system
+impulse response.
+
+So there, of course, there's a
+very strong parallel between
+
+continuous time and
+discrete time.
+
+Now, just as we did in
+continuous-time, let's begin
+
+the discussion by first
+concentrating on periodic--
+
+the representation through
+complex exponentials of
+
+periodic sequences, and then
+we'll generalize that
+
+discussion to the
+representation
+
+of aperiodic signals.
+
+So let's consider first a
+periodic signal, or in
+
+general, signals which
+are periodic.
+
+Period denoted by capital N.
+And then, of course, the
+
+fundamental frequency is 2
+pi divided by capital N.
+
+Now, we can consider
+exponentials which have this
+
+as a fundamental frequency, or
+which are harmonics of that,
+
+and that would correspond
+to the class of complex
+
+exponentials of the form
+e to the jk omega 0 n.
+
+So these complex exponentials
+then, as k varies, are complex
+
+exponentials that are
+harmonically related, all of
+
+which are periodic with the
+same period capital N.
+
+Although the fundamental
+period is
+
+different for each of these.
+
+Each of them being related
+by an integer amount.
+
+Now, again, just as we did in
+continuous time, we can
+
+consider attempting to build our
+periodic signal out of a
+
+linear combination of these.
+
+And so we consider a periodic
+signal, which is a weighted
+
+sum of these complex
+exponentials.
+
+And, of course, this
+periodic signal--
+
+this is a periodic signal.
+
+This can be verified, more or
+less, in a straightforward way
+
+by substitution.
+
+And, of course, one of the
+things that we'll want to
+
+address shortly is how broad a
+class of signals, again, can
+
+be represented by this sum?
+
+And another question obviously
+will be, how do we determine
+
+the coefficients a sub k?
+
+However, before we do that, let
+me focus on an important
+
+distinction between
+continuous-time and
+
+discrete-time in the context of
+these complex exponentials
+
+and this representation.
+
+When we talked about complex
+exponentials and sinusoids
+
+early in the course, one of the
+differences that we saw
+
+between continuous-time and
+discrete-time is that in
+
+continuous-time, as we vary the
+frequency variable, we see
+
+different complex exponentials
+as omega varies.
+
+Whereas, in discrete-time, we
+saw, in fact, that there was a
+
+periodicity.
+
+Or said another way, it's
+straightforward to verify that
+
+if we think of this class
+of complex exponentials.
+
+That, in fact, if we consider
+varying k by adding to it
+
+capital N, where capital N is
+the period of the fundamental
+
+complex exponential.
+
+Then in fact, if we replace k by
+k plus capital N, we'll see
+
+exactly the same complex
+exponentials over again.
+
+Now, what does that say?
+
+What it says is that if I
+consider this class of complex
+
+exponentials, as k varies from
+0 through capital N minus 1,
+
+we will see all of the ones
+that there are to see.
+
+There aren't anymore.
+
+And so, in fact, if we can
+build x of n out of this
+
+linear combination, then we
+better be able to do it as k
+
+varies from 0 up to N minus 1.
+
+Because beyond that, we'll
+simply see the same complex
+
+exponentials over again.
+
+So, for example, if k takes on
+the value capital N, that will
+
+be exactly the same complex
+exponential as if
+
+k is equal to 0.
+
+So in fact, this sum ranges
+only over capital N of the
+
+distinct complex exponentials.
+
+Let's say, for example, from
+0 to capital N minus 1 .
+
+Although, in fact, since these
+complex exponentials repeat in
+
+k, I could actually consider
+instead of from 0 to N minus
+
+1, I could consider from
+1 to N, or from 2 to
+
+N plus 1, or whatever.
+
+Or said another way, in this
+representation, I could
+
+alternatively choose k outside
+this range, thinking of these
+
+coefficients simply as
+periodically repeating in k
+
+because of the fact that these
+complex exponentials
+
+periodically repeat in k.
+
+So, in fact, in place of this
+expression, it will be common
+
+in writing the Fourier series
+expression to write it as I've
+
+indicated here, where the
+implication is that these
+
+Fourier coefficients
+periodically repeat as k
+
+continues to repeat outside
+the interval from
+
+0 to N minus 1.
+
+And so this notation, in fact,
+says that what we're going to
+
+use is k ranging over one
+period of this periodic
+
+sequence, which is the Fourier
+series coefficients.
+
+So the expression that we have
+then for the Fourier series
+
+I've repeated here.
+
+And the implication
+now is that the
+
+a sub k's are periodic.
+
+They periodically repeat
+because, of course, these
+
+exponentials periodically
+repeat.
+
+This indicates that we only
+use them over one period.
+
+And now we can inquire as
+to how we determine the
+
+coefficients a sub k.
+
+Well, we can formally go through
+this much as we did in
+
+the continuous-time case.
+
+And we do, in fact, do that in
+the text, which involves
+
+substituting some sums and
+interchanging the orders of
+
+summation, et cetera.
+
+But let me draw your attention
+to the fact that this, in
+
+fact, can be thought of as
+capital N equations and
+
+capital N unknowns.
+
+In other words, we know x of n
+over a period, and so we know
+
+what the left-hand side of this
+is for capital N values.
+
+And we'd like to determine
+these constants a sub k.
+
+Well, it turns out that there
+is a nice convenient
+
+closed-form expression
+for that.
+
+And, in fact, if we evaluate
+the closed-form expression
+
+through any of a variety of
+algebraic manipulations, we
+
+end up then with the
+analysis equation.
+
+And the analysis equation, which
+tells us how to get the
+
+coefficients a sub k from x of n
+is what I've indicated here.
+
+And so this tells us how from
+x of n to get the a sub k's.
+
+And, of course, the first
+equation tells us how x of n
+
+is built up out of
+the a sub k.
+
+Notice incidentally that there
+is a strong duality between
+
+these two equations.
+
+And that's a duality that we'll
+return to, actually
+
+toward the end of the
+next lecture.
+
+Now, there is a real difference
+between the way
+
+those equations look and the
+way the continuous-time
+
+Fourier series looked.
+
+In the continuous-time case,
+let me remind you that it
+
+required an infinite number of
+coefficients to build up this
+
+continuous-time function.
+
+And so this was not simply a
+matter of identifying how to
+
+invert capital N or a finite
+number of equations and a
+
+finite number of unknowns.
+
+And the analysis equation was
+an integration as opposed to
+
+the synthesis equation,
+which is a summation.
+
+So there is a real difference
+there between the
+
+continuous-time and
+discrete-time cases.
+
+And the difference arises, to
+a large extent, because of
+
+this notion that in
+discrete-time, the complex
+
+exponentials are periodic
+in their frequency.
+
+So we have then to summarize the
+synthesis equation and the
+
+analysis equation for the
+discrete-time Fourier series.
+
+Again, x of n, our original
+signal is periodic.
+
+And, of course, the complex
+exponentials
+
+involved are periodic.
+
+They're periodic
+obviously in n.
+
+But in contrast to
+continuous-time,
+
+these repeat in k.
+
+In other words, as k omega 0
+goes outside a range that
+
+covers a 2 pi interval.
+
+And because of that, we're
+imposing, in a sense, the
+
+interpretation that
+the a sub k's are
+
+likewise a periodic sequence.
+
+And in fact, if we look at the
+analysis equation, as we let k
+
+vary outside the range from 0
+to N minus 1, what you can
+
+easily verify by substitution in
+here is that this sequence
+
+will, in fact, periodically
+repeat.
+
+So to underscore the difference
+between the
+
+continuous-time and
+discrete-time cases, we have
+
+this periodicity in the time
+domain, and that's a
+
+periodicity that is, of course,
+true in discrete-time
+
+and it's also true in
+continuous-time if we replace
+
+the integer variable by the
+discrete-time time variable.
+
+And we also, in discrete-time,
+have this periodicity in k, or
+
+in k omega 0.
+
+And correspondingly, a
+periodicity in the Fourier
+
+coefficients.
+
+And that is a set of properties
+that does not
+
+happen in continuous-time.
+
+And it is that that essentially
+leads to all of
+
+the important differences
+between discrete-time Fourier
+
+representations and
+continuous-time Fourier
+
+representations.
+
+Now, just quickly, let me draw
+your attention to the issue of
+
+convergence and when a sequence
+can and can't be
+
+represented, et cetera.
+
+And recall that in the
+continuous-time case, we
+
+focused on convergence in the
+context either of conditions,
+
+which I referred to as square
+integrability, or another set
+
+of conditions, which were the
+Dirichlet conditions.
+
+And there was this issue about
+when the signal does and
+
+doesn't converge at
+discontinuities, et cetera.
+
+Let me just simply draw your
+attention to the fact that in
+
+the discrete-time case, what we
+have is the representation
+
+of the periodic signal
+as a sum of a
+
+finite number of terms.
+
+This represents capital
+N equations
+
+and capital N unknowns.
+
+If we consider earth the partial
+sum, namely taking a
+
+smaller number of terms, then
+simply what happens is as the
+
+number of terms increases to the
+finite number required to
+
+represent x of n, we simply end
+up with the partial sum
+
+representing the finite
+[? length ?] sequence.
+
+What all that boils down to
+is the statement that in
+
+discrete-time there really are
+no convergence issues as there
+
+were in continuous-time.
+
+OK, well let's look at an
+example of the Fourier series
+
+representation for a
+particular signal.
+
+And the one that I've picked
+here is a simple one.
+
+Namely, a constant, a sine
+term, and a cosine term.
+
+Now, for this particular
+example, we can expand this
+
+out directly in terms of complex
+exponentials and
+
+essentially recognize this as a
+sum of complex exponentials.
+
+It's examined in more detail
+in Example 5.2 in the text.
+
+And if we look at the Fourier
+series coefficients, we can
+
+either look at it in terms of
+real and imaginary parts or
+
+magnitude and angle.
+
+On the left side here, I have
+the real part of the Fourier
+
+coefficients.
+
+And let me draw your attention
+to the fact that I've drawn
+
+this to specifically illuminate
+the periodicity of
+
+the Fourier series coefficients
+with a period of
+
+capital N.
+
+So here are the Fourier
+coefficients.
+
+And, in fact, it's this line
+that represents the DC, or
+
+constant term, and these two
+lines that represent the
+
+cosine term.
+
+And of course, these are the
+three terms that are required.
+
+Or equivalently, this one,
+this one, and this one.
+
+And then because of the
+periodicity of the Fourier
+
+series coefficients, this simply
+periodically repeats.
+
+So here is the real part
+and below it I show
+
+the imaginary part.
+
+And in the imaginary part,
+incidentally let me draw your
+
+attention to the fact that it's
+this term and this term
+
+in the imaginary part that
+represent the sinusoid.
+
+Whereas it's the symmetric terms
+in the real part the
+
+represent the cosine.
+
+OK, let's look at
+another example.
+
+This is another example from the
+text, and one that we'll
+
+be making frequent reference to
+in this particular lecture.
+
+And what it is, is
+a square wave.
+
+And I've expressed the Fourier
+series coefficients, which are
+
+algebraically developed
+in the text.
+
+I've expressed the Fourier
+series coefficients as samples
+
+of an envelope function.
+
+And so I've expressed it as
+samples of this particular
+
+function, which is referred
+to as a sin
+
+nx over sin x function.
+
+And let me just compare it to
+a continuous-time example,
+
+which is the continuous-time
+square wave, where with the
+
+continuous-times square wave the
+form of the Fourier series
+
+coefficients was as samples of
+what we refer to as a sin x
+
+over x function.
+
+Now, the sin nx over sin x
+function, which is the
+
+envelope of the Fourier series
+coefficients for the
+
+discrete-time periodic square
+wave plays the role--
+
+and we'll see it very often
+in discrete-time--
+
+that sin x over x does
+in continuous-time.
+
+And, in fact, we should
+understand right from the
+
+beginning that the sin x over
+x envelope couldn't possibly
+
+be the envelope of the
+discrete-time Fourier series
+
+coefficients.
+
+And one obvious reason is
+that it is not periodic.
+
+What we require, of course, from
+the discussion that I've
+
+just gone through is
+periodicity of the
+
+coefficients.
+
+And then consequently, also
+periodicity of the envelope in
+
+the discrete-time case.
+
+So once again, if we look back
+at the algebraic expression
+
+that I have, it's samples of
+the sin nx over sine x
+
+function that represent the
+Fourier series coefficients of
+
+this periodic square wave.
+
+Now, in the representation in
+the continuous-time case, we
+
+essentially had used the concept
+of an envelope to
+
+represent the Fourier series
+coefficients, and the notion
+
+that the Fourier series
+coefficients were samples of
+
+an envelope.
+
+And that is the same notion
+that we'll be using in
+
+discrete-time.
+
+So again for this square wave
+example, then what we have is
+
+an envelope function, the sin
+nx over sin x envelope
+
+function for a particular
+value of the period.
+
+Here indicated with a period
+of 10 samples.
+
+These samples of this envelope
+function would then represent
+
+the Fourier series
+coefficients.
+
+If we increased the period, then
+we would simply have a
+
+finer spacing on the samples
+of the envelope function to
+
+get the Fourier series
+coefficients.
+
+And likewise, if we increase the
+period still further, what
+
+we would have is an even
+finer spacing.
+
+So actually, as the period
+increases, and recall we used
+
+this in continuous-time also.
+
+As the period increases, we can
+view the Fourier series
+
+coefficients as samples
+of an envelope.
+
+And as the period increases,
+the sample spacing
+
+gets finer and finer.
+
+And in fact, as the period
+goes off essentially to
+
+infinity, the samples of the
+envelope, in effect, become
+
+the envelope.
+
+And recall also that this was
+essentially the trick that we
+
+used in continuous-time to allow
+us to develop or utilize
+
+the Fourier series to provide a
+representation of aperiodic
+
+signals as a linear combination
+of complex
+
+exponentials.
+
+In particular, what we did in
+the continuous-time case when
+
+we had an aperiodic signal was
+to consider constructing a
+
+periodic signal for which
+the aperiodic
+
+signal was one period.
+
+And then we developed the notion
+that since the periodic
+
+signal has a Fourier series, and
+since as the period of the
+
+periodic signal increases and
+goes to infinity, the periodic
+
+signal represents the
+aperiodic signal.
+
+Then, essentially, the Fourier
+series provides us with a
+
+representation.
+
+Now, we can do exactly
+the same thing in the
+
+discrete-time case.
+
+The statement is exactly the
+same, except that in the
+
+discrete-time case, instead of t
+as the independent variable,
+
+we simply make exactly the same
+statement, but with our
+
+discrete-time variable n.
+
+So the basic notion then in
+representing a discrete-time
+
+aperiodic signal is to first
+construct a periodic signal.
+
+Here we have the aperiodic
+signal.
+
+We construct a periodic signal
+by simply periodically
+
+replicating the aperiodic
+signal.
+
+The periodic signal and the
+aperiodic signal are identical
+
+for one period.
+
+And as the period goes off to
+infinity, it's the Fourier
+
+series representation of the
+periodic signal that provides
+
+a representation of the
+aperiodic signal.
+
+Again, to return to the example
+that we have been kind
+
+of working through
+this lecture.
+
+Namely, the periodic
+square wave.
+
+If we have an aperiodic signal,
+which is a rectangle,
+
+and we construct a
+periodic signal.
+
+And now we consider
+letting this
+
+period increase to infinity.
+
+We would first have this set
+of samples of the envelope.
+
+As the period increases, we
+would decrease the sample
+
+spacing to this set
+of samples.
+
+As the period increases further,
+it would be this set
+
+of samples.
+
+And as the period goes off to
+infinity, it's every point on
+
+the envelope.
+
+In fact, what the representation
+of the
+
+aperiodic signal is,
+is the envelope.
+
+OK, well, so that's
+the basic notion.
+
+It's no different than
+what we did in the
+
+continuous-time case.
+
+And mathematically, it develops
+in very much the same
+
+way as in the continuous-time
+case.
+
+Specifically, here is our
+representation through the
+
+Fourier series of the--
+
+here is a representation through
+the envelope function.
+
+And this is the Fourier series
+synthesis equation where the
+
+equation below tells us how we
+get these Fourier coefficients
+
+or the envelope from x of n.
+
+Now, x tilde of n is the
+periodic signal.
+
+And we know that over one
+period, which is the only
+
+interval over which we use it,
+in fact, this is identical to
+
+the aperiodic signal.
+
+And so, in fact, we can rewrite
+this equation simply
+
+by substituting in instead
+of x tilde, the original
+
+aperiodic signal.
+
+And now we can use infinite
+limits on this sum.
+
+And what we would want to
+examine, mathematically, is
+
+what happens to the top equation
+as we let the period
+
+go off to infinity?
+
+And what happens is exactly
+identical, mathematically, to
+
+continuous-time.
+
+I won't belabor the details.
+
+Essentially it's this sum that
+goes to an integral.
+
+Omega 0, which is the
+fundamental frequency, is
+
+going towards 0.
+
+In fact, becomes the
+differential in the integral.
+
+And in the second equation,
+of course, this then
+
+becomes x of omega.
+
+And as N goes to infinity then,
+what the Fourier series
+
+becomes is the Fourier transform
+as summarized by the
+
+bottom two equations.
+
+So although there is a little
+bit of mathematical trickery.
+
+Or let's not call it trickery,
+but subtlety, to be tracked
+
+through in detail.
+
+The important conceptual thing
+to think about is this notion
+
+that we take the aperiodic
+signal, form a periodic
+
+signal, let the period
+go off to infinity.
+
+In which case, the Fourier
+series coefficients become
+
+these envelopes functions.
+
+And incidentally,
+mathematically, one of the
+
+sums ends up going
+to an integral.
+
+So what we have then is the
+discrete-time Fourier
+
+transform, which is a
+representation of
+
+an aperiodic signal.
+
+And we have the synthesis
+equation, which I show as the
+
+top equation on this
+transparency.
+
+And this is the integral that
+the Fourier series synthesis
+
+equation went to as the period
+went off to infinity.
+
+And we have the corresponding
+analysis equation, which is
+
+shown below, where this tells
+us the Fourier transform.
+
+In effect, the envelope or the
+Fourier series coefficients of
+
+that periodic signal.
+
+And here represented in terms
+of the aperiodic signal.
+
+So we have the analysis
+equation
+
+and synthesis equation.
+
+There are a number of
+things to focus on
+
+as you look at this.
+
+And we'll talk about some of its
+properties actually in the
+
+next lecture.
+
+But some of the points that I'd
+like you to think about
+
+and focus on is the fact that
+now there is somewhat of an
+
+imbalance or lack of duality
+between the time domain and
+
+frequency domain.
+
+x of n, which is our
+aperiodic signal,
+
+is of course, discrete.
+
+It's Fourier transform, x of
+omega, is a function of a
+
+continuous variable.
+
+Omega is a continuous
+variable.
+
+That is essentially what
+represents the envelope.
+
+Also, in the time domain
+x of n is aperiodic.
+
+It's not a periodic function.
+
+However, in the frequency
+domain, remember that the
+
+Fourier series coefficients
+were always periodic.
+
+Well, this envelope function
+then is also periodic with a
+
+period in omega of 2 pi.
+
+Once again, the reason for the
+periodicity, it all stems back
+
+to the fact that when we talk
+about complex exponentials--
+
+and recall back to the
+early lectures.
+
+In discrete-time, as the
+frequency variable covers a
+
+range of 2 pi, when you proceed
+past that range, you
+
+simply see the same complex
+exponentials
+
+over and over again.
+
+And so obviously, anything that
+we do with them would
+
+have to be periodic in that
+frequency variable.
+
+All right, notationally, we'll,
+again, represent the
+
+discrete-time Fourier
+transform pair
+
+as I indicated here.
+
+And since it's a complex
+function of frequency may, on
+
+occasion, want to either
+represent it in rectangular
+
+form as I indicate in this
+equation, or in polar form as
+
+I indicate in this equation.
+
+Let's look at an example.
+
+And, of course, one example that
+we can look at is the one
+
+that has kind of been tracking
+us through this lecture, which
+
+is the example of a rectangle.
+
+Now, the rectangle, if we refer
+back to our argument of
+
+how we get a Fourier
+representation for an
+
+aperiodic signal, we would form
+a periodic signal where
+
+this is repeated.
+
+And that's our square
+wave example.
+
+As the period goes to infinity,
+the Fourier
+
+transform of this is represented
+by the envelope of
+
+those Fourier series
+coefficients, and that was our
+
+sin nx over sin x function,
+which in this particular case,
+
+for these particular numbers, is
+sin 5 omega over 2 divided
+
+by sin omega over 2.
+
+And notice, of course,
+as we would expect--
+
+notice that this is a periodic
+function of the frequency
+
+variable omega repeating, of
+course, with a period of 2 pi.
+
+Whereas, in the time domain,
+the function was not a
+
+periodic function,
+it's aperiodic.
+
+Now, let's look at
+another example.
+
+Let's look at an example which
+is another signal that has
+
+kind of popped its head up
+from time to time as the
+
+lectures have gone along.
+
+A signal which is another
+aperiodic signal, which is a
+
+decaying exponential of this
+form with the factor a chosen
+
+between 0 and 1.
+
+And you can work out the algebra
+at your leisure.
+
+Basically, if we substitute
+into the Fourier transform
+
+analysis equation, it's this
+sum that we evaluate.
+
+Because we have a unit step here
+which shuts this off for
+
+n less than 0, we can change
+the limits on the sum.
+
+This then corresponds to the sum
+over an infinite number of
+
+terms of a geometric series.
+
+And that, as we've seen before,
+is 1 divided by 1
+
+minus a e to the
+minus j omega.
+
+So let's look at what
+that looks like.
+
+Here then we have, again, the
+expression in the time domain
+
+and the expression in the
+frequency domain.
+
+And let's, in particular, focus
+on what the magnitude of
+
+the Fourier transform
+looks like.
+
+It's as we show here.
+
+And for the particular values
+of a that I pick, namely
+
+between 0 and 1, it's
+larger at the origin
+
+than it is at pi.
+
+And then, of course,
+it is periodic.
+
+And the periodicity is inherent
+in the Fourier
+
+transform in discrete-time, so
+we really might only need to
+
+look at this either from minus
+pi to pi, or from 0 to 2 pi.
+
+The periodicity, of course,
+would imply what the rest of
+
+this is for other
+values of omega.
+
+Let me also draw your attention
+while we're on it to
+
+the fact that--
+
+observe that if a were, in
+fact, negative, then this
+
+value would be less
+than this value.
+
+And in fact, for a negative, the
+magnitude of the frequency
+
+response would look like this
+except shifted by an amount in
+
+omega equal to pi.
+
+And this example will come up
+and play an important role in
+
+our discussion next time, so
+try to keep it in mind.
+
+And in fact, work it out
+more carefully between
+
+now and next time.
+
+And also, if you have a chance,
+focus on this issue of
+
+how it looks with a positive as
+compared with a negative.
+
+Now, we developed the Fourier
+transform by beginning with
+
+the Fourier series.
+
+We did that in continuous-time
+also.
+
+What I'd like to do now, just as
+we did in continuous-time,
+
+is now absorb the Fourier series
+within the broader
+
+framework of the Fourier
+transform.
+
+And there are two relationships
+between the
+
+Fourier series and the Fourier
+transform, which are identical
+
+to relationships that we had in
+the continuous-time case.
+
+Let me remind you that in
+continuous-time we had the
+
+statement that if we have a
+periodic signal, that in fact
+
+the Fourier series coefficients
+of that periodic
+
+signal is proportional to
+samples of the Fourier
+
+transform of one period.
+
+Well, in fact, let me remind you
+flows easily from all the
+
+things that we built up so far,
+because of the fact that
+
+the Fourier transform
+essentially, by definition, of
+
+the way we developed it, is
+what we get as the Fourier
+
+series coefficients, as we focus
+on one period, and then
+
+let the period go
+off to infinity.
+
+Well, looking at one period, the
+Fourier transform of that
+
+then is the envelope of the
+Fourier series coefficients.
+
+And so in continuous-time, we
+have this relationship.
+
+And in discrete-time, we
+have precisely the same
+
+relationship, except that here
+we're talking about an integer
+
+variable as opposed to the
+continuous variable, and a
+
+period of capital N as opposed
+to a period of t0.
+
+OK, so once again, if we return
+to our example, or if
+
+we return to a periodic
+signal.
+
+If we have a periodic signal
+and we consider the Fourier
+
+transform of one period, the
+Fourier series coefficients of
+
+this periodic signal are,
+in fact, samples--
+
+as stated mathematically in the
+bottom equation, samples
+
+of the Fourier transform
+of one period.
+
+So x of omega is the Fourier
+transform of one period.
+
+a sub k's are the Fourier series
+coefficients of the
+
+periodic signal.
+
+And this relationship simply
+says they're related except
+
+for scale factor through
+samples along
+
+the frequency axis.
+
+And, of course, we saw this
+in the context of
+
+our square wave example.
+
+In the square wave example, we
+have a periodic signal, which
+
+is a periodic square wave.
+
+And the Fourier transform
+of one period, in fact,
+
+represents the envelope.
+
+And here we have the
+envelope function.
+
+Represents the envelope of the
+Fourier series coefficients.
+
+And the Fourier series
+coefficients are samples.
+
+So what we have then is a
+relationship back to the
+
+Fourier series coefficients
+from the Fourier transform
+
+that tells us that for a
+periodic signal now, the
+
+periodic signal--
+
+the Fourier series coefficients
+are related, are
+
+samples of the Fourier transform
+of one period.
+
+Now, finally, to kind of bring
+things back in a circle and
+
+exactly identical to what we
+did in the continuous-time
+
+case, we can finally absorb
+the Fourier series in
+
+discrete-time.
+
+We can absorb it into
+the framework
+
+of the Fourier transform.
+
+Now, remember or recall how we
+did that when we tried to do a
+
+similar sort of thing
+in continuous-time.
+
+In continuous-time, what we
+essentially did is to develop
+
+that, more or less,
+by definition.
+
+We have a periodic signal.
+
+The periodic signal is
+represented through a Fourier
+
+series and Fourier series
+coefficients.
+
+Essentially what I pointed
+out at that time
+
+was that if we define--
+
+take it as a definition, the
+Fourier transform of the
+
+periodic signal as an impulse
+train where the amplitudes of
+
+the impulses are proportional
+to the Fourier series
+
+coefficients.
+
+If we take that impulse train
+representation and simply plug
+
+it into the Fourier transform
+synthesis equation, what we
+
+end up with is the Fourier
+series synthesis equation.
+
+So in continuous-time, we had
+used this definition of the
+
+continuous-time Fourier
+transform
+
+of a periodic signal.
+
+And again, in discrete-time,
+it's simply a matter of using
+
+exactly the same expression.
+
+And using, instead, the
+appropriate variables related
+
+to discrete-time rather than
+the variables related to
+
+continuous-time.
+
+So in discrete-time, if we have
+a periodic signal, the
+
+Fourier transform of that
+periodic signal is defined as
+
+an impulse train where the
+amplitudes of the impulses are
+
+proportional to the Fourier
+series coefficients.
+
+If this expression is
+substituted into the synthesis
+
+equation for the Fourier
+transform, that will simply
+
+then reduce to the synthesis
+equation
+
+for the Fourier series.
+
+So once more returning to our
+example, which is the square
+
+wave example that we've
+carried through these
+
+lectures, or through this
+lecture, we can see that
+
+really what we're talking
+about really is
+
+a notational change.
+
+Here is the periodic signal and
+below it are the Fourier
+
+series coefficients, where
+I've removed the envelope
+
+function and just indicate the
+amplitudes of the coefficients
+
+indexed, of course, on the
+coefficient number.
+
+And so this represents
+a bar graph.
+
+And if instead of talking
+about the Fourier series
+
+coefficients, what I want to
+talk about is the Fourier
+
+transform, the Fourier
+transform, in essence,
+
+corresponds to simply redrawing
+that using impulses
+
+and using an axis that is
+essentially indexed on the
+
+fundamental frequency omega 0,
+rather than on the Fourier
+
+series coefficient number k.
+
+OK, so to summarize,
+what we've done is
+
+to pretty much parallel--
+
+somewhat more quickly, the kind
+of development that we
+
+went through for continuous-time
+representation
+
+through complex exponentials,
+paralleled that for the
+
+discrete-time case.
+
+And pretty much the conceptual
+underpinnings of the
+
+development are identical
+in discrete-time and in
+
+continuous-time.
+
+We saw that there are some
+major differences, or
+
+important differences between
+continuous-time and
+
+discrete-time.
+
+And the difference, essentially
+
+relates to two aspects.
+
+One aspect is the fact that in
+discrete-time, we have a
+
+discrete representation in the
+time domain, whereas the
+
+independent variable in the
+frequency domain is a
+
+continuous variable.
+
+Whereas in continuous-time for
+the Fourier transform, we had
+
+a duality between the time
+domain and frequency domain.
+
+The other very important
+difference tied back to the
+
+difference between complex
+exponentials, continuous-time
+
+and discrete-time.
+
+In continuous-time, complex
+exponentials, as you vary the
+
+frequency, generate distinct
+time functions.
+
+In discrete-time, as you vary
+the frequency, once you've
+
+covered a frequency interval of
+2 pi, then you've seen all
+
+the ones there are to see.
+
+There are no more.
+
+And this, in effect, imposes a
+periodicity on the Fourier
+
+domain representation of
+discrete-time signals.
+
+And some of those differences
+and, of course, lots of the
+
+similarities will surface,
+both as we use this
+
+representation and as we develop
+further properties.
+
+In the next lecture, what
+we'll do is to focus in,
+
+again, on the Fourier transform,
+the discrete-time
+
+Fourier transform, develop
+or illuminate some of the
+
+properties of the Fourier
+transform, and then see how
+
+these properties can be used
+for a number of things.
+
+For example, how the properties
+as they were in
+
+continuous-time can be used to
+efficiently generate the
+
+solution and analyze linear
+constant coefficient
+
+difference equations.
+
+And then beyond that, the
+concepts of filtering and
+
+modulation.
+
+And both the properties and
+interpretation, which will
+
+very strongly parallel the kinds
+of developments along
+
+those lines that we did
+in the last lecture.
+
+Thank you.
\ No newline at end of file
diff --git a/ToEFkUxFURg.txt b/ToEFkUxFURg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f20838961e3147a2349bd7da99ee8243145210cf
--- /dev/null
+++ b/ToEFkUxFURg.txt
@@ -0,0 +1,9283 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi I'm Jim Roberge and I'm with the
+
+ align:start position:0%
+hi I'm Jim Roberge and I'm with the
+ 
+
+ align:start position:0%
+hi I'm Jim Roberge and I'm with the
+Department of electrical engineering and
+
+ align:start position:0%
+Department of electrical engineering and
+ 
+
+ align:start position:0%
+Department of electrical engineering and
+computer science at
+
+ align:start position:0%
+computer science at
+ 
+
+ align:start position:0%
+computer science at
+MIT I'd like to welcome you to our
+
+ align:start position:0%
+MIT I'd like to welcome you to our
+ 
+
+ align:start position:0%
+MIT I'd like to welcome you to our
+subject on feedback
+
+ align:start position:0%
+subject on feedback
+ 
+
+ align:start position:0%
+subject on feedback
+systems the material we'll be covering
+
+ align:start position:0%
+systems the material we'll be covering
+ 
+
+ align:start position:0%
+systems the material we'll be covering
+is in the field known as classical Fe
+
+ align:start position:0%
+is in the field known as classical Fe
+ 
+
+ align:start position:0%
+is in the field known as classical Fe
+feedback techniques and I'd like to
+
+ align:start position:0%
+feedback techniques and I'd like to
+ 
+
+ align:start position:0%
+feedback techniques and I'd like to
+point out that there's a very real
+
+ align:start position:0%
+point out that there's a very real
+ 
+
+ align:start position:0%
+point out that there's a very real
+difference between this category of
+
+ align:start position:0%
+difference between this category of
+ 
+
+ align:start position:0%
+difference between this category of
+material classical feedback techniques
+
+ align:start position:0%
+material classical feedback techniques
+ 
+
+ align:start position:0%
+material classical feedback techniques
+and what's now known as modern control
+
+ align:start position:0%
+and what's now known as modern control
+ 
+
+ align:start position:0%
+and what's now known as modern control
+techniques there's another subject in
+
+ align:start position:0%
+techniques there's another subject in
+ 
+
+ align:start position:0%
+techniques there's another subject in
+this series one given by Professor
+
+ align:start position:0%
+this series one given by Professor
+ 
+
+ align:start position:0%
+this series one given by Professor
+Athens also here at MIT that covers one
+
+ align:start position:0%
+Athens also here at MIT that covers one
+ 
+
+ align:start position:0%
+Athens also here at MIT that covers one
+aspect of modern control but we won't be
+
+ align:start position:0%
+aspect of modern control but we won't be
+ 
+
+ align:start position:0%
+aspect of modern control but we won't be
+looking into those sorts of of things I
+
+ align:start position:0%
+looking into those sorts of of things I
+ 
+
+ align:start position:0%
+looking into those sorts of of things I
+think one of the fundamental differences
+
+ align:start position:0%
+think one of the fundamental differences
+ 
+
+ align:start position:0%
+think one of the fundamental differences
+between classical control and modern
+
+ align:start position:0%
+between classical control and modern
+ 
+
+ align:start position:0%
+between classical control and modern
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+theory is that uh an underlying
+
+ align:start position:0%
+theory is that uh an underlying
+ 
+
+ align:start position:0%
+theory is that uh an underlying
+assumption in many of the ideas in
+
+ align:start position:0%
+assumption in many of the ideas in
+ 
+
+ align:start position:0%
+assumption in many of the ideas in
+modern control is that you're able to
+
+ align:start position:0%
+modern control is that you're able to
+ 
+
+ align:start position:0%
+modern control is that you're able to
+make decisions on a time scale very fast
+
+ align:start position:0%
+make decisions on a time scale very fast
+ 
+
+ align:start position:0%
+make decisions on a time scale very fast
+compared to the Dynamics of the systems
+
+ align:start position:0%
+compared to the Dynamics of the systems
+ 
+
+ align:start position:0%
+compared to the Dynamics of the systems
+involved uh you're then able to do
+
+ align:start position:0%
+involved uh you're then able to do
+ 
+
+ align:start position:0%
+involved uh you're then able to do
+optimization a lot of the techniques in
+
+ align:start position:0%
+optimization a lot of the techniques in
+ 
+
+ align:start position:0%
+optimization a lot of the techniques in
+modern control theory come from the
+
+ align:start position:0%
+modern control theory come from the
+ 
+
+ align:start position:0%
+modern control theory come from the
+calculus of variations and what you're
+
+ align:start position:0%
+calculus of variations and what you're
+ 
+
+ align:start position:0%
+calculus of variations and what you're
+able to do is really explore the effects
+
+ align:start position:0%
+able to do is really explore the effects
+ 
+
+ align:start position:0%
+able to do is really explore the effects
+of a given strategy for control in a
+
+ align:start position:0%
+of a given strategy for control in a
+ 
+
+ align:start position:0%
+of a given strategy for control in a
+short period of time compared to the
+
+ align:start position:0%
+short period of time compared to the
+ 
+
+ align:start position:0%
+short period of time compared to the
+Dynamics of the system before the system
+
+ align:start position:0%
+Dynamics of the system before the system
+ 
+
+ align:start position:0%
+Dynamics of the system before the system
+changes very much uh this kind of an
+
+ align:start position:0%
+changes very much uh this kind of an
+ 
+
+ align:start position:0%
+changes very much uh this kind of an
+approach is is very good if for example
+
+ align:start position:0%
+approach is is very good if for example
+ 
+
+ align:start position:0%
+approach is is very good if for example
+you have a a satellite in orbit around
+
+ align:start position:0%
+you have a a satellite in orbit around
+ 
+
+ align:start position:0%
+you have a a satellite in orbit around
+the Earth and you'd like to figure out
+
+ align:start position:0%
+the Earth and you'd like to figure out
+ 
+
+ align:start position:0%
+the Earth and you'd like to figure out
+what's the optimum trajectory to get to
+
+ align:start position:0%
+what's the optimum trajectory to get to
+ 
+
+ align:start position:0%
+what's the optimum trajectory to get to
+the Moon a minimum fuel trajectory or
+
+ align:start position:0%
+the Moon a minimum fuel trajectory or
+ 
+
+ align:start position:0%
+the Moon a minimum fuel trajectory or
+something like that because you
+
+ align:start position:0%
+something like that because you
+ 
+
+ align:start position:0%
+something like that because you
+recognize that that trip is going to
+
+ align:start position:0%
+recognize that that trip is going to
+ 
+
+ align:start position:0%
+recognize that that trip is going to
+take you several days and yet we
+
+ align:start position:0%
+take you several days and yet we
+ 
+
+ align:start position:0%
+take you several days and yet we
+currently have the ability to do
+
+ align:start position:0%
+currently have the ability to do
+ 
+
+ align:start position:0%
+currently have the ability to do
+calculations uh of of simulations of
+
+ align:start position:0%
+calculations uh of of simulations of
+ 
+
+ align:start position:0%
+calculations uh of of simulations of
+that sort of of dynamic system in a very
+
+ align:start position:0%
+that sort of of dynamic system in a very
+ 
+
+ align:start position:0%
+that sort of of dynamic system in a very
+very short period of time and so we can
+
+ align:start position:0%
+very short period of time and so we can
+ 
+
+ align:start position:0%
+very short period of time and so we can
+investigate in detail the effects of
+
+ align:start position:0%
+investigate in detail the effects of
+ 
+
+ align:start position:0%
+investigate in detail the effects of
+various control
+
+ align:start position:0%
+various control
+ 
+
+ align:start position:0%
+various control
+strategies however if we look at at
+
+ align:start position:0%
+strategies however if we look at at
+ 
+
+ align:start position:0%
+strategies however if we look at at
+another kind of system of interest for
+
+ align:start position:0%
+another kind of system of interest for
+ 
+
+ align:start position:0%
+another kind of system of interest for
+example a high-speed amplifier uh
+
+ align:start position:0%
+example a high-speed amplifier uh
+ 
+
+ align:start position:0%
+example a high-speed amplifier uh
+suppose we're worrying about a 100
+
+ align:start position:0%
+suppose we're worrying about a 100
+ 
+
+ align:start position:0%
+suppose we're worrying about a 100
+megahertz type of operational amplifier
+
+ align:start position:0%
+megahertz type of operational amplifier
+ 
+
+ align:start position:0%
+megahertz type of operational amplifier
+we're really not able to make decisions
+
+ align:start position:0%
+we're really not able to make decisions
+ 
+
+ align:start position:0%
+we're really not able to make decisions
+on a time scale fast compared to the
+
+ align:start position:0%
+on a time scale fast compared to the
+ 
+
+ align:start position:0%
+on a time scale fast compared to the
+Dynamics of that system for basically
+
+ align:start position:0%
+Dynamics of that system for basically
+ 
+
+ align:start position:0%
+Dynamics of that system for basically
+fundamental reasons if we had devices
+
+ align:start position:0%
+fundamental reasons if we had devices
+ 
+
+ align:start position:0%
+fundamental reasons if we had devices
+that allowed us to make decis decisions
+
+ align:start position:0%
+that allowed us to make decis decisions
+ 
+
+ align:start position:0%
+that allowed us to make decis decisions
+on that sort of a rapid time scale why
+
+ align:start position:0%
+on that sort of a rapid time scale why
+ 
+
+ align:start position:0%
+on that sort of a rapid time scale why
+what we do is redesign our amplifier to
+
+ align:start position:0%
+what we do is redesign our amplifier to
+ 
+
+ align:start position:0%
+what we do is redesign our amplifier to
+use those devices and thereby increase
+
+ align:start position:0%
+use those devices and thereby increase
+ 
+
+ align:start position:0%
+use those devices and thereby increase
+the speed of the amplifier so in certain
+
+ align:start position:0%
+the speed of the amplifier so in certain
+ 
+
+ align:start position:0%
+the speed of the amplifier so in certain
+applications in a very large class of
+
+ align:start position:0%
+applications in a very large class of
+ 
+
+ align:start position:0%
+applications in a very large class of
+important applications we find that this
+
+ align:start position:0%
+important applications we find that this
+ 
+
+ align:start position:0%
+important applications we find that this
+disparity between the Dynamics of the
+
+ align:start position:0%
+disparity between the Dynamics of the
+ 
+
+ align:start position:0%
+disparity between the Dynamics of the
+system and the speed with which we can
+
+ align:start position:0%
+system and the speed with which we can
+ 
+
+ align:start position:0%
+system and the speed with which we can
+make decisions doesn't exist and we're
+
+ align:start position:0%
+make decisions doesn't exist and we're
+ 
+
+ align:start position:0%
+make decisions doesn't exist and we're
+forced to use other control techniques
+
+ align:start position:0%
+forced to use other control techniques
+ 
+
+ align:start position:0%
+forced to use other control techniques
+we'll be looking at at those kinds of of
+
+ align:start position:0%
+we'll be looking at at those kinds of of
+ 
+
+ align:start position:0%
+we'll be looking at at those kinds of of
+classical control techniques or what we
+
+ align:start position:0%
+classical control techniques or what we
+ 
+
+ align:start position:0%
+classical control techniques or what we
+might call ient control
+
+ align:start position:0%
+might call ient control
+ 
+
+ align:start position:0%
+might call ient control
+theory the this material has been
+
+ align:start position:0%
+theory the this material has been
+ 
+
+ align:start position:0%
+theory the this material has been
+available for a a period of time in fact
+
+ align:start position:0%
+available for a a period of time in fact
+ 
+
+ align:start position:0%
+available for a a period of time in fact
+I think the pioneering work in classical
+
+ align:start position:0%
+I think the pioneering work in classical
+ 
+
+ align:start position:0%
+I think the pioneering work in classical
+control theory was done starting during
+
+ align:start position:0%
+control theory was done starting during
+ 
+
+ align:start position:0%
+control theory was done starting during
+the second world war principally at Bell
+
+ align:start position:0%
+the second world war principally at Bell
+ 
+
+ align:start position:0%
+the second world war principally at Bell
+Laboratories and here at MIT in the
+
+ align:start position:0%
+Laboratories and here at MIT in the
+ 
+
+ align:start position:0%
+Laboratories and here at MIT in the
+radiation laboratory and we'll be
+
+ align:start position:0%
+radiation laboratory and we'll be
+ 
+
+ align:start position:0%
+radiation laboratory and we'll be
+basically reviewing some of that
+
+ align:start position:0%
+basically reviewing some of that
+ 
+
+ align:start position:0%
+basically reviewing some of that
+material and seeing how it applies to a
+
+ align:start position:0%
+material and seeing how it applies to a
+ 
+
+ align:start position:0%
+material and seeing how it applies to a
+collection of modern systems what we're
+
+ align:start position:0%
+collection of modern systems what we're
+ 
+
+ align:start position:0%
+collection of modern systems what we're
+one of the themes throughout this
+
+ align:start position:0%
+one of the themes throughout this
+ 
+
+ align:start position:0%
+one of the themes throughout this
+subject will be the application of the
+
+ align:start position:0%
+subject will be the application of the
+ 
+
+ align:start position:0%
+subject will be the application of the
+techniques we're discussing to real
+
+ align:start position:0%
+techniques we're discussing to real
+ 
+
+ align:start position:0%
+techniques we're discussing to real
+world kinds of systems I think there's a
+
+ align:start position:0%
+world kinds of systems I think there's a
+ 
+
+ align:start position:0%
+world kinds of systems I think there's a
+a tendency to feel that the techniques
+
+ align:start position:0%
+a tendency to feel that the techniques
+ 
+
+ align:start position:0%
+a tendency to feel that the techniques
+we have are very special purpose very
+
+ align:start position:0%
+we have are very special purpose very
+ 
+
+ align:start position:0%
+we have are very special purpose very
+dedicated to single kinds of
+
+ align:start position:0%
+dedicated to single kinds of
+ 
+
+ align:start position:0%
+dedicated to single kinds of
+applications but we'll see that's just
+
+ align:start position:0%
+applications but we'll see that's just
+ 
+
+ align:start position:0%
+applications but we'll see that's just
+not true we'll develop analytic and
+
+ align:start position:0%
+not true we'll develop analytic and
+ 
+
+ align:start position:0%
+not true we'll develop analytic and
+design techniques and then we'll
+
+ align:start position:0%
+design techniques and then we'll
+ 
+
+ align:start position:0%
+design techniques and then we'll
+illustrate those analytic and design
+
+ align:start position:0%
+illustrate those analytic and design
+ 
+
+ align:start position:0%
+illustrate those analytic and design
+techniques by applying them to a very
+
+ align:start position:0%
+techniques by applying them to a very
+ 
+
+ align:start position:0%
+techniques by applying them to a very
+wide range of systems we'll look at at
+
+ align:start position:0%
+wide range of systems we'll look at at
+ 
+
+ align:start position:0%
+wide range of systems we'll look at at
+purely electronic systems operational
+
+ align:start position:0%
+purely electronic systems operational
+ 
+
+ align:start position:0%
+purely electronic systems operational
+amplifiers for example and we'll see how
+
+ align:start position:0%
+amplifiers for example and we'll see how
+ 
+
+ align:start position:0%
+amplifiers for example and we'll see how
+we apply the techniques we've developed
+
+ align:start position:0%
+we apply the techniques we've developed
+ 
+
+ align:start position:0%
+we apply the techniques we've developed
+to those kinds of of circuits uh we'll
+
+ align:start position:0%
+to those kinds of of circuits uh we'll
+ 
+
+ align:start position:0%
+to those kinds of of circuits uh we'll
+look at some examples of mechanical
+
+ align:start position:0%
+look at some examples of mechanical
+ 
+
+ align:start position:0%
+look at some examples of mechanical
+systems Servo mechanisms are are systems
+
+ align:start position:0%
+systems Servo mechanisms are are systems
+ 
+
+ align:start position:0%
+systems Servo mechanisms are are systems
+where at least one of the variables is a
+
+ align:start position:0%
+where at least one of the variables is a
+ 
+
+ align:start position:0%
+where at least one of the variables is a
+mechanical one and we'll look at how we
+
+ align:start position:0%
+mechanical one and we'll look at how we
+ 
+
+ align:start position:0%
+mechanical one and we'll look at how we
+apply some of these ideas to certain
+
+ align:start position:0%
+apply some of these ideas to certain
+ 
+
+ align:start position:0%
+apply some of these ideas to certain
+kinds of of Servo
+
+ align:start position:0%
+kinds of of Servo
+ 
+
+ align:start position:0%
+kinds of of Servo
+mechanisms so we'll see a a variety of
+
+ align:start position:0%
+mechanisms so we'll see a a variety of
+ 
+
+ align:start position:0%
+mechanisms so we'll see a a variety of
+applications for the technique that
+
+ align:start position:0%
+applications for the technique that
+ 
+
+ align:start position:0%
+applications for the technique that
+we'll develop and we'll illustrate many
+
+ align:start position:0%
+we'll develop and we'll illustrate many
+ 
+
+ align:start position:0%
+we'll develop and we'll illustrate many
+of these applications with actual
+
+ align:start position:0%
+of these applications with actual
+ 
+
+ align:start position:0%
+of these applications with actual
+operating systems we'll we'll see a
+
+ align:start position:0%
+operating systems we'll we'll see a
+ 
+
+ align:start position:0%
+operating systems we'll we'll see a
+number of of examples of that sort of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing the I'd like to indicate some of
+
+ align:start position:0%
+thing the I'd like to indicate some of
+ 
+
+ align:start position:0%
+thing the I'd like to indicate some of
+the additional material that we'll have
+
+ align:start position:0%
+the additional material that we'll have
+ 
+
+ align:start position:0%
+the additional material that we'll have
+for the course besides the videotape
+
+ align:start position:0%
+for the course besides the videotape
+ 
+
+ align:start position:0%
+for the course besides the videotape
+material the book that we'll use is this
+
+ align:start position:0%
+material the book that we'll use is this
+ 
+
+ align:start position:0%
+material the book that we'll use is this
+one it's called operational amplifiers
+
+ align:start position:0%
+one it's called operational amplifiers
+ 
+
+ align:start position:0%
+one it's called operational amplifiers
+theory and practice but that's really
+
+ align:start position:0%
+theory and practice but that's really
+ 
+
+ align:start position:0%
+theory and practice but that's really
+somewhat of a misnomer this is basically
+
+ align:start position:0%
+somewhat of a misnomer this is basically
+ 
+
+ align:start position:0%
+somewhat of a misnomer this is basically
+a collection of things that I had wanted
+
+ align:start position:0%
+a collection of things that I had wanted
+ 
+
+ align:start position:0%
+a collection of things that I had wanted
+to write for quite a while and a large
+
+ align:start position:0%
+to write for quite a while and a large
+ 
+
+ align:start position:0%
+to write for quite a while and a large
+part of the text does really deal with
+
+ align:start position:0%
+part of the text does really deal with
+ 
+
+ align:start position:0%
+part of the text does really deal with
+classical feedback in particular we'll
+
+ align:start position:0%
+classical feedback in particular we'll
+ 
+
+ align:start position:0%
+classical feedback in particular we'll
+be concentrating on the materials in
+
+ align:start position:0%
+be concentrating on the materials in
+ 
+
+ align:start position:0%
+be concentrating on the materials in
+chapters 1 through six in the book uh
+
+ align:start position:0%
+chapters 1 through six in the book uh
+ 
+
+ align:start position:0%
+chapters 1 through six in the book uh
+the material in Chapter 13 gets back to
+
+ align:start position:0%
+the material in Chapter 13 gets back to
+ 
+
+ align:start position:0%
+the material in Chapter 13 gets back to
+classical feedback Concepts and we'll
+
+ align:start position:0%
+classical feedback Concepts and we'll
+ 
+
+ align:start position:0%
+classical feedback Concepts and we'll
+look at that in detail and then we'll
+
+ align:start position:0%
+look at that in detail and then we'll
+ 
+
+ align:start position:0%
+look at that in detail and then we'll
+use certain examples from chapters 11
+
+ align:start position:0%
+use certain examples from chapters 11
+ 
+
+ align:start position:0%
+use certain examples from chapters 11
+and 12 out of this book so we'll cover
+
+ align:start position:0%
+and 12 out of this book so we'll cover
+ 
+
+ align:start position:0%
+and 12 out of this book so we'll cover
+cover about half the material in the
+
+ align:start position:0%
+cover about half the material in the
+ 
+
+ align:start position:0%
+cover about half the material in the
+book as we go through the the
+
+ align:start position:0%
+book as we go through the the
+ 
+
+ align:start position:0%
+book as we go through the the
+subject the we will also have problems
+
+ align:start position:0%
+subject the we will also have problems
+ 
+
+ align:start position:0%
+subject the we will also have problems
+in the subject that are basically taken
+
+ align:start position:0%
+in the subject that are basically taken
+ 
+
+ align:start position:0%
+in the subject that are basically taken
+from the book in most cases and so the
+
+ align:start position:0%
+from the book in most cases and so the
+ 
+
+ align:start position:0%
+from the book in most cases and so the
+book is is very very closely linked to
+
+ align:start position:0%
+book is is very very closely linked to
+ 
+
+ align:start position:0%
+book is is very very closely linked to
+to the subject this book and the subject
+
+ align:start position:0%
+to the subject this book and the subject
+ 
+
+ align:start position:0%
+to the subject this book and the subject
+for that matter are ones used here at
+
+ align:start position:0%
+for that matter are ones used here at
+ 
+
+ align:start position:0%
+for that matter are ones used here at
+MIT in a subject called 6302 which is
+
+ align:start position:0%
+MIT in a subject called 6302 which is
+ 
+
+ align:start position:0%
+MIT in a subject called 6302 which is
+again entitled feedback systems and the
+
+ align:start position:0%
+again entitled feedback systems and the
+ 
+
+ align:start position:0%
+again entitled feedback systems and the
+material I'll be presenting has been
+
+ align:start position:0%
+material I'll be presenting has been
+ 
+
+ align:start position:0%
+material I'll be presenting has been
+abstracted from that subject for use
+
+ align:start position:0%
+abstracted from that subject for use
+ 
+
+ align:start position:0%
+abstracted from that subject for use
+here in addition to the text we'll have
+
+ align:start position:0%
+here in addition to the text we'll have
+ 
+
+ align:start position:0%
+here in addition to the text we'll have
+a study guide the study guide will
+
+ align:start position:0%
+a study guide the study guide will
+ 
+
+ align:start position:0%
+a study guide the study guide will
+include the visuals that we use here the
+
+ align:start position:0%
+include the visuals that we use here the
+ 
+
+ align:start position:0%
+include the visuals that we use here the
+Blackboard material as well as the view
+
+ align:start position:0%
+Blackboard material as well as the view
+ 
+
+ align:start position:0%
+Blackboard material as well as the view
+graphs that we use uh the study guide
+
+ align:start position:0%
+graphs that we use uh the study guide
+ 
+
+ align:start position:0%
+graphs that we use uh the study guide
+will list the problems that will be
+
+ align:start position:0%
+will list the problems that will be
+ 
+
+ align:start position:0%
+will list the problems that will be
+expected uh that will be assigned in
+
+ align:start position:0%
+expected uh that will be assigned in
+ 
+
+ align:start position:0%
+expected uh that will be assigned in
+conjunction with the various lectures
+
+ align:start position:0%
+conjunction with the various lectures
+ 
+
+ align:start position:0%
+conjunction with the various lectures
+and we'll also have solutions to the
+
+ align:start position:0%
+and we'll also have solutions to the
+ 
+
+ align:start position:0%
+and we'll also have solutions to the
+problems included in the study guide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'd like to spend just a moment talking
+
+ align:start position:0%
+I'd like to spend just a moment talking
+ 
+
+ align:start position:0%
+I'd like to spend just a moment talking
+about the prerequisites I anticipate for
+
+ align:start position:0%
+about the prerequisites I anticipate for
+ 
+
+ align:start position:0%
+about the prerequisites I anticipate for
+participation in the
+
+ align:start position:0%
+participation in the
+ 
+
+ align:start position:0%
+participation in the
+subject
+
+ align:start position:0%
+subject
+ 
+
+ align:start position:0%
+subject
+uh we'd like you to have a reasonable
+
+ align:start position:0%
+uh we'd like you to have a reasonable
+ 
+
+ align:start position:0%
+uh we'd like you to have a reasonable
+background in linear system
+
+ align:start position:0%
+background in linear system
+ 
+
+ align:start position:0%
+background in linear system
+manipulations uh basically at an S plane
+
+ align:start position:0%
+manipulations uh basically at an S plane
+ 
+
+ align:start position:0%
+manipulations uh basically at an S plane
+level you should be familiar with the
+
+ align:start position:0%
+level you should be familiar with the
+ 
+
+ align:start position:0%
+level you should be familiar with the
+usual kinds of sane manipulations how do
+
+ align:start position:0%
+usual kinds of sane manipulations how do
+ 
+
+ align:start position:0%
+usual kinds of sane manipulations how do
+you uh find the magnitude and phase for
+
+ align:start position:0%
+you uh find the magnitude and phase for
+ 
+
+ align:start position:0%
+you uh find the magnitude and phase for
+for purely sinusoidal exitation for
+
+ align:start position:0%
+for purely sinusoidal exitation for
+ 
+
+ align:start position:0%
+for purely sinusoidal exitation for
+example if you're given a pole zero plot
+
+ align:start position:0%
+example if you're given a pole zero plot
+ 
+
+ align:start position:0%
+example if you're given a pole zero plot
+for a system transfer function that sort
+
+ align:start position:0%
+for a system transfer function that sort
+ 
+
+ align:start position:0%
+for a system transfer function that sort
+of thing so we'd like to have a
+
+ align:start position:0%
+of thing so we'd like to have a
+ 
+
+ align:start position:0%
+of thing so we'd like to have a
+reasonably good appreciation of of
+
+ align:start position:0%
+reasonably good appreciation of of
+ 
+
+ align:start position:0%
+reasonably good appreciation of of
+linear system Concepts but we won't
+
+ align:start position:0%
+linear system Concepts but we won't
+ 
+
+ align:start position:0%
+linear system Concepts but we won't
+really depend particularly heavily on on
+
+ align:start position:0%
+really depend particularly heavily on on
+ 
+
+ align:start position:0%
+really depend particularly heavily on on
+using a big Sledgehammer of llas to
+
+ align:start position:0%
+using a big Sledgehammer of llas to
+ 
+
+ align:start position:0%
+using a big Sledgehammer of llas to
+attack the systems we'll spend very
+
+ align:start position:0%
+attack the systems we'll spend very
+ 
+
+ align:start position:0%
+attack the systems we'll spend very
+little time actually doing things like
+
+ align:start position:0%
+little time actually doing things like
+ 
+
+ align:start position:0%
+little time actually doing things like
+uh partial fraction expansions in order
+
+ align:start position:0%
+uh partial fraction expansions in order
+ 
+
+ align:start position:0%
+uh partial fraction expansions in order
+to take inverse transforms and that that
+
+ align:start position:0%
+to take inverse transforms and that that
+ 
+
+ align:start position:0%
+to take inverse transforms and that that
+sort of thing so while you do have to
+
+ align:start position:0%
+sort of thing so while you do have to
+ 
+
+ align:start position:0%
+sort of thing so while you do have to
+have an appreciation of trans functions
+
+ align:start position:0%
+have an appreciation of trans functions
+ 
+
+ align:start position:0%
+have an appreciation of trans functions
+of the significance of various pole zero
+
+ align:start position:0%
+of the significance of various pole zero
+ 
+
+ align:start position:0%
+of the significance of various pole zero
+configurations and that sort of thing we
+
+ align:start position:0%
+configurations and that sort of thing we
+ 
+
+ align:start position:0%
+configurations and that sort of thing we
+really won't be spending very much time
+
+ align:start position:0%
+really won't be spending very much time
+ 
+
+ align:start position:0%
+really won't be spending very much time
+looking at the formal mathematics of
+
+ align:start position:0%
+looking at the formal mathematics of
+ 
+
+ align:start position:0%
+looking at the formal mathematics of
+llas kinds of
+
+ align:start position:0%
+llas kinds of
+ 
+
+ align:start position:0%
+llas kinds of
+manipulations also really because
+
+ align:start position:0%
+manipulations also really because
+ 
+
+ align:start position:0%
+manipulations also really because
+they're you we use them so frequently
+
+ align:start position:0%
+they're you we use them so frequently
+ 
+
+ align:start position:0%
+they're you we use them so frequently
+for examples you should be able to look
+
+ align:start position:0%
+for examples you should be able to look
+ 
+
+ align:start position:0%
+for examples you should be able to look
+at an operational amplifier connection
+
+ align:start position:0%
+at an operational amplifier connection
+ 
+
+ align:start position:0%
+at an operational amplifier connection
+and decide that if the amplifier had
+
+ align:start position:0%
+and decide that if the amplifier had
+ 
+
+ align:start position:0%
+and decide that if the amplifier had
+ideal characteristics the usual kinds of
+
+ align:start position:0%
+ideal characteristics the usual kinds of
+ 
+
+ align:start position:0%
+ideal characteristics the usual kinds of
+things that we list in connection with
+
+ align:start position:0%
+things that we list in connection with
+ 
+
+ align:start position:0%
+things that we list in connection with
+an operation amplifier very high open
+
+ align:start position:0%
+an operation amplifier very high open
+ 
+
+ align:start position:0%
+an operation amplifier very high open
+loop gain very high input impedance very
+
+ align:start position:0%
+loop gain very high input impedance very
+ 
+
+ align:start position:0%
+loop gain very high input impedance very
+low output impedance the usual kinds of
+
+ align:start position:0%
+low output impedance the usual kinds of
+ 
+
+ align:start position:0%
+low output impedance the usual kinds of
+good things that we talk about in
+
+ align:start position:0%
+good things that we talk about in
+ 
+
+ align:start position:0%
+good things that we talk about in
+connection with operational amplifiers
+
+ align:start position:0%
+connection with operational amplifiers
+ 
+
+ align:start position:0%
+connection with operational amplifiers
+given those constraints that the
+
+ align:start position:0%
+given those constraints that the
+ 
+
+ align:start position:0%
+given those constraints that the
+amplifier is effectively ideal you ought
+
+ align:start position:0%
+amplifier is effectively ideal you ought
+ 
+
+ align:start position:0%
+amplifier is effectively ideal you ought
+to be able to predict what the ideal
+
+ align:start position:0%
+to be able to predict what the ideal
+ 
+
+ align:start position:0%
+to be able to predict what the ideal
+closed loop gain should be by looking at
+
+ align:start position:0%
+closed loop gain should be by looking at
+ 
+
+ align:start position:0%
+closed loop gain should be by looking at
+the topology for at least relatively
+
+ align:start position:0%
+the topology for at least relatively
+ 
+
+ align:start position:0%
+the topology for at least relatively
+straightforward operational amplifier
+
+ align:start position:0%
+straightforward operational amplifier
+ 
+
+ align:start position:0%
+straightforward operational amplifier
+configurations again that's a talent
+
+ align:start position:0%
+configurations again that's a talent
+ 
+
+ align:start position:0%
+configurations again that's a talent
+that I think most of you have
+
+ align:start position:0%
+that I think most of you have
+ 
+
+ align:start position:0%
+that I think most of you have
+operational amplifiers are so so all
+
+ align:start position:0%
+operational amplifiers are so so all
+ 
+
+ align:start position:0%
+operational amplifiers are so so all
+prev vasive at present that most people
+
+ align:start position:0%
+prev vasive at present that most people
+ 
+
+ align:start position:0%
+prev vasive at present that most people
+have picked up the facility to look at a
+
+ align:start position:0%
+have picked up the facility to look at a
+ 
+
+ align:start position:0%
+have picked up the facility to look at a
+connection and and see what the
+
+ align:start position:0%
+connection and and see what the
+ 
+
+ align:start position:0%
+connection and and see what the
+objective of the connection is if you
+
+ align:start position:0%
+objective of the connection is if you
+ 
+
+ align:start position:0%
+objective of the connection is if you
+have any concerns about that I go
+
+ align:start position:0%
+have any concerns about that I go
+ 
+
+ align:start position:0%
+have any concerns about that I go
+through those those kinds of
+
+ align:start position:0%
+through those those kinds of
+ 
+
+ align:start position:0%
+through those those kinds of
+calculations in chapter one and I
+
+ align:start position:0%
+calculations in chapter one and I
+ 
+
+ align:start position:0%
+calculations in chapter one and I
+encourage you to review the material
+
+ align:start position:0%
+encourage you to review the material
+ 
+
+ align:start position:0%
+encourage you to review the material
+there in order to gain that that degree
+
+ align:start position:0%
+there in order to gain that that degree
+ 
+
+ align:start position:0%
+there in order to gain that that degree
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+facility Well what do we mean by a
+
+ align:start position:0%
+facility Well what do we mean by a
+ 
+
+ align:start position:0%
+facility Well what do we mean by a
+feedback system since that's what we're
+
+ align:start position:0%
+feedback system since that's what we're
+ 
+
+ align:start position:0%
+feedback system since that's what we're
+going to be studying throughout this
+
+ align:start position:0%
+going to be studying throughout this
+ 
+
+ align:start position:0%
+going to be studying throughout this
+subject I think a feedback system is one
+
+ align:start position:0%
+subject I think a feedback system is one
+ 
+
+ align:start position:0%
+subject I think a feedback system is one
+where we attempt to control an output
+
+ align:start position:0%
+where we attempt to control an output
+ 
+
+ align:start position:0%
+where we attempt to control an output
+variable in response to a command but
+
+ align:start position:0%
+variable in response to a command but
+ 
+
+ align:start position:0%
+variable in response to a command but
+the important distinction in a feedback
+
+ align:start position:0%
+the important distinction in a feedback
+ 
+
+ align:start position:0%
+the important distinction in a feedback
+system is that at least part of the
+
+ align:start position:0%
+system is that at least part of the
+ 
+
+ align:start position:0%
+system is that at least part of the
+information used to control the output
+
+ align:start position:0%
+information used to control the output
+ 
+
+ align:start position:0%
+information used to control the output
+variable itself is made by is derived
+
+ align:start position:0%
+variable itself is made by is derived
+ 
+
+ align:start position:0%
+variable itself is made by is derived
+from measurements that we make on the
+
+ align:start position:0%
+from measurements that we make on the
+ 
+
+ align:start position:0%
+from measurements that we make on the
+output variable so this idea of of
+
+ align:start position:0%
+output variable so this idea of of
+ 
+
+ align:start position:0%
+output variable so this idea of of
+looking at the variable that we're
+
+ align:start position:0%
+looking at the variable that we're
+ 
+
+ align:start position:0%
+looking at the variable that we're
+trying to control and using that
+
+ align:start position:0%
+trying to control and using that
+ 
+
+ align:start position:0%
+trying to control and using that
+information at least in part to control
+
+ align:start position:0%
+information at least in part to control
+ 
+
+ align:start position:0%
+information at least in part to control
+the variable itself is Central to the
+
+ align:start position:0%
+the variable itself is Central to the
+ 
+
+ align:start position:0%
+the variable itself is Central to the
+idea of feedback systems there's
+
+ align:start position:0%
+idea of feedback systems there's
+ 
+
+ align:start position:0%
+idea of feedback systems there's
+certainly many examples of those that
+
+ align:start position:0%
+certainly many examples of those that
+ 
+
+ align:start position:0%
+certainly many examples of those that
+we're all familiar with we can look at
+
+ align:start position:0%
+we're all familiar with we can look at
+ 
+
+ align:start position:0%
+we're all familiar with we can look at
+at most electronic amplifiers audio
+
+ align:start position:0%
+at most electronic amplifiers audio
+ 
+
+ align:start position:0%
+at most electronic amplifiers audio
+amplifiers for example in entertainment
+
+ align:start position:0%
+amplifiers for example in entertainment
+ 
+
+ align:start position:0%
+amplifiers for example in entertainment
+systems include feedback it's very
+
+ align:start position:0%
+systems include feedback it's very
+ 
+
+ align:start position:0%
+systems include feedback it's very
+difficult to get the kinds of
+
+ align:start position:0%
+difficult to get the kinds of
+ 
+
+ align:start position:0%
+difficult to get the kinds of
+characteristics we'd like to have in a
+
+ align:start position:0%
+characteristics we'd like to have in a
+ 
+
+ align:start position:0%
+characteristics we'd like to have in a
+good quality audio amplifier without
+
+ align:start position:0%
+good quality audio amplifier without
+ 
+
+ align:start position:0%
+good quality audio amplifier without
+using feedback we've certainly all seen
+
+ align:start position:0%
+using feedback we've certainly all seen
+ 
+
+ align:start position:0%
+using feedback we've certainly all seen
+numerous examples of mechanical systems
+
+ align:start position:0%
+numerous examples of mechanical systems
+ 
+
+ align:start position:0%
+numerous examples of mechanical systems
+uh ways for example Le of of moving
+
+ align:start position:0%
+uh ways for example Le of of moving
+ 
+
+ align:start position:0%
+uh ways for example Le of of moving
+aircraft control surfaces in response to
+
+ align:start position:0%
+aircraft control surfaces in response to
+ 
+
+ align:start position:0%
+aircraft control surfaces in response to
+commands from the cockpit um ways of of
+
+ align:start position:0%
+commands from the cockpit um ways of of
+ 
+
+ align:start position:0%
+commands from the cockpit um ways of of
+pointing radar antenna again in response
+
+ align:start position:0%
+pointing radar antenna again in response
+ 
+
+ align:start position:0%
+pointing radar antenna again in response
+to commands generated elsewhere so we've
+
+ align:start position:0%
+to commands generated elsewhere so we've
+ 
+
+ align:start position:0%
+to commands generated elsewhere so we've
+seen examples of mechanical systems of
+
+ align:start position:0%
+seen examples of mechanical systems of
+ 
+
+ align:start position:0%
+seen examples of mechanical systems of
+that kind uh there's also a very
+
+ align:start position:0%
+that kind uh there's also a very
+ 
+
+ align:start position:0%
+that kind uh there's also a very
+important class of feedback system known
+
+ align:start position:0%
+important class of feedback system known
+ 
+
+ align:start position:0%
+important class of feedback system known
+as a regulator and we're familiar with
+
+ align:start position:0%
+as a regulator and we're familiar with
+ 
+
+ align:start position:0%
+as a regulator and we're familiar with
+examples of those a home heating system
+
+ align:start position:0%
+examples of those a home heating system
+ 
+
+ align:start position:0%
+examples of those a home heating system
+where you measure the temperature of of
+
+ align:start position:0%
+where you measure the temperature of of
+ 
+
+ align:start position:0%
+where you measure the temperature of of
+a room and control a furnace in in order
+
+ align:start position:0%
+a room and control a furnace in in order
+ 
+
+ align:start position:0%
+a room and control a furnace in in order
+to maintain that room temperature at at
+
+ align:start position:0%
+to maintain that room temperature at at
+ 
+
+ align:start position:0%
+to maintain that room temperature at at
+some set point value uh similarly the uh
+
+ align:start position:0%
+some set point value uh similarly the uh
+ 
+
+ align:start position:0%
+some set point value uh similarly the uh
+system involving the iris that regulates
+
+ align:start position:0%
+system involving the iris that regulates
+ 
+
+ align:start position:0%
+system involving the iris that regulates
+the amount of light that strikes your
+
+ align:start position:0%
+the amount of light that strikes your
+ 
+
+ align:start position:0%
+the amount of light that strikes your
+retina here again it's a feedback system
+
+ align:start position:0%
+retina here again it's a feedback system
+ 
+
+ align:start position:0%
+retina here again it's a feedback system
+uh somehow you measure the total light
+
+ align:start position:0%
+uh somehow you measure the total light
+ 
+
+ align:start position:0%
+uh somehow you measure the total light
+flux striking your retina and the iris
+
+ align:start position:0%
+flux striking your retina and the iris
+ 
+
+ align:start position:0%
+flux striking your retina and the iris
+reacts in a way to regulate that total
+
+ align:start position:0%
+reacts in a way to regulate that total
+ 
+
+ align:start position:0%
+reacts in a way to regulate that total
+amount of light flux that that hits the
+
+ align:start position:0%
+amount of light flux that that hits the
+ 
+
+ align:start position:0%
+amount of light flux that that hits the
+retina so here's a biological example of
+
+ align:start position:0%
+retina so here's a biological example of
+ 
+
+ align:start position:0%
+retina so here's a biological example of
+a feedback system interestingly enough
+
+ align:start position:0%
+a feedback system interestingly enough
+ 
+
+ align:start position:0%
+a feedback system interestingly enough
+you can make measurements on that system
+
+ align:start position:0%
+you can make measurements on that system
+ 
+
+ align:start position:0%
+you can make measurements on that system
+uh by appropriately stimulating it you
+
+ align:start position:0%
+uh by appropriately stimulating it you
+ 
+
+ align:start position:0%
+uh by appropriately stimulating it you
+can get the same sorts of instabilities
+
+ align:start position:0%
+can get the same sorts of instabilities
+ 
+
+ align:start position:0%
+can get the same sorts of instabilities
+that we often times see in in man-made
+
+ align:start position:0%
+that we often times see in in man-made
+ 
+
+ align:start position:0%
+that we often times see in in man-made
+Control
+
+ align:start position:0%
+Control
+ 
+
+ align:start position:0%
+Control
+Systems I'd like to show some elements
+
+ align:start position:0%
+Systems I'd like to show some elements
+ 
+
+ align:start position:0%
+Systems I'd like to show some elements
+that are common to many of the kinds of
+
+ align:start position:0%
+that are common to many of the kinds of
+ 
+
+ align:start position:0%
+that are common to many of the kinds of
+feedback systems that we're going to
+
+ align:start position:0%
+feedback systems that we're going to
+ 
+
+ align:start position:0%
+feedback systems that we're going to
+examine here we have a sort of
+
+ align:start position:0%
+examine here we have a sort of
+ 
+
+ align:start position:0%
+examine here we have a sort of
+diagrammatic representation of a
+
+ align:start position:0%
+diagrammatic representation of a
+ 
+
+ align:start position:0%
+diagrammatic representation of a
+feedback system we have an input
+
+ align:start position:0%
+feedback system we have an input
+ 
+
+ align:start position:0%
+feedback system we have an input
+variable and of of course an output
+
+ align:start position:0%
+variable and of of course an output
+ 
+
+ align:start position:0%
+variable and of of course an output
+variable and the objective is certainly
+
+ align:start position:0%
+variable and the objective is certainly
+ 
+
+ align:start position:0%
+variable and the objective is certainly
+to make the output variable be some
+
+ align:start position:0%
+to make the output variable be some
+ 
+
+ align:start position:0%
+to make the output variable be some
+known relationship to the input applied
+
+ align:start position:0%
+known relationship to the input applied
+ 
+
+ align:start position:0%
+known relationship to the input applied
+to the system and the way we accomplish
+
+ align:start position:0%
+to the system and the way we accomplish
+ 
+
+ align:start position:0%
+to the system and the way we accomplish
+that is by measuring the output
+
+ align:start position:0%
+that is by measuring the output
+ 
+
+ align:start position:0%
+that is by measuring the output
+obtaining some measure of what the
+
+ align:start position:0%
+obtaining some measure of what the
+ 
+
+ align:start position:0%
+obtaining some measure of what the
+output's value is or or certain
+
+ align:start position:0%
+output's value is or or certain
+ 
+
+ align:start position:0%
+output's value is or or certain
+characteristics of the output we do that
+
+ align:start position:0%
+characteristics of the output we do that
+ 
+
+ align:start position:0%
+characteristics of the output we do that
+with a measuring or a feedback element
+
+ align:start position:0%
+with a measuring or a feedback element
+ 
+
+ align:start position:0%
+with a measuring or a feedback element
+and what we do is compare our measure of
+
+ align:start position:0%
+and what we do is compare our measure of
+ 
+
+ align:start position:0%
+and what we do is compare our measure of
+the output variable with the applied
+
+ align:start position:0%
+the output variable with the applied
+ 
+
+ align:start position:0%
+the output variable with the applied
+input variable so we have some sort of a
+
+ align:start position:0%
+input variable so we have some sort of a
+ 
+
+ align:start position:0%
+input variable so we have some sort of a
+comparator that develops an
+
+ align:start position:0%
+comparator that develops an
+ 
+
+ align:start position:0%
+comparator that develops an
+error the error being the difference
+
+ align:start position:0%
+error the error being the difference
+ 
+
+ align:start position:0%
+error the error being the difference
+between the input or the command
+
+ align:start position:0%
+between the input or the command
+ 
+
+ align:start position:0%
+between the input or the command
+variable and our measure of the output
+
+ align:start position:0%
+variable and our measure of the output
+ 
+
+ align:start position:0%
+variable and our measure of the output
+variable we then amplify that error
+
+ align:start position:0%
+variable we then amplify that error
+ 
+
+ align:start position:0%
+variable we then amplify that error
+signal and change the output Drive the
+
+ align:start position:0%
+signal and change the output Drive the
+ 
+
+ align:start position:0%
+signal and change the output Drive the
+output as a function of the Amplified
+
+ align:start position:0%
+output as a function of the Amplified
+ 
+
+ align:start position:0%
+output as a function of the Amplified
+error signal and of course the objective
+
+ align:start position:0%
+error signal and of course the objective
+ 
+
+ align:start position:0%
+error signal and of course the objective
+is to drive the output variable in such
+
+ align:start position:0%
+is to drive the output variable in such
+ 
+
+ align:start position:0%
+is to drive the output variable in such
+a direction to reduce the error signal
+
+ align:start position:0%
+a direction to reduce the error signal
+ 
+
+ align:start position:0%
+a direction to reduce the error signal
+to make the
+
+ align:start position:0%
+to make the
+ 
+
+ align:start position:0%
+to make the
+measured function of the output variable
+
+ align:start position:0%
+measured function of the output variable
+ 
+
+ align:start position:0%
+measured function of the output variable
+uh be in better agreement with our input
+
+ align:start position:0%
+uh be in better agreement with our input
+ 
+
+ align:start position:0%
+uh be in better agreement with our input
+so the system works to drive the output
+
+ align:start position:0%
+so the system works to drive the output
+ 
+
+ align:start position:0%
+so the system works to drive the output
+uh in such a way that the error tends
+
+ align:start position:0%
+uh in such a way that the error tends
+ 
+
+ align:start position:0%
+uh in such a way that the error tends
+toward zero and that's at times
+
+ align:start position:0%
+toward zero and that's at times
+ 
+
+ align:start position:0%
+toward zero and that's at times
+Complicated by disturbances that may be
+
+ align:start position:0%
+Complicated by disturbances that may be
+ 
+
+ align:start position:0%
+Complicated by disturbances that may be
+applied to the system at some point I
+
+ align:start position:0%
+applied to the system at some point I
+ 
+
+ align:start position:0%
+applied to the system at some point I
+happen to have shown the disturbances
+
+ align:start position:0%
+happen to have shown the disturbances
+ 
+
+ align:start position:0%
+happen to have shown the disturbances
+here in in conjunction Junction with the
+
+ align:start position:0%
+here in in conjunction Junction with the
+ 
+
+ align:start position:0%
+here in in conjunction Junction with the
+amplifying element but that's not
+
+ align:start position:0%
+amplifying element but that's not
+ 
+
+ align:start position:0%
+amplifying element but that's not
+necessary the important point is that uh
+
+ align:start position:0%
+necessary the important point is that uh
+ 
+
+ align:start position:0%
+necessary the important point is that uh
+our attempts to make the output or the
+
+ align:start position:0%
+our attempts to make the output or the
+ 
+
+ align:start position:0%
+our attempts to make the output or the
+measure of the output correspond to the
+
+ align:start position:0%
+measure of the output correspond to the
+ 
+
+ align:start position:0%
+measure of the output correspond to the
+input may be Complicated by disturbances
+
+ align:start position:0%
+input may be Complicated by disturbances
+ 
+
+ align:start position:0%
+input may be Complicated by disturbances
+that are applied to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system I think we can look at a a fairly
+
+ align:start position:0%
+system I think we can look at a a fairly
+ 
+
+ align:start position:0%
+system I think we can look at a a fairly
+familiar example and see how it
+
+ align:start position:0%
+familiar example and see how it
+ 
+
+ align:start position:0%
+familiar example and see how it
+corresponds to that uh sort of
+
+ align:start position:0%
+corresponds to that uh sort of
+ 
+
+ align:start position:0%
+corresponds to that uh sort of
+diagrammatic representation of a typical
+
+ align:start position:0%
+diagrammatic representation of a typical
+ 
+
+ align:start position:0%
+diagrammatic representation of a typical
+feedback system system here we have a
+
+ align:start position:0%
+feedback system system here we have a
+ 
+
+ align:start position:0%
+feedback system system here we have a
+rather familiar operational amplifier
+
+ align:start position:0%
+rather familiar operational amplifier
+ 
+
+ align:start position:0%
+rather familiar operational amplifier
+connection this is called a
+
+ align:start position:0%
+connection this is called a
+ 
+
+ align:start position:0%
+connection this is called a
+non-inverting amplifier connection we
+
+ align:start position:0%
+non-inverting amplifier connection we
+ 
+
+ align:start position:0%
+non-inverting amplifier connection we
+have an input voltage V subi which I
+
+ align:start position:0%
+have an input voltage V subi which I
+ 
+
+ align:start position:0%
+have an input voltage V subi which I
+apply to the non-inverting input
+
+ align:start position:0%
+apply to the non-inverting input
+ 
+
+ align:start position:0%
+apply to the non-inverting input
+terminal of our operational
+
+ align:start position:0%
+terminal of our operational
+ 
+
+ align:start position:0%
+terminal of our operational
+amplifier the quantity a is the open
+
+ align:start position:0%
+amplifier the quantity a is the open
+ 
+
+ align:start position:0%
+amplifier the quantity a is the open
+loop gain or the open loop transfer
+
+ align:start position:0%
+loop gain or the open loop transfer
+ 
+
+ align:start position:0%
+loop gain or the open loop transfer
+function of the operational
+
+ align:start position:0%
+function of the operational
+ 
+
+ align:start position:0%
+function of the operational
+amplifier and we then get an output from
+
+ align:start position:0%
+amplifier and we then get an output from
+ 
+
+ align:start position:0%
+amplifier and we then get an output from
+our operational amplifier that output is
+
+ align:start position:0%
+our operational amplifier that output is
+ 
+
+ align:start position:0%
+our operational amplifier that output is
+attenuated by a network involving the
+
+ align:start position:0%
+attenuated by a network involving the
+ 
+
+ align:start position:0%
+attenuated by a network involving the
+resistors R1 and
+
+ align:start position:0%
+resistors R1 and
+ 
+
+ align:start position:0%
+resistors R1 and
+R2 and the voltage at the output of that
+
+ align:start position:0%
+R2 and the voltage at the output of that
+ 
+
+ align:start position:0%
+R2 and the voltage at the output of that
+Network we'll call V subf that's
+
+ align:start position:0%
+Network we'll call V subf that's
+ 
+
+ align:start position:0%
+Network we'll call V subf that's
+actually the voltage fed back in this
+
+ align:start position:0%
+actually the voltage fed back in this
+ 
+
+ align:start position:0%
+actually the voltage fed back in this
+particular system uh we also then get an
+
+ align:start position:0%
+particular system uh we also then get an
+ 
+
+ align:start position:0%
+particular system uh we also then get an
+error which is really the difference
+
+ align:start position:0%
+error which is really the difference
+ 
+
+ align:start position:0%
+error which is really the difference
+between the input voltage VI and our
+
+ align:start position:0%
+between the input voltage VI and our
+ 
+
+ align:start position:0%
+between the input voltage VI and our
+measure of the output here we have the
+
+ align:start position:0%
+measure of the output here we have the
+ 
+
+ align:start position:0%
+measure of the output here we have the
+output voltage our measure of the output
+
+ align:start position:0%
+output voltage our measure of the output
+ 
+
+ align:start position:0%
+output voltage our measure of the output
+involves in this case simply the
+
+ align:start position:0%
+involves in this case simply the
+ 
+
+ align:start position:0%
+involves in this case simply the
+attenuation ratio of the r1r2 network
+
+ align:start position:0%
+attenuation ratio of the r1r2 network
+ 
+
+ align:start position:0%
+attenuation ratio of the r1r2 network
+that assumes that uh the amplifier is is
+
+ align:start position:0%
+that assumes that uh the amplifier is is
+ 
+
+ align:start position:0%
+that assumes that uh the amplifier is is
+ideal in the sense that it doesn't load
+
+ align:start position:0%
+ideal in the sense that it doesn't load
+ 
+
+ align:start position:0%
+ideal in the sense that it doesn't load
+this network we generate an error
+
+ align:start position:0%
+this network we generate an error
+ 
+
+ align:start position:0%
+this network we generate an error
+voltage proportional to the difference
+
+ align:start position:0%
+voltage proportional to the difference
+ 
+
+ align:start position:0%
+voltage proportional to the difference
+between the input and the fedback
+
+ align:start position:0%
+between the input and the fedback
+ 
+
+ align:start position:0%
+between the input and the fedback
+voltage so we see aside from the
+
+ align:start position:0%
+voltage so we see aside from the
+ 
+
+ align:start position:0%
+voltage so we see aside from the
+disturbance that I indicated as a
+
+ align:start position:0%
+disturbance that I indicated as a
+ 
+
+ align:start position:0%
+disturbance that I indicated as a
+possibility in our in our diagrammatic
+
+ align:start position:0%
+possibility in our in our diagrammatic
+ 
+
+ align:start position:0%
+possibility in our in our diagrammatic
+feedback system here we have the the
+
+ align:start position:0%
+feedback system here we have the the
+ 
+
+ align:start position:0%
+feedback system here we have the the
+elements Central to a feedback system an
+
+ align:start position:0%
+elements Central to a feedback system an
+ 
+
+ align:start position:0%
+elements Central to a feedback system an
+input an output a measure of the output
+
+ align:start position:0%
+input an output a measure of the output
+ 
+
+ align:start position:0%
+input an output a measure of the output
+an error that's the difference between
+
+ align:start position:0%
+an error that's the difference between
+ 
+
+ align:start position:0%
+an error that's the difference between
+the input and that measure of the output
+
+ align:start position:0%
+the input and that measure of the output
+ 
+
+ align:start position:0%
+the input and that measure of the output
+and then the amplifying element that
+
+ align:start position:0%
+and then the amplifying element that
+ 
+
+ align:start position:0%
+and then the amplifying element that
+amplifies the error signal and drives
+
+ align:start position:0%
+amplifies the error signal and drives
+ 
+
+ align:start position:0%
+amplifies the error signal and drives
+the output
+
+ align:start position:0%
+the output
+ 
+
+ align:start position:0%
+the output
+accordingly I'd like to indicate a
+
+ align:start position:0%
+accordingly I'd like to indicate a
+ 
+
+ align:start position:0%
+accordingly I'd like to indicate a
+notation that I'll use throughout the
+
+ align:start position:0%
+notation that I'll use throughout the
+ 
+
+ align:start position:0%
+notation that I'll use throughout the
+subject and what we will do is the
+
+ align:start position:0%
+subject and what we will do is the
+ 
+
+ align:start position:0%
+subject and what we will do is the
+following we use a combination of a
+
+ align:start position:0%
+following we use a combination of a
+ 
+
+ align:start position:0%
+following we use a combination of a
+variable and its subscript to indicate
+
+ align:start position:0%
+variable and its subscript to indicate
+ 
+
+ align:start position:0%
+variable and its subscript to indicate
+the class of variable that we're dealing
+
+ align:start position:0%
+the class of variable that we're dealing
+ 
+
+ align:start position:0%
+the class of variable that we're dealing
+with and this will become important
+
+ align:start position:0%
+with and this will become important
+ 
+
+ align:start position:0%
+with and this will become important
+later on as we look at a wider variety
+
+ align:start position:0%
+later on as we look at a wider variety
+ 
+
+ align:start position:0%
+later on as we look at a wider variety
+of systems but uh the notation is as
+
+ align:start position:0%
+of systems but uh the notation is as
+ 
+
+ align:start position:0%
+of systems but uh the notation is as
+follows if we use a lowercase variable
+
+ align:start position:0%
+follows if we use a lowercase variable
+ 
+
+ align:start position:0%
+follows if we use a lowercase variable
+and a capital subscript we're talking
+
+ align:start position:0%
+and a capital subscript we're talking
+ 
+
+ align:start position:0%
+and a capital subscript we're talking
+about a total variable or time variable
+
+ align:start position:0%
+about a total variable or time variable
+ 
+
+ align:start position:0%
+about a total variable or time variable
+in many cases we'll be
+
+ align:start position:0%
+in many cases we'll be
+ 
+
+ align:start position:0%
+in many cases we'll be
+linearizing uh as one technique for
+
+ align:start position:0%
+linearizing uh as one technique for
+ 
+
+ align:start position:0%
+linearizing uh as one technique for
+analyzing systems and when we do that we
+
+ align:start position:0%
+analyzing systems and when we do that we
+ 
+
+ align:start position:0%
+analyzing systems and when we do that we
+very frequently find it convenient to
+
+ align:start position:0%
+very frequently find it convenient to
+ 
+
+ align:start position:0%
+very frequently find it convenient to
+decompose a total variable into a sum of
+
+ align:start position:0%
+decompose a total variable into a sum of
+ 
+
+ align:start position:0%
+decompose a total variable into a sum of
+an operating Point variable and an
+
+ align:start position:0%
+an operating Point variable and an
+ 
+
+ align:start position:0%
+an operating Point variable and an
+incremental component about that
+
+ align:start position:0%
+incremental component about that
+ 
+
+ align:start position:0%
+incremental component about that
+operating
+
+ align:start position:0%
+operating
+ 
+
+ align:start position:0%
+operating
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+the way we designate an operating point
+
+ align:start position:0%
+the way we designate an operating point
+ 
+
+ align:start position:0%
+the way we designate an operating point
+is capital V uh sub capital I we use
+
+ align:start position:0%
+is capital V uh sub capital I we use
+ 
+
+ align:start position:0%
+is capital V uh sub capital I we use
+capitals on both the variable and the
+
+ align:start position:0%
+capitals on both the variable and the
+ 
+
+ align:start position:0%
+capitals on both the variable and the
+subscript uh we then uh will designate
+
+ align:start position:0%
+subscript uh we then uh will designate
+ 
+
+ align:start position:0%
+subscript uh we then uh will designate
+the incremental component about that
+
+ align:start position:0%
+the incremental component about that
+ 
+
+ align:start position:0%
+the incremental component about that
+operating Point by a lowercase variable
+
+ align:start position:0%
+operating Point by a lowercase variable
+ 
+
+ align:start position:0%
+operating Point by a lowercase variable
+and a lowercase
+
+ align:start position:0%
+and a lowercase
+ 
+
+ align:start position:0%
+and a lowercase
+subscript and the final permutation uh
+
+ align:start position:0%
+subscript and the final permutation uh
+ 
+
+ align:start position:0%
+subscript and the final permutation uh
+the capital variable and the lowercase
+
+ align:start position:0%
+the capital variable and the lowercase
+ 
+
+ align:start position:0%
+the capital variable and the lowercase
+subscript we'll use for a frequency
+
+ align:start position:0%
+subscript we'll use for a frequency
+ 
+
+ align:start position:0%
+subscript we'll use for a frequency
+domain representation a complex
+
+ align:start position:0%
+domain representation a complex
+ 
+
+ align:start position:0%
+domain representation a complex
+amplitude or a llas transform that sort
+
+ align:start position:0%
+amplitude or a llas transform that sort
+ 
+
+ align:start position:0%
+amplitude or a llas transform that sort
+of thing and you notice that's the
+
+ align:start position:0%
+of thing and you notice that's the
+ 
+
+ align:start position:0%
+of thing and you notice that's the
+notation I've used here uh that allows
+
+ align:start position:0%
+notation I've used here uh that allows
+ 
+
+ align:start position:0%
+notation I've used here uh that allows
+us the possibility of talking about a
+
+ align:start position:0%
+us the possibility of talking about a
+ 
+
+ align:start position:0%
+us the possibility of talking about a
+transfer function for the amplifier uh
+
+ align:start position:0%
+transfer function for the amplifier uh
+ 
+
+ align:start position:0%
+transfer function for the amplifier uh
+we'll see very rapidly not actually in
+
+ align:start position:0%
+we'll see very rapidly not actually in
+ 
+
+ align:start position:0%
+we'll see very rapidly not actually in
+in this session but very shortly we'll
+
+ align:start position:0%
+in this session but very shortly we'll
+ 
+
+ align:start position:0%
+in this session but very shortly we'll
+see that we'll begin to worry about how
+
+ align:start position:0%
+see that we'll begin to worry about how
+ 
+
+ align:start position:0%
+see that we'll begin to worry about how
+these systems be cave when the quantity
+
+ align:start position:0%
+these systems be cave when the quantity
+ 
+
+ align:start position:0%
+these systems be cave when the quantity
+a is frequency dependent by using the
+
+ align:start position:0%
+a is frequency dependent by using the
+ 
+
+ align:start position:0%
+a is frequency dependent by using the
+complex amplitude of the frequency
+
+ align:start position:0%
+complex amplitude of the frequency
+ 
+
+ align:start position:0%
+complex amplitude of the frequency
+domain notation uh where we allow
+
+ align:start position:0%
+domain notation uh where we allow
+ 
+
+ align:start position:0%
+domain notation uh where we allow
+ourselves that
+
+ align:start position:0%
+ourselves that
+ 
+
+ align:start position:0%
+ourselves that
+capability well let's go ahead and and
+
+ align:start position:0%
+capability well let's go ahead and and
+ 
+
+ align:start position:0%
+capability well let's go ahead and and
+develop the closed loop gain for this
+
+ align:start position:0%
+develop the closed loop gain for this
+ 
+
+ align:start position:0%
+develop the closed loop gain for this
+very simple non-inverting operational
+
+ align:start position:0%
+very simple non-inverting operational
+ 
+
+ align:start position:0%
+very simple non-inverting operational
+amplifier
+
+ align:start position:0%
+amplifier
+ 
+
+ align:start position:0%
+amplifier
+configuration the amplifier of course
+
+ align:start position:0%
+configuration the amplifier of course
+ 
+
+ align:start position:0%
+configuration the amplifier of course
+provides an output V out that's equal to
+
+ align:start position:0%
+provides an output V out that's equal to
+ 
+
+ align:start position:0%
+provides an output V out that's equal to
+its open loop gain or or open Loop
+
+ align:start position:0%
+its open loop gain or or open Loop
+ 
+
+ align:start position:0%
+its open loop gain or or open Loop
+transfer function times the differential
+
+ align:start position:0%
+transfer function times the differential
+ 
+
+ align:start position:0%
+transfer function times the differential
+voltage applied to the operational
+
+ align:start position:0%
+voltage applied to the operational
+ 
+
+ align:start position:0%
+voltage applied to the operational
+amplifier so the output voltage is
+
+ align:start position:0%
+amplifier so the output voltage is
+ 
+
+ align:start position:0%
+amplifier so the output voltage is
+simply a times the differential input
+
+ align:start position:0%
+simply a times the differential input
+ 
+
+ align:start position:0%
+simply a times the differential input
+voltage that voltage is VE in our
+
+ align:start position:0%
+voltage that voltage is VE in our
+ 
+
+ align:start position:0%
+voltage that voltage is VE in our
+schematic diagram and the voltage ve is
+
+ align:start position:0%
+schematic diagram and the voltage ve is
+ 
+
+ align:start position:0%
+schematic diagram and the voltage ve is
+simply equal to the difference between
+
+ align:start position:0%
+simply equal to the difference between
+ 
+
+ align:start position:0%
+simply equal to the difference between
+the input voltage applied to the overall
+
+ align:start position:0%
+the input voltage applied to the overall
+ 
+
+ align:start position:0%
+the input voltage applied to the overall
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+VI and our measure of the output v subf
+
+ align:start position:0%
+VI and our measure of the output v subf
+ 
+
+ align:start position:0%
+VI and our measure of the output v subf
+v subf in turn
+
+ align:start position:0%
+v subf in turn
+ 
+
+ align:start position:0%
+v subf in turn
+uh is the attenuated version of the
+
+ align:start position:0%
+uh is the attenuated version of the
+ 
+
+ align:start position:0%
+uh is the attenuated version of the
+output in this particular system R1 over
+
+ align:start position:0%
+output in this particular system R1 over
+ 
+
+ align:start position:0%
+output in this particular system R1 over
+R1 + R2 time V out again this
+
+ align:start position:0%
+R1 + R2 time V out again this
+ 
+
+ align:start position:0%
+R1 + R2 time V out again this
+presupposes that there's no loading at
+
+ align:start position:0%
+presupposes that there's no loading at
+ 
+
+ align:start position:0%
+presupposes that there's no loading at
+the input of the amplifier so that
+
+ align:start position:0%
+the input of the amplifier so that
+ 
+
+ align:start position:0%
+the input of the amplifier so that
+the attenuating network the r1r2 network
+
+ align:start position:0%
+the attenuating network the r1r2 network
+ 
+
+ align:start position:0%
+the attenuating network the r1r2 network
+isn't affected because of of input
+
+ align:start position:0%
+isn't affected because of of input
+ 
+
+ align:start position:0%
+isn't affected because of of input
+impedance associated with the
+
+ align:start position:0%
+impedance associated with the
+ 
+
+ align:start position:0%
+impedance associated with the
+operational amplifier we're able to
+
+ align:start position:0%
+operational amplifier we're able to
+ 
+
+ align:start position:0%
+operational amplifier we're able to
+write the voltage VF as simply being
+
+ align:start position:0%
+write the voltage VF as simply being
+ 
+
+ align:start position:0%
+write the voltage VF as simply being
+equal to R1 / R1 + R2 time V out U I'd
+
+ align:start position:0%
+equal to R1 / R1 + R2 time V out U I'd
+ 
+
+ align:start position:0%
+equal to R1 / R1 + R2 time V out U I'd
+like to introduce a notation again that
+
+ align:start position:0%
+like to introduce a notation again that
+ 
+
+ align:start position:0%
+like to introduce a notation again that
+we'll use almost universally throughout
+
+ align:start position:0%
+we'll use almost universally throughout
+ 
+
+ align:start position:0%
+we'll use almost universally throughout
+the subject uh let's call this fraction
+
+ align:start position:0%
+the subject uh let's call this fraction
+ 
+
+ align:start position:0%
+the subject uh let's call this fraction
+F uh in general the relationship between
+
+ align:start position:0%
+F uh in general the relationship between
+ 
+
+ align:start position:0%
+F uh in general the relationship between
+the output variable and the quantity
+
+ align:start position:0%
+the output variable and the quantity
+ 
+
+ align:start position:0%
+the output variable and the quantity
+that we feedback in our feedback system
+
+ align:start position:0%
+that we feedback in our feedback system
+ 
+
+ align:start position:0%
+that we feedback in our feedback system
+is ftimes V out the uh fedback quantity
+
+ align:start position:0%
+is ftimes V out the uh fedback quantity
+ 
+
+ align:start position:0%
+is ftimes V out the uh fedback quantity
+is f the feedback function times V out
+
+ align:start position:0%
+is f the feedback function times V out
+ 
+
+ align:start position:0%
+is f the feedback function times V out
+again I emphasize the fact that this
+
+ align:start position:0%
+again I emphasize the fact that this
+ 
+
+ align:start position:0%
+again I emphasize the fact that this
+expression is true only in the case
+
+ align:start position:0%
+expression is true only in the case
+ 
+
+ align:start position:0%
+expression is true only in the case
+where we can ignore loading in the
+
+ align:start position:0%
+where we can ignore loading in the
+ 
+
+ align:start position:0%
+where we can ignore loading in the
+operational amplifier at the input of
+
+ align:start position:0%
+operational amplifier at the input of
+ 
+
+ align:start position:0%
+operational amplifier at the input of
+the operational amplifier we could
+
+ align:start position:0%
+the operational amplifier we could
+ 
+
+ align:start position:0%
+the operational amplifier we could
+certainly get some modified F some
+
+ align:start position:0%
+certainly get some modified F some
+ 
+
+ align:start position:0%
+certainly get some modified F some
+different value for f if we did have to
+
+ align:start position:0%
+different value for f if we did have to
+ 
+
+ align:start position:0%
+different value for f if we did have to
+worry about
+
+ align:start position:0%
+worry about
+ 
+
+ align:start position:0%
+worry about
+loading uh we can then combine these
+
+ align:start position:0%
+loading uh we can then combine these
+ 
+
+ align:start position:0%
+loading uh we can then combine these
+equations and conclude that V out is
+
+ align:start position:0%
+equations and conclude that V out is
+ 
+
+ align:start position:0%
+equations and conclude that V out is
+equal to a * VI minus FV out Simply
+
+ align:start position:0%
+equal to a * VI minus FV out Simply
+ 
+
+ align:start position:0%
+equal to a * VI minus FV out Simply
+combining these equations and that
+
+ align:start position:0%
+combining these equations and that
+ 
+
+ align:start position:0%
+combining these equations and that
+allows us to write the closed loop
+
+ align:start position:0%
+allows us to write the closed loop
+ 
+
+ align:start position:0%
+allows us to write the closed loop
+transfer function V out over VI and we
+
+ align:start position:0%
+transfer function V out over VI and we
+ 
+
+ align:start position:0%
+transfer function V out over VI and we
+use that expression often enough so that
+
+ align:start position:0%
+use that expression often enough so that
+ 
+
+ align:start position:0%
+use that expression often enough so that
+I'd like to introduce again a standard
+
+ align:start position:0%
+I'd like to introduce again a standard
+ 
+
+ align:start position:0%
+I'd like to introduce again a standard
+notation that we'll use for the closed
+
+ align:start position:0%
+notation that we'll use for the closed
+ 
+
+ align:start position:0%
+notation that we'll use for the closed
+loop gain or the Clos Loop transfer
+
+ align:start position:0%
+loop gain or the Clos Loop transfer
+ 
+
+ align:start position:0%
+loop gain or the Clos Loop transfer
+function of our operational amplifier uh
+
+ align:start position:0%
+function of our operational amplifier uh
+ 
+
+ align:start position:0%
+function of our operational amplifier uh
+it at times will be a function of of S
+
+ align:start position:0%
+it at times will be a function of of S
+ 
+
+ align:start position:0%
+it at times will be a function of of S
+the complex variable s uh but anyway our
+
+ align:start position:0%
+the complex variable s uh but anyway our
+ 
+
+ align:start position:0%
+the complex variable s uh but anyway our
+closed loop transfer function will be
+
+ align:start position:0%
+closed loop transfer function will be
+ 
+
+ align:start position:0%
+closed loop transfer function will be
+capital A and that's equal to little a
+
+ align:start position:0%
+capital A and that's equal to little a
+ 
+
+ align:start position:0%
+capital A and that's equal to little a
+in this case the open loop transfer
+
+ align:start position:0%
+in this case the open loop transfer
+ 
+
+ align:start position:0%
+in this case the open loop transfer
+function or the open loop gain of the
+
+ align:start position:0%
+function or the open loop gain of the
+ 
+
+ align:start position:0%
+function or the open loop gain of the
+operational amplifier over 1 plus AF
+
+ align:start position:0%
+operational amplifier over 1 plus AF
+ 
+
+ align:start position:0%
+operational amplifier over 1 plus AF
+that's simply the result of combining
+
+ align:start position:0%
+that's simply the result of combining
+ 
+
+ align:start position:0%
+that's simply the result of combining
+this set of
+
+ align:start position:0%
+this set of
+ 
+
+ align:start position:0%
+this set of
+equations we'll frequently find that
+
+ align:start position:0%
+equations we'll frequently find that
+ 
+
+ align:start position:0%
+equations we'll frequently find that
+it's convenient to indicate the
+
+ align:start position:0%
+it's convenient to indicate the
+ 
+
+ align:start position:0%
+it's convenient to indicate the
+relationships that exist in a feedback
+
+ align:start position:0%
+relationships that exist in a feedback
+ 
+
+ align:start position:0%
+relationships that exist in a feedback
+system in terms of a a pictorial
+
+ align:start position:0%
+system in terms of a a pictorial
+ 
+
+ align:start position:0%
+system in terms of a a pictorial
+representation and that sort of
+
+ align:start position:0%
+representation and that sort of
+ 
+
+ align:start position:0%
+representation and that sort of
+pictorial representation is known as a
+
+ align:start position:0%
+pictorial representation is known as a
+ 
+
+ align:start position:0%
+pictorial representation is known as a
+block
+
+ align:start position:0%
+block
+ 
+
+ align:start position:0%
+block
+diagram and I have an example here of a
+
+ align:start position:0%
+diagram and I have an example here of a
+ 
+
+ align:start position:0%
+diagram and I have an example here of a
+block diagram the reason that we do this
+
+ align:start position:0%
+block diagram the reason that we do this
+ 
+
+ align:start position:0%
+block diagram the reason that we do this
+is is not because it gives us any
+
+ align:start position:0%
+is is not because it gives us any
+ 
+
+ align:start position:0%
+is is not because it gives us any
+information that we didn't have before
+
+ align:start position:0%
+information that we didn't have before
+ 
+
+ align:start position:0%
+information that we didn't have before
+in fact we can certainly construct a
+
+ align:start position:0%
+in fact we can certainly construct a
+ 
+
+ align:start position:0%
+in fact we can certainly construct a
+block diagram by looking at the
+
+ align:start position:0%
+block diagram by looking at the
+ 
+
+ align:start position:0%
+block diagram by looking at the
+equations that describe the behavior of
+
+ align:start position:0%
+equations that describe the behavior of
+ 
+
+ align:start position:0%
+equations that describe the behavior of
+the system we can go back and forth
+
+ align:start position:0%
+the system we can go back and forth
+ 
+
+ align:start position:0%
+the system we can go back and forth
+readily between those quantities but uh
+
+ align:start position:0%
+readily between those quantities but uh
+ 
+
+ align:start position:0%
+readily between those quantities but uh
+oftentimes
+
+ align:start position:0%
+oftentimes
+ 
+
+ align:start position:0%
+oftentimes
+the topology that we see when we get a
+
+ align:start position:0%
+the topology that we see when we get a
+ 
+
+ align:start position:0%
+the topology that we see when we get a
+block diagram or when we develop a block
+
+ align:start position:0%
+block diagram or when we develop a block
+ 
+
+ align:start position:0%
+block diagram or when we develop a block
+diagram gives us a very nice feeling for
+
+ align:start position:0%
+diagram gives us a very nice feeling for
+ 
+
+ align:start position:0%
+diagram gives us a very nice feeling for
+the way signals are interacting in a
+
+ align:start position:0%
+the way signals are interacting in a
+ 
+
+ align:start position:0%
+the way signals are interacting in a
+feedback system and so I think the
+
+ align:start position:0%
+feedback system and so I think the
+ 
+
+ align:start position:0%
+feedback system and so I think the
+advantage is that kind of insight that
+
+ align:start position:0%
+advantage is that kind of insight that
+ 
+
+ align:start position:0%
+advantage is that kind of insight that
+the pictorial representation very
+
+ align:start position:0%
+the pictorial representation very
+ 
+
+ align:start position:0%
+the pictorial representation very
+frequently gives us and here's an
+
+ align:start position:0%
+frequently gives us and here's an
+ 
+
+ align:start position:0%
+frequently gives us and here's an
+example of a simple block diagram in
+
+ align:start position:0%
+example of a simple block diagram in
+ 
+
+ align:start position:0%
+example of a simple block diagram in
+fact one for the system we've just
+
+ align:start position:0%
+fact one for the system we've just
+ 
+
+ align:start position:0%
+fact one for the system we've just
+described uh there are three kinds of of
+
+ align:start position:0%
+described uh there are three kinds of of
+ 
+
+ align:start position:0%
+described uh there are three kinds of of
+elements if you will in a block diagram
+
+ align:start position:0%
+elements if you will in a block diagram
+ 
+
+ align:start position:0%
+elements if you will in a block diagram
+there are lines and lines represent
+
+ align:start position:0%
+there are lines and lines represent
+ 
+
+ align:start position:0%
+there are lines and lines represent
+variables in our block diagram uh for
+
+ align:start position:0%
+variables in our block diagram uh for
+ 
+
+ align:start position:0%
+variables in our block diagram uh for
+example this line represents the output
+
+ align:start position:0%
+example this line represents the output
+ 
+
+ align:start position:0%
+example this line represents the output
+V out this point in the block diagram is
+
+ align:start position:0%
+V out this point in the block diagram is
+ 
+
+ align:start position:0%
+V out this point in the block diagram is
+equal to the difference between V out
+
+ align:start position:0%
+equal to the difference between V out
+ 
+
+ align:start position:0%
+equal to the difference between V out
+time F and
+
+ align:start position:0%
+time F and
+ 
+
+ align:start position:0%
+time F and
+VI and that's simply equal to the
+
+ align:start position:0%
+VI and that's simply equal to the
+ 
+
+ align:start position:0%
+VI and that's simply equal to the
+quantity V which we mentioned earlier uh
+
+ align:start position:0%
+quantity V which we mentioned earlier uh
+ 
+
+ align:start position:0%
+quantity V which we mentioned earlier uh
+so a line represents a variable we have
+
+ align:start position:0%
+so a line represents a variable we have
+ 
+
+ align:start position:0%
+so a line represents a variable we have
+blocks and blocks simply scale variables
+
+ align:start position:0%
+blocks and blocks simply scale variables
+ 
+
+ align:start position:0%
+blocks and blocks simply scale variables
+here we have V out going into a block
+
+ align:start position:0%
+here we have V out going into a block
+ 
+
+ align:start position:0%
+here we have V out going into a block
+that provid provides a gain of F and the
+
+ align:start position:0%
+that provid provides a gain of F and the
+ 
+
+ align:start position:0%
+that provid provides a gain of F and the
+output of that block is then the
+
+ align:start position:0%
+output of that block is then the
+ 
+
+ align:start position:0%
+output of that block is then the
+quantity V subf that we mentioned
+
+ align:start position:0%
+quantity V subf that we mentioned
+ 
+
+ align:start position:0%
+quantity V subf that we mentioned
+earlier we also have the Third Kind of
+
+ align:start position:0%
+earlier we also have the Third Kind of
+ 
+
+ align:start position:0%
+earlier we also have the Third Kind of
+element a summing point where we
+
+ align:start position:0%
+element a summing point where we
+ 
+
+ align:start position:0%
+element a summing point where we
+algebraically combine variables here we
+
+ align:start position:0%
+algebraically combine variables here we
+ 
+
+ align:start position:0%
+algebraically combine variables here we
+have VI and VF we get the output of our
+
+ align:start position:0%
+have VI and VF we get the output of our
+ 
+
+ align:start position:0%
+have VI and VF we get the output of our
+summing Point as being equal to the
+
+ align:start position:0%
+summing Point as being equal to the
+ 
+
+ align:start position:0%
+summing Point as being equal to the
+difference between VI and VF VI minus VF
+
+ align:start position:0%
+difference between VI and VF VI minus VF
+ 
+
+ align:start position:0%
+difference between VI and VF VI minus VF
+and that's
+
+ align:start position:0%
+and that's
+ 
+
+ align:start position:0%
+and that's
+V so here we have a pictorial way of of
+
+ align:start position:0%
+V so here we have a pictorial way of of
+ 
+
+ align:start position:0%
+V so here we have a pictorial way of of
+representing our our
+
+ align:start position:0%
+representing our our
+ 
+
+ align:start position:0%
+representing our our
+system the closed loop transfer function
+
+ align:start position:0%
+system the closed loop transfer function
+ 
+
+ align:start position:0%
+system the closed loop transfer function
+for this configuration then we can get
+
+ align:start position:0%
+for this configuration then we can get
+ 
+
+ align:start position:0%
+for this configuration then we can get
+the following
+
+ align:start position:0%
+the following
+ 
+
+ align:start position:0%
+the following
+way we've already derived this
+
+ align:start position:0%
+way we've already derived this
+ 
+
+ align:start position:0%
+way we've already derived this
+expression with uh by going through the
+
+ align:start position:0%
+expression with uh by going through the
+ 
+
+ align:start position:0%
+expression with uh by going through the
+algebraic
+
+ align:start position:0%
+algebraic
+ 
+
+ align:start position:0%
+algebraic
+manipulation and we can also get that
+
+ align:start position:0%
+manipulation and we can also get that
+ 
+
+ align:start position:0%
+manipulation and we can also get that
+picture tally we may find out that what
+
+ align:start position:0%
+picture tally we may find out that what
+ 
+
+ align:start position:0%
+picture tally we may find out that what
+we do is develop a a block diagram by a
+
+ align:start position:0%
+we do is develop a a block diagram by a
+ 
+
+ align:start position:0%
+we do is develop a a block diagram by a
+series of manipulations that reduce a
+
+ align:start position:0%
+series of manipulations that reduce a
+ 
+
+ align:start position:0%
+series of manipulations that reduce a
+more complicated block
+
+ align:start position:0%
+more complicated block
+ 
+
+ align:start position:0%
+more complicated block
+diagram we there's examples of that in
+
+ align:start position:0%
+diagram we there's examples of that in
+ 
+
+ align:start position:0%
+diagram we there's examples of that in
+the the text and in fact some of the
+
+ align:start position:0%
+the the text and in fact some of the
+ 
+
+ align:start position:0%
+the the text and in fact some of the
+homework problems associated with this
+
+ align:start position:0%
+homework problems associated with this
+ 
+
+ align:start position:0%
+homework problems associated with this
+session will have you go through some
+
+ align:start position:0%
+session will have you go through some
+ 
+
+ align:start position:0%
+session will have you go through some
+block diagram
+
+ align:start position:0%
+block diagram
+ 
+
+ align:start position:0%
+block diagram
+manipulations but we may find out that
+
+ align:start position:0%
+manipulations but we may find out that
+ 
+
+ align:start position:0%
+manipulations but we may find out that
+for a more complicated system we start
+
+ align:start position:0%
+for a more complicated system we start
+ 
+
+ align:start position:0%
+for a more complicated system we start
+with a more General block diagram one
+
+ align:start position:0%
+with a more General block diagram one
+ 
+
+ align:start position:0%
+with a more General block diagram one
+that has possibly multiple Loops or
+
+ align:start position:0%
+that has possibly multiple Loops or
+ 
+
+ align:start position:0%
+that has possibly multiple Loops or
+something but we're always able to go
+
+ align:start position:0%
+something but we're always able to go
+ 
+
+ align:start position:0%
+something but we're always able to go
+through a series of manipulations at
+
+ align:start position:0%
+through a series of manipulations at
+ 
+
+ align:start position:0%
+through a series of manipulations at
+least for linear systems uh until we
+
+ align:start position:0%
+least for linear systems uh until we
+ 
+
+ align:start position:0%
+least for linear systems uh until we
+finally get our block diagram down to
+
+ align:start position:0%
+finally get our block diagram down to
+ 
+
+ align:start position:0%
+finally get our block diagram down to
+this form uh here it came out directly
+
+ align:start position:0%
+this form uh here it came out directly
+ 
+
+ align:start position:0%
+this form uh here it came out directly
+we notice there a very nice one: one
+
+ align:start position:0%
+we notice there a very nice one: one
+ 
+
+ align:start position:0%
+we notice there a very nice one: one
+correspondence between that block
+
+ align:start position:0%
+correspondence between that block
+ 
+
+ align:start position:0%
+correspondence between that block
+diagram and the actual system that we
+
+ align:start position:0%
+diagram and the actual system that we
+ 
+
+ align:start position:0%
+diagram and the actual system that we
+started with uh we have the input we
+
+ align:start position:0%
+started with uh we have the input we
+ 
+
+ align:start position:0%
+started with uh we have the input we
+have VF uh we have F time V out all
+
+ align:start position:0%
+have VF uh we have F time V out all
+ 
+
+ align:start position:0%
+have VF uh we have F time V out all
+appearing in the block diagram the
+
+ align:start position:0%
+appearing in the block diagram the
+ 
+
+ align:start position:0%
+appearing in the block diagram the
+function of the summing point in the
+
+ align:start position:0%
+function of the summing point in the
+ 
+
+ align:start position:0%
+function of the summing point in the
+block diagram is performed of course by
+
+ align:start position:0%
+block diagram is performed of course by
+ 
+
+ align:start position:0%
+block diagram is performed of course by
+the differential input on the
+
+ align:start position:0%
+the differential input on the
+ 
+
+ align:start position:0%
+the differential input on the
+operational amplifier here so here
+
+ align:start position:0%
+operational amplifier here so here
+ 
+
+ align:start position:0%
+operational amplifier here so here
+there's a very very nice onetoone
+
+ align:start position:0%
+there's a very very nice onetoone
+ 
+
+ align:start position:0%
+there's a very very nice onetoone
+correspondence between the physical
+
+ align:start position:0%
+correspondence between the physical
+ 
+
+ align:start position:0%
+correspondence between the physical
+system and the block diagram that almost
+
+ align:start position:0%
+system and the block diagram that almost
+ 
+
+ align:start position:0%
+system and the block diagram that almost
+perfect match doesn't always exist but
+
+ align:start position:0%
+perfect match doesn't always exist but
+ 
+
+ align:start position:0%
+perfect match doesn't always exist but
+frequently does in any case we can by
+
+ align:start position:0%
+frequently does in any case we can by
+ 
+
+ align:start position:0%
+frequently does in any case we can by
+using block diagram manipulations that
+
+ align:start position:0%
+using block diagram manipulations that
+ 
+
+ align:start position:0%
+using block diagram manipulations that
+we'll look at reduce a complicated
+
+ align:start position:0%
+we'll look at reduce a complicated
+ 
+
+ align:start position:0%
+we'll look at reduce a complicated
+system uh generally to this sort of of
+
+ align:start position:0%
+system uh generally to this sort of of
+ 
+
+ align:start position:0%
+system uh generally to this sort of of
+configuration where we have an input a
+
+ align:start position:0%
+configuration where we have an input a
+ 
+
+ align:start position:0%
+configuration where we have an input a
+single path between the input and the
+
+ align:start position:0%
+single path between the input and the
+ 
+
+ align:start position:0%
+single path between the input and the
+output and we'll try to stick with a
+
+ align:start position:0%
+output and we'll try to stick with a
+ 
+
+ align:start position:0%
+output and we'll try to stick with a
+notation where we use a lowercase a for
+
+ align:start position:0%
+notation where we use a lowercase a for
+ 
+
+ align:start position:0%
+notation where we use a lowercase a for
+that path and then a single feedback
+
+ align:start position:0%
+that path and then a single feedback
+ 
+
+ align:start position:0%
+that path and then a single feedback
+path from the output back to the summing
+
+ align:start position:0%
+path from the output back to the summing
+ 
+
+ align:start position:0%
+path from the output back to the summing
+point and we'll try to use the notation
+
+ align:start position:0%
+point and we'll try to use the notation
+ 
+
+ align:start position:0%
+point and we'll try to use the notation
+F uh pretty much generally for that
+
+ align:start position:0%
+F uh pretty much generally for that
+ 
+
+ align:start position:0%
+F uh pretty much generally for that
+feedback path or feed feedback transfer
+
+ align:start position:0%
+feedback path or feed feedback transfer
+ 
+
+ align:start position:0%
+feedback path or feed feedback transfer
+function when we've reduced the system
+
+ align:start position:0%
+function when we've reduced the system
+ 
+
+ align:start position:0%
+function when we've reduced the system
+to this configuration it of course Abyss
+
+ align:start position:0%
+to this configuration it of course Abyss
+ 
+
+ align:start position:0%
+to this configuration it of course Abyss
+exactly the equations that we've written
+
+ align:start position:0%
+exactly the equations that we've written
+ 
+
+ align:start position:0%
+exactly the equations that we've written
+down here and so we can by inspection
+
+ align:start position:0%
+down here and so we can by inspection
+ 
+
+ align:start position:0%
+down here and so we can by inspection
+write the closed loop gain we can
+
+ align:start position:0%
+write the closed loop gain we can
+ 
+
+ align:start position:0%
+write the closed loop gain we can
+recognize that the ratio the
+
+ align:start position:0%
+recognize that the ratio the
+ 
+
+ align:start position:0%
+recognize that the ratio the
+relationship between the output and the
+
+ align:start position:0%
+relationship between the output and the
+ 
+
+ align:start position:0%
+relationship between the output and the
+input V out over VI which is by
+
+ align:start position:0%
+input V out over VI which is by
+ 
+
+ align:start position:0%
+input V out over VI which is by
+definition capital A the closed loop
+
+ align:start position:0%
+definition capital A the closed loop
+ 
+
+ align:start position:0%
+definition capital A the closed loop
+gain of the system is always equal to
+
+ align:start position:0%
+gain of the system is always equal to
+ 
+
+ align:start position:0%
+gain of the system is always equal to
+the forward path a over 1 plus
+
+ align:start position:0%
+the forward path a over 1 plus
+ 
+
+ align:start position:0%
+the forward path a over 1 plus
+AF if we have this standard form a
+
+ align:start position:0%
+AF if we have this standard form a
+ 
+
+ align:start position:0%
+AF if we have this standard form a
+forward path a a feedback path F uh and
+
+ align:start position:0%
+forward path a a feedback path F uh and
+ 
+
+ align:start position:0%
+forward path a a feedback path F uh and
+an inversion associated with the
+
+ align:start position:0%
+an inversion associated with the
+ 
+
+ align:start position:0%
+an inversion associated with the
+feedback path that's shown here at the
+
+ align:start position:0%
+feedback path that's shown here at the
+ 
+
+ align:start position:0%
+feedback path that's shown here at the
+summing
+
+ align:start position:0%
+summing
+ 
+
+ align:start position:0%
+summing
+point the quantity AF that appears in
+
+ align:start position:0%
+point the quantity AF that appears in
+ 
+
+ align:start position:0%
+point the quantity AF that appears in
+this expression is a very important one
+
+ align:start position:0%
+this expression is a very important one
+ 
+
+ align:start position:0%
+this expression is a very important one
+for feedback systems and as we'll see
+
+ align:start position:0%
+for feedback systems and as we'll see
+ 
+
+ align:start position:0%
+for feedback systems and as we'll see
+that quantity the AF product controls
+
+ align:start position:0%
+that quantity the AF product controls
+ 
+
+ align:start position:0%
+that quantity the AF product controls
+many of the important parameters that we
+
+ align:start position:0%
+many of the important parameters that we
+ 
+
+ align:start position:0%
+many of the important parameters that we
+associate with a feedback
+
+ align:start position:0%
+associate with a feedback
+ 
+
+ align:start position:0%
+associate with a feedback
+system and in fact it has a name we call
+
+ align:start position:0%
+system and in fact it has a name we call
+ 
+
+ align:start position:0%
+system and in fact it has a name we call
+the loop transmission for a feedback
+
+ align:start position:0%
+the loop transmission for a feedback
+ 
+
+ align:start position:0%
+the loop transmission for a feedback
+system in this standard form uh the
+
+ align:start position:0%
+system in this standard form uh the
+ 
+
+ align:start position:0%
+system in this standard form uh the
+quantity minus AF is the loop
+
+ align:start position:0%
+quantity minus AF is the loop
+ 
+
+ align:start position:0%
+quantity minus AF is the loop
+transmission Loop transmission has a
+
+ align:start position:0%
+transmission Loop transmission has a
+ 
+
+ align:start position:0%
+transmission Loop transmission has a
+very very nice physical significance
+
+ align:start position:0%
+very very nice physical significance
+ 
+
+ align:start position:0%
+very very nice physical significance
+let's go into our system either on a
+
+ align:start position:0%
+let's go into our system either on a
+ 
+
+ align:start position:0%
+let's go into our system either on a
+block diagram level or the actual
+
+ align:start position:0%
+block diagram level or the actual
+ 
+
+ align:start position:0%
+block diagram level or the actual
+physical
+
+ align:start position:0%
+physical
+ 
+
+ align:start position:0%
+physical
+system and what we can do is break the
+
+ align:start position:0%
+system and what we can do is break the
+ 
+
+ align:start position:0%
+system and what we can do is break the
+loop actually we break break the loop at
+
+ align:start position:0%
+loop actually we break break the loop at
+ 
+
+ align:start position:0%
+loop actually we break break the loop at
+any point let's say
+
+ align:start position:0%
+any point let's say
+ 
+
+ align:start position:0%
+any point let's say
+here and we suppress all inputs so we'd
+
+ align:start position:0%
+here and we suppress all inputs so we'd
+ 
+
+ align:start position:0%
+here and we suppress all inputs so we'd
+set VI to
+
+ align:start position:0%
+set VI to
+ 
+
+ align:start position:0%
+set VI to
+zero and then we test the system by
+
+ align:start position:0%
+zero and then we test the system by
+ 
+
+ align:start position:0%
+zero and then we test the system by
+applying a test
+
+ align:start position:0%
+applying a test
+ 
+
+ align:start position:0%
+applying a test
+generator let's put one in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here and we observe the signal that the
+
+ align:start position:0%
+here and we observe the signal that the
+ 
+
+ align:start position:0%
+here and we observe the signal that the
+loop returns uh in response to a test
+
+ align:start position:0%
+loop returns uh in response to a test
+ 
+
+ align:start position:0%
+loop returns uh in response to a test
+signal well let's look at the signal vo
+
+ align:start position:0%
+signal well let's look at the signal vo
+ 
+
+ align:start position:0%
+signal well let's look at the signal vo
+that's the signal that comes back at the
+
+ align:start position:0%
+that's the signal that comes back at the
+ 
+
+ align:start position:0%
+that's the signal that comes back at the
+point where we had opened the loop or
+
+ align:start position:0%
+point where we had opened the loop or
+ 
+
+ align:start position:0%
+point where we had opened the loop or
+broken the loop and the relationship
+
+ align:start position:0%
+broken the loop and the relationship
+ 
+
+ align:start position:0%
+broken the loop and the relationship
+between V out and VT is simply ftimes
+
+ align:start position:0%
+between V out and VT is simply ftimes
+ 
+
+ align:start position:0%
+between V out and VT is simply ftimes
+minus we get an inversion associated
+
+ align:start position:0%
+minus we get an inversion associated
+ 
+
+ align:start position:0%
+minus we get an inversion associated
+with the the summing point so we have f
+
+ align:start position:0%
+with the the summing point so we have f
+ 
+
+ align:start position:0%
+with the the summing point so we have f
+* -1 * a or minus AF for the signal
+
+ align:start position:0%
+* -1 * a or minus AF for the signal
+ 
+
+ align:start position:0%
+* -1 * a or minus AF for the signal
+returned by the loop when we test it
+
+ align:start position:0%
+returned by the loop when we test it
+ 
+
+ align:start position:0%
+returned by the loop when we test it
+minus AF is the Loop transmission of
+
+ align:start position:0%
+minus AF is the Loop transmission of
+ 
+
+ align:start position:0%
+minus AF is the Loop transmission of
+this system we can do that very easily
+
+ align:start position:0%
+this system we can do that very easily
+ 
+
+ align:start position:0%
+this system we can do that very easily
+on a block diagram basis we can do the
+
+ align:start position:0%
+on a block diagram basis we can do the
+ 
+
+ align:start position:0%
+on a block diagram basis we can do the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+thing in our physical system uh there
+
+ align:start position:0%
+thing in our physical system uh there
+ 
+
+ align:start position:0%
+thing in our physical system uh there
+may be a practical problem associated
+
+ align:start position:0%
+may be a practical problem associated
+ 
+
+ align:start position:0%
+may be a practical problem associated
+with breaking the loop but uh there may
+
+ align:start position:0%
+with breaking the loop but uh there may
+ 
+
+ align:start position:0%
+with breaking the loop but uh there may
+be uh the amplifier May saturate or
+
+ align:start position:0%
+be uh the amplifier May saturate or
+ 
+
+ align:start position:0%
+be uh the amplifier May saturate or
+something like that but at least if we
+
+ align:start position:0%
+something like that but at least if we
+ 
+
+ align:start position:0%
+something like that but at least if we
+ignore that for a moment conceptually we
+
+ align:start position:0%
+ignore that for a moment conceptually we
+ 
+
+ align:start position:0%
+ignore that for a moment conceptually we
+can determine the loop transmission by
+
+ align:start position:0%
+can determine the loop transmission by
+ 
+
+ align:start position:0%
+can determine the loop transmission by
+exactly the same kind of of manipulation
+
+ align:start position:0%
+exactly the same kind of of manipulation
+ 
+
+ align:start position:0%
+exactly the same kind of of manipulation
+we break the loop possibly here is a
+
+ align:start position:0%
+we break the loop possibly here is a
+ 
+
+ align:start position:0%
+we break the loop possibly here is a
+good place we suppress the input source
+
+ align:start position:0%
+good place we suppress the input source
+ 
+
+ align:start position:0%
+good place we suppress the input source
+make that voltage source zero apply a
+
+ align:start position:0%
+make that voltage source zero apply a
+ 
+
+ align:start position:0%
+make that voltage source zero apply a
+test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+signal and again find out that we when
+
+ align:start position:0%
+signal and again find out that we when
+ 
+
+ align:start position:0%
+signal and again find out that we when
+when we observe the signal that comes
+
+ align:start position:0%
+when we observe the signal that comes
+ 
+
+ align:start position:0%
+when we observe the signal that comes
+back in response to a test why we get
+
+ align:start position:0%
+back in response to a test why we get
+ 
+
+ align:start position:0%
+back in response to a test why we get
+the test signal times an attenuation
+
+ align:start position:0%
+the test signal times an attenuation
+ 
+
+ align:start position:0%
+the test signal times an attenuation
+ratio R1 over R1 + R2 we get an
+
+ align:start position:0%
+ratio R1 over R1 + R2 we get an
+ 
+
+ align:start position:0%
+ratio R1 over R1 + R2 we get an
+inversion because the signal happens to
+
+ align:start position:0%
+inversion because the signal happens to
+ 
+
+ align:start position:0%
+inversion because the signal happens to
+go in to the inverting input of our
+
+ align:start position:0%
+go in to the inverting input of our
+ 
+
+ align:start position:0%
+go in to the inverting input of our
+operational amplifier and uh then the
+
+ align:start position:0%
+operational amplifier and uh then the
+ 
+
+ align:start position:0%
+operational amplifier and uh then the
+signal returned is a * f * the inversion
+
+ align:start position:0%
+signal returned is a * f * the inversion
+ 
+
+ align:start position:0%
+signal returned is a * f * the inversion
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+AF providing a and F both have the same
+
+ align:start position:0%
+AF providing a and F both have the same
+ 
+
+ align:start position:0%
+AF providing a and F both have the same
+sign the polarity or the sign associated
+
+ align:start position:0%
+sign the polarity or the sign associated
+ 
+
+ align:start position:0%
+sign the polarity or the sign associated
+with the loop transmission is
+
+ align:start position:0%
+with the loop transmission is
+ 
+
+ align:start position:0%
+with the loop transmission is
+negative and so this is an example of a
+
+ align:start position:0%
+negative and so this is an example of a
+ 
+
+ align:start position:0%
+negative and so this is an example of a
+negative feedback system and in general
+
+ align:start position:0%
+negative feedback system and in general
+ 
+
+ align:start position:0%
+negative feedback system and in general
+those will be the kinds we're studying
+
+ align:start position:0%
+those will be the kinds we're studying
+ 
+
+ align:start position:0%
+those will be the kinds we're studying
+we could also look at positive feedback
+
+ align:start position:0%
+we could also look at positive feedback
+ 
+
+ align:start position:0%
+we could also look at positive feedback
+systems we'll see an occasional example
+
+ align:start position:0%
+systems we'll see an occasional example
+ 
+
+ align:start position:0%
+systems we'll see an occasional example
+of a positive feedback system but
+
+ align:start position:0%
+of a positive feedback system but
+ 
+
+ align:start position:0%
+of a positive feedback system but
+generally for our purposes they're not
+
+ align:start position:0%
+generally for our purposes they're not
+ 
+
+ align:start position:0%
+generally for our purposes they're not
+quite as useful and so we'll focus our
+
+ align:start position:0%
+quite as useful and so we'll focus our
+ 
+
+ align:start position:0%
+quite as useful and so we'll focus our
+attention principally on negative
+
+ align:start position:0%
+attention principally on negative
+ 
+
+ align:start position:0%
+attention principally on negative
+feedback systems if we're concerned
+
+ align:start position:0%
+feedback systems if we're concerned
+ 
+
+ align:start position:0%
+feedback systems if we're concerned
+about whether a system is a negative
+
+ align:start position:0%
+about whether a system is a negative
+ 
+
+ align:start position:0%
+about whether a system is a negative
+feedback system or not there's a fairly
+
+ align:start position:0%
+feedback system or not there's a fairly
+ 
+
+ align:start position:0%
+feedback system or not there's a fairly
+nice test we could for example start
+
+ align:start position:0%
+nice test we could for example start
+ 
+
+ align:start position:0%
+nice test we could for example start
+with a system uh start with a a value of
+
+ align:start position:0%
+with a system uh start with a a value of
+ 
+
+ align:start position:0%
+with a system uh start with a a value of
+f equal to zero and then let F go toward
+
+ align:start position:0%
+f equal to zero and then let F go toward
+ 
+
+ align:start position:0%
+f equal to zero and then let F go toward
+the value that it actually has in the
+
+ align:start position:0%
+the value that it actually has in the
+ 
+
+ align:start position:0%
+the value that it actually has in the
+system if under those conditions the
+
+ align:start position:0%
+system if under those conditions the
+ 
+
+ align:start position:0%
+system if under those conditions the
+magnitude of the closed loop gain the
+
+ align:start position:0%
+magnitude of the closed loop gain the
+ 
+
+ align:start position:0%
+magnitude of the closed loop gain the
+magnitude of capital A decreases as we
+
+ align:start position:0%
+magnitude of capital A decreases as we
+ 
+
+ align:start position:0%
+magnitude of capital A decreases as we
+increase F from zero toward its actual
+
+ align:start position:0%
+increase F from zero toward its actual
+ 
+
+ align:start position:0%
+increase F from zero toward its actual
+value we have a negative feedback system
+
+ align:start position:0%
+value we have a negative feedback system
+ 
+
+ align:start position:0%
+value we have a negative feedback system
+and so that's a an easy way to test to
+
+ align:start position:0%
+and so that's a an easy way to test to
+ 
+
+ align:start position:0%
+and so that's a an easy way to test to
+see if a feedback system is in fact a
+
+ align:start position:0%
+see if a feedback system is in fact a
+ 
+
+ align:start position:0%
+see if a feedback system is in fact a
+negative feedback
+
+ align:start position:0%
+negative feedback
+ 
+
+ align:start position:0%
+negative feedback
+system well why do we do this what's our
+
+ align:start position:0%
+system well why do we do this what's our
+ 
+
+ align:start position:0%
+system well why do we do this what's our
+interest in building feedback
+
+ align:start position:0%
+interest in building feedback
+ 
+
+ align:start position:0%
+interest in building feedback
+systems let's again look at our closed
+
+ align:start position:0%
+systems let's again look at our closed
+ 
+
+ align:start position:0%
+systems let's again look at our closed
+loop gain
+
+ align:start position:0%
+loop gain
+ 
+
+ align:start position:0%
+loop gain
+expression the part that's valuable to
+
+ align:start position:0%
+expression the part that's valuable to
+ 
+
+ align:start position:0%
+expression the part that's valuable to
+us is the following suppose we have a
+
+ align:start position:0%
+us is the following suppose we have a
+ 
+
+ align:start position:0%
+us is the following suppose we have a
+sufficiently large AF product suppose
+
+ align:start position:0%
+sufficiently large AF product suppose
+ 
+
+ align:start position:0%
+sufficiently large AF product suppose
+the magnitude of AF is much much larger
+
+ align:start position:0%
+the magnitude of AF is much much larger
+ 
+
+ align:start position:0%
+the magnitude of AF is much much larger
+than one well then our closed loop gain
+
+ align:start position:0%
+than one well then our closed loop gain
+ 
+
+ align:start position:0%
+than one well then our closed loop gain
+expression in in evaluating the closed
+
+ align:start position:0%
+expression in in evaluating the closed
+ 
+
+ align:start position:0%
+expression in in evaluating the closed
+loop gain expression we're able to
+
+ align:start position:0%
+loop gain expression we're able to
+ 
+
+ align:start position:0%
+loop gain expression we're able to
+ignore the one in the in the denominator
+
+ align:start position:0%
+ignore the one in the in the denominator
+ 
+
+ align:start position:0%
+ignore the one in the in the denominator
+compared to the AF
+
+ align:start position:0%
+compared to the AF
+ 
+
+ align:start position:0%
+compared to the AF
+product and consequently the denominator
+
+ align:start position:0%
+product and consequently the denominator
+ 
+
+ align:start position:0%
+product and consequently the denominator
+is approximately equal to AF as a result
+
+ align:start position:0%
+is approximately equal to AF as a result
+ 
+
+ align:start position:0%
+is approximately equal to AF as a result
+capital A is simply approximately equal
+
+ align:start position:0%
+capital A is simply approximately equal
+ 
+
+ align:start position:0%
+capital A is simply approximately equal
+to 1/
+
+ align:start position:0%
+to 1/
+ 
+
+ align:start position:0%
+to 1/
+F that's the feature that we're really
+
+ align:start position:0%
+F that's the feature that we're really
+ 
+
+ align:start position:0%
+F that's the feature that we're really
+looking for and the reason is as follows
+
+ align:start position:0%
+looking for and the reason is as follows
+ 
+
+ align:start position:0%
+looking for and the reason is as follows
+the quantity a which is the forward path
+
+ align:start position:0%
+the quantity a which is the forward path
+ 
+
+ align:start position:0%
+the quantity a which is the forward path
+of our feedback system very frequently
+
+ align:start position:0%
+of our feedback system very frequently
+ 
+
+ align:start position:0%
+of our feedback system very frequently
+isn't particularly well known usually
+
+ align:start position:0%
+isn't particularly well known usually
+ 
+
+ align:start position:0%
+isn't particularly well known usually
+the gain the active elements in our
+
+ align:start position:0%
+the gain the active elements in our
+ 
+
+ align:start position:0%
+the gain the active elements in our
+feedback system are concentrated in the
+
+ align:start position:0%
+feedback system are concentrated in the
+ 
+
+ align:start position:0%
+feedback system are concentrated in the
+forward
+
+ align:start position:0%
+forward
+ 
+
+ align:start position:0%
+forward
+path and as a result because of
+
+ align:start position:0%
+path and as a result because of
+ 
+
+ align:start position:0%
+path and as a result because of
+uncertainties associated with the active
+
+ align:start position:0%
+uncertainties associated with the active
+ 
+
+ align:start position:0%
+uncertainties associated with the active
+elements possibly temp temperature or
+
+ align:start position:0%
+elements possibly temp temperature or
+ 
+
+ align:start position:0%
+elements possibly temp temperature or
+time time dependencies associated with
+
+ align:start position:0%
+time time dependencies associated with
+ 
+
+ align:start position:0%
+time time dependencies associated with
+their characteristics this quantity may
+
+ align:start position:0%
+their characteristics this quantity may
+ 
+
+ align:start position:0%
+their characteristics this quantity may
+not be particularly well known
+
+ align:start position:0%
+not be particularly well known
+ 
+
+ align:start position:0%
+not be particularly well known
+conversely we very frequently find that
+
+ align:start position:0%
+conversely we very frequently find that
+ 
+
+ align:start position:0%
+conversely we very frequently find that
+it's possible to mechanize the function
+
+ align:start position:0%
+it's possible to mechanize the function
+ 
+
+ align:start position:0%
+it's possible to mechanize the function
+f the feedback transfer function uh by
+
+ align:start position:0%
+f the feedback transfer function uh by
+ 
+
+ align:start position:0%
+f the feedback transfer function uh by
+means of stable passive components uh in
+
+ align:start position:0%
+means of stable passive components uh in
+ 
+
+ align:start position:0%
+means of stable passive components uh in
+our particular example we used a
+
+ align:start position:0%
+our particular example we used a
+ 
+
+ align:start position:0%
+our particular example we used a
+resistive attenuator in order to
+
+ align:start position:0%
+resistive attenuator in order to
+ 
+
+ align:start position:0%
+resistive attenuator in order to
+mechanize the the feedback element well
+
+ align:start position:0%
+mechanize the the feedback element well
+ 
+
+ align:start position:0%
+mechanize the the feedback element well
+we can buy passive components we can buy
+
+ align:start position:0%
+we can buy passive components we can buy
+ 
+
+ align:start position:0%
+we can buy passive components we can buy
+resistors with ratios that are known to
+
+ align:start position:0%
+resistors with ratios that are known to
+ 
+
+ align:start position:0%
+resistors with ratios that are known to
+almost any degree of precision we want
+
+ align:start position:0%
+almost any degree of precision we want
+ 
+
+ align:start position:0%
+almost any degree of precision we want
+if we go to a resistor manufacturer with
+
+ align:start position:0%
+if we go to a resistor manufacturer with
+ 
+
+ align:start position:0%
+if we go to a resistor manufacturer with
+a large enough pile of gold they'll give
+
+ align:start position:0%
+a large enough pile of gold they'll give
+ 
+
+ align:start position:0%
+a large enough pile of gold they'll give
+us resistors whose ratio can be
+
+ align:start position:0%
+us resistors whose ratio can be
+ 
+
+ align:start position:0%
+us resistors whose ratio can be
+controlled to a part in a million if we
+
+ align:start position:0%
+controlled to a part in a million if we
+ 
+
+ align:start position:0%
+controlled to a part in a million if we
+care to do that it's very very difficult
+
+ align:start position:0%
+care to do that it's very very difficult
+ 
+
+ align:start position:0%
+care to do that it's very very difficult
+in fact impossible to build an amplifier
+
+ align:start position:0%
+in fact impossible to build an amplifier
+ 
+
+ align:start position:0%
+in fact impossible to build an amplifier
+not using feedback techniques where the
+
+ align:start position:0%
+not using feedback techniques where the
+ 
+
+ align:start position:0%
+not using feedback techniques where the
+gain of the amplifier itself is
+
+ align:start position:0%
+gain of the amplifier itself is
+ 
+
+ align:start position:0%
+gain of the amplifier itself is
+controlled uh to a part in the million
+
+ align:start position:0%
+controlled uh to a part in the million
+ 
+
+ align:start position:0%
+controlled uh to a part in the million
+we just find out that that's not a
+
+ align:start position:0%
+we just find out that that's not a
+ 
+
+ align:start position:0%
+we just find out that that's not a
+possible thing to do no matter how much
+
+ align:start position:0%
+possible thing to do no matter how much
+ 
+
+ align:start position:0%
+possible thing to do no matter how much
+money you have so what we do by using
+
+ align:start position:0%
+money you have so what we do by using
+ 
+
+ align:start position:0%
+money you have so what we do by using
+feedback is find a way to make the
+
+ align:start position:0%
+feedback is find a way to make the
+ 
+
+ align:start position:0%
+feedback is find a way to make the
+closed loop gain the gain with feedback
+
+ align:start position:0%
+closed loop gain the gain with feedback
+ 
+
+ align:start position:0%
+closed loop gain the gain with feedback
+dependent on a quantity that we may be
+
+ align:start position:0%
+dependent on a quantity that we may be
+ 
+
+ align:start position:0%
+dependent on a quantity that we may be
+able to Define very precisely or specify
+
+ align:start position:0%
+able to Define very precisely or specify
+ 
+
+ align:start position:0%
+able to Define very precisely or specify
+very precisely and we make ourselves
+
+ align:start position:0%
+very precisely and we make ourselves
+ 
+
+ align:start position:0%
+very precisely and we make ourselves
+largely insensitive to variations in a
+
+ align:start position:0%
+largely insensitive to variations in a
+ 
+
+ align:start position:0%
+largely insensitive to variations in a
+subject only to the constraint that a is
+
+ align:start position:0%
+subject only to the constraint that a is
+ 
+
+ align:start position:0%
+subject only to the constraint that a is
+big enough so that the AF product is
+
+ align:start position:0%
+big enough so that the AF product is
+ 
+
+ align:start position:0%
+big enough so that the AF product is
+large compared to one if we're able to
+
+ align:start position:0%
+large compared to one if we're able to
+ 
+
+ align:start position:0%
+large compared to one if we're able to
+do that if we're able to say well a is
+
+ align:start position:0%
+do that if we're able to say well a is
+ 
+
+ align:start position:0%
+do that if we're able to say well a is
+big enough then in fact we can make or
+
+ align:start position:0%
+big enough then in fact we can make or
+ 
+
+ align:start position:0%
+big enough then in fact we can make or
+the forward path a little a is large
+
+ align:start position:0%
+the forward path a little a is large
+ 
+
+ align:start position:0%
+the forward path a little a is large
+enough we're able to make the closed
+
+ align:start position:0%
+enough we're able to make the closed
+ 
+
+ align:start position:0%
+enough we're able to make the closed
+loop gain dependent on the well-known
+
+ align:start position:0%
+loop gain dependent on the well-known
+ 
+
+ align:start position:0%
+loop gain dependent on the well-known
+characteristics of the feedback element
+
+ align:start position:0%
+characteristics of the feedback element
+ 
+
+ align:start position:0%
+characteristics of the feedback element
+we can emphasize that concept by
+
+ align:start position:0%
+we can emphasize that concept by
+ 
+
+ align:start position:0%
+we can emphasize that concept by
+calculating
+
+ align:start position:0%
+calculating
+ 
+
+ align:start position:0%
+calculating
+the change that occurs in closed loop
+
+ align:start position:0%
+the change that occurs in closed loop
+ 
+
+ align:start position:0%
+the change that occurs in closed loop
+gain as a function of changes in open
+
+ align:start position:0%
+gain as a function of changes in open
+ 
+
+ align:start position:0%
+gain as a function of changes in open
+loop gain and again we start with our
+
+ align:start position:0%
+loop gain and again we start with our
+ 
+
+ align:start position:0%
+loop gain and again we start with our
+forward path transmission we start with
+
+ align:start position:0%
+forward path transmission we start with
+ 
+
+ align:start position:0%
+forward path transmission we start with
+our expression for the closed loop gain
+
+ align:start position:0%
+our expression for the closed loop gain
+ 
+
+ align:start position:0%
+our expression for the closed loop gain
+capital A being equal to the forward
+
+ align:start position:0%
+capital A being equal to the forward
+ 
+
+ align:start position:0%
+capital A being equal to the forward
+path over 1 minus the loop
+
+ align:start position:0%
+path over 1 minus the loop
+ 
+
+ align:start position:0%
+path over 1 minus the loop
+transmission and if we differentiate
+
+ align:start position:0%
+transmission and if we differentiate
+ 
+
+ align:start position:0%
+transmission and if we differentiate
+this expression we get that the da is
+
+ align:start position:0%
+this expression we get that the da is
+ 
+
+ align:start position:0%
+this expression we get that the da is
+equal to Da little da over 1 + AF SAR
+
+ align:start position:0%
+equal to Da little da over 1 + AF SAR
+ 
+
+ align:start position:0%
+equal to Da little da over 1 + AF SAR
+well we're not interested really in in
+
+ align:start position:0%
+well we're not interested really in in
+ 
+
+ align:start position:0%
+well we're not interested really in in
+relationships between absolute changes
+
+ align:start position:0%
+relationships between absolute changes
+ 
+
+ align:start position:0%
+relationships between absolute changes
+in the forward path gain and the closed
+
+ align:start position:0%
+in the forward path gain and the closed
+ 
+
+ align:start position:0%
+in the forward path gain and the closed
+loop gain but rather in the relationship
+
+ align:start position:0%
+loop gain but rather in the relationship
+ 
+
+ align:start position:0%
+loop gain but rather in the relationship
+between fractional changes in the
+
+ align:start position:0%
+between fractional changes in the
+ 
+
+ align:start position:0%
+between fractional changes in the
+forward path gain and in the closed loop
+
+ align:start position:0%
+forward path gain and in the closed loop
+ 
+
+ align:start position:0%
+forward path gain and in the closed loop
+gain so what we'll do is divide this
+
+ align:start position:0%
+gain so what we'll do is divide this
+ 
+
+ align:start position:0%
+gain so what we'll do is divide this
+expression we'll divide the left side by
+
+ align:start position:0%
+expression we'll divide the left side by
+ 
+
+ align:start position:0%
+expression we'll divide the left side by
+capital A we'll divide the right side by
+
+ align:start position:0%
+capital A we'll divide the right side by
+ 
+
+ align:start position:0%
+capital A we'll divide the right side by
+the equivalent for for Capital a little
+
+ align:start position:0%
+the equivalent for for Capital a little
+ 
+
+ align:start position:0%
+the equivalent for for Capital a little
+a over 1 plus a f when we do that we
+
+ align:start position:0%
+a over 1 plus a f when we do that we
+ 
+
+ align:start position:0%
+a over 1 plus a f when we do that we
+find out that the fractional change in
+
+ align:start position:0%
+find out that the fractional change in
+ 
+
+ align:start position:0%
+find out that the fractional change in
+closed loop gain da over cap a is equal
+
+ align:start position:0%
+closed loop gain da over cap a is equal
+ 
+
+ align:start position:0%
+closed loop gain da over cap a is equal
+to the fractional change in forward path
+
+ align:start position:0%
+to the fractional change in forward path
+ 
+
+ align:start position:0%
+to the fractional change in forward path
+gain little da over little a times an
+
+ align:start position:0%
+gain little da over little a times an
+ 
+
+ align:start position:0%
+gain little da over little a times an
+attenuation Factor 1 over 1 +
+
+ align:start position:0%
+attenuation Factor 1 over 1 +
+ 
+
+ align:start position:0%
+attenuation Factor 1 over 1 +
+AF this quantity we'll call call the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+desensitivity and what it does is
+
+ align:start position:0%
+desensitivity and what it does is
+ 
+
+ align:start position:0%
+desensitivity and what it does is
+indicate how our feedback topology
+
+ align:start position:0%
+indicate how our feedback topology
+ 
+
+ align:start position:0%
+indicate how our feedback topology
+desensitizes the Clos Loop gain to
+
+ align:start position:0%
+desensitizes the Clos Loop gain to
+ 
+
+ align:start position:0%
+desensitizes the Clos Loop gain to
+changes in the forward path gain this is
+
+ align:start position:0%
+changes in the forward path gain this is
+ 
+
+ align:start position:0%
+changes in the forward path gain this is
+again is is a very important quantity
+
+ align:start position:0%
+again is is a very important quantity
+ 
+
+ align:start position:0%
+again is is a very important quantity
+clearly we're interested in having
+
+ align:start position:0%
+clearly we're interested in having
+ 
+
+ align:start position:0%
+clearly we're interested in having
+systems that have large desensitivity so
+
+ align:start position:0%
+systems that have large desensitivity so
+ 
+
+ align:start position:0%
+systems that have large desensitivity so
+that we can tolerate large changes in
+
+ align:start position:0%
+that we can tolerate large changes in
+ 
+
+ align:start position:0%
+that we can tolerate large changes in
+the forward path gain and get minimal
+
+ align:start position:0%
+the forward path gain and get minimal
+ 
+
+ align:start position:0%
+the forward path gain and get minimal
+changes in the closed loop gain of the
+
+ align:start position:0%
+changes in the closed loop gain of the
+ 
+
+ align:start position:0%
+changes in the closed loop gain of the
+system so we'll be looking one of our
+
+ align:start position:0%
+system so we'll be looking one of our
+ 
+
+ align:start position:0%
+system so we'll be looking one of our
+design objectives very frequently we'll
+
+ align:start position:0%
+design objectives very frequently we'll
+ 
+
+ align:start position:0%
+design objectives very frequently we'll
+be to build systems that have large
+
+ align:start position:0%
+be to build systems that have large
+ 
+
+ align:start position:0%
+be to build systems that have large
+values for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+desensitivity uh notice that the
+
+ align:start position:0%
+desensitivity uh notice that the
+ 
+
+ align:start position:0%
+desensitivity uh notice that the
+desensitivity is obtained really only in
+
+ align:start position:0%
+desensitivity is obtained really only in
+ 
+
+ align:start position:0%
+desensitivity is obtained really only in
+exchange for starting with a greater
+
+ align:start position:0%
+exchange for starting with a greater
+ 
+
+ align:start position:0%
+exchange for starting with a greater
+amount of forward path gain than we
+
+ align:start position:0%
+amount of forward path gain than we
+ 
+
+ align:start position:0%
+amount of forward path gain than we
+actually need we're designing a system
+
+ align:start position:0%
+actually need we're designing a system
+ 
+
+ align:start position:0%
+actually need we're designing a system
+that that has a final closed loop G gain
+
+ align:start position:0%
+that that has a final closed loop G gain
+ 
+
+ align:start position:0%
+that that has a final closed loop G gain
+that's a over 1 + AF capital A is little
+
+ align:start position:0%
+that's a over 1 + AF capital A is little
+ 
+
+ align:start position:0%
+that's a over 1 + AF capital A is little
+a over 1 plus AF however we start with a
+
+ align:start position:0%
+a over 1 plus AF however we start with a
+ 
+
+ align:start position:0%
+a over 1 plus AF however we start with a
+forward path gain of little a so our
+
+ align:start position:0%
+forward path gain of little a so our
+ 
+
+ align:start position:0%
+forward path gain of little a so our
+feedback topology attenuates the gain
+
+ align:start position:0%
+feedback topology attenuates the gain
+ 
+
+ align:start position:0%
+feedback topology attenuates the gain
+below that which we started with by a
+
+ align:start position:0%
+below that which we started with by a
+ 
+
+ align:start position:0%
+below that which we started with by a
+factor of 1 plus AF and that's precisely
+
+ align:start position:0%
+factor of 1 plus AF and that's precisely
+ 
+
+ align:start position:0%
+factor of 1 plus AF and that's precisely
+the amount of desensitivity we get so we
+
+ align:start position:0%
+the amount of desensitivity we get so we
+ 
+
+ align:start position:0%
+the amount of desensitivity we get so we
+get desensitivity only in exchange for
+
+ align:start position:0%
+get desensitivity only in exchange for
+ 
+
+ align:start position:0%
+get desensitivity only in exchange for
+starting with a forward path gain that's
+
+ align:start position:0%
+starting with a forward path gain that's
+ 
+
+ align:start position:0%
+starting with a forward path gain that's
+larger than we actually
+
+ align:start position:0%
+larger than we actually
+ 
+
+ align:start position:0%
+larger than we actually
+need so that that's the price we have to
+
+ align:start position:0%
+need so that that's the price we have to
+ 
+
+ align:start position:0%
+need so that that's the price we have to
+pay in order order to achieve the
+
+ align:start position:0%
+pay in order order to achieve the
+ 
+
+ align:start position:0%
+pay in order order to achieve the
+desensitivity we're interested
+
+ align:start position:0%
+desensitivity we're interested
+ 
+
+ align:start position:0%
+desensitivity we're interested
+in I think
+
+ align:start position:0%
+in I think
+ 
+
+ align:start position:0%
+in I think
+the the ability to automatically
+
+ align:start position:0%
+the the ability to automatically
+ 
+
+ align:start position:0%
+the the ability to automatically
+desensitize a system to changes in
+
+ align:start position:0%
+desensitize a system to changes in
+ 
+
+ align:start position:0%
+desensitize a system to changes in
+forward path gain is the only property
+
+ align:start position:0%
+forward path gain is the only property
+ 
+
+ align:start position:0%
+forward path gain is the only property
+that that's really intrinsic to a
+
+ align:start position:0%
+that that's really intrinsic to a
+ 
+
+ align:start position:0%
+that that's really intrinsic to a
+feedback topology I think there's a a
+
+ align:start position:0%
+feedback topology I think there's a a
+ 
+
+ align:start position:0%
+feedback topology I think there's a a
+tendency on the part of of people when
+
+ align:start position:0%
+tendency on the part of of people when
+ 
+
+ align:start position:0%
+tendency on the part of of people when
+they begin to worry about feedback
+
+ align:start position:0%
+they begin to worry about feedback
+ 
+
+ align:start position:0%
+they begin to worry about feedback
+systems to associate almost magical
+
+ align:start position:0%
+systems to associate almost magical
+ 
+
+ align:start position:0%
+systems to associate almost magical
+properties with them and that's just not
+
+ align:start position:0%
+properties with them and that's just not
+ 
+
+ align:start position:0%
+properties with them and that's just not
+true uh feedback generally doesn't allow
+
+ align:start position:0%
+true uh feedback generally doesn't allow
+ 
+
+ align:start position:0%
+true uh feedback generally doesn't allow
+you to do do uh uh many of the things
+
+ align:start position:0%
+you to do do uh uh many of the things
+ 
+
+ align:start position:0%
+you to do do uh uh many of the things
+that that you can't do without feedback
+
+ align:start position:0%
+that that you can't do without feedback
+ 
+
+ align:start position:0%
+that that you can't do without feedback
+for example feedback never gives you a
+
+ align:start position:0%
+for example feedback never gives you a
+ 
+
+ align:start position:0%
+for example feedback never gives you a
+mechanism for detecting signals that you
+
+ align:start position:0%
+mechanism for detecting signals that you
+ 
+
+ align:start position:0%
+mechanism for detecting signals that you
+couldn't detect by other methods maybe a
+
+ align:start position:0%
+couldn't detect by other methods maybe a
+ 
+
+ align:start position:0%
+couldn't detect by other methods maybe a
+certain detection schemes may be more
+
+ align:start position:0%
+certain detection schemes may be more
+ 
+
+ align:start position:0%
+certain detection schemes may be more
+conveniently realized as feedback to
+
+ align:start position:0%
+conveniently realized as feedback to
+ 
+
+ align:start position:0%
+conveniently realized as feedback to
+apologies but we can't use feedback as
+
+ align:start position:0%
+apologies but we can't use feedback as
+ 
+
+ align:start position:0%
+apologies but we can't use feedback as
+some sort of Salvation to rescue signals
+
+ align:start position:0%
+some sort of Salvation to rescue signals
+ 
+
+ align:start position:0%
+some sort of Salvation to rescue signals
+from noise that we couldn't do otherwise
+
+ align:start position:0%
+from noise that we couldn't do otherwise
+ 
+
+ align:start position:0%
+from noise that we couldn't do otherwise
+there's a whole collection of those
+
+ align:start position:0%
+there's a whole collection of those
+ 
+
+ align:start position:0%
+there's a whole collection of those
+sorts of things that uh at first there's
+
+ align:start position:0%
+sorts of things that uh at first there's
+ 
+
+ align:start position:0%
+sorts of things that uh at first there's
+a hope that feedback might help with in
+
+ align:start position:0%
+a hope that feedback might help with in
+ 
+
+ align:start position:0%
+a hope that feedback might help with in
+reality
+
+ align:start position:0%
+reality
+ 
+
+ align:start position:0%
+reality
+feedback doesn't offer that sort of
+
+ align:start position:0%
+feedback doesn't offer that sort of
+ 
+
+ align:start position:0%
+feedback doesn't offer that sort of
+Panacea the only thing it does do I
+
+ align:start position:0%
+Panacea the only thing it does do I
+ 
+
+ align:start position:0%
+Panacea the only thing it does do I
+believe the only fundamental property of
+
+ align:start position:0%
+believe the only fundamental property of
+ 
+
+ align:start position:0%
+believe the only fundamental property of
+feedback is that it gives us
+
+ align:start position:0%
+feedback is that it gives us
+ 
+
+ align:start position:0%
+feedback is that it gives us
+desensitivity in exchange for excess
+
+ align:start position:0%
+desensitivity in exchange for excess
+ 
+
+ align:start position:0%
+desensitivity in exchange for excess
+forward path
+
+ align:start position:0%
+forward path
+ 
+
+ align:start position:0%
+forward path
+gain one of the other features of
+
+ align:start position:0%
+gain one of the other features of
+ 
+
+ align:start position:0%
+gain one of the other features of
+feedback systems another feature is that
+
+ align:start position:0%
+feedback systems another feature is that
+ 
+
+ align:start position:0%
+feedback systems another feature is that
+feedback systems frequently give us ways
+
+ align:start position:0%
+feedback systems frequently give us ways
+ 
+
+ align:start position:0%
+feedback systems frequently give us ways
+of modifying input and output impedances
+
+ align:start position:0%
+of modifying input and output impedances
+ 
+
+ align:start position:0%
+of modifying input and output impedances
+associated with systems uh either
+
+ align:start position:0%
+associated with systems uh either
+ 
+
+ align:start position:0%
+associated with systems uh either
+mechanical impedances for example uh
+
+ align:start position:0%
+mechanical impedances for example uh
+ 
+
+ align:start position:0%
+mechanical impedances for example uh
+compliances or stiffnesses in in
+
+ align:start position:0%
+compliances or stiffnesses in in
+ 
+
+ align:start position:0%
+compliances or stiffnesses in in
+mechanical systems or the equivalent
+
+ align:start position:0%
+mechanical systems or the equivalent
+ 
+
+ align:start position:0%
+mechanical systems or the equivalent
+electrical input and output in pences
+
+ align:start position:0%
+electrical input and output in pences
+ 
+
+ align:start position:0%
+electrical input and output in pences
+and I'd like to look at at that for a
+
+ align:start position:0%
+and I'd like to look at at that for a
+ 
+
+ align:start position:0%
+and I'd like to look at at that for a
+moment here we have again A Familiar
+
+ align:start position:0%
+moment here we have again A Familiar
+ 
+
+ align:start position:0%
+moment here we have again A Familiar
+operational amplifier configuration and
+
+ align:start position:0%
+operational amplifier configuration and
+ 
+
+ align:start position:0%
+operational amplifier configuration and
+input uh I've indicated the operational
+
+ align:start position:0%
+input uh I've indicated the operational
+ 
+
+ align:start position:0%
+input uh I've indicated the operational
+amplifier now as a dependent generator
+
+ align:start position:0%
+amplifier now as a dependent generator
+ 
+
+ align:start position:0%
+amplifier now as a dependent generator
+uh whose magnitude is a times the error
+
+ align:start position:0%
+uh whose magnitude is a times the error
+ 
+
+ align:start position:0%
+uh whose magnitude is a times the error
+voltage and then some output resistance
+
+ align:start position:0%
+voltage and then some output resistance
+ 
+
+ align:start position:0%
+voltage and then some output resistance
+are out uh the output voltage and I feed
+
+ align:start position:0%
+are out uh the output voltage and I feed
+ 
+
+ align:start position:0%
+are out uh the output voltage and I feed
+that back to the inverting input
+
+ align:start position:0%
+that back to the inverting input
+ 
+
+ align:start position:0%
+that back to the inverting input
+terminal of the operational amplifier so
+
+ align:start position:0%
+terminal of the operational amplifier so
+ 
+
+ align:start position:0%
+terminal of the operational amplifier so
+this is a familiar follower
+
+ align:start position:0%
+this is a familiar follower
+ 
+
+ align:start position:0%
+this is a familiar follower
+connection I've also indicated a test
+
+ align:start position:0%
+connection I've also indicated a test
+ 
+
+ align:start position:0%
+connection I've also indicated a test
+source that can apply disturbance in
+
+ align:start position:0%
+source that can apply disturbance in
+ 
+
+ align:start position:0%
+source that can apply disturbance in
+this case a disturbing current and what
+
+ align:start position:0%
+this case a disturbing current and what
+ 
+
+ align:start position:0%
+this case a disturbing current and what
+I'll do is use that disturbing current
+
+ align:start position:0%
+I'll do is use that disturbing current
+ 
+
+ align:start position:0%
+I'll do is use that disturbing current
+to test the output impedance or output
+
+ align:start position:0%
+to test the output impedance or output
+ 
+
+ align:start position:0%
+to test the output impedance or output
+resistance of our configuration so what
+
+ align:start position:0%
+resistance of our configuration so what
+ 
+
+ align:start position:0%
+resistance of our configuration so what
+we'll do is is effectively measure the
+
+ align:start position:0%
+we'll do is is effectively measure the
+ 
+
+ align:start position:0%
+we'll do is is effectively measure the
+output resistance of this configuration
+
+ align:start position:0%
+output resistance of this configuration
+ 
+
+ align:start position:0%
+output resistance of this configuration
+by determining the relationship between
+
+ align:start position:0%
+by determining the relationship between
+ 
+
+ align:start position:0%
+by determining the relationship between
+changes in output voltage and changes in
+
+ align:start position:0%
+changes in output voltage and changes in
+ 
+
+ align:start position:0%
+changes in output voltage and changes in
+this disturb being current that's of
+
+ align:start position:0%
+this disturb being current that's of
+ 
+
+ align:start position:0%
+this disturb being current that's of
+course by definition the output
+
+ align:start position:0%
+course by definition the output
+ 
+
+ align:start position:0%
+course by definition the output
+resistance of our configuration well
+
+ align:start position:0%
+resistance of our configuration well
+ 
+
+ align:start position:0%
+resistance of our configuration well
+first let's make a block diagram for
+
+ align:start position:0%
+first let's make a block diagram for
+ 
+
+ align:start position:0%
+first let's make a block diagram for
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+system we do that we have our input
+
+ align:start position:0%
+system we do that we have our input
+ 
+
+ align:start position:0%
+system we do that we have our input
+voltage uh we get an error that in this
+
+ align:start position:0%
+voltage uh we get an error that in this
+ 
+
+ align:start position:0%
+voltage uh we get an error that in this
+case is the difference between the
+
+ align:start position:0%
+case is the difference between the
+ 
+
+ align:start position:0%
+case is the difference between the
+output voltage and the input voltage
+
+ align:start position:0%
+output voltage and the input voltage
+ 
+
+ align:start position:0%
+output voltage and the input voltage
+since we have a direct feedback
+
+ align:start position:0%
+since we have a direct feedback
+ 
+
+ align:start position:0%
+since we have a direct feedback
+Connection in our system in other words
+
+ align:start position:0%
+Connection in our system in other words
+ 
+
+ align:start position:0%
+Connection in our system in other words
+we have an F of one for this particular
+
+ align:start position:0%
+we have an F of one for this particular
+ 
+
+ align:start position:0%
+we have an F of one for this particular
+system remember there's a wire directly
+
+ align:start position:0%
+system remember there's a wire directly
+ 
+
+ align:start position:0%
+system remember there's a wire directly
+back from the output to the inverting
+
+ align:start position:0%
+back from the output to the inverting
+ 
+
+ align:start position:0%
+back from the output to the inverting
+input
+
+ align:start position:0%
+input
+ 
+
+ align:start position:0%
+input
+we get an error voltage that's the
+
+ align:start position:0%
+we get an error voltage that's the
+ 
+
+ align:start position:0%
+we get an error voltage that's the
+difference between those two quantities
+
+ align:start position:0%
+difference between those two quantities
+ 
+
+ align:start position:0%
+difference between those two quantities
+the dependent generator associated with
+
+ align:start position:0%
+the dependent generator associated with
+ 
+
+ align:start position:0%
+the dependent generator associated with
+the operational amplifier provides an
+
+ align:start position:0%
+the operational amplifier provides an
+ 
+
+ align:start position:0%
+the operational amplifier provides an
+output voltage that's a times the error
+
+ align:start position:0%
+output voltage that's a times the error
+ 
+
+ align:start position:0%
+output voltage that's a times the error
+voltage but there's another term besides
+
+ align:start position:0%
+voltage but there's another term besides
+ 
+
+ align:start position:0%
+voltage but there's another term besides
+the output voltage of the of the
+
+ align:start position:0%
+the output voltage of the of the
+ 
+
+ align:start position:0%
+the output voltage of the of the
+dependent
+
+ align:start position:0%
+dependent
+ 
+
+ align:start position:0%
+dependent
+generator associated with v out in
+
+ align:start position:0%
+generator associated with v out in
+ 
+
+ align:start position:0%
+generator associated with v out in
+particular the drop across this
+
+ align:start position:0%
+particular the drop across this
+ 
+
+ align:start position:0%
+particular the drop across this
+resistance R out the output resistance
+
+ align:start position:0%
+resistance R out the output resistance
+ 
+
+ align:start position:0%
+resistance R out the output resistance
+associated with the operational
+
+ align:start position:0%
+associated with the operational
+ 
+
+ align:start position:0%
+associated with the operational
+amplifier and since the input current
+
+ align:start position:0%
+amplifier and since the input current
+ 
+
+ align:start position:0%
+amplifier and since the input current
+the amplifier is assumed to be zero the
+
+ align:start position:0%
+the amplifier is assumed to be zero the
+ 
+
+ align:start position:0%
+the amplifier is assumed to be zero the
+disturbing current ID all flows through
+
+ align:start position:0%
+disturbing current ID all flows through
+ 
+
+ align:start position:0%
+disturbing current ID all flows through
+the output resistance of the amplifier
+
+ align:start position:0%
+the output resistance of the amplifier
+ 
+
+ align:start position:0%
+the output resistance of the amplifier
+and we can model that in our block
+
+ align:start position:0%
+and we can model that in our block
+ 
+
+ align:start position:0%
+and we can model that in our block
+diagram form by taking ID scaling it by
+
+ align:start position:0%
+diagram form by taking ID scaling it by
+ 
+
+ align:start position:0%
+diagram form by taking ID scaling it by
+the output resistance this variable is
+
+ align:start position:0%
+the output resistance this variable is
+ 
+
+ align:start position:0%
+the output resistance this variable is
+then the voltage across the output
+
+ align:start position:0%
+then the voltage across the output
+ 
+
+ align:start position:0%
+then the voltage across the output
+resistance R not we add that voltage to
+
+ align:start position:0%
+resistance R not we add that voltage to
+ 
+
+ align:start position:0%
+resistance R not we add that voltage to
+the voltage from the dependent generator
+
+ align:start position:0%
+the voltage from the dependent generator
+ 
+
+ align:start position:0%
+the voltage from the dependent generator
+to get the actual output voltage of the
+
+ align:start position:0%
+to get the actual output voltage of the
+ 
+
+ align:start position:0%
+to get the actual output voltage of the
+amplifier and we feed that back
+
+ align:start position:0%
+amplifier and we feed that back
+ 
+
+ align:start position:0%
+amplifier and we feed that back
+well here's a system that has actually a
+
+ align:start position:0%
+well here's a system that has actually a
+ 
+
+ align:start position:0%
+well here's a system that has actually a
+desired input and then a disturbance and
+
+ align:start position:0%
+desired input and then a disturbance and
+ 
+
+ align:start position:0%
+desired input and then a disturbance and
+we can write the output for our system
+
+ align:start position:0%
+we can write the output for our system
+ 
+
+ align:start position:0%
+we can write the output for our system
+uh as the superposition of the responses
+
+ align:start position:0%
+uh as the superposition of the responses
+ 
+
+ align:start position:0%
+uh as the superposition of the responses
+to the desired input and the response to
+
+ align:start position:0%
+to the desired input and the response to
+ 
+
+ align:start position:0%
+to the desired input and the response to
+the disturbing current if we do that uh
+
+ align:start position:0%
+the disturbing current if we do that uh
+ 
+
+ align:start position:0%
+the disturbing current if we do that uh
+we get the output and now let's do the
+
+ align:start position:0%
+we get the output and now let's do the
+ 
+
+ align:start position:0%
+we get the output and now let's do the
+component dependent on the input voltage
+
+ align:start position:0%
+component dependent on the input voltage
+ 
+
+ align:start position:0%
+component dependent on the input voltage
+when we have this the our standard
+
+ align:start position:0%
+when we have this the our standard
+ 
+
+ align:start position:0%
+when we have this the our standard
+feedback topology a forward path a
+
+ align:start position:0%
+feedback topology a forward path a
+ 
+
+ align:start position:0%
+feedback topology a forward path a
+feedback path uh the result is always
+
+ align:start position:0%
+feedback path uh the result is always
+ 
+
+ align:start position:0%
+feedback path uh the result is always
+the same the expression is always the
+
+ align:start position:0%
+the same the expression is always the
+ 
+
+ align:start position:0%
+the same the expression is always the
+same it's the forward path over one
+
+ align:start position:0%
+same it's the forward path over one
+ 
+
+ align:start position:0%
+same it's the forward path over one
+minus the loop transmission so let's see
+
+ align:start position:0%
+minus the loop transmission so let's see
+ 
+
+ align:start position:0%
+minus the loop transmission so let's see
+the forward path is a uh the loop
+
+ align:start position:0%
+the forward path is a uh the loop
+ 
+
+ align:start position:0%
+the forward path is a uh the loop
+transmission is minus a there's nothing
+
+ align:start position:0%
+transmission is minus a there's nothing
+ 
+
+ align:start position:0%
+transmission is minus a there's nothing
+else in the loop so the relationship
+
+ align:start position:0%
+else in the loop so the relationship
+ 
+
+ align:start position:0%
+else in the loop so the relationship
+between V out and VI is the forward path
+
+ align:start position:0%
+between V out and VI is the forward path
+ 
+
+ align:start position:0%
+between V out and VI is the forward path
+a over one minus the loop transmission 1
+
+ align:start position:0%
+a over one minus the loop transmission 1
+ 
+
+ align:start position:0%
+a over one minus the loop transmission 1
++ a v out is a over 1 + a * VI and now
+
+ align:start position:0%
++ a v out is a over 1 + a * VI and now
+ 
+
+ align:start position:0%
++ a v out is a over 1 + a * VI and now
+we have another component that component
+
+ align:start position:0%
+we have another component that component
+ 
+
+ align:start position:0%
+we have another component that component
+being proportional to
+
+ align:start position:0%
+being proportional to
+ 
+
+ align:start position:0%
+being proportional to
+IID well there's a scale factor before
+
+ align:start position:0%
+IID well there's a scale factor before
+ 
+
+ align:start position:0%
+IID well there's a scale factor before
+we even get into the loop associated
+
+ align:start position:0%
+we even get into the loop associated
+ 
+
+ align:start position:0%
+we even get into the loop associated
+with ID that scale factor is R not we
+
+ align:start position:0%
+with ID that scale factor is R not we
+ 
+
+ align:start position:0%
+with ID that scale factor is R not we
+can drag it out in front in our
+
+ align:start position:0%
+can drag it out in front in our
+ 
+
+ align:start position:0%
+can drag it out in front in our
+expression and then we can calculate the
+
+ align:start position:0%
+expression and then we can calculate the
+ 
+
+ align:start position:0%
+expression and then we can calculate the
+transfer function or the gain from this
+
+ align:start position:0%
+transfer function or the gain from this
+ 
+
+ align:start position:0%
+transfer function or the gain from this
+this point to the output the forward
+
+ align:start position:0%
+this point to the output the forward
+ 
+
+ align:start position:0%
+this point to the output the forward
+path for that transfer function or that
+
+ align:start position:0%
+path for that transfer function or that
+ 
+
+ align:start position:0%
+path for that transfer function or that
+gain is simply one and and again the
+
+ align:start position:0%
+gain is simply one and and again the
+ 
+
+ align:start position:0%
+gain is simply one and and again the
+loop transmission doesn't change the
+
+ align:start position:0%
+loop transmission doesn't change the
+ 
+
+ align:start position:0%
+loop transmission doesn't change the
+loop transmission for a feedback system
+
+ align:start position:0%
+loop transmission for a feedback system
+ 
+
+ align:start position:0%
+loop transmission for a feedback system
+is an intrinsic property a fundamental
+
+ align:start position:0%
+is an intrinsic property a fundamental
+ 
+
+ align:start position:0%
+is an intrinsic property a fundamental
+property of the system has nothing to do
+
+ align:start position:0%
+property of the system has nothing to do
+ 
+
+ align:start position:0%
+property of the system has nothing to do
+with what we consider the input and the
+
+ align:start position:0%
+with what we consider the input and the
+ 
+
+ align:start position:0%
+with what we consider the input and the
+output of the system uh and so we get
+
+ align:start position:0%
+output of the system uh and so we get
+ 
+
+ align:start position:0%
+output of the system uh and so we get
+the same denominator expression uh 1 + a
+
+ align:start position:0%
+the same denominator expression uh 1 + a
+ 
+
+ align:start position:0%
+the same denominator expression uh 1 + a
+or 1 minus the loop transmission get R
+
+ align:start position:0%
+or 1 minus the loop transmission get R
+ 
+
+ align:start position:0%
+or 1 minus the loop transmission get R
+KN * 1 over 1 + a and that's the scale
+
+ align:start position:0%
+KN * 1 over 1 + a and that's the scale
+ 
+
+ align:start position:0%
+KN * 1 over 1 + a and that's the scale
+factor that links output voltage to
+
+ align:start position:0%
+factor that links output voltage to
+ 
+
+ align:start position:0%
+factor that links output voltage to
+disturbing current and what we see see
+
+ align:start position:0%
+disturbing current and what we see see
+ 
+
+ align:start position:0%
+disturbing current and what we see see
+is that fine we get an output voltage
+
+ align:start position:0%
+is that fine we get an output voltage
+ 
+
+ align:start position:0%
+is that fine we get an output voltage
+that's very nearly equal to the input
+
+ align:start position:0%
+that's very nearly equal to the input
+ 
+
+ align:start position:0%
+that's very nearly equal to the input
+voltage at least in the case where a is
+
+ align:start position:0%
+voltage at least in the case where a is
+ 
+
+ align:start position:0%
+voltage at least in the case where a is
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+large we get an output resistance the
+
+ align:start position:0%
+large we get an output resistance the
+ 
+
+ align:start position:0%
+large we get an output resistance the
+ratio between changes and output voltage
+
+ align:start position:0%
+ratio between changes and output voltage
+ 
+
+ align:start position:0%
+ratio between changes and output voltage
+and disturbing currents that's simply
+
+ align:start position:0%
+and disturbing currents that's simply
+ 
+
+ align:start position:0%
+and disturbing currents that's simply
+equal to the open loop output resistance
+
+ align:start position:0%
+equal to the open loop output resistance
+ 
+
+ align:start position:0%
+equal to the open loop output resistance
+the resistance that the amplifier would
+
+ align:start position:0%
+the resistance that the amplifier would
+ 
+
+ align:start position:0%
+the resistance that the amplifier would
+display in the absence of
+
+ align:start position:0%
+display in the absence of
+ 
+
+ align:start position:0%
+display in the absence of
+feedback divided by a very familiar
+
+ align:start position:0%
+feedback divided by a very familiar
+ 
+
+ align:start position:0%
+feedback divided by a very familiar
+expression one minus the loop
+
+ align:start position:0%
+expression one minus the loop
+ 
+
+ align:start position:0%
+expression one minus the loop
+transmission we get R out over one the
+
+ align:start position:0%
+transmission we get R out over one the
+ 
+
+ align:start position:0%
+transmission we get R out over one the
+open loop output resistance over one
+
+ align:start position:0%
+open loop output resistance over one
+ 
+
+ align:start position:0%
+open loop output resistance over one
+minus the loop transmission for the
+
+ align:start position:0%
+minus the loop transmission for the
+ 
+
+ align:start position:0%
+minus the loop transmission for the
+output resistance with
+
+ align:start position:0%
+output resistance with
+ 
+
+ align:start position:0%
+output resistance with
+feedback uh here in contrast to the
+
+ align:start position:0%
+feedback uh here in contrast to the
+ 
+
+ align:start position:0%
+feedback uh here in contrast to the
+desensitivity issue we're able to
+
+ align:start position:0%
+desensitivity issue we're able to
+ 
+
+ align:start position:0%
+desensitivity issue we're able to
+accomplish this sort of thing at least
+
+ align:start position:0%
+accomplish this sort of thing at least
+ 
+
+ align:start position:0%
+accomplish this sort of thing at least
+conceptually without feedback consider
+
+ align:start position:0%
+conceptually without feedback consider
+ 
+
+ align:start position:0%
+conceptually without feedback consider
+the following let's take exactly the the
+
+ align:start position:0%
+the following let's take exactly the the
+ 
+
+ align:start position:0%
+the following let's take exactly the the
+same amplifier in other words an
+
+ align:start position:0%
+same amplifier in other words an
+ 
+
+ align:start position:0%
+same amplifier in other words an
+amplifier that has this
+
+ align:start position:0%
+amplifier that has this
+ 
+
+ align:start position:0%
+amplifier that has this
+model uh we have a dependent generator
+
+ align:start position:0%
+model uh we have a dependent generator
+ 
+
+ align:start position:0%
+model uh we have a dependent generator
+in here whose magnitude is a Time the
+
+ align:start position:0%
+in here whose magnitude is a Time the
+ 
+
+ align:start position:0%
+in here whose magnitude is a Time the
+voltage applied to the amplifier and
+
+ align:start position:0%
+voltage applied to the amplifier and
+ 
+
+ align:start position:0%
+voltage applied to the amplifier and
+then let me in a very Brute Force way
+
+ align:start position:0%
+then let me in a very Brute Force way
+ 
+
+ align:start position:0%
+then let me in a very Brute Force way
+load the amplifier with a resistor whose
+
+ align:start position:0%
+load the amplifier with a resistor whose
+ 
+
+ align:start position:0%
+load the amplifier with a resistor whose
+value is R out divided a in that case we
+
+ align:start position:0%
+value is R out divided a in that case we
+ 
+
+ align:start position:0%
+value is R out divided a in that case we
+would find let's see when we went to
+
+ align:start position:0%
+would find let's see when we went to
+ 
+
+ align:start position:0%
+would find let's see when we went to
+calculate the gain from here to here uh
+
+ align:start position:0%
+calculate the gain from here to here uh
+ 
+
+ align:start position:0%
+calculate the gain from here to here uh
+V out over VI we'd get the gain
+
+ align:start position:0%
+V out over VI we'd get the gain
+ 
+
+ align:start position:0%
+V out over VI we'd get the gain
+associated with the dependent generator
+
+ align:start position:0%
+associated with the dependent generator
+ 
+
+ align:start position:0%
+associated with the dependent generator
+which is a and now we' get an
+
+ align:start position:0%
+which is a and now we' get an
+ 
+
+ align:start position:0%
+which is a and now we' get an
+attenuation ratio that's dependent on R
+
+ align:start position:0%
+attenuation ratio that's dependent on R
+ 
+
+ align:start position:0%
+attenuation ratio that's dependent on R
+KN over a a and the output resistance of
+
+ align:start position:0%
+KN over a a and the output resistance of
+ 
+
+ align:start position:0%
+KN over a a and the output resistance of
+the amplifier that's our attenuation
+
+ align:start position:0%
+the amplifier that's our attenuation
+ 
+
+ align:start position:0%
+the amplifier that's our attenuation
+ratio we have an external resistor R
+
+ align:start position:0%
+ratio we have an external resistor R
+ 
+
+ align:start position:0%
+ratio we have an external resistor R
+over a there's an internal resistor
+
+ align:start position:0%
+over a there's an internal resistor
+ 
+
+ align:start position:0%
+over a there's an internal resistor
+that's R and so we get an attenuation
+
+ align:start position:0%
+that's R and so we get an attenuation
+ 
+
+ align:start position:0%
+that's R and so we get an attenuation
+ratio r/ a / R plus r over a and if we
+
+ align:start position:0%
+ratio r/ a / R plus r over a and if we
+ 
+
+ align:start position:0%
+ratio r/ a / R plus r over a and if we
+simplify this expression a bit we find
+
+ align:start position:0%
+simplify this expression a bit we find
+ 
+
+ align:start position:0%
+simplify this expression a bit we find
+that the gain for this expression for
+
+ align:start position:0%
+that the gain for this expression for
+ 
+
+ align:start position:0%
+that the gain for this expression for
+for this configuration exactly as it was
+
+ align:start position:0%
+for this configuration exactly as it was
+ 
+
+ align:start position:0%
+for this configuration exactly as it was
+up here the relationship between output
+
+ align:start position:0%
+up here the relationship between output
+ 
+
+ align:start position:0%
+up here the relationship between output
+voltage and input voltage is simply a
+
+ align:start position:0%
+voltage and input voltage is simply a
+ 
+
+ align:start position:0%
+voltage and input voltage is simply a
+over 1+ a similarly if we calculated the
+
+ align:start position:0%
+over 1+ a similarly if we calculated the
+ 
+
+ align:start position:0%
+over 1+ a similarly if we calculated the
+output resistance of this configuration
+
+ align:start position:0%
+output resistance of this configuration
+ 
+
+ align:start position:0%
+output resistance of this configuration
+it would be R out over a uh in parallel
+
+ align:start position:0%
+it would be R out over a uh in parallel
+ 
+
+ align:start position:0%
+it would be R out over a uh in parallel
+with r out and if we simplify that we'd
+
+ align:start position:0%
+with r out and if we simplify that we'd
+ 
+
+ align:start position:0%
+with r out and if we simplify that we'd
+find out it was R out over 1 plus a so
+
+ align:start position:0%
+find out it was R out over 1 plus a so
+ 
+
+ align:start position:0%
+find out it was R out over 1 plus a so
+here conceptually is a topology that
+
+ align:start position:0%
+here conceptually is a topology that
+ 
+
+ align:start position:0%
+here conceptually is a topology that
+gives us both the same voltage gain and
+
+ align:start position:0%
+gives us both the same voltage gain and
+ 
+
+ align:start position:0%
+gives us both the same voltage gain and
+the same output
+
+ align:start position:0%
+the same output
+ 
+
+ align:start position:0%
+the same output
+resistance as the feedback
+
+ align:start position:0%
+resistance as the feedback
+ 
+
+ align:start position:0%
+resistance as the feedback
+topology um this isn't to imply that
+
+ align:start position:0%
+topology um this isn't to imply that
+ 
+
+ align:start position:0%
+topology um this isn't to imply that
+this is a a good solution in fact I
+
+ align:start position:0%
+this is a a good solution in fact I
+ 
+
+ align:start position:0%
+this is a a good solution in fact I
+think we appreciate that loading an
+
+ align:start position:0%
+think we appreciate that loading an
+ 
+
+ align:start position:0%
+think we appreciate that loading an
+operational amplifier with a resistor
+
+ align:start position:0%
+operational amplifier with a resistor
+ 
+
+ align:start position:0%
+operational amplifier with a resistor
+whose magnitude is its output resistance
+
+ align:start position:0%
+whose magnitude is its output resistance
+ 
+
+ align:start position:0%
+whose magnitude is its output resistance
+which may be ohms divided by its open
+
+ align:start position:0%
+which may be ohms divided by its open
+ 
+
+ align:start position:0%
+which may be ohms divided by its open
+loop gain which may be hundreds of
+
+ align:start position:0%
+loop gain which may be hundreds of
+ 
+
+ align:start position:0%
+loop gain which may be hundreds of
+thousands uh is probably a a quite an
+
+ align:start position:0%
+thousands uh is probably a a quite an
+ 
+
+ align:start position:0%
+thousands uh is probably a a quite an
+impractical thing to do but at least
+
+ align:start position:0%
+impractical thing to do but at least
+ 
+
+ align:start position:0%
+impractical thing to do but at least
+conceptually at least on a block diagram
+
+ align:start position:0%
+conceptually at least on a block diagram
+ 
+
+ align:start position:0%
+conceptually at least on a block diagram
+or a mathematical level we're able to
+
+ align:start position:0%
+or a mathematical level we're able to
+ 
+
+ align:start position:0%
+or a mathematical level we're able to
+get the same performance with a topology
+
+ align:start position:0%
+get the same performance with a topology
+ 
+
+ align:start position:0%
+get the same performance with a topology
+that doesn't include feedback we don't
+
+ align:start position:0%
+that doesn't include feedback we don't
+ 
+
+ align:start position:0%
+that doesn't include feedback we don't
+do any worse with a feedback solution
+
+ align:start position:0%
+do any worse with a feedback solution
+ 
+
+ align:start position:0%
+do any worse with a feedback solution
+but we don't do any better in terms
+
+ align:start position:0%
+but we don't do any better in terms
+ 
+
+ align:start position:0%
+but we don't do any better in terms
+terms of scaling impedances and so forth
+
+ align:start position:0%
+terms of scaling impedances and so forth
+ 
+
+ align:start position:0%
+terms of scaling impedances and so forth
+I went through this sort of a discussion
+
+ align:start position:0%
+I went through this sort of a discussion
+ 
+
+ align:start position:0%
+I went through this sort of a discussion
+one time when I presented this material
+
+ align:start position:0%
+one time when I presented this material
+ 
+
+ align:start position:0%
+one time when I presented this material
+at MIT and a student of mine who was a
+
+ align:start position:0%
+at MIT and a student of mine who was a
+ 
+
+ align:start position:0%
+at MIT and a student of mine who was a
+very gifted student and in fact was kind
+
+ align:start position:0%
+very gifted student and in fact was kind
+ 
+
+ align:start position:0%
+very gifted student and in fact was kind
+enough to do some reviewing of my book
+
+ align:start position:0%
+enough to do some reviewing of my book
+ 
+
+ align:start position:0%
+enough to do some reviewing of my book
+in in Note Form uh came up to me after
+
+ align:start position:0%
+in in Note Form uh came up to me after
+ 
+
+ align:start position:0%
+in in Note Form uh came up to me after
+the lecture and said Jim you know you
+
+ align:start position:0%
+the lecture and said Jim you know you
+ 
+
+ align:start position:0%
+the lecture and said Jim you know you
+sort of really give Aid and comfort to
+
+ align:start position:0%
+sort of really give Aid and comfort to
+ 
+
+ align:start position:0%
+sort of really give Aid and comfort to
+the enemies a feedback by that kind of
+
+ align:start position:0%
+the enemies a feedback by that kind of
+ 
+
+ align:start position:0%
+the enemies a feedback by that kind of
+presentation he said I think a better
+
+ align:start position:0%
+presentation he said I think a better
+ 
+
+ align:start position:0%
+presentation he said I think a better
+way to look at it is that uh what you do
+
+ align:start position:0%
+way to look at it is that uh what you do
+ 
+
+ align:start position:0%
+way to look at it is that uh what you do
+is you build a feedback system really to
+
+ align:start position:0%
+is you build a feedback system really to
+ 
+
+ align:start position:0%
+is you build a feedback system really to
+take advant of its fundamental property
+
+ align:start position:0%
+take advant of its fundamental property
+ 
+
+ align:start position:0%
+take advant of its fundamental property
+the desensitivity and you find out that
+
+ align:start position:0%
+the desensitivity and you find out that
+ 
+
+ align:start position:0%
+the desensitivity and you find out that
+you get a whole lot of other things to
+
+ align:start position:0%
+you get a whole lot of other things to
+ 
+
+ align:start position:0%
+you get a whole lot of other things to
+go along with it for example it gives
+
+ align:start position:0%
+go along with it for example it gives
+ 
+
+ align:start position:0%
+go along with it for example it gives
+you a way of scaling impedances uh we'll
+
+ align:start position:0%
+you a way of scaling impedances uh we'll
+ 
+
+ align:start position:0%
+you a way of scaling impedances uh we'll
+see next time it gives us a way of of
+
+ align:start position:0%
+see next time it gives us a way of of
+ 
+
+ align:start position:0%
+see next time it gives us a way of of
+dealing with certain kinds of noise in a
+
+ align:start position:0%
+dealing with certain kinds of noise in a
+ 
+
+ align:start position:0%
+dealing with certain kinds of noise in a
+convenient method it doesn't give us a
+
+ align:start position:0%
+convenient method it doesn't give us a
+ 
+
+ align:start position:0%
+convenient method it doesn't give us a
+way of eliminating noise it doesn't give
+
+ align:start position:0%
+way of eliminating noise it doesn't give
+ 
+
+ align:start position:0%
+way of eliminating noise it doesn't give
+us a way of improving signal and noise
+
+ align:start position:0%
+us a way of improving signal and noise
+ 
+
+ align:start position:0%
+us a way of improving signal and noise
+ratio beyond what we could do with an
+
+ align:start position:0%
+ratio beyond what we could do with an
+ 
+
+ align:start position:0%
+ratio beyond what we could do with an
+open loop solution but it gives us a
+
+ align:start position:0%
+open loop solution but it gives us a
+ 
+
+ align:start position:0%
+open loop solution but it gives us a
+very convenient way to handle certain
+
+ align:start position:0%
+very convenient way to handle certain
+ 
+
+ align:start position:0%
+very convenient way to handle certain
+kinds of noises and and I think that's a
+
+ align:start position:0%
+kinds of noises and and I think that's a
+ 
+
+ align:start position:0%
+kinds of noises and and I think that's a
+good way to look at it we build a
+
+ align:start position:0%
+good way to look at it we build a
+ 
+
+ align:start position:0%
+good way to look at it we build a
+feedback system uh for it its
+
+ align:start position:0%
+feedback system uh for it its
+ 
+
+ align:start position:0%
+feedback system uh for it its
+fundamental advantage that of
+
+ align:start position:0%
+fundamental advantage that of
+ 
+
+ align:start position:0%
+fundamental advantage that of
+desensitivity we happen to get a lot of
+
+ align:start position:0%
+desensitivity we happen to get a lot of
+ 
+
+ align:start position:0%
+desensitivity we happen to get a lot of
+other things thrown in for
+
+ align:start position:0%
+other things thrown in for
+ 
+
+ align:start position:0%
+other things thrown in for
+free returning for a moment to the issue
+
+ align:start position:0%
+free returning for a moment to the issue
+ 
+
+ align:start position:0%
+free returning for a moment to the issue
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+impedances uh a number of people make a
+
+ align:start position:0%
+impedances uh a number of people make a
+ 
+
+ align:start position:0%
+impedances uh a number of people make a
+big big issue about uh topologies
+
+ align:start position:0%
+big big issue about uh topologies
+ 
+
+ align:start position:0%
+big big issue about uh topologies
+involved with impedance modification and
+
+ align:start position:0%
+involved with impedance modification and
+ 
+
+ align:start position:0%
+involved with impedance modification and
+they talk about shunt feedback and
+
+ align:start position:0%
+they talk about shunt feedback and
+ 
+
+ align:start position:0%
+they talk about shunt feedback and
+series feedback and and all those kinds
+
+ align:start position:0%
+series feedback and and all those kinds
+ 
+
+ align:start position:0%
+series feedback and and all those kinds
+of things and I I just happened not to
+
+ align:start position:0%
+of things and I I just happened not to
+ 
+
+ align:start position:0%
+of things and I I just happened not to
+believe that I think or not to believe
+
+ align:start position:0%
+believe that I think or not to believe
+ 
+
+ align:start position:0%
+believe that I think or not to believe
+that's the right approach I think that
+
+ align:start position:0%
+that's the right approach I think that
+ 
+
+ align:start position:0%
+that's the right approach I think that
+that feedback is feedback and the way
+
+ align:start position:0%
+that feedback is feedback and the way
+ 
+
+ align:start position:0%
+that feedback is feedback and the way
+that impedance scaling
+
+ align:start position:0%
+that impedance scaling
+ 
+
+ align:start position:0%
+that impedance scaling
+occurs uh is very very easy what or it's
+
+ align:start position:0%
+occurs uh is very very easy what or it's
+ 
+
+ align:start position:0%
+occurs uh is very very easy what or it's
+easy to see what happens is that
+
+ align:start position:0%
+easy to see what happens is that
+ 
+
+ align:start position:0%
+easy to see what happens is that
+feedback scales the impedance level of a
+
+ align:start position:0%
+feedback scales the impedance level of a
+ 
+
+ align:start position:0%
+feedback scales the impedance level of a
+system either at its output or its input
+
+ align:start position:0%
+system either at its output or its input
+ 
+
+ align:start position:0%
+system either at its output or its input
+and the scaling factor is always the
+
+ align:start position:0%
+and the scaling factor is always the
+ 
+
+ align:start position:0%
+and the scaling factor is always the
+same it's always one minus the loop
+
+ align:start position:0%
+same it's always one minus the loop
+ 
+
+ align:start position:0%
+same it's always one minus the loop
+transmission now does it lower the
+
+ align:start position:0%
+transmission now does it lower the
+ 
+
+ align:start position:0%
+transmission now does it lower the
+impedance or does it raise the impedance
+
+ align:start position:0%
+impedance or does it raise the impedance
+ 
+
+ align:start position:0%
+impedance or does it raise the impedance
+well all we have to do is look at the
+
+ align:start position:0%
+well all we have to do is look at the
+ 
+
+ align:start position:0%
+well all we have to do is look at the
+topology we don't have to assign names
+
+ align:start position:0%
+topology we don't have to assign names
+ 
+
+ align:start position:0%
+topology we don't have to assign names
+with it to this and so forth
+
+ align:start position:0%
+with it to this and so forth
+ 
+
+ align:start position:0%
+with it to this and so forth
+uh here we have a topology where we're
+
+ align:start position:0%
+uh here we have a topology where we're
+ 
+
+ align:start position:0%
+uh here we have a topology where we're
+bringing back the output we're applying
+
+ align:start position:0%
+bringing back the output we're applying
+ 
+
+ align:start position:0%
+bringing back the output we're applying
+our our input signal uh in a location
+
+ align:start position:0%
+our our input signal uh in a location
+ 
+
+ align:start position:0%
+our our input signal uh in a location
+where the input impedance should be very
+
+ align:start position:0%
+where the input impedance should be very
+ 
+
+ align:start position:0%
+where the input impedance should be very
+very high uh we'd find out that if we
+
+ align:start position:0%
+very high uh we'd find out that if we
+ 
+
+ align:start position:0%
+very high uh we'd find out that if we
+looked at this configuration we would
+
+ align:start position:0%
+looked at this configuration we would
+ 
+
+ align:start position:0%
+looked at this configuration we would
+get a very high input impedance we'd
+
+ align:start position:0%
+get a very high input impedance we'd
+ 
+
+ align:start position:0%
+get a very high input impedance we'd
+scale the input impedance in the absence
+
+ align:start position:0%
+scale the input impedance in the absence
+ 
+
+ align:start position:0%
+scale the input impedance in the absence
+of feedback by a factor of one minus the
+
+ align:start position:0%
+of feedback by a factor of one minus the
+ 
+
+ align:start position:0%
+of feedback by a factor of one minus the
+loop transmission we'd up it but we're
+
+ align:start position:0%
+loop transmission we'd up it but we're
+ 
+
+ align:start position:0%
+loop transmission we'd up it but we're
+bringing back information about the
+
+ align:start position:0%
+bringing back information about the
+ 
+
+ align:start position:0%
+bringing back information about the
+output voltage uh the implication being
+
+ align:start position:0%
+output voltage uh the implication being
+ 
+
+ align:start position:0%
+output voltage uh the implication being
+we're trying to hold the output voltage
+
+ align:start position:0%
+we're trying to hold the output voltage
+ 
+
+ align:start position:0%
+we're trying to hold the output voltage
+fixed in order to do that we need a low
+
+ align:start position:0%
+fixed in order to do that we need a low
+ 
+
+ align:start position:0%
+fixed in order to do that we need a low
+output impedance uh or that's what we're
+
+ align:start position:0%
+output impedance uh or that's what we're
+ 
+
+ align:start position:0%
+output impedance uh or that's what we're
+trying to accomplish and so when we look
+
+ align:start position:0%
+trying to accomplish and so when we look
+ 
+
+ align:start position:0%
+trying to accomplish and so when we look
+to the output impedance we find that
+
+ align:start position:0%
+to the output impedance we find that
+ 
+
+ align:start position:0%
+to the output impedance we find that
+it's the output impedance in the absence
+
+ align:start position:0%
+it's the output impedance in the absence
+ 
+
+ align:start position:0%
+it's the output impedance in the absence
+of feedback this time divided by one
+
+ align:start position:0%
+of feedback this time divided by one
+ 
+
+ align:start position:0%
+of feedback this time divided by one
+minus the loop transmission let's look
+
+ align:start position:0%
+minus the loop transmission let's look
+ 
+
+ align:start position:0%
+minus the loop transmission let's look
+at another
+
+ align:start position:0%
+at another
+ 
+
+ align:start position:0%
+at another
+topology let's ask what's the impedance
+
+ align:start position:0%
+topology let's ask what's the impedance
+ 
+
+ align:start position:0%
+topology let's ask what's the impedance
+what impedance do we see at this point
+
+ align:start position:0%
+what impedance do we see at this point
+ 
+
+ align:start position:0%
+what impedance do we see at this point
+well what what are we doing here here we
+
+ align:start position:0%
+well what what are we doing here here we
+ 
+
+ align:start position:0%
+well what what are we doing here here we
+have a configuration where we ground one
+
+ align:start position:0%
+have a configuration where we ground one
+ 
+
+ align:start position:0%
+have a configuration where we ground one
+input terminal to the operational
+
+ align:start position:0%
+input terminal to the operational
+ 
+
+ align:start position:0%
+input terminal to the operational
+amplifier we apply our test signal uh to
+
+ align:start position:0%
+amplifier we apply our test signal uh to
+ 
+
+ align:start position:0%
+amplifier we apply our test signal uh to
+the other point but notice of course
+
+ align:start position:0%
+the other point but notice of course
+ 
+
+ align:start position:0%
+the other point but notice of course
+that that the feedback in the system
+
+ align:start position:0%
+that that the feedback in the system
+ 
+
+ align:start position:0%
+that that the feedback in the system
+should fight to keep the voltage between
+
+ align:start position:0%
+should fight to keep the voltage between
+ 
+
+ align:start position:0%
+should fight to keep the voltage between
+these two terminals very small we have a
+
+ align:start position:0%
+these two terminals very small we have a
+ 
+
+ align:start position:0%
+these two terminals very small we have a
+very high gain operational amplifier
+
+ align:start position:0%
+very high gain operational amplifier
+ 
+
+ align:start position:0%
+very high gain operational amplifier
+that should show up as having a very
+
+ align:start position:0%
+that should show up as having a very
+ 
+
+ align:start position:0%
+that should show up as having a very
+small input resistance we can see how
+
+ align:start position:0%
+small input resistance we can see how
+ 
+
+ align:start position:0%
+small input resistance we can see how
+that happens let's apply a a test volt
+
+ align:start position:0%
+that happens let's apply a a test volt
+ 
+
+ align:start position:0%
+that happens let's apply a a test volt
+Vol in order to really determine the
+
+ align:start position:0%
+Vol in order to really determine the
+ 
+
+ align:start position:0%
+Vol in order to really determine the
+input resistance if we apply a test
+
+ align:start position:0%
+input resistance if we apply a test
+ 
+
+ align:start position:0%
+input resistance if we apply a test
+voltage generator measure the resultant
+
+ align:start position:0%
+voltage generator measure the resultant
+ 
+
+ align:start position:0%
+voltage generator measure the resultant
+input current the ratio of those two uh
+
+ align:start position:0%
+input current the ratio of those two uh
+ 
+
+ align:start position:0%
+input current the ratio of those two uh
+is simply equal to the input
+
+ align:start position:0%
+is simply equal to the input
+ 
+
+ align:start position:0%
+is simply equal to the input
+resistance if I apply a test voltage VI
+
+ align:start position:0%
+resistance if I apply a test voltage VI
+ 
+
+ align:start position:0%
+resistance if I apply a test voltage VI
+over here the amplifier assuming its
+
+ align:start position:0%
+over here the amplifier assuming its
+ 
+
+ align:start position:0%
+over here the amplifier assuming its
+output resistance is zero gives me a
+
+ align:start position:0%
+output resistance is zero gives me a
+ 
+
+ align:start position:0%
+output resistance is zero gives me a
+voltage minus a * VI over here
+
+ align:start position:0%
+voltage minus a * VI over here
+ 
+
+ align:start position:0%
+voltage minus a * VI over here
+consequently the current through the
+
+ align:start position:0%
+consequently the current through the
+ 
+
+ align:start position:0%
+consequently the current through the
+resistor which is equal to the input
+
+ align:start position:0%
+resistor which is equal to the input
+ 
+
+ align:start position:0%
+resistor which is equal to the input
+current current is simply equal to the
+
+ align:start position:0%
+current current is simply equal to the
+ 
+
+ align:start position:0%
+current current is simply equal to the
+voltage here minus the voltage here that
+
+ align:start position:0%
+voltage here minus the voltage here that
+ 
+
+ align:start position:0%
+voltage here minus the voltage here that
+quantity is 1 + a * VI uh divided by the
+
+ align:start position:0%
+quantity is 1 + a * VI uh divided by the
+ 
+
+ align:start position:0%
+quantity is 1 + a * VI uh divided by the
+resistor value current here is this
+
+ align:start position:0%
+resistor value current here is this
+ 
+
+ align:start position:0%
+resistor value current here is this
+voltage minus that voltage divided by
+
+ align:start position:0%
+voltage minus that voltage divided by
+ 
+
+ align:start position:0%
+voltage minus that voltage divided by
+R if I take the ratio then VI over RI
+
+ align:start position:0%
+R if I take the ratio then VI over RI
+ 
+
+ align:start position:0%
+R if I take the ratio then VI over RI
+I'm sorry VI over II which is equal to
+
+ align:start position:0%
+I'm sorry VI over II which is equal to
+ 
+
+ align:start position:0%
+I'm sorry VI over II which is equal to
+the input resistance this may be a
+
+ align:start position:0%
+the input resistance this may be a
+ 
+
+ align:start position:0%
+the input resistance this may be a
+little bit confusing but R subi I'm now
+
+ align:start position:0%
+little bit confusing but R subi I'm now
+ 
+
+ align:start position:0%
+little bit confusing but R subi I'm now
+implying as the input resistance for the
+
+ align:start position:0%
+implying as the input resistance for the
+ 
+
+ align:start position:0%
+implying as the input resistance for the
+configur duration it's simply equal to R
+
+ align:start position:0%
+configur duration it's simply equal to R
+ 
+
+ align:start position:0%
+configur duration it's simply equal to R
+/ 1 + a in other words what we've done
+
+ align:start position:0%
+/ 1 + a in other words what we've done
+ 
+
+ align:start position:0%
+/ 1 + a in other words what we've done
+is lower the input resistance uh by a
+
+ align:start position:0%
+is lower the input resistance uh by a
+ 
+
+ align:start position:0%
+is lower the input resistance uh by a
+factor of one minus the loop
+
+ align:start position:0%
+factor of one minus the loop
+ 
+
+ align:start position:0%
+factor of one minus the loop
+transmission compared to the value that
+
+ align:start position:0%
+transmission compared to the value that
+ 
+
+ align:start position:0%
+transmission compared to the value that
+we'd see without feedback if the if the
+
+ align:start position:0%
+we'd see without feedback if the if the
+ 
+
+ align:start position:0%
+we'd see without feedback if the if the
+amplifier gain were zero we'd have no
+
+ align:start position:0%
+amplifier gain were zero we'd have no
+ 
+
+ align:start position:0%
+amplifier gain were zero we'd have no
+feedback uh this point would always
+
+ align:start position:0%
+feedback uh this point would always
+ 
+
+ align:start position:0%
+feedback uh this point would always
+remain grounded we'd see an input
+
+ align:start position:0%
+remain grounded we'd see an input
+ 
+
+ align:start position:0%
+remain grounded we'd see an input
+resistance simply equal to R uh feedback
+
+ align:start position:0%
+resistance simply equal to R uh feedback
+ 
+
+ align:start position:0%
+resistance simply equal to R uh feedback
+scales that by an amount one minus Loop
+
+ align:start position:0%
+scales that by an amount one minus Loop
+ 
+
+ align:start position:0%
+scales that by an amount one minus Loop
+Transmission in this case it lowers it
+
+ align:start position:0%
+Transmission in this case it lowers it
+ 
+
+ align:start position:0%
+Transmission in this case it lowers it
+we have a tool
+
+ align:start position:0%
+we have a tool
+ 
+
+ align:start position:0%
+we have a tool
+where what we're doing is is designing
+
+ align:start position:0%
+where what we're doing is is designing
+ 
+
+ align:start position:0%
+where what we're doing is is designing
+for a low impedance at this point
+
+ align:start position:0%
+for a low impedance at this point
+ 
+
+ align:start position:0%
+for a low impedance at this point
+because of that topology we scale lower
+
+ align:start position:0%
+because of that topology we scale lower
+ 
+
+ align:start position:0%
+because of that topology we scale lower
+the effective resistance by a factor of
+
+ align:start position:0%
+the effective resistance by a factor of
+ 
+
+ align:start position:0%
+the effective resistance by a factor of
+one minus the loop transmission so we
+
+ align:start position:0%
+one minus the loop transmission so we
+ 
+
+ align:start position:0%
+one minus the loop transmission so we
+can simply look at the topology see if
+
+ align:start position:0%
+can simply look at the topology see if
+ 
+
+ align:start position:0%
+can simply look at the topology see if
+we're trying to increase or decrease a
+
+ align:start position:0%
+we're trying to increase or decrease a
+ 
+
+ align:start position:0%
+we're trying to increase or decrease a
+resistance or an impedance uh by virtue
+
+ align:start position:0%
+resistance or an impedance uh by virtue
+ 
+
+ align:start position:0%
+resistance or an impedance uh by virtue
+of the topology and the scale factor is
+
+ align:start position:0%
+of the topology and the scale factor is
+ 
+
+ align:start position:0%
+of the topology and the scale factor is
+always one minus the loop transmission
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next time we'll continue our discussion
+
+ align:start position:0%
+next time we'll continue our discussion
+ 
+
+ align:start position:0%
+next time we'll continue our discussion
+of the properties of feedback systems in
+
+ align:start position:0%
+of the properties of feedback systems in
+ 
+
+ align:start position:0%
+of the properties of feedback systems in
+particular we'll see how feedback
+
+ align:start position:0%
+particular we'll see how feedback
+ 
+
+ align:start position:0%
+particular we'll see how feedback
+systems do affect the noise associated
+
+ align:start position:0%
+systems do affect the noise associated
+ 
+
+ align:start position:0%
+systems do affect the noise associated
+with a a system we'll also look at at
+
+ align:start position:0%
+with a a system we'll also look at at
+ 
+
+ align:start position:0%
+with a a system we'll also look at at
+how feedback can be used to moderate the
+
+ align:start position:0%
+how feedback can be used to moderate the
+ 
+
+ align:start position:0%
+how feedback can be used to moderate the
+effects of certain kinds of
+
+ align:start position:0%
+effects of certain kinds of
+ 
+
+ align:start position:0%
+effects of certain kinds of
+nonlinearities in a system thank you
\ No newline at end of file
diff --git a/TtaWB0bL3zQ.txt b/TtaWB0bL3zQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2229211717624f513c0f78f158fc0b36cf5a9446
--- /dev/null
+++ b/TtaWB0bL3zQ.txt
@@ -0,0 +1,3043 @@
+align:start position:0%
+ 
+what I wanted to demonstrate is this how
+
+ align:start position:0%
+what I wanted to demonstrate is this how
+ 
+
+ align:start position:0%
+what I wanted to demonstrate is this how
+this press works I want to show you how
+
+ align:start position:0%
+this press works I want to show you how
+ 
+
+ align:start position:0%
+this press works I want to show you how
+to make a water a proper water filter
+
+ align:start position:0%
+to make a water a proper water filter
+ 
+
+ align:start position:0%
+to make a water a proper water filter
+and this is ceramic water filter that
+
+ align:start position:0%
+and this is ceramic water filter that
+ 
+
+ align:start position:0%
+and this is ceramic water filter that
+I'm going to create here and that's
+
+ align:start position:0%
+I'm going to create here and that's
+ 
+
+ align:start position:0%
+I'm going to create here and that's
+essentially a focus of the first talk
+
+ align:start position:0%
+essentially a focus of the first talk
+ 
+
+ align:start position:0%
+essentially a focus of the first talk
+this is a bisque fired filters made with
+
+ align:start position:0%
+this is a bisque fired filters made with
+ 
+
+ align:start position:0%
+this is a bisque fired filters made with
+clay and sawdust dry clay dry sawdust
+
+ align:start position:0%
+clay and sawdust dry clay dry sawdust
+ 
+
+ align:start position:0%
+clay and sawdust dry clay dry sawdust
+about 50/50 and when the sawdust burns
+
+ align:start position:0%
+about 50/50 and when the sawdust burns
+ 
+
+ align:start position:0%
+about 50/50 and when the sawdust burns
+out it leaves pores now the clay is
+
+ align:start position:0%
+out it leaves pores now the clay is
+ 
+
+ align:start position:0%
+out it leaves pores now the clay is
+naturally porous but the sawdust allows
+
+ align:start position:0%
+naturally porous but the sawdust allows
+ 
+
+ align:start position:0%
+naturally porous but the sawdust allows
+for more porosity and so the water can
+
+ align:start position:0%
+for more porosity and so the water can
+ 
+
+ align:start position:0%
+for more porosity and so the water can
+flow through if you have water that's
+
+ align:start position:0%
+flow through if you have water that's
+ 
+
+ align:start position:0%
+flow through if you have water that's
+contaminated with microbes and pathogens
+
+ align:start position:0%
+contaminated with microbes and pathogens
+ 
+
+ align:start position:0%
+contaminated with microbes and pathogens
+that might create things like cholera
+
+ align:start position:0%
+that might create things like cholera
+ 
+
+ align:start position:0%
+that might create things like cholera
+coli Giardia you can put that water into
+
+ align:start position:0%
+coli Giardia you can put that water into
+ 
+
+ align:start position:0%
+coli Giardia you can put that water into
+this filter a filter about one to three
+
+ align:start position:0%
+this filter a filter about one to three
+ 
+
+ align:start position:0%
+this filter a filter about one to three
+liters an hour and that water is
+
+ align:start position:0%
+liters an hour and that water is
+ 
+
+ align:start position:0%
+liters an hour and that water is
+rendered renders about 95 percent free
+
+ align:start position:0%
+rendered renders about 95 percent free
+ 
+
+ align:start position:0%
+rendered renders about 95 percent free
+of those those contaminants we add a
+
+ align:start position:0%
+of those those contaminants we add a
+ 
+
+ align:start position:0%
+of those those contaminants we add a
+small amount of colloidal silver to the
+
+ align:start position:0%
+small amount of colloidal silver to the
+ 
+
+ align:start position:0%
+small amount of colloidal silver to the
+filter by brushing it on usually it's a
+
+ align:start position:0%
+filter by brushing it on usually it's a
+ 
+
+ align:start position:0%
+filter by brushing it on usually it's a
+less than a gram with about 500
+
+ align:start position:0%
+less than a gram with about 500
+ 
+
+ align:start position:0%
+less than a gram with about 500
+milliliters of water that silver acts as
+
+ align:start position:0%
+milliliters of water that silver acts as
+ 
+
+ align:start position:0%
+milliliters of water that silver acts as
+a natural antimicrobial and will render
+
+ align:start position:0%
+a natural antimicrobial and will render
+ 
+
+ align:start position:0%
+a natural antimicrobial and will render
+in earth to approximately the remaining
+
+ align:start position:0%
+in earth to approximately the remaining
+ 
+
+ align:start position:0%
+in earth to approximately the remaining
+four four and a half to five percent of
+
+ align:start position:0%
+four four and a half to five percent of
+ 
+
+ align:start position:0%
+four four and a half to five percent of
+the bad stuff that's in that water so
+
+ align:start position:0%
+the bad stuff that's in that water so
+ 
+
+ align:start position:0%
+the bad stuff that's in that water so
+this is one of those approaches that
+
+ align:start position:0%
+this is one of those approaches that
+ 
+
+ align:start position:0%
+this is one of those approaches that
+allows us to have potable water or
+
+ align:start position:0%
+allows us to have potable water or
+ 
+
+ align:start position:0%
+allows us to have potable water or
+adequate access to clean water a few
+
+ align:start position:0%
+adequate access to clean water a few
+ 
+
+ align:start position:0%
+adequate access to clean water a few
+years ago I was working with some
+
+ align:start position:0%
+years ago I was working with some
+ 
+
+ align:start position:0%
+years ago I was working with some
+undergrad engineering students and I
+
+ align:start position:0%
+undergrad engineering students and I
+ 
+
+ align:start position:0%
+undergrad engineering students and I
+said look I have this dilemma
+
+ align:start position:0%
+said look I have this dilemma
+ 
+
+ align:start position:0%
+said look I have this dilemma
+here's the here's the situation with
+
+ align:start position:0%
+here's the here's the situation with
+ 
+
+ align:start position:0%
+here's the here's the situation with
+this big press that's used
+
+ align:start position:0%
+this big press that's used
+ 
+
+ align:start position:0%
+this big press that's used
+conventionally to make these filters but
+
+ align:start position:0%
+conventionally to make these filters but
+ 
+
+ align:start position:0%
+conventionally to make these filters but
+it's really tough to to take with me on
+
+ align:start position:0%
+it's really tough to to take with me on
+ 
+
+ align:start position:0%
+it's really tough to to take with me on
+the road can you make one that fits in a
+
+ align:start position:0%
+the road can you make one that fits in a
+ 
+
+ align:start position:0%
+the road can you make one that fits in a
+suitcase they say yeah can you make one
+
+ align:start position:0%
+suitcase they say yeah can you make one
+ 
+
+ align:start position:0%
+suitcase they say yeah can you make one
+that makes the same size filters yeah
+
+ align:start position:0%
+that makes the same size filters yeah
+ 
+
+ align:start position:0%
+that makes the same size filters yeah
+can you make one that doesn't cost any
+
+ align:start position:0%
+can you make one that doesn't cost any
+ 
+
+ align:start position:0%
+can you make one that doesn't cost any
+money or cost as little as possible they
+
+ align:start position:0%
+money or cost as little as possible they
+ 
+
+ align:start position:0%
+money or cost as little as possible they
+said well wait maybe and they did it
+
+ align:start position:0%
+said well wait maybe and they did it
+ 
+
+ align:start position:0%
+said well wait maybe and they did it
+this is the the filter press it was
+
+ align:start position:0%
+this is the the filter press it was
+ 
+
+ align:start position:0%
+this is the the filter press it was
+collapsed earlier I assembled this and
+
+ align:start position:0%
+collapsed earlier I assembled this and
+ 
+
+ align:start position:0%
+collapsed earlier I assembled this and
+they made this out of repurposed
+
+ align:start position:0%
+they made this out of repurposed
+ 
+
+ align:start position:0%
+they made this out of repurposed
+materials but also some of the materials
+
+ align:start position:0%
+materials but also some of the materials
+ 
+
+ align:start position:0%
+materials but also some of the materials
+I gave them which was this Bell the male
+
+ align:start position:0%
+I gave them which was this Bell the male
+ 
+
+ align:start position:0%
+I gave them which was this Bell the male
+and female molds here so I'll
+
+ align:start position:0%
+and female molds here so I'll
+ 
+
+ align:start position:0%
+and female molds here so I'll
+demonstrate how this this works to make
+
+ align:start position:0%
+demonstrate how this this works to make
+ 
+
+ align:start position:0%
+demonstrate how this this works to make
+a filter usually again the filters are
+
+ align:start position:0%
+a filter usually again the filters are
+ 
+
+ align:start position:0%
+a filter usually again the filters are
+made on a full-sized press but this is a
+
+ align:start position:0%
+made on a full-sized press but this is a
+ 
+
+ align:start position:0%
+made on a full-sized press but this is a
+smaller press
+
+ align:start position:0%
+smaller press
+ 
+
+ align:start position:0%
+smaller press
+so this is both the prototype and the
+
+ align:start position:0%
+so this is both the prototype and the
+ 
+
+ align:start position:0%
+so this is both the prototype and the
+final product and the only one in
+
+ align:start position:0%
+final product and the only one in
+ 
+
+ align:start position:0%
+final product and the only one in
+existence cool thing about this is one
+
+ align:start position:0%
+existence cool thing about this is one
+ 
+
+ align:start position:0%
+existence cool thing about this is one
+person can operate it usually with those
+
+ align:start position:0%
+person can operate it usually with those
+ 
+
+ align:start position:0%
+person can operate it usually with those
+big presses it's easier if two people
+
+ align:start position:0%
+big presses it's easier if two people
+ 
+
+ align:start position:0%
+big presses it's easier if two people
+operates it but one person can do very
+
+ align:start position:0%
+operates it but one person can do very
+ 
+
+ align:start position:0%
+operates it but one person can do very
+well so this is a male mold this is
+
+ align:start position:0%
+well so this is a male mold this is
+ 
+
+ align:start position:0%
+well so this is a male mold this is
+essentially very lightweight steel this
+
+ align:start position:0%
+essentially very lightweight steel this
+ 
+
+ align:start position:0%
+essentially very lightweight steel this
+is so we have this is this Bell form and
+
+ align:start position:0%
+is so we have this is this Bell form and
+ 
+
+ align:start position:0%
+is so we have this is this Bell form and
+what we're going to do is put the clay
+
+ align:start position:0%
+what we're going to do is put the clay
+ 
+
+ align:start position:0%
+what we're going to do is put the clay
+in the middle and we'll make the filter
+
+ align:start position:0%
+in the middle and we'll make the filter
+ 
+
+ align:start position:0%
+in the middle and we'll make the filter
+this way so this is this is the the
+
+ align:start position:0%
+this way so this is this is the the
+ 
+
+ align:start position:0%
+this way so this is this is the the
+metal mold the bottom of the mold I'm
+
+ align:start position:0%
+metal mold the bottom of the mold I'm
+ 
+
+ align:start position:0%
+metal mold the bottom of the mold I'm
+going to put this thank you put this
+
+ align:start position:0%
+going to put this thank you put this
+ 
+
+ align:start position:0%
+going to put this thank you put this
+plastic down as release agent because
+
+ align:start position:0%
+plastic down as release agent because
+ 
+
+ align:start position:0%
+plastic down as release agent because
+the clay will stick to the metal won't
+
+ align:start position:0%
+the clay will stick to the metal won't
+ 
+
+ align:start position:0%
+the clay will stick to the metal won't
+doesn't like to stick to the plastic and
+
+ align:start position:0%
+doesn't like to stick to the plastic and
+ 
+
+ align:start position:0%
+doesn't like to stick to the plastic and
+have this bat there's a bevel in it and
+
+ align:start position:0%
+have this bat there's a bevel in it and
+ 
+
+ align:start position:0%
+have this bat there's a bevel in it and
+approximate the same angle as the the
+
+ align:start position:0%
+approximate the same angle as the the
+ 
+
+ align:start position:0%
+approximate the same angle as the the
+Bell then I'm gonna put this clay so I'm
+
+ align:start position:0%
+Bell then I'm gonna put this clay so I'm
+ 
+
+ align:start position:0%
+Bell then I'm gonna put this clay so I'm
+gonna put the second piece of plastic on
+
+ align:start position:0%
+gonna put the second piece of plastic on
+ 
+
+ align:start position:0%
+gonna put the second piece of plastic on
+and then I'll put the this top part
+
+ align:start position:0%
+and then I'll put the this top part
+ 
+
+ align:start position:0%
+and then I'll put the this top part
+what's interesting is that the original
+
+ align:start position:0%
+what's interesting is that the original
+ 
+
+ align:start position:0%
+what's interesting is that the original
+traditional approach to these larger
+
+ align:start position:0%
+traditional approach to these larger
+ 
+
+ align:start position:0%
+traditional approach to these larger
+presses used concrete molds and then
+
+ align:start position:0%
+presses used concrete molds and then
+ 
+
+ align:start position:0%
+presses used concrete molds and then
+they move to light later weight metal
+
+ align:start position:0%
+they move to light later weight metal
+ 
+
+ align:start position:0%
+they move to light later weight metal
+molds and so this is the same exact mold
+
+ align:start position:0%
+molds and so this is the same exact mold
+ 
+
+ align:start position:0%
+molds and so this is the same exact mold
+that one would find on a larger press
+
+ align:start position:0%
+that one would find on a larger press
+ 
+
+ align:start position:0%
+that one would find on a larger press
+now this is the part that sometimes gets
+
+ align:start position:0%
+now this is the part that sometimes gets
+ 
+
+ align:start position:0%
+now this is the part that sometimes gets
+tricky because you got to make sure both
+
+ align:start position:0%
+tricky because you got to make sure both
+ 
+
+ align:start position:0%
+tricky because you got to make sure both
+of these sides are latched down take
+
+ align:start position:0%
+of these sides are latched down take
+ 
+
+ align:start position:0%
+of these sides are latched down take
+this arm and tighten up the the jack and
+
+ align:start position:0%
+this arm and tighten up the the jack and
+ 
+
+ align:start position:0%
+this arm and tighten up the the jack and
+then with just a simple
+
+ align:start position:0%
+then with just a simple
+ 
+
+ align:start position:0%
+then with just a simple
+this is a fun part I like to say you
+
+ align:start position:0%
+this is a fun part I like to say you
+ 
+
+ align:start position:0%
+this is a fun part I like to say you
+have to get up to get down right you
+
+ align:start position:0%
+have to get up to get down right you
+ 
+
+ align:start position:0%
+have to get up to get down right you
+have to push this thing up in order for
+
+ align:start position:0%
+have to push this thing up in order for
+ 
+
+ align:start position:0%
+have to push this thing up in order for
+it to have resistance and push back down
+
+ align:start position:0%
+it to have resistance and push back down
+ 
+
+ align:start position:0%
+it to have resistance and push back down
+at this point I am going to release the
+
+ align:start position:0%
+at this point I am going to release the
+ 
+
+ align:start position:0%
+at this point I am going to release the
+pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+certainly this machine this press
+
+ align:start position:0%
+certainly this machine this press
+ 
+
+ align:start position:0%
+certainly this machine this press
+portable press wouldn't necessarily work
+
+ align:start position:0%
+portable press wouldn't necessarily work
+ 
+
+ align:start position:0%
+portable press wouldn't necessarily work
+well for a proper production facility
+
+ align:start position:0%
+well for a proper production facility
+ 
+
+ align:start position:0%
+well for a proper production facility
+where you want to crank out lots of
+
+ align:start position:0%
+where you want to crank out lots of
+ 
+
+ align:start position:0%
+where you want to crank out lots of
+filters in a day or in a week but
+
+ align:start position:0%
+filters in a day or in a week but
+ 
+
+ align:start position:0%
+filters in a day or in a week but
+certainly to establish a facility in a
+
+ align:start position:0%
+certainly to establish a facility in a
+ 
+
+ align:start position:0%
+certainly to establish a facility in a
+community that needs clean water using
+
+ align:start position:0%
+community that needs clean water using
+ 
+
+ align:start position:0%
+community that needs clean water using
+this technology we can use this press to
+
+ align:start position:0%
+this technology we can use this press to
+ 
+
+ align:start position:0%
+this technology we can use this press to
+create filters very quickly and create
+
+ align:start position:0%
+create filters very quickly and create
+ 
+
+ align:start position:0%
+create filters very quickly and create
+give us a give ourselves a baseline of
+
+ align:start position:0%
+give us a give ourselves a baseline of
+ 
+
+ align:start position:0%
+give us a give ourselves a baseline of
+not only the clay but the how the
+
+ align:start position:0%
+not only the clay but the how the
+ 
+
+ align:start position:0%
+not only the clay but the how the
+filtration works lift this back up take
+
+ align:start position:0%
+filtration works lift this back up take
+ 
+
+ align:start position:0%
+filtration works lift this back up take
+the bell off there's our filter just
+
+ align:start position:0%
+the bell off there's our filter just
+ 
+
+ align:start position:0%
+the bell off there's our filter just
+takes a little bit of clean up at this
+
+ align:start position:0%
+takes a little bit of clean up at this
+ 
+
+ align:start position:0%
+takes a little bit of clean up at this
+point again I'm using my thumb just to
+
+ align:start position:0%
+point again I'm using my thumb just to
+ 
+
+ align:start position:0%
+point again I'm using my thumb just to
+pull some of this extra off but I could
+
+ align:start position:0%
+pull some of this extra off but I could
+ 
+
+ align:start position:0%
+pull some of this extra off but I could
+certainly use and this is what you would
+
+ align:start position:0%
+certainly use and this is what you would
+ 
+
+ align:start position:0%
+certainly use and this is what you would
+do in a the production facility would be
+
+ align:start position:0%
+do in a the production facility would be
+ 
+
+ align:start position:0%
+do in a the production facility would be
+to take a clay Tolan to clean this up as
+
+ align:start position:0%
+to take a clay Tolan to clean this up as
+ 
+
+ align:start position:0%
+to take a clay Tolan to clean this up as
+well and then because this bat is wider
+
+ align:start position:0%
+well and then because this bat is wider
+ 
+
+ align:start position:0%
+well and then because this bat is wider
+than the base I simply lift and there's
+
+ align:start position:0%
+than the base I simply lift and there's
+ 
+
+ align:start position:0%
+than the base I simply lift and there's
+the filter I can lay this place this
+
+ align:start position:0%
+the filter I can lay this place this
+ 
+
+ align:start position:0%
+the filter I can lay this place this
+down on a shelf in the studio or in the
+
+ align:start position:0%
+down on a shelf in the studio or in the
+ 
+
+ align:start position:0%
+down on a shelf in the studio or in the
+facility another worker would clean it
+
+ align:start position:0%
+facility another worker would clean it
+ 
+
+ align:start position:0%
+facility another worker would clean it
+up smooth up some of the edges perhaps
+
+ align:start position:0%
+up smooth up some of the edges perhaps
+ 
+
+ align:start position:0%
+up smooth up some of the edges perhaps
+stamp it with a date and a number so we
+
+ align:start position:0%
+stamp it with a date and a number so we
+ 
+
+ align:start position:0%
+stamp it with a date and a number so we
+can track the way that it put it
+
+ align:start position:0%
+can track the way that it put it
+ 
+
+ align:start position:0%
+can track the way that it put it
+operates we let it dry then we fire we
+
+ align:start position:0%
+operates we let it dry then we fire we
+ 
+
+ align:start position:0%
+operates we let it dry then we fire we
+put it in the kiln we fired to about 860
+
+ align:start position:0%
+put it in the kiln we fired to about 860
+ 
+
+ align:start position:0%
+put it in the kiln we fired to about 860
+six degrees C and what happens then is
+
+ align:start position:0%
+six degrees C and what happens then is
+ 
+
+ align:start position:0%
+six degrees C and what happens then is
+the sawdust burns out which then creates
+
+ align:start position:0%
+the sawdust burns out which then creates
+ 
+
+ align:start position:0%
+the sawdust burns out which then creates
+a more porous vessel that allows the
+
+ align:start position:0%
+a more porous vessel that allows the
+ 
+
+ align:start position:0%
+a more porous vessel that allows the
+water to flow at a more rapid pace than
+
+ align:start position:0%
+water to flow at a more rapid pace than
+ 
+
+ align:start position:0%
+water to flow at a more rapid pace than
+it would if it wasn't as porous this is
+
+ align:start position:0%
+it would if it wasn't as porous this is
+ 
+
+ align:start position:0%
+it would if it wasn't as porous this is
+ready to make another filter I could put
+
+ align:start position:0%
+ready to make another filter I could put
+ 
+
+ align:start position:0%
+ready to make another filter I could put
+plastic down another bat down we could
+
+ align:start position:0%
+plastic down another bat down we could
+ 
+
+ align:start position:0%
+plastic down another bat down we could
+continue to make filters as long as we
+
+ align:start position:0%
+continue to make filters as long as we
+ 
+
+ align:start position:0%
+continue to make filters as long as we
+had clay so with one person that was
+
+ align:start position:0%
+had clay so with one person that was
+ 
+
+ align:start position:0%
+had clay so with one person that was
+what about a ten minute time frame with
+
+ align:start position:0%
+what about a ten minute time frame with
+ 
+
+ align:start position:0%
+what about a ten minute time frame with
+two people you could move much more
+
+ align:start position:0%
+two people you could move much more
+ 
+
+ align:start position:0%
+two people you could move much more
+quickly but the reason I wanted to
+
+ align:start position:0%
+quickly but the reason I wanted to
+ 
+
+ align:start position:0%
+quickly but the reason I wanted to
+demonstrate this to you is to show you
+
+ align:start position:0%
+demonstrate this to you is to show you
+ 
+
+ align:start position:0%
+demonstrate this to you is to show you
+in real time what it takes to create a
+
+ align:start position:0%
+in real time what it takes to create a
+ 
+
+ align:start position:0%
+in real time what it takes to create a
+water filter what if you designed houses
+
+ align:start position:0%
+water filter what if you designed houses
+ 
+
+ align:start position:0%
+water filter what if you designed houses
+what if you designed shelters what if
+
+ align:start position:0%
+what if you designed shelters what if
+ 
+
+ align:start position:0%
+what if you designed shelters what if
+you designed access to water as if you
+
+ align:start position:0%
+you designed access to water as if you
+ 
+
+ align:start position:0%
+you designed access to water as if you
+really cared about people getting it not
+
+ align:start position:0%
+really cared about people getting it not
+ 
+
+ align:start position:0%
+really cared about people getting it not
+that you cared about making money from
+
+ align:start position:0%
+that you cared about making money from
+ 
+
+ align:start position:0%
+that you cared about making money from
+it or that you were interested in fame
+
+ align:start position:0%
+it or that you were interested in fame
+ 
+
+ align:start position:0%
+it or that you were interested in fame
+or that you were just doing it to do it
+
+ align:start position:0%
+or that you were just doing it to do it
+ 
+
+ align:start position:0%
+or that you were just doing it to do it
+what if you gave a damn about the
+
+ align:start position:0%
+what if you gave a damn about the
+ 
+
+ align:start position:0%
+what if you gave a damn about the
+situation what if he cared in in more
+
+ align:start position:0%
+situation what if he cared in in more
+ 
+
+ align:start position:0%
+situation what if he cared in in more
+direct ways what would that look like in
+
+ align:start position:0%
+direct ways what would that look like in
+ 
+
+ align:start position:0%
+direct ways what would that look like in
+ways that would be affordable to people
+
+ align:start position:0%
+ways that would be affordable to people
+ 
+
+ align:start position:0%
+ways that would be affordable to people
+who need it but also appropriate in
+
+ align:start position:0%
+who need it but also appropriate in
+ 
+
+ align:start position:0%
+who need it but also appropriate in
+terms of appropriate technology the idea
+
+ align:start position:0%
+terms of appropriate technology the idea
+ 
+
+ align:start position:0%
+terms of appropriate technology the idea
+that materials and practices and
+
+ align:start position:0%
+that materials and practices and
+ 
+
+ align:start position:0%
+that materials and practices and
+processes that allow for things like
+
+ align:start position:0%
+processes that allow for things like
+ 
+
+ align:start position:0%
+processes that allow for things like
+shelter and food and water access to
+
+ align:start position:0%
+shelter and food and water access to
+ 
+
+ align:start position:0%
+shelter and food and water access to
+happen do not complicate a cultural set
+
+ align:start position:0%
+happen do not complicate a cultural set
+ 
+
+ align:start position:0%
+happen do not complicate a cultural set
+of rules and practices right it's
+
+ align:start position:0%
+of rules and practices right it's
+ 
+
+ align:start position:0%
+of rules and practices right it's
+appropriate for the culture it's
+
+ align:start position:0%
+appropriate for the culture it's
+ 
+
+ align:start position:0%
+appropriate for the culture it's
+appropriate for the situation thinking
+
+ align:start position:0%
+appropriate for the situation thinking
+ 
+
+ align:start position:0%
+appropriate for the situation thinking
+about culture as the way we do things
+
+ align:start position:0%
+about culture as the way we do things
+ 
+
+ align:start position:0%
+about culture as the way we do things
+around here right so does the cup does
+
+ align:start position:0%
+around here right so does the cup does
+ 
+
+ align:start position:0%
+around here right so does the cup does
+the technology interrupt the way we do
+
+ align:start position:0%
+the technology interrupt the way we do
+ 
+
+ align:start position:0%
+the technology interrupt the way we do
+things around and does it pose confusion
+
+ align:start position:0%
+things around and does it pose confusion
+ 
+
+ align:start position:0%
+things around and does it pose confusion
+so this is the gentleman who invented or
+
+ align:start position:0%
+so this is the gentleman who invented or
+ 
+
+ align:start position:0%
+so this is the gentleman who invented or
+was credited with coming up with the
+
+ align:start position:0%
+was credited with coming up with the
+ 
+
+ align:start position:0%
+was credited with coming up with the
+approach that dr. Fran dimas' Regas he's
+
+ align:start position:0%
+approach that dr. Fran dimas' Regas he's
+ 
+
+ align:start position:0%
+approach that dr. Fran dimas' Regas he's
+from Guatemala and as a first response
+
+ align:start position:0%
+from Guatemala and as a first response
+ 
+
+ align:start position:0%
+from Guatemala and as a first response
+to natural disasters Missouri Gustad if
+
+ align:start position:0%
+to natural disasters Missouri Gustad if
+ 
+
+ align:start position:0%
+to natural disasters Missouri Gustad if
+we had this porous vessel that allowed
+
+ align:start position:0%
+we had this porous vessel that allowed
+ 
+
+ align:start position:0%
+we had this porous vessel that allowed
+for water to flow through that the
+
+ align:start position:0%
+for water to flow through that the
+ 
+
+ align:start position:0%
+for water to flow through that the
+contaminated water to flow through at a
+
+ align:start position:0%
+contaminated water to flow through at a
+ 
+
+ align:start position:0%
+contaminated water to flow through at a
+fairly rapid pace we might be able to
+
+ align:start position:0%
+fairly rapid pace we might be able to
+ 
+
+ align:start position:0%
+fairly rapid pace we might be able to
+produce adequate access to clean water
+
+ align:start position:0%
+produce adequate access to clean water
+ 
+
+ align:start position:0%
+produce adequate access to clean water
+to potable water after natural disasters
+
+ align:start position:0%
+to potable water after natural disasters
+ 
+
+ align:start position:0%
+to potable water after natural disasters
+and so Mazza Regas then
+
+ align:start position:0%
+and so Mazza Regas then
+ 
+
+ align:start position:0%
+and so Mazza Regas then
+was contacted by Ron Rivera Ron was
+
+ align:start position:0%
+was contacted by Ron Rivera Ron was
+ 
+
+ align:start position:0%
+was contacted by Ron Rivera Ron was
+working with Potter's for peace at the
+
+ align:start position:0%
+working with Potter's for peace at the
+ 
+
+ align:start position:0%
+working with Potter's for peace at the
+time and this was in the late 80s early
+
+ align:start position:0%
+time and this was in the late 80s early
+ 
+
+ align:start position:0%
+time and this was in the late 80s early
+90s and Ron learned the process and
+
+ align:start position:0%
+90s and Ron learned the process and
+ 
+
+ align:start position:0%
+90s and Ron learned the process and
+started setting up water filter
+
+ align:start position:0%
+started setting up water filter
+ 
+
+ align:start position:0%
+started setting up water filter
+production facility through Potter's for
+
+ align:start position:0%
+production facility through Potter's for
+ 
+
+ align:start position:0%
+production facility through Potter's for
+peace met Ron Rivera a number of years
+
+ align:start position:0%
+peace met Ron Rivera a number of years
+ 
+
+ align:start position:0%
+peace met Ron Rivera a number of years
+ago at a conference and several months
+
+ align:start position:0%
+ago at a conference and several months
+ 
+
+ align:start position:0%
+ago at a conference and several months
+late after I met him he passed away he
+
+ align:start position:0%
+late after I met him he passed away he
+ 
+
+ align:start position:0%
+late after I met him he passed away he
+was working in Nigeria to help a
+
+ align:start position:0%
+was working in Nigeria to help a
+ 
+
+ align:start position:0%
+was working in Nigeria to help a
+community set up a water filter
+
+ align:start position:0%
+community set up a water filter
+ 
+
+ align:start position:0%
+community set up a water filter
+production facility so that they
+
+ align:start position:0%
+production facility so that they
+ 
+
+ align:start position:0%
+production facility so that they
+wouldn't contract malaria and would not
+
+ align:start position:0%
+wouldn't contract malaria and would not
+ 
+
+ align:start position:0%
+wouldn't contract malaria and would not
+die from malaria Ron came back from that
+
+ align:start position:0%
+die from malaria Ron came back from that
+ 
+
+ align:start position:0%
+die from malaria Ron came back from that
+trip and died from a very rare and
+
+ align:start position:0%
+trip and died from a very rare and
+ 
+
+ align:start position:0%
+trip and died from a very rare and
+difficult strain of malaria so he gave
+
+ align:start position:0%
+difficult strain of malaria so he gave
+ 
+
+ align:start position:0%
+difficult strain of malaria so he gave
+his life so that others could have clean
+
+ align:start position:0%
+his life so that others could have clean
+ 
+
+ align:start position:0%
+his life so that others could have clean
+water and whenever I give a presentation
+
+ align:start position:0%
+water and whenever I give a presentation
+ 
+
+ align:start position:0%
+water and whenever I give a presentation
+I always think of that very special
+
+ align:start position:0%
+I always think of that very special
+ 
+
+ align:start position:0%
+I always think of that very special
+moment meeting Ron but the idea is that
+
+ align:start position:0%
+moment meeting Ron but the idea is that
+ 
+
+ align:start position:0%
+moment meeting Ron but the idea is that
+it's possible for this technology to be
+
+ align:start position:0%
+it's possible for this technology to be
+ 
+
+ align:start position:0%
+it's possible for this technology to be
+passed along to folks so that they can
+
+ align:start position:0%
+passed along to folks so that they can
+ 
+
+ align:start position:0%
+passed along to folks so that they can
+add use it to to move throughout world
+
+ align:start position:0%
+add use it to to move throughout world
+ 
+
+ align:start position:0%
+add use it to to move throughout world
+the world and through communities to to
+
+ align:start position:0%
+the world and through communities to to
+ 
+
+ align:start position:0%
+the world and through communities to to
+to help other other people this is a
+
+ align:start position:0%
+to help other other people this is a
+ 
+
+ align:start position:0%
+to help other other people this is a
+cross-section there's a drawing that
+
+ align:start position:0%
+cross-section there's a drawing that
+ 
+
+ align:start position:0%
+cross-section there's a drawing that
+Manny did of the filter inside the
+
+ align:start position:0%
+Manny did of the filter inside the
+ 
+
+ align:start position:0%
+Manny did of the filter inside the
+receptacle you see the addition of a
+
+ align:start position:0%
+receptacle you see the addition of a
+ 
+
+ align:start position:0%
+receptacle you see the addition of a
+spigot and a lid and these are two
+
+ align:start position:0%
+spigot and a lid and these are two
+ 
+
+ align:start position:0%
+spigot and a lid and these are two
+important components you need a spigot
+
+ align:start position:0%
+important components you need a spigot
+ 
+
+ align:start position:0%
+important components you need a spigot
+to get the water out and a lid to keep
+
+ align:start position:0%
+to get the water out and a lid to keep
+ 
+
+ align:start position:0%
+to get the water out and a lid to keep
+hands and other things entering into the
+
+ align:start position:0%
+hands and other things entering into the
+ 
+
+ align:start position:0%
+hands and other things entering into the
+into the filter contamination is is a
+
+ align:start position:0%
+into the filter contamination is is a
+ 
+
+ align:start position:0%
+into the filter contamination is is a
+big issue right these filters as you see
+
+ align:start position:0%
+big issue right these filters as you see
+ 
+
+ align:start position:0%
+big issue right these filters as you see
+here if they were sitting in a count on
+
+ align:start position:0%
+here if they were sitting in a count on
+ 
+
+ align:start position:0%
+here if they were sitting in a count on
+a counter in a kitchen you can put
+
+ align:start position:0%
+a counter in a kitchen you can put
+ 
+
+ align:start position:0%
+a counter in a kitchen you can put
+anything in the your hands can touch
+
+ align:start position:0%
+anything in the your hands can touch
+ 
+
+ align:start position:0%
+anything in the your hands can touch
+them external things could touch them
+
+ align:start position:0%
+them external things could touch them
+ 
+
+ align:start position:0%
+them external things could touch them
+and and you can contaminate the water
+
+ align:start position:0%
+and and you can contaminate the water
+ 
+
+ align:start position:0%
+and and you can contaminate the water
+even the water that is flowing through
+
+ align:start position:0%
+even the water that is flowing through
+ 
+
+ align:start position:0%
+even the water that is flowing through
+can get contaminated so a lid is
+
+ align:start position:0%
+can get contaminated so a lid is
+ 
+
+ align:start position:0%
+can get contaminated so a lid is
+necessary I don't know if you can hear
+
+ align:start position:0%
+necessary I don't know if you can hear
+ 
+
+ align:start position:0%
+necessary I don't know if you can hear
+but this one is dripping quite loudly
+
+ align:start position:0%
+but this one is dripping quite loudly
+ 
+
+ align:start position:0%
+but this one is dripping quite loudly
+now that the water is flowing we have
+
+ align:start position:0%
+now that the water is flowing we have
+ 
+
+ align:start position:0%
+now that the water is flowing we have
+some dirty water that we were using
+
+ align:start position:0%
+some dirty water that we were using
+ 
+
+ align:start position:0%
+some dirty water that we were using
+earlier and we filled these filters up
+
+ align:start position:0%
+earlier and we filled these filters up
+ 
+
+ align:start position:0%
+earlier and we filled these filters up
+I'm going to lift this one up so you can
+
+ align:start position:0%
+I'm going to lift this one up so you can
+ 
+
+ align:start position:0%
+I'm going to lift this one up so you can
+see it okay you can't see the
+
+ align:start position:0%
+see it okay you can't see the
+ 
+
+ align:start position:0%
+see it okay you can't see the
+cross-section this is the cross-section
+
+ align:start position:0%
+cross-section this is the cross-section
+ 
+
+ align:start position:0%
+cross-section this is the cross-section
+here's the spigot I don't have the lid
+
+ align:start position:0%
+here's the spigot I don't have the lid
+ 
+
+ align:start position:0%
+here's the spigot I don't have the lid
+but I'll lift this up you'll notice the
+
+ align:start position:0%
+but I'll lift this up you'll notice the
+ 
+
+ align:start position:0%
+but I'll lift this up you'll notice the
+bell shape and you should see the water
+
+ align:start position:0%
+bell shape and you should see the water
+ 
+
+ align:start position:0%
+bell shape and you should see the water
+dripping from the filter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you see that and if you come up later
+
+ align:start position:0%
+you see that and if you come up later
+ 
+
+ align:start position:0%
+you see that and if you come up later
+after we give this little chat you'll be
+
+ align:start position:0%
+after we give this little chat you'll be
+ 
+
+ align:start position:0%
+after we give this little chat you'll be
+able to see the clean water that's in
+
+ align:start position:0%
+able to see the clean water that's in
+ 
+
+ align:start position:0%
+able to see the clean water that's in
+there so this is a point of views water
+
+ align:start position:0%
+there so this is a point of views water
+ 
+
+ align:start position:0%
+there so this is a point of views water
+filter it's placed in the point in which
+
+ align:start position:0%
+filter it's placed in the point in which
+ 
+
+ align:start position:0%
+filter it's placed in the point in which
+it will be used in the home usually in a
+
+ align:start position:0%
+it will be used in the home usually in a
+ 
+
+ align:start position:0%
+it will be used in the home usually in a
+kitchen and you the idea is that you
+
+ align:start position:0%
+kitchen and you the idea is that you
+ 
+
+ align:start position:0%
+kitchen and you the idea is that you
+would fill it up in the morning or in
+
+ align:start position:0%
+would fill it up in the morning or in
+ 
+
+ align:start position:0%
+would fill it up in the morning or in
+the evening I'm sorry before you go to
+
+ align:start position:0%
+the evening I'm sorry before you go to
+ 
+
+ align:start position:0%
+the evening I'm sorry before you go to
+sleep it will filter through the night
+
+ align:start position:0%
+sleep it will filter through the night
+ 
+
+ align:start position:0%
+sleep it will filter through the night
+and in the morning you have water for
+
+ align:start position:0%
+and in the morning you have water for
+ 
+
+ align:start position:0%
+and in the morning you have water for
+cooking and drinking you fill it up
+
+ align:start position:0%
+cooking and drinking you fill it up
+ 
+
+ align:start position:0%
+cooking and drinking you fill it up
+again sometime during the day and then
+
+ align:start position:0%
+again sometime during the day and then
+ 
+
+ align:start position:0%
+again sometime during the day and then
+you have another batch of water in the
+
+ align:start position:0%
+you have another batch of water in the
+ 
+
+ align:start position:0%
+you have another batch of water in the
+evening so again point of views water
+
+ align:start position:0%
+evening so again point of views water
+ 
+
+ align:start position:0%
+evening so again point of views water
+filters these filters again the
+
+ align:start position:0%
+filters these filters again the
+ 
+
+ align:start position:0%
+filters these filters again the
+technology is the same the idea is the
+
+ align:start position:0%
+technology is the same the idea is the
+ 
+
+ align:start position:0%
+technology is the same the idea is the
+same but because clay and needs are
+
+ align:start position:0%
+same but because clay and needs are
+ 
+
+ align:start position:0%
+same but because clay and needs are
+different in different locations various
+
+ align:start position:0%
+different in different locations various
+ 
+
+ align:start position:0%
+different in different locations various
+organizations have set up facilities
+
+ align:start position:0%
+organizations have set up facilities
+ 
+
+ align:start position:0%
+organizations have set up facilities
+under different names but using the same
+
+ align:start position:0%
+under different names but using the same
+ 
+
+ align:start position:0%
+under different names but using the same
+technology the same idea because the
+
+ align:start position:0%
+technology the same idea because the
+ 
+
+ align:start position:0%
+technology the same idea because the
+need for clean water is a global need
+
+ align:start position:0%
+need for clean water is a global need
+ 
+
+ align:start position:0%
+need for clean water is a global need
+the right to what access to water is a
+
+ align:start position:0%
+the right to what access to water is a
+ 
+
+ align:start position:0%
+the right to what access to water is a
+basic human right so this little girl
+
+ align:start position:0%
+basic human right so this little girl
+ 
+
+ align:start position:0%
+basic human right so this little girl
+and her the other two children in the
+
+ align:start position:0%
+and her the other two children in the
+ 
+
+ align:start position:0%
+and her the other two children in the
+image are drinking water like they do
+
+ align:start position:0%
+image are drinking water like they do
+ 
+
+ align:start position:0%
+image are drinking water like they do
+every day I can go right to that water
+
+ align:start position:0%
+every day I can go right to that water
+ 
+
+ align:start position:0%
+every day I can go right to that water
+fountain down the hallway and get a
+
+ align:start position:0%
+fountain down the hallway and get a
+ 
+
+ align:start position:0%
+fountain down the hallway and get a
+drink of water where my water bottle is
+
+ align:start position:0%
+drink of water where my water bottle is
+ 
+
+ align:start position:0%
+drink of water where my water bottle is
+here somewhere I can drink out of that
+
+ align:start position:0%
+here somewhere I can drink out of that
+ 
+
+ align:start position:0%
+here somewhere I can drink out of that
+you know many of you have water bottles
+
+ align:start position:0%
+you know many of you have water bottles
+ 
+
+ align:start position:0%
+you know many of you have water bottles
+this is the same water that you see in
+
+ align:start position:0%
+this is the same water that you see in
+ 
+
+ align:start position:0%
+this is the same water that you see in
+the background this water is the same
+
+ align:start position:0%
+the background this water is the same
+ 
+
+ align:start position:0%
+the background this water is the same
+water where the cows have defecated
+
+ align:start position:0%
+water where the cows have defecated
+ 
+
+ align:start position:0%
+water where the cows have defecated
+where people have thrown away whatever
+
+ align:start position:0%
+where people have thrown away whatever
+ 
+
+ align:start position:0%
+where people have thrown away whatever
+it is they're throwing away in that
+
+ align:start position:0%
+it is they're throwing away in that
+ 
+
+ align:start position:0%
+it is they're throwing away in that
+water this little girl is in Honduras
+
+ align:start position:0%
+water this little girl is in Honduras
+ 
+
+ align:start position:0%
+water this little girl is in Honduras
+this gentleman is getting water for his
+
+ align:start position:0%
+this gentleman is getting water for his
+ 
+
+ align:start position:0%
+this gentleman is getting water for his
+family as well and that box has a little
+
+ align:start position:0%
+family as well and that box has a little
+ 
+
+ align:start position:0%
+family as well and that box has a little
+opening on the face on the plane facing
+
+ align:start position:0%
+opening on the face on the plane facing
+ 
+
+ align:start position:0%
+opening on the face on the plane facing
+us he reaches his hand and puts a few
+
+ align:start position:0%
+us he reaches his hand and puts a few
+ 
+
+ align:start position:0%
+us he reaches his hand and puts a few
+coins in there and the water comes out
+
+ align:start position:0%
+coins in there and the water comes out
+ 
+
+ align:start position:0%
+coins in there and the water comes out
+of that long tube water's been sitting
+
+ align:start position:0%
+of that long tube water's been sitting
+ 
+
+ align:start position:0%
+of that long tube water's been sitting
+in some sort of receptacle reservoir
+
+ align:start position:0%
+in some sort of receptacle reservoir
+ 
+
+ align:start position:0%
+in some sort of receptacle reservoir
+underneath he fills up the containers in
+
+ align:start position:0%
+underneath he fills up the containers in
+ 
+
+ align:start position:0%
+underneath he fills up the containers in
+the back of his truck and then drives
+
+ align:start position:0%
+the back of his truck and then drives
+ 
+
+ align:start position:0%
+the back of his truck and then drives
+those containers home then has to figure
+
+ align:start position:0%
+those containers home then has to figure
+ 
+
+ align:start position:0%
+those containers home then has to figure
+out how to get the water into his house
+
+ align:start position:0%
+out how to get the water into his house
+ 
+
+ align:start position:0%
+out how to get the water into his house
+and that's to figure out how to get make
+
+ align:start position:0%
+and that's to figure out how to get make
+ 
+
+ align:start position:0%
+and that's to figure out how to get make
+sure the water is clean and safe to
+
+ align:start position:0%
+sure the water is clean and safe to
+ 
+
+ align:start position:0%
+sure the water is clean and safe to
+drink this gentleman is in South Texas
+
+ align:start position:0%
+drink this gentleman is in South Texas
+ 
+
+ align:start position:0%
+drink this gentleman is in South Texas
+outside of Laredo half a million people
+
+ align:start position:0%
+outside of Laredo half a million people
+ 
+
+ align:start position:0%
+outside of Laredo half a million people
+do not have utilities paved roads and
+
+ align:start position:0%
+do not have utilities paved roads and
+ 
+
+ align:start position:0%
+do not have utilities paved roads and
+housing that's up to code in South Texas
+
+ align:start position:0%
+housing that's up to code in South Texas
+ 
+
+ align:start position:0%
+housing that's up to code in South Texas
+from El Paso to Brownsville and 150
+
+ align:start position:0%
+from El Paso to Brownsville and 150
+ 
+
+ align:start position:0%
+from El Paso to Brownsville and 150
+miles north at green swath that you see
+
+ align:start position:0%
+miles north at green swath that you see
+ 
+
+ align:start position:0%
+miles north at green swath that you see
+in that map that's South Texas half a
+
+ align:start position:0%
+in that map that's South Texas half a
+ 
+
+ align:start position:0%
+in that map that's South Texas half a
+million people they don't have adequate
+
+ align:start position:0%
+million people they don't have adequate
+ 
+
+ align:start position:0%
+million people they don't have adequate
+access to clean water either and so my
+
+ align:start position:0%
+access to clean water either and so my
+ 
+
+ align:start position:0%
+access to clean water either and so my
+colleague at Texas A&M Oscar muñoz is is
+
+ align:start position:0%
+colleague at Texas A&M Oscar muñoz is is
+ 
+
+ align:start position:0%
+colleague at Texas A&M Oscar muñoz is is
+the director of the colonias program and
+
+ align:start position:0%
+the director of the colonias program and
+ 
+
+ align:start position:0%
+the director of the colonias program and
+works with communities along that along
+
+ align:start position:0%
+works with communities along that along
+ 
+
+ align:start position:0%
+works with communities along that along
+that region social practice and public
+
+ align:start position:0%
+that region social practice and public
+ 
+
+ align:start position:0%
+that region social practice and public
+pedagogy linking those to this notion of
+
+ align:start position:0%
+pedagogy linking those to this notion of
+ 
+
+ align:start position:0%
+pedagogy linking those to this notion of
+inter intentionally disruptive
+
+ align:start position:0%
+inter intentionally disruptive
+ 
+
+ align:start position:0%
+inter intentionally disruptive
+responsibility social practice being a
+
+ align:start position:0%
+responsibility social practice being a
+ 
+
+ align:start position:0%
+responsibility social practice being a
+term that grows out of a number of moves
+
+ align:start position:0%
+term that grows out of a number of moves
+ 
+
+ align:start position:0%
+term that grows out of a number of moves
+in contemporary art where we have been
+
+ align:start position:0%
+in contemporary art where we have been
+ 
+
+ align:start position:0%
+in contemporary art where we have been
+theorized by people like Clare Bishop
+
+ align:start position:0%
+theorized by people like Clare Bishop
+ 
+
+ align:start position:0%
+theorized by people like Clare Bishop
+and Pablo ellebra
+
+ align:start position:0%
+and Pablo ellebra
+ 
+
+ align:start position:0%
+and Pablo ellebra
+and others to think about the way in
+
+ align:start position:0%
+and others to think about the way in
+ 
+
+ align:start position:0%
+and others to think about the way in
+which artists or our artistic practices
+
+ align:start position:0%
+which artists or our artistic practices
+ 
+
+ align:start position:0%
+which artists or our artistic practices
+intersect with social issues and
+
+ align:start position:0%
+intersect with social issues and
+ 
+
+ align:start position:0%
+intersect with social issues and
+conventions from other disciplines to
+
+ align:start position:0%
+conventions from other disciplines to
+ 
+
+ align:start position:0%
+conventions from other disciplines to
+make positive change or to enact change
+
+ align:start position:0%
+make positive change or to enact change
+ 
+
+ align:start position:0%
+make positive change or to enact change
+in through intentional amongst public
+
+ align:start position:0%
+in through intentional amongst public
+ 
+
+ align:start position:0%
+in through intentional amongst public
+pedagogy very much like what we did this
+
+ align:start position:0%
+pedagogy very much like what we did this
+ 
+
+ align:start position:0%
+pedagogy very much like what we did this
+after this morning we were out
+
+ align:start position:0%
+after this morning we were out
+ 
+
+ align:start position:0%
+after this morning we were out
+essentially on the sidewalk now we're on
+
+ align:start position:0%
+essentially on the sidewalk now we're on
+ 
+
+ align:start position:0%
+essentially on the sidewalk now we're on
+the patio that overlooked the sidewalk
+
+ align:start position:0%
+the patio that overlooked the sidewalk
+ 
+
+ align:start position:0%
+the patio that overlooked the sidewalk
+mixing clay and sawdust in preparation
+
+ align:start position:0%
+mixing clay and sawdust in preparation
+ 
+
+ align:start position:0%
+mixing clay and sawdust in preparation
+for making water filters and people
+
+ align:start position:0%
+for making water filters and people
+ 
+
+ align:start position:0%
+for making water filters and people
+stopped and said what do you when what
+
+ align:start position:0%
+stopped and said what do you when what
+ 
+
+ align:start position:0%
+stopped and said what do you when what
+are you doing right there you have
+
+ align:start position:0%
+are you doing right there you have
+ 
+
+ align:start position:0%
+are you doing right there you have
+developed a relationship this
+
+ align:start position:0%
+developed a relationship this
+ 
+
+ align:start position:0%
+developed a relationship this
+interchange by asking a question and
+
+ align:start position:0%
+interchange by asking a question and
+ 
+
+ align:start position:0%
+interchange by asking a question and
+responding in this back and forth and
+
+ align:start position:0%
+responding in this back and forth and
+ 
+
+ align:start position:0%
+responding in this back and forth and
+back and forth there's some learning
+
+ align:start position:0%
+back and forth there's some learning
+ 
+
+ align:start position:0%
+back and forth there's some learning
+that goes on in both directions and
+
+ align:start position:0%
+that goes on in both directions and
+ 
+
+ align:start position:0%
+that goes on in both directions and
+talking to folks about the water filters
+
+ align:start position:0%
+talking to folks about the water filters
+ 
+
+ align:start position:0%
+talking to folks about the water filters
+through a public forum in a public space
+
+ align:start position:0%
+through a public forum in a public space
+ 
+
+ align:start position:0%
+through a public forum in a public space
+is one form that we might consider
+
+ align:start position:0%
+is one form that we might consider
+ 
+
+ align:start position:0%
+is one form that we might consider
+public pedagogy and when I moved it to
+
+ align:start position:0%
+public pedagogy and when I moved it to
+ 
+
+ align:start position:0%
+public pedagogy and when I moved it to
+Penn State I decided to put a name to
+
+ align:start position:0%
+Penn State I decided to put a name to
+ 
+
+ align:start position:0%
+Penn State I decided to put a name to
+these performances collaborative
+
+ align:start position:0%
+these performances collaborative
+ 
+
+ align:start position:0%
+these performances collaborative
+creative resistance I mean Larry and I
+
+ align:start position:0%
+creative resistance I mean Larry and I
+ 
+
+ align:start position:0%
+creative resistance I mean Larry and I
+were talking about titles and sometimes
+
+ align:start position:0%
+were talking about titles and sometimes
+ 
+
+ align:start position:0%
+were talking about titles and sometimes
+the titles enough to tease and pull
+
+ align:start position:0%
+the titles enough to tease and pull
+ 
+
+ align:start position:0%
+the titles enough to tease and pull
+folks in but the idea of how might we
+
+ align:start position:0%
+folks in but the idea of how might we
+ 
+
+ align:start position:0%
+folks in but the idea of how might we
+collaboratively work together to resist
+
+ align:start position:0%
+collaboratively work together to resist
+ 
+
+ align:start position:0%
+collaboratively work together to resist
+those hegemonic forces or to disrupt
+
+ align:start position:0%
+those hegemonic forces or to disrupt
+ 
+
+ align:start position:0%
+those hegemonic forces or to disrupt
+what others might find acceptable so
+
+ align:start position:0%
+what others might find acceptable so
+ 
+
+ align:start position:0%
+what others might find acceptable so
+with a small grant from the Institute
+
+ align:start position:0%
+with a small grant from the Institute
+ 
+
+ align:start position:0%
+with a small grant from the Institute
+for the Arts and Humanities I did a
+
+ align:start position:0%
+for the Arts and Humanities I did a
+ 
+
+ align:start position:0%
+for the Arts and Humanities I did a
+performance in front of the
+
+ align:start position:0%
+performance in front of the
+ 
+
+ align:start position:0%
+performance in front of the
+Palmer Museum of Art so there's a
+
+ align:start position:0%
+Palmer Museum of Art so there's a
+ 
+
+ align:start position:0%
+Palmer Museum of Art so there's a
+proximity to the museum Art Museum so
+
+ align:start position:0%
+proximity to the museum Art Museum so
+ 
+
+ align:start position:0%
+proximity to the museum Art Museum so
+maybe it's more art like because it's
+
+ align:start position:0%
+maybe it's more art like because it's
+ 
+
+ align:start position:0%
+maybe it's more art like because it's
+closer to the museum I'm not necessarily
+
+ align:start position:0%
+closer to the museum I'm not necessarily
+ 
+
+ align:start position:0%
+closer to the museum I'm not necessarily
+saying that but it was a wonderful open
+
+ align:start position:0%
+saying that but it was a wonderful open
+ 
+
+ align:start position:0%
+saying that but it was a wonderful open
+space that allowed for the middle of
+
+ align:start position:0%
+space that allowed for the middle of
+ 
+
+ align:start position:0%
+space that allowed for the middle of
+campus to to stumble upon and I was it
+
+ align:start position:0%
+campus to to stumble upon and I was it
+ 
+
+ align:start position:0%
+campus to to stumble upon and I was it
+was a Friday afternoon in the middle of
+
+ align:start position:0%
+was a Friday afternoon in the middle of
+ 
+
+ align:start position:0%
+was a Friday afternoon in the middle of
+April set up the press started making
+
+ align:start position:0%
+April set up the press started making
+ 
+
+ align:start position:0%
+April set up the press started making
+filters people stopped by students in
+
+ align:start position:0%
+filters people stopped by students in
+ 
+
+ align:start position:0%
+filters people stopped by students in
+art education and in the School of
+
+ align:start position:0%
+art education and in the School of
+ 
+
+ align:start position:0%
+art education and in the School of
+Visual Arts volunteered to sieve sawdust
+
+ align:start position:0%
+Visual Arts volunteered to sieve sawdust
+ 
+
+ align:start position:0%
+Visual Arts volunteered to sieve sawdust
+and to mix the clay although I knew this
+
+ align:start position:0%
+and to mix the clay although I knew this
+ 
+
+ align:start position:0%
+and to mix the clay although I knew this
+would probably happen I didn't count on
+
+ align:start position:0%
+would probably happen I didn't count on
+ 
+
+ align:start position:0%
+would probably happen I didn't count on
+it happening to the degree that it did
+
+ align:start position:0%
+it happening to the degree that it did
+ 
+
+ align:start position:0%
+it happening to the degree that it did
+in the background of this image and in
+
+ align:start position:0%
+in the background of this image and in
+ 
+
+ align:start position:0%
+in the background of this image and in
+the very foreground you probably see
+
+ align:start position:0%
+the very foreground you probably see
+ 
+
+ align:start position:0%
+the very foreground you probably see
+people who are a little younger than
+
+ align:start position:0%
+people who are a little younger than
+ 
+
+ align:start position:0%
+people who are a little younger than
+what you might expect to see on college
+
+ align:start position:0%
+what you might expect to see on college
+ 
+
+ align:start position:0%
+what you might expect to see on college
+campuses these are children who came
+
+ align:start position:0%
+campuses these are children who came
+ 
+
+ align:start position:0%
+campuses these are children who came
+from the local daycare center on campus
+
+ align:start position:0%
+from the local daycare center on campus
+ 
+
+ align:start position:0%
+from the local daycare center on campus
+and from the local elementary schools
+
+ align:start position:0%
+and from the local elementary schools
+ 
+
+ align:start position:0%
+and from the local elementary schools
+the day care folks knew I was gonna do
+
+ align:start position:0%
+the day care folks knew I was gonna do
+ 
+
+ align:start position:0%
+the day care folks knew I was gonna do
+it because I had talked to them but the
+
+ align:start position:0%
+it because I had talked to them but the
+ 
+
+ align:start position:0%
+it because I had talked to them but the
+people the kids from the elementary
+
+ align:start position:0%
+people the kids from the elementary
+ 
+
+ align:start position:0%
+people the kids from the elementary
+schools their teachers and the kids
+
+ align:start position:0%
+schools their teachers and the kids
+ 
+
+ align:start position:0%
+schools their teachers and the kids
+thought they were going inside the
+
+ align:start position:0%
+thought they were going inside the
+ 
+
+ align:start position:0%
+thought they were going inside the
+museum to see art but when they got off
+
+ align:start position:0%
+museum to see art but when they got off
+ 
+
+ align:start position:0%
+museum to see art but when they got off
+the bus and they saw this guy with the
+
+ align:start position:0%
+the bus and they saw this guy with the
+ 
+
+ align:start position:0%
+the bus and they saw this guy with the
+fedora wedging clay and using this big
+
+ align:start position:0%
+fedora wedging clay and using this big
+ 
+
+ align:start position:0%
+fedora wedging clay and using this big
+guillotine looking machine in the middle
+
+ align:start position:0%
+guillotine looking machine in the middle
+ 
+
+ align:start position:0%
+guillotine looking machine in the middle
+of campus they would have they'd rather
+
+ align:start position:0%
+of campus they would have they'd rather
+ 
+
+ align:start position:0%
+of campus they would have they'd rather
+stay outside and talk to that guy we had
+
+ align:start position:0%
+stay outside and talk to that guy we had
+ 
+
+ align:start position:0%
+stay outside and talk to that guy we had
+wonderful conversations about adequate
+
+ align:start position:0%
+wonderful conversations about adequate
+ 
+
+ align:start position:0%
+wonderful conversations about adequate
+access to clean water former student Sam
+
+ align:start position:0%
+access to clean water former student Sam
+ 
+
+ align:start position:0%
+access to clean water former student Sam
+Bachman who's a ceramic artist
+
+ align:start position:0%
+Bachman who's a ceramic artist
+ 
+
+ align:start position:0%
+Bachman who's a ceramic artist
+dual-degree studio art and art education
+
+ align:start position:0%
+dual-degree studio art and art education
+ 
+
+ align:start position:0%
+dual-degree studio art and art education
+you can have class anywhere you can
+
+ align:start position:0%
+you can have class anywhere you can
+ 
+
+ align:start position:0%
+you can have class anywhere you can
+engage education anywhere you can have
+
+ align:start position:0%
+engage education anywhere you can have
+ 
+
+ align:start position:0%
+engage education anywhere you can have
+learning anywhere if education is a
+
+ align:start position:0%
+learning anywhere if education is a
+ 
+
+ align:start position:0%
+learning anywhere if education is a
+relationship teaching and learning is a
+
+ align:start position:0%
+relationship teaching and learning is a
+ 
+
+ align:start position:0%
+relationship teaching and learning is a
+relationship that's negotiated between
+
+ align:start position:0%
+relationship that's negotiated between
+ 
+
+ align:start position:0%
+relationship that's negotiated between
+multiple parties and there's as much
+
+ align:start position:0%
+multiple parties and there's as much
+ 
+
+ align:start position:0%
+multiple parties and there's as much
+learning going on from whoever thinks
+
+ align:start position:0%
+learning going on from whoever thinks
+ 
+
+ align:start position:0%
+learning going on from whoever thinks
+they might be the teacher as there is
+
+ align:start position:0%
+they might be the teacher as there is
+ 
+
+ align:start position:0%
+they might be the teacher as there is
+from folks who might initially think
+
+ align:start position:0%
+from folks who might initially think
+ 
+
+ align:start position:0%
+from folks who might initially think
+they're the learner everyone in that
+
+ align:start position:0%
+they're the learner everyone in that
+ 
+
+ align:start position:0%
+they're the learner everyone in that
+relationship is learning and teaching
+
+ align:start position:0%
+relationship is learning and teaching
+ 
+
+ align:start position:0%
+relationship is learning and teaching
+simultaneously
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/U2DvFy2qM74.txt b/U2DvFy2qM74.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e82c8bad73f20992b03d44de707cc88073aa08a9
--- /dev/null
+++ b/U2DvFy2qM74.txt
@@ -0,0 +1,651 @@
+align:start position:0%
+ 
+so there's a lot of
+
+ align:start position:0%
+so there's a lot of
+ 
+
+ align:start position:0%
+so there's a lot of
+images in the class partly because we're
+
+ align:start position:0%
+images in the class partly because we're
+ 
+
+ align:start position:0%
+images in the class partly because we're
+studying these materials and
+
+ align:start position:0%
+studying these materials and
+ 
+
+ align:start position:0%
+studying these materials and
+you can see just with the ones sitting
+
+ align:start position:0%
+you can see just with the ones sitting
+ 
+
+ align:start position:0%
+you can see just with the ones sitting
+in front of me they they have this
+
+ align:start position:0%
+in front of me they they have this
+ 
+
+ align:start position:0%
+in front of me they they have this
+porous cellular structure so i show lots
+
+ align:start position:0%
+porous cellular structure so i show lots
+ 
+
+ align:start position:0%
+porous cellular structure so i show lots
+of images of materials
+
+ align:start position:0%
+of images of materials
+ 
+
+ align:start position:0%
+of images of materials
+we also look at how excuse me how the
+
+ align:start position:0%
+we also look at how excuse me how the
+ 
+
+ align:start position:0%
+we also look at how excuse me how the
+images deform
+
+ align:start position:0%
+images deform
+ 
+
+ align:start position:0%
+images deform
+under load and i think perhaps that's
+
+ align:start position:0%
+under load and i think perhaps that's
+ 
+
+ align:start position:0%
+under load and i think perhaps that's
+something that might be a little
+
+ align:start position:0%
+something that might be a little
+ 
+
+ align:start position:0%
+something that might be a little
+unexpected
+
+ align:start position:0%
+unexpected
+ 
+
+ align:start position:0%
+unexpected
+so for instance we have a stage in the
+
+ align:start position:0%
+so for instance we have a stage in the
+ 
+
+ align:start position:0%
+so for instance we have a stage in the
+electron microscope where we can
+
+ align:start position:0%
+electron microscope where we can
+ 
+
+ align:start position:0%
+electron microscope where we can
+actually deform things in the microscope
+
+ align:start position:0%
+actually deform things in the microscope
+ 
+
+ align:start position:0%
+actually deform things in the microscope
+so we and the stage is set up that it
+
+ align:start position:0%
+so we and the stage is set up that it
+ 
+
+ align:start position:0%
+so we and the stage is set up that it
+has a load cell on it
+
+ align:start position:0%
+has a load cell on it
+ 
+
+ align:start position:0%
+has a load cell on it
+and we can also measure how much it
+
+ align:start position:0%
+and we can also measure how much it
+ 
+
+ align:start position:0%
+and we can also measure how much it
+deforms the materials so we can actually
+
+ align:start position:0%
+deforms the materials so we can actually
+ 
+
+ align:start position:0%
+deforms the materials so we can actually
+watch the materials
+
+ align:start position:0%
+watch the materials
+ 
+
+ align:start position:0%
+watch the materials
+as they're deforming so even though the
+
+ align:start position:0%
+as they're deforming so even though the
+ 
+
+ align:start position:0%
+as they're deforming so even though the
+cells may be
+
+ align:start position:0%
+cells may be
+ 
+
+ align:start position:0%
+cells may be
+you know 100 micron kind of size you can
+
+ align:start position:0%
+you know 100 micron kind of size you can
+ 
+
+ align:start position:0%
+you know 100 micron kind of size you can
+watch how they deform and how they fail
+
+ align:start position:0%
+watch how they deform and how they fail
+ 
+
+ align:start position:0%
+watch how they deform and how they fail
+and you can learn a lot about the
+
+ align:start position:0%
+and you can learn a lot about the
+ 
+
+ align:start position:0%
+and you can learn a lot about the
+mechanics from these sorts of
+
+ align:start position:0%
+mechanics from these sorts of
+ 
+
+ align:start position:0%
+mechanics from these sorts of
+observations
+
+ align:start position:0%
+observations
+ 
+
+ align:start position:0%
+observations
+so we have both video of
+
+ align:start position:0%
+so we have both video of
+ 
+
+ align:start position:0%
+so we have both video of
+these deformations and also there's
+
+ align:start position:0%
+these deformations and also there's
+ 
+
+ align:start position:0%
+these deformations and also there's
+still photography
+
+ align:start position:0%
+still photography
+ 
+
+ align:start position:0%
+still photography
+you know at different time points that
+
+ align:start position:0%
+you know at different time points that
+ 
+
+ align:start position:0%
+you know at different time points that
+we show
+
+ align:start position:0%
+we show
+ 
+
+ align:start position:0%
+we show
+you know another kind of interesting
+
+ align:start position:0%
+you know another kind of interesting
+ 
+
+ align:start position:0%
+you know another kind of interesting
+little video clip that i show in the
+
+ align:start position:0%
+little video clip that i show in the
+ 
+
+ align:start position:0%
+little video clip that i show in the
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+is we look at the interactions between
+
+ align:start position:0%
+is we look at the interactions between
+ 
+
+ align:start position:0%
+is we look at the interactions between
+biological cells
+
+ align:start position:0%
+biological cells
+ 
+
+ align:start position:0%
+biological cells
+and tissue engineering scaffolds so for
+
+ align:start position:0%
+and tissue engineering scaffolds so for
+ 
+
+ align:start position:0%
+and tissue engineering scaffolds so for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+uh people who've looked at trying to
+
+ align:start position:0%
+uh people who've looked at trying to
+ 
+
+ align:start position:0%
+uh people who've looked at trying to
+heal
+
+ align:start position:0%
+heal
+ 
+
+ align:start position:0%
+heal
+say burns in skin where there's a large
+
+ align:start position:0%
+say burns in skin where there's a large
+ 
+
+ align:start position:0%
+say burns in skin where there's a large
+area of skin missing
+
+ align:start position:0%
+area of skin missing
+ 
+
+ align:start position:0%
+area of skin missing
+one of the ways that you can do that is
+
+ align:start position:0%
+one of the ways that you can do that is
+ 
+
+ align:start position:0%
+one of the ways that you can do that is
+by using a collagen based
+
+ align:start position:0%
+by using a collagen based
+ 
+
+ align:start position:0%
+by using a collagen based
+tissue engineering scaffold and when
+
+ align:start position:0%
+tissue engineering scaffold and when
+ 
+
+ align:start position:0%
+tissue engineering scaffold and when
+when you have a burn in your skin
+
+ align:start position:0%
+when you have a burn in your skin
+ 
+
+ align:start position:0%
+when you have a burn in your skin
+and it just heals the normal way and you
+
+ align:start position:0%
+and it just heals the normal way and you
+ 
+
+ align:start position:0%
+and it just heals the normal way and you
+get all the scar tissue forming
+
+ align:start position:0%
+get all the scar tissue forming
+ 
+
+ align:start position:0%
+get all the scar tissue forming
+that scar tissue is thought to form in
+
+ align:start position:0%
+that scar tissue is thought to form in
+ 
+
+ align:start position:0%
+that scar tissue is thought to form in
+conjunction with a process of what's
+
+ align:start position:0%
+conjunction with a process of what's
+ 
+
+ align:start position:0%
+conjunction with a process of what's
+called wound contraction
+
+ align:start position:0%
+called wound contraction
+ 
+
+ align:start position:0%
+called wound contraction
+so cells will actually migrate into the
+
+ align:start position:0%
+so cells will actually migrate into the
+ 
+
+ align:start position:0%
+so cells will actually migrate into the
+wound bed and actually mechanically
+
+ align:start position:0%
+wound bed and actually mechanically
+ 
+
+ align:start position:0%
+wound bed and actually mechanically
+pull the edges of the wound together and
+
+ align:start position:0%
+pull the edges of the wound together and
+ 
+
+ align:start position:0%
+pull the edges of the wound together and
+that partly closes the wound and then
+
+ align:start position:0%
+that partly closes the wound and then
+ 
+
+ align:start position:0%
+that partly closes the wound and then
+scar forms as well and those
+
+ align:start position:0%
+scar forms as well and those
+ 
+
+ align:start position:0%
+scar forms as well and those
+two processes are thought to be related
+
+ align:start position:0%
+two processes are thought to be related
+ 
+
+ align:start position:0%
+two processes are thought to be related
+to each other
+
+ align:start position:0%
+to each other
+ 
+
+ align:start position:0%
+to each other
+so i've done a collaboration with
+
+ align:start position:0%
+so i've done a collaboration with
+ 
+
+ align:start position:0%
+so i've done a collaboration with
+professor yanni anas here at mit who
+
+ align:start position:0%
+professor yanni anas here at mit who
+ 
+
+ align:start position:0%
+professor yanni anas here at mit who
+developed one of these scaffolds for
+
+ align:start position:0%
+developed one of these scaffolds for
+ 
+
+ align:start position:0%
+developed one of these scaffolds for
+burn patients and he and i have been
+
+ align:start position:0%
+burn patients and he and i have been
+ 
+
+ align:start position:0%
+burn patients and he and i have been
+interested in this wound contraction
+
+ align:start position:0%
+interested in this wound contraction
+ 
+
+ align:start position:0%
+interested in this wound contraction
+problem and it turns out if you just put
+
+ align:start position:0%
+problem and it turns out if you just put
+ 
+
+ align:start position:0%
+problem and it turns out if you just put
+fibroblasts
+
+ align:start position:0%
+fibroblasts
+ 
+
+ align:start position:0%
+fibroblasts
+skin cells into a dish of culture medium
+
+ align:start position:0%
+skin cells into a dish of culture medium
+ 
+
+ align:start position:0%
+skin cells into a dish of culture medium
+with one of these tissue engineering
+
+ align:start position:0%
+with one of these tissue engineering
+ 
+
+ align:start position:0%
+with one of these tissue engineering
+scaffolds
+
+ align:start position:0%
+scaffolds
+ 
+
+ align:start position:0%
+scaffolds
+they will contract the scaffold and you
+
+ align:start position:0%
+they will contract the scaffold and you
+ 
+
+ align:start position:0%
+they will contract the scaffold and you
+can use
+
+ align:start position:0%
+can use
+ 
+
+ align:start position:0%
+can use
+an optical microscope to actually watch
+
+ align:start position:0%
+an optical microscope to actually watch
+ 
+
+ align:start position:0%
+an optical microscope to actually watch
+the cells do this
+
+ align:start position:0%
+the cells do this
+ 
+
+ align:start position:0%
+the cells do this
+so you can focus on an individual cell
+
+ align:start position:0%
+so you can focus on an individual cell
+ 
+
+ align:start position:0%
+so you can focus on an individual cell
+and you can see the cell elongating you
+
+ align:start position:0%
+and you can see the cell elongating you
+ 
+
+ align:start position:0%
+and you can see the cell elongating you
+can see the scaffold itself
+
+ align:start position:0%
+can see the scaffold itself
+ 
+
+ align:start position:0%
+can see the scaffold itself
+contracting and you can see this whole
+
+ align:start position:0%
+contracting and you can see this whole
+ 
+
+ align:start position:0%
+contracting and you can see this whole
+process so this is one of the little
+
+ align:start position:0%
+process so this is one of the little
+ 
+
+ align:start position:0%
+process so this is one of the little
+video
+
+ align:start position:0%
+video
+ 
+
+ align:start position:0%
+video
+clips that we show in class and the
+
+ align:start position:0%
+clips that we show in class and the
+ 
+
+ align:start position:0%
+clips that we show in class and the
+students always
+
+ align:start position:0%
+students always
+ 
+
+ align:start position:0%
+students always
+find that kind of fascinating
\ No newline at end of file
diff --git a/UbjZgxIjQfk.txt b/UbjZgxIjQfk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8f0066a8a020085e4db2e978241c9d15366064d4
--- /dev/null
+++ b/UbjZgxIjQfk.txt
@@ -0,0 +1,8911 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu settle down a weekend
+
+ align:start position:0%
+ocw.mit.edu settle down a weekend
+ 
+
+ align:start position:0%
+ocw.mit.edu settle down a weekend
+doesn't begin until at least after the
+
+ align:start position:0%
+doesn't begin until at least after the
+ 
+
+ align:start position:0%
+doesn't begin until at least after the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lecture work first then play couple of
+
+ align:start position:0%
+lecture work first then play couple of
+ 
+
+ align:start position:0%
+lecture work first then play couple of
+announcements next Tuesday Quiz 2 based
+
+ align:start position:0%
+announcements next Tuesday Quiz 2 based
+ 
+
+ align:start position:0%
+announcements next Tuesday Quiz 2 based
+on the subject matter of homework 2 um
+
+ align:start position:0%
+on the subject matter of homework 2 um
+ 
+
+ align:start position:0%
+on the subject matter of homework 2 um
+the periodic table test will be on
+
+ align:start position:0%
+the periodic table test will be on
+ 
+
+ align:start position:0%
+the periodic table test will be on
+Thursday and it's going to be not before
+
+ align:start position:0%
+Thursday and it's going to be not before
+ 
+
+ align:start position:0%
+Thursday and it's going to be not before
+too long we'll have time for the monthly
+
+ align:start position:0%
+too long we'll have time for the monthly
+ 
+
+ align:start position:0%
+too long we'll have time for the monthly
+test the first monthly test the
+
+ align:start position:0%
+test the first monthly test the
+ 
+
+ align:start position:0%
+test the first monthly test the
+pneumonics contest deadline is uh week
+
+ align:start position:0%
+pneumonics contest deadline is uh week
+ 
+
+ align:start position:0%
+pneumonics contest deadline is uh week
+from today 5:00 send it to me by email
+
+ align:start position:0%
+from today 5:00 send it to me by email
+ 
+
+ align:start position:0%
+from today 5:00 send it to me by email
+if you want to win that hot tie or that
+
+ align:start position:0%
+if you want to win that hot tie or that
+ 
+
+ align:start position:0%
+if you want to win that hot tie or that
+hot
+
+ align:start position:0%
+hot
+ 
+
+ align:start position:0%
+hot
+scarf um it's come to my attention that
+
+ align:start position:0%
+scarf um it's come to my attention that
+ 
+
+ align:start position:0%
+scarf um it's come to my attention that
+people are moving freely about
+
+ align:start position:0%
+people are moving freely about
+ 
+
+ align:start position:0%
+people are moving freely about
+recitations without uh arranging through
+
+ align:start position:0%
+recitations without uh arranging through
+ 
+
+ align:start position:0%
+recitations without uh arranging through
+my office and some of the recitation
+
+ align:start position:0%
+my office and some of the recitation
+ 
+
+ align:start position:0%
+my office and some of the recitation
+sections are uh uncomfortably large
+
+ align:start position:0%
+sections are uh uncomfortably large
+ 
+
+ align:start position:0%
+sections are uh uncomfortably large
+which defeats the purpose of the
+
+ align:start position:0%
+which defeats the purpose of the
+ 
+
+ align:start position:0%
+which defeats the purpose of the
+recitation uh in part I mean we want you
+
+ align:start position:0%
+recitation uh in part I mean we want you
+ 
+
+ align:start position:0%
+recitation uh in part I mean we want you
+to have access to the instructor and if
+
+ align:start position:0%
+to have access to the instructor and if
+ 
+
+ align:start position:0%
+to have access to the instructor and if
+we've got 30 students there instead of
+
+ align:start position:0%
+we've got 30 students there instead of
+ 
+
+ align:start position:0%
+we've got 30 students there instead of
+20 that uh dilutes your access so uh we
+
+ align:start position:0%
+20 that uh dilutes your access so uh we
+ 
+
+ align:start position:0%
+20 that uh dilutes your access so uh we
+insist that you go to the section that
+
+ align:start position:0%
+insist that you go to the section that
+ 
+
+ align:start position:0%
+insist that you go to the section that
+you're assigned to and if you must
+
+ align:start position:0%
+you're assigned to and if you must
+ 
+
+ align:start position:0%
+you're assigned to and if you must
+change because youve got a EUR up or
+
+ align:start position:0%
+change because youve got a EUR up or
+ 
+
+ align:start position:0%
+change because youve got a EUR up or
+you've got a some other activity um
+
+ align:start position:0%
+you've got a some other activity um
+ 
+
+ align:start position:0%
+you've got a some other activity um
+please do it through my office so that
+
+ align:start position:0%
+please do it through my office so that
+ 
+
+ align:start position:0%
+please do it through my office so that
+we can uh make the learning experience
+
+ align:start position:0%
+we can uh make the learning experience
+ 
+
+ align:start position:0%
+we can uh make the learning experience
+good for uh the the majority and not
+
+ align:start position:0%
+good for uh the the majority and not
+ 
+
+ align:start position:0%
+good for uh the the majority and not
+just for the the
+
+ align:start position:0%
+just for the the
+ 
+
+ align:start position:0%
+just for the the
+few um oh there was something else I
+
+ align:start position:0%
+few um oh there was something else I
+ 
+
+ align:start position:0%
+few um oh there was something else I
+think yes I just uh just learned
+
+ align:start position:0%
+think yes I just uh just learned
+ 
+
+ align:start position:0%
+think yes I just uh just learned
+yesterday that to my somewhat
+
+ align:start position:0%
+yesterday that to my somewhat
+ 
+
+ align:start position:0%
+yesterday that to my somewhat
+disappointment you know my favorite
+
+ align:start position:0%
+disappointment you know my favorite
+ 
+
+ align:start position:0%
+disappointment you know my favorite
+transuranic element is 111 because it
+
+ align:start position:0%
+transuranic element is 111 because it
+ 
+
+ align:start position:0%
+transuranic element is 111 because it
+goes as unium but uh it has been
+
+ align:start position:0%
+goes as unium but uh it has been
+ 
+
+ align:start position:0%
+goes as unium but uh it has been
+isolated by the team in uh darad in
+
+ align:start position:0%
+isolated by the team in uh darad in
+ 
+
+ align:start position:0%
+isolated by the team in uh darad in
+Germany and they have proposed the name
+
+ align:start position:0%
+Germany and they have proposed the name
+ 
+
+ align:start position:0%
+Germany and they have proposed the name
+renum after villam renken who is the uh
+
+ align:start position:0%
+renum after villam renken who is the uh
+ 
+
+ align:start position:0%
+renum after villam renken who is the uh
+discoverer of X-rays and that's now
+
+ align:start position:0%
+discoverer of X-rays and that's now
+ 
+
+ align:start position:0%
+discoverer of X-rays and that's now
+before the international Union of pure
+
+ align:start position:0%
+before the international Union of pure
+ 
+
+ align:start position:0%
+before the international Union of pure
+and applied chemistry so maybe before uh
+
+ align:start position:0%
+and applied chemistry so maybe before uh
+ 
+
+ align:start position:0%
+and applied chemistry so maybe before uh
+the fall is out we'll have to change I
+
+ align:start position:0%
+the fall is out we'll have to change I
+ 
+
+ align:start position:0%
+the fall is out we'll have to change I
+already showed you that this is now darh
+
+ align:start position:0%
+already showed you that this is now darh
+ 
+
+ align:start position:0%
+already showed you that this is now darh
+stadium so we're going to have a whole
+
+ align:start position:0%
+stadium so we're going to have a whole
+ 
+
+ align:start position:0%
+stadium so we're going to have a whole
+bunch of looks like M nearium so there
+
+ align:start position:0%
+bunch of looks like M nearium so there
+ 
+
+ align:start position:0%
+bunch of looks like M nearium so there
+there going to be a whole bunch of
+
+ align:start position:0%
+there going to be a whole bunch of
+ 
+
+ align:start position:0%
+there going to be a whole bunch of
+German names along here pretty soon so
+
+ align:start position:0%
+German names along here pretty soon so
+ 
+
+ align:start position:0%
+German names along here pretty soon so
+somebody better get busy over in
+
+ align:start position:0%
+somebody better get busy over in
+ 
+
+ align:start position:0%
+somebody better get busy over in
+Berkeley what are they doing there huh
+
+ align:start position:0%
+Berkeley what are they doing there huh
+ 
+
+ align:start position:0%
+Berkeley what are they doing there huh
+what's going on anybody
+
+ align:start position:0%
+what's going on anybody
+ 
+
+ align:start position:0%
+what's going on anybody
+know people are
+
+ align:start position:0%
+know people are
+ 
+
+ align:start position:0%
+know people are
+sleeping okay so la let's get to the
+
+ align:start position:0%
+sleeping okay so la let's get to the
+ 
+
+ align:start position:0%
+sleeping okay so la let's get to the
+lesson last day last day we studied the
+
+ align:start position:0%
+lesson last day last day we studied the
+ 
+
+ align:start position:0%
+lesson last day last day we studied the
+bore model for one electron atoms and uh
+
+ align:start position:0%
+bore model for one electron atoms and uh
+ 
+
+ align:start position:0%
+bore model for one electron atoms and uh
+the bore model showed us that through
+
+ align:start position:0%
+the bore model showed us that through
+ 
+
+ align:start position:0%
+the bore model showed us that through
+the quantum condition all of these
+
+ align:start position:0%
+the quantum condition all of these
+ 
+
+ align:start position:0%
+the quantum condition all of these
+quantities uh were Quant qued they were
+
+ align:start position:0%
+quantities uh were Quant qued they were
+ 
+
+ align:start position:0%
+quantities uh were Quant qued they were
+functions of the quantum number n and
+
+ align:start position:0%
+functions of the quantum number n and
+ 
+
+ align:start position:0%
+functions of the quantum number n and
+later in the lecture we began to look
+
+ align:start position:0%
+later in the lecture we began to look
+ 
+
+ align:start position:0%
+later in the lecture we began to look
+for reconciliation between the bore
+
+ align:start position:0%
+for reconciliation between the bore
+ 
+
+ align:start position:0%
+for reconciliation between the bore
+model and balmer's Analysis of angstroms
+
+ align:start position:0%
+model and balmer's Analysis of angstroms
+ 
+
+ align:start position:0%
+model and balmer's Analysis of angstroms
+spectral line study of atomic hydrogen
+
+ align:start position:0%
+spectral line study of atomic hydrogen
+ 
+
+ align:start position:0%
+spectral line study of atomic hydrogen
+and so we looked at the prism
+
+ align:start position:0%
+and so we looked at the prism
+ 
+
+ align:start position:0%
+and so we looked at the prism
+spectrograph and the gas discharge tube
+
+ align:start position:0%
+spectrograph and the gas discharge tube
+ 
+
+ align:start position:0%
+spectrograph and the gas discharge tube
+and I showed you the energetics of what
+
+ align:start position:0%
+and I showed you the energetics of what
+ 
+
+ align:start position:0%
+and I showed you the energetics of what
+goes on in there and towards the end of
+
+ align:start position:0%
+goes on in there and towards the end of
+ 
+
+ align:start position:0%
+goes on in there and towards the end of
+the lecture we started talking about the
+
+ align:start position:0%
+the lecture we started talking about the
+ 
+
+ align:start position:0%
+the lecture we started talking about the
+actual energetics of collision and I
+
+ align:start position:0%
+actual energetics of collision and I
+ 
+
+ align:start position:0%
+actual energetics of collision and I
+want to return to that so let's put up
+
+ align:start position:0%
+want to return to that so let's put up
+ 
+
+ align:start position:0%
+want to return to that so let's put up
+that uh sketch again where we're looking
+
+ align:start position:0%
+that uh sketch again where we're looking
+ 
+
+ align:start position:0%
+that uh sketch again where we're looking
+at the incident electron and this is the
+
+ align:start position:0%
+at the incident electron and this is the
+ 
+
+ align:start position:0%
+at the incident electron and this is the
+electron that is accelerating off the
+
+ align:start position:0%
+electron that is accelerating off the
+ 
+
+ align:start position:0%
+electron that is accelerating off the
+cathode there's electrons all over and I
+
+ align:start position:0%
+cathode there's electrons all over and I
+ 
+
+ align:start position:0%
+cathode there's electrons all over and I
+want to make sure we're not confusing
+
+ align:start position:0%
+want to make sure we're not confusing
+ 
+
+ align:start position:0%
+want to make sure we're not confusing
+one electron for another so this
+
+ align:start position:0%
+one electron for another so this
+ 
+
+ align:start position:0%
+one electron for another so this
+electron I'm talking about here is this
+
+ align:start position:0%
+electron I'm talking about here is this
+ 
+
+ align:start position:0%
+electron I'm talking about here is this
+one that is moving off the cathode and
+
+ align:start position:0%
+one that is moving off the cathode and
+ 
+
+ align:start position:0%
+one that is moving off the cathode and
+towards the anode and on root is going
+
+ align:start position:0%
+towards the anode and on root is going
+ 
+
+ align:start position:0%
+towards the anode and on root is going
+to collide with some Atomic hydrogen so
+
+ align:start position:0%
+to collide with some Atomic hydrogen so
+ 
+
+ align:start position:0%
+to collide with some Atomic hydrogen so
+this is the instant an electron and it
+
+ align:start position:0%
+this is the instant an electron and it
+ 
+
+ align:start position:0%
+this is the instant an electron and it
+has it has kinetic energy it has kinetic
+
+ align:start position:0%
+has it has kinetic energy it has kinetic
+ 
+
+ align:start position:0%
+has it has kinetic energy it has kinetic
+energy of I'm going to denote it e
+
+ align:start position:0%
+energy of I'm going to denote it e
+ 
+
+ align:start position:0%
+energy of I'm going to denote it e
+incident 12 MV squared it's not bound
+
+ align:start position:0%
+incident 12 MV squared it's not bound
+ 
+
+ align:start position:0%
+incident 12 MV squared it's not bound
+it's moving along and let's sub script
+
+ align:start position:0%
+it's moving along and let's sub script
+ 
+
+ align:start position:0%
+it's moving along and let's sub script
+this as well incident velocity incident
+
+ align:start position:0%
+this as well incident velocity incident
+ 
+
+ align:start position:0%
+this as well incident velocity incident
+velocity electron rest Mass incident
+
+ align:start position:0%
+velocity electron rest Mass incident
+ 
+
+ align:start position:0%
+velocity electron rest Mass incident
+energy and it's going to collide with a
+
+ align:start position:0%
+energy and it's going to collide with a
+ 
+
+ align:start position:0%
+energy and it's going to collide with a
+hydrogen atom at some point and I'm
+
+ align:start position:0%
+hydrogen atom at some point and I'm
+ 
+
+ align:start position:0%
+hydrogen atom at some point and I'm
+going to draw the hydrogen atom
+
+ align:start position:0%
+going to draw the hydrogen atom
+ 
+
+ align:start position:0%
+going to draw the hydrogen atom
+schematically like this with a proton in
+
+ align:start position:0%
+schematically like this with a proton in
+ 
+
+ align:start position:0%
+schematically like this with a proton in
+the nucleus and a lone electron in some
+
+ align:start position:0%
+the nucleus and a lone electron in some
+ 
+
+ align:start position:0%
+the nucleus and a lone electron in some
+orbit here and if the energy if the
+
+ align:start position:0%
+orbit here and if the energy if the
+ 
+
+ align:start position:0%
+orbit here and if the energy if the
+energy of the incident electron is
+
+ align:start position:0%
+energy of the incident electron is
+ 
+
+ align:start position:0%
+energy of the incident electron is
+greater than the energy required for
+
+ align:start position:0%
+greater than the energy required for
+ 
+
+ align:start position:0%
+greater than the energy required for
+some transition within the uh hydrogen
+
+ align:start position:0%
+some transition within the uh hydrogen
+ 
+
+ align:start position:0%
+some transition within the uh hydrogen
+then it's possible that this electron
+
+ align:start position:0%
+then it's possible that this electron
+ 
+
+ align:start position:0%
+then it's possible that this electron
+will capture some of the energy from the
+
+ align:start position:0%
+will capture some of the energy from the
+ 
+
+ align:start position:0%
+will capture some of the energy from the
+instant electron on and be excited to
+
+ align:start position:0%
+instant electron on and be excited to
+ 
+
+ align:start position:0%
+instant electron on and be excited to
+some other state so let's put that on
+
+ align:start position:0%
+some other state so let's put that on
+ 
+
+ align:start position:0%
+some other state so let's put that on
+let's call this some initial State and
+
+ align:start position:0%
+let's call this some initial State and
+ 
+
+ align:start position:0%
+let's call this some initial State and
+let's call this some final State and
+
+ align:start position:0%
+let's call this some final State and
+ 
+
+ align:start position:0%
+let's call this some final State and
+that's only going to occur when this
+
+ align:start position:0%
+that's only going to occur when this
+ 
+
+ align:start position:0%
+that's only going to occur when this
+incident energy is greater than the
+
+ align:start position:0%
+incident energy is greater than the
+ 
+
+ align:start position:0%
+incident energy is greater than the
+energy of transition so we've got two
+
+ align:start position:0%
+energy of transition so we've got two
+ 
+
+ align:start position:0%
+energy of transition so we've got two
+electrons here here's a moving electron
+
+ align:start position:0%
+electrons here here's a moving electron
+ 
+
+ align:start position:0%
+electrons here here's a moving electron
+free electron this one is bound so this
+
+ align:start position:0%
+free electron this one is bound so this
+ 
+
+ align:start position:0%
+free electron this one is bound so this
+is in the Target or in the
+
+ align:start position:0%
+is in the Target or in the
+ 
+
+ align:start position:0%
+is in the Target or in the
+specimen which in this case is atomic
+
+ align:start position:0%
+specimen which in this case is atomic
+ 
+
+ align:start position:0%
+specimen which in this case is atomic
+hydrogen so let's look at what happens
+
+ align:start position:0%
+hydrogen so let's look at what happens
+ 
+
+ align:start position:0%
+hydrogen so let's look at what happens
+here the excitation occurs and we can
+
+ align:start position:0%
+here the excitation occurs and we can
+ 
+
+ align:start position:0%
+here the excitation occurs and we can
+get the energy required for this uh
+
+ align:start position:0%
+get the energy required for this uh
+ 
+
+ align:start position:0%
+get the energy required for this uh
+transition by using the bore model the
+
+ align:start position:0%
+transition by using the bore model the
+ 
+
+ align:start position:0%
+transition by using the bore model the
+bore model gives this value it gives the
+
+ align:start position:0%
+bore model gives this value it gives the
+ 
+
+ align:start position:0%
+bore model gives this value it gives the
+value as I think came right out of the
+
+ align:start position:0%
+value as I think came right out of the
+ 
+
+ align:start position:0%
+value as I think came right out of the
+the postulates the Delta e of transition
+
+ align:start position:0%
+the postulates the Delta e of transition
+ 
+
+ align:start position:0%
+the postulates the Delta e of transition
+is going to equal minus K I'm putting it
+
+ align:start position:0%
+is going to equal minus K I'm putting it
+ 
+
+ align:start position:0%
+is going to equal minus K I'm putting it
+up generally z^2 to I allow for uh
+
+ align:start position:0%
+up generally z^2 to I allow for uh
+ 
+
+ align:start position:0%
+up generally z^2 to I allow for uh
+higher Z level one electron atoms and
+
+ align:start position:0%
+higher Z level one electron atoms and
+ 
+
+ align:start position:0%
+higher Z level one electron atoms and
+it's one over
+
+ align:start position:0%
+it's one over
+ 
+
+ align:start position:0%
+it's one over
+final quantum number squared minus one
+
+ align:start position:0%
+final quantum number squared minus one
+ 
+
+ align:start position:0%
+final quantum number squared minus one
+over initial quantum number squared so
+
+ align:start position:0%
+over initial quantum number squared so
+ 
+
+ align:start position:0%
+over initial quantum number squared so
+that gives you the amount of energy and
+
+ align:start position:0%
+that gives you the amount of energy and
+ 
+
+ align:start position:0%
+that gives you the amount of energy and
+that energy is going to be taken away
+
+ align:start position:0%
+that energy is going to be taken away
+ 
+
+ align:start position:0%
+that energy is going to be taken away
+from the kinetic energy of the incident
+
+ align:start position:0%
+from the kinetic energy of the incident
+ 
+
+ align:start position:0%
+from the kinetic energy of the incident
+electron which then will make its merry
+
+ align:start position:0%
+electron which then will make its merry
+ 
+
+ align:start position:0%
+electron which then will make its merry
+way off after the collision and I'm
+
+ align:start position:0%
+way off after the collision and I'm
+ 
+
+ align:start position:0%
+way off after the collision and I'm
+purposely making that Vector shorter to
+
+ align:start position:0%
+purposely making that Vector shorter to
+ 
+
+ align:start position:0%
+purposely making that Vector shorter to
+indicate that this electron has been
+
+ align:start position:0%
+indicate that this electron has been
+ 
+
+ align:start position:0%
+indicate that this electron has been
+slowed and we call this electron the
+
+ align:start position:0%
+slowed and we call this electron the
+ 
+
+ align:start position:0%
+slowed and we call this electron the
+scattered
+
+ align:start position:0%
+scattered
+ 
+
+ align:start position:0%
+scattered
+electron scattered by the collision with
+
+ align:start position:0%
+electron scattered by the collision with
+ 
+
+ align:start position:0%
+electron scattered by the collision with
+the target hydrogen and it has kinetic
+
+ align:start position:0%
+the target hydrogen and it has kinetic
+ 
+
+ align:start position:0%
+the target hydrogen and it has kinetic
+energy e sub scattered as 12 M v^2
+
+ align:start position:0%
+energy e sub scattered as 12 M v^2
+ 
+
+ align:start position:0%
+energy e sub scattered as 12 M v^2
+scattered the mass of the electron
+
+ align:start position:0%
+scattered the mass of the electron
+ 
+
+ align:start position:0%
+scattered the mass of the electron
+doesn't change but its velocity
+
+ align:start position:0%
+doesn't change but its velocity
+ 
+
+ align:start position:0%
+doesn't change but its velocity
+certainly decreases as a result of this
+
+ align:start position:0%
+certainly decreases as a result of this
+ 
+
+ align:start position:0%
+certainly decreases as a result of this
+Collision but that's not the end of the
+
+ align:start position:0%
+Collision but that's not the end of the
+ 
+
+ align:start position:0%
+Collision but that's not the end of the
+story that's not the end of the story uh
+
+ align:start position:0%
+story that's not the end of the story uh
+ 
+
+ align:start position:0%
+story that's not the end of the story uh
+what happens here is that this electron
+
+ align:start position:0%
+what happens here is that this electron
+ 
+
+ align:start position:0%
+what happens here is that this electron
+that's excited is there in an
+
+ align:start position:0%
+that's excited is there in an
+ 
+
+ align:start position:0%
+that's excited is there in an
+unsustainable basis it's just a on shot
+
+ align:start position:0%
+unsustainable basis it's just a on shot
+ 
+
+ align:start position:0%
+unsustainable basis it's just a on shot
+deal so the electron wants to fall back
+
+ align:start position:0%
+deal so the electron wants to fall back
+ 
+
+ align:start position:0%
+deal so the electron wants to fall back
+down to the lower energy State and it
+
+ align:start position:0%
+down to the lower energy State and it
+ 
+
+ align:start position:0%
+down to the lower energy State and it
+does so it falls back down and when it
+
+ align:start position:0%
+does so it falls back down and when it
+ 
+
+ align:start position:0%
+does so it falls back down and when it
+does so it gives off that energy in the
+
+ align:start position:0%
+does so it gives off that energy in the
+ 
+
+ align:start position:0%
+does so it gives off that energy in the
+form of a photon so we have a an emitted
+
+ align:start position:0%
+form of a photon so we have a an emitted
+ 
+
+ align:start position:0%
+form of a photon so we have a an emitted
+Photon and it has energy H new or HC
+
+ align:start position:0%
+Photon and it has energy H new or HC
+ 
+
+ align:start position:0%
+Photon and it has energy H new or HC
+over Lambda or
+
+ align:start position:0%
+over Lambda or
+ 
+
+ align:start position:0%
+over Lambda or
+HC new
+
+ align:start position:0%
+HC new
+ 
+
+ align:start position:0%
+HC new
+bar and it is the set of these emitted
+
+ align:start position:0%
+bar and it is the set of these emitted
+ 
+
+ align:start position:0%
+bar and it is the set of these emitted
+photons that anstrom
+
+ align:start position:0%
+photons that anstrom
+ 
+
+ align:start position:0%
+photons that anstrom
+studied anstrom was studying these
+
+ align:start position:0%
+studied anstrom was studying these
+ 
+
+ align:start position:0%
+studied anstrom was studying these
+emitted photons and clearly there's some
+
+ align:start position:0%
+emitted photons and clearly there's some
+ 
+
+ align:start position:0%
+emitted photons and clearly there's some
+relationship between the wavelengths
+
+ align:start position:0%
+relationship between the wavelengths
+ 
+
+ align:start position:0%
+relationship between the wavelengths
+that he observed and the energy levels
+
+ align:start position:0%
+that he observed and the energy levels
+ 
+
+ align:start position:0%
+that he observed and the energy levels
+within the atomic hydrogen and all of
+
+ align:start position:0%
+within the atomic hydrogen and all of
+ 
+
+ align:start position:0%
+within the atomic hydrogen and all of
+this this whole process is subject to uh
+
+ align:start position:0%
+this this whole process is subject to uh
+ 
+
+ align:start position:0%
+this this whole process is subject to uh
+conservation so let's get that up Let's
+
+ align:start position:0%
+conservation so let's get that up Let's
+ 
+
+ align:start position:0%
+conservation so let's get that up Let's
+uh make sure that we don't violate any
+
+ align:start position:0%
+uh make sure that we don't violate any
+ 
+
+ align:start position:0%
+uh make sure that we don't violate any
+basic laws so we're going to say that
+
+ align:start position:0%
+basic laws so we're going to say that
+ 
+
+ align:start position:0%
+basic laws so we're going to say that
+the energy of the incident electron will
+
+ align:start position:0%
+the energy of the incident electron will
+ 
+
+ align:start position:0%
+the energy of the incident electron will
+then be spread
+
+ align:start position:0%
+then be spread
+ 
+
+ align:start position:0%
+then be spread
+across
+
+ align:start position:0%
+across
+ 
+
+ align:start position:0%
+across
+the electron energy of transition within
+
+ align:start position:0%
+the electron energy of transition within
+ 
+
+ align:start position:0%
+the electron energy of transition within
+the Target and whatever is left over
+
+ align:start position:0%
+the Target and whatever is left over
+ 
+
+ align:start position:0%
+the Target and whatever is left over
+will remain with the electron at some
+
+ align:start position:0%
+will remain with the electron at some
+ 
+
+ align:start position:0%
+will remain with the electron at some
+reduced value and what I've shown here
+
+ align:start position:0%
+reduced value and what I've shown here
+ 
+
+ align:start position:0%
+reduced value and what I've shown here
+I'm applying it to the experiment that
+
+ align:start position:0%
+I'm applying it to the experiment that
+ 
+
+ align:start position:0%
+I'm applying it to the experiment that
+anstrom conducted in which he
+
+ align:start position:0%
+anstrom conducted in which he
+ 
+
+ align:start position:0%
+anstrom conducted in which he
+accelerated electrons but it's the same
+
+ align:start position:0%
+accelerated electrons but it's the same
+ 
+
+ align:start position:0%
+accelerated electrons but it's the same
+calculation for any particle so this is
+
+ align:start position:0%
+calculation for any particle so this is
+ 
+
+ align:start position:0%
+calculation for any particle so this is
+for all incident particles be subject to
+
+ align:start position:0%
+for all incident particles be subject to
+ 
+
+ align:start position:0%
+for all incident particles be subject to
+this all incident
+
+ align:start position:0%
+this all incident
+ 
+
+ align:start position:0%
+this all incident
+particles all incident particles so it
+
+ align:start position:0%
+particles all incident particles so it
+ 
+
+ align:start position:0%
+particles all incident particles so it
+could be uh obviously electrons we could
+
+ align:start position:0%
+could be uh obviously electrons we could
+ 
+
+ align:start position:0%
+could be uh obviously electrons we could
+accelerate protons we could accelerate
+
+ align:start position:0%
+accelerate protons we could accelerate
+ 
+
+ align:start position:0%
+accelerate protons we could accelerate
+neutrons we could accelerate alpha
+
+ align:start position:0%
+neutrons we could accelerate alpha
+ 
+
+ align:start position:0%
+neutrons we could accelerate alpha
+particles we could accelerate argon ions
+
+ align:start position:0%
+particles we could accelerate argon ions
+ 
+
+ align:start position:0%
+particles we could accelerate argon ions
+there's a host of incident particles
+
+ align:start position:0%
+there's a host of incident particles
+ 
+
+ align:start position:0%
+there's a host of incident particles
+consider them only as bearers of energy
+
+ align:start position:0%
+consider them only as bearers of energy
+ 
+
+ align:start position:0%
+consider them only as bearers of energy
+they're energy transfer vehicles and
+
+ align:start position:0%
+they're energy transfer vehicles and
+ 
+
+ align:start position:0%
+they're energy transfer vehicles and
+they transfer energy here provided that
+
+ align:start position:0%
+they transfer energy here provided that
+ 
+
+ align:start position:0%
+they transfer energy here provided that
+the energy is high enough to cause
+
+ align:start position:0%
+the energy is high enough to cause
+ 
+
+ align:start position:0%
+the energy is high enough to cause
+excitation our another way of looking at
+
+ align:start position:0%
+excitation our another way of looking at
+ 
+
+ align:start position:0%
+excitation our another way of looking at
+it conceptually is this is a probe beam
+
+ align:start position:0%
+it conceptually is this is a probe beam
+ 
+
+ align:start position:0%
+it conceptually is this is a probe beam
+a probe beam or maybe a
+
+ align:start position:0%
+a probe beam or maybe a
+ 
+
+ align:start position:0%
+a probe beam or maybe a
+stimulus and the integral of the energy
+
+ align:start position:0%
+stimulus and the integral of the energy
+ 
+
+ align:start position:0%
+stimulus and the integral of the energy
+of the particle after interaction and
+
+ align:start position:0%
+of the particle after interaction and
+ 
+
+ align:start position:0%
+of the particle after interaction and
+the emitted photons that collectivity is
+
+ align:start position:0%
+the emitted photons that collectivity is
+ 
+
+ align:start position:0%
+the emitted photons that collectivity is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+response this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+response okay this is the response so
+
+ align:start position:0%
+response okay this is the response so
+ 
+
+ align:start position:0%
+response okay this is the response so
+what does this mean this means that we
+
+ align:start position:0%
+what does this mean this means that we
+ 
+
+ align:start position:0%
+what does this mean this means that we
+could interrogate some atom of unknown
+
+ align:start position:0%
+could interrogate some atom of unknown
+ 
+
+ align:start position:0%
+could interrogate some atom of unknown
+identity and on the basis of these
+
+ align:start position:0%
+identity and on the basis of these
+ 
+
+ align:start position:0%
+identity and on the basis of these
+values infer deduce the identity of that
+
+ align:start position:0%
+values infer deduce the identity of that
+ 
+
+ align:start position:0%
+values infer deduce the identity of that
+species and we talked at the end of last
+
+ align:start position:0%
+species and we talked at the end of last
+ 
+
+ align:start position:0%
+species and we talked at the end of last
+day about how this is applied in
+
+ align:start position:0%
+day about how this is applied in
+ 
+
+ align:start position:0%
+day about how this is applied in
+analyzing the chemical composition of
+
+ align:start position:0%
+analyzing the chemical composition of
+ 
+
+ align:start position:0%
+analyzing the chemical composition of
+stars so the radiation goes a long way
+
+ align:start position:0%
+stars so the radiation goes a long way
+ 
+
+ align:start position:0%
+stars so the radiation goes a long way
+and we're able to use the information
+
+ align:start position:0%
+and we're able to use the information
+ 
+
+ align:start position:0%
+and we're able to use the information
+contained therein to conduct
+
+ align:start position:0%
+contained therein to conduct
+ 
+
+ align:start position:0%
+contained therein to conduct
+analyses
+
+ align:start position:0%
+analyses
+ 
+
+ align:start position:0%
+analyses
+so let's see how this will help us
+
+ align:start position:0%
+so let's see how this will help us
+ 
+
+ align:start position:0%
+so let's see how this will help us
+reconcile the bore model to balmer's
+
+ align:start position:0%
+reconcile the bore model to balmer's
+ 
+
+ align:start position:0%
+reconcile the bore model to balmer's
+analysis of enstrom's data so let's see
+
+ align:start position:0%
+analysis of enstrom's data so let's see
+ 
+
+ align:start position:0%
+analysis of enstrom's data so let's see
+I think we have to go back to to the
+
+ align:start position:0%
+I think we have to go back to to the
+ 
+
+ align:start position:0%
+I think we have to go back to to the
+bore model if we go over to
+
+ align:start position:0%
+bore model if we go over to
+ 
+
+ align:start position:0%
+bore model if we go over to
+bore this thing's decided that it wants
+
+ align:start position:0%
+bore this thing's decided that it wants
+ 
+
+ align:start position:0%
+bore this thing's decided that it wants
+to sleep ah finally see it's Friday the
+
+ align:start position:0%
+to sleep ah finally see it's Friday the
+ 
+
+ align:start position:0%
+to sleep ah finally see it's Friday the
+computer's decided it's going to goof
+
+ align:start position:0%
+computer's decided it's going to goof
+ 
+
+ align:start position:0%
+computer's decided it's going to goof
+off a little bit so we're going to use
+
+ align:start position:0%
+off a little bit so we're going to use
+ 
+
+ align:start position:0%
+off a little bit so we're going to use
+uh postulate number six in order to help
+
+ align:start position:0%
+uh postulate number six in order to help
+ 
+
+ align:start position:0%
+uh postulate number six in order to help
+elucidate what's going on here so we can
+
+ align:start position:0%
+elucidate what's going on here so we can
+ 
+
+ align:start position:0%
+elucidate what's going on here so we can
+then resume here and say that Delta e of
+
+ align:start position:0%
+then resume here and say that Delta e of
+ 
+
+ align:start position:0%
+then resume here and say that Delta e of
+the transition is the energy of the
+
+ align:start position:0%
+the transition is the energy of the
+ 
+
+ align:start position:0%
+the transition is the energy of the
+final State minus the energy of the
+
+ align:start position:0%
+final State minus the energy of the
+ 
+
+ align:start position:0%
+final State minus the energy of the
+initial State that's always the case we
+
+ align:start position:0%
+initial State that's always the case we
+ 
+
+ align:start position:0%
+initial State that's always the case we
+always say that the difference goes
+
+ align:start position:0%
+always say that the difference goes
+ 
+
+ align:start position:0%
+always say that the difference goes
+final minus initial and we can represent
+
+ align:start position:0%
+final minus initial and we can represent
+ 
+
+ align:start position:0%
+final minus initial and we can represent
+that as the product kz^ 2 1 / N Final
+
+ align:start position:0%
+that as the product kz^ 2 1 / N Final
+ 
+
+ align:start position:0%
+that as the product kz^ 2 1 / N Final
+squ - 1 over initial squared and
+
+ align:start position:0%
+squ - 1 over initial squared and
+ 
+
+ align:start position:0%
+squ - 1 over initial squared and
+conservation of energy says that must be
+
+ align:start position:0%
+conservation of energy says that must be
+ 
+
+ align:start position:0%
+conservation of energy says that must be
+the value of the energy imparted to the
+
+ align:start position:0%
+the value of the energy imparted to the
+ 
+
+ align:start position:0%
+the value of the energy imparted to the
+emitted Photon so the emitted
+
+ align:start position:0%
+emitted Photon so the emitted
+ 
+
+ align:start position:0%
+emitted Photon so the emitted
+Photon e of the photon this is
+
+ align:start position:0%
+Photon e of the photon this is
+ 
+
+ align:start position:0%
+Photon e of the photon this is
+emitted when the electron Cascades back
+
+ align:start position:0%
+emitted when the electron Cascades back
+ 
+
+ align:start position:0%
+emitted when the electron Cascades back
+down and that will be HC over Lambda so
+
+ align:start position:0%
+down and that will be HC over Lambda so
+ 
+
+ align:start position:0%
+down and that will be HC over Lambda so
+let's flip this thing around let's flip
+
+ align:start position:0%
+let's flip this thing around let's flip
+ 
+
+ align:start position:0%
+let's flip this thing around let's flip
+this thing around and what we'll get
+
+ align:start position:0%
+this thing around and what we'll get
+ 
+
+ align:start position:0%
+this thing around and what we'll get
+then is new bar or 1 over Lambda then
+
+ align:start position:0%
+then is new bar or 1 over Lambda then
+ 
+
+ align:start position:0%
+then is new bar or 1 over Lambda then
+will be kz^ 2 over the product of the
+
+ align:start position:0%
+will be kz^ 2 over the product of the
+ 
+
+ align:start position:0%
+will be kz^ 2 over the product of the
+plank constant times the speed of light
+
+ align:start position:0%
+plank constant times the speed of light
+ 
+
+ align:start position:0%
+plank constant times the speed of light
+1 / N Final squar minus 1/ n initial
+
+ align:start position:0%
+1 / N Final squar minus 1/ n initial
+ 
+
+ align:start position:0%
+1 / N Final squar minus 1/ n initial
+squared now for the Balmer series for
+
+ align:start position:0%
+squared now for the Balmer series for
+ 
+
+ align:start position:0%
+squared now for the Balmer series for
+bmer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+series we we had this set of lines for
+
+ align:start position:0%
+series we we had this set of lines for
+ 
+
+ align:start position:0%
+series we we had this set of lines for
+which the N member was always n equal 2
+
+ align:start position:0%
+which the N member was always n equal 2
+ 
+
+ align:start position:0%
+which the N member was always n equal 2
+so we're dealing with atomic hydrogen so
+
+ align:start position:0%
+so we're dealing with atomic hydrogen so
+ 
+
+ align:start position:0%
+so we're dealing with atomic hydrogen so
+let's put Z equals one and let's put the
+
+ align:start position:0%
+let's put Z equals one and let's put the
+ 
+
+ align:start position:0%
+let's put Z equals one and let's put the
+final State as Nal 2 and furthermore if
+
+ align:start position:0%
+final State as Nal 2 and furthermore if
+ 
+
+ align:start position:0%
+final State as Nal 2 and furthermore if
+we evaluate K Over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+HC using values that we already know we
+
+ align:start position:0%
+HC using values that we already know we
+ 
+
+ align:start position:0%
+HC using values that we already know we
+get 1.1 * 10 7 reciprocal meters so if
+
+ align:start position:0%
+get 1.1 * 10 7 reciprocal meters so if
+ 
+
+ align:start position:0%
+get 1.1 * 10 7 reciprocal meters so if
+you put all that in you get 1 1 *
+
+ align:start position:0%
+you put all that in you get 1 1 *
+ 
+
+ align:start position:0%
+you put all that in you get 1 1 *
+10us excuse me 10 + 7 1 / 2^ 2 - 1 over
+
+ align:start position:0%
+10us excuse me 10 + 7 1 / 2^ 2 - 1 over
+ 
+
+ align:start position:0%
+10us excuse me 10 + 7 1 / 2^ 2 - 1 over
+n i squared and ni has to be greater
+
+ align:start position:0%
+n i squared and ni has to be greater
+ 
+
+ align:start position:0%
+n i squared and ni has to be greater
+than NF so that necessarily means that
+
+ align:start position:0%
+than NF so that necessarily means that
+ 
+
+ align:start position:0%
+than NF so that necessarily means that
+it must begin at three could go four
+
+ align:start position:0%
+it must begin at three could go four
+ 
+
+ align:start position:0%
+it must begin at three could go four
+five Etc well that's exactly the Balmer
+
+ align:start position:0%
+five Etc well that's exactly the Balmer
+ 
+
+ align:start position:0%
+five Etc well that's exactly the Balmer
+formula we've got the Balmer lines out
+
+ align:start position:0%
+formula we've got the Balmer lines out
+ 
+
+ align:start position:0%
+formula we've got the Balmer lines out
+of the bore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model identical to Balmer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so bore has been able to reconcile with
+
+ align:start position:0%
+so bore has been able to reconcile with
+ 
+
+ align:start position:0%
+so bore has been able to reconcile with
+enstrom's data taken a half a century
+
+ align:start position:0%
+enstrom's data taken a half a century
+ 
+
+ align:start position:0%
+enstrom's data taken a half a century
+earlier but furthermore bore suggests
+
+ align:start position:0%
+earlier but furthermore bore suggests
+ 
+
+ align:start position:0%
+earlier but furthermore bore suggests
+other experiments for example doesn't it
+
+ align:start position:0%
+other experiments for example doesn't it
+ 
+
+ align:start position:0%
+other experiments for example doesn't it
+bother you that the lines end at n
+
+ align:start position:0%
+bother you that the lines end at n
+ 
+
+ align:start position:0%
+bother you that the lines end at n
+equals 2 you know that according to the
+
+ align:start position:0%
+equals 2 you know that according to the
+ 
+
+ align:start position:0%
+equals 2 you know that according to the
+energetics here the electrons have to
+
+ align:start position:0%
+energetics here the electrons have to
+ 
+
+ align:start position:0%
+energetics here the electrons have to
+keep cascading down at n equals one I
+
+ align:start position:0%
+keep cascading down at n equals one I
+ 
+
+ align:start position:0%
+keep cascading down at n equals one I
+mean is there's something funny going on
+
+ align:start position:0%
+mean is there's something funny going on
+ 
+
+ align:start position:0%
+mean is there's something funny going on
+in in Sweden maybe the electrons in
+
+ align:start position:0%
+in in Sweden maybe the electrons in
+ 
+
+ align:start position:0%
+in in Sweden maybe the electrons in
+Sweden are they're a little bit ner
+
+ align:start position:0%
+Sweden are they're a little bit ner
+ 
+
+ align:start position:0%
+Sweden are they're a little bit ner
+nervous maybe it's winter maybe they're
+
+ align:start position:0%
+nervous maybe it's winter maybe they're
+ 
+
+ align:start position:0%
+nervous maybe it's winter maybe they're
+afraid to go down to n equals 1 how come
+
+ align:start position:0%
+afraid to go down to n equals 1 how come
+ 
+
+ align:start position:0%
+afraid to go down to n equals 1 how come
+we only get n equals
+
+ align:start position:0%
+we only get n equals
+ 
+
+ align:start position:0%
+we only get n equals
+2 well let's look for a second here
+
+ align:start position:0%
+2 well let's look for a second here
+ 
+
+ align:start position:0%
+2 well let's look for a second here
+uh see look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this the sleep function is kicking in
+
+ align:start position:0%
+this the sleep function is kicking in
+ 
+
+ align:start position:0%
+this the sleep function is kicking in
+huh I see the hard drive there we go all
+
+ align:start position:0%
+huh I see the hard drive there we go all
+ 
+
+ align:start position:0%
+huh I see the hard drive there we go all
+right so let's for a moment take a look
+
+ align:start position:0%
+right so let's for a moment take a look
+ 
+
+ align:start position:0%
+right so let's for a moment take a look
+at the electromagnetic spectrum this is
+
+ align:start position:0%
+at the electromagnetic spectrum this is
+ 
+
+ align:start position:0%
+at the electromagnetic spectrum this is
+taken from your book and you see again
+
+ align:start position:0%
+taken from your book and you see again
+ 
+
+ align:start position:0%
+taken from your book and you see again
+I've thinking about you all the time I
+
+ align:start position:0%
+I've thinking about you all the time I
+ 
+
+ align:start position:0%
+I've thinking about you all the time I
+got out my pens and just and and I've
+
+ align:start position:0%
+got out my pens and just and and I've
+ 
+
+ align:start position:0%
+got out my pens and just and and I've
+colored it in doctor says this is good
+
+ align:start position:0%
+colored it in doctor says this is good
+ 
+
+ align:start position:0%
+colored it in doctor says this is good
+it's very good so here we are with uh
+
+ align:start position:0%
+it's very good so here we are with uh
+ 
+
+ align:start position:0%
+it's very good so here we are with uh
+wavelength on the upper uh Trace showing
+
+ align:start position:0%
+wavelength on the upper uh Trace showing
+ 
+
+ align:start position:0%
+wavelength on the upper uh Trace showing
+wavelength increasing from uh right to
+
+ align:start position:0%
+wavelength increasing from uh right to
+ 
+
+ align:start position:0%
+wavelength increasing from uh right to
+left and energy increases from left to
+
+ align:start position:0%
+left and energy increases from left to
+ 
+
+ align:start position:0%
+left and energy increases from left to
+right so high energy is low wavelength
+
+ align:start position:0%
+right so high energy is low wavelength
+ 
+
+ align:start position:0%
+right so high energy is low wavelength
+one point here that irritates me the the
+
+ align:start position:0%
+one point here that irritates me the the
+ 
+
+ align:start position:0%
+one point here that irritates me the the
+SI unit of uh frequency is Hertz which
+
+ align:start position:0%
+SI unit of uh frequency is Hertz which
+ 
+
+ align:start position:0%
+SI unit of uh frequency is Hertz which
+means um beats per second it's uh it's
+
+ align:start position:0%
+means um beats per second it's uh it's
+ 
+
+ align:start position:0%
+means um beats per second it's uh it's
+not the per second I this is a little
+
+ align:start position:0%
+not the per second I this is a little
+ 
+
+ align:start position:0%
+not the per second I this is a little
+sloppiness on the part of the textbook
+
+ align:start position:0%
+sloppiness on the part of the textbook
+ 
+
+ align:start position:0%
+sloppiness on the part of the textbook
+and so here what we've got is at the
+
+ align:start position:0%
+and so here what we've got is at the
+ 
+
+ align:start position:0%
+and so here what we've got is at the
+very very low end of wavelength very
+
+ align:start position:0%
+very very low end of wavelength very
+ 
+
+ align:start position:0%
+very very low end of wavelength very
+high energy or gamma rays cosmic rays
+
+ align:start position:0%
+high energy or gamma rays cosmic rays
+ 
+
+ align:start position:0%
+high energy or gamma rays cosmic rays
+and then over here at the low end of
+
+ align:start position:0%
+and then over here at the low end of
+ 
+
+ align:start position:0%
+and then over here at the low end of
+energy are the gentle uh forms of
+
+ align:start position:0%
+energy are the gentle uh forms of
+ 
+
+ align:start position:0%
+energy are the gentle uh forms of
+radiation radio TV microwaves over here
+
+ align:start position:0%
+radiation radio TV microwaves over here
+ 
+
+ align:start position:0%
+radiation radio TV microwaves over here
+and then in the center as it's drawn is
+
+ align:start position:0%
+and then in the center as it's drawn is
+ 
+
+ align:start position:0%
+and then in the center as it's drawn is
+visible light and I want to expand that
+
+ align:start position:0%
+visible light and I want to expand that
+ 
+
+ align:start position:0%
+visible light and I want to expand that
+and here's the visible spectrum which in
+
+ align:start position:0%
+and here's the visible spectrum which in
+ 
+
+ align:start position:0%
+and here's the visible spectrum which in
+round numbers I'd like you to know a
+
+ align:start position:0%
+round numbers I'd like you to know a
+ 
+
+ align:start position:0%
+round numbers I'd like you to know a
+little bit of this I think an educated
+
+ align:start position:0%
+little bit of this I think an educated
+ 
+
+ align:start position:0%
+little bit of this I think an educated
+person should should know a few things
+
+ align:start position:0%
+person should should know a few things
+ 
+
+ align:start position:0%
+person should should know a few things
+here and round numbers visible spectrum
+
+ align:start position:0%
+here and round numbers visible spectrum
+ 
+
+ align:start position:0%
+here and round numbers visible spectrum
+runs from about 400 nanometers up to
+
+ align:start position:0%
+runs from about 400 nanometers up to
+ 
+
+ align:start position:0%
+runs from about 400 nanometers up to
+about 700 nanometers and so visible the
+
+ align:start position:0%
+about 700 nanometers and so visible the
+ 
+
+ align:start position:0%
+about 700 nanometers and so visible the
+the the blue is low wavelength it's high
+
+ align:start position:0%
+the the blue is low wavelength it's high
+ 
+
+ align:start position:0%
+the the blue is low wavelength it's high
+energy and red is uh High wavelength low
+
+ align:start position:0%
+energy and red is uh High wavelength low
+ 
+
+ align:start position:0%
+energy and red is uh High wavelength low
+energy and here it is H staggered from
+
+ align:start position:0%
+energy and here it is H staggered from
+ 
+
+ align:start position:0%
+energy and here it is H staggered from
+uh one end to the other and so what we
+
+ align:start position:0%
+uh one end to the other and so what we
+ 
+
+ align:start position:0%
+uh one end to the other and so what we
+have here is actually uh an indication
+
+ align:start position:0%
+have here is actually uh an indication
+ 
+
+ align:start position:0%
+have here is actually uh an indication
+of what our photo detectors are capable
+
+ align:start position:0%
+of what our photo detectors are capable
+ 
+
+ align:start position:0%
+of what our photo detectors are capable
+of sensing we're tuned to operate here
+
+ align:start position:0%
+of sensing we're tuned to operate here
+ 
+
+ align:start position:0%
+of sensing we're tuned to operate here
+and it's no accident that our we're
+
+ align:start position:0%
+and it's no accident that our we're
+ 
+
+ align:start position:0%
+and it's no accident that our we're
+maximally positioned here in green very
+
+ align:start position:0%
+maximally positioned here in green very
+ 
+
+ align:start position:0%
+maximally positioned here in green very
+sensitive in the green we don't have
+
+ align:start position:0%
+sensitive in the green we don't have
+ 
+
+ align:start position:0%
+sensitive in the green we don't have
+uniform sensitivity it Maxes in green so
+
+ align:start position:0%
+uniform sensitivity it Maxes in green so
+ 
+
+ align:start position:0%
+uniform sensitivity it Maxes in green so
+the green pointer is a very good pointer
+
+ align:start position:0%
+the green pointer is a very good pointer
+ 
+
+ align:start position:0%
+the green pointer is a very good pointer
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+use so um now let's go over to the let's
+
+ align:start position:0%
+use so um now let's go over to the let's
+ 
+
+ align:start position:0%
+use so um now let's go over to the let's
+go over to the experiment oh we can
+
+ align:start position:0%
+go over to the experiment oh we can
+ 
+
+ align:start position:0%
+go over to the experiment oh we can
+convert this to electron volts by the
+
+ align:start position:0%
+convert this to electron volts by the
+ 
+
+ align:start position:0%
+convert this to electron volts by the
+way I think electron volts is a good
+
+ align:start position:0%
+way I think electron volts is a good
+ 
+
+ align:start position:0%
+way I think electron volts is a good
+good way to do this and you can see that
+
+ align:start position:0%
+good way to do this and you can see that
+ 
+
+ align:start position:0%
+good way to do this and you can see that
+visible spectrum spans roughly 2 to
+
+ align:start position:0%
+visible spectrum spans roughly 2 to
+ 
+
+ align:start position:0%
+visible spectrum spans roughly 2 to
+three electron volts two to three
+
+ align:start position:0%
+three electron volts two to three
+ 
+
+ align:start position:0%
+three electron volts two to three
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+volts and think about it I mean think
+
+ align:start position:0%
+volts and think about it I mean think
+ 
+
+ align:start position:0%
+volts and think about it I mean think
+already this little Paradigm here I've
+
+ align:start position:0%
+already this little Paradigm here I've
+ 
+
+ align:start position:0%
+already this little Paradigm here I've
+shown you something excites something
+
+ align:start position:0%
+shown you something excites something
+ 
+
+ align:start position:0%
+shown you something excites something
+gives off Photon what about the inverse
+
+ align:start position:0%
+gives off Photon what about the inverse
+ 
+
+ align:start position:0%
+gives off Photon what about the inverse
+Photon comes in something
+
+ align:start position:0%
+Photon comes in something
+ 
+
+ align:start position:0%
+Photon comes in something
+excites wouldn't it make sense to have
+
+ align:start position:0%
+excites wouldn't it make sense to have
+ 
+
+ align:start position:0%
+excites wouldn't it make sense to have
+photo detectors that operate at around
+
+ align:start position:0%
+photo detectors that operate at around
+ 
+
+ align:start position:0%
+photo detectors that operate at around
+two to three electron volts
+
+ align:start position:0%
+two to three electron volts
+ 
+
+ align:start position:0%
+two to three electron volts
+we're going to see later on in 3091 that
+
+ align:start position:0%
+we're going to see later on in 3091 that
+ 
+
+ align:start position:0%
+we're going to see later on in 3091 that
+semiconductors have band gaps roughly in
+
+ align:start position:0%
+semiconductors have band gaps roughly in
+ 
+
+ align:start position:0%
+semiconductors have band gaps roughly in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+regime okay so what's this have to do
+
+ align:start position:0%
+regime okay so what's this have to do
+ 
+
+ align:start position:0%
+regime okay so what's this have to do
+with uh n equals 2 well this is taken
+
+ align:start position:0%
+with uh n equals 2 well this is taken
+ 
+
+ align:start position:0%
+with uh n equals 2 well this is taken
+from your uh textbook and here's the
+
+ align:start position:0%
+from your uh textbook and here's the
+ 
+
+ align:start position:0%
+from your uh textbook and here's the
+Balmer series ending in nals 2 if you
+
+ align:start position:0%
+Balmer series ending in nals 2 if you
+ 
+
+ align:start position:0%
+Balmer series ending in nals 2 if you
+convert these transitions Nal 3 to Nal 2
+
+ align:start position:0%
+convert these transitions Nal 3 to Nal 2
+ 
+
+ align:start position:0%
+convert these transitions Nal 3 to Nal 2
+that turns out to give you a an energy
+
+ align:start position:0%
+that turns out to give you a an energy
+ 
+
+ align:start position:0%
+that turns out to give you a an energy
+on the order of something between 400
+
+ align:start position:0%
+on the order of something between 400
+ 
+
+ align:start position:0%
+on the order of something between 400
+and 700 nanometers and what was the
+
+ align:start position:0%
+and 700 nanometers and what was the
+ 
+
+ align:start position:0%
+and 700 nanometers and what was the
+sensor that uh anstrom was using he was
+
+ align:start position:0%
+sensor that uh anstrom was using he was
+ 
+
+ align:start position:0%
+sensor that uh anstrom was using he was
+using photographic film and photographic
+
+ align:start position:0%
+using photographic film and photographic
+ 
+
+ align:start position:0%
+using photographic film and photographic
+film is sensitive in the visible so the
+
+ align:start position:0%
+film is sensitive in the visible so the
+ 
+
+ align:start position:0%
+film is sensitive in the visible so the
+electrons in Sweden were falling down to
+
+ align:start position:0%
+electrons in Sweden were falling down to
+ 
+
+ align:start position:0%
+electrons in Sweden were falling down to
+n equals 1 but look what happens when
+
+ align:start position:0%
+n equals 1 but look what happens when
+ 
+
+ align:start position:0%
+n equals 1 but look what happens when
+you fall down to n equals 1 look at
+
+ align:start position:0%
+you fall down to n equals 1 look at
+ 
+
+ align:start position:0%
+you fall down to n equals 1 look at
+these wavelengths 100 nanometers well
+
+ align:start position:0%
+these wavelengths 100 nanometers well
+ 
+
+ align:start position:0%
+these wavelengths 100 nanometers well
+where's 100 nanometers put you 100
+
+ align:start position:0%
+where's 100 nanometers put you 100
+ 
+
+ align:start position:0%
+where's 100 nanometers put you 100
+nanometers put you way over here you're
+
+ align:start position:0%
+nanometers put you way over here you're
+ 
+
+ align:start position:0%
+nanometers put you way over here you're
+in the ultraviolet so the photographic
+
+ align:start position:0%
+in the ultraviolet so the photographic
+ 
+
+ align:start position:0%
+in the ultraviolet so the photographic
+detector doesn't pick them up and
+
+ align:start position:0%
+detector doesn't pick them up and
+ 
+
+ align:start position:0%
+detector doesn't pick them up and
+likewise some of the some of the
+
+ align:start position:0%
+likewise some of the some of the
+ 
+
+ align:start position:0%
+likewise some of the some of the
+electrons were promoted even higher than
+
+ align:start position:0%
+electrons were promoted even higher than
+ 
+
+ align:start position:0%
+electrons were promoted even higher than
+Nal 4 Nal 5 and on their way down they
+
+ align:start position:0%
+Nal 4 Nal 5 and on their way down they
+ 
+
+ align:start position:0%
+Nal 4 Nal 5 and on their way down they
+were landing on n equals 3 so you say
+
+ align:start position:0%
+were landing on n equals 3 so you say
+ 
+
+ align:start position:0%
+were landing on n equals 3 so you say
+well why didn't why didn't he get a set
+
+ align:start position:0%
+well why didn't why didn't he get a set
+ 
+
+ align:start position:0%
+well why didn't why didn't he get a set
+of lines where sometimes you get 1 over
+
+ align:start position:0%
+of lines where sometimes you get 1 over
+ 
+
+ align:start position:0%
+of lines where sometimes you get 1 over
+3^ squared well let's take a look let's
+
+ align:start position:0%
+3^ squared well let's take a look let's
+ 
+
+ align:start position:0%
+3^ squared well let's take a look let's
+take a look if you go down to Nal 3
+
+ align:start position:0%
+take a look if you go down to Nal 3
+ 
+
+ align:start position:0%
+take a look if you go down to Nal 3
+that's called the postion series and
+
+ align:start position:0%
+that's called the postion series and
+ 
+
+ align:start position:0%
+that's called the postion series and
+look at these numbers these 1800
+
+ align:start position:0%
+look at these numbers these 1800
+ 
+
+ align:start position:0%
+look at these numbers these 1800
+1875 nanom 1875 nanometers that puts you
+
+ align:start position:0%
+1875 nanom 1875 nanometers that puts you
+ 
+
+ align:start position:0%
+1875 nanom 1875 nanometers that puts you
+way over here in the infrared so n
+
+ align:start position:0%
+way over here in the infrared so n
+ 
+
+ align:start position:0%
+way over here in the infrared so n
+equals 2 those four lines end up right
+
+ align:start position:0%
+equals 2 those four lines end up right
+ 
+
+ align:start position:0%
+equals 2 those four lines end up right
+in the middle of the visible spectrum
+
+ align:start position:0%
+in the middle of the visible spectrum
+ 
+
+ align:start position:0%
+in the middle of the visible spectrum
+and that's why the lines that angstrom
+
+ align:start position:0%
+and that's why the lines that angstrom
+ 
+
+ align:start position:0%
+and that's why the lines that angstrom
+measured were in that regime so we can
+
+ align:start position:0%
+measured were in that regime so we can
+ 
+
+ align:start position:0%
+measured were in that regime so we can
+generalize all of this in the following
+
+ align:start position:0%
+generalize all of this in the following
+ 
+
+ align:start position:0%
+generalize all of this in the following
+equation new bar which is the wave
+
+ align:start position:0%
+equation new bar which is the wave
+ 
+
+ align:start position:0%
+equation new bar which is the wave
+number goes as R * z^ 2
+
+ align:start position:0%
+number goes as R * z^ 2
+ 
+
+ align:start position:0%
+number goes as R * z^ 2
+1 / n f^ 2us 1 over n i 2 and this is
+
+ align:start position:0%
+1 / n f^ 2us 1 over n i 2 and this is
+ 
+
+ align:start position:0%
+1 / n f^ 2us 1 over n i 2 and this is
+known as the ridberg
+
+ align:start position:0%
+known as the ridberg
+ 
+
+ align:start position:0%
+known as the ridberg
+equation ridberg
+
+ align:start position:0%
+equation ridberg
+ 
+
+ align:start position:0%
+equation ridberg
+equation in honor of Professor ridberg
+
+ align:start position:0%
+equation in honor of Professor ridberg
+ 
+
+ align:start position:0%
+equation in honor of Professor ridberg
+another Swede he was at the University
+
+ align:start position:0%
+another Swede he was at the University
+ 
+
+ align:start position:0%
+another Swede he was at the University
+of Lund and he was also active in
+
+ align:start position:0%
+of Lund and he was also active in
+ 
+
+ align:start position:0%
+of Lund and he was also active in
+spectroscopy and so we uh encapsulate
+
+ align:start position:0%
+spectroscopy and so we uh encapsulate
+ 
+
+ align:start position:0%
+spectroscopy and so we uh encapsulate
+everything that's on this uh on this
+
+ align:start position:0%
+everything that's on this uh on this
+ 
+
+ align:start position:0%
+everything that's on this uh on this
+slide here is in this equation and more
+
+ align:start position:0%
+slide here is in this equation and more
+ 
+
+ align:start position:0%
+slide here is in this equation and more
+so because this allows for higher Z
+
+ align:start position:0%
+so because this allows for higher Z
+ 
+
+ align:start position:0%
+so because this allows for higher Z
+elements besides just Elemental
+
+ align:start position:0%
+elements besides just Elemental
+ 
+
+ align:start position:0%
+elements besides just Elemental
+hydrogen well there's still more
+
+ align:start position:0%
+hydrogen well there's still more
+ 
+
+ align:start position:0%
+hydrogen well there's still more
+evidence there's still more evidence in
+
+ align:start position:0%
+evidence there's still more evidence in
+ 
+
+ align:start position:0%
+evidence there's still more evidence in
+support of
+
+ align:start position:0%
+support of
+ 
+
+ align:start position:0%
+support of
+bore let's take a look at that bore was
+
+ align:start position:0%
+bore let's take a look at that bore was
+ 
+
+ align:start position:0%
+bore let's take a look at that bore was
+really Riding High this was good but it
+
+ align:start position:0%
+really Riding High this was good but it
+ 
+
+ align:start position:0%
+really Riding High this was good but it
+gets better it gets better there's the
+
+ align:start position:0%
+gets better it gets better there's the
+ 
+
+ align:start position:0%
+gets better it gets better there's the
+Frank Herz experiment the Frank Herz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experiment Frank Herz experiment expent
+
+ align:start position:0%
+experiment Frank Herz experiment expent
+ 
+
+ align:start position:0%
+experiment Frank Herz experiment expent
+was performed in
+
+ align:start position:0%
+was performed in
+ 
+
+ align:start position:0%
+was performed in
+Berlin around 1912 to 1914 so it was
+
+ align:start position:0%
+Berlin around 1912 to 1914 so it was
+ 
+
+ align:start position:0%
+Berlin around 1912 to 1914 so it was
+published around
+
+ align:start position:0%
+published around
+ 
+
+ align:start position:0%
+published around
+1914 and what Frank and Herz did was
+
+ align:start position:0%
+1914 and what Frank and Herz did was
+ 
+
+ align:start position:0%
+1914 and what Frank and Herz did was
+operate a gas discharge tube but instead
+
+ align:start position:0%
+operate a gas discharge tube but instead
+ 
+
+ align:start position:0%
+operate a gas discharge tube but instead
+of running it with hydrogen they filled
+
+ align:start position:0%
+of running it with hydrogen they filled
+ 
+
+ align:start position:0%
+of running it with hydrogen they filled
+it with mercury vapor now Mercury as
+
+ align:start position:0%
+it with mercury vapor now Mercury as
+ 
+
+ align:start position:0%
+it with mercury vapor now Mercury as
+you'll learn later in its Vapor State
+
+ align:start position:0%
+you'll learn later in its Vapor State
+ 
+
+ align:start position:0%
+you'll learn later in its Vapor State
+exists as the single atom it's like
+
+ align:start position:0%
+exists as the single atom it's like
+ 
+
+ align:start position:0%
+exists as the single atom it's like
+helium single atom whereas hydrogen
+
+ align:start position:0%
+helium single atom whereas hydrogen
+ 
+
+ align:start position:0%
+helium single atom whereas hydrogen
+there is atomic hydrogen there's there's
+
+ align:start position:0%
+there is atomic hydrogen there's there's
+ 
+
+ align:start position:0%
+there is atomic hydrogen there's there's
+a molecular hydrogen so they operated
+
+ align:start position:0%
+a molecular hydrogen so they operated
+ 
+
+ align:start position:0%
+a molecular hydrogen so they operated
+gas discharge
+
+ align:start position:0%
+gas discharge
+ 
+
+ align:start position:0%
+gas discharge
+tube gas discharge tube with mercury
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vapor and what did they
+
+ align:start position:0%
+vapor and what did they
+ 
+
+ align:start position:0%
+vapor and what did they
+find what did they find what they found
+
+ align:start position:0%
+find what did they find what they found
+ 
+
+ align:start position:0%
+find what did they find what they found
+was that when they Vari so let's let's
+
+ align:start position:0%
+was that when they Vari so let's let's
+ 
+
+ align:start position:0%
+was that when they Vari so let's let's
+draw this little schematic here they've
+
+ align:start position:0%
+draw this little schematic here they've
+ 
+
+ align:start position:0%
+draw this little schematic here they've
+got a variable voltage power supply
+
+ align:start position:0%
+got a variable voltage power supply
+ 
+
+ align:start position:0%
+got a variable voltage power supply
+feeding electrodes we've got mercury in
+
+ align:start position:0%
+feeding electrodes we've got mercury in
+ 
+
+ align:start position:0%
+feeding electrodes we've got mercury in
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+cathode
+
+ align:start position:0%
+cathode
+ 
+
+ align:start position:0%
+cathode
+anode and they put a an ammeter in the
+
+ align:start position:0%
+anode and they put a an ammeter in the
+ 
+
+ align:start position:0%
+anode and they put a an ammeter in the
+circuit and they measured the current
+
+ align:start position:0%
+circuit and they measured the current
+ 
+
+ align:start position:0%
+circuit and they measured the current
+voltage
+
+ align:start position:0%
+voltage
+ 
+
+ align:start position:0%
+voltage
+characteristic so here's the current
+
+ align:start position:0%
+characteristic so here's the current
+ 
+
+ align:start position:0%
+characteristic so here's the current
+that goes through the cell electrons
+
+ align:start position:0%
+that goes through the cell electrons
+ 
+
+ align:start position:0%
+that goes through the cell electrons
+moving off the cathode shooting across
+
+ align:start position:0%
+moving off the cathode shooting across
+ 
+
+ align:start position:0%
+moving off the cathode shooting across
+to the anode and they measured the
+
+ align:start position:0%
+to the anode and they measured the
+ 
+
+ align:start position:0%
+to the anode and they measured the
+current as a function of
+
+ align:start position:0%
+current as a function of
+ 
+
+ align:start position:0%
+current as a function of
+voltage and what they found was that at
+
+ align:start position:0%
+voltage and what they found was that at
+ 
+
+ align:start position:0%
+voltage and what they found was that at
+low voltage you get low current and at
+
+ align:start position:0%
+low voltage you get low current and at
+ 
+
+ align:start position:0%
+low voltage you get low current and at
+higher voltage you get higher current as
+
+ align:start position:0%
+higher voltage you get higher current as
+ 
+
+ align:start position:0%
+higher voltage you get higher current as
+you would expect some kind of an ohic
+
+ align:start position:0%
+you would expect some kind of an ohic
+ 
+
+ align:start position:0%
+you would expect some kind of an ohic
+Behavior up to some critical voltage and
+
+ align:start position:0%
+Behavior up to some critical voltage and
+ 
+
+ align:start position:0%
+Behavior up to some critical voltage and
+at that point the current dropped to
+
+ align:start position:0%
+at that point the current dropped to
+ 
+
+ align:start position:0%
+at that point the current dropped to
+almost zero and the tube started glowing
+
+ align:start position:0%
+almost zero and the tube started glowing
+ 
+
+ align:start position:0%
+almost zero and the tube started glowing
+blinding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+white this turns out to be about 4.9
+
+ align:start position:0%
+white this turns out to be about 4.9
+ 
+
+ align:start position:0%
+white this turns out to be about 4.9
+volts 4.9 volts they continued raising
+
+ align:start position:0%
+volts 4.9 volts they continued raising
+ 
+
+ align:start position:0%
+volts 4.9 volts they continued raising
+the voltage and again now they've got
+
+ align:start position:0%
+the voltage and again now they've got
+ 
+
+ align:start position:0%
+the voltage and again now they've got
+current going through the ameter is
+
+ align:start position:0%
+current going through the ameter is
+ 
+
+ align:start position:0%
+current going through the ameter is
+registering current the tube is glowing
+
+ align:start position:0%
+registering current the tube is glowing
+ 
+
+ align:start position:0%
+registering current the tube is glowing
+and now the current is rising until
+
+ align:start position:0%
+and now the current is rising until
+ 
+
+ align:start position:0%
+and now the current is rising until
+another critical voltage and it falls
+
+ align:start position:0%
+another critical voltage and it falls
+ 
+
+ align:start position:0%
+another critical voltage and it falls
+again and now the tube is glowing even
+
+ align:start position:0%
+again and now the tube is glowing even
+ 
+
+ align:start position:0%
+again and now the tube is glowing even
+brighter and this is 6.7 volts and just
+
+ align:start position:0%
+brighter and this is 6.7 volts and just
+ 
+
+ align:start position:0%
+brighter and this is 6.7 volts and just
+for your information you look on the
+
+ align:start position:0%
+for your information you look on the
+ 
+
+ align:start position:0%
+for your information you look on the
+periodic table today and it turns out
+
+ align:start position:0%
+periodic table today and it turns out
+ 
+
+ align:start position:0%
+periodic table today and it turns out
+that the ionization voltage for um
+
+ align:start position:0%
+that the ionization voltage for um
+ 
+
+ align:start position:0%
+that the ionization voltage for um
+Mercury is about 10.4 10.4 EV is the
+
+ align:start position:0%
+Mercury is about 10.4 10.4 EV is the
+ 
+
+ align:start position:0%
+Mercury is about 10.4 10.4 EV is the
+ionization energy so this is below the
+
+ align:start position:0%
+ionization energy so this is below the
+ 
+
+ align:start position:0%
+ionization energy so this is below the
+ionization energy so what's going on
+
+ align:start position:0%
+ionization energy so what's going on
+ 
+
+ align:start position:0%
+ionization energy so what's going on
+here what they reasoned was that they
+
+ align:start position:0%
+here what they reasoned was that they
+ 
+
+ align:start position:0%
+here what they reasoned was that they
+were exciting bound electrons within
+
+ align:start position:0%
+were exciting bound electrons within
+ 
+
+ align:start position:0%
+were exciting bound electrons within
+Mercury and furthermore that there are
+
+ align:start position:0%
+Mercury and furthermore that there are
+ 
+
+ align:start position:0%
+Mercury and furthermore that there are
+critical voltages associated with
+
+ align:start position:0%
+critical voltages associated with
+ 
+
+ align:start position:0%
+critical voltages associated with
+critical energies conclusion there are
+
+ align:start position:0%
+critical energies conclusion there are
+ 
+
+ align:start position:0%
+critical energies conclusion there are
+quantized energy levels within Mercury
+
+ align:start position:0%
+quantized energy levels within Mercury
+ 
+
+ align:start position:0%
+quantized energy levels within Mercury
+which is to say that the bore postulate
+
+ align:start position:0%
+which is to say that the bore postulate
+ 
+
+ align:start position:0%
+which is to say that the bore postulate
+of quantization applies not only to a
+
+ align:start position:0%
+of quantization applies not only to a
+ 
+
+ align:start position:0%
+of quantization applies not only to a
+one electron atom but it applies to
+
+ align:start position:0%
+one electron atom but it applies to
+ 
+
+ align:start position:0%
+one electron atom but it applies to
+multi-electron atoms well it applies to
+
+ align:start position:0%
+multi-electron atoms well it applies to
+ 
+
+ align:start position:0%
+multi-electron atoms well it applies to
+multi-electron atoms doesn't that mean
+
+ align:start position:0%
+multi-electron atoms doesn't that mean
+ 
+
+ align:start position:0%
+multi-electron atoms doesn't that mean
+it applies to everything so they
+
+ align:start position:0%
+it applies to everything so they
+ 
+
+ align:start position:0%
+it applies to everything so they
+concluded from this experiment
+
+ align:start position:0%
+concluded from this experiment
+ 
+
+ align:start position:0%
+concluded from this experiment
+quantization
+
+ align:start position:0%
+quantization
+ 
+
+ align:start position:0%
+quantization
+quantization of
+
+ align:start position:0%
+quantization of
+ 
+
+ align:start position:0%
+quantization of
+energies quantization of
+
+ align:start position:0%
+energies quantization of
+ 
+
+ align:start position:0%
+energies quantization of
+energies of electrons in multi-electron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+atoms so the bore model doesn't apply to
+
+ align:start position:0%
+atoms so the bore model doesn't apply to
+ 
+
+ align:start position:0%
+atoms so the bore model doesn't apply to
+multi electron atoms but the assumption
+
+ align:start position:0%
+multi electron atoms but the assumption
+ 
+
+ align:start position:0%
+multi electron atoms but the assumption
+that energy is quantized in
+
+ align:start position:0%
+that energy is quantized in
+ 
+
+ align:start position:0%
+that energy is quantized in
+multi-electron atoms is the Assumption
+
+ align:start position:0%
+multi-electron atoms is the Assumption
+ 
+
+ align:start position:0%
+multi-electron atoms is the Assumption
+of energy quantization extends to
+
+ align:start position:0%
+of energy quantization extends to
+ 
+
+ align:start position:0%
+of energy quantization extends to
+multi-electron atoms so this was really
+
+ align:start position:0%
+multi-electron atoms so this was really
+ 
+
+ align:start position:0%
+multi-electron atoms so this was really
+really good bore was writing very very
+
+ align:start position:0%
+really good bore was writing very very
+ 
+
+ align:start position:0%
+really good bore was writing very very
+high but all good things come to an end
+
+ align:start position:0%
+high but all good things come to an end
+ 
+
+ align:start position:0%
+high but all good things come to an end
+there were problems with the bore model
+
+ align:start position:0%
+there were problems with the bore model
+ 
+
+ align:start position:0%
+there were problems with the bore model
+too so now let's look at limitations
+
+ align:start position:0%
+too so now let's look at limitations
+ 
+
+ align:start position:0%
+too so now let's look at limitations
+want to look at
+
+ align:start position:0%
+want to look at
+ 
+
+ align:start position:0%
+want to look at
+limitations of the bore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model limitation of
+
+ align:start position:0%
+model limitation of
+ 
+
+ align:start position:0%
+model limitation of
+bore okay first of all there's data out
+
+ align:start position:0%
+bore okay first of all there's data out
+ 
+
+ align:start position:0%
+bore okay first of all there's data out
+there there's data out there already
+
+ align:start position:0%
+there there's data out there already
+ 
+
+ align:start position:0%
+there there's data out there already
+first uh
+
+ align:start position:0%
+first uh
+ 
+
+ align:start position:0%
+first uh
+1887 1887 Michaelson and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Morley Michaelson and
+
+ align:start position:0%
+Morley Michaelson and
+ 
+
+ align:start position:0%
+Morley Michaelson and
+Morley this work was distinguished by
+
+ align:start position:0%
+Morley this work was distinguished by
+ 
+
+ align:start position:0%
+Morley this work was distinguished by
+the fact that it was done in the United
+
+ align:start position:0%
+the fact that it was done in the United
+ 
+
+ align:start position:0%
+the fact that it was done in the United
+States you notice most of everything
+
+ align:start position:0%
+States you notice most of everything
+ 
+
+ align:start position:0%
+States you notice most of everything
+I've shown you up until now was done in
+
+ align:start position:0%
+I've shown you up until now was done in
+ 
+
+ align:start position:0%
+I've shown you up until now was done in
+Europe with one exception the milikan
+
+ align:start position:0%
+Europe with one exception the milikan
+ 
+
+ align:start position:0%
+Europe with one exception the milikan
+experiment in Chicago everything else is
+
+ align:start position:0%
+experiment in Chicago everything else is
+ 
+
+ align:start position:0%
+experiment in Chicago everything else is
+European science but Michaelson had
+
+ align:start position:0%
+European science but Michaelson had
+ 
+
+ align:start position:0%
+European science but Michaelson had
+immigrated to the United States and was
+
+ align:start position:0%
+immigrated to the United States and was
+ 
+
+ align:start position:0%
+immigrated to the United States and was
+really really clever he was a brilliant
+
+ align:start position:0%
+really really clever he was a brilliant
+ 
+
+ align:start position:0%
+really really clever he was a brilliant
+inventor was doing military research for
+
+ align:start position:0%
+inventor was doing military research for
+ 
+
+ align:start position:0%
+inventor was doing military research for
+the Navy back in the early 1880s he
+
+ align:start position:0%
+the Navy back in the early 1880s he
+ 
+
+ align:start position:0%
+the Navy back in the early 1880s he
+invented the
+
+ align:start position:0%
+invented the
+ 
+
+ align:start position:0%
+invented the
+interferometer and he was the first to
+
+ align:start position:0%
+interferometer and he was the first to
+ 
+
+ align:start position:0%
+interferometer and he was the first to
+make accurate measurements of the speed
+
+ align:start position:0%
+make accurate measurements of the speed
+ 
+
+ align:start position:0%
+make accurate measurements of the speed
+of light the Michaelson interferometer
+
+ align:start position:0%
+of light the Michaelson interferometer
+ 
+
+ align:start position:0%
+of light the Michaelson interferometer
+and he was uh he uh eventually worked at
+
+ align:start position:0%
+and he was uh he uh eventually worked at
+ 
+
+ align:start position:0%
+and he was uh he uh eventually worked at
+the uh case School of applied science in
+
+ align:start position:0%
+the uh case School of applied science in
+ 
+
+ align:start position:0%
+the uh case School of applied science in
+Cleveland which ultimately
+
+ align:start position:0%
+Cleveland which ultimately
+ 
+
+ align:start position:0%
+Cleveland which ultimately
+became case Western Reserve University
+
+ align:start position:0%
+became case Western Reserve University
+ 
+
+ align:start position:0%
+became case Western Reserve University
+after a number of transitions so he was
+
+ align:start position:0%
+after a number of transitions so he was
+ 
+
+ align:start position:0%
+after a number of transitions so he was
+working at case in Cleveland and doing
+
+ align:start position:0%
+working at case in Cleveland and doing
+ 
+
+ align:start position:0%
+working at case in Cleveland and doing
+very very high uh Precision spectroscopy
+
+ align:start position:0%
+very very high uh Precision spectroscopy
+ 
+
+ align:start position:0%
+very very high uh Precision spectroscopy
+that was his Forte he was a brilliant
+
+ align:start position:0%
+that was his Forte he was a brilliant
+ 
+
+ align:start position:0%
+that was his Forte he was a brilliant
+experimentalist knew how to make
+
+ align:start position:0%
+experimentalist knew how to make
+ 
+
+ align:start position:0%
+experimentalist knew how to make
+equipment that was highly accurate and
+
+ align:start position:0%
+equipment that was highly accurate and
+ 
+
+ align:start position:0%
+equipment that was highly accurate and
+what he found was that one of enstrom's
+
+ align:start position:0%
+what he found was that one of enstrom's
+ 
+
+ align:start position:0%
+what he found was that one of enstrom's
+lines the line the line associated with
+
+ align:start position:0%
+lines the line the line associated with
+ 
+
+ align:start position:0%
+lines the line the line associated with
+the transition 3:2 if you look really
+
+ align:start position:0%
+the transition 3:2 if you look really
+ 
+
+ align:start position:0%
+the transition 3:2 if you look really
+really carefully now remember anstrom
+
+ align:start position:0%
+really carefully now remember anstrom
+ 
+
+ align:start position:0%
+really carefully now remember anstrom
+made the measurements by looking at
+
+ align:start position:0%
+made the measurements by looking at
+ 
+
+ align:start position:0%
+made the measurements by looking at
+light hitting a photographic plate and
+
+ align:start position:0%
+light hitting a photographic plate and
+ 
+
+ align:start position:0%
+light hitting a photographic plate and
+that light doesn't come down nice and
+
+ align:start position:0%
+that light doesn't come down nice and
+ 
+
+ align:start position:0%
+that light doesn't come down nice and
+sharp there's a little bit of of uh
+
+ align:start position:0%
+sharp there's a little bit of of uh
+ 
+
+ align:start position:0%
+sharp there's a little bit of of uh
+scatter in the data so you get this fat
+
+ align:start position:0%
+scatter in the data so you get this fat
+ 
+
+ align:start position:0%
+scatter in the data so you get this fat
+line but the positions of Center to
+
+ align:start position:0%
+line but the positions of Center to
+ 
+
+ align:start position:0%
+line but the positions of Center to
+Center on the lines follow that set of
+
+ align:start position:0%
+Center on the lines follow that set of
+ 
+
+ align:start position:0%
+Center on the lines follow that set of
+four uh numbers that we were looking at
+
+ align:start position:0%
+four uh numbers that we were looking at
+ 
+
+ align:start position:0%
+four uh numbers that we were looking at
+yesterday now when Michaelson redid the
+
+ align:start position:0%
+yesterday now when Michaelson redid the
+ 
+
+ align:start position:0%
+yesterday now when Michaelson redid the
+work remember anstrom did his
+
+ align:start position:0%
+work remember anstrom did his
+ 
+
+ align:start position:0%
+work remember anstrom did his
+experiments in 1853 Michaelson looks
+
+ align:start position:0%
+experiments in 1853 Michaelson looks
+ 
+
+ align:start position:0%
+experiments in 1853 Michaelson looks
+very very carefully and sees that it's
+
+ align:start position:0%
+very very carefully and sees that it's
+ 
+
+ align:start position:0%
+very very carefully and sees that it's
+not one line but it's two lines two
+
+ align:start position:0%
+not one line but it's two lines two
+ 
+
+ align:start position:0%
+not one line but it's two lines two
+lines very close together so the 3:2
+
+ align:start position:0%
+lines very close together so the 3:2
+ 
+
+ align:start position:0%
+lines very close together so the 3:2
+line is in fact a
+
+ align:start position:0%
+line is in fact a
+ 
+
+ align:start position:0%
+line is in fact a
+dublet it's a dublet that is to say two
+
+ align:start position:0%
+dublet it's a dublet that is to say two
+ 
+
+ align:start position:0%
+dublet it's a dublet that is to say two
+lines very very close together but from
+
+ align:start position:0%
+lines very very close together but from
+ 
+
+ align:start position:0%
+lines very very close together but from
+a distance it looks like a line and then
+
+ align:start position:0%
+a distance it looks like a line and then
+ 
+
+ align:start position:0%
+a distance it looks like a line and then
+if you've got really accurate uh
+
+ align:start position:0%
+if you've got really accurate uh
+ 
+
+ align:start position:0%
+if you've got really accurate uh
+instrumentation you discover that it's a
+
+ align:start position:0%
+instrumentation you discover that it's a
+ 
+
+ align:start position:0%
+instrumentation you discover that it's a
+dublet and that's a problem that's a
+
+ align:start position:0%
+dublet and that's a problem that's a
+ 
+
+ align:start position:0%
+dublet and that's a problem that's a
+problem because if you look at this term
+
+ align:start position:0%
+problem because if you look at this term
+ 
+
+ align:start position:0%
+problem because if you look at this term
+scheme here if we've got a doublet it
+
+ align:start position:0%
+scheme here if we've got a doublet it
+ 
+
+ align:start position:0%
+scheme here if we've got a doublet it
+means that you've got two different
+
+ align:start position:0%
+means that you've got two different
+ 
+
+ align:start position:0%
+means that you've got two different
+transitions so the bore model is saying
+
+ align:start position:0%
+transitions so the bore model is saying
+ 
+
+ align:start position:0%
+transitions so the bore model is saying
+you go from Nal 2 up to Nal 3 and when
+
+ align:start position:0%
+you go from Nal 2 up to Nal 3 and when
+ 
+
+ align:start position:0%
+you go from Nal 2 up to Nal 3 and when
+you fall from three back down to two you
+
+ align:start position:0%
+you fall from three back down to two you
+ 
+
+ align:start position:0%
+you fall from three back down to two you
+give off a photon and that Photon has a
+
+ align:start position:0%
+give off a photon and that Photon has a
+ 
+
+ align:start position:0%
+give off a photon and that Photon has a
+unique value of wavelength but they're
+
+ align:start position:0%
+unique value of wavelength but they're
+ 
+
+ align:start position:0%
+unique value of wavelength but they're
+measuring two but they're very close so
+
+ align:start position:0%
+measuring two but they're very close so
+ 
+
+ align:start position:0%
+measuring two but they're very close so
+what that suggests is that maybe there
+
+ align:start position:0%
+what that suggests is that maybe there
+ 
+
+ align:start position:0%
+what that suggests is that maybe there
+are two levels that are really really
+
+ align:start position:0%
+are two levels that are really really
+ 
+
+ align:start position:0%
+are two levels that are really really
+close together and sometimes the
+
+ align:start position:0%
+close together and sometimes the
+ 
+
+ align:start position:0%
+close together and sometimes the
+electron falls from the higher level and
+
+ align:start position:0%
+electron falls from the higher level and
+ 
+
+ align:start position:0%
+electron falls from the higher level and
+sometimes it falls from the lower level
+
+ align:start position:0%
+sometimes it falls from the lower level
+ 
+
+ align:start position:0%
+sometimes it falls from the lower level
+but in any event there must be more than
+
+ align:start position:0%
+but in any event there must be more than
+ 
+
+ align:start position:0%
+but in any event there must be more than
+one level but very close together so
+
+ align:start position:0%
+one level but very close together so
+ 
+
+ align:start position:0%
+one level but very close together so
+bore is silent on that now the other
+
+ align:start position:0%
+bore is silent on that now the other
+ 
+
+ align:start position:0%
+bore is silent on that now the other
+possibility is that you know two is the
+
+ align:start position:0%
+possibility is that you know two is the
+ 
+
+ align:start position:0%
+possibility is that you know two is the
+problem we don't know maybe there maybe
+
+ align:start position:0%
+problem we don't know maybe there maybe
+ 
+
+ align:start position:0%
+problem we don't know maybe there maybe
+there are maybe this has got two lines
+
+ align:start position:0%
+there are maybe this has got two lines
+ 
+
+ align:start position:0%
+there are maybe this has got two lines
+and this has one so that's the point
+
+ align:start position:0%
+and this has one so that's the point
+ 
+
+ align:start position:0%
+and this has one so that's the point
+first of all by the way uh uh Michaelson
+
+ align:start position:0%
+first of all by the way uh uh Michaelson
+ 
+
+ align:start position:0%
+first of all by the way uh uh Michaelson
+was uh awarded the Nobel Prize in
+
+ align:start position:0%
+was uh awarded the Nobel Prize in
+ 
+
+ align:start position:0%
+was uh awarded the Nobel Prize in
+1907 not for this observation he got it
+
+ align:start position:0%
+1907 not for this observation he got it
+ 
+
+ align:start position:0%
+1907 not for this observation he got it
+for the uh measurement of the speed of
+
+ align:start position:0%
+for the uh measurement of the speed of
+ 
+
+ align:start position:0%
+for the uh measurement of the speed of
+light why I'm putting it down is you're
+
+ align:start position:0%
+light why I'm putting it down is you're
+ 
+
+ align:start position:0%
+light why I'm putting it down is you're
+going to see everybody today we're
+
+ align:start position:0%
+going to see everybody today we're
+ 
+
+ align:start position:0%
+going to see everybody today we're
+giving out nobels like they're going out
+
+ align:start position:0%
+giving out nobels like they're going out
+ 
+
+ align:start position:0%
+giving out nobels like they're going out
+of style so everybody gets a Nobel today
+
+ align:start position:0%
+of style so everybody gets a Nobel today
+ 
+
+ align:start position:0%
+of style so everybody gets a Nobel today
+it's not like Oprah we're not giving
+
+ align:start position:0%
+it's not like Oprah we're not giving
+ 
+
+ align:start position:0%
+it's not like Oprah we're not giving
+everybody a car but we're going to give
+
+ align:start position:0%
+everybody a car but we're going to give
+ 
+
+ align:start position:0%
+everybody a car but we're going to give
+everybody an Nobel okay so that's the
+
+ align:start position:0%
+everybody an Nobel okay so that's the
+ 
+
+ align:start position:0%
+everybody an Nobel okay so that's the
+first piece of bad news for bore these
+
+ align:start position:0%
+first piece of bad news for bore these
+ 
+
+ align:start position:0%
+first piece of bad news for bore these
+are headaches for boar okay number two
+
+ align:start position:0%
+are headaches for boar okay number two
+ 
+
+ align:start position:0%
+are headaches for boar okay number two
+number two is
+
+ align:start position:0%
+number two is
+ 
+
+ align:start position:0%
+number two is
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+1896 um Pete
+
+ align:start position:0%
+1896 um Pete
+ 
+
+ align:start position:0%
+1896 um Pete
+Zan Pete Zan who was a postdoc at
+
+ align:start position:0%
+Zan Pete Zan who was a postdoc at
+ 
+
+ align:start position:0%
+Zan Pete Zan who was a postdoc at
+Liden in the
+
+ align:start position:0%
+Liden in the
+ 
+
+ align:start position:0%
+Liden in the
+Netherlands he was a postto at Leiden in
+
+ align:start position:0%
+Netherlands he was a postto at Leiden in
+ 
+
+ align:start position:0%
+Netherlands he was a postto at Leiden in
+the Netherlands and what he did these
+
+ align:start position:0%
+the Netherlands and what he did these
+ 
+
+ align:start position:0%
+the Netherlands and what he did these
+people were so creative I mean they were
+
+ align:start position:0%
+people were so creative I mean they were
+ 
+
+ align:start position:0%
+people were so creative I mean they were
+so excited about science so he works
+
+ align:start position:0%
+so excited about science so he works
+ 
+
+ align:start position:0%
+so excited about science so he works
+with a gas discharge tube and he takes
+
+ align:start position:0%
+with a gas discharge tube and he takes
+ 
+
+ align:start position:0%
+with a gas discharge tube and he takes
+the gas discharge tube and he puts it
+
+ align:start position:0%
+the gas discharge tube and he puts it
+ 
+
+ align:start position:0%
+the gas discharge tube and he puts it
+into a magnetic field he makes a
+
+ align:start position:0%
+into a magnetic field he makes a
+ 
+
+ align:start position:0%
+into a magnetic field he makes a
+magnetic field by wrapping uh conductor
+
+ align:start position:0%
+magnetic field by wrapping uh conductor
+ 
+
+ align:start position:0%
+magnetic field by wrapping uh conductor
+around the tube and passing current
+
+ align:start position:0%
+around the tube and passing current
+ 
+
+ align:start position:0%
+around the tube and passing current
+through the conductor and he by playing
+
+ align:start position:0%
+through the conductor and he by playing
+ 
+
+ align:start position:0%
+through the conductor and he by playing
+with the value of the current through
+
+ align:start position:0%
+with the value of the current through
+ 
+
+ align:start position:0%
+with the value of the current through
+the coil he changes the intensity of
+
+ align:start position:0%
+the coil he changes the intensity of
+ 
+
+ align:start position:0%
+the coil he changes the intensity of
+magnetic field and then goes through the
+
+ align:start position:0%
+magnetic field and then goes through the
+ 
+
+ align:start position:0%
+magnetic field and then goes through the
+experiments with the prism spectrograph
+
+ align:start position:0%
+experiments with the prism spectrograph
+ 
+
+ align:start position:0%
+experiments with the prism spectrograph
+okay so he measures gas discharge
+
+ align:start position:0%
+okay so he measures gas discharge
+ 
+
+ align:start position:0%
+okay so he measures gas discharge
+tube same thing all over again gas
+
+ align:start position:0%
+tube same thing all over again gas
+ 
+
+ align:start position:0%
+tube same thing all over again gas
+discharge tube in a magnetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+field and what he observes is the
+
+ align:start position:0%
+field and what he observes is the
+ 
+
+ align:start position:0%
+field and what he observes is the
+following if I just schematically if
+
+ align:start position:0%
+following if I just schematically if
+ 
+
+ align:start position:0%
+following if I just schematically if
+this is the photographic plate and
+
+ align:start position:0%
+this is the photographic plate and
+ 
+
+ align:start position:0%
+this is the photographic plate and
+you've got multiple lines on the
+
+ align:start position:0%
+you've got multiple lines on the
+ 
+
+ align:start position:0%
+you've got multiple lines on the
+photographic plate
+
+ align:start position:0%
+photographic plate
+ 
+
+ align:start position:0%
+photographic plate
+this is no magnetic field what we've
+
+ align:start position:0%
+this is no magnetic field what we've
+ 
+
+ align:start position:0%
+this is no magnetic field what we've
+seen before what he finds is that in the
+
+ align:start position:0%
+seen before what he finds is that in the
+ 
+
+ align:start position:0%
+seen before what he finds is that in the
+magnetic
+
+ align:start position:0%
+magnetic
+ 
+
+ align:start position:0%
+magnetic
+field some of these lines actually and
+
+ align:start position:0%
+field some of these lines actually and
+ 
+
+ align:start position:0%
+field some of these lines actually and
+this is not to scale some of these lines
+
+ align:start position:0%
+this is not to scale some of these lines
+ 
+
+ align:start position:0%
+this is not to scale some of these lines
+actually show up as doublets triplets
+
+ align:start position:0%
+actually show up as doublets triplets
+ 
+
+ align:start position:0%
+actually show up as doublets triplets
+but only in the applied magnetic field
+
+ align:start position:0%
+but only in the applied magnetic field
+ 
+
+ align:start position:0%
+but only in the applied magnetic field
+so we call this line
+
+ align:start position:0%
+so we call this line
+ 
+
+ align:start position:0%
+so we call this line
+splitting which is even different from
+
+ align:start position:0%
+splitting which is even different from
+ 
+
+ align:start position:0%
+splitting which is even different from
+what Morley said Morley just said
+
+ align:start position:0%
+what Morley said Morley just said
+ 
+
+ align:start position:0%
+what Morley said Morley just said
+Michaelson and Morley observed that null
+
+ align:start position:0%
+Michaelson and Morley observed that null
+ 
+
+ align:start position:0%
+Michaelson and Morley observed that null
+magnetic field if you look carefully
+
+ align:start position:0%
+magnetic field if you look carefully
+ 
+
+ align:start position:0%
+magnetic field if you look carefully
+there's multiple lines what Zeman sees
+
+ align:start position:0%
+there's multiple lines what Zeman sees
+ 
+
+ align:start position:0%
+there's multiple lines what Zeman sees
+is that single line null magnetic field
+
+ align:start position:0%
+is that single line null magnetic field
+ 
+
+ align:start position:0%
+is that single line null magnetic field
+apply a magnetic field you see a line
+
+ align:start position:0%
+apply a magnetic field you see a line
+ 
+
+ align:start position:0%
+apply a magnetic field you see a line
+splitting and furthermore he found that
+
+ align:start position:0%
+splitting and furthermore he found that
+ 
+
+ align:start position:0%
+splitting and furthermore he found that
+the intensity of the magnetic field
+
+ align:start position:0%
+the intensity of the magnetic field
+ 
+
+ align:start position:0%
+the intensity of the magnetic field
+affected the degree of splitting higher
+
+ align:start position:0%
+affected the degree of splitting higher
+ 
+
+ align:start position:0%
+affected the degree of splitting higher
+the magnetic field the greater the
+
+ align:start position:0%
+the magnetic field the greater the
+ 
+
+ align:start position:0%
+the magnetic field the greater the
+degree of splitting line splitting
+
+ align:start position:0%
+degree of splitting line splitting
+ 
+
+ align:start position:0%
+degree of splitting line splitting
+proportional to
+
+ align:start position:0%
+proportional to
+ 
+
+ align:start position:0%
+proportional to
+intensity of magnetic
+
+ align:start position:0%
+intensity of magnetic
+ 
+
+ align:start position:0%
+intensity of magnetic
+field so this is called the Zan
+
+ align:start position:0%
+field so this is called the Zan
+ 
+
+ align:start position:0%
+field so this is called the Zan
+effect and that's not bad for a postto
+
+ align:start position:0%
+effect and that's not bad for a postto
+ 
+
+ align:start position:0%
+effect and that's not bad for a postto
+cuz he got he got a Nobel in
+
+ align:start position:0%
+cuz he got he got a Nobel in
+ 
+
+ align:start position:0%
+cuz he got he got a Nobel in
+1902 and they were only offered for the
+
+ align:start position:0%
+1902 and they were only offered for the
+ 
+
+ align:start position:0%
+1902 and they were only offered for the
+first time in 1901 so talk about a
+
+ align:start position:0%
+first time in 1901 so talk about a
+ 
+
+ align:start position:0%
+first time in 1901 so talk about a
+meteoric rise and people obviously on
+
+ align:start position:0%
+meteoric rise and people obviously on
+ 
+
+ align:start position:0%
+meteoric rise and people obviously on
+the Nobel committee thought this was
+
+ align:start position:0%
+the Nobel committee thought this was
+ 
+
+ align:start position:0%
+the Nobel committee thought this was
+pretty good work so you know how's how's
+
+ align:start position:0%
+pretty good work so you know how's how's
+ 
+
+ align:start position:0%
+pretty good work so you know how's how's
+the Bor model going to describe this
+
+ align:start position:0%
+the Bor model going to describe this
+ 
+
+ align:start position:0%
+the Bor model going to describe this
+it's it can't it's uh it's incapable of
+
+ align:start position:0%
+it's it can't it's uh it's incapable of
+ 
+
+ align:start position:0%
+it's it can't it's uh it's incapable of
+describing this
+
+ align:start position:0%
+describing this
+ 
+
+ align:start position:0%
+describing this
+effect there's more people are looking
+
+ align:start position:0%
+effect there's more people are looking
+ 
+
+ align:start position:0%
+effect there's more people are looking
+they're they're working hard so
+
+ align:start position:0%
+they're they're working hard so
+ 
+
+ align:start position:0%
+they're they're working hard so
+1913 I'm even going to give you the the
+
+ align:start position:0%
+1913 I'm even going to give you the the
+ 
+
+ align:start position:0%
+1913 I'm even going to give you the the
+month November 1913 why am I giving you
+
+ align:start position:0%
+month November 1913 why am I giving you
+ 
+
+ align:start position:0%
+month November 1913 why am I giving you
+the month because the paper was
+
+ align:start position:0%
+the month because the paper was
+ 
+
+ align:start position:0%
+the month because the paper was
+published in July of
+
+ align:start position:0%
+published in July of
+ 
+
+ align:start position:0%
+published in July of
+1913 B's paper July 1913 November 19133
+
+ align:start position:0%
+1913 B's paper July 1913 November 19133
+ 
+
+ align:start position:0%
+1913 B's paper July 1913 November 19133
+there's a fellow by the name of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Stark and he's doing some work at aen in
+
+ align:start position:0%
+Stark and he's doing some work at aen in
+ 
+
+ align:start position:0%
+Stark and he's doing some work at aen in
+Germany and analogous to what Zeman was
+
+ align:start position:0%
+Germany and analogous to what Zeman was
+ 
+
+ align:start position:0%
+Germany and analogous to what Zeman was
+doing Stark takes the gas discharge to
+
+ align:start position:0%
+doing Stark takes the gas discharge to
+ 
+
+ align:start position:0%
+doing Stark takes the gas discharge to
+and he puts it between plates that are
+
+ align:start position:0%
+and he puts it between plates that are
+ 
+
+ align:start position:0%
+and he puts it between plates that are
+connected to a power supply so then he
+
+ align:start position:0%
+connected to a power supply so then he
+ 
+
+ align:start position:0%
+connected to a power supply so then he
+subjects the gas in the tube to an
+
+ align:start position:0%
+subjects the gas in the tube to an
+ 
+
+ align:start position:0%
+subjects the gas in the tube to an
+electric field and what does he observe
+
+ align:start position:0%
+electric field and what does he observe
+ 
+
+ align:start position:0%
+electric field and what does he observe
+line splitting and how is the line
+
+ align:start position:0%
+line splitting and how is the line
+ 
+
+ align:start position:0%
+line splitting and how is the line
+splitting the more intense the applied
+
+ align:start position:0%
+splitting the more intense the applied
+ 
+
+ align:start position:0%
+splitting the more intense the applied
+electric field the greater the line
+
+ align:start position:0%
+electric field the greater the line
+ 
+
+ align:start position:0%
+electric field the greater the line
+splitting so same thing line
+
+ align:start position:0%
+splitting so same thing line
+ 
+
+ align:start position:0%
+splitting so same thing line
+splitting line splitting in electric
+
+ align:start position:0%
+splitting line splitting in electric
+ 
+
+ align:start position:0%
+splitting line splitting in electric
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+it's known as the Stark
+
+ align:start position:0%
+it's known as the Stark
+ 
+
+ align:start position:0%
+it's known as the Stark
+effect and uh you guess that he gets a
+
+ align:start position:0%
+effect and uh you guess that he gets a
+ 
+
+ align:start position:0%
+effect and uh you guess that he gets a
+Nobel everybody's getting
+
+ align:start position:0%
+Nobel everybody's getting
+ 
+
+ align:start position:0%
+Nobel everybody's getting
+noells 1919 he gets an nobell for the
+
+ align:start position:0%
+noells 1919 he gets an nobell for the
+ 
+
+ align:start position:0%
+noells 1919 he gets an nobell for the
+Stark effect so all of this is adding up
+
+ align:start position:0%
+Stark effect so all of this is adding up
+ 
+
+ align:start position:0%
+Stark effect so all of this is adding up
+to you know there's good there's good
+
+ align:start position:0%
+to you know there's good there's good
+ 
+
+ align:start position:0%
+to you know there's good there's good
+news here bore was able to give us a
+
+ align:start position:0%
+news here bore was able to give us a
+ 
+
+ align:start position:0%
+news here bore was able to give us a
+sense of what was going on in the
+
+ align:start position:0%
+sense of what was going on in the
+ 
+
+ align:start position:0%
+sense of what was going on in the
+angstrom experiment but there's a lot of
+
+ align:start position:0%
+angstrom experiment but there's a lot of
+ 
+
+ align:start position:0%
+angstrom experiment but there's a lot of
+stuff here indicating that it's an
+
+ align:start position:0%
+stuff here indicating that it's an
+ 
+
+ align:start position:0%
+stuff here indicating that it's an
+incomplete model so 1916 a theoretician
+
+ align:start position:0%
+incomplete model so 1916 a theoretician
+ 
+
+ align:start position:0%
+incomplete model so 1916 a theoretician
+comes to the rescue Arnold
+
+ align:start position:0%
+comes to the rescue Arnold
+ 
+
+ align:start position:0%
+comes to the rescue Arnold
+sommerfeld Arnold sommerfeld he was a
+
+ align:start position:0%
+sommerfeld Arnold sommerfeld he was a
+ 
+
+ align:start position:0%
+sommerfeld Arnold sommerfeld he was a
+professor of physics in
+
+ align:start position:0%
+professor of physics in
+ 
+
+ align:start position:0%
+professor of physics in
+Munich
+
+ align:start position:0%
+Munich
+ 
+
+ align:start position:0%
+Munich
+and he proposed some modifications to
+
+ align:start position:0%
+and he proposed some modifications to
+ 
+
+ align:start position:0%
+and he proposed some modifications to
+the bore model he liked the bore model
+
+ align:start position:0%
+the bore model he liked the bore model
+ 
+
+ align:start position:0%
+the bore model he liked the bore model
+he didn't want to throw it out he liked
+
+ align:start position:0%
+he didn't want to throw it out he liked
+ 
+
+ align:start position:0%
+he didn't want to throw it out he liked
+the concept of a planetary model but
+
+ align:start position:0%
+the concept of a planetary model but
+ 
+
+ align:start position:0%
+the concept of a planetary model but
+then he looked to maybe he looked to the
+
+ align:start position:0%
+then he looked to maybe he looked to the
+ 
+
+ align:start position:0%
+then he looked to maybe he looked to the
+heavens you know Kepler's laws of
+
+ align:start position:0%
+heavens you know Kepler's laws of
+ 
+
+ align:start position:0%
+heavens you know Kepler's laws of
+planetary motion what's the orbit that
+
+ align:start position:0%
+planetary motion what's the orbit that
+ 
+
+ align:start position:0%
+planetary motion what's the orbit that
+the planets describe it's ellips liip
+
+ align:start position:0%
+the planets describe it's ellips liip
+ 
+
+ align:start position:0%
+the planets describe it's ellips liip
+oil so some are said how about this
+
+ align:start position:0%
+oil so some are said how about this
+ 
+
+ align:start position:0%
+oil so some are said how about this
+suppose just suppose and this is not to
+
+ align:start position:0%
+suppose just suppose and this is not to
+ 
+
+ align:start position:0%
+suppose just suppose and this is not to
+scale it's going to be exaggerated so
+
+ align:start position:0%
+scale it's going to be exaggerated so
+ 
+
+ align:start position:0%
+scale it's going to be exaggerated so
+you get a sense of it suppose in
+
+ align:start position:0%
+you get a sense of it suppose in
+ 
+
+ align:start position:0%
+you get a sense of it suppose in
+addition to a spherical orbit suppose
+
+ align:start position:0%
+addition to a spherical orbit suppose
+ 
+
+ align:start position:0%
+addition to a spherical orbit suppose
+the electron might describe an
+
+ align:start position:0%
+the electron might describe an
+ 
+
+ align:start position:0%
+the electron might describe an
+elliptical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orbit now overall this is roughly the
+
+ align:start position:0%
+orbit now overall this is roughly the
+ 
+
+ align:start position:0%
+orbit now overall this is roughly the
+same it's not super elliptical it's just
+
+ align:start position:0%
+same it's not super elliptical it's just
+ 
+
+ align:start position:0%
+same it's not super elliptical it's just
+mildly elliptical but just enough that
+
+ align:start position:0%
+mildly elliptical but just enough that
+ 
+
+ align:start position:0%
+mildly elliptical but just enough that
+it's not exactly spherical so this could
+
+ align:start position:0%
+it's not exactly spherical so this could
+ 
+
+ align:start position:0%
+it's not exactly spherical so this could
+give you sort of have your cake and eat
+
+ align:start position:0%
+give you sort of have your cake and eat
+ 
+
+ align:start position:0%
+give you sort of have your cake and eat
+it too you could say this this is the
+
+ align:start position:0%
+it too you could say this this is the
+ 
+
+ align:start position:0%
+it too you could say this this is the
+principal quantum number of bore it's n
+
+ align:start position:0%
+principal quantum number of bore it's n
+ 
+
+ align:start position:0%
+principal quantum number of bore it's n
+but within n there's a little bit of
+
+ align:start position:0%
+but within n there's a little bit of
+ 
+
+ align:start position:0%
+but within n there's a little bit of
+fine
+
+ align:start position:0%
+fine
+ 
+
+ align:start position:0%
+fine
+structure fine structure that is to say
+
+ align:start position:0%
+structure fine structure that is to say
+ 
+
+ align:start position:0%
+structure fine structure that is to say
+there are details there that the first
+
+ align:start position:0%
+there are details there that the first
+ 
+
+ align:start position:0%
+there are details there that the first
+past didn't quite
+
+ align:start position:0%
+past didn't quite
+ 
+
+ align:start position:0%
+past didn't quite
+capture so suppose we have more than one
+
+ align:start position:0%
+capture so suppose we have more than one
+ 
+
+ align:start position:0%
+capture so suppose we have more than one
+maybe we have a plurality of elliptical
+
+ align:start position:0%
+maybe we have a plurality of elliptical
+ 
+
+ align:start position:0%
+maybe we have a plurality of elliptical
+orbits
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have elliptical orbits but they're
+
+ align:start position:0%
+so we have elliptical orbits but they're
+ 
+
+ align:start position:0%
+so we have elliptical orbits but they're
+roughly of the same Dimension as the
+
+ align:start position:0%
+roughly of the same Dimension as the
+ 
+
+ align:start position:0%
+roughly of the same Dimension as the
+original circular orbit and he says this
+
+ align:start position:0%
+original circular orbit and he says this
+ 
+
+ align:start position:0%
+original circular orbit and he says this
+we have sort of a band a band and he
+
+ align:start position:0%
+we have sort of a band a band and he
+ 
+
+ align:start position:0%
+we have sort of a band a band and he
+calls this a
+
+ align:start position:0%
+calls this a
+ 
+
+ align:start position:0%
+calls this a
+shell a shell
+
+ align:start position:0%
+shell a shell
+ 
+
+ align:start position:0%
+shell a shell
+containing multiple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orbits which he termed orbitals to
+
+ align:start position:0%
+orbits which he termed orbitals to
+ 
+
+ align:start position:0%
+orbits which he termed orbitals to
+distinguish them from the circular
+
+ align:start position:0%
+distinguish them from the circular
+ 
+
+ align:start position:0%
+distinguish them from the circular
+orbits of
+
+ align:start position:0%
+orbits of
+ 
+
+ align:start position:0%
+orbits of
+bore why do you call it a shell model he
+
+ align:start position:0%
+bore why do you call it a shell model he
+ 
+
+ align:start position:0%
+bore why do you call it a shell model he
+said think about the eggshell the
+
+ align:start position:0%
+said think about the eggshell the
+ 
+
+ align:start position:0%
+said think about the eggshell the
+eggshell we can describe it but the
+
+ align:start position:0%
+eggshell we can describe it but the
+ 
+
+ align:start position:0%
+eggshell we can describe it but the
+eggshell itself has some thickness so
+
+ align:start position:0%
+eggshell itself has some thickness so
+ 
+
+ align:start position:0%
+eggshell itself has some thickness so
+this is a a sense of what what
+
+ align:start position:0%
+this is a a sense of what what
+ 
+
+ align:start position:0%
+this is a a sense of what what
+summerfelt was giving us so he says how
+
+ align:start position:0%
+summerfelt was giving us so he says how
+ 
+
+ align:start position:0%
+summerfelt was giving us so he says how
+am I going to capture these ideas
+
+ align:start position:0%
+am I going to capture these ideas
+ 
+
+ align:start position:0%
+am I going to capture these ideas
+quantitatively well the shell could be
+
+ align:start position:0%
+quantitatively well the shell could be
+ 
+
+ align:start position:0%
+quantitatively well the shell could be
+captured by the quantity n but these
+
+ align:start position:0%
+captured by the quantity n but these
+ 
+
+ align:start position:0%
+captured by the quantity n but these
+orbitals some of them circular some of
+
+ align:start position:0%
+orbitals some of them circular some of
+ 
+
+ align:start position:0%
+orbitals some of them circular some of
+them elliptical I'm going to need new
+
+ align:start position:0%
+them elliptical I'm going to need new
+ 
+
+ align:start position:0%
+them elliptical I'm going to need new
+quantum numbers new quantum numbers
+
+ align:start position:0%
+quantum numbers new quantum numbers
+ 
+
+ align:start position:0%
+quantum numbers new quantum numbers
+in order to capture these new
+
+ align:start position:0%
+in order to capture these new
+ 
+
+ align:start position:0%
+in order to capture these new
+ideas and so let's take a look at the
+
+ align:start position:0%
+ideas and so let's take a look at the
+ 
+
+ align:start position:0%
+ideas and so let's take a look at the
+quantum numbers that uh sommerfeld gave
+
+ align:start position:0%
+quantum numbers that uh sommerfeld gave
+ 
+
+ align:start position:0%
+quantum numbers that uh sommerfeld gave
+us so the first one is n and it is as it
+
+ align:start position:0%
+us so the first one is n and it is as it
+ 
+
+ align:start position:0%
+us so the first one is n and it is as it
+was in the case of the bore model so
+
+ align:start position:0%
+was in the case of the bore model so
+ 
+
+ align:start position:0%
+was in the case of the bore model so
+this is called the principal shell Quant
+
+ align:start position:0%
+this is called the principal shell Quant
+ 
+
+ align:start position:0%
+this is called the principal shell Quant
+the principal uh quantum number or the
+
+ align:start position:0%
+the principal uh quantum number or the
+ 
+
+ align:start position:0%
+the principal uh quantum number or the
+uh shell quantum number principal or
+
+ align:start position:0%
+uh shell quantum number principal or
+ 
+
+ align:start position:0%
+uh shell quantum number principal or
+shell quantum number and it talks about
+
+ align:start position:0%
+shell quantum number and it talks about
+ 
+
+ align:start position:0%
+shell quantum number and it talks about
+size it talks about size the size of
+
+ align:start position:0%
+size it talks about size the size of
+ 
+
+ align:start position:0%
+size it talks about size the size of
+that is to say the distance from the
+
+ align:start position:0%
+that is to say the distance from the
+ 
+
+ align:start position:0%
+that is to say the distance from the
+nucleus to the
+
+ align:start position:0%
+nucleus to the
+ 
+
+ align:start position:0%
+nucleus to the
+shell and it takes values 1 2 three and
+
+ align:start position:0%
+shell and it takes values 1 2 three and
+ 
+
+ align:start position:0%
+shell and it takes values 1 2 three and
+so on up to infinity and infinity we're
+
+ align:start position:0%
+so on up to infinity and infinity we're
+ 
+
+ align:start position:0%
+so on up to infinity and infinity we're
+talking about a free electron okay and
+
+ align:start position:0%
+talking about a free electron okay and
+ 
+
+ align:start position:0%
+talking about a free electron okay and
+in parallel there's another notation
+
+ align:start position:0%
+in parallel there's another notation
+ 
+
+ align:start position:0%
+in parallel there's another notation
+that's used the
+
+ align:start position:0%
+that's used the
+ 
+
+ align:start position:0%
+that's used the
+spectroscopists came up with their own
+
+ align:start position:0%
+spectroscopists came up with their own
+ 
+
+ align:start position:0%
+spectroscopists came up with their own
+notation they don't like numbers the
+
+ align:start position:0%
+notation they don't like numbers the
+ 
+
+ align:start position:0%
+notation they don't like numbers the
+spectroscopists use letters but you know
+
+ align:start position:0%
+spectroscopists use letters but you know
+ 
+
+ align:start position:0%
+spectroscopists use letters but you know
+the spectroscopist they're funny Bunch
+
+ align:start position:0%
+the spectroscopist they're funny Bunch
+ 
+
+ align:start position:0%
+the spectroscopist they're funny Bunch
+you know they're very suspicious so
+
+ align:start position:0%
+you know they're very suspicious so
+ 
+
+ align:start position:0%
+you know they're very suspicious so
+here's what happened if you look on this
+
+ align:start position:0%
+here's what happened if you look on this
+ 
+
+ align:start position:0%
+here's what happened if you look on this
+chart here for a while we thought Balmer
+
+ align:start position:0%
+chart here for a while we thought Balmer
+ 
+
+ align:start position:0%
+chart here for a while we thought Balmer
+was the bottom of the barrel but that's
+
+ align:start position:0%
+was the bottom of the barrel but that's
+ 
+
+ align:start position:0%
+was the bottom of the barrel but that's
+n equals 2 and then when the detectors
+
+ align:start position:0%
+n equals 2 and then when the detectors
+ 
+
+ align:start position:0%
+n equals 2 and then when the detectors
+got better we saw that n equals 1 so the
+
+ align:start position:0%
+got better we saw that n equals 1 so the
+ 
+
+ align:start position:0%
+got better we saw that n equals 1 so the
+spectroscopist said what if somebody
+
+ align:start position:0%
+spectroscopist said what if somebody
+ 
+
+ align:start position:0%
+spectroscopist said what if somebody
+comes along with an even better detector
+
+ align:start position:0%
+comes along with an even better detector
+ 
+
+ align:start position:0%
+comes along with an even better detector
+and finds transitions to energy levels
+
+ align:start position:0%
+and finds transitions to energy levels
+ 
+
+ align:start position:0%
+and finds transitions to energy levels
+below that which we are calling
+
+ align:start position:0%
+below that which we are calling
+ 
+
+ align:start position:0%
+below that which we are calling
+one so we're going to get ready we're
+
+ align:start position:0%
+one so we're going to get ready we're
+ 
+
+ align:start position:0%
+one so we're going to get ready we're
+going to give letters to these and they
+
+ align:start position:0%
+going to give letters to these and they
+ 
+
+ align:start position:0%
+going to give letters to these and they
+started with the letter k because it's
+
+ align:start position:0%
+started with the letter k because it's
+ 
+
+ align:start position:0%
+started with the letter k because it's
+somewhere in the middle of the alphabet
+
+ align:start position:0%
+somewhere in the middle of the alphabet
+ 
+
+ align:start position:0%
+somewhere in the middle of the alphabet
+so if we ever discover an energy level
+
+ align:start position:0%
+so if we ever discover an energy level
+ 
+
+ align:start position:0%
+so if we ever discover an energy level
+lower than n equals 1 we can use the
+
+ align:start position:0%
+lower than n equals 1 we can use the
+ 
+
+ align:start position:0%
+lower than n equals 1 we can use the
+letter it will be the J so there's K LM
+
+ align:start position:0%
+letter it will be the J so there's K LM
+ 
+
+ align:start position:0%
+letter it will be the J so there's K LM
+and this notation is used to this day
+
+ align:start position:0%
+and this notation is used to this day
+ 
+
+ align:start position:0%
+and this notation is used to this day
+when we talk about x-rays x-rays
+
+ align:start position:0%
+when we talk about x-rays x-rays
+ 
+
+ align:start position:0%
+when we talk about x-rays x-rays
+generated by electrons falling down to
+
+ align:start position:0%
+generated by electrons falling down to
+ 
+
+ align:start position:0%
+generated by electrons falling down to
+ground state are called K xrays so this
+
+ align:start position:0%
+ground state are called K xrays so this
+ 
+
+ align:start position:0%
+ground state are called K xrays so this
+is the other notation for the values
+
+ align:start position:0%
+is the other notation for the values
+ 
+
+ align:start position:0%
+is the other notation for the values
+that the N can take now let's get into
+
+ align:start position:0%
+that the N can take now let's get into
+ 
+
+ align:start position:0%
+that the N can take now let's get into
+the contributions of uh sufel he called
+
+ align:start position:0%
+the contributions of uh sufel he called
+ 
+
+ align:start position:0%
+the contributions of uh sufel he called
+the next quantum number lowercase L and
+
+ align:start position:0%
+the next quantum number lowercase L and
+ 
+
+ align:start position:0%
+the next quantum number lowercase L and
+this is the orbital quantum number the
+
+ align:start position:0%
+this is the orbital quantum number the
+ 
+
+ align:start position:0%
+this is the orbital quantum number the
+orbital quantum number and it describes
+
+ align:start position:0%
+orbital quantum number and it describes
+ 
+
+ align:start position:0%
+orbital quantum number and it describes
+the shape of the orbital remember I said
+
+ align:start position:0%
+the shape of the orbital remember I said
+ 
+
+ align:start position:0%
+the shape of the orbital remember I said
+we needed some way to distinguish purely
+
+ align:start position:0%
+we needed some way to distinguish purely
+ 
+
+ align:start position:0%
+we needed some way to distinguish purely
+circular from elliptical or other shaped
+
+ align:start position:0%
+circular from elliptical or other shaped
+ 
+
+ align:start position:0%
+circular from elliptical or other shaped
+orbitals and the orbital quantum number
+
+ align:start position:0%
+orbitals and the orbital quantum number
+ 
+
+ align:start position:0%
+orbitals and the orbital quantum number
+takes values 0 1 2 up to the value of n
+
+ align:start position:0%
+takes values 0 1 2 up to the value of n
+ 
+
+ align:start position:0%
+takes values 0 1 2 up to the value of n
+minus1 up to the value n minus one and
+
+ align:start position:0%
+minus1 up to the value n minus one and
+ 
+
+ align:start position:0%
+minus1 up to the value n minus one and
+the spectroscopists use letters they
+
+ align:start position:0%
+the spectroscopists use letters they
+ 
+
+ align:start position:0%
+the spectroscopists use letters they
+don't they refuse used to use numbers
+
+ align:start position:0%
+don't they refuse used to use numbers
+ 
+
+ align:start position:0%
+don't they refuse used to use numbers
+they're very numero phobic so they use
+
+ align:start position:0%
+they're very numero phobic so they use
+ 
+
+ align:start position:0%
+they're very numero phobic so they use
+lowercase letters to distinguish the
+
+ align:start position:0%
+lowercase letters to distinguish the
+ 
+
+ align:start position:0%
+lowercase letters to distinguish the
+orbital quantum number from the
+
+ align:start position:0%
+orbital quantum number from the
+ 
+
+ align:start position:0%
+orbital quantum number from the
+principal quantum number and so when uh
+
+ align:start position:0%
+principal quantum number and so when uh
+ 
+
+ align:start position:0%
+principal quantum number and so when uh
+L equals zero it's lowercase s for Sharp
+
+ align:start position:0%
+L equals zero it's lowercase s for Sharp
+ 
+
+ align:start position:0%
+L equals zero it's lowercase s for Sharp
+because these would be very sharp lines
+
+ align:start position:0%
+because these would be very sharp lines
+ 
+
+ align:start position:0%
+because these would be very sharp lines
+then P for uh L equal 1 which is
+
+ align:start position:0%
+then P for uh L equal 1 which is
+ 
+
+ align:start position:0%
+then P for uh L equal 1 which is
+principal D for Lal 2 which stands for
+
+ align:start position:0%
+principal D for Lal 2 which stands for
+ 
+
+ align:start position:0%
+principal D for Lal 2 which stands for
+diffuse and F which stands for
+
+ align:start position:0%
+diffuse and F which stands for
+ 
+
+ align:start position:0%
+diffuse and F which stands for
+fundamental Because by the the time you
+
+ align:start position:0%
+fundamental Because by the the time you
+ 
+
+ align:start position:0%
+fundamental Because by the the time you
+get up to F level you've got such
+
+ align:start position:0%
+get up to F level you've got such
+ 
+
+ align:start position:0%
+get up to F level you've got such
+compression that all of the spectral
+
+ align:start position:0%
+compression that all of the spectral
+ 
+
+ align:start position:0%
+compression that all of the spectral
+lines are starting to look very similar
+
+ align:start position:0%
+lines are starting to look very similar
+ 
+
+ align:start position:0%
+lines are starting to look very similar
+to those of hydrogen which is the
+
+ align:start position:0%
+to those of hydrogen which is the
+ 
+
+ align:start position:0%
+to those of hydrogen which is the
+fundamental spectrum of all time and
+
+ align:start position:0%
+fundamental spectrum of all time and
+ 
+
+ align:start position:0%
+fundamental spectrum of all time and
+then after that they go GH because they
+
+ align:start position:0%
+then after that they go GH because they
+ 
+
+ align:start position:0%
+then after that they go GH because they
+ran out of ideas so they that was it
+
+ align:start position:0%
+ran out of ideas so they that was it
+ 
+
+ align:start position:0%
+ran out of ideas so they that was it
+okay so um now let's take a look when L
+
+ align:start position:0%
+okay so um now let's take a look when L
+ 
+
+ align:start position:0%
+okay so um now let's take a look when L
+equals z l equals z this means you have
+
+ align:start position:0%
+equals z l equals z this means you have
+ 
+
+ align:start position:0%
+equals z l equals z this means you have
+a spherical or circular a spherical
+
+ align:start position:0%
+a spherical or circular a spherical
+ 
+
+ align:start position:0%
+a spherical or circular a spherical
+orbital or a circular orbit and that's
+
+ align:start position:0%
+orbital or a circular orbit and that's
+ 
+
+ align:start position:0%
+orbital or a circular orbit and that's
+easy to remember because o is think of
+
+ align:start position:0%
+easy to remember because o is think of
+ 
+
+ align:start position:0%
+easy to remember because o is think of
+it as perfect sphere all right when l
+
+ align:start position:0%
+it as perfect sphere all right when l
+ 
+
+ align:start position:0%
+it as perfect sphere all right when l
+equals 1 this is
+
+ align:start position:0%
+equals 1 this is
+ 
+
+ align:start position:0%
+equals 1 this is
+elliptical you have an elliptical orbit
+
+ align:start position:0%
+elliptical you have an elliptical orbit
+ 
+
+ align:start position:0%
+elliptical you have an elliptical orbit
+you can think of that you know zero is
+
+ align:start position:0%
+you can think of that you know zero is
+ 
+
+ align:start position:0%
+you can think of that you know zero is
+zero and one think of that as there's
+
+ align:start position:0%
+zero and one think of that as there's
+ 
+
+ align:start position:0%
+zero and one think of that as there's
+some elongation okay and when L equals 2
+
+ align:start position:0%
+some elongation okay and when L equals 2
+ 
+
+ align:start position:0%
+some elongation okay and when L equals 2
+when L equals 2 I'll show you these
+
+ align:start position:0%
+when L equals 2 I'll show you these
+ 
+
+ align:start position:0%
+when L equals 2 I'll show you these
+later in the in about a week's time
+
+ align:start position:0%
+later in the in about a week's time
+ 
+
+ align:start position:0%
+later in the in about a week's time
+they're just much more complex you get
+
+ align:start position:0%
+they're just much more complex you get
+ 
+
+ align:start position:0%
+they're just much more complex you get
+dumbbell shaped donut shaped and all
+
+ align:start position:0%
+dumbbell shaped donut shaped and all
+ 
+
+ align:start position:0%
+dumbbell shaped donut shaped and all
+sorts of things so just say they're more
+
+ align:start position:0%
+sorts of things so just say they're more
+ 
+
+ align:start position:0%
+sorts of things so just say they're more
+complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so those are the numbers associated with
+
+ align:start position:0%
+so those are the numbers associated with
+ 
+
+ align:start position:0%
+so those are the numbers associated with
+certain shapes of the uh orbital then
+
+ align:start position:0%
+certain shapes of the uh orbital then
+ 
+
+ align:start position:0%
+certain shapes of the uh orbital then
+the the next quantum number he gave us
+
+ align:start position:0%
+the the next quantum number he gave us
+ 
+
+ align:start position:0%
+the the next quantum number he gave us
+was m m which is the magnetic quantum
+
+ align:start position:0%
+was m m which is the magnetic quantum
+ 
+
+ align:start position:0%
+was m m which is the magnetic quantum
+number it's the magnetic quantum number
+
+ align:start position:0%
+number it's the magnetic quantum number
+ 
+
+ align:start position:0%
+number it's the magnetic quantum number
+and it speaks to the question of
+
+ align:start position:0%
+and it speaks to the question of
+ 
+
+ align:start position:0%
+and it speaks to the question of
+orientation
+
+ align:start position:0%
+orientation
+ 
+
+ align:start position:0%
+orientation
+orientation and the admissible values of
+
+ align:start position:0%
+orientation and the admissible values of
+ 
+
+ align:start position:0%
+orientation and the admissible values of
+M are l l minus one through zero down
+
+ align:start position:0%
+M are l l minus one through zero down
+ 
+
+ align:start position:0%
+M are l l minus one through zero down
+to minus l so spanning from plus L to
+
+ align:start position:0%
+to minus l so spanning from plus L to
+ 
+
+ align:start position:0%
+to minus l so spanning from plus L to
+minus L and of course L is subject to
+
+ align:start position:0%
+minus L and of course L is subject to
+ 
+
+ align:start position:0%
+minus L and of course L is subject to
+values of n so in the case of n equals 1
+
+ align:start position:0%
+values of n so in the case of n equals 1
+ 
+
+ align:start position:0%
+values of n so in the case of n equals 1
+when n equals 1 L can equal only
+
+ align:start position:0%
+when n equals 1 L can equal only
+ 
+
+ align:start position:0%
+when n equals 1 L can equal only
+zero so if L is zero then this value M
+
+ align:start position:0%
+zero so if L is zero then this value M
+ 
+
+ align:start position:0%
+zero so if L is zero then this value M
+must always be
+
+ align:start position:0%
+must always be
+ 
+
+ align:start position:0%
+must always be
+zero and indeed this confirms the
+
+ align:start position:0%
+zero and indeed this confirms the
+ 
+
+ align:start position:0%
+zero and indeed this confirms the
+observations there was no line splitting
+
+ align:start position:0%
+observations there was no line splitting
+ 
+
+ align:start position:0%
+observations there was no line splitting
+in a magnetic field for the ground state
+
+ align:start position:0%
+in a magnetic field for the ground state
+ 
+
+ align:start position:0%
+in a magnetic field for the ground state
+say wasn't seen what happens when n
+
+ align:start position:0%
+say wasn't seen what happens when n
+ 
+
+ align:start position:0%
+say wasn't seen what happens when n
+equals 2 when n equals 2 well L can take
+
+ align:start position:0%
+equals 2 when n equals 2 well L can take
+ 
+
+ align:start position:0%
+equals 2 when n equals 2 well L can take
+values of 1 and zero all right one and
+
+ align:start position:0%
+values of 1 and zero all right one and
+ 
+
+ align:start position:0%
+values of 1 and zero all right one and
+zero so what do we have we have now Nal
+
+ align:start position:0%
+zero so what do we have we have now Nal
+ 
+
+ align:start position:0%
+zero so what do we have we have now Nal
+2 L equals one so M can now go one Z and
+
+ align:start position:0%
+2 L equals one so M can now go one Z and
+ 
+
+ align:start position:0%
+2 L equals one so M can now go one Z and
+minus one 1 Z and minus one so this is
+
+ align:start position:0%
+minus one 1 Z and minus one so this is
+ 
+
+ align:start position:0%
+minus one 1 Z and minus one so this is
+the one case where there is some value
+
+ align:start position:0%
+the one case where there is some value
+ 
+
+ align:start position:0%
+the one case where there is some value
+in thinking about the cartisian
+
+ align:start position:0%
+in thinking about the cartisian
+ 
+
+ align:start position:0%
+in thinking about the cartisian
+equivalent of this it's very dangerous
+
+ align:start position:0%
+equivalent of this it's very dangerous
+ 
+
+ align:start position:0%
+equivalent of this it's very dangerous
+when you're talking about uh Quantum
+
+ align:start position:0%
+when you're talking about uh Quantum
+ 
+
+ align:start position:0%
+when you're talking about uh Quantum
+ideas to try to ascribe physical
+
+ align:start position:0%
+ideas to try to ascribe physical
+ 
+
+ align:start position:0%
+ideas to try to ascribe physical
+attributes to them because in many cases
+
+ align:start position:0%
+attributes to them because in many cases
+ 
+
+ align:start position:0%
+attributes to them because in many cases
+it just doesn't doesn't work but in this
+
+ align:start position:0%
+it just doesn't doesn't work but in this
+ 
+
+ align:start position:0%
+it just doesn't doesn't work but in this
+case I think it does so let's look at
+
+ align:start position:0%
+case I think it does so let's look at
+ 
+
+ align:start position:0%
+case I think it does so let's look at
+three values of the magnetic quantum
+
+ align:start position:0%
+three values of the magnetic quantum
+ 
+
+ align:start position:0%
+three values of the magnetic quantum
+number when we have an elliptical
+
+ align:start position:0%
+number when we have an elliptical
+ 
+
+ align:start position:0%
+number when we have an elliptical
+orbital right so one way of thinking
+
+ align:start position:0%
+orbital right so one way of thinking
+ 
+
+ align:start position:0%
+orbital right so one way of thinking
+about it is here are the three principal
+
+ align:start position:0%
+about it is here are the three principal
+ 
+
+ align:start position:0%
+about it is here are the three principal
+coordinate directions x y and z now I
+
+ align:start position:0%
+coordinate directions x y and z now I
+ 
+
+ align:start position:0%
+coordinate directions x y and z now I
+don't know where real X lies but once I
+
+ align:start position:0%
+don't know where real X lies but once I
+ 
+
+ align:start position:0%
+don't know where real X lies but once I
+choose X I can use the right hand rule
+
+ align:start position:0%
+choose X I can use the right hand rule
+ 
+
+ align:start position:0%
+choose X I can use the right hand rule
+and I know where Y and Z have to be
+
+ align:start position:0%
+and I know where Y and Z have to be
+ 
+
+ align:start position:0%
+and I know where Y and Z have to be
+they're orthogonal so if this is X this
+
+ align:start position:0%
+they're orthogonal so if this is X this
+ 
+
+ align:start position:0%
+they're orthogonal so if this is X this
+is y this is
+
+ align:start position:0%
+is y this is
+ 
+
+ align:start position:0%
+is y this is
+z I have a non spherical non-axis
+
+ align:start position:0%
+z I have a non spherical non-axis
+ 
+
+ align:start position:0%
+z I have a non spherical non-axis
+symmetric orbital so for Simplicity I'm
+
+ align:start position:0%
+symmetric orbital so for Simplicity I'm
+ 
+
+ align:start position:0%
+symmetric orbital so for Simplicity I'm
+going to just make
+
+ align:start position:0%
+going to just make
+ 
+
+ align:start position:0%
+going to just make
+it elongated okay well what does this
+
+ align:start position:0%
+it elongated okay well what does this
+ 
+
+ align:start position:0%
+it elongated okay well what does this
+say it says M can go 1 0 minus one which
+
+ align:start position:0%
+say it says M can go 1 0 minus one which
+ 
+
+ align:start position:0%
+say it says M can go 1 0 minus one which
+to my mind represents the fact that
+
+ align:start position:0%
+to my mind represents the fact that
+ 
+
+ align:start position:0%
+to my mind represents the fact that
+there are three principal coordinate
+
+ align:start position:0%
+there are three principal coordinate
+ 
+
+ align:start position:0%
+there are three principal coordinate
+directions in which you can Orient that
+
+ align:start position:0%
+directions in which you can Orient that
+ 
+
+ align:start position:0%
+directions in which you can Orient that
+so I think this is a nice example of
+
+ align:start position:0%
+so I think this is a nice example of
+ 
+
+ align:start position:0%
+so I think this is a nice example of
+mathematics imitating reality okay after
+
+ align:start position:0%
+mathematics imitating reality okay after
+ 
+
+ align:start position:0%
+mathematics imitating reality okay after
+that it gets uh it gets very messy and
+
+ align:start position:0%
+that it gets uh it gets very messy and
+ 
+
+ align:start position:0%
+that it gets uh it gets very messy and
+then the last quantum number this is
+
+ align:start position:0%
+then the last quantum number this is
+ 
+
+ align:start position:0%
+then the last quantum number this is
+where this is where
+
+ align:start position:0%
+where this is where
+ 
+
+ align:start position:0%
+where this is where
+um uh sommerfeld left it but uh I'll
+
+ align:start position:0%
+um uh sommerfeld left it but uh I'll
+ 
+
+ align:start position:0%
+um uh sommerfeld left it but uh I'll
+finish by introducing the last quantum
+
+ align:start position:0%
+finish by introducing the last quantum
+ 
+
+ align:start position:0%
+finish by introducing the last quantum
+number the last quantum number came a
+
+ align:start position:0%
+number the last quantum number came a
+ 
+
+ align:start position:0%
+number the last quantum number came a
+little bit later it's lowercase s which
+
+ align:start position:0%
+little bit later it's lowercase s which
+ 
+
+ align:start position:0%
+little bit later it's lowercase s which
+is the spin quantum
+
+ align:start position:0%
+is the spin quantum
+ 
+
+ align:start position:0%
+is the spin quantum
+number and it represents the fact that
+
+ align:start position:0%
+number and it represents the fact that
+ 
+
+ align:start position:0%
+number and it represents the fact that
+electron is considered to have Spin and
+
+ align:start position:0%
+electron is considered to have Spin and
+ 
+
+ align:start position:0%
+electron is considered to have Spin and
+it takes values plus or minus 12 and
+
+ align:start position:0%
+it takes values plus or minus 12 and
+ 
+
+ align:start position:0%
+it takes values plus or minus 12 and
+here's the here's the basis for this uh
+
+ align:start position:0%
+here's the here's the basis for this uh
+ 
+
+ align:start position:0%
+here's the here's the basis for this uh
+value here I want to put this all
+
+ align:start position:0%
+value here I want to put this all
+ 
+
+ align:start position:0%
+value here I want to put this all
+together so I'm doing a little bit of
+
+ align:start position:0%
+together so I'm doing a little bit of
+ 
+
+ align:start position:0%
+together so I'm doing a little bit of
+Back to the Future because this is 1916
+
+ align:start position:0%
+Back to the Future because this is 1916
+ 
+
+ align:start position:0%
+Back to the Future because this is 1916
+that's where summerell leaves it this
+
+ align:start position:0%
+that's where summerell leaves it this
+ 
+
+ align:start position:0%
+that's where summerell leaves it this
+comes about 1925 but I want you to have
+
+ align:start position:0%
+comes about 1925 but I want you to have
+ 
+
+ align:start position:0%
+comes about 1925 but I want you to have
+all quantum numbers and then we can move
+
+ align:start position:0%
+all quantum numbers and then we can move
+ 
+
+ align:start position:0%
+all quantum numbers and then we can move
+forward and what introduced this was an
+
+ align:start position:0%
+forward and what introduced this was an
+ 
+
+ align:start position:0%
+forward and what introduced this was an
+exp experiment conducted by Stern and
+
+ align:start position:0%
+exp experiment conducted by Stern and
+ 
+
+ align:start position:0%
+exp experiment conducted by Stern and
+gerac in
+
+ align:start position:0%
+gerac in
+ 
+
+ align:start position:0%
+gerac in
+Frankfurt uh and that was done around
+
+ align:start position:0%
+Frankfurt uh and that was done around
+ 
+
+ align:start position:0%
+Frankfurt uh and that was done around
+1921 we can wake this up we'll have a
+
+ align:start position:0%
+1921 we can wake this up we'll have a
+ 
+
+ align:start position:0%
+1921 we can wake this up we'll have a
+look at
+
+ align:start position:0%
+look at
+ 
+
+ align:start position:0%
+look at
+it oh this is cute this is uh I think
+
+ align:start position:0%
+it oh this is cute this is uh I think
+ 
+
+ align:start position:0%
+it oh this is cute this is uh I think
+it's cute we'll see you don't laugh at
+
+ align:start position:0%
+it's cute we'll see you don't laugh at
+ 
+
+ align:start position:0%
+it's cute we'll see you don't laugh at
+any of my jokes but here's this is um
+
+ align:start position:0%
+any of my jokes but here's this is um
+ 
+
+ align:start position:0%
+any of my jokes but here's this is um
+this is sommerfeld on the occasion of
+
+ align:start position:0%
+this is sommerfeld on the occasion of
+ 
+
+ align:start position:0%
+this is sommerfeld on the occasion of
+his 80th birthday and as the custom for
+
+ align:start position:0%
+his 80th birthday and as the custom for
+ 
+
+ align:start position:0%
+his 80th birthday and as the custom for
+the for a uh a birthday is so uh
+
+ align:start position:0%
+the for a uh a birthday is so uh
+ 
+
+ align:start position:0%
+the for a uh a birthday is so uh
+momentous is this people from all over
+
+ align:start position:0%
+momentous is this people from all over
+ 
+
+ align:start position:0%
+momentous is this people from all over
+the world get together for a party and
+
+ align:start position:0%
+the world get together for a party and
+ 
+
+ align:start position:0%
+the world get together for a party and
+they accompan this with a two or three
+
+ align:start position:0%
+they accompan this with a two or three
+ 
+
+ align:start position:0%
+they accompan this with a two or three
+day Affair in which people give
+
+ align:start position:0%
+day Affair in which people give
+ 
+
+ align:start position:0%
+day Affair in which people give
+scientific papers in honor of the
+
+ align:start position:0%
+scientific papers in honor of the
+ 
+
+ align:start position:0%
+scientific papers in honor of the
+celebrant so this is taken from the book
+
+ align:start position:0%
+celebrant so this is taken from the book
+ 
+
+ align:start position:0%
+celebrant so this is taken from the book
+that was published on the occasion of
+
+ align:start position:0%
+that was published on the occasion of
+ 
+
+ align:start position:0%
+that was published on the occasion of
+sommerfeld's 80th birthday and since
+
+ align:start position:0%
+sommerfeld's 80th birthday and since
+ 
+
+ align:start position:0%
+sommerfeld's 80th birthday and since
+sommerfeld was the one that proposed
+
+ align:start position:0%
+sommerfeld was the one that proposed
+ 
+
+ align:start position:0%
+sommerfeld was the one that proposed
+that orbits could be spherical or
+
+ align:start position:0%
+that orbits could be spherical or
+ 
+
+ align:start position:0%
+that orbits could be spherical or
+elliptical they as a as a a gag said
+
+ align:start position:0%
+elliptical they as a as a a gag said
+ 
+
+ align:start position:0%
+elliptical they as a as a a gag said
+that well here's sommerfeld and then
+
+ align:start position:0%
+that well here's sommerfeld and then
+ 
+
+ align:start position:0%
+that well here's sommerfeld and then
+here's sommerfeld somewhat distended so
+
+ align:start position:0%
+here's sommerfeld somewhat distended so
+ 
+
+ align:start position:0%
+here's sommerfeld somewhat distended so
+this is L equals 0 and this is lals 1
+
+ align:start position:0%
+this is L equals 0 and this is lals 1
+ 
+
+ align:start position:0%
+this is L equals 0 and this is lals 1
+and um this was accompanied by the
+
+ align:start position:0%
+and um this was accompanied by the
+ 
+
+ align:start position:0%
+and um this was accompanied by the
+inscription that said sommerfeld was the
+
+ align:start position:0%
+inscription that said sommerfeld was the
+ 
+
+ align:start position:0%
+inscription that said sommerfeld was the
+one who taught us that the circle is the
+
+ align:start position:0%
+one who taught us that the circle is the
+ 
+
+ align:start position:0%
+one who taught us that the circle is the
+degenerate form of the ellipse and that
+
+ align:start position:0%
+degenerate form of the ellipse and that
+ 
+
+ align:start position:0%
+degenerate form of the ellipse and that
+was really funny that's that's 1920s
+
+ align:start position:0%
+was really funny that's that's 1920s
+ 
+
+ align:start position:0%
+was really funny that's that's 1920s
+geek humor that was oh roaring see but
+
+ align:start position:0%
+geek humor that was oh roaring see but
+ 
+
+ align:start position:0%
+geek humor that was oh roaring see but
+clearly it doesn't age well you're not
+
+ align:start position:0%
+clearly it doesn't age well you're not
+ 
+
+ align:start position:0%
+clearly it doesn't age well you're not
+you're not you're not sensing this okay
+
+ align:start position:0%
+you're not you're not sensing this okay
+ 
+
+ align:start position:0%
+you're not you're not sensing this okay
+here's the stern gerac experiment very
+
+ align:start position:0%
+here's the stern gerac experiment very
+ 
+
+ align:start position:0%
+here's the stern gerac experiment very
+very cool experiment they were doing
+
+ align:start position:0%
+very cool experiment they were doing
+ 
+
+ align:start position:0%
+very cool experiment they were doing
+studies in the early 20s to try to
+
+ align:start position:0%
+studies in the early 20s to try to
+ 
+
+ align:start position:0%
+studies in the early 20s to try to
+validate Maxwell's equations so what
+
+ align:start position:0%
+validate Maxwell's equations so what
+ 
+
+ align:start position:0%
+validate Maxwell's equations so what
+they've got over here is a furnace with
+
+ align:start position:0%
+they've got over here is a furnace with
+ 
+
+ align:start position:0%
+they've got over here is a furnace with
+a Cru ible of liquid metal and the metal
+
+ align:start position:0%
+a Cru ible of liquid metal and the metal
+ 
+
+ align:start position:0%
+a Cru ible of liquid metal and the metal
+has obviously a vapor pressure above it
+
+ align:start position:0%
+has obviously a vapor pressure above it
+ 
+
+ align:start position:0%
+has obviously a vapor pressure above it
+and there's a slit here and they've got
+
+ align:start position:0%
+and there's a slit here and they've got
+ 
+
+ align:start position:0%
+and there's a slit here and they've got
+a beam it's like a physical vapor
+
+ align:start position:0%
+a beam it's like a physical vapor
+ 
+
+ align:start position:0%
+a beam it's like a physical vapor
+deposition and so they're shooting metal
+
+ align:start position:0%
+deposition and so they're shooting metal
+ 
+
+ align:start position:0%
+deposition and so they're shooting metal
+in a beam over to a cooled substrate
+
+ align:start position:0%
+in a beam over to a cooled substrate
+ 
+
+ align:start position:0%
+in a beam over to a cooled substrate
+here and they're analyzing the deposit
+
+ align:start position:0%
+here and they're analyzing the deposit
+ 
+
+ align:start position:0%
+here and they're analyzing the deposit
+okay so if you shoot a beam and he's got
+
+ align:start position:0%
+okay so if you shoot a beam and he's got
+ 
+
+ align:start position:0%
+okay so if you shoot a beam and he's got
+a slit you should just get the shadow of
+
+ align:start position:0%
+a slit you should just get the shadow of
+ 
+
+ align:start position:0%
+a slit you should just get the shadow of
+the slit so now let's get interesting
+
+ align:start position:0%
+the slit so now let's get interesting
+ 
+
+ align:start position:0%
+the slit so now let's get interesting
+let's test Maxwell's equations so they
+
+ align:start position:0%
+let's test Maxwell's equations so they
+ 
+
+ align:start position:0%
+let's test Maxwell's equations so they
+send the beam through a Divergent
+
+ align:start position:0%
+send the beam through a Divergent
+ 
+
+ align:start position:0%
+send the beam through a Divergent
+magnetic field you can see the South
+
+ align:start position:0%
+magnetic field you can see the South
+ 
+
+ align:start position:0%
+magnetic field you can see the South
+Pole comes to a point and the North Pole
+
+ align:start position:0%
+Pole comes to a point and the North Pole
+ 
+
+ align:start position:0%
+Pole comes to a point and the North Pole
+is uh a curve so the field lines have to
+
+ align:start position:0%
+is uh a curve so the field lines have to
+ 
+
+ align:start position:0%
+is uh a curve so the field lines have to
+diverge so they were asking questions
+
+ align:start position:0%
+diverge so they were asking questions
+ 
+
+ align:start position:0%
+diverge so they were asking questions
+like what happens if you take a beam of
+
+ align:start position:0%
+like what happens if you take a beam of
+ 
+
+ align:start position:0%
+like what happens if you take a beam of
+metal and send it through and here's
+
+ align:start position:0%
+metal and send it through and here's
+ 
+
+ align:start position:0%
+metal and send it through and here's
+what they found what they found was
+
+ align:start position:0%
+what they found what they found was
+ 
+
+ align:start position:0%
+what they found what they found was
+really really interesting if you
+
+ align:start position:0%
+really really interesting if you
+ 
+
+ align:start position:0%
+really really interesting if you
+take a a
+
+ align:start position:0%
+take a a
+ 
+
+ align:start position:0%
+take a a
+metal and send it with no magnetic
+
+ align:start position:0%
+metal and send it with no magnetic
+ 
+
+ align:start position:0%
+metal and send it with no magnetic
+field you look at what you get on the
+
+ align:start position:0%
+field you look at what you get on the
+ 
+
+ align:start position:0%
+field you look at what you get on the
+substrate this is the shadow of the slit
+
+ align:start position:0%
+substrate this is the shadow of the slit
+ 
+
+ align:start position:0%
+substrate this is the shadow of the slit
+in other words if you send it through a
+
+ align:start position:0%
+in other words if you send it through a
+ 
+
+ align:start position:0%
+in other words if you send it through a
+narrow slit this will be the deposit of
+
+ align:start position:0%
+narrow slit this will be the deposit of
+ 
+
+ align:start position:0%
+narrow slit this will be the deposit of
+the metal when B does not equal zero
+
+ align:start position:0%
+the metal when B does not equal zero
+ 
+
+ align:start position:0%
+the metal when B does not equal zero
+they observe a deflection so now the
+
+ align:start position:0%
+they observe a deflection so now the
+ 
+
+ align:start position:0%
+they observe a deflection so now the
+question is if here's the rest position
+
+ align:start position:0%
+question is if here's the rest position
+ 
+
+ align:start position:0%
+question is if here's the rest position
+of the beam in which direction should
+
+ align:start position:0%
+of the beam in which direction should
+ 
+
+ align:start position:0%
+of the beam in which direction should
+the deflection
+
+ align:start position:0%
+the deflection
+ 
+
+ align:start position:0%
+the deflection
+go and so some would argue well it
+
+ align:start position:0%
+go and so some would argue well it
+ 
+
+ align:start position:0%
+go and so some would argue well it
+should go up and some argued that it
+
+ align:start position:0%
+should go up and some argued that it
+ 
+
+ align:start position:0%
+should go up and some argued that it
+that it should go down and what they
+
+ align:start position:0%
+that it should go down and what they
+ 
+
+ align:start position:0%
+that it should go down and what they
+found
+
+ align:start position:0%
+found
+ 
+
+ align:start position:0%
+found
+was two they found two a single beam
+
+ align:start position:0%
+was two they found two a single beam
+ 
+
+ align:start position:0%
+was two they found two a single beam
+split into two
+
+ align:start position:0%
+split into two
+ 
+
+ align:start position:0%
+split into two
+and this really vexed people in fact
+
+ align:start position:0%
+and this really vexed people in fact
+ 
+
+ align:start position:0%
+and this really vexed people in fact
+here are the data this is a very grainy
+
+ align:start position:0%
+here are the data this is a very grainy
+ 
+
+ align:start position:0%
+here are the data this is a very grainy
+reproduction from their paper that dark
+
+ align:start position:0%
+reproduction from their paper that dark
+ 
+
+ align:start position:0%
+reproduction from their paper that dark
+line is the uh trace of the deposit in
+
+ align:start position:0%
+line is the uh trace of the deposit in
+ 
+
+ align:start position:0%
+line is the uh trace of the deposit in
+this case it's silver they're sending
+
+ align:start position:0%
+this case it's silver they're sending
+ 
+
+ align:start position:0%
+this case it's silver they're sending
+silver through with no magnetic field
+
+ align:start position:0%
+silver through with no magnetic field
+ 
+
+ align:start position:0%
+silver through with no magnetic field
+and now here it is with the magnetic
+
+ align:start position:0%
+and now here it is with the magnetic
+ 
+
+ align:start position:0%
+and now here it is with the magnetic
+field on and this is a grading and
+
+ align:start position:0%
+field on and this is a grading and
+ 
+
+ align:start position:0%
+field on and this is a grading and
+they're measuring separation so the
+
+ align:start position:0%
+they're measuring separation so the
+ 
+
+ align:start position:0%
+they're measuring separation so the
+silver beam splits into two it goes up
+
+ align:start position:0%
+silver beam splits into two it goes up
+ 
+
+ align:start position:0%
+silver beam splits into two it goes up
+and down so gsmith and backck come along
+
+ align:start position:0%
+and down so gsmith and backck come along
+ 
+
+ align:start position:0%
+and down so gsmith and backck come along
+let's get these guys on here first this
+
+ align:start position:0%
+let's get these guys on here first this
+ 
+
+ align:start position:0%
+let's get these guys on here first this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+Stern and
+
+ align:start position:0%
+Stern and
+ 
+
+ align:start position:0%
+Stern and
+gerac
+
+ align:start position:0%
+gerac
+ 
+
+ align:start position:0%
+gerac
+1921 and uh yeah so they're they're
+
+ align:start position:0%
+1921 and uh yeah so they're they're
+ 
+
+ align:start position:0%
+1921 and uh yeah so they're they're
+working on that one and then comes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um goodsmith and Ulen Beck also at Liden
+
+ align:start position:0%
+um goodsmith and Ulen Beck also at Liden
+ 
+
+ align:start position:0%
+um goodsmith and Ulen Beck also at Liden
+again they were at Liden they were two
+
+ align:start position:0%
+again they were at Liden they were two
+ 
+
+ align:start position:0%
+again they were at Liden they were two
+graduate students and they said we can
+
+ align:start position:0%
+graduate students and they said we can
+ 
+
+ align:start position:0%
+graduate students and they said we can
+explain that watch this crazy as it
+
+ align:start position:0%
+explain that watch this crazy as it
+ 
+
+ align:start position:0%
+explain that watch this crazy as it
+sounds
+
+ align:start position:0%
+sounds
+ 
+
+ align:start position:0%
+sounds
+here's the electron moving around they
+
+ align:start position:0%
+here's the electron moving around they
+ 
+
+ align:start position:0%
+here's the electron moving around they
+said the electron just doesn't move it
+
+ align:start position:0%
+said the electron just doesn't move it
+ 
+
+ align:start position:0%
+said the electron just doesn't move it
+spins said what if the electron is
+
+ align:start position:0%
+spins said what if the electron is
+ 
+
+ align:start position:0%
+spins said what if the electron is
+spinning as it moves around the nucleus
+
+ align:start position:0%
+spinning as it moves around the nucleus
+ 
+
+ align:start position:0%
+spinning as it moves around the nucleus
+all right and if you use the right hand
+
+ align:start position:0%
+all right and if you use the right hand
+ 
+
+ align:start position:0%
+all right and if you use the right hand
+rule if it's spinning clockwise well
+
+ align:start position:0%
+rule if it's spinning clockwise well
+ 
+
+ align:start position:0%
+rule if it's spinning clockwise well
+it's spinning up but maybe an electron
+
+ align:start position:0%
+it's spinning up but maybe an electron
+ 
+
+ align:start position:0%
+it's spinning up but maybe an electron
+we don't know where the absolute up or
+
+ align:start position:0%
+we don't know where the absolute up or
+ 
+
+ align:start position:0%
+we don't know where the absolute up or
+the absolute down is some electrons
+
+ align:start position:0%
+the absolute down is some electrons
+ 
+
+ align:start position:0%
+the absolute down is some electrons
+might be spinning anticlockwise in which
+
+ align:start position:0%
+might be spinning anticlockwise in which
+ 
+
+ align:start position:0%
+might be spinning anticlockwise in which
+case they're spin down and silver is
+
+ align:start position:0%
+case they're spin down and silver is
+ 
+
+ align:start position:0%
+case they're spin down and silver is
+atomic number 47 so it has an odd number
+
+ align:start position:0%
+atomic number 47 so it has an odd number
+ 
+
+ align:start position:0%
+atomic number 47 so it has an odd number
+of electrons so it it can't get a spin
+
+ align:start position:0%
+of electrons so it it can't get a spin
+ 
+
+ align:start position:0%
+of electrons so it it can't get a spin
+up electron cancelling a spin down
+
+ align:start position:0%
+up electron cancelling a spin down
+ 
+
+ align:start position:0%
+up electron cancelling a spin down
+electron it has a Net nonpaired Spin and
+
+ align:start position:0%
+electron it has a Net nonpaired Spin and
+ 
+
+ align:start position:0%
+electron it has a Net nonpaired Spin and
+they said well since we don't know what
+
+ align:start position:0%
+they said well since we don't know what
+ 
+
+ align:start position:0%
+they said well since we don't know what
+the absolute is some half of the half of
+
+ align:start position:0%
+the absolute is some half of the half of
+ 
+
+ align:start position:0%
+the absolute is some half of the half of
+the silvers are spin up and half of the
+
+ align:start position:0%
+the silvers are spin up and half of the
+ 
+
+ align:start position:0%
+the silvers are spin up and half of the
+silvers are spin down and that's why you
+
+ align:start position:0%
+silvers are spin down and that's why you
+ 
+
+ align:start position:0%
+silvers are spin down and that's why you
+get this so let's give a fourth quantum
+
+ align:start position:0%
+get this so let's give a fourth quantum
+ 
+
+ align:start position:0%
+get this so let's give a fourth quantum
+number let's call it plus or minus a
+
+ align:start position:0%
+number let's call it plus or minus a
+ 
+
+ align:start position:0%
+number let's call it plus or minus a
+half and you can say this is crazy but
+
+ align:start position:0%
+half and you can say this is crazy but
+ 
+
+ align:start position:0%
+half and you can say this is crazy but
+it explains those results and uh they
+
+ align:start position:0%
+it explains those results and uh they
+ 
+
+ align:start position:0%
+it explains those results and uh they
+actually were here during World War II
+
+ align:start position:0%
+actually were here during World War II
+ 
+
+ align:start position:0%
+actually were here during World War II
+both of them they work down just around
+
+ align:start position:0%
+both of them they work down just around
+ 
+
+ align:start position:0%
+both of them they work down just around
+the the corner here in the rad lab
+
+ align:start position:0%
+the the corner here in the rad lab
+ 
+
+ align:start position:0%
+the the corner here in the rad lab
+radiation laboratory where radar was
+
+ align:start position:0%
+radiation laboratory where radar was
+ 
+
+ align:start position:0%
+radiation laboratory where radar was
+discovered it's around building four
+
+ align:start position:0%
+discovered it's around building four
+ 
+
+ align:start position:0%
+discovered it's around building four
+first floor uh there's a plaque there
+
+ align:start position:0%
+first floor uh there's a plaque there
+ 
+
+ align:start position:0%
+first floor uh there's a plaque there
+indicating it okay well let's let's jump
+
+ align:start position:0%
+indicating it okay well let's let's jump
+ 
+
+ align:start position:0%
+indicating it okay well let's let's jump
+ahead I'm going to talk a little bit
+
+ align:start position:0%
+ahead I'm going to talk a little bit
+ 
+
+ align:start position:0%
+ahead I'm going to talk a little bit
+about hydrogen in uh energy and I want
+
+ align:start position:0%
+about hydrogen in uh energy and I want
+ 
+
+ align:start position:0%
+about hydrogen in uh energy and I want
+to talk about the Hindenburg the
+
+ align:start position:0%
+to talk about the Hindenburg the
+ 
+
+ align:start position:0%
+to talk about the Hindenburg the
+Hindenburg was a giant a giant rigid uh
+
+ align:start position:0%
+Hindenburg was a giant a giant rigid uh
+ 
+
+ align:start position:0%
+Hindenburg was a giant a giant rigid uh
+Airship to give you sense of scale was
+
+ align:start position:0%
+Airship to give you sense of scale was
+ 
+
+ align:start position:0%
+Airship to give you sense of scale was
+almost as long as a Titanic 135 fet in
+
+ align:start position:0%
+almost as long as a Titanic 135 fet in
+ 
+
+ align:start position:0%
+almost as long as a Titanic 135 fet in
+diameter 84 feet long at this is a 747
+
+ align:start position:0%
+diameter 84 feet long at this is a 747
+ 
+
+ align:start position:0%
+diameter 84 feet long at this is a 747
+dwarfed 7 million cubic feet of gas 112
+
+ align:start position:0%
+dwarfed 7 million cubic feet of gas 112
+ 
+
+ align:start position:0%
+dwarfed 7 million cubic feet of gas 112
+tons of useful lift but they inflated it
+
+ align:start position:0%
+tons of useful lift but they inflated it
+ 
+
+ align:start position:0%
+tons of useful lift but they inflated it
+with hydrogen because the Nazis had come
+
+ align:start position:0%
+with hydrogen because the Nazis had come
+ 
+
+ align:start position:0%
+with hydrogen because the Nazis had come
+to power most of the helium was to be
+
+ align:start position:0%
+to power most of the helium was to be
+ 
+
+ align:start position:0%
+to power most of the helium was to be
+found in the United States and Congress
+
+ align:start position:0%
+found in the United States and Congress
+ 
+
+ align:start position:0%
+found in the United States and Congress
+passed the helium Control Act which
+
+ align:start position:0%
+passed the helium Control Act which
+ 
+
+ align:start position:0%
+passed the helium Control Act which
+forbad the sale of helium to Germany so
+
+ align:start position:0%
+forbad the sale of helium to Germany so
+ 
+
+ align:start position:0%
+forbad the sale of helium to Germany so
+the engineers said okay we'll use
+
+ align:start position:0%
+the engineers said okay we'll use
+ 
+
+ align:start position:0%
+the engineers said okay we'll use
+hydrogen so they filled this thing with
+
+ align:start position:0%
+hydrogen so they filled this thing with
+ 
+
+ align:start position:0%
+hydrogen so they filled this thing with
+atom uh with molecular
+
+ align:start position:0%
+atom uh with molecular
+ 
+
+ align:start position:0%
+atom uh with molecular
+hydrogen and I mean it it was a it was a
+
+ align:start position:0%
+hydrogen and I mean it it was a it was a
+ 
+
+ align:start position:0%
+hydrogen and I mean it it was a it was a
+fantastic Boon I mean these are posters
+
+ align:start position:0%
+fantastic Boon I mean these are posters
+ 
+
+ align:start position:0%
+fantastic Boon I mean these are posters
+from that era 2 and A2 days to Europe
+
+ align:start position:0%
+from that era 2 and A2 days to Europe
+ 
+
+ align:start position:0%
+from that era 2 and A2 days to Europe
+only 2 and A2 days much faster than
+
+ align:start position:0%
+only 2 and A2 days much faster than
+ 
+
+ align:start position:0%
+only 2 and A2 days much faster than
+going by ship now here's a here's a
+
+ align:start position:0%
+going by ship now here's a here's a
+ 
+
+ align:start position:0%
+going by ship now here's a here's a
+sketch this is in German and now over
+
+ align:start position:0%
+sketch this is in German and now over
+ 
+
+ align:start position:0%
+sketch this is in German and now over
+the North Atlantic there's the the tip
+
+ align:start position:0%
+the North Atlantic there's the the tip
+ 
+
+ align:start position:0%
+the North Atlantic there's the the tip
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Manhattan there's a nice shot of uh the
+
+ align:start position:0%
+Manhattan there's a nice shot of uh the
+ 
+
+ align:start position:0%
+Manhattan there's a nice shot of uh the
+Airship over uh
+
+ align:start position:0%
+Airship over uh
+ 
+
+ align:start position:0%
+Airship over uh
+Manhattan so it made 10 transatlantic
+
+ align:start position:0%
+Manhattan so it made 10 transatlantic
+ 
+
+ align:start position:0%
+Manhattan so it made 10 transatlantic
+flights in 36 carrying almost a th
+
+ align:start position:0%
+flights in 36 carrying almost a th
+ 
+
+ align:start position:0%
+flights in 36 carrying almost a th
+passengers cruising speed 78 miles an
+
+ align:start position:0%
+passengers cruising speed 78 miles an
+ 
+
+ align:start position:0%
+passengers cruising speed 78 miles an
+hour they only flew in the
+
+ align:start position:0%
+hour they only flew in the
+ 
+
+ align:start position:0%
+hour they only flew in the
+summer so it's the arrival of the first
+
+ align:start position:0%
+summer so it's the arrival of the first
+ 
+
+ align:start position:0%
+summer so it's the arrival of the first
+flight to the US on May 6th 1937 and
+
+ align:start position:0%
+flight to the US on May 6th 1937 and
+ 
+
+ align:start position:0%
+flight to the US on May 6th 1937 and
+it's docking at Lake Hurst uh New Jersey
+
+ align:start position:0%
+it's docking at Lake Hurst uh New Jersey
+ 
+
+ align:start position:0%
+it's docking at Lake Hurst uh New Jersey
+the docking was moved if you go to the
+
+ align:start position:0%
+the docking was moved if you go to the
+ 
+
+ align:start position:0%
+the docking was moved if you go to the
+top of the Empire State Building and you
+
+ align:start position:0%
+top of the Empire State Building and you
+ 
+
+ align:start position:0%
+top of the Empire State Building and you
+look out you'll see these
+
+ align:start position:0%
+look out you'll see these
+ 
+
+ align:start position:0%
+look out you'll see these
+protrusions those protrusions were put
+
+ align:start position:0%
+protrusions those protrusions were put
+ 
+
+ align:start position:0%
+protrusions those protrusions were put
+there in the expectation that Zeppelin
+
+ align:start position:0%
+there in the expectation that Zeppelin
+ 
+
+ align:start position:0%
+there in the expectation that Zeppelin
+airships derable airships would Dock at
+
+ align:start position:0%
+airships derable airships would Dock at
+ 
+
+ align:start position:0%
+airships derable airships would Dock at
+the Empire State Building people would
+
+ align:start position:0%
+the Empire State Building people would
+ 
+
+ align:start position:0%
+the Empire State Building people would
+get off take the elevator next thing you
+
+ align:start position:0%
+get off take the elevator next thing you
+ 
+
+ align:start position:0%
+get off take the elevator next thing you
+know you're on Fifth Avenue when they
+
+ align:start position:0%
+know you're on Fifth Avenue when they
+ 
+
+ align:start position:0%
+know you're on Fifth Avenue when they
+tried to dock these things the air
+
+ align:start position:0%
+tried to dock these things the air
+ 
+
+ align:start position:0%
+tried to dock these things the air
+currents were so turbulent that it was
+
+ align:start position:0%
+currents were so turbulent that it was
+ 
+
+ align:start position:0%
+currents were so turbulent that it was
+unsafe to do so so they made this
+
+ align:start position:0%
+unsafe to do so so they made this
+ 
+
+ align:start position:0%
+unsafe to do so so they made this
+docking station across the across the
+
+ align:start position:0%
+docking station across the across the
+ 
+
+ align:start position:0%
+docking station across the across the
+river in Lakehurst so this is what
+
+ align:start position:0%
+river in Lakehurst so this is what
+ 
+
+ align:start position:0%
+river in Lakehurst so this is what
+happens uh 36 dead that's that's not
+
+ align:start position:0%
+happens uh 36 dead that's that's not
+ 
+
+ align:start position:0%
+happens uh 36 dead that's that's not
+what's amazing it's amazing that the
+
+ align:start position:0%
+what's amazing it's amazing that the
+ 
+
+ align:start position:0%
+what's amazing it's amazing that the
+majority of people disembarked what I
+
+ align:start position:0%
+majority of people disembarked what I
+ 
+
+ align:start position:0%
+majority of people disembarked what I
+want to tell you is it was not an
+
+ align:start position:0%
+want to tell you is it was not an
+ 
+
+ align:start position:0%
+want to tell you is it was not an
+explosion it did the Hindenberg did not
+
+ align:start position:0%
+explosion it did the Hindenberg did not
+ 
+
+ align:start position:0%
+explosion it did the Hindenberg did not
+explode there was an aluminum grand
+
+ align:start position:0%
+explode there was an aluminum grand
+ 
+
+ align:start position:0%
+explode there was an aluminum grand
+piano on there they had ballrooms they
+
+ align:start position:0%
+piano on there they had ballrooms they
+ 
+
+ align:start position:0%
+piano on there they had ballrooms they
+had restaurants I mean you're there for
+
+ align:start position:0%
+had restaurants I mean you're there for
+ 
+
+ align:start position:0%
+had restaurants I mean you're there for
+2 and a half days you're dressed it's
+
+ align:start position:0%
+2 and a half days you're dressed it's
+ 
+
+ align:start position:0%
+2 and a half days you're dressed it's
+it's elegant the aluminum piano melted
+
+ align:start position:0%
+it's elegant the aluminum piano melted
+ 
+
+ align:start position:0%
+it's elegant the aluminum piano melted
+they figured what happened was there was
+
+ align:start position:0%
+they figured what happened was there was
+ 
+
+ align:start position:0%
+they figured what happened was there was
+an electric discharge in the vicinity of
+
+ align:start position:0%
+an electric discharge in the vicinity of
+ 
+
+ align:start position:0%
+an electric discharge in the vicinity of
+a tiny hydrogen leak hydrogen's a tiny
+
+ align:start position:0%
+a tiny hydrogen leak hydrogen's a tiny
+ 
+
+ align:start position:0%
+a tiny hydrogen leak hydrogen's a tiny
+molecule and some hydrogen must have
+
+ align:start position:0%
+molecule and some hydrogen must have
+ 
+
+ align:start position:0%
+molecule and some hydrogen must have
+been leaking and they think it may have
+
+ align:start position:0%
+been leaking and they think it may have
+ 
+
+ align:start position:0%
+been leaking and they think it may have
+been something like a St Elmo's Fire or
+
+ align:start position:0%
+been something like a St Elmo's Fire or
+ 
+
+ align:start position:0%
+been something like a St Elmo's Fire or
+something like that just a high
+
+ align:start position:0%
+something like that just a high
+ 
+
+ align:start position:0%
+something like that just a high
+electrical discharge and The Misfortune
+
+ align:start position:0%
+electrical discharge and The Misfortune
+ 
+
+ align:start position:0%
+electrical discharge and The Misfortune
+that this thing caught so here's the
+
+ align:start position:0%
+that this thing caught so here's the
+ 
+
+ align:start position:0%
+that this thing caught so here's the
+analysis the skin was made of resin and
+
+ align:start position:0%
+analysis the skin was made of resin and
+ 
+
+ align:start position:0%
+analysis the skin was made of resin and
+it was finished with a lacquer dope to
+
+ align:start position:0%
+it was finished with a lacquer dope to
+ 
+
+ align:start position:0%
+it was finished with a lacquer dope to
+make it water
+
+ align:start position:0%
+make it water
+ 
+
+ align:start position:0%
+make it water
+repellent and to make it Glow they used
+
+ align:start position:0%
+repellent and to make it Glow they used
+ 
+
+ align:start position:0%
+repellent and to make it Glow they used
+aluminum powder in in the lacquer dope
+
+ align:start position:0%
+aluminum powder in in the lacquer dope
+ 
+
+ align:start position:0%
+aluminum powder in in the lacquer dope
+and then they put iron oxide on the
+
+ align:start position:0%
+and then they put iron oxide on the
+ 
+
+ align:start position:0%
+and then they put iron oxide on the
+inside Lord knows why so you basically
+
+ align:start position:0%
+inside Lord knows why so you basically
+ 
+
+ align:start position:0%
+inside Lord knows why so you basically
+have the elements of a thermite reaction
+
+ align:start position:0%
+have the elements of a thermite reaction
+ 
+
+ align:start position:0%
+have the elements of a thermite reaction
+this is what the shuttle uses in its
+
+ align:start position:0%
+this is what the shuttle uses in its
+ 
+
+ align:start position:0%
+this is what the shuttle uses in its
+solid rocket
+
+ align:start position:0%
+solid rocket
+ 
+
+ align:start position:0%
+solid rocket
+boosters so once this thing caught it
+
+ align:start position:0%
+boosters so once this thing caught it
+ 
+
+ align:start position:0%
+boosters so once this thing caught it
+was it was the skin that went and of
+
+ align:start position:0%
+was it was the skin that went and of
+ 
+
+ align:start position:0%
+was it was the skin that went and of
+course this meant the end of rigid
+
+ align:start position:0%
+course this meant the end of rigid
+ 
+
+ align:start position:0%
+course this meant the end of rigid
+airships and commercial air
+
+ align:start position:0%
+airships and commercial air
+ 
+
+ align:start position:0%
+airships and commercial air
+transportation and to point out that it
+
+ align:start position:0%
+transportation and to point out that it
+ 
+
+ align:start position:0%
+transportation and to point out that it
+wasn't the hydrogen if that had exploded
+
+ align:start position:0%
+wasn't the hydrogen if that had exploded
+ 
+
+ align:start position:0%
+wasn't the hydrogen if that had exploded
+it it would have been a very different
+
+ align:start position:0%
+it it would have been a very different
+ 
+
+ align:start position:0%
+it it would have been a very different
+uh scene this is 1956 a US Navy Airship
+
+ align:start position:0%
+uh scene this is 1956 a US Navy Airship
+ 
+
+ align:start position:0%
+uh scene this is 1956 a US Navy Airship
+derable filled with helium same thing
+
+ align:start position:0%
+derable filled with helium same thing
+ 
+
+ align:start position:0%
+derable filled with helium same thing
+but it had a two ply cotton envelope
+
+ align:start position:0%
+but it had a two ply cotton envelope
+ 
+
+ align:start position:0%
+but it had a two ply cotton envelope
+gasoline fire away it goes so it was the
+
+ align:start position:0%
+gasoline fire away it goes so it was the
+ 
+
+ align:start position:0%
+gasoline fire away it goes so it was the
+skin in fact 100% hydrogen will quench
+
+ align:start position:0%
+skin in fact 100% hydrogen will quench
+ 
+
+ align:start position:0%
+skin in fact 100% hydrogen will quench
+flame it's like running a carburetor too
+
+ align:start position:0%
+flame it's like running a carburetor too
+ 
+
+ align:start position:0%
+flame it's like running a carburetor too
+rich you choke you need fuel plus
+
+ align:start position:0%
+rich you choke you need fuel plus
+ 
+
+ align:start position:0%
+rich you choke you need fuel plus
+oxidant you cannot get 7 million cubic
+
+ align:start position:0%
+oxidant you cannot get 7 million cubic
+ 
+
+ align:start position:0%
+oxidant you cannot get 7 million cubic
+feet of oxygen to the site to sustain
+
+ align:start position:0%
+feet of oxygen to the site to sustain
+ 
+
+ align:start position:0%
+feet of oxygen to the site to sustain
+the explosion besides you're working
+
+ align:start position:0%
+the explosion besides you're working
+ 
+
+ align:start position:0%
+the explosion besides you're working
+with only 20% oxygen in air this I put
+
+ align:start position:0%
+with only 20% oxygen in air this I put
+ 
+
+ align:start position:0%
+with only 20% oxygen in air this I put
+up I blew it up cuz I thought this would
+
+ align:start position:0%
+up I blew it up cuz I thought this would
+ 
+
+ align:start position:0%
+up I blew it up cuz I thought this would
+look sort of like modern art you know
+
+ align:start position:0%
+look sort of like modern art you know
+ 
+
+ align:start position:0%
+look sort of like modern art you know
+rashan so there it is this is a Roman
+
+ align:start position:0%
+rashan so there it is this is a Roman
+ 
+
+ align:start position:0%
+rashan so there it is this is a Roman
+Candle it's not an explosion if this had
+
+ align:start position:0%
+Candle it's not an explosion if this had
+ 
+
+ align:start position:0%
+Candle it's not an explosion if this had
+been an explosion it would have been
+
+ align:start position:0%
+been an explosion it would have been
+ 
+
+ align:start position:0%
+been an explosion it would have been
+totally different so this is
+
+ align:start position:0%
+totally different so this is
+ 
+
+ align:start position:0%
+totally different so this is
+stochiometry this is a limited reaction
+
+ align:start position:0%
+stochiometry this is a limited reaction
+ 
+
+ align:start position:0%
+stochiometry this is a limited reaction
+there was not enough oxygen to keep it
+
+ align:start position:0%
+there was not enough oxygen to keep it
+ 
+
+ align:start position:0%
+there was not enough oxygen to keep it
+going so there it is have a nice weekend
\ No newline at end of file
diff --git a/VHjH6A9InR4.txt b/VHjH6A9InR4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..075c094b97341bf81b151c1766a75125ca81e551
--- /dev/null
+++ b/VHjH6A9InR4.txt
@@ -0,0 +1,2595 @@
+align:start position:0%
+ 
+hello everybody and welcome to our last
+
+ align:start position:0%
+hello everybody and welcome to our last
+ 
+
+ align:start position:0%
+hello everybody and welcome to our last
+video at least for a while on music
+
+ align:start position:0%
+video at least for a while on music
+ 
+
+ align:start position:0%
+video at least for a while on music
+representation and I want to talk about
+
+ align:start position:0%
+representation and I want to talk about
+ 
+
+ align:start position:0%
+representation and I want to talk about
+a remarkable tool created by a
+
+ align:start position:0%
+a remarkable tool created by a
+ 
+
+ align:start position:0%
+a remarkable tool created by a
+researcher at Stanford Craig Stuart Sapp
+
+ align:start position:0%
+researcher at Stanford Craig Stuart Sapp
+ 
+
+ align:start position:0%
+researcher at Stanford Craig Stuart Sapp
+that he calls the Rosetta
+
+ align:start position:0%
+that he calls the Rosetta
+ 
+
+ align:start position:0%
+that he calls the Rosetta
+Stone I'm going to be skipping a few
+
+ align:start position:0%
+Stone I'm going to be skipping a few
+ 
+
+ align:start position:0%
+Stone I'm going to be skipping a few
+slides from his presentation and if
+
+ align:start position:0%
+slides from his presentation and if
+ 
+
+ align:start position:0%
+slides from his presentation and if
+added a few other things but in this
+
+ align:start position:0%
+added a few other things but in this
+ 
+
+ align:start position:0%
+added a few other things but in this
+module I will also present his entirety
+
+ align:start position:0%
+module I will also present his entirety
+ 
+
+ align:start position:0%
+module I will also present his entirety
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+slides that he has given and my hats off
+
+ align:start position:0%
+slides that he has given and my hats off
+ 
+
+ align:start position:0%
+slides that he has given and my hats off
+to Craig sap for all he's done and his
+
+ align:start position:0%
+to Craig sap for all he's done and his
+ 
+
+ align:start position:0%
+to Craig sap for all he's done and his
+generosity so the Rosetta Stone was a
+
+ align:start position:0%
+generosity so the Rosetta Stone was a
+ 
+
+ align:start position:0%
+generosity so the Rosetta Stone was a
+stone discovered in I think 1799 and
+
+ align:start position:0%
+stone discovered in I think 1799 and
+ 
+
+ align:start position:0%
+stone discovered in I think 1799 and
+deciphered over the next uh I 10 years
+
+ align:start position:0%
+deciphered over the next uh I 10 years
+ 
+
+ align:start position:0%
+deciphered over the next uh I 10 years
+or so that was a remarkable
+
+ align:start position:0%
+or so that was a remarkable
+ 
+
+ align:start position:0%
+or so that was a remarkable
+um Discovery because up until that point
+
+ align:start position:0%
+um Discovery because up until that point
+ 
+
+ align:start position:0%
+um Discovery because up until that point
+Egyptian hieroglyphics such as those
+
+ align:start position:0%
+Egyptian hieroglyphics such as those
+ 
+
+ align:start position:0%
+Egyptian hieroglyphics such as those
+highlighted here were not legible by
+
+ align:start position:0%
+highlighted here were not legible by
+ 
+
+ align:start position:0%
+highlighted here were not legible by
+anybody living at that point but the
+
+ align:start position:0%
+anybody living at that point but the
+ 
+
+ align:start position:0%
+anybody living at that point but the
+Rosetta Stone had two forms of Egyptian
+
+ align:start position:0%
+Rosetta Stone had two forms of Egyptian
+ 
+
+ align:start position:0%
+Rosetta Stone had two forms of Egyptian
+hieroglyphics and also in the top two
+
+ align:start position:0%
+hieroglyphics and also in the top two
+ 
+
+ align:start position:0%
+hieroglyphics and also in the top two
+sections and also at the bottom the
+
+ align:start position:0%
+sections and also at the bottom the
+ 
+
+ align:start position:0%
+sections and also at the bottom the
+exact same text in Greek and so since
+
+ align:start position:0%
+exact same text in Greek and so since
+ 
+
+ align:start position:0%
+exact same text in Greek and so since
+people knew how to read ancient Greek
+
+ align:start position:0%
+people knew how to read ancient Greek
+ 
+
+ align:start position:0%
+people knew how to read ancient Greek
+they were able to go through each of the
+
+ align:start position:0%
+they were able to go through each of the
+ 
+
+ align:start position:0%
+they were able to go through each of the
+signs of ancient Greek and figure out
+
+ align:start position:0%
+signs of ancient Greek and figure out
+ 
+
+ align:start position:0%
+signs of ancient Greek and figure out
+what the signs of the hieroglyphics and
+
+ align:start position:0%
+what the signs of the hieroglyphics and
+ 
+
+ align:start position:0%
+what the signs of the hieroglyphics and
+the two forms of writing
+
+ align:start position:0%
+the two forms of writing
+ 
+
+ align:start position:0%
+the two forms of writing
+meant Craig saps Rosetta Stone allows us
+
+ align:start position:0%
+meant Craig saps Rosetta Stone allows us
+ 
+
+ align:start position:0%
+meant Craig saps Rosetta Stone allows us
+to look at how different digital
+
+ align:start position:0%
+to look at how different digital
+ 
+
+ align:start position:0%
+to look at how different digital
+representations of Music work by
+
+ align:start position:0%
+representations of Music work by
+ 
+
+ align:start position:0%
+representations of Music work by
+encoding the exact same melody in I
+
+ align:start position:0%
+encoding the exact same melody in I
+ 
+
+ align:start position:0%
+encoding the exact same melody in I
+think almost two dozen different formats
+
+ align:start position:0%
+think almost two dozen different formats
+ 
+
+ align:start position:0%
+think almost two dozen different formats
+these aren't all formats that have ever
+
+ align:start position:0%
+these aren't all formats that have ever
+ 
+
+ align:start position:0%
+these aren't all formats that have ever
+been used but it's a good chunk of them
+
+ align:start position:0%
+been used but it's a good chunk of them
+ 
+
+ align:start position:0%
+been used but it's a good chunk of them
+so here's the melody and it has um some
+
+ align:start position:0%
+so here's the melody and it has um some
+ 
+
+ align:start position:0%
+so here's the melody and it has um some
+interesting things here it has different
+
+ align:start position:0%
+interesting things here it has different
+ 
+
+ align:start position:0%
+interesting things here it has different
+octaves it has uh key signature time
+
+ align:start position:0%
+octaves it has uh key signature time
+ 
+
+ align:start position:0%
+octaves it has uh key signature time
+signature has beaming information the
+
+ align:start position:0%
+signature has beaming information the
+ 
+
+ align:start position:0%
+signature has beaming information the
+only thing it really well some of the
+
+ align:start position:0%
+only thing it really well some of the
+ 
+
+ align:start position:0%
+only thing it really well some of the
+things it doesn't have Are chords and
+
+ align:start position:0%
+things it doesn't have Are chords and
+ 
+
+ align:start position:0%
+things it doesn't have Are chords and
+triplets and things like that but once
+
+ align:start position:0%
+triplets and things like that but once
+ 
+
+ align:start position:0%
+triplets and things like that but once
+you see how this melody is encoded in a
+
+ align:start position:0%
+you see how this melody is encoded in a
+ 
+
+ align:start position:0%
+you see how this melody is encoded in a
+lot of formats you can figure out how
+
+ align:start position:0%
+lot of formats you can figure out how
+ 
+
+ align:start position:0%
+lot of formats you can figure out how
+all the other things might be encoded in
+
+ align:start position:0%
+all the other things might be encoded in
+ 
+
+ align:start position:0%
+all the other things might be encoded in
+those formats
+
+ align:start position:0%
+those formats
+ 
+
+ align:start position:0%
+those formats
+so here's an example of a code that's uh
+
+ align:start position:0%
+so here's an example of a code that's uh
+ 
+
+ align:start position:0%
+so here's an example of a code that's uh
+not used as much today but was once very
+
+ align:start position:0%
+not used as much today but was once very
+ 
+
+ align:start position:0%
+not used as much today but was once very
+important uh plain and easy code and you
+
+ align:start position:0%
+important uh plain and easy code and you
+ 
+
+ align:start position:0%
+important uh plain and easy code and you
+can see that we have something like I
+
+ align:start position:0%
+can see that we have something like I
+ 
+
+ align:start position:0%
+can see that we have something like I
+can decipher okay maybe that's a g on
+
+ align:start position:0%
+can decipher okay maybe that's a g on
+ 
+
+ align:start position:0%
+can decipher okay maybe that's a g on
+clef on line two and then we have a flat
+
+ align:start position:0%
+clef on line two and then we have a flat
+ 
+
+ align:start position:0%
+clef on line two and then we have a flat
+on the on b 2 four and then we have an
+
+ align:start position:0%
+on the on b 2 four and then we have an
+ 
+
+ align:start position:0%
+on the on b 2 four and then we have an
+eighth note with a DOT on c um and then
+
+ align:start position:0%
+eighth note with a DOT on c um and then
+ 
+
+ align:start position:0%
+eighth note with a DOT on c um and then
+uh I I guess the three means 302 note
+
+ align:start position:0%
+uh I I guess the three means 302 note
+ 
+
+ align:start position:0%
+uh I I guess the three means 302 note
+DC and there's a little bracket around
+
+ align:start position:0%
+DC and there's a little bracket around
+ 
+
+ align:start position:0%
+DC and there's a little bracket around
+it and that probably means they're beam
+
+ align:start position:0%
+it and that probably means they're beam
+ 
+
+ align:start position:0%
+it and that probably means they're beam
+together then we have two eighth notes
+
+ align:start position:0%
+together then we have two eighth notes
+ 
+
+ align:start position:0%
+together then we have two eighth notes
+on C beam together have slash means new
+
+ align:start position:0%
+on C beam together have slash means new
+ 
+
+ align:start position:0%
+on C beam together have slash means new
+measure and so on throughout the whole
+
+ align:start position:0%
+measure and so on throughout the whole
+ 
+
+ align:start position:0%
+measure and so on throughout the whole
+thing we can see um that oh maybe octave
+
+ align:start position:0%
+thing we can see um that oh maybe octave
+ 
+
+ align:start position:0%
+thing we can see um that oh maybe octave
+isn't encoded here or um something like
+
+ align:start position:0%
+isn't encoded here or um something like
+ 
+
+ align:start position:0%
+isn't encoded here or um something like
+that and um we can figure out how those
+
+ align:start position:0%
+that and um we can figure out how those
+ 
+
+ align:start position:0%
+that and um we can figure out how those
+go here is another format this is uh
+
+ align:start position:0%
+go here is another format this is uh
+ 
+
+ align:start position:0%
+go here is another format this is uh
+primarily used for folk songs called ABC
+
+ align:start position:0%
+primarily used for folk songs called ABC
+ 
+
+ align:start position:0%
+primarily used for folk songs called ABC
+and we can see that um well example
+
+ align:start position:0%
+and we can see that um well example
+ 
+
+ align:start position:0%
+and we can see that um well example
+maybe that's the title of the piece 24 K
+
+ align:start position:0%
+maybe that's the title of the piece 24 K
+ 
+
+ align:start position:0%
+maybe that's the title of the piece 24 K
+is key is f l means the smallest
+
+ align:start position:0%
+is key is f l means the smallest
+ 
+
+ align:start position:0%
+is key is f l means the smallest
+possible encoding is a 16th note then we
+
+ align:start position:0%
+possible encoding is a 16th note then we
+ 
+
+ align:start position:0%
+possible encoding is a 16th note then we
+see that c is worth three of those 16th
+
+ align:start position:0%
+see that c is worth three of those 16th
+ 
+
+ align:start position:0%
+see that c is worth three of those 16th
+D is worth I guess 1 half C is 1/2 C is
+
+ align:start position:0%
+D is worth I guess 1 half C is 1/2 C is
+ 
+
+ align:start position:0%
+D is worth I guess 1 half C is 1/2 C is
+worth two of those that's eth note C is
+
+ align:start position:0%
+worth two of those that's eth note C is
+ 
+
+ align:start position:0%
+worth two of those that's eth note C is
+worth two of those we have a bar line
+
+ align:start position:0%
+worth two of those we have a bar line
+ 
+
+ align:start position:0%
+worth two of those we have a bar line
+and so on and we can see that the high C
+
+ align:start position:0%
+and so on and we can see that the high C
+ 
+
+ align:start position:0%
+and so on and we can see that the high C
+is encoded with c with a um apostrophe
+
+ align:start position:0%
+is encoded with c with a um apostrophe
+ 
+
+ align:start position:0%
+is encoded with c with a um apostrophe
+after
+
+ align:start position:0%
+after
+ 
+
+ align:start position:0%
+after
+it this is what's called dar's code it
+
+ align:start position:0%
+it this is what's called dar's code it
+ 
+
+ align:start position:0%
+it this is what's called dar's code it
+was once highly used but it hasn't
+
+ align:start position:0%
+was once highly used but it hasn't
+ 
+
+ align:start position:0%
+was once highly used but it hasn't
+really been used very much recently
+
+ align:start position:0%
+really been used very much recently
+ 
+
+ align:start position:0%
+really been used very much recently
+and well I don't know how to read dar's
+
+ align:start position:0%
+and well I don't know how to read dar's
+ 
+
+ align:start position:0%
+and well I don't know how to read dar's
+code but uh I think that the numbers
+
+ align:start position:0%
+code but uh I think that the numbers
+ 
+
+ align:start position:0%
+code but uh I think that the numbers
+represent pitch here we have an eth with
+
+ align:start position:0%
+represent pitch here we have an eth with
+ 
+
+ align:start position:0%
+represent pitch here we have an eth with
+a DOT and t means 302 I'm guessing and
+
+ align:start position:0%
+a DOT and t means 302 I'm guessing and
+ 
+
+ align:start position:0%
+a DOT and t means 302 I'm guessing and
+so on we have some rs's which might mean
+
+ align:start position:0%
+so on we have some rs's which might mean
+ 
+
+ align:start position:0%
+so on we have some rs's which might mean
+16th note this is Guido music notation
+
+ align:start position:0%
+16th note this is Guido music notation
+ 
+
+ align:start position:0%
+16th note this is Guido music notation
+which uses uh backslashes to indicate
+
+ align:start position:0%
+which uses uh backslashes to indicate
+ 
+
+ align:start position:0%
+which uses uh backslashes to indicate
+certain kinds of musical elements we can
+
+ align:start position:0%
+certain kinds of musical elements we can
+ 
+
+ align:start position:0%
+certain kinds of musical elements we can
+see CS Keys meters are encoded in here
+
+ align:start position:0%
+see CS Keys meters are encoded in here
+ 
+
+ align:start position:0%
+see CS Keys meters are encoded in here
+uh bar lines are explicitly encoded it
+
+ align:start position:0%
+uh bar lines are explicitly encoded it
+ 
+
+ align:start position:0%
+uh bar lines are explicitly encoded it
+looks like you put a slash before a a
+
+ align:start position:0%
+looks like you put a slash before a a
+ 
+
+ align:start position:0%
+looks like you put a slash before a a
+beat a duration and there's some dur
+
+ align:start position:0%
+beat a duration and there's some dur
+ 
+
+ align:start position:0%
+beat a duration and there's some dur
+notes that don't have durations but they
+
+ align:start position:0%
+notes that don't have durations but they
+ 
+
+ align:start position:0%
+notes that don't have durations but they
+seem to be the same duration as before
+
+ align:start position:0%
+seem to be the same duration as before
+ 
+
+ align:start position:0%
+seem to be the same duration as before
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+I think it looks like underscores our
+
+ align:start position:0%
+I think it looks like underscores our
+ 
+
+ align:start position:0%
+I think it looks like underscores our
+rest this is Muse data which Michael
+
+ align:start position:0%
+rest this is Muse data which Michael
+ 
+
+ align:start position:0%
+rest this is Muse data which Michael
+good said was one of the um inspiration
+
+ align:start position:0%
+good said was one of the um inspiration
+ 
+
+ align:start position:0%
+good said was one of the um inspiration
+behind music XML it's a little bit
+
+ align:start position:0%
+behind music XML it's a little bit
+ 
+
+ align:start position:0%
+behind music XML it's a little bit
+bigger format takes more space uh it was
+
+ align:start position:0%
+bigger format takes more space uh it was
+ 
+
+ align:start position:0%
+bigger format takes more space uh it was
+one of what we used to use a lot these
+
+ align:start position:0%
+one of what we used to use a lot these
+ 
+
+ align:start position:0%
+one of what we used to use a lot these
+fixed position encodings so that if
+
+ align:start position:0%
+fixed position encodings so that if
+ 
+
+ align:start position:0%
+fixed position encodings so that if
+you're writing in a monus baced font
+
+ align:start position:0%
+you're writing in a monus baced font
+ 
+
+ align:start position:0%
+you're writing in a monus baced font
+every single place uh has a particular
+
+ align:start position:0%
+every single place uh has a particular
+ 
+
+ align:start position:0%
+every single place uh has a particular
+meaning so you can look at column 8 or
+
+ align:start position:0%
+meaning so you can look at column 8 or
+ 
+
+ align:start position:0%
+meaning so you can look at column 8 or
+something like that and see the duration
+
+ align:start position:0%
+something like that and see the duration
+ 
+
+ align:start position:0%
+something like that and see the duration
+and then this was a a major positive
+
+ align:start position:0%
+and then this was a a major positive
+ 
+
+ align:start position:0%
+and then this was a a major positive
+step because it encodes duration in
+
+ align:start position:0%
+step because it encodes duration in
+ 
+
+ align:start position:0%
+step because it encodes duration in
+terms of the number of uh something the
+
+ align:start position:0%
+terms of the number of uh something the
+ 
+
+ align:start position:0%
+terms of the number of uh something the
+number of 30 second notes and also
+
+ align:start position:0%
+number of 30 second notes and also
+ 
+
+ align:start position:0%
+number of 30 second notes and also
+separately the the look of the duration
+
+ align:start position:0%
+separately the the look of the duration
+ 
+
+ align:start position:0%
+separately the the look of the duration
+and so you can still see that in music
+
+ align:start position:0%
+and so you can still see that in music
+ 
+
+ align:start position:0%
+and so you can still see that in music
+XML and formats that are still in use
+
+ align:start position:0%
+XML and formats that are still in use
+ 
+
+ align:start position:0%
+XML and formats that are still in use
+today I really like the use of these uh
+
+ align:start position:0%
+today I really like the use of these uh
+ 
+
+ align:start position:0%
+today I really like the use of these uh
+left and right square brackets to
+
+ align:start position:0%
+left and right square brackets to
+ 
+
+ align:start position:0%
+left and right square brackets to
+indicate the start and an end of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beams humdrum is a code that we have
+
+ align:start position:0%
+beams humdrum is a code that we have
+ 
+
+ align:start position:0%
+beams humdrum is a code that we have
+encountered a couple times and here it
+
+ align:start position:0%
+encountered a couple times and here it
+ 
+
+ align:start position:0%
+encountered a couple times and here it
+is and maybe it's easier with humdrum to
+
+ align:start position:0%
+is and maybe it's easier with humdrum to
+ 
+
+ align:start position:0%
+is and maybe it's easier with humdrum to
+rotate the musical examples so we can
+
+ align:start position:0%
+rotate the musical examples so we can
+ 
+
+ align:start position:0%
+rotate the musical examples so we can
+see how things go maybe maybe not but we
+
+ align:start position:0%
+see how things go maybe maybe not but we
+ 
+
+ align:start position:0%
+see how things go maybe maybe not but we
+can see that there's L's and J's that
+
+ align:start position:0%
+can see that there's L's and J's that
+ 
+
+ align:start position:0%
+can see that there's L's and J's that
+represent the starts and ends of beams
+
+ align:start position:0%
+represent the starts and ends of beams
+ 
+
+ align:start position:0%
+represent the starts and ends of beams
+and different octaves are represented by
+
+ align:start position:0%
+and different octaves are represented by
+ 
+
+ align:start position:0%
+and different octaves are represented by
+doubling or tripling the
+
+ align:start position:0%
+doubling or tripling the
+ 
+
+ align:start position:0%
+doubling or tripling the
+letter little Pond is actually a set of
+
+ align:start position:0%
+letter little Pond is actually a set of
+ 
+
+ align:start position:0%
+letter little Pond is actually a set of
+macros for the scheme programming
+
+ align:start position:0%
+macros for the scheme programming
+ 
+
+ align:start position:0%
+macros for the scheme programming
+language which is a kind of variant on
+
+ align:start position:0%
+language which is a kind of variant on
+ 
+
+ align:start position:0%
+language which is a kind of variant on
+list and so you can actually write
+
+ align:start position:0%
+list and so you can actually write
+ 
+
+ align:start position:0%
+list and so you can actually write
+computer code in Lily Pond and here we
+
+ align:start position:0%
+computer code in Lily Pond and here we
+ 
+
+ align:start position:0%
+computer code in Lily Pond and here we
+have the same representation you can see
+
+ align:start position:0%
+have the same representation you can see
+ 
+
+ align:start position:0%
+have the same representation you can see
+again backs slashes indicating uh starts
+
+ align:start position:0%
+again backs slashes indicating uh starts
+ 
+
+ align:start position:0%
+again backs slashes indicating uh starts
+of larger musical elements time
+
+ align:start position:0%
+of larger musical elements time
+ 
+
+ align:start position:0%
+of larger musical elements time
+signatures bar lines that are explicitly
+
+ align:start position:0%
+signatures bar lines that are explicitly
+ 
+
+ align:start position:0%
+signatures bar lines that are explicitly
+encoded with what they look like and so
+
+ align:start position:0%
+encoded with what they look like and so
+ 
+
+ align:start position:0%
+encoded with what they look like and so
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+melisma was an interesting uh code
+
+ align:start position:0%
+melisma was an interesting uh code
+ 
+
+ align:start position:0%
+melisma was an interesting uh code
+format that's a little bit similar to
+
+ align:start position:0%
+format that's a little bit similar to
+ 
+
+ align:start position:0%
+format that's a little bit similar to
+what we might have with midi and what
+
+ align:start position:0%
+what we might have with midi and what
+ 
+
+ align:start position:0%
+what we might have with midi and what
+we're doing here is we're encoding only
+
+ align:start position:0%
+we're doing here is we're encoding only
+ 
+
+ align:start position:0%
+we're doing here is we're encoding only
+uh the numeric duration so we can say
+
+ align:start position:0%
+uh the numeric duration so we can say
+ 
+
+ align:start position:0%
+uh the numeric duration so we can say
+that I guess uh
+
+ align:start position:0%
+that I guess uh
+ 
+
+ align:start position:0%
+that I guess uh
+125 is a 302nd note and we can figure
+
+ align:start position:0%
+125 is a 302nd note and we can figure
+ 
+
+ align:start position:0%
+125 is a 302nd note and we can figure
+out from there that 500 is an eighth
+
+ align:start position:0%
+out from there that 500 is an eighth
+ 
+
+ align:start position:0%
+out from there that 500 is an eighth
+note and so on and on the far right
+
+ align:start position:0%
+note and so on and on the far right
+ 
+
+ align:start position:0%
+note and so on and on the far right
+column we have the pitch encoded so
+
+ align:start position:0%
+column we have the pitch encoded so
+ 
+
+ align:start position:0%
+column we have the pitch encoded so
+we're losing here
+
+ align:start position:0%
+we're losing here
+ 
+
+ align:start position:0%
+we're losing here
+beams and some other things we we're
+
+ align:start position:0%
+beams and some other things we we're
+ 
+
+ align:start position:0%
+beams and some other things we we're
+actually been losing the clef and the
+
+ align:start position:0%
+actually been losing the clef and the
+ 
+
+ align:start position:0%
+actually been losing the clef and the
+time seure but we do have an info tag
+
+ align:start position:0%
+time seure but we do have an info tag
+ 
+
+ align:start position:0%
+time seure but we do have an info tag
+that tells us a key
+
+ align:start position:0%
+that tells us a key
+ 
+
+ align:start position:0%
+that tells us a key
+signature algro is a more compact
+
+ align:start position:0%
+signature algro is a more compact
+ 
+
+ align:start position:0%
+signature algro is a more compact
+version the same format looks like we
+
+ align:start position:0%
+version the same format looks like we
+ 
+
+ align:start position:0%
+version the same format looks like we
+have midi numbers 72 74 72 um for C DC
+
+ align:start position:0%
+have midi numbers 72 74 72 um for C DC
+ 
+
+ align:start position:0%
+have midi numbers 72 74 72 um for C DC
+and so on and um I believe 64 is
+
+ align:start position:0%
+and so on and um I believe 64 is
+ 
+
+ align:start position:0%
+and so on and um I believe 64 is
+encoding the velocity that is having how
+
+ align:start position:0%
+encoding the velocity that is having how
+ 
+
+ align:start position:0%
+encoding the velocity that is having how
+loud each note is and since we haven't
+
+ align:start position:0%
+loud each note is and since we haven't
+ 
+
+ align:start position:0%
+loud each note is and since we haven't
+encoded any Dynamics here they're all
+
+ align:start position:0%
+encoded any Dynamics here they're all
+ 
+
+ align:start position:0%
+encoded any Dynamics here they're all
+64s and we have toward the end start and
+
+ align:start position:0%
+64s and we have toward the end start and
+ 
+
+ align:start position:0%
+64s and we have toward the end start and
+end offsets of each note I think if we
+
+ align:start position:0%
+end offsets of each note I think if we
+ 
+
+ align:start position:0%
+end offsets of each note I think if we
+can go through Note One 2 3 4 five 6 7 8
+
+ align:start position:0%
+can go through Note One 2 3 4 five 6 7 8
+ 
+
+ align:start position:0%
+can go through Note One 2 3 4 five 6 7 8
+nine would be a rest and at 1 two 3 4
+
+ align:start position:0%
+nine would be a rest and at 1 two 3 4
+ 
+
+ align:start position:0%
+nine would be a rest and at 1 two 3 4
+five 6 7 8 um we have there sorry we're
+
+ align:start position:0%
+five 6 7 8 um we have there sorry we're
+ 
+
+ align:start position:0%
+five 6 7 8 um we have there sorry we're
+not doing start and end we're doing
+
+ align:start position:0%
+not doing start and end we're doing
+ 
+
+ align:start position:0%
+not doing start and end we're doing
+start offset and duration and there we
+
+ align:start position:0%
+start offset and duration and there we
+ 
+
+ align:start position:0%
+start offset and duration and there we
+have have a start offset Note 8 of 2.5
+
+ align:start position:0%
+have have a start offset Note 8 of 2.5
+ 
+
+ align:start position:0%
+have have a start offset Note 8 of 2.5
+duration of one and then the next
+
+ align:start position:0%
+duration of one and then the next
+ 
+
+ align:start position:0%
+duration of one and then the next
+element does not start at 3.5 but it
+
+ align:start position:0%
+element does not start at 3.5 but it
+ 
+
+ align:start position:0%
+element does not start at 3.5 but it
+just starts at 3.75 so we're not even
+
+ align:start position:0%
+just starts at 3.75 so we're not even
+ 
+
+ align:start position:0%
+just starts at 3.75 so we're not even
+encoding rests we're saying that they
+
+ align:start position:0%
+encoding rests we're saying that they
+ 
+
+ align:start position:0%
+encoding rests we're saying that they
+are gaps in the
+
+ align:start position:0%
+are gaps in the
+ 
+
+ align:start position:0%
+are gaps in the
+musical
+
+ align:start position:0%
+musical
+ 
+
+ align:start position:0%
+musical
+format director musicus is also a list
+
+ align:start position:0%
+format director musicus is also a list
+ 
+
+ align:start position:0%
+format director musicus is also a list
+based format I believe that's why we
+
+ align:start position:0%
+based format I believe that's why we
+ 
+
+ align:start position:0%
+based format I believe that's why we
+have all these extra parentheses where
+
+ align:start position:0%
+have all these extra parentheses where
+ 
+
+ align:start position:0%
+have all these extra parentheses where
+we're loading things into a stack and we
+
+ align:start position:0%
+we're loading things into a stack and we
+ 
+
+ align:start position:0%
+we're loading things into a stack and we
+can see that we're encoding uh the meter
+
+ align:start position:0%
+can see that we're encoding uh the meter
+ 
+
+ align:start position:0%
+can see that we're encoding uh the meter
+after the first note it's kind of
+
+ align:start position:0%
+after the first note it's kind of
+ 
+
+ align:start position:0%
+after the first note it's kind of
+interesting and um 302 notes are one
+
+ align:start position:0%
+interesting and um 302 notes are one
+ 
+
+ align:start position:0%
+interesting and um 302 notes are one
+over 32 that's kind of nice um the
+
+ align:start position:0%
+over 32 that's kind of nice um the
+ 
+
+ align:start position:0%
+over 32 that's kind of nice um the
+dotted uh eighth note is 316th notes
+
+ align:start position:0%
+dotted uh eighth note is 316th notes
+ 
+
+ align:start position:0%
+dotted uh eighth note is 316th notes
+wrong long so we see 316th can be
+
+ align:start position:0%
+wrong long so we see 316th can be
+ 
+
+ align:start position:0%
+wrong long so we see 316th can be
+interesting for
+
+ align:start position:0%
+interesting for
+ 
+
+ align:start position:0%
+interesting for
+ahead score has come up at least once in
+
+ align:start position:0%
+ahead score has come up at least once in
+ 
+
+ align:start position:0%
+ahead score has come up at least once in
+class it is perhaps the best uh most
+
+ align:start position:0%
+class it is perhaps the best uh most
+ 
+
+ align:start position:0%
+class it is perhaps the best uh most
+beautiful music editor ever
+
+ align:start position:0%
+beautiful music editor ever
+ 
+
+ align:start position:0%
+beautiful music editor ever
+this is how a user might input
+
+ align:start position:0%
+this is how a user might input
+ 
+
+ align:start position:0%
+this is how a user might input
+score and it makes it a little bit
+
+ align:start position:0%
+score and it makes it a little bit
+ 
+
+ align:start position:0%
+score and it makes it a little bit
+easier to enter things you're putting
+
+ align:start position:0%
+easier to enter things you're putting
+ 
+
+ align:start position:0%
+easier to enter things you're putting
+slashes between notes and so on and then
+
+ align:start position:0%
+slashes between notes and so on and then
+ 
+
+ align:start position:0%
+slashes between notes and so on and then
+it generates an internal syntax that uh
+
+ align:start position:0%
+it generates an internal syntax that uh
+ 
+
+ align:start position:0%
+it generates an internal syntax that uh
+specifies exactly where on the page
+
+ align:start position:0%
+specifies exactly where on the page
+ 
+
+ align:start position:0%
+specifies exactly where on the page
+every note is and so musical engravers
+
+ align:start position:0%
+every note is and so musical engravers
+ 
+
+ align:start position:0%
+every note is and so musical engravers
+really like working with score because
+
+ align:start position:0%
+really like working with score because
+ 
+
+ align:start position:0%
+really like working with score because
+you can precisely move things around
+
+ align:start position:0%
+you can precisely move things around
+ 
+
+ align:start position:0%
+you can precisely move things around
+probably a professional engraver would
+
+ align:start position:0%
+probably a professional engraver would
+ 
+
+ align:start position:0%
+probably a professional engraver would
+have moved the C at the beginning of the
+
+ align:start position:0%
+have moved the C at the beginning of the
+ 
+
+ align:start position:0%
+have moved the C at the beginning of the
+second measure a little bit to the right
+
+ align:start position:0%
+second measure a little bit to the right
+ 
+
+ align:start position:0%
+second measure a little bit to the right
+because it's a little bit close to that
+
+ align:start position:0%
+because it's a little bit close to that
+ 
+
+ align:start position:0%
+because it's a little bit close to that
+bar line and you might confuse the bar
+
+ align:start position:0%
+bar line and you might confuse the bar
+ 
+
+ align:start position:0%
+bar line and you might confuse the bar
+line for a stem so score is sometimes
+
+ align:start position:0%
+line for a stem so score is sometimes
+ 
+
+ align:start position:0%
+line for a stem so score is sometimes
+still used even though it hasn't been
+
+ align:start position:0%
+still used even though it hasn't been
+ 
+
+ align:start position:0%
+still used even though it hasn't been
+updated in
+
+ align:start position:0%
+updated in
+ 
+
+ align:start position:0%
+updated in
+decades this is music XML as we've seen
+
+ align:start position:0%
+decades this is music XML as we've seen
+ 
+
+ align:start position:0%
+decades this is music XML as we've seen
+from Michael Good's presentation it is
+
+ align:start position:0%
+from Michael Good's presentation it is
+ 
+
+ align:start position:0%
+from Michael Good's presentation it is
+uh much more verbose format um things
+
+ align:start position:0%
+uh much more verbose format um things
+ 
+
+ align:start position:0%
+uh much more verbose format um things
+are uh displayed you know it takes a lot
+
+ align:start position:0%
+are uh displayed you know it takes a lot
+ 
+
+ align:start position:0%
+are uh displayed you know it takes a lot
+more space to do it but music XML was
+
+ align:start position:0%
+more space to do it but music XML was
+ 
+
+ align:start position:0%
+more space to do it but music XML was
+invented around the year 2000 some of
+
+ align:start position:0%
+invented around the year 2000 some of
+ 
+
+ align:start position:0%
+invented around the year 2000 some of
+these other formats were around since
+
+ align:start position:0%
+these other formats were around since
+ 
+
+ align:start position:0%
+these other formats were around since
+the 80s so there's a lot more space on
+
+ align:start position:0%
+the 80s so there's a lot more space on
+ 
+
+ align:start position:0%
+the 80s so there's a lot more space on
+the hard drive well there are hard
+
+ align:start position:0%
+the hard drive well there are hard
+ 
+
+ align:start position:0%
+the hard drive well there are hard
+drives now um to be able to store all
+
+ align:start position:0%
+drives now um to be able to store all
+ 
+
+ align:start position:0%
+drives now um to be able to store all
+this information so here craigp has
+
+ align:start position:0%
+this information so here craigp has
+ 
+
+ align:start position:0%
+this information so here craigp has
+simply highlighted the part uh one
+
+ align:start position:0%
+simply highlighted the part uh one
+ 
+
+ align:start position:0%
+simply highlighted the part uh one
+measure in order to see how this would
+
+ align:start position:0%
+measure in order to see how this would
+ 
+
+ align:start position:0%
+measure in order to see how this would
+work in music
+
+ align:start position:0%
+work in music
+ 
+
+ align:start position:0%
+work in music
+XML Mei is another format you can't
+
+ align:start position:0%
+XML Mei is another format you can't
+ 
+
+ align:start position:0%
+XML Mei is another format you can't
+really see things here but it's very
+
+ align:start position:0%
+really see things here but it's very
+ 
+
+ align:start position:0%
+really see things here but it's very
+similar to music XML it's um
+
+ align:start position:0%
+similar to music XML it's um
+ 
+
+ align:start position:0%
+similar to music XML it's um
+as we said it's the format or as Michael
+
+ align:start position:0%
+as we said it's the format or as Michael
+ 
+
+ align:start position:0%
+as we said it's the format or as Michael
+good said is a format mostly used by
+
+ align:start position:0%
+good said is a format mostly used by
+ 
+
+ align:start position:0%
+good said is a format mostly used by
+professional musicologists and almost
+
+ align:start position:0%
+professional musicologists and almost
+ 
+
+ align:start position:0%
+professional musicologists and almost
+nobody else for for encoding common
+
+ align:start position:0%
+nobody else for for encoding common
+ 
+
+ align:start position:0%
+nobody else for for encoding common
+western music notation I don't see it as
+
+ align:start position:0%
+western music notation I don't see it as
+ 
+
+ align:start position:0%
+western music notation I don't see it as
+having advantages over music XML and in
+
+ align:start position:0%
+having advantages over music XML and in
+ 
+
+ align:start position:0%
+having advantages over music XML and in
+fact uh has many disadvantages because
+
+ align:start position:0%
+fact uh has many disadvantages because
+ 
+
+ align:start position:0%
+fact uh has many disadvantages because
+it's not supported by many formats but
+
+ align:start position:0%
+it's not supported by many formats but
+ 
+
+ align:start position:0%
+it's not supported by many formats but
+Mei can also encode music such as
+
+ align:start position:0%
+Mei can also encode music such as
+ 
+
+ align:start position:0%
+Mei can also encode music such as
+Medieval music um which uses different
+
+ align:start position:0%
+Medieval music um which uses different
+ 
+
+ align:start position:0%
+Medieval music um which uses different
+representation format so it has a
+
+ align:start position:0%
+representation format so it has a
+ 
+
+ align:start position:0%
+representation format so it has a
+particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Niche this is a standard midi file
+
+ align:start position:0%
+Niche this is a standard midi file
+ 
+
+ align:start position:0%
+Niche this is a standard midi file
+represented in binary and it's a little
+
+ align:start position:0%
+represented in binary and it's a little
+ 
+
+ align:start position:0%
+represented in binary and it's a little
+bit unfair to compare the two because
+
+ align:start position:0%
+bit unfair to compare the two because
+ 
+
+ align:start position:0%
+bit unfair to compare the two because
+it's a binary format so we can't really
+
+ align:start position:0%
+it's a binary format so we can't really
+ 
+
+ align:start position:0%
+it's a binary format so we can't really
+see anything but look at what's um been
+
+ align:start position:0%
+see anything but look at what's um been
+ 
+
+ align:start position:0%
+see anything but look at what's um been
+highlighted here we begin with
+
+ align:start position:0%
+highlighted here we begin with
+ 
+
+ align:start position:0%
+highlighted here we begin with
+0090 which is the indication for a note
+
+ align:start position:0%
+0090 which is the indication for a note
+ 
+
+ align:start position:0%
+0090 which is the indication for a note
+off so we're ending the previous note if
+
+ align:start position:0%
+off so we're ending the previous note if
+ 
+
+ align:start position:0%
+off so we're ending the previous note if
+we go to the beginning of the next line
+
+ align:start position:0%
+we go to the beginning of the next line
+ 
+
+ align:start position:0%
+we go to the beginning of the next line
+we can see ad0 which is the beginning of
+
+ align:start position:0%
+we can see ad0 which is the beginning of
+ 
+
+ align:start position:0%
+we can see ad0 which is the beginning of
+a note on and then 4D which let's see if
+
+ align:start position:0%
+a note on and then 4D which let's see if
+ 
+
+ align:start position:0%
+a note on and then 4D which let's see if
+I can still wear my heximal so 4 * 16 is
+
+ align:start position:0%
+I can still wear my heximal so 4 * 16 is
+ 
+
+ align:start position:0%
+I can still wear my heximal so 4 * 16 is
+64 add D to that that is uh what was
+
+ align:start position:0%
+64 add D to that that is uh what was
+ 
+
+ align:start position:0%
+64 add D to that that is uh what was
+that I don't know 14 13 and so you end
+
+ align:start position:0%
+that I don't know 14 13 and so you end
+ 
+
+ align:start position:0%
+that I don't know 14 13 and so you end
+up somewhere around 70 uh 78 or so which
+
+ align:start position:0%
+up somewhere around 70 uh 78 or so which
+ 
+
+ align:start position:0%
+up somewhere around 70 uh 78 or so which
+is the representation of the note F and
+
+ align:start position:0%
+is the representation of the note F and
+ 
+
+ align:start position:0%
+is the representation of the note F and
+then the 40 after that is 64 in
+
+ align:start position:0%
+then the 40 after that is 64 in
+ 
+
+ align:start position:0%
+then the 40 after that is 64 in
+um uh in in decimal and so that would be
+
+ align:start position:0%
+um uh in in decimal and so that would be
+ 
+
+ align:start position:0%
+um uh in in decimal and so that would be
+the velocity how hard we're hitting
+
+ align:start position:0%
+the velocity how hard we're hitting
+ 
+
+ align:start position:0%
+the velocity how hard we're hitting
+since velocity hasn't been encoded in
+
+ align:start position:0%
+since velocity hasn't been encoded in
+ 
+
+ align:start position:0%
+since velocity hasn't been encoded in
+this and there's a number between 0 and
+
+ align:start position:0%
+this and there's a number between 0 and
+ 
+
+ align:start position:0%
+this and there's a number between 0 and
+127 64 seems a pretty good number and
+
+ align:start position:0%
+127 64 seems a pretty good number and
+ 
+
+ align:start position:0%
+127 64 seems a pretty good number and
+then we state that the note is turned
+
+ align:start position:0%
+then we state that the note is turned
+ 
+
+ align:start position:0%
+then we state that the note is turned
+off with the 90 and we say it's turned
+
+ align:start position:0%
+off with the 90 and we say it's turned
+ 
+
+ align:start position:0%
+off with the 90 and we say it's turned
+off after a certain amount of time so
+
+ align:start position:0%
+off after a certain amount of time so
+ 
+
+ align:start position:0%
+off after a certain amount of time so
+how much time has passed and you'll see
+
+ align:start position:0%
+how much time has passed and you'll see
+ 
+
+ align:start position:0%
+how much time has passed and you'll see
+this 51 seems to be a represent
+
+ align:start position:0%
+this 51 seems to be a represent
+ 
+
+ align:start position:0%
+this 51 seems to be a represent
+of the length of a 16th
+
+ align:start position:0%
+of the length of a 16th
+ 
+
+ align:start position:0%
+of the length of a 16th
+note if you really want to look at midi
+
+ align:start position:0%
+note if you really want to look at midi
+ 
+
+ align:start position:0%
+note if you really want to look at midi
+you want to use a translator there's one
+
+ align:start position:0%
+you want to use a translator there's one
+ 
+
+ align:start position:0%
+you want to use a translator there's one
+in music 21 there's one other places
+
+ align:start position:0%
+in music 21 there's one other places
+ 
+
+ align:start position:0%
+in music 21 there's one other places
+that will translate this format into a
+
+ align:start position:0%
+that will translate this format into a
+ 
+
+ align:start position:0%
+that will translate this format into a
+series of events like no on no offs
+
+ align:start position:0%
+series of events like no on no offs
+ 
+
+ align:start position:0%
+series of events like no on no offs
+pitch bends and the time Deltas which
+
+ align:start position:0%
+pitch bends and the time Deltas which
+ 
+
+ align:start position:0%
+pitch bends and the time Deltas which
+move us forward in time that will allow
+
+ align:start position:0%
+move us forward in time that will allow
+ 
+
+ align:start position:0%
+move us forward in time that will allow
+you to actually give this uh particular
+
+ align:start position:0%
+you to actually give this uh particular
+ 
+
+ align:start position:0%
+you to actually give this uh particular
+a fair
+
+ align:start position:0%
+a fair
+ 
+
+ align:start position:0%
+a fair
+shape you can see also this is nith
+
+ align:start position:0%
+shape you can see also this is nith
+ 
+
+ align:start position:0%
+shape you can see also this is nith
+format which has um which craigp has uh
+
+ align:start position:0%
+format which has um which craigp has uh
+ 
+
+ align:start position:0%
+format which has um which craigp has uh
+translated some of the um some of the
+
+ align:start position:0%
+translated some of the um some of the
+ 
+
+ align:start position:0%
+translated some of the um some of the
+hexad decimals into particular uh
+
+ align:start position:0%
+hexad decimals into particular uh
+ 
+
+ align:start position:0%
+hexad decimals into particular uh
+letters so that we can see what they are
+
+ align:start position:0%
+letters so that we can see what they are
+ 
+
+ align:start position:0%
+letters so that we can see what they are
+um somewhere in the middle of the page I
+
+ align:start position:0%
+um somewhere in the middle of the page I
+ 
+
+ align:start position:0%
+um somewhere in the middle of the page I
+see CLA I see fing fingering I see a
+
+ align:start position:0%
+see CLA I see fing fingering I see a
+ 
+
+ align:start position:0%
+see CLA I see fing fingering I see a
+font change glissant harp uh I'm not
+
+ align:start position:0%
+font change glissant harp uh I'm not
+ 
+
+ align:start position:0%
+font change glissant harp uh I'm not
+sure that this is oh this these are just
+
+ align:start position:0%
+sure that this is oh this these are just
+ 
+
+ align:start position:0%
+sure that this is oh this these are just
+all the things that could be in here so
+
+ align:start position:0%
+all the things that could be in here so
+ 
+
+ align:start position:0%
+all the things that could be in here so
+we haven't even gotten to encoding the
+
+ align:start position:0%
+we haven't even gotten to encoding the
+ 
+
+ align:start position:0%
+we haven't even gotten to encoding the
+uh the piece yet but basically niif
+
+ align:start position:0%
+uh the piece yet but basically niif
+ 
+
+ align:start position:0%
+uh the piece yet but basically niif
+encodes where each shape is on the page
+
+ align:start position:0%
+encodes where each shape is on the page
+ 
+
+ align:start position:0%
+encodes where each shape is on the page
+it is a format used by music scanners
+
+ align:start position:0%
+it is a format used by music scanners
+ 
+
+ align:start position:0%
+it is a format used by music scanners
+it's not used very much anymore but the
+
+ align:start position:0%
+it's not used very much anymore but the
+ 
+
+ align:start position:0%
+it's not used very much anymore but the
+idea is that it's much more important to
+
+ align:start position:0%
+idea is that it's much more important to
+ 
+
+ align:start position:0%
+idea is that it's much more important to
+get an exact representation of what the
+
+ align:start position:0%
+get an exact representation of what the
+ 
+
+ align:start position:0%
+get an exact representation of what the
+page looks like rather than what it
+
+ align:start position:0%
+page looks like rather than what it
+ 
+
+ align:start position:0%
+page looks like rather than what it
+might
+
+ align:start position:0%
+might
+ 
+
+ align:start position:0%
+might
+encode the last format which uh in this
+
+ align:start position:0%
+encode the last format which uh in this
+ 
+
+ align:start position:0%
+encode the last format which uh in this
+presentation Flex outputs first isn't
+
+ align:start position:0%
+presentation Flex outputs first isn't
+ 
+
+ align:start position:0%
+presentation Flex outputs first isn't
+really a digital format at all but is
+
+ align:start position:0%
+really a digital format at all but is
+ 
+
+ align:start position:0%
+really a digital format at all but is
+the Braille music code which is US
+
+ align:start position:0%
+the Braille music code which is US
+ 
+
+ align:start position:0%
+the Braille music code which is US
+encoding of music notation that was
+
+ align:start position:0%
+encoding of music notation that was
+ 
+
+ align:start position:0%
+encoding of music notation that was
+created by Louis proud um at about the
+
+ align:start position:0%
+created by Louis proud um at about the
+ 
+
+ align:start position:0%
+created by Louis proud um at about the
+same time that he created the text
+
+ align:start position:0%
+same time that he created the text
+ 
+
+ align:start position:0%
+same time that he created the text
+Braille so he was really interested in
+
+ align:start position:0%
+Braille so he was really interested in
+ 
+
+ align:start position:0%
+Braille so he was really interested in
+music en coding also and we can see some
+
+ align:start position:0%
+music en coding also and we can see some
+ 
+
+ align:start position:0%
+music en coding also and we can see some
+parts of Braille that does encode a clef
+
+ align:start position:0%
+parts of Braille that does encode a clef
+ 
+
+ align:start position:0%
+parts of Braille that does encode a clef
+even though it's not really used um in
+
+ align:start position:0%
+even though it's not really used um in
+ 
+
+ align:start position:0%
+even though it's not really used um in
+the reading because we're going to
+
+ align:start position:0%
+the reading because we're going to
+ 
+
+ align:start position:0%
+the reading because we're going to
+encode specific notes why encoded cleff
+
+ align:start position:0%
+encode specific notes why encoded cleff
+ 
+
+ align:start position:0%
+encode specific notes why encoded cleff
+because um
+
+ align:start position:0%
+because um
+ 
+
+ align:start position:0%
+because um
+because blind and uh visually impaired
+
+ align:start position:0%
+because blind and uh visually impaired
+ 
+
+ align:start position:0%
+because blind and uh visually impaired
+musicians often need to talk to
+
+ align:start position:0%
+musicians often need to talk to
+ 
+
+ align:start position:0%
+musicians often need to talk to
+musicians who have sight so it's easy to
+
+ align:start position:0%
+musicians who have sight so it's easy to
+ 
+
+ align:start position:0%
+musicians who have sight so it's easy to
+say well you know it's in trouble clap
+
+ align:start position:0%
+say well you know it's in trouble clap
+ 
+
+ align:start position:0%
+say well you know it's in trouble clap
+and there's one flat key signature and
+
+ align:start position:0%
+and there's one flat key signature and
+ 
+
+ align:start position:0%
+and there's one flat key signature and
+so on um so there's a time signature and
+
+ align:start position:0%
+so on um so there's a time signature and
+ 
+
+ align:start position:0%
+so on um so there's a time signature and
+then that's not October 5th it's octave
+
+ align:start position:0%
+then that's not October 5th it's octave
+ 
+
+ align:start position:0%
+then that's not October 5th it's octave
+5 we set the octave we see that there's
+
+ align:start position:0%
+5 we set the octave we see that there's
+ 
+
+ align:start position:0%
+5 we set the octave we see that there's
+a C8 we encode in augmentation dot d32
+
+ align:start position:0%
+a C8 we encode in augmentation dot d32
+ 
+
+ align:start position:0%
+a C8 we encode in augmentation dot d32
+C32
+
+ align:start position:0%
+C32
+ 
+
+ align:start position:0%
+C32
+c16th uh
+
+ align:start position:0%
+c16th uh
+ 
+
+ align:start position:0%
+c16th uh
+F16 and so on and so there's um
+
+ align:start position:0%
+F16 and so on and so there's um
+ 
+
+ align:start position:0%
+F16 and so on and so there's um
+interestingly we can usually get both
+
+ align:start position:0%
+interestingly we can usually get both
+ 
+
+ align:start position:0%
+interestingly we can usually get both
+the note and the duration into a six dot
+
+ align:start position:0%
+the note and the duration into a six dot
+ 
+
+ align:start position:0%
+the note and the duration into a six dot
+segment which would represent six b six
+
+ align:start position:0%
+segment which would represent six b six
+ 
+
+ align:start position:0%
+segment which would represent six b six
+bits or less than a bite so it's a very
+
+ align:start position:0%
+bits or less than a bite so it's a very
+ 
+
+ align:start position:0%
+bits or less than a bite so it's a very
+efficient encoding that makes it reading
+
+ align:start position:0%
+efficient encoding that makes it reading
+ 
+
+ align:start position:0%
+efficient encoding that makes it reading
+music with your fingers very
+
+ align:start position:0%
+music with your fingers very
+ 
+
+ align:start position:0%
+music with your fingers very
+fast if you want to know more about the
+
+ align:start position:0%
+fast if you want to know more about the
+ 
+
+ align:start position:0%
+fast if you want to know more about the
+Rosetta Stone and these various musical
+
+ align:start position:0%
+Rosetta Stone and these various musical
+ 
+
+ align:start position:0%
+Rosetta Stone and these various musical
+encodings I have also included cra saps
+
+ align:start position:0%
+encodings I have also included cra saps
+ 
+
+ align:start position:0%
+encodings I have also included cra saps
+which I'll video thanks for watching
\ No newline at end of file
diff --git a/WAc7fQ1qzAc.txt b/WAc7fQ1qzAc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c6461070e1a1544b42b7bb86f8f3aa52ea4f5f45
--- /dev/null
+++ b/WAc7fQ1qzAc.txt
@@ -0,0 +1,14995 @@
+align:start position:0%
+ 
+Labs based on electronic structure and
+
+ align:start position:0%
+Labs based on electronic structure and
+ 
+
+ align:start position:0%
+Labs based on electronic structure and
+this will cover the next two
+
+ align:start position:0%
+this will cover the next two
+ 
+
+ align:start position:0%
+this will cover the next two
+computational lab and on Thursday we'll
+
+ align:start position:0%
+computational lab and on Thursday we'll
+ 
+
+ align:start position:0%
+computational lab and on Thursday we'll
+start looking at some of the finite
+
+ align:start position:0%
+start looking at some of the finite
+ 
+
+ align:start position:0%
+start looking at some of the finite
+temperature ideas that are based on the
+
+ align:start position:0%
+temperature ideas that are based on the
+ 
+
+ align:start position:0%
+temperature ideas that are based on the
+energy models that we have seen um this
+
+ align:start position:0%
+energy models that we have seen um this
+ 
+
+ align:start position:0%
+energy models that we have seen um this
+by the way is robertto bajo missing a
+
+ align:start position:0%
+by the way is robertto bajo missing a
+ 
+
+ align:start position:0%
+by the way is robertto bajo missing a
+penalty shot um okay so U reminder of
+
+ align:start position:0%
+penalty shot um okay so U reminder of
+ 
+
+ align:start position:0%
+penalty shot um okay so U reminder of
+what we have seen in the last class um
+
+ align:start position:0%
+what we have seen in the last class um
+ 
+
+ align:start position:0%
+what we have seen in the last class um
+we have introduced the idea of pseudo
+
+ align:start position:0%
+we have introduced the idea of pseudo
+ 
+
+ align:start position:0%
+we have introduced the idea of pseudo
+Potentials in order to remove the cost
+
+ align:start position:0%
+Potentials in order to remove the cost
+ 
+
+ align:start position:0%
+Potentials in order to remove the cost
+of carrying out calculation that include
+
+ align:start position:0%
+of carrying out calculation that include
+ 
+
+ align:start position:0%
+of carrying out calculation that include
+the core electrons that are very many
+
+ align:start position:0%
+the core electrons that are very many
+ 
+
+ align:start position:0%
+the core electrons that are very many
+especially in s of larger atoms and that
+
+ align:start position:0%
+especially in s of larger atoms and that
+ 
+
+ align:start position:0%
+especially in s of larger atoms and that
+have exceedingly High um oscillations
+
+ align:start position:0%
+have exceedingly High um oscillations
+ 
+
+ align:start position:0%
+have exceedingly High um oscillations
+around the nucleus duing to the
+
+ align:start position:0%
+around the nucleus duing to the
+ 
+
+ align:start position:0%
+around the nucleus duing to the
+orthogonality constraint what we have
+
+ align:start position:0%
+orthogonality constraint what we have
+ 
+
+ align:start position:0%
+orthogonality constraint what we have
+done is we have substituted what would
+
+ align:start position:0%
+done is we have substituted what would
+ 
+
+ align:start position:0%
+done is we have substituted what would
+be the Z over R cumic potential with
+
+ align:start position:0%
+be the Z over R cumic potential with
+ 
+
+ align:start position:0%
+be the Z over R cumic potential with
+inside the core region of the nucleus at
+
+ align:start position:0%
+inside the core region of the nucleus at
+ 
+
+ align:start position:0%
+inside the core region of the nucleus at
+pseudo potential that is a potential
+
+ align:start position:0%
+pseudo potential that is a potential
+ 
+
+ align:start position:0%
+pseudo potential that is a potential
+that reproduces the effect of the
+
+ align:start position:0%
+that reproduces the effect of the
+ 
+
+ align:start position:0%
+that reproduces the effect of the
+nucleus and of the frozen core electrons
+
+ align:start position:0%
+nucleus and of the frozen core electrons
+ 
+
+ align:start position:0%
+nucleus and of the frozen core electrons
+and as you can see this pseudo potential
+
+ align:start position:0%
+and as you can see this pseudo potential
+ 
+
+ align:start position:0%
+and as you can see this pseudo potential
+tend to be repulsive close to the origin
+
+ align:start position:0%
+tend to be repulsive close to the origin
+ 
+
+ align:start position:0%
+tend to be repulsive close to the origin
+basically again reproducing the sort of
+
+ align:start position:0%
+basically again reproducing the sort of
+ 
+
+ align:start position:0%
+basically again reproducing the sort of
+angular momentum push outwards of the
+
+ align:start position:0%
+angular momentum push outwards of the
+ 
+
+ align:start position:0%
+angular momentum push outwards of the
+core electrons uh to the valence
+
+ align:start position:0%
+core electrons uh to the valence
+ 
+
+ align:start position:0%
+core electrons uh to the valence
+electrons and in order to make this
+
+ align:start position:0%
+electrons and in order to make this
+ 
+
+ align:start position:0%
+electrons and in order to make this
+pseudo potential very accurate there has
+
+ align:start position:0%
+pseudo potential very accurate there has
+ 
+
+ align:start position:0%
+pseudo potential very accurate there has
+been this idea that has been developed
+
+ align:start position:0%
+been this idea that has been developed
+ 
+
+ align:start position:0%
+been this idea that has been developed
+of Norm conserving potential that will
+
+ align:start position:0%
+of Norm conserving potential that will
+ 
+
+ align:start position:0%
+of Norm conserving potential that will
+act differently on the different
+
+ align:start position:0%
+act differently on the different
+ 
+
+ align:start position:0%
+act differently on the different
+components of a valence electronic wave
+
+ align:start position:0%
+components of a valence electronic wave
+ 
+
+ align:start position:0%
+components of a valence electronic wave
+function so you have a incoming
+
+ align:start position:0%
+function so you have a incoming
+ 
+
+ align:start position:0%
+function so you have a incoming
+electrons or you have a sort of ground
+
+ align:start position:0%
+electrons or you have a sort of ground
+ 
+
+ align:start position:0%
+electrons or you have a sort of ground
+state valence wave function you can
+
+ align:start position:0%
+state valence wave function you can
+ 
+
+ align:start position:0%
+state valence wave function you can
+decompose it you can decide how much of
+
+ align:start position:0%
+decompose it you can decide how much of
+ 
+
+ align:start position:0%
+decompose it you can decide how much of
+it as s p or D component and you can act
+
+ align:start position:0%
+it as s p or D component and you can act
+ 
+
+ align:start position:0%
+it as s p or D component and you can act
+differently on the different slices of
+
+ align:start position:0%
+differently on the different slices of
+ 
+
+ align:start position:0%
+differently on the different slices of
+this wave function and so with this
+
+ align:start position:0%
+this wave function and so with this
+ 
+
+ align:start position:0%
+this wave function and so with this
+basically we can solve a new problem in
+
+ align:start position:0%
+basically we can solve a new problem in
+ 
+
+ align:start position:0%
+basically we can solve a new problem in
+an effective external potential in which
+
+ align:start position:0%
+an effective external potential in which
+ 
+
+ align:start position:0%
+an effective external potential in which
+the lowest energy ground state will
+
+ align:start position:0%
+the lowest energy ground state will
+ 
+
+ align:start position:0%
+the lowest energy ground state will
+actually be identical in energy to the
+
+ align:start position:0%
+actually be identical in energy to the
+ 
+
+ align:start position:0%
+actually be identical in energy to the
+valence ion state of the original
+
+ align:start position:0%
+valence ion state of the original
+ 
+
+ align:start position:0%
+valence ion state of the original
+so-called all electron atom the atom
+
+ align:start position:0%
+so-called all electron atom the atom
+ 
+
+ align:start position:0%
+so-called all electron atom the atom
+with all its electrons and the wave
+
+ align:start position:0%
+with all its electrons and the wave
+ 
+
+ align:start position:0%
+with all its electrons and the wave
+function for this pseudo atom will be
+
+ align:start position:0%
+function for this pseudo atom will be
+ 
+
+ align:start position:0%
+function for this pseudo atom will be
+identical to the wave function of the
+
+ align:start position:0%
+identical to the wave function of the
+ 
+
+ align:start position:0%
+identical to the wave function of the
+real atom outside of the core radius
+
+ align:start position:0%
+real atom outside of the core radius
+ 
+
+ align:start position:0%
+real atom outside of the core radius
+outside in this case three Atomic unit
+
+ align:start position:0%
+outside in this case three Atomic unit
+ 
+
+ align:start position:0%
+outside in this case three Atomic unit
+in this slide so this was sort of one
+
+ align:start position:0%
+in this slide so this was sort of one
+ 
+
+ align:start position:0%
+in this slide so this was sort of one
+the first important technical tools that
+
+ align:start position:0%
+the first important technical tools that
+ 
+
+ align:start position:0%
+the first important technical tools that
+were introduced in the 70s and 80s to
+
+ align:start position:0%
+were introduced in the 70s and 80s to
+ 
+
+ align:start position:0%
+were introduced in the 70s and 80s to
+make this calculation clearly feasible
+
+ align:start position:0%
+make this calculation clearly feasible
+ 
+
+ align:start position:0%
+make this calculation clearly feasible
+um the other sort of idea that I want to
+
+ align:start position:0%
+um the other sort of idea that I want to
+ 
+
+ align:start position:0%
+um the other sort of idea that I want to
+sort of remind you uh is that whenever
+
+ align:start position:0%
+sort of remind you uh is that whenever
+ 
+
+ align:start position:0%
+sort of remind you uh is that whenever
+we deal with extended systems solids
+
+ align:start position:0%
+we deal with extended systems solids
+ 
+
+ align:start position:0%
+we deal with extended systems solids
+liquids and in particular when we have
+
+ align:start position:0%
+liquids and in particular when we have
+ 
+
+ align:start position:0%
+liquids and in particular when we have
+periodic boundary condition that is we
+
+ align:start position:0%
+periodic boundary condition that is we
+ 
+
+ align:start position:0%
+periodic boundary condition that is we
+have a unit cell periodically repeated
+
+ align:start position:0%
+have a unit cell periodically repeated
+ 
+
+ align:start position:0%
+have a unit cell periodically repeated
+in all Dimension the Ian states of
+
+ align:start position:0%
+in all Dimension the Ian states of
+ 
+
+ align:start position:0%
+in all Dimension the Ian states of
+aronian take the form of block theorem
+
+ align:start position:0%
+aronian take the form of block theorem
+ 
+
+ align:start position:0%
+aronian take the form of block theorem
+and get classified according to two
+
+ align:start position:0%
+and get classified according to two
+ 
+
+ align:start position:0%
+and get classified according to two
+quantum numbers a discrete number the
+
+ align:start position:0%
+quantum numbers a discrete number the
+ 
+
+ align:start position:0%
+quantum numbers a discrete number the
+bond index number n and a continuous
+
+ align:start position:0%
+bond index number n and a continuous
+ 
+
+ align:start position:0%
+bond index number n and a continuous
+number K and the overall igen States can
+
+ align:start position:0%
+number K and the overall igen States can
+ 
+
+ align:start position:0%
+number K and the overall igen States can
+be written as a product of two function
+
+ align:start position:0%
+be written as a product of two function
+ 
+
+ align:start position:0%
+be written as a product of two function
+one is just a plain wave that has the
+
+ align:start position:0%
+one is just a plain wave that has the
+ 
+
+ align:start position:0%
+one is just a plain wave that has the
+periodicity of the so-called Crystal
+
+ align:start position:0%
+periodicity of the so-called Crystal
+ 
+
+ align:start position:0%
+periodicity of the so-called Crystal
+momentum K one of these quantum numbers
+
+ align:start position:0%
+momentum K one of these quantum numbers
+ 
+
+ align:start position:0%
+momentum K one of these quantum numbers
+and the other is the periodic part of
+
+ align:start position:0%
+and the other is the periodic part of
+ 
+
+ align:start position:0%
+and the other is the periodic part of
+this block orbital written here as U and
+
+ align:start position:0%
+this block orbital written here as U and
+ 
+
+ align:start position:0%
+this block orbital written here as U and
+that this this is a function with the
+
+ align:start position:0%
+that this this is a function with the
+ 
+
+ align:start position:0%
+that this this is a function with the
+same periodicity of your unit cell so
+
+ align:start position:0%
+same periodicity of your unit cell so
+ 
+
+ align:start position:0%
+same periodicity of your unit cell so
+overall the orbital itself The KES
+
+ align:start position:0%
+overall the orbital itself The KES
+ 
+
+ align:start position:0%
+overall the orbital itself The KES
+orbital p uh can have any periodicity
+
+ align:start position:0%
+orbital p uh can have any periodicity
+ 
+
+ align:start position:0%
+orbital p uh can have any periodicity
+but it can always be decomposed into a
+
+ align:start position:0%
+but it can always be decomposed into a
+ 
+
+ align:start position:0%
+but it can always be decomposed into a
+part of a well defined wavelength times
+
+ align:start position:0%
+part of a well defined wavelength times
+ 
+
+ align:start position:0%
+part of a well defined wavelength times
+a periodic a periodic part uh periodic
+
+ align:start position:0%
+a periodic a periodic part uh periodic
+ 
+
+ align:start position:0%
+a periodic a periodic part uh periodic
+part is going to be smooth again we
+
+ align:start position:0%
+part is going to be smooth again we
+ 
+
+ align:start position:0%
+part is going to be smooth again we
+don't have any more core electrons so
+
+ align:start position:0%
+don't have any more core electrons so
+ 
+
+ align:start position:0%
+don't have any more core electrons so
+close to the nuclei it will look just as
+
+ align:start position:0%
+close to the nuclei it will look just as
+ 
+
+ align:start position:0%
+close to the nuclei it will look just as
+1 S 2 s to P orbitals and that periodic
+
+ align:start position:0%
+1 S 2 s to P orbitals and that periodic
+ 
+
+ align:start position:0%
+1 S 2 s to P orbitals and that periodic
+part can actually be expanded in a set
+
+ align:start position:0%
+part can actually be expanded in a set
+ 
+
+ align:start position:0%
+part can actually be expanded in a set
+of plane waves uh plane waves that need
+
+ align:start position:0%
+of plane waves uh plane waves that need
+ 
+
+ align:start position:0%
+of plane waves uh plane waves that need
+to satisfy the periodic boundary
+
+ align:start position:0%
+to satisfy the periodic boundary
+ 
+
+ align:start position:0%
+to satisfy the periodic boundary
+condition of our system and so we have
+
+ align:start position:0%
+condition of our system and so we have
+ 
+
+ align:start position:0%
+condition of our system and so we have
+seen that we can write the functions e
+
+ align:start position:0%
+seen that we can write the functions e
+ 
+
+ align:start position:0%
+seen that we can write the functions e
+to the igr where the G is a linear
+
+ align:start position:0%
+to the igr where the G is a linear
+ 
+
+ align:start position:0%
+to the igr where the G is a linear
+combination of primitive reciprocal
+
+ align:start position:0%
+combination of primitive reciprocal
+ 
+
+ align:start position:0%
+combination of primitive reciprocal
+latis vectors with integer coefficient
+
+ align:start position:0%
+latis vectors with integer coefficient
+ 
+
+ align:start position:0%
+latis vectors with integer coefficient
+and all those G vectors are such that e
+
+ align:start position:0%
+and all those G vectors are such that e
+ 
+
+ align:start position:0%
+and all those G vectors are such that e
+to the i r has the same periodicity of
+
+ align:start position:0%
+to the i r has the same periodicity of
+ 
+
+ align:start position:0%
+to the i r has the same periodicity of
+your direct lce and these are the
+
+ align:start position:0%
+your direct lce and these are the
+ 
+
+ align:start position:0%
+your direct lce and these are the
+coefficient of this series expansion and
+
+ align:start position:0%
+coefficient of this series expansion and
+ 
+
+ align:start position:0%
+coefficient of this series expansion and
+uh we sort of can systematically improve
+
+ align:start position:0%
+uh we sort of can systematically improve
+ 
+
+ align:start position:0%
+uh we sort of can systematically improve
+the quality of this basic set expansion
+
+ align:start position:0%
+the quality of this basic set expansion
+ 
+
+ align:start position:0%
+the quality of this basic set expansion
+by increasing the number of G vectors
+
+ align:start position:0%
+by increasing the number of G vectors
+ 
+
+ align:start position:0%
+by increasing the number of G vectors
+that we use and we can do that
+
+ align:start position:0%
+that we use and we can do that
+ 
+
+ align:start position:0%
+that we use and we can do that
+systematically by taking G vectors with
+
+ align:start position:0%
+systematically by taking G vectors with
+ 
+
+ align:start position:0%
+systematically by taking G vectors with
+longer and longer lengths or as we say
+
+ align:start position:0%
+longer and longer lengths or as we say
+ 
+
+ align:start position:0%
+longer and longer lengths or as we say
+with higher and higher energy cut off uh
+
+ align:start position:0%
+with higher and higher energy cut off uh
+ 
+
+ align:start position:0%
+with higher and higher energy cut off uh
+because higher and higher energy cut
+
+ align:start position:0%
+because higher and higher energy cut
+ 
+
+ align:start position:0%
+because higher and higher energy cut
+offs or longer and longer moduli for the
+
+ align:start position:0%
+offs or longer and longer moduli for the
+ 
+
+ align:start position:0%
+offs or longer and longer moduli for the
+G vectors corresponds to plane waves
+
+ align:start position:0%
+G vectors corresponds to plane waves
+ 
+
+ align:start position:0%
+G vectors corresponds to plane waves
+with finer and finer periodicity so with
+
+ align:start position:0%
+with finer and finer periodicity so with
+ 
+
+ align:start position:0%
+with finer and finer periodicity so with
+finer and finer resolution so this is a
+
+ align:start position:0%
+finer and finer resolution so this is a
+ 
+
+ align:start position:0%
+finer and finer resolution so this is a
+distinct advantage of plane waves uh and
+
+ align:start position:0%
+distinct advantage of plane waves uh and
+ 
+
+ align:start position:0%
+distinct advantage of plane waves uh and
+in addition this U basis sets do not
+
+ align:start position:0%
+in addition this U basis sets do not
+ 
+
+ align:start position:0%
+in addition this U basis sets do not
+depend on Atomic position so when we
+
+ align:start position:0%
+depend on Atomic position so when we
+ 
+
+ align:start position:0%
+depend on Atomic position so when we
+calculate forces say to do molecular
+
+ align:start position:0%
+calculate forces say to do molecular
+ 
+
+ align:start position:0%
+calculate forces say to do molecular
+Dynamics or structural relaxation
+
+ align:start position:0%
+Dynamics or structural relaxation
+ 
+
+ align:start position:0%
+Dynamics or structural relaxation
+calculation we don't need to take into
+
+ align:start position:0%
+calculation we don't need to take into
+ 
+
+ align:start position:0%
+calculation we don't need to take into
+account the fact that the basic set
+
+ align:start position:0%
+account the fact that the basic set
+ 
+
+ align:start position:0%
+account the fact that the basic set
+changes with the position of the atoms
+
+ align:start position:0%
+changes with the position of the atoms
+ 
+
+ align:start position:0%
+changes with the position of the atoms
+uh plane waves are not the only choices
+
+ align:start position:0%
+uh plane waves are not the only choices
+ 
+
+ align:start position:0%
+uh plane waves are not the only choices
+there are a number of other choices that
+
+ align:start position:0%
+there are a number of other choices that
+ 
+
+ align:start position:0%
+there are a number of other choices that
+are very successful in particular a lot
+
+ align:start position:0%
+are very successful in particular a lot
+ 
+
+ align:start position:0%
+are very successful in particular a lot
+of the quantum chemistry code use
+
+ align:start position:0%
+of the quantum chemistry code use
+ 
+
+ align:start position:0%
+of the quantum chemistry code use
+gaussian basis sets so atom centered
+
+ align:start position:0%
+gaussian basis sets so atom centered
+ 
+
+ align:start position:0%
+gaussian basis sets so atom centered
+orbitals that decay as gausian this is
+
+ align:start position:0%
+orbitals that decay as gausian this is
+ 
+
+ align:start position:0%
+orbitals that decay as gausian this is
+very convenient to do calculation like
+
+ align:start position:0%
+very convenient to do calculation like
+ 
+
+ align:start position:0%
+very convenient to do calculation like
+the exchange term in Harry fol but of
+
+ align:start position:0%
+the exchange term in Harry fol but of
+ 
+
+ align:start position:0%
+the exchange term in Harry fol but of
+course you could have just a finite
+
+ align:start position:0%
+course you could have just a finite
+ 
+
+ align:start position:0%
+course you could have just a finite
+difference representation so you could
+
+ align:start position:0%
+difference representation so you could
+ 
+
+ align:start position:0%
+difference representation so you could
+represent your orbitals on a grid of
+
+ align:start position:0%
+represent your orbitals on a grid of
+ 
+
+ align:start position:0%
+represent your orbitals on a grid of
+points in real space that tends to be
+
+ align:start position:0%
+points in real space that tends to be
+ 
+
+ align:start position:0%
+points in real space that tends to be
+very efficient to do parallel
+
+ align:start position:0%
+very efficient to do parallel
+ 
+
+ align:start position:0%
+very efficient to do parallel
+calculation but it's very difficult to
+
+ align:start position:0%
+calculation but it's very difficult to
+ 
+
+ align:start position:0%
+calculation but it's very difficult to
+do um accurate calculation of the second
+
+ align:start position:0%
+do um accurate calculation of the second
+ 
+
+ align:start position:0%
+do um accurate calculation of the second
+derivative if you remember when you
+
+ align:start position:0%
+derivative if you remember when you
+ 
+
+ align:start position:0%
+derivative if you remember when you
+expand a function in plain waves you
+
+ align:start position:0%
+expand a function in plain waves you
+ 
+
+ align:start position:0%
+expand a function in plain waves you
+have an analytic expression for the
+
+ align:start position:0%
+have an analytic expression for the
+ 
+
+ align:start position:0%
+have an analytic expression for the
+second derivative just because the the
+
+ align:start position:0%
+second derivative just because the the
+ 
+
+ align:start position:0%
+second derivative just because the the
+first and second derivative of a plane
+
+ align:start position:0%
+first and second derivative of a plane
+ 
+
+ align:start position:0%
+first and second derivative of a plane
+waves are just IG or minus g s time the
+
+ align:start position:0%
+waves are just IG or minus g s time the
+ 
+
+ align:start position:0%
+waves are just IG or minus g s time the
+plane wave itself and that's very
+
+ align:start position:0%
+plane wave itself and that's very
+ 
+
+ align:start position:0%
+plane wave itself and that's very
+important and so that's that's when sort
+
+ align:start position:0%
+important and so that's that's when sort
+ 
+
+ align:start position:0%
+important and so that's that's when sort
+of real space representation become a
+
+ align:start position:0%
+of real space representation become a
+ 
+
+ align:start position:0%
+of real space representation become a
+little bit trickier and then there are a
+
+ align:start position:0%
+little bit trickier and then there are a
+ 
+
+ align:start position:0%
+little bit trickier and then there are a
+number of sort of you know uh more
+
+ align:start position:0%
+number of sort of you know uh more
+ 
+
+ align:start position:0%
+number of sort of you know uh more
+approximate approaches based on a number
+
+ align:start position:0%
+approximate approaches based on a number
+ 
+
+ align:start position:0%
+approximate approaches based on a number
+of sort of atomic like localized
+
+ align:start position:0%
+of sort of atomic like localized
+ 
+
+ align:start position:0%
+of sort of atomic like localized
+orbitals or there are a number of sort
+
+ align:start position:0%
+orbitals or there are a number of sort
+ 
+
+ align:start position:0%
+orbitals or there are a number of sort
+of accurate approaches that are based
+
+ align:start position:0%
+of accurate approaches that are based
+ 
+
+ align:start position:0%
+of accurate approaches that are based
+usually on a
+
+ align:start position:0%
+usually on a
+ 
+
+ align:start position:0%
+usually on a
+combination of a basic set that has
+
+ align:start position:0%
+combination of a basic set that has
+ 
+
+ align:start position:0%
+combination of a basic set that has
+plain wave like characteristic in the
+
+ align:start position:0%
+plain wave like characteristic in the
+ 
+
+ align:start position:0%
+plain wave like characteristic in the
+region sort of far away from the nuclei
+
+ align:start position:0%
+region sort of far away from the nuclei
+ 
+
+ align:start position:0%
+region sort of far away from the nuclei
+and then it has Atomic like
+
+ align:start position:0%
+and then it has Atomic like
+ 
+
+ align:start position:0%
+and then it has Atomic like
+characteristic in the region inside the
+
+ align:start position:0%
+characteristic in the region inside the
+ 
+
+ align:start position:0%
+characteristic in the region inside the
+nuclei and this tends to be the most
+
+ align:start position:0%
+nuclei and this tends to be the most
+ 
+
+ align:start position:0%
+nuclei and this tends to be the most
+accurate but also slightly more
+
+ align:start position:0%
+accurate but also slightly more
+ 
+
+ align:start position:0%
+accurate but also slightly more
+expensive approaches okay this concludes
+
+ align:start position:0%
+expensive approaches okay this concludes
+ 
+
+ align:start position:0%
+expensive approaches okay this concludes
+one of sort of the technical points that
+
+ align:start position:0%
+one of sort of the technical points that
+ 
+
+ align:start position:0%
+one of sort of the technical points that
+you need to be careful in a practical
+
+ align:start position:0%
+you need to be careful in a practical
+ 
+
+ align:start position:0%
+you need to be careful in a practical
+calculation uh the other point that sort
+
+ align:start position:0%
+calculation uh the other point that sort
+ 
+
+ align:start position:0%
+calculation uh the other point that sort
+of comes over and over again has to do
+
+ align:start position:0%
+of comes over and over again has to do
+ 
+
+ align:start position:0%
+of comes over and over again has to do
+with BL enzone integration uh let me
+
+ align:start position:0%
+with BL enzone integration uh let me
+ 
+
+ align:start position:0%
+with BL enzone integration uh let me
+give you first the example of a molecule
+
+ align:start position:0%
+give you first the example of a molecule
+ 
+
+ align:start position:0%
+give you first the example of a molecule
+say if you're calculating the electronic
+
+ align:start position:0%
+say if you're calculating the electronic
+ 
+
+ align:start position:0%
+say if you're calculating the electronic
+structure of a molecule uh in the course
+
+ align:start position:0%
+structure of a molecule uh in the course
+ 
+
+ align:start position:0%
+structure of a molecule uh in the course
+of your calculation you'll need to
+
+ align:start position:0%
+of your calculation you'll need to
+ 
+
+ align:start position:0%
+of your calculation you'll need to
+calculate integrated quantity like the
+
+ align:start position:0%
+calculate integrated quantity like the
+ 
+
+ align:start position:0%
+calculate integrated quantity like the
+charge density the charge density of a
+
+ align:start position:0%
+charge density the charge density of a
+ 
+
+ align:start position:0%
+charge density the charge density of a
+molecule is going to be the sum of the
+
+ align:start position:0%
+molecule is going to be the sum of the
+ 
+
+ align:start position:0%
+molecule is going to be the sum of the
+square modulus moduli of all the single
+
+ align:start position:0%
+square modulus moduli of all the single
+ 
+
+ align:start position:0%
+square modulus moduli of all the single
+particle orbitals so if you are sort of
+
+ align:start position:0%
+particle orbitals so if you are sort of
+ 
+
+ align:start position:0%
+particle orbitals so if you are sort of
+you know studying a molecule like just
+
+ align:start position:0%
+you know studying a molecule like just
+ 
+
+ align:start position:0%
+you know studying a molecule like just
+hydrogen 2 well you just take the sort
+
+ align:start position:0%
+hydrogen 2 well you just take the sort
+ 
+
+ align:start position:0%
+hydrogen 2 well you just take the sort
+of sum of the square module of the first
+
+ align:start position:0%
+of sum of the square module of the first
+ 
+
+ align:start position:0%
+of sum of the square module of the first
+orbital you have more orbital more
+
+ align:start position:0%
+orbital you have more orbital more
+ 
+
+ align:start position:0%
+orbital you have more orbital more
+complex molecule you need to sum over
+
+ align:start position:0%
+complex molecule you need to sum over
+ 
+
+ align:start position:0%
+complex molecule you need to sum over
+all the orbitals up to the homo the
+
+ align:start position:0%
+all the orbitals up to the homo the
+ 
+
+ align:start position:0%
+all the orbitals up to the homo the
+highest occupied molecular orbital you
+
+ align:start position:0%
+highest occupied molecular orbital you
+ 
+
+ align:start position:0%
+highest occupied molecular orbital you
+do a calculation in a solid you have to
+
+ align:start position:0%
+do a calculation in a solid you have to
+ 
+
+ align:start position:0%
+do a calculation in a solid you have to
+do exactly the same thing that is you
+
+ align:start position:0%
+do exactly the same thing that is you
+ 
+
+ align:start position:0%
+do exactly the same thing that is you
+need to calculate the charge density by
+
+ align:start position:0%
+need to calculate the charge density by
+ 
+
+ align:start position:0%
+need to calculate the charge density by
+summing all over the occupied
+
+ align:start position:0%
+summing all over the occupied
+ 
+
+ align:start position:0%
+summing all over the occupied
+States now as I said what are the
+
+ align:start position:0%
+States now as I said what are the
+ 
+
+ align:start position:0%
+States now as I said what are the
+quantum numbers that describe a solid
+
+ align:start position:0%
+quantum numbers that describe a solid
+ 
+
+ align:start position:0%
+quantum numbers that describe a solid
+are a bond index n and a continuous
+
+ align:start position:0%
+are a bond index n and a continuous
+ 
+
+ align:start position:0%
+are a bond index n and a continuous
+index K that we call the Quasi momentum
+
+ align:start position:0%
+index K that we call the Quasi momentum
+ 
+
+ align:start position:0%
+index K that we call the Quasi momentum
+and we us represent say the energy of
+
+ align:start position:0%
+and we us represent say the energy of
+ 
+
+ align:start position:0%
+and we us represent say the energy of
+the states in a solid with a band
+
+ align:start position:0%
+the states in a solid with a band
+ 
+
+ align:start position:0%
+the states in a solid with a band
+diagram and I've plotted here on the
+
+ align:start position:0%
+diagram and I've plotted here on the
+ 
+
+ align:start position:0%
+diagram and I've plotted here on the
+left the band diagram for
+
+ align:start position:0%
+left the band diagram for
+ 
+
+ align:start position:0%
+left the band diagram for
+silicon uh in particular what we are
+
+ align:start position:0%
+silicon uh in particular what we are
+ 
+
+ align:start position:0%
+silicon uh in particular what we are
+looking here is in the bran zone of
+
+ align:start position:0%
+looking here is in the bran zone of
+ 
+
+ align:start position:0%
+looking here is in the bran zone of
+silicon along certain High symmetry
+
+ align:start position:0%
+silicon along certain High symmetry
+ 
+
+ align:start position:0%
+silicon along certain High symmetry
+Direction I presume this is these are
+
+ align:start position:0%
+Direction I presume this is these are
+ 
+
+ align:start position:0%
+Direction I presume this is these are
+sort of high symmetry points like gamma
+
+ align:start position:0%
+sort of high symmetry points like gamma
+ 
+
+ align:start position:0%
+sort of high symmetry points like gamma
+would be 0 0 0 L would be uh 1/2 1/2 1/2
+
+ align:start position:0%
+would be 0 0 0 L would be uh 1/2 1/2 1/2
+ 
+
+ align:start position:0%
+would be 0 0 0 L would be uh 1/2 1/2 1/2
+uh hope this is correct this should be X
+
+ align:start position:0%
+uh hope this is correct this should be X
+ 
+
+ align:start position:0%
+uh hope this is correct this should be X
+that is 1 0 0 so we plot the energies of
+
+ align:start position:0%
+that is 1 0 0 so we plot the energies of
+ 
+
+ align:start position:0%
+that is 1 0 0 so we plot the energies of
+all the occupied bonds of silicon in
+
+ align:start position:0%
+all the occupied bonds of silicon in
+ 
+
+ align:start position:0%
+all the occupied bonds of silicon in
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+direction along the Bren Zone um silicon
+
+ align:start position:0%
+direction along the Bren Zone um silicon
+ 
+
+ align:start position:0%
+direction along the Bren Zone um silicon
+has two atoms per unit cell each atom
+
+ align:start position:0%
+has two atoms per unit cell each atom
+ 
+
+ align:start position:0%
+has two atoms per unit cell each atom
+has four valence electrons so we have
+
+ align:start position:0%
+has four valence electrons so we have
+ 
+
+ align:start position:0%
+has four valence electrons so we have
+eight valence electron per unit cell uh
+
+ align:start position:0%
+eight valence electron per unit cell uh
+ 
+
+ align:start position:0%
+eight valence electron per unit cell uh
+it's a system in which uh there is
+
+ align:start position:0%
+it's a system in which uh there is
+ 
+
+ align:start position:0%
+it's a system in which uh there is
+basically spin degeneracy so there is
+
+ align:start position:0%
+basically spin degeneracy so there is
+ 
+
+ align:start position:0%
+basically spin degeneracy so there is
+really sort of the same spal part for
+
+ align:start position:0%
+really sort of the same spal part for
+ 
+
+ align:start position:0%
+really sort of the same spal part for
+spin up and spin down so what we usually
+
+ align:start position:0%
+spin up and spin down so what we usually
+ 
+
+ align:start position:0%
+spin up and spin down so what we usually
+say is that we can accommodate two
+
+ align:start position:0%
+say is that we can accommodate two
+ 
+
+ align:start position:0%
+say is that we can accommodate two
+electrons for each space orbital and
+
+ align:start position:0%
+electrons for each space orbital and
+ 
+
+ align:start position:0%
+electrons for each space orbital and
+they will just have different spin
+
+ align:start position:0%
+they will just have different spin
+ 
+
+ align:start position:0%
+they will just have different spin
+quantum number so with this eight
+
+ align:start position:0%
+quantum number so with this eight
+ 
+
+ align:start position:0%
+quantum number so with this eight
+valence electron we end up with four
+
+ align:start position:0%
+valence electron we end up with four
+ 
+
+ align:start position:0%
+valence electron we end up with four
+bonds and sometimes because of symmetry
+
+ align:start position:0%
+bonds and sometimes because of symmetry
+ 
+
+ align:start position:0%
+bonds and sometimes because of symmetry
+you have degeneracy but you see that
+
+ align:start position:0%
+you have degeneracy but you see that
+ 
+
+ align:start position:0%
+you have degeneracy but you see that
+somewhere like here at a sort of you
+
+ align:start position:0%
+somewhere like here at a sort of you
+ 
+
+ align:start position:0%
+somewhere like here at a sort of you
+know arbitrary low symmetry point in the
+
+ align:start position:0%
+know arbitrary low symmetry point in the
+ 
+
+ align:start position:0%
+know arbitrary low symmetry point in the
+Brian Zone you can clearly see uh for
+
+ align:start position:0%
+Brian Zone you can clearly see uh for
+ 
+
+ align:start position:0%
+Brian Zone you can clearly see uh for
+for bands so if we want to calculate the
+
+ align:start position:0%
+for bands so if we want to calculate the
+ 
+
+ align:start position:0%
+for bands so if we want to calculate the
+charge density of this system we need to
+
+ align:start position:0%
+charge density of this system we need to
+ 
+
+ align:start position:0%
+charge density of this system we need to
+sum over all the possible occupied
+
+ align:start position:0%
+sum over all the possible occupied
+ 
+
+ align:start position:0%
+sum over all the possible occupied
+states that is we need to sum over all
+
+ align:start position:0%
+states that is we need to sum over all
+ 
+
+ align:start position:0%
+states that is we need to sum over all
+the four bonds and that's trivial but we
+
+ align:start position:0%
+the four bonds and that's trivial but we
+ 
+
+ align:start position:0%
+the four bonds and that's trivial but we
+also need to integrate over all the
+
+ align:start position:0%
+also need to integrate over all the
+ 
+
+ align:start position:0%
+also need to integrate over all the
+possible K vectors that is we need to
+
+ align:start position:0%
+possible K vectors that is we need to
+ 
+
+ align:start position:0%
+possible K vectors that is we need to
+make an integral in the brn zone uh that
+
+ align:start position:0%
+make an integral in the brn zone uh that
+ 
+
+ align:start position:0%
+make an integral in the brn zone uh that
+is we need to sort of really sum over
+
+ align:start position:0%
+is we need to sort of really sum over
+ 
+
+ align:start position:0%
+is we need to sort of really sum over
+all these possible States okay an
+
+ align:start position:0%
+all these possible States okay an
+ 
+
+ align:start position:0%
+all these possible States okay an
+integral is is obviously an analytical
+
+ align:start position:0%
+integral is is obviously an analytical
+ 
+
+ align:start position:0%
+integral is is obviously an analytical
+operation in practice on a computer what
+
+ align:start position:0%
+operation in practice on a computer what
+ 
+
+ align:start position:0%
+operation in practice on a computer what
+we do is just we discretize that
+
+ align:start position:0%
+we do is just we discretize that
+ 
+
+ align:start position:0%
+we do is just we discretize that
+integral and we take a sum so it means
+
+ align:start position:0%
+integral and we take a sum so it means
+ 
+
+ align:start position:0%
+integral and we take a sum so it means
+that and again I'll use two Dimension as
+
+ align:start position:0%
+that and again I'll use two Dimension as
+ 
+
+ align:start position:0%
+that and again I'll use two Dimension as
+an example it means that If This Were My
+
+ align:start position:0%
+an example it means that If This Were My
+ 
+
+ align:start position:0%
+an example it means that If This Were My
+bran zone two dimensional bran Zone and
+
+ align:start position:0%
+bran zone two dimensional bran Zone and
+ 
+
+ align:start position:0%
+bran zone two dimensional bran Zone and
+my K Vector can be anywhere in this bran
+
+ align:start position:0%
+my K Vector can be anywhere in this bran
+ 
+
+ align:start position:0%
+my K Vector can be anywhere in this bran
+Zona what I would need to do is an
+
+ align:start position:0%
+Zona what I would need to do is an
+ 
+
+ align:start position:0%
+Zona what I would need to do is an
+integral over all the possibility inside
+
+ align:start position:0%
+integral over all the possibility inside
+ 
+
+ align:start position:0%
+integral over all the possibility inside
+there but in practice what I'll do I'll
+
+ align:start position:0%
+there but in practice what I'll do I'll
+ 
+
+ align:start position:0%
+there but in practice what I'll do I'll
+just take a
+
+ align:start position:0%
+just take a
+ 
+
+ align:start position:0%
+just take a
+discretization and I'll calculate my
+
+ align:start position:0%
+discretization and I'll calculate my
+ 
+
+ align:start position:0%
+discretization and I'll calculate my
+band structure at each one of these
+
+ align:start position:0%
+band structure at each one of these
+ 
+
+ align:start position:0%
+band structure at each one of these
+points say a regular equispaced mesh of
+
+ align:start position:0%
+points say a regular equispaced mesh of
+ 
+
+ align:start position:0%
+points say a regular equispaced mesh of
+K points and that's a an expensive
+
+ align:start position:0%
+K points and that's a an expensive
+ 
+
+ align:start position:0%
+K points and that's a an expensive
+operation so each calculation at each K
+
+ align:start position:0%
+operation so each calculation at each K
+ 
+
+ align:start position:0%
+operation so each calculation at each K
+point will require a self-consistent
+
+ align:start position:0%
+point will require a self-consistent
+ 
+
+ align:start position:0%
+point will require a self-consistent
+diagonalization of your problem and so
+
+ align:start position:0%
+diagonalization of your problem and so
+ 
+
+ align:start position:0%
+diagonalization of your problem and so
+really the cost of your calculation is
+
+ align:start position:0%
+really the cost of your calculation is
+ 
+
+ align:start position:0%
+really the cost of your calculation is
+linearly scaling in the number of K
+
+ align:start position:0%
+linearly scaling in the number of K
+ 
+
+ align:start position:0%
+linearly scaling in the number of K
+points so in reality you want to use uh
+
+ align:start position:0%
+points so in reality you want to use uh
+ 
+
+ align:start position:0%
+points so in reality you want to use uh
+as few K points as possible um for a
+
+ align:start position:0%
+as few K points as possible um for a
+ 
+
+ align:start position:0%
+as few K points as possible um for a
+system like a semiconductor or an
+
+ align:start position:0%
+system like a semiconductor or an
+ 
+
+ align:start position:0%
+system like a semiconductor or an
+insulator in which if you want the band
+
+ align:start position:0%
+insulator in which if you want the band
+ 
+
+ align:start position:0%
+insulator in which if you want the band
+structure is very smooth uh it becomes
+
+ align:start position:0%
+structure is very smooth uh it becomes
+ 
+
+ align:start position:0%
+structure is very smooth uh it becomes
+fairly easy to integrate that smooth
+
+ align:start position:0%
+fairly easy to integrate that smooth
+ 
+
+ align:start position:0%
+fairly easy to integrate that smooth
+bands with very coarse meshes so for
+
+ align:start position:0%
+bands with very coarse meshes so for
+ 
+
+ align:start position:0%
+bands with very coarse meshes so for
+something like Silicon you might be
+
+ align:start position:0%
+something like Silicon you might be
+ 
+
+ align:start position:0%
+something like Silicon you might be
+already very happy when you start to
+
+ align:start position:0%
+already very happy when you start to
+ 
+
+ align:start position:0%
+already very happy when you start to
+sample the threedimensional Brian zon
+
+ align:start position:0%
+sample the threedimensional Brian zon
+ 
+
+ align:start position:0%
+sample the threedimensional Brian zon
+with a uniform mes of K points that
+
+ align:start position:0%
+with a uniform mes of K points that
+ 
+
+ align:start position:0%
+with a uniform mes of K points that
+could have four K points in each
+
+ align:start position:0%
+could have four K points in each
+ 
+
+ align:start position:0%
+could have four K points in each
+Direction 4 by 4X 4 6X 6X 6 8X 8 by 8
+
+ align:start position:0%
+Direction 4 by 4X 4 6X 6X 6 8X 8 by 8
+ 
+
+ align:start position:0%
+Direction 4 by 4X 4 6X 6X 6 8X 8 by 8
+this is sort of the order of magnitude
+
+ align:start position:0%
+this is sort of the order of magnitude
+ 
+
+ align:start position:0%
+this is sort of the order of magnitude
+of the K points that you need to use uh
+
+ align:start position:0%
+of the K points that you need to use uh
+ 
+
+ align:start position:0%
+of the K points that you need to use uh
+if you were to study for a moment a unit
+
+ align:start position:0%
+if you were to study for a moment a unit
+ 
+
+ align:start position:0%
+if you were to study for a moment a unit
+cell of silicon you might want to study
+
+ align:start position:0%
+cell of silicon you might want to study
+ 
+
+ align:start position:0%
+cell of silicon you might want to study
+say a vacancy formation energy like you
+
+ align:start position:0%
+say a vacancy formation energy like you
+ 
+
+ align:start position:0%
+say a vacancy formation energy like you
+were doing in your first computational
+
+ align:start position:0%
+were doing in your first computational
+ 
+
+ align:start position:0%
+were doing in your first computational
+lab then you're not going to use a
+
+ align:start position:0%
+lab then you're not going to use a
+ 
+
+ align:start position:0%
+lab then you're not going to use a
+two atom unit cell you're going to use a
+
+ align:start position:0%
+two atom unit cell you're going to use a
+ 
+
+ align:start position:0%
+two atom unit cell you're going to use a
+larger unit cell and without sort of
+
+ align:start position:0%
+larger unit cell and without sort of
+ 
+
+ align:start position:0%
+larger unit cell and without sort of
+dwelling that much on it suppose that
+
+ align:start position:0%
+dwelling that much on it suppose that
+ 
+
+ align:start position:0%
+dwelling that much on it suppose that
+again in two Dimension you double the
+
+ align:start position:0%
+again in two Dimension you double the
+ 
+
+ align:start position:0%
+again in two Dimension you double the
+size of your unit cell um what's really
+
+ align:start position:0%
+size of your unit cell um what's really
+ 
+
+ align:start position:0%
+size of your unit cell um what's really
+happening is that the reciprocal latis
+
+ align:start position:0%
+happening is that the reciprocal latis
+ 
+
+ align:start position:0%
+happening is that the reciprocal latis
+vectors will become 1/2 in length so
+
+ align:start position:0%
+vectors will become 1/2 in length so
+ 
+
+ align:start position:0%
+vectors will become 1/2 in length so
+remember this General concept when you
+
+ align:start position:0%
+remember this General concept when you
+ 
+
+ align:start position:0%
+remember this General concept when you
+sort of increase the size of the unit
+
+ align:start position:0%
+sort of increase the size of the unit
+ 
+
+ align:start position:0%
+sort of increase the size of the unit
+cell the reciprocal cell becom smaller
+
+ align:start position:0%
+cell the reciprocal cell becom smaller
+ 
+
+ align:start position:0%
+cell the reciprocal cell becom smaller
+suppose that we have doubled we have
+
+ align:start position:0%
+suppose that we have doubled we have
+ 
+
+ align:start position:0%
+suppose that we have doubled we have
+gone from two atoms in each uh two atoms
+
+ align:start position:0%
+gone from two atoms in each uh two atoms
+ 
+
+ align:start position:0%
+gone from two atoms in each uh two atoms
+in our unit cell to well if we are in
+
+ align:start position:0%
+in our unit cell to well if we are in
+ 
+
+ align:start position:0%
+in our unit cell to well if we are in
+two Dimension eight atoms in the unit
+
+ align:start position:0%
+two Dimension eight atoms in the unit
+ 
+
+ align:start position:0%
+two Dimension eight atoms in the unit
+cell we have doubled uh in real space in
+
+ align:start position:0%
+cell we have doubled uh in real space in
+ 
+
+ align:start position:0%
+cell we have doubled uh in real space in
+reciprocal space our bran Zone becomes
+
+ align:start position:0%
+reciprocal space our bran Zone becomes
+ 
+
+ align:start position:0%
+reciprocal space our bran Zone becomes
+uh four times as small and so if we want
+
+ align:start position:0%
+uh four times as small and so if we want
+ 
+
+ align:start position:0%
+uh four times as small and so if we want
+to keep the same quality of integration
+
+ align:start position:0%
+to keep the same quality of integration
+ 
+
+ align:start position:0%
+to keep the same quality of integration
+actually it means that our K Point
+
+ align:start position:0%
+actually it means that our K Point
+ 
+
+ align:start position:0%
+actually it means that our K Point
+sampling needs only to be 1/4 the number
+
+ align:start position:0%
+sampling needs only to be 1/4 the number
+ 
+
+ align:start position:0%
+sampling needs only to be 1/4 the number
+of points that we had before that is we
+
+ align:start position:0%
+of points that we had before that is we
+ 
+
+ align:start position:0%
+of points that we had before that is we
+still use the blue points that are
+
+ align:start position:0%
+still use the blue points that are
+ 
+
+ align:start position:0%
+still use the blue points that are
+included in this sort of smaller
+
+ align:start position:0%
+included in this sort of smaller
+ 
+
+ align:start position:0%
+included in this sort of smaller
+blackish unit cell so that also means
+
+ align:start position:0%
+blackish unit cell so that also means
+ 
+
+ align:start position:0%
+blackish unit cell so that also means
+that say if 64k points is a good number
+
+ align:start position:0%
+that say if 64k points is a good number
+ 
+
+ align:start position:0%
+that say if 64k points is a good number
+for a regular sort of unit cell of two
+
+ align:start position:0%
+for a regular sort of unit cell of two
+ 
+
+ align:start position:0%
+for a regular sort of unit cell of two
+atoms of silicon if now you're going to
+
+ align:start position:0%
+atoms of silicon if now you're going to
+ 
+
+ align:start position:0%
+atoms of silicon if now you're going to
+use a say a unit cell that has maybe 128
+
+ align:start position:0%
+use a say a unit cell that has maybe 128
+ 
+
+ align:start position:0%
+use a say a unit cell that has maybe 128
+atoms much larger to calculate a Vance
+
+ align:start position:0%
+atoms much larger to calculate a Vance
+ 
+
+ align:start position:0%
+atoms much larger to calculate a Vance
+information energy you really need only
+
+ align:start position:0%
+information energy you really need only
+ 
+
+ align:start position:0%
+information energy you really need only
+one k point to calculate your total
+
+ align:start position:0%
+one k point to calculate your total
+ 
+
+ align:start position:0%
+one k point to calculate your total
+energy with the same accuracy so there
+
+ align:start position:0%
+energy with the same accuracy so there
+ 
+
+ align:start position:0%
+energy with the same accuracy so there
+is this general idea of scaling and
+
+ align:start position:0%
+is this general idea of scaling and
+ 
+
+ align:start position:0%
+is this general idea of scaling and
+folding you make your real space
+
+ align:start position:0%
+folding you make your real space
+ 
+
+ align:start position:0%
+folding you make your real space
+calculation larger you actually need to
+
+ align:start position:0%
+calculation larger you actually need to
+ 
+
+ align:start position:0%
+calculation larger you actually need to
+use fewer K points and if you are
+
+ align:start position:0%
+use fewer K points and if you are
+ 
+
+ align:start position:0%
+use fewer K points and if you are
+familiar with sort of some of the solid
+
+ align:start position:0%
+familiar with sort of some of the solid
+ 
+
+ align:start position:0%
+familiar with sort of some of the solid
+state ideas that also just means that
+
+ align:start position:0%
+state ideas that also just means that
+ 
+
+ align:start position:0%
+state ideas that also just means that
+when you double the size of your unit
+
+ align:start position:0%
+when you double the size of your unit
+ 
+
+ align:start position:0%
+when you double the size of your unit
+cell you're really
+
+ align:start position:0%
+cell you're really
+ 
+
+ align:start position:0%
+cell you're really
+refolding some of this band structure in
+
+ align:start position:0%
+refolding some of this band structure in
+ 
+
+ align:start position:0%
+refolding some of this band structure in
+a smaller space so you actually sum over
+
+ align:start position:0%
+a smaller space so you actually sum over
+ 
+
+ align:start position:0%
+a smaller space so you actually sum over
+a number of bands that increases
+
+ align:start position:0%
+a number of bands that increases
+ 
+
+ align:start position:0%
+a number of bands that increases
+uh the situation is slightly more
+
+ align:start position:0%
+uh the situation is slightly more
+ 
+
+ align:start position:0%
+uh the situation is slightly more
+complex for something like a metal uh
+
+ align:start position:0%
+complex for something like a metal uh
+ 
+
+ align:start position:0%
+complex for something like a metal uh
+the sort of fundamental difference when
+
+ align:start position:0%
+the sort of fundamental difference when
+ 
+
+ align:start position:0%
+the sort of fundamental difference when
+you deal with a metal as opposed to a
+
+ align:start position:0%
+you deal with a metal as opposed to a
+ 
+
+ align:start position:0%
+you deal with a metal as opposed to a
+semiconductor or an insulator is that
+
+ align:start position:0%
+semiconductor or an insulator is that
+ 
+
+ align:start position:0%
+semiconductor or an insulator is that
+there is something called a thy energy
+
+ align:start position:0%
+there is something called a thy energy
+ 
+
+ align:start position:0%
+there is something called a thy energy
+that is now there isn't anymore a gap
+
+ align:start position:0%
+that is now there isn't anymore a gap
+ 
+
+ align:start position:0%
+that is now there isn't anymore a gap
+okay so the total charge density is
+
+ align:start position:0%
+okay so the total charge density is
+ 
+
+ align:start position:0%
+okay so the total charge density is
+again given by a sum of the states sum
+
+ align:start position:0%
+again given by a sum of the states sum
+ 
+
+ align:start position:0%
+again given by a sum of the states sum
+of over all the bands and integral over
+
+ align:start position:0%
+of over all the bands and integral over
+ 
+
+ align:start position:0%
+of over all the bands and integral over
+all the k
+
+ align:start position:0%
+all the k
+ 
+
+ align:start position:0%
+all the k
+space um but really the total charge
+
+ align:start position:0%
+space um but really the total charge
+ 
+
+ align:start position:0%
+space um but really the total charge
+density and so the you know ultimate
+
+ align:start position:0%
+density and so the you know ultimate
+ 
+
+ align:start position:0%
+density and so the you know ultimate
+integral that would be the number of
+
+ align:start position:0%
+integral that would be the number of
+ 
+
+ align:start position:0%
+integral that would be the number of
+electrons depends really on where we
+
+ align:start position:0%
+electrons depends really on where we
+ 
+
+ align:start position:0%
+electrons depends really on where we
+stop and there isn't anymore a sort of
+
+ align:start position:0%
+stop and there isn't anymore a sort of
+ 
+
+ align:start position:0%
+stop and there isn't anymore a sort of
+natural separation between empty and
+
+ align:start position:0%
+natural separation between empty and
+ 
+
+ align:start position:0%
+natural separation between empty and
+occupied States so there is going to be
+
+ align:start position:0%
+occupied States so there is going to be
+ 
+
+ align:start position:0%
+occupied States so there is going to be
+in a metal an energy level that
+
+ align:start position:0%
+in a metal an energy level that
+ 
+
+ align:start position:0%
+in a metal an energy level that
+determines what is occupied and what is
+
+ align:start position:0%
+determines what is occupied and what is
+ 
+
+ align:start position:0%
+determines what is occupied and what is
+empty and that's the firy energy so for
+
+ align:start position:0%
+empty and that's the firy energy so for
+ 
+
+ align:start position:0%
+empty and that's the firy energy so for
+copper that I think has you know 11
+
+ align:start position:0%
+copper that I think has you know 11
+ 
+
+ align:start position:0%
+copper that I think has you know 11
+electrons uh per unit cell sort of FCC
+
+ align:start position:0%
+electrons uh per unit cell sort of FCC
+ 
+
+ align:start position:0%
+electrons uh per unit cell sort of FCC
+metal with one atom per uh one atom in
+
+ align:start position:0%
+metal with one atom per uh one atom in
+ 
+
+ align:start position:0%
+metal with one atom per uh one atom in
+each unit cell what we really need to do
+
+ align:start position:0%
+each unit cell what we really need to do
+ 
+
+ align:start position:0%
+each unit cell what we really need to do
+in a electronic Str calculation is find
+
+ align:start position:0%
+in a electronic Str calculation is find
+ 
+
+ align:start position:0%
+in a electronic Str calculation is find
+what is this energy level that is find
+
+ align:start position:0%
+what is this energy level that is find
+ 
+
+ align:start position:0%
+what is this energy level that is find
+what is this fery energy such that the
+
+ align:start position:0%
+what is this fery energy such that the
+ 
+
+ align:start position:0%
+what is this fery energy such that the
+integral over all the state below that
+
+ align:start position:0%
+integral over all the state below that
+ 
+
+ align:start position:0%
+integral over all the state below that
+level gives us the right charge density
+
+ align:start position:0%
+level gives us the right charge density
+ 
+
+ align:start position:0%
+level gives us the right charge density
+in particular the right number of
+
+ align:start position:0%
+in particular the right number of
+ 
+
+ align:start position:0%
+in particular the right number of
+electrons and this is sort of one of the
+
+ align:start position:0%
+electrons and this is sort of one of the
+ 
+
+ align:start position:0%
+electrons and this is sort of one of the
+difficulties that come out in metas
+
+ align:start position:0%
+difficulties that come out in metas
+ 
+
+ align:start position:0%
+difficulties that come out in metas
+because now what you're trying to do is
+
+ align:start position:0%
+because now what you're trying to do is
+ 
+
+ align:start position:0%
+because now what you're trying to do is
+you are trying to integrate bands below
+
+ align:start position:0%
+you are trying to integrate bands below
+ 
+
+ align:start position:0%
+you are trying to integrate bands below
+a level below the black line and so you
+
+ align:start position:0%
+a level below the black line and so you
+ 
+
+ align:start position:0%
+a level below the black line and so you
+really introduce a discontinuity in your
+
+ align:start position:0%
+really introduce a discontinuity in your
+ 
+
+ align:start position:0%
+really introduce a discontinuity in your
+integral and so to calculate integrals
+
+ align:start position:0%
+integral and so to calculate integrals
+ 
+
+ align:start position:0%
+integral and so to calculate integrals
+of discontinuous function usually
+
+ align:start position:0%
+of discontinuous function usually
+ 
+
+ align:start position:0%
+of discontinuous function usually
+requires a much finer accuracy in your
+
+ align:start position:0%
+requires a much finer accuracy in your
+ 
+
+ align:start position:0%
+requires a much finer accuracy in your
+kpoint sampling and so the calculation
+
+ align:start position:0%
+kpoint sampling and so the calculation
+ 
+
+ align:start position:0%
+kpoint sampling and so the calculation
+tend to become much more expensive
+
+ align:start position:0%
+tend to become much more expensive
+ 
+
+ align:start position:0%
+tend to become much more expensive
+nothing else uh sort of the general
+
+ align:start position:0%
+nothing else uh sort of the general
+ 
+
+ align:start position:0%
+nothing else uh sort of the general
+solution to this problem besides using a
+
+ align:start position:0%
+solution to this problem besides using a
+ 
+
+ align:start position:0%
+solution to this problem besides using a
+larger number of K points and paying
+
+ align:start position:0%
+larger number of K points and paying
+ 
+
+ align:start position:0%
+larger number of K points and paying
+particular accuracy to this sampling
+
+ align:start position:0%
+particular accuracy to this sampling
+ 
+
+ align:start position:0%
+particular accuracy to this sampling
+issue is that of introducing what is
+
+ align:start position:0%
+issue is that of introducing what is
+ 
+
+ align:start position:0%
+issue is that of introducing what is
+called a finite electronic temperature
+
+ align:start position:0%
+called a finite electronic temperature
+ 
+
+ align:start position:0%
+called a finite electronic temperature
+so what is actually done in sort of
+
+ align:start position:0%
+so what is actually done in sort of
+ 
+
+ align:start position:0%
+so what is actually done in sort of
+every practical calculation is introduce
+
+ align:start position:0%
+every practical calculation is introduce
+ 
+
+ align:start position:0%
+every practical calculation is introduce
+a small amount of temperature so that in
+
+ align:start position:0%
+a small amount of temperature so that in
+ 
+
+ align:start position:0%
+a small amount of temperature so that in
+reality this sharp discontinuity
+
+ align:start position:0%
+reality this sharp discontinuity
+ 
+
+ align:start position:0%
+reality this sharp discontinuity
+becomes smoother because when you have
+
+ align:start position:0%
+becomes smoother because when you have
+ 
+
+ align:start position:0%
+becomes smoother because when you have
+an electronic temperature States above
+
+ align:start position:0%
+an electronic temperature States above
+ 
+
+ align:start position:0%
+an electronic temperature States above
+the firy energy can be slightly occupied
+
+ align:start position:0%
+the firy energy can be slightly occupied
+ 
+
+ align:start position:0%
+the firy energy can be slightly occupied
+with a sort of f occupation and States
+
+ align:start position:0%
+with a sort of f occupation and States
+ 
+
+ align:start position:0%
+with a sort of f occupation and States
+just below the FY energy can be slightly
+
+ align:start position:0%
+just below the FY energy can be slightly
+ 
+
+ align:start position:0%
+just below the FY energy can be slightly
+EMP empty so to summarize I mean we need
+
+ align:start position:0%
+EMP empty so to summarize I mean we need
+ 
+
+ align:start position:0%
+EMP empty so to summarize I mean we need
+to be careful uh in a sort of sampling
+
+ align:start position:0%
+to be careful uh in a sort of sampling
+ 
+
+ align:start position:0%
+to be careful uh in a sort of sampling
+and that's the other sort of fundamental
+
+ align:start position:0%
+and that's the other sort of fundamental
+ 
+
+ align:start position:0%
+and that's the other sort of fundamental
+parameter of your calculation if you're
+
+ align:start position:0%
+parameter of your calculation if you're
+ 
+
+ align:start position:0%
+parameter of your calculation if you're
+dealing with a metal you need to be
+
+ align:start position:0%
+dealing with a metal you need to be
+ 
+
+ align:start position:0%
+dealing with a metal you need to be
+particularly careful and you need to use
+
+ align:start position:0%
+particularly careful and you need to use
+ 
+
+ align:start position:0%
+particularly careful and you need to use
+electronic temper
+
+ align:start position:0%
+electronic temper
+ 
+
+ align:start position:0%
+electronic temper
+techniques um if you are
+
+ align:start position:0%
+techniques um if you are
+ 
+
+ align:start position:0%
+techniques um if you are
+using sort of if you're studying an
+
+ align:start position:0%
+using sort of if you're studying an
+ 
+
+ align:start position:0%
+using sort of if you're studying an
+insulator or a semiconductor what you'll
+
+ align:start position:0%
+insulator or a semiconductor what you'll
+ 
+
+ align:start position:0%
+insulator or a semiconductor what you'll
+usually do is just use a regular
+
+ align:start position:0%
+usually do is just use a regular
+ 
+
+ align:start position:0%
+usually do is just use a regular
+equispaced mesh of K points and that are
+
+ align:start position:0%
+equispaced mesh of K points and that are
+ 
+
+ align:start position:0%
+equispaced mesh of K points and that are
+sort of known in the community with a
+
+ align:start position:0%
+sort of known in the community with a
+ 
+
+ align:start position:0%
+sort of known in the community with a
+technical name they are called monos P
+
+ align:start position:0%
+technical name they are called monos P
+ 
+
+ align:start position:0%
+technical name they are called monos P
+grids for some very good reason actually
+
+ align:start position:0%
+grids for some very good reason actually
+ 
+
+ align:start position:0%
+grids for some very good reason actually
+there are sort of some actually fairly
+
+ align:start position:0%
+there are sort of some actually fairly
+ 
+
+ align:start position:0%
+there are sort of some actually fairly
+beautiful symmetry thoughts on why uh
+
+ align:start position:0%
+beautiful symmetry thoughts on why uh
+ 
+
+ align:start position:0%
+beautiful symmetry thoughts on why uh
+equ spaced Co mesh can work very well
+
+ align:start position:0%
+equ spaced Co mesh can work very well
+ 
+
+ align:start position:0%
+equ spaced Co mesh can work very well
+but in practice is nothing else than
+
+ align:start position:0%
+but in practice is nothing else than
+ 
+
+ align:start position:0%
+but in practice is nothing else than
+choosing the Blue Points inside the
+
+ align:start position:0%
+choosing the Blue Points inside the
+ 
+
+ align:start position:0%
+choosing the Blue Points inside the
+green bran Zone um if you are studing
+
+ align:start position:0%
+green bran Zone um if you are studing
+ 
+
+ align:start position:0%
+green bran Zone um if you are studing
+really large system uh you can actually
+
+ align:start position:0%
+really large system uh you can actually
+ 
+
+ align:start position:0%
+really large system uh you can actually
+reduce yourself to sampling only one
+
+ align:start position:0%
+reduce yourself to sampling only one
+ 
+
+ align:start position:0%
+reduce yourself to sampling only one
+point in the bonial brenzone has become
+
+ align:start position:0%
+point in the bonial brenzone has become
+ 
+
+ align:start position:0%
+point in the bonial brenzone has become
+so small just just taking uh sort of you
+
+ align:start position:0%
+so small just just taking uh sort of you
+ 
+
+ align:start position:0%
+so small just just taking uh sort of you
+know um uh how do you call it a Mina um
+
+ align:start position:0%
+know um uh how do you call it a Mina um
+ 
+
+ align:start position:0%
+know um uh how do you call it a Mina um
+the theorem of the Mina that is you can
+
+ align:start position:0%
+the theorem of the Mina that is you can
+ 
+
+ align:start position:0%
+the theorem of the Mina that is you can
+substitute the integral with the value
+
+ align:start position:0%
+substitute the integral with the value
+ 
+
+ align:start position:0%
+substitute the integral with the value
+of the function at one point and sort of
+
+ align:start position:0%
+of the function at one point and sort of
+ 
+
+ align:start position:0%
+of the function at one point and sort of
+usually you have two choices you can
+
+ align:start position:0%
+usually you have two choices you can
+ 
+
+ align:start position:0%
+usually you have two choices you can
+just use the gamma point this means 0 0
+
+ align:start position:0%
+just use the gamma point this means 0 0
+ 
+
+ align:start position:0%
+just use the gamma point this means 0 0
+0 that has a computational Advantage
+
+ align:start position:0%
+0 that has a computational Advantage
+ 
+
+ align:start position:0%
+0 that has a computational Advantage
+when you sample things at the gamma
+
+ align:start position:0%
+when you sample things at the gamma
+ 
+
+ align:start position:0%
+when you sample things at the gamma
+point you can choose your wave functions
+
+ align:start position:0%
+point you can choose your wave functions
+ 
+
+ align:start position:0%
+point you can choose your wave functions
+to be real instead of complex and so you
+
+ align:start position:0%
+to be real instead of complex and so you
+ 
+
+ align:start position:0%
+to be real instead of complex and so you
+have right away your computational cost
+
+ align:start position:0%
+have right away your computational cost
+ 
+
+ align:start position:0%
+have right away your computational cost
+or you can choose sort of what could be
+
+ align:start position:0%
+or you can choose sort of what could be
+ 
+
+ align:start position:0%
+or you can choose sort of what could be
+the best single point for your given
+
+ align:start position:0%
+the best single point for your given
+ 
+
+ align:start position:0%
+the best single point for your given
+symmetry that's sometimes called the
+
+ align:start position:0%
+symmetry that's sometimes called the
+ 
+
+ align:start position:0%
+symmetry that's sometimes called the
+balesi point and that can be a again
+
+ align:start position:0%
+balesi point and that can be a again
+ 
+
+ align:start position:0%
+balesi point and that can be a again
+sort of useful if you need to do a
+
+ align:start position:0%
+sort of useful if you need to do a
+ 
+
+ align:start position:0%
+sort of useful if you need to do a
+accurate calculation in a large scale
+
+ align:start position:0%
+accurate calculation in a large scale
+ 
+
+ align:start position:0%
+accurate calculation in a large scale
+system okay once you have sort of Set uh
+
+ align:start position:0%
+system okay once you have sort of Set uh
+ 
+
+ align:start position:0%
+system okay once you have sort of Set uh
+these two fundamental parameters you're
+
+ align:start position:0%
+these two fundamental parameters you're
+ 
+
+ align:start position:0%
+these two fundamental parameters you're
+really ready to do actually a practical
+
+ align:start position:0%
+really ready to do actually a practical
+ 
+
+ align:start position:0%
+really ready to do actually a practical
+calculation and so as I said you know we
+
+ align:start position:0%
+calculation and so as I said you know we
+ 
+
+ align:start position:0%
+calculation and so as I said you know we
+have a self-consistent hamiltonian and
+
+ align:start position:0%
+have a self-consistent hamiltonian and
+ 
+
+ align:start position:0%
+have a self-consistent hamiltonian and
+so what you need to do is you need to
+
+ align:start position:0%
+so what you need to do is you need to
+ 
+
+ align:start position:0%
+so what you need to do is you need to
+iterate your problem until the igen
+
+ align:start position:0%
+iterate your problem until the igen
+ 
+
+ align:start position:0%
+iterate your problem until the igen
+states that you find give you a charge
+
+ align:start position:0%
+states that you find give you a charge
+ 
+
+ align:start position:0%
+states that you find give you a charge
+density that is identical to the charge
+
+ align:start position:0%
+density that is identical to the charge
+ 
+
+ align:start position:0%
+density that is identical to the charge
+density that you have done before so in
+
+ align:start position:0%
+density that you have done before so in
+ 
+
+ align:start position:0%
+density that you have done before so in
+practice how would your electronic
+
+ align:start position:0%
+practice how would your electronic
+ 
+
+ align:start position:0%
+practice how would your electronic
+structure code work well first you would
+
+ align:start position:0%
+structure code work well first you would
+ 
+
+ align:start position:0%
+structure code work well first you would
+tell your code where the atoms are okay
+
+ align:start position:0%
+tell your code where the atoms are okay
+ 
+
+ align:start position:0%
+tell your code where the atoms are okay
+so you need to specify the position of
+
+ align:start position:0%
+so you need to specify the position of
+ 
+
+ align:start position:0%
+so you need to specify the position of
+the atom suppose that you're studying
+
+ align:start position:0%
+the atom suppose that you're studying
+ 
+
+ align:start position:0%
+the atom suppose that you're studying
+silicon uh you could you know sort of
+
+ align:start position:0%
+silicon uh you could you know sort of
+ 
+
+ align:start position:0%
+silicon uh you could you know sort of
+since you know actually what is the
+
+ align:start position:0%
+since you know actually what is the
+ 
+
+ align:start position:0%
+since you know actually what is the
+structure of silicon you could already
+
+ align:start position:0%
+structure of silicon you could already
+ 
+
+ align:start position:0%
+structure of silicon you could already
+put them in the origin and in the
+
+ align:start position:0%
+put them in the origin and in the
+ 
+
+ align:start position:0%
+put them in the origin and in the
+position 1/4 1/4 1/4 and then you need
+
+ align:start position:0%
+position 1/4 1/4 1/4 and then you need
+ 
+
+ align:start position:0%
+position 1/4 1/4 1/4 and then you need
+to specify in particular which flavor of
+
+ align:start position:0%
+to specify in particular which flavor of
+ 
+
+ align:start position:0%
+to specify in particular which flavor of
+nonlocal pseudo potential you're going
+
+ align:start position:0%
+nonlocal pseudo potential you're going
+ 
+
+ align:start position:0%
+nonlocal pseudo potential you're going
+to use that is there will be a library
+
+ align:start position:0%
+to use that is there will be a library
+ 
+
+ align:start position:0%
+to use that is there will be a library
+of pseudo potential that basically
+
+ align:start position:0%
+of pseudo potential that basically
+ 
+
+ align:start position:0%
+of pseudo potential that basically
+represent a silicon atom with all the
+
+ align:start position:0%
+represent a silicon atom with all the
+ 
+
+ align:start position:0%
+represent a silicon atom with all the
+core electrons Frozen and there are sort
+
+ align:start position:0%
+core electrons Frozen and there are sort
+ 
+
+ align:start position:0%
+core electrons Frozen and there are sort
+of a number of technicalities that
+
+ align:start position:0%
+of a number of technicalities that
+ 
+
+ align:start position:0%
+of a number of technicalities that
+you'll see in the lab on which one you
+
+ align:start position:0%
+you'll see in the lab on which one you
+ 
+
+ align:start position:0%
+you'll see in the lab on which one you
+should choose but they are sort of more
+
+ align:start position:0%
+should choose but they are sort of more
+ 
+
+ align:start position:0%
+should choose but they are sort of more
+or less all the same at least from from
+
+ align:start position:0%
+or less all the same at least from from
+ 
+
+ align:start position:0%
+or less all the same at least from from
+this point of view once the coder knows
+
+ align:start position:0%
+this point of view once the coder knows
+ 
+
+ align:start position:0%
+this point of view once the coder knows
+where the atoms are that is know the
+
+ align:start position:0%
+where the atoms are that is know the
+ 
+
+ align:start position:0%
+where the atoms are that is know the
+position of the atoms inside the unit
+
+ align:start position:0%
+position of the atoms inside the unit
+ 
+
+ align:start position:0%
+position of the atoms inside the unit
+cell knows what is the shape of the unit
+
+ align:start position:0%
+cell knows what is the shape of the unit
+ 
+
+ align:start position:0%
+cell knows what is the shape of the unit
+cell and what is the length of the
+
+ align:start position:0%
+cell and what is the length of the
+ 
+
+ align:start position:0%
+cell and what is the length of the
+direct latis vectors this infinite array
+
+ align:start position:0%
+direct latis vectors this infinite array
+ 
+
+ align:start position:0%
+direct latis vectors this infinite array
+of atoms the infinite crystalline or
+
+ align:start position:0%
+of atoms the infinite crystalline or
+ 
+
+ align:start position:0%
+of atoms the infinite crystalline or
+amorphous or disordered extended system
+
+ align:start position:0%
+amorphous or disordered extended system
+ 
+
+ align:start position:0%
+amorphous or disordered extended system
+is set and what we really need to do is
+
+ align:start position:0%
+is set and what we really need to do is
+ 
+
+ align:start position:0%
+is set and what we really need to do is
+throw the electrons in and let the
+
+ align:start position:0%
+throw the electrons in and let the
+ 
+
+ align:start position:0%
+throw the electrons in and let the
+electron find their own ground state and
+
+ align:start position:0%
+electron find their own ground state and
+ 
+
+ align:start position:0%
+electron find their own ground state and
+so we need to make sure that we have the
+
+ align:start position:0%
+so we need to make sure that we have the
+ 
+
+ align:start position:0%
+so we need to make sure that we have the
+right basis set cut off that is we're
+
+ align:start position:0%
+right basis set cut off that is we're
+ 
+
+ align:start position:0%
+right basis set cut off that is we're
+going to describe the orbitals aculate
+
+ align:start position:0%
+going to describe the orbitals aculate
+ 
+
+ align:start position:0%
+going to describe the orbitals aculate
+we have the right sampling and at this
+
+ align:start position:0%
+we have the right sampling and at this
+ 
+
+ align:start position:0%
+we have the right sampling and at this
+point we can sort of start the
+
+ align:start position:0%
+point we can sort of start the
+ 
+
+ align:start position:0%
+point we can sort of start the
+self-consistent procedure and in the
+
+ align:start position:0%
+self-consistent procedure and in the
+ 
+
+ align:start position:0%
+self-consistent procedure and in the
+sort of simplest form well we first need
+
+ align:start position:0%
+sort of simplest form well we first need
+ 
+
+ align:start position:0%
+sort of simplest form well we first need
+to figure out what is our aonian
+
+ align:start position:0%
+to figure out what is our aonian
+ 
+
+ align:start position:0%
+to figure out what is our aonian
+operator the aonian remember depends on
+
+ align:start position:0%
+operator the aonian remember depends on
+ 
+
+ align:start position:0%
+operator the aonian remember depends on
+the charge density itself because some
+
+ align:start position:0%
+the charge density itself because some
+ 
+
+ align:start position:0%
+the charge density itself because some
+of the terms in the aonian like the
+
+ align:start position:0%
+of the terms in the aonian like the
+ 
+
+ align:start position:0%
+of the terms in the aonian like the
+hearty energy the AR potential or the
+
+ align:start position:0%
+hearty energy the AR potential or the
+ 
+
+ align:start position:0%
+hearty energy the AR potential or the
+exchange correlation potential depend on
+
+ align:start position:0%
+exchange correlation potential depend on
+ 
+
+ align:start position:0%
+exchange correlation potential depend on
+the density so we need to pick an
+
+ align:start position:0%
+the density so we need to pick an
+ 
+
+ align:start position:0%
+the density so we need to pick an
+initial guess for a trial charge density
+
+ align:start position:0%
+initial guess for a trial charge density
+ 
+
+ align:start position:0%
+initial guess for a trial charge density
+it could just be a superposition of
+
+ align:start position:0%
+it could just be a superposition of
+ 
+
+ align:start position:0%
+it could just be a superposition of
+atomic charge density once we have the
+
+ align:start position:0%
+atomic charge density once we have the
+ 
+
+ align:start position:0%
+atomic charge density once we have the
+charge density we can construct the
+
+ align:start position:0%
+charge density we can construct the
+ 
+
+ align:start position:0%
+charge density we can construct the
+aonian The KES miltonian the kinetic
+
+ align:start position:0%
+aonian The KES miltonian the kinetic
+ 
+
+ align:start position:0%
+aonian The KES miltonian the kinetic
+energy operator is we always know it but
+
+ align:start position:0%
+energy operator is we always know it but
+ 
+
+ align:start position:0%
+energy operator is we always know it but
+we can construct this Harry and exchange
+
+ align:start position:0%
+we can construct this Harry and exchange
+ 
+
+ align:start position:0%
+we can construct this Harry and exchange
+correlation terms that depend on the
+
+ align:start position:0%
+correlation terms that depend on the
+ 
+
+ align:start position:0%
+correlation terms that depend on the
+charge density and then we'll have the
+
+ align:start position:0%
+charge density and then we'll have the
+ 
+
+ align:start position:0%
+charge density and then we'll have the
+external potential that is given by this
+
+ align:start position:0%
+external potential that is given by this
+ 
+
+ align:start position:0%
+external potential that is given by this
+array of nonlocal pseudo potential at
+
+ align:start position:0%
+array of nonlocal pseudo potential at
+ 
+
+ align:start position:0%
+array of nonlocal pseudo potential at
+this point we have the aonian and we try
+
+ align:start position:0%
+this point we have the aonian and we try
+ 
+
+ align:start position:0%
+this point we have the aonian and we try
+to find the lowest energy I States for
+
+ align:start position:0%
+to find the lowest energy I States for
+ 
+
+ align:start position:0%
+to find the lowest energy I States for
+the amonium in particular we just need
+
+ align:start position:0%
+the amonium in particular we just need
+ 
+
+ align:start position:0%
+the amonium in particular we just need
+to calculate uh number of states that is
+
+ align:start position:0%
+to calculate uh number of states that is
+ 
+
+ align:start position:0%
+to calculate uh number of states that is
+equal to the number of occupied orbitals
+
+ align:start position:0%
+equal to the number of occupied orbitals
+ 
+
+ align:start position:0%
+equal to the number of occupied orbitals
+if we are dealing with a semiconductor
+
+ align:start position:0%
+if we are dealing with a semiconductor
+ 
+
+ align:start position:0%
+if we are dealing with a semiconductor
+or it's equal to the number of sort of
+
+ align:start position:0%
+or it's equal to the number of sort of
+ 
+
+ align:start position:0%
+or it's equal to the number of sort of
+you know electrons plus 20 30% in a
+
+ align:start position:0%
+you know electrons plus 20 30% in a
+ 
+
+ align:start position:0%
+you know electrons plus 20 30% in a
+metal to make sure that at different
+
+ align:start position:0%
+metal to make sure that at different
+ 
+
+ align:start position:0%
+metal to make sure that at different
+points in the bran Z Zone we calculate
+
+ align:start position:0%
+points in the bran Z Zone we calculate
+ 
+
+ align:start position:0%
+points in the bran Z Zone we calculate
+all the bonds that that could be below
+
+ align:start position:0%
+all the bonds that that could be below
+ 
+
+ align:start position:0%
+all the bonds that that could be below
+our firy energy so we solve this and
+
+ align:start position:0%
+our firy energy so we solve this and
+ 
+
+ align:start position:0%
+our firy energy so we solve this and
+this is really the expansive step and I
+
+ align:start position:0%
+this is really the expansive step and I
+ 
+
+ align:start position:0%
+this is really the expansive step and I
+mean very expensive step in any
+
+ align:start position:0%
+mean very expensive step in any
+ 
+
+ align:start position:0%
+mean very expensive step in any
+electronic structural calculation and
+
+ align:start position:0%
+electronic structural calculation and
+ 
+
+ align:start position:0%
+electronic structural calculation and
+there are sort of you know a number of
+
+ align:start position:0%
+there are sort of you know a number of
+ 
+
+ align:start position:0%
+there are sort of you know a number of
+ways of
+
+ align:start position:0%
+ways of
+ 
+
+ align:start position:0%
+ways of
+diagonalizing a matrix solving this I
+
+ align:start position:0%
+diagonalizing a matrix solving this I
+ 
+
+ align:start position:0%
+diagonalizing a matrix solving this I
+State equation in a basic set that tends
+
+ align:start position:0%
+State equation in a basic set that tends
+ 
+
+ align:start position:0%
+State equation in a basic set that tends
+to be very large when you do sort of a
+
+ align:start position:0%
+to be very large when you do sort of a
+ 
+
+ align:start position:0%
+to be very large when you do sort of a
+realistic calculation even for silicon
+
+ align:start position:0%
+realistic calculation even for silicon
+ 
+
+ align:start position:0%
+realistic calculation even for silicon
+you could have hundreds of plane waves
+
+ align:start position:0%
+you could have hundreds of plane waves
+ 
+
+ align:start position:0%
+you could have hundreds of plane waves
+so hundreds of basic set elements and
+
+ align:start position:0%
+so hundreds of basic set elements and
+ 
+
+ align:start position:0%
+so hundreds of basic set elements and
+you know large scale calculation like
+
+ align:start position:0%
+you know large scale calculation like
+ 
+
+ align:start position:0%
+you know large scale calculation like
+you would do in research would contain
+
+ align:start position:0%
+you would do in research would contain
+ 
+
+ align:start position:0%
+you would do in research would contain
+tens of thousands of plane waves and
+
+ align:start position:0%
+tens of thousands of plane waves and
+ 
+
+ align:start position:0%
+tens of thousands of plane waves and
+actually uh you
+
+ align:start position:0%
+actually uh you
+ 
+
+ align:start position:0%
+actually uh you
+don't you can't really diagonalize on a
+
+ align:start position:0%
+don't you can't really diagonalize on a
+ 
+
+ align:start position:0%
+don't you can't really diagonalize on a
+regular computer even a matrix that has
+
+ align:start position:0%
+regular computer even a matrix that has
+ 
+
+ align:start position:0%
+regular computer even a matrix that has
+you know start start if you think a
+
+ align:start position:0%
+you know start start if you think a
+ 
+
+ align:start position:0%
+you know start start if you think a
+matrix that has uh a dimension of 1,000
+
+ align:start position:0%
+matrix that has uh a dimension of 1,000
+ 
+
+ align:start position:0%
+matrix that has uh a dimension of 1,000
+requires 1 million
+
+ align:start position:0%
+requires 1 million
+ 
+
+ align:start position:0%
+requires 1 million
+elements okay and you know one uh one
+
+ align:start position:0%
+elements okay and you know one uh one
+ 
+
+ align:start position:0%
+elements okay and you know one uh one
+number a complex number requires 16
+
+ align:start position:0%
+number a complex number requires 16
+ 
+
+ align:start position:0%
+number a complex number requires 16
+bytes so just a matrix that has
+
+ align:start position:0%
+bytes so just a matrix that has
+ 
+
+ align:start position:0%
+bytes so just a matrix that has
+1,000 side will require 16 megabytes to
+
+ align:start position:0%
+1,000 side will require 16 megabytes to
+ 
+
+ align:start position:0%
+1,000 side will require 16 megabytes to
+be described and this number explodes
+
+ align:start position:0%
+be described and this number explodes
+ 
+
+ align:start position:0%
+be described and this number explodes
+quadratically very quickly so you can't
+
+ align:start position:0%
+quadratically very quickly so you can't
+ 
+
+ align:start position:0%
+quadratically very quickly so you can't
+construct the full aonian and you don't
+
+ align:start position:0%
+construct the full aonian and you don't
+ 
+
+ align:start position:0%
+construct the full aonian and you don't
+want to calculate if you have a matrix
+
+ align:start position:0%
+want to calculate if you have a matrix
+ 
+
+ align:start position:0%
+want to calculate if you have a matrix
+of Dimension 1,000 it will have a th000
+
+ align:start position:0%
+of Dimension 1,000 it will have a th000
+ 
+
+ align:start position:0%
+of Dimension 1,000 it will have a th000
+IG state
+
+ align:start position:0%
+IG state
+ 
+
+ align:start position:0%
+IG state
+but you only care say if you are
+
+ align:start position:0%
+but you only care say if you are
+ 
+
+ align:start position:0%
+but you only care say if you are
+studying silicon on the lowest four I
+
+ align:start position:0%
+studying silicon on the lowest four I
+ 
+
+ align:start position:0%
+studying silicon on the lowest four I
+States so you want to have numerical
+
+ align:start position:0%
+States so you want to have numerical
+ 
+
+ align:start position:0%
+States so you want to have numerical
+techniques that calculate for you only
+
+ align:start position:0%
+techniques that calculate for you only
+ 
+
+ align:start position:0%
+techniques that calculate for you only
+the lowest energy I States and there are
+
+ align:start position:0%
+the lowest energy I States and there are
+ 
+
+ align:start position:0%
+the lowest energy I States and there are
+a number of them that are well
+
+ align:start position:0%
+a number of them that are well
+ 
+
+ align:start position:0%
+a number of them that are well
+established so now you have obtained
+
+ align:start position:0%
+established so now you have obtained
+ 
+
+ align:start position:0%
+established so now you have obtained
+with one of these techniques your lowest
+
+ align:start position:0%
+with one of these techniques your lowest
+ 
+
+ align:start position:0%
+with one of these techniques your lowest
+energy I States and you sum the square
+
+ align:start position:0%
+energy I States and you sum the square
+ 
+
+ align:start position:0%
+energy I States and you sum the square
+moduli to obtain the new charge density
+
+ align:start position:0%
+moduli to obtain the new charge density
+ 
+
+ align:start position:0%
+moduli to obtain the new charge density
+and with this you go back to this step
+
+ align:start position:0%
+and with this you go back to this step
+ 
+
+ align:start position:0%
+and with this you go back to this step
+you construct the hamiltonian operator
+
+ align:start position:0%
+you construct the hamiltonian operator
+ 
+
+ align:start position:0%
+you construct the hamiltonian operator
+again you diagonalize new density and
+
+ align:start position:0%
+again you diagonalize new density and
+ 
+
+ align:start position:0%
+again you diagonalize new density and
+iterate um of course actually so a
+
+ align:start position:0%
+iterate um of course actually so a
+ 
+
+ align:start position:0%
+iterate um of course actually so a
+recipe like this would most likely never
+
+ align:start position:0%
+recipe like this would most likely never
+ 
+
+ align:start position:0%
+recipe like this would most likely never
+converge so one needs to develop U
+
+ align:start position:0%
+converge so one needs to develop U
+ 
+
+ align:start position:0%
+converge so one needs to develop U
+mixing approach mixing approaches that
+
+ align:start position:0%
+mixing approach mixing approaches that
+ 
+
+ align:start position:0%
+mixing approach mixing approaches that
+sort of make the change in the charge
+
+ align:start position:0%
+sort of make the change in the charge
+ 
+
+ align:start position:0%
+sort of make the change in the charge
+density at every iterative step smoother
+
+ align:start position:0%
+density at every iterative step smoother
+ 
+
+ align:start position:0%
+density at every iterative step smoother
+than what I've described so if you
+
+ align:start position:0%
+than what I've described so if you
+ 
+
+ align:start position:0%
+than what I've described so if you
+calculate a new charge density and you
+
+ align:start position:0%
+calculate a new charge density and you
+ 
+
+ align:start position:0%
+calculate a new charge density and you
+diagonalize it again your second new
+
+ align:start position:0%
+diagonalize it again your second new
+ 
+
+ align:start position:0%
+diagonalize it again your second new
+charge density will be even more
+
+ align:start position:0%
+charge density will be even more
+ 
+
+ align:start position:0%
+charge density will be even more
+different from anything that you have
+
+ align:start position:0%
+different from anything that you have
+ 
+
+ align:start position:0%
+different from anything that you have
+obtained before so what you really do is
+
+ align:start position:0%
+obtained before so what you really do is
+ 
+
+ align:start position:0%
+obtained before so what you really do is
+you need to find some schemes to evolve
+
+ align:start position:0%
+you need to find some schemes to evolve
+ 
+
+ align:start position:0%
+you need to find some schemes to evolve
+in a very smooth way your charge density
+
+ align:start position:0%
+in a very smooth way your charge density
+ 
+
+ align:start position:0%
+in a very smooth way your charge density
+so maybe once you have calculated the
+
+ align:start position:0%
+so maybe once you have calculated the
+ 
+
+ align:start position:0%
+so maybe once you have calculated the
+new sum of igen States you don't take
+
+ align:start position:0%
+new sum of igen States you don't take
+ 
+
+ align:start position:0%
+new sum of igen States you don't take
+that as a new charge density but you
+
+ align:start position:0%
+that as a new charge density but you
+ 
+
+ align:start position:0%
+that as a new charge density but you
+just update your old charge density with
+
+ align:start position:0%
+just update your old charge density with
+ 
+
+ align:start position:0%
+just update your old charge density with
+you know sort of 10% of what you have
+
+ align:start position:0%
+you know sort of 10% of what you have
+ 
+
+ align:start position:0%
+you know sort of 10% of what you have
+calculated now to try to make the
+
+ align:start position:0%
+calculated now to try to make the
+ 
+
+ align:start position:0%
+calculated now to try to make the
+iteration to selfconsistent very smooth
+
+ align:start position:0%
+iteration to selfconsistent very smooth
+ 
+
+ align:start position:0%
+iteration to selfconsistent very smooth
+and I have to say a lot of you know the
+
+ align:start position:0%
+and I have to say a lot of you know the
+ 
+
+ align:start position:0%
+and I have to say a lot of you know the
+KN how in electronic structural
+
+ align:start position:0%
+KN how in electronic structural
+ 
+
+ align:start position:0%
+KN how in electronic structural
+calculation in the '90s has really gone
+
+ align:start position:0%
+calculation in the '90s has really gone
+ 
+
+ align:start position:0%
+calculation in the '90s has really gone
+into trying to find sort of mixing
+
+ align:start position:0%
+into trying to find sort of mixing
+ 
+
+ align:start position:0%
+into trying to find sort of mixing
+approaches that evolve our charge
+
+ align:start position:0%
+approaches that evolve our charge
+ 
+
+ align:start position:0%
+approaches that evolve our charge
+density to self-consistency and that
+
+ align:start position:0%
+density to self-consistency and that
+ 
+
+ align:start position:0%
+density to self-consistency and that
+converge under a large variety of
+
+ align:start position:0%
+converge under a large variety of
+ 
+
+ align:start position:0%
+converge under a large variety of
+circumstances for large or complex
+
+ align:start position:0%
+circumstances for large or complex
+ 
+
+ align:start position:0%
+circumstances for large or complex
+system especially for
+
+ align:start position:0%
+system especially for
+ 
+
+ align:start position:0%
+system especially for
+Metals um so so strip to the bare uh
+
+ align:start position:0%
+Metals um so so strip to the bare uh
+ 
+
+ align:start position:0%
+Metals um so so strip to the bare uh
+elements an electronic structur code
+
+ align:start position:0%
+elements an electronic structur code
+ 
+
+ align:start position:0%
+elements an electronic structur code
+really needs to do two things needs to
+
+ align:start position:0%
+really needs to do two things needs to
+ 
+
+ align:start position:0%
+really needs to do two things needs to
+diagonalize inexpensively an aonian that
+
+ align:start position:0%
+diagonalize inexpensively an aonian that
+ 
+
+ align:start position:0%
+diagonalize inexpensively an aonian that
+expressed on a plane wave basis as a
+
+ align:start position:0%
+expressed on a plane wave basis as a
+ 
+
+ align:start position:0%
+expressed on a plane wave basis as a
+very large order and I just mentioned
+
+ align:start position:0%
+very large order and I just mentioned
+ 
+
+ align:start position:0%
+very large order and I just mentioned
+the names of some of the algorith things
+
+ align:start position:0%
+the names of some of the algorith things
+ 
+
+ align:start position:0%
+the names of some of the algorith things
+like The Davids and the Lanos or some of
+
+ align:start position:0%
+like The Davids and the Lanos or some of
+ 
+
+ align:start position:0%
+like The Davids and the Lanos or some of
+the conjugate gradient algorithm are all
+
+ align:start position:0%
+the conjugate gradient algorithm are all
+ 
+
+ align:start position:0%
+the conjugate gradient algorithm are all
+algorithms that give us uh with
+
+ align:start position:0%
+algorithms that give us uh with
+ 
+
+ align:start position:0%
+algorithms that give us uh with
+reasonable cost the lowest energy igen
+
+ align:start position:0%
+reasonable cost the lowest energy igen
+ 
+
+ align:start position:0%
+reasonable cost the lowest energy igen
+states of that amoni and then once you
+
+ align:start position:0%
+states of that amoni and then once you
+ 
+
+ align:start position:0%
+states of that amoni and then once you
+have that igen states you need to
+
+ align:start position:0%
+have that igen states you need to
+ 
+
+ align:start position:0%
+have that igen states you need to
+calculate charge density and you need to
+
+ align:start position:0%
+calculate charge density and you need to
+ 
+
+ align:start position:0%
+calculate charge density and you need to
+have a mixing strategy you need to have
+
+ align:start position:0%
+have a mixing strategy you need to have
+ 
+
+ align:start position:0%
+have a mixing strategy you need to have
+a strategy to evolve your charge density
+
+ align:start position:0%
+a strategy to evolve your charge density
+ 
+
+ align:start position:0%
+a strategy to evolve your charge density
+towards self-consistency and that is
+
+ align:start position:0%
+towards self-consistency and that is
+ 
+
+ align:start position:0%
+towards self-consistency and that is
+also a very tricky
+
+ align:start position:0%
+also a very tricky
+ 
+
+ align:start position:0%
+also a very tricky
+approach um there is a sort of
+
+ align:start position:0%
+approach um there is a sort of
+ 
+
+ align:start position:0%
+approach um there is a sort of
+completely different approach to the
+
+ align:start position:0%
+completely different approach to the
+ 
+
+ align:start position:0%
+completely different approach to the
+problem that sees
+
+ align:start position:0%
+problem that sees
+ 
+
+ align:start position:0%
+problem that sees
+the solution the ground state solution
+
+ align:start position:0%
+the solution the ground state solution
+ 
+
+ align:start position:0%
+the solution the ground state solution
+not as a self-consistent iteration but
+
+ align:start position:0%
+not as a self-consistent iteration but
+ 
+
+ align:start position:0%
+not as a self-consistent iteration but
+as as a nonlinear direct minimization of
+
+ align:start position:0%
+as as a nonlinear direct minimization of
+ 
+
+ align:start position:0%
+as as a nonlinear direct minimization of
+the functional U if you remember we have
+
+ align:start position:0%
+the functional U if you remember we have
+ 
+
+ align:start position:0%
+the functional U if you remember we have
+the energy functional I think it's
+
+ align:start position:0%
+the energy functional I think it's
+ 
+
+ align:start position:0%
+the energy functional I think it's
+written here in the next slide no it's
+
+ align:start position:0%
+written here in the next slide no it's
+ 
+
+ align:start position:0%
+written here in the next slide no it's
+not we have sort of written the density
+
+ align:start position:0%
+not we have sort of written the density
+ 
+
+ align:start position:0%
+not we have sort of written the density
+functional Theory energy functional and
+
+ align:start position:0%
+functional Theory energy functional and
+ 
+
+ align:start position:0%
+functional Theory energy functional and
+it is a well defined expression of the
+
+ align:start position:0%
+it is a well defined expression of the
+ 
+
+ align:start position:0%
+it is a well defined expression of the
+orbitals only it will be in one of the S
+
+ align:start position:0%
+orbitals only it will be in one of the S
+ 
+
+ align:start position:0%
+orbitals only it will be in one of the S
+of following slides will pick it up
+
+ align:start position:0%
+of following slides will pick it up
+ 
+
+ align:start position:0%
+of following slides will pick it up
+again and so we can also see that
+
+ align:start position:0%
+again and so we can also see that
+ 
+
+ align:start position:0%
+again and so we can also see that
+problem as the problem of a
+
+ align:start position:0%
+problem as the problem of a
+ 
+
+ align:start position:0%
+problem as the problem of a
+minimization of that function in a space
+
+ align:start position:0%
+minimization of that function in a space
+ 
+
+ align:start position:0%
+minimization of that function in a space
+that is very large because the sort of
+
+ align:start position:0%
+that is very large because the sort of
+ 
+
+ align:start position:0%
+that is very large because the sort of
+variables that we really deal with are
+
+ align:start position:0%
+variables that we really deal with are
+ 
+
+ align:start position:0%
+variables that we really deal with are
+the coefficients of our plane wave
+
+ align:start position:0%
+the coefficients of our plane wave
+ 
+
+ align:start position:0%
+the coefficients of our plane wave
+expansion but in principle and I'll show
+
+ align:start position:0%
+expansion but in principle and I'll show
+ 
+
+ align:start position:0%
+expansion but in principle and I'll show
+you that in a moment we can actually
+
+ align:start position:0%
+you that in a moment we can actually
+ 
+
+ align:start position:0%
+you that in a moment we can actually
+write out a minimization algorithm the
+
+ align:start position:0%
+write out a minimization algorithm the
+ 
+
+ align:start position:0%
+write out a minimization algorithm the
+advantage of this approach if if it's
+
+ align:start position:0%
+advantage of this approach if if it's
+ 
+
+ align:start position:0%
+advantage of this approach if if it's
+done properly it has always a solution
+
+ align:start position:0%
+done properly it has always a solution
+ 
+
+ align:start position:0%
+done properly it has always a solution
+if you keep minimizing your energy at
+
+ align:start position:0%
+if you keep minimizing your energy at
+ 
+
+ align:start position:0%
+if you keep minimizing your energy at
+the end you will get to a global or to a
+
+ align:start position:0%
+the end you will get to a global or to a
+ 
+
+ align:start position:0%
+the end you will get to a global or to a
+local minimum so these approach tend to
+
+ align:start position:0%
+local minimum so these approach tend to
+ 
+
+ align:start position:0%
+local minimum so these approach tend to
+sort of converge under every
+
+ align:start position:0%
+sort of converge under every
+ 
+
+ align:start position:0%
+sort of converge under every
+circumstances if done properly and done
+
+ align:start position:0%
+circumstances if done properly and done
+ 
+
+ align:start position:0%
+circumstances if done properly and done
+properly is not is not trivial uh but
+
+ align:start position:0%
+properly is not is not trivial uh but
+ 
+
+ align:start position:0%
+properly is not is not trivial uh but
+then sort of you know the efficiency of
+
+ align:start position:0%
+then sort of you know the efficiency of
+ 
+
+ align:start position:0%
+then sort of you know the efficiency of
+the different things is really system
+
+ align:start position:0%
+the different things is really system
+ 
+
+ align:start position:0%
+the different things is really system
+dependent and I guess without wanting to
+
+ align:start position:0%
+dependent and I guess without wanting to
+ 
+
+ align:start position:0%
+dependent and I guess without wanting to
+bore you with sort of mats just I wanted
+
+ align:start position:0%
+bore you with sort of mats just I wanted
+ 
+
+ align:start position:0%
+bore you with sort of mats just I wanted
+to remind you again what happens in our
+
+ align:start position:0%
+to remind you again what happens in our
+ 
+
+ align:start position:0%
+to remind you again what happens in our
+computer that is what happens when we
+
+ align:start position:0%
+computer that is what happens when we
+ 
+
+ align:start position:0%
+computer that is what happens when we
+say we want to solve this I State
+
+ align:start position:0%
+say we want to solve this I State
+ 
+
+ align:start position:0%
+say we want to solve this I State
+equation supposing that say we are in a
+
+ align:start position:0%
+equation supposing that say we are in a
+ 
+
+ align:start position:0%
+equation supposing that say we are in a
+uh self-consistent diagonalization
+
+ align:start position:0%
+uh self-consistent diagonalization
+ 
+
+ align:start position:0%
+uh self-consistent diagonalization
+approach and as always you have to
+
+ align:start position:0%
+approach and as always you have to
+ 
+
+ align:start position:0%
+approach and as always you have to
+remember we expand our W function in a
+
+ align:start position:0%
+remember we expand our W function in a
+ 
+
+ align:start position:0%
+remember we expand our W function in a
+well defined set of orbit that is our
+
+ align:start position:0%
+well defined set of orbit that is our
+ 
+
+ align:start position:0%
+well defined set of orbit that is our
+basis set I've represented here them as
+
+ align:start position:0%
+basis set I've represented here them as
+ 
+
+ align:start position:0%
+basis set I've represented here them as
+five and it could be plane waves it
+
+ align:start position:0%
+five and it could be plane waves it
+ 
+
+ align:start position:0%
+five and it could be plane waves it
+could be Atomic orbitals we'll use plane
+
+ align:start position:0%
+could be Atomic orbitals we'll use plane
+ 
+
+ align:start position:0%
+could be Atomic orbitals we'll use plane
+waves all the time so really in our
+
+ align:start position:0%
+waves all the time so really in our
+ 
+
+ align:start position:0%
+waves all the time so really in our
+computer our unknowns are these
+
+ align:start position:0%
+computer our unknowns are these
+ 
+
+ align:start position:0%
+computer our unknowns are these
+coefficients of this basic set expansion
+
+ align:start position:0%
+coefficients of this basic set expansion
+ 
+
+ align:start position:0%
+coefficients of this basic set expansion
+and so our igen state equation once we
+
+ align:start position:0%
+and so our igen state equation once we
+ 
+
+ align:start position:0%
+and so our igen state equation once we
+multiply on the left by FM star and
+
+ align:start position:0%
+multiply on the left by FM star and
+ 
+
+ align:start position:0%
+multiply on the left by FM star and
+integrate uh is really a matrix problem
+
+ align:start position:0%
+integrate uh is really a matrix problem
+ 
+
+ align:start position:0%
+integrate uh is really a matrix problem
+so I written it here is just the same
+
+ align:start position:0%
+so I written it here is just the same
+ 
+
+ align:start position:0%
+so I written it here is just the same
+igen function equation written over
+
+ align:start position:0%
+igen function equation written over
+ 
+
+ align:start position:0%
+igen function equation written over
+there and if we call hmn the Matrix
+
+ align:start position:0%
+there and if we call hmn the Matrix
+ 
+
+ align:start position:0%
+there and if we call hmn the Matrix
+element of the aonian between say two
+
+ align:start position:0%
+element of the aonian between say two
+ 
+
+ align:start position:0%
+element of the aonian between say two
+plane waves of different wavelength this
+
+ align:start position:0%
+plane waves of different wavelength this
+ 
+
+ align:start position:0%
+plane waves of different wavelength this
+is what our problem is it's just a
+
+ align:start position:0%
+is what our problem is it's just a
+ 
+
+ align:start position:0%
+is what our problem is it's just a
+linear algebra problem we need to find
+
+ align:start position:0%
+linear algebra problem we need to find
+ 
+
+ align:start position:0%
+linear algebra problem we need to find
+the igen values for which there is a
+
+ align:start position:0%
+the igen values for which there is a
+ 
+
+ align:start position:0%
+the igen values for which there is a
+possible solution and the possible
+
+ align:start position:0%
+possible solution and the possible
+ 
+
+ align:start position:0%
+possible solution and the possible
+solution will be igen States and I state
+
+ align:start position:0%
+solution will be igen States and I state
+ 
+
+ align:start position:0%
+solution will be igen States and I state
+is nothing else than an appropriate set
+
+ align:start position:0%
+is nothing else than an appropriate set
+ 
+
+ align:start position:0%
+is nothing else than an appropriate set
+of coefficients that satisfy this
+
+ align:start position:0%
+of coefficients that satisfy this
+ 
+
+ align:start position:0%
+of coefficients that satisfy this
+equation and those coefficients put back
+
+ align:start position:0%
+equation and those coefficients put back
+ 
+
+ align:start position:0%
+equation and those coefficients put back
+in here will give us actually what are
+
+ align:start position:0%
+in here will give us actually what are
+ 
+
+ align:start position:0%
+in here will give us actually what are
+the full igen states of our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem okay so this was the sort of
+
+ align:start position:0%
+problem okay so this was the sort of
+ 
+
+ align:start position:0%
+problem okay so this was the sort of
+self-consistent diagonalization as I
+
+ align:start position:0%
+self-consistent diagonalization as I
+ 
+
+ align:start position:0%
+self-consistent diagonalization as I
+just said a moment ago we can also look
+
+ align:start position:0%
+just said a moment ago we can also look
+ 
+
+ align:start position:0%
+just said a moment ago we can also look
+at the problem as a non linear
+
+ align:start position:0%
+at the problem as a non linear
+ 
+
+ align:start position:0%
+at the problem as a non linear
+minimization problem once you know we
+
+ align:start position:0%
+minimization problem once you know we
+ 
+
+ align:start position:0%
+minimization problem once you know we
+have decided on an approximation for our
+
+ align:start position:0%
+have decided on an approximation for our
+ 
+
+ align:start position:0%
+have decided on an approximation for our
+exchange correlation functional could be
+
+ align:start position:0%
+exchange correlation functional could be
+ 
+
+ align:start position:0%
+exchange correlation functional could be
+a local density approximation could be a
+
+ align:start position:0%
+a local density approximation could be a
+ 
+
+ align:start position:0%
+a local density approximation could be a
+generalized gradient approximation this
+
+ align:start position:0%
+generalized gradient approximation this
+ 
+
+ align:start position:0%
+generalized gradient approximation this
+is a well defined quantity in which
+
+ align:start position:0%
+is a well defined quantity in which
+ 
+
+ align:start position:0%
+is a well defined quantity in which
+again the external potential is given by
+
+ align:start position:0%
+again the external potential is given by
+ 
+
+ align:start position:0%
+again the external potential is given by
+this array of nonlocal pseudo potential
+
+ align:start position:0%
+this array of nonlocal pseudo potential
+ 
+
+ align:start position:0%
+this array of nonlocal pseudo potential
+and the hearty energy is just a
+
+ align:start position:0%
+and the hearty energy is just a
+ 
+
+ align:start position:0%
+and the hearty energy is just a
+functional of the charge density and the
+
+ align:start position:0%
+functional of the charge density and the
+ 
+
+ align:start position:0%
+functional of the charge density and the
+charge density itself is just a sum of
+
+ align:start position:0%
+charge density itself is just a sum of
+ 
+
+ align:start position:0%
+charge density itself is just a sum of
+the square modulus of the orbitals so in
+
+ align:start position:0%
+the square modulus of the orbitals so in
+ 
+
+ align:start position:0%
+the square modulus of the orbitals so in
+reality this energy is a functional of
+
+ align:start position:0%
+reality this energy is a functional of
+ 
+
+ align:start position:0%
+reality this energy is a functional of
+the s or in other terms is nothing else
+
+ align:start position:0%
+the s or in other terms is nothing else
+ 
+
+ align:start position:0%
+the s or in other terms is nothing else
+than a very complex function of those C1
+
+ align:start position:0%
+than a very complex function of those C1
+ 
+
+ align:start position:0%
+than a very complex function of those C1
+to CN coefficients of each vectors so
+
+ align:start position:0%
+to CN coefficients of each vectors so
+ 
+
+ align:start position:0%
+to CN coefficients of each vectors so
+this is nothing eless than a
+
+ align:start position:0%
+this is nothing eless than a
+ 
+
+ align:start position:0%
+this is nothing eless than a
+minimization problem again on a number
+
+ align:start position:0%
+minimization problem again on a number
+ 
+
+ align:start position:0%
+minimization problem again on a number
+of variables that can be a thousand if
+
+ align:start position:0%
+of variables that can be a thousand if
+ 
+
+ align:start position:0%
+of variables that can be a thousand if
+you're studying two atoms of silicon and
+
+ align:start position:0%
+you're studying two atoms of silicon and
+ 
+
+ align:start position:0%
+you're studying two atoms of silicon and
+it can be in the tens or hundreds of
+
+ align:start position:0%
+it can be in the tens or hundreds of
+ 
+
+ align:start position:0%
+it can be in the tens or hundreds of
+thousands if you start to do really
+
+ align:start position:0%
+thousands if you start to do really
+ 
+
+ align:start position:0%
+thousands if you start to do really
+serious calculation so again it's a sort
+
+ align:start position:0%
+serious calculation so again it's a sort
+ 
+
+ align:start position:0%
+serious calculation so again it's a sort
+of Fairly complex Pro problem a huge
+
+ align:start position:0%
+of Fairly complex Pro problem a huge
+ 
+
+ align:start position:0%
+of Fairly complex Pro problem a huge
+number of variables that you need to
+
+ align:start position:0%
+number of variables that you need to
+ 
+
+ align:start position:0%
+number of variables that you need to
+deal with and uh um a nonlinear
+
+ align:start position:0%
+deal with and uh um a nonlinear
+ 
+
+ align:start position:0%
+deal with and uh um a nonlinear
+expression for the energy but again in
+
+ align:start position:0%
+expression for the energy but again in
+ 
+
+ align:start position:0%
+expression for the energy but again in
+principle if we have this explicit
+
+ align:start position:0%
+principle if we have this explicit
+ 
+
+ align:start position:0%
+principle if we have this explicit
+expression for the energy e of
+
+ align:start position:0%
+expression for the energy e of
+ 
+
+ align:start position:0%
+expression for the energy e of
+P where the P that we consider are only
+
+ align:start position:0%
+P where the P that we consider are only
+ 
+
+ align:start position:0%
+P where the P that we consider are only
+the occupied orbitals what we can do is
+
+ align:start position:0%
+the occupied orbitals what we can do is
+ 
+
+ align:start position:0%
+the occupied orbitals what we can do is
+nothing else than take the functional
+
+ align:start position:0%
+nothing else than take the functional
+ 
+
+ align:start position:0%
+nothing else than take the functional
+derivative with respect to the consider
+
+ align:start position:0%
+derivative with respect to the consider
+ 
+
+ align:start position:0%
+derivative with respect to the consider
+them real here just to to avoid sort of
+
+ align:start position:0%
+them real here just to to avoid sort of
+ 
+
+ align:start position:0%
+them real here just to to avoid sort of
+complex conjugate numbers and at the end
+
+ align:start position:0%
+complex conjugate numbers and at the end
+ 
+
+ align:start position:0%
+complex conjugate numbers and at the end
+this is nothing else than calculates the
+
+ align:start position:0%
+this is nothing else than calculates the
+ 
+
+ align:start position:0%
+this is nothing else than calculates the
+derivative of the energy with respect to
+
+ align:start position:0%
+derivative of the energy with respect to
+ 
+
+ align:start position:0%
+derivative of the energy with respect to
+all the
+
+ align:start position:0%
+all the
+ 
+
+ align:start position:0%
+all the
+coefficients say for I that goes one up
+
+ align:start position:0%
+coefficients say for I that goes one up
+ 
+
+ align:start position:0%
+coefficients say for I that goes one up
+to the cut
+
+ align:start position:0%
+to the cut
+ 
+
+ align:start position:0%
+to the cut
+off all the coefficients of all the
+
+ align:start position:0%
+off all the coefficients of all the
+ 
+
+ align:start position:0%
+off all the coefficients of all the
+occupied
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orbitals so you see the larg your system
+
+ align:start position:0%
+orbitals so you see the larg your system
+ 
+
+ align:start position:0%
+orbitals so you see the larg your system
+becomes the
+
+ align:start position:0%
+becomes the
+ 
+
+ align:start position:0%
+becomes the
+more basis elements you'll need to use I
+
+ align:start position:0%
+more basis elements you'll need to use I
+ 
+
+ align:start position:0%
+more basis elements you'll need to use I
+mean if you double the size of your
+
+ align:start position:0%
+mean if you double the size of your
+ 
+
+ align:start position:0%
+mean if you double the size of your
+system you if you look at the math you
+
+ align:start position:0%
+system you if you look at the math you
+ 
+
+ align:start position:0%
+system you if you look at the math you
+actually need twice the number of plain
+
+ align:start position:0%
+actually need twice the number of plain
+ 
+
+ align:start position:0%
+actually need twice the number of plain
+waves as it makes sense to describe a
+
+ align:start position:0%
+waves as it makes sense to describe a
+ 
+
+ align:start position:0%
+waves as it makes sense to describe a
+charge density or a wave function with
+
+ align:start position:0%
+charge density or a wave function with
+ 
+
+ align:start position:0%
+charge density or a wave function with
+the same resolution so you double the
+
+ align:start position:0%
+the same resolution so you double the
+ 
+
+ align:start position:0%
+the same resolution so you double the
+size of your system the number of plane
+
+ align:start position:0%
+size of your system the number of plane
+ 
+
+ align:start position:0%
+size of your system the number of plane
+waves to describe a single particle
+
+ align:start position:0%
+waves to describe a single particle
+ 
+
+ align:start position:0%
+waves to describe a single particle
+orbital becomes twice as large but now
+
+ align:start position:0%
+orbital becomes twice as large but now
+ 
+
+ align:start position:0%
+orbital becomes twice as large but now
+you will also have twice as many
+
+ align:start position:0%
+you will also have twice as many
+ 
+
+ align:start position:0%
+you will also have twice as many
+occupied orbitals so just the number of
+
+ align:start position:0%
+occupied orbitals so just the number of
+ 
+
+ align:start position:0%
+occupied orbitals so just the number of
+this coefficient has become four times
+
+ align:start position:0%
+this coefficient has become four times
+ 
+
+ align:start position:0%
+this coefficient has become four times
+as large so again you know this
+
+ align:start position:0%
+as large so again you know this
+ 
+
+ align:start position:0%
+as large so again you know this
+calculation becomes very expensive very
+
+ align:start position:0%
+calculation becomes very expensive very
+ 
+
+ align:start position:0%
+calculation becomes very expensive very
+quickly but again this is well defined I
+
+ align:start position:0%
+quickly but again this is well defined I
+ 
+
+ align:start position:0%
+quickly but again this is well defined I
+mean we can just actually write
+
+ align:start position:0%
+mean we can just actually write
+ 
+
+ align:start position:0%
+mean we can just actually write
+explicitly the nonlinear function of the
+
+ align:start position:0%
+explicitly the nonlinear function of the
+ 
+
+ align:start position:0%
+explicitly the nonlinear function of the
+previous slide in terms of the
+
+ align:start position:0%
+previous slide in terms of the
+ 
+
+ align:start position:0%
+previous slide in terms of the
+coefficients of the plane waves this is
+
+ align:start position:0%
+coefficients of the plane waves this is
+ 
+
+ align:start position:0%
+coefficients of the plane waves this is
+actually done in one of the uh article
+
+ align:start position:0%
+actually done in one of the uh article
+ 
+
+ align:start position:0%
+actually done in one of the uh article
+posted there is a review of modern
+
+ align:start position:0%
+posted there is a review of modern
+ 
+
+ align:start position:0%
+posted there is a review of modern
+physics by Mike pay and coor coworkers
+
+ align:start position:0%
+physics by Mike pay and coor coworkers
+ 
+
+ align:start position:0%
+physics by Mike pay and coor coworkers
+among other John johanos that here at
+
+ align:start position:0%
+among other John johanos that here at
+ 
+
+ align:start position:0%
+among other John johanos that here at
+MIT and they actually work out the
+
+ align:start position:0%
+MIT and they actually work out the
+ 
+
+ align:start position:0%
+MIT and they actually work out the
+algebra of all these derivatives and
+
+ align:start position:0%
+algebra of all these derivatives and
+ 
+
+ align:start position:0%
+algebra of all these derivatives and
+then once you have the derivatives you
+
+ align:start position:0%
+then once you have the derivatives you
+ 
+
+ align:start position:0%
+then once you have the derivatives you
+have the gradients and you know how to
+
+ align:start position:0%
+have the gradients and you know how to
+ 
+
+ align:start position:0%
+have the gradients and you know how to
+move along and go to the minimum
+
+ align:start position:0%
+move along and go to the minimum
+ 
+
+ align:start position:0%
+move along and go to the minimum
+following the gradients the only
+
+ align:start position:0%
+following the gradients the only
+ 
+
+ align:start position:0%
+following the gradients the only
+difference with a sort of regular
+
+ align:start position:0%
+difference with a sort of regular
+ 
+
+ align:start position:0%
+difference with a sort of regular
+minimization problem is that this is a
+
+ align:start position:0%
+minimization problem is that this is a
+ 
+
+ align:start position:0%
+minimization problem is that this is a
+constraint problem that is what we have
+
+ align:start position:0%
+constraint problem that is what we have
+ 
+
+ align:start position:0%
+constraint problem that is what we have
+because these are really electrons are
+
+ align:start position:0%
+because these are really electrons are
+ 
+
+ align:start position:0%
+because these are really electrons are
+not just sort of arbitrary functions the
+
+ align:start position:0%
+not just sort of arbitrary functions the
+ 
+
+ align:start position:0%
+not just sort of arbitrary functions the
+electrons need to be meaningful Quantum
+
+ align:start position:0%
+electrons need to be meaningful Quantum
+ 
+
+ align:start position:0%
+electrons need to be meaningful Quantum
+States so they need to be uton normal so
+
+ align:start position:0%
+States so they need to be uton normal so
+ 
+
+ align:start position:0%
+States so they need to be uton normal so
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+derivatives with respect to the C need
+
+ align:start position:0%
+derivatives with respect to the C need
+ 
+
+ align:start position:0%
+derivatives with respect to the C need
+actually to take place on the hypers
+
+ align:start position:0%
+actually to take place on the hypers
+ 
+
+ align:start position:0%
+actually to take place on the hypers
+surface where these conditions are
+
+ align:start position:0%
+surface where these conditions are
+ 
+
+ align:start position:0%
+surface where these conditions are
+satisfied that is if you were to evolve
+
+ align:start position:0%
+satisfied that is if you were to evolve
+ 
+
+ align:start position:0%
+satisfied that is if you were to evolve
+the coefficients of the plane waves what
+
+ align:start position:0%
+the coefficients of the plane waves what
+ 
+
+ align:start position:0%
+the coefficients of the plane waves what
+you would find is that as soon as you
+
+ align:start position:0%
+you would find is that as soon as you
+ 
+
+ align:start position:0%
+you would find is that as soon as you
+have sort of change them by a little
+
+ align:start position:0%
+have sort of change them by a little
+ 
+
+ align:start position:0%
+have sort of change them by a little
+amount your orbitals per se are not
+
+ align:start position:0%
+amount your orbitals per se are not
+ 
+
+ align:start position:0%
+amount your orbitals per se are not
+going to be oron normal anymore so this
+
+ align:start position:0%
+going to be oron normal anymore so this
+ 
+
+ align:start position:0%
+going to be oron normal anymore so this
+constraint is sort of fundamental and
+
+ align:start position:0%
+constraint is sort of fundamental and
+ 
+
+ align:start position:0%
+constraint is sort of fundamental and
+this is what ultimately limits sort of
+
+ align:start position:0%
+this is what ultimately limits sort of
+ 
+
+ align:start position:0%
+this is what ultimately limits sort of
+or determines the computational costs of
+
+ align:start position:0%
+or determines the computational costs of
+ 
+
+ align:start position:0%
+or determines the computational costs of
+our calculation because again if we
+
+ align:start position:0%
+our calculation because again if we
+ 
+
+ align:start position:0%
+our calculation because again if we
+double the size of the system we'll have
+
+ align:start position:0%
+double the size of the system we'll have
+ 
+
+ align:start position:0%
+double the size of the system we'll have
+twice as many plain waves and we'll have
+
+ align:start position:0%
+twice as many plain waves and we'll have
+ 
+
+ align:start position:0%
+twice as many plain waves and we'll have
+twice as many occupied orbitals so we
+
+ align:start position:0%
+twice as many occupied orbitals so we
+ 
+
+ align:start position:0%
+twice as many occupied orbitals so we
+have already a cost of force but those
+
+ align:start position:0%
+have already a cost of force but those
+ 
+
+ align:start position:0%
+have already a cost of force but those
+occupied orbitals will need to be
+
+ align:start position:0%
+occupied orbitals will need to be
+ 
+
+ align:start position:0%
+occupied orbitals will need to be
+orthogonal to each other and so the
+
+ align:start position:0%
+orthogonal to each other and so the
+ 
+
+ align:start position:0%
+orthogonal to each other and so the
+number of this Matrix elements that you
+
+ align:start position:0%
+number of this Matrix elements that you
+ 
+
+ align:start position:0%
+number of this Matrix elements that you
+need to calculate has become also twice
+
+ align:start position:0%
+need to calculate has become also twice
+ 
+
+ align:start position:0%
+need to calculate has become also twice
+or the number of orbitals in this Matrix
+
+ align:start position:0%
+or the number of orbitals in this Matrix
+ 
+
+ align:start position:0%
+or the number of orbitals in this Matrix
+have become twice so the number of
+
+ align:start position:0%
+have become twice so the number of
+ 
+
+ align:start position:0%
+have become twice so the number of
+Matrix elements has become four times as
+
+ align:start position:0%
+Matrix elements has become four times as
+ 
+
+ align:start position:0%
+Matrix elements has become four times as
+large you see we double the size of the
+
+ align:start position:0%
+large you see we double the size of the
+ 
+
+ align:start position:0%
+large you see we double the size of the
+system we'll have twice as many orbitals
+
+ align:start position:0%
+system we'll have twice as many orbitals
+ 
+
+ align:start position:0%
+system we'll have twice as many orbitals
+here twice as many orbitals here and
+
+ align:start position:0%
+here twice as many orbitals here and
+ 
+
+ align:start position:0%
+here twice as many orbitals here and
+this integral is going to take place on
+
+ align:start position:0%
+this integral is going to take place on
+ 
+
+ align:start position:0%
+this integral is going to take place on
+a region in space that's twice as large
+
+ align:start position:0%
+a region in space that's twice as large
+ 
+
+ align:start position:0%
+a region in space that's twice as large
+so 2 by 2 by two gives us a factor of F
+
+ align:start position:0%
+so 2 by 2 by two gives us a factor of F
+ 
+
+ align:start position:0%
+so 2 by 2 by two gives us a factor of F
+and so gives us the ultimate cubic
+
+ align:start position:0%
+and so gives us the ultimate cubic
+ 
+
+ align:start position:0%
+and so gives us the ultimate cubic
+scaling cost of density functional
+
+ align:start position:0%
+scaling cost of density functional
+ 
+
+ align:start position:0%
+scaling cost of density functional
+calculation you go from two atoms of
+
+ align:start position:0%
+calculation you go from two atoms of
+ 
+
+ align:start position:0%
+calculation you go from two atoms of
+silicon to four atoms of silicon your
+
+ align:start position:0%
+silicon to four atoms of silicon your
+ 
+
+ align:start position:0%
+silicon to four atoms of silicon your
+calculation has become eight times more
+
+ align:start position:0%
+calculation has become eight times more
+ 
+
+ align:start position:0%
+calculation has become eight times more
+expensive uh Harry F in his sort of you
+
+ align:start position:0%
+expensive uh Harry F in his sort of you
+ 
+
+ align:start position:0%
+expensive uh Harry F in his sort of you
+know original formulation scales as the
+
+ align:start position:0%
+know original formulation scales as the
+ 
+
+ align:start position:0%
+know original formulation scales as the
+fourth power at other Quantum cany
+
+ align:start position:0%
+fourth power at other Quantum cany
+ 
+
+ align:start position:0%
+fourth power at other Quantum cany
+approach scale as the fifth sixth or
+
+ align:start position:0%
+approach scale as the fifth sixth or
+ 
+
+ align:start position:0%
+approach scale as the fifth sixth or
+seventh power so it becomes very easy to
+
+ align:start position:0%
+seventh power so it becomes very easy to
+ 
+
+ align:start position:0%
+seventh power so it becomes very easy to
+sort of reach really the limit of
+
+ align:start position:0%
+sort of reach really the limit of
+ 
+
+ align:start position:0%
+sort of reach really the limit of
+calculation that you can do on a regular
+
+ align:start position:0%
+calculation that you can do on a regular
+ 
+
+ align:start position:0%
+calculation that you can do on a regular
+computer or even on a regular super
+
+ align:start position:0%
+computer or even on a regular super
+ 
+
+ align:start position:0%
+computer or even on a regular super
+computer and there is a lot of effort to
+
+ align:start position:0%
+computer and there is a lot of effort to
+ 
+
+ align:start position:0%
+computer and there is a lot of effort to
+develop what are called linear scaling
+
+ align:start position:0%
+develop what are called linear scaling
+ 
+
+ align:start position:0%
+develop what are called linear scaling
+approaches that is electronic struction
+
+ align:start position:0%
+approaches that is electronic struction
+ 
+
+ align:start position:0%
+approaches that is electronic struction
+algorithm that scale linearly as the
+
+ align:start position:0%
+algorithm that scale linearly as the
+ 
+
+ align:start position:0%
+algorithm that scale linearly as the
+size of the system and somehow they are
+
+ align:start position:0%
+size of the system and somehow they are
+ 
+
+ align:start position:0%
+size of the system and somehow they are
+all based on the idea that sort of
+
+ align:start position:0%
+all based on the idea that sort of
+ 
+
+ align:start position:0%
+all based on the idea that sort of
+physics or quantum mechanics is local so
+
+ align:start position:0%
+physics or quantum mechanics is local so
+ 
+
+ align:start position:0%
+physics or quantum mechanics is local so
+if your orbital at the end is ultimately
+
+ align:start position:0%
+if your orbital at the end is ultimately
+ 
+
+ align:start position:0%
+if your orbital at the end is ultimately
+localized in a certain region of space
+
+ align:start position:0%
+localized in a certain region of space
+ 
+
+ align:start position:0%
+localized in a certain region of space
+it will be automatically orthogonal to
+
+ align:start position:0%
+it will be automatically orthogonal to
+ 
+
+ align:start position:0%
+it will be automatically orthogonal to
+orbitals that are very far away because
+
+ align:start position:0%
+orbitals that are very far away because
+ 
+
+ align:start position:0%
+orbitals that are very far away because
+if this is localized somewhere here and
+
+ align:start position:0%
+if this is localized somewhere here and
+ 
+
+ align:start position:0%
+if this is localized somewhere here and
+this p is localized somewhere there
+
+ align:start position:0%
+this p is localized somewhere there
+ 
+
+ align:start position:0%
+this p is localized somewhere there
+their overlap will be Zero by definition
+
+ align:start position:0%
+their overlap will be Zero by definition
+ 
+
+ align:start position:0%
+their overlap will be Zero by definition
+and so we don't need to worry about
+
+ align:start position:0%
+and so we don't need to worry about
+ 
+
+ align:start position:0%
+and so we don't need to worry about
+orthogonality so somehow locality of
+
+ align:start position:0%
+orthogonality so somehow locality of
+ 
+
+ align:start position:0%
+orthogonality so somehow locality of
+physics locality of quantum mechanics in
+
+ align:start position:0%
+physics locality of quantum mechanics in
+ 
+
+ align:start position:0%
+physics locality of quantum mechanics in
+principle tells us that there are sort
+
+ align:start position:0%
+principle tells us that there are sort
+ 
+
+ align:start position:0%
+principle tells us that there are sort
+of linear scaling uh approaches that
+
+ align:start position:0%
+of linear scaling uh approaches that
+ 
+
+ align:start position:0%
+of linear scaling uh approaches that
+could work although none of them have
+
+ align:start position:0%
+could work although none of them have
+ 
+
+ align:start position:0%
+could work although none of them have
+really made into sort of you know
+
+ align:start position:0%
+really made into sort of you know
+ 
+
+ align:start position:0%
+really made into sort of you know
+production electronic structure at this
+
+ align:start position:0%
+production electronic structure at this
+ 
+
+ align:start position:0%
+production electronic structure at this
+stage although there is a lot of ongoing
+
+ align:start position:0%
+stage although there is a lot of ongoing
+ 
+
+ align:start position:0%
+stage although there is a lot of ongoing
+effort in many in many
+
+ align:start position:0%
+effort in many in many
+ 
+
+ align:start position:0%
+effort in many in many
+groups okay so with this sort of we
+
+ align:start position:0%
+groups okay so with this sort of we
+ 
+
+ align:start position:0%
+groups okay so with this sort of we
+conclude also all the
+
+ align:start position:0%
+conclude also all the
+ 
+
+ align:start position:0%
+conclude also all the
+technicalities and what we'll do in the
+
+ align:start position:0%
+technicalities and what we'll do in the
+ 
+
+ align:start position:0%
+technicalities and what we'll do in the
+rest of the class we'll give you a sort
+
+ align:start position:0%
+rest of the class we'll give you a sort
+ 
+
+ align:start position:0%
+rest of the class we'll give you a sort
+of Panorama of what typical applications
+
+ align:start position:0%
+of Panorama of what typical applications
+ 
+
+ align:start position:0%
+of Panorama of what typical applications
+of density functional Theory calculation
+
+ align:start position:0%
+of density functional Theory calculation
+ 
+
+ align:start position:0%
+of density functional Theory calculation
+are going to are going to do and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um um I'll I'll I'll go very quickly
+
+ align:start position:0%
+um um I'll I'll I'll go very quickly
+ 
+
+ align:start position:0%
+um um I'll I'll I'll go very quickly
+over this I have here sort of you know
+
+ align:start position:0%
+over this I have here sort of you know
+ 
+
+ align:start position:0%
+over this I have here sort of you know
+cases in which we could be interested in
+
+ align:start position:0%
+cases in which we could be interested in
+ 
+
+ align:start position:0%
+cases in which we could be interested in
+structural
+
+ align:start position:0%
+structural
+ 
+
+ align:start position:0%
+structural
+excitations so when you start warming up
+
+ align:start position:0%
+excitations so when you start warming up
+ 
+
+ align:start position:0%
+excitations so when you start warming up
+a system a molecule or a solid you start
+
+ align:start position:0%
+a system a molecule or a solid you start
+ 
+
+ align:start position:0%
+a system a molecule or a solid you start
+exciting the different normal modes of
+
+ align:start position:0%
+exciting the different normal modes of
+ 
+
+ align:start position:0%
+exciting the different normal modes of
+your molecule or of a solid I shown you
+
+ align:start position:0%
+your molecule or of a solid I shown you
+ 
+
+ align:start position:0%
+your molecule or of a solid I shown you
+some of the possibilities for something
+
+ align:start position:0%
+some of the possibilities for something
+ 
+
+ align:start position:0%
+some of the possibilities for something
+like a carbon nanot tube it could start
+
+ align:start position:0%
+like a carbon nanot tube it could start
+ 
+
+ align:start position:0%
+like a carbon nanot tube it could start
+Bend we have a bending mode up there we
+
+ align:start position:0%
+Bend we have a bending mode up there we
+ 
+
+ align:start position:0%
+Bend we have a bending mode up there we
+have a pinching mode or we have a
+
+ align:start position:0%
+have a pinching mode or we have a
+ 
+
+ align:start position:0%
+have a pinching mode or we have a
+breathing mode so these are all the
+
+ align:start position:0%
+breathing mode so these are all the
+ 
+
+ align:start position:0%
+breathing mode so these are all the
+possible structural excitation and you
+
+ align:start position:0%
+possible structural excitation and you
+ 
+
+ align:start position:0%
+possible structural excitation and you
+can actually calculate these structural
+
+ align:start position:0%
+can actually calculate these structural
+ 
+
+ align:start position:0%
+can actually calculate these structural
+excitations using T fanal Theory and
+
+ align:start position:0%
+excitations using T fanal Theory and
+ 
+
+ align:start position:0%
+excitations using T fanal Theory and
+I've given here a comparison between um
+
+ align:start position:0%
+I've given here a comparison between um
+ 
+
+ align:start position:0%
+I've given here a comparison between um
+the case of diamond
+
+ align:start position:0%
+the case of diamond
+ 
+
+ align:start position:0%
+the case of diamond
+uh what is calculated with a sort of you
+
+ align:start position:0%
+uh what is calculated with a sort of you
+ 
+
+ align:start position:0%
+uh what is calculated with a sort of you
+know state of the art such a code like
+
+ align:start position:0%
+know state of the art such a code like
+ 
+
+ align:start position:0%
+know state of the art such a code like
+you are going to see in your uh in your
+
+ align:start position:0%
+you are going to see in your uh in your
+ 
+
+ align:start position:0%
+you are going to see in your uh in your
+laboratory and what is measured actually
+
+ align:start position:0%
+laboratory and what is measured actually
+ 
+
+ align:start position:0%
+laboratory and what is measured actually
+with Neutron scattering the the red dots
+
+ align:start position:0%
+with Neutron scattering the the red dots
+ 
+
+ align:start position:0%
+with Neutron scattering the the red dots
+so you see without really any input
+
+ align:start position:0%
+so you see without really any input
+ 
+
+ align:start position:0%
+so you see without really any input
+parameters and once you have really pH
+
+ align:start position:0%
+parameters and once you have really pH
+ 
+
+ align:start position:0%
+parameters and once you have really pH
+on dispersion you can calculate all the
+
+ align:start position:0%
+on dispersion you can calculate all the
+ 
+
+ align:start position:0%
+on dispersion you can calculate all the
+thermodynamics of solids that is really
+
+ align:start position:0%
+thermodynamics of solids that is really
+ 
+
+ align:start position:0%
+thermodynamics of solids that is really
+basically based on the statistics of
+
+ align:start position:0%
+basically based on the statistics of
+ 
+
+ align:start position:0%
+basically based on the statistics of
+excitation of this vibrational degrees
+
+ align:start position:0%
+excitation of this vibrational degrees
+ 
+
+ align:start position:0%
+excitation of this vibrational degrees
+of freedom so you could calculate say
+
+ align:start position:0%
+of freedom so you could calculate say
+ 
+
+ align:start position:0%
+of freedom so you could calculate say
+how your elastic constant or your bulk
+
+ align:start position:0%
+how your elastic constant or your bulk
+ 
+
+ align:start position:0%
+how your elastic constant or your bulk
+modulus changes with temperature and you
+
+ align:start position:0%
+modulus changes with temperature and you
+ 
+
+ align:start position:0%
+modulus changes with temperature and you
+know this is the calculated Black line
+
+ align:start position:0%
+know this is the calculated Black line
+ 
+
+ align:start position:0%
+know this is the calculated Black line
+and you could compare it with
+
+ align:start position:0%
+and you could compare it with
+ 
+
+ align:start position:0%
+and you could compare it with
+experiments or you know you could take
+
+ align:start position:0%
+experiments or you know you could take
+ 
+
+ align:start position:0%
+experiments or you know you could take
+one of your slabs like you know you have
+
+ align:start position:0%
+one of your slabs like you know you have
+ 
+
+ align:start position:0%
+one of your slabs like you know you have
+seen in the first laboratory in which
+
+ align:start position:0%
+seen in the first laboratory in which
+ 
+
+ align:start position:0%
+seen in the first laboratory in which
+you were calculating the surface energy
+
+ align:start position:0%
+you were calculating the surface energy
+ 
+
+ align:start position:0%
+you were calculating the surface energy
+and you could actually put it in motion
+
+ align:start position:0%
+and you could actually put it in motion
+ 
+
+ align:start position:0%
+and you could actually put it in motion
+you could follow at a given temperature
+
+ align:start position:0%
+you could follow at a given temperature
+ 
+
+ align:start position:0%
+you could follow at a given temperature
+the Dynamics of the atoms and you want
+
+ align:start position:0%
+the Dynamics of the atoms and you want
+ 
+
+ align:start position:0%
+the Dynamics of the atoms and you want
+to have slab that thick enough so the
+
+ align:start position:0%
+to have slab that thick enough so the
+ 
+
+ align:start position:0%
+to have slab that thick enough so the
+atoms in the middle really act as bulk
+
+ align:start position:0%
+atoms in the middle really act as bulk
+ 
+
+ align:start position:0%
+atoms in the middle really act as bulk
+atoms they don't see the presence of the
+
+ align:start position:0%
+atoms they don't see the presence of the
+ 
+
+ align:start position:0%
+atoms they don't see the presence of the
+surface and then it becomes very easy to
+
+ align:start position:0%
+surface and then it becomes very easy to
+ 
+
+ align:start position:0%
+surface and then it becomes very easy to
+investigate what's happening on the
+
+ align:start position:0%
+investigate what's happening on the
+ 
+
+ align:start position:0%
+investigate what's happening on the
+surface and so you can have sort of you
+
+ align:start position:0%
+surface and so you can have sort of you
+ 
+
+ align:start position:0%
+surface and so you can have sort of you
+know a snapshot of sort of how the atoms
+
+ align:start position:0%
+know a snapshot of sort of how the atoms
+ 
+
+ align:start position:0%
+know a snapshot of sort of how the atoms
+are moving on the sort of outer layers
+
+ align:start position:0%
+are moving on the sort of outer layers
+ 
+
+ align:start position:0%
+are moving on the sort of outer layers
+what are the sort of typical
+
+ align:start position:0%
+what are the sort of typical
+ 
+
+ align:start position:0%
+what are the sort of typical
+displacements or typical mean square
+
+ align:start position:0%
+displacements or typical mean square
+ 
+
+ align:start position:0%
+displacements or typical mean square
+displacements or you can say study how
+
+ align:start position:0%
+displacements or you can say study how
+ 
+
+ align:start position:0%
+displacements or you can say study how
+the distance between the layers evolve
+
+ align:start position:0%
+the distance between the layers evolve
+ 
+
+ align:start position:0%
+the distance between the layers evolve
+with temperature so you can look at say
+
+ align:start position:0%
+with temperature so you can look at say
+ 
+
+ align:start position:0%
+with temperature so you can look at say
+how as you increase the temperature of
+
+ align:start position:0%
+how as you increase the temperature of
+ 
+
+ align:start position:0%
+how as you increase the temperature of
+your slab the distance between the
+
+ align:start position:0%
+your slab the distance between the
+ 
+
+ align:start position:0%
+your slab the distance between the
+Surface layer and the second layer
+
+ align:start position:0%
+Surface layer and the second layer
+ 
+
+ align:start position:0%
+Surface layer and the second layer
+changes with temperature and this would
+
+ align:start position:0%
+changes with temperature and this would
+ 
+
+ align:start position:0%
+changes with temperature and this would
+be the computation and here we have the
+
+ align:start position:0%
+be the computation and here we have the
+ 
+
+ align:start position:0%
+be the computation and here we have the
+experimental value and sort of there are
+
+ align:start position:0%
+experimental value and sort of there are
+ 
+
+ align:start position:0%
+experimental value and sort of there are
+sort of lots of interesting physics that
+
+ align:start position:0%
+sort of lots of interesting physics that
+ 
+
+ align:start position:0%
+sort of lots of interesting physics that
+takes place uh again if you look at the
+
+ align:start position:0%
+takes place uh again if you look at the
+ 
+
+ align:start position:0%
+takes place uh again if you look at the
+distance between the second and third
+
+ align:start position:0%
+distance between the second and third
+ 
+
+ align:start position:0%
+distance between the second and third
+layer is the red line above and the
+
+ align:start position:0%
+layer is the red line above and the
+ 
+
+ align:start position:0%
+layer is the red line above and the
+system expands there and you know sort
+
+ align:start position:0%
+system expands there and you know sort
+ 
+
+ align:start position:0%
+system expands there and you know sort
+of with computation you can actually
+
+ align:start position:0%
+of with computation you can actually
+ 
+
+ align:start position:0%
+of with computation you can actually
+probe your system deeper and deeper
+
+ align:start position:0%
+probe your system deeper and deeper
+ 
+
+ align:start position:0%
+probe your system deeper and deeper
+where experiment starts to become very
+
+ align:start position:0%
+where experiment starts to become very
+ 
+
+ align:start position:0%
+where experiment starts to become very
+difficult it's almost impossible to look
+
+ align:start position:0%
+difficult it's almost impossible to look
+ 
+
+ align:start position:0%
+difficult it's almost impossible to look
+at what the fourth layer in a surface do
+
+ align:start position:0%
+at what the fourth layer in a surface do
+ 
+
+ align:start position:0%
+at what the fourth layer in a surface do
+and what the fifth layer of a surface do
+
+ align:start position:0%
+and what the fifth layer of a surface do
+ 
+
+ align:start position:0%
+and what the fifth layer of a surface do
+okay I think in order to keep the
+
+ align:start position:0%
+okay I think in order to keep the
+ 
+
+ align:start position:0%
+okay I think in order to keep the
+balance of the lecture I actually switch
+
+ align:start position:0%
+balance of the lecture I actually switch
+ 
+
+ align:start position:0%
+balance of the lecture I actually switch
+on to to Professor Cedar part so he can
+
+ align:start position:0%
+on to to Professor Cedar part so he can
+ 
+
+ align:start position:0%
+on to to Professor Cedar part so he can
+show you some of the other application
+
+ align:start position:0%
+show you some of the other application
+ 
+
+ align:start position:0%
+show you some of the other application
+and um if we have time either in one of
+
+ align:start position:0%
+and um if we have time either in one of
+ 
+
+ align:start position:0%
+and um if we have time either in one of
+the next class I'll show you some of
+
+ align:start position:0%
+the next class I'll show you some of
+ 
+
+ align:start position:0%
+the next class I'll show you some of
+some some of the other
+
+ align:start position:0%
+some some of the other
+ 
+
+ align:start position:0%
+some some of the other
+um applications that we have mentioned
+
+ align:start position:0%
+um applications that we have mentioned
+ 
+
+ align:start position:0%
+um applications that we have mentioned
+so I think I'll I'll pass over the
+
+ align:start position:0%
+so I think I'll I'll pass over the
+ 
+
+ align:start position:0%
+so I think I'll I'll pass over the
+lecture to to Professor Cedar and
+
+ align:start position:0%
+lecture to to Professor Cedar and
+ 
+
+ align:start position:0%
+lecture to to Professor Cedar and
+uh okay so uh professor marzari already
+
+ align:start position:0%
+uh okay so uh professor marzari already
+ 
+
+ align:start position:0%
+uh okay so uh professor marzari already
+gave
+
+ align:start position:0%
+gave
+ 
+
+ align:start position:0%
+gave
+you sort of some generic applications
+
+ align:start position:0%
+you sort of some generic applications
+ 
+
+ align:start position:0%
+you sort of some generic applications
+what I want to do for the rest of the
+
+ align:start position:0%
+what I want to do for the rest of the
+ 
+
+ align:start position:0%
+what I want to do for the rest of the
+class is um actually give you some
+
+ align:start position:0%
+class is um actually give you some
+ 
+
+ align:start position:0%
+class is um actually give you some
+numbers and um really look seriously at
+
+ align:start position:0%
+numbers and um really look seriously at
+ 
+
+ align:start position:0%
+numbers and um really look seriously at
+um what the typical accuracies are that
+
+ align:start position:0%
+um what the typical accuracies are that
+ 
+
+ align:start position:0%
+um what the typical accuracies are that
+you can expect from what we'll call
+
+ align:start position:0%
+you can expect from what we'll call
+ 
+
+ align:start position:0%
+you can expect from what we'll call
+density functional Theory what we mean
+
+ align:start position:0%
+density functional Theory what we mean
+ 
+
+ align:start position:0%
+density functional Theory what we mean
+with that isort of standard density
+
+ align:start position:0%
+with that isort of standard density
+ 
+
+ align:start position:0%
+with that isort of standard density
+functional Theory um as we kind of
+
+ align:start position:0%
+functional Theory um as we kind of
+ 
+
+ align:start position:0%
+functional Theory um as we kind of
+explained it to you in the class you
+
+ align:start position:0%
+explained it to you in the class you
+ 
+
+ align:start position:0%
+explained it to you in the class you
+know in the local density or generalized
+
+ align:start position:0%
+know in the local density or generalized
+ 
+
+ align:start position:0%
+know in the local density or generalized
+gradient approximation uh so these are
+
+ align:start position:0%
+gradient approximation uh so these are
+ 
+
+ align:start position:0%
+gradient approximation uh so these are
+sort of Staples of electronic structure
+
+ align:start position:0%
+sort of Staples of electronic structure
+ 
+
+ align:start position:0%
+sort of Staples of electronic structure
+methods now that doesn't mean that there
+
+ align:start position:0%
+methods now that doesn't mean that there
+ 
+
+ align:start position:0%
+methods now that doesn't mean that there
+are in some cases not already better
+
+ align:start position:0%
+are in some cases not already better
+ 
+
+ align:start position:0%
+are in some cases not already better
+forms out there uh but they're often
+
+ align:start position:0%
+forms out there uh but they're often
+ 
+
+ align:start position:0%
+forms out there uh but they're often
+very much in the research stage and
+
+ align:start position:0%
+very much in the research stage and
+ 
+
+ align:start position:0%
+very much in the research stage and
+there wouldn't be things that you would
+
+ align:start position:0%
+there wouldn't be things that you would
+ 
+
+ align:start position:0%
+there wouldn't be things that you would
+either easily do on real problems you
+
+ align:start position:0%
+either easily do on real problems you
+ 
+
+ align:start position:0%
+either easily do on real problems you
+wouldn't easily get your hands on them
+
+ align:start position:0%
+wouldn't easily get your hands on them
+ 
+
+ align:start position:0%
+wouldn't easily get your hands on them
+and you wouldn't necessarily easily
+
+ align:start position:0%
+and you wouldn't necessarily easily
+ 
+
+ align:start position:0%
+and you wouldn't necessarily easily
+learn from from them so again what we're
+
+ align:start position:0%
+learn from from them so again what we're
+ 
+
+ align:start position:0%
+learn from from them so again what we're
+going to talk about is the kind of
+
+ align:start position:0%
+going to talk about is the kind of
+ 
+
+ align:start position:0%
+going to talk about is the kind of
+standard um staple of electronic
+
+ align:start position:0%
+standard um staple of electronic
+ 
+
+ align:start position:0%
+standard um staple of electronic
+structure um before I did that I want to
+
+ align:start position:0%
+structure um before I did that I want to
+ 
+
+ align:start position:0%
+structure um before I did that I want to
+say a little bit about a topic we
+
+ align:start position:0%
+say a little bit about a topic we
+ 
+
+ align:start position:0%
+say a little bit about a topic we
+haven't touched about which is uh the
+
+ align:start position:0%
+haven't touched about which is uh the
+ 
+
+ align:start position:0%
+haven't touched about which is uh the
+what they What's called the spin
+
+ align:start position:0%
+what they What's called the spin
+ 
+
+ align:start position:0%
+what they What's called the spin
+polarized version of density functional
+
+ align:start position:0%
+polarized version of density functional
+ 
+
+ align:start position:0%
+polarized version of density functional
+Theory um if you remember the hornberg
+
+ align:start position:0%
+Theory um if you remember the hornberg
+ 
+
+ align:start position:0%
+Theory um if you remember the hornberg
+home theorem everything is in in essence
+
+ align:start position:0%
+home theorem everything is in in essence
+ 
+
+ align:start position:0%
+home theorem everything is in in essence
+expressed in terms of the charge density
+
+ align:start position:0%
+expressed in terms of the charge density
+ 
+
+ align:start position:0%
+expressed in terms of the charge density
+okay everything is a function of the
+
+ align:start position:0%
+okay everything is a function of the
+ 
+
+ align:start position:0%
+okay everything is a function of the
+charge density and the electron spin
+
+ align:start position:0%
+charge density and the electron spin
+ 
+
+ align:start position:0%
+charge density and the electron spin
+never explicitly appears in there um but
+
+ align:start position:0%
+never explicitly appears in there um but
+ 
+
+ align:start position:0%
+never explicitly appears in there um but
+of course electrons have spin uh if you
+
+ align:start position:0%
+of course electrons have spin uh if you
+ 
+
+ align:start position:0%
+of course electrons have spin uh if you
+don't consider any coupling with the
+
+ align:start position:0%
+don't consider any coupling with the
+ 
+
+ align:start position:0%
+don't consider any coupling with the
+angular momentum it's really just up or
+
+ align:start position:0%
+angular momentum it's really just up or
+ 
+
+ align:start position:0%
+angular momentum it's really just up or
+down spin so plus or minus um a half the
+
+ align:start position:0%
+down spin so plus or minus um a half the
+ 
+
+ align:start position:0%
+down spin so plus or minus um a half the
+Bor magnet none um and we'll treat here
+
+ align:start position:0%
+Bor magnet none um and we'll treat here
+ 
+
+ align:start position:0%
+Bor magnet none um and we'll treat here
+in the lecture spin as a scalar quantity
+
+ align:start position:0%
+in the lecture spin as a scalar quantity
+ 
+
+ align:start position:0%
+in the lecture spin as a scalar quantity
+uh so really spin is just up or down uh
+
+ align:start position:0%
+uh so really spin is just up or down uh
+ 
+
+ align:start position:0%
+uh so really spin is just up or down uh
+plus one or minus one or plus a half or
+
+ align:start position:0%
+plus one or minus one or plus a half or
+ 
+
+ align:start position:0%
+plus one or minus one or plus a half or
+minus a half in in the appropriate units
+
+ align:start position:0%
+minus a half in in the appropriate units
+ 
+
+ align:start position:0%
+minus a half in in the appropriate units
+in Reality Skin spin as soon as it
+
+ align:start position:0%
+in Reality Skin spin as soon as it
+ 
+
+ align:start position:0%
+in Reality Skin spin as soon as it
+couples to the angular momentum U
+
+ align:start position:0%
+couples to the angular momentum U
+ 
+
+ align:start position:0%
+couples to the angular momentum U
+becomes a vector quantity okay also as
+
+ align:start position:0%
+becomes a vector quantity okay also as
+ 
+
+ align:start position:0%
+becomes a vector quantity okay also as
+soon as it couples to an electric to a
+
+ align:start position:0%
+soon as it couples to an electric to a
+ 
+
+ align:start position:0%
+soon as it couples to an electric to a
+magnetic field from the environment
+
+ align:start position:0%
+magnetic field from the environment
+ 
+
+ align:start position:0%
+magnetic field from the environment
+becomes a vector quantity and people do
+
+ align:start position:0%
+becomes a vector quantity and people do
+ 
+
+ align:start position:0%
+becomes a vector quantity and people do
+that now already treating spin as a
+
+ align:start position:0%
+that now already treating spin as a
+ 
+
+ align:start position:0%
+that now already treating spin as a
+vector quantity but most codes that you
+
+ align:start position:0%
+vector quantity but most codes that you
+ 
+
+ align:start position:0%
+vector quantity but most codes that you
+you that you will use uh spin will
+
+ align:start position:0%
+you that you will use uh spin will
+ 
+
+ align:start position:0%
+you that you will use uh spin will
+simply be treated as a scaler which is
+
+ align:start position:0%
+simply be treated as a scaler which is
+ 
+
+ align:start position:0%
+simply be treated as a scaler which is
+fine for um most purposes um we tend to
+
+ align:start position:0%
+fine for um most purposes um we tend to
+ 
+
+ align:start position:0%
+fine for um most purposes um we tend to
+refer to them as um
+
+ align:start position:0%
+refer to them as um
+ 
+
+ align:start position:0%
+refer to them as um
+uh just up and down Spin and I'll often
+
+ align:start position:0%
+uh just up and down Spin and I'll often
+ 
+
+ align:start position:0%
+uh just up and down Spin and I'll often
+write that with the either up and down
+
+ align:start position:0%
+write that with the either up and down
+ 
+
+ align:start position:0%
+write that with the either up and down
+um Arrow um now why um do you actually
+
+ align:start position:0%
+um Arrow um now why um do you actually
+ 
+
+ align:start position:0%
+um Arrow um now why um do you actually
+need uh to treat the electron spin uh
+
+ align:start position:0%
+need uh to treat the electron spin uh
+ 
+
+ align:start position:0%
+need uh to treat the electron spin uh
+let me just sort of give you a refresher
+
+ align:start position:0%
+let me just sort of give you a refresher
+ 
+
+ align:start position:0%
+let me just sort of give you a refresher
+of of um why you need to deal with the
+
+ align:start position:0%
+of of um why you need to deal with the
+ 
+
+ align:start position:0%
+of of um why you need to deal with the
+spin uh well the reason is the Pauling
+
+ align:start position:0%
+spin uh well the reason is the Pauling
+ 
+
+ align:start position:0%
+spin uh well the reason is the Pauling
+Exclusion Principle really is that you
+
+ align:start position:0%
+Exclusion Principle really is that you
+ 
+
+ align:start position:0%
+Exclusion Principle really is that you
+know the polling Exclusion Principle
+
+ align:start position:0%
+know the polling Exclusion Principle
+ 
+
+ align:start position:0%
+know the polling Exclusion Principle
+tells you that two electrons cannot be
+
+ align:start position:0%
+tells you that two electrons cannot be
+ 
+
+ align:start position:0%
+tells you that two electrons cannot be
+in exactly the same Quantum State
+
+ align:start position:0%
+in exactly the same Quantum State
+ 
+
+ align:start position:0%
+in exactly the same Quantum State
+remember that
+
+ align:start position:0%
+remember that
+ 
+
+ align:start position:0%
+remember that
+so that means that if you have
+
+ align:start position:0%
+so that means that if you have
+ 
+
+ align:start position:0%
+so that means that if you have
+two up electrons approaching each other
+
+ align:start position:0%
+two up electrons approaching each other
+ 
+
+ align:start position:0%
+two up electrons approaching each other
+versus say an up and a down
+
+ align:start position:0%
+versus say an up and a down
+ 
+
+ align:start position:0%
+versus say an up and a down
+electron okay these will approach each
+
+ align:start position:0%
+electron okay these will approach each
+ 
+
+ align:start position:0%
+electron okay these will approach each
+other differently because these
+
+ align:start position:0%
+other differently because these
+ 
+
+ align:start position:0%
+other differently because these
+two are in the same spin state so if you
+
+ align:start position:0%
+two are in the same spin state so if you
+ 
+
+ align:start position:0%
+two are in the same spin state so if you
+bring them very close together they
+
+ align:start position:0%
+bring them very close together they
+ 
+
+ align:start position:0%
+bring them very close together they
+essentially not get the same coordinate
+
+ align:start position:0%
+essentially not get the same coordinate
+ 
+
+ align:start position:0%
+essentially not get the same coordinate
+as well so they almost have the same
+
+ align:start position:0%
+as well so they almost have the same
+ 
+
+ align:start position:0%
+as well so they almost have the same
+Quant numbers now and the poly Exclusion
+
+ align:start position:0%
+Quant numbers now and the poly Exclusion
+ 
+
+ align:start position:0%
+Quant numbers now and the poly Exclusion
+Principle prevents that so the poly
+
+ align:start position:0%
+Principle prevents that so the poly
+ 
+
+ align:start position:0%
+Principle prevents that so the poly
+Exclusion Principle keeps electrons with
+
+ align:start position:0%
+Exclusion Principle keeps electrons with
+ 
+
+ align:start position:0%
+Exclusion Principle keeps electrons with
+parallel spin essentially away from each
+
+ align:start position:0%
+parallel spin essentially away from each
+ 
+
+ align:start position:0%
+parallel spin essentially away from each
+other okay whereas if you have electrons
+
+ align:start position:0%
+other okay whereas if you have electrons
+ 
+
+ align:start position:0%
+other okay whereas if you have electrons
+with anti- parallel spin even if these
+
+ align:start position:0%
+with anti- parallel spin even if these
+ 
+
+ align:start position:0%
+with anti- parallel spin even if these
+are at the same position they don't have
+
+ align:start position:0%
+are at the same position they don't have
+ 
+
+ align:start position:0%
+are at the same position they don't have
+the same spin so they don't have the
+
+ align:start position:0%
+the same spin so they don't have the
+ 
+
+ align:start position:0%
+the same spin so they don't have the
+same set of quantum numbers so the poly
+
+ align:start position:0%
+same set of quantum numbers so the poly
+ 
+
+ align:start position:0%
+same set of quantum numbers so the poly
+Exclusion Principle doesn't act on them
+
+ align:start position:0%
+Exclusion Principle doesn't act on them
+ 
+
+ align:start position:0%
+Exclusion Principle doesn't act on them
+and you know the poly excusion principle
+
+ align:start position:0%
+and you know the poly excusion principle
+ 
+
+ align:start position:0%
+and you know the poly excusion principle
+is essentially something that keeps the
+
+ align:start position:0%
+is essentially something that keeps the
+ 
+
+ align:start position:0%
+is essentially something that keeps the
+electrons away um without an explicit
+
+ align:start position:0%
+electrons away um without an explicit
+ 
+
+ align:start position:0%
+electrons away um without an explicit
+term for it in the hamiltonian it's not
+
+ align:start position:0%
+term for it in the hamiltonian it's not
+ 
+
+ align:start position:0%
+term for it in the hamiltonian it's not
+like you know the columbic interaction
+
+ align:start position:0%
+like you know the columbic interaction
+ 
+
+ align:start position:0%
+like you know the columbic interaction
+of course keeps electrons away from each
+
+ align:start position:0%
+of course keeps electrons away from each
+ 
+
+ align:start position:0%
+of course keeps electrons away from each
+other but the PO Exclusion Principle is
+
+ align:start position:0%
+other but the PO Exclusion Principle is
+ 
+
+ align:start position:0%
+other but the PO Exclusion Principle is
+essentially something on top of that
+
+ align:start position:0%
+essentially something on top of that
+ 
+
+ align:start position:0%
+essentially something on top of that
+that comes from anti- symmetrizing the
+
+ align:start position:0%
+that comes from anti- symmetrizing the
+ 
+
+ align:start position:0%
+that comes from anti- symmetrizing the
+wave function you don't see it directly
+
+ align:start position:0%
+wave function you don't see it directly
+ 
+
+ align:start position:0%
+wave function you don't see it directly
+in the form as a term in the form of the
+
+ align:start position:0%
+in the form as a term in the form of the
+ 
+
+ align:start position:0%
+in the form as a term in the form of the
+hamiltonian and if you remember
+
+ align:start position:0%
+hamiltonian and if you remember
+ 
+
+ align:start position:0%
+hamiltonian and if you remember
+consequences of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it's going to take forever um of the
+
+ align:start position:0%
+um it's going to take forever um of the
+ 
+
+ align:start position:0%
+um it's going to take forever um of the
+PO exent principle it's h rule that if
+
+ align:start position:0%
+PO exent principle it's h rule that if
+ 
+
+ align:start position:0%
+PO exent principle it's h rule that if
+you have you know if you remember Atomic
+
+ align:start position:0%
+you have you know if you remember Atomic
+ 
+
+ align:start position:0%
+you have you know if you remember Atomic
+D level say for example um if you
+
+ align:start position:0%
+D level say for example um if you
+ 
+
+ align:start position:0%
+D level say for example um if you
+add electrons to like say 5D levels
+
+ align:start position:0%
+add electrons to like say 5D levels
+ 
+
+ align:start position:0%
+add electrons to like say 5D levels
+you're going to add them with parallel
+
+ align:start position:0%
+you're going to add them with parallel
+ 
+
+ align:start position:0%
+you're going to add them with parallel
+spin first because again then the poly
+
+ align:start position:0%
+spin first because again then the poly
+ 
+
+ align:start position:0%
+spin first because again then the poly
+exclusion um principle satisfied and
+
+ align:start position:0%
+exclusion um principle satisfied and
+ 
+
+ align:start position:0%
+exclusion um principle satisfied and
+then you start filling them with anti
+
+ align:start position:0%
+then you start filling them with anti
+ 
+
+ align:start position:0%
+then you start filling them with anti
+paral the anti- parallel levels okay so
+
+ align:start position:0%
+paral the anti- parallel levels okay so
+ 
+
+ align:start position:0%
+paral the anti- parallel levels okay so
+this is going to carry over in atoms uh
+
+ align:start position:0%
+this is going to carry over in atoms uh
+ 
+
+ align:start position:0%
+this is going to carry over in atoms uh
+in solids I'm sorry um basically if
+
+ align:start position:0%
+in solids I'm sorry um basically if
+ 
+
+ align:start position:0%
+in solids I'm sorry um basically if
+those five say let's focus on D levels
+
+ align:start position:0%
+those five say let's focus on D levels
+ 
+
+ align:start position:0%
+those five say let's focus on D levels
+if they remain
+
+ align:start position:0%
+if they remain
+ 
+
+ align:start position:0%
+if they remain
+degenerate so they remain roughly at the
+
+ align:start position:0%
+degenerate so they remain roughly at the
+ 
+
+ align:start position:0%
+degenerate so they remain roughly at the
+same level you going to fill them
+
+ align:start position:0%
+same level you going to fill them
+ 
+
+ align:start position:0%
+same level you going to fill them
+according to Huns Rule and that's what
+
+ align:start position:0%
+according to Huns Rule and that's what
+ 
+
+ align:start position:0%
+according to Huns Rule and that's what
+I've shown here so in solids these you
+
+ align:start position:0%
+I've shown here so in solids these you
+ 
+
+ align:start position:0%
+I've shown here so in solids these you
+know these D levels will split a little
+
+ align:start position:0%
+know these D levels will split a little
+ 
+
+ align:start position:0%
+know these D levels will split a little
+which is what I've shown here but if
+
+ align:start position:0%
+which is what I've shown here but if
+ 
+
+ align:start position:0%
+which is what I've shown here but if
+they don't split a lot okay then you're
+
+ align:start position:0%
+they don't split a lot okay then you're
+ 
+
+ align:start position:0%
+they don't split a lot okay then you're
+actually going to fill them with
+
+ align:start position:0%
+actually going to fill them with
+ 
+
+ align:start position:0%
+actually going to fill them with
+parallel Spin and so if that's the case
+
+ align:start position:0%
+parallel Spin and so if that's the case
+ 
+
+ align:start position:0%
+parallel Spin and so if that's the case
+you have a lot of Magnetic Moment on
+
+ align:start position:0%
+you have a lot of Magnetic Moment on
+ 
+
+ align:start position:0%
+you have a lot of Magnetic Moment on
+your iron okay you have five electron
+
+ align:start position:0%
+your iron okay you have five electron
+ 
+
+ align:start position:0%
+your iron okay you have five electron
+spins here uh you have no down spin so
+
+ align:start position:0%
+spins here uh you have no down spin so
+ 
+
+ align:start position:0%
+spins here uh you have no down spin so
+you have a strong Magnetic Moment and
+
+ align:start position:0%
+you have a strong Magnetic Moment and
+ 
+
+ align:start position:0%
+you have a strong Magnetic Moment and
+I'll show you in a second where that
+
+ align:start position:0%
+I'll show you in a second where that
+ 
+
+ align:start position:0%
+I'll show you in a second where that
+becomes important uh on the other hand
+
+ align:start position:0%
+becomes important uh on the other hand
+ 
+
+ align:start position:0%
+becomes important uh on the other hand
+let's say you're in an environment that
+
+ align:start position:0%
+let's say you're in an environment that
+ 
+
+ align:start position:0%
+let's say you're in an environment that
+splits off two of these okay puts them
+
+ align:start position:0%
+splits off two of these okay puts them
+ 
+
+ align:start position:0%
+splits off two of these okay puts them
+much higher um at some point you won't
+
+ align:start position:0%
+much higher um at some point you won't
+ 
+
+ align:start position:0%
+much higher um at some point you won't
+satisfy Hun's rule anymore because the
+
+ align:start position:0%
+satisfy Hun's rule anymore because the
+ 
+
+ align:start position:0%
+satisfy Hun's rule anymore because the
+energy cost of let's say you know after
+
+ align:start position:0%
+energy cost of let's say you know after
+ 
+
+ align:start position:0%
+energy cost of let's say you know after
+you put in these three green
+
+ align:start position:0%
+you put in these three green
+ 
+
+ align:start position:0%
+you put in these three green
+electrons now you have to add two more
+
+ align:start position:0%
+electrons now you have to add two more
+ 
+
+ align:start position:0%
+electrons now you have to add two more
+say if you have five electrons to fill
+
+ align:start position:0%
+say if you have five electrons to fill
+ 
+
+ align:start position:0%
+say if you have five electrons to fill
+them with parall spin you would have to
+
+ align:start position:0%
+them with parall spin you would have to
+ 
+
+ align:start position:0%
+them with parall spin you would have to
+put them
+
+ align:start position:0%
+put them
+ 
+
+ align:start position:0%
+put them
+here but since those levers are so much
+
+ align:start position:0%
+here but since those levers are so much
+ 
+
+ align:start position:0%
+here but since those levers are so much
+higher um you know you basically want to
+
+ align:start position:0%
+higher um you know you basically want to
+ 
+
+ align:start position:0%
+higher um you know you basically want to
+pay the exchange penalty they call it
+
+ align:start position:0%
+pay the exchange penalty they call it
+ 
+
+ align:start position:0%
+pay the exchange penalty they call it
+the Hun rule penalty to put them in a
+
+ align:start position:0%
+the Hun rule penalty to put them in a
+ 
+
+ align:start position:0%
+the Hun rule penalty to put them in a
+lower orbital and you put them in with
+
+ align:start position:0%
+lower orbital and you put them in with
+ 
+
+ align:start position:0%
+lower orbital and you put them in with
+anti parallel so in some sense whether
+
+ align:start position:0%
+anti parallel so in some sense whether
+ 
+
+ align:start position:0%
+anti parallel so in some sense whether
+you get a lot of magnetic spin uh a lot
+
+ align:start position:0%
+you get a lot of magnetic spin uh a lot
+ 
+
+ align:start position:0%
+you get a lot of magnetic spin uh a lot
+of Magnetic Moment left over depends on
+
+ align:start position:0%
+of Magnetic Moment left over depends on
+ 
+
+ align:start position:0%
+of Magnetic Moment left over depends on
+how much your orbitals uh will split in
+
+ align:start position:0%
+how much your orbitals uh will split in
+ 
+
+ align:start position:0%
+how much your orbitals uh will split in
+the end but I'm going to show you in the
+
+ align:start position:0%
+the end but I'm going to show you in the
+ 
+
+ align:start position:0%
+the end but I'm going to show you in the
+end that that it can actually have
+
+ align:start position:0%
+end that that it can actually have
+ 
+
+ align:start position:0%
+end that that it can actually have
+significant consequences on the physical
+
+ align:start position:0%
+significant consequences on the physical
+ 
+
+ align:start position:0%
+significant consequences on the physical
+properties of your material
+
+ align:start position:0%
+properties of your material
+ 
+
+ align:start position:0%
+properties of your material
+so your in your density functional
+
+ align:start position:0%
+so your in your density functional
+ 
+
+ align:start position:0%
+so your in your density functional
+Theory calculation you will carry a
+
+ align:start position:0%
+Theory calculation you will carry a
+ 
+
+ align:start position:0%
+Theory calculation you will carry a
+Magnetic Moment locally when the up
+
+ align:start position:0%
+Magnetic Moment locally when the up
+ 
+
+ align:start position:0%
+Magnetic Moment locally when the up
+density and the down density are not the
+
+ align:start position:0%
+density and the down density are not the
+ 
+
+ align:start position:0%
+density and the down density are not the
+same and so I've sort of already given
+
+ align:start position:0%
+same and so I've sort of already given
+ 
+
+ align:start position:0%
+same and so I've sort of already given
+away here how this problem is dealt with
+
+ align:start position:0%
+away here how this problem is dealt with
+ 
+
+ align:start position:0%
+away here how this problem is dealt with
+in density functional
+
+ align:start position:0%
+in density functional
+ 
+
+ align:start position:0%
+in density functional
+Theory um the interesting thing is that
+
+ align:start position:0%
+Theory um the interesting thing is that
+ 
+
+ align:start position:0%
+Theory um the interesting thing is that
+if you think about it very hard uh you
+
+ align:start position:0%
+if you think about it very hard uh you
+ 
+
+ align:start position:0%
+if you think about it very hard uh you
+shouldn't have to deal with spin in
+
+ align:start position:0%
+shouldn't have to deal with spin in
+ 
+
+ align:start position:0%
+shouldn't have to deal with spin in
+density functional Theory um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay some might put me back at my old
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture okay you know in principle
+
+ align:start position:0%
+picture okay you know in principle
+ 
+
+ align:start position:0%
+picture okay you know in principle
+remember that we told you that Professor
+
+ align:start position:0%
+remember that we told you that Professor
+ 
+
+ align:start position:0%
+remember that we told you that Professor
+marari told you that the energy and the
+
+ align:start position:0%
+marari told you that the energy and the
+ 
+
+ align:start position:0%
+marari told you that the energy and the
+potential is a function of the charge
+
+ align:start position:0%
+potential is a function of the charge
+ 
+
+ align:start position:0%
+potential is a function of the charge
+density okay so the charge density
+
+ align:start position:0%
+density okay so the charge density
+ 
+
+ align:start position:0%
+density okay so the charge density
+itself should actually also contain the
+
+ align:start position:0%
+itself should actually also contain the
+ 
+
+ align:start position:0%
+itself should actually also contain the
+information about electron Spin and
+
+ align:start position:0%
+information about electron Spin and
+ 
+
+ align:start position:0%
+information about electron Spin and
+Magnetic Moment even though it doesn't
+
+ align:start position:0%
+Magnetic Moment even though it doesn't
+ 
+
+ align:start position:0%
+Magnetic Moment even though it doesn't
+explicitly contain that okay but for a
+
+ align:start position:0%
+explicitly contain that okay but for a
+ 
+
+ align:start position:0%
+explicitly contain that okay but for a
+given charge density there would
+
+ align:start position:0%
+given charge density there would
+ 
+
+ align:start position:0%
+given charge density there would
+probably be a certain amount of spin
+
+ align:start position:0%
+probably be a certain amount of spin
+ 
+
+ align:start position:0%
+probably be a certain amount of spin
+polarization so it should all be in that
+
+ align:start position:0%
+polarization so it should all be in that
+ 
+
+ align:start position:0%
+polarization so it should all be in that
+functional but remember that's the
+
+ align:start position:0%
+functional but remember that's the
+ 
+
+ align:start position:0%
+functional but remember that's the
+functional that we don't know and so um
+
+ align:start position:0%
+functional that we don't know and so um
+ 
+
+ align:start position:0%
+functional that we don't know and so um
+in practice that doesn't work very well
+
+ align:start position:0%
+in practice that doesn't work very well
+ 
+
+ align:start position:0%
+in practice that doesn't work very well
+so what we do is we really help dense
+
+ align:start position:0%
+so what we do is we really help dense
+ 
+
+ align:start position:0%
+so what we do is we really help dense
+the functional Theory Along by treating
+
+ align:start position:0%
+the functional Theory Along by treating
+ 
+
+ align:start position:0%
+the functional Theory Along by treating
+the up and the down density separately
+
+ align:start position:0%
+the up and the down density separately
+ 
+
+ align:start position:0%
+the up and the down density separately
+but again you should keep in mind that
+
+ align:start position:0%
+but again you should keep in mind that
+ 
+
+ align:start position:0%
+but again you should keep in mind that
+in principle in the formalism of density
+
+ align:start position:0%
+in principle in the formalism of density
+ 
+
+ align:start position:0%
+in principle in the formalism of density
+functional Theory you wouldn't have to
+
+ align:start position:0%
+functional Theory you wouldn't have to
+ 
+
+ align:start position:0%
+functional Theory you wouldn't have to
+do that so if you do um what's called
+
+ align:start position:0%
+do that so if you do um what's called
+ 
+
+ align:start position:0%
+do that so if you do um what's called
+say the local spin density approximation
+
+ align:start position:0%
+say the local spin density approximation
+ 
+
+ align:start position:0%
+say the local spin density approximation
+which is the spin polarized version of
+
+ align:start position:0%
+which is the spin polarized version of
+ 
+
+ align:start position:0%
+which is the spin polarized version of
+the local density approximation it so
+
+ align:start position:0%
+the local density approximation it so
+ 
+
+ align:start position:0%
+the local density approximation it so
+goes under name LSD Luc see in the Sky
+
+ align:start position:0%
+goes under name LSD Luc see in the Sky
+ 
+
+ align:start position:0%
+goes under name LSD Luc see in the Sky
+with Diamonds or
+
+ align:start position:0%
+with Diamonds or
+ 
+
+ align:start position:0%
+with Diamonds or
+lsda uh and there's a version of that
+
+ align:start position:0%
+lsda uh and there's a version of that
+ 
+
+ align:start position:0%
+lsda uh and there's a version of that
+for the GGA which nobody often people
+
+ align:start position:0%
+for the GGA which nobody often people
+ 
+
+ align:start position:0%
+for the GGA which nobody often people
+will just call it LDA or or GGA but they
+
+ align:start position:0%
+will just call it LDA or or GGA but they
+ 
+
+ align:start position:0%
+will just call it LDA or or GGA but they
+will call it sometimes spin polarized
+
+ align:start position:0%
+will call it sometimes spin polarized
+ 
+
+ align:start position:0%
+will call it sometimes spin polarized
+LDA or GGA what you do there is that you
+
+ align:start position:0%
+LDA or GGA what you do there is that you
+ 
+
+ align:start position:0%
+LDA or GGA what you do there is that you
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+separate density for the up electrons
+
+ align:start position:0%
+separate density for the up electrons
+ 
+
+ align:start position:0%
+separate density for the up electrons
+and a separate density for the down
+
+ align:start position:0%
+and a separate density for the down
+ 
+
+ align:start position:0%
+and a separate density for the down
+electrons okay and the two will interact
+
+ align:start position:0%
+electrons okay and the two will interact
+ 
+
+ align:start position:0%
+electrons okay and the two will interact
+differently so the up up will up will
+
+ align:start position:0%
+differently so the up up will up will
+ 
+
+ align:start position:0%
+differently so the up up will up will
+interact differently with up with with
+
+ align:start position:0%
+interact differently with up with with
+ 
+
+ align:start position:0%
+interact differently with up with with
+up than up with down okay and that comes
+
+ align:start position:0%
+up than up with down okay and that comes
+ 
+
+ align:start position:0%
+up than up with down okay and that comes
+from the way the exchange correlation
+
+ align:start position:0%
+from the way the exchange correlation
+ 
+
+ align:start position:0%
+from the way the exchange correlation
+potentials are defined um so
+
+ align:start position:0%
+potentials are defined um so
+ 
+
+ align:start position:0%
+potentials are defined um so
+um I think Professor marari mentioned
+
+ align:start position:0%
+um I think Professor marari mentioned
+ 
+
+ align:start position:0%
+um I think Professor marari mentioned
+restricted and unrestricted heart ful uh
+
+ align:start position:0%
+restricted and unrestricted heart ful uh
+ 
+
+ align:start position:0%
+restricted and unrestricted heart ful uh
+before very briefly and this is
+
+ align:start position:0%
+before very briefly and this is
+ 
+
+ align:start position:0%
+before very briefly and this is
+essentially the same idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um um sort of one quick tip I want to
+
+ align:start position:0%
+um um sort of one quick tip I want to
+ 
+
+ align:start position:0%
+um um sort of one quick tip I want to
+give you is that um if you have spin
+
+ align:start position:0%
+give you is that um if you have spin
+ 
+
+ align:start position:0%
+give you is that um if you have spin
+polarized materials um it's often much
+
+ align:start position:0%
+polarized materials um it's often much
+ 
+
+ align:start position:0%
+polarized materials um it's often much
+more useful to look at spin densities
+
+ align:start position:0%
+more useful to look at spin densities
+ 
+
+ align:start position:0%
+more useful to look at spin densities
+than at charge densities um one of the
+
+ align:start position:0%
+than at charge densities um one of the
+ 
+
+ align:start position:0%
+than at charge densities um one of the
+really cool things about doing quantum
+
+ align:start position:0%
+really cool things about doing quantum
+ 
+
+ align:start position:0%
+really cool things about doing quantum
+mechanics is that you can actually look
+
+ align:start position:0%
+mechanics is that you can actually look
+ 
+
+ align:start position:0%
+mechanics is that you can actually look
+at the charge these and look at the
+
+ align:start position:0%
+at the charge these and look at the
+ 
+
+ align:start position:0%
+at the charge these and look at the
+electrons which you know most people get
+
+ align:start position:0%
+electrons which you know most people get
+ 
+
+ align:start position:0%
+electrons which you know most people get
+very excited about that the first time
+
+ align:start position:0%
+very excited about that the first time
+ 
+
+ align:start position:0%
+very excited about that the first time
+they do quantum mechanics it's kind of
+
+ align:start position:0%
+they do quantum mechanics it's kind of
+ 
+
+ align:start position:0%
+they do quantum mechanics it's kind of
+cool you can look at where the electrons
+
+ align:start position:0%
+cool you can look at where the electrons
+ 
+
+ align:start position:0%
+cool you can look at where the electrons
+go well the first thing you learn is
+
+ align:start position:0%
+go well the first thing you learn is
+ 
+
+ align:start position:0%
+go well the first thing you learn is
+that you don't see much uh when you look
+
+ align:start position:0%
+that you don't see much uh when you look
+ 
+
+ align:start position:0%
+that you don't see much uh when you look
+at charge denes you typically see big
+
+ align:start position:0%
+at charge denes you typically see big
+ 
+
+ align:start position:0%
+at charge denes you typically see big
+blobs of charge and and it's very hard
+
+ align:start position:0%
+blobs of charge and and it's very hard
+ 
+
+ align:start position:0%
+blobs of charge and and it's very hard
+to see any fine structure of bonding in
+
+ align:start position:0%
+to see any fine structure of bonding in
+ 
+
+ align:start position:0%
+to see any fine structure of bonding in
+Blobs of charge density and I wanted to
+
+ align:start position:0%
+Blobs of charge density and I wanted to
+ 
+
+ align:start position:0%
+Blobs of charge density and I wanted to
+show you an example here's lithium
+
+ align:start position:0%
+show you an example here's lithium
+ 
+
+ align:start position:0%
+show you an example here's lithium
+Cobalt oxide is a transition metal oxide
+
+ align:start position:0%
+Cobalt oxide is a transition metal oxide
+ 
+
+ align:start position:0%
+Cobalt oxide is a transition metal oxide
+it's a a layered material layers of
+
+ align:start position:0%
+it's a a layered material layers of
+ 
+
+ align:start position:0%
+it's a a layered material layers of
+oxygen here the red things and then
+
+ align:start position:0%
+oxygen here the red things and then
+ 
+
+ align:start position:0%
+oxygen here the red things and then
+layers of cob and layers of lithium and
+
+ align:start position:0%
+layers of cob and layers of lithium and
+ 
+
+ align:start position:0%
+layers of cob and layers of lithium and
+you know if you plot the charge density
+
+ align:start position:0%
+you know if you plot the charge density
+ 
+
+ align:start position:0%
+you know if you plot the charge density
+in a plane this is actually a plane in
+
+ align:start position:0%
+in a plane this is actually a plane in
+ 
+
+ align:start position:0%
+in a plane this is actually a plane in
+this in the plane of the figure if you
+
+ align:start position:0%
+this in the plane of the figure if you
+ 
+
+ align:start position:0%
+this in the plane of the figure if you
+look at the charge this is a picture of
+
+ align:start position:0%
+look at the charge this is a picture of
+ 
+
+ align:start position:0%
+look at the charge this is a picture of
+the charge density you know you see big
+
+ align:start position:0%
+the charge density you know you see big
+ 
+
+ align:start position:0%
+the charge density you know you see big
+blobs I mean you see the oxygen layers
+
+ align:start position:0%
+blobs I mean you see the oxygen layers
+ 
+
+ align:start position:0%
+blobs I mean you see the oxygen layers
+here remember the oxygen are two minus
+
+ align:start position:0%
+here remember the oxygen are two minus
+ 
+
+ align:start position:0%
+here remember the oxygen are two minus
+so remember that you're showing only the
+
+ align:start position:0%
+so remember that you're showing only the
+ 
+
+ align:start position:0%
+so remember that you're showing only the
+veence electrons so these have a lot of
+
+ align:start position:0%
+veence electrons so these have a lot of
+ 
+
+ align:start position:0%
+veence electrons so these have a lot of
+veence electrons in them so you see a
+
+ align:start position:0%
+veence electrons in them so you see a
+ 
+
+ align:start position:0%
+veence electrons in them so you see a
+lot of intensity um Cobalt has somewhat
+
+ align:start position:0%
+lot of intensity um Cobalt has somewhat
+ 
+
+ align:start position:0%
+lot of intensity um Cobalt has somewhat
+less veence electrons on it so you see
+
+ align:start position:0%
+less veence electrons on it so you see
+ 
+
+ align:start position:0%
+less veence electrons on it so you see
+less intensity there and lithium is
+
+ align:start position:0%
+less intensity there and lithium is
+ 
+
+ align:start position:0%
+less intensity there and lithium is
+ionized to lithium plus so it has no
+
+ align:start position:0%
+ionized to lithium plus so it has no
+ 
+
+ align:start position:0%
+ionized to lithium plus so it has no
+veence electrons on it so you see almost
+
+ align:start position:0%
+veence electrons on it so you see almost
+ 
+
+ align:start position:0%
+veence electrons on it so you see almost
+nothing
+
+ align:start position:0%
+nothing
+ 
+
+ align:start position:0%
+nothing
+here but in Ence this do give you a lot
+
+ align:start position:0%
+here but in Ence this do give you a lot
+ 
+
+ align:start position:0%
+here but in Ence this do give you a lot
+of detail um if you actually take a
+
+ align:start position:0%
+of detail um if you actually take a
+ 
+
+ align:start position:0%
+of detail um if you actually take a
+material like
+
+ align:start position:0%
+material like
+ 
+
+ align:start position:0%
+material like
+this and rather than plot the charge
+
+ align:start position:0%
+this and rather than plot the charge
+ 
+
+ align:start position:0%
+this and rather than plot the charge
+density you plot the spin polarization
+
+ align:start position:0%
+density you plot the spin polarization
+ 
+
+ align:start position:0%
+density you plot the spin polarization
+density so that say up minus down or
+
+ align:start position:0%
+density so that say up minus down or
+ 
+
+ align:start position:0%
+density so that say up minus down or
+down minus up okay so it's how much
+
+ align:start position:0%
+down minus up okay so it's how much
+ 
+
+ align:start position:0%
+down minus up okay so it's how much
+Magnetic Moment there is locally you get
+
+ align:start position:0%
+Magnetic Moment there is locally you get
+ 
+
+ align:start position:0%
+Magnetic Moment there is locally you get
+much cleaner pictures this is the same
+
+ align:start position:0%
+much cleaner pictures this is the same
+ 
+
+ align:start position:0%
+much cleaner pictures this is the same
+picture it's a slightly different
+
+ align:start position:0%
+picture it's a slightly different
+ 
+
+ align:start position:0%
+picture it's a slightly different
+material it's with different ions in it
+
+ align:start position:0%
+material it's with different ions in it
+ 
+
+ align:start position:0%
+material it's with different ions in it
+it's with nickel and manganese in it um
+
+ align:start position:0%
+it's with nickel and manganese in it um
+ 
+
+ align:start position:0%
+it's with nickel and manganese in it um
+but you know here's the oxygen by the
+
+ align:start position:0%
+but you know here's the oxygen by the
+ 
+
+ align:start position:0%
+but you know here's the oxygen by the
+way I should have told you red is the
+
+ align:start position:0%
+way I should have told you red is the
+ 
+
+ align:start position:0%
+way I should have told you red is the
+neutral color in these pictures so it's
+
+ align:start position:0%
+neutral color in these pictures so it's
+ 
+
+ align:start position:0%
+neutral color in these pictures so it's
+zero um so now you don't see the oxygen
+
+ align:start position:0%
+zero um so now you don't see the oxygen
+ 
+
+ align:start position:0%
+zero um so now you don't see the oxygen
+at all and the reason is oxygen doesn't
+
+ align:start position:0%
+at all and the reason is oxygen doesn't
+ 
+
+ align:start position:0%
+at all and the reason is oxygen doesn't
+have spin it's a filled shell every time
+
+ align:start position:0%
+have spin it's a filled shell every time
+ 
+
+ align:start position:0%
+have spin it's a filled shell every time
+you have filled shells you don't have
+
+ align:start position:0%
+you have filled shells you don't have
+ 
+
+ align:start position:0%
+you have filled shells you don't have
+spin so looking at spin density often
+
+ align:start position:0%
+spin so looking at spin density often
+ 
+
+ align:start position:0%
+spin so looking at spin density often
+allows you to filter out certain ions
+
+ align:start position:0%
+allows you to filter out certain ions
+ 
+
+ align:start position:0%
+allows you to filter out certain ions
+and you Lally the transition metals then
+
+ align:start position:0%
+and you Lally the transition metals then
+ 
+
+ align:start position:0%
+and you Lally the transition metals then
+to have spin on them and you see that
+
+ align:start position:0%
+to have spin on them and you see that
+ 
+
+ align:start position:0%
+to have spin on them and you see that
+very clearly um so it's often a a trick
+
+ align:start position:0%
+very clearly um so it's often a a trick
+ 
+
+ align:start position:0%
+very clearly um so it's often a a trick
+that I just wanted to share with you
+
+ align:start position:0%
+that I just wanted to share with you
+ 
+
+ align:start position:0%
+that I just wanted to share with you
+uh okay so what I want to go in sort of
+
+ align:start position:0%
+uh okay so what I want to go in sort of
+ 
+
+ align:start position:0%
+uh okay so what I want to go in sort of
+the last half hour is go through um the
+
+ align:start position:0%
+the last half hour is go through um the
+ 
+
+ align:start position:0%
+the last half hour is go through um the
+kind of numerical accuracy and then
+
+ align:start position:0%
+kind of numerical accuracy and then
+ 
+
+ align:start position:0%
+kind of numerical accuracy and then
+slowly try to connect that to the
+
+ align:start position:0%
+slowly try to connect that to the
+ 
+
+ align:start position:0%
+slowly try to connect that to the
+physical accuracy uh that you get in
+
+ align:start position:0%
+physical accuracy uh that you get in
+ 
+
+ align:start position:0%
+physical accuracy uh that you get in
+properties so you know if you want to
+
+ align:start position:0%
+properties so you know if you want to
+ 
+
+ align:start position:0%
+properties so you know if you want to
+use the abonal methods and density
+
+ align:start position:0%
+use the abonal methods and density
+ 
+
+ align:start position:0%
+use the abonal methods and density
+functional Theory to get to engineering
+
+ align:start position:0%
+functional Theory to get to engineering
+ 
+
+ align:start position:0%
+functional Theory to get to engineering
+properties a lot of steps you have to
+
+ align:start position:0%
+properties a lot of steps you have to
+ 
+
+ align:start position:0%
+properties a lot of steps you have to
+make because in the end we calculate
+
+ align:start position:0%
+make because in the end we calculate
+ 
+
+ align:start position:0%
+make because in the end we calculate
+simple things you know we calculate
+
+ align:start position:0%
+simple things you know we calculate
+ 
+
+ align:start position:0%
+simple things you know we calculate
+charge densities and band structures and
+
+ align:start position:0%
+charge densities and band structures and
+ 
+
+ align:start position:0%
+charge densities and band structures and
+energies and you know you'll talk later
+
+ align:start position:0%
+energies and you know you'll talk later
+ 
+
+ align:start position:0%
+energies and you know you'll talk later
+to somebody and they want to know like
+
+ align:start position:0%
+to somebody and they want to know like
+ 
+
+ align:start position:0%
+to somebody and they want to know like
+you know what's the corrosion resistance
+
+ align:start position:0%
+you know what's the corrosion resistance
+ 
+
+ align:start position:0%
+you know what's the corrosion resistance
+of this and corrosion resistance is not
+
+ align:start position:0%
+of this and corrosion resistance is not
+ 
+
+ align:start position:0%
+of this and corrosion resistance is not
+a Quantum operator um so you need to
+
+ align:start position:0%
+a Quantum operator um so you need to
+ 
+
+ align:start position:0%
+a Quantum operator um so you need to
+take a lot of steps to go from these
+
+ align:start position:0%
+take a lot of steps to go from these
+ 
+
+ align:start position:0%
+take a lot of steps to go from these
+simple what I would call primitive
+
+ align:start position:0%
+simple what I would call primitive
+ 
+
+ align:start position:0%
+simple what I would call primitive
+output to engineering properties but
+
+ align:start position:0%
+output to engineering properties but
+ 
+
+ align:start position:0%
+output to engineering properties but
+before you even take that step you need
+
+ align:start position:0%
+before you even take that step you need
+ 
+
+ align:start position:0%
+before you even take that step you need
+to understand the kind of accuracy how
+
+ align:start position:0%
+to understand the kind of accuracy how
+ 
+
+ align:start position:0%
+to understand the kind of accuracy how
+reliable your output is and so I
+
+ align:start position:0%
+reliable your output is and so I
+ 
+
+ align:start position:0%
+reliable your output is and so I
+collected a lot of results um and you
+
+ align:start position:0%
+collected a lot of results um and you
+ 
+
+ align:start position:0%
+collected a lot of results um and you
+know I was going to start with the
+
+ align:start position:0%
+know I was going to start with the
+ 
+
+ align:start position:0%
+know I was going to start with the
+simple things the energies of the atoms
+
+ align:start position:0%
+simple things the energies of the atoms
+ 
+
+ align:start position:0%
+simple things the energies of the atoms
+um so here's a collection it looks like
+
+ align:start position:0%
+um so here's a collection it looks like
+ 
+
+ align:start position:0%
+um so here's a collection it looks like
+a bunch of numbers but there's a very
+
+ align:start position:0%
+a bunch of numbers but there's a very
+ 
+
+ align:start position:0%
+a bunch of numbers but there's a very
+systematic Trend in it so what I show
+
+ align:start position:0%
+systematic Trend in it so what I show
+ 
+
+ align:start position:0%
+systematic Trend in it so what I show
+for a bunch of atoms and these all
+
+ align:start position:0%
+for a bunch of atoms and these all
+ 
+
+ align:start position:0%
+for a bunch of atoms and these all
+should have a minus sign in front of
+
+ align:start position:0%
+should have a minus sign in front of
+ 
+
+ align:start position:0%
+should have a minus sign in front of
+them because the if you sum up all the
+
+ align:start position:0%
+them because the if you sum up all the
+ 
+
+ align:start position:0%
+them because the if you sum up all the
+electronic states in the atom they're
+
+ align:start position:0%
+electronic states in the atom they're
+ 
+
+ align:start position:0%
+electronic states in the atom they're
+obviously bind binding so um it should
+
+ align:start position:0%
+obviously bind binding so um it should
+ 
+
+ align:start position:0%
+obviously bind binding so um it should
+be negative so there's always the
+
+ align:start position:0%
+be negative so there's always the
+ 
+
+ align:start position:0%
+be negative so there's always the
+experimental line at least for most of
+
+ align:start position:0%
+experimental line at least for most of
+ 
+
+ align:start position:0%
+experimental line at least for most of
+them um the LDA number and then the GGA
+
+ align:start position:0%
+them um the LDA number and then the GGA
+ 
+
+ align:start position:0%
+them um the LDA number and then the GGA
+with a fairly recent implementation of
+
+ align:start position:0%
+with a fairly recent implementation of
+ 
+
+ align:start position:0%
+with a fairly recent implementation of
+the exchange correlation function and so
+
+ align:start position:0%
+the exchange correlation function and so
+ 
+
+ align:start position:0%
+the exchange correlation function and so
+if you look carefully at the numbers um
+
+ align:start position:0%
+if you look carefully at the numbers um
+ 
+
+ align:start position:0%
+if you look carefully at the numbers um
+let's take one here let's take carbon
+
+ align:start position:0%
+let's take one here let's take carbon
+ 
+
+ align:start position:0%
+let's take one here let's take carbon
+for example so experiment is 27 275 688
+
+ align:start position:0%
+for example so experiment is 27 275 688
+ 
+
+ align:start position:0%
+for example so experiment is 27 275 688
+oops that wasn't good um
+
+ align:start position:0%
+oops that wasn't good um
+ 
+
+ align:start position:0%
+oops that wasn't good um
+LDA The Binding energy is somewhat
+
+ align:start position:0%
+LDA The Binding energy is somewhat
+ 
+
+ align:start position:0%
+LDA The Binding energy is somewhat
+weaker it's almost is an electron volt
+
+ align:start position:0%
+weaker it's almost is an electron volt
+ 
+
+ align:start position:0%
+weaker it's almost is an electron volt
+weaker and GGA is slightly closer uh to
+
+ align:start position:0%
+weaker and GGA is slightly closer uh to
+ 
+
+ align:start position:0%
+weaker and GGA is slightly closer uh to
+the experiment um that's typically what
+
+ align:start position:0%
+the experiment um that's typically what
+ 
+
+ align:start position:0%
+the experiment um that's typically what
+you'll see if you look at all the other
+
+ align:start position:0%
+you'll see if you look at all the other
+ 
+
+ align:start position:0%
+you'll see if you look at all the other
+atoms you'll see a very systematic Trend
+
+ align:start position:0%
+atoms you'll see a very systematic Trend
+ 
+
+ align:start position:0%
+atoms you'll see a very systematic Trend
+okay in the ldan the atoms the electrons
+
+ align:start position:0%
+okay in the ldan the atoms the electrons
+ 
+
+ align:start position:0%
+okay in the ldan the atoms the electrons
+are not strong are not bound enough in
+
+ align:start position:0%
+are not strong are not bound enough in
+ 
+
+ align:start position:0%
+are not strong are not bound enough in
+the GGA they are somewhat closer um to
+
+ align:start position:0%
+the GGA they are somewhat closer um to
+ 
+
+ align:start position:0%
+the GGA they are somewhat closer um to
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experiment um it gets more interesting
+
+ align:start position:0%
+experiment um it gets more interesting
+ 
+
+ align:start position:0%
+experiment um it gets more interesting
+when you look at molecules uh because
+
+ align:start position:0%
+when you look at molecules uh because
+ 
+
+ align:start position:0%
+when you look at molecules uh because
+now you can talk about a physical
+
+ align:start position:0%
+now you can talk about a physical
+ 
+
+ align:start position:0%
+now you can talk about a physical
+binding energy and so the one we we look
+
+ align:start position:0%
+binding energy and so the one we we look
+ 
+
+ align:start position:0%
+binding energy and so the one we we look
+at here is for very simple uh diatomic
+
+ align:start position:0%
+at here is for very simple uh diatomic
+ 
+
+ align:start position:0%
+at here is for very simple uh diatomic
+Mo molecules what's their binding energy
+
+ align:start position:0%
+Mo molecules what's their binding energy
+ 
+
+ align:start position:0%
+Mo molecules what's their binding energy
+so what's their energy to pull them
+
+ align:start position:0%
+so what's their energy to pull them
+ 
+
+ align:start position:0%
+so what's their energy to pull them
+apart so you know if you think about it
+
+ align:start position:0%
+apart so you know if you think about it
+ 
+
+ align:start position:0%
+apart so you know if you think about it
+if you have a molecule as a you know and
+
+ align:start position:0%
+if you have a molecule as a you know and
+ 
+
+ align:start position:0%
+if you have a molecule as a you know and
+ab this is the this the vector between
+
+ align:start position:0%
+ab this is the this the vector between
+ 
+
+ align:start position:0%
+ab this is the this the vector between
+them you know you'll have sort of
+
+ align:start position:0%
+them you know you'll have sort of
+ 
+
+ align:start position:0%
+them you know you'll have sort of
+something that looks like this uh and so
+
+ align:start position:0%
+something that looks like this uh and so
+ 
+
+ align:start position:0%
+something that looks like this uh and so
+we're looking at what's that well depth
+
+ align:start position:0%
+we're looking at what's that well depth
+ 
+
+ align:start position:0%
+we're looking at what's that well depth
+here The Binding
+
+ align:start position:0%
+here The Binding
+ 
+
+ align:start position:0%
+here The Binding
+energy okay if you look at hydrogen H2
+
+ align:start position:0%
+energy okay if you look at hydrogen H2
+ 
+
+ align:start position:0%
+energy okay if you look at hydrogen H2
+you have the experimental number here
+
+ align:start position:0%
+you have the experimental number here
+ 
+
+ align:start position:0%
+you have the experimental number here
+the LDA number you see now that the LDA
+
+ align:start position:0%
+the LDA number you see now that the LDA
+ 
+
+ align:start position:0%
+the LDA number you see now that the LDA
+number that the binding is too strong
+
+ align:start position:0%
+number that the binding is too strong
+ 
+
+ align:start position:0%
+number that the binding is too strong
+the H2 molecule is bound too strongly
+
+ align:start position:0%
+the H2 molecule is bound too strongly
+ 
+
+ align:start position:0%
+the H2 molecule is bound too strongly
+it's not so bad it's only about 5% in
+
+ align:start position:0%
+it's not so bad it's only about 5% in
+ 
+
+ align:start position:0%
+it's not so bad it's only about 5% in
+hydrogen and the GGA The Binding is too
+
+ align:start position:0%
+hydrogen and the GGA The Binding is too
+ 
+
+ align:start position:0%
+hydrogen and the GGA The Binding is too
+weak okay for reference I've also put
+
+ align:start position:0%
+weak okay for reference I've also put
+ 
+
+ align:start position:0%
+weak okay for reference I've also put
+uncorrected heart Fu in here Professor
+
+ align:start position:0%
+uncorrected heart Fu in here Professor
+ 
+
+ align:start position:0%
+uncorrected heart Fu in here Professor
+marar showed you essentially what heart
+
+ align:start position:0%
+marar showed you essentially what heart
+ 
+
+ align:start position:0%
+marar showed you essentially what heart
+refu is uh which is essentially having
+
+ align:start position:0%
+refu is uh which is essentially having
+ 
+
+ align:start position:0%
+refu is uh which is essentially having
+the heart ter so the self-consistent
+
+ align:start position:0%
+the heart ter so the self-consistent
+ 
+
+ align:start position:0%
+the heart ter so the self-consistent
+colum interaction from the other
+
+ align:start position:0%
+colum interaction from the other
+ 
+
+ align:start position:0%
+colum interaction from the other
+electrons and the exact exchange but no
+
+ align:start position:0%
+electrons and the exact exchange but no
+ 
+
+ align:start position:0%
+electrons and the exact exchange but no
+correlation effects okay um this is an
+
+ align:start position:0%
+correlation effects okay um this is an
+ 
+
+ align:start position:0%
+correlation effects okay um this is an
+interesting one that you will actually
+
+ align:start position:0%
+interesting one that you will actually
+ 
+
+ align:start position:0%
+interesting one that you will actually
+often use or
+
+ align:start position:0%
+often use or
+ 
+
+ align:start position:0%
+often use or
+two anytime you look at oxidation
+
+ align:start position:0%
+two anytime you look at oxidation
+ 
+
+ align:start position:0%
+two anytime you look at oxidation
+reactions for example experiment oxygen
+
+ align:start position:0%
+reactions for example experiment oxygen
+ 
+
+ align:start position:0%
+reactions for example experiment oxygen
+is only about minus 5.2 EV binding LDA
+
+ align:start position:0%
+is only about minus 5.2 EV binding LDA
+ 
+
+ align:start position:0%
+is only about minus 5.2 EV binding LDA
+binds it by a whopping 7 and a
+
+ align:start position:0%
+binds it by a whopping 7 and a
+ 
+
+ align:start position:0%
+binds it by a whopping 7 and a
+half okay so you're more than two
+
+ align:start position:0%
+half okay so you're more than two
+ 
+
+ align:start position:0%
+half okay so you're more than two
+electron volt
+
+ align:start position:0%
+electron volt
+ 
+
+ align:start position:0%
+electron volt
+uh GGA gets you a little closer in this
+
+ align:start position:0%
+uh GGA gets you a little closer in this
+ 
+
+ align:start position:0%
+uh GGA gets you a little closer in this
+case Okay um heartre uncorrected heart
+
+ align:start position:0%
+case Okay um heartre uncorrected heart
+ 
+
+ align:start position:0%
+case Okay um heartre uncorrected heart
+refu is is is off the charts okay and
+
+ align:start position:0%
+refu is is is off the charts okay and
+ 
+
+ align:start position:0%
+refu is is is off the charts okay and
+this is something you'll generically see
+
+ align:start position:0%
+this is something you'll generically see
+ 
+
+ align:start position:0%
+this is something you'll generically see
+uncorrected heart refu very few people
+
+ align:start position:0%
+uncorrected heart refu very few people
+ 
+
+ align:start position:0%
+uncorrected heart refu very few people
+would actually use that anymore it's
+
+ align:start position:0%
+would actually use that anymore it's
+ 
+
+ align:start position:0%
+would actually use that anymore it's
+sort of for binding energies way off the
+
+ align:start position:0%
+sort of for binding energies way off the
+ 
+
+ align:start position:0%
+sort of for binding energies way off the
+charts um you know these things are
+
+ align:start position:0%
+charts um you know these things are
+ 
+
+ align:start position:0%
+charts um you know these things are
+important if you now let's say you want
+
+ align:start position:0%
+important if you now let's say you want
+ 
+
+ align:start position:0%
+important if you now let's say you want
+to look at an oxidation reaction so that
+
+ align:start position:0%
+to look at an oxidation reaction so that
+ 
+
+ align:start position:0%
+to look at an oxidation reaction so that
+means that at some point you're going to
+
+ align:start position:0%
+means that at some point you're going to
+ 
+
+ align:start position:0%
+means that at some point you're going to
+calculate the state of an
+
+ align:start position:0%
+calculate the state of an
+ 
+
+ align:start position:0%
+calculate the state of an
+oxide and compare the chemical potential
+
+ align:start position:0%
+oxide and compare the chemical potential
+ 
+
+ align:start position:0%
+oxide and compare the chemical potential
+of the oxygen there to that of oxygen
+
+ align:start position:0%
+of the oxygen there to that of oxygen
+ 
+
+ align:start position:0%
+of the oxygen there to that of oxygen
+gas okay so of course you have a big
+
+ align:start position:0%
+gas okay so of course you have a big
+ 
+
+ align:start position:0%
+gas okay so of course you have a big
+error in the oxygen
+
+ align:start position:0%
+error in the oxygen
+ 
+
+ align:start position:0%
+error in the oxygen
+gas the question is how much of that
+
+ align:start position:0%
+gas the question is how much of that
+ 
+
+ align:start position:0%
+gas the question is how much of that
+error carries over to the solid if you
+
+ align:start position:0%
+error carries over to the solid if you
+ 
+
+ align:start position:0%
+error carries over to the solid if you
+make exactly the same error in the solid
+
+ align:start position:0%
+make exactly the same error in the solid
+ 
+
+ align:start position:0%
+make exactly the same error in the solid
+then the reaction energy is perfect
+
+ align:start position:0%
+then the reaction energy is perfect
+ 
+
+ align:start position:0%
+then the reaction energy is perfect
+because you're going to subtract the two
+
+ align:start position:0%
+because you're going to subtract the two
+ 
+
+ align:start position:0%
+because you're going to subtract the two
+and a lot of practical things you do
+
+ align:start position:0%
+and a lot of practical things you do
+ 
+
+ align:start position:0%
+and a lot of practical things you do
+with density functional T depend on
+
+ align:start position:0%
+with density functional T depend on
+ 
+
+ align:start position:0%
+with density functional T depend on
+error counts
+
+ align:start position:0%
+error counts
+ 
+
+ align:start position:0%
+error counts
+ation okay the thing is that you will
+
+ align:start position:0%
+ation okay the thing is that you will
+ 
+
+ align:start position:0%
+ation okay the thing is that you will
+have more airor cancellation as the
+
+ align:start position:0%
+have more airor cancellation as the
+ 
+
+ align:start position:0%
+have more airor cancellation as the
+states that you subtract are more
+
+ align:start position:0%
+states that you subtract are more
+ 
+
+ align:start position:0%
+states that you subtract are more
+physical are more physically similar but
+
+ align:start position:0%
+physical are more physically similar but
+ 
+
+ align:start position:0%
+physical are more physically similar but
+the problem is let's say you look at
+
+ align:start position:0%
+the problem is let's say you look at
+ 
+
+ align:start position:0%
+the problem is let's say you look at
+oxidation of a metal aluminum plus
+
+ align:start position:0%
+oxidation of a metal aluminum plus
+ 
+
+ align:start position:0%
+oxidation of a metal aluminum plus
+oxygen going to aluminum oxygen oxide
+
+ align:start position:0%
+oxygen going to aluminum oxygen oxide
+ 
+
+ align:start position:0%
+oxygen going to aluminum oxygen oxide
+the oxygen in aluminum oxide is very
+
+ align:start position:0%
+the oxygen in aluminum oxide is very
+ 
+
+ align:start position:0%
+the oxygen in aluminum oxide is very
+different from the oxygen in the O2
+
+ align:start position:0%
+different from the oxygen in the O2
+ 
+
+ align:start position:0%
+different from the oxygen in the O2
+molecule so not all the error will
+
+ align:start position:0%
+molecule so not all the error will
+ 
+
+ align:start position:0%
+molecule so not all the error will
+cancel you know let's say it was so bad
+
+ align:start position:0%
+cancel you know let's say it was so bad
+ 
+
+ align:start position:0%
+cancel you know let's say it was so bad
+that you kept two EV
+
+ align:start position:0%
+that you kept two EV
+ 
+
+ align:start position:0%
+that you kept two EV
+error in so 2 EV error in the in the
+
+ align:start position:0%
+error in so 2 EV error in the in the
+ 
+
+ align:start position:0%
+error in so 2 EV error in the in the
+molecule is one EV per oxygen if you
+
+ align:start position:0%
+molecule is one EV per oxygen if you
+ 
+
+ align:start position:0%
+molecule is one EV per oxygen if you
+want to think of it that way you know if
+
+ align:start position:0%
+want to think of it that way you know if
+ 
+
+ align:start position:0%
+want to think of it that way you know if
+you don't if you're not careful about
+
+ align:start position:0%
+you don't if you're not careful about
+ 
+
+ align:start position:0%
+you don't if you're not careful about
+that's an enormous effect uh think about
+
+ align:start position:0%
+that's an enormous effect uh think about
+ 
+
+ align:start position:0%
+that's an enormous effect uh think about
+it the chemical potential which relates
+
+ align:start position:0%
+it the chemical potential which relates
+ 
+
+ align:start position:0%
+it the chemical potential which relates
+directly to the energy goes like the
+
+ align:start position:0%
+directly to the energy goes like the
+ 
+
+ align:start position:0%
+directly to the energy goes like the
+logarithm of the partial pressure of
+
+ align:start position:0%
+logarithm of the partial pressure of
+ 
+
+ align:start position:0%
+logarithm of the partial pressure of
+oxygen okay remember that mu is Mu plus
+
+ align:start position:0%
+oxygen okay remember that mu is Mu plus
+ 
+
+ align:start position:0%
+oxygen okay remember that mu is Mu plus
+RT log P so if you now invert that that
+
+ align:start position:0%
+RT log P so if you now invert that that
+ 
+
+ align:start position:0%
+RT log P so if you now invert that that
+means you're if you want to calculate
+
+ align:start position:0%
+means you're if you want to calculate
+ 
+
+ align:start position:0%
+means you're if you want to calculate
+say a partial pressure of oxygen at
+
+ align:start position:0%
+say a partial pressure of oxygen at
+ 
+
+ align:start position:0%
+say a partial pressure of oxygen at
+which something oxidized
+
+ align:start position:0%
+which something oxidized
+ 
+
+ align:start position:0%
+which something oxidized
+your oxygen pressure goes exponentially
+
+ align:start position:0%
+your oxygen pressure goes exponentially
+ 
+
+ align:start position:0%
+your oxygen pressure goes exponentially
+with the
+
+ align:start position:0%
+with the
+ 
+
+ align:start position:0%
+with the
+energetics okay so if you have a 1 EV
+
+ align:start position:0%
+energetics okay so if you have a 1 EV
+ 
+
+ align:start position:0%
+energetics okay so if you have a 1 EV
+error at room temperature your error in
+
+ align:start position:0%
+error at room temperature your error in
+ 
+
+ align:start position:0%
+error at room temperature your error in
+the oxygen
+
+ align:start position:0%
+the oxygen
+ 
+
+ align:start position:0%
+the oxygen
+pressure is the exponential of 1 EV over
+
+ align:start position:0%
+pressure is the exponential of 1 EV over
+ 
+
+ align:start position:0%
+pressure is the exponential of 1 EV over
+KT which you know is off the
+
+ align:start position:0%
+KT which you know is off the
+ 
+
+ align:start position:0%
+KT which you know is off the
+charts so you have to be a little
+
+ align:start position:0%
+charts so you have to be a little
+ 
+
+ align:start position:0%
+charts so you have to be a little
+careful with these kind of um error
+
+ align:start position:0%
+careful with these kind of um error
+ 
+
+ align:start position:0%
+careful with these kind of um error
+calibrations
+
+ align:start position:0%
+calibrations
+ 
+
+ align:start position:0%
+calibrations
+fortunately uh we'll see later when we
+
+ align:start position:0%
+fortunately uh we'll see later when we
+ 
+
+ align:start position:0%
+fortunately uh we'll see later when we
+look at reaction between solid most of
+
+ align:start position:0%
+look at reaction between solid most of
+ 
+
+ align:start position:0%
+look at reaction between solid most of
+the error tends to cancel and we get
+
+ align:start position:0%
+the error tends to cancel and we get
+ 
+
+ align:start position:0%
+the error tends to cancel and we get
+much much better accuracy if all our
+
+ align:start position:0%
+much much better accuracy if all our
+ 
+
+ align:start position:0%
+much much better accuracy if all our
+reaction energies were wrong by one EV
+
+ align:start position:0%
+reaction energies were wrong by one EV
+ 
+
+ align:start position:0%
+reaction energies were wrong by one EV
+uh you know we wouldn't be here we'd be
+
+ align:start position:0%
+uh you know we wouldn't be here we'd be
+ 
+
+ align:start position:0%
+uh you know we wouldn't be here we'd be
+out of business um but you have to keep
+
+ align:start position:0%
+out of business um but you have to keep
+ 
+
+ align:start position:0%
+out of business um but you have to keep
+in mind that you get less error
+
+ align:start position:0%
+in mind that you get less error
+ 
+
+ align:start position:0%
+in mind that you get less error
+cancellation as the states you're
+
+ align:start position:0%
+cancellation as the states you're
+ 
+
+ align:start position:0%
+cancellation as the states you're
+comparing are different the more they're
+
+ align:start position:0%
+comparing are different the more they're
+ 
+
+ align:start position:0%
+comparing are different the more they're
+different the less error cancellation
+
+ align:start position:0%
+different the less error cancellation
+ 
+
+ align:start position:0%
+different the less error cancellation
+that's sort of a rule of thumb and so
+
+ align:start position:0%
+that's sort of a rule of thumb and so
+ 
+
+ align:start position:0%
+that's sort of a rule of thumb and so
+going from a gas to a solid is a
+
+ align:start position:0%
+going from a gas to a solid is a
+ 
+
+ align:start position:0%
+going from a gas to a solid is a
+significant difference you know often
+
+ align:start position:0%
+significant difference you know often
+ 
+
+ align:start position:0%
+significant difference you know often
+what people do is that you know if you
+
+ align:start position:0%
+what people do is that you know if you
+ 
+
+ align:start position:0%
+what people do is that you know if you
+want to get practical results they'll
+
+ align:start position:0%
+want to get practical results they'll
+ 
+
+ align:start position:0%
+want to get practical results they'll
+add a correction to this which they fit
+
+ align:start position:0%
+add a correction to this which they fit
+ 
+
+ align:start position:0%
+add a correction to this which they fit
+at one
+
+ align:start position:0%
+at one
+ 
+
+ align:start position:0%
+at one
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+okay so these are the small molecules
+
+ align:start position:0%
+okay so these are the small molecules
+ 
+
+ align:start position:0%
+okay so these are the small molecules
+let's go to the
+
+ align:start position:0%
+let's go to the
+ 
+
+ align:start position:0%
+let's go to the
+solids um here I don't have the binding
+
+ align:start position:0%
+solids um here I don't have the binding
+ 
+
+ align:start position:0%
+solids um here I don't have the binding
+energies but I have the lattice
+
+ align:start position:0%
+energies but I have the lattice
+ 
+
+ align:start position:0%
+energies but I have the lattice
+parameters but you'll see something
+
+ align:start position:0%
+parameters but you'll see something
+ 
+
+ align:start position:0%
+parameters but you'll see something
+that's very um consistent with the
+
+ align:start position:0%
+that's very um consistent with the
+ 
+
+ align:start position:0%
+that's very um consistent with the
+molecules um if you look at the lce
+
+ align:start position:0%
+molecules um if you look at the lce
+ 
+
+ align:start position:0%
+molecules um if you look at the lce
+parameters you compare say the
+
+ align:start position:0%
+parameters you compare say the
+ 
+
+ align:start position:0%
+parameters you compare say the
+experimental ones versus the LDA ones
+
+ align:start position:0%
+experimental ones versus the LDA ones
+ 
+
+ align:start position:0%
+experimental ones versus the LDA ones
+what you'll see is that the LDA ones
+
+ align:start position:0%
+what you'll see is that the LDA ones
+ 
+
+ align:start position:0%
+what you'll see is that the LDA ones
+almost always and I think all always in
+
+ align:start position:0%
+almost always and I think all always in
+ 
+
+ align:start position:0%
+almost always and I think all always in
+this case are
+
+ align:start position:0%
+this case are
+ 
+
+ align:start position:0%
+this case are
+smaller actually yeah because the the
+
+ align:start position:0%
+smaller actually yeah because the the
+ 
+
+ align:start position:0%
+smaller actually yeah because the the
+difference is actually negative uh the
+
+ align:start position:0%
+difference is actually negative uh the
+ 
+
+ align:start position:0%
+difference is actually negative uh the
+GGA results are always
+
+ align:start position:0%
+GGA results are always
+ 
+
+ align:start position:0%
+GGA results are always
+bigger okay um this is rather consistent
+
+ align:start position:0%
+bigger okay um this is rather consistent
+ 
+
+ align:start position:0%
+bigger okay um this is rather consistent
+whatever material you do you will find
+
+ align:start position:0%
+whatever material you do you will find
+ 
+
+ align:start position:0%
+whatever material you do you will find
+uh almost always that the
+
+ align:start position:0%
+uh almost always that the
+ 
+
+ align:start position:0%
+uh almost always that the
+LDA uh gives you lat parameters that are
+
+ align:start position:0%
+LDA uh gives you lat parameters that are
+ 
+
+ align:start position:0%
+LDA uh gives you lat parameters that are
+too small by a factor of a percent
+
+ align:start position:0%
+too small by a factor of a percent
+ 
+
+ align:start position:0%
+too small by a factor of a percent
+sometimes 2% uh and so people refer to
+
+ align:start position:0%
+sometimes 2% uh and so people refer to
+ 
+
+ align:start position:0%
+sometimes 2% uh and so people refer to
+as that as the overbinding of LDA LDA
+
+ align:start position:0%
+as that as the overbinding of LDA LDA
+ 
+
+ align:start position:0%
+as that as the overbinding of LDA LDA
+binds somewhat too strongly remember you
+
+ align:start position:0%
+binds somewhat too strongly remember you
+ 
+
+ align:start position:0%
+binds somewhat too strongly remember you
+saw that in the molecules as well oxygen
+
+ align:start position:0%
+saw that in the molecules as well oxygen
+ 
+
+ align:start position:0%
+saw that in the molecules as well oxygen
+had a 7 EV binding energy and it should
+
+ align:start position:0%
+had a 7 EV binding energy and it should
+ 
+
+ align:start position:0%
+had a 7 EV binding energy and it should
+only have a 5 EV binding energy and so
+
+ align:start position:0%
+only have a 5 EV binding energy and so
+ 
+
+ align:start position:0%
+only have a 5 EV binding energy and so
+in solids the way that comes out is that
+
+ align:start position:0%
+in solids the way that comes out is that
+ 
+
+ align:start position:0%
+in solids the way that comes out is that
+your equilibrium lus parameter is
+
+ align:start position:0%
+your equilibrium lus parameter is
+ 
+
+ align:start position:0%
+your equilibrium lus parameter is
+slightly too small um actually I'm not
+
+ align:start position:0%
+slightly too small um actually I'm not
+ 
+
+ align:start position:0%
+slightly too small um actually I'm not
+sure that I know of a single result
+
+ align:start position:0%
+sure that I know of a single result
+ 
+
+ align:start position:0%
+sure that I know of a single result
+where LDA gives a l par that's too big
+
+ align:start position:0%
+where LDA gives a l par that's too big
+ 
+
+ align:start position:0%
+where LDA gives a l par that's too big
+I've seen that on some occasions in
+
+ align:start position:0%
+I've seen that on some occasions in
+ 
+
+ align:start position:0%
+I've seen that on some occasions in
+papers but it's almost always an
+
+ align:start position:0%
+papers but it's almost always an
+ 
+
+ align:start position:0%
+papers but it's almost always an
+indication that the people did the
+
+ align:start position:0%
+indication that the people did the
+ 
+
+ align:start position:0%
+indication that the people did the
+calculation
+
+ align:start position:0%
+calculation
+ 
+
+ align:start position:0%
+calculation
+wrong okay actually ND that agrees with
+
+ align:start position:0%
+wrong okay actually ND that agrees with
+ 
+
+ align:start position:0%
+wrong okay actually ND that agrees with
+experiment is usually wrong a wrong
+
+ align:start position:0%
+experiment is usually wrong a wrong
+ 
+
+ align:start position:0%
+experiment is usually wrong a wrong
+calculation GGA is much more um
+
+ align:start position:0%
+calculation GGA is much more um
+ 
+
+ align:start position:0%
+calculation GGA is much more um
+unpredictable the ones that I've shown
+
+ align:start position:0%
+unpredictable the ones that I've shown
+ 
+
+ align:start position:0%
+unpredictable the ones that I've shown
+here because they're simple metals and
+
+ align:start position:0%
+here because they're simple metals and
+ 
+
+ align:start position:0%
+here because they're simple metals and
+semiconductors give you a latus
+
+ align:start position:0%
+semiconductors give you a latus
+ 
+
+ align:start position:0%
+semiconductors give you a latus
+parameter that's too large in GGA it's
+
+ align:start position:0%
+parameter that's too large in GGA it's
+ 
+
+ align:start position:0%
+parameter that's too large in GGA it's
+actually also possible to give a
+
+ align:start position:0%
+actually also possible to give a
+ 
+
+ align:start position:0%
+actually also possible to give a
+parameter that's too small though it's
+
+ align:start position:0%
+parameter that's too small though it's
+ 
+
+ align:start position:0%
+parameter that's too small though it's
+rare most of the time you're on the
+
+ align:start position:0%
+rare most of the time you're on the
+ 
+
+ align:start position:0%
+rare most of the time you're on the
+higher side but it's less predictable
+
+ align:start position:0%
+higher side but it's less predictable
+ 
+
+ align:start position:0%
+higher side but it's less predictable
+and that's sort of slightly problematic
+
+ align:start position:0%
+and that's sort of slightly problematic
+ 
+
+ align:start position:0%
+and that's sort of slightly problematic
+with the GGA you know in LDA you know a
+
+ align:start position:0%
+with the GGA you know in LDA you know a
+ 
+
+ align:start position:0%
+with the GGA you know in LDA you know a
+good guess of the latus param you
+
+ align:start position:0%
+good guess of the latus param you
+ 
+
+ align:start position:0%
+good guess of the latus param you
+calculate your latus parameter and you
+
+ align:start position:0%
+calculate your latus parameter and you
+ 
+
+ align:start position:0%
+calculate your latus parameter and you
+know you're on the low side you always
+
+ align:start position:0%
+know you're on the low side you always
+ 
+
+ align:start position:0%
+know you're on the low side you always
+know that the real ad par is going to be
+
+ align:start position:0%
+know that the real ad par is going to be
+ 
+
+ align:start position:0%
+know that the real ad par is going to be
+bigger in GGA it's slightly more
+
+ align:start position:0%
+bigger in GGA it's slightly more
+ 
+
+ align:start position:0%
+bigger in GGA it's slightly more
+difficult to predict on which side you
+
+ align:start position:0%
+difficult to predict on which side you
+ 
+
+ align:start position:0%
+difficult to predict on which side you
+are uh though in metals you do tend to
+
+ align:start position:0%
+are uh though in metals you do tend to
+ 
+
+ align:start position:0%
+are uh though in metals you do tend to
+be on the high
+
+ align:start position:0%
+be on the high
+ 
+
+ align:start position:0%
+be on the high
+side um that actually has consequences
+
+ align:start position:0%
+side um that actually has consequences
+ 
+
+ align:start position:0%
+side um that actually has consequences
+for other properties like the bulk
+
+ align:start position:0%
+for other properties like the bulk
+ 
+
+ align:start position:0%
+for other properties like the bulk
+modulus um if you compare say the
+
+ align:start position:0%
+modulus um if you compare say the
+ 
+
+ align:start position:0%
+modulus um if you compare say the
+experimental bulk modulus to the LDA one
+
+ align:start position:0%
+experimental bulk modulus to the LDA one
+ 
+
+ align:start position:0%
+experimental bulk modulus to the LDA one
+what you'll find is that in almost all
+
+ align:start position:0%
+what you'll find is that in almost all
+ 
+
+ align:start position:0%
+what you'll find is that in almost all
+cases and I think in all cases that I've
+
+ align:start position:0%
+cases and I think in all cases that I've
+ 
+
+ align:start position:0%
+cases and I think in all cases that I've
+shown well case except silicon um the
+
+ align:start position:0%
+shown well case except silicon um the
+ 
+
+ align:start position:0%
+shown well case except silicon um the
+LDA bulk modulus is too large so the
+
+ align:start position:0%
+LDA bulk modulus is too large so the
+ 
+
+ align:start position:0%
+LDA bulk modulus is too large so the
+material is too stiff that means and
+
+ align:start position:0%
+material is too stiff that means and
+ 
+
+ align:start position:0%
+material is too stiff that means and
+that kind of goes together with the
+
+ align:start position:0%
+that kind of goes together with the
+ 
+
+ align:start position:0%
+that kind of goes together with the
+overbinding you know remember the
+
+ align:start position:0%
+overbinding you know remember the
+ 
+
+ align:start position:0%
+overbinding you know remember the
+bonding energy is too high the lattice
+
+ align:start position:0%
+bonding energy is too high the lattice
+ 
+
+ align:start position:0%
+bonding energy is too high the lattice
+parameter too small all that is kind of
+
+ align:start position:0%
+parameter too small all that is kind of
+ 
+
+ align:start position:0%
+parameter too small all that is kind of
+in agreement with the material also
+
+ align:start position:0%
+in agreement with the material also
+ 
+
+ align:start position:0%
+in agreement with the material also
+being too stiff as you compress a
+
+ align:start position:0%
+being too stiff as you compress a
+ 
+
+ align:start position:0%
+being too stiff as you compress a
+material it gets stiffer okay GGA most
+
+ align:start position:0%
+material it gets stiffer okay GGA most
+ 
+
+ align:start position:0%
+material it gets stiffer okay GGA most
+of the time if you see from deviation
+
+ align:start position:0%
+of the time if you see from deviation
+ 
+
+ align:start position:0%
+of the time if you see from deviation
+has to be on the other side okay it
+
+ align:start position:0%
+has to be on the other side okay it
+ 
+
+ align:start position:0%
+has to be on the other side okay it
+tends to be too soft and and you know
+
+ align:start position:0%
+tends to be too soft and and you know
+ 
+
+ align:start position:0%
+tends to be too soft and and you know
+bulk modulus effects that will transfer
+
+ align:start position:0%
+bulk modulus effects that will transfer
+ 
+
+ align:start position:0%
+bulk modulus effects that will transfer
+for example also into vibrational
+
+ align:start position:0%
+for example also into vibrational
+ 
+
+ align:start position:0%
+for example also into vibrational
+frequencies okay in material you know
+
+ align:start position:0%
+frequencies okay in material you know
+ 
+
+ align:start position:0%
+frequencies okay in material you know
+when you're too hard too stiff you'll
+
+ align:start position:0%
+when you're too hard too stiff you'll
+ 
+
+ align:start position:0%
+when you're too hard too stiff you'll
+have higher vibrational frequency when
+
+ align:start position:0%
+have higher vibrational frequency when
+ 
+
+ align:start position:0%
+have higher vibrational frequency when
+you're too soft you'll have lower
+
+ align:start position:0%
+you're too soft you'll have lower
+ 
+
+ align:start position:0%
+you're too soft you'll have lower
+vibrational
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequencies okay you know here's the
+
+ align:start position:0%
+frequencies okay you know here's the
+ 
+
+ align:start position:0%
+frequencies okay you know here's the
+same for oxides you're not exactly
+
+ align:start position:0%
+same for oxides you're not exactly
+ 
+
+ align:start position:0%
+same for oxides you're not exactly
+learning a lot new by looking at them
+
+ align:start position:0%
+learning a lot new by looking at them
+ 
+
+ align:start position:0%
+learning a lot new by looking at them
+except that in oxides the erors just
+
+ align:start position:0%
+except that in oxides the erors just
+ 
+
+ align:start position:0%
+except that in oxides the erors just
+tend to be slightly larger um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so here's a summary for geometry
+
+ align:start position:0%
+okay so here's a summary for geometry
+ 
+
+ align:start position:0%
+okay so here's a summary for geometry
+prediction um you almost always and I
+
+ align:start position:0%
+prediction um you almost always and I
+ 
+
+ align:start position:0%
+prediction um you almost always and I
+would probably say oh was underpredict
+
+ align:start position:0%
+would probably say oh was underpredict
+ 
+
+ align:start position:0%
+would probably say oh was underpredict
+with LDA less systematic error with GGA
+
+ align:start position:0%
+with LDA less systematic error with GGA
+ 
+
+ align:start position:0%
+with LDA less systematic error with GGA
+um for normal materials like
+
+ align:start position:0%
+um for normal materials like
+ 
+
+ align:start position:0%
+um for normal materials like
+semiconductors metals often your errors
+
+ align:start position:0%
+semiconductors metals often your errors
+ 
+
+ align:start position:0%
+semiconductors metals often your errors
+are confined to order 1 to
+
+ align:start position:0%
+are confined to order 1 to
+ 
+
+ align:start position:0%
+are confined to order 1 to
+2% um in transition metal oxides and I
+
+ align:start position:0%
+2% um in transition metal oxides and I
+ 
+
+ align:start position:0%
+2% um in transition metal oxides and I
+have a chance I'll say a little more
+
+ align:start position:0%
+have a chance I'll say a little more
+ 
+
+ align:start position:0%
+have a chance I'll say a little more
+about that later because they have
+
+ align:start position:0%
+about that later because they have
+ 
+
+ align:start position:0%
+about that later because they have
+electronic structures where the LDA and
+
+ align:start position:0%
+electronic structures where the LDA and
+ 
+
+ align:start position:0%
+electronic structures where the LDA and
+GGA approximations are particularly
+
+ align:start position:0%
+GGA approximations are particularly
+ 
+
+ align:start position:0%
+GGA approximations are particularly
+harsh on uh you tend to have somewhat
+
+ align:start position:0%
+harsh on uh you tend to have somewhat
+ 
+
+ align:start position:0%
+harsh on uh you tend to have somewhat
+bigger errors uh but I may say a little
+
+ align:start position:0%
+bigger errors uh but I may say a little
+ 
+
+ align:start position:0%
+bigger errors uh but I may say a little
+more about that if we get to it okay so
+
+ align:start position:0%
+more about that if we get to it okay so
+ 
+
+ align:start position:0%
+more about that if we get to it okay so
+I I want to say something about
+
+ align:start position:0%
+I I want to say something about
+ 
+
+ align:start position:0%
+I I want to say something about
+predicting structure and about the
+
+ align:start position:0%
+predicting structure and about the
+ 
+
+ align:start position:0%
+predicting structure and about the
+energy scale that's required um so this
+
+ align:start position:0%
+energy scale that's required um so this
+ 
+
+ align:start position:0%
+energy scale that's required um so this
+is often something you want to do you
+
+ align:start position:0%
+is often something you want to do you
+ 
+
+ align:start position:0%
+is often something you want to do you
+want to know like you know if I put my
+
+ align:start position:0%
+want to know like you know if I put my
+ 
+
+ align:start position:0%
+want to know like you know if I put my
+energies in this Arrangement is that
+
+ align:start position:0%
+energies in this Arrangement is that
+ 
+
+ align:start position:0%
+energies in this Arrangement is that
+lower in energy than some other
+
+ align:start position:0%
+lower in energy than some other
+ 
+
+ align:start position:0%
+lower in energy than some other
+Arrangement so I can kind of predict
+
+ align:start position:0%
+Arrangement so I can kind of predict
+ 
+
+ align:start position:0%
+Arrangement so I can kind of predict
+what the most stable Arrangement is so
+
+ align:start position:0%
+what the most stable Arrangement is so
+ 
+
+ align:start position:0%
+what the most stable Arrangement is so
+that could either be crystal structure
+
+ align:start position:0%
+that could either be crystal structure
+ 
+
+ align:start position:0%
+that could either be crystal structure
+but it's the same for if you look say at
+
+ align:start position:0%
+but it's the same for if you look say at
+ 
+
+ align:start position:0%
+but it's the same for if you look say at
+a surface um so I wanted to give you a
+
+ align:start position:0%
+a surface um so I wanted to give you a
+ 
+
+ align:start position:0%
+a surface um so I wanted to give you a
+feeling for the scale of energetic
+
+ align:start position:0%
+feeling for the scale of energetic
+ 
+
+ align:start position:0%
+feeling for the scale of energetic
+differences uh so for vadium I've listed
+
+ align:start position:0%
+differences uh so for vadium I've listed
+ 
+
+ align:start position:0%
+differences uh so for vadium I've listed
+the atomic energy here in Reed Bergs
+
+ align:start position:0%
+the atomic energy here in Reed Bergs
+ 
+
+ align:start position:0%
+the atomic energy here in Reed Bergs
+this is the energy of all its electrons
+
+ align:start position:0%
+this is the energy of all its electrons
+ 
+
+ align:start position:0%
+this is the energy of all its electrons
+so not just the veence electrons
+
+ align:start position:0%
+so not just the veence electrons
+ 
+
+ align:start position:0%
+so not just the veence electrons
+actually um the energy for FCC vadium so
+
+ align:start position:0%
+actually um the energy for FCC vadium so
+ 
+
+ align:start position:0%
+actually um the energy for FCC vadium so
+remember the first line is the
+
+ align:start position:0%
+remember the first line is the
+ 
+
+ align:start position:0%
+remember the first line is the
+atom not not in a
+
+ align:start position:0%
+atom not not in a
+ 
+
+ align:start position:0%
+atom not not in a
+solid the second line is the FCC
+
+ align:start position:0%
+solid the second line is the FCC
+ 
+
+ align:start position:0%
+solid the second line is the FCC
+iron uh and the third line is BCC iron
+
+ align:start position:0%
+iron uh and the third line is BCC iron
+ 
+
+ align:start position:0%
+iron uh and the third line is BCC iron
+so look at the differences first of all
+
+ align:start position:0%
+so look at the differences first of all
+ 
+
+ align:start position:0%
+so look at the differences first of all
+if you go from the atom to the solid
+
+ align:start position:0%
+if you go from the atom to the solid
+ 
+
+ align:start position:0%
+if you go from the atom to the solid
+your first Force digits don't even
+
+ align:start position:0%
+your first Force digits don't even
+ 
+
+ align:start position:0%
+your first Force digits don't even
+change you know and again that's a
+
+ align:start position:0%
+change you know and again that's a
+ 
+
+ align:start position:0%
+change you know and again that's a
+reflection of well a lot of your deep
+
+ align:start position:0%
+reflection of well a lot of your deep
+ 
+
+ align:start position:0%
+reflection of well a lot of your deep
+core states don't change but you would
+
+ align:start position:0%
+core states don't change but you would
+ 
+
+ align:start position:0%
+core states don't change but you would
+see something similar even with a pseudo
+
+ align:start position:0%
+see something similar even with a pseudo
+ 
+
+ align:start position:0%
+see something similar even with a pseudo
+potential approximation where you all
+
+ align:start position:0%
+potential approximation where you all
+ 
+
+ align:start position:0%
+potential approximation where you all
+deal with the veence electrons you know
+
+ align:start position:0%
+deal with the veence electrons you know
+ 
+
+ align:start position:0%
+deal with the veence electrons you know
+so the cohesive
+
+ align:start position:0%
+so the cohesive
+ 
+
+ align:start position:0%
+so the cohesive
+energy is only 0.3%
+
+ align:start position:0%
+energy is only 0.3%
+ 
+
+ align:start position:0%
+energy is only 0.3%
+of the total
+
+ align:start position:0%
+of the total
+ 
+
+ align:start position:0%
+of the total
+energy okay so if you're calculating the
+
+ align:start position:0%
+energy okay so if you're calculating the
+ 
+
+ align:start position:0%
+energy okay so if you're calculating the
+reason I'm saying this if you're
+
+ align:start position:0%
+reason I'm saying this if you're
+ 
+
+ align:start position:0%
+reason I'm saying this if you're
+calculating the cohesive energy by first
+
+ align:start position:0%
+calculating the cohesive energy by first
+ 
+
+ align:start position:0%
+calculating the cohesive energy by first
+calculating the total energy of a solid
+
+ align:start position:0%
+calculating the total energy of a solid
+ 
+
+ align:start position:0%
+calculating the total energy of a solid
+and then calculating the atomic energy
+
+ align:start position:0%
+and then calculating the atomic energy
+ 
+
+ align:start position:0%
+and then calculating the atomic energy
+you'd better do these things damn
+
+ align:start position:0%
+you'd better do these things damn
+ 
+
+ align:start position:0%
+you'd better do these things damn
+accurate because you're going to
+
+ align:start position:0%
+accurate because you're going to
+ 
+
+ align:start position:0%
+accurate because you're going to
+subtract them and most of what you
+
+ align:start position:0%
+subtract them and most of what you
+ 
+
+ align:start position:0%
+subtract them and most of what you
+subtract is the same so to get any
+
+ align:start position:0%
+subtract is the same so to get any
+ 
+
+ align:start position:0%
+subtract is the same so to get any
+significance in your result you need to
+
+ align:start position:0%
+significance in your result you need to
+ 
+
+ align:start position:0%
+significance in your result you need to
+have high numerical
+
+ align:start position:0%
+have high numerical
+ 
+
+ align:start position:0%
+have high numerical
+accuracy okay and that's not a big
+
+ align:start position:0%
+accuracy okay and that's not a big
+ 
+
+ align:start position:0%
+accuracy okay and that's not a big
+problem with a lot of codes but I want
+
+ align:start position:0%
+problem with a lot of codes but I want
+ 
+
+ align:start position:0%
+problem with a lot of codes but I want
+you to keep that in mind but you know
+
+ align:start position:0%
+you to keep that in mind but you know
+ 
+
+ align:start position:0%
+you to keep that in mind but you know
+few people care about the cohesive
+
+ align:start position:0%
+few people care about the cohesive
+ 
+
+ align:start position:0%
+few people care about the cohesive
+energy let's say you want to know
+
+ align:start position:0%
+energy let's say you want to know
+ 
+
+ align:start position:0%
+energy let's say you want to know
+whether venarum you know is FCC or
+
+ align:start position:0%
+whether venarum you know is FCC or
+ 
+
+ align:start position:0%
+whether venarum you know is FCC or
+BCC um so you could calculate it as BCC
+
+ align:start position:0%
+BCC um so you could calculate it as BCC
+ 
+
+ align:start position:0%
+BCC um so you could calculate it as BCC
+now the FCC BCC difference is only
+
+ align:start position:0%
+now the FCC BCC difference is only
+ 
+
+ align:start position:0%
+now the FCC BCC difference is only
+0.001% of the total energy and these are
+
+ align:start position:0%
+0.001% of the total energy and these are
+ 
+
+ align:start position:0%
+0.001% of the total energy and these are
+not complicated structures so in many
+
+ align:start position:0%
+not complicated structures so in many
+ 
+
+ align:start position:0%
+not complicated structures so in many
+cases we're going to work with energy
+
+ align:start position:0%
+cases we're going to work with energy
+ 
+
+ align:start position:0%
+cases we're going to work with energy
+differences that are fractions of like
+
+ align:start position:0%
+differences that are fractions of like
+ 
+
+ align:start position:0%
+differences that are fractions of like
+so that are 10 Theus 6 10- 7 times the
+
+ align:start position:0%
+so that are 10 Theus 6 10- 7 times the
+ 
+
+ align:start position:0%
+so that are 10 Theus 6 10- 7 times the
+total energy so it's sort of telling you
+
+ align:start position:0%
+total energy so it's sort of telling you
+ 
+
+ align:start position:0%
+total energy so it's sort of telling you
+something about how much numerical
+
+ align:start position:0%
+something about how much numerical
+ 
+
+ align:start position:0%
+something about how much numerical
+accuracy um um you need if you want to
+
+ align:start position:0%
+accuracy um um you need if you want to
+ 
+
+ align:start position:0%
+accuracy um um you need if you want to
+look at mixing energies you know let's
+
+ align:start position:0%
+look at mixing energies you know let's
+ 
+
+ align:start position:0%
+look at mixing energies you know let's
+say I mix vadium with something else
+
+ align:start position:0%
+say I mix vadium with something else
+ 
+
+ align:start position:0%
+say I mix vadium with something else
+platinum and you want to know what's the
+
+ align:start position:0%
+platinum and you want to know what's the
+ 
+
+ align:start position:0%
+platinum and you want to know what's the
+mixing enpy because that sets the whole
+
+ align:start position:0%
+mixing enpy because that sets the whole
+ 
+
+ align:start position:0%
+mixing enpy because that sets the whole
+temperature scale for mixing the whole
+
+ align:start position:0%
+temperature scale for mixing the whole
+ 
+
+ align:start position:0%
+temperature scale for mixing the whole
+phase diagram topology uh that tends to
+
+ align:start position:0%
+phase diagram topology uh that tends to
+ 
+
+ align:start position:0%
+phase diagram topology uh that tends to
+be a fraction 10- 6 10- 7 of the total
+
+ align:start position:0%
+be a fraction 10- 6 10- 7 of the total
+ 
+
+ align:start position:0%
+be a fraction 10- 6 10- 7 of the total
+energy um so my my former visor used to
+
+ align:start position:0%
+energy um so my my former visor used to
+ 
+
+ align:start position:0%
+energy um so my my former visor used to
+compare this to let's say you want to
+
+ align:start position:0%
+compare this to let's say you want to
+ 
+
+ align:start position:0%
+compare this to let's say you want to
+know the weight of a captain a captain
+
+ align:start position:0%
+know the weight of a captain a captain
+ 
+
+ align:start position:0%
+know the weight of a captain a captain
+that like you know sails a big super
+
+ align:start position:0%
+that like you know sails a big super
+ 
+
+ align:start position:0%
+that like you know sails a big super
+tanker it's like weighing the tanker
+
+ align:start position:0%
+tanker it's like weighing the tanker
+ 
+
+ align:start position:0%
+tanker it's like weighing the tanker
+with the captain and without the captain
+
+ align:start position:0%
+with the captain and without the captain
+ 
+
+ align:start position:0%
+with the captain and without the captain
+and looking at the difference and that's
+
+ align:start position:0%
+and looking at the difference and that's
+ 
+
+ align:start position:0%
+and looking at the difference and that's
+the weight of the captain you know
+
+ align:start position:0%
+the weight of the captain you know
+ 
+
+ align:start position:0%
+the weight of the captain you know
+you're almost at a kind of relative
+
+ align:start position:0%
+you're almost at a kind of relative
+ 
+
+ align:start position:0%
+you're almost at a kind of relative
+scale um like that here
+
+ align:start position:0%
+scale um like that here
+ 
+
+ align:start position:0%
+scale um like that here
+so the cute thing really is that all
+
+ align:start position:0%
+so the cute thing really is that all
+ 
+
+ align:start position:0%
+so the cute thing really is that all
+these approximations we make to density
+
+ align:start position:0%
+these approximations we make to density
+ 
+
+ align:start position:0%
+these approximations we make to density
+functional Theory are obviously not this
+
+ align:start position:0%
+functional Theory are obviously not this
+ 
+
+ align:start position:0%
+functional Theory are obviously not this
+accurate you know the total energy is
+
+ align:start position:0%
+accurate you know the total energy is
+ 
+
+ align:start position:0%
+accurate you know the total energy is
+not accurate up to a fraction of 10us 6
+
+ align:start position:0%
+not accurate up to a fraction of 10us 6
+ 
+
+ align:start position:0%
+not accurate up to a fraction of 10us 6
+the only reason we're here and we can
+
+ align:start position:0%
+the only reason we're here and we can
+ 
+
+ align:start position:0%
+the only reason we're here and we can
+get physical Behavior right is because a
+
+ align:start position:0%
+get physical Behavior right is because a
+ 
+
+ align:start position:0%
+get physical Behavior right is because a
+lot of the error the density functional
+
+ align:start position:0%
+lot of the error the density functional
+ 
+
+ align:start position:0%
+lot of the error the density functional
+Theory makes in LDA and GDA is
+
+ align:start position:0%
+Theory makes in LDA and GDA is
+ 
+
+ align:start position:0%
+Theory makes in LDA and GDA is
+systematic and so a lot of it cancels
+
+ align:start position:0%
+systematic and so a lot of it cancels
+ 
+
+ align:start position:0%
+systematic and so a lot of it cancels
+away when you take energy differences
+
+ align:start position:0%
+away when you take energy differences
+ 
+
+ align:start position:0%
+away when you take energy differences
+okay when I do FCC and BCC vadium yes I
+
+ align:start position:0%
+okay when I do FCC and BCC vadium yes I
+ 
+
+ align:start position:0%
+okay when I do FCC and BCC vadium yes I
+may have an error of 10 to minus 4 and
+
+ align:start position:0%
+may have an error of 10 to minus 4 and
+ 
+
+ align:start position:0%
+may have an error of 10 to minus 4 and
+the energy but most of it cancels away
+
+ align:start position:0%
+the energy but most of it cancels away
+ 
+
+ align:start position:0%
+the energy but most of it cancels away
+when I take the energy difference and
+
+ align:start position:0%
+when I take the energy difference and
+ 
+
+ align:start position:0%
+when I take the energy difference and
+that's why we're lucky
+
+ align:start position:0%
+that's why we're lucky
+ 
+
+ align:start position:0%
+that's why we're lucky
+but you have to keep that in mind
+
+ align:start position:0%
+but you have to keep that in mind
+ 
+
+ align:start position:0%
+but you have to keep that in mind
+because again the less cancellation you
+
+ align:start position:0%
+because again the less cancellation you
+ 
+
+ align:start position:0%
+because again the less cancellation you
+have the bigger your error um on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+result okay so again let me show you how
+
+ align:start position:0%
+result okay so again let me show you how
+ 
+
+ align:start position:0%
+result okay so again let me show you how
+well or how badly it does so I I did a
+
+ align:start position:0%
+well or how badly it does so I I did a
+ 
+
+ align:start position:0%
+well or how badly it does so I I did a
+very simple thing I looked at um how
+
+ align:start position:0%
+very simple thing I looked at um how
+ 
+
+ align:start position:0%
+very simple thing I looked at um how
+well does it predict say the structure
+
+ align:start position:0%
+well does it predict say the structure
+ 
+
+ align:start position:0%
+well does it predict say the structure
+of the elements um this is done in GGA a
+
+ align:start position:0%
+of the elements um this is done in GGA a
+ 
+
+ align:start position:0%
+of the elements um this is done in GGA a
+standard shudo potential method um so
+
+ align:start position:0%
+standard shudo potential method um so
+ 
+
+ align:start position:0%
+standard shudo potential method um so
+this comes out you may have to look at
+
+ align:start position:0%
+this comes out you may have to look at
+ 
+
+ align:start position:0%
+this comes out you may have to look at
+your handout because this is extremely
+
+ align:start position:0%
+your handout because this is extremely
+ 
+
+ align:start position:0%
+your handout because this is extremely
+fuzzy on the screen um in red I did
+
+ align:start position:0%
+fuzzy on the screen um in red I did
+ 
+
+ align:start position:0%
+fuzzy on the screen um in red I did
+metals that are experimentally FCC and
+
+ align:start position:0%
+metals that are experimentally FCC and
+ 
+
+ align:start position:0%
+metals that are experimentally FCC and
+in green I did metals that are
+
+ align:start position:0%
+in green I did metals that are
+ 
+
+ align:start position:0%
+in green I did metals that are
+experimentally BCC now what I show you
+
+ align:start position:0%
+experimentally BCC now what I show you
+ 
+
+ align:start position:0%
+experimentally BCC now what I show you
+is the calculated energy difference
+
+ align:start position:0%
+is the calculated energy difference
+ 
+
+ align:start position:0%
+is the calculated energy difference
+between FCC and BCC and it's actually
+
+ align:start position:0%
+between FCC and BCC and it's actually
+ 
+
+ align:start position:0%
+between FCC and BCC and it's actually
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+line below every
+
+ align:start position:0%
+line below every
+ 
+
+ align:start position:0%
+line below every
+element kind of like this
+
+ align:start position:0%
+element kind of like this
+ 
+
+ align:start position:0%
+element kind of like this
+and so when that's positive the BCC
+
+ align:start position:0%
+and so when that's positive the BCC
+ 
+
+ align:start position:0%
+and so when that's positive the BCC
+energy is higher than FCC so it's going
+
+ align:start position:0%
+energy is higher than FCC so it's going
+ 
+
+ align:start position:0%
+energy is higher than FCC so it's going
+to FCC is preferred over BCC if it's
+
+ align:start position:0%
+to FCC is preferred over BCC if it's
+ 
+
+ align:start position:0%
+to FCC is preferred over BCC if it's
+negative like here okay then BCC is
+
+ align:start position:0%
+negative like here okay then BCC is
+ 
+
+ align:start position:0%
+negative like here okay then BCC is
+preferred over FCC and so if you look so
+
+ align:start position:0%
+preferred over FCC and so if you look so
+ 
+
+ align:start position:0%
+preferred over FCC and so if you look so
+the color is the experimental result the
+
+ align:start position:0%
+the color is the experimental result the
+ 
+
+ align:start position:0%
+the color is the experimental result the
+number is calculated um so if you if you
+
+ align:start position:0%
+number is calculated um so if you if you
+ 
+
+ align:start position:0%
+number is calculated um so if you if you
+look at them carefully they're all
+
+ align:start position:0%
+look at them carefully they're all
+ 
+
+ align:start position:0%
+look at them carefully they're all
+correct it's negative when we have green
+
+ align:start position:0%
+correct it's negative when we have green
+ 
+
+ align:start position:0%
+correct it's negative when we have green
+it's it's positive when we have um red
+
+ align:start position:0%
+it's it's positive when we have um red
+ 
+
+ align:start position:0%
+it's it's positive when we have um red
+um you can do a more subtle comparison
+
+ align:start position:0%
+um you can do a more subtle comparison
+ 
+
+ align:start position:0%
+um you can do a more subtle comparison
+look at the difference between hcp
+
+ align:start position:0%
+look at the difference between hcp
+ 
+
+ align:start position:0%
+look at the difference between hcp
+hexagonal clo pack and FCC and the
+
+ align:start position:0%
+hexagonal clo pack and FCC and the
+ 
+
+ align:start position:0%
+hexagonal clo pack and FCC and the
+reason that that's more subtle is hcp
+
+ align:start position:0%
+reason that that's more subtle is hcp
+ 
+
+ align:start position:0%
+reason that that's more subtle is hcp
+and FCC are much more alike you know
+
+ align:start position:0%
+and FCC are much more alike you know
+ 
+
+ align:start position:0%
+and FCC are much more alike you know
+they're all close packed it's just a
+
+ align:start position:0%
+they're all close packed it's just a
+ 
+
+ align:start position:0%
+they're all close packed it's just a
+difference in stacking ABAB versus ABC
+
+ align:start position:0%
+difference in stacking ABAB versus ABC
+ 
+
+ align:start position:0%
+difference in stacking ABAB versus ABC
+ABC um and so again you'll see that
+
+ align:start position:0%
+ABC um and so again you'll see that
+ 
+
+ align:start position:0%
+ABC um and so again you'll see that
+they're all
+
+ align:start position:0%
+they're all
+ 
+
+ align:start position:0%
+they're all
+correct um the red ones are the FCC ones
+
+ align:start position:0%
+correct um the red ones are the FCC ones
+ 
+
+ align:start position:0%
+correct um the red ones are the FCC ones
+they're the ones where that first line
+
+ align:start position:0%
+they're the ones where that first line
+ 
+
+ align:start position:0%
+they're the ones where that first line
+is positive by the way that numbers in
+
+ align:start position:0%
+is positive by the way that numbers in
+ 
+
+ align:start position:0%
+is positive by the way that numbers in
+KJ per mole here um the yellow ones that
+
+ align:start position:0%
+KJ per mole here um the yellow ones that
+ 
+
+ align:start position:0%
+KJ per mole here um the yellow ones that
+number is negative okay so we get the
+
+ align:start position:0%
+number is negative okay so we get the
+ 
+
+ align:start position:0%
+number is negative okay so we get the
+structure of the elements um essentially
+
+ align:start position:0%
+structure of the elements um essentially
+ 
+
+ align:start position:0%
+structure of the elements um essentially
+correct um there are notable
+
+ align:start position:0%
+correct um there are notable
+ 
+
+ align:start position:0%
+correct um there are notable
+exceptions um in LDA iron is wrong iron
+
+ align:start position:0%
+exceptions um in LDA iron is wrong iron
+ 
+
+ align:start position:0%
+exceptions um in LDA iron is wrong iron
+is FCC in LDA not BCC but in GGA that's
+
+ align:start position:0%
+is FCC in LDA not BCC but in GGA that's
+ 
+
+ align:start position:0%
+is FCC in LDA not BCC but in GGA that's
+corrected um and then there are you know
+
+ align:start position:0%
+corrected um and then there are you know
+ 
+
+ align:start position:0%
+corrected um and then there are you know
+the weirdos if you go deep down in the
+
+ align:start position:0%
+the weirdos if you go deep down in the
+ 
+
+ align:start position:0%
+the weirdos if you go deep down in the
+periodic table um you know especially F
+
+ align:start position:0%
+periodic table um you know especially F
+ 
+
+ align:start position:0%
+periodic table um you know especially F
+electron Metals uh have um the F states
+
+ align:start position:0%
+electron Metals uh have um the F states
+ 
+
+ align:start position:0%
+electron Metals uh have um the F states
+are extremely localized even in metals
+
+ align:start position:0%
+are extremely localized even in metals
+ 
+
+ align:start position:0%
+are extremely localized even in metals
+and so electron correlation becomes very
+
+ align:start position:0%
+and so electron correlation becomes very
+ 
+
+ align:start position:0%
+and so electron correlation becomes very
+important here and I may say a little
+
+ align:start position:0%
+important here and I may say a little
+ 
+
+ align:start position:0%
+important here and I may say a little
+more about that and so there you'll
+
+ align:start position:0%
+more about that and so there you'll
+ 
+
+ align:start position:0%
+more about that and so there you'll
+start to see failures of LDA and GGA and
+
+ align:start position:0%
+start to see failures of LDA and GGA and
+ 
+
+ align:start position:0%
+start to see failures of LDA and GGA and
+you know an important one like is
+
+ align:start position:0%
+you know an important one like is
+ 
+
+ align:start position:0%
+you know an important one like is
+plutonium you know plutonium is kind of
+
+ align:start position:0%
+plutonium you know plutonium is kind of
+ 
+
+ align:start position:0%
+plutonium you know plutonium is kind of
+important for obvious reasons especially
+
+ align:start position:0%
+important for obvious reasons especially
+ 
+
+ align:start position:0%
+important for obvious reasons especially
+if you work at National Labs these days
+
+ align:start position:0%
+if you work at National Labs these days
+ 
+
+ align:start position:0%
+if you work at National Labs these days
+um and so people are building more
+
+ align:start position:0%
+um and so people are building more
+ 
+
+ align:start position:0%
+um and so people are building more
+sophisticated Mets to deal with
+
+ align:start position:0%
+sophisticated Mets to deal with
+ 
+
+ align:start position:0%
+sophisticated Mets to deal with
+materials such as
+
+ align:start position:0%
+materials such as
+ 
+
+ align:start position:0%
+materials such as
+plutonium typically when you work with f
+
+ align:start position:0%
+plutonium typically when you work with f
+ 
+
+ align:start position:0%
+plutonium typically when you work with f
+electron Metals sometimes you'll get the
+
+ align:start position:0%
+electron Metals sometimes you'll get the
+ 
+
+ align:start position:0%
+electron Metals sometimes you'll get the
+answer right sometimes you won't but you
+
+ align:start position:0%
+answer right sometimes you won't but you
+ 
+
+ align:start position:0%
+answer right sometimes you won't but you
+should be a little more uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+careful um let me skip this you can get
+
+ align:start position:0%
+careful um let me skip this you can get
+ 
+
+ align:start position:0%
+careful um let me skip this you can get
+the the most of the time you'll get the
+
+ align:start position:0%
+the the most of the time you'll get the
+ 
+
+ align:start position:0%
+the the most of the time you'll get the
+um structure of compounds right um if
+
+ align:start position:0%
+um structure of compounds right um if
+ 
+
+ align:start position:0%
+um structure of compounds right um if
+you go to transition metal oxides so I
+
+ align:start position:0%
+you go to transition metal oxides so I
+ 
+
+ align:start position:0%
+you go to transition metal oxides so I
+sort of went from metallic elements not
+
+ align:start position:0%
+sort of went from metallic elements not
+ 
+
+ align:start position:0%
+sort of went from metallic elements not
+to transition metal oxides most of the
+
+ align:start position:0%
+to transition metal oxides most of the
+ 
+
+ align:start position:0%
+to transition metal oxides most of the
+time you'll also get the structure right
+
+ align:start position:0%
+time you'll also get the structure right
+ 
+
+ align:start position:0%
+time you'll also get the structure right
+but things get more subtle um in
+
+ align:start position:0%
+but things get more subtle um in
+ 
+
+ align:start position:0%
+but things get more subtle um in
+transition metal oxides the transition
+
+ align:start position:0%
+transition metal oxides the transition
+ 
+
+ align:start position:0%
+transition metal oxides the transition
+metal has local D States and I showed
+
+ align:start position:0%
+metal has local D States and I showed
+ 
+
+ align:start position:0%
+metal has local D States and I showed
+you before they often have significant
+
+ align:start position:0%
+you before they often have significant
+ 
+
+ align:start position:0%
+you before they often have significant
+spin polarization so the first thing you
+
+ align:start position:0%
+spin polarization so the first thing you
+ 
+
+ align:start position:0%
+spin polarization so the first thing you
+need to do is turn spin polarization on
+
+ align:start position:0%
+need to do is turn spin polarization on
+ 
+
+ align:start position:0%
+need to do is turn spin polarization on
+or you really get the wrong answer but
+
+ align:start position:0%
+or you really get the wrong answer but
+ 
+
+ align:start position:0%
+or you really get the wrong answer but
+it often gets worse uh remember that
+
+ align:start position:0%
+it often gets worse uh remember that
+ 
+
+ align:start position:0%
+it often gets worse uh remember that
+your spin is a scaler so it's up or down
+
+ align:start position:0%
+your spin is a scaler so it's up or down
+ 
+
+ align:start position:0%
+your spin is a scaler so it's up or down
+so now you have a spatial degree of
+
+ align:start position:0%
+so now you have a spatial degree of
+ 
+
+ align:start position:0%
+so now you have a spatial degree of
+freedom of how to organize that spin on
+
+ align:start position:0%
+freedom of how to organize that spin on
+ 
+
+ align:start position:0%
+freedom of how to organize that spin on
+the ions you know if you have a bunch of
+
+ align:start position:0%
+the ions you know if you have a bunch of
+ 
+
+ align:start position:0%
+the ions you know if you have a bunch of
+ions you could put them all with the
+
+ align:start position:0%
+ions you could put them all with the
+ 
+
+ align:start position:0%
+ions you could put them all with the
+same direction that's a
+
+ align:start position:0%
+same direction that's a
+ 
+
+ align:start position:0%
+same direction that's a
+ferromagnet okay or you would could
+
+ align:start position:0%
+ferromagnet okay or you would could
+ 
+
+ align:start position:0%
+ferromagnet okay or you would could
+could put them with sort of alternating
+
+ align:start position:0%
+could put them with sort of alternating
+ 
+
+ align:start position:0%
+could put them with sort of alternating
+Direction as a kind of
+
+ align:start position:0%
+Direction as a kind of
+ 
+
+ align:start position:0%
+Direction as a kind of
+antiferromagnet and then there's many
+
+ align:start position:0%
+antiferromagnet and then there's many
+ 
+
+ align:start position:0%
+antiferromagnet and then there's many
+ways to make them
+
+ align:start position:0%
+ways to make them
+ 
+
+ align:start position:0%
+ways to make them
+antiferromagnetic and unfortunately in
+
+ align:start position:0%
+antiferromagnetic and unfortunately in
+ 
+
+ align:start position:0%
+antiferromagnetic and unfortunately in
+transition metal oxide it often matter
+
+ align:start position:0%
+transition metal oxide it often matter
+ 
+
+ align:start position:0%
+transition metal oxide it often matter
+because there's not only a strong spin
+
+ align:start position:0%
+because there's not only a strong spin
+ 
+
+ align:start position:0%
+because there's not only a strong spin
+polarization effect on the energy but
+
+ align:start position:0%
+polarization effect on the energy but
+ 
+
+ align:start position:0%
+polarization effect on the energy but
+there's a fairly strong effect of the
+
+ align:start position:0%
+there's a fairly strong effect of the
+ 
+
+ align:start position:0%
+there's a fairly strong effect of the
+interaction between spins on different
+
+ align:start position:0%
+interaction between spins on different
+ 
+
+ align:start position:0%
+interaction between spins on different
+ions and I'm showing you a result here
+
+ align:start position:0%
+ions and I'm showing you a result here
+ 
+
+ align:start position:0%
+ions and I'm showing you a result here
+uh this is a simple crystal structure
+
+ align:start position:0%
+uh this is a simple crystal structure
+ 
+
+ align:start position:0%
+uh this is a simple crystal structure
+it's a structure of lithium manganese
+
+ align:start position:0%
+it's a structure of lithium manganese
+ 
+
+ align:start position:0%
+it's a structure of lithium manganese
+oxide it's an ordered rock salt these
+
+ align:start position:0%
+oxide it's an ordered rock salt these
+ 
+
+ align:start position:0%
+oxide it's an ordered rock salt these
+are still very simple um but the the
+
+ align:start position:0%
+are still very simple um but the the
+ 
+
+ align:start position:0%
+are still very simple um but the the
+correct answer I'm showing the
+
+ align:start position:0%
+correct answer I'm showing the
+ 
+
+ align:start position:0%
+correct answer I'm showing the
+comparison here between two structures
+
+ align:start position:0%
+comparison here between two structures
+ 
+
+ align:start position:0%
+comparison here between two structures
+only labeled by their symmetry
+
+ align:start position:0%
+only labeled by their symmetry
+ 
+
+ align:start position:0%
+only labeled by their symmetry
+unfortunately one is c2m and one is pmmn
+
+ align:start position:0%
+unfortunately one is c2m and one is pmmn
+ 
+
+ align:start position:0%
+unfortunately one is c2m and one is pmmn
+um there're rather similar structures
+
+ align:start position:0%
+um there're rather similar structures
+ 
+
+ align:start position:0%
+um there're rather similar structures
+but one is utomic and one is monoclinic
+
+ align:start position:0%
+but one is utomic and one is monoclinic
+ 
+
+ align:start position:0%
+but one is utomic and one is monoclinic
+um the correct answer is pmmn is the
+
+ align:start position:0%
+um the correct answer is pmmn is the
+ 
+
+ align:start position:0%
+um the correct answer is pmmn is the
+real crystal structure if you do a
+
+ align:start position:0%
+real crystal structure if you do a
+ 
+
+ align:start position:0%
+real crystal structure if you do a
+non-spin polarized calculation so that's
+
+ align:start position:0%
+non-spin polarized calculation so that's
+ 
+
+ align:start position:0%
+non-spin polarized calculation so that's
+not even allowing spin on the ions you
+
+ align:start position:0%
+not even allowing spin on the ions you
+ 
+
+ align:start position:0%
+not even allowing spin on the ions you
+get a whopping error I mean c2m is lower
+
+ align:start position:0%
+get a whopping error I mean c2m is lower
+ 
+
+ align:start position:0%
+get a whopping error I mean c2m is lower
+in energy by 250 M electon volt per form
+
+ align:start position:0%
+in energy by 250 M electon volt per form
+ 
+
+ align:start position:0%
+in energy by 250 M electon volt per form
+M unit that's very large you know in
+
+ align:start position:0%
+M unit that's very large you know in
+ 
+
+ align:start position:0%
+M unit that's very large you know in
+kilj that'd be 25 KJ per mole um it's a
+
+ align:start position:0%
+kilj that'd be 25 KJ per mole um it's a
+ 
+
+ align:start position:0%
+kilj that'd be 25 KJ per mole um it's a
+very large error if you turn on spin
+
+ align:start position:0%
+very large error if you turn on spin
+ 
+
+ align:start position:0%
+very large error if you turn on spin
+polarization but make a ferromagnetic
+
+ align:start position:0%
+polarization but make a ferromagnetic
+ 
+
+ align:start position:0%
+polarization but make a ferromagnetic
+there degenerate and if you make an
+
+ align:start position:0%
+there degenerate and if you make an
+ 
+
+ align:start position:0%
+there degenerate and if you make an
+antier I uh this one is the lowest in
+
+ align:start position:0%
+antier I uh this one is the lowest in
+ 
+
+ align:start position:0%
+antier I uh this one is the lowest in
+energy okay now here's a very common
+
+ align:start position:0%
+energy okay now here's a very common
+ 
+
+ align:start position:0%
+energy okay now here's a very common
+mistake people make um if you take this
+
+ align:start position:0%
+mistake people make um if you take this
+ 
+
+ align:start position:0%
+mistake people make um if you take this
+material at room temperature it's
+
+ align:start position:0%
+material at room temperature it's
+ 
+
+ align:start position:0%
+material at room temperature it's
+paramagnetic so people say well it's
+
+ align:start position:0%
+paramagnetic so people say well it's
+ 
+
+ align:start position:0%
+paramagnetic so people say well it's
+paramagnetic so I shouldn't have any
+
+ align:start position:0%
+paramagnetic so I shouldn't have any
+ 
+
+ align:start position:0%
+paramagnetic so I shouldn't have any
+spin polarization there's no net moment
+
+ align:start position:0%
+spin polarization there's no net moment
+ 
+
+ align:start position:0%
+spin polarization there's no net moment
+that is so wrong okay because a
+
+ align:start position:0%
+that is so wrong okay because a
+ 
+
+ align:start position:0%
+that is so wrong okay because a
+paramagnet still has a local moment the
+
+ align:start position:0%
+paramagnet still has a local moment the
+ 
+
+ align:start position:0%
+paramagnet still has a local moment the
+ions still have a moment on them it's
+
+ align:start position:0%
+ions still have a moment on them it's
+ 
+
+ align:start position:0%
+ions still have a moment on them it's
+just randomly oriented okay so you still
+
+ align:start position:0%
+just randomly oriented okay so you still
+ 
+
+ align:start position:0%
+just randomly oriented okay so you still
+need to rep represent that
+
+ align:start position:0%
+need to rep represent that
+ 
+
+ align:start position:0%
+need to rep represent that
+moment okay because turns out that's the
+
+ align:start position:0%
+moment okay because turns out that's the
+ 
+
+ align:start position:0%
+moment okay because turns out that's the
+biggest effect on the energy is the fact
+
+ align:start position:0%
+biggest effect on the energy is the fact
+ 
+
+ align:start position:0%
+biggest effect on the energy is the fact
+that you have that local moment it's not
+
+ align:start position:0%
+that you have that local moment it's not
+ 
+
+ align:start position:0%
+that you have that local moment it's not
+necessarily how they're arranged you can
+
+ align:start position:0%
+necessarily how they're arranged you can
+ 
+
+ align:start position:0%
+necessarily how they're arranged you can
+actually see that here how they're
+
+ align:start position:0%
+actually see that here how they're
+ 
+
+ align:start position:0%
+actually see that here how they're
+arranged makes you go from this
+
+ align:start position:0%
+arranged makes you go from this
+ 
+
+ align:start position:0%
+arranged makes you go from this
+difference to this difference but
+
+ align:start position:0%
+difference to this difference but
+ 
+
+ align:start position:0%
+difference to this difference but
+turning on the local moment makes you go
+
+ align:start position:0%
+turning on the local moment makes you go
+ 
+
+ align:start position:0%
+turning on the local moment makes you go
+from this difference to that
+
+ align:start position:0%
+from this difference to that
+ 
+
+ align:start position:0%
+from this difference to that
+difference okay so never fall in that
+
+ align:start position:0%
+difference okay so never fall in that
+ 
+
+ align:start position:0%
+difference okay so never fall in that
+trap it's really only uh non-magnetic
+
+ align:start position:0%
+trap it's really only uh non-magnetic
+ 
+
+ align:start position:0%
+trap it's really only uh non-magnetic
+materials or diamagnetic materials for
+
+ align:start position:0%
+materials or diamagnetic materials for
+ 
+
+ align:start position:0%
+materials or diamagnetic materials for
+which you don't really need uh spin
+
+ align:start position:0%
+which you don't really need uh spin
+ 
+
+ align:start position:0%
+which you don't really need uh spin
+polariz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now why is this effect so important um
+
+ align:start position:0%
+now why is this effect so important um
+ 
+
+ align:start position:0%
+now why is this effect so important um
+It's really because if you spin polarize
+
+ align:start position:0%
+It's really because if you spin polarize
+ 
+
+ align:start position:0%
+It's really because if you spin polarize
+an ion um you fill different
+
+ align:start position:0%
+an ion um you fill different
+ 
+
+ align:start position:0%
+an ion um you fill different
+orbitals I mean I've shown that here
+
+ align:start position:0%
+orbitals I mean I've shown that here
+ 
+
+ align:start position:0%
+orbitals I mean I've shown that here
+with a bunch of D orbitals and this is
+
+ align:start position:0%
+with a bunch of D orbitals and this is
+ 
+
+ align:start position:0%
+with a bunch of D orbitals and this is
+typically how they split in most oxides
+
+ align:start position:0%
+typically how they split in most oxides
+ 
+
+ align:start position:0%
+typically how they split in most oxides
+every time an ion is octahedral five D
+
+ align:start position:0%
+every time an ion is octahedral five D
+ 
+
+ align:start position:0%
+every time an ion is octahedral five D
+orbitals tend to split in pairs of three
+
+ align:start position:0%
+orbitals tend to split in pairs of three
+ 
+
+ align:start position:0%
+orbitals tend to split in pairs of three
+two okay three down two up in some cases
+
+ align:start position:0%
+two okay three down two up in some cases
+ 
+
+ align:start position:0%
+two okay three down two up in some cases
+two down three up um but let's say you
+
+ align:start position:0%
+two down three up um but let's say you
+ 
+
+ align:start position:0%
+two down three up um but let's say you
+have to put four five electrons in there
+
+ align:start position:0%
+have to put four five electrons in there
+ 
+
+ align:start position:0%
+have to put four five electrons in there
+how many do I have I'm missing a couple
+
+ align:start position:0%
+how many do I have I'm missing a couple
+ 
+
+ align:start position:0%
+how many do I have I'm missing a couple
+no four electrons if you put them what's
+
+ align:start position:0%
+no four electrons if you put them what's
+ 
+
+ align:start position:0%
+no four electrons if you put them what's
+called high spin so all parallel spin
+
+ align:start position:0%
+called high spin so all parallel spin
+ 
+
+ align:start position:0%
+called high spin so all parallel spin
+you put them like this if you put them
+
+ align:start position:0%
+you put them like this if you put them
+ 
+
+ align:start position:0%
+you put them like this if you put them
+low spin you put them like this so here
+
+ align:start position:0%
+low spin you put them like this so here
+ 
+
+ align:start position:0%
+low spin you put them like this so here
+you have no moment
+
+ align:start position:0%
+you have no moment
+ 
+
+ align:start position:0%
+you have no moment
+so these two ions have different
+
+ align:start position:0%
+so these two ions have different
+ 
+
+ align:start position:0%
+so these two ions have different
+chemical properties because the
+
+ align:start position:0%
+chemical properties because the
+ 
+
+ align:start position:0%
+chemical properties because the
+electrons occupy different orbitals
+
+ align:start position:0%
+electrons occupy different orbitals
+ 
+
+ align:start position:0%
+electrons occupy different orbitals
+these are different D orbitals and so um
+
+ align:start position:0%
+these are different D orbitals and so um
+ 
+
+ align:start position:0%
+these are different D orbitals and so um
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+this orbital points in a different
+
+ align:start position:0%
+this orbital points in a different
+ 
+
+ align:start position:0%
+this orbital points in a different
+direction for example than this one okay
+
+ align:start position:0%
+direction for example than this one okay
+ 
+
+ align:start position:0%
+direction for example than this one okay
+so by spin polarizing you create
+
+ align:start position:0%
+so by spin polarizing you create
+ 
+
+ align:start position:0%
+so by spin polarizing you create
+essentially a different Dion it's not
+
+ align:start position:0%
+essentially a different Dion it's not
+ 
+
+ align:start position:0%
+essentially a different Dion it's not
+it's not really an issue of magnetism
+
+ align:start position:0%
+it's not really an issue of magnetism
+ 
+
+ align:start position:0%
+it's not really an issue of magnetism
+because magnetic effects tend to be
+
+ align:start position:0%
+because magnetic effects tend to be
+ 
+
+ align:start position:0%
+because magnetic effects tend to be
+small in materials but it's the fact
+
+ align:start position:0%
+small in materials but it's the fact
+ 
+
+ align:start position:0%
+small in materials but it's the fact
+that you create chemically a different n
+
+ align:start position:0%
+that you create chemically a different n
+ 
+
+ align:start position:0%
+that you create chemically a different n
+because you fill different
+
+ align:start position:0%
+because you fill different
+ 
+
+ align:start position:0%
+because you fill different
+levels okay that's really why these
+
+ align:start position:0%
+levels okay that's really why these
+ 
+
+ align:start position:0%
+levels okay that's really why these
+energy differences are so big
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I sort of want to end with showing
+
+ align:start position:0%
+okay I sort of want to end with showing
+ 
+
+ align:start position:0%
+okay I sort of want to end with showing
+you some reaction energies very quickly
+
+ align:start position:0%
+you some reaction energies very quickly
+ 
+
+ align:start position:0%
+you some reaction energies very quickly
+uh and I'm going to sort of make it
+
+ align:start position:0%
+uh and I'm going to sort of make it
+ 
+
+ align:start position:0%
+uh and I'm going to sort of make it
+systematically harder so here's a simple
+
+ align:start position:0%
+systematically harder so here's a simple
+ 
+
+ align:start position:0%
+systematically harder so here's a simple
+one a metal lithium BCC with another
+
+ align:start position:0%
+one a metal lithium BCC with another
+ 
+
+ align:start position:0%
+one a metal lithium BCC with another
+metal aluminum forming a lithium
+
+ align:start position:0%
+metal aluminum forming a lithium
+ 
+
+ align:start position:0%
+metal aluminum forming a lithium
+aluminum compound here's the
+
+ align:start position:0%
+aluminum compound here's the
+ 
+
+ align:start position:0%
+aluminum compound here's the
+experimental reaction energy here's the
+
+ align:start position:0%
+experimental reaction energy here's the
+ 
+
+ align:start position:0%
+experimental reaction energy here's the
+LDA one 10% off okay that's classic
+
+ align:start position:0%
+LDA one 10% off okay that's classic
+ 
+
+ align:start position:0%
+LDA one 10% off okay that's classic
+metallic reaction energies you know
+
+ align:start position:0%
+metallic reaction energies you know
+ 
+
+ align:start position:0%
+metallic reaction energies you know
+you're somewhere in the range 5 to
+
+ align:start position:0%
+you're somewhere in the range 5 to
+ 
+
+ align:start position:0%
+you're somewhere in the range 5 to
+15% uh the one I show here copper gold
+
+ align:start position:0%
+15% uh the one I show here copper gold
+ 
+
+ align:start position:0%
+15% uh the one I show here copper gold
+is a notably exception where you're over
+
+ align:start position:0%
+is a notably exception where you're over
+ 
+
+ align:start position:0%
+is a notably exception where you're over
+50% off but um most of them it's much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simpler um so in metals you tend to get
+
+ align:start position:0%
+simpler um so in metals you tend to get
+ 
+
+ align:start position:0%
+simpler um so in metals you tend to get
+very good reaction energies uh I want to
+
+ align:start position:0%
+very good reaction energies uh I want to
+ 
+
+ align:start position:0%
+very good reaction energies uh I want to
+show you the the case where things go
+
+ align:start position:0%
+show you the the case where things go
+ 
+
+ align:start position:0%
+show you the the case where things go
+wrong uh where your errors become bigger
+
+ align:start position:0%
+wrong uh where your errors become bigger
+ 
+
+ align:start position:0%
+wrong uh where your errors become bigger
+is in Redux reactions and I've shown
+
+ align:start position:0%
+is in Redux reactions and I've shown
+ 
+
+ align:start position:0%
+is in Redux reactions and I've shown
+sort of here three different ones
+
+ align:start position:0%
+sort of here three different ones
+ 
+
+ align:start position:0%
+sort of here three different ones
+they're all related they're essentially
+
+ align:start position:0%
+they're all related they're essentially
+ 
+
+ align:start position:0%
+they're all related they're essentially
+a reaction between between an oxide or
+
+ align:start position:0%
+a reaction between between an oxide or
+ 
+
+ align:start position:0%
+a reaction between between an oxide or
+in this case a phosphate with a metal to
+
+ align:start position:0%
+in this case a phosphate with a metal to
+ 
+
+ align:start position:0%
+in this case a phosphate with a metal to
+react the two together and if you look
+
+ align:start position:0%
+react the two together and if you look
+ 
+
+ align:start position:0%
+react the two together and if you look
+at the reaction energies you're not
+
+ align:start position:0%
+at the reaction energies you're not
+ 
+
+ align:start position:0%
+at the reaction energies you're not
+considerably off GGA gives you 2.8
+
+ align:start position:0%
+considerably off GGA gives you 2.8
+ 
+
+ align:start position:0%
+considerably off GGA gives you 2.8
+electron volts for this reaction
+
+ align:start position:0%
+electron volts for this reaction
+ 
+
+ align:start position:0%
+electron volts for this reaction
+experiment is
+
+ align:start position:0%
+experiment is
+ 
+
+ align:start position:0%
+experiment is
+3.5 this one which is very similar you
+
+ align:start position:0%
+3.5 this one which is very similar you
+ 
+
+ align:start position:0%
+3.5 this one which is very similar you
+know the error is 30% you get 3.3
+
+ align:start position:0%
+know the error is 30% you get 3.3
+ 
+
+ align:start position:0%
+know the error is 30% you get 3.3
+electron volt experiment is
+
+ align:start position:0%
+electron volt experiment is
+ 
+
+ align:start position:0%
+electron volt experiment is
+4.6 why is that well it has to do with
+
+ align:start position:0%
+4.6 why is that well it has to do with
+ 
+
+ align:start position:0%
+4.6 why is that well it has to do with
+the lack of error cancellation if you
+
+ align:start position:0%
+the lack of error cancellation if you
+ 
+
+ align:start position:0%
+the lack of error cancellation if you
+look in detail what happens to the
+
+ align:start position:0%
+look in detail what happens to the
+ 
+
+ align:start position:0%
+look in detail what happens to the
+electronic structure in these materials
+
+ align:start position:0%
+electronic structure in these materials
+ 
+
+ align:start position:0%
+electronic structure in these materials
+these are Redux reactions so if you do
+
+ align:start position:0%
+these are Redux reactions so if you do
+ 
+
+ align:start position:0%
+these are Redux reactions so if you do
+the the math on the Veen and believe me
+
+ align:start position:0%
+the the math on the Veen and believe me
+ 
+
+ align:start position:0%
+the the math on the Veen and believe me
+this iron here is 3
+
+ align:start position:0%
+this iron here is 3
+ 
+
+ align:start position:0%
+this iron here is 3
+plus you know phosphor is 5 plus oxygen
+
+ align:start position:0%
+plus you know phosphor is 5 plus oxygen
+ 
+
+ align:start position:0%
+plus you know phosphor is 5 plus oxygen
+is 2 minus so you can do the math iron
+
+ align:start position:0%
+is 2 minus so you can do the math iron
+ 
+
+ align:start position:0%
+is 2 minus so you can do the math iron
+here is 2 plus and lithium is 1 plus so
+
+ align:start position:0%
+here is 2 plus and lithium is 1 plus so
+ 
+
+ align:start position:0%
+here is 2 plus and lithium is 1 plus so
+what has happened in this reaction well
+
+ align:start position:0%
+what has happened in this reaction well
+ 
+
+ align:start position:0%
+what has happened in this reaction well
+you've taken essentially an electron
+
+ align:start position:0%
+you've taken essentially an electron
+ 
+
+ align:start position:0%
+you've taken essentially an electron
+from lithium in its metallic
+
+ align:start position:0%
+from lithium in its metallic
+ 
+
+ align:start position:0%
+from lithium in its metallic
+State okay and put it on the iron 3+ to
+
+ align:start position:0%
+State okay and put it on the iron 3+ to
+ 
+
+ align:start position:0%
+State okay and put it on the iron 3+ to
+make iron 2+ so essentially you've
+
+ align:start position:0%
+make iron 2+ so essentially you've
+ 
+
+ align:start position:0%
+make iron 2+ so essentially you've
+transferred an electron from metallic
+
+ align:start position:0%
+transferred an electron from metallic
+ 
+
+ align:start position:0%
+transferred an electron from metallic
+lithium and ironize the lithium to the
+
+ align:start position:0%
+lithium and ironize the lithium to the
+ 
+
+ align:start position:0%
+lithium and ironize the lithium to the
+iron to reduce it from 3+ to 2+ but
+
+ align:start position:0%
+iron to reduce it from 3+ to 2+ but
+ 
+
+ align:start position:0%
+iron to reduce it from 3+ to 2+ but
+think about what's that doing that
+
+ align:start position:0%
+think about what's that doing that
+ 
+
+ align:start position:0%
+think about what's that doing that
+electron in lithium you know lithium is
+
+ align:start position:0%
+electron in lithium you know lithium is
+ 
+
+ align:start position:0%
+electron in lithium you know lithium is
+there in the alkali metals that's the N
+
+ align:start position:0%
+there in the alkali metals that's the N
+ 
+
+ align:start position:0%
+there in the alkali metals that's the N
+electron so that's a a wide Del
+
+ align:start position:0%
+electron so that's a a wide Del
+ 
+
+ align:start position:0%
+electron so that's a a wide Del
+localized orbital and thing is metallic
+
+ align:start position:0%
+localized orbital and thing is metallic
+ 
+
+ align:start position:0%
+localized orbital and thing is metallic
+and you're transferring it to a
+
+ align:start position:0%
+and you're transferring it to a
+ 
+
+ align:start position:0%
+and you're transferring it to a
+localized D State on the
+
+ align:start position:0%
+localized D State on the
+ 
+
+ align:start position:0%
+localized D State on the
+iron so that electron is essentially
+
+ align:start position:0%
+iron so that electron is essentially
+ 
+
+ align:start position:0%
+iron so that electron is essentially
+being transferred between extremely
+
+ align:start position:0%
+being transferred between extremely
+ 
+
+ align:start position:0%
+being transferred between extremely
+different states and this is what's
+
+ align:start position:0%
+different states and this is what's
+ 
+
+ align:start position:0%
+different states and this is what's
+killing you okay because you transfer
+
+ align:start position:0%
+killing you okay because you transfer
+ 
+
+ align:start position:0%
+killing you okay because you transfer
+between such different states you start
+
+ align:start position:0%
+between such different states you start
+ 
+
+ align:start position:0%
+between such different states you start
+losing a lot of the sort of cancellation
+
+ align:start position:0%
+losing a lot of the sort of cancellation
+ 
+
+ align:start position:0%
+losing a lot of the sort of cancellation
+of errors that you need that's the
+
+ align:start position:0%
+of errors that you need that's the
+ 
+
+ align:start position:0%
+of errors that you need that's the
+functional Theory um and in
+
+ align:start position:0%
+functional Theory um and in
+ 
+
+ align:start position:0%
+functional Theory um and in
+particular the error here comes from
+
+ align:start position:0%
+particular the error here comes from
+ 
+
+ align:start position:0%
+particular the error here comes from
+something quite particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um uh it comes from the self inter what
+
+ align:start position:0%
+um uh it comes from the self inter what
+ 
+
+ align:start position:0%
+um uh it comes from the self inter what
+we called a self- interaction error um
+
+ align:start position:0%
+we called a self- interaction error um
+ 
+
+ align:start position:0%
+we called a self- interaction error um
+so I'm trying to sort of make you
+
+ align:start position:0%
+so I'm trying to sort of make you
+ 
+
+ align:start position:0%
+so I'm trying to sort of make you
+understand where these errors comes from
+
+ align:start position:0%
+understand where these errors comes from
+ 
+
+ align:start position:0%
+understand where these errors comes from
+so that when you work on your
+
+ align:start position:0%
+so that when you work on your
+ 
+
+ align:start position:0%
+so that when you work on your
+application you get a bit of a feeling
+
+ align:start position:0%
+application you get a bit of a feeling
+ 
+
+ align:start position:0%
+application you get a bit of a feeling
+for um if you remember how we solve all
+
+ align:start position:0%
+for um if you remember how we solve all
+ 
+
+ align:start position:0%
+for um if you remember how we solve all
+these quantum mechanical equations we
+
+ align:start position:0%
+these quantum mechanical equations we
+ 
+
+ align:start position:0%
+these quantum mechanical equations we
+reduce them to one electron equations
+
+ align:start position:0%
+reduce them to one electron equations
+ 
+
+ align:start position:0%
+reduce them to one electron equations
+where you know you have the kinetic
+
+ align:start position:0%
+where you know you have the kinetic
+ 
+
+ align:start position:0%
+where you know you have the kinetic
+energy the nuclear potential then this
+
+ align:start position:0%
+energy the nuclear potential then this
+ 
+
+ align:start position:0%
+energy the nuclear potential then this
+effective potential which remember what
+
+ align:start position:0%
+effective potential which remember what
+ 
+
+ align:start position:0%
+effective potential which remember what
+all goes in there their effective
+
+ align:start position:0%
+all goes in there their effective
+ 
+
+ align:start position:0%
+all goes in there their effective
+potential that's the one that has the
+
+ align:start position:0%
+potential that's the one that has the
+ 
+
+ align:start position:0%
+potential that's the one that has the
+exchange correlation in it but it also
+
+ align:start position:0%
+exchange correlation in it but it also
+ 
+
+ align:start position:0%
+exchange correlation in it but it also
+has the hearty field so the columbic
+
+ align:start position:0%
+has the hearty field so the columbic
+ 
+
+ align:start position:0%
+has the hearty field so the columbic
+field from all the electrons well that
+
+ align:start position:0%
+field from all the electrons well that
+ 
+
+ align:start position:0%
+field from all the electrons well that
+that field includes the electron
+
+ align:start position:0%
+that field includes the electron
+ 
+
+ align:start position:0%
+that field includes the electron
+itself okay that's the sort of vity in
+
+ align:start position:0%
+itself okay that's the sort of vity in
+ 
+
+ align:start position:0%
+itself okay that's the sort of vity in
+essence when you calculate the charge
+
+ align:start position:0%
+essence when you calculate the charge
+ 
+
+ align:start position:0%
+essence when you calculate the charge
+density that's the charge density of all
+
+ align:start position:0%
+density that's the charge density of all
+ 
+
+ align:start position:0%
+density that's the charge density of all
+the electrons when you then calculate
+
+ align:start position:0%
+the electrons when you then calculate
+ 
+
+ align:start position:0%
+the electrons when you then calculate
+the potential coming from that charge
+
+ align:start position:0%
+the potential coming from that charge
+ 
+
+ align:start position:0%
+the potential coming from that charge
+density that's the potential coming from
+
+ align:start position:0%
+density that's the potential coming from
+ 
+
+ align:start position:0%
+density that's the potential coming from
+all all the electrons but you operate
+
+ align:start position:0%
+all all the electrons but you operate
+ 
+
+ align:start position:0%
+all all the electrons but you operate
+that now on a single electron so the
+
+ align:start position:0%
+that now on a single electron so the
+ 
+
+ align:start position:0%
+that now on a single electron so the
+electron is feeling its own
+
+ align:start position:0%
+electron is feeling its own
+ 
+
+ align:start position:0%
+electron is feeling its own
+potential okay part of the exchange
+
+ align:start position:0%
+potential okay part of the exchange
+ 
+
+ align:start position:0%
+potential okay part of the exchange
+correlation um term corrects for that
+
+ align:start position:0%
+correlation um term corrects for that
+ 
+
+ align:start position:0%
+correlation um term corrects for that
+but not all of it and the problem is
+
+ align:start position:0%
+but not all of it and the problem is
+ 
+
+ align:start position:0%
+but not all of it and the problem is
+that the correction doesn't operate as
+
+ align:start position:0%
+that the correction doesn't operate as
+ 
+
+ align:start position:0%
+that the correction doesn't operate as
+well on different forms of the charge
+
+ align:start position:0%
+well on different forms of the charge
+ 
+
+ align:start position:0%
+well on different forms of the charge
+density you know in a
+
+ align:start position:0%
+density you know in a
+ 
+
+ align:start position:0%
+density you know in a
+metal you have a small self interaction
+
+ align:start position:0%
+metal you have a small self interaction
+ 
+
+ align:start position:0%
+metal you have a small self interaction
+error and the reason if you look at a
+
+ align:start position:0%
+error and the reason if you look at a
+ 
+
+ align:start position:0%
+error and the reason if you look at a
+state in a metal sort of very
+
+ align:start position:0%
+state in a metal sort of very
+ 
+
+ align:start position:0%
+state in a metal sort of very
+delocalized so very spread out charge
+
+ align:start position:0%
+delocalized so very spread out charge
+ 
+
+ align:start position:0%
+delocalized so very spread out charge
+density so if you want to think of it
+
+ align:start position:0%
+density so if you want to think of it
+ 
+
+ align:start position:0%
+density so if you want to think of it
+when the the part of the electron here
+
+ align:start position:0%
+when the the part of the electron here
+ 
+
+ align:start position:0%
+when the the part of the electron here
+doesn't feel much of the charge density
+
+ align:start position:0%
+doesn't feel much of the charge density
+ 
+
+ align:start position:0%
+doesn't feel much of the charge density
+coming of the potential coming from that
+
+ align:start position:0%
+coming of the potential coming from that
+ 
+
+ align:start position:0%
+coming of the potential coming from that
+piece of the charge Den because they're
+
+ align:start position:0%
+piece of the charge Den because they're
+ 
+
+ align:start position:0%
+piece of the charge Den because they're
+very far
+
+ align:start position:0%
+very far
+ 
+
+ align:start position:0%
+very far
+away okay whereas if you do a very
+
+ align:start position:0%
+away okay whereas if you do a very
+ 
+
+ align:start position:0%
+away okay whereas if you do a very
+localized
+
+ align:start position:0%
+localized
+ 
+
+ align:start position:0%
+localized
+state in some sense then the potential
+
+ align:start position:0%
+state in some sense then the potential
+ 
+
+ align:start position:0%
+state in some sense then the potential
+is from the electron is very high where
+
+ align:start position:0%
+is from the electron is very high where
+ 
+
+ align:start position:0%
+is from the electron is very high where
+the electron itself is sitting okay
+
+ align:start position:0%
+the electron itself is sitting okay
+ 
+
+ align:start position:0%
+the electron itself is sitting okay
+because it's all very close you know if
+
+ align:start position:0%
+because it's all very close you know if
+ 
+
+ align:start position:0%
+because it's all very close you know if
+you put a an electron in a Delta
+
+ align:start position:0%
+you put a an electron in a Delta
+ 
+
+ align:start position:0%
+you put a an electron in a Delta
+function if you could if you didn't have
+
+ align:start position:0%
+function if you could if you didn't have
+ 
+
+ align:start position:0%
+function if you could if you didn't have
+an uncertainty principle okay and you
+
+ align:start position:0%
+an uncertainty principle okay and you
+ 
+
+ align:start position:0%
+an uncertainty principle okay and you
+calculate its potential it's basically
+
+ align:start position:0%
+calculate its potential it's basically
+ 
+
+ align:start position:0%
+calculate its potential it's basically
+sitting on top of itself then you'd have
+
+ align:start position:0%
+sitting on top of itself then you'd have
+ 
+
+ align:start position:0%
+sitting on top of itself then you'd have
+an infinite self inter self interaction
+
+ align:start position:0%
+an infinite self inter self interaction
+ 
+
+ align:start position:0%
+an infinite self inter self interaction
+so the more local the state is the more
+
+ align:start position:0%
+so the more local the state is the more
+ 
+
+ align:start position:0%
+so the more local the state is the more
+self interaction you have and the
+
+ align:start position:0%
+self interaction you have and the
+ 
+
+ align:start position:0%
+self interaction you have and the
+exchange correlation functional can't
+
+ align:start position:0%
+exchange correlation functional can't
+ 
+
+ align:start position:0%
+exchange correlation functional can't
+quite uh correct these two in the same
+
+ align:start position:0%
+quite uh correct these two in the same
+ 
+
+ align:start position:0%
+quite uh correct these two in the same
+way and remember that the exchange
+
+ align:start position:0%
+way and remember that the exchange
+ 
+
+ align:start position:0%
+way and remember that the exchange
+correlation correction comes from
+
+ align:start position:0%
+correlation correction comes from
+ 
+
+ align:start position:0%
+correlation correction comes from
+homogeneous charge
+
+ align:start position:0%
+homogeneous charge
+ 
+
+ align:start position:0%
+homogeneous charge
+densities okay so it tends to correct
+
+ align:start position:0%
+densities okay so it tends to correct
+ 
+
+ align:start position:0%
+densities okay so it tends to correct
+the metallic State better uh than the
+
+ align:start position:0%
+the metallic State better uh than the
+ 
+
+ align:start position:0%
+the metallic State better uh than the
+localized State and so this is why that
+
+ align:start position:0%
+localized State and so this is why that
+ 
+
+ align:start position:0%
+localized State and so this is why that
+Redux reaction I showed you had a big
+
+ align:start position:0%
+Redux reaction I showed you had a big
+ 
+
+ align:start position:0%
+Redux reaction I showed you had a big
+error because we were trans transing
+
+ align:start position:0%
+error because we were trans transing
+ 
+
+ align:start position:0%
+error because we were trans transing
+from a state that was metallic the
+
+ align:start position:0%
+from a state that was metallic the
+ 
+
+ align:start position:0%
+from a state that was metallic the
+electron went from the lithium state to
+
+ align:start position:0%
+electron went from the lithium state to
+ 
+
+ align:start position:0%
+electron went from the lithium state to
+the transition metal State okay and
+
+ align:start position:0%
+the transition metal State okay and
+ 
+
+ align:start position:0%
+the transition metal State okay and
+somehow the self interaction error
+
+ align:start position:0%
+somehow the self interaction error
+ 
+
+ align:start position:0%
+somehow the self interaction error
+doesn't cancel um and you will see
+
+ align:start position:0%
+doesn't cancel um and you will see
+ 
+
+ align:start position:0%
+doesn't cancel um and you will see
+things like that whenever you transfer
+
+ align:start position:0%
+things like that whenever you transfer
+ 
+
+ align:start position:0%
+things like that whenever you transfer
+electrons between quite different states
+
+ align:start position:0%
+electrons between quite different states
+ 
+
+ align:start position:0%
+electrons between quite different states
+so that's something to keep in mind um
+
+ align:start position:0%
+so that's something to keep in mind um
+ 
+
+ align:start position:0%
+so that's something to keep in mind um
+I'm running out of time here so yeah let
+
+ align:start position:0%
+I'm running out of time here so yeah let
+ 
+
+ align:start position:0%
+I'm running out of time here so yeah let
+me stop here
+
+ align:start position:0%
+me stop here
+ 
+
+ align:start position:0%
+me stop here
+um so I'm summarizing here this is the
+
+ align:start position:0%
+um so I'm summarizing here this is the
+ 
+
+ align:start position:0%
+um so I'm summarizing here this is the
+stuff I went over before uh in general
+
+ align:start position:0%
+stuff I went over before uh in general
+ 
+
+ align:start position:0%
+stuff I went over before uh in general
+you do pretty well um I think if you if
+
+ align:start position:0%
+you do pretty well um I think if you if
+ 
+
+ align:start position:0%
+you do pretty well um I think if you if
+I'd given this summary 10 years ago I
+
+ align:start position:0%
+I'd given this summary 10 years ago I
+ 
+
+ align:start position:0%
+I'd given this summary 10 years ago I
+would have been even more optimistic
+
+ align:start position:0%
+would have been even more optimistic
+ 
+
+ align:start position:0%
+would have been even more optimistic
+because most people worked on metals and
+
+ align:start position:0%
+because most people worked on metals and
+ 
+
+ align:start position:0%
+because most people worked on metals and
+semiconductors um which tend to be
+
+ align:start position:0%
+semiconductors um which tend to be
+ 
+
+ align:start position:0%
+semiconductors um which tend to be
+fairly delocalized States so LDA and GDA
+
+ align:start position:0%
+fairly delocalized States so LDA and GDA
+ 
+
+ align:start position:0%
+fairly delocalized States so LDA and GDA
+do quite well I think as we dig into
+
+ align:start position:0%
+do quite well I think as we dig into
+ 
+
+ align:start position:0%
+do quite well I think as we dig into
+more complicated materials uh we have
+
+ align:start position:0%
+more complicated materials uh we have
+ 
+
+ align:start position:0%
+more complicated materials uh we have
+learned more about the errors of LDA and
+
+ align:start position:0%
+learned more about the errors of LDA and
+ 
+
+ align:start position:0%
+learned more about the errors of LDA and
+GGA um but on sort of classic Metals you
+
+ align:start position:0%
+GGA um but on sort of classic Metals you
+ 
+
+ align:start position:0%
+GGA um but on sort of classic Metals you
+do pretty well with lce constants
+
+ align:start position:0%
+do pretty well with lce constants
+ 
+
+ align:start position:0%
+do pretty well with lce constants
+reaction energies and cohesive energies
+
+ align:start position:0%
+reaction energies and cohesive energies
+ 
+
+ align:start position:0%
+reaction energies and cohesive energies
+um but now there is a series of methods
+
+ align:start position:0%
+um but now there is a series of methods
+ 
+
+ align:start position:0%
+um but now there is a series of methods
+under development and if we have some
+
+ align:start position:0%
+under development and if we have some
+ 
+
+ align:start position:0%
+under development and if we have some
+time we might sort of just Broach them
+
+ align:start position:0%
+time we might sort of just Broach them
+ 
+
+ align:start position:0%
+time we might sort of just Broach them
+uh to deal better with the correlation
+
+ align:start position:0%
+uh to deal better with the correlation
+ 
+
+ align:start position:0%
+uh to deal better with the correlation
+energy with the self interaction energy
+
+ align:start position:0%
+energy with the self interaction energy
+ 
+
+ align:start position:0%
+energy with the self interaction energy
+uh to solve these problems of both
+
+ align:start position:0%
+uh to solve these problems of both
+ 
+
+ align:start position:0%
+uh to solve these problems of both
+energetics and also electronic structure
+
+ align:start position:0%
+energetics and also electronic structure
+ 
+
+ align:start position:0%
+energetics and also electronic structure
+things such as the band so I'll end here
+
+ align:start position:0%
+things such as the band so I'll end here
+ 
+
+ align:start position:0%
+things such as the band so I'll end here
+and uh remember on Tuesday we have lab
+
+ align:start position:0%
+and uh remember on Tuesday we have lab
+ 
+
+ align:start position:0%
+and uh remember on Tuesday we have lab
+so you meet in the lab and then Thursday
+
+ align:start position:0%
+so you meet in the lab and then Thursday
+ 
+
+ align:start position:0%
+so you meet in the lab and then Thursday
+we'll be back here
\ No newline at end of file
diff --git a/WF9ftfGEGYw.txt b/WF9ftfGEGYw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1e7f5c4c4821e13ed706e79ce10ed19e4cf85224
--- /dev/null
+++ b/WF9ftfGEGYw.txt
@@ -0,0 +1,8539 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu let's get
+
+ align:start position:0%
+ocw.mit.edu let's get
+ 
+
+ align:start position:0%
+ocw.mit.edu let's get
+started um one announcement and that is
+
+ align:start position:0%
+started um one announcement and that is
+ 
+
+ align:start position:0%
+started um one announcement and that is
+that uh reminder about the celebration
+
+ align:start position:0%
+that uh reminder about the celebration
+ 
+
+ align:start position:0%
+that uh reminder about the celebration
+of learning on Wednesday
+
+ align:start position:0%
+of learning on Wednesday
+ 
+
+ align:start position:0%
+of learning on Wednesday
+October 2nd test two it'll have H
+
+ align:start position:0%
+October 2nd test two it'll have H
+ 
+
+ align:start position:0%
+October 2nd test two it'll have H
+coverage spanning lecture 7 through 17 7
+
+ align:start position:0%
+coverage spanning lecture 7 through 17 7
+ 
+
+ align:start position:0%
+coverage spanning lecture 7 through 17 7
+through 17 uh so the material that the
+
+ align:start position:0%
+through 17 uh so the material that the
+ 
+
+ align:start position:0%
+through 17 uh so the material that the
+new material that I'm going to introduce
+
+ align:start position:0%
+new material that I'm going to introduce
+ 
+
+ align:start position:0%
+new material that I'm going to introduce
+today will not be covered but certainly
+
+ align:start position:0%
+today will not be covered but certainly
+ 
+
+ align:start position:0%
+today will not be covered but certainly
+this little review is uh
+
+ align:start position:0%
+this little review is uh
+ 
+
+ align:start position:0%
+this little review is uh
+worthwhile um and going back to seven
+
+ align:start position:0%
+worthwhile um and going back to seven
+ 
+
+ align:start position:0%
+worthwhile um and going back to seven
+with the beginning of ionics so um what
+
+ align:start position:0%
+with the beginning of ionics so um what
+ 
+
+ align:start position:0%
+with the beginning of ionics so um what
+I wanted to do today was just uh set the
+
+ align:start position:0%
+I wanted to do today was just uh set the
+ 
+
+ align:start position:0%
+I wanted to do today was just uh set the
+stage briefly review where we were last
+
+ align:start position:0%
+stage briefly review where we were last
+ 
+
+ align:start position:0%
+stage briefly review where we were last
+day where we looked at the emission
+
+ align:start position:0%
+day where we looked at the emission
+ 
+
+ align:start position:0%
+day where we looked at the emission
+spectrum of a Target in an x-ray tube so
+
+ align:start position:0%
+spectrum of a Target in an x-ray tube so
+ 
+
+ align:start position:0%
+spectrum of a Target in an x-ray tube so
+here I've plotted uh intensity versus
+
+ align:start position:0%
+here I've plotted uh intensity versus
+ 
+
+ align:start position:0%
+here I've plotted uh intensity versus
+wave length so long wavelength this is
+
+ align:start position:0%
+wave length so long wavelength this is
+ 
+
+ align:start position:0%
+wave length so long wavelength this is
+low energy energy is increasing from
+
+ align:start position:0%
+low energy energy is increasing from
+ 
+
+ align:start position:0%
+low energy energy is increasing from
+right to left and what we see is a
+
+ align:start position:0%
+right to left and what we see is a
+ 
+
+ align:start position:0%
+right to left and what we see is a
+family of nested curves uh each taken a
+
+ align:start position:0%
+family of nested curves uh each taken a
+ 
+
+ align:start position:0%
+family of nested curves uh each taken a
+different plate voltage low voltage
+
+ align:start position:0%
+different plate voltage low voltage
+ 
+
+ align:start position:0%
+different plate voltage low voltage
+gives us uh low intensity high voltage
+
+ align:start position:0%
+gives us uh low intensity high voltage
+ 
+
+ align:start position:0%
+gives us uh low intensity high voltage
+gives us high intensity so we see this
+
+ align:start position:0%
+gives us high intensity so we see this
+ 
+
+ align:start position:0%
+gives us high intensity so we see this
+whale-shaped background which we refer
+
+ align:start position:0%
+whale-shaped background which we refer
+ 
+
+ align:start position:0%
+whale-shaped background which we refer
+to as the continuous Spectrum or brim
+
+ align:start position:0%
+to as the continuous Spectrum or brim
+ 
+
+ align:start position:0%
+to as the continuous Spectrum or brim
+straing and then once we reach a
+
+ align:start position:0%
+straing and then once we reach a
+ 
+
+ align:start position:0%
+straing and then once we reach a
+critical voltage Beyond which we start
+
+ align:start position:0%
+critical voltage Beyond which we start
+ 
+
+ align:start position:0%
+critical voltage Beyond which we start
+to see this second set of uh lines here
+
+ align:start position:0%
+to see this second set of uh lines here
+ 
+
+ align:start position:0%
+to see this second set of uh lines here
+which I've indicated in uh fuchsia and
+
+ align:start position:0%
+which I've indicated in uh fuchsia and
+ 
+
+ align:start position:0%
+which I've indicated in uh fuchsia and
+this is the characteristic spectrum and
+
+ align:start position:0%
+this is the characteristic spectrum and
+ 
+
+ align:start position:0%
+this is the characteristic spectrum and
+it's quantized it's not continuous we
+
+ align:start position:0%
+it's quantized it's not continuous we
+ 
+
+ align:start position:0%
+it's quantized it's not continuous we
+have discrete values of uh wavelength
+
+ align:start position:0%
+have discrete values of uh wavelength
+ 
+
+ align:start position:0%
+have discrete values of uh wavelength
+associated with energy transitions
+
+ align:start position:0%
+associated with energy transitions
+ 
+
+ align:start position:0%
+associated with energy transitions
+within the Target and those transitions
+
+ align:start position:0%
+within the Target and those transitions
+ 
+
+ align:start position:0%
+within the Target and those transitions
+are prompted by the ejection of inner
+
+ align:start position:0%
+are prompted by the ejection of inner
+ 
+
+ align:start position:0%
+are prompted by the ejection of inner
+shell electrons and that doesn't occur
+
+ align:start position:0%
+shell electrons and that doesn't occur
+ 
+
+ align:start position:0%
+shell electrons and that doesn't occur
+until you get to a certain critical uh
+
+ align:start position:0%
+until you get to a certain critical uh
+ 
+
+ align:start position:0%
+until you get to a certain critical uh
+plate voltage which translates into a
+
+ align:start position:0%
+plate voltage which translates into a
+ 
+
+ align:start position:0%
+plate voltage which translates into a
+certain critical ballistic uh energy on
+
+ align:start position:0%
+certain critical ballistic uh energy on
+ 
+
+ align:start position:0%
+certain critical ballistic uh energy on
+the part of the inant in electrons and
+
+ align:start position:0%
+the part of the inant in electrons and
+ 
+
+ align:start position:0%
+the part of the inant in electrons and
+there are a few features here that we
+
+ align:start position:0%
+there are a few features here that we
+ 
+
+ align:start position:0%
+there are a few features here that we
+can point out um the various discrete
+
+ align:start position:0%
+can point out um the various discrete
+ 
+
+ align:start position:0%
+can point out um the various discrete
+wavelengths of the characteristic
+
+ align:start position:0%
+wavelengths of the characteristic
+ 
+
+ align:start position:0%
+wavelengths of the characteristic
+Spectrum are calculable the K Alpha and
+
+ align:start position:0%
+Spectrum are calculable the K Alpha and
+ 
+
+ align:start position:0%
+Spectrum are calculable the K Alpha and
+the L Alpha lines are calculable by
+
+ align:start position:0%
+the L Alpha lines are calculable by
+ 
+
+ align:start position:0%
+the L Alpha lines are calculable by
+Mosley's law which is given here uh
+
+ align:start position:0%
+Mosley's law which is given here uh
+ 
+
+ align:start position:0%
+Mosley's law which is given here uh
+where the NF and ni are associated with
+
+ align:start position:0%
+where the NF and ni are associated with
+ 
+
+ align:start position:0%
+where the NF and ni are associated with
+the particular transition for K lines
+
+ align:start position:0%
+the particular transition for K lines
+ 
+
+ align:start position:0%
+the particular transition for K lines
+it's the transition from two to one and
+
+ align:start position:0%
+it's the transition from two to one and
+ 
+
+ align:start position:0%
+it's the transition from two to one and
+screening factor is one for the K Alpha
+
+ align:start position:0%
+screening factor is one for the K Alpha
+ 
+
+ align:start position:0%
+screening factor is one for the K Alpha
+transition for the L Alpha transition
+
+ align:start position:0%
+transition for the L Alpha transition
+ 
+
+ align:start position:0%
+transition for the L Alpha transition
+it's uh from 3 to two and the screening
+
+ align:start position:0%
+it's uh from 3 to two and the screening
+ 
+
+ align:start position:0%
+it's uh from 3 to two and the screening
+factor in that case is 7.4 so we can
+
+ align:start position:0%
+factor in that case is 7.4 so we can
+ 
+
+ align:start position:0%
+factor in that case is 7.4 so we can
+calculate these discrete values and the
+
+ align:start position:0%
+calculate these discrete values and the
+ 
+
+ align:start position:0%
+calculate these discrete values and the
+other point that we can calculate on
+
+ align:start position:0%
+other point that we can calculate on
+ 
+
+ align:start position:0%
+other point that we can calculate on
+this curve is the Leading Edge of the
+
+ align:start position:0%
+this curve is the Leading Edge of the
+ 
+
+ align:start position:0%
+this curve is the Leading Edge of the
+continuous Spectrum the Leading Edge of
+
+ align:start position:0%
+continuous Spectrum the Leading Edge of
+ 
+
+ align:start position:0%
+continuous Spectrum the Leading Edge of
+the continuous spectrum is the uh
+
+ align:start position:0%
+the continuous spectrum is the uh
+ 
+
+ align:start position:0%
+the continuous spectrum is the uh
+designated here as the shortest
+
+ align:start position:0%
+designated here as the shortest
+ 
+
+ align:start position:0%
+designated here as the shortest
+wavelength which obviously is the
+
+ align:start position:0%
+wavelength which obviously is the
+ 
+
+ align:start position:0%
+wavelength which obviously is the
+highest energy and that derives from
+
+ align:start position:0%
+highest energy and that derives from
+ 
+
+ align:start position:0%
+highest energy and that derives from
+Total transfer of incident ballistic
+
+ align:start position:0%
+Total transfer of incident ballistic
+ 
+
+ align:start position:0%
+Total transfer of incident ballistic
+energy of the electron to Photon and
+
+ align:start position:0%
+energy of the electron to Photon and
+ 
+
+ align:start position:0%
+energy of the electron to Photon and
+capture of the electron and that's the
+
+ align:start position:0%
+capture of the electron and that's the
+ 
+
+ align:start position:0%
+capture of the electron and that's the
+shortest wavelength given by the Dwayne
+
+ align:start position:0%
+shortest wavelength given by the Dwayne
+ 
+
+ align:start position:0%
+shortest wavelength given by the Dwayne
+hunt law which is
+
+ align:start position:0%
+hunt law which is
+ 
+
+ align:start position:0%
+hunt law which is
+12,400 over the plate voltage giving you
+
+ align:start position:0%
+12,400 over the plate voltage giving you
+ 
+
+ align:start position:0%
+12,400 over the plate voltage giving you
+a value of wavelength and angstroms so I
+
+ align:start position:0%
+a value of wavelength and angstroms so I
+ 
+
+ align:start position:0%
+a value of wavelength and angstroms so I
+think we're ready now to uh probe Atomic
+
+ align:start position:0%
+think we're ready now to uh probe Atomic
+ 
+
+ align:start position:0%
+think we're ready now to uh probe Atomic
+arrangement with x-rays and in order to
+
+ align:start position:0%
+arrangement with x-rays and in order to
+ 
+
+ align:start position:0%
+arrangement with x-rays and in order to
+do so we're going to rely on two um
+
+ align:start position:0%
+do so we're going to rely on two um
+ 
+
+ align:start position:0%
+do so we're going to rely on two um
+important uh factors first of all we're
+
+ align:start position:0%
+important uh factors first of all we're
+ 
+
+ align:start position:0%
+important uh factors first of all we're
+going to model we're going to model the
+
+ align:start position:0%
+going to model we're going to model the
+ 
+
+ align:start position:0%
+going to model we're going to model the
+crystal as an array of mirrors in other
+
+ align:start position:0%
+crystal as an array of mirrors in other
+ 
+
+ align:start position:0%
+crystal as an array of mirrors in other
+words we're going to look at the atoms
+
+ align:start position:0%
+words we're going to look at the atoms
+ 
+
+ align:start position:0%
+words we're going to look at the atoms
+in the Crystal and consider each atom as
+
+ align:start position:0%
+in the Crystal and consider each atom as
+ 
+
+ align:start position:0%
+in the Crystal and consider each atom as
+acting as a
+
+ align:start position:0%
+acting as a
+ 
+
+ align:start position:0%
+acting as a
+mirror so this will give us features
+
+ align:start position:0%
+mirror so this will give us features
+ 
+
+ align:start position:0%
+mirror so this will give us features
+that we can exploit in a very simple
+
+ align:start position:0%
+that we can exploit in a very simple
+ 
+
+ align:start position:0%
+that we can exploit in a very simple
+model so let's model atoms let's model
+
+ align:start position:0%
+model so let's model atoms let's model
+ 
+
+ align:start position:0%
+model so let's model atoms let's model
+atoms as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mirrors and that's going to allow us to
+
+ align:start position:0%
+mirrors and that's going to allow us to
+ 
+
+ align:start position:0%
+mirrors and that's going to allow us to
+use the laws of specular
+
+ align:start position:0%
+use the laws of specular
+ 
+
+ align:start position:0%
+use the laws of specular
+reflection the laws of specular
+
+ align:start position:0%
+reflection the laws of specular
+ 
+
+ align:start position:0%
+reflection the laws of specular
+reflection and the one that we most
+
+ align:start position:0%
+reflection and the one that we most
+ 
+
+ align:start position:0%
+reflection and the one that we most
+critically rely on is that the angle of
+
+ align:start position:0%
+critically rely on is that the angle of
+ 
+
+ align:start position:0%
+critically rely on is that the angle of
+incidence equals the angle of reflection
+
+ align:start position:0%
+incidence equals the angle of reflection
+ 
+
+ align:start position:0%
+incidence equals the angle of reflection
+the angle of incidence equals the angle
+
+ align:start position:0%
+the angle of incidence equals the angle
+ 
+
+ align:start position:0%
+the angle of incidence equals the angle
+of reflection so that's the first thing
+
+ align:start position:0%
+of reflection so that's the first thing
+ 
+
+ align:start position:0%
+of reflection so that's the first thing
+that we uh uh use and then the second
+
+ align:start position:0%
+that we uh uh use and then the second
+ 
+
+ align:start position:0%
+that we uh uh use and then the second
+thing that we use is interference
+
+ align:start position:0%
+thing that we use is interference
+ 
+
+ align:start position:0%
+thing that we use is interference
+criteria we're going to
+
+ align:start position:0%
+criteria we're going to
+ 
+
+ align:start position:0%
+criteria we're going to
+apply interference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+criteria so let's take a look at what
+
+ align:start position:0%
+criteria so let's take a look at what
+ 
+
+ align:start position:0%
+criteria so let's take a look at what
+mean by that uh we have two
+
+ align:start position:0%
+mean by that uh we have two
+ 
+
+ align:start position:0%
+mean by that uh we have two
+possibilities we can have multiple beams
+
+ align:start position:0%
+possibilities we can have multiple beams
+ 
+
+ align:start position:0%
+possibilities we can have multiple beams
+coming in Phase or we can have multiple
+
+ align:start position:0%
+coming in Phase or we can have multiple
+ 
+
+ align:start position:0%
+coming in Phase or we can have multiple
+beams coming out of phase and so here's
+
+ align:start position:0%
+beams coming out of phase and so here's
+ 
+
+ align:start position:0%
+beams coming out of phase and so here's
+what we talk about I'm going to show
+
+ align:start position:0%
+what we talk about I'm going to show
+ 
+
+ align:start position:0%
+what we talk about I'm going to show
+little sketch where I'm plotting
+
+ align:start position:0%
+little sketch where I'm plotting
+ 
+
+ align:start position:0%
+little sketch where I'm plotting
+amplitude ude this is some
+
+ align:start position:0%
+amplitude ude this is some
+ 
+
+ align:start position:0%
+amplitude ude this is some
+electromagnetic signal amplitude versus
+
+ align:start position:0%
+electromagnetic signal amplitude versus
+ 
+
+ align:start position:0%
+electromagnetic signal amplitude versus
+time amplitude versus time so let's look
+
+ align:start position:0%
+time amplitude versus time so let's look
+ 
+
+ align:start position:0%
+time amplitude versus time so let's look
+at two rays here's one this is amplitude
+
+ align:start position:0%
+at two rays here's one this is amplitude
+ 
+
+ align:start position:0%
+at two rays here's one this is amplitude
+versus time and a second one in Phase so
+
+ align:start position:0%
+versus time and a second one in Phase so
+ 
+
+ align:start position:0%
+versus time and a second one in Phase so
+I'm going to draw it directly beneath
+
+ align:start position:0%
+I'm going to draw it directly beneath
+ 
+
+ align:start position:0%
+I'm going to draw it directly beneath
+and so the crests line up the troughs
+
+ align:start position:0%
+and so the crests line up the troughs
+ 
+
+ align:start position:0%
+and so the crests line up the troughs
+line up so if I take Ray one plus Ray 2
+
+ align:start position:0%
+line up so if I take Ray one plus Ray 2
+ 
+
+ align:start position:0%
+line up so if I take Ray one plus Ray 2
+I'm going to add them and I will get the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intensification the additive sum of
+
+ align:start position:0%
+intensification the additive sum of
+ 
+
+ align:start position:0%
+intensification the additive sum of
+amplitudes because they're in Phase so
+
+ align:start position:0%
+amplitudes because they're in Phase so
+ 
+
+ align:start position:0%
+amplitudes because they're in Phase so
+this is called
+
+ align:start position:0%
+this is called
+ 
+
+ align:start position:0%
+this is called
+inphase radiation summing or the other
+
+ align:start position:0%
+inphase radiation summing or the other
+ 
+
+ align:start position:0%
+inphase radiation summing or the other
+term applied to this is constructive
+
+ align:start position:0%
+term applied to this is constructive
+ 
+
+ align:start position:0%
+term applied to this is constructive
+interference constructive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interference that's the one extreme The
+
+ align:start position:0%
+interference that's the one extreme The
+ 
+
+ align:start position:0%
+interference that's the one extreme The
+Other Extreme is totally out of phase so
+
+ align:start position:0%
+Other Extreme is totally out of phase so
+ 
+
+ align:start position:0%
+Other Extreme is totally out of phase so
+in that case Ray one I'll draw as I did
+
+ align:start position:0%
+in that case Ray one I'll draw as I did
+ 
+
+ align:start position:0%
+in that case Ray one I'll draw as I did
+before but Ray two I'll draw
+
+ align:start position:0%
+before but Ray two I'll draw
+ 
+
+ align:start position:0%
+before but Ray two I'll draw
+symmetrically opposite so that in Ray
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two the crest of Ray two aligns with the
+
+ align:start position:0%
+two the crest of Ray two aligns with the
+ 
+
+ align:start position:0%
+two the crest of Ray two aligns with the
+trough of Ray one the trough of Ray 2
+
+ align:start position:0%
+trough of Ray one the trough of Ray 2
+ 
+
+ align:start position:0%
+trough of Ray one the trough of Ray 2
+aligns with the crest of Ray one and for
+
+ align:start position:0%
+aligns with the crest of Ray one and for
+ 
+
+ align:start position:0%
+aligns with the crest of Ray one and for
+argument sake let's say that these are
+
+ align:start position:0%
+argument sake let's say that these are
+ 
+
+ align:start position:0%
+argument sake let's say that these are
+equal in amplitude so if I have two rays
+
+ align:start position:0%
+equal in amplitude so if I have two rays
+ 
+
+ align:start position:0%
+equal in amplitude so if I have two rays
+equal in amplitude and they interfere
+
+ align:start position:0%
+equal in amplitude and they interfere
+ 
+
+ align:start position:0%
+equal in amplitude and they interfere
+but they're perfectly out of phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I add these two signals what I will
+
+ align:start position:0%
+if I add these two signals what I will
+ 
+
+ align:start position:0%
+if I add these two signals what I will
+get is nothing they will
+
+ align:start position:0%
+get is nothing they will
+ 
+
+ align:start position:0%
+get is nothing they will
+cancel complete cancellation so this is
+
+ align:start position:0%
+cancel complete cancellation so this is
+ 
+
+ align:start position:0%
+cancel complete cancellation so this is
+called destructive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interference destructive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interference and those are the only two
+
+ align:start position:0%
+interference and those are the only two
+ 
+
+ align:start position:0%
+interference and those are the only two
+principles we need and we can describe
+
+ align:start position:0%
+principles we need and we can describe
+ 
+
+ align:start position:0%
+principles we need and we can describe
+at a very reasonable level what's going
+
+ align:start position:0%
+at a very reasonable level what's going
+ 
+
+ align:start position:0%
+at a very reasonable level what's going
+on inside a crystal which is being
+
+ align:start position:0%
+on inside a crystal which is being
+ 
+
+ align:start position:0%
+on inside a crystal which is being
+irradiated by electromagnetic radiation
+
+ align:start position:0%
+irradiated by electromagnetic radiation
+ 
+
+ align:start position:0%
+irradiated by electromagnetic radiation
+in the X region of the spectrum that's
+
+ align:start position:0%
+in the X region of the spectrum that's
+ 
+
+ align:start position:0%
+in the X region of the spectrum that's
+all I'm going to use is these two ideas
+
+ align:start position:0%
+all I'm going to use is these two ideas
+ 
+
+ align:start position:0%
+all I'm going to use is these two ideas
+so let's now go to a simple model here
+
+ align:start position:0%
+so let's now go to a simple model here
+ 
+
+ align:start position:0%
+so let's now go to a simple model here
+of a crystal so we'll draw some atoms
+
+ align:start position:0%
+of a crystal so we'll draw some atoms
+ 
+
+ align:start position:0%
+of a crystal so we'll draw some atoms
+here there's the top plane let's go down
+
+ align:start position:0%
+here there's the top plane let's go down
+ 
+
+ align:start position:0%
+here there's the top plane let's go down
+a second and I'll make this cubic
+
+ align:start position:0%
+a second and I'll make this cubic
+ 
+
+ align:start position:0%
+a second and I'll make this cubic
+so here's two planes of atoms and let's
+
+ align:start position:0%
+so here's two planes of atoms and let's
+ 
+
+ align:start position:0%
+so here's two planes of atoms and let's
+say I've got incident light coming in at
+
+ align:start position:0%
+say I've got incident light coming in at
+ 
+
+ align:start position:0%
+say I've got incident light coming in at
+some angle Theta here's some incident
+
+ align:start position:0%
+some angle Theta here's some incident
+ 
+
+ align:start position:0%
+some angle Theta here's some incident
+light coming in at some angle
+
+ align:start position:0%
+light coming in at some angle
+ 
+
+ align:start position:0%
+light coming in at some angle
+Theta and so one Ray I'm showing
+
+ align:start position:0%
+Theta and so one Ray I'm showing
+ 
+
+ align:start position:0%
+Theta and so one Ray I'm showing
+striking this atom and if I observe the
+
+ align:start position:0%
+striking this atom and if I observe the
+ 
+
+ align:start position:0%
+striking this atom and if I observe the
+laws of specular reflection this will
+
+ align:start position:0%
+laws of specular reflection this will
+ 
+
+ align:start position:0%
+laws of specular reflection this will
+reflect from the mirror at The Identical
+
+ align:start position:0%
+reflect from the mirror at The Identical
+ 
+
+ align:start position:0%
+reflect from the mirror at The Identical
+angle so the angle of reflection equals
+
+ align:start position:0%
+angle so the angle of reflection equals
+ 
+
+ align:start position:0%
+angle so the angle of reflection equals
+the angle of incidence and let's put a
+
+ align:start position:0%
+the angle of incidence and let's put a
+ 
+
+ align:start position:0%
+the angle of incidence and let's put a
+second Ray let's put a second Ray coming
+
+ align:start position:0%
+second Ray let's put a second Ray coming
+ 
+
+ align:start position:0%
+second Ray let's put a second Ray coming
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+here and it too will uh reflect at the
+
+ align:start position:0%
+here and it too will uh reflect at the
+ 
+
+ align:start position:0%
+here and it too will uh reflect at the
+same angle and come out like
+
+ align:start position:0%
+same angle and come out like
+ 
+
+ align:start position:0%
+same angle and come out like
+so oh there's a cell phone somebody's
+
+ align:start position:0%
+so oh there's a cell phone somebody's
+ 
+
+ align:start position:0%
+so oh there's a cell phone somebody's
+leaving the room let's go I want the
+
+ align:start position:0%
+leaving the room let's go I want the
+ 
+
+ align:start position:0%
+leaving the room let's go I want the
+cell phones off no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compromises show some respect for your
+
+ align:start position:0%
+compromises show some respect for your
+ 
+
+ align:start position:0%
+compromises show some respect for your
+classmates it's rude it's disrespectful
+
+ align:start position:0%
+classmates it's rude it's disrespectful
+ 
+
+ align:start position:0%
+classmates it's rude it's disrespectful
+to me it's disrespectful to the class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+don't get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it that happens on Wednesday I will tear
+
+ align:start position:0%
+it that happens on Wednesday I will tear
+ 
+
+ align:start position:0%
+it that happens on Wednesday I will tear
+up your paper in front of your eyes and
+
+ align:start position:0%
+up your paper in front of your eyes and
+ 
+
+ align:start position:0%
+up your paper in front of your eyes and
+give you a zero mark my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+words
+
+ align:start position:0%
+words
+ 
+
+ align:start position:0%
+words
+so I want to look at what happens when I
+
+ align:start position:0%
+so I want to look at what happens when I
+ 
+
+ align:start position:0%
+so I want to look at what happens when I
+have light coming
+
+ align:start position:0%
+have light coming
+ 
+
+ align:start position:0%
+have light coming
+in at a particular angle and furthermore
+
+ align:start position:0%
+in at a particular angle and furthermore
+ 
+
+ align:start position:0%
+in at a particular angle and furthermore
+I want to specify that I have uh inphase
+
+ align:start position:0%
+I want to specify that I have uh inphase
+ 
+
+ align:start position:0%
+I want to specify that I have uh inphase
+radiation inphase radiation which is a
+
+ align:start position:0%
+radiation inphase radiation which is a
+ 
+
+ align:start position:0%
+radiation inphase radiation which is a
+also termed coherent so I have inphase
+
+ align:start position:0%
+also termed coherent so I have inphase
+ 
+
+ align:start position:0%
+also termed coherent so I have inphase
+incident coherent radiation and
+
+ align:start position:0%
+incident coherent radiation and
+ 
+
+ align:start position:0%
+incident coherent radiation and
+furthermore I want it
+
+ align:start position:0%
+furthermore I want it
+ 
+
+ align:start position:0%
+furthermore I want it
+monochromatic monochromatic so these are
+
+ align:start position:0%
+monochromatic monochromatic so these are
+ 
+
+ align:start position:0%
+monochromatic monochromatic so these are
+X-rays that are coherent and
+
+ align:start position:0%
+X-rays that are coherent and
+ 
+
+ align:start position:0%
+X-rays that are coherent and
+monochromatic monochromatic means a
+
+ align:start position:0%
+monochromatic monochromatic means a
+ 
+
+ align:start position:0%
+monochromatic monochromatic means a
+single wav length a single wavelength so
+
+ align:start position:0%
+single wav length a single wavelength so
+ 
+
+ align:start position:0%
+single wav length a single wavelength so
+here's the incident radiation on the
+
+ align:start position:0%
+here's the incident radiation on the
+ 
+
+ align:start position:0%
+here's the incident radiation on the
+left
+
+ align:start position:0%
+left
+ 
+
+ align:start position:0%
+left
+this is the incident radiation on the
+
+ align:start position:0%
+this is the incident radiation on the
+ 
+
+ align:start position:0%
+this is the incident radiation on the
+left and this is the reflected radiation
+
+ align:start position:0%
+left and this is the reflected radiation
+ 
+
+ align:start position:0%
+left and this is the reflected radiation
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+right and uh what do I want to see here
+
+ align:start position:0%
+right and uh what do I want to see here
+ 
+
+ align:start position:0%
+right and uh what do I want to see here
+I want to see what are the conditions to
+
+ align:start position:0%
+I want to see what are the conditions to
+ 
+
+ align:start position:0%
+I want to see what are the conditions to
+give me constructive interference
+
+ align:start position:0%
+give me constructive interference
+ 
+
+ align:start position:0%
+give me constructive interference
+because I don't want destructive
+
+ align:start position:0%
+because I don't want destructive
+ 
+
+ align:start position:0%
+because I don't want destructive
+interference if I have destructive
+
+ align:start position:0%
+interference if I have destructive
+ 
+
+ align:start position:0%
+interference if I have destructive
+interference I won't see anything so uh
+
+ align:start position:0%
+interference I won't see anything so uh
+ 
+
+ align:start position:0%
+interference I won't see anything so uh
+let's mark this by showing some kind of
+
+ align:start position:0%
+let's mark this by showing some kind of
+ 
+
+ align:start position:0%
+let's mark this by showing some kind of
+a way form what I'll do is show just the
+
+ align:start position:0%
+a way form what I'll do is show just the
+ 
+
+ align:start position:0%
+a way form what I'll do is show just the
+first sinusoid I'll show the first
+
+ align:start position:0%
+first sinusoid I'll show the first
+ 
+
+ align:start position:0%
+first sinusoid I'll show the first
+sinusoid and then I'll show the same on
+
+ align:start position:0%
+sinusoid and then I'll show the same on
+ 
+
+ align:start position:0%
+sinusoid and then I'll show the same on
+the second Ray so what I'm trying to
+
+ align:start position:0%
+the second Ray so what I'm trying to
+ 
+
+ align:start position:0%
+the second Ray so what I'm trying to
+indicate is that I have inphase
+
+ align:start position:0%
+indicate is that I have inphase
+ 
+
+ align:start position:0%
+indicate is that I have inphase
+radiation coming down from the left and
+
+ align:start position:0%
+radiation coming down from the left and
+ 
+
+ align:start position:0%
+radiation coming down from the left and
+then over here I want to indicate that I
+
+ align:start position:0%
+then over here I want to indicate that I
+ 
+
+ align:start position:0%
+then over here I want to indicate that I
+have inphase radiation leaving so again
+
+ align:start position:0%
+have inphase radiation leaving so again
+ 
+
+ align:start position:0%
+have inphase radiation leaving so again
+I'll indicate the sinusoids in the same
+
+ align:start position:0%
+I'll indicate the sinusoids in the same
+ 
+
+ align:start position:0%
+I'll indicate the sinusoids in the same
+position so there's an issue here you
+
+ align:start position:0%
+position so there's an issue here you
+ 
+
+ align:start position:0%
+position so there's an issue here you
+can see Ray one travels a shorter
+
+ align:start position:0%
+can see Ray one travels a shorter
+ 
+
+ align:start position:0%
+can see Ray one travels a shorter
+distance than Ray 2 Ray 2 has to go
+
+ align:start position:0%
+distance than Ray 2 Ray 2 has to go
+ 
+
+ align:start position:0%
+distance than Ray 2 Ray 2 has to go
+farther so I can actually calculate how
+
+ align:start position:0%
+farther so I can actually calculate how
+ 
+
+ align:start position:0%
+farther so I can actually calculate how
+far that is if I drop a normal from here
+
+ align:start position:0%
+far that is if I drop a normal from here
+ 
+
+ align:start position:0%
+far that is if I drop a normal from here
+and a normal from here I can label this
+
+ align:start position:0%
+and a normal from here I can label this
+ 
+
+ align:start position:0%
+and a normal from here I can label this
+a b and c and we can see that Ray two
+
+ align:start position:0%
+a b and c and we can see that Ray two
+ 
+
+ align:start position:0%
+a b and c and we can see that Ray two
+has to travel a farther distance a B
+
+ align:start position:0%
+has to travel a farther distance a B
+ 
+
+ align:start position:0%
+has to travel a farther distance a B
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+BC now what's the condition of ab plus
+
+ align:start position:0%
+BC now what's the condition of ab plus
+ 
+
+ align:start position:0%
+BC now what's the condition of ab plus
+BC to ensure that these two are in Phase
+
+ align:start position:0%
+BC to ensure that these two are in Phase
+ 
+
+ align:start position:0%
+BC to ensure that these two are in Phase
+they must equal some path length that is
+
+ align:start position:0%
+they must equal some path length that is
+ 
+
+ align:start position:0%
+they must equal some path length that is
+a whole number of wavelengths otherwise
+
+ align:start position:0%
+a whole number of wavelengths otherwise
+ 
+
+ align:start position:0%
+a whole number of wavelengths otherwise
+I will get some amount of destructive
+
+ align:start position:0%
+I will get some amount of destructive
+ 
+
+ align:start position:0%
+I will get some amount of destructive
+interference and N of course is a whole
+
+ align:start position:0%
+interference and N of course is a whole
+ 
+
+ align:start position:0%
+interference and N of course is a whole
+number I don't care it's one two and so
+
+ align:start position:0%
+number I don't care it's one two and so
+ 
+
+ align:start position:0%
+number I don't care it's one two and so
+on and actually we can call this this is
+
+ align:start position:0%
+on and actually we can call this this is
+ 
+
+ align:start position:0%
+on and actually we can call this this is
+the order of the reflection this is the
+
+ align:start position:0%
+the order of the reflection this is the
+ 
+
+ align:start position:0%
+the order of the reflection this is the
+order of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reflection and if I go through the uh
+
+ align:start position:0%
+reflection and if I go through the uh
+ 
+
+ align:start position:0%
+reflection and if I go through the uh
+math um we know what Theta is what's
+
+ align:start position:0%
+math um we know what Theta is what's
+ 
+
+ align:start position:0%
+math um we know what Theta is what's
+this distance between successive planes
+
+ align:start position:0%
+this distance between successive planes
+ 
+
+ align:start position:0%
+this distance between successive planes
+if I'm showing you adjacent hkl plane
+
+ align:start position:0%
+if I'm showing you adjacent hkl plane
+ 
+
+ align:start position:0%
+if I'm showing you adjacent hkl plane
+then this distance here is d as we've
+
+ align:start position:0%
+then this distance here is d as we've
+ 
+
+ align:start position:0%
+then this distance here is d as we've
+defined it before this is the distance
+
+ align:start position:0%
+defined it before this is the distance
+ 
+
+ align:start position:0%
+defined it before this is the distance
+between adjacent hkl planes and if I go
+
+ align:start position:0%
+between adjacent hkl planes and if I go
+ 
+
+ align:start position:0%
+between adjacent hkl planes and if I go
+through the trigonometry here n Lambda
+
+ align:start position:0%
+through the trigonometry here n Lambda
+ 
+
+ align:start position:0%
+through the trigonometry here n Lambda
+will equal 2 *
+
+ align:start position:0%
+will equal 2 *
+ 
+
+ align:start position:0%
+will equal 2 *
+d s of
+
+ align:start position:0%
+d s of
+ 
+
+ align:start position:0%
+d s of
+theta we got the angle Theta we know the
+
+ align:start position:0%
+theta we got the angle Theta we know the
+ 
+
+ align:start position:0%
+theta we got the angle Theta we know the
+distance between successive planes if n
+
+ align:start position:0%
+distance between successive planes if n
+ 
+
+ align:start position:0%
+distance between successive planes if n
+Lambda equals 2D sin Theta this path
+
+ align:start position:0%
+Lambda equals 2D sin Theta this path
+ 
+
+ align:start position:0%
+Lambda equals 2D sin Theta this path
+length will be such that constructive
+
+ align:start position:0%
+length will be such that constructive
+ 
+
+ align:start position:0%
+length will be such that constructive
+interference will occur in inphase
+
+ align:start position:0%
+interference will occur in inphase
+ 
+
+ align:start position:0%
+interference will occur in inphase
+radiation will be reflected as
+
+ align:start position:0%
+radiation will be reflected as
+ 
+
+ align:start position:0%
+radiation will be reflected as
+such and this is called brags
+
+ align:start position:0%
+such and this is called brags
+ 
+
+ align:start position:0%
+such and this is called brags
+law this is Bragg's law it's the
+
+ align:start position:0%
+law this is Bragg's law it's the
+ 
+
+ align:start position:0%
+law this is Bragg's law it's the
+condition for constructive interference
+
+ align:start position:0%
+condition for constructive interference
+ 
+
+ align:start position:0%
+condition for constructive interference
+in a
+
+ align:start position:0%
+in a
+ 
+
+ align:start position:0%
+in a
+crystal condition for constructive
+
+ align:start position:0%
+crystal condition for constructive
+ 
+
+ align:start position:0%
+crystal condition for constructive
+interference in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crystal and in 3091 in 3091 what we're
+
+ align:start position:0%
+crystal and in 3091 in 3091 what we're
+ 
+
+ align:start position:0%
+crystal and in 3091 in 3091 what we're
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+do in 3091 we're going to neglect higher
+
+ align:start position:0%
+do in 3091 we're going to neglect higher
+ 
+
+ align:start position:0%
+do in 3091 we're going to neglect higher
+order Reflections in 3091 we neglect
+
+ align:start position:0%
+order Reflections in 3091 we neglect
+ 
+
+ align:start position:0%
+order Reflections in 3091 we neglect
+higher order Reflections so let's just
+
+ align:start position:0%
+higher order Reflections so let's just
+ 
+
+ align:start position:0%
+higher order Reflections so let's just
+put D equals 1 so excuse me Nal 1 so
+
+ align:start position:0%
+put D equals 1 so excuse me Nal 1 so
+ 
+
+ align:start position:0%
+put D equals 1 so excuse me Nal 1 so
+Bragg's law for 3091 will simply be
+
+ align:start position:0%
+Bragg's law for 3091 will simply be
+ 
+
+ align:start position:0%
+Bragg's law for 3091 will simply be
+Lambda =
+
+ align:start position:0%
+Lambda =
+ 
+
+ align:start position:0%
+Lambda =
+2D sin
+
+ align:start position:0%
+2D sin
+ 
+
+ align:start position:0%
+2D sin
+Theta that's the brag
+
+ align:start position:0%
+Theta that's the brag
+ 
+
+ align:start position:0%
+Theta that's the brag
+condition now um suppose I have a new uh
+
+ align:start position:0%
+condition now um suppose I have a new uh
+ 
+
+ align:start position:0%
+condition now um suppose I have a new uh
+system and I find that I have now atoms
+
+ align:start position:0%
+system and I find that I have now atoms
+ 
+
+ align:start position:0%
+system and I find that I have now atoms
+here let's say I go from a simple cubic
+
+ align:start position:0%
+here let's say I go from a simple cubic
+ 
+
+ align:start position:0%
+here let's say I go from a simple cubic
+to a body centered cubic well in body
+
+ align:start position:0%
+to a body centered cubic well in body
+ 
+
+ align:start position:0%
+to a body centered cubic well in body
+centered cubic there are atoms here I
+
+ align:start position:0%
+centered cubic there are atoms here I
+ 
+
+ align:start position:0%
+centered cubic there are atoms here I
+know they're in a different plane
+
+ align:start position:0%
+know they're in a different plane
+ 
+
+ align:start position:0%
+know they're in a different plane
+relative to the board but relative to
+
+ align:start position:0%
+relative to the board but relative to
+ 
+
+ align:start position:0%
+relative to the board but relative to
+the horizontal there's a plane of atoms
+
+ align:start position:0%
+the horizontal there's a plane of atoms
+ 
+
+ align:start position:0%
+the horizontal there's a plane of atoms
+at this location so let's see what
+
+ align:start position:0%
+at this location so let's see what
+ 
+
+ align:start position:0%
+at this location so let's see what
+happens in this case in this case if I
+
+ align:start position:0%
+happens in this case in this case if I
+ 
+
+ align:start position:0%
+happens in this case in this case if I
+have a third Ray that comes in let's
+
+ align:start position:0%
+have a third Ray that comes in let's
+ 
+
+ align:start position:0%
+have a third Ray that comes in let's
+call it Ray three and Ray three also is
+
+ align:start position:0%
+call it Ray three and Ray three also is
+ 
+
+ align:start position:0%
+call it Ray three and Ray three also is
+in Phase with Ray one and Ray two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the reflected ray three I can
+
+ align:start position:0%
+this is the reflected ray three I can
+ 
+
+ align:start position:0%
+this is the reflected ray three I can
+Define the additional path length of Ray
+
+ align:start position:0%
+Define the additional path length of Ray
+ 
+
+ align:start position:0%
+Define the additional path length of Ray
+three as d e f and what we see is that
+
+ align:start position:0%
+three as d e f and what we see is that
+ 
+
+ align:start position:0%
+three as d e f and what we see is that
+it turns out then that D plus e f if n
+
+ align:start position:0%
+it turns out then that D plus e f if n
+ 
+
+ align:start position:0%
+it turns out then that D plus e f if n
+equals 1 this is going to be 1 12 a
+
+ align:start position:0%
+equals 1 this is going to be 1 12 a
+ 
+
+ align:start position:0%
+equals 1 this is going to be 1 12 a
+wavelength if AB plus BC is one
+
+ align:start position:0%
+wavelength if AB plus BC is one
+ 
+
+ align:start position:0%
+wavelength if AB plus BC is one
+wavelength this is one half wavelength
+
+ align:start position:0%
+wavelength this is one half wavelength
+ 
+
+ align:start position:0%
+wavelength this is one half wavelength
+and what that means is that the
+
+ align:start position:0%
+and what that means is that the
+ 
+
+ align:start position:0%
+and what that means is that the
+reflected
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reflected ray three is perfectly out of
+
+ align:start position:0%
+reflected ray three is perfectly out of
+ 
+
+ align:start position:0%
+reflected ray three is perfectly out of
+phase perfectly out of
+
+ align:start position:0%
+phase perfectly out of
+ 
+
+ align:start position:0%
+phase perfectly out of
+phase with Rays one and
+
+ align:start position:0%
+phase with Rays one and
+ 
+
+ align:start position:0%
+phase with Rays one and
+two with one and two so that means we're
+
+ align:start position:0%
+two with one and two so that means we're
+ 
+
+ align:start position:0%
+two with one and two so that means we're
+going to get destructive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interference we're going to get
+
+ align:start position:0%
+interference we're going to get
+ 
+
+ align:start position:0%
+interference we're going to get
+destructive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interference and that means if we put a
+
+ align:start position:0%
+interference and that means if we put a
+ 
+
+ align:start position:0%
+interference and that means if we put a
+detector if we if we park a detector
+
+ align:start position:0%
+detector if we if we park a detector
+ 
+
+ align:start position:0%
+detector if we if we park a detector
+right here we will measure zero
+
+ align:start position:0%
+right here we will measure zero
+ 
+
+ align:start position:0%
+right here we will measure zero
+intensity so we
+
+ align:start position:0%
+intensity so we
+ 
+
+ align:start position:0%
+intensity so we
+measure zero intensity at that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+angle so now what I want to do is I want
+
+ align:start position:0%
+angle so now what I want to do is I want
+ 
+
+ align:start position:0%
+angle so now what I want to do is I want
+to I want to generalize what we've
+
+ align:start position:0%
+to I want to generalize what we've
+ 
+
+ align:start position:0%
+to I want to generalize what we've
+observed here I want to generalize this
+
+ align:start position:0%
+observed here I want to generalize this
+ 
+
+ align:start position:0%
+observed here I want to generalize this
+analysis and if I generalize this
+
+ align:start position:0%
+analysis and if I generalize this
+ 
+
+ align:start position:0%
+analysis and if I generalize this
+analysis what I get is that if I take
+
+ align:start position:0%
+analysis what I get is that if I take
+ 
+
+ align:start position:0%
+analysis what I get is that if I take
+the interference Criterion
+
+ align:start position:0%
+the interference Criterion
+ 
+
+ align:start position:0%
+the interference Criterion
+if I take the interference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Criterion and I combine it with the
+
+ align:start position:0%
+Criterion and I combine it with the
+ 
+
+ align:start position:0%
+Criterion and I combine it with the
+crystal
+
+ align:start position:0%
+crystal
+ 
+
+ align:start position:0%
+crystal
+structure I combine it with the crystal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure what's that give me it gives
+
+ align:start position:0%
+structure what's that give me it gives
+ 
+
+ align:start position:0%
+structure what's that give me it gives
+me the set of expected
+
+ align:start position:0%
+me the set of expected
+ 
+
+ align:start position:0%
+me the set of expected
+Reflections the set of
+
+ align:start position:0%
+Reflections the set of
+ 
+
+ align:start position:0%
+Reflections the set of
+expected reflections
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so in essence this is a fingerprint
+
+ align:start position:0%
+and so in essence this is a fingerprint
+ 
+
+ align:start position:0%
+and so in essence this is a fingerprint
+of the crystal
+
+ align:start position:0%
+of the crystal
+ 
+
+ align:start position:0%
+of the crystal
+structure fingerprint of the crystal
+
+ align:start position:0%
+structure fingerprint of the crystal
+ 
+
+ align:start position:0%
+structure fingerprint of the crystal
+structure it's not a fingerprint of the
+
+ align:start position:0%
+structure it's not a fingerprint of the
+ 
+
+ align:start position:0%
+structure it's not a fingerprint of the
+chemical
+
+ align:start position:0%
+chemical
+ 
+
+ align:start position:0%
+chemical
+identity okay it doesn't say anything
+
+ align:start position:0%
+identity okay it doesn't say anything
+ 
+
+ align:start position:0%
+identity okay it doesn't say anything
+about identity but any crystal structure
+
+ align:start position:0%
+about identity but any crystal structure
+ 
+
+ align:start position:0%
+about identity but any crystal structure
+of this description will give the
+
+ align:start position:0%
+of this description will give the
+ 
+
+ align:start position:0%
+of this description will give the
+Reflections at the same set of angles
+
+ align:start position:0%
+Reflections at the same set of angles
+ 
+
+ align:start position:0%
+Reflections at the same set of angles
+any crystal structure of this
+
+ align:start position:0%
+any crystal structure of this
+ 
+
+ align:start position:0%
+any crystal structure of this
+description will give no reflections at
+
+ align:start position:0%
+description will give no reflections at
+ 
+
+ align:start position:0%
+description will give no reflections at
+the same set of
+
+ align:start position:0%
+the same set of
+ 
+
+ align:start position:0%
+the same set of
+angles
+
+ align:start position:0%
+angles
+ 
+
+ align:start position:0%
+angles
+so this for example will show you what
+
+ align:start position:0%
+so this for example will show you what
+ 
+
+ align:start position:0%
+so this for example will show you what
+would happen in the case
+
+ align:start position:0%
+would happen in the case
+ 
+
+ align:start position:0%
+would happen in the case
+of 00
+
+ align:start position:0%
+of 00
+ 
+
+ align:start position:0%
+of 00
+01 001 we saw
+
+ align:start position:0%
+01 001 we saw
+ 
+
+ align:start position:0%
+01 001 we saw
+reflects 001 we saw reflects in in
+
+ align:start position:0%
+reflects 001 we saw reflects in in
+ 
+
+ align:start position:0%
+reflects 001 we saw reflects in in
+simple cubic okay at the given angle
+
+ align:start position:0%
+simple cubic okay at the given angle
+ 
+
+ align:start position:0%
+simple cubic okay at the given angle
+Theta
+
+ align:start position:0%
+Theta
+ 
+
+ align:start position:0%
+Theta
+o1 but it does not reflect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does not
+
+ align:start position:0%
+does not
+ 
+
+ align:start position:0%
+does not
+reflect in body centered cubic at Theta
+
+ align:start position:0%
+reflect in body centered cubic at Theta
+ 
+
+ align:start position:0%
+reflect in body centered cubic at Theta
+o1 because in body centered cubic there
+
+ align:start position:0%
+o1 because in body centered cubic there
+ 
+
+ align:start position:0%
+o1 because in body centered cubic there
+are atoms at
+
+ align:start position:0%
+are atoms at
+ 
+
+ align:start position:0%
+are atoms at
+O2 and atoms at O2 will be totally out
+
+ align:start position:0%
+O2 and atoms at O2 will be totally out
+ 
+
+ align:start position:0%
+O2 and atoms at O2 will be totally out
+of phase with the reflection that's
+
+ align:start position:0%
+of phase with the reflection that's
+ 
+
+ align:start position:0%
+of phase with the reflection that's
+coming off of o1 so we will see no
+
+ align:start position:0%
+coming off of o1 so we will see no
+ 
+
+ align:start position:0%
+coming off of o1 so we will see no
+reflection at
+
+ align:start position:0%
+reflection at
+ 
+
+ align:start position:0%
+reflection at
+o1 and likewise with FC FCC also has
+
+ align:start position:0%
+o1 and likewise with FC FCC also has
+ 
+
+ align:start position:0%
+o1 and likewise with FC FCC also has
+atoms at the midpoint on each face
+
+ align:start position:0%
+atoms at the midpoint on each face
+ 
+
+ align:start position:0%
+atoms at the midpoint on each face
+so does not reflect in BCC and FCC both
+
+ align:start position:0%
+so does not reflect in BCC and FCC both
+ 
+
+ align:start position:0%
+so does not reflect in BCC and FCC both
+of them so now I can start to
+
+ align:start position:0%
+of them so now I can start to
+ 
+
+ align:start position:0%
+of them so now I can start to
+distinguish I can distinguish which are
+
+ align:start position:0%
+distinguish I can distinguish which are
+ 
+
+ align:start position:0%
+distinguish I can distinguish which are
+which and now let's take a look at some
+
+ align:start position:0%
+which and now let's take a look at some
+ 
+
+ align:start position:0%
+which and now let's take a look at some
+opportunity to uh make sense of this oh
+
+ align:start position:0%
+opportunity to uh make sense of this oh
+ 
+
+ align:start position:0%
+opportunity to uh make sense of this oh
+here's here's just a a figure that I
+
+ align:start position:0%
+here's here's just a a figure that I
+ 
+
+ align:start position:0%
+here's here's just a a figure that I
+took from one of the texts just showing
+
+ align:start position:0%
+took from one of the texts just showing
+ 
+
+ align:start position:0%
+took from one of the texts just showing
+what I've drawn on the board I think we
+
+ align:start position:0%
+what I've drawn on the board I think we
+ 
+
+ align:start position:0%
+what I've drawn on the board I think we
+can zoom through this okay so now this
+
+ align:start position:0%
+can zoom through this okay so now this
+ 
+
+ align:start position:0%
+can zoom through this okay so now this
+is on the handout this is the selection
+
+ align:start position:0%
+is on the handout this is the selection
+ 
+
+ align:start position:0%
+is on the handout this is the selection
+rules for reflection in cubic crystals
+
+ align:start position:0%
+rules for reflection in cubic crystals
+ 
+
+ align:start position:0%
+rules for reflection in cubic crystals
+what has happened here is that the
+
+ align:start position:0%
+what has happened here is that the
+ 
+
+ align:start position:0%
+what has happened here is that the
+geometric
+
+ align:start position:0%
+geometric
+ 
+
+ align:start position:0%
+geometric
+analysis along these lines has been
+
+ align:start position:0%
+analysis along these lines has been
+ 
+
+ align:start position:0%
+analysis along these lines has been
+performed taking into account the atom
+
+ align:start position:0%
+performed taking into account the atom
+ 
+
+ align:start position:0%
+performed taking into account the atom
+positions and what do we see we see that
+
+ align:start position:0%
+positions and what do we see we see that
+ 
+
+ align:start position:0%
+positions and what do we see we see that
+simple cubic we get Reflections at every
+
+ align:start position:0%
+simple cubic we get Reflections at every
+ 
+
+ align:start position:0%
+simple cubic we get Reflections at every
+plane at every index body centered cubic
+
+ align:start position:0%
+plane at every index body centered cubic
+ 
+
+ align:start position:0%
+plane at every index body centered cubic
+is not reflecting the one because we've
+
+ align:start position:0%
+is not reflecting the one because we've
+ 
+
+ align:start position:0%
+is not reflecting the one because we've
+shown already that the Reflection from
+
+ align:start position:0%
+shown already that the Reflection from
+ 
+
+ align:start position:0%
+shown already that the Reflection from
+20 at that angle is perfectly out of
+
+ align:start position:0%
+20 at that angle is perfectly out of
+ 
+
+ align:start position:0%
+20 at that angle is perfectly out of
+phase so the computations have been done
+
+ align:start position:0%
+phase so the computations have been done
+ 
+
+ align:start position:0%
+phase so the computations have been done
+and likewise FCC so this is indicating
+
+ align:start position:0%
+and likewise FCC so this is indicating
+ 
+
+ align:start position:0%
+and likewise FCC so this is indicating
+that you won't see a 10 reflection in
+
+ align:start position:0%
+that you won't see a 10 reflection in
+ 
+
+ align:start position:0%
+that you won't see a 10 reflection in
+face centered cubic or body centered
+
+ align:start position:0%
+face centered cubic or body centered
+ 
+
+ align:start position:0%
+face centered cubic or body centered
+cubic and we go down to 0 uh one one
+
+ align:start position:0%
+cubic and we go down to 0 uh one one
+ 
+
+ align:start position:0%
+cubic and we go down to 0 uh one one
+simple cubic reflects body centered
+
+ align:start position:0%
+simple cubic reflects body centered
+ 
+
+ align:start position:0%
+simple cubic reflects body centered
+cubic reflects but face centered cubic
+
+ align:start position:0%
+cubic reflects but face centered cubic
+ 
+
+ align:start position:0%
+cubic reflects but face centered cubic
+doesn't reflect so you can't look at any
+
+ align:start position:0%
+doesn't reflect so you can't look at any
+ 
+
+ align:start position:0%
+doesn't reflect so you can't look at any
+single line you have to look at the
+
+ align:start position:0%
+single line you have to look at the
+ 
+
+ align:start position:0%
+single line you have to look at the
+entire pattern and so on and there's a
+
+ align:start position:0%
+entire pattern and so on and there's a
+ 
+
+ align:start position:0%
+entire pattern and so on and there's a
+simple way of of codifying all of this
+
+ align:start position:0%
+simple way of of codifying all of this
+ 
+
+ align:start position:0%
+simple way of of codifying all of this
+simple cubic all all of the indices are
+
+ align:start position:0%
+simple cubic all all of the indices are
+ 
+
+ align:start position:0%
+simple cubic all all of the indices are
+reflecting in body centered cubic if you
+
+ align:start position:0%
+reflecting in body centered cubic if you
+ 
+
+ align:start position:0%
+reflecting in body centered cubic if you
+go through this pattern what we're
+
+ align:start position:0%
+go through this pattern what we're
+ 
+
+ align:start position:0%
+go through this pattern what we're
+looking at is the sum of h^2 + K2 + L S
+
+ align:start position:0%
+looking at is the sum of h^2 + K2 + L S
+ 
+
+ align:start position:0%
+looking at is the sum of h^2 + K2 + L S
+and that gives you a nice sequence 1 2 3
+
+ align:start position:0%
+and that gives you a nice sequence 1 2 3
+ 
+
+ align:start position:0%
+and that gives you a nice sequence 1 2 3
+4 5 and so on and what you see with BCC
+
+ align:start position:0%
+4 5 and so on and what you see with BCC
+ 
+
+ align:start position:0%
+4 5 and so on and what you see with BCC
+is you have the sequence 2 4 6 8 10 the
+
+ align:start position:0%
+is you have the sequence 2 4 6 8 10 the
+ 
+
+ align:start position:0%
+is you have the sequence 2 4 6 8 10 the
+sum of H + K plus L is even so that's a
+
+ align:start position:0%
+sum of H + K plus L is even so that's a
+ 
+
+ align:start position:0%
+sum of H + K plus L is even so that's a
+way of capturing what's going on in this
+
+ align:start position:0%
+way of capturing what's going on in this
+ 
+
+ align:start position:0%
+way of capturing what's going on in this
+uh series and for face centered cubic it
+
+ align:start position:0%
+uh series and for face centered cubic it
+ 
+
+ align:start position:0%
+uh series and for face centered cubic it
+turns out that the planes that reflect
+
+ align:start position:0%
+turns out that the planes that reflect
+ 
+
+ align:start position:0%
+turns out that the planes that reflect
+are either all even numbers or all odd
+
+ align:start position:0%
+are either all even numbers or all odd
+ 
+
+ align:start position:0%
+are either all even numbers or all odd
+numbers so for example face centered
+
+ align:start position:0%
+numbers so for example face centered
+ 
+
+ align:start position:0%
+numbers so for example face centered
+cubic you see 111 those are all odd 20
+
+ align:start position:0%
+cubic you see 111 those are all odd 20
+ 
+
+ align:start position:0%
+cubic you see 111 those are all odd 20
+zero is termed uh in this calculation as
+
+ align:start position:0%
+zero is termed uh in this calculation as
+ 
+
+ align:start position:0%
+zero is termed uh in this calculation as
+being an even number so two is even zero
+
+ align:start position:0%
+being an even number so two is even zero
+ 
+
+ align:start position:0%
+being an even number so two is even zero
+is even and zero is even so uh three and
+
+ align:start position:0%
+is even and zero is even so uh three and
+ 
+
+ align:start position:0%
+is even and zero is even so uh three and
+four reflect five and six do not eight
+
+ align:start position:0%
+four reflect five and six do not eight
+ 
+
+ align:start position:0%
+four reflect five and six do not eight
+does that's 220 and so on 8 11 12 16 so
+
+ align:start position:0%
+does that's 220 and so on 8 11 12 16 so
+ 
+
+ align:start position:0%
+does that's 220 and so on 8 11 12 16 so
+this is a set of selection criteria that
+
+ align:start position:0%
+this is a set of selection criteria that
+ 
+
+ align:start position:0%
+this is a set of selection criteria that
+have been tabulated for your convenience
+
+ align:start position:0%
+have been tabulated for your convenience
+ 
+
+ align:start position:0%
+have been tabulated for your convenience
+and now what we can do now what we can
+
+ align:start position:0%
+and now what we can do now what we can
+ 
+
+ align:start position:0%
+and now what we can do now what we can
+do is go into some example uh using this
+
+ align:start position:0%
+do is go into some example uh using this
+ 
+
+ align:start position:0%
+do is go into some example uh using this
+technique in order to index a crystal
+
+ align:start position:0%
+technique in order to index a crystal
+ 
+
+ align:start position:0%
+technique in order to index a crystal
+and so I want to show you uh two
+
+ align:start position:0%
+and so I want to show you uh two
+ 
+
+ align:start position:0%
+and so I want to show you uh two
+different techniques that allow us to
+
+ align:start position:0%
+different techniques that allow us to
+ 
+
+ align:start position:0%
+different techniques that allow us to
+determine the crystal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structure the first one is called
+
+ align:start position:0%
+structure the first one is called
+ 
+
+ align:start position:0%
+structure the first one is called
+diffractometry the first one is called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diffractometry and since it's done with
+
+ align:start position:0%
+diffractometry and since it's done with
+ 
+
+ align:start position:0%
+diffractometry and since it's done with
+x-rays it's also known as X-ray
+
+ align:start position:0%
+x-rays it's also known as X-ray
+ 
+
+ align:start position:0%
+x-rays it's also known as X-ray
+defraction
+
+ align:start position:0%
+defraction
+ 
+
+ align:start position:0%
+defraction
+xrd and the characteristics of X-ray
+
+ align:start position:0%
+xrd and the characteristics of X-ray
+ 
+
+ align:start position:0%
+xrd and the characteristics of X-ray
+defraction are we use radiation of fixed
+
+ align:start position:0%
+defraction are we use radiation of fixed
+ 
+
+ align:start position:0%
+defraction are we use radiation of fixed
+wavelength and we vary the
+
+ align:start position:0%
+wavelength and we vary the
+ 
+
+ align:start position:0%
+wavelength and we vary the
+angle variable angle so look at this
+
+ align:start position:0%
+angle variable angle so look at this
+ 
+
+ align:start position:0%
+angle variable angle so look at this
+cartoon here if we have fixed wavelength
+
+ align:start position:0%
+cartoon here if we have fixed wavelength
+ 
+
+ align:start position:0%
+cartoon here if we have fixed wavelength
+and we're varying the angle I'm going to
+
+ align:start position:0%
+and we're varying the angle I'm going to
+ 
+
+ align:start position:0%
+and we're varying the angle I'm going to
+be moving the Crystal this is how I'm
+
+ align:start position:0%
+be moving the Crystal this is how I'm
+ 
+
+ align:start position:0%
+be moving the Crystal this is how I'm
+going to get variable angle what I'm
+
+ align:start position:0%
+going to get variable angle what I'm
+ 
+
+ align:start position:0%
+going to get variable angle what I'm
+saying is variable angle of incidence in
+
+ align:start position:0%
+saying is variable angle of incidence in
+ 
+
+ align:start position:0%
+saying is variable angle of incidence in
+other words I want to probe all of the
+
+ align:start position:0%
+other words I want to probe all of the
+ 
+
+ align:start position:0%
+other words I want to probe all of the
+incident angles and build a library of
+
+ align:start position:0%
+incident angles and build a library of
+ 
+
+ align:start position:0%
+incident angles and build a library of
+responses for a given incident angle
+
+ align:start position:0%
+responses for a given incident angle
+ 
+
+ align:start position:0%
+responses for a given incident angle
+what's the intensity of the reflected
+
+ align:start position:0%
+what's the intensity of the reflected
+ 
+
+ align:start position:0%
+what's the intensity of the reflected
+radiation and the way I do that is to
+
+ align:start position:0%
+radiation and the way I do that is to
+ 
+
+ align:start position:0%
+radiation and the way I do that is to
+park the beam and rotate the specimen
+
+ align:start position:0%
+park the beam and rotate the specimen
+ 
+
+ align:start position:0%
+park the beam and rotate the specimen
+and ultimately I end up with a plot that
+
+ align:start position:0%
+and ultimately I end up with a plot that
+ 
+
+ align:start position:0%
+and ultimately I end up with a plot that
+looks like this plot that looks like
+
+ align:start position:0%
+looks like this plot that looks like
+ 
+
+ align:start position:0%
+looks like this plot that looks like
+this intensity versus angle this is
+
+ align:start position:0%
+this intensity versus angle this is
+ 
+
+ align:start position:0%
+this intensity versus angle this is
+angle of reflected
+
+ align:start position:0%
+angle of reflected
+ 
+
+ align:start position:0%
+angle of reflected
+okay so now we're going to decide if the
+
+ align:start position:0%
+okay so now we're going to decide if the
+ 
+
+ align:start position:0%
+okay so now we're going to decide if the
+pattern we observe conforms to this set
+
+ align:start position:0%
+pattern we observe conforms to this set
+ 
+
+ align:start position:0%
+pattern we observe conforms to this set
+of rules up
+
+ align:start position:0%
+of rules up
+ 
+
+ align:start position:0%
+of rules up
+here and by making that comparison we
+
+ align:start position:0%
+here and by making that comparison we
+ 
+
+ align:start position:0%
+here and by making that comparison we
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+deduce which of these three Crystal
+
+ align:start position:0%
+deduce which of these three Crystal
+ 
+
+ align:start position:0%
+deduce which of these three Crystal
+structures the crystal belongs to and
+
+ align:start position:0%
+structures the crystal belongs to and
+ 
+
+ align:start position:0%
+structures the crystal belongs to and
+I'm I'm keeping this as a very narrow
+
+ align:start position:0%
+I'm I'm keeping this as a very narrow
+ 
+
+ align:start position:0%
+I'm I'm keeping this as a very narrow
+set I'm saying this is 3091 so we
+
+ align:start position:0%
+set I'm saying this is 3091 so we
+ 
+
+ align:start position:0%
+set I'm saying this is 3091 so we
+confine ourselves to the universe of
+
+ align:start position:0%
+confine ourselves to the universe of
+ 
+
+ align:start position:0%
+confine ourselves to the universe of
+cubic crystals if you want to get more
+
+ align:start position:0%
+cubic crystals if you want to get more
+ 
+
+ align:start position:0%
+cubic crystals if you want to get more
+General then it could be any one of the
+
+ align:start position:0%
+General then it could be any one of the
+ 
+
+ align:start position:0%
+General then it could be any one of the
+crystals that comes out of the 14 brav
+
+ align:start position:0%
+crystals that comes out of the 14 brav
+ 
+
+ align:start position:0%
+crystals that comes out of the 14 brav
+luses plus a range of
+
+ align:start position:0%
+luses plus a range of
+ 
+
+ align:start position:0%
+luses plus a range of
+bases so there's a huge database out
+
+ align:start position:0%
+bases so there's a huge database out
+ 
+
+ align:start position:0%
+bases so there's a huge database out
+there that has values of intensity
+
+ align:start position:0%
+there that has values of intensity
+ 
+
+ align:start position:0%
+there that has values of intensity
+versus angle
+
+ align:start position:0%
+versus angle
+ 
+
+ align:start position:0%
+versus angle
+for thousands and thousands of metals
+
+ align:start position:0%
+for thousands and thousands of metals
+ 
+
+ align:start position:0%
+for thousands and thousands of metals
+and compounds huge amount of minerology
+
+ align:start position:0%
+and compounds huge amount of minerology
+ 
+
+ align:start position:0%
+and compounds huge amount of minerology
+in this database and so when you bring a
+
+ align:start position:0%
+in this database and so when you bring a
+ 
+
+ align:start position:0%
+in this database and so when you bring a
+specimen of unknown Providence you're
+
+ align:start position:0%
+specimen of unknown Providence you're
+ 
+
+ align:start position:0%
+specimen of unknown Providence you're
+able to use this technique and infer
+
+ align:start position:0%
+able to use this technique and infer
+ 
+
+ align:start position:0%
+able to use this technique and infer
+what the constituents are so first of
+
+ align:start position:0%
+what the constituents are so first of
+ 
+
+ align:start position:0%
+what the constituents are so first of
+all let's take a look at what the uh
+
+ align:start position:0%
+all let's take a look at what the uh
+ 
+
+ align:start position:0%
+all let's take a look at what the uh
+what the specimen look looks like I
+
+ align:start position:0%
+what the specimen look looks like I
+ 
+
+ align:start position:0%
+what the specimen look looks like I
+can't take a few atoms what we use is a
+
+ align:start position:0%
+can't take a few atoms what we use is a
+ 
+
+ align:start position:0%
+can't take a few atoms what we use is a
+powdered
+
+ align:start position:0%
+powdered
+ 
+
+ align:start position:0%
+powdered
+specimen powdered
+
+ align:start position:0%
+specimen powdered
+ 
+
+ align:start position:0%
+specimen powdered
+specimen so we grind the material into a
+
+ align:start position:0%
+specimen so we grind the material into a
+ 
+
+ align:start position:0%
+specimen so we grind the material into a
+fine powder and we put it in a
+
+ align:start position:0%
+fine powder and we put it in a
+ 
+
+ align:start position:0%
+fine powder and we put it in a
+silicate a silicate
+
+ align:start position:0%
+silicate a silicate
+ 
+
+ align:start position:0%
+silicate a silicate
+glass
+
+ align:start position:0%
+glass
+ 
+
+ align:start position:0%
+glass
+holder and the silicate glass holder
+
+ align:start position:0%
+holder and the silicate glass holder
+ 
+
+ align:start position:0%
+holder and the silicate glass holder
+looks something like
+
+ align:start position:0%
+looks something like
+ 
+
+ align:start position:0%
+looks something like
+this it's a very narrow tube this is not
+
+ align:start position:0%
+this it's a very narrow tube this is not
+ 
+
+ align:start position:0%
+this it's a very narrow tube this is not
+to scale definitely not to scale this
+
+ align:start position:0%
+to scale definitely not to scale this
+ 
+
+ align:start position:0%
+to scale definitely not to scale this
+Dimension here
+
+ align:start position:0%
+Dimension here
+ 
+
+ align:start position:0%
+Dimension here
+is about a tenth of a millimeter it's a
+
+ align:start position:0%
+is about a tenth of a millimeter it's a
+ 
+
+ align:start position:0%
+is about a tenth of a millimeter it's a
+very narrow tube a tenth of a millimeter
+
+ align:start position:0%
+very narrow tube a tenth of a millimeter
+ 
+
+ align:start position:0%
+very narrow tube a tenth of a millimeter
+made of silicate glass it's an oxide
+
+ align:start position:0%
+made of silicate glass it's an oxide
+ 
+
+ align:start position:0%
+made of silicate glass it's an oxide
+glass cousin of window glass why do we
+
+ align:start position:0%
+glass cousin of window glass why do we
+ 
+
+ align:start position:0%
+glass cousin of window glass why do we
+choose it not because it's transparent
+
+ align:start position:0%
+choose it not because it's transparent
+ 
+
+ align:start position:0%
+choose it not because it's transparent
+visible light we don't care we're
+
+ align:start position:0%
+visible light we don't care we're
+ 
+
+ align:start position:0%
+visible light we don't care we're
+shooting x-rays through this thing for
+
+ align:start position:0%
+shooting x-rays through this thing for
+ 
+
+ align:start position:0%
+shooting x-rays through this thing for
+heaven's sakes why do we choose this
+
+ align:start position:0%
+heaven's sakes why do we choose this
+ 
+
+ align:start position:0%
+heaven's sakes why do we choose this
+because it's a morphus and it doesn't
+
+ align:start position:0%
+because it's a morphus and it doesn't
+ 
+
+ align:start position:0%
+because it's a morphus and it doesn't
+have a crystal structure of its own if
+
+ align:start position:0%
+have a crystal structure of its own if
+ 
+
+ align:start position:0%
+have a crystal structure of its own if
+we're trying to radiate the contents of
+
+ align:start position:0%
+we're trying to radiate the contents of
+ 
+
+ align:start position:0%
+we're trying to radiate the contents of
+this and the the tube itself has a
+
+ align:start position:0%
+this and the the tube itself has a
+ 
+
+ align:start position:0%
+this and the the tube itself has a
+crystal structure how we going to sort
+
+ align:start position:0%
+crystal structure how we going to sort
+ 
+
+ align:start position:0%
+crystal structure how we going to sort
+out what's the contents from the
+
+ align:start position:0%
+out what's the contents from the
+ 
+
+ align:start position:0%
+out what's the contents from the
+container so this is a morphus no long
+
+ align:start position:0%
+container so this is a morphus no long
+ 
+
+ align:start position:0%
+container so this is a morphus no long
+range order and inside we put
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+little grains of powder in here okay so
+
+ align:start position:0%
+little grains of powder in here okay so
+ 
+
+ align:start position:0%
+little grains of powder in here okay so
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+powder the powder Dimension is on the
+
+ align:start position:0%
+powder the powder Dimension is on the
+ 
+
+ align:start position:0%
+powder the powder Dimension is on the
+order of about oh 50
+
+ align:start position:0%
+order of about oh 50
+ 
+
+ align:start position:0%
+order of about oh 50
+micrometers 50
+
+ align:start position:0%
+micrometers 50
+ 
+
+ align:start position:0%
+micrometers 50
+micrometers and uh oh the wall thickness
+
+ align:start position:0%
+micrometers and uh oh the wall thickness
+ 
+
+ align:start position:0%
+micrometers and uh oh the wall thickness
+I didn't mention that that's one/ 100th
+
+ align:start position:0%
+I didn't mention that that's one/ 100th
+ 
+
+ align:start position:0%
+I didn't mention that that's one/ 100th
+of a millimeter
+
+ align:start position:0%
+of a millimeter
+ 
+
+ align:start position:0%
+of a millimeter
+saying it's paper thin is an
+
+ align:start position:0%
+saying it's paper thin is an
+ 
+
+ align:start position:0%
+saying it's paper thin is an
+exaggeration it's 100th of a millimeter
+
+ align:start position:0%
+exaggeration it's 100th of a millimeter
+ 
+
+ align:start position:0%
+exaggeration it's 100th of a millimeter
+and this distance is about oh 2
+
+ align:start position:0%
+and this distance is about oh 2
+ 
+
+ align:start position:0%
+and this distance is about oh 2
+cm so you grind in a mortar and pestl
+
+ align:start position:0%
+cm so you grind in a mortar and pestl
+ 
+
+ align:start position:0%
+cm so you grind in a mortar and pestl
+drop the powder in here and then this
+
+ align:start position:0%
+drop the powder in here and then this
+ 
+
+ align:start position:0%
+drop the powder in here and then this
+goes into the diffractometer and is
+
+ align:start position:0%
+goes into the diffractometer and is
+ 
+
+ align:start position:0%
+goes into the diffractometer and is
+irradiated and we're going to turn this
+
+ align:start position:0%
+irradiated and we're going to turn this
+ 
+
+ align:start position:0%
+irradiated and we're going to turn this
+in order to present as many different
+
+ align:start position:0%
+in order to present as many different
+ 
+
+ align:start position:0%
+in order to present as many different
+angles as possible we have many grains
+
+ align:start position:0%
+angles as possible we have many grains
+ 
+
+ align:start position:0%
+angles as possible we have many grains
+in here and each grain the the theory is
+
+ align:start position:0%
+in here and each grain the the theory is
+ 
+
+ align:start position:0%
+in here and each grain the the theory is
+if we grind These Fine enough each one
+
+ align:start position:0%
+if we grind These Fine enough each one
+ 
+
+ align:start position:0%
+if we grind These Fine enough each one
+of these can act as a single Crystal so
+
+ align:start position:0%
+of these can act as a single Crystal so
+ 
+
+ align:start position:0%
+of these can act as a single Crystal so
+now light is coming in and reflecting
+
+ align:start position:0%
+now light is coming in and reflecting
+ 
+
+ align:start position:0%
+now light is coming in and reflecting
+off this but the its cousin is sitting
+
+ align:start position:0%
+off this but the its cousin is sitting
+ 
+
+ align:start position:0%
+off this but the its cousin is sitting
+at a slightly different angle and so I'm
+
+ align:start position:0%
+at a slightly different angle and so I'm
+ 
+
+ align:start position:0%
+at a slightly different angle and so I'm
+going to try to through the mix of
+
+ align:start position:0%
+going to try to through the mix of
+ 
+
+ align:start position:0%
+going to try to through the mix of
+powder and the rotation of the specimen
+
+ align:start position:0%
+powder and the rotation of the specimen
+ 
+
+ align:start position:0%
+powder and the rotation of the specimen
+try to get all of the different incident
+
+ align:start position:0%
+try to get all of the different incident
+ 
+
+ align:start position:0%
+try to get all of the different incident
+angles so that I will get as many
+
+ align:start position:0%
+angles so that I will get as many
+ 
+
+ align:start position:0%
+angles so that I will get as many
+reflected angles as
+
+ align:start position:0%
+reflected angles as
+ 
+
+ align:start position:0%
+reflected angles as
+possible I I worked with this my PhD
+
+ align:start position:0%
+possible I I worked with this my PhD
+ 
+
+ align:start position:0%
+possible I I worked with this my PhD
+thesis and it was the the material was
+
+ align:start position:0%
+thesis and it was the the material was
+ 
+
+ align:start position:0%
+thesis and it was the the material was
+was sensitive to moisture in the air so
+
+ align:start position:0%
+was sensitive to moisture in the air so
+ 
+
+ align:start position:0%
+was sensitive to moisture in the air so
+I had to work in a glove box had these
+
+ align:start position:0%
+I had to work in a glove box had these
+ 
+
+ align:start position:0%
+I had to work in a glove box had these
+big thick rubber gloves on and and and
+
+ align:start position:0%
+big thick rubber gloves on and and and
+ 
+
+ align:start position:0%
+big thick rubber gloves on and and and
+holding something like this only it's re
+
+ align:start position:0%
+holding something like this only it's re
+ 
+
+ align:start position:0%
+holding something like this only it's re
+in real life it's about this big and
+
+ align:start position:0%
+in real life it's about this big and
+ 
+
+ align:start position:0%
+in real life it's about this big and
+you're inside the glove box and it's
+
+ align:start position:0%
+you're inside the glove box and it's
+ 
+
+ align:start position:0%
+you're inside the glove box and it's
+Toronto and it's August and perspiration
+
+ align:start position:0%
+Toronto and it's August and perspiration
+ 
+
+ align:start position:0%
+Toronto and it's August and perspiration
+is pouring you're supposed to be crying
+
+ align:start position:0%
+is pouring you're supposed to be crying
+ 
+
+ align:start position:0%
+is pouring you're supposed to be crying
+now the perspiration is pouring down my
+
+ align:start position:0%
+now the perspiration is pouring down my
+ 
+
+ align:start position:0%
+now the perspiration is pouring down my
+face and and I have to I have to get the
+
+ align:start position:0%
+face and and I have to I have to get the
+ 
+
+ align:start position:0%
+face and and I have to I have to get the
+powder to fall in here and I I got to
+
+ align:start position:0%
+powder to fall in here and I I got to
+ 
+
+ align:start position:0%
+powder to fall in here and I I got to
+flick this a little bit right and flick
+
+ align:start position:0%
+flick this a little bit right and flick
+ 
+
+ align:start position:0%
+flick this a little bit right and flick
+it one more time and then it breaks off
+
+ align:start position:0%
+it one more time and then it breaks off
+ 
+
+ align:start position:0%
+it one more time and then it breaks off
+and you start you laugh now it's not
+
+ align:start position:0%
+and you start you laugh now it's not
+ 
+
+ align:start position:0%
+and you start you laugh now it's not
+funny and that's that's the way that's
+
+ align:start position:0%
+funny and that's that's the way that's
+ 
+
+ align:start position:0%
+funny and that's that's the way that's
+the way that's how science goes so
+
+ align:start position:0%
+the way that's how science goes so
+ 
+
+ align:start position:0%
+the way that's how science goes so
+anyway so what happens now we take this
+
+ align:start position:0%
+anyway so what happens now we take this
+ 
+
+ align:start position:0%
+anyway so what happens now we take this
+and I'm going to give you the top view
+
+ align:start position:0%
+and I'm going to give you the top view
+ 
+
+ align:start position:0%
+and I'm going to give you the top view
+the top view of the
+
+ align:start position:0%
+the top view of the
+ 
+
+ align:start position:0%
+the top view of the
+diffractometer the top view of the
+
+ align:start position:0%
+diffractometer the top view of the
+ 
+
+ align:start position:0%
+diffractometer the top view of the
+diffractometer it's it's essentially a
+
+ align:start position:0%
+diffractometer it's it's essentially a
+ 
+
+ align:start position:0%
+diffractometer it's it's essentially a
+combination of an x-ray generator a
+
+ align:start position:0%
+combination of an x-ray generator a
+ 
+
+ align:start position:0%
+combination of an x-ray generator a
+specimen holder and a detector okay so
+
+ align:start position:0%
+specimen holder and a detector okay so
+ 
+
+ align:start position:0%
+specimen holder and a detector okay so
+the top view has x-ray coming in this is
+
+ align:start position:0%
+the top view has x-ray coming in this is
+ 
+
+ align:start position:0%
+the top view has x-ray coming in this is
+monochromatic x-ray Lambda Lambda some
+
+ align:start position:0%
+monochromatic x-ray Lambda Lambda some
+ 
+
+ align:start position:0%
+monochromatic x-ray Lambda Lambda some
+Lambda fixed okay monochromatic x-ray
+
+ align:start position:0%
+Lambda fixed okay monochromatic x-ray
+ 
+
+ align:start position:0%
+Lambda fixed okay monochromatic x-ray
+coming in top view has this sitting in a
+
+ align:start position:0%
+coming in top view has this sitting in a
+ 
+
+ align:start position:0%
+coming in top view has this sitting in a
+in a Carousel and this Carousel spins
+
+ align:start position:0%
+in a Carousel and this Carousel spins
+ 
+
+ align:start position:0%
+in a Carousel and this Carousel spins
+and then I have a detector and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+detector the the detector itself moves
+
+ align:start position:0%
+detector the the detector itself moves
+ 
+
+ align:start position:0%
+detector the the detector itself moves
+through a variety of angles and so here
+
+ align:start position:0%
+through a variety of angles and so here
+ 
+
+ align:start position:0%
+through a variety of angles and so here
+we have an incidence angle and here we
+
+ align:start position:0%
+we have an incidence angle and here we
+ 
+
+ align:start position:0%
+we have an incidence angle and here we
+have a reflectance angle and ultimately
+
+ align:start position:0%
+have a reflectance angle and ultimately
+ 
+
+ align:start position:0%
+have a reflectance angle and ultimately
+we get a plot of intensity versus
+
+ align:start position:0%
+we get a plot of intensity versus
+ 
+
+ align:start position:0%
+we get a plot of intensity versus
+reflected angle from this specimen and
+
+ align:start position:0%
+reflected angle from this specimen and
+ 
+
+ align:start position:0%
+reflected angle from this specimen and
+that's how this thing works and here's
+
+ align:start position:0%
+that's how this thing works and here's
+ 
+
+ align:start position:0%
+that's how this thing works and here's
+what the output could look like you'll
+
+ align:start position:0%
+what the output could look like you'll
+ 
+
+ align:start position:0%
+what the output could look like you'll
+have nothing and then you'll have Peaks
+
+ align:start position:0%
+have nothing and then you'll have Peaks
+ 
+
+ align:start position:0%
+have nothing and then you'll have Peaks
+at discrete lines Why at certain angles
+
+ align:start position:0%
+at discrete lines Why at certain angles
+ 
+
+ align:start position:0%
+at discrete lines Why at certain angles
+the brag condition is satisfied at other
+
+ align:start position:0%
+the brag condition is satisfied at other
+ 
+
+ align:start position:0%
+the brag condition is satisfied at other
+angles the brag condition is not
+
+ align:start position:0%
+angles the brag condition is not
+ 
+
+ align:start position:0%
+angles the brag condition is not
+satisfied so these are the brag Peaks
+
+ align:start position:0%
+satisfied so these are the brag Peaks
+ 
+
+ align:start position:0%
+satisfied so these are the brag Peaks
+associated with magical angles right and
+
+ align:start position:0%
+associated with magical angles right and
+ 
+
+ align:start position:0%
+associated with magical angles right and
+what are the magical angles they are the
+
+ align:start position:0%
+what are the magical angles they are the
+ 
+
+ align:start position:0%
+what are the magical angles they are the
+angles associated with those
+
+ align:start position:0%
+angles associated with those
+ 
+
+ align:start position:0%
+angles associated with those
+planes so this is how we're trying to
+
+ align:start position:0%
+planes so this is how we're trying to
+ 
+
+ align:start position:0%
+planes so this is how we're trying to
+make sense of what's going on here
+
+ align:start position:0%
+make sense of what's going on here
+ 
+
+ align:start position:0%
+make sense of what's going on here
+so I wanted to give you uh the thrill of
+
+ align:start position:0%
+so I wanted to give you uh the thrill of
+ 
+
+ align:start position:0%
+so I wanted to give you uh the thrill of
+Discovery so we're going to do a Virtual
+
+ align:start position:0%
+Discovery so we're going to do a Virtual
+ 
+
+ align:start position:0%
+Discovery so we're going to do a Virtual
+Lab here so what I've got for you is a
+
+ align:start position:0%
+Lab here so what I've got for you is a
+ 
+
+ align:start position:0%
+Lab here so what I've got for you is a
+data set this is a data set if you flip
+
+ align:start position:0%
+data set this is a data set if you flip
+ 
+
+ align:start position:0%
+data set this is a data set if you flip
+over your sheet this is all you get the
+
+ align:start position:0%
+over your sheet this is all you get the
+ 
+
+ align:start position:0%
+over your sheet this is all you get the
+output now for reasons I I don't want to
+
+ align:start position:0%
+output now for reasons I I don't want to
+ 
+
+ align:start position:0%
+output now for reasons I I don't want to
+go into the angles are are often
+
+ align:start position:0%
+go into the angles are are often
+ 
+
+ align:start position:0%
+go into the angles are are often
+reported as 2 Theta instead of theta and
+
+ align:start position:0%
+reported as 2 Theta instead of theta and
+ 
+
+ align:start position:0%
+reported as 2 Theta instead of theta and
+it has to do with the the geometry of
+
+ align:start position:0%
+it has to do with the the geometry of
+ 
+
+ align:start position:0%
+it has to do with the the geometry of
+this specimen and blah blah blah but
+
+ align:start position:0%
+this specimen and blah blah blah but
+ 
+
+ align:start position:0%
+this specimen and blah blah blah but
+that's not important so we've got a
+
+ align:start position:0%
+that's not important so we've got a
+ 
+
+ align:start position:0%
+that's not important so we've got a
+copper Target in the X-ray generator
+
+ align:start position:0%
+copper Target in the X-ray generator
+ 
+
+ align:start position:0%
+copper Target in the X-ray generator
+which means we will have
+
+ align:start position:0%
+which means we will have
+ 
+
+ align:start position:0%
+which means we will have
+monochromatic light Lambda 1.54 one8
+
+ align:start position:0%
+monochromatic light Lambda 1.54 one8
+ 
+
+ align:start position:0%
+monochromatic light Lambda 1.54 one8
+angstrom so we know that and remember we
+
+ align:start position:0%
+angstrom so we know that and remember we
+ 
+
+ align:start position:0%
+angstrom so we know that and remember we
+said we had to fix our Lambda so we've
+
+ align:start position:0%
+said we had to fix our Lambda so we've
+ 
+
+ align:start position:0%
+said we had to fix our Lambda so we've
+done that we've rotated the specimen
+
+ align:start position:0%
+done that we've rotated the specimen
+ 
+
+ align:start position:0%
+done that we've rotated the specimen
+variable Theta and these are the Peaks I
+
+ align:start position:0%
+variable Theta and these are the Peaks I
+ 
+
+ align:start position:0%
+variable Theta and these are the Peaks I
+I don't care about the intensities all
+
+ align:start position:0%
+I don't care about the intensities all
+ 
+
+ align:start position:0%
+I don't care about the intensities all
+I'm doing right now is telling you these
+
+ align:start position:0%
+I'm doing right now is telling you these
+ 
+
+ align:start position:0%
+I'm doing right now is telling you these
+are the Peaks that I got so how do we
+
+ align:start position:0%
+are the Peaks that I got so how do we
+ 
+
+ align:start position:0%
+are the Peaks that I got so how do we
+take that and infer what the crystal is
+
+ align:start position:0%
+take that and infer what the crystal is
+ 
+
+ align:start position:0%
+take that and infer what the crystal is
+well you know you go to the library and
+
+ align:start position:0%
+well you know you go to the library and
+ 
+
+ align:start position:0%
+well you know you go to the library and
+get all these uh self-help books I
+
+ align:start position:0%
+get all these uh self-help books I
+ 
+
+ align:start position:0%
+get all these uh self-help books I
+haven't had the time to write a full
+
+ align:start position:0%
+haven't had the time to write a full
+ 
+
+ align:start position:0%
+haven't had the time to write a full
+self-help book but I got this one
+
+ align:start position:0%
+self-help book but I got this one
+ 
+
+ align:start position:0%
+self-help book but I got this one
+self-help sheet here so this is my
+
+ align:start position:0%
+self-help sheet here so this is my
+ 
+
+ align:start position:0%
+self-help sheet here so this is my
+program you won't find this in any books
+
+ align:start position:0%
+program you won't find this in any books
+ 
+
+ align:start position:0%
+program you won't find this in any books
+this I'm giving to you special okay so I
+
+ align:start position:0%
+this I'm giving to you special okay so I
+ 
+
+ align:start position:0%
+this I'm giving to you special okay so I
+want to walk through this and show you
+
+ align:start position:0%
+want to walk through this and show you
+ 
+
+ align:start position:0%
+want to walk through this and show you
+how to take that data set and index the
+
+ align:start position:0%
+how to take that data set and index the
+ 
+
+ align:start position:0%
+how to take that data set and index the
+crystal the question we're trying to
+
+ align:start position:0%
+crystal the question we're trying to
+ 
+
+ align:start position:0%
+crystal the question we're trying to
+answer is what is the crystal structure
+
+ align:start position:0%
+answer is what is the crystal structure
+ 
+
+ align:start position:0%
+answer is what is the crystal structure
+and you only got three answers it's
+
+ align:start position:0%
+and you only got three answers it's
+ 
+
+ align:start position:0%
+and you only got three answers it's
+either going to be simple cubic body
+
+ align:start position:0%
+either going to be simple cubic body
+ 
+
+ align:start position:0%
+either going to be simple cubic body
+centered cubic or face centered cubic
+
+ align:start position:0%
+centered cubic or face centered cubic
+ 
+
+ align:start position:0%
+centered cubic or face centered cubic
+okay and that's the data set that's all
+
+ align:start position:0%
+okay and that's the data set that's all
+ 
+
+ align:start position:0%
+okay and that's the data set that's all
+you got plus your mind okay so let's go
+
+ align:start position:0%
+you got plus your mind okay so let's go
+ 
+
+ align:start position:0%
+you got plus your mind okay so let's go
+so it says start with the 2 Theta values
+
+ align:start position:0%
+so it says start with the 2 Theta values
+ 
+
+ align:start position:0%
+so it says start with the 2 Theta values
+and generate a set of sin squ Theta
+
+ align:start position:0%
+and generate a set of sin squ Theta
+ 
+
+ align:start position:0%
+and generate a set of sin squ Theta
+values oh I should perhaps tell you how
+
+ align:start position:0%
+values oh I should perhaps tell you how
+ 
+
+ align:start position:0%
+values oh I should perhaps tell you how
+I came up with this what's the what's
+
+ align:start position:0%
+I came up with this what's the what's
+ 
+
+ align:start position:0%
+I came up with this what's the what's
+the underlying principle yeah here's the
+
+ align:start position:0%
+the underlying principle yeah here's the
+ 
+
+ align:start position:0%
+the underlying principle yeah here's the
+underlying uh principle uh I don't like
+
+ align:start position:0%
+underlying uh principle uh I don't like
+ 
+
+ align:start position:0%
+underlying uh principle uh I don't like
+that piece of chalk this one here okay
+
+ align:start position:0%
+that piece of chalk this one here okay
+ 
+
+ align:start position:0%
+that piece of chalk this one here okay
+here's the underlying principle to solve
+
+ align:start position:0%
+here's the underlying principle to solve
+ 
+
+ align:start position:0%
+here's the underlying principle to solve
+the puzzle all I did was I took these
+
+ align:start position:0%
+the puzzle all I did was I took these
+ 
+
+ align:start position:0%
+the puzzle all I did was I took these
+two equations I took the brags law which
+
+ align:start position:0%
+two equations I took the brags law which
+ 
+
+ align:start position:0%
+two equations I took the brags law which
+is Lambda equal 2D sin Theta and I took
+
+ align:start position:0%
+is Lambda equal 2D sin Theta and I took
+ 
+
+ align:start position:0%
+is Lambda equal 2D sin Theta and I took
+the formula for the the D spacing
+
+ align:start position:0%
+the formula for the the D spacing
+ 
+
+ align:start position:0%
+the formula for the the D spacing
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+planes which you saw two days ago which
+
+ align:start position:0%
+planes which you saw two days ago which
+ 
+
+ align:start position:0%
+planes which you saw two days ago which
+is the ratio of the lattice constant
+
+ align:start position:0%
+is the ratio of the lattice constant
+ 
+
+ align:start position:0%
+is the ratio of the lattice constant
+divided by the sum of the
+
+ align:start position:0%
+divided by the sum of the
+ 
+
+ align:start position:0%
+divided by the sum of the
+squares of the Miller indices of the
+
+ align:start position:0%
+squares of the Miller indices of the
+ 
+
+ align:start position:0%
+squares of the Miller indices of the
+plane so if I take those two equations
+
+ align:start position:0%
+plane so if I take those two equations
+ 
+
+ align:start position:0%
+plane so if I take those two equations
+and put them together I can get the
+
+ align:start position:0%
+and put them together I can get the
+ 
+
+ align:start position:0%
+and put them together I can get the
+following relationship Lambda 2 over 4
+
+ align:start position:0%
+following relationship Lambda 2 over 4
+ 
+
+ align:start position:0%
+following relationship Lambda 2 over 4
+a^ 2
+
+ align:start position:0%
+a^ 2
+ 
+
+ align:start position:0%
+a^ 2
+equals sin^2 Theta over h² + k^ 2 + l^
+
+ align:start position:0%
+equals sin^2 Theta over h² + k^ 2 + l^
+ 
+
+ align:start position:0%
+equals sin^2 Theta over h² + k^ 2 + l^
+2 now look at the left side of this
+
+ align:start position:0%
+2 now look at the left side of this
+ 
+
+ align:start position:0%
+2 now look at the left side of this
+equation Lambda is the wavelength of the
+
+ align:start position:0%
+equation Lambda is the wavelength of the
+ 
+
+ align:start position:0%
+equation Lambda is the wavelength of the
+incident radiation and that's fixed we
+
+ align:start position:0%
+incident radiation and that's fixed we
+ 
+
+ align:start position:0%
+incident radiation and that's fixed we
+fixed that in the experiment so this is
+
+ align:start position:0%
+fixed that in the experiment so this is
+ 
+
+ align:start position:0%
+fixed that in the experiment so this is
+a constant it's
+
+ align:start position:0%
+a constant it's
+ 
+
+ align:start position:0%
+a constant it's
+fixed a is the lattice constant of the
+
+ align:start position:0%
+fixed a is the lattice constant of the
+ 
+
+ align:start position:0%
+fixed a is the lattice constant of the
+crystal right that's
+
+ align:start position:0%
+crystal right that's
+ 
+
+ align:start position:0%
+crystal right that's
+the that's the crystal property so
+
+ align:start position:0%
+the that's the crystal property so
+ 
+
+ align:start position:0%
+the that's the crystal property so
+that's fixed so that means that the
+
+ align:start position:0%
+that's fixed so that means that the
+ 
+
+ align:start position:0%
+that's fixed so that means that the
+ratio of Lambda 2 over 4 a^2 is a
+
+ align:start position:0%
+ratio of Lambda 2 over 4 a^2 is a
+ 
+
+ align:start position:0%
+ratio of Lambda 2 over 4 a^2 is a
+constant well when I went to school what
+
+ align:start position:0%
+constant well when I went to school what
+ 
+
+ align:start position:0%
+constant well when I went to school what
+they taught me in math was that if the
+
+ align:start position:0%
+they taught me in math was that if the
+ 
+
+ align:start position:0%
+they taught me in math was that if the
+left hand side of the equation is
+
+ align:start position:0%
+left hand side of the equation is
+ 
+
+ align:start position:0%
+left hand side of the equation is
+constant the right hand side of the
+
+ align:start position:0%
+constant the right hand side of the
+ 
+
+ align:start position:0%
+constant the right hand side of the
+equation is constant so that means even
+
+ align:start position:0%
+equation is constant so that means even
+ 
+
+ align:start position:0%
+equation is constant so that means even
+though Theta is varying with hkl this
+
+ align:start position:0%
+though Theta is varying with hkl this
+ 
+
+ align:start position:0%
+though Theta is varying with hkl this
+ratio varies in such a way as to remain
+
+ align:start position:0%
+ratio varies in such a way as to remain
+ 
+
+ align:start position:0%
+ratio varies in such a way as to remain
+constant that's the key so whatever hkl
+
+ align:start position:0%
+constant that's the key so whatever hkl
+ 
+
+ align:start position:0%
+constant that's the key so whatever hkl
+is at that Theta the the sin squ of that
+
+ align:start position:0%
+is at that Theta the the sin squ of that
+ 
+
+ align:start position:0%
+is at that Theta the the sin squ of that
+angle over the H2 + K2 + L S remains
+
+ align:start position:0%
+angle over the H2 + K2 + L S remains
+ 
+
+ align:start position:0%
+angle over the H2 + K2 + L S remains
+constant as you go through all of the
+
+ align:start position:0%
+constant as you go through all of the
+ 
+
+ align:start position:0%
+constant as you go through all of the
+lines so this is the underlying
+
+ align:start position:0%
+lines so this is the underlying
+ 
+
+ align:start position:0%
+lines so this is the underlying
+principle okay so so let's go let's go
+
+ align:start position:0%
+principle okay so so let's go let's go
+ 
+
+ align:start position:0%
+principle okay so so let's go let's go
+into this so first thing I want to do is
+
+ align:start position:0%
+into this so first thing I want to do is
+ 
+
+ align:start position:0%
+into this so first thing I want to do is
+I want to build sin squ Theta so there
+
+ align:start position:0%
+I want to build sin squ Theta so there
+ 
+
+ align:start position:0%
+I want to build sin squ Theta so there
+they are those are the Theta values and
+
+ align:start position:0%
+they are those are the Theta values and
+ 
+
+ align:start position:0%
+they are those are the Theta values and
+now I've taken them divided them by two
+
+ align:start position:0%
+now I've taken them divided them by two
+ 
+
+ align:start position:0%
+now I've taken them divided them by two
+and then squared uh taken the sign and
+
+ align:start position:0%
+and then squared uh taken the sign and
+ 
+
+ align:start position:0%
+and then squared uh taken the sign and
+then squared it so now I got a new
+
+ align:start position:0%
+then squared it so now I got a new
+ 
+
+ align:start position:0%
+then squared it so now I got a new
+column and then and then it says
+
+ align:start position:0%
+column and then and then it says
+ 
+
+ align:start position:0%
+column and then and then it says
+normalize by dividing sin^2 Theta by the
+
+ align:start position:0%
+normalize by dividing sin^2 Theta by the
+ 
+
+ align:start position:0%
+normalize by dividing sin^2 Theta by the
+first member of the column so all I did
+
+ align:start position:0%
+first member of the column so all I did
+ 
+
+ align:start position:0%
+first member of the column so all I did
+was I took everything divided it by 143
+
+ align:start position:0%
+was I took everything divided it by 143
+ 
+
+ align:start position:0%
+was I took everything divided it by 143
+so this 0143 divided 0143 is 1 this as
+
+ align:start position:0%
+so this 0143 divided 0143 is 1 this as
+ 
+
+ align:start position:0%
+so this 0143 divided 0143 is 1 this as
+you can see 190 divided by 140 is about
+
+ align:start position:0%
+you can see 190 divided by 140 is about
+ 
+
+ align:start position:0%
+you can see 190 divided by 140 is about
+134 and so on okay why because look I'm
+
+ align:start position:0%
+134 and so on okay why because look I'm
+ 
+
+ align:start position:0%
+134 and so on okay why because look I'm
+going to this going to
+
+ align:start position:0%
+going to this going to
+ 
+
+ align:start position:0%
+going to this going to
+this what's the next thing clear the
+
+ align:start position:0%
+this what's the next thing clear the
+ 
+
+ align:start position:0%
+this what's the next thing clear the
+fractions from the normalized column I
+
+ align:start position:0%
+fractions from the normalized column I
+ 
+
+ align:start position:0%
+fractions from the normalized column I
+don't like this I don't like 1 1.34 and
+
+ align:start position:0%
+don't like this I don't like 1 1.34 and
+ 
+
+ align:start position:0%
+don't like this I don't like 1 1.34 and
+so on 1.34 to me allowing for some
+
+ align:start position:0%
+so on 1.34 to me allowing for some
+ 
+
+ align:start position:0%
+so on 1.34 to me allowing for some
+experimental error is roughly one and
+
+ align:start position:0%
+experimental error is roughly one and
+ 
+
+ align:start position:0%
+experimental error is roughly one and
+a3d isn't it it's roughly 4/3 and that's
+
+ align:start position:0%
+a3d isn't it it's roughly 4/3 and that's
+ 
+
+ align:start position:0%
+a3d isn't it it's roughly 4/3 and that's
+2.67 that's roughly 8/3 so why not
+
+ align:start position:0%
+2.67 that's roughly 8/3 so why not
+ 
+
+ align:start position:0%
+2.67 that's roughly 8/3 so why not
+multiply the whole darn column by three
+
+ align:start position:0%
+multiply the whole darn column by three
+ 
+
+ align:start position:0%
+multiply the whole darn column by three
+and throw away the little residuals and
+
+ align:start position:0%
+and throw away the little residuals and
+ 
+
+ align:start position:0%
+and throw away the little residuals and
+sure enough you get a set of whole
+
+ align:start position:0%
+sure enough you get a set of whole
+ 
+
+ align:start position:0%
+sure enough you get a set of whole
+numbers 3 4 8 11 12 and so on this is
+
+ align:start position:0%
+numbers 3 4 8 11 12 and so on this is
+ 
+
+ align:start position:0%
+numbers 3 4 8 11 12 and so on this is
+good we're getting somewhere so now it
+
+ align:start position:0%
+good we're getting somewhere so now it
+ 
+
+ align:start position:0%
+good we're getting somewhere so now it
+says speculate this is where you get to
+
+ align:start position:0%
+says speculate this is where you get to
+ 
+
+ align:start position:0%
+says speculate this is where you get to
+participate speculate on the hkl values
+
+ align:start position:0%
+participate speculate on the hkl values
+ 
+
+ align:start position:0%
+participate speculate on the hkl values
+that if expressed as H2 + K2 + L2 would
+
+ align:start position:0%
+that if expressed as H2 + K2 + L2 would
+ 
+
+ align:start position:0%
+that if expressed as H2 + K2 + L2 would
+generate the sequence of the clear fr
+
+ align:start position:0%
+generate the sequence of the clear fr
+ 
+
+ align:start position:0%
+generate the sequence of the clear fr
+column and remember what you have to go
+
+ align:start position:0%
+column and remember what you have to go
+ 
+
+ align:start position:0%
+column and remember what you have to go
+on you've got that set of simple cubic
+
+ align:start position:0%
+on you've got that set of simple cubic
+ 
+
+ align:start position:0%
+on you've got that set of simple cubic
+face centered cubic body centered cubic
+
+ align:start position:0%
+face centered cubic body centered cubic
+ 
+
+ align:start position:0%
+face centered cubic body centered cubic
+so what set of hk's would give you this
+
+ align:start position:0%
+so what set of hk's would give you this
+ 
+
+ align:start position:0%
+so what set of hk's would give you this
+well what would what sum of integers
+
+ align:start position:0%
+well what would what sum of integers
+ 
+
+ align:start position:0%
+well what would what sum of integers
+squares would give you three I wonder
+
+ align:start position:0%
+squares would give you three I wonder
+ 
+
+ align:start position:0%
+squares would give you three I wonder
+maybe one one one how about four and so
+
+ align:start position:0%
+maybe one one one how about four and so
+ 
+
+ align:start position:0%
+maybe one one one how about four and so
+you can see what's going on here this
+
+ align:start position:0%
+you can see what's going on here this
+ 
+
+ align:start position:0%
+you can see what's going on here this
+this I've gotten from the Theta and this
+
+ align:start position:0%
+this I've gotten from the Theta and this
+ 
+
+ align:start position:0%
+this I've gotten from the Theta and this
+is my
+
+ align:start position:0%
+is my
+ 
+
+ align:start position:0%
+is my
+speculation just trying
+
+ align:start position:0%
+speculation just trying
+ 
+
+ align:start position:0%
+speculation just trying
+and now here's the punch line compute
+
+ align:start position:0%
+and now here's the punch line compute
+ 
+
+ align:start position:0%
+and now here's the punch line compute
+for each Theta the value of this the sin
+
+ align:start position:0%
+for each Theta the value of this the sin
+ 
+
+ align:start position:0%
+for each Theta the value of this the sin
+squ Theta over h2+ a uh K2 + L2 and if
+
+ align:start position:0%
+squ Theta over h2+ a uh K2 + L2 and if
+ 
+
+ align:start position:0%
+squ Theta over h2+ a uh K2 + L2 and if
+you get a constant Bingo you must have
+
+ align:start position:0%
+you get a constant Bingo you must have
+ 
+
+ align:start position:0%
+you get a constant Bingo you must have
+hit the jackpot so let's do it well
+
+ align:start position:0%
+hit the jackpot so let's do it well
+ 
+
+ align:start position:0%
+hit the jackpot so let's do it well
+sin^2 Theta is this h^2 + k^2 + L S is <
+
+ align:start position:0%
+sin^2 Theta is this h^2 + k^2 + L S is <
+ 
+
+ align:start position:0%
+sin^2 Theta is this h^2 + k^2 + L S is <
+TK of 3 that's
+
+ align:start position:0%
+TK of 3 that's
+ 
+
+ align:start position:0%
+TK of 3 that's
+0477 you do it for the next one next one
+
+ align:start position:0%
+0477 you do it for the next one next one
+ 
+
+ align:start position:0%
+0477 you do it for the next one next one
+next one allowing for experimental error
+
+ align:start position:0%
+next one allowing for experimental error
+ 
+
+ align:start position:0%
+next one allowing for experimental error
+I got a constant so what does that say
+
+ align:start position:0%
+I got a constant so what does that say
+ 
+
+ align:start position:0%
+I got a constant so what does that say
+it says that my speculation of what the
+
+ align:start position:0%
+it says that my speculation of what the
+ 
+
+ align:start position:0%
+it says that my speculation of what the
+hk's are is good it's self-consistent
+
+ align:start position:0%
+hk's are is good it's self-consistent
+ 
+
+ align:start position:0%
+hk's are is good it's self-consistent
+and what do I know those are all even or
+
+ align:start position:0%
+and what do I know those are all even or
+ 
+
+ align:start position:0%
+and what do I know those are all even or
+they're either all even or all odd
+
+ align:start position:0%
+they're either all even or all odd
+ 
+
+ align:start position:0%
+they're either all even or all odd
+that's the sequence for face centered
+
+ align:start position:0%
+that's the sequence for face centered
+ 
+
+ align:start position:0%
+that's the sequence for face centered
+cubic that's the sequence for face
+
+ align:start position:0%
+cubic that's the sequence for face
+ 
+
+ align:start position:0%
+cubic that's the sequence for face
+centered cubic so on this basis I can
+
+ align:start position:0%
+centered cubic so on this basis I can
+ 
+
+ align:start position:0%
+centered cubic so on this basis I can
+say that I've got something that's face
+
+ align:start position:0%
+say that I've got something that's face
+ 
+
+ align:start position:0%
+say that I've got something that's face
+centered
+
+ align:start position:0%
+centered
+ 
+
+ align:start position:0%
+centered
+cubic so I'm happy about that but
+
+ align:start position:0%
+cubic so I'm happy about that but
+ 
+
+ align:start position:0%
+cubic so I'm happy about that but
+furthermore what else can I get well I
+
+ align:start position:0%
+furthermore what else can I get well I
+ 
+
+ align:start position:0%
+furthermore what else can I get well I
+know the Lambda value and I know this
+
+ align:start position:0%
+know the Lambda value and I know this
+ 
+
+ align:start position:0%
+know the Lambda value and I know this
+thing this is that uh this is that
+
+ align:start position:0%
+thing this is that uh this is that
+ 
+
+ align:start position:0%
+thing this is that uh this is that
+constant there right so what I can do is
+
+ align:start position:0%
+constant there right so what I can do is
+ 
+
+ align:start position:0%
+constant there right so what I can do is
+I can take this constant and plug it
+
+ align:start position:0%
+I can take this constant and plug it
+ 
+
+ align:start position:0%
+I can take this constant and plug it
+into this equation and furthermore I can
+
+ align:start position:0%
+into this equation and furthermore I can
+ 
+
+ align:start position:0%
+into this equation and furthermore I can
+determine that the a whatever this
+
+ align:start position:0%
+determine that the a whatever this
+ 
+
+ align:start position:0%
+determine that the a whatever this
+Crystal is is going to be Lambda of
+
+ align:start position:0%
+Crystal is is going to be Lambda of
+ 
+
+ align:start position:0%
+Crystal is is going to be Lambda of
+copper K Alpha divided by 2 * square
+
+ align:start position:0%
+copper K Alpha divided by 2 * square
+ 
+
+ align:start position:0%
+copper K Alpha divided by 2 * square
+root of that
+
+ align:start position:0%
+root of that
+ 
+
+ align:start position:0%
+root of that
+constant and if I plug in the numbers I
+
+ align:start position:0%
+constant and if I plug in the numbers I
+ 
+
+ align:start position:0%
+constant and if I plug in the numbers I
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+3.53 angstroms 3 .53 angstroms so it's
+
+ align:start position:0%
+3.53 angstroms 3 .53 angstroms so it's
+ 
+
+ align:start position:0%
+3.53 angstroms 3 .53 angstroms so it's
+FCC it's 3.53 angstroms if I look at it
+
+ align:start position:0%
+FCC it's 3.53 angstroms if I look at it
+ 
+
+ align:start position:0%
+FCC it's 3.53 angstroms if I look at it
+and it looks metallic I'm going to say
+
+ align:start position:0%
+and it looks metallic I'm going to say
+ 
+
+ align:start position:0%
+and it looks metallic I'm going to say
+it's nickel because I happen to know
+
+ align:start position:0%
+it's nickel because I happen to know
+ 
+
+ align:start position:0%
+it's nickel because I happen to know
+that nickel has a lattice constant of
+
+ align:start position:0%
+that nickel has a lattice constant of
+ 
+
+ align:start position:0%
+that nickel has a lattice constant of
+3.53 angstroms I know it's I got to do
+
+ align:start position:0%
+3.53 angstroms I know it's I got to do
+ 
+
+ align:start position:0%
+3.53 angstroms I know it's I got to do
+some other things but certainly that
+
+ align:start position:0%
+some other things but certainly that
+ 
+
+ align:start position:0%
+some other things but certainly that
+makes me thinking think about whether
+
+ align:start position:0%
+makes me thinking think about whether
+ 
+
+ align:start position:0%
+makes me thinking think about whether
+I've got nickel present so here's the
+
+ align:start position:0%
+I've got nickel present so here's the
+ 
+
+ align:start position:0%
+I've got nickel present so here's the
+here's the Gambit that's how you're
+
+ align:start position:0%
+here's the Gambit that's how you're
+ 
+
+ align:start position:0%
+here's the Gambit that's how you're
+going to solve these problems you're
+
+ align:start position:0%
+going to solve these problems you're
+ 
+
+ align:start position:0%
+going to solve these problems you're
+going to go through this this set of
+
+ align:start position:0%
+going to go through this this set of
+ 
+
+ align:start position:0%
+going to go through this this set of
+operations and go through this set of
+
+ align:start position:0%
+operations and go through this set of
+ 
+
+ align:start position:0%
+operations and go through this set of
+operations so just to recap if you're
+
+ align:start position:0%
+operations so just to recap if you're
+ 
+
+ align:start position:0%
+operations so just to recap if you're
+going to look at this simple cubic the
+
+ align:start position:0%
+going to look at this simple cubic the
+ 
+
+ align:start position:0%
+going to look at this simple cubic the
+hkl sequence is 1 2 3 4 5 6 8 9 because
+
+ align:start position:0%
+hkl sequence is 1 2 3 4 5 6 8 9 because
+ 
+
+ align:start position:0%
+hkl sequence is 1 2 3 4 5 6 8 9 because
+there's no sum of integers that will
+
+ align:start position:0%
+there's no sum of integers that will
+ 
+
+ align:start position:0%
+there's no sum of integers that will
+give you seven if you sum squares of
+
+ align:start position:0%
+give you seven if you sum squares of
+ 
+
+ align:start position:0%
+give you seven if you sum squares of
+integers okay so it give you all the
+
+ align:start position:0%
+integers okay so it give you all the
+ 
+
+ align:start position:0%
+integers okay so it give you all the
+lines but this is H2 + k^2 + L2 in
+
+ align:start position:0%
+lines but this is H2 + k^2 + L2 in
+ 
+
+ align:start position:0%
+lines but this is H2 + k^2 + L2 in
+ascending value all right body centered
+
+ align:start position:0%
+ascending value all right body centered
+ 
+
+ align:start position:0%
+ascending value all right body centered
+cubic body centered cubic has to be 2 4
+
+ align:start position:0%
+cubic body centered cubic has to be 2 4
+ 
+
+ align:start position:0%
+cubic body centered cubic has to be 2 4
+6 8 10 12 14 16 but when you first do
+
+ align:start position:0%
+6 8 10 12 14 16 but when you first do
+ 
+
+ align:start position:0%
+6 8 10 12 14 16 but when you first do
+this you don't know because you divide
+
+ align:start position:0%
+this you don't know because you divide
+ 
+
+ align:start position:0%
+this you don't know because you divide
+by the first s squared and so you don't
+
+ align:start position:0%
+by the first s squared and so you don't
+ 
+
+ align:start position:0%
+by the first s squared and so you don't
+know it's 2 468 you could end up with
+
+ align:start position:0%
+know it's 2 468 you could end up with
+ 
+
+ align:start position:0%
+know it's 2 468 you could end up with
+one 2 3 4 now don't we have a problem
+
+ align:start position:0%
+one 2 3 4 now don't we have a problem
+ 
+
+ align:start position:0%
+one 2 3 4 now don't we have a problem
+the simple cubic is going 1 2 3 4 and
+
+ align:start position:0%
+the simple cubic is going 1 2 3 4 and
+ 
+
+ align:start position:0%
+the simple cubic is going 1 2 3 4 and
+body centered cubic is going 1 2 3 4 but
+
+ align:start position:0%
+body centered cubic is going 1 2 3 4 but
+ 
+
+ align:start position:0%
+body centered cubic is going 1 2 3 4 but
+watch this
+
+ align:start position:0%
+watch this
+ 
+
+ align:start position:0%
+watch this
+perseverance half of 10 is five half of
+
+ align:start position:0%
+perseverance half of 10 is five half of
+ 
+
+ align:start position:0%
+perseverance half of 10 is five half of
+12 is six half of 14 is seven
+
+ align:start position:0%
+12 is six half of 14 is seven
+ 
+
+ align:start position:0%
+12 is six half of 14 is seven
+Bingo if you guess that something when
+
+ align:start position:0%
+Bingo if you guess that something when
+ 
+
+ align:start position:0%
+Bingo if you guess that something when
+you divide through you get a sequence
+
+ align:start position:0%
+you divide through you get a sequence
+ 
+
+ align:start position:0%
+you divide through you get a sequence
+that gives you 1 2 3 4 5 6 7 you know
+
+ align:start position:0%
+that gives you 1 2 3 4 5 6 7 you know
+ 
+
+ align:start position:0%
+that gives you 1 2 3 4 5 6 7 you know
+that it can't be simple cubic because
+
+ align:start position:0%
+that it can't be simple cubic because
+ 
+
+ align:start position:0%
+that it can't be simple cubic because
+there is no sum of integer squares that
+
+ align:start position:0%
+there is no sum of integer squares that
+ 
+
+ align:start position:0%
+there is no sum of integer squares that
+gives you seven this seven in fact must
+
+ align:start position:0%
+gives you seven this seven in fact must
+ 
+
+ align:start position:0%
+gives you seven this seven in fact must
+be 14 / two this is body centered cubic
+
+ align:start position:0%
+be 14 / two this is body centered cubic
+ 
+
+ align:start position:0%
+be 14 / two this is body centered cubic
+face centered cubic is the easiest one
+
+ align:start position:0%
+face centered cubic is the easiest one
+ 
+
+ align:start position:0%
+face centered cubic is the easiest one
+to pick off because it gives you 3 4 8
+
+ align:start position:0%
+to pick off because it gives you 3 4 8
+ 
+
+ align:start position:0%
+to pick off because it gives you 3 4 8
+11 12 and I mean I just need to see
+
+ align:start position:0%
+11 12 and I mean I just need to see
+ 
+
+ align:start position:0%
+11 12 and I mean I just need to see
+three four and I'm done I always check
+
+ align:start position:0%
+three four and I'm done I always check
+ 
+
+ align:start position:0%
+three four and I'm done I always check
+for FCC first I always check for FCC
+
+ align:start position:0%
+for FCC first I always check for FCC
+ 
+
+ align:start position:0%
+for FCC first I always check for FCC
+first so anyways that's how that's how
+
+ align:start position:0%
+first so anyways that's how that's how
+ 
+
+ align:start position:0%
+first so anyways that's how that's how
+defract cometry works and it allows you
+
+ align:start position:0%
+defract cometry works and it allows you
+ 
+
+ align:start position:0%
+defract cometry works and it allows you
+to index crystals and determine their
+
+ align:start position:0%
+to index crystals and determine their
+ 
+
+ align:start position:0%
+to index crystals and determine their
+crystal structure and more broadly
+
+ align:start position:0%
+crystal structure and more broadly
+ 
+
+ align:start position:0%
+crystal structure and more broadly
+speaking there's a database of all sorts
+
+ align:start position:0%
+speaking there's a database of all sorts
+ 
+
+ align:start position:0%
+speaking there's a database of all sorts
+of uh minerals and compounds and so on
+
+ align:start position:0%
+of uh minerals and compounds and so on
+ 
+
+ align:start position:0%
+of uh minerals and compounds and so on
+let's look at the second technique the
+
+ align:start position:0%
+let's look at the second technique the
+ 
+
+ align:start position:0%
+let's look at the second technique the
+second technique is called Loi
+
+ align:start position:0%
+second technique is called Loi
+ 
+
+ align:start position:0%
+second technique is called Loi
+defraction Loi defraction named after
+
+ align:start position:0%
+defraction Loi defraction named after
+ 
+
+ align:start position:0%
+defraction Loi defraction named after
+Max Loi who got the Nobel he was the
+
+ align:start position:0%
+Max Loi who got the Nobel he was the
+ 
+
+ align:start position:0%
+Max Loi who got the Nobel he was the
+first person to demonstrate uh x-ray
+
+ align:start position:0%
+first person to demonstrate uh x-ray
+ 
+
+ align:start position:0%
+first person to demonstrate uh x-ray
+identification of crystal structure got
+
+ align:start position:0%
+identification of crystal structure got
+ 
+
+ align:start position:0%
+identification of crystal structure got
+the Nobel in 1912 1912 for this and in
+
+ align:start position:0%
+the Nobel in 1912 1912 for this and in
+ 
+
+ align:start position:0%
+the Nobel in 1912 1912 for this and in
+La we fixed the angle the specimen is
+
+ align:start position:0%
+La we fixed the angle the specimen is
+ 
+
+ align:start position:0%
+La we fixed the angle the specimen is
+stationary and
+
+ align:start position:0%
+stationary and
+ 
+
+ align:start position:0%
+stationary and
+variable variable wavelength radiation
+
+ align:start position:0%
+variable variable wavelength radiation
+ 
+
+ align:start position:0%
+variable variable wavelength radiation
+so how do we get variable wavelength
+
+ align:start position:0%
+so how do we get variable wavelength
+ 
+
+ align:start position:0%
+so how do we get variable wavelength
+radiation look at that Spectrum up there
+
+ align:start position:0%
+radiation look at that Spectrum up there
+ 
+
+ align:start position:0%
+radiation look at that Spectrum up there
+you see the brem straing the brem
+
+ align:start position:0%
+you see the brem straing the brem
+ 
+
+ align:start position:0%
+you see the brem straing the brem
+straling gives you a range of wavelength
+
+ align:start position:0%
+straling gives you a range of wavelength
+ 
+
+ align:start position:0%
+straling gives you a range of wavelength
+so when we're how do we get
+
+ align:start position:0%
+so when we're how do we get
+ 
+
+ align:start position:0%
+so when we're how do we get
+monochromatic radiation how do we get
+
+ align:start position:0%
+monochromatic radiation how do we get
+ 
+
+ align:start position:0%
+monochromatic radiation how do we get
+monochromatic X-rays and don't tell me
+
+ align:start position:0%
+monochromatic X-rays and don't tell me
+ 
+
+ align:start position:0%
+monochromatic X-rays and don't tell me
+we we buy an x-ray laser how do we get
+
+ align:start position:0%
+we we buy an x-ray laser how do we get
+ 
+
+ align:start position:0%
+we we buy an x-ray laser how do we get
+monochromatic x-rays well it's really
+
+ align:start position:0%
+monochromatic x-rays well it's really
+ 
+
+ align:start position:0%
+monochromatic x-rays well it's really
+cool what you do is you
+
+ align:start position:0%
+cool what you do is you
+ 
+
+ align:start position:0%
+cool what you do is you
+take you take this briem straling with
+
+ align:start position:0%
+take you take this briem straling with
+ 
+
+ align:start position:0%
+take you take this briem straling with
+everything on
+
+ align:start position:0%
+everything on
+ 
+
+ align:start position:0%
+everything on
+it and you present it to a single
+
+ align:start position:0%
+it and you present it to a single
+ 
+
+ align:start position:0%
+it and you present it to a single
+Crystal you present it to a single
+
+ align:start position:0%
+Crystal you present it to a single
+ 
+
+ align:start position:0%
+Crystal you present it to a single
+Crystal and then you park over here this
+
+ align:start position:0%
+Crystal and then you park over here this
+ 
+
+ align:start position:0%
+Crystal and then you park over here this
+is the entrance slit to your defract
+
+ align:start position:0%
+is the entrance slit to your defract
+ 
+
+ align:start position:0%
+is the entrance slit to your defract
+tometer what will go through that
+
+ align:start position:0%
+tometer what will go through that
+ 
+
+ align:start position:0%
+tometer what will go through that
+entrance
+
+ align:start position:0%
+entrance
+ 
+
+ align:start position:0%
+entrance
+slit there's only one wavelength that
+
+ align:start position:0%
+slit there's only one wavelength that
+ 
+
+ align:start position:0%
+slit there's only one wavelength that
+will go through that entrance slit and
+
+ align:start position:0%
+will go through that entrance slit and
+ 
+
+ align:start position:0%
+will go through that entrance slit and
+that's the wavelength that satisfies the
+
+ align:start position:0%
+that's the wavelength that satisfies the
+ 
+
+ align:start position:0%
+that's the wavelength that satisfies the
+brag condition for this lattice spacing
+
+ align:start position:0%
+brag condition for this lattice spacing
+ 
+
+ align:start position:0%
+brag condition for this lattice spacing
+at this angle so what I can do is I can
+
+ align:start position:0%
+at this angle so what I can do is I can
+ 
+
+ align:start position:0%
+at this angle so what I can do is I can
+make a a single Crystal monochrometer
+
+ align:start position:0%
+make a a single Crystal monochrometer
+ 
+
+ align:start position:0%
+make a a single Crystal monochrometer
+that basically takes this characteristic
+
+ align:start position:0%
+that basically takes this characteristic
+ 
+
+ align:start position:0%
+that basically takes this characteristic
+Spectrum on top of the brm straing sends
+
+ align:start position:0%
+Spectrum on top of the brm straing sends
+ 
+
+ align:start position:0%
+Spectrum on top of the brm straing sends
+that in I present a single cryst
+
+ align:start position:0%
+that in I present a single cryst
+ 
+
+ align:start position:0%
+that in I present a single cryst
+and there's only one wavelength of light
+
+ align:start position:0%
+and there's only one wavelength of light
+ 
+
+ align:start position:0%
+and there's only one wavelength of light
+that will come out of here that
+
+ align:start position:0%
+that will come out of here that
+ 
+
+ align:start position:0%
+that will come out of here that
+satisfies the brag condition for this D
+
+ align:start position:0%
+satisfies the brag condition for this D
+ 
+
+ align:start position:0%
+satisfies the brag condition for this D
+spacing and this angle so the single
+
+ align:start position:0%
+spacing and this angle so the single
+ 
+
+ align:start position:0%
+spacing and this angle so the single
+Crystal acts as a monochrometer very
+
+ align:start position:0%
+Crystal acts as a monochrometer very
+ 
+
+ align:start position:0%
+Crystal acts as a monochrometer very
+cool very cool so this is called a
+
+ align:start position:0%
+cool very cool so this is called a
+ 
+
+ align:start position:0%
+cool very cool so this is called a
+single
+
+ align:start position:0%
+single
+ 
+
+ align:start position:0%
+single
+Crystal monochrometer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just use brags law that's all well in
+
+ align:start position:0%
+just use brags law that's all well in
+ 
+
+ align:start position:0%
+just use brags law that's all well in
+this case we just we take the whole the
+
+ align:start position:0%
+this case we just we take the whole the
+ 
+
+ align:start position:0%
+this case we just we take the whole the
+whole mess everything and here's what
+
+ align:start position:0%
+whole mess everything and here's what
+ 
+
+ align:start position:0%
+whole mess everything and here's what
+the specimen looks like the specimen
+
+ align:start position:0%
+the specimen looks like the specimen
+ 
+
+ align:start position:0%
+the specimen looks like the specimen
+goes into a a a darkened uh box it's
+
+ align:start position:0%
+goes into a a a darkened uh box it's
+ 
+
+ align:start position:0%
+goes into a a a darkened uh box it's
+called a camera
+
+ align:start position:0%
+called a camera
+ 
+
+ align:start position:0%
+called a camera
+obscura camera
+
+ align:start position:0%
+obscura camera
+ 
+
+ align:start position:0%
+obscura camera
+obscura and what happens is I can put
+
+ align:start position:0%
+obscura and what happens is I can put
+ 
+
+ align:start position:0%
+obscura and what happens is I can put
+the specimen on the front here so the
+
+ align:start position:0%
+the specimen on the front here so the
+ 
+
+ align:start position:0%
+the specimen on the front here so the
+specimen is on the front this is some
+
+ align:start position:0%
+specimen is on the front this is some
+ 
+
+ align:start position:0%
+specimen is on the front this is some
+Crystal relatively thin and I put film
+
+ align:start position:0%
+Crystal relatively thin and I put film
+ 
+
+ align:start position:0%
+Crystal relatively thin and I put film
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+back films on the back so I have film
+
+ align:start position:0%
+back films on the back so I have film
+ 
+
+ align:start position:0%
+back films on the back so I have film
+that's sensitive to uh X-ray and now I
+
+ align:start position:0%
+that's sensitive to uh X-ray and now I
+ 
+
+ align:start position:0%
+that's sensitive to uh X-ray and now I
+send the beam in so this is white
+
+ align:start position:0%
+send the beam in so this is white
+ 
+
+ align:start position:0%
+send the beam in so this is white
+x-ray white x-ray white x-ray meaning
+
+ align:start position:0%
+x-ray white x-ray white x-ray meaning
+ 
+
+ align:start position:0%
+x-ray white x-ray white x-ray meaning
+it's variable wavelength it's the whole
+
+ align:start position:0%
+it's variable wavelength it's the whole
+ 
+
+ align:start position:0%
+it's variable wavelength it's the whole
+Spectrum okay and what happens is the
+
+ align:start position:0%
+Spectrum okay and what happens is the
+ 
+
+ align:start position:0%
+Spectrum okay and what happens is the
+white x-ray interacts with the specimen
+
+ align:start position:0%
+white x-ray interacts with the specimen
+ 
+
+ align:start position:0%
+white x-ray interacts with the specimen
+and shoots off at different angles
+
+ align:start position:0%
+and shoots off at different angles
+ 
+
+ align:start position:0%
+and shoots off at different angles
+because I've got different initial
+
+ align:start position:0%
+because I've got different initial
+ 
+
+ align:start position:0%
+because I've got different initial
+wavelengths so each wavelength will be
+
+ align:start position:0%
+wavelengths so each wavelength will be
+ 
+
+ align:start position:0%
+wavelengths so each wavelength will be
+defract at its own special angle and so
+
+ align:start position:0%
+defract at its own special angle and so
+ 
+
+ align:start position:0%
+defract at its own special angle and so
+what happens is we end up with a spot
+
+ align:start position:0%
+what happens is we end up with a spot
+ 
+
+ align:start position:0%
+what happens is we end up with a spot
+pattern
+
+ align:start position:0%
+pattern
+ 
+
+ align:start position:0%
+pattern
+on the film we end up with a spot
+
+ align:start position:0%
+on the film we end up with a spot
+ 
+
+ align:start position:0%
+on the film we end up with a spot
+pattern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and spot pattern spot pattern is the
+
+ align:start position:0%
+and spot pattern spot pattern is the
+ 
+
+ align:start position:0%
+and spot pattern spot pattern is the
+output and the symmetry of the spot
+
+ align:start position:0%
+output and the symmetry of the spot
+ 
+
+ align:start position:0%
+output and the symmetry of the spot
+pattern I'm not going to take you into k
+
+ align:start position:0%
+pattern I'm not going to take you into k
+ 
+
+ align:start position:0%
+pattern I'm not going to take you into k
+space and so on but and let me simply
+
+ align:start position:0%
+space and so on but and let me simply
+ 
+
+ align:start position:0%
+space and so on but and let me simply
+tell you that all you need to appreciate
+
+ align:start position:0%
+tell you that all you need to appreciate
+ 
+
+ align:start position:0%
+tell you that all you need to appreciate
+at this point is that the Symmetry in
+
+ align:start position:0%
+at this point is that the Symmetry in
+ 
+
+ align:start position:0%
+at this point is that the Symmetry in
+the spot pattern is
+
+ align:start position:0%
+the spot pattern is
+ 
+
+ align:start position:0%
+the spot pattern is
+imitative is imitative of the symmetry
+
+ align:start position:0%
+imitative is imitative of the symmetry
+ 
+
+ align:start position:0%
+imitative is imitative of the symmetry
+in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crystal symmetry in the
+
+ align:start position:0%
+crystal symmetry in the
+ 
+
+ align:start position:0%
+crystal symmetry in the
+crystal so let me say something about
+
+ align:start position:0%
+crystal so let me say something about
+ 
+
+ align:start position:0%
+crystal so let me say something about
+Atomic symmetry uh and this is basic all
+
+ align:start position:0%
+Atomic symmetry uh and this is basic all
+ 
+
+ align:start position:0%
+Atomic symmetry uh and this is basic all
+we're talking about here is rotational
+
+ align:start position:0%
+we're talking about here is rotational
+ 
+
+ align:start position:0%
+we're talking about here is rotational
+symmetry because we're looking at
+
+ align:start position:0%
+symmetry because we're looking at
+ 
+
+ align:start position:0%
+symmetry because we're looking at
+something uh on edge so for example if I
+
+ align:start position:0%
+something uh on edge so for example if I
+ 
+
+ align:start position:0%
+something uh on edge so for example if I
+gave you the o1 plane if I gave you the
+
+ align:start position:0%
+gave you the o1 plane if I gave you the
+ 
+
+ align:start position:0%
+gave you the o1 plane if I gave you the
+o1 plane in a cubic Crystal it looks
+
+ align:start position:0%
+o1 plane in a cubic Crystal it looks
+ 
+
+ align:start position:0%
+o1 plane in a cubic Crystal it looks
+like this all right so now what I want
+
+ align:start position:0%
+like this all right so now what I want
+ 
+
+ align:start position:0%
+like this all right so now what I want
+to do is look at
+
+ align:start position:0%
+to do is look at
+ 
+
+ align:start position:0%
+to do is look at
+rotation rotation above about a normal
+
+ align:start position:0%
+rotation rotation above about a normal
+ 
+
+ align:start position:0%
+rotation rotation above about a normal
+axis rotation about a normal axis so I'm
+
+ align:start position:0%
+axis rotation about a normal axis so I'm
+ 
+
+ align:start position:0%
+axis rotation about a normal axis so I'm
+going to put a normal axis right here at
+
+ align:start position:0%
+going to put a normal axis right here at
+ 
+
+ align:start position:0%
+going to put a normal axis right here at
+the center and I'm going to rotate this
+
+ align:start position:0%
+the center and I'm going to rotate this
+ 
+
+ align:start position:0%
+the center and I'm going to rotate this
+and I'm going to ask you the question
+
+ align:start position:0%
+and I'm going to ask you the question
+ 
+
+ align:start position:0%
+and I'm going to ask you the question
+how through what angle do I have to
+
+ align:start position:0%
+how through what angle do I have to
+ 
+
+ align:start position:0%
+how through what angle do I have to
+rotate this in order to get this back so
+
+ align:start position:0%
+rotate this in order to get this back so
+ 
+
+ align:start position:0%
+rotate this in order to get this back so
+if you close your eyes and I start
+
+ align:start position:0%
+if you close your eyes and I start
+ 
+
+ align:start position:0%
+if you close your eyes and I start
+rotating suppose I rotate at 45 degrees
+
+ align:start position:0%
+rotating suppose I rotate at 45 degrees
+ 
+
+ align:start position:0%
+rotating suppose I rotate at 45 degrees
+you open your eyes you're going to see
+
+ align:start position:0%
+you open your eyes you're going to see
+ 
+
+ align:start position:0%
+you open your eyes you're going to see
+that you're going to know something's
+
+ align:start position:0%
+that you're going to know something's
+ 
+
+ align:start position:0%
+that you're going to know something's
+moved how many degrees do I have to
+
+ align:start position:0%
+moved how many degrees do I have to
+ 
+
+ align:start position:0%
+moved how many degrees do I have to
+rotate before I get this back 90 right
+
+ align:start position:0%
+rotate before I get this back 90 right
+ 
+
+ align:start position:0%
+rotate before I get this back 90 right
+so if I rotate 90° I will end up with
+
+ align:start position:0%
+so if I rotate 90° I will end up with
+ 
+
+ align:start position:0%
+so if I rotate 90° I will end up with
+this and these are indistinguishable so
+
+ align:start position:0%
+this and these are indistinguishable so
+ 
+
+ align:start position:0%
+this and these are indistinguishable so
+90° is what I need to rotate and the
+
+ align:start position:0%
+90° is what I need to rotate and the
+ 
+
+ align:start position:0%
+90° is what I need to rotate and the
+crystallographers instead of talking
+
+ align:start position:0%
+crystallographers instead of talking
+ 
+
+ align:start position:0%
+crystallographers instead of talking
+about the angle of rotation to restore
+
+ align:start position:0%
+about the angle of rotation to restore
+ 
+
+ align:start position:0%
+about the angle of rotation to restore
+what you're looking at they talk about
+
+ align:start position:0%
+what you're looking at they talk about
+ 
+
+ align:start position:0%
+what you're looking at they talk about
+fold and fold is simply
+
+ align:start position:0%
+fold and fold is simply
+ 
+
+ align:start position:0%
+fold and fold is simply
+360° divided by this angle so we say
+
+ align:start position:0%
+360° divided by this angle so we say
+ 
+
+ align:start position:0%
+360° divided by this angle so we say
+that this has fourfold rotational
+
+ align:start position:0%
+that this has fourfold rotational
+ 
+
+ align:start position:0%
+that this has fourfold rotational
+symmetry this has four-fold symmetry
+
+ align:start position:0%
+symmetry this has four-fold symmetry
+ 
+
+ align:start position:0%
+symmetry this has four-fold symmetry
+suppose I look at
+
+ align:start position:0%
+suppose I look at
+ 
+
+ align:start position:0%
+suppose I look at
+011 011 is the uh diagonal isn't it so
+
+ align:start position:0%
+011 011 is the uh diagonal isn't it so
+ 
+
+ align:start position:0%
+011 011 is the uh diagonal isn't it so
+this is a and this is square < TK of 2 a
+
+ align:start position:0%
+this is a and this is square < TK of 2 a
+ 
+
+ align:start position:0%
+this is a and this is square < TK of 2 a
+and now if I put an axis in the center
+
+ align:start position:0%
+and now if I put an axis in the center
+ 
+
+ align:start position:0%
+and now if I put an axis in the center
+through what angle do I have to rotate
+
+ align:start position:0%
+through what angle do I have to rotate
+ 
+
+ align:start position:0%
+through what angle do I have to rotate
+before I get this back that's 180 right
+
+ align:start position:0%
+before I get this back that's 180 right
+ 
+
+ align:start position:0%
+before I get this back that's 180 right
+180 so this has twofold
+
+ align:start position:0%
+180 so this has twofold
+ 
+
+ align:start position:0%
+180 so this has twofold
+symmetry okay and finally uh let's do
+
+ align:start position:0%
+symmetry okay and finally uh let's do
+ 
+
+ align:start position:0%
+symmetry okay and finally uh let's do
+111 the 111 plane looks like this and so
+
+ align:start position:0%
+111 the 111 plane looks like this and so
+ 
+
+ align:start position:0%
+111 the 111 plane looks like this and so
+obviously this you'd have to go through
+
+ align:start position:0%
+obviously this you'd have to go through
+ 
+
+ align:start position:0%
+obviously this you'd have to go through
+120 and this would exhibit three-fold
+
+ align:start position:0%
+120 and this would exhibit three-fold
+ 
+
+ align:start position:0%
+120 and this would exhibit three-fold
+symmetry so for example suppose remember
+
+ align:start position:0%
+symmetry so for example suppose remember
+ 
+
+ align:start position:0%
+symmetry so for example suppose remember
+I showed you that uh Crystal of the um
+
+ align:start position:0%
+I showed you that uh Crystal of the um
+ 
+
+ align:start position:0%
+I showed you that uh Crystal of the um
+silicon single Crystal silicon the
+
+ align:start position:0%
+silicon single Crystal silicon the
+ 
+
+ align:start position:0%
+silicon single Crystal silicon the
+single Crystal
+
+ align:start position:0%
+single Crystal
+ 
+
+ align:start position:0%
+single Crystal
+silicon let's say we've cut it and we
+
+ align:start position:0%
+silicon let's say we've cut it and we
+ 
+
+ align:start position:0%
+silicon let's say we've cut it and we
+want to find out what plane we cut it on
+
+ align:start position:0%
+want to find out what plane we cut it on
+ 
+
+ align:start position:0%
+want to find out what plane we cut it on
+how suppose we want to ensure that we
+
+ align:start position:0%
+how suppose we want to ensure that we
+ 
+
+ align:start position:0%
+how suppose we want to ensure that we
+have cut it so that the 111 plane is
+
+ align:start position:0%
+have cut it so that the 111 plane is
+ 
+
+ align:start position:0%
+have cut it so that the 111 plane is
+parallel to the surface one way of
+
+ align:start position:0%
+parallel to the surface one way of
+ 
+
+ align:start position:0%
+parallel to the surface one way of
+determining this would be to put the
+
+ align:start position:0%
+determining this would be to put the
+ 
+
+ align:start position:0%
+determining this would be to put the
+single Crystal of silicon into a laow
+
+ align:start position:0%
+single Crystal of silicon into a laow
+ 
+
+ align:start position:0%
+single Crystal of silicon into a laow
+unit and irradiate it and if indeed we
+
+ align:start position:0%
+unit and irradiate it and if indeed we
+ 
+
+ align:start position:0%
+unit and irradiate it and if indeed we
+have the 111 plane we will see a spot
+
+ align:start position:0%
+have the 111 plane we will see a spot
+ 
+
+ align:start position:0%
+have the 111 plane we will see a spot
+pattern that exhibits three-fold
+
+ align:start position:0%
+pattern that exhibits three-fold
+ 
+
+ align:start position:0%
+pattern that exhibits three-fold
+symmetry so this allows us to do
+
+ align:start position:0%
+symmetry so this allows us to do
+ 
+
+ align:start position:0%
+symmetry so this allows us to do
+indexing the other thing we can do is we
+
+ align:start position:0%
+indexing the other thing we can do is we
+ 
+
+ align:start position:0%
+indexing the other thing we can do is we
+can put the specimen on the back and and
+
+ align:start position:0%
+can put the specimen on the back and and
+ 
+
+ align:start position:0%
+can put the specimen on the back and and
+have the film on the front and we end up
+
+ align:start position:0%
+have the film on the front and we end up
+ 
+
+ align:start position:0%
+have the film on the front and we end up
+with what's known as lowiy back scatter
+
+ align:start position:0%
+with what's known as lowiy back scatter
+ 
+
+ align:start position:0%
+with what's known as lowiy back scatter
+so let's take a look at a few more
+
+ align:start position:0%
+so let's take a look at a few more
+ 
+
+ align:start position:0%
+so let's take a look at a few more
+symmetries here's uh this is going back
+
+ align:start position:0%
+symmetries here's uh this is going back
+ 
+
+ align:start position:0%
+symmetries here's uh this is going back
+to some eer prints uh I don't think I
+
+ align:start position:0%
+to some eer prints uh I don't think I
+ 
+
+ align:start position:0%
+to some eer prints uh I don't think I
+showed you this one the other day so
+
+ align:start position:0%
+showed you this one the other day so
+ 
+
+ align:start position:0%
+showed you this one the other day so
+what's this what's that crystal
+
+ align:start position:0%
+what's this what's that crystal
+ 
+
+ align:start position:0%
+what's this what's that crystal
+structure that simple Cub it's not
+
+ align:start position:0%
+structure that simple Cub it's not
+ 
+
+ align:start position:0%
+structure that simple Cub it's not
+simple cubic pardon me it's either body
+
+ align:start position:0%
+simple cubic pardon me it's either body
+ 
+
+ align:start position:0%
+simple cubic pardon me it's either body
+centered cubic or face centered cubic
+
+ align:start position:0%
+centered cubic or face centered cubic
+ 
+
+ align:start position:0%
+centered cubic or face centered cubic
+the two are the same in two Dimensions
+
+ align:start position:0%
+the two are the same in two Dimensions
+ 
+
+ align:start position:0%
+the two are the same in two Dimensions
+right so this would exhibit fourfold
+
+ align:start position:0%
+right so this would exhibit fourfold
+ 
+
+ align:start position:0%
+right so this would exhibit fourfold
+symmetry this pattern exhibits four-fold
+
+ align:start position:0%
+symmetry this pattern exhibits four-fold
+ 
+
+ align:start position:0%
+symmetry this pattern exhibits four-fold
+symmetry
+
+ align:start position:0%
+symmetry
+ 
+
+ align:start position:0%
+symmetry
+right this
+
+ align:start position:0%
+right this
+ 
+
+ align:start position:0%
+right this
+one symmetry now symmetry three-fold
+
+ align:start position:0%
+one symmetry now symmetry three-fold
+ 
+
+ align:start position:0%
+one symmetry now symmetry three-fold
+symmetry right 120 look I even tried it
+
+ align:start position:0%
+symmetry right 120 look I even tried it
+ 
+
+ align:start position:0%
+symmetry right 120 look I even tried it
+I rotated this I actually programmed
+
+ align:start position:0%
+I rotated this I actually programmed
+ 
+
+ align:start position:0%
+I rotated this I actually programmed
+Photoshop I said rotate 120° Bingo now
+
+ align:start position:0%
+Photoshop I said rotate 120° Bingo now
+ 
+
+ align:start position:0%
+Photoshop I said rotate 120° Bingo now
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+see so now these are some La patterns of
+
+ align:start position:0%
+see so now these are some La patterns of
+ 
+
+ align:start position:0%
+see so now these are some La patterns of
+various crystals this is what you see in
+
+ align:start position:0%
+various crystals this is what you see in
+ 
+
+ align:start position:0%
+various crystals this is what you see in
+the Lai uh unit three different crystals
+
+ align:start position:0%
+the Lai uh unit three different crystals
+ 
+
+ align:start position:0%
+the Lai uh unit three different crystals
+here okay so let's look what do we see
+
+ align:start position:0%
+here okay so let's look what do we see
+ 
+
+ align:start position:0%
+here okay so let's look what do we see
+how about this
+
+ align:start position:0%
+how about this
+ 
+
+ align:start position:0%
+how about this
+one okay this you won't be able to tell
+
+ align:start position:0%
+one okay this you won't be able to tell
+ 
+
+ align:start position:0%
+one okay this you won't be able to tell
+the crystal structure all you can see is
+
+ align:start position:0%
+the crystal structure all you can see is
+ 
+
+ align:start position:0%
+the crystal structure all you can see is
+the pattern all you can ask from this is
+
+ align:start position:0%
+the pattern all you can ask from this is
+ 
+
+ align:start position:0%
+the pattern all you can ask from this is
+what is the pattern so which of these
+
+ align:start position:0%
+what is the pattern so which of these
+ 
+
+ align:start position:0%
+what is the pattern so which of these
+symmetries do we have is this fourfold
+
+ align:start position:0%
+symmetries do we have is this fourfold
+ 
+
+ align:start position:0%
+symmetries do we have is this fourfold
+threefold or
+
+ align:start position:0%
+threefold or
+ 
+
+ align:start position:0%
+threefold or
+twofold this looks like fourfold 90
+
+ align:start position:0%
+twofold this looks like fourfold 90
+ 
+
+ align:start position:0%
+twofold this looks like fourfold 90
+degre pretty good okay this one
+
+ align:start position:0%
+degre pretty good okay this one
+ 
+
+ align:start position:0%
+degre pretty good okay this one
+here yeah well six you're right you can
+
+ align:start position:0%
+here yeah well six you're right you can
+ 
+
+ align:start position:0%
+here yeah well six you're right you can
+say six it looks like 60 but in fact uh
+
+ align:start position:0%
+say six it looks like 60 but in fact uh
+ 
+
+ align:start position:0%
+say six it looks like 60 but in fact uh
+it's you need to go the full there there
+
+ align:start position:0%
+it's you need to go the full there there
+ 
+
+ align:start position:0%
+it's you need to go the full there there
+other other reasons you have to go into
+
+ align:start position:0%
+other other reasons you have to go into
+ 
+
+ align:start position:0%
+other other reasons you have to go into
+that this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+twofold remember this so this one is you
+
+ align:start position:0%
+twofold remember this so this one is you
+ 
+
+ align:start position:0%
+twofold remember this so this one is you
+can see this is a 60° angle but you can
+
+ align:start position:0%
+can see this is a 60° angle but you can
+ 
+
+ align:start position:0%
+can see this is a 60° angle but you can
+see this has three-fold symmetry so this
+
+ align:start position:0%
+see this has three-fold symmetry so this
+ 
+
+ align:start position:0%
+see this has three-fold symmetry so this
+gets back somebody uh said 60° but you
+
+ align:start position:0%
+gets back somebody uh said 60° but you
+ 
+
+ align:start position:0%
+gets back somebody uh said 60° but you
+can see this pattern is requires because
+
+ align:start position:0%
+can see this pattern is requires because
+ 
+
+ align:start position:0%
+can see this pattern is requires because
+of the basis here in fact it requires
+
+ align:start position:0%
+of the basis here in fact it requires
+ 
+
+ align:start position:0%
+of the basis here in fact it requires
+120° what about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one exactly it's onefold this this has
+
+ align:start position:0%
+one exactly it's onefold this this has
+ 
+
+ align:start position:0%
+one exactly it's onefold this this has
+translational symmetry but no rotational
+
+ align:start position:0%
+translational symmetry but no rotational
+ 
+
+ align:start position:0%
+translational symmetry but no rotational
+symmetry obviously if you go 90 degrees
+
+ align:start position:0%
+symmetry obviously if you go 90 degrees
+ 
+
+ align:start position:0%
+symmetry obviously if you go 90 degrees
+the dogs are going to be pointing up and
+
+ align:start position:0%
+the dogs are going to be pointing up and
+ 
+
+ align:start position:0%
+the dogs are going to be pointing up and
+down if you go 180 degrees it's not
+
+ align:start position:0%
+down if you go 180 degrees it's not
+ 
+
+ align:start position:0%
+down if you go 180 degrees it's not
+going to work either you have to go this
+
+ align:start position:0%
+going to work either you have to go this
+ 
+
+ align:start position:0%
+going to work either you have to go this
+is this has rotational uh onefold
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to jump over this I think I
+
+ align:start position:0%
+I'm going to jump over this I think I
+ 
+
+ align:start position:0%
+I'm going to jump over this I think I
+see we're getting close to and all right
+
+ align:start position:0%
+see we're getting close to and all right
+ 
+
+ align:start position:0%
+see we're getting close to and all right
+so now here's another uh symmetry this
+
+ align:start position:0%
+so now here's another uh symmetry this
+ 
+
+ align:start position:0%
+so now here's another uh symmetry this
+is the inverse of the dogs the dogs have
+
+ align:start position:0%
+is the inverse of the dogs the dogs have
+ 
+
+ align:start position:0%
+is the inverse of the dogs the dogs have
+no rotational symmetry but translational
+
+ align:start position:0%
+no rotational symmetry but translational
+ 
+
+ align:start position:0%
+no rotational symmetry but translational
+symmetry this pattern here has
+
+ align:start position:0%
+symmetry this pattern here has
+ 
+
+ align:start position:0%
+symmetry this pattern here has
+rotational symmetry but no translational
+
+ align:start position:0%
+rotational symmetry but no translational
+ 
+
+ align:start position:0%
+rotational symmetry but no translational
+symmetry it's called Penrose tile
+
+ align:start position:0%
+symmetry it's called Penrose tile
+ 
+
+ align:start position:0%
+symmetry it's called Penrose tile
+Penrose tile and in particular there's
+
+ align:start position:0%
+Penrose tile and in particular there's
+ 
+
+ align:start position:0%
+Penrose tile and in particular there's
+the rotation symmetry right and how many
+
+ align:start position:0%
+the rotation symmetry right and how many
+ 
+
+ align:start position:0%
+the rotation symmetry right and how many
+how many turns do we go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here it has fivefold symmetry
+
+ align:start position:0%
+here it has fivefold symmetry
+ 
+
+ align:start position:0%
+here it has fivefold symmetry
+five that's very
+
+ align:start position:0%
+five that's very
+ 
+
+ align:start position:0%
+five that's very
+weird fivefold
+
+ align:start position:0%
+weird fivefold
+ 
+
+ align:start position:0%
+weird fivefold
+symmetry now this doesn't conform to any
+
+ align:start position:0%
+symmetry now this doesn't conform to any
+ 
+
+ align:start position:0%
+symmetry now this doesn't conform to any
+rules of
+
+ align:start position:0%
+rules of
+ 
+
+ align:start position:0%
+rules of
+crystallography doesn't conform to any
+
+ align:start position:0%
+crystallography doesn't conform to any
+ 
+
+ align:start position:0%
+crystallography doesn't conform to any
+such a such a such a a pattern is called
+
+ align:start position:0%
+such a such a such a a pattern is called
+ 
+
+ align:start position:0%
+such a such a such a a pattern is called
+the AP periodic we saw that it's you
+
+ align:start position:0%
+the AP periodic we saw that it's you
+ 
+
+ align:start position:0%
+the AP periodic we saw that it's you
+couldn't make bathroom ties of this
+
+ align:start position:0%
+couldn't make bathroom ties of this
+ 
+
+ align:start position:0%
+couldn't make bathroom ties of this
+shape you'd have to have other shapes
+
+ align:start position:0%
+shape you'd have to have other shapes
+ 
+
+ align:start position:0%
+shape you'd have to have other shapes
+that would feed into the fit into the
+
+ align:start position:0%
+that would feed into the fit into the
+ 
+
+ align:start position:0%
+that would feed into the fit into the
+interstices and so on there's another
+
+ align:start position:0%
+interstices and so on there's another
+ 
+
+ align:start position:0%
+interstices and so on there's another
+one see it fills it fills to space but
+
+ align:start position:0%
+one see it fills it fills to space but
+ 
+
+ align:start position:0%
+one see it fills it fills to space but
+you you have to add some extra but it
+
+ align:start position:0%
+you you have to add some extra but it
+ 
+
+ align:start position:0%
+you you have to add some extra but it
+has fivefold symmetry if you take this
+
+ align:start position:0%
+has fivefold symmetry if you take this
+ 
+
+ align:start position:0%
+has fivefold symmetry if you take this
+whole pattern and rotate at 72 degrees
+
+ align:start position:0%
+whole pattern and rotate at 72 degrees
+ 
+
+ align:start position:0%
+whole pattern and rotate at 72 degrees
+you'll get it back so it has rotational
+
+ align:start position:0%
+you'll get it back so it has rotational
+ 
+
+ align:start position:0%
+you'll get it back so it has rotational
+symmetry okay so now I'm going to show
+
+ align:start position:0%
+symmetry okay so now I'm going to show
+ 
+
+ align:start position:0%
+symmetry okay so now I'm going to show
+you something that was really
+
+ align:start position:0%
+you something that was really
+ 
+
+ align:start position:0%
+you something that was really
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+unexpected so so far we over here in the
+
+ align:start position:0%
+unexpected so so far we over here in the
+ 
+
+ align:start position:0%
+unexpected so so far we over here in the
+top left we're studying ordered solids
+
+ align:start position:0%
+top left we're studying ordered solids
+ 
+
+ align:start position:0%
+top left we're studying ordered solids
+which they have a unit cell they're
+
+ align:start position:0%
+which they have a unit cell they're
+ 
+
+ align:start position:0%
+which they have a unit cell they're
+periodic and we call them a crystal and
+
+ align:start position:0%
+periodic and we call them a crystal and
+ 
+
+ align:start position:0%
+periodic and we call them a crystal and
+pretty soon we're going to start
+
+ align:start position:0%
+pretty soon we're going to start
+ 
+
+ align:start position:0%
+pretty soon we're going to start
+studying disordered solids which form
+
+ align:start position:0%
+studying disordered solids which form
+ 
+
+ align:start position:0%
+studying disordered solids which form
+glasses in 1982 there was a a fellow by
+
+ align:start position:0%
+glasses in 1982 there was a a fellow by
+ 
+
+ align:start position:0%
+glasses in 1982 there was a a fellow by
+the name of Dan sheckman who was uh on
+
+ align:start position:0%
+the name of Dan sheckman who was uh on
+ 
+
+ align:start position:0%
+the name of Dan sheckman who was uh on
+sabatical from the tech neon in Israel
+
+ align:start position:0%
+sabatical from the tech neon in Israel
+ 
+
+ align:start position:0%
+sabatical from the tech neon in Israel
+and he was working down at the National
+
+ align:start position:0%
+and he was working down at the National
+ 
+
+ align:start position:0%
+and he was working down at the National
+Bureau of Standards it was called NBS in
+
+ align:start position:0%
+Bureau of Standards it was called NBS in
+ 
+
+ align:start position:0%
+Bureau of Standards it was called NBS in
+those days it's now known as the
+
+ align:start position:0%
+those days it's now known as the
+ 
+
+ align:start position:0%
+those days it's now known as the
+National Institute of Standards and
+
+ align:start position:0%
+National Institute of Standards and
+ 
+
+ align:start position:0%
+National Institute of Standards and
+technology sometimes you'll see This
+
+ align:start position:0%
+technology sometimes you'll see This
+ 
+
+ align:start position:0%
+technology sometimes you'll see This
+Acronym nist and they're down in
+
+ align:start position:0%
+Acronym nist and they're down in
+ 
+
+ align:start position:0%
+Acronym nist and they're down in
+Gaithersburg Maryland
+
+ align:start position:0%
+Gaithersburg Maryland
+ 
+
+ align:start position:0%
+Gaithersburg Maryland
+and sheckman and and John Khan and
+
+ align:start position:0%
+and sheckman and and John Khan and
+ 
+
+ align:start position:0%
+and sheckman and and John Khan and
+co-workers were were looking at a set of
+
+ align:start position:0%
+co-workers were were looking at a set of
+ 
+
+ align:start position:0%
+co-workers were were looking at a set of
+Alloys from the aluminum manganese
+
+ align:start position:0%
+Alloys from the aluminum manganese
+ 
+
+ align:start position:0%
+Alloys from the aluminum manganese
+system and they were very highly
+
+ align:start position:0%
+system and they were very highly
+ 
+
+ align:start position:0%
+system and they were very highly
+ordered over the range of composition
+
+ align:start position:0%
+ordered over the range of composition
+ 
+
+ align:start position:0%
+ordered over the range of composition
+pure aluminum is FCC pure manganes has
+
+ align:start position:0%
+pure aluminum is FCC pure manganes has
+ 
+
+ align:start position:0%
+pure aluminum is FCC pure manganes has
+multiple Crystal structures so the
+
+ align:start position:0%
+multiple Crystal structures so the
+ 
+
+ align:start position:0%
+multiple Crystal structures so the
+question is what happens when you take
+
+ align:start position:0%
+question is what happens when you take
+ 
+
+ align:start position:0%
+question is what happens when you take
+something that's not face centered cubic
+
+ align:start position:0%
+something that's not face centered cubic
+ 
+
+ align:start position:0%
+something that's not face centered cubic
+and alloy it with something that is face
+
+ align:start position:0%
+and alloy it with something that is face
+ 
+
+ align:start position:0%
+and alloy it with something that is face
+centered cubic well initially it retains
+
+ align:start position:0%
+centered cubic well initially it retains
+ 
+
+ align:start position:0%
+centered cubic well initially it retains
+aluminum retains its face Center cubic
+
+ align:start position:0%
+aluminum retains its face Center cubic
+ 
+
+ align:start position:0%
+aluminum retains its face Center cubic
+crystal structure but after a while you
+
+ align:start position:0%
+crystal structure but after a while you
+ 
+
+ align:start position:0%
+crystal structure but after a while you
+get to such a high manganese level that
+
+ align:start position:0%
+get to such a high manganese level that
+ 
+
+ align:start position:0%
+get to such a high manganese level that
+the crystal structure changes and over
+
+ align:start position:0%
+the crystal structure changes and over
+ 
+
+ align:start position:0%
+the crystal structure changes and over
+certain ranges of composition these
+
+ align:start position:0%
+certain ranges of composition these
+ 
+
+ align:start position:0%
+certain ranges of composition these
+Alloys are amorphous they're glass
+
+ align:start position:0%
+Alloys are amorphous they're glass
+ 
+
+ align:start position:0%
+Alloys are amorphous they're glass
+formers but then came something totally
+
+ align:start position:0%
+formers but then came something totally
+ 
+
+ align:start position:0%
+formers but then came something totally
+unexpected when sheckman prepared the
+
+ align:start position:0%
+unexpected when sheckman prepared the
+ 
+
+ align:start position:0%
+unexpected when sheckman prepared the
+alloy that contained 25% manganese he
+
+ align:start position:0%
+alloy that contained 25% manganese he
+ 
+
+ align:start position:0%
+alloy that contained 25% manganese he
+got something extremely weird in the
+
+ align:start position:0%
+got something extremely weird in the
+ 
+
+ align:start position:0%
+got something extremely weird in the
+X-ray defraction pattern he got
+
+ align:start position:0%
+X-ray defraction pattern he got
+ 
+
+ align:start position:0%
+X-ray defraction pattern he got
+five-fold symmetry in his X-ray
+
+ align:start position:0%
+five-fold symmetry in his X-ray
+ 
+
+ align:start position:0%
+five-fold symmetry in his X-ray
+defraction pattern five-fold symmetry
+
+ align:start position:0%
+defraction pattern five-fold symmetry
+ 
+
+ align:start position:0%
+defraction pattern five-fold symmetry
+so this LAX translational symmetry it's
+
+ align:start position:0%
+so this LAX translational symmetry it's
+ 
+
+ align:start position:0%
+so this LAX translational symmetry it's
+AP periodic these were termed quasi
+
+ align:start position:0%
+AP periodic these were termed quasi
+ 
+
+ align:start position:0%
+AP periodic these were termed quasi
+crystals and this caused a a a storm in
+
+ align:start position:0%
+crystals and this caused a a a storm in
+ 
+
+ align:start position:0%
+crystals and this caused a a a storm in
+the material science community in the
+
+ align:start position:0%
+the material science community in the
+ 
+
+ align:start position:0%
+the material science community in the
+mid 80s all kinds of NSF programs
+
+ align:start position:0%
+mid 80s all kinds of NSF programs
+ 
+
+ align:start position:0%
+mid 80s all kinds of NSF programs
+Department of Defense programs were
+
+ align:start position:0%
+Department of Defense programs were
+ 
+
+ align:start position:0%
+Department of Defense programs were
+funding Research into quasi crystals to
+
+ align:start position:0%
+funding Research into quasi crystals to
+ 
+
+ align:start position:0%
+funding Research into quasi crystals to
+try to figure out well they might have
+
+ align:start position:0%
+try to figure out well they might have
+ 
+
+ align:start position:0%
+try to figure out well they might have
+some unique properties maybe they have
+
+ align:start position:0%
+some unique properties maybe they have
+ 
+
+ align:start position:0%
+some unique properties maybe they have
+conductivities maybe they have
+
+ align:start position:0%
+conductivities maybe they have
+ 
+
+ align:start position:0%
+conductivities maybe they have
+ductilities maybe they have corrosion
+
+ align:start position:0%
+ductilities maybe they have corrosion
+ 
+
+ align:start position:0%
+ductilities maybe they have corrosion
+resistance that is unknown in classical
+
+ align:start position:0%
+resistance that is unknown in classical
+ 
+
+ align:start position:0%
+resistance that is unknown in classical
+face centered body centered simple cubic
+
+ align:start position:0%
+face centered body centered simple cubic
+ 
+
+ align:start position:0%
+face centered body centered simple cubic
+Alloys so here's uh one of sheckman
+
+ align:start position:0%
+Alloys so here's uh one of sheckman
+ 
+
+ align:start position:0%
+Alloys so here's uh one of sheckman
+uh lowii
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+patterns look at that it's so
+
+ align:start position:0%
+patterns look at that it's so
+ 
+
+ align:start position:0%
+patterns look at that it's so
+weird there were jokes about this you
+
+ align:start position:0%
+weird there were jokes about this you
+ 
+
+ align:start position:0%
+weird there were jokes about this you
+know Gaithersburg if you know the
+
+ align:start position:0%
+know Gaithersburg if you know the
+ 
+
+ align:start position:0%
+know Gaithersburg if you know the
+geography gaitherburg is not far from um
+
+ align:start position:0%
+geography gaitherburg is not far from um
+ 
+
+ align:start position:0%
+geography gaitherburg is not far from um
+Washington so some people joke that this
+
+ align:start position:0%
+Washington so some people joke that this
+ 
+
+ align:start position:0%
+Washington so some people joke that this
+had five-fold symmetry because the
+
+ align:start position:0%
+had five-fold symmetry because the
+ 
+
+ align:start position:0%
+had five-fold symmetry because the
+research was funded by the Pentagon
+
+ align:start position:0%
+research was funded by the Pentagon
+ 
+
+ align:start position:0%
+research was funded by the Pentagon
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+um and this is this is really something
+
+ align:start position:0%
+um and this is this is really something
+ 
+
+ align:start position:0%
+um and this is this is really something
+this is the pages from shech man's lab
+
+ align:start position:0%
+this is the pages from shech man's lab
+ 
+
+ align:start position:0%
+this is the pages from shech man's lab
+notebook April 8th 1982 aluminum 25%
+
+ align:start position:0%
+notebook April 8th 1982 aluminum 25%
+ 
+
+ align:start position:0%
+notebook April 8th 1982 aluminum 25%
+manganese and he's analyzing his
+
+ align:start position:0%
+manganese and he's analyzing his
+ 
+
+ align:start position:0%
+manganese and he's analyzing his
+defraction patterns and he's going nuts
+
+ align:start position:0%
+defraction patterns and he's going nuts
+ 
+
+ align:start position:0%
+defraction patterns and he's going nuts
+and he writes tfold exclamation point
+
+ align:start position:0%
+and he writes tfold exclamation point
+ 
+
+ align:start position:0%
+and he writes tfold exclamation point
+triple and it was real it was real it
+
+ align:start position:0%
+triple and it was real it was real it
+ 
+
+ align:start position:0%
+triple and it was real it was real it
+was very very uh uh exciting so that's
+
+ align:start position:0%
+was very very uh uh exciting so that's
+ 
+
+ align:start position:0%
+was very very uh uh exciting so that's
+that's what quasi crystals is about so
+
+ align:start position:0%
+that's what quasi crystals is about so
+ 
+
+ align:start position:0%
+that's what quasi crystals is about so
+what you can see is how using La you can
+
+ align:start position:0%
+what you can see is how using La you can
+ 
+
+ align:start position:0%
+what you can see is how using La you can
+infer that and then you have to go in
+
+ align:start position:0%
+infer that and then you have to go in
+ 
+
+ align:start position:0%
+infer that and then you have to go in
+and determine what the lce constant so
+
+ align:start position:0%
+and determine what the lce constant so
+ 
+
+ align:start position:0%
+and determine what the lce constant so
+on Last Thing Before You Go somebody I I
+
+ align:start position:0%
+on Last Thing Before You Go somebody I I
+ 
+
+ align:start position:0%
+on Last Thing Before You Go somebody I I
+ran out of time last day what what's the
+
+ align:start position:0%
+ran out of time last day what what's the
+ 
+
+ align:start position:0%
+ran out of time last day what what's the
+connection between seven up and lithium
+
+ align:start position:0%
+connection between seven up and lithium
+ 
+
+ align:start position:0%
+connection between seven up and lithium
+before Mosley people referred to things
+
+ align:start position:0%
+before Mosley people referred to things
+ 
+
+ align:start position:0%
+before Mosley people referred to things
+according to their atomic mass so the
+
+ align:start position:0%
+according to their atomic mass so the
+ 
+
+ align:start position:0%
+according to their atomic mass so the
+atomic mass of lithium is seven that's
+
+ align:start position:0%
+atomic mass of lithium is seven that's
+ 
+
+ align:start position:0%
+atomic mass of lithium is seven that's
+why it's seven I have this on good
+
+ align:start position:0%
+why it's seven I have this on good
+ 
+
+ align:start position:0%
+why it's seven I have this on good
+authority from people in the lithium
+
+ align:start position:0%
+authority from people in the lithium
+ 
+
+ align:start position:0%
+authority from people in the lithium
+industry all right have a good weekend
\ No newline at end of file
diff --git a/WxkwkGEVu-E.txt b/WxkwkGEVu-E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..83d2c4bacb7a8414c728fb4e8396779dccc38c83
--- /dev/null
+++ b/WxkwkGEVu-E.txt
@@ -0,0 +1,275 @@
+align:start position:0%
+ 
+when we discussed the rolling of the
+
+ align:start position:0%
+when we discussed the rolling of the
+ 
+
+ align:start position:0%
+when we discussed the rolling of the
+wheel we chose a reference frame fixed
+
+ align:start position:0%
+wheel we chose a reference frame fixed
+ 
+
+ align:start position:0%
+wheel we chose a reference frame fixed
+to the ground so that was our what we
+
+ align:start position:0%
+to the ground so that was our what we
+ 
+
+ align:start position:0%
+to the ground so that was our what we
+called frame a and in that reference
+
+ align:start position:0%
+called frame a and in that reference
+ 
+
+ align:start position:0%
+called frame a and in that reference
+frame the motion of the point p on the
+
+ align:start position:0%
+frame the motion of the point p on the
+ 
+
+ align:start position:0%
+frame the motion of the point p on the
+rim was quite complicated now what we'd
+
+ align:start position:0%
+rim was quite complicated now what we'd
+ 
+
+ align:start position:0%
+rim was quite complicated now what we'd
+like to look at it in the reference
+
+ align:start position:0%
+like to look at it in the reference
+ 
+
+ align:start position:0%
+like to look at it in the reference
+frame moving with the centre of mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we call that frame CM now the
+
+ align:start position:0%
+and we call that frame CM now the
+ 
+
+ align:start position:0%
+and we call that frame CM now the
+picture there is much easier because the
+
+ align:start position:0%
+picture there is much easier because the
+ 
+
+ align:start position:0%
+picture there is much easier because the
+object is in that reference frame the
+
+ align:start position:0%
+object is in that reference frame the
+ 
+
+ align:start position:0%
+object is in that reference frame the
+center of mass is not moving and the
+
+ align:start position:0%
+center of mass is not moving and the
+ 
+
+ align:start position:0%
+center of mass is not moving and the
+point P on the rim the object is just
+
+ align:start position:0%
+point P on the rim the object is just
+ 
+
+ align:start position:0%
+point P on the rim the object is just
+undergoing circular motion so in that
+
+ align:start position:0%
+undergoing circular motion so in that
+ 
+
+ align:start position:0%
+undergoing circular motion so in that
+frame the velocity of that point P in
+
+ align:start position:0%
+frame the velocity of that point P in
+ 
+
+ align:start position:0%
+frame the velocity of that point P in
+the center-of-mass frame is just tangent
+
+ align:start position:0%
+the center-of-mass frame is just tangent
+ 
+
+ align:start position:0%
+the center-of-mass frame is just tangent
+to the circle and as the object moves
+
+ align:start position:0%
+to the circle and as the object moves
+ 
+
+ align:start position:0%
+to the circle and as the object moves
+around at a later time the velocity is
+
+ align:start position:0%
+around at a later time the velocity is
+ 
+
+ align:start position:0%
+around at a later time the velocity is
+always tangential and in this reference
+
+ align:start position:0%
+always tangential and in this reference
+ 
+
+ align:start position:0%
+always tangential and in this reference
+frame it's just pure circular motion and
+
+ align:start position:0%
+frame it's just pure circular motion and
+ 
+
+ align:start position:0%
+frame it's just pure circular motion and
+we know that the speed in that reference
+
+ align:start position:0%
+we know that the speed in that reference
+ 
+
+ align:start position:0%
+we know that the speed in that reference
+frame is given by the radius of the
+
+ align:start position:0%
+frame is given by the radius of the
+ 
+
+ align:start position:0%
+frame is given by the radius of the
+wheel times the rate d theta/dt and here
+
+ align:start position:0%
+wheel times the rate d theta/dt and here
+ 
+
+ align:start position:0%
+wheel times the rate d theta/dt and here
+let's define the variable theta this way
+
+ align:start position:0%
+let's define the variable theta this way
+ 
+
+ align:start position:0%
+let's define the variable theta this way
+and so in this frame what's happening is
+
+ align:start position:0%
+and so in this frame what's happening is
+ 
+
+ align:start position:0%
+and so in this frame what's happening is
+pure circular motion now we know our law
+
+ align:start position:0%
+pure circular motion now we know our law
+ 
+
+ align:start position:0%
+pure circular motion now we know our law
+of addition of velocity tells us that
+
+ align:start position:0%
+of addition of velocity tells us that
+ 
+
+ align:start position:0%
+of addition of velocity tells us that
+the velocity in the frame fixed to the
+
+ align:start position:0%
+the velocity in the frame fixed to the
+ 
+
+ align:start position:0%
+the velocity in the frame fixed to the
+ground of that point is equal to the
+
+ align:start position:0%
+ground of that point is equal to the
+ 
+
+ align:start position:0%
+ground of that point is equal to the
+velocity of the center of mass plus the
+
+ align:start position:0%
+velocity of the center of mass plus the
+ 
+
+ align:start position:0%
+velocity of the center of mass plus the
+velocity of the object the point on the
+
+ align:start position:0%
+velocity of the object the point on the
+ 
+
+ align:start position:0%
+velocity of the object the point on the
+rim in the center-of-mass frame now what
+
+ align:start position:0%
+rim in the center-of-mass frame now what
+ 
+
+ align:start position:0%
+rim in the center-of-mass frame now what
+we want to do now is draw a picture
+
+ align:start position:0%
+we want to do now is draw a picture
+ 
+
+ align:start position:0%
+we want to do now is draw a picture
+which illustrates this law of addition
+
+ align:start position:0%
+which illustrates this law of addition
+ 
+
+ align:start position:0%
+which illustrates this law of addition
+of velocities
\ No newline at end of file
diff --git a/YP_B0AapU0c.txt b/YP_B0AapU0c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f636c8fae0e0af1fcb85d127f676deb105ad48b8
--- /dev/null
+++ b/YP_B0AapU0c.txt
@@ -0,0 +1,7207 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ocw.mit.edu
+ 
+
+ align:start position:0%
+ocw.mit.edu
+so you know basically the last few weeks
+
+ align:start position:0%
+so you know basically the last few weeks
+ 
+
+ align:start position:0%
+so you know basically the last few weeks
+we've been doing derivatives now we're
+
+ align:start position:0%
+we've been doing derivatives now we're
+ 
+
+ align:start position:0%
+we've been doing derivatives now we're
+going to do integral
+
+ align:start position:0%
+going to do integral
+ 
+
+ align:start position:0%
+going to do integral
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so okay so more precisely we're going to
+
+ align:start position:0%
+so okay so more precisely we're going to
+ 
+
+ align:start position:0%
+so okay so more precisely we're going to
+be talking about double
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integrals okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just to motivate the
+
+ align:start position:0%
+so just to motivate the
+ 
+
+ align:start position:0%
+so just to motivate the
+notion let me just remind you that when
+
+ align:start position:0%
+notion let me just remind you that when
+ 
+
+ align:start position:0%
+notion let me just remind you that when
+you have a function of one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variable say F
+
+ align:start position:0%
+variable say F
+ 
+
+ align:start position:0%
+variable say F
+ofx and if you take its
+
+ align:start position:0%
+ofx and if you take its
+ 
+
+ align:start position:0%
+ofx and if you take its
+integral from say A to B of f ofx
+
+ align:start position:0%
+integral from say A to B of f ofx
+ 
+
+ align:start position:0%
+integral from say A to B of f ofx
+DX well that corresponds to the
+
+ align:start position:0%
+DX well that corresponds to the
+ 
+
+ align:start position:0%
+DX well that corresponds to the
+area
+
+ align:start position:0%
+area
+ 
+
+ align:start position:0%
+area
+below the graph of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F over the interval from A to
+
+ align:start position:0%
+F over the interval from A to
+ 
+
+ align:start position:0%
+F over the interval from A to
+B okay so the
+
+ align:start position:0%
+B okay so the
+ 
+
+ align:start position:0%
+B okay so the
+picture is something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like you have a you have B you have the
+
+ align:start position:0%
+like you have a you have B you have the
+ 
+
+ align:start position:0%
+like you have a you have B you have the
+graph of
+
+ align:start position:0%
+graph of
+ 
+
+ align:start position:0%
+graph of
+F
+
+ align:start position:0%
+F
+ 
+
+ align:start position:0%
+F
+and then with the integral
+
+ align:start position:0%
+and then with the integral
+ 
+
+ align:start position:0%
+and then with the integral
+measures is the
+
+ align:start position:0%
+measures is the
+ 
+
+ align:start position:0%
+measures is the
+area of the this
+
+ align:start position:0%
+area of the this
+ 
+
+ align:start position:0%
+area of the this
+region and when we say the area of this
+
+ align:start position:0%
+region and when we say the area of this
+ 
+
+ align:start position:0%
+region and when we say the area of this
+region of course if f is positive that's
+
+ align:start position:0%
+region of course if f is positive that's
+ 
+
+ align:start position:0%
+region of course if f is positive that's
+what happens if f is negative then we
+
+ align:start position:0%
+what happens if f is negative then we
+ 
+
+ align:start position:0%
+what happens if f is negative then we
+count negatively the area below the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x-axis so now when you have a function
+
+ align:start position:0%
+x-axis so now when you have a function
+ 
+
+ align:start position:0%
+x-axis so now when you have a function
+of two
+
+ align:start position:0%
+of two
+ 
+
+ align:start position:0%
+of two
+variables then you can try to do the
+
+ align:start position:0%
+variables then you can try to do the
+ 
+
+ align:start position:0%
+variables then you can try to do the
+same thing namely you can plot its graph
+
+ align:start position:0%
+same thing namely you can plot its graph
+ 
+
+ align:start position:0%
+same thing namely you can plot its graph
+its graph will be a surface in space and
+
+ align:start position:0%
+its graph will be a surface in space and
+ 
+
+ align:start position:0%
+its graph will be a surface in space and
+then we can try to look for the volume
+
+ align:start position:0%
+then we can try to look for the volume
+ 
+
+ align:start position:0%
+then we can try to look for the volume
+below the graph and that's what we will
+
+ align:start position:0%
+below the graph and that's what we will
+ 
+
+ align:start position:0%
+below the graph and that's what we will
+call the double integ
+
+ align:start position:0%
+call the double integ
+ 
+
+ align:start position:0%
+call the double integ
+of a function over a certain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+region okay
+
+ align:start position:0%
+region okay
+ 
+
+ align:start position:0%
+region okay
+so let's say that we have a
+
+ align:start position:0%
+so let's say that we have a
+ 
+
+ align:start position:0%
+so let's say that we have a
+function of two variables X and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y then we'll look at the volume that's
+
+ align:start position:0%
+Y then we'll look at the volume that's
+ 
+
+ align:start position:0%
+Y then we'll look at the volume that's
+below the
+
+ align:start position:0%
+below the
+ 
+
+ align:start position:0%
+below the
+graph Z equals f of x y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's dra a picture for what this
+
+ align:start position:0%
+so let's dra a picture for what this
+ 
+
+ align:start position:0%
+so let's dra a picture for what this
+means I have a function of X and Y I can
+
+ align:start position:0%
+means I have a function of X and Y I can
+ 
+
+ align:start position:0%
+means I have a function of X and Y I can
+draw its graph the graph will be you
+
+ align:start position:0%
+draw its graph the graph will be you
+ 
+
+ align:start position:0%
+draw its graph the graph will be you
+know the surface with equation Z equals
+
+ align:start position:0%
+know the surface with equation Z equals
+ 
+
+ align:start position:0%
+know the surface with equation Z equals
+f of x and
+
+ align:start position:0%
+f of x and
+ 
+
+ align:start position:0%
+f of x and
+y and while I have to decide where I
+
+ align:start position:0%
+y and while I have to decide where I
+ 
+
+ align:start position:0%
+y and while I have to decide where I
+will integrate the function so for that
+
+ align:start position:0%
+will integrate the function so for that
+ 
+
+ align:start position:0%
+will integrate the function so for that
+I will choose some region in the XY
+
+ align:start position:0%
+I will choose some region in the XY
+ 
+
+ align:start position:0%
+I will choose some region in the XY
+plane
+
+ align:start position:0%
+plane
+ 
+
+ align:start position:0%
+plane
+and I will integrate the function on
+
+ align:start position:0%
+and I will integrate the function on
+ 
+
+ align:start position:0%
+and I will integrate the function on
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+region so it's over a region R in the XY
+
+ align:start position:0%
+region so it's over a region R in the XY
+ 
+
+ align:start position:0%
+region so it's over a region R in the XY
+plane so I have this region R and I look
+
+ align:start position:0%
+plane so I have this region R and I look
+ 
+
+ align:start position:0%
+plane so I have this region R and I look
+at the piece of the graph that is above
+
+ align:start position:0%
+at the piece of the graph that is above
+ 
+
+ align:start position:0%
+at the piece of the graph that is above
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+region and we'll try to compute the
+
+ align:start position:0%
+region and we'll try to compute the
+ 
+
+ align:start position:0%
+region and we'll try to compute the
+volume of this solid
+
+ align:start position:0%
+volume of this solid
+ 
+
+ align:start position:0%
+volume of this solid
+here okay that's what the double
+
+ align:start position:0%
+here okay that's what the double
+ 
+
+ align:start position:0%
+here okay that's what the double
+integral will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measure so we'll call
+
+ align:start position:0%
+measure so we'll call
+ 
+
+ align:start position:0%
+measure so we'll call
+that the double integral of our Orion R
+
+ align:start position:0%
+that the double integral of our Orion R
+ 
+
+ align:start position:0%
+that the double integral of our Orion R
+of f of XY d a and I will have to
+
+ align:start position:0%
+of f of XY d a and I will have to
+ 
+
+ align:start position:0%
+of f of XY d a and I will have to
+explain what the notation means so da
+
+ align:start position:0%
+explain what the notation means so da
+ 
+
+ align:start position:0%
+explain what the notation means so da
+here stands for a piece of area a stands
+
+ align:start position:0%
+here stands for a piece of area a stands
+ 
+
+ align:start position:0%
+here stands for a piece of area a stands
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+area and well it's a double integral so
+
+ align:start position:0%
+area and well it's a double integral so
+ 
+
+ align:start position:0%
+area and well it's a double integral so
+that's why we have two integral signs
+
+ align:start position:0%
+that's why we have two integral signs
+ 
+
+ align:start position:0%
+that's why we have two integral signs
+and we'll have have to indicate somehow
+
+ align:start position:0%
+and we'll have have to indicate somehow
+ 
+
+ align:start position:0%
+and we'll have have to indicate somehow
+the region over which we're integrating
+
+ align:start position:0%
+the region over which we're integrating
+ 
+
+ align:start position:0%
+the region over which we're integrating
+okay we'll come up with more concrete
+
+ align:start position:0%
+okay we'll come up with more concrete
+ 
+
+ align:start position:0%
+okay we'll come up with more concrete
+notations when we see how to actually
+
+ align:start position:0%
+notations when we see how to actually
+ 
+
+ align:start position:0%
+notations when we see how to actually
+compute these things but that's the
+
+ align:start position:0%
+compute these things but that's the
+ 
+
+ align:start position:0%
+compute these things but that's the
+basic
+
+ align:start position:0%
+basic
+ 
+
+ align:start position:0%
+basic
+definition okay so actually how do well
+
+ align:start position:0%
+definition okay so actually how do well
+ 
+
+ align:start position:0%
+definition okay so actually how do well
+I mean that's not really much of a
+
+ align:start position:0%
+I mean that's not really much of a
+ 
+
+ align:start position:0%
+I mean that's not really much of a
+definition yet how do we actually you
+
+ align:start position:0%
+definition yet how do we actually you
+ 
+
+ align:start position:0%
+definition yet how do we actually you
+know Define this
+
+ align:start position:0%
+know Define this
+ 
+
+ align:start position:0%
+know Define this
+rigorously well remember the integral in
+
+ align:start position:0%
+rigorously well remember the integral in
+ 
+
+ align:start position:0%
+rigorously well remember the integral in
+one variable you probably saw a
+
+ align:start position:0%
+one variable you probably saw a
+ 
+
+ align:start position:0%
+one variable you probably saw a
+definition where you take your interval
+
+ align:start position:0%
+definition where you take your interval
+ 
+
+ align:start position:0%
+definition where you take your interval
+from A to B and you cut it into little
+
+ align:start position:0%
+from A to B and you cut it into little
+ 
+
+ align:start position:0%
+from A to B and you cut it into little
+pieces and then for each little piece
+
+ align:start position:0%
+pieces and then for each little piece
+ 
+
+ align:start position:0%
+pieces and then for each little piece
+you take the value of the function and
+
+ align:start position:0%
+you take the value of the function and
+ 
+
+ align:start position:0%
+you take the value of the function and
+you multiply by the width of the piece
+
+ align:start position:0%
+you multiply by the width of the piece
+ 
+
+ align:start position:0%
+you multiply by the width of the piece
+that gives you a
+
+ align:start position:0%
+that gives you a
+ 
+
+ align:start position:0%
+that gives you a
+rectangular slice and then you sum all
+
+ align:start position:0%
+rectangular slice and then you sum all
+ 
+
+ align:start position:0%
+rectangular slice and then you sum all
+of these rectangular slices together so
+
+ align:start position:0%
+of these rectangular slices together so
+ 
+
+ align:start position:0%
+of these rectangular slices together so
+here we'll do the same
+
+ align:start position:0%
+here we'll do the same
+ 
+
+ align:start position:0%
+here we'll do the same
+thing okay so well let me put a picture
+
+ align:start position:0%
+thing okay so well let me put a picture
+ 
+
+ align:start position:0%
+thing okay so well let me put a picture
+up and explain what it
+
+ align:start position:0%
+up and explain what it
+ 
+
+ align:start position:0%
+up and explain what it
+does so we are going to cut our region
+
+ align:start position:0%
+does so we are going to cut our region
+ 
+
+ align:start position:0%
+does so we are going to cut our region
+into little pieces say little rectangles
+
+ align:start position:0%
+into little pieces say little rectangles
+ 
+
+ align:start position:0%
+into little pieces say little rectangles
+or actually anything we want
+
+ align:start position:0%
+or actually anything we want
+ 
+
+ align:start position:0%
+or actually anything we want
+and then for each
+
+ align:start position:0%
+and then for each
+ 
+
+ align:start position:0%
+and then for each
+piece with a small area Delta a we'll
+
+ align:start position:0%
+piece with a small area Delta a we'll
+ 
+
+ align:start position:0%
+piece with a small area Delta a we'll
+take the area Delta a times the value of
+
+ align:start position:0%
+take the area Delta a times the value of
+ 
+
+ align:start position:0%
+take the area Delta a times the value of
+a function in there that will give us
+
+ align:start position:0%
+a function in there that will give us
+ 
+
+ align:start position:0%
+a function in there that will give us
+the volume of a small box that sits
+
+ align:start position:0%
+the volume of a small box that sits
+ 
+
+ align:start position:0%
+the volume of a small box that sits
+under the graph and then we'll add all
+
+ align:start position:0%
+under the graph and then we'll add all
+ 
+
+ align:start position:0%
+under the graph and then we'll add all
+these boxes together that gives us an
+
+ align:start position:0%
+these boxes together that gives us an
+ 
+
+ align:start position:0%
+these boxes together that gives us an
+estimate of the volume and then to get
+
+ align:start position:0%
+estimate of the volume and then to get
+ 
+
+ align:start position:0%
+estimate of the volume and then to get
+actually the integral the integral will
+
+ align:start position:0%
+actually the integral the integral will
+ 
+
+ align:start position:0%
+actually the integral the integral will
+be defined as a limit as we subdivide
+
+ align:start position:0%
+be defined as a limit as we subdivide
+ 
+
+ align:start position:0%
+be defined as a limit as we subdivide
+into smaller and smaller boxes and we
+
+ align:start position:0%
+into smaller and smaller boxes and we
+ 
+
+ align:start position:0%
+into smaller and smaller boxes and we
+sum more and more
+
+ align:start position:0%
+sum more and more
+ 
+
+ align:start position:0%
+sum more and more
+pieces okay
+
+ align:start position:0%
+pieces okay
+ 
+
+ align:start position:0%
+pieces okay
+so actually what we do oh I still have a
+
+ align:start position:0%
+so actually what we do oh I still have a
+ 
+
+ align:start position:0%
+so actually what we do oh I still have a
+I still have a board
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so the actual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definition
+
+ align:start position:0%
+definition
+ 
+
+ align:start position:0%
+definition
+involves cutting R into small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pieces of area that's called Delta a
+
+ align:start position:0%
+pieces of area that's called Delta a
+ 
+
+ align:start position:0%
+pieces of area that's called Delta a
+maybe Delta a i the area of the if pce
+
+ align:start position:0%
+maybe Delta a i the area of the if pce
+ 
+
+ align:start position:0%
+maybe Delta a i the area of the if pce
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+then okay so maybe in the XY
+
+ align:start position:0%
+then okay so maybe in the XY
+ 
+
+ align:start position:0%
+then okay so maybe in the XY
+plane we have our region and we'll cut
+
+ align:start position:0%
+plane we have our region and we'll cut
+ 
+
+ align:start position:0%
+plane we have our region and we'll cut
+it maybe using some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grid okay and then we'll have each small
+
+ align:start position:0%
+grid okay and then we'll have each small
+ 
+
+ align:start position:0%
+grid okay and then we'll have each small
+piece each small piece will have
+
+ align:start position:0%
+piece each small piece will have
+ 
+
+ align:start position:0%
+piece each small piece will have
+AA Delta
+
+ align:start position:0%
+AA Delta
+ 
+
+ align:start position:0%
+AA Delta
+a Delta a i and it will be at some
+
+ align:start position:0%
+a Delta a i and it will be at some
+ 
+
+ align:start position:0%
+a Delta a i and it will be at some
+point let's call it x i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yi y i x
+
+ align:start position:0%
+Yi y i x
+ 
+
+ align:start position:0%
+Yi y i x
+i and then we'll consider the sum over
+
+ align:start position:0%
+i and then we'll consider the sum over
+ 
+
+ align:start position:0%
+i and then we'll consider the sum over
+all the
+
+ align:start position:0%
+all the
+ 
+
+ align:start position:0%
+all the
+pieces of F at that point x i y i times
+
+ align:start position:0%
+pieces of F at that point x i y i times
+ 
+
+ align:start position:0%
+pieces of F at that point x i y i times
+the area of a small
+
+ align:start position:0%
+the area of a small
+ 
+
+ align:start position:0%
+the area of a small
+piece so what that corresponds to in the
+
+ align:start position:0%
+piece so what that corresponds to in the
+ 
+
+ align:start position:0%
+piece so what that corresponds to in the
+threedimensional picture is just I sum
+
+ align:start position:0%
+threedimensional picture is just I sum
+ 
+
+ align:start position:0%
+threedimensional picture is just I sum
+the volumes of all of the little columns
+
+ align:start position:0%
+the volumes of all of the little columns
+ 
+
+ align:start position:0%
+the volumes of all of the little columns
+that sit under the
+
+ align:start position:0%
+that sit under the
+ 
+
+ align:start position:0%
+that sit under the
+graph okay and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then so what I do is actually I take the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit as the you know the size of the
+
+ align:start position:0%
+limit as the you know the size of the
+ 
+
+ align:start position:0%
+limit as the you know the size of the
+pieces tends to zero so I have more and
+
+ align:start position:0%
+pieces tends to zero so I have more and
+ 
+
+ align:start position:0%
+pieces tends to zero so I have more and
+more smaller and smaller
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pieces
+
+ align:start position:0%
+pieces
+ 
+
+ align:start position:0%
+pieces
+and that gives me the double
+
+ align:start position:0%
+and that gives me the double
+ 
+
+ align:start position:0%
+and that gives me the double
+integral okay Sor that's not a very good
+
+ align:start position:0%
+integral okay Sor that's not a very good
+ 
+
+ align:start position:0%
+integral okay Sor that's not a very good
+sentence but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whatever
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay so that's the definition of
+
+ align:start position:0%
+so okay so that's the definition of
+ 
+
+ align:start position:0%
+so okay so that's the definition of
+course we'll have to see how to compute
+
+ align:start position:0%
+course we'll have to see how to compute
+ 
+
+ align:start position:0%
+course we'll have to see how to compute
+it we don't actually compute it you know
+
+ align:start position:0%
+it we don't actually compute it you know
+ 
+
+ align:start position:0%
+it we don't actually compute it you know
+when you compute an integral in single
+
+ align:start position:0%
+when you compute an integral in single
+ 
+
+ align:start position:0%
+when you compute an integral in single
+variable calculus you don't do that you
+
+ align:start position:0%
+variable calculus you don't do that you
+ 
+
+ align:start position:0%
+variable calculus you don't do that you
+don't cut into little pieces and sum the
+
+ align:start position:0%
+don't cut into little pieces and sum the
+ 
+
+ align:start position:0%
+don't cut into little pieces and sum the
+pieces together you've learned how to
+
+ align:start position:0%
+pieces together you've learned how to
+ 
+
+ align:start position:0%
+pieces together you've learned how to
+integrate functions using various
+
+ align:start position:0%
+integrate functions using various
+ 
+
+ align:start position:0%
+integrate functions using various
+formulas and similar here we'll learn
+
+ align:start position:0%
+formulas and similar here we'll learn
+ 
+
+ align:start position:0%
+formulas and similar here we'll learn
+how to actually compute these things
+
+ align:start position:0%
+how to actually compute these things
+ 
+
+ align:start position:0%
+how to actually compute these things
+without doing that cutting into small
+
+ align:start position:0%
+without doing that cutting into small
+ 
+
+ align:start position:0%
+without doing that cutting into small
+pieces but okay any questions first
+
+ align:start position:0%
+pieces but okay any questions first
+ 
+
+ align:start position:0%
+pieces but okay any questions first
+about the concept or what the definition
+
+ align:start position:0%
+about the concept or what the definition
+ 
+
+ align:start position:0%
+about the concept or what the definition
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes well so we'll have to learn which
+
+ align:start position:0%
+yes well so we'll have to learn which
+ 
+
+ align:start position:0%
+yes well so we'll have to learn which
+tricks work and how exactly but so what
+
+ align:start position:0%
+tricks work and how exactly but so what
+ 
+
+ align:start position:0%
+tricks work and how exactly but so what
+we'll do actually is we'll reduce the
+
+ align:start position:0%
+we'll do actually is we'll reduce the
+ 
+
+ align:start position:0%
+we'll do actually is we'll reduce the
+calculation of a double integral to two
+
+ align:start position:0%
+calculation of a double integral to two
+ 
+
+ align:start position:0%
+calculation of a double integral to two
+calculations of single integrals and so
+
+ align:start position:0%
+calculations of single integrals and so
+ 
+
+ align:start position:0%
+calculations of single integrals and so
+for these certainly all the tricks
+
+ align:start position:0%
+for these certainly all the tricks
+ 
+
+ align:start position:0%
+for these certainly all the tricks
+you've learned in single variable
+
+ align:start position:0%
+you've learned in single variable
+ 
+
+ align:start position:0%
+you've learned in single variable
+calculus will come in
+
+ align:start position:0%
+calculus will come in
+ 
+
+ align:start position:0%
+calculus will come in
+handy okay so yes that's a strong signal
+
+ align:start position:0%
+handy okay so yes that's a strong signal
+ 
+
+ align:start position:0%
+handy okay so yes that's a strong signal
+by the way that if you forgotten
+
+ align:start position:0%
+by the way that if you forgotten
+ 
+
+ align:start position:0%
+by the way that if you forgotten
+everything about single variable
+
+ align:start position:0%
+everything about single variable
+ 
+
+ align:start position:0%
+everything about single variable
+calculus now might be a good time to
+
+ align:start position:0%
+calculus now might be a good time to
+ 
+
+ align:start position:0%
+calculus now might be a good time to
+actually brush up on you know
+
+ align:start position:0%
+actually brush up on you know
+ 
+
+ align:start position:0%
+actually brush up on you know
+integrals
+
+ align:start position:0%
+integrals
+ 
+
+ align:start position:0%
+integrals
+um you know the usual integrals and the
+
+ align:start position:0%
+um you know the usual integrals and the
+ 
+
+ align:start position:0%
+um you know the usual integrals and the
+usual substition substitution tricks and
+
+ align:start position:0%
+usual substition substitution tricks and
+ 
+
+ align:start position:0%
+usual substition substitution tricks and
+easy trig in particular this will be
+
+ align:start position:0%
+easy trig in particular this will be
+ 
+
+ align:start position:0%
+easy trig in particular this will be
+very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+useful okay so yes so how do we compute
+
+ align:start position:0%
+useful okay so yes so how do we compute
+ 
+
+ align:start position:0%
+useful okay so yes so how do we compute
+these things that's what we have to come
+
+ align:start position:0%
+these things that's what we have to come
+ 
+
+ align:start position:0%
+these things that's what we have to come
+up with
+
+ align:start position:0%
+up with
+ 
+
+ align:start position:0%
+up with
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+well you know going back to what we did
+
+ align:start position:0%
+well you know going back to what we did
+ 
+
+ align:start position:0%
+well you know going back to what we did
+with derivatives to understand
+
+ align:start position:0%
+with derivatives to understand
+ 
+
+ align:start position:0%
+with derivatives to understand
+variations of functions and derivatives
+
+ align:start position:0%
+variations of functions and derivatives
+ 
+
+ align:start position:0%
+variations of functions and derivatives
+what we did was really we took slices
+
+ align:start position:0%
+what we did was really we took slices
+ 
+
+ align:start position:0%
+what we did was really we took slices
+parallel to an excess or another one so
+
+ align:start position:0%
+parallel to an excess or another one so
+ 
+
+ align:start position:0%
+parallel to an excess or another one so
+in fact here the key is also the same so
+
+ align:start position:0%
+in fact here the key is also the same so
+ 
+
+ align:start position:0%
+in fact here the key is also the same so
+what we're going to do is instead of
+
+ align:start position:0%
+what we're going to do is instead of
+ 
+
+ align:start position:0%
+what we're going to do is instead of
+cutting into a lot of small boxes like
+
+ align:start position:0%
+cutting into a lot of small boxes like
+ 
+
+ align:start position:0%
+cutting into a lot of small boxes like
+that and summing completely at random
+
+ align:start position:0%
+that and summing completely at random
+ 
+
+ align:start position:0%
+that and summing completely at random
+will actually somehow scan our region
+
+ align:start position:0%
+will actually somehow scan our region
+ 
+
+ align:start position:0%
+will actually somehow scan our region
+scan through our by planes okay so let
+
+ align:start position:0%
+scan through our by planes okay so let
+ 
+
+ align:start position:0%
+scan through our by planes okay so let
+me put up actually a slightly different
+
+ align:start position:0%
+me put up actually a slightly different
+ 
+
+ align:start position:0%
+me put up actually a slightly different
+picture up
+
+ align:start position:0%
+picture up
+ 
+
+ align:start position:0%
+picture up
+here so what I'm going to do is I'm
+
+ align:start position:0%
+here so what I'm going to do is I'm
+ 
+
+ align:start position:0%
+here so what I'm going to do is I'm
+going to take planes say in the specture
+
+ align:start position:0%
+going to take planes say in the specture
+ 
+
+ align:start position:0%
+going to take planes say in the specture
+parallel to the YZ plane I'll take a
+
+ align:start position:0%
+parallel to the YZ plane I'll take a
+ 
+
+ align:start position:0%
+parallel to the YZ plane I'll take a
+moving plane that scans from the back to
+
+ align:start position:0%
+moving plane that scans from the back to
+ 
+
+ align:start position:0%
+moving plane that scans from the back to
+the front or from the front to the
+
+ align:start position:0%
+the front or from the front to the
+ 
+
+ align:start position:0%
+the front or from the front to the
+back so that means you know I set a
+
+ align:start position:0%
+back so that means you know I set a
+ 
+
+ align:start position:0%
+back so that means you know I set a
+value of x0 of X and I I look at the
+
+ align:start position:0%
+value of x0 of X and I I look at the
+ 
+
+ align:start position:0%
+value of x0 of X and I I look at the
+slice xals x0 and then I will do that
+
+ align:start position:0%
+slice xals x0 and then I will do that
+ 
+
+ align:start position:0%
+slice xals x0 and then I will do that
+for all values of x0 so now in each
+
+ align:start position:0%
+for all values of x0 so now in each
+ 
+
+ align:start position:0%
+for all values of x0 so now in each
+slice well I get what looks a lot like a
+
+ align:start position:0%
+slice well I get what looks a lot like a
+ 
+
+ align:start position:0%
+slice well I get what looks a lot like a
+single variable integral okay and that
+
+ align:start position:0%
+single variable integral okay and that
+ 
+
+ align:start position:0%
+single variable integral okay and that
+integral will tell me what is the area
+
+ align:start position:0%
+integral will tell me what is the area
+ 
+
+ align:start position:0%
+integral will tell me what is the area
+in this well I guess was supposed to be
+
+ align:start position:0%
+in this well I guess was supposed to be
+ 
+
+ align:start position:0%
+in this well I guess was supposed to be
+green but it all comes as black so uh
+
+ align:start position:0%
+green but it all comes as black so uh
+ 
+
+ align:start position:0%
+green but it all comes as black so uh
+let's say the black shaded
+
+ align:start position:0%
+let's say the black shaded
+ 
+
+ align:start position:0%
+let's say the black shaded
+slice and then when I add all of these
+
+ align:start position:0%
+slice and then when I add all of these
+ 
+
+ align:start position:0%
+slice and then when I add all of these
+areas together as the value of x changes
+
+ align:start position:0%
+areas together as the value of x changes
+ 
+
+ align:start position:0%
+areas together as the value of x changes
+I will get the
+
+ align:start position:0%
+I will get the
+ 
+
+ align:start position:0%
+I will get the
+volume okay let me try to explain that
+
+ align:start position:0%
+volume okay let me try to explain that
+ 
+
+ align:start position:0%
+volume okay let me try to explain that
+again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compute this integral what we do is
+
+ align:start position:0%
+compute this integral what we do is
+ 
+
+ align:start position:0%
+compute this integral what we do is
+actually we
+
+ align:start position:0%
+actually we
+ 
+
+ align:start position:0%
+actually we
+take
+
+ align:start position:0%
+take
+ 
+
+ align:start position:0%
+take
+slices
+
+ align:start position:0%
+slices
+ 
+
+ align:start position:0%
+slices
+so let's consider let's call S of X the
+
+ align:start position:0%
+so let's consider let's call S of X the
+ 
+
+ align:start position:0%
+so let's consider let's call S of X the
+area of a
+
+ align:start position:0%
+area of a
+ 
+
+ align:start position:0%
+area of a
+slice
+
+ align:start position:0%
+slice
+ 
+
+ align:start position:0%
+slice
+through well by um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by a plane parallel to the YZ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane okay so on the picture s of X is
+
+ align:start position:0%
+plane okay so on the picture s of X is
+ 
+
+ align:start position:0%
+plane okay so on the picture s of X is
+just the area of this thing in the in
+
+ align:start position:0%
+just the area of this thing in the in
+ 
+
+ align:start position:0%
+just the area of this thing in the in
+the vertical
+
+ align:start position:0%
+the vertical
+ 
+
+ align:start position:0%
+the vertical
+wall now if you sum all of these well
+
+ align:start position:0%
+wall now if you sum all of these well
+ 
+
+ align:start position:0%
+wall now if you sum all of these well
+let's see why does that work so if you
+
+ align:start position:0%
+let's see why does that work so if you
+ 
+
+ align:start position:0%
+let's see why does that work so if you
+take the region between two parallel
+
+ align:start position:0%
+take the region between two parallel
+ 
+
+ align:start position:0%
+take the region between two parallel
+slices that are very close to each each
+
+ align:start position:0%
+slices that are very close to each each
+ 
+
+ align:start position:0%
+slices that are very close to each each
+other what's the volume between these
+
+ align:start position:0%
+other what's the volume between these
+ 
+
+ align:start position:0%
+other what's the volume between these
+two things well it's essentially s of X
+
+ align:start position:0%
+two things well it's essentially s of X
+ 
+
+ align:start position:0%
+two things well it's essentially s of X
+the thickness of this very slice and the
+
+ align:start position:0%
+the thickness of this very slice and the
+ 
+
+ align:start position:0%
+the thickness of this very slice and the
+thickness would be Delta X or DX if you
+
+ align:start position:0%
+thickness would be Delta X or DX if you
+ 
+
+ align:start position:0%
+thickness would be Delta X or DX if you
+take a limit with more and more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slices okay
+
+ align:start position:0%
+slices okay
+ 
+
+ align:start position:0%
+slices okay
+so then the
+
+ align:start position:0%
+so then the
+ 
+
+ align:start position:0%
+so then the
+volume will be the integral of s of X
+
+ align:start position:0%
+volume will be the integral of s of X
+ 
+
+ align:start position:0%
+volume will be the integral of s of X
+DX from well what would be the range for
+
+ align:start position:0%
+DX from well what would be the range for
+ 
+
+ align:start position:0%
+DX from well what would be the range for
+X well we would have to start at the
+
+ align:start position:0%
+X well we would have to start at the
+ 
+
+ align:start position:0%
+X well we would have to start at the
+very lowest value of x that ever happens
+
+ align:start position:0%
+very lowest value of x that ever happens
+ 
+
+ align:start position:0%
+very lowest value of x that ever happens
+in our region and we' have to go all the
+
+ align:start position:0%
+in our region and we' have to go all the
+ 
+
+ align:start position:0%
+in our region and we' have to go all the
+way to the very largest value of x okay
+
+ align:start position:0%
+way to the very largest value of x okay
+ 
+
+ align:start position:0%
+way to the very largest value of x okay
+from the very far back to the very far
+
+ align:start position:0%
+from the very far back to the very far
+ 
+
+ align:start position:0%
+from the very far back to the very far
+front so on this picture we probably
+
+ align:start position:0%
+front so on this picture we probably
+ 
+
+ align:start position:0%
+front so on this picture we probably
+start you know over here at the back and
+
+ align:start position:0%
+start you know over here at the back and
+ 
+
+ align:start position:0%
+start you know over here at the back and
+with end over here at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+front
+
+ align:start position:0%
+front
+ 
+
+ align:start position:0%
+front
+so let me just say from you know the
+
+ align:start position:0%
+so let me just say from you know the
+ 
+
+ align:start position:0%
+so let me just say from you know the
+minimum x to the maximum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X and now how do we find S of X well s
+
+ align:start position:0%
+X and now how do we find S of X well s
+ 
+
+ align:start position:0%
+X and now how do we find S of X well s
+of X will be actually again an integral
+
+ align:start position:0%
+of X will be actually again an integral
+ 
+
+ align:start position:0%
+of X will be actually again an integral
+but now it's an integral over the
+
+ align:start position:0%
+but now it's an integral over the
+ 
+
+ align:start position:0%
+but now it's an integral over the
+variable y because when we look at this
+
+ align:start position:0%
+variable y because when we look at this
+ 
+
+ align:start position:0%
+variable y because when we look at this
+slice what changes from left to height
+
+ align:start position:0%
+slice what changes from left to height
+ 
+
+ align:start position:0%
+slice what changes from left to height
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+well let me actually write that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down for a given
+
+ align:start position:0%
+down for a given
+ 
+
+ align:start position:0%
+down for a given
+X the area s of X you can compute as an
+
+ align:start position:0%
+X the area s of X you can compute as an
+ 
+
+ align:start position:0%
+X the area s of X you can compute as an
+integral of f of
+
+ align:start position:0%
+integral of f of
+ 
+
+ align:start position:0%
+integral of f of
+XY
+
+ align:start position:0%
+XY
+ 
+
+ align:start position:0%
+XY
+Dy okay well now X is a constant and Y
+
+ align:start position:0%
+Dy okay well now X is a constant and Y
+ 
+
+ align:start position:0%
+Dy okay well now X is a constant and Y
+will be the variable of
+
+ align:start position:0%
+will be the variable of
+ 
+
+ align:start position:0%
+will be the variable of
+integration what are what's the range
+
+ align:start position:0%
+integration what are what's the range
+ 
+
+ align:start position:0%
+integration what are what's the range
+for y well it's from you know the
+
+ align:start position:0%
+for y well it's from you know the
+ 
+
+ align:start position:0%
+for y well it's from you know the
+leftmost point here to the rightmost
+
+ align:start position:0%
+leftmost point here to the rightmost
+ 
+
+ align:start position:0%
+leftmost point here to the rightmost
+point here on the given
+
+ align:start position:0%
+point here on the given
+ 
+
+ align:start position:0%
+point here on the given
+slice so there's a big catch here that's
+
+ align:start position:0%
+slice so there's a big catch here that's
+ 
+
+ align:start position:0%
+slice so there's a big catch here that's
+a very important thing to
+
+ align:start position:0%
+a very important thing to
+ 
+
+ align:start position:0%
+a very important thing to
+remember what is the range of
+
+ align:start position:0%
+remember what is the range of
+ 
+
+ align:start position:0%
+remember what is the range of
+integration the range of integration for
+
+ align:start position:0%
+integration the range of integration for
+ 
+
+ align:start position:0%
+integration the range of integration for
+y depends actually on X see if I took a
+
+ align:start position:0%
+y depends actually on X see if I took a
+ 
+
+ align:start position:0%
+y depends actually on X see if I took a
+slice if I take this slice that's
+
+ align:start position:0%
+slice if I take this slice that's
+ 
+
+ align:start position:0%
+slice if I take this slice that's
+pictured on that diagram then the range
+
+ align:start position:0%
+pictured on that diagram then the range
+ 
+
+ align:start position:0%
+pictured on that diagram then the range
+for y goes all the way from the very
+
+ align:start position:0%
+for y goes all the way from the very
+ 
+
+ align:start position:0%
+for y goes all the way from the very
+left to the very right but if I take a
+
+ align:start position:0%
+left to the very right but if I take a
+ 
+
+ align:start position:0%
+left to the very right but if I take a
+slice that say near the very front
+
+ align:start position:0%
+slice that say near the very front
+ 
+
+ align:start position:0%
+slice that say near the very front
+then in fact only a very small segment
+
+ align:start position:0%
+then in fact only a very small segment
+ 
+
+ align:start position:0%
+then in fact only a very small segment
+of it will be in my region so the range
+
+ align:start position:0%
+of it will be in my region so the range
+ 
+
+ align:start position:0%
+of it will be in my region so the range
+of values for y will be much less let me
+
+ align:start position:0%
+of values for y will be much less let me
+ 
+
+ align:start position:0%
+of values for y will be much less let me
+actually draw a 2d picture of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so remember we fix X and we VAR sorry
+
+ align:start position:0%
+it so remember we fix X and we VAR sorry
+ 
+
+ align:start position:0%
+it so remember we fix X and we VAR sorry
+so we fix a value of
+
+ align:start position:0%
+so we fix a value of
+ 
+
+ align:start position:0%
+so we fix a value of
+x okay and for a given value of x what
+
+ align:start position:0%
+x okay and for a given value of x what
+ 
+
+ align:start position:0%
+x okay and for a given value of x what
+we'll do is we'll slice our graph by
+
+ align:start position:0%
+we'll do is we'll slice our graph by
+ 
+
+ align:start position:0%
+we'll do is we'll slice our graph by
+this plane parallel to the YZ plane so
+
+ align:start position:0%
+this plane parallel to the YZ plane so
+ 
+
+ align:start position:0%
+this plane parallel to the YZ plane so
+now imagine the graph is sitting above
+
+ align:start position:0%
+now imagine the graph is sitting above
+ 
+
+ align:start position:0%
+now imagine the graph is sitting above
+that and that's the region
+
+ align:start position:0%
+that and that's the region
+ 
+
+ align:start position:0%
+that and that's the region
+R I have the region R and I'm I have the
+
+ align:start position:0%
+R I have the region R and I'm I have the
+ 
+
+ align:start position:0%
+R I have the region R and I'm I have the
+graph of a function above this region
+
+ align:start position:0%
+graph of a function above this region
+ 
+
+ align:start position:0%
+graph of a function above this region
+R and I'm trying to find the area
+
+ align:start position:0%
+R and I'm trying to find the area
+ 
+
+ align:start position:0%
+R and I'm trying to find the area
+between this segment and the graph above
+
+ align:start position:0%
+between this segment and the graph above
+ 
+
+ align:start position:0%
+between this segment and the graph above
+it in this vertical
+
+ align:start position:0%
+it in this vertical
+ 
+
+ align:start position:0%
+it in this vertical
+plane well to do that I have to
+
+ align:start position:0%
+plane well to do that I have to
+ 
+
+ align:start position:0%
+plane well to do that I have to
+integrate from
+
+ align:start position:0%
+integrate from
+ 
+
+ align:start position:0%
+integrate from
+y for y going
+
+ align:start position:0%
+y for y going
+ 
+
+ align:start position:0%
+y for y going
+from here to
+
+ align:start position:0%
+from here to
+ 
+
+ align:start position:0%
+from here to
+here right I want the area of a piece
+
+ align:start position:0%
+here right I want the area of a piece
+ 
+
+ align:start position:0%
+here right I want the area of a piece
+that sits above this red segment and so
+
+ align:start position:0%
+that sits above this red segment and so
+ 
+
+ align:start position:0%
+that sits above this red segment and so
+in particular the end points the extreme
+
+ align:start position:0%
+in particular the end points the extreme
+ 
+
+ align:start position:0%
+in particular the end points the extreme
+values for y depend on X because see if
+
+ align:start position:0%
+values for y depend on X because see if
+ 
+
+ align:start position:0%
+values for y depend on X because see if
+I slice here
+
+ align:start position:0%
+I slice here
+ 
+
+ align:start position:0%
+I slice here
+instead well my bounce for y will be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smaller okay so now if I put the two
+
+ align:start position:0%
+smaller okay so now if I put the two
+ 
+
+ align:start position:0%
+smaller okay so now if I put the two
+things together what I will get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+actually a formula where I have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integrate over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X an
+
+ align:start position:0%
+X an
+ 
+
+ align:start position:0%
+X an
+integral over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y
+
+ align:start position:0%
+y
+ 
+
+ align:start position:0%
+y
+okay and so this is called an iterated
+
+ align:start position:0%
+okay and so this is called an iterated
+ 
+
+ align:start position:0%
+okay and so this is called an iterated
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+because we iterate twice the process of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+taking an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral okay so
+
+ align:start position:0%
+integral okay so
+ 
+
+ align:start position:0%
+integral okay so
+again what's important to realize here I
+
+ align:start position:0%
+again what's important to realize here I
+ 
+
+ align:start position:0%
+again what's important to realize here I
+mean I'm going to save at several times
+
+ align:start position:0%
+mean I'm going to save at several times
+ 
+
+ align:start position:0%
+mean I'm going to save at several times
+over the next few days but that's
+
+ align:start position:0%
+over the next few days but that's
+ 
+
+ align:start position:0%
+over the next few days but that's
+because it's the single most important
+
+ align:start position:0%
+because it's the single most important
+ 
+
+ align:start position:0%
+because it's the single most important
+thing to remember about double
+
+ align:start position:0%
+thing to remember about double
+ 
+
+ align:start position:0%
+thing to remember about double
+integrals the bounds here are just going
+
+ align:start position:0%
+integrals the bounds here are just going
+ 
+
+ align:start position:0%
+integrals the bounds here are just going
+to be numbers okay
+
+ align:start position:0%
+to be numbers okay
+ 
+
+ align:start position:0%
+to be numbers okay
+because the question that I'm asking
+
+ align:start position:0%
+because the question that I'm asking
+ 
+
+ align:start position:0%
+because the question that I'm asking
+myself here is what is the first value
+
+ align:start position:0%
+myself here is what is the first value
+ 
+
+ align:start position:0%
+myself here is what is the first value
+of x by which I might want to slice and
+
+ align:start position:0%
+of x by which I might want to slice and
+ 
+
+ align:start position:0%
+of x by which I might want to slice and
+what is the last value of x you know
+
+ align:start position:0%
+what is the last value of x you know
+ 
+
+ align:start position:0%
+what is the last value of x you know
+which range of X do I want to look at to
+
+ align:start position:0%
+which range of X do I want to look at to
+ 
+
+ align:start position:0%
+which range of X do I want to look at to
+take my red slices and the answer is I
+
+ align:start position:0%
+take my red slices and the answer is I
+ 
+
+ align:start position:0%
+take my red slices and the answer is I
+would go all the way from here that's my
+
+ align:start position:0%
+would go all the way from here that's my
+ 
+
+ align:start position:0%
+would go all the way from here that's my
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+slice
+
+ align:start position:0%
+slice
+ 
+
+ align:start position:0%
+slice
+to somewhere here that's my last
+
+ align:start position:0%
+to somewhere here that's my last
+ 
+
+ align:start position:0%
+to somewhere here that's my last
+slice for any value in between these I
+
+ align:start position:0%
+slice for any value in between these I
+ 
+
+ align:start position:0%
+slice for any value in between these I
+will have some sort some red segment and
+
+ align:start position:0%
+will have some sort some red segment and
+ 
+
+ align:start position:0%
+will have some sort some red segment and
+I will want to integrate over that on
+
+ align:start position:0%
+I will want to integrate over that on
+ 
+
+ align:start position:0%
+I will want to integrate over that on
+the other hand here the bounce will
+
+ align:start position:0%
+the other hand here the bounce will
+ 
+
+ align:start position:0%
+the other hand here the bounce will
+depend on the outer variable
+
+ align:start position:0%
+depend on the outer variable
+ 
+
+ align:start position:0%
+depend on the outer variable
+X because if I fix a value of x what the
+
+ align:start position:0%
+X because if I fix a value of x what the
+ 
+
+ align:start position:0%
+X because if I fix a value of x what the
+values of Y will be depends on X in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+general okay so I think probably we
+
+ align:start position:0%
+general okay so I think probably we
+ 
+
+ align:start position:0%
+general okay so I think probably we
+should do lots of examples to convince
+
+ align:start position:0%
+should do lots of examples to convince
+ 
+
+ align:start position:0%
+should do lots of examples to convince
+ourselves you know and see how it
+
+ align:start position:0%
+ourselves you know and see how it
+ 
+
+ align:start position:0%
+ourselves you know and see how it
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry yeah it's it's called an iterated
+
+ align:start position:0%
+sorry yeah it's it's called an iterated
+ 
+
+ align:start position:0%
+sorry yeah it's it's called an iterated
+integral because first we integrate Y
+
+ align:start position:0%
+integral because first we integrate Y
+ 
+
+ align:start position:0%
+integral because first we integrate Y
+and then we integrate again over X
+
+ align:start position:0%
+and then we integrate again over X
+ 
+
+ align:start position:0%
+and then we integrate again over X
+okay so we can do that
+
+ align:start position:0%
+okay so we can do that
+ 
+
+ align:start position:0%
+okay so we can do that
+well I mean y depends on X or X depends
+
+ align:start position:0%
+well I mean y depends on X or X depends
+ 
+
+ align:start position:0%
+well I mean y depends on X or X depends
+no actually X and Y vary independently
+
+ align:start position:0%
+no actually X and Y vary independently
+ 
+
+ align:start position:0%
+no actually X and Y vary independently
+of each other inside here
+
+ align:start position:0%
+of each other inside here
+ 
+
+ align:start position:0%
+of each other inside here
+what is more complicated is how the
+
+ align:start position:0%
+what is more complicated is how the
+ 
+
+ align:start position:0%
+what is more complicated is how the
+bounds on y depend on X but actually you
+
+ align:start position:0%
+bounds on y depend on X but actually you
+ 
+
+ align:start position:0%
+bounds on y depend on X but actually you
+could also do it the other way around
+
+ align:start position:0%
+could also do it the other way around
+ 
+
+ align:start position:0%
+could also do it the other way around
+first integrate over X and then over Y
+
+ align:start position:0%
+first integrate over X and then over Y
+ 
+
+ align:start position:0%
+first integrate over X and then over Y
+and then the bounce for X would depend
+
+ align:start position:0%
+and then the bounce for X would depend
+ 
+
+ align:start position:0%
+and then the bounce for X would depend
+on y we'll see that on an example yes
+
+ align:start position:0%
+on y we'll see that on an example yes
+ 
+
+ align:start position:0%
+on y we'll see that on an example yes
+for your y
+
+ align:start position:0%
+for your y
+ 
+
+ align:start position:0%
+for your y
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values so for y I'm using the range of
+
+ align:start position:0%
+values so for y I'm using the range of
+ 
+
+ align:start position:0%
+values so for y I'm using the range of
+values for y that corresponds to the
+
+ align:start position:0%
+values for y that corresponds to the
+ 
+
+ align:start position:0%
+values for y that corresponds to the
+given value of
+
+ align:start position:0%
+given value of
+ 
+
+ align:start position:0%
+given value of
+x okay remember this is just like a plot
+
+ align:start position:0%
+x okay remember this is just like a plot
+ 
+
+ align:start position:0%
+x okay remember this is just like a plot
+in the XY plane above that we have the
+
+ align:start position:0%
+in the XY plane above that we have the
+ 
+
+ align:start position:0%
+in the XY plane above that we have the
+graph maybe I should draw a picture here
+
+ align:start position:0%
+graph maybe I should draw a picture here
+ 
+
+ align:start position:0%
+graph maybe I should draw a picture here
+instead for a given value of x so that's
+
+ align:start position:0%
+instead for a given value of x so that's
+ 
+
+ align:start position:0%
+instead for a given value of x so that's
+a given slice I have a range of values
+
+ align:start position:0%
+a given slice I have a range of values
+ 
+
+ align:start position:0%
+a given slice I have a range of values
+for y that is from you know in this
+
+ align:start position:0%
+for y that is from you know in this
+ 
+
+ align:start position:0%
+for y that is from you know in this
+picture it's the leftmost point on that
+
+ align:start position:0%
+picture it's the leftmost point on that
+ 
+
+ align:start position:0%
+picture it's the leftmost point on that
+slice to the rightmost point on that
+
+ align:start position:0%
+slice to the rightmost point on that
+ 
+
+ align:start position:0%
+slice to the rightmost point on that
+slice so where I start and where I stop
+
+ align:start position:0%
+slice so where I start and where I stop
+ 
+
+ align:start position:0%
+slice so where I start and where I stop
+depends on the value of
+
+ align:start position:0%
+depends on the value of
+ 
+
+ align:start position:0%
+depends on the value of
+x does that make
+
+ align:start position:0%
+x does that make
+ 
+
+ align:start position:0%
+x does that make
+sense kind of okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh no more
+
+ align:start position:0%
+okay uh no more
+ 
+
+ align:start position:0%
+okay uh no more
+questions no
+
+ align:start position:0%
+questions no
+ 
+
+ align:start position:0%
+questions no
+okay so let's do a first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example so let's say that we want to
+
+ align:start position:0%
+example so let's say that we want to
+ 
+
+ align:start position:0%
+example so let's say that we want to
+integrate the function 1 minus
+
+ align:start position:0%
+integrate the function 1 minus
+ 
+
+ align:start position:0%
+integrate the function 1 minus
+xus
+
+ align:start position:0%
+xus
+ 
+
+ align:start position:0%
+xus
+y^2 over the
+
+ align:start position:0%
+y^2 over the
+ 
+
+ align:start position:0%
+y^2 over the
+region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+defined by X between 0 and 1 and y
+
+ align:start position:0%
+defined by X between 0 and 1 and y
+ 
+
+ align:start position:0%
+defined by X between 0 and 1 and y
+between 0 and
+
+ align:start position:0%
+between 0 and
+ 
+
+ align:start position:0%
+between 0 and
+one so what does that mean
+
+ align:start position:0%
+one so what does that mean
+ 
+
+ align:start position:0%
+one so what does that mean
+geometrically well Z = 1 - X2 - y^ 2 and
+
+ align:start position:0%
+geometrically well Z = 1 - X2 - y^ 2 and
+ 
+
+ align:start position:0%
+geometrically well Z = 1 - X2 - y^ 2 and
+it's a variation on you know something I
+
+ align:start position:0%
+it's a variation on you know something I
+ 
+
+ align:start position:0%
+it's a variation on you know something I
+think actually we've plotted that one
+
+ align:start position:0%
+think actually we've plotted that one
+ 
+
+ align:start position:0%
+think actually we've plotted that one
+right when we that was our first example
+
+ align:start position:0%
+right when we that was our first example
+ 
+
+ align:start position:0%
+right when we that was our first example
+of a function of two variables
+
+ align:start position:0%
+of a function of two variables
+ 
+
+ align:start position:0%
+of a function of two variables
+possibly and so we saw that the graph is
+
+ align:start position:0%
+possibly and so we saw that the graph is
+ 
+
+ align:start position:0%
+possibly and so we saw that the graph is
+this paraboloid pointing downwards okay
+
+ align:start position:0%
+this paraboloid pointing downwards okay
+ 
+
+ align:start position:0%
+this paraboloid pointing downwards okay
+it's what you get by taking a parabol
+
+ align:start position:0%
+it's what you get by taking a parabol
+ 
+
+ align:start position:0%
+it's what you get by taking a parabol
+Parabola and rotating it and now what
+
+ align:start position:0%
+Parabola and rotating it and now what
+ 
+
+ align:start position:0%
+Parabola and rotating it and now what
+we're asking is what is the volume
+
+ align:start position:0%
+we're asking is what is the volume
+ 
+
+ align:start position:0%
+we're asking is what is the volume
+between the paraboloid and the XY plane
+
+ align:start position:0%
+between the paraboloid and the XY plane
+ 
+
+ align:start position:0%
+between the paraboloid and the XY plane
+over the square of side one in the XY
+
+ align:start position:0%
+over the square of side one in the XY
+ 
+
+ align:start position:0%
+over the square of side one in the XY
+plane X and Y between 0 and
+
+ align:start position:0%
+plane X and Y between 0 and
+ 
+
+ align:start position:0%
+plane X and Y between 0 and
+one okay so what we'll do is
+
+ align:start position:0%
+one okay so what we'll do is
+ 
+
+ align:start position:0%
+one okay so what we'll do is
+we'll so see here I've tried to
+
+ align:start position:0%
+we'll so see here I've tried to
+ 
+
+ align:start position:0%
+we'll so see here I've tried to
+represent the square and we'll just
+
+ align:start position:0%
+represent the square and we'll just
+ 
+
+ align:start position:0%
+represent the square and we'll just
+sum the areas of the for slices as say x
+
+ align:start position:0%
+sum the areas of the for slices as say x
+ 
+
+ align:start position:0%
+sum the areas of the for slices as say x
+varies from 0 to
+
+ align:start position:0%
+varies from 0 to
+ 
+
+ align:start position:0%
+varies from 0 to
+one and here of course setting up a
+
+ align:start position:0%
+one and here of course setting up a
+ 
+
+ align:start position:0%
+one and here of course setting up a
+bounds will be easy because no matter
+
+ align:start position:0%
+bounds will be easy because no matter
+ 
+
+ align:start position:0%
+bounds will be easy because no matter
+what x I take y still goes from Z to
+
+ align:start position:0%
+what x I take y still goes from Z to
+ 
+
+ align:start position:0%
+what x I take y still goes from Z to
+one see it's easiest to do double
+
+ align:start position:0%
+one see it's easiest to do double
+ 
+
+ align:start position:0%
+one see it's easiest to do double
+integrals when the region is just a
+
+ align:start position:0%
+integrals when the region is just a
+ 
+
+ align:start position:0%
+integrals when the region is just a
+rectangle in the XY plane because then
+
+ align:start position:0%
+rectangle in the XY plane because then
+ 
+
+ align:start position:0%
+rectangle in the XY plane because then
+you don't have to worry too much about
+
+ align:start position:0%
+you don't have to worry too much about
+ 
+
+ align:start position:0%
+you don't have to worry too much about
+what are the
+
+ align:start position:0%
+what are the
+ 
+
+ align:start position:0%
+what are the
+ranges okay
+
+ align:start position:0%
+ranges okay
+ 
+
+ align:start position:0%
+ranges okay
+so let's do it well that would
+
+ align:start position:0%
+so let's do it well that would
+ 
+
+ align:start position:0%
+so let's do it well that would
+be the integral from 0 to 1 of the
+
+ align:start position:0%
+be the integral from 0 to 1 of the
+ 
+
+ align:start position:0%
+be the integral from 0 to 1 of the
+integral from 0 to
+
+ align:start position:0%
+integral from 0 to
+ 
+
+ align:start position:0%
+integral from 0 to
+1 of 1 - x - y^ 2 Dy DX okay so I'm
+
+ align:start position:0%
+1 of 1 - x - y^ 2 Dy DX okay so I'm
+ 
+
+ align:start position:0%
+1 of 1 - x - y^ 2 Dy DX okay so I'm
+dropping the parentheses but if you
+
+ align:start position:0%
+dropping the parentheses but if you
+ 
+
+ align:start position:0%
+dropping the parentheses but if you
+still want to see them I'm going to put
+
+ align:start position:0%
+still want to see them I'm going to put
+ 
+
+ align:start position:0%
+still want to see them I'm going to put
+them in you know very
+
+ align:start position:0%
+them in you know very
+ 
+
+ align:start position:0%
+them in you know very
+thin so that you see what it means but
+
+ align:start position:0%
+thin so that you see what it means but
+ 
+
+ align:start position:0%
+thin so that you see what it means but
+actually the convention is we won't put
+
+ align:start position:0%
+actually the convention is we won't put
+ 
+
+ align:start position:0%
+actually the convention is we won't put
+these parentheses in there
+
+ align:start position:0%
+these parentheses in there
+ 
+
+ align:start position:0%
+these parentheses in there
+anymore okay so what this means is first
+
+ align:start position:0%
+anymore okay so what this means is first
+ 
+
+ align:start position:0%
+anymore okay so what this means is first
+I will integrate 1 - x - y^ 2 over y
+
+ align:start position:0%
+I will integrate 1 - x - y^ 2 over y
+ 
+
+ align:start position:0%
+I will integrate 1 - x - y^ 2 over y
+ranging from 0 to 1 with X held fixed so
+
+ align:start position:0%
+ranging from 0 to 1 with X held fixed so
+ 
+
+ align:start position:0%
+ranging from 0 to 1 with X held fixed so
+what that represents is the area in this
+
+ align:start position:0%
+what that represents is the area in this
+ 
+
+ align:start position:0%
+what that represents is the area in this
+slice so see here actually I've drawn
+
+ align:start position:0%
+slice so see here actually I've drawn
+ 
+
+ align:start position:0%
+slice so see here actually I've drawn
+well what happens is actually the
+
+ align:start position:0%
+well what happens is actually the
+ 
+
+ align:start position:0%
+well what happens is actually the
+function takes positive and negative
+
+ align:start position:0%
+function takes positive and negative
+ 
+
+ align:start position:0%
+function takes positive and negative
+values so in fact I will be counting
+
+ align:start position:0%
+values so in fact I will be counting
+ 
+
+ align:start position:0%
+values so in fact I will be counting
+positively this part of the area and I
+
+ align:start position:0%
+positively this part of the area and I
+ 
+
+ align:start position:0%
+positively this part of the area and I
+will be counting negatively this part of
+
+ align:start position:0%
+will be counting negatively this part of
+ 
+
+ align:start position:0%
+will be counting negatively this part of
+the area I mean as usual when I do an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what I
+
+ align:start position:0%
+so what I
+ 
+
+ align:start position:0%
+so what I
+will do to evaluate
+
+ align:start position:0%
+will do to evaluate
+ 
+
+ align:start position:0%
+will do to evaluate
+this I will first do What's called the
+
+ align:start position:0%
+this I will first do What's called the
+ 
+
+ align:start position:0%
+this I will first do What's called the
+inner
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral so to do the inner integral
+
+ align:start position:0%
+integral so to do the inner integral
+ 
+
+ align:start position:0%
+integral so to do the inner integral
+well it's pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+easy how do I integrate
+
+ align:start position:0%
+easy how do I integrate
+ 
+
+ align:start position:0%
+easy how do I integrate
+this well
+
+ align:start position:0%
+this well
+ 
+
+ align:start position:0%
+this well
+becomes so what's the integral of one
+
+ align:start position:0%
+becomes so what's the integral of one
+ 
+
+ align:start position:0%
+becomes so what's the integral of one
+it's y just the only thing to remember
+
+ align:start position:0%
+it's y just the only thing to remember
+ 
+
+ align:start position:0%
+it's y just the only thing to remember
+is we're integrating with respect to y
+
+ align:start position:0%
+is we're integrating with respect to y
+ 
+
+ align:start position:0%
+is we're integrating with respect to y
+not to X okay the integral of x s
+
+ align:start position:0%
+not to X okay the integral of x s
+ 
+
+ align:start position:0%
+not to X okay the integral of x s
+is x 2 *
+
+ align:start position:0%
+is x 2 *
+ 
+
+ align:start position:0%
+is x 2 *
+Y and the integral of y^2
+
+ align:start position:0%
+Y and the integral of y^2
+ 
+
+ align:start position:0%
+Y and the integral of y^2
+is y cubed over
+
+ align:start position:0%
+is y cubed over
+ 
+
+ align:start position:0%
+is y cubed over
+3 okay and then we plug in the bounds
+
+ align:start position:0%
+3 okay and then we plug in the bounds
+ 
+
+ align:start position:0%
+3 okay and then we plug in the bounds
+which are zero and one in this
+
+ align:start position:0%
+which are zero and one in this
+ 
+
+ align:start position:0%
+which are zero and one in this
+case and so when you plug y = 1 you will
+
+ align:start position:0%
+case and so when you plug y = 1 you will
+ 
+
+ align:start position:0%
+case and so when you plug y = 1 you will
+get 1 - x^2 -
+
+ align:start position:0%
+get 1 - x^2 -
+ 
+
+ align:start position:0%
+get 1 - x^2 -
+1/3
+
+ align:start position:0%
+1/3
+ 
+
+ align:start position:0%
+1/3
+minus well for y = 0 you get 0 0 0 so
+
+ align:start position:0%
+minus well for y = 0 you get 0 0 0 so
+ 
+
+ align:start position:0%
+minus well for y = 0 you get 0 0 0 so
+nothing changes because you're left with
+
+ align:start position:0%
+nothing changes because you're left with
+ 
+
+ align:start position:0%
+nothing changes because you're left with
+2/3 minus
+
+ align:start position:0%
+2/3 minus
+ 
+
+ align:start position:0%
+2/3 minus
+x^2 okay and that's a function of X only
+
+ align:start position:0%
+x^2 okay and that's a function of X only
+ 
+
+ align:start position:0%
+x^2 okay and that's a function of X only
+here you shouldn't see any y's anymore
+
+ align:start position:0%
+here you shouldn't see any y's anymore
+ 
+
+ align:start position:0%
+here you shouldn't see any y's anymore
+because y was your integration variable
+
+ align:start position:0%
+because y was your integration variable
+ 
+
+ align:start position:0%
+because y was your integration variable
+but you still have X you still have X
+
+ align:start position:0%
+but you still have X you still have X
+ 
+
+ align:start position:0%
+but you still have X you still have X
+because the area of this shaded slice
+
+ align:start position:0%
+because the area of this shaded slice
+ 
+
+ align:start position:0%
+because the area of this shaded slice
+depends of course on the value of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so now the second thing to do is to
+
+ align:start position:0%
+and so now the second thing to do is to
+ 
+
+ align:start position:0%
+and so now the second thing to do is to
+do the outer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral so now we integrate from 0 to
+
+ align:start position:0%
+integral so now we integrate from 0 to
+ 
+
+ align:start position:0%
+integral so now we integrate from 0 to
+1 what we got which is 2/3 -
+
+ align:start position:0%
+1 what we got which is 2/3 -
+ 
+
+ align:start position:0%
+1 what we got which is 2/3 -
+x^2
+
+ align:start position:0%
+x^2
+ 
+
+ align:start position:0%
+x^2
+DX okay and we know how to compute that
+
+ align:start position:0%
+DX okay and we know how to compute that
+ 
+
+ align:start position:0%
+DX okay and we know how to compute that
+because that integrates to 2/3 xus 1/3 x
+
+ align:start position:0%
+because that integrates to 2/3 xus 1/3 x
+ 
+
+ align:start position:0%
+because that integrates to 2/3 xus 1/3 x
+cubed between 0 and 1 and I let you do
+
+ align:start position:0%
+cubed between 0 and 1 and I let you do
+ 
+
+ align:start position:0%
+cubed between 0 and 1 and I let you do
+the computation you will find it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1/3 okay so that's the final
+
+ align:start position:0%
+1/3 okay so that's the final
+ 
+
+ align:start position:0%
+1/3 okay so that's the final
+answer so that's the general pattern see
+
+ align:start position:0%
+answer so that's the general pattern see
+ 
+
+ align:start position:0%
+answer so that's the general pattern see
+we when we have a double integral to
+
+ align:start position:0%
+we when we have a double integral to
+ 
+
+ align:start position:0%
+we when we have a double integral to
+compute first we want to set it up
+
+ align:start position:0%
+compute first we want to set it up
+ 
+
+ align:start position:0%
+compute first we want to set it up
+carefully we want to find what will be
+
+ align:start position:0%
+carefully we want to find what will be
+ 
+
+ align:start position:0%
+carefully we want to find what will be
+the bounds in X and Y and here that was
+
+ align:start position:0%
+the bounds in X and Y and here that was
+ 
+
+ align:start position:0%
+the bounds in X and Y and here that was
+actually pretty easy because our region
+
+ align:start position:0%
+actually pretty easy because our region
+ 
+
+ align:start position:0%
+actually pretty easy because our region
+was very
+
+ align:start position:0%
+was very
+ 
+
+ align:start position:0%
+was very
+simple then we want to compute the inner
+
+ align:start position:0%
+simple then we want to compute the inner
+ 
+
+ align:start position:0%
+simple then we want to compute the inner
+integral and then we compute the outer
+
+ align:start position:0%
+integral and then we compute the outer
+ 
+
+ align:start position:0%
+integral and then we compute the outer
+integral and that's
+
+ align:start position:0%
+integral and that's
+ 
+
+ align:start position:0%
+integral and that's
+it okay any questions at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no okay so by the way we started with a
+
+ align:start position:0%
+no okay so by the way we started with a
+ 
+
+ align:start position:0%
+no okay so by the way we started with a
+DA in the notation right here we had
+
+ align:start position:0%
+DA in the notation right here we had
+ 
+
+ align:start position:0%
+DA in the notation right here we had
+da and that somehow became a Dy
+
+ align:start position:0%
+da and that somehow became a Dy
+ 
+
+ align:start position:0%
+da and that somehow became a Dy
+DX Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so da a became Dy DX because when we do
+
+ align:start position:0%
+so da a became Dy DX because when we do
+ 
+
+ align:start position:0%
+so da a became Dy DX because when we do
+the iterated integral this way what
+
+ align:start position:0%
+the iterated integral this way what
+ 
+
+ align:start position:0%
+the iterated integral this way what
+we're actually doing is that we're
+
+ align:start position:0%
+we're actually doing is that we're
+ 
+
+ align:start position:0%
+we're actually doing is that we're
+slicing our region into small
+
+ align:start position:0%
+slicing our region into small
+ 
+
+ align:start position:0%
+slicing our region into small
+rectangles Okay now what's the area of
+
+ align:start position:0%
+rectangles Okay now what's the area of
+ 
+
+ align:start position:0%
+rectangles Okay now what's the area of
+this small rectangle here well it's the
+
+ align:start position:0%
+this small rectangle here well it's the
+ 
+
+ align:start position:0%
+this small rectangle here well it's the
+product of its width time its height so
+
+ align:start position:0%
+product of its width time its height so
+ 
+
+ align:start position:0%
+product of its width time its height so
+that's Delta X time Delta y
+
+ align:start position:0%
+that's Delta X time Delta y
+ 
+
+ align:start position:0%
+that's Delta X time Delta y
+okay so Delta a equals Delta X Delta y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+became so actually it's not just becomes
+
+ align:start position:0%
+became so actually it's not just becomes
+ 
+
+ align:start position:0%
+became so actually it's not just becomes
+it's really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal for the small rectangles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for um now it became dydx not DX d y
+
+ align:start position:0%
+for um now it became dydx not DX d y
+ 
+
+ align:start position:0%
+for um now it became dydx not DX d y
+well that's a question of in which order
+
+ align:start position:0%
+well that's a question of in which order
+ 
+
+ align:start position:0%
+well that's a question of in which order
+we do the iterated integral it's up to
+
+ align:start position:0%
+we do the iterated integral it's up to
+ 
+
+ align:start position:0%
+we do the iterated integral it's up to
+us to decide whether we want to
+
+ align:start position:0%
+us to decide whether we want to
+ 
+
+ align:start position:0%
+us to decide whether we want to
+integrate x first then y or Y first then
+
+ align:start position:0%
+integrate x first then y or Y first then
+ 
+
+ align:start position:0%
+integrate x first then y or Y first then
+X but as we'll see very soon that is an
+
+ align:start position:0%
+X but as we'll see very soon that is an
+ 
+
+ align:start position:0%
+X but as we'll see very soon that is an
+important decision when it comes to
+
+ align:start position:0%
+important decision when it comes to
+ 
+
+ align:start position:0%
+important decision when it comes to
+setting up the bounds of integration
+
+ align:start position:0%
+setting up the bounds of integration
+ 
+
+ align:start position:0%
+setting up the bounds of integration
+here it doesn't matter but in general we
+
+ align:start position:0%
+here it doesn't matter but in general we
+ 
+
+ align:start position:0%
+here it doesn't matter but in general we
+have to be very careful about in which
+
+ align:start position:0%
+have to be very careful about in which
+ 
+
+ align:start position:0%
+have to be very careful about in which
+order we'll do
+
+ align:start position:0%
+order we'll do
+ 
+
+ align:start position:0%
+order we'll do
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+yes will always work sorry yeah it well
+
+ align:start position:0%
+yes will always work sorry yeah it well
+ 
+
+ align:start position:0%
+yes will always work sorry yeah it well
+in principle it always works both ways
+
+ align:start position:0%
+in principle it always works both ways
+ 
+
+ align:start position:0%
+in principle it always works both ways
+sometimes it will be that you know
+
+ align:start position:0%
+sometimes it will be that you know
+ 
+
+ align:start position:0%
+sometimes it will be that you know
+because the region has a strange shape
+
+ align:start position:0%
+because the region has a strange shape
+ 
+
+ align:start position:0%
+because the region has a strange shape
+you can actually set it up more easily
+
+ align:start position:0%
+you can actually set it up more easily
+ 
+
+ align:start position:0%
+you can actually set it up more easily
+one way than the other sometimes it will
+
+ align:start position:0%
+one way than the other sometimes it will
+ 
+
+ align:start position:0%
+one way than the other sometimes it will
+also be that the function here you
+
+ align:start position:0%
+also be that the function here you
+ 
+
+ align:start position:0%
+also be that the function here you
+actually know how to integrate in one
+
+ align:start position:0%
+actually know how to integrate in one
+ 
+
+ align:start position:0%
+actually know how to integrate in one
+way but not the other so the theory is
+
+ align:start position:0%
+way but not the other so the theory is
+ 
+
+ align:start position:0%
+way but not the other so the theory is
+that it should work both ways in
+
+ align:start position:0%
+that it should work both ways in
+ 
+
+ align:start position:0%
+that it should work both ways in
+practice one of the two calculations may
+
+ align:start position:0%
+practice one of the two calculations may
+ 
+
+ align:start position:0%
+practice one of the two calculations may
+be much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+harder
+
+ align:start position:0%
+harder
+ 
+
+ align:start position:0%
+harder
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's do another
+
+ align:start position:0%
+let's do another
+ 
+
+ align:start position:0%
+let's do another
+example let's say that what I wanted to
+
+ align:start position:0%
+example let's say that what I wanted to
+ 
+
+ align:start position:0%
+example let's say that what I wanted to
+know was you know not actually what I
+
+ align:start position:0%
+know was you know not actually what I
+ 
+
+ align:start position:0%
+know was you know not actually what I
+computed namely the volume below the
+
+ align:start position:0%
+computed namely the volume below the
+ 
+
+ align:start position:0%
+computed namely the volume below the
+paraboloid but also the negative of some
+
+ align:start position:0%
+paraboloid but also the negative of some
+ 
+
+ align:start position:0%
+paraboloid but also the negative of some
+part that's you know in the corner
+
+ align:start position:0%
+part that's you know in the corner
+ 
+
+ align:start position:0%
+part that's you know in the corner
+towards me but let's say really what I
+
+ align:start position:0%
+towards me but let's say really what I
+ 
+
+ align:start position:0%
+towards me but let's say really what I
+wanted was just the volume between the
+
+ align:start position:0%
+wanted was just the volume between the
+ 
+
+ align:start position:0%
+wanted was just the volume between the
+paraboloid and the XY plane so looking
+
+ align:start position:0%
+paraboloid and the XY plane so looking
+ 
+
+ align:start position:0%
+paraboloid and the XY plane so looking
+only at the part of it that sits above
+
+ align:start position:0%
+only at the part of it that sits above
+ 
+
+ align:start position:0%
+only at the part of it that sits above
+the XY plane so that means instead of
+
+ align:start position:0%
+the XY plane so that means instead of
+ 
+
+ align:start position:0%
+the XY plane so that means instead of
+integrating over the entire square of
+
+ align:start position:0%
+integrating over the entire square of
+ 
+
+ align:start position:0%
+integrating over the entire square of
+size one I should just integrate over
+
+ align:start position:0%
+size one I should just integrate over
+ 
+
+ align:start position:0%
+size one I should just integrate over
+the quarter disk right I should stop
+
+ align:start position:0%
+the quarter disk right I should stop
+ 
+
+ align:start position:0%
+the quarter disk right I should stop
+integrating where my paraboloid hits the
+
+ align:start position:0%
+integrating where my paraboloid hits the
+ 
+
+ align:start position:0%
+integrating where my paraboloid hits the
+XY plane so let me draw another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture so let's say I wanted to
+
+ align:start position:0%
+picture so let's say I wanted to
+ 
+
+ align:start position:0%
+picture so let's say I wanted to
+integrate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+so let's call this example two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry so it's the same we're going to do
+
+ align:start position:0%
+sorry so it's the same we're going to do
+ 
+
+ align:start position:0%
+sorry so it's the same we're going to do
+the same function but over a different
+
+ align:start position:0%
+the same function but over a different
+ 
+
+ align:start position:0%
+the same function but over a different
+region and the region will just be
+
+ align:start position:0%
+region and the region will just be
+ 
+
+ align:start position:0%
+region and the region will just be
+now this quarter dis here okay so maybe
+
+ align:start position:0%
+now this quarter dis here okay so maybe
+ 
+
+ align:start position:0%
+now this quarter dis here okay so maybe
+I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should draw a picture in the XY
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane that's my new region r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so in principle it will be the same
+
+ align:start position:0%
+okay so in principle it will be the same
+ 
+
+ align:start position:0%
+okay so in principle it will be the same
+integral but what changes is the
+
+ align:start position:0%
+integral but what changes is the
+ 
+
+ align:start position:0%
+integral but what changes is the
+bounds why do the bounds change while
+
+ align:start position:0%
+bounds why do the bounds change while
+ 
+
+ align:start position:0%
+bounds why do the bounds change while
+the bounds change because now if I set
+
+ align:start position:0%
+the bounds change because now if I set
+ 
+
+ align:start position:0%
+the bounds change because now if I set
+if I fix some value of x then I will
+
+ align:start position:0%
+if I fix some value of x then I will
+ 
+
+ align:start position:0%
+if I fix some value of x then I will
+want to integrate this part of the slice
+
+ align:start position:0%
+want to integrate this part of the slice
+ 
+
+ align:start position:0%
+want to integrate this part of the slice
+that's above the XY plane and I don't
+
+ align:start position:0%
+that's above the XY plane and I don't
+ 
+
+ align:start position:0%
+that's above the XY plane and I don't
+want to take this part that's actually
+
+ align:start position:0%
+want to take this part that's actually
+ 
+
+ align:start position:0%
+want to take this part that's actually
+outside of my dis so I should stop
+
+ align:start position:0%
+outside of my dis so I should stop
+ 
+
+ align:start position:0%
+outside of my dis so I should stop
+integrating over y when y reaches this
+
+ align:start position:0%
+integrating over y when y reaches this
+ 
+
+ align:start position:0%
+integrating over y when y reaches this
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+here okay on that picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here on this picture it tells me for a
+
+ align:start position:0%
+here on this picture it tells me for a
+ 
+
+ align:start position:0%
+here on this picture it tells me for a
+fixed value of x the range of values for
+
+ align:start position:0%
+fixed value of x the range of values for
+ 
+
+ align:start position:0%
+fixed value of x the range of values for
+y should go only from here to here so
+
+ align:start position:0%
+y should go only from here to here so
+ 
+
+ align:start position:0%
+y should go only from here to here so
+that's from here to less than
+
+ align:start position:0%
+that's from here to less than
+ 
+
+ align:start position:0%
+that's from here to less than
+one okay
+
+ align:start position:0%
+one okay
+ 
+
+ align:start position:0%
+one okay
+so for given
+
+ align:start position:0%
+so for given
+ 
+
+ align:start position:0%
+so for given
+X the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+range of
+
+ align:start position:0%
+range of
+ 
+
+ align:start position:0%
+range of
+Y is
+
+ align:start position:0%
+Y is
+ 
+
+ align:start position:0%
+Y is
+well so what's the lowest value of y
+
+ align:start position:0%
+well so what's the lowest value of y
+ 
+
+ align:start position:0%
+well so what's the lowest value of y
+that I will want to look at it's still
+
+ align:start position:0%
+that I will want to look at it's still
+ 
+
+ align:start position:0%
+that I will want to look at it's still
+Zero from y equal Z to what's the value
+
+ align:start position:0%
+Zero from y equal Z to what's the value
+ 
+
+ align:start position:0%
+Zero from y equal Z to what's the value
+of y here well I have to solve in the
+
+ align:start position:0%
+of y here well I have to solve in the
+ 
+
+ align:start position:0%
+of y here well I have to solve in the
+equation of a circle
+
+ align:start position:0%
+equation of a circle
+ 
+
+ align:start position:0%
+equation of a circle
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so if I'm here this is X2 + Y2 = 1 that
+
+ align:start position:0%
+so if I'm here this is X2 + Y2 = 1 that
+ 
+
+ align:start position:0%
+so if I'm here this is X2 + Y2 = 1 that
+means Y is square root of 1 - x^
+
+ align:start position:0%
+means Y is square root of 1 - x^
+ 
+
+ align:start position:0%
+means Y is square root of 1 - x^
+2 okay so I will integrate from y = 0 to
+
+ align:start position:0%
+2 okay so I will integrate from y = 0 to
+ 
+
+ align:start position:0%
+2 okay so I will integrate from y = 0 to
+Y = < TK of 1 -
+
+ align:start position:0%
+Y = < TK of 1 -
+ 
+
+ align:start position:0%
+Y = < TK of 1 -
+x^2 and now you see how the Bound for y
+
+ align:start position:0%
+x^2 and now you see how the Bound for y
+ 
+
+ align:start position:0%
+x^2 and now you see how the Bound for y
+will depend on the value of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x okay so while I erase I will let you
+
+ align:start position:0%
+x okay so while I erase I will let you
+ 
+
+ align:start position:0%
+x okay so while I erase I will let you
+think about what is the Bound for X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now it's a trick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I claim that what we'll
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do so we'll write this as an iterated
+
+ align:start position:0%
+do so we'll write this as an iterated
+ 
+
+ align:start position:0%
+do so we'll write this as an iterated
+integral first Dy then
+
+ align:start position:0%
+integral first Dy then
+ 
+
+ align:start position:0%
+integral first Dy then
+DX and we said for a fixed value of x
+
+ align:start position:0%
+DX and we said for a fixed value of x
+ 
+
+ align:start position:0%
+DX and we said for a fixed value of x
+the range for y is from 0 to sare root
+
+ align:start position:0%
+the range for y is from 0 to sare root
+ 
+
+ align:start position:0%
+the range for y is from 0 to sare root
+of 1us x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s what about the range for X well the
+
+ align:start position:0%
+s what about the range for X well the
+ 
+
+ align:start position:0%
+s what about the range for X well the
+range for X should just be numbers okay
+
+ align:start position:0%
+range for X should just be numbers okay
+ 
+
+ align:start position:0%
+range for X should just be numbers okay
+remember the question I have to ask now
+
+ align:start position:0%
+remember the question I have to ask now
+ 
+
+ align:start position:0%
+remember the question I have to ask now
+is if I look at all of these yellow
+
+ align:start position:0%
+is if I look at all of these yellow
+ 
+
+ align:start position:0%
+is if I look at all of these yellow
+slices which one is the first one that I
+
+ align:start position:0%
+slices which one is the first one that I
+ 
+
+ align:start position:0%
+slices which one is the first one that I
+want to consider which one is the last
+
+ align:start position:0%
+want to consider which one is the last
+ 
+
+ align:start position:0%
+want to consider which one is the last
+one that I want to consider so the
+
+ align:start position:0%
+one that I want to consider so the
+ 
+
+ align:start position:0%
+one that I want to consider so the
+smallest value of x that I want to
+
+ align:start position:0%
+smallest value of x that I want to
+ 
+
+ align:start position:0%
+smallest value of x that I want to
+is zero again and then I will have there
+
+ align:start position:0%
+is zero again and then I will have there
+ 
+
+ align:start position:0%
+is zero again and then I will have there
+I will actually have a pretty big slice
+
+ align:start position:0%
+I will actually have a pretty big slice
+ 
+
+ align:start position:0%
+I will actually have a pretty big slice
+and I will get smaller and smaller and
+
+ align:start position:0%
+and I will get smaller and smaller and
+ 
+
+ align:start position:0%
+and I will get smaller and smaller and
+smaller slices and it stops I have to
+
+ align:start position:0%
+smaller slices and it stops I have to
+ 
+
+ align:start position:0%
+smaller slices and it stops I have to
+stop when x equals 1 afterwards there's
+
+ align:start position:0%
+stop when x equals 1 afterwards there's
+ 
+
+ align:start position:0%
+stop when x equals 1 afterwards there's
+nothing else to
+
+ align:start position:0%
+nothing else to
+ 
+
+ align:start position:0%
+nothing else to
+integrate
+
+ align:start position:0%
+integrate
+ 
+
+ align:start position:0%
+integrate
+so X goes from Zer to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one okay and
+
+ align:start position:0%
+one okay and
+ 
+
+ align:start position:0%
+one okay and
+now see how in the inner integral the
+
+ align:start position:0%
+now see how in the inner integral the
+ 
+
+ align:start position:0%
+now see how in the inner integral the
+bounds depend on X in the outer one you
+
+ align:start position:0%
+bounds depend on X in the outer one you
+ 
+
+ align:start position:0%
+bounds depend on X in the outer one you
+just get numbers
+
+ align:start position:0%
+just get numbers
+ 
+
+ align:start position:0%
+just get numbers
+because the questions that you have to
+
+ align:start position:0%
+because the questions that you have to
+ 
+
+ align:start position:0%
+because the questions that you have to
+ask to set up this one and to set up
+
+ align:start position:0%
+ask to set up this one and to set up
+ 
+
+ align:start position:0%
+ask to set up this one and to set up
+that one are different here the question
+
+ align:start position:0%
+that one are different here the question
+ 
+
+ align:start position:0%
+that one are different here the question
+is if I fix a given X if I look at a
+
+ align:start position:0%
+is if I fix a given X if I look at a
+ 
+
+ align:start position:0%
+is if I fix a given X if I look at a
+given slice what's the range for y here
+
+ align:start position:0%
+given slice what's the range for y here
+ 
+
+ align:start position:0%
+given slice what's the range for y here
+the question is what's the First Slice
+
+ align:start position:0%
+the question is what's the First Slice
+ 
+
+ align:start position:0%
+the question is what's the First Slice
+what is the last
+
+ align:start position:0%
+what is the last
+ 
+
+ align:start position:0%
+what is the last
+slice does that make
+
+ align:start position:0%
+slice does that make
+ 
+
+ align:start position:0%
+slice does that make
+sense everyone happy with it okay very
+
+ align:start position:0%
+sense everyone happy with it okay very
+ 
+
+ align:start position:0%
+sense everyone happy with it okay very
+good so now how do we compute that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we do the inner integral so that's
+
+ align:start position:0%
+well we do the inner integral so that's
+ 
+
+ align:start position:0%
+well we do the inner integral so that's
+integral from 0 to square root of 1 - x^
+
+ align:start position:0%
+integral from 0 to square root of 1 - x^
+ 
+
+ align:start position:0%
+integral from 0 to square root of 1 - x^
+2 of 1 - x 2 - y^ 2
+
+ align:start position:0%
+2 of 1 - x 2 - y^ 2
+ 
+
+ align:start position:0%
+2 of 1 - x 2 - y^ 2
+Dy and well that integrates to y - x^2 y
+
+ align:start position:0%
+Dy and well that integrates to y - x^2 y
+ 
+
+ align:start position:0%
+Dy and well that integrates to y - x^2 y
+- y Cub 3 from 0 to otk of 1 - x^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then that
+
+ align:start position:0%
+and then that
+ 
+
+ align:start position:0%
+and then that
+becomes well root of 1 - x^ 2 - x^ 2un
+
+ align:start position:0%
+becomes well root of 1 - x^ 2 - x^ 2un
+ 
+
+ align:start position:0%
+becomes well root of 1 - x^ 2 - x^ 2un
+of 1 - x^ 2 - 1 - x 2 to the three
+
+ align:start position:0%
+of 1 - x^ 2 - 1 - x 2 to the three
+ 
+
+ align:start position:0%
+of 1 - x^ 2 - 1 - x 2 to the three
+halves over three and actually if you
+
+ align:start position:0%
+halves over three and actually if you
+ 
+
+ align:start position:0%
+halves over three and actually if you
+look at it for long enough see this is 1
+
+ align:start position:0%
+look at it for long enough see this is 1
+ 
+
+ align:start position:0%
+look at it for long enough see this is 1
+- x 2 * sare root of 1 - x^ 2 so
+
+ align:start position:0%
+- x 2 * sare root of 1 - x^ 2 so
+ 
+
+ align:start position:0%
+- x 2 * sare root of 1 - x^ 2 so
+actually that's
+
+ align:start position:0%
+actually that's
+ 
+
+ align:start position:0%
+actually that's
+also so in fact that simplifies to 2/3
+
+ align:start position:0%
+also so in fact that simplifies to 2/3
+ 
+
+ align:start position:0%
+also so in fact that simplifies to 2/3
+of 1 - x^2 to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3es okay let me redo that
+
+ align:start position:0%
+3es okay let me redo that
+ 
+
+ align:start position:0%
+3es okay let me redo that
+maybe slightly differently this was 1 -
+
+ align:start position:0%
+maybe slightly differently this was 1 -
+ 
+
+ align:start position:0%
+maybe slightly differently this was 1 -
+x^ 2 * y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so 1 - x^ 2 * y becomes < TK 1 - x^ 2
+
+ align:start position:0%
+so 1 - x^ 2 * y becomes < TK 1 - x^ 2
+ 
+
+ align:start position:0%
+so 1 - x^ 2 * y becomes < TK 1 - x^ 2
+oops X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus YB 3 and then when I take yal 0 I
+
+ align:start position:0%
+minus YB 3 and then when I take yal 0 I
+ 
+
+ align:start position:0%
+minus YB 3 and then when I take yal 0 I
+get Z so I don't subtract anything okay
+
+ align:start position:0%
+get Z so I don't subtract anything okay
+ 
+
+ align:start position:0%
+get Z so I don't subtract anything okay
+so now you see this is 1 - x^2 to the
+
+ align:start position:0%
+so now you see this is 1 - x^2 to the
+ 
+
+ align:start position:0%
+so now you see this is 1 - x^2 to the
+three halesus a thir of it so you're
+
+ align:start position:0%
+three halesus a thir of it so you're
+ 
+
+ align:start position:0%
+three halesus a thir of it so you're
+left with
+
+ align:start position:0%
+left with
+ 
+
+ align:start position:0%
+left with
+2/3
+
+ align:start position:0%
+2/3
+ 
+
+ align:start position:0%
+2/3
+okay so that's the inner
+
+ align:start position:0%
+okay so that's the inner
+ 
+
+ align:start position:0%
+okay so that's the inner
+integral the outer integral is integral
+
+ align:start position:0%
+integral the outer integral is integral
+ 
+
+ align:start position:0%
+integral the outer integral is integral
+from 0 to 1 of 2/3 of
+
+ align:start position:0%
+from 0 to 1 of 2/3 of
+ 
+
+ align:start position:0%
+from 0 to 1 of 2/3 of
+1 - X2 to the
+
+ align:start position:0%
+1 - X2 to the
+ 
+
+ align:start position:0%
+1 - X2 to the
+3es
+
+ align:start position:0%
+3es
+ 
+
+ align:start position:0%
+3es
+DX
+
+ align:start position:0%
+DX
+ 
+
+ align:start position:0%
+DX
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well I let you see if you remember
+
+ align:start position:0%
+well I let you see if you remember
+ 
+
+ align:start position:0%
+well I let you see if you remember
+single variable integrals by trying to
+
+ align:start position:0%
+single variable integrals by trying to
+ 
+
+ align:start position:0%
+single variable integrals by trying to
+figure out how this actually comes out
+
+ align:start position:0%
+figure out how this actually comes out
+ 
+
+ align:start position:0%
+figure out how this actually comes out
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be is it pi/ two or Pi 8
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually I think it's p
+
+ align:start position:0%
+actually I think it's p
+ 
+
+ align:start position:0%
+actually I think it's p
+eight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H okay well I guess we have to do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I wrote something on my notes but
+
+ align:start position:0%
+then I wrote something on my notes but
+ 
+
+ align:start position:0%
+then I wrote something on my notes but
+it's not very clear okay so how do we
+
+ align:start position:0%
+it's not very clear okay so how do we
+ 
+
+ align:start position:0%
+it's not very clear okay so how do we
+compute this thing well we have to do
+
+ align:start position:0%
+compute this thing well we have to do
+ 
+
+ align:start position:0%
+compute this thing well we have to do
+trig substitution that's the only way I
+
+ align:start position:0%
+trig substitution that's the only way I
+ 
+
+ align:start position:0%
+trig substitution that's the only way I
+know to compute an integral like that
+
+ align:start position:0%
+know to compute an integral like that
+ 
+
+ align:start position:0%
+know to compute an integral like that
+okay so we'll set x equal sin Theta and
+
+ align:start position:0%
+okay so we'll set x equal sin Theta and
+ 
+
+ align:start position:0%
+okay so we'll set x equal sin Theta and
+then square root of 1 - x^2 will be
+
+ align:start position:0%
+then square root of 1 - x^2 will be
+ 
+
+ align:start position:0%
+then square root of 1 - x^2 will be
+cosine Theta we're using sin square plus
+
+ align:start position:0%
+cosine Theta we're using sin square plus
+ 
+
+ align:start position:0%
+cosine Theta we're using sin square plus
+cosine Square equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 and so that will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+become so 2/3 remains 2/3 1 - x^ 2 to
+
+ align:start position:0%
+become so 2/3 remains 2/3 1 - x^ 2 to
+ 
+
+ align:start position:0%
+become so 2/3 remains 2/3 1 - x^ 2 to
+the 3es becomes cosine Cub Theta
+
+ align:start position:0%
+the 3es becomes cosine Cub Theta
+ 
+
+ align:start position:0%
+the 3es becomes cosine Cub Theta
+DX well s if x is sin Theta then DX is
+
+ align:start position:0%
+DX well s if x is sin Theta then DX is
+ 
+
+ align:start position:0%
+DX well s if x is sin Theta then DX is
+cosine Theta D Theta so that's cosine
+
+ align:start position:0%
+cosine Theta D Theta so that's cosine
+ 
+
+ align:start position:0%
+cosine Theta D Theta so that's cosine
+Theta D Theta and well if you do things
+
+ align:start position:0%
+Theta D Theta and well if you do things
+ 
+
+ align:start position:0%
+Theta D Theta and well if you do things
+subtitution the way I do them then you
+
+ align:start position:0%
+subtitution the way I do them then you
+ 
+
+ align:start position:0%
+subtitution the way I do them then you
+should worry about the bounce for Theta
+
+ align:start position:0%
+should worry about the bounce for Theta
+ 
+
+ align:start position:0%
+should worry about the bounce for Theta
+which will be 0 to pi/ 2 or you can you
+
+ align:start position:0%
+which will be 0 to pi/ 2 or you can you
+ 
+
+ align:start position:0%
+which will be 0 to pi/ 2 or you can you
+know also just plug in the bounce at the
+
+ align:start position:0%
+know also just plug in the bounce at the
+ 
+
+ align:start position:0%
+know also just plug in the bounce at the
+end um so now you have
+
+ align:start position:0%
+end um so now you have
+ 
+
+ align:start position:0%
+end um so now you have
+the 2/3 time the integral from 0 to Pi /
+
+ align:start position:0%
+the 2/3 time the integral from 0 to Pi /
+ 
+
+ align:start position:0%
+the 2/3 time the integral from 0 to Pi /
+2 of cosine to 4 Theta D
+
+ align:start position:0%
+2 of cosine to 4 Theta D
+ 
+
+ align:start position:0%
+2 of cosine to 4 Theta D
+Theta and how do you integrate that well
+
+ align:start position:0%
+Theta and how do you integrate that well
+ 
+
+ align:start position:0%
+Theta and how do you integrate that well
+you have to use double angle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formulas okay so cosine to the 4
+
+ align:start position:0%
+formulas okay so cosine to the 4
+ 
+
+ align:start position:0%
+formulas okay so cosine to the 4
+remember cosine Square Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is 1 + cosine 2 Theta over 2 and we want
+
+ align:start position:0%
+is 1 + cosine 2 Theta over 2 and we want
+ 
+
+ align:start position:0%
+is 1 + cosine 2 Theta over 2 and we want
+the square of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it and so that will give
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+us of well we'll
+
+ align:start position:0%
+us of well we'll
+ 
+
+ align:start position:0%
+us of well we'll
+have actually
+
+ align:start position:0%
+have actually
+ 
+
+ align:start position:0%
+have actually
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+qu+ 12 cosine 2 Theta + 1 cosine S 2
+
+ align:start position:0%
+qu+ 12 cosine 2 Theta + 1 cosine S 2
+ 
+
+ align:start position:0%
+qu+ 12 cosine 2 Theta + 1 cosine S 2
+Theta D
+
+ align:start position:0%
+Theta D
+ 
+
+ align:start position:0%
+Theta D
+Theta and how will you handle this guy
+
+ align:start position:0%
+Theta and how will you handle this guy
+ 
+
+ align:start position:0%
+Theta and how will you handle this guy
+while using again for double angle
+
+ align:start position:0%
+while using again for double angle
+ 
+
+ align:start position:0%
+while using again for double angle
+formula okay so it's getting slightly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nasty so but I don't know any simpler
+
+ align:start position:0%
+nasty so but I don't know any simpler
+ 
+
+ align:start position:0%
+nasty so but I don't know any simpler
+solution except for one simpler solution
+
+ align:start position:0%
+solution except for one simpler solution
+ 
+
+ align:start position:0%
+solution except for one simpler solution
+which is you have a table of integrals
+
+ align:start position:0%
+which is you have a table of integrals
+ 
+
+ align:start position:0%
+which is you have a table of integrals
+of this form Inside thees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yes uh no I don't think so because if
+
+ align:start position:0%
+Yes uh no I don't think so because if
+ 
+
+ align:start position:0%
+Yes uh no I don't think so because if
+you take 1 12 * cosine half * 2 you will
+
+ align:start position:0%
+you take 1 12 * cosine half * 2 you will
+ 
+
+ align:start position:0%
+you take 1 12 * cosine half * 2 you will
+still have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+half okay so if you do again the double
+
+ align:start position:0%
+half okay so if you do again the double
+ 
+
+ align:start position:0%
+half okay so if you do again the double
+angle formula I think I'm not going to
+
+ align:start position:0%
+angle formula I think I'm not going to
+ 
+
+ align:start position:0%
+angle formula I think I'm not going to
+bother to do
+
+ align:start position:0%
+bother to do
+ 
+
+ align:start position:0%
+bother to do
+it I claim you will get at the
+
+ align:start position:0%
+it I claim you will get at the
+ 
+
+ align:start position:0%
+it I claim you will get at the
+end Pi
+
+ align:start position:0%
+end Pi
+ 
+
+ align:start position:0%
+end Pi
+over8 because I say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so okay so
+
+ align:start position:0%
+so so okay so
+ 
+
+ align:start position:0%
+so so okay so
+exercise continue calculating and get pi
+
+ align:start position:0%
+exercise continue calculating and get pi
+ 
+
+ align:start position:0%
+exercise continue calculating and get pi
+over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+8 okay now what does this show us well
+
+ align:start position:0%
+8 okay now what does this show us well
+ 
+
+ align:start position:0%
+8 okay now what does this show us well
+this shows us us actually that this is
+
+ align:start position:0%
+this shows us us actually that this is
+ 
+
+ align:start position:0%
+this shows us us actually that this is
+probably not the right way to do this
+
+ align:start position:0%
+probably not the right way to do this
+ 
+
+ align:start position:0%
+probably not the right way to do this
+okay the right way to do this will be to
+
+ align:start position:0%
+okay the right way to do this will be to
+ 
+
+ align:start position:0%
+okay the right way to do this will be to
+integrate it in polar coordinates and
+
+ align:start position:0%
+integrate it in polar coordinates and
+ 
+
+ align:start position:0%
+integrate it in polar coordinates and
+that's what we'll learn how to do
+
+ align:start position:0%
+that's what we'll learn how to do
+ 
+
+ align:start position:0%
+that's what we'll learn how to do
+tomorrow okay
+
+ align:start position:0%
+tomorrow okay
+ 
+
+ align:start position:0%
+tomorrow okay
+so we'll actually see how to do it with
+
+ align:start position:0%
+so we'll actually see how to do it with
+ 
+
+ align:start position:0%
+so we'll actually see how to do it with
+much less
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trig
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that will be
+
+ align:start position:0%
+so that will be
+ 
+
+ align:start position:0%
+so that will be
+easier in polar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coordinates so we'll see that
+
+ align:start position:0%
+coordinates so we'll see that
+ 
+
+ align:start position:0%
+coordinates so we'll see that
+tomorrow okay so but you know we are
+
+ align:start position:0%
+tomorrow okay so but you know we are
+ 
+
+ align:start position:0%
+tomorrow okay so but you know we are
+almost there I mean here you just use
+
+ align:start position:0%
+almost there I mean here you just use
+ 
+
+ align:start position:0%
+almost there I mean here you just use
+the double angle again and then you can
+
+ align:start position:0%
+the double angle again and then you can
+ 
+
+ align:start position:0%
+the double angle again and then you can
+get it and it's it's pretty
+
+ align:start position:0%
+get it and it's it's pretty
+ 
+
+ align:start position:0%
+get it and it's it's pretty
+straightforward
+
+ align:start position:0%
+straightforward
+ 
+
+ align:start position:0%
+straightforward
+okay so one thing that's kind of
+
+ align:start position:0%
+okay so one thing that's kind of
+ 
+
+ align:start position:0%
+okay so one thing that's kind of
+interesting to
+
+ align:start position:0%
+interesting to
+ 
+
+ align:start position:0%
+interesting to
+know is we can exchange the order of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integration so if we have an integral
+
+ align:start position:0%
+integration so if we have an integral
+ 
+
+ align:start position:0%
+integration so if we have an integral
+given to us in the order Dy DX we can
+
+ align:start position:0%
+given to us in the order Dy DX we can
+ 
+
+ align:start position:0%
+given to us in the order Dy DX we can
+switch it to DX Dy but we have to be
+
+ align:start position:0%
+switch it to DX Dy but we have to be
+ 
+
+ align:start position:0%
+switch it to DX Dy but we have to be
+extremely careful with the
+
+ align:start position:0%
+extremely careful with the
+ 
+
+ align:start position:0%
+extremely careful with the
+bounds see you certainly cannot just
+
+ align:start position:0%
+bounds see you certainly cannot just
+ 
+
+ align:start position:0%
+bounds see you certainly cannot just
+swap the bounds of the inner and outer
+
+ align:start position:0%
+swap the bounds of the inner and outer
+ 
+
+ align:start position:0%
+swap the bounds of the inner and outer
+because there you would end up you know
+
+ align:start position:0%
+because there you would end up you know
+ 
+
+ align:start position:0%
+because there you would end up you know
+having this square root of 1 - x square
+
+ align:start position:0%
+having this square root of 1 - x square
+ 
+
+ align:start position:0%
+having this square root of 1 - x square
+on the outside and you would never get a
+
+ align:start position:0%
+on the outside and you would never get a
+ 
+
+ align:start position:0%
+on the outside and you would never get a
+number out of that so that cannot work
+
+ align:start position:0%
+number out of that so that cannot work
+ 
+
+ align:start position:0%
+number out of that so that cannot work
+it's more complicated than that okay so
+
+ align:start position:0%
+it's more complicated than that okay so
+ 
+
+ align:start position:0%
+it's more complicated than that okay so
+well here's a first baby
+
+ align:start position:0%
+well here's a first baby
+ 
+
+ align:start position:0%
+well here's a first baby
+example certainly if I do integral from
+
+ align:start position:0%
+example certainly if I do integral from
+ 
+
+ align:start position:0%
+example certainly if I do integral from
+0 to 1 integral from 0 to two DX
+
+ align:start position:0%
+0 to 1 integral from 0 to two DX
+ 
+
+ align:start position:0%
+0 to 1 integral from 0 to two DX
+dy I can there I can certainly
+
+ align:start position:0%
+dy I can there I can certainly
+ 
+
+ align:start position:0%
+dy I can there I can certainly
+switch the bounce without thinking too
+
+ align:start position:0%
+switch the bounce without thinking too
+ 
+
+ align:start position:0%
+switch the bounce without thinking too
+much what's the reason for that well the
+
+ align:start position:0%
+much what's the reason for that well the
+ 
+
+ align:start position:0%
+much what's the reason for that well the
+reason for that is you know this
+
+ align:start position:0%
+reason for that is you know this
+ 
+
+ align:start position:0%
+reason for that is you know this
+corresponds in both cases to integrating
+
+ align:start position:0%
+corresponds in both cases to integrating
+ 
+
+ align:start position:0%
+corresponds in both cases to integrating
+x from 0 to two and Y from 0 to 1 it's a
+
+ align:start position:0%
+x from 0 to two and Y from 0 to 1 it's a
+ 
+
+ align:start position:0%
+x from 0 to two and Y from 0 to 1 it's a
+rectangle so if I slice it this way you
+
+ align:start position:0%
+rectangle so if I slice it this way you
+ 
+
+ align:start position:0%
+rectangle so if I slice it this way you
+see that y goes from 0 to one for any X
+
+ align:start position:0%
+see that y goes from 0 to one for any X
+ 
+
+ align:start position:0%
+see that y goes from 0 to one for any X
+between 0 and two it's this guy if I
+
+ align:start position:0%
+between 0 and two it's this guy if I
+ 
+
+ align:start position:0%
+between 0 and two it's this guy if I
+slice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it that way then X goes from 0 to two
+
+ align:start position:0%
+it that way then X goes from 0 to two
+ 
+
+ align:start position:0%
+it that way then X goes from 0 to two
+for any value of y between 0 and one and
+
+ align:start position:0%
+for any value of y between 0 and one and
+ 
+
+ align:start position:0%
+for any value of y between 0 and one and
+it's this one so here it works but in
+
+ align:start position:0%
+it's this one so here it works but in
+ 
+
+ align:start position:0%
+it's this one so here it works but in
+general I I have to draw a picture of my
+
+ align:start position:0%
+general I I have to draw a picture of my
+ 
+
+ align:start position:0%
+general I I have to draw a picture of my
+region and see how the slices look like
+
+ align:start position:0%
+region and see how the slices look like
+ 
+
+ align:start position:0%
+region and see how the slices look like
+both
+
+ align:start position:0%
+both
+ 
+
+ align:start position:0%
+both
+ways okay so let's
+
+ align:start position:0%
+ways okay so let's
+ 
+
+ align:start position:0%
+ways okay so let's
+do a more interesting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one let's say that I want to compute
+
+ align:start position:0%
+one let's say that I want to compute
+ 
+
+ align:start position:0%
+one let's say that I want to compute
+integral from 0 to 1 of integral from X
+
+ align:start position:0%
+integral from 0 to 1 of integral from X
+ 
+
+ align:start position:0%
+integral from 0 to 1 of integral from X
+to square root of x of e to the Y over Y
+
+ align:start position:0%
+to square root of x of e to the Y over Y
+ 
+
+ align:start position:0%
+to square root of x of e to the Y over Y
+and Dy
+
+ align:start position:0%
+and Dy
+ 
+
+ align:start position:0%
+and Dy
+DX so why did I choose this guy I choose
+
+ align:start position:0%
+DX so why did I choose this guy I choose
+ 
+
+ align:start position:0%
+DX so why did I choose this guy I choose
+this guy because as far as I can tell
+
+ align:start position:0%
+this guy because as far as I can tell
+ 
+
+ align:start position:0%
+this guy because as far as I can tell
+there's no way to integrate e to the Y
+
+ align:start position:0%
+there's no way to integrate e to the Y
+ 
+
+ align:start position:0%
+there's no way to integrate e to the Y
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+y so this is an integral but you cannot
+
+ align:start position:0%
+y so this is an integral but you cannot
+ 
+
+ align:start position:0%
+y so this is an integral but you cannot
+compute this
+
+ align:start position:0%
+compute this
+ 
+
+ align:start position:0%
+compute this
+way so it's a good example for why this
+
+ align:start position:0%
+way so it's a good example for why this
+ 
+
+ align:start position:0%
+way so it's a good example for why this
+can be useful so if you do it this way
+
+ align:start position:0%
+can be useful so if you do it this way
+ 
+
+ align:start position:0%
+can be useful so if you do it this way
+you're stuck immediately so instead
+
+ align:start position:0%
+you're stuck immediately so instead
+ 
+
+ align:start position:0%
+you're stuck immediately so instead
+we'll try to switch the order but to
+
+ align:start position:0%
+we'll try to switch the order but to
+ 
+
+ align:start position:0%
+we'll try to switch the order but to
+switch the order we have to understand
+
+ align:start position:0%
+switch the order we have to understand
+ 
+
+ align:start position:0%
+switch the order we have to understand
+what do these bounds
+
+ align:start position:0%
+what do these bounds
+ 
+
+ align:start position:0%
+what do these bounds
+mean okay so let's draw a picture of the
+
+ align:start position:0%
+mean okay so let's draw a picture of the
+ 
+
+ align:start position:0%
+mean okay so let's draw a picture of the
+region
+
+ align:start position:0%
+region
+ 
+
+ align:start position:0%
+region
+well what we're saying is y goes from y
+
+ align:start position:0%
+well what we're saying is y goes from y
+ 
+
+ align:start position:0%
+well what we're saying is y goes from y
+= x to Y = root of x well let's
+
+ align:start position:0%
+= x to Y = root of x well let's
+ 
+
+ align:start position:0%
+= x to Y = root of x well let's
+draw Y =
+
+ align:start position:0%
+draw Y =
+ 
+
+ align:start position:0%
+draw Y =
+X and Y = square root of
+
+ align:start position:0%
+X and Y = square root of
+ 
+
+ align:start position:0%
+X and Y = square root of
+x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's well maybe I should
+
+ align:start position:0%
+it's well maybe I should
+ 
+
+ align:start position:0%
+it's well maybe I should
+actually put this here y = x to Y = root
+
+ align:start position:0%
+actually put this here y = x to Y = root
+ 
+
+ align:start position:0%
+actually put this here y = x to Y = root
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+x okay and so I will go for each value
+
+ align:start position:0%
+x okay and so I will go for each value
+ 
+
+ align:start position:0%
+x okay and so I will go for each value
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+x I will go from yal X to Y = root of x
+
+ align:start position:0%
+x I will go from yal X to Y = root of x
+ 
+
+ align:start position:0%
+x I will go from yal X to Y = root of x
+and I will do that for values of X that
+
+ align:start position:0%
+and I will do that for values of X that
+ 
+
+ align:start position:0%
+and I will do that for values of X that
+go from xal
+
+ align:start position:0%
+go from xal
+ 
+
+ align:start position:0%
+go from xal
+0 to xal 1 which happens to be exactly
+
+ align:start position:0%
+0 to xal 1 which happens to be exactly
+ 
+
+ align:start position:0%
+0 to xal 1 which happens to be exactly
+where these things
+
+ align:start position:0%
+where these things
+ 
+
+ align:start position:0%
+where these things
+intersect so my region will consist of
+
+ align:start position:0%
+intersect so my region will consist of
+ 
+
+ align:start position:0%
+intersect so my region will consist of
+all this okay so now if I want to do it
+
+ align:start position:0%
+all this okay so now if I want to do it
+ 
+
+ align:start position:0%
+all this okay so now if I want to do it
+the other around I have to decompose my
+
+ align:start position:0%
+the other around I have to decompose my
+ 
+
+ align:start position:0%
+the other around I have to decompose my
+region the other way around I have
+
+ align:start position:0%
+region the other way around I have
+ 
+
+ align:start position:0%
+region the other way around I have
+to so my goal now is to Rite this as an
+
+ align:start position:0%
+to so my goal now is to Rite this as an
+ 
+
+ align:start position:0%
+to so my goal now is to Rite this as an
+integral well it's still the same
+
+ align:start position:0%
+integral well it's still the same
+ 
+
+ align:start position:0%
+integral well it's still the same
+function it's still e to the Y over y
+
+ align:start position:0%
+function it's still e to the Y over y
+ 
+
+ align:start position:0%
+function it's still e to the Y over y
+but now I want to integrate DX d y so
+
+ align:start position:0%
+but now I want to integrate DX d y so
+ 
+
+ align:start position:0%
+but now I want to integrate DX d y so
+how do I integrate over X well I fix a
+
+ align:start position:0%
+how do I integrate over X well I fix a
+ 
+
+ align:start position:0%
+how do I integrate over X well I fix a
+value of
+
+ align:start position:0%
+value of
+ 
+
+ align:start position:0%
+value of
+y and for that value of y what's the
+
+ align:start position:0%
+y and for that value of y what's the
+ 
+
+ align:start position:0%
+y and for that value of y what's the
+range for X well the range for X is from
+
+ align:start position:0%
+range for X well the range for X is from
+ 
+
+ align:start position:0%
+range for X well the range for X is from
+here to
+
+ align:start position:0%
+here to
+ 
+
+ align:start position:0%
+here to
+here okay what's the value of x here
+
+ align:start position:0%
+here okay what's the value of x here
+ 
+
+ align:start position:0%
+here okay what's the value of x here
+let's start with the easy
+
+ align:start position:0%
+let's start with the easy
+ 
+
+ align:start position:0%
+let's start with the easy
+one this is xal y what about this one
+
+ align:start position:0%
+one this is xal y what about this one
+ 
+
+ align:start position:0%
+one this is xal y what about this one
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+xal X =
+
+ align:start position:0%
+xal X =
+ 
+
+ align:start position:0%
+xal X =
+y^2 okay
+
+ align:start position:0%
+y^2 okay
+ 
+
+ align:start position:0%
+y^2 okay
+so X goes from y^2 to Y and then what
+
+ align:start position:0%
+so X goes from y^2 to Y and then what
+ 
+
+ align:start position:0%
+so X goes from y^2 to Y and then what
+about y well I have to start at the
+
+ align:start position:0%
+about y well I have to start at the
+ 
+
+ align:start position:0%
+about y well I have to start at the
+bottom of my region that's yal 0 to the
+
+ align:start position:0%
+bottom of my region that's yal 0 to the
+ 
+
+ align:start position:0%
+bottom of my region that's yal 0 to the
+top which is at yal 1 so y goes from 0
+
+ align:start position:0%
+top which is at yal 1 so y goes from 0
+ 
+
+ align:start position:0%
+top which is at yal 1 so y goes from 0
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+one so see switching the bounds is not
+
+ align:start position:0%
+one so see switching the bounds is not
+ 
+
+ align:start position:0%
+one so see switching the bounds is not
+completely
+
+ align:start position:0%
+completely
+ 
+
+ align:start position:0%
+completely
+obvious that took a little bit of
+
+ align:start position:0%
+obvious that took a little bit of
+ 
+
+ align:start position:0%
+obvious that took a little bit of
+work but now that we've done that
+
+ align:start position:0%
+work but now that we've done that
+ 
+
+ align:start position:0%
+work but now that we've done that
+well just to see how it goes it's
+
+ align:start position:0%
+well just to see how it goes it's
+ 
+
+ align:start position:0%
+well just to see how it goes it's
+actually going to be much easier to
+
+ align:start position:0%
+actually going to be much easier to
+ 
+
+ align:start position:0%
+actually going to be much easier to
+integrate
+
+ align:start position:0%
+integrate
+ 
+
+ align:start position:0%
+integrate
+because in our
+
+ align:start position:0%
+because in our
+ 
+
+ align:start position:0%
+because in our
+integral well what's the integral of e
+
+ align:start position:0%
+integral well what's the integral of e
+ 
+
+ align:start position:0%
+integral well what's the integral of e
+to the y y with respect to X it's just
+
+ align:start position:0%
+to the y y with respect to X it's just
+ 
+
+ align:start position:0%
+to the y y with respect to X it's just
+that time x
+
+ align:start position:0%
+that time x
+ 
+
+ align:start position:0%
+that time x
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+from X = y^2 to Y so that will be well
+
+ align:start position:0%
+from X = y^2 to Y so that will be well
+ 
+
+ align:start position:0%
+from X = y^2 to Y so that will be well
+if I plug xal y I will get e to Y minus
+
+ align:start position:0%
+if I plug xal y I will get e to Y minus
+ 
+
+ align:start position:0%
+if I plug xal y I will get e to Y minus
+if I plug x = y^ 2 I will get e to y y *
+
+ align:start position:0%
+if I plug x = y^ 2 I will get e to y y *
+ 
+
+ align:start position:0%
+if I plug x = y^ 2 I will get e to y y *
+y^
+
+ align:start position:0%
+y^
+ 
+
+ align:start position:0%
+y^
+2 the y *
+
+ align:start position:0%
+2 the y *
+ 
+
+ align:start position:0%
+2 the y *
+y okay so now if I do the outer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral I will have integral from 0 to
+
+ align:start position:0%
+integral I will have integral from 0 to
+ 
+
+ align:start position:0%
+integral I will have integral from 0 to
+one of e to Yus y e to
+
+ align:start position:0%
+one of e to Yus y e to
+ 
+
+ align:start position:0%
+one of e to Yus y e to
+y d y and that one actually is a little
+
+ align:start position:0%
+y d y and that one actually is a little
+ 
+
+ align:start position:0%
+y d y and that one actually is a little
+bit easier
+
+ align:start position:0%
+bit easier
+ 
+
+ align:start position:0%
+bit easier
+so we know how to integrate e to the Y
+
+ align:start position:0%
+so we know how to integrate e to the Y
+ 
+
+ align:start position:0%
+so we know how to integrate e to the Y
+we don't quite know how to integrate y e
+
+ align:start position:0%
+we don't quite know how to integrate y e
+ 
+
+ align:start position:0%
+we don't quite know how to integrate y e
+to the Y but let's
+
+ align:start position:0%
+to the Y but let's
+ 
+
+ align:start position:0%
+to the Y but let's
+try so let's see what's the derivative
+
+ align:start position:0%
+try so let's see what's the derivative
+ 
+
+ align:start position:0%
+try so let's see what's the derivative
+of y e to the
+
+ align:start position:0%
+of y e to the
+ 
+
+ align:start position:0%
+of y e to the
+Y well by the product rule that 1 * e to
+
+ align:start position:0%
+Y well by the product rule that 1 * e to
+ 
+
+ align:start position:0%
+Y well by the product rule that 1 * e to
+Y
+
+ align:start position:0%
+Y
+ 
+
+ align:start position:0%
+Y
+plus 1 y * the derivative of e to the Y
+
+ align:start position:0%
+plus 1 y * the derivative of e to the Y
+ 
+
+ align:start position:0%
+plus 1 y * the derivative of e to the Y
+is y e to Y so if we do okay let's put a
+
+ align:start position:0%
+is y e to Y so if we do okay let's put a
+ 
+
+ align:start position:0%
+is y e to Y so if we do okay let's put a
+minus sign in
+
+ align:start position:0%
+minus sign in
+ 
+
+ align:start position:0%
+minus sign in
+front well that's almost what we want
+
+ align:start position:0%
+front well that's almost what we want
+ 
+
+ align:start position:0%
+front well that's almost what we want
+except we have a minus E to the Y
+
+ align:start position:0%
+except we have a minus E to the Y
+ 
+
+ align:start position:0%
+except we have a minus E to the Y
+instead of a plus e to the Y so we need
+
+ align:start position:0%
+instead of a plus e to the Y so we need
+ 
+
+ align:start position:0%
+instead of a plus e to the Y so we need
+to add 2 e to the Y and I claim that the
+
+ align:start position:0%
+to add 2 e to the Y and I claim that the
+ 
+
+ align:start position:0%
+to add 2 e to the Y and I claim that the
+anti-derivative okay if you got lost you
+
+ align:start position:0%
+anti-derivative okay if you got lost you
+ 
+
+ align:start position:0%
+anti-derivative okay if you got lost you
+can also do it by integrating by Parts
+
+ align:start position:0%
+can also do it by integrating by Parts
+ 
+
+ align:start position:0%
+can also do it by integrating by Parts
+by taking the derivative of y and
+
+ align:start position:0%
+by taking the derivative of y and
+ 
+
+ align:start position:0%
+by taking the derivative of y and
+integrating this guy um or the you know
+
+ align:start position:0%
+integrating this guy um or the you know
+ 
+
+ align:start position:0%
+integrating this guy um or the you know
+that works just you know your first
+
+ align:start position:0%
+that works just you know your first
+ 
+
+ align:start position:0%
+that works just you know your first
+guess would be maybe let's try minus y e
+
+ align:start position:0%
+guess would be maybe let's try minus y e
+ 
+
+ align:start position:0%
+guess would be maybe let's try minus y e
+to the Y take the dative of that compare
+
+ align:start position:0%
+to the Y take the dative of that compare
+ 
+
+ align:start position:0%
+to the Y take the dative of that compare
+see what you need to to do to fix and so
+
+ align:start position:0%
+see what you need to to do to fix and so
+ 
+
+ align:start position:0%
+see what you need to to do to fix and so
+if you take that between Z and one you
+
+ align:start position:0%
+if you take that between Z and one you
+ 
+
+ align:start position:0%
+if you take that between Z and one you
+will eventually get e minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 okay
+
+ align:start position:0%
+2 okay
+ 
+
+ align:start position:0%
+2 okay
+so tomorrow we are going to see how to
+
+ align:start position:0%
+so tomorrow we are going to see how to
+ 
+
+ align:start position:0%
+so tomorrow we are going to see how to
+do double integrals in polar coordinates
+
+ align:start position:0%
+do double integrals in polar coordinates
+ 
+
+ align:start position:0%
+do double integrals in polar coordinates
+and also applications of double
+
+ align:start position:0%
+and also applications of double
+ 
+
+ align:start position:0%
+and also applications of double
+integrals how to use use them for
+
+ align:start position:0%
+integrals how to use use them for
+ 
+
+ align:start position:0%
+integrals how to use use them for
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+things
\ No newline at end of file
diff --git a/YTFcnBEiVgs.txt b/YTFcnBEiVgs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0af037d297d468d68c84aceab9f2f1cb10e56232
--- /dev/null
+++ b/YTFcnBEiVgs.txt
@@ -0,0 +1,16539 @@
+align:start position:0%
+ 
+okay maybe we'll go ahead and get
+
+ align:start position:0%
+okay maybe we'll go ahead and get
+ 
+
+ align:start position:0%
+okay maybe we'll go ahead and get
+started at least with the announcements
+
+ align:start position:0%
+started at least with the announcements
+ 
+
+ align:start position:0%
+started at least with the announcements
+uh yeah hopefully everybody's recovered
+
+ align:start position:0%
+uh yeah hopefully everybody's recovered
+ 
+
+ align:start position:0%
+uh yeah hopefully everybody's recovered
+from their Thanksgiving
+
+ align:start position:0%
+from their Thanksgiving
+ 
+
+ align:start position:0%
+from their Thanksgiving
+feast and uh looks like people are
+
+ align:start position:0%
+feast and uh looks like people are
+ 
+
+ align:start position:0%
+feast and uh looks like people are
+sleeping in today um what I'm showing up
+
+ align:start position:0%
+sleeping in today um what I'm showing up
+ 
+
+ align:start position:0%
+sleeping in today um what I'm showing up
+here is the um sort of the schedule to
+
+ align:start position:0%
+here is the um sort of the schedule to
+ 
+
+ align:start position:0%
+here is the um sort of the schedule to
+orient us uh this is lecture 22 going
+
+ align:start position:0%
+orient us uh this is lecture 22 going
+ 
+
+ align:start position:0%
+orient us uh this is lecture 22 going
+talk about pilicides uh device contacts
+
+ align:start position:0%
+talk about pilicides uh device contacts
+ 
+
+ align:start position:0%
+talk about pilicides uh device contacts
+and I've added in um new material this
+
+ align:start position:0%
+and I've added in um new material this
+ 
+
+ align:start position:0%
+and I've added in um new material this
+year on novel gate materials
+
+ align:start position:0%
+year on novel gate materials
+ 
+
+ align:start position:0%
+year on novel gate materials
+and part of this is covered um the first
+
+ align:start position:0%
+and part of this is covered um the first
+ 
+
+ align:start position:0%
+and part of this is covered um the first
+two topics are covered in chapter 11 and
+
+ align:start position:0%
+two topics are covered in chapter 11 and
+ 
+
+ align:start position:0%
+two topics are covered in chapter 11 and
+then we have one more lecture which is
+
+ align:start position:0%
+then we have one more lecture which is
+ 
+
+ align:start position:0%
+then we have one more lecture which is
+on um strain silicon and silicon
+
+ align:start position:0%
+on um strain silicon and silicon
+ 
+
+ align:start position:0%
+on um strain silicon and silicon
+geranium growth and processing uh and
+
+ align:start position:0%
+geranium growth and processing uh and
+ 
+
+ align:start position:0%
+geranium growth and processing uh and
+then next week we have um two class
+
+ align:start position:0%
+then next week we have um two class
+ 
+
+ align:start position:0%
+then next week we have um two class
+periods uh scheduled there'll be um four
+
+ align:start position:0%
+periods uh scheduled there'll be um four
+ 
+
+ align:start position:0%
+periods uh scheduled there'll be um four
+speakers in each and those will be your
+
+ align:start position:0%
+speakers in each and those will be your
+ 
+
+ align:start position:0%
+speakers in each and those will be your
+um the oral reports and the student
+
+ align:start position:0%
+um the oral reports and the student
+ 
+
+ align:start position:0%
+um the oral reports and the student
+reports uh given on Tuesday and Thursday
+
+ align:start position:0%
+reports uh given on Tuesday and Thursday
+ 
+
+ align:start position:0%
+reports uh given on Tuesday and Thursday
+in fact I have a a slightly better uh
+
+ align:start position:0%
+in fact I have a a slightly better uh
+ 
+
+ align:start position:0%
+in fact I have a a slightly better uh
+version of this schedule I think in this
+
+ align:start position:0%
+version of this schedule I think in this
+ 
+
+ align:start position:0%
+version of this schedule I think in this
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+um uh in this Excel file and this is
+
+ align:start position:0%
+um uh in this Excel file and this is
+ 
+
+ align:start position:0%
+um uh in this Excel file and this is
+posted up on the web by the way so on
+
+ align:start position:0%
+posted up on the web by the way so on
+ 
+
+ align:start position:0%
+posted up on the web by the way so on
+December 7th we have these four speakers
+
+ align:start position:0%
+December 7th we have these four speakers
+ 
+
+ align:start position:0%
+December 7th we have these four speakers
+we're going to hear um short
+
+ align:start position:0%
+we're going to hear um short
+ 
+
+ align:start position:0%
+we're going to hear um short
+presentations about 16 minutes each um
+
+ align:start position:0%
+presentations about 16 minutes each um
+ 
+
+ align:start position:0%
+presentations about 16 minutes each um
+from these four students on everything
+
+ align:start position:0%
+from these four students on everything
+ 
+
+ align:start position:0%
+from these four students on everything
+from high K going to diffusion in G
+
+ align:start position:0%
+from high K going to diffusion in G
+ 
+
+ align:start position:0%
+from high K going to diffusion in G
+maride and then on the Thursday the 9th
+
+ align:start position:0%
+maride and then on the Thursday the 9th
+ 
+
+ align:start position:0%
+maride and then on the Thursday the 9th
+we have um these four students uh
+
+ align:start position:0%
+we have um these four students uh
+ 
+
+ align:start position:0%
+we have um these four students uh
+scheduled and I just want to remind
+
+ align:start position:0%
+scheduled and I just want to remind
+ 
+
+ align:start position:0%
+scheduled and I just want to remind
+people if you're doing an oral report
+
+ align:start position:0%
+people if you're doing an oral report
+ 
+
+ align:start position:0%
+people if you're doing an oral report
+you're expected to um provide handouts
+
+ align:start position:0%
+you're expected to um provide handouts
+ 
+
+ align:start position:0%
+you're expected to um provide handouts
+the same kind of type of handout that I
+
+ align:start position:0%
+the same kind of type of handout that I
+ 
+
+ align:start position:0%
+the same kind of type of handout that I
+use during lecture and if you need help
+
+ align:start position:0%
+use during lecture and if you need help
+ 
+
+ align:start position:0%
+use during lecture and if you need help
+um in making Xerox copies contact my
+
+ align:start position:0%
+um in making Xerox copies contact my
+ 
+
+ align:start position:0%
+um in making Xerox copies contact my
+assistant her uh her contact information
+
+ align:start position:0%
+assistant her uh her contact information
+ 
+
+ align:start position:0%
+assistant her uh her contact information
+is published on the web make sure you
+
+ align:start position:0%
+is published on the web make sure you
+ 
+
+ align:start position:0%
+is published on the web make sure you
+get to her early enough don't uh don't
+
+ align:start position:0%
+get to her early enough don't uh don't
+ 
+
+ align:start position:0%
+get to her early enough don't uh don't
+give her the the job the same day uh
+
+ align:start position:0%
+give her the the job the same day uh
+ 
+
+ align:start position:0%
+give her the the job the same day uh
+that morning but maybe the day before it
+
+ align:start position:0%
+that morning but maybe the day before it
+ 
+
+ align:start position:0%
+that morning but maybe the day before it
+would be good um and also if you're
+
+ align:start position:0%
+would be good um and also if you're
+ 
+
+ align:start position:0%
+would be good um and also if you're
+doing a written report they are due on
+
+ align:start position:0%
+doing a written report they are due on
+ 
+
+ align:start position:0%
+doing a written report they are due on
+Thursday December 9th um in class if you
+
+ align:start position:0%
+Thursday December 9th um in class if you
+ 
+
+ align:start position:0%
+Thursday December 9th um in class if you
+have any questions about the final
+
+ align:start position:0%
+have any questions about the final
+ 
+
+ align:start position:0%
+have any questions about the final
+project just uh please email me or
+
+ align:start position:0%
+project just uh please email me or
+ 
+
+ align:start position:0%
+project just uh please email me or
+contact me after
+
+ align:start position:0%
+contact me after
+ 
+
+ align:start position:0%
+contact me after
+class okay so that's uh sort of the
+
+ align:start position:0%
+class okay so that's uh sort of the
+ 
+
+ align:start position:0%
+class okay so that's uh sort of the
+bookkeeping uh and to remind people
+
+ align:start position:0%
+bookkeeping uh and to remind people
+ 
+
+ align:start position:0%
+bookkeeping uh and to remind people
+about the final project let's um let's
+
+ align:start position:0%
+about the final project let's um let's
+ 
+
+ align:start position:0%
+about the final project let's um let's
+go on and start uh we can start today's
+
+ align:start position:0%
+go on and start uh we can start today's
+ 
+
+ align:start position:0%
+go on and start uh we can start today's
+lecture um this uh the notes for uh
+
+ align:start position:0%
+lecture um this uh the notes for uh
+ 
+
+ align:start position:0%
+lecture um this uh the notes for uh
+today's lecture are given in handout
+
+ align:start position:0%
+today's lecture are given in handout
+ 
+
+ align:start position:0%
+today's lecture are given in handout
+36 and today we want to talk about uh
+
+ align:start position:0%
+36 and today we want to talk about uh
+ 
+
+ align:start position:0%
+36 and today we want to talk about uh
+sort of um couple of device a couple of
+
+ align:start position:0%
+sort of um couple of device a couple of
+ 
+
+ align:start position:0%
+sort of um couple of device a couple of
+areas the formation of suicides I've
+
+ align:start position:0%
+areas the formation of suicides I've
+ 
+
+ align:start position:0%
+areas the formation of suicides I've
+referred suicides a number of times in
+
+ align:start position:0%
+referred suicides a number of times in
+ 
+
+ align:start position:0%
+referred suicides a number of times in
+the course but we really haven't gotten
+
+ align:start position:0%
+the course but we really haven't gotten
+ 
+
+ align:start position:0%
+the course but we really haven't gotten
+a chance to talk about what they are now
+
+ align:start position:0%
+a chance to talk about what they are now
+ 
+
+ align:start position:0%
+a chance to talk about what they are now
+we'll find out uh how we make contact
+
+ align:start position:0%
+we'll find out uh how we make contact
+ 
+
+ align:start position:0%
+we'll find out uh how we make contact
+how we make uh the structures that make
+
+ align:start position:0%
+how we make uh the structures that make
+ 
+
+ align:start position:0%
+how we make uh the structures that make
+good electrical contact in the device
+
+ align:start position:0%
+good electrical contact in the device
+ 
+
+ align:start position:0%
+good electrical contact in the device
+and as I mentioned I've added a new
+
+ align:start position:0%
+and as I mentioned I've added a new
+ 
+
+ align:start position:0%
+and as I mentioned I've added a new
+module this year on novel gate materials
+
+ align:start position:0%
+module this year on novel gate materials
+ 
+
+ align:start position:0%
+module this year on novel gate materials
+and we started some of that last time so
+
+ align:start position:0%
+and we started some of that last time so
+ 
+
+ align:start position:0%
+and we started some of that last time so
+so far we've talked about how to get
+
+ align:start position:0%
+so far we've talked about how to get
+ 
+
+ align:start position:0%
+so far we've talked about how to get
+these uh insulating and doped regions
+
+ align:start position:0%
+these uh insulating and doped regions
+ 
+
+ align:start position:0%
+these uh insulating and doped regions
+inside the device we've talked about
+
+ align:start position:0%
+inside the device we've talked about
+ 
+
+ align:start position:0%
+inside the device we've talked about
+oxidation implantation diffusion thin
+
+ align:start position:0%
+oxidation implantation diffusion thin
+ 
+
+ align:start position:0%
+oxidation implantation diffusion thin
+film deposition uh and how we etch
+
+ align:start position:0%
+film deposition uh and how we etch
+ 
+
+ align:start position:0%
+film deposition uh and how we etch
+structures
+
+ align:start position:0%
+structures
+ 
+
+ align:start position:0%
+structures
+uh but at this point uh in the device
+
+ align:start position:0%
+uh but at this point uh in the device
+ 
+
+ align:start position:0%
+uh but at this point uh in the device
+fabrication of the seamoss flow we need
+
+ align:start position:0%
+fabrication of the seamoss flow we need
+ 
+
+ align:start position:0%
+fabrication of the seamoss flow we need
+some way to make a good electrical
+
+ align:start position:0%
+some way to make a good electrical
+ 
+
+ align:start position:0%
+some way to make a good electrical
+contact and I put good electrical
+
+ align:start position:0%
+contact and I put good electrical
+ 
+
+ align:start position:0%
+contact and I put good electrical
+contact in quotes because it's it's
+
+ align:start position:0%
+contact in quotes because it's it's
+ 
+
+ align:start position:0%
+contact in quotes because it's it's
+somewhat uh you know nebulous but we'll
+
+ align:start position:0%
+somewhat uh you know nebulous but we'll
+ 
+
+ align:start position:0%
+somewhat uh you know nebulous but we'll
+see in in in this lecture what we mean
+
+ align:start position:0%
+see in in in this lecture what we mean
+ 
+
+ align:start position:0%
+see in in in this lecture what we mean
+by good electrical contact to doped
+
+ align:start position:0%
+by good electrical contact to doped
+ 
+
+ align:start position:0%
+by good electrical contact to doped
+regions and so this this lecture is kind
+
+ align:start position:0%
+regions and so this this lecture is kind
+ 
+
+ align:start position:0%
+regions and so this this lecture is kind
+of the first link to the backend
+
+ align:start position:0%
+of the first link to the backend
+ 
+
+ align:start position:0%
+of the first link to the backend
+technology course the contact itself is
+
+ align:start position:0%
+technology course the contact itself is
+ 
+
+ align:start position:0%
+technology course the contact itself is
+still generally considered part of the
+
+ align:start position:0%
+still generally considered part of the
+ 
+
+ align:start position:0%
+still generally considered part of the
+front end because you're contacting to
+
+ align:start position:0%
+front end because you're contacting to
+ 
+
+ align:start position:0%
+front end because you're contacting to
+silicon and then beyond that everything
+
+ align:start position:0%
+silicon and then beyond that everything
+ 
+
+ align:start position:0%
+silicon and then beyond that everything
+uh is in the 6.77 three which is the
+
+ align:start position:0%
+uh is in the 6.77 three which is the
+ 
+
+ align:start position:0%
+uh is in the 6.77 three which is the
+backend technology um this is just a
+
+ align:start position:0%
+backend technology um this is just a
+ 
+
+ align:start position:0%
+backend technology um this is just a
+schematic I've shown a couple of
+
+ align:start position:0%
+schematic I've shown a couple of
+ 
+
+ align:start position:0%
+schematic I've shown a couple of
+different times to point out to you what
+
+ align:start position:0%
+different times to point out to you what
+ 
+
+ align:start position:0%
+different times to point out to you what
+I mean by the contact you're familiar
+
+ align:start position:0%
+I mean by the contact you're familiar
+ 
+
+ align:start position:0%
+I mean by the contact you're familiar
+with this by now we have the Silicon
+
+ align:start position:0%
+with this by now we have the Silicon
+ 
+
+ align:start position:0%
+with this by now we have the Silicon
+source and the Silicon heavily dope
+
+ align:start position:0%
+source and the Silicon heavily dope
+ 
+
+ align:start position:0%
+source and the Silicon heavily dope
+drain uh here's the gate material and I
+
+ align:start position:0%
+drain uh here's the gate material and I
+ 
+
+ align:start position:0%
+drain uh here's the gate material and I
+need some way of of uh making a a
+
+ align:start position:0%
+need some way of of uh making a a
+ 
+
+ align:start position:0%
+need some way of of uh making a a
+contact between this electrical
+
+ align:start position:0%
+contact between this electrical
+ 
+
+ align:start position:0%
+contact between this electrical
+connection here this metal line uh and
+
+ align:start position:0%
+connection here this metal line uh and
+ 
+
+ align:start position:0%
+connection here this metal line uh and
+the Silicon itself and you can see that
+
+ align:start position:0%
+the Silicon itself and you can see that
+ 
+
+ align:start position:0%
+the Silicon itself and you can see that
+can consist of several different
+
+ align:start position:0%
+can consist of several different
+ 
+
+ align:start position:0%
+can consist of several different
+materials uh in this particular picture
+
+ align:start position:0%
+materials uh in this particular picture
+ 
+
+ align:start position:0%
+materials uh in this particular picture
+these dark uh sort of dark regions um
+
+ align:start position:0%
+these dark uh sort of dark regions um
+ 
+
+ align:start position:0%
+these dark uh sort of dark regions um
+contacting the Silicon are going to be
+
+ align:start position:0%
+contacting the Silicon are going to be
+ 
+
+ align:start position:0%
+contacting the Silicon are going to be
+made of pilicide and we'll talk today
+
+ align:start position:0%
+made of pilicide and we'll talk today
+ 
+
+ align:start position:0%
+made of pilicide and we'll talk today
+about how you fabricate those pilicides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let me also I want to talk about
+
+ align:start position:0%
+um let me also I want to talk about
+ 
+
+ align:start position:0%
+um let me also I want to talk about
+local interconnects sometimes the
+
+ align:start position:0%
+local interconnects sometimes the
+ 
+
+ align:start position:0%
+local interconnects sometimes the
+contacts themselves are also used for
+
+ align:start position:0%
+contacts themselves are also used for
+ 
+
+ align:start position:0%
+contacts themselves are also used for
+something called local interconnect and
+
+ align:start position:0%
+something called local interconnect and
+ 
+
+ align:start position:0%
+something called local interconnect and
+I should point out here this is an
+
+ align:start position:0%
+I should point out here this is an
+ 
+
+ align:start position:0%
+I should point out here this is an
+example of a local interconnect um you
+
+ align:start position:0%
+example of a local interconnect um you
+ 
+
+ align:start position:0%
+example of a local interconnect um you
+know where I've I've got uh a contact
+
+ align:start position:0%
+know where I've I've got uh a contact
+ 
+
+ align:start position:0%
+know where I've I've got uh a contact
+region that is being used to
+
+ align:start position:0%
+region that is being used to
+ 
+
+ align:start position:0%
+region that is being used to
+interconnect from one layer to the next
+
+ align:start position:0%
+interconnect from one layer to the next
+ 
+
+ align:start position:0%
+interconnect from one layer to the next
+or locally from uh one part of the
+
+ align:start position:0%
+or locally from uh one part of the
+ 
+
+ align:start position:0%
+or locally from uh one part of the
+device to a neighboring device but not
+
+ align:start position:0%
+device to a neighboring device but not
+ 
+
+ align:start position:0%
+device to a neighboring device but not
+across the whole chip these are called
+
+ align:start position:0%
+across the whole chip these are called
+ 
+
+ align:start position:0%
+across the whole chip these are called
+Global interconnects because these wires
+
+ align:start position:0%
+Global interconnects because these wires
+ 
+
+ align:start position:0%
+Global interconnects because these wires
+go potentially across the entire chip up
+
+ align:start position:0%
+go potentially across the entire chip up
+ 
+
+ align:start position:0%
+go potentially across the entire chip up
+here but this this is a a local
+
+ align:start position:0%
+here but this this is a a local
+ 
+
+ align:start position:0%
+here but this this is a a local
+interconnect it only extends over a very
+
+ align:start position:0%
+interconnect it only extends over a very
+ 
+
+ align:start position:0%
+interconnect it only extends over a very
+small
+
+ align:start position:0%
+small
+ 
+
+ align:start position:0%
+small
+distance in fact on slide number two of
+
+ align:start position:0%
+distance in fact on slide number two of
+ 
+
+ align:start position:0%
+distance in fact on slide number two of
+your handout I've got an example of a
+
+ align:start position:0%
+your handout I've got an example of a
+ 
+
+ align:start position:0%
+your handout I've got an example of a
+local interconnect and and what it might
+
+ align:start position:0%
+local interconnect and and what it might
+ 
+
+ align:start position:0%
+local interconnect and and what it might
+uh uh might consist of this is just the
+
+ align:start position:0%
+uh uh might consist of this is just the
+ 
+
+ align:start position:0%
+uh uh might consist of this is just the
+circuit schematic if you have taken uh
+
+ align:start position:0%
+circuit schematic if you have taken uh
+ 
+
+ align:start position:0%
+circuit schematic if you have taken uh
+electrical engineering course as you
+
+ align:start position:0%
+electrical engineering course as you
+ 
+
+ align:start position:0%
+electrical engineering course as you
+know this is a bipolar transistor with
+
+ align:start position:0%
+know this is a bipolar transistor with
+ 
+
+ align:start position:0%
+know this is a bipolar transistor with
+the base and the emitter this little
+
+ align:start position:0%
+the base and the emitter this little
+ 
+
+ align:start position:0%
+the base and the emitter this little
+arrow represents the emitter region and
+
+ align:start position:0%
+arrow represents the emitter region and
+ 
+
+ align:start position:0%
+arrow represents the emitter region and
+you see in this circuit schematic that
+
+ align:start position:0%
+you see in this circuit schematic that
+ 
+
+ align:start position:0%
+you see in this circuit schematic that
+the emitter of this transistor is
+
+ align:start position:0%
+the emitter of this transistor is
+ 
+
+ align:start position:0%
+the emitter of this transistor is
+connected by a wire to a resistor
+
+ align:start position:0%
+connected by a wire to a resistor
+ 
+
+ align:start position:0%
+connected by a wire to a resistor
+R uh well this is the circuit schematic
+
+ align:start position:0%
+R uh well this is the circuit schematic
+ 
+
+ align:start position:0%
+R uh well this is the circuit schematic
+and below is the actual implementation
+
+ align:start position:0%
+and below is the actual implementation
+ 
+
+ align:start position:0%
+and below is the actual implementation
+of this circuit in Silicon uh and in
+
+ align:start position:0%
+of this circuit in Silicon uh and in
+ 
+
+ align:start position:0%
+of this circuit in Silicon uh and in
+fact we if you recognize the you know
+
+ align:start position:0%
+fact we if you recognize the you know
+ 
+
+ align:start position:0%
+fact we if you recognize the you know
+that this is an npn device and this
+
+ align:start position:0%
+that this is an npn device and this
+ 
+
+ align:start position:0%
+that this is an npn device and this
+little n region right here is the
+
+ align:start position:0%
+little n region right here is the
+ 
+
+ align:start position:0%
+little n region right here is the
+emitter this is the p type base shown
+
+ align:start position:0%
+emitter this is the p type base shown
+ 
+
+ align:start position:0%
+emitter this is the p type base shown
+here in in red and this is the n type
+
+ align:start position:0%
+here in in red and this is the n type
+ 
+
+ align:start position:0%
+here in in red and this is the n type
+collector and what you see here is this
+
+ align:start position:0%
+collector and what you see here is this
+ 
+
+ align:start position:0%
+collector and what you see here is this
+emitter region has a a w has a um a
+
+ align:start position:0%
+emitter region has a a w has a um a
+ 
+
+ align:start position:0%
+emitter region has a a w has a um a
+metal contact to it and it is connected
+
+ align:start position:0%
+metal contact to it and it is connected
+ 
+
+ align:start position:0%
+metal contact to it and it is connected
+locally to this ptype tub region which
+
+ align:start position:0%
+locally to this ptype tub region which
+ 
+
+ align:start position:0%
+locally to this ptype tub region which
+is in fact a resistor this is a resistor
+
+ align:start position:0%
+is in fact a resistor this is a resistor
+ 
+
+ align:start position:0%
+is in fact a resistor this is a resistor
+because the current can flow from this
+
+ align:start position:0%
+because the current can flow from this
+ 
+
+ align:start position:0%
+because the current can flow from this
+metal uh contact here through the the
+
+ align:start position:0%
+metal uh contact here through the the
+ 
+
+ align:start position:0%
+metal uh contact here through the the
+ptype region has a certain sheet
+
+ align:start position:0%
+ptype region has a certain sheet
+ 
+
+ align:start position:0%
+ptype region has a certain sheet
+resistance or a certain resistance and
+
+ align:start position:0%
+resistance or a certain resistance and
+ 
+
+ align:start position:0%
+resistance or a certain resistance and
+out this other end so this is sort of an
+
+ align:start position:0%
+out this other end so this is sort of an
+ 
+
+ align:start position:0%
+out this other end so this is sort of an
+example example of using a a very short
+
+ align:start position:0%
+example example of using a a very short
+ 
+
+ align:start position:0%
+example example of using a a very short
+metal wire could might even end up being
+
+ align:start position:0%
+metal wire could might even end up being
+ 
+
+ align:start position:0%
+metal wire could might even end up being
+suicide or something having a very short
+
+ align:start position:0%
+suicide or something having a very short
+ 
+
+ align:start position:0%
+suicide or something having a very short
+metal wire locally on the chip to do
+
+ align:start position:0%
+metal wire locally on the chip to do
+ 
+
+ align:start position:0%
+metal wire locally on the chip to do
+interconnect from say uh one neighboring
+
+ align:start position:0%
+interconnect from say uh one neighboring
+ 
+
+ align:start position:0%
+interconnect from say uh one neighboring
+device in this case a transistor to
+
+ align:start position:0%
+device in this case a transistor to
+ 
+
+ align:start position:0%
+device in this case a transistor to
+another neighboring device uh a resistor
+
+ align:start position:0%
+another neighboring device uh a resistor
+ 
+
+ align:start position:0%
+another neighboring device uh a resistor
+um so that's what we mean by local
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interconnect talk a little bit about
+
+ align:start position:0%
+interconnect talk a little bit about
+ 
+
+ align:start position:0%
+interconnect talk a little bit about
+historically about how contacts were
+
+ align:start position:0%
+historically about how contacts were
+ 
+
+ align:start position:0%
+historically about how contacts were
+made and this is shown on slide three um
+
+ align:start position:0%
+made and this is shown on slide three um
+ 
+
+ align:start position:0%
+made and this is shown on slide three um
+in the early days if this was uh the
+
+ align:start position:0%
+in the early days if this was uh the
+ 
+
+ align:start position:0%
+in the early days if this was uh the
+brain or the source of a of a transistor
+
+ align:start position:0%
+brain or the source of a of a transistor
+ 
+
+ align:start position:0%
+brain or the source of a of a transistor
+a moset uh we simply people simply use
+
+ align:start position:0%
+a moset uh we simply people simply use
+ 
+
+ align:start position:0%
+a moset uh we simply people simply use
+aluminum which was the metal of choice
+
+ align:start position:0%
+aluminum which was the metal of choice
+ 
+
+ align:start position:0%
+aluminum which was the metal of choice
+directly on Silicon to make both the
+
+ align:start position:0%
+directly on Silicon to make both the
+ 
+
+ align:start position:0%
+directly on Silicon to make both the
+contact and the interconnect material so
+
+ align:start position:0%
+contact and the interconnect material so
+ 
+
+ align:start position:0%
+contact and the interconnect material so
+it was convenient you could contact the
+
+ align:start position:0%
+it was convenient you could contact the
+ 
+
+ align:start position:0%
+it was convenient you could contact the
+Silicon with aluminum and then you could
+
+ align:start position:0%
+Silicon with aluminum and then you could
+ 
+
+ align:start position:0%
+Silicon with aluminum and then you could
+run wires along the Chip And That Could
+
+ align:start position:0%
+run wires along the Chip And That Could
+ 
+
+ align:start position:0%
+run wires along the Chip And That Could
+interconnect the various
+
+ align:start position:0%
+interconnect the various
+ 
+
+ align:start position:0%
+interconnect the various
+devices the advantages of aluminum has a
+
+ align:start position:0%
+devices the advantages of aluminum has a
+ 
+
+ align:start position:0%
+devices the advantages of aluminum has a
+low resistivity it's the second lowest
+
+ align:start position:0%
+low resistivity it's the second lowest
+ 
+
+ align:start position:0%
+low resistivity it's the second lowest
+of all the metal candidates copper being
+
+ align:start position:0%
+of all the metal candidates copper being
+ 
+
+ align:start position:0%
+of all the metal candidates copper being
+the lowest um and it it has very good
+
+ align:start position:0%
+the lowest um and it it has very good
+ 
+
+ align:start position:0%
+the lowest um and it it has very good
+adhesion to silicon and to silicon
+
+ align:start position:0%
+adhesion to silicon and to silicon
+ 
+
+ align:start position:0%
+adhesion to silicon and to silicon
+dioxide uh it's a very stable metal and
+
+ align:start position:0%
+dioxide uh it's a very stable metal and
+ 
+
+ align:start position:0%
+dioxide uh it's a very stable metal and
+it makes good electrical contact to
+
+ align:start position:0%
+it makes good electrical contact to
+ 
+
+ align:start position:0%
+it makes good electrical contact to
+heavily doped silicon as long as the
+
+ align:start position:0%
+heavily doped silicon as long as the
+ 
+
+ align:start position:0%
+heavily doped silicon as long as the
+Silicon is heavily
+
+ align:start position:0%
+Silicon is heavily
+ 
+
+ align:start position:0%
+Silicon is heavily
+doped why why does it do that well
+
+ align:start position:0%
+doped why why does it do that well
+ 
+
+ align:start position:0%
+doped why why does it do that well
+aluminum tends to reduce any native
+
+ align:start position:0%
+aluminum tends to reduce any native
+ 
+
+ align:start position:0%
+aluminum tends to reduce any native
+oxide present on Silicon you know if you
+
+ align:start position:0%
+oxide present on Silicon you know if you
+ 
+
+ align:start position:0%
+oxide present on Silicon you know if you
+take a silicon wafer and you do an HF
+
+ align:start position:0%
+take a silicon wafer and you do an HF
+ 
+
+ align:start position:0%
+take a silicon wafer and you do an HF
+dip you'll get rid of any native oxide
+
+ align:start position:0%
+dip you'll get rid of any native oxide
+ 
+
+ align:start position:0%
+dip you'll get rid of any native oxide
+but if you let it sit for any period a
+
+ align:start position:0%
+but if you let it sit for any period a
+ 
+
+ align:start position:0%
+but if you let it sit for any period a
+few minutes an hour or so you grow a a
+
+ align:start position:0%
+few minutes an hour or so you grow a a
+ 
+
+ align:start position:0%
+few minutes an hour or so you grow a a
+thin natural native oxide S2 at room
+
+ align:start position:0%
+thin natural native oxide S2 at room
+ 
+
+ align:start position:0%
+thin natural native oxide S2 at room
+temperature on Silicon mainly be about
+
+ align:start position:0%
+temperature on Silicon mainly be about
+ 
+
+ align:start position:0%
+temperature on Silicon mainly be about
+10 anstrom thick but it's still there
+
+ align:start position:0%
+10 anstrom thick but it's still there
+ 
+
+ align:start position:0%
+10 anstrom thick but it's still there
+the nice thing about aluminum is that it
+
+ align:start position:0%
+the nice thing about aluminum is that it
+ 
+
+ align:start position:0%
+the nice thing about aluminum is that it
+tends to reduce or or eat up that oxide
+
+ align:start position:0%
+tends to reduce or or eat up that oxide
+ 
+
+ align:start position:0%
+tends to reduce or or eat up that oxide
+uh on the silicon and it forms a very
+
+ align:start position:0%
+uh on the silicon and it forms a very
+ 
+
+ align:start position:0%
+uh on the silicon and it forms a very
+thin layer of
+
+ align:start position:0%
+thin layer of
+ 
+
+ align:start position:0%
+thin layer of
+al203 but this layer is quite thin and
+
+ align:start position:0%
+al203 but this layer is quite thin and
+ 
+
+ align:start position:0%
+al203 but this layer is quite thin and
+the aluminum itself can diffuse right
+
+ align:start position:0%
+the aluminum itself can diffuse right
+ 
+
+ align:start position:0%
+the aluminum itself can diffuse right
+through it so this enables you to form a
+
+ align:start position:0%
+through it so this enables you to form a
+ 
+
+ align:start position:0%
+through it so this enables you to form a
+very good Electrical uh contact without
+
+ align:start position:0%
+very good Electrical uh contact without
+ 
+
+ align:start position:0%
+very good Electrical uh contact without
+having an intervening layer of of oxide
+
+ align:start position:0%
+having an intervening layer of of oxide
+ 
+
+ align:start position:0%
+having an intervening layer of of oxide
+uh some metals you might put down and um
+
+ align:start position:0%
+uh some metals you might put down and um
+ 
+
+ align:start position:0%
+uh some metals you might put down and um
+they won't eat through them the the
+
+ align:start position:0%
+they won't eat through them the the
+ 
+
+ align:start position:0%
+they won't eat through them the the
+Silicon native oxide the S2 and then
+
+ align:start position:0%
+Silicon native oxide the S2 and then
+ 
+
+ align:start position:0%
+Silicon native oxide the S2 and then
+they'll just be sitting there and you
+
+ align:start position:0%
+they'll just be sitting there and you
+ 
+
+ align:start position:0%
+they'll just be sitting there and you
+won't get a good electrical contact L
+
+ align:start position:0%
+won't get a good electrical contact L
+ 
+
+ align:start position:0%
+won't get a good electrical contact L
+has this property that eats through that
+
+ align:start position:0%
+has this property that eats through that
+ 
+
+ align:start position:0%
+has this property that eats through that
+little native oxide uh so you get a good
+
+ align:start position:0%
+little native oxide uh so you get a good
+ 
+
+ align:start position:0%
+little native oxide uh so you get a good
+um a good contact so it was a convenient
+
+ align:start position:0%
+um a good contact so it was a convenient
+ 
+
+ align:start position:0%
+um a good contact so it was a convenient
+uh and a good material for people to use
+
+ align:start position:0%
+uh and a good material for people to use
+ 
+
+ align:start position:0%
+uh and a good material for people to use
+for many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+years slide four just shows you some of
+
+ align:start position:0%
+years slide four just shows you some of
+ 
+
+ align:start position:0%
+years slide four just shows you some of
+the basic properties of interconnect
+
+ align:start position:0%
+the basic properties of interconnect
+ 
+
+ align:start position:0%
+the basic properties of interconnect
+materials just so you get oriented
+
+ align:start position:0%
+materials just so you get oriented
+ 
+
+ align:start position:0%
+materials just so you get oriented
+um here is aluminum on the top again one
+
+ align:start position:0%
+um here is aluminum on the top again one
+ 
+
+ align:start position:0%
+um here is aluminum on the top again one
+of the most popular for many years the
+
+ align:start position:0%
+of the most popular for many years the
+ 
+
+ align:start position:0%
+of the most popular for many years the
+resistivity is listed in the second
+
+ align:start position:0%
+resistivity is listed in the second
+ 
+
+ align:start position:0%
+resistivity is listed in the second
+column somewhere around 2.7 to3 micro
+
+ align:start position:0%
+column somewhere around 2.7 to3 micro
+ 
+
+ align:start position:0%
+column somewhere around 2.7 to3 micro
+ohm centimeter for the resistivity again
+
+ align:start position:0%
+ohm centimeter for the resistivity again
+ 
+
+ align:start position:0%
+ohm centimeter for the resistivity again
+the resistivity is is a property of the
+
+ align:start position:0%
+the resistivity is is a property of the
+ 
+
+ align:start position:0%
+the resistivity is is a property of the
+material uh and this show the the last
+
+ align:start position:0%
+material uh and this show the the last
+ 
+
+ align:start position:0%
+material uh and this show the the last
+column shows the melting point so it is
+
+ align:start position:0%
+column shows the melting point so it is
+ 
+
+ align:start position:0%
+column shows the melting point so it is
+a low melting point
+
+ align:start position:0%
+a low melting point
+ 
+
+ align:start position:0%
+a low melting point
+material um the only other metal of
+
+ align:start position:0%
+material um the only other metal of
+ 
+
+ align:start position:0%
+material um the only other metal of
+consequence that has a low resistivity
+
+ align:start position:0%
+consequence that has a low resistivity
+ 
+
+ align:start position:0%
+consequence that has a low resistivity
+is copper which is shown here the third
+
+ align:start position:0%
+is copper which is shown here the third
+ 
+
+ align:start position:0%
+is copper which is shown here the third
+one uh the third row uh that's about 1.7
+
+ align:start position:0%
+one uh the third row uh that's about 1.7
+ 
+
+ align:start position:0%
+one uh the third row uh that's about 1.7
+to2 two micro centimeter copper has a
+
+ align:start position:0%
+to2 two micro centimeter copper has a
+ 
+
+ align:start position:0%
+to2 two micro centimeter copper has a
+much higher melting point copper has
+
+ align:start position:0%
+much higher melting point copper has
+ 
+
+ align:start position:0%
+much higher melting point copper has
+other difficulties associated with its
+
+ align:start position:0%
+other difficulties associated with its
+ 
+
+ align:start position:0%
+other difficulties associated with its
+integration uh copper if it gets into
+
+ align:start position:0%
+integration uh copper if it gets into
+ 
+
+ align:start position:0%
+integration uh copper if it gets into
+silicon can be a deep level so it can
+
+ align:start position:0%
+silicon can be a deep level so it can
+ 
+
+ align:start position:0%
+silicon can be a deep level so it can
+cause lifetime problems um copper
+
+ align:start position:0%
+cause lifetime problems um copper
+ 
+
+ align:start position:0%
+cause lifetime problems um copper
+oxidizes very readily even at room
+
+ align:start position:0%
+oxidizes very readily even at room
+ 
+
+ align:start position:0%
+oxidizes very readily even at room
+temperature so you need to protect it
+
+ align:start position:0%
+temperature so you need to protect it
+ 
+
+ align:start position:0%
+temperature so you need to protect it
+you you've um you're all aware of that
+
+ align:start position:0%
+you you've um you're all aware of that
+ 
+
+ align:start position:0%
+you you've um you're all aware of that
+uh and copper is more difficult to
+
+ align:start position:0%
+uh and copper is more difficult to
+ 
+
+ align:start position:0%
+uh and copper is more difficult to
+deposit um than aluminum so uh but
+
+ align:start position:0%
+deposit um than aluminum so uh but
+ 
+
+ align:start position:0%
+deposit um than aluminum so uh but
+copper is the material of choice for
+
+ align:start position:0%
+copper is the material of choice for
+ 
+
+ align:start position:0%
+copper is the material of choice for
+today's interconnect I think I brought
+
+ align:start position:0%
+today's interconnect I think I brought
+ 
+
+ align:start position:0%
+today's interconnect I think I brought
+uh a wafer from Intel about halfway
+
+ align:start position:0%
+uh a wafer from Intel about halfway
+ 
+
+ align:start position:0%
+uh a wafer from Intel about halfway
+through the course a 12-in wafer and
+
+ align:start position:0%
+through the course a 12-in wafer and
+ 
+
+ align:start position:0%
+through the course a 12-in wafer and
+showed it to you and you notice it was
+
+ align:start position:0%
+showed it to you and you notice it was
+ 
+
+ align:start position:0%
+showed it to you and you notice it was
+all Co pretty copper colored it's
+
+ align:start position:0%
+all Co pretty copper colored it's
+ 
+
+ align:start position:0%
+all Co pretty copper colored it's
+because the the modern interconnect
+
+ align:start position:0%
+because the the modern interconnect
+ 
+
+ align:start position:0%
+because the the modern interconnect
+material is copper uh a few places are
+
+ align:start position:0%
+material is copper uh a few places are
+ 
+
+ align:start position:0%
+material is copper uh a few places are
+still using aluminum aluminum was
+
+ align:start position:0%
+still using aluminum aluminum was
+ 
+
+ align:start position:0%
+still using aluminum aluminum was
+historically what's used copper was
+
+ align:start position:0%
+historically what's used copper was
+ 
+
+ align:start position:0%
+historically what's used copper was
+introduced uh well in research in the
+
+ align:start position:0%
+introduced uh well in research in the
+ 
+
+ align:start position:0%
+introduced uh well in research in the
+mid 80s and in production about 10 years
+
+ align:start position:0%
+mid 80s and in production about 10 years
+ 
+
+ align:start position:0%
+mid 80s and in production about 10 years
+uh past
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh on slide four I'm showing um
+
+ align:start position:0%
+that uh on slide four I'm showing um
+ 
+
+ align:start position:0%
+that uh on slide four I'm showing um
+some basic physics that you may be may
+
+ align:start position:0%
+some basic physics that you may be may
+ 
+
+ align:start position:0%
+some basic physics that you may be may
+or may not be familiar with but you need
+
+ align:start position:0%
+or may not be familiar with but you need
+ 
+
+ align:start position:0%
+or may not be familiar with but you need
+to understand the basics of it in order
+
+ align:start position:0%
+to understand the basics of it in order
+ 
+
+ align:start position:0%
+to understand the basics of it in order
+to understand what we mean by a good
+
+ align:start position:0%
+to understand what we mean by a good
+ 
+
+ align:start position:0%
+to understand what we mean by a good
+electrical contact there um contacts can
+
+ align:start position:0%
+electrical contact there um contacts can
+ 
+
+ align:start position:0%
+electrical contact there um contacts can
+to to a semiconductor can be sort of
+
+ align:start position:0%
+to to a semiconductor can be sort of
+ 
+
+ align:start position:0%
+to to a semiconductor can be sort of
+divided into roughly two classes there's
+
+ align:start position:0%
+divided into roughly two classes there's
+ 
+
+ align:start position:0%
+divided into roughly two classes there's
+an OM contact and a shocky contact um a
+
+ align:start position:0%
+an OM contact and a shocky contact um a
+ 
+
+ align:start position:0%
+an OM contact and a shocky contact um a
+shocky contact is shown here and and if
+
+ align:start position:0%
+shocky contact is shown here and and if
+ 
+
+ align:start position:0%
+shocky contact is shown here and and if
+you just look at the current this this
+
+ align:start position:0%
+you just look at the current this this
+ 
+
+ align:start position:0%
+you just look at the current this this
+little uh schematic shows the current
+
+ align:start position:0%
+little uh schematic shows the current
+ 
+
+ align:start position:0%
+little uh schematic shows the current
+that flows in the device or through the
+
+ align:start position:0%
+that flows in the device or through the
+ 
+
+ align:start position:0%
+that flows in the device or through the
+device as a function of the voltage that
+
+ align:start position:0%
+device as a function of the voltage that
+ 
+
+ align:start position:0%
+device as a function of the voltage that
+you apply shocky contact is is a
+
+ align:start position:0%
+you apply shocky contact is is a
+ 
+
+ align:start position:0%
+you apply shocky contact is is a
+rectifier um it is uh when you apply a
+
+ align:start position:0%
+rectifier um it is uh when you apply a
+ 
+
+ align:start position:0%
+rectifier um it is uh when you apply a
+large voltage in One Direction the
+
+ align:start position:0%
+large voltage in One Direction the
+ 
+
+ align:start position:0%
+large voltage in One Direction the
+reverse Direction not much current flows
+
+ align:start position:0%
+reverse Direction not much current flows
+ 
+
+ align:start position:0%
+reverse Direction not much current flows
+so that's not a very useful way to make
+
+ align:start position:0%
+so that's not a very useful way to make
+ 
+
+ align:start position:0%
+so that's not a very useful way to make
+a a contact to a device if you apply a
+
+ align:start position:0%
+a a contact to a device if you apply a
+ 
+
+ align:start position:0%
+a a contact to a device if you apply a
+small voltage the other direction you
+
+ align:start position:0%
+small voltage the other direction you
+ 
+
+ align:start position:0%
+small voltage the other direction you
+get a little current and then you apply
+
+ align:start position:0%
+get a little current and then you apply
+ 
+
+ align:start position:0%
+get a little current and then you apply
+above a certain threshold voltage and
+
+ align:start position:0%
+above a certain threshold voltage and
+ 
+
+ align:start position:0%
+above a certain threshold voltage and
+you get a lot of current um it's
+
+ align:start position:0%
+you get a lot of current um it's
+ 
+
+ align:start position:0%
+you get a lot of current um it's
+basically a
+
+ align:start position:0%
+basically a
+ 
+
+ align:start position:0%
+basically a
+diode and um you uh the current
+
+ align:start position:0%
+diode and um you uh the current
+ 
+
+ align:start position:0%
+diode and um you uh the current
+transport is by the sort of thermionic
+
+ align:start position:0%
+transport is by the sort of thermionic
+ 
+
+ align:start position:0%
+transport is by the sort of thermionic
+or thermal emission over this barrier uh
+
+ align:start position:0%
+or thermal emission over this barrier uh
+ 
+
+ align:start position:0%
+or thermal emission over this barrier uh
+so this is not considered consider
+
+ align:start position:0%
+so this is not considered consider
+ 
+
+ align:start position:0%
+so this is not considered consider
+desirable for making a good contact UM
+
+ align:start position:0%
+desirable for making a good contact UM
+ 
+
+ align:start position:0%
+desirable for making a good contact UM
+an OM contact uh on the other side or a
+
+ align:start position:0%
+an OM contact uh on the other side or a
+ 
+
+ align:start position:0%
+an OM contact uh on the other side or a
+tunneling contact uh occurs when you can
+
+ align:start position:0%
+tunneling contact uh occurs when you can
+ 
+
+ align:start position:0%
+tunneling contact uh occurs when you can
+actually Tunnel right through this
+
+ align:start position:0%
+actually Tunnel right through this
+ 
+
+ align:start position:0%
+actually Tunnel right through this
+barrier the barrier is so thin um that
+
+ align:start position:0%
+barrier the barrier is so thin um that
+ 
+
+ align:start position:0%
+barrier the barrier is so thin um that
+you can actually Tunnel right through it
+
+ align:start position:0%
+you can actually Tunnel right through it
+ 
+
+ align:start position:0%
+you can actually Tunnel right through it
+the depletion region is very uh very
+
+ align:start position:0%
+the depletion region is very uh very
+ 
+
+ align:start position:0%
+the depletion region is very uh very
+thin and um if you do high make high
+
+ align:start position:0%
+thin and um if you do high make high
+ 
+
+ align:start position:0%
+thin and um if you do high make high
+doping right near the metal you you can
+
+ align:start position:0%
+doping right near the metal you you can
+ 
+
+ align:start position:0%
+doping right near the metal you you can
+uh reduce this depletion layer width and
+
+ align:start position:0%
+uh reduce this depletion layer width and
+ 
+
+ align:start position:0%
+uh reduce this depletion layer width and
+you enables this tunneling and so if you
+
+ align:start position:0%
+you enables this tunneling and so if you
+ 
+
+ align:start position:0%
+you enables this tunneling and so if you
+look at the current voltage
+
+ align:start position:0%
+look at the current voltage
+ 
+
+ align:start position:0%
+look at the current voltage
+characteristics so current plotted on
+
+ align:start position:0%
+characteristics so current plotted on
+ 
+
+ align:start position:0%
+characteristics so current plotted on
+the Y axis voltage on the x-axis you see
+
+ align:start position:0%
+the Y axis voltage on the x-axis you see
+ 
+
+ align:start position:0%
+the Y axis voltage on the x-axis you see
+it's very symmetrical and you get a very
+
+ align:start position:0%
+it's very symmetrical and you get a very
+ 
+
+ align:start position:0%
+it's very symmetrical and you get a very
+very high current for a very small
+
+ align:start position:0%
+very high current for a very small
+ 
+
+ align:start position:0%
+very high current for a very small
+voltage in either direction so this is
+
+ align:start position:0%
+voltage in either direction so this is
+ 
+
+ align:start position:0%
+voltage in either direction so this is
+considered desirable this is what we
+
+ align:start position:0%
+considered desirable this is what we
+ 
+
+ align:start position:0%
+considered desirable this is what we
+want we want that om contact uh and it
+
+ align:start position:0%
+want we want that om contact uh and it
+ 
+
+ align:start position:0%
+want we want that om contact uh and it
+tends to happen uh particularly with
+
+ align:start position:0%
+tends to happen uh particularly with
+ 
+
+ align:start position:0%
+tends to happen uh particularly with
+aluminum and most metals if you make the
+
+ align:start position:0%
+aluminum and most metals if you make the
+ 
+
+ align:start position:0%
+aluminum and most metals if you make the
+Surface doping uh very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+high a concept that we want to talk
+
+ align:start position:0%
+high a concept that we want to talk
+ 
+
+ align:start position:0%
+high a concept that we want to talk
+about H is shown here on slide six it's
+
+ align:start position:0%
+about H is shown here on slide six it's
+ 
+
+ align:start position:0%
+about H is shown here on slide six it's
+called the specific contact resistivity
+
+ align:start position:0%
+called the specific contact resistivity
+ 
+
+ align:start position:0%
+called the specific contact resistivity
+and we usually use the Greek letter row
+
+ align:start position:0%
+and we usually use the Greek letter row
+ 
+
+ align:start position:0%
+and we usually use the Greek letter row
+subc um the definition of it is is given
+
+ align:start position:0%
+subc um the definition of it is is given
+ 
+
+ align:start position:0%
+subc um the definition of it is is given
+here it's it's defined as being
+
+ align:start position:0%
+here it's it's defined as being
+ 
+
+ align:start position:0%
+here it's it's defined as being
+equivalent to the derivative of the
+
+ align:start position:0%
+equivalent to the derivative of the
+ 
+
+ align:start position:0%
+equivalent to the derivative of the
+voltage Uh current density
+
+ align:start position:0%
+voltage Uh current density
+ 
+
+ align:start position:0%
+voltage Uh current density
+characteristics at a metal semiconductor
+
+ align:start position:0%
+characteristics at a metal semiconductor
+ 
+
+ align:start position:0%
+characteristics at a metal semiconductor
+contact so it's partial V the voltage by
+
+ align:start position:0%
+contact so it's partial V the voltage by
+ 
+
+ align:start position:0%
+contact so it's partial V the voltage by
+partial J um basically um and so um
+
+ align:start position:0%
+partial J um basically um and so um
+ 
+
+ align:start position:0%
+partial J um basically um and so um
+we're uh for we usually assume a
+
+ align:start position:0%
+we're uh for we usually assume a
+ 
+
+ align:start position:0%
+we're uh for we usually assume a
+structure where the current density is
+
+ align:start position:0%
+structure where the current density is
+ 
+
+ align:start position:0%
+structure where the current density is
+uniform across some contact area um then
+
+ align:start position:0%
+uniform across some contact area um then
+ 
+
+ align:start position:0%
+uniform across some contact area um then
+you can calculate the contact resistance
+
+ align:start position:0%
+you can calculate the contact resistance
+ 
+
+ align:start position:0%
+you can calculate the contact resistance
+R in ohms so R would have the units of
+
+ align:start position:0%
+R in ohms so R would have the units of
+ 
+
+ align:start position:0%
+R in ohms so R would have the units of
+ohms uh from the specific contact
+
+ align:start position:0%
+ohms uh from the specific contact
+ 
+
+ align:start position:0%
+ohms uh from the specific contact
+resistivity by the following equation
+
+ align:start position:0%
+resistivity by the following equation
+ 
+
+ align:start position:0%
+resistivity by the following equation
+the resistance of a given contact in
+
+ align:start position:0%
+the resistance of a given contact in
+ 
+
+ align:start position:0%
+the resistance of a given contact in
+ohms is just the voltage divided by the
+
+ align:start position:0%
+ohms is just the voltage divided by the
+ 
+
+ align:start position:0%
+ohms is just the voltage divided by the
+current flowing through that that
+
+ align:start position:0%
+current flowing through that that
+ 
+
+ align:start position:0%
+current flowing through that that
+contact and you can calculate it by row
+
+ align:start position:0%
+contact and you can calculate it by row
+ 
+
+ align:start position:0%
+contact and you can calculate it by row
+subc which typically has units of ohm
+
+ align:start position:0%
+subc which typically has units of ohm
+ 
+
+ align:start position:0%
+subc which typically has units of ohm
+centimet squared or ohm Micron squared
+
+ align:start position:0%
+centimet squared or ohm Micron squared
+ 
+
+ align:start position:0%
+centimet squared or ohm Micron squared
+so it's got a units of resistance times
+
+ align:start position:0%
+so it's got a units of resistance times
+ 
+
+ align:start position:0%
+so it's got a units of resistance times
+an area and divided by the area of the
+
+ align:start position:0%
+an area and divided by the area of the
+ 
+
+ align:start position:0%
+an area and divided by the area of the
+contract contact so if someone tells you
+
+ align:start position:0%
+contract contact so if someone tells you
+ 
+
+ align:start position:0%
+contract contact so if someone tells you
+oh I've made a contact that has a
+
+ align:start position:0%
+oh I've made a contact that has a
+ 
+
+ align:start position:0%
+oh I've made a contact that has a
+certain contact specific contact
+
+ align:start position:0%
+certain contact specific contact
+ 
+
+ align:start position:0%
+certain contact specific contact
+resistivity uh 10us 7 ohm cmet squared
+
+ align:start position:0%
+resistivity uh 10us 7 ohm cmet squared
+ 
+
+ align:start position:0%
+resistivity uh 10us 7 ohm cmet squared
+then you can design your contact
+
+ align:start position:0%
+then you can design your contact
+ 
+
+ align:start position:0%
+then you can design your contact
+area as you need to to get the right to
+
+ align:start position:0%
+area as you need to to get the right to
+ 
+
+ align:start position:0%
+area as you need to to get the right to
+get the right contact resistance in ohms
+
+ align:start position:0%
+get the right contact resistance in ohms
+ 
+
+ align:start position:0%
+get the right contact resistance in ohms
+um and basically what this tells you is
+
+ align:start position:0%
+um and basically what this tells you is
+ 
+
+ align:start position:0%
+um and basically what this tells you is
+and you notice you it's uh the total
+
+ align:start position:0%
+and you notice you it's uh the total
+ 
+
+ align:start position:0%
+and you notice you it's uh the total
+resistance of a contact in ohms is
+
+ align:start position:0%
+resistance of a contact in ohms is
+ 
+
+ align:start position:0%
+resistance of a contact in ohms is
+inversely proportional to area so if I
+
+ align:start position:0%
+inversely proportional to area so if I
+ 
+
+ align:start position:0%
+inversely proportional to area so if I
+make a smaller contact area for a given
+
+ align:start position:0%
+make a smaller contact area for a given
+ 
+
+ align:start position:0%
+make a smaller contact area for a given
+specific contact resistivity you're
+
+ align:start position:0%
+specific contact resistivity you're
+ 
+
+ align:start position:0%
+specific contact resistivity you're
+going to have a higher resistance and
+
+ align:start position:0%
+going to have a higher resistance and
+ 
+
+ align:start position:0%
+going to have a higher resistance and
+this is a problem if I'm scaling devices
+
+ align:start position:0%
+this is a problem if I'm scaling devices
+ 
+
+ align:start position:0%
+this is a problem if I'm scaling devices
+right I'm packing more and more devices
+
+ align:start position:0%
+right I'm packing more and more devices
+ 
+
+ align:start position:0%
+right I'm packing more and more devices
+on the chip it means I want to make the
+
+ align:start position:0%
+on the chip it means I want to make the
+ 
+
+ align:start position:0%
+on the chip it means I want to make the
+total area occupied by every device
+
+ align:start position:0%
+total area occupied by every device
+ 
+
+ align:start position:0%
+total area occupied by every device
+smaller that means I need to make the
+
+ align:start position:0%
+smaller that means I need to make the
+ 
+
+ align:start position:0%
+smaller that means I need to make the
+contact area smaller but if I leave the
+
+ align:start position:0%
+contact area smaller but if I leave the
+ 
+
+ align:start position:0%
+contact area smaller but if I leave the
+resist contact resistivity the same I
+
+ align:start position:0%
+resist contact resistivity the same I
+ 
+
+ align:start position:0%
+resist contact resistivity the same I
+don't do anything different about how I
+
+ align:start position:0%
+don't do anything different about how I
+ 
+
+ align:start position:0%
+don't do anything different about how I
+make the contact then as I'm scaling
+
+ align:start position:0%
+make the contact then as I'm scaling
+ 
+
+ align:start position:0%
+make the contact then as I'm scaling
+these devices of course the area of the
+
+ align:start position:0%
+these devices of course the area of the
+ 
+
+ align:start position:0%
+these devices of course the area of the
+contact is going down uh uh to make get
+
+ align:start position:0%
+contact is going down uh uh to make get
+ 
+
+ align:start position:0%
+contact is going down uh uh to make get
+more of these devices on the chip that
+
+ align:start position:0%
+more of these devices on the chip that
+ 
+
+ align:start position:0%
+more of these devices on the chip that
+means the
+
+ align:start position:0%
+means the
+ 
+
+ align:start position:0%
+means the
+resistance is good is going up uh as
+
+ align:start position:0%
+resistance is good is going up uh as
+ 
+
+ align:start position:0%
+resistance is good is going up uh as
+devices are scale and we'll we'll see
+
+ align:start position:0%
+devices are scale and we'll we'll see
+ 
+
+ align:start position:0%
+devices are scale and we'll we'll see
+some specific numbers um on the numbers
+
+ align:start position:0%
+some specific numbers um on the numbers
+ 
+
+ align:start position:0%
+some specific numbers um on the numbers
+on this this is a problem as we scale
+
+ align:start position:0%
+on this this is a problem as we scale
+ 
+
+ align:start position:0%
+on this this is a problem as we scale
+unless we scale row subc unless we do
+
+ align:start position:0%
+unless we scale row subc unless we do
+ 
+
+ align:start position:0%
+unless we scale row subc unless we do
+something to make better contacts as we
+
+ align:start position:0%
+something to make better contacts as we
+ 
+
+ align:start position:0%
+something to make better contacts as we
+scale devices just because of this
+
+ align:start position:0%
+scale devices just because of this
+ 
+
+ align:start position:0%
+scale devices just because of this
+geometric Factor as I make the area the
+
+ align:start position:0%
+geometric Factor as I make the area the
+ 
+
+ align:start position:0%
+geometric Factor as I make the area the
+current goes through smaller uh the
+
+ align:start position:0%
+current goes through smaller uh the
+ 
+
+ align:start position:0%
+current goes through smaller uh the
+resistance of that contact goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up um so the second type of contact
+
+ align:start position:0%
+up um so the second type of contact
+ 
+
+ align:start position:0%
+up um so the second type of contact
+again this is one that's not generally
+
+ align:start position:0%
+again this is one that's not generally
+ 
+
+ align:start position:0%
+again this is one that's not generally
+considered desirable but we need to
+
+ align:start position:0%
+considered desirable but we need to
+ 
+
+ align:start position:0%
+considered desirable but we need to
+understand a little the physics of it um
+
+ align:start position:0%
+understand a little the physics of it um
+ 
+
+ align:start position:0%
+understand a little the physics of it um
+is a shocky
+
+ align:start position:0%
+is a shocky
+ 
+
+ align:start position:0%
+is a shocky
+contact and that's uh the energy band
+
+ align:start position:0%
+contact and that's uh the energy band
+ 
+
+ align:start position:0%
+contact and that's uh the energy band
+diagram for that um is shown here where
+
+ align:start position:0%
+diagram for that um is shown here where
+ 
+
+ align:start position:0%
+diagram for that um is shown here where
+the metal is is is on the left and the
+
+ align:start position:0%
+the metal is is is on the left and the
+ 
+
+ align:start position:0%
+the metal is is is on the left and the
+semiconductor is on the
+
+ align:start position:0%
+semiconductor is on the
+ 
+
+ align:start position:0%
+semiconductor is on the
+right and uh a shocky contact is
+
+ align:start position:0%
+right and uh a shocky contact is
+ 
+
+ align:start position:0%
+right and uh a shocky contact is
+governed by thermionic emission so it's
+
+ align:start position:0%
+governed by thermionic emission so it's
+ 
+
+ align:start position:0%
+governed by thermionic emission so it's
+it's a thermo thermionic process
+
+ align:start position:0%
+it's a thermo thermionic process
+ 
+
+ align:start position:0%
+it's a thermo thermionic process
+emitting carriers over this
+
+ align:start position:0%
+emitting carriers over this
+ 
+
+ align:start position:0%
+emitting carriers over this
+barrier um and we know from the
+
+ align:start position:0%
+barrier um and we know from the
+ 
+
+ align:start position:0%
+barrier um and we know from the
+Richardson equation we can write
+
+ align:start position:0%
+Richardson equation we can write
+ 
+
+ align:start position:0%
+Richardson equation we can write
+thermionic emission current density J uh
+
+ align:start position:0%
+thermionic emission current density J uh
+ 
+
+ align:start position:0%
+thermionic emission current density J uh
+as being uh proportional to some the
+
+ align:start position:0%
+as being uh proportional to some the
+ 
+
+ align:start position:0%
+as being uh proportional to some the
+temperature squared some constant a star
+
+ align:start position:0%
+temperature squared some constant a star
+ 
+
+ align:start position:0%
+temperature squared some constant a star
+but most importantly it goes
+
+ align:start position:0%
+but most importantly it goes
+ 
+
+ align:start position:0%
+but most importantly it goes
+exponentially like the barrier height so
+
+ align:start position:0%
+exponentially like the barrier height so
+ 
+
+ align:start position:0%
+exponentially like the barrier height so
+it's e to the minus qfb over KT where
+
+ align:start position:0%
+it's e to the minus qfb over KT where
+ 
+
+ align:start position:0%
+it's e to the minus qfb over KT where
+the barrier height is is is just the um
+
+ align:start position:0%
+the barrier height is is is just the um
+ 
+
+ align:start position:0%
+the barrier height is is is just the um
+sort of the band bending it's this
+
+ align:start position:0%
+sort of the band bending it's this
+ 
+
+ align:start position:0%
+sort of the band bending it's this
+barrier uh between the fairy level in
+
+ align:start position:0%
+barrier uh between the fairy level in
+ 
+
+ align:start position:0%
+barrier uh between the fairy level in
+the semiconductor and the fmy level uh
+
+ align:start position:0%
+the semiconductor and the fmy level uh
+ 
+
+ align:start position:0%
+the semiconductor and the fmy level uh
+in in the metal um so that's going to
+
+ align:start position:0%
+in in the metal um so that's going to
+ 
+
+ align:start position:0%
+in in the metal um so that's going to
+tend to be a property of the doping in
+
+ align:start position:0%
+tend to be a property of the doping in
+ 
+
+ align:start position:0%
+tend to be a property of the doping in
+the semiconductor and what kind of metal
+
+ align:start position:0%
+the semiconductor and what kind of metal
+ 
+
+ align:start position:0%
+the semiconductor and what kind of metal
+you put on
+
+ align:start position:0%
+you put on
+ 
+
+ align:start position:0%
+you put on
+it uh so if we take this equation for
+
+ align:start position:0%
+it uh so if we take this equation for
+ 
+
+ align:start position:0%
+it uh so if we take this equation for
+this this current equation which we know
+
+ align:start position:0%
+this this current equation which we know
+ 
+
+ align:start position:0%
+this this current equation which we know
+the current voltage characteristic is
+
+ align:start position:0%
+the current voltage characteristic is
+ 
+
+ align:start position:0%
+the current voltage characteristic is
+exponential uh in in the applied voltage
+
+ align:start position:0%
+exponential uh in in the applied voltage
+ 
+
+ align:start position:0%
+exponential uh in in the applied voltage
+and we just uh use the cont the the
+
+ align:start position:0%
+and we just uh use the cont the the
+ 
+
+ align:start position:0%
+and we just uh use the cont the the
+definition of Ros Sub C you can
+
+ align:start position:0%
+definition of Ros Sub C you can
+ 
+
+ align:start position:0%
+definition of Ros Sub C you can
+calculate as show on the bottom here of
+
+ align:start position:0%
+calculate as show on the bottom here of
+ 
+
+ align:start position:0%
+calculate as show on the bottom here of
+of slide seven um what the specific
+
+ align:start position:0%
+of slide seven um what the specific
+ 
+
+ align:start position:0%
+of slide seven um what the specific
+contact resistivity should look like for
+
+ align:start position:0%
+contact resistivity should look like for
+ 
+
+ align:start position:0%
+contact resistivity should look like for
+a shocky barrier and you see it goes
+
+ align:start position:0%
+a shocky barrier and you see it goes
+ 
+
+ align:start position:0%
+a shocky barrier and you see it goes
+exponentially like the barrier height so
+
+ align:start position:0%
+exponentially like the barrier height so
+ 
+
+ align:start position:0%
+exponentially like the barrier height so
+we change that barrier height we can
+
+ align:start position:0%
+we change that barrier height we can
+ 
+
+ align:start position:0%
+we change that barrier height we can
+change uh row
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subc so what what we do in practice is
+
+ align:start position:0%
+subc so what what we do in practice is
+ 
+
+ align:start position:0%
+subc so what what we do in practice is
+um we uh we look at that equation and we
+
+ align:start position:0%
+um we uh we look at that equation and we
+ 
+
+ align:start position:0%
+um we uh we look at that equation and we
+try to get into a different regime
+
+ align:start position:0%
+try to get into a different regime
+ 
+
+ align:start position:0%
+try to get into a different regime
+instead of being in the regime where
+
+ align:start position:0%
+instead of being in the regime where
+ 
+
+ align:start position:0%
+instead of being in the regime where
+we're dominated by tunneling over this
+
+ align:start position:0%
+we're dominated by tunneling over this
+ 
+
+ align:start position:0%
+we're dominated by tunneling over this
+barrier by um thermionic emission rather
+
+ align:start position:0%
+barrier by um thermionic emission rather
+ 
+
+ align:start position:0%
+barrier by um thermionic emission rather
+excuse me over the barrier if we make
+
+ align:start position:0%
+excuse me over the barrier if we make
+ 
+
+ align:start position:0%
+excuse me over the barrier if we make
+the barrier distance really narrow you
+
+ align:start position:0%
+the barrier distance really narrow you
+ 
+
+ align:start position:0%
+the barrier distance really narrow you
+know uh really small you know from your
+
+ align:start position:0%
+know uh really small you know from your
+ 
+
+ align:start position:0%
+know uh really small you know from your
+quantum mechanics classes that you can
+
+ align:start position:0%
+quantum mechanics classes that you can
+ 
+
+ align:start position:0%
+quantum mechanics classes that you can
+actually get quantum mechanical
+
+ align:start position:0%
+actually get quantum mechanical
+ 
+
+ align:start position:0%
+actually get quantum mechanical
+tunneling through the
+
+ align:start position:0%
+tunneling through the
+ 
+
+ align:start position:0%
+tunneling through the
+barrier so here on slide eight what I've
+
+ align:start position:0%
+barrier so here on slide eight what I've
+ 
+
+ align:start position:0%
+barrier so here on slide eight what I've
+shown is a tunneling Contex it's a
+
+ align:start position:0%
+shown is a tunneling Contex it's a
+ 
+
+ align:start position:0%
+shown is a tunneling Contex it's a
+shocky contact in the limit of very very
+
+ align:start position:0%
+shocky contact in the limit of very very
+ 
+
+ align:start position:0%
+shocky contact in the limit of very very
+high doping um so we form you see we
+
+ align:start position:0%
+high doping um so we form you see we
+ 
+
+ align:start position:0%
+high doping um so we form you see we
+still have this barrier 5B um but the
+
+ align:start position:0%
+still have this barrier 5B um but the
+ 
+
+ align:start position:0%
+still have this barrier 5B um but the
+distance the depletion layer thickness
+
+ align:start position:0%
+distance the depletion layer thickness
+ 
+
+ align:start position:0%
+distance the depletion layer thickness
+in the semiconductor is very very small
+
+ align:start position:0%
+in the semiconductor is very very small
+ 
+
+ align:start position:0%
+in the semiconductor is very very small
+and that happens uh when you make the
+
+ align:start position:0%
+and that happens uh when you make the
+ 
+
+ align:start position:0%
+and that happens uh when you make the
+doping High um so in fact for a
+
+ align:start position:0%
+doping High um so in fact for a
+ 
+
+ align:start position:0%
+doping High um so in fact for a
+tunneling contact if you go back to your
+
+ align:start position:0%
+tunneling contact if you go back to your
+ 
+
+ align:start position:0%
+tunneling contact if you go back to your
+quantum mechanics you know if you have a
+
+ align:start position:0%
+quantum mechanics you know if you have a
+ 
+
+ align:start position:0%
+quantum mechanics you know if you have a
+certain barrier height
+
+ align:start position:0%
+certain barrier height
+ 
+
+ align:start position:0%
+certain barrier height
+FB um and uh a certain uh barrier
+
+ align:start position:0%
+FB um and uh a certain uh barrier
+ 
+
+ align:start position:0%
+FB um and uh a certain uh barrier
+thickness uh Act
+
+ align:start position:0%
+thickness uh Act
+ 
+
+ align:start position:0%
+thickness uh Act
+XD um that the tunneling current is
+
+ align:start position:0%
+XD um that the tunneling current is
+ 
+
+ align:start position:0%
+XD um that the tunneling current is
+exponentially dependent on those two
+
+ align:start position:0%
+exponentially dependent on those two
+ 
+
+ align:start position:0%
+exponentially dependent on those two
+quantities it looks something like
+
+ align:start position:0%
+quantities it looks something like
+ 
+
+ align:start position:0%
+quantities it looks something like
+this so how do I make the depletion
+
+ align:start position:0%
+this so how do I make the depletion
+ 
+
+ align:start position:0%
+this so how do I make the depletion
+layer thickness small in the
+
+ align:start position:0%
+layer thickness small in the
+ 
+
+ align:start position:0%
+layer thickness small in the
+semiconductor when I put a metal contact
+
+ align:start position:0%
+semiconductor when I put a metal contact
+ 
+
+ align:start position:0%
+semiconductor when I put a metal contact
+to it well again if you're going back to
+
+ align:start position:0%
+to it well again if you're going back to
+ 
+
+ align:start position:0%
+to it well again if you're going back to
+some of your basic electrostatics XD is
+
+ align:start position:0%
+some of your basic electrostatics XD is
+ 
+
+ align:start position:0%
+some of your basic electrostatics XD is
+inversely proportional to the doping or
+
+ align:start position:0%
+inversely proportional to the doping or
+ 
+
+ align:start position:0%
+inversely proportional to the doping or
+the square root of the doping so all I
+
+ align:start position:0%
+the square root of the doping so all I
+ 
+
+ align:start position:0%
+the square root of the doping so all I
+need to do to make XD small is to pump
+
+ align:start position:0%
+need to do to make XD small is to pump
+ 
+
+ align:start position:0%
+need to do to make XD small is to pump
+up this doping very high the doping in
+
+ align:start position:0%
+up this doping very high the doping in
+ 
+
+ align:start position:0%
+up this doping very high the doping in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+semiconductor um
+
+ align:start position:0%
+semiconductor um
+ 
+
+ align:start position:0%
+semiconductor um
+so when the doping is high enough uh XD
+
+ align:start position:0%
+so when the doping is high enough uh XD
+ 
+
+ align:start position:0%
+so when the doping is high enough uh XD
+will become
+
+ align:start position:0%
+will become
+ 
+
+ align:start position:0%
+will become
+small um and then when XD gets less than
+
+ align:start position:0%
+small um and then when XD gets less than
+ 
+
+ align:start position:0%
+small um and then when XD gets less than
+about say two nanometers or so in in
+
+ align:start position:0%
+about say two nanometers or so in in
+ 
+
+ align:start position:0%
+about say two nanometers or so in in
+this equation you get a very large
+
+ align:start position:0%
+this equation you get a very large
+ 
+
+ align:start position:0%
+this equation you get a very large
+tunneling current basically um so what
+
+ align:start position:0%
+tunneling current basically um so what
+ 
+
+ align:start position:0%
+tunneling current basically um so what
+people do in practice is you dope very
+
+ align:start position:0%
+people do in practice is you dope very
+ 
+
+ align:start position:0%
+people do in practice is you dope very
+heavily above say above uh mid 10 of the
+
+ align:start position:0%
+heavily above say above uh mid 10 of the
+ 
+
+ align:start position:0%
+heavily above say above uh mid 10 of the
+19th you get uh quantum mechanical
+
+ align:start position:0%
+19th you get uh quantum mechanical
+ 
+
+ align:start position:0%
+19th you get uh quantum mechanical
+tunneling and that's really what's
+
+ align:start position:0%
+tunneling and that's really what's
+ 
+
+ align:start position:0%
+tunneling and that's really what's
+dominating um so if you put these
+
+ align:start position:0%
+dominating um so if you put these
+ 
+
+ align:start position:0%
+dominating um so if you put these
+numbers uh and you in here and you you
+
+ align:start position:0%
+numbers uh and you in here and you you
+ 
+
+ align:start position:0%
+numbers uh and you in here and you you
+look look at the definition of the
+
+ align:start position:0%
+look look at the definition of the
+ 
+
+ align:start position:0%
+look look at the definition of the
+specific contact resistivity you get an
+
+ align:start position:0%
+specific contact resistivity you get an
+ 
+
+ align:start position:0%
+specific contact resistivity you get an
+equation like was shown at the bottom of
+
+ align:start position:0%
+equation like was shown at the bottom of
+ 
+
+ align:start position:0%
+equation like was shown at the bottom of
+uh page eight here and you can see again
+
+ align:start position:0%
+uh page eight here and you can see again
+ 
+
+ align:start position:0%
+uh page eight here and you can see again
+it depends exponentially on the barrier
+
+ align:start position:0%
+it depends exponentially on the barrier
+ 
+
+ align:start position:0%
+it depends exponentially on the barrier
+height um uh and and inversely
+
+ align:start position:0%
+height um uh and and inversely
+ 
+
+ align:start position:0%
+height um uh and and inversely
+exponentially on the doping so for low
+
+ align:start position:0%
+exponentially on the doping so for low
+ 
+
+ align:start position:0%
+exponentially on the doping so for low
+contact resistivity to get this number
+
+ align:start position:0%
+contact resistivity to get this number
+ 
+
+ align:start position:0%
+contact resistivity to get this number
+down I need a small barrier so you would
+
+ align:start position:0%
+down I need a small barrier so you would
+ 
+
+ align:start position:0%
+down I need a small barrier so you would
+choose um a particular metal that gives
+
+ align:start position:0%
+choose um a particular metal that gives
+ 
+
+ align:start position:0%
+choose um a particular metal that gives
+you a relatively small barrier height 5B
+
+ align:start position:0%
+you a relatively small barrier height 5B
+ 
+
+ align:start position:0%
+you a relatively small barrier height 5B
+and you need more most importantly very
+
+ align:start position:0%
+and you need more most importantly very
+ 
+
+ align:start position:0%
+and you need more most importantly very
+high doping so you need to pump up the
+
+ align:start position:0%
+high doping so you need to pump up the
+ 
+
+ align:start position:0%
+high doping so you need to pump up the
+doping um as high as possible and then
+
+ align:start position:0%
+doping um as high as possible and then
+ 
+
+ align:start position:0%
+doping um as high as possible and then
+you'll get IV characteristic that is
+
+ align:start position:0%
+you'll get IV characteristic that is
+ 
+
+ align:start position:0%
+you'll get IV characteristic that is
+essentially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+omic so here um I'm just doing the uh a
+
+ align:start position:0%
+omic so here um I'm just doing the uh a
+ 
+
+ align:start position:0%
+omic so here um I'm just doing the uh a
+simple calculation um on uh on slide
+
+ align:start position:0%
+simple calculation um on uh on slide
+ 
+
+ align:start position:0%
+simple calculation um on uh on slide
+nine here's an
+
+ align:start position:0%
+nine here's an
+ 
+
+ align:start position:0%
+nine here's an
+example uh if we use the expression for
+
+ align:start position:0%
+example uh if we use the expression for
+ 
+
+ align:start position:0%
+example uh if we use the expression for
+the the specific contact resistivity at
+
+ align:start position:0%
+the the specific contact resistivity at
+ 
+
+ align:start position:0%
+the the specific contact resistivity at
+very high doping levels uh where we have
+
+ align:start position:0%
+very high doping levels uh where we have
+ 
+
+ align:start position:0%
+very high doping levels uh where we have
+tunneling dominate so we we we can write
+
+ align:start position:0%
+tunneling dominate so we we we can write
+ 
+
+ align:start position:0%
+tunneling dominate so we we we can write
+that expression that I just showed on
+
+ align:start position:0%
+that expression that I just showed on
+ 
+
+ align:start position:0%
+that expression that I just showed on
+the PRI prior page saying that row C is
+
+ align:start position:0%
+the PRI prior page saying that row C is
+ 
+
+ align:start position:0%
+the PRI prior page saying that row C is
+row c0 some pre-exponential times the
+
+ align:start position:0%
+row c0 some pre-exponential times the
+ 
+
+ align:start position:0%
+row c0 some pre-exponential times the
+exponential dependence on 5B and
+
+ align:start position:0%
+exponential dependence on 5B and
+ 
+
+ align:start position:0%
+exponential dependence on 5B and
+ND and where this um this this com this
+
+ align:start position:0%
+ND and where this um this this com this
+ 
+
+ align:start position:0%
+ND and where this um this this com this
+uh exponential U multiplier C1 is given
+
+ align:start position:0%
+uh exponential U multiplier C1 is given
+ 
+
+ align:start position:0%
+uh exponential U multiplier C1 is given
+by this number 7 x 10 the
+
+ align:start position:0%
+by this number 7 x 10 the
+ 
+
+ align:start position:0%
+by this number 7 x 10 the
+10th so now let's say I assume I have a
+
+ align:start position:0%
+10th so now let's say I assume I have a
+ 
+
+ align:start position:0%
+10th so now let's say I assume I have a
+a metal semiconductor contact where the
+
+ align:start position:0%
+a metal semiconductor contact where the
+ 
+
+ align:start position:0%
+a metal semiconductor contact where the
+barrier height is 6 electron volts um
+
+ align:start position:0%
+barrier height is 6 electron volts um
+ 
+
+ align:start position:0%
+barrier height is 6 electron volts um
+and uh row c0 this number is about 10- 7
+
+ align:start position:0%
+and uh row c0 this number is about 10- 7
+ 
+
+ align:start position:0%
+and uh row c0 this number is about 10- 7
+ohm that's a little hard to read but
+
+ align:start position:0%
+ohm that's a little hard to read but
+ 
+
+ align:start position:0%
+ohm that's a little hard to read but
+that's ohm cenim squar for an aluminum
+
+ align:start position:0%
+that's ohm cenim squar for an aluminum
+ 
+
+ align:start position:0%
+that's ohm cenim squar for an aluminum
+silicon
+
+ align:start position:0%
+silicon
+ 
+
+ align:start position:0%
+silicon
+contact so the question is if I change
+
+ align:start position:0%
+contact so the question is if I change
+ 
+
+ align:start position:0%
+contact so the question is if I change
+the doping from9 to20 by a factor of 10
+
+ align:start position:0%
+the doping from9 to20 by a factor of 10
+ 
+
+ align:start position:0%
+the doping from9 to20 by a factor of 10
+how much does row C go down just to give
+
+ align:start position:0%
+how much does row C go down just to give
+ 
+
+ align:start position:0%
+how much does row C go down just to give
+us an example of how much you you
+
+ align:start position:0%
+us an example of how much you you
+ 
+
+ align:start position:0%
+us an example of how much you you
+benefit yourself and again this is an
+
+ align:start position:0%
+benefit yourself and again this is an
+ 
+
+ align:start position:0%
+benefit yourself and again this is an
+exponential relationship so you expect a
+
+ align:start position:0%
+exponential relationship so you expect a
+ 
+
+ align:start position:0%
+exponential relationship so you expect a
+big change so in this case the first
+
+ align:start position:0%
+big change so in this case the first
+ 
+
+ align:start position:0%
+big change so in this case the first
+case I have a doping of 10 of the 19th
+
+ align:start position:0%
+case I have a doping of 10 of the 19th
+ 
+
+ align:start position:0%
+case I have a doping of 10 of the 19th
+you plug in all these numbers you put in
+
+ align:start position:0%
+you plug in all these numbers you put in
+ 
+
+ align:start position:0%
+you plug in all these numbers you put in
+the square root of 10 of 19th down here
+
+ align:start position:0%
+the square root of 10 of 19th down here
+ 
+
+ align:start position:0%
+the square root of 10 of 19th down here
+and you get um a row C of about 6 * 10us
+
+ align:start position:0%
+and you get um a row C of about 6 * 10us
+ 
+
+ align:start position:0%
+and you get um a row C of about 6 * 10us
+2 ohm cenim squar
+
+ align:start position:0%
+2 ohm cenim squar
+ 
+
+ align:start position:0%
+2 ohm cenim squar
+that's a pretty big number as it turns
+
+ align:start position:0%
+that's a pretty big number as it turns
+ 
+
+ align:start position:0%
+that's a pretty big number as it turns
+out if you plug in a standard size of a
+
+ align:start position:0%
+out if you plug in a standard size of a
+ 
+
+ align:start position:0%
+out if you plug in a standard size of a
+contact on a silicon chip that's a 10 of
+
+ align:start position:0%
+contact on a silicon chip that's a 10 of
+ 
+
+ align:start position:0%
+contact on a silicon chip that's a 10 of
+a 19 at 10 of 20 you do the same sort of
+
+ align:start position:0%
+a 19 at 10 of 20 you do the same sort of
+ 
+
+ align:start position:0%
+a 19 at 10 of 20 you do the same sort of
+thing and you do the math and now you
+
+ align:start position:0%
+thing and you do the math and now you
+ 
+
+ align:start position:0%
+thing and you do the math and now you
+get about 6 * 10us 6m cenim squar so
+
+ align:start position:0%
+get about 6 * 10us 6m cenim squar so
+ 
+
+ align:start position:0%
+get about 6 * 10us 6m cenim squar so
+that's a b a factor of 9,000 lower so it
+
+ align:start position:0%
+that's a b a factor of 9,000 lower so it
+ 
+
+ align:start position:0%
+that's a b a factor of 9,000 lower so it
+changed by almost fours of magnitude the
+
+ align:start position:0%
+changed by almost fours of magnitude the
+ 
+
+ align:start position:0%
+changed by almost fours of magnitude the
+contact resistivity um just by drop
+
+ align:start position:0%
+contact resistivity um just by drop
+ 
+
+ align:start position:0%
+contact resistivity um just by drop
+upping the doping by a factor of 10 so
+
+ align:start position:0%
+upping the doping by a factor of 10 so
+ 
+
+ align:start position:0%
+upping the doping by a factor of 10 so
+you got four orders of magnitude um
+
+ align:start position:0%
+you got four orders of magnitude um
+ 
+
+ align:start position:0%
+you got four orders of magnitude um
+that's dramatic difference um so this is
+
+ align:start position:0%
+that's dramatic difference um so this is
+ 
+
+ align:start position:0%
+that's dramatic difference um so this is
+this is this tells you you need to have
+
+ align:start position:0%
+this is this tells you you need to have
+ 
+
+ align:start position:0%
+this is this tells you you need to have
+if you're going to get reasonable
+
+ align:start position:0%
+if you're going to get reasonable
+ 
+
+ align:start position:0%
+if you're going to get reasonable
+contacts in Silicon technology unless
+
+ align:start position:0%
+contacts in Silicon technology unless
+ 
+
+ align:start position:0%
+contacts in Silicon technology unless
+you want huge devices with you know
+
+ align:start position:0%
+you want huge devices with you know
+ 
+
+ align:start position:0%
+you want huge devices with you know
+where where the whole chip is dominated
+
+ align:start position:0%
+where where the whole chip is dominated
+ 
+
+ align:start position:0%
+where where the whole chip is dominated
+by contacts which is ridiculous you
+
+ align:start position:0%
+by contacts which is ridiculous you
+ 
+
+ align:start position:0%
+by contacts which is ridiculous you
+won't be able to get enough devices on
+
+ align:start position:0%
+won't be able to get enough devices on
+ 
+
+ align:start position:0%
+won't be able to get enough devices on
+your chip you're going to have to get
+
+ align:start position:0%
+your chip you're going to have to get
+ 
+
+ align:start position:0%
+your chip you're going to have to get
+the doping in the sourc drain regions
+
+ align:start position:0%
+the doping in the sourc drain regions
+ 
+
+ align:start position:0%
+the doping in the sourc drain regions
+high at least 10 to the 20 or higher um
+
+ align:start position:0%
+high at least 10 to the 20 or higher um
+ 
+
+ align:start position:0%
+high at least 10 to the 20 or higher um
+this number itself itself is still
+
+ align:start position:0%
+this number itself itself is still
+ 
+
+ align:start position:0%
+this number itself itself is still
+considered a little bit uh on the too
+
+ align:start position:0%
+considered a little bit uh on the too
+ 
+
+ align:start position:0%
+considered a little bit uh on the too
+high of a side for a contact resistance
+
+ align:start position:0%
+high of a side for a contact resistance
+ 
+
+ align:start position:0%
+high of a side for a contact resistance
+but it's just interesting to look at
+
+ align:start position:0%
+but it's just interesting to look at
+ 
+
+ align:start position:0%
+but it's just interesting to look at
+these numbers and and in fact I've taken
+
+ align:start position:0%
+these numbers and and in fact I've taken
+ 
+
+ align:start position:0%
+these numbers and and in fact I've taken
+on the next slide uh figure 11-7 from
+
+ align:start position:0%
+on the next slide uh figure 11-7 from
+ 
+
+ align:start position:0%
+on the next slide uh figure 11-7 from
+your text and you can see that these
+
+ align:start position:0%
+your text and you can see that these
+ 
+
+ align:start position:0%
+your text and you can see that these
+numbers are in pretty good agreement
+
+ align:start position:0%
+numbers are in pretty good agreement
+ 
+
+ align:start position:0%
+numbers are in pretty good agreement
+with what people have
+
+ align:start position:0%
+with what people have
+ 
+
+ align:start position:0%
+with what people have
+measured um here on on on slide 10 uh I
+
+ align:start position:0%
+measured um here on on on slide 10 uh I
+ 
+
+ align:start position:0%
+measured um here on on on slide 10 uh I
+took this from your text that shows um
+
+ align:start position:0%
+took this from your text that shows um
+ 
+
+ align:start position:0%
+took this from your text that shows um
+the uh contact resistivity uh in ohm
+
+ align:start position:0%
+the uh contact resistivity uh in ohm
+ 
+
+ align:start position:0%
+the uh contact resistivity uh in ohm
+centimet squared uh as a function of
+
+ align:start position:0%
+centimet squared uh as a function of
+ 
+
+ align:start position:0%
+centimet squared uh as a function of
+doping here and you can see the doping
+
+ align:start position:0%
+doping here and you can see the doping
+ 
+
+ align:start position:0%
+doping here and you can see the doping
+up on this uh scale here uh for a couple
+
+ align:start position:0%
+up on this uh scale here uh for a couple
+ 
+
+ align:start position:0%
+up on this uh scale here uh for a couple
+different uh two different metal systems
+
+ align:start position:0%
+different uh two different metal systems
+ 
+
+ align:start position:0%
+different uh two different metal systems
+one is the aluminum uh contact to n type
+
+ align:start position:0%
+one is the aluminum uh contact to n type
+ 
+
+ align:start position:0%
+one is the aluminum uh contact to n type
+silicon and the other is platinum
+
+ align:start position:0%
+silicon and the other is platinum
+ 
+
+ align:start position:0%
+silicon and the other is platinum
+silicide to n type silicon and the data
+
+ align:start position:0%
+silicide to n type silicon and the data
+ 
+
+ align:start position:0%
+silicide to n type silicon and the data
+is the uh the bullets uh that people
+
+ align:start position:0%
+is the uh the bullets uh that people
+ 
+
+ align:start position:0%
+is the uh the bullets uh that people
+have measured like these open squares
+
+ align:start position:0%
+have measured like these open squares
+ 
+
+ align:start position:0%
+have measured like these open squares
+are for aluminum contacting n type
+
+ align:start position:0%
+are for aluminum contacting n type
+ 
+
+ align:start position:0%
+are for aluminum contacting n type
+silicon and the theoretical uh curve is
+
+ align:start position:0%
+silicon and the theoretical uh curve is
+ 
+
+ align:start position:0%
+silicon and the theoretical uh curve is
+shown here uh with the solid line
+
+ align:start position:0%
+shown here uh with the solid line
+ 
+
+ align:start position:0%
+shown here uh with the solid line
+there's there you can see there's
+
+ align:start position:0%
+there's there you can see there's
+ 
+
+ align:start position:0%
+there's there you can see there's
+reasonable agreement notice here this is
+
+ align:start position:0%
+reasonable agreement notice here this is
+ 
+
+ align:start position:0%
+reasonable agreement notice here this is
+a um uh a log log scale so we're getting
+
+ align:start position:0%
+a um uh a log log scale so we're getting
+ 
+
+ align:start position:0%
+a um uh a log log scale so we're getting
+an exponential dependence in the heavily
+
+ align:start position:0%
+an exponential dependence in the heavily
+ 
+
+ align:start position:0%
+an exponential dependence in the heavily
+dope regime so again as I doping is
+
+ align:start position:0%
+dope regime so again as I doping is
+ 
+
+ align:start position:0%
+dope regime so again as I doping is
+increasing to the left on this x-axis so
+
+ align:start position:0%
+increasing to the left on this x-axis so
+ 
+
+ align:start position:0%
+increasing to the left on this x-axis so
+here's a doping of 10 of a 19th here's a
+
+ align:start position:0%
+here's a doping of 10 of a 19th here's a
+ 
+
+ align:start position:0%
+here's a doping of 10 of a 19th here's a
+doping of 10 of the 20 and we see uh a
+
+ align:start position:0%
+doping of 10 of the 20 and we see uh a
+ 
+
+ align:start position:0%
+doping of 10 of the 20 and we see uh a
+number of orders of magnitude basically
+
+ align:start position:0%
+number of orders of magnitude basically
+ 
+
+ align:start position:0%
+number of orders of magnitude basically
+fours of magnitude uh drop as I go from
+
+ align:start position:0%
+fours of magnitude uh drop as I go from
+ 
+
+ align:start position:0%
+fours of magnitude uh drop as I go from
+10 of 19 to 10 of
+
+ align:start position:0%
+10 of 19 to 10 of
+ 
+
+ align:start position:0%
+10 of 19 to 10 of
+20 so you say okay that's not a big deal
+
+ align:start position:0%
+20 so you say okay that's not a big deal
+ 
+
+ align:start position:0%
+20 so you say okay that's not a big deal
+I just keep increasing the doping in my
+
+ align:start position:0%
+I just keep increasing the doping in my
+ 
+
+ align:start position:0%
+I just keep increasing the doping in my
+source drain regions over time the
+
+ align:start position:0%
+source drain regions over time the
+ 
+
+ align:start position:0%
+source drain regions over time the
+problem is we know that there are
+
+ align:start position:0%
+problem is we know that there are
+ 
+
+ align:start position:0%
+problem is we know that there are
+electrical solubility limits we cannot
+
+ align:start position:0%
+electrical solubility limits we cannot
+ 
+
+ align:start position:0%
+electrical solubility limits we cannot
+just arbitrarily keep increasing doping
+
+ align:start position:0%
+just arbitrarily keep increasing doping
+ 
+
+ align:start position:0%
+just arbitrarily keep increasing doping
+we're trying to find ways to do it but
+
+ align:start position:0%
+we're trying to find ways to do it but
+ 
+
+ align:start position:0%
+we're trying to find ways to do it but
+you know if you do an implant you do a
+
+ align:start position:0%
+you know if you do an implant you do a
+ 
+
+ align:start position:0%
+you know if you do an implant you do a
+certain anal you get doping up to a
+
+ align:start position:0%
+certain anal you get doping up to a
+ 
+
+ align:start position:0%
+certain anal you get doping up to a
+certain value maybe uh depending on the
+
+ align:start position:0%
+certain value maybe uh depending on the
+ 
+
+ align:start position:0%
+certain value maybe uh depending on the
+dope it maybe in the low 20s maybe 2 to
+
+ align:start position:0%
+dope it maybe in the low 20s maybe 2 to
+ 
+
+ align:start position:0%
+dope it maybe in the low 20s maybe 2 to
+four times 10 of a 20 beyond that it's
+
+ align:start position:0%
+four times 10 of a 20 beyond that it's
+ 
+
+ align:start position:0%
+four times 10 of a 20 beyond that it's
+very hard to to go much further so the
+
+ align:start position:0%
+very hard to to go much further so the
+ 
+
+ align:start position:0%
+very hard to to go much further so the
+problem is that row C is not really
+
+ align:start position:0%
+problem is that row C is not really
+ 
+
+ align:start position:0%
+problem is that row C is not really
+scaling because of the do doe the dopent
+
+ align:start position:0%
+scaling because of the do doe the dopent
+ 
+
+ align:start position:0%
+scaling because of the do doe the dopent
+electrical solubility limit so the
+
+ align:start position:0%
+electrical solubility limit so the
+ 
+
+ align:start position:0%
+electrical solubility limit so the
+contact privity doesn't scale as we as
+
+ align:start position:0%
+contact privity doesn't scale as we as
+ 
+
+ align:start position:0%
+contact privity doesn't scale as we as
+we as we shrink technology this is a
+
+ align:start position:0%
+we as we shrink technology this is a
+ 
+
+ align:start position:0%
+we as we shrink technology this is a
+major problem people are looking for new
+
+ align:start position:0%
+major problem people are looking for new
+ 
+
+ align:start position:0%
+major problem people are looking for new
+methods new materials whatever uh some
+
+ align:start position:0%
+methods new materials whatever uh some
+ 
+
+ align:start position:0%
+methods new materials whatever uh some
+way of getting the doping up or a new
+
+ align:start position:0%
+way of getting the doping up or a new
+ 
+
+ align:start position:0%
+way of getting the doping up or a new
+method of making content that's kind of
+
+ align:start position:0%
+method of making content that's kind of
+ 
+
+ align:start position:0%
+method of making content that's kind of
+a fundamental
+
+ align:start position:0%
+a fundamental
+ 
+
+ align:start position:0%
+a fundamental
+issue in fact here on slide 11 I'm
+
+ align:start position:0%
+issue in fact here on slide 11 I'm
+ 
+
+ align:start position:0%
+issue in fact here on slide 11 I'm
+showing you um I show this is really one
+
+ align:start position:0%
+showing you um I show this is really one
+ 
+
+ align:start position:0%
+showing you um I show this is really one
+of the concerns uh this is a table that
+
+ align:start position:0%
+of the concerns uh this is a table that
+ 
+
+ align:start position:0%
+of the concerns uh this is a table that
+I took table 71a from the 20033
+
+ align:start position:0%
+I took table 71a from the 20033
+ 
+
+ align:start position:0%
+I took table 71a from the 20033
+international technology roadmap per
+
+ align:start position:0%
+international technology roadmap per
+ 
+
+ align:start position:0%
+international technology roadmap per
+semic not because I've shown this before
+
+ align:start position:0%
+semic not because I've shown this before
+ 
+
+ align:start position:0%
+semic not because I've shown this before
+but we hadn't gotten to this contact
+
+ align:start position:0%
+but we hadn't gotten to this contact
+ 
+
+ align:start position:0%
+but we hadn't gotten to this contact
+stage and um just to remind you in the
+
+ align:start position:0%
+stage and um just to remind you in the
+ 
+
+ align:start position:0%
+stage and um just to remind you in the
+upper right corner this is what the
+
+ align:start position:0%
+upper right corner this is what the
+ 
+
+ align:start position:0%
+upper right corner this is what the
+mosfet looks like and these black
+
+ align:start position:0%
+mosfet looks like and these black
+ 
+
+ align:start position:0%
+mosfet looks like and these black
+regions are going to be suicides either
+
+ align:start position:0%
+regions are going to be suicides either
+ 
+
+ align:start position:0%
+regions are going to be suicides either
+Cobalt silicide or nickel silicide we'll
+
+ align:start position:0%
+Cobalt silicide or nickel silicide we'll
+ 
+
+ align:start position:0%
+Cobalt silicide or nickel silicide we'll
+talk more about that but the point is
+
+ align:start position:0%
+talk more about that but the point is
+ 
+
+ align:start position:0%
+talk more about that but the point is
+there a contact between a metal and a
+
+ align:start position:0%
+there a contact between a metal and a
+ 
+
+ align:start position:0%
+there a contact between a metal and a
+heav heavily dope semiconductor which is
+
+ align:start position:0%
+heav heavily dope semiconductor which is
+ 
+
+ align:start position:0%
+heav heavily dope semiconductor which is
+silicon and if you look at some of the
+
+ align:start position:0%
+silicon and if you look at some of the
+ 
+
+ align:start position:0%
+silicon and if you look at some of the
+requirements here on the itrs road map
+
+ align:start position:0%
+requirements here on the itrs road map
+ 
+
+ align:start position:0%
+requirements here on the itrs road map
+here we are in two let's say a year ago
+
+ align:start position:0%
+here we are in two let's say a year ago
+ 
+
+ align:start position:0%
+here we are in two let's say a year ago
+2003 look at the contact the maximum
+
+ align:start position:0%
+2003 look at the contact the maximum
+ 
+
+ align:start position:0%
+2003 look at the contact the maximum
+contact resistivity so this is the row C
+
+ align:start position:0%
+contact resistivity so this is the row C
+ 
+
+ align:start position:0%
+contact resistivity so this is the row C
+this this um uh row this right here is
+
+ align:start position:0%
+this this um uh row this right here is
+ 
+
+ align:start position:0%
+this this um uh row this right here is
+represented what we call row C in 2003
+
+ align:start position:0%
+represented what we call row C in 2003
+ 
+
+ align:start position:0%
+represented what we call row C in 2003
+they wanted to have about 2 * 10 Theus
+
+ align:start position:0%
+they wanted to have about 2 * 10 Theus
+ 
+
+ align:start position:0%
+they wanted to have about 2 * 10 Theus
+7th mm centimeter squar and you notice
+
+ align:start position:0%
+7th mm centimeter squar and you notice
+ 
+
+ align:start position:0%
+7th mm centimeter squar and you notice
+it's sort of a light orange color which
+
+ align:start position:0%
+it's sort of a light orange color which
+ 
+
+ align:start position:0%
+it's sort of a light orange color which
+means uh according to our key that there
+
+ align:start position:0%
+means uh according to our key that there
+ 
+
+ align:start position:0%
+means uh according to our key that there
+is an inter interim Solution on how to
+
+ align:start position:0%
+is an inter interim Solution on how to
+ 
+
+ align:start position:0%
+is an inter interim Solution on how to
+get to this is known uh but if you go to
+
+ align:start position:0%
+get to this is known uh but if you go to
+ 
+
+ align:start position:0%
+get to this is known uh but if you go to
+2004 they want you want to lower it in
+
+ align:start position:0%
+2004 they want you want to lower it in
+ 
+
+ align:start position:0%
+2004 they want you want to lower it in
+according to the itrs to about 1.6 *
+
+ align:start position:0%
+according to the itrs to about 1.6 *
+ 
+
+ align:start position:0%
+according to the itrs to about 1.6 *
+10us 7 that's all in yellow which means
+
+ align:start position:0%
+10us 7 that's all in yellow which means
+ 
+
+ align:start position:0%
+10us 7 that's all in yellow which means
+their manufacturable Solutions are known
+
+ align:start position:0%
+their manufacturable Solutions are known
+ 
+
+ align:start position:0%
+their manufacturable Solutions are known
+they haven't yet been in integrated and
+
+ align:start position:0%
+they haven't yet been in integrated and
+ 
+
+ align:start position:0%
+they haven't yet been in integrated and
+when we get to 2008 in the red to get
+
+ align:start position:0%
+when we get to 2008 in the red to get
+ 
+
+ align:start position:0%
+when we get to 2008 in the red to get
+down to about 8 * 10- 7 ohm cenm squ
+
+ align:start position:0%
+down to about 8 * 10- 7 ohm cenm squ
+ 
+
+ align:start position:0%
+down to about 8 * 10- 7 ohm cenm squ
+there aren't any known solutions that
+
+ align:start position:0%
+there aren't any known solutions that
+ 
+
+ align:start position:0%
+there aren't any known solutions that
+are manufacturable so we're we're coming
+
+ align:start position:0%
+are manufacturable so we're we're coming
+ 
+
+ align:start position:0%
+are manufacturable so we're we're coming
+up against the red brick wall here um
+
+ align:start position:0%
+up against the red brick wall here um
+ 
+
+ align:start position:0%
+up against the red brick wall here um
+because the um the the device
+
+ align:start position:0%
+because the um the the device
+ 
+
+ align:start position:0%
+because the um the the device
+scaling the need to make the contact
+
+ align:start position:0%
+scaling the need to make the contact
+ 
+
+ align:start position:0%
+scaling the need to make the contact
+size smaller means that we need to drop
+
+ align:start position:0%
+size smaller means that we need to drop
+ 
+
+ align:start position:0%
+size smaller means that we need to drop
+row C uh at this rate and it's just
+
+ align:start position:0%
+row C uh at this rate and it's just
+ 
+
+ align:start position:0%
+row C uh at this rate and it's just
+nobody yes knows yet how to make a
+
+ align:start position:0%
+nobody yes knows yet how to make a
+ 
+
+ align:start position:0%
+nobody yes knows yet how to make a
+contact that has 8 time 10us 7 ohms cmet
+
+ align:start position:0%
+contact that has 8 time 10us 7 ohms cmet
+ 
+
+ align:start position:0%
+contact that has 8 time 10us 7 ohms cmet
+squ for the specific resistivity um so
+
+ align:start position:0%
+squ for the specific resistivity um so
+ 
+
+ align:start position:0%
+squ for the specific resistivity um so
+it's the contacts that are really
+
+ align:start position:0%
+it's the contacts that are really
+ 
+
+ align:start position:0%
+it's the contacts that are really
+hurting us look at the the the sheet
+
+ align:start position:0%
+hurting us look at the the the sheet
+ 
+
+ align:start position:0%
+hurting us look at the the the sheet
+resist you might be concerned about well
+
+ align:start position:0%
+resist you might be concerned about well
+ 
+
+ align:start position:0%
+resist you might be concerned about well
+how about the resistance of the metal
+
+ align:start position:0%
+how about the resistance of the metal
+ 
+
+ align:start position:0%
+how about the resistance of the metal
+itself resistance of the metal of of the
+
+ align:start position:0%
+itself resistance of the metal of of the
+ 
+
+ align:start position:0%
+itself resistance of the metal of of the
+electrons flowing through the metal is
+
+ align:start position:0%
+electrons flowing through the metal is
+ 
+
+ align:start position:0%
+electrons flowing through the metal is
+not a real big problem you look at the
+
+ align:start position:0%
+not a real big problem you look at the
+ 
+
+ align:start position:0%
+not a real big problem you look at the
+the the contact pilicide sheet
+
+ align:start position:0%
+the the contact pilicide sheet
+ 
+
+ align:start position:0%
+the the contact pilicide sheet
+resistance in ohms per square um needs
+
+ align:start position:0%
+resistance in ohms per square um needs
+ 
+
+ align:start position:0%
+resistance in ohms per square um needs
+to be in this range of 6 to 10 uh ohms
+
+ align:start position:0%
+to be in this range of 6 to 10 uh ohms
+ 
+
+ align:start position:0%
+to be in this range of 6 to 10 uh ohms
+per square that's not a problem none of
+
+ align:start position:0%
+per square that's not a problem none of
+ 
+
+ align:start position:0%
+per square that's not a problem none of
+that that's all in white which means
+
+ align:start position:0%
+that that's all in white which means
+ 
+
+ align:start position:0%
+that that's all in white which means
+people know how to do that the real
+
+ align:start position:0%
+people know how to do that the real
+ 
+
+ align:start position:0%
+people know how to do that the real
+problem is making these really good uh
+
+ align:start position:0%
+problem is making these really good uh
+ 
+
+ align:start position:0%
+problem is making these really good uh
+low resistivity uh
+
+ align:start position:0%
+low resistivity uh
+ 
+
+ align:start position:0%
+low resistivity uh
+contacts to the Silicon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I just want to show an example of how
+
+ align:start position:0%
+uh I just want to show an example of how
+ 
+
+ align:start position:0%
+uh I just want to show an example of how
+so you get a feel for how the numbers
+
+ align:start position:0%
+so you get a feel for how the numbers
+ 
+
+ align:start position:0%
+so you get a feel for how the numbers
+work uh of how one does a contact
+
+ align:start position:0%
+work uh of how one does a contact
+ 
+
+ align:start position:0%
+work uh of how one does a contact
+resistance calculation this is uh for a
+
+ align:start position:0%
+resistance calculation this is uh for a
+ 
+
+ align:start position:0%
+resistance calculation this is uh for a
+mosfet this is shown on uh slide 12 of
+
+ align:start position:0%
+mosfet this is shown on uh slide 12 of
+ 
+
+ align:start position:0%
+mosfet this is shown on uh slide 12 of
+your handouts um again this is a
+
+ align:start position:0%
+your handouts um again this is a
+ 
+
+ align:start position:0%
+your handouts um again this is a
+cross-section view of a moset so on the
+
+ align:start position:0%
+cross-section view of a moset so on the
+ 
+
+ align:start position:0%
+cross-section view of a moset so on the
+left you can imagine this region as
+
+ align:start position:0%
+left you can imagine this region as
+ 
+
+ align:start position:0%
+left you can imagine this region as
+being the heavily dope Source in the
+
+ align:start position:0%
+being the heavily dope Source in the
+ 
+
+ align:start position:0%
+being the heavily dope Source in the
+middle uh shown in Orange is the the
+
+ align:start position:0%
+middle uh shown in Orange is the the
+ 
+
+ align:start position:0%
+middle uh shown in Orange is the the
+gate uh and this is the heavily dope
+
+ align:start position:0%
+gate uh and this is the heavily dope
+ 
+
+ align:start position:0%
+gate uh and this is the heavily dope
+drain and these black regions are metal
+
+ align:start position:0%
+drain and these black regions are metal
+ 
+
+ align:start position:0%
+drain and these black regions are metal
+good Miss silicide but there's a metal
+
+ align:start position:0%
+good Miss silicide but there's a metal
+ 
+
+ align:start position:0%
+good Miss silicide but there's a metal
+region um and I'm showing the dimension
+
+ align:start position:0%
+region um and I'm showing the dimension
+ 
+
+ align:start position:0%
+region um and I'm showing the dimension
+of the contact so the region over which
+
+ align:start position:0%
+of the contact so the region over which
+ 
+
+ align:start position:0%
+of the contact so the region over which
+the metal is in contact with the Silicon
+
+ align:start position:0%
+the metal is in contact with the Silicon
+ 
+
+ align:start position:0%
+the metal is in contact with the Silicon
+in this Dimension is 02 microns wide
+
+ align:start position:0%
+in this Dimension is 02 microns wide
+ 
+
+ align:start position:0%
+in this Dimension is 02 microns wide
+okay now into the page or into the board
+
+ align:start position:0%
+okay now into the page or into the board
+ 
+
+ align:start position:0%
+okay now into the page or into the board
+we're assuming that it's one micron and
+
+ align:start position:0%
+we're assuming that it's one micron and
+ 
+
+ align:start position:0%
+we're assuming that it's one micron and
+in fact this is a cross-section view of
+
+ align:start position:0%
+in fact this is a cross-section view of
+ 
+
+ align:start position:0%
+in fact this is a cross-section view of
+the device if you were to look down on
+
+ align:start position:0%
+the device if you were to look down on
+ 
+
+ align:start position:0%
+the device if you were to look down on
+the device a top view this is what you
+
+ align:start position:0%
+the device a top view this is what you
+ 
+
+ align:start position:0%
+the device a top view this is what you
+would see this would be your Source um
+
+ align:start position:0%
+would see this would be your Source um
+ 
+
+ align:start position:0%
+would see this would be your Source um
+contact region here's your gate in the
+
+ align:start position:0%
+contact region here's your gate in the
+ 
+
+ align:start position:0%
+contact region here's your gate in the
+orange and here's the drain and again we
+
+ align:start position:0%
+orange and here's the drain and again we
+ 
+
+ align:start position:0%
+orange and here's the drain and again we
+the region over which we have to make
+
+ align:start position:0%
+the region over which we have to make
+ 
+
+ align:start position:0%
+the region over which we have to make
+the metal contact is assumed to be 02
+
+ align:start position:0%
+the metal contact is assumed to be 02
+ 
+
+ align:start position:0%
+the metal contact is assumed to be 02
+microns in this Direction with uh and
+
+ align:start position:0%
+microns in this Direction with uh and
+ 
+
+ align:start position:0%
+microns in this Direction with uh and
+one micron in this direction so the area
+
+ align:start position:0%
+one micron in this direction so the area
+ 
+
+ align:start position:0%
+one micron in this direction so the area
+of this contact clearly if if the
+
+ align:start position:0%
+of this contact clearly if if the
+ 
+
+ align:start position:0%
+of this contact clearly if if the
+current is going to go flow through it
+
+ align:start position:0%
+current is going to go flow through it
+ 
+
+ align:start position:0%
+current is going to go flow through it
+the area is going to be 02 * 1 square
+
+ align:start position:0%
+the area is going to be 02 * 1 square
+ 
+
+ align:start position:0%
+the area is going to be 02 * 1 square
+microns or 02 Micron squar so that's the
+
+ align:start position:0%
+microns or 02 Micron squar so that's the
+ 
+
+ align:start position:0%
+microns or 02 Micron squar so that's the
+area assuming we go back to
+
+ align:start position:0%
+area assuming we go back to
+ 
+
+ align:start position:0%
+area assuming we go back to
+itrs uh assuming we are here roughly in
+
+ align:start position:0%
+itrs uh assuming we are here roughly in
+ 
+
+ align:start position:0%
+itrs uh assuming we are here roughly in
+2002 uh and the contact resistivity is
+
+ align:start position:0%
+2002 uh and the contact resistivity is
+ 
+
+ align:start position:0%
+2002 uh and the contact resistivity is
+about 2 * 10- 7 ohm cimet squar okay so
+
+ align:start position:0%
+about 2 * 10- 7 ohm cimet squar okay so
+ 
+
+ align:start position:0%
+about 2 * 10- 7 ohm cimet squar okay so
+I'm assuming this as specific contact
+
+ align:start position:0%
+I'm assuming this as specific contact
+ 
+
+ align:start position:0%
+I'm assuming this as specific contact
+resistivity then I can calculate the
+
+ align:start position:0%
+resistivity then I can calculate the
+ 
+
+ align:start position:0%
+resistivity then I can calculate the
+resistance of of just the drain contact
+
+ align:start position:0%
+resistance of of just the drain contact
+ 
+
+ align:start position:0%
+resistance of of just the drain contact
+itself the resistance is just that row C
+
+ align:start position:0%
+itself the resistance is just that row C
+ 
+
+ align:start position:0%
+itself the resistance is just that row C
+divided by the area of that contact and
+
+ align:start position:0%
+divided by the area of that contact and
+ 
+
+ align:start position:0%
+divided by the area of that contact and
+you get um 100
+
+ align:start position:0%
+you get um 100
+ 
+
+ align:start position:0%
+you get um 100
+ohms so the um a resistance of for the
+
+ align:start position:0%
+ohms so the um a resistance of for the
+ 
+
+ align:start position:0%
+ohms so the um a resistance of for the
+current just to flow through this
+
+ align:start position:0%
+current just to flow through this
+ 
+
+ align:start position:0%
+current just to flow through this
+contact is 100 Ohms on the drain side
+
+ align:start position:0%
+contact is 100 Ohms on the drain side
+ 
+
+ align:start position:0%
+contact is 100 Ohms on the drain side
+it's going to be 100 Ohms on the source
+
+ align:start position:0%
+it's going to be 100 Ohms on the source
+ 
+
+ align:start position:0%
+it's going to be 100 Ohms on the source
+side as well so that's 200 SS right
+
+ align:start position:0%
+side as well so that's 200 SS right
+ 
+
+ align:start position:0%
+side as well so that's 200 SS right
+there just give you a rough idea uh and
+
+ align:start position:0%
+there just give you a rough idea uh and
+ 
+
+ align:start position:0%
+there just give you a rough idea uh and
+this is equivalent to the itrs 2003 uh
+
+ align:start position:0%
+this is equivalent to the itrs 2003 uh
+ 
+
+ align:start position:0%
+this is equivalent to the itrs 2003 uh
+requirement so we're talking about 200
+
+ align:start position:0%
+requirement so we're talking about 200
+ 
+
+ align:start position:0%
+requirement so we're talking about 200
+ohms of the total resistance of the
+
+ align:start position:0%
+ohms of the total resistance of the
+ 
+
+ align:start position:0%
+ohms of the total resistance of the
+device just being due to the contacts uh
+
+ align:start position:0%
+device just being due to the contacts uh
+ 
+
+ align:start position:0%
+device just being due to the contacts uh
+because of the size and that's that's a
+
+ align:start position:0%
+because of the size and that's that's a
+ 
+
+ align:start position:0%
+because of the size and that's that's a
+reasonably large resistance so we'll
+
+ align:start position:0%
+reasonably large resistance so we'll
+ 
+
+ align:start position:0%
+reasonably large resistance so we'll
+we'll see that the contact resistance
+
+ align:start position:0%
+we'll see that the contact resistance
+ 
+
+ align:start position:0%
+we'll see that the contact resistance
+actually does dominate again what you
+
+ align:start position:0%
+actually does dominate again what you
+ 
+
+ align:start position:0%
+actually does dominate again what you
+could say was we'll just make the
+
+ align:start position:0%
+could say was we'll just make the
+ 
+
+ align:start position:0%
+could say was we'll just make the
+contact wider which you can do but that
+
+ align:start position:0%
+contact wider which you can do but that
+ 
+
+ align:start position:0%
+contact wider which you can do but that
+means your chip ends up being larger you
+
+ align:start position:0%
+means your chip ends up being larger you
+ 
+
+ align:start position:0%
+means your chip ends up being larger you
+can't put as many devices uh on the chip
+
+ align:start position:0%
+can't put as many devices uh on the chip
+ 
+
+ align:start position:0%
+can't put as many devices uh on the chip
+so there's a fundamental tradeoff here
+
+ align:start position:0%
+so there's a fundamental tradeoff here
+ 
+
+ align:start position:0%
+so there's a fundamental tradeoff here
+unless we can get this Rosy number down
+
+ align:start position:0%
+unless we can get this Rosy number down
+ 
+
+ align:start position:0%
+unless we can get this Rosy number down
+and that's exactly why this number is
+
+ align:start position:0%
+and that's exactly why this number is
+ 
+
+ align:start position:0%
+and that's exactly why this number is
+dropping with time people want to drop
+
+ align:start position:0%
+dropping with time people want to drop
+ 
+
+ align:start position:0%
+dropping with time people want to drop
+because they want to be able to continue
+
+ align:start position:0%
+because they want to be able to continue
+ 
+
+ align:start position:0%
+because they want to be able to continue
+to scale the area of the device uh it's
+
+ align:start position:0%
+to scale the area of the device uh it's
+ 
+
+ align:start position:0%
+to scale the area of the device uh it's
+a problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+though uh on slide 13 I'm showing you a
+
+ align:start position:0%
+though uh on slide 13 I'm showing you a
+ 
+
+ align:start position:0%
+though uh on slide 13 I'm showing you a
+structure if you if you are studying
+
+ align:start position:0%
+structure if you if you are studying
+ 
+
+ align:start position:0%
+structure if you if you are studying
+contacts or if you ever make devices you
+
+ align:start position:0%
+contacts or if you ever make devices you
+ 
+
+ align:start position:0%
+contacts or if you ever make devices you
+always want to know what is my contact
+
+ align:start position:0%
+always want to know what is my contact
+ 
+
+ align:start position:0%
+always want to know what is my contact
+resistance uh and this is a classic
+
+ align:start position:0%
+resistance uh and this is a classic
+ 
+
+ align:start position:0%
+resistance uh and this is a classic
+structure to actually measure contact
+
+ align:start position:0%
+structure to actually measure contact
+ 
+
+ align:start position:0%
+structure to actually measure contact
+resistance it's called Uh a structure uh
+
+ align:start position:0%
+resistance it's called Uh a structure uh
+ 
+
+ align:start position:0%
+resistance it's called Uh a structure uh
+I took this particular picture out of
+
+ align:start position:0%
+I took this particular picture out of
+ 
+
+ align:start position:0%
+I took this particular picture out of
+your textbook uh figure
+
+ align:start position:0%
+your textbook uh figure
+ 
+
+ align:start position:0%
+your textbook uh figure
+11-35 there's a reference to it um in
+
+ align:start position:0%
+11-35 there's a reference to it um in
+ 
+
+ align:start position:0%
+11-35 there's a reference to it um in
+your textbook a paper that an article
+
+ align:start position:0%
+your textbook a paper that an article
+ 
+
+ align:start position:0%
+your textbook a paper that an article
+that talks about it in much more detail
+
+ align:start position:0%
+that talks about it in much more detail
+ 
+
+ align:start position:0%
+that talks about it in much more detail
+on on how it's actually made um on the
+
+ align:start position:0%
+on on how it's actually made um on the
+ 
+
+ align:start position:0%
+on on how it's actually made um on the
+left hand side is sort of showing the um
+
+ align:start position:0%
+left hand side is sort of showing the um
+ 
+
+ align:start position:0%
+left hand side is sort of showing the um
+the the mask layout in order to make one
+
+ align:start position:0%
+the the mask layout in order to make one
+ 
+
+ align:start position:0%
+the the mask layout in order to make one
+of these structures and what you do is
+
+ align:start position:0%
+of these structures and what you do is
+ 
+
+ align:start position:0%
+of these structures and what you do is
+you have these dark regions here that
+
+ align:start position:0%
+you have these dark regions here that
+ 
+
+ align:start position:0%
+you have these dark regions here that
+are that are funny shaped uh are
+
+ align:start position:0%
+are that are funny shaped uh are
+ 
+
+ align:start position:0%
+are that are funny shaped uh are
+considered to be um the N plus region
+
+ align:start position:0%
+considered to be um the N plus region
+ 
+
+ align:start position:0%
+considered to be um the N plus region
+that you want want a contact so that
+
+ align:start position:0%
+that you want want a contact so that
+ 
+
+ align:start position:0%
+that you want want a contact so that
+would be called The N plus diffusion uh
+
+ align:start position:0%
+would be called The N plus diffusion uh
+ 
+
+ align:start position:0%
+would be called The N plus diffusion uh
+has this particular shape um the uh Dash
+
+ align:start position:0%
+has this particular shape um the uh Dash
+ 
+
+ align:start position:0%
+has this particular shape um the uh Dash
+lines represent the metal uh so that
+
+ align:start position:0%
+lines represent the metal uh so that
+ 
+
+ align:start position:0%
+lines represent the metal uh so that
+would be the metal level so this is
+
+ align:start position:0%
+would be the metal level so this is
+ 
+
+ align:start position:0%
+would be the metal level so this is
+going to take uh at least three masks to
+
+ align:start position:0%
+going to take uh at least three masks to
+ 
+
+ align:start position:0%
+going to take uh at least three masks to
+patter and these little square regions
+
+ align:start position:0%
+patter and these little square regions
+ 
+
+ align:start position:0%
+patter and these little square regions
+uh with the X's going through them are
+
+ align:start position:0%
+uh with the X's going through them are
+ 
+
+ align:start position:0%
+uh with the X's going through them are
+the contacts so that's the region where
+
+ align:start position:0%
+the contacts so that's the region where
+ 
+
+ align:start position:0%
+the contacts so that's the region where
+um one layer uh contacts uh um the layer
+
+ align:start position:0%
+um one layer uh contacts uh um the layer
+ 
+
+ align:start position:0%
+um one layer uh contacts uh um the layer
+above it or below it so this is sort of
+
+ align:start position:0%
+above it or below it so this is sort of
+ 
+
+ align:start position:0%
+above it or below it so this is sort of
+a planer view if you want more of a
+
+ align:start position:0%
+a planer view if you want more of a
+ 
+
+ align:start position:0%
+a planer view if you want more of a
+bird's eye view of actually how it's how
+
+ align:start position:0%
+bird's eye view of actually how it's how
+ 
+
+ align:start position:0%
+bird's eye view of actually how it's how
+it looks you can look on the right hand
+
+ align:start position:0%
+it looks you can look on the right hand
+ 
+
+ align:start position:0%
+it looks you can look on the right hand
+side and um these L-shaped brackets are
+
+ align:start position:0%
+side and um these L-shaped brackets are
+ 
+
+ align:start position:0%
+side and um these L-shaped brackets are
+are made of metal so there's one here uh
+
+ align:start position:0%
+are made of metal so there's one here uh
+ 
+
+ align:start position:0%
+are made of metal so there's one here uh
+and one here and basically it you for
+
+ align:start position:0%
+and one here and basically it you for
+ 
+
+ align:start position:0%
+and one here and basically it you for
+perform a fourpoint uh kind of
+
+ align:start position:0%
+perform a fourpoint uh kind of
+ 
+
+ align:start position:0%
+perform a fourpoint uh kind of
+measurement what you're doing is this
+
+ align:start position:0%
+measurement what you're doing is this
+ 
+
+ align:start position:0%
+measurement what you're doing is this
+little region here that square in the
+
+ align:start position:0%
+little region here that square in the
+ 
+
+ align:start position:0%
+little region here that square in the
+center that has a dimension of L in one
+
+ align:start position:0%
+center that has a dimension of L in one
+ 
+
+ align:start position:0%
+center that has a dimension of L in one
+in one dimension by L in the other so
+
+ align:start position:0%
+in one dimension by L in the other so
+ 
+
+ align:start position:0%
+in one dimension by L in the other so
+this is an L by L Square the current
+
+ align:start position:0%
+this is an L by L Square the current
+ 
+
+ align:start position:0%
+this is an L by L Square the current
+then comes through on this leg so if the
+
+ align:start position:0%
+then comes through on this leg so if the
+ 
+
+ align:start position:0%
+then comes through on this leg so if the
+current flows through diffusion then it
+
+ align:start position:0%
+current flows through diffusion then it
+ 
+
+ align:start position:0%
+current flows through diffusion then it
+flows up through this square the square
+
+ align:start position:0%
+flows up through this square the square
+ 
+
+ align:start position:0%
+flows up through this square the square
+contact and it flows out through probe
+
+ align:start position:0%
+contact and it flows out through probe
+ 
+
+ align:start position:0%
+contact and it flows out through probe
+number two on the metal so you put an
+
+ align:start position:0%
+number two on the metal so you put an
+ 
+
+ align:start position:0%
+number two on the metal so you put an
+ammeter here uh you put an ameter
+
+ align:start position:0%
+ammeter here uh you put an ameter
+ 
+
+ align:start position:0%
+ammeter here uh you put an ameter
+between probes two and three and you
+
+ align:start position:0%
+between probes two and three and you
+ 
+
+ align:start position:0%
+between probes two and three and you
+measure that current that's flowing
+
+ align:start position:0%
+measure that current that's flowing
+ 
+
+ align:start position:0%
+measure that current that's flowing
+through that square contact and then you
+
+ align:start position:0%
+through that square contact and then you
+ 
+
+ align:start position:0%
+through that square contact and then you
+put a voltmeter between probes one and
+
+ align:start position:0%
+put a voltmeter between probes one and
+ 
+
+ align:start position:0%
+put a voltmeter between probes one and
+four um and you measure the voltage drop
+
+ align:start position:0%
+four um and you measure the voltage drop
+ 
+
+ align:start position:0%
+four um and you measure the voltage drop
+across that face and then you just
+
+ align:start position:0%
+across that face and then you just
+ 
+
+ align:start position:0%
+across that face and then you just
+divide V divided by um uh I whatever you
+
+ align:start position:0%
+divide V divided by um uh I whatever you
+ 
+
+ align:start position:0%
+divide V divided by um uh I whatever you
+measure the measured voltage between 1
+
+ align:start position:0%
+measure the measured voltage between 1
+ 
+
+ align:start position:0%
+measure the measured voltage between 1
+and four divided by the current flowing
+
+ align:start position:0%
+and four divided by the current flowing
+ 
+
+ align:start position:0%
+and four divided by the current flowing
+between two and three and that is your
+
+ align:start position:0%
+between two and three and that is your
+ 
+
+ align:start position:0%
+between two and three and that is your
+uh resistance and that's going to be
+
+ align:start position:0%
+uh resistance and that's going to be
+ 
+
+ align:start position:0%
+uh resistance and that's going to be
+equivalent to row C divided by um the
+
+ align:start position:0%
+equivalent to row C divided by um the
+ 
+
+ align:start position:0%
+equivalent to row C divided by um the
+area of the contact l squ so this is a
+
+ align:start position:0%
+area of the contact l squ so this is a
+ 
+
+ align:start position:0%
+area of the contact l squ so this is a
+very common way to do it you might say
+
+ align:start position:0%
+very common way to do it you might say
+ 
+
+ align:start position:0%
+very common way to do it you might say
+well why do you go to the effort of
+
+ align:start position:0%
+well why do you go to the effort of
+ 
+
+ align:start position:0%
+well why do you go to the effort of
+making you know having separate probes
+
+ align:start position:0%
+making you know having separate probes
+ 
+
+ align:start position:0%
+making you know having separate probes
+why don't you just put you know uh um
+
+ align:start position:0%
+why don't you just put you know uh um
+ 
+
+ align:start position:0%
+why don't you just put you know uh um
+you know measure the current and the and
+
+ align:start position:0%
+you know measure the current and the and
+ 
+
+ align:start position:0%
+you know measure the current and the and
+the voltage um uh at the same uh uh on
+
+ align:start position:0%
+the voltage um uh at the same uh uh on
+ 
+
+ align:start position:0%
+the voltage um uh at the same uh uh on
+the same prob points and the reason you
+
+ align:start position:0%
+the same prob points and the reason you
+ 
+
+ align:start position:0%
+the same prob points and the reason you
+do this is because you don't want to
+
+ align:start position:0%
+do this is because you don't want to
+ 
+
+ align:start position:0%
+do this is because you don't want to
+have extra contact resistance say of
+
+ align:start position:0%
+have extra contact resistance say of
+ 
+
+ align:start position:0%
+have extra contact resistance say of
+your probes going down down uh and
+
+ align:start position:0%
+your probes going down down uh and
+ 
+
+ align:start position:0%
+your probes going down down uh and
+there's always a voltage drop there so
+
+ align:start position:0%
+there's always a voltage drop there so
+ 
+
+ align:start position:0%
+there's always a voltage drop there so
+this uh the probes through which you um
+
+ align:start position:0%
+this uh the probes through which you um
+ 
+
+ align:start position:0%
+this uh the probes through which you um
+Force the current are separate from the
+
+ align:start position:0%
+Force the current are separate from the
+ 
+
+ align:start position:0%
+Force the current are separate from the
+probes for which you measure the voltage
+
+ align:start position:0%
+probes for which you measure the voltage
+ 
+
+ align:start position:0%
+probes for which you measure the voltage
+so that therefore you're only measuring
+
+ align:start position:0%
+so that therefore you're only measuring
+ 
+
+ align:start position:0%
+so that therefore you're only measuring
+really the voltage drop uh across this
+
+ align:start position:0%
+really the voltage drop uh across this
+ 
+
+ align:start position:0%
+really the voltage drop uh across this
+uh the contact face the square face so
+
+ align:start position:0%
+uh the contact face the square face so
+ 
+
+ align:start position:0%
+uh the contact face the square face so
+this a very common structure the celvin
+
+ align:start position:0%
+this a very common structure the celvin
+ 
+
+ align:start position:0%
+this a very common structure the celvin
+structure you'll find on a lot of test
+
+ align:start position:0%
+structure you'll find on a lot of test
+ 
+
+ align:start position:0%
+structure you'll find on a lot of test
+masks and test circuits that people use
+
+ align:start position:0%
+masks and test circuits that people use
+ 
+
+ align:start position:0%
+masks and test circuits that people use
+to measure the contact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resistivity here's an example shown on
+
+ align:start position:0%
+resistivity here's an example shown on
+ 
+
+ align:start position:0%
+resistivity here's an example shown on
+on slide 11 uh using a cross pit Kelvin
+
+ align:start position:0%
+on slide 11 uh using a cross pit Kelvin
+ 
+
+ align:start position:0%
+on slide 11 uh using a cross pit Kelvin
+structure and you have a one micron by
+
+ align:start position:0%
+structure and you have a one micron by
+ 
+
+ align:start position:0%
+structure and you have a one micron by
+one micron opening uh you find that you
+
+ align:start position:0%
+one micron opening uh you find that you
+ 
+
+ align:start position:0%
+one micron opening uh you find that you
+get a current of 10 microamps through
+
+ align:start position:0%
+get a current of 10 microamps through
+ 
+
+ align:start position:0%
+get a current of 10 microamps through
+the contact so that's
+
+ align:start position:0%
+the contact so that's
+ 
+
+ align:start position:0%
+the contact so that's
+i23 uh when you measure a voltage drop
+
+ align:start position:0%
+i23 uh when you measure a voltage drop
+ 
+
+ align:start position:0%
+i23 uh when you measure a voltage drop
+of about uh 320 microvolts what is the
+
+ align:start position:0%
+of about uh 320 microvolts what is the
+ 
+
+ align:start position:0%
+of about uh 320 microvolts what is the
+specific contact
+
+ align:start position:0%
+specific contact
+ 
+
+ align:start position:0%
+specific contact
+resistivity um so you just divide the
+
+ align:start position:0%
+resistivity um so you just divide the
+ 
+
+ align:start position:0%
+resistivity um so you just divide the
+voltage drop divided by the current um
+
+ align:start position:0%
+voltage drop divided by the current um
+ 
+
+ align:start position:0%
+voltage drop divided by the current um
+and that gives you a resistance number
+
+ align:start position:0%
+and that gives you a resistance number
+ 
+
+ align:start position:0%
+and that gives you a resistance number
+in fact that's 32 ohms and by by
+
+ align:start position:0%
+in fact that's 32 ohms and by by
+ 
+
+ align:start position:0%
+in fact that's 32 ohms and by by
+definition that's equal to row C divided
+
+ align:start position:0%
+definition that's equal to row C divided
+ 
+
+ align:start position:0%
+definition that's equal to row C divided
+by the area of the contact so you can
+
+ align:start position:0%
+by the area of the contact so you can
+ 
+
+ align:start position:0%
+by the area of the contact so you can
+solve for row C here just by multiplying
+
+ align:start position:0%
+solve for row C here just by multiplying
+ 
+
+ align:start position:0%
+solve for row C here just by multiplying
+32 ohms by the area of the contact and
+
+ align:start position:0%
+32 ohms by the area of the contact and
+ 
+
+ align:start position:0%
+32 ohms by the area of the contact and
+you get 3.2 * 10- 7 ohm cenm squ it's
+
+ align:start position:0%
+you get 3.2 * 10- 7 ohm cenm squ it's
+ 
+
+ align:start position:0%
+you get 3.2 * 10- 7 ohm cenm squ it's
+pretty close to the itrs requirement
+
+ align:start position:0%
+pretty close to the itrs requirement
+ 
+
+ align:start position:0%
+pretty close to the itrs requirement
+still a little bit High still about a
+
+ align:start position:0%
+still a little bit High still about a
+ 
+
+ align:start position:0%
+still a little bit High still about a
+factor of two too high but it just gives
+
+ align:start position:0%
+factor of two too high but it just gives
+ 
+
+ align:start position:0%
+factor of two too high but it just gives
+you an idea typically you use several
+
+ align:start position:0%
+you an idea typically you use several
+ 
+
+ align:start position:0%
+you an idea typically you use several
+different dimensions so you use a 1 by
+
+ align:start position:0%
+different dimensions so you use a 1 by
+ 
+
+ align:start position:0%
+different dimensions so you use a 1 by
+one a 5x5 and a 10x10 Square uh and you
+
+ align:start position:0%
+one a 5x5 and a 10x10 Square uh and you
+ 
+
+ align:start position:0%
+one a 5x5 and a 10x10 Square uh and you
+make sure you get the same specific
+
+ align:start position:0%
+make sure you get the same specific
+ 
+
+ align:start position:0%
+make sure you get the same specific
+contact resistivity number over all of
+
+ align:start position:0%
+contact resistivity number over all of
+ 
+
+ align:start position:0%
+contact resistivity number over all of
+those um because sometimes you can have
+
+ align:start position:0%
+those um because sometimes you can have
+ 
+
+ align:start position:0%
+those um because sometimes you can have
+current crowding effects when I drew it
+
+ align:start position:0%
+current crowding effects when I drew it
+ 
+
+ align:start position:0%
+current crowding effects when I drew it
+in this picture here on on page 13 I
+
+ align:start position:0%
+in this picture here on on page 13 I
+ 
+
+ align:start position:0%
+in this picture here on on page 13 I
+said the current is uniformly going
+
+ align:start position:0%
+said the current is uniformly going
+ 
+
+ align:start position:0%
+said the current is uniformly going
+through that face so you can imagine
+
+ align:start position:0%
+through that face so you can imagine
+ 
+
+ align:start position:0%
+through that face so you can imagine
+like a flow of water uniformly flowing
+
+ align:start position:0%
+like a flow of water uniformly flowing
+ 
+
+ align:start position:0%
+like a flow of water uniformly flowing
+with the same flux all across the face
+
+ align:start position:0%
+with the same flux all across the face
+ 
+
+ align:start position:0%
+with the same flux all across the face
+that may or may not be true depending on
+
+ align:start position:0%
+that may or may not be true depending on
+ 
+
+ align:start position:0%
+that may or may not be true depending on
+the series resistance of this n plus
+
+ align:start position:0%
+the series resistance of this n plus
+ 
+
+ align:start position:0%
+the series resistance of this n plus
+diffusion and things like that so um you
+
+ align:start position:0%
+diffusion and things like that so um you
+ 
+
+ align:start position:0%
+diffusion and things like that so um you
+want to use different areas and for
+
+ align:start position:0%
+want to use different areas and for
+ 
+
+ align:start position:0%
+want to use different areas and for
+different size areas you should get the
+
+ align:start position:0%
+different size areas you should get the
+ 
+
+ align:start position:0%
+different size areas you should get the
+same number if you don't and you
+
+ align:start position:0%
+same number if you don't and you
+ 
+
+ align:start position:0%
+same number if you don't and you
+probably have current crowding effects
+
+ align:start position:0%
+probably have current crowding effects
+ 
+
+ align:start position:0%
+probably have current crowding effects
+and you need a more sophisticated
+
+ align:start position:0%
+and you need a more sophisticated
+ 
+
+ align:start position:0%
+and you need a more sophisticated
+two-dimensional
+
+ align:start position:0%
+two-dimensional
+ 
+
+ align:start position:0%
+two-dimensional
+model so that's a typical way that
+
+ align:start position:0%
+model so that's a typical way that
+ 
+
+ align:start position:0%
+model so that's a typical way that
+people would measure um their contact
+
+ align:start position:0%
+people would measure um their contact
+ 
+
+ align:start position:0%
+people would measure um their contact
+resistance so that sort of introduces
+
+ align:start position:0%
+resistance so that sort of introduces
+ 
+
+ align:start position:0%
+resistance so that sort of introduces
+the whole idea of scaling and why we
+
+ align:start position:0%
+the whole idea of scaling and why we
+ 
+
+ align:start position:0%
+the whole idea of scaling and why we
+want to do this um I want to bring up
+
+ align:start position:0%
+want to do this um I want to bring up
+ 
+
+ align:start position:0%
+want to do this um I want to bring up
+some other requirements we we said it's
+
+ align:start position:0%
+some other requirements we we said it's
+ 
+
+ align:start position:0%
+some other requirements we we said it's
+good it's important to make a low
+
+ align:start position:0%
+good it's important to make a low
+ 
+
+ align:start position:0%
+good it's important to make a low
+resistance contact but there are other
+
+ align:start position:0%
+resistance contact but there are other
+ 
+
+ align:start position:0%
+resistance contact but there are other
+requirements besides that um so clearly
+
+ align:start position:0%
+requirements besides that um so clearly
+ 
+
+ align:start position:0%
+requirements besides that um so clearly
+we need to have a high doping
+
+ align:start position:0%
+we need to have a high doping
+ 
+
+ align:start position:0%
+we need to have a high doping
+concentration at the interface that's
+
+ align:start position:0%
+concentration at the interface that's
+ 
+
+ align:start position:0%
+concentration at the interface that's
+going to allow the electrical tunneling
+
+ align:start position:0%
+going to allow the electrical tunneling
+ 
+
+ align:start position:0%
+going to allow the electrical tunneling
+to take place you need to be the
+
+ align:start position:0%
+to take place you need to be the
+ 
+
+ align:start position:0%
+to take place you need to be the
+interface has to be free of contamin as
+
+ align:start position:0%
+interface has to be free of contamin as
+ 
+
+ align:start position:0%
+interface has to be free of contamin as
+I me mentioned you want to get rid of
+
+ align:start position:0%
+I me mentioned you want to get rid of
+ 
+
+ align:start position:0%
+I me mentioned you want to get rid of
+the Native oxide so you preferably use a
+
+ align:start position:0%
+the Native oxide so you preferably use a
+ 
+
+ align:start position:0%
+the Native oxide so you preferably use a
+metal that will kind of eat away if
+
+ align:start position:0%
+metal that will kind of eat away if
+ 
+
+ align:start position:0%
+metal that will kind of eat away if
+there is any little native oxide that
+
+ align:start position:0%
+there is any little native oxide that
+ 
+
+ align:start position:0%
+there is any little native oxide that
+will eat it away and you clearly don't
+
+ align:start position:0%
+will eat it away and you clearly don't
+ 
+
+ align:start position:0%
+will eat it away and you clearly don't
+want residues you don't want a lot of
+
+ align:start position:0%
+want residues you don't want a lot of
+ 
+
+ align:start position:0%
+want residues you don't want a lot of
+excess carbon or other things at the
+
+ align:start position:0%
+excess carbon or other things at the
+ 
+
+ align:start position:0%
+excess carbon or other things at the
+interface because that's going to cause
+
+ align:start position:0%
+interface because that's going to cause
+ 
+
+ align:start position:0%
+interface because that's going to cause
+an increase in your contact resistance
+
+ align:start position:0%
+an increase in your contact resistance
+ 
+
+ align:start position:0%
+an increase in your contact resistance
+you don't want nitride or oxide there
+
+ align:start position:0%
+you don't want nitride or oxide there
+ 
+
+ align:start position:0%
+you don't want nitride or oxide there
+that's one thing to get low contact
+
+ align:start position:0%
+that's one thing to get low contact
+ 
+
+ align:start position:0%
+that's one thing to get low contact
+resistance the second thing you want is
+
+ align:start position:0%
+resistance the second thing you want is
+ 
+
+ align:start position:0%
+resistance the second thing you want is
+good thermal stability um you don't want
+
+ align:start position:0%
+good thermal stability um you don't want
+ 
+
+ align:start position:0%
+good thermal stability um you don't want
+the contact structure to change or
+
+ align:start position:0%
+the contact structure to change or
+ 
+
+ align:start position:0%
+the contact structure to change or
+degrade in some way during the process
+
+ align:start position:0%
+degrade in some way during the process
+ 
+
+ align:start position:0%
+degrade in some way during the process
+after all there will be subsequent
+
+ align:start position:0%
+after all there will be subsequent
+ 
+
+ align:start position:0%
+after all there will be subsequent
+thermal processing once you make those
+
+ align:start position:0%
+thermal processing once you make those
+ 
+
+ align:start position:0%
+thermal processing once you make those
+contacts you still have to make all that
+
+ align:start position:0%
+contacts you still have to make all that
+ 
+
+ align:start position:0%
+contacts you still have to make all that
+multi-level metal okay and those
+
+ align:start position:0%
+multi-level metal okay and those
+ 
+
+ align:start position:0%
+multi-level metal okay and those
+multi-level metal schemes involved you
+
+ align:start position:0%
+multi-level metal schemes involved you
+ 
+
+ align:start position:0%
+multi-level metal schemes involved you
+know uh uh in knealing steps or
+
+ align:start position:0%
+know uh uh in knealing steps or
+ 
+
+ align:start position:0%
+know uh uh in knealing steps or
+deposition steps that could be in the
+
+ align:start position:0%
+deposition steps that could be in the
+ 
+
+ align:start position:0%
+deposition steps that could be in the
+range of four to 500 Degrees so you
+
+ align:start position:0%
+range of four to 500 Degrees so you
+ 
+
+ align:start position:0%
+range of four to 500 Degrees so you
+don't want the anything weird happening
+
+ align:start position:0%
+don't want the anything weird happening
+ 
+
+ align:start position:0%
+don't want the anything weird happening
+down in your contact when you heat the
+
+ align:start position:0%
+down in your contact when you heat the
+ 
+
+ align:start position:0%
+down in your contact when you heat the
+thing um and in particular uh you're
+
+ align:start position:0%
+thing um and in particular uh you're
+ 
+
+ align:start position:0%
+thing um and in particular uh you're
+also very concerned about Junction
+
+ align:start position:0%
+also very concerned about Junction
+ 
+
+ align:start position:0%
+also very concerned about Junction
+leakage remember this Electrical uh
+
+ align:start position:0%
+leakage remember this Electrical uh
+ 
+
+ align:start position:0%
+leakage remember this Electrical uh
+metal this metal making electrical
+
+ align:start position:0%
+metal this metal making electrical
+ 
+
+ align:start position:0%
+metal this metal making electrical
+contact to a p and Junction this is
+
+ align:start position:0%
+contact to a p and Junction this is
+ 
+
+ align:start position:0%
+contact to a p and Junction this is
+right this is an N plus P Junction um so
+
+ align:start position:0%
+right this is an N plus P Junction um so
+ 
+
+ align:start position:0%
+right this is an N plus P Junction um so
+you don't you want it to be uh
+
+ align:start position:0%
+you don't you want it to be uh
+ 
+
+ align:start position:0%
+you don't you want it to be uh
+ultimately this n plus P Junction to
+
+ align:start position:0%
+ultimately this n plus P Junction to
+ 
+
+ align:start position:0%
+ultimately this n plus P Junction to
+have good Junction characteristics and
+
+ align:start position:0%
+have good Junction characteristics and
+ 
+
+ align:start position:0%
+have good Junction characteristics and
+and low leakage uh in the Silicon
+
+ align:start position:0%
+and low leakage uh in the Silicon
+ 
+
+ align:start position:0%
+and low leakage uh in the Silicon
+underneath the
+
+ align:start position:0%
+underneath the
+ 
+
+ align:start position:0%
+underneath the
+contact so here on slide 15 I'm showing
+
+ align:start position:0%
+contact so here on slide 15 I'm showing
+ 
+
+ align:start position:0%
+contact so here on slide 15 I'm showing
+an example of a figure I took out of the
+
+ align:start position:0%
+an example of a figure I took out of the
+ 
+
+ align:start position:0%
+an example of a figure I took out of the
+text where something very bad has
+
+ align:start position:0%
+text where something very bad has
+ 
+
+ align:start position:0%
+text where something very bad has
+happened um which is called spiking of
+
+ align:start position:0%
+happened um which is called spiking of
+ 
+
+ align:start position:0%
+happened um which is called spiking of
+the metal and you can see what's
+
+ align:start position:0%
+the metal and you can see what's
+ 
+
+ align:start position:0%
+the metal and you can see what's
+happened this is the metal aluminum is
+
+ align:start position:0%
+happened this is the metal aluminum is
+ 
+
+ align:start position:0%
+happened this is the metal aluminum is
+shown here um and this is my n plus
+
+ align:start position:0%
+shown here um and this is my n plus
+ 
+
+ align:start position:0%
+shown here um and this is my n plus
+drain or source and this aluminum has uh
+
+ align:start position:0%
+drain or source and this aluminum has uh
+ 
+
+ align:start position:0%
+drain or source and this aluminum has uh
+this um uh chip has been heated up and
+
+ align:start position:0%
+this um uh chip has been heated up and
+ 
+
+ align:start position:0%
+this um uh chip has been heated up and
+the aluminum has actually spiked through
+
+ align:start position:0%
+the aluminum has actually spiked through
+ 
+
+ align:start position:0%
+the aluminum has actually spiked through
+uh the the the junction it's actually
+
+ align:start position:0%
+uh the the the junction it's actually
+ 
+
+ align:start position:0%
+uh the the the junction it's actually
+touching now the ptype Silicon so it's
+
+ align:start position:0%
+touching now the ptype Silicon so it's
+ 
+
+ align:start position:0%
+touching now the ptype Silicon so it's
+really shorted out um it's essentially
+
+ align:start position:0%
+really shorted out um it's essentially
+ 
+
+ align:start position:0%
+really shorted out um it's essentially
+shorted out this uh PN
+
+ align:start position:0%
+shorted out this uh PN
+ 
+
+ align:start position:0%
+shorted out this uh PN
+Junction uh it's created a lot of Noid
+
+ align:start position:0%
+Junction uh it's created a lot of Noid
+ 
+
+ align:start position:0%
+Junction uh it's created a lot of Noid
+and this is a big problem and that's
+
+ align:start position:0%
+and this is a big problem and that's
+ 
+
+ align:start position:0%
+and this is a big problem and that's
+because aluminum has a finite solubility
+
+ align:start position:0%
+because aluminum has a finite solubility
+ 
+
+ align:start position:0%
+because aluminum has a finite solubility
+for silicon the Silicon actually gets
+
+ align:start position:0%
+for silicon the Silicon actually gets
+ 
+
+ align:start position:0%
+for silicon the Silicon actually gets
+sucked into the aluminum uh and causes
+
+ align:start position:0%
+sucked into the aluminum uh and causes
+ 
+
+ align:start position:0%
+sucked into the aluminum uh and causes
+the spiking of effect and this is one
+
+ align:start position:0%
+the spiking of effect and this is one
+ 
+
+ align:start position:0%
+the spiking of effect and this is one
+reason why um if you have a very deep
+
+ align:start position:0%
+reason why um if you have a very deep
+ 
+
+ align:start position:0%
+reason why um if you have a very deep
+Junction that's many microns deep well a
+
+ align:start position:0%
+Junction that's many microns deep well a
+ 
+
+ align:start position:0%
+Junction that's many microns deep well a
+little it would never Spike because it
+
+ align:start position:0%
+little it would never Spike because it
+ 
+
+ align:start position:0%
+little it would never Spike because it
+never gets that deep but um now the
+
+ align:start position:0%
+never gets that deep but um now the
+ 
+
+ align:start position:0%
+never gets that deep but um now the
+Junctions are very shallow they're 0.1
+
+ align:start position:0%
+Junctions are very shallow they're 0.1
+ 
+
+ align:start position:0%
+Junctions are very shallow they're 0.1
+Micron or less people never put aluminum
+
+ align:start position:0%
+Micron or less people never put aluminum
+ 
+
+ align:start position:0%
+Micron or less people never put aluminum
+directly in contact with silicon so in
+
+ align:start position:0%
+directly in contact with silicon so in
+ 
+
+ align:start position:0%
+directly in contact with silicon so in
+the old days this is way how this is the
+
+ align:start position:0%
+the old days this is way how this is the
+ 
+
+ align:start position:0%
+the old days this is way how this is the
+way people made contacts today if you do
+
+ align:start position:0%
+way people made contacts today if you do
+ 
+
+ align:start position:0%
+way people made contacts today if you do
+this with any kind of reasonably shallow
+
+ align:start position:0%
+this with any kind of reasonably shallow
+ 
+
+ align:start position:0%
+this with any kind of reasonably shallow
+Junction you're going to when you go to
+
+ align:start position:0%
+Junction you're going to when you go to
+ 
+
+ align:start position:0%
+Junction you're going to when you go to
+heat the thing up to do the final
+
+ align:start position:0%
+heat the thing up to do the final
+ 
+
+ align:start position:0%
+heat the thing up to do the final
+forming gasal you're going to spike The
+
+ align:start position:0%
+forming gasal you're going to spike The
+ 
+
+ align:start position:0%
+forming gasal you're going to spike The
+Junction and you're going to destroy the
+
+ align:start position:0%
+Junction and you're going to destroy the
+ 
+
+ align:start position:0%
+Junction and you're going to destroy the
+device
+
+ align:start position:0%
+device
+ 
+
+ align:start position:0%
+device
+uh here's an example on on slide 16 of
+
+ align:start position:0%
+uh here's an example on on slide 16 of
+ 
+
+ align:start position:0%
+uh here's an example on on slide 16 of
+uh of what happens in some extreme cases
+
+ align:start position:0%
+uh of what happens in some extreme cases
+ 
+
+ align:start position:0%
+uh of what happens in some extreme cases
+of Junction spiking what we're actually
+
+ align:start position:0%
+of Junction spiking what we're actually
+ 
+
+ align:start position:0%
+of Junction spiking what we're actually
+looking at what I showed you here in the
+
+ align:start position:0%
+looking at what I showed you here in the
+ 
+
+ align:start position:0%
+looking at what I showed you here in the
+prior slide this is a cross-section view
+
+ align:start position:0%
+prior slide this is a cross-section view
+ 
+
+ align:start position:0%
+prior slide this is a cross-section view
+you can see the way the aluminum has
+
+ align:start position:0%
+you can see the way the aluminum has
+ 
+
+ align:start position:0%
+you can see the way the aluminum has
+created uh has spiked into the Silicon
+
+ align:start position:0%
+created uh has spiked into the Silicon
+ 
+
+ align:start position:0%
+created uh has spiked into the Silicon
+um in fact if you look sort of in in in
+
+ align:start position:0%
+um in fact if you look sort of in in in
+ 
+
+ align:start position:0%
+um in fact if you look sort of in in in
+plan view at a tilt angle of about 45
+
+ align:start position:0%
+plan view at a tilt angle of about 45
+ 
+
+ align:start position:0%
+plan view at a tilt angle of about 45
+degrees U this is a contact region and
+
+ align:start position:0%
+degrees U this is a contact region and
+ 
+
+ align:start position:0%
+degrees U this is a contact region and
+around it is uh oxide um these are 5x5
+
+ align:start position:0%
+around it is uh oxide um these are 5x5
+ 
+
+ align:start position:0%
+around it is uh oxide um these are 5x5
+Micron holes so they're fairly large uh
+
+ align:start position:0%
+Micron holes so they're fairly large uh
+ 
+
+ align:start position:0%
+Micron holes so they're fairly large uh
+these were analed by rapid thermal
+
+ align:start position:0%
+these were analed by rapid thermal
+ 
+
+ align:start position:0%
+these were analed by rapid thermal
+processing and then the aluminum layer
+
+ align:start position:0%
+processing and then the aluminum layer
+ 
+
+ align:start position:0%
+processing and then the aluminum layer
+was removed just to see what happened uh
+
+ align:start position:0%
+was removed just to see what happened uh
+ 
+
+ align:start position:0%
+was removed just to see what happened uh
+and in fact this was a Neal for 10
+
+ align:start position:0%
+and in fact this was a Neal for 10
+ 
+
+ align:start position:0%
+and in fact this was a Neal for 10
+minutes at 425 so this is aluminum
+
+ align:start position:0%
+minutes at 425 so this is aluminum
+ 
+
+ align:start position:0%
+minutes at 425 so this is aluminum
+directly in contact with silicon at 10
+
+ align:start position:0%
+directly in contact with silicon at 10
+ 
+
+ align:start position:0%
+directly in contact with silicon at 10
+minutes at 425 you can see it's created
+
+ align:start position:0%
+minutes at 425 you can see it's created
+ 
+
+ align:start position:0%
+minutes at 425 you can see it's created
+all these voids because the this there's
+
+ align:start position:0%
+all these voids because the this there's
+ 
+
+ align:start position:0%
+all these voids because the this there's
+a solubility of silicon in aluminum
+
+ align:start position:0%
+a solubility of silicon in aluminum
+ 
+
+ align:start position:0%
+a solubility of silicon in aluminum
+silicon from the substrate has actually
+
+ align:start position:0%
+silicon from the substrate has actually
+ 
+
+ align:start position:0%
+silicon from the substrate has actually
+gone up into the aluminum and it leaves
+
+ align:start position:0%
+gone up into the aluminum and it leaves
+ 
+
+ align:start position:0%
+gone up into the aluminum and it leaves
+behind voids uh which are end up being
+
+ align:start position:0%
+behind voids uh which are end up being
+ 
+
+ align:start position:0%
+behind voids uh which are end up being
+filled by the overlying uh aluminum and
+
+ align:start position:0%
+filled by the overlying uh aluminum and
+ 
+
+ align:start position:0%
+filled by the overlying uh aluminum and
+when you etge the aluminum off you get
+
+ align:start position:0%
+when you etge the aluminum off you get
+ 
+
+ align:start position:0%
+when you etge the aluminum off you get
+all see all these
+
+ align:start position:0%
+all see all these
+ 
+
+ align:start position:0%
+all see all these
+holes um so and if you do RTP at a lower
+
+ align:start position:0%
+holes um so and if you do RTP at a lower
+ 
+
+ align:start position:0%
+holes um so and if you do RTP at a lower
+temperature here 350 for 10 seconds you
+
+ align:start position:0%
+temperature here 350 for 10 seconds you
+ 
+
+ align:start position:0%
+temperature here 350 for 10 seconds you
+don't see nearly as many spikes nearly
+
+ align:start position:0%
+don't see nearly as many spikes nearly
+ 
+
+ align:start position:0%
+don't see nearly as many spikes nearly
+as many holes but 350 for 10 seconds is
+
+ align:start position:0%
+as many holes but 350 for 10 seconds is
+ 
+
+ align:start position:0%
+as many holes but 350 for 10 seconds is
+really too low for any kind of backend
+
+ align:start position:0%
+really too low for any kind of backend
+ 
+
+ align:start position:0%
+really too low for any kind of backend
+processing so this is why you never put
+
+ align:start position:0%
+processing so this is why you never put
+ 
+
+ align:start position:0%
+processing so this is why you never put
+aluminum directly in contact uh with
+
+ align:start position:0%
+aluminum directly in contact uh with
+ 
+
+ align:start position:0%
+aluminum directly in contact uh with
+silicon unless you're making a really
+
+ align:start position:0%
+silicon unless you're making a really
+ 
+
+ align:start position:0%
+silicon unless you're making a really
+deep Junction like a micron deep
+
+ align:start position:0%
+deep Junction like a micron deep
+ 
+
+ align:start position:0%
+deep Junction like a micron deep
+Junction you have some kind of device
+
+ align:start position:0%
+Junction you have some kind of device
+ 
+
+ align:start position:0%
+Junction you have some kind of device
+but in mosfets today the typical drain
+
+ align:start position:0%
+but in mosfets today the typical drain
+ 
+
+ align:start position:0%
+but in mosfets today the typical drain
+Source drain Junctions are
+
+ align:start position:0%
+Source drain Junctions are
+ 
+
+ align:start position:0%
+Source drain Junctions are
+microns um so this is sort of a classic
+
+ align:start position:0%
+microns um so this is sort of a classic
+ 
+
+ align:start position:0%
+microns um so this is sort of a classic
+case uh of Junction
+
+ align:start position:0%
+case uh of Junction
+ 
+
+ align:start position:0%
+case uh of Junction
+spiking there are a couple different
+
+ align:start position:0%
+spiking there are a couple different
+ 
+
+ align:start position:0%
+spiking there are a couple different
+solutions people have come up with over
+
+ align:start position:0%
+solutions people have come up with over
+ 
+
+ align:start position:0%
+solutions people have come up with over
+the years one of them is shown here on
+
+ align:start position:0%
+the years one of them is shown here on
+ 
+
+ align:start position:0%
+the years one of them is shown here on
+slide um 17 although it's not perfect
+
+ align:start position:0%
+slide um 17 although it's not perfect
+ 
+
+ align:start position:0%
+slide um 17 although it's not perfect
+people had the idea of well don't use
+
+ align:start position:0%
+people had the idea of well don't use
+ 
+
+ align:start position:0%
+people had the idea of well don't use
+pure aluminum use an alloy of aluminum
+
+ align:start position:0%
+pure aluminum use an alloy of aluminum
+ 
+
+ align:start position:0%
+pure aluminum use an alloy of aluminum
+with one to 2% silicon and since we said
+
+ align:start position:0%
+with one to 2% silicon and since we said
+ 
+
+ align:start position:0%
+with one to 2% silicon and since we said
+that the Silicon is soluble in the
+
+ align:start position:0%
+that the Silicon is soluble in the
+ 
+
+ align:start position:0%
+that the Silicon is soluble in the
+aluminum if you put silicon in the metal
+
+ align:start position:0%
+aluminum if you put silicon in the metal
+ 
+
+ align:start position:0%
+aluminum if you put silicon in the metal
+itself so you when you sputter you don't
+
+ align:start position:0%
+itself so you when you sputter you don't
+ 
+
+ align:start position:0%
+itself so you when you sputter you don't
+sputter pure aluminum you sputter an
+
+ align:start position:0%
+sputter pure aluminum you sputter an
+ 
+
+ align:start position:0%
+sputter pure aluminum you sputter an
+alloy of aluminum and silicon then you
+
+ align:start position:0%
+alloy of aluminum and silicon then you
+ 
+
+ align:start position:0%
+alloy of aluminum and silicon then you
+think well okay it won't suck up any any
+
+ align:start position:0%
+think well okay it won't suck up any any
+ 
+
+ align:start position:0%
+think well okay it won't suck up any any
+silicon from the substrate because it's
+
+ align:start position:0%
+silicon from the substrate because it's
+ 
+
+ align:start position:0%
+silicon from the substrate because it's
+already in equilibrium it's already um
+
+ align:start position:0%
+already in equilibrium it's already um
+ 
+
+ align:start position:0%
+already in equilibrium it's already um
+you know it's already got all the
+
+ align:start position:0%
+you know it's already got all the
+ 
+
+ align:start position:0%
+you know it's already got all the
+Silicon it needs the the aluminum uh tic
+
+ align:start position:0%
+Silicon it needs the the aluminum uh tic
+ 
+
+ align:start position:0%
+Silicon it needs the the aluminum uh tic
+so it's not a problem but uh it's still
+
+ align:start position:0%
+so it's not a problem but uh it's still
+ 
+
+ align:start position:0%
+so it's not a problem but uh it's still
+a bit of an issue is that um the Silicon
+
+ align:start position:0%
+a bit of an issue is that um the Silicon
+ 
+
+ align:start position:0%
+a bit of an issue is that um the Silicon
+itself can actually precipitate out of
+
+ align:start position:0%
+itself can actually precipitate out of
+ 
+
+ align:start position:0%
+itself can actually precipitate out of
+the aluminum this is an example that's
+
+ align:start position:0%
+the aluminum this is an example that's
+ 
+
+ align:start position:0%
+the aluminum this is an example that's
+been um uh it's been heated uh and and
+
+ align:start position:0%
+been um uh it's been heated uh and and
+ 
+
+ align:start position:0%
+been um uh it's been heated uh and and
+uh then they remove the aluminum film
+
+ align:start position:0%
+uh then they remove the aluminum film
+ 
+
+ align:start position:0%
+uh then they remove the aluminum film
+and you get these little silicon
+
+ align:start position:0%
+and you get these little silicon
+ 
+
+ align:start position:0%
+and you get these little silicon
+precipitates which can increase the
+
+ align:start position:0%
+precipitates which can increase the
+ 
+
+ align:start position:0%
+precipitates which can increase the
+specific contact resistance especially
+
+ align:start position:0%
+specific contact resistance especially
+ 
+
+ align:start position:0%
+specific contact resistance especially
+an end type silicon so it's making an an
+
+ align:start position:0%
+an end type silicon so it's making an an
+ 
+
+ align:start position:0%
+an end type silicon so it's making an an
+aluminum 1% silicon contact to Silicon
+
+ align:start position:0%
+aluminum 1% silicon contact to Silicon
+ 
+
+ align:start position:0%
+aluminum 1% silicon contact to Silicon
+which was again after pure aluminum
+
+ align:start position:0%
+which was again after pure aluminum
+ 
+
+ align:start position:0%
+which was again after pure aluminum
+people did the aluminum 1% silicon
+
+ align:start position:0%
+people did the aluminum 1% silicon
+ 
+
+ align:start position:0%
+people did the aluminum 1% silicon
+solution uh was a solution maybe in the
+
+ align:start position:0%
+solution uh was a solution maybe in the
+ 
+
+ align:start position:0%
+solution uh was a solution maybe in the
+1980s or so but again it's still not
+
+ align:start position:0%
+1980s or so but again it's still not
+ 
+
+ align:start position:0%
+1980s or so but again it's still not
+something that people typically do
+
+ align:start position:0%
+something that people typically do
+ 
+
+ align:start position:0%
+something that people typically do
+because you're going to get a higher
+
+ align:start position:0%
+because you're going to get a higher
+ 
+
+ align:start position:0%
+because you're going to get a higher
+contact resistance and you can still get
+
+ align:start position:0%
+contact resistance and you can still get
+ 
+
+ align:start position:0%
+contact resistance and you can still get
+spiking it's not a perfect um not a
+
+ align:start position:0%
+spiking it's not a perfect um not a
+ 
+
+ align:start position:0%
+spiking it's not a perfect um not a
+perfect
+
+ align:start position:0%
+perfect
+ 
+
+ align:start position:0%
+perfect
+solution but that was one uh solu ution
+
+ align:start position:0%
+solution but that was one uh solu ution
+ 
+
+ align:start position:0%
+solution but that was one uh solu ution
+that people did use at one
+
+ align:start position:0%
+that people did use at one
+ 
+
+ align:start position:0%
+that people did use at one
+point the way people go today is to form
+
+ align:start position:0%
+point the way people go today is to form
+ 
+
+ align:start position:0%
+point the way people go today is to form
+what they call a barrier layer and a
+
+ align:start position:0%
+what they call a barrier layer and a
+ 
+
+ align:start position:0%
+what they call a barrier layer and a
+barrier layer does exactly what the name
+
+ align:start position:0%
+barrier layer does exactly what the name
+ 
+
+ align:start position:0%
+barrier layer does exactly what the name
+says it forms a barrier between this
+
+ align:start position:0%
+says it forms a barrier between this
+ 
+
+ align:start position:0%
+says it forms a barrier between this
+aluminum and the Silicon um the barrier
+
+ align:start position:0%
+aluminum and the Silicon um the barrier
+ 
+
+ align:start position:0%
+aluminum and the Silicon um the barrier
+is has a very low specific contact
+
+ align:start position:0%
+is has a very low specific contact
+ 
+
+ align:start position:0%
+is has a very low specific contact
+resistivity so it still makes a good
+
+ align:start position:0%
+resistivity so it still makes a good
+ 
+
+ align:start position:0%
+resistivity so it still makes a good
+contact but it doesn't allow the
+
+ align:start position:0%
+contact but it doesn't allow the
+ 
+
+ align:start position:0%
+contact but it doesn't allow the
+aluminum or the Silicon to talk to each
+
+ align:start position:0%
+aluminum or the Silicon to talk to each
+ 
+
+ align:start position:0%
+aluminum or the Silicon to talk to each
+other so you cannot get this void
+
+ align:start position:0%
+other so you cannot get this void
+ 
+
+ align:start position:0%
+other so you cannot get this void
+formation you can't get the spiking so
+
+ align:start position:0%
+formation you can't get the spiking so
+ 
+
+ align:start position:0%
+formation you can't get the spiking so
+um typical barrier layers might be a
+
+ align:start position:0%
+um typical barrier layers might be a
+ 
+
+ align:start position:0%
+um typical barrier layers might be a
+thin layer of titanium say a thousand
+
+ align:start position:0%
+thin layer of titanium say a thousand
+ 
+
+ align:start position:0%
+thin layer of titanium say a thousand
+anrs of a titanium is often used uh or
+
+ align:start position:0%
+anrs of a titanium is often used uh or
+ 
+
+ align:start position:0%
+anrs of a titanium is often used uh or
+you sputter TI tungsten or maybe Tha
+
+ align:start position:0%
+you sputter TI tungsten or maybe Tha
+ 
+
+ align:start position:0%
+you sputter TI tungsten or maybe Tha
+silicide so in between the heavily dope
+
+ align:start position:0%
+silicide so in between the heavily dope
+ 
+
+ align:start position:0%
+silicide so in between the heavily dope
+silicon you now have an
+
+ align:start position:0%
+silicon you now have an
+ 
+
+ align:start position:0%
+silicon you now have an
+interlayer um of this material uh that
+
+ align:start position:0%
+interlayer um of this material uh that
+ 
+
+ align:start position:0%
+interlayer um of this material uh that
+forms a barrier so this prevents the
+
+ align:start position:0%
+forms a barrier so this prevents the
+ 
+
+ align:start position:0%
+forms a barrier so this prevents the
+chemical inter diffusion between the
+
+ align:start position:0%
+chemical inter diffusion between the
+ 
+
+ align:start position:0%
+chemical inter diffusion between the
+silicon and the and the aluminum
+
+ align:start position:0%
+silicon and the and the aluminum
+ 
+
+ align:start position:0%
+silicon and the and the aluminum
+generally has low stress you pick a
+
+ align:start position:0%
+generally has low stress you pick a
+ 
+
+ align:start position:0%
+generally has low stress you pick a
+material that has good adhesion so it
+
+ align:start position:0%
+material that has good adhesion so it
+ 
+
+ align:start position:0%
+material that has good adhesion so it
+doesn't peel off um and uh of course
+
+ align:start position:0%
+doesn't peel off um and uh of course
+ 
+
+ align:start position:0%
+doesn't peel off um and uh of course
+good electrical conductivity and low
+
+ align:start position:0%
+good electrical conductivity and low
+ 
+
+ align:start position:0%
+good electrical conductivity and low
+contact resistance silicon aluminum so
+
+ align:start position:0%
+contact resistance silicon aluminum so
+ 
+
+ align:start position:0%
+contact resistance silicon aluminum so
+that's to satisfy all these things and
+
+ align:start position:0%
+that's to satisfy all these things and
+ 
+
+ align:start position:0%
+that's to satisfy all these things and
+uh these are raised these these
+
+ align:start position:0%
+uh these are raised these these
+ 
+
+ align:start position:0%
+uh these are raised these these
+materials titanium and tit tungen have
+
+ align:start position:0%
+materials titanium and tit tungen have
+ 
+
+ align:start position:0%
+materials titanium and tit tungen have
+reasonable contact resistivity they is
+
+ align:start position:0%
+reasonable contact resistivity they is
+ 
+
+ align:start position:0%
+reasonable contact resistivity they is
+still not low enough to meet the a lot
+
+ align:start position:0%
+still not low enough to meet the a lot
+ 
+
+ align:start position:0%
+still not low enough to meet the a lot
+of the itrs requirements in the future
+
+ align:start position:0%
+of the itrs requirements in the future
+ 
+
+ align:start position:0%
+of the itrs requirements in the future
+but today they're uh they're good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enough uh this is just I I took on on uh
+
+ align:start position:0%
+enough uh this is just I I took on on uh
+ 
+
+ align:start position:0%
+enough uh this is just I I took on on uh
+slide 19 I took from a different
+
+ align:start position:0%
+slide 19 I took from a different
+ 
+
+ align:start position:0%
+slide 19 I took from a different
+textbook this is a figure from mayor and
+
+ align:start position:0%
+textbook this is a figure from mayor and
+ 
+
+ align:start position:0%
+textbook this is a figure from mayor and
+Lao I had mentioned mayor and lao's
+
+ align:start position:0%
+Lao I had mentioned mayor and lao's
+ 
+
+ align:start position:0%
+Lao I had mentioned mayor and lao's
+textbook at the very beginning of this
+
+ align:start position:0%
+textbook at the very beginning of this
+ 
+
+ align:start position:0%
+textbook at the very beginning of this
+course so you have a reference to it and
+
+ align:start position:0%
+course so you have a reference to it and
+ 
+
+ align:start position:0%
+course so you have a reference to it and
+this is just an example of uh in his
+
+ align:start position:0%
+this is just an example of uh in his
+ 
+
+ align:start position:0%
+this is just an example of uh in his
+book how he's saying a titanium may work
+
+ align:start position:0%
+book how he's saying a titanium may work
+ 
+
+ align:start position:0%
+book how he's saying a titanium may work
+as a sacrificial barrier uh may or may
+
+ align:start position:0%
+as a sacrificial barrier uh may or may
+ 
+
+ align:start position:0%
+as a sacrificial barrier uh may or may
+not exactly work this way but it's it's
+
+ align:start position:0%
+not exactly work this way but it's it's
+ 
+
+ align:start position:0%
+not exactly work this way but it's it's
+one potential U methodology you can
+
+ align:start position:0%
+one potential U methodology you can
+ 
+
+ align:start position:0%
+one potential U methodology you can
+imagine having a thin layer of titanium
+
+ align:start position:0%
+imagine having a thin layer of titanium
+ 
+
+ align:start position:0%
+imagine having a thin layer of titanium
+with aluminum on top when you heat the
+
+ align:start position:0%
+with aluminum on top when you heat the
+ 
+
+ align:start position:0%
+with aluminum on top when you heat the
+structure um you may get uh formation of
+
+ align:start position:0%
+structure um you may get uh formation of
+ 
+
+ align:start position:0%
+structure um you may get uh formation of
+tial3 uh for some time and Portion and
+
+ align:start position:0%
+tial3 uh for some time and Portion and
+ 
+
+ align:start position:0%
+tial3 uh for some time and Portion and
+then you heat it a little bit longer and
+
+ align:start position:0%
+then you heat it a little bit longer and
+ 
+
+ align:start position:0%
+then you heat it a little bit longer and
+all the titanium uh is
+
+ align:start position:0%
+all the titanium uh is
+ 
+
+ align:start position:0%
+all the titanium uh is
+consumed um and then here you at this
+
+ align:start position:0%
+consumed um and then here you at this
+ 
+
+ align:start position:0%
+consumed um and then here you at this
+point in D you can start to get the
+
+ align:start position:0%
+point in D you can start to get the
+ 
+
+ align:start position:0%
+point in D you can start to get the
+aluminum uh incursion um so the idea is
+
+ align:start position:0%
+aluminum uh incursion um so the idea is
+ 
+
+ align:start position:0%
+aluminum uh incursion um so the idea is
+you put down enough titanium that you're
+
+ align:start position:0%
+you put down enough titanium that you're
+ 
+
+ align:start position:0%
+you put down enough titanium that you're
+not going to end up uh with a spiking
+
+ align:start position:0%
+not going to end up uh with a spiking
+ 
+
+ align:start position:0%
+not going to end up uh with a spiking
+problem and typically uh for if you want
+
+ align:start position:0%
+problem and typically uh for if you want
+ 
+
+ align:start position:0%
+problem and typically uh for if you want
+to anal uh typical forming gas anal 450
+
+ align:start position:0%
+to anal uh typical forming gas anal 450
+ 
+
+ align:start position:0%
+to anal uh typical forming gas anal 450
+or so a th000 an of titanium seems to be
+
+ align:start position:0%
+or so a th000 an of titanium seems to be
+ 
+
+ align:start position:0%
+or so a th000 an of titanium seems to be
+adequate uh barrier layer but again it
+
+ align:start position:0%
+adequate uh barrier layer but again it
+ 
+
+ align:start position:0%
+adequate uh barrier layer but again it
+depends on your your backend uh thermal
+
+ align:start position:0%
+depends on your your backend uh thermal
+ 
+
+ align:start position:0%
+depends on your your backend uh thermal
+budget
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slide 20 is just another example saying
+
+ align:start position:0%
+slide 20 is just another example saying
+ 
+
+ align:start position:0%
+slide 20 is just another example saying
+that when you depending on the barrier
+
+ align:start position:0%
+that when you depending on the barrier
+ 
+
+ align:start position:0%
+that when you depending on the barrier
+layer that you choose you have to be
+
+ align:start position:0%
+layer that you choose you have to be
+ 
+
+ align:start position:0%
+layer that you choose you have to be
+careful um a lot of these materials for
+
+ align:start position:0%
+careful um a lot of these materials for
+ 
+
+ align:start position:0%
+careful um a lot of these materials for
+barrier layers TI tungsten uh or Ty
+
+ align:start position:0%
+barrier layers TI tungsten uh or Ty
+ 
+
+ align:start position:0%
+barrier layers TI tungsten uh or Ty
+nitride are very often um they're
+
+ align:start position:0%
+nitride are very often um they're
+ 
+
+ align:start position:0%
+nitride are very often um they're
+they're poly crystallin basically and
+
+ align:start position:0%
+they're poly crystallin basically and
+ 
+
+ align:start position:0%
+they're poly crystallin basically and
+what can happen if you're not careful is
+
+ align:start position:0%
+what can happen if you're not careful is
+ 
+
+ align:start position:0%
+what can happen if you're not careful is
+the aluminum can actually diffuse
+
+ align:start position:0%
+the aluminum can actually diffuse
+ 
+
+ align:start position:0%
+the aluminum can actually diffuse
+through uh the long grain boundaries and
+
+ align:start position:0%
+through uh the long grain boundaries and
+ 
+
+ align:start position:0%
+through uh the long grain boundaries and
+can still uh make its way to the silicon
+
+ align:start position:0%
+can still uh make its way to the silicon
+ 
+
+ align:start position:0%
+can still uh make its way to the silicon
+and end up causing problems so people
+
+ align:start position:0%
+and end up causing problems so people
+ 
+
+ align:start position:0%
+and end up causing problems so people
+often when they deposit these material
+
+ align:start position:0%
+often when they deposit these material
+ 
+
+ align:start position:0%
+often when they deposit these material
+they sometimes sputter them in an
+
+ align:start position:0%
+they sometimes sputter them in an
+ 
+
+ align:start position:0%
+they sometimes sputter them in an
+ambient that has some impurity could be
+
+ align:start position:0%
+ambient that has some impurity could be
+ 
+
+ align:start position:0%
+ambient that has some impurity could be
+nitrogen is is one of the most common
+
+ align:start position:0%
+nitrogen is is one of the most common
+ 
+
+ align:start position:0%
+nitrogen is is one of the most common
+sometimes people actually do sputter tii
+
+ align:start position:0%
+sometimes people actually do sputter tii
+ 
+
+ align:start position:0%
+sometimes people actually do sputter tii
+tungsten and then they expose it to air
+
+ align:start position:0%
+tungsten and then they expose it to air
+ 
+
+ align:start position:0%
+tungsten and then they expose it to air
+for a period few minutes or half an hour
+
+ align:start position:0%
+for a period few minutes or half an hour
+ 
+
+ align:start position:0%
+for a period few minutes or half an hour
+then they put the aluminum on top the
+
+ align:start position:0%
+then they put the aluminum on top the
+ 
+
+ align:start position:0%
+then they put the aluminum on top the
+idea is that these um either nitrogen or
+
+ align:start position:0%
+idea is that these um either nitrogen or
+ 
+
+ align:start position:0%
+idea is that these um either nitrogen or
+oxygen impurities are going to end up
+
+ align:start position:0%
+oxygen impurities are going to end up
+ 
+
+ align:start position:0%
+oxygen impurities are going to end up
+being um very high concentration in
+
+ align:start position:0%
+being um very high concentration in
+ 
+
+ align:start position:0%
+being um very high concentration in
+these grain
+
+ align:start position:0%
+these grain
+ 
+
+ align:start position:0%
+these grain
+boundaries uh this is called like a
+
+ align:start position:0%
+boundaries uh this is called like a
+ 
+
+ align:start position:0%
+boundaries uh this is called like a
+stuffed barrier by stuffing the grain
+
+ align:start position:0%
+stuffed barrier by stuffing the grain
+ 
+
+ align:start position:0%
+stuffed barrier by stuffing the grain
+boundaries it helps prevent the aluminum
+
+ align:start position:0%
+boundaries it helps prevent the aluminum
+ 
+
+ align:start position:0%
+boundaries it helps prevent the aluminum
+from diffusing down in and and getting
+
+ align:start position:0%
+from diffusing down in and and getting
+ 
+
+ align:start position:0%
+from diffusing down in and and getting
+to the Silicon um so again we're going
+
+ align:start position:0%
+to the Silicon um so again we're going
+ 
+
+ align:start position:0%
+to the Silicon um so again we're going
+to do a heat treatment you're going to
+
+ align:start position:0%
+to do a heat treatment you're going to
+ 
+
+ align:start position:0%
+to do a heat treatment you're going to
+put aluminum on top here you need to try
+
+ align:start position:0%
+put aluminum on top here you need to try
+ 
+
+ align:start position:0%
+put aluminum on top here you need to try
+to uh prevent the incursion of the
+
+ align:start position:0%
+to uh prevent the incursion of the
+ 
+
+ align:start position:0%
+to uh prevent the incursion of the
+aluminum so uh how you do the sputtering
+
+ align:start position:0%
+aluminum so uh how you do the sputtering
+ 
+
+ align:start position:0%
+aluminum so uh how you do the sputtering
+of the barrier layer is actually very
+
+ align:start position:0%
+of the barrier layer is actually very
+ 
+
+ align:start position:0%
+of the barrier layer is actually very
+important what ambient you use will
+
+ align:start position:0%
+important what ambient you use will
+ 
+
+ align:start position:0%
+important what ambient you use will
+determine whether it's a good barrier
+
+ align:start position:0%
+determine whether it's a good barrier
+ 
+
+ align:start position:0%
+determine whether it's a good barrier
+layer or or a poor barrier layer and how
+
+ align:start position:0%
+layer or or a poor barrier layer and how
+ 
+
+ align:start position:0%
+layer or or a poor barrier layer and how
+long it's going to stand up so it's a
+
+ align:start position:0%
+long it's going to stand up so it's a
+ 
+
+ align:start position:0%
+long it's going to stand up so it's a
+lot of it quasi empirical um uh you know
+
+ align:start position:0%
+lot of it quasi empirical um uh you know
+ 
+
+ align:start position:0%
+lot of it quasi empirical um uh you know
+just testing of what works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on this page 21 I'm showing um a classic
+
+ align:start position:0%
+on this page 21 I'm showing um a classic
+ 
+
+ align:start position:0%
+on this page 21 I'm showing um a classic
+process that was developed a number of
+
+ align:start position:0%
+process that was developed a number of
+ 
+
+ align:start position:0%
+process that was developed a number of
+years ago called the salicide process
+
+ align:start position:0%
+years ago called the salicide process
+ 
+
+ align:start position:0%
+years ago called the salicide process
+and this is something you need to be
+
+ align:start position:0%
+and this is something you need to be
+ 
+
+ align:start position:0%
+and this is something you need to be
+familiar with um salicide uh is stands
+
+ align:start position:0%
+familiar with um salicide uh is stands
+ 
+
+ align:start position:0%
+familiar with um salicide uh is stands
+for uh the S comes from self-aligned
+
+ align:start position:0%
+for uh the S comes from self-aligned
+ 
+
+ align:start position:0%
+for uh the S comes from self-aligned
+pilicide process and you'll see when we
+
+ align:start position:0%
+pilicide process and you'll see when we
+ 
+
+ align:start position:0%
+pilicide process and you'll see when we
+go through it what we mean by um
+
+ align:start position:0%
+go through it what we mean by um
+ 
+
+ align:start position:0%
+go through it what we mean by um
+self-aligned so we start here uh with
+
+ align:start position:0%
+self-aligned so we start here uh with
+ 
+
+ align:start position:0%
+self-aligned so we start here uh with
+our naked device ready to be contacted
+
+ align:start position:0%
+our naked device ready to be contacted
+ 
+
+ align:start position:0%
+our naked device ready to be contacted
+we don't have any contacts we just have
+
+ align:start position:0%
+we don't have any contacts we just have
+ 
+
+ align:start position:0%
+we don't have any contacts we just have
+n plus source and drain and you have a
+
+ align:start position:0%
+n plus source and drain and you have a
+ 
+
+ align:start position:0%
+n plus source and drain and you have a
+heavily dope polysilicon layer okay we
+
+ align:start position:0%
+heavily dope polysilicon layer okay we
+ 
+
+ align:start position:0%
+heavily dope polysilicon layer okay we
+then form our oxide spacers so you know
+
+ align:start position:0%
+then form our oxide spacers so you know
+ 
+
+ align:start position:0%
+then form our oxide spacers so you know
+how to form sidewall spacers now you
+
+ align:start position:0%
+how to form sidewall spacers now you
+ 
+
+ align:start position:0%
+how to form sidewall spacers now you
+deposit a conformal layer of sio2 say
+
+ align:start position:0%
+deposit a conformal layer of sio2 say
+ 
+
+ align:start position:0%
+deposit a conformal layer of sio2 say
+low temperature oxide and then you etch
+
+ align:start position:0%
+low temperature oxide and then you etch
+ 
+
+ align:start position:0%
+low temperature oxide and then you etch
+it back and isotropically so you end up
+
+ align:start position:0%
+it back and isotropically so you end up
+ 
+
+ align:start position:0%
+it back and isotropically so you end up
+with these little stringers on on the
+
+ align:start position:0%
+with these little stringers on on the
+ 
+
+ align:start position:0%
+with these little stringers on on the
+edges which we call sidewalls okay those
+
+ align:start position:0%
+edges which we call sidewalls okay those
+ 
+
+ align:start position:0%
+edges which we call sidewalls okay those
+are critical um so they're going to uh
+
+ align:start position:0%
+are critical um so they're going to uh
+ 
+
+ align:start position:0%
+are critical um so they're going to uh
+they're going to form sort of a blocking
+
+ align:start position:0%
+they're going to form sort of a blocking
+ 
+
+ align:start position:0%
+they're going to form sort of a blocking
+uh region which will be critical in in
+
+ align:start position:0%
+uh region which will be critical in in
+ 
+
+ align:start position:0%
+uh region which will be critical in in
+the salicide process you then deposit
+
+ align:start position:0%
+the salicide process you then deposit
+ 
+
+ align:start position:0%
+the salicide process you then deposit
+metal M over everything so you can do
+
+ align:start position:0%
+metal M over everything so you can do
+ 
+
+ align:start position:0%
+metal M over everything so you can do
+some kind of PVD deposition and here's
+
+ align:start position:0%
+some kind of PVD deposition and here's
+ 
+
+ align:start position:0%
+some kind of PVD deposition and here's
+your titanium layer that goes everywhere
+
+ align:start position:0%
+your titanium layer that goes everywhere
+ 
+
+ align:start position:0%
+your titanium layer that goes everywhere
+obviously across the whole wafer and
+
+ align:start position:0%
+obviously across the whole wafer and
+ 
+
+ align:start position:0%
+obviously across the whole wafer and
+then you do a magic anal at the right
+
+ align:start position:0%
+then you do a magic anal at the right
+ 
+
+ align:start position:0%
+then you do a magic anal at the right
+temperature and this anal uh is such
+
+ align:start position:0%
+temperature and this anal uh is such
+ 
+
+ align:start position:0%
+temperature and this anal uh is such
+that wherever the metal the titanium is
+
+ align:start position:0%
+that wherever the metal the titanium is
+ 
+
+ align:start position:0%
+that wherever the metal the titanium is
+contacting the Silicon you form a metal
+
+ align:start position:0%
+contacting the Silicon you form a metal
+ 
+
+ align:start position:0%
+contacting the Silicon you form a metal
+pilicide say TI
+
+ align:start position:0%
+pilicide say TI
+ 
+
+ align:start position:0%
+pilicide say TI
+si2 only so it only forms where it's in
+
+ align:start position:0%
+si2 only so it only forms where it's in
+ 
+
+ align:start position:0%
+si2 only so it only forms where it's in
+contact with silicon which is right here
+
+ align:start position:0%
+contact with silicon which is right here
+ 
+
+ align:start position:0%
+contact with silicon which is right here
+this dark region and on top of the gate
+
+ align:start position:0%
+this dark region and on top of the gate
+ 
+
+ align:start position:0%
+this dark region and on top of the gate
+so on the source gate and drains where
+
+ align:start position:0%
+so on the source gate and drains where
+ 
+
+ align:start position:0%
+so on the source gate and drains where
+it's in contact with silicon remember
+
+ align:start position:0%
+it's in contact with silicon remember
+ 
+
+ align:start position:0%
+it's in contact with silicon remember
+the the sil the the polysilicon uh gate
+
+ align:start position:0%
+the the sil the the polysilicon uh gate
+ 
+
+ align:start position:0%
+the the sil the the polysilicon uh gate
+will also react um you have titanium
+
+ align:start position:0%
+will also react um you have titanium
+ 
+
+ align:start position:0%
+will also react um you have titanium
+disilicide everywhere else you have
+
+ align:start position:0%
+disilicide everywhere else you have
+ 
+
+ align:start position:0%
+disilicide everywhere else you have
+still remaining some unreacted metal
+
+ align:start position:0%
+still remaining some unreacted metal
+ 
+
+ align:start position:0%
+still remaining some unreacted metal
+okay so still sitting there and now the
+
+ align:start position:0%
+okay so still sitting there and now the
+ 
+
+ align:start position:0%
+okay so still sitting there and now the
+key to the process is that you dip it in
+
+ align:start position:0%
+key to the process is that you dip it in
+ 
+
+ align:start position:0%
+key to the process is that you dip it in
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+solution sometimes it's HF sometimes
+
+ align:start position:0%
+solution sometimes it's HF sometimes
+ 
+
+ align:start position:0%
+solution sometimes it's HF sometimes
+it's sulfuric uh that removes unreacted
+
+ align:start position:0%
+it's sulfuric uh that removes unreacted
+ 
+
+ align:start position:0%
+it's sulfuric uh that removes unreacted
+metal but that does not Edge uh the the
+
+ align:start position:0%
+metal but that does not Edge uh the the
+ 
+
+ align:start position:0%
+metal but that does not Edge uh the the
+pilicide itself so we've created a
+
+ align:start position:0%
+pilicide itself so we've created a
+ 
+
+ align:start position:0%
+pilicide itself so we've created a
+material a titanium dilde or a metal
+
+ align:start position:0%
+material a titanium dilde or a metal
+ 
+
+ align:start position:0%
+material a titanium dilde or a metal
+dilde that because of the virtue of of
+
+ align:start position:0%
+dilde that because of the virtue of of
+ 
+
+ align:start position:0%
+dilde that because of the virtue of of
+its uh its chemical structure it now
+
+ align:start position:0%
+its uh its chemical structure it now
+ 
+
+ align:start position:0%
+its uh its chemical structure it now
+stands up to the edge which will remove
+
+ align:start position:0%
+stands up to the edge which will remove
+ 
+
+ align:start position:0%
+stands up to the edge which will remove
+the unreacted metal so uh the the reason
+
+ align:start position:0%
+the unreacted metal so uh the the reason
+ 
+
+ align:start position:0%
+the unreacted metal so uh the the reason
+it's called self align you notice I did
+
+ align:start position:0%
+it's called self align you notice I did
+ 
+
+ align:start position:0%
+it's called self align you notice I did
+not have to do any photolithography to
+
+ align:start position:0%
+not have to do any photolithography to
+ 
+
+ align:start position:0%
+not have to do any photolithography to
+pattern this metal the metal was
+
+ align:start position:0%
+pattern this metal the metal was
+ 
+
+ align:start position:0%
+pattern this metal the metal was
+deposited over the entire chip it was
+
+ align:start position:0%
+deposited over the entire chip it was
+ 
+
+ align:start position:0%
+deposited over the entire chip it was
+reacted with the silicon and then it was
+
+ align:start position:0%
+reacted with the silicon and then it was
+ 
+
+ align:start position:0%
+reacted with the silicon and then it was
+just etched off in a blanket etch so
+
+ align:start position:0%
+just etched off in a blanket etch so
+ 
+
+ align:start position:0%
+just etched off in a blanket etch so
+there's no photo resist step here to
+
+ align:start position:0%
+there's no photo resist step here to
+ 
+
+ align:start position:0%
+there's no photo resist step here to
+pattern this
+
+ align:start position:0%
+pattern this
+ 
+
+ align:start position:0%
+pattern this
+metal that's why it's self align because
+
+ align:start position:0%
+metal that's why it's self align because
+ 
+
+ align:start position:0%
+metal that's why it's self align because
+wherever there's Expos exposed silicon
+
+ align:start position:0%
+wherever there's Expos exposed silicon
+ 
+
+ align:start position:0%
+wherever there's Expos exposed silicon
+you will end up with a metal contact
+
+ align:start position:0%
+you will end up with a metal contact
+ 
+
+ align:start position:0%
+you will end up with a metal contact
+aligned to that exposed silicon without
+
+ align:start position:0%
+aligned to that exposed silicon without
+ 
+
+ align:start position:0%
+aligned to that exposed silicon without
+having to do another lithography step um
+
+ align:start position:0%
+having to do another lithography step um
+ 
+
+ align:start position:0%
+having to do another lithography step um
+so this was a this was a really great
+
+ align:start position:0%
+so this was a this was a really great
+ 
+
+ align:start position:0%
+so this was a this was a really great
+invention um you save yourself in
+
+ align:start position:0%
+invention um you save yourself in
+ 
+
+ align:start position:0%
+invention um you save yourself in
+alignment tolerance so it's very good
+
+ align:start position:0%
+alignment tolerance so it's very good
+ 
+
+ align:start position:0%
+alignment tolerance so it's very good
+alignment you are you form a low
+
+ align:start position:0%
+alignment you are you form a low
+ 
+
+ align:start position:0%
+alignment you are you form a low
+resistance contact to the source drain
+
+ align:start position:0%
+resistance contact to the source drain
+ 
+
+ align:start position:0%
+resistance contact to the source drain
+and to the gate
+
+ align:start position:0%
+and to the gate
+ 
+
+ align:start position:0%
+and to the gate
+simultaneously um so this this is kind
+
+ align:start position:0%
+simultaneously um so this this is kind
+ 
+
+ align:start position:0%
+simultaneously um so this this is kind
+of salicide process was a big
+
+ align:start position:0%
+of salicide process was a big
+ 
+
+ align:start position:0%
+of salicide process was a big
+breakthrough in in in seamless
+
+ align:start position:0%
+breakthrough in in in seamless
+ 
+
+ align:start position:0%
+breakthrough in in in seamless
+technology uh say in around the 80s or
+
+ align:start position:0%
+technology uh say in around the 80s or
+ 
+
+ align:start position:0%
+technology uh say in around the 80s or
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slide 21 22 I just took from a different
+
+ align:start position:0%
+slide 21 22 I just took from a different
+ 
+
+ align:start position:0%
+slide 21 22 I just took from a different
+text it has a slightly different type of
+
+ align:start position:0%
+text it has a slightly different type of
+ 
+
+ align:start position:0%
+text it has a slightly different type of
+drawing maybe it's easier to understand
+
+ align:start position:0%
+drawing maybe it's easier to understand
+ 
+
+ align:start position:0%
+drawing maybe it's easier to understand
+they have a little different notation
+
+ align:start position:0%
+they have a little different notation
+ 
+
+ align:start position:0%
+they have a little different notation
+it's the exact same process it's the
+
+ align:start position:0%
+it's the exact same process it's the
+ 
+
+ align:start position:0%
+it's the exact same process it's the
+basic salicide process you have an N
+
+ align:start position:0%
+basic salicide process you have an N
+ 
+
+ align:start position:0%
+basic salicide process you have an N
+plus source and drain you form your
+
+ align:start position:0%
+plus source and drain you form your
+ 
+
+ align:start position:0%
+plus source and drain you form your
+spacers um you uh uh react the metal it
+
+ align:start position:0%
+spacers um you uh uh react the metal it
+ 
+
+ align:start position:0%
+spacers um you uh uh react the metal it
+does not react hopefully it does not
+
+ align:start position:0%
+does not react hopefully it does not
+ 
+
+ align:start position:0%
+does not react hopefully it does not
+creep up the sidewall which is a problem
+
+ align:start position:0%
+creep up the sidewall which is a problem
+ 
+
+ align:start position:0%
+creep up the sidewall which is a problem
+uh you then selectively remove the
+
+ align:start position:0%
+uh you then selectively remove the
+ 
+
+ align:start position:0%
+uh you then selectively remove the
+unreacted metal form put your dialectric
+
+ align:start position:0%
+unreacted metal form put your dialectric
+ 
+
+ align:start position:0%
+unreacted metal form put your dialectric
+down every where else and putting your
+
+ align:start position:0%
+down every where else and putting your
+ 
+
+ align:start position:0%
+down every where else and putting your
+metal contacts um so that's a a basic uh
+
+ align:start position:0%
+metal contacts um so that's a a basic uh
+ 
+
+ align:start position:0%
+metal contacts um so that's a a basic uh
+metal contact scheme that that people
+
+ align:start position:0%
+metal contact scheme that that people
+ 
+
+ align:start position:0%
+metal contact scheme that that people
+use um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today what do people use which materials
+
+ align:start position:0%
+today what do people use which materials
+ 
+
+ align:start position:0%
+today what do people use which materials
+are commonly used well um some of them
+
+ align:start position:0%
+are commonly used well um some of them
+ 
+
+ align:start position:0%
+are commonly used well um some of them
+are shown here on slide 23 the first one
+
+ align:start position:0%
+are shown here on slide 23 the first one
+ 
+
+ align:start position:0%
+are shown here on slide 23 the first one
+that was used um historically was Ty
+
+ align:start position:0%
+that was used um historically was Ty
+ 
+
+ align:start position:0%
+that was used um historically was Ty
+silicide uh tyde was very good because
+
+ align:start position:0%
+silicide uh tyde was very good because
+ 
+
+ align:start position:0%
+silicide uh tyde was very good because
+it has a low resistivity phase um and
+
+ align:start position:0%
+it has a low resistivity phase um and
+ 
+
+ align:start position:0%
+it has a low resistivity phase um and
+we're talking about maybe a 15 micro ohm
+
+ align:start position:0%
+we're talking about maybe a 15 micro ohm
+ 
+
+ align:start position:0%
+we're talking about maybe a 15 micro ohm
+centimeter
+
+ align:start position:0%
+centimeter
+ 
+
+ align:start position:0%
+centimeter
+um for a particular phase that's formed
+
+ align:start position:0%
+um for a particular phase that's formed
+ 
+
+ align:start position:0%
+um for a particular phase that's formed
+with on a particular type of
+
+ align:start position:0%
+with on a particular type of
+ 
+
+ align:start position:0%
+with on a particular type of
+analing uh uh there's a little
+
+ align:start position:0%
+analing uh uh there's a little
+ 
+
+ align:start position:0%
+analing uh uh there's a little
+difficulty though as people make the
+
+ align:start position:0%
+difficulty though as people make the
+ 
+
+ align:start position:0%
+difficulty though as people make the
+polysilicon gate length
+
+ align:start position:0%
+polysilicon gate length
+ 
+
+ align:start position:0%
+polysilicon gate length
+shorter it's harder and harder to get
+
+ align:start position:0%
+shorter it's harder and harder to get
+ 
+
+ align:start position:0%
+shorter it's harder and harder to get
+this particular phase to form this is
+
+ align:start position:0%
+this particular phase to form this is
+ 
+
+ align:start position:0%
+this particular phase to form this is
+called the narrow line effect or the
+
+ align:start position:0%
+called the narrow line effect or the
+ 
+
+ align:start position:0%
+called the narrow line effect or the
+narrow width effect usually the narrow
+
+ align:start position:0%
+narrow width effect usually the narrow
+ 
+
+ align:start position:0%
+narrow width effect usually the narrow
+line effect uh thilde also has a
+
+ align:start position:0%
+line effect uh thilde also has a
+ 
+
+ align:start position:0%
+line effect uh thilde also has a
+tendency to agglomerate when it's very
+
+ align:start position:0%
+tendency to agglomerate when it's very
+ 
+
+ align:start position:0%
+tendency to agglomerate when it's very
+thin at higher in kneeling temperature
+
+ align:start position:0%
+thin at higher in kneeling temperature
+ 
+
+ align:start position:0%
+thin at higher in kneeling temperature
+so it's not that thermally stable so for
+
+ align:start position:0%
+so it's not that thermally stable so for
+ 
+
+ align:start position:0%
+so it's not that thermally stable so for
+a number of reasons particularly the
+
+ align:start position:0%
+a number of reasons particularly the
+ 
+
+ align:start position:0%
+a number of reasons particularly the
+narrow line effect uh industry moved uh
+
+ align:start position:0%
+narrow line effect uh industry moved uh
+ 
+
+ align:start position:0%
+narrow line effect uh industry moved uh
+a number of years ago primarily from TY
+
+ align:start position:0%
+a number of years ago primarily from TY
+ 
+
+ align:start position:0%
+a number of years ago primarily from TY
+silicide although some people may still
+
+ align:start position:0%
+silicide although some people may still
+ 
+
+ align:start position:0%
+silicide although some people may still
+use it to Cobalt disilicide it does not
+
+ align:start position:0%
+use it to Cobalt disilicide it does not
+ 
+
+ align:start position:0%
+use it to Cobalt disilicide it does not
+have that n narrow line
+
+ align:start position:0%
+have that n narrow line
+ 
+
+ align:start position:0%
+have that n narrow line
+effect um but it it gives you a slightly
+
+ align:start position:0%
+effect um but it it gives you a slightly
+ 
+
+ align:start position:0%
+effect um but it it gives you a slightly
+higher resistivity it's a little more
+
+ align:start position:0%
+higher resistivity it's a little more
+ 
+
+ align:start position:0%
+higher resistivity it's a little more
+sensitive to surface contaminants the
+
+ align:start position:0%
+sensitive to surface contaminants the
+ 
+
+ align:start position:0%
+sensitive to surface contaminants the
+beauty of Thai is again the titanium you
+
+ align:start position:0%
+beauty of Thai is again the titanium you
+ 
+
+ align:start position:0%
+beauty of Thai is again the titanium you
+know eats its way through things through
+
+ align:start position:0%
+know eats its way through things through
+ 
+
+ align:start position:0%
+know eats its way through things through
+oxides it'll reduce oxides so uh Cobalt
+
+ align:start position:0%
+oxides it'll reduce oxides so uh Cobalt
+ 
+
+ align:start position:0%
+oxides it'll reduce oxides so uh Cobalt
+you have to have a really clean
+
+ align:start position:0%
+you have to have a really clean
+ 
+
+ align:start position:0%
+you have to have a really clean
+interface um Cobalt has a little less
+
+ align:start position:0%
+interface um Cobalt has a little less
+ 
+
+ align:start position:0%
+interface um Cobalt has a little less
+lateral encroach over the oxide spacer
+
+ align:start position:0%
+lateral encroach over the oxide spacer
+ 
+
+ align:start position:0%
+lateral encroach over the oxide spacer
+and I'll show pictures of that uh so
+
+ align:start position:0%
+and I'll show pictures of that uh so
+ 
+
+ align:start position:0%
+and I'll show pictures of that uh so
+Cobalt was used and is still used uh in
+
+ align:start position:0%
+Cobalt was used and is still used uh in
+ 
+
+ align:start position:0%
+Cobalt was used and is still used uh in
+in some processes the latest pilicide
+
+ align:start position:0%
+in some processes the latest pilicide
+ 
+
+ align:start position:0%
+in some processes the latest pilicide
+that people are exploring in research
+
+ align:start position:0%
+that people are exploring in research
+ 
+
+ align:start position:0%
+that people are exploring in research
+and development and at some point will
+
+ align:start position:0%
+and development and at some point will
+ 
+
+ align:start position:0%
+and development and at some point will
+probably be in production is nickel
+
+ align:start position:0%
+probably be in production is nickel
+ 
+
+ align:start position:0%
+probably be in production is nickel
+silicide um nickel silicide has the
+
+ align:start position:0%
+silicide um nickel silicide has the
+ 
+
+ align:start position:0%
+silicide um nickel silicide has the
+lowest silicon consumption in order to
+
+ align:start position:0%
+lowest silicon consumption in order to
+ 
+
+ align:start position:0%
+lowest silicon consumption in order to
+do this you need to react and you need
+
+ align:start position:0%
+do this you need to react and you need
+ 
+
+ align:start position:0%
+do this you need to react and you need
+to consume some of the silicon and you
+
+ align:start position:0%
+to consume some of the silicon and you
+ 
+
+ align:start position:0%
+to consume some of the silicon and you
+don't want to consume very much of that
+
+ align:start position:0%
+don't want to consume very much of that
+ 
+
+ align:start position:0%
+don't want to consume very much of that
+shallow Junction so nickel is good
+
+ align:start position:0%
+shallow Junction so nickel is good
+ 
+
+ align:start position:0%
+shallow Junction so nickel is good
+because of that it it can be formed at
+
+ align:start position:0%
+because of that it it can be formed at
+ 
+
+ align:start position:0%
+because of that it it can be formed at
+very low temperatures and it doesn't it
+
+ align:start position:0%
+very low temperatures and it doesn't it
+ 
+
+ align:start position:0%
+very low temperatures and it doesn't it
+doesn't have very bad narrow line effect
+
+ align:start position:0%
+doesn't have very bad narrow line effect
+ 
+
+ align:start position:0%
+doesn't have very bad narrow line effect
+for suiciding the gate big problem with
+
+ align:start position:0%
+for suiciding the gate big problem with
+ 
+
+ align:start position:0%
+for suiciding the gate big problem with
+nickel uh is uh the thermal you have to
+
+ align:start position:0%
+nickel uh is uh the thermal you have to
+ 
+
+ align:start position:0%
+nickel uh is uh the thermal you have to
+be careful of your thermal budget and
+
+ align:start position:0%
+be careful of your thermal budget and
+ 
+
+ align:start position:0%
+be careful of your thermal budget and
+watch out for nickel nickel is a very
+
+ align:start position:0%
+watch out for nickel nickel is a very
+ 
+
+ align:start position:0%
+watch out for nickel nickel is a very
+fast diffuser remember in Silicon nickel
+
+ align:start position:0%
+fast diffuser remember in Silicon nickel
+ 
+
+ align:start position:0%
+fast diffuser remember in Silicon nickel
+is also a deep
+
+ align:start position:0%
+is also a deep
+ 
+
+ align:start position:0%
+is also a deep
+level um so nickel contamination of
+
+ align:start position:0%
+level um so nickel contamination of
+ 
+
+ align:start position:0%
+level um so nickel contamination of
+equipment and of the of the Wafers is an
+
+ align:start position:0%
+equipment and of the of the Wafers is an
+ 
+
+ align:start position:0%
+equipment and of the of the Wafers is an
+issue and people need to deal with this
+
+ align:start position:0%
+issue and people need to deal with this
+ 
+
+ align:start position:0%
+issue and people need to deal with this
+um but nickel suicide is uh becoming
+
+ align:start position:0%
+um but nickel suicide is uh becoming
+ 
+
+ align:start position:0%
+um but nickel suicide is uh becoming
+more and more uh prevalent uh in
+
+ align:start position:0%
+more and more uh prevalent uh in
+ 
+
+ align:start position:0%
+more and more uh prevalent uh in
+research and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+development I mentioned there there was
+
+ align:start position:0%
+development I mentioned there there was
+ 
+
+ align:start position:0%
+development I mentioned there there was
+a problem with this
+
+ align:start position:0%
+a problem with this
+ 
+
+ align:start position:0%
+a problem with this
+encroachment um over the spacer and uh
+
+ align:start position:0%
+encroachment um over the spacer and uh
+ 
+
+ align:start position:0%
+encroachment um over the spacer and uh
+this is Illustrated on on uh slide
+
+ align:start position:0%
+this is Illustrated on on uh slide
+ 
+
+ align:start position:0%
+this is Illustrated on on uh slide
+24 um on the left hand side I'm showing
+
+ align:start position:0%
+24 um on the left hand side I'm showing
+ 
+
+ align:start position:0%
+24 um on the left hand side I'm showing
+the case of uh uh Cobalt uh
+
+ align:start position:0%
+the case of uh uh Cobalt uh
+ 
+
+ align:start position:0%
+the case of uh uh Cobalt uh
+disilicide uh formation where it's the
+
+ align:start position:0%
+disilicide uh formation where it's the
+ 
+
+ align:start position:0%
+disilicide uh formation where it's the
+metal that diffuses so you can imagine
+
+ align:start position:0%
+metal that diffuses so you can imagine
+ 
+
+ align:start position:0%
+metal that diffuses so you can imagine
+that you have this metal that's
+
+ align:start position:0%
+that you have this metal that's
+ 
+
+ align:start position:0%
+that you have this metal that's
+deposited everywhere and you're going to
+
+ align:start position:0%
+deposited everywhere and you're going to
+ 
+
+ align:start position:0%
+deposited everywhere and you're going to
+form a reaction between the metal and
+
+ align:start position:0%
+form a reaction between the metal and
+ 
+
+ align:start position:0%
+form a reaction between the metal and
+the Silicon the question is um how does
+
+ align:start position:0%
+the Silicon the question is um how does
+ 
+
+ align:start position:0%
+the Silicon the question is um how does
+the reaction occur does the metal
+
+ align:start position:0%
+the reaction occur does the metal
+ 
+
+ align:start position:0%
+the reaction occur does the metal
+diffuse in and and meet the Silicon down
+
+ align:start position:0%
+diffuse in and and meet the Silicon down
+ 
+
+ align:start position:0%
+diffuse in and and meet the Silicon down
+at this interface or vice versa well it
+
+ align:start position:0%
+at this interface or vice versa well it
+ 
+
+ align:start position:0%
+at this interface or vice versa well it
+depends on uh on the particular type of
+
+ align:start position:0%
+depends on uh on the particular type of
+ 
+
+ align:start position:0%
+depends on uh on the particular type of
+uh of pilicide in the case of cobalt
+
+ align:start position:0%
+uh of pilicide in the case of cobalt
+ 
+
+ align:start position:0%
+uh of pilicide in the case of cobalt
+dilde the metal diffuses through the
+
+ align:start position:0%
+dilde the metal diffuses through the
+ 
+
+ align:start position:0%
+dilde the metal diffuses through the
+pilicide into this to this interface
+
+ align:start position:0%
+pilicide into this to this interface
+ 
+
+ align:start position:0%
+pilicide into this to this interface
+here and then reacts um so you get
+
+ align:start position:0%
+here and then reacts um so you get
+ 
+
+ align:start position:0%
+here and then reacts um so you get
+pilicide reaction or formation at the
+
+ align:start position:0%
+pilicide reaction or formation at the
+ 
+
+ align:start position:0%
+pilicide reaction or formation at the
+bottom here so you're less likely to
+
+ align:start position:0%
+bottom here so you're less likely to
+ 
+
+ align:start position:0%
+bottom here so you're less likely to
+have creep up uh in the case of um TI
+
+ align:start position:0%
+have creep up uh in the case of um TI
+ 
+
+ align:start position:0%
+have creep up uh in the case of um TI
+titanium dilde in fact what happens is
+
+ align:start position:0%
+titanium dilde in fact what happens is
+ 
+
+ align:start position:0%
+titanium dilde in fact what happens is
+the Silicon is what's the fast diffuser
+
+ align:start position:0%
+the Silicon is what's the fast diffuser
+ 
+
+ align:start position:0%
+the Silicon is what's the fast diffuser
+through the tii silicide it diffuses up
+
+ align:start position:0%
+through the tii silicide it diffuses up
+ 
+
+ align:start position:0%
+through the tii silicide it diffuses up
+and meets the metal so um if you do it
+
+ align:start position:0%
+and meets the metal so um if you do it
+ 
+
+ align:start position:0%
+and meets the metal so um if you do it
+long enough and if you have a short
+
+ align:start position:0%
+long enough and if you have a short
+ 
+
+ align:start position:0%
+long enough and if you have a short
+enough spacer you can see the disilicide
+
+ align:start position:0%
+enough spacer you can see the disilicide
+ 
+
+ align:start position:0%
+enough spacer you can see the disilicide
+can creep and grow uh up from the source
+
+ align:start position:0%
+can creep and grow uh up from the source
+ 
+
+ align:start position:0%
+can creep and grow uh up from the source
+and drain down from the gate and
+
+ align:start position:0%
+and drain down from the gate and
+ 
+
+ align:start position:0%
+and drain down from the gate and
+eventually you may actually bridge and
+
+ align:start position:0%
+eventually you may actually bridge and
+ 
+
+ align:start position:0%
+eventually you may actually bridge and
+and then you have a big problem because
+
+ align:start position:0%
+and then you have a big problem because
+ 
+
+ align:start position:0%
+and then you have a big problem because
+then your gate is electrically sorted to
+
+ align:start position:0%
+then your gate is electrically sorted to
+ 
+
+ align:start position:0%
+then your gate is electrically sorted to
+your source and drain and then your
+
+ align:start position:0%
+your source and drain and then your
+ 
+
+ align:start position:0%
+your source and drain and then your
+device is dead um so um Titanium bcide
+
+ align:start position:0%
+device is dead um so um Titanium bcide
+ 
+
+ align:start position:0%
+device is dead um so um Titanium bcide
+has a little more tendency to do this um
+
+ align:start position:0%
+has a little more tendency to do this um
+ 
+
+ align:start position:0%
+has a little more tendency to do this um
+than the Cobalt disilicide this is part
+
+ align:start position:0%
+than the Cobalt disilicide this is part
+ 
+
+ align:start position:0%
+than the Cobalt disilicide this is part
+of the region people uh went to Cobalt
+
+ align:start position:0%
+of the region people uh went to Cobalt
+ 
+
+ align:start position:0%
+of the region people uh went to Cobalt
+despite fact it has a slightly higher um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resistivity um slide 25 is just a kind
+
+ align:start position:0%
+resistivity um slide 25 is just a kind
+ 
+
+ align:start position:0%
+resistivity um slide 25 is just a kind
+of an illustration of some of the
+
+ align:start position:0%
+of an illustration of some of the
+ 
+
+ align:start position:0%
+of an illustration of some of the
+kinetics of what's Happening um when you
+
+ align:start position:0%
+kinetics of what's Happening um when you
+ 
+
+ align:start position:0%
+kinetics of what's Happening um when you
+have uh Titanium on Silicon that's
+
+ align:start position:0%
+have uh Titanium on Silicon that's
+ 
+
+ align:start position:0%
+have uh Titanium on Silicon that's
+reacting here we have a certain
+
+ align:start position:0%
+reacting here we have a certain
+ 
+
+ align:start position:0%
+reacting here we have a certain
+thickness of tha suicide that's already
+
+ align:start position:0%
+thickness of tha suicide that's already
+ 
+
+ align:start position:0%
+thickness of tha suicide that's already
+formed uh people do model this there are
+
+ align:start position:0%
+formed uh people do model this there are
+ 
+
+ align:start position:0%
+formed uh people do model this there are
+silicidation models in Supreme 4 not
+
+ align:start position:0%
+silicidation models in Supreme 4 not
+ 
+
+ align:start position:0%
+silicidation models in Supreme 4 not
+necessarily uh perfectly accurate but uh
+
+ align:start position:0%
+necessarily uh perfectly accurate but uh
+ 
+
+ align:start position:0%
+necessarily uh perfectly accurate but uh
+what what people model is the sil
+
+ align:start position:0%
+what what people model is the sil
+ 
+
+ align:start position:0%
+what what people model is the sil
+diffusion of the Silicon from the bulk
+
+ align:start position:0%
+diffusion of the Silicon from the bulk
+ 
+
+ align:start position:0%
+diffusion of the Silicon from the bulk
+through the titanium dilde up here to
+
+ align:start position:0%
+through the titanium dilde up here to
+ 
+
+ align:start position:0%
+through the titanium dilde up here to
+this uh top interface and form a new a
+
+ align:start position:0%
+this uh top interface and form a new a
+ 
+
+ align:start position:0%
+this uh top interface and form a new a
+new layer of titanium
+
+ align:start position:0%
+new layer of titanium
+ 
+
+ align:start position:0%
+new layer of titanium
+dside um so this is what might happen in
+
+ align:start position:0%
+dside um so this is what might happen in
+ 
+
+ align:start position:0%
+dside um so this is what might happen in
+um an inner ambient now if you if you do
+
+ align:start position:0%
+um an inner ambient now if you if you do
+ 
+
+ align:start position:0%
+um an inner ambient now if you if you do
+the anal in a nitriding ambient so in an
+
+ align:start position:0%
+the anal in a nitriding ambient so in an
+ 
+
+ align:start position:0%
+the anal in a nitriding ambient so in an
+ambient that has nitrogen and at the
+
+ align:start position:0%
+ambient that has nitrogen and at the
+ 
+
+ align:start position:0%
+ambient that has nitrogen and at the
+same time you're forming thaide at this
+
+ align:start position:0%
+same time you're forming thaide at this
+ 
+
+ align:start position:0%
+same time you're forming thaide at this
+interface you can be reacting the
+
+ align:start position:0%
+interface you can be reacting the
+ 
+
+ align:start position:0%
+interface you can be reacting the
+titanium is fairly reactive you can be
+
+ align:start position:0%
+titanium is fairly reactive you can be
+ 
+
+ align:start position:0%
+titanium is fairly reactive you can be
+reacting in form Ty nitride up here at
+
+ align:start position:0%
+reacting in form Ty nitride up here at
+ 
+
+ align:start position:0%
+reacting in form Ty nitride up here at
+the top interface so this would be in a
+
+ align:start position:0%
+the top interface so this would be in a
+ 
+
+ align:start position:0%
+the top interface so this would be in a
+nitrogen ambient you can get
+
+ align:start position:0%
+nitrogen ambient you can get
+ 
+
+ align:start position:0%
+nitrogen ambient you can get
+simultaneous formation of tys silicide
+
+ align:start position:0%
+simultaneous formation of tys silicide
+ 
+
+ align:start position:0%
+simultaneous formation of tys silicide
+down here and then Ty nitride on on top
+
+ align:start position:0%
+down here and then Ty nitride on on top
+ 
+
+ align:start position:0%
+down here and then Ty nitride on on top
+of the titanium titanium is very
+
+ align:start position:0%
+of the titanium titanium is very
+ 
+
+ align:start position:0%
+of the titanium titanium is very
+reactive so it's It's Not Unusual to try
+
+ align:start position:0%
+reactive so it's It's Not Unusual to try
+ 
+
+ align:start position:0%
+reactive so it's It's Not Unusual to try
+to form a Ty nitride to prevent it from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oxidizing slide 26 just shows you some
+
+ align:start position:0%
+oxidizing slide 26 just shows you some
+ 
+
+ align:start position:0%
+oxidizing slide 26 just shows you some
+of the different uses of pilicide uh in
+
+ align:start position:0%
+of the different uses of pilicide uh in
+ 
+
+ align:start position:0%
+of the different uses of pilicide uh in
+Silicon technology and I've actually
+
+ align:start position:0%
+Silicon technology and I've actually
+ 
+
+ align:start position:0%
+Silicon technology and I've actually
+updated it added a fourth one so
+
+ align:start position:0%
+updated it added a fourth one so
+ 
+
+ align:start position:0%
+updated it added a fourth one so
+pilicides are used as you can see to
+
+ align:start position:0%
+pilicides are used as you can see to
+ 
+
+ align:start position:0%
+pilicides are used as you can see to
+strap the poly and the reason you do
+
+ align:start position:0%
+strap the poly and the reason you do
+ 
+
+ align:start position:0%
+strap the poly and the reason you do
+that is you're trying to reduce the
+
+ align:start position:0%
+that is you're trying to reduce the
+ 
+
+ align:start position:0%
+that is you're trying to reduce the
+resistance of the gate so you you form a
+
+ align:start position:0%
+resistance of the gate so you you form a
+ 
+
+ align:start position:0%
+resistance of the gate so you you form a
+little pilicide during the the salicide
+
+ align:start position:0%
+little pilicide during the the salicide
+ 
+
+ align:start position:0%
+little pilicide during the the salicide
+process strap the Junctions well what
+
+ align:start position:0%
+process strap the Junctions well what
+ 
+
+ align:start position:0%
+process strap the Junctions well what
+does that mean again you're going to
+
+ align:start position:0%
+does that mean again you're going to
+ 
+
+ align:start position:0%
+does that mean again you're going to
+reduce the the the the sheet resistance
+
+ align:start position:0%
+reduce the the the the sheet resistance
+ 
+
+ align:start position:0%
+reduce the the the the sheet resistance
+of this Junction by forming a thin layer
+
+ align:start position:0%
+of this Junction by forming a thin layer
+ 
+
+ align:start position:0%
+of this Junction by forming a thin layer
+uh it also forms a barrier layer as we
+
+ align:start position:0%
+uh it also forms a barrier layer as we
+ 
+
+ align:start position:0%
+uh it also forms a barrier layer as we
+mentioned it can be used as a local
+
+ align:start position:0%
+mentioned it can be used as a local
+ 
+
+ align:start position:0%
+mentioned it can be used as a local
+interconnect here the pilicide has
+
+ align:start position:0%
+interconnect here the pilicide has
+ 
+
+ align:start position:0%
+interconnect here the pilicide has
+actually uh been formed Above This oxide
+
+ align:start position:0%
+actually uh been formed Above This oxide
+ 
+
+ align:start position:0%
+actually uh been formed Above This oxide
+so some some silicon must have been
+
+ align:start position:0%
+so some some silicon must have been
+ 
+
+ align:start position:0%
+so some some silicon must have been
+deposited prior to
+
+ align:start position:0%
+deposited prior to
+ 
+
+ align:start position:0%
+deposited prior to
+that um and uh finally it can be used as
+
+ align:start position:0%
+that um and uh finally it can be used as
+ 
+
+ align:start position:0%
+that um and uh finally it can be used as
+a gate material and I i' uh at the end
+
+ align:start position:0%
+a gate material and I i' uh at the end
+ 
+
+ align:start position:0%
+a gate material and I i' uh at the end
+I've added a few slides that show you
+
+ align:start position:0%
+I've added a few slides that show you
+ 
+
+ align:start position:0%
+I've added a few slides that show you
+that people are actually using suicides
+
+ align:start position:0%
+that people are actually using suicides
+ 
+
+ align:start position:0%
+that people are actually using suicides
+um as as metal gates uh this is a table
+
+ align:start position:0%
+um as as metal gates uh this is a table
+ 
+
+ align:start position:0%
+um as as metal gates uh this is a table
+here shown on slide 26 of some of the
+
+ align:start position:0%
+here shown on slide 26 of some of the
+ 
+
+ align:start position:0%
+here shown on slide 26 of some of the
+common pilicides and some of their
+
+ align:start position:0%
+common pilicides and some of their
+ 
+
+ align:start position:0%
+common pilicides and some of their
+important uh properties so um here you
+
+ align:start position:0%
+important uh properties so um here you
+ 
+
+ align:start position:0%
+important uh properties so um here you
+notice for tyde there are two
+
+ align:start position:0%
+notice for tyde there are two
+ 
+
+ align:start position:0%
+notice for tyde there are two
+phases there is a phase called the c49
+
+ align:start position:0%
+phases there is a phase called the c49
+ 
+
+ align:start position:0%
+phases there is a phase called the c49
+phase that forms at low temperatures so
+
+ align:start position:0%
+phase that forms at low temperatures so
+ 
+
+ align:start position:0%
+phase that forms at low temperatures so
+if you were to kneel the titanium and
+
+ align:start position:0%
+if you were to kneel the titanium and
+ 
+
+ align:start position:0%
+if you were to kneel the titanium and
+react it with silicon say between 500 to
+
+ align:start position:0%
+react it with silicon say between 500 to
+ 
+
+ align:start position:0%
+react it with silicon say between 500 to
+to 700 say around 600 you get a a
+
+ align:start position:0%
+to 700 say around 600 you get a a
+ 
+
+ align:start position:0%
+to 700 say around 600 you get a a
+resistivity of about 60 to 70 micro ohm
+
+ align:start position:0%
+resistivity of about 60 to 70 micro ohm
+ 
+
+ align:start position:0%
+resistivity of about 60 to 70 micro ohm
+centimeter that's too high uh for um the
+
+ align:start position:0%
+centimeter that's too high uh for um the
+ 
+
+ align:start position:0%
+centimeter that's too high uh for um the
+film resistivity for most applications
+
+ align:start position:0%
+film resistivity for most applications
+ 
+
+ align:start position:0%
+film resistivity for most applications
+so people typically do a low temperature
+
+ align:start position:0%
+so people typically do a low temperature
+ 
+
+ align:start position:0%
+so people typically do a low temperature
+inal to form the c49 phase they then
+
+ align:start position:0%
+inal to form the c49 phase they then
+ 
+
+ align:start position:0%
+inal to form the c49 phase they then
+etch off all the unreacted titanium they
+
+ align:start position:0%
+etch off all the unreacted titanium they
+ 
+
+ align:start position:0%
+etch off all the unreacted titanium they
+put it back in the RTA and they pop it
+
+ align:start position:0%
+put it back in the RTA and they pop it
+ 
+
+ align:start position:0%
+put it back in the RTA and they pop it
+up to 800 or 900 to do a high
+
+ align:start position:0%
+up to 800 or 900 to do a high
+ 
+
+ align:start position:0%
+up to 800 or 900 to do a high
+temperature knel to form the c-54 phase
+
+ align:start position:0%
+temperature knel to form the c-54 phase
+ 
+
+ align:start position:0%
+temperature knel to form the c-54 phase
+uh so they get the which has a a much
+
+ align:start position:0%
+uh so they get the which has a a much
+ 
+
+ align:start position:0%
+uh so they get the which has a a much
+lower um sheet
+
+ align:start position:0%
+lower um sheet
+ 
+
+ align:start position:0%
+lower um sheet
+resistance nice thing about TI silicide
+
+ align:start position:0%
+resistance nice thing about TI silicide
+ 
+
+ align:start position:0%
+resistance nice thing about TI silicide
+it's reasonably stable maybe up to about
+
+ align:start position:0%
+it's reasonably stable maybe up to about
+ 
+
+ align:start position:0%
+it's reasonably stable maybe up to about
+800 900 Degrees something like that um
+
+ align:start position:0%
+800 900 Degrees something like that um
+ 
+
+ align:start position:0%
+800 900 Degrees something like that um
+it does consume a fair amount of silicon
+
+ align:start position:0%
+it does consume a fair amount of silicon
+ 
+
+ align:start position:0%
+it does consume a fair amount of silicon
+so it consumes 2.2 or 2.3 or so
+
+ align:start position:0%
+so it consumes 2.2 or 2.3 or so
+ 
+
+ align:start position:0%
+so it consumes 2.2 or 2.3 or so
+nanometers of silicon per every
+
+ align:start position:0%
+nanometers of silicon per every
+ 
+
+ align:start position:0%
+nanometers of silicon per every
+nanometer of metal that's consumed but
+
+ align:start position:0%
+nanometer of metal that's consumed but
+ 
+
+ align:start position:0%
+nanometer of metal that's consumed but
+depending on how thick of a silicide
+
+ align:start position:0%
+depending on how thick of a silicide
+ 
+
+ align:start position:0%
+depending on how thick of a silicide
+you're trying to form you may eat into
+
+ align:start position:0%
+you're trying to form you may eat into
+ 
+
+ align:start position:0%
+you're trying to form you may eat into
+your Junction if you have a very shallow
+
+ align:start position:0%
+your Junction if you have a very shallow
+ 
+
+ align:start position:0%
+your Junction if you have a very shallow
+Junction you have to watch out you don't
+
+ align:start position:0%
+Junction you have to watch out you don't
+ 
+
+ align:start position:0%
+Junction you have to watch out you don't
+want to eat in too far um uh so Cobalt
+
+ align:start position:0%
+want to eat in too far um uh so Cobalt
+ 
+
+ align:start position:0%
+want to eat in too far um uh so Cobalt
+disilicide uh is another example here
+
+ align:start position:0%
+disilicide uh is another example here
+ 
+
+ align:start position:0%
+disilicide uh is another example here
+you can see um it's got somewhat higher
+
+ align:start position:0%
+you can see um it's got somewhat higher
+ 
+
+ align:start position:0%
+you can see um it's got somewhat higher
+resistivity um this is the temperature
+
+ align:start position:0%
+resistivity um this is the temperature
+ 
+
+ align:start position:0%
+resistivity um this is the temperature
+at which is formed um it consumes um a
+
+ align:start position:0%
+at which is formed um it consumes um a
+ 
+
+ align:start position:0%
+at which is formed um it consumes um a
+little bit less uh than the case of of
+
+ align:start position:0%
+little bit less uh than the case of of
+ 
+
+ align:start position:0%
+little bit less uh than the case of of
+titanium the modern suicide that I
+
+ align:start position:0%
+titanium the modern suicide that I
+ 
+
+ align:start position:0%
+titanium the modern suicide that I
+mentioned here is this nickel suicide ni
+
+ align:start position:0%
+mentioned here is this nickel suicide ni
+ 
+
+ align:start position:0%
+mentioned here is this nickel suicide ni
+si uh it's formed at very low
+
+ align:start position:0%
+si uh it's formed at very low
+ 
+
+ align:start position:0%
+si uh it's formed at very low
+temperatures 450 or 500 um and it has a
+
+ align:start position:0%
+temperatures 450 or 500 um and it has a
+ 
+
+ align:start position:0%
+temperatures 450 or 500 um and it has a
+low consumption only 1.8 NM uh of
+
+ align:start position:0%
+low consumption only 1.8 NM uh of
+ 
+
+ align:start position:0%
+low consumption only 1.8 NM uh of
+silicon consumed per nanm of metal uh
+
+ align:start position:0%
+silicon consumed per nanm of metal uh
+ 
+
+ align:start position:0%
+silicon consumed per nanm of metal uh
+one thing about this though if you look
+
+ align:start position:0%
+one thing about this though if you look
+ 
+
+ align:start position:0%
+one thing about this though if you look
+at the stability temperature look at
+
+ align:start position:0%
+at the stability temperature look at
+ 
+
+ align:start position:0%
+at the stability temperature look at
+this column here called stable on
+
+ align:start position:0%
+this column here called stable on
+ 
+
+ align:start position:0%
+this column here called stable on
+Silicon be very careful people have
+
+ align:start position:0%
+Silicon be very careful people have
+ 
+
+ align:start position:0%
+Silicon be very careful people have
+listed nickel pilicide is being stable
+
+ align:start position:0%
+listed nickel pilicide is being stable
+ 
+
+ align:start position:0%
+listed nickel pilicide is being stable
+up to about
+
+ align:start position:0%
+up to about
+ 
+
+ align:start position:0%
+up to about
+650 may not even be stable that high
+
+ align:start position:0%
+650 may not even be stable that high
+ 
+
+ align:start position:0%
+650 may not even be stable that high
+maybe 600 or so so unlike some of these
+
+ align:start position:0%
+maybe 600 or so so unlike some of these
+ 
+
+ align:start position:0%
+maybe 600 or so so unlike some of these
+others uh which you can heat up Ty
+
+ align:start position:0%
+others uh which you can heat up Ty
+ 
+
+ align:start position:0%
+others uh which you can heat up Ty
+silicide or platinum you can heat up to
+
+ align:start position:0%
+silicide or platinum you can heat up to
+ 
+
+ align:start position:0%
+silicide or platinum you can heat up to
+800 or so you cannot do that with nickel
+
+ align:start position:0%
+800 or so you cannot do that with nickel
+ 
+
+ align:start position:0%
+800 or so you cannot do that with nickel
+pilicide so if you're using a nickel
+
+ align:start position:0%
+pilicide so if you're using a nickel
+ 
+
+ align:start position:0%
+pilicide so if you're using a nickel
+pilicide process you're going to be
+
+ align:start position:0%
+pilicide process you're going to be
+ 
+
+ align:start position:0%
+pilicide process you're going to be
+limited to a lower back end
+
+ align:start position:0%
+limited to a lower back end
+ 
+
+ align:start position:0%
+limited to a lower back end
+uh lower backend temperature but you can
+
+ align:start position:0%
+uh lower backend temperature but you can
+ 
+
+ align:start position:0%
+uh lower backend temperature but you can
+get reasonably low uh sheet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resistance um slide 27 I just want to
+
+ align:start position:0%
+resistance um slide 27 I just want to
+ 
+
+ align:start position:0%
+resistance um slide 27 I just want to
+show you an example uh and we'll go
+
+ align:start position:0%
+show you an example uh and we'll go
+ 
+
+ align:start position:0%
+show you an example uh and we'll go
+through these sort of calculations at
+
+ align:start position:0%
+through these sort of calculations at
+ 
+
+ align:start position:0%
+through these sort of calculations at
+the end of a lecture but um I want to go
+
+ align:start position:0%
+the end of a lecture but um I want to go
+ 
+
+ align:start position:0%
+the end of a lecture but um I want to go
+on and do the gate material um work
+
+ align:start position:0%
+on and do the gate material um work
+ 
+
+ align:start position:0%
+on and do the gate material um work
+first but what this is is a
+
+ align:start position:0%
+first but what this is is a
+ 
+
+ align:start position:0%
+first but what this is is a
+cross-section of a
+
+ align:start position:0%
+cross-section of a
+ 
+
+ align:start position:0%
+cross-section of a
+mosfet and there are and we've seen this
+
+ align:start position:0%
+mosfet and there are and we've seen this
+ 
+
+ align:start position:0%
+mosfet and there are and we've seen this
+uh we've seen this cross-section t
+
+ align:start position:0%
+uh we've seen this cross-section t
+ 
+
+ align:start position:0%
+uh we've seen this cross-section t
+number of times now in our class we now
+
+ align:start position:0%
+number of times now in our class we now
+ 
+
+ align:start position:0%
+number of times now in our class we now
+have enough ammunition that we can
+
+ align:start position:0%
+have enough ammunition that we can
+ 
+
+ align:start position:0%
+have enough ammunition that we can
+actually go sit down and calculate all
+
+ align:start position:0%
+actually go sit down and calculate all
+ 
+
+ align:start position:0%
+actually go sit down and calculate all
+these resistances or estimate them um uh
+
+ align:start position:0%
+these resistances or estimate them um uh
+ 
+
+ align:start position:0%
+these resistances or estimate them um uh
+given a certain given a geometry of a
+
+ align:start position:0%
+given a certain given a geometry of a
+ 
+
+ align:start position:0%
+given a certain given a geometry of a
+particular device so the resistance that
+
+ align:start position:0%
+particular device so the resistance that
+ 
+
+ align:start position:0%
+particular device so the resistance that
+we really uh when we scale the the
+
+ align:start position:0%
+we really uh when we scale the the
+ 
+
+ align:start position:0%
+we really uh when we scale the the
+channel length we really trying to scale
+
+ align:start position:0%
+channel length we really trying to scale
+ 
+
+ align:start position:0%
+channel length we really trying to scale
+is the channel resistance R Chan okay
+
+ align:start position:0%
+is the channel resistance R Chan okay
+ 
+
+ align:start position:0%
+is the channel resistance R Chan okay
+that's fine we make the channel shorter
+
+ align:start position:0%
+that's fine we make the channel shorter
+ 
+
+ align:start position:0%
+that's fine we make the channel shorter
+we can reduce that resistance but the
+
+ align:start position:0%
+we can reduce that resistance but the
+ 
+
+ align:start position:0%
+we can reduce that resistance but the
+problem is what happens to all if we
+
+ align:start position:0%
+problem is what happens to all if we
+ 
+
+ align:start position:0%
+problem is what happens to all if we
+don't do something to all these other
+
+ align:start position:0%
+don't do something to all these other
+ 
+
+ align:start position:0%
+don't do something to all these other
+parasitic resistances the net resistance
+
+ align:start position:0%
+parasitic resistances the net resistance
+ 
+
+ align:start position:0%
+parasitic resistances the net resistance
+of the device is really not going to go
+
+ align:start position:0%
+of the device is really not going to go
+ 
+
+ align:start position:0%
+of the device is really not going to go
+down by very much uh so there are three
+
+ align:start position:0%
+down by very much uh so there are three
+ 
+
+ align:start position:0%
+down by very much uh so there are three
+resistances we really want to be able to
+
+ align:start position:0%
+resistances we really want to be able to
+ 
+
+ align:start position:0%
+resistances we really want to be able to
+think about um one is this little
+
+ align:start position:0%
+think about um one is this little
+ 
+
+ align:start position:0%
+think about um one is this little
+resistor right here which is the
+
+ align:start position:0%
+resistor right here which is the
+ 
+
+ align:start position:0%
+resistor right here which is the
+resistance associated with the source
+
+ align:start position:0%
+resistance associated with the source
+ 
+
+ align:start position:0%
+resistance associated with the source
+drain extension okay it has a certain
+
+ align:start position:0%
+drain extension okay it has a certain
+ 
+
+ align:start position:0%
+drain extension okay it has a certain
+sheet resistance uh it's dope to a
+
+ align:start position:0%
+sheet resistance uh it's dope to a
+ 
+
+ align:start position:0%
+sheet resistance uh it's dope to a
+certain level it has a certain Junction
+
+ align:start position:0%
+certain level it has a certain Junction
+ 
+
+ align:start position:0%
+certain level it has a certain Junction
+depth it's usually very shallow so this
+
+ align:start position:0%
+depth it's usually very shallow so this
+ 
+
+ align:start position:0%
+depth it's usually very shallow so this
+resistance of a sour TR extension uh is
+
+ align:start position:0%
+resistance of a sour TR extension uh is
+ 
+
+ align:start position:0%
+resistance of a sour TR extension uh is
+one resistance we have to calculate the
+
+ align:start position:0%
+one resistance we have to calculate the
+ 
+
+ align:start position:0%
+one resistance we have to calculate the
+second one is the uh the resistance of
+
+ align:start position:0%
+second one is the uh the resistance of
+ 
+
+ align:start position:0%
+second one is the uh the resistance of
+this region here are that and generally
+
+ align:start position:0%
+this region here are that and generally
+ 
+
+ align:start position:0%
+this region here are that and generally
+this region has been silicided you
+
+ align:start position:0%
+this region has been silicided you
+ 
+
+ align:start position:0%
+this region has been silicided you
+notice the sourc Trin extension is under
+
+ align:start position:0%
+notice the sourc Trin extension is under
+ 
+
+ align:start position:0%
+notice the sourc Trin extension is under
+the spacer right by definition so it's
+
+ align:start position:0%
+the spacer right by definition so it's
+ 
+
+ align:start position:0%
+the spacer right by definition so it's
+not silicided so the current has to flow
+
+ align:start position:0%
+not silicided so the current has to flow
+ 
+
+ align:start position:0%
+not silicided so the current has to flow
+strictly through the Silicon so it'll
+
+ align:start position:0%
+strictly through the Silicon so it'll
+ 
+
+ align:start position:0%
+strictly through the Silicon so it'll
+have a certain higher resistivity in
+
+ align:start position:0%
+have a certain higher resistivity in
+ 
+
+ align:start position:0%
+have a certain higher resistivity in
+this case this region is is blue it's
+
+ align:start position:0%
+this case this region is is blue it's
+ 
+
+ align:start position:0%
+this case this region is is blue it's
+been silicided so it's going to have a
+
+ align:start position:0%
+been silicided so it's going to have a
+ 
+
+ align:start position:0%
+been silicided so it's going to have a
+lower resistivity it's got a metal on
+
+ align:start position:0%
+lower resistivity it's got a metal on
+ 
+
+ align:start position:0%
+lower resistivity it's got a metal on
+top of it uh so that's the second
+
+ align:start position:0%
+top of it uh so that's the second
+ 
+
+ align:start position:0%
+top of it uh so that's the second
+resistor we need to calculate the third
+
+ align:start position:0%
+resistor we need to calculate the third
+ 
+
+ align:start position:0%
+resistor we need to calculate the third
+one is the resistance of the contact
+
+ align:start position:0%
+one is the resistance of the contact
+ 
+
+ align:start position:0%
+one is the resistance of the contact
+itself so it's the contact resistance
+
+ align:start position:0%
+itself so it's the contact resistance
+ 
+
+ align:start position:0%
+itself so it's the contact resistance
+from the current flowing through the
+
+ align:start position:0%
+from the current flowing through the
+ 
+
+ align:start position:0%
+from the current flowing through the
+Silicon up into the metal um and that we
+
+ align:start position:0%
+Silicon up into the metal um and that we
+ 
+
+ align:start position:0%
+Silicon up into the metal um and that we
+calculate if we know the area and the
+
+ align:start position:0%
+calculate if we know the area and the
+ 
+
+ align:start position:0%
+calculate if we know the area and the
+specific contact resistivity so all
+
+ align:start position:0%
+specific contact resistivity so all
+ 
+
+ align:start position:0%
+specific contact resistivity so all
+three of these The sourc Strand
+
+ align:start position:0%
+three of these The sourc Strand
+ 
+
+ align:start position:0%
+three of these The sourc Strand
+extension resistance the silicide
+
+ align:start position:0%
+extension resistance the silicide
+ 
+
+ align:start position:0%
+extension resistance the silicide
+resistance uh and the contact resistance
+
+ align:start position:0%
+resistance uh and the contact resistance
+ 
+
+ align:start position:0%
+resistance uh and the contact resistance
+all three are going to add up and give
+
+ align:start position:0%
+all three are going to add up and give
+ 
+
+ align:start position:0%
+all three are going to add up and give
+us different contributions depending on
+
+ align:start position:0%
+us different contributions depending on
+ 
+
+ align:start position:0%
+us different contributions depending on
+the geometry so I want to go through a
+
+ align:start position:0%
+the geometry so I want to go through a
+ 
+
+ align:start position:0%
+the geometry so I want to go through a
+calculation of this I'm going to hold
+
+ align:start position:0%
+calculation of this I'm going to hold
+ 
+
+ align:start position:0%
+calculation of this I'm going to hold
+off for now because I want to make sure
+
+ align:start position:0%
+off for now because I want to make sure
+ 
+
+ align:start position:0%
+off for now because I want to make sure
+we cover the um the the novel gate
+
+ align:start position:0%
+we cover the um the the novel gate
+ 
+
+ align:start position:0%
+we cover the um the the novel gate
+material uh aspects but um we'll come
+
+ align:start position:0%
+material uh aspects but um we'll come
+ 
+
+ align:start position:0%
+material uh aspects but um we'll come
+back to this and you'll you should be
+
+ align:start position:0%
+back to this and you'll you should be
+ 
+
+ align:start position:0%
+back to this and you'll you should be
+able to sit down at this point and
+
+ align:start position:0%
+able to sit down at this point and
+ 
+
+ align:start position:0%
+able to sit down at this point and
+culate all three of these things and see
+
+ align:start position:0%
+culate all three of these things and see
+ 
+
+ align:start position:0%
+culate all three of these things and see
+what they look like for modern
+
+ align:start position:0%
+what they look like for modern
+ 
+
+ align:start position:0%
+what they look like for modern
+technology let's go on for now to slide
+
+ align:start position:0%
+technology let's go on for now to slide
+ 
+
+ align:start position:0%
+technology let's go on for now to slide
+um there's one more oh by the way I I I
+
+ align:start position:0%
+um there's one more oh by the way I I I
+ 
+
+ align:start position:0%
+um there's one more oh by the way I I I
+I sort of um didn't tell you the whole
+
+ align:start position:0%
+I sort of um didn't tell you the whole
+ 
+
+ align:start position:0%
+I sort of um didn't tell you the whole
+truth I said there are three resistors
+
+ align:start position:0%
+truth I said there are three resistors
+ 
+
+ align:start position:0%
+truth I said there are three resistors
+this one this one and this one it's not
+
+ align:start position:0%
+this one this one and this one it's not
+ 
+
+ align:start position:0%
+this one this one and this one it's not
+quite that simple these back of the
+
+ align:start position:0%
+quite that simple these back of the
+ 
+
+ align:start position:0%
+quite that simple these back of the
+envelope calculations are terrific
+
+ align:start position:0%
+envelope calculations are terrific
+ 
+
+ align:start position:0%
+envelope calculations are terrific
+because you can do them in five minutes
+
+ align:start position:0%
+because you can do them in five minutes
+ 
+
+ align:start position:0%
+because you can do them in five minutes
+in class or in 10 minutes in your office
+
+ align:start position:0%
+in class or in 10 minutes in your office
+ 
+
+ align:start position:0%
+in class or in 10 minutes in your office
+or whatever there is another resistance
+
+ align:start position:0%
+or whatever there is another resistance
+ 
+
+ align:start position:0%
+or whatever there is another resistance
+called the spreading resistance and uh
+
+ align:start position:0%
+called the spreading resistance and uh
+ 
+
+ align:start position:0%
+called the spreading resistance and uh
+that's actually pictured it cannot be
+
+ align:start position:0%
+that's actually pictured it cannot be
+ 
+
+ align:start position:0%
+that's actually pictured it cannot be
+calculated by hand but it's actually
+
+ align:start position:0%
+calculated by hand but it's actually
+ 
+
+ align:start position:0%
+calculated by hand but it's actually
+pictured on on page
+
+ align:start position:0%
+pictured on on page
+ 
+
+ align:start position:0%
+pictured on on page
+28 um here just to give you an idea this
+
+ align:start position:0%
+28 um here just to give you an idea this
+ 
+
+ align:start position:0%
+28 um here just to give you an idea this
+first was discussed by uh Ming and Lynch
+
+ align:start position:0%
+first was discussed by uh Ming and Lynch
+ 
+
+ align:start position:0%
+first was discussed by uh Ming and Lynch
+back in the in in the late 80s but what
+
+ align:start position:0%
+back in the in in the late 80s but what
+ 
+
+ align:start position:0%
+back in the in in the late 80s but what
+it is is um you have this channel region
+
+ align:start position:0%
+it is is um you have this channel region
+ 
+
+ align:start position:0%
+it is is um you have this channel region
+that's very very thin typically the the
+
+ align:start position:0%
+that's very very thin typically the the
+ 
+
+ align:start position:0%
+that's very very thin typically the the
+channel where the electrons of the holes
+
+ align:start position:0%
+channel where the electrons of the holes
+ 
+
+ align:start position:0%
+channel where the electrons of the holes
+are traversing across and they're going
+
+ align:start position:0%
+are traversing across and they're going
+ 
+
+ align:start position:0%
+are traversing across and they're going
+uh across the gate length that's maybe
+
+ align:start position:0%
+uh across the gate length that's maybe
+ 
+
+ align:start position:0%
+uh across the gate length that's maybe
+only 30 angstroms thick um that's where
+
+ align:start position:0%
+only 30 angstroms thick um that's where
+ 
+
+ align:start position:0%
+only 30 angstroms thick um that's where
+the current is all flowing in in in the
+
+ align:start position:0%
+the current is all flowing in in in the
+ 
+
+ align:start position:0%
+the current is all flowing in in in the
+Chan a very very high density of
+
+ align:start position:0%
+Chan a very very high density of
+ 
+
+ align:start position:0%
+Chan a very very high density of
+carriers the current then spreads out as
+
+ align:start position:0%
+carriers the current then spreads out as
+ 
+
+ align:start position:0%
+carriers the current then spreads out as
+it goes into the sourc drain extension
+
+ align:start position:0%
+it goes into the sourc drain extension
+ 
+
+ align:start position:0%
+it goes into the sourc drain extension
+this this is such an old paper it's
+
+ align:start position:0%
+this this is such an old paper it's
+ 
+
+ align:start position:0%
+this this is such an old paper it's
+before they had sourc drain extensions
+
+ align:start position:0%
+before they had sourc drain extensions
+ 
+
+ align:start position:0%
+before they had sourc drain extensions
+but you can imagine it then spreads out
+
+ align:start position:0%
+but you can imagine it then spreads out
+ 
+
+ align:start position:0%
+but you can imagine it then spreads out
+here into this region over a certain
+
+ align:start position:0%
+here into this region over a certain
+ 
+
+ align:start position:0%
+here into this region over a certain
+distance and how far it spreads out and
+
+ align:start position:0%
+distance and how far it spreads out and
+ 
+
+ align:start position:0%
+distance and how far it spreads out and
+exactly how it spreads out depends on
+
+ align:start position:0%
+exactly how it spreads out depends on
+ 
+
+ align:start position:0%
+exactly how it spreads out depends on
+the doping and the geometry of the
+
+ align:start position:0%
+the doping and the geometry of the
+ 
+
+ align:start position:0%
+the doping and the geometry of the
+structure it's a very two-dimensional
+
+ align:start position:0%
+structure it's a very two-dimensional
+ 
+
+ align:start position:0%
+structure it's a very two-dimensional
+problem you can't calculate it by hand
+
+ align:start position:0%
+problem you can't calculate it by hand
+ 
+
+ align:start position:0%
+problem you can't calculate it by hand
+so um this that's called the RSP here in
+
+ align:start position:0%
+so um this that's called the RSP here in
+ 
+
+ align:start position:0%
+so um this that's called the RSP here in
+this little um diagram where where he
+
+ align:start position:0%
+this little um diagram where where he
+ 
+
+ align:start position:0%
+this little um diagram where where he
+wrote down the different resistances so
+
+ align:start position:0%
+wrote down the different resistances so
+ 
+
+ align:start position:0%
+wrote down the different resistances so
+our spreading
+
+ align:start position:0%
+our spreading
+ 
+
+ align:start position:0%
+our spreading
+is one that generally has to be computed
+
+ align:start position:0%
+is one that generally has to be computed
+ 
+
+ align:start position:0%
+is one that generally has to be computed
+either by a two-dimensional simulator or
+
+ align:start position:0%
+either by a two-dimensional simulator or
+ 
+
+ align:start position:0%
+either by a two-dimensional simulator or
+you have to get it out of uh test
+
+ align:start position:0%
+you have to get it out of uh test
+ 
+
+ align:start position:0%
+you have to get it out of uh test
+devices or some kind of test structures
+
+ align:start position:0%
+devices or some kind of test structures
+ 
+
+ align:start position:0%
+devices or some kind of test structures
+it's not something you can simply
+
+ align:start position:0%
+it's not something you can simply
+ 
+
+ align:start position:0%
+it's not something you can simply
+calculate by hand but it is a major
+
+ align:start position:0%
+calculate by hand but it is a major
+ 
+
+ align:start position:0%
+calculate by hand but it is a major
+contri it can be a major contribution uh
+
+ align:start position:0%
+contri it can be a major contribution uh
+ 
+
+ align:start position:0%
+contri it can be a major contribution uh
+to the total series resistance so it's
+
+ align:start position:0%
+to the total series resistance so it's
+ 
+
+ align:start position:0%
+to the total series resistance so it's
+something we need to we need to be
+
+ align:start position:0%
+something we need to we need to be
+ 
+
+ align:start position:0%
+something we need to we need to be
+concerned about but I just want to point
+
+ align:start position:0%
+concerned about but I just want to point
+ 
+
+ align:start position:0%
+concerned about but I just want to point
+out that so th those three resistances
+
+ align:start position:0%
+out that so th those three resistances
+ 
+
+ align:start position:0%
+out that so th those three resistances
+we can calculate by hand that gives you
+
+ align:start position:0%
+we can calculate by hand that gives you
+ 
+
+ align:start position:0%
+we can calculate by hand that gives you
+the minimum series resistance of the
+
+ align:start position:0%
+the minimum series resistance of the
+ 
+
+ align:start position:0%
+the minimum series resistance of the
+device there'll always be a little extra
+
+ align:start position:0%
+device there'll always be a little extra
+ 
+
+ align:start position:0%
+device there'll always be a little extra
+which is spreading resistance which you
+
+ align:start position:0%
+which is spreading resistance which you
+ 
+
+ align:start position:0%
+which is spreading resistance which you
+you have to simulate uh in a two
+
+ align:start position:0%
+you have to simulate uh in a two
+ 
+
+ align:start position:0%
+you have to simulate uh in a two
+dimensional Tor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simulator that's how we make contacts I
+
+ align:start position:0%
+simulator that's how we make contacts I
+ 
+
+ align:start position:0%
+simulator that's how we make contacts I
+just wanted to go on and spend um the
+
+ align:start position:0%
+just wanted to go on and spend um the
+ 
+
+ align:start position:0%
+just wanted to go on and spend um the
+most of the remaining time of the
+
+ align:start position:0%
+most of the remaining time of the
+ 
+
+ align:start position:0%
+most of the remaining time of the
+lecture and talk about um something else
+
+ align:start position:0%
+lecture and talk about um something else
+ 
+
+ align:start position:0%
+lecture and talk about um something else
+that's come up in the last three or four
+
+ align:start position:0%
+that's come up in the last three or four
+ 
+
+ align:start position:0%
+that's come up in the last three or four
+years which is um related directly to
+
+ align:start position:0%
+years which is um related directly to
+ 
+
+ align:start position:0%
+years which is um related directly to
+the context because it turns out uh we
+
+ align:start position:0%
+the context because it turns out uh we
+ 
+
+ align:start position:0%
+the context because it turns out uh we
+can also use pilicides not only for the
+
+ align:start position:0%
+can also use pilicides not only for the
+ 
+
+ align:start position:0%
+can also use pilicides not only for the
+context but we can also fully s asde the
+
+ align:start position:0%
+context but we can also fully s asde the
+ 
+
+ align:start position:0%
+context but we can also fully s asde the
+gate and use it for the gate and I I
+
+ align:start position:0%
+gate and use it for the gate and I I
+ 
+
+ align:start position:0%
+gate and use it for the gate and I I
+think I T I I showed you this slide last
+
+ align:start position:0%
+think I T I I showed you this slide last
+ 
+
+ align:start position:0%
+think I T I I showed you this slide last
+last time page 29 was taken directly
+
+ align:start position:0%
+last time page 29 was taken directly
+ 
+
+ align:start position:0%
+last time page 29 was taken directly
+from the last lecture I just wanted to
+
+ align:start position:0%
+from the last lecture I just wanted to
+ 
+
+ align:start position:0%
+from the last lecture I just wanted to
+remind you that there are some new gate
+
+ align:start position:0%
+remind you that there are some new gate
+ 
+
+ align:start position:0%
+remind you that there are some new gate
+materials that are coming
+
+ align:start position:0%
+materials that are coming
+ 
+
+ align:start position:0%
+materials that are coming
+along this is the more classical old
+
+ align:start position:0%
+along this is the more classical old
+ 
+
+ align:start position:0%
+along this is the more classical old
+older technology the CL you know the
+
+ align:start position:0%
+older technology the CL you know the
+ 
+
+ align:start position:0%
+older technology the CL you know the
+traditional technology this is a photo
+
+ align:start position:0%
+traditional technology this is a photo
+ 
+
+ align:start position:0%
+traditional technology this is a photo
+from Intel uh device it's a somewhat
+
+ align:start position:0%
+from Intel uh device it's a somewhat
+ 
+
+ align:start position:0%
+from Intel uh device it's a somewhat
+older uh Tech uh photo now this was uh
+
+ align:start position:0%
+older uh Tech uh photo now this was uh
+ 
+
+ align:start position:0%
+older uh Tech uh photo now this was uh
+published back in in about five years
+
+ align:start position:0%
+published back in in about five years
+ 
+
+ align:start position:0%
+published back in in about five years
+ago in 2000 uh and what it shows is what
+
+ align:start position:0%
+ago in 2000 uh and what it shows is what
+ 
+
+ align:start position:0%
+ago in 2000 uh and what it shows is what
+we've just exactly been talking about
+
+ align:start position:0%
+we've just exactly been talking about
+ 
+
+ align:start position:0%
+we've just exactly been talking about
+here's the polysilicon gate these are
+
+ align:start position:0%
+here's the polysilicon gate these are
+ 
+
+ align:start position:0%
+here's the polysilicon gate these are
+the sidewall spacers you know how to
+
+ align:start position:0%
+the sidewall spacers you know how to
+ 
+
+ align:start position:0%
+the sidewall spacers you know how to
+form them and this is the pilicide in
+
+ align:start position:0%
+form them and this is the pilicide in
+ 
+
+ align:start position:0%
+form them and this is the pilicide in
+the source you can see it looks very
+
+ align:start position:0%
+the source you can see it looks very
+ 
+
+ align:start position:0%
+the source you can see it looks very
+dark because it's been pilicide and the
+
+ align:start position:0%
+dark because it's been pilicide and the
+ 
+
+ align:start position:0%
+dark because it's been pilicide and the
+pilicide in the drain and the pilicide
+
+ align:start position:0%
+pilicide in the drain and the pilicide
+ 
+
+ align:start position:0%
+pilicide in the drain and the pilicide
+that's been formed on the gate so that
+
+ align:start position:0%
+that's been formed on the gate so that
+ 
+
+ align:start position:0%
+that's been formed on the gate so that
+was a salside process just by the
+
+ align:start position:0%
+was a salside process just by the
+ 
+
+ align:start position:0%
+was a salside process just by the
+process exactly what we just talked
+
+ align:start position:0%
+process exactly what we just talked
+ 
+
+ align:start position:0%
+process exactly what we just talked
+about that's the classical type of
+
+ align:start position:0%
+about that's the classical type of
+ 
+
+ align:start position:0%
+about that's the classical type of
+structure we talked last time though
+
+ align:start position:0%
+structure we talked last time though
+ 
+
+ align:start position:0%
+structure we talked last time though
+that um polysilicon can only be doped so
+
+ align:start position:0%
+that um polysilicon can only be doped so
+ 
+
+ align:start position:0%
+that um polysilicon can only be doped so
+high and maybe you can get it to 10 to
+
+ align:start position:0%
+high and maybe you can get it to 10 to
+ 
+
+ align:start position:0%
+high and maybe you can get it to 10 to
+the 20 or or mid 10 of 20 but that's not
+
+ align:start position:0%
+the 20 or or mid 10 of 20 but that's not
+ 
+
+ align:start position:0%
+the 20 or or mid 10 of 20 but that's not
+enough carriers to prevent depletion of
+
+ align:start position:0%
+enough carriers to prevent depletion of
+ 
+
+ align:start position:0%
+enough carriers to prevent depletion of
+a poly silic at very high gate bind es
+
+ align:start position:0%
+a poly silic at very high gate bind es
+ 
+
+ align:start position:0%
+a poly silic at very high gate bind es
+um uh and you get a polysilicon
+
+ align:start position:0%
+um uh and you get a polysilicon
+ 
+
+ align:start position:0%
+um uh and you get a polysilicon
+depletion effect so people are concerned
+
+ align:start position:0%
+depletion effect so people are concerned
+ 
+
+ align:start position:0%
+depletion effect so people are concerned
+they want to they want to get rid of
+
+ align:start position:0%
+they want to they want to get rid of
+ 
+
+ align:start position:0%
+they want to they want to get rid of
+poly as the gate material it doesn't
+
+ align:start position:0%
+poly as the gate material it doesn't
+ 
+
+ align:start position:0%
+poly as the gate material it doesn't
+have enough carriers poly silicon may
+
+ align:start position:0%
+have enough carriers poly silicon may
+ 
+
+ align:start position:0%
+have enough carriers poly silicon may
+only have maybe five time 10 of 20
+
+ align:start position:0%
+only have maybe five time 10 of 20
+ 
+
+ align:start position:0%
+only have maybe five time 10 of 20
+electrons per cubic centimeter they
+
+ align:start position:0%
+electrons per cubic centimeter they
+ 
+
+ align:start position:0%
+electrons per cubic centimeter they
+would like to replace the poly with a
+
+ align:start position:0%
+would like to replace the poly with a
+ 
+
+ align:start position:0%
+would like to replace the poly with a
+gate with a metal gate um a metal has 10
+
+ align:start position:0%
+gate with a metal gate um a metal has 10
+ 
+
+ align:start position:0%
+gate with a metal gate um a metal has 10
+of 23rd says three of magnitude higher
+
+ align:start position:0%
+of 23rd says three of magnitude higher
+ 
+
+ align:start position:0%
+of 23rd says three of magnitude higher
+carriers so it's not going to get
+
+ align:start position:0%
+carriers so it's not going to get
+ 
+
+ align:start position:0%
+carriers so it's not going to get
+depleted um so they want to remove the
+
+ align:start position:0%
+depleted um so they want to remove the
+ 
+
+ align:start position:0%
+depleted um so they want to remove the
+semiconductor from the gate uh but poly
+
+ align:start position:0%
+semiconductor from the gate uh but poly
+ 
+
+ align:start position:0%
+semiconductor from the gate uh but poly
+is a extremely easy material to
+
+ align:start position:0%
+is a extremely easy material to
+ 
+
+ align:start position:0%
+is a extremely easy material to
+integrate people know how to etch it
+
+ align:start position:0%
+integrate people know how to etch it
+ 
+
+ align:start position:0%
+integrate people know how to etch it
+it's not reactive with
+
+ align:start position:0%
+it's not reactive with
+ 
+
+ align:start position:0%
+it's not reactive with
+sio2 um that's not the case for Metals
+
+ align:start position:0%
+sio2 um that's not the case for Metals
+ 
+
+ align:start position:0%
+sio2 um that's not the case for Metals
+so here's an example last time I in fact
+
+ align:start position:0%
+so here's an example last time I in fact
+ 
+
+ align:start position:0%
+so here's an example last time I in fact
+I went through a process called the
+
+ align:start position:0%
+I went through a process called the
+ 
+
+ align:start position:0%
+I went through a process called the
+replacement gate process where we showed
+
+ align:start position:0%
+replacement gate process where we showed
+ 
+
+ align:start position:0%
+replacement gate process where we showed
+they actually used poly they dug it out
+
+ align:start position:0%
+they actually used poly they dug it out
+ 
+
+ align:start position:0%
+they actually used poly they dug it out
+at the very end of the process they they
+
+ align:start position:0%
+at the very end of the process they they
+ 
+
+ align:start position:0%
+at the very end of the process they they
+they etched out the poly and they
+
+ align:start position:0%
+they etched out the poly and they
+ 
+
+ align:start position:0%
+they etched out the poly and they
+replaced it with a high K material like
+
+ align:start position:0%
+replaced it with a high K material like
+ 
+
+ align:start position:0%
+replaced it with a high K material like
+halfin dioxide and it's high nitride um
+
+ align:start position:0%
+halfin dioxide and it's high nitride um
+ 
+
+ align:start position:0%
+halfin dioxide and it's high nitride um
+gate so this was an example of something
+
+ align:start position:0%
+gate so this was an example of something
+ 
+
+ align:start position:0%
+gate so this was an example of something
+published about six months ago so people
+
+ align:start position:0%
+published about six months ago so people
+ 
+
+ align:start position:0%
+published about six months ago so people
+are thinking of replacing poly uh but
+
+ align:start position:0%
+are thinking of replacing poly uh but
+ 
+
+ align:start position:0%
+are thinking of replacing poly uh but
+it's got a lot of complex process
+
+ align:start position:0%
+it's got a lot of complex process
+ 
+
+ align:start position:0%
+it's got a lot of complex process
+integration an easier process
+
+ align:start position:0%
+integration an easier process
+ 
+
+ align:start position:0%
+integration an easier process
+integration that people are considered
+
+ align:start position:0%
+integration that people are considered
+ 
+
+ align:start position:0%
+integration that people are considered
+considering is rather than digging the
+
+ align:start position:0%
+considering is rather than digging the
+ 
+
+ align:start position:0%
+considering is rather than digging the
+poly out and whenever you etch out the
+
+ align:start position:0%
+poly out and whenever you etch out the
+ 
+
+ align:start position:0%
+poly out and whenever you etch out the
+poly always expose uh the very sensitive
+
+ align:start position:0%
+poly always expose uh the very sensitive
+ 
+
+ align:start position:0%
+poly always expose uh the very sensitive
+uh oxide silicon interface so it's
+
+ align:start position:0%
+uh oxide silicon interface so it's
+ 
+
+ align:start position:0%
+uh oxide silicon interface so it's
+typically you know from an integration
+
+ align:start position:0%
+typically you know from an integration
+ 
+
+ align:start position:0%
+typically you know from an integration
+point of view digging out the poly is
+
+ align:start position:0%
+point of view digging out the poly is
+ 
+
+ align:start position:0%
+point of view digging out the poly is
+not that desirable they said well well
+
+ align:start position:0%
+not that desirable they said well well
+ 
+
+ align:start position:0%
+not that desirable they said well well
+why don't we just take the poly silicon
+
+ align:start position:0%
+why don't we just take the poly silicon
+ 
+
+ align:start position:0%
+why don't we just take the poly silicon
+and fully react it with a metal and
+
+ align:start position:0%
+and fully react it with a metal and
+ 
+
+ align:start position:0%
+and fully react it with a metal and
+convert it from polysilicon into
+
+ align:start position:0%
+convert it from polysilicon into
+ 
+
+ align:start position:0%
+convert it from polysilicon into
+acide put enough metal there instead of
+
+ align:start position:0%
+acide put enough metal there instead of
+ 
+
+ align:start position:0%
+acide put enough metal there instead of
+in this case they only put a very thin
+
+ align:start position:0%
+in this case they only put a very thin
+ 
+
+ align:start position:0%
+in this case they only put a very thin
+amount of metal so it only reacts to
+
+ align:start position:0%
+amount of metal so it only reacts to
+ 
+
+ align:start position:0%
+amount of metal so it only reacts to
+form maybe several hundred angstroms of
+
+ align:start position:0%
+form maybe several hundred angstroms of
+ 
+
+ align:start position:0%
+form maybe several hundred angstroms of
+pilicide people are saying all right
+
+ align:start position:0%
+pilicide people are saying all right
+ 
+
+ align:start position:0%
+pilicide people are saying all right
+well put enough metal on top of that
+
+ align:start position:0%
+well put enough metal on top of that
+ 
+
+ align:start position:0%
+well put enough metal on top of that
+make it really thick um you know a metal
+
+ align:start position:0%
+make it really thick um you know a metal
+ 
+
+ align:start position:0%
+make it really thick um you know a metal
+and so that it re and reacted at a high
+
+ align:start position:0%
+and so that it re and reacted at a high
+ 
+
+ align:start position:0%
+and so that it re and reacted at a high
+enough temperature for a long enough
+
+ align:start position:0%
+enough temperature for a long enough
+ 
+
+ align:start position:0%
+enough temperature for a long enough
+time that the metal um reaction takes
+
+ align:start position:0%
+time that the metal um reaction takes
+ 
+
+ align:start position:0%
+time that the metal um reaction takes
+place throughout the entire pole and you
+
+ align:start position:0%
+place throughout the entire pole and you
+ 
+
+ align:start position:0%
+place throughout the entire pole and you
+get a pilicide all the way down to the
+
+ align:start position:0%
+get a pilicide all the way down to the
+ 
+
+ align:start position:0%
+get a pilicide all the way down to the
+gate um gate interface and here's an
+
+ align:start position:0%
+gate um gate interface and here's an
+ 
+
+ align:start position:0%
+gate um gate interface and here's an
+example of uh nickel pilicide fully
+
+ align:start position:0%
+example of uh nickel pilicide fully
+ 
+
+ align:start position:0%
+example of uh nickel pilicide fully
+silicided gate that was published about
+
+ align:start position:0%
+silicided gate that was published about
+ 
+
+ align:start position:0%
+silicided gate that was published about
+6 month ago uh by analing at 450° and
+
+ align:start position:0%
+6 month ago uh by analing at 450° and
+ 
+
+ align:start position:0%
+6 month ago uh by analing at 450° and
+using a thick enough layer of of nickel
+
+ align:start position:0%
+using a thick enough layer of of nickel
+ 
+
+ align:start position:0%
+using a thick enough layer of of nickel
+so not only are pilicides being used in
+
+ align:start position:0%
+so not only are pilicides being used in
+ 
+
+ align:start position:0%
+so not only are pilicides being used in
+the source and drain but they're also
+
+ align:start position:0%
+the source and drain but they're also
+ 
+
+ align:start position:0%
+the source and drain but they're also
+being used fully in the gate now this is
+
+ align:start position:0%
+being used fully in the gate now this is
+ 
+
+ align:start position:0%
+being used fully in the gate now this is
+different from the salicide
+
+ align:start position:0%
+different from the salicide
+ 
+
+ align:start position:0%
+different from the salicide
+process one reason would be is um the
+
+ align:start position:0%
+process one reason would be is um the
+ 
+
+ align:start position:0%
+process one reason would be is um the
+gate's usually reasonably tall right the
+
+ align:start position:0%
+gate's usually reasonably tall right the
+ 
+
+ align:start position:0%
+gate's usually reasonably tall right the
+gate may be uh a thousand anrs tall
+
+ align:start position:0%
+gate may be uh a thousand anrs tall
+ 
+
+ align:start position:0%
+gate may be uh a thousand anrs tall
+something like that so you need to put
+
+ align:start position:0%
+something like that so you need to put
+ 
+
+ align:start position:0%
+something like that so you need to put
+enough metal down that you can suicide
+
+ align:start position:0%
+enough metal down that you can suicide
+ 
+
+ align:start position:0%
+enough metal down that you can suicide
+all the way through a th angstroms now
+
+ align:start position:0%
+all the way through a th angstroms now
+ 
+
+ align:start position:0%
+all the way through a th angstroms now
+on a source and drain you don't want to
+
+ align:start position:0%
+on a source and drain you don't want to
+ 
+
+ align:start position:0%
+on a source and drain you don't want to
+be suiciding down aums right because I
+
+ align:start position:0%
+be suiciding down aums right because I
+ 
+
+ align:start position:0%
+be suiciding down aums right because I
+said the junction depth is about a th
+
+ align:start position:0%
+said the junction depth is about a th
+ 
+
+ align:start position:0%
+said the junction depth is about a th
+aums so if you're going to do a foozy
+
+ align:start position:0%
+aums so if you're going to do a foozy
+ 
+
+ align:start position:0%
+aums so if you're going to do a foozy
+process for the gate you actually need
+
+ align:start position:0%
+process for the gate you actually need
+ 
+
+ align:start position:0%
+process for the gate you actually need
+to have two different suiciding steps
+
+ align:start position:0%
+to have two different suiciding steps
+ 
+
+ align:start position:0%
+to have two different suiciding steps
+you need to have a step when you would
+
+ align:start position:0%
+you need to have a step when you would
+ 
+
+ align:start position:0%
+you need to have a step when you would
+pilicide with a very thin amount of
+
+ align:start position:0%
+pilicide with a very thin amount of
+ 
+
+ align:start position:0%
+pilicide with a very thin amount of
+metal would pilicide the source and
+
+ align:start position:0%
+metal would pilicide the source and
+ 
+
+ align:start position:0%
+metal would pilicide the source and
+drain you need to cover them and protect
+
+ align:start position:0%
+drain you need to cover them and protect
+ 
+
+ align:start position:0%
+drain you need to cover them and protect
+them then and then open up the gate and
+
+ align:start position:0%
+them then and then open up the gate and
+ 
+
+ align:start position:0%
+them then and then open up the gate and
+use a thick amount of metal to try to
+
+ align:start position:0%
+use a thick amount of metal to try to
+ 
+
+ align:start position:0%
+use a thick amount of metal to try to
+fully slow aside the gate so it's a
+
+ align:start position:0%
+fully slow aside the gate so it's a
+ 
+
+ align:start position:0%
+fully slow aside the gate so it's a
+little it's still tricky it's not as
+
+ align:start position:0%
+little it's still tricky it's not as
+ 
+
+ align:start position:0%
+little it's still tricky it's not as
+simple as using the oldfashioned
+
+ align:start position:0%
+simple as using the oldfashioned
+ 
+
+ align:start position:0%
+simple as using the oldfashioned
+salicide process where the thickness
+
+ align:start position:0%
+salicide process where the thickness
+ 
+
+ align:start position:0%
+salicide process where the thickness
+that you siloc side on the gate was the
+
+ align:start position:0%
+that you siloc side on the gate was the
+ 
+
+ align:start position:0%
+that you siloc side on the gate was the
+same as the thickness you went in the
+
+ align:start position:0%
+same as the thickness you went in the
+ 
+
+ align:start position:0%
+same as the thickness you went in the
+source and drain it's it's different
+
+ align:start position:0%
+source and drain it's it's different
+ 
+
+ align:start position:0%
+source and drain it's it's different
+from that but it's not quite as
+
+ align:start position:0%
+from that but it's not quite as
+ 
+
+ align:start position:0%
+from that but it's not quite as
+complicated as completely replacing the
+
+ align:start position:0%
+complicated as completely replacing the
+ 
+
+ align:start position:0%
+complicated as completely replacing the
+gate um in in the in the etch out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process fact I've got here um showing
+
+ align:start position:0%
+process fact I've got here um showing
+ 
+
+ align:start position:0%
+process fact I've got here um showing
+here you on slide 30 some very fairly
+
+ align:start position:0%
+here you on slide 30 some very fairly
+ 
+
+ align:start position:0%
+here you on slide 30 some very fairly
+recent results from the last couple of
+
+ align:start position:0%
+recent results from the last couple of
+ 
+
+ align:start position:0%
+recent results from the last couple of
+years of how people have made nickel
+
+ align:start position:0%
+years of how people have made nickel
+ 
+
+ align:start position:0%
+years of how people have made nickel
+silicided foozy f fues is the acronym
+
+ align:start position:0%
+silicided foozy f fues is the acronym
+ 
+
+ align:start position:0%
+silicided foozy f fues is the acronym
+for fully suicided um gate how they've
+
+ align:start position:0%
+for fully suicided um gate how they've
+ 
+
+ align:start position:0%
+for fully suicided um gate how they've
+made this uh in this particular article
+
+ align:start position:0%
+made this uh in this particular article
+ 
+
+ align:start position:0%
+made this uh in this particular article
+came out uh iedm two years ago from uh
+
+ align:start position:0%
+came out uh iedm two years ago from uh
+ 
+
+ align:start position:0%
+came out uh iedm two years ago from uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+AMD and what they're showing here is a
+
+ align:start position:0%
+AMD and what they're showing here is a
+ 
+
+ align:start position:0%
+AMD and what they're showing here is a
+method to form this so they do the
+
+ align:start position:0%
+method to form this so they do the
+ 
+
+ align:start position:0%
+method to form this so they do the
+standard uh transistor fabrication or
+
+ align:start position:0%
+standard uh transistor fabrication or
+ 
+
+ align:start position:0%
+standard uh transistor fabrication or
+flow here so this is their poly gate um
+
+ align:start position:0%
+flow here so this is their poly gate um
+ 
+
+ align:start position:0%
+flow here so this is their poly gate um
+and here they've actually formed a
+
+ align:start position:0%
+and here they've actually formed a
+ 
+
+ align:start position:0%
+and here they've actually formed a
+little bit of pilicide in the source and
+
+ align:start position:0%
+little bit of pilicide in the source and
+ 
+
+ align:start position:0%
+little bit of pilicide in the source and
+drain and a little bit on top of the
+
+ align:start position:0%
+drain and a little bit on top of the
+ 
+
+ align:start position:0%
+drain and a little bit on top of the
+gate so they did the standard salicide
+
+ align:start position:0%
+gate so they did the standard salicide
+ 
+
+ align:start position:0%
+gate so they did the standard salicide
+process at this
+
+ align:start position:0%
+process at this
+ 
+
+ align:start position:0%
+process at this
+point now they have to do a planarizing
+
+ align:start position:0%
+point now they have to do a planarizing
+ 
+
+ align:start position:0%
+point now they have to do a planarizing
+step so to get from here to here what
+
+ align:start position:0%
+step so to get from here to here what
+ 
+
+ align:start position:0%
+step so to get from here to here what
+they had to do is they had to put um
+
+ align:start position:0%
+they had to do is they had to put um
+ 
+
+ align:start position:0%
+they had to do is they had to put um
+metal and maybe some other harder
+
+ align:start position:0%
+metal and maybe some other harder
+ 
+
+ align:start position:0%
+metal and maybe some other harder
+material uh not sorry uh uh they had to
+
+ align:start position:0%
+material uh not sorry uh uh they had to
+ 
+
+ align:start position:0%
+material uh not sorry uh uh they had to
+put yeah contact material and then maybe
+
+ align:start position:0%
+put yeah contact material and then maybe
+ 
+
+ align:start position:0%
+put yeah contact material and then maybe
+a dialectric over over the entire thing
+
+ align:start position:0%
+a dialectric over over the entire thing
+ 
+
+ align:start position:0%
+a dialectric over over the entire thing
+and then CMP it down so it's planarized
+
+ align:start position:0%
+and then CMP it down so it's planarized
+ 
+
+ align:start position:0%
+and then CMP it down so it's planarized
+because you know they're going to get uh
+
+ align:start position:0%
+because you know they're going to get uh
+ 
+
+ align:start position:0%
+because you know they're going to get uh
+deposition everywhere so they planarize
+
+ align:start position:0%
+deposition everywhere so they planarize
+ 
+
+ align:start position:0%
+deposition everywhere so they planarize
+it um uh and they expose then the in the
+
+ align:start position:0%
+it um uh and they expose then the in the
+ 
+
+ align:start position:0%
+it um uh and they expose then the in the
+planarizing process they expose the uh
+
+ align:start position:0%
+planarizing process they expose the uh
+ 
+
+ align:start position:0%
+planarizing process they expose the uh
+the the poly silic gate and they can
+
+ align:start position:0%
+the the poly silic gate and they can
+ 
+
+ align:start position:0%
+the the poly silic gate and they can
+then put down metal here and a thick
+
+ align:start position:0%
+then put down metal here and a thick
+ 
+
+ align:start position:0%
+then put down metal here and a thick
+layer metal and reacted all the way to
+
+ align:start position:0%
+layer metal and reacted all the way to
+ 
+
+ align:start position:0%
+layer metal and reacted all the way to
+the interface so here they have this
+
+ align:start position:0%
+the interface so here they have this
+ 
+
+ align:start position:0%
+the interface so here they have this
+this uh very thick region uh where the
+
+ align:start position:0%
+this uh very thick region uh where the
+ 
+
+ align:start position:0%
+this uh very thick region uh where the
+entire gate has been suicided and you
+
+ align:start position:0%
+entire gate has been suicided and you
+ 
+
+ align:start position:0%
+entire gate has been suicided and you
+notice during this last process here on
+
+ align:start position:0%
+notice during this last process here on
+ 
+
+ align:start position:0%
+notice during this last process here on
+the right um there's no suiciding
+
+ align:start position:0%
+the right um there's no suiciding
+ 
+
+ align:start position:0%
+the right um there's no suiciding
+happening down in the source and drain
+
+ align:start position:0%
+happening down in the source and drain
+ 
+
+ align:start position:0%
+happening down in the source and drain
+because that's all been protected during
+
+ align:start position:0%
+because that's all been protected during
+ 
+
+ align:start position:0%
+because that's all been protected during
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+process um so it's certainly easier than
+
+ align:start position:0%
+process um so it's certainly easier than
+ 
+
+ align:start position:0%
+process um so it's certainly easier than
+the than the replacement gate scheme
+
+ align:start position:0%
+the than the replacement gate scheme
+ 
+
+ align:start position:0%
+the than the replacement gate scheme
+that I showed last time and it also
+
+ align:start position:0%
+that I showed last time and it also
+ 
+
+ align:start position:0%
+that I showed last time and it also
+avoids the pbd damage to the gate oxide
+
+ align:start position:0%
+avoids the pbd damage to the gate oxide
+ 
+
+ align:start position:0%
+avoids the pbd damage to the gate oxide
+if I'm going to etch this gate out um
+
+ align:start position:0%
+if I'm going to etch this gate out um
+ 
+
+ align:start position:0%
+if I'm going to etch this gate out um
+and I have to dep positive metal by pbd
+
+ align:start position:0%
+and I have to dep positive metal by pbd
+ 
+
+ align:start position:0%
+and I have to dep positive metal by pbd
+your your pbd processes can be very um
+
+ align:start position:0%
+your your pbd processes can be very um
+ 
+
+ align:start position:0%
+your your pbd processes can be very um
+energetic right you often use uh some
+
+ align:start position:0%
+energetic right you often use uh some
+ 
+
+ align:start position:0%
+energetic right you often use uh some
+kind of sputtering where you have ions
+
+ align:start position:0%
+kind of sputtering where you have ions
+ 
+
+ align:start position:0%
+kind of sputtering where you have ions
+and you can cause damage to the the gate
+
+ align:start position:0%
+and you can cause damage to the the gate
+ 
+
+ align:start position:0%
+and you can cause damage to the the gate
+oxide this doesn't have that at all
+
+ align:start position:0%
+oxide this doesn't have that at all
+ 
+
+ align:start position:0%
+oxide this doesn't have that at all
+because when you deposit the nickel the
+
+ align:start position:0%
+because when you deposit the nickel the
+ 
+
+ align:start position:0%
+because when you deposit the nickel the
+nickel's going on up here and then it it
+
+ align:start position:0%
+nickel's going on up here and then it it
+ 
+
+ align:start position:0%
+nickel's going on up here and then it it
+diffuses in a suiciding process to get
+
+ align:start position:0%
+diffuses in a suiciding process to get
+ 
+
+ align:start position:0%
+diffuses in a suiciding process to get
+down to the
+
+ align:start position:0%
+down to the
+ 
+
+ align:start position:0%
+down to the
+bottom here's an example of uh electron
+
+ align:start position:0%
+bottom here's an example of uh electron
+ 
+
+ align:start position:0%
+bottom here's an example of uh electron
+micrograph of of one of those devices
+
+ align:start position:0%
+micrograph of of one of those devices
+ 
+
+ align:start position:0%
+micrograph of of one of those devices
+this gate has been fully suicided so
+
+ align:start position:0%
+this gate has been fully suicided so
+ 
+
+ align:start position:0%
+this gate has been fully suicided so
+this is all nickel suicide is very thin
+
+ align:start position:0%
+this is all nickel suicide is very thin
+ 
+
+ align:start position:0%
+this is all nickel suicide is very thin
+white layer is the gate oxide uh very
+
+ align:start position:0%
+white layer is the gate oxide uh very
+ 
+
+ align:start position:0%
+white layer is the gate oxide uh very
+thin and this layer here is the Silicon
+
+ align:start position:0%
+thin and this layer here is the Silicon
+ 
+
+ align:start position:0%
+thin and this layer here is the Silicon
+Channel this is an SOI device um so
+
+ align:start position:0%
+Channel this is an SOI device um so
+ 
+
+ align:start position:0%
+Channel this is an SOI device um so
+here's this is the Silicon Channel and
+
+ align:start position:0%
+here's this is the Silicon Channel and
+ 
+
+ align:start position:0%
+here's this is the Silicon Channel and
+this is the the buried insulator the
+
+ align:start position:0%
+this is the the buried insulator the
+ 
+
+ align:start position:0%
+this is the the buried insulator the
+buried
+
+ align:start position:0%
+buried
+ 
+
+ align:start position:0%
+buried
+oxide and these are uh uh sidewall
+
+ align:start position:0%
+oxide and these are uh uh sidewall
+ 
+
+ align:start position:0%
+oxide and these are uh uh sidewall
+spacer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+layers this is just another image here
+
+ align:start position:0%
+layers this is just another image here
+ 
+
+ align:start position:0%
+layers this is just another image here
+on on slide 31 another image of that
+
+ align:start position:0%
+on on slide 31 another image of that
+ 
+
+ align:start position:0%
+on on slide 31 another image of that
+gate uh they've made a very short
+
+ align:start position:0%
+gate uh they've made a very short
+ 
+
+ align:start position:0%
+gate uh they've made a very short
+Channel device only something like uh 30
+
+ align:start position:0%
+Channel device only something like uh 30
+ 
+
+ align:start position:0%
+Channel device only something like uh 30
+between uh 35 and 40 nanometers um it's
+
+ align:start position:0%
+between uh 35 and 40 nanometers um it's
+ 
+
+ align:start position:0%
+between uh 35 and 40 nanometers um it's
+a very uh uh ultra thin body device or
+
+ align:start position:0%
+a very uh uh ultra thin body device or
+ 
+
+ align:start position:0%
+a very uh uh ultra thin body device or
+reasonably thin body device this is a
+
+ align:start position:0%
+reasonably thin body device this is a
+ 
+
+ align:start position:0%
+reasonably thin body device this is a
+SOI it's only 25 nmet thick and they
+
+ align:start position:0%
+SOI it's only 25 nmet thick and they
+ 
+
+ align:start position:0%
+SOI it's only 25 nmet thick and they
+have uh oxide and and uh nitride spacers
+
+ align:start position:0%
+have uh oxide and and uh nitride spacers
+ 
+
+ align:start position:0%
+have uh oxide and and uh nitride spacers
+on either side the point they were
+
+ align:start position:0%
+on either side the point they were
+ 
+
+ align:start position:0%
+on either side the point they were
+trying to make with this was that the
+
+ align:start position:0%
+trying to make with this was that the
+ 
+
+ align:start position:0%
+trying to make with this was that the
+nickel did not diffuse into the Silicon
+
+ align:start position:0%
+nickel did not diffuse into the Silicon
+ 
+
+ align:start position:0%
+nickel did not diffuse into the Silicon
+of course it's a little hard to tell
+
+ align:start position:0%
+of course it's a little hard to tell
+ 
+
+ align:start position:0%
+of course it's a little hard to tell
+from this uh the nice thing about it if
+
+ align:start position:0%
+from this uh the nice thing about it if
+ 
+
+ align:start position:0%
+from this uh the nice thing about it if
+you zoom in at this point right here and
+
+ align:start position:0%
+you zoom in at this point right here and
+ 
+
+ align:start position:0%
+you zoom in at this point right here and
+you zoom in on the gate oxide um so this
+
+ align:start position:0%
+you zoom in on the gate oxide um so this
+ 
+
+ align:start position:0%
+you zoom in on the gate oxide um so this
+is the gate dialectric uh which is uh
+
+ align:start position:0%
+is the gate dialectric uh which is uh
+ 
+
+ align:start position:0%
+is the gate dialectric uh which is uh
+shown here by this amorphous material
+
+ align:start position:0%
+shown here by this amorphous material
+ 
+
+ align:start position:0%
+shown here by this amorphous material
+it's about 2.1 nanm thick that's their
+
+ align:start position:0%
+it's about 2.1 nanm thick that's their
+ 
+
+ align:start position:0%
+it's about 2.1 nanm thick that's their
+gate dialectric this is the metal gate
+
+ align:start position:0%
+gate dialectric this is the metal gate
+ 
+
+ align:start position:0%
+gate dialectric this is the metal gate
+now it's nickel suicide it went down and
+
+ align:start position:0%
+now it's nickel suicide it went down and
+ 
+
+ align:start position:0%
+now it's nickel suicide it went down and
+it stopped at the gate stopped reacting
+
+ align:start position:0%
+it stopped at the gate stopped reacting
+ 
+
+ align:start position:0%
+it stopped at the gate stopped reacting
+at the gate dialectric and this is the
+
+ align:start position:0%
+at the gate dialectric and this is the
+ 
+
+ align:start position:0%
+at the gate dialectric and this is the
+Silicon channel uh region it's
+
+ align:start position:0%
+Silicon channel uh region it's
+ 
+
+ align:start position:0%
+Silicon channel uh region it's
+reasonably smooth people were concerned
+
+ align:start position:0%
+reasonably smooth people were concerned
+ 
+
+ align:start position:0%
+reasonably smooth people were concerned
+that the nickel might diffuse in and
+
+ align:start position:0%
+that the nickel might diffuse in and
+ 
+
+ align:start position:0%
+that the nickel might diffuse in and
+react with the oxide but according to
+
+ align:start position:0%
+react with the oxide but according to
+ 
+
+ align:start position:0%
+react with the oxide but according to
+this particular temperature and time
+
+ align:start position:0%
+this particular temperature and time
+ 
+
+ align:start position:0%
+this particular temperature and time
+that they did they get a reasonably
+
+ align:start position:0%
+that they did they get a reasonably
+ 
+
+ align:start position:0%
+that they did they get a reasonably
+smooth um uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interface remember you can you care
+
+ align:start position:0%
+interface remember you can you care
+ 
+
+ align:start position:0%
+interface remember you can you care
+about because it's going to be the
+
+ align:start position:0%
+about because it's going to be the
+ 
+
+ align:start position:0%
+about because it's going to be the
+channel the carriers are going to be
+
+ align:start position:0%
+channel the carriers are going to be
+ 
+
+ align:start position:0%
+channel the carriers are going to be
+flowing right right in the sil
+
+ align:start position:0%
+flowing right right in the sil
+ 
+
+ align:start position:0%
+flowing right right in the sil
+underneath this so you don't want to get
+
+ align:start position:0%
+underneath this so you don't want to get
+ 
+
+ align:start position:0%
+underneath this so you don't want to get
+any nickel into that
+
+ align:start position:0%
+any nickel into that
+ 
+
+ align:start position:0%
+any nickel into that
+channel this is um on slide 32 that same
+
+ align:start position:0%
+channel this is um on slide 32 that same
+ 
+
+ align:start position:0%
+channel this is um on slide 32 that same
+paper they also did some uh uh o
+
+ align:start position:0%
+paper they also did some uh uh o
+ 
+
+ align:start position:0%
+paper they also did some uh uh o
+analysis remember we talked about OJ
+
+ align:start position:0%
+analysis remember we talked about OJ
+ 
+
+ align:start position:0%
+analysis remember we talked about OJ
+spectroscopy as being a means of
+
+ align:start position:0%
+spectroscopy as being a means of
+ 
+
+ align:start position:0%
+spectroscopy as being a means of
+measuring the composition by by going
+
+ align:start position:0%
+measuring the composition by by going
+ 
+
+ align:start position:0%
+measuring the composition by by going
+through a device so this is a vertical
+
+ align:start position:0%
+through a device so this is a vertical
+ 
+
+ align:start position:0%
+through a device so this is a vertical
+scan through the device um so what
+
+ align:start position:0%
+scan through the device um so what
+ 
+
+ align:start position:0%
+scan through the device um so what
+they're actually doing is um
+
+ align:start position:0%
+they're actually doing is um
+ 
+
+ align:start position:0%
+they're actually doing is um
+going back here they're taking uh the uh
+
+ align:start position:0%
+going back here they're taking uh the uh
+ 
+
+ align:start position:0%
+going back here they're taking uh the uh
+doing the OJ experiment and they're
+
+ align:start position:0%
+doing the OJ experiment and they're
+ 
+
+ align:start position:0%
+doing the OJ experiment and they're
+sputtering right through here and
+
+ align:start position:0%
+sputtering right through here and
+ 
+
+ align:start position:0%
+sputtering right through here and
+through the center of the gate they're
+
+ align:start position:0%
+through the center of the gate they're
+ 
+
+ align:start position:0%
+through the center of the gate they're
+looking at what comes off what elements
+
+ align:start position:0%
+looking at what comes off what elements
+ 
+
+ align:start position:0%
+looking at what comes off what elements
+um uh What uh what they see uh what OJ
+
+ align:start position:0%
+um uh What uh what they see uh what OJ
+ 
+
+ align:start position:0%
+um uh What uh what they see uh what OJ
+electrons uh as they sputter so um here
+
+ align:start position:0%
+electrons uh as they sputter so um here
+ 
+
+ align:start position:0%
+electrons uh as they sputter so um here
+we see Atomic concentration in
+
+ align:start position:0%
+we see Atomic concentration in
+ 
+
+ align:start position:0%
+we see Atomic concentration in
+percent as a function of depth
+
+ align:start position:0%
+percent as a function of depth
+ 
+
+ align:start position:0%
+percent as a function of depth
+essentially so this is the surface over
+
+ align:start position:0%
+essentially so this is the surface over
+ 
+
+ align:start position:0%
+essentially so this is the surface over
+here and you can see that the red line
+
+ align:start position:0%
+here and you can see that the red line
+ 
+
+ align:start position:0%
+here and you can see that the red line
+is the nickel the blue is the Silicon uh
+
+ align:start position:0%
+is the nickel the blue is the Silicon uh
+ 
+
+ align:start position:0%
+is the nickel the blue is the Silicon uh
+this is the this is the thickness of the
+
+ align:start position:0%
+this is the this is the thickness of the
+ 
+
+ align:start position:0%
+this is the this is the thickness of the
+gate uh from the surface surface here to
+
+ align:start position:0%
+gate uh from the surface surface here to
+ 
+
+ align:start position:0%
+gate uh from the surface surface here to
+this point here to the gate
+
+ align:start position:0%
+this point here to the gate
+ 
+
+ align:start position:0%
+this point here to the gate
+oxide um and uh what you see is there's
+
+ align:start position:0%
+oxide um and uh what you see is there's
+ 
+
+ align:start position:0%
+oxide um and uh what you see is there's
+um uh quite a bit of silicidation this
+
+ align:start position:0%
+um uh quite a bit of silicidation this
+ 
+
+ align:start position:0%
+um uh quite a bit of silicidation this
+is mostly um nickel silicide uh it looks
+
+ align:start position:0%
+is mostly um nickel silicide uh it looks
+ 
+
+ align:start position:0%
+is mostly um nickel silicide uh it looks
+like here there's a little bit of
+
+ align:start position:0%
+like here there's a little bit of
+ 
+
+ align:start position:0%
+like here there's a little bit of
+silicon uh or here you have the uh
+
+ align:start position:0%
+silicon uh or here you have the uh
+ 
+
+ align:start position:0%
+silicon uh or here you have the uh
+silicon in the sio2 and then then uh
+
+ align:start position:0%
+silicon in the sio2 and then then uh
+ 
+
+ align:start position:0%
+silicon in the sio2 and then then uh
+this is the oxide beneath so you just
+
+ align:start position:0%
+this is the oxide beneath so you just
+ 
+
+ align:start position:0%
+this is the oxide beneath so you just
+get some idea this looks like it's
+
+ align:start position:0%
+get some idea this looks like it's
+ 
+
+ align:start position:0%
+get some idea this looks like it's
+fairly stochiometric almost one: one
+
+ align:start position:0%
+fairly stochiometric almost one: one
+ 
+
+ align:start position:0%
+fairly stochiometric almost one: one
+silicon to Nickel maybe a little bit
+
+ align:start position:0%
+silicon to Nickel maybe a little bit
+ 
+
+ align:start position:0%
+silicon to Nickel maybe a little bit
+nickel rich
+
+ align:start position:0%
+nickel rich
+ 
+
+ align:start position:0%
+nickel rich
+again using the types of techniques we
+
+ align:start position:0%
+again using the types of techniques we
+ 
+
+ align:start position:0%
+again using the types of techniques we
+talked about in our characterization uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lectures uh this is a different paper
+
+ align:start position:0%
+lectures uh this is a different paper
+ 
+
+ align:start position:0%
+lectures uh this is a different paper
+this is a paper that last paper was from
+
+ align:start position:0%
+this is a paper that last paper was from
+ 
+
+ align:start position:0%
+this is a paper that last paper was from
+uh iedm um 2002 by a applied uh by
+
+ align:start position:0%
+uh iedm um 2002 by a applied uh by
+ 
+
+ align:start position:0%
+uh iedm um 2002 by a applied uh by
+AMD um IBM the same year also published
+
+ align:start position:0%
+AMD um IBM the same year also published
+ 
+
+ align:start position:0%
+AMD um IBM the same year also published
+at the same conference uh nickel
+
+ align:start position:0%
+at the same conference uh nickel
+ 
+
+ align:start position:0%
+at the same conference uh nickel
+silicide foozy Gates uh this time they
+
+ align:start position:0%
+silicide foozy Gates uh this time they
+ 
+
+ align:start position:0%
+silicide foozy Gates uh this time they
+did them uh not only on fully depleted
+
+ align:start position:0%
+did them uh not only on fully depleted
+ 
+
+ align:start position:0%
+did them uh not only on fully depleted
+SOI I just showed you uh a silicon
+
+ align:start position:0%
+SOI I just showed you uh a silicon
+ 
+
+ align:start position:0%
+SOI I just showed you uh a silicon
+insulator device they also did it on a a
+
+ align:start position:0%
+insulator device they also did it on a a
+ 
+
+ align:start position:0%
+insulator device they also did it on a a
+device which is called a finfet we
+
+ align:start position:0%
+device which is called a finfet we
+ 
+
+ align:start position:0%
+device which is called a finfet we
+haven't had any time really to go into
+
+ align:start position:0%
+haven't had any time really to go into
+ 
+
+ align:start position:0%
+haven't had any time really to go into
+these new types of devices but there are
+
+ align:start position:0%
+these new types of devices but there are
+ 
+
+ align:start position:0%
+these new types of devices but there are
+um there are silicon mosfets these days
+
+ align:start position:0%
+um there are silicon mosfets these days
+ 
+
+ align:start position:0%
+um there are silicon mosfets these days
+that are not being made in a planer
+
+ align:start position:0%
+that are not being made in a planer
+ 
+
+ align:start position:0%
+that are not being made in a planer
+structure uh there's a device that's
+
+ align:start position:0%
+structure uh there's a device that's
+ 
+
+ align:start position:0%
+structure uh there's a device that's
+that's very non-planar called the finfet
+
+ align:start position:0%
+that's very non-planar called the finfet
+ 
+
+ align:start position:0%
+that's very non-planar called the finfet
+when in fact people form a fin and the
+
+ align:start position:0%
+when in fact people form a fin and the
+ 
+
+ align:start position:0%
+when in fact people form a fin and the
+channel of the device is actually into
+
+ align:start position:0%
+channel of the device is actually into
+ 
+
+ align:start position:0%
+channel of the device is actually into
+the PO into the page so it's into the
+
+ align:start position:0%
+the PO into the page so it's into the
+ 
+
+ align:start position:0%
+the PO into the page so it's into the
+board and the electrons actually flow
+
+ align:start position:0%
+board and the electrons actually flow
+ 
+
+ align:start position:0%
+board and the electrons actually flow
+along the sidewalls electrons actually
+
+ align:start position:0%
+along the sidewalls electrons actually
+ 
+
+ align:start position:0%
+along the sidewalls electrons actually
+flow right along here and you have a
+
+ align:start position:0%
+flow right along here and you have a
+ 
+
+ align:start position:0%
+flow right along here and you have a
+gate on the right side and a gate on the
+
+ align:start position:0%
+gate on the right side and a gate on the
+ 
+
+ align:start position:0%
+gate on the right side and a gate on the
+left side in fact the gate kind of wraps
+
+ align:start position:0%
+left side in fact the gate kind of wraps
+ 
+
+ align:start position:0%
+left side in fact the gate kind of wraps
+around um so this whole thing ends up
+
+ align:start position:0%
+around um so this whole thing ends up
+ 
+
+ align:start position:0%
+around um so this whole thing ends up
+being a channel and a source and drainer
+
+ align:start position:0%
+being a channel and a source and drainer
+ 
+
+ align:start position:0%
+being a channel and a source and drainer
+into the board uh this is a device that
+
+ align:start position:0%
+into the board uh this is a device that
+ 
+
+ align:start position:0%
+into the board uh this is a device that
+has uh some advantages although it's a
+
+ align:start position:0%
+has uh some advantages although it's a
+ 
+
+ align:start position:0%
+has uh some advantages although it's a
+little tricky to make uh it's a it's a
+
+ align:start position:0%
+little tricky to make uh it's a it's a
+ 
+
+ align:start position:0%
+little tricky to make uh it's a it's a
+Doublegate device you end end up getting
+
+ align:start position:0%
+Doublegate device you end end up getting
+ 
+
+ align:start position:0%
+Doublegate device you end end up getting
+kind of two channels in this thin
+
+ align:start position:0%
+kind of two channels in this thin
+ 
+
+ align:start position:0%
+kind of two channels in this thin
+silicon film so they made a fin fit and
+
+ align:start position:0%
+silicon film so they made a fin fit and
+ 
+
+ align:start position:0%
+silicon film so they made a fin fit and
+they demonstrated they could make a
+
+ align:start position:0%
+they demonstrated they could make a
+ 
+
+ align:start position:0%
+they demonstrated they could make a
+nickel suicide uh uh gate uh going all
+
+ align:start position:0%
+nickel suicide uh uh gate uh going all
+ 
+
+ align:start position:0%
+nickel suicide uh uh gate uh going all
+the way around uh that that fin in fact
+
+ align:start position:0%
+the way around uh that that fin in fact
+ 
+
+ align:start position:0%
+the way around uh that that fin in fact
+this is the gate dialectric shown here
+
+ align:start position:0%
+this is the gate dialectric shown here
+ 
+
+ align:start position:0%
+this is the gate dialectric shown here
+this um on morphis looking region with
+
+ align:start position:0%
+this um on morphis looking region with
+ 
+
+ align:start position:0%
+this um on morphis looking region with
+nickel suicide on the outside again
+
+ align:start position:0%
+nickel suicide on the outside again
+ 
+
+ align:start position:0%
+nickel suicide on the outside again
+using a foozy process where they put
+
+ align:start position:0%
+using a foozy process where they put
+ 
+
+ align:start position:0%
+using a foozy process where they put
+poly everywhere put down the appropriate
+
+ align:start position:0%
+poly everywhere put down the appropriate
+ 
+
+ align:start position:0%
+poly everywhere put down the appropriate
+amount of nickel and then reacted it uh
+
+ align:start position:0%
+amount of nickel and then reacted it uh
+ 
+
+ align:start position:0%
+amount of nickel and then reacted it uh
+and the reaction stopped right when it
+
+ align:start position:0%
+and the reaction stopped right when it
+ 
+
+ align:start position:0%
+and the reaction stopped right when it
+hit the gate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dialectric uh an interesting thing that
+
+ align:start position:0%
+dialectric uh an interesting thing that
+ 
+
+ align:start position:0%
+dialectric uh an interesting thing that
+was also done in this paper if you end
+
+ align:start position:0%
+was also done in this paper if you end
+ 
+
+ align:start position:0%
+was also done in this paper if you end
+up wanting to do research in this area
+
+ align:start position:0%
+up wanting to do research in this area
+ 
+
+ align:start position:0%
+up wanting to do research in this area
+uh is shown here on slide 34 uh this is
+
+ align:start position:0%
+uh is shown here on slide 34 uh this is
+ 
+
+ align:start position:0%
+uh is shown here on slide 34 uh this is
+called something called gate work
+
+ align:start position:0%
+called something called gate work
+ 
+
+ align:start position:0%
+called something called gate work
+function engineering we haven't really
+
+ align:start position:0%
+function engineering we haven't really
+ 
+
+ align:start position:0%
+function engineering we haven't really
+talked about it but um the uh the work
+
+ align:start position:0%
+talked about it but um the uh the work
+ 
+
+ align:start position:0%
+talked about it but um the uh the work
+function between the metal I think we
+
+ align:start position:0%
+function between the metal I think we
+ 
+
+ align:start position:0%
+function between the metal I think we
+may have talked about we've talked about
+
+ align:start position:0%
+may have talked about we've talked about
+ 
+
+ align:start position:0%
+may have talked about we've talked about
+um threshold voltage control the work
+
+ align:start position:0%
+um threshold voltage control the work
+ 
+
+ align:start position:0%
+um threshold voltage control the work
+function or uh which is a property of
+
+ align:start position:0%
+function or uh which is a property of
+ 
+
+ align:start position:0%
+function or uh which is a property of
+the metal material to a certain extent
+
+ align:start position:0%
+the metal material to a certain extent
+ 
+
+ align:start position:0%
+the metal material to a certain extent
+and the Silicon that determines the
+
+ align:start position:0%
+and the Silicon that determines the
+ 
+
+ align:start position:0%
+and the Silicon that determines the
+threshold voltage of a transistor the
+
+ align:start position:0%
+threshold voltage of a transistor the
+ 
+
+ align:start position:0%
+threshold voltage of a transistor the
+voltage at which the transistor turns on
+
+ align:start position:0%
+voltage at which the transistor turns on
+ 
+
+ align:start position:0%
+voltage at which the transistor turns on
+so that's a very important property um
+
+ align:start position:0%
+so that's a very important property um
+ 
+
+ align:start position:0%
+so that's a very important property um
+people have been using n plus poly and
+
+ align:start position:0%
+people have been using n plus poly and
+ 
+
+ align:start position:0%
+people have been using n plus poly and
+p+ Poly on n fets and p fets for years
+
+ align:start position:0%
+p+ Poly on n fets and p fets for years
+ 
+
+ align:start position:0%
+p+ Poly on n fets and p fets for years
+because it has it has the right work
+
+ align:start position:0%
+because it has it has the right work
+ 
+
+ align:start position:0%
+because it has it has the right work
+function the problem with poly as we've
+
+ align:start position:0%
+function the problem with poly as we've
+ 
+
+ align:start position:0%
+function the problem with poly as we've
+mentioned is U doesn't have enough
+
+ align:start position:0%
+mentioned is U doesn't have enough
+ 
+
+ align:start position:0%
+mentioned is U doesn't have enough
+carries it tends to deplete so people
+
+ align:start position:0%
+carries it tends to deplete so people
+ 
+
+ align:start position:0%
+carries it tends to deplete so people
+want to use Metals the problem with
+
+ align:start position:0%
+want to use Metals the problem with
+ 
+
+ align:start position:0%
+want to use Metals the problem with
+Metals is what work function do they
+
+ align:start position:0%
+Metals is what work function do they
+ 
+
+ align:start position:0%
+Metals is what work function do they
+have well they have the work function
+
+ align:start position:0%
+have well they have the work function
+ 
+
+ align:start position:0%
+have well they have the work function
+typically of the metal which is a
+
+ align:start position:0%
+typically of the metal which is a
+ 
+
+ align:start position:0%
+typically of the metal which is a
+property of the metal so and there are
+
+ align:start position:0%
+property of the metal so and there are
+ 
+
+ align:start position:0%
+property of the metal so and there are
+only so many metals in the world there
+
+ align:start position:0%
+only so many metals in the world there
+ 
+
+ align:start position:0%
+only so many metals in the world there
+are only so many pilicides in the world
+
+ align:start position:0%
+are only so many pilicides in the world
+ 
+
+ align:start position:0%
+are only so many pilicides in the world
+but what IBM has shown in this
+
+ align:start position:0%
+but what IBM has shown in this
+ 
+
+ align:start position:0%
+but what IBM has shown in this
+particular paper is that they can adjust
+
+ align:start position:0%
+particular paper is that they can adjust
+ 
+
+ align:start position:0%
+particular paper is that they can adjust
+slightly the effective work function of
+
+ align:start position:0%
+slightly the effective work function of
+ 
+
+ align:start position:0%
+slightly the effective work function of
+that gate stack
+
+ align:start position:0%
+that gate stack
+ 
+
+ align:start position:0%
+that gate stack
+so the effective work function in
+
+ align:start position:0%
+so the effective work function in
+ 
+
+ align:start position:0%
+so the effective work function in
+between this uh this metal gate and the
+
+ align:start position:0%
+between this uh this metal gate and the
+ 
+
+ align:start position:0%
+between this uh this metal gate and the
+Silicon uh material they said they can
+
+ align:start position:0%
+Silicon uh material they said they can
+ 
+
+ align:start position:0%
+Silicon uh material they said they can
+adjust it to a certain extent by how
+
+ align:start position:0%
+adjust it to a certain extent by how
+ 
+
+ align:start position:0%
+adjust it to a certain extent by how
+much they dope the polysilicon uh prior
+
+ align:start position:0%
+much they dope the polysilicon uh prior
+ 
+
+ align:start position:0%
+much they dope the polysilicon uh prior
+to the pilicide reaction and this is
+
+ align:start position:0%
+to the pilicide reaction and this is
+ 
+
+ align:start position:0%
+to the pilicide reaction and this is
+just a a table that I took right out of
+
+ align:start position:0%
+just a a table that I took right out of
+ 
+
+ align:start position:0%
+just a a table that I took right out of
+that paper uh for the case of nickel
+
+ align:start position:0%
+that paper uh for the case of nickel
+ 
+
+ align:start position:0%
+that paper uh for the case of nickel
+pilicide what they found is depending
+
+ align:start position:0%
+pilicide what they found is depending
+ 
+
+ align:start position:0%
+pilicide what they found is depending
+exactly on how much doping they put into
+
+ align:start position:0%
+exactly on how much doping they put into
+ 
+
+ align:start position:0%
+exactly on how much doping they put into
+the gate to begin with say if they don't
+
+ align:start position:0%
+the gate to begin with say if they don't
+ 
+
+ align:start position:0%
+the gate to begin with say if they don't
+dope it uh or if they put in one20 2 E20
+
+ align:start position:0%
+dope it uh or if they put in one20 2 E20
+ 
+
+ align:start position:0%
+dope it uh or if they put in one20 2 E20
+or 4 E20 um the effective work function
+
+ align:start position:0%
+or 4 E20 um the effective work function
+ 
+
+ align:start position:0%
+or 4 E20 um the effective work function
+that they measure with respect to the
+
+ align:start position:0%
+that they measure with respect to the
+ 
+
+ align:start position:0%
+that they measure with respect to the
+sil condu conduction man is shown here
+
+ align:start position:0%
+sil condu conduction man is shown here
+ 
+
+ align:start position:0%
+sil condu conduction man is shown here
+it can be varied Maybe by about 100
+
+ align:start position:0%
+it can be varied Maybe by about 100
+ 
+
+ align:start position:0%
+it can be varied Maybe by about 100
+molts maybe a little more uh something
+
+ align:start position:0%
+molts maybe a little more uh something
+ 
+
+ align:start position:0%
+molts maybe a little more uh something
+like that I guess the nickel pilicide
+
+ align:start position:0%
+like that I guess the nickel pilicide
+ 
+
+ align:start position:0%
+like that I guess the nickel pilicide
+was zero so it's a little more maybe a
+
+ align:start position:0%
+was zero so it's a little more maybe a
+ 
+
+ align:start position:0%
+was zero so it's a little more maybe a
+couple hundred Mill volts it can be
+
+ align:start position:0%
+couple hundred Mill volts it can be
+ 
+
+ align:start position:0%
+couple hundred Mill volts it can be
+varied uh by whether you put doping in
+
+ align:start position:0%
+varied uh by whether you put doping in
+ 
+
+ align:start position:0%
+varied uh by whether you put doping in
+or not and by how much doping uh and
+
+ align:start position:0%
+or not and by how much doping uh and
+ 
+
+ align:start position:0%
+or not and by how much doping uh and
+this is important because you need this
+
+ align:start position:0%
+this is important because you need this
+ 
+
+ align:start position:0%
+this is important because you need this
+flexibility in being able to adjust your
+
+ align:start position:0%
+flexibility in being able to adjust your
+ 
+
+ align:start position:0%
+flexibility in being able to adjust your
+threshold voltage so fosy gates are also
+
+ align:start position:0%
+threshold voltage so fosy gates are also
+ 
+
+ align:start position:0%
+threshold voltage so fosy gates are also
+interesting not just because it's a
+
+ align:start position:0%
+interesting not just because it's a
+ 
+
+ align:start position:0%
+interesting not just because it's a
+little easier to integrate the the
+
+ align:start position:0%
+little easier to integrate the the
+ 
+
+ align:start position:0%
+little easier to integrate the the
+processing the front end processing is
+
+ align:start position:0%
+processing the front end processing is
+ 
+
+ align:start position:0%
+processing the front end processing is
+what we're all familiar with everyone
+
+ align:start position:0%
+what we're all familiar with everyone
+ 
+
+ align:start position:0%
+what we're all familiar with everyone
+knows how to etch a poly gate and and
+
+ align:start position:0%
+knows how to etch a poly gate and and
+ 
+
+ align:start position:0%
+knows how to etch a poly gate and and
+make a good poly gate um and you can
+
+ align:start position:0%
+make a good poly gate um and you can
+ 
+
+ align:start position:0%
+make a good poly gate um and you can
+convert it to pilicide but depending on
+
+ align:start position:0%
+convert it to pilicide but depending on
+ 
+
+ align:start position:0%
+convert it to pilicide but depending on
+how you dope it you may be able to
+
+ align:start position:0%
+how you dope it you may be able to
+ 
+
+ align:start position:0%
+how you dope it you may be able to
+control the VT uh or adjust the VT a
+
+ align:start position:0%
+control the VT uh or adjust the VT a
+ 
+
+ align:start position:0%
+control the VT uh or adjust the VT a
+little bit uh still a very tricky
+
+ align:start position:0%
+little bit uh still a very tricky
+ 
+
+ align:start position:0%
+little bit uh still a very tricky
+process uh the reaction temperature um
+
+ align:start position:0%
+process uh the reaction temperature um
+ 
+
+ align:start position:0%
+process uh the reaction temperature um
+or the thermal stability temperature is
+
+ align:start position:0%
+or the thermal stability temperature is
+ 
+
+ align:start position:0%
+or the thermal stability temperature is
+is reasonably low so you cannot take
+
+ align:start position:0%
+is reasonably low so you cannot take
+ 
+
+ align:start position:0%
+is reasonably low so you cannot take
+these and then take them to a backend
+
+ align:start position:0%
+these and then take them to a backend
+ 
+
+ align:start position:0%
+these and then take them to a backend
+process that is too hot uh so this is
+
+ align:start position:0%
+process that is too hot uh so this is
+ 
+
+ align:start position:0%
+process that is too hot uh so this is
+very much a research it was only
+
+ align:start position:0%
+very much a research it was only
+ 
+
+ align:start position:0%
+very much a research it was only
+published by IBM a couple years ago it's
+
+ align:start position:0%
+published by IBM a couple years ago it's
+ 
+
+ align:start position:0%
+published by IBM a couple years ago it's
+uh certainly not ready necessarily for
+
+ align:start position:0%
+uh certainly not ready necessarily for
+ 
+
+ align:start position:0%
+uh certainly not ready necessarily for
+manufacturing right now perhaps in the
+
+ align:start position:0%
+manufacturing right now perhaps in the
+ 
+
+ align:start position:0%
+manufacturing right now perhaps in the
+near future but just give you an idea of
+
+ align:start position:0%
+near future but just give you an idea of
+ 
+
+ align:start position:0%
+near future but just give you an idea of
+of the types of things that people are
+
+ align:start position:0%
+of the types of things that people are
+ 
+
+ align:start position:0%
+of the types of things that people are
+um concerned about with
+
+ align:start position:0%
+um concerned about with
+ 
+
+ align:start position:0%
+um concerned about with
+suiciding uh before I go through the
+
+ align:start position:0%
+suiciding uh before I go through the
+ 
+
+ align:start position:0%
+suiciding uh before I go through the
+summary let's let's take a few minutes
+
+ align:start position:0%
+summary let's let's take a few minutes
+ 
+
+ align:start position:0%
+summary let's let's take a few minutes
+because we we have um a couple minutes
+
+ align:start position:0%
+because we we have um a couple minutes
+ 
+
+ align:start position:0%
+because we we have um a couple minutes
+right now I just want to kind of go
+
+ align:start position:0%
+right now I just want to kind of go
+ 
+
+ align:start position:0%
+right now I just want to kind of go
+through with you very briefly if we if
+
+ align:start position:0%
+through with you very briefly if we if
+ 
+
+ align:start position:0%
+through with you very briefly if we if
+we back up a little bit um here onto
+
+ align:start position:0%
+we back up a little bit um here onto
+ 
+
+ align:start position:0%
+we back up a little bit um here onto
+slide number
+
+ align:start position:0%
+slide number
+ 
+
+ align:start position:0%
+slide number
+27 and you can sit down and and and do
+
+ align:start position:0%
+27 and you can sit down and and and do
+ 
+
+ align:start position:0%
+27 and you can sit down and and and do
+this back of the envelope calculation
+
+ align:start position:0%
+this back of the envelope calculation
+ 
+
+ align:start position:0%
+this back of the envelope calculation
+yourself over the next couple days it's
+
+ align:start position:0%
+yourself over the next couple days it's
+ 
+
+ align:start position:0%
+yourself over the next couple days it's
+not a homework assignment but I think
+
+ align:start position:0%
+not a homework assignment but I think
+ 
+
+ align:start position:0%
+not a homework assignment but I think
+it's something you should do um uh What
+
+ align:start position:0%
+it's something you should do um uh What
+ 
+
+ align:start position:0%
+it's something you should do um uh What
+uh how to calculate these three
+
+ align:start position:0%
+uh how to calculate these three
+ 
+
+ align:start position:0%
+uh how to calculate these three
+resistances uh and then we can we can
+
+ align:start position:0%
+resistances uh and then we can we can
+ 
+
+ align:start position:0%
+resistances uh and then we can we can
+talk about it and go through it next
+
+ align:start position:0%
+talk about it and go through it next
+ 
+
+ align:start position:0%
+talk about it and go through it next
+time but what I want you to calculate is
+
+ align:start position:0%
+time but what I want you to calculate is
+ 
+
+ align:start position:0%
+time but what I want you to calculate is
+you're given uh everything you need to
+
+ align:start position:0%
+you're given uh everything you need to
+ 
+
+ align:start position:0%
+you're given uh everything you need to
+calculate the contact resistance you're
+
+ align:start position:0%
+calculate the contact resistance you're
+ 
+
+ align:start position:0%
+calculate the contact resistance you're
+given the specific contact resistivity
+
+ align:start position:0%
+given the specific contact resistivity
+ 
+
+ align:start position:0%
+given the specific contact resistivity
+row C and you're given the area of the
+
+ align:start position:0%
+row C and you're given the area of the
+ 
+
+ align:start position:0%
+row C and you're given the area of the
+contact so you know exactly how to
+
+ align:start position:0%
+contact so you know exactly how to
+ 
+
+ align:start position:0%
+contact so you know exactly how to
+calculate that you just do a simple
+
+ align:start position:0%
+calculate that you just do a simple
+ 
+
+ align:start position:0%
+calculate that you just do a simple
+division and you can calculate this
+
+ align:start position:0%
+division and you can calculate this
+ 
+
+ align:start position:0%
+division and you can calculate this
+resistor the contact resistance uh
+
+ align:start position:0%
+resistor the contact resistance uh
+ 
+
+ align:start position:0%
+resistor the contact resistance uh
+you're given the sheet resistance of the
+
+ align:start position:0%
+you're given the sheet resistance of the
+ 
+
+ align:start position:0%
+you're given the sheet resistance of the
+pilicide this blow region you have its
+
+ align:start position:0%
+pilicide this blow region you have its
+ 
+
+ align:start position:0%
+pilicide this blow region you have its
+sheet resistance
+
+ align:start position:0%
+sheet resistance
+ 
+
+ align:start position:0%
+sheet resistance
+um uh or it's resistivity I'm sorry 15 *
+
+ align:start position:0%
+um uh or it's resistivity I'm sorry 15 *
+ 
+
+ align:start position:0%
+um uh or it's resistivity I'm sorry 15 *
+10us 6 ohm centimeter and you know it's
+
+ align:start position:0%
+10us 6 ohm centimeter and you know it's
+ 
+
+ align:start position:0%
+10us 6 ohm centimeter and you know it's
+thickness so resistivity divided by
+
+ align:start position:0%
+thickness so resistivity divided by
+ 
+
+ align:start position:0%
+thickness so resistivity divided by
+thickness you can get sheet resistance
+
+ align:start position:0%
+thickness you can get sheet resistance
+ 
+
+ align:start position:0%
+thickness you can get sheet resistance
+and then you can figure out how many
+
+ align:start position:0%
+and then you can figure out how many
+ 
+
+ align:start position:0%
+and then you can figure out how many
+squares the current has to flow through
+
+ align:start position:0%
+squares the current has to flow through
+ 
+
+ align:start position:0%
+squares the current has to flow through
+so you should be able to contact to
+
+ align:start position:0%
+so you should be able to contact to
+ 
+
+ align:start position:0%
+so you should be able to contact to
+calculate this resistance uh of the
+
+ align:start position:0%
+calculate this resistance uh of the
+ 
+
+ align:start position:0%
+calculate this resistance uh of the
+psilocin regions and then the little
+
+ align:start position:0%
+psilocin regions and then the little
+ 
+
+ align:start position:0%
+psilocin regions and then the little
+resistor here of the source drain
+
+ align:start position:0%
+resistor here of the source drain
+ 
+
+ align:start position:0%
+resistor here of the source drain
+extensions um we are given their
+
+ align:start position:0%
+extensions um we are given their
+ 
+
+ align:start position:0%
+extensions um we are given their
+resistivity and again it's thickness so
+
+ align:start position:0%
+resistivity and again it's thickness so
+ 
+
+ align:start position:0%
+resistivity and again it's thickness so
+we should be able to calculate a sheet
+
+ align:start position:0%
+we should be able to calculate a sheet
+ 
+
+ align:start position:0%
+we should be able to calculate a sheet
+resist
+
+ align:start position:0%
+resist
+ 
+
+ align:start position:0%
+resist
+and from that figure out that so you get
+
+ align:start position:0%
+and from that figure out that so you get
+ 
+
+ align:start position:0%
+and from that figure out that so you get
+the ohm square and the number of squares
+
+ align:start position:0%
+the ohm square and the number of squares
+ 
+
+ align:start position:0%
+the ohm square and the number of squares
+and you get a resistor so one two and
+
+ align:start position:0%
+and you get a resistor so one two and
+ 
+
+ align:start position:0%
+and you get a resistor so one two and
+three resistors corresponding to this
+
+ align:start position:0%
+three resistors corresponding to this
+ 
+
+ align:start position:0%
+three resistors corresponding to this
+contact resistance the resistance of the
+
+ align:start position:0%
+contact resistance the resistance of the
+ 
+
+ align:start position:0%
+contact resistance the resistance of the
+current flowing through this sheet and
+
+ align:start position:0%
+current flowing through this sheet and
+ 
+
+ align:start position:0%
+current flowing through this sheet and
+the resistance throwing through through
+
+ align:start position:0%
+the resistance throwing through through
+ 
+
+ align:start position:0%
+the resistance throwing through through
+the source Trin extension uh you'll get
+
+ align:start position:0%
+the source Trin extension uh you'll get
+ 
+
+ align:start position:0%
+the source Trin extension uh you'll get
+three numbers and you get just get an
+
+ align:start position:0%
+three numbers and you get just get an
+ 
+
+ align:start position:0%
+three numbers and you get just get an
+idea of the order of magnitude of those
+
+ align:start position:0%
+idea of the order of magnitude of those
+ 
+
+ align:start position:0%
+idea of the order of magnitude of those
+numbers and how they compare um so you
+
+ align:start position:0%
+numbers and how they compare um so you
+ 
+
+ align:start position:0%
+numbers and how they compare um so you
+have time between now and next lecture
+
+ align:start position:0%
+have time between now and next lecture
+ 
+
+ align:start position:0%
+have time between now and next lecture
+do that we'll go through it at the
+
+ align:start position:0%
+do that we'll go through it at the
+ 
+
+ align:start position:0%
+do that we'll go through it at the
+beginning of of of the last lecture uh
+
+ align:start position:0%
+beginning of of of the last lecture uh
+ 
+
+ align:start position:0%
+beginning of of of the last lecture uh
+next time but it it's just an
+
+ align:start position:0%
+next time but it it's just an
+ 
+
+ align:start position:0%
+next time but it it's just an
+interesting uh interesting comparison
+
+ align:start position:0%
+interesting uh interesting comparison
+ 
+
+ align:start position:0%
+interesting uh interesting comparison
+between those three
+
+ align:start position:0%
+between those three
+ 
+
+ align:start position:0%
+between those three
+numbers okay so uh let me finish up by
+
+ align:start position:0%
+numbers okay so uh let me finish up by
+ 
+
+ align:start position:0%
+numbers okay so uh let me finish up by
+um kind of summarizing on this this
+
+ align:start position:0%
+um kind of summarizing on this this
+ 
+
+ align:start position:0%
+um kind of summarizing on this this
+topic um what we talked about today we
+
+ align:start position:0%
+topic um what we talked about today we
+ 
+
+ align:start position:0%
+topic um what we talked about today we
+need good uh device contacts that have
+
+ align:start position:0%
+need good uh device contacts that have
+ 
+
+ align:start position:0%
+need good uh device contacts that have
+certain requirements a low specific
+
+ align:start position:0%
+certain requirements a low specific
+ 
+
+ align:start position:0%
+certain requirements a low specific
+contact resistance row C very good
+
+ align:start position:0%
+contact resistance row C very good
+ 
+
+ align:start position:0%
+contact resistance row C very good
+thermal stability so when you heat them
+
+ align:start position:0%
+thermal stability so when you heat them
+ 
+
+ align:start position:0%
+thermal stability so when you heat them
+up they don't Spike or do anything
+
+ align:start position:0%
+up they don't Spike or do anything
+ 
+
+ align:start position:0%
+up they don't Spike or do anything
+unusual uh in general you want to get
+
+ align:start position:0%
+unusual uh in general you want to get
+ 
+
+ align:start position:0%
+unusual uh in general you want to get
+the high doping concentration of the
+
+ align:start position:0%
+the high doping concentration of the
+ 
+
+ align:start position:0%
+the high doping concentration of the
+Silicon right at the interface that will
+
+ align:start position:0%
+Silicon right at the interface that will
+ 
+
+ align:start position:0%
+Silicon right at the interface that will
+tend to lower the contact resistance by
+
+ align:start position:0%
+tend to lower the contact resistance by
+ 
+
+ align:start position:0%
+tend to lower the contact resistance by
+inducing quantum mechanical
+
+ align:start position:0%
+inducing quantum mechanical
+ 
+
+ align:start position:0%
+inducing quantum mechanical
+tunneling uh the the the however there
+
+ align:start position:0%
+tunneling uh the the the however there
+ 
+
+ align:start position:0%
+tunneling uh the the the however there
+is a fundamental limit on how much
+
+ align:start position:0%
+is a fundamental limit on how much
+ 
+
+ align:start position:0%
+is a fundamental limit on how much
+doping we can activate in Silicon this
+
+ align:start position:0%
+doping we can activate in Silicon this
+ 
+
+ align:start position:0%
+doping we can activate in Silicon this
+puts a limit on the contact resistance
+
+ align:start position:0%
+puts a limit on the contact resistance
+ 
+
+ align:start position:0%
+puts a limit on the contact resistance
+and on the sheet resistance uh and on
+
+ align:start position:0%
+and on the sheet resistance uh and on
+ 
+
+ align:start position:0%
+and on the sheet resistance uh and on
+the parasitic resistance in fact it's
+
+ align:start position:0%
+the parasitic resistance in fact it's
+ 
+
+ align:start position:0%
+the parasitic resistance in fact it's
+the contact resistance that's really a
+
+ align:start position:0%
+the contact resistance that's really a
+ 
+
+ align:start position:0%
+the contact resistance that's really a
+big problem if you look in the itrs
+
+ align:start position:0%
+big problem if you look in the itrs
+ 
+
+ align:start position:0%
+big problem if you look in the itrs
+there's a lot of concern uh about how to
+
+ align:start position:0%
+there's a lot of concern uh about how to
+ 
+
+ align:start position:0%
+there's a lot of concern uh about how to
+lower that the so-called self-aligned
+
+ align:start position:0%
+lower that the so-called self-aligned
+ 
+
+ align:start position:0%
+lower that the so-called self-aligned
+silicide process or also abbreviated
+
+ align:start position:0%
+silicide process or also abbreviated
+ 
+
+ align:start position:0%
+silicide process or also abbreviated
+salicide it's been the main stay of
+
+ align:start position:0%
+salicide it's been the main stay of
+ 
+
+ align:start position:0%
+salicide it's been the main stay of
+technology for many many years now
+
+ align:start position:0%
+technology for many many years now
+ 
+
+ align:start position:0%
+technology for many many years now
+um it it has a lot of advantages it's
+
+ align:start position:0%
+um it it has a lot of advantages it's
+ 
+
+ align:start position:0%
+um it it has a lot of advantages it's
+self-aligned it reduces the sheet
+
+ align:start position:0%
+self-aligned it reduces the sheet
+ 
+
+ align:start position:0%
+self-aligned it reduces the sheet
+resistance of the deep Source drain
+
+ align:start position:0%
+resistance of the deep Source drain
+ 
+
+ align:start position:0%
+resistance of the deep Source drain
+region it reduces the gate sheet
+
+ align:start position:0%
+region it reduces the gate sheet
+ 
+
+ align:start position:0%
+region it reduces the gate sheet
+resistance because you put you pilicide
+
+ align:start position:0%
+resistance because you put you pilicide
+ 
+
+ align:start position:0%
+resistance because you put you pilicide
+on the gate and also provides a local
+
+ align:start position:0%
+on the gate and also provides a local
+ 
+
+ align:start position:0%
+on the gate and also provides a local
+interconnect layer so it's been a very
+
+ align:start position:0%
+interconnect layer so it's been a very
+ 
+
+ align:start position:0%
+interconnect layer so it's been a very
+uh good
+
+ align:start position:0%
+uh good
+ 
+
+ align:start position:0%
+uh good
+Workhorse um pilicides can also function
+
+ align:start position:0%
+Workhorse um pilicides can also function
+ 
+
+ align:start position:0%
+Workhorse um pilicides can also function
+as a barrier layer to prevent spiking
+
+ align:start position:0%
+as a barrier layer to prevent spiking
+ 
+
+ align:start position:0%
+as a barrier layer to prevent spiking
+potentially um pilicides do consume
+
+ align:start position:0%
+potentially um pilicides do consume
+ 
+
+ align:start position:0%
+potentially um pilicides do consume
+silicon that's one problem with
+
+ align:start position:0%
+silicon that's one problem with
+ 
+
+ align:start position:0%
+silicon that's one problem with
+them uh and as you move the metal closer
+
+ align:start position:0%
+them uh and as you move the metal closer
+ 
+
+ align:start position:0%
+them uh and as you move the metal closer
+to the F depletion region it's a big
+
+ align:start position:0%
+to the F depletion region it's a big
+ 
+
+ align:start position:0%
+to the F depletion region it's a big
+problem uh because you get tend to get
+
+ align:start position:0%
+problem uh because you get tend to get
+ 
+
+ align:start position:0%
+problem uh because you get tend to get
+more leakage than the fact this is why
+
+ align:start position:0%
+more leakage than the fact this is why
+ 
+
+ align:start position:0%
+more leakage than the fact this is why
+people use deep sour strain regions to
+
+ align:start position:0%
+people use deep sour strain regions to
+ 
+
+ align:start position:0%
+people use deep sour strain regions to
+allow a thick enough uh region in
+
+ align:start position:0%
+allow a thick enough uh region in
+ 
+
+ align:start position:0%
+allow a thick enough uh region in
+between the depletion region and the
+
+ align:start position:0%
+between the depletion region and the
+ 
+
+ align:start position:0%
+between the depletion region and the
+point and where the pilicide is formed
+
+ align:start position:0%
+point and where the pilicide is formed
+ 
+
+ align:start position:0%
+point and where the pilicide is formed
+while so you can get a reasonable
+
+ align:start position:0%
+while so you can get a reasonable
+ 
+
+ align:start position:0%
+while so you can get a reasonable
+pilicide with low Junction uh leakage
+
+ align:start position:0%
+pilicide with low Junction uh leakage
+ 
+
+ align:start position:0%
+pilicide with low Junction uh leakage
+because um because Junctions are scaling
+
+ align:start position:0%
+because um because Junctions are scaling
+ 
+
+ align:start position:0%
+because um because Junctions are scaling
+to be thinner and thinner especially in
+
+ align:start position:0%
+to be thinner and thinner especially in
+ 
+
+ align:start position:0%
+to be thinner and thinner especially in
+fully depleted s SOI people are moving
+
+ align:start position:0%
+fully depleted s SOI people are moving
+ 
+
+ align:start position:0%
+fully depleted s SOI people are moving
+towards nickel pilicide because it
+
+ align:start position:0%
+towards nickel pilicide because it
+ 
+
+ align:start position:0%
+towards nickel pilicide because it
+consumes a lot less silicon per
+
+ align:start position:0%
+consumes a lot less silicon per
+ 
+
+ align:start position:0%
+consumes a lot less silicon per
+thickness of pilicide than say Tha
+
+ align:start position:0%
+thickness of pilicide than say Tha
+ 
+
+ align:start position:0%
+thickness of pilicide than say Tha
+pilicide or Cobalt pilicides so for
+
+ align:start position:0%
+pilicide or Cobalt pilicides so for
+ 
+
+ align:start position:0%
+pilicide or Cobalt pilicides so for
+fully depleted SOI nickel pde has a lot
+
+ align:start position:0%
+fully depleted SOI nickel pde has a lot
+ 
+
+ align:start position:0%
+fully depleted SOI nickel pde has a lot
+of advantages and the last thing which
+
+ align:start position:0%
+of advantages and the last thing which
+ 
+
+ align:start position:0%
+of advantages and the last thing which
+isn't in the summary we just talked
+
+ align:start position:0%
+isn't in the summary we just talked
+ 
+
+ align:start position:0%
+isn't in the summary we just talked
+about is that silicides are even being
+
+ align:start position:0%
+about is that silicides are even being
+ 
+
+ align:start position:0%
+about is that silicides are even being
+considered to be fully uh suicided uh
+
+ align:start position:0%
+considered to be fully uh suicided uh
+ 
+
+ align:start position:0%
+considered to be fully uh suicided uh
+purpose for the gate and uh that's
+
+ align:start position:0%
+purpose for the gate and uh that's
+ 
+
+ align:start position:0%
+purpose for the gate and uh that's
+something that's in research right now
+
+ align:start position:0%
+something that's in research right now
+ 
+
+ align:start position:0%
+something that's in research right now
+you may see in production over the next
+
+ align:start position:0%
+you may see in production over the next
+ 
+
+ align:start position:0%
+you may see in production over the next
+uh you know three or four years or so um
+
+ align:start position:0%
+uh you know three or four years or so um
+ 
+
+ align:start position:0%
+uh you know three or four years or so um
+so that's all I have um for this lecture
+
+ align:start position:0%
+so that's all I have um for this lecture
+ 
+
+ align:start position:0%
+so that's all I have um for this lecture
+take a look at that simple calculation
+
+ align:start position:0%
+take a look at that simple calculation
+ 
+
+ align:start position:0%
+take a look at that simple calculation
+example by hand and um uh then next time
+
+ align:start position:0%
+example by hand and um uh then next time
+ 
+
+ align:start position:0%
+example by hand and um uh then next time
+uh will meet for the for the final
+
+ align:start position:0%
+uh will meet for the for the final
+ 
+
+ align:start position:0%
+uh will meet for the for the final
+lecture and again I announced at the
+
+ align:start position:0%
+lecture and again I announced at the
+ 
+
+ align:start position:0%
+lecture and again I announced at the
+beginning um the people who are going to
+
+ align:start position:0%
+beginning um the people who are going to
+ 
+
+ align:start position:0%
+beginning um the people who are going to
+be speaking in the order it's also
+
+ align:start position:0%
+be speaking in the order it's also
+ 
+
+ align:start position:0%
+be speaking in the order it's also
+posted on the website but if you have
+
+ align:start position:0%
+posted on the website but if you have
+ 
+
+ align:start position:0%
+posted on the website but if you have
+any questions um about your oral report
+
+ align:start position:0%
+any questions um about your oral report
+ 
+
+ align:start position:0%
+any questions um about your oral report
+or whatever um please get back to me
+
+ align:start position:0%
+or whatever um please get back to me
+ 
+
+ align:start position:0%
+or whatever um please get back to me
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thanks
\ No newline at end of file
diff --git a/YZpYxeeb6hA.txt b/YZpYxeeb6hA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f2218cd49585d10690a58887bd06d63cdf57d495
--- /dev/null
+++ b/YZpYxeeb6hA.txt
@@ -0,0 +1,16475 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right thanks for coming you guys uh
+
+ align:start position:0%
+all right thanks for coming you guys uh
+ 
+
+ align:start position:0%
+all right thanks for coming you guys uh
+my name is bus Leonard I'm Carter I'm
+
+ align:start position:0%
+my name is bus Leonard I'm Carter I'm
+ 
+
+ align:start position:0%
+my name is bus Leonard I'm Carter I'm
+Brianna and Roser is not here right now
+
+ align:start position:0%
+Brianna and Roser is not here right now
+ 
+
+ align:start position:0%
+Brianna and Roser is not here right now
+and our team lead is uh Ken um and we're
+
+ align:start position:0%
+and our team lead is uh Ken um and we're
+ 
+
+ align:start position:0%
+and our team lead is uh Ken um and we're
+uh working on OJ
+
+ align:start position:0%
+uh working on OJ
+ 
+
+ align:start position:0%
+uh working on OJ
+sealer um for a community in Nicaragua
+
+ align:start position:0%
+sealer um for a community in Nicaragua
+ 
+
+ align:start position:0%
+sealer um for a community in Nicaragua
+uh we were partnered with uh the NGO ASO
+
+ align:start position:0%
+uh we were partnered with uh the NGO ASO
+ 
+
+ align:start position:0%
+uh we were partnered with uh the NGO ASO
+Phoenix uh which is
+
+ align:start position:0%
+Phoenix uh which is
+ 
+
+ align:start position:0%
+Phoenix uh which is
+uh a organization that does a rural
+
+ align:start position:0%
+uh a organization that does a rural
+ 
+
+ align:start position:0%
+uh a organization that does a rural
+sustainable development projects um with
+
+ align:start position:0%
+sustainable development projects um with
+ 
+
+ align:start position:0%
+sustainable development projects um with
+multiple communities uh in
+
+ align:start position:0%
+multiple communities uh in
+ 
+
+ align:start position:0%
+multiple communities uh in
+Nicaragua and they do projects such that
+
+ align:start position:0%
+Nicaragua and they do projects such that
+ 
+
+ align:start position:0%
+Nicaragua and they do projects such that
+promote clean water uh electricity
+
+ align:start position:0%
+promote clean water uh electricity
+ 
+
+ align:start position:0%
+promote clean water uh electricity
+income generation and also educational
+
+ align:start position:0%
+income generation and also educational
+ 
+
+ align:start position:0%
+income generation and also educational
+projects that uh help the community be
+
+ align:start position:0%
+projects that uh help the community be
+ 
+
+ align:start position:0%
+projects that uh help the community be
+healthy uh so our project uh centers
+
+ align:start position:0%
+healthy uh so our project uh centers
+ 
+
+ align:start position:0%
+healthy uh so our project uh centers
+around the community ELR BL that we
+
+ align:start position:0%
+around the community ELR BL that we
+ 
+
+ align:start position:0%
+around the community ELR BL that we
+visited while we were down there and
+
+ align:start position:0%
+visited while we were down there and
+ 
+
+ align:start position:0%
+visited while we were down there and
+they have a large orange Harvest crop
+
+ align:start position:0%
+they have a large orange Harvest crop
+ 
+
+ align:start position:0%
+they have a large orange Harvest crop
+that they get and there's no market for
+
+ align:start position:0%
+that they get and there's no market for
+ 
+
+ align:start position:0%
+that they get and there's no market for
+the oranges
+
+ align:start position:0%
+the oranges
+ 
+
+ align:start position:0%
+the oranges
+um during the harvest season because
+
+ align:start position:0%
+um during the harvest season because
+ 
+
+ align:start position:0%
+um during the harvest season because
+everybody's harvesting oranges so the
+
+ align:start position:0%
+everybody's harvesting oranges so the
+ 
+
+ align:start position:0%
+everybody's harvesting oranges so the
+idea is to create a way for them to sell
+
+ align:start position:0%
+idea is to create a way for them to sell
+ 
+
+ align:start position:0%
+idea is to create a way for them to sell
+the oranges or a product from the
+
+ align:start position:0%
+the oranges or a product from the
+ 
+
+ align:start position:0%
+the oranges or a product from the
+oranges in the offseason to generate
+
+ align:start position:0%
+oranges in the offseason to generate
+ 
+
+ align:start position:0%
+oranges in the offseason to generate
+income and they were introduced a
+
+ align:start position:0%
+income and they were introduced a
+ 
+
+ align:start position:0%
+income and they were introduced a
+pasteurization process to preserve uh
+
+ align:start position:0%
+pasteurization process to preserve uh
+ 
+
+ align:start position:0%
+pasteurization process to preserve uh
+the orange juice by uh oo Phoenix and
+
+ align:start position:0%
+the orange juice by uh oo Phoenix and
+ 
+
+ align:start position:0%
+the orange juice by uh oo Phoenix and
+through a the University of Managua so
+
+ align:start position:0%
+through a the University of Managua so
+ 
+
+ align:start position:0%
+through a the University of Managua so
+that that process is in place and we are
+
+ align:start position:0%
+that that process is in place and we are
+ 
+
+ align:start position:0%
+that that process is in place and we are
+trying to develop a way for them to seal
+
+ align:start position:0%
+trying to develop a way for them to seal
+ 
+
+ align:start position:0%
+trying to develop a way for them to seal
+a plastic bag uh in order to preserve
+
+ align:start position:0%
+a plastic bag uh in order to preserve
+ 
+
+ align:start position:0%
+a plastic bag uh in order to preserve
+the juice and this is actually staming
+
+ align:start position:0%
+the juice and this is actually staming
+ 
+
+ align:start position:0%
+the juice and this is actually staming
+off of a project that was started during
+
+ align:start position:0%
+off of a project that was started during
+ 
+
+ align:start position:0%
+off of a project that was started during
+last year's daab energy class um and you
+
+ align:start position:0%
+last year's daab energy class um and you
+ 
+
+ align:start position:0%
+last year's daab energy class um and you
+see that project pictured at the bottom
+
+ align:start position:0%
+see that project pictured at the bottom
+ 
+
+ align:start position:0%
+see that project pictured at the bottom
+here and uh our our specifications that
+
+ align:start position:0%
+here and uh our our specifications that
+ 
+
+ align:start position:0%
+here and uh our our specifications that
+we want to achieve with our project is
+
+ align:start position:0%
+we want to achieve with our project is
+ 
+
+ align:start position:0%
+we want to achieve with our project is
+to have it the device be able to run off
+
+ align:start position:0%
+to have it the device be able to run off
+ 
+
+ align:start position:0%
+to have it the device be able to run off
+120 volts of AC current and uh while and
+
+ align:start position:0%
+120 volts of AC current and uh while and
+ 
+
+ align:start position:0%
+120 volts of AC current and uh while and
+the seal should be done while removing
+
+ align:start position:0%
+the seal should be done while removing
+ 
+
+ align:start position:0%
+the seal should be done while removing
+the air from the bag so there's no air
+
+ align:start position:0%
+the air from the bag so there's no air
+ 
+
+ align:start position:0%
+the air from the bag so there's no air
+in the bag um to prevent spoiling of the
+
+ align:start position:0%
+in the bag um to prevent spoiling of the
+ 
+
+ align:start position:0%
+in the bag um to prevent spoiling of the
+juice um after it's sealed uh before
+
+ align:start position:0%
+juice um after it's sealed uh before
+ 
+
+ align:start position:0%
+juice um after it's sealed uh before
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+sold uh and we also want to create and
+
+ align:start position:0%
+sold uh and we also want to create and
+ 
+
+ align:start position:0%
+sold uh and we also want to create and
+maintain the uh durable userfriendly
+
+ align:start position:0%
+maintain the uh durable userfriendly
+ 
+
+ align:start position:0%
+maintain the uh durable userfriendly
+interface that was began last year's
+
+ align:start position:0%
+interface that was began last year's
+ 
+
+ align:start position:0%
+interface that was began last year's
+with last year's
+
+ align:start position:0%
+with last year's
+ 
+
+ align:start position:0%
+with last year's
+project um so this is a bigger picture
+
+ align:start position:0%
+project um so this is a bigger picture
+ 
+
+ align:start position:0%
+project um so this is a bigger picture
+of last year's project and it sealed
+
+ align:start position:0%
+of last year's project and it sealed
+ 
+
+ align:start position:0%
+of last year's project and it sealed
+bags nicely and all but there's uh
+
+ align:start position:0%
+bags nicely and all but there's uh
+ 
+
+ align:start position:0%
+bags nicely and all but there's uh
+several areas that we feel need
+
+ align:start position:0%
+several areas that we feel need
+ 
+
+ align:start position:0%
+several areas that we feel need
+improving on before it can actually
+
+ align:start position:0%
+improving on before it can actually
+ 
+
+ align:start position:0%
+improving on before it can actually
+really be used uh the first one is the
+
+ align:start position:0%
+really be used uh the first one is the
+ 
+
+ align:start position:0%
+really be used uh the first one is the
+power supply um between last year and
+
+ align:start position:0%
+power supply um between last year and
+ 
+
+ align:start position:0%
+power supply um between last year and
+this year the community that we're
+
+ align:start position:0%
+this year the community that we're
+ 
+
+ align:start position:0%
+this year the community that we're
+working
+
+ align:start position:0%
+working
+ 
+
+ align:start position:0%
+working
+in um got rid of all their 12vt
+
+ align:start position:0%
+in um got rid of all their 12vt
+ 
+
+ align:start position:0%
+in um got rid of all their 12vt
+batteries like that because they got a
+
+ align:start position:0%
+batteries like that because they got a
+ 
+
+ align:start position:0%
+batteries like that because they got a
+micro hydr grid and so now they're
+
+ align:start position:0%
+micro hydr grid and so now they're
+ 
+
+ align:start position:0%
+micro hydr grid and so now they're
+running in 120 AC so we need to make it
+
+ align:start position:0%
+running in 120 AC so we need to make it
+ 
+
+ align:start position:0%
+running in 120 AC so we need to make it
+actually be able to run on the power
+
+ align:start position:0%
+actually be able to run on the power
+ 
+
+ align:start position:0%
+actually be able to run on the power
+that they have um I mentioned removing
+
+ align:start position:0%
+that they have um I mentioned removing
+ 
+
+ align:start position:0%
+that they have um I mentioned removing
+all the air from the bags the
+
+ align:start position:0%
+all the air from the bags the
+ 
+
+ align:start position:0%
+all the air from the bags the
+preservation process isn't very strong
+
+ align:start position:0%
+preservation process isn't very strong
+ 
+
+ align:start position:0%
+preservation process isn't very strong
+so it's a key part of making sure the
+
+ align:start position:0%
+so it's a key part of making sure the
+ 
+
+ align:start position:0%
+so it's a key part of making sure the
+orange juice stays good um the wide flat
+
+ align:start position:0%
+orange juice stays good um the wide flat
+ 
+
+ align:start position:0%
+orange juice stays good um the wide flat
+surface that they're sealing on here
+
+ align:start position:0%
+surface that they're sealing on here
+ 
+
+ align:start position:0%
+surface that they're sealing on here
+makes it very very diff ult to do that
+
+ align:start position:0%
+makes it very very diff ult to do that
+ 
+
+ align:start position:0%
+makes it very very diff ult to do that
+um so we wanted to improve that as well
+
+ align:start position:0%
+um so we wanted to improve that as well
+ 
+
+ align:start position:0%
+um so we wanted to improve that as well
+um and then when we talk about um
+
+ align:start position:0%
+um and then when we talk about um
+ 
+
+ align:start position:0%
+um and then when we talk about um
+comfort in using it um the light that
+
+ align:start position:0%
+comfort in using it um the light that
+ 
+
+ align:start position:0%
+comfort in using it um the light that
+indicated whether something is hot or
+
+ align:start position:0%
+indicated whether something is hot or
+ 
+
+ align:start position:0%
+indicated whether something is hot or
+not was right about here and you would
+
+ align:start position:0%
+not was right about here and you would
+ 
+
+ align:start position:0%
+not was right about here and you would
+use it from the other side was very
+
+ align:start position:0%
+use it from the other side was very
+ 
+
+ align:start position:0%
+use it from the other side was very
+difficult to see um there's a latch
+
+ align:start position:0%
+difficult to see um there's a latch
+ 
+
+ align:start position:0%
+difficult to see um there's a latch
+that's really difficult to open um and
+
+ align:start position:0%
+that's really difficult to open um and
+ 
+
+ align:start position:0%
+that's really difficult to open um and
+trying to get the bags to get all the
+
+ align:start position:0%
+trying to get the bags to get all the
+ 
+
+ align:start position:0%
+trying to get the bags to get all the
+air out because the Y flat surface was
+
+ align:start position:0%
+air out because the Y flat surface was
+ 
+
+ align:start position:0%
+air out because the Y flat surface was
+also very difficult and um the control
+
+ align:start position:0%
+also very difficult and um the control
+ 
+
+ align:start position:0%
+also very difficult and um the control
+the timing circuit there that they they
+
+ align:start position:0%
+the timing circuit there that they they
+ 
+
+ align:start position:0%
+the timing circuit there that they they
+used an outof thebox timing circuit um
+
+ align:start position:0%
+used an outof thebox timing circuit um
+ 
+
+ align:start position:0%
+used an outof thebox timing circuit um
+mainly I think because of limited time
+
+ align:start position:0%
+mainly I think because of limited time
+ 
+
+ align:start position:0%
+mainly I think because of limited time
+um that cost $26 so we're also designing
+
+ align:start position:0%
+um that cost $26 so we're also designing
+ 
+
+ align:start position:0%
+um that cost $26 so we're also designing
+a simplified timing circuit built out of
+
+ align:start position:0%
+a simplified timing circuit built out of
+ 
+
+ align:start position:0%
+a simplified timing circuit built out of
+just components that is only going to be
+
+ align:start position:0%
+just components that is only going to be
+ 
+
+ align:start position:0%
+just components that is only going to be
+a couple
+
+ align:start position:0%
+a couple
+ 
+
+ align:start position:0%
+a couple
+dollars so we wanted to First go into um
+
+ align:start position:0%
+dollars so we wanted to First go into um
+ 
+
+ align:start position:0%
+dollars so we wanted to First go into um
+experimentation and see what needed to
+
+ align:start position:0%
+experimentation and see what needed to
+ 
+
+ align:start position:0%
+experimentation and see what needed to
+be done to uh I guess get a good seal on
+
+ align:start position:0%
+be done to uh I guess get a good seal on
+ 
+
+ align:start position:0%
+be done to uh I guess get a good seal on
+a bag um so we first started off with
+
+ align:start position:0%
+a bag um so we first started off with
+ 
+
+ align:start position:0%
+a bag um so we first started off with
+what type of plastic do we need uh we
+
+ align:start position:0%
+what type of plastic do we need uh we
+ 
+
+ align:start position:0%
+what type of plastic do we need uh we
+basically tested we got some plastic
+
+ align:start position:0%
+basically tested we got some plastic
+ 
+
+ align:start position:0%
+basically tested we got some plastic
+from uh Nicaragua and we brought it back
+
+ align:start position:0%
+from uh Nicaragua and we brought it back
+ 
+
+ align:start position:0%
+from uh Nicaragua and we brought it back
+and it turned out to be uh 25,000 of an
+
+ align:start position:0%
+and it turned out to be uh 25,000 of an
+ 
+
+ align:start position:0%
+and it turned out to be uh 25,000 of an
+inch um so we're testing with 25,000 of
+
+ align:start position:0%
+inch um so we're testing with 25,000 of
+ 
+
+ align:start position:0%
+inch um so we're testing with 25,000 of
+an inch and 45,000 of an inch uh that
+
+ align:start position:0%
+an inch and 45,000 of an inch uh that
+ 
+
+ align:start position:0%
+an inch and 45,000 of an inch uh that
+because um there's various Plastics
+
+ align:start position:0%
+because um there's various Plastics
+ 
+
+ align:start position:0%
+because um there's various Plastics
+there and so we wanted to uh test with
+
+ align:start position:0%
+there and so we wanted to uh test with
+ 
+
+ align:start position:0%
+there and so we wanted to uh test with
+multiple types of plastic to uh
+
+ align:start position:0%
+multiple types of plastic to uh
+ 
+
+ align:start position:0%
+multiple types of plastic to uh
+accommodate that
+
+ align:start position:0%
+accommodate that
+ 
+
+ align:start position:0%
+accommodate that
+um in addition to that we wanted to see
+
+ align:start position:0%
+um in addition to that we wanted to see
+ 
+
+ align:start position:0%
+um in addition to that we wanted to see
+what temperature was needed to fully
+
+ align:start position:0%
+what temperature was needed to fully
+ 
+
+ align:start position:0%
+what temperature was needed to fully
+steal plastic so we used the uh standard
+
+ align:start position:0%
+steal plastic so we used the uh standard
+ 
+
+ align:start position:0%
+steal plastic so we used the uh standard
+impulse or the uh industry um standard
+
+ align:start position:0%
+impulse or the uh industry um standard
+ 
+
+ align:start position:0%
+impulse or the uh industry um standard
+which is the impul sealer to seal a bag
+
+ align:start position:0%
+which is the impul sealer to seal a bag
+ 
+
+ align:start position:0%
+which is the impul sealer to seal a bag
+and we used a thermal couple to
+
+ align:start position:0%
+and we used a thermal couple to
+ 
+
+ align:start position:0%
+and we used a thermal couple to
+determine the temperature we got a
+
+ align:start position:0%
+determine the temperature we got a
+ 
+
+ align:start position:0%
+determine the temperature we got a
+temperature of about 195 Celsius and you
+
+ align:start position:0%
+temperature of about 195 Celsius and you
+ 
+
+ align:start position:0%
+temperature of about 195 Celsius and you
+can see uh gets a good seal like this
+
+ align:start position:0%
+can see uh gets a good seal like this
+ 
+
+ align:start position:0%
+can see uh gets a good seal like this
+you pass this around if you want um the
+
+ align:start position:0%
+you pass this around if you want um the
+ 
+
+ align:start position:0%
+you pass this around if you want um the
+water should be orange juice but uh but
+
+ align:start position:0%
+water should be orange juice but uh but
+ 
+
+ align:start position:0%
+water should be orange juice but uh but
+yeah so we got um 195 Celsius that's the
+
+ align:start position:0%
+yeah so we got um 195 Celsius that's the
+ 
+
+ align:start position:0%
+yeah so we got um 195 Celsius that's the
+temperature we need to hit um
+
+ align:start position:0%
+temperature we need to hit um
+ 
+
+ align:start position:0%
+temperature we need to hit um
+and in addition to the temperature
+
+ align:start position:0%
+and in addition to the temperature
+ 
+
+ align:start position:0%
+and in addition to the temperature
+another factor is pressure how much
+
+ align:start position:0%
+another factor is pressure how much
+ 
+
+ align:start position:0%
+another factor is pressure how much
+force do you need to put down on a nyron
+
+ align:start position:0%
+force do you need to put down on a nyron
+ 
+
+ align:start position:0%
+force do you need to put down on a nyron
+wire to get a good
+
+ align:start position:0%
+wire to get a good
+ 
+
+ align:start position:0%
+wire to get a good
+seal so we used a for uh Force plate
+
+ align:start position:0%
+seal so we used a for uh Force plate
+ 
+
+ align:start position:0%
+seal so we used a for uh Force plate
+sensor and push down on it um we got
+
+ align:start position:0%
+sensor and push down on it um we got
+ 
+
+ align:start position:0%
+sensor and push down on it um we got
+about 56 Newtons which uh translates to
+
+ align:start position:0%
+about 56 Newtons which uh translates to
+ 
+
+ align:start position:0%
+about 56 Newtons which uh translates to
+about 169 kilopascals on The nyron Wire
+
+ align:start position:0%
+about 169 kilopascals on The nyron Wire
+ 
+
+ align:start position:0%
+about 169 kilopascals on The nyron Wire
+um and you can see over here with if you
+
+ align:start position:0%
+um and you can see over here with if you
+ 
+
+ align:start position:0%
+um and you can see over here with if you
+don't apply enough pressure you get a um
+
+ align:start position:0%
+don't apply enough pressure you get a um
+ 
+
+ align:start position:0%
+don't apply enough pressure you get a um
+sort of like a perforated uh line where
+
+ align:start position:0%
+sort of like a perforated uh line where
+ 
+
+ align:start position:0%
+sort of like a perforated uh line where
+there's seals like uh there's a lot of
+
+ align:start position:0%
+there's seals like uh there's a lot of
+ 
+
+ align:start position:0%
+there's seals like uh there's a lot of
+gaps between the seals so this is not a
+
+ align:start position:0%
+gaps between the seals so this is not a
+ 
+
+ align:start position:0%
+gaps between the seals so this is not a
+good seal because there wasn't enough
+
+ align:start position:0%
+good seal because there wasn't enough
+ 
+
+ align:start position:0%
+good seal because there wasn't enough
+pressure although the time was perfect
+
+ align:start position:0%
+pressure although the time was perfect
+ 
+
+ align:start position:0%
+pressure although the time was perfect
+um with this with a 6 kg weight you got
+
+ align:start position:0%
+um with this with a 6 kg weight you got
+ 
+
+ align:start position:0%
+um with this with a 6 kg weight you got
+a good solid seal um on the on the bag
+
+ align:start position:0%
+a good solid seal um on the on the bag
+ 
+
+ align:start position:0%
+a good solid seal um on the on the bag
+everything looks good uh water did not
+
+ align:start position:0%
+everything looks good uh water did not
+ 
+
+ align:start position:0%
+everything looks good uh water did not
+leak and that is
+
+ align:start position:0%
+leak and that is
+ 
+
+ align:start position:0%
+leak and that is
+ideal uh in terms of timing we also want
+
+ align:start position:0%
+ideal uh in terms of timing we also want
+ 
+
+ align:start position:0%
+ideal uh in terms of timing we also want
+to make sure you apply the right amount
+
+ align:start position:0%
+to make sure you apply the right amount
+ 
+
+ align:start position:0%
+to make sure you apply the right amount
+of time or else it melts the plastic
+
+ align:start position:0%
+of time or else it melts the plastic
+ 
+
+ align:start position:0%
+of time or else it melts the plastic
+will melt uh so what we did was we had a
+
+ align:start position:0%
+will melt uh so what we did was we had a
+ 
+
+ align:start position:0%
+will melt uh so what we did was we had a
+standard weight we applied it to um our
+
+ align:start position:0%
+standard weight we applied it to um our
+ 
+
+ align:start position:0%
+standard weight we applied it to um our
+rig and tested uh with a constant
+
+ align:start position:0%
+rig and tested uh with a constant
+ 
+
+ align:start position:0%
+rig and tested uh with a constant
+voltage different timing um s we ran we
+
+ align:start position:0%
+voltage different timing um s we ran we
+ 
+
+ align:start position:0%
+voltage different timing um s we ran we
+ran the the device for a certain amount
+
+ align:start position:0%
+ran the the device for a certain amount
+ 
+
+ align:start position:0%
+ran the the device for a certain amount
+of time and then increased it slowly so
+
+ align:start position:0%
+of time and then increased it slowly so
+ 
+
+ align:start position:0%
+of time and then increased it slowly so
+you can see as you increase more time
+
+ align:start position:0%
+you can see as you increase more time
+ 
+
+ align:start position:0%
+you can see as you increase more time
+this was enough this wasn't enough uh
+
+ align:start position:0%
+this was enough this wasn't enough uh
+ 
+
+ align:start position:0%
+this was enough this wasn't enough uh
+pressure because you see the dimples but
+
+ align:start position:0%
+pressure because you see the dimples but
+ 
+
+ align:start position:0%
+pressure because you see the dimples but
+you can see over time that it's a very
+
+ align:start position:0%
+you can see over time that it's a very
+ 
+
+ align:start position:0%
+you can see over time that it's a very
+small seal to one that's uh melted and
+
+ align:start position:0%
+small seal to one that's uh melted and
+ 
+
+ align:start position:0%
+small seal to one that's uh melted and
+so with various um weights and various
+
+ align:start position:0%
+so with various um weights and various
+ 
+
+ align:start position:0%
+so with various um weights and various
+voltages and varying the time we got um
+
+ align:start position:0%
+voltages and varying the time we got um
+ 
+
+ align:start position:0%
+voltages and varying the time we got um
+figured out exactly what we
+
+ align:start position:0%
+figured out exactly what we
+ 
+
+ align:start position:0%
+figured out exactly what we
+need um so in terms of power and voltage
+
+ align:start position:0%
+need um so in terms of power and voltage
+ 
+
+ align:start position:0%
+need um so in terms of power and voltage
+I'll pass it off to ban um so before I
+
+ align:start position:0%
+I'll pass it off to ban um so before I
+ 
+
+ align:start position:0%
+I'll pass it off to ban um so before I
+get into our different tests of power
+
+ align:start position:0%
+get into our different tests of power
+ 
+
+ align:start position:0%
+get into our different tests of power
+and voltage might notice that it says
+
+ align:start position:0%
+and voltage might notice that it says
+ 
+
+ align:start position:0%
+and voltage might notice that it says
+like 5 volts to 10 volts 12 volts but we
+
+ align:start position:0%
+like 5 volts to 10 volts 12 volts but we
+ 
+
+ align:start position:0%
+like 5 volts to 10 volts 12 volts but we
+were talking about 120 Vols AC um this
+
+ align:start position:0%
+were talking about 120 Vols AC um this
+ 
+
+ align:start position:0%
+were talking about 120 Vols AC um this
+is because we've decided that the best
+
+ align:start position:0%
+is because we've decided that the best
+ 
+
+ align:start position:0%
+is because we've decided that the best
+way to run something off the wall power
+
+ align:start position:0%
+way to run something off the wall power
+ 
+
+ align:start position:0%
+way to run something off the wall power
+is actually just to buy an adapter and
+
+ align:start position:0%
+is actually just to buy an adapter and
+ 
+
+ align:start position:0%
+is actually just to buy an adapter and
+plug it in and convert it to 12 volts DC
+
+ align:start position:0%
+plug it in and convert it to 12 volts DC
+ 
+
+ align:start position:0%
+plug it in and convert it to 12 volts DC
+um running something off the wall makes
+
+ align:start position:0%
+um running something off the wall makes
+ 
+
+ align:start position:0%
+um running something off the wall makes
+it very difficult to have our timing
+
+ align:start position:0%
+it very difficult to have our timing
+ 
+
+ align:start position:0%
+it very difficult to have our timing
+circuit work we probably have to um
+
+ align:start position:0%
+circuit work we probably have to um
+ 
+
+ align:start position:0%
+circuit work we probably have to um
+Rectify that into DC anyway way um the
+
+ align:start position:0%
+Rectify that into DC anyway way um the
+ 
+
+ align:start position:0%
+Rectify that into DC anyway way um the
+120 volts with our nichrome that's like
+
+ align:start position:0%
+120 volts with our nichrome that's like
+ 
+
+ align:start position:0%
+120 volts with our nichrome that's like
+a 4 ohm resistor would have to add
+
+ align:start position:0%
+a 4 ohm resistor would have to add
+ 
+
+ align:start position:0%
+a 4 ohm resistor would have to add
+either more resistors that would do
+
+ align:start position:0%
+either more resistors that would do
+ 
+
+ align:start position:0%
+either more resistors that would do
+nothing for the heating and be expensive
+
+ align:start position:0%
+nothing for the heating and be expensive
+ 
+
+ align:start position:0%
+nothing for the heating and be expensive
+because they'd have to be big Power
+
+ align:start position:0%
+because they'd have to be big Power
+ 
+
+ align:start position:0%
+because they'd have to be big Power
+resistors um or lots more nyron wire
+
+ align:start position:0%
+resistors um or lots more nyron wire
+ 
+
+ align:start position:0%
+resistors um or lots more nyron wire
+which would again be expensive um if we
+
+ align:start position:0%
+which would again be expensive um if we
+ 
+
+ align:start position:0%
+which would again be expensive um if we
+built our own adapter The price came out
+
+ align:start position:0%
+built our own adapter The price came out
+ 
+
+ align:start position:0%
+built our own adapter The price came out
+to just about the same as what 12vt 34
+
+ align:start position:0%
+to just about the same as what 12vt 34
+ 
+
+ align:start position:0%
+to just about the same as what 12vt 34
+amp adapters are selling for and it
+
+ align:start position:0%
+amp adapters are selling for and it
+ 
+
+ align:start position:0%
+amp adapters are selling for and it
+would be more complicated and harder to
+
+ align:start position:0%
+would be more complicated and harder to
+ 
+
+ align:start position:0%
+would be more complicated and harder to
+replace such so um it turns out that the
+
+ align:start position:0%
+replace such so um it turns out that the
+ 
+
+ align:start position:0%
+replace such so um it turns out that the
+best solution to running it Off the Wall
+
+ align:start position:0%
+best solution to running it Off the Wall
+ 
+
+ align:start position:0%
+best solution to running it Off the Wall
+is just to buy an adapter and run it off
+
+ align:start position:0%
+is just to buy an adapter and run it off
+ 
+
+ align:start position:0%
+is just to buy an adapter and run it off
+the 12 volt set anyways um so we did
+
+ align:start position:0%
+the 12 volt set anyways um so we did
+ 
+
+ align:start position:0%
+the 12 volt set anyways um so we did
+tests with power and voltage or power
+
+ align:start position:0%
+tests with power and voltage or power
+ 
+
+ align:start position:0%
+tests with power and voltage or power
+controlled by what voltage we were
+
+ align:start position:0%
+controlled by what voltage we were
+ 
+
+ align:start position:0%
+controlled by what voltage we were
+putting across a resistor and um the
+
+ align:start position:0%
+putting across a resistor and um the
+ 
+
+ align:start position:0%
+putting across a resistor and um the
+time that we left it on for um these are
+
+ align:start position:0%
+time that we left it on for um these are
+ 
+
+ align:start position:0%
+time that we left it on for um these are
+just a couple samples there see at 5
+
+ align:start position:0%
+just a couple samples there see at 5
+ 
+
+ align:start position:0%
+just a couple samples there see at 5
+volts even when we were doing it for a
+
+ align:start position:0%
+volts even when we were doing it for a
+ 
+
+ align:start position:0%
+volts even when we were doing it for a
+minute we didn't get hot enough to melt
+
+ align:start position:0%
+minute we didn't get hot enough to melt
+ 
+
+ align:start position:0%
+minute we didn't get hot enough to melt
+the bag at all I know the pictures
+
+ align:start position:0%
+the bag at all I know the pictures
+ 
+
+ align:start position:0%
+the bag at all I know the pictures
+aren't really great but um bear with us
+
+ align:start position:0%
+aren't really great but um bear with us
+ 
+
+ align:start position:0%
+aren't really great but um bear with us
+at 10 volts we had a good seal in just
+
+ align:start position:0%
+at 10 volts we had a good seal in just
+ 
+
+ align:start position:0%
+at 10 volts we had a good seal in just
+20 seconds and at 12 Vol um by the time
+
+ align:start position:0%
+20 seconds and at 12 Vol um by the time
+ 
+
+ align:start position:0%
+20 seconds and at 12 Vol um by the time
+it was 14 seconds we were already
+
+ align:start position:0%
+it was 14 seconds we were already
+ 
+
+ align:start position:0%
+it was 14 seconds we were already
+sealing it too much so this was giving
+
+ align:start position:0%
+sealing it too much so this was giving
+ 
+
+ align:start position:0%
+sealing it too much so this was giving
+us a good idea of our tradeoffs between
+
+ align:start position:0%
+us a good idea of our tradeoffs between
+ 
+
+ align:start position:0%
+us a good idea of our tradeoffs between
+how much power we're using what range of
+
+ align:start position:0%
+how much power we're using what range of
+ 
+
+ align:start position:0%
+how much power we're using what range of
+powers and times we can use um I think
+
+ align:start position:0%
+powers and times we can use um I think
+ 
+
+ align:start position:0%
+powers and times we can use um I think
+we did get a good seal of the 12 volts
+
+ align:start position:0%
+we did get a good seal of the 12 volts
+ 
+
+ align:start position:0%
+we did get a good seal of the 12 volts
+at about like 8 or 10 seconds um but
+
+ align:start position:0%
+at about like 8 or 10 seconds um but
+ 
+
+ align:start position:0%
+at about like 8 or 10 seconds um but
+didn't really have
+
+ align:start position:0%
+didn't really have
+ 
+
+ align:start position:0%
+didn't really have
+at all visic picture of that to show you
+
+ align:start position:0%
+at all visic picture of that to show you
+ 
+
+ align:start position:0%
+at all visic picture of that to show you
+um so um that was the experimentation
+
+ align:start position:0%
+um so um that was the experimentation
+ 
+
+ align:start position:0%
+um so um that was the experimentation
+that we did and we wanted to um use this
+
+ align:start position:0%
+that we did and we wanted to um use this
+ 
+
+ align:start position:0%
+that we did and we wanted to um use this
+results into our design so when we
+
+ align:start position:0%
+results into our design so when we
+ 
+
+ align:start position:0%
+results into our design so when we
+designed our product we wanted to take
+
+ align:start position:0%
+designed our product we wanted to take
+ 
+
+ align:start position:0%
+designed our product we wanted to take
+two things in mind functionality and
+
+ align:start position:0%
+two things in mind functionality and
+ 
+
+ align:start position:0%
+two things in mind functionality and
+usability um thing about functionality
+
+ align:start position:0%
+usability um thing about functionality
+ 
+
+ align:start position:0%
+usability um thing about functionality
+is we want the users to be uh looking
+
+ align:start position:0%
+is we want the users to be uh looking
+ 
+
+ align:start position:0%
+is we want the users to be uh looking
+down the product so they can use it uh
+
+ align:start position:0%
+down the product so they can use it uh
+ 
+
+ align:start position:0%
+down the product so they can use it uh
+on a table and they also want a um a
+
+ align:start position:0%
+on a table and they also want a um a
+ 
+
+ align:start position:0%
+on a table and they also want a um a
+nice latch system um so as you can see
+
+ align:start position:0%
+nice latch system um so as you can see
+ 
+
+ align:start position:0%
+nice latch system um so as you can see
+over here we have uh an angled product
+
+ align:start position:0%
+over here we have uh an angled product
+ 
+
+ align:start position:0%
+over here we have uh an angled product
+um and since it's angled you can look
+
+ align:start position:0%
+um and since it's angled you can look
+ 
+
+ align:start position:0%
+um and since it's angled you can look
+down on it use it easily um it should be
+
+ align:start position:0%
+down on it use it easily um it should be
+ 
+
+ align:start position:0%
+down on it use it easily um it should be
+taller but yeah um and with this angled
+
+ align:start position:0%
+taller but yeah um and with this angled
+ 
+
+ align:start position:0%
+taller but yeah um and with this angled
+uh plane you can have the bag hanging
+
+ align:start position:0%
+uh plane you can have the bag hanging
+ 
+
+ align:start position:0%
+uh plane you can have the bag hanging
+down as such so that the liquid will be
+
+ align:start position:0%
+down as such so that the liquid will be
+ 
+
+ align:start position:0%
+down as such so that the liquid will be
+um in the bag and that you can get a
+
+ align:start position:0%
+um in the bag and that you can get a
+ 
+
+ align:start position:0%
+um in the bag and that you can get a
+good airtight seal here um and then
+
+ align:start position:0%
+good airtight seal here um and then
+ 
+
+ align:start position:0%
+good airtight seal here um and then
+another bonus is that the excess juice
+
+ align:start position:0%
+another bonus is that the excess juice
+ 
+
+ align:start position:0%
+another bonus is that the excess juice
+that you we're sealing through juice in
+
+ align:start position:0%
+that you we're sealing through juice in
+ 
+
+ align:start position:0%
+that you we're sealing through juice in
+order to get an airtight seal um the
+
+ align:start position:0%
+order to get an airtight seal um the
+ 
+
+ align:start position:0%
+order to get an airtight seal um the
+extra juice you can just let run off
+
+ align:start position:0%
+extra juice you can just let run off
+ 
+
+ align:start position:0%
+extra juice you can just let run off
+after you make this seal you can have a
+
+ align:start position:0%
+after you make this seal you can have a
+ 
+
+ align:start position:0%
+after you make this seal you can have a
+pot sitting right here to catch the
+
+ align:start position:0%
+pot sitting right here to catch the
+ 
+
+ align:start position:0%
+pot sitting right here to catch the
+excess juice um so that's another and
+
+ align:start position:0%
+excess juice um so that's another and
+ 
+
+ align:start position:0%
+excess juice um so that's another and
+the spr there Springs in this arm
+
+ align:start position:0%
+the spr there Springs in this arm
+ 
+
+ align:start position:0%
+the spr there Springs in this arm
+um that allow you once you have once we
+
+ align:start position:0%
+um that allow you once you have once we
+ 
+
+ align:start position:0%
+um that allow you once you have once we
+have a latch system that will uh keep
+
+ align:start position:0%
+have a latch system that will uh keep
+ 
+
+ align:start position:0%
+have a latch system that will uh keep
+the same Force for every seal uh so
+
+ align:start position:0%
+the same Force for every seal uh so
+ 
+
+ align:start position:0%
+the same Force for every seal uh so
+you'll know that you have enough force
+
+ align:start position:0%
+you'll know that you have enough force
+ 
+
+ align:start position:0%
+you'll know that you have enough force
+and that given the timing circuit it'll
+
+ align:start position:0%
+and that given the timing circuit it'll
+ 
+
+ align:start position:0%
+and that given the timing circuit it'll
+run for the same amount of time so the
+
+ align:start position:0%
+run for the same amount of time so the
+ 
+
+ align:start position:0%
+run for the same amount of time so the
+seals will all be the same um and then
+
+ align:start position:0%
+seals will all be the same um and then
+ 
+
+ align:start position:0%
+seals will all be the same um and then
+more on the latch system um the the
+
+ align:start position:0%
+more on the latch system um the the
+ 
+
+ align:start position:0%
+more on the latch system um the the
+Springs also provide some give uh that
+
+ align:start position:0%
+Springs also provide some give uh that
+ 
+
+ align:start position:0%
+Springs also provide some give uh that
+will allow this to be compressed a
+
+ align:start position:0%
+will allow this to be compressed a
+ 
+
+ align:start position:0%
+will allow this to be compressed a
+little bit more than um the the
+
+ align:start position:0%
+little bit more than um the the
+ 
+
+ align:start position:0%
+little bit more than um the the
+necessary Force for a seal so we can
+
+ align:start position:0%
+necessary Force for a seal so we can
+ 
+
+ align:start position:0%
+necessary Force for a seal so we can
+just have a simple rotating um thing out
+
+ align:start position:0%
+just have a simple rotating um thing out
+ 
+
+ align:start position:0%
+just have a simple rotating um thing out
+of uh sheet metal um something that's
+
+ align:start position:0%
+of uh sheet metal um something that's
+ 
+
+ align:start position:0%
+of uh sheet metal um something that's
+readily available in Nicaragua um and
+
+ align:start position:0%
+readily available in Nicaragua um and
+ 
+
+ align:start position:0%
+readily available in Nicaragua um and
+then you can slide it over uh like the
+
+ align:start position:0%
+then you can slide it over uh like the
+ 
+
+ align:start position:0%
+then you can slide it over uh like the
+picture and then when you want it off
+
+ align:start position:0%
+picture and then when you want it off
+ 
+
+ align:start position:0%
+picture and then when you want it off
+you can press down slide it back off and
+
+ align:start position:0%
+you can press down slide it back off and
+ 
+
+ align:start position:0%
+you can press down slide it back off and
+you'll be ready to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have some uh future things that we
+
+ align:start position:0%
+so we have some uh future things that we
+ 
+
+ align:start position:0%
+so we have some uh future things that we
+need to uh work on um one thing would be
+
+ align:start position:0%
+need to uh work on um one thing would be
+ 
+
+ align:start position:0%
+need to uh work on um one thing would be
+combining the ergonomics uh the
+
+ align:start position:0%
+combining the ergonomics uh the
+ 
+
+ align:start position:0%
+combining the ergonomics uh the
+usability of this product in addition to
+
+ align:start position:0%
+usability of this product in addition to
+ 
+
+ align:start position:0%
+usability of this product in addition to
+the functionality um we were doing a
+
+ align:start position:0%
+the functionality um we were doing a
+ 
+
+ align:start position:0%
+the functionality um we were doing a
+sample test on a basically just two
+
+ align:start position:0%
+sample test on a basically just two
+ 
+
+ align:start position:0%
+sample test on a basically just two
+pieces of wood testing uh putting weight
+
+ align:start position:0%
+pieces of wood testing uh putting weight
+ 
+
+ align:start position:0%
+pieces of wood testing uh putting weight
+on top and so we need to add an ncon
+
+ align:start position:0%
+on top and so we need to add an ncon
+ 
+
+ align:start position:0%
+on top and so we need to add an ncon
+wire onto the uh base of this so that we
+
+ align:start position:0%
+wire onto the uh base of this so that we
+ 
+
+ align:start position:0%
+wire onto the uh base of this so that we
+can actually seal bags with this design
+
+ align:start position:0%
+can actually seal bags with this design
+ 
+
+ align:start position:0%
+can actually seal bags with this design
+um in addition that we need to finalize
+
+ align:start position:0%
+um in addition that we need to finalize
+ 
+
+ align:start position:0%
+um in addition that we need to finalize
+the circuitry and uh design a housing
+
+ align:start position:0%
+the circuitry and uh design a housing
+ 
+
+ align:start position:0%
+the circuitry and uh design a housing
+device for the electronics that we would
+
+ align:start position:0%
+device for the electronics that we would
+ 
+
+ align:start position:0%
+device for the electronics that we would
+be placing on the side um in addition to
+
+ align:start position:0%
+be placing on the side um in addition to
+ 
+
+ align:start position:0%
+be placing on the side um in addition to
+that once we have this completed uh
+
+ align:start position:0%
+that once we have this completed uh
+ 
+
+ align:start position:0%
+that once we have this completed uh
+basically just get users to test it make
+
+ align:start position:0%
+basically just get users to test it make
+ 
+
+ align:start position:0%
+basically just get users to test it make
+sure it's um intuitive easy to use and a
+
+ align:start position:0%
+sure it's um intuitive easy to use and a
+ 
+
+ align:start position:0%
+sure it's um intuitive easy to use and a
+great product overall um we'd like to
+
+ align:start position:0%
+great product overall um we'd like to
+ 
+
+ align:start position:0%
+great product overall um we'd like to
+thank uh Ken am meets daab overall um
+
+ align:start position:0%
+thank uh Ken am meets daab overall um
+ 
+
+ align:start position:0%
+thank uh Ken am meets daab overall um
+and our community partner also Phoenix
+
+ align:start position:0%
+and our community partner also Phoenix
+ 
+
+ align:start position:0%
+and our community partner also Phoenix
+uh are there any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+so you're sealing through juice right
+
+ align:start position:0%
+so you're sealing through juice right
+ 
+
+ align:start position:0%
+so you're sealing through juice right
+now are you testing that by sealing
+
+ align:start position:0%
+now are you testing that by sealing
+ 
+
+ align:start position:0%
+now are you testing that by sealing
+through water yes can you seal through
+
+ align:start position:0%
+through water yes can you seal through
+ 
+
+ align:start position:0%
+through water yes can you seal through
+pulp that's a good question we have yet
+
+ align:start position:0%
+pulp that's a good question we have yet
+ 
+
+ align:start position:0%
+pulp that's a good question we have yet
+to test that
+
+ align:start position:0%
+to test that
+ 
+
+ align:start position:0%
+to test that
+okay it's probably time to buy some
+
+ align:start position:0%
+okay it's probably time to buy some
+ 
+
+ align:start position:0%
+okay it's probably time to buy some
+lunch
+
+ align:start position:0%
+lunch
+ 
+
+ align:start position:0%
+lunch
+juice and yeah I would buy the like this
+
+ align:start position:0%
+juice and yeah I would buy the like this
+ 
+
+ align:start position:0%
+juice and yeah I would buy the like this
+super extra ping version and then throw
+
+ align:start position:0%
+super extra ping version and then throw
+ 
+
+ align:start position:0%
+super extra ping version and then throw
+some like sticks and rocks into it
+
+ align:start position:0%
+some like sticks and rocks into it
+ 
+
+ align:start position:0%
+some like sticks and rocks into it
+measure and and at one point it would be
+
+ align:start position:0%
+measure and and at one point it would be
+ 
+
+ align:start position:0%
+measure and and at one point it would be
+worth it to test like actually squeeze
+
+ align:start position:0%
+worth it to test like actually squeeze
+ 
+
+ align:start position:0%
+worth it to test like actually squeeze
+your own juice cuz it's not that hard to
+
+ align:start position:0%
+your own juice cuz it's not that hard to
+ 
+
+ align:start position:0%
+your own juice cuz it's not that hard to
+make a bit and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any other
+
+ align:start position:0%
+any other
+ 
+
+ align:start position:0%
+any other
+questions how important is the latch
+
+ align:start position:0%
+questions how important is the latch
+ 
+
+ align:start position:0%
+questions how important is the latch
+mechanism like why can't you just hold
+
+ align:start position:0%
+mechanism like why can't you just hold
+ 
+
+ align:start position:0%
+mechanism like why can't you just hold
+it um we wanted it to be able to I guess
+
+ align:start position:0%
+it um we wanted it to be able to I guess
+ 
+
+ align:start position:0%
+it um we wanted it to be able to I guess
+be easily used by one person ideally so
+
+ align:start position:0%
+be easily used by one person ideally so
+ 
+
+ align:start position:0%
+be easily used by one person ideally so
+if they have you want we're not sure
+
+ align:start position:0%
+if they have you want we're not sure
+ 
+
+ align:start position:0%
+if they have you want we're not sure
+that this um like there could be cases
+
+ align:start position:0%
+that this um like there could be cases
+ 
+
+ align:start position:0%
+that this um like there could be cases
+if they're filling like liter bags or 2
+
+ align:start position:0%
+if they're filling like liter bags or 2
+ 
+
+ align:start position:0%
+if they're filling like liter bags or 2
+lit bags of juice if they're selling it
+
+ align:start position:0%
+lit bags of juice if they're selling it
+ 
+
+ align:start position:0%
+lit bags of juice if they're selling it
+to restaurants for um kind of like whole
+
+ align:start position:0%
+to restaurants for um kind of like whole
+ 
+
+ align:start position:0%
+to restaurants for um kind of like whole
+sale like to restaurants this Force
+
+ align:start position:0%
+sale like to restaurants this Force
+ 
+
+ align:start position:0%
+sale like to restaurants this Force
+pressing down might not be enough to
+
+ align:start position:0%
+pressing down might not be enough to
+ 
+
+ align:start position:0%
+pressing down might not be enough to
+hold the bag so they might need to be
+
+ align:start position:0%
+hold the bag so they might need to be
+ 
+
+ align:start position:0%
+hold the bag so they might need to be
+holding the bag pressing a button so you
+
+ align:start position:0%
+holding the bag pressing a button so you
+ 
+
+ align:start position:0%
+holding the bag pressing a button so you
+want you want to be able to do one thing
+
+ align:start position:0%
+want you want to be able to do one thing
+ 
+
+ align:start position:0%
+want you want to be able to do one thing
+at a time with your free hand in
+
+ align:start position:0%
+at a time with your free hand in
+ 
+
+ align:start position:0%
+at a time with your free hand in
+addition to that you also want to have a
+
+ align:start position:0%
+addition to that you also want to have a
+ 
+
+ align:start position:0%
+addition to that you also want to have a
+Conant force uh for each seal so there
+
+ align:start position:0%
+Conant force uh for each seal so there
+ 
+
+ align:start position:0%
+Conant force uh for each seal so there
+can be variable forces if you like push
+
+ align:start position:0%
+can be variable forces if you like push
+ 
+
+ align:start position:0%
+can be variable forces if you like push
+harder less than each time we're I'm
+
+ align:start position:0%
+harder less than each time we're I'm
+ 
+
+ align:start position:0%
+harder less than each time we're I'm
+going to say that it's also might be
+
+ align:start position:0%
+going to say that it's also might be
+ 
+
+ align:start position:0%
+going to say that it's also might be
+easy for these guys to remember like how
+
+ align:start position:0%
+easy for these guys to remember like how
+ 
+
+ align:start position:0%
+easy for these guys to remember like how
+much force they always put enough force
+
+ align:start position:0%
+much force they always put enough force
+ 
+
+ align:start position:0%
+much force they always put enough force
+on it but when I when I was doing some
+
+ align:start position:0%
+on it but when I when I was doing some
+ 
+
+ align:start position:0%
+on it but when I when I was doing some
+tests I wasn't always getting enough
+
+ align:start position:0%
+tests I wasn't always getting enough
+ 
+
+ align:start position:0%
+tests I wasn't always getting enough
+force on there and the people who are
+
+ align:start position:0%
+force on there and the people who are
+ 
+
+ align:start position:0%
+force on there and the people who are
+doing this are women and girls so it's
+
+ align:start position:0%
+doing this are women and girls so it's
+ 
+
+ align:start position:0%
+doing this are women and girls so it's
+um like even like 9 10 12 year old girls
+
+ align:start position:0%
+um like even like 9 10 12 year old girls
+ 
+
+ align:start position:0%
+um like even like 9 10 12 year old girls
+being able to latch it down prevents
+
+ align:start position:0%
+being able to latch it down prevents
+ 
+
+ align:start position:0%
+being able to latch it down prevents
+from having to hold all the pressure
+
+ align:start position:0%
+from having to hold all the pressure
+ 
+
+ align:start position:0%
+from having to hold all the pressure
+there all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+device no this is a new arm we left the
+
+ align:start position:0%
+device no this is a new arm we left the
+ 
+
+ align:start position:0%
+device no this is a new arm we left the
+uh last year's model in nicaragu with
+
+ align:start position:0%
+uh last year's model in nicaragu with
+ 
+
+ align:start position:0%
+uh last year's model in nicaragu with
+House of
+
+ align:start position:0%
+House of
+ 
+
+ align:start position:0%
+House of
+Phoenix and it it works off the 12vt
+
+ align:start position:0%
+Phoenix and it it works off the 12vt
+ 
+
+ align:start position:0%
+Phoenix and it it works off the 12vt
+battery I'm not sure if it's being used
+
+ align:start position:0%
+battery I'm not sure if it's being used
+ 
+
+ align:start position:0%
+battery I'm not sure if it's being used
+um in another Community we delivered it
+
+ align:start position:0%
+um in another Community we delivered it
+ 
+
+ align:start position:0%
+um in another Community we delivered it
+a last L not orange juice season at the
+
+ align:start position:0%
+a last L not orange juice season at the
+ 
+
+ align:start position:0%
+a last L not orange juice season at the
+moment so exactly right now it's not
+
+ align:start position:0%
+moment so exactly right now it's not
+ 
+
+ align:start position:0%
+moment so exactly right now it's not
+being used I don't know whether they
+
+ align:start position:0%
+being used I don't know whether they
+ 
+
+ align:start position:0%
+being used I don't know whether they
+will take it out to the community to use
+
+ align:start position:0%
+will take it out to the community to use
+ 
+
+ align:start position:0%
+will take it out to the community to use
+it when it becomes orange last year's
+
+ align:start position:0%
+it when it becomes orange last year's
+ 
+
+ align:start position:0%
+it when it becomes orange last year's
+project also did not have the
+
+ align:start position:0%
+project also did not have the
+ 
+
+ align:start position:0%
+project also did not have the
+specification to remove the air so using
+
+ align:start position:0%
+specification to remove the air so using
+ 
+
+ align:start position:0%
+specification to remove the air so using
+that while removing the air is also more
+
+ align:start position:0%
+that while removing the air is also more
+ 
+
+ align:start position:0%
+that while removing the air is also more
+difficult the feedback that you have is
+
+ align:start position:0%
+difficult the feedback that you have is
+ 
+
+ align:start position:0%
+difficult the feedback that you have is
+based on is from the field or from your
+
+ align:start position:0%
+based on is from the field or from your
+ 
+
+ align:start position:0%
+based on is from the field or from your
+own from our spring break trip down to
+
+ align:start position:0%
+own from our spring break trip down to
+ 
+
+ align:start position:0%
+own from our spring break trip down to
+Nicaragua and fact finding there with in
+
+ align:start position:0%
+Nicaragua and fact finding there with in
+ 
+
+ align:start position:0%
+Nicaragua and fact finding there with in
+ELR with
+
+ align:start position:0%
+ELR with
+ 
+
+ align:start position:0%
+ELR with
+yeah do you have any show pictures of
+
+ align:start position:0%
+yeah do you have any show pictures of
+ 
+
+ align:start position:0%
+yeah do you have any show pictures of
+that testing yeah we we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pictures no no thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+while you're doing it one thing that you
+
+ align:start position:0%
+while you're doing it one thing that you
+ 
+
+ align:start position:0%
+while you're doing it one thing that you
+might want to think about is is since
+
+ align:start position:0%
+might want to think about is is since
+ 
+
+ align:start position:0%
+might want to think about is is since
+you're trying to create sort of at least
+
+ align:start position:0%
+you're trying to create sort of at least
+ 
+
+ align:start position:0%
+you're trying to create sort of at least
+notionally sterile stuff um you might
+
+ align:start position:0%
+notionally sterile stuff um you might
+ 
+
+ align:start position:0%
+notionally sterile stuff um you might
+want to start it might be time to start
+
+ align:start position:0%
+want to start it might be time to start
+ 
+
+ align:start position:0%
+want to start it might be time to start
+thinking about segregating this thing
+
+ align:start position:0%
+thinking about segregating this thing
+ 
+
+ align:start position:0%
+thinking about segregating this thing
+into the stuff you have to keep clean
+
+ align:start position:0%
+into the stuff you have to keep clean
+ 
+
+ align:start position:0%
+into the stuff you have to keep clean
+and the stuff you don't have to keep
+
+ align:start position:0%
+and the stuff you don't have to keep
+ 
+
+ align:start position:0%
+and the stuff you don't have to keep
+clean
+
+ align:start position:0%
+clean
+ 
+
+ align:start position:0%
+clean
+isz like having to reach over with your
+
+ align:start position:0%
+isz like having to reach over with your
+ 
+
+ align:start position:0%
+isz like having to reach over with your
+you know your sterile hand that's in all
+
+ align:start position:0%
+you know your sterile hand that's in all
+ 
+
+ align:start position:0%
+you know your sterile hand that's in all
+the juice and and all the stuff you're
+
+ align:start position:0%
+the juice and and all the stuff you're
+ 
+
+ align:start position:0%
+the juice and and all the stuff you're
+trying to reclaim and like reach over
+
+ align:start position:0%
+trying to reclaim and like reach over
+ 
+
+ align:start position:0%
+trying to reclaim and like reach over
+and hit the button on the top of the
+
+ align:start position:0%
+and hit the button on the top of the
+ 
+
+ align:start position:0%
+and hit the button on the top of the
+timer is going to become a drag if that
+
+ align:start position:0%
+timer is going to become a drag if that
+ 
+
+ align:start position:0%
+timer is going to become a drag if that
+like that button somehow has to stay
+
+ align:start position:0%
+like that button somehow has to stay
+ 
+
+ align:start position:0%
+like that button somehow has to stay
+clean like if you can give them things
+
+ align:start position:0%
+clean like if you can give them things
+ 
+
+ align:start position:0%
+clean like if you can give them things
+like foot pedals and elbow switches and
+
+ align:start position:0%
+like foot pedals and elbow switches and
+ 
+
+ align:start position:0%
+like foot pedals and elbow switches and
+you know stuff so that you know just to
+
+ align:start position:0%
+you know stuff so that you know just to
+ 
+
+ align:start position:0%
+you know stuff so that you know just to
+think about the process and like how
+
+ align:start position:0%
+think about the process and like how
+ 
+
+ align:start position:0%
+think about the process and like how
+you're going to keep the clean stuff
+
+ align:start position:0%
+you're going to keep the clean stuff
+ 
+
+ align:start position:0%
+you're going to keep the clean stuff
+clean and not and sort of minimize the
+
+ align:start position:0%
+clean and not and sort of minimize the
+ 
+
+ align:start position:0%
+clean and not and sort of minimize the
+amount of stuff you actually have to use
+
+ align:start position:0%
+amount of stuff you actually have to use
+ 
+
+ align:start position:0%
+amount of stuff you actually have to use
+sterile make it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um there aren't devices that use low
+
+ align:start position:0%
+um there aren't devices that use low
+ 
+
+ align:start position:0%
+um there aren't devices that use low
+power like this I'm not sure what the
+
+ align:start position:0%
+power like this I'm not sure what the
+ 
+
+ align:start position:0%
+power like this I'm not sure what the
+price point for the impulse sealer is
+
+ align:start position:0%
+price point for the impulse sealer is
+ 
+
+ align:start position:0%
+price point for the impulse sealer is
+but running it off batteries or their
+
+ align:start position:0%
+but running it off batteries or their
+ 
+
+ align:start position:0%
+but running it off batteries or their
+Micah hydrog grid you can't use that it
+
+ align:start position:0%
+Micah hydrog grid you can't use that it
+ 
+
+ align:start position:0%
+Micah hydrog grid you can't use that it
+uses more power than there there's a
+
+ align:start position:0%
+uses more power than there there's a
+ 
+
+ align:start position:0%
+uses more power than there there's a
+limit to the amount of power that any
+
+ align:start position:0%
+limit to the amount of power that any
+ 
+
+ align:start position:0%
+limit to the amount of power that any
+like device theyve run off the micro
+
+ align:start position:0%
+like device theyve run off the micro
+ 
+
+ align:start position:0%
+like device theyve run off the micro
+hydrog grid that asop Phoenix has
+
+ align:start position:0%
+hydrog grid that asop Phoenix has
+ 
+
+ align:start position:0%
+hydrog grid that asop Phoenix has
+installed um is allowed to draw so also
+
+ align:start position:0%
+installed um is allowed to draw so also
+ 
+
+ align:start position:0%
+installed um is allowed to draw so also
+Phoenix uh doesn't allow use of irons or
+
+ align:start position:0%
+Phoenix uh doesn't allow use of irons or
+ 
+
+ align:start position:0%
+Phoenix uh doesn't allow use of irons or
+like hair dryers or hair straighteners
+
+ align:start position:0%
+like hair dryers or hair straighteners
+ 
+
+ align:start position:0%
+like hair dryers or hair straighteners
+or anything that's heavy power intensive
+
+ align:start position:0%
+or anything that's heavy power intensive
+ 
+
+ align:start position:0%
+or anything that's heavy power intensive
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+that um when we compare what we have to
+
+ align:start position:0%
+that um when we compare what we have to
+ 
+
+ align:start position:0%
+that um when we compare what we have to
+the design that was made last year I
+
+ align:start position:0%
+the design that was made last year I
+ 
+
+ align:start position:0%
+the design that was made last year I
+think were probably
+
+ align:start position:0%
+think were probably
+ 
+
+ align:start position:0%
+think were probably
+about $10 less which not if you know
+
+ align:start position:0%
+about $10 less which not if you know
+ 
+
+ align:start position:0%
+about $10 less which not if you know
+include a battery I think that makes
+
+ align:start position:0%
+include a battery I think that makes
+ 
+
+ align:start position:0%
+include a battery I think that makes
+around $40 instead of around
+
+ align:start position:0%
+around $40 instead of around
+ 
+
+ align:start position:0%
+around $40 instead of around
+$50
+
+ align:start position:0%
+$50
+ 
+
+ align:start position:0%
+$50
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which no it it instead of sealing um our
+
+ align:start position:0%
+which no it it instead of sealing um our
+ 
+
+ align:start position:0%
+which no it it instead of sealing um our
+slight about the commercial one so use a
+
+ align:start position:0%
+slight about the commercial one so use a
+ 
+
+ align:start position:0%
+slight about the commercial one so use a
+some large amount of power for about
+
+ align:start position:0%
+some large amount of power for about
+ 
+
+ align:start position:0%
+some large amount of power for about
+half a second this will use um like 30
+
+ align:start position:0%
+half a second this will use um like 30
+ 
+
+ align:start position:0%
+half a second this will use um like 30
+Watts for more like 10
+
+ align:start position:0%
+Watts for more like 10
+ 
+
+ align:start position:0%
+Watts for more like 10
+seconds so these are are uh um the
+
+ align:start position:0%
+seconds so these are are uh um the
+ 
+
+ align:start position:0%
+seconds so these are are uh um the
+photos working in the field in uh the
+
+ align:start position:0%
+photos working in the field in uh the
+ 
+
+ align:start position:0%
+photos working in the field in uh the
+house we stayed in El BL a group of
+
+ align:start position:0%
+house we stayed in El BL a group of
+ 
+
+ align:start position:0%
+house we stayed in El BL a group of
+about 18 8 to 10 of the women of the
+
+ align:start position:0%
+about 18 8 to 10 of the women of the
+ 
+
+ align:start position:0%
+about 18 8 to 10 of the women of the
+Town came and uh we gave a demonstration
+
+ align:start position:0%
+Town came and uh we gave a demonstration
+ 
+
+ align:start position:0%
+Town came and uh we gave a demonstration
+of how it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works roll through so this is we found
+
+ align:start position:0%
+works roll through so this is we found
+ 
+
+ align:start position:0%
+works roll through so this is we found
+out that there were no 12vt batteries so
+
+ align:start position:0%
+out that there were no 12vt batteries so
+ 
+
+ align:start position:0%
+out that there were no 12vt batteries so
+we strung up a bunch of AA and AAA
+
+ align:start position:0%
+we strung up a bunch of AA and AAA
+ 
+
+ align:start position:0%
+we strung up a bunch of AA and AAA
+batteries just to be able to do the
+
+ align:start position:0%
+batteries just to be able to do the
+ 
+
+ align:start position:0%
+batteries just to be able to do the
+demonstration so we got like somewhere
+
+ align:start position:0%
+demonstration so we got like somewhere
+ 
+
+ align:start position:0%
+demonstration so we got like somewhere
+between like six and 10 bags of that for
+
+ align:start position:0%
+between like six and 10 bags of that for
+ 
+
+ align:start position:0%
+between like six and 10 bags of that for
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+batteries
+
+ align:start position:0%
+batteries
+ 
+
+ align:start position:0%
+batteries
+pictures so this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process then they they actually got to
+
+ align:start position:0%
+process then they they actually got to
+ 
+
+ align:start position:0%
+process then they they actually got to
+seal a few
+
+ align:start position:0%
+seal a few
+ 
+
+ align:start position:0%
+seal a few
+bags um
+
+ align:start position:0%
+bags um
+ 
+
+ align:start position:0%
+bags um
+themselves let me know if you have any
+
+ align:start position:0%
+themselves let me know if you have any
+ 
+
+ align:start position:0%
+themselves let me know if you have any
+questions as we're going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through do you have any sense about like
+
+ align:start position:0%
+through do you have any sense about like
+ 
+
+ align:start position:0%
+through do you have any sense about like
+aim accept amount
+
+ align:start position:0%
+aim accept amount
+ 
+
+ align:start position:0%
+aim accept amount
+of thing we heard from the Community
+
+ align:start position:0%
+of thing we heard from the Community
+ 
+
+ align:start position:0%
+of thing we heard from the Community
+Partners that they didn't want any air
+
+ align:start position:0%
+Partners that they didn't want any air
+ 
+
+ align:start position:0%
+Partners that they didn't want any air
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so uh in terms of like room for air
+
+ align:start position:0%
+so uh in terms of like room for air
+ 
+
+ align:start position:0%
+so uh in terms of like room for air
+we're we're not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure I wonder if there's a correlation
+
+ align:start position:0%
+sure I wonder if there's a correlation
+ 
+
+ align:start position:0%
+sure I wonder if there's a correlation
+between like the size of that bar that
+
+ align:start position:0%
+between like the size of that bar that
+ 
+
+ align:start position:0%
+between like the size of that bar that
+it's hanging off of and how much air you
+
+ align:start position:0%
+it's hanging off of and how much air you
+ 
+
+ align:start position:0%
+it's hanging off of and how much air you
+know like presumably if you make a
+
+ align:start position:0%
+know like presumably if you make a
+ 
+
+ align:start position:0%
+know like presumably if you make a
+really sharp edge can so ideally we're
+
+ align:start position:0%
+really sharp edge can so ideally we're
+ 
+
+ align:start position:0%
+really sharp edge can so ideally we're
+going to have the ncon wire close as
+
+ align:start position:0%
+going to have the ncon wire close as
+ 
+
+ align:start position:0%
+going to have the ncon wire close as
+close to the edge as possible to get as
+
+ align:start position:0%
+close to the edge as possible to get as
+ 
+
+ align:start position:0%
+close to the edge as possible to get as
+clean as seel as possible um cuz the
+
+ align:start position:0%
+clean as seel as possible um cuz the
+ 
+
+ align:start position:0%
+clean as seel as possible um cuz the
+more the further it the further in it is
+
+ align:start position:0%
+more the further it the further in it is
+ 
+
+ align:start position:0%
+more the further it the further in it is
+the more overlap there is so there's
+
+ align:start position:0%
+the more overlap there is so there's
+ 
+
+ align:start position:0%
+the more overlap there is so there's
+going to be potentially more air um cuz
+
+ align:start position:0%
+going to be potentially more air um cuz
+ 
+
+ align:start position:0%
+going to be potentially more air um cuz
+easier to get a like clamp it like this
+
+ align:start position:0%
+easier to get a like clamp it like this
+ 
+
+ align:start position:0%
+easier to get a like clamp it like this
+versus top
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but and that's actually the last well
+
+ align:start position:0%
+but and that's actually the last well
+ 
+
+ align:start position:0%
+but and that's actually the last well
+now yeah tried to run it off solar as
+
+ align:start position:0%
+now yeah tried to run it off solar as
+ 
+
+ align:start position:0%
+now yeah tried to run it off solar as
+well but this is getting away from the
+
+ align:start position:0%
+well but this is getting away from the
+ 
+
+ align:start position:0%
+well but this is getting away from the
+presentation and more so how many bags
+
+ align:start position:0%
+presentation and more so how many bags
+ 
+
+ align:start position:0%
+presentation and more so how many bags
+have you guys sealed over the course of
+
+ align:start position:0%
+have you guys sealed over the course of
+ 
+
+ align:start position:0%
+have you guys sealed over the course of
+the semester oh including the testing
+
+ align:start position:0%
+the semester oh including the testing
+ 
+
+ align:start position:0%
+the semester oh including the testing
+where we were just
+
+ align:start position:0%
+where we were just
+ 
+
+ align:start position:0%
+where we were just
+down five gallons with orange juice or
+
+ align:start position:0%
+down five gallons with orange juice or
+ 
+
+ align:start position:0%
+down five gallons with orange juice or
+five gallons worth of water and 100 bags
+
+ align:start position:0%
+five gallons worth of water and 100 bags
+ 
+
+ align:start position:0%
+five gallons worth of water and 100 bags
+we usually just a real process or it
+
+ align:start position:0%
+we usually just a real process or it
+ 
+
+ align:start position:0%
+we usually just a real process or it
+just one off one off every now and then
+
+ align:start position:0%
+just one off one off every now and then
+ 
+
+ align:start position:0%
+just one off one off every now and then
+uh we've been ceiling bags um the size
+
+ align:start position:0%
+uh we've been ceiling bags um the size
+ 
+
+ align:start position:0%
+uh we've been ceiling bags um the size
+of at least 20 or so but that was with
+
+ align:start position:0%
+of at least 20 or so but that was with
+ 
+
+ align:start position:0%
+of at least 20 or so but that was with
+our kind of works like model so we
+
+ align:start position:0%
+our kind of works like model so we
+ 
+
+ align:start position:0%
+our kind of works like model so we
+haven't combined the sealer with this
+
+ align:start position:0%
+haven't combined the sealer with this
+ 
+
+ align:start position:0%
+haven't combined the sealer with this
+ergonomic um application of it yet to
+
+ align:start position:0%
+ergonomic um application of it yet to
+ 
+
+ align:start position:0%
+ergonomic um application of it yet to
+have something that are those
+
+ align:start position:0%
+have something that are those
+ 
+
+ align:start position:0%
+have something that are those
+bags the individual bags locally
+
+ align:start position:0%
+bags the individual bags locally
+ 
+
+ align:start position:0%
+bags the individual bags locally
+available or do you get it in a long
+
+ align:start position:0%
+available or do you get it in a long
+ 
+
+ align:start position:0%
+available or do you get it in a long
+tube they get in a long tube okay and we
+
+ align:start position:0%
+tube they get in a long tube okay and we
+ 
+
+ align:start position:0%
+tube they get in a long tube okay and we
+have about 6 ft of that tube
+
+ align:start position:0%
+have about 6 ft of that tube
+ 
+
+ align:start position:0%
+have about 6 ft of that tube
+here you thought about how that how that
+
+ align:start position:0%
+here you thought about how that how that
+ 
+
+ align:start position:0%
+here you thought about how that how that
+could change the process a little bit
+
+ align:start position:0%
+could change the process a little bit
+ 
+
+ align:start position:0%
+could change the process a little bit
+fill the whole tube with orange juice SE
+
+ align:start position:0%
+fill the whole tube with orange juice SE
+ 
+
+ align:start position:0%
+fill the whole tube with orange juice SE
+seal
+
+ align:start position:0%
+seal
+ 
+
+ align:start position:0%
+seal
+cut we have the long tube and that's for
+
+ align:start position:0%
+cut we have the long tube and that's for
+ 
+
+ align:start position:0%
+cut we have the long tube and that's for
+like the individual size servs we
+
+ align:start position:0%
+like the individual size servs we
+ 
+
+ align:start position:0%
+like the individual size servs we
+weren't sure that that would always be
+
+ align:start position:0%
+weren't sure that that would always be
+ 
+
+ align:start position:0%
+weren't sure that that would always be
+what they would get especially if
+
+ align:start position:0%
+what they would get especially if
+ 
+
+ align:start position:0%
+what they would get especially if
+they're like one or two lit bags so we
+
+ align:start position:0%
+they're like one or two lit bags so we
+ 
+
+ align:start position:0%
+they're like one or two lit bags so we
+wanted something I think we were trying
+
+ align:start position:0%
+wanted something I think we were trying
+ 
+
+ align:start position:0%
+wanted something I think we were trying
+to go a little more flexible rather than
+
+ align:start position:0%
+to go a little more flexible rather than
+ 
+
+ align:start position:0%
+to go a little more flexible rather than
+specifically
+
+ align:start position:0%
+specifically
+ 
+
+ align:start position:0%
+specifically
+for that would only be Advantage with
+
+ align:start position:0%
+for that would only be Advantage with
+ 
+
+ align:start position:0%
+for that would only be Advantage with
+the long
+
+ align:start position:0%
+the long
+ 
+
+ align:start position:0%
+the long
+tube you can still use that process
+
+ align:start position:0%
+tube you can still use that process
+ 
+
+ align:start position:0%
+tube you can still use that process
+right and yeah or if you had a extra
+
+ align:start position:0%
+right and yeah or if you had a extra
+ 
+
+ align:start position:0%
+right and yeah or if you had a extra
+add-ons to hold to support part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two that's actually
+
+ align:start position:0%
+two that's actually
+ 
+
+ align:start position:0%
+two that's actually
+something in the Middle where
+
+ align:start position:0%
+something in the Middle where
+ 
+
+ align:start position:0%
+something in the Middle where
+you where all you have filled above what
+
+ align:start position:0%
+you where all you have filled above what
+ 
+
+ align:start position:0%
+you where all you have filled above what
+you're ceiling is like another half a
+
+ align:start position:0%
+you're ceiling is like another half a
+ 
+
+ align:start position:0%
+you're ceiling is like another half a
+bag worth of orange juice or something
+
+ align:start position:0%
+bag worth of orange juice or something
+ 
+
+ align:start position:0%
+bag worth of orange juice or something
+so you don't have to hold like you're
+
+ align:start position:0%
+so you don't have to hold like you're
+ 
+
+ align:start position:0%
+so you don't have to hold like you're
+filling one lit bags you don't want to
+
+ align:start position:0%
+filling one lit bags you don't want to
+ 
+
+ align:start position:0%
+filling one lit bags you don't want to
+have to hold 50 lbs of bags above this
+
+ align:start position:0%
+have to hold 50 lbs of bags above this
+ 
+
+ align:start position:0%
+have to hold 50 lbs of bags above this
+thing but if you if you have it sort of
+
+ align:start position:0%
+thing but if you if you have it sort of
+ 
+
+ align:start position:0%
+thing but if you if you have it sort of
+as a continuous process so you've only
+
+ align:start position:0%
+as a continuous process so you've only
+ 
+
+ align:start position:0%
+as a continuous process so you've only
+got like a half a bags worth of stuff
+
+ align:start position:0%
+got like a half a bags worth of stuff
+ 
+
+ align:start position:0%
+got like a half a bags worth of stuff
+supported above no matter what size the
+
+ align:start position:0%
+supported above no matter what size the
+ 
+
+ align:start position:0%
+supported above no matter what size the
+bag is and then you keep filling it you
+
+ align:start position:0%
+bag is and then you keep filling it you
+ 
+
+ align:start position:0%
+bag is and then you keep filling it you
+know once you've made that last seal
+
+ align:start position:0%
+know once you've made that last seal
+ 
+
+ align:start position:0%
+know once you've made that last seal
+then it makes the support problems a
+
+ align:start position:0%
+then it makes the support problems a
+ 
+
+ align:start position:0%
+then it makes the support problems a
+little bit easier might be too late to
+
+ align:start position:0%
+little bit easier might be too late to
+ 
+
+ align:start position:0%
+little bit easier might be too late to
+start thinking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and does the once the orange juice is
+
+ align:start position:0%
+and does the once the orange juice is
+ 
+
+ align:start position:0%
+and does the once the orange juice is
+sealed does it need
+
+ align:start position:0%
+sealed does it need
+ 
+
+ align:start position:0%
+sealed does it need
+Refrigeration no no they have as long as
+
+ align:start position:0%
+Refrigeration no no they have as long as
+ 
+
+ align:start position:0%
+Refrigeration no no they have as long as
+there's no pasturization process that
+
+ align:start position:0%
+there's no pasturization process that
+ 
+
+ align:start position:0%
+there's no pasturization process that
+comes before as long as there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no is there a standard for the size of
+
+ align:start position:0%
+no is there a standard for the size of
+ 
+
+ align:start position:0%
+no is there a standard for the size of
+bubble that can be that can remain or
+
+ align:start position:0%
+bubble that can be that can remain or
+ 
+
+ align:start position:0%
+bubble that can be that can remain or
+does it have to be absolutely no
+
+ align:start position:0%
+does it have to be absolutely no
+ 
+
+ align:start position:0%
+does it have to be absolutely no
+um Ste we were not
+
+ align:start position:0%
+um Ste we were not
+ 
+
+ align:start position:0%
+um Ste we were not
+sure you guys were going to look into
+
+ align:start position:0%
+sure you guys were going to look into
+ 
+
+ align:start position:0%
+sure you guys were going to look into
+that did you make any progress there um
+
+ align:start position:0%
+that did you make any progress there um
+ 
+
+ align:start position:0%
+that did you make any progress there um
+I think I think the most answer we got
+
+ align:start position:0%
+I think I think the most answer we got
+ 
+
+ align:start position:0%
+I think I think the most answer we got
+was that yes the air needs to be removed
+
+ align:start position:0%
+was that yes the air needs to be removed
+ 
+
+ align:start position:0%
+was that yes the air needs to be removed
+there needs to be no air and whether
+
+ align:start position:0%
+there needs to be no air and whether
+ 
+
+ align:start position:0%
+there needs to be no air and whether
+that's a like overstating the um
+
+ align:start position:0%
+that's a like overstating the um
+ 
+
+ align:start position:0%
+that's a like overstating the um
+requirement or actually there really
+
+ align:start position:0%
+requirement or actually there really
+ 
+
+ align:start position:0%
+requirement or actually there really
+actually needs to be no air that's where
+
+ align:start position:0%
+actually needs to be no air that's where
+ 
+
+ align:start position:0%
+actually needs to be no air that's where
+we're unsure I think so we're making our
+
+ align:start position:0%
+we're unsure I think so we're making our
+ 
+
+ align:start position:0%
+we're unsure I think so we're making our
+goal be there is actually no air you
+
+ align:start position:0%
+goal be there is actually no air you
+ 
+
+ align:start position:0%
+goal be there is actually no air you
+started testing to see if you can
+
+ align:start position:0%
+started testing to see if you can
+ 
+
+ align:start position:0%
+started testing to see if you can
+actually successfully seal with zero air
+
+ align:start position:0%
+actually successfully seal with zero air
+ 
+
+ align:start position:0%
+actually successfully seal with zero air
+or zero noticeable air I think we did
+
+ align:start position:0%
+or zero noticeable air I think we did
+ 
+
+ align:start position:0%
+or zero noticeable air I think we did
+one with our
+
+ align:start position:0%
+one with our
+ 
+
+ align:start position:0%
+one with our
+um flat flat one that wasn't even that
+
+ align:start position:0%
+um flat flat one that wasn't even that
+ 
+
+ align:start position:0%
+um flat flat one that wasn't even that
+we had no air in
+
+ align:start position:0%
+we had no air in
+ 
+
+ align:start position:0%
+we had no air in
+um yeah how how crazy is their
+
+ align:start position:0%
+um yeah how how crazy is their
+ 
+
+ align:start position:0%
+um yeah how how crazy is their
+pasteurization
+
+ align:start position:0%
+pasteurization
+ 
+
+ align:start position:0%
+pasteurization
+process like throw it in a pot boil it
+
+ align:start position:0%
+process like throw it in a pot boil it
+ 
+
+ align:start position:0%
+process like throw it in a pot boil it
+for 10 minutes and then put in the back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I bet it depends a lot more on
+
+ align:start position:0%
+so I bet it depends a lot more on
+ 
+
+ align:start position:0%
+so I bet it depends a lot more on
+keeping the clean room clean then on how
+
+ align:start position:0%
+keeping the clean room clean then on how
+ 
+
+ align:start position:0%
+keeping the clean room clean then on how
+much air is in the B because there's air
+
+ align:start position:0%
+much air is in the B because there's air
+ 
+
+ align:start position:0%
+much air is in the B because there's air
+in a bottle of Sunny delay there's air
+
+ align:start position:0%
+in a bottle of Sunny delay there's air
+ 
+
+ align:start position:0%
+in a bottle of Sunny delay there's air
+at the top of you know like there's air
+
+ align:start position:0%
+at the top of you know like there's air
+ 
+
+ align:start position:0%
+at the top of you know like there's air
+at the top of a b of a jar pickles there
+
+ align:start position:0%
+at the top of a b of a jar pickles there
+ 
+
+ align:start position:0%
+at the top of a b of a jar pickles there
+you know if it's pasteurized and it's
+
+ align:start position:0%
+you know if it's pasteurized and it's
+ 
+
+ align:start position:0%
+you know if it's pasteurized and it's
+highly acid then you're trying to you
+
+ align:start position:0%
+highly acid then you're trying to you
+ 
+
+ align:start position:0%
+highly acid then you're trying to you
+know what's left that you're trying to
+
+ align:start position:0%
+know what's left that you're trying to
+ 
+
+ align:start position:0%
+know what's left that you're trying to
+to get rid ofm but air doesn't help that
+
+ align:start position:0%
+to get rid ofm but air doesn't help that
+ 
+
+ align:start position:0%
+to get rid ofm but air doesn't help that
+I don't know
+
+ align:start position:0%
+I don't know
+ 
+
+ align:start position:0%
+I don't know
+yeah try to find it'd be it'd be good to
+
+ align:start position:0%
+yeah try to find it'd be it'd be good to
+ 
+
+ align:start position:0%
+yeah try to find it'd be it'd be good to
+both be able to answer that and also
+
+ align:start position:0%
+both be able to answer that and also
+ 
+
+ align:start position:0%
+both be able to answer that and also
+know like even if you have the answer
+
+ align:start position:0%
+know like even if you have the answer
+ 
+
+ align:start position:0%
+know like even if you have the answer
+that air is okay if they are convinced
+
+ align:start position:0%
+that air is okay if they are convinced
+ 
+
+ align:start position:0%
+that air is okay if they are convinced
+that air is not
+
+ align:start position:0%
+that air is not
+ 
+
+ align:start position:0%
+that air is not
+okay that may be a knockout blow and so
+
+ align:start position:0%
+okay that may be a knockout blow and so
+ 
+
+ align:start position:0%
+okay that may be a knockout blow and so
+practicing to make sure the ergonomics
+
+ align:start position:0%
+practicing to make sure the ergonomics
+ 
+
+ align:start position:0%
+practicing to make sure the ergonomics
+and whatever your process are set up
+
+ align:start position:0%
+and whatever your process are set up
+ 
+
+ align:start position:0%
+and whatever your process are set up
+such that you can actually ensure that
+
+ align:start position:0%
+such that you can actually ensure that
+ 
+
+ align:start position:0%
+such that you can actually ensure that
+most of the time you're getting a bag
+
+ align:start position:0%
+most of the time you're getting a bag
+ 
+
+ align:start position:0%
+most of the time you're getting a bag
+with no air visible I think would be
+
+ align:start position:0%
+with no air visible I think would be
+ 
+
+ align:start position:0%
+with no air visible I think would be
+good to to practice that a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bunch I heard you guys talk
+
+ align:start position:0%
+bunch I heard you guys talk
+ 
+
+ align:start position:0%
+bunch I heard you guys talk
+about you guys um I'm not sure if I
+
+ align:start position:0%
+about you guys um I'm not sure if I
+ 
+
+ align:start position:0%
+about you guys um I'm not sure if I
+missed it but are you planning on
+
+ align:start position:0%
+missed it but are you planning on
+ 
+
+ align:start position:0%
+missed it but are you planning on
+keeping sort of
+
+ align:start position:0%
+keeping sort of
+ 
+
+ align:start position:0%
+keeping sort of
+surface I'm just wondering like the gets
+
+ align:start position:0%
+surface I'm just wondering like the gets
+ 
+
+ align:start position:0%
+surface I'm just wondering like the gets
+away it probably wouldn't we directly
+
+ align:start position:0%
+away it probably wouldn't we directly
+ 
+
+ align:start position:0%
+away it probably wouldn't we directly
+would like that um this was an earlier
+
+ align:start position:0%
+would like that um this was an earlier
+ 
+
+ align:start position:0%
+would like that um this was an earlier
+model we've got it um covered in PL PL
+
+ align:start position:0%
+model we've got it um covered in PL PL
+ 
+
+ align:start position:0%
+model we've got it um covered in PL PL
+de um probably one the way we're going
+
+ align:start position:0%
+de um probably one the way we're going
+ 
+
+ align:start position:0%
+de um probably one the way we're going
+to go last year's was painted or
+
+ align:start position:0%
+to go last year's was painted or
+ 
+
+ align:start position:0%
+to go last year's was painted or
+lacquered
+
+ align:start position:0%
+lacquered
+ 
+
+ align:start position:0%
+lacquered
+or um so it definitely be some kind of
+
+ align:start position:0%
+or um so it definitely be some kind of
+ 
+
+ align:start position:0%
+or um so it definitely be some kind of
+more wiped downable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surface it's not the end of the
+
+ align:start position:0%
+surface it's not the end of the
+ 
+
+ align:start position:0%
+surface it's not the end of the
+world and as long as it you know what
+
+ align:start position:0%
+world and as long as it you know what
+ 
+
+ align:start position:0%
+world and as long as it you know what
+kills wood is going wet dry wet dry wet
+
+ align:start position:0%
+kills wood is going wet dry wet dry wet
+ 
+
+ align:start position:0%
+kills wood is going wet dry wet dry wet
+dry wet dry over and over and over again
+
+ align:start position:0%
+dry wet dry over and over and over again
+ 
+
+ align:start position:0%
+dry wet dry over and over and over again
+but if you're going to run it all day
+
+ align:start position:0%
+but if you're going to run it all day
+ 
+
+ align:start position:0%
+but if you're going to run it all day
+long wet it's not the end of the
+
+ align:start position:0%
+long wet it's not the end of the
+ 
+
+ align:start position:0%
+long wet it's not the end of the
+world you know wooden cutting for are
+
+ align:start position:0%
+world you know wooden cutting for are
+ 
+
+ align:start position:0%
+world you know wooden cutting for are
+clean cleanable you just might not want
+
+ align:start position:0%
+clean cleanable you just might not want
+ 
+
+ align:start position:0%
+clean cleanable you just might not want
+to make it out of something you know
+
+ align:start position:0%
+to make it out of something you know
+ 
+
+ align:start position:0%
+to make it out of something you know
+it's it's nice to be able to make the
+
+ align:start position:0%
+it's it's nice to be able to make the
+ 
+
+ align:start position:0%
+it's it's nice to be able to make the
+surfaces flat so you can clean them so
+
+ align:start position:0%
+surfaces flat so you can clean them so
+ 
+
+ align:start position:0%
+surfaces flat so you can clean them so
+like really soft Pine or Nick and and
+
+ align:start position:0%
+like really soft Pine or Nick and and
+ 
+
+ align:start position:0%
+like really soft Pine or Nick and and
+harder stuff but harder wood would
+
+ align:start position:0%
+harder stuff but harder wood would
+ 
+
+ align:start position:0%
+harder stuff but harder wood would
+probably be
+
+ align:start position:0%
+probably be
+ 
+
+ align:start position:0%
+probably be
+okay I think one of their Mains also was
+
+ align:start position:0%
+okay I think one of their Mains also was
+ 
+
+ align:start position:0%
+okay I think one of their Mains also was
+capturing the Overflow juice yeah in
+
+ align:start position:0%
+capturing the Overflow juice yeah in
+ 
+
+ align:start position:0%
+capturing the Overflow juice yeah in
+that case you want a very sterile
+
+ align:start position:0%
+that case you want a very sterile
+ 
+
+ align:start position:0%
+that case you want a very sterile
+surface and or as clean as you can get
+
+ align:start position:0%
+surface and or as clean as you can get
+ 
+
+ align:start position:0%
+surface and or as clean as you can get
+and if you have an extra 8 in off your
+
+ align:start position:0%
+and if you have an extra 8 in off your
+ 
+
+ align:start position:0%
+and if you have an extra 8 in off your
+roll of plastic or 6 in off your roll of
+
+ align:start position:0%
+roll of plastic or 6 in off your roll of
+ 
+
+ align:start position:0%
+roll of plastic or 6 in off your roll of
+plastic you can just wrap that but
+
+ align:start position:0%
+plastic you can just wrap that but
+ 
+
+ align:start position:0%
+plastic you can just wrap that but
+bottom portion with that it's like kind
+
+ align:start position:0%
+bottom portion with that it's like kind
+ 
+
+ align:start position:0%
+bottom portion with that it's like kind
+of your runoff shape then you don't
+
+ align:start position:0%
+of your runoff shape then you don't
+ 
+
+ align:start position:0%
+of your runoff shape then you don't
+actually have to worry about uh cleaning
+
+ align:start position:0%
+actually have to worry about uh cleaning
+ 
+
+ align:start position:0%
+actually have to worry about uh cleaning
+your wood as as much as you would have
+
+ align:start position:0%
+your wood as as much as you would have
+ 
+
+ align:start position:0%
+your wood as as much as you would have
+it's also nice for normally overflow to
+
+ align:start position:0%
+it's also nice for normally overflow to
+ 
+
+ align:start position:0%
+it's also nice for normally overflow to
+like soak into the device rather than
+
+ align:start position:0%
+like soak into the device rather than
+ 
+
+ align:start position:0%
+like soak into the device rather than
+being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+replayed prob the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay thanks you guys
+
+ align:start position:0%
+yeah okay thanks you guys
+ 
+
+ align:start position:0%
+yeah okay thanks you guys
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi uh we're the charcoal group um I'm
+
+ align:start position:0%
+hi uh we're the charcoal group um I'm
+ 
+
+ align:start position:0%
+hi uh we're the charcoal group um I'm
+Vian I'm Jessica and I'm Kurt um and our
+
+ align:start position:0%
+Vian I'm Jessica and I'm Kurt um and our
+ 
+
+ align:start position:0%
+Vian I'm Jessica and I'm Kurt um and our
+project mentors are Amelia raise your
+
+ align:start position:0%
+project mentors are Amelia raise your
+ 
+
+ align:start position:0%
+project mentors are Amelia raise your
+hand and Steve over there okay um so
+
+ align:start position:0%
+hand and Steve over there okay um so
+ 
+
+ align:start position:0%
+hand and Steve over there okay um so
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+oh okay our main
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motive sorry okay our main
+
+ align:start position:0%
+motive sorry okay our main
+ 
+
+ align:start position:0%
+motive sorry okay our main
+motivation for our project um stems from
+
+ align:start position:0%
+motivation for our project um stems from
+ 
+
+ align:start position:0%
+motivation for our project um stems from
+the work we did with a nicar aan based
+
+ align:start position:0%
+the work we did with a nicar aan based
+ 
+
+ align:start position:0%
+the work we did with a nicar aan based
+NGO called group of Phoenix and more
+
+ align:start position:0%
+NGO called group of Phoenix and more
+ 
+
+ align:start position:0%
+NGO called group of Phoenix and more
+specifically we worked with a
+
+ align:start position:0%
+specifically we worked with a
+ 
+
+ align:start position:0%
+specifically we worked with a
+Cooperative called the muera solaras
+
+ align:start position:0%
+Cooperative called the muera solaras
+ 
+
+ align:start position:0%
+Cooperative called the muera solaras
+which is the solar
+
+ align:start position:0%
+which is the solar
+ 
+
+ align:start position:0%
+which is the solar
+woman um basically we introduced um the
+
+ align:start position:0%
+woman um basically we introduced um the
+ 
+
+ align:start position:0%
+woman um basically we introduced um the
+idea of dlabs uh aggro waste charcoal
+
+ align:start position:0%
+idea of dlabs uh aggro waste charcoal
+ 
+
+ align:start position:0%
+idea of dlabs uh aggro waste charcoal
+and for those of you aren't familiar
+
+ align:start position:0%
+and for those of you aren't familiar
+ 
+
+ align:start position:0%
+and for those of you aren't familiar
+with it it's basically a process of
+
+ align:start position:0%
+with it it's basically a process of
+ 
+
+ align:start position:0%
+with it it's basically a process of
+making charcoal um out of aggro or
+
+ align:start position:0%
+making charcoal um out of aggro or
+ 
+
+ align:start position:0%
+making charcoal um out of aggro or
+biomass instead of wood so you know you
+
+ align:start position:0%
+biomass instead of wood so you know you
+ 
+
+ align:start position:0%
+biomass instead of wood so you know you
+reduce deforestation and um it burns a
+
+ align:start position:0%
+reduce deforestation and um it burns a
+ 
+
+ align:start position:0%
+reduce deforestation and um it burns a
+lot cleaner um we really want wanted to
+
+ align:start position:0%
+lot cleaner um we really want wanted to
+ 
+
+ align:start position:0%
+lot cleaner um we really want wanted to
+um improve this process so that the
+
+ align:start position:0%
+um improve this process so that the
+ 
+
+ align:start position:0%
+um improve this process so that the
+women would feel more comfortable
+
+ align:start position:0%
+women would feel more comfortable
+ 
+
+ align:start position:0%
+women would feel more comfortable
+integrating this into their everyday
+
+ align:start position:0%
+integrating this into their everyday
+ 
+
+ align:start position:0%
+integrating this into their everyday
+lives or possibly using this as a
+
+ align:start position:0%
+lives or possibly using this as a
+ 
+
+ align:start position:0%
+lives or possibly using this as a
+business activity for them um right now
+
+ align:start position:0%
+business activity for them um right now
+ 
+
+ align:start position:0%
+business activity for them um right now
+there is a general discomfort with the
+
+ align:start position:0%
+there is a general discomfort with the
+ 
+
+ align:start position:0%
+there is a general discomfort with the
+process and just can talk to you a
+
+ align:start position:0%
+process and just can talk to you a
+ 
+
+ align:start position:0%
+process and just can talk to you a
+little bit more about those
+
+ align:start position:0%
+little bit more about those
+ 
+
+ align:start position:0%
+little bit more about those
+specifics so what was really unique to
+
+ align:start position:0%
+specifics so what was really unique to
+ 
+
+ align:start position:0%
+specifics so what was really unique to
+our group was that we had the language
+
+ align:start position:0%
+our group was that we had the language
+ 
+
+ align:start position:0%
+our group was that we had the language
+um to get the direct feedback from the
+
+ align:start position:0%
+um to get the direct feedback from the
+ 
+
+ align:start position:0%
+um to get the direct feedback from the
+women so we didn't have to go through a
+
+ align:start position:0%
+women so we didn't have to go through a
+ 
+
+ align:start position:0%
+women so we didn't have to go through a
+third person instead you know I was able
+
+ align:start position:0%
+third person instead you know I was able
+ 
+
+ align:start position:0%
+third person instead you know I was able
+to interpret exactly what they were
+
+ align:start position:0%
+to interpret exactly what they were
+ 
+
+ align:start position:0%
+to interpret exactly what they were
+saying and you I see I've highlighted
+
+ align:start position:0%
+saying and you I see I've highlighted
+ 
+
+ align:start position:0%
+saying and you I see I've highlighted
+here that the biggest issue for them
+
+ align:start position:0%
+here that the biggest issue for them
+ 
+
+ align:start position:0%
+here that the biggest issue for them
+today is still covering the barrel
+
+ align:start position:0%
+today is still covering the barrel
+ 
+
+ align:start position:0%
+today is still covering the barrel
+because they cannot bathe afterwards
+
+ align:start position:0%
+because they cannot bathe afterwards
+ 
+
+ align:start position:0%
+because they cannot bathe afterwards
+after dealing with so much heat of the
+
+ align:start position:0%
+after dealing with so much heat of the
+ 
+
+ align:start position:0%
+after dealing with so much heat of the
+barrel um they say that the heat is too
+
+ align:start position:0%
+barrel um they say that the heat is too
+ 
+
+ align:start position:0%
+barrel um they say that the heat is too
+intensive for them and then they you
+
+ align:start position:0%
+intensive for them and then they you
+ 
+
+ align:start position:0%
+intensive for them and then they you
+know would bathe with cold water and
+
+ align:start position:0%
+know would bathe with cold water and
+ 
+
+ align:start position:0%
+know would bathe with cold water and
+then they would get sick afterwards so
+
+ align:start position:0%
+then they would get sick afterwards so
+ 
+
+ align:start position:0%
+then they would get sick afterwards so
+that's the biggest gap for them right
+
+ align:start position:0%
+that's the biggest gap for them right
+ 
+
+ align:start position:0%
+that's the biggest gap for them right
+now even when we um discussed uh the
+
+ align:start position:0%
+now even when we um discussed uh the
+ 
+
+ align:start position:0%
+now even when we um discussed uh the
+different project ideas that we had uh
+
+ align:start position:0%
+different project ideas that we had uh
+ 
+
+ align:start position:0%
+different project ideas that we had uh
+to to make the charcoal process better
+
+ align:start position:0%
+to to make the charcoal process better
+ 
+
+ align:start position:0%
+to to make the charcoal process better
+they still brought us back to we really
+
+ align:start position:0%
+they still brought us back to we really
+ 
+
+ align:start position:0%
+they still brought us back to we really
+want you to work on the barrel um do
+
+ align:start position:0%
+want you to work on the barrel um do
+ 
+
+ align:start position:0%
+want you to work on the barrel um do
+something so that it doesn't feel so hot
+
+ align:start position:0%
+something so that it doesn't feel so hot
+ 
+
+ align:start position:0%
+something so that it doesn't feel so hot
+sorry can do you want to um like run
+
+ align:start position:0%
+sorry can do you want to um like run
+ 
+
+ align:start position:0%
+sorry can do you want to um like run
+through the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+current um so we're going to show you a
+
+ align:start position:0%
+current um so we're going to show you a
+ 
+
+ align:start position:0%
+current um so we're going to show you a
+video of um the women doing a charcoal
+
+ align:start position:0%
+video of um the women doing a charcoal
+ 
+
+ align:start position:0%
+video of um the women doing a charcoal
+burn
+
+ align:start position:0%
+burn
+ 
+
+ align:start position:0%
+burn
+there well I can't pass forward but this
+
+ align:start position:0%
+there well I can't pass forward but this
+ 
+
+ align:start position:0%
+there well I can't pass forward but this
+is the third charcoal burn that the
+
+ align:start position:0%
+is the third charcoal burn that the
+ 
+
+ align:start position:0%
+is the third charcoal burn that the
+women are doing by themselves we trained
+
+ align:start position:0%
+women are doing by themselves we trained
+ 
+
+ align:start position:0%
+women are doing by themselves we trained
+them and then we had them do the first
+
+ align:start position:0%
+them and then we had them do the first
+ 
+
+ align:start position:0%
+them and then we had them do the first
+two by themselves they were successful
+
+ align:start position:0%
+two by themselves they were successful
+ 
+
+ align:start position:0%
+two by themselves they were successful
+this is the third one and you can see
+
+ align:start position:0%
+this is the third one and you can see
+ 
+
+ align:start position:0%
+this is the third one and you can see
+that even in the third trial there's
+
+ align:start position:0%
+that even in the third trial there's
+ 
+
+ align:start position:0%
+that even in the third trial there's
+still some
+
+ align:start position:0%
+still some
+ 
+
+ align:start position:0%
+still some
+uncoordination um in the barrel ceiling
+
+ align:start position:0%
+uncoordination um in the barrel ceiling
+ 
+
+ align:start position:0%
+uncoordination um in the barrel ceiling
+this is a current design where the
+
+ align:start position:0%
+this is a current design where the
+ 
+
+ align:start position:0%
+this is a current design where the
+barrel sits on top of the bricks and you
+
+ align:start position:0%
+barrel sits on top of the bricks and you
+ 
+
+ align:start position:0%
+barrel sits on top of the bricks and you
+have to tilt and kick and sometimes kick
+
+ align:start position:0%
+have to tilt and kick and sometimes kick
+ 
+
+ align:start position:0%
+have to tilt and kick and sometimes kick
+too much and so what we can see here are
+
+ align:start position:0%
+too much and so what we can see here are
+ 
+
+ align:start position:0%
+too much and so what we can see here are
+the main points the main pain points of
+
+ align:start position:0%
+the main points the main pain points of
+ 
+
+ align:start position:0%
+the main points the main pain points of
+the process which are stop that right
+
+ align:start position:0%
+the process which are stop that right
+ 
+
+ align:start position:0%
+the process which are stop that right
+now which are the heat intensity of the
+
+ align:start position:0%
+now which are the heat intensity of the
+ 
+
+ align:start position:0%
+now which are the heat intensity of the
+process which is what they've ident
+
+ align:start position:0%
+process which is what they've ident
+ 
+
+ align:start position:0%
+process which is what they've ident
+ified and of course the safety issue and
+
+ align:start position:0%
+ified and of course the safety issue and
+ 
+
+ align:start position:0%
+ified and of course the safety issue and
+we realize that we need to address these
+
+ align:start position:0%
+we realize that we need to address these
+ 
+
+ align:start position:0%
+we realize that we need to address these
+two concerns while still meeting the
+
+ align:start position:0%
+two concerns while still meeting the
+ 
+
+ align:start position:0%
+two concerns while still meeting the
+same quality of a chargo
+
+ align:start position:0%
+same quality of a chargo
+ 
+
+ align:start position:0%
+same quality of a chargo
+burn great so in order to um meet these
+
+ align:start position:0%
+burn great so in order to um meet these
+ 
+
+ align:start position:0%
+burn great so in order to um meet these
+criteria that Jess just highlighted um
+
+ align:start position:0%
+criteria that Jess just highlighted um
+ 
+
+ align:start position:0%
+criteria that Jess just highlighted um
+our design submerges the uh bricks on
+
+ align:start position:0%
+our design submerges the uh bricks on
+ 
+
+ align:start position:0%
+our design submerges the uh bricks on
+which the barrel sits into the ground
+
+ align:start position:0%
+which the barrel sits into the ground
+ 
+
+ align:start position:0%
+which the barrel sits into the ground
+and um so basically what we've done here
+
+ align:start position:0%
+and um so basically what we've done here
+ 
+
+ align:start position:0%
+and um so basically what we've done here
+I can show you on our model here this is
+
+ align:start position:0%
+I can show you on our model here this is
+ 
+
+ align:start position:0%
+I can show you on our model here this is
+uh one of the uh ideas the charcoal burn
+
+ align:start position:0%
+uh one of the uh ideas the charcoal burn
+ 
+
+ align:start position:0%
+uh one of the uh ideas the charcoal burn
+is that it's uh it uses commonly
+
+ align:start position:0%
+is that it's uh it uses commonly
+ 
+
+ align:start position:0%
+is that it's uh it uses commonly
+available materials like a oil drum so
+
+ align:start position:0%
+available materials like a oil drum so
+ 
+
+ align:start position:0%
+available materials like a oil drum so
+I've used a Natty Ice um Can here too In
+
+ align:start position:0%
+I've used a Natty Ice um Can here too In
+ 
+
+ align:start position:0%
+I've used a Natty Ice um Can here too In
+The Same Spirit um and the uh so instead
+
+ align:start position:0%
+The Same Spirit um and the uh so instead
+ 
+
+ align:start position:0%
+The Same Spirit um and the uh so instead
+of sitting on top of the ground it now
+
+ align:start position:0%
+of sitting on top of the ground it now
+ 
+
+ align:start position:0%
+of sitting on top of the ground it now
+sits on bricks that are submerged into
+
+ align:start position:0%
+sits on bricks that are submerged into
+ 
+
+ align:start position:0%
+sits on bricks that are submerged into
+holes
+
+ align:start position:0%
+holes
+ 
+
+ align:start position:0%
+holes
+and uh so the design is pretty simple
+
+ align:start position:0%
+and uh so the design is pretty simple
+ 
+
+ align:start position:0%
+and uh so the design is pretty simple
+there is a Dugout hole there's six
+
+ align:start position:0%
+there is a Dugout hole there's six
+ 
+
+ align:start position:0%
+there is a Dugout hole there's six
+bricks that line three channels which
+
+ align:start position:0%
+bricks that line three channels which
+ 
+
+ align:start position:0%
+bricks that line three channels which
+allow for air flow in this space right
+
+ align:start position:0%
+allow for air flow in this space right
+ 
+
+ align:start position:0%
+allow for air flow in this space right
+here the um the ground and the barrel
+
+ align:start position:0%
+here the um the ground and the barrel
+ 
+
+ align:start position:0%
+here the um the ground and the barrel
+form a seal so the uh the barrel does
+
+ align:start position:0%
+form a seal so the uh the barrel does
+ 
+
+ align:start position:0%
+form a seal so the uh the barrel does
+not move once it's been um lit on
+
+ align:start position:0%
+not move once it's been um lit on
+ 
+
+ align:start position:0%
+not move once it's been um lit on
+fire and we've uh calculated the air
+
+ align:start position:0%
+fire and we've uh calculated the air
+ 
+
+ align:start position:0%
+fire and we've uh calculated the air
+flow so that uh there is sufficient air
+
+ align:start position:0%
+flow so that uh there is sufficient air
+ 
+
+ align:start position:0%
+flow so that uh there is sufficient air
+flow through those channels uh into the
+
+ align:start position:0%
+flow through those channels uh into the
+ 
+
+ align:start position:0%
+flow through those channels uh into the
+holes that are at the bottom of the
+
+ align:start position:0%
+holes that are at the bottom of the
+ 
+
+ align:start position:0%
+holes that are at the bottom of the
+barrel so that um the so that the while
+
+ align:start position:0%
+barrel so that um the so that the while
+ 
+
+ align:start position:0%
+barrel so that um the so that the while
+it's burning there's enough
+
+ align:start position:0%
+it's burning there's enough
+ 
+
+ align:start position:0%
+it's burning there's enough
+air and uh so to work on Sealing these
+
+ align:start position:0%
+air and uh so to work on Sealing these
+ 
+
+ align:start position:0%
+air and uh so to work on Sealing these
+channels we have um we've come up with
+
+ align:start position:0%
+channels we have um we've come up with
+ 
+
+ align:start position:0%
+channels we have um we've come up with
+these uh metal plates right here so
+
+ align:start position:0%
+these uh metal plates right here so
+ 
+
+ align:start position:0%
+these uh metal plates right here so
+essentially this is just uh sheet metal
+
+ align:start position:0%
+essentially this is just uh sheet metal
+ 
+
+ align:start position:0%
+essentially this is just uh sheet metal
+and it has these uh handles on top we
+
+ align:start position:0%
+and it has these uh handles on top we
+ 
+
+ align:start position:0%
+and it has these uh handles on top we
+call them and they can be pushed in
+
+ align:start position:0%
+call them and they can be pushed in
+ 
+
+ align:start position:0%
+call them and they can be pushed in
+underneath the uh uh over rather the
+
+ align:start position:0%
+underneath the uh uh over rather the
+ 
+
+ align:start position:0%
+underneath the uh uh over rather the
+three channels to seal them and just
+
+ align:start position:0%
+three channels to seal them and just
+ 
+
+ align:start position:0%
+three channels to seal them and just
+with a little bit of sand it forms a
+
+ align:start position:0%
+with a little bit of sand it forms a
+ 
+
+ align:start position:0%
+with a little bit of sand it forms a
+seal around the whole Barrel um so
+
+ align:start position:0%
+seal around the whole Barrel um so
+ 
+
+ align:start position:0%
+seal around the whole Barrel um so
+eliminates the need for tilting the
+
+ align:start position:0%
+eliminates the need for tilting the
+ 
+
+ align:start position:0%
+eliminates the need for tilting the
+barrel kicking it kicking out the bricks
+
+ align:start position:0%
+barrel kicking it kicking out the bricks
+ 
+
+ align:start position:0%
+barrel kicking it kicking out the bricks
+and all that and we experimented with a
+
+ align:start position:0%
+and all that and we experimented with a
+ 
+
+ align:start position:0%
+and all that and we experimented with a
+number of uh shapes here at the top so
+
+ align:start position:0%
+number of uh shapes here at the top so
+ 
+
+ align:start position:0%
+number of uh shapes here at the top so
+this is a semicircular we also have a
+
+ align:start position:0%
+this is a semicircular we also have a
+ 
+
+ align:start position:0%
+this is a semicircular we also have a
+triangular shapes and then diff various
+
+ align:start position:0%
+triangular shapes and then diff various
+ 
+
+ align:start position:0%
+triangular shapes and then diff various
+types of handles which Jessica will go
+
+ align:start position:0%
+types of handles which Jessica will go
+ 
+
+ align:start position:0%
+types of handles which Jessica will go
+into um in a second so an overview of
+
+ align:start position:0%
+into um in a second so an overview of
+ 
+
+ align:start position:0%
+into um in a second so an overview of
+the benefits of this design compared to
+
+ align:start position:0%
+the benefits of this design compared to
+ 
+
+ align:start position:0%
+the benefits of this design compared to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+existing um the existing portion of the
+
+ align:start position:0%
+existing um the existing portion of the
+ 
+
+ align:start position:0%
+existing um the existing portion of the
+process that we're trying to fit are
+
+ align:start position:0%
+process that we're trying to fit are
+ 
+
+ align:start position:0%
+process that we're trying to fit are
+first that it minimizes the heat
+
+ align:start position:0%
+first that it minimizes the heat
+ 
+
+ align:start position:0%
+first that it minimizes the heat
+exposure because the uh the Flaming
+
+ align:start position:0%
+exposure because the uh the Flaming
+ 
+
+ align:start position:0%
+exposure because the uh the Flaming
+Barrel is now in the ground and there's
+
+ align:start position:0%
+Barrel is now in the ground and there's
+ 
+
+ align:start position:0%
+Barrel is now in the ground and there's
+no space for the there there's minimized
+
+ align:start position:0%
+no space for the there there's minimized
+ 
+
+ align:start position:0%
+no space for the there there's minimized
+space for this heat to come out the
+
+ align:start position:0%
+space for this heat to come out the
+ 
+
+ align:start position:0%
+space for this heat to come out the
+second is that one person can seal the
+
+ align:start position:0%
+second is that one person can seal the
+ 
+
+ align:start position:0%
+second is that one person can seal the
+um the barrel rather than needing to and
+
+ align:start position:0%
+um the barrel rather than needing to and
+ 
+
+ align:start position:0%
+um the barrel rather than needing to and
+we can show a video of that right
+
+ align:start position:0%
+we can show a video of that right
+ 
+
+ align:start position:0%
+we can show a video of that right
+now although I'm yeah
+
+ align:start position:0%
+now although I'm yeah
+ 
+
+ align:start position:0%
+now although I'm yeah
+you so this is
+
+ align:start position:0%
+you so this is
+ 
+
+ align:start position:0%
+you so this is
+the entire process uh
+
+ align:start position:0%
+the entire process uh
+ 
+
+ align:start position:0%
+the entire process uh
+we and I'll talk through this um third
+
+ align:start position:0%
+we and I'll talk through this um third
+ 
+
+ align:start position:0%
+we and I'll talk through this um third
+is that we you can still light the
+
+ align:start position:0%
+is that we you can still light the
+ 
+
+ align:start position:0%
+is that we you can still light the
+barrel through the
+
+ align:start position:0%
+barrel through the
+ 
+
+ align:start position:0%
+barrel through the
+channels and um the barrel doesn't move
+
+ align:start position:0%
+channels and um the barrel doesn't move
+ 
+
+ align:start position:0%
+channels and um the barrel doesn't move
+once it's on fire and flaming so um as
+
+ align:start position:0%
+once it's on fire and flaming so um as
+ 
+
+ align:start position:0%
+once it's on fire and flaming so um as
+you can see all Jessica is doing here is
+
+ align:start position:0%
+you can see all Jessica is doing here is
+ 
+
+ align:start position:0%
+you can see all Jessica is doing here is
+just pushing the uh the the plates in at
+
+ align:start position:0%
+just pushing the uh the the plates in at
+ 
+
+ align:start position:0%
+just pushing the uh the the plates in at
+a safe distance and um with minimal
+
+ align:start position:0%
+a safe distance and um with minimal
+ 
+
+ align:start position:0%
+a safe distance and um with minimal
+exposure to heat basically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and so from our experiment we were
+
+ align:start position:0%
+um and so from our experiment we were
+ 
+
+ align:start position:0%
+um and so from our experiment we were
+able to conclude
+
+ align:start position:0%
+able to conclude
+ 
+
+ align:start position:0%
+able to conclude
+um what designs of sheet and handles
+
+ align:start position:0%
+um what designs of sheet and handles
+ 
+
+ align:start position:0%
+um what designs of sheet and handles
+were better equipped to meet our project
+
+ align:start position:0%
+were better equipped to meet our project
+ 
+
+ align:start position:0%
+were better equipped to meet our project
+attributes we wanted to be able to steer
+
+ align:start position:0%
+attributes we wanted to be able to steer
+ 
+
+ align:start position:0%
+attributes we wanted to be able to steer
+the sheet and the better design for that
+
+ align:start position:0%
+the sheet and the better design for that
+ 
+
+ align:start position:0%
+the sheet and the better design for that
+was a semicircular plate um in terms of
+
+ align:start position:0%
+was a semicircular plate um in terms of
+ 
+
+ align:start position:0%
+was a semicircular plate um in terms of
+maneuvering and being precise about
+
+ align:start position:0%
+maneuvering and being precise about
+ 
+
+ align:start position:0%
+maneuvering and being precise about
+where the sheet was going the lipped
+
+ align:start position:0%
+where the sheet was going the lipped
+ 
+
+ align:start position:0%
+where the sheet was going the lipped
+handle which is this one right here
+
+ align:start position:0%
+handle which is this one right here
+ 
+
+ align:start position:0%
+handle which is this one right here
+allowed for the wood to come in and kind
+
+ align:start position:0%
+allowed for the wood to come in and kind
+ 
+
+ align:start position:0%
+allowed for the wood to come in and kind
+of fit right there um just enough to be
+
+ align:start position:0%
+of fit right there um just enough to be
+ 
+
+ align:start position:0%
+of fit right there um just enough to be
+able to to maneuver the sheet into where
+
+ align:start position:0%
+able to to maneuver the sheet into where
+ 
+
+ align:start position:0%
+able to to maneuver the sheet into where
+we wanted
+
+ align:start position:0%
+we wanted
+ 
+
+ align:start position:0%
+we wanted
+it uh the lifting potential of the LIF
+
+ align:start position:0%
+it uh the lifting potential of the LIF
+ 
+
+ align:start position:0%
+it uh the lifting potential of the LIF
+handle allowed us to sort of Kick the
+
+ align:start position:0%
+handle allowed us to sort of Kick the
+ 
+
+ align:start position:0%
+handle allowed us to sort of Kick the
+sheet up a little bit if it ever got
+
+ align:start position:0%
+sheet up a little bit if it ever got
+ 
+
+ align:start position:0%
+sheet up a little bit if it ever got
+stuck right before the brick um and the
+
+ align:start position:0%
+stuck right before the brick um and the
+ 
+
+ align:start position:0%
+stuck right before the brick um and the
+Three Sheets worked equally as well um
+
+ align:start position:0%
+Three Sheets worked equally as well um
+ 
+
+ align:start position:0%
+Three Sheets worked equally as well um
+to diminish the heat exposure and to uh
+
+ align:start position:0%
+to diminish the heat exposure and to uh
+ 
+
+ align:start position:0%
+to diminish the heat exposure and to uh
+lessen the time that it took to seal the
+
+ align:start position:0%
+lessen the time that it took to seal the
+ 
+
+ align:start position:0%
+lessen the time that it took to seal the
+barrel now stepping back for a second
+
+ align:start position:0%
+barrel now stepping back for a second
+ 
+
+ align:start position:0%
+barrel now stepping back for a second
+the sheet metal is only one of three uh
+
+ align:start position:0%
+the sheet metal is only one of three uh
+ 
+
+ align:start position:0%
+the sheet metal is only one of three uh
+ceiling Barrel ceiling alter that we're
+
+ align:start position:0%
+ceiling Barrel ceiling alter that we're
+ 
+
+ align:start position:0%
+ceiling Barrel ceiling alter that we're
+considering right now the other two are
+
+ align:start position:0%
+considering right now the other two are
+ 
+
+ align:start position:0%
+considering right now the other two are
+inserting a break into the channel of
+
+ align:start position:0%
+inserting a break into the channel of
+ 
+
+ align:start position:0%
+inserting a break into the channel of
+The Dugout and covering the rest with
+
+ align:start position:0%
+The Dugout and covering the rest with
+ 
+
+ align:start position:0%
+The Dugout and covering the rest with
+sand and the third is even simpler than
+
+ align:start position:0%
+sand and the third is even simpler than
+ 
+
+ align:start position:0%
+sand and the third is even simpler than
+that just shoveling in or pouring in
+
+ align:start position:0%
+that just shoveling in or pouring in
+ 
+
+ align:start position:0%
+that just shoveling in or pouring in
+sand into the three holes um and of
+
+ align:start position:0%
+sand into the three holes um and of
+ 
+
+ align:start position:0%
+sand into the three holes um and of
+course on the left we have different
+
+ align:start position:0%
+course on the left we have different
+ 
+
+ align:start position:0%
+course on the left we have different
+sort of design spec spe excuse me
+
+ align:start position:0%
+sort of design spec spe excuse me
+ 
+
+ align:start position:0%
+sort of design spec spe excuse me
+specifications that we want this to meet
+
+ align:start position:0%
+specifications that we want this to meet
+ 
+
+ align:start position:0%
+specifications that we want this to meet
+because it's part of the process that
+
+ align:start position:0%
+because it's part of the process that
+ 
+
+ align:start position:0%
+because it's part of the process that
+before was most heat intensive um you'll
+
+ align:start position:0%
+before was most heat intensive um you'll
+ 
+
+ align:start position:0%
+before was most heat intensive um you'll
+see there's an even spread right now of
+
+ align:start position:0%
+see there's an even spread right now of
+ 
+
+ align:start position:0%
+see there's an even spread right now of
+all the three uh designs for example the
+
+ align:start position:0%
+all the three uh designs for example the
+ 
+
+ align:start position:0%
+all the three uh designs for example the
+sheet metal is best in diminishing or in
+
+ align:start position:0%
+sheet metal is best in diminishing or in
+ 
+
+ align:start position:0%
+sheet metal is best in diminishing or in
+lessening the time that it takes to seal
+
+ align:start position:0%
+lessening the time that it takes to seal
+ 
+
+ align:start position:0%
+lessening the time that it takes to seal
+but the sand could be done from farthest
+
+ align:start position:0%
+but the sand could be done from farthest
+ 
+
+ align:start position:0%
+but the sand could be done from farthest
+away you just sort of take the sand and
+
+ align:start position:0%
+away you just sort of take the sand and
+ 
+
+ align:start position:0%
+away you just sort of take the sand and
+throw it into the barrel throw it in
+
+ align:start position:0%
+throw it into the barrel throw it in
+ 
+
+ align:start position:0%
+throw it into the barrel throw it in
+along the side but this is due to the
+
+ align:start position:0%
+along the side but this is due to the
+ 
+
+ align:start position:0%
+along the side but this is due to the
+metrics of the attributes right for
+
+ align:start position:0%
+metrics of the attributes right for
+ 
+
+ align:start position:0%
+metrics of the attributes right for
+example the labor intensity we consider
+
+ align:start position:0%
+example the labor intensity we consider
+ 
+
+ align:start position:0%
+example the labor intensity we consider
+that it's easier to seal the hole but
+
+ align:start position:0%
+that it's easier to seal the hole but
+ 
+
+ align:start position:0%
+that it's easier to seal the hole but
+you do have to spend some time finding
+
+ align:start position:0%
+you do have to spend some time finding
+ 
+
+ align:start position:0%
+you do have to spend some time finding
+the sheet metal which is readily
+
+ align:start position:0%
+the sheet metal which is readily
+ 
+
+ align:start position:0%
+the sheet metal which is readily
+available in Nicaragua but you still
+
+ align:start position:0%
+available in Nicaragua but you still
+ 
+
+ align:start position:0%
+available in Nicaragua but you still
+have to make and manufacture the sheet
+
+ align:start position:0%
+have to make and manufacture the sheet
+ 
+
+ align:start position:0%
+have to make and manufacture the sheet
+um the sheet metal with the handles only
+
+ align:start position:0%
+um the sheet metal with the handles only
+ 
+
+ align:start position:0%
+um the sheet metal with the handles only
+once
+
+ align:start position:0%
+once
+ 
+
+ align:start position:0%
+once
+though so in our experiment we concluded
+
+ align:start position:0%
+though so in our experiment we concluded
+ 
+
+ align:start position:0%
+though so in our experiment we concluded
+that um our Dugout was successful in um
+
+ align:start position:0%
+that um our Dugout was successful in um
+ 
+
+ align:start position:0%
+that um our Dugout was successful in um
+addressing the need to reduce heat
+
+ align:start position:0%
+addressing the need to reduce heat
+ 
+
+ align:start position:0%
+addressing the need to reduce heat
+exposure um it channels all the heat
+
+ align:start position:0%
+exposure um it channels all the heat
+ 
+
+ align:start position:0%
+exposure um it channels all the heat
+down into the Dugout instead of um at
+
+ align:start position:0%
+down into the Dugout instead of um at
+ 
+
+ align:start position:0%
+down into the Dugout instead of um at
+the people working on it um we also were
+
+ align:start position:0%
+the people working on it um we also were
+ 
+
+ align:start position:0%
+the people working on it um we also were
+able to decrease a safety risk of the
+
+ align:start position:0%
+able to decrease a safety risk of the
+ 
+
+ align:start position:0%
+able to decrease a safety risk of the
+tip and kick method um our sheet metal
+
+ align:start position:0%
+tip and kick method um our sheet metal
+ 
+
+ align:start position:0%
+tip and kick method um our sheet metal
+seals were also successful in in um
+
+ align:start position:0%
+seals were also successful in in um
+ 
+
+ align:start position:0%
+seals were also successful in in um
+creating a seal and um resulting in a
+
+ align:start position:0%
+creating a seal and um resulting in a
+ 
+
+ align:start position:0%
+creating a seal and um resulting in a
+quality burn we did get some really good
+
+ align:start position:0%
+quality burn we did get some really good
+ 
+
+ align:start position:0%
+quality burn we did get some really good
+carbonized material out of this burn um
+
+ align:start position:0%
+carbonized material out of this burn um
+ 
+
+ align:start position:0%
+carbonized material out of this burn um
+but there are definitely still
+
+ align:start position:0%
+but there are definitely still
+ 
+
+ align:start position:0%
+but there are definitely still
+improvements to be made um we can still
+
+ align:start position:0%
+improvements to be made um we can still
+ 
+
+ align:start position:0%
+improvements to be made um we can still
+work on the maneuverability and handling
+
+ align:start position:0%
+work on the maneuverability and handling
+ 
+
+ align:start position:0%
+work on the maneuverability and handling
+of these seals with the handles and um
+
+ align:start position:0%
+of these seals with the handles and um
+ 
+
+ align:start position:0%
+of these seals with the handles and um
+we can also work on adding a little more
+
+ align:start position:0%
+we can also work on adding a little more
+ 
+
+ align:start position:0%
+we can also work on adding a little more
+distance between the person and the
+
+ align:start position:0%
+distance between the person and the
+ 
+
+ align:start position:0%
+distance between the person and the
+barrel and so we're at our next steps um
+
+ align:start position:0%
+barrel and so we're at our next steps um
+ 
+
+ align:start position:0%
+barrel and so we're at our next steps um
+which are going to be to send the
+
+ align:start position:0%
+which are going to be to send the
+ 
+
+ align:start position:0%
+which are going to be to send the
+document the process of our new Barrel
+
+ align:start position:0%
+document the process of our new Barrel
+ 
+
+ align:start position:0%
+document the process of our new Barrel
+design or charcoal making design to the
+
+ align:start position:0%
+design or charcoal making design to the
+ 
+
+ align:start position:0%
+design or charcoal making design to the
+women and they're going to make a
+
+ align:start position:0%
+women and they're going to make a
+ 
+
+ align:start position:0%
+women and they're going to make a
+charcoal burn early next week we're
+
+ align:start position:0%
+charcoal burn early next week we're
+ 
+
+ align:start position:0%
+charcoal burn early next week we're
+going to phone call them and talk to
+
+ align:start position:0%
+going to phone call them and talk to
+ 
+
+ align:start position:0%
+going to phone call them and talk to
+them directly I'll talk to them directly
+
+ align:start position:0%
+them directly I'll talk to them directly
+ 
+
+ align:start position:0%
+them directly I'll talk to them directly
+and get their feedback on what the heat
+
+ align:start position:0%
+and get their feedback on what the heat
+ 
+
+ align:start position:0%
+and get their feedback on what the heat
+experience was and see how they've um
+
+ align:start position:0%
+experience was and see how they've um
+ 
+
+ align:start position:0%
+experience was and see how they've um
+how they can explain that and whether
+
+ align:start position:0%
+how they can explain that and whether
+ 
+
+ align:start position:0%
+how they can explain that and whether
+it's better or worse um and finally
+
+ align:start position:0%
+it's better or worse um and finally
+ 
+
+ align:start position:0%
+it's better or worse um and finally
+we're going to continue to look at
+
+ align:start position:0%
+we're going to continue to look at
+ 
+
+ align:start position:0%
+we're going to continue to look at
+improving the sheet metal design um and
+
+ align:start position:0%
+improving the sheet metal design um and
+ 
+
+ align:start position:0%
+improving the sheet metal design um and
+seeing how we can manufacture it easier
+
+ align:start position:0%
+seeing how we can manufacture it easier
+ 
+
+ align:start position:0%
+seeing how we can manufacture it easier
+or how we can just get it um a better
+
+ align:start position:0%
+or how we can just get it um a better
+ 
+
+ align:start position:0%
+or how we can just get it um a better
+design so we can man maneuver it better
+
+ align:start position:0%
+design so we can man maneuver it better
+ 
+
+ align:start position:0%
+design so we can man maneuver it better
+and finally of course we're here to
+
+ align:start position:0%
+and finally of course we're here to
+ 
+
+ align:start position:0%
+and finally of course we're here to
+incorporate your input so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions questions yes Benji have you
+
+ align:start position:0%
+questions questions yes Benji have you
+ 
+
+ align:start position:0%
+questions questions yes Benji have you
+been able to talk to them about the
+
+ align:start position:0%
+been able to talk to them about the
+ 
+
+ align:start position:0%
+been able to talk to them about the
+three different options of how to seal
+
+ align:start position:0%
+three different options of how to seal
+ 
+
+ align:start position:0%
+three different options of how to seal
+the holes like in terms of like would
+
+ align:start position:0%
+the holes like in terms of like would
+ 
+
+ align:start position:0%
+the holes like in terms of like would
+you rather make a plate or would you
+
+ align:start position:0%
+you rather make a plate or would you
+ 
+
+ align:start position:0%
+you rather make a plate or would you
+rather just like f
+
+ align:start position:0%
+rather just like f
+ 
+
+ align:start position:0%
+rather just like f
+the so no the answer is no um not about
+
+ align:start position:0%
+the so no the answer is no um not about
+ 
+
+ align:start position:0%
+the so no the answer is no um not about
+those three specific designs but um in
+
+ align:start position:0%
+those three specific designs but um in
+ 
+
+ align:start position:0%
+those three specific designs but um in
+our conv ation with Lindsay which is
+
+ align:start position:0%
+our conv ation with Lindsay which is
+ 
+
+ align:start position:0%
+our conv ation with Lindsay which is
+sort of their project coordinator
+
+ align:start position:0%
+sort of their project coordinator
+ 
+
+ align:start position:0%
+sort of their project coordinator
+oraison R liaison with the community um
+
+ align:start position:0%
+oraison R liaison with the community um
+ 
+
+ align:start position:0%
+oraison R liaison with the community um
+she says that she continues to say that
+
+ align:start position:0%
+she says that she continues to say that
+ 
+
+ align:start position:0%
+she says that she continues to say that
+the the heat of it is the biggest
+
+ align:start position:0%
+the the heat of it is the biggest
+ 
+
+ align:start position:0%
+the the heat of it is the biggest
+exposure so rather than have them do the
+
+ align:start position:0%
+exposure so rather than have them do the
+ 
+
+ align:start position:0%
+exposure so rather than have them do the
+test trials and all the experimentation
+
+ align:start position:0%
+test trials and all the experimentation
+ 
+
+ align:start position:0%
+test trials and all the experimentation
+of like which feels best or taking all
+
+ align:start position:0%
+of like which feels best or taking all
+ 
+
+ align:start position:0%
+of like which feels best or taking all
+this data that we've been taking we try
+
+ align:start position:0%
+this data that we've been taking we try
+ 
+
+ align:start position:0%
+this data that we've been taking we try
+to get the data first and then submit
+
+ align:start position:0%
+to get the data first and then submit
+ 
+
+ align:start position:0%
+to get the data first and then submit
+our conclusive you know recommendation
+
+ align:start position:0%
+our conclusive you know recommendation
+ 
+
+ align:start position:0%
+our conclusive you know recommendation
+to them and then that's what they're
+
+ align:start position:0%
+to them and then that's what they're
+ 
+
+ align:start position:0%
+to them and then that's what they're
+going to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+week how are you actually going to
+
+ align:start position:0%
+week how are you actually going to
+ 
+
+ align:start position:0%
+week how are you actually going to
+communicate them your idea do you need
+
+ align:start position:0%
+communicate them your idea do you need
+ 
+
+ align:start position:0%
+communicate them your idea do you need
+to describe the ho with dig as well yeah
+
+ align:start position:0%
+to describe the ho with dig as well yeah
+ 
+
+ align:start position:0%
+to describe the ho with dig as well yeah
+right now um when you train a community
+
+ align:start position:0%
+right now um when you train a community
+ 
+
+ align:start position:0%
+right now um when you train a community
+to make a charcoal burn there's a Nifty
+
+ align:start position:0%
+to make a charcoal burn there's a Nifty
+ 
+
+ align:start position:0%
+to make a charcoal burn there's a Nifty
+document with diagrams that daab has
+
+ align:start position:0%
+document with diagrams that daab has
+ 
+
+ align:start position:0%
+document with diagrams that daab has
+produced um that tells them you know how
+
+ align:start position:0%
+produced um that tells them you know how
+ 
+
+ align:start position:0%
+produced um that tells them you know how
+to make the holes or how to set up the
+
+ align:start position:0%
+to make the holes or how to set up the
+ 
+
+ align:start position:0%
+to make the holes or how to set up the
+bricks and all the process and so we're
+
+ align:start position:0%
+bricks and all the process and so we're
+ 
+
+ align:start position:0%
+bricks and all the process and so we're
+going to do that they've already been
+
+ align:start position:0%
+going to do that they've already been
+ 
+
+ align:start position:0%
+going to do that they've already been
+trained with that and they have that
+
+ align:start position:0%
+trained with that and they have that
+ 
+
+ align:start position:0%
+trained with that and they have that
+document we train them over spring break
+
+ align:start position:0%
+document we train them over spring break
+ 
+
+ align:start position:0%
+document we train them over spring break
+and so we're just going to sort of an
+
+ align:start position:0%
+and so we're just going to sort of an
+ 
+
+ align:start position:0%
+and so we're just going to sort of an
+addendum an appendix to what the new
+
+ align:start position:0%
+addendum an appendix to what the new
+ 
+
+ align:start position:0%
+addendum an appendix to what the new
+process should be and how they should
+
+ align:start position:0%
+process should be and how they should
+ 
+
+ align:start position:0%
+process should be and how they should
+dig the hole and all that so they can do
+
+ align:start position:0%
+dig the hole and all that so they can do
+ 
+
+ align:start position:0%
+dig the hole and all that so they can do
+their charcoal next week and we have all
+
+ align:start position:0%
+their charcoal next week and we have all
+ 
+
+ align:start position:0%
+their charcoal next week and we have all
+the specifications for the whole um
+
+ align:start position:0%
+the specifications for the whole um
+ 
+
+ align:start position:0%
+the specifications for the whole um
+based on like air flow right so that we
+
+ align:start position:0%
+based on like air flow right so that we
+ 
+
+ align:start position:0%
+based on like air flow right so that we
+can s them exactly so we can send them
+
+ align:start position:0%
+can s them exactly so we can send them
+ 
+
+ align:start position:0%
+can s them exactly so we can send them
+um very very exact uh so they did before
+
+ align:start position:0%
+um very very exact uh so they did before
+ 
+
+ align:start position:0%
+um very very exact uh so they did before
+with the original document they were
+
+ align:start position:0%
+with the original document they were
+ 
+
+ align:start position:0%
+with the original document they were
+able to go through it without any
+
+ align:start position:0%
+able to go through it without any
+ 
+
+ align:start position:0%
+able to go through it without any
+training or no we were there to train
+
+ align:start position:0%
+training or no we were there to train
+ 
+
+ align:start position:0%
+training or no we were there to train
+them personally you can yeah you it's
+
+ align:start position:0%
+them personally you can yeah you it's
+ 
+
+ align:start position:0%
+them personally you can yeah you it's
+hard to communicate just with a document
+
+ align:start position:0%
+hard to communicate just with a document
+ 
+
+ align:start position:0%
+hard to communicate just with a document
+of step-by-step instructions even though
+
+ align:start position:0%
+of step-by-step instructions even though
+ 
+
+ align:start position:0%
+of step-by-step instructions even though
+they're really well drafted because they
+
+ align:start position:0%
+they're really well drafted because they
+ 
+
+ align:start position:0%
+they're really well drafted because they
+still have questions on it's really
+
+ align:start position:0%
+still have questions on it's really
+ 
+
+ align:start position:0%
+still have questions on it's really
+about understanding the why of things
+
+ align:start position:0%
+about understanding the why of things
+ 
+
+ align:start position:0%
+about understanding the why of things
+but now that they understand the why of
+
+ align:start position:0%
+but now that they understand the why of
+ 
+
+ align:start position:0%
+but now that they understand the why of
+things like why it has to be sealed at a
+
+ align:start position:0%
+things like why it has to be sealed at a
+ 
+
+ align:start position:0%
+things like why it has to be sealed at a
+certain time now it's a matter of just
+
+ align:start position:0%
+certain time now it's a matter of just
+ 
+
+ align:start position:0%
+certain time now it's a matter of just
+saying instead of mounting the barrel on
+
+ align:start position:0%
+saying instead of mounting the barrel on
+ 
+
+ align:start position:0%
+saying instead of mounting the barrel on
+the bricks instead make a hole insert
+
+ align:start position:0%
+the bricks instead make a hole insert
+ 
+
+ align:start position:0%
+the bricks instead make a hole insert
+bricks and put the barrel on top okay my
+
+ align:start position:0%
+bricks and put the barrel on top okay my
+ 
+
+ align:start position:0%
+bricks and put the barrel on top okay my
+expectation is that it's going be more
+
+ align:start position:0%
+expectation is that it's going be more
+ 
+
+ align:start position:0%
+expectation is that it's going be more
+chall
+
+ align:start position:0%
+chall
+ 
+
+ align:start position:0%
+chall
+yeah and it seems sorry it seems like
+
+ align:start position:0%
+yeah and it seems sorry it seems like
+ 
+
+ align:start position:0%
+yeah and it seems sorry it seems like
+how do you if you're going to plug the
+
+ align:start position:0%
+how do you if you're going to plug the
+ 
+
+ align:start position:0%
+how do you if you're going to plug the
+hole with a with a third brick how do
+
+ align:start position:0%
+hole with a with a third brick how do
+ 
+
+ align:start position:0%
+hole with a with a third brick how do
+you get the brick
+
+ align:start position:0%
+you get the brick
+ 
+
+ align:start position:0%
+you get the brick
+there well I mean that that does that
+
+ align:start position:0%
+there well I mean that that does that
+ 
+
+ align:start position:0%
+there well I mean that that does that
+inevitably involve your hand a half an
+
+ align:start position:0%
+inevitably involve your hand a half an
+ 
+
+ align:start position:0%
+inevitably involve your hand a half an
+inch away from the barral sure so that
+
+ align:start position:0%
+inch away from the barral sure so that
+ 
+
+ align:start position:0%
+inch away from the barral sure so that
+you can make other construtions that
+
+ align:start position:0%
+you can make other construtions that
+ 
+
+ align:start position:0%
+you can make other construtions that
+we've considered like a reach sort of
+
+ align:start position:0%
+we've considered like a reach sort of
+ 
+
+ align:start position:0%
+we've considered like a reach sort of
+like the things that you use to reach
+
+ align:start position:0%
+like the things that you use to reach
+ 
+
+ align:start position:0%
+like the things that you use to reach
+really far away and just grab it and put
+
+ align:start position:0%
+really far away and just grab it and put
+ 
+
+ align:start position:0%
+really far away and just grab it and put
+it there but um the simplest design is
+
+ align:start position:0%
+it there but um the simplest design is
+ 
+
+ align:start position:0%
+it there but um the simplest design is
+that you know when I'll show you the
+
+ align:start position:0%
+that you know when I'll show you the
+ 
+
+ align:start position:0%
+that you know when I'll show you the
+picture when you can walk right next to
+
+ align:start position:0%
+picture when you can walk right next to
+ 
+
+ align:start position:0%
+picture when you can walk right next to
+the barrel um you can sort of stand
+
+ align:start position:0%
+the barrel um you can sort of stand
+ 
+
+ align:start position:0%
+the barrel um you can sort of stand
+right here and you're not feeling any
+
+ align:start position:0%
+right here and you're not feeling any
+ 
+
+ align:start position:0%
+right here and you're not feeling any
+heat so you can if you just drop in the
+
+ align:start position:0%
+heat so you can if you just drop in the
+ 
+
+ align:start position:0%
+heat so you can if you just drop in the
+brake you're technically not feeling any
+
+ align:start position:0%
+brake you're technically not feeling any
+ 
+
+ align:start position:0%
+brake you're technically not feeling any
+heat over you whereas even with the
+
+ align:start position:0%
+heat over you whereas even with the
+ 
+
+ align:start position:0%
+heat over you whereas even with the
+sheet metal design you're directly in
+
+ align:start position:0%
+sheet metal design you're directly in
+ 
+
+ align:start position:0%
+sheet metal design you're directly in
+front of the channel That that does have
+
+ align:start position:0%
+front of the channel That that does have
+ 
+
+ align:start position:0%
+front of the channel That that does have
+the heat coming out of it if that makes
+
+ align:start position:0%
+the heat coming out of it if that makes
+ 
+
+ align:start position:0%
+the heat coming out of it if that makes
+any sense yeah I'm just surprised that
+
+ align:start position:0%
+any sense yeah I'm just surprised that
+ 
+
+ align:start position:0%
+any sense yeah I'm just surprised that
+you're getting so much heat out of the
+
+ align:start position:0%
+you're getting so much heat out of the
+ 
+
+ align:start position:0%
+you're getting so much heat out of the
+channel comparatively I think a lot of
+
+ align:start position:0%
+channel comparatively I think a lot of
+ 
+
+ align:start position:0%
+channel comparatively I think a lot of
+it is smoke too that Jess is talking
+
+ align:start position:0%
+it is smoke too that Jess is talking
+ 
+
+ align:start position:0%
+it is smoke too that Jess is talking
+about a lot of smoke comes out of the
+
+ align:start position:0%
+about a lot of smoke comes out of the
+ 
+
+ align:start position:0%
+about a lot of smoke comes out of the
+chanels and comparatively remember that
+
+ align:start position:0%
+chanels and comparatively remember that
+ 
+
+ align:start position:0%
+chanels and comparatively remember that
+it was all on bricks before so all the
+
+ align:start position:0%
+it was all on bricks before so all the
+ 
+
+ align:start position:0%
+it was all on bricks before so all the
+heat was radiating out of the bottom and
+
+ align:start position:0%
+heat was radiating out of the bottom and
+ 
+
+ align:start position:0%
+heat was radiating out of the bottom and
+that was going right to their feet to
+
+ align:start position:0%
+that was going right to their feet to
+ 
+
+ align:start position:0%
+that was going right to their feet to
+their ankles and whatnot and CU there's
+
+ align:start position:0%
+their ankles and whatnot and CU there's
+ 
+
+ align:start position:0%
+their ankles and whatnot and CU there's
+I mean if there's no if it's just as
+
+ align:start position:0%
+I mean if there's no if it's just as
+ 
+
+ align:start position:0%
+I mean if there's no if it's just as
+easy for them to bring nine bricks as
+
+ align:start position:0%
+easy for them to bring nine bricks as
+ 
+
+ align:start position:0%
+easy for them to bring nine bricks as
+six bricks then the you know the easiest
+
+ align:start position:0%
+six bricks then the you know the easiest
+ 
+
+ align:start position:0%
+six bricks then the you know the easiest
+way to tell them how wide the hole
+
+ align:start position:0%
+way to tell them how wide the hole
+ 
+
+ align:start position:0%
+way to tell them how wide the hole
+should be is that it should be a brick
+
+ align:start position:0%
+should be is that it should be a brick
+ 
+
+ align:start position:0%
+should be is that it should be a brick
+wide yeah right just you measure it with
+
+ align:start position:0%
+wide yeah right just you measure it with
+ 
+
+ align:start position:0%
+wide yeah right just you measure it with
+the bricks you're about to use to plug
+
+ align:start position:0%
+the bricks you're about to use to plug
+ 
+
+ align:start position:0%
+the bricks you're about to use to plug
+it but if can't get there to put the
+
+ align:start position:0%
+it but if can't get there to put the
+ 
+
+ align:start position:0%
+it but if can't get there to put the
+brick in then that whole efficiency is
+
+ align:start position:0%
+brick in then that whole efficiency is
+ 
+
+ align:start position:0%
+brick in then that whole efficiency is
+not working right so that's why for the
+
+ align:start position:0%
+not working right so that's why for the
+ 
+
+ align:start position:0%
+not working right so that's why for the
+time being we still prefer the solution
+
+ align:start position:0%
+time being we still prefer the solution
+ 
+
+ align:start position:0%
+time being we still prefer the solution
+with the metal Su so Jess you you tested
+
+ align:start position:0%
+with the metal Su so Jess you you tested
+ 
+
+ align:start position:0%
+with the metal Su so Jess you you tested
+with a hot Barrel putting the bricks
+
+ align:start position:0%
+with a hot Barrel putting the bricks
+ 
+
+ align:start position:0%
+with a hot Barrel putting the bricks
+in the Barr no no we've time tested that
+
+ align:start position:0%
+in the Barr no no we've time tested that
+ 
+
+ align:start position:0%
+in the Barr no no we've time tested that
+okay cuz I I question that you wouldn't
+
+ align:start position:0%
+okay cuz I I question that you wouldn't
+ 
+
+ align:start position:0%
+okay cuz I I question that you wouldn't
+be exposed to heat by putting a brick in
+
+ align:start position:0%
+be exposed to heat by putting a brick in
+ 
+
+ align:start position:0%
+be exposed to heat by putting a brick in
+in our video um I was significantly
+
+ align:start position:0%
+in our video um I was significantly
+ 
+
+ align:start position:0%
+in our video um I was significantly
+close with the sheet metal and um and I
+
+ align:start position:0%
+close with the sheet metal and um and I
+ 
+
+ align:start position:0%
+close with the sheet metal and um and I
+had to be over the over the channel so I
+
+ align:start position:0%
+had to be over the over the channel so I
+ 
+
+ align:start position:0%
+had to be over the over the channel so I
+can only imagine them being on the side
+
+ align:start position:0%
+can only imagine them being on the side
+ 
+
+ align:start position:0%
+can only imagine them being on the side
+of it where the smoke isn't Rising would
+
+ align:start position:0%
+of it where the smoke isn't Rising would
+ 
+
+ align:start position:0%
+of it where the smoke isn't Rising would
+be better but that is actually what
+
+ align:start position:0%
+be better but that is actually what
+ 
+
+ align:start position:0%
+be better but that is actually what
+we're going to be testing on Monday
+
+ align:start position:0%
+we're going to be testing on Monday
+ 
+
+ align:start position:0%
+we're going to be testing on Monday
+which is we're going to have two um
+
+ align:start position:0%
+which is we're going to have two um
+ 
+
+ align:start position:0%
+which is we're going to have two um
+we're going to do two barrels and we're
+
+ align:start position:0%
+we're going to do two barrels and we're
+ 
+
+ align:start position:0%
+we're going to do two barrels and we're
+going to be testing the thermometer
+
+ align:start position:0%
+going to be testing the thermometer
+ 
+
+ align:start position:0%
+going to be testing the thermometer
+readings like along the different points
+
+ align:start position:0%
+readings like along the different points
+ 
+
+ align:start position:0%
+readings like along the different points
+around the barrel at different
+
+ align:start position:0%
+around the barrel at different
+ 
+
+ align:start position:0%
+around the barrel at different
+distances are you converging no we'll be
+
+ align:start position:0%
+distances are you converging no we'll be
+ 
+
+ align:start position:0%
+distances are you converging no we'll be
+testing where it's hottest so if there
+
+ align:start position:0%
+testing where it's hottest so if there
+ 
+
+ align:start position:0%
+testing where it's hottest so if there
+is a really significant difference
+
+ align:start position:0%
+is a really significant difference
+ 
+
+ align:start position:0%
+is a really significant difference
+between right above the right above the
+
+ align:start position:0%
+between right above the right above the
+ 
+
+ align:start position:0%
+between right above the right above the
+channel and here then we know that this
+
+ align:start position:0%
+channel and here then we know that this
+ 
+
+ align:start position:0%
+channel and here then we know that this
+is like a safer area or a better area
+
+ align:start position:0%
+is like a safer area or a better area
+ 
+
+ align:start position:0%
+is like a safer area or a better area
+for them to work with how how do you
+
+ align:start position:0%
+for them to work with how how do you
+ 
+
+ align:start position:0%
+for them to work with how how do you
+test that there's a like high resolution
+
+ align:start position:0%
+test that there's a like high resolution
+ 
+
+ align:start position:0%
+test that there's a like high resolution
+thermometer that we're borrowing from
+
+ align:start position:0%
+thermometer that we're borrowing from
+ 
+
+ align:start position:0%
+thermometer that we're borrowing from
+2671 and uh from papardo and uh it one
+
+ align:start position:0%
+2671 and uh from papardo and uh it one
+ 
+
+ align:start position:0%
+2671 and uh from papardo and uh it one
+of the like The Improv gunet no no it's
+
+ align:start position:0%
+of the like The Improv gunet no no it's
+ 
+
+ align:start position:0%
+of the like The Improv gunet no no it's
+just like ambient
+
+ align:start position:0%
+just like ambient
+ 
+
+ align:start position:0%
+just like ambient
+tempature so is that measuring air
+
+ align:start position:0%
+tempature so is that measuring air
+ 
+
+ align:start position:0%
+tempature so is that measuring air
+temperature or
+
+ align:start position:0%
+temperature or
+ 
+
+ align:start position:0%
+temperature or
+sens temperature on skin or Surface no
+
+ align:start position:0%
+sens temperature on skin or Surface no
+ 
+
+ align:start position:0%
+sens temperature on skin or Surface no
+not on skin or Surface just like you can
+
+ align:start position:0%
+not on skin or Surface just like you can
+ 
+
+ align:start position:0%
+not on skin or Surface just like you can
+just hold it so air temperature like
+
+ align:start position:0%
+just hold it so air temperature like
+ 
+
+ align:start position:0%
+just hold it so air temperature like
+ambient
+
+ align:start position:0%
+ambient
+ 
+
+ align:start position:0%
+ambient
+temperature I'm not sure I haven't
+
+ align:start position:0%
+temperature I'm not sure I haven't
+ 
+
+ align:start position:0%
+temperature I'm not sure I haven't
+looked at it but that's what the
+
+ align:start position:0%
+looked at it but that's what the
+ 
+
+ align:start position:0%
+looked at it but that's what the
+description says there's a surface one
+
+ align:start position:0%
+description says there's a surface one
+ 
+
+ align:start position:0%
+description says there's a surface one
+that depends on like the surface the
+
+ align:start position:0%
+that depends on like the surface the
+ 
+
+ align:start position:0%
+that depends on like the surface the
+surface roughness and the surface like
+
+ align:start position:0%
+surface roughness and the surface like
+ 
+
+ align:start position:0%
+surface roughness and the surface like
+change of temperature too right in the
+
+ align:start position:0%
+change of temperature too right in the
+ 
+
+ align:start position:0%
+change of temperature too right in the
+material but this one is just supposed
+
+ align:start position:0%
+material but this one is just supposed
+ 
+
+ align:start position:0%
+material but this one is just supposed
+to be able to hold it up Ian if you have
+
+ align:start position:0%
+to be able to hold it up Ian if you have
+ 
+
+ align:start position:0%
+to be able to hold it up Ian if you have
+something metallic and you have a source
+
+ align:start position:0%
+something metallic and you have a source
+ 
+
+ align:start position:0%
+something metallic and you have a source
+most likely radiating to it you're not
+
+ align:start position:0%
+most likely radiating to it you're not
+ 
+
+ align:start position:0%
+most likely radiating to it you're not
+going to measure any heat off of that
+
+ align:start position:0%
+going to measure any heat off of that
+ 
+
+ align:start position:0%
+going to measure any heat off of that
+the emittance of metal is going to be so
+
+ align:start position:0%
+the emittance of metal is going to be so
+ 
+
+ align:start position:0%
+the emittance of metal is going to be so
+low or the absorptions of the thermales
+
+ align:start position:0%
+low or the absorptions of the thermales
+ 
+
+ align:start position:0%
+low or the absorptions of the thermales
+going to be so low so um when you see
+
+ align:start position:0%
+going to be so low so um when you see
+ 
+
+ align:start position:0%
+going to be so low so um when you see
+your smoke coming out of it just
+
+ align:start position:0%
+your smoke coming out of it just
+ 
+
+ align:start position:0%
+your smoke coming out of it just
+continue um so smoke is coming out of
+
+ align:start position:0%
+continue um so smoke is coming out of
+ 
+
+ align:start position:0%
+continue um so smoke is coming out of
+the channels at the bottom right so is
+
+ align:start position:0%
+the channels at the bottom right so is
+ 
+
+ align:start position:0%
+the channels at the bottom right so is
+that happening the entire time or only
+
+ align:start position:0%
+that happening the entire time or only
+ 
+
+ align:start position:0%
+that happening the entire time or only
+after you seal the top only after you
+
+ align:start position:0%
+after you seal the top only after you
+ 
+
+ align:start position:0%
+after you seal the top only after you
+seal the to is there any reason you
+
+ align:start position:0%
+seal the to is there any reason you
+ 
+
+ align:start position:0%
+seal the to is there any reason you
+can't seal the bottom first then seal
+
+ align:start position:0%
+can't seal the bottom first then seal
+ 
+
+ align:start position:0%
+can't seal the bottom first then seal
+the top uh the top is just more of a
+
+ align:start position:0%
+the top uh the top is just more of a
+ 
+
+ align:start position:0%
+the top uh the top is just more of a
+like there's actually Fire coming out of
+
+ align:start position:0%
+like there's actually Fire coming out of
+ 
+
+ align:start position:0%
+like there's actually Fire coming out of
+it and if the wind changes Direction
+
+ align:start position:0%
+it and if the wind changes Direction
+ 
+
+ align:start position:0%
+it and if the wind changes Direction
+really quickly then if you're standing
+
+ align:start position:0%
+really quickly then if you're standing
+ 
+
+ align:start position:0%
+really quickly then if you're standing
+close to the m
+
+ align:start position:0%
+close to the m
+ 
+
+ align:start position:0%
+close to the m
+you could actually be pretty close to
+
+ align:start position:0%
+you could actually be pretty close to
+ 
+
+ align:start position:0%
+you could actually be pretty close to
+open flame so the way um the way it's uh
+
+ align:start position:0%
+open flame so the way um the way it's uh
+ 
+
+ align:start position:0%
+open flame so the way um the way it's uh
+the way the barrel is sealed now is with
+
+ align:start position:0%
+the way the barrel is sealed now is with
+ 
+
+ align:start position:0%
+the way the barrel is sealed now is with
+the top first and then kicking out the
+
+ align:start position:0%
+the top first and then kicking out the
+ 
+
+ align:start position:0%
+the top first and then kicking out the
+brakes afterwards so we've just stuck
+
+ align:start position:0%
+brakes afterwards so we've just stuck
+ 
+
+ align:start position:0%
+brakes afterwards so we've just stuck
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+yeah but you don't want this thing going
+
+ align:start position:0%
+yeah but you don't want this thing going
+ 
+
+ align:start position:0%
+yeah but you don't want this thing going
+wiggling back and forth with the top is
+
+ align:start position:0%
+wiggling back and forth with the top is
+ 
+
+ align:start position:0%
+wiggling back and forth with the top is
+open because maybe some Embers come
+
+ align:start position:0%
+open because maybe some Embers come
+ 
+
+ align:start position:0%
+open because maybe some Embers come
+flying out or something like that but if
+
+ align:start position:0%
+flying out or something like that but if
+ 
+
+ align:start position:0%
+flying out or something like that but if
+you're not wiggling a barrel uh maybe
+
+ align:start position:0%
+you're not wiggling a barrel uh maybe
+ 
+
+ align:start position:0%
+you're not wiggling a barrel uh maybe
+you can just seal the bottom first and
+
+ align:start position:0%
+you can just seal the bottom first and
+ 
+
+ align:start position:0%
+you can just seal the bottom first and
+smoke buing out of the bottom and then
+
+ align:start position:0%
+smoke buing out of the bottom and then
+ 
+
+ align:start position:0%
+smoke buing out of the bottom and then
+you can seal the top I think cuz like
+
+ align:start position:0%
+you can seal the top I think cuz like
+ 
+
+ align:start position:0%
+you can seal the top I think cuz like
+smoke is still coming out at like kind
+
+ align:start position:0%
+smoke is still coming out at like kind
+ 
+
+ align:start position:0%
+smoke is still coming out at like kind
+of like eye level when when the top is
+
+ align:start position:0%
+of like eye level when when the top is
+ 
+
+ align:start position:0%
+of like eye level when when the top is
+open so our intuition tells us to seal
+
+ align:start position:0%
+open so our intuition tells us to seal
+ 
+
+ align:start position:0%
+open so our intuition tells us to seal
+the top first before
+
+ align:start position:0%
+the top first before
+ 
+
+ align:start position:0%
+the top first before
+we well maybe that's another experiment
+
+ align:start position:0%
+we well maybe that's another experiment
+ 
+
+ align:start position:0%
+we well maybe that's another experiment
+yeah yeah absolutely so that's worth
+
+ align:start position:0%
+yeah yeah absolutely so that's worth
+ 
+
+ align:start position:0%
+yeah yeah absolutely so that's worth
+well experiment yeah and the point about
+
+ align:start position:0%
+well experiment yeah and the point about
+ 
+
+ align:start position:0%
+well experiment yeah and the point about
+you know measuring heat is complicated
+
+ align:start position:0%
+you know measuring heat is complicated
+ 
+
+ align:start position:0%
+you know measuring heat is complicated
+and so you because it's it's coming at
+
+ align:start position:0%
+and so you because it's it's coming at
+ 
+
+ align:start position:0%
+and so you because it's it's coming at
+you in two different ways and your
+
+ align:start position:0%
+you in two different ways and your
+ 
+
+ align:start position:0%
+you in two different ways and your
+measurement devices might only measure
+
+ align:start position:0%
+measurement devices might only measure
+ 
+
+ align:start position:0%
+measurement devices might only measure
+one or the other of those ways and you
+
+ align:start position:0%
+one or the other of those ways and you
+ 
+
+ align:start position:0%
+one or the other of those ways and you
+might want to try a bunch of different
+
+ align:start position:0%
+might want to try a bunch of different
+ 
+
+ align:start position:0%
+might want to try a bunch of different
+ways I mean
+
+ align:start position:0%
+ways I mean
+ 
+
+ align:start position:0%
+ways I mean
+it's because what you're going to be
+
+ align:start position:0%
+it's because what you're going to be
+ 
+
+ align:start position:0%
+it's because what you're going to be
+getting is radiant heat M as as Focus as
+
+ align:start position:0%
+getting is radiant heat M as as Focus as
+ 
+
+ align:start position:0%
+getting is radiant heat M as as Focus as
+this sounds you might actually get a
+
+ align:start position:0%
+this sounds you might actually get a
+ 
+
+ align:start position:0%
+this sounds you might actually get a
+more useful measurement by like you know
+
+ align:start position:0%
+more useful measurement by like you know
+ 
+
+ align:start position:0%
+more useful measurement by like you know
+you know yeah either how hot does it
+
+ align:start position:0%
+you know yeah either how hot does it
+ 
+
+ align:start position:0%
+you know yeah either how hot does it
+feel or like you know if you want to get
+
+ align:start position:0%
+feel or like you know if you want to get
+ 
+
+ align:start position:0%
+feel or like you know if you want to get
+some kind of integrated measurement you
+
+ align:start position:0%
+some kind of integrated measurement you
+ 
+
+ align:start position:0%
+some kind of integrated measurement you
+know you buy like you know three
+
+ align:start position:0%
+know you buy like you know three
+ 
+
+ align:start position:0%
+know you buy like you know three
+cantelopes cuz those at least look like
+
+ align:start position:0%
+cantelopes cuz those at least look like
+ 
+
+ align:start position:0%
+cantelopes cuz those at least look like
+human beings and will absorb radiated
+
+ align:start position:0%
+human beings and will absorb radiated
+ 
+
+ align:start position:0%
+human beings and will absorb radiated
+heat about the same would where you put
+
+ align:start position:0%
+heat about the same would where you put
+ 
+
+ align:start position:0%
+heat about the same would where you put
+them around the thing and then measure
+
+ align:start position:0%
+them around the thing and then measure
+ 
+
+ align:start position:0%
+them around the thing and then measure
+how hot they get 15 minutes later you
+
+ align:start position:0%
+how hot they get 15 minutes later you
+ 
+
+ align:start position:0%
+how hot they get 15 minutes later you
+know you've got to do you know something
+
+ align:start position:0%
+know you've got to do you know something
+ 
+
+ align:start position:0%
+know you've got to do you know something
+but you need an absorber that looks like
+
+ align:start position:0%
+but you need an absorber that looks like
+ 
+
+ align:start position:0%
+but you need an absorber that looks like
+a a person looks like skin um because
+
+ align:start position:0%
+a a person looks like skin um because
+ 
+
+ align:start position:0%
+a a person looks like skin um because
+like you know it's the metal is going to
+
+ align:start position:0%
+like you know it's the metal is going to
+ 
+
+ align:start position:0%
+like you know it's the metal is going to
+reflect all the all the radi you heat
+
+ align:start position:0%
+reflect all the all the radi you heat
+ 
+
+ align:start position:0%
+reflect all the all the radi you heat
+sure so the thermal couple won't see it
+
+ align:start position:0%
+sure so the thermal couple won't see it
+ 
+
+ align:start position:0%
+sure so the thermal couple won't see it
+so another way to do that is to just
+
+ align:start position:0%
+so another way to do that is to just
+ 
+
+ align:start position:0%
+so another way to do that is to just
+grab half or a third of the barrel
+
+ align:start position:0%
+grab half or a third of the barrel
+ 
+
+ align:start position:0%
+grab half or a third of the barrel
+vertically in tin foil and use some sort
+
+ align:start position:0%
+vertically in tin foil and use some sort
+ 
+
+ align:start position:0%
+vertically in tin foil and use some sort
+of uh metallic wire to strap the tin tin
+
+ align:start position:0%
+of uh metallic wire to strap the tin tin
+ 
+
+ align:start position:0%
+of uh metallic wire to strap the tin tin
+foil with like one3 of the barrel or
+
+ align:start position:0%
+foil with like one3 of the barrel or
+ 
+
+ align:start position:0%
+foil with like one3 of the barrel or
+half the barrel and that will act as a
+
+ align:start position:0%
+half the barrel and that will act as a
+ 
+
+ align:start position:0%
+half the barrel and that will act as a
+huge radiation Shield so if you want to
+
+ align:start position:0%
+huge radiation Shield so if you want to
+ 
+
+ align:start position:0%
+huge radiation Shield so if you want to
+that would just tell you if you're if
+
+ align:start position:0%
+that would just tell you if you're if
+ 
+
+ align:start position:0%
+that would just tell you if you're if
+the heat is coming from hot air coming
+
+ align:start position:0%
+the heat is coming from hot air coming
+ 
+
+ align:start position:0%
+the heat is coming from hot air coming
+out from the bottom or from radiation
+
+ align:start position:0%
+out from the bottom or from radiation
+ 
+
+ align:start position:0%
+out from the bottom or from radiation
+off the barrel and then you would know
+
+ align:start position:0%
+off the barrel and then you would know
+ 
+
+ align:start position:0%
+off the barrel and then you would know
+actually what your problem is sure so
+
+ align:start position:0%
+actually what your problem is sure so
+ 
+
+ align:start position:0%
+actually what your problem is sure so
+that would be a good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+test any other comments especially on
+
+ align:start position:0%
+test any other comments especially on
+ 
+
+ align:start position:0%
+test any other comments especially on
+the sheet metal seal and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whatnot I just wouldn't Bank on the
+
+ align:start position:0%
+whatnot I just wouldn't Bank on the
+ 
+
+ align:start position:0%
+whatnot I just wouldn't Bank on the
+women being able to do a test early next
+
+ align:start position:0%
+women being able to do a test early next
+ 
+
+ align:start position:0%
+women being able to do a test early next
+week
+
+ align:start position:0%
+week
+ 
+
+ align:start position:0%
+week
+as part of your critical path sure
+
+ align:start position:0%
+as part of your critical path sure
+ 
+
+ align:start position:0%
+as part of your critical path sure
+Lindsay did already say that they wanted
+
+ align:start position:0%
+Lindsay did already say that they wanted
+ 
+
+ align:start position:0%
+Lindsay did already say that they wanted
+to do a burn that's why we are not
+
+ align:start position:0%
+to do a burn that's why we are not
+ 
+
+ align:start position:0%
+to do a burn that's why we are not
+counting on it but it can happen but
+
+ align:start position:0%
+counting on it but it can happen but
+ 
+
+ align:start position:0%
+counting on it but it can happen but
+yeah yeah absolutely but I think you
+
+ align:start position:0%
+yeah yeah absolutely but I think you
+ 
+
+ align:start position:0%
+yeah yeah absolutely but I think you
+should try to make that happen but also
+
+ align:start position:0%
+should try to make that happen but also
+ 
+
+ align:start position:0%
+should try to make that happen but also
+if it takes them a week to make it
+
+ align:start position:0%
+if it takes them a week to make it
+ 
+
+ align:start position:0%
+if it takes them a week to make it
+happen right be able to work with that
+
+ align:start position:0%
+happen right be able to work with that
+ 
+
+ align:start position:0%
+happen right be able to work with that
+too yeah one thing I noticed when you're
+
+ align:start position:0%
+too yeah one thing I noticed when you're
+ 
+
+ align:start position:0%
+too yeah one thing I noticed when you're
+showing the video of you sliding the
+
+ align:start position:0%
+showing the video of you sliding the
+ 
+
+ align:start position:0%
+showing the video of you sliding the
+covers on over next to presy it looked
+
+ align:start position:0%
+covers on over next to presy it looked
+ 
+
+ align:start position:0%
+covers on over next to presy it looked
+like it would be useful to have to have
+
+ align:start position:0%
+like it would be useful to have to have
+ 
+
+ align:start position:0%
+like it would be useful to have to have
+a way to pick up up the front of the
+
+ align:start position:0%
+a way to pick up up the front of the
+ 
+
+ align:start position:0%
+a way to pick up up the front of the
+shet with with a simple stick and so I
+
+ align:start position:0%
+shet with with a simple stick and so I
+ 
+
+ align:start position:0%
+shet with with a simple stick and so I
+think you could do that simply by
+
+ align:start position:0%
+think you could do that simply by
+ 
+
+ align:start position:0%
+think you could do that simply by
+putting sry putting another Block in the
+
+ align:start position:0%
+putting sry putting another Block in the
+ 
+
+ align:start position:0%
+putting sry putting another Block in the
+back so you had another lever point so
+
+ align:start position:0%
+back so you had another lever point so
+ 
+
+ align:start position:0%
+back so you had another lever point so
+you can push the stick in here and
+
+ align:start position:0%
+you can push the stick in here and
+ 
+
+ align:start position:0%
+you can push the stick in here and
+effectively pick it up like that to
+
+ align:start position:0%
+effectively pick it up like that to
+ 
+
+ align:start position:0%
+effectively pick it up like that to
+slide it over the brids because it looks
+
+ align:start position:0%
+slide it over the brids because it looks
+ 
+
+ align:start position:0%
+slide it over the brids because it looks
+yeah t SL the gr it's a good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea that would need to be as far back
+
+ align:start position:0%
+idea that would need to be as far back
+ 
+
+ align:start position:0%
+idea that would need to be as far back
+towards the back Edge yeah one of our
+
+ align:start position:0%
+towards the back Edge yeah one of our
+ 
+
+ align:start position:0%
+towards the back Edge yeah one of our
+designs actually after this experiment
+
+ align:start position:0%
+designs actually after this experiment
+ 
+
+ align:start position:0%
+designs actually after this experiment
+was um to sort of like make a a hole
+
+ align:start position:0%
+was um to sort of like make a a hole
+ 
+
+ align:start position:0%
+was um to sort of like make a a hole
+insert where you could put in the the
+
+ align:start position:0%
+insert where you could put in the the
+ 
+
+ align:start position:0%
+insert where you could put in the the
+hole the wood but it was mostly for like
+
+ align:start position:0%
+hole the wood but it was mostly for like
+ 
+
+ align:start position:0%
+hole the wood but it was mostly for like
+more yeah and then on the flip side
+
+ align:start position:0%
+more yeah and then on the flip side
+ 
+
+ align:start position:0%
+more yeah and then on the flip side
+Trying to minimize how much metal is
+
+ align:start position:0%
+Trying to minimize how much metal is
+ 
+
+ align:start position:0%
+Trying to minimize how much metal is
+used is also important because it's
+
+ align:start position:0%
+used is also important because it's
+ 
+
+ align:start position:0%
+used is also important because it's
+expensive so in the design that Jessica
+
+ align:start position:0%
+expensive so in the design that Jessica
+ 
+
+ align:start position:0%
+expensive so in the design that Jessica
+just referenced uh you take your sheet
+
+ align:start position:0%
+just referenced uh you take your sheet
+ 
+
+ align:start position:0%
+just referenced uh you take your sheet
+and it would have to be thinner than
+
+ align:start position:0%
+and it would have to be thinner than
+ 
+
+ align:start position:0%
+and it would have to be thinner than
+this and then you could cut it like here
+
+ align:start position:0%
+this and then you could cut it like here
+ 
+
+ align:start position:0%
+this and then you could cut it like here
+and then there and leave a certain point
+
+ align:start position:0%
+and then there and leave a certain point
+ 
+
+ align:start position:0%
+and then there and leave a certain point
+there and just bend those two um edges
+
+ align:start position:0%
+there and just bend those two um edges
+ 
+
+ align:start position:0%
+there and just bend those two um edges
+together and just them once yeah and but
+
+ align:start position:0%
+together and just them once yeah and but
+ 
+
+ align:start position:0%
+together and just them once yeah and but
+and I also wonder like if the bricks are
+
+ align:start position:0%
+and I also wonder like if the bricks are
+ 
+
+ align:start position:0%
+and I also wonder like if the bricks are
+decently sealed against the um grass if
+
+ align:start position:0%
+decently sealed against the um grass if
+ 
+
+ align:start position:0%
+decently sealed against the um grass if
+you could make your devices
+
+ align:start position:0%
+you could make your devices
+ 
+
+ align:start position:0%
+you could make your devices
+significantly smaller to just cover the
+
+ align:start position:0%
+significantly smaller to just cover the
+ 
+
+ align:start position:0%
+significantly smaller to just cover the
+hole and not the whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+area you sand the way
+
+ align:start position:0%
+area you sand the way
+ 
+
+ align:start position:0%
+area you sand the way
+around uh yeah
+
+ align:start position:0%
+around uh yeah
+ 
+
+ align:start position:0%
+around uh yeah
+yeah so I can't forward to it
+
+ align:start position:0%
+yeah so I can't forward to it
+ 
+
+ align:start position:0%
+yeah so I can't forward to it
+but if you if you exit at a PowerPoint
+
+ align:start position:0%
+but if you if you exit at a PowerPoint
+ 
+
+ align:start position:0%
+but if you if you exit at a PowerPoint
+you might be able to load it in quick
+
+ align:start position:0%
+you might be able to load it in quick
+ 
+
+ align:start position:0%
+you might be able to load it in quick
+time or whatever
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+too yeah it's it's totally like you
+
+ align:start position:0%
+too yeah it's it's totally like you
+ 
+
+ align:start position:0%
+too yeah it's it's totally like you
+don't want to be rocking the barrel but
+
+ align:start position:0%
+don't want to be rocking the barrel but
+ 
+
+ align:start position:0%
+don't want to be rocking the barrel but
+we don't we don't like they they did a
+
+ align:start position:0%
+we don't we don't like they they did a
+ 
+
+ align:start position:0%
+we don't we don't like they they did a
+different order than we do in the video
+
+ align:start position:0%
+different order than we do in the video
+ 
+
+ align:start position:0%
+different order than we do in the video
+so we normally just put the lid on top
+
+ align:start position:0%
+so we normally just put the lid on top
+ 
+
+ align:start position:0%
+so we normally just put the lid on top
+but then we drop it down before we put
+
+ align:start position:0%
+but then we drop it down before we put
+ 
+
+ align:start position:0%
+but then we drop it down before we put
+the sand so you don't have sand falling
+
+ align:start position:0%
+the sand so you don't have sand falling
+ 
+
+ align:start position:0%
+the sand so you don't have sand falling
+off when you're rocking it um so you
+
+ align:start position:0%
+off when you're rocking it um so you
+ 
+
+ align:start position:0%
+off when you're rocking it um so you
+don't you think I that's why I said like
+
+ align:start position:0%
+don't you think I that's why I said like
+ 
+
+ align:start position:0%
+don't you think I that's why I said like
+they should try it cuz you don't have to
+
+ align:start position:0%
+they should try it cuz you don't have to
+ 
+
+ align:start position:0%
+they should try it cuz you don't have to
+put the lid on top
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first what are you looking for just to
+
+ align:start position:0%
+first what are you looking for just to
+ 
+
+ align:start position:0%
+first what are you looking for just to
+show them oh the ceiling theiling yeah
+
+ align:start position:0%
+show them oh the ceiling theiling yeah
+ 
+
+ align:start position:0%
+show them oh the ceiling theiling yeah
+he asked for what the thing look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like and what happened here was that the
+
+ align:start position:0%
+like and what happened here was that the
+ 
+
+ align:start position:0%
+like and what happened here was that the
+grass um is a lot fluffier here than in
+
+ align:start position:0%
+grass um is a lot fluffier here than in
+ 
+
+ align:start position:0%
+grass um is a lot fluffier here than in
+Nicaragua like over there it's kind of
+
+ align:start position:0%
+Nicaragua like over there it's kind of
+ 
+
+ align:start position:0%
+Nicaragua like over there it's kind of
+burnt out kind of dry kind of just not
+
+ align:start position:0%
+burnt out kind of dry kind of just not
+ 
+
+ align:start position:0%
+burnt out kind of dry kind of just not
+that much grass um and so we know that
+
+ align:start position:0%
+that much grass um and so we know that
+ 
+
+ align:start position:0%
+that much grass um and so we know that
+like there won't be that much like air
+
+ align:start position:0%
+like there won't be that much like air
+ 
+
+ align:start position:0%
+like there won't be that much like air
+holes through the grass that we'll have
+
+ align:start position:0%
+holes through the grass that we'll have
+ 
+
+ align:start position:0%
+holes through the grass that we'll have
+to seal stand all the way around
+
+ align:start position:0%
+to seal stand all the way around
+ 
+
+ align:start position:0%
+to seal stand all the way around
+excessively like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that any other questions or thoughts
+
+ align:start position:0%
+that any other questions or thoughts
+ 
+
+ align:start position:0%
+that any other questions or thoughts
+or how much harder
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is uh we didn't think it was really a
+
+ align:start position:0%
+is uh we didn't think it was really a
+ 
+
+ align:start position:0%
+is uh we didn't think it was really a
+problem um in our experimentation it
+
+ align:start position:0%
+problem um in our experimentation it
+ 
+
+ align:start position:0%
+problem um in our experimentation it
+didn't like you can still have uh like
+
+ align:start position:0%
+didn't like you can still have uh like
+ 
+
+ align:start position:0%
+didn't like you can still have uh like
+strands of the biomass come out through
+
+ align:start position:0%
+strands of the biomass come out through
+ 
+
+ align:start position:0%
+strands of the biomass come out through
+through the channels and then just light
+
+ align:start position:0%
+through the channels and then just light
+ 
+
+ align:start position:0%
+through the channels and then just light
+them right there and in fact it may even
+
+ align:start position:0%
+them right there and in fact it may even
+ 
+
+ align:start position:0%
+them right there and in fact it may even
+be easier because there's no wind
+
+ align:start position:0%
+be easier because there's no wind
+ 
+
+ align:start position:0%
+be easier because there's no wind
+passing through um so it wasn't didn't
+
+ align:start position:0%
+passing through um so it wasn't didn't
+ 
+
+ align:start position:0%
+passing through um so it wasn't didn't
+take us that
+
+ align:start position:0%
+take us that
+ 
+
+ align:start position:0%
+take us that
+long it's probably either the same or
+
+ align:start position:0%
+long it's probably either the same or
+ 
+
+ align:start position:0%
+long it's probably either the same or
+easier than the current method on Ono's
+
+ align:start position:0%
+easier than the current method on Ono's
+ 
+
+ align:start position:0%
+easier than the current method on Ono's
+clock it was 14 seconds which is more or
+
+ align:start position:0%
+clock it was 14 seconds which is more or
+ 
+
+ align:start position:0%
+clock it was 14 seconds which is more or
+less what it took us with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other great thank you thanks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so hello everyone we're group of Phoenix
+
+ align:start position:0%
+so hello everyone we're group of Phoenix
+ 
+
+ align:start position:0%
+so hello everyone we're group of Phoenix
+well we're the other part of group of
+
+ align:start position:0%
+well we're the other part of group of
+ 
+
+ align:start position:0%
+well we're the other part of group of
+Phoenix we all travel together we
+
+ align:start position:0%
+Phoenix we all travel together we
+ 
+
+ align:start position:0%
+Phoenix we all travel together we
+sprinted two projects um I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Juan we're pretty
+
+ align:start position:0%
+Juan we're pretty
+ 
+
+ align:start position:0%
+Juan we're pretty
+awesome have electricity too um cool so
+
+ align:start position:0%
+awesome have electricity too um cool so
+ 
+
+ align:start position:0%
+awesome have electricity too um cool so
+I'm Juan I'm Liz I'm Sid
+
+ align:start position:0%
+I'm Juan I'm Liz I'm Sid
+ 
+
+ align:start position:0%
+I'm Juan I'm Liz I'm Sid
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+our and our mentors are Amilia and Steve
+
+ align:start position:0%
+our and our mentors are Amilia and Steve
+ 
+
+ align:start position:0%
+our and our mentors are Amilia and Steve
+um so I just start with um currently
+
+ align:start position:0%
+um so I just start with um currently
+ 
+
+ align:start position:0%
+um so I just start with um currently
+we're working with uh the comparative in
+
+ align:start position:0%
+we're working with uh the comparative in
+ 
+
+ align:start position:0%
+we're working with uh the comparative in
+saana Grande that makes the they make
+
+ align:start position:0%
+saana Grande that makes the they make
+ 
+
+ align:start position:0%
+saana Grande that makes the they make
+solar cells they make solar panels and
+
+ align:start position:0%
+solar cells they make solar panels and
+ 
+
+ align:start position:0%
+solar cells they make solar panels and
+forough they use it for home power and
+
+ align:start position:0%
+forough they use it for home power and
+ 
+
+ align:start position:0%
+forough they use it for home power and
+also for as individual cellone Chargers
+
+ align:start position:0%
+also for as individual cellone Chargers
+ 
+
+ align:start position:0%
+also for as individual cellone Chargers
+currently this is these are the large
+
+ align:start position:0%
+currently this is these are the large
+ 
+
+ align:start position:0%
+currently this is these are the large
+solar panels that they make they're 60
+
+ align:start position:0%
+solar panels that they make they're 60
+ 
+
+ align:start position:0%
+solar panels that they make they're 60
+watts um the you can see each solar cell
+
+ align:start position:0%
+watts um the you can see each solar cell
+ 
+
+ align:start position:0%
+watts um the you can see each solar cell
+is like is is donated and all the solar
+
+ align:start position:0%
+is like is is donated and all the solar
+ 
+
+ align:start position:0%
+is like is is donated and all the solar
+cells that are used AR donator and
+
+ align:start position:0%
+cells that are used AR donator and
+ 
+
+ align:start position:0%
+cells that are used AR donator and
+they're about about 500 cells per box
+
+ align:start position:0%
+they're about about 500 cells per box
+ 
+
+ align:start position:0%
+they're about about 500 cells per box
+well they do have to be bought though
+
+ align:start position:0%
+well they do have to be bought though
+ 
+
+ align:start position:0%
+well they do have to be bought though
+they're about a do oh sorry they're buy
+
+ align:start position:0%
+they're about a do oh sorry they're buy
+ 
+
+ align:start position:0%
+they're about a do oh sorry they're buy
+but they're bought for aot for a lower
+
+ align:start position:0%
+but they're bought for aot for a lower
+ 
+
+ align:start position:0%
+but they're bought for aot for a lower
+price because they're um rejects they're
+
+ align:start position:0%
+price because they're um rejects they're
+ 
+
+ align:start position:0%
+price because they're um rejects they're
+rejects from the factory here in the
+
+ align:start position:0%
+rejects from the factory here in the
+ 
+
+ align:start position:0%
+rejects from the factory here in the
+US the problem is that they're really
+
+ align:start position:0%
+US the problem is that they're really
+ 
+
+ align:start position:0%
+US the problem is that they're really
+fragile and a lot of them break on the
+
+ align:start position:0%
+fragile and a lot of them break on the
+ 
+
+ align:start position:0%
+fragile and a lot of them break on the
+shipping there and so right now they're
+
+ align:start position:0%
+shipping there and so right now they're
+ 
+
+ align:start position:0%
+shipping there and so right now they're
+also making um sorry so right now
+
+ align:start position:0%
+also making um sorry so right now
+ 
+
+ align:start position:0%
+also making um sorry so right now
+they're also making solar cell phone
+
+ align:start position:0%
+they're also making solar cell phone
+ 
+
+ align:start position:0%
+they're also making solar cell phone
+chargers but to make the solar cell
+
+ align:start position:0%
+chargers but to make the solar cell
+ 
+
+ align:start position:0%
+chargers but to make the solar cell
+phone charg
+
+ align:start position:0%
+phone charg
+ 
+
+ align:start position:0%
+phone charg
+they need to cut each individual cell so
+
+ align:start position:0%
+they need to cut each individual cell so
+ 
+
+ align:start position:0%
+they need to cut each individual cell so
+they can get a really high so they can
+
+ align:start position:0%
+they can get a really high so they can
+ 
+
+ align:start position:0%
+they can get a really high so they can
+get a high enough voltage but still have
+
+ align:start position:0%
+get a high enough voltage but still have
+ 
+
+ align:start position:0%
+get a high enough voltage but still have
+a small enough solar panel that it's uh
+
+ align:start position:0%
+a small enough solar panel that it's uh
+ 
+
+ align:start position:0%
+a small enough solar panel that it's uh
+transportable
+
+ align:start position:0%
+transportable
+ 
+
+ align:start position:0%
+transportable
+um yeah so this is just oh well this a
+
+ align:start position:0%
+um yeah so this is just oh well this a
+ 
+
+ align:start position:0%
+um yeah so this is just oh well this a
+landscape of the the place where we are
+
+ align:start position:0%
+landscape of the the place where we are
+ 
+
+ align:start position:0%
+landscape of the the place where we are
+we can see there is no Grid in a lot of
+
+ align:start position:0%
+we can see there is no Grid in a lot of
+ 
+
+ align:start position:0%
+we can see there is no Grid in a lot of
+the houses but a lot of people still
+
+ align:start position:0%
+the houses but a lot of people still
+ 
+
+ align:start position:0%
+the houses but a lot of people still
+have cell phones and so some of them
+
+ align:start position:0%
+have cell phones and so some of them
+ 
+
+ align:start position:0%
+have cell phones and so some of them
+have to walk up to two or 3 km to charge
+
+ align:start position:0%
+have to walk up to two or 3 km to charge
+ 
+
+ align:start position:0%
+have to walk up to two or 3 km to charge
+of cell phones and they pay 10 C which
+
+ align:start position:0%
+of cell phones and they pay 10 C which
+ 
+
+ align:start position:0%
+of cell phones and they pay 10 C which
+is about 50 cents per charge
+
+ align:start position:0%
+is about 50 cents per charge
+ 
+
+ align:start position:0%
+is about 50 cents per charge
+um so that is where that is how we want
+
+ align:start position:0%
+um so that is where that is how we want
+ 
+
+ align:start position:0%
+um so that is where that is how we want
+to I guess help the project this is an
+
+ align:start position:0%
+to I guess help the project this is an
+ 
+
+ align:start position:0%
+to I guess help the project this is an
+example of a Chinese made self charger
+
+ align:start position:0%
+example of a Chinese made self charger
+ 
+
+ align:start position:0%
+example of a Chinese made self charger
+that they they have used um as you can
+
+ align:start position:0%
+that they they have used um as you can
+ 
+
+ align:start position:0%
+that they they have used um as you can
+see it it charges and it comes with um
+
+ align:start position:0%
+see it it charges and it comes with um
+ 
+
+ align:start position:0%
+see it it charges and it comes with um
+an extra battery and it charges the
+
+ align:start position:0%
+an extra battery and it charges the
+ 
+
+ align:start position:0%
+an extra battery and it charges the
+extra battery in that device but this
+
+ align:start position:0%
+extra battery in that device but this
+ 
+
+ align:start position:0%
+extra battery in that device but this
+only fits uh one it only fits Nokia cell
+
+ align:start position:0%
+only fits uh one it only fits Nokia cell
+ 
+
+ align:start position:0%
+only fits uh one it only fits Nokia cell
+phones and two is just imported so this
+
+ align:start position:0%
+phones and two is just imported so this
+ 
+
+ align:start position:0%
+phones and two is just imported so this
+is not we don't think it's really
+
+ align:start position:0%
+is not we don't think it's really
+ 
+
+ align:start position:0%
+is not we don't think it's really
+helping the I just the the job market in
+
+ align:start position:0%
+helping the I just the the job market in
+ 
+
+ align:start position:0%
+helping the I just the the job market in
+the area
+
+ align:start position:0%
+the area
+ 
+
+ align:start position:0%
+the area
+it cost $20 oh it also costs $20 so so
+
+ align:start position:0%
+it cost $20 oh it also costs $20 so so
+ 
+
+ align:start position:0%
+it cost $20 oh it also costs $20 so so
+our goal is to make so this is why I
+
+ align:start position:0%
+our goal is to make so this is why I
+ 
+
+ align:start position:0%
+our goal is to make so this is why I
+guess we're this is why we want to make
+
+ align:start position:0%
+guess we're this is why we want to make
+ 
+
+ align:start position:0%
+guess we're this is why we want to make
+a cell phone charger so we want to make
+
+ align:start position:0%
+a cell phone charger so we want to make
+ 
+
+ align:start position:0%
+a cell phone charger so we want to make
+one that is um can hopefully compete
+
+ align:start position:0%
+one that is um can hopefully compete
+ 
+
+ align:start position:0%
+one that is um can hopefully compete
+with this um not obviously like initial
+
+ align:start position:0%
+with this um not obviously like initial
+ 
+
+ align:start position:0%
+with this um not obviously like initial
+manufacturing cost but at least in like
+
+ align:start position:0%
+manufacturing cost but at least in like
+ 
+
+ align:start position:0%
+manufacturing cost but at least in like
+end cost to their own manufacturing cost
+
+ align:start position:0%
+end cost to their own manufacturing cost
+ 
+
+ align:start position:0%
+end cost to their own manufacturing cost
+can reduce their time currently it takes
+
+ align:start position:0%
+can reduce their time currently it takes
+ 
+
+ align:start position:0%
+can reduce their time currently it takes
+them 24 hours to make uh the small cell
+
+ align:start position:0%
+them 24 hours to make uh the small cell
+ 
+
+ align:start position:0%
+them 24 hours to make uh the small cell
+phone
+
+ align:start position:0%
+phone
+ 
+
+ align:start position:0%
+phone
+chargers and it can
+
+ align:start position:0%
+chargers and it can
+ 
+
+ align:start position:0%
+chargers and it can
+also um so time and it can also be trans
+
+ align:start position:0%
+also um so time and it can also be trans
+ 
+
+ align:start position:0%
+also um so time and it can also be trans
+portable
+
+ align:start position:0%
+portable
+ 
+
+ align:start position:0%
+portable
+and charge their cell phones and charge
+
+ align:start position:0%
+and charge their cell phones and charge
+ 
+
+ align:start position:0%
+and charge their cell phones and charge
+all the different types of cell phones
+
+ align:start position:0%
+all the different types of cell phones
+ 
+
+ align:start position:0%
+all the different types of cell phones
+that they
+
+ align:start position:0%
+that they
+ 
+
+ align:start position:0%
+that they
+have okay so um as Quan said uh
+
+ align:start position:0%
+have okay so um as Quan said uh
+ 
+
+ align:start position:0%
+have okay so um as Quan said uh
+basically uh the solar cells uh output
+
+ align:start position:0%
+basically uh the solar cells uh output
+ 
+
+ align:start position:0%
+basically uh the solar cells uh output
+.5 volts each and this is your original
+
+ align:start position:0%
+.5 volts each and this is your original
+ 
+
+ align:start position:0%
+.5 volts each and this is your original
+cell uh the way they do it right now is
+
+ align:start position:0%
+cell uh the way they do it right now is
+ 
+
+ align:start position:0%
+cell uh the way they do it right now is
+uh that they cut up these cells uh into
+
+ align:start position:0%
+uh that they cut up these cells uh into
+ 
+
+ align:start position:0%
+uh that they cut up these cells uh into
+four parts across like that and then
+
+ align:start position:0%
+four parts across like that and then
+ 
+
+ align:start position:0%
+four parts across like that and then
+connect them in series so you can step
+
+ align:start position:0%
+connect them in series so you can step
+ 
+
+ align:start position:0%
+connect them in series so you can step
+up your voltage uh unfortunately what
+
+ align:start position:0%
+up your voltage uh unfortunately what
+ 
+
+ align:start position:0%
+up your voltage uh unfortunately what
+ends up happening is when you're cutting
+
+ align:start position:0%
+ends up happening is when you're cutting
+ 
+
+ align:start position:0%
+ends up happening is when you're cutting
+these cells as one mentioned they're
+
+ align:start position:0%
+these cells as one mentioned they're
+ 
+
+ align:start position:0%
+these cells as one mentioned they're
+very fragile so you end up wasting a lot
+
+ align:start position:0%
+very fragile so you end up wasting a lot
+ 
+
+ align:start position:0%
+very fragile so you end up wasting a lot
+of your cells and that actually is the
+
+ align:start position:0%
+of your cells and that actually is the
+ 
+
+ align:start position:0%
+of your cells and that actually is the
+largest like they spend the most amount
+
+ align:start position:0%
+largest like they spend the most amount
+ 
+
+ align:start position:0%
+largest like they spend the most amount
+of their money uh in cutting the cells
+
+ align:start position:0%
+of their money uh in cutting the cells
+ 
+
+ align:start position:0%
+of their money uh in cutting the cells
+and then using the silicone but we'll
+
+ align:start position:0%
+and then using the silicone but we'll
+ 
+
+ align:start position:0%
+and then using the silicone but we'll
+get into that later um so we decided
+
+ align:start position:0%
+get into that later um so we decided
+ 
+
+ align:start position:0%
+get into that later um so we decided
+that it would be helpful if they could
+
+ align:start position:0%
+that it would be helpful if they could
+ 
+
+ align:start position:0%
+that it would be helpful if they could
+just use the original cells instead of
+
+ align:start position:0%
+just use the original cells instead of
+ 
+
+ align:start position:0%
+just use the original cells instead of
+cutting them and so we thought that if
+
+ align:start position:0%
+cutting them and so we thought that if
+ 
+
+ align:start position:0%
+cutting them and so we thought that if
+they just connected three of these cells
+
+ align:start position:0%
+they just connected three of these cells
+ 
+
+ align:start position:0%
+they just connected three of these cells
+in series you could go up to 1.5 volts
+
+ align:start position:0%
+in series you could go up to 1.5 volts
+ 
+
+ align:start position:0%
+in series you could go up to 1.5 volts
+which is about like a normal pencil cell
+
+ align:start position:0%
+which is about like a normal pencil cell
+ 
+
+ align:start position:0%
+which is about like a normal pencil cell
+and then we thought we would just step
+
+ align:start position:0%
+and then we thought we would just step
+ 
+
+ align:start position:0%
+and then we thought we would just step
+up that voltage to 5 Vols which is what
+
+ align:start position:0%
+up that voltage to 5 Vols which is what
+ 
+
+ align:start position:0%
+up that voltage to 5 Vols which is what
+a cell phone charger uses um to do that
+
+ align:start position:0%
+a cell phone charger uses um to do that
+ 
+
+ align:start position:0%
+a cell phone charger uses um to do that
+we bought so this is the circuitry that
+
+ align:start position:0%
+we bought so this is the circuitry that
+ 
+
+ align:start position:0%
+we bought so this is the circuitry that
+we're using
+
+ align:start position:0%
+we're using
+ 
+
+ align:start position:0%
+we're using
+um so essentially like a lot of I mean
+
+ align:start position:0%
+um so essentially like a lot of I mean
+ 
+
+ align:start position:0%
+um so essentially like a lot of I mean
+we couldn't actually make the step up uh
+
+ align:start position:0%
+we couldn't actually make the step up uh
+ 
+
+ align:start position:0%
+we couldn't actually make the step up uh
+we tried but we failed uh so we decided
+
+ align:start position:0%
+we tried but we failed uh so we decided
+ 
+
+ align:start position:0%
+we tried but we failed uh so we decided
+to just buy it like off the shelf and so
+
+ align:start position:0%
+to just buy it like off the shelf and so
+ 
+
+ align:start position:0%
+to just buy it like off the shelf and so
+this is how our RedBoard looks um
+
+ align:start position:0%
+this is how our RedBoard looks um
+ 
+
+ align:start position:0%
+this is how our RedBoard looks um
+essentially this would be our input
+
+ align:start position:0%
+essentially this would be our input
+ 
+
+ align:start position:0%
+essentially this would be our input
+right here uh and this would be 1.5 DC
+
+ align:start position:0%
+right here uh and this would be 1.5 DC
+ 
+
+ align:start position:0%
+right here uh and this would be 1.5 DC
+input and then you'd have a 5vt DC
+
+ align:start position:0%
+input and then you'd have a 5vt DC
+ 
+
+ align:start position:0%
+input and then you'd have a 5vt DC
+output coming in from here um and
+
+ align:start position:0%
+output coming in from here um and
+ 
+
+ align:start position:0%
+output coming in from here um and
+basically your solar cells would be
+
+ align:start position:0%
+basically your solar cells would be
+ 
+
+ align:start position:0%
+basically your solar cells would be
+connected but so your solar cells are
+
+ align:start position:0%
+connected but so your solar cells are
+ 
+
+ align:start position:0%
+connected but so your solar cells are
+here this little thing fits into this
+
+ align:start position:0%
+here this little thing fits into this
+ 
+
+ align:start position:0%
+here this little thing fits into this
+depression right here and then so your
+
+ align:start position:0%
+depression right here and then so your
+ 
+
+ align:start position:0%
+depression right here and then so your
+panels are connected in series you have
+
+ align:start position:0%
+panels are connected in series you have
+ 
+
+ align:start position:0%
+panels are connected in series you have
+two wires
+
+ align:start position:0%
+two wires
+ 
+
+ align:start position:0%
+two wires
+connecting to these
+
+ align:start position:0%
+connecting to these
+ 
+
+ align:start position:0%
+connecting to these
+terminals it steps up to 5 volts and
+
+ align:start position:0%
+terminals it steps up to 5 volts and
+ 
+
+ align:start position:0%
+terminals it steps up to 5 volts and
+goes out to connect to this thing
+
+ align:start position:0%
+goes out to connect to this thing
+ 
+
+ align:start position:0%
+goes out to connect to this thing
+this thing then goes into your Nokia SL
+
+ align:start position:0%
+this thing then goes into your Nokia SL
+ 
+
+ align:start position:0%
+this thing then goes into your Nokia SL
+whatever phone you have and then charges
+
+ align:start position:0%
+whatever phone you have and then charges
+ 
+
+ align:start position:0%
+whatever phone you have and then charges
+to your phone um is the video next one
+
+ align:start position:0%
+to your phone um is the video next one
+ 
+
+ align:start position:0%
+to your phone um is the video next one
+uh make sure my volume's on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now yeah so we kind of like made a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+video okay so we're switching on the
+
+ align:start position:0%
+video okay so we're switching on the
+ 
+
+ align:start position:0%
+video okay so we're switching on the
+light so so three cells right
+
+ align:start position:0%
+light so so three cells right
+ 
+
+ align:start position:0%
+light so so three cells right
+here and now we're going to measure the
+
+ align:start position:0%
+here and now we're going to measure the
+ 
+
+ align:start position:0%
+here and now we're going to measure the
+voltage out by the solar
+
+ align:start position:0%
+voltage out by the solar
+ 
+
+ align:start position:0%
+voltage out by the solar
+cells it's 1.6 volts that's
+
+ align:start position:0%
+cells it's 1.6 volts that's
+ 
+
+ align:start position:0%
+cells it's 1.6 volts that's
+good now going to measure the voltage I
+
+ align:start position:0%
+good now going to measure the voltage I
+ 
+
+ align:start position:0%
+good now going to measure the voltage I
+put it after we step
+
+ align:start position:0%
+put it after we step
+ 
+
+ align:start position:0%
+put it after we step
+up can you guys hear that at all or is
+
+ align:start position:0%
+up can you guys hear that at all or is
+ 
+
+ align:start position:0%
+up can you guys hear that at all or is
+it that's
+
+ align:start position:0%
+it that's
+ 
+
+ align:start position:0%
+it that's
+good now one's going to plug in the cell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phone okay and it says charging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3.8 which is the voltage across the
+
+ align:start position:0%
+3.8 which is the voltage across the
+ 
+
+ align:start position:0%
+3.8 which is the voltage across the
+battery so it makes sense that when it's
+
+ align:start position:0%
+battery so it makes sense that when it's
+ 
+
+ align:start position:0%
+battery so it makes sense that when it's
+plugged in it's 3.8 volts instead of
+
+ align:start position:0%
+plugged in it's 3.8 volts instead of
+ 
+
+ align:start position:0%
+plugged in it's 3.8 volts instead of
+five and yeah so that's basically like
+
+ align:start position:0%
+five and yeah so that's basically like
+ 
+
+ align:start position:0%
+five and yeah so that's basically like
+the works like um yeah I think that's
+
+ align:start position:0%
+the works like um yeah I think that's
+ 
+
+ align:start position:0%
+the works like um yeah I think that's
+pretty much looks like yeah and then
+
+ align:start position:0%
+pretty much looks like yeah and then
+ 
+
+ align:start position:0%
+pretty much looks like yeah and then
+we've also been talking to the community
+
+ align:start position:0%
+we've also been talking to the community
+ 
+
+ align:start position:0%
+we've also been talking to the community
+on Fir we're hoping we can talk to them
+
+ align:start position:0%
+on Fir we're hoping we can talk to them
+ 
+
+ align:start position:0%
+on Fir we're hoping we can talk to them
+on the phone soon this week they haven't
+
+ align:start position:0%
+on the phone soon this week they haven't
+ 
+
+ align:start position:0%
+on the phone soon this week they haven't
+really been in contact cuz it's Holy
+
+ align:start position:0%
+really been in contact cuz it's Holy
+ 
+
+ align:start position:0%
+really been in contact cuz it's Holy
+Week um but we sent them this in Spanish
+
+ align:start position:0%
+Week um but we sent them this in Spanish
+ 
+
+ align:start position:0%
+Week um but we sent them this in Spanish
+and some other instructions about kind
+
+ align:start position:0%
+and some other instructions about kind
+ 
+
+ align:start position:0%
+and some other instructions about kind
+of what we've been working on so we can
+
+ align:start position:0%
+of what we've been working on so we can
+ 
+
+ align:start position:0%
+of what we've been working on so we can
+hope to get their feedback um we like
+
+ align:start position:0%
+hope to get their feedback um we like
+ 
+
+ align:start position:0%
+hope to get their feedback um we like
+this is our kind of looks like model you
+
+ align:start position:0%
+this is our kind of looks like model you
+ 
+
+ align:start position:0%
+this is our kind of looks like model you
+saw housed kind of can put the stuff
+
+ align:start position:0%
+saw housed kind of can put the stuff
+ 
+
+ align:start position:0%
+saw housed kind of can put the stuff
+into this indentation here um so that
+
+ align:start position:0%
+into this indentation here um so that
+ 
+
+ align:start position:0%
+into this indentation here um so that
+when it's not in use or when it's you
+
+ align:start position:0%
+when it's not in use or when it's you
+ 
+
+ align:start position:0%
+when it's not in use or when it's you
+know noon it can be completely flat this
+
+ align:start position:0%
+know noon it can be completely flat this
+ 
+
+ align:start position:0%
+know noon it can be completely flat this
+also protects all of the um the
+
+ align:start position:0%
+also protects all of the um the
+ 
+
+ align:start position:0%
+also protects all of the um the
+circuitry from the uh like rain and that
+
+ align:start position:0%
+circuitry from the uh like rain and that
+ 
+
+ align:start position:0%
+circuitry from the uh like rain and that
+kind of thing um there could be notches
+
+ align:start position:0%
+kind of thing um there could be notches
+ 
+
+ align:start position:0%
+kind of thing um there could be notches
+added to the sides so that for instance
+
+ align:start position:0%
+added to the sides so that for instance
+ 
+
+ align:start position:0%
+added to the sides so that for instance
+you could make it lower by you know
+
+ align:start position:0%
+you could make it lower by you know
+ 
+
+ align:start position:0%
+you could make it lower by you know
+lowering these and it could be like that
+
+ align:start position:0%
+lowering these and it could be like that
+ 
+
+ align:start position:0%
+lowering these and it could be like that
+and stay still um and it's also just
+
+ align:start position:0%
+and stay still um and it's also just
+ 
+
+ align:start position:0%
+and stay still um and it's also just
+something they can really simply make
+
+ align:start position:0%
+something they can really simply make
+ 
+
+ align:start position:0%
+something they can really simply make
+they also make other things with wood in
+
+ align:start position:0%
+they also make other things with wood in
+ 
+
+ align:start position:0%
+they also make other things with wood in
+the same Center so they have all the
+
+ align:start position:0%
+the same Center so they have all the
+ 
+
+ align:start position:0%
+the same Center so they have all the
+materials um it's pretty low cost and
+
+ align:start position:0%
+materials um it's pretty low cost and
+ 
+
+ align:start position:0%
+materials um it's pretty low cost and
+you can add you know we have a hole here
+
+ align:start position:0%
+you can add you know we have a hole here
+ 
+
+ align:start position:0%
+you can add you know we have a hole here
+for security you can see in the picture
+
+ align:start position:0%
+for security you can see in the picture
+ 
+
+ align:start position:0%
+for security you can see in the picture
+um so that if they want to kind of like
+
+ align:start position:0%
+um so that if they want to kind of like
+ 
+
+ align:start position:0%
+um so that if they want to kind of like
+tie it up and lock it to something while
+
+ align:start position:0%
+tie it up and lock it to something while
+ 
+
+ align:start position:0%
+tie it up and lock it to something while
+it's charging they can do that um it's
+
+ align:start position:0%
+it's charging they can do that um it's
+ 
+
+ align:start position:0%
+it's charging they can do that um it's
+pretty portable but it's also like not
+
+ align:start position:0%
+pretty portable but it's also like not
+ 
+
+ align:start position:0%
+pretty portable but it's also like not
+so small this when just stick it in our
+
+ align:start position:0%
+so small this when just stick it in our
+ 
+
+ align:start position:0%
+so small this when just stick it in our
+pocket and run away with
+
+ align:start position:0%
+pocket and run away with
+ 
+
+ align:start position:0%
+pocket and run away with
+it um it's adjustable and just easy for
+
+ align:start position:0%
+it um it's adjustable and just easy for
+ 
+
+ align:start position:0%
+it um it's adjustable and just easy for
+them to make so we're hoping that they
+
+ align:start position:0%
+them to make so we're hoping that they
+ 
+
+ align:start position:0%
+them to make so we're hoping that they
+like it they can easily change the looks
+
+ align:start position:0%
+like it they can easily change the looks
+ 
+
+ align:start position:0%
+like it they can easily change the looks
+like design as well um most of how we're
+
+ align:start position:0%
+like design as well um most of how we're
+ 
+
+ align:start position:0%
+like design as well um most of how we're
+trying to help them is the act like cuz
+
+ align:start position:0%
+trying to help them is the act like cuz
+ 
+
+ align:start position:0%
+trying to help them is the act like cuz
+they're pretty capable of coming up with
+
+ align:start position:0%
+they're pretty capable of coming up with
+ 
+
+ align:start position:0%
+they're pretty capable of coming up with
+things like this themselves but this is
+
+ align:start position:0%
+things like this themselves but this is
+ 
+
+ align:start position:0%
+things like this themselves but this is
+just kind of a
+
+ align:start position:0%
+just kind of a
+ 
+
+ align:start position:0%
+just kind of a
+suggestion um we've also been talking
+
+ align:start position:0%
+suggestion um we've also been talking
+ 
+
+ align:start position:0%
+suggestion um we've also been talking
+with some other people who are working
+
+ align:start position:0%
+with some other people who are working
+ 
+
+ align:start position:0%
+with some other people who are working
+on the other aspects of the solar panels
+
+ align:start position:0%
+on the other aspects of the solar panels
+ 
+
+ align:start position:0%
+on the other aspects of the solar panels
+like the like trying to make the uh
+
+ align:start position:0%
+like the like trying to make the uh
+ 
+
+ align:start position:0%
+like the like trying to make the uh
+application of the glass on top easier
+
+ align:start position:0%
+application of the glass on top easier
+ 
+
+ align:start position:0%
+application of the glass on top easier
+and things like that so other people
+
+ align:start position:0%
+and things like that so other people
+ 
+
+ align:start position:0%
+and things like that so other people
+have that part covered so we're focusing
+
+ align:start position:0%
+have that part covered so we're focusing
+ 
+
+ align:start position:0%
+have that part covered so we're focusing
+a lot on just making it actually be able
+
+ align:start position:0%
+a lot on just making it actually be able
+ 
+
+ align:start position:0%
+a lot on just making it actually be able
+to charge a cell phone
+
+ align:start position:0%
+to charge a cell phone
+ 
+
+ align:start position:0%
+to charge a cell phone
+and what we're looking to do next is um
+
+ align:start position:0%
+and what we're looking to do next is um
+ 
+
+ align:start position:0%
+and what we're looking to do next is um
+like right now it's on the breadboard
+
+ align:start position:0%
+like right now it's on the breadboard
+ 
+
+ align:start position:0%
+like right now it's on the breadboard
+and it's definitely like if you handed
+
+ align:start position:0%
+and it's definitely like if you handed
+ 
+
+ align:start position:0%
+and it's definitely like if you handed
+this to a customer and we're like don't
+
+ align:start position:0%
+this to a customer and we're like don't
+ 
+
+ align:start position:0%
+this to a customer and we're like don't
+break it like something's going to come
+
+ align:start position:0%
+break it like something's going to come
+ 
+
+ align:start position:0%
+break it like something's going to come
+out and then they won't know what to do
+
+ align:start position:0%
+out and then they won't know what to do
+ 
+
+ align:start position:0%
+out and then they won't know what to do
+with it so we have to make it more kind
+
+ align:start position:0%
+with it so we have to make it more kind
+ 
+
+ align:start position:0%
+with it so we have to make it more kind
+of uh able to be actually give to
+
+ align:start position:0%
+of uh able to be actually give to
+ 
+
+ align:start position:0%
+of uh able to be actually give to
+somebody and not break uh so more
+
+ align:start position:0%
+somebody and not break uh so more
+ 
+
+ align:start position:0%
+somebody and not break uh so more
+durable I guess uh we need to be able to
+
+ align:start position:0%
+durable I guess uh we need to be able to
+ 
+
+ align:start position:0%
+durable I guess uh we need to be able to
+make it easy to explain so that because
+
+ align:start position:0%
+make it easy to explain so that because
+ 
+
+ align:start position:0%
+make it easy to explain so that because
+we might not have anybody down there
+
+ align:start position:0%
+we might not have anybody down there
+ 
+
+ align:start position:0%
+we might not have anybody down there
+showing them they they can still learn
+
+ align:start position:0%
+showing them they they can still learn
+ 
+
+ align:start position:0%
+showing them they they can still learn
+how to do it they have a mechanic uh I
+
+ align:start position:0%
+how to do it they have a mechanic uh I
+ 
+
+ align:start position:0%
+how to do it they have a mechanic uh I
+mean an an engineer who's been trained
+
+ align:start position:0%
+mean an an engineer who's been trained
+ 
+
+ align:start position:0%
+mean an an engineer who's been trained
+and should know how to put this together
+
+ align:start position:0%
+and should know how to put this together
+ 
+
+ align:start position:0%
+and should know how to put this together
+reasonably well and he's definitely
+
+ align:start position:0%
+reasonably well and he's definitely
+ 
+
+ align:start position:0%
+reasonably well and he's definitely
+better at soldering than we are so it
+
+ align:start position:0%
+better at soldering than we are so it
+ 
+
+ align:start position:0%
+better at soldering than we are so it
+should be
+
+ align:start position:0%
+should be
+ 
+
+ align:start position:0%
+should be
+doable thank you yeah and like to be
+
+ align:start position:0%
+doable thank you yeah and like to be
+ 
+
+ align:start position:0%
+doable thank you yeah and like to be
+clear like this is uh this is just a
+
+ align:start position:0%
+clear like this is uh this is just a
+ 
+
+ align:start position:0%
+clear like this is uh this is just a
+model of this is actually going to be a
+
+ align:start position:0%
+model of this is actually going to be a
+ 
+
+ align:start position:0%
+model of this is actually going to be a
+solar panel like this is not wood in
+
+ align:start position:0%
+solar panel like this is not wood in
+ 
+
+ align:start position:0%
+solar panel like this is not wood in
+case people were kind of confused this
+
+ align:start position:0%
+case people were kind of confused this
+ 
+
+ align:start position:0%
+case people were kind of confused this
+is this is the solar panel but since our
+
+ align:start position:0%
+is this is the solar panel but since our
+ 
+
+ align:start position:0%
+is this is the solar panel but since our
+project focuses on like converting the
+
+ align:start position:0%
+project focuses on like converting the
+ 
+
+ align:start position:0%
+project focuses on like converting the
+voltage to a cell phone charging voltage
+
+ align:start position:0%
+voltage to a cell phone charging voltage
+ 
+
+ align:start position:0%
+voltage to a cell phone charging voltage
+we decided to just like go with this
+
+ align:start position:0%
+we decided to just like go with this
+ 
+
+ align:start position:0%
+we decided to just like go with this
+just to show you guys how it's going to
+
+ align:start position:0%
+just to show you guys how it's going to
+ 
+
+ align:start position:0%
+just to show you guys how it's going to
+look uh when solar panel is in fact
+
+ align:start position:0%
+look uh when solar panel is in fact
+ 
+
+ align:start position:0%
+look uh when solar panel is in fact
+installed yeah pretty much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it uh
+
+ align:start position:0%
+it uh
+ 
+
+ align:start position:0%
+it uh
+three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah pretty much basic
+
+ align:start position:0%
+yeah yeah pretty much basic
+ 
+
+ align:start position:0%
+yeah yeah pretty much basic
+yeah what's the cost of your circuitry
+
+ align:start position:0%
+yeah what's the cost of your circuitry
+ 
+
+ align:start position:0%
+yeah what's the cost of your circuitry
+said um so so we estimate so like uh the
+
+ align:start position:0%
+said um so so we estimate so like uh the
+ 
+
+ align:start position:0%
+said um so so we estimate so like uh the
+right now we bought five of each if you
+
+ align:start position:0%
+right now we bought five of each if you
+ 
+
+ align:start position:0%
+right now we bought five of each if you
+buy like large scale uh like sorry like
+
+ align:start position:0%
+buy like large scale uh like sorry like
+ 
+
+ align:start position:0%
+buy like large scale uh like sorry like
+wholesale uh I think this I think this
+
+ align:start position:0%
+wholesale uh I think this I think this
+ 
+
+ align:start position:0%
+wholesale uh I think this I think this
+thing should cost about four dollar like
+
+ align:start position:0%
+thing should cost about four dollar like
+ 
+
+ align:start position:0%
+thing should cost about four dollar like
+this entire it cost us like6 this is
+
+ align:start position:0%
+this entire it cost us like6 this is
+ 
+
+ align:start position:0%
+this entire it cost us like6 this is
+about six for us but I think it should
+
+ align:start position:0%
+about six for us but I think it should
+ 
+
+ align:start position:0%
+about six for us but I think it should
+cost four uh and then so the connectors
+
+ align:start position:0%
+cost four uh and then so the connectors
+ 
+
+ align:start position:0%
+cost four uh and then so the connectors
+are actually more expensive um but
+
+ align:start position:0%
+are actually more expensive um but
+ 
+
+ align:start position:0%
+are actually more expensive um but
+that's because so there are two ways to
+
+ align:start position:0%
+that's because so there are two ways to
+ 
+
+ align:start position:0%
+that's because so there are two ways to
+do it either you buy the whole thing cut
+
+ align:start position:0%
+do it either you buy the whole thing cut
+ 
+
+ align:start position:0%
+do it either you buy the whole thing cut
+it off but that doesn't make any sense
+
+ align:start position:0%
+it off but that doesn't make any sense
+ 
+
+ align:start position:0%
+it off but that doesn't make any sense
+right so I lo when we looked it up
+
+ align:start position:0%
+right so I lo when we looked it up
+ 
+
+ align:start position:0%
+right so I lo when we looked it up
+online you can buy like about 10 of them
+
+ align:start position:0%
+online you can buy like about 10 of them
+ 
+
+ align:start position:0%
+online you can buy like about 10 of them
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+$7 um but they're probably cheaper ways
+
+ align:start position:0%
+$7 um but they're probably cheaper ways
+ 
+
+ align:start position:0%
+$7 um but they're probably cheaper ways
+to buy them uh maybe May if he contacted
+
+ align:start position:0%
+to buy them uh maybe May if he contacted
+ 
+
+ align:start position:0%
+to buy them uh maybe May if he contacted
+the company asked them about it we we're
+
+ align:start position:0%
+the company asked them about it we we're
+ 
+
+ align:start position:0%
+the company asked them about it we we're
+still deciding uh how to get them for
+
+ align:start position:0%
+still deciding uh how to get them for
+ 
+
+ align:start position:0%
+still deciding uh how to get them for
+cheap but we can definitely I think this
+
+ align:start position:0%
+cheap but we can definitely I think this
+ 
+
+ align:start position:0%
+cheap but we can definitely I think this
+should be about a dollar Max like if you
+
+ align:start position:0%
+should be about a dollar Max like if you
+ 
+
+ align:start position:0%
+should be about a dollar Max like if you
+just buy it so and then when you add in
+
+ align:start position:0%
+just buy it so and then when you add in
+ 
+
+ align:start position:0%
+just buy it so and then when you add in
+their um like the time they'll use like
+
+ align:start position:0%
+their um like the time they'll use like
+ 
+
+ align:start position:0%
+their um like the time they'll use like
+it probably will take them about 8 hours
+
+ align:start position:0%
+it probably will take them about 8 hours
+ 
+
+ align:start position:0%
+it probably will take them about 8 hours
+now CU they won't have to cut sales so
+
+ align:start position:0%
+now CU they won't have to cut sales so
+ 
+
+ align:start position:0%
+now CU they won't have to cut sales so
+uh that'll you know add another $4 or
+
+ align:start position:0%
+uh that'll you know add another $4 or
+ 
+
+ align:start position:0%
+uh that'll you know add another $4 or
+something cuz they like getting paid
+
+ align:start position:0%
+something cuz they like getting paid
+ 
+
+ align:start position:0%
+something cuz they like getting paid
+about 50 cents an hour I think so it'll
+
+ align:start position:0%
+about 50 cents an hour I think so it'll
+ 
+
+ align:start position:0%
+about 50 cents an hour I think so it'll
+definitely be able to compete with the
+
+ align:start position:0%
+definitely be able to compete with the
+ 
+
+ align:start position:0%
+definitely be able to compete with the
+current one no problem yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question sorry I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry so um so basically the the concept
+
+ align:start position:0%
+sorry so um so basically the the concept
+ 
+
+ align:start position:0%
+sorry so um so basically the the concept
+the like the reason we decided to put in
+
+ align:start position:0%
+the like the reason we decided to put in
+ 
+
+ align:start position:0%
+the like the reason we decided to put in
+the depression underneath was that like
+
+ align:start position:0%
+the depression underneath was that like
+ 
+
+ align:start position:0%
+the depression underneath was that like
+uh if it did rain it wouldn't be
+
+ align:start position:0%
+uh if it did rain it wouldn't be
+ 
+
+ align:start position:0%
+uh if it did rain it wouldn't be
+immediately affected uh that being said
+
+ align:start position:0%
+immediately affected uh that being said
+ 
+
+ align:start position:0%
+immediately affected uh that being said
+like this isn't going to protect it
+
+ align:start position:0%
+like this isn't going to protect it
+ 
+
+ align:start position:0%
+like this isn't going to protect it
+against like if you like leave it out in
+
+ align:start position:0%
+against like if you like leave it out in
+ 
+
+ align:start position:0%
+against like if you like leave it out in
+the rain it's not going to protect it so
+
+ align:start position:0%
+the rain it's not going to protect it so
+ 
+
+ align:start position:0%
+the rain it's not going to protect it so
+uh I guess the concept is that you leave
+
+ align:start position:0%
+uh I guess the concept is that you leave
+ 
+
+ align:start position:0%
+uh I guess the concept is that you leave
+it out only when it's bright but if it
+
+ align:start position:0%
+it out only when it's bright but if it
+ 
+
+ align:start position:0%
+it out only when it's bright but if it
+suddenly starts to rain it'll give you a
+
+ align:start position:0%
+suddenly starts to rain it'll give you a
+ 
+
+ align:start position:0%
+suddenly starts to rain it'll give you a
+certain amount of protection against it
+
+ align:start position:0%
+certain amount of protection against it
+ 
+
+ align:start position:0%
+certain amount of protection against it
+before you can you know take it back in
+
+ align:start position:0%
+before you can you know take it back in
+ 
+
+ align:start position:0%
+before you can you know take it back in
+and the solar cells themselves uh to be
+
+ align:start position:0%
+and the solar cells themselves uh to be
+ 
+
+ align:start position:0%
+and the solar cells themselves uh to be
+clear are not going to be just like be
+
+ align:start position:0%
+clear are not going to be just like be
+ 
+
+ align:start position:0%
+clear are not going to be just like be
+the way we had them a pel like they
+
+ align:start position:0%
+the way we had them a pel like they
+ 
+
+ align:start position:0%
+the way we had them a pel like they
+they'll still do the process of with
+
+ align:start position:0%
+they'll still do the process of with
+ 
+
+ align:start position:0%
+they'll still do the process of with
+with like a silicone and glass on top um
+
+ align:start position:0%
+with like a silicone and glass on top um
+ 
+
+ align:start position:0%
+with like a silicone and glass on top um
+because that's necessary you can't I
+
+ align:start position:0%
+because that's necessary you can't I
+ 
+
+ align:start position:0%
+because that's necessary you can't I
+mean the cells get damaged if you don't
+
+ align:start position:0%
+mean the cells get damaged if you don't
+ 
+
+ align:start position:0%
+mean the cells get damaged if you don't
+uh incapsulate them right I mean just to
+
+ align:start position:0%
+uh incapsulate them right I mean just to
+ 
+
+ align:start position:0%
+uh incapsulate them right I mean just to
+be clear just so we I realized we didn't
+
+ align:start position:0%
+be clear just so we I realized we didn't
+ 
+
+ align:start position:0%
+be clear just so we I realized we didn't
+explain like how the panel looks uh the
+
+ align:start position:0%
+explain like how the panel looks uh the
+ 
+
+ align:start position:0%
+explain like how the panel looks uh the
+way the panel looks is that like you
+
+ align:start position:0%
+way the panel looks is that like you
+ 
+
+ align:start position:0%
+way the panel looks is that like you
+have uh the three solar cells in series
+
+ align:start position:0%
+have uh the three solar cells in series
+ 
+
+ align:start position:0%
+have uh the three solar cells in series
+which are then encapsulated in silicone
+
+ align:start position:0%
+which are then encapsulated in silicone
+ 
+
+ align:start position:0%
+which are then encapsulated in silicone
+uh you have an aluminum frame yeah right
+
+ align:start position:0%
+uh you have an aluminum frame yeah right
+ 
+
+ align:start position:0%
+uh you have an aluminum frame yeah right
+so you have like an aluminum frame you
+
+ align:start position:0%
+so you have like an aluminum frame you
+ 
+
+ align:start position:0%
+so you have like an aluminum frame you
+have these cells in series uh and
+
+ align:start position:0%
+have these cells in series uh and
+ 
+
+ align:start position:0%
+have these cells in series uh and
+they're encapsulated by silicone uh you
+
+ align:start position:0%
+they're encapsulated by silicone uh you
+ 
+
+ align:start position:0%
+they're encapsulated by silicone uh you
+then uh pressure you put pressure on a
+
+ align:start position:0%
+then uh pressure you put pressure on a
+ 
+
+ align:start position:0%
+then uh pressure you put pressure on a
+glass frame on top of it and leave it
+
+ align:start position:0%
+glass frame on top of it and leave it
+ 
+
+ align:start position:0%
+glass frame on top of it and leave it
+like set um and then you have like a
+
+ align:start position:0%
+like set um and then you have like a
+ 
+
+ align:start position:0%
+like set um and then you have like a
+plastic sheet underneath so this is
+
+ align:start position:0%
+plastic sheet underneath so this is
+ 
+
+ align:start position:0%
+plastic sheet underneath so this is
+basically waterproof uh and this is what
+
+ align:start position:0%
+basically waterproof uh and this is what
+ 
+
+ align:start position:0%
+basically waterproof uh and this is what
+we're talking about will be here cuz
+
+ align:start position:0%
+we're talking about will be here cuz
+ 
+
+ align:start position:0%
+we're talking about will be here cuz
+these are the kinds of panels that they
+
+ align:start position:0%
+these are the kinds of panels that they
+ 
+
+ align:start position:0%
+these are the kinds of panels that they
+stick on their roofs and you use for
+
+ align:start position:0%
+stick on their roofs and you use for
+ 
+
+ align:start position:0%
+stick on their roofs and you use for
+power except like in our case you'd have
+
+ align:start position:0%
+power except like in our case you'd have
+ 
+
+ align:start position:0%
+power except like in our case you'd have
+only three cells as opposed to yeah so
+
+ align:start position:0%
+only three cells as opposed to yeah so
+ 
+
+ align:start position:0%
+only three cells as opposed to yeah so
+it's a lot less time a lot of the
+
+ align:start position:0%
+it's a lot less time a lot of the
+ 
+
+ align:start position:0%
+it's a lot less time a lot of the
+problems with the big ones is when you
+
+ align:start position:0%
+problems with the big ones is when you
+ 
+
+ align:start position:0%
+problems with the big ones is when you
+uh encapsulate it you have to push it
+
+ align:start position:0%
+uh encapsulate it you have to push it
+ 
+
+ align:start position:0%
+uh encapsulate it you have to push it
+down and make sure that there's no air
+
+ align:start position:0%
+down and make sure that there's no air
+ 
+
+ align:start position:0%
+down and make sure that there's no air
+bubbles and it's really hard on a big
+
+ align:start position:0%
+bubbles and it's really hard on a big
+ 
+
+ align:start position:0%
+bubbles and it's really hard on a big
+panel to make sure there's no bubbles
+
+ align:start position:0%
+panel to make sure there's no bubbles
+ 
+
+ align:start position:0%
+panel to make sure there's no bubbles
+but on the smaller ones it's mostly The
+
+ align:start position:0%
+but on the smaller ones it's mostly The
+ 
+
+ align:start position:0%
+but on the smaller ones it's mostly The
+Cutting that they said they're they
+
+ align:start position:0%
+Cutting that they said they're they
+ 
+
+ align:start position:0%
+Cutting that they said they're they
+really need to get rid of so that's what
+
+ align:start position:0%
+really need to get rid of so that's what
+ 
+
+ align:start position:0%
+really need to get rid of so that's what
+our goal was yeah I mean the goal
+
+ align:start position:0%
+our goal was yeah I mean the goal
+ 
+
+ align:start position:0%
+our goal was yeah I mean the goal
+basically like Liz said is to eliminate
+
+ align:start position:0%
+basically like Liz said is to eliminate
+ 
+
+ align:start position:0%
+basically like Liz said is to eliminate
+cutting the cells because that's a pain
+
+ align:start position:0%
+cutting the cells because that's a pain
+ 
+
+ align:start position:0%
+cutting the cells because that's a pain
+it's a pain and they break uh they said
+
+ align:start position:0%
+it's a pain and they break uh they said
+ 
+
+ align:start position:0%
+it's a pain and they break uh they said
+like you know if they have five cells
+
+ align:start position:0%
+like you know if they have five cells
+ 
+
+ align:start position:0%
+like you know if they have five cells
+they'll break or ever like and so they
+
+ align:start position:0%
+they'll break or ever like and so they
+ 
+
+ align:start position:0%
+they'll break or ever like and so they
+won't break these cuz they're just full
+
+ align:start position:0%
+won't break these cuz they're just full
+ 
+
+ align:start position:0%
+won't break these cuz they're just full
+cyles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right ask this question but have you
+
+ align:start position:0%
+right ask this question but have you
+ 
+
+ align:start position:0%
+right ask this question but have you
+tried in lab pointing that hallogen la
+
+ align:start position:0%
+tried in lab pointing that hallogen la
+ 
+
+ align:start position:0%
+tried in lab pointing that hallogen la
+at the solar cell and actually fully
+
+ align:start position:0%
+at the solar cell and actually fully
+ 
+
+ align:start position:0%
+at the solar cell and actually fully
+charging the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phone the efficiency on that is so
+
+ align:start position:0%
+phone the efficiency on that is so
+ 
+
+ align:start position:0%
+phone the efficiency on that is so
+horrifying as to be I mean it's like
+
+ align:start position:0%
+horrifying as to be I mean it's like
+ 
+
+ align:start position:0%
+horrifying as to be I mean it's like
+.01% I mean it's like 10 amps 15 amps at
+
+ align:start position:0%
+.01% I mean it's like 10 amps 15 amps at
+ 
+
+ align:start position:0%
+.01% I mean it's like 10 amps 15 amps at
+120 volts to get like a mowatt into the
+
+ align:start position:0%
+120 volts to get like a mowatt into the
+ 
+
+ align:start position:0%
+120 volts to get like a mowatt into the
+phone which is crazy but you should try
+
+ align:start position:0%
+phone which is crazy but you should try
+ 
+
+ align:start position:0%
+phone which is crazy but you should try
+it yeah we we actually got like the
+
+ align:start position:0%
+it yeah we we actually got like the
+ 
+
+ align:start position:0%
+it yeah we we actually got like the
+video we showed you was yesterday so uh
+
+ align:start position:0%
+video we showed you was yesterday so uh
+ 
+
+ align:start position:0%
+video we showed you was yesterday so uh
+we're probably going to try that over
+
+ align:start position:0%
+we're probably going to try that over
+ 
+
+ align:start position:0%
+we're probably going to try that over
+the weekend yeah yeah you should just
+
+ align:start position:0%
+the weekend yeah yeah you should just
+ 
+
+ align:start position:0%
+the weekend yeah yeah you should just
+set it I mean find a phone that'll
+
+ align:start position:0%
+set it I mean find a phone that'll
+ 
+
+ align:start position:0%
+set it I mean find a phone that'll
+actually give you like a some kind of
+
+ align:start position:0%
+actually give you like a some kind of
+ 
+
+ align:start position:0%
+actually give you like a some kind of
+decent readout of how charged it is and
+
+ align:start position:0%
+decent readout of how charged it is and
+ 
+
+ align:start position:0%
+decent readout of how charged it is and
+run it for you know half an hour and see
+
+ align:start position:0%
+run it for you know half an hour and see
+ 
+
+ align:start position:0%
+run it for you know half an hour and see
+how see how much the charge improves
+
+ align:start position:0%
+how see how much the charge improves
+ 
+
+ align:start position:0%
+how see how much the charge improves
+over a half an hour or or take out the
+
+ align:start position:0%
+over a half an hour or or take out the
+ 
+
+ align:start position:0%
+over a half an hour or or take out the
+battery measure the voltage on the Cell
+
+ align:start position:0%
+battery measure the voltage on the Cell
+ 
+
+ align:start position:0%
+battery measure the voltage on the Cell
+at a couple different times or something
+
+ align:start position:0%
+at a couple different times or something
+ 
+
+ align:start position:0%
+at a couple different times or something
+we did a rough calculation based on it
+
+ align:start position:0%
+we did a rough calculation based on it
+ 
+
+ align:start position:0%
+we did a rough calculation based on it
+should have about 100 milliamp Uh
+
+ align:start position:0%
+should have about 100 milliamp Uh
+ 
+
+ align:start position:0%
+should have about 100 milliamp Uh
+current and like how long that should
+
+ align:start position:0%
+current and like how long that should
+ 
+
+ align:start position:0%
+current and like how long that should
+take and it'll be longer than the China
+
+ align:start position:0%
+take and it'll be longer than the China
+ 
+
+ align:start position:0%
+take and it'll be longer than the China
+One the China One's about 5 hours and
+
+ align:start position:0%
+One the China One's about 5 hours and
+ 
+
+ align:start position:0%
+One the China One's about 5 hours and
+this hopefully will be like 7even or 8
+
+ align:start position:0%
+this hopefully will be like 7even or 8
+ 
+
+ align:start position:0%
+this hopefully will be like 7even or 8
+hours but we have not tested this so
+
+ align:start position:0%
+hours but we have not tested this so
+ 
+
+ align:start position:0%
+hours but we have not tested this so
+that could be a big problem we have to
+
+ align:start position:0%
+that could be a big problem we have to
+ 
+
+ align:start position:0%
+that could be a big problem we have to
+figure that out you may just find that
+
+ align:start position:0%
+figure that out you may just find that
+ 
+
+ align:start position:0%
+figure that out you may just find that
+you need to have storage in your thing
+
+ align:start position:0%
+you need to have storage in your thing
+ 
+
+ align:start position:0%
+you need to have storage in your thing
+there not enough if there's not enough
+
+ align:start position:0%
+there not enough if there's not enough
+ 
+
+ align:start position:0%
+there not enough if there's not enough
+current coming out of that thing to
+
+ align:start position:0%
+current coming out of that thing to
+ 
+
+ align:start position:0%
+current coming out of that thing to
+charge in real time you may have to add
+
+ align:start position:0%
+charge in real time you may have to add
+ 
+
+ align:start position:0%
+charge in real time you may have to add
+a battery to that so that you can store
+
+ align:start position:0%
+a battery to that so that you can store
+ 
+
+ align:start position:0%
+a battery to that so that you can store
+a little bit and then charge your phone
+
+ align:start position:0%
+a little bit and then charge your phone
+ 
+
+ align:start position:0%
+a little bit and then charge your phone
+on and we have also been testing uh the
+
+ align:start position:0%
+on and we have also been testing uh the
+ 
+
+ align:start position:0%
+on and we have also been testing uh the
+voltage necessary to actually get enough
+
+ align:start position:0%
+voltage necessary to actually get enough
+ 
+
+ align:start position:0%
+voltage necessary to actually get enough
+voltage to put to like so we can get
+
+ align:start position:0%
+voltage to put to like so we can get
+ 
+
+ align:start position:0%
+voltage to put to like so we can get
+enough voltage that it can be stepped up
+
+ align:start position:0%
+enough voltage that it can be stepped up
+ 
+
+ align:start position:0%
+enough voltage that it can be stepped up
+to 5 volts and right now we're getting
+
+ align:start position:0%
+to 5 volts and right now we're getting
+ 
+
+ align:start position:0%
+to 5 volts and right now we're getting
+that is 1.2 volts is the minimum
+
+ align:start position:0%
+that is 1.2 volts is the minimum
+ 
+
+ align:start position:0%
+that is 1.2 volts is the minimum
+according to the Circuit we should be a
+
+ align:start position:0%
+according to the Circuit we should be a
+ 
+
+ align:start position:0%
+according to the Circuit we should be a
+we should be able to step up to 5 volts
+
+ align:start position:0%
+we should be able to step up to 5 volts
+ 
+
+ align:start position:0%
+we should be able to step up to 5 volts
+using only 27 volts so we're going to
+
+ align:start position:0%
+using only 27 volts so we're going to
+ 
+
+ align:start position:0%
+using only 27 volts so we're going to
+keep trying that but but it also
+
+ align:start position:0%
+keep trying that but but it also
+ 
+
+ align:start position:0%
+keep trying that but but it also
+shouldn't be much of a problem because
+
+ align:start position:0%
+shouldn't be much of a problem because
+ 
+
+ align:start position:0%
+shouldn't be much of a problem because
+in the kin Sun like it is a volt and a
+
+ align:start position:0%
+in the kin Sun like it is a volt and a
+ 
+
+ align:start position:0%
+in the kin Sun like it is a volt and a
+half like it would have to be like
+
+ align:start position:0%
+half like it would have to be like
+ 
+
+ align:start position:0%
+half like it would have to be like
+sunset for it to be that low and who's
+
+ align:start position:0%
+sunset for it to be that low and who's
+ 
+
+ align:start position:0%
+sunset for it to be that low and who's
+charging their solar cell phone at that
+
+ align:start position:0%
+charging their solar cell phone at that
+ 
+
+ align:start position:0%
+charging their solar cell phone at that
+hour yeah but I mean yeah so we're
+
+ align:start position:0%
+hour yeah but I mean yeah so we're
+ 
+
+ align:start position:0%
+hour yeah but I mean yeah so we're
+definitely going to try that though just
+
+ align:start position:0%
+definitely going to try that though just
+ 
+
+ align:start position:0%
+definitely going to try that though just
+try and charge the cell phone uh part of
+
+ align:start position:0%
+try and charge the cell phone uh part of
+ 
+
+ align:start position:0%
+try and charge the cell phone uh part of
+our initial plan was actually to have a
+
+ align:start position:0%
+our initial plan was actually to have a
+ 
+
+ align:start position:0%
+our initial plan was actually to have a
+separate uh energy uh storage device
+
+ align:start position:0%
+separate uh energy uh storage device
+ 
+
+ align:start position:0%
+separate uh energy uh storage device
+like in our system but uh we decided
+
+ align:start position:0%
+like in our system but uh we decided
+ 
+
+ align:start position:0%
+like in our system but uh we decided
+that that would like increase costs uh
+
+ align:start position:0%
+that that would like increase costs uh
+ 
+
+ align:start position:0%
+that that would like increase costs uh
+and so we thought that if you could do
+
+ align:start position:0%
+and so we thought that if you could do
+ 
+
+ align:start position:0%
+and so we thought that if you could do
+it without that yeah so but yeah that's
+
+ align:start position:0%
+it without that yeah so but yeah that's
+ 
+
+ align:start position:0%
+it without that yeah so but yeah that's
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+yeah any feedback from Maro or others at
+
+ align:start position:0%
+yeah any feedback from Maro or others at
+ 
+
+ align:start position:0%
+yeah any feedback from Maro or others at
+group of Phoenix yet we really need to
+
+ align:start position:0%
+group of Phoenix yet we really need to
+ 
+
+ align:start position:0%
+group of Phoenix yet we really need to
+talk to them like they they're not very
+
+ align:start position:0%
+talk to them like they they're not very
+ 
+
+ align:start position:0%
+talk to them like they they're not very
+good at getting back to us okay so I
+
+ align:start position:0%
+good at getting back to us okay so I
+ 
+
+ align:start position:0%
+good at getting back to us okay so I
+would encourage you to use the phone
+
+ align:start position:0%
+would encourage you to use the phone
+ 
+
+ align:start position:0%
+would encourage you to use the phone
+next week we want prob just call them we
+
+ align:start position:0%
+next week we want prob just call them we
+ 
+
+ align:start position:0%
+next week we want prob just call them we
+have a lot of questions that a
+
+ align:start position:0%
+have a lot of questions that a
+ 
+
+ align:start position:0%
+have a lot of questions that a
+conversation will be really helpful
+
+ align:start position:0%
+conversation will be really helpful
+ 
+
+ align:start position:0%
+conversation will be really helpful
+so so how many non noia phones did you
+
+ align:start position:0%
+so so how many non noia phones did you
+ 
+
+ align:start position:0%
+so so how many non noia phones did you
+see when you were there um we only
+
+ align:start position:0%
+see when you were there um we only
+ 
+
+ align:start position:0%
+see when you were there um we only
+actually saw two kinds of cell phones we
+
+ align:start position:0%
+actually saw two kinds of cell phones we
+ 
+
+ align:start position:0%
+actually saw two kinds of cell phones we
+saw Nokia and a ZTE phone and a ZTE E
+
+ align:start position:0%
+saw Nokia and a ZTE phone and a ZTE E
+ 
+
+ align:start position:0%
+saw Nokia and a ZTE phone and a ZTE E
+phone um can be in a similar way it's
+
+ align:start position:0%
+phone um can be in a similar way it's
+ 
+
+ align:start position:0%
+phone um can be in a similar way it's
+it's the same voltage
+
+ align:start position:0%
+it's the same voltage
+ 
+
+ align:start position:0%
+it's the same voltage
+input yeah it's a different connector um
+
+ align:start position:0%
+input yeah it's a different connector um
+ 
+
+ align:start position:0%
+input yeah it's a different connector um
+we could also do this with a USB charger
+
+ align:start position:0%
+we could also do this with a USB charger
+ 
+
+ align:start position:0%
+we could also do this with a USB charger
+but the Nokia phone does can't be
+
+ align:start position:0%
+but the Nokia phone does can't be
+ 
+
+ align:start position:0%
+but the Nokia phone does can't be
+charged via USB so we just use that um
+
+ align:start position:0%
+charged via USB so we just use that um
+ 
+
+ align:start position:0%
+charged via USB so we just use that um
+we're waiting Lindsay the woman who's
+
+ align:start position:0%
+we're waiting Lindsay the woman who's
+ 
+
+ align:start position:0%
+we're waiting Lindsay the woman who's
+the likely on that the other group was
+
+ align:start position:0%
+the likely on that the other group was
+ 
+
+ align:start position:0%
+the likely on that the other group was
+talking about said that she has like a
+
+ align:start position:0%
+talking about said that she has like a
+ 
+
+ align:start position:0%
+talking about said that she has like a
+spreadsheet with what kind of SES
+
+ align:start position:0%
+spreadsheet with what kind of SES
+ 
+
+ align:start position:0%
+spreadsheet with what kind of SES
+everyone has but we're trying to get
+
+ align:start position:0%
+everyone has but we're trying to get
+ 
+
+ align:start position:0%
+everyone has but we're trying to get
+that from her right but we asked a lot
+
+ align:start position:0%
+that from her right but we asked a lot
+ 
+
+ align:start position:0%
+that from her right but we asked a lot
+of people and those are the only two SES
+
+ align:start position:0%
+of people and those are the only two SES
+ 
+
+ align:start position:0%
+of people and those are the only two SES
+we found right so I mean right now these
+
+ align:start position:0%
+we found right so I mean right now these
+ 
+
+ align:start position:0%
+we found right so I mean right now these
+are the two Conn conectors we have this
+
+ align:start position:0%
+are the two Conn conectors we have this
+ 
+
+ align:start position:0%
+are the two Conn conectors we have this
+one charg is a knock in and this one's a
+
+ align:start position:0%
+one charg is a knock in and this one's a
+ 
+
+ align:start position:0%
+one charg is a knock in and this one's a
+USB charger
+
+ align:start position:0%
+USB charger
+ 
+
+ align:start position:0%
+USB charger
+so any more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay well thank you
+
+ align:start position:0%
+questions okay well thank you
+ 
+
+ align:start position:0%
+questions okay well thank you
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+than as we speak we're actually going to
+
+ align:start position:0%
+than as we speak we're actually going to
+ 
+
+ align:start position:0%
+than as we speak we're actually going to
+pass around the little zip log bags of
+
+ align:start position:0%
+pass around the little zip log bags of
+ 
+
+ align:start position:0%
+pass around the little zip log bags of
+the experiments we did with the rice and
+
+ align:start position:0%
+the experiments we did with the rice and
+ 
+
+ align:start position:0%
+the experiments we did with the rice and
+um the NGO that we worked with was
+
+ align:start position:0%
+um the NGO that we worked with was
+ 
+
+ align:start position:0%
+um the NGO that we worked with was
+called ASA prar and we are actually part
+
+ align:start position:0%
+called ASA prar and we are actually part
+ 
+
+ align:start position:0%
+called ASA prar and we are actually part
+of the class that went to El Salvador
+
+ align:start position:0%
+of the class that went to El Salvador
+ 
+
+ align:start position:0%
+of the class that went to El Salvador
+and not
+
+ align:start position:0%
+and not
+ 
+
+ align:start position:0%
+and not
+Nicaragua um we worked in a community
+
+ align:start position:0%
+Nicaragua um we worked in a community
+ 
+
+ align:start position:0%
+Nicaragua um we worked in a community
+called La Magdalena in El Salvador and
+
+ align:start position:0%
+called La Magdalena in El Salvador and
+ 
+
+ align:start position:0%
+called La Magdalena in El Salvador and
+the NGO is currently introducing rice
+
+ align:start position:0%
+the NGO is currently introducing rice
+ 
+
+ align:start position:0%
+the NGO is currently introducing rice
+cultivation in the community um both to
+
+ align:start position:0%
+cultivation in the community um both to
+ 
+
+ align:start position:0%
+cultivation in the community um both to
+be used as a source of income and also
+
+ align:start position:0%
+be used as a source of income and also
+ 
+
+ align:start position:0%
+be used as a source of income and also
+as nutrition and in order for um the
+
+ align:start position:0%
+as nutrition and in order for um the
+ 
+
+ align:start position:0%
+as nutrition and in order for um the
+rice to be ready for consumption uh it
+
+ align:start position:0%
+rice to be ready for consumption uh it
+ 
+
+ align:start position:0%
+rice to be ready for consumption uh it
+needs to be processed and the process
+
+ align:start position:0%
+needs to be processed and the process
+ 
+
+ align:start position:0%
+needs to be processed and the process
+involves uh threshing and dehusking and
+
+ align:start position:0%
+involves uh threshing and dehusking and
+ 
+
+ align:start position:0%
+involves uh threshing and dehusking and
+current methods of dehusking are very um
+
+ align:start position:0%
+current methods of dehusking are very um
+ 
+
+ align:start position:0%
+current methods of dehusking are very um
+time and money intensive they usually
+
+ align:start position:0%
+time and money intensive they usually
+ 
+
+ align:start position:0%
+time and money intensive they usually
+involve a 2 to three hour bus ride to a
+
+ align:start position:0%
+involve a 2 to three hour bus ride to a
+ 
+
+ align:start position:0%
+involve a 2 to three hour bus ride to a
+mill um where The Rice can be processed
+
+ align:start position:0%
+mill um where The Rice can be processed
+ 
+
+ align:start position:0%
+mill um where The Rice can be processed
+and um it costs about $3 to4 we found
+
+ align:start position:0%
+and um it costs about $3 to4 we found
+ 
+
+ align:start position:0%
+and um it costs about $3 to4 we found
+out which is um about um a daily salary
+
+ align:start position:0%
+out which is um about um a daily salary
+ 
+
+ align:start position:0%
+out which is um about um a daily salary
+so our design challenge is to develop a
+
+ align:start position:0%
+so our design challenge is to develop a
+ 
+
+ align:start position:0%
+so our design challenge is to develop a
+method that's um for more local faster
+
+ align:start position:0%
+method that's um for more local faster
+ 
+
+ align:start position:0%
+method that's um for more local faster
+and cheaper way of De husking rice um
+
+ align:start position:0%
+and cheaper way of De husking rice um
+ 
+
+ align:start position:0%
+and cheaper way of De husking rice um
+the two most important project
+
+ align:start position:0%
+the two most important project
+ 
+
+ align:start position:0%
+the two most important project
+specifications that we focused on were
+
+ align:start position:0%
+specifications that we focused on were
+ 
+
+ align:start position:0%
+specifications that we focused on were
+the efficiency which refers to the
+
+ align:start position:0%
+the efficiency which refers to the
+ 
+
+ align:start position:0%
+the efficiency which refers to the
+amount of rice that's successfully
+
+ align:start position:0%
+amount of rice that's successfully
+ 
+
+ align:start position:0%
+amount of rice that's successfully
+dehusked and also how gentle the uh
+
+ align:start position:0%
+dehusked and also how gentle the uh
+ 
+
+ align:start position:0%
+dehusked and also how gentle the uh
+process is meaning um we wanted to
+
+ align:start position:0%
+process is meaning um we wanted to
+ 
+
+ align:start position:0%
+process is meaning um we wanted to
+minimize the amount of rice that's
+
+ align:start position:0%
+minimize the amount of rice that's
+ 
+
+ align:start position:0%
+minimize the amount of rice that's
+broken or cut in half and some of the
+
+ align:start position:0%
+broken or cut in half and some of the
+ 
+
+ align:start position:0%
+broken or cut in half and some of the
+other specifications we looked at were
+
+ align:start position:0%
+other specifications we looked at were
+ 
+
+ align:start position:0%
+other specifications we looked at were
+safety affordability of course um
+
+ align:start position:0%
+safety affordability of course um
+ 
+
+ align:start position:0%
+safety affordability of course um
+durability um and also um Aesthetics
+
+ align:start position:0%
+durability um and also um Aesthetics
+ 
+
+ align:start position:0%
+durability um and also um Aesthetics
+um we approached the problem by
+
+ align:start position:0%
+um we approached the problem by
+ 
+
+ align:start position:0%
+um we approached the problem by
+brainstorming uh we researched some
+
+ align:start position:0%
+brainstorming uh we researched some
+ 
+
+ align:start position:0%
+brainstorming uh we researched some
+existing technologies that people use in
+
+ align:start position:0%
+existing technologies that people use in
+ 
+
+ align:start position:0%
+existing technologies that people use in
+regions that rice is grown some of them
+
+ align:start position:0%
+regions that rice is grown some of them
+ 
+
+ align:start position:0%
+regions that rice is grown some of them
+are more simple some of them involve uh
+
+ align:start position:0%
+are more simple some of them involve uh
+ 
+
+ align:start position:0%
+are more simple some of them involve uh
+heavy machinery uh what we concluded
+
+ align:start position:0%
+heavy machinery uh what we concluded
+ 
+
+ align:start position:0%
+heavy machinery uh what we concluded
+though is that all of these Technologies
+
+ align:start position:0%
+though is that all of these Technologies
+ 
+
+ align:start position:0%
+though is that all of these Technologies
+use friction in order to get the husk
+
+ align:start position:0%
+use friction in order to get the husk
+ 
+
+ align:start position:0%
+use friction in order to get the husk
+from the rice and it's a matter of um
+
+ align:start position:0%
+from the rice and it's a matter of um
+ 
+
+ align:start position:0%
+from the rice and it's a matter of um
+adjusting the amount of friction we have
+
+ align:start position:0%
+adjusting the amount of friction we have
+ 
+
+ align:start position:0%
+adjusting the amount of friction we have
+in order to get the husk off but um not
+
+ align:start position:0%
+in order to get the husk off but um not
+ 
+
+ align:start position:0%
+in order to get the husk off but um not
+break the rice grain
+
+ align:start position:0%
+break the rice grain
+ 
+
+ align:start position:0%
+break the rice grain
+and some of the ideas we ran through
+
+ align:start position:0%
+and some of the ideas we ran through
+ 
+
+ align:start position:0%
+and some of the ideas we ran through
+were um pepper grinder where we have
+
+ align:start position:0%
+were um pepper grinder where we have
+ 
+
+ align:start position:0%
+were um pepper grinder where we have
+cylinders rotating together um rubbing
+
+ align:start position:0%
+cylinders rotating together um rubbing
+ 
+
+ align:start position:0%
+cylinders rotating together um rubbing
+together uh plates that can be made from
+
+ align:start position:0%
+together uh plates that can be made from
+ 
+
+ align:start position:0%
+together uh plates that can be made from
+different materials U mortar and pestil
+
+ align:start position:0%
+different materials U mortar and pestil
+ 
+
+ align:start position:0%
+different materials U mortar and pestil
+idea which is used but it's um a lot
+
+ align:start position:0%
+idea which is used but it's um a lot
+ 
+
+ align:start position:0%
+idea which is used but it's um a lot
+more energy intensive and not as
+
+ align:start position:0%
+more energy intensive and not as
+ 
+
+ align:start position:0%
+more energy intensive and not as
+efficient and also the Molina which is a
+
+ align:start position:0%
+efficient and also the Molina which is a
+ 
+
+ align:start position:0%
+efficient and also the Molina which is a
+a corn maill that's currently used in El
+
+ align:start position:0%
+a corn maill that's currently used in El
+ 
+
+ align:start position:0%
+a corn maill that's currently used in El
+Salvador um to grain corn and that's um
+
+ align:start position:0%
+Salvador um to grain corn and that's um
+ 
+
+ align:start position:0%
+Salvador um to grain corn and that's um
+basically two circular plates that um
+
+ align:start position:0%
+basically two circular plates that um
+ 
+
+ align:start position:0%
+basically two circular plates that um
+rub together and that's what we actually
+
+ align:start position:0%
+rub together and that's what we actually
+ 
+
+ align:start position:0%
+rub together and that's what we actually
+have over
+
+ align:start position:0%
+have over
+ 
+
+ align:start position:0%
+have over
+there um so Amy Smith actually had
+
+ align:start position:0%
+there um so Amy Smith actually had
+ 
+
+ align:start position:0%
+there um so Amy Smith actually had
+visited this community before we had and
+
+ align:start position:0%
+visited this community before we had and
+ 
+
+ align:start position:0%
+visited this community before we had and
+she had looked at this Molina and um
+
+ align:start position:0%
+she had looked at this Molina and um
+ 
+
+ align:start position:0%
+she had looked at this Molina and um
+inserted a black inner tube in between
+
+ align:start position:0%
+inserted a black inner tube in between
+ 
+
+ align:start position:0%
+inserted a black inner tube in between
+the two metal Parts um so we used that
+
+ align:start position:0%
+the two metal Parts um so we used that
+ 
+
+ align:start position:0%
+the two metal Parts um so we used that
+kind of as our standard when we were
+
+ align:start position:0%
+kind of as our standard when we were
+ 
+
+ align:start position:0%
+kind of as our standard when we were
+looking at um how we could go about
+
+ align:start position:0%
+looking at um how we could go about
+ 
+
+ align:start position:0%
+looking at um how we could go about
+improving this process um so we use this
+
+ align:start position:0%
+improving this process um so we use this
+ 
+
+ align:start position:0%
+improving this process um so we use this
+Peart um with these attributes to kind
+
+ align:start position:0%
+Peart um with these attributes to kind
+ 
+
+ align:start position:0%
+Peart um with these attributes to kind
+of figure out which one would be the
+
+ align:start position:0%
+of figure out which one would be the
+ 
+
+ align:start position:0%
+of figure out which one would be the
+most feasible to do this semester
+
+ align:start position:0%
+most feasible to do this semester
+ 
+
+ align:start position:0%
+most feasible to do this semester
+um and which one would be the most um
+
+ align:start position:0%
+um and which one would be the most um
+ 
+
+ align:start position:0%
+um and which one would be the most um
+efficient for the community to use
+
+ align:start position:0%
+efficient for the community to use
+ 
+
+ align:start position:0%
+efficient for the community to use
+overall um in the end we chose to modify
+
+ align:start position:0%
+overall um in the end we chose to modify
+ 
+
+ align:start position:0%
+overall um in the end we chose to modify
+the existing Molino um by inserting a
+
+ align:start position:0%
+the existing Molino um by inserting a
+ 
+
+ align:start position:0%
+the existing Molino um by inserting a
+different material in between the plates
+
+ align:start position:0%
+different material in between the plates
+ 
+
+ align:start position:0%
+different material in between the plates
+right now we have um the two leather
+
+ align:start position:0%
+right now we have um the two leather
+ 
+
+ align:start position:0%
+right now we have um the two leather
+inserts in there if oh
+
+ align:start position:0%
+inserts in there if oh
+ 
+
+ align:start position:0%
+inserts in there if oh
+bu so they kind of we kind of just add
+
+ align:start position:0%
+bu so they kind of we kind of just add
+ 
+
+ align:start position:0%
+bu so they kind of we kind of just add
+like a circular insert in between them
+
+ align:start position:0%
+like a circular insert in between them
+ 
+
+ align:start position:0%
+like a circular insert in between them
+um the advantages of using the Molino is
+
+ align:start position:0%
+um the advantages of using the Molino is
+ 
+
+ align:start position:0%
+um the advantages of using the Molino is
+that our community partner as a
+
+ align:start position:0%
+that our community partner as a
+ 
+
+ align:start position:0%
+that our community partner as a
+is actually um Distributing the molos to
+
+ align:start position:0%
+is actually um Distributing the molos to
+ 
+
+ align:start position:0%
+is actually um Distributing the molos to
+the community to use for um corn to make
+
+ align:start position:0%
+the community to use for um corn to make
+ 
+
+ align:start position:0%
+the community to use for um corn to make
+cornmeal um to grind yaka to and like so
+
+ align:start position:0%
+cornmeal um to grind yaka to and like so
+ 
+
+ align:start position:0%
+cornmeal um to grind yaka to and like so
+it's very multifunctional for them and
+
+ align:start position:0%
+it's very multifunctional for them and
+ 
+
+ align:start position:0%
+it's very multifunctional for them and
+although the cost is $20 as a proar is
+
+ align:start position:0%
+although the cost is $20 as a proar is
+ 
+
+ align:start position:0%
+although the cost is $20 as a proar is
+funding this um distribution to the
+
+ align:start position:0%
+funding this um distribution to the
+ 
+
+ align:start position:0%
+funding this um distribution to the
+communities um and as it is now either
+
+ align:start position:0%
+communities um and as it is now either
+ 
+
+ align:start position:0%
+communities um and as it is now either
+one family will use it or a whole
+
+ align:start position:0%
+one family will use it or a whole
+ 
+
+ align:start position:0%
+one family will use it or a whole
+Community will use it so it's available
+
+ align:start position:0%
+Community will use it so it's available
+ 
+
+ align:start position:0%
+Community will use it so it's available
+to a lot of people um it's pretty
+
+ align:start position:0%
+to a lot of people um it's pretty
+ 
+
+ align:start position:0%
+to a lot of people um it's pretty
+durable the metal is pretty rigid um and
+
+ align:start position:0%
+durable the metal is pretty rigid um and
+ 
+
+ align:start position:0%
+durable the metal is pretty rigid um and
+it's not labor intensive it's just a
+
+ align:start position:0%
+it's not labor intensive it's just a
+ 
+
+ align:start position:0%
+it's not labor intensive it's just a
+hand crank that you use um a few of the
+
+ align:start position:0%
+hand crank that you use um a few of the
+ 
+
+ align:start position:0%
+hand crank that you use um a few of the
+challenges with the moino though is that
+
+ align:start position:0%
+challenges with the moino though is that
+ 
+
+ align:start position:0%
+challenges with the moino though is that
+when you just do it without any insert
+
+ align:start position:0%
+when you just do it without any insert
+ 
+
+ align:start position:0%
+when you just do it without any insert
+it cracks or um breaks the rice so
+
+ align:start position:0%
+it cracks or um breaks the rice so
+ 
+
+ align:start position:0%
+it cracks or um breaks the rice so
+people don't really necessarily want
+
+ align:start position:0%
+people don't really necessarily want
+ 
+
+ align:start position:0%
+people don't really necessarily want
+broken rice um and it wears the material
+
+ align:start position:0%
+broken rice um and it wears the material
+ 
+
+ align:start position:0%
+broken rice um and it wears the material
+down if you put something in there we
+
+ align:start position:0%
+down if you put something in there we
+ 
+
+ align:start position:0%
+down if you put something in there we
+kind of need a durble material that will
+
+ align:start position:0%
+kind of need a durble material that will
+ 
+
+ align:start position:0%
+kind of need a durble material that will
+withstand this
+
+ align:start position:0%
+withstand this
+ 
+
+ align:start position:0%
+withstand this
+turning um so we decided upon five
+
+ align:start position:0%
+turning um so we decided upon five
+ 
+
+ align:start position:0%
+turning um so we decided upon five
+different materials that we wanted to
+
+ align:start position:0%
+different materials that we wanted to
+ 
+
+ align:start position:0%
+different materials that we wanted to
+test um and we looked at leather rubber
+
+ align:start position:0%
+test um and we looked at leather rubber
+ 
+
+ align:start position:0%
+test um and we looked at leather rubber
+metal wood and fabric um and based on
+
+ align:start position:0%
+metal wood and fabric um and based on
+ 
+
+ align:start position:0%
+metal wood and fabric um and based on
+those we looked at the cost residue
+
+ align:start position:0%
+those we looked at the cost residue
+ 
+
+ align:start position:0%
+those we looked at the cost residue
+durability and availability of those um
+
+ align:start position:0%
+durability and availability of those um
+ 
+
+ align:start position:0%
+durability and availability of those um
+we brought back leather and rubber from
+
+ align:start position:0%
+we brought back leather and rubber from
+ 
+
+ align:start position:0%
+we brought back leather and rubber from
+El Salvador um so we actually could use
+
+ align:start position:0%
+El Salvador um so we actually could use
+ 
+
+ align:start position:0%
+El Salvador um so we actually could use
+stuff that was aail available in those
+
+ align:start position:0%
+stuff that was aail available in those
+ 
+
+ align:start position:0%
+stuff that was aail available in those
+communities and Missy will talk to you
+
+ align:start position:0%
+communities and Missy will talk to you
+ 
+
+ align:start position:0%
+communities and Missy will talk to you
+about what we found so we did a quite a
+
+ align:start position:0%
+about what we found so we did a quite a
+ 
+
+ align:start position:0%
+about what we found so we did a quite a
+few experiments where the main variables
+
+ align:start position:0%
+few experiments where the main variables
+ 
+
+ align:start position:0%
+few experiments where the main variables
+that we were really testing were what
+
+ align:start position:0%
+that we were really testing were what
+ 
+
+ align:start position:0%
+that we were really testing were what
+type of material that we wanted to use
+
+ align:start position:0%
+type of material that we wanted to use
+ 
+
+ align:start position:0%
+type of material that we wanted to use
+and then also how many turns of the
+
+ align:start position:0%
+and then also how many turns of the
+ 
+
+ align:start position:0%
+and then also how many turns of the
+Molina that we were going to do um
+
+ align:start position:0%
+Molina that we were going to do um
+ 
+
+ align:start position:0%
+Molina that we were going to do um
+so first to just highlight the um main
+
+ align:start position:0%
+so first to just highlight the um main
+ 
+
+ align:start position:0%
+so first to just highlight the um main
+steps of the experiments that we did
+
+ align:start position:0%
+steps of the experiments that we did
+ 
+
+ align:start position:0%
+steps of the experiments that we did
+first we inserted the material and then
+
+ align:start position:0%
+first we inserted the material and then
+ 
+
+ align:start position:0%
+first we inserted the material and then
+in order to be able to accurately
+
+ align:start position:0%
+in order to be able to accurately
+ 
+
+ align:start position:0%
+in order to be able to accurately
+measure how much space there actually
+
+ align:start position:0%
+measure how much space there actually
+ 
+
+ align:start position:0%
+measure how much space there actually
+existed in between the uh sides of the
+
+ align:start position:0%
+existed in between the uh sides of the
+ 
+
+ align:start position:0%
+existed in between the uh sides of the
+Molino and the um insert we tightened it
+
+ align:start position:0%
+Molino and the um insert we tightened it
+ 
+
+ align:start position:0%
+Molino and the um insert we tightened it
+as far as we could once we uh inserted
+
+ align:start position:0%
+as far as we could once we uh inserted
+ 
+
+ align:start position:0%
+as far as we could once we uh inserted
+the material and then we measured it
+
+ align:start position:0%
+the material and then we measured it
+ 
+
+ align:start position:0%
+the material and then we measured it
+from the number of turns out so uh how
+
+ align:start position:0%
+from the number of turns out so uh how
+ 
+
+ align:start position:0%
+from the number of turns out so uh how
+much we actually loosened it from the
+
+ align:start position:0%
+much we actually loosened it from the
+ 
+
+ align:start position:0%
+much we actually loosened it from the
+most type position and then we used the
+
+ align:start position:0%
+most type position and then we used the
+ 
+
+ align:start position:0%
+most type position and then we used the
+same amount of rice for each experiment
+
+ align:start position:0%
+same amount of rice for each experiment
+ 
+
+ align:start position:0%
+same amount of rice for each experiment
+50 g and we ran it through and once the
+
+ align:start position:0%
+50 g and we ran it through and once the
+ 
+
+ align:start position:0%
+50 g and we ran it through and once the
+had gone through the Molino we uh sifted
+
+ align:start position:0%
+had gone through the Molino we uh sifted
+ 
+
+ align:start position:0%
+had gone through the Molino we uh sifted
+it through to get rid of the really
+
+ align:start position:0%
+it through to get rid of the really
+ 
+
+ align:start position:0%
+it through to get rid of the really
+crushed pieces and then we winnowed it
+
+ align:start position:0%
+crushed pieces and then we winnowed it
+ 
+
+ align:start position:0%
+crushed pieces and then we winnowed it
+so essentially just uh tossing the rice
+
+ align:start position:0%
+so essentially just uh tossing the rice
+ 
+
+ align:start position:0%
+so essentially just uh tossing the rice
+up uh so the air will catch and blow the
+
+ align:start position:0%
+up uh so the air will catch and blow the
+ 
+
+ align:start position:0%
+up uh so the air will catch and blow the
+husks away so you can get rid of the
+
+ align:start position:0%
+husks away so you can get rid of the
+ 
+
+ align:start position:0%
+husks away so you can get rid of the
+husks and then we separated the rice
+
+ align:start position:0%
+husks and then we separated the rice
+ 
+
+ align:start position:0%
+husks and then we separated the rice
+into four main components being the rice
+
+ align:start position:0%
+into four main components being the rice
+ 
+
+ align:start position:0%
+into four main components being the rice
+that was still husk the rice that was
+
+ align:start position:0%
+that was still husk the rice that was
+ 
+
+ align:start position:0%
+that was still husk the rice that was
+whole the rice that was crushed or
+
+ align:start position:0%
+whole the rice that was crushed or
+ 
+
+ align:start position:0%
+whole the rice that was crushed or
+broken and then also if there were any
+
+ align:start position:0%
+broken and then also if there were any
+ 
+
+ align:start position:0%
+broken and then also if there were any
+husks left as well and then we noted um
+
+ align:start position:0%
+husks left as well and then we noted um
+ 
+
+ align:start position:0%
+husks left as well and then we noted um
+and you'll see the bags themselves are
+
+ align:start position:0%
+and you'll see the bags themselves are
+ 
+
+ align:start position:0%
+and you'll see the bags themselves are
+labeled as they're going passing around
+
+ align:start position:0%
+labeled as they're going passing around
+ 
+
+ align:start position:0%
+labeled as they're going passing around
+um how many turns that it took and then
+
+ align:start position:0%
+um how many turns that it took and then
+ 
+
+ align:start position:0%
+um how many turns that it took and then
+uh the number the weight of the still
+
+ align:start position:0%
+uh the number the weight of the still
+ 
+
+ align:start position:0%
+uh the number the weight of the still
+husk rice the weight of the husk rice
+
+ align:start position:0%
+husk rice the weight of the husk rice
+ 
+
+ align:start position:0%
+husk rice the weight of the husk rice
+and if it was in pieces and such so this
+
+ align:start position:0%
+and if it was in pieces and such so this
+ 
+
+ align:start position:0%
+and if it was in pieces and such so this
+is a we don't like this picture is a
+
+ align:start position:0%
+is a we don't like this picture is a
+ 
+
+ align:start position:0%
+is a we don't like this picture is a
+picture of the rice that has still
+
+ align:start position:0%
+picture of the rice that has still
+ 
+
+ align:start position:0%
+picture of the rice that has still
+husked a whole uh grain of H dehusked
+
+ align:start position:0%
+husked a whole uh grain of H dehusked
+ 
+
+ align:start position:0%
+husked a whole uh grain of H dehusked
+rice a broken grain and then some of the
+
+ align:start position:0%
+rice a broken grain and then some of the
+ 
+
+ align:start position:0%
+rice a broken grain and then some of the
+particles that we used to Siff through
+
+ align:start position:0%
+particles that we used to Siff through
+ 
+
+ align:start position:0%
+particles that we used to Siff through
+to get rid
+
+ align:start position:0%
+to get rid
+ 
+
+ align:start position:0%
+to get rid
+of and so one of the experiments we used
+
+ align:start position:0%
+of and so one of the experiments we used
+ 
+
+ align:start position:0%
+of and so one of the experiments we used
+with the honeycomb rubber is what we
+
+ align:start position:0%
+with the honeycomb rubber is what we
+ 
+
+ align:start position:0%
+with the honeycomb rubber is what we
+called it uh
+
+ align:start position:0%
+called it uh
+ 
+
+ align:start position:0%
+called it uh
+that's pictures kind of self-explanatory
+
+ align:start position:0%
+that's pictures kind of self-explanatory
+ 
+
+ align:start position:0%
+that's pictures kind of self-explanatory
+why we call it that but um so we did a
+
+ align:start position:0%
+why we call it that but um so we did a
+ 
+
+ align:start position:0%
+why we call it that but um so we did a
+couple experiments with this and you can
+
+ align:start position:0%
+couple experiments with this and you can
+ 
+
+ align:start position:0%
+couple experiments with this and you can
+see in the pictures that we have uh
+
+ align:start position:0%
+see in the pictures that we have uh
+ 
+
+ align:start position:0%
+see in the pictures that we have uh
+whether the it's kind of hard to see
+
+ align:start position:0%
+whether the it's kind of hard to see
+ 
+
+ align:start position:0%
+whether the it's kind of hard to see
+from these pictures but but um once
+
+ align:start position:0%
+from these pictures but but um once
+ 
+
+ align:start position:0%
+from these pictures but but um once
+we've separated it through what how much
+
+ align:start position:0%
+we've separated it through what how much
+ 
+
+ align:start position:0%
+we've separated it through what how much
+of the rice is still husk how much of
+
+ align:start position:0%
+of the rice is still husk how much of
+ 
+
+ align:start position:0%
+of the rice is still husk how much of
+the rice has been dehusked based on the
+
+ align:start position:0%
+the rice has been dehusked based on the
+ 
+
+ align:start position:0%
+the rice has been dehusked based on the
+number of turns what we noted about the
+
+ align:start position:0%
+number of turns what we noted about the
+ 
+
+ align:start position:0%
+number of turns what we noted about the
+rubber though is that we weren't very
+
+ align:start position:0%
+rubber though is that we weren't very
+ 
+
+ align:start position:0%
+rubber though is that we weren't very
+sure how hazardous the residue that
+
+ align:start position:0%
+sure how hazardous the residue that
+ 
+
+ align:start position:0%
+sure how hazardous the residue that
+might end up on the rice would be
+
+ align:start position:0%
+might end up on the rice would be
+ 
+
+ align:start position:0%
+might end up on the rice would be
+because it's not an organic material uh
+
+ align:start position:0%
+because it's not an organic material uh
+ 
+
+ align:start position:0%
+because it's not an organic material uh
+we also noted that this rubber cost
+
+ align:start position:0%
+we also noted that this rubber cost
+ 
+
+ align:start position:0%
+we also noted that this rubber cost
+about $6 per square foot so it's not too
+
+ align:start position:0%
+about $6 per square foot so it's not too
+ 
+
+ align:start position:0%
+about $6 per square foot so it's not too
+expensive um another we decid to flip
+
+ align:start position:0%
+expensive um another we decid to flip
+ 
+
+ align:start position:0%
+expensive um another we decid to flip
+that rubber around and decided to test
+
+ align:start position:0%
+that rubber around and decided to test
+ 
+
+ align:start position:0%
+that rubber around and decided to test
+with the different textures and uh the
+
+ align:start position:0%
+with the different textures and uh the
+ 
+
+ align:start position:0%
+with the different textures and uh the
+same thing happens with this rubber
+
+ align:start position:0%
+same thing happens with this rubber
+ 
+
+ align:start position:0%
+same thing happens with this rubber
+again it's not organic so we we did a
+
+ align:start position:0%
+again it's not organic so we we did a
+ 
+
+ align:start position:0%
+again it's not organic so we we did a
+quick little data sheet uh based on the
+
+ align:start position:0%
+quick little data sheet uh based on the
+ 
+
+ align:start position:0%
+quick little data sheet uh based on the
+number of turns and the mass we started
+
+ align:start position:0%
+number of turns and the mass we started
+ 
+
+ align:start position:0%
+number of turns and the mass we started
+with and then the mess that was broken
+
+ align:start position:0%
+with and then the mess that was broken
+ 
+
+ align:start position:0%
+with and then the mess that was broken
+and just to get an idea um then we
+
+ align:start position:0%
+and just to get an idea um then we
+ 
+
+ align:start position:0%
+and just to get an idea um then we
+continued on with leather which was the
+
+ align:start position:0%
+continued on with leather which was the
+ 
+
+ align:start position:0%
+continued on with leather which was the
+kind um since it's organic and a little
+
+ align:start position:0%
+kind um since it's organic and a little
+ 
+
+ align:start position:0%
+kind um since it's organic and a little
+bit cheaper than the rubber made us feel
+
+ align:start position:0%
+bit cheaper than the rubber made us feel
+ 
+
+ align:start position:0%
+bit cheaper than the rubber made us feel
+a little bit better as the one we kind
+
+ align:start position:0%
+a little bit better as the one we kind
+ 
+
+ align:start position:0%
+a little bit better as the one we kind
+of preferred uh and it's very readily
+
+ align:start position:0%
+of preferred uh and it's very readily
+ 
+
+ align:start position:0%
+of preferred uh and it's very readily
+tested um but we were trying to decide
+
+ align:start position:0%
+tested um but we were trying to decide
+ 
+
+ align:start position:0%
+tested um but we were trying to decide
+how many layers of the leather we should
+
+ align:start position:0%
+how many layers of the leather we should
+ 
+
+ align:start position:0%
+how many layers of the leather we should
+um put
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so all right so as we did the
+
+ align:start position:0%
+so all right so as we did the
+ 
+
+ align:start position:0%
+so all right so as we did the
+experiments with the leather sometimes
+
+ align:start position:0%
+experiments with the leather sometimes
+ 
+
+ align:start position:0%
+experiments with the leather sometimes
+we processed it through twice sometimes
+
+ align:start position:0%
+we processed it through twice sometimes
+ 
+
+ align:start position:0%
+we processed it through twice sometimes
+we did different number of turns with
+
+ align:start position:0%
+we did different number of turns with
+ 
+
+ align:start position:0%
+we did different number of turns with
+different layers and you can see most of
+
+ align:start position:0%
+different layers and you can see most of
+ 
+
+ align:start position:0%
+different layers and you can see most of
+them are relatively the same somewhere a
+
+ align:start position:0%
+them are relatively the same somewhere a
+ 
+
+ align:start position:0%
+them are relatively the same somewhere a
+little bit better um but But ultimately
+
+ align:start position:0%
+little bit better um but But ultimately
+ 
+
+ align:start position:0%
+little bit better um but But ultimately
+we decided um well we decided that the
+
+ align:start position:0%
+we decided um well we decided that the
+ 
+
+ align:start position:0%
+we decided um well we decided that the
+material wasn't the biggest part but we
+
+ align:start position:0%
+material wasn't the biggest part but we
+ 
+
+ align:start position:0%
+material wasn't the biggest part but we
+still decided to test with uh duct tape
+
+ align:start position:0%
+still decided to test with uh duct tape
+ 
+
+ align:start position:0%
+still decided to test with uh duct tape
+which we found unfortunately wore away
+
+ align:start position:0%
+which we found unfortunately wore away
+ 
+
+ align:start position:0%
+which we found unfortunately wore away
+relatively quickly and then we tried for
+
+ align:start position:0%
+relatively quickly and then we tried for
+ 
+
+ align:start position:0%
+relatively quickly and then we tried for
+the heck of it a flat sheet metal
+
+ align:start position:0%
+the heck of it a flat sheet metal
+ 
+
+ align:start position:0%
+the heck of it a flat sheet metal
+surface and essentially that was a
+
+ align:start position:0%
+surface and essentially that was a
+ 
+
+ align:start position:0%
+surface and essentially that was a
+disaster so I'll hand it over to Benji
+
+ align:start position:0%
+disaster so I'll hand it over to Benji
+ 
+
+ align:start position:0%
+disaster so I'll hand it over to Benji
+um so the so one of the reasons that we
+
+ align:start position:0%
+um so the so one of the reasons that we
+ 
+
+ align:start position:0%
+um so the so one of the reasons that we
+decided to go against the flat metal was
+
+ align:start position:0%
+decided to go against the flat metal was
+ 
+
+ align:start position:0%
+decided to go against the flat metal was
+because the rice wasn't actually fed in
+
+ align:start position:0%
+because the rice wasn't actually fed in
+ 
+
+ align:start position:0%
+because the rice wasn't actually fed in
+into the Molino um the way that the
+
+ align:start position:0%
+into the Molino um the way that the
+ 
+
+ align:start position:0%
+into the Molino um the way that the
+plate the way that the back plate is
+
+ align:start position:0%
+plate the way that the back plate is
+ 
+
+ align:start position:0%
+plate the way that the back plate is
+designed and shaped the it feeds in the
+
+ align:start position:0%
+designed and shaped the it feeds in the
+ 
+
+ align:start position:0%
+designed and shaped the it feeds in the
+rice and so we decided to just focus on
+
+ align:start position:0%
+rice and so we decided to just focus on
+ 
+
+ align:start position:0%
+rice and so we decided to just focus on
+the one side of um on the back side of
+
+ align:start position:0%
+the one side of um on the back side of
+ 
+
+ align:start position:0%
+the one side of um on the back side of
+the Molino and just adding the material
+
+ align:start position:0%
+the Molino and just adding the material
+ 
+
+ align:start position:0%
+the Molino and just adding the material
+there um so as you can see like we have
+
+ align:start position:0%
+there um so as you can see like we have
+ 
+
+ align:start position:0%
+there um so as you can see like we have
+a lot of the tests and um we did a lot
+
+ align:start position:0%
+a lot of the tests and um we did a lot
+ 
+
+ align:start position:0%
+a lot of the tests and um we did a lot
+of tests but actually there was no
+
+ align:start position:0%
+of tests but actually there was no
+ 
+
+ align:start position:0%
+of tests but actually there was no
+conclusive like awesome material that
+
+ align:start position:0%
+conclusive like awesome material that
+ 
+
+ align:start position:0%
+conclusive like awesome material that
+was way better at husting the rice than
+
+ align:start position:0%
+was way better at husting the rice than
+ 
+
+ align:start position:0%
+was way better at husting the rice than
+the others um and so basically we said
+
+ align:start position:0%
+the others um and so basically we said
+ 
+
+ align:start position:0%
+the others um and so basically we said
+okay well the the we noticed that the
+
+ align:start position:0%
+okay well the the we noticed that the
+ 
+
+ align:start position:0%
+okay well the the we noticed that the
+most important variable for deciding
+
+ align:start position:0%
+most important variable for deciding
+ 
+
+ align:start position:0%
+most important variable for deciding
+that was the number of turns away from
+
+ align:start position:0%
+that was the number of turns away from
+ 
+
+ align:start position:0%
+that was the number of turns away from
+you know from tightening it and so we
+
+ align:start position:0%
+you know from tightening it and so we
+ 
+
+ align:start position:0%
+you know from tightening it and so we
+said well you know we still have to
+
+ align:start position:0%
+said well you know we still have to
+ 
+
+ align:start position:0%
+said well you know we still have to
+decide on a material so we wanted to um
+
+ align:start position:0%
+decide on a material so we wanted to um
+ 
+
+ align:start position:0%
+decide on a material so we wanted to um
+optimize how much how much rice was
+
+ align:start position:0%
+optimize how much how much rice was
+ 
+
+ align:start position:0%
+optimize how much how much rice was
+broken um and also just think about uh
+
+ align:start position:0%
+broken um and also just think about uh
+ 
+
+ align:start position:0%
+broken um and also just think about uh
+the robustness and the availability of
+
+ align:start position:0%
+the robustness and the availability of
+ 
+
+ align:start position:0%
+the robustness and the availability of
+the material um and so we decided on
+
+ align:start position:0%
+the material um and so we decided on
+ 
+
+ align:start position:0%
+the material um and so we decided on
+choosing leather um because it's
+
+ align:start position:0%
+choosing leather um because it's
+ 
+
+ align:start position:0%
+choosing leather um because it's
+availability and because of um because
+
+ align:start position:0%
+availability and because of um because
+ 
+
+ align:start position:0%
+availability and because of um because
+it is organic it's much safer um and so
+
+ align:start position:0%
+it is organic it's much safer um and so
+ 
+
+ align:start position:0%
+it is organic it's much safer um and so
+going we did a couple more uh
+
+ align:start position:0%
+going we did a couple more uh
+ 
+
+ align:start position:0%
+going we did a couple more uh
+uh exploratory test with the leather um
+
+ align:start position:0%
+uh exploratory test with the leather um
+ 
+
+ align:start position:0%
+uh exploratory test with the leather um
+and trying to decide how soft we wanted
+
+ align:start position:0%
+and trying to decide how soft we wanted
+ 
+
+ align:start position:0%
+and trying to decide how soft we wanted
+to make the leather effectively like how
+
+ align:start position:0%
+to make the leather effectively like how
+ 
+
+ align:start position:0%
+to make the leather effectively like how
+it interacts with the rice and so we
+
+ align:start position:0%
+it interacts with the rice and so we
+ 
+
+ align:start position:0%
+it interacts with the rice and so we
+tried with two pieces of leather um
+
+ align:start position:0%
+tried with two pieces of leather um
+ 
+
+ align:start position:0%
+tried with two pieces of leather um
+glued together and then three pieces
+
+ align:start position:0%
+glued together and then three pieces
+ 
+
+ align:start position:0%
+glued together and then three pieces
+together and um unsurprisingly we
+
+ align:start position:0%
+together and um unsurprisingly we
+ 
+
+ align:start position:0%
+together and um unsurprisingly we
+actually found that they were very
+
+ align:start position:0%
+actually found that they were very
+ 
+
+ align:start position:0%
+actually found that they were very
+similar as well um so you know so we
+
+ align:start position:0%
+similar as well um so you know so we
+ 
+
+ align:start position:0%
+similar as well um so you know so we
+decided on going with two pieces of
+
+ align:start position:0%
+decided on going with two pieces of
+ 
+
+ align:start position:0%
+decided on going with two pieces of
+leather rather than the three because
+
+ align:start position:0%
+leather rather than the three because
+ 
+
+ align:start position:0%
+leather rather than the three because
+it's just it's less material it's less
+
+ align:start position:0%
+it's just it's less material it's less
+ 
+
+ align:start position:0%
+it's just it's less material it's less
+expensive um and so going forward we're
+
+ align:start position:0%
+expensive um and so going forward we're
+ 
+
+ align:start position:0%
+expensive um and so going forward we're
+going to be optimizing that sort of two-
+
+ align:start position:0%
+going to be optimizing that sort of two-
+ 
+
+ align:start position:0%
+going to be optimizing that sort of two-
+layer uh process
+
+ align:start position:0%
+layer uh process
+ 
+
+ align:start position:0%
+layer uh process
+um or you know how we're going to be
+
+ align:start position:0%
+um or you know how we're going to be
+ 
+
+ align:start position:0%
+um or you know how we're going to be
+gluing those together you know what type
+
+ align:start position:0%
+gluing those together you know what type
+ 
+
+ align:start position:0%
+gluing those together you know what type
+of glue um or if we're going to sew them
+
+ align:start position:0%
+of glue um or if we're going to sew them
+ 
+
+ align:start position:0%
+of glue um or if we're going to sew them
+together because the glue might not be
+
+ align:start position:0%
+together because the glue might not be
+ 
+
+ align:start position:0%
+together because the glue might not be
+available um and so we'll be looking at
+
+ align:start position:0%
+available um and so we'll be looking at
+ 
+
+ align:start position:0%
+available um and so we'll be looking at
+those sort of details of um of that
+
+ align:start position:0%
+those sort of details of um of that
+ 
+
+ align:start position:0%
+those sort of details of um of that
+leather material um but also we want to
+
+ align:start position:0%
+leather material um but also we want to
+ 
+
+ align:start position:0%
+leather material um but also we want to
+look at the process of how it's being uh
+
+ align:start position:0%
+look at the process of how it's being uh
+ 
+
+ align:start position:0%
+look at the process of how it's being uh
+how it's being put through the mill um
+
+ align:start position:0%
+how it's being put through the mill um
+ 
+
+ align:start position:0%
+how it's being put through the mill um
+so not only changing the material but
+
+ align:start position:0%
+so not only changing the material but
+ 
+
+ align:start position:0%
+so not only changing the material but
+also thinking well if we change the
+
+ align:start position:0%
+also thinking well if we change the
+ 
+
+ align:start position:0%
+also thinking well if we change the
+number of turns to you know say three
+
+ align:start position:0%
+number of turns to you know say three
+ 
+
+ align:start position:0%
+number of turns to you know say three
+times more than usual and then going
+
+ align:start position:0%
+times more than usual and then going
+ 
+
+ align:start position:0%
+times more than usual and then going
+through it twice you know does that
+
+ align:start position:0%
+through it twice you know does that
+ 
+
+ align:start position:0%
+through it twice you know does that
+change the results at all like is it
+
+ align:start position:0%
+change the results at all like is it
+ 
+
+ align:start position:0%
+change the results at all like is it
+more gentle with um with the rice if you
+
+ align:start position:0%
+more gentle with um with the rice if you
+ 
+
+ align:start position:0%
+more gentle with um with the rice if you
+process through it twice while husking
+
+ align:start position:0%
+process through it twice while husking
+ 
+
+ align:start position:0%
+process through it twice while husking
+more of the material um so we'll be
+
+ align:start position:0%
+more of the material um so we'll be
+ 
+
+ align:start position:0%
+more of the material um so we'll be
+looking at that or if we can do anything
+
+ align:start position:0%
+looking at that or if we can do anything
+ 
+
+ align:start position:0%
+looking at that or if we can do anything
+to the right prior to actually running
+
+ align:start position:0%
+to the right prior to actually running
+ 
+
+ align:start position:0%
+to the right prior to actually running
+it through the mill that would make it
+
+ align:start position:0%
+it through the mill that would make it
+ 
+
+ align:start position:0%
+it through the mill that would make it
+more effective um for dehusking it um so
+
+ align:start position:0%
+more effective um for dehusking it um so
+ 
+
+ align:start position:0%
+more effective um for dehusking it um so
+that's about it if you guys have any
+
+ align:start position:0%
+that's about it if you guys have any
+ 
+
+ align:start position:0%
+that's about it if you guys have any
+questions we can also show how this is
+
+ align:start position:0%
+questions we can also show how this is
+ 
+
+ align:start position:0%
+questions we can also show how this is
+working so far to you one reason was for
+
+ align:start position:0%
+working so far to you one reason was for
+ 
+
+ align:start position:0%
+working so far to you one reason was for
+explaining it to Community Partners it's
+
+ align:start position:0%
+explaining it to Community Partners it's
+ 
+
+ align:start position:0%
+explaining it to Community Partners it's
+a lot easier to say six turns from as
+
+ align:start position:0%
+a lot easier to say six turns from as
+ 
+
+ align:start position:0%
+a lot easier to say six turns from as
+tight as you can tighten it as opposed
+
+ align:start position:0%
+tight as you can tighten it as opposed
+ 
+
+ align:start position:0%
+tight as you can tighten it as opposed
+to 3 mm in between cuz we don't want to
+
+ align:start position:0%
+to 3 mm in between cuz we don't want to
+ 
+
+ align:start position:0%
+to 3 mm in between cuz we don't want to
+use exact measurements that and also
+
+ align:start position:0%
+use exact measurements that and also
+ 
+
+ align:start position:0%
+use exact measurements that and also
+kind of gave us um using different
+
+ align:start position:0%
+kind of gave us um using different
+ 
+
+ align:start position:0%
+kind of gave us um using different
+materials gave us a lot of flexibility
+
+ align:start position:0%
+materials gave us a lot of flexibility
+ 
+
+ align:start position:0%
+materials gave us a lot of flexibility
+with how much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+weend so this is
+
+ align:start position:0%
+weend so this is
+ 
+
+ align:start position:0%
+weend so this is
+the talking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and then how many turns should we do
+
+ align:start position:0%
+so and then how many turns should we do
+ 
+
+ align:start position:0%
+so and then how many turns should we do
+three three so
+
+ align:start position:0%
+three three so
+ 
+
+ align:start position:0%
+three three so
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+two maybe we can do a little more so
+
+ align:start position:0%
+two maybe we can do a little more so
+ 
+
+ align:start position:0%
+two maybe we can do a little more so
+it's easier
+
+ align:start position:0%
+it's easier
+ 
+
+ align:start position:0%
+it's easier
+after yeah four
+
+ align:start position:0%
+after yeah four
+ 
+
+ align:start position:0%
+after yeah four
+and and it takes a little bit of um like
+
+ align:start position:0%
+and and it takes a little bit of um like
+ 
+
+ align:start position:0%
+and and it takes a little bit of um like
+the first two turns and the last two
+
+ align:start position:0%
+the first two turns and the last two
+ 
+
+ align:start position:0%
+the first two turns and the last two
+turns are um very awkward yeah a little
+
+ align:start position:0%
+turns are um very awkward yeah a little
+ 
+
+ align:start position:0%
+turns are um very awkward yeah a little
+bit difficult it takes a while for it to
+
+ align:start position:0%
+bit difficult it takes a while for it to
+ 
+
+ align:start position:0%
+bit difficult it takes a while for it to
+start because it just um needs some
+
+ align:start position:0%
+start because it just um needs some
+ 
+
+ align:start position:0%
+start because it just um needs some
+amount of rice to to be in there see
+
+ align:start position:0%
+amount of rice to to be in there see
+ 
+
+ align:start position:0%
+amount of rice to to be in there see
+like we you do
+
+ align:start position:0%
+like we you do
+ 
+
+ align:start position:0%
+like we you do
+just from the little bit that has come
+
+ align:start position:0%
+just from the little bit that has come
+ 
+
+ align:start position:0%
+just from the little bit that has come
+out already there's a lot of broken
+
+ align:start position:0%
+out already there's a lot of broken
+ 
+
+ align:start position:0%
+out already there's a lot of broken
+pieces so like with with this setup
+
+ align:start position:0%
+pieces so like with with this setup
+ 
+
+ align:start position:0%
+pieces so like with with this setup
+we've done it at like four five six
+
+ align:start position:0%
+we've done it at like four five six
+ 
+
+ align:start position:0%
+we've done it at like four five six
+turns just because we found that like
+
+ align:start position:0%
+turns just because we found that like
+ 
+
+ align:start position:0%
+turns just because we found that like
+having the race not actually dehus oh
+
+ align:start position:0%
+having the race not actually dehus oh
+ 
+
+ align:start position:0%
+having the race not actually dehus oh
+it's against this we'd rather have rice
+
+ align:start position:0%
+it's against this we'd rather have rice
+ 
+
+ align:start position:0%
+it's against this we'd rather have rice
+not de hust as opposed to like a lot of
+
+ align:start position:0%
+not de hust as opposed to like a lot of
+ 
+
+ align:start position:0%
+not de hust as opposed to like a lot of
+broken
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pieces think a few people can do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it um I'm I'm not sure if you guys also
+
+ align:start position:0%
+it um I'm I'm not sure if you guys also
+ 
+
+ align:start position:0%
+it um I'm I'm not sure if you guys also
+saw the bag that was just it broken so
+
+ align:start position:0%
+saw the bag that was just it broken so
+ 
+
+ align:start position:0%
+saw the bag that was just it broken so
+basically it still hust it still hust it
+
+ align:start position:0%
+basically it still hust it still hust it
+ 
+
+ align:start position:0%
+basically it still hust it still hust it
+without this material but um it's
+
+ align:start position:0%
+without this material but um it's
+ 
+
+ align:start position:0%
+without this material but um it's
+actually much more effective at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Le from a shoe do you know how they made
+
+ align:start position:0%
+Le from a shoe do you know how they made
+ 
+
+ align:start position:0%
+Le from a shoe do you know how they made
+it cuz leather tanning I mean that
+
+ align:start position:0%
+it cuz leather tanning I mean that
+ 
+
+ align:start position:0%
+it cuz leather tanning I mean that
+leather could be the most toxic thing
+
+ align:start position:0%
+leather could be the most toxic thing
+ 
+
+ align:start position:0%
+leather could be the most toxic thing
+you have yeah conceivably I mean like
+
+ align:start position:0%
+you have yeah conceivably I mean like
+ 
+
+ align:start position:0%
+you have yeah conceivably I mean like
+one of the things that is used in
+
+ align:start position:0%
+one of the things that is used in
+ 
+
+ align:start position:0%
+one of the things that is used in
+leather tanning is like chromium sulfate
+
+ align:start position:0%
+leather tanning is like chromium sulfate
+ 
+
+ align:start position:0%
+leather tanning is like chromium sulfate
+as the tanning agent so like it's just
+
+ align:start position:0%
+as the tanning agent so like it's just
+ 
+
+ align:start position:0%
+as the tanning agent so like it's just
+worth finding out I mean the another
+
+ align:start position:0%
+worth finding out I mean the another
+ 
+
+ align:start position:0%
+worth finding out I mean the another
+option is tannning which comes from oak
+
+ align:start position:0%
+option is tannning which comes from oak
+ 
+
+ align:start position:0%
+option is tannning which comes from oak
+trees guess have a lot of O Tre Salvador
+
+ align:start position:0%
+trees guess have a lot of O Tre Salvador
+ 
+
+ align:start position:0%
+trees guess have a lot of O Tre Salvador
+but um yeah it's worth finding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out cu it would be sad to poison
+
+ align:start position:0%
+out cu it would be sad to poison
+ 
+
+ align:start position:0%
+out cu it would be sad to poison
+everybody
+
+ align:start position:0%
+everybody
+ 
+
+ align:start position:0%
+everybody
+right it's hard to get invited back
+
+ align:start position:0%
+right it's hard to get invited back
+ 
+
+ align:start position:0%
+right it's hard to get invited back
+after well they can't invite you back
+
+ align:start position:0%
+after well they can't invite you back
+ 
+
+ align:start position:0%
+after well they can't invite you back
+after they're all dead we've been also
+
+ align:start position:0%
+after they're all dead we've been also
+ 
+
+ align:start position:0%
+after they're all dead we've been also
+we've been um we've been waiting for
+
+ align:start position:0%
+we've been um we've been waiting for
+ 
+
+ align:start position:0%
+we've been um we've been waiting for
+them to respond to
+
+ align:start position:0%
+them to respond to
+ 
+
+ align:start position:0%
+them to respond to
+um questions but some of the questions
+
+ align:start position:0%
+um questions but some of the questions
+ 
+
+ align:start position:0%
+um questions but some of the questions
+um that we've been trying to get answers
+
+ align:start position:0%
+um that we've been trying to get answers
+ 
+
+ align:start position:0%
+um that we've been trying to get answers
+to are like how many how many people may
+
+ align:start position:0%
+to are like how many how many people may
+ 
+
+ align:start position:0%
+to are like how many how many people may
+meet the how many people can use it
+
+ align:start position:0%
+meet the how many people can use it
+ 
+
+ align:start position:0%
+meet the how many people can use it
+would it be a family or whole community
+
+ align:start position:0%
+would it be a family or whole community
+ 
+
+ align:start position:0%
+would it be a family or whole community
+and how much rice do they consume how
+
+ align:start position:0%
+and how much rice do they consume how
+ 
+
+ align:start position:0%
+and how much rice do they consume how
+much right can they grow and I think
+
+ align:start position:0%
+much right can they grow and I think
+ 
+
+ align:start position:0%
+much right can they grow and I think
+that's going to it's going to be
+
+ align:start position:0%
+that's going to it's going to be
+ 
+
+ align:start position:0%
+that's going to it's going to be
+important for us to know in terms of the
+
+ align:start position:0%
+important for us to know in terms of the
+ 
+
+ align:start position:0%
+important for us to know in terms of the
+material and how durable the material is
+
+ align:start position:0%
+material and how durable the material is
+ 
+
+ align:start position:0%
+material and how durable the material is
+and do every does each family have um a
+
+ align:start position:0%
+and do every does each family have um a
+ 
+
+ align:start position:0%
+and do every does each family have um a
+piece of this leather or is it
+
+ align:start position:0%
+piece of this leather or is it
+ 
+
+ align:start position:0%
+piece of this leather or is it
+permanently attached to the
+
+ align:start position:0%
+permanently attached to the
+ 
+
+ align:start position:0%
+permanently attached to the
+so those are a lot of questions that we
+
+ align:start position:0%
+so those are a lot of questions that we
+ 
+
+ align:start position:0%
+so those are a lot of questions that we
+still I just wouldn't take for granted
+
+ align:start position:0%
+still I just wouldn't take for granted
+ 
+
+ align:start position:0%
+still I just wouldn't take for granted
+what isn't isn't toxic based on like cuz
+
+ align:start position:0%
+what isn't isn't toxic based on like cuz
+ 
+
+ align:start position:0%
+what isn't isn't toxic based on like cuz
+the rubber could be fine for all we know
+
+ align:start position:0%
+the rubber could be fine for all we know
+ 
+
+ align:start position:0%
+the rubber could be fine for all we know
+and the leather could be we're not sure
+
+ align:start position:0%
+and the leather could be we're not sure
+ 
+
+ align:start position:0%
+and the leather could be we're not sure
+poisonous um and and if what comes off
+
+ align:start position:0%
+poisonous um and and if what comes off
+ 
+
+ align:start position:0%
+poisonous um and and if what comes off
+is stuff that you can wash off then it's
+
+ align:start position:0%
+is stuff that you can wash off then it's
+ 
+
+ align:start position:0%
+is stuff that you can wash off then it's
+not the end well the problem with the
+
+ align:start position:0%
+not the end well the problem with the
+ 
+
+ align:start position:0%
+not the end well the problem with the
+inner tube was that it was leaving like
+
+ align:start position:0%
+inner tube was that it was leaving like
+ 
+
+ align:start position:0%
+inner tube was that it was leaving like
+a black residue on the right right yeah
+
+ align:start position:0%
+a black residue on the right right yeah
+ 
+
+ align:start position:0%
+a black residue on the right right yeah
+if if it's like marking with a crayon on
+
+ align:start position:0%
+if if it's like marking with a crayon on
+ 
+
+ align:start position:0%
+if if it's like marking with a crayon on
+each one but if there's like you know a
+
+ align:start position:0%
+each one but if there's like you know a
+ 
+
+ align:start position:0%
+each one but if there's like you know a
+little bit of rubber dust that comes off
+
+ align:start position:0%
+little bit of rubber dust that comes off
+ 
+
+ align:start position:0%
+little bit of rubber dust that comes off
+but it's not adhering to anything then
+
+ align:start position:0%
+but it's not adhering to anything then
+ 
+
+ align:start position:0%
+but it's not adhering to anything then
+you can wash it off yellow whatever yeah
+
+ align:start position:0%
+you can wash it off yellow whatever yeah
+ 
+
+ align:start position:0%
+you can wash it off yellow whatever yeah
+yeah so it's just worth exper you know
+
+ align:start position:0%
+yeah so it's just worth exper you know
+ 
+
+ align:start position:0%
+yeah so it's just worth exper you know
+actually finding out what the what
+
+ align:start position:0%
+actually finding out what the what
+ 
+
+ align:start position:0%
+actually finding out what the what
+chemicals are actually present cuz it
+
+ align:start position:0%
+chemicals are actually present cuz it
+ 
+
+ align:start position:0%
+chemicals are actually present cuz it
+might be that you could eat you know a
+
+ align:start position:0%
+might be that you could eat you know a
+ 
+
+ align:start position:0%
+might be that you could eat you know a
+loaf of that rubber and you'd be fine
+
+ align:start position:0%
+loaf of that rubber and you'd be fine
+ 
+
+ align:start position:0%
+loaf of that rubber and you'd be fine
+but if you chew on the leather for a
+
+ align:start position:0%
+but if you chew on the leather for a
+ 
+
+ align:start position:0%
+but if you chew on the leather for a
+little bit and get SI it's just hard to
+
+ align:start position:0%
+little bit and get SI it's just hard to
+ 
+
+ align:start position:0%
+little bit and get SI it's just hard to
+control that you know what I mean like
+
+ align:start position:0%
+control that you know what I mean like
+ 
+
+ align:start position:0%
+control that you know what I mean like
+the shops will be do different I yeah
+
+ align:start position:0%
+the shops will be do different I yeah
+ 
+
+ align:start position:0%
+the shops will be do different I yeah
+well I think I think it's worth figuring
+
+ align:start position:0%
+well I think I think it's worth figuring
+ 
+
+ align:start position:0%
+well I think I think it's worth figuring
+out like worst case scenario this
+
+ align:start position:0%
+out like worst case scenario this
+ 
+
+ align:start position:0%
+out like worst case scenario this
+leather is tanned with whatever chemical
+
+ align:start position:0%
+leather is tanned with whatever chemical
+ 
+
+ align:start position:0%
+leather is tanned with whatever chemical
+Steve just mentioned is that something
+
+ align:start position:0%
+Steve just mentioned is that something
+ 
+
+ align:start position:0%
+Steve just mentioned is that something
+that's going to get absorbed into the
+
+ align:start position:0%
+that's going to get absorbed into the
+ 
+
+ align:start position:0%
+that's going to get absorbed into the
+rice or something that's going to be
+
+ align:start position:0%
+rice or something that's going to be
+ 
+
+ align:start position:0%
+rice or something that's going to be
+washed off during processing if it's
+
+ align:start position:0%
+washed off during processing if it's
+ 
+
+ align:start position:0%
+washed off during processing if it's
+going to get absorbed maybe we need to
+
+ align:start position:0%
+going to get absorbed maybe we need to
+ 
+
+ align:start position:0%
+going to get absorbed maybe we need to
+knock this leather out as a contender
+
+ align:start position:0%
+knock this leather out as a contender
+ 
+
+ align:start position:0%
+knock this leather out as a contender
+and find something similar cuz it seemed
+
+ align:start position:0%
+and find something similar cuz it seemed
+ 
+
+ align:start position:0%
+and find something similar cuz it seemed
+like different materials all seem to
+
+ align:start position:0%
+like different materials all seem to
+ 
+
+ align:start position:0%
+like different materials all seem to
+work basically the same and so you know
+
+ align:start position:0%
+work basically the same and so you know
+ 
+
+ align:start position:0%
+work basically the same and so you know
+would an old t-shirt work just as well
+
+ align:start position:0%
+would an old t-shirt work just as well
+ 
+
+ align:start position:0%
+would an old t-shirt work just as well
+or something I don't know how did fabric
+
+ align:start position:0%
+or something I don't know how did fabric
+ 
+
+ align:start position:0%
+or something I don't know how did fabric
+work did you try yeah so that's the
+
+ align:start position:0%
+work did you try yeah so that's the
+ 
+
+ align:start position:0%
+work did you try yeah so that's the
+reason we did the the duct tape was like
+
+ align:start position:0%
+reason we did the the duct tape was like
+ 
+
+ align:start position:0%
+reason we did the the duct tape was like
+not as an actual sort of design but just
+
+ align:start position:0%
+not as an actual sort of design but just
+ 
+
+ align:start position:0%
+not as an actual sort of design but just
+to see how long it lasts because it is
+
+ align:start position:0%
+to see how long it lasts because it is
+ 
+
+ align:start position:0%
+to see how long it lasts because it is
+like generally wear resistant but it
+
+ align:start position:0%
+like generally wear resistant but it
+ 
+
+ align:start position:0%
+like generally wear resistant but it
+does wear and like we tried this um
+
+ align:start position:0%
+does wear and like we tried this um
+ 
+
+ align:start position:0%
+does wear and like we tried this um
+foam material and that it like you can
+
+ align:start position:0%
+foam material and that it like you can
+ 
+
+ align:start position:0%
+foam material and that it like you can
+see that with 50 g with the 50 with even
+
+ align:start position:0%
+see that with 50 g with the 50 with even
+ 
+
+ align:start position:0%
+see that with 50 g with the 50 with even
+running like this much of 50 g with the
+
+ align:start position:0%
+running like this much of 50 g with the
+ 
+
+ align:start position:0%
+running like this much of 50 g with the
+duct tape you could tell that it was
+
+ align:start position:0%
+duct tape you could tell that it was
+ 
+
+ align:start position:0%
+duct tape you could tell that it was
+worn and like they actually do tests
+
+ align:start position:0%
+worn and like they actually do tests
+ 
+
+ align:start position:0%
+worn and like they actually do tests
+with um between Denim and Leather like
+
+ align:start position:0%
+with um between Denim and Leather like
+ 
+
+ align:start position:0%
+with um between Denim and Leather like
+for motorcycles and like they simulate
+
+ align:start position:0%
+for motorcycles and like they simulate
+ 
+
+ align:start position:0%
+for motorcycles and like they simulate
+someone falling down and like the
+
+ align:start position:0%
+someone falling down and like the
+ 
+
+ align:start position:0%
+someone falling down and like the
+leather lasts for 90 ft of dragging
+
+ align:start position:0%
+leather lasts for 90 ft of dragging
+ 
+
+ align:start position:0%
+leather lasts for 90 ft of dragging
+while denim lasts for five wow so and
+
+ align:start position:0%
+while denim lasts for five wow so and
+ 
+
+ align:start position:0%
+while denim lasts for five wow so and
+denim is like very durable right like
+
+ align:start position:0%
+denim is like very durable right like
+ 
+
+ align:start position:0%
+denim is like very durable right like
+but the inside I don't know if Benji
+
+ align:start position:0%
+but the inside I don't know if Benji
+ 
+
+ align:start position:0%
+but the inside I don't know if Benji
+showed you about the inside of these
+
+ align:start position:0%
+showed you about the inside of these
+ 
+
+ align:start position:0%
+showed you about the inside of these
+kind of small
+
+ align:start position:0%
+kind of small
+ 
+
+ align:start position:0%
+kind of small
+can oh yeah I it's like you're trying to
+
+ align:start position:0%
+can oh yeah I it's like you're trying to
+ 
+
+ align:start position:0%
+can oh yeah I it's like you're trying to
+gr grind sandpaper it's going to wreck
+
+ align:start position:0%
+gr grind sandpaper it's going to wreck
+ 
+
+ align:start position:0%
+gr grind sandpaper it's going to wreck
+whatever you put it both sides are brid
+
+ align:start position:0%
+whatever you put it both sides are brid
+ 
+
+ align:start position:0%
+whatever you put it both sides are brid
+so there a reason why that thing's made
+
+ align:start position:0%
+so there a reason why that thing's made
+ 
+
+ align:start position:0%
+so there a reason why that thing's made
+out of metal
+
+ align:start position:0%
+out of metal
+ 
+
+ align:start position:0%
+out of metal
+yeah so that's why we were looking at
+
+ align:start position:0%
+yeah so that's why we were looking at
+ 
+
+ align:start position:0%
+yeah so that's why we were looking at
+doing flat metal um so that that was
+
+ align:start position:0%
+doing flat metal um so that that was
+ 
+
+ align:start position:0%
+doing flat metal um so that that was
+more durable but you know like I
+
+ align:start position:0%
+more durable but you know like I
+ 
+
+ align:start position:0%
+more durable but you know like I
+mentioned we need the we need the design
+
+ align:start position:0%
+mentioned we need the we need the design
+ 
+
+ align:start position:0%
+mentioned we need the we need the design
+on the inner part um to to pull the rice
+
+ align:start position:0%
+on the inner part um to to pull the rice
+ 
+
+ align:start position:0%
+on the inner part um to to pull the rice
+out otherwise two pie grinding against
+
+ align:start position:0%
+out otherwise two pie grinding against
+ 
+
+ align:start position:0%
+out otherwise two pie grinding against
+each other no R so even if you made the
+
+ align:start position:0%
+each other no R so even if you made the
+ 
+
+ align:start position:0%
+each other no R so even if you made the
+the in
+
+ align:start position:0%
+the in
+ 
+
+ align:start position:0%
+the in
+uh the one the metal piece that goes on
+
+ align:start position:0%
+uh the one the metal piece that goes on
+ 
+
+ align:start position:0%
+uh the one the metal piece that goes on
+this side did you make the inner hole
+
+ align:start position:0%
+this side did you make the inner hole
+ 
+
+ align:start position:0%
+this side did you make the inner hole
+big enough so that um the rice could
+
+ align:start position:0%
+big enough so that um the rice could
+ 
+
+ align:start position:0%
+big enough so that um the rice could
+come out through yeah so you so it needs
+
+ align:start position:0%
+come out through yeah so you so it needs
+ 
+
+ align:start position:0%
+come out through yeah so you so it needs
+the like the this cutting in yeah the
+
+ align:start position:0%
+the like the this cutting in yeah the
+ 
+
+ align:start position:0%
+the like the this cutting in yeah the
+dimension like it can't actually just be
+
+ align:start position:0%
+dimension like it can't actually just be
+ 
+
+ align:start position:0%
+dimension like it can't actually just be
+a flat surface no matter how big the
+
+ align:start position:0%
+a flat surface no matter how big the
+ 
+
+ align:start position:0%
+a flat surface no matter how big the
+hole is because the rice isn't allowed
+
+ align:start position:0%
+hole is because the rice isn't allowed
+ 
+
+ align:start position:0%
+hole is because the rice isn't allowed
+to like feed into it these ridges like
+
+ align:start position:0%
+to like feed into it these ridges like
+ 
+
+ align:start position:0%
+to like feed into it these ridges like
+wear the material down a lot it's on
+
+ align:start position:0%
+wear the material down a lot it's on
+ 
+
+ align:start position:0%
+wear the material down a lot it's on
+both sides of this have you found I I
+
+ align:start position:0%
+both sides of this have you found I I
+ 
+
+ align:start position:0%
+both sides of this have you found I I
+didn't go look I was too busy looking up
+
+ align:start position:0%
+didn't go look I was too busy looking up
+ 
+
+ align:start position:0%
+didn't go look I was too busy looking up
+how you tan leather while you were
+
+ align:start position:0%
+how you tan leather while you were
+ 
+
+ align:start position:0%
+how you tan leather while you were
+talking but the um but there are all
+
+ align:start position:0%
+talking but the um but there are all
+ 
+
+ align:start position:0%
+talking but the um but there are all
+over YouTube there are videos of like
+
+ align:start position:0%
+over YouTube there are videos of like
+ 
+
+ align:start position:0%
+over YouTube there are videos of like
+how manufacturing processes happen
+
+ align:start position:0%
+how manufacturing processes happen
+ 
+
+ align:start position:0%
+how manufacturing processes happen
+usually they're put up by the people who
+
+ align:start position:0%
+usually they're put up by the people who
+ 
+
+ align:start position:0%
+usually they're put up by the people who
+build the equipment um and it'd be I'm
+
+ align:start position:0%
+build the equipment um and it'd be I'm
+ 
+
+ align:start position:0%
+build the equipment um and it'd be I'm
+curious how they actually like how rice
+
+ align:start position:0%
+curious how they actually like how rice
+ 
+
+ align:start position:0%
+curious how they actually like how rice
+actually gets husk yeah so they do it
+
+ align:start position:0%
+actually gets husk yeah so they do it
+ 
+
+ align:start position:0%
+actually gets husk yeah so they do it
+they do it with like rollers basically
+
+ align:start position:0%
+they do it with like rollers basically
+ 
+
+ align:start position:0%
+they do it with like rollers basically
+like rubber rollers a lot of times um
+
+ align:start position:0%
+like rubber rollers a lot of times um
+ 
+
+ align:start position:0%
+like rubber rollers a lot of times um
+which is it's a totally different
+
+ align:start position:0%
+which is it's a totally different
+ 
+
+ align:start position:0%
+which is it's a totally different
+geometry that we're dealing with um but
+
+ align:start position:0%
+geometry that we're dealing with um but
+ 
+
+ align:start position:0%
+geometry that we're dealing with um but
+like you said it's like the friction
+
+ align:start position:0%
+like you said it's like the friction
+ 
+
+ align:start position:0%
+like you said it's like the friction
+yeah I just wonder if there's pieces of
+
+ align:start position:0%
+yeah I just wonder if there's pieces of
+ 
+
+ align:start position:0%
+yeah I just wonder if there's pieces of
+that you can steel there's you know like
+
+ align:start position:0%
+that you can steel there's you know like
+ 
+
+ align:start position:0%
+that you can steel there's you know like
+like if that's too Co but a flat plate
+
+ align:start position:0%
+like if that's too Co but a flat plate
+ 
+
+ align:start position:0%
+like if that's too Co but a flat plate
+with a single slot cut in it would get
+
+ align:start position:0%
+with a single slot cut in it would get
+ 
+
+ align:start position:0%
+with a single slot cut in it would get
+you you know would you know like if you
+
+ align:start position:0%
+you you know would you know like if you
+ 
+
+ align:start position:0%
+you you know would you know like if you
+had if you had groups cut in it that
+
+ align:start position:0%
+had if you had groups cut in it that
+ 
+
+ align:start position:0%
+had if you had groups cut in it that
+happen to be about the right size for a
+
+ align:start position:0%
+happen to be about the right size for a
+ 
+
+ align:start position:0%
+happen to be about the right size for a
+grain of rice or something um it it
+
+ align:start position:0%
+grain of rice or something um it it
+ 
+
+ align:start position:0%
+grain of rice or something um it it
+would help you out but I don't know just
+
+ align:start position:0%
+would help you out but I don't know just
+ 
+
+ align:start position:0%
+would help you out but I don't know just
+wondering if there are tricks this might
+
+ align:start position:0%
+wondering if there are tricks this might
+ 
+
+ align:start position:0%
+wondering if there are tricks this might
+be too far out but what about like a
+
+ align:start position:0%
+be too far out but what about like a
+ 
+
+ align:start position:0%
+be too far out but what about like a
+tumbling process instead of a grinding
+
+ align:start position:0%
+tumbling process instead of a grinding
+ 
+
+ align:start position:0%
+tumbling process instead of a grinding
+process yeah the um the Marine there's a
+
+ align:start position:0%
+process yeah the um the Marine there's a
+ 
+
+ align:start position:0%
+process yeah the um the Marine there's a
+team also doing Maringa seed husking and
+
+ align:start position:0%
+team also doing Maringa seed husking and
+ 
+
+ align:start position:0%
+team also doing Maringa seed husking and
+daab design I believe um but the MinGa
+
+ align:start position:0%
+daab design I believe um but the MinGa
+ 
+
+ align:start position:0%
+daab design I believe um but the MinGa
+is actually very soft and it doesn't end
+
+ align:start position:0%
+is actually very soft and it doesn't end
+ 
+
+ align:start position:0%
+is actually very soft and it doesn't end
+up getting damaged by the Tumblers
+
+ align:start position:0%
+up getting damaged by the Tumblers
+ 
+
+ align:start position:0%
+up getting damaged by the Tumblers
+whereas the hus the husks are actually
+
+ align:start position:0%
+whereas the hus the husks are actually
+ 
+
+ align:start position:0%
+whereas the hus the husks are actually
+pretty soft and the rice is hard so if
+
+ align:start position:0%
+pretty soft and the rice is hard so if
+ 
+
+ align:start position:0%
+pretty soft and the rice is hard so if
+there were tumblers like just from
+
+ align:start position:0%
+there were tumblers like just from
+ 
+
+ align:start position:0%
+there were tumblers like just from
+looking at it the rice would probably
+
+ align:start position:0%
+looking at it the rice would probably
+ 
+
+ align:start position:0%
+looking at it the rice would probably
+get more crushed whereas the hus
+
+ align:start position:0%
+get more crushed whereas the hus
+ 
+
+ align:start position:0%
+get more crushed whereas the hus
+probably would really as
+
+ align:start position:0%
+probably would really as
+ 
+
+ align:start position:0%
+probably would really as
+much um cuz we found that the soft
+
+ align:start position:0%
+much um cuz we found that the soft
+ 
+
+ align:start position:0%
+much um cuz we found that the soft
+materials really like give and allow the
+
+ align:start position:0%
+materials really like give and allow the
+ 
+
+ align:start position:0%
+materials really like give and allow the
+hus to come off with the friction but
+
+ align:start position:0%
+hus to come off with the friction but
+ 
+
+ align:start position:0%
+hus to come off with the friction but
+not damage the rce as much so try to
+
+ align:start position:0%
+not damage the rce as much so try to
+ 
+
+ align:start position:0%
+not damage the rce as much so try to
+push her softer as opposed to kind of
+
+ align:start position:0%
+push her softer as opposed to kind of
+ 
+
+ align:start position:0%
+push her softer as opposed to kind of
+like that h
+
+ align:start position:0%
+like that h
+ 
+
+ align:start position:0%
+like that h
+right what's wrong with broken
+
+ align:start position:0%
+right what's wrong with broken
+ 
+
+ align:start position:0%
+right what's wrong with broken
+race that's something that we actually
+
+ align:start position:0%
+race that's something that we actually
+ 
+
+ align:start position:0%
+race that's something that we actually
+uh that we wanted to ask the community
+
+ align:start position:0%
+uh that we wanted to ask the community
+ 
+
+ align:start position:0%
+uh that we wanted to ask the community
+um I got to get to mushy probably get
+
+ align:start position:0%
+um I got to get to mushy probably get
+ 
+
+ align:start position:0%
+um I got to get to mushy probably get
+mush well part of the reason they they
+
+ align:start position:0%
+mush well part of the reason they they
+ 
+
+ align:start position:0%
+mush well part of the reason they they
+want to use like this as a tool in their
+
+ align:start position:0%
+want to use like this as a tool in their
+ 
+
+ align:start position:0%
+want to use like this as a tool in their
+communities they want to sell race too
+
+ align:start position:0%
+communities they want to sell race too
+ 
+
+ align:start position:0%
+communities they want to sell race too
+so I would assume we haven't been in
+
+ align:start position:0%
+so I would assume we haven't been in
+ 
+
+ align:start position:0%
+so I would assume we haven't been in
+contact really with our community
+
+ align:start position:0%
+contact really with our community
+ 
+
+ align:start position:0%
+contact really with our community
+partner we haven't gotten back to us but
+
+ align:start position:0%
+partner we haven't gotten back to us but
+ 
+
+ align:start position:0%
+partner we haven't gotten back to us but
+um we' assume that they'd want to sell
+
+ align:start position:0%
+um we' assume that they'd want to sell
+ 
+
+ align:start position:0%
+um we' assume that they'd want to sell
+whole grain Asos to one question I think
+
+ align:start position:0%
+whole grain Asos to one question I think
+ 
+
+ align:start position:0%
+whole grain Asos to one question I think
+I this last time I you have one question
+
+ align:start position:0%
+I this last time I you have one question
+ 
+
+ align:start position:0%
+I this last time I you have one question
+you might want to ask is um what their
+
+ align:start position:0%
+you might want to ask is um what their
+ 
+
+ align:start position:0%
+you might want to ask is um what their
+expectations are for broken rice if they
+
+ align:start position:0%
+expectations are for broken rice if they
+ 
+
+ align:start position:0%
+expectations are for broken rice if they
+already from the mill if they get 25%
+
+ align:start position:0%
+already from the mill if they get 25%
+ 
+
+ align:start position:0%
+already from the mill if they get 25%
+broken R already and they
+
+ align:start position:0%
+broken R already and they
+ 
+
+ align:start position:0%
+broken R already and they
+just yeah so I would get on the phone
+
+ align:start position:0%
+just yeah so I would get on the phone
+ 
+
+ align:start position:0%
+just yeah so I would get on the phone
+next week do hopefully you reach them um
+
+ align:start position:0%
+next week do hopefully you reach them um
+ 
+
+ align:start position:0%
+next week do hopefully you reach them um
+if you end whatever material you end up
+
+ align:start position:0%
+if you end whatever material you end up
+ 
+
+ align:start position:0%
+if you end whatever material you end up
+with whether it's leather or something
+
+ align:start position:0%
+with whether it's leather or something
+ 
+
+ align:start position:0%
+with whether it's leather or something
+else uh figuring out just how long it
+
+ align:start position:0%
+else uh figuring out just how long it
+ 
+
+ align:start position:0%
+else uh figuring out just how long it
+does last so how many grams you can
+
+ align:start position:0%
+does last so how many grams you can
+ 
+
+ align:start position:0%
+does last so how many grams you can
+process before you need to rep it and
+
+ align:start position:0%
+process before you need to rep it and
+ 
+
+ align:start position:0%
+process before you need to rep it and
+then getting like a both both for your
+
+ align:start position:0%
+then getting like a both both for your
+ 
+
+ align:start position:0%
+then getting like a both both for your
+users that they know we should beess
+
+ align:start position:0%
+users that they know we should beess
+ 
+
+ align:start position:0%
+users that they know we should beess
+replacing it this often and also so you
+
+ align:start position:0%
+replacing it this often and also so you
+ 
+
+ align:start position:0%
+replacing it this often and also so you
+can get a cost estimate for like we're
+
+ align:start position:0%
+can get a cost estimate for like we're
+ 
+
+ align:start position:0%
+can get a cost estimate for like we're
+going to in a year you know or this many
+
+ align:start position:0%
+going to in a year you know or this many
+ 
+
+ align:start position:0%
+going to in a year you know or this many
+tons of rice we're going to need this
+
+ align:start position:0%
+tons of rice we're going to need this
+ 
+
+ align:start position:0%
+tons of rice we're going to need this
+much leather or whatever it is be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+useful did you bring the rice back from
+
+ align:start position:0%
+useful did you bring the rice back from
+ 
+
+ align:start position:0%
+useful did you bring the rice back from
+those Salvador no or is it from like a
+
+ align:start position:0%
+those Salvador no or is it from like a
+ 
+
+ align:start position:0%
+those Salvador no or is it from like a
+farm nearby where the price come from it
+
+ align:start position:0%
+farm nearby where the price come from it
+ 
+
+ align:start position:0%
+farm nearby where the price come from it
+is from a farm Texas but I mean from
+
+ align:start position:0%
+is from a farm Texas but I mean from
+ 
+
+ align:start position:0%
+is from a farm Texas but I mean from
+comparisons they are very similar yeah
+
+ align:start position:0%
+comparisons they are very similar yeah
+ 
+
+ align:start position:0%
+comparisons they are very similar yeah
+nobody's going to let you bring a sack
+
+ align:start position:0%
+nobody's going to let you bring a sack
+ 
+
+ align:start position:0%
+nobody's going to let you bring a sack
+of un hus
+
+ align:start position:0%
+of un hus
+ 
+
+ align:start position:0%
+of un hus
+right if you did you did it hidden in a
+
+ align:start position:0%
+right if you did you did it hidden in a
+ 
+
+ align:start position:0%
+right if you did you did it hidden in a
+p up sock all right thanks you guys
\ No newline at end of file
diff --git a/Y_lWzD2vigk.txt b/Y_lWzD2vigk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9358fe00d91d886b01dbbf192c0d838b125ffde6
--- /dev/null
+++ b/Y_lWzD2vigk.txt
@@ -0,0 +1,7586 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu well hope you had a good
+
+ align:start position:0%
+ocw.mit.edu well hope you had a good
+ 
+
+ align:start position:0%
+ocw.mit.edu well hope you had a good
+Thanksgiving uh so this uh this this is
+
+ align:start position:0%
+Thanksgiving uh so this uh this this is
+ 
+
+ align:start position:0%
+Thanksgiving uh so this uh this this is
+partly review a day even uh Wednesday
+
+ align:start position:0%
+partly review a day even uh Wednesday
+ 
+
+ align:start position:0%
+partly review a day even uh Wednesday
+even more review Wednesday evening uh or
+
+ align:start position:0%
+even more review Wednesday evening uh or
+ 
+
+ align:start position:0%
+even more review Wednesday evening uh or
+Wednesday at 4 we'll be I'll be here for
+
+ align:start position:0%
+Wednesday at 4 we'll be I'll be here for
+ 
+
+ align:start position:0%
+Wednesday at 4 we'll be I'll be here for
+any questions and then the exam is
+
+ align:start position:0%
+any questions and then the exam is
+ 
+
+ align:start position:0%
+any questions and then the exam is
+Thursday at 7:30 in Walker top floor of
+
+ align:start position:0%
+Thursday at 7:30 in Walker top floor of
+ 
+
+ align:start position:0%
+Thursday at 7:30 in Walker top floor of
+Walker this time not not the same
+
+ align:start position:0%
+Walker this time not not the same
+ 
+
+ align:start position:0%
+Walker this time not not the same
+54100 okay and then uh no lectures after
+
+ align:start position:0%
+54100 okay and then uh no lectures after
+ 
+
+ align:start position:0%
+54100 okay and then uh no lectures after
+that holiday whatever yes uh right T you
+
+ align:start position:0%
+that holiday whatever yes uh right T you
+ 
+
+ align:start position:0%
+that holiday whatever yes uh right T you
+get a chance to do something catch up
+
+ align:start position:0%
+get a chance to do something catch up
+ 
+
+ align:start position:0%
+get a chance to do something catch up
+with all those other courses that that
+
+ align:start position:0%
+with all those other courses that that
+ 
+
+ align:start position:0%
+with all those other courses that that
+that are being neglected in favor of
+
+ align:start position:0%
+that are being neglected in favor of
+ 
+
+ align:start position:0%
+that are being neglected in favor of
+18085 right okay so here's a bit of
+
+ align:start position:0%
+18085 right okay so here's a bit of
+ 
+
+ align:start position:0%
+18085 right okay so here's a bit of
+review right away we we've really had
+
+ align:start position:0%
+review right away we we've really had
+ 
+
+ align:start position:0%
+review right away we we've really had
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+cases uh we started with 4A series that
+
+ align:start position:0%
+cases uh we started with 4A series that
+ 
+
+ align:start position:0%
+cases uh we started with 4A series that
+was periodic functions and then discrete
+
+ align:start position:0%
+was periodic functions and then discrete
+ 
+
+ align:start position:0%
+was periodic functions and then discrete
+4 a series also periodic in a way
+
+ align:start position:0%
+4 a series also periodic in a way
+ 
+
+ align:start position:0%
+4 a series also periodic in a way
+because W to the nth was one so that the
+
+ align:start position:0%
+because W to the nth was one so that the
+ 
+
+ align:start position:0%
+because W to the nth was one so that the
+the we have n numbers and then if we
+
+ align:start position:0%
+the we have n numbers and then if we
+ 
+
+ align:start position:0%
+the we have n numbers and then if we
+could repeat them if we wanted so those
+
+ align:start position:0%
+could repeat them if we wanted so those
+ 
+
+ align:start position:0%
+could repeat them if we wanted so those
+are the two that
+
+ align:start position:0%
+are the two that
+ 
+
+ align:start position:0%
+are the two that
+repeat uh this is the F ofx this is all
+
+ align:start position:0%
+repeat uh this is the F ofx this is all
+ 
+
+ align:start position:0%
+repeat uh this is the F ofx this is all
+X so that would be the fora integral
+
+ align:start position:0%
+X so that would be the fora integral
+ 
+
+ align:start position:0%
+X so that would be the fora integral
+that we did just last week fora integral
+
+ align:start position:0%
+that we did just last week fora integral
+ 
+
+ align:start position:0%
+that we did just last week fora integral
+transform and this was the well these
+
+ align:start position:0%
+transform and this was the well these
+ 
+
+ align:start position:0%
+transform and this was the well these
+are all this is the discrete all the way
+
+ align:start position:0%
+are all this is the discrete all the way
+ 
+
+ align:start position:0%
+are all this is the discrete all the way
+so that's oh you you can see these pair
+
+ align:start position:0%
+so that's oh you you can see these pair
+ 
+
+ align:start position:0%
+so that's oh you you can see these pair
+off right the the
+
+ align:start position:0%
+off right the the
+ 
+
+ align:start position:0%
+off right the the
+for the periodic this the periodic
+
+ align:start position:0%
+for the periodic this the periodic
+ 
+
+ align:start position:0%
+for the periodic this the periodic
+function the two Pi periodic function
+
+ align:start position:0%
+function the two Pi periodic function
+ 
+
+ align:start position:0%
+function the two Pi periodic function
+has 4 a coefficients for all K so Vice
+
+ align:start position:0%
+has 4 a coefficients for all K so Vice
+ 
+
+ align:start position:0%
+has 4 a coefficients for all K so Vice
+so that's the pair that we started with
+
+ align:start position:0%
+so that's the pair that we started with
+ 
+
+ align:start position:0%
+so that's the pair that we started with
+Section 41 this sort of
+
+ align:start position:0%
+Section 41 this sort of
+ 
+
+ align:start position:0%
+Section 41 this sort of
+pairs I don't know whether to say with
+
+ align:start position:0%
+pairs I don't know whether to say with
+ 
+
+ align:start position:0%
+pairs I don't know whether to say with
+itself I mean the the the it's we start
+
+ align:start position:0%
+itself I mean the the the it's we start
+ 
+
+ align:start position:0%
+itself I mean the the the it's we start
+with n numbers and we end with n numbers
+
+ align:start position:0%
+with n numbers and we end with n numbers
+ 
+
+ align:start position:0%
+with n numbers and we end with n numbers
+we have n numbers in physical space and
+
+ align:start position:0%
+we have n numbers in physical space and
+ 
+
+ align:start position:0%
+we have n numbers in physical space and
+we have n numbers in uh frequency space
+
+ align:start position:0%
+we have n numbers in uh frequency space
+ 
+
+ align:start position:0%
+we have n numbers in uh frequency space
+right so we we called those so those
+
+ align:start position:0%
+right so we we called those so those
+ 
+
+ align:start position:0%
+right so we we called those so those
+went to
+
+ align:start position:0%
+went to
+ 
+
+ align:start position:0%
+went to
+c0 up to CN minus one and
+
+ align:start position:0%
+c0 up to CN minus one and
+ 
+
+ align:start position:0%
+c0 up to CN minus one and
+this all X pair for the function paired
+
+ align:start position:0%
+this all X pair for the function paired
+ 
+
+ align:start position:0%
+this all X pair for the function paired
+off with itself or with with this went
+
+ align:start position:0%
+off with itself or with with this went
+ 
+
+ align:start position:0%
+off with itself or with with this went
+to F Well maybe I used small F I guess I
+
+ align:start position:0%
+to F Well maybe I used small F I guess I
+ 
+
+ align:start position:0%
+to F Well maybe I used small F I guess I
+did in in in last week so that and I
+
+ align:start position:0%
+did in in in last week so that and I
+ 
+
+ align:start position:0%
+did in in in last week so that and I
+call called it's for a transform fat of
+
+ align:start position:0%
+call called it's for a transform fat of
+ 
+
+ align:start position:0%
+call called it's for a transform fat of
+K all
+
+ align:start position:0%
+K all
+ 
+
+ align:start position:0%
+K all
+K so that's the pairing kind of inside n
+
+ align:start position:0%
+K so that's the pairing kind of inside n
+ 
+
+ align:start position:0%
+K so that's the pairing kind of inside n
+dimensional space with the 4A Matrix
+
+ align:start position:0%
+dimensional space with the 4A Matrix
+ 
+
+ align:start position:0%
+dimensional space with the 4A Matrix
+this is the pairing of the formula for f
+
+ align:start position:0%
+this is the pairing of the formula for f
+ 
+
+ align:start position:0%
+this is the pairing of the formula for f
+and it's similar formula for fat and
+
+ align:start position:0%
+and it's similar formula for fat and
+ 
+
+ align:start position:0%
+and it's similar formula for fat and
+these are the guys that connect with
+
+ align:start position:0%
+these are the guys that connect with
+ 
+
+ align:start position:0%
+these are the guys that connect with
+each other okay so that's that's what we
+
+ align:start position:0%
+each other okay so that's that's what we
+ 
+
+ align:start position:0%
+each other okay so that's that's what we
+know what we haven't done is anything in
+
+ align:start position:0%
+know what we haven't done is anything in
+ 
+
+ align:start position:0%
+know what we haven't done is anything in
+two dimensions
+
+ align:start position:0%
+two dimensions
+ 
+
+ align:start position:0%
+two dimensions
+so I would like to include that today I
+
+ align:start position:0%
+so I would like to include that today I
+ 
+
+ align:start position:0%
+so I would like to include that today I
+I think my real message about 2D and I'm
+
+ align:start position:0%
+I think my real message about 2D and I'm
+ 
+
+ align:start position:0%
+I think my real message about 2D and I'm
+not going to included on the exam but
+
+ align:start position:0%
+not going to included on the exam but
+ 
+
+ align:start position:0%
+not going to included on the exam but
+you might wonder okay does two can the
+
+ align:start position:0%
+you might wonder okay does two can the
+ 
+
+ align:start position:0%
+you might wonder okay does two can the
+can I have a function of X and Y and
+
+ align:start position:0%
+can I have a function of X and Y and
+ 
+
+ align:start position:0%
+can I have a function of X and Y and
+will the whole setup work and the answer
+
+ align:start position:0%
+will the whole setup work and the answer
+ 
+
+ align:start position:0%
+will the whole setup work and the answer
+is yes so so really my message is not to
+
+ align:start position:0%
+is yes so so really my message is not to
+ 
+
+ align:start position:0%
+is yes so so really my message is not to
+be uh afraid in any way of 2D it's just
+
+ align:start position:0%
+be uh afraid in any way of 2D it's just
+ 
+
+ align:start position:0%
+be uh afraid in any way of 2D it's just
+the same formulas with with XY or two
+
+ align:start position:0%
+the same formulas with with XY or two
+ 
+
+ align:start position:0%
+the same formulas with with XY or two
+indices k L yeah you'll see that okay
+
+ align:start position:0%
+indices k L yeah you'll see that okay
+ 
+
+ align:start position:0%
+indices k L yeah you'll see that okay
+now now for the new part what's a
+
+ align:start position:0%
+now now for the new part what's a
+ 
+
+ align:start position:0%
+now now for the new part what's a
+convolution
+
+ align:start position:0%
+convolution
+ 
+
+ align:start position:0%
+convolution
+equation that's my word for an equation
+
+ align:start position:0%
+equation that's my word for an equation
+ 
+
+ align:start position:0%
+equation that's my word for an equation
+where instead of doing a convolution and
+
+ align:start position:0%
+where instead of doing a convolution and
+ 
+
+ align:start position:0%
+where instead of doing a convolution and
+finding the right hand
+
+ align:start position:0%
+finding the right hand
+ 
+
+ align:start position:0%
+finding the right hand
+side instead we're given the right hand
+
+ align:start position:0%
+side instead we're given the right hand
+ 
+
+ align:start position:0%
+side instead we're given the right hand
+side and it's the convolution is in the
+
+ align:start position:0%
+side and it's the convolution is in the
+ 
+
+ align:start position:0%
+side and it's the convolution is in the
+the unknown is in the convolution so let
+
+ align:start position:0%
+the unknown is in the convolution so let
+ 
+
+ align:start position:0%
+the unknown is in the convolution so let
+me let me write examples of convolution
+
+ align:start position:0%
+me let me write examples of convolution
+ 
+
+ align:start position:0%
+me let me write examples of convolution
+equ equation every one of these would
+
+ align:start position:0%
+equ equation every one of these would
+ 
+
+ align:start position:0%
+equ equation every one of these would
+have a allow a convolution so the
+
+ align:start position:0%
+have a allow a convolution so the
+ 
+
+ align:start position:0%
+have a allow a convolution so the
+convolution equation would be something
+
+ align:start position:0%
+convolution equation would be something
+ 
+
+ align:start position:0%
+convolution equation would be something
+like the integral of f ofx f of T U for
+
+ align:start position:0%
+like the integral of f ofx f of T U for
+ 
+
+ align:start position:0%
+like the integral of f ofx f of T U for
+the unknown at x minus t is oh no sorry
+
+ align:start position:0%
+the unknown at x minus t is oh no sorry
+ 
+
+ align:start position:0%
+the unknown at x minus t is oh no sorry
+F will be the right hand side F of well
+
+ align:start position:0%
+F will be the right hand side F of well
+ 
+
+ align:start position:0%
+F will be the right hand side F of well
+can I yeah better if I put it on the
+
+ align:start position:0%
+can I yeah better if I put it on the
+ 
+
+ align:start position:0%
+can I yeah better if I put it on the
+right hand side if I'm going to call it
+
+ align:start position:0%
+right hand side if I'm going to call it
+ 
+
+ align:start position:0%
+right hand side if I'm going to call it
+the right hand side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this would be some so I call it often
+
+ align:start position:0%
+so this would be some so I call it often
+ 
+
+ align:start position:0%
+so this would be some so I call it often
+k for kernel is is sometimes the word
+
+ align:start position:0%
+k for kernel is is sometimes the word
+ 
+
+ align:start position:0%
+k for kernel is is sometimes the word
+okay so what I'm saying is equations
+
+ align:start position:0%
+okay so what I'm saying is equations
+ 
+
+ align:start position:0%
+okay so what I'm saying is equations
+come this way that the this is really K
+
+ align:start position:0%
+come this way that the this is really K
+ 
+
+ align:start position:0%
+come this way that the this is really K
+convolved with
+
+ align:start position:0%
+convolved with
+ 
+
+ align:start position:0%
+convolved with
+u equals F you see the only novelty is
+
+ align:start position:0%
+u equals F you see the only novelty is
+ 
+
+ align:start position:0%
+u equals F you see the only novelty is
+the unknown is here so that that's why
+
+ align:start position:0%
+the unknown is here so that that's why
+ 
+
+ align:start position:0%
+the unknown is here so that that's why
+the word deconvolution is up there
+
+ align:start position:0%
+the word deconvolution is up there
+ 
+
+ align:start position:0%
+the word deconvolution is up there
+because that's what we have have to do
+
+ align:start position:0%
+because that's what we have have to do
+ 
+
+ align:start position:0%
+because that's what we have have to do
+we have to undo the convolution this
+
+ align:start position:0%
+we have to undo the convolution this
+ 
+
+ align:start position:0%
+we have to undo the convolution this
+unknown function is convolved with a
+
+ align:start position:0%
+unknown function is convolved with a
+ 
+
+ align:start position:0%
+unknown function is convolved with a
+known K is known some known kernel that
+
+ align:start position:0%
+known K is known some known kernel that
+ 
+
+ align:start position:0%
+known K is known some known kernel that
+tells us the point spread of the of the
+
+ align:start position:0%
+tells us the point spread of the of the
+ 
+
+ align:start position:0%
+tells us the point spread of the of the
+telescope or whatever we're doing and
+
+ align:start position:0%
+telescope or whatever we're doing and
+ 
+
+ align:start position:0%
+telescope or whatever we're doing and
+gives us the output that we're looking
+
+ align:start position:0%
+gives us the output that we're looking
+ 
+
+ align:start position:0%
+gives us the output that we're looking
+at and then we have to find the
+
+ align:start position:0%
+at and then we have to find the
+ 
+
+ align:start position:0%
+at and then we have to find the
+input okay can I write down the similar
+
+ align:start position:0%
+input okay can I write down the similar
+ 
+
+ align:start position:0%
+input okay can I write down the similar
+equations for the other three here and
+
+ align:start position:0%
+equations for the other three here and
+ 
+
+ align:start position:0%
+equations for the other three here and
+then we'll just think how would we how
+
+ align:start position:0%
+then we'll just think how would we how
+ 
+
+ align:start position:0%
+then we'll just think how would we how
+would we find you how would we solve
+
+ align:start position:0%
+would we find you how would we solve
+ 
+
+ align:start position:0%
+would we find you how would we solve
+them so the the equation here might be
+
+ align:start position:0%
+them so the the equation here might be
+ 
+
+ align:start position:0%
+them so the the equation here might be
+that uh some kernel circle circle
+
+ align:start position:0%
+that uh some kernel circle circle
+ 
+
+ align:start position:0%
+that uh some kernel circle circle
+convolved with the unknown U is some
+
+ align:start position:0%
+convolved with the unknown U is some
+ 
+
+ align:start position:0%
+convolved with the unknown U is some
+y these are now
+
+ align:start position:0%
+y these are now
+ 
+
+ align:start position:0%
+y these are now
+vectors this is
+
+ align:start position:0%
+vectors this is
+ 
+
+ align:start position:0%
+vectors this is
+known this is known and those the end
+
+ align:start position:0%
+known this is known and those the end
+ 
+
+ align:start position:0%
+known this is known and those the end
+components of U are unknown okay so that
+
+ align:start position:0%
+components of U are unknown okay so that
+ 
+
+ align:start position:0%
+components of U are unknown okay so that
+would be a same problem here what would
+
+ align:start position:0%
+would be a same problem here what would
+ 
+
+ align:start position:0%
+would be a same problem here what would
+be here same thing now the integral will
+
+ align:start position:0%
+be here same thing now the integral will
+ 
+
+ align:start position:0%
+be here same thing now the integral will
+go from the only difference is the
+
+ align:start position:0%
+go from the only difference is the
+ 
+
+ align:start position:0%
+go from the only difference is the
+integral will go from minus infinity to
+
+ align:start position:0%
+integral will go from minus infinity to
+ 
+
+ align:start position:0%
+integral will go from minus infinity to
+Infinity K of T U of xus T dtal F
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ofx and finally regular
+
+ align:start position:0%
+ofx and finally regular
+ 
+
+ align:start position:0%
+ofx and finally regular
+convolution
+
+ align:start position:0%
+convolution
+ 
+
+ align:start position:0%
+convolution
+uh what am I going to call it k k would
+
+ align:start position:0%
+uh what am I going to call it k k would
+ 
+
+ align:start position:0%
+uh what am I going to call it k k would
+be a sequence maybe I'll maybe I should
+
+ align:start position:0%
+be a sequence maybe I'll maybe I should
+ 
+
+ align:start position:0%
+be a sequence maybe I'll maybe I should
+call it a known convolved with u unknown
+
+ align:start position:0%
+call it a known convolved with u unknown
+ 
+
+ align:start position:0%
+call it a known convolved with u unknown
+is some C
+
+ align:start position:0%
+is some C
+ 
+
+ align:start position:0%
+is some C
+known yeah so those would be four
+
+ align:start position:0%
+known yeah so those would be four
+ 
+
+ align:start position:0%
+known yeah so those would be four
+equations what what you might say wait a
+
+ align:start position:0%
+equations what what you might say wait a
+ 
+
+ align:start position:0%
+equations what what you might say wait a
+minute where has Professor Strang come
+
+ align:start position:0%
+minute where has Professor Strang come
+ 
+
+ align:start position:0%
+minute where has Professor Strang come
+up with these problems at the last week
+
+ align:start position:0%
+up with these problems at the last week
+ 
+
+ align:start position:0%
+up with these problems at the last week
+of the course but these are exactly the
+
+ align:start position:0%
+of the course but these are exactly the
+ 
+
+ align:start position:0%
+of the course but these are exactly the
+type of problems that we know and love
+
+ align:start position:0%
+type of problems that we know and love
+ 
+
+ align:start position:0%
+type of problems that we know and love
+these are these come from constant
+
+ align:start position:0%
+these are these come from constant
+ 
+
+ align:start position:0%
+these are these come from constant
+coefficient time invariant shift
+
+ align:start position:0%
+coefficient time invariant shift
+ 
+
+ align:start position:0%
+coefficient time invariant shift
+invariant linear problems LTI linear
+
+ align:start position:0%
+invariant linear problems LTI linear
+ 
+
+ align:start position:0%
+invariant linear problems LTI linear
+time invariant and uh my lecture uh wedy
+
+ align:start position:0%
+time invariant and uh my lecture uh wedy
+ 
+
+ align:start position:0%
+time invariant and uh my lecture uh wedy
+just before Thanksgiving took a
+
+ align:start position:0%
+just before Thanksgiving took a
+ 
+
+ align:start position:0%
+just before Thanksgiving took a
+differential equation for you and found
+
+ align:start position:0%
+differential equation for you and found
+ 
+
+ align:start position:0%
+differential equation for you and found
+and put it in this form I I'll come back
+
+ align:start position:0%
+and put it in this form I I'll come back
+ 
+
+ align:start position:0%
+and put it in this form I I'll come back
+to that yeah so suddenly we're seeing I
+
+ align:start position:0%
+to that yeah so suddenly we're seeing I
+ 
+
+ align:start position:0%
+to that yeah so suddenly we're seeing I
+mean we're we're actually seeing some
+
+ align:start position:0%
+mean we're we're actually seeing some
+ 
+
+ align:start position:0%
+mean we're we're actually seeing some
+new things but also it includes all the
+
+ align:start position:0%
+new things but also it includes all the
+ 
+
+ align:start position:0%
+new things but also it includes all the
+old ones these are all the linear all
+
+ align:start position:0%
+old ones these are all the linear all
+ 
+
+ align:start position:0%
+old ones these are all the linear all
+the best problems in the world World
+
+ align:start position:0%
+the best problems in the world World
+ 
+
+ align:start position:0%
+the best problems in the world World
+these linear constant coefficient
+
+ align:start position:0%
+these linear constant coefficient
+ 
+
+ align:start position:0%
+these linear constant coefficient
+problems time invariant of of any of
+
+ align:start position:0%
+problems time invariant of of any of
+ 
+
+ align:start position:0%
+problems time invariant of of any of
+these types this one was an integral
+
+ align:start position:0%
+these types this one was an integral
+ 
+
+ align:start position:0%
+these types this one was an integral
+from minus pi to Pi of course where this
+
+ align:start position:0%
+from minus pi to Pi of course where this
+ 
+
+ align:start position:0%
+from minus pi to Pi of course where this
+one went all the way yeah so that's this
+
+ align:start position:0%
+one went all the way yeah so that's this
+ 
+
+ align:start position:0%
+one went all the way yeah so that's this
+is not uh brand new stuff but uh it sort
+
+ align:start position:0%
+is not uh brand new stuff but uh it sort
+ 
+
+ align:start position:0%
+is not uh brand new stuff but uh it sort
+of looks new and uh now the question is
+
+ align:start position:0%
+of looks new and uh now the question is
+ 
+
+ align:start position:0%
+of looks new and uh now the question is
+so my immediate question is before doing
+
+ align:start position:0%
+so my immediate question is before doing
+ 
+
+ align:start position:0%
+so my immediate question is before doing
+any example How would how would you
+
+ align:start position:0%
+any example How would how would you
+ 
+
+ align:start position:0%
+any example How would how would you
+solve such an equation and I saw on Old
+
+ align:start position:0%
+solve such an equation and I saw on Old
+ 
+
+ align:start position:0%
+solve such an equation and I saw on Old
+exams some of this sort for example let
+
+ align:start position:0%
+exams some of this sort for example let
+ 
+
+ align:start position:0%
+exams some of this sort for example let
+me focus on this one uh let me instead
+
+ align:start position:0%
+me focus on this one uh let me instead
+ 
+
+ align:start position:0%
+me focus on this one uh let me instead
+of K there I'm not used to using k for a
+
+ align:start position:0%
+of K there I'm not used to using k for a
+ 
+
+ align:start position:0%
+of K there I'm not used to using k for a
+vector let me I'm used to well maybe
+
+ align:start position:0%
+vector let me I'm used to well maybe
+ 
+
+ align:start position:0%
+vector let me I'm used to well maybe
+maybe I'll use C for the vector there so
+
+ align:start position:0%
+maybe I'll use C for the vector there so
+ 
+
+ align:start position:0%
+maybe I'll use C for the vector there so
+this is this is n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equations and unknowns oh it's capital L
+
+ align:start position:0%
+equations and unknowns oh it's capital L
+ 
+
+ align:start position:0%
+equations and unknowns oh it's capital L
+is our usual here for for the number and
+
+ align:start position:0%
+is our usual here for for the number and
+ 
+
+ align:start position:0%
+is our usual here for for the number and
+n u n unknown use it's it's a matrix
+
+ align:start position:0%
+n u n unknown use it's it's a matrix
+ 
+
+ align:start position:0%
+n u n unknown use it's it's a matrix
+equation with a circulent matrix so it's
+
+ align:start position:0%
+equation with a circulent matrix so it's
+ 
+
+ align:start position:0%
+equation with a circulent matrix so it's
+a all these equations are the sort of
+
+ align:start position:0%
+a all these equations are the sort of
+ 
+
+ align:start position:0%
+a all these equations are the sort of
+the special best kind because they're
+
+ align:start position:0%
+the special best kind because they're
+ 
+
+ align:start position:0%
+the special best kind because they're
+convolutions and now tell me the main
+
+ align:start position:0%
+convolutions and now tell me the main
+ 
+
+ align:start position:0%
+convolutions and now tell me the main
+point how do we solve equations like
+
+ align:start position:0%
+point how do we solve equations like
+ 
+
+ align:start position:0%
+point how do we solve equations like
+this how do we do a
+
+ align:start position:0%
+this how do we do a
+ 
+
+ align:start position:0%
+this how do we do a
+deconvolution to to so the unknown is
+
+ align:start position:0%
+deconvolution to to so the unknown is
+ 
+
+ align:start position:0%
+deconvolution to to so the unknown is
+convolved with C here it's convolved
+
+ align:start position:0%
+convolved with C here it's convolved
+ 
+
+ align:start position:0%
+convolved with C here it's convolved
+with K it's convolved with a how do we
+
+ align:start position:0%
+with K it's convolved with a how do we
+ 
+
+ align:start position:0%
+with K it's convolved with a how do we
+UNC deconvolve it to get you by itself
+
+ align:start position:0%
+UNC deconvolve it to get you by itself
+ 
+
+ align:start position:0%
+UNC deconvolve it to get you by itself
+so what's the what's the central idea
+
+ align:start position:0%
+so what's the what's the central idea
+ 
+
+ align:start position:0%
+so what's the what's the central idea
+here central idea go into frequency
+
+ align:start position:0%
+here central idea go into frequency
+ 
+
+ align:start position:0%
+here central idea go into frequency
+space use the convolution rule in
+
+ align:start position:0%
+space use the convolution rule in
+ 
+
+ align:start position:0%
+space use the convolution rule in
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+space where these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transform uh we're looking at multip
+
+ align:start position:0%
+transform uh we're looking at multip
+ 
+
+ align:start position:0%
+transform uh we're looking at multip
+ation and multiplication we can undo we
+
+ align:start position:0%
+ation and multiplication we can undo we
+ 
+
+ align:start position:0%
+ation and multiplication we can undo we
+can Dem
+
+ align:start position:0%
+can Dem
+ 
+
+ align:start position:0%
+can Dem
+multiply Dem multiply is just a a big
+
+ align:start position:0%
+multiply Dem multiply is just a a big
+ 
+
+ align:start position:0%
+multiply Dem multiply is just a a big
+word for divide right so that's the
+
+ align:start position:0%
+word for divide right so that's the
+ 
+
+ align:start position:0%
+word for divide right so that's the
+point get into that space and that's
+
+ align:start position:0%
+point get into that space and that's
+ 
+
+ align:start position:0%
+point get into that space and that's
+what we've been doing all the time I
+
+ align:start position:0%
+what we've been doing all the time I
+ 
+
+ align:start position:0%
+what we've been doing all the time I
+better get one example the the example
+
+ align:start position:0%
+better get one example the the example
+ 
+
+ align:start position:0%
+better get one example the the example
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+um from Wednesday just up here so just
+
+ align:start position:0%
+um from Wednesday just up here so just
+ 
+
+ align:start position:0%
+um from Wednesday just up here so just
+so you see it this won't look like a
+
+ align:start position:0%
+so you see it this won't look like a
+ 
+
+ align:start position:0%
+so you see it this won't look like a
+convolution equation but you do you
+
+ align:start position:0%
+convolution equation but you do you
+ 
+
+ align:start position:0%
+convolution equation but you do you
+remember it was my - U Prime + a^ 2 U =
+
+ align:start position:0%
+remember it was my - U Prime + a^ 2 U =
+ 
+
+ align:start position:0%
+remember it was my - U Prime + a^ 2 U =
+some f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ofx so that's a constant it's certainly
+
+ align:start position:0%
+ofx so that's a constant it's certainly
+ 
+
+ align:start position:0%
+ofx so that's a constant it's certainly
+constant coefficient linear time
+
+ align:start position:0%
+constant coefficient linear time
+ 
+
+ align:start position:0%
+constant coefficient linear time
+invariant right okay and how did we
+
+ align:start position:0%
+invariant right okay and how did we
+ 
+
+ align:start position:0%
+invariant right okay and how did we
+solve that we took 48 transforms so this
+
+ align:start position:0%
+solve that we took 48 transforms so this
+ 
+
+ align:start position:0%
+solve that we took 48 transforms so this
+was this was the second derivative the
+
+ align:start position:0%
+was this was the second derivative the
+ 
+
+ align:start position:0%
+was this was the second derivative the
+48 transform what do the SEC rule for
+
+ align:start position:0%
+48 transform what do the SEC rule for
+ 
+
+ align:start position:0%
+48 transform what do the SEC rule for
+the fora transform of derivative every
+
+ align:start position:0%
+the fora transform of derivative every
+ 
+
+ align:start position:0%
+the fora transform of derivative every
+derivative brings down an i K in the
+
+ align:start position:0%
+derivative brings down an i K in the
+ 
+
+ align:start position:0%
+derivative brings down an i K in the
+transform so we get i k twice so k s i^
+
+ align:start position:0%
+transform so we get i k twice so k s i^
+ 
+
+ align:start position:0%
+transform so we get i k twice so k s i^
+2 cancels the minus1 so it's so that's
+
+ align:start position:0%
+2 cancels the minus1 so it's so that's
+ 
+
+ align:start position:0%
+2 cancels the minus1 so it's so that's
+the transform of minus U Prime this is
+
+ align:start position:0%
+the transform of minus U Prime this is
+ 
+
+ align:start position:0%
+the transform of minus U Prime this is
+the transform of ordinary a s u just a
+
+ align:start position:0%
+the transform of ordinary a s u just a
+ 
+
+ align:start position:0%
+the transform of ordinary a s u just a
+squ and this is fat so we've got into
+
+ align:start position:0%
+squ and this is fat so we've got into
+ 
+
+ align:start position:0%
+squ and this is fat so we've got into
+frequency space where we just seeing a
+
+ align:start position:0%
+frequency space where we just seeing a
+ 
+
+ align:start position:0%
+frequency space where we just seeing a
+multiplication
+
+ align:start position:0%
+multiplication
+ 
+
+ align:start position:0%
+multiplication
+K2 + a 2
+
+ align:start position:0%
+K2 + a 2
+ 
+
+ align:start position:0%
+K2 + a 2
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+hat of this is U hat of k equals fat of
+
+ align:start position:0%
+hat of this is U hat of k equals fat of
+ 
+
+ align:start position:0%
+hat of this is U hat of k equals fat of
+K right this
+
+ align:start position:0%
+K right this
+ 
+
+ align:start position:0%
+K right this
+is uh oh well sorry we were yeah yeah no
+
+ align:start position:0%
+is uh oh well sorry we were yeah yeah no
+ 
+
+ align:start position:0%
+is uh oh well sorry we were yeah yeah no
+that's right F of K
+
+ align:start position:0%
+that's right F of K
+ 
+
+ align:start position:0%
+that's right F of K
+right so we're in frequency space where
+
+ align:start position:0%
+right so we're in frequency space where
+ 
+
+ align:start position:0%
+right so we're in frequency space where
+we just see a multiplication so again
+
+ align:start position:0%
+we just see a multiplication so again
+ 
+
+ align:start position:0%
+we just see a multiplication so again
+this is now we just Dem multiply just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divide and then we have the answer
+
+ align:start position:0%
+divide and then we have the answer
+ 
+
+ align:start position:0%
+divide and then we have the answer
+answer but we have it transform and then
+
+ align:start position:0%
+answer but we have it transform and then
+ 
+
+ align:start position:0%
+answer but we have it transform and then
+we have to transform back so we have to
+
+ align:start position:0%
+we have to transform back so we have to
+ 
+
+ align:start position:0%
+we have to transform back so we have to
+do the the for transform to get to the
+
+ align:start position:0%
+do the the for transform to get to the
+ 
+
+ align:start position:0%
+do the the for transform to get to the
+I'll say the inverse forier trans
+
+ align:start position:0%
+I'll say the inverse forier trans
+ 
+
+ align:start position:0%
+I'll say the inverse forier trans
+transform to get back to U of X the
+
+ align:start position:0%
+transform to get back to U of X the
+ 
+
+ align:start position:0%
+transform to get back to U of X the
+answer that that's the model that's the
+
+ align:start position:0%
+answer that that's the model that's the
+ 
+
+ align:start position:0%
+answer that that's the model that's the
+model and that's maybe the one that
+
+ align:start position:0%
+model and that's maybe the one that
+ 
+
+ align:start position:0%
+model and that's maybe the one that
+we've seen now we're able to think about
+
+ align:start position:0%
+we've seen now we're able to think about
+ 
+
+ align:start position:0%
+we've seen now we're able to think about
+uh uh all these all these four types
+
+ align:start position:0%
+uh uh all these all these four types
+ 
+
+ align:start position:0%
+uh uh all these all these four types
+right yeah yeah okay so what was the key
+
+ align:start position:0%
+right yeah yeah okay so what was the key
+ 
+
+ align:start position:0%
+right yeah yeah okay so what was the key
+idea get into frequency space and then
+
+ align:start position:0%
+idea get into frequency space and then
+ 
+
+ align:start position:0%
+idea get into frequency space and then
+then it's just a then the the equation
+
+ align:start position:0%
+then it's just a then the the equation
+ 
+
+ align:start position:0%
+then it's just a then the the equation
+is just a multiplication so the solution
+
+ align:start position:0%
+is just a multiplication so the solution
+ 
+
+ align:start position:0%
+is just a multiplication so the solution
+is just a division so can I do that now
+
+ align:start position:0%
+is just a division so can I do that now
+ 
+
+ align:start position:0%
+is just a division so can I do that now
+with these four examples just to see so
+
+ align:start position:0%
+with these four examples just to see so
+ 
+
+ align:start position:0%
+with these four examples just to see so
+this is like bringing the pieces
+
+ align:start position:0%
+this is like bringing the pieces
+ 
+
+ align:start position:0%
+this is like bringing the pieces
+together okay and deconvolution is a
+
+ align:start position:0%
+together okay and deconvolution is a
+ 
+
+ align:start position:0%
+together okay and deconvolution is a
+very key thing to do okay so I'll take
+
+ align:start position:0%
+very key thing to do okay so I'll take
+ 
+
+ align:start position:0%
+very key thing to do okay so I'll take
+all four of those and bring them into
+
+ align:start position:0%
+all four of those and bring them into
+ 
+
+ align:start position:0%
+all four of those and bring them into
+frequency space so this will be maybe uh
+
+ align:start position:0%
+frequency space so this will be maybe uh
+ 
+
+ align:start position:0%
+frequency space so this will be maybe uh
+maybe uh you'll let me use K hat of oh K
+
+ align:start position:0%
+maybe uh you'll let me use K hat of oh K
+ 
+
+ align:start position:0%
+maybe uh you'll let me use K hat of oh K
+hat of K that's not too good uh well I'm
+
+ align:start position:0%
+hat of K that's not too good uh well I'm
+ 
+
+ align:start position:0%
+hat of K that's not too good uh well I'm
+stuck with it you you yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H what am I doing here and this two Pi
+
+ align:start position:0%
+H what am I doing here and this two Pi
+ 
+
+ align:start position:0%
+H what am I doing here and this two Pi
+periodic one that's that's the one I
+
+ align:start position:0%
+periodic one that's that's the one I
+ 
+
+ align:start position:0%
+periodic one that's that's the one I
+started with but now I've got got I'm
+
+ align:start position:0%
+started with but now I've got got I'm
+ 
+
+ align:start position:0%
+started with but now I've got got I'm
+I'm using hats and so on I didn't do
+
+ align:start position:0%
+I'm using hats and so on I didn't do
+ 
+
+ align:start position:0%
+I'm using hats and so on I didn't do
+that in in uh section
+
+ align:start position:0%
+that in in uh section
+ 
+
+ align:start position:0%
+that in in uh section
+4.1 uh what the heck am I G to what
+
+ align:start position:0%
+4.1 uh what the heck am I G to what
+ 
+
+ align:start position:0%
+4.1 uh what the heck am I G to what
+notation am I going to do this is and I
+
+ align:start position:0%
+notation am I going to do this is and I
+ 
+
+ align:start position:0%
+notation am I going to do this is and I
+really didn't do uh convolution that
+
+ align:start position:0%
+really didn't do uh convolution that
+ 
+
+ align:start position:0%
+really didn't do uh convolution that
+much for functions so let me jump to
+
+ align:start position:0%
+much for functions so let me jump to
+ 
+
+ align:start position:0%
+much for functions so let me jump to
+here let me I'll come back it's it's has
+
+ align:start position:0%
+here let me I'll come back it's it's has
+ 
+
+ align:start position:0%
+here let me I'll come back it's it's has
+follows exactly the same pattern so let
+
+ align:start position:0%
+follows exactly the same pattern so let
+ 
+
+ align:start position:0%
+follows exactly the same pattern so let
+me jump to this one okay so I have a
+
+ align:start position:0%
+me jump to this one okay so I have a
+ 
+
+ align:start position:0%
+me jump to this one okay so I have a
+convolution equation
+
+ align:start position:0%
+convolution equation
+ 
+
+ align:start position:0%
+convolution equation
+now this is one where I you could you
+
+ align:start position:0%
+now this is one where I you could you
+ 
+
+ align:start position:0%
+now this is one where I you could you
+know you you could you could do this one
+
+ align:start position:0%
+know you you could you could do this one
+ 
+
+ align:start position:0%
+know you you could you could do this one
+this this is you know this could appear
+
+ align:start position:0%
+this this is you know this could appear
+ 
+
+ align:start position:0%
+this this is you know this could appear
+on the quiz because because I can do all
+
+ align:start position:0%
+on the quiz because because I can do all
+ 
+
+ align:start position:0%
+on the quiz because because I can do all
+of it so what is this
+
+ align:start position:0%
+of it so what is this
+ 
+
+ align:start position:0%
+of it so what is this
+convolution okay it's I've got n
+
+ align:start position:0%
+convolution okay it's I've got n
+ 
+
+ align:start position:0%
+convolution okay it's I've got n
+equations n unknowns let me write them
+
+ align:start position:0%
+equations n unknowns let me write them
+ 
+
+ align:start position:0%
+equations n unknowns let me write them
+in Matrix form just so you see it that
+
+ align:start position:0%
+in Matrix form just so you see it that
+ 
+
+ align:start position:0%
+in Matrix form just so you see it that
+way too c not C1 C2 C3 make n equal 4
+
+ align:start position:0%
+way too c not C1 C2 C3 make n equal 4
+ 
+
+ align:start position:0%
+way too c not C1 C2 C3 make n equal 4
+and then these are uh th this
+
+ align:start position:0%
+and then these are uh th this
+ 
+
+ align:start position:0%
+and then these are uh th this
+convolution has c not C2
+
+ align:start position:0%
+convolution has c not C2
+ 
+
+ align:start position:0%
+convolution has c not C2
+C1 C3 C2 C1 c not this will be C3 C3 C3
+
+ align:start position:0%
+C1 C3 C2 C1 c not this will be C3 C3 C3
+ 
+
+ align:start position:0%
+C1 C3 C2 C1 c not this will be C3 C3 C3
+I'm writing down all the right numbers
+
+ align:start position:0%
+I'm writing down all the right numbers
+ 
+
+ align:start position:0%
+I'm writing down all the right numbers
+in the right places so that when I do
+
+ align:start position:0%
+in the right places so that when I do
+ 
+
+ align:start position:0%
+in the right places so that when I do
+that multiplication with the unknown you
+
+ align:start position:0%
+that multiplication with the unknown you
+ 
+
+ align:start position:0%
+that multiplication with the unknown you
+not you
+
+ align:start position:0%
+not you
+ 
+
+ align:start position:0%
+not you
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+u 2 and
+
+ align:start position:0%
+u 2 and
+ 
+
+ align:start position:0%
+u 2 and
+u3 I get the the right hand the known
+
+ align:start position:0%
+u3 I get the the right hand the known
+ 
+
+ align:start position:0%
+u3 I get the the right hand the known
+right hand side maybe B would be a
+
+ align:start position:0%
+right hand side maybe B would be a
+ 
+
+ align:start position:0%
+right hand side maybe B would be a
+little better because we're more used to
+
+ align:start position:0%
+little better because we're more used to
+ 
+
+ align:start position:0%
+little better because we're more used to
+B as the as a known it's it's just an ax
+
+ align:start position:0%
+B as the as a known it's it's just an ax
+ 
+
+ align:start position:0%
+B as the as a known it's it's just an ax
+equal B problem or an au U equal B
+
+ align:start position:0%
+equal B problem or an au U equal B
+ 
+
+ align:start position:0%
+equal B problem or an au U equal B
+problem but uh it looks like a
+
+ align:start position:0%
+problem but uh it looks like a
+ 
+
+ align:start position:0%
+problem but uh it looks like a
+convolution but now it's just a matrix
+
+ align:start position:0%
+convolution but now it's just a matrix
+ 
+
+ align:start position:0%
+convolution but now it's just a matrix
+multiplication so this is just B KN B1
+
+ align:start position:0%
+multiplication so this is just B KN B1
+ 
+
+ align:start position:0%
+multiplication so this is just B KN B1
+B2
+
+ align:start position:0%
+B2
+ 
+
+ align:start position:0%
+B2
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay that's our
+
+ align:start position:0%
+okay that's our
+ 
+
+ align:start position:0%
+okay that's our
+equation special type of Matrix
+
+ align:start position:0%
+equation special type of Matrix
+ 
+
+ align:start position:0%
+equation special type of Matrix
+circulent Matrix so this is just
+
+ align:start position:0%
+circulent Matrix so this is just
+ 
+
+ align:start position:0%
+circulent Matrix so this is just
+literally the same as C circularly
+
+ align:start position:0%
+literally the same as C circularly
+ 
+
+ align:start position:0%
+literally the same as C circularly
+convolved with u equals B I just wrote
+
+ align:start position:0%
+convolved with u equals B I just wrote
+ 
+
+ align:start position:0%
+convolved with u equals B I just wrote
+it out in Matrix
+
+ align:start position:0%
+it out in Matrix
+ 
+
+ align:start position:0%
+it out in Matrix
+language so you could call matlb with
+
+ align:start position:0%
+language so you could call matlb with
+ 
+
+ align:start position:0%
+language so you could call matlb with
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+Matrix and and uh you know so one way to
+
+ align:start position:0%
+Matrix and and uh you know so one way to
+ 
+
+ align:start position:0%
+Matrix and and uh you know so one way to
+answer it would be get the invert The
+
+ align:start position:0%
+answer it would be get the invert The
+ 
+
+ align:start position:0%
+answer it would be get the invert The
+Matrix but if it was
+
+ align:start position:0%
+Matrix but if it was
+ 
+
+ align:start position:0%
+Matrix but if it was
+large uh I A Better Way would be switch
+
+ align:start position:0%
+large uh I A Better Way would be switch
+ 
+
+ align:start position:0%
+large uh I A Better Way would be switch
+over to frequency space so now here here
+
+ align:start position:0%
+over to frequency space so now here here
+ 
+
+ align:start position:0%
+over to frequency space so now here here
+think now what happens when I switch
+
+ align:start position:0%
+think now what happens when I switch
+ 
+
+ align:start position:0%
+think now what happens when I switch
+these vectors to frequency space it
+
+ align:start position:0%
+these vectors to frequency space it
+ 
+
+ align:start position:0%
+these vectors to frequency space it
+becomes a multiplication so this go
+
+ align:start position:0%
+becomes a multiplication so this go
+ 
+
+ align:start position:0%
+becomes a multiplication so this go
+becomes a multiplication
+
+ align:start position:0%
+becomes a multiplication
+ 
+
+ align:start position:0%
+becomes a multiplication
+what now what so C I want the Fier the
+
+ align:start position:0%
+what now what so C I want the Fier the
+ 
+
+ align:start position:0%
+what now what so C I want the Fier the
+from the C's what do I what am I going
+
+ align:start position:0%
+from the C's what do I what am I going
+ 
+
+ align:start position:0%
+from the C's what do I what am I going
+to so this is
+
+ align:start position:0%
+to so this is
+ 
+
+ align:start position:0%
+to so this is
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+uh you these are all in in the the con
+
+ align:start position:0%
+uh you these are all in in the the con
+ 
+
+ align:start position:0%
+uh you these are all in in the the con
+in the space where it's a convolution
+
+ align:start position:0%
+in the space where it's a convolution
+ 
+
+ align:start position:0%
+in the space where it's a convolution
+what am I going to call it where it's in
+
+ align:start position:0%
+what am I going to call it where it's in
+ 
+
+ align:start position:0%
+what am I going to call it where it's in
+the space where it's a multiplication I
+
+ align:start position:0%
+the space where it's a multiplication I
+ 
+
+ align:start position:0%
+the space where it's a multiplication I
+better I just need three new names uh
+
+ align:start position:0%
+better I just need three new names uh
+ 
+
+ align:start position:0%
+better I just need three new names uh
+maybe I'll use C hat U hat and B hat hat
+
+ align:start position:0%
+maybe I'll use C hat U hat and B hat hat
+ 
+
+ align:start position:0%
+maybe I'll use C hat U hat and B hat hat
+just because there's no doubt in
+
+ align:start position:0%
+just because there's no doubt in
+ 
+
+ align:start position:0%
+just because there's no doubt in
+anybody's mind that when you see that
+
+ align:start position:0%
+anybody's mind that when you see that
+ 
+
+ align:start position:0%
+anybody's mind that when you see that
+hat you've gone into frequency space now
+
+ align:start position:0%
+hat you've gone into frequency space now
+ 
+
+ align:start position:0%
+hat you've gone into frequency space now
+what's the equation in frequency
+
+ align:start position:0%
+what's the equation in frequency
+ 
+
+ align:start position:0%
+what's the equation in frequency
+space and then I'll do an
+
+ align:start position:0%
+space and then I'll do an
+ 
+
+ align:start position:0%
+space and then I'll do an
+example what what it's a
+
+ align:start position:0%
+example what what it's a
+ 
+
+ align:start position:0%
+example what what it's a
+multiplication but I don't usually see a
+
+ align:start position:0%
+multiplication but I don't usually see a
+ 
+
+ align:start position:0%
+multiplication but I don't usually see a
+vector and nothing there and what what's
+
+ align:start position:0%
+vector and nothing there and what what's
+ 
+
+ align:start position:0%
+vector and nothing there and what what's
+what is what's the multiplication in
+
+ align:start position:0%
+what is what's the multiplication in
+ 
+
+ align:start position:0%
+what is what's the multiplication in
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's component by component
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c0 u0 equal B 0 C hat one U Hat 1 equal
+
+ align:start position:0%
+c0 u0 equal B 0 C hat one U Hat 1 equal
+ 
+
+ align:start position:0%
+c0 u0 equal B 0 C hat one U Hat 1 equal
+B hat one C Hat 2 U Hat 2 equal B Hat 2
+
+ align:start position:0%
+B hat one C Hat 2 U Hat 2 equal B Hat 2
+ 
+
+ align:start position:0%
+B hat one C Hat 2 U Hat 2 equal B Hat 2
+and finally C hat 3 U hat 3 equal B hat
+
+ align:start position:0%
+and finally C hat 3 U hat 3 equal B hat
+ 
+
+ align:start position:0%
+and finally C hat 3 U hat 3 equal B hat
+3 and there might be I don't swear that
+
+ align:start position:0%
+3 and there might be I don't swear that
+ 
+
+ align:start position:0%
+3 and there might be I don't swear that
+there isn't a 1 over4 somewhere
+
+ align:start position:0%
+there isn't a 1 over4 somewhere
+ 
+
+ align:start position:0%
+there isn't a 1 over4 somewhere
+right but the point is we're in uh
+
+ align:start position:0%
+right but the point is we're in uh
+ 
+
+ align:start position:0%
+right but the point is we're in uh
+frequency space now we just have a
+
+ align:start position:0%
+frequency space now we just have a
+ 
+
+ align:start position:0%
+frequency space now we just have a
+component by component each component of
+
+ align:start position:0%
+component by component each component of
+ 
+
+ align:start position:0%
+component by component each component of
+c times each component each component of
+
+ align:start position:0%
+c times each component each component of
+ 
+
+ align:start position:0%
+c times each component each component of
+C hat times each component of U hat
+
+ align:start position:0%
+C hat times each component of U hat
+ 
+
+ align:start position:0%
+C hat times each component of U hat
+gives us a component of b hat now we're
+
+ align:start position:0%
+gives us a component of b hat now we're
+ 
+
+ align:start position:0%
+gives us a component of b hat now we're
+ready for deconvolution just divide so
+
+ align:start position:0%
+ready for deconvolution just divide so
+ 
+
+ align:start position:0%
+ready for deconvolution just divide so
+now you have obviously
+
+ align:start position:0%
+now you have obviously
+ 
+
+ align:start position:0%
+now you have obviously
+I don't have to write all these B hat
+
+ align:start position:0%
+I don't have to write all these B hat
+ 
+
+ align:start position:0%
+I don't have to write all these B hat
+zero over C hat zero right I just do a
+
+ align:start position:0%
+zero over C hat zero right I just do a
+ 
+
+ align:start position:0%
+zero over C hat zero right I just do a
+division so on down to U hat 3 is B hat
+
+ align:start position:0%
+division so on down to U hat 3 is B hat
+ 
+
+ align:start position:0%
+division so on down to U hat 3 is B hat
+is the third component of b divided by
+
+ align:start position:0%
+is the third component of b divided by
+ 
+
+ align:start position:0%
+is the third component of b divided by
+the third component of
+
+ align:start position:0%
+the third component of
+ 
+
+ align:start position:0%
+the third component of
+C okay now don't forget here that that
+
+ align:start position:0%
+C okay now don't forget here that that
+ 
+
+ align:start position:0%
+C okay now don't forget here that that
+in going from here to here I had to
+
+ align:start position:0%
+in going from here to here I had to
+ 
+
+ align:start position:0%
+in going from here to here I had to
+figure out what's the C hats
+
+ align:start position:0%
+figure out what's the C hats
+ 
+
+ align:start position:0%
+figure out what's the C hats
+were right I had to do
+
+ align:start position:0%
+were right I had to do
+ 
+
+ align:start position:0%
+were right I had to do
+the for the for Matrix or or the inverse
+
+ align:start position:0%
+the for the for Matrix or or the inverse
+ 
+
+ align:start position:0%
+the for the for Matrix or or the inverse
+for Matrix to go from C to C hat from B
+
+ align:start position:0%
+for Matrix to go from C to C hat from B
+ 
+
+ align:start position:0%
+for Matrix to go from C to C hat from B
+to be hat so everything got for
+
+ align:start position:0%
+to be hat so everything got for
+ 
+
+ align:start position:0%
+to be hat so everything got for
+transformed but the the the
+
+ align:start position:0%
+transformed but the the the
+ 
+
+ align:start position:0%
+transformed but the the the
+the the object was to make the equation
+
+ align:start position:0%
+the the object was to make the equation
+ 
+
+ align:start position:0%
+the the object was to make the equation
+easy and of course now we've got four
+
+ align:start position:0%
+easy and of course now we've got four
+ 
+
+ align:start position:0%
+easy and of course now we've got four
+trivial equations that we just solve
+
+ align:start position:0%
+trivial equations that we just solve
+ 
+
+ align:start position:0%
+trivial equations that we just solve
+that way all right can I let me see if I
+
+ align:start position:0%
+that way all right can I let me see if I
+ 
+
+ align:start position:0%
+that way all right can I let me see if I
+can just pull this down with some
+
+ align:start position:0%
+can just pull this down with some
+ 
+
+ align:start position:0%
+can just pull this down with some
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+when is a Circ when is this here's a
+
+ align:start position:0%
+when is a Circ when is this here's a
+ 
+
+ align:start position:0%
+when is a Circ when is this here's a
+good question when is that when is a
+
+ align:start position:0%
+good question when is that when is a
+ 
+
+ align:start position:0%
+good question when is that when is a
+circulent matrix
+
+ align:start position:0%
+circulent matrix
+ 
+
+ align:start position:0%
+circulent matrix
+invertible when what's the when will
+
+ align:start position:0%
+invertible when what's the when will
+ 
+
+ align:start position:0%
+invertible when what's the when will
+this method
+
+ align:start position:0%
+this method
+ 
+
+ align:start position:0%
+this method
+work the the circular Matrix could fail
+
+ align:start position:0%
+work the the circular Matrix could fail
+ 
+
+ align:start position:0%
+work the the circular Matrix could fail
+to be invertible how would I know
+
+ align:start position:0%
+to be invertible how would I know
+ 
+
+ align:start position:0%
+to be invertible how would I know
+that sorry if it's singular and how
+
+ align:start position:0%
+that sorry if it's singular and how
+ 
+
+ align:start position:0%
+that sorry if it's singular and how
+would I if I proceed this way here I've
+
+ align:start position:0%
+would I if I proceed this way here I've
+ 
+
+ align:start position:0%
+would I if I proceed this way here I've
+got an
+
+ align:start position:0%
+got an
+ 
+
+ align:start position:0%
+got an
+answer but if it's singular not really
+
+ align:start position:0%
+answer but if it's singular not really
+ 
+
+ align:start position:0%
+answer but if it's singular not really
+expecting to get an answer let me lift
+
+ align:start position:0%
+expecting to get an answer let me lift
+ 
+
+ align:start position:0%
+expecting to get an answer let me lift
+the board a little uh so where
+
+ align:start position:0%
+the board a little uh so where
+ 
+
+ align:start position:0%
+the board a little uh so where
+would where would the where would I get
+
+ align:start position:0%
+would where would the where would I get
+ 
+
+ align:start position:0%
+would where would the where would I get
+oops have to stop this method in in uh
+
+ align:start position:0%
+oops have to stop this method in in uh
+ 
+
+ align:start position:0%
+oops have to stop this method in in uh
+in solving those four equations where
+
+ align:start position:0%
+in solving those four equations where
+ 
+
+ align:start position:0%
+in solving those four equations where
+would I learn it is
+
+ align:start position:0%
+would I learn it is
+ 
+
+ align:start position:0%
+would I learn it is
+singular what could go wrong in
+
+ align:start position:0%
+singular what could go wrong in
+ 
+
+ align:start position:0%
+singular what could go wrong in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+yes that's right that always in math the
+
+ align:start position:0%
+yes that's right that always in math the
+ 
+
+ align:start position:0%
+yes that's right that always in math the
+question is
+
+ align:start position:0%
+question is
+ 
+
+ align:start position:0%
+question is
+are you dividing by zero so the the the
+
+ align:start position:0%
+are you dividing by zero so the the the
+ 
+
+ align:start position:0%
+are you dividing by zero so the the the
+question of whether the Matrix is
+
+ align:start position:0%
+question of whether the Matrix is
+ 
+
+ align:start position:0%
+question of whether the Matrix is
+singular is the same as the question of
+
+ align:start position:0%
+singular is the same as the question of
+ 
+
+ align:start position:0%
+singular is the same as the question of
+whether c not hat c not one C not2 and C
+
+ align:start position:0%
+whether c not hat c not one C not2 and C
+ 
+
+ align:start position:0%
+whether c not hat c not one C not2 and C
+not3 C sorry c not hat C1 hat C2 hat and
+
+ align:start position:0%
+not3 C sorry c not hat C1 hat C2 hat and
+ 
+
+ align:start position:0%
+not3 C sorry c not hat C1 hat C2 hat and
+C3 hat can't be zero that's in fact even
+
+ align:start position:0%
+C3 hat can't be zero that's in fact even
+ 
+
+ align:start position:0%
+C3 hat can't be zero that's in fact even
+better those numbers are the those four
+
+ align:start position:0%
+better those numbers are the those four
+ 
+
+ align:start position:0%
+better those numbers are the those four
+numbers those four C hats are actually
+
+ align:start position:0%
+numbers those four C hats are actually
+ 
+
+ align:start position:0%
+numbers those four C hats are actually
+the igen value values of the Matrix
+
+ align:start position:0%
+the igen value values of the Matrix
+ 
+
+ align:start position:0%
+the igen value values of the Matrix
+we've switched what the f transform did
+
+ align:start position:0%
+we've switched what the f transform did
+ 
+
+ align:start position:0%
+we've switched what the f transform did
+was switch over to the Igan values and
+
+ align:start position:0%
+was switch over to the Igan values and
+ 
+
+ align:start position:0%
+was switch over to the Igan values and
+igen vectors and there that's the whole
+
+ align:start position:0%
+igen vectors and there that's the whole
+ 
+
+ align:start position:0%
+igen vectors and there that's the whole
+message of those guys is you follow each
+
+ align:start position:0%
+message of those guys is you follow each
+ 
+
+ align:start position:0%
+message of those guys is you follow each
+one separately just the way we're doing
+
+ align:start position:0%
+one separately just the way we're doing
+ 
+
+ align:start position:0%
+one separately just the way we're doing
+here so this is the component of the b
+
+ align:start position:0%
+here so this is the component of the b
+ 
+
+ align:start position:0%
+here so this is the component of the b
+in the four IG Vector directions those
+
+ align:start position:0%
+in the four IG Vector directions those
+ 
+
+ align:start position:0%
+in the four IG Vector directions those
+are the four igen values and I have to
+
+ align:start position:0%
+are the four igen values and I have to
+ 
+
+ align:start position:0%
+are the four igen values and I have to
+divide by
+
+ align:start position:0%
+divide by
+ 
+
+ align:start position:0%
+divide by
+them you see it's the idea was like we
+
+ align:start position:0%
+them you see it's the idea was like we
+ 
+
+ align:start position:0%
+them you see it's the idea was like we
+diagonalized The Matrix we we've had
+
+ align:start position:0%
+diagonalized The Matrix we we've had
+ 
+
+ align:start position:0%
+diagonalized The Matrix we we've had
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+Matrix which is which is full and we
+
+ align:start position:0%
+Matrix which is which is full and we
+ 
+
+ align:start position:0%
+Matrix which is which is full and we
+uh take by taking for a transforms
+
+ align:start position:0%
+uh take by taking for a transforms
+ 
+
+ align:start position:0%
+uh take by taking for a transforms
+that's the same thing as as as putting
+
+ align:start position:0%
+that's the same thing as as as putting
+ 
+
+ align:start position:0%
+that's the same thing as as as putting
+in the I vectors switching The Matrix to
+
+ align:start position:0%
+in the I vectors switching The Matrix to
+ 
+
+ align:start position:0%
+in the I vectors switching The Matrix to
+this diagonal matrix right our our our
+
+ align:start position:0%
+this diagonal matrix right our our our
+ 
+
+ align:start position:0%
+this diagonal matrix right our our our
+problem has become like the the the
+
+ align:start position:0%
+problem has become like the the the
+ 
+
+ align:start position:0%
+problem has become like the the the
+diagonalized form is c not hat down to
+
+ align:start position:0%
+diagonalized form is c not hat down to
+ 
+
+ align:start position:0%
+diagonalized form is c not hat down to
+C3 hat sitting on the diagonal all zeros
+
+ align:start position:0%
+C3 hat sitting on the diagonal all zeros
+ 
+
+ align:start position:0%
+C3 hat sitting on the diagonal all zeros
+elsewhere that's when we switched when
+
+ align:start position:0%
+elsewhere that's when we switched when
+ 
+
+ align:start position:0%
+elsewhere that's when we switched when
+we did 4 a transform we were switching
+
+ align:start position:0%
+we did 4 a transform we were switching
+ 
+
+ align:start position:0%
+we did 4 a transform we were switching
+to igen vectors okay so that's the
+
+ align:start position:0%
+to igen vectors okay so that's the
+ 
+
+ align:start position:0%
+to igen vectors okay so that's the
+message that that the test for for
+
+ align:start position:0%
+message that that the test for for
+ 
+
+ align:start position:0%
+message that that the test for for
+Singularity is the for8 some the
+
+ align:start position:0%
+Singularity is the for8 some the
+ 
+
+ align:start position:0%
+Singularity is the for8 some the
+transform of C hits
+
+ align:start position:0%
+transform of C hits
+ 
+
+ align:start position:0%
+transform of C hits
+zero then we're in trouble let let me do
+
+ align:start position:0%
+zero then we're in trouble let let me do
+ 
+
+ align:start position:0%
+zero then we're in trouble let let me do
+an example you know let me do an example
+
+ align:start position:0%
+an example you know let me do an example
+ 
+
+ align:start position:0%
+an example you know let me do an example
+you know okay here's so finally now we
+
+ align:start position:0%
+you know okay here's so finally now we
+ 
+
+ align:start position:0%
+you know okay here's so finally now we
+get a numerical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example the example we really know is
+
+ align:start position:0%
+example the example we really know is
+ 
+
+ align:start position:0%
+example the example we really know is
+this one right the I as I start writing
+
+ align:start position:0%
+this one right the I as I start writing
+ 
+
+ align:start position:0%
+this one right the I as I start writing
+that you may say in your mind oh no not
+
+ align:start position:0%
+that you may say in your mind oh no not
+ 
+
+ align:start position:0%
+that you may say in your mind oh no not
+again but uh give it to me one more week
+
+ align:start position:0%
+again but uh give it to me one more week
+ 
+
+ align:start position:0%
+again but uh give it to me one more week
+with these matrices but it'll be the C
+
+ align:start position:0%
+with these matrices but it'll be the C
+ 
+
+ align:start position:0%
+with these matrices but it'll be the C
+Matrix so it's going to be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+circulent recognize
+
+ align:start position:0%
+circulent recognize
+ 
+
+ align:start position:0%
+circulent recognize
+this and got those minus ones in the
+
+ align:start position:0%
+this and got those minus ones in the
+ 
+
+ align:start position:0%
+this and got those minus ones in the
+corners too okay let's go back to day
+
+ align:start position:0%
+corners too okay let's go back to day
+ 
+
+ align:start position:0%
+corners too okay let's go back to day
+one is that matrics
+
+ align:start position:0%
+one is that matrics
+ 
+
+ align:start position:0%
+one is that matrics
+invertible yes or
+
+ align:start position:0%
+invertible yes or
+ 
+
+ align:start position:0%
+invertible yes or
+no please no everybody knows that Matrix
+
+ align:start position:0%
+no please no everybody knows that Matrix
+ 
+
+ align:start position:0%
+no please no everybody knows that Matrix
+is not invertible and do you remember
+
+ align:start position:0%
+is not invertible and do you remember
+ 
+
+ align:start position:0%
+is not invertible and do you remember
+what's in the null
+
+ align:start position:0%
+what's in the null
+ 
+
+ align:start position:0%
+what's in the null
+space yes what's the vector in the null
+
+ align:start position:0%
+space yes what's the vector in the null
+ 
+
+ align:start position:0%
+space yes what's the vector in the null
+space of that Matrix all ones now when I
+
+ align:start position:0%
+space of that Matrix all ones now when I
+ 
+
+ align:start position:0%
+space of that Matrix all ones now when I
+take just think now when I take 4A
+
+ align:start position:0%
+take just think now when I take 4A
+ 
+
+ align:start position:0%
+take just think now when I take 4A
+transform that all
+
+ align:start position:0%
+transform that all
+ 
+
+ align:start position:0%
+transform that all
+ones is going to transform to
+
+ align:start position:0%
+ones is going to transform to
+ 
+
+ align:start position:0%
+ones is going to transform to
+what it's going to transform to the
+
+ align:start position:0%
+what it's going to transform to the
+ 
+
+ align:start position:0%
+what it's going to transform to the
+Delta it'll transform to the one that is
+
+ align:start position:0%
+Delta it'll transform to the one that is
+ 
+
+ align:start position:0%
+Delta it'll transform to the one that is
+like one z0 or maybe it's four z00 Z but
+
+ align:start position:0%
+like one z0 or maybe it's four z00 Z but
+ 
+
+ align:start position:0%
+like one z0 or maybe it's four z00 Z but
+it's it's the that well
+
+ align:start position:0%
+it's it's the that well
+ 
+
+ align:start position:0%
+it's it's the that well
+okay now I'm ready to take uh so here's
+
+ align:start position:0%
+okay now I'm ready to take uh so here's
+ 
+
+ align:start position:0%
+okay now I'm ready to take uh so here's
+my C
+
+ align:start position:0%
+my C
+ 
+
+ align:start position:0%
+my C
+can I take the so what's my method now
+
+ align:start position:0%
+can I take the so what's my method now
+ 
+
+ align:start position:0%
+can I take the so what's my method now
+I'm going to do this method and I'm
+
+ align:start position:0%
+I'm going to do this method and I'm
+ 
+
+ align:start position:0%
+I'm going to do this method and I'm
+going to run
+
+ align:start position:0%
+going to run
+ 
+
+ align:start position:0%
+going to run
+into this thing is going to be zero
+
+ align:start position:0%
+into this thing is going to be zero
+ 
+
+ align:start position:0%
+into this thing is going to be zero
+because that's the igen value that goes
+
+ align:start position:0%
+because that's the igen value that goes
+ 
+
+ align:start position:0%
+because that's the igen value that goes
+with the 11111 column the constant the
+
+ align:start position:0%
+with the 11111 column the constant the
+ 
+
+ align:start position:0%
+with the 11111 column the constant the
+the the zero frequency in the in
+
+ align:start position:0%
+the the zero frequency in the in
+ 
+
+ align:start position:0%
+the the zero frequency in the in
+frequency space you'll see it happen so
+
+ align:start position:0%
+frequency space you'll see it happen so
+ 
+
+ align:start position:0%
+frequency space you'll see it happen so
+let's take the 4 a transform of
+
+ align:start position:0%
+let's take the 4 a transform of
+ 
+
+ align:start position:0%
+let's take the 4 a transform of
+that and then we would have to take the
+
+ align:start position:0%
+that and then we would have to take the
+ 
+
+ align:start position:0%
+that and then we would have to take the
+for a transform of the right hand side B
+
+ align:start position:0%
+for a transform of the right hand side B
+ 
+
+ align:start position:0%
+for a transform of the right hand side B
+whatever ever that happened to be but
+
+ align:start position:0%
+whatever ever that happened to be but
+ 
+
+ align:start position:0%
+whatever ever that happened to be but
+but it's always the left side the
+
+ align:start position:0%
+but it's always the left side the
+ 
+
+ align:start position:0%
+but it's always the left side the
+singular or not Matrix I believe will be
+
+ align:start position:0%
+singular or not Matrix I believe will be
+ 
+
+ align:start position:0%
+singular or not Matrix I believe will be
+singular here so okay just to remind me
+
+ align:start position:0%
+singular here so okay just to remind me
+ 
+
+ align:start position:0%
+singular here so okay just to remind me
+how do I take transforms of this
+
+ align:start position:0%
+how do I take transforms of this
+ 
+
+ align:start position:0%
+how do I take transforms of this
+guy gosh we have to be able to do that
+
+ align:start position:0%
+guy gosh we have to be able to do that
+ 
+
+ align:start position:0%
+guy gosh we have to be able to do that
+that's section 4 well 4.3 isn't it yeah
+
+ align:start position:0%
+that's section 4 well 4.3 isn't it yeah
+ 
+
+ align:start position:0%
+that's section 4 well 4.3 isn't it yeah
+the the DFT of that of that Vector uh
+
+ align:start position:0%
+the the DFT of that of that Vector uh
+ 
+
+ align:start position:0%
+the the DFT of that of that Vector uh
+what do I
+
+ align:start position:0%
+what do I
+ 
+
+ align:start position:0%
+what do I
+get um yes how do I take the DFT of a of
+
+ align:start position:0%
+get um yes how do I take the DFT of a of
+ 
+
+ align:start position:0%
+get um yes how do I take the DFT of a of
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+vector I multiply by The forier Matrix
+
+ align:start position:0%
+vector I multiply by The forier Matrix
+ 
+
+ align:start position:0%
+vector I multiply by The forier Matrix
+right yes yes so I have to multiply
+
+ align:start position:0%
+right yes yes so I have to multiply
+ 
+
+ align:start position:0%
+right yes yes so I have to multiply
+multiply that thing by The forier Matrix
+
+ align:start position:0%
+multiply that thing by The forier Matrix
+ 
+
+ align:start position:0%
+multiply that thing by The forier Matrix
+to so to get C
+
+ align:start position:0%
+to so to get C
+ 
+
+ align:start position:0%
+to so to get C
+hat this was Big C for the Matrix little
+
+ align:start position:0%
+hat this was Big C for the Matrix little
+ 
+
+ align:start position:0%
+hat this was Big C for the Matrix little
+C for the vector that goes into it into
+
+ align:start position:0%
+C for the vector that goes into it into
+ 
+
+ align:start position:0%
+C for the vector that goes into it into
+column zero and C hat for its transform
+
+ align:start position:0%
+column zero and C hat for its transform
+ 
+
+ align:start position:0%
+column zero and C hat for its transform
+okay so so it's trans what now here
+
+ align:start position:0%
+okay so so it's trans what now here
+ 
+
+ align:start position:0%
+okay so so it's trans what now here
+comes the fre matx that we know 1 i i 2
+
+ align:start position:0%
+comes the fre matx that we know 1 i i 2
+ 
+
+ align:start position:0%
+comes the fre matx that we know 1 i i 2
+I CU 1 I 2 I4 I6 1 I Cube I6 and
+
+ align:start position:0%
+I CU 1 I 2 I4 I6 1 I Cube I6 and
+ 
+
+ align:start position:0%
+I CU 1 I 2 I4 I6 1 I Cube I6 and
+I9 so I'm I want to transform that c to
+
+ align:start position:0%
+I9 so I'm I want to transform that c to
+ 
+
+ align:start position:0%
+I9 so I'm I want to transform that c to
+get to find out C hat okay and what do I
+
+ align:start position:0%
+get to find out C hat okay and what do I
+ 
+
+ align:start position:0%
+get to find out C hat okay and what do I
+get up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there what's the first component the
+
+ align:start position:0%
+there what's the first component the
+ 
+
+ align:start position:0%
+there what's the first component the
+zeroth component I should say of the of
+
+ align:start position:0%
+zeroth component I should say of the of
+ 
+
+ align:start position:0%
+zeroth component I should say of the of
+the of
+
+ align:start position:0%
+the of
+ 
+
+ align:start position:0%
+the of
+when I take this guy this four this
+
+ align:start position:0%
+when I take this guy this four this
+ 
+
+ align:start position:0%
+when I take this guy this four this
+Vector with four components and I get
+
+ align:start position:0%
+Vector with four components and I get
+ 
+
+ align:start position:0%
+Vector with four components and I get
+back four components the frequency
+
+ align:start position:0%
+back four components the frequency
+ 
+
+ align:start position:0%
+back four components the frequency
+components what's the first one ones
+
+ align:start position:0%
+components what's the first one ones
+ 
+
+ align:start position:0%
+components what's the first one ones
+times this what am I getting zero that's
+
+ align:start position:0%
+times this what am I getting zero that's
+ 
+
+ align:start position:0%
+times this what am I getting zero that's
+what I expected that tells me the Matrix
+
+ align:start position:0%
+what I expected that tells me the Matrix
+ 
+
+ align:start position:0%
+what I expected that tells me the Matrix
+is not going to be invertible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because in a different
+
+ align:start position:0%
+because in a different
+ 
+
+ align:start position:0%
+because in a different
+language I'm finding the igen values and
+
+ align:start position:0%
+language I'm finding the igen values and
+ 
+
+ align:start position:0%
+language I'm finding the igen values and
+that's one of them and if if an igen
+
+ align:start position:0%
+that's one of them and if if an igen
+ 
+
+ align:start position:0%
+that's one of them and if if an igen
+value is zero that means the igen vector
+
+ align:start position:0%
+value is zero that means the igen vector
+ 
+
+ align:start position:0%
+value is zero that means the igen vector
+is getting knocked out completely and
+
+ align:start position:0%
+is getting knocked out completely and
+ 
+
+ align:start position:0%
+is getting knocked out completely and
+there's no no way c a c inverse could
+
+ align:start position:0%
+there's no no way c a c inverse could
+ 
+
+ align:start position:0%
+there's no no way c a c inverse could
+recover when that ion Vector is gone
+
+ align:start position:0%
+recover when that ion Vector is gone
+ 
+
+ align:start position:0%
+recover when that ion Vector is gone
+okay let's do the other ones two minus
+
+ align:start position:0%
+okay let's do the other ones two minus
+ 
+
+ align:start position:0%
+okay let's do the other ones two minus
+I nothing what do I get for that what do
+
+ align:start position:0%
+I nothing what do I get for that what do
+ 
+
+ align:start position:0%
+I nothing what do I get for that what do
+I what's the other one here
+
+ align:start position:0%
+I what's the other one here
+ 
+
+ align:start position:0%
+I what's the other one here
+two this is minus I and that's plus I I
+
+ align:start position:0%
+two this is minus I and that's plus I I
+ 
+
+ align:start position:0%
+two this is minus I and that's plus I I
+think so I think it's just two
+
+ align:start position:0%
+think so I think it's just two
+ 
+
+ align:start position:0%
+think so I think it's just two
+all right this is two i^ 2 can I write
+
+ align:start position:0%
+all right this is two i^ 2 can I write
+ 
+
+ align:start position:0%
+all right this is two i^ 2 can I write
+in some of these just so I have a little
+
+ align:start position:0%
+in some of these just so I have a little
+ 
+
+ align:start position:0%
+in some of these just so I have a little
+i^2 is - one and I4 is one and that's
+
+ align:start position:0%
+i^2 is - one and I4 is one and that's
+ 
+
+ align:start position:0%
+i^2 is - one and I4 is one and that's
+minus one so that's 2 + one + one I
+
+ align:start position:0%
+minus one so that's 2 + one + one I
+ 
+
+ align:start position:0%
+minus one so that's 2 + one + one I
+think is
+
+ align:start position:0%
+think is
+ 
+
+ align:start position:0%
+think is
+four and then I cubed is the same as
+
+ align:start position:0%
+four and then I cubed is the same as
+ 
+
+ align:start position:0%
+four and then I cubed is the same as
+minus I and I 9th is the same as plus I
+
+ align:start position:0%
+minus I and I 9th is the same as plus I
+ 
+
+ align:start position:0%
+minus I and I 9th is the same as plus I
+so I think I'm getting 2 + I nothing
+
+ align:start position:0%
+so I think I'm getting 2 + I nothing
+ 
+
+ align:start position:0%
+so I think I'm getting 2 + I nothing
+minus I 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's my claim my claim is that
+
+ align:start position:0%
+so what's my claim my claim is that
+ 
+
+ align:start position:0%
+so what's my claim my claim is that
+these are the four igen values that the
+
+ align:start position:0%
+these are the four igen values that the
+ 
+
+ align:start position:0%
+these are the four igen values that the
+fora forier diagonalizes these problems
+
+ align:start position:0%
+fora forier diagonalizes these problems
+ 
+
+ align:start position:0%
+fora forier diagonalizes these problems
+that's what it comes to forier
+
+ align:start position:0%
+that's what it comes to forier
+ 
+
+ align:start position:0%
+that's what it comes to forier
+diagonalizes all constant coefficient
+
+ align:start position:0%
+diagonalizes all constant coefficient
+ 
+
+ align:start position:0%
+diagonalizes all constant coefficient
+shift inv variant linear problems and
+
+ align:start position:0%
+shift inv variant linear problems and
+ 
+
+ align:start position:0%
+shift inv variant linear problems and
+tells us here the igen values so 0242
+
+ align:start position:0%
+tells us here the igen values so 0242
+ 
+
+ align:start position:0%
+tells us here the igen values so 0242
+would you like to how do I check the
+
+ align:start position:0%
+would you like to how do I check the
+ 
+
+ align:start position:0%
+would you like to how do I check the
+igen values of a matrix let's just
+
+ align:start position:0%
+igen values of a matrix let's just
+ 
+
+ align:start position:0%
+igen values of a matrix let's just
+remember if if if I give you four
+
+ align:start position:0%
+remember if if if I give you four
+ 
+
+ align:start position:0%
+remember if if if I give you four
+numbers and I say those are the igen
+
+ align:start position:0%
+numbers and I say those are the igen
+ 
+
+ align:start position:0%
+numbers and I say those are the igen
+values and and you look at that Matrix
+
+ align:start position:0%
+values and and you look at that Matrix
+ 
+
+ align:start position:0%
+values and and you look at that Matrix
+what Quick Check does everybody
+
+ align:start position:0%
+what Quick Check does everybody
+ 
+
+ align:start position:0%
+what Quick Check does everybody
+do compute the the trace add up the
+
+ align:start position:0%
+do compute the the trace add up the
+ 
+
+ align:start position:0%
+do compute the the trace add up the
+diagonal of the Matrix add up the
+
+ align:start position:0%
+diagonal of the Matrix add up the
+ 
+
+ align:start position:0%
+diagonal of the Matrix add up the
+proposed igen values they better be the
+
+ align:start position:0%
+proposed igen values they better be the
+ 
+
+ align:start position:0%
+proposed igen values they better be the
+same and they are I get eight both ways
+
+ align:start position:0%
+same and they are I get eight both ways
+ 
+
+ align:start position:0%
+same and they are I get eight both ways
+that doesn't mean of course that these
+
+ align:start position:0%
+that doesn't mean of course that these
+ 
+
+ align:start position:0%
+that doesn't mean of course that these
+four numbers are right but they I think
+
+ align:start position:0%
+four numbers are right but they I think
+ 
+
+ align:start position:0%
+four numbers are right but they I think
+they are yeah yeah so those added up to
+
+ align:start position:0%
+they are yeah yeah so those added up to
+ 
+
+ align:start position:0%
+they are yeah yeah so those added up to
+eight those numbers added up to eight
+
+ align:start position:0%
+eight those numbers added up to eight
+ 
+
+ align:start position:0%
+eight those numbers added up to eight
+and uh yep uh the and the these are real
+
+ align:start position:0%
+and uh yep uh the and the these are real
+ 
+
+ align:start position:0%
+and uh yep uh the and the these are real
+they came out real and how did I know
+
+ align:start position:0%
+they came out real and how did I know
+ 
+
+ align:start position:0%
+they came out real and how did I know
+that would happen from The
+
+ align:start position:0%
+that would happen from The
+ 
+
+ align:start position:0%
+that would happen from The
+Matrix when what what
+
+ align:start position:0%
+Matrix when what what
+ 
+
+ align:start position:0%
+Matrix when what what
+matrices am I certain to get real igen
+
+ align:start position:0%
+matrices am I certain to get real igen
+ 
+
+ align:start position:0%
+matrices am I certain to get real igen
+values
+
+ align:start position:0%
+values
+ 
+
+ align:start position:0%
+values
+for symmetric right now what about I
+
+ align:start position:0%
+for symmetric right now what about I
+ 
+
+ align:start position:0%
+for symmetric right now what about I
+heard the word positive of course that's
+
+ align:start position:0%
+heard the word positive of course that's
+ 
+
+ align:start position:0%
+heard the word positive of course that's
+the other question I have to ask is this
+
+ align:start position:0%
+the other question I have to ask is this
+ 
+
+ align:start position:0%
+the other question I have to ask is this
+Matrix positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definite okay everybody this is the
+
+ align:start position:0%
+definite okay everybody this is the
+ 
+
+ align:start position:0%
+definite okay everybody this is the
+language we've learned in 18085 is that
+
+ align:start position:0%
+language we've learned in 18085 is that
+ 
+
+ align:start position:0%
+language we've learned in 18085 is that
+Matrix positive definite yes or no no
+
+ align:start position:0%
+Matrix positive definite yes or no no
+ 
+
+ align:start position:0%
+Matrix positive definite yes or no no
+what is it it's positive semi definite
+
+ align:start position:0%
+what is it it's positive semi definite
+ 
+
+ align:start position:0%
+what is it it's positive semi definite
+how how what does that tell me about the
+
+ align:start position:0%
+how how what does that tell me about the
+ 
+
+ align:start position:0%
+how how what does that tell me about the
+igen
+
+ align:start position:0%
+igen
+ 
+
+ align:start position:0%
+igen
+values there one is zero that's why it's
+
+ align:start position:0%
+values there one is zero that's why it's
+ 
+
+ align:start position:0%
+values there one is zero that's why it's
+not positive definite but the others are
+
+ align:start position:0%
+not positive definite but the others are
+ 
+
+ align:start position:0%
+not positive definite but the others are
+positive so that sure enough all in
+
+ align:start position:0%
+positive so that sure enough all in
+ 
+
+ align:start position:0%
+positive so that sure enough all in
+other words what we've done here
+
+ align:start position:0%
+other words what we've done here
+ 
+
+ align:start position:0%
+other words what we've done here
+in that for that Matrix that came on day
+
+ align:start position:0%
+in that for that Matrix that came on day
+ 
+
+ align:start position:0%
+in that for that Matrix that came on day
+one and now we're seeing it on Day N
+
+ align:start position:0%
+one and now we're seeing it on Day N
+ 
+
+ align:start position:0%
+one and now we're seeing it on Day N
+minus one
+
+ align:start position:0%
+minus one
+ 
+
+ align:start position:0%
+minus one
+here uh uh we we're seeing it sort of in
+
+ align:start position:0%
+here uh uh we we're seeing it sort of in
+ 
+
+ align:start position:0%
+here uh uh we we're seeing it sort of in
+a new way because at that time we didn't
+
+ align:start position:0%
+a new way because at that time we didn't
+ 
+
+ align:start position:0%
+a new way because at that time we didn't
+know these for uh I were the igen
+
+ align:start position:0%
+know these for uh I were the igen
+ 
+
+ align:start position:0%
+know these for uh I were the igen
+vectors of that Matrix but they are and
+
+ align:start position:0%
+vectors of that Matrix but they are and
+ 
+
+ align:start position:0%
+vectors of that Matrix but they are and
+uh and uh we're coming to the same
+
+ align:start position:0%
+uh and uh we're coming to the same
+ 
+
+ align:start position:0%
+uh and uh we're coming to the same
+conclusion we came to on day one that
+
+ align:start position:0%
+conclusion we came to on day one that
+ 
+
+ align:start position:0%
+conclusion we came to on day one that
+the that the Matrix is positive semi
+
+ align:start position:0%
+the that the Matrix is positive semi
+ 
+
+ align:start position:0%
+the that the Matrix is positive semi
+semi-definite and that we know its zigen
+
+ align:start position:0%
+semi-definite and that we know its zigen
+ 
+
+ align:start position:0%
+semi-definite and that we know its zigen
+values and we can actually oh let me
+
+ align:start position:0%
+values and we can actually oh let me
+ 
+
+ align:start position:0%
+values and we can actually oh let me
+even take it one more step just because
+
+ align:start position:0%
+even take it one more step just because
+ 
+
+ align:start position:0%
+even take it one more step just because
+this example is so perfect some rightand
+
+ align:start position:0%
+this example is so perfect some rightand
+ 
+
+ align:start position:0%
+this example is so perfect some rightand
+sides we could solve for right if if I
+
+ align:start position:0%
+sides we could solve for right if if I
+ 
+
+ align:start position:0%
+sides we could solve for right if if I
+have a matrix that's
+
+ align:start position:0%
+have a matrix that's
+ 
+
+ align:start position:0%
+have a matrix that's
+singular Way Way Back even I think was
+
+ align:start position:0%
+singular Way Way Back even I think was
+ 
+
+ align:start position:0%
+singular Way Way Back even I think was
+like a worked example in section 1.1 I
+
+ align:start position:0%
+like a worked example in section 1.1 I
+ 
+
+ align:start position:0%
+like a worked example in section 1.1 I
+could ask the question when is CX equal
+
+ align:start position:0%
+could ask the question when is CX equal
+ 
+
+ align:start position:0%
+could ask the question when is CX equal
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+solvable because there are some right
+
+ align:start position:0%
+solvable because there are some right
+ 
+
+ align:start position:0%
+solvable because there are some right
+hand sides it'll work because if I just
+
+ align:start position:0%
+hand sides it'll work because if I just
+ 
+
+ align:start position:0%
+hand sides it'll work because if I just
+take an X and multiply by C I'll get a
+
+ align:start position:0%
+take an X and multiply by C I'll get a
+ 
+
+ align:start position:0%
+take an X and multiply by C I'll get a
+right hand side that that works but
+
+ align:start position:0%
+right hand side that that works but
+ 
+
+ align:start position:0%
+right hand side that that works but
+uh so which right which B's for which
+
+ align:start position:0%
+uh so which right which B's for which
+ 
+
+ align:start position:0%
+uh so which right which B's for which
+vectors right hand sides B will my
+
+ align:start position:0%
+vectors right hand sides B will my
+ 
+
+ align:start position:0%
+vectors right hand sides B will my
+method
+
+ align:start position:0%
+method
+ 
+
+ align:start position:0%
+method
+work the ones that
+
+ align:start position:0%
+work the ones that
+ 
+
+ align:start position:0%
+work the ones that
+have yeah the ones that have which what
+
+ align:start position:0%
+have yeah the ones that have which what
+ 
+
+ align:start position:0%
+have yeah the ones that have which what
+what do I need with these C's c not C1
+
+ align:start position:0%
+what do I need with these C's c not C1
+ 
+
+ align:start position:0%
+what do I need with these C's c not C1
+C2 and C3 for my solution to be
+
+ align:start position:0%
+C2 and C3 for my solution to be
+ 
+
+ align:start position:0%
+C2 and C3 for my solution to be
+possible I need B not hat equals z I
+
+ align:start position:0%
+possible I need B not hat equals z I
+ 
+
+ align:start position:0%
+possible I need B not hat equals z I
+need B not hat equals z then what does
+
+ align:start position:0%
+need B not hat equals z then what does
+ 
+
+ align:start position:0%
+need B not hat equals z then what does
+that say that means that the B the
+
+ align:start position:0%
+that say that means that the B the
+ 
+
+ align:start position:0%
+that say that means that the B the
+vector B has none of no constant term in
+
+ align:start position:0%
+vector B has none of no constant term in
+ 
+
+ align:start position:0%
+vector B has none of no constant term in
+is in in the 4 Series it means that the
+
+ align:start position:0%
+is in in the 4 Series it means that the
+ 
+
+ align:start position:0%
+is in in the 4 Series it means that the
+vector B is orthogonal to the 1111 V
+
+ align:start position:0%
+vector B is orthogonal to the 1111 V
+ 
+
+ align:start position:0%
+vector B is orthogonal to the 1111 V
+Vector yeah so this is like a subtle
+
+ align:start position:0%
+Vector yeah so this is like a subtle
+ 
+
+ align:start position:0%
+Vector yeah so this is like a subtle
+point but just just driving home the
+
+ align:start position:0%
+point but just just driving home the
+ 
+
+ align:start position:0%
+point but just just driving home the
+point that what for does is diagonalize
+
+ align:start position:0%
+point that what for does is diagonalize
+ 
+
+ align:start position:0%
+point that what for does is diagonalize
+everything it diagonalizes all the
+
+ align:start position:0%
+everything it diagonalizes all the
+ 
+
+ align:start position:0%
+everything it diagonalizes all the
+important problems of all the simplest
+
+ align:start position:0%
+important problems of all the simplest
+ 
+
+ align:start position:0%
+important problems of all the simplest
+problems of of uh differential equations
+
+ align:start position:0%
+problems of of uh differential equations
+ 
+
+ align:start position:0%
+problems of of uh differential equations
+you know I mean this is like
+
+ align:start position:0%
+you know I mean this is like
+ 
+
+ align:start position:0%
+you know I mean this is like
+1803 looked looked at from F's point of
+
+ align:start position:0%
+1803 looked looked at from F's point of
+ 
+
+ align:start position:0%
+1803 looked looked at from F's point of
+view okay what more could I do with that
+
+ align:start position:0%
+view okay what more could I do with that
+ 
+
+ align:start position:0%
+view okay what more could I do with that
+equation I think you you really are
+
+ align:start position:0%
+equation I think you you really are
+ 
+
+ align:start position:0%
+equation I think you you really are
+seeing all the good stuff here the
+
+ align:start position:0%
+seeing all the good stuff here the
+ 
+
+ align:start position:0%
+seeing all the good stuff here the
+you're seeing the Matrix we're
+
+ align:start position:0%
+you're seeing the Matrix we're
+ 
+
+ align:start position:0%
+you're seeing the Matrix we're
+recognizing it as a circulent we're
+
+ align:start position:0%
+recognizing it as a circulent we're
+ 
+
+ align:start position:0%
+recognizing it as a circulent we're
+realizing that we could take its fre a
+
+ align:start position:0%
+realizing that we could take its fre a
+ 
+
+ align:start position:0%
+realizing that we could take its fre a
+transform we get the igen
+
+ align:start position:0%
+transform we get the igen
+ 
+
+ align:start position:0%
+transform we get the igen
+values We're diagonalizing The Matrix
+
+ align:start position:0%
+values We're diagonalizing The Matrix
+ 
+
+ align:start position:0%
+values We're diagonalizing The Matrix
+the convolution becomes a multiplication
+
+ align:start position:0%
+the convolution becomes a multiplication
+ 
+
+ align:start position:0%
+the convolution becomes a multiplication
+and the solution becomes inversion
+
+ align:start position:0%
+and the solution becomes inversion
+ 
+
+ align:start position:0%
+and the solution becomes inversion
+becomes
+
+ align:start position:0%
+becomes
+ 
+
+ align:start position:0%
+becomes
+Division I hope you see that this is
+
+ align:start position:0%
+Division I hope you see that this is
+ 
+
+ align:start position:0%
+Division I hope you see that this is
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+uh that's really a model problem for for
+
+ align:start position:0%
+uh that's really a model problem for for
+ 
+
+ align:start position:0%
+uh that's really a model problem for for
+this course
+
+ align:start position:0%
+this course
+ 
+
+ align:start position:0%
+this course
+okay yeah questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good uh would I give you a 6x6 for a
+
+ align:start position:0%
+good uh would I give you a 6x6 for a
+ 
+
+ align:start position:0%
+good uh would I give you a 6x6 for a
+matrix on a test probably not no you I
+
+ align:start position:0%
+matrix on a test probably not no you I
+ 
+
+ align:start position:0%
+matrix on a test probably not no you I
+just about could I mean it's a 6x6 is
+
+ align:start position:0%
+just about could I mean it's a 6x6 is
+ 
+
+ align:start position:0%
+just about could I mean it's a 6x6 is
+like those are pretty decent numbers
+
+ align:start position:0%
+like those are pretty decent numbers
+ 
+
+ align:start position:0%
+like those are pretty decent numbers
+right the those six roots of unity but
+
+ align:start position:0%
+right the those six roots of unity but
+ 
+
+ align:start position:0%
+right the those six roots of unity but
+not quite right yeah yeah yeah so 4x4 5
+
+ align:start position:0%
+not quite right yeah yeah yeah so 4x4 5
+ 
+
+ align:start position:0%
+not quite right yeah yeah yeah so 4x4 5
+by5 would not be nice certainly who
+
+ align:start position:0%
+by5 would not be nice certainly who
+ 
+
+ align:start position:0%
+by5 would not be nice certainly who
+knows the cosine of 72
+
+ align:start position:0%
+knows the cosine of 72
+ 
+
+ align:start position:0%
+knows the cosine of 72
+degrees crazy but 60 degrees we could do
+
+ align:start position:0%
+degrees crazy but 60 degrees we could do
+ 
+
+ align:start position:0%
+degrees crazy but 60 degrees we could do
+so the the 4A Matrix would be full of
+
+ align:start position:0%
+so the the 4A Matrix would be full of
+ 
+
+ align:start position:0%
+so the the 4A Matrix would be full of
+square roots of 3 over two and one over
+
+ align:start position:0%
+square roots of 3 over two and one over
+ 
+
+ align:start position:0%
+square roots of 3 over two and one over
+two and I's so on but it it wouldn't be
+
+ align:start position:0%
+two and I's so on but it it wouldn't be
+ 
+
+ align:start position:0%
+two and I's so on but it it wouldn't be
+as nice so really 4x4 is sort of the
+
+ align:start position:0%
+as nice so really 4x4 is sort of the
+ 
+
+ align:start position:0%
+as nice so really 4x4 is sort of the
+model yeah yeah so 4x4 is that model um
+
+ align:start position:0%
+model yeah yeah so 4x4 is that model um
+ 
+
+ align:start position:0%
+model yeah yeah so 4x4 is that model um
+other questions because this is really a
+
+ align:start position:0%
+other questions because this is really a
+ 
+
+ align:start position:0%
+other questions because this is really a
+key example
+
+ align:start position:0%
+key example
+ 
+
+ align:start position:0%
+key example
+yeah when I calculated the igen values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah ah because this Matrix I know
+
+ align:start position:0%
+yeah ah because this Matrix I know
+ 
+
+ align:start position:0%
+yeah ah because this Matrix I know
+everything about that Matrix when I know
+
+ align:start position:0%
+everything about that Matrix when I know
+ 
+
+ align:start position:0%
+everything about that Matrix when I know
+its first Vector
+
+ align:start position:0%
+its first Vector
+ 
+
+ align:start position:0%
+its first Vector
+because yeah it's because it's a
+
+ align:start position:0%
+because yeah it's because it's a
+ 
+
+ align:start position:0%
+because yeah it's because it's a
+circulent matrix it's because that
+
+ align:start position:0%
+circulent matrix it's because that
+ 
+
+ align:start position:0%
+circulent matrix it's because that
+Matrix is is expressing convolution with
+
+ align:start position:0%
+Matrix is is expressing convolution with
+ 
+
+ align:start position:0%
+Matrix is is expressing convolution with
+with this Vector 2 -1 0
+
+ align:start position:0%
+with this Vector 2 -1 0
+ 
+
+ align:start position:0%
+with this Vector 2 -1 0
+-1 that that circulent Matrix
+
+ align:start position:0%
+-1 that that circulent Matrix
+ 
+
+ align:start position:0%
+-1 that that circulent Matrix
+essentially is is built from four
+
+ align:start position:0%
+essentially is is built from four
+ 
+
+ align:start position:0%
+essentially is is built from four
+numbers right yeah yeah and they go in
+
+ align:start position:0%
+numbers right yeah yeah and they go in
+ 
+
+ align:start position:0%
+numbers right yeah yeah and they go in
+the zeroth column right yeah yeah yeah
+
+ align:start position:0%
+the zeroth column right yeah yeah yeah
+ 
+
+ align:start position:0%
+the zeroth column right yeah yeah yeah
+right so uh um so there's an example
+
+ align:start position:0%
+right so uh um so there's an example
+ 
+
+ align:start position:0%
+right so uh um so there's an example
+where we could like do everything now uh
+
+ align:start position:0%
+where we could like do everything now uh
+ 
+
+ align:start position:0%
+where we could like do everything now uh
+and and let me just remember that with
+
+ align:start position:0%
+and and let me just remember that with
+ 
+
+ align:start position:0%
+and and let me just remember that with
+this example we could do everything so
+
+ align:start position:0%
+this example we could do everything so
+ 
+
+ align:start position:0%
+this example we could do everything so
+this is an example of you could say this
+
+ align:start position:0%
+this is an example of you could say this
+ 
+
+ align:start position:0%
+this is an example of you could say this
+type of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem uh but with a very special
+
+ align:start position:0%
+problem uh but with a very special
+ 
+
+ align:start position:0%
+problem uh but with a very special
+kernel there so it turned out to be it
+
+ align:start position:0%
+kernel there so it turned out to be it
+ 
+
+ align:start position:0%
+kernel there so it turned out to be it
+looks like an integral equation here but
+
+ align:start position:0%
+looks like an integral equation here but
+ 
+
+ align:start position:0%
+looks like an integral equation here but
+if that kernel involves Delta functions
+
+ align:start position:0%
+if that kernel involves Delta functions
+ 
+
+ align:start position:0%
+if that kernel involves Delta functions
+and so on then it can be just a
+
+ align:start position:0%
+and so on then it can be just a
+ 
+
+ align:start position:0%
+and so on then it can be just a
+differential equation and then that's
+
+ align:start position:0%
+differential equation and then that's
+ 
+
+ align:start position:0%
+differential equation and then that's
+what we got there so we we went all we
+
+ align:start position:0%
+what we got there so we we went all we
+ 
+
+ align:start position:0%
+what we got there so we we went all we
+got we took all the same steps we did
+
+ align:start position:0%
+got we took all the same steps we did
+ 
+
+ align:start position:0%
+got we took all the same steps we did
+here we did here we took the 4A
+
+ align:start position:0%
+here we did here we took the 4A
+ 
+
+ align:start position:0%
+here we did here we took the 4A
+transform we and and and I emphasized
+
+ align:start position:0%
+transform we and and and I emphasized
+ 
+
+ align:start position:0%
+transform we and and and I emphasized
+there uh just to remember Wednesday uh
+
+ align:start position:0%
+there uh just to remember Wednesday uh
+ 
+
+ align:start position:0%
+there uh just to remember Wednesday uh
+this was a Delta function when I took
+
+ align:start position:0%
+this was a Delta function when I took
+ 
+
+ align:start position:0%
+this was a Delta function when I took
+the 4A transform that I got a one so
+
+ align:start position:0%
+the 4A transform that I got a one so
+ 
+
+ align:start position:0%
+the 4A transform that I got a one so
+this was one over this and I did the
+
+ align:start position:0%
+this was one over this and I did the
+ 
+
+ align:start position:0%
+this was one over this and I did the
+inverse transform and I got back to the
+
+ align:start position:0%
+inverse transform and I got back to the
+ 
+
+ align:start position:0%
+inverse transform and I got back to the
+function that I drew which was e to the
+
+ align:start position:0%
+function that I drew which was e to the
+ 
+
+ align:start position:0%
+function that I drew which was e to the
+minus a x over 2 a and and and even so
+
+ align:start position:0%
+minus a x over 2 a and and and even so
+ 
+
+ align:start position:0%
+minus a x over 2 a and and and even so
+yeah so th this was the this was the
+
+ align:start position:0%
+yeah so th this was the this was the
+ 
+
+ align:start position:0%
+yeah so th this was the this was the
+answer U of
+
+ align:start position:0%
+answer U of
+ 
+
+ align:start position:0%
+answer U of
+X so I was able to do that be I mean
+
+ align:start position:0%
+X so I was able to do that be I mean
+ 
+
+ align:start position:0%
+X so I was able to do that be I mean
+this step is easy that step is easy that
+
+ align:start position:0%
+this step is easy that step is easy that
+ 
+
+ align:start position:0%
+this step is easy that step is easy that
+step is easy the division is easy and
+
+ align:start position:0%
+step is easy the division is easy and
+ 
+
+ align:start position:0%
+step is easy the division is easy and
+then I just recognized this as
+
+ align:start position:0%
+then I just recognized this as
+ 
+
+ align:start position:0%
+then I just recognized this as
+the as the transform of this one that
+
+ align:start position:0%
+the as the transform of this one that
+ 
+
+ align:start position:0%
+the as the transform of this one that
+this example that we had done uh once I
+
+ align:start position:0%
+this example that we had done uh once I
+ 
+
+ align:start position:0%
+this example that we had done uh once I
+divided by a 2 a so that you should be
+
+ align:start position:0%
+divided by a 2 a so that you should be
+ 
+
+ align:start position:0%
+divided by a 2 a so that you should be
+able to do this so th those are two that
+
+ align:start position:0%
+able to do this so th those are two that
+ 
+
+ align:start position:0%
+able to do this so th those are two that
+you should really be able to do I I'm
+
+ align:start position:0%
+you should really be able to do I I'm
+ 
+
+ align:start position:0%
+you should really be able to do I I'm
+not going to obviously I'm not going to
+
+ align:start position:0%
+not going to obviously I'm not going to
+ 
+
+ align:start position:0%
+not going to obviously I'm not going to
+ask you a 2d problem on the exam or even
+
+ align:start position:0%
+ask you a 2d problem on the exam or even
+ 
+
+ align:start position:0%
+ask you a 2d problem on the exam or even
+on on a homework but uh but now if
+
+ align:start position:0%
+on on a homework but uh but now if
+ 
+
+ align:start position:0%
+on on a homework but uh but now if
+you'll allow me I'd like to spend a few
+
+ align:start position:0%
+you'll allow me I'd like to spend a few
+ 
+
+ align:start position:0%
+you'll allow me I'd like to spend a few
+minutes to get into 2D because
+
+ align:start position:0%
+minutes to get into 2D because
+ 
+
+ align:start position:0%
+minutes to get into 2D because
+really you've got the main thoughts
+
+ align:start position:0%
+really you've got the main thoughts
+ 
+
+ align:start position:0%
+really you've got the main thoughts
+here that Fier is the same as finding
+
+ align:start position:0%
+here that Fier is the same as finding
+ 
+
+ align:start position:0%
+here that Fier is the same as finding
+igen vectors and igen values yeah that
+
+ align:start position:0%
+igen vectors and igen values yeah that
+ 
+
+ align:start position:0%
+igen vectors and igen values yeah that
+that's the main thought for for for
+
+ align:start position:0%
+that's the main thought for for for
+ 
+
+ align:start position:0%
+that's the main thought for for for
+these LTI problems okay now suppose I
+
+ align:start position:0%
+these LTI problems okay now suppose I
+ 
+
+ align:start position:0%
+these LTI problems okay now suppose I
+have let's just get the formalities
+
+ align:start position:0%
+have let's just get the formalities
+ 
+
+ align:start position:0%
+have let's just get the formalities
+straight here suppose I have a function
+
+ align:start position:0%
+straight here suppose I have a function
+ 
+
+ align:start position:0%
+straight here suppose I have a function
+of X and
+
+ align:start position:0%
+of X and
+ 
+
+ align:start position:0%
+of X and
+Y 2 pi periodic in X and in y so so if I
+
+ align:start position:0%
+Y 2 pi periodic in X and in y so so if I
+ 
+
+ align:start position:0%
+Y 2 pi periodic in X and in y so so if I
+bump X by 2 pi or if I bump y by 2 pi oh
+
+ align:start position:0%
+bump X by 2 pi or if I bump y by 2 pi oh
+ 
+
+ align:start position:0%
+bump X by 2 pi or if I bump y by 2 pi oh
+I'm using capital F for for the periodic
+
+ align:start position:0%
+I'm using capital F for for the periodic
+ 
+
+ align:start position:0%
+I'm using capital F for for the periodic
+guys so let me stay with capital f x y +
+
+ align:start position:0%
+guys so let me stay with capital f x y +
+ 
+
+ align:start position:0%
+guys so let me stay with capital f x y +
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+pi
+
+ align:start position:0%
+pi
+ 
+
+ align:start position:0%
+pi
+okay so I have a function this is
+
+ align:start position:0%
+okay so I have a function this is
+ 
+
+ align:start position:0%
+okay so I have a function this is
+given this is it's in 2D now and I want
+
+ align:start position:0%
+given this is it's in 2D now and I want
+ 
+
+ align:start position:0%
+given this is it's in 2D now and I want
+to write it fora Series so I'm just
+
+ align:start position:0%
+to write it fora Series so I'm just
+ 
+
+ align:start position:0%
+to write it fora Series so I'm just
+asking the question what does the 4A
+
+ align:start position:0%
+asking the question what does the 4A
+ 
+
+ align:start position:0%
+asking the question what does the 4A
+series look like for a function of two
+
+ align:start position:0%
+series look like for a function of two
+ 
+
+ align:start position:0%
+series look like for a function of two
+variables the point is it's going to be
+
+ align:start position:0%
+variables the point is it's going to be
+ 
+
+ align:start position:0%
+variables the point is it's going to be
+it's going to be nice answer and and and
+
+ align:start position:0%
+it's going to be nice answer and and and
+ 
+
+ align:start position:0%
+it's going to be nice answer and and and
+so everything you know what you know how
+
+ align:start position:0%
+so everything you know what you know how
+ 
+
+ align:start position:0%
+so everything you know what you know how
+to do in 1D you can do in 2D so I let me
+
+ align:start position:0%
+to do in 1D you can do in 2D so I let me
+ 
+
+ align:start position:0%
+to do in 1D you can do in 2D so I let me
+write the
+
+ align:start position:0%
+write the
+ 
+
+ align:start position:0%
+write the
+complex form the e to the i stuff so so
+
+ align:start position:0%
+complex form the e to the i stuff so so
+ 
+
+ align:start position:0%
+complex form the e to the i stuff so so
+what would I write how would I write
+
+ align:start position:0%
+what would I write how would I write
+ 
+
+ align:start position:0%
+what would I write how would I write
+this I would write that as a
+
+ align:start position:0%
+this I would write that as a
+ 
+
+ align:start position:0%
+this I would write that as a
+sum but it'll have I I'll make it a
+
+ align:start position:0%
+sum but it'll have I I'll make it a
+ 
+
+ align:start position:0%
+sum but it'll have I I'll make it a
+double sum I'll write two sigmas just to
+
+ align:start position:0%
+double sum I'll write two sigmas just to
+ 
+
+ align:start position:0%
+double sum I'll write two sigmas just to
+emphasize that we're summing from k
+
+ align:start position:0%
+emphasize that we're summing from k
+ 
+
+ align:start position:0%
+emphasize that we're summing from k
+equal minus infinity to INF infinity and
+
+ align:start position:0%
+equal minus infinity to INF infinity and
+ 
+
+ align:start position:0%
+equal minus infinity to INF infinity and
+from L equal minus infinity to Infinity
+
+ align:start position:0%
+from L equal minus infinity to Infinity
+ 
+
+ align:start position:0%
+from L equal minus infinity to Infinity
+we have coefficient CK
+
+ align:start position:0%
+we have coefficient CK
+ 
+
+ align:start position:0%
+we have coefficient CK
+L they depend on two indices this is the
+
+ align:start position:0%
+L they depend on two indices this is the
+ 
+
+ align:start position:0%
+L they depend on two indices this is the
+pattern to know multiplying our e to the
+
+ align:start position:0%
+pattern to know multiplying our e to the
+ 
+
+ align:start position:0%
+pattern to know multiplying our e to the
+I KX and our e to the i l
+
+ align:start position:0%
+I KX and our e to the i l
+ 
+
+ align:start position:0%
+I KX and our e to the i l
+y right good
+
+ align:start position:0%
+y right good
+ 
+
+ align:start position:0%
+y right good
+good that so all right let me ask you
+
+ align:start position:0%
+good that so all right let me ask you
+ 
+
+ align:start position:0%
+good that so all right let me ask you
+how would I find
+
+ align:start position:0%
+how would I find
+ 
+
+ align:start position:0%
+how would I find
+c23 just just just to know that we we
+
+ align:start position:0%
+c23 just just just to know that we we
+ 
+
+ align:start position:0%
+c23 just just just to know that we we
+could find all these coefficients find
+
+ align:start position:0%
+could find all these coefficients find
+ 
+
+ align:start position:0%
+could find all these coefficients find
+formulas for them we could do examples
+
+ align:start position:0%
+formulas for them we could do examples
+ 
+
+ align:start position:0%
+formulas for them we could do examples
+how would I find c23 so this is my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f I know F I want to find c23 what's the
+
+ align:start position:0%
+f I know F I want to find c23 what's the
+ 
+
+ align:start position:0%
+f I know F I want to find c23 what's the
+magic
+
+ align:start position:0%
+magic
+ 
+
+ align:start position:0%
+magic
+trick and I'm 2 pi periodic so all
+
+ align:start position:0%
+trick and I'm 2 pi periodic so all
+ 
+
+ align:start position:0%
+trick and I'm 2 pi periodic so all
+integrals all the integrals and I'm
+
+ align:start position:0%
+integrals all the integrals and I'm
+ 
+
+ align:start position:0%
+integrals all the integrals and I'm
+giving you a hint of course I'm going to
+
+ align:start position:0%
+giving you a hint of course I'm going to
+ 
+
+ align:start position:0%
+giving you a hint of course I'm going to
+integrate and the integrals will all go
+
+ align:start position:0%
+integrate and the integrals will all go
+ 
+
+ align:start position:0%
+integrate and the integrals will all go
+from minus pi to Pi in X and in y
+
+ align:start position:0%
+from minus pi to Pi in X and in y
+ 
+
+ align:start position:0%
+from minus pi to Pi in X and in y
+they'll integrate over the period Square
+
+ align:start position:0%
+they'll integrate over the period Square
+ 
+
+ align:start position:0%
+they'll integrate over the period Square
+here's the period Square from from
+
+ align:start position:0%
+here's the period Square from from
+ 
+
+ align:start position:0%
+here's the period Square from from
+there's the center X Direction y
+
+ align:start position:0%
+there's the center X Direction y
+ 
+
+ align:start position:0%
+there's the center X Direction y
+direction goes out to Pi and goes up to
+
+ align:start position:0%
+direction goes out to Pi and goes up to
+ 
+
+ align:start position:0%
+direction goes out to Pi and goes up to
+Pi so all integrals will be over X and
+
+ align:start position:0%
+Pi so all integrals will be over X and
+ 
+
+ align:start position:0%
+Pi so all integrals will be over X and
+DX d y but what do I integr
+
+ align:start position:0%
+DX d y but what do I integr
+ 
+
+ align:start position:0%
+DX d y but what do I integr
+to find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c23 well these guys are orthogonal
+
+ align:start position:0%
+c23 well these guys are orthogonal
+ 
+
+ align:start position:0%
+c23 well these guys are orthogonal
+that's the that was that's what's making
+
+ align:start position:0%
+that's the that was that's what's making
+ 
+
+ align:start position:0%
+that's the that was that's what's making
+everything work they're orthogonal and
+
+ align:start position:0%
+everything work they're orthogonal and
+ 
+
+ align:start position:0%
+everything work they're orthogonal and
+very special so I use orthogonality what
+
+ align:start position:0%
+very special so I use orthogonality what
+ 
+
+ align:start position:0%
+very special so I use orthogonality what
+do I do I multiply by just tell me what
+
+ align:start position:0%
+do I do I multiply by just tell me what
+ 
+
+ align:start position:0%
+do I do I multiply by just tell me what
+to multiply
+
+ align:start position:0%
+to multiply
+ 
+
+ align:start position:0%
+to multiply
+by by this and integrate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what is it that I multiply by if
+
+ align:start position:0%
+okay what is it that I multiply by if
+ 
+
+ align:start position:0%
+okay what is it that I multiply by if
+I'm shooting for
+
+ align:start position:0%
+I'm shooting for
+ 
+
+ align:start position:0%
+I'm shooting for
+c23 for
+
+ align:start position:0%
+c23 for
+ 
+
+ align:start position:0%
+c23 for
+example e to
+
+ align:start position:0%
+example e to
+ 
+
+ align:start position:0%
+example e to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+2x is it e to the
+
+ align:start position:0%
+2x is it e to the
+ 
+
+ align:start position:0%
+2x is it e to the
+i2x minus right it's I multiply by e to
+
+ align:start position:0%
+i2x minus right it's I multiply by e to
+ 
+
+ align:start position:0%
+i2x minus right it's I multiply by e to
+the minus
+
+ align:start position:0%
+the minus
+ 
+
+ align:start position:0%
+the minus
+i2x E to the minus I3
+
+ align:start position:0%
+i2x E to the minus I3
+ 
+
+ align:start position:0%
+i2x E to the minus I3
+Y and integrate
+
+ align:start position:0%
+Y and integrate
+ 
+
+ align:start position:0%
+Y and integrate
+yeah so when I multiply by that and
+
+ align:start position:0%
+yeah so when I multiply by that and
+ 
+
+ align:start position:0%
+yeah so when I multiply by that and
+integrate everything will go except the
+
+ align:start position:0%
+integrate everything will go except the
+ 
+
+ align:start position:0%
+integrate everything will go except the
+c23 term which will be multiplied by one
+
+ align:start position:0%
+c23 term which will be multiplied by one
+ 
+
+ align:start position:0%
+c23 term which will be multiplied by one
+so I'll just have c23 times probably Pi
+
+ align:start position:0%
+so I'll just have c23 times probably Pi
+ 
+
+ align:start position:0%
+so I'll just have c23 times probably Pi
+2 pi^ 2 I guess 2 pi will come in from
+
+ align:start position:0%
+2 pi^ 2 I guess 2 pi will come in from
+ 
+
+ align:start position:0%
+2 pi^ 2 I guess 2 pi will come in from
+both integrals so C the formula will be
+
+ align:start position:0%
+both integrals so C the formula will be
+ 
+
+ align:start position:0%
+both integrals so C the formula will be
+ckl ckl will be do you want me to write
+
+ align:start position:0%
+ckl ckl will be do you want me to write
+ 
+
+ align:start position:0%
+ckl ckl will be do you want me to write
+this formula I'll write it here and then
+
+ align:start position:0%
+this formula I'll write it here and then
+ 
+
+ align:start position:0%
+this formula I'll write it here and then
+forget it right away ckl will be
+
+ align:start position:0%
+forget it right away ckl will be
+ 
+
+ align:start position:0%
+forget it right away ckl will be
+1 2i^ 2 the integral of my
+
+ align:start position:0%
+1 2i^ 2 the integral of my
+ 
+
+ align:start position:0%
+1 2i^ 2 the integral of my
+function time my e to Theus I KX time my
+
+ align:start position:0%
+function time my e to Theus I KX time my
+ 
+
+ align:start position:0%
+function time my e to Theus I KX time my
+eus l y DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dy so that that just makes the point
+
+ align:start position:0%
+Dy so that that just makes the point
+ 
+
+ align:start position:0%
+Dy so that that just makes the point
+that there's nothing new here is just up
+
+ align:start position:0%
+that there's nothing new here is just up
+ 
+
+ align:start position:0%
+that there's nothing new here is just up
+a dimension but the formulas all look
+
+ align:start position:0%
+a dimension but the formulas all look
+ 
+
+ align:start position:0%
+a dimension but the formulas all look
+the same and if if F was a well what
+
+ align:start position:0%
+the same and if if F was a well what
+ 
+
+ align:start position:0%
+the same and if if F was a well what
+would if if f is a Delta function if f
+
+ align:start position:0%
+would if if f is a Delta function if f
+ 
+
+ align:start position:0%
+would if if f is a Delta function if f
+is now a 2d Delta function yeah we we
+
+ align:start position:0%
+is now a 2d Delta function yeah we we
+ 
+
+ align:start position:0%
+is now a 2d Delta function yeah we we
+haven't done Delta functions in 2D why
+
+ align:start position:0%
+haven't done Delta functions in 2D why
+ 
+
+ align:start position:0%
+haven't done Delta functions in 2D why
+don't we so what's suppose f is the
+
+ align:start position:0%
+don't we so what's suppose f is the
+ 
+
+ align:start position:0%
+don't we so what's suppose f is the
+Delta function in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2D then what are the
+
+ align:start position:0%
+2D then what are the
+ 
+
+ align:start position:0%
+2D then what are the
+coefficients what's what do you think
+
+ align:start position:0%
+coefficients what's what do you think
+ 
+
+ align:start position:0%
+coefficients what's what do you think
+this means this Delta function in in 2D
+
+ align:start position:0%
+this means this Delta function in in 2D
+ 
+
+ align:start position:0%
+this means this Delta function in in 2D
+so if I put in the Delta here and I
+
+ align:start position:0%
+so if I put in the Delta here and I
+ 
+
+ align:start position:0%
+so if I put in the Delta here and I
+integrate and what do I get
+
+ align:start position:0%
+integrate and what do I get
+ 
+
+ align:start position:0%
+integrate and what do I get
+then so if this guy is a Delta a
+
+ align:start position:0%
+then so if this guy is a Delta a
+ 
+
+ align:start position:0%
+then so if this guy is a Delta a
+two-dimensional Delta function the rule
+
+ align:start position:0%
+two-dimensional Delta function the rule
+ 
+
+ align:start position:0%
+two-dimensional Delta function the rule
+is that when I integrate over over a
+
+ align:start position:0%
+is that when I integrate over over a
+ 
+
+ align:start position:0%
+is that when I integrate over over a
+region that includes the spike so it's a
+
+ align:start position:0%
+region that includes the spike so it's a
+ 
+
+ align:start position:0%
+region that includes the spike so it's a
+spike sitting up above a plane now
+
+ align:start position:0%
+spike sitting up above a plane now
+ 
+
+ align:start position:0%
+spike sitting up above a plane now
+instead of sitting above a line it's
+
+ align:start position:0%
+instead of sitting above a line it's
+ 
+
+ align:start position:0%
+instead of sitting above a line it's
+sitting above a plane then I get the
+
+ align:start position:0%
+sitting above a plane then I get the
+ 
+
+ align:start position:0%
+sitting above a plane then I get the
+value so this is the Delta function at
+
+ align:start position:0%
+value so this is the Delta function at
+ 
+
+ align:start position:0%
+value so this is the Delta function at
+the origin so I get the value of this at
+
+ align:start position:0%
+the origin so I get the value of this at
+ 
+
+ align:start position:0%
+the origin so I get the value of this at
+the origin so what answer do I get I get
+
+ align:start position:0%
+the origin so what answer do I get I get
+ 
+
+ align:start position:0%
+the origin so what answer do I get I get
+one out of the integral and then I just
+
+ align:start position:0%
+one out of the integral and then I just
+ 
+
+ align:start position:0%
+one out of the integral and then I just
+have this constant so it's constant
+
+ align:start position:0%
+have this constant so it's constant
+ 
+
+ align:start position:0%
+have this constant so it's constant
+again and it's just
+
+ align:start position:0%
+again and it's just
+ 
+
+ align:start position:0%
+again and it's just
+one so the 48 the 48 trans for a
+
+ align:start position:0%
+one so the 48 the 48 trans for a
+ 
+
+ align:start position:0%
+one so the 48 the 48 trans for a
+coefficients of the Delta function are
+
+ align:start position:0%
+coefficients of the Delta function are
+ 
+
+ align:start position:0%
+coefficients of the Delta function are
+constant all frequencies they're the
+
+ align:start position:0%
+constant all frequencies they're the
+ 
+
+ align:start position:0%
+constant all frequencies they're the
+same what about a line of Delta
+
+ align:start position:0%
+same what about a line of Delta
+ 
+
+ align:start position:0%
+same what about a line of Delta
+functions and what does that mean what
+
+ align:start position:0%
+functions and what does that mean what
+ 
+
+ align:start position:0%
+functions and what does that mean what
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+yeah let me let me try to draw Delta of
+
+ align:start position:0%
+yeah let me let me try to draw Delta of
+ 
+
+ align:start position:0%
+yeah let me let me try to draw Delta of
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+suppose suppose I have a function of x
+
+ align:start position:0%
+suppose suppose I have a function of x
+ 
+
+ align:start position:0%
+suppose suppose I have a function of x
+and y d it's just worth imagining a line
+
+ align:start position:0%
+and y d it's just worth imagining a line
+ 
+
+ align:start position:0%
+and y d it's just worth imagining a line
+of Delta functions so so I'm in the XY
+
+ align:start position:0%
+of Delta functions so so I'm in the XY
+ 
+
+ align:start position:0%
+of Delta functions so so I'm in the XY
+let me look again at this
+
+ align:start position:0%
+let me look again at this
+ 
+
+ align:start position:0%
+let me look again at this
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+uh I have Delta functions all along this
+
+ align:start position:0%
+uh I have Delta functions all along this
+ 
+
+ align:start position:0%
+uh I have Delta functions all along this
+line now this is here's a crazy czy
+
+ align:start position:0%
+line now this is here's a crazy czy
+ 
+
+ align:start position:0%
+line now this is here's a crazy czy
+example just to just to say well there
+
+ align:start position:0%
+example just to just to say well there
+ 
+
+ align:start position:0%
+example just to just to say well there
+is something new in
+
+ align:start position:0%
+is something new in
+ 
+
+ align:start position:0%
+is something new in
+2D so previously my Delta function was
+
+ align:start position:0%
+2D so previously my Delta function was
+ 
+
+ align:start position:0%
+2D so previously my Delta function was
+just at that point and the all integrals
+
+ align:start position:0%
+just at that point and the all integrals
+ 
+
+ align:start position:0%
+just at that point and the all integrals
+just picked out the value at that point
+
+ align:start position:0%
+just picked out the value at that point
+ 
+
+ align:start position:0%
+just picked out the value at that point
+but now think of uh Delta functions a
+
+ align:start position:0%
+but now think of uh Delta functions a
+ 
+
+ align:start position:0%
+but now think of uh Delta functions a
+sort of line of spikes going up here and
+
+ align:start position:0%
+sort of line of spikes going up here and
+ 
+
+ align:start position:0%
+sort of line of spikes going up here and
+then of course it's periodic
+
+ align:start position:0%
+then of course it's periodic
+ 
+
+ align:start position:0%
+then of course it's periodic
+everything's periodic so that line
+
+ align:start position:0%
+everything's periodic so that line
+ 
+
+ align:start position:0%
+everything's periodic so that line
+continues and this line appears here and
+
+ align:start position:0%
+continues and this line appears here and
+ 
+
+ align:start position:0%
+continues and this line appears here and
+the line appears here but I only have to
+
+ align:start position:0%
+the line appears here but I only have to
+ 
+
+ align:start position:0%
+the line appears here but I only have to
+focus on one period
+
+ align:start position:0%
+focus on one period
+ 
+
+ align:start position:0%
+focus on one period
+Square what what's what's my answer
+
+ align:start position:0%
+Square what what's what's my answer
+ 
+
+ align:start position:0%
+Square what what's what's my answer
+now if this function suddenly changes
+
+ align:start position:0%
+now if this function suddenly changes
+ 
+
+ align:start position:0%
+now if this function suddenly changes
+from a one point Delta function to a
+
+ align:start position:0%
+from a one point Delta function to a
+ 
+
+ align:start position:0%
+from a one point Delta function to a
+line of Delta functions now tell me what
+
+ align:start position:0%
+line of Delta functions now tell me what
+ 
+
+ align:start position:0%
+line of Delta functions now tell me what
+the coefficients are what are the 4A
+
+ align:start position:0%
+the coefficients are what are the 4A
+ 
+
+ align:start position:0%
+the coefficients are what are the 4A
+coefficients in 2D for a line of Delta
+
+ align:start position:0%
+coefficients in 2D for a line of Delta
+ 
+
+ align:start position:0%
+coefficients in 2D for a line of Delta
+functions a straight line of Delta
+
+ align:start position:0%
+functions a straight line of Delta
+ 
+
+ align:start position:0%
+functions a straight line of Delta
+functions going up the Y AIS
+
+ align:start position:0%
+functions going up the Y AIS
+ 
+
+ align:start position:0%
+functions going up the Y AIS
+what it'll be let's
+
+ align:start position:0%
+what it'll be let's
+ 
+
+ align:start position:0%
+what it'll be let's
+see what yeah what do I
+
+ align:start position:0%
+see what yeah what do I
+ 
+
+ align:start position:0%
+see what yeah what do I
+do I'm going to integrate oh yeah what
+
+ align:start position:0%
+do I'm going to integrate oh yeah what
+ 
+
+ align:start position:0%
+do I'm going to integrate oh yeah what
+is it good
+
+ align:start position:0%
+is it good
+ 
+
+ align:start position:0%
+is it good
+question okay so what is
+
+ align:start position:0%
+question okay so what is
+ 
+
+ align:start position:0%
+question okay so what is
+a when do I get zero and when do I not
+
+ align:start position:0%
+a when do I get zero and when do I not
+ 
+
+ align:start position:0%
+a when do I get zero and when do I not
+get zero out of this one yeah tell me
+
+ align:start position:0%
+get zero out of this one yeah tell me
+ 
+
+ align:start position:0%
+get zero out of this one yeah tell me
+first when do I get zero out of this
+
+ align:start position:0%
+first when do I get zero out of this
+ 
+
+ align:start position:0%
+first when do I get zero out of this
+integral well when do I not what am I
+
+ align:start position:0%
+integral well when do I not what am I
+ 
+
+ align:start position:0%
+integral well when do I not what am I
+what am I doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here help I said 2D was easy and I've
+
+ align:start position:0%
+here help I said 2D was easy and I've
+ 
+
+ align:start position:0%
+here help I said 2D was easy and I've
+got in over my head here uh so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+look I can do the X intergral right we
+
+ align:start position:0%
+look I can do the X intergral right we
+ 
+
+ align:start position:0%
+look I can do the X intergral right we
+all know how to do the X
+
+ align:start position:0%
+all know how to do the X
+ 
+
+ align:start position:0%
+all know how to do the X
+integral yes is that right if I
+
+ align:start position:0%
+integral yes is that right if I
+ 
+
+ align:start position:0%
+integral yes is that right if I
+integrate with respect to x what do I
+
+ align:start position:0%
+integrate with respect to x what do I
+ 
+
+ align:start position:0%
+integrate with respect to x what do I
+get let's see I'll keep that one over 2
+
+ align:start position:0%
+get let's see I'll keep that one over 2
+ 
+
+ align:start position:0%
+get let's see I'll keep that one over 2
+pi Square now I'm trying to do this
+
+ align:start position:0%
+pi Square now I'm trying to do this
+ 
+
+ align:start position:0%
+pi Square now I'm trying to do this
+integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do I get a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one if I get a one from the X integral
+
+ align:start position:0%
+one if I get a one from the X integral
+ 
+
+ align:start position:0%
+one if I get a one from the X integral
+so that leaves so then I'm down to one
+
+ align:start position:0%
+so that leaves so then I'm down to one
+ 
+
+ align:start position:0%
+so that leaves so then I'm down to one
+integral just the Y integral is left e
+
+ align:start position:0%
+integral just the Y integral is left e
+ 
+
+ align:start position:0%
+integral just the Y integral is left e
+the minus i l y Dy right I did the X
+
+ align:start position:0%
+the minus i l y Dy right I did the X
+ 
+
+ align:start position:0%
+the minus i l y Dy right I did the X
+part which said okay take that value at
+
+ align:start position:0%
+part which said okay take that value at
+ 
+
+ align:start position:0%
+part which said okay take that value at
+x equals z which was one so the X
+
+ align:start position:0%
+x equals z which was one so the X
+ 
+
+ align:start position:0%
+x equals z which was one so the X
+integral was one good
+
+ align:start position:0%
+integral was one good
+ 
+
+ align:start position:0%
+integral was one good
+and now I've got down to this part now
+
+ align:start position:0%
+and now I've got down to this part now
+ 
+
+ align:start position:0%
+and now I've got down to this part now
+what is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral it's
+
+ align:start position:0%
+integral it's
+ 
+
+ align:start position:0%
+integral it's
+two wait a
+
+ align:start position:0%
+two wait a
+ 
+
+ align:start position:0%
+two wait a
+minute depends on L doesn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it when L yeah so it's it's going to
+
+ align:start position:0%
+it when L yeah so it's it's going to
+ 
+
+ align:start position:0%
+it when L yeah so it's it's going to
+depend on whether L is zero or not is
+
+ align:start position:0%
+depend on whether L is zero or not is
+ 
+
+ align:start position:0%
+depend on whether L is zero or not is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+right yeah it's sort of
+
+ align:start position:0%
+right yeah it's sort of
+ 
+
+ align:start position:0%
+right yeah it's sort of
+interesting if L is zero then I'm
+
+ align:start position:0%
+interesting if L is zero then I'm
+ 
+
+ align:start position:0%
+interesting if L is zero then I'm
+getting then this this is a 2 pi so the
+
+ align:start position:0%
+getting then this this is a 2 pi so the
+ 
+
+ align:start position:0%
+getting then this this is a 2 pi so the
+answer so I'm getting
+
+ align:start position:0%
+answer so I'm getting
+ 
+
+ align:start position:0%
+answer so I'm getting
+ck0 when L is zero I'm getting a two Pi
+
+ align:start position:0%
+ck0 when L is zero I'm getting a two Pi
+ 
+
+ align:start position:0%
+ck0 when L is zero I'm getting a two Pi
+out of that if L is zero this is I'm
+
+ align:start position:0%
+out of that if L is zero this is I'm
+ 
+
+ align:start position:0%
+out of that if L is zero this is I'm
+integrating one I get a 2 pi cancels one
+
+ align:start position:0%
+integrating one I get a 2 pi cancels one
+ 
+
+ align:start position:0%
+integrating one I get a 2 pi cancels one
+of those I get a one over 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pi and and otherwise the other
+
+ align:start position:0%
+pi and and otherwise the other
+ 
+
+ align:start position:0%
+pi and and otherwise the other
+CK's when L is not zero or
+
+ align:start position:0%
+CK's when L is not zero or
+ 
+
+ align:start position:0%
+CK's when L is not zero or
+what just zero I think the the integral
+
+ align:start position:0%
+what just zero I think the the integral
+ 
+
+ align:start position:0%
+what just zero I think the the integral
+of this thing this is a periodic guy if
+
+ align:start position:0%
+of this thing this is a periodic guy if
+ 
+
+ align:start position:0%
+of this thing this is a periodic guy if
+I integrate it from from minus pi to Pi
+
+ align:start position:0%
+I integrate it from from minus pi to Pi
+ 
+
+ align:start position:0%
+I integrate it from from minus pi to Pi
+it's zero what am I I'm making a big
+
+ align:start position:0%
+it's zero what am I I'm making a big
+ 
+
+ align:start position:0%
+it's zero what am I I'm making a big
+deal out of something that isn't
+
+ align:start position:0%
+deal out of something that isn't
+ 
+
+ align:start position:0%
+deal out of something that isn't
+shouldn't be a big deal the the Delta of
+
+ align:start position:0%
+shouldn't be a big deal the the Delta of
+ 
+
+ align:start position:0%
+shouldn't be a big deal the the Delta of
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+function this is just it's fora series
+
+ align:start position:0%
+function this is just it's fora series
+ 
+
+ align:start position:0%
+function this is just it's fora series
+is just the one we know sum of e to the
+
+ align:start position:0%
+is just the one we know sum of e to the
+ 
+
+ align:start position:0%
+is just the one we know sum of e to the
+I kx's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do you see what's happened
+
+ align:start position:0%
+do you see what's happened
+ 
+
+ align:start position:0%
+do you see what's happened
+here it was supposed to be a double sum
+
+ align:start position:0%
+here it was supposed to be a double sum
+ 
+
+ align:start position:0%
+here it was supposed to be a double sum
+but the ones when L wasn't zero aren't
+
+ align:start position:0%
+but the ones when L wasn't zero aren't
+ 
+
+ align:start position:0%
+but the ones when L wasn't zero aren't
+there the only ones yeah so I'm back to
+
+ align:start position:0%
+there the only ones yeah so I'm back to
+ 
+
+ align:start position:0%
+there the only ones yeah so I'm back to
+the if for a line of spikes a line of
+
+ align:start position:0%
+the if for a line of spikes a line of
+ 
+
+ align:start position:0%
+the if for a line of spikes a line of
+Deltas I'm back to so it only depended
+
+ align:start position:0%
+Deltas I'm back to so it only depended
+ 
+
+ align:start position:0%
+Deltas I'm back to so it only depended
+on X so the 4A series is just the one I
+
+ align:start position:0%
+on X so the 4A series is just the one I
+ 
+
+ align:start position:0%
+on X so the 4A series is just the one I
+already know all
+
+ align:start position:0%
+already know all
+ 
+
+ align:start position:0%
+already know all
+ones when there's no when when L is zero
+
+ align:start position:0%
+ones when there's no when when L is zero
+ 
+
+ align:start position:0%
+ones when there's no when when L is zero
+all all ones are one over two pies all
+
+ align:start position:0%
+all all ones are one over two pies all
+ 
+
+ align:start position:0%
+all all ones are one over two pies all
+constant when L is is is zero but
+
+ align:start position:0%
+constant when L is is is zero but
+ 
+
+ align:start position:0%
+constant when L is is is zero but
+there's no there's no y uh there's no
+
+ align:start position:0%
+there's no there's no y uh there's no
+ 
+
+ align:start position:0%
+there's no there's no y uh there's no
+oscillation in the y direction okay um
+
+ align:start position:0%
+oscillation in the y direction okay um
+ 
+
+ align:start position:0%
+oscillation in the y direction okay um
+I'm
+
+ align:start position:0%
+I'm
+ 
+
+ align:start position:0%
+I'm
+uh I don't know why I got into that
+
+ align:start position:0%
+uh I don't know why I got into that
+ 
+
+ align:start position:0%
+uh I don't know why I got into that
+example but because the conclusion was
+
+ align:start position:0%
+example but because the conclusion was
+ 
+
+ align:start position:0%
+example but because the conclusion was
+just it's the it's the 4 a series that
+
+ align:start position:0%
+just it's the it's the 4 a series that
+ 
+
+ align:start position:0%
+just it's the it's the 4 a series that
+we already know and it doesn't depend on
+
+ align:start position:0%
+we already know and it doesn't depend on
+ 
+
+ align:start position:0%
+we already know and it doesn't depend on
+L because the function didn't depend on
+
+ align:start position:0%
+L because the function didn't depend on
+ 
+
+ align:start position:0%
+L because the function didn't depend on
+why right okay then we could imagine
+
+ align:start position:0%
+why right okay then we could imagine
+ 
+
+ align:start position:0%
+why right okay then we could imagine
+Delta functions in other positions or
+
+ align:start position:0%
+Delta functions in other positions or
+ 
+
+ align:start position:0%
+Delta functions in other positions or
+the or a general function okay so that's
+
+ align:start position:0%
+the or a general function okay so that's
+ 
+
+ align:start position:0%
+the or a general function okay so that's
+2D uh would I want to tackle a 2d
+
+ align:start position:0%
+2D uh would I want to tackle a 2d
+ 
+
+ align:start position:0%
+2D uh would I want to tackle a 2d
+ha we've got two minutes that's two one
+
+ align:start position:0%
+ha we've got two minutes that's two one
+ 
+
+ align:start position:0%
+ha we've got two minutes that's two one
+dimension a minute right okay uh what
+
+ align:start position:0%
+dimension a minute right okay uh what
+ 
+
+ align:start position:0%
+dimension a minute right okay uh what
+happens what's a 2d discrete convolution
+
+ align:start position:0%
+happens what's a 2d discrete convolution
+ 
+
+ align:start position:0%
+happens what's a 2d discrete convolution
+what's a 2d discrete convolution now you
+
+ align:start position:0%
+what's a 2d discrete convolution now you
+ 
+
+ align:start position:0%
+what's a 2d discrete convolution now you
+might say okay why is Professor Strang
+
+ align:start position:0%
+might say okay why is Professor Strang
+ 
+
+ align:start position:0%
+might say okay why is Professor Strang
+inventing these problems because a 2d
+
+ align:start position:0%
+inventing these problems because a 2d
+ 
+
+ align:start position:0%
+inventing these problems because a 2d
+discrete convolution is the core idea of
+
+ align:start position:0%
+discrete convolution is the core idea of
+ 
+
+ align:start position:0%
+discrete convolution is the core idea of
+image processing if I have an image what
+
+ align:start position:0%
+image processing if I have an image what
+ 
+
+ align:start position:0%
+image processing if I have an image what
+what does image processing do image
+
+ align:start position:0%
+what does image processing do image
+ 
+
+ align:start position:0%
+what does image processing do image
+processing takes my image it it
+
+ align:start position:0%
+processing takes my image it it
+ 
+
+ align:start position:0%
+processing takes my image it it
+separates it into pixels right that's
+
+ align:start position:0%
+separates it into pixels right that's
+ 
+
+ align:start position:0%
+separates it into pixels right that's
+that's all the image is bunch of pixels
+
+ align:start position:0%
+that's all the image is bunch of pixels
+ 
+
+ align:start position:0%
+that's all the image is bunch of pixels
+then many 2D image process in processing
+
+ align:start position:0%
+then many 2D image process in processing
+ 
+
+ align:start position:0%
+then many 2D image process in processing
+algorithms will take jpeg old jpeg for
+
+ align:start position:0%
+algorithms will take jpeg old jpeg for
+ 
+
+ align:start position:0%
+algorithms will take jpeg old jpeg for
+example would take an 8
+
+ align:start position:0%
+example would take an 8
+ 
+
+ align:start position:0%
+example would take an 8
+by8 8 by8 2D in other words 8 by8 2D is
+
+ align:start position:0%
+by8 8 by8 2D in other words 8 by8 2D is
+ 
+
+ align:start position:0%
+by8 8 by8 2D in other words 8 by8 2D is
+the main point set of pixels and
+
+ align:start position:0%
+the main point set of pixels and
+ 
+
+ align:start position:0%
+the main point set of pixels and
+transform it do a 2d transform so what
+
+ align:start position:0%
+transform it do a 2d transform so what
+ 
+
+ align:start position:0%
+transform it do a 2d transform so what
+is a 2d transform what is what would be
+
+ align:start position:0%
+is a 2d transform what is what would be
+ 
+
+ align:start position:0%
+is a 2d transform what is what would be
+the 2D transform that would correspond
+
+ align:start position:0%
+the 2D transform that would correspond
+ 
+
+ align:start position:0%
+the 2D transform that would correspond
+to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first of all how big's the
+
+ align:start position:0%
+first of all how big's the
+ 
+
+ align:start position:0%
+first of all how big's the
+Matrix just just so we get an idea I I
+
+ align:start position:0%
+Matrix just just so we get an idea I I
+ 
+
+ align:start position:0%
+Matrix just just so we get an idea I I
+probably won't get to the end of this
+
+ align:start position:0%
+probably won't get to the end of this
+ 
+
+ align:start position:0%
+probably won't get to the end of this
+example but just so in 1D my Matrix was
+
+ align:start position:0%
+example but just so in 1D my Matrix was
+ 
+
+ align:start position:0%
+example but just so in 1D my Matrix was
+4x4 now I've got so that was for four
+
+ align:start position:0%
+4x4 now I've got so that was for four
+ 
+
+ align:start position:0%
+4x4 now I've got so that was for four
+points on a line now I've
+
+ align:start position:0%
+points on a line now I've
+ 
+
+ align:start position:0%
+points on a line now I've
+got I've got a a square of points so how
+
+ align:start position:0%
+got I've got a a square of points so how
+ 
+
+ align:start position:0%
+got I've got a a square of points so how
+big is my
+
+ align:start position:0%
+big is my
+ 
+
+ align:start position:0%
+big is my
+Matrix 16 right 16 by 16 because it's
+
+ align:start position:0%
+Matrix 16 right 16 by 16 because it's
+ 
+
+ align:start position:0%
+Matrix 16 right 16 by 16 because it's
+operating on 16
+
+ align:start position:0%
+operating on 16
+ 
+
+ align:start position:0%
+operating on 16
+pixels it's operating on 16 pixels where
+
+ align:start position:0%
+pixels it's operating on 16 pixels where
+ 
+
+ align:start position:0%
+pixels it's operating on 16 pixels where
+where in 1D it only had four to act on
+
+ align:start position:0%
+where in 1D it only had four to act on
+ 
+
+ align:start position:0%
+where in 1D it only had four to act on
+so I'm going to end up with a 16 by 16
+
+ align:start position:0%
+so I'm going to end up with a 16 by 16
+ 
+
+ align:start position:0%
+so I'm going to end up with a 16 by 16
+Matrix here and I
+
+ align:start position:0%
+Matrix here and I
+ 
+
+ align:start position:0%
+Matrix here and I
+think uh let me see what do I
+
+ align:start position:0%
+think uh let me see what do I
+ 
+
+ align:start position:0%
+think uh let me see what do I
+need oh wait a minute uh
+
+ align:start position:0%
+need oh wait a minute uh
+ 
+
+ align:start position:0%
+need oh wait a minute uh
+oh yeah I think it time's up here uh
+
+ align:start position:0%
+oh yeah I think it time's up here uh
+ 
+
+ align:start position:0%
+oh yeah I think it time's up here uh
+yeah because my C is has my C got to
+
+ align:start position:0%
+yeah because my C is has my C got to
+ 
+
+ align:start position:0%
+yeah because my C is has my C got to
+have 16 components yes my U has to have
+
+ align:start position:0%
+have 16 components yes my U has to have
+ 
+
+ align:start position:0%
+have 16 components yes my U has to have
+16 my right hand side has got these 16
+
+ align:start position:0%
+16 my right hand side has got these 16
+ 
+
+ align:start position:0%
+16 my right hand side has got these 16
+components yeah so I'm up to 16 but a
+
+ align:start position:0%
+components yeah so I'm up to 16 but a
+ 
+
+ align:start position:0%
+components yeah so I'm up to 16 but a
+very special circulent of a circulent
+
+ align:start position:0%
+very special circulent of a circulent
+ 
+
+ align:start position:0%
+very special circulent of a circulent
+it'll be a circulent of a circulent
+
+ align:start position:0%
+it'll be a circulent of a circulent
+ 
+
+ align:start position:0%
+it'll be a circulent of a circulent
+somehow okay enough for 2D I'll see you
+
+ align:start position:0%
+somehow okay enough for 2D I'll see you
+ 
+
+ align:start position:0%
+somehow okay enough for 2D I'll see you
+Wednesday and we're back to reality okay
\ No newline at end of file
diff --git a/Yap0AKRczf0.txt b/Yap0AKRczf0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..17dad87d34300598fefd44bf3e2eeccd1d1ce93f
--- /dev/null
+++ b/Yap0AKRczf0.txt
@@ -0,0 +1,10755 @@
+align:start position:0%
+ 
+let's get started how is everyone
+
+ align:start position:0%
+let's get started how is everyone
+ 
+
+ align:start position:0%
+let's get started how is everyone
+you know why you're so excited because
+
+ align:start position:0%
+you know why you're so excited because
+ 
+
+ align:start position:0%
+you know why you're so excited because
+it's a goody bag day
+
+ align:start position:0%
+it's a goody bag day
+ 
+
+ align:start position:0%
+it's a goody bag day
+and i i'm not i'm not
+
+ align:start position:0%
+and i i'm not i'm not
+ 
+
+ align:start position:0%
+and i i'm not i'm not
+going to deny you a weekend of goody bag
+
+ align:start position:0%
+going to deny you a weekend of goody bag
+ 
+
+ align:start position:0%
+going to deny you a weekend of goody bag
+action which is why you're getting it
+
+ align:start position:0%
+action which is why you're getting it
+ 
+
+ align:start position:0%
+action which is why you're getting it
+today even though
+
+ align:start position:0%
+today even though
+ 
+
+ align:start position:0%
+today even though
+the topic in the goody bag is
+
+ align:start position:0%
+the topic in the goody bag is
+ 
+
+ align:start position:0%
+the topic in the goody bag is
+crystallography
+
+ align:start position:0%
+crystallography
+ 
+
+ align:start position:0%
+crystallography
+we will not start talking about
+
+ align:start position:0%
+we will not start talking about
+ 
+
+ align:start position:0%
+we will not start talking about
+crystallography
+
+ align:start position:0%
+crystallography
+ 
+
+ align:start position:0%
+crystallography
+until monday but i didn't want to wait i
+
+ align:start position:0%
+until monday but i didn't want to wait i
+ 
+
+ align:start position:0%
+until monday but i didn't want to wait i
+know you didn't want to wait to have
+
+ align:start position:0%
+know you didn't want to wait to have
+ 
+
+ align:start position:0%
+know you didn't want to wait to have
+these models
+
+ align:start position:0%
+these models
+ 
+
+ align:start position:0%
+these models
+um in your hands because it's an
+
+ align:start position:0%
+um in your hands because it's an
+ 
+
+ align:start position:0%
+um in your hands because it's an
+enhancement of your weekend activities
+
+ align:start position:0%
+enhancement of your weekend activities
+ 
+
+ align:start position:0%
+enhancement of your weekend activities
+so the goody bag again just sort of like
+
+ align:start position:0%
+so the goody bag again just sort of like
+ 
+
+ align:start position:0%
+so the goody bag again just sort of like
+last time i'm giving it out to you today
+
+ align:start position:0%
+last time i'm giving it out to you today
+ 
+
+ align:start position:0%
+last time i'm giving it out to you today
+but the topic will start on monday
+
+ align:start position:0%
+but the topic will start on monday
+ 
+
+ align:start position:0%
+but the topic will start on monday
+um today instead we're going to talk
+
+ align:start position:0%
+um today instead we're going to talk
+ 
+
+ align:start position:0%
+um today instead we're going to talk
+about metals
+
+ align:start position:0%
+about metals
+ 
+
+ align:start position:0%
+about metals
+and metallic bonding and the properties
+
+ align:start position:0%
+and metallic bonding and the properties
+ 
+
+ align:start position:0%
+and metallic bonding and the properties
+of metals that are related to the kind
+
+ align:start position:0%
+of metals that are related to the kind
+ 
+
+ align:start position:0%
+of metals that are related to the kind
+of bond that you get in metals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you know we kind of motivated
+
+ align:start position:0%
+and you know we kind of motivated
+ 
+
+ align:start position:0%
+and you know we kind of motivated
+band theory of solids with conductivity
+
+ align:start position:0%
+band theory of solids with conductivity
+ 
+
+ align:start position:0%
+band theory of solids with conductivity
+and we talked about conductivity there's
+
+ align:start position:0%
+and we talked about conductivity there's
+ 
+
+ align:start position:0%
+and we talked about conductivity there's
+a chart
+
+ align:start position:0%
+a chart
+ 
+
+ align:start position:0%
+a chart
+of conductivity and there's some
+
+ align:start position:0%
+of conductivity and there's some
+ 
+
+ align:start position:0%
+of conductivity and there's some
+elements in there some elements and some
+
+ align:start position:0%
+elements in there some elements and some
+ 
+
+ align:start position:0%
+elements in there some elements and some
+uh some materials that are more
+
+ align:start position:0%
+uh some materials that are more
+ 
+
+ align:start position:0%
+uh some materials that are more
+complicated
+
+ align:start position:0%
+complicated
+ 
+
+ align:start position:0%
+complicated
+right like glass isn't necessarily one
+
+ align:start position:0%
+right like glass isn't necessarily one
+ 
+
+ align:start position:0%
+right like glass isn't necessarily one
+element or silica
+
+ align:start position:0%
+element or silica
+ 
+
+ align:start position:0%
+element or silica
+there's diamonds silicon germanium
+
+ align:start position:0%
+there's diamonds silicon germanium
+ 
+
+ align:start position:0%
+there's diamonds silicon germanium
+copper and we talked about
+
+ align:start position:0%
+copper and we talked about
+ 
+
+ align:start position:0%
+copper and we talked about
+insulators semiconductors and i've
+
+ align:start position:0%
+insulators semiconductors and i've
+ 
+
+ align:start position:0%
+insulators semiconductors and i've
+mentioned metals
+
+ align:start position:0%
+mentioned metals
+ 
+
+ align:start position:0%
+mentioned metals
+and that's what i want to focus on today
+
+ align:start position:0%
+and that's what i want to focus on today
+ 
+
+ align:start position:0%
+and that's what i want to focus on today
+we did this in the context of the bands
+
+ align:start position:0%
+we did this in the context of the bands
+ 
+
+ align:start position:0%
+we did this in the context of the bands
+right so remember here you've got your
+
+ align:start position:0%
+right so remember here you've got your
+ 
+
+ align:start position:0%
+right so remember here you've got your
+your um conduction band and here you've
+
+ align:start position:0%
+your um conduction band and here you've
+ 
+
+ align:start position:0%
+your um conduction band and here you've
+got your valence band and the valence
+
+ align:start position:0%
+got your valence band and the valence
+ 
+
+ align:start position:0%
+got your valence band and the valence
+band is filled
+
+ align:start position:0%
+band is filled
+ 
+
+ align:start position:0%
+band is filled
+and so if there's a large gap that's the
+
+ align:start position:0%
+and so if there's a large gap that's the
+ 
+
+ align:start position:0%
+and so if there's a large gap that's the
+gap
+
+ align:start position:0%
+gap
+ 
+
+ align:start position:0%
+gap
+if it's large like you know over three
+
+ align:start position:0%
+if it's large like you know over three
+ 
+
+ align:start position:0%
+if it's large like you know over three
+and a half ev
+
+ align:start position:0%
+and a half ev
+ 
+
+ align:start position:0%
+and a half ev
+then it's an insulator and then the
+
+ align:start position:0%
+then it's an insulator and then the
+ 
+
+ align:start position:0%
+then it's an insulator and then the
+the one in between we talked about a lot
+
+ align:start position:0%
+the one in between we talked about a lot
+ 
+
+ align:start position:0%
+the one in between we talked about a lot
+on wednesday
+
+ align:start position:0%
+on wednesday
+ 
+
+ align:start position:0%
+on wednesday
+that you know if if this is your gap and
+
+ align:start position:0%
+that you know if if this is your gap and
+ 
+
+ align:start position:0%
+that you know if if this is your gap and
+it's say
+
+ align:start position:0%
+it's say
+ 
+
+ align:start position:0%
+it's say
+between you know zero
+
+ align:start position:0%
+between you know zero
+ 
+
+ align:start position:0%
+between you know zero
+uh to 3.5 ev then
+
+ align:start position:0%
+uh to 3.5 ev then
+ 
+
+ align:start position:0%
+uh to 3.5 ev then
+that's a semiconductor and so you know
+
+ align:start position:0%
+that's a semiconductor and so you know
+ 
+
+ align:start position:0%
+that's a semiconductor and so you know
+that's what we talked about that's in
+
+ align:start position:0%
+that's what we talked about that's in
+ 
+
+ align:start position:0%
+that's what we talked about that's in
+your goodie bag we talked a lot about
+
+ align:start position:0%
+your goodie bag we talked a lot about
+ 
+
+ align:start position:0%
+your goodie bag we talked a lot about
+semiconductors
+
+ align:start position:0%
+semiconductors
+ 
+
+ align:start position:0%
+semiconductors
+and then we talked about how well if you
+
+ align:start position:0%
+and then we talked about how well if you
+ 
+
+ align:start position:0%
+and then we talked about how well if you
+have some kind of
+
+ align:start position:0%
+have some kind of
+ 
+
+ align:start position:0%
+have some kind of
+band that is filled in the middle there
+
+ align:start position:0%
+band that is filled in the middle there
+ 
+
+ align:start position:0%
+band that is filled in the middle there
+so it's it doesn't have to be filled in
+
+ align:start position:0%
+so it's it doesn't have to be filled in
+ 
+
+ align:start position:0%
+so it's it doesn't have to be filled in
+the middle it could be filled here it
+
+ align:start position:0%
+the middle it could be filled here it
+ 
+
+ align:start position:0%
+the middle it could be filled here it
+could be filled up here
+
+ align:start position:0%
+could be filled up here
+ 
+
+ align:start position:0%
+could be filled up here
+but the point is that the filling of
+
+ align:start position:0%
+but the point is that the filling of
+ 
+
+ align:start position:0%
+but the point is that the filling of
+electrons does not
+
+ align:start position:0%
+electrons does not
+ 
+
+ align:start position:0%
+electrons does not
+stop where there's a forbidden zone
+
+ align:start position:0%
+stop where there's a forbidden zone
+ 
+
+ align:start position:0%
+stop where there's a forbidden zone
+of states right where there's no states
+
+ align:start position:0%
+of states right where there's no states
+ 
+
+ align:start position:0%
+of states right where there's no states
+that's what this is that's what a gap is
+
+ align:start position:0%
+that's what this is that's what a gap is
+ 
+
+ align:start position:0%
+that's what this is that's what a gap is
+it's a gap of electron
+
+ align:start position:0%
+it's a gap of electron
+ 
+
+ align:start position:0%
+it's a gap of electron
+freedom right whereas in a metal there
+
+ align:start position:0%
+freedom right whereas in a metal there
+ 
+
+ align:start position:0%
+freedom right whereas in a metal there
+is no such thing because you fill
+
+ align:start position:0%
+is no such thing because you fill
+ 
+
+ align:start position:0%
+is no such thing because you fill
+up to a point where then right above
+
+ align:start position:0%
+up to a point where then right above
+ 
+
+ align:start position:0%
+up to a point where then right above
+that infinitesimally tiny bit of energy
+
+ align:start position:0%
+that infinitesimally tiny bit of energy
+ 
+
+ align:start position:0%
+that infinitesimally tiny bit of energy
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+there's a free state right there's a
+
+ align:start position:0%
+there's a free state right there's a
+ 
+
+ align:start position:0%
+there's a free state right there's a
+free state so you're in the middle of a
+
+ align:start position:0%
+free state so you're in the middle of a
+ 
+
+ align:start position:0%
+free state so you're in the middle of a
+band
+
+ align:start position:0%
+band
+ 
+
+ align:start position:0%
+band
+and that's a metal well i mean this is
+
+ align:start position:0%
+and that's a metal well i mean this is
+ 
+
+ align:start position:0%
+and that's a metal well i mean this is
+you know so
+
+ align:start position:0%
+you know so
+ 
+
+ align:start position:0%
+you know so
+so we should say that the gap here has
+
+ align:start position:0%
+so we should say that the gap here has
+ 
+
+ align:start position:0%
+so we should say that the gap here has
+to be greater than zero here the gap
+
+ align:start position:0%
+to be greater than zero here the gap
+ 
+
+ align:start position:0%
+to be greater than zero here the gap
+would be equal to zero
+
+ align:start position:0%
+would be equal to zero
+ 
+
+ align:start position:0%
+would be equal to zero
+there's no gap you can't define a gap in
+
+ align:start position:0%
+there's no gap you can't define a gap in
+ 
+
+ align:start position:0%
+there's no gap you can't define a gap in
+a metal
+
+ align:start position:0%
+a metal
+ 
+
+ align:start position:0%
+a metal
+and we talked about semiconductor
+
+ align:start position:0%
+and we talked about semiconductor
+ 
+
+ align:start position:0%
+and we talked about semiconductor
+problems i looked up
+
+ align:start position:0%
+problems i looked up
+ 
+
+ align:start position:0%
+problems i looked up
+just for fun you know i mean why not
+
+ align:start position:0%
+just for fun you know i mean why not
+ 
+
+ align:start position:0%
+just for fun you know i mean why not
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+of course you do it late at night you
+
+ align:start position:0%
+of course you do it late at night you
+ 
+
+ align:start position:0%
+of course you do it late at night you
+look up old exam problems and you play
+
+ align:start position:0%
+look up old exam problems and you play
+ 
+
+ align:start position:0%
+look up old exam problems and you play
+with them
+
+ align:start position:0%
+with them
+ 
+
+ align:start position:0%
+with them
+and you know okay so from last exam
+
+ align:start position:0%
+and you know okay so from last exam
+ 
+
+ align:start position:0%
+and you know okay so from last exam
+right so this is for the semiconductors
+
+ align:start position:0%
+right so this is for the semiconductors
+ 
+
+ align:start position:0%
+right so this is for the semiconductors
+we had oh here's a good question
+
+ align:start position:0%
+we had oh here's a good question
+ 
+
+ align:start position:0%
+we had oh here's a good question
+2.8 centimeters cubed
+
+ align:start position:0%
+2.8 centimeters cubed
+ 
+
+ align:start position:0%
+2.8 centimeters cubed
+of uh pure germanium
+
+ align:start position:0%
+of uh pure germanium
+ 
+
+ align:start position:0%
+of uh pure germanium
+now i want to highlight this because
+
+ align:start position:0%
+now i want to highlight this because
+ 
+
+ align:start position:0%
+now i want to highlight this because
+there's one more thing i want to say
+
+ align:start position:0%
+there's one more thing i want to say
+ 
+
+ align:start position:0%
+there's one more thing i want to say
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+semiconductors before i move on uh now
+
+ align:start position:0%
+semiconductors before i move on uh now
+ 
+
+ align:start position:0%
+semiconductors before i move on uh now
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+it's doped and that's what we spent a
+
+ align:start position:0%
+it's doped and that's what we spent a
+ 
+
+ align:start position:0%
+it's doped and that's what we spent a
+lot of time talking about on wednesday
+
+ align:start position:0%
+lot of time talking about on wednesday
+ 
+
+ align:start position:0%
+lot of time talking about on wednesday
+it's doped
+
+ align:start position:0%
+it's doped
+ 
+
+ align:start position:0%
+it's doped
+with 50 micrograms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay of selenium that was the problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the first part of the problem is how
+
+ align:start position:0%
+and the first part of the problem is how
+ 
+
+ align:start position:0%
+and the first part of the problem is how
+many carriers are produced
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what and the same question it's like are
+
+ align:start position:0%
+what and the same question it's like are
+ 
+
+ align:start position:0%
+what and the same question it's like are
+they n-type because then tight or are
+
+ align:start position:0%
+they n-type because then tight or are
+ 
+
+ align:start position:0%
+they n-type because then tight or are
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+p-type what type of carriers those are
+
+ align:start position:0%
+p-type what type of carriers those are
+ 
+
+ align:start position:0%
+p-type what type of carriers those are
+things we can now answer
+
+ align:start position:0%
+things we can now answer
+ 
+
+ align:start position:0%
+things we can now answer
+based on what we learned on wednesday
+
+ align:start position:0%
+based on what we learned on wednesday
+ 
+
+ align:start position:0%
+based on what we learned on wednesday
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+you know you oh then you have this and
+
+ align:start position:0%
+you know you oh then you have this and
+ 
+
+ align:start position:0%
+you know you oh then you have this and
+you say aha i know where to start
+
+ align:start position:0%
+you say aha i know where to start
+ 
+
+ align:start position:0%
+you say aha i know where to start
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+everything starts here right and and so
+
+ align:start position:0%
+everything starts here right and and so
+ 
+
+ align:start position:0%
+everything starts here right and and so
+pure germanium
+
+ align:start position:0%
+pure germanium
+ 
+
+ align:start position:0%
+pure germanium
+is doped well first of all where am i
+
+ align:start position:0%
+is doped well first of all where am i
+ 
+
+ align:start position:0%
+is doped well first of all where am i
+this is my map
+
+ align:start position:0%
+this is my map
+ 
+
+ align:start position:0%
+this is my map
+right germanium is there and now it's
+
+ align:start position:0%
+right germanium is there and now it's
+ 
+
+ align:start position:0%
+right germanium is there and now it's
+doped with
+
+ align:start position:0%
+doped with
+ 
+
+ align:start position:0%
+doped with
+selenium is selenium to the right or to
+
+ align:start position:0%
+selenium is selenium to the right or to
+ 
+
+ align:start position:0%
+selenium is selenium to the right or to
+the left in the period
+
+ align:start position:0%
+the left in the period
+ 
+
+ align:start position:0%
+the left in the period
+it's to the right right and so
+
+ align:start position:0%
+it's to the right right and so
+ 
+
+ align:start position:0%
+it's to the right right and so
+right away you know if you put a
+
+ align:start position:0%
+right away you know if you put a
+ 
+
+ align:start position:0%
+right away you know if you put a
+selenium in there
+
+ align:start position:0%
+selenium in there
+ 
+
+ align:start position:0%
+selenium in there
+instead of germanium so if you take your
+
+ align:start position:0%
+instead of germanium so if you take your
+ 
+
+ align:start position:0%
+instead of germanium so if you take your
+germanium
+
+ align:start position:0%
+germanium
+ 
+
+ align:start position:0%
+germanium
+and put a selenium atom in it's gonna
+
+ align:start position:0%
+and put a selenium atom in it's gonna
+ 
+
+ align:start position:0%
+and put a selenium atom in it's gonna
+it's gonna if it's a dopant it's gonna
+
+ align:start position:0%
+it's gonna if it's a dopant it's gonna
+ 
+
+ align:start position:0%
+it's gonna if it's a dopant it's gonna
+be in the bonding network that germanium
+
+ align:start position:0%
+be in the bonding network that germanium
+ 
+
+ align:start position:0%
+be in the bonding network that germanium
+was but
+
+ align:start position:0%
+was but
+ 
+
+ align:start position:0%
+was but
+add electrons to it if it's to the right
+
+ align:start position:0%
+add electrons to it if it's to the right
+ 
+
+ align:start position:0%
+add electrons to it if it's to the right
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and so you know that it's gonna be an
+
+ align:start position:0%
+and so you know that it's gonna be an
+ 
+
+ align:start position:0%
+and so you know that it's gonna be an
+n-type material
+
+ align:start position:0%
+n-type material
+ 
+
+ align:start position:0%
+n-type material
+and if you do the math the number
+
+ align:start position:0%
+and if you do the math the number
+ 
+
+ align:start position:0%
+and if you do the math the number
+of carriers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to 7.6 times 10 to the 20th
+
+ align:start position:0%
+is equal to 7.6 times 10 to the 20th
+ 
+
+ align:start position:0%
+is equal to 7.6 times 10 to the 20th
+per centimeter cube now
+
+ align:start position:0%
+per centimeter cube now
+ 
+
+ align:start position:0%
+per centimeter cube now
+here's something important that is twice
+
+ align:start position:0%
+here's something important that is twice
+ 
+
+ align:start position:0%
+here's something important that is twice
+as many selenium atoms
+
+ align:start position:0%
+as many selenium atoms
+ 
+
+ align:start position:0%
+as many selenium atoms
+twice as many because it's two over from
+
+ align:start position:0%
+twice as many because it's two over from
+ 
+
+ align:start position:0%
+twice as many because it's two over from
+germanium
+
+ align:start position:0%
+germanium
+ 
+
+ align:start position:0%
+germanium
+so it had two extra electrons for each
+
+ align:start position:0%
+so it had two extra electrons for each
+ 
+
+ align:start position:0%
+so it had two extra electrons for each
+dopant atom
+
+ align:start position:0%
+dopant atom
+ 
+
+ align:start position:0%
+dopant atom
+right so the way you solve these
+
+ align:start position:0%
+right so the way you solve these
+ 
+
+ align:start position:0%
+right so the way you solve these
+problems you figure out how many
+
+ align:start position:0%
+problems you figure out how many
+ 
+
+ align:start position:0%
+problems you figure out how many
+selenium atoms are there per centimeter
+
+ align:start position:0%
+selenium atoms are there per centimeter
+ 
+
+ align:start position:0%
+selenium atoms are there per centimeter
+cubed
+
+ align:start position:0%
+cubed
+ 
+
+ align:start position:0%
+cubed
+and how many electrons for each of those
+
+ align:start position:0%
+and how many electrons for each of those
+ 
+
+ align:start position:0%
+and how many electrons for each of those
+acted
+
+ align:start position:0%
+acted
+ 
+
+ align:start position:0%
+acted
+as a free carrier dope as good as a
+
+ align:start position:0%
+as a free carrier dope as good as a
+ 
+
+ align:start position:0%
+as a free carrier dope as good as a
+dopant remember dopants simply
+
+ align:start position:0%
+dopant remember dopants simply
+ 
+
+ align:start position:0%
+dopant remember dopants simply
+give you carriers either up there
+
+ align:start position:0%
+give you carriers either up there
+ 
+
+ align:start position:0%
+give you carriers either up there
+if it's n-type or down here if it's
+
+ align:start position:0%
+if it's n-type or down here if it's
+ 
+
+ align:start position:0%
+if it's n-type or down here if it's
+p-type
+
+ align:start position:0%
+p-type
+ 
+
+ align:start position:0%
+p-type
+okay and this is n-type
+
+ align:start position:0%
+okay and this is n-type
+ 
+
+ align:start position:0%
+okay and this is n-type
+and type okay so that's a nice
+
+ align:start position:0%
+and type okay so that's a nice
+ 
+
+ align:start position:0%
+and type okay so that's a nice
+now the reason i wanted to do this is
+
+ align:start position:0%
+now the reason i wanted to do this is
+ 
+
+ align:start position:0%
+now the reason i wanted to do this is
+because again it is
+
+ align:start position:0%
+because again it is
+ 
+
+ align:start position:0%
+because again it is
+net you can never have enough fun doing
+
+ align:start position:0%
+net you can never have enough fun doing
+ 
+
+ align:start position:0%
+net you can never have enough fun doing
+problems like this and looking up old
+
+ align:start position:0%
+problems like this and looking up old
+ 
+
+ align:start position:0%
+problems like this and looking up old
+exams and stuff
+
+ align:start position:0%
+exams and stuff
+ 
+
+ align:start position:0%
+exams and stuff
+but i also wanted to go back to this
+
+ align:start position:0%
+but i also wanted to go back to this
+ 
+
+ align:start position:0%
+but i also wanted to go back to this
+picture that i drew for you on wednesday
+
+ align:start position:0%
+picture that i drew for you on wednesday
+ 
+
+ align:start position:0%
+picture that i drew for you on wednesday
+okay so this picture was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the number of carriers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and remember these are electrons that
+
+ align:start position:0%
+and remember these are electrons that
+ 
+
+ align:start position:0%
+and remember these are electrons that
+carry
+
+ align:start position:0%
+carry
+ 
+
+ align:start position:0%
+carry
+current right and we sort of drew
+
+ align:start position:0%
+current right and we sort of drew
+ 
+
+ align:start position:0%
+current right and we sort of drew
+something that looked like this
+
+ align:start position:0%
+something that looked like this
+ 
+
+ align:start position:0%
+something that looked like this
+now remember this is
+
+ align:start position:0%
+now remember this is
+ 
+
+ align:start position:0%
+now remember this is
+right these are thermally activated and
+
+ align:start position:0%
+right these are thermally activated and
+ 
+
+ align:start position:0%
+right these are thermally activated and
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+thermally activated activated
+
+ align:start position:0%
+thermally activated activated
+ 
+
+ align:start position:0%
+thermally activated activated
+and these are from dopants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now which is if i put dopants in
+
+ align:start position:0%
+now which is if i put dopants in
+ 
+
+ align:start position:0%
+now which is if i put dopants in
+and then i can get you a constant number
+
+ align:start position:0%
+and then i can get you a constant number
+ 
+
+ align:start position:0%
+and then i can get you a constant number
+of carriers because it's just defined by
+
+ align:start position:0%
+of carriers because it's just defined by
+ 
+
+ align:start position:0%
+of carriers because it's just defined by
+how much of the impurity i mixed in
+
+ align:start position:0%
+how much of the impurity i mixed in
+ 
+
+ align:start position:0%
+how much of the impurity i mixed in
+how much impurity and i can control that
+
+ align:start position:0%
+how much impurity and i can control that
+ 
+
+ align:start position:0%
+how much impurity and i can control that
+really carefully which means i can
+
+ align:start position:0%
+really carefully which means i can
+ 
+
+ align:start position:0%
+really carefully which means i can
+control the number of carriers
+
+ align:start position:0%
+control the number of carriers
+ 
+
+ align:start position:0%
+control the number of carriers
+and then eventually thermally excited
+
+ align:start position:0%
+and then eventually thermally excited
+ 
+
+ align:start position:0%
+and then eventually thermally excited
+carriers will just start to dominate
+
+ align:start position:0%
+carriers will just start to dominate
+ 
+
+ align:start position:0%
+carriers will just start to dominate
+but this is this ability to dope with
+
+ align:start position:0%
+but this is this ability to dope with
+ 
+
+ align:start position:0%
+but this is this ability to dope with
+chemistry
+
+ align:start position:0%
+chemistry
+ 
+
+ align:start position:0%
+chemistry
+is what enabled the semiconductor
+
+ align:start position:0%
+is what enabled the semiconductor
+ 
+
+ align:start position:0%
+is what enabled the semiconductor
+revolution now
+
+ align:start position:0%
+revolution now
+ 
+
+ align:start position:0%
+revolution now
+is that okay what's going on over here
+
+ align:start position:0%
+is that okay what's going on over here
+ 
+
+ align:start position:0%
+is that okay what's going on over here
+what's going on in this part here right
+
+ align:start position:0%
+what's going on in this part here right
+ 
+
+ align:start position:0%
+what's going on in this part here right
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+you know what's going on there because
+
+ align:start position:0%
+you know what's going on there because
+ 
+
+ align:start position:0%
+you know what's going on there because
+we drew this picture
+
+ align:start position:0%
+we drew this picture
+ 
+
+ align:start position:0%
+we drew this picture
+on wednesday because if i have an
+
+ align:start position:0%
+on wednesday because if i have an
+ 
+
+ align:start position:0%
+on wednesday because if i have an
+end type if that's my vbm and that's my
+
+ align:start position:0%
+end type if that's my vbm and that's my
+ 
+
+ align:start position:0%
+end type if that's my vbm and that's my
+cbm
+
+ align:start position:0%
+cbm
+ 
+
+ align:start position:0%
+cbm
+the way this works is you introduce a
+
+ align:start position:0%
+the way this works is you introduce a
+ 
+
+ align:start position:0%
+the way this works is you introduce a
+donor level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's how doping works
+
+ align:start position:0%
+right that's how doping works
+ 
+
+ align:start position:0%
+right that's how doping works
+right the the electrons from selenium go
+
+ align:start position:0%
+right the the electrons from selenium go
+ 
+
+ align:start position:0%
+right the the electrons from selenium go
+into here
+
+ align:start position:0%
+into here
+ 
+
+ align:start position:0%
+into here
+and then you have enough thermal energy
+
+ align:start position:0%
+and then you have enough thermal energy
+ 
+
+ align:start position:0%
+and then you have enough thermal energy
+to get them up to there
+
+ align:start position:0%
+to get them up to there
+ 
+
+ align:start position:0%
+to get them up to there
+and that's where they're free carriers
+
+ align:start position:0%
+and that's where they're free carriers
+ 
+
+ align:start position:0%
+and that's where they're free carriers
+that's where they can
+
+ align:start position:0%
+that's where they can
+ 
+
+ align:start position:0%
+that's where they can
+carry electricity and so at a certain
+
+ align:start position:0%
+carry electricity and so at a certain
+ 
+
+ align:start position:0%
+carry electricity and so at a certain
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+below which right at a certain
+
+ align:start position:0%
+below which right at a certain
+ 
+
+ align:start position:0%
+below which right at a certain
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+if you're lower than that well there's
+
+ align:start position:0%
+if you're lower than that well there's
+ 
+
+ align:start position:0%
+if you're lower than that well there's
+not even enough thermal energy to get
+
+ align:start position:0%
+not even enough thermal energy to get
+ 
+
+ align:start position:0%
+not even enough thermal energy to get
+from here to here
+
+ align:start position:0%
+from here to here
+ 
+
+ align:start position:0%
+from here to here
+right not even enough to do that so it's
+
+ align:start position:0%
+right not even enough to do that so it's
+ 
+
+ align:start position:0%
+right not even enough to do that so it's
+got to go down eventually that's what
+
+ align:start position:0%
+got to go down eventually that's what
+ 
+
+ align:start position:0%
+got to go down eventually that's what
+that part is
+
+ align:start position:0%
+that part is
+ 
+
+ align:start position:0%
+that part is
+and then one other thing i want to say
+
+ align:start position:0%
+and then one other thing i want to say
+ 
+
+ align:start position:0%
+and then one other thing i want to say
+about this plot
+
+ align:start position:0%
+about this plot
+ 
+
+ align:start position:0%
+about this plot
+is that we have names for this these are
+
+ align:start position:0%
+is that we have names for this these are
+ 
+
+ align:start position:0%
+is that we have names for this these are
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+intrinsic carriers intrinsic
+
+ align:start position:0%
+intrinsic carriers intrinsic
+ 
+
+ align:start position:0%
+intrinsic carriers intrinsic
+and these are called extrinsic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well i mean that kind of makes sense
+
+ align:start position:0%
+well i mean that kind of makes sense
+ 
+
+ align:start position:0%
+well i mean that kind of makes sense
+it's that's actually a pretty good way
+
+ align:start position:0%
+it's that's actually a pretty good way
+ 
+
+ align:start position:0%
+it's that's actually a pretty good way
+to name them
+
+ align:start position:0%
+to name them
+ 
+
+ align:start position:0%
+to name them
+because you know intrinsic means i
+
+ align:start position:0%
+because you know intrinsic means i
+ 
+
+ align:start position:0%
+because you know intrinsic means i
+didn't need to do anything it's
+
+ align:start position:0%
+didn't need to do anything it's
+ 
+
+ align:start position:0%
+didn't need to do anything it's
+about pure germanium pure germanium
+
+ align:start position:0%
+about pure germanium pure germanium
+ 
+
+ align:start position:0%
+about pure germanium pure germanium
+intrinsic
+
+ align:start position:0%
+intrinsic
+ 
+
+ align:start position:0%
+intrinsic
+i didn't do anything to the material
+
+ align:start position:0%
+i didn't do anything to the material
+ 
+
+ align:start position:0%
+i didn't do anything to the material
+okay and so but it's still you can get
+
+ align:start position:0%
+okay and so but it's still you can get
+ 
+
+ align:start position:0%
+okay and so but it's still you can get
+carriers from thermal activation
+
+ align:start position:0%
+carriers from thermal activation
+ 
+
+ align:start position:0%
+carriers from thermal activation
+above the gap whereas if it's extrinsic
+
+ align:start position:0%
+above the gap whereas if it's extrinsic
+ 
+
+ align:start position:0%
+above the gap whereas if it's extrinsic
+it means i did something external i
+
+ align:start position:0%
+it means i did something external i
+ 
+
+ align:start position:0%
+it means i did something external i
+added dopants those are extrinsically
+
+ align:start position:0%
+added dopants those are extrinsically
+ 
+
+ align:start position:0%
+added dopants those are extrinsically
+doped
+
+ align:start position:0%
+doped
+ 
+
+ align:start position:0%
+doped
+okay so those are just important uh
+
+ align:start position:0%
+okay so those are just important uh
+ 
+
+ align:start position:0%
+okay so those are just important uh
+distinguishing factors now i'm going to
+
+ align:start position:0%
+distinguishing factors now i'm going to
+ 
+
+ align:start position:0%
+distinguishing factors now i'm going to
+come back to this plot later i want to
+
+ align:start position:0%
+come back to this plot later i want to
+ 
+
+ align:start position:0%
+come back to this plot later i want to
+talk about metals metals are all the way
+
+ align:start position:0%
+talk about metals metals are all the way
+ 
+
+ align:start position:0%
+talk about metals metals are all the way
+over here
+
+ align:start position:0%
+over here
+ 
+
+ align:start position:0%
+over here
+those are semiconductors and doping them
+
+ align:start position:0%
+those are semiconductors and doping them
+ 
+
+ align:start position:0%
+those are semiconductors and doping them
+or thermal activation gets me
+
+ align:start position:0%
+or thermal activation gets me
+ 
+
+ align:start position:0%
+or thermal activation gets me
+carriers which gets me this conductivity
+
+ align:start position:0%
+carriers which gets me this conductivity
+ 
+
+ align:start position:0%
+carriers which gets me this conductivity
+range but metals are
+
+ align:start position:0%
+range but metals are
+ 
+
+ align:start position:0%
+range but metals are
+much much much higher metals are much
+
+ align:start position:0%
+much much much higher metals are much
+ 
+
+ align:start position:0%
+much much much higher metals are much
+much much higher
+
+ align:start position:0%
+much much higher
+ 
+
+ align:start position:0%
+much much higher
+why what is going on in metals that's so
+
+ align:start position:0%
+why what is going on in metals that's so
+ 
+
+ align:start position:0%
+why what is going on in metals that's so
+special
+
+ align:start position:0%
+special
+ 
+
+ align:start position:0%
+special
+okay well the way we understand
+
+ align:start position:0%
+okay well the way we understand
+ 
+
+ align:start position:0%
+okay well the way we understand
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+is from the bonds so what is happening
+
+ align:start position:0%
+is from the bonds so what is happening
+ 
+
+ align:start position:0%
+is from the bonds so what is happening
+in a metal there's a there's aluminum
+
+ align:start position:0%
+in a metal there's a there's aluminum
+ 
+
+ align:start position:0%
+in a metal there's a there's aluminum
+there's aluminum
+
+ align:start position:0%
+there's aluminum
+ 
+
+ align:start position:0%
+there's aluminum
+there's aluminum and there's aluminum
+
+ align:start position:0%
+there's aluminum and there's aluminum
+ 
+
+ align:start position:0%
+there's aluminum and there's aluminum
+for us this is all we see now
+
+ align:start position:0%
+for us this is all we see now
+ 
+
+ align:start position:0%
+for us this is all we see now
+we don't see any of this anymore we only
+
+ align:start position:0%
+we don't see any of this anymore we only
+ 
+
+ align:start position:0%
+we don't see any of this anymore we only
+see atoms and electrons
+
+ align:start position:0%
+see atoms and electrons
+ 
+
+ align:start position:0%
+see atoms and electrons
+because those are the building blocks
+
+ align:start position:0%
+because those are the building blocks
+ 
+
+ align:start position:0%
+because those are the building blocks
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+those are the building blocks and and
+
+ align:start position:0%
+those are the building blocks and and
+ 
+
+ align:start position:0%
+those are the building blocks and and
+the thing is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we write down all the orbitals of an
+
+ align:start position:0%
+if we write down all the orbitals of an
+ 
+
+ align:start position:0%
+if we write down all the orbitals of an
+aluminum atom there's the core
+
+ align:start position:0%
+aluminum atom there's the core
+ 
+
+ align:start position:0%
+aluminum atom there's the core
+there's the shell there's another
+
+ align:start position:0%
+there's the shell there's another
+ 
+
+ align:start position:0%
+there's the shell there's another
+there's these ones out here way out here
+
+ align:start position:0%
+there's these ones out here way out here
+ 
+
+ align:start position:0%
+there's these ones out here way out here
+right in the case of aluminum three of
+
+ align:start position:0%
+right in the case of aluminum three of
+ 
+
+ align:start position:0%
+right in the case of aluminum three of
+them that are really really
+
+ align:start position:0%
+them that are really really
+ 
+
+ align:start position:0%
+them that are really really
+kind of weakly bonded right they're way
+
+ align:start position:0%
+kind of weakly bonded right they're way
+ 
+
+ align:start position:0%
+kind of weakly bonded right they're way
+out there they're loose
+
+ align:start position:0%
+out there they're loose
+ 
+
+ align:start position:0%
+out there they're loose
+they have they have the ability to come
+
+ align:start position:0%
+they have they have the ability to come
+ 
+
+ align:start position:0%
+they have they have the ability to come
+off easily we talked about this in the
+
+ align:start position:0%
+off easily we talked about this in the
+ 
+
+ align:start position:0%
+off easily we talked about this in the
+context of other properties
+
+ align:start position:0%
+context of other properties
+ 
+
+ align:start position:0%
+context of other properties
+right uh uh you know the
+
+ align:start position:0%
+right uh uh you know the
+ 
+
+ align:start position:0%
+right uh uh you know the
+the polarizability the electronegativity
+
+ align:start position:0%
+the polarizability the electronegativity
+ 
+
+ align:start position:0%
+the polarizability the electronegativity
+right all of this feeds in everything is
+
+ align:start position:0%
+right all of this feeds in everything is
+ 
+
+ align:start position:0%
+right all of this feeds in everything is
+determined
+
+ align:start position:0%
+determined
+ 
+
+ align:start position:0%
+determined
+by where these electrons are and then
+
+ align:start position:0%
+by where these electrons are and then
+ 
+
+ align:start position:0%
+by where these electrons are and then
+also as i mentioned
+
+ align:start position:0%
+also as i mentioned
+ 
+
+ align:start position:0%
+also as i mentioned
+by how the atoms arrange that comes next
+
+ align:start position:0%
+by how the atoms arrange that comes next
+ 
+
+ align:start position:0%
+by how the atoms arrange that comes next
+week
+
+ align:start position:0%
+week
+ 
+
+ align:start position:0%
+week
+so but if they're really really kind of
+
+ align:start position:0%
+so but if they're really really kind of
+ 
+
+ align:start position:0%
+so but if they're really really kind of
+almost free
+
+ align:start position:0%
+almost free
+ 
+
+ align:start position:0%
+almost free
+then you can kind of picture it like
+
+ align:start position:0%
+then you can kind of picture it like
+ 
+
+ align:start position:0%
+then you can kind of picture it like
+this let's dial it back to sodium
+
+ align:start position:0%
+this let's dial it back to sodium
+ 
+
+ align:start position:0%
+this let's dial it back to sodium
+and you can you can kind of picture a
+
+ align:start position:0%
+and you can you can kind of picture a
+ 
+
+ align:start position:0%
+and you can you can kind of picture a
+metal as
+
+ align:start position:0%
+metal as
+ 
+
+ align:start position:0%
+metal as
+truly free electrons right they're truly
+
+ align:start position:0%
+truly free electrons right they're truly
+ 
+
+ align:start position:0%
+truly free electrons right they're truly
+free they're not
+
+ align:start position:0%
+free they're not
+ 
+
+ align:start position:0%
+free they're not
+they're not in they're they're in the
+
+ align:start position:0%
+they're not in they're they're in the
+ 
+
+ align:start position:0%
+they're not in they're they're in the
+middle of that band and they've got all
+
+ align:start position:0%
+middle of that band and they've got all
+ 
+
+ align:start position:0%
+middle of that band and they've got all
+this freedom because the states are free
+
+ align:start position:0%
+this freedom because the states are free
+ 
+
+ align:start position:0%
+this freedom because the states are free
+all around them
+
+ align:start position:0%
+all around them
+ 
+
+ align:start position:0%
+all around them
+and they're basically not really that
+
+ align:start position:0%
+and they're basically not really that
+ 
+
+ align:start position:0%
+and they're basically not really that
+attached to any one
+
+ align:start position:0%
+attached to any one
+ 
+
+ align:start position:0%
+attached to any one
+atom or another and this is really
+
+ align:start position:0%
+atom or another and this is really
+ 
+
+ align:start position:0%
+atom or another and this is really
+the picture of the metallic bond so
+
+ align:start position:0%
+the picture of the metallic bond so
+ 
+
+ align:start position:0%
+the picture of the metallic bond so
+let's use let's go over here
+
+ align:start position:0%
+let's use let's go over here
+ 
+
+ align:start position:0%
+let's use let's go over here
+and it's they're so
+
+ align:start position:0%
+and it's they're so
+ 
+
+ align:start position:0%
+and it's they're so
+they're so free when these atoms come
+
+ align:start position:0%
+they're so free when these atoms come
+ 
+
+ align:start position:0%
+they're so free when these atoms come
+together with those
+
+ align:start position:0%
+together with those
+ 
+
+ align:start position:0%
+together with those
+very very loosely bound outer electrons
+
+ align:start position:0%
+very very loosely bound outer electrons
+ 
+
+ align:start position:0%
+very very loosely bound outer electrons
+those those electrons
+
+ align:start position:0%
+those those electrons
+ 
+
+ align:start position:0%
+those those electrons
+are so free we actually call it a c we
+
+ align:start position:0%
+are so free we actually call it a c we
+ 
+
+ align:start position:0%
+are so free we actually call it a c we
+call it the electron c
+
+ align:start position:0%
+call it the electron c
+ 
+
+ align:start position:0%
+call it the electron c
+it's a simplified way to think about it
+
+ align:start position:0%
+it's a simplified way to think about it
+ 
+
+ align:start position:0%
+it's a simplified way to think about it
+but it's a good picture
+
+ align:start position:0%
+but it's a good picture
+ 
+
+ align:start position:0%
+but it's a good picture
+to start with so in metals
+
+ align:start position:0%
+to start with so in metals
+ 
+
+ align:start position:0%
+to start with so in metals
+you've got this electron c electron
+
+ align:start position:0%
+you've got this electron c electron
+ 
+
+ align:start position:0%
+you've got this electron c electron
+c we'll call it a model because it's a
+
+ align:start position:0%
+c we'll call it a model because it's a
+ 
+
+ align:start position:0%
+c we'll call it a model because it's a
+way of thinking
+
+ align:start position:0%
+way of thinking
+ 
+
+ align:start position:0%
+way of thinking
+and in this model you've got a positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charge
+
+ align:start position:0%
+charge
+ 
+
+ align:start position:0%
+charge
+nuclei so you got positively charged new
+
+ align:start position:0%
+nuclei so you got positively charged new
+ 
+
+ align:start position:0%
+nuclei so you got positively charged new
+guy why because they've lost an electron
+
+ align:start position:0%
+guy why because they've lost an electron
+ 
+
+ align:start position:0%
+guy why because they've lost an electron
+to the c
+
+ align:start position:0%
+to the c
+ 
+
+ align:start position:0%
+to the c
+they've lost it those outer ones have
+
+ align:start position:0%
+they've lost it those outer ones have
+ 
+
+ align:start position:0%
+they've lost it those outer ones have
+gone well
+
+ align:start position:0%
+gone well
+ 
+
+ align:start position:0%
+gone well
+they're not gone because there's others
+
+ align:start position:0%
+they're not gone because there's others
+ 
+
+ align:start position:0%
+they're not gone because there's others
+around too but they're all just kind of
+
+ align:start position:0%
+around too but they're all just kind of
+ 
+
+ align:start position:0%
+around too but they're all just kind of
+roaming free
+
+ align:start position:0%
+roaming free
+ 
+
+ align:start position:0%
+roaming free
+and so you're left with these positive
+
+ align:start position:0%
+and so you're left with these positive
+ 
+
+ align:start position:0%
+and so you're left with these positive
+charges
+
+ align:start position:0%
+charges
+ 
+
+ align:start position:0%
+charges
+right and these are the cations
+
+ align:start position:0%
+right and these are the cations
+ 
+
+ align:start position:0%
+right and these are the cations
+positively charged nuclei are cations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and they're in a sea of electrons
+
+ align:start position:0%
+right and they're in a sea of electrons
+ 
+
+ align:start position:0%
+right and they're in a sea of electrons
+and so this is because the valence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrons is not tightly bound this is
+
+ align:start position:0%
+electrons is not tightly bound this is
+ 
+
+ align:start position:0%
+electrons is not tightly bound this is
+what i've been saying but this is why
+
+ align:start position:0%
+what i've been saying but this is why
+ 
+
+ align:start position:0%
+what i've been saying but this is why
+you get it
+
+ align:start position:0%
+you get it
+ 
+
+ align:start position:0%
+you get it
+cations so positive charge nuclei these
+
+ align:start position:0%
+cations so positive charge nuclei these
+ 
+
+ align:start position:0%
+cations so positive charge nuclei these
+are cations
+
+ align:start position:0%
+are cations
+ 
+
+ align:start position:0%
+are cations
+in a sea of electrons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now so if you think about a metal in
+
+ align:start position:0%
+now so if you think about a metal in
+ 
+
+ align:start position:0%
+now so if you think about a metal in
+this way
+
+ align:start position:0%
+this way
+ 
+
+ align:start position:0%
+this way
+then you understand a lot of the
+
+ align:start position:0%
+then you understand a lot of the
+ 
+
+ align:start position:0%
+then you understand a lot of the
+properties of metals
+
+ align:start position:0%
+properties of metals
+ 
+
+ align:start position:0%
+properties of metals
+this is a very useful way to think about
+
+ align:start position:0%
+this is a very useful way to think about
+ 
+
+ align:start position:0%
+this is a very useful way to think about
+metals
+
+ align:start position:0%
+metals
+ 
+
+ align:start position:0%
+metals
+and and it it let's go back to our
+
+ align:start position:0%
+and and it it let's go back to our
+ 
+
+ align:start position:0%
+and and it it let's go back to our
+pictures of bonding let me use this
+
+ align:start position:0%
+pictures of bonding let me use this
+ 
+
+ align:start position:0%
+pictures of bonding let me use this
+board here
+
+ align:start position:0%
+board here
+ 
+
+ align:start position:0%
+board here
+we'll put it right under here and we're
+
+ align:start position:0%
+we'll put it right under here and we're
+ 
+
+ align:start position:0%
+we'll put it right under here and we're
+going to finish
+
+ align:start position:0%
+going to finish
+ 
+
+ align:start position:0%
+going to finish
+what we started we're going to finish
+
+ align:start position:0%
+what we started we're going to finish
+ 
+
+ align:start position:0%
+what we started we're going to finish
+what we started
+
+ align:start position:0%
+what we started
+ 
+
+ align:start position:0%
+what we started
+because remember we talked about
+
+ align:start position:0%
+because remember we talked about
+ 
+
+ align:start position:0%
+because remember we talked about
+covalent
+
+ align:start position:0%
+covalent
+ 
+
+ align:start position:0%
+covalent
+we talked about ionic and then we did
+
+ align:start position:0%
+we talked about ionic and then we did
+ 
+
+ align:start position:0%
+we talked about ionic and then we did
+all these intermolecular forces and the
+
+ align:start position:0%
+all these intermolecular forces and the
+ 
+
+ align:start position:0%
+all these intermolecular forces and the
+bonding
+
+ align:start position:0%
+bonding
+ 
+
+ align:start position:0%
+bonding
+that comes about from those but we
+
+ align:start position:0%
+that comes about from those but we
+ 
+
+ align:start position:0%
+that comes about from those but we
+didn't do metallic so if i do covalent
+
+ align:start position:0%
+didn't do metallic so if i do covalent
+ 
+
+ align:start position:0%
+didn't do metallic so if i do covalent
+over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i do ionic over here well okay
+
+ align:start position:0%
+and i do ionic over here well okay
+ 
+
+ align:start position:0%
+and i do ionic over here well okay
+covalent we know right these
+
+ align:start position:0%
+covalent we know right these
+ 
+
+ align:start position:0%
+covalent we know right these
+are maybe h that's a covalent bond
+
+ align:start position:0%
+are maybe h that's a covalent bond
+ 
+
+ align:start position:0%
+are maybe h that's a covalent bond
+that's a nonpolar
+
+ align:start position:0%
+that's a nonpolar
+ 
+
+ align:start position:0%
+that's a nonpolar
+kind of covalent bond carrying is
+
+ align:start position:0%
+kind of covalent bond carrying is
+ 
+
+ align:start position:0%
+kind of covalent bond carrying is
+sharing oh you could have hf
+
+ align:start position:0%
+sharing oh you could have hf
+ 
+
+ align:start position:0%
+sharing oh you could have hf
+right where it's sort of like you know
+
+ align:start position:0%
+right where it's sort of like you know
+ 
+
+ align:start position:0%
+right where it's sort of like you know
+it's a little less sharing
+
+ align:start position:0%
+it's a little less sharing
+ 
+
+ align:start position:0%
+it's a little less sharing
+but it you know it's still a covalent
+
+ align:start position:0%
+but it you know it's still a covalent
+ 
+
+ align:start position:0%
+but it you know it's still a covalent
+bond it's a polar covalent bond
+
+ align:start position:0%
+bond it's a polar covalent bond
+ 
+
+ align:start position:0%
+bond it's a polar covalent bond
+right and i mean now in the ionic sense
+
+ align:start position:0%
+right and i mean now in the ionic sense
+ 
+
+ align:start position:0%
+right and i mean now in the ionic sense
+you have sodium chloride we did that
+
+ align:start position:0%
+you have sodium chloride we did that
+ 
+
+ align:start position:0%
+you have sodium chloride we did that
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+where you literally chlorine is like
+
+ align:start position:0%
+where you literally chlorine is like
+ 
+
+ align:start position:0%
+where you literally chlorine is like
+give me and so i'm just like okay
+
+ align:start position:0%
+give me and so i'm just like okay
+ 
+
+ align:start position:0%
+give me and so i'm just like okay
+and that's it that's the relationship
+
+ align:start position:0%
+and that's it that's the relationship
+ 
+
+ align:start position:0%
+and that's it that's the relationship
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but see now here let's take sodium and
+
+ align:start position:0%
+but see now here let's take sodium and
+ 
+
+ align:start position:0%
+but see now here let's take sodium and
+let's just put a bunch of them around
+
+ align:start position:0%
+let's just put a bunch of them around
+ 
+
+ align:start position:0%
+let's just put a bunch of them around
+well but see if i've got an electron c
+
+ align:start position:0%
+well but see if i've got an electron c
+ 
+
+ align:start position:0%
+well but see if i've got an electron c
+then my electrons
+
+ align:start position:0%
+then my electrons
+ 
+
+ align:start position:0%
+then my electrons
+are simply wandering around
+
+ align:start position:0%
+are simply wandering around
+ 
+
+ align:start position:0%
+are simply wandering around
+in the c so every ion
+
+ align:start position:0%
+in the c so every ion
+ 
+
+ align:start position:0%
+in the c so every ion
+has this kind of ocean of electrons
+
+ align:start position:0%
+has this kind of ocean of electrons
+ 
+
+ align:start position:0%
+has this kind of ocean of electrons
+around it
+
+ align:start position:0%
+around it
+ 
+
+ align:start position:0%
+around it
+they're not attached it'd be like if you
+
+ align:start position:0%
+they're not attached it'd be like if you
+ 
+
+ align:start position:0%
+they're not attached it'd be like if you
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+how are you going to parent well i'm
+
+ align:start position:0%
+how are you going to parent well i'm
+ 
+
+ align:start position:0%
+how are you going to parent well i'm
+going to pair i'm going to tell
+
+ align:start position:0%
+going to pair i'm going to tell
+ 
+
+ align:start position:0%
+going to pair i'm going to tell
+you know you can only go into the
+
+ align:start position:0%
+you know you can only go into the
+ 
+
+ align:start position:0%
+you know you can only go into the
+backyard
+
+ align:start position:0%
+backyard
+ 
+
+ align:start position:0%
+backyard
+and play that's it right you are
+
+ align:start position:0%
+and play that's it right you are
+ 
+
+ align:start position:0%
+and play that's it right you are
+confined to be in the backyard
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and and now you say well okay if but
+
+ align:start position:0%
+um and and now you say well okay if but
+ 
+
+ align:start position:0%
+um and and now you say well okay if but
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+if i'm a proton and i'm parenting an
+
+ align:start position:0%
+if i'm a proton and i'm parenting an
+ 
+
+ align:start position:0%
+if i'm a proton and i'm parenting an
+election i say you know what you can be
+
+ align:start position:0%
+election i say you know what you can be
+ 
+
+ align:start position:0%
+election i say you know what you can be
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+any yard it doesn't matter don't even
+
+ align:start position:0%
+any yard it doesn't matter don't even
+ 
+
+ align:start position:0%
+any yard it doesn't matter don't even
+come home
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't care like another kid's going to
+
+ align:start position:0%
+i don't care like another kid's going to
+ 
+
+ align:start position:0%
+i don't care like another kid's going to
+come into my backyard at some point
+
+ align:start position:0%
+come into my backyard at some point
+ 
+
+ align:start position:0%
+come into my backyard at some point
+so it's all good
+
+ align:start position:0%
+so it's all good
+ 
+
+ align:start position:0%
+so it's all good
+that's the that is the relationship
+
+ align:start position:0%
+that's the that is the relationship
+ 
+
+ align:start position:0%
+that's the that is the relationship
+of a metal of inside of a metal
+
+ align:start position:0%
+of a metal of inside of a metal
+ 
+
+ align:start position:0%
+of a metal of inside of a metal
+maybe here it's like the two houses
+
+ align:start position:0%
+maybe here it's like the two houses
+ 
+
+ align:start position:0%
+maybe here it's like the two houses
+switched kids i don't know what's going
+
+ align:start position:0%
+switched kids i don't know what's going
+ 
+
+ align:start position:0%
+switched kids i don't know what's going
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+no one of them just took the kid but
+
+ align:start position:0%
+no one of them just took the kid but
+ 
+
+ align:start position:0%
+no one of them just took the kid but
+anyway
+
+ align:start position:0%
+anyway
+ 
+
+ align:start position:0%
+anyway
+all right i'm going too far but here's
+
+ align:start position:0%
+all right i'm going too far but here's
+ 
+
+ align:start position:0%
+all right i'm going too far but here's
+yo i want to give you that sense that
+
+ align:start position:0%
+yo i want to give you that sense that
+ 
+
+ align:start position:0%
+yo i want to give you that sense that
+they're just roaming around in a sea
+
+ align:start position:0%
+they're just roaming around in a sea
+ 
+
+ align:start position:0%
+they're just roaming around in a sea
+they're roaming around they're roaming
+
+ align:start position:0%
+they're roaming around they're roaming
+ 
+
+ align:start position:0%
+they're roaming around they're roaming
+around now
+
+ align:start position:0%
+around now
+ 
+
+ align:start position:0%
+around now
+here's the point i've got a sea of
+
+ align:start position:0%
+here's the point i've got a sea of
+ 
+
+ align:start position:0%
+here's the point i've got a sea of
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+oh oh we can finish our table
+
+ align:start position:0%
+oh oh we can finish our table
+ 
+
+ align:start position:0%
+oh oh we can finish our table
+i'm gonna finish that table we started
+
+ align:start position:0%
+i'm gonna finish that table we started
+ 
+
+ align:start position:0%
+i'm gonna finish that table we started
+the table let's finish the table
+
+ align:start position:0%
+the table let's finish the table
+ 
+
+ align:start position:0%
+the table let's finish the table
+because now if i have metallic all right
+
+ align:start position:0%
+because now if i have metallic all right
+ 
+
+ align:start position:0%
+because now if i have metallic all right
+and i have this kind of um
+
+ align:start position:0%
+and i have this kind of um
+ 
+
+ align:start position:0%
+and i have this kind of um
+you know this kind of setup here right
+
+ align:start position:0%
+you know this kind of setup here right
+ 
+
+ align:start position:0%
+you know this kind of setup here right
+that's the picture
+
+ align:start position:0%
+that's the picture
+ 
+
+ align:start position:0%
+that's the picture
+that's the model and here i have cation
+
+ align:start position:0%
+that's the model and here i have cation
+ 
+
+ align:start position:0%
+that's the model and here i have cation
+remember our table slash delocalized
+
+ align:start position:0%
+remember our table slash delocalized
+ 
+
+ align:start position:0%
+remember our table slash delocalized
+d lok d localized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrons and the bonding strength for
+
+ align:start position:0%
+electrons and the bonding strength for
+ 
+
+ align:start position:0%
+electrons and the bonding strength for
+this table
+
+ align:start position:0%
+this table
+ 
+
+ align:start position:0%
+this table
+in kilojoules per mole is 75 to a
+
+ align:start position:0%
+in kilojoules per mole is 75 to a
+ 
+
+ align:start position:0%
+in kilojoules per mole is 75 to a
+thousand
+
+ align:start position:0%
+thousand
+ 
+
+ align:start position:0%
+thousand
+that's a big range we'll talk about that
+
+ align:start position:0%
+that's a big range we'll talk about that
+ 
+
+ align:start position:0%
+that's a big range we'll talk about that
+and there's an example iron we finished
+
+ align:start position:0%
+and there's an example iron we finished
+ 
+
+ align:start position:0%
+and there's an example iron we finished
+our table
+
+ align:start position:0%
+our table
+ 
+
+ align:start position:0%
+our table
+that's it that's the last century now
+
+ align:start position:0%
+that's it that's the last century now
+ 
+
+ align:start position:0%
+that's it that's the last century now
+this remember
+
+ align:start position:0%
+this remember
+ 
+
+ align:start position:0%
+this remember
+this part of the table was the basis of
+
+ align:start position:0%
+this part of the table was the basis of
+ 
+
+ align:start position:0%
+this part of the table was the basis of
+attraction
+
+ align:start position:0%
+attraction
+ 
+
+ align:start position:0%
+attraction
+remember that and we filled this out for
+
+ align:start position:0%
+remember that and we filled this out for
+ 
+
+ align:start position:0%
+remember that and we filled this out for
+all the other types of bonds
+
+ align:start position:0%
+all the other types of bonds
+ 
+
+ align:start position:0%
+all the other types of bonds
+the basis of attraction and
+
+ align:start position:0%
+the basis of attraction and
+ 
+
+ align:start position:0%
+the basis of attraction and
+i want to point out that every single
+
+ align:start position:0%
+i want to point out that every single
+ 
+
+ align:start position:0%
+i want to point out that every single
+basis we have covered involves the same
+
+ align:start position:0%
+basis we have covered involves the same
+ 
+
+ align:start position:0%
+basis we have covered involves the same
+thing understanding what electrons are
+
+ align:start position:0%
+thing understanding what electrons are
+ 
+
+ align:start position:0%
+thing understanding what electrons are
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+what is the electronic
+
+ align:start position:0%
+what is the electronic
+ 
+
+ align:start position:0%
+what is the electronic
+structure that's the fundamental
+
+ align:start position:0%
+structure that's the fundamental
+ 
+
+ align:start position:0%
+structure that's the fundamental
+principle
+
+ align:start position:0%
+principle
+ 
+
+ align:start position:0%
+principle
+of of this class right that's the key
+
+ align:start position:0%
+of of this class right that's the key
+ 
+
+ align:start position:0%
+of of this class right that's the key
+component the key ingredient that's in
+
+ align:start position:0%
+component the key ingredient that's in
+ 
+
+ align:start position:0%
+component the key ingredient that's in
+all of our recipes
+
+ align:start position:0%
+all of our recipes
+ 
+
+ align:start position:0%
+all of our recipes
+what are those electrons doing that
+
+ align:start position:0%
+what are those electrons doing that
+ 
+
+ align:start position:0%
+what are those electrons doing that
+leads us to
+
+ align:start position:0%
+leads us to
+ 
+
+ align:start position:0%
+leads us to
+every single one of those kinds of bonds
+
+ align:start position:0%
+every single one of those kinds of bonds
+ 
+
+ align:start position:0%
+every single one of those kinds of bonds
+including metallic all right so now you
+
+ align:start position:0%
+including metallic all right so now you
+ 
+
+ align:start position:0%
+including metallic all right so now you
+can you can imagine
+
+ align:start position:0%
+can you can imagine
+ 
+
+ align:start position:0%
+can you can imagine
+how this controls the properties right
+
+ align:start position:0%
+how this controls the properties right
+ 
+
+ align:start position:0%
+how this controls the properties right
+now but and but first they say
+
+ align:start position:0%
+now but and but first they say
+ 
+
+ align:start position:0%
+now but and but first they say
+well if i had a group one metal if i had
+
+ align:start position:0%
+well if i had a group one metal if i had
+ 
+
+ align:start position:0%
+well if i had a group one metal if i had
+a group one metal then i've got
+
+ align:start position:0%
+a group one metal then i've got
+ 
+
+ align:start position:0%
+a group one metal then i've got
+two i've got one right like sodium but
+
+ align:start position:0%
+two i've got one right like sodium but
+ 
+
+ align:start position:0%
+two i've got one right like sodium but
+if i go over to magnesium
+
+ align:start position:0%
+if i go over to magnesium
+ 
+
+ align:start position:0%
+if i go over to magnesium
+you can see that i've got a higher
+
+ align:start position:0%
+you can see that i've got a higher
+ 
+
+ align:start position:0%
+you can see that i've got a higher
+charge because
+
+ align:start position:0%
+charge because
+ 
+
+ align:start position:0%
+charge because
+both of those electrons are likely to
+
+ align:start position:0%
+both of those electrons are likely to
+ 
+
+ align:start position:0%
+both of those electrons are likely to
+leave and wander around in the sea
+
+ align:start position:0%
+leave and wander around in the sea
+ 
+
+ align:start position:0%
+leave and wander around in the sea
+of electrons so that would be what
+
+ align:start position:0%
+of electrons so that would be what
+ 
+
+ align:start position:0%
+of electrons so that would be what
+magnesium looks like in terms of this
+
+ align:start position:0%
+magnesium looks like in terms of this
+ 
+
+ align:start position:0%
+magnesium looks like in terms of this
+this electron c model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the thing is that that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the c this picture is what helps us
+
+ align:start position:0%
+the c this picture is what helps us
+ 
+
+ align:start position:0%
+the c this picture is what helps us
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+the properties of metals and that's what
+
+ align:start position:0%
+the properties of metals and that's what
+ 
+
+ align:start position:0%
+the properties of metals and that's what
+i want to talk about
+
+ align:start position:0%
+i want to talk about
+ 
+
+ align:start position:0%
+i want to talk about
+that's what i want to talk about and and
+
+ align:start position:0%
+that's what i want to talk about and and
+ 
+
+ align:start position:0%
+that's what i want to talk about and and
+these are some of the properties right
+
+ align:start position:0%
+these are some of the properties right
+ 
+
+ align:start position:0%
+these are some of the properties right
+you can go through
+
+ align:start position:0%
+you can go through
+ 
+
+ align:start position:0%
+you can go through
+metals and there's a whole range of
+
+ align:start position:0%
+metals and there's a whole range of
+ 
+
+ align:start position:0%
+metals and there's a whole range of
+properties but these are some of the
+
+ align:start position:0%
+properties but these are some of the
+ 
+
+ align:start position:0%
+properties but these are some of the
+ones that are pretty consistent
+
+ align:start position:0%
+ones that are pretty consistent
+ 
+
+ align:start position:0%
+ones that are pretty consistent
+they are reflective they're shiny there
+
+ align:start position:0%
+they are reflective they're shiny there
+ 
+
+ align:start position:0%
+they are reflective they're shiny there
+are literally settings in like photo
+
+ align:start position:0%
+are literally settings in like photo
+ 
+
+ align:start position:0%
+are literally settings in like photo
+you know photo apps metallic
+
+ align:start position:0%
+you know photo apps metallic
+ 
+
+ align:start position:0%
+you know photo apps metallic
+make it look metallic right
+
+ align:start position:0%
+make it look metallic right
+ 
+
+ align:start position:0%
+make it look metallic right
+because metals are are shiny
+
+ align:start position:0%
+because metals are are shiny
+ 
+
+ align:start position:0%
+because metals are are shiny
+they have luster why the
+
+ align:start position:0%
+they have luster why the
+ 
+
+ align:start position:0%
+they have luster why the
+the high they have high electrical
+
+ align:start position:0%
+the high they have high electrical
+ 
+
+ align:start position:0%
+the high they have high electrical
+connectivity that's the thing we talked
+
+ align:start position:0%
+connectivity that's the thing we talked
+ 
+
+ align:start position:0%
+connectivity that's the thing we talked
+about a lot already
+
+ align:start position:0%
+about a lot already
+ 
+
+ align:start position:0%
+about a lot already
+they have uh high thermal conductivity
+
+ align:start position:0%
+they have uh high thermal conductivity
+ 
+
+ align:start position:0%
+they have uh high thermal conductivity
+i'll mention that
+
+ align:start position:0%
+i'll mention that
+ 
+
+ align:start position:0%
+i'll mention that
+high heat capacity they're malleable and
+
+ align:start position:0%
+high heat capacity they're malleable and
+ 
+
+ align:start position:0%
+high heat capacity they're malleable and
+ductile
+
+ align:start position:0%
+ductile
+ 
+
+ align:start position:0%
+ductile
+all of these and many more properties of
+
+ align:start position:0%
+all of these and many more properties of
+ 
+
+ align:start position:0%
+all of these and many more properties of
+metals
+
+ align:start position:0%
+metals
+ 
+
+ align:start position:0%
+metals
+can be explained from this one
+
+ align:start position:0%
+can be explained from this one
+ 
+
+ align:start position:0%
+can be explained from this one
+simple picture of the electron c
+
+ align:start position:0%
+simple picture of the electron c
+ 
+
+ align:start position:0%
+simple picture of the electron c
+from this one simple picture okay
+
+ align:start position:0%
+from this one simple picture okay
+ 
+
+ align:start position:0%
+from this one simple picture okay
+so let's start so if i if i think about
+
+ align:start position:0%
+so let's start so if i if i think about
+ 
+
+ align:start position:0%
+so let's start so if i if i think about
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let's look at these top three okay so
+
+ align:start position:0%
+let's look at these top three okay so
+ 
+
+ align:start position:0%
+let's look at these top three okay so
+i'll start
+
+ align:start position:0%
+i'll start
+ 
+
+ align:start position:0%
+i'll start
+why is a metal shiny why isn't metal
+
+ align:start position:0%
+why is a metal shiny why isn't metal
+ 
+
+ align:start position:0%
+why is a metal shiny why isn't metal
+shiny
+
+ align:start position:0%
+shiny
+ 
+
+ align:start position:0%
+shiny
+well it goes back to the thing we've
+
+ align:start position:0%
+well it goes back to the thing we've
+ 
+
+ align:start position:0%
+well it goes back to the thing we've
+been talking about all along
+
+ align:start position:0%
+been talking about all along
+ 
+
+ align:start position:0%
+been talking about all along
+you know or or certainly in a lot of
+
+ align:start position:0%
+you know or or certainly in a lot of
+ 
+
+ align:start position:0%
+you know or or certainly in a lot of
+parts right with the bohr model and
+
+ align:start position:0%
+parts right with the bohr model and
+ 
+
+ align:start position:0%
+parts right with the bohr model and
+atoms and electrons getting excited the
+
+ align:start position:0%
+atoms and electrons getting excited the
+ 
+
+ align:start position:0%
+atoms and electrons getting excited the
+semiconductors and
+
+ align:start position:0%
+semiconductors and
+ 
+
+ align:start position:0%
+semiconductors and
+and leds right
+
+ align:start position:0%
+and leds right
+ 
+
+ align:start position:0%
+and leds right
+it has to do with how photons interact
+
+ align:start position:0%
+it has to do with how photons interact
+ 
+
+ align:start position:0%
+it has to do with how photons interact
+with the material
+
+ align:start position:0%
+with the material
+ 
+
+ align:start position:0%
+with the material
+but see now i've got these electrons
+
+ align:start position:0%
+but see now i've got these electrons
+ 
+
+ align:start position:0%
+but see now i've got these electrons
+that are sitting out there at any energy
+
+ align:start position:0%
+that are sitting out there at any energy
+ 
+
+ align:start position:0%
+that are sitting out there at any energy
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+ready for the photon there's not there's
+
+ align:start position:0%
+ready for the photon there's not there's
+ 
+
+ align:start position:0%
+ready for the photon there's not there's
+no gap
+
+ align:start position:0%
+no gap
+ 
+
+ align:start position:0%
+no gap
+right so so i've got electrons sitting
+
+ align:start position:0%
+right so so i've got electrons sitting
+ 
+
+ align:start position:0%
+right so so i've got electrons sitting
+around in the sea
+
+ align:start position:0%
+around in the sea
+ 
+
+ align:start position:0%
+around in the sea
+and they're ready for anything any kind
+
+ align:start position:0%
+and they're ready for anything any kind
+ 
+
+ align:start position:0%
+and they're ready for anything any kind
+of energy that hits them well they've
+
+ align:start position:0%
+of energy that hits them well they've
+ 
+
+ align:start position:0%
+of energy that hits them well they've
+got room to be excited
+
+ align:start position:0%
+got room to be excited
+ 
+
+ align:start position:0%
+got room to be excited
+right they've got room to be excited and
+
+ align:start position:0%
+right they've got room to be excited and
+ 
+
+ align:start position:0%
+right they've got room to be excited and
+it's it's that
+
+ align:start position:0%
+it's it's that
+ 
+
+ align:start position:0%
+it's it's that
+combined with other things but it's that
+
+ align:start position:0%
+combined with other things but it's that
+ 
+
+ align:start position:0%
+combined with other things but it's that
+that is a big part of why metals
+
+ align:start position:0%
+that is a big part of why metals
+ 
+
+ align:start position:0%
+that is a big part of why metals
+have their shininess those electrons can
+
+ align:start position:0%
+have their shininess those electrons can
+ 
+
+ align:start position:0%
+have their shininess those electrons can
+be excited
+
+ align:start position:0%
+be excited
+ 
+
+ align:start position:0%
+be excited
+in almost any way right because there's
+
+ align:start position:0%
+in almost any way right because there's
+ 
+
+ align:start position:0%
+in almost any way right because there's
+an infinite number of states right there
+
+ align:start position:0%
+an infinite number of states right there
+ 
+
+ align:start position:0%
+an infinite number of states right there
+there's no gap
+
+ align:start position:0%
+there's no gap
+ 
+
+ align:start position:0%
+there's no gap
+right so the way they can respond to
+
+ align:start position:0%
+right so the way they can respond to
+ 
+
+ align:start position:0%
+right so the way they can respond to
+energy from photons
+
+ align:start position:0%
+energy from photons
+ 
+
+ align:start position:0%
+energy from photons
+is is um is extremely diverse and and
+
+ align:start position:0%
+is is um is extremely diverse and and
+ 
+
+ align:start position:0%
+is is um is extremely diverse and and
+you can imagine if i'm a photon and i
+
+ align:start position:0%
+you can imagine if i'm a photon and i
+ 
+
+ align:start position:0%
+you can imagine if i'm a photon and i
+excite an electron
+
+ align:start position:0%
+excite an electron
+ 
+
+ align:start position:0%
+excite an electron
+it doesn't matter what the wavelength is
+
+ align:start position:0%
+it doesn't matter what the wavelength is
+ 
+
+ align:start position:0%
+it doesn't matter what the wavelength is
+that electron can fall back down and
+
+ align:start position:0%
+that electron can fall back down and
+ 
+
+ align:start position:0%
+that electron can fall back down and
+re-emit the same
+
+ align:start position:0%
+re-emit the same
+ 
+
+ align:start position:0%
+re-emit the same
+energy photon right okay
+
+ align:start position:0%
+energy photon right okay
+ 
+
+ align:start position:0%
+energy photon right okay
+so that's uh so that's luster by the way
+
+ align:start position:0%
+so that's uh so that's luster by the way
+ 
+
+ align:start position:0%
+so that's uh so that's luster by the way
+but now you know and you really should
+
+ align:start position:0%
+but now you know and you really should
+ 
+
+ align:start position:0%
+but now you know and you really should
+do this
+
+ align:start position:0%
+do this
+ 
+
+ align:start position:0%
+do this
+you i just said you know you have this
+
+ align:start position:0%
+you i just said you know you have this
+ 
+
+ align:start position:0%
+you i just said you know you have this
+i've got electrons
+
+ align:start position:0%
+i've got electrons
+ 
+
+ align:start position:0%
+i've got electrons
+i shine photons on these they might come
+
+ align:start position:0%
+i shine photons on these they might come
+ 
+
+ align:start position:0%
+i shine photons on these they might come
+up and go back down
+
+ align:start position:0%
+up and go back down
+ 
+
+ align:start position:0%
+up and go back down
+at any you know there's all this room
+
+ align:start position:0%
+at any you know there's all this room
+ 
+
+ align:start position:0%
+at any you know there's all this room
+here for electrons to be excited there's
+
+ align:start position:0%
+here for electrons to be excited there's
+ 
+
+ align:start position:0%
+here for electrons to be excited there's
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+there's no gap whereas in diamond
+
+ align:start position:0%
+there's no gap whereas in diamond
+ 
+
+ align:start position:0%
+there's no gap whereas in diamond
+in diamond i've got this huge gap
+
+ align:start position:0%
+in diamond i've got this huge gap
+ 
+
+ align:start position:0%
+in diamond i've got this huge gap
+right remember diamond is an insulator
+
+ align:start position:0%
+right remember diamond is an insulator
+ 
+
+ align:start position:0%
+right remember diamond is an insulator
+diamond has a gap of 5.5 electron volts
+
+ align:start position:0%
+diamond has a gap of 5.5 electron volts
+ 
+
+ align:start position:0%
+diamond has a gap of 5.5 electron volts
+roughly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now you know why diamonds are
+
+ align:start position:0%
+now you know why diamonds are
+ 
+
+ align:start position:0%
+now you know why diamonds are
+transparent it's of course
+
+ align:start position:0%
+transparent it's of course
+ 
+
+ align:start position:0%
+transparent it's of course
+the electrons of course because
+
+ align:start position:0%
+the electrons of course because
+ 
+
+ align:start position:0%
+the electrons of course because
+if you if i shine photons on this and
+
+ align:start position:0%
+if you if i shine photons on this and
+ 
+
+ align:start position:0%
+if you if i shine photons on this and
+those photons are in
+
+ align:start position:0%
+those photons are in
+ 
+
+ align:start position:0%
+those photons are in
+the visible you know that even if i go
+
+ align:start position:0%
+the visible you know that even if i go
+ 
+
+ align:start position:0%
+the visible you know that even if i go
+all the way up to purple photons
+
+ align:start position:0%
+all the way up to purple photons
+ 
+
+ align:start position:0%
+all the way up to purple photons
+they're not that high so any time i try
+
+ align:start position:0%
+they're not that high so any time i try
+ 
+
+ align:start position:0%
+they're not that high so any time i try
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+so i'm shining photons on my diamond and
+
+ align:start position:0%
+so i'm shining photons on my diamond and
+ 
+
+ align:start position:0%
+so i'm shining photons on my diamond and
+those electrons are like can i go here
+
+ align:start position:0%
+those electrons are like can i go here
+ 
+
+ align:start position:0%
+those electrons are like can i go here
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+can i go here no can i go here no you
+
+ align:start position:0%
+can i go here no can i go here no you
+ 
+
+ align:start position:0%
+can i go here no can i go here no you
+have to shine a very
+
+ align:start position:0%
+have to shine a very
+ 
+
+ align:start position:0%
+have to shine a very
+high energy photon to excite an electron
+
+ align:start position:0%
+high energy photon to excite an electron
+ 
+
+ align:start position:0%
+high energy photon to excite an electron
+in diamond
+
+ align:start position:0%
+in diamond
+ 
+
+ align:start position:0%
+in diamond
+that's why it's transparent right
+
+ align:start position:0%
+that's why it's transparent right
+ 
+
+ align:start position:0%
+that's why it's transparent right
+that's the reason when you go to the
+
+ align:start position:0%
+that's the reason when you go to the
+ 
+
+ align:start position:0%
+that's the reason when you go to the
+store to buy diamonds you should ask
+
+ align:start position:0%
+store to buy diamonds you should ask
+ 
+
+ align:start position:0%
+store to buy diamonds you should ask
+them about the electrons
+
+ align:start position:0%
+them about the electrons
+ 
+
+ align:start position:0%
+them about the electrons
+that's what's making it all work
+
+ align:start position:0%
+that's what's making it all work
+ 
+
+ align:start position:0%
+that's what's making it all work
+that's what explains the properties
+
+ align:start position:0%
+that's what explains the properties
+ 
+
+ align:start position:0%
+that's what explains the properties
+okay but back to metals now okay so
+
+ align:start position:0%
+okay but back to metals now okay so
+ 
+
+ align:start position:0%
+okay but back to metals now okay so
+that's uh luster
+
+ align:start position:0%
+that's uh luster
+ 
+
+ align:start position:0%
+that's uh luster
+what about electrical connectivity well
+
+ align:start position:0%
+what about electrical connectivity well
+ 
+
+ align:start position:0%
+what about electrical connectivity well
+it's the same thing it comes from the c
+
+ align:start position:0%
+it's the same thing it comes from the c
+ 
+
+ align:start position:0%
+it's the same thing it comes from the c
+it comes from the c now if i take a wire
+
+ align:start position:0%
+it comes from the c now if i take a wire
+ 
+
+ align:start position:0%
+it comes from the c now if i take a wire
+of copper and
+
+ align:start position:0%
+of copper and
+ 
+
+ align:start position:0%
+of copper and
+i look at this as a sea of electrons
+
+ align:start position:0%
+i look at this as a sea of electrons
+ 
+
+ align:start position:0%
+i look at this as a sea of electrons
+so i'm not drawing the ions they're in
+
+ align:start position:0%
+so i'm not drawing the ions they're in
+ 
+
+ align:start position:0%
+so i'm not drawing the ions they're in
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+i'm just drawing the fact that i've got
+
+ align:start position:0%
+i'm just drawing the fact that i've got
+ 
+
+ align:start position:0%
+i'm just drawing the fact that i've got
+this sort of ocean of electrons
+
+ align:start position:0%
+this sort of ocean of electrons
+ 
+
+ align:start position:0%
+this sort of ocean of electrons
+that are fairly free right
+
+ align:start position:0%
+that are fairly free right
+ 
+
+ align:start position:0%
+that are fairly free right
+what well what what is happening when i
+
+ align:start position:0%
+what well what what is happening when i
+ 
+
+ align:start position:0%
+what well what what is happening when i
+when i
+
+ align:start position:0%
+when i
+ 
+
+ align:start position:0%
+when i
+try to when i try to move
+
+ align:start position:0%
+try to when i try to move
+ 
+
+ align:start position:0%
+try to when i try to move
+them the way you do it is with some kind
+
+ align:start position:0%
+them the way you do it is with some kind
+ 
+
+ align:start position:0%
+them the way you do it is with some kind
+of electromagnetic
+
+ align:start position:0%
+of electromagnetic
+ 
+
+ align:start position:0%
+of electromagnetic
+force right you know some kind of force
+
+ align:start position:0%
+force right you know some kind of force
+ 
+
+ align:start position:0%
+force right you know some kind of force
+and what that means is that i have a
+
+ align:start position:0%
+and what that means is that i have a
+ 
+
+ align:start position:0%
+and what that means is that i have a
+charge
+
+ align:start position:0%
+charge
+ 
+
+ align:start position:0%
+charge
+that this doesn't like right so like
+
+ align:start position:0%
+that this doesn't like right so like
+ 
+
+ align:start position:0%
+that this doesn't like right so like
+it's a repulsive charge over here
+
+ align:start position:0%
+it's a repulsive charge over here
+ 
+
+ align:start position:0%
+it's a repulsive charge over here
+it's going to push one of these into the
+
+ align:start position:0%
+it's going to push one of these into the
+ 
+
+ align:start position:0%
+it's going to push one of these into the
+other one
+
+ align:start position:0%
+other one
+ 
+
+ align:start position:0%
+other one
+but then that's going to feel that's
+
+ align:start position:0%
+but then that's going to feel that's
+ 
+
+ align:start position:0%
+but then that's going to feel that's
+going to feel a force is going to move
+
+ align:start position:0%
+going to feel a force is going to move
+ 
+
+ align:start position:0%
+going to feel a force is going to move
+and then that's going to push this one
+
+ align:start position:0%
+and then that's going to push this one
+ 
+
+ align:start position:0%
+and then that's going to push this one
+and that's going to push that one and so
+
+ align:start position:0%
+and that's going to push that one and so
+ 
+
+ align:start position:0%
+and that's going to push that one and so
+forth
+
+ align:start position:0%
+forth
+ 
+
+ align:start position:0%
+forth
+that's how electricity works right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the actual movement of the electrons
+
+ align:start position:0%
+so the actual movement of the electrons
+ 
+
+ align:start position:0%
+so the actual movement of the electrons
+could be slow in the material
+
+ align:start position:0%
+could be slow in the material
+ 
+
+ align:start position:0%
+could be slow in the material
+uh but the but the the current right you
+
+ align:start position:0%
+uh but the but the the current right you
+ 
+
+ align:start position:0%
+uh but the but the the current right you
+can push a lot of current through
+
+ align:start position:0%
+can push a lot of current through
+ 
+
+ align:start position:0%
+can push a lot of current through
+right because these ones over here feel
+
+ align:start position:0%
+right because these ones over here feel
+ 
+
+ align:start position:0%
+right because these ones over here feel
+pretty quickly
+
+ align:start position:0%
+pretty quickly
+ 
+
+ align:start position:0%
+pretty quickly
+the forces you applied over there but
+
+ align:start position:0%
+the forces you applied over there but
+ 
+
+ align:start position:0%
+the forces you applied over there but
+they only feel it
+
+ align:start position:0%
+they only feel it
+ 
+
+ align:start position:0%
+they only feel it
+they only feel it if you can get this
+
+ align:start position:0%
+they only feel it if you can get this
+ 
+
+ align:start position:0%
+they only feel it if you can get this
+freedom
+
+ align:start position:0%
+freedom
+ 
+
+ align:start position:0%
+freedom
+if those electrons are not free they're
+
+ align:start position:0%
+if those electrons are not free they're
+ 
+
+ align:start position:0%
+if those electrons are not free they're
+going to feel this
+
+ align:start position:0%
+going to feel this
+ 
+
+ align:start position:0%
+going to feel this
+this repulsion they're going to be like
+
+ align:start position:0%
+this repulsion they're going to be like
+ 
+
+ align:start position:0%
+this repulsion they're going to be like
+you know what i'm stuck in my state
+
+ align:start position:0%
+you know what i'm stuck in my state
+ 
+
+ align:start position:0%
+you know what i'm stuck in my state
+i'm stuck in this in this full valence
+
+ align:start position:0%
+i'm stuck in this in this full valence
+ 
+
+ align:start position:0%
+i'm stuck in this in this full valence
+band i got nowhere to go
+
+ align:start position:0%
+band i got nowhere to go
+ 
+
+ align:start position:0%
+band i got nowhere to go
+sorry you know put your energy into the
+
+ align:start position:0%
+sorry you know put your energy into the
+ 
+
+ align:start position:0%
+sorry you know put your energy into the
+atom
+
+ align:start position:0%
+atom
+ 
+
+ align:start position:0%
+atom
+or something else i don't know but i'm
+
+ align:start position:0%
+or something else i don't know but i'm
+ 
+
+ align:start position:0%
+or something else i don't know but i'm
+not moving
+
+ align:start position:0%
+not moving
+ 
+
+ align:start position:0%
+not moving
+ah but if it's a c then you can push
+
+ align:start position:0%
+ah but if it's a c then you can push
+ 
+
+ align:start position:0%
+ah but if it's a c then you can push
+them and they can push each other
+
+ align:start position:0%
+them and they can push each other
+ 
+
+ align:start position:0%
+them and they can push each other
+right and that's the same thing it's a
+
+ align:start position:0%
+right and that's the same thing it's a
+ 
+
+ align:start position:0%
+right and that's the same thing it's a
+conceptual picture but it's the same
+
+ align:start position:0%
+conceptual picture but it's the same
+ 
+
+ align:start position:0%
+conceptual picture but it's the same
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+as almost an infinite number of free
+
+ align:start position:0%
+as almost an infinite number of free
+ 
+
+ align:start position:0%
+as almost an infinite number of free
+states that's what that means
+
+ align:start position:0%
+states that's what that means
+ 
+
+ align:start position:0%
+states that's what that means
+right that's what that means now
+
+ align:start position:0%
+right that's what that means now
+ 
+
+ align:start position:0%
+right that's what that means now
+if you got copper we see copper now
+
+ align:start position:0%
+if you got copper we see copper now
+ 
+
+ align:start position:0%
+if you got copper we see copper now
+as something like argon with
+
+ align:start position:0%
+as something like argon with
+ 
+
+ align:start position:0%
+as something like argon with
+those d electrons filled 3d 10
+
+ align:start position:0%
+those d electrons filled 3d 10
+ 
+
+ align:start position:0%
+those d electrons filled 3d 10
+and an s electron here
+
+ align:start position:0%
+and an s electron here
+ 
+
+ align:start position:0%
+and an s electron here
+and so if it's a copper wire those d
+
+ align:start position:0%
+and so if it's a copper wire those d
+ 
+
+ align:start position:0%
+and so if it's a copper wire those d
+electrons it's all filled up in there
+
+ align:start position:0%
+electrons it's all filled up in there
+ 
+
+ align:start position:0%
+electrons it's all filled up in there
+and they act as a way of
+
+ align:start position:0%
+and they act as a way of
+ 
+
+ align:start position:0%
+and they act as a way of
+shielding it's a beautiful shielding so
+
+ align:start position:0%
+shielding it's a beautiful shielding so
+ 
+
+ align:start position:0%
+shielding it's a beautiful shielding so
+that this is even more free and less
+
+ align:start position:0%
+that this is even more free and less
+ 
+
+ align:start position:0%
+that this is even more free and less
+interested in staying around
+
+ align:start position:0%
+interested in staying around
+ 
+
+ align:start position:0%
+interested in staying around
+right so copper is such a great
+
+ align:start position:0%
+right so copper is such a great
+ 
+
+ align:start position:0%
+right so copper is such a great
+conductor and that whole
+
+ align:start position:0%
+conductor and that whole
+ 
+
+ align:start position:0%
+conductor and that whole
+column is such a great conductor and
+
+ align:start position:0%
+column is such a great conductor and
+ 
+
+ align:start position:0%
+column is such a great conductor and
+this is by the way
+
+ align:start position:0%
+this is by the way
+ 
+
+ align:start position:0%
+this is by the way
+um oh such a good thing to do on a
+
+ align:start position:0%
+um oh such a good thing to do on a
+ 
+
+ align:start position:0%
+um oh such a good thing to do on a
+friday night i'm so glad it's friday
+
+ align:start position:0%
+friday night i'm so glad it's friday
+ 
+
+ align:start position:0%
+friday night i'm so glad it's friday
+look at this
+
+ align:start position:0%
+look at this
+ 
+
+ align:start position:0%
+look at this
+ptable.com huh
+
+ align:start position:0%
+ptable.com huh
+ 
+
+ align:start position:0%
+ptable.com huh
+you could spend hours on this i do
+
+ align:start position:0%
+you could spend hours on this i do
+ 
+
+ align:start position:0%
+you could spend hours on this i do
+spend hours on this
+
+ align:start position:0%
+spend hours on this
+ 
+
+ align:start position:0%
+spend hours on this
+property electrical conductivity and
+
+ align:start position:0%
+property electrical conductivity and
+ 
+
+ align:start position:0%
+property electrical conductivity and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+it shows you like dark green is high
+
+ align:start position:0%
+it shows you like dark green is high
+ 
+
+ align:start position:0%
+it shows you like dark green is high
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+dark green is high and and then like no
+
+ align:start position:0%
+dark green is high and and then like no
+ 
+
+ align:start position:0%
+dark green is high and and then like no
+coloring is low
+
+ align:start position:0%
+coloring is low
+ 
+
+ align:start position:0%
+coloring is low
+and then you can just click around and
+
+ align:start position:0%
+and then you can just click around and
+ 
+
+ align:start position:0%
+and then you can just click around and
+you just click around
+
+ align:start position:0%
+you just click around
+ 
+
+ align:start position:0%
+you just click around
+i can do it now but i'll i would never
+
+ align:start position:0%
+i can do it now but i'll i would never
+ 
+
+ align:start position:0%
+i can do it now but i'll i would never
+leave
+
+ align:start position:0%
+leave
+ 
+
+ align:start position:0%
+leave
+but you go there and you can click on
+
+ align:start position:0%
+but you go there and you can click on
+ 
+
+ align:start position:0%
+but you go there and you can click on
+different properties and see the trends
+
+ align:start position:0%
+different properties and see the trends
+ 
+
+ align:start position:0%
+different properties and see the trends
+in the periodic table and it's a
+
+ align:start position:0%
+in the periodic table and it's a
+ 
+
+ align:start position:0%
+in the periodic table and it's a
+beautiful thing
+
+ align:start position:0%
+beautiful thing
+ 
+
+ align:start position:0%
+beautiful thing
+and you now can understand them because
+
+ align:start position:0%
+and you now can understand them because
+ 
+
+ align:start position:0%
+and you now can understand them because
+of the ways
+
+ align:start position:0%
+of the ways
+ 
+
+ align:start position:0%
+of the ways
+in which electrons behave
+
+ align:start position:0%
+in which electrons behave
+ 
+
+ align:start position:0%
+in which electrons behave
+so you can see look at this there's
+
+ align:start position:0%
+so you can see look at this there's
+ 
+
+ align:start position:0%
+so you can see look at this there's
+copper right so there's copper
+
+ align:start position:0%
+copper right so there's copper
+ 
+
+ align:start position:0%
+copper right so there's copper
+and below that we've got silver and gold
+
+ align:start position:0%
+and below that we've got silver and gold
+ 
+
+ align:start position:0%
+and below that we've got silver and gold
+and this is a really high
+
+ align:start position:0%
+and this is a really high
+ 
+
+ align:start position:0%
+and this is a really high
+set of elements right the electrical
+
+ align:start position:0%
+set of elements right the electrical
+ 
+
+ align:start position:0%
+set of elements right the electrical
+conductivity
+
+ align:start position:0%
+conductivity
+ 
+
+ align:start position:0%
+conductivity
+in these three elements is super high
+
+ align:start position:0%
+in these three elements is super high
+ 
+
+ align:start position:0%
+in these three elements is super high
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this is why because each k in each case
+
+ align:start position:0%
+this is why because each k in each case
+ 
+
+ align:start position:0%
+this is why because each k in each case
+you're going down but you're filling the
+
+ align:start position:0%
+you're going down but you're filling the
+ 
+
+ align:start position:0%
+you're going down but you're filling the
+d's
+
+ align:start position:0%
+d's
+ 
+
+ align:start position:0%
+d's
+oh and then you're even filling f's
+
+ align:start position:0%
+oh and then you're even filling f's
+ 
+
+ align:start position:0%
+oh and then you're even filling f's
+screening further away
+
+ align:start position:0%
+screening further away
+ 
+
+ align:start position:0%
+screening further away
+really free s electrons high
+
+ align:start position:0%
+really free s electrons high
+ 
+
+ align:start position:0%
+really free s electrons high
+conductivity
+
+ align:start position:0%
+conductivity
+ 
+
+ align:start position:0%
+conductivity
+electron c right very easy to
+
+ align:start position:0%
+electron c right very easy to
+ 
+
+ align:start position:0%
+electron c right very easy to
+very easy to push them around now okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this also also goes back
+
+ align:start position:0%
+this also also goes back
+ 
+
+ align:start position:0%
+this also also goes back
+to this picture because remember i snuck
+
+ align:start position:0%
+to this picture because remember i snuck
+ 
+
+ align:start position:0%
+to this picture because remember i snuck
+it in
+
+ align:start position:0%
+it in
+ 
+
+ align:start position:0%
+it in
+because it was on the graph and i didn't
+
+ align:start position:0%
+because it was on the graph and i didn't
+ 
+
+ align:start position:0%
+because it was on the graph and i didn't
+take it out
+
+ align:start position:0%
+take it out
+ 
+
+ align:start position:0%
+take it out
+but there was a a picture of silicon
+
+ align:start position:0%
+but there was a a picture of silicon
+ 
+
+ align:start position:0%
+but there was a a picture of silicon
+where i showed
+
+ align:start position:0%
+where i showed
+ 
+
+ align:start position:0%
+where i showed
+silicon increasing its intrinsic carrier
+
+ align:start position:0%
+silicon increasing its intrinsic carrier
+ 
+
+ align:start position:0%
+silicon increasing its intrinsic carrier
+concentration with temperature
+
+ align:start position:0%
+concentration with temperature
+ 
+
+ align:start position:0%
+concentration with temperature
+and on top of that was a metal i think
+
+ align:start position:0%
+and on top of that was a metal i think
+ 
+
+ align:start position:0%
+and on top of that was a metal i think
+it was tungsten
+
+ align:start position:0%
+it was tungsten
+ 
+
+ align:start position:0%
+it was tungsten
+now if you draw the metal it would be
+
+ align:start position:0%
+now if you draw the metal it would be
+ 
+
+ align:start position:0%
+now if you draw the metal it would be
+way up
+
+ align:start position:0%
+way up
+ 
+
+ align:start position:0%
+way up
+it would be way up right here because
+
+ align:start position:0%
+it would be way up right here because
+ 
+
+ align:start position:0%
+it would be way up right here because
+it's higher
+
+ align:start position:0%
+it's higher
+ 
+
+ align:start position:0%
+it's higher
+but it went this way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wow but now you know why it's totally
+
+ align:start position:0%
+wow but now you know why it's totally
+ 
+
+ align:start position:0%
+wow but now you know why it's totally
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+right the reason is totally different
+
+ align:start position:0%
+right the reason is totally different
+ 
+
+ align:start position:0%
+right the reason is totally different
+than why this changes
+
+ align:start position:0%
+than why this changes
+ 
+
+ align:start position:0%
+than why this changes
+but you can understand it for the same
+
+ align:start position:0%
+but you can understand it for the same
+ 
+
+ align:start position:0%
+but you can understand it for the same
+route
+
+ align:start position:0%
+route
+ 
+
+ align:start position:0%
+route
+which is the behavior of the electrons
+
+ align:start position:0%
+which is the behavior of the electrons
+ 
+
+ align:start position:0%
+which is the behavior of the electrons
+so in a metal
+
+ align:start position:0%
+so in a metal
+ 
+
+ align:start position:0%
+so in a metal
+in a semiconductor this temperature
+
+ align:start position:0%
+in a semiconductor this temperature
+ 
+
+ align:start position:0%
+in a semiconductor this temperature
+dependence
+
+ align:start position:0%
+dependence
+ 
+
+ align:start position:0%
+dependence
+uh here i've taken the temperature
+
+ align:start position:0%
+uh here i've taken the temperature
+ 
+
+ align:start position:0%
+uh here i've taken the temperature
+independence away because i've doped it
+
+ align:start position:0%
+independence away because i've doped it
+ 
+
+ align:start position:0%
+independence away because i've doped it
+but here that's the thermal activation
+
+ align:start position:0%
+but here that's the thermal activation
+ 
+
+ align:start position:0%
+but here that's the thermal activation
+into a place of freedom into a place
+
+ align:start position:0%
+into a place of freedom into a place
+ 
+
+ align:start position:0%
+into a place of freedom into a place
+where they can they can be free in the
+
+ align:start position:0%
+where they can they can be free in the
+ 
+
+ align:start position:0%
+where they can they can be free in the
+conduction ban
+
+ align:start position:0%
+conduction ban
+ 
+
+ align:start position:0%
+conduction ban
+here they're already totally free so
+
+ align:start position:0%
+here they're already totally free so
+ 
+
+ align:start position:0%
+here they're already totally free so
+what's happening well when i increase
+
+ align:start position:0%
+what's happening well when i increase
+ 
+
+ align:start position:0%
+what's happening well when i increase
+the temperature
+
+ align:start position:0%
+the temperature
+ 
+
+ align:start position:0%
+the temperature
+i'm increasing the vibrations
+
+ align:start position:0%
+i'm increasing the vibrations
+ 
+
+ align:start position:0%
+i'm increasing the vibrations
+you can imagine if these electrons are
+
+ align:start position:0%
+you can imagine if these electrons are
+ 
+
+ align:start position:0%
+you can imagine if these electrons are
+trying to do their thing
+
+ align:start position:0%
+trying to do their thing
+ 
+
+ align:start position:0%
+trying to do their thing
+and they're in like a sea of electrons
+
+ align:start position:0%
+and they're in like a sea of electrons
+ 
+
+ align:start position:0%
+and they're in like a sea of electrons
+the last thing i want to do if i'm
+
+ align:start position:0%
+the last thing i want to do if i'm
+ 
+
+ align:start position:0%
+the last thing i want to do if i'm
+moving along is to see some
+
+ align:start position:0%
+moving along is to see some
+ 
+
+ align:start position:0%
+moving along is to see some
+big ion moving around
+
+ align:start position:0%
+big ion moving around
+ 
+
+ align:start position:0%
+big ion moving around
+and if it moves more then it's going to
+
+ align:start position:0%
+and if it moves more then it's going to
+ 
+
+ align:start position:0%
+and if it moves more then it's going to
+make me more upset
+
+ align:start position:0%
+make me more upset
+ 
+
+ align:start position:0%
+make me more upset
+and get in my way that's temperature
+
+ align:start position:0%
+and get in my way that's temperature
+ 
+
+ align:start position:0%
+and get in my way that's temperature
+but that's why this goes down and not up
+
+ align:start position:0%
+but that's why this goes down and not up
+ 
+
+ align:start position:0%
+but that's why this goes down and not up
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+for metals the more thermal energy you
+
+ align:start position:0%
+for metals the more thermal energy you
+ 
+
+ align:start position:0%
+for metals the more thermal energy you
+put in the more those
+
+ align:start position:0%
+put in the more those
+ 
+
+ align:start position:0%
+put in the more those
+ions those positive charges are positive
+
+ align:start position:0%
+ions those positive charges are positive
+ 
+
+ align:start position:0%
+ions those positive charges are positive
+right are going to interfere with the
+
+ align:start position:0%
+right are going to interfere with the
+ 
+
+ align:start position:0%
+right are going to interfere with the
+electrons being free
+
+ align:start position:0%
+electrons being free
+ 
+
+ align:start position:0%
+electrons being free
+right oh we are understanding things
+
+ align:start position:0%
+right oh we are understanding things
+ 
+
+ align:start position:0%
+right oh we are understanding things
+we understood why these have now you
+
+ align:start position:0%
+we understood why these have now you
+ 
+
+ align:start position:0%
+we understood why these have now you
+might say why are these different
+
+ align:start position:0%
+might say why are these different
+ 
+
+ align:start position:0%
+might say why are these different
+that's complicated relativity
+
+ align:start position:0%
+that's complicated relativity
+ 
+
+ align:start position:0%
+that's complicated relativity
+not part of this class but if you want
+
+ align:start position:0%
+not part of this class but if you want
+ 
+
+ align:start position:0%
+not part of this class but if you want
+to understand why these are different
+
+ align:start position:0%
+to understand why these are different
+ 
+
+ align:start position:0%
+to understand why these are different
+from each they're all really high
+
+ align:start position:0%
+from each they're all really high
+ 
+
+ align:start position:0%
+from each they're all really high
+why are they different it's more it goes
+
+ align:start position:0%
+why are they different it's more it goes
+ 
+
+ align:start position:0%
+why are they different it's more it goes
+beyond the scope of this class but it's
+
+ align:start position:0%
+beyond the scope of this class but it's
+ 
+
+ align:start position:0%
+beyond the scope of this class but it's
+also a very interesting story that has
+
+ align:start position:0%
+also a very interesting story that has
+ 
+
+ align:start position:0%
+also a very interesting story that has
+to do with
+
+ align:start position:0%
+to do with
+ 
+
+ align:start position:0%
+to do with
+uh on the one hand relativistic effects
+
+ align:start position:0%
+uh on the one hand relativistic effects
+ 
+
+ align:start position:0%
+uh on the one hand relativistic effects
+okay now there's another thing which is
+
+ align:start position:0%
+okay now there's another thing which is
+ 
+
+ align:start position:0%
+okay now there's another thing which is
+that if i go back to that table
+
+ align:start position:0%
+that if i go back to that table
+ 
+
+ align:start position:0%
+that if i go back to that table
+and i did this i really did this a lot i
+
+ align:start position:0%
+and i did this i really did this a lot i
+ 
+
+ align:start position:0%
+and i did this i really did this a lot i
+clicked back and forth
+
+ align:start position:0%
+clicked back and forth
+ 
+
+ align:start position:0%
+clicked back and forth
+between okay electrical now look up here
+
+ align:start position:0%
+between okay electrical now look up here
+ 
+
+ align:start position:0%
+between okay electrical now look up here
+thermal electrical thermal electrical
+
+ align:start position:0%
+thermal electrical thermal electrical
+ 
+
+ align:start position:0%
+thermal electrical thermal electrical
+and you can click you go and you can
+
+ align:start position:0%
+and you can click you go and you can
+ 
+
+ align:start position:0%
+and you can click you go and you can
+watch the table
+
+ align:start position:0%
+watch the table
+ 
+
+ align:start position:0%
+watch the table
+and do that for like five minutes or so
+
+ align:start position:0%
+and do that for like five minutes or so
+ 
+
+ align:start position:0%
+and do that for like five minutes or so
+and what you'll find
+
+ align:start position:0%
+and what you'll find
+ 
+
+ align:start position:0%
+and what you'll find
+is almost nothing changes
+
+ align:start position:0%
+is almost nothing changes
+ 
+
+ align:start position:0%
+is almost nothing changes
+you can't do that with very many
+
+ align:start position:0%
+you can't do that with very many
+ 
+
+ align:start position:0%
+you can't do that with very many
+properties but for metals
+
+ align:start position:0%
+properties but for metals
+ 
+
+ align:start position:0%
+properties but for metals
+and those two properties they're almost
+
+ align:start position:0%
+and those two properties they're almost
+ 
+
+ align:start position:0%
+and those two properties they're almost
+identical again
+
+ align:start position:0%
+identical again
+ 
+
+ align:start position:0%
+identical again
+it goes back to the sea it goes back to
+
+ align:start position:0%
+it goes back to the sea it goes back to
+ 
+
+ align:start position:0%
+it goes back to the sea it goes back to
+the sea because
+
+ align:start position:0%
+the sea because
+ 
+
+ align:start position:0%
+the sea because
+you know if you have electrons
+
+ align:start position:0%
+you know if you have electrons
+ 
+
+ align:start position:0%
+you know if you have electrons
+that are free in a material
+
+ align:start position:0%
+that are free in a material
+ 
+
+ align:start position:0%
+that are free in a material
+you you can also those can carry not
+
+ align:start position:0%
+you you can also those can carry not
+ 
+
+ align:start position:0%
+you you can also those can carry not
+just electricity
+
+ align:start position:0%
+just electricity
+ 
+
+ align:start position:0%
+just electricity
+but those can be the dominant carriers
+
+ align:start position:0%
+but those can be the dominant carriers
+ 
+
+ align:start position:0%
+but those can be the dominant carriers
+of thermal energy as well and i'm not
+
+ align:start position:0%
+of thermal energy as well and i'm not
+ 
+
+ align:start position:0%
+of thermal energy as well and i'm not
+going to go into those details i just
+
+ align:start position:0%
+going to go into those details i just
+ 
+
+ align:start position:0%
+going to go into those details i just
+want to mention it
+
+ align:start position:0%
+want to mention it
+ 
+
+ align:start position:0%
+want to mention it
+so this is actually called the vitamin
+
+ align:start position:0%
+so this is actually called the vitamin
+ 
+
+ align:start position:0%
+so this is actually called the vitamin
+franzla
+
+ align:start position:0%
+franzla
+ 
+
+ align:start position:0%
+franzla
+and it
+
+ align:start position:0%
+and it
+ 
+
+ align:start position:0%
+and it
+basically says for these
+
+ align:start position:0%
+basically says for these
+ 
+
+ align:start position:0%
+basically says for these
+for metals that the
+
+ align:start position:0%
+for metals that the
+ 
+
+ align:start position:0%
+for metals that the
+thermal let's see okay i'll just write
+
+ align:start position:0%
+thermal let's see okay i'll just write
+ 
+
+ align:start position:0%
+thermal let's see okay i'll just write
+it here
+
+ align:start position:0%
+it here
+ 
+
+ align:start position:0%
+it here
+thermal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divided by electrical
+
+ align:start position:0%
+divided by electrical
+ 
+
+ align:start position:0%
+divided by electrical
+conductivity for both conductivities
+
+ align:start position:0%
+conductivity for both conductivities
+ 
+
+ align:start position:0%
+conductivity for both conductivities
+okay i'm putting it in parentheses it
+
+ align:start position:0%
+okay i'm putting it in parentheses it
+ 
+
+ align:start position:0%
+okay i'm putting it in parentheses it
+should be thermal conductivity
+
+ align:start position:0%
+should be thermal conductivity
+ 
+
+ align:start position:0%
+should be thermal conductivity
+divided by electrical conductivity goes
+
+ align:start position:0%
+divided by electrical conductivity goes
+ 
+
+ align:start position:0%
+divided by electrical conductivity goes
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+some constant
+
+ align:start position:0%
+some constant
+ 
+
+ align:start position:0%
+some constant
+times the temperature and look at
+
+ align:start position:0%
+times the temperature and look at
+ 
+
+ align:start position:0%
+times the temperature and look at
+so so if you look at that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can look at it by toggling back
+
+ align:start position:0%
+so you can look at it by toggling back
+ 
+
+ align:start position:0%
+so you can look at it by toggling back
+and forth and see how similar these are
+
+ align:start position:0%
+and forth and see how similar these are
+ 
+
+ align:start position:0%
+and forth and see how similar these are
+you can also just plot stuff or find
+
+ align:start position:0%
+you can also just plot stuff or find
+ 
+
+ align:start position:0%
+you can also just plot stuff or find
+plots of stuff here's one
+
+ align:start position:0%
+plots of stuff here's one
+ 
+
+ align:start position:0%
+plots of stuff here's one
+electrical conductivity this is at some
+
+ align:start position:0%
+electrical conductivity this is at some
+ 
+
+ align:start position:0%
+electrical conductivity this is at some
+fixed temperature orders of magnitude
+
+ align:start position:0%
+fixed temperature orders of magnitude
+ 
+
+ align:start position:0%
+fixed temperature orders of magnitude
+variation orders of magnitude variation
+
+ align:start position:0%
+variation orders of magnitude variation
+ 
+
+ align:start position:0%
+variation orders of magnitude variation
+tons and tons of different materials
+
+ align:start position:0%
+tons and tons of different materials
+ 
+
+ align:start position:0%
+tons and tons of different materials
+this is the vitamin france law
+
+ align:start position:0%
+this is the vitamin france law
+ 
+
+ align:start position:0%
+this is the vitamin france law
+and it all now you know that law is
+
+ align:start position:0%
+and it all now you know that law is
+ 
+
+ align:start position:0%
+and it all now you know that law is
+simply
+
+ align:start position:0%
+simply
+ 
+
+ align:start position:0%
+simply
+a result of the fact that these free
+
+ align:start position:0%
+a result of the fact that these free
+ 
+
+ align:start position:0%
+a result of the fact that these free
+electrons can carry both
+
+ align:start position:0%
+electrons can carry both
+ 
+
+ align:start position:0%
+electrons can carry both
+electrical their charge as well as
+
+ align:start position:0%
+electrical their charge as well as
+ 
+
+ align:start position:0%
+electrical their charge as well as
+thermal energy
+
+ align:start position:0%
+thermal energy
+ 
+
+ align:start position:0%
+thermal energy
+and that the way they carry those are
+
+ align:start position:0%
+and that the way they carry those are
+ 
+
+ align:start position:0%
+and that the way they carry those are
+are dependent on the material dependent
+
+ align:start position:0%
+are dependent on the material dependent
+ 
+
+ align:start position:0%
+are dependent on the material dependent
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+the number of electrons and the way they
+
+ align:start position:0%
+the number of electrons and the way they
+ 
+
+ align:start position:0%
+the number of electrons and the way they
+bond and all that but if they carry it
+
+ align:start position:0%
+bond and all that but if they carry it
+ 
+
+ align:start position:0%
+bond and all that but if they carry it
+in one way for one it carries it in the
+
+ align:start position:0%
+in one way for one it carries it in the
+ 
+
+ align:start position:0%
+in one way for one it carries it in the
+same way for the other right
+
+ align:start position:0%
+same way for the other right
+ 
+
+ align:start position:0%
+same way for the other right
+so that's okay look at all these things
+
+ align:start position:0%
+so that's okay look at all these things
+ 
+
+ align:start position:0%
+so that's okay look at all these things
+now notice here
+
+ align:start position:0%
+now notice here
+ 
+
+ align:start position:0%
+now notice here
+this word that's used a lot alloy alloy
+
+ align:start position:0%
+this word that's used a lot alloy alloy
+ 
+
+ align:start position:0%
+this word that's used a lot alloy alloy
+alloy these are all you know okay alloy
+
+ align:start position:0%
+alloy these are all you know okay alloy
+ 
+
+ align:start position:0%
+alloy these are all you know okay alloy
+and i mentioned the word alloy on
+
+ align:start position:0%
+and i mentioned the word alloy on
+ 
+
+ align:start position:0%
+and i mentioned the word alloy on
+wednesday because i said if you wanted
+
+ align:start position:0%
+wednesday because i said if you wanted
+ 
+
+ align:start position:0%
+wednesday because i said if you wanted
+to make a good blue
+
+ align:start position:0%
+to make a good blue
+ 
+
+ align:start position:0%
+to make a good blue
+a good blue led you had gallium nitride
+
+ align:start position:0%
+a good blue led you had gallium nitride
+ 
+
+ align:start position:0%
+a good blue led you had gallium nitride
+but it was a little too high
+
+ align:start position:0%
+but it was a little too high
+ 
+
+ align:start position:0%
+but it was a little too high
+in its band gas so they alloyed it with
+
+ align:start position:0%
+in its band gas so they alloyed it with
+ 
+
+ align:start position:0%
+in its band gas so they alloyed it with
+other then that meant mixing in
+
+ align:start position:0%
+other then that meant mixing in
+ 
+
+ align:start position:0%
+other then that meant mixing in
+well that is done for metals
+
+ align:start position:0%
+well that is done for metals
+ 
+
+ align:start position:0%
+well that is done for metals
+that is done for metals in a very wide
+
+ align:start position:0%
+that is done for metals in a very wide
+ 
+
+ align:start position:0%
+that is done for metals in a very wide
+range
+
+ align:start position:0%
+range
+ 
+
+ align:start position:0%
+range
+why because the metal properties that
+
+ align:start position:0%
+why because the metal properties that
+ 
+
+ align:start position:0%
+why because the metal properties that
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+you may like some of but you may not
+
+ align:start position:0%
+you may like some of but you may not
+ 
+
+ align:start position:0%
+you may like some of but you may not
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+others right so like for copper
+
+ align:start position:0%
+others right so like for copper
+ 
+
+ align:start position:0%
+others right so like for copper
+it's um you know it's it's got this
+
+ align:start position:0%
+it's um you know it's it's got this
+ 
+
+ align:start position:0%
+it's um you know it's it's got this
+really high conductivity
+
+ align:start position:0%
+really high conductivity
+ 
+
+ align:start position:0%
+really high conductivity
+but maybe you don't want it to be so
+
+ align:start position:0%
+but maybe you don't want it to be so
+ 
+
+ align:start position:0%
+but maybe you don't want it to be so
+malleable what does that mean
+
+ align:start position:0%
+malleable what does that mean
+ 
+
+ align:start position:0%
+malleable what does that mean
+we'll see in 10 minutes malleable
+
+ align:start position:0%
+we'll see in 10 minutes malleable
+ 
+
+ align:start position:0%
+we'll see in 10 minutes malleable
+ductile
+
+ align:start position:0%
+ductile
+ 
+
+ align:start position:0%
+ductile
+but but so what do you do well you alloy
+
+ align:start position:0%
+but but so what do you do well you alloy
+ 
+
+ align:start position:0%
+but but so what do you do well you alloy
+it right
+
+ align:start position:0%
+it right
+ 
+
+ align:start position:0%
+it right
+and so here's an example brass well
+
+ align:start position:0%
+and so here's an example brass well
+ 
+
+ align:start position:0%
+and so here's an example brass well
+we know brass but now you know brass now
+
+ align:start position:0%
+we know brass but now you know brass now
+ 
+
+ align:start position:0%
+we know brass but now you know brass now
+you really know brass you didn't know
+
+ align:start position:0%
+you really know brass you didn't know
+ 
+
+ align:start position:0%
+you really know brass you didn't know
+brass you don't know
+
+ align:start position:0%
+brass you don't know
+ 
+
+ align:start position:0%
+brass you don't know
+anyone or anything until you see it as
+
+ align:start position:0%
+anyone or anything until you see it as
+ 
+
+ align:start position:0%
+anyone or anything until you see it as
+an atom
+
+ align:start position:0%
+an atom
+ 
+
+ align:start position:0%
+an atom
+and electrons that is how you know
+
+ align:start position:0%
+and electrons that is how you know
+ 
+
+ align:start position:0%
+and electrons that is how you know
+someone
+
+ align:start position:0%
+someone
+ 
+
+ align:start position:0%
+someone
+copper with zinc substituted in a two to
+
+ align:start position:0%
+copper with zinc substituted in a two to
+ 
+
+ align:start position:0%
+copper with zinc substituted in a two to
+one ratio copper to zinc
+
+ align:start position:0%
+one ratio copper to zinc
+ 
+
+ align:start position:0%
+one ratio copper to zinc
+the conductivity drops those electrons
+
+ align:start position:0%
+the conductivity drops those electrons
+ 
+
+ align:start position:0%
+the conductivity drops those electrons
+are not as free but they're still pretty
+
+ align:start position:0%
+are not as free but they're still pretty
+ 
+
+ align:start position:0%
+are not as free but they're still pretty
+free
+
+ align:start position:0%
+free
+ 
+
+ align:start position:0%
+free
+maybe they're a little more tied up in
+
+ align:start position:0%
+maybe they're a little more tied up in
+ 
+
+ align:start position:0%
+maybe they're a little more tied up in
+the bonding and maybe what you've done
+
+ align:start position:0%
+the bonding and maybe what you've done
+ 
+
+ align:start position:0%
+the bonding and maybe what you've done
+by alloying is changed its mechanical
+
+ align:start position:0%
+by alloying is changed its mechanical
+ 
+
+ align:start position:0%
+by alloying is changed its mechanical
+properties
+
+ align:start position:0%
+properties
+ 
+
+ align:start position:0%
+properties
+because i kind of want something
+
+ align:start position:0%
+because i kind of want something
+ 
+
+ align:start position:0%
+because i kind of want something
+copper-like but i want it to have
+
+ align:start position:0%
+copper-like but i want it to have
+ 
+
+ align:start position:0%
+copper-like but i want it to have
+different mechanical properties so i
+
+ align:start position:0%
+different mechanical properties so i
+ 
+
+ align:start position:0%
+different mechanical properties so i
+alloy it
+
+ align:start position:0%
+alloy it
+ 
+
+ align:start position:0%
+alloy it
+and and this is really how how
+
+ align:start position:0%
+and and this is really how how
+ 
+
+ align:start position:0%
+and and this is really how how
+we think about materials design i need
+
+ align:start position:0%
+we think about materials design i need
+ 
+
+ align:start position:0%
+we think about materials design i need
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+to have let's say a certain set of
+
+ align:start position:0%
+to have let's say a certain set of
+ 
+
+ align:start position:0%
+to have let's say a certain set of
+properties well i don't have them all
+
+ align:start position:0%
+properties well i don't have them all
+ 
+
+ align:start position:0%
+properties well i don't have them all
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and i don't have them all here but how
+
+ align:start position:0%
+and i don't have them all here but how
+ 
+
+ align:start position:0%
+and i don't have them all here but how
+can i use a combination
+
+ align:start position:0%
+can i use a combination
+ 
+
+ align:start position:0%
+can i use a combination
+right how can i how can i use a
+
+ align:start position:0%
+right how can i how can i use a
+ 
+
+ align:start position:0%
+right how can i how can i use a
+combination to get what i want
+
+ align:start position:0%
+combination to get what i want
+ 
+
+ align:start position:0%
+combination to get what i want
+bronze is copper with tin four to one
+
+ align:start position:0%
+bronze is copper with tin four to one
+ 
+
+ align:start position:0%
+bronze is copper with tin four to one
+ratio copper it's in connectivity drops
+
+ align:start position:0%
+ratio copper it's in connectivity drops
+ 
+
+ align:start position:0%
+ratio copper it's in connectivity drops
+even more
+
+ align:start position:0%
+even more
+ 
+
+ align:start position:0%
+even more
+it's not so simple right it's not so
+
+ align:start position:0%
+it's not so simple right it's not so
+ 
+
+ align:start position:0%
+it's not so simple right it's not so
+simple as
+
+ align:start position:0%
+simple as
+ 
+
+ align:start position:0%
+simple as
+oh if it's four to one then maybe it's
+
+ align:start position:0%
+oh if it's four to one then maybe it's
+ 
+
+ align:start position:0%
+oh if it's four to one then maybe it's
+like 20 no
+
+ align:start position:0%
+like 20 no
+ 
+
+ align:start position:0%
+like 20 no
+because it has to do with what happens
+
+ align:start position:0%
+because it has to do with what happens
+ 
+
+ align:start position:0%
+because it has to do with what happens
+to the freedom
+
+ align:start position:0%
+to the freedom
+ 
+
+ align:start position:0%
+to the freedom
+of these electrons that's what it has to
+
+ align:start position:0%
+of these electrons that's what it has to
+ 
+
+ align:start position:0%
+of these electrons that's what it has to
+do with and that's more complicated
+
+ align:start position:0%
+do with and that's more complicated
+ 
+
+ align:start position:0%
+do with and that's more complicated
+but maybe i've changed the properties in
+
+ align:start position:0%
+but maybe i've changed the properties in
+ 
+
+ align:start position:0%
+but maybe i've changed the properties in
+another way that i really like
+
+ align:start position:0%
+another way that i really like
+ 
+
+ align:start position:0%
+another way that i really like
+well those are substitutional
+
+ align:start position:0%
+well those are substitutional
+ 
+
+ align:start position:0%
+well those are substitutional
+substitutional alloys means i took one
+
+ align:start position:0%
+substitutional alloys means i took one
+ 
+
+ align:start position:0%
+substitutional alloys means i took one
+of the coppers out
+
+ align:start position:0%
+of the coppers out
+ 
+
+ align:start position:0%
+of the coppers out
+and i replaced it with something else
+
+ align:start position:0%
+and i replaced it with something else
+ 
+
+ align:start position:0%
+and i replaced it with something else
+here's brass with zinc in there
+
+ align:start position:0%
+here's brass with zinc in there
+ 
+
+ align:start position:0%
+here's brass with zinc in there
+you can also have interstitial alloys
+
+ align:start position:0%
+you can also have interstitial alloys
+ 
+
+ align:start position:0%
+you can also have interstitial alloys
+and interstitial alloys so if we we'll
+
+ align:start position:0%
+and interstitial alloys so if we we'll
+ 
+
+ align:start position:0%
+and interstitial alloys so if we we'll
+be coming back to this when we talk
+
+ align:start position:0%
+be coming back to this when we talk
+ 
+
+ align:start position:0%
+be coming back to this when we talk
+about crystals next week
+
+ align:start position:0%
+about crystals next week
+ 
+
+ align:start position:0%
+about crystals next week
+but alloys actually when we talk about
+
+ align:start position:0%
+but alloys actually when we talk about
+ 
+
+ align:start position:0%
+but alloys actually when we talk about
+defects
+
+ align:start position:0%
+defects
+ 
+
+ align:start position:0%
+defects
+so you can have substitutional
+
+ align:start position:0%
+so you can have substitutional
+ 
+
+ align:start position:0%
+so you can have substitutional
+substitutional
+
+ align:start position:0%
+substitutional
+ 
+
+ align:start position:0%
+substitutional
+and you can have interstitial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is just a preview interstitial
+
+ align:start position:0%
+this is just a preview interstitial
+ 
+
+ align:start position:0%
+this is just a preview interstitial
+this is just a preview we're not going
+
+ align:start position:0%
+this is just a preview we're not going
+ 
+
+ align:start position:0%
+this is just a preview we're not going
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+testing on this or thinking about this
+
+ align:start position:0%
+testing on this or thinking about this
+ 
+
+ align:start position:0%
+testing on this or thinking about this
+much until we get to actually
+
+ align:start position:0%
+much until we get to actually
+ 
+
+ align:start position:0%
+much until we get to actually
+putting these things in to a crystal
+
+ align:start position:0%
+putting these things in to a crystal
+ 
+
+ align:start position:0%
+putting these things in to a crystal
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+as as defects but right now i just want
+
+ align:start position:0%
+as as defects but right now i just want
+ 
+
+ align:start position:0%
+as as defects but right now i just want
+to make sure you
+
+ align:start position:0%
+to make sure you
+ 
+
+ align:start position:0%
+to make sure you
+you know you kind of see them for the
+
+ align:start position:0%
+you know you kind of see them for the
+ 
+
+ align:start position:0%
+you know you kind of see them for the
+first time substitutional
+
+ align:start position:0%
+first time substitutional
+ 
+
+ align:start position:0%
+first time substitutional
+interstitial why would you want one well
+
+ align:start position:0%
+interstitial why would you want one well
+ 
+
+ align:start position:0%
+interstitial why would you want one well
+it depends on what properties you're
+
+ align:start position:0%
+it depends on what properties you're
+ 
+
+ align:start position:0%
+it depends on what properties you're
+trying to change
+
+ align:start position:0%
+trying to change
+ 
+
+ align:start position:0%
+trying to change
+in this case i've got i really like iron
+
+ align:start position:0%
+in this case i've got i really like iron
+ 
+
+ align:start position:0%
+in this case i've got i really like iron
+it's really cheap it's it's
+
+ align:start position:0%
+it's really cheap it's it's
+ 
+
+ align:start position:0%
+it's really cheap it's it's
+it's a cool material but i need it to be
+
+ align:start position:0%
+it's a cool material but i need it to be
+ 
+
+ align:start position:0%
+it's a cool material but i need it to be
+stronger
+
+ align:start position:0%
+stronger
+ 
+
+ align:start position:0%
+stronger
+and that's called steel and if you just
+
+ align:start position:0%
+and that's called steel and if you just
+ 
+
+ align:start position:0%
+and that's called steel and if you just
+put a little bit of carbon
+
+ align:start position:0%
+put a little bit of carbon
+ 
+
+ align:start position:0%
+put a little bit of carbon
+really not much like a percent by weight
+
+ align:start position:0%
+really not much like a percent by weight
+ 
+
+ align:start position:0%
+really not much like a percent by weight
+you can dramatically change the
+
+ align:start position:0%
+you can dramatically change the
+ 
+
+ align:start position:0%
+you can dramatically change the
+mechanical properties of iron
+
+ align:start position:0%
+mechanical properties of iron
+ 
+
+ align:start position:0%
+mechanical properties of iron
+you can make it a much stronger material
+
+ align:start position:0%
+you can make it a much stronger material
+ 
+
+ align:start position:0%
+you can make it a much stronger material
+there's a massive massive range
+
+ align:start position:0%
+there's a massive massive range
+ 
+
+ align:start position:0%
+there's a massive massive range
+of properties and part of why metals are
+
+ align:start position:0%
+of properties and part of why metals are
+ 
+
+ align:start position:0%
+of properties and part of why metals are
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh tunable is because of the electron c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well i just came across this article
+
+ align:start position:0%
+well i just came across this article
+ 
+
+ align:start position:0%
+well i just came across this article
+actually and i thought i'd show you this
+
+ align:start position:0%
+actually and i thought i'd show you this
+ 
+
+ align:start position:0%
+actually and i thought i'd show you this
+just literally yesterday is that
+
+ align:start position:0%
+just literally yesterday is that
+ 
+
+ align:start position:0%
+just literally yesterday is that
+yesterday
+
+ align:start position:0%
+yesterday
+ 
+
+ align:start position:0%
+yesterday
+um i thought it was an interesting
+
+ align:start position:0%
+um i thought it was an interesting
+ 
+
+ align:start position:0%
+um i thought it was an interesting
+example car wars still getting stronger
+
+ align:start position:0%
+example car wars still getting stronger
+ 
+
+ align:start position:0%
+example car wars still getting stronger
+lighter to curb aluminum rise well
+
+ align:start position:0%
+lighter to curb aluminum rise well
+ 
+
+ align:start position:0%
+lighter to curb aluminum rise well
+see the thing is that you know as you
+
+ align:start position:0%
+see the thing is that you know as you
+ 
+
+ align:start position:0%
+see the thing is that you know as you
+want cars to be lighter
+
+ align:start position:0%
+want cars to be lighter
+ 
+
+ align:start position:0%
+want cars to be lighter
+think fuel efficiency or range if it's
+
+ align:start position:0%
+think fuel efficiency or range if it's
+ 
+
+ align:start position:0%
+think fuel efficiency or range if it's
+electric
+
+ align:start position:0%
+electric
+ 
+
+ align:start position:0%
+electric
+right um you got to use lighter metals
+
+ align:start position:0%
+right um you got to use lighter metals
+ 
+
+ align:start position:0%
+right um you got to use lighter metals
+and aluminum is lighter but aluminum is
+
+ align:start position:0%
+and aluminum is lighter but aluminum is
+ 
+
+ align:start position:0%
+and aluminum is lighter but aluminum is
+more than twice as much as steel
+
+ align:start position:0%
+more than twice as much as steel
+ 
+
+ align:start position:0%
+more than twice as much as steel
+it's a lot lighter though so so there's
+
+ align:start position:0%
+it's a lot lighter though so so there's
+ 
+
+ align:start position:0%
+it's a lot lighter though so so there's
+there's a lot of interest
+
+ align:start position:0%
+there's a lot of interest
+ 
+
+ align:start position:0%
+there's a lot of interest
+in making steel that's just iron with
+
+ align:start position:0%
+in making steel that's just iron with
+ 
+
+ align:start position:0%
+in making steel that's just iron with
+carbon interstitial
+
+ align:start position:0%
+carbon interstitial
+ 
+
+ align:start position:0%
+carbon interstitial
+and making steel stronger you can see
+
+ align:start position:0%
+and making steel stronger you can see
+ 
+
+ align:start position:0%
+and making steel stronger you can see
+newest alloy that's what caught my
+
+ align:start position:0%
+newest alloy that's what caught my
+ 
+
+ align:start position:0%
+newest alloy that's what caught my
+attention
+
+ align:start position:0%
+attention
+ 
+
+ align:start position:0%
+attention
+newest alloy they've come up with
+
+ align:start position:0%
+newest alloy they've come up with
+ 
+
+ align:start position:0%
+newest alloy they've come up with
+something to add to iron
+
+ align:start position:0%
+something to add to iron
+ 
+
+ align:start position:0%
+something to add to iron
+to make its mechanical properties really
+
+ align:start position:0%
+to make its mechanical properties really
+ 
+
+ align:start position:0%
+to make its mechanical properties really
+really good
+
+ align:start position:0%
+really good
+ 
+
+ align:start position:0%
+really good
+at a very very thin layer
+
+ align:start position:0%
+at a very very thin layer
+ 
+
+ align:start position:0%
+at a very very thin layer
+right because they need steel to be even
+
+ align:start position:0%
+right because they need steel to be even
+ 
+
+ align:start position:0%
+right because they need steel to be even
+stronger
+
+ align:start position:0%
+stronger
+ 
+
+ align:start position:0%
+stronger
+in a much thinner layer otherwise it's
+
+ align:start position:0%
+in a much thinner layer otherwise it's
+ 
+
+ align:start position:0%
+in a much thinner layer otherwise it's
+too heavy and you've got to make it
+
+ align:start position:0%
+too heavy and you've got to make it
+ 
+
+ align:start position:0%
+too heavy and you've got to make it
+really thin
+
+ align:start position:0%
+really thin
+ 
+
+ align:start position:0%
+really thin
+and really strong those are going to be
+
+ align:start position:0%
+and really strong those are going to be
+ 
+
+ align:start position:0%
+and really strong those are going to be
+alloys okay
+
+ align:start position:0%
+alloys okay
+ 
+
+ align:start position:0%
+alloys okay
+back to our property list now um
+
+ align:start position:0%
+back to our property list now um
+ 
+
+ align:start position:0%
+back to our property list now um
+malleability and ductility why
+
+ align:start position:0%
+malleability and ductility why
+ 
+
+ align:start position:0%
+malleability and ductility why
+are metals malleable and ductile
+
+ align:start position:0%
+are metals malleable and ductile
+ 
+
+ align:start position:0%
+are metals malleable and ductile
+well i thought this was a good place for
+
+ align:start position:0%
+well i thought this was a good place for
+ 
+
+ align:start position:0%
+well i thought this was a good place for
+a video
+
+ align:start position:0%
+a video
+ 
+
+ align:start position:0%
+a video
+because i really like i think it's a
+
+ align:start position:0%
+because i really like i think it's a
+ 
+
+ align:start position:0%
+because i really like i think it's a
+really simple explanation
+
+ align:start position:0%
+really simple explanation
+ 
+
+ align:start position:0%
+really simple explanation
+of malleability and ductility as it
+
+ align:start position:0%
+of malleability and ductility as it
+ 
+
+ align:start position:0%
+of malleability and ductility as it
+relates to the electron c
+
+ align:start position:0%
+relates to the electron c
+ 
+
+ align:start position:0%
+relates to the electron c
+so let's watch this it's like a minute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+long
+
+ align:start position:0%
+long
+ 
+
+ align:start position:0%
+long
+they violently repel each other breaking
+
+ align:start position:0%
+they violently repel each other breaking
+ 
+
+ align:start position:0%
+they violently repel each other breaking
+the crystal apart
+
+ align:start position:0%
+the crystal apart
+ 
+
+ align:start position:0%
+the crystal apart
+that's an ionic trap if you hit a metal
+
+ align:start position:0%
+that's an ionic trap if you hit a metal
+ 
+
+ align:start position:0%
+that's an ionic trap if you hit a metal
+with a hammer
+
+ align:start position:0%
+with a hammer
+ 
+
+ align:start position:0%
+with a hammer
+it doesn't break it just dents metals
+
+ align:start position:0%
+it doesn't break it just dents metals
+ 
+
+ align:start position:0%
+it doesn't break it just dents metals
+are able to deform in response to an
+
+ align:start position:0%
+are able to deform in response to an
+ 
+
+ align:start position:0%
+are able to deform in response to an
+applied force
+
+ align:start position:0%
+applied force
+ 
+
+ align:start position:0%
+applied force
+the mobile sea of electrons shields the
+
+ align:start position:0%
+the mobile sea of electrons shields the
+ 
+
+ align:start position:0%
+the mobile sea of electrons shields the
+cations from each other
+
+ align:start position:0%
+cations from each other
+ 
+
+ align:start position:0%
+cations from each other
+preventing violent repulsion and
+
+ align:start position:0%
+preventing violent repulsion and
+ 
+
+ align:start position:0%
+preventing violent repulsion and
+allowing the metal to change
+
+ align:start position:0%
+allowing the metal to change
+ 
+
+ align:start position:0%
+allowing the metal to change
+shape the most malleable metal is gold
+
+ align:start position:0%
+shape the most malleable metal is gold
+ 
+
+ align:start position:0%
+shape the most malleable metal is gold
+a similar property to the malleability
+
+ align:start position:0%
+a similar property to the malleability
+ 
+
+ align:start position:0%
+a similar property to the malleability
+of metals
+
+ align:start position:0%
+of metals
+ 
+
+ align:start position:0%
+of metals
+is their ability to be pulled into long
+
+ align:start position:0%
+is their ability to be pulled into long
+ 
+
+ align:start position:0%
+is their ability to be pulled into long
+thin wires
+
+ align:start position:0%
+thin wires
+ 
+
+ align:start position:0%
+thin wires
+we call this ductility ionic compounds
+
+ align:start position:0%
+we call this ductility ionic compounds
+ 
+
+ align:start position:0%
+we call this ductility ionic compounds
+are not ductal
+
+ align:start position:0%
+are not ductal
+ 
+
+ align:start position:0%
+are not ductal
+for the same reason they are not
+
+ align:start position:0%
+for the same reason they are not
+ 
+
+ align:start position:0%
+for the same reason they are not
+malleable in general
+
+ align:start position:0%
+malleable in general
+ 
+
+ align:start position:0%
+malleable in general
+if an ionic compound is forced into a
+
+ align:start position:0%
+if an ionic compound is forced into a
+ 
+
+ align:start position:0%
+if an ionic compound is forced into a
+long cylinder
+
+ align:start position:0%
+long cylinder
+ 
+
+ align:start position:0%
+long cylinder
+it breaks apart because of the repulsion
+
+ align:start position:0%
+it breaks apart because of the repulsion
+ 
+
+ align:start position:0%
+it breaks apart because of the repulsion
+of like ions
+
+ align:start position:0%
+of like ions
+ 
+
+ align:start position:0%
+of like ions
+in contrast a metal can be pulled into a
+
+ align:start position:0%
+in contrast a metal can be pulled into a
+ 
+
+ align:start position:0%
+in contrast a metal can be pulled into a
+long cylindrical shape
+
+ align:start position:0%
+long cylindrical shape
+ 
+
+ align:start position:0%
+long cylindrical shape
+because the cations can line up shielded
+
+ align:start position:0%
+because the cations can line up shielded
+ 
+
+ align:start position:0%
+because the cations can line up shielded
+from each other
+
+ align:start position:0%
+from each other
+ 
+
+ align:start position:0%
+from each other
+as the fluid-like sea of electrons flows
+
+ align:start position:0%
+as the fluid-like sea of electrons flows
+ 
+
+ align:start position:0%
+as the fluid-like sea of electrons flows
+around them
+
+ align:start position:0%
+around them
+ 
+
+ align:start position:0%
+around them
+that's my favorite part the most ductile
+
+ align:start position:0%
+that's my favorite part the most ductile
+ 
+
+ align:start position:0%
+that's my favorite part the most ductile
+metal
+
+ align:start position:0%
+metal
+ 
+
+ align:start position:0%
+metal
+oh the most ductile metal what is it
+
+ align:start position:0%
+oh the most ductile metal what is it
+ 
+
+ align:start position:0%
+oh the most ductile metal what is it
+they never know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's platinum but see now okay okay now
+
+ align:start position:0%
+it's platinum but see now okay okay now
+ 
+
+ align:start position:0%
+it's platinum but see now okay okay now
+that's a
+
+ align:start position:0%
+that's a
+ 
+
+ align:start position:0%
+that's a
+i just gave it away okay
+
+ align:start position:0%
+i just gave it away okay
+ 
+
+ align:start position:0%
+i just gave it away okay
+ductile malleable sea of electrons
+
+ align:start position:0%
+ductile malleable sea of electrons
+ 
+
+ align:start position:0%
+ductile malleable sea of electrons
+sea of electrons because did you see
+
+ align:start position:0%
+sea of electrons because did you see
+ 
+
+ align:start position:0%
+sea of electrons because did you see
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+flowing around you're moving the atom
+
+ align:start position:0%
+flowing around you're moving the atom
+ 
+
+ align:start position:0%
+flowing around you're moving the atom
+that was like a dance thing
+
+ align:start position:0%
+that was like a dance thing
+ 
+
+ align:start position:0%
+that was like a dance thing
+that could be like a new dance move that
+
+ align:start position:0%
+that could be like a new dance move that
+ 
+
+ align:start position:0%
+that could be like a new dance move that
+you try out tonight the sea of electrons
+
+ align:start position:0%
+you try out tonight the sea of electrons
+ 
+
+ align:start position:0%
+you try out tonight the sea of electrons
+dance move i'm just saying
+
+ align:start position:0%
+dance move i'm just saying
+ 
+
+ align:start position:0%
+dance move i'm just saying
+that so the sea of elect i'm not gonna
+
+ align:start position:0%
+that so the sea of elect i'm not gonna
+ 
+
+ align:start position:0%
+that so the sea of elect i'm not gonna
+do it again but the sea of electrons
+
+ align:start position:0%
+do it again but the sea of electrons
+ 
+
+ align:start position:0%
+do it again but the sea of electrons
+is able to move around the ions as
+
+ align:start position:0%
+is able to move around the ions as
+ 
+
+ align:start position:0%
+is able to move around the ions as
+they're distorting because the metal
+
+ align:start position:0%
+they're distorting because the metal
+ 
+
+ align:start position:0%
+they're distorting because the metal
+bond is not so directional
+
+ align:start position:0%
+bond is not so directional
+ 
+
+ align:start position:0%
+bond is not so directional
+the metal bond is not so directional
+
+ align:start position:0%
+the metal bond is not so directional
+ 
+
+ align:start position:0%
+the metal bond is not so directional
+because think about it what is holding
+
+ align:start position:0%
+because think about it what is holding
+ 
+
+ align:start position:0%
+because think about it what is holding
+the metal together
+
+ align:start position:0%
+the metal together
+ 
+
+ align:start position:0%
+the metal together
+it's these interactions between the
+
+ align:start position:0%
+it's these interactions between the
+ 
+
+ align:start position:0%
+it's these interactions between the
+house and the kids that are roaming all
+
+ align:start position:0%
+house and the kids that are roaming all
+ 
+
+ align:start position:0%
+house and the kids that are roaming all
+over the place
+
+ align:start position:0%
+over the place
+ 
+
+ align:start position:0%
+over the place
+there's a kid over there over there it
+
+ align:start position:0%
+there's a kid over there over there it
+ 
+
+ align:start position:0%
+there's a kid over there over there it
+doesn't matter just give me a
+
+ align:start position:0%
+doesn't matter just give me a
+ 
+
+ align:start position:0%
+doesn't matter just give me a
+give me a little bit of positive you
+
+ align:start position:0%
+give me a little bit of positive you
+ 
+
+ align:start position:0%
+give me a little bit of positive you
+know a little bit of negative charge so
+
+ align:start position:0%
+know a little bit of negative charge so
+ 
+
+ align:start position:0%
+know a little bit of negative charge so
+i can feel an attraction
+
+ align:start position:0%
+i can feel an attraction
+ 
+
+ align:start position:0%
+i can feel an attraction
+but that's the metal that's why
+
+ align:start position:0%
+but that's the metal that's why
+ 
+
+ align:start position:0%
+but that's the metal that's why
+it is so able to deform in the way it
+
+ align:start position:0%
+it is so able to deform in the way it
+ 
+
+ align:start position:0%
+it is so able to deform in the way it
+does
+
+ align:start position:0%
+does
+ 
+
+ align:start position:0%
+does
+right because those atoms are moving
+
+ align:start position:0%
+right because those atoms are moving
+ 
+
+ align:start position:0%
+right because those atoms are moving
+around and the electrons are just kind
+
+ align:start position:0%
+around and the electrons are just kind
+ 
+
+ align:start position:0%
+around and the electrons are just kind
+of there as this happy c and the bonding
+
+ align:start position:0%
+of there as this happy c and the bonding
+ 
+
+ align:start position:0%
+of there as this happy c and the bonding
+remains it doesn't break that's the key
+
+ align:start position:0%
+remains it doesn't break that's the key
+ 
+
+ align:start position:0%
+remains it doesn't break that's the key
+otherwise this thing would just crack so
+
+ align:start position:0%
+otherwise this thing would just crack so
+ 
+
+ align:start position:0%
+otherwise this thing would just crack so
+why are pulling
+
+ align:start position:0%
+why are pulling
+ 
+
+ align:start position:0%
+why are pulling
+check this one out you can take a 10
+
+ align:start position:0%
+check this one out you can take a 10
+ 
+
+ align:start position:0%
+check this one out you can take a 10
+centimeter
+
+ align:start position:0%
+centimeter
+ 
+
+ align:start position:0%
+centimeter
+by one centimeter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+platinum rod and you can spin that into
+
+ align:start position:0%
+platinum rod and you can spin that into
+ 
+
+ align:start position:0%
+platinum rod and you can spin that into
+a wire and this is done
+
+ align:start position:0%
+a wire and this is done
+ 
+
+ align:start position:0%
+a wire and this is done
+this is a very thin case for effect but
+
+ align:start position:0%
+this is a very thin case for effect but
+ 
+
+ align:start position:0%
+this is a very thin case for effect but
+you can make
+
+ align:start position:0%
+you can make
+ 
+
+ align:start position:0%
+you can make
+a 0.006 millimeter
+
+ align:start position:0%
+a 0.006 millimeter
+ 
+
+ align:start position:0%
+a 0.006 millimeter
+diameter wire and you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+27.77 kilometers of wire
+
+ align:start position:0%
+27.77 kilometers of wire
+ 
+
+ align:start position:0%
+27.77 kilometers of wire
+now that's because of ductility the only
+
+ align:start position:0%
+now that's because of ductility the only
+ 
+
+ align:start position:0%
+now that's because of ductility the only
+reason i can get from
+
+ align:start position:0%
+reason i can get from
+ 
+
+ align:start position:0%
+reason i can get from
+point a to point b there is because i'm
+
+ align:start position:0%
+point a to point b there is because i'm
+ 
+
+ align:start position:0%
+point a to point b there is because i'm
+not breaking this apart and that's how
+
+ align:start position:0%
+not breaking this apart and that's how
+ 
+
+ align:start position:0%
+not breaking this apart and that's how
+thin i can get
+
+ align:start position:0%
+thin i can get
+ 
+
+ align:start position:0%
+thin i can get
+27 millimeter sorry diameter
+
+ align:start position:0%
+27 millimeter sorry diameter
+ 
+
+ align:start position:0%
+27 millimeter sorry diameter
+when i pull it and i thought that was a
+
+ align:start position:0%
+when i pull it and i thought that was a
+ 
+
+ align:start position:0%
+when i pull it and i thought that was a
+really good example of
+
+ align:start position:0%
+really good example of
+ 
+
+ align:start position:0%
+really good example of
+why this matters because
+
+ align:start position:0%
+why this matters because
+ 
+
+ align:start position:0%
+why this matters because
+maybe you've noticed but wires are
+
+ align:start position:0%
+maybe you've noticed but wires are
+ 
+
+ align:start position:0%
+maybe you've noticed but wires are
+really important to us
+
+ align:start position:0%
+really important to us
+ 
+
+ align:start position:0%
+really important to us
+right we use them a lot and and so
+
+ align:start position:0%
+right we use them a lot and and so
+ 
+
+ align:start position:0%
+right we use them a lot and and so
+you know you just saw a cartoon with
+
+ align:start position:0%
+you know you just saw a cartoon with
+ 
+
+ align:start position:0%
+you know you just saw a cartoon with
+electrons
+
+ align:start position:0%
+electrons
+ 
+
+ align:start position:0%
+electrons
+here's a cartoon that i thought was
+
+ align:start position:0%
+here's a cartoon that i thought was
+ 
+
+ align:start position:0%
+here's a cartoon that i thought was
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+um that shows kind of a wire pulling set
+
+ align:start position:0%
+um that shows kind of a wire pulling set
+ 
+
+ align:start position:0%
+um that shows kind of a wire pulling set
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+so now this is there's
+
+ align:start position:0%
+so now this is there's
+ 
+
+ align:start position:0%
+so now this is there's
+eye reducing the diameter that's a
+
+ align:start position:0%
+eye reducing the diameter that's a
+ 
+
+ align:start position:0%
+eye reducing the diameter that's a
+double further reduction can take place
+
+ align:start position:0%
+double further reduction can take place
+ 
+
+ align:start position:0%
+double further reduction can take place
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+extra dyes the drawn wire is finally
+
+ align:start position:0%
+extra dyes the drawn wire is finally
+ 
+
+ align:start position:0%
+extra dyes the drawn wire is finally
+wound on a spool
+
+ align:start position:0%
+wound on a spool
+ 
+
+ align:start position:0%
+wound on a spool
+this transformation elongates the wire
+
+ align:start position:0%
+this transformation elongates the wire
+ 
+
+ align:start position:0%
+this transformation elongates the wire
+one meter of 5.5 millimeter wire rod
+
+ align:start position:0%
+one meter of 5.5 millimeter wire rod
+ 
+
+ align:start position:0%
+one meter of 5.5 millimeter wire rod
+can be drawn to 30 meters with one
+
+ align:start position:0%
+can be drawn to 30 meters with one
+ 
+
+ align:start position:0%
+can be drawn to 30 meters with one
+millimeter diameter
+
+ align:start position:0%
+millimeter diameter
+ 
+
+ align:start position:0%
+millimeter diameter
+or 484 meters with 0.25 millimeters damp
+
+ align:start position:0%
+or 484 meters with 0.25 millimeters damp
+ 
+
+ align:start position:0%
+or 484 meters with 0.25 millimeters damp
+okay now that is a cartoon
+
+ align:start position:0%
+okay now that is a cartoon
+ 
+
+ align:start position:0%
+okay now that is a cartoon
+and um and i think you know it's always
+
+ align:start position:0%
+and um and i think you know it's always
+ 
+
+ align:start position:0%
+and um and i think you know it's always
+good when you see cartoons like this
+
+ align:start position:0%
+good when you see cartoons like this
+ 
+
+ align:start position:0%
+good when you see cartoons like this
+you know you don't know go look up what
+
+ align:start position:0%
+you know you don't know go look up what
+ 
+
+ align:start position:0%
+you know you don't know go look up what
+the real deal is
+
+ align:start position:0%
+the real deal is
+ 
+
+ align:start position:0%
+the real deal is
+what does it really look like to draw
+
+ align:start position:0%
+what does it really look like to draw
+ 
+
+ align:start position:0%
+what does it really look like to draw
+wires and i found
+
+ align:start position:0%
+wires and i found
+ 
+
+ align:start position:0%
+wires and i found
+pretty cool so this is an actual wire
+
+ align:start position:0%
+pretty cool so this is an actual wire
+ 
+
+ align:start position:0%
+pretty cool so this is an actual wire
+drawing plant
+
+ align:start position:0%
+drawing plant
+ 
+
+ align:start position:0%
+drawing plant
+okay and this is what it looks like now
+
+ align:start position:0%
+okay and this is what it looks like now
+ 
+
+ align:start position:0%
+okay and this is what it looks like now
+there's no audio here but i just want to
+
+ align:start position:0%
+there's no audio here but i just want to
+ 
+
+ align:start position:0%
+there's no audio here but i just want to
+show you the magnitude those are huge
+
+ align:start position:0%
+show you the magnitude those are huge
+ 
+
+ align:start position:0%
+show you the magnitude those are huge
+towers that are melting metals to give
+
+ align:start position:0%
+towers that are melting metals to give
+ 
+
+ align:start position:0%
+towers that are melting metals to give
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+this first rod right and then it goes
+
+ align:start position:0%
+this first rod right and then it goes
+ 
+
+ align:start position:0%
+this first rod right and then it goes
+through one
+
+ align:start position:0%
+through one
+ 
+
+ align:start position:0%
+through one
+after the other and look at it being
+
+ align:start position:0%
+after the other and look at it being
+ 
+
+ align:start position:0%
+after the other and look at it being
+pulled being pulled in at some diameter
+
+ align:start position:0%
+pulled being pulled in at some diameter
+ 
+
+ align:start position:0%
+pulled being pulled in at some diameter
+and it comes out at a different diameter
+
+ align:start position:0%
+and it comes out at a different diameter
+ 
+
+ align:start position:0%
+and it comes out at a different diameter
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but i wanted to show you the scope and
+
+ align:start position:0%
+but i wanted to show you the scope and
+ 
+
+ align:start position:0%
+but i wanted to show you the scope and
+size of this okay so there
+
+ align:start position:0%
+size of this okay so there
+ 
+
+ align:start position:0%
+size of this okay so there
+is this is just one of there's a person
+
+ align:start position:0%
+is this is just one of there's a person
+ 
+
+ align:start position:0%
+is this is just one of there's a person
+and so you get a sense of the
+
+ align:start position:0%
+and so you get a sense of the
+ 
+
+ align:start position:0%
+and so you get a sense of the
+of the size and then you can also see
+
+ align:start position:0%
+of the size and then you can also see
+ 
+
+ align:start position:0%
+of the size and then you can also see
+something when you go visit these
+
+ align:start position:0%
+something when you go visit these
+ 
+
+ align:start position:0%
+something when you go visit these
+factories
+
+ align:start position:0%
+factories
+ 
+
+ align:start position:0%
+factories
+and i have visited these factories
+
+ align:start position:0%
+and i have visited these factories
+ 
+
+ align:start position:0%
+and i have visited these factories
+there's always a lot of this happening
+
+ align:start position:0%
+there's always a lot of this happening
+ 
+
+ align:start position:0%
+there's always a lot of this happening
+why things are getting really hot right
+
+ align:start position:0%
+why things are getting really hot right
+ 
+
+ align:start position:0%
+why things are getting really hot right
+when you're spinning things like wire at
+
+ align:start position:0%
+when you're spinning things like wire at
+ 
+
+ align:start position:0%
+when you're spinning things like wire at
+a very high velocity
+
+ align:start position:0%
+a very high velocity
+ 
+
+ align:start position:0%
+a very high velocity
+things heat up so you get water all over
+
+ align:start position:0%
+things heat up so you get water all over
+ 
+
+ align:start position:0%
+things heat up so you get water all over
+the place right so there's water
+
+ align:start position:0%
+the place right so there's water
+ 
+
+ align:start position:0%
+the place right so there's water
+being sprayed in factories all over the
+
+ align:start position:0%
+being sprayed in factories all over the
+ 
+
+ align:start position:0%
+being sprayed in factories all over the
+place
+
+ align:start position:0%
+place
+ 
+
+ align:start position:0%
+place
+because you got to keep stuff cool or
+
+ align:start position:0%
+because you got to keep stuff cool or
+ 
+
+ align:start position:0%
+because you got to keep stuff cool or
+there's water baths that you run these
+
+ align:start position:0%
+there's water baths that you run these
+ 
+
+ align:start position:0%
+there's water baths that you run these
+things through
+
+ align:start position:0%
+things through
+ 
+
+ align:start position:0%
+things through
+right and then you got to think about
+
+ align:start position:0%
+right and then you got to think about
+ 
+
+ align:start position:0%
+right and then you got to think about
+well does this thing interact with water
+
+ align:start position:0%
+well does this thing interact with water
+ 
+
+ align:start position:0%
+well does this thing interact with water
+how does the water play a role it all
+
+ align:start position:0%
+how does the water play a role it all
+ 
+
+ align:start position:0%
+how does the water play a role it all
+comes down to the electrons
+
+ align:start position:0%
+comes down to the electrons
+ 
+
+ align:start position:0%
+comes down to the electrons
+and it once they've actually drawn the
+
+ align:start position:0%
+and it once they've actually drawn the
+ 
+
+ align:start position:0%
+and it once they've actually drawn the
+wire out over this huge factory
+
+ align:start position:0%
+wire out over this huge factory
+ 
+
+ align:start position:0%
+wire out over this huge factory
+they can actually weave it back together
+
+ align:start position:0%
+they can actually weave it back together
+ 
+
+ align:start position:0%
+they can actually weave it back together
+so i found this this is the same factory
+
+ align:start position:0%
+so i found this this is the same factory
+ 
+
+ align:start position:0%
+so i found this this is the same factory
+now these things here are doing the
+
+ align:start position:0%
+now these things here are doing the
+ 
+
+ align:start position:0%
+now these things here are doing the
+opposite so these are huge drums
+
+ align:start position:0%
+opposite so these are huge drums
+ 
+
+ align:start position:0%
+opposite so these are huge drums
+about the size of a person and each of
+
+ align:start position:0%
+about the size of a person and each of
+ 
+
+ align:start position:0%
+about the size of a person and each of
+these got
+
+ align:start position:0%
+these got
+ 
+
+ align:start position:0%
+these got
+a wire that was drawn right
+
+ align:start position:0%
+a wire that was drawn right
+ 
+
+ align:start position:0%
+a wire that was drawn right
+and now again because of the ductility
+
+ align:start position:0%
+and now again because of the ductility
+ 
+
+ align:start position:0%
+and now again because of the ductility
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+you can also move the wires play with
+
+ align:start position:0%
+you can also move the wires play with
+ 
+
+ align:start position:0%
+you can also move the wires play with
+the wires and you can weave them
+
+ align:start position:0%
+the wires and you can weave them
+ 
+
+ align:start position:0%
+the wires and you can weave them
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+you can weave them right back together
+
+ align:start position:0%
+you can weave them right back together
+ 
+
+ align:start position:0%
+you can weave them right back together
+into a thread that looks like that which
+
+ align:start position:0%
+into a thread that looks like that which
+ 
+
+ align:start position:0%
+into a thread that looks like that which
+we all have seen
+
+ align:start position:0%
+we all have seen
+ 
+
+ align:start position:0%
+we all have seen
+you know i think many many times all of
+
+ align:start position:0%
+you know i think many many times all of
+ 
+
+ align:start position:0%
+you know i think many many times all of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+processing all of this manufacturability
+
+ align:start position:0%
+processing all of this manufacturability
+ 
+
+ align:start position:0%
+processing all of this manufacturability
+has to do with the electron c
+
+ align:start position:0%
+has to do with the electron c
+ 
+
+ align:start position:0%
+has to do with the electron c
+that's why we have wires okay
+
+ align:start position:0%
+that's why we have wires okay
+ 
+
+ align:start position:0%
+that's why we have wires okay
+now a couple more small points
+
+ align:start position:0%
+now a couple more small points
+ 
+
+ align:start position:0%
+now a couple more small points
+so we're going to go back to this
+
+ align:start position:0%
+so we're going to go back to this
+ 
+
+ align:start position:0%
+so we're going to go back to this
+picture because
+
+ align:start position:0%
+picture because
+ 
+
+ align:start position:0%
+picture because
+this is how we started um
+
+ align:start position:0%
+this is how we started um
+ 
+
+ align:start position:0%
+this is how we started um
+and when this is that 1d
+
+ align:start position:0%
+and when this is that 1d
+ 
+
+ align:start position:0%
+and when this is that 1d
+remember that 1d model that we used
+
+ align:start position:0%
+remember that 1d model that we used
+ 
+
+ align:start position:0%
+remember that 1d model that we used
+to introduce band theory all right
+
+ align:start position:0%
+to introduce band theory all right
+ 
+
+ align:start position:0%
+to introduce band theory all right
+and i want to go back to this
+
+ align:start position:0%
+and i want to go back to this
+ 
+
+ align:start position:0%
+and i want to go back to this
+um because what you can see
+
+ align:start position:0%
+um because what you can see
+ 
+
+ align:start position:0%
+um because what you can see
+is that you know
+
+ align:start position:0%
+is that you know
+ 
+
+ align:start position:0%
+is that you know
+if i if i think about this as
+
+ align:start position:0%
+if i if i think about this as
+ 
+
+ align:start position:0%
+if i if i think about this as
+bonding and anti-bonding orbitals all
+
+ align:start position:0%
+bonding and anti-bonding orbitals all
+ 
+
+ align:start position:0%
+bonding and anti-bonding orbitals all
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+mixed in here then you can also get a
+
+ align:start position:0%
+mixed in here then you can also get a
+ 
+
+ align:start position:0%
+mixed in here then you can also get a
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+but just like in the the the dimers that
+
+ align:start position:0%
+but just like in the the the dimers that
+ 
+
+ align:start position:0%
+but just like in the the the dimers that
+we made
+
+ align:start position:0%
+we made
+ 
+
+ align:start position:0%
+we made
+right n2 o2
+
+ align:start position:0%
+right n2 o2
+ 
+
+ align:start position:0%
+right n2 o2
+right remember no bond order
+
+ align:start position:0%
+right remember no bond order
+ 
+
+ align:start position:0%
+right remember no bond order
+right it counts how many electrons are
+
+ align:start position:0%
+right it counts how many electrons are
+ 
+
+ align:start position:0%
+right it counts how many electrons are
+in an antibonding orbital doesn't just
+
+ align:start position:0%
+in an antibonding orbital doesn't just
+ 
+
+ align:start position:0%
+in an antibonding orbital doesn't just
+because it's in an anti-bonding orbital
+
+ align:start position:0%
+because it's in an anti-bonding orbital
+ 
+
+ align:start position:0%
+because it's in an anti-bonding orbital
+doesn't mean it's not there
+
+ align:start position:0%
+doesn't mean it's not there
+ 
+
+ align:start position:0%
+doesn't mean it's not there
+in the system it's the same with these
+
+ align:start position:0%
+in the system it's the same with these
+ 
+
+ align:start position:0%
+in the system it's the same with these
+metal bands
+
+ align:start position:0%
+metal bands
+ 
+
+ align:start position:0%
+metal bands
+right some of them may be good for
+
+ align:start position:0%
+right some of them may be good for
+ 
+
+ align:start position:0%
+right some of them may be good for
+bonding some of them may not
+
+ align:start position:0%
+bonding some of them may not
+ 
+
+ align:start position:0%
+bonding some of them may not
+but just like in the dimers the bond
+
+ align:start position:0%
+but just like in the dimers the bond
+ 
+
+ align:start position:0%
+but just like in the dimers the bond
+order is related to
+
+ align:start position:0%
+order is related to
+ 
+
+ align:start position:0%
+order is related to
+you know the strength of that bond
+
+ align:start position:0%
+you know the strength of that bond
+ 
+
+ align:start position:0%
+you know the strength of that bond
+remember right and then no it's like a
+
+ align:start position:0%
+remember right and then no it's like a
+ 
+
+ align:start position:0%
+remember right and then no it's like a
+bond order of two and a half and then if
+
+ align:start position:0%
+bond order of two and a half and then if
+ 
+
+ align:start position:0%
+bond order of two and a half and then if
+i took an electron
+
+ align:start position:0%
+i took an electron
+ 
+
+ align:start position:0%
+i took an electron
+out it actually got stronger the bonding
+
+ align:start position:0%
+out it actually got stronger the bonding
+ 
+
+ align:start position:0%
+out it actually got stronger the bonding
+got stronger
+
+ align:start position:0%
+got stronger
+ 
+
+ align:start position:0%
+got stronger
+it's the same thing in the case you can
+
+ align:start position:0%
+it's the same thing in the case you can
+ 
+
+ align:start position:0%
+it's the same thing in the case you can
+think about this the same way
+
+ align:start position:0%
+think about this the same way
+ 
+
+ align:start position:0%
+think about this the same way
+in metals you have a band i mean some of
+
+ align:start position:0%
+in metals you have a band i mean some of
+ 
+
+ align:start position:0%
+in metals you have a band i mean some of
+these orbitals are not going to be
+
+ align:start position:0%
+these orbitals are not going to be
+ 
+
+ align:start position:0%
+these orbitals are not going to be
+bonding orbitals and some of them are
+
+ align:start position:0%
+bonding orbitals and some of them are
+ 
+
+ align:start position:0%
+bonding orbitals and some of them are
+going to be much more about the bonding
+
+ align:start position:0%
+going to be much more about the bonding
+ 
+
+ align:start position:0%
+going to be much more about the bonding
+and and so that's going to relate to
+
+ align:start position:0%
+and and so that's going to relate to
+ 
+
+ align:start position:0%
+and and so that's going to relate to
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+like boiling point right so like
+
+ align:start position:0%
+like boiling point right so like
+ 
+
+ align:start position:0%
+like boiling point right so like
+you know metals have boiling points too
+
+ align:start position:0%
+you know metals have boiling points too
+ 
+
+ align:start position:0%
+you know metals have boiling points too
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and so if you look now go back to the
+
+ align:start position:0%
+and so if you look now go back to the
+ 
+
+ align:start position:0%
+and so if you look now go back to the
+periodic table
+
+ align:start position:0%
+periodic table
+ 
+
+ align:start position:0%
+periodic table
+remember the highest electrical
+
+ align:start position:0%
+remember the highest electrical
+ 
+
+ align:start position:0%
+remember the highest electrical
+conductivity was here well that had to
+
+ align:start position:0%
+conductivity was here well that had to
+ 
+
+ align:start position:0%
+conductivity was here well that had to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+with with that right there right with
+
+ align:start position:0%
+with with that right there right with
+ 
+
+ align:start position:0%
+with with that right there right with
+the the position
+
+ align:start position:0%
+the the position
+ 
+
+ align:start position:0%
+the the position
+with the filling of the orbitals to give
+
+ align:start position:0%
+with the filling of the orbitals to give
+ 
+
+ align:start position:0%
+with the filling of the orbitals to give
+me the freest electron i can imagine
+
+ align:start position:0%
+me the freest electron i can imagine
+ 
+
+ align:start position:0%
+me the freest electron i can imagine
+right after those d orbitals are filled
+
+ align:start position:0%
+right after those d orbitals are filled
+ 
+
+ align:start position:0%
+right after those d orbitals are filled
+that s
+
+ align:start position:0%
+that s
+ 
+
+ align:start position:0%
+that s
+but but if i'm thinking about whether i
+
+ align:start position:0%
+but but if i'm thinking about whether i
+ 
+
+ align:start position:0%
+but but if i'm thinking about whether i
+filled anti-bonding orbitals
+
+ align:start position:0%
+filled anti-bonding orbitals
+ 
+
+ align:start position:0%
+filled anti-bonding orbitals
+because now i'm thinking about the
+
+ align:start position:0%
+because now i'm thinking about the
+ 
+
+ align:start position:0%
+because now i'm thinking about the
+strength of the bonds you see a
+
+ align:start position:0%
+strength of the bonds you see a
+ 
+
+ align:start position:0%
+strength of the bonds you see a
+different trend and you see
+
+ align:start position:0%
+different trend and you see
+ 
+
+ align:start position:0%
+different trend and you see
+something that you would expect first of
+
+ align:start position:0%
+something that you would expect first of
+ 
+
+ align:start position:0%
+something that you would expect first of
+all you see a huge variability
+
+ align:start position:0%
+all you see a huge variability
+ 
+
+ align:start position:0%
+all you see a huge variability
+but you see that the ones that are
+
+ align:start position:0%
+but you see that the ones that are
+ 
+
+ align:start position:0%
+but you see that the ones that are
+strongest the highest boiling points
+
+ align:start position:0%
+strongest the highest boiling points
+ 
+
+ align:start position:0%
+strongest the highest boiling points
+are going to be the ones where you fill
+
+ align:start position:0%
+are going to be the ones where you fill
+ 
+
+ align:start position:0%
+are going to be the ones where you fill
+that band
+
+ align:start position:0%
+that band
+ 
+
+ align:start position:0%
+that band
+those those bands roughly halfway
+
+ align:start position:0%
+those those bands roughly halfway
+ 
+
+ align:start position:0%
+those those bands roughly halfway
+right and this is also why
+
+ align:start position:0%
+right and this is also why
+ 
+
+ align:start position:0%
+right and this is also why
+you know in a metallic bond in a
+
+ align:start position:0%
+you know in a metallic bond in a
+ 
+
+ align:start position:0%
+you know in a metallic bond in a
+metallic bond
+
+ align:start position:0%
+metallic bond
+ 
+
+ align:start position:0%
+metallic bond
+you've got this enormous range right so
+
+ align:start position:0%
+you've got this enormous range right so
+ 
+
+ align:start position:0%
+you've got this enormous range right so
+you've got
+
+ align:start position:0%
+you've got
+ 
+
+ align:start position:0%
+you've got
+um you know it's the weakest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for elements like you know for elements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with near empty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+near empty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+valence
+
+ align:start position:0%
+valence
+ 
+
+ align:start position:0%
+valence
+shells right valence subshells
+
+ align:start position:0%
+shells right valence subshells
+ 
+
+ align:start position:0%
+shells right valence subshells
+i don't think you know like uh okay
+
+ align:start position:0%
+i don't think you know like uh okay
+ 
+
+ align:start position:0%
+i don't think you know like uh okay
+cesium
+
+ align:start position:0%
+cesium
+ 
+
+ align:start position:0%
+cesium
+is an example uh or
+
+ align:start position:0%
+is an example uh or
+ 
+
+ align:start position:0%
+is an example uh or
+near full
+
+ align:start position:0%
+near full
+ 
+
+ align:start position:0%
+near full
+like for example in mercury now
+
+ align:start position:0%
+like for example in mercury now
+ 
+
+ align:start position:0%
+like for example in mercury now
+mercury is actually a liquid at room
+
+ align:start position:0%
+mercury is actually a liquid at room
+ 
+
+ align:start position:0%
+mercury is actually a liquid at room
+temperature because of this
+
+ align:start position:0%
+temperature because of this
+ 
+
+ align:start position:0%
+temperature because of this
+right there it is there it is right
+
+ align:start position:0%
+right there it is there it is right
+ 
+
+ align:start position:0%
+right there it is there it is right
+you know why because i've i've
+
+ align:start position:0%
+you know why because i've i've
+ 
+
+ align:start position:0%
+you know why because i've i've
+remembered like the beryllium dimer
+
+ align:start position:0%
+remembered like the beryllium dimer
+ 
+
+ align:start position:0%
+remembered like the beryllium dimer
+right like i filled all these electrons
+
+ align:start position:0%
+right like i filled all these electrons
+ 
+
+ align:start position:0%
+right like i filled all these electrons
+in there
+
+ align:start position:0%
+in there
+ 
+
+ align:start position:0%
+in there
+and and they're they're causing this
+
+ align:start position:0%
+and and they're they're causing this
+ 
+
+ align:start position:0%
+and and they're they're causing this
+really weak bonding
+
+ align:start position:0%
+really weak bonding
+ 
+
+ align:start position:0%
+really weak bonding
+right this really weak bonding because i
+
+ align:start position:0%
+right this really weak bonding because i
+ 
+
+ align:start position:0%
+right this really weak bonding because i
+had to put all of them into the
+
+ align:start position:0%
+had to put all of them into the
+ 
+
+ align:start position:0%
+had to put all of them into the
+antibonding orbitals
+
+ align:start position:0%
+antibonding orbitals
+ 
+
+ align:start position:0%
+antibonding orbitals
+i couldn't do this trick that right over
+
+ align:start position:0%
+i couldn't do this trick that right over
+ 
+
+ align:start position:0%
+i couldn't do this trick that right over
+here right one column next to it
+
+ align:start position:0%
+here right one column next to it
+ 
+
+ align:start position:0%
+here right one column next to it
+these guys can have tricks where they
+
+ align:start position:0%
+these guys can have tricks where they
+ 
+
+ align:start position:0%
+these guys can have tricks where they
+you know now this is this is bonding
+
+ align:start position:0%
+you know now this is this is bonding
+ 
+
+ align:start position:0%
+you know now this is this is bonding
+strength this is not electrical
+
+ align:start position:0%
+strength this is not electrical
+ 
+
+ align:start position:0%
+strength this is not electrical
+conductivity
+
+ align:start position:0%
+conductivity
+ 
+
+ align:start position:0%
+conductivity
+right but here they're filling the d and
+
+ align:start position:0%
+right but here they're filling the d and
+ 
+
+ align:start position:0%
+right but here they're filling the d and
+then the s
+
+ align:start position:0%
+then the s
+ 
+
+ align:start position:0%
+then the s
+is free not here here they're all filled
+
+ align:start position:0%
+is free not here here they're all filled
+ 
+
+ align:start position:0%
+is free not here here they're all filled
+bonding and anti-bonding
+
+ align:start position:0%
+bonding and anti-bonding
+ 
+
+ align:start position:0%
+bonding and anti-bonding
+no tricks now uh
+
+ align:start position:0%
+no tricks now uh
+ 
+
+ align:start position:0%
+no tricks now uh
+if you look at the the melting
+
+ align:start position:0%
+if you look at the the melting
+ 
+
+ align:start position:0%
+if you look at the the melting
+temperature that's why the one of the
+
+ align:start position:0%
+temperature that's why the one of the
+ 
+
+ align:start position:0%
+temperature that's why the one of the
+strongest elements would be tungsten
+
+ align:start position:0%
+strongest elements would be tungsten
+ 
+
+ align:start position:0%
+strongest elements would be tungsten
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+strongest would be
+
+ align:start position:0%
+strongest would be
+ 
+
+ align:start position:0%
+strongest would be
+example tungsten where you've got
+
+ align:start position:0%
+example tungsten where you've got
+ 
+
+ align:start position:0%
+example tungsten where you've got
+a range of melting the melting point of
+
+ align:start position:0%
+a range of melting the melting point of
+ 
+
+ align:start position:0%
+a range of melting the melting point of
+tungsten
+
+ align:start position:0%
+tungsten
+ 
+
+ align:start position:0%
+tungsten
+and this is not the same as the boiling
+
+ align:start position:0%
+and this is not the same as the boiling
+ 
+
+ align:start position:0%
+and this is not the same as the boiling
+point the melting point of tungsten
+
+ align:start position:0%
+point the melting point of tungsten
+ 
+
+ align:start position:0%
+point the melting point of tungsten
+is 36 80 degrees c
+
+ align:start position:0%
+is 36 80 degrees c
+ 
+
+ align:start position:0%
+is 36 80 degrees c
+that's a liquid at room temperature
+
+ align:start position:0%
+that's a liquid at room temperature
+ 
+
+ align:start position:0%
+that's a liquid at room temperature
+and the melting point of cesium
+
+ align:start position:0%
+and the melting point of cesium
+ 
+
+ align:start position:0%
+and the melting point of cesium
+is 28 degrees c
+
+ align:start position:0%
+is 28 degrees c
+ 
+
+ align:start position:0%
+is 28 degrees c
+look at that range and it all has to do
+
+ align:start position:0%
+look at that range and it all has to do
+ 
+
+ align:start position:0%
+look at that range and it all has to do
+with how these electrons are filling the
+
+ align:start position:0%
+with how these electrons are filling the
+ 
+
+ align:start position:0%
+with how these electrons are filling the
+metallic bands and more than that
+
+ align:start position:0%
+metallic bands and more than that
+ 
+
+ align:start position:0%
+metallic bands and more than that
+because it also has to do with the way
+
+ align:start position:0%
+because it also has to do with the way
+ 
+
+ align:start position:0%
+because it also has to do with the way
+the atoms come together
+
+ align:start position:0%
+the atoms come together
+ 
+
+ align:start position:0%
+the atoms come together
+and that is going to be the topic of
+
+ align:start position:0%
+and that is going to be the topic of
+ 
+
+ align:start position:0%
+and that is going to be the topic of
+next week now that would
+
+ align:start position:0%
+next week now that would
+ 
+
+ align:start position:0%
+next week now that would
+would have been a perfect line to end on
+
+ align:start position:0%
+would have been a perfect line to end on
+ 
+
+ align:start position:0%
+would have been a perfect line to end on
+because i said the words next week but i
+
+ align:start position:0%
+because i said the words next week but i
+ 
+
+ align:start position:0%
+because i said the words next week but i
+just want to make one more point
+
+ align:start position:0%
+just want to make one more point
+ 
+
+ align:start position:0%
+just want to make one more point
+i can't stop because there's one more
+
+ align:start position:0%
+i can't stop because there's one more
+ 
+
+ align:start position:0%
+i can't stop because there's one more
+thing i want to show
+
+ align:start position:0%
+thing i want to show
+ 
+
+ align:start position:0%
+thing i want to show
+very quickly in one minute and that is
+
+ align:start position:0%
+very quickly in one minute and that is
+ 
+
+ align:start position:0%
+very quickly in one minute and that is
+you know going back to this picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right if you're thinking about filling
+
+ align:start position:0%
+right if you're thinking about filling
+ 
+
+ align:start position:0%
+right if you're thinking about filling
+right and i've got like my 3s remember
+
+ align:start position:0%
+right and i've got like my 3s remember
+ 
+
+ align:start position:0%
+right and i've got like my 3s remember
+i've got like my 3s
+
+ align:start position:0%
+i've got like my 3s
+ 
+
+ align:start position:0%
+i've got like my 3s
+okay and okay let's
+
+ align:start position:0%
+okay and okay let's
+ 
+
+ align:start position:0%
+okay and okay let's
+let's put 2p here and then
+
+ align:start position:0%
+let's put 2p here and then
+ 
+
+ align:start position:0%
+let's put 2p here and then
+3s and 3p now remember
+
+ align:start position:0%
+3s and 3p now remember
+ 
+
+ align:start position:0%
+3s and 3p now remember
+for metals for a lot of these metals
+
+ align:start position:0%
+for metals for a lot of these metals
+ 
+
+ align:start position:0%
+for metals for a lot of these metals
+what ends up happening
+
+ align:start position:0%
+what ends up happening
+ 
+
+ align:start position:0%
+what ends up happening
+is what i showed you before on wednesday
+
+ align:start position:0%
+is what i showed you before on wednesday
+ 
+
+ align:start position:0%
+is what i showed you before on wednesday
+which is that
+
+ align:start position:0%
+which is that
+ 
+
+ align:start position:0%
+which is that
+you get actually an overlap of this so
+
+ align:start position:0%
+you get actually an overlap of this so
+ 
+
+ align:start position:0%
+you get actually an overlap of this so
+you get a band
+
+ align:start position:0%
+you get a band
+ 
+
+ align:start position:0%
+you get a band
+that would be the 3s 3p band
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sodium magnesium aluminum these are all
+
+ align:start position:0%
+sodium magnesium aluminum these are all
+ 
+
+ align:start position:0%
+sodium magnesium aluminum these are all
+come together like this to form a single
+
+ align:start position:0%
+come together like this to form a single
+ 
+
+ align:start position:0%
+come together like this to form a single
+band
+
+ align:start position:0%
+band
+ 
+
+ align:start position:0%
+band
+now remember i don't need you to know
+
+ align:start position:0%
+now remember i don't need you to know
+ 
+
+ align:start position:0%
+now remember i don't need you to know
+how to do this
+
+ align:start position:0%
+how to do this
+ 
+
+ align:start position:0%
+how to do this
+we would tell you if it does this or not
+
+ align:start position:0%
+we would tell you if it does this or not
+ 
+
+ align:start position:0%
+we would tell you if it does this or not
+right we talked about that i'm not going
+
+ align:start position:0%
+right we talked about that i'm not going
+ 
+
+ align:start position:0%
+right we talked about that i'm not going
+to ask you to know
+
+ align:start position:0%
+to ask you to know
+ 
+
+ align:start position:0%
+to ask you to know
+you know how these come together do they
+
+ align:start position:0%
+you know how these come together do they
+ 
+
+ align:start position:0%
+you know how these come together do they
+form a continuous band or not
+
+ align:start position:0%
+form a continuous band or not
+ 
+
+ align:start position:0%
+form a continuous band or not
+but in this case they do for that row
+
+ align:start position:0%
+but in this case they do for that row
+ 
+
+ align:start position:0%
+but in this case they do for that row
+and so you know
+
+ align:start position:0%
+and so you know
+ 
+
+ align:start position:0%
+and so you know
+i've got eight electrons eight electron
+
+ align:start position:0%
+i've got eight electrons eight electron
+ 
+
+ align:start position:0%
+i've got eight electrons eight electron
+capacity
+
+ align:start position:0%
+capacity
+ 
+
+ align:start position:0%
+capacity
+in that band per atom
+
+ align:start position:0%
+in that band per atom
+ 
+
+ align:start position:0%
+in that band per atom
+that's the capacity of the band so now i
+
+ align:start position:0%
+that's the capacity of the band so now i
+ 
+
+ align:start position:0%
+that's the capacity of the band so now i
+want to talk about how is this band
+
+ align:start position:0%
+want to talk about how is this band
+ 
+
+ align:start position:0%
+want to talk about how is this band
+filled well for sodium
+
+ align:start position:0%
+filled well for sodium
+ 
+
+ align:start position:0%
+filled well for sodium
+i'm gonna fill it 1 8 because it's got
+
+ align:start position:0%
+i'm gonna fill it 1 8 because it's got
+ 
+
+ align:start position:0%
+i'm gonna fill it 1 8 because it's got
+just one electron that it's putting into
+
+ align:start position:0%
+just one electron that it's putting into
+ 
+
+ align:start position:0%
+just one electron that it's putting into
+that band
+
+ align:start position:0%
+that band
+ 
+
+ align:start position:0%
+that band
+right and for magnesium right for
+
+ align:start position:0%
+right and for magnesium right for
+ 
+
+ align:start position:0%
+right and for magnesium right for
+magnesium
+
+ align:start position:0%
+magnesium
+ 
+
+ align:start position:0%
+magnesium
+i'm going to fill it with two electrons
+
+ align:start position:0%
+i'm going to fill it with two electrons
+ 
+
+ align:start position:0%
+i'm going to fill it with two electrons
+and aluminum
+
+ align:start position:0%
+and aluminum
+ 
+
+ align:start position:0%
+and aluminum
+would be three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so on okay so so it goes back to the
+
+ align:start position:0%
+and so on okay so so it goes back to the
+ 
+
+ align:start position:0%
+and so on okay so so it goes back to the
+same picture as before we're filling the
+
+ align:start position:0%
+same picture as before we're filling the
+ 
+
+ align:start position:0%
+same picture as before we're filling the
+bands
+
+ align:start position:0%
+bands
+ 
+
+ align:start position:0%
+bands
+but now we've got 10 to the 23rd 24th
+
+ align:start position:0%
+but now we've got 10 to the 23rd 24th
+ 
+
+ align:start position:0%
+but now we've got 10 to the 23rd 24th
+atoms
+
+ align:start position:0%
+atoms
+ 
+
+ align:start position:0%
+atoms
+and so we think about filling the bands
+
+ align:start position:0%
+and so we think about filling the bands
+ 
+
+ align:start position:0%
+and so we think about filling the bands
+as you know
+
+ align:start position:0%
+as you know
+ 
+
+ align:start position:0%
+as you know
+how what's the occupancy per atom that
+
+ align:start position:0%
+how what's the occupancy per atom that
+ 
+
+ align:start position:0%
+how what's the occupancy per atom that
+you could put in there
+
+ align:start position:0%
+you could put in there
+ 
+
+ align:start position:0%
+you could put in there
+right and so i could tell you if i had a
+
+ align:start position:0%
+right and so i could tell you if i had a
+ 
+
+ align:start position:0%
+right and so i could tell you if i had a
+mole of sodium how many electrons i have
+
+ align:start position:0%
+mole of sodium how many electrons i have
+ 
+
+ align:start position:0%
+mole of sodium how many electrons i have
+in this band right it's a mole
+
+ align:start position:0%
+in this band right it's a mole
+ 
+
+ align:start position:0%
+in this band right it's a mole
+right and how did you fill it and that
+
+ align:start position:0%
+right and how did you fill it and that
+ 
+
+ align:start position:0%
+right and how did you fill it and that
+ties into what i just talked about which
+
+ align:start position:0%
+ties into what i just talked about which
+ 
+
+ align:start position:0%
+ties into what i just talked about which
+is how that
+
+ align:start position:0%
+is how that
+ 
+
+ align:start position:0%
+is how that
+relates to bonding strength okay now we
+
+ align:start position:0%
+relates to bonding strength okay now we
+ 
+
+ align:start position:0%
+relates to bonding strength okay now we
+can stop
+
+ align:start position:0%
+can stop
+ 
+
+ align:start position:0%
+can stop
+on monday we will start talking about
+
+ align:start position:0%
+on monday we will start talking about
+ 
+
+ align:start position:0%
+on monday we will start talking about
+crystals
+
+ align:start position:0%
+crystals
+ 
+
+ align:start position:0%
+crystals
+have a very good weekend
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/ZCqgBRoH_Tk.txt b/ZCqgBRoH_Tk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5b5b29f20d46bdd793994bc513b65571bb390e54
--- /dev/null
+++ b/ZCqgBRoH_Tk.txt
@@ -0,0 +1,1627 @@
+align:start position:0%
+ 
+so the engineering of birds is a course
+
+ align:start position:0%
+so the engineering of birds is a course
+ 
+
+ align:start position:0%
+so the engineering of birds is a course
+uh that's something we call a freshman
+
+ align:start position:0%
+uh that's something we call a freshman
+ 
+
+ align:start position:0%
+uh that's something we call a freshman
+uh Service Learning freshman seminar and
+
+ align:start position:0%
+uh Service Learning freshman seminar and
+ 
+
+ align:start position:0%
+uh Service Learning freshman seminar and
+so there there's really two things going
+
+ align:start position:0%
+so there there's really two things going
+ 
+
+ align:start position:0%
+so there there's really two things going
+on here freshman seminars are set up so
+
+ align:start position:0%
+on here freshman seminars are set up so
+ 
+
+ align:start position:0%
+on here freshman seminars are set up so
+that they're a small learning group um
+
+ align:start position:0%
+that they're a small learning group um
+ 
+
+ align:start position:0%
+that they're a small learning group um
+in the core MIT freshman year the
+
+ align:start position:0%
+in the core MIT freshman year the
+ 
+
+ align:start position:0%
+in the core MIT freshman year the
+students mostly are in much larger
+
+ align:start position:0%
+students mostly are in much larger
+ 
+
+ align:start position:0%
+students mostly are in much larger
+lecture courses with say 200 students in
+
+ align:start position:0%
+lecture courses with say 200 students in
+ 
+
+ align:start position:0%
+lecture courses with say 200 students in
+a lecture and the seminars are set up to
+
+ align:start position:0%
+a lecture and the seminars are set up to
+ 
+
+ align:start position:0%
+a lecture and the seminars are set up to
+be in a smaller group there's at most
+
+ align:start position:0%
+be in a smaller group there's at most
+ 
+
+ align:start position:0%
+be in a smaller group there's at most
+eight students and typically I have half
+
+ align:start position:0%
+eight students and typically I have half
+ 
+
+ align:start position:0%
+eight students and typically I have half
+a dozen students in the seminar I've
+
+ align:start position:0%
+a dozen students in the seminar I've
+ 
+
+ align:start position:0%
+a dozen students in the seminar I've
+done it for a few years now um so one
+
+ align:start position:0%
+done it for a few years now um so one
+ 
+
+ align:start position:0%
+done it for a few years now um so one
+one goal is to have a smaller group of
+
+ align:start position:0%
+one goal is to have a smaller group of
+ 
+
+ align:start position:0%
+one goal is to have a smaller group of
+students and for them to get to know a
+
+ align:start position:0%
+students and for them to get to know a
+ 
+
+ align:start position:0%
+students and for them to get to know a
+faculty member bit more personal level
+
+ align:start position:0%
+faculty member bit more personal level
+ 
+
+ align:start position:0%
+faculty member bit more personal level
+uh the other thing we do is we try to do
+
+ align:start position:0%
+uh the other thing we do is we try to do
+ 
+
+ align:start position:0%
+uh the other thing we do is we try to do
+do some community service project so
+
+ align:start position:0%
+do some community service project so
+ 
+
+ align:start position:0%
+do some community service project so
+we've done uh several of these freshman
+
+ align:start position:0%
+we've done uh several of these freshman
+ 
+
+ align:start position:0%
+we've done uh several of these freshman
+seminars they they've been on different
+
+ align:start position:0%
+seminars they they've been on different
+ 
+
+ align:start position:0%
+seminars they they've been on different
+topics each year but uh what we do is is
+
+ align:start position:0%
+topics each year but uh what we do is is
+ 
+
+ align:start position:0%
+topics each year but uh what we do is is
+we do a service project for the Boston
+
+ align:start position:0%
+we do a service project for the Boston
+ 
+
+ align:start position:0%
+we do a service project for the Boston
+Nature Center which is run by the
+
+ align:start position:0%
+Nature Center which is run by the
+ 
+
+ align:start position:0%
+Nature Center which is run by the
+Massachusetts Autobon society and me
+
+ align:start position:0%
+Massachusetts Autobon society and me
+ 
+
+ align:start position:0%
+Massachusetts Autobon society and me
+personally I love Natural History I love
+
+ align:start position:0%
+personally I love Natural History I love
+ 
+
+ align:start position:0%
+personally I love Natural History I love
+trees and plants and birds and all this
+
+ align:start position:0%
+trees and plants and birds and all this
+ 
+
+ align:start position:0%
+trees and plants and birds and all this
+stuff so every year when I choose a
+
+ align:start position:0%
+stuff so every year when I choose a
+ 
+
+ align:start position:0%
+stuff so every year when I choose a
+topic I I just pick something that I'm
+
+ align:start position:0%
+topic I I just pick something that I'm
+ 
+
+ align:start position:0%
+topic I I just pick something that I'm
+interested in and I know a little bit
+
+ align:start position:0%
+interested in and I know a little bit
+ 
+
+ align:start position:0%
+interested in and I know a little bit
+about from an engineering point of view
+
+ align:start position:0%
+about from an engineering point of view
+ 
+
+ align:start position:0%
+about from an engineering point of view
+and we we develop educational displays
+
+ align:start position:0%
+and we we develop educational displays
+ 
+
+ align:start position:0%
+and we we develop educational displays
+and give them to the Nature Center um at
+
+ align:start position:0%
+and give them to the Nature Center um at
+ 
+
+ align:start position:0%
+and give them to the Nature Center um at
+the end of the year so that that's kind
+
+ align:start position:0%
+the end of the year so that that's kind
+ 
+
+ align:start position:0%
+the end of the year so that that's kind
+of the um the overview of what we're
+
+ align:start position:0%
+of the um the overview of what we're
+ 
+
+ align:start position:0%
+of the um the overview of what we're
+trying to do uh in particular the the
+
+ align:start position:0%
+trying to do uh in particular the the
+ 
+
+ align:start position:0%
+trying to do uh in particular the the
+one we did this last fall on the
+
+ align:start position:0%
+one we did this last fall on the
+ 
+
+ align:start position:0%
+one we did this last fall on the
+engineering of birds we developed a
+
+ align:start position:0%
+engineering of birds we developed a
+ 
+
+ align:start position:0%
+engineering of birds we developed a
+number of PowerPoint presentations so
+
+ align:start position:0%
+number of PowerPoint presentations so
+ 
+
+ align:start position:0%
+number of PowerPoint presentations so
+one was on bird nests and one was on how
+
+ align:start position:0%
+one was on bird nests and one was on how
+ 
+
+ align:start position:0%
+one was on bird nests and one was on how
+birds fly and one was on bird migration
+
+ align:start position:0%
+birds fly and one was on bird migration
+ 
+
+ align:start position:0%
+birds fly and one was on bird migration
+uh so they were on different topics that
+
+ align:start position:0%
+uh so they were on different topics that
+ 
+
+ align:start position:0%
+uh so they were on different topics that
+had some kind of engineering content to
+
+ align:start position:0%
+had some kind of engineering content to
+ 
+
+ align:start position:0%
+had some kind of engineering content to
+them the idea is that the students learn
+
+ align:start position:0%
+them the idea is that the students learn
+ 
+
+ align:start position:0%
+them the idea is that the students learn
+some engineering principles while
+
+ align:start position:0%
+some engineering principles while
+ 
+
+ align:start position:0%
+some engineering principles while
+they're putting together some community
+
+ align:start position:0%
+they're putting together some community
+ 
+
+ align:start position:0%
+they're putting together some community
+service project so what we do in the
+
+ align:start position:0%
+service project so what we do in the
+ 
+
+ align:start position:0%
+service project so what we do in the
+course is the first time we meet we meet
+
+ align:start position:0%
+course is the first time we meet we meet
+ 
+
+ align:start position:0%
+course is the first time we meet we meet
+here at MIT and I just describe what the
+
+ align:start position:0%
+here at MIT and I just describe what the
+ 
+
+ align:start position:0%
+here at MIT and I just describe what the
+topic is that we're going to be
+
+ align:start position:0%
+topic is that we're going to be
+ 
+
+ align:start position:0%
+topic is that we're going to be
+discussing so this past year it was
+
+ align:start position:0%
+discussing so this past year it was
+ 
+
+ align:start position:0%
+discussing so this past year it was
+Birds um and then the second week we we
+
+ align:start position:0%
+Birds um and then the second week we we
+ 
+
+ align:start position:0%
+Birds um and then the second week we we
+meet once a week um and the second week
+
+ align:start position:0%
+meet once a week um and the second week
+ 
+
+ align:start position:0%
+meet once a week um and the second week
+uh we went out to the Nature Center and
+
+ align:start position:0%
+uh we went out to the Nature Center and
+ 
+
+ align:start position:0%
+uh we went out to the Nature Center and
+we met with the people there we talk to
+
+ align:start position:0%
+we met with the people there we talk to
+ 
+
+ align:start position:0%
+we met with the people there we talk to
+them about what they would like us to do
+
+ align:start position:0%
+them about what they would like us to do
+ 
+
+ align:start position:0%
+them about what they would like us to do
+and what the sorts of things that we
+
+ align:start position:0%
+and what the sorts of things that we
+ 
+
+ align:start position:0%
+and what the sorts of things that we
+were thinking of doing so we had a a
+
+ align:start position:0%
+were thinking of doing so we had a a
+ 
+
+ align:start position:0%
+were thinking of doing so we had a a
+meeting with the people there we looked
+
+ align:start position:0%
+meeting with the people there we looked
+ 
+
+ align:start position:0%
+meeting with the people there we looked
+around the Nature Center uh we've done
+
+ align:start position:0%
+around the Nature Center uh we've done
+ 
+
+ align:start position:0%
+around the Nature Center uh we've done
+this the last couple of years and we
+
+ align:start position:0%
+this the last couple of years and we
+ 
+
+ align:start position:0%
+this the last couple of years and we
+looked at the projects from the previous
+
+ align:start position:0%
+looked at the projects from the previous
+ 
+
+ align:start position:0%
+looked at the projects from the previous
+years so the students this year could
+
+ align:start position:0%
+years so the students this year could
+ 
+
+ align:start position:0%
+years so the students this year could
+kind of see what we've done in the past
+
+ align:start position:0%
+kind of see what we've done in the past
+ 
+
+ align:start position:0%
+kind of see what we've done in the past
+so we usually have some of these field
+
+ align:start position:0%
+so we usually have some of these field
+ 
+
+ align:start position:0%
+so we usually have some of these field
+trips and you know depending on what the
+
+ align:start position:0%
+trips and you know depending on what the
+ 
+
+ align:start position:0%
+trips and you know depending on what the
+project is we we do different field
+
+ align:start position:0%
+project is we we do different field
+ 
+
+ align:start position:0%
+project is we we do different field
+trips um and then we come back to MIT
+
+ align:start position:0%
+trips um and then we come back to MIT
+ 
+
+ align:start position:0%
+trips um and then we come back to MIT
+and we have you know the next week we
+
+ align:start position:0%
+and we have you know the next week we
+ 
+
+ align:start position:0%
+and we have you know the next week we
+usually discuss what the projects are
+
+ align:start position:0%
+usually discuss what the projects are
+ 
+
+ align:start position:0%
+usually discuss what the projects are
+going to be and I assign the students
+
+ align:start position:0%
+going to be and I assign the students
+ 
+
+ align:start position:0%
+going to be and I assign the students
+into groups so typically they do it in
+
+ align:start position:0%
+into groups so typically they do it in
+ 
+
+ align:start position:0%
+into groups so typically they do it in
+pairs so we might have three pairs of
+
+ align:start position:0%
+pairs so we might have three pairs of
+ 
+
+ align:start position:0%
+pairs so we might have three pairs of
+students do three projects and then I
+
+ align:start position:0%
+students do three projects and then I
+ 
+
+ align:start position:0%
+students do three projects and then I
+try to give them some material some
+
+ align:start position:0%
+try to give them some material some
+ 
+
+ align:start position:0%
+try to give them some material some
+background material and information and
+
+ align:start position:0%
+background material and information and
+ 
+
+ align:start position:0%
+background material and information and
+then they they put together some sort of
+
+ align:start position:0%
+then they they put together some sort of
+ 
+
+ align:start position:0%
+then they they put together some sort of
+a poster or this year it was a
+
+ align:start position:0%
+a poster or this year it was a
+ 
+
+ align:start position:0%
+a poster or this year it was a
+PowerPoint presentation and they have a
+
+ align:start position:0%
+PowerPoint presentation and they have a
+ 
+
+ align:start position:0%
+PowerPoint presentation and they have a
+couple of weeks to work on it and then
+
+ align:start position:0%
+couple of weeks to work on it and then
+ 
+
+ align:start position:0%
+couple of weeks to work on it and then
+they bring it back and we have a session
+
+ align:start position:0%
+they bring it back and we have a session
+ 
+
+ align:start position:0%
+they bring it back and we have a session
+where we we kind everybody kind of
+
+ align:start position:0%
+where we we kind everybody kind of
+ 
+
+ align:start position:0%
+where we we kind everybody kind of
+critiques the what people have got so
+
+ align:start position:0%
+critiques the what people have got so
+ 
+
+ align:start position:0%
+critiques the what people have got so
+far and then they go away and they work
+
+ align:start position:0%
+far and then they go away and they work
+ 
+
+ align:start position:0%
+far and then they go away and they work
+on it on it again and then by the end of
+
+ align:start position:0%
+on it on it again and then by the end of
+ 
+
+ align:start position:0%
+on it on it again and then by the end of
+the term they've got something pretty
+
+ align:start position:0%
+the term they've got something pretty
+ 
+
+ align:start position:0%
+the term they've got something pretty
+much put together and I I sort of help
+
+ align:start position:0%
+much put together and I I sort of help
+ 
+
+ align:start position:0%
+much put together and I I sort of help
+them edit it at the end of the term so
+
+ align:start position:0%
+them edit it at the end of the term so
+ 
+
+ align:start position:0%
+them edit it at the end of the term so
+so it's a combination of um getting to
+
+ align:start position:0%
+so it's a combination of um getting to
+ 
+
+ align:start position:0%
+so it's a combination of um getting to
+go out and do some field trips and then
+
+ align:start position:0%
+go out and do some field trips and then
+ 
+
+ align:start position:0%
+go out and do some field trips and then
+putting together some educational
+
+ align:start position:0%
+putting together some educational
+ 
+
+ align:start position:0%
+putting together some educational
+displays and I try and explain
+
+ align:start position:0%
+displays and I try and explain
+ 
+
+ align:start position:0%
+displays and I try and explain
+engineering principles that they need to
+
+ align:start position:0%
+engineering principles that they need to
+ 
+
+ align:start position:0%
+engineering principles that they need to
+to make their displays uh put their
+
+ align:start position:0%
+to make their displays uh put their
+ 
+
+ align:start position:0%
+to make their displays uh put their
+displays together so the way this course
+
+ align:start position:0%
+displays together so the way this course
+ 
+
+ align:start position:0%
+displays together so the way this course
+fits into the curriculum is that it's
+
+ align:start position:0%
+fits into the curriculum is that it's
+ 
+
+ align:start position:0%
+fits into the curriculum is that it's
+really set up for freshman and it's part
+
+ align:start position:0%
+really set up for freshman and it's part
+ 
+
+ align:start position:0%
+really set up for freshman and it's part
+of the freshman year uh so it it it's
+
+ align:start position:0%
+of the freshman year uh so it it it's
+ 
+
+ align:start position:0%
+of the freshman year uh so it it it's
+sort of a uh sort of complements the
+
+ align:start position:0%
+sort of a uh sort of complements the
+ 
+
+ align:start position:0%
+sort of a uh sort of complements the
+more hardcore you know physics and
+
+ align:start position:0%
+more hardcore you know physics and
+ 
+
+ align:start position:0%
+more hardcore you know physics and
+chemistry and math that the students are
+
+ align:start position:0%
+chemistry and math that the students are
+ 
+
+ align:start position:0%
+chemistry and math that the students are
+taking but in in in another sense it's a
+
+ align:start position:0%
+taking but in in in another sense it's a
+ 
+
+ align:start position:0%
+taking but in in in another sense it's a
+way of of sort of showing freshman
+
+ align:start position:0%
+way of of sort of showing freshman
+ 
+
+ align:start position:0%
+way of of sort of showing freshman
+students something about the materials
+
+ align:start position:0%
+students something about the materials
+ 
+
+ align:start position:0%
+students something about the materials
+department and so it's a way to
+
+ align:start position:0%
+department and so it's a way to
+ 
+
+ align:start position:0%
+department and so it's a way to
+introduce students to this department
+
+ align:start position:0%
+introduce students to this department
+ 
+
+ align:start position:0%
+introduce students to this department
+and I find almost every year I do it at
+
+ align:start position:0%
+and I find almost every year I do it at
+ 
+
+ align:start position:0%
+and I find almost every year I do it at
+least one or two of the students ends up
+
+ align:start position:0%
+least one or two of the students ends up
+ 
+
+ align:start position:0%
+least one or two of the students ends up
+majoring in Material Science and
+
+ align:start position:0%
+majoring in Material Science and
+ 
+
+ align:start position:0%
+majoring in Material Science and
+Engineering I mean one of the things I
+
+ align:start position:0%
+Engineering I mean one of the things I
+ 
+
+ align:start position:0%
+Engineering I mean one of the things I
+find is that when freshmen come to MIT
+
+ align:start position:0%
+find is that when freshmen come to MIT
+ 
+
+ align:start position:0%
+find is that when freshmen come to MIT
+you know they're all excited it's MIT
+
+ align:start position:0%
+you know they're all excited it's MIT
+ 
+
+ align:start position:0%
+you know they're all excited it's MIT
+it's engineering science this is great
+
+ align:start position:0%
+it's engineering science this is great
+ 
+
+ align:start position:0%
+it's engineering science this is great
+um but they don't really have a good
+
+ align:start position:0%
+um but they don't really have a good
+ 
+
+ align:start position:0%
+um but they don't really have a good
+idea about what the different types of
+
+ align:start position:0%
+idea about what the different types of
+ 
+
+ align:start position:0%
+idea about what the different types of
+engineering do so during their freshman
+
+ align:start position:0%
+engineering do so during their freshman
+ 
+
+ align:start position:0%
+engineering do so during their freshman
+year they all take a common core and
+
+ align:start position:0%
+year they all take a common core and
+ 
+
+ align:start position:0%
+year they all take a common core and
+then towards the end of the spring term
+
+ align:start position:0%
+then towards the end of the spring term
+ 
+
+ align:start position:0%
+then towards the end of the spring term
+they have to choose a major and a lot of
+
+ align:start position:0%
+they have to choose a major and a lot of
+ 
+
+ align:start position:0%
+they have to choose a major and a lot of
+them don't really know what material
+
+ align:start position:0%
+them don't really know what material
+ 
+
+ align:start position:0%
+them don't really know what material
+science in engineering is or what
+
+ align:start position:0%
+science in engineering is or what
+ 
+
+ align:start position:0%
+science in engineering is or what
+chemical engineering is or what
+
+ align:start position:0%
+chemical engineering is or what
+ 
+
+ align:start position:0%
+chemical engineering is or what
+mechanical engineering is and this gives
+
+ align:start position:0%
+mechanical engineering is and this gives
+ 
+
+ align:start position:0%
+mechanical engineering is and this gives
+them kind of a taste of what material
+
+ align:start position:0%
+them kind of a taste of what material
+ 
+
+ align:start position:0%
+them kind of a taste of what material
+scientist do and I think they find that
+
+ align:start position:0%
+scientist do and I think they find that
+ 
+
+ align:start position:0%
+scientist do and I think they find that
+that quite useful so so this course is
+
+ align:start position:0%
+that quite useful so so this course is
+ 
+
+ align:start position:0%
+that quite useful so so this course is
+taught in such a way that every year we
+
+ align:start position:0%
+taught in such a way that every year we
+ 
+
+ align:start position:0%
+taught in such a way that every year we
+we do a different topic and we produce
+
+ align:start position:0%
+we do a different topic and we produce
+ 
+
+ align:start position:0%
+we do a different topic and we produce
+different displays for the Nature Center
+
+ align:start position:0%
+different displays for the Nature Center
+ 
+
+ align:start position:0%
+different displays for the Nature Center
+and for the Science Museum and the way
+
+ align:start position:0%
+and for the Science Museum and the way
+ 
+
+ align:start position:0%
+and for the Science Museum and the way
+it really started was I got an email
+
+ align:start position:0%
+it really started was I got an email
+ 
+
+ align:start position:0%
+it really started was I got an email
+from somebody in the public service
+
+ align:start position:0%
+from somebody in the public service
+ 
+
+ align:start position:0%
+from somebody in the public service
+center saying would I like to teach a
+
+ align:start position:0%
+center saying would I like to teach a
+ 
+
+ align:start position:0%
+center saying would I like to teach a
+service learning freshman seminar and I
+
+ align:start position:0%
+service learning freshman seminar and I
+ 
+
+ align:start position:0%
+service learning freshman seminar and I
+had done freshman seminars before but
+
+ align:start position:0%
+had done freshman seminars before but
+ 
+
+ align:start position:0%
+had done freshman seminars before but
+more in a just a seminar format um and I
+
+ align:start position:0%
+more in a just a seminar format um and I
+ 
+
+ align:start position:0%
+more in a just a seminar format um and I
+hadn't really done the service learning
+
+ align:start position:0%
+hadn't really done the service learning
+ 
+
+ align:start position:0%
+hadn't really done the service learning
+component and so I had to kind of think
+
+ align:start position:0%
+component and so I had to kind of think
+ 
+
+ align:start position:0%
+component and so I had to kind of think
+about well what would that actually mean
+
+ align:start position:0%
+about well what would that actually mean
+ 
+
+ align:start position:0%
+about well what would that actually mean
+I mean I my my background is in
+
+ align:start position:0%
+I mean I my my background is in
+ 
+
+ align:start position:0%
+I mean I my my background is in
+mechanics which is kind of Hardcore
+
+ align:start position:0%
+mechanics which is kind of Hardcore
+ 
+
+ align:start position:0%
+mechanics which is kind of Hardcore
+equations and you know doing experiments
+
+ align:start position:0%
+equations and you know doing experiments
+ 
+
+ align:start position:0%
+equations and you know doing experiments
+it wasn't obvious to me at first how I
+
+ align:start position:0%
+it wasn't obvious to me at first how I
+ 
+
+ align:start position:0%
+it wasn't obvious to me at first how I
+was going to make a service learning
+
+ align:start position:0%
+was going to make a service learning
+ 
+
+ align:start position:0%
+was going to make a service learning
+piece of this but as I said I I do love
+
+ align:start position:0%
+piece of this but as I said I I do love
+ 
+
+ align:start position:0%
+piece of this but as I said I I do love
+nature stuff I go bird watching and you
+
+ align:start position:0%
+nature stuff I go bird watching and you
+ 
+
+ align:start position:0%
+nature stuff I go bird watching and you
+know like to go walking in the woods
+
+ align:start position:0%
+know like to go walking in the woods
+ 
+
+ align:start position:0%
+know like to go walking in the woods
+that kind of stuff um and so I knew that
+
+ align:start position:0%
+that kind of stuff um and so I knew that
+ 
+
+ align:start position:0%
+that kind of stuff um and so I knew that
+the mass audabon was opening a new
+
+ align:start position:0%
+the mass audabon was opening a new
+ 
+
+ align:start position:0%
+the mass audabon was opening a new
+Nature Center and in fact it's just down
+
+ align:start position:0%
+Nature Center and in fact it's just down
+ 
+
+ align:start position:0%
+Nature Center and in fact it's just down
+the street from where I live it's it's
+
+ align:start position:0%
+the street from where I live it's it's
+ 
+
+ align:start position:0%
+the street from where I live it's it's
+very close to where I live and I had
+
+ align:start position:0%
+very close to where I live and I had
+ 
+
+ align:start position:0%
+very close to where I live and I had
+sort of gone to talk to the people there
+
+ align:start position:0%
+sort of gone to talk to the people there
+ 
+
+ align:start position:0%
+sort of gone to talk to the people there
+just to kind of find out about what they
+
+ align:start position:0%
+just to kind of find out about what they
+ 
+
+ align:start position:0%
+just to kind of find out about what they
+were doing and and uh I talked to my
+
+ align:start position:0%
+were doing and and uh I talked to my
+ 
+
+ align:start position:0%
+were doing and and uh I talked to my
+partner and we were you know we were
+
+ align:start position:0%
+partner and we were you know we were
+ 
+
+ align:start position:0%
+partner and we were you know we were
+thinking about what I could do she's
+
+ align:start position:0%
+thinking about what I could do she's
+ 
+
+ align:start position:0%
+thinking about what I could do she's
+actually involved with Service Learning
+
+ align:start position:0%
+actually involved with Service Learning
+ 
+
+ align:start position:0%
+actually involved with Service Learning
+at the Harvard Medical School and uh and
+
+ align:start position:0%
+at the Harvard Medical School and uh and
+ 
+
+ align:start position:0%
+at the Harvard Medical School and uh and
+she suggested you know you could you
+
+ align:start position:0%
+she suggested you know you could you
+ 
+
+ align:start position:0%
+she suggested you know you could you
+could do some educational things on this
+
+ align:start position:0%
+could do some educational things on this
+ 
+
+ align:start position:0%
+could do some educational things on this
+nature stuff that you do your research
+
+ align:start position:0%
+nature stuff that you do your research
+ 
+
+ align:start position:0%
+nature stuff that you do your research
+on so the idea behind Service Learning
+
+ align:start position:0%
+on so the idea behind Service Learning
+ 
+
+ align:start position:0%
+on so the idea behind Service Learning
+is to teach students some academic
+
+ align:start position:0%
+is to teach students some academic
+ 
+
+ align:start position:0%
+is to teach students some academic
+subject but to incorporate a community
+
+ align:start position:0%
+subject but to incorporate a community
+ 
+
+ align:start position:0%
+subject but to incorporate a community
+service aspect into it and there's
+
+ align:start position:0%
+service aspect into it and there's
+ 
+
+ align:start position:0%
+service aspect into it and there's
+various ways that people do this and
+
+ align:start position:0%
+various ways that people do this and
+ 
+
+ align:start position:0%
+various ways that people do this and
+what we've been doing is developing
+
+ align:start position:0%
+what we've been doing is developing
+ 
+
+ align:start position:0%
+what we've been doing is developing
+these educational projects for the
+
+ align:start position:0%
+these educational projects for the
+ 
+
+ align:start position:0%
+these educational projects for the
+Nature Center and for the science museum
+
+ align:start position:0%
+Nature Center and for the science museum
+ 
+
+ align:start position:0%
+Nature Center and for the science museum
+but one of the nice features that I
+
+ align:start position:0%
+but one of the nice features that I
+ 
+
+ align:start position:0%
+but one of the nice features that I
+found about it is it's a way of engaging
+
+ align:start position:0%
+found about it is it's a way of engaging
+ 
+
+ align:start position:0%
+found about it is it's a way of engaging
+the students it's a way of sort of
+
+ align:start position:0%
+the students it's a way of sort of
+ 
+
+ align:start position:0%
+the students it's a way of sort of
+giving them a project and it's not just
+
+ align:start position:0%
+giving them a project and it's not just
+ 
+
+ align:start position:0%
+giving them a project and it's not just
+a madeup project of something that I
+
+ align:start position:0%
+a madeup project of something that I
+ 
+
+ align:start position:0%
+a madeup project of something that I
+said you know go away and do this it's
+
+ align:start position:0%
+said you know go away and do this it's
+ 
+
+ align:start position:0%
+said you know go away and do this it's
+something that they feel somebody's
+
+ align:start position:0%
+something that they feel somebody's
+ 
+
+ align:start position:0%
+something that they feel somebody's
+actually going to make use of it
+
+ align:start position:0%
+actually going to make use of it
+ 
+
+ align:start position:0%
+actually going to make use of it
+actually makes a difference to somebody
+
+ align:start position:0%
+actually makes a difference to somebody
+ 
+
+ align:start position:0%
+actually makes a difference to somebody
+and one of the things I find is is by
+
+ align:start position:0%
+and one of the things I find is is by
+ 
+
+ align:start position:0%
+and one of the things I find is is by
+the end of the term uh it's sort of a
+
+ align:start position:0%
+the end of the term uh it's sort of a
+ 
+
+ align:start position:0%
+the end of the term uh it's sort of a
+win-win win situation you know I I get a
+
+ align:start position:0%
+win-win win situation you know I I get a
+ 
+
+ align:start position:0%
+win-win win situation you know I I get a
+big kick out of it just because I like
+
+ align:start position:0%
+big kick out of it just because I like
+ 
+
+ align:start position:0%
+big kick out of it just because I like
+doing these things but the students feel
+
+ align:start position:0%
+doing these things but the students feel
+ 
+
+ align:start position:0%
+doing these things but the students feel
+they've actually made something they've
+
+ align:start position:0%
+they've actually made something they've
+ 
+
+ align:start position:0%
+they've actually made something they've
+actually created something and they've
+
+ align:start position:0%
+actually created something and they've
+ 
+
+ align:start position:0%
+actually created something and they've
+given it to the Nature Center the
+
+ align:start position:0%
+given it to the Nature Center the
+ 
+
+ align:start position:0%
+given it to the Nature Center the
+Science Museum and and they're going to
+
+ align:start position:0%
+Science Museum and and they're going to
+ 
+
+ align:start position:0%
+Science Museum and and they're going to
+make use of it and then the Nature
+
+ align:start position:0%
+make use of it and then the Nature
+ 
+
+ align:start position:0%
+make use of it and then the Nature
+Center and the science museum feel like
+
+ align:start position:0%
+Center and the science museum feel like
+ 
+
+ align:start position:0%
+Center and the science museum feel like
+you know just out of the blue we've
+
+ align:start position:0%
+you know just out of the blue we've
+ 
+
+ align:start position:0%
+you know just out of the blue we've
+dropped in and and done something for
+
+ align:start position:0%
+dropped in and and done something for
+ 
+
+ align:start position:0%
+dropped in and and done something for
+them that they can use with school
+
+ align:start position:0%
+them that they can use with school
+ 
+
+ align:start position:0%
+them that they can use with school
+groups or with you know groups that come
+
+ align:start position:0%
+groups or with you know groups that come
+ 
+
+ align:start position:0%
+groups or with you know groups that come
+through their facilities so it's a
+
+ align:start position:0%
+through their facilities so it's a
+ 
+
+ align:start position:0%
+through their facilities so it's a
+really nice um a nice combination of of
+
+ align:start position:0%
+really nice um a nice combination of of
+ 
+
+ align:start position:0%
+really nice um a nice combination of of
+sort of giving the students sort of
+
+ align:start position:0%
+sort of giving the students sort of
+ 
+
+ align:start position:0%
+sort of giving the students sort of
+motivating the students and giving them
+
+ align:start position:0%
+motivating the students and giving them
+ 
+
+ align:start position:0%
+motivating the students and giving them
+a a concrete thing to work on that
+
+ align:start position:0%
+a a concrete thing to work on that
+ 
+
+ align:start position:0%
+a a concrete thing to work on that
+somebody else is going to use and then
+
+ align:start position:0%
+somebody else is going to use and then
+ 
+
+ align:start position:0%
+somebody else is going to use and then
+trying to benefit some group in the
+
+ align:start position:0%
+trying to benefit some group in the
+ 
+
+ align:start position:0%
+trying to benefit some group in the
+Community as well so i' I've enjoyed
+
+ align:start position:0%
+Community as well so i' I've enjoyed
+ 
+
+ align:start position:0%
+Community as well so i' I've enjoyed
+doing it uh for that
+
+ align:start position:0%
+doing it uh for that
+ 
+
+ align:start position:0%
+doing it uh for that
+reason
\ No newline at end of file
diff --git a/_KbfL3lVgag.txt b/_KbfL3lVgag.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2916a47509824ea15f7422c8e39a73a735c92ad5
--- /dev/null
+++ b/_KbfL3lVgag.txt
@@ -0,0 +1,6651 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when we introduced the discrete forier
+
+ align:start position:0%
+when we introduced the discrete forier
+ 
+
+ align:start position:0%
+when we introduced the discrete forier
+transform one of the important aspects
+
+ align:start position:0%
+transform one of the important aspects
+ 
+
+ align:start position:0%
+transform one of the important aspects
+of that transform that I stressed was
+
+ align:start position:0%
+of that transform that I stressed was
+ 
+
+ align:start position:0%
+of that transform that I stressed was
+the fact that the discret forier
+
+ align:start position:0%
+the fact that the discret forier
+ 
+
+ align:start position:0%
+the fact that the discret forier
+transform as opposed to the forier or Z
+
+ align:start position:0%
+transform as opposed to the forier or Z
+ 
+
+ align:start position:0%
+transform as opposed to the forier or Z
+transform actually has implications in
+
+ align:start position:0%
+transform actually has implications in
+ 
+
+ align:start position:0%
+transform actually has implications in
+terms of implementing discrete time
+
+ align:start position:0%
+terms of implementing discrete time
+ 
+
+ align:start position:0%
+terms of implementing discrete time
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+systems I commented or suggested that in
+
+ align:start position:0%
+systems I commented or suggested that in
+ 
+
+ align:start position:0%
+systems I commented or suggested that in
+fact a linear system or a digital filter
+
+ align:start position:0%
+fact a linear system or a digital filter
+ 
+
+ align:start position:0%
+fact a linear system or a digital filter
+could be implemented explicit licitly by
+
+ align:start position:0%
+could be implemented explicit licitly by
+ 
+
+ align:start position:0%
+could be implemented explicit licitly by
+Computing the discrete forier transform
+
+ align:start position:0%
+Computing the discrete forier transform
+ 
+
+ align:start position:0%
+Computing the discrete forier transform
+of a unit sample response and an input
+
+ align:start position:0%
+of a unit sample response and an input
+ 
+
+ align:start position:0%
+of a unit sample response and an input
+sequence multiplying these transforms
+
+ align:start position:0%
+sequence multiplying these transforms
+ 
+
+ align:start position:0%
+sequence multiplying these transforms
+together and then Computing the inverse
+
+ align:start position:0%
+together and then Computing the inverse
+ 
+
+ align:start position:0%
+together and then Computing the inverse
+discrete forier
+
+ align:start position:0%
+discrete forier
+ 
+
+ align:start position:0%
+discrete forier
+transform there is a very efficient
+
+ align:start position:0%
+transform there is a very efficient
+ 
+
+ align:start position:0%
+transform there is a very efficient
+algorithm in fact for computing the
+
+ align:start position:0%
+algorithm in fact for computing the
+ 
+
+ align:start position:0%
+algorithm in fact for computing the
+discrete 4A transform and so it will
+
+ align:start position:0%
+discrete 4A transform and so it will
+ 
+
+ align:start position:0%
+discrete 4A transform and so it will
+turn out and we won't see this right
+
+ align:start position:0%
+turn out and we won't see this right
+ 
+
+ align:start position:0%
+turn out and we won't see this right
+away but we'll see it toward the end of
+
+ align:start position:0%
+away but we'll see it toward the end of
+ 
+
+ align:start position:0%
+away but we'll see it toward the end of
+this set of cures it will turn out that
+
+ align:start position:0%
+this set of cures it will turn out that
+ 
+
+ align:start position:0%
+this set of cures it will turn out that
+in fact that's a very efficient way
+
+ align:start position:0%
+in fact that's a very efficient way
+ 
+
+ align:start position:0%
+in fact that's a very efficient way
+often of implementing a convolution or
+
+ align:start position:0%
+often of implementing a convolution or
+ 
+
+ align:start position:0%
+often of implementing a convolution or
+implementing a digital
+
+ align:start position:0%
+implementing a digital
+ 
+
+ align:start position:0%
+implementing a digital
+filter well in the last lecture we saw
+
+ align:start position:0%
+filter well in the last lecture we saw
+ 
+
+ align:start position:0%
+filter well in the last lecture we saw
+that Computing discrete forier
+
+ align:start position:0%
+that Computing discrete forier
+ 
+
+ align:start position:0%
+that Computing discrete forier
+transforms multiplying those together
+
+ align:start position:0%
+transforms multiplying those together
+ 
+
+ align:start position:0%
+transforms multiplying those together
+and then Computing the inverse discrete
+
+ align:start position:0%
+and then Computing the inverse discrete
+ 
+
+ align:start position:0%
+and then Computing the inverse discrete
+forier transform doesn't give us a
+
+ align:start position:0%
+forier transform doesn't give us a
+ 
+
+ align:start position:0%
+forier transform doesn't give us a
+convolution in the usual sense so in
+
+ align:start position:0%
+convolution in the usual sense so in
+ 
+
+ align:start position:0%
+convolution in the usual sense so in
+other words it doesn't give us a linear
+
+ align:start position:0%
+other words it doesn't give us a linear
+ 
+
+ align:start position:0%
+other words it doesn't give us a linear
+convolution ution it gives us a circular
+
+ align:start position:0%
+convolution ution it gives us a circular
+ 
+
+ align:start position:0%
+convolution ution it gives us a circular
+convolution and one of the important
+
+ align:start position:0%
+convolution and one of the important
+ 
+
+ align:start position:0%
+convolution and one of the important
+considerations in using the discrete
+
+ align:start position:0%
+considerations in using the discrete
+ 
+
+ align:start position:0%
+considerations in using the discrete
+forier transform to implement a digital
+
+ align:start position:0%
+forier transform to implement a digital
+ 
+
+ align:start position:0%
+forier transform to implement a digital
+filter or a discrete time system is to
+
+ align:start position:0%
+filter or a discrete time system is to
+ 
+
+ align:start position:0%
+filter or a discrete time system is to
+account for this circularity or to
+
+ align:start position:0%
+account for this circularity or to
+ 
+
+ align:start position:0%
+account for this circularity or to
+modify the circular convolution so that
+
+ align:start position:0%
+modify the circular convolution so that
+ 
+
+ align:start position:0%
+modify the circular convolution so that
+it looks like a linear
+
+ align:start position:0%
+it looks like a linear
+ 
+
+ align:start position:0%
+it looks like a linear
+convolution so in this lecture what I
+
+ align:start position:0%
+convolution so in this lecture what I
+ 
+
+ align:start position:0%
+convolution so in this lecture what I
+would like to concentrate on in fact
+
+ align:start position:0%
+would like to concentrate on in fact
+ 
+
+ align:start position:0%
+would like to concentrate on in fact
+entirely for the whole lecture is a
+
+ align:start position:0%
+entirely for the whole lecture is a
+ 
+
+ align:start position:0%
+entirely for the whole lecture is a
+discussion of circular convolution with
+
+ align:start position:0%
+discussion of circular convolution with
+ 
+
+ align:start position:0%
+discussion of circular convolution with
+the hope that at the end of this lecture
+
+ align:start position:0%
+the hope that at the end of this lecture
+ 
+
+ align:start position:0%
+the hope that at the end of this lecture
+there will be a very intuitive feeling
+
+ align:start position:0%
+there will be a very intuitive feeling
+ 
+
+ align:start position:0%
+there will be a very intuitive feeling
+for what circular convolution means and
+
+ align:start position:0%
+for what circular convolution means and
+ 
+
+ align:start position:0%
+for what circular convolution means and
+then also how you can use circular
+
+ align:start position:0%
+then also how you can use circular
+ 
+
+ align:start position:0%
+then also how you can use circular
+convolution to implement a linear
+
+ align:start position:0%
+convolution to implement a linear
+ 
+
+ align:start position:0%
+convolution to implement a linear
+convolution and consequently to
+
+ align:start position:0%
+convolution and consequently to
+ 
+
+ align:start position:0%
+convolution and consequently to
+implement a discrete time linear system
+
+ align:start position:0%
+implement a discrete time linear system
+ 
+
+ align:start position:0%
+implement a discrete time linear system
+for example to implement a digital
+
+ align:start position:0%
+for example to implement a digital
+ 
+
+ align:start position:0%
+for example to implement a digital
+filter well first of all to remind you
+
+ align:start position:0%
+filter well first of all to remind you
+ 
+
+ align:start position:0%
+filter well first of all to remind you
+of the con Evolution property that we
+
+ align:start position:0%
+of the con Evolution property that we
+ 
+
+ align:start position:0%
+of the con Evolution property that we
+derived last
+
+ align:start position:0%
+derived last
+ 
+
+ align:start position:0%
+derived last
+time we found that multiplying discrete
+
+ align:start position:0%
+time we found that multiplying discrete
+ 
+
+ align:start position:0%
+time we found that multiplying discrete
+forier transforms leads to a circular
+
+ align:start position:0%
+forier transforms leads to a circular
+ 
+
+ align:start position:0%
+forier transforms leads to a circular
+convolution which we denoted with an an
+
+ align:start position:0%
+convolution which we denoted with an an
+ 
+
+ align:start position:0%
+convolution which we denoted with an an
+n and a circle around it meaning an
+
+ align:start position:0%
+n and a circle around it meaning an
+ 
+
+ align:start position:0%
+n and a circle around it meaning an
+endpoint circuit
+
+ align:start position:0%
+endpoint circuit
+ 
+
+ align:start position:0%
+endpoint circuit
+convolution and what that basically
+
+ align:start position:0%
+convolution and what that basically
+ 
+
+ align:start position:0%
+convolution and what that basically
+corresponded to was a periodic
+
+ align:start position:0%
+corresponded to was a periodic
+ 
+
+ align:start position:0%
+corresponded to was a periodic
+convolution of two periodic sequences
+
+ align:start position:0%
+convolution of two periodic sequences
+ 
+
+ align:start position:0%
+convolution of two periodic sequences
+which are generated from these finite
+
+ align:start position:0%
+which are generated from these finite
+ 
+
+ align:start position:0%
+which are generated from these finite
+length sequences by periodically
+
+ align:start position:0%
+length sequences by periodically
+ 
+
+ align:start position:0%
+length sequences by periodically
+repeating them with a period of capital
+
+ align:start position:0%
+repeating them with a period of capital
+ 
+
+ align:start position:0%
+repeating them with a period of capital
+n and then finally extracting one
+
+ align:start position:0%
+n and then finally extracting one
+ 
+
+ align:start position:0%
+n and then finally extracting one
+endpoint period from that the result
+
+ align:start position:0%
+endpoint period from that the result
+ 
+
+ align:start position:0%
+endpoint period from that the result
+being the circular convolution of X1 of
+
+ align:start position:0%
+being the circular convolution of X1 of
+ 
+
+ align:start position:0%
+being the circular convolution of X1 of
+n with X2 of
+
+ align:start position:0%
+n with X2 of
+ 
+
+ align:start position:0%
+n with X2 of
+n notationally also I sometimes rewrote
+
+ align:start position:0%
+n notationally also I sometimes rewrote
+ 
+
+ align:start position:0%
+n notationally also I sometimes rewrote
+this in a slightly different
+
+ align:start position:0%
+this in a slightly different
+ 
+
+ align:start position:0%
+this in a slightly different
+way where the periodic sequence X1
+
+ align:start position:0%
+way where the periodic sequence X1
+ 
+
+ align:start position:0%
+way where the periodic sequence X1
+Matilda of M or n could also be written
+
+ align:start position:0%
+Matilda of M or n could also be written
+ 
+
+ align:start position:0%
+Matilda of M or n could also be written
+with a modular notation a double
+
+ align:start position:0%
+with a modular notation a double
+ 
+
+ align:start position:0%
+with a modular notation a double
+parentheses and a subscript capital N
+
+ align:start position:0%
+parentheses and a subscript capital N
+ 
+
+ align:start position:0%
+parentheses and a subscript capital N
+indicating that X1 of n or
+
+ align:start position:0%
+indicating that X1 of n or
+ 
+
+ align:start position:0%
+indicating that X1 of n or
+M X1 Tilda of M is generated from X1 of
+
+ align:start position:0%
+M X1 Tilda of M is generated from X1 of
+ 
+
+ align:start position:0%
+M X1 Tilda of M is generated from X1 of
+M by simply taking this argument modulo
+
+ align:start position:0%
+M by simply taking this argument modulo
+ 
+
+ align:start position:0%
+M by simply taking this argument modulo
+capital m capital N so this is an
+
+ align:start position:0%
+capital m capital N so this is an
+ 
+
+ align:start position:0%
+capital m capital N so this is an
+alternative way of writing this and
+
+ align:start position:0%
+alternative way of writing this and
+ 
+
+ align:start position:0%
+alternative way of writing this and
+finally I pointed out in the last
+
+ align:start position:0%
+finally I pointed out in the last
+ 
+
+ align:start position:0%
+finally I pointed out in the last
+lecture that if we just look at this
+
+ align:start position:0%
+lecture that if we just look at this
+ 
+
+ align:start position:0%
+lecture that if we just look at this
+expression we see that X1 Tilda of M or
+
+ align:start position:0%
+expression we see that X1 Tilda of M or
+ 
+
+ align:start position:0%
+expression we see that X1 Tilda of M or
+equivalently X1 of M modulo capital
+
+ align:start position:0%
+equivalently X1 of M modulo capital
+ 
+
+ align:start position:0%
+equivalently X1 of M modulo capital
+n Only involves values of this argument
+
+ align:start position:0%
+n Only involves values of this argument
+ 
+
+ align:start position:0%
+n Only involves values of this argument
+from zero to capital n minus1 and
+
+ align:start position:0%
+from zero to capital n minus1 and
+ 
+
+ align:start position:0%
+from zero to capital n minus1 and
+consequently as an alternative we can
+
+ align:start position:0%
+consequently as an alternative we can
+ 
+
+ align:start position:0%
+consequently as an alternative we can
+replace here X1 of M so this was an
+
+ align:start position:0%
+replace here X1 of M so this was an
+ 
+
+ align:start position:0%
+replace here X1 of M so this was an
+expression for circular convolution
+
+ align:start position:0%
+expression for circular convolution
+ 
+
+ align:start position:0%
+expression for circular convolution
+of the two finite length sequences X1 of
+
+ align:start position:0%
+of the two finite length sequences X1 of
+ 
+
+ align:start position:0%
+of the two finite length sequences X1 of
+N and X2 of n to remind you of how the
+
+ align:start position:0%
+N and X2 of n to remind you of how the
+ 
+
+ align:start position:0%
+N and X2 of n to remind you of how the
+mechanics of the circular convolution
+
+ align:start position:0%
+mechanics of the circular convolution
+ 
+
+ align:start position:0%
+mechanics of the circular convolution
+are carried out I showed you last time
+
+ align:start position:0%
+are carried out I showed you last time
+ 
+
+ align:start position:0%
+are carried out I showed you last time
+the circular
+
+ align:start position:0%
+the circular
+ 
+
+ align:start position:0%
+the circular
+convolution of one finite length
+
+ align:start position:0%
+convolution of one finite length
+ 
+
+ align:start position:0%
+convolution of one finite length
+sequence X1 of M and X2 of M and let me
+
+ align:start position:0%
+sequence X1 of M and X2 of M and let me
+ 
+
+ align:start position:0%
+sequence X1 of M and X2 of M and let me
+ress a couple of important points first
+
+ align:start position:0%
+ress a couple of important points first
+ 
+
+ align:start position:0%
+ress a couple of important points first
+of all we form from X1 of M
+
+ align:start position:0%
+of all we form from X1 of M
+ 
+
+ align:start position:0%
+of all we form from X1 of M
+of rather from X2 of M X2 of n minus m
+
+ align:start position:0%
+of rather from X2 of M X2 of n minus m
+ 
+
+ align:start position:0%
+of rather from X2 of M X2 of n minus m
+modul capital n and for example if
+
+ align:start position:0%
+modul capital n and for example if
+ 
+
+ align:start position:0%
+modul capital n and for example if
+little n equals z so that we're looking
+
+ align:start position:0%
+little n equals z so that we're looking
+ 
+
+ align:start position:0%
+little n equals z so that we're looking
+at X2 of minus m modulo capital N that
+
+ align:start position:0%
+at X2 of minus m modulo capital N that
+ 
+
+ align:start position:0%
+at X2 of minus m modulo capital N that
+corresponds to flipping this over and
+
+ align:start position:0%
+corresponds to flipping this over and
+ 
+
+ align:start position:0%
+corresponds to flipping this over and
+then taking the values modulo capital N
+
+ align:start position:0%
+then taking the values modulo capital N
+ 
+
+ align:start position:0%
+then taking the values modulo capital N
+which basically corresponds to flipping
+
+ align:start position:0%
+which basically corresponds to flipping
+ 
+
+ align:start position:0%
+which basically corresponds to flipping
+this over the points that come off the
+
+ align:start position:0%
+this over the points that come off the
+ 
+
+ align:start position:0%
+this over the points that come off the
+end get wrapped around back on to this
+
+ align:start position:0%
+end get wrapped around back on to this
+ 
+
+ align:start position:0%
+end get wrapped around back on to this
+side as I've Illustrated
+
+ align:start position:0%
+side as I've Illustrated
+ 
+
+ align:start position:0%
+side as I've Illustrated
+here then if we shift and and I've
+
+ align:start position:0%
+here then if we shift and and I've
+ 
+
+ align:start position:0%
+here then if we shift and and I've
+indicated with these dashed lines what
+
+ align:start position:0%
+indicated with these dashed lines what
+ 
+
+ align:start position:0%
+indicated with these dashed lines what
+would correspond to the periodic
+
+ align:start position:0%
+would correspond to the periodic
+ 
+
+ align:start position:0%
+would correspond to the periodic
+extension of this although it's the
+
+ align:start position:0%
+extension of this although it's the
+ 
+
+ align:start position:0%
+extension of this although it's the
+interval from0 to capital N minus one
+
+ align:start position:0%
+interval from0 to capital N minus one
+ 
+
+ align:start position:0%
+interval from0 to capital N minus one
+which is the interval that I want to
+
+ align:start position:0%
+which is the interval that I want to
+ 
+
+ align:start position:0%
+which is the interval that I want to
+focus on all right well now as we change
+
+ align:start position:0%
+focus on all right well now as we change
+ 
+
+ align:start position:0%
+focus on all right well now as we change
+n if this is generally n minus M that
+
+ align:start position:0%
+n if this is generally n minus M that
+ 
+
+ align:start position:0%
+n if this is generally n minus M that
+corresponds to a shift left or right of
+
+ align:start position:0%
+corresponds to a shift left or right of
+ 
+
+ align:start position:0%
+corresponds to a shift left or right of
+this sequence and if let's say we look
+
+ align:start position:0%
+this sequence and if let's say we look
+ 
+
+ align:start position:0%
+this sequence and if let's say we look
+at X2 of 1 - M modul capital N that
+
+ align:start position:0%
+at X2 of 1 - M modul capital N that
+ 
+
+ align:start position:0%
+at X2 of 1 - M modul capital N that
+corresponds to shifting this sequence to
+
+ align:start position:0%
+corresponds to shifting this sequence to
+ 
+
+ align:start position:0%
+corresponds to shifting this sequence to
+the right by one point and as this point
+
+ align:start position:0%
+the right by one point and as this point
+ 
+
+ align:start position:0%
+the right by one point and as this point
+falls off the end it wraps around to the
+
+ align:start position:0%
+falls off the end it wraps around to the
+ 
+
+ align:start position:0%
+falls off the end it wraps around to the
+other side which is what I've
+
+ align:start position:0%
+other side which is what I've
+ 
+
+ align:start position:0%
+other side which is what I've
+Illustrated here and then if we shift so
+
+ align:start position:0%
+Illustrated here and then if we shift so
+ 
+
+ align:start position:0%
+Illustrated here and then if we shift so
+that little n is equal to two another
+
+ align:start position:0%
+that little n is equal to two another
+ 
+
+ align:start position:0%
+that little n is equal to two another
+Point wraps around the end as I've
+
+ align:start position:0%
+Point wraps around the end as I've
+ 
+
+ align:start position:0%
+Point wraps around the end as I've
+indicated Etc and that's the kind of
+
+ align:start position:0%
+indicated Etc and that's the kind of
+ 
+
+ align:start position:0%
+indicated Etc and that's the kind of
+shifted that gets carried out in other
+
+ align:start position:0%
+shifted that gets carried out in other
+ 
+
+ align:start position:0%
+shifted that gets carried out in other
+words it's a circular shift that's
+
+ align:start position:0%
+words it's a circular shift that's
+ 
+
+ align:start position:0%
+words it's a circular shift that's
+implemented to form the convolution then
+
+ align:start position:0%
+implemented to form the convolution then
+ 
+
+ align:start position:0%
+implemented to form the convolution then
+for example for little n equals 1 we
+
+ align:start position:0%
+for example for little n equals 1 we
+ 
+
+ align:start position:0%
+for example for little n equals 1 we
+multiply this set of values by this set
+
+ align:start position:0%
+multiply this set of values by this set
+ 
+
+ align:start position:0%
+multiply this set of values by this set
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+values and carry out the sum and as I
+
+ align:start position:0%
+values and carry out the sum and as I
+ 
+
+ align:start position:0%
+values and carry out the sum and as I
+indicated last time it's straightforward
+
+ align:start position:0%
+indicated last time it's straightforward
+ 
+
+ align:start position:0%
+indicated last time it's straightforward
+to see that the answer comes out to be
+
+ align:start position:0%
+to see that the answer comes out to be
+ 
+
+ align:start position:0%
+to see that the answer comes out to be
+Unity over the interval 0 to capital N
+
+ align:start position:0%
+Unity over the interval 0 to capital N
+ 
+
+ align:start position:0%
+Unity over the interval 0 to capital N
+minus one but the important point and
+
+ align:start position:0%
+minus one but the important point and
+ 
+
+ align:start position:0%
+minus one but the important point and
+the important picture that I tried to
+
+ align:start position:0%
+the important picture that I tried to
+ 
+
+ align:start position:0%
+the important picture that I tried to
+last time was the notion of thinking of
+
+ align:start position:0%
+last time was the notion of thinking of
+ 
+
+ align:start position:0%
+last time was the notion of thinking of
+the sequences as being wrapped around a
+
+ align:start position:0%
+the sequences as being wrapped around a
+ 
+
+ align:start position:0%
+the sequences as being wrapped around a
+cylinder X1 of n wrapped around a
+
+ align:start position:0%
+cylinder X1 of n wrapped around a
+ 
+
+ align:start position:0%
+cylinder X1 of n wrapped around a
+cylinder X2 of minus n wrapped around a
+
+ align:start position:0%
+cylinder X2 of minus n wrapped around a
+ 
+
+ align:start position:0%
+cylinder X2 of minus n wrapped around a
+cylinder one cylinder put inside the
+
+ align:start position:0%
+cylinder one cylinder put inside the
+ 
+
+ align:start position:0%
+cylinder one cylinder put inside the
+other and then as we form the
+
+ align:start position:0%
+other and then as we form the
+ 
+
+ align:start position:0%
+other and then as we form the
+convolution the cylinders are turned
+
+ align:start position:0%
+convolution the cylinders are turned
+ 
+
+ align:start position:0%
+convolution the cylinders are turned
+with respect to each other and the
+
+ align:start position:0%
+with respect to each other and the
+ 
+
+ align:start position:0%
+with respect to each other and the
+values
+
+ align:start position:0%
+values
+ 
+
+ align:start position:0%
+values
+multiplied successive values multiplied
+
+ align:start position:0%
+multiplied successive values multiplied
+ 
+
+ align:start position:0%
+multiplied successive values multiplied
+and then added around the cylinder and
+
+ align:start position:0%
+and then added around the cylinder and
+ 
+
+ align:start position:0%
+and then added around the cylinder and
+that's the picture of Circ cular
+
+ align:start position:0%
+that's the picture of Circ cular
+ 
+
+ align:start position:0%
+that's the picture of Circ cular
+convolution now there are other ways of
+
+ align:start position:0%
+convolution now there are other ways of
+ 
+
+ align:start position:0%
+convolution now there are other ways of
+looking at circular
+
+ align:start position:0%
+looking at circular
+ 
+
+ align:start position:0%
+looking at circular
+convolution and one of them can be
+
+ align:start position:0%
+convolution and one of them can be
+ 
+
+ align:start position:0%
+convolution and one of them can be
+suggested by referring back to this view
+
+ align:start position:0%
+suggested by referring back to this view
+ 
+
+ align:start position:0%
+suggested by referring back to this view
+graph we saw that we could express the
+
+ align:start position:0%
+graph we saw that we could express the
+ 
+
+ align:start position:0%
+graph we saw that we could express the
+circular
+
+ align:start position:0%
+circular
+ 
+
+ align:start position:0%
+circular
+convolution in this form or
+
+ align:start position:0%
+convolution in this form or
+ 
+
+ align:start position:0%
+convolution in this form or
+equivalently what this means what this
+
+ align:start position:0%
+equivalently what this means what this
+ 
+
+ align:start position:0%
+equivalently what this means what this
+equation means is is or can be
+
+ align:start position:0%
+equation means is is or can be
+ 
+
+ align:start position:0%
+equation means is is or can be
+interpreted as is as the linear
+
+ align:start position:0%
+interpreted as is as the linear
+ 
+
+ align:start position:0%
+interpreted as is as the linear
+convolution of X1 of N and X2 Tilda of n
+
+ align:start position:0%
+convolution of X1 of N and X2 Tilda of n
+ 
+
+ align:start position:0%
+convolution of X1 of N and X2 Tilda of n
+or equivalently X2 of n modulo capital n
+
+ align:start position:0%
+or equivalently X2 of n modulo capital n
+ 
+
+ align:start position:0%
+or equivalently X2 of n modulo capital n
+and then one period extracted from
+
+ align:start position:0%
+and then one period extracted from
+ 
+
+ align:start position:0%
+and then one period extracted from
+that so in fact another way of looking
+
+ align:start position:0%
+that so in fact another way of looking
+ 
+
+ align:start position:0%
+that so in fact another way of looking
+at circular convolution would be to form
+
+ align:start position:0%
+at circular convolution would be to form
+ 
+
+ align:start position:0%
+at circular convolution would be to form
+the linear convolution of X1 of n with
+
+ align:start position:0%
+the linear convolution of X1 of n with
+ 
+
+ align:start position:0%
+the linear convolution of X1 of n with
+the periodic
+
+ align:start position:0%
+the periodic
+ 
+
+ align:start position:0%
+the periodic
+part of X2 of N Carry Out that linear
+
+ align:start position:0%
+part of X2 of N Carry Out that linear
+ 
+
+ align:start position:0%
+part of X2 of N Carry Out that linear
+convolution and then extract one period
+
+ align:start position:0%
+convolution and then extract one period
+ 
+
+ align:start position:0%
+convolution and then extract one period
+which is what this function R sub
+
+ align:start position:0%
+which is what this function R sub
+ 
+
+ align:start position:0%
+which is what this function R sub
+capital N of n is
+
+ align:start position:0%
+capital N of n is
+ 
+
+ align:start position:0%
+capital N of n is
+doing how can we get the periodic
+
+ align:start position:0%
+doing how can we get the periodic
+ 
+
+ align:start position:0%
+doing how can we get the periodic
+sequence from X2 of n well we could do
+
+ align:start position:0%
+sequence from X2 of n well we could do
+ 
+
+ align:start position:0%
+sequence from X2 of n well we could do
+that for example by convolving X2 of n
+
+ align:start position:0%
+that for example by convolving X2 of n
+ 
+
+ align:start position:0%
+that for example by convolving X2 of n
+with a pulse train where the spacing of
+
+ align:start position:0%
+with a pulse train where the spacing of
+ 
+
+ align:start position:0%
+with a pulse train where the spacing of
+the pulses is capital n and that's
+
+ align:start position:0%
+the pulses is capital n and that's
+ 
+
+ align:start position:0%
+the pulses is capital n and that's
+Illustrated on on the next view
+
+ align:start position:0%
+Illustrated on on the next view
+ 
+
+ align:start position:0%
+Illustrated on on the next view
+graph so that from the equation that we
+
+ align:start position:0%
+graph so that from the equation that we
+ 
+
+ align:start position:0%
+graph so that from the equation that we
+just saw one
+
+ align:start position:0%
+just saw one
+ 
+
+ align:start position:0%
+just saw one
+possible way of thinking of circular
+
+ align:start position:0%
+possible way of thinking of circular
+ 
+
+ align:start position:0%
+possible way of thinking of circular
+convolution is
+
+ align:start position:0%
+convolution is
+ 
+
+ align:start position:0%
+convolution is
+as the generation of the periodic
+
+ align:start position:0%
+as the generation of the periodic
+ 
+
+ align:start position:0%
+as the generation of the periodic
+function X2 of n by convolving X2 of n
+
+ align:start position:0%
+function X2 of n by convolving X2 of n
+ 
+
+ align:start position:0%
+function X2 of n by convolving X2 of n
+with a pulse train then a linear
+
+ align:start position:0%
+with a pulse train then a linear
+ 
+
+ align:start position:0%
+with a pulse train then a linear
+convolution of that with X1 of N and
+
+ align:start position:0%
+convolution of that with X1 of N and
+ 
+
+ align:start position:0%
+convolution of that with X1 of N and
+then finally extracting one period which
+
+ align:start position:0%
+then finally extracting one period which
+ 
+
+ align:start position:0%
+then finally extracting one period which
+is what this function multiplying X3
+
+ align:start position:0%
+is what this function multiplying X3
+ 
+
+ align:start position:0%
+is what this function multiplying X3
+Tilda of n does so we could generate a
+
+ align:start position:0%
+Tilda of n does so we could generate a
+ 
+
+ align:start position:0%
+Tilda of n does so we could generate a
+pulse Train by taking a system whose
+
+ align:start position:0%
+pulse Train by taking a system whose
+ 
+
+ align:start position:0%
+pulse Train by taking a system whose
+unit sample response is one at a spacing
+
+ align:start position:0%
+unit sample response is one at a spacing
+ 
+
+ align:start position:0%
+unit sample response is one at a spacing
+of capital n and it's zero
+
+ align:start position:0%
+of capital n and it's zero
+ 
+
+ align:start position:0%
+of capital n and it's zero
+otherwise kicking that system with a
+
+ align:start position:0%
+otherwise kicking that system with a
+ 
+
+ align:start position:0%
+otherwise kicking that system with a
+unit sample in which case we get this
+
+ align:start position:0%
+unit sample in which case we get this
+ 
+
+ align:start position:0%
+unit sample in which case we get this
+pulse train out
+
+ align:start position:0%
+pulse train out
+ 
+
+ align:start position:0%
+pulse train out
+using that as the exitation to a system
+
+ align:start position:0%
+using that as the exitation to a system
+ 
+
+ align:start position:0%
+using that as the exitation to a system
+whose unit sample response is X2 of N
+
+ align:start position:0%
+whose unit sample response is X2 of N
+ 
+
+ align:start position:0%
+whose unit sample response is X2 of N
+and what we'll get then is X2 of n
+
+ align:start position:0%
+and what we'll get then is X2 of n
+ 
+
+ align:start position:0%
+and what we'll get then is X2 of n
+convolved with this pulse train or X2 of
+
+ align:start position:0%
+convolved with this pulse train or X2 of
+ 
+
+ align:start position:0%
+convolved with this pulse train or X2 of
+n repeated at intervals of capital N but
+
+ align:start position:0%
+n repeated at intervals of capital N but
+ 
+
+ align:start position:0%
+n repeated at intervals of capital N but
+that's X2 Tila of n that's the periodic
+
+ align:start position:0%
+that's X2 Tila of n that's the periodic
+ 
+
+ align:start position:0%
+that's X2 Tila of n that's the periodic
+sequence that we want that's the
+
+ align:start position:0%
+sequence that we want that's the
+ 
+
+ align:start position:0%
+sequence that we want that's the
+periodic counterpart of X2 of N and so
+
+ align:start position:0%
+periodic counterpart of X2 of N and so
+ 
+
+ align:start position:0%
+periodic counterpart of X2 of N and so
+that is what we have
+
+ align:start position:0%
+that is what we have
+ 
+
+ align:start position:0%
+that is what we have
+here using that as the input to a system
+
+ align:start position:0%
+here using that as the input to a system
+ 
+
+ align:start position:0%
+here using that as the input to a system
+whose unit sample response is X1 of N
+
+ align:start position:0%
+whose unit sample response is X1 of N
+ 
+
+ align:start position:0%
+whose unit sample response is X1 of N
+and then the output is the periodic
+
+ align:start position:0%
+and then the output is the periodic
+ 
+
+ align:start position:0%
+and then the output is the periodic
+convolution of X1 of n with X2 of n we
+
+ align:start position:0%
+convolution of X1 of n with X2 of n we
+ 
+
+ align:start position:0%
+convolution of X1 of n with X2 of n we
+extract one period and we get finally
+
+ align:start position:0%
+extract one period and we get finally
+ 
+
+ align:start position:0%
+extract one period and we get finally
+the circular convolution of the finite
+
+ align:start position:0%
+the circular convolution of the finite
+ 
+
+ align:start position:0%
+the circular convolution of the finite
+length sequences X1 of N and X2 of
+
+ align:start position:0%
+length sequences X1 of N and X2 of
+ 
+
+ align:start position:0%
+length sequences X1 of N and X2 of
+n well the fact that we could view the
+
+ align:start position:0%
+n well the fact that we could view the
+ 
+
+ align:start position:0%
+n well the fact that we could view the
+circular convolution in terms of of a
+
+ align:start position:0%
+circular convolution in terms of of a
+ 
+
+ align:start position:0%
+circular convolution in terms of of a
+Cascade of systems of this type leads to
+
+ align:start position:0%
+Cascade of systems of this type leads to
+ 
+
+ align:start position:0%
+Cascade of systems of this type leads to
+a very important and interesting
+
+ align:start position:0%
+a very important and interesting
+ 
+
+ align:start position:0%
+a very important and interesting
+interpretation of circular
+
+ align:start position:0%
+interpretation of circular
+ 
+
+ align:start position:0%
+interpretation of circular
+convolution in
+
+ align:start position:0%
+convolution in
+ 
+
+ align:start position:0%
+convolution in
+particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's look
+
+ align:start position:0%
+let's look
+ 
+
+ align:start position:0%
+let's look
+at these
+
+ align:start position:0%
+at these
+ 
+
+ align:start position:0%
+at these
+systems cascaded as they are here so we
+
+ align:start position:0%
+systems cascaded as they are here so we
+ 
+
+ align:start position:0%
+systems cascaded as they are here so we
+have then the Cascade of these three
+
+ align:start position:0%
+have then the Cascade of these three
+ 
+
+ align:start position:0%
+have then the Cascade of these three
+systems to generate the circular
+
+ align:start position:0%
+systems to generate the circular
+ 
+
+ align:start position:0%
+systems to generate the circular
+convolution which is X3 of n the
+
+ align:start position:0%
+convolution which is X3 of n the
+ 
+
+ align:start position:0%
+convolution which is X3 of n the
+circular convolution of X1 of N and X2
+
+ align:start position:0%
+circular convolution of X1 of N and X2
+ 
+
+ align:start position:0%
+circular convolution of X1 of N and X2
+of n so this then is three systems
+
+ align:start position:0%
+of n so this then is three systems
+ 
+
+ align:start position:0%
+of n so this then is three systems
+linear shift and variance systems in
+
+ align:start position:0%
+linear shift and variance systems in
+ 
+
+ align:start position:0%
+linear shift and variance systems in
+Cascade and one of the important things
+
+ align:start position:0%
+Cascade and one of the important things
+ 
+
+ align:start position:0%
+Cascade and one of the important things
+that we know about linear shift and
+
+ align:start position:0%
+that we know about linear shift and
+ 
+
+ align:start position:0%
+that we know about linear shift and
+variance systems which are cascaded is
+
+ align:start position:0%
+variance systems which are cascaded is
+ 
+
+ align:start position:0%
+variance systems which are cascaded is
+that the order in which they're cascaded
+
+ align:start position:0%
+that the order in which they're cascaded
+ 
+
+ align:start position:0%
+that the order in which they're cascaded
+is irrelevant that's something we showed
+
+ align:start position:0%
+is irrelevant that's something we showed
+ 
+
+ align:start position:0%
+is irrelevant that's something we showed
+in one of the early lectures so in fact
+
+ align:start position:0%
+in one of the early lectures so in fact
+ 
+
+ align:start position:0%
+in one of the early lectures so in fact
+we can interchange the order of these
+
+ align:start position:0%
+we can interchange the order of these
+ 
+
+ align:start position:0%
+we can interchange the order of these
+systems any way that we want
+
+ align:start position:0%
+systems any way that we want
+ 
+
+ align:start position:0%
+systems any way that we want
+to and in particular let's interchange
+
+ align:start position:0%
+to and in particular let's interchange
+ 
+
+ align:start position:0%
+to and in particular let's interchange
+the order of these systems by taking
+
+ align:start position:0%
+the order of these systems by taking
+ 
+
+ align:start position:0%
+the order of these systems by taking
+this system which generates the pulse
+
+ align:start position:0%
+this system which generates the pulse
+ 
+
+ align:start position:0%
+this system which generates the pulse
+train putting that at the end of this
+
+ align:start position:0%
+train putting that at the end of this
+ 
+
+ align:start position:0%
+train putting that at the end of this
+Cascade
+
+ align:start position:0%
+Cascade
+ 
+
+ align:start position:0%
+Cascade
+chain so that instead of this Cascade
+
+ align:start position:0%
+chain so that instead of this Cascade
+ 
+
+ align:start position:0%
+chain so that instead of this Cascade
+then we have X2 of n cascaded with X1 of
+
+ align:start position:0%
+then we have X2 of n cascaded with X1 of
+ 
+
+ align:start position:0%
+then we have X2 of n cascaded with X1 of
+n cascaded with p subc capital N of N
+
+ align:start position:0%
+n cascaded with p subc capital N of N
+ 
+
+ align:start position:0%
+n cascaded with p subc capital N of N
+and then of course R subn to extract the
+
+ align:start position:0%
+and then of course R subn to extract the
+ 
+
+ align:start position:0%
+and then of course R subn to extract the
+single
+
+ align:start position:0%
+single
+ 
+
+ align:start position:0%
+single
+period Well what does this
+
+ align:start position:0%
+period Well what does this
+ 
+
+ align:start position:0%
+period Well what does this
+mean this means that I can equivalently
+
+ align:start position:0%
+mean this means that I can equivalently
+ 
+
+ align:start position:0%
+mean this means that I can equivalently
+form the circular convolution of X1 of N
+
+ align:start position:0%
+form the circular convolution of X1 of N
+ 
+
+ align:start position:0%
+form the circular convolution of X1 of N
+and X2 of n by first forming the linear
+
+ align:start position:0%
+and X2 of n by first forming the linear
+ 
+
+ align:start position:0%
+and X2 of n by first forming the linear
+convolution of X1 and X2 that's of
+
+ align:start position:0%
+convolution of X1 and X2 that's of
+ 
+
+ align:start position:0%
+convolution of X1 and X2 that's of
+course what the impulse response of
+
+ align:start position:0%
+course what the impulse response of
+ 
+
+ align:start position:0%
+course what the impulse response of
+these two systems in Cascade
+
+ align:start position:0%
+these two systems in Cascade
+ 
+
+ align:start position:0%
+these two systems in Cascade
+is and then using that as the exitation
+
+ align:start position:0%
+is and then using that as the exitation
+ 
+
+ align:start position:0%
+is and then using that as the exitation
+to a system whose unit sample response
+
+ align:start position:0%
+to a system whose unit sample response
+ 
+
+ align:start position:0%
+to a system whose unit sample response
+is a pulse train so I can think of this
+
+ align:start position:0%
+is a pulse train so I can think of this
+ 
+
+ align:start position:0%
+is a pulse train so I can think of this
+then as the linear
+
+ align:start position:0%
+then as the linear
+ 
+
+ align:start position:0%
+then as the linear
+convolution that convolved with a pulse
+
+ align:start position:0%
+convolution that convolved with a pulse
+ 
+
+ align:start position:0%
+convolution that convolved with a pulse
+train one period extracted and the
+
+ align:start position:0%
+train one period extracted and the
+ 
+
+ align:start position:0%
+train one period extracted and the
+result is a circular
+
+ align:start position:0%
+result is a circular
+ 
+
+ align:start position:0%
+result is a circular
+convolution that's a very useful and
+
+ align:start position:0%
+convolution that's a very useful and
+ 
+
+ align:start position:0%
+convolution that's a very useful and
+important interpretation of circular
+
+ align:start position:0%
+important interpretation of circular
+ 
+
+ align:start position:0%
+important interpretation of circular
+convolution and the way to sort of say
+
+ align:start position:0%
+convolution and the way to sort of say
+ 
+
+ align:start position:0%
+convolution and the way to sort of say
+it in words this is isn't exactly
+
+ align:start position:0%
+it in words this is isn't exactly
+ 
+
+ align:start position:0%
+it in words this is isn't exactly
+correct but more or less the way to say
+
+ align:start position:0%
+correct but more or less the way to say
+ 
+
+ align:start position:0%
+correct but more or less the way to say
+it in words is that the circular
+
+ align:start position:0%
+it in words is that the circular
+ 
+
+ align:start position:0%
+it in words is that the circular
+convolution can be formed from a linear
+
+ align:start position:0%
+convolution can be formed from a linear
+ 
+
+ align:start position:0%
+convolution can be formed from a linear
+convolution plus
+
+ align:start position:0%
+convolution plus
+ 
+
+ align:start position:0%
+convolution plus
+aliasing you see this linear convolution
+
+ align:start position:0%
+aliasing you see this linear convolution
+ 
+
+ align:start position:0%
+aliasing you see this linear convolution
+in general is going to be longer than
+
+ align:start position:0%
+in general is going to be longer than
+ 
+
+ align:start position:0%
+in general is going to be longer than
+capital N the output of this system is
+
+ align:start position:0%
+capital N the output of this system is
+ 
+
+ align:start position:0%
+capital N the output of this system is
+this linear convolution repeated over
+
+ align:start position:0%
+this linear convolution repeated over
+ 
+
+ align:start position:0%
+this linear convolution repeated over
+and over again added up over and over
+
+ align:start position:0%
+and over again added up over and over
+ 
+
+ align:start position:0%
+and over again added up over and over
+again with a spacing of capital N so
+
+ align:start position:0%
+again with a spacing of capital N so
+ 
+
+ align:start position:0%
+again with a spacing of capital N so
+there is an interference if you want to
+
+ align:start position:0%
+there is an interference if you want to
+ 
+
+ align:start position:0%
+there is an interference if you want to
+call it that between the successive
+
+ align:start position:0%
+call it that between the successive
+ 
+
+ align:start position:0%
+call it that between the successive
+replicas of this linear convolution as
+
+ align:start position:0%
+replicas of this linear convolution as
+ 
+
+ align:start position:0%
+replicas of this linear convolution as
+they come out of this system that's the
+
+ align:start position:0%
+they come out of this system that's the
+ 
+
+ align:start position:0%
+they come out of this system that's the
+aliasing that it's why aliasing is stuck
+
+ align:start position:0%
+aliasing that it's why aliasing is stuck
+ 
+
+ align:start position:0%
+aliasing that it's why aliasing is stuck
+into that that phrase but the way to to
+
+ align:start position:0%
+into that that phrase but the way to to
+ 
+
+ align:start position:0%
+into that that phrase but the way to to
+sort of summarize it or think about it
+
+ align:start position:0%
+sort of summarize it or think about it
+ 
+
+ align:start position:0%
+sort of summarize it or think about it
+is as circular convolution corresponding
+
+ align:start position:0%
+is as circular convolution corresponding
+ 
+
+ align:start position:0%
+is as circular convolution corresponding
+to linear convolution plus
+
+ align:start position:0%
+to linear convolution plus
+ 
+
+ align:start position:0%
+to linear convolution plus
+aliasing so here it is said again
+
+ align:start position:0%
+aliasing so here it is said again
+ 
+
+ align:start position:0%
+aliasing so here it is said again
+circular con olution equals linear
+
+ align:start position:0%
+circular con olution equals linear
+ 
+
+ align:start position:0%
+circular con olution equals linear
+convolution plus aliasing what I mean by
+
+ align:start position:0%
+convolution plus aliasing what I mean by
+ 
+
+ align:start position:0%
+convolution plus aliasing what I mean by
+that is that if I have the linear
+
+ align:start position:0%
+that is that if I have the linear
+ 
+
+ align:start position:0%
+that is that if I have the linear
+convolution of X1 of N and X2 of
+
+ align:start position:0%
+convolution of X1 of N and X2 of
+ 
+
+ align:start position:0%
+convolution of X1 of N and X2 of
+n which I'm denoting by X3 hat of N and
+
+ align:start position:0%
+n which I'm denoting by X3 hat of N and
+ 
+
+ align:start position:0%
+n which I'm denoting by X3 hat of N and
+I want the circular convolution the
+
+ align:start position:0%
+I want the circular convolution the
+ 
+
+ align:start position:0%
+I want the circular convolution the
+endpoint circular convolution of X1 of n
+
+ align:start position:0%
+endpoint circular convolution of X1 of n
+ 
+
+ align:start position:0%
+endpoint circular convolution of X1 of n
+with X2 of
+
+ align:start position:0%
+with X2 of
+ 
+
+ align:start position:0%
+with X2 of
+n i can get the circular convolution
+
+ align:start position:0%
+n i can get the circular convolution
+ 
+
+ align:start position:0%
+n i can get the circular convolution
+from the linear
+
+ align:start position:0%
+from the linear
+ 
+
+ align:start position:0%
+from the linear
+convolution by taking the linear
+
+ align:start position:0%
+convolution by taking the linear
+ 
+
+ align:start position:0%
+convolution by taking the linear
+convolution and convolving it with a
+
+ align:start position:0%
+convolution and convolving it with a
+ 
+
+ align:start position:0%
+convolution and convolving it with a
+pulse train with a spacing of capital N
+
+ align:start position:0%
+pulse train with a spacing of capital N
+ 
+
+ align:start position:0%
+pulse train with a spacing of capital N
+or equivalently adding it to itself
+
+ align:start position:0%
+or equivalently adding it to itself
+ 
+
+ align:start position:0%
+or equivalently adding it to itself
+delayed by capital N to capital N minus
+
+ align:start position:0%
+delayed by capital N to capital N minus
+ 
+
+ align:start position:0%
+delayed by capital N to capital N minus
+capital N minus 2 capital N Etc and then
+
+ align:start position:0%
+capital N minus 2 capital N Etc and then
+ 
+
+ align:start position:0%
+capital N minus 2 capital N Etc and then
+extracting a single period and often
+
+ align:start position:0%
+extracting a single period and often
+ 
+
+ align:start position:0%
+extracting a single period and often
+when you carry out a circular
+
+ align:start position:0%
+when you carry out a circular
+ 
+
+ align:start position:0%
+when you carry out a circular
+convolution of two sequences or want to
+
+ align:start position:0%
+convolution of two sequences or want to
+ 
+
+ align:start position:0%
+convolution of two sequences or want to
+examine proper properties of circular
+
+ align:start position:0%
+examine proper properties of circular
+ 
+
+ align:start position:0%
+examine proper properties of circular
+convolution the notion or interpretation
+
+ align:start position:0%
+convolution the notion or interpretation
+ 
+
+ align:start position:0%
+convolution the notion or interpretation
+of circular convolution as linear
+
+ align:start position:0%
+of circular convolution as linear
+ 
+
+ align:start position:0%
+of circular convolution as linear
+convolution plus Al aliasing is an
+
+ align:start position:0%
+convolution plus Al aliasing is an
+ 
+
+ align:start position:0%
+convolution plus Al aliasing is an
+extremely useful sort of picture to
+
+ align:start position:0%
+extremely useful sort of picture to
+ 
+
+ align:start position:0%
+extremely useful sort of picture to
+have so it's the kind of phrase that you
+
+ align:start position:0%
+have so it's the kind of phrase that you
+ 
+
+ align:start position:0%
+have so it's the kind of phrase that you
+should refer you should repeat to
+
+ align:start position:0%
+should refer you should repeat to
+ 
+
+ align:start position:0%
+should refer you should repeat to
+yourself two or three times for a week
+
+ align:start position:0%
+yourself two or three times for a week
+ 
+
+ align:start position:0%
+yourself two or three times for a week
+before you go to bed and uh in a short
+
+ align:start position:0%
+before you go to bed and uh in a short
+ 
+
+ align:start position:0%
+before you go to bed and uh in a short
+time you'll understand the relationship
+
+ align:start position:0%
+time you'll understand the relationship
+ 
+
+ align:start position:0%
+time you'll understand the relationship
+between circular convolution and linear
+
+ align:start position:0%
+between circular convolution and linear
+ 
+
+ align:start position:0%
+between circular convolution and linear
+convolution well well let's look at a
+
+ align:start position:0%
+convolution well well let's look at a
+ 
+
+ align:start position:0%
+convolution well well let's look at a
+couple of examples of
+
+ align:start position:0%
+couple of examples of
+ 
+
+ align:start position:0%
+couple of examples of
+this here is a sequence X1 of n it's a
+
+ align:start position:0%
+this here is a sequence X1 of n it's a
+ 
+
+ align:start position:0%
+this here is a sequence X1 of n it's a
+Sixpoint
+
+ align:start position:0%
+Sixpoint
+ 
+
+ align:start position:0%
+Sixpoint
+sequence and let's carry out the
+
+ align:start position:0%
+sequence and let's carry out the
+ 
+
+ align:start position:0%
+sequence and let's carry out the
+circular convolution of this sequence
+
+ align:start position:0%
+circular convolution of this sequence
+ 
+
+ align:start position:0%
+circular convolution of this sequence
+with itself that makes it a relatively
+
+ align:start position:0%
+with itself that makes it a relatively
+ 
+
+ align:start position:0%
+with itself that makes it a relatively
+straightforward
+
+ align:start position:0%
+straightforward
+ 
+
+ align:start position:0%
+straightforward
+example and let's do that by using the
+
+ align:start position:0%
+example and let's do that by using the
+ 
+
+ align:start position:0%
+example and let's do that by using the
+notion that circular convolution is
+
+ align:start position:0%
+notion that circular convolution is
+ 
+
+ align:start position:0%
+notion that circular convolution is
+linear convolution plus
+
+ align:start position:0%
+linear convolution plus
+ 
+
+ align:start position:0%
+linear convolution plus
+aliasing so we want first of all to form
+
+ align:start position:0%
+aliasing so we want first of all to form
+ 
+
+ align:start position:0%
+aliasing so we want first of all to form
+the linear convolution of X1 of N and X2
+
+ align:start position:0%
+the linear convolution of X1 of N and X2
+ 
+
+ align:start position:0%
+the linear convolution of X1 of N and X2
+of N and as you should recall from
+
+ align:start position:0%
+of N and as you should recall from
+ 
+
+ align:start position:0%
+of N and as you should recall from
+similar examples in the earlier lectures
+
+ align:start position:0%
+similar examples in the earlier lectures
+ 
+
+ align:start position:0%
+similar examples in the earlier lectures
+and examples that you've worked in the
+
+ align:start position:0%
+and examples that you've worked in the
+ 
+
+ align:start position:0%
+and examples that you've worked in the
+study guide the linear convolution of
+
+ align:start position:0%
+study guide the linear convolution of
+ 
+
+ align:start position:0%
+study guide the linear convolution of
+this sequence with itself is a
+
+ align:start position:0%
+this sequence with itself is a
+ 
+
+ align:start position:0%
+this sequence with itself is a
+triangular sequence we of course take
+
+ align:start position:0%
+triangular sequence we of course take
+ 
+
+ align:start position:0%
+triangular sequence we of course take
+this sequence flip it over and slide it
+
+ align:start position:0%
+this sequence flip it over and slide it
+ 
+
+ align:start position:0%
+this sequence flip it over and slide it
+past the itself and as we slide along we
+
+ align:start position:0%
+past the itself and as we slide along we
+ 
+
+ align:start position:0%
+past the itself and as we slide along we
+accumulate more and more
+
+ align:start position:0%
+accumulate more and more
+ 
+
+ align:start position:0%
+accumulate more and more
+points and so the linear convolution of
+
+ align:start position:0%
+points and so the linear convolution of
+ 
+
+ align:start position:0%
+points and so the linear convolution of
+X1 of n with X2 of N is a triangular
+
+ align:start position:0%
+X1 of n with X2 of N is a triangular
+ 
+
+ align:start position:0%
+X1 of n with X2 of N is a triangular
+sequence as I've indicated
+
+ align:start position:0%
+sequence as I've indicated
+ 
+
+ align:start position:0%
+sequence as I've indicated
+here well now to form the circular
+
+ align:start position:0%
+here well now to form the circular
+ 
+
+ align:start position:0%
+here well now to form the circular
+convolution of X1 of N and X2 of
+
+ align:start position:0%
+convolution of X1 of N and X2 of
+ 
+
+ align:start position:0%
+convolution of X1 of N and X2 of
+n what we need to do is repeat this
+
+ align:start position:0%
+n what we need to do is repeat this
+ 
+
+ align:start position:0%
+n what we need to do is repeat this
+triangular sequence over and over again
+
+ align:start position:0%
+triangular sequence over and over again
+ 
+
+ align:start position:0%
+triangular sequence over and over again
+added to itself with a delay of capital
+
+ align:start position:0%
+added to itself with a delay of capital
+ 
+
+ align:start position:0%
+added to itself with a delay of capital
+n and capital N in this case is six so
+
+ align:start position:0%
+n and capital N in this case is six so
+ 
+
+ align:start position:0%
+n and capital N in this case is six so
+we want this sequence repeated over and
+
+ align:start position:0%
+we want this sequence repeated over and
+ 
+
+ align:start position:0%
+we want this sequence repeated over and
+over again and added to itself with a
+
+ align:start position:0%
+over again and added to itself with a
+ 
+
+ align:start position:0%
+over again and added to itself with a
+spacing of six and then 12 and then 18
+
+ align:start position:0%
+spacing of six and then 12 and then 18
+ 
+
+ align:start position:0%
+spacing of six and then 12 and then 18
+Etc or equivalently we want the linear
+
+ align:start position:0%
+Etc or equivalently we want the linear
+ 
+
+ align:start position:0%
+Etc or equivalently we want the linear
+convolution convolved with a pulse train
+
+ align:start position:0%
+convolution convolved with a pulse train
+ 
+
+ align:start position:0%
+convolution convolved with a pulse train
+where the spacing of the pulses is
+
+ align:start position:0%
+where the spacing of the pulses is
+ 
+
+ align:start position:0%
+where the spacing of the pulses is
+capital N which in this case is six so
+
+ align:start position:0%
+capital N which in this case is six so
+ 
+
+ align:start position:0%
+capital N which in this case is six so
+I've indicated here the envelope of the
+
+ align:start position:0%
+I've indicated here the envelope of the
+ 
+
+ align:start position:0%
+I've indicated here the envelope of the
+Triangular sequence that's the envelope
+
+ align:start position:0%
+Triangular sequence that's the envelope
+ 
+
+ align:start position:0%
+Triangular sequence that's the envelope
+here the envelope of the Triangular
+
+ align:start position:0%
+here the envelope of the Triangular
+ 
+
+ align:start position:0%
+here the envelope of the Triangular
+sequence and you can see that if we
+
+ align:start position:0%
+sequence and you can see that if we
+ 
+
+ align:start position:0%
+sequence and you can see that if we
+overlap these triangles by a spacing of
+
+ align:start position:0%
+overlap these triangles by a spacing of
+ 
+
+ align:start position:0%
+overlap these triangles by a spacing of
+six then in fact these points will get
+
+ align:start position:0%
+six then in fact these points will get
+ 
+
+ align:start position:0%
+six then in fact these points will get
+added to these points or when we add up
+
+ align:start position:0%
+added to these points or when we add up
+ 
+
+ align:start position:0%
+added to these points or when we add up
+the triangles they'll always add up to
+
+ align:start position:0%
+the triangles they'll always add up to
+ 
+
+ align:start position:0%
+the triangles they'll always add up to
+one so when we carry out this
+
+ align:start position:0%
+one so when we carry out this
+ 
+
+ align:start position:0%
+one so when we carry out this
+convolution what we end up with are
+
+ align:start position:0%
+convolution what we end up with are
+ 
+
+ align:start position:0%
+convolution what we end up with are
+values that are constant from minus
+
+ align:start position:0%
+values that are constant from minus
+ 
+
+ align:start position:0%
+values that are constant from minus
+infinity to plus infinity that's due to
+
+ align:start position:0%
+infinity to plus infinity that's due to
+ 
+
+ align:start position:0%
+infinity to plus infinity that's due to
+the convolution with this
+
+ align:start position:0%
+the convolution with this
+ 
+
+ align:start position:0%
+the convolution with this
+term finally to form the endpoint or six
+
+ align:start position:0%
+term finally to form the endpoint or six
+ 
+
+ align:start position:0%
+term finally to form the endpoint or six
+point in this case circuit
+
+ align:start position:0%
+point in this case circuit
+ 
+
+ align:start position:0%
+point in this case circuit
+convolution what we want to extract are
+
+ align:start position:0%
+convolution what we want to extract are
+ 
+
+ align:start position:0%
+convolution what we want to extract are
+are the six points of this sequence 1 2
+
+ align:start position:0%
+are the six points of this sequence 1 2
+ 
+
+ align:start position:0%
+are the six points of this sequence 1 2
+3 4 5 six those six points set the rest
+
+ align:start position:0%
+3 4 5 six those six points set the rest
+ 
+
+ align:start position:0%
+3 4 5 six those six points set the rest
+to zero and the result is as I've
+
+ align:start position:0%
+to zero and the result is as I've
+ 
+
+ align:start position:0%
+to zero and the result is as I've
+indicated here so this then is the
+
+ align:start position:0%
+indicated here so this then is the
+ 
+
+ align:start position:0%
+indicated here so this then is the
+endpoint circular convolution of X1 of n
+
+ align:start position:0%
+endpoint circular convolution of X1 of n
+ 
+
+ align:start position:0%
+endpoint circular convolution of X1 of n
+with X2 of n this is the linear
+
+ align:start position:0%
+with X2 of n this is the linear
+ 
+
+ align:start position:0%
+with X2 of n this is the linear
+convolution of X1 of n with X2 of
+
+ align:start position:0%
+convolution of X1 of n with X2 of
+ 
+
+ align:start position:0%
+convolution of X1 of n with X2 of
+n it should be clear that or relatively
+
+ align:start position:0%
+n it should be clear that or relatively
+ 
+
+ align:start position:0%
+n it should be clear that or relatively
+clear that
+
+ align:start position:0%
+clear that
+ 
+
+ align:start position:0%
+clear that
+this is in fact the way the circular
+
+ align:start position:0%
+this is in fact the way the circular
+ 
+
+ align:start position:0%
+this is in fact the way the circular
+convolution comes out because if you
+
+ align:start position:0%
+convolution comes out because if you
+ 
+
+ align:start position:0%
+convolution comes out because if you
+imagine flipping this and sliding it
+
+ align:start position:0%
+imagine flipping this and sliding it
+ 
+
+ align:start position:0%
+imagine flipping this and sliding it
+modulo capital N or equivalently taking
+
+ align:start position:0%
+modulo capital N or equivalently taking
+ 
+
+ align:start position:0%
+modulo capital N or equivalently taking
+this sequence and wrapping it around the
+
+ align:start position:0%
+this sequence and wrapping it around the
+ 
+
+ align:start position:0%
+this sequence and wrapping it around the
+cylinder no matter how you twist the
+
+ align:start position:0%
+cylinder no matter how you twist the
+ 
+
+ align:start position:0%
+cylinder no matter how you twist the
+cylinder you always see the same points
+
+ align:start position:0%
+cylinder you always see the same points
+ 
+
+ align:start position:0%
+cylinder you always see the same points
+so in fact by by evaluating the circular
+
+ align:start position:0%
+so in fact by by evaluating the circular
+ 
+
+ align:start position:0%
+so in fact by by evaluating the circular
+convolution using modulus arguments you
+
+ align:start position:0%
+convolution using modulus arguments you
+ 
+
+ align:start position:0%
+convolution using modulus arguments you
+would of course come up with the same
+
+ align:start position:0%
+would of course come up with the same
+ 
+
+ align:start position:0%
+would of course come up with the same
+result but we see here how it comes out
+
+ align:start position:0%
+result but we see here how it comes out
+ 
+
+ align:start position:0%
+result but we see here how it comes out
+of this notion of linear convolution
+
+ align:start position:0%
+of this notion of linear convolution
+ 
+
+ align:start position:0%
+of this notion of linear convolution
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+aliasing all right well let's look at
+
+ align:start position:0%
+aliasing all right well let's look at
+ 
+
+ align:start position:0%
+aliasing all right well let's look at
+another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example actually it's the same example
+
+ align:start position:0%
+example actually it's the same example
+ 
+
+ align:start position:0%
+example actually it's the same example
+but with one slight change to it here
+
+ align:start position:0%
+but with one slight change to it here
+ 
+
+ align:start position:0%
+but with one slight change to it here
+again I have the example of X1 of n
+
+ align:start position:0%
+again I have the example of X1 of n
+ 
+
+ align:start position:0%
+again I have the example of X1 of n
+equal to X2 of N and again we take both
+
+ align:start position:0%
+equal to X2 of N and again we take both
+ 
+
+ align:start position:0%
+equal to X2 of N and again we take both
+of them as a box car sequence in other
+
+ align:start position:0%
+of them as a box car sequence in other
+ 
+
+ align:start position:0%
+of them as a box car sequence in other
+words rectangular or constant value in
+
+ align:start position:0%
+words rectangular or constant value in
+ 
+
+ align:start position:0%
+words rectangular or constant value in
+the interval 0 to n minus1 and zero
+
+ align:start position:0%
+the interval 0 to n minus1 and zero
+ 
+
+ align:start position:0%
+the interval 0 to n minus1 and zero
+outside that
+
+ align:start position:0%
+outside that
+ 
+
+ align:start position:0%
+outside that
+interval again of course then we have
+
+ align:start position:0%
+interval again of course then we have
+ 
+
+ align:start position:0%
+interval again of course then we have
+the linear convolution of these
+
+ align:start position:0%
+the linear convolution of these
+ 
+
+ align:start position:0%
+the linear convolution of these
+two as a
+
+ align:start position:0%
+two as a
+ 
+
+ align:start position:0%
+two as a
+triangle which is what I've denoted
+
+ align:start position:0%
+triangle which is what I've denoted
+ 
+
+ align:start position:0%
+triangle which is what I've denoted
+here and now let's look not at the
+
+ align:start position:0%
+here and now let's look not at the
+ 
+
+ align:start position:0%
+here and now let's look not at the
+endpoint circular
+
+ align:start position:0%
+endpoint circular
+ 
+
+ align:start position:0%
+endpoint circular
+convolution but at the 2 N Point
+
+ align:start position:0%
+convolution but at the 2 N Point
+ 
+
+ align:start position:0%
+convolution but at the 2 N Point
+circular convolution of X1 of n with X2
+
+ align:start position:0%
+circular convolution of X1 of n with X2
+ 
+
+ align:start position:0%
+circular convolution of X1 of n with X2
+event in that case we want this
+
+ align:start position:0%
+event in that case we want this
+ 
+
+ align:start position:0%
+event in that case we want this
+triangular
+
+ align:start position:0%
+triangular
+ 
+
+ align:start position:0%
+triangular
+sequence repeated and added to itself
+
+ align:start position:0%
+sequence repeated and added to itself
+ 
+
+ align:start position:0%
+sequence repeated and added to itself
+not with a spacing of capital n as in
+
+ align:start position:0%
+not with a spacing of capital n as in
+ 
+
+ align:start position:0%
+not with a spacing of capital n as in
+the previous example but with a spacing
+
+ align:start position:0%
+the previous example but with a spacing
+ 
+
+ align:start position:0%
+the previous example but with a spacing
+of 2 capital
+
+ align:start position:0%
+of 2 capital
+ 
+
+ align:start position:0%
+of 2 capital
+N because we're doing a two capital N
+
+ align:start position:0%
+N because we're doing a two capital N
+ 
+
+ align:start position:0%
+N because we're doing a two capital N
+Point circular convolution well if we do
+
+ align:start position:0%
+Point circular convolution well if we do
+ 
+
+ align:start position:0%
+Point circular convolution well if we do
+that then we end up with this triangular
+
+ align:start position:0%
+that then we end up with this triangular
+ 
+
+ align:start position:0%
+that then we end up with this triangular
+sequence added to itself starting here
+
+ align:start position:0%
+sequence added to itself starting here
+ 
+
+ align:start position:0%
+sequence added to itself starting here
+finishing over there there or in general
+
+ align:start position:0%
+finishing over there there or in general
+ 
+
+ align:start position:0%
+finishing over there there or in general
+if we convolve it with this pulse train
+
+ align:start position:0%
+if we convolve it with this pulse train
+ 
+
+ align:start position:0%
+if we convolve it with this pulse train
+then the resulting periodic sequence
+
+ align:start position:0%
+then the resulting periodic sequence
+ 
+
+ align:start position:0%
+then the resulting periodic sequence
+that we end up with is has triangular
+
+ align:start position:0%
+that we end up with is has triangular
+ 
+
+ align:start position:0%
+that we end up with is has triangular
+periods to it with a period now not of
+
+ align:start position:0%
+periods to it with a period now not of
+ 
+
+ align:start position:0%
+periods to it with a period now not of
+capital n as we had in the previous
+
+ align:start position:0%
+capital n as we had in the previous
+ 
+
+ align:start position:0%
+capital n as we had in the previous
+example but of two capital
+
+ align:start position:0%
+example but of two capital
+ 
+
+ align:start position:0%
+example but of two capital
+N finally to get the circular
+
+ align:start position:0%
+N finally to get the circular
+ 
+
+ align:start position:0%
+N finally to get the circular
+convolution we see that or we recall
+
+ align:start position:0%
+convolution we see that or we recall
+ 
+
+ align:start position:0%
+convolution we see that or we recall
+that we want to extract one period perod
+
+ align:start position:0%
+that we want to extract one period perod
+ 
+
+ align:start position:0%
+that we want to extract one period perod
+of this so we extract the period from
+
+ align:start position:0%
+of this so we extract the period from
+ 
+
+ align:start position:0%
+of this so we extract the period from
+zero to 2 Capital
+
+ align:start position:0%
+zero to 2 Capital
+ 
+
+ align:start position:0%
+zero to 2 Capital
+nus1 so we have 0 to 2 capital n minus1
+
+ align:start position:0%
+nus1 so we have 0 to 2 capital n minus1
+ 
+
+ align:start position:0%
+nus1 so we have 0 to 2 capital n minus1
+and this result then is the two Endo
+
+ align:start position:0%
+and this result then is the two Endo
+ 
+
+ align:start position:0%
+and this result then is the two Endo
+circular convolution of X1 of n with X2
+
+ align:start position:0%
+circular convolution of X1 of n with X2
+ 
+
+ align:start position:0%
+circular convolution of X1 of n with X2
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+n it's interesting to note that in this
+
+ align:start position:0%
+n it's interesting to note that in this
+ 
+
+ align:start position:0%
+n it's interesting to note that in this
+case the circular
+
+ align:start position:0%
+case the circular
+ 
+
+ align:start position:0%
+case the circular
+convolution in fact came out looking
+
+ align:start position:0%
+convolution in fact came out looking
+ 
+
+ align:start position:0%
+convolution in fact came out looking
+like the linear convolution of X1 of N
+
+ align:start position:0%
+like the linear convolution of X1 of N
+ 
+
+ align:start position:0%
+like the linear convolution of X1 of N
+and X2 of N and the reason for that we
+
+ align:start position:0%
+and X2 of N and the reason for that we
+ 
+
+ align:start position:0%
+and X2 of N and the reason for that we
+see is that when we did the convolution
+
+ align:start position:0%
+see is that when we did the convolution
+ 
+
+ align:start position:0%
+see is that when we did the convolution
+with this pulse train we chose the
+
+ align:start position:0%
+with this pulse train we chose the
+ 
+
+ align:start position:0%
+with this pulse train we chose the
+spacing of the pulse train large enough
+
+ align:start position:0%
+spacing of the pulse train large enough
+ 
+
+ align:start position:0%
+spacing of the pulse train large enough
+so that there was no interference from
+
+ align:start position:0%
+so that there was no interference from
+ 
+
+ align:start position:0%
+so that there was no interference from
+successive replicas of this linear
+
+ align:start position:0%
+successive replicas of this linear
+ 
+
+ align:start position:0%
+successive replicas of this linear
+convolution well that suggests an
+
+ align:start position:0%
+convolution well that suggests an
+ 
+
+ align:start position:0%
+convolution well that suggests an
+interesting thing it suggests that we
+
+ align:start position:0%
+interesting thing it suggests that we
+ 
+
+ align:start position:0%
+interesting thing it suggests that we
+could in fact imp Implement a linear
+
+ align:start position:0%
+could in fact imp Implement a linear
+ 
+
+ align:start position:0%
+could in fact imp Implement a linear
+convolution from a circular
+
+ align:start position:0%
+convolution from a circular
+ 
+
+ align:start position:0%
+convolution from a circular
+convolution if we're careful enough to
+
+ align:start position:0%
+convolution if we're careful enough to
+ 
+
+ align:start position:0%
+convolution if we're careful enough to
+pick the length of the circular
+
+ align:start position:0%
+pick the length of the circular
+ 
+
+ align:start position:0%
+pick the length of the circular
+convolution long enough now what does
+
+ align:start position:0%
+convolution long enough now what does
+ 
+
+ align:start position:0%
+convolution long enough now what does
+long enough mean well long enough means
+
+ align:start position:0%
+long enough mean well long enough means
+ 
+
+ align:start position:0%
+long enough mean well long enough means
+that the length of the circular
+
+ align:start position:0%
+that the length of the circular
+ 
+
+ align:start position:0%
+that the length of the circular
+convolution has to be longer than the
+
+ align:start position:0%
+convolution has to be longer than the
+ 
+
+ align:start position:0%
+convolution has to be longer than the
+length of the linear
+
+ align:start position:0%
+length of the linear
+ 
+
+ align:start position:0%
+length of the linear
+convolution you can show incidentally
+
+ align:start position:0%
+convolution you can show incidentally
+ 
+
+ align:start position:0%
+convolution you can show incidentally
+and you'll see this in more detail in
+
+ align:start position:0%
+and you'll see this in more detail in
+ 
+
+ align:start position:0%
+and you'll see this in more detail in
+this text that if you have one sequence
+
+ align:start position:0%
+this text that if you have one sequence
+ 
+
+ align:start position:0%
+this text that if you have one sequence
+of length capital n and another sequence
+
+ align:start position:0%
+of length capital n and another sequence
+ 
+
+ align:start position:0%
+of length capital n and another sequence
+of length capital M then the linear
+
+ align:start position:0%
+of length capital M then the linear
+ 
+
+ align:start position:0%
+of length capital M then the linear
+convolution of the two is always going
+
+ align:start position:0%
+convolution of the two is always going
+ 
+
+ align:start position:0%
+convolution of the two is always going
+to be shorter than or equal to n + m
+
+ align:start position:0%
+to be shorter than or equal to n + m
+ 
+
+ align:start position:0%
+to be shorter than or equal to n + m
+minus one points so if we do the
+
+ align:start position:0%
+minus one points so if we do the
+ 
+
+ align:start position:0%
+minus one points so if we do the
+circular convolution on the basis of n +
+
+ align:start position:0%
+circular convolution on the basis of n +
+ 
+
+ align:start position:0%
+circular convolution on the basis of n +
+m minus one or n plus M well take n plus
+
+ align:start position:0%
+m minus one or n plus M well take n plus
+ 
+
+ align:start position:0%
+m minus one or n plus M well take n plus
+M that will certainly work then the
+
+ align:start position:0%
+M that will certainly work then the
+ 
+
+ align:start position:0%
+M that will certainly work then the
+circular convolution will end up
+
+ align:start position:0%
+circular convolution will end up
+ 
+
+ align:start position:0%
+circular convolution will end up
+corresponding to a linear convolution
+
+ align:start position:0%
+corresponding to a linear convolution
+ 
+
+ align:start position:0%
+corresponding to a linear convolution
+and this is the way that we can carry
+
+ align:start position:0%
+and this is the way that we can carry
+ 
+
+ align:start position:0%
+and this is the way that we can carry
+out a linear convolution using circular
+
+ align:start position:0%
+out a linear convolution using circular
+ 
+
+ align:start position:0%
+out a linear convolution using circular
+convolution this is commonly referred to
+
+ align:start position:0%
+convolution this is commonly referred to
+ 
+
+ align:start position:0%
+convolution this is commonly referred to
+as padding with zeros and what that
+
+ align:start position:0%
+as padding with zeros and what that
+ 
+
+ align:start position:0%
+as padding with zeros and what that
+means is treating this endpoint sequence
+
+ align:start position:0%
+means is treating this endpoint sequence
+ 
+
+ align:start position:0%
+means is treating this endpoint sequence
+not as an endpoint sequence when we
+
+ align:start position:0%
+not as an endpoint sequence when we
+ 
+
+ align:start position:0%
+not as an endpoint sequence when we
+compute the
+
+ align:start position:0%
+compute the
+ 
+
+ align:start position:0%
+compute the
+DFT but as a sequence of length 2
+
+ align:start position:0%
+DFT but as a sequence of length 2
+ 
+
+ align:start position:0%
+DFT but as a sequence of length 2
+capital N so that if we computed a two
+
+ align:start position:0%
+capital N so that if we computed a two
+ 
+
+ align:start position:0%
+capital N so that if we computed a two
+capital N Point DFT of this sequence
+
+ align:start position:0%
+capital N Point DFT of this sequence
+ 
+
+ align:start position:0%
+capital N Point DFT of this sequence
+panning out with capital N
+
+ align:start position:0%
+panning out with capital N
+ 
+
+ align:start position:0%
+panning out with capital N
+zeros multiplied that DFT together with
+
+ align:start position:0%
+zeros multiplied that DFT together with
+ 
+
+ align:start position:0%
+zeros multiplied that DFT together with
+itself and then computed the inverse
+
+ align:start position:0%
+itself and then computed the inverse
+ 
+
+ align:start position:0%
+itself and then computed the inverse
+DFT what we would get in fact because of
+
+ align:start position:0%
+DFT what we would get in fact because of
+ 
+
+ align:start position:0%
+DFT what we would get in fact because of
+the fact that we pan it out with zeros
+
+ align:start position:0%
+the fact that we pan it out with zeros
+ 
+
+ align:start position:0%
+the fact that we pan it out with zeros
+is a two endpoint circular convolution
+
+ align:start position:0%
+is a two endpoint circular convolution
+ 
+
+ align:start position:0%
+is a two endpoint circular convolution
+which would correspond to the linear
+
+ align:start position:0%
+which would correspond to the linear
+ 
+
+ align:start position:0%
+which would correspond to the linear
+convolution
+
+ align:start position:0%
+convolution
+ 
+
+ align:start position:0%
+convolution
+so this is the way then that we can
+
+ align:start position:0%
+so this is the way then that we can
+ 
+
+ align:start position:0%
+so this is the way then that we can
+modify a circular convolution so that it
+
+ align:start position:0%
+modify a circular convolution so that it
+ 
+
+ align:start position:0%
+modify a circular convolution so that it
+implements for us a linear
+
+ align:start position:0%
+implements for us a linear
+ 
+
+ align:start position:0%
+implements for us a linear
+convolution and when we actually
+
+ align:start position:0%
+convolution and when we actually
+ 
+
+ align:start position:0%
+convolution and when we actually
+Implement a digital filter or a discrete
+
+ align:start position:0%
+Implement a digital filter or a discrete
+ 
+
+ align:start position:0%
+Implement a digital filter or a discrete
+time system using an explicit
+
+ align:start position:0%
+time system using an explicit
+ 
+
+ align:start position:0%
+time system using an explicit
+computation of the discrete fora
+
+ align:start position:0%
+computation of the discrete fora
+ 
+
+ align:start position:0%
+computation of the discrete fora
+transform then of course this is what we
+
+ align:start position:0%
+transform then of course this is what we
+ 
+
+ align:start position:0%
+transform then of course this is what we
+have to do to avoid the circular
+
+ align:start position:0%
+have to do to avoid the circular
+ 
+
+ align:start position:0%
+have to do to avoid the circular
+convolution since what we want in that
+
+ align:start position:0%
+convolution since what we want in that
+ 
+
+ align:start position:0%
+convolution since what we want in that
+case is a linear
+
+ align:start position:0%
+case is a linear
+ 
+
+ align:start position:0%
+case is a linear
+convolution well it's important very
+
+ align:start position:0%
+convolution well it's important very
+ 
+
+ align:start position:0%
+convolution well it's important very
+important to keep straight first of all
+
+ align:start position:0%
+important to keep straight first of all
+ 
+
+ align:start position:0%
+important to keep straight first of all
+the properties of circular convolution
+
+ align:start position:0%
+the properties of circular convolution
+ 
+
+ align:start position:0%
+the properties of circular convolution
+sometimes in fact circular convolution
+
+ align:start position:0%
+sometimes in fact circular convolution
+ 
+
+ align:start position:0%
+sometimes in fact circular convolution
+is what you would like to
+
+ align:start position:0%
+is what you would like to
+ 
+
+ align:start position:0%
+is what you would like to
+get the notion the relationship between
+
+ align:start position:0%
+get the notion the relationship between
+ 
+
+ align:start position:0%
+get the notion the relationship between
+circular and linear convolution mainly
+
+ align:start position:0%
+circular and linear convolution mainly
+ 
+
+ align:start position:0%
+circular and linear convolution mainly
+this notion of circular convolution
+
+ align:start position:0%
+this notion of circular convolution
+ 
+
+ align:start position:0%
+this notion of circular convolution
+being equal to linear convolution plus
+
+ align:start position:0%
+being equal to linear convolution plus
+ 
+
+ align:start position:0%
+being equal to linear convolution plus
+aliasing and then finally the way in
+
+ align:start position:0%
+aliasing and then finally the way in
+ 
+
+ align:start position:0%
+aliasing and then finally the way in
+which you can use a circular convolution
+
+ align:start position:0%
+which you can use a circular convolution
+ 
+
+ align:start position:0%
+which you can use a circular convolution
+to actually implement a linear
+
+ align:start position:0%
+to actually implement a linear
+ 
+
+ align:start position:0%
+to actually implement a linear
+convolution now what I'd like to do is
+
+ align:start position:0%
+convolution now what I'd like to do is
+ 
+
+ align:start position:0%
+convolution now what I'd like to do is
+really cement this by illustrating these
+
+ align:start position:0%
+really cement this by illustrating these
+ 
+
+ align:start position:0%
+really cement this by illustrating these
+Notions finally with a film which will
+
+ align:start position:0%
+Notions finally with a film which will
+ 
+
+ align:start position:0%
+Notions finally with a film which will
+depict a number of things it's actually
+
+ align:start position:0%
+depict a number of things it's actually
+ 
+
+ align:start position:0%
+depict a number of things it's actually
+the continuation of a film that you saw
+
+ align:start position:0%
+the continuation of a film that you saw
+ 
+
+ align:start position:0%
+the continuation of a film that you saw
+in the first lecture that we had on
+
+ align:start position:0%
+in the first lecture that we had on
+ 
+
+ align:start position:0%
+in the first lecture that we had on
+discreet time
+
+ align:start position:0%
+discreet time
+ 
+
+ align:start position:0%
+discreet time
+convolution we'll show first of all
+
+ align:start position:0%
+convolution we'll show first of all
+ 
+
+ align:start position:0%
+convolution we'll show first of all
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+convolution as just exactly as you had
+
+ align:start position:0%
+convolution as just exactly as you had
+ 
+
+ align:start position:0%
+convolution as just exactly as you had
+seen
+
+ align:start position:0%
+seen
+ 
+
+ align:start position:0%
+seen
+before second of all periodic or
+
+ align:start position:0%
+before second of all periodic or
+ 
+
+ align:start position:0%
+before second of all periodic or
+circular convolution and the difference
+
+ align:start position:0%
+circular convolution and the difference
+ 
+
+ align:start position:0%
+circular convolution and the difference
+between them the third thing that the
+
+ align:start position:0%
+between them the third thing that the
+ 
+
+ align:start position:0%
+between them the third thing that the
+film will illustrate is the relationship
+
+ align:start position:0%
+film will illustrate is the relationship
+ 
+
+ align:start position:0%
+film will illustrate is the relationship
+between linear convolution and periodic
+
+ align:start position:0%
+between linear convolution and periodic
+ 
+
+ align:start position:0%
+between linear convolution and periodic
+or circular convolution namely the
+
+ align:start position:0%
+or circular convolution namely the
+ 
+
+ align:start position:0%
+or circular convolution namely the
+notion of circular convolution as linear
+
+ align:start position:0%
+notion of circular convolution as linear
+ 
+
+ align:start position:0%
+notion of circular convolution as linear
+convolution plus
+
+ align:start position:0%
+convolution plus
+ 
+
+ align:start position:0%
+convolution plus
+aliasing and finally the fourth thing
+
+ align:start position:0%
+aliasing and finally the fourth thing
+ 
+
+ align:start position:0%
+aliasing and finally the fourth thing
+that it will illustrate is this notion
+
+ align:start position:0%
+that it will illustrate is this notion
+ 
+
+ align:start position:0%
+that it will illustrate is this notion
+of panning with zeros so that a circular
+
+ align:start position:0%
+of panning with zeros so that a circular
+ 
+
+ align:start position:0%
+of panning with zeros so that a circular
+convolution can be used to implement a
+
+ align:start position:0%
+convolution can be used to implement a
+ 
+
+ align:start position:0%
+convolution can be used to implement a
+linear convolution so let's go to the
+
+ align:start position:0%
+linear convolution so let's go to the
+ 
+
+ align:start position:0%
+linear convolution so let's go to the
+film now and go through these various
+
+ align:start position:0%
+film now and go through these various
+ 
+
+ align:start position:0%
+film now and go through these various
+examples with the hope that uh at the
+
+ align:start position:0%
+examples with the hope that uh at the
+ 
+
+ align:start position:0%
+examples with the hope that uh at the
+end of this the Notions and
+
+ align:start position:0%
+end of this the Notions and
+ 
+
+ align:start position:0%
+end of this the Notions and
+relationships will really be very Vivid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay the convolution sum then we have is
+
+ align:start position:0%
+okay the convolution sum then we have is
+ 
+
+ align:start position:0%
+okay the convolution sum then we have is
+the sum of X of k h of n minus K and so
+
+ align:start position:0%
+the sum of X of k h of n minus K and so
+ 
+
+ align:start position:0%
+the sum of X of k h of n minus K and so
+what we would like to illustrate is the
+
+ align:start position:0%
+what we would like to illustrate is the
+ 
+
+ align:start position:0%
+what we would like to illustrate is the
+operation of evaluating this sum on the
+
+ align:start position:0%
+operation of evaluating this sum on the
+ 
+
+ align:start position:0%
+operation of evaluating this sum on the
+top we have X of K on the bottom we have
+
+ align:start position:0%
+top we have X of K on the bottom we have
+ 
+
+ align:start position:0%
+top we have X of K on the bottom we have
+H of k h of K being an exponential and
+
+ align:start position:0%
+H of k h of K being an exponential and
+ 
+
+ align:start position:0%
+H of k h of K being an exponential and
+now we see h of minus K namely h of K
+
+ align:start position:0%
+now we see h of minus K namely h of K
+ 
+
+ align:start position:0%
+now we see h of minus K namely h of K
+flipped over as we shift h of K to the
+
+ align:start position:0%
+flipped over as we shift h of K to the
+ 
+
+ align:start position:0%
+flipped over as we shift h of K to the
+left Cor responding to Nal minus1 then
+
+ align:start position:0%
+left Cor responding to Nal minus1 then
+ 
+
+ align:start position:0%
+left Cor responding to Nal minus1 then
+back to
+
+ align:start position:0%
+back to
+ 
+
+ align:start position:0%
+back to
+zero and now to the
+
+ align:start position:0%
+zero and now to the
+ 
+
+ align:start position:0%
+zero and now to the
+right so we have H of 1 minus K and then
+
+ align:start position:0%
+right so we have H of 1 minus K and then
+ 
+
+ align:start position:0%
+right so we have H of 1 minus K and then
+to form y of n we want the product of H
+
+ align:start position:0%
+to form y of n we want the product of H
+ 
+
+ align:start position:0%
+to form y of n we want the product of H
+of minus K shifted with X of K that
+
+ align:start position:0%
+of minus K shifted with X of K that
+ 
+
+ align:start position:0%
+of minus K shifted with X of K that
+product summed from minus infinity to
+
+ align:start position:0%
+product summed from minus infinity to
+ 
+
+ align:start position:0%
+product summed from minus infinity to
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+infinity so here we see X of K * h of 1
+
+ align:start position:0%
+infinity so here we see X of K * h of 1
+ 
+
+ align:start position:0%
+infinity so here we see X of K * h of 1
+- k 2 - K 3 - k etc those multiplied and
+
+ align:start position:0%
+- k 2 - K 3 - k etc those multiplied and
+ 
+
+ align:start position:0%
+- k 2 - K 3 - k etc those multiplied and
+then summed from minus infinity to plus
+
+ align:start position:0%
+then summed from minus infinity to plus
+ 
+
+ align:start position:0%
+then summed from minus infinity to plus
+infinity we see during this portion that
+
+ align:start position:0%
+infinity we see during this portion that
+ 
+
+ align:start position:0%
+infinity we see during this portion that
+more and more values of H are engaged
+
+ align:start position:0%
+more and more values of H are engaged
+ 
+
+ align:start position:0%
+more and more values of H are engaged
+with nonzero values of X and so y of n
+
+ align:start position:0%
+with nonzero values of X and so y of n
+ 
+
+ align:start position:0%
+with nonzero values of X and so y of n
+grows until we reach the point where
+
+ align:start position:0%
+grows until we reach the point where
+ 
+
+ align:start position:0%
+grows until we reach the point where
+values fall off the end of the nonzero
+
+ align:start position:0%
+values fall off the end of the nonzero
+ 
+
+ align:start position:0%
+values fall off the end of the nonzero
+values of X where y of n
+
+ align:start position:0%
+values of X where y of n
+ 
+
+ align:start position:0%
+values of X where y of n
+decays so this then is an illustration
+
+ align:start position:0%
+decays so this then is an illustration
+ 
+
+ align:start position:0%
+decays so this then is an illustration
+of the linear convolution of X of K with
+
+ align:start position:0%
+of the linear convolution of X of K with
+ 
+
+ align:start position:0%
+of the linear convolution of X of K with
+h of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K now what we'd like to compare this
+
+ align:start position:0%
+K now what we'd like to compare this
+ 
+
+ align:start position:0%
+K now what we'd like to compare this
+with is periodic convolution where the
+
+ align:start position:0%
+with is periodic convolution where the
+ 
+
+ align:start position:0%
+with is periodic convolution where the
+sum is of a similar form but the
+
+ align:start position:0%
+sum is of a similar form but the
+ 
+
+ align:start position:0%
+sum is of a similar form but the
+arguments are taken modulo capital
+
+ align:start position:0%
+arguments are taken modulo capital
+ 
+
+ align:start position:0%
+arguments are taken modulo capital
+M and in this case then the shifting is
+
+ align:start position:0%
+M and in this case then the shifting is
+ 
+
+ align:start position:0%
+M and in this case then the shifting is
+a circular shifting rather than a linear
+
+ align:start position:0%
+a circular shifting rather than a linear
+ 
+
+ align:start position:0%
+a circular shifting rather than a linear
+shifting on the top again we have X of K
+
+ align:start position:0%
+shifting on the top again we have X of K
+ 
+
+ align:start position:0%
+shifting on the top again we have X of K
+modulo M on the bottom h of k modulo m
+
+ align:start position:0%
+modulo M on the bottom h of k modulo m
+ 
+
+ align:start position:0%
+modulo M on the bottom h of k modulo m
+now h of minus k modul m and we see that
+
+ align:start position:0%
+now h of minus k modul m and we see that
+ 
+
+ align:start position:0%
+now h of minus k modul m and we see that
+it as we shift the shift is circular
+
+ align:start position:0%
+it as we shift the shift is circular
+ 
+
+ align:start position:0%
+it as we shift the shift is circular
+modulo capital M so there's zero h of 0
+
+ align:start position:0%
+modulo capital M so there's zero h of 0
+ 
+
+ align:start position:0%
+modulo capital M so there's zero h of 0
+- K modul capital
+
+ align:start position:0%
+- K modul capital
+ 
+
+ align:start position:0%
+- K modul capital
+m h of 1 - K modul capital M that was
+
+ align:start position:0%
+m h of 1 - K modul capital M that was
+ 
+
+ align:start position:0%
+m h of 1 - K modul capital M that was
+shifted to the right circularly by
+
+ align:start position:0%
+shifted to the right circularly by
+ 
+
+ align:start position:0%
+shifted to the right circularly by
+one and now we want to look at the sum
+
+ align:start position:0%
+one and now we want to look at the sum
+ 
+
+ align:start position:0%
+one and now we want to look at the sum
+from 0o to M minus one of the product of
+
+ align:start position:0%
+from 0o to M minus one of the product of
+ 
+
+ align:start position:0%
+from 0o to M minus one of the product of
+those and the thing to notice is that
+
+ align:start position:0%
+those and the thing to notice is that
+ 
+
+ align:start position:0%
+those and the thing to notice is that
+since X of K is of length capital M as
+
+ align:start position:0%
+since X of K is of length capital M as
+ 
+
+ align:start position:0%
+since X of K is of length capital M as
+we implement the circular shift of H of
+
+ align:start position:0%
+we implement the circular shift of H of
+ 
+
+ align:start position:0%
+we implement the circular shift of H of
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+K the values of H of K or h of minus K
+
+ align:start position:0%
+K the values of H of K or h of minus K
+ 
+
+ align:start position:0%
+K the values of H of K or h of minus K
+are always engaged with unity values of
+
+ align:start position:0%
+are always engaged with unity values of
+ 
+
+ align:start position:0%
+are always engaged with unity values of
+X and consequently y always comes out to
+
+ align:start position:0%
+X and consequently y always comes out to
+ 
+
+ align:start position:0%
+X and consequently y always comes out to
+have the same
+
+ align:start position:0%
+have the same
+ 
+
+ align:start position:0%
+have the same
+value to see the relationship between
+
+ align:start position:0%
+value to see the relationship between
+ 
+
+ align:start position:0%
+value to see the relationship between
+the periodic and AP periodic convolution
+
+ align:start position:0%
+the periodic and AP periodic convolution
+ 
+
+ align:start position:0%
+the periodic and AP periodic convolution
+namely the aliasing relationship we can
+
+ align:start position:0%
+namely the aliasing relationship we can
+ 
+
+ align:start position:0%
+namely the aliasing relationship we can
+simply look at
+
+ align:start position:0%
+simply look at
+ 
+
+ align:start position:0%
+simply look at
+the AP periodic convolution or linear
+
+ align:start position:0%
+the AP periodic convolution or linear
+ 
+
+ align:start position:0%
+the AP periodic convolution or linear
+convolution take the second M values
+
+ align:start position:0%
+convolution take the second M values
+ 
+
+ align:start position:0%
+convolution take the second M values
+added to the first M
+
+ align:start position:0%
+added to the first M
+ 
+
+ align:start position:0%
+added to the first M
+values and when we carry out that sum
+
+ align:start position:0%
+values and when we carry out that sum
+ 
+
+ align:start position:0%
+values and when we carry out that sum
+what we get is a constant in general the
+
+ align:start position:0%
+what we get is a constant in general the
+ 
+
+ align:start position:0%
+what we get is a constant in general the
+relationship is that the circular
+
+ align:start position:0%
+relationship is that the circular
+ 
+
+ align:start position:0%
+relationship is that the circular
+convolution is y of n plus y of n Plus
+
+ align:start position:0%
+convolution is y of n plus y of n Plus
+ 
+
+ align:start position:0%
+convolution is y of n plus y of n Plus
+capital m y of n plus 2 capital M
+
+ align:start position:0%
+capital m y of n plus 2 capital M
+ 
+
+ align:start position:0%
+capital m y of n plus 2 capital M
+Etc next what we would like to
+
+ align:start position:0%
+Etc next what we would like to
+ 
+
+ align:start position:0%
+Etc next what we would like to
+illustrate is the fact that the linear
+
+ align:start position:0%
+illustrate is the fact that the linear
+ 
+
+ align:start position:0%
+illustrate is the fact that the linear
+convolution can be obtained from a
+
+ align:start position:0%
+convolution can be obtained from a
+ 
+
+ align:start position:0%
+convolution can be obtained from a
+circular convolution if we pad out with
+
+ align:start position:0%
+circular convolution if we pad out with
+ 
+
+ align:start position:0%
+circular convolution if we pad out with
+zeros so now we're going to implement
+
+ align:start position:0%
+zeros so now we're going to implement
+ 
+
+ align:start position:0%
+zeros so now we're going to implement
+the circular
+
+ align:start position:0%
+the circular
+ 
+
+ align:start position:0%
+the circular
+convolution but notice that we've padded
+
+ align:start position:0%
+convolution but notice that we've padded
+ 
+
+ align:start position:0%
+convolution but notice that we've padded
+X of K out with a number of zeros in
+
+ align:start position:0%
+X of K out with a number of zeros in
+ 
+
+ align:start position:0%
+X of K out with a number of zeros in
+that case as we do the circular shifting
+
+ align:start position:0%
+that case as we do the circular shifting
+ 
+
+ align:start position:0%
+that case as we do the circular shifting
+of H the values on the right are
+
+ align:start position:0%
+of H the values on the right are
+ 
+
+ align:start position:0%
+of H the values on the right are
+multiplied only by the zero values that
+
+ align:start position:0%
+multiplied only by the zero values that
+ 
+
+ align:start position:0%
+multiplied only by the zero values that
+we appended x with and so this looks
+
+ align:start position:0%
+we appended x with and so this looks
+ 
+
+ align:start position:0%
+we appended x with and so this looks
+exactly the same as if we were sliding H
+
+ align:start position:0%
+exactly the same as if we were sliding H
+ 
+
+ align:start position:0%
+exactly the same as if we were sliding H
+in from the leftand end and so what
+
+ align:start position:0%
+in from the leftand end and so what
+ 
+
+ align:start position:0%
+in from the leftand end and so what
+results then is the linear convolution
+
+ align:start position:0%
+results then is the linear convolution
+ 
+
+ align:start position:0%
+results then is the linear convolution
+although we're implementing a circular
+
+ align:start position:0%
+although we're implementing a circular
+ 
+
+ align:start position:0%
+although we're implementing a circular
+convolution because of the fact that
+
+ align:start position:0%
+convolution because of the fact that
+ 
+
+ align:start position:0%
+convolution because of the fact that
+we've augmented with zeros the resulting
+
+ align:start position:0%
+we've augmented with zeros the resulting
+ 
+
+ align:start position:0%
+we've augmented with zeros the resulting
+answer is exactly the same as the linear
+
+ align:start position:0%
+answer is exactly the same as the linear
+ 
+
+ align:start position:0%
+answer is exactly the same as the linear
+convolution of X of n with h of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n all right well hopefully through that
+
+ align:start position:0%
+n all right well hopefully through that
+ 
+
+ align:start position:0%
+n all right well hopefully through that
+through the film you get to you got to
+
+ align:start position:0%
+through the film you get to you got to
+ 
+
+ align:start position:0%
+through the film you get to you got to
+see the Dynamics of convolution and
+
+ align:start position:0%
+see the Dynamics of convolution and
+ 
+
+ align:start position:0%
+see the Dynamics of convolution and
+these relationships that I've been
+
+ align:start position:0%
+these relationships that I've been
+ 
+
+ align:start position:0%
+these relationships that I've been
+trying so hard to
+
+ align:start position:0%
+trying so hard to
+ 
+
+ align:start position:0%
+trying so hard to
+stress and now if we return to to the
+
+ align:start position:0%
+stress and now if we return to to the
+ 
+
+ align:start position:0%
+stress and now if we return to to the
+example that we were talking about
+
+ align:start position:0%
+example that we were talking about
+ 
+
+ align:start position:0%
+example that we were talking about
+before the
+
+ align:start position:0%
+before the
+ 
+
+ align:start position:0%
+before the
+film it should be clear that through
+
+ align:start position:0%
+film it should be clear that through
+ 
+
+ align:start position:0%
+film it should be clear that through
+this notion of panning with zeros we can
+
+ align:start position:0%
+this notion of panning with zeros we can
+ 
+
+ align:start position:0%
+this notion of panning with zeros we can
+Implement a linear convolution and
+
+ align:start position:0%
+Implement a linear convolution and
+ 
+
+ align:start position:0%
+Implement a linear convolution and
+thereby Implement a discrete time linear
+
+ align:start position:0%
+thereby Implement a discrete time linear
+ 
+
+ align:start position:0%
+thereby Implement a discrete time linear
+shift and variance system using circular
+
+ align:start position:0%
+shift and variance system using circular
+ 
+
+ align:start position:0%
+shift and variance system using circular
+convolution or equivalently Computing
+
+ align:start position:0%
+convolution or equivalently Computing
+ 
+
+ align:start position:0%
+convolution or equivalently Computing
+dfts multiplying and Computing the
+
+ align:start position:0%
+dfts multiplying and Computing the
+ 
+
+ align:start position:0%
+dfts multiplying and Computing the
+inverse
+
+ align:start position:0%
+inverse
+ 
+
+ align:start position:0%
+inverse
+DFT well well there's only one hitch to
+
+ align:start position:0%
+DFT well well there's only one hitch to
+ 
+
+ align:start position:0%
+DFT well well there's only one hitch to
+that and that's the following suppose
+
+ align:start position:0%
+that and that's the following suppose
+ 
+
+ align:start position:0%
+that and that's the following suppose
+that what I wanted to implement
+
+ align:start position:0%
+that what I wanted to implement
+ 
+
+ align:start position:0%
+that what I wanted to implement
+was the was a discrete time system let's
+
+ align:start position:0%
+was the was a discrete time system let's
+ 
+
+ align:start position:0%
+was the was a discrete time system let's
+take the impulse response as this
+
+ align:start position:0%
+take the impulse response as this
+ 
+
+ align:start position:0%
+take the impulse response as this
+sequence X1 of N and let's say that the
+
+ align:start position:0%
+sequence X1 of N and let's say that the
+ 
+
+ align:start position:0%
+sequence X1 of N and let's say that the
+input to the filter was also a sequence
+
+ align:start position:0%
+input to the filter was also a sequence
+ 
+
+ align:start position:0%
+input to the filter was also a sequence
+of length capital N or capital M then on
+
+ align:start position:0%
+of length capital N or capital M then on
+ 
+
+ align:start position:0%
+of length capital N or capital M then on
+the basis of everything we've been
+
+ align:start position:0%
+the basis of everything we've been
+ 
+
+ align:start position:0%
+the basis of everything we've been
+saying in this lecture clearly we could
+
+ align:start position:0%
+saying in this lecture clearly we could
+ 
+
+ align:start position:0%
+saying in this lecture clearly we could
+do the
+
+ align:start position:0%
+do the
+ 
+
+ align:start position:0%
+do the
+convolution by pading out with enough
+
+ align:start position:0%
+convolution by pading out with enough
+ 
+
+ align:start position:0%
+convolution by pading out with enough
+zeros Computing the discrete 4A
+
+ align:start position:0%
+zeros Computing the discrete 4A
+ 
+
+ align:start position:0%
+zeros Computing the discrete 4A
+transform multiplying and inverse
+
+ align:start position:0%
+transform multiplying and inverse
+ 
+
+ align:start position:0%
+transform multiplying and inverse
+transforming however in order to do that
+
+ align:start position:0%
+transforming however in order to do that
+ 
+
+ align:start position:0%
+transforming however in order to do that
+obviously for the input we before we
+
+ align:start position:0%
+obviously for the input we before we
+ 
+
+ align:start position:0%
+obviously for the input we before we
+compute the discrete 4A transform we
+
+ align:start position:0%
+compute the discrete 4A transform we
+ 
+
+ align:start position:0%
+compute the discrete 4A transform we
+have to wait until the entire input
+
+ align:start position:0%
+have to wait until the entire input
+ 
+
+ align:start position:0%
+have to wait until the entire input
+comes in in other words we need a buffer
+
+ align:start position:0%
+comes in in other words we need a buffer
+ 
+
+ align:start position:0%
+comes in in other words we need a buffer
+that's long enough to hold the entire
+
+ align:start position:0%
+that's long enough to hold the entire
+ 
+
+ align:start position:0%
+that's long enough to hold the entire
+input furthermore what we need to do is
+
+ align:start position:0%
+input furthermore what we need to do is
+ 
+
+ align:start position:0%
+input furthermore what we need to do is
+compute a forier transform discrete
+
+ align:start position:0%
+compute a forier transform discrete
+ 
+
+ align:start position:0%
+compute a forier transform discrete
+forier transform that is at least as
+
+ align:start position:0%
+forier transform that is at least as
+ 
+
+ align:start position:0%
+forier transform that is at least as
+long as the input data in fact as long
+
+ align:start position:0%
+long as the input data in fact as long
+ 
+
+ align:start position:0%
+long as the input data in fact as long
+as the input data plus the length of the
+
+ align:start position:0%
+as the input data plus the length of the
+ 
+
+ align:start position:0%
+as the input data plus the length of the
+unit sample response now obviously if we
+
+ align:start position:0%
+unit sample response now obviously if we
+ 
+
+ align:start position:0%
+unit sample response now obviously if we
+want to filter some signal like let's
+
+ align:start position:0%
+want to filter some signal like let's
+ 
+
+ align:start position:0%
+want to filter some signal like let's
+say B one of Beethoven Symphonies
+
+ align:start position:0%
+say B one of Beethoven Symphonies
+ 
+
+ align:start position:0%
+say B one of Beethoven Symphonies
+clearly we're not first of all going to
+
+ align:start position:0%
+clearly we're not first of all going to
+ 
+
+ align:start position:0%
+clearly we're not first of all going to
+want to buffer the entire input
+
+ align:start position:0%
+want to buffer the entire input
+ 
+
+ align:start position:0%
+want to buffer the entire input
+signal second of all you can imagine
+
+ align:start position:0%
+signal second of all you can imagine
+ 
+
+ align:start position:0%
+signal second of all you can imagine
+computationally that at say a 10 khz or
+
+ align:start position:0%
+computationally that at say a 10 khz or
+ 
+
+ align:start position:0%
+computationally that at say a 10 khz or
+20 khz sampling rate we'd be talking
+
+ align:start position:0%
+20 khz sampling rate we'd be talking
+ 
+
+ align:start position:0%
+20 khz sampling rate we'd be talking
+about a discrete forier transform that's
+
+ align:start position:0%
+about a discrete forier transform that's
+ 
+
+ align:start position:0%
+about a discrete forier transform that's
+that's astronomical in length so if we
+
+ align:start position:0%
+that's astronomical in length so if we
+ 
+
+ align:start position:0%
+that's astronomical in length so if we
+want to implement a digital filter or a
+
+ align:start position:0%
+want to implement a digital filter or a
+ 
+
+ align:start position:0%
+want to implement a digital filter or a
+discrete time system using this kind of
+
+ align:start position:0%
+discrete time system using this kind of
+ 
+
+ align:start position:0%
+discrete time system using this kind of
+approach then we would like to have some
+
+ align:start position:0%
+approach then we would like to have some
+ 
+
+ align:start position:0%
+approach then we would like to have some
+strategy y that avoids the problem of
+
+ align:start position:0%
+strategy y that avoids the problem of
+ 
+
+ align:start position:0%
+strategy y that avoids the problem of
+having to buffer the entire input and
+
+ align:start position:0%
+having to buffer the entire input and
+ 
+
+ align:start position:0%
+having to buffer the entire input and
+one way of doing that is by sectioning
+
+ align:start position:0%
+one way of doing that is by sectioning
+ 
+
+ align:start position:0%
+one way of doing that is by sectioning
+the input
+
+ align:start position:0%
+the input
+ 
+
+ align:start position:0%
+the input
+signal so that suppose we had as an
+
+ align:start position:0%
+signal so that suppose we had as an
+ 
+
+ align:start position:0%
+signal so that suppose we had as an
+example a unit sample response which was
+
+ align:start position:0%
+example a unit sample response which was
+ 
+
+ align:start position:0%
+example a unit sample response which was
+of length capital M so it runs from zero
+
+ align:start position:0%
+of length capital M so it runs from zero
+ 
+
+ align:start position:0%
+of length capital M so it runs from zero
+to capital N minus one we have an input
+
+ align:start position:0%
+to capital N minus one we have an input
+ 
+
+ align:start position:0%
+to capital N minus one we have an input
+signal that's arbitrarily long starts at
+
+ align:start position:0%
+signal that's arbitrarily long starts at
+ 
+
+ align:start position:0%
+signal that's arbitrarily long starts at
+zero let's say and runs on uh for an
+
+ align:start position:0%
+zero let's say and runs on uh for an
+ 
+
+ align:start position:0%
+zero let's say and runs on uh for an
+indefinite length we could imagine
+
+ align:start position:0%
+indefinite length we could imagine
+ 
+
+ align:start position:0%
+indefinite length we could imagine
+sectioning the input sectioning X of n
+
+ align:start position:0%
+sectioning the input sectioning X of n
+ 
+
+ align:start position:0%
+sectioning the input sectioning X of n
+into sections of some length and let's
+
+ align:start position:0%
+into sections of some length and let's
+ 
+
+ align:start position:0%
+into sections of some length and let's
+call the length capital
+
+ align:start position:0%
+call the length capital
+ 
+
+ align:start position:0%
+call the length capital
+L so that we have a number of sections
+
+ align:start position:0%
+L so that we have a number of sections
+ 
+
+ align:start position:0%
+L so that we have a number of sections
+of length capital
+
+ align:start position:0%
+of length capital
+ 
+
+ align:start position:0%
+of length capital
+L now we know and you should recall from
+
+ align:start position:0%
+L now we know and you should recall from
+ 
+
+ align:start position:0%
+L now we know and you should recall from
+when we discussed
+
+ align:start position:0%
+when we discussed
+ 
+
+ align:start position:0%
+when we discussed
+convolution that the convolution of a
+
+ align:start position:0%
+convolution that the convolution of a
+ 
+
+ align:start position:0%
+convolution that the convolution of a
+sum
+
+ align:start position:0%
+sum
+ 
+
+ align:start position:0%
+sum
+the convolution of H of n with a sum of
+
+ align:start position:0%
+the convolution of H of n with a sum of
+ 
+
+ align:start position:0%
+the convolution of H of n with a sum of
+things is equal to the sum of the
+
+ align:start position:0%
+things is equal to the sum of the
+ 
+
+ align:start position:0%
+things is equal to the sum of the
+convolutions so that if we generated a
+
+ align:start position:0%
+convolutions so that if we generated a
+ 
+
+ align:start position:0%
+convolutions so that if we generated a
+set of
+
+ align:start position:0%
+set of
+ 
+
+ align:start position:0%
+set of
+sequences each one corresponding to a
+
+ align:start position:0%
+sequences each one corresponding to a
+ 
+
+ align:start position:0%
+sequences each one corresponding to a
+different section of the
+
+ align:start position:0%
+different section of the
+ 
+
+ align:start position:0%
+different section of the
+input we could convolve each of those
+
+ align:start position:0%
+input we could convolve each of those
+ 
+
+ align:start position:0%
+input we could convolve each of those
+with h of
+
+ align:start position:0%
+with h of
+ 
+
+ align:start position:0%
+with h of
+N and then add the resulting
+
+ align:start position:0%
+N and then add the resulting
+ 
+
+ align:start position:0%
+N and then add the resulting
+convolutions together to form the output
+
+ align:start position:0%
+convolutions together to form the output
+ 
+
+ align:start position:0%
+convolutions together to form the output
+y of n so if we section the input X of n
+
+ align:start position:0%
+y of n so if we section the input X of n
+ 
+
+ align:start position:0%
+y of n so if we section the input X of n
+we can then form a set of sequences each
+
+ align:start position:0%
+we can then form a set of sequences each
+ 
+
+ align:start position:0%
+we can then form a set of sequences each
+one of which corresponds to one of these
+
+ align:start position:0%
+one of which corresponds to one of these
+ 
+
+ align:start position:0%
+one of which corresponds to one of these
+sections and is zero outside the
+
+ align:start position:0%
+sections and is zero outside the
+ 
+
+ align:start position:0%
+sections and is zero outside the
+interval that I've indicated for each
+
+ align:start position:0%
+interval that I've indicated for each
+ 
+
+ align:start position:0%
+interval that I've indicated for each
+one of these colored sections and we
+
+ align:start position:0%
+one of these colored sections and we
+ 
+
+ align:start position:0%
+one of these colored sections and we
+would end up with a set of
+
+ align:start position:0%
+would end up with a set of
+ 
+
+ align:start position:0%
+would end up with a set of
+subsequences which would for example
+
+ align:start position:0%
+subsequences which would for example
+ 
+
+ align:start position:0%
+subsequences which would for example
+look like this x0 of n corresponding to
+
+ align:start position:0%
+look like this x0 of n corresponding to
+ 
+
+ align:start position:0%
+look like this x0 of n corresponding to
+the first L points and zero afterwards
+
+ align:start position:0%
+the first L points and zero afterwards
+ 
+
+ align:start position:0%
+the first L points and zero afterwards
+X1 of n corresponding to the second L
+
+ align:start position:0%
+X1 of n corresponding to the second L
+ 
+
+ align:start position:0%
+X1 of n corresponding to the second L
+points and zero afterwards and before X2
+
+ align:start position:0%
+points and zero afterwards and before X2
+ 
+
+ align:start position:0%
+points and zero afterwards and before X2
+of n the next set of L points X3 of n
+
+ align:start position:0%
+of n the next set of L points X3 of n
+ 
+
+ align:start position:0%
+of n the next set of L points X3 of n
+the next set of L points and we could
+
+ align:start position:0%
+the next set of L points and we could
+ 
+
+ align:start position:0%
+the next set of L points and we could
+continue on like
+
+ align:start position:0%
+continue on like
+ 
+
+ align:start position:0%
+continue on like
+that implement the
+
+ align:start position:0%
+that implement the
+ 
+
+ align:start position:0%
+that implement the
+convolution of each one of these
+
+ align:start position:0%
+convolution of each one of these
+ 
+
+ align:start position:0%
+convolution of each one of these
+sections with the unit sample
+
+ align:start position:0%
+sections with the unit sample
+ 
+
+ align:start position:0%
+sections with the unit sample
+response and then add the resulting
+
+ align:start position:0%
+response and then add the resulting
+ 
+
+ align:start position:0%
+response and then add the resulting
+outputs together in that case the length
+
+ align:start position:0%
+outputs together in that case the length
+ 
+
+ align:start position:0%
+outputs together in that case the length
+transform that we would need to compute
+
+ align:start position:0%
+transform that we would need to compute
+ 
+
+ align:start position:0%
+transform that we would need to compute
+the C the linear convolution of this lpo
+
+ align:start position:0%
+the C the linear convolution of this lpo
+ 
+
+ align:start position:0%
+the C the linear convolution of this lpo
+section with the input h of n would be
+
+ align:start position:0%
+section with the input h of n would be
+ 
+
+ align:start position:0%
+section with the input h of n would be
+where H of n was of length M would be a
+
+ align:start position:0%
+where H of n was of length M would be a
+ 
+
+ align:start position:0%
+where H of n was of length M would be a
+DFT of length l+ M minus one L plus M
+
+ align:start position:0%
+DFT of length l+ M minus one L plus M
+ 
+
+ align:start position:0%
+DFT of length l+ M minus one L plus M
+certainly works but it turns out L plus
+
+ align:start position:0%
+certainly works but it turns out L plus
+ 
+
+ align:start position:0%
+certainly works but it turns out L plus
+M minus one is
+
+ align:start position:0%
+M minus one is
+ 
+
+ align:start position:0%
+M minus one is
+enough now obviously we have to make
+
+ align:start position:0%
+enough now obviously we have to make
+ 
+
+ align:start position:0%
+enough now obviously we have to make
+sure that we line up if we have the
+
+ align:start position:0%
+sure that we line up if we have the
+ 
+
+ align:start position:0%
+sure that we line up if we have the
+input sections delayed by a certain
+
+ align:start position:0%
+input sections delayed by a certain
+ 
+
+ align:start position:0%
+input sections delayed by a certain
+amount we have to make sure that we line
+
+ align:start position:0%
+amount we have to make sure that we line
+ 
+
+ align:start position:0%
+amount we have to make sure that we line
+up the output
+
+ align:start position:0%
+up the output
+ 
+
+ align:start position:0%
+up the output
+sections and what we end up with
+
+ align:start position:0%
+sections and what we end up with
+ 
+
+ align:start position:0%
+sections and what we end up with
+then is a set of output
+
+ align:start position:0%
+then is a set of output
+ 
+
+ align:start position:0%
+then is a set of output
+subsequences which correspond to the
+
+ align:start position:0%
+subsequences which correspond to the
+ 
+
+ align:start position:0%
+subsequences which correspond to the
+convolution of each one of the input
+
+ align:start position:0%
+convolution of each one of the input
+ 
+
+ align:start position:0%
+convolution of each one of the input
+sections with h of
+
+ align:start position:0%
+sections with h of
+ 
+
+ align:start position:0%
+sections with h of
+n now we started out with sections of
+
+ align:start position:0%
+n now we started out with sections of
+ 
+
+ align:start position:0%
+n now we started out with sections of
+length L we convolve those with a unit
+
+ align:start position:0%
+length L we convolve those with a unit
+ 
+
+ align:start position:0%
+length L we convolve those with a unit
+sample response of length
+
+ align:start position:0%
+sample response of length
+ 
+
+ align:start position:0%
+sample response of length
+M the resulting length of the
+
+ align:start position:0%
+M the resulting length of the
+ 
+
+ align:start position:0%
+M the resulting length of the
+convolution will be L + m minus one
+
+ align:start position:0%
+convolution will be L + m minus one
+ 
+
+ align:start position:0%
+convolution will be L + m minus one
+we've seen that in a variety of
+
+ align:start position:0%
+we've seen that in a variety of
+ 
+
+ align:start position:0%
+we've seen that in a variety of
+ways and consequently when we consider
+
+ align:start position:0%
+ways and consequently when we consider
+ 
+
+ align:start position:0%
+ways and consequently when we consider
+adding up the outputs from the
+
+ align:start position:0%
+adding up the outputs from the
+ 
+
+ align:start position:0%
+adding up the outputs from the
+convolution with each one of the
+
+ align:start position:0%
+convolution with each one of the
+ 
+
+ align:start position:0%
+convolution with each one of the
+subsections if this is the point that
+
+ align:start position:0%
+subsections if this is the point that
+ 
+
+ align:start position:0%
+subsections if this is the point that
+corresponds to L this is just exactly
+
+ align:start position:0%
+corresponds to L this is just exactly
+ 
+
+ align:start position:0%
+corresponds to L this is just exactly
+the right delay
+
+ align:start position:0%
+the right delay
+ 
+
+ align:start position:0%
+the right delay
+we notice that there's a tail out of the
+
+ align:start position:0%
+we notice that there's a tail out of the
+ 
+
+ align:start position:0%
+we notice that there's a tail out of the
+convolution in this section that
+
+ align:start position:0%
+convolution in this section that
+ 
+
+ align:start position:0%
+convolution in this section that
+overlaps into the first M minus one or M
+
+ align:start position:0%
+overlaps into the first M minus one or M
+ 
+
+ align:start position:0%
+overlaps into the first M minus one or M
+Points of it's m minus one points
+
+ align:start position:0%
+Points of it's m minus one points
+ 
+
+ align:start position:0%
+Points of it's m minus one points
+actually of this
+
+ align:start position:0%
+actually of this
+ 
+
+ align:start position:0%
+actually of this
+section likewise there are Min minus one
+
+ align:start position:0%
+section likewise there are Min minus one
+ 
+
+ align:start position:0%
+section likewise there are Min minus one
+points at the tail of this one that
+
+ align:start position:0%
+points at the tail of this one that
+ 
+
+ align:start position:0%
+points at the tail of this one that
+overlap into the first M Points here so
+
+ align:start position:0%
+overlap into the first M Points here so
+ 
+
+ align:start position:0%
+overlap into the first M Points here so
+that when we add up the output
+
+ align:start position:0%
+that when we add up the output
+ 
+
+ align:start position:0%
+that when we add up the output
+subsequence sequences what we have is an
+
+ align:start position:0%
+subsequence sequences what we have is an
+ 
+
+ align:start position:0%
+subsequence sequences what we have is an
+overlap between the tail of this section
+
+ align:start position:0%
+overlap between the tail of this section
+ 
+
+ align:start position:0%
+overlap between the tail of this section
+and the beginning of this one since this
+
+ align:start position:0%
+and the beginning of this one since this
+ 
+
+ align:start position:0%
+and the beginning of this one since this
+starts at L and this runs longer than L
+
+ align:start position:0%
+starts at L and this runs longer than L
+ 
+
+ align:start position:0%
+starts at L and this runs longer than L
+similarly an overlap from the tail of
+
+ align:start position:0%
+similarly an overlap from the tail of
+ 
+
+ align:start position:0%
+similarly an overlap from the tail of
+this into the beginning of this one and
+
+ align:start position:0%
+this into the beginning of this one and
+ 
+
+ align:start position:0%
+this into the beginning of this one and
+that continues on because of that this
+
+ align:start position:0%
+that continues on because of that this
+ 
+
+ align:start position:0%
+that continues on because of that this
+technique for sectioning and then adding
+
+ align:start position:0%
+technique for sectioning and then adding
+ 
+
+ align:start position:0%
+technique for sectioning and then adding
+the results together is often referred
+
+ align:start position:0%
+the results together is often referred
+ 
+
+ align:start position:0%
+the results together is often referred
+to as the overlap ad method because we
+
+ align:start position:0%
+to as the overlap ad method because we
+ 
+
+ align:start position:0%
+to as the overlap ad method because we
+overlap the outputs and then add these
+
+ align:start position:0%
+overlap the outputs and then add these
+ 
+
+ align:start position:0%
+overlap the outputs and then add these
+together these pieces will add these
+
+ align:start position:0%
+together these pieces will add these
+ 
+
+ align:start position:0%
+together these pieces will add these
+blue pieces will add Etc down the
+
+ align:start position:0%
+blue pieces will add Etc down the
+ 
+
+ align:start position:0%
+blue pieces will add Etc down the
+line there's also another method for
+
+ align:start position:0%
+line there's also another method for
+ 
+
+ align:start position:0%
+line there's also another method for
+sectioning using circular convolution
+
+ align:start position:0%
+sectioning using circular convolution
+ 
+
+ align:start position:0%
+sectioning using circular convolution
+and fitting the outputs together which
+
+ align:start position:0%
+and fitting the outputs together which
+ 
+
+ align:start position:0%
+and fitting the outputs together which
+is a method that is referred to as the
+
+ align:start position:0%
+is a method that is referred to as the
+ 
+
+ align:start position:0%
+is a method that is referred to as the
+overlap save method and that method is
+
+ align:start position:0%
+overlap save method and that method is
+ 
+
+ align:start position:0%
+overlap save method and that method is
+discussed in some detail in the text and
+
+ align:start position:0%
+discussed in some detail in the text and
+ 
+
+ align:start position:0%
+discussed in some detail in the text and
+responds basically to implementing a
+
+ align:start position:0%
+responds basically to implementing a
+ 
+
+ align:start position:0%
+responds basically to implementing a
+circular convolution of the sections
+
+ align:start position:0%
+circular convolution of the sections
+ 
+
+ align:start position:0%
+circular convolution of the sections
+rather than a linear convolution as we
+
+ align:start position:0%
+rather than a linear convolution as we
+ 
+
+ align:start position:0%
+rather than a linear convolution as we
+did here the linear convolution we could
+
+ align:start position:0%
+did here the linear convolution we could
+ 
+
+ align:start position:0%
+did here the linear convolution we could
+get from a circular convolution by
+
+ align:start position:0%
+get from a circular convolution by
+ 
+
+ align:start position:0%
+get from a circular convolution by
+padding with zeros alternatively we can
+
+ align:start position:0%
+padding with zeros alternatively we can
+ 
+
+ align:start position:0%
+padding with zeros alternatively we can
+take the circular convolution and
+
+ align:start position:0%
+take the circular convolution and
+ 
+
+ align:start position:0%
+take the circular convolution and
+discard the points that don't correspond
+
+ align:start position:0%
+discard the points that don't correspond
+ 
+
+ align:start position:0%
+discard the points that don't correspond
+to a linear
+
+ align:start position:0%
+to a linear
+ 
+
+ align:start position:0%
+to a linear
+convolution well there are a variety of
+
+ align:start position:0%
+convolution well there are a variety of
+ 
+
+ align:start position:0%
+convolution well there are a variety of
+techniques of this type the important
+
+ align:start position:0%
+techniques of this type the important
+ 
+
+ align:start position:0%
+techniques of this type the important
+point though is that circular
+
+ align:start position:0%
+point though is that circular
+ 
+
+ align:start position:0%
+point though is that circular
+convolution can in fact be used to
+
+ align:start position:0%
+convolution can in fact be used to
+ 
+
+ align:start position:0%
+convolution can in fact be used to
+implement linear convolution it can be
+
+ align:start position:0%
+implement linear convolution it can be
+ 
+
+ align:start position:0%
+implement linear convolution it can be
+used to implement digital filters or
+
+ align:start position:0%
+used to implement digital filters or
+ 
+
+ align:start position:0%
+used to implement digital filters or
+discrete time linear systems and in fact
+
+ align:start position:0%
+discrete time linear systems and in fact
+ 
+
+ align:start position:0%
+discrete time linear systems and in fact
+although this there's nothing that we've
+
+ align:start position:0%
+although this there's nothing that we've
+ 
+
+ align:start position:0%
+although this there's nothing that we've
+said that clearly makes this obvious in
+
+ align:start position:0%
+said that clearly makes this obvious in
+ 
+
+ align:start position:0%
+said that clearly makes this obvious in
+fact there are very efficient ways of
+
+ align:start position:0%
+fact there are very efficient ways of
+ 
+
+ align:start position:0%
+fact there are very efficient ways of
+computing the discrete 4ier
+
+ align:start position:0%
+computing the discrete 4ier
+ 
+
+ align:start position:0%
+computing the discrete 4ier
+transform which in fact make this notion
+
+ align:start position:0%
+transform which in fact make this notion
+ 
+
+ align:start position:0%
+transform which in fact make this notion
+of computing the transform multiplying
+
+ align:start position:0%
+of computing the transform multiplying
+ 
+
+ align:start position:0%
+of computing the transform multiplying
+an inverse transforming a efficient
+
+ align:start position:0%
+an inverse transforming a efficient
+ 
+
+ align:start position:0%
+an inverse transforming a efficient
+method an efficient method for
+
+ align:start position:0%
+method an efficient method for
+ 
+
+ align:start position:0%
+method an efficient method for
+implementing a digital
+
+ align:start position:0%
+implementing a digital
+ 
+
+ align:start position:0%
+implementing a digital
+filter all right well this concludes our
+
+ align:start position:0%
+filter all right well this concludes our
+ 
+
+ align:start position:0%
+filter all right well this concludes our
+discussion of the discret forier
+
+ align:start position:0%
+discussion of the discret forier
+ 
+
+ align:start position:0%
+discussion of the discret forier
+transform toward the end of this set of
+
+ align:start position:0%
+transform toward the end of this set of
+ 
+
+ align:start position:0%
+transform toward the end of this set of
+lectures we'll return actually to the
+
+ align:start position:0%
+lectures we'll return actually to the
+ 
+
+ align:start position:0%
+lectures we'll return actually to the
+discret forier transform again where at
+
+ align:start position:0%
+discret forier transform again where at
+ 
+
+ align:start position:0%
+discret forier transform again where at
+that time what we'll want to talk about
+
+ align:start position:0%
+that time what we'll want to talk about
+ 
+
+ align:start position:0%
+that time what we'll want to talk about
+is specifically the computation of the
+
+ align:start position:0%
+is specifically the computation of the
+ 
+
+ align:start position:0%
+is specifically the computation of the
+discret 4A transform which leads to
+
+ align:start position:0%
+discret 4A transform which leads to
+ 
+
+ align:start position:0%
+discret 4A transform which leads to
+Notions such as the fast 4A transform
+
+ align:start position:0%
+Notions such as the fast 4A transform
+ 
+
+ align:start position:0%
+Notions such as the fast 4A transform
+algorithm it's that computational
+
+ align:start position:0%
+algorithm it's that computational
+ 
+
+ align:start position:0%
+algorithm it's that computational
+efficiency that makes some of these
+
+ align:start position:0%
+efficiency that makes some of these
+ 
+
+ align:start position:0%
+efficiency that makes some of these
+ideas that we've talked about in the
+
+ align:start position:0%
+ideas that we've talked about in the
+ 
+
+ align:start position:0%
+ideas that we've talked about in the
+last few lectures so important in terms
+
+ align:start position:0%
+last few lectures so important in terms
+ 
+
+ align:start position:0%
+last few lectures so important in terms
+of implementing digital filters thank
+
+ align:start position:0%
+of implementing digital filters thank
+ 
+
+ align:start position:0%
+of implementing digital filters thank
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/_UBh66KVAJI.txt b/_UBh66KVAJI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..549a50572ae3eea4f122092681d7e58d897c730d
--- /dev/null
+++ b/_UBh66KVAJI.txt
@@ -0,0 +1,1824 @@
+align:start position:0%
+ 
+hi welcome back to recitation today
+
+ align:start position:0%
+hi welcome back to recitation today
+ 
+
+ align:start position:0%
+hi welcome back to recitation today
+we're going to do a couple of exercises
+
+ align:start position:0%
+we're going to do a couple of exercises
+ 
+
+ align:start position:0%
+we're going to do a couple of exercises
+on Computing average values and
+
+ align:start position:0%
+on Computing average values and
+ 
+
+ align:start position:0%
+on Computing average values and
+probabilities so using using integration
+
+ align:start position:0%
+probabilities so using using integration
+ 
+
+ align:start position:0%
+probabilities so using using integration
+so for this problem I'm going to let R
+
+ align:start position:0%
+so for this problem I'm going to let R
+ 
+
+ align:start position:0%
+so for this problem I'm going to let R
+be the name of the region that's bounded
+
+ align:start position:0%
+be the name of the region that's bounded
+ 
+
+ align:start position:0%
+be the name of the region that's bounded
+above by the curve by the line I guess
+
+ align:start position:0%
+above by the curve by the line I guess
+ 
+
+ align:start position:0%
+above by the curve by the line I guess
+yals X and Below by the curve yal X
+
+ align:start position:0%
+yals X and Below by the curve yal X
+ 
+
+ align:start position:0%
+yals X and Below by the curve yal X
+cubed so I have a little picture of R
+
+ align:start position:0%
+cubed so I have a little picture of R
+ 
+
+ align:start position:0%
+cubed so I have a little picture of R
+here it's you know lives all in the in
+
+ align:start position:0%
+here it's you know lives all in the in
+ 
+
+ align:start position:0%
+here it's you know lives all in the in
+the first quadrant there it's just this
+
+ align:start position:0%
+the first quadrant there it's just this
+ 
+
+ align:start position:0%
+the first quadrant there it's just this
+little sliver um so the first part of
+
+ align:start position:0%
+little sliver um so the first part of
+ 
+
+ align:start position:0%
+little sliver um so the first part of
+the question is if I if I look at all
+
+ align:start position:0%
+the question is if I if I look at all
+ 
+
+ align:start position:0%
+the question is if I if I look at all
+the points in R what's the average x
+
+ align:start position:0%
+the points in R what's the average x
+ 
+
+ align:start position:0%
+the points in R what's the average x
+coordinate of those points what's the
+
+ align:start position:0%
+coordinate of those points what's the
+ 
+
+ align:start position:0%
+coordinate of those points what's the
+average value of the of the x coordinate
+
+ align:start position:0%
+average value of the of the x coordinate
+ 
+
+ align:start position:0%
+average value of the of the x coordinate
+and the second problem is if I choose a
+
+ align:start position:0%
+and the second problem is if I choose a
+ 
+
+ align:start position:0%
+and the second problem is if I choose a
+point at random somewhere in R what's
+
+ align:start position:0%
+point at random somewhere in R what's
+ 
+
+ align:start position:0%
+point at random somewhere in R what's
+the probability that its x coordinate is
+
+ align:start position:0%
+the probability that its x coordinate is
+ 
+
+ align:start position:0%
+the probability that its x coordinate is
+larger than 1/2 so what's what's the
+
+ align:start position:0%
+larger than 1/2 so what's what's the
+ 
+
+ align:start position:0%
+larger than 1/2 so what's what's the
+probability that it that it lies on the
+
+ align:start position:0%
+probability that it that it lies on the
+ 
+
+ align:start position:0%
+probability that it that it lies on the
+right hand side of R so why don't you
+
+ align:start position:0%
+right hand side of R so why don't you
+ 
+
+ align:start position:0%
+right hand side of R so why don't you
+pause the video take a couple minutes to
+
+ align:start position:0%
+pause the video take a couple minutes to
+ 
+
+ align:start position:0%
+pause the video take a couple minutes to
+work through these problems come back
+
+ align:start position:0%
+work through these problems come back
+ 
+
+ align:start position:0%
+work through these problems come back
+and we can work on them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together all right welcome back so
+
+ align:start position:0%
+together all right welcome back so
+ 
+
+ align:start position:0%
+together all right welcome back so
+hopefully you've you've had a chance to
+
+ align:start position:0%
+hopefully you've you've had a chance to
+ 
+
+ align:start position:0%
+hopefully you've you've had a chance to
+to get some good work done on these
+
+ align:start position:0%
+to get some good work done on these
+ 
+
+ align:start position:0%
+to get some good work done on these
+questions so let's start to work through
+
+ align:start position:0%
+questions so let's start to work through
+ 
+
+ align:start position:0%
+questions so let's start to work through
+them so remember to compute the the
+
+ align:start position:0%
+them so remember to compute the the
+ 
+
+ align:start position:0%
+them so remember to compute the the
+average value of of a function over some
+
+ align:start position:0%
+average value of of a function over some
+ 
+
+ align:start position:0%
+average value of of a function over some
+region what you need to do is you need
+
+ align:start position:0%
+region what you need to do is you need
+ 
+
+ align:start position:0%
+region what you need to do is you need
+to compute a weighted average and the
+
+ align:start position:0%
+to compute a weighted average and the
+ 
+
+ align:start position:0%
+to compute a weighted average and the
+weighting here is that you have you have
+
+ align:start position:0%
+weighting here is that you have you have
+ 
+
+ align:start position:0%
+weighting here is that you have you have
+to consider the fact that you know for X
+
+ align:start position:0%
+to consider the fact that you know for X
+ 
+
+ align:start position:0%
+to consider the fact that you know for X
+very near zero there aren't very many
+
+ align:start position:0%
+very near zero there aren't very many
+ 
+
+ align:start position:0%
+very near zero there aren't very many
+points in r in this little corner right
+
+ align:start position:0%
+points in r in this little corner right
+ 
+
+ align:start position:0%
+points in r in this little corner right
+and for X very near one there aren't
+
+ align:start position:0%
+and for X very near one there aren't
+ 
+
+ align:start position:0%
+and for X very near one there aren't
+very many points there either in the
+
+ align:start position:0%
+very many points there either in the
+ 
+
+ align:start position:0%
+very many points there either in the
+middle the this region is a little
+
+ align:start position:0%
+middle the this region is a little
+ 
+
+ align:start position:0%
+middle the this region is a little
+higher so there so there are there are
+
+ align:start position:0%
+higher so there so there are there are
+ 
+
+ align:start position:0%
+higher so there so there are there are
+more points there so those points will
+
+ align:start position:0%
+more points there so those points will
+ 
+
+ align:start position:0%
+more points there so those points will
+sort of weigh more when you when you
+
+ align:start position:0%
+sort of weigh more when you when you
+ 
+
+ align:start position:0%
+sort of weigh more when you when you
+take the average of all points than the
+
+ align:start position:0%
+take the average of all points than the
+ 
+
+ align:start position:0%
+take the average of all points than the
+points near the edges so the way we
+
+ align:start position:0%
+points near the edges so the way we
+ 
+
+ align:start position:0%
+points near the edges so the way we
+account for that is we have this this
+
+ align:start position:0%
+account for that is we have this this
+ 
+
+ align:start position:0%
+account for that is we have this this
+weight function that is the the in our
+
+ align:start position:0%
+weight function that is the the in our
+ 
+
+ align:start position:0%
+weight function that is the the in our
+case since we're interested in the x
+
+ align:start position:0%
+case since we're interested in the x
+ 
+
+ align:start position:0%
+case since we're interested in the x
+coordinate the weight at a given x
+
+ align:start position:0%
+coordinate the weight at a given x
+ 
+
+ align:start position:0%
+coordinate the weight at a given x
+coordinate is the the slice of the how
+
+ align:start position:0%
+coordinate is the the slice of the how
+ 
+
+ align:start position:0%
+coordinate is the the slice of the how
+much of the region lies above that x
+
+ align:start position:0%
+much of the region lies above that x
+ 
+
+ align:start position:0%
+much of the region lies above that x
+coordinate what you know the the the
+
+ align:start position:0%
+coordinate what you know the the the
+ 
+
+ align:start position:0%
+coordinate what you know the the the
+area of a little rectangle above that x
+
+ align:start position:0%
+area of a little rectangle above that x
+ 
+
+ align:start position:0%
+area of a little rectangle above that x
+coordinate says how tells you how many
+
+ align:start position:0%
+coordinate says how tells you how many
+ 
+
+ align:start position:0%
+coordinate says how tells you how many
+of the points have that have that x
+
+ align:start position:0%
+of the points have that have that x
+ 
+
+ align:start position:0%
+of the points have that have that x
+coordinate um so then we we want to
+
+ align:start position:0%
+coordinate um so then we we want to
+ 
+
+ align:start position:0%
+coordinate um so then we we want to
+average the the function X right because
+
+ align:start position:0%
+average the the function X right because
+ 
+
+ align:start position:0%
+average the the function X right because
+we're interested in the x coordinate so
+
+ align:start position:0%
+we're interested in the x coordinate so
+ 
+
+ align:start position:0%
+we're interested in the x coordinate so
+the function we're averaging is X um
+
+ align:start position:0%
+the function we're averaging is X um
+ 
+
+ align:start position:0%
+the function we're averaging is X um
+over this over this region with that
+
+ align:start position:0%
+over this over this region with that
+ 
+
+ align:start position:0%
+over this over this region with that
+waiting so all right so let's write down
+
+ align:start position:0%
+waiting so all right so let's write down
+ 
+
+ align:start position:0%
+waiting so all right so let's write down
+what that means so we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have want
+
+ align:start position:0%
+have want
+ 
+
+ align:start position:0%
+have want
+average of the function f ofx and f ofx
+
+ align:start position:0%
+average of the function f ofx and f ofx
+ 
+
+ align:start position:0%
+average of the function f ofx and f ofx
+the thing we're Computing the average of
+
+ align:start position:0%
+the thing we're Computing the average of
+ 
+
+ align:start position:0%
+the thing we're Computing the average of
+is just the x coordinate so it's just
+
+ align:start position:0%
+is just the x coordinate so it's just
+ 
+
+ align:start position:0%
+is just the x coordinate so it's just
+the function value X
+
+ align:start position:0%
+the function value X
+ 
+
+ align:start position:0%
+the function value X
+over R so we want that the average of
+
+ align:start position:0%
+over R so we want that the average of
+ 
+
+ align:start position:0%
+over R so we want that the average of
+this function f ofx over R so what we
+
+ align:start position:0%
+this function f ofx over R so what we
+ 
+
+ align:start position:0%
+this function f ofx over R so what we
+need to compute is the so so we have two
+
+ align:start position:0%
+need to compute is the so so we have two
+ 
+
+ align:start position:0%
+need to compute is the so so we have two
+integrals we need to compute right so we
+
+ align:start position:0%
+integrals we need to compute right so we
+ 
+
+ align:start position:0%
+integrals we need to compute right so we
+need one integral that is the the
+
+ align:start position:0%
+need one integral that is the the
+ 
+
+ align:start position:0%
+need one integral that is the the
+numerator and so that numerator um so
+
+ align:start position:0%
+numerator and so that numerator um so
+ 
+
+ align:start position:0%
+numerator and so that numerator um so
+I'm going to just write average for the
+
+ align:start position:0%
+I'm going to just write average for the
+ 
+
+ align:start position:0%
+I'm going to just write average for the
+average that we want so the numerator is
+
+ align:start position:0%
+average that we want so the numerator is
+ 
+
+ align:start position:0%
+average that we want so the numerator is
+the integral okay and so we have to
+
+ align:start position:0%
+the integral okay and so we have to
+ 
+
+ align:start position:0%
+the integral okay and so we have to
+integrate we have to take all possible X
+
+ align:start position:0%
+integrate we have to take all possible X
+ 
+
+ align:start position:0%
+integrate we have to take all possible X
+values into consideration so X going
+
+ align:start position:0%
+values into consideration so X going
+ 
+
+ align:start position:0%
+values into consideration so X going
+that in this case that's X going from 0
+
+ align:start position:0%
+that in this case that's X going from 0
+ 
+
+ align:start position:0%
+that in this case that's X going from 0
+to 1 and now we want to multiply the
+
+ align:start position:0%
+to 1 and now we want to multiply the
+ 
+
+ align:start position:0%
+to 1 and now we want to multiply the
+function that we're averaging which in
+
+ align:start position:0%
+function that we're averaging which in
+ 
+
+ align:start position:0%
+function that we're averaging which in
+this case is X by the appropriate weight
+
+ align:start position:0%
+this case is X by the appropriate weight
+ 
+
+ align:start position:0%
+this case is X by the appropriate weight
+function and the weight function is how
+
+ align:start position:0%
+function and the weight function is how
+ 
+
+ align:start position:0%
+function and the weight function is how
+much of the region is associated with
+
+ align:start position:0%
+much of the region is associated with
+ 
+
+ align:start position:0%
+much of the region is associated with
+that x value and that's the height of
+
+ align:start position:0%
+that x value and that's the height of
+ 
+
+ align:start position:0%
+that x value and that's the height of
+this little rectangle which in this case
+
+ align:start position:0%
+this little rectangle which in this case
+ 
+
+ align:start position:0%
+this little rectangle which in this case
+is x - x cubed
+
+ align:start position:0%
+is x - x cubed
+ 
+
+ align:start position:0%
+is x - x cubed
+DX okay but then this is an average we
+
+ align:start position:0%
+DX okay but then this is an average we
+ 
+
+ align:start position:0%
+DX okay but then this is an average we
+have to divide by the the total weight
+
+ align:start position:0%
+have to divide by the the total weight
+ 
+
+ align:start position:0%
+have to divide by the the total weight
+of the region the weight in this case is
+
+ align:start position:0%
+of the region the weight in this case is
+ 
+
+ align:start position:0%
+of the region the weight in this case is
+just the area
+
+ align:start position:0%
+just the area
+ 
+
+ align:start position:0%
+just the area
+um so so we have to divide by the
+
+ align:start position:0%
+um so so we have to divide by the
+ 
+
+ align:start position:0%
+um so so we have to divide by the
+integral from 0 to 1 of just this x - x
+
+ align:start position:0%
+integral from 0 to 1 of just this x - x
+ 
+
+ align:start position:0%
+integral from 0 to 1 of just this x - x
+Cub DX okay so we have to compute these
+
+ align:start position:0%
+Cub DX okay so we have to compute these
+ 
+
+ align:start position:0%
+Cub DX okay so we have to compute these
+two integrals and then we have to to
+
+ align:start position:0%
+two integrals and then we have to to
+ 
+
+ align:start position:0%
+two integrals and then we have to to
+take their ratio so let's do them
+
+ align:start position:0%
+take their ratio so let's do them
+ 
+
+ align:start position:0%
+take their ratio so let's do them
+separately so the first one is well the
+
+ align:start position:0%
+separately so the first one is well the
+ 
+
+ align:start position:0%
+separately so the first one is well the
+second one is actually a little simpler
+
+ align:start position:0%
+second one is actually a little simpler
+ 
+
+ align:start position:0%
+second one is actually a little simpler
+the one in the the denominator so let's
+
+ align:start position:0%
+the one in the the denominator so let's
+ 
+
+ align:start position:0%
+the one in the the denominator so let's
+handle that first so the integral from 0
+
+ align:start position:0%
+handle that first so the integral from 0
+ 
+
+ align:start position:0%
+handle that first so the integral from 0
+to 1 of x - x cubed DX well this is a
+
+ align:start position:0%
+to 1 of x - x cubed DX well this is a
+ 
+
+ align:start position:0%
+to 1 of x - x cubed DX well this is a
+pretty easy integral it's x^2 / 2 - x 4
+
+ align:start position:0%
+pretty easy integral it's x^2 / 2 - x 4
+ 
+
+ align:start position:0%
+pretty easy integral it's x^2 / 2 - x 4
+over 4 between zero and one so that's a
+
+ align:start position:0%
+over 4 between zero and one so that's a
+ 
+
+ align:start position:0%
+over 4 between zero and one so that's a
+half minus a quarter so that's minus
+
+ align:start position:0%
+half minus a quarter so that's minus
+ 
+
+ align:start position:0%
+half minus a quarter so that's minus
+well when you put in zero you just get
+
+ align:start position:0%
+well when you put in zero you just get
+ 
+
+ align:start position:0%
+well when you put in zero you just get
+zero so that's a
+
+ align:start position:0%
+zero so that's a
+ 
+
+ align:start position:0%
+zero so that's a
+quarter and the first one the top the
+
+ align:start position:0%
+quarter and the first one the top the
+ 
+
+ align:start position:0%
+quarter and the first one the top the
+numerator is it's the integral from 0 to
+
+ align:start position:0%
+numerator is it's the integral from 0 to
+ 
+
+ align:start position:0%
+numerator is it's the integral from 0 to
+1 okay we can multiply through so that's
+
+ align:start position:0%
+1 okay we can multiply through so that's
+ 
+
+ align:start position:0%
+1 okay we can multiply through so that's
+x^2 - x 4th
+
+ align:start position:0%
+x^2 - x 4th
+ 
+
+ align:start position:0%
+x^2 - x 4th
+DX so that integral from 0 to one again
+
+ align:start position:0%
+DX so that integral from 0 to one again
+ 
+
+ align:start position:0%
+DX so that integral from 0 to one again
+is X Cub over 3 - x the 5 over
+
+ align:start position:0%
+is X Cub over 3 - x the 5 over
+ 
+
+ align:start position:0%
+is X Cub over 3 - x the 5 over
+5 between 0o and one we put in zero we
+
+ align:start position:0%
+5 between 0o and one we put in zero we
+ 
+
+ align:start position:0%
+5 between 0o and one we put in zero we
+get zero put in one we get a third minus
+
+ align:start position:0%
+get zero put in one we get a third minus
+ 
+
+ align:start position:0%
+get zero put in one we get a third minus
+a fifth so that's common
+
+ align:start position:0%
+a fifth so that's common
+ 
+
+ align:start position:0%
+a fifth so that's common
+denominator 15 2
+
+ align:start position:0%
+denominator 15 2
+ 
+
+ align:start position:0%
+denominator 15 2
+15 okay so the numerator of our average
+
+ align:start position:0%
+15 okay so the numerator of our average
+ 
+
+ align:start position:0%
+15 okay so the numerator of our average
+value is 215 the denominator is
+
+ align:start position:0%
+value is 215 the denominator is
+ 
+
+ align:start position:0%
+value is 215 the denominator is
+1/4 so this so the average value we're
+
+ align:start position:0%
+1/4 so this so the average value we're
+ 
+
+ align:start position:0%
+1/4 so this so the average value we're
+interested in is
+
+ align:start position:0%
+interested in is
+ 
+
+ align:start position:0%
+interested in is
+25 / 1
+
+ align:start position:0%
+25 / 1
+ 
+
+ align:start position:0%
+25 / 1
+qu which is 8 15 so the average x
+
+ align:start position:0%
+qu which is 8 15 so the average x
+ 
+
+ align:start position:0%
+qu which is 8 15 so the average x
+coordinate is just so 81 15 is just a
+
+ align:start position:0%
+coordinate is just so 81 15 is just a
+ 
+
+ align:start position:0%
+coordinate is just so 81 15 is just a
+tiny bit larger than a half right so so
+
+ align:start position:0%
+tiny bit larger than a half right so so
+ 
+
+ align:start position:0%
+tiny bit larger than a half right so so
+this is saying somehow the the average x
+
+ align:start position:0%
+this is saying somehow the the average x
+ 
+
+ align:start position:0%
+this is saying somehow the the average x
+coordinate is just slightly shifted to
+
+ align:start position:0%
+coordinate is just slightly shifted to
+ 
+
+ align:start position:0%
+coordinate is just slightly shifted to
+the right of 1/2 so this I may have
+
+ align:start position:0%
+the right of 1/2 so this I may have
+ 
+
+ align:start position:0%
+the right of 1/2 so this I may have
+drawn this region sort of symmetrically
+
+ align:start position:0%
+drawn this region sort of symmetrically
+ 
+
+ align:start position:0%
+drawn this region sort of symmetrically
+but in in fact it's a little bit uh
+
+ align:start position:0%
+but in in fact it's a little bit uh
+ 
+
+ align:start position:0%
+but in in fact it's a little bit uh
+shifted to to the right there so that's
+
+ align:start position:0%
+shifted to to the right there so that's
+ 
+
+ align:start position:0%
+shifted to to the right there so that's
+the uh the first part of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem for the second part we want to
+
+ align:start position:0%
+problem for the second part we want to
+ 
+
+ align:start position:0%
+problem for the second part we want to
+compute the probability so okay so we
+
+ align:start position:0%
+compute the probability so okay so we
+ 
+
+ align:start position:0%
+compute the probability so okay so we
+choose a point at random in the set R
+
+ align:start position:0%
+choose a point at random in the set R
+ 
+
+ align:start position:0%
+choose a point at random in the set R
+and we want to know what's the
+
+ align:start position:0%
+and we want to know what's the
+ 
+
+ align:start position:0%
+and we want to know what's the
+probability that its x coordinate is
+
+ align:start position:0%
+probability that its x coordinate is
+ 
+
+ align:start position:0%
+probability that its x coordinate is
+larger
+
+ align:start position:0%
+larger
+ 
+
+ align:start position:0%
+larger
+than2 well since all points are are you
+
+ align:start position:0%
+than2 well since all points are are you
+ 
+
+ align:start position:0%
+than2 well since all points are are you
+know equally likely all regions the
+
+ align:start position:0%
+know equally likely all regions the
+ 
+
+ align:start position:0%
+know equally likely all regions the
+probability is just a is just has to do
+
+ align:start position:0%
+probability is just a is just has to do
+ 
+
+ align:start position:0%
+probability is just a is just has to do
+with the area of the region what we
+
+ align:start position:0%
+with the area of the region what we
+ 
+
+ align:start position:0%
+with the area of the region what we
+really want to know is what's the area
+
+ align:start position:0%
+really want to know is what's the area
+ 
+
+ align:start position:0%
+really want to know is what's the area
+of R to the right of the line xal 12 so
+
+ align:start position:0%
+of R to the right of the line xal 12 so
+ 
+
+ align:start position:0%
+of R to the right of the line xal 12 so
+that's the the good region and then we
+
+ align:start position:0%
+that's the the good region and then we
+ 
+
+ align:start position:0%
+that's the the good region and then we
+want to know how much of the entire
+
+ align:start position:0%
+want to know how much of the entire
+ 
+
+ align:start position:0%
+want to know how much of the entire
+region is that so we want to know the
+
+ align:start position:0%
+region is that so we want to know the
+ 
+
+ align:start position:0%
+region is that so we want to know the
+the area of the good region to the right
+
+ align:start position:0%
+the area of the good region to the right
+ 
+
+ align:start position:0%
+the area of the good region to the right
+of2 divided by the total area now
+
+ align:start position:0%
+of2 divided by the total area now
+ 
+
+ align:start position:0%
+of2 divided by the total area now
+luckily we've already computed the total
+
+ align:start position:0%
+luckily we've already computed the total
+ 
+
+ align:start position:0%
+luckily we've already computed the total
+area right here this is this was this
+
+ align:start position:0%
+area right here this is this was this
+ 
+
+ align:start position:0%
+area right here this is this was this
+denominator that we had over here so we
+
+ align:start position:0%
+denominator that we had over here so we
+ 
+
+ align:start position:0%
+denominator that we had over here so we
+just need we just need the numerator of
+
+ align:start position:0%
+just need we just need the numerator of
+ 
+
+ align:start position:0%
+just need we just need the numerator of
+that fraction so let's go over here let
+
+ align:start position:0%
+that fraction so let's go over here let
+ 
+
+ align:start position:0%
+that fraction so let's go over here let
+me let me write that down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+equals so I'm going to put good area in
+
+ align:start position:0%
+equals so I'm going to put good area in
+ 
+
+ align:start position:0%
+equals so I'm going to put good area in
+quotation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+marks so what I mean by good area is the
+
+ align:start position:0%
+marks so what I mean by good area is the
+ 
+
+ align:start position:0%
+marks so what I mean by good area is the
+area of the set of points that satisfies
+
+ align:start position:0%
+area of the set of points that satisfies
+ 
+
+ align:start position:0%
+area of the set of points that satisfies
+our condition and in our case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the good area is just we so a point
+
+ align:start position:0%
+the good area is just we so a point
+ 
+
+ align:start position:0%
+the good area is just we so a point
+we're interested in if it's x coordinate
+
+ align:start position:0%
+we're interested in if it's x coordinate
+ 
+
+ align:start position:0%
+we're interested in if it's x coordinate
+is bigger than a half so we just want to
+
+ align:start position:0%
+is bigger than a half so we just want to
+ 
+
+ align:start position:0%
+is bigger than a half so we just want to
+to take the the part of this region to
+
+ align:start position:0%
+to take the the part of this region to
+ 
+
+ align:start position:0%
+to take the the part of this region to
+the right of2 so in order to compute
+
+ align:start position:0%
+the right of2 so in order to compute
+ 
+
+ align:start position:0%
+the right of2 so in order to compute
+that we just you know take this integral
+
+ align:start position:0%
+that we just you know take this integral
+ 
+
+ align:start position:0%
+that we just you know take this integral
+from 1/2 to one instead of from zero to
+
+ align:start position:0%
+from 1/2 to one instead of from zero to
+ 
+
+ align:start position:0%
+from 1/2 to one instead of from zero to
+one so we're only counting those points
+
+ align:start position:0%
+one so we're only counting those points
+ 
+
+ align:start position:0%
+one so we're only counting those points
+to the right of2
+
+ align:start position:0%
+to the right of2
+ 
+
+ align:start position:0%
+to the right of2
+and then we want the you know the area
+
+ align:start position:0%
+and then we want the you know the area
+ 
+
+ align:start position:0%
+and then we want the you know the area
+between these two curves on that region
+
+ align:start position:0%
+between these two curves on that region
+ 
+
+ align:start position:0%
+between these two curves on that region
+okay so and again this is a fairly
+
+ align:start position:0%
+okay so and again this is a fairly
+ 
+
+ align:start position:0%
+okay so and again this is a fairly
+simple integral to compute so this gives
+
+ align:start position:0%
+simple integral to compute so this gives
+ 
+
+ align:start position:0%
+simple integral to compute so this gives
+me x^2 over 2 - x 4 over 4 between 12
+
+ align:start position:0%
+me x^2 over 2 - x 4 over 4 between 12
+ 
+
+ align:start position:0%
+me x^2 over 2 - x 4 over 4 between 12
+and 1 all right so this is maybe a tiny
+
+ align:start position:0%
+and 1 all right so this is maybe a tiny
+ 
+
+ align:start position:0%
+and 1 all right so this is maybe a tiny
+bit hairy so this gives me 12 minus a
+
+ align:start position:0%
+bit hairy so this gives me 12 minus a
+ 
+
+ align:start position:0%
+bit hairy so this gives me 12 minus a
+quarter minus well we put in a half here
+
+ align:start position:0%
+quarter minus well we put in a half here
+ 
+
+ align:start position:0%
+quarter minus well we put in a half here
+we get 1 18
+
+ align:start position:0%
+we get 1 18
+ 
+
+ align:start position:0%
+we get 1 18
+minus 12 to the 4th is a 16th / 4 is 1
+
+ align:start position:0%
+minus 12 to the 4th is a 16th / 4 is 1
+ 
+
+ align:start position:0%
+minus 12 to the 4th is a 16th / 4 is 1
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+64 so this is all going to be in
+
+ align:start position:0%
+64 so this is all going to be in
+ 
+
+ align:start position:0%
+64 so this is all going to be in
+64ths so okay so let's see 32 64s minus
+
+ align:start position:0%
+64ths so okay so let's see 32 64s minus
+ 
+
+ align:start position:0%
+64ths so okay so let's see 32 64s minus
+16 64s - 8 64s + 1 if I just put it all
+
+ align:start position:0%
+16 64s - 8 64s + 1 if I just put it all
+ 
+
+ align:start position:0%
+16 64s - 8 64s + 1 if I just put it all
+over that common denominator all right
+
+ align:start position:0%
+over that common denominator all right
+ 
+
+ align:start position:0%
+over that common denominator all right
+so I think that looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+9 64s if I did that right so okay so
+
+ align:start position:0%
+9 64s if I did that right so okay so
+ 
+
+ align:start position:0%
+9 64s if I did that right so okay so
+that's the good area and then the
+
+ align:start position:0%
+that's the good area and then the
+ 
+
+ align:start position:0%
+that's the good area and then the
+probability that I want I have to divide
+
+ align:start position:0%
+probability that I want I have to divide
+ 
+
+ align:start position:0%
+probability that I want I have to divide
+the good area by the total area and we
+
+ align:start position:0%
+the good area by the total area and we
+ 
+
+ align:start position:0%
+the good area by the total area and we
+saw before that the total area was 1/4
+
+ align:start position:0%
+saw before that the total area was 1/4
+ 
+
+ align:start position:0%
+saw before that the total area was 1/4
+that was what this computation was so
+
+ align:start position:0%
+that was what this computation was so
+ 
+
+ align:start position:0%
+that was what this computation was so
+the total area is 1/4 so the
+
+ align:start position:0%
+the total area is 1/4 so the
+ 
+
+ align:start position:0%
+the total area is 1/4 so the
+probability I'm just going to write p r
+
+ align:start position:0%
+probability I'm just going to write p r
+ 
+
+ align:start position:0%
+probability I'm just going to write p r
+for probability that we're interested in
+
+ align:start position:0%
+for probability that we're interested in
+ 
+
+ align:start position:0%
+for probability that we're interested in
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+9 over
+
+ align:start position:0%
+9 over
+ 
+
+ align:start position:0%
+9 over
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+divided 1 over
+
+ align:start position:0%
+divided 1 over
+ 
+
+ align:start position:0%
+divided 1 over
+4 which is 9 over
+
+ align:start position:0%
+4 which is 9 over
+ 
+
+ align:start position:0%
+4 which is 9 over
+16 okay so this says it so 9 over 16 is
+
+ align:start position:0%
+16 okay so this says it so 9 over 16 is
+ 
+
+ align:start position:0%
+16 okay so this says it so 9 over 16 is
+also a little bit bigger than a half so
+
+ align:start position:0%
+also a little bit bigger than a half so
+ 
+
+ align:start position:0%
+also a little bit bigger than a half so
+this is a different way of saying our
+
+ align:start position:0%
+this is a different way of saying our
+ 
+
+ align:start position:0%
+this is a different way of saying our
+region there's a little bit more of it
+
+ align:start position:0%
+region there's a little bit more of it
+ 
+
+ align:start position:0%
+region there's a little bit more of it
+to the right than there is to the left
+
+ align:start position:0%
+to the right than there is to the left
+ 
+
+ align:start position:0%
+to the right than there is to the left
+you know so it's slightly more likely
+
+ align:start position:0%
+you know so it's slightly more likely
+ 
+
+ align:start position:0%
+you know so it's slightly more likely
+that a that a random point is to the
+
+ align:start position:0%
+that a that a random point is to the
+ 
+
+ align:start position:0%
+that a that a random point is to the
+right of the line Y equals 1/2 than it
+
+ align:start position:0%
+right of the line Y equals 1/2 than it
+ 
+
+ align:start position:0%
+right of the line Y equals 1/2 than it
+is to the left of that line so just to
+
+ align:start position:0%
+is to the left of that line so just to
+ 
+
+ align:start position:0%
+is to the left of that line so just to
+sum up we had these two different uh
+
+ align:start position:0%
+sum up we had these two different uh
+ 
+
+ align:start position:0%
+sum up we had these two different uh
+problem s that we did concerning this
+
+ align:start position:0%
+problem s that we did concerning this
+ 
+
+ align:start position:0%
+problem s that we did concerning this
+region R so first we computed the
+
+ align:start position:0%
+region R so first we computed the
+ 
+
+ align:start position:0%
+region R so first we computed the
+average value of the x coordinate of a
+
+ align:start position:0%
+average value of the x coordinate of a
+ 
+
+ align:start position:0%
+average value of the x coordinate of a
+point in this region so that was that
+
+ align:start position:0%
+point in this region so that was that
+ 
+
+ align:start position:0%
+point in this region so that was that
+was part a we computed the average value
+
+ align:start position:0%
+was part a we computed the average value
+ 
+
+ align:start position:0%
+was part a we computed the average value
+of the x coordinate and that was over
+
+ align:start position:0%
+of the x coordinate and that was over
+ 
+
+ align:start position:0%
+of the x coordinate and that was over
+here so we had to you know do this the
+
+ align:start position:0%
+here so we had to you know do this the
+ 
+
+ align:start position:0%
+here so we had to you know do this the
+weighted average of the x coordinate
+
+ align:start position:0%
+weighted average of the x coordinate
+ 
+
+ align:start position:0%
+weighted average of the x coordinate
+divided by the the total area and then
+
+ align:start position:0%
+divided by the the total area and then
+ 
+
+ align:start position:0%
+divided by the the total area and then
+second we computed the probability that
+
+ align:start position:0%
+second we computed the probability that
+ 
+
+ align:start position:0%
+second we computed the probability that
+a randomly chosen Point has x coordinate
+
+ align:start position:0%
+a randomly chosen Point has x coordinate
+ 
+
+ align:start position:0%
+a randomly chosen Point has x coordinate
+larger than2 and we did that over
+
+ align:start position:0%
+larger than2 and we did that over
+ 
+
+ align:start position:0%
+larger than2 and we did that over
+here and for that we needed to to
+
+ align:start position:0%
+here and for that we needed to to
+ 
+
+ align:start position:0%
+here and for that we needed to to
+compute the area of the of the good
+
+ align:start position:0%
+compute the area of the of the good
+ 
+
+ align:start position:0%
+compute the area of the of the good
+region which was the part to the right
+
+ align:start position:0%
+region which was the part to the right
+ 
+
+ align:start position:0%
+region which was the part to the right
+of the line yal 1/2 and then we needed
+
+ align:start position:0%
+of the line yal 1/2 and then we needed
+ 
+
+ align:start position:0%
+of the line yal 1/2 and then we needed
+to divide it by the total area so I'll
+
+ align:start position:0%
+to divide it by the total area so I'll
+ 
+
+ align:start position:0%
+to divide it by the total area so I'll
+end there
\ No newline at end of file
diff --git a/_gqsatXDIJ4.txt b/_gqsatXDIJ4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9fb7cc5a016897449d36f3750a978e78ebb01b7d
--- /dev/null
+++ b/_gqsatXDIJ4.txt
@@ -0,0 +1,6019 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mentioned that a lot of what we're
+
+ align:start position:0%
+I mentioned that a lot of what we're
+ 
+
+ align:start position:0%
+I mentioned that a lot of what we're
+going to do when we model Solutions is
+
+ align:start position:0%
+going to do when we model Solutions is
+ 
+
+ align:start position:0%
+going to do when we model Solutions is
+bookkeeping so this is a really
+
+ align:start position:0%
+bookkeeping so this is a really
+ 
+
+ align:start position:0%
+bookkeeping so this is a really
+important quantity that we're going to
+
+ align:start position:0%
+important quantity that we're going to
+ 
+
+ align:start position:0%
+important quantity that we're going to
+track and I'm going to introduce it
+
+ align:start position:0%
+track and I'm going to introduce it
+ 
+
+ align:start position:0%
+track and I'm going to introduce it
+partial molar properties and we're going
+
+ align:start position:0%
+partial molar properties and we're going
+ 
+
+ align:start position:0%
+partial molar properties and we're going
+to use them the notation as in the text
+
+ align:start position:0%
+to use them the notation as in the text
+ 
+
+ align:start position:0%
+to use them the notation as in the text
+so the partial molar
+
+ align:start position:0%
+so the partial molar
+ 
+
+ align:start position:0%
+so the partial molar
+property for some generic State function
+
+ align:start position:0%
+property for some generic State function
+ 
+
+ align:start position:0%
+property for some generic State function
+we're using B here because it could
+
+ align:start position:0%
+we're using B here because it could
+ 
+
+ align:start position:0%
+we're using B here because it could
+stand in for any state function
+
+ align:start position:0%
+stand in for any state function
+ 
+
+ align:start position:0%
+stand in for any state function
+is the partial
+
+ align:start position:0%
+is the partial
+ 
+
+ align:start position:0%
+is the partial
+of the total B which is an extensive
+
+ align:start position:0%
+of the total B which is an extensive
+ 
+
+ align:start position:0%
+of the total B which is an extensive
+State function with moles of component k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at fixed temperature fixed pressure
+
+ align:start position:0%
+at fixed temperature fixed pressure
+ 
+
+ align:start position:0%
+at fixed temperature fixed pressure
+and fixed moles of
+
+ align:start position:0%
+and fixed moles of
+ 
+
+ align:start position:0%
+and fixed moles of
+everything that's not k J not equal to K
+
+ align:start position:0%
+everything that's not k J not equal to K
+ 
+
+ align:start position:0%
+everything that's not k J not equal to K
+so B is an extensive property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+extensive property
+
+ align:start position:0%
+extensive property
+ 
+
+ align:start position:0%
+extensive property
+n a k is moles of K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and B Bar of K
+
+ align:start position:0%
+and B Bar of K
+ 
+
+ align:start position:0%
+and B Bar of K
+equals a partial molar property
+
+ align:start position:0%
+equals a partial molar property
+ 
+
+ align:start position:0%
+equals a partial molar property
+sometimes I'll just
+
+ align:start position:0%
+sometimes I'll just
+ 
+
+ align:start position:0%
+sometimes I'll just
+call this pmps
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+um kind of formal looking but it's not
+
+ align:start position:0%
+um kind of formal looking but it's not
+ 
+
+ align:start position:0%
+um kind of formal looking but it's not
+it's not a hard concept
+
+ align:start position:0%
+it's not a hard concept
+ 
+
+ align:start position:0%
+it's not a hard concept
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know you could think of this in many
+
+ align:start position:0%
+you know you could think of this in many
+ 
+
+ align:start position:0%
+you know you could think of this in many
+different ways you could think of the
+
+ align:start position:0%
+different ways you could think of the
+ 
+
+ align:start position:0%
+different ways you could think of the
+extensive property as the total amount
+
+ align:start position:0%
+extensive property as the total amount
+ 
+
+ align:start position:0%
+extensive property as the total amount
+of money in all of our pockets right now
+
+ align:start position:0%
+of money in all of our pockets right now
+ 
+
+ align:start position:0%
+of money in all of our pockets right now
+um but we each have different amounts of
+
+ align:start position:0%
+um but we each have different amounts of
+ 
+
+ align:start position:0%
+um but we each have different amounts of
+money in our pockets right so our our
+
+ align:start position:0%
+money in our pockets right so our our
+ 
+
+ align:start position:0%
+money in our pockets right so our our
+own contribution to the total amount of
+
+ align:start position:0%
+own contribution to the total amount of
+ 
+
+ align:start position:0%
+own contribution to the total amount of
+money in all of our pockets right now
+
+ align:start position:0%
+money in all of our pockets right now
+ 
+
+ align:start position:0%
+money in all of our pockets right now
+would be our partial you know personal
+
+ align:start position:0%
+would be our partial you know personal
+ 
+
+ align:start position:0%
+would be our partial you know personal
+property I guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can think of this as as the total
+
+ align:start position:0%
+you can think of this as as the total
+ 
+
+ align:start position:0%
+you can think of this as as the total
+area in my whole neighborhood land area
+
+ align:start position:0%
+area in my whole neighborhood land area
+ 
+
+ align:start position:0%
+area in my whole neighborhood land area
+but um each of our houses has a
+
+ align:start position:0%
+but um each of our houses has a
+ 
+
+ align:start position:0%
+but um each of our houses has a
+different lot size so we each have a
+
+ align:start position:0%
+different lot size so we each have a
+ 
+
+ align:start position:0%
+different lot size so we each have a
+different contribution to the total land
+
+ align:start position:0%
+different contribution to the total land
+ 
+
+ align:start position:0%
+different contribution to the total land
+area
+
+ align:start position:0%
+area
+ 
+
+ align:start position:0%
+area
+in my neighborhood over here in West
+
+ align:start position:0%
+in my neighborhood over here in West
+ 
+
+ align:start position:0%
+in my neighborhood over here in West
+Cambridge and so forth and so on so you
+
+ align:start position:0%
+Cambridge and so forth and so on so you
+ 
+
+ align:start position:0%
+Cambridge and so forth and so on so you
+know this bookkeeping is kind of formal
+
+ align:start position:0%
+know this bookkeeping is kind of formal
+ 
+
+ align:start position:0%
+know this bookkeeping is kind of formal
+but the concept is is familiar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're gonna make sure we know what the
+
+ align:start position:0%
+we're gonna make sure we know what the
+ 
+
+ align:start position:0%
+we're gonna make sure we know what the
+total differential
+
+ align:start position:0%
+total differential
+ 
+
+ align:start position:0%
+total differential
+of property B is
+
+ align:start position:0%
+of property B is
+ 
+
+ align:start position:0%
+of property B is
+we have these coefficients the b d t f x
+
+ align:start position:0%
+we have these coefficients the b d t f x
+ 
+
+ align:start position:0%
+we have these coefficients the b d t f x
+pre p
+
+ align:start position:0%
+pre p
+ 
+
+ align:start position:0%
+pre p
+and mole number
+
+ align:start position:0%
+and mole number
+ 
+
+ align:start position:0%
+and mole number
+DET plus d b d p
+
+ align:start position:0%
+DET plus d b d p
+ 
+
+ align:start position:0%
+DET plus d b d p
+f x t
+
+ align:start position:0%
+f x t
+ 
+
+ align:start position:0%
+f x t
+and mole number
+
+ align:start position:0%
+and mole number
+ 
+
+ align:start position:0%
+and mole number
+and here's where uh we get to use the
+
+ align:start position:0%
+and here's where uh we get to use the
+ 
+
+ align:start position:0%
+and here's where uh we get to use the
+partial mole of properties plus b i d n
+
+ align:start position:0%
+partial mole of properties plus b i d n
+ 
+
+ align:start position:0%
+partial mole of properties plus b i d n
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+so as defined here it's a coefficient
+
+ align:start position:0%
+so as defined here it's a coefficient
+ 
+
+ align:start position:0%
+so as defined here it's a coefficient
+right partial molar property is just
+
+ align:start position:0%
+right partial molar property is just
+ 
+
+ align:start position:0%
+right partial molar property is just
+coefficient
+
+ align:start position:0%
+coefficient
+ 
+
+ align:start position:0%
+coefficient
+foreign
+
+ align:start position:0%
+foreign
+ 
+
+ align:start position:0%
+foreign
+clarification for a pure phase
+
+ align:start position:0%
+clarification for a pure phase
+ 
+
+ align:start position:0%
+clarification for a pure phase
+for a pure phase right you only have one
+
+ align:start position:0%
+for a pure phase right you only have one
+ 
+
+ align:start position:0%
+for a pure phase right you only have one
+component its mole fraction is one
+
+ align:start position:0%
+component its mole fraction is one
+ 
+
+ align:start position:0%
+component its mole fraction is one
+and the partial molar property is simply
+
+ align:start position:0%
+and the partial molar property is simply
+ 
+
+ align:start position:0%
+and the partial molar property is simply
+the molar property there's no partial
+
+ align:start position:0%
+the molar property there's no partial
+ 
+
+ align:start position:0%
+the molar property there's no partial
+involved
+
+ align:start position:0%
+involved
+ 
+
+ align:start position:0%
+involved
+all right one thing about pmps is pmps
+
+ align:start position:0%
+all right one thing about pmps is pmps
+ 
+
+ align:start position:0%
+all right one thing about pmps is pmps
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're intensive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're independent of the system size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm going to use some illustrations
+
+ align:start position:0%
+and I'm going to use some illustrations
+ 
+
+ align:start position:0%
+and I'm going to use some illustrations
+to to sort of tell you what I mean there
+
+ align:start position:0%
+to to sort of tell you what I mean there
+ 
+
+ align:start position:0%
+to to sort of tell you what I mean there
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see how do we know they're
+
+ align:start position:0%
+let's see how do we know they're
+ 
+
+ align:start position:0%
+let's see how do we know they're
+intensive
+
+ align:start position:0%
+intensive
+ 
+
+ align:start position:0%
+intensive
+a PMP is an extensive quantity divided
+
+ align:start position:0%
+a PMP is an extensive quantity divided
+ 
+
+ align:start position:0%
+a PMP is an extensive quantity divided
+by an extensive quantity
+
+ align:start position:0%
+by an extensive quantity
+ 
+
+ align:start position:0%
+by an extensive quantity
+so if I imagine
+
+ align:start position:0%
+so if I imagine
+ 
+
+ align:start position:0%
+so if I imagine
+um this is a partial mole of property um
+
+ align:start position:0%
+um this is a partial mole of property um
+ 
+
+ align:start position:0%
+um this is a partial mole of property um
+and the system is
+
+ align:start position:0%
+and the system is
+ 
+
+ align:start position:0%
+and the system is
+is a given size and I double the system
+
+ align:start position:0%
+is a given size and I double the system
+ 
+
+ align:start position:0%
+is a given size and I double the system
+size
+
+ align:start position:0%
+size
+ 
+
+ align:start position:0%
+size
+then both the numerator and the
+
+ align:start position:0%
+then both the numerator and the
+ 
+
+ align:start position:0%
+then both the numerator and the
+denominator here will double
+
+ align:start position:0%
+denominator here will double
+ 
+
+ align:start position:0%
+denominator here will double
+and the Intensive parcel molar property
+
+ align:start position:0%
+and the Intensive parcel molar property
+ 
+
+ align:start position:0%
+and the Intensive parcel molar property
+will remain unchanged
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um but there are there are kind of
+
+ align:start position:0%
+um but there are there are kind of
+ 
+
+ align:start position:0%
+um but there are there are kind of
+useful consequences of this so let's
+
+ align:start position:0%
+useful consequences of this so let's
+ 
+
+ align:start position:0%
+useful consequences of this so let's
+let's imagine a system made out of um
+
+ align:start position:0%
+let's imagine a system made out of um
+ 
+
+ align:start position:0%
+let's imagine a system made out of um
+triangles and
+
+ align:start position:0%
+triangles and
+ 
+
+ align:start position:0%
+triangles and
+circles so for example
+
+ align:start position:0%
+circles so for example
+ 
+
+ align:start position:0%
+circles so for example
+let's imagine a system with X Circle
+
+ align:start position:0%
+let's imagine a system with X Circle
+ 
+
+ align:start position:0%
+let's imagine a system with X Circle
+equals x triangle and it's 50 50 just
+
+ align:start position:0%
+equals x triangle and it's 50 50 just
+ 
+
+ align:start position:0%
+equals x triangle and it's 50 50 just
+just to be specific
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so let's imagine three different
+
+ align:start position:0%
+um so let's imagine three different
+ 
+
+ align:start position:0%
+um so let's imagine three different
+systems here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we have
+
+ align:start position:0%
+here we have
+ 
+
+ align:start position:0%
+here we have
+one two three four
+
+ align:start position:0%
+one two three four
+ 
+
+ align:start position:0%
+one two three four
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+five circles
+
+ align:start position:0%
+five circles
+ 
+
+ align:start position:0%
+five circles
+and we have five triangles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if we have B Circle
+
+ align:start position:0%
+and if we have B Circle
+ 
+
+ align:start position:0%
+and if we have B Circle
+equals seven
+
+ align:start position:0%
+equals seven
+ 
+
+ align:start position:0%
+equals seven
+and B
+
+ align:start position:0%
+and B
+ 
+
+ align:start position:0%
+and B
+triangle I'm just making up numbers here
+
+ align:start position:0%
+triangle I'm just making up numbers here
+ 
+
+ align:start position:0%
+triangle I'm just making up numbers here
+it doesn't matter what numbers I used
+
+ align:start position:0%
+it doesn't matter what numbers I used
+ 
+
+ align:start position:0%
+it doesn't matter what numbers I used
+and for T and P constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this case total amount of B
+
+ align:start position:0%
+in this case total amount of B
+ 
+
+ align:start position:0%
+in this case total amount of B
+because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B Circle and circle plus b triangle n
+
+ align:start position:0%
+B Circle and circle plus b triangle n
+ 
+
+ align:start position:0%
+B Circle and circle plus b triangle n
+triangle
+
+ align:start position:0%
+triangle
+ 
+
+ align:start position:0%
+triangle
+and this is seven
+
+ align:start position:0%
+and this is seven
+ 
+
+ align:start position:0%
+and this is seven
+times five plus
+
+ align:start position:0%
+times five plus
+ 
+
+ align:start position:0%
+times five plus
+four times five
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's considered a slightly different
+
+ align:start position:0%
+let's considered a slightly different
+ 
+
+ align:start position:0%
+let's considered a slightly different
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+let's make the system a little smaller
+
+ align:start position:0%
+let's make the system a little smaller
+ 
+
+ align:start position:0%
+let's make the system a little smaller
+let's have three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moles of each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in this case the total amount of B
+
+ align:start position:0%
+in this case the total amount of B
+ 
+
+ align:start position:0%
+in this case the total amount of B
+again is some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B of i n of I
+
+ align:start position:0%
+B of i n of I
+ 
+
+ align:start position:0%
+B of i n of I
+equals seven times three
+
+ align:start position:0%
+equals seven times three
+ 
+
+ align:start position:0%
+equals seven times three
+plus four times three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then of course you can keep on going
+
+ align:start position:0%
+and then of course you can keep on going
+ 
+
+ align:start position:0%
+and then of course you can keep on going
+here let's imagine
+
+ align:start position:0%
+here let's imagine
+ 
+
+ align:start position:0%
+here let's imagine
+one Circle
+
+ align:start position:0%
+one Circle
+ 
+
+ align:start position:0%
+one Circle
+and one triangle
+
+ align:start position:0%
+and one triangle
+ 
+
+ align:start position:0%
+and one triangle
+the total amount of V equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seven plus
+
+ align:start position:0%
+seven plus
+ 
+
+ align:start position:0%
+seven plus
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so why am I telling you this right why
+
+ align:start position:0%
+so why am I telling you this right why
+ 
+
+ align:start position:0%
+so why am I telling you this right why
+do we just go through this exercise with
+
+ align:start position:0%
+do we just go through this exercise with
+ 
+
+ align:start position:0%
+do we just go through this exercise with
+circles and triangles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it's because we're going to add up
+
+ align:start position:0%
+um it's because we're going to add up
+ 
+
+ align:start position:0%
+um it's because we're going to add up
+partial molar properties a lot we're
+
+ align:start position:0%
+partial molar properties a lot we're
+ 
+
+ align:start position:0%
+partial molar properties a lot we're
+going to be doing this quite a lot and
+
+ align:start position:0%
+going to be doing this quite a lot and
+ 
+
+ align:start position:0%
+going to be doing this quite a lot and
+um it comes back to this the whole
+
+ align:start position:0%
+um it comes back to this the whole
+ 
+
+ align:start position:0%
+um it comes back to this the whole
+is the sum of the contributions of the
+
+ align:start position:0%
+is the sum of the contributions of the
+ 
+
+ align:start position:0%
+is the sum of the contributions of the
+parts according to this bookkeeping
+
+ align:start position:0%
+parts according to this bookkeeping
+ 
+
+ align:start position:0%
+parts according to this bookkeeping
+scheme
+
+ align:start position:0%
+scheme
+ 
+
+ align:start position:0%
+scheme
+it's according to this bookkeeping
+
+ align:start position:0%
+it's according to this bookkeeping
+ 
+
+ align:start position:0%
+it's according to this bookkeeping
+scheme
+
+ align:start position:0%
+scheme
+ 
+
+ align:start position:0%
+scheme
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's keep going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we need some mathematical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between the whole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is the total amount of B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the p m P's
+
+ align:start position:0%
+and the p m P's
+ 
+
+ align:start position:0%
+and the p m P's
+so we're gonna
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're gonna consider scaling
+
+ align:start position:0%
+we're gonna consider scaling
+ 
+
+ align:start position:0%
+we're gonna consider scaling
+the system size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by a scaling Factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is a unit this thing I'll just
+
+ align:start position:0%
+and this is a unit this thing I'll just
+ 
+
+ align:start position:0%
+and this is a unit this thing I'll just
+use Lambda so imagine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+is a function of temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the scaled system size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well if we imagine let's say doubling
+
+ align:start position:0%
+well if we imagine let's say doubling
+ 
+
+ align:start position:0%
+well if we imagine let's say doubling
+the amount of moles of everybody
+
+ align:start position:0%
+the amount of moles of everybody
+ 
+
+ align:start position:0%
+the amount of moles of everybody
+we simply double all extensive
+
+ align:start position:0%
+we simply double all extensive
+ 
+
+ align:start position:0%
+we simply double all extensive
+quantities
+
+ align:start position:0%
+quantities
+ 
+
+ align:start position:0%
+quantities
+and that holds for any you know it
+
+ align:start position:0%
+and that holds for any you know it
+ 
+
+ align:start position:0%
+and that holds for any you know it
+doesn't have to be double it could be
+
+ align:start position:0%
+doesn't have to be double it could be
+ 
+
+ align:start position:0%
+doesn't have to be double it could be
+triple it could be have could be any
+
+ align:start position:0%
+triple it could be have could be any
+ 
+
+ align:start position:0%
+triple it could be have could be any
+Factor so
+
+ align:start position:0%
+Factor so
+ 
+
+ align:start position:0%
+Factor so
+we have this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I If I multiply by some constant
+
+ align:start position:0%
+so if I If I multiply by some constant
+ 
+
+ align:start position:0%
+so if I If I multiply by some constant
+scale factor the size of the system it's
+
+ align:start position:0%
+scale factor the size of the system it's
+ 
+
+ align:start position:0%
+scale factor the size of the system it's
+the same thing as multiplying the
+
+ align:start position:0%
+the same thing as multiplying the
+ 
+
+ align:start position:0%
+the same thing as multiplying the
+overall extensive quantity by that same
+
+ align:start position:0%
+overall extensive quantity by that same
+ 
+
+ align:start position:0%
+overall extensive quantity by that same
+scale factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to use this so this is not
+
+ align:start position:0%
+I'm going to use this so this is not
+ 
+
+ align:start position:0%
+I'm going to use this so this is not
+just you know for fun this becomes
+
+ align:start position:0%
+just you know for fun this becomes
+ 
+
+ align:start position:0%
+just you know for fun this becomes
+useful but I will sort of call out for
+
+ align:start position:0%
+useful but I will sort of call out for
+ 
+
+ align:start position:0%
+useful but I will sort of call out for
+those of you who are mathematically
+
+ align:start position:0%
+those of you who are mathematically
+ 
+
+ align:start position:0%
+those of you who are mathematically
+inclined but that means that b Prime
+
+ align:start position:0%
+inclined but that means that b Prime
+ 
+
+ align:start position:0%
+inclined but that means that b Prime
+is a homogeneous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the MKS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of order
+
+ align:start position:0%
+of order
+ 
+
+ align:start position:0%
+of order
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+so for those of you who do like real
+
+ align:start position:0%
+so for those of you who do like real
+ 
+
+ align:start position:0%
+so for those of you who do like real
+analysis and stuff that that comes in
+
+ align:start position:0%
+analysis and stuff that that comes in
+ 
+
+ align:start position:0%
+analysis and stuff that that comes in
+but never mind okay so what we're going
+
+ align:start position:0%
+but never mind okay so what we're going
+ 
+
+ align:start position:0%
+but never mind okay so what we're going
+to do with that is we're going to take
+
+ align:start position:0%
+to do with that is we're going to take
+ 
+
+ align:start position:0%
+to do with that is we're going to take
+the derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+total derivative d d Lambda
+
+ align:start position:0%
+total derivative d d Lambda
+ 
+
+ align:start position:0%
+total derivative d d Lambda
+of both sides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's see the left hand side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is going to give us d B
+
+ align:start position:0%
+is going to give us d B
+ 
+
+ align:start position:0%
+is going to give us d B
+D Lambda
+
+ align:start position:0%
+D Lambda
+ 
+
+ align:start position:0%
+D Lambda
+equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+Lambda n of K
+
+ align:start position:0%
+Lambda n of K
+ 
+
+ align:start position:0%
+Lambda n of K
+just using the chain rule here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is chain Rule
+
+ align:start position:0%
+this is chain Rule
+ 
+
+ align:start position:0%
+this is chain Rule
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+this is our definition of partial mode
+
+ align:start position:0%
+this is our definition of partial mode
+ 
+
+ align:start position:0%
+this is our definition of partial mode
+of property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this derivative is really easy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay right hand side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d d Lambda
+
+ align:start position:0%
+d d Lambda
+ 
+
+ align:start position:0%
+d d Lambda
+times Lambda
+
+ align:start position:0%
+times Lambda
+ 
+
+ align:start position:0%
+times Lambda
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+t p
+
+ align:start position:0%
+t p
+ 
+
+ align:start position:0%
+t p
+n of K and that is also an easy
+
+ align:start position:0%
+n of K and that is also an easy
+ 
+
+ align:start position:0%
+n of K and that is also an easy
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+that's B
+
+ align:start position:0%
+that's B
+ 
+
+ align:start position:0%
+that's B
+t p
+
+ align:start position:0%
+t p
+ 
+
+ align:start position:0%
+t p
+and okay so I took the total derivative
+
+ align:start position:0%
+and okay so I took the total derivative
+ 
+
+ align:start position:0%
+and okay so I took the total derivative
+of the left hand side and the right hand
+
+ align:start position:0%
+of the left hand side and the right hand
+ 
+
+ align:start position:0%
+of the left hand side and the right hand
+side
+
+ align:start position:0%
+side
+ 
+
+ align:start position:0%
+side
+and I'm going to then compare them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay again this is exactly what we were
+
+ align:start position:0%
+okay again this is exactly what we were
+ 
+
+ align:start position:0%
+okay again this is exactly what we were
+doing with circles and triangles
+
+ align:start position:0%
+doing with circles and triangles
+ 
+
+ align:start position:0%
+doing with circles and triangles
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+total extensive quantity
+
+ align:start position:0%
+total extensive quantity
+ 
+
+ align:start position:0%
+total extensive quantity
+for a system is the sum of the partial
+
+ align:start position:0%
+for a system is the sum of the partial
+ 
+
+ align:start position:0%
+for a system is the sum of the partial
+molar properties times the mul numbers
+
+ align:start position:0%
+molar properties times the mul numbers
+ 
+
+ align:start position:0%
+molar properties times the mul numbers
+there we go circles and triangles
+
+ align:start position:0%
+there we go circles and triangles
+ 
+
+ align:start position:0%
+there we go circles and triangles
+scaling with system size and this is
+
+ align:start position:0%
+scaling with system size and this is
+ 
+
+ align:start position:0%
+scaling with system size and this is
+called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an Euler equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think it's the only one we're going to
+
+ align:start position:0%
+I think it's the only one we're going to
+ 
+
+ align:start position:0%
+I think it's the only one we're going to
+use in this class so you don't have to
+
+ align:start position:0%
+use in this class so you don't have to
+ 
+
+ align:start position:0%
+use in this class so you don't have to
+worry so much about you know that
+
+ align:start position:0%
+worry so much about you know that
+ 
+
+ align:start position:0%
+worry so much about you know that
+there's this category of equations
+
+ align:start position:0%
+there's this category of equations
+ 
+
+ align:start position:0%
+there's this category of equations
+called Euler equations in thermal but
+
+ align:start position:0%
+called Euler equations in thermal but
+ 
+
+ align:start position:0%
+called Euler equations in thermal but
+you know you might encounter them if not
+
+ align:start position:0%
+you know you might encounter them if not
+ 
+
+ align:start position:0%
+you know you might encounter them if not
+now than in a later class and and that's
+
+ align:start position:0%
+now than in a later class and and that's
+ 
+
+ align:start position:0%
+now than in a later class and and that's
+what this is
+
+ align:start position:0%
+what this is
+ 
+
+ align:start position:0%
+what this is
+it is the consequence of that first or
+
+ align:start position:0%
+it is the consequence of that first or
+ 
+
+ align:start position:0%
+it is the consequence of that first or
+order homogeneous property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where does it stated a little more
+
+ align:start position:0%
+where does it stated a little more
+ 
+
+ align:start position:0%
+where does it stated a little more
+colloquially extensive properties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a solution phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+made up of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+mole
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+weighted
+
+ align:start position:0%
+weighted
+ 
+
+ align:start position:0%
+weighted
+pmps
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's what it means so for example this
+
+ align:start position:0%
+that's what it means so for example this
+ 
+
+ align:start position:0%
+that's what it means so for example this
+is the one we'll be using almost
+
+ align:start position:0%
+is the one we'll be using almost
+ 
+
+ align:start position:0%
+is the one we'll be using almost
+to the exclusion of any other in this
+
+ align:start position:0%
+to the exclusion of any other in this
+ 
+
+ align:start position:0%
+to the exclusion of any other in this
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+the Gibbs free energy of a system
+
+ align:start position:0%
+the Gibbs free energy of a system
+ 
+
+ align:start position:0%
+the Gibbs free energy of a system
+is going to be the sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of these PMP times the whole numbers
+
+ align:start position:0%
+of these PMP times the whole numbers
+ 
+
+ align:start position:0%
+of these PMP times the whole numbers
+and because Gibbs free energy is so
+
+ align:start position:0%
+and because Gibbs free energy is so
+ 
+
+ align:start position:0%
+and because Gibbs free energy is so
+special we have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+special expression for the molar Gibbs
+
+ align:start position:0%
+special expression for the molar Gibbs
+ 
+
+ align:start position:0%
+special expression for the molar Gibbs
+free energy and its chemical potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that gives free energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PMP
+
+ align:start position:0%
+PMP
+ 
+
+ align:start position:0%
+PMP
+is the chemical potential so you've seen
+
+ align:start position:0%
+is the chemical potential so you've seen
+ 
+
+ align:start position:0%
+is the chemical potential so you've seen
+this expression before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you ever see someone add up the
+
+ align:start position:0%
+so if you ever see someone add up the
+ 
+
+ align:start position:0%
+so if you ever see someone add up the
+Gibbs free energy of a system and they
+
+ align:start position:0%
+Gibbs free energy of a system and they
+ 
+
+ align:start position:0%
+Gibbs free energy of a system and they
+just jump right to this you know where
+
+ align:start position:0%
+just jump right to this you know where
+ 
+
+ align:start position:0%
+just jump right to this you know where
+it comes from
+
+ align:start position:0%
+it comes from
+ 
+
+ align:start position:0%
+it comes from
+the sum of the chemical potentials
+
+ align:start position:0%
+the sum of the chemical potentials
+ 
+
+ align:start position:0%
+the sum of the chemical potentials
+weighted by the mole numbers
+
+ align:start position:0%
+weighted by the mole numbers
+ 
+
+ align:start position:0%
+weighted by the mole numbers
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+unfortunately we have to continue with
+
+ align:start position:0%
+unfortunately we have to continue with
+ 
+
+ align:start position:0%
+unfortunately we have to continue with
+more equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what we're doing here is we're
+
+ align:start position:0%
+so what we're doing here is we're
+ 
+
+ align:start position:0%
+so what we're doing here is we're
+building up to these useful Expressions
+
+ align:start position:0%
+building up to these useful Expressions
+ 
+
+ align:start position:0%
+building up to these useful Expressions
+which you can use you will use on the
+
+ align:start position:0%
+which you can use you will use on the
+ 
+
+ align:start position:0%
+which you can use you will use on the
+homework for instance without
+
+ align:start position:0%
+homework for instance without
+ 
+
+ align:start position:0%
+homework for instance without
+necessarily knowing where they come from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have an Euler equation
+
+ align:start position:0%
+so we have an Euler equation
+ 
+
+ align:start position:0%
+so we have an Euler equation
+which is like
+
+ align:start position:0%
+which is like
+ 
+
+ align:start position:0%
+which is like
+the one we just
+
+ align:start position:0%
+the one we just
+ 
+
+ align:start position:0%
+the one we just
+derived which is the total amount of B
+
+ align:start position:0%
+derived which is the total amount of B
+ 
+
+ align:start position:0%
+derived which is the total amount of B
+equals the sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the partial molar B
+
+ align:start position:0%
+of the partial molar B
+ 
+
+ align:start position:0%
+of the partial molar B
+times the mole numbers
+
+ align:start position:0%
+times the mole numbers
+ 
+
+ align:start position:0%
+times the mole numbers
+and then we're going to use the chain
+
+ align:start position:0%
+and then we're going to use the chain
+ 
+
+ align:start position:0%
+and then we're going to use the chain
+rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're going to calculate the total
+
+ align:start position:0%
+and we're going to calculate the total
+ 
+
+ align:start position:0%
+and we're going to calculate the total
+derivative DB and that's going to be
+
+ align:start position:0%
+derivative DB and that's going to be
+ 
+
+ align:start position:0%
+derivative DB and that's going to be
+equal to chain rule stuff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b k d n of K plus n of K
+
+ align:start position:0%
+b k d n of K plus n of K
+ 
+
+ align:start position:0%
+b k d n of K plus n of K
+d d
+
+ align:start position:0%
+d d
+ 
+
+ align:start position:0%
+d d
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and that's relatively straightforward
+
+ align:start position:0%
+and that's relatively straightforward
+ 
+
+ align:start position:0%
+and that's relatively straightforward
+and we're going to use a coefficient
+
+ align:start position:0%
+and we're going to use a coefficient
+ 
+
+ align:start position:0%
+and we're going to use a coefficient
+relation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the coefficient relation is at D B at
+
+ align:start position:0%
+the coefficient relation is at D B at
+ 
+
+ align:start position:0%
+the coefficient relation is at D B at
+constant temperature and pressure
+
+ align:start position:0%
+constant temperature and pressure
+ 
+
+ align:start position:0%
+constant temperature and pressure
+equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that was from the beginning when we
+
+ align:start position:0%
+that was from the beginning when we
+ 
+
+ align:start position:0%
+that was from the beginning when we
+defined the partial molar property and
+
+ align:start position:0%
+defined the partial molar property and
+ 
+
+ align:start position:0%
+defined the partial molar property and
+so what we're going to do is we're going
+
+ align:start position:0%
+so what we're going to do is we're going
+ 
+
+ align:start position:0%
+so what we're going to do is we're going
+to Simply compare
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compare these Expressions this and this
+
+ align:start position:0%
+compare these Expressions this and this
+ 
+
+ align:start position:0%
+compare these Expressions this and this
+and we find that one of these two sums
+
+ align:start position:0%
+and we find that one of these two sums
+ 
+
+ align:start position:0%
+and we find that one of these two sums
+is zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is called a Gibbs duhammer equation
+
+ align:start position:0%
+this is called a Gibbs duhammer equation
+ 
+
+ align:start position:0%
+this is called a Gibbs duhammer equation
+and by the way I really would not be
+
+ align:start position:0%
+and by the way I really would not be
+ 
+
+ align:start position:0%
+and by the way I really would not be
+spending the time on this if it didn't
+
+ align:start position:0%
+spending the time on this if it didn't
+ 
+
+ align:start position:0%
+spending the time on this if it didn't
+end up in a really useful place so if
+
+ align:start position:0%
+end up in a really useful place so if
+ 
+
+ align:start position:0%
+end up in a really useful place so if
+you're wondering why on Earth you signed
+
+ align:start position:0%
+you're wondering why on Earth you signed
+ 
+
+ align:start position:0%
+you're wondering why on Earth you signed
+up for a classroom analysis
+
+ align:start position:0%
+up for a classroom analysis
+ 
+
+ align:start position:0%
+up for a classroom analysis
+um all I can say is this is a class on
+
+ align:start position:0%
+um all I can say is this is a class on
+ 
+
+ align:start position:0%
+um all I can say is this is a class on
+Thermo and this is part of it and I'm
+
+ align:start position:0%
+Thermo and this is part of it and I'm
+ 
+
+ align:start position:0%
+Thermo and this is part of it and I'm
+including it because it's going to take
+
+ align:start position:0%
+including it because it's going to take
+ 
+
+ align:start position:0%
+including it because it's going to take
+us somewhere really useful okay right
+
+ align:start position:0%
+us somewhere really useful okay right
+ 
+
+ align:start position:0%
+us somewhere really useful okay right
+and that's excuse making this is uh
+
+ align:start position:0%
+and that's excuse making this is uh
+ 
+
+ align:start position:0%
+and that's excuse making this is uh
+Thermo so ndbk what on Earth does this
+
+ align:start position:0%
+Thermo so ndbk what on Earth does this
+ 
+
+ align:start position:0%
+Thermo so ndbk what on Earth does this
+mean it means that you can't change are
+
+ align:start position:0%
+mean it means that you can't change are
+ 
+
+ align:start position:0%
+mean it means that you can't change are
+the partial amount of properties
+
+ align:start position:0%
+the partial amount of properties
+ 
+
+ align:start position:0%
+the partial amount of properties
+independently of each other
+
+ align:start position:0%
+independently of each other
+ 
+
+ align:start position:0%
+independently of each other
+if you have two components
+
+ align:start position:0%
+if you have two components
+ 
+
+ align:start position:0%
+if you have two components
+let's say the sum runs over two
+
+ align:start position:0%
+let's say the sum runs over two
+ 
+
+ align:start position:0%
+let's say the sum runs over two
+there's a linkage between how The Parson
+
+ align:start position:0%
+there's a linkage between how The Parson
+ 
+
+ align:start position:0%
+there's a linkage between how The Parson
+model properties of one change
+
+ align:start position:0%
+model properties of one change
+ 
+
+ align:start position:0%
+model properties of one change
+when the part partial molar properties
+
+ align:start position:0%
+when the part partial molar properties
+ 
+
+ align:start position:0%
+when the part partial molar properties
+of the other change
+
+ align:start position:0%
+of the other change
+ 
+
+ align:start position:0%
+of the other change
+right there's this equation that relates
+
+ align:start position:0%
+right there's this equation that relates
+ 
+
+ align:start position:0%
+right there's this equation that relates
+those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me take that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the Gibbs do have equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are constraints
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+the variation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of intensive properties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right or in other words they express
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how the partial molar properties
+
+ align:start position:0%
+how the partial molar properties
+ 
+
+ align:start position:0%
+how the partial molar properties
+covary right that's a that's a term from
+
+ align:start position:0%
+covary right that's a that's a term from
+ 
+
+ align:start position:0%
+covary right that's a that's a term from
+optimization they covariate with system
+
+ align:start position:0%
+optimization they covariate with system
+ 
+
+ align:start position:0%
+optimization they covariate with system
+composition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in other words it's a differential
+
+ align:start position:0%
+in other words it's a differential
+ 
+
+ align:start position:0%
+in other words it's a differential
+equation right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right an equation that describes how
+
+ align:start position:0%
+right an equation that describes how
+ 
+
+ align:start position:0%
+right an equation that describes how
+things covary with each other is it
+
+ align:start position:0%
+things covary with each other is it
+ 
+
+ align:start position:0%
+things covary with each other is it
+differential equation that's what it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so now we're going to move
+
+ align:start position:0%
+all right so now we're going to move
+ 
+
+ align:start position:0%
+all right so now we're going to move
+towards um
+
+ align:start position:0%
+towards um
+ 
+
+ align:start position:0%
+towards um
+uh let's see partial properties of
+
+ align:start position:0%
+uh let's see partial properties of
+ 
+
+ align:start position:0%
+uh let's see partial properties of
+mixing and so forth and we will finally
+
+ align:start position:0%
+mixing and so forth and we will finally
+ 
+
+ align:start position:0%
+mixing and so forth and we will finally
+get to graphical interpretation which is
+
+ align:start position:0%
+get to graphical interpretation which is
+ 
+
+ align:start position:0%
+get to graphical interpretation which is
+why we're doing all this so for example
+
+ align:start position:0%
+why we're doing all this so for example
+ 
+
+ align:start position:0%
+why we're doing all this so for example
+gives to him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for Gibbs for your energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if anyone's wondering
+
+ align:start position:0%
+if anyone's wondering
+ 
+
+ align:start position:0%
+if anyone's wondering
+what's with Gibbs how can he gets his
+
+ align:start position:0%
+what's with Gibbs how can he gets his
+ 
+
+ align:start position:0%
+what's with Gibbs how can he gets his
+name on everything
+
+ align:start position:0%
+name on everything
+ 
+
+ align:start position:0%
+name on everything
+um he's one of the most important and
+
+ align:start position:0%
+um he's one of the most important and
+ 
+
+ align:start position:0%
+um he's one of the most important and
+prolific American scientists ever
+
+ align:start position:0%
+prolific American scientists ever
+ 
+
+ align:start position:0%
+prolific American scientists ever
+and he was a thermodynamics researcher
+
+ align:start position:0%
+and he was a thermodynamics researcher
+ 
+
+ align:start position:0%
+and he was a thermodynamics researcher
+obviously in the late 19th century and
+
+ align:start position:0%
+obviously in the late 19th century and
+ 
+
+ align:start position:0%
+obviously in the late 19th century and
+he spent his career at Yale
+
+ align:start position:0%
+he spent his career at Yale
+ 
+
+ align:start position:0%
+he spent his career at Yale
+um and uh yeah his name is all over
+
+ align:start position:0%
+um and uh yeah his name is all over
+ 
+
+ align:start position:0%
+um and uh yeah his name is all over
+classical pharaoh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Euler
+
+ align:start position:0%
+Euler
+ 
+
+ align:start position:0%
+Euler
+or that gives us the following the total
+
+ align:start position:0%
+or that gives us the following the total
+ 
+
+ align:start position:0%
+or that gives us the following the total
+gives free energy
+
+ align:start position:0%
+gives free energy
+ 
+
+ align:start position:0%
+gives free energy
+is the sum
+
+ align:start position:0%
+is the sum
+ 
+
+ align:start position:0%
+is the sum
+of mu of k n of K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a chain rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gives us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+TG equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mu k d n of K plus n of K D mu of K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we combine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the combined statement
+
+ align:start position:0%
+the combined statement
+ 
+
+ align:start position:0%
+the combined statement
+that's it
+
+ align:start position:0%
+that's it
+ 
+
+ align:start position:0%
+that's it
+the combined statement is a
+
+ align:start position:0%
+the combined statement is a
+ 
+
+ align:start position:0%
+the combined statement is a
+coefficient relation right d g
+
+ align:start position:0%
+coefficient relation right d g
+ 
+
+ align:start position:0%
+coefficient relation right d g
+equals minus s DT plus v d p
+
+ align:start position:0%
+equals minus s DT plus v d p
+ 
+
+ align:start position:0%
+equals minus s DT plus v d p
+first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mu of K
+
+ align:start position:0%
+mu of K
+ 
+
+ align:start position:0%
+mu of K
+d n of K
+
+ align:start position:0%
+d n of K
+ 
+
+ align:start position:0%
+d n of K
+and I'm going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use these and I get the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n of K D mu of K
+
+ align:start position:0%
+n of K D mu of K
+ 
+
+ align:start position:0%
+n of K D mu of K
+equals minus s
+
+ align:start position:0%
+equals minus s
+ 
+
+ align:start position:0%
+equals minus s
+g t
+
+ align:start position:0%
+g t
+ 
+
+ align:start position:0%
+g t
+plus v
+
+ align:start position:0%
+plus v
+ 
+
+ align:start position:0%
+plus v
+DP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or if I want to divide through by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the total number of moles I get an
+
+ align:start position:0%
+the total number of moles I get an
+ 
+
+ align:start position:0%
+the total number of moles I get an
+equivalent statement
+
+ align:start position:0%
+equivalent statement
+ 
+
+ align:start position:0%
+equivalent statement
+mole fraction
+
+ align:start position:0%
+mole fraction
+ 
+
+ align:start position:0%
+mole fraction
+D mu of K
+
+ align:start position:0%
+D mu of K
+ 
+
+ align:start position:0%
+D mu of K
+equals molar entropy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are
+
+ align:start position:0%
+these are
+ 
+
+ align:start position:0%
+these are
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+gives to him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again you see what these are is there
+
+ align:start position:0%
+so again you see what these are is there
+ 
+
+ align:start position:0%
+so again you see what these are is there
+constraints on how the intensive
+
+ align:start position:0%
+constraints on how the intensive
+ 
+
+ align:start position:0%
+constraints on how the intensive
+properties are varying
+
+ align:start position:0%
+properties are varying
+ 
+
+ align:start position:0%
+properties are varying
+as intensive property is not pressure
+
+ align:start position:0%
+as intensive property is not pressure
+ 
+
+ align:start position:0%
+as intensive property is not pressure
+temperature and chemical potential we
+
+ align:start position:0%
+temperature and chemical potential we
+ 
+
+ align:start position:0%
+temperature and chemical potential we
+can't all vary independently of each
+
+ align:start position:0%
+can't all vary independently of each
+ 
+
+ align:start position:0%
+can't all vary independently of each
+other we have these constraints
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's move on
+
+ align:start position:0%
+let's move on
+ 
+
+ align:start position:0%
+let's move on
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is really like Actuarial
+
+ align:start position:0%
+and this is really like Actuarial
+ 
+
+ align:start position:0%
+and this is really like Actuarial
+science we just keep on coming up with
+
+ align:start position:0%
+science we just keep on coming up with
+ 
+
+ align:start position:0%
+science we just keep on coming up with
+these bookkeeping schemes
+
+ align:start position:0%
+these bookkeeping schemes
+ 
+
+ align:start position:0%
+these bookkeeping schemes
+and uh we have to stick with it so we're
+
+ align:start position:0%
+and uh we have to stick with it so we're
+ 
+
+ align:start position:0%
+and uh we have to stick with it so we're
+going to have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something called
+
+ align:start position:0%
+something called
+ 
+
+ align:start position:0%
+something called
+the mixing quantities so the change due
+
+ align:start position:0%
+the mixing quantities so the change due
+ 
+
+ align:start position:0%
+the mixing quantities so the change due
+to mixing
+
+ align:start position:0%
+to mixing
+ 
+
+ align:start position:0%
+to mixing
+is going to be the total quantity
+
+ align:start position:0%
+is going to be the total quantity
+ 
+
+ align:start position:0%
+is going to be the total quantity
+in the solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus what you started with before you
+
+ align:start position:0%
+minus what you started with before you
+ 
+
+ align:start position:0%
+minus what you started with before you
+made the solution
+
+ align:start position:0%
+made the solution
+ 
+
+ align:start position:0%
+made the solution
+appear
+
+ align:start position:0%
+appear
+ 
+
+ align:start position:0%
+appear
+components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we talked about this last time that in
+
+ align:start position:0%
+we talked about this last time that in
+ 
+
+ align:start position:0%
+we talked about this last time that in
+general the the whole is not simply the
+
+ align:start position:0%
+general the the whole is not simply the
+ 
+
+ align:start position:0%
+general the the whole is not simply the
+sum of the parts when you make a
+
+ align:start position:0%
+sum of the parts when you make a
+ 
+
+ align:start position:0%
+sum of the parts when you make a
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+and there were some examples given of
+
+ align:start position:0%
+and there were some examples given of
+ 
+
+ align:start position:0%
+and there were some examples given of
+you know materials which
+
+ align:start position:0%
+you know materials which
+ 
+
+ align:start position:0%
+you know materials which
+for example get bigger than you would
+
+ align:start position:0%
+for example get bigger than you would
+ 
+
+ align:start position:0%
+for example get bigger than you would
+expect or smaller than you would expect
+
+ align:start position:0%
+expect or smaller than you would expect
+ 
+
+ align:start position:0%
+expect or smaller than you would expect
+and so forth so
+
+ align:start position:0%
+and so forth so
+ 
+
+ align:start position:0%
+and so forth so
+um we're just going to capture that
+
+ align:start position:0%
+um we're just going to capture that
+ 
+
+ align:start position:0%
+um we're just going to capture that
+change here
+
+ align:start position:0%
+change here
+ 
+
+ align:start position:0%
+change here
+and um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to write
+
+ align:start position:0%
+we're going to write
+ 
+
+ align:start position:0%
+we're going to write
+the total B using partial molar
+
+ align:start position:0%
+the total B using partial molar
+ 
+
+ align:start position:0%
+the total B using partial molar
+properties as we just learned how to do
+
+ align:start position:0%
+properties as we just learned how to do
+ 
+
+ align:start position:0%
+properties as we just learned how to do
+BK n of K
+
+ align:start position:0%
+BK n of K
+ 
+
+ align:start position:0%
+BK n of K
+and then we're going to introduce even
+
+ align:start position:0%
+and then we're going to introduce even
+ 
+
+ align:start position:0%
+and then we're going to introduce even
+more notation and say
+
+ align:start position:0%
+more notation and say
+ 
+
+ align:start position:0%
+more notation and say
+for the pure components you had
+
+ align:start position:0%
+for the pure components you had
+ 
+
+ align:start position:0%
+for the pure components you had
+pure
+
+ align:start position:0%
+pure
+ 
+
+ align:start position:0%
+pure
+molar properties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're going to group terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're going to Define that
+
+ align:start position:0%
+and we're going to Define that
+ 
+
+ align:start position:0%
+and we're going to Define that
+as Delta
+
+ align:start position:0%
+as Delta
+ 
+
+ align:start position:0%
+as Delta
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+partial molar property due to mixing
+
+ align:start position:0%
+partial molar property due to mixing
+ 
+
+ align:start position:0%
+partial molar property due to mixing
+oof
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change in p m p
+
+ align:start position:0%
+change in p m p
+ 
+
+ align:start position:0%
+change in p m p
+due to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mixing
+
+ align:start position:0%
+mixing
+ 
+
+ align:start position:0%
+mixing
+my goodness all right
+
+ align:start position:0%
+my goodness all right
+ 
+
+ align:start position:0%
+my goodness all right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+is this all right let me give an analogy
+
+ align:start position:0%
+is this all right let me give an analogy
+ 
+
+ align:start position:0%
+is this all right let me give an analogy
+I don't know whether this helps
+
+ align:start position:0%
+I don't know whether this helps
+ 
+
+ align:start position:0%
+I don't know whether this helps
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's imagine this is um
+
+ align:start position:0%
+let's imagine this is um
+ 
+
+ align:start position:0%
+let's imagine this is um
+personal space we're calculating here uh
+
+ align:start position:0%
+personal space we're calculating here uh
+ 
+
+ align:start position:0%
+personal space we're calculating here uh
+the the area occupied by a crowd of
+
+ align:start position:0%
+the the area occupied by a crowd of
+ 
+
+ align:start position:0%
+the the area occupied by a crowd of
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+and you could Define a personal space as
+
+ align:start position:0%
+and you could Define a personal space as
+ 
+
+ align:start position:0%
+and you could Define a personal space as
+the exclusive area around everybody
+
+ align:start position:0%
+the exclusive area around everybody
+ 
+
+ align:start position:0%
+the exclusive area around everybody
+such that the total area is everyone's
+
+ align:start position:0%
+such that the total area is everyone's
+ 
+
+ align:start position:0%
+such that the total area is everyone's
+personal space added up right that does
+
+ align:start position:0%
+personal space added up right that does
+ 
+
+ align:start position:0%
+personal space added up right that does
+that make sense imagine a crowd of
+
+ align:start position:0%
+that make sense imagine a crowd of
+ 
+
+ align:start position:0%
+that make sense imagine a crowd of
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+what this is is
+
+ align:start position:0%
+what this is is
+ 
+
+ align:start position:0%
+what this is is
+um an expression acknowledgment that
+
+ align:start position:0%
+um an expression acknowledgment that
+ 
+
+ align:start position:0%
+um an expression acknowledgment that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+your personal space in a given crowd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+varies
+
+ align:start position:0%
+varies
+ 
+
+ align:start position:0%
+varies
+with the crowd
+
+ align:start position:0%
+with the crowd
+ 
+
+ align:start position:0%
+with the crowd
+so if you are
+
+ align:start position:0%
+so if you are
+ 
+
+ align:start position:0%
+so if you are
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if your crowd is uh a dispersal
+
+ align:start position:0%
+if your crowd is uh a dispersal
+ 
+
+ align:start position:0%
+if your crowd is uh a dispersal
+dispersal of people uh in Killian Court
+
+ align:start position:0%
+dispersal of people uh in Killian Court
+ 
+
+ align:start position:0%
+dispersal of people uh in Killian Court
+uh on a sunny day
+
+ align:start position:0%
+uh on a sunny day
+ 
+
+ align:start position:0%
+uh on a sunny day
+you're going to have a lot of personal
+
+ align:start position:0%
+you're going to have a lot of personal
+ 
+
+ align:start position:0%
+you're going to have a lot of personal
+space per person right
+
+ align:start position:0%
+space per person right
+ 
+
+ align:start position:0%
+space per person right
+um it would be very very strange to go
+
+ align:start position:0%
+um it would be very very strange to go
+ 
+
+ align:start position:0%
+um it would be very very strange to go
+up to somebody
+
+ align:start position:0%
+up to somebody
+ 
+
+ align:start position:0%
+up to somebody
+who is sitting there having a picnic and
+
+ align:start position:0%
+who is sitting there having a picnic and
+ 
+
+ align:start position:0%
+who is sitting there having a picnic and
+to sit so that your shoulders are
+
+ align:start position:0%
+to sit so that your shoulders are
+ 
+
+ align:start position:0%
+to sit so that your shoulders are
+rubbing and you don't know the person
+
+ align:start position:0%
+rubbing and you don't know the person
+ 
+
+ align:start position:0%
+rubbing and you don't know the person
+right a total stranger Killian courts
+
+ align:start position:0%
+right a total stranger Killian courts
+ 
+
+ align:start position:0%
+right a total stranger Killian courts
+wide open and sunny and you go sit with
+
+ align:start position:0%
+wide open and sunny and you go sit with
+ 
+
+ align:start position:0%
+wide open and sunny and you go sit with
+your shoulders rubbing and that's the
+
+ align:start position:0%
+your shoulders rubbing and that's the
+ 
+
+ align:start position:0%
+your shoulders rubbing and that's the
+space you take and that would be very
+
+ align:start position:0%
+space you take and that would be very
+ 
+
+ align:start position:0%
+space you take and that would be very
+unusual
+
+ align:start position:0%
+unusual
+ 
+
+ align:start position:0%
+unusual
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but same people on a crowded subway car
+
+ align:start position:0%
+but same people on a crowded subway car
+ 
+
+ align:start position:0%
+but same people on a crowded subway car
+or on a dance floor right you might have
+
+ align:start position:0%
+or on a dance floor right you might have
+ 
+
+ align:start position:0%
+or on a dance floor right you might have
+a very different
+
+ align:start position:0%
+a very different
+ 
+
+ align:start position:0%
+a very different
+personal space
+
+ align:start position:0%
+personal space
+ 
+
+ align:start position:0%
+personal space
+so your personal space is not fixed by
+
+ align:start position:0%
+so your personal space is not fixed by
+ 
+
+ align:start position:0%
+so your personal space is not fixed by
+you you know who you are you know as a
+
+ align:start position:0%
+you you know who you are you know as a
+ 
+
+ align:start position:0%
+you you know who you are you know as a
+person
+
+ align:start position:0%
+person
+ 
+
+ align:start position:0%
+person
+it's determined by um the solution you
+
+ align:start position:0%
+it's determined by um the solution you
+ 
+
+ align:start position:0%
+it's determined by um the solution you
+find yourself in
+
+ align:start position:0%
+find yourself in
+ 
+
+ align:start position:0%
+find yourself in
+in different solutions will result in
+
+ align:start position:0%
+in different solutions will result in
+ 
+
+ align:start position:0%
+in different solutions will result in
+different personal space
+
+ align:start position:0%
+different personal space
+ 
+
+ align:start position:0%
+different personal space
+space per area per person and we have
+
+ align:start position:0%
+space per area per person and we have
+ 
+
+ align:start position:0%
+space per area per person and we have
+this term Delta B of K personal the
+
+ align:start position:0%
+this term Delta B of K personal the
+ 
+
+ align:start position:0%
+this term Delta B of K personal the
+property of mixing to capture how that
+
+ align:start position:0%
+property of mixing to capture how that
+ 
+
+ align:start position:0%
+property of mixing to capture how that
+changes right so how does your personal
+
+ align:start position:0%
+changes right so how does your personal
+ 
+
+ align:start position:0%
+changes right so how does your personal
+space change from your you know ideal
+
+ align:start position:0%
+space change from your you know ideal
+ 
+
+ align:start position:0%
+space change from your you know ideal
+situation where you're in a field by
+
+ align:start position:0%
+situation where you're in a field by
+ 
+
+ align:start position:0%
+situation where you're in a field by
+yourself
+
+ align:start position:0%
+yourself
+ 
+
+ align:start position:0%
+yourself
+um if you're in a crowded subway car or
+
+ align:start position:0%
+um if you're in a crowded subway car or
+ 
+
+ align:start position:0%
+um if you're in a crowded subway car or
+you're surrounded by a crowd of people
+
+ align:start position:0%
+you're surrounded by a crowd of people
+ 
+
+ align:start position:0%
+you're surrounded by a crowd of people
+who who you like
+
+ align:start position:0%
+who who you like
+ 
+
+ align:start position:0%
+who who you like
+right maybe your personal space shrinks
+
+ align:start position:0%
+right maybe your personal space shrinks
+ 
+
+ align:start position:0%
+right maybe your personal space shrinks
+or you're surrounded by a crowd of
+
+ align:start position:0%
+or you're surrounded by a crowd of
+ 
+
+ align:start position:0%
+or you're surrounded by a crowd of
+people who you don't really like maybe
+
+ align:start position:0%
+people who you don't really like maybe
+ 
+
+ align:start position:0%
+people who you don't really like maybe
+your personal space expands
+
+ align:start position:0%
+your personal space expands
+ 
+
+ align:start position:0%
+your personal space expands
+and there's going to be analogies for
+
+ align:start position:0%
+and there's going to be analogies for
+ 
+
+ align:start position:0%
+and there's going to be analogies for
+all of these in Therma when a molecule
+
+ align:start position:0%
+all of these in Therma when a molecule
+ 
+
+ align:start position:0%
+all of these in Therma when a molecule
+is surmounted by other molecules that
+
+ align:start position:0%
+is surmounted by other molecules that
+ 
+
+ align:start position:0%
+is surmounted by other molecules that
+that it likes or that it wants to bond
+
+ align:start position:0%
+that it likes or that it wants to bond
+ 
+
+ align:start position:0%
+that it likes or that it wants to bond
+with it's it's process volume is going
+
+ align:start position:0%
+with it's it's process volume is going
+ 
+
+ align:start position:0%
+with it's it's process volume is going
+to shrink a little bit is volume for
+
+ align:start position:0%
+to shrink a little bit is volume for
+ 
+
+ align:start position:0%
+to shrink a little bit is volume for
+molecular shrink a little bit and if a
+
+ align:start position:0%
+molecular shrink a little bit and if a
+ 
+
+ align:start position:0%
+molecular shrink a little bit and if a
+molecule is surrounded by molecules that
+
+ align:start position:0%
+molecule is surrounded by molecules that
+ 
+
+ align:start position:0%
+molecule is surrounded by molecules that
+it doesn't want to bond with
+
+ align:start position:0%
+it doesn't want to bond with
+ 
+
+ align:start position:0%
+it doesn't want to bond with
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+partial molar volume will expand a
+
+ align:start position:0%
+partial molar volume will expand a
+ 
+
+ align:start position:0%
+partial molar volume will expand a
+little bit so these these Concepts
+
+ align:start position:0%
+little bit so these these Concepts
+ 
+
+ align:start position:0%
+little bit so these these Concepts
+depend on the surroundings
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's make this specific again Gibbs
+
+ align:start position:0%
+so let's make this specific again Gibbs
+ 
+
+ align:start position:0%
+so let's make this specific again Gibbs
+free energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the total give us free energy of a
+
+ align:start position:0%
+the total give us free energy of a
+ 
+
+ align:start position:0%
+the total give us free energy of a
+system is equal to
+
+ align:start position:0%
+system is equal to
+ 
+
+ align:start position:0%
+system is equal to
+the sum
+
+ align:start position:0%
+the sum
+ 
+
+ align:start position:0%
+the sum
+of partial molar Gibbs free energy
+
+ align:start position:0%
+of partial molar Gibbs free energy
+ 
+
+ align:start position:0%
+of partial molar Gibbs free energy
+times mole number
+
+ align:start position:0%
+times mole number
+ 
+
+ align:start position:0%
+times mole number
+is because it gives a special it has its
+
+ align:start position:0%
+is because it gives a special it has its
+ 
+
+ align:start position:0%
+is because it gives a special it has its
+own term chemical potential
+
+ align:start position:0%
+own term chemical potential
+ 
+
+ align:start position:0%
+own term chemical potential
+time command number
+
+ align:start position:0%
+time command number
+ 
+
+ align:start position:0%
+time command number
+and according to our uh new
+
+ align:start position:0%
+and according to our uh new
+ 
+
+ align:start position:0%
+and according to our uh new
+bookkeeping scheme this is the chemical
+
+ align:start position:0%
+bookkeeping scheme this is the chemical
+ 
+
+ align:start position:0%
+bookkeeping scheme this is the chemical
+potential of the pure stuff
+
+ align:start position:0%
+potential of the pure stuff
+ 
+
+ align:start position:0%
+potential of the pure stuff
+plus however it changed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when it entered the solution phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we'll divide
+
+ align:start position:0%
+and then we'll divide
+ 
+
+ align:start position:0%
+and then we'll divide
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+by the total mole count
+
+ align:start position:0%
+by the total mole count
+ 
+
+ align:start position:0%
+by the total mole count
+and we get Gibbs free energy equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay and again this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the pure
+
+ align:start position:0%
+the pure
+ 
+
+ align:start position:0%
+the pure
+components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the change upon mixing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we have two more slides and we're
+
+ align:start position:0%
+okay we have two more slides and we're
+ 
+
+ align:start position:0%
+okay we have two more slides and we're
+going to get to the very very useful
+
+ align:start position:0%
+going to get to the very very useful
+ 
+
+ align:start position:0%
+going to get to the very very useful
+graphical interpretation of all this
+
+ align:start position:0%
+graphical interpretation of all this
+ 
+
+ align:start position:0%
+graphical interpretation of all this
+how do we calculate these things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you're going to do a little bit of
+
+ align:start position:0%
+so you're going to do a little bit of
+ 
+
+ align:start position:0%
+so you're going to do a little bit of
+this on the pset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're going to do the case
+
+ align:start position:0%
+so we're going to do the case
+ 
+
+ align:start position:0%
+so we're going to do the case
+of chemical potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a binary system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+binary system
+
+ align:start position:0%
+binary system
+ 
+
+ align:start position:0%
+binary system
+okay so binary system Delta G due to
+
+ align:start position:0%
+okay so binary system Delta G due to
+ 
+
+ align:start position:0%
+okay so binary system Delta G due to
+mixing equals
+
+ align:start position:0%
+mixing equals
+ 
+
+ align:start position:0%
+mixing equals
+Delta Mu of One X One Plus Delta Mu of 2
+
+ align:start position:0%
+Delta Mu of One X One Plus Delta Mu of 2
+ 
+
+ align:start position:0%
+Delta Mu of One X One Plus Delta Mu of 2
+x 2. I only have two components that's
+
+ align:start position:0%
+x 2. I only have two components that's
+ 
+
+ align:start position:0%
+x 2. I only have two components that's
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+and so here this is gets
+
+ align:start position:0%
+and so here this is gets
+ 
+
+ align:start position:0%
+and so here this is gets
+you really have to know your D's of
+
+ align:start position:0%
+you really have to know your D's of
+ 
+
+ align:start position:0%
+you really have to know your D's of
+thermodynamics here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the change
+
+ align:start position:0%
+the change
+ 
+
+ align:start position:0%
+the change
+of the given free energy of mixing
+
+ align:start position:0%
+of the given free energy of mixing
+ 
+
+ align:start position:0%
+of the given free energy of mixing
+for fixed pressure and temperature
+
+ align:start position:0%
+for fixed pressure and temperature
+ 
+
+ align:start position:0%
+for fixed pressure and temperature
+as a system composition varies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again the change of the Gibbs free
+
+ align:start position:0%
+so again the change of the Gibbs free
+ 
+
+ align:start position:0%
+so again the change of the Gibbs free
+energy of mixing
+
+ align:start position:0%
+energy of mixing
+ 
+
+ align:start position:0%
+energy of mixing
+at fixed pressure and temperature as the
+
+ align:start position:0%
+at fixed pressure and temperature as the
+ 
+
+ align:start position:0%
+at fixed pressure and temperature as the
+system composition varies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you say what about the chain rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+that thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals zero
+
+ align:start position:0%
+equals zero
+ 
+
+ align:start position:0%
+equals zero
+if I give to him so I'm left with these
+
+ align:start position:0%
+if I give to him so I'm left with these
+ 
+
+ align:start position:0%
+if I give to him so I'm left with these
+two terms here
+
+ align:start position:0%
+two terms here
+ 
+
+ align:start position:0%
+two terms here
+then I'm going to use
+
+ align:start position:0%
+then I'm going to use
+ 
+
+ align:start position:0%
+then I'm going to use
+x 1 plus x 2 equals one which means what
+
+ align:start position:0%
+x 1 plus x 2 equals one which means what
+ 
+
+ align:start position:0%
+x 1 plus x 2 equals one which means what
+d x 1 equals minus dx2 it's a binary
+
+ align:start position:0%
+d x 1 equals minus dx2 it's a binary
+ 
+
+ align:start position:0%
+d x 1 equals minus dx2 it's a binary
+system so there's only one composition
+
+ align:start position:0%
+system so there's only one composition
+ 
+
+ align:start position:0%
+system so there's only one composition
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+get the following d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DTG DT Delta G Max
+
+ align:start position:0%
+DTG DT Delta G Max
+ 
+
+ align:start position:0%
+DTG DT Delta G Max
+d x two I chose X2 here is my
+
+ align:start position:0%
+d x two I chose X2 here is my
+ 
+
+ align:start position:0%
+d x two I chose X2 here is my
+independent variable at fixed pressure
+
+ align:start position:0%
+independent variable at fixed pressure
+ 
+
+ align:start position:0%
+independent variable at fixed pressure
+and temperature
+
+ align:start position:0%
+and temperature
+ 
+
+ align:start position:0%
+and temperature
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+Delta Mu of two minus Delta
+
+ align:start position:0%
+Delta Mu of two minus Delta
+ 
+
+ align:start position:0%
+Delta Mu of two minus Delta
+U of one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I'm going to eliminate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta Mu of one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using the above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's the above
+
+ align:start position:0%
+what's the above
+ 
+
+ align:start position:0%
+what's the above
+that's the above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I get the following
+
+ align:start position:0%
+and I get the following
+ 
+
+ align:start position:0%
+and I get the following
+Delta Mu of 2
+
+ align:start position:0%
+Delta Mu of 2
+ 
+
+ align:start position:0%
+Delta Mu of 2
+equals Delta G
+
+ align:start position:0%
+equals Delta G
+ 
+
+ align:start position:0%
+equals Delta G
+mix
+
+ align:start position:0%
+mix
+ 
+
+ align:start position:0%
+mix
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+1 minus X 2.
+
+ align:start position:0%
+1 minus X 2.
+ 
+
+ align:start position:0%
+1 minus X 2.
+D Delta g mix
+
+ align:start position:0%
+D Delta g mix
+ 
+
+ align:start position:0%
+D Delta g mix
+d x 2.
+
+ align:start position:0%
+d x 2.
+ 
+
+ align:start position:0%
+d x 2.
+and believe it or not this is really
+
+ align:start position:0%
+and believe it or not this is really
+ 
+
+ align:start position:0%
+and believe it or not this is really
+useful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+likewise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for Delta
+
+ align:start position:0%
+for Delta
+ 
+
+ align:start position:0%
+for Delta
+mu of one
+
+ align:start position:0%
+mu of one
+ 
+
+ align:start position:0%
+mu of one
+all right and um let me just show you
+
+ align:start position:0%
+all right and um let me just show you
+ 
+
+ align:start position:0%
+all right and um let me just show you
+why it's really useful and we can come
+
+ align:start position:0%
+why it's really useful and we can come
+ 
+
+ align:start position:0%
+why it's really useful and we can come
+back for questions it's really useful
+
+ align:start position:0%
+back for questions it's really useful
+ 
+
+ align:start position:0%
+back for questions it's really useful
+because we have a graphical
+
+ align:start position:0%
+because we have a graphical
+ 
+
+ align:start position:0%
+because we have a graphical
+interpretation of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graphical interpretation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of p m P's
+
+ align:start position:0%
+of p m P's
+ 
+
+ align:start position:0%
+of p m P's
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+solution models
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we're going to do this for a case
+
+ align:start position:0%
+we're going to do this for a case
+ 
+
+ align:start position:0%
+we're going to do this for a case
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Delta G
+
+ align:start position:0%
+Delta G
+ 
+
+ align:start position:0%
+Delta G
+mix
+
+ align:start position:0%
+mix
+ 
+
+ align:start position:0%
+mix
+and Delta
+
+ align:start position:0%
+and Delta
+ 
+
+ align:start position:0%
+and Delta
+the Delta Mu K so let's draw a plot let
+
+ align:start position:0%
+the Delta Mu K so let's draw a plot let
+ 
+
+ align:start position:0%
+the Delta Mu K so let's draw a plot let
+me show you what I mean here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+'s a solution model I'm just going to
+
+ align:start position:0%
+'s a solution model I'm just going to
+ 
+
+ align:start position:0%
+'s a solution model I'm just going to
+draw anything I'm going to draw imagine
+
+ align:start position:0%
+draw anything I'm going to draw imagine
+ 
+
+ align:start position:0%
+draw anything I'm going to draw imagine
+someone gave you this data or um
+
+ align:start position:0%
+someone gave you this data or um
+ 
+
+ align:start position:0%
+someone gave you this data or um
+you figure this out yourself something
+
+ align:start position:0%
+you figure this out yourself something
+ 
+
+ align:start position:0%
+you figure this out yourself something
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+here's here's the solution model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something right it's some trend of
+
+ align:start position:0%
+something right it's some trend of
+ 
+
+ align:start position:0%
+something right it's some trend of
+thermodynamics with what
+
+ align:start position:0%
+thermodynamics with what
+ 
+
+ align:start position:0%
+thermodynamics with what
+with system composition
+
+ align:start position:0%
+with system composition
+ 
+
+ align:start position:0%
+with system composition
+and so this is X2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we have some solution model
+
+ align:start position:0%
+all right so we have some solution model
+ 
+
+ align:start position:0%
+all right so we have some solution model
+and we're going to imagine sitting here
+
+ align:start position:0%
+and we're going to imagine sitting here
+ 
+
+ align:start position:0%
+and we're going to imagine sitting here
+at um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's imagine sitting here
+
+ align:start position:0%
+let's imagine sitting here
+ 
+
+ align:start position:0%
+let's imagine sitting here
+at this composition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me just go ahead and draw these
+
+ align:start position:0%
+let me just go ahead and draw these
+ 
+
+ align:start position:0%
+let me just go ahead and draw these
+tangents and then we'll come back to why
+
+ align:start position:0%
+tangents and then we'll come back to why
+ 
+
+ align:start position:0%
+tangents and then we'll come back to why
+they matter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so there's a point on the
+
+ align:start position:0%
+all right so there's a point on the
+ 
+
+ align:start position:0%
+all right so there's a point on the
+Curve
+
+ align:start position:0%
+Curve
+ 
+
+ align:start position:0%
+Curve
+and my overall system composition
+
+ align:start position:0%
+and my overall system composition
+ 
+
+ align:start position:0%
+and my overall system composition
+this intercept here I'm going to label
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and a label
+
+ align:start position:0%
+this and a label
+ 
+
+ align:start position:0%
+this and a label
+this over here
+
+ align:start position:0%
+this over here
+ 
+
+ align:start position:0%
+this over here
+and also label
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this over here
+
+ align:start position:0%
+this over here
+ 
+
+ align:start position:0%
+this over here
+I'm going to label and I give these
+
+ align:start position:0%
+I'm going to label and I give these
+ 
+
+ align:start position:0%
+I'm going to label and I give these
+number labels p
+
+ align:start position:0%
+number labels p
+ 
+
+ align:start position:0%
+number labels p
+s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and Q
+
+ align:start position:0%
+and Q
+ 
+
+ align:start position:0%
+and Q
+so here's my system
+
+ align:start position:0%
+so here's my system
+ 
+
+ align:start position:0%
+so here's my system
+composition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's my system composition
+
+ align:start position:0%
+here's my system composition
+ 
+
+ align:start position:0%
+here's my system composition
+there's a tangent line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a tangent line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we have a
+
+ align:start position:0%
+and we have a
+ 
+
+ align:start position:0%
+and we have a
+solution model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+Delta G mixed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is um it's just the the height of this
+
+ align:start position:0%
+is um it's just the the height of this
+ 
+
+ align:start position:0%
+is um it's just the the height of this
+curve it's just you know
+
+ align:start position:0%
+curve it's just you know
+ 
+
+ align:start position:0%
+curve it's just you know
+QR
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's that's that that length
+
+ align:start position:0%
+right that's that's that that length
+ 
+
+ align:start position:0%
+right that's that's that that length
+the curve evaluated at p
+
+ align:start position:0%
+the curve evaluated at p
+ 
+
+ align:start position:0%
+the curve evaluated at p
+quantity one minus X2
+
+ align:start position:0%
+quantity one minus X2
+ 
+
+ align:start position:0%
+quantity one minus X2
+equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PR
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's just that length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the slope
+
+ align:start position:0%
+and the slope
+ 
+
+ align:start position:0%
+and the slope
+D Delta g mix dx2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's rise over run right so the rise is
+
+ align:start position:0%
+it's rise over run right so the rise is
+ 
+
+ align:start position:0%
+it's rise over run right so the rise is
+r s
+
+ align:start position:0%
+r s
+ 
+
+ align:start position:0%
+r s
+and the run is PR
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so I'm going to plug these
+
+ align:start position:0%
+and so I'm going to plug these
+ 
+
+ align:start position:0%
+and so I'm going to plug these
+geometries into the expression which we
+
+ align:start position:0%
+geometries into the expression which we
+ 
+
+ align:start position:0%
+geometries into the expression which we
+derived on the previous slide you have q
+
+ align:start position:0%
+derived on the previous slide you have q
+ 
+
+ align:start position:0%
+derived on the previous slide you have q
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+plus p r
+
+ align:start position:0%
+plus p r
+ 
+
+ align:start position:0%
+plus p r
+times r s
+
+ align:start position:0%
+times r s
+ 
+
+ align:start position:0%
+times r s
+over p r
+
+ align:start position:0%
+over p r
+ 
+
+ align:start position:0%
+over p r
+and this blank segments cancel each
+
+ align:start position:0%
+and this blank segments cancel each
+ 
+
+ align:start position:0%
+and this blank segments cancel each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+and you get q r
+
+ align:start position:0%
+and you get q r
+ 
+
+ align:start position:0%
+and you get q r
+plus RS so this distance plus this
+
+ align:start position:0%
+plus RS so this distance plus this
+ 
+
+ align:start position:0%
+plus RS so this distance plus this
+distance which of course is
+
+ align:start position:0%
+distance which of course is
+ 
+
+ align:start position:0%
+distance which of course is
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+q s
+
+ align:start position:0%
+q s
+ 
+
+ align:start position:0%
+q s
+what does that mean
+
+ align:start position:0%
+what does that mean
+ 
+
+ align:start position:0%
+what does that mean
+it means that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this point here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this intercept
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is Delta
+
+ align:start position:0%
+is Delta
+ 
+
+ align:start position:0%
+is Delta
+mu 2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and likewise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for Delta U1 The Intercept over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is Delta V1
+
+ align:start position:0%
+is Delta V1
+ 
+
+ align:start position:0%
+is Delta V1
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+right that means if we have a solution
+
+ align:start position:0%
+right that means if we have a solution
+ 
+
+ align:start position:0%
+right that means if we have a solution
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+some data some curve
+
+ align:start position:0%
+some data some curve
+ 
+
+ align:start position:0%
+some data some curve
+if we draw the tangent of that
+
+ align:start position:0%
+if we draw the tangent of that
+ 
+
+ align:start position:0%
+if we draw the tangent of that
+we can pick out the partial molar
+
+ align:start position:0%
+we can pick out the partial molar
+ 
+
+ align:start position:0%
+we can pick out the partial molar
+properties of component one component
+
+ align:start position:0%
+properties of component one component
+ 
+
+ align:start position:0%
+properties of component one component
+Two by The Intercept of the tangent
+
+ align:start position:0%
+Two by The Intercept of the tangent
+ 
+
+ align:start position:0%
+Two by The Intercept of the tangent
+on the left hand axis and the right hand
+
+ align:start position:0%
+on the left hand axis and the right hand
+ 
+
+ align:start position:0%
+on the left hand axis and the right hand
+axis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that's where I'm going to leave it for
+
+ align:start position:0%
+that's where I'm going to leave it for
+ 
+
+ align:start position:0%
+that's where I'm going to leave it for
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+either this is kind of mysterious and
+
+ align:start position:0%
+either this is kind of mysterious and
+ 
+
+ align:start position:0%
+either this is kind of mysterious and
+and wasn't worth the effort
+
+ align:start position:0%
+and wasn't worth the effort
+ 
+
+ align:start position:0%
+and wasn't worth the effort
+um in which case I would ask you just to
+
+ align:start position:0%
+um in which case I would ask you just to
+ 
+
+ align:start position:0%
+um in which case I would ask you just to
+hold on
+
+ align:start position:0%
+hold on
+ 
+
+ align:start position:0%
+hold on
+uh or it now starts to make sense
+
+ align:start position:0%
+uh or it now starts to make sense
+ 
+
+ align:start position:0%
+uh or it now starts to make sense
+um if you've seen the common tangent
+
+ align:start position:0%
+um if you've seen the common tangent
+ 
+
+ align:start position:0%
+um if you've seen the common tangent
+construction before in which case you
+
+ align:start position:0%
+construction before in which case you
+ 
+
+ align:start position:0%
+construction before in which case you
+know I'll say all right well we'll you
+
+ align:start position:0%
+know I'll say all right well we'll you
+ 
+
+ align:start position:0%
+know I'll say all right well we'll you
+know we'll get there
+
+ align:start position:0%
+know we'll get there
+ 
+
+ align:start position:0%
+know we'll get there
+um right
+
+ align:start position:0%
+um right
+ 
+
+ align:start position:0%
+um right
+so this was a bunch of math around
+
+ align:start position:0%
+so this was a bunch of math around
+ 
+
+ align:start position:0%
+so this was a bunch of math around
+solution modeling
\ No newline at end of file
diff --git a/a66tfLdr6oY.txt b/a66tfLdr6oY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6f6871676622e774c2d4df228a45aa26e7a73de9
--- /dev/null
+++ b/a66tfLdr6oY.txt
@@ -0,0 +1,14795 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT
+opencourseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so we've been talking about
+
+ align:start position:0%
+ocw.mit.edu so we've been talking about
+ 
+
+ align:start position:0%
+ocw.mit.edu so we've been talking about
+this K Square test and um the name k
+
+ align:start position:0%
+this K Square test and um the name k
+ 
+
+ align:start position:0%
+this K Square test and um the name k
+Square comes from the fact that we build
+
+ align:start position:0%
+Square comes from the fact that we build
+ 
+
+ align:start position:0%
+Square comes from the fact that we build
+a test statistic that has a sympotic
+
+ align:start position:0%
+a test statistic that has a sympotic
+ 
+
+ align:start position:0%
+a test statistic that has a sympotic
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+by the K squ
+
+ align:start position:0%
+by the K squ
+ 
+
+ align:start position:0%
+by the K squ
+distribution let's just give it another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shot okay and uh um this test who has
+
+ align:start position:0%
+shot okay and uh um this test who has
+ 
+
+ align:start position:0%
+shot okay and uh um this test who has
+actually ever encountered the K Square
+
+ align:start position:0%
+actually ever encountered the K Square
+ 
+
+ align:start position:0%
+actually ever encountered the K Square
+test outside of a stats
+
+ align:start position:0%
+test outside of a stats
+ 
+
+ align:start position:0%
+test outside of a stats
+classroom all right so some people have
+
+ align:start position:0%
+classroom all right so some people have
+ 
+
+ align:start position:0%
+classroom all right so some people have
+right it's a fairly common uh test that
+
+ align:start position:0%
+right it's a fairly common uh test that
+ 
+
+ align:start position:0%
+right it's a fairly common uh test that
+you might encounter and it was
+
+ align:start position:0%
+you might encounter and it was
+ 
+
+ align:start position:0%
+you might encounter and it was
+essentially to test if given some uh
+
+ align:start position:0%
+essentially to test if given some uh
+ 
+
+ align:start position:0%
+essentially to test if given some uh
+data with a fixed probability Mass
+
+ align:start position:0%
+data with a fixed probability Mass
+ 
+
+ align:start position:0%
+data with a fixed probability Mass
+function right so discrete distribution
+
+ align:start position:0%
+function right so discrete distribution
+ 
+
+ align:start position:0%
+function right so discrete distribution
+you wanted to test if it was given the
+
+ align:start position:0%
+you wanted to test if it was given the
+ 
+
+ align:start position:0%
+you wanted to test if it was given the
+pmf was equal to a set value P KN or if
+
+ align:start position:0%
+pmf was equal to a set value P KN or if
+ 
+
+ align:start position:0%
+pmf was equal to a set value P KN or if
+it was different from P KN and the way
+
+ align:start position:0%
+it was different from P KN and the way
+ 
+
+ align:start position:0%
+it was different from P KN and the way
+the K Square arose here was by uh
+
+ align:start position:0%
+the K Square arose here was by uh
+ 
+
+ align:start position:0%
+the K Square arose here was by uh
+looking at uh Walt's test and
+
+ align:start position:0%
+looking at uh Walt's test and
+ 
+
+ align:start position:0%
+looking at uh Walt's test and
+essentially if you write so WT is the
+
+ align:start position:0%
+essentially if you write so WT is the
+ 
+
+ align:start position:0%
+essentially if you write so WT is the
+one that has the K Square as the
+
+ align:start position:0%
+one that has the K Square as the
+ 
+
+ align:start position:0%
+one that has the K Square as the
+limiting distribution and if you invert
+
+ align:start position:0%
+limiting distribution and if you invert
+ 
+
+ align:start position:0%
+limiting distribution and if you invert
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+uh cence Matrix the Astic cence Matrix
+
+ align:start position:0%
+uh cence Matrix the Astic cence Matrix
+ 
+
+ align:start position:0%
+uh cence Matrix the Astic cence Matrix
+so you compute the Fisher information
+
+ align:start position:0%
+so you compute the Fisher information
+ 
+
+ align:start position:0%
+so you compute the Fisher information
+which in this particular case does not
+
+ align:start position:0%
+which in this particular case does not
+ 
+
+ align:start position:0%
+which in this particular case does not
+exist for the mul multinomial
+
+ align:start position:0%
+exist for the mul multinomial
+ 
+
+ align:start position:0%
+exist for the mul multinomial
+distribution but we found a trick on how
+
+ align:start position:0%
+distribution but we found a trick on how
+ 
+
+ align:start position:0%
+distribution but we found a trick on how
+to do this we removed the part that
+
+ align:start position:0%
+to do this we removed the part that
+ 
+
+ align:start position:0%
+to do this we removed the part that
+forbid it to be invertible then we found
+
+ align:start position:0%
+forbid it to be invertible then we found
+ 
+
+ align:start position:0%
+forbid it to be invertible then we found
+this K Square distribution so in way we
+
+ align:start position:0%
+this K Square distribution so in way we
+ 
+
+ align:start position:0%
+this K Square distribution so in way we
+have this test statistic which you might
+
+ align:start position:0%
+have this test statistic which you might
+ 
+
+ align:start position:0%
+have this test statistic which you might
+have learned as a blackbox lry list but
+
+ align:start position:0%
+have learned as a blackbox lry list but
+ 
+
+ align:start position:0%
+have learned as a blackbox lry list but
+going through the math which might have
+
+ align:start position:0%
+going through the math which might have
+ 
+
+ align:start position:0%
+going through the math which might have
+been slightly imp plasant I acknowledge
+
+ align:start position:0%
+been slightly imp plasant I acknowledge
+ 
+
+ align:start position:0%
+been slightly imp plasant I acknowledge
+but really told you why you should do
+
+ align:start position:0%
+but really told you why you should do
+ 
+
+ align:start position:0%
+but really told you why you should do
+this particular normalization so uh
+
+ align:start position:0%
+this particular normalization so uh
+ 
+
+ align:start position:0%
+this particular normalization so uh
+since some of you requested a little
+
+ align:start position:0%
+since some of you requested a little
+ 
+
+ align:start position:0%
+since some of you requested a little
+more uh you know practical examples of
+
+ align:start position:0%
+more uh you know practical examples of
+ 
+
+ align:start position:0%
+more uh you know practical examples of
+how those things work let me show you a
+
+ align:start position:0%
+how those things work let me show you a
+ 
+
+ align:start position:0%
+how those things work let me show you a
+couple uh the first one is um the uh you
+
+ align:start position:0%
+couple uh the first one is um the uh you
+ 
+
+ align:start position:0%
+couple uh the first one is um the uh you
+want to answer the question well you
+
+ align:start position:0%
+want to answer the question well you
+ 
+
+ align:start position:0%
+want to answer the question well you
+know when should I be born to be
+
+ align:start position:0%
+know when should I be born to be
+ 
+
+ align:start position:0%
+know when should I be born to be
+successful right and uh you know some
+
+ align:start position:0%
+successful right and uh you know some
+ 
+
+ align:start position:0%
+successful right and uh you know some
+people believe in zodiac and so Fortune
+
+ align:start position:0%
+people believe in zodiac and so Fortune
+ 
+
+ align:start position:0%
+people believe in zodiac and so Fortune
+Magazine actually collected the signs of
+
+ align:start position:0%
+Magazine actually collected the signs of
+ 
+
+ align:start position:0%
+Magazine actually collected the signs of
+256 hazs of the Fortune 500 right those
+
+ align:start position:0%
+256 hazs of the Fortune 500 right those
+ 
+
+ align:start position:0%
+256 hazs of the Fortune 500 right those
+were taken randomly and they were
+
+ align:start position:0%
+were taken randomly and they were
+ 
+
+ align:start position:0%
+were taken randomly and they were
+collected there and you can see this
+
+ align:start position:0%
+collected there and you can see this
+ 
+
+ align:start position:0%
+collected there and you can see this
+this this the count of number of CEOs
+
+ align:start position:0%
+this this the count of number of CEOs
+ 
+
+ align:start position:0%
+this this the count of number of CEOs
+that have a particular zodiac sign and
+
+ align:start position:0%
+that have a particular zodiac sign and
+ 
+
+ align:start position:0%
+that have a particular zodiac sign and
+if this was completely uniformly
+
+ align:start position:0%
+if this was completely uniformly
+ 
+
+ align:start position:0%
+if this was completely uniformly
+distributed you should actually get a
+
+ align:start position:0%
+distributed you should actually get a
+ 
+
+ align:start position:0%
+distributed you should actually get a
+number that's around 256 divided by 12
+
+ align:start position:0%
+number that's around 256 divided by 12
+ 
+
+ align:start position:0%
+number that's around 256 divided by 12
+which in this case is
+
+ align:start position:0%
+which in this case is
+ 
+
+ align:start position:0%
+which in this case is
+2133 okay and you can see that there's
+
+ align:start position:0%
+2133 okay and you can see that there's
+ 
+
+ align:start position:0%
+2133 okay and you can see that there's
+uh numbers that you know are probably in
+
+ align:start position:0%
+uh numbers that you know are probably in
+ 
+
+ align:start position:0%
+uh numbers that you know are probably in
+the vicinity but see look at this guy
+
+ align:start position:0%
+the vicinity but see look at this guy
+ 
+
+ align:start position:0%
+the vicinity but see look at this guy
+pieces right that's 29 so whose piece is
+
+ align:start position:0%
+pieces right that's 29 so whose piece is
+ 
+
+ align:start position:0%
+pieces right that's 29 so whose piece is
+here all right and um all right so give
+
+ align:start position:0%
+here all right and um all right so give
+ 
+
+ align:start position:0%
+here all right and um all right so give
+me your information and uh we'll meet
+
+ align:start position:0%
+me your information and uh we'll meet
+ 
+
+ align:start position:0%
+me your information and uh we'll meet
+again in 10 years and so uh basically
+
+ align:start position:0%
+again in 10 years and so uh basically
+ 
+
+ align:start position:0%
+again in 10 years and so uh basically
+you might want to test if actually the
+
+ align:start position:0%
+you might want to test if actually the
+ 
+
+ align:start position:0%
+you might want to test if actually the
+fact that it's uniformly distributed is
+
+ align:start position:0%
+fact that it's uniformly distributed is
+ 
+
+ align:start position:0%
+fact that it's uniformly distributed is
+a valid assumption now this is clearly a
+
+ align:start position:0%
+a valid assumption now this is clearly a
+ 
+
+ align:start position:0%
+a valid assumption now this is clearly a
+random variable I pick a random CEO and
+
+ align:start position:0%
+random variable I pick a random CEO and
+ 
+
+ align:start position:0%
+random variable I pick a random CEO and
+I measure uh uh what is um zodiac sign
+
+ align:start position:0%
+I measure uh uh what is um zodiac sign
+ 
+
+ align:start position:0%
+I measure uh uh what is um zodiac sign
+is and I want to know if this so it's a
+
+ align:start position:0%
+is and I want to know if this so it's a
+ 
+
+ align:start position:0%
+is and I want to know if this so it's a
+probability over I don't know 12 Zodiac
+
+ align:start position:0%
+probability over I don't know 12 Zodiac
+ 
+
+ align:start position:0%
+probability over I don't know 12 Zodiac
+signs and I want to know if it's uniform
+
+ align:start position:0%
+signs and I want to know if it's uniform
+ 
+
+ align:start position:0%
+signs and I want to know if it's uniform
+or not right uniform sounds like it
+
+ align:start position:0%
+or not right uniform sounds like it
+ 
+
+ align:start position:0%
+or not right uniform sounds like it
+should be the status quo if you're
+
+ align:start position:0%
+should be the status quo if you're
+ 
+
+ align:start position:0%
+should be the status quo if you're
+reasonable and uh and maybe there's
+
+ align:start position:0%
+reasonable and uh and maybe there's
+ 
+
+ align:start position:0%
+reasonable and uh and maybe there's
+actually something that moves away uh so
+
+ align:start position:0%
+actually something that moves away uh so
+ 
+
+ align:start position:0%
+actually something that moves away uh so
+you know we could uh do this in view of
+
+ align:start position:0%
+you know we could uh do this in view of
+ 
+
+ align:start position:0%
+you know we could uh do this in view of
+this data is there evidence that one is
+
+ align:start position:0%
+this data is there evidence that one is
+ 
+
+ align:start position:0%
+this data is there evidence that one is
+different here's another example where
+
+ align:start position:0%
+different here's another example where
+ 
+
+ align:start position:0%
+different here's another example where
+you might want to apply the cas Square
+
+ align:start position:0%
+you might want to apply the cas Square
+ 
+
+ align:start position:0%
+you might want to apply the cas Square
+test right so as I said The Benchmark
+
+ align:start position:0%
+test right so as I said The Benchmark
+ 
+
+ align:start position:0%
+test right so as I said The Benchmark
+distribution was the uniform
+
+ align:start position:0%
+distribution was the uniform
+ 
+
+ align:start position:0%
+distribution was the uniform
+distribution for the zxn and that's
+
+ align:start position:0%
+distribution for the zxn and that's
+ 
+
+ align:start position:0%
+distribution for the zxn and that's
+usually the one I gave you one over K
+
+ align:start position:0%
+usually the one I gave you one over K
+ 
+
+ align:start position:0%
+usually the one I gave you one over K
+one over K because well that's sort of
+
+ align:start position:0%
+one over K because well that's sort of
+ 
+
+ align:start position:0%
+one over K because well that's sort of
+the zero uh you know the central point
+
+ align:start position:0%
+the zero uh you know the central point
+ 
+
+ align:start position:0%
+the zero uh you know the central point
+for all distributions right that's the
+
+ align:start position:0%
+for all distributions right that's the
+ 
+
+ align:start position:0%
+for all distributions right that's the
+point that's right at the center of what
+
+ align:start position:0%
+point that's right at the center of what
+ 
+
+ align:start position:0%
+point that's right at the center of what
+we call the Simplex uh but you can have
+
+ align:start position:0%
+we call the Simplex uh but you can have
+ 
+
+ align:start position:0%
+we call the Simplex uh but you can have
+another Benchmark that sort of makes
+
+ align:start position:0%
+another Benchmark that sort of makes
+ 
+
+ align:start position:0%
+another Benchmark that sort of makes
+sense right so for example this is an
+
+ align:start position:0%
+sense right so for example this is an
+ 
+
+ align:start position:0%
+sense right so for example this is an
+actual data set where
+
+ align:start position:0%
+actual data set where
+ 
+
+ align:start position:0%
+actual data set where
+2575 jurors were identified with
+
+ align:start position:0%
+2575 jurors were identified with
+ 
+
+ align:start position:0%
+2575 jurors were identified with
+identified racial group were uh
+
+ align:start position:0%
+identified racial group were uh
+ 
+
+ align:start position:0%
+identified racial group were uh
+collected and you actually might want to
+
+ align:start position:0%
+collected and you actually might want to
+ 
+
+ align:start position:0%
+collected and you actually might want to
+know if you know juries in this country
+
+ align:start position:0%
+know if you know juries in this country
+ 
+
+ align:start position:0%
+know if you know juries in this country
+are actually representative of the
+
+ align:start position:0%
+are actually representative of the
+ 
+
+ align:start position:0%
+are actually representative of the
+actual uh uh uh population and so here
+
+ align:start position:0%
+actual uh uh uh population and so here
+ 
+
+ align:start position:0%
+actual uh uh uh population and so here
+of course the population is not
+
+ align:start position:0%
+of course the population is not
+ 
+
+ align:start position:0%
+of course the population is not
+uniformly distributed uh according to
+
+ align:start position:0%
+uniformly distributed uh according to
+ 
+
+ align:start position:0%
+uniformly distributed uh according to
+racial group and the way you actually do
+
+ align:start position:0%
+racial group and the way you actually do
+ 
+
+ align:start position:0%
+racial group and the way you actually do
+it is you actually go on Wikipedia for
+
+ align:start position:0%
+it is you actually go on Wikipedia for
+ 
+
+ align:start position:0%
+it is you actually go on Wikipedia for
+example and you look at the demographics
+
+ align:start position:0%
+example and you look at the demographics
+ 
+
+ align:start position:0%
+example and you look at the demographics
+of the United States and you find that
+
+ align:start position:0%
+of the United States and you find that
+ 
+
+ align:start position:0%
+of the United States and you find that
+the proportion of white is uh 72% black
+
+ align:start position:0%
+the proportion of white is uh 72% black
+ 
+
+ align:start position:0%
+the proportion of white is uh 72% black
+is 7% Hispanic is 12 and other is uh uh
+
+ align:start position:0%
+is 7% Hispanic is 12 and other is uh uh
+ 
+
+ align:start position:0%
+is 7% Hispanic is 12 and other is uh uh
+uh well uh about uh nine um percent so
+
+ align:start position:0%
+uh well uh about uh nine um percent so
+ 
+
+ align:start position:0%
+uh well uh about uh nine um percent so
+that's a total of one and this is what
+
+ align:start position:0%
+that's a total of one and this is what
+ 
+
+ align:start position:0%
+that's a total of one and this is what
+we actually measured for uh some jurors
+
+ align:start position:0%
+we actually measured for uh some jurors
+ 
+
+ align:start position:0%
+we actually measured for uh some jurors
+so for this guy you can actually run the
+
+ align:start position:0%
+so for this guy you can actually run the
+ 
+
+ align:start position:0%
+so for this guy you can actually run the
+K Square test right you have the
+
+ align:start position:0%
+K Square test right you have the
+ 
+
+ align:start position:0%
+K Square test right you have the
+estimated proportion which comes from
+
+ align:start position:0%
+estimated proportion which comes from
+ 
+
+ align:start position:0%
+estimated proportion which comes from
+the first line you have the tested
+
+ align:start position:0%
+the first line you have the tested
+ 
+
+ align:start position:0%
+the first line you have the tested
+proportion p 0 that comes from the
+
+ align:start position:0%
+proportion p 0 that comes from the
+ 
+
+ align:start position:0%
+proportion p 0 that comes from the
+second line and you might want to check
+
+ align:start position:0%
+second line and you might want to check
+ 
+
+ align:start position:0%
+second line and you might want to check
+if those things actually correspond to
+
+ align:start position:0%
+if those things actually correspond to
+ 
+
+ align:start position:0%
+if those things actually correspond to
+each other okay so I'm not going to do
+
+ align:start position:0%
+each other okay so I'm not going to do
+ 
+
+ align:start position:0%
+each other okay so I'm not going to do
+it for you but I sort of invite you to
+
+ align:start position:0%
+it for you but I sort of invite you to
+ 
+
+ align:start position:0%
+it for you but I sort of invite you to
+do it and test and see how this compares
+
+ align:start position:0%
+do it and test and see how this compares
+ 
+
+ align:start position:0%
+do it and test and see how this compares
+to the quantales of the appropriate Kare
+
+ align:start position:0%
+to the quantales of the appropriate Kare
+ 
+
+ align:start position:0%
+to the quantales of the appropriate Kare
+distribution and see what you can
+
+ align:start position:0%
+distribution and see what you can
+ 
+
+ align:start position:0%
+distribution and see what you can
+conclude from those two
+
+ align:start position:0%
+conclude from those two
+ 
+
+ align:start position:0%
+conclude from those two
+things all right so uh this was the
+
+ align:start position:0%
+things all right so uh this was the
+ 
+
+ align:start position:0%
+things all right so uh this was the
+multinomial case so uh this is
+
+ align:start position:0%
+multinomial case so uh this is
+ 
+
+ align:start position:0%
+multinomial case so uh this is
+essentially what we did we computed the
+
+ align:start position:0%
+essentially what we did we computed the
+ 
+
+ align:start position:0%
+essentially what we did we computed the
+mle under the right constraint and that
+
+ align:start position:0%
+mle under the right constraint and that
+ 
+
+ align:start position:0%
+mle under the right constraint and that
+was our test statistic that converges to
+
+ align:start position:0%
+was our test statistic that converges to
+ 
+
+ align:start position:0%
+was our test statistic that converges to
+the C Square distribution so if you've
+
+ align:start position:0%
+the C Square distribution so if you've
+ 
+
+ align:start position:0%
+the C Square distribution so if you've
+seen it before that's all that was given
+
+ align:start position:0%
+seen it before that's all that was given
+ 
+
+ align:start position:0%
+seen it before that's all that was given
+to you now we know why the normalization
+
+ align:start position:0%
+to you now we know why the normalization
+ 
+
+ align:start position:0%
+to you now we know why the normalization
+here is P J and p j^ s or square root of
+
+ align:start position:0%
+here is P J and p j^ s or square root of
+ 
+
+ align:start position:0%
+here is P J and p j^ s or square root of
+p j or even one right I mean it's not
+
+ align:start position:0%
+p j or even one right I mean it's not
+ 
+
+ align:start position:0%
+p j or even one right I mean it's not
+clear that this should be the right
+
+ align:start position:0%
+clear that this should be the right
+ 
+
+ align:start position:0%
+clear that this should be the right
+normalization but we know that's what
+
+ align:start position:0%
+normalization but we know that's what
+ 
+
+ align:start position:0%
+normalization but we know that's what
+comes from taking the right
+
+ align:start position:0%
+comes from taking the right
+ 
+
+ align:start position:0%
+comes from taking the right
+normalization which comes from the
+
+ align:start position:0%
+normalization which comes from the
+ 
+
+ align:start position:0%
+normalization which comes from the
+Fisher information all right okay so uh
+
+ align:start position:0%
+Fisher information all right okay so uh
+ 
+
+ align:start position:0%
+Fisher information all right okay so uh
+um the thing I wanted to move on to so
+
+ align:start position:0%
+um the thing I wanted to move on to so
+ 
+
+ align:start position:0%
+um the thing I wanted to move on to so
+we've basically covered uh K Square test
+
+ align:start position:0%
+we've basically covered uh K Square test
+ 
+
+ align:start position:0%
+we've basically covered uh K Square test
+are there any questions about k k Square
+
+ align:start position:0%
+are there any questions about k k Square
+ 
+
+ align:start position:0%
+are there any questions about k k Square
+test and for those of you who were not
+
+ align:start position:0%
+test and for those of you who were not
+ 
+
+ align:start position:0%
+test and for those of you who were not
+here on Thursday I'm really just I I do
+
+ align:start position:0%
+here on Thursday I'm really just I I do
+ 
+
+ align:start position:0%
+here on Thursday I'm really just I I do
+not pretend I just did it right that's
+
+ align:start position:0%
+not pretend I just did it right that's
+ 
+
+ align:start position:0%
+not pretend I just did it right that's
+something we did last Thursday right but
+
+ align:start position:0%
+something we did last Thursday right but
+ 
+
+ align:start position:0%
+something we did last Thursday right but
+are there any questions that arose when
+
+ align:start position:0%
+are there any questions that arose when
+ 
+
+ align:start position:0%
+are there any questions that arose when
+you were reading your notes things that
+
+ align:start position:0%
+you were reading your notes things that
+ 
+
+ align:start position:0%
+you were reading your notes things that
+you didn't understand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes so so it's it's not so it's not the
+
+ align:start position:0%
+yes so so it's it's not so it's not the
+ 
+
+ align:start position:0%
+yes so so it's it's not so it's not the
+Fisher the Fisher information does not
+
+ align:start position:0%
+Fisher the Fisher information does not
+ 
+
+ align:start position:0%
+Fisher the Fisher information does not
+exist in this case and so there's no
+
+ align:start position:0%
+exist in this case and so there's no
+ 
+
+ align:start position:0%
+exist in this case and so there's no
+appropriate name for this is the pseudo
+
+ align:start position:0%
+appropriate name for this is the pseudo
+ 
+
+ align:start position:0%
+appropriate name for this is the pseudo
+inverse of the Astic ciance Matrix and
+
+ align:start position:0%
+inverse of the Astic ciance Matrix and
+ 
+
+ align:start position:0%
+inverse of the Astic ciance Matrix and
+that's what it is and there's um I don't
+
+ align:start position:0%
+that's what it is and there's um I don't
+ 
+
+ align:start position:0%
+that's what it is and there's um I don't
+know if I mentioned it last time but
+
+ align:start position:0%
+know if I mentioned it last time but
+ 
+
+ align:start position:0%
+know if I mentioned it last time but
+there's this entire field that uses you
+
+ align:start position:0%
+there's this entire field that uses you
+ 
+
+ align:start position:0%
+there's this entire field that uses you
+know for people who are really aspire to
+
+ align:start position:0%
+know for people who are really aspire to
+ 
+
+ align:start position:0%
+know for people who are really aspire to
+differential geometry but are stuck in a
+
+ align:start position:0%
+differential geometry but are stuck in a
+ 
+
+ align:start position:0%
+differential geometry but are stuck in a
+stats department and there's this thing
+
+ align:start position:0%
+stats department and there's this thing
+ 
+
+ align:start position:0%
+stats department and there's this thing
+called information geometry which is
+
+ align:start position:0%
+called information geometry which is
+ 
+
+ align:start position:0%
+called information geometry which is
+essentially studying the manifolds uh
+
+ align:start position:0%
+essentially studying the manifolds uh
+ 
+
+ align:start position:0%
+essentially studying the manifolds uh
+Associated to the Fisher information
+
+ align:start position:0%
+Associated to the Fisher information
+ 
+
+ align:start position:0%
+Associated to the Fisher information
+matric and the uh the the the metric
+
+ align:start position:0%
+matric and the uh the the the metric
+ 
+
+ align:start position:0%
+matric and the uh the the the metric
+that's associated to Fisher information
+
+ align:start position:0%
+that's associated to Fisher information
+ 
+
+ align:start position:0%
+that's associated to Fisher information
+right and so those of course can be
+
+ align:start position:0%
+right and so those of course can be
+ 
+
+ align:start position:0%
+right and so those of course can be
+lower dimensional manifolds it not only
+
+ align:start position:0%
+lower dimensional manifolds it not only
+ 
+
+ align:start position:0%
+lower dimensional manifolds it not only
+distorts the geometry but forces
+
+ align:start position:0%
+distorts the geometry but forces
+ 
+
+ align:start position:0%
+distorts the geometry but forces
+everything to live on the lower
+
+ align:start position:0%
+everything to live on the lower
+ 
+
+ align:start position:0%
+everything to live on the lower
+Dimension which is what happens when
+
+ align:start position:0%
+Dimension which is what happens when
+ 
+
+ align:start position:0%
+Dimension which is what happens when
+your fure information does not exist and
+
+ align:start position:0%
+your fure information does not exist and
+ 
+
+ align:start position:0%
+your fure information does not exist and
+so you know there's a bunch of things
+
+ align:start position:0%
+so you know there's a bunch of things
+ 
+
+ align:start position:0%
+so you know there's a bunch of things
+that you can study what this manifold
+
+ align:start position:0%
+that you can study what this manifold
+ 
+
+ align:start position:0%
+that you can study what this manifold
+looks like Etc but no there's no
+
+ align:start position:0%
+looks like Etc but no there's no
+ 
+
+ align:start position:0%
+looks like Etc but no there's no
+particular terminology here about uh
+
+ align:start position:0%
+particular terminology here about uh
+ 
+
+ align:start position:0%
+particular terminology here about uh
+about going
+
+ align:start position:0%
+about going
+ 
+
+ align:start position:0%
+about going
+here uh to be fair within the scope of
+
+ align:start position:0%
+here uh to be fair within the scope of
+ 
+
+ align:start position:0%
+here uh to be fair within the scope of
+this class this is the
+
+ align:start position:0%
+this class this is the
+ 
+
+ align:start position:0%
+this class this is the
+only case where you mul multinomial Cas
+
+ align:start position:0%
+only case where you mul multinomial Cas
+ 
+
+ align:start position:0%
+only case where you mul multinomial Cas
+is the only case where you typically see
+
+ align:start position:0%
+is the only case where you typically see
+ 
+
+ align:start position:0%
+is the only case where you typically see
+um uh uh a lack of Fisher information
+
+ align:start position:0%
+um uh uh a lack of Fisher information
+ 
+
+ align:start position:0%
+um uh uh a lack of Fisher information
+Matrix and that's just because we have
+
+ align:start position:0%
+Matrix and that's just because we have
+ 
+
+ align:start position:0%
+Matrix and that's just because we have
+this extra constraints that the sum of
+
+ align:start position:0%
+this extra constraints that the sum of
+ 
+
+ align:start position:0%
+this extra constraints that the sum of
+the parameters should be one and if you
+
+ align:start position:0%
+the parameters should be one and if you
+ 
+
+ align:start position:0%
+the parameters should be one and if you
+have an extra constraint that seems like
+
+ align:start position:0%
+have an extra constraint that seems like
+ 
+
+ align:start position:0%
+have an extra constraint that seems like
+it's actually removed one degree of
+
+ align:start position:0%
+it's actually removed one degree of
+ 
+
+ align:start position:0%
+it's actually removed one degree of
+Freedom this will happen inevitably and
+
+ align:start position:0%
+Freedom this will happen inevitably and
+ 
+
+ align:start position:0%
+Freedom this will happen inevitably and
+so maybe what you can do is repar
+
+ align:start position:0%
+so maybe what you can do is repar
+ 
+
+ align:start position:0%
+so maybe what you can do is repar
+reparameterize so if I actually
+
+ align:start position:0%
+reparameterize so if I actually
+ 
+
+ align:start position:0%
+reparameterize so if I actually
+reparameterize everything in for in in
+
+ align:start position:0%
+reparameterize everything in for in in
+ 
+
+ align:start position:0%
+reparameterize everything in for in in
+function of P1 to PK minus one and then
+
+ align:start position:0%
+function of P1 to PK minus one and then
+ 
+
+ align:start position:0%
+function of P1 to PK minus one and then
+one minus the sum this would not have
+
+ align:start position:0%
+one minus the sum this would not have
+ 
+
+ align:start position:0%
+one minus the sum this would not have
+happened because I have only a ky
+
+ align:start position:0%
+happened because I have only a ky
+ 
+
+ align:start position:0%
+happened because I have only a ky
+dimensional space so there's tricks
+
+ align:start position:0%
+dimensional space so there's tricks
+ 
+
+ align:start position:0%
+dimensional space so there's tricks
+around this to make it exist if you want
+
+ align:start position:0%
+around this to make it exist if you want
+ 
+
+ align:start position:0%
+around this to make it exist if you want
+it to
+
+ align:start position:0%
+it to
+ 
+
+ align:start position:0%
+it to
+exist any other
+
+ align:start position:0%
+exist any other
+ 
+
+ align:start position:0%
+exist any other
+question all right so let's move on to
+
+ align:start position:0%
+question all right so let's move on to
+ 
+
+ align:start position:0%
+question all right so let's move on to
+students T tasks uh we mentioned that
+
+ align:start position:0%
+students T tasks uh we mentioned that
+ 
+
+ align:start position:0%
+students T tasks uh we mentioned that
+last time right so essentially uh you've
+
+ align:start position:0%
+last time right so essentially uh you've
+ 
+
+ align:start position:0%
+last time right so essentially uh you've
+probably done it more even in in
+
+ align:start position:0%
+probably done it more even in in
+ 
+
+ align:start position:0%
+probably done it more even in in
+homework than you've done it in uh in
+
+ align:start position:0%
+homework than you've done it in uh in
+ 
+
+ align:start position:0%
+homework than you've done it in uh in
+lectures but just quickly um this is
+
+ align:start position:0%
+lectures but just quickly um this is
+ 
+
+ align:start position:0%
+lectures but just quickly um this is
+essentially the test that's the test
+
+ align:start position:0%
+essentially the test that's the test
+ 
+
+ align:start position:0%
+essentially the test that's the test
+when we have an actual data that comes
+
+ align:start position:0%
+when we have an actual data that comes
+ 
+
+ align:start position:0%
+when we have an actual data that comes
+from a normal distribution there's no
+
+ align:start position:0%
+from a normal distribution there's no
+ 
+
+ align:start position:0%
+from a normal distribution there's no
+Central limit theorem that exists this
+
+ align:start position:0%
+Central limit theorem that exists this
+ 
+
+ align:start position:0%
+Central limit theorem that exists this
+is really to account for the fact that
+
+ align:start position:0%
+is really to account for the fact that
+ 
+
+ align:start position:0%
+is really to account for the fact that
+for smaller sample sizes uh it might be
+
+ align:start position:0%
+for smaller sample sizes uh it might be
+ 
+
+ align:start position:0%
+for smaller sample sizes uh it might be
+the case that it's not exactly true that
+
+ align:start position:0%
+the case that it's not exactly true that
+ 
+
+ align:start position:0%
+the case that it's not exactly true that
+when I look at X n
+
+ align:start position:0%
+when I look at X n
+ 
+
+ align:start position:0%
+when I look at X n
+barus mu divid so if I look at xn bar
+
+ align:start position:0%
+barus mu divid so if I look at xn bar
+ 
+
+ align:start position:0%
+barus mu divid so if I look at xn bar
+minus mu ID Sigma * of n then this thing
+
+ align:start position:0%
+minus mu ID Sigma * of n then this thing
+ 
+
+ align:start position:0%
+minus mu ID Sigma * of n then this thing
+should have n01 distribution
+
+ align:start position:0%
+should have n01 distribution
+ 
+
+ align:start position:0%
+should have n01 distribution
+approximately right by the central Lim
+
+ align:start position:0%
+approximately right by the central Lim
+ 
+
+ align:start position:0%
+approximately right by the central Lim
+theorem so that's for n large but if n
+
+ align:start position:0%
+theorem so that's for n large but if n
+ 
+
+ align:start position:0%
+theorem so that's for n large but if n
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+small then it's still
+
+ align:start position:0%
+small then it's still
+ 
+
+ align:start position:0%
+small then it's still
+true when the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data is n mu Sigma squ
+
+ align:start position:0%
+data is n mu Sigma squ
+ 
+
+ align:start position:0%
+data is n mu Sigma squ
+then it's true that square root of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n so here it's
+
+ align:start position:0%
+n so here it's
+ 
+
+ align:start position:0%
+n so here it's
+approximately and this is always
+
+ align:start position:0%
+approximately and this is always
+ 
+
+ align:start position:0%
+approximately and this is always
+true but I don't know Sigma in practice
+
+ align:start position:0%
+true but I don't know Sigma in practice
+ 
+
+ align:start position:0%
+true but I don't know Sigma in practice
+right maybe mu comes from my um maybe mu
+
+ align:start position:0%
+right maybe mu comes from my um maybe mu
+ 
+
+ align:start position:0%
+right maybe mu comes from my um maybe mu
+comes from my mu not right maybe
+
+ align:start position:0%
+comes from my mu not right maybe
+ 
+
+ align:start position:0%
+comes from my mu not right maybe
+something from the the test statistic
+
+ align:start position:0%
+something from the the test statistic
+ 
+
+ align:start position:0%
+something from the the test statistic
+where mu actually is here but for this
+
+ align:start position:0%
+where mu actually is here but for this
+ 
+
+ align:start position:0%
+where mu actually is here but for this
+guy I'm going to have inevitably to find
+
+ align:start position:0%
+guy I'm going to have inevitably to find
+ 
+
+ align:start position:0%
+guy I'm going to have inevitably to find
+an estimator and now in this case for
+
+ align:start position:0%
+an estimator and now in this case for
+ 
+
+ align:start position:0%
+an estimator and now in this case for
+small n this is no longer true and what
+
+ align:start position:0%
+small n this is no longer true and what
+ 
+
+ align:start position:0%
+small n this is no longer true and what
+the T statistic is doing is essentially
+
+ align:start position:0%
+the T statistic is doing is essentially
+ 
+
+ align:start position:0%
+the T statistic is doing is essentially
+telling you what the distribution of
+
+ align:start position:0%
+telling you what the distribution of
+ 
+
+ align:start position:0%
+telling you what the distribution of
+this guy is all right so the truth what
+
+ align:start position:0%
+this guy is all right so the truth what
+ 
+
+ align:start position:0%
+this guy is all right so the truth what
+you should say is that now this guy has
+
+ align:start position:0%
+you should say is that now this guy has
+ 
+
+ align:start position:0%
+you should say is that now this guy has
+a t distribution with n minus one
+
+ align:start position:0%
+a t distribution with n minus one
+ 
+
+ align:start position:0%
+a t distribution with n minus one
+degrees of freedom that's basically the
+
+ align:start position:0%
+degrees of freedom that's basically the
+ 
+
+ align:start position:0%
+degrees of freedom that's basically the
+you know laundry list stats that you
+
+ align:start position:0%
+you know laundry list stats that you
+ 
+
+ align:start position:0%
+you know laundry list stats that you
+would learn it says just look at a
+
+ align:start position:0%
+would learn it says just look at a
+ 
+
+ align:start position:0%
+would learn it says just look at a
+different table that's what it is but we
+
+ align:start position:0%
+different table that's what it is but we
+ 
+
+ align:start position:0%
+different table that's what it is but we
+actually defined was a what a t
+
+ align:start position:0%
+actually defined was a what a t
+ 
+
+ align:start position:0%
+actually defined was a what a t
+distribution was and a t
+
+ align:start position:0%
+distribution was and a t
+ 
+
+ align:start position:0%
+distribution was and a t
+distribution is basically something that
+
+ align:start position:0%
+distribution is basically something that
+ 
+
+ align:start position:0%
+distribution is basically something that
+has the same distribution as some
+
+ align:start position:0%
+has the same distribution as some
+ 
+
+ align:start position:0%
+has the same distribution as some
+n01 divided by the square root of a k
+
+ align:start position:0%
+n01 divided by the square root of a k
+ 
+
+ align:start position:0%
+n01 divided by the square root of a k
+squ with d degrees of freedom divided by
+
+ align:start position:0%
+squ with d degrees of freedom divided by
+ 
+
+ align:start position:0%
+squ with d degrees of freedom divided by
+D and that's a t distribution with d
+
+ align:start position:0%
+D and that's a t distribution with d
+ 
+
+ align:start position:0%
+D and that's a t distribution with d
+degrees of freedom right and those two
+
+ align:start position:0%
+degrees of freedom right and those two
+ 
+
+ align:start position:0%
+degrees of freedom right and those two
+have to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent okay and so what I need to
+
+ align:start position:0%
+independent okay and so what I need to
+ 
+
+ align:start position:0%
+independent okay and so what I need to
+check is that this guy over there is of
+
+ align:start position:0%
+check is that this guy over there is of
+ 
+
+ align:start position:0%
+check is that this guy over there is of
+this form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's look at the numerator well
+
+ align:start position:0%
+okay so let's look at the numerator well
+ 
+
+ align:start position:0%
+okay so let's look at the numerator well
+s root of n xn bar minus mu what is the
+
+ align:start position:0%
+s root of n xn bar minus mu what is the
+ 
+
+ align:start position:0%
+s root of n xn bar minus mu what is the
+distribution of this thing is it an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n01 n0 Sigma squ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so I'm not going to put it here so
+
+ align:start position:0%
+right so I'm not going to put it here so
+ 
+
+ align:start position:0%
+right so I'm not going to put it here so
+if I want this guy to be in 01 I need to
+
+ align:start position:0%
+if I want this guy to be in 01 I need to
+ 
+
+ align:start position:0%
+if I want this guy to be in 01 I need to
+divide by Sigma that's what we have over
+
+ align:start position:0%
+divide by Sigma that's what we have over
+ 
+
+ align:start position:0%
+divide by Sigma that's what we have over
+there so that's my n01 that's going to
+
+ align:start position:0%
+there so that's my n01 that's going to
+ 
+
+ align:start position:0%
+there so that's my n01 that's going to
+play the role of this guy here so if I
+
+ align:start position:0%
+play the role of this guy here so if I
+ 
+
+ align:start position:0%
+play the role of this guy here so if I
+want to go a little further I need to
+
+ align:start position:0%
+want to go a little further I need to
+ 
+
+ align:start position:0%
+want to go a little further I need to
+just say okay now I need to have square
+
+ align:start position:0%
+just say okay now I need to have square
+ 
+
+ align:start position:0%
+just say okay now I need to have square
+root of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+N and I need to find something here that
+
+ align:start position:0%
+N and I need to find something here that
+ 
+
+ align:start position:0%
+N and I need to find something here that
+looks like my K square root of K Square
+
+ align:start position:0%
+looks like my K square root of K Square
+ 
+
+ align:start position:0%
+looks like my K square root of K Square
+divided by yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no that's just in distribution uh so I
+
+ align:start position:0%
+no that's just in distribution uh so I
+ 
+
+ align:start position:0%
+no that's just in distribution uh so I
+don't know that's uh let's just write it
+
+ align:start position:0%
+don't know that's uh let's just write it
+ 
+
+ align:start position:0%
+don't know that's uh let's just write it
+like that if you
+
+ align:start position:0%
+like that if you
+ 
+
+ align:start position:0%
+like that if you
+want um I mean yeah that's not really
+
+ align:start position:0%
+want um I mean yeah that's not really
+ 
+
+ align:start position:0%
+want um I mean yeah that's not really
+appropriate to have usually you write
+
+ align:start position:0%
+appropriate to have usually you write
+ 
+
+ align:start position:0%
+appropriate to have usually you write
+only one Distribution on the right hand
+
+ align:start position:0%
+only one Distribution on the right hand
+ 
+
+ align:start position:0%
+only one Distribution on the right hand
+side of this twiddle thing so not just
+
+ align:start position:0%
+side of this twiddle thing so not just
+ 
+
+ align:start position:0%
+side of this twiddle thing so not just
+this complicated function of
+
+ align:start position:0%
+this complicated function of
+ 
+
+ align:start position:0%
+this complicated function of
+distributions I mean this is more like
+
+ align:start position:0%
+distributions I mean this is more like
+ 
+
+ align:start position:0%
+distributions I mean this is more like
+to explain okay and so usually you thing
+
+ align:start position:0%
+to explain okay and so usually you thing
+ 
+
+ align:start position:0%
+to explain okay and so usually you thing
+you should say is that t is equal to
+
+ align:start position:0%
+you should say is that t is equal to
+ 
+
+ align:start position:0%
+you should say is that t is equal to
+this x ided square root of Zid by D
+
+ align:start position:0%
+this x ided square root of Zid by D
+ 
+
+ align:start position:0%
+this x ided square root of Zid by D
+where X has normal distribution Z has K
+
+ align:start position:0%
+where X has normal distribution Z has K
+ 
+
+ align:start position:0%
+where X has normal distribution Z has K
+Square distribution with the degrees of
+
+ align:start position:0%
+Square distribution with the degrees of
+ 
+
+ align:start position:0%
+Square distribution with the degrees of
+freedom okay so what do I need here well
+
+ align:start position:0%
+freedom okay so what do I need here well
+ 
+
+ align:start position:0%
+freedom okay so what do I need here well
+I need to have something which looks
+
+ align:start position:0%
+I need to have something which looks
+ 
+
+ align:start position:0%
+I need to have something which looks
+like my Sigma hat right so somehow
+
+ align:start position:0%
+like my Sigma hat right so somehow
+ 
+
+ align:start position:0%
+like my Sigma hat right so somehow
+inevitably I'm going to need to have
+
+ align:start position:0%
+inevitably I'm going to need to have
+ 
+
+ align:start position:0%
+inevitably I'm going to need to have
+Sigma
+
+ align:start position:0%
+Sigma
+ 
+
+ align:start position:0%
+Sigma
+hat now of course I need to divide this
+
+ align:start position:0%
+hat now of course I need to divide this
+ 
+
+ align:start position:0%
+hat now of course I need to divide this
+by my Sigma so that my Sigma goes
+
+ align:start position:0%
+by my Sigma so that my Sigma goes
+ 
+
+ align:start position:0%
+by my Sigma so that my Sigma goes
+away and so now this thing here uh sorry
+
+ align:start position:0%
+away and so now this thing here uh sorry
+ 
+
+ align:start position:0%
+away and so now this thing here uh sorry
+I should move on to the right okay and
+
+ align:start position:0%
+I should move on to the right okay and
+ 
+
+ align:start position:0%
+I should move on to the right okay and
+so this thing here so Sigma hat is is a
+
+ align:start position:0%
+so this thing here so Sigma hat is is a
+ 
+
+ align:start position:0%
+so this thing here so Sigma hat is is a
+square root of SN and now I'm almost
+
+ align:start position:0%
+square root of SN and now I'm almost
+ 
+
+ align:start position:0%
+square root of SN and now I'm almost
+there so this thing is actually equal to
+
+ align:start position:0%
+there so this thing is actually equal to
+ 
+
+ align:start position:0%
+there so this thing is actually equal to
+uh s root of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+right but this thing
+
+ align:start position:0%
+right but this thing
+ 
+
+ align:start position:0%
+right but this thing
+here is actually not a
+
+ align:start position:0%
+here is actually not a
+ 
+
+ align:start position:0%
+here is actually not a
+uh so this thing here follows a
+
+ align:start position:0%
+uh so this thing here follows a
+ 
+
+ align:start position:0%
+uh so this thing here follows a
+distribution which is actually a c
+
+ align:start position:0%
+distribution which is actually a c
+ 
+
+ align:start position:0%
+distribution which is actually a c
+square square root of a k Square
+
+ align:start position:0%
+square square root of a k Square
+ 
+
+ align:start position:0%
+square square root of a k Square
+distribution divided by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and yeah that's a square root uh K
+
+ align:start position:0%
+and yeah that's a square root uh K
+ 
+
+ align:start position:0%
+and yeah that's a square root uh K
+Square distribution with n minus one
+
+ align:start position:0%
+Square distribution with n minus one
+ 
+
+ align:start position:0%
+Square distribution with n minus one
+degrees of freedom divided by n because
+
+ align:start position:0%
+degrees of freedom divided by n because
+ 
+
+ align:start position:0%
+degrees of freedom divided by n because
+Sigma hat is equal to 1 / n sum from I =
+
+ align:start position:0%
+Sigma hat is equal to 1 / n sum from I =
+ 
+
+ align:start position:0%
+Sigma hat is equal to 1 / n sum from I =
+1 to n x i - xar squared and we just
+
+ align:start position:0%
+1 to n x i - xar squared and we just
+ 
+
+ align:start position:0%
+1 to n x i - xar squared and we just
+said that this part here was a k Square
+
+ align:start position:0%
+said that this part here was a k Square
+ 
+
+ align:start position:0%
+said that this part here was a k Square
+distrib we didn't just say it we said it
+
+ align:start position:0%
+distrib we didn't just say it we said it
+ 
+
+ align:start position:0%
+distrib we didn't just say it we said it
+a few lectures back that this thing was
+
+ align:start position:0%
+a few lectures back that this thing was
+ 
+
+ align:start position:0%
+a few lectures back that this thing was
+the K Square distribution and the fact
+
+ align:start position:0%
+the K Square distribution and the fact
+ 
+
+ align:start position:0%
+the K Square distribution and the fact
+that the presence of this xn bar xar
+
+ align:start position:0%
+that the presence of this xn bar xar
+ 
+
+ align:start position:0%
+that the presence of this xn bar xar
+here was actually removing one degree of
+
+ align:start position:0%
+here was actually removing one degree of
+ 
+
+ align:start position:0%
+here was actually removing one degree of
+freedom from this
+
+ align:start position:0%
+freedom from this
+ 
+
+ align:start position:0%
+freedom from this
+sum okay so this guy here has the same
+
+ align:start position:0%
+sum okay so this guy here has the same
+ 
+
+ align:start position:0%
+sum okay so this guy here has the same
+distribution as a k s n minus one /
+
+ align:start position:0%
+distribution as a k s n minus one /
+ 
+
+ align:start position:0%
+distribution as a k s n minus one /
+n so now I need to actually still
+
+ align:start position:0%
+n so now I need to actually still
+ 
+
+ align:start position:0%
+n so now I need to actually still
+arrange this thing a little bit to have
+
+ align:start position:0%
+arrange this thing a little bit to have
+ 
+
+ align:start position:0%
+arrange this thing a little bit to have
+a t distribution I should not see n here
+
+ align:start position:0%
+a t distribution I should not see n here
+ 
+
+ align:start position:0%
+a t distribution I should not see n here
+but I should see n minus one right the D
+
+ align:start position:0%
+but I should see n minus one right the D
+ 
+
+ align:start position:0%
+but I should see n minus one right the D
+here is the same as this D here and so
+
+ align:start position:0%
+here is the same as this D here and so
+ 
+
+ align:start position:0%
+here is the same as this D here and so
+let me make the correction so that this
+
+ align:start position:0%
+let me make the correction so that this
+ 
+
+ align:start position:0%
+let me make the correction so that this
+actually happens well if I actually
+
+ align:start position:0%
+actually happens well if I actually
+ 
+
+ align:start position:0%
+actually happens well if I actually
+write this to be equal to uh so if I
+
+ align:start position:0%
+write this to be equal to uh so if I
+ 
+
+ align:start position:0%
+write this to be equal to uh so if I
+write square root of n minus one as on
+
+ align:start position:0%
+write square root of n minus one as on
+ 
+
+ align:start position:0%
+write square root of n minus one as on
+the slide times
+
+ align:start position:0%
+the slide times
+ 
+
+ align:start position:0%
+the slide times
+xnar minus mu divided by well let me
+
+ align:start position:0%
+xnar minus mu divided by well let me
+ 
+
+ align:start position:0%
+xnar minus mu divided by well let me
+write it as square root of SN which is
+
+ align:start position:0%
+write it as square root of SN which is
+ 
+
+ align:start position:0%
+write it as square root of SN which is
+my Sigma hat
+
+ align:start position:0%
+my Sigma hat
+ 
+
+ align:start position:0%
+my Sigma hat
+then uh what this thing is actually
+
+ align:start position:0%
+then uh what this thing is actually
+ 
+
+ align:start position:0%
+then uh what this thing is actually
+equal to well it's uh it's it follows a
+
+ align:start position:0%
+equal to well it's uh it's it follows a
+ 
+
+ align:start position:0%
+equal to well it's uh it's it follows a
+n01 divided by the square root of my K
+
+ align:start position:0%
+n01 divided by the square root of my K
+ 
+
+ align:start position:0%
+n01 divided by the square root of my K
+Square distribution with n minus1
+
+ align:start position:0%
+Square distribution with n minus1
+ 
+
+ align:start position:0%
+Square distribution with n minus1
+degrees of freedom and here the fact
+
+ align:start position:0%
+degrees of freedom and here the fact
+ 
+
+ align:start position:0%
+degrees of freedom and here the fact
+that I multiply by square Ro of n minus
+
+ align:start position:0%
+that I multiply by square Ro of n minus
+ 
+
+ align:start position:0%
+that I multiply by square Ro of n minus
+one and I have the square root of n here
+
+ align:start position:0%
+one and I have the square root of n here
+ 
+
+ align:start position:0%
+one and I have the square root of n here
+is essentially the same as dividing here
+
+ align:start position:0%
+is essentially the same as dividing here
+ 
+
+ align:start position:0%
+is essentially the same as dividing here
+by n minus one
+
+ align:start position:0%
+by n minus one
+ 
+
+ align:start position:0%
+by n minus one
+right and that's my TN
+
+ align:start position:0%
+right and that's my TN
+ 
+
+ align:start position:0%
+right and that's my TN
+distribution my T distribution with n
+
+ align:start position:0%
+distribution my T distribution with n
+ 
+
+ align:start position:0%
+distribution my T distribution with n
+minus one degrees of freedom just by
+
+ align:start position:0%
+minus one degrees of freedom just by
+ 
+
+ align:start position:0%
+minus one degrees of freedom just by
+definition of what this thing is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes uh this guy I'm sorry that's Sigma
+
+ align:start position:0%
+yes uh this guy I'm sorry that's Sigma
+ 
+
+ align:start position:0%
+yes uh this guy I'm sorry that's Sigma
+Square thank you
+
+ align:start position:0%
+Square thank you
+ 
+
+ align:start position:0%
+Square thank you
+that's just that's the estimator of the
+
+ align:start position:0%
+that's just that's the estimator of the
+ 
+
+ align:start position:0%
+that's just that's the estimator of the
+variance not the estimator of the
+
+ align:start position:0%
+variance not the estimator of the
+ 
+
+ align:start position:0%
+variance not the estimator of the
+standard deviation and when I want to
+
+ align:start position:0%
+standard deviation and when I want to
+ 
+
+ align:start position:0%
+standard deviation and when I want to
+divide I divide by standard deviation
+
+ align:start position:0%
+divide I divide by standard deviation
+ 
+
+ align:start position:0%
+divide I divide by standard deviation
+thank
+
+ align:start position:0%
+thank
+ 
+
+ align:start position:0%
+thank
+you any other question or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remark the estimator for the
+
+ align:start position:0%
+remark the estimator for the
+ 
+
+ align:start position:0%
+remark the estimator for the
+variance oh yes you're right so there's
+
+ align:start position:0%
+variance oh yes you're right so there's
+ 
+
+ align:start position:0%
+variance oh yes you're right so there's
+a sigma Square here
+
+ align:start position:0%
+a sigma Square here
+ 
+
+ align:start position:0%
+a sigma Square here
+is that what you're asking yes yeah
+
+ align:start position:0%
+is that what you're asking yes yeah
+ 
+
+ align:start position:0%
+is that what you're asking yes yeah
+absolutely and that's where it get
+
+ align:start position:0%
+absolutely and that's where it get
+ 
+
+ align:start position:0%
+absolutely and that's where it get
+cancels here it gets canceled
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay so this is really a sigma Square
+
+ align:start position:0%
+okay so this is really a sigma Square
+ 
+
+ align:start position:0%
+okay so this is really a sigma Square
+Times K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Square okay so the fact that it's Sigma
+
+ align:start position:0%
+Square okay so the fact that it's Sigma
+ 
+
+ align:start position:0%
+Square okay so the fact that it's Sigma
+square is just because I can pull out
+
+ align:start position:0%
+square is just because I can pull out
+ 
+
+ align:start position:0%
+square is just because I can pull out
+Sigma squar and just make those guys n
+
+ align:start position:0%
+Sigma squar and just make those guys n
+ 
+
+ align:start position:0%
+Sigma squar and just make those guys n
+zer1 right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so that's my uh T distribution
+
+ align:start position:0%
+all right so that's my uh T distribution
+ 
+
+ align:start position:0%
+all right so that's my uh T distribution
+now that I actually have a pivotal
+
+ align:start position:0%
+now that I actually have a pivotal
+ 
+
+ align:start position:0%
+now that I actually have a pivotal
+distribution what I do is that I form
+
+ align:start position:0%
+distribution what I do is that I form
+ 
+
+ align:start position:0%
+distribution what I do is that I form
+the statistic uh here I called it uh T
+
+ align:start position:0%
+the statistic uh here I called it uh T
+ 
+
+ align:start position:0%
+the statistic uh here I called it uh T
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Tilda okay and what is this thing I know
+
+ align:start position:0%
+Tilda okay and what is this thing I know
+ 
+
+ align:start position:0%
+Tilda okay and what is this thing I know
+that this has a pivotal distribution so
+
+ align:start position:0%
+that this has a pivotal distribution so
+ 
+
+ align:start position:0%
+that this has a pivotal distribution so
+for example I know that the probability
+
+ align:start position:0%
+for example I know that the probability
+ 
+
+ align:start position:0%
+for example I know that the probability
+uh that t and Tilda in absolute value
+
+ align:start position:0%
+uh that t and Tilda in absolute value
+ 
+
+ align:start position:0%
+uh that t and Tilda in absolute value
+exceeds some number that I'm going to
+
+ align:start position:0%
+exceeds some number that I'm going to
+ 
+
+ align:start position:0%
+exceeds some number that I'm going to
+call Q Alpha over two for the TN minus
+
+ align:start position:0%
+call Q Alpha over two for the TN minus
+ 
+
+ align:start position:0%
+call Q Alpha over two for the TN minus
+one is equal to Alpha right so that's
+
+ align:start position:0%
+one is equal to Alpha right so that's
+ 
+
+ align:start position:0%
+one is equal to Alpha right so that's
+basically remember the T distribution
+
+ align:start position:0%
+basically remember the T distribution
+ 
+
+ align:start position:0%
+basically remember the T distribution
+has the same shape as the gaussian
+
+ align:start position:0%
+has the same shape as the gaussian
+ 
+
+ align:start position:0%
+has the same shape as the gaussian
+distribution what I'm finding is for
+
+ align:start position:0%
+distribution what I'm finding is for
+ 
+
+ align:start position:0%
+distribution what I'm finding is for
+this T distribution some number Q Alpha
+
+ align:start position:0%
+this T distribution some number Q Alpha
+ 
+
+ align:start position:0%
+this T distribution some number Q Alpha
+over 2 of TN minus one and minus Q Alpha
+
+ align:start position:0%
+over 2 of TN minus one and minus Q Alpha
+ 
+
+ align:start position:0%
+over 2 of TN minus one and minus Q Alpha
+over 2 of TN minus one so those are
+
+ align:start position:0%
+over 2 of TN minus one so those are
+ 
+
+ align:start position:0%
+over 2 of TN minus one so those are
+different from the gaussian one such
+
+ align:start position:0%
+different from the gaussian one such
+ 
+
+ align:start position:0%
+different from the gaussian one such
+that the area under the curve here is
+
+ align:start position:0%
+that the area under the curve here is
+ 
+
+ align:start position:0%
+that the area under the curve here is
+Alpha over two on each side so that the
+
+ align:start position:0%
+Alpha over two on each side so that the
+ 
+
+ align:start position:0%
+Alpha over two on each side so that the
+probability that my absolute value
+
+ align:start position:0%
+probability that my absolute value
+ 
+
+ align:start position:0%
+probability that my absolute value
+exceeds this number is equal to Alpha
+
+ align:start position:0%
+exceeds this number is equal to Alpha
+ 
+
+ align:start position:0%
+exceeds this number is equal to Alpha
+and that's what I'm going to use to
+
+ align:start position:0%
+and that's what I'm going to use to
+ 
+
+ align:start position:0%
+and that's what I'm going to use to
+reject the test right so now my test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+become for h0 say mu is equal to some
+
+ align:start position:0%
+become for h0 say mu is equal to some
+ 
+
+ align:start position:0%
+become for h0 say mu is equal to some
+mu0
+
+ align:start position:0%
+mu0
+ 
+
+ align:start position:0%
+mu0
+versus
+
+ align:start position:0%
+versus
+ 
+
+ align:start position:0%
+versus
+H1 mu is not equal to mu0 is well uh the
+
+ align:start position:0%
+H1 mu is not equal to mu0 is well uh the
+ 
+
+ align:start position:0%
+H1 mu is not equal to mu0 is well uh the
+rejection region is going to be equal to
+
+ align:start position:0%
+rejection region is going to be equal to
+ 
+
+ align:start position:0%
+rejection region is going to be equal to
+the set on which square root of n minus
+
+ align:start position:0%
+the set on which square root of n minus
+ 
+
+ align:start position:0%
+the set on which square root of n minus
+one time xnar minus mu 0 this time
+
+ align:start position:0%
+one time xnar minus mu 0 this time
+ 
+
+ align:start position:0%
+one time xnar minus mu 0 this time
+divided by square Ro T of SN exceeds in
+
+ align:start position:0%
+divided by square Ro T of SN exceeds in
+ 
+
+ align:start position:0%
+divided by square Ro T of SN exceeds in
+absolute value exceeds Q sorry there's
+
+ align:start position:0%
+absolute value exceeds Q sorry there's
+ 
+
+ align:start position:0%
+absolute value exceeds Q sorry there's
+already here exed Q Alpha 2 of TN minus
+
+ align:start position:0%
+already here exed Q Alpha 2 of TN minus
+ 
+
+ align:start position:0%
+already here exed Q Alpha 2 of TN minus
+one okay so I reject when this thing
+
+ align:start position:0%
+one okay so I reject when this thing
+ 
+
+ align:start position:0%
+one okay so I reject when this thing
+increases the same as the Gan case
+
+ align:start position:0%
+increases the same as the Gan case
+ 
+
+ align:start position:0%
+increases the same as the Gan case
+except that rather than reading my
+
+ align:start position:0%
+except that rather than reading my
+ 
+
+ align:start position:0%
+except that rather than reading my
+quenes from the Gan table I read them
+
+ align:start position:0%
+quenes from the Gan table I read them
+ 
+
+ align:start position:0%
+quenes from the Gan table I read them
+from the student
+
+ align:start position:0%
+from the student
+ 
+
+ align:start position:0%
+from the student
+table it's just the same thing so
+
+ align:start position:0%
+table it's just the same thing so
+ 
+
+ align:start position:0%
+table it's just the same thing so
+they're just going to be a little bit
+
+ align:start position:0%
+they're just going to be a little bit
+ 
+
+ align:start position:0%
+they're just going to be a little bit
+farther right so this guy here is just
+
+ align:start position:0%
+farther right so this guy here is just
+ 
+
+ align:start position:0%
+farther right so this guy here is just
+going to be a little bigger than the one
+
+ align:start position:0%
+going to be a little bigger than the one
+ 
+
+ align:start position:0%
+going to be a little bigger than the one
+for the gussan one because it's going to
+
+ align:start position:0%
+for the gussan one because it's going to
+ 
+
+ align:start position:0%
+for the gussan one because it's going to
+require me a little more evidence in my
+
+ align:start position:0%
+require me a little more evidence in my
+ 
+
+ align:start position:0%
+require me a little more evidence in my
+data to be able to reject because I have
+
+ align:start position:0%
+data to be able to reject because I have
+ 
+
+ align:start position:0%
+data to be able to reject because I have
+to account for the fluctuations of Sigma
+
+ align:start position:0%
+to account for the fluctuations of Sigma
+ 
+
+ align:start position:0%
+to account for the fluctuations of Sigma
+hat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so of course students test is used
+
+ align:start position:0%
+okay so of course students test is used
+ 
+
+ align:start position:0%
+okay so of course students test is used
+everywhere people use only T tests right
+
+ align:start position:0%
+everywhere people use only T tests right
+ 
+
+ align:start position:0%
+everywhere people use only T tests right
+that's basically if you look at any data
+
+ align:start position:0%
+that's basically if you look at any data
+ 
+
+ align:start position:0%
+that's basically if you look at any data
+point any uh uh output even if you had
+
+ align:start position:0%
+point any uh uh output even if you had
+ 
+
+ align:start position:0%
+point any uh uh output even if you had
+500 observations if you look at the
+
+ align:start position:0%
+500 observations if you look at the
+ 
+
+ align:start position:0%
+500 observations if you look at the
+statistical software output it's going
+
+ align:start position:0%
+statistical software output it's going
+ 
+
+ align:start position:0%
+statistical software output it's going
+to say t test and the reason why you see
+
+ align:start position:0%
+to say t test and the reason why you see
+ 
+
+ align:start position:0%
+to say t test and the reason why you see
+T Test is because sort of somehow it's
+
+ align:start position:0%
+T Test is because sort of somehow it's
+ 
+
+ align:start position:0%
+T Test is because sort of somehow it's
+felt like it's not not asymptotic you
+
+ align:start position:0%
+felt like it's not not asymptotic you
+ 
+
+ align:start position:0%
+felt like it's not not asymptotic you
+don't need to actually do you know to be
+
+ align:start position:0%
+don't need to actually do you know to be
+ 
+
+ align:start position:0%
+don't need to actually do you know to be
+particularly careful and anyway if n is
+
+ align:start position:0%
+particularly careful and anyway if n is
+ 
+
+ align:start position:0%
+particularly careful and anyway if n is
+equal to 500 since the two curves are
+
+ align:start position:0%
+equal to 500 since the two curves are
+ 
+
+ align:start position:0%
+equal to 500 since the two curves are
+above each other it's basically the same
+
+ align:start position:0%
+above each other it's basically the same
+ 
+
+ align:start position:0%
+above each other it's basically the same
+thing so it doesn't really change
+
+ align:start position:0%
+thing so it doesn't really change
+ 
+
+ align:start position:0%
+thing so it doesn't really change
+anything so why not using the T Test so
+
+ align:start position:0%
+anything so why not using the T Test so
+ 
+
+ align:start position:0%
+anything so why not using the T Test so
+it's not asymptotic it doesn't require
+
+ align:start position:0%
+it's not asymptotic it doesn't require
+ 
+
+ align:start position:0%
+it's not asymptotic it doesn't require
+Central theorum to to kick in and so in
+
+ align:start position:0%
+Central theorum to to kick in and so in
+ 
+
+ align:start position:0%
+Central theorum to to kick in and so in
+particular it can be run if you have 15
+
+ align:start position:0%
+particular it can be run if you have 15
+ 
+
+ align:start position:0%
+particular it can be run if you have 15
+observations now of course the drawback
+
+ align:start position:0%
+observations now of course the drawback
+ 
+
+ align:start position:0%
+observations now of course the drawback
+of the student test is that it relies on
+
+ align:start position:0%
+of the student test is that it relies on
+ 
+
+ align:start position:0%
+of the student test is that it relies on
+the assumption that the the sample is
+
+ align:start position:0%
+the assumption that the the sample is
+ 
+
+ align:start position:0%
+the assumption that the the sample is
+gaussin and that's something we really
+
+ align:start position:0%
+gaussin and that's something we really
+ 
+
+ align:start position:0%
+gaussin and that's something we really
+need to keep in mind if you have a small
+
+ align:start position:0%
+need to keep in mind if you have a small
+ 
+
+ align:start position:0%
+need to keep in mind if you have a small
+sample size there's no magic going on
+
+ align:start position:0%
+sample size there's no magic going on
+ 
+
+ align:start position:0%
+sample size there's no magic going on
+it's not like student T Test allows you
+
+ align:start position:0%
+it's not like student T Test allows you
+ 
+
+ align:start position:0%
+it's not like student T Test allows you
+to get rid of this ASM totic normality
+
+ align:start position:0%
+to get rid of this ASM totic normality
+ 
+
+ align:start position:0%
+to get rid of this ASM totic normality
+it sort of assumes that it's built in it
+
+ align:start position:0%
+it sort of assumes that it's built in it
+ 
+
+ align:start position:0%
+it sort of assumes that it's built in it
+assumes that your data has a gaussin
+
+ align:start position:0%
+assumes that your data has a gaussin
+ 
+
+ align:start position:0%
+assumes that your data has a gaussin
+distribution so if you have 15
+
+ align:start position:0%
+distribution so if you have 15
+ 
+
+ align:start position:0%
+distribution so if you have 15
+observations what are you going to do
+
+ align:start position:0%
+observations what are you going to do
+ 
+
+ align:start position:0%
+observations what are you going to do
+you want to test if the mean is equal to
+
+ align:start position:0%
+you want to test if the mean is equal to
+ 
+
+ align:start position:0%
+you want to test if the mean is equal to
+zero or not equal to zero but you have
+
+ align:start position:0%
+zero or not equal to zero but you have
+ 
+
+ align:start position:0%
+zero or not equal to zero but you have
+only 15
+
+ align:start position:0%
+only 15
+ 
+
+ align:start position:0%
+only 15
+observations you have to somehow assume
+
+ align:start position:0%
+observations you have to somehow assume
+ 
+
+ align:start position:0%
+observations you have to somehow assume
+that your data is gussan but if the data
+
+ align:start position:0%
+that your data is gussan but if the data
+ 
+
+ align:start position:0%
+that your data is gussan but if the data
+is G to you this is not math you
+
+ align:start position:0%
+is G to you this is not math you
+ 
+
+ align:start position:0%
+is G to you this is not math you
+actually have to check that it's gum and
+
+ align:start position:0%
+actually have to check that it's gum and
+ 
+
+ align:start position:0%
+actually have to check that it's gum and
+so we're going to have to find tests
+
+ align:start position:0%
+so we're going to have to find tests
+ 
+
+ align:start position:0%
+so we're going to have to find tests
+that given some
+
+ align:start position:0%
+that given some
+ 
+
+ align:start position:0%
+that given some
+data tells us whether it's gaussian or
+
+ align:start position:0%
+data tells us whether it's gaussian or
+ 
+
+ align:start position:0%
+data tells us whether it's gaussian or
+not if I have 15 observations eight of
+
+ align:start position:0%
+not if I have 15 observations eight of
+ 
+
+ align:start position:0%
+not if I have 15 observations eight of
+them are equal to plus one and seven of
+
+ align:start position:0%
+them are equal to plus one and seven of
+ 
+
+ align:start position:0%
+them are equal to plus one and seven of
+them are equal to minus one then it's
+
+ align:start position:0%
+them are equal to minus one then it's
+ 
+
+ align:start position:0%
+them are equal to minus one then it's
+pretty unlikely that you're going to be
+
+ align:start position:0%
+pretty unlikely that you're going to be
+ 
+
+ align:start position:0%
+pretty unlikely that you're going to be
+able to conclude that your data has a
+
+ align:start position:0%
+able to conclude that your data has a
+ 
+
+ align:start position:0%
+able to conclude that your data has a
+gaan distribution however if you see
+
+ align:start position:0%
+gaan distribution however if you see
+ 
+
+ align:start position:0%
+gaan distribution however if you see
+some sort of spread around some value
+
+ align:start position:0%
+some sort of spread around some value
+ 
+
+ align:start position:0%
+some sort of spread around some value
+you form a histogram maybe and it sort
+
+ align:start position:0%
+you form a histogram maybe and it sort
+ 
+
+ align:start position:0%
+you form a histogram maybe and it sort
+of looks like it's a gussan one you
+
+ align:start position:0%
+of looks like it's a gussan one you
+ 
+
+ align:start position:0%
+of looks like it's a gussan one you
+might want to say it's gussan right
+
+ align:start position:0%
+might want to say it's gussan right
+ 
+
+ align:start position:0%
+might want to say it's gussan right
+right and so how do we make this more
+
+ align:start position:0%
+right and so how do we make this more
+ 
+
+ align:start position:0%
+right and so how do we make this more
+quantitative well the sad answer to this
+
+ align:start position:0%
+quantitative well the sad answer to this
+ 
+
+ align:start position:0%
+quantitative well the sad answer to this
+question is that there will be some test
+
+ align:start position:0%
+question is that there will be some test
+ 
+
+ align:start position:0%
+question is that there will be some test
+that make it quantitative but here if
+
+ align:start position:0%
+that make it quantitative but here if
+ 
+
+ align:start position:0%
+that make it quantitative but here if
+you think about it for one second what
+
+ align:start position:0%
+you think about it for one second what
+ 
+
+ align:start position:0%
+you think about it for one second what
+is going to be your null hypothesis your
+
+ align:start position:0%
+is going to be your null hypothesis your
+ 
+
+ align:start position:0%
+is going to be your null hypothesis your
+null hypothesis since it's one point
+
+ align:start position:0%
+null hypothesis since it's one point
+ 
+
+ align:start position:0%
+null hypothesis since it's one point
+it's going to be that it's gussan and
+
+ align:start position:0%
+it's going to be that it's gussan and
+ 
+
+ align:start position:0%
+it's going to be that it's gussan and
+then it's the alternative is going to be
+
+ align:start position:0%
+then it's the alternative is going to be
+ 
+
+ align:start position:0%
+then it's the alternative is going to be
+that it's not gussan so what it means is
+
+ align:start position:0%
+that it's not gussan so what it means is
+ 
+
+ align:start position:0%
+that it's not gussan so what it means is
+that for the first time in your
+
+ align:start position:0%
+that for the first time in your
+ 
+
+ align:start position:0%
+that for the first time in your
+statisticians life you're going to want
+
+ align:start position:0%
+statisticians life you're going to want
+ 
+
+ align:start position:0%
+statisticians life you're going to want
+to conclude that the H zero is the true
+
+ align:start position:0%
+to conclude that the H zero is the true
+ 
+
+ align:start position:0%
+to conclude that the H zero is the true
+one you're definitely not going to want
+
+ align:start position:0%
+one you're definitely not going to want
+ 
+
+ align:start position:0%
+one you're definitely not going to want
+to say that it's not gaussian because
+
+ align:start position:0%
+to say that it's not gaussian because
+ 
+
+ align:start position:0%
+to say that it's not gaussian because
+then everything you know is sort of
+
+ align:start position:0%
+then everything you know is sort of
+ 
+
+ align:start position:0%
+then everything you know is sort of
+falling apart and so it's kind of a
+
+ align:start position:0%
+falling apart and so it's kind of a
+ 
+
+ align:start position:0%
+falling apart and so it's kind of a
+weird thing where you're sort of going
+
+ align:start position:0%
+weird thing where you're sort of going
+ 
+
+ align:start position:0%
+weird thing where you're sort of going
+to be seeking tests that have no power
+
+ align:start position:0%
+to be seeking tests that have no power
+ 
+
+ align:start position:0%
+to be seeking tests that have no power
+basically you're going to want tests
+
+ align:start position:0%
+basically you're going to want tests
+ 
+
+ align:start position:0%
+basically you're going to want tests
+that and that's what that's the nature
+
+ align:start position:0%
+that and that's what that's the nature
+ 
+
+ align:start position:0%
+that and that's what that's the nature
+the amount of Alternatives the number of
+
+ align:start position:0%
+the amount of Alternatives the number of
+ 
+
+ align:start position:0%
+the amount of Alternatives the number of
+ways you can be not gaussian is so huge
+
+ align:start position:0%
+ways you can be not gaussian is so huge
+ 
+
+ align:start position:0%
+ways you can be not gaussian is so huge
+that all tests are sort of bound to have
+
+ align:start position:0%
+that all tests are sort of bound to have
+ 
+
+ align:start position:0%
+that all tests are sort of bound to have
+very low power and so that's why people
+
+ align:start position:0%
+very low power and so that's why people
+ 
+
+ align:start position:0%
+very low power and so that's why people
+are pretty happy with the IDE that
+
+ align:start position:0%
+are pretty happy with the IDE that
+ 
+
+ align:start position:0%
+are pretty happy with the IDE that
+things is Galan because it's very hard
+
+ align:start position:0%
+things is Galan because it's very hard
+ 
+
+ align:start position:0%
+things is Galan because it's very hard
+to find a test that's going to reject
+
+ align:start position:0%
+to find a test that's going to reject
+ 
+
+ align:start position:0%
+to find a test that's going to reject
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+hypothesis all right and so we're even
+
+ align:start position:0%
+hypothesis all right and so we're even
+ 
+
+ align:start position:0%
+hypothesis all right and so we're even
+going to find some tests that are visual
+
+ align:start position:0%
+going to find some tests that are visual
+ 
+
+ align:start position:0%
+going to find some tests that are visual
+where you're going to be able to say
+
+ align:start position:0%
+where you're going to be able to say
+ 
+
+ align:start position:0%
+where you're going to be able to say
+Well it sort of looks Gan to me if it's
+
+ align:start position:0%
+Well it sort of looks Gan to me if it's
+ 
+
+ align:start position:0%
+Well it sort of looks Gan to me if it's
+all allows allows you to to deal with
+
+ align:start position:0%
+all allows allows you to to deal with
+ 
+
+ align:start position:0%
+all allows allows you to to deal with
+the borderline cases pretty efficiently
+
+ align:start position:0%
+the borderline cases pretty efficiently
+ 
+
+ align:start position:0%
+the borderline cases pretty efficiently
+we'll see actually a particular example
+
+ align:start position:0%
+we'll see actually a particular example
+ 
+
+ align:start position:0%
+we'll see actually a particular example
+right so this theory of testing whether
+
+ align:start position:0%
+right so this theory of testing whether
+ 
+
+ align:start position:0%
+right so this theory of testing whether
+data comes from a particular
+
+ align:start position:0%
+data comes from a particular
+ 
+
+ align:start position:0%
+data comes from a particular
+distribution is called goodness to fit
+
+ align:start position:0%
+distribution is called goodness to fit
+ 
+
+ align:start position:0%
+distribution is called goodness to fit
+is this this distribution a good fit for
+
+ align:start position:0%
+is this this distribution a good fit for
+ 
+
+ align:start position:0%
+is this this distribution a good fit for
+my data that's the goodness of fit test
+
+ align:start position:0%
+my data that's the goodness of fit test
+ 
+
+ align:start position:0%
+my data that's the goodness of fit test
+we have just seen a goodness of fit test
+
+ align:start position:0%
+we have just seen a goodness of fit test
+ 
+
+ align:start position:0%
+we have just seen a goodness of fit test
+what was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it yeah the the the the K Square test
+
+ align:start position:0%
+it yeah the the the the K Square test
+ 
+
+ align:start position:0%
+it yeah the the the the K Square test
+right the K Square test we were given a
+
+ align:start position:0%
+right the K Square test we were given a
+ 
+
+ align:start position:0%
+right the K Square test we were given a
+candidate pmf and we were testing if
+
+ align:start position:0%
+candidate pmf and we were testing if
+ 
+
+ align:start position:0%
+candidate pmf and we were testing if
+this was a good fit for our data that
+
+ align:start position:0%
+this was a good fit for our data that
+ 
+
+ align:start position:0%
+this was a good fit for our data that
+was a goodness of f test so of course
+
+ align:start position:0%
+was a goodness of f test so of course
+ 
+
+ align:start position:0%
+was a goodness of f test so of course
+multinomial is one example but really
+
+ align:start position:0%
+multinomial is one example but really
+ 
+
+ align:start position:0%
+multinomial is one example but really
+what we have back of our mind is I want
+
+ align:start position:0%
+what we have back of our mind is I want
+ 
+
+ align:start position:0%
+what we have back of our mind is I want
+to test if my data is gussan that's
+
+ align:start position:0%
+to test if my data is gussan that's
+ 
+
+ align:start position:0%
+to test if my data is gussan that's
+basically the usual thing and just like
+
+ align:start position:0%
+basically the usual thing and just like
+ 
+
+ align:start position:0%
+basically the usual thing and just like
+you always see T Test as a standard
+
+ align:start position:0%
+you always see T Test as a standard
+ 
+
+ align:start position:0%
+you always see T Test as a standard
+output from statistical software whether
+
+ align:start position:0%
+output from statistical software whether
+ 
+
+ align:start position:0%
+output from statistical software whether
+you ask for it or not there will be a
+
+ align:start position:0%
+you ask for it or not there will be a
+ 
+
+ align:start position:0%
+you ask for it or not there will be a
+test for normality whether you ask it or
+
+ align:start position:0%
+test for normality whether you ask it or
+ 
+
+ align:start position:0%
+test for normality whether you ask it or
+not uh from any statistical software
+
+ align:start position:0%
+not uh from any statistical software
+ 
+
+ align:start position:0%
+not uh from any statistical software
+output all right so a goodness of f test
+
+ align:start position:0%
+output all right so a goodness of f test
+ 
+
+ align:start position:0%
+output all right so a goodness of f test
+looks as follows you're given there's a
+
+ align:start position:0%
+looks as follows you're given there's a
+ 
+
+ align:start position:0%
+looks as follows you're given there's a
+random variable X and you're given IID
+
+ align:start position:0%
+random variable X and you're given IID
+ 
+
+ align:start position:0%
+random variable X and you're given IID
+copies of X right X1 to xn they come
+
+ align:start position:0%
+copies of X right X1 to xn they come
+ 
+
+ align:start position:0%
+copies of X right X1 to xn they come
+from the same distribution and you're
+
+ align:start position:0%
+from the same distribution and you're
+ 
+
+ align:start position:0%
+from the same distribution and you're
+going to ask the following question that
+
+ align:start position:0%
+going to ask the following question that
+ 
+
+ align:start position:0%
+going to ask the following question that
+x x have a standard normal distribution
+
+ align:start position:0%
+x x have a standard normal distribution
+ 
+
+ align:start position:0%
+x x have a standard normal distribution
+right so for T distribution that's
+
+ align:start position:0%
+right so for T distribution that's
+ 
+
+ align:start position:0%
+right so for T distribution that's
+definitely the kind of questions you may
+
+ align:start position:0%
+definitely the kind of questions you may
+ 
+
+ align:start position:0%
+definitely the kind of questions you may
+want to ask does X have a uniform
+
+ align:start position:0%
+want to ask does X have a uniform
+ 
+
+ align:start position:0%
+want to ask does X have a uniform
+Distribution on 01 right that's
+
+ align:start position:0%
+Distribution on 01 right that's
+ 
+
+ align:start position:0%
+Distribution on 01 right that's
+different from the distribution one
+
+ align:start position:0%
+different from the distribution one
+ 
+
+ align:start position:0%
+different from the distribution one
+overk one overk it's the continuous
+
+ align:start position:0%
+overk one overk it's the continuous
+ 
+
+ align:start position:0%
+overk one overk it's the continuous
+notion of of uniform uh uniformity all
+
+ align:start position:0%
+notion of of uniform uh uniformity all
+ 
+
+ align:start position:0%
+notion of of uniform uh uniformity all
+right and for example you might want to
+
+ align:start position:0%
+right and for example you might want to
+ 
+
+ align:start position:0%
+right and for example you might want to
+test that so there's actually a nice
+
+ align:start position:0%
+test that so there's actually a nice
+ 
+
+ align:start position:0%
+test that so there's actually a nice
+exercise which is if you look at the P
+
+ align:start position:0%
+exercise which is if you look at the P
+ 
+
+ align:start position:0%
+exercise which is if you look at the P
+values right so we've defined what the P
+
+ align:start position:0%
+values right so we've defined what the P
+ 
+
+ align:start position:0%
+values right so we've defined what the P
+values were and it turn the P value is a
+
+ align:start position:0%
+values were and it turn the P value is a
+ 
+
+ align:start position:0%
+values were and it turn the P value is a
+number between zero and one right and
+
+ align:start position:0%
+number between zero and one right and
+ 
+
+ align:start position:0%
+number between zero and one right and
+you could actually ask yourself what is
+
+ align:start position:0%
+you could actually ask yourself what is
+ 
+
+ align:start position:0%
+you could actually ask yourself what is
+the distribution of the P value under
+
+ align:start position:0%
+the distribution of the P value under
+ 
+
+ align:start position:0%
+the distribution of the P value under
+the null right so it's a the P value is
+
+ align:start position:0%
+the null right so it's a the P value is
+ 
+
+ align:start position:0%
+the null right so it's a the P value is
+a random a random number is the
+
+ align:start position:0%
+a random a random number is the
+ 
+
+ align:start position:0%
+a random a random number is the
+probability right so the P value let's
+
+ align:start position:0%
+probability right so the P value let's
+ 
+
+ align:start position:0%
+probability right so the P value let's
+look at um um the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+test h0 mu is equal to Z versus H1 mu is
+
+ align:start position:0%
+test h0 mu is equal to Z versus H1 mu is
+ 
+
+ align:start position:0%
+test h0 mu is equal to Z versus H1 mu is
+say not equal to zero and um I know that
+
+ align:start position:0%
+say not equal to zero and um I know that
+ 
+
+ align:start position:0%
+say not equal to zero and um I know that
+the P value is uh uh so I'm going to
+
+ align:start position:0%
+the P value is uh uh so I'm going to
+ 
+
+ align:start position:0%
+the P value is uh uh so I'm going to
+form what I'm going to look at xnar
+
+ align:start position:0%
+form what I'm going to look at xnar
+ 
+
+ align:start position:0%
+form what I'm going to look at xnar
+minus mu ided by uh time root of n ID
+
+ align:start position:0%
+minus mu ided by uh time root of n ID
+ 
+
+ align:start position:0%
+minus mu ided by uh time root of n ID
+let's say that we know Sigma for one
+
+ align:start position:0%
+let's say that we know Sigma for one
+ 
+
+ align:start position:0%
+let's say that we know Sigma for one
+second right uh then the P value is the
+
+ align:start position:0%
+second right uh then the P value is the
+ 
+
+ align:start position:0%
+second right uh then the P value is the
+probability that this is say
+
+ align:start position:0%
+probability that this is say
+ 
+
+ align:start position:0%
+probability that this is say
+larger than squ root of n little xn bar
+
+ align:start position:0%
+larger than squ root of n little xn bar
+ 
+
+ align:start position:0%
+larger than squ root of n little xn bar
+minus mu minus zero actually in this
+
+ align:start position:0%
+minus mu minus zero actually in this
+ 
+
+ align:start position:0%
+minus mu minus zero actually in this
+case
+
+ align:start position:0%
+case
+ 
+
+ align:start position:0%
+case
+right divided by
+
+ align:start position:0%
+right divided by
+ 
+
+ align:start position:0%
+right divided by
+Sigma where this guy is the observed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so now you could say
+
+ align:start position:0%
+right okay so now you could say
+ 
+
+ align:start position:0%
+right okay so now you could say
+well how is that a random variable right
+
+ align:start position:0%
+well how is that a random variable right
+ 
+
+ align:start position:0%
+well how is that a random variable right
+it's just a number uh it's just a
+
+ align:start position:0%
+it's just a number uh it's just a
+ 
+
+ align:start position:0%
+it's just a number uh it's just a
+probability of something but then I can
+
+ align:start position:0%
+probability of something but then I can
+ 
+
+ align:start position:0%
+probability of something but then I can
+view this as a function of this guy here
+
+ align:start position:0%
+view this as a function of this guy here
+ 
+
+ align:start position:0%
+view this as a function of this guy here
+when I plug plug it back it when I plug
+
+ align:start position:0%
+when I plug plug it back it when I plug
+ 
+
+ align:start position:0%
+when I plug plug it back it when I plug
+it back to be a random variable so how
+
+ align:start position:0%
+it back to be a random variable so how
+ 
+
+ align:start position:0%
+it back to be a random variable so how
+what I mean by this is that if I look at
+
+ align:start position:0%
+what I mean by this is that if I look at
+ 
+
+ align:start position:0%
+what I mean by this is that if I look at
+this value here this if I if I say say
+
+ align:start position:0%
+this value here this if I if I say say
+ 
+
+ align:start position:0%
+this value here this if I if I say say
+that f is the
+
+ align:start position:0%
+that f is the
+ 
+
+ align:start position:0%
+that f is the
+CDF of
+
+ align:start position:0%
+CDF of
+ 
+
+ align:start position:0%
+CDF of
+n01 right so the P value is the
+
+ align:start position:0%
+n01 right so the P value is the
+ 
+
+ align:start position:0%
+n01 right so the P value is the
+probability that it exceeds this so
+
+ align:start position:0%
+probability that it exceeds this so
+ 
+
+ align:start position:0%
+probability that it exceeds this so
+that's the probability that I'm on
+
+ align:start position:0%
+that's the probability that I'm on
+ 
+
+ align:start position:0%
+that's the probability that I'm on
+either here or
+
+ align:start position:0%
+either here or
+ 
+
+ align:start position:0%
+either here or
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay no it's not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right this is a big X and this is a
+
+ align:start position:0%
+right this is a big X and this is a
+ 
+
+ align:start position:0%
+right this is a big X and this is a
+small X this is just where you plug in
+
+ align:start position:0%
+small X this is just where you plug in
+ 
+
+ align:start position:0%
+small X this is just where you plug in
+your data do I have right P value is the
+
+ align:start position:0%
+your data do I have right P value is the
+ 
+
+ align:start position:0%
+your data do I have right P value is the
+probability you have more evidence
+
+ align:start position:0%
+probability you have more evidence
+ 
+
+ align:start position:0%
+probability you have more evidence
+against your Al your null than what you
+
+ align:start position:0%
+against your Al your null than what you
+ 
+
+ align:start position:0%
+against your Al your null than what you
+already have okay so now I can write in
+
+ align:start position:0%
+already have okay so now I can write in
+ 
+
+ align:start position:0%
+already have okay so now I can write in
+in terms of cumulative distribution
+
+ align:start position:0%
+in terms of cumulative distribution
+ 
+
+ align:start position:0%
+in terms of cumulative distribution
+functions right so this is what this is
+
+ align:start position:0%
+functions right so this is what this is
+ 
+
+ align:start position:0%
+functions right so this is what this is
+f of this guy which is minus this thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here well it's basically two times this
+
+ align:start position:0%
+here well it's basically two times this
+ 
+
+ align:start position:0%
+here well it's basically two times this
+guy five of minus squ root of
+
+ align:start position:0%
+guy five of minus squ root of
+ 
+
+ align:start position:0%
+guy five of minus squ root of
+n xn
+
+ align:start position:0%
+n xn
+ 
+
+ align:start position:0%
+n xn
+bar divided by Sigma
+
+ align:start position:0%
+bar divided by Sigma
+ 
+
+ align:start position:0%
+bar divided by Sigma
+right that's the value of my P that's my
+
+ align:start position:0%
+right that's the value of my P that's my
+ 
+
+ align:start position:0%
+right that's the value of my P that's my
+P value if you give me data I'm going to
+
+ align:start position:0%
+P value if you give me data I'm going to
+ 
+
+ align:start position:0%
+P value if you give me data I'm going to
+compute the average and plug it in there
+
+ align:start position:0%
+compute the average and plug it in there
+ 
+
+ align:start position:0%
+compute the average and plug it in there
+and it's going to spit out the P value
+
+ align:start position:0%
+and it's going to spit out the P value
+ 
+
+ align:start position:0%
+and it's going to spit out the P value
+everybody
+
+ align:start position:0%
+everybody
+ 
+
+ align:start position:0%
+everybody
+agrees so now I can view this if I start
+
+ align:start position:0%
+agrees so now I can view this if I start
+ 
+
+ align:start position:0%
+agrees so now I can view this if I start
+now looking back I say well where does
+
+ align:start position:0%
+now looking back I say well where does
+ 
+
+ align:start position:0%
+now looking back I say well where does
+this data come from well it could be a
+
+ align:start position:0%
+this data come from well it could be a
+ 
+
+ align:start position:0%
+this data come from well it could be a
+random variable right it it came from
+
+ align:start position:0%
+random variable right it it came from
+ 
+
+ align:start position:0%
+random variable right it it came from
+realization of this thing so I can try
+
+ align:start position:0%
+realization of this thing so I can try
+ 
+
+ align:start position:0%
+realization of this thing so I can try
+to I can think of this
+
+ align:start position:0%
+to I can think of this
+ 
+
+ align:start position:0%
+to I can think of this
+value or now this is a random variable
+
+ align:start position:0%
+value or now this is a random variable
+ 
+
+ align:start position:0%
+value or now this is a random variable
+because I just plugged in a random
+
+ align:start position:0%
+because I just plugged in a random
+ 
+
+ align:start position:0%
+because I just plugged in a random
+variable in here
+
+ align:start position:0%
+variable in here
+ 
+
+ align:start position:0%
+variable in here
+right so now I view my P value as a
+
+ align:start position:0%
+right so now I view my P value as a
+ 
+
+ align:start position:0%
+right so now I view my P value as a
+random
+
+ align:start position:0%
+random
+ 
+
+ align:start position:0%
+random
+variable right so I keep on switching
+
+ align:start position:0%
+variable right so I keep on switching
+ 
+
+ align:start position:0%
+variable right so I keep on switching
+from small X to large x everybody agrees
+
+ align:start position:0%
+from small X to large x everybody agrees
+ 
+
+ align:start position:0%
+from small X to large x everybody agrees
+what I'm doing here so I just wrote it
+
+ align:start position:0%
+what I'm doing here so I just wrote it
+ 
+
+ align:start position:0%
+what I'm doing here so I just wrote it
+as a deterministic function of some
+
+ align:start position:0%
+as a deterministic function of some
+ 
+
+ align:start position:0%
+as a deterministic function of some
+deterministic number and now the number
+
+ align:start position:0%
+deterministic number and now the number
+ 
+
+ align:start position:0%
+deterministic number and now the number
+the function stays deterministic but the
+
+ align:start position:0%
+the function stays deterministic but the
+ 
+
+ align:start position:0%
+the function stays deterministic but the
+number becomes random and so now I can
+
+ align:start position:0%
+number becomes random and so now I can
+ 
+
+ align:start position:0%
+number becomes random and so now I can
+think of this as some statistic of my
+
+ align:start position:0%
+think of this as some statistic of my
+ 
+
+ align:start position:0%
+think of this as some statistic of my
+data and I could say well what is the
+
+ align:start position:0%
+data and I could say well what is the
+ 
+
+ align:start position:0%
+data and I could say well what is the
+distribution of this random
+
+ align:start position:0%
+distribution of this random
+ 
+
+ align:start position:0%
+distribution of this random
+variable now if my data is actually
+
+ align:start position:0%
+variable now if my data is actually
+ 
+
+ align:start position:0%
+variable now if my data is actually
+normally distributed so I'm actually
+
+ align:start position:0%
+normally distributed so I'm actually
+ 
+
+ align:start position:0%
+normally distributed so I'm actually
+under the null so under the
+
+ align:start position:0%
+under the null so under the
+ 
+
+ align:start position:0%
+under the null so under the
+null that means that xn bar time of n ID
+
+ align:start position:0%
+null that means that xn bar time of n ID
+ 
+
+ align:start position:0%
+null that means that xn bar time of n ID
+Sigma has what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normal yeah well it was Sigma I I assume
+
+ align:start position:0%
+normal yeah well it was Sigma I I assume
+ 
+
+ align:start position:0%
+normal yeah well it was Sigma I I assume
+I knew it right so it's n01 right I
+
+ align:start position:0%
+I knew it right so it's n01 right I
+ 
+
+ align:start position:0%
+I knew it right so it's n01 right I
+divided by Sigma here okay so now I have
+
+ align:start position:0%
+divided by Sigma here okay so now I have
+ 
+
+ align:start position:0%
+divided by Sigma here okay so now I have
+this random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+variable and uh so my random variable is
+
+ align:start position:0%
+variable and uh so my random variable is
+ 
+
+ align:start position:0%
+variable and uh so my random variable is
+now two five of minus absolute value of
+
+ align:start position:0%
+now two five of minus absolute value of
+ 
+
+ align:start position:0%
+now two five of minus absolute value of
+a gan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and I'm actually interested
+
+ align:start position:0%
+okay and I'm actually interested
+ 
+
+ align:start position:0%
+okay and I'm actually interested
+in the distribution of this thing okay I
+
+ align:start position:0%
+in the distribution of this thing okay I
+ 
+
+ align:start position:0%
+in the distribution of this thing okay I
+could ask that anybody has an idea of
+
+ align:start position:0%
+could ask that anybody has an idea of
+ 
+
+ align:start position:0%
+could ask that anybody has an idea of
+how you would want to tackle this thing
+
+ align:start position:0%
+how you would want to tackle this thing
+ 
+
+ align:start position:0%
+how you would want to tackle this thing
+if I ask you what is the distribution of
+
+ align:start position:0%
+if I ask you what is the distribution of
+ 
+
+ align:start position:0%
+if I ask you what is the distribution of
+a random variable how do you tackle this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question there's basically two ways one
+
+ align:start position:0%
+question there's basically two ways one
+ 
+
+ align:start position:0%
+question there's basically two ways one
+is to try to find something that looks
+
+ align:start position:0%
+is to try to find something that looks
+ 
+
+ align:start position:0%
+is to try to find something that looks
+like the expectation
+
+ align:start position:0%
+like the expectation
+ 
+
+ align:start position:0%
+like the expectation
+of H of
+
+ align:start position:0%
+of H of
+ 
+
+ align:start position:0%
+of H of
+X for all H and you try to write this
+
+ align:start position:0%
+X for all H and you try to write this
+ 
+
+ align:start position:0%
+X for all H and you try to write this
+using change of variables as something
+
+ align:start position:0%
+using change of variables as something
+ 
+
+ align:start position:0%
+using change of variables as something
+that looks like integral of H of x p of
+
+ align:start position:0%
+that looks like integral of H of x p of
+ 
+
+ align:start position:0%
+that looks like integral of H of x p of
+X DX and then you say well that's the
+
+ align:start position:0%
+X DX and then you say well that's the
+ 
+
+ align:start position:0%
+X DX and then you say well that's the
+density right if you can write this for
+
+ align:start position:0%
+density right if you can write this for
+ 
+
+ align:start position:0%
+density right if you can write this for
+any H then that's the way you would do
+
+ align:start position:0%
+any H then that's the way you would do
+ 
+
+ align:start position:0%
+any H then that's the way you would do
+it but there's a much simpler way that
+
+ align:start position:0%
+it but there's a much simpler way that
+ 
+
+ align:start position:0%
+it but there's a much simpler way that
+does not involve changing uh variables
+
+ align:start position:0%
+does not involve changing uh variables
+ 
+
+ align:start position:0%
+does not involve changing uh variables
+Etc you just try to compute the
+
+ align:start position:0%
+Etc you just try to compute the
+ 
+
+ align:start position:0%
+Etc you just try to compute the
+cumulative distribution function right
+
+ align:start position:0%
+cumulative distribution function right
+ 
+
+ align:start position:0%
+cumulative distribution function right
+so let's try to compute the probability
+
+ align:start position:0%
+so let's try to compute the probability
+ 
+
+ align:start position:0%
+so let's try to compute the probability
+that 2 pi
+
+ align:start position:0%
+that 2 pi
+ 
+
+ align:start position:0%
+that 2 pi
+minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n01 is less than
+
+ align:start position:0%
+n01 is less than
+ 
+
+ align:start position:0%
+n01 is less than
+T and maybe we can find something we
+
+ align:start position:0%
+T and maybe we can find something we
+ 
+
+ align:start position:0%
+T and maybe we can find something we
+know okay well that's equal to what
+
+ align:start position:0%
+know okay well that's equal to what
+ 
+
+ align:start position:0%
+know okay well that's equal to what
+that's the probability that a minus n0
+
+ align:start position:0%
+that's the probability that a minus n0
+ 
+
+ align:start position:0%
+that's the probability that a minus n0
+well let's say that an
+
+ align:start position:0%
+well let's say that an
+ 
+
+ align:start position:0%
+well let's say that an
+n01 AB sorry n01 absolute value is
+
+ align:start position:0%
+n01 AB sorry n01 absolute value is
+ 
+
+ align:start position:0%
+n01 AB sorry n01 absolute value is
+greater than uh
+
+ align:start position:0%
+greater than uh
+ 
+
+ align:start position:0%
+greater than uh
+minus F
+
+ align:start position:0%
+minus F
+ 
+
+ align:start position:0%
+minus F
+inverse of t over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+right and that's basic that's what well
+
+ align:start position:0%
+right and that's basic that's what well
+ 
+
+ align:start position:0%
+right and that's basic that's what well
+is just the same thing that we had
+
+ align:start position:0%
+is just the same thing that we had
+ 
+
+ align:start position:0%
+is just the same thing that we had
+before it's equal to so if I look
+
+ align:start position:0%
+before it's equal to so if I look
+ 
+
+ align:start position:0%
+before it's equal to so if I look
+again this is the probability that I'm
+
+ align:start position:0%
+again this is the probability that I'm
+ 
+
+ align:start position:0%
+again this is the probability that I'm
+actually on this side or that side of
+
+ align:start position:0%
+actually on this side or that side of
+ 
+
+ align:start position:0%
+actually on this side or that side of
+this number and this number is what it's
+
+ align:start position:0%
+this number and this number is what it's
+ 
+
+ align:start position:0%
+this number and this number is what it's
+um minus
+
+ align:start position:0%
+um minus
+ 
+
+ align:start position:0%
+um minus
+5 of T
+
+ align:start position:0%
+5 of T
+ 
+
+ align:start position:0%
+5 of T
+over2 why do I have a minus here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's fine okay so it's actually not
+
+ align:start position:0%
+that's fine okay so it's actually not
+ 
+
+ align:start position:0%
+that's fine okay so it's actually not
+this it's actually the probability my
+
+ align:start position:0%
+this it's actually the probability my
+ 
+
+ align:start position:0%
+this it's actually the probability my
+absolute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value oh because F inverse okay uh
+
+ align:start position:0%
+value oh because F inverse okay uh
+ 
+
+ align:start position:0%
+value oh because F inverse okay uh
+because fi inverse is uh so I'm going to
+
+ align:start position:0%
+because fi inverse is uh so I'm going to
+ 
+
+ align:start position:0%
+because fi inverse is uh so I'm going to
+look at T between uh zero and so this
+
+ align:start position:0%
+look at T between uh zero and so this
+ 
+
+ align:start position:0%
+look at T between uh zero and so this
+number is ranging between zero and one
+
+ align:start position:0%
+number is ranging between zero and one
+ 
+
+ align:start position:0%
+number is ranging between zero and one
+so it means that this number is ranging
+
+ align:start position:0%
+so it means that this number is ranging
+ 
+
+ align:start position:0%
+so it means that this number is ranging
+between zero well the probability that
+
+ align:start position:0%
+between zero well the probability that
+ 
+
+ align:start position:0%
+between zero well the probability that
+something is less than t should be
+
+ align:start position:0%
+something is less than t should be
+ 
+
+ align:start position:0%
+something is less than t should be
+ranging between uh the numbers that this
+
+ align:start position:0%
+ranging between uh the numbers that this
+ 
+
+ align:start position:0%
+ranging between uh the numbers that this
+guy takes to uh so that's between zero
+
+ align:start position:0%
+guy takes to uh so that's between zero
+ 
+
+ align:start position:0%
+guy takes to uh so that's between zero
+and two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right right because this thing takes
+
+ align:start position:0%
+right right because this thing takes
+ 
+
+ align:start position:0%
+right right because this thing takes
+values between zero and two I want to
+
+ align:start position:0%
+values between zero and two I want to
+ 
+
+ align:start position:0%
+values between zero and two I want to
+see Zero and one though
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you're right thank you so this is
+
+ align:start position:0%
+yeah you're right thank you so this is
+ 
+
+ align:start position:0%
+yeah you're right thank you so this is
+always some number which is less than
+
+ align:start position:0%
+always some number which is less than
+ 
+
+ align:start position:0%
+always some number which is less than
+zero so the probability that the Gan is
+
+ align:start position:0%
+zero so the probability that the Gan is
+ 
+
+ align:start position:0%
+zero so the probability that the Gan is
+less than this number is always less
+
+ align:start position:0%
+less than this number is always less
+ 
+
+ align:start position:0%
+less than this number is always less
+than probability it's less than zero
+
+ align:start position:0%
+than probability it's less than zero
+ 
+
+ align:start position:0%
+than probability it's less than zero
+which is one half so T only has to be
+
+ align:start position:0%
+which is one half so T only has to be
+ 
+
+ align:start position:0%
+which is one half so T only has to be
+between zero and one thank
+
+ align:start position:0%
+between zero and one thank
+ 
+
+ align:start position:0%
+between zero and one thank
+you and so now for t uh uh between zero
+
+ align:start position:0%
+you and so now for t uh uh between zero
+ 
+
+ align:start position:0%
+you and so now for t uh uh between zero
+and one then this guy is actually
+
+ align:start position:0%
+and one then this guy is actually
+ 
+
+ align:start position:0%
+and one then this guy is actually
+becoming something which is positive for
+
+ align:start position:0%
+becoming something which is positive for
+ 
+
+ align:start position:0%
+becoming something which is positive for
+the same reason as before and so that's
+
+ align:start position:0%
+the same reason as before and so that's
+ 
+
+ align:start position:0%
+the same reason as before and so that's
+what that's just basically two
+
+ align:start position:0%
+what that's just basically two
+ 
+
+ align:start position:0%
+what that's just basically two
+times uh
+
+ align:start position:0%
+times uh
+ 
+
+ align:start position:0%
+times uh
+uh F of f
+
+ align:start position:0%
+uh F of f
+ 
+
+ align:start position:0%
+uh F of f
+inverse of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t/2 okay that's just playing with the
+
+ align:start position:0%
+t/2 okay that's just playing with the
+ 
+
+ align:start position:0%
+t/2 okay that's just playing with the
+Symmetry a little bit you can look at
+
+ align:start position:0%
+Symmetry a little bit you can look at
+ 
+
+ align:start position:0%
+Symmetry a little bit you can look at
+the areas under the curve and so what it
+
+ align:start position:0%
+the areas under the curve and so what it
+ 
+
+ align:start position:0%
+the areas under the curve and so what it
+means is that those two guys cancel this
+
+ align:start position:0%
+means is that those two guys cancel this
+ 
+
+ align:start position:0%
+means is that those two guys cancel this
+is the identity and so this is equal to
+
+ align:start position:0%
+is the identity and so this is equal to
+ 
+
+ align:start position:0%
+is the identity and so this is equal to
+T so which distribution has a has a
+
+ align:start position:0%
+T so which distribution has a has a
+ 
+
+ align:start position:0%
+T so which distribution has a has a
+density as a sorry which distribution
+
+ align:start position:0%
+density as a sorry which distribution
+ 
+
+ align:start position:0%
+density as a sorry which distribution
+has a uh cumulative distribution
+
+ align:start position:0%
+has a uh cumulative distribution
+ 
+
+ align:start position:0%
+has a uh cumulative distribution
+function which which is equal to T for T
+
+ align:start position:0%
+function which which is equal to T for T
+ 
+
+ align:start position:0%
+function which which is equal to T for T
+between 0 and
+
+ align:start position:0%
+between 0 and
+ 
+
+ align:start position:0%
+between 0 and
+one that's the uniform distribution
+
+ align:start position:0%
+one that's the uniform distribution
+ 
+
+ align:start position:0%
+one that's the uniform distribution
+right so it means that this guy follows
+
+ align:start position:0%
+right so it means that this guy follows
+ 
+
+ align:start position:0%
+right so it means that this guy follows
+a uniform Distribution on the interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+01 okay and you can actually check that
+
+ align:start position:0%
+01 okay and you can actually check that
+ 
+
+ align:start position:0%
+01 okay and you can actually check that
+for any test you're going to come up
+
+ align:start position:0%
+for any test you're going to come up
+ 
+
+ align:start position:0%
+for any test you're going to come up
+with this is going to be the case your P
+
+ align:start position:0%
+with this is going to be the case your P
+ 
+
+ align:start position:0%
+with this is going to be the case your P
+value under the null will have a
+
+ align:start position:0%
+value under the null will have a
+ 
+
+ align:start position:0%
+value under the null will have a
+distribution which is
+
+ align:start position:0%
+distribution which is
+ 
+
+ align:start position:0%
+distribution which is
+uniform so now if somebody shows up and
+
+ align:start position:0%
+uniform so now if somebody shows up and
+ 
+
+ align:start position:0%
+uniform so now if somebody shows up and
+says here's my test it's awesome it just
+
+ align:start position:0%
+says here's my test it's awesome it just
+ 
+
+ align:start position:0%
+says here's my test it's awesome it just
+works great I don't I'm not going to
+
+ align:start position:0%
+works great I don't I'm not going to
+ 
+
+ align:start position:0%
+works great I don't I'm not going to
+explain to you how I built it it's a
+
+ align:start position:0%
+explain to you how I built it it's a
+ 
+
+ align:start position:0%
+explain to you how I built it it's a
+complicated statistics that involve
+
+ align:start position:0%
+complicated statistics that involve
+ 
+
+ align:start position:0%
+complicated statistics that involve
+moments of order
+
+ align:start position:0%
+moments of order
+ 
+
+ align:start position:0%
+moments of order
+27 and I'm like okay you know how am I
+
+ align:start position:0%
+27 and I'm like okay you know how am I
+ 
+
+ align:start position:0%
+27 and I'm like okay you know how am I
+going to test that your test statistic
+
+ align:start position:0%
+going to test that your test statistic
+ 
+
+ align:start position:0%
+going to test that your test statistic
+actually makes sense well one thing I
+
+ align:start position:0%
+actually makes sense well one thing I
+ 
+
+ align:start position:0%
+actually makes sense well one thing I
+can do is to run a bunch of data draw a
+
+ align:start position:0%
+can do is to run a bunch of data draw a
+ 
+
+ align:start position:0%
+can do is to run a bunch of data draw a
+bunch of samples compute your test
+
+ align:start position:0%
+bunch of samples compute your test
+ 
+
+ align:start position:0%
+bunch of samples compute your test
+statistic compute the P value and check
+
+ align:start position:0%
+statistic compute the P value and check
+ 
+
+ align:start position:0%
+statistic compute the P value and check
+if my PV value has a uniform
+
+ align:start position:0%
+if my PV value has a uniform
+ 
+
+ align:start position:0%
+if my PV value has a uniform
+Distribution on the interval
+
+ align:start position:0%
+Distribution on the interval
+ 
+
+ align:start position:0%
+Distribution on the interval
+01 but for that I need you have a test
+
+ align:start position:0%
+01 but for that I need you have a test
+ 
+
+ align:start position:0%
+01 but for that I need you have a test
+that's allowed given a bunch of
+
+ align:start position:0%
+that's allowed given a bunch of
+ 
+
+ align:start position:0%
+that's allowed given a bunch of
+observations can tell me whether they're
+
+ align:start position:0%
+observations can tell me whether they're
+ 
+
+ align:start position:0%
+observations can tell me whether they're
+actually distributed uniformly on the
+
+ align:start position:0%
+actually distributed uniformly on the
+ 
+
+ align:start position:0%
+actually distributed uniformly on the
+interval 01 and again one thing I could
+
+ align:start position:0%
+interval 01 and again one thing I could
+ 
+
+ align:start position:0%
+interval 01 and again one thing I could
+do is build a histogram and see if it
+
+ align:start position:0%
+do is build a histogram and see if it
+ 
+
+ align:start position:0%
+do is build a histogram and see if it
+looks like that of a uniform but I could
+
+ align:start position:0%
+looks like that of a uniform but I could
+ 
+
+ align:start position:0%
+looks like that of a uniform but I could
+also try to be slightly more
+
+ align:start position:0%
+also try to be slightly more
+ 
+
+ align:start position:0%
+also try to be slightly more
+quantitative about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this for two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tests no it's it's uniform under the
+
+ align:start position:0%
+tests no it's it's uniform under the
+ 
+
+ align:start position:0%
+tests no it's it's uniform under the
+null right so because my my test
+
+ align:start position:0%
+null right so because my my test
+ 
+
+ align:start position:0%
+null right so because my my test
+statistic was built under the null and
+
+ align:start position:0%
+statistic was built under the null and
+ 
+
+ align:start position:0%
+statistic was built under the null and
+so I have to be able to plug in the
+
+ align:start position:0%
+so I have to be able to plug in the
+ 
+
+ align:start position:0%
+so I have to be able to plug in the
+right value in there otherwise it's
+
+ align:start position:0%
+right value in there otherwise it's
+ 
+
+ align:start position:0%
+right value in there otherwise it's
+going to shift everything for this
+
+ align:start position:0%
+going to shift everything for this
+ 
+
+ align:start position:0%
+going to shift everything for this
+particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+test that's the P value right that's the
+
+ align:start position:0%
+test that's the P value right that's the
+ 
+
+ align:start position:0%
+test that's the P value right that's the
+definition of the P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value right so the probability that my
+
+ align:start position:0%
+value right so the probability that my
+ 
+
+ align:start position:0%
+value right so the probability that my
+test statistic exceeds what I've
+
+ align:start position:0%
+test statistic exceeds what I've
+ 
+
+ align:start position:0%
+test statistic exceeds what I've
+actually observed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so my my P value is just this
+
+ align:start position:0%
+yeah so my my P value is just this
+ 
+
+ align:start position:0%
+yeah so my my P value is just this
+number when I just plug in the values
+
+ align:start position:0%
+number when I just plug in the values
+ 
+
+ align:start position:0%
+number when I just plug in the values
+that I observe here right that's one
+
+ align:start position:0%
+that I observe here right that's one
+ 
+
+ align:start position:0%
+that I observe here right that's one
+number for every data set you're going
+
+ align:start position:0%
+number for every data set you're going
+ 
+
+ align:start position:0%
+number for every data set you're going
+to give me is going to be one number now
+
+ align:start position:0%
+to give me is going to be one number now
+ 
+
+ align:start position:0%
+to give me is going to be one number now
+what I can do is for generate a bunch of
+
+ align:start position:0%
+what I can do is for generate a bunch of
+ 
+
+ align:start position:0%
+what I can do is for generate a bunch of
+data sets of size n like 200 of them and
+
+ align:start position:0%
+data sets of size n like 200 of them and
+ 
+
+ align:start position:0%
+data sets of size n like 200 of them and
+then I'm going to have a new sample of
+
+ align:start position:0%
+then I'm going to have a new sample of
+ 
+
+ align:start position:0%
+then I'm going to have a new sample of
+size 200 which is just the sample of 200
+
+ align:start position:0%
+size 200 which is just the sample of 200
+ 
+
+ align:start position:0%
+size 200 which is just the sample of 200
+P value
+
+ align:start position:0%
+P value
+ 
+
+ align:start position:0%
+P value
+and I want to test if those P values
+
+ align:start position:0%
+and I want to test if those P values
+ 
+
+ align:start position:0%
+and I want to test if those P values
+have a uniform distribution okay because
+
+ align:start position:0%
+have a uniform distribution okay because
+ 
+
+ align:start position:0%
+have a uniform distribution okay because
+that's the distribution they should be
+
+ align:start position:0%
+that's the distribution they should be
+ 
+
+ align:start position:0%
+that's the distribution they should be
+having all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay this one we've already seen
+
+ align:start position:0%
+right okay this one we've already seen
+ 
+
+ align:start position:0%
+right okay this one we've already seen
+do X have a pmf with you know 30% 50%
+
+ align:start position:0%
+do X have a pmf with you know 30% 50%
+ 
+
+ align:start position:0%
+do X have a pmf with you know 30% 50%
+and 20% right that's something I could
+
+ align:start position:0%
+and 20% right that's something I could
+ 
+
+ align:start position:0%
+and 20% right that's something I could
+try to test uh that looks like your uh
+
+ align:start position:0%
+try to test uh that looks like your uh
+ 
+
+ align:start position:0%
+try to test uh that looks like your uh
+great Point distribution for this class
+
+ align:start position:0%
+great Point distribution for this class
+ 
+
+ align:start position:0%
+great Point distribution for this class
+uh all right U well not exactly but that
+
+ align:start position:0%
+uh all right U well not exactly but that
+ 
+
+ align:start position:0%
+uh all right U well not exactly but that
+looks like it all right so um so all
+
+ align:start position:0%
+looks like it all right so um so all
+ 
+
+ align:start position:0%
+looks like it all right so um so all
+these things are know are known as
+
+ align:start position:0%
+these things are know are known as
+ 
+
+ align:start position:0%
+these things are know are known as
+goodness of fit test the goodness of fit
+
+ align:start position:0%
+goodness of fit test the goodness of fit
+ 
+
+ align:start position:0%
+goodness of fit test the goodness of fit
+test is something that want to know if
+
+ align:start position:0%
+test is something that want to know if
+ 
+
+ align:start position:0%
+test is something that want to know if
+the data that you have at hand has a
+
+ align:start position:0%
+the data that you have at hand has a
+ 
+
+ align:start position:0%
+the data that you have at hand has a
+follows a hypothesized distribution all
+
+ align:start position:0%
+follows a hypothesized distribution all
+ 
+
+ align:start position:0%
+follows a hypothesized distribution all
+right so it's not a parametric test it's
+
+ align:start position:0%
+right so it's not a parametric test it's
+ 
+
+ align:start position:0%
+right so it's not a parametric test it's
+not a test that says is my mean equal to
+
+ align:start position:0%
+not a test that says is my mean equal to
+ 
+
+ align:start position:0%
+not a test that says is my mean equal to
+25 or not is my proportion of heads
+
+ align:start position:0%
+25 or not is my proportion of heads
+ 
+
+ align:start position:0%
+25 or not is my proportion of heads
+larger than 1 half or not it's something
+
+ align:start position:0%
+larger than 1 half or not it's something
+ 
+
+ align:start position:0%
+larger than 1 half or not it's something
+that says is my distribution this
+
+ align:start position:0%
+that says is my distribution this
+ 
+
+ align:start position:0%
+that says is my distribution this
+particular thing all
+
+ align:start position:0%
+particular thing all
+ 
+
+ align:start position:0%
+particular thing all
+right so I'm going to going to write
+
+ align:start position:0%
+right so I'm going to going to write
+ 
+
+ align:start position:0%
+right so I'm going to going to write
+them as goodness of a goof here so here
+
+ align:start position:0%
+them as goodness of a goof here so here
+ 
+
+ align:start position:0%
+them as goodness of a goof here so here
+there's you don't need to have
+
+ align:start position:0%
+there's you don't need to have
+ 
+
+ align:start position:0%
+there's you don't need to have
+parametric modeling to do
+
+ align:start position:0%
+parametric modeling to do
+ 
+
+ align:start position:0%
+parametric modeling to do
+that so how do I work right so if I
+
+ align:start position:0%
+that so how do I work right so if I
+ 
+
+ align:start position:0%
+that so how do I work right so if I
+don't have any parametric modeling I
+
+ align:start position:0%
+don't have any parametric modeling I
+ 
+
+ align:start position:0%
+don't have any parametric modeling I
+need to have something which is somewhat
+
+ align:start position:0%
+need to have something which is somewhat
+ 
+
+ align:start position:0%
+need to have something which is somewhat
+non-parametric right something that's
+
+ align:start position:0%
+non-parametric right something that's
+ 
+
+ align:start position:0%
+non-parametric right something that's
+goes beyond Computing the mean and the
+
+ align:start position:0%
+goes beyond Computing the mean and the
+ 
+
+ align:start position:0%
+goes beyond Computing the mean and the
+standard deviation something that
+
+ align:start position:0%
+standard deviation something that
+ 
+
+ align:start position:0%
+standard deviation something that
+computes some intrinsic non-parametric
+
+ align:start position:0%
+computes some intrinsic non-parametric
+ 
+
+ align:start position:0%
+computes some intrinsic non-parametric
+aspect of my data and just like here we
+
+ align:start position:0%
+aspect of my data and just like here we
+ 
+
+ align:start position:0%
+aspect of my data and just like here we
+made this computation what we did is we
+
+ align:start position:0%
+made this computation what we did is we
+ 
+
+ align:start position:0%
+made this computation what we did is we
+said
+
+ align:start position:0%
+said
+ 
+
+ align:start position:0%
+said
+well if I actually check that the CDF of
+
+ align:start position:0%
+well if I actually check that the CDF of
+ 
+
+ align:start position:0%
+well if I actually check that the CDF of
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+data has that of my P value is uniform
+
+ align:start position:0%
+data has that of my P value is uniform
+ 
+
+ align:start position:0%
+data has that of my P value is uniform
+then I know it's uniform so it means
+
+ align:start position:0%
+then I know it's uniform so it means
+ 
+
+ align:start position:0%
+then I know it's uniform so it means
+that the cumulative distribution
+
+ align:start position:0%
+that the cumulative distribution
+ 
+
+ align:start position:0%
+that the cumulative distribution
+function has an intrinsic value about it
+
+ align:start position:0%
+function has an intrinsic value about it
+ 
+
+ align:start position:0%
+function has an intrinsic value about it
+captures the entire distribution right
+
+ align:start position:0%
+captures the entire distribution right
+ 
+
+ align:start position:0%
+captures the entire distribution right
+everything I need to know about my
+
+ align:start position:0%
+everything I need to know about my
+ 
+
+ align:start position:0%
+everything I need to know about my
+distribution is captured by the
+
+ align:start position:0%
+distribution is captured by the
+ 
+
+ align:start position:0%
+distribution is captured by the
+cumulative distribution function now I
+
+ align:start position:0%
+cumulative distribution function now I
+ 
+
+ align:start position:0%
+cumulative distribution function now I
+have an empirical way of computing I
+
+ align:start position:0%
+have an empirical way of computing I
+ 
+
+ align:start position:0%
+have an empirical way of computing I
+have a data driven way of computing an
+
+ align:start position:0%
+have a data driven way of computing an
+ 
+
+ align:start position:0%
+have a data driven way of computing an
+estimate for the cumulative distribution
+
+ align:start position:0%
+estimate for the cumulative distribution
+ 
+
+ align:start position:0%
+estimate for the cumulative distribution
+function which is using the old
+
+ align:start position:0%
+function which is using the old
+ 
+
+ align:start position:0%
+function which is using the old
+statistical trick which consists in
+
+ align:start position:0%
+statistical trick which consists in
+ 
+
+ align:start position:0%
+statistical trick which consists in
+replacing Expectations by averages all
+
+ align:start position:0%
+replacing Expectations by averages all
+ 
+
+ align:start position:0%
+replacing Expectations by averages all
+right so as I said the the cumulative
+
+ align:start position:0%
+right so as I said the the cumulative
+ 
+
+ align:start position:0%
+right so as I said the the cumulative
+distribution function for any
+
+ align:start position:0%
+distribution function for any
+ 
+
+ align:start position:0%
+distribution function for any
+distribution we for any random variable
+
+ align:start position:0%
+distribution we for any random variable
+ 
+
+ align:start position:0%
+distribution we for any random variable
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um right so F of
+
+ align:start position:0%
+um right so F of
+ 
+
+ align:start position:0%
+um right so F of
+T is the probability that X is less than
+
+ align:start position:0%
+T is the probability that X is less than
+ 
+
+ align:start position:0%
+T is the probability that X is less than
+or equal to T which is equal to the
+
+ align:start position:0%
+or equal to T which is equal to the
+ 
+
+ align:start position:0%
+or equal to T which is equal to the
+expectation of the indicator that X is
+
+ align:start position:0%
+expectation of the indicator that X is
+ 
+
+ align:start position:0%
+expectation of the indicator that X is
+less than or equal to
+
+ align:start position:0%
+less than or equal to
+ 
+
+ align:start position:0%
+less than or equal to
+T right that's the definition of a
+
+ align:start position:0%
+T right that's the definition of a
+ 
+
+ align:start position:0%
+T right that's the definition of a
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+and so here I'm just going to
+
+ align:start position:0%
+and so here I'm just going to
+ 
+
+ align:start position:0%
+and so here I'm just going to
+replace expectation by the
+
+ align:start position:0%
+replace expectation by the
+ 
+
+ align:start position:0%
+replace expectation by the
+average right that's my usual
+
+ align:start position:0%
+average right that's my usual
+ 
+
+ align:start position:0%
+average right that's my usual
+statistical trick and so my estimator FN
+
+ align:start position:0%
+statistical trick and so my estimator FN
+ 
+
+ align:start position:0%
+statistical trick and so my estimator FN
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+uh the distribution is going to be 1/ n
+
+ align:start position:0%
+uh the distribution is going to be 1/ n
+ 
+
+ align:start position:0%
+uh the distribution is going to be 1/ n
+sum from IAL 1 to n of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+indicators okay and this is called the
+
+ align:start position:0%
+indicators okay and this is called the
+ 
+
+ align:start position:0%
+indicators okay and this is called the
+empirical uh CDF is just the data
+
+ align:start position:0%
+empirical uh CDF is just the data
+ 
+
+ align:start position:0%
+empirical uh CDF is just the data
+version of the CDF
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I just replace this expectation
+
+ align:start position:0%
+okay so I just replace this expectation
+ 
+
+ align:start position:0%
+okay so I just replace this expectation
+here by an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+average
+
+ align:start position:0%
+average
+ 
+
+ align:start position:0%
+average
+okay now when I sum
+
+ align:start position:0%
+okay now when I sum
+ 
+
+ align:start position:0%
+okay now when I sum
+indicators I'm actually counting the
+
+ align:start position:0%
+indicators I'm actually counting the
+ 
+
+ align:start position:0%
+indicators I'm actually counting the
+number of them that satisfy something so
+
+ align:start position:0%
+number of them that satisfy something so
+ 
+
+ align:start position:0%
+number of them that satisfy something so
+if you look at what this guy
+
+ align:start position:0%
+if you look at what this guy
+ 
+
+ align:start position:0%
+if you look at what this guy
+is this is the number of XIs
+
+ align:start position:0%
+is this is the number of XIs
+ 
+
+ align:start position:0%
+is this is the number of XIs
+that is less than T
+
+ align:start position:0%
+that is less than T
+ 
+
+ align:start position:0%
+that is less than T
+right and so if I divide by n it's the
+
+ align:start position:0%
+right and so if I divide by n it's the
+ 
+
+ align:start position:0%
+right and so if I divide by n it's the
+proportion of observations that I have
+
+ align:start position:0%
+proportion of observations that I have
+ 
+
+ align:start position:0%
+proportion of observations that I have
+that are less than
+
+ align:start position:0%
+that are less than
+ 
+
+ align:start position:0%
+that are less than
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+okay that's what the empirical
+
+ align:start position:0%
+okay that's what the empirical
+ 
+
+ align:start position:0%
+okay that's what the empirical
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+so that's what's written here the number
+
+ align:start position:0%
+so that's what's written here the number
+ 
+
+ align:start position:0%
+so that's what's written here the number
+of of data points that are less than T
+
+ align:start position:0%
+of of data points that are less than T
+ 
+
+ align:start position:0%
+of of data points that are less than T
+and so this is going to be something
+
+ align:start position:0%
+and so this is going to be something
+ 
+
+ align:start position:0%
+and so this is going to be something
+that's sort of try to estimate one or
+
+ align:start position:0%
+that's sort of try to estimate one or
+ 
+
+ align:start position:0%
+that's sort of try to estimate one or
+the other and the law of large number
+
+ align:start position:0%
+the other and the law of large number
+ 
+
+ align:start position:0%
+the other and the law of large number
+actually tells me that for any given T
+
+ align:start position:0%
+actually tells me that for any given T
+ 
+
+ align:start position:0%
+actually tells me that for any given T
+if n is large enough FN of T it should
+
+ align:start position:0%
+if n is large enough FN of T it should
+ 
+
+ align:start position:0%
+if n is large enough FN of T it should
+be close to F of T right because it's an
+
+ align:start position:0%
+be close to F of T right because it's an
+ 
+
+ align:start position:0%
+be close to F of T right because it's an
+average and this entire thing this
+
+ align:start position:0%
+average and this entire thing this
+ 
+
+ align:start position:0%
+average and this entire thing this
+entire statistical trick which consists
+
+ align:start position:0%
+entire statistical trick which consists
+ 
+
+ align:start position:0%
+entire statistical trick which consists
+in replacing Expectations by averages is
+
+ align:start position:0%
+in replacing Expectations by averages is
+ 
+
+ align:start position:0%
+in replacing Expectations by averages is
+justified by the law of large number
+
+ align:start position:0%
+justified by the law of large number
+ 
+
+ align:start position:0%
+justified by the law of large number
+every time we used it that was because
+
+ align:start position:0%
+every time we used it that was because
+ 
+
+ align:start position:0%
+every time we used it that was because
+the law of large number sort of
+
+ align:start position:0%
+the law of large number sort of
+ 
+
+ align:start position:0%
+the law of large number sort of
+guaranteed to us that the average was
+
+ align:start position:0%
+guaranteed to us that the average was
+ 
+
+ align:start position:0%
+guaranteed to us that the average was
+close to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectation Okay so so law of large
+
+ align:start position:0%
+expectation Okay so so law of large
+ 
+
+ align:start position:0%
+expectation Okay so so law of large
+numbers tell me that FN of T converges
+
+ align:start position:0%
+numbers tell me that FN of T converges
+ 
+
+ align:start position:0%
+numbers tell me that FN of T converges
+so that's the strong law says that
+
+ align:start position:0%
+so that's the strong law says that
+ 
+
+ align:start position:0%
+so that's the strong law says that
+almost surely actually FN of T goes to F
+
+ align:start position:0%
+almost surely actually FN of T goes to F
+ 
+
+ align:start position:0%
+almost surely actually FN of T goes to F
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+okay and that's just for any given T
+
+ align:start position:0%
+okay and that's just for any given T
+ 
+
+ align:start position:0%
+okay and that's just for any given T
+everybody is there any question about
+
+ align:start position:0%
+everybody is there any question about
+ 
+
+ align:start position:0%
+everybody is there any question about
+this right that averages converge to
+
+ align:start position:0%
+this right that averages converge to
+ 
+
+ align:start position:0%
+this right that averages converge to
+expectation That's the Law of L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number and almost surely we could say in
+
+ align:start position:0%
+number and almost surely we could say in
+ 
+
+ align:start position:0%
+number and almost surely we could say in
+probability it's the same that would be
+
+ align:start position:0%
+probability it's the same that would be
+ 
+
+ align:start position:0%
+probability it's the same that would be
+the weak low of large number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now this is fine for any given T the
+
+ align:start position:0%
+now this is fine for any given T the
+ 
+
+ align:start position:0%
+now this is fine for any given T the
+average converges to the two right it
+
+ align:start position:0%
+average converges to the two right it
+ 
+
+ align:start position:0%
+average converges to the two right it
+just happens that this random variable
+
+ align:start position:0%
+just happens that this random variable
+ 
+
+ align:start position:0%
+just happens that this random variable
+is indexed by T and I could do it for T
+
+ align:start position:0%
+is indexed by T and I could do it for T
+ 
+
+ align:start position:0%
+is indexed by T and I could do it for T
+equals 1 or two or 25 and just check it
+
+ align:start position:0%
+equals 1 or two or 25 and just check it
+ 
+
+ align:start position:0%
+equals 1 or two or 25 and just check it
+again but I might want to check it for
+
+ align:start position:0%
+again but I might want to check it for
+ 
+
+ align:start position:0%
+again but I might want to check it for
+all T's at
+
+ align:start position:0%
+all T's at
+ 
+
+ align:start position:0%
+all T's at
+once and that's actually a different
+
+ align:start position:0%
+once and that's actually a different
+ 
+
+ align:start position:0%
+once and that's actually a different
+result that's called a uniform result I
+
+ align:start position:0%
+result that's called a uniform result I
+ 
+
+ align:start position:0%
+result that's called a uniform result I
+want this to hold for all T at the same
+
+ align:start position:0%
+want this to hold for all T at the same
+ 
+
+ align:start position:0%
+want this to hold for all T at the same
+time and it may be the case that it
+
+ align:start position:0%
+time and it may be the case that it
+ 
+
+ align:start position:0%
+time and it may be the case that it
+works for for each T individually but
+
+ align:start position:0%
+works for for each T individually but
+ 
+
+ align:start position:0%
+works for for each T individually but
+not for all T's at the same time What
+
+ align:start position:0%
+not for all T's at the same time What
+ 
+
+ align:start position:0%
+not for all T's at the same time What
+could happen is that for T equals 1 it
+
+ align:start position:0%
+could happen is that for T equals 1 it
+ 
+
+ align:start position:0%
+could happen is that for T equals 1 it
+converges at a certain rate and for T
+
+ align:start position:0%
+converges at a certain rate and for T
+ 
+
+ align:start position:0%
+converges at a certain rate and for T
+equals 2 it converges at a bit of a
+
+ align:start position:0%
+equals 2 it converges at a bit of a
+ 
+
+ align:start position:0%
+equals 2 it converges at a bit of a
+slower rate and for T equals three at a
+
+ align:start position:0%
+slower rate and for T equals three at a
+ 
+
+ align:start position:0%
+slower rate and for T equals three at a
+slower rate and slower rate and so as T
+
+ align:start position:0%
+slower rate and slower rate and so as T
+ 
+
+ align:start position:0%
+slower rate and slower rate and so as T
+goes to Infinity the rate is going to
+
+ align:start position:0%
+goes to Infinity the rate is going to
+ 
+
+ align:start position:0%
+goes to Infinity the rate is going to
+vanish and nothing is going to converge
+
+ align:start position:0%
+vanish and nothing is going to converge
+ 
+
+ align:start position:0%
+vanish and nothing is going to converge
+that could happen I could make this
+
+ align:start position:0%
+that could happen I could make this
+ 
+
+ align:start position:0%
+that could happen I could make this
+happen at a finite Point there's many
+
+ align:start position:0%
+happen at a finite Point there's many
+ 
+
+ align:start position:0%
+happen at a finite Point there's many
+ways where I could make this happen
+
+ align:start position:0%
+ways where I could make this happen
+ 
+
+ align:start position:0%
+ways where I could make this happen
+right let's see how that could work I
+
+ align:start position:0%
+right let's see how that could work I
+ 
+
+ align:start position:0%
+right let's see how that could work I
+could say um well actually no I still
+
+ align:start position:0%
+could say um well actually no I still
+ 
+
+ align:start position:0%
+could say um well actually no I still
+need to have this at Infinity for some
+
+ align:start position:0%
+need to have this at Infinity for some
+ 
+
+ align:start position:0%
+need to have this at Infinity for some
+reason
+
+ align:start position:0%
+reason
+ 
+
+ align:start position:0%
+reason
+okay so turns out that this is still
+
+ align:start position:0%
+okay so turns out that this is still
+ 
+
+ align:start position:0%
+okay so turns out that this is still
+true uniformly and this is actually a
+
+ align:start position:0%
+true uniformly and this is actually a
+ 
+
+ align:start position:0%
+true uniformly and this is actually a
+much more complicated result than the
+
+ align:start position:0%
+much more complicated result than the
+ 
+
+ align:start position:0%
+much more complicated result than the
+law of number it's called gleno Canali
+
+ align:start position:0%
+law of number it's called gleno Canali
+ 
+
+ align:start position:0%
+law of number it's called gleno Canali
+theorem and the gleno Canali theorem
+
+ align:start position:0%
+theorem and the gleno Canali theorem
+ 
+
+ align:start position:0%
+theorem and the gleno Canali theorem
+tells me
+
+ align:start position:0%
+tells me
+ 
+
+ align:start position:0%
+tells me
+that for all T's at once FN converges to
+
+ align:start position:0%
+that for all T's at once FN converges to
+ 
+
+ align:start position:0%
+that for all T's at once FN converges to
+F okay so let me just tell you show you
+
+ align:start position:0%
+F okay so let me just tell you show you
+ 
+
+ align:start position:0%
+F okay so let me just tell you show you
+quickly why this is just a little bit
+
+ align:start position:0%
+quickly why this is just a little bit
+ 
+
+ align:start position:0%
+quickly why this is just a little bit
+stronger than the one that
+
+ align:start position:0%
+stronger than the one that
+ 
+
+ align:start position:0%
+stronger than the one that
+we we had so remember if soup is
+
+ align:start position:0%
+we we had so remember if soup is
+ 
+
+ align:start position:0%
+we we had so remember if soup is
+confusing you think of Max is just a Max
+
+ align:start position:0%
+confusing you think of Max is just a Max
+ 
+
+ align:start position:0%
+confusing you think of Max is just a Max
+over an infinite set and so what we know
+
+ align:start position:0%
+over an infinite set and so what we know
+ 
+
+ align:start position:0%
+over an infinite set and so what we know
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+FN of T minus goes to F of
+
+ align:start position:0%
+FN of T minus goes to F of
+ 
+
+ align:start position:0%
+FN of T minus goes to F of
+t as n goes to infinity and let's say
+
+ align:start position:0%
+t as n goes to infinity and let's say
+ 
+
+ align:start position:0%
+t as n goes to infinity and let's say
+almost surely okay and that's the lar
+
+ align:start position:0%
+almost surely okay and that's the lar
+ 
+
+ align:start position:0%
+almost surely okay and that's the lar
+large numbers which is equivalent to
+
+ align:start position:0%
+large numbers which is equivalent to
+ 
+
+ align:start position:0%
+large numbers which is equivalent to
+saying that FN of T minus F of
+
+ align:start position:0%
+saying that FN of T minus F of
+ 
+
+ align:start position:0%
+saying that FN of T minus F of
+t as n goes to Infinity converges almost
+
+ align:start position:0%
+t as n goes to Infinity converges almost
+ 
+
+ align:start position:0%
+t as n goes to Infinity converges almost
+surely to zero right this is the same
+
+ align:start position:0%
+surely to zero right this is the same
+ 
+
+ align:start position:0%
+surely to zero right this is the same
+thing now I want this to happen for all
+
+ align:start position:0%
+thing now I want this to happen for all
+ 
+
+ align:start position:0%
+thing now I want this to happen for all
+T's at once okay and so what I'm going
+
+ align:start position:0%
+T's at once okay and so what I'm going
+ 
+
+ align:start position:0%
+T's at once okay and so what I'm going
+to do oh and this is actually equivalent
+
+ align:start position:0%
+to do oh and this is actually equivalent
+ 
+
+ align:start position:0%
+to do oh and this is actually equivalent
+to this and so what I'm going to do is
+
+ align:start position:0%
+to this and so what I'm going to do is
+ 
+
+ align:start position:0%
+to this and so what I'm going to do is
+I'm going to make it a little stronger
+
+ align:start position:0%
+I'm going to make it a little stronger
+ 
+
+ align:start position:0%
+I'm going to make it a little stronger
+so here the arrow only goes one way and
+
+ align:start position:0%
+so here the arrow only goes one way and
+ 
+
+ align:start position:0%
+so here the arrow only goes one way and
+this is where the soup for T and R of FN
+
+ align:start position:0%
+this is where the soup for T and R of FN
+ 
+
+ align:start position:0%
+this is where the soup for T and R of FN
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T okay and you can actually show that
+
+ align:start position:0%
+T okay and you can actually show that
+ 
+
+ align:start position:0%
+T okay and you can actually show that
+this happens also almost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surely okay now maybe OB shirle is a bit
+
+ align:start position:0%
+surely okay now maybe OB shirle is a bit
+ 
+
+ align:start position:0%
+surely okay now maybe OB shirle is a bit
+more difficult to get a Gras on does can
+
+ align:start position:0%
+more difficult to get a Gras on does can
+ 
+
+ align:start position:0%
+more difficult to get a Gras on does can
+somebody does somebody have would like
+
+ align:start position:0%
+somebody does somebody have would like
+ 
+
+ align:start position:0%
+somebody does somebody have would like
+does anybody want to see an like why
+
+ align:start position:0%
+does anybody want to see an like why
+ 
+
+ align:start position:0%
+does anybody want to see an like why
+this statement for the soup is strictly
+
+ align:start position:0%
+this statement for the soup is strictly
+ 
+
+ align:start position:0%
+this statement for the soup is strictly
+stronger than the one that holds
+
+ align:start position:0%
+stronger than the one that holds
+ 
+
+ align:start position:0%
+stronger than the one that holds
+indivually for
+
+ align:start position:0%
+indivually for
+ 
+
+ align:start position:0%
+indivually for
+all you want to see that okay so let's
+
+ align:start position:0%
+all you want to see that okay so let's
+ 
+
+ align:start position:0%
+all you want to see that okay so let's
+do this so forget about almost surely
+
+ align:start position:0%
+do this so forget about almost surely
+ 
+
+ align:start position:0%
+do this so forget about almost surely
+for one second let's just do it for
+
+ align:start position:0%
+for one second let's just do it for
+ 
+
+ align:start position:0%
+for one second let's just do it for
+improbability right the fact that FN of
+
+ align:start position:0%
+improbability right the fact that FN of
+ 
+
+ align:start position:0%
+improbability right the fact that FN of
+T converges
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to f f f of t for all T in probability
+
+ align:start position:0%
+to f f f of t for all T in probability
+ 
+
+ align:start position:0%
+to f f f of t for all T in probability
+means that this goes to zero as then
+
+ align:start position:0%
+means that this goes to zero as then
+ 
+
+ align:start position:0%
+means that this goes to zero as then
+goes to Infinity for any Epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right for any Epsilon and T we know we
+
+ align:start position:0%
+right for any Epsilon and T we know we
+ 
+
+ align:start position:0%
+right for any Epsilon and T we know we
+have this that's the convergence and
+
+ align:start position:0%
+have this that's the convergence and
+ 
+
+ align:start position:0%
+have this that's the convergence and
+probability now what I want is to put a
+
+ align:start position:0%
+probability now what I want is to put a
+ 
+
+ align:start position:0%
+probability now what I want is to put a
+soup
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here right
+
+ align:start position:0%
+here right
+ 
+
+ align:start position:0%
+here right
+the probability that the soup is larger
+
+ align:start position:0%
+the probability that the soup is larger
+ 
+
+ align:start position:0%
+the probability that the soup is larger
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+Epsilon might be actually always larger
+
+ align:start position:0%
+Epsilon might be actually always larger
+ 
+
+ align:start position:0%
+Epsilon might be actually always larger
+than uh never go to to zero in some
+
+ align:start position:0%
+than uh never go to to zero in some
+ 
+
+ align:start position:0%
+than uh never go to to zero in some
+cases right it could be the case that
+
+ align:start position:0%
+cases right it could be the case that
+ 
+
+ align:start position:0%
+cases right it could be the case that
+for each given T I can make n large
+
+ align:start position:0%
+for each given T I can make n large
+ 
+
+ align:start position:0%
+for each given T I can make n large
+enough so that this is small so that
+
+ align:start position:0%
+enough so that this is small so that
+ 
+
+ align:start position:0%
+enough so that this is small so that
+this probability becomes small but then
+
+ align:start position:0%
+this probability becomes small but then
+ 
+
+ align:start position:0%
+this probability becomes small but then
+maybe it's an N of T right so this here
+
+ align:start position:0%
+maybe it's an N of T right so this here
+ 
+
+ align:start position:0%
+maybe it's an N of T right so this here
+means that for any say uh maybe I
+
+ align:start position:0%
+means that for any say uh maybe I
+ 
+
+ align:start position:0%
+means that for any say uh maybe I
+shouldn't put the let me put a Delta
+
+ align:start position:0%
+shouldn't put the let me put a Delta
+ 
+
+ align:start position:0%
+shouldn't put the let me put a Delta
+here so for any
+
+ align:start position:0%
+here so for any
+ 
+
+ align:start position:0%
+here so for any
+Epsilon so for any T there and for any
+
+ align:start position:0%
+Epsilon so for any T there and for any
+ 
+
+ align:start position:0%
+Epsilon so for any T there and for any
+Epsilon there exists n which could
+
+ align:start position:0%
+Epsilon there exists n which could
+ 
+
+ align:start position:0%
+Epsilon there exists n which could
+depend on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the on both Epsilon and
+
+ align:start position:0%
+the on both Epsilon and
+ 
+
+ align:start position:0%
+the on both Epsilon and
+t such that the probability that FN T
+
+ align:start position:0%
+t such that the probability that FN T
+ 
+
+ align:start position:0%
+t such that the probability that FN T
+minus F of
+
+ align:start position:0%
+minus F of
+ 
+
+ align:start position:0%
+minus F of
+T exceeding uh Delta is less than
+
+ align:start position:0%
+T exceeding uh Delta is less than
+ 
+
+ align:start position:0%
+T exceeding uh Delta is less than
+Epsilon T there exist an n and a Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no that's for all Delta
+
+ align:start position:0%
+no that's for all Delta
+ 
+
+ align:start position:0%
+no that's for all Delta
+sorry so uh right so this is true right
+
+ align:start position:0%
+sorry so uh right so this is true right
+ 
+
+ align:start position:0%
+sorry so uh right so this is true right
+so that's that's what this this limit
+
+ align:start position:0%
+so that's that's what this this limit
+ 
+
+ align:start position:0%
+so that's that's what this this limit
+statement actually
+
+ align:start position:0%
+statement actually
+ 
+
+ align:start position:0%
+statement actually
+means but it could be the case that now
+
+ align:start position:0%
+means but it could be the case that now
+ 
+
+ align:start position:0%
+means but it could be the case that now
+when I take the soup over T maybe that n
+
+ align:start position:0%
+when I take the soup over T maybe that n
+ 
+
+ align:start position:0%
+when I take the soup over T maybe that n
+of T is something that looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T or maybe well integer part of T it
+
+ align:start position:0%
+T or maybe well integer part of T it
+ 
+
+ align:start position:0%
+T or maybe well integer part of T it
+could be right I don't say anything it's
+
+ align:start position:0%
+could be right I don't say anything it's
+ 
+
+ align:start position:0%
+could be right I don't say anything it's
+just an N that depends on T So if this n
+
+ align:start position:0%
+just an N that depends on T So if this n
+ 
+
+ align:start position:0%
+just an N that depends on T So if this n
+is just
+
+ align:start position:0%
+is just
+ 
+
+ align:start position:0%
+is just
+T maybe T over Epsilon right because I
+
+ align:start position:0%
+T maybe T over Epsilon right because I
+ 
+
+ align:start position:0%
+T maybe T over Epsilon right because I
+want Epsilon something like this well
+
+ align:start position:0%
+want Epsilon something like this well
+ 
+
+ align:start position:0%
+want Epsilon something like this well
+that means that if I want this to hold
+
+ align:start position:0%
+that means that if I want this to hold
+ 
+
+ align:start position:0%
+that means that if I want this to hold
+for all T's at once I'm going to have to
+
+ align:start position:0%
+for all T's at once I'm going to have to
+ 
+
+ align:start position:0%
+for all T's at once I'm going to have to
+go for the T the N that works for all
+
+ align:start position:0%
+go for the T the N that works for all
+ 
+
+ align:start position:0%
+go for the T the N that works for all
+T's at once but there's no such n that
+
+ align:start position:0%
+T's at once but there's no such n that
+ 
+
+ align:start position:0%
+T's at once but there's no such n that
+works for all T's at once this is the
+
+ align:start position:0%
+works for all T's at once this is the
+ 
+
+ align:start position:0%
+works for all T's at once this is the
+only n that works is
+
+ align:start position:0%
+only n that works is
+ 
+
+ align:start position:0%
+only n that works is
+infinity and so I cannot make this
+
+ align:start position:0%
+infinity and so I cannot make this
+ 
+
+ align:start position:0%
+infinity and so I cannot make this
+happen for all of them what Leno can
+
+ align:start position:0%
+happen for all of them what Leno can
+ 
+
+ align:start position:0%
+happen for all of them what Leno can
+tell tells you it's actually this is not
+
+ align:start position:0%
+tell tells you it's actually this is not
+ 
+
+ align:start position:0%
+tell tells you it's actually this is not
+something that holds like this that the
+
+ align:start position:0%
+something that holds like this that the
+ 
+
+ align:start position:0%
+something that holds like this that the
+N that depends on T there's actually one
+
+ align:start position:0%
+N that depends on T there's actually one
+ 
+
+ align:start position:0%
+N that depends on T there's actually one
+largest n that works for all the t's at
+
+ align:start position:0%
+largest n that works for all the t's at
+ 
+
+ align:start position:0%
+largest n that works for all the t's at
+once and that's
+
+ align:start position:0%
+once and that's
+ 
+
+ align:start position:0%
+once and that's
+it okay so just so you know why this is
+
+ align:start position:0%
+it okay so just so you know why this is
+ 
+
+ align:start position:0%
+it okay so just so you know why this is
+actually a stronger statement and uh and
+
+ align:start position:0%
+actually a stronger statement and uh and
+ 
+
+ align:start position:0%
+actually a stronger statement and uh and
+uh uh that's basically how how it works
+
+ align:start position:0%
+uh uh that's basically how how it works
+ 
+
+ align:start position:0%
+uh uh that's basically how how it works
+any other
+
+ align:start position:0%
+any other
+ 
+
+ align:start position:0%
+any other
+question yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no well the random variable does have
+
+ align:start position:0%
+no well the random variable does have
+ 
+
+ align:start position:0%
+no well the random variable does have
+finite mean and finite variance because
+
+ align:start position:0%
+finite mean and finite variance because
+ 
+
+ align:start position:0%
+finite mean and finite variance because
+the random variable is an indicator so
+
+ align:start position:0%
+the random variable is an indicator so
+ 
+
+ align:start position:0%
+the random variable is an indicator so
+it has everything you want this is one
+
+ align:start position:0%
+it has everything you want this is one
+ 
+
+ align:start position:0%
+it has everything you want this is one
+of the nicest random variables this is a
+
+ align:start position:0%
+of the nicest random variables this is a
+ 
+
+ align:start position:0%
+of the nicest random variables this is a
+Burly random variable right so here when
+
+ align:start position:0%
+Burly random variable right so here when
+ 
+
+ align:start position:0%
+Burly random variable right so here when
+I say law of large number uh that this
+
+ align:start position:0%
+I say law of large number uh that this
+ 
+
+ align:start position:0%
+I say law of large number uh that this
+holds uh where did I write this I think
+
+ align:start position:0%
+holds uh where did I write this I think
+ 
+
+ align:start position:0%
+holds uh where did I write this I think
+I erased it yeah the one over there this
+
+ align:start position:0%
+I erased it yeah the one over there this
+ 
+
+ align:start position:0%
+I erased it yeah the one over there this
+is actually low of large numbers for
+
+ align:start position:0%
+is actually low of large numbers for
+ 
+
+ align:start position:0%
+is actually low of large numbers for
+burnly random variables they have
+
+ align:start position:0%
+burnly random variables they have
+ 
+
+ align:start position:0%
+burnly random variables they have
+everything you want they're
+
+ align:start position:0%
+everything you want they're
+ 
+
+ align:start position:0%
+everything you want they're
+bounded yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you mean this one for all Epsilon and
+
+ align:start position:0%
+so you mean this one for all Epsilon and
+ 
+
+ align:start position:0%
+so you mean this one for all Epsilon and
+all T so you fix them now then the
+
+ align:start position:0%
+all T so you fix them now then the
+ 
+
+ align:start position:0%
+all T so you fix them now then the
+probability that I oh sorry uh that was
+
+ align:start position:0%
+probability that I oh sorry uh that was
+ 
+
+ align:start position:0%
+probability that I oh sorry uh that was
+Delta right I changed this Epsilon to
+
+ align:start position:0%
+Delta right I changed this Epsilon to
+ 
+
+ align:start position:0%
+Delta right I changed this Epsilon to
+Delta at some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point oh so then the second line says
+
+ align:start position:0%
+point oh so then the second line says
+ 
+
+ align:start position:0%
+point oh so then the second line says
+that for all so this is so the way you
+
+ align:start position:0%
+that for all so this is so the way you
+ 
+
+ align:start position:0%
+that for all so this is so the way you
+so this I'm just rewriting in terms of
+
+ align:start position:0%
+so this I'm just rewriting in terms of
+ 
+
+ align:start position:0%
+so this I'm just rewriting in terms of
+Epsilon Delta what this n goes uh goes
+
+ align:start position:0%
+Epsilon Delta what this n goes uh goes
+ 
+
+ align:start position:0%
+Epsilon Delta what this n goes uh goes
+to Infinity means so that means that
+
+ align:start position:0%
+to Infinity means so that means that
+ 
+
+ align:start position:0%
+to Infinity means so that means that
+that for any um well for any T and and
+
+ align:start position:0%
+that for any um well for any T and and
+ 
+
+ align:start position:0%
+that for any um well for any T and and
+Delta right so that's the same as this
+
+ align:start position:0%
+Delta right so that's the same as this
+ 
+
+ align:start position:0%
+Delta right so that's the same as this
+guy here then here I'm just going back
+
+ align:start position:0%
+guy here then here I'm just going back
+ 
+
+ align:start position:0%
+guy here then here I'm just going back
+to rewriting this it says that for any
+
+ align:start position:0%
+to rewriting this it says that for any
+ 
+
+ align:start position:0%
+to rewriting this it says that for any
+Epsilon there exist an n large enough uh
+
+ align:start position:0%
+Epsilon there exist an n large enough uh
+ 
+
+ align:start position:0%
+Epsilon there exist an n large enough uh
+such that well n larger than this thing
+
+ align:start position:0%
+such that well n larger than this thing
+ 
+
+ align:start position:0%
+such that well n larger than this thing
+basically such that this thing is less
+
+ align:start position:0%
+basically such that this thing is less
+ 
+
+ align:start position:0%
+basically such that this thing is less
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+absolon
+
+ align:start position:0%
+absolon
+ 
+
+ align:start position:0%
+absolon
+okay so gleno can tell tells us that not
+
+ align:start position:0%
+okay so gleno can tell tells us that not
+ 
+
+ align:start position:0%
+okay so gleno can tell tells us that not
+only is this thing is good idea
+
+ align:start position:0%
+only is this thing is good idea
+ 
+
+ align:start position:0%
+only is this thing is good idea
+pointwise but it's also a good idea
+
+ align:start position:0%
+pointwise but it's also a good idea
+ 
+
+ align:start position:0%
+pointwise but it's also a good idea
+uniformly and all it's saying is if you
+
+ align:start position:0%
+uniformly and all it's saying is if you
+ 
+
+ align:start position:0%
+uniformly and all it's saying is if you
+you actually were happy with just this
+
+ align:start position:0%
+you actually were happy with just this
+ 
+
+ align:start position:0%
+you actually were happy with just this
+result you should be even happier with
+
+ align:start position:0%
+result you should be even happier with
+ 
+
+ align:start position:0%
+result you should be even happier with
+that result and this both of these
+
+ align:start position:0%
+that result and this both of these
+ 
+
+ align:start position:0%
+that result and this both of these
+results only tell you one thing they're
+
+ align:start position:0%
+results only tell you one thing they're
+ 
+
+ align:start position:0%
+results only tell you one thing they're
+just telling you that the empirical CDF
+
+ align:start position:0%
+just telling you that the empirical CDF
+ 
+
+ align:start position:0%
+just telling you that the empirical CDF
+is a good estimator of the
+
+ align:start position:0%
+is a good estimator of the
+ 
+
+ align:start position:0%
+is a good estimator of the
+CDF okay now since those F those
+
+ align:start position:0%
+CDF okay now since those F those
+ 
+
+ align:start position:0%
+CDF okay now since those F those
+indicators are burnly distributions I
+
+ align:start position:0%
+indicators are burnly distributions I
+ 
+
+ align:start position:0%
+indicators are burnly distributions I
+can actually do even
+
+ align:start position:0%
+can actually do even
+ 
+
+ align:start position:0%
+can actually do even
+more so let me get this guy here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so those guys uh FN of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T this guy is a burnly distribution what
+
+ align:start position:0%
+T this guy is a burnly distribution what
+ 
+
+ align:start position:0%
+T this guy is a burnly distribution what
+is the parameter of this burnly
+
+ align:start position:0%
+is the parameter of this burnly
+ 
+
+ align:start position:0%
+is the parameter of this burnly
+distribution what is the probability
+
+ align:start position:0%
+distribution what is the probability
+ 
+
+ align:start position:0%
+distribution what is the probability
+that takes value one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F of T right it's just the probability
+
+ align:start position:0%
+F of T right it's just the probability
+ 
+
+ align:start position:0%
+F of T right it's just the probability
+that this thing happens which is f of
+
+ align:start position:0%
+that this thing happens which is f of
+ 
+
+ align:start position:0%
+that this thing happens which is f of
+T so in particular the
+
+ align:start position:0%
+T so in particular the
+ 
+
+ align:start position:0%
+T so in particular the
+variance of this
+
+ align:start position:0%
+variance of this
+ 
+
+ align:start position:0%
+variance of this
+guy is the variance of this burnly so
+
+ align:start position:0%
+guy is the variance of this burnly so
+ 
+
+ align:start position:0%
+guy is the variance of this burnly so
+it's F of
+
+ align:start position:0%
+it's F of
+ 
+
+ align:start position:0%
+it's F of
+t one minus F of T and I can use that in
+
+ align:start position:0%
+t one minus F of T and I can use that in
+ 
+
+ align:start position:0%
+t one minus F of T and I can use that in
+my central limit theorem and my name
+
+ align:start position:0%
+my central limit theorem and my name
+ 
+
+ align:start position:0%
+my central limit theorem and my name
+Central theorem is just going to tell me
+
+ align:start position:0%
+Central theorem is just going to tell me
+ 
+
+ align:start position:0%
+Central theorem is just going to tell me
+that if I look at the average of random
+
+ align:start position:0%
+that if I look at the average of random
+ 
+
+ align:start position:0%
+that if I look at the average of random
+variables I remove their mean right so
+
+ align:start position:0%
+variables I remove their mean right so
+ 
+
+ align:start position:0%
+variables I remove their mean right so
+look at square root of
+
+ align:start position:0%
+look at square root of
+ 
+
+ align:start position:0%
+look at square root of
+n FN of T which I could really write as
+
+ align:start position:0%
+n FN of T which I could really write as
+ 
+
+ align:start position:0%
+n FN of T which I could really write as
+xn bar right that's really just an xn
+
+ align:start position:0%
+xn bar right that's really just an xn
+ 
+
+ align:start position:0%
+xn bar right that's really just an xn
+bar minus the expectation which is f of
+
+ align:start position:0%
+bar minus the expectation which is f of
+ 
+
+ align:start position:0%
+bar minus the expectation which is f of
+T that comes from this guy now if I
+
+ align:start position:0%
+T that comes from this guy now if I
+ 
+
+ align:start position:0%
+T that comes from this guy now if I
+divide by square root of the
+
+ align:start position:0%
+divide by square root of the
+ 
+
+ align:start position:0%
+divide by square root of the
+variance that's my square root P1 minus
+
+ align:start position:0%
+variance that's my square root P1 minus
+ 
+
+ align:start position:0%
+variance that's my square root P1 minus
+P then this guy by the central limit
+
+ align:start position:0%
+P then this guy by the central limit
+ 
+
+ align:start position:0%
+P then this guy by the central limit
+theorem goes to some
+
+ align:start position:0%
+theorem goes to some
+ 
+
+ align:start position:0%
+theorem goes to some
+n01 okay which is the same thing as you
+
+ align:start position:0%
+n01 okay which is the same thing as you
+ 
+
+ align:start position:0%
+n01 okay which is the same thing as you
+see there except that the variance was
+
+ align:start position:0%
+see there except that the variance was
+ 
+
+ align:start position:0%
+see there except that the variance was
+put on the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side okay do I
+
+ align:start position:0%
+side okay do I
+ 
+
+ align:start position:0%
+side okay do I
+have the same thing uniformly in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t right can I write something that holds
+
+ align:start position:0%
+t right can I write something that holds
+ 
+
+ align:start position:0%
+t right can I write something that holds
+uniformly in t well if you think about
+
+ align:start position:0%
+uniformly in t well if you think about
+ 
+
+ align:start position:0%
+uniformly in t well if you think about
+it for one second it's unlikely it's
+
+ align:start position:0%
+it for one second it's unlikely it's
+ 
+
+ align:start position:0%
+it for one second it's unlikely it's
+going to go too well in the sense that
+
+ align:start position:0%
+going to go too well in the sense that
+ 
+
+ align:start position:0%
+going to go too well in the sense that
+it's unlikely that the supremum of those
+
+ align:start position:0%
+it's unlikely that the supremum of those
+ 
+
+ align:start position:0%
+it's unlikely that the supremum of those
+random variables over T is going to also
+
+ align:start position:0%
+random variables over T is going to also
+ 
+
+ align:start position:0%
+random variables over T is going to also
+be a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gaussian right and the reason
+
+ align:start position:0%
+gaussian right and the reason
+ 
+
+ align:start position:0%
+gaussian right and the reason
+is that uh well actually the reason is
+
+ align:start position:0%
+is that uh well actually the reason is
+ 
+
+ align:start position:0%
+is that uh well actually the reason is
+that this thing is actually a stochastic
+
+ align:start position:0%
+that this thing is actually a stochastic
+ 
+
+ align:start position:0%
+that this thing is actually a stochastic
+process index by T A stochastic process
+
+ align:start position:0%
+process index by T A stochastic process
+ 
+
+ align:start position:0%
+process index by T A stochastic process
+is just a sequence in random variables
+
+ align:start position:0%
+is just a sequence in random variables
+ 
+
+ align:start position:0%
+is just a sequence in random variables
+that's indexed by say time one the one
+
+ align:start position:0%
+that's indexed by say time one the one
+ 
+
+ align:start position:0%
+that's indexed by say time one the one
+that's the most famous is the brown
+
+ align:start position:0%
+that's the most famous is the brown
+ 
+
+ align:start position:0%
+that's the most famous is the brown
+brown and motion and it's basically a
+
+ align:start position:0%
+brown and motion and it's basically a
+ 
+
+ align:start position:0%
+brown and motion and it's basically a
+bunch
+
+ align:start position:0%
+bunch
+ 
+
+ align:start position:0%
+bunch
+of gausson increments right so when you
+
+ align:start position:0%
+of gausson increments right so when you
+ 
+
+ align:start position:0%
+of gausson increments right so when you
+go from T to just t a little after that
+
+ align:start position:0%
+go from T to just t a little after that
+ 
+
+ align:start position:0%
+go from T to just t a little after that
+you have just add some gum to the thing
+
+ align:start position:0%
+you have just add some gum to the thing
+ 
+
+ align:start position:0%
+you have just add some gum to the thing
+and uh and here it's basically the same
+
+ align:start position:0%
+and uh and here it's basically the same
+ 
+
+ align:start position:0%
+and uh and here it's basically the same
+thing that's happening and you would
+
+ align:start position:0%
+thing that's happening and you would
+ 
+
+ align:start position:0%
+thing that's happening and you would
+sort of expect since each of this guy is
+
+ align:start position:0%
+sort of expect since each of this guy is
+ 
+
+ align:start position:0%
+sort of expect since each of this guy is
+gaussian you would expect to see
+
+ align:start position:0%
+gaussian you would expect to see
+ 
+
+ align:start position:0%
+gaussian you would expect to see
+something that looks like a brown in
+
+ align:start position:0%
+something that looks like a brown in
+ 
+
+ align:start position:0%
+something that looks like a brown in
+motion at the end but it's not exactly a
+
+ align:start position:0%
+motion at the end but it's not exactly a
+ 
+
+ align:start position:0%
+motion at the end but it's not exactly a
+brown motion it's something that's
+
+ align:start position:0%
+brown motion it's something that's
+ 
+
+ align:start position:0%
+brown motion it's something that's
+called a brownan bridge so if you've
+
+ align:start position:0%
+called a brownan bridge so if you've
+ 
+
+ align:start position:0%
+called a brownan bridge so if you've
+seen the brown motion is something if I
+
+ align:start position:0%
+seen the brown motion is something if I
+ 
+
+ align:start position:0%
+seen the brown motion is something if I
+make it start at zero for example so
+
+ align:start position:0%
+make it start at zero for example so
+ 
+
+ align:start position:0%
+make it start at zero for example so
+this is the value of my brown and motion
+
+ align:start position:0%
+this is the value of my brown and motion
+ 
+
+ align:start position:0%
+this is the value of my brown and motion
+let's write it uh so this is one
+
+ align:start position:0%
+let's write it uh so this is one
+ 
+
+ align:start position:0%
+let's write it uh so this is one
+path one realization of a brown motion
+
+ align:start position:0%
+path one realization of a brown motion
+ 
+
+ align:start position:0%
+path one realization of a brown motion
+let's call it W of t as T increases so
+
+ align:start position:0%
+let's call it W of t as T increases so
+ 
+
+ align:start position:0%
+let's call it W of t as T increases so
+it's let's say it starts at zero and it
+
+ align:start position:0%
+it's let's say it starts at zero and it
+ 
+
+ align:start position:0%
+it's let's say it starts at zero and it
+looks like something like
+
+ align:start position:0%
+looks like something like
+ 
+
+ align:start position:0%
+looks like something like
+this right so that's what brown motion
+
+ align:start position:0%
+this right so that's what brown motion
+ 
+
+ align:start position:0%
+this right so that's what brown motion
+looks like it's just something that's
+
+ align:start position:0%
+looks like it's just something that's
+ 
+
+ align:start position:0%
+looks like it's just something that's
+pretty nasty and uh but it it's I mean
+
+ align:start position:0%
+pretty nasty and uh but it it's I mean
+ 
+
+ align:start position:0%
+pretty nasty and uh but it it's I mean
+it looks pretty nasty it's not
+
+ align:start position:0%
+it looks pretty nasty it's not
+ 
+
+ align:start position:0%
+it looks pretty nasty it's not
+continuous Etc but it's actually very um
+
+ align:start position:0%
+continuous Etc but it's actually very um
+ 
+
+ align:start position:0%
+continuous Etc but it's actually very um
+very benign uh in some average way okay
+
+ align:start position:0%
+very benign uh in some average way okay
+ 
+
+ align:start position:0%
+very benign uh in some average way okay
+and so Brown motion is just something
+
+ align:start position:0%
+and so Brown motion is just something
+ 
+
+ align:start position:0%
+and so Brown motion is just something
+what you should view this as if I sum
+
+ align:start position:0%
+what you should view this as if I sum
+ 
+
+ align:start position:0%
+what you should view this as if I sum
+some random
+
+ align:start position:0%
+some random
+ 
+
+ align:start position:0%
+some random
+variable uh that are gan and then I look
+
+ align:start position:0%
+variable uh that are gan and then I look
+ 
+
+ align:start position:0%
+variable uh that are gan and then I look
+at at this farther from farther and
+
+ align:start position:0%
+at at this farther from farther and
+ 
+
+ align:start position:0%
+at at this farther from farther and
+further it's going to look like
+
+ align:start position:0%
+further it's going to look like
+ 
+
+ align:start position:0%
+further it's going to look like
+this and so here I cannot have a brown
+
+ align:start position:0%
+this and so here I cannot have a brown
+ 
+
+ align:start position:0%
+this and so here I cannot have a brown
+Motion in the end because what is the
+
+ align:start position:0%
+Motion in the end because what is the
+ 
+
+ align:start position:0%
+Motion in the end because what is the
+value at what is the variance of FN of T
+
+ align:start position:0%
+value at what is the variance of FN of T
+ 
+
+ align:start position:0%
+value at what is the variance of FN of T
+minus F of T at T is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one sorry at T is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinity it's zero right the variance
+
+ align:start position:0%
+Infinity it's zero right the variance
+ 
+
+ align:start position:0%
+Infinity it's zero right the variance
+goes from zero at T is negative Infinity
+
+ align:start position:0%
+goes from zero at T is negative Infinity
+ 
+
+ align:start position:0%
+goes from zero at T is negative Infinity
+because at negative Infinity F of T is
+
+ align:start position:0%
+because at negative Infinity F of T is
+ 
+
+ align:start position:0%
+because at negative Infinity F of T is
+going to zero and at F at T as T goes to
+
+ align:start position:0%
+going to zero and at F at T as T goes to
+ 
+
+ align:start position:0%
+going to zero and at F at T as T goes to
+plus infinity F of T is going to one
+
+ align:start position:0%
+plus infinity F of T is going to one
+ 
+
+ align:start position:0%
+plus infinity F of T is going to one
+which means that the variance of this
+
+ align:start position:0%
+which means that the variance of this
+ 
+
+ align:start position:0%
+which means that the variance of this
+guy as T goes from negative Infinity to
+
+ align:start position:0%
+guy as T goes from negative Infinity to
+ 
+
+ align:start position:0%
+guy as T goes from negative Infinity to
+plus infinity is pinned to be zero on
+
+ align:start position:0%
+plus infinity is pinned to be zero on
+ 
+
+ align:start position:0%
+plus infinity is pinned to be zero on
+each side and so my brownon motion
+
+ align:start position:0%
+each side and so my brownon motion
+ 
+
+ align:start position:0%
+each side and so my brownon motion
+cannot surate when I describe it bar
+
+ align:start position:0%
+cannot surate when I describe it bar
+ 
+
+ align:start position:0%
+cannot surate when I describe it bar
+motion I'm just like adding more and
+
+ align:start position:0%
+motion I'm just like adding more and
+ 
+
+ align:start position:0%
+motion I'm just like adding more and
+more entropy to the thing is going all
+
+ align:start position:0%
+more entropy to the thing is going all
+ 
+
+ align:start position:0%
+more entropy to the thing is going all
+over the place but here what I want is
+
+ align:start position:0%
+over the place but here what I want is
+ 
+
+ align:start position:0%
+over the place but here what I want is
+that as I go back it should go back to
+
+ align:start position:0%
+that as I go back it should go back to
+ 
+
+ align:start position:0%
+that as I go back it should go back to
+essentially zero it should be pinned
+
+ align:start position:0%
+essentially zero it should be pinned
+ 
+
+ align:start position:0%
+essentially zero it should be pinned
+down to a specific value at the end and
+
+ align:start position:0%
+down to a specific value at the end and
+ 
+
+ align:start position:0%
+down to a specific value at the end and
+that's actually called The Brown Bridge
+
+ align:start position:0%
+that's actually called The Brown Bridge
+ 
+
+ align:start position:0%
+that's actually called The Brown Bridge
+it's a brown motion that's conditioned
+
+ align:start position:0%
+it's a brown motion that's conditioned
+ 
+
+ align:start position:0%
+it's a brown motion that's conditioned
+to come back to where it started
+
+ align:start position:0%
+to come back to where it started
+ 
+
+ align:start position:0%
+to come back to where it started
+essentially now you don't need to
+
+ align:start position:0%
+essentially now you don't need to
+ 
+
+ align:start position:0%
+essentially now you don't need to
+understand Brown Bridges to understand
+
+ align:start position:0%
+understand Brown Bridges to understand
+ 
+
+ align:start position:0%
+understand Brown Bridges to understand
+what I'm going to be telling you what
+
+ align:start position:0%
+what I'm going to be telling you what
+ 
+
+ align:start position:0%
+what I'm going to be telling you what
+the only thing I want to communicate to
+
+ align:start position:0%
+the only thing I want to communicate to
+ 
+
+ align:start position:0%
+the only thing I want to communicate to
+you is that this guy here when I say A
+
+ align:start position:0%
+you is that this guy here when I say A
+ 
+
+ align:start position:0%
+you is that this guy here when I say A
+Brandon bridge I can go to any
+
+ align:start position:0%
+Brandon bridge I can go to any
+ 
+
+ align:start position:0%
+Brandon bridge I can go to any
+probabilist and they can tell you all
+
+ align:start position:0%
+probabilist and they can tell you all
+ 
+
+ align:start position:0%
+probabilist and they can tell you all
+the probability uh uh uh properties of
+
+ align:start position:0%
+the probability uh uh uh properties of
+ 
+
+ align:start position:0%
+the probability uh uh uh properties of
+this stochastic process it can tell me
+
+ align:start position:0%
+this stochastic process it can tell me
+ 
+
+ align:start position:0%
+this stochastic process it can tell me
+the probability it takes any value at
+
+ align:start position:0%
+the probability it takes any value at
+ 
+
+ align:start position:0%
+the probability it takes any value at
+any point in particular it can tell me
+
+ align:start position:0%
+any point in particular it can tell me
+ 
+
+ align:start position:0%
+any point in particular it can tell me
+the supremum between zero and one of
+
+ align:start position:0%
+the supremum between zero and one of
+ 
+
+ align:start position:0%
+the supremum between zero and one of
+this guy it can tell me what the
+
+ align:start position:0%
+this guy it can tell me what the
+ 
+
+ align:start position:0%
+this guy it can tell me what the
+cumulative distribution function of this
+
+ align:start position:0%
+cumulative distribution function of this
+ 
+
+ align:start position:0%
+cumulative distribution function of this
+thing is can tell me what the density of
+
+ align:start position:0%
+thing is can tell me what the density of
+ 
+
+ align:start position:0%
+thing is can tell me what the density of
+this thing is it can tell me everything
+
+ align:start position:0%
+this thing is it can tell me everything
+ 
+
+ align:start position:0%
+this thing is it can tell me everything
+so it means that if I want to compute
+
+ align:start position:0%
+so it means that if I want to compute
+ 
+
+ align:start position:0%
+so it means that if I want to compute
+probabilities on this object here which
+
+ align:start position:0%
+probabilities on this object here which
+ 
+
+ align:start position:0%
+probabilities on this object here which
+is the maximum value that this guy can
+
+ align:start position:0%
+is the maximum value that this guy can
+ 
+
+ align:start position:0%
+is the maximum value that this guy can
+take over a certain period of time which
+
+ align:start position:0%
+take over a certain period of time which
+ 
+
+ align:start position:0%
+take over a certain period of time which
+is basically this random variable right
+
+ align:start position:0%
+is basically this random variable right
+ 
+
+ align:start position:0%
+is basically this random variable right
+if I look at the value here it's a
+
+ align:start position:0%
+if I look at the value here it's a
+ 
+
+ align:start position:0%
+if I look at the value here it's a
+random variable that fluctuates it can
+
+ align:start position:0%
+random variable that fluctuates it can
+ 
+
+ align:start position:0%
+random variable that fluctuates it can
+tell me where it is with high
+
+ align:start position:0%
+tell me where it is with high
+ 
+
+ align:start position:0%
+tell me where it is with high
+probability can tell me the quintales of
+
+ align:start position:0%
+probability can tell me the quintales of
+ 
+
+ align:start position:0%
+probability can tell me the quintales of
+this thing and it tell can tell me which
+
+ align:start position:0%
+this thing and it tell can tell me which
+ 
+
+ align:start position:0%
+this thing and it tell can tell me which
+is useful because I can build a table
+
+ align:start position:0%
+is useful because I can build a table
+ 
+
+ align:start position:0%
+is useful because I can build a table
+and use it to compute my quenes and form
+
+ align:start position:0%
+and use it to compute my quenes and form
+ 
+
+ align:start position:0%
+and use it to compute my quenes and form
+test from it okay so that's what
+
+ align:start position:0%
+test from it okay so that's what
+ 
+
+ align:start position:0%
+test from it okay so that's what
+actually is quite nice it says that if I
+
+ align:start position:0%
+actually is quite nice it says that if I
+ 
+
+ align:start position:0%
+actually is quite nice it says that if I
+look at the square root of nfn hat now I
+
+ align:start position:0%
+look at the square root of nfn hat now I
+ 
+
+ align:start position:0%
+look at the square root of nfn hat now I
+soup over T I get something that looks
+
+ align:start position:0%
+soup over T I get something that looks
+ 
+
+ align:start position:0%
+soup over T I get something that looks
+like the soup of this gausin but it's
+
+ align:start position:0%
+like the soup of this gausin but it's
+ 
+
+ align:start position:0%
+like the soup of this gausin but it's
+not really soup of gin it's soup of a
+
+ align:start position:0%
+not really soup of gin it's soup of a
+ 
+
+ align:start position:0%
+not really soup of gin it's soup of a
+brown motion now there's something you
+
+ align:start position:0%
+brown motion now there's something you
+ 
+
+ align:start position:0%
+brown motion now there's something you
+should be very careful here I cheated a
+
+ align:start position:0%
+should be very careful here I cheated a
+ 
+
+ align:start position:0%
+should be very careful here I cheated a
+little bit I I didn't cheat I can do
+
+ align:start position:0%
+little bit I I didn't cheat I can do
+ 
+
+ align:start position:0%
+little bit I I didn't cheat I can do
+whatever I want but my notation might be
+
+ align:start position:0%
+whatever I want but my notation might be
+ 
+
+ align:start position:0%
+whatever I want but my notation might be
+a little
+
+ align:start position:0%
+a little
+ 
+
+ align:start position:0%
+a little
+confusing everybody sees that this T
+
+ align:start position:0%
+confusing everybody sees that this T
+ 
+
+ align:start position:0%
+confusing everybody sees that this T
+here is not the same as this T
+
+ align:start position:0%
+here is not the same as this T
+ 
+
+ align:start position:0%
+here is not the same as this T
+here can somebody see that right just
+
+ align:start position:0%
+here can somebody see that right just
+ 
+
+ align:start position:0%
+here can somebody see that right just
+because first of all this guy is between
+
+ align:start position:0%
+because first of all this guy is between
+ 
+
+ align:start position:0%
+because first of all this guy is between
+zero and one and this guy is between is
+
+ align:start position:0%
+zero and one and this guy is between is
+ 
+
+ align:start position:0%
+zero and one and this guy is between is
+all in all of
+
+ align:start position:0%
+all in all of
+ 
+
+ align:start position:0%
+all in all of
+R what is this T
+
+ align:start position:0%
+R what is this T
+ 
+
+ align:start position:0%
+R what is this T
+here as a function of this T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here this guy is f of this guy okay so
+
+ align:start position:0%
+here this guy is f of this guy okay so
+ 
+
+ align:start position:0%
+here this guy is f of this guy okay so
+really if I wanted to be completely
+
+ align:start position:0%
+really if I wanted to be completely
+ 
+
+ align:start position:0%
+really if I wanted to be completely
+transparent and not you know save the
+
+ align:start position:0%
+transparent and not you know save the
+ 
+
+ align:start position:0%
+transparent and not you know save the
+keys of my keyboard I would write this
+
+ align:start position:0%
+keys of my keyboard I would write this
+ 
+
+ align:start position:0%
+keys of my keyboard I would write this
+as sorry soup over T of FN T minus F of
+
+ align:start position:0%
+as sorry soup over T of FN T minus F of
+ 
+
+ align:start position:0%
+as sorry soup over T of FN T minus F of
+T goes to in distribution as n goes to
+
+ align:start position:0%
+T goes to in distribution as n goes to
+ 
+
+ align:start position:0%
+T goes to in distribution as n goes to
+Infinity the supremum over T again in R
+
+ align:start position:0%
+Infinity the supremum over T again in R
+ 
+
+ align:start position:0%
+Infinity the supremum over T again in R
+so this guy is for T in the entire real
+
+ align:start position:0%
+so this guy is for T in the entire real
+ 
+
+ align:start position:0%
+so this guy is for T in the entire real
+line this guy is for T in the entire
+
+ align:start position:0%
+line this guy is for T in the entire
+ 
+
+ align:start position:0%
+line this guy is for T in the entire
+real line but now I should write B of
+
+ align:start position:0%
+real line but now I should write B of
+ 
+
+ align:start position:0%
+real line but now I should write B of
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F of T exactly so really the T here is f
+
+ align:start position:0%
+F of T exactly so really the T here is f
+ 
+
+ align:start position:0%
+F of T exactly so really the T here is f
+of the original one and so that's a
+
+ align:start position:0%
+of the original one and so that's a
+ 
+
+ align:start position:0%
+of the original one and so that's a
+brown motion that's a brownland bridge
+
+ align:start position:0%
+brown motion that's a brownland bridge
+ 
+
+ align:start position:0%
+brown motion that's a brownland bridge
+where when T goes to Infinity the
+
+ align:start position:0%
+where when T goes to Infinity the
+ 
+
+ align:start position:0%
+where when T goes to Infinity the
+brownon bridge goes from zero to one and
+
+ align:start position:0%
+brownon bridge goes from zero to one and
+ 
+
+ align:start position:0%
+brownon bridge goes from zero to one and
+it looks like this a brownland bridge at
+
+ align:start position:0%
+it looks like this a brownland bridge at
+ 
+
+ align:start position:0%
+it looks like this a brownland bridge at
+zero is zero at one is
+
+ align:start position:0%
+zero is zero at one is
+ 
+
+ align:start position:0%
+zero is zero at one is
+zero it does this but it doesn't stray
+
+ align:start position:0%
+zero it does this but it doesn't stray
+ 
+
+ align:start position:0%
+zero it does this but it doesn't stray
+too far because I condition it to come
+
+ align:start position:0%
+too far because I condition it to come
+ 
+
+ align:start position:0%
+too far because I condition it to come
+back to this point that's what a
+
+ align:start position:0%
+back to this point that's what a
+ 
+
+ align:start position:0%
+back to this point that's what a
+Browning bridge is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so in particular I can
+
+ align:start position:0%
+okay so in particular I can
+ 
+
+ align:start position:0%
+okay so in particular I can
+find a distribution for this guy and I
+
+ align:start position:0%
+find a distribution for this guy and I
+ 
+
+ align:start position:0%
+find a distribution for this guy and I
+can use this to build a test which is
+
+ align:start position:0%
+can use this to build a test which is
+ 
+
+ align:start position:0%
+can use this to build a test which is
+called the kov smof
+
+ align:start position:0%
+called the kov smof
+ 
+
+ align:start position:0%
+called the kov smof
+test okay so the idea is the following
+
+ align:start position:0%
+test okay so the idea is the following
+ 
+
+ align:start position:0%
+test okay so the idea is the following
+it says well if I were if I want to test
+
+ align:start position:0%
+it says well if I were if I want to test
+ 
+
+ align:start position:0%
+it says well if I were if I want to test
+some distribution fot some distribution
+
+ align:start position:0%
+some distribution fot some distribution
+ 
+
+ align:start position:0%
+some distribution fot some distribution
+that has a particular CD f f not and I
+
+ align:start position:0%
+that has a particular CD f f not and I
+ 
+
+ align:start position:0%
+that has a particular CD f f not and I
+plug it in under the null then this guy
+
+ align:start position:0%
+plug it in under the null then this guy
+ 
+
+ align:start position:0%
+plug it in under the null then this guy
+should have pretty much the same
+
+ align:start position:0%
+should have pretty much the same
+ 
+
+ align:start position:0%
+should have pretty much the same
+distribution as this supreme of brown
+
+ align:start position:0%
+distribution as this supreme of brown
+ 
+
+ align:start position:0%
+distribution as this supreme of brown
+and Bridge and so if I see this to be
+
+ align:start position:0%
+and Bridge and so if I see this to be
+ 
+
+ align:start position:0%
+and Bridge and so if I see this to be
+much larger than it should be when it's
+
+ align:start position:0%
+much larger than it should be when it's
+ 
+
+ align:start position:0%
+much larger than it should be when it's
+the Supreme of brown and bridge I'm
+
+ align:start position:0%
+the Supreme of brown and bridge I'm
+ 
+
+ align:start position:0%
+the Supreme of brown and bridge I'm
+actually going to reject my
+
+ align:start position:0%
+actually going to reject my
+ 
+
+ align:start position:0%
+actually going to reject my
+hypothesis
+
+ align:start position:0%
+hypothesis
+ 
+
+ align:start position:0%
+hypothesis
+okay so here's the test I want to test
+
+ align:start position:0%
+okay so here's the test I want to test
+ 
+
+ align:start position:0%
+okay so here's the test I want to test
+whether
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h0o f is equal to F0 and you will see
+
+ align:start position:0%
+h0o f is equal to F0 and you will see
+ 
+
+ align:start position:0%
+h0o f is equal to F0 and you will see
+that most of the the um goodness of fit
+
+ align:start position:0%
+that most of the the um goodness of fit
+ 
+
+ align:start position:0%
+that most of the the um goodness of fit
+tests are formulated mathematically in
+
+ align:start position:0%
+tests are formulated mathematically in
+ 
+
+ align:start position:0%
+tests are formulated mathematically in
+terms of the cumulative distrib function
+
+ align:start position:0%
+terms of the cumulative distrib function
+ 
+
+ align:start position:0%
+terms of the cumulative distrib function
+I could formulate them in terms of
+
+ align:start position:0%
+I could formulate them in terms of
+ 
+
+ align:start position:0%
+I could formulate them in terms of
+probability density function or just
+
+ align:start position:0%
+probability density function or just
+ 
+
+ align:start position:0%
+probability density function or just
+write X follows n01 but that's the way
+
+ align:start position:0%
+write X follows n01 but that's the way
+ 
+
+ align:start position:0%
+write X follows n01 but that's the way
+we write it we formulate them in terms
+
+ align:start position:0%
+we write it we formulate them in terms
+ 
+
+ align:start position:0%
+we write it we formulate them in terms
+of cumulative distribution function
+
+ align:start position:0%
+of cumulative distribution function
+ 
+
+ align:start position:0%
+of cumulative distribution function
+because that's what we have a handle on
+
+ align:start position:0%
+because that's what we have a handle on
+ 
+
+ align:start position:0%
+because that's what we have a handle on
+through the empirical cumulative
+
+ align:start position:0%
+through the empirical cumulative
+ 
+
+ align:start position:0%
+through the empirical cumulative
+distribution function okay and then
+
+ align:start position:0%
+distribution function okay and then
+ 
+
+ align:start position:0%
+distribution function okay and then
+that's versus
+
+ align:start position:0%
+that's versus
+ 
+
+ align:start position:0%
+that's versus
+H1 f is not equal to
+
+ align:start position:0%
+H1 f is not equal to
+ 
+
+ align:start position:0%
+H1 f is not equal to
+F0 okay so now I have my empirical CDF
+
+ align:start position:0%
+F0 okay so now I have my empirical CDF
+ 
+
+ align:start position:0%
+F0 okay so now I have my empirical CDF
+and I hope that for all T's FN of T
+
+ align:start position:0%
+and I hope that for all T's FN of T
+ 
+
+ align:start position:0%
+and I hope that for all T's FN of T
+should be close to F0 of t
+
+ align:start position:0%
+should be close to F0 of t
+ 
+
+ align:start position:0%
+should be close to F0 of t
+uh okay let me write it like this I put
+
+ align:start position:0%
+uh okay let me write it like this I put
+ 
+
+ align:start position:0%
+uh okay let me write it like this I put
+it to on the exponent because uh
+
+ align:start position:0%
+it to on the exponent because uh
+ 
+
+ align:start position:0%
+it to on the exponent because uh
+otherwise that would be a have F the
+
+ align:start position:0%
+otherwise that would be a have F the
+ 
+
+ align:start position:0%
+otherwise that would be a have F the
+empirical distribution function based on
+
+ align:start position:0%
+empirical distribution function based on
+ 
+
+ align:start position:0%
+empirical distribution function based on
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+observations all right so uh now I
+
+ align:start position:0%
+observations all right so uh now I
+ 
+
+ align:start position:0%
+observations all right so uh now I
+formed the following test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statistic okay so my test statistic is
+
+ align:start position:0%
+statistic okay so my test statistic is
+ 
+
+ align:start position:0%
+statistic okay so my test statistic is
+TN which is the supremum over T in the
+
+ align:start position:0%
+TN which is the supremum over T in the
+ 
+
+ align:start position:0%
+TN which is the supremum over T in the
+real line of s root of n FN of T minus F
+
+ align:start position:0%
+real line of s root of n FN of T minus F
+ 
+
+ align:start position:0%
+real line of s root of n FN of T minus F
+of t uh sorry F0 of T so I can compute
+
+ align:start position:0%
+of t uh sorry F0 of T so I can compute
+ 
+
+ align:start position:0%
+of t uh sorry F0 of T so I can compute
+everything I know this from the data and
+
+ align:start position:0%
+everything I know this from the data and
+ 
+
+ align:start position:0%
+everything I know this from the data and
+this is the one that comes from my uh
+
+ align:start position:0%
+this is the one that comes from my uh
+ 
+
+ align:start position:0%
+this is the one that comes from my uh
+null hypothesis I can compute this thing
+
+ align:start position:0%
+null hypothesis I can compute this thing
+ 
+
+ align:start position:0%
+null hypothesis I can compute this thing
+and I know that if this is true this
+
+ align:start position:0%
+and I know that if this is true this
+ 
+
+ align:start position:0%
+and I know that if this is true this
+should actually be the supremum of a
+
+ align:start position:0%
+should actually be the supremum of a
+ 
+
+ align:start position:0%
+should actually be the supremum of a
+brown and Bridge pretty
+
+ align:start position:0%
+brown and Bridge pretty
+ 
+
+ align:start position:0%
+brown and Bridge pretty
+much okay and so the korov smov test
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+simply
+
+ align:start position:0%
+simply
+ 
+
+ align:start position:0%
+simply
+reject if this guy TN in absolute value
+
+ align:start position:0%
+reject if this guy TN in absolute value
+ 
+
+ align:start position:0%
+reject if this guy TN in absolute value
+right this no actually not in absolute
+
+ align:start position:0%
+right this no actually not in absolute
+ 
+
+ align:start position:0%
+right this no actually not in absolute
+value this is just already absolute
+
+ align:start position:0%
+value this is just already absolute
+ 
+
+ align:start position:0%
+value this is just already absolute
+valued then this guy should be what well
+
+ align:start position:0%
+valued then this guy should be what well
+ 
+
+ align:start position:0%
+valued then this guy should be what well
+it should be larger than the Q Alpha
+
+ align:start position:0%
+it should be larger than the Q Alpha
+ 
+
+ align:start position:0%
+it should be larger than the Q Alpha
+over two distribution that I have but
+
+ align:start position:0%
+over two distribution that I have but
+ 
+
+ align:start position:0%
+over two distribution that I have but
+now rather than putting n01 or TN this
+
+ align:start position:0%
+now rather than putting n01 or TN this
+ 
+
+ align:start position:0%
+now rather than putting n01 or TN this
+is here whatever notation I have for
+
+ align:start position:0%
+is here whatever notation I have for
+ 
+
+ align:start position:0%
+is here whatever notation I have for
+supremum of brownan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bridge okay just like I did for any
+
+ align:start position:0%
+bridge okay just like I did for any
+ 
+
+ align:start position:0%
+bridge okay just like I did for any
+pivotal distribution right that was the
+
+ align:start position:0%
+pivotal distribution right that was the
+ 
+
+ align:start position:0%
+pivotal distribution right that was the
+same recipe every single time I formed a
+
+ align:start position:0%
+same recipe every single time I formed a
+ 
+
+ align:start position:0%
+same recipe every single time I formed a
+test statistic such that the asmic
+
+ align:start position:0%
+test statistic such that the asmic
+ 
+
+ align:start position:0%
+test statistic such that the asmic
+distribution did not depend on anything
+
+ align:start position:0%
+distribution did not depend on anything
+ 
+
+ align:start position:0%
+distribution did not depend on anything
+I know and then I would just reject when
+
+ align:start position:0%
+I know and then I would just reject when
+ 
+
+ align:start position:0%
+I know and then I would just reject when
+this pivotal distribution was larger
+
+ align:start position:0%
+this pivotal distribution was larger
+ 
+
+ align:start position:0%
+this pivotal distribution was larger
+than something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes do you know what a brown and Bridge
+
+ align:start position:0%
+yes do you know what a brown and Bridge
+ 
+
+ align:start position:0%
+yes do you know what a brown and Bridge
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+or Okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this thing
+
+ align:start position:0%
+so this thing
+ 
+
+ align:start position:0%
+so this thing
+here is think of it as being a gaan
+
+ align:start position:0%
+here is think of it as being a gaan
+ 
+
+ align:start position:0%
+here is think of it as being a gaan
+right so for all T you have a gaan
+
+ align:start position:0%
+right so for all T you have a gaan
+ 
+
+ align:start position:0%
+right so for all T you have a gaan
+distribution okay now a bran
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion so if I so if I had a brown
+
+ align:start position:0%
+motion so if I so if I had a brown
+ 
+
+ align:start position:0%
+motion so if I so if I had a brown
+motion I need to tell you what the so
+
+ align:start position:0%
+motion I need to tell you what the so
+ 
+
+ align:start position:0%
+motion I need to tell you what the so
+it's basically a brown motion is
+
+ align:start position:0%
+it's basically a brown motion is
+ 
+
+ align:start position:0%
+it's basically a brown motion is
+something that looks like this it's some
+
+ align:start position:0%
+something that looks like this it's some
+ 
+
+ align:start position:0%
+something that looks like this it's some
+random variable that's indexed by T I
+
+ align:start position:0%
+random variable that's indexed by T I
+ 
+
+ align:start position:0%
+random variable that's indexed by T I
+want say the expectation of XT to be
+
+ align:start position:0%
+want say the expectation of XT to be
+ 
+
+ align:start position:0%
+want say the expectation of XT to be
+equal to zero for all
+
+ align:start position:0%
+equal to zero for all
+ 
+
+ align:start position:0%
+equal to zero for all
+T okay and what I want is that the
+
+ align:start position:0%
+T okay and what I want is that the
+ 
+
+ align:start position:0%
+T okay and what I want is that the
+increments have a certain distribution
+
+ align:start position:0%
+increments have a certain distribution
+ 
+
+ align:start position:0%
+increments have a certain distribution
+okay so what I want is that um the
+
+ align:start position:0%
+okay so what I want is that um the
+ 
+
+ align:start position:0%
+okay so what I want is that um the
+expectation of
+
+ align:start position:0%
+expectation of
+ 
+
+ align:start position:0%
+expectation of
+x t minus
+
+ align:start position:0%
+x t minus
+ 
+
+ align:start position:0%
+x t minus
+XS follows some distribution which is n0
+
+ align:start position:0%
+XS follows some distribution which is n0
+ 
+
+ align:start position:0%
+XS follows some distribution which is n0
+T minus s okay so the increments are
+
+ align:start position:0%
+T minus s okay so the increments are
+ 
+
+ align:start position:0%
+T minus s okay so the increments are
+bigger as I go farther in terms of
+
+ align:start position:0%
+bigger as I go farther in terms of
+ 
+
+ align:start position:0%
+bigger as I go farther in terms of
+variability and I also want some coant
+
+ align:start position:0%
+variability and I also want some coant
+ 
+
+ align:start position:0%
+variability and I also want some coant
+structure between the two right so what
+
+ align:start position:0%
+structure between the two right so what
+ 
+
+ align:start position:0%
+structure between the two right so what
+I want is that the ciance between Xs and
+
+ align:start position:0%
+I want is that the ciance between Xs and
+ 
+
+ align:start position:0%
+I want is that the ciance between Xs and
+XT is actually equal to the minimum of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+SNT
+
+ align:start position:0%
+SNT
+ 
+
+ align:start position:0%
+SNT
+uh yeah
+
+ align:start position:0%
+uh yeah
+ 
+
+ align:start position:0%
+uh yeah
+maybe uh yeah that should be that okay
+
+ align:start position:0%
+maybe uh yeah that should be that okay
+ 
+
+ align:start position:0%
+maybe uh yeah that should be that okay
+so this is you know you open a
+
+ align:start position:0%
+so this is you know you open a
+ 
+
+ align:start position:0%
+so this is you know you open a
+probability book that's what it's going
+
+ align:start position:0%
+probability book that's what it's going
+ 
+
+ align:start position:0%
+probability book that's what it's going
+to look like so in particular you can
+
+ align:start position:0%
+to look like so in particular you can
+ 
+
+ align:start position:0%
+to look like so in particular you can
+see if I put zero here as T goes to in
+
+ align:start position:0%
+see if I put zero here as T goes to in
+ 
+
+ align:start position:0%
+see if I put zero here as T goes to in
+and x0 is equal to zero it has zero
+
+ align:start position:0%
+and x0 is equal to zero it has zero
+ 
+
+ align:start position:0%
+and x0 is equal to zero it has zero
+variance and it's so in particular it
+
+ align:start position:0%
+variance and it's so in particular it
+ 
+
+ align:start position:0%
+variance and it's so in particular it
+means that
+
+ align:start position:0%
+means that
+ 
+
+ align:start position:0%
+means that
+XT if I look only at the teth one it has
+
+ align:start position:0%
+XT if I look only at the teth one it has
+ 
+
+ align:start position:0%
+XT if I look only at the teth one it has
+some normal
+
+ align:start position:0%
+some normal
+ 
+
+ align:start position:0%
+some normal
+distribution with variance T so this is
+
+ align:start position:0%
+distribution with variance T so this is
+ 
+
+ align:start position:0%
+distribution with variance T so this is
+something that just blows
+
+ align:start position:0%
+something that just blows
+ 
+
+ align:start position:0%
+something that just blows
+up so this guy here it looks like it's
+
+ align:start position:0%
+up so this guy here it looks like it's
+ 
+
+ align:start position:0%
+up so this guy here it looks like it's
+going to be a brown motion because when
+
+ align:start position:0%
+going to be a brown motion because when
+ 
+
+ align:start position:0%
+going to be a brown motion because when
+I look at the left hand side it has a
+
+ align:start position:0%
+I look at the left hand side it has a
+ 
+
+ align:start position:0%
+I look at the left hand side it has a
+normal distribution now there's a bunch
+
+ align:start position:0%
+normal distribution now there's a bunch
+ 
+
+ align:start position:0%
+normal distribution now there's a bunch
+of other things you need to check if is
+
+ align:start position:0%
+of other things you need to check if is
+ 
+
+ align:start position:0%
+of other things you need to check if is
+the fact that you have this Co variance
+
+ align:start position:0%
+the fact that you have this Co variance
+ 
+
+ align:start position:0%
+the fact that you have this Co variance
+for example which I did not tell you but
+
+ align:start position:0%
+for example which I did not tell you but
+ 
+
+ align:start position:0%
+for example which I did not tell you but
+it should look somewhat somewhat like
+
+ align:start position:0%
+it should look somewhat somewhat like
+ 
+
+ align:start position:0%
+it should look somewhat somewhat like
+that and in particular when I look at
+
+ align:start position:0%
+that and in particular when I look at
+ 
+
+ align:start position:0%
+that and in particular when I look at
+the uh normal with mean zero and and
+
+ align:start position:0%
+the uh normal with mean zero and and
+ 
+
+ align:start position:0%
+the uh normal with mean zero and and
+variance here then it's clear that this
+
+ align:start position:0%
+variance here then it's clear that this
+ 
+
+ align:start position:0%
+variance here then it's clear that this
+guy does not have a variance that's
+
+ align:start position:0%
+guy does not have a variance that's
+ 
+
+ align:start position:0%
+guy does not have a variance that's
+going to go to Infinity just like the
+
+ align:start position:0%
+going to go to Infinity just like the
+ 
+
+ align:start position:0%
+going to go to Infinity just like the
+variance of this guy we know that the
+
+ align:start position:0%
+variance of this guy we know that the
+ 
+
+ align:start position:0%
+variance of this guy we know that the
+variance is is forced to be back to
+
+ align:start position:0%
+variance is is forced to be back to
+ 
+
+ align:start position:0%
+variance is is forced to be back to
+zero okay and so in particular we have
+
+ align:start position:0%
+zero okay and so in particular we have
+ 
+
+ align:start position:0%
+zero okay and so in particular we have
+something that has mean zero always
+
+ align:start position:0%
+something that has mean zero always
+ 
+
+ align:start position:0%
+something that has mean zero always
+whose variance has to be zero at zero
+
+ align:start position:0%
+whose variance has to be zero at zero
+ 
+
+ align:start position:0%
+whose variance has to be zero at zero
+and uh variance sorry at tal negative
+
+ align:start position:0%
+and uh variance sorry at tal negative
+ 
+
+ align:start position:0%
+and uh variance sorry at tal negative
+infinity and variance one at tal plus
+
+ align:start position:0%
+infinity and variance one at tal plus
+ 
+
+ align:start position:0%
+infinity and variance one at tal plus
+infinity sorry variance zero at T equals
+
+ align:start position:0%
+infinity sorry variance zero at T equals
+ 
+
+ align:start position:0%
+infinity sorry variance zero at T equals
+plus infinity and so I have to basically
+
+ align:start position:0%
+plus infinity and so I have to basically
+ 
+
+ align:start position:0%
+plus infinity and so I have to basically
+force it to be equal to zero on at each
+
+ align:start position:0%
+force it to be equal to zero on at each
+ 
+
+ align:start position:0%
+force it to be equal to zero on at each
+end so the brown motion here tends to
+
+ align:start position:0%
+end so the brown motion here tends to
+ 
+
+ align:start position:0%
+end so the brown motion here tends to
+just go to Infinity somewhere whereas
+
+ align:start position:0%
+just go to Infinity somewhere whereas
+ 
+
+ align:start position:0%
+just go to Infinity somewhere whereas
+this guy force it to come back now
+
+ align:start position:0%
+this guy force it to come back now
+ 
+
+ align:start position:0%
+this guy force it to come back now
+everything I describ to you is on the
+
+ align:start position:0%
+everything I describ to you is on the
+ 
+
+ align:start position:0%
+everything I describ to you is on the
+scale zero negative Infinity to plus
+
+ align:start position:0%
+scale zero negative Infinity to plus
+ 
+
+ align:start position:0%
+scale zero negative Infinity to plus
+infinity but since everything depends of
+
+ align:start position:0%
+infinity but since everything depends of
+ 
+
+ align:start position:0%
+infinity but since everything depends of
+on F of T I can actually just put that
+
+ align:start position:0%
+on F of T I can actually just put that
+ 
+
+ align:start position:0%
+on F of T I can actually just put that
+back into a scale which is zero and one
+
+ align:start position:0%
+back into a scale which is zero and one
+ 
+
+ align:start position:0%
+back into a scale which is zero and one
+by a a simple change of variable it's
+
+ align:start position:0%
+by a a simple change of variable it's
+ 
+
+ align:start position:0%
+by a a simple change of variable it's
+like it's called change of time for the
+
+ align:start position:0%
+like it's called change of time for the
+ 
+
+ align:start position:0%
+like it's called change of time for the
+brown
+
+ align:start position:0%
+brown
+ 
+
+ align:start position:0%
+brown
+motion okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah I mean that definitely it's
+
+ align:start position:0%
+yeah yeah I mean that definitely it's
+ 
+
+ align:start position:0%
+yeah yeah I mean that definitely it's
+going to be I mean by symmetry you can
+
+ align:start position:0%
+going to be I mean by symmetry you can
+ 
+
+ align:start position:0%
+going to be I mean by symmetry you can
+probably infer all the things right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah so I don't know exact there's an
+
+ align:start position:0%
+so yeah so I don't know exact there's an
+ 
+
+ align:start position:0%
+so yeah so I don't know exact there's an
+explicit formula for the and it's simple
+
+ align:start position:0%
+explicit formula for the and it's simple
+ 
+
+ align:start position:0%
+explicit formula for the and it's simple
+that's what I can tell you but I don't
+
+ align:start position:0%
+that's what I can tell you but I don't
+ 
+
+ align:start position:0%
+that's what I can tell you but I don't
+know what the explicit at the top of my
+
+ align:start position:0%
+know what the explicit at the top of my
+ 
+
+ align:start position:0%
+know what the explicit at the top of my
+head what the explicit formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no uh well the brownland bridge this is
+
+ align:start position:0%
+no uh well the brownland bridge this is
+ 
+
+ align:start position:0%
+no uh well the brownland bridge this is
+the Supreme of you're right so this is
+
+ align:start position:0%
+the Supreme of you're right so this is
+ 
+
+ align:start position:0%
+the Supreme of you're right so this is
+yes so right
+
+ align:start position:0%
+yes so right
+ 
+
+ align:start position:0%
+yes so right
+so this will be this form for the
+
+ align:start position:0%
+so this will be this form for the
+ 
+
+ align:start position:0%
+so this will be this form for the
+variance for sure because this is only
+
+ align:start position:0%
+variance for sure because this is only
+ 
+
+ align:start position:0%
+variance for sure because this is only
+marginal distribution that don't take
+
+ align:start position:0%
+marginal distribution that don't take
+ 
+
+ align:start position:0%
+marginal distribution that don't take
+right the process is not just what is
+
+ align:start position:0%
+right the process is not just what is
+ 
+
+ align:start position:0%
+right the process is not just what is
+the distribution at each instant T it's
+
+ align:start position:0%
+the distribution at each instant T it's
+ 
+
+ align:start position:0%
+the distribution at each instant T it's
+also how do those distributions interact
+
+ align:start position:0%
+also how do those distributions interact
+ 
+
+ align:start position:0%
+also how do those distributions interact
+with each other right in terms of
+
+ align:start position:0%
+with each other right in terms of
+ 
+
+ align:start position:0%
+with each other right in terms of
+variance but for the marginal
+
+ align:start position:0%
+variance but for the marginal
+ 
+
+ align:start position:0%
+variance but for the marginal
+distributions at each instant T right
+
+ align:start position:0%
+distributions at each instant T right
+ 
+
+ align:start position:0%
+distributions at each instant T right
+the variance is f of T1 minus F of T
+
+ align:start position:0%
+the variance is f of T1 minus F of T
+ 
+
+ align:start position:0%
+the variance is f of T1 minus F of T
+that's not going to we're not going to
+
+ align:start position:0%
+that's not going to we're not going to
+ 
+
+ align:start position:0%
+that's not going to we're not going to
+escape that uh but then the cience
+
+ align:start position:0%
+escape that uh but then the cience
+ 
+
+ align:start position:0%
+escape that uh but then the cience
+structure between those guys is a little
+
+ align:start position:0%
+structure between those guys is a little
+ 
+
+ align:start position:0%
+structure between those guys is a little
+more complicated but yes you're right
+
+ align:start position:0%
+more complicated but yes you're right
+ 
+
+ align:start position:0%
+more complicated but yes you're right
+for marginal that's enough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah it could be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinity um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay because uh what I did I erase it
+
+ align:start position:0%
+okay because uh what I did I erase it
+ 
+
+ align:start position:0%
+okay because uh what I did I erase it
+yeah because here I didn't say the
+
+ align:start position:0%
+yeah because here I didn't say the
+ 
+
+ align:start position:0%
+yeah because here I didn't say the
+supremum of the absolute value of a
+
+ align:start position:0%
+supremum of the absolute value of a
+ 
+
+ align:start position:0%
+supremum of the absolute value of a
+brownon bridge I just said the Supreme
+
+ align:start position:0%
+brownon bridge I just said the Supreme
+ 
+
+ align:start position:0%
+brownon bridge I just said the Supreme
+of a brownland bridge but you're right
+
+ align:start position:0%
+of a brownland bridge but you're right
+ 
+
+ align:start position:0%
+of a brownland bridge but you're right
+let's just do this like
+
+ align:start position:0%
+let's just do this like
+ 
+
+ align:start position:0%
+let's just do this like
+that and then uh and then it's uh it's
+
+ align:start position:0%
+that and then uh and then it's uh it's
+ 
+
+ align:start position:0%
+that and then uh and then it's uh it's
+probably
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cleaner right so yeah actually well I
+
+ align:start position:0%
+cleaner right so yeah actually well I
+ 
+
+ align:start position:0%
+cleaner right so yeah actually well I
+should be Q Alpha so uh uh this is
+
+ align:start position:0%
+should be Q Alpha so uh uh this is
+ 
+
+ align:start position:0%
+should be Q Alpha so uh uh this is
+basically you're right so this is think
+
+ align:start position:0%
+basically you're right so this is think
+ 
+
+ align:start position:0%
+basically you're right so this is think
+of it as being one-sided uh and there's
+
+ align:start position:0%
+of it as being one-sided uh and there's
+ 
+
+ align:start position:0%
+of it as being one-sided uh and there's
+actually no symmetry for the supremum
+
+ align:start position:0%
+actually no symmetry for the supremum
+ 
+
+ align:start position:0%
+actually no symmetry for the supremum
+right so I mean the supremum is not
+
+ align:start position:0%
+right so I mean the supremum is not
+ 
+
+ align:start position:0%
+right so I mean the supremum is not
+symmetric around zero and so uh so
+
+ align:start position:0%
+symmetric around zero and so uh so
+ 
+
+ align:start position:0%
+symmetric around zero and so uh so
+you're right I should not use Alpha over
+
+ align:start position:0%
+you're right I should not use Alpha over
+ 
+
+ align:start position:0%
+you're right I should not use Alpha over
+two thank
+
+ align:start position:0%
+two thank
+ 
+
+ align:start position:0%
+two thank
+you any other
+
+ align:start position:0%
+you any other
+ 
+
+ align:start position:0%
+you any other
+question this should be Alpha yeah I
+
+ align:start position:0%
+question this should be Alpha yeah I
+ 
+
+ align:start position:0%
+question this should be Alpha yeah I
+mean those slides were written with
+
+ align:start position:0%
+mean those slides were written with
+ 
+
+ align:start position:0%
+mean those slides were written with
+minus Alpha and I have not replaced all
+
+ align:start position:0%
+minus Alpha and I have not replaced all
+ 
+
+ align:start position:0%
+minus Alpha and I have not replaced all
+instances of one minus Alpha by Alpha I
+
+ align:start position:0%
+instances of one minus Alpha by Alpha I
+ 
+
+ align:start position:0%
+instances of one minus Alpha by Alpha I
+mean except this guy is still the well
+
+ align:start position:0%
+mean except this guy is still the well
+ 
+
+ align:start position:0%
+mean except this guy is still the well
+it depends on how you want to call it
+
+ align:start position:0%
+it depends on how you want to call it
+ 
+
+ align:start position:0%
+it depends on how you want to call it
+but this is still the probability that Z
+
+ align:start position:0%
+but this is still the probability that Z
+ 
+
+ align:start position:0%
+but this is still the probability that Z
+the probability at Z exits this guy
+
+ align:start position:0%
+the probability at Z exits this guy
+ 
+
+ align:start position:0%
+the probability at Z exits this guy
+should be
+
+ align:start position:0%
+should be
+ 
+
+ align:start position:0%
+should be
+Alpha okay and this can be found in
+
+ align:start position:0%
+Alpha okay and this can be found in
+ 
+
+ align:start position:0%
+Alpha okay and this can be found in
+tables and we can compute the P value
+
+ align:start position:0%
+tables and we can compute the P value
+ 
+
+ align:start position:0%
+tables and we can compute the P value
+just like we did
+
+ align:start position:0%
+just like we did
+ 
+
+ align:start position:0%
+just like we did
+before but we have to simulate it
+
+ align:start position:0%
+before but we have to simulate it
+ 
+
+ align:start position:0%
+before but we have to simulate it
+because it's not going to depend on the
+
+ align:start position:0%
+because it's not going to depend on the
+ 
+
+ align:start position:0%
+because it's not going to depend on the
+cumulative distribution function of a
+
+ align:start position:0%
+cumulative distribution function of a
+ 
+
+ align:start position:0%
+cumulative distribution function of a
+gin like it did for the usual gin test
+
+ align:start position:0%
+gin like it did for the usual gin test
+ 
+
+ align:start position:0%
+gin like it did for the usual gin test
+something that's more complicated and
+
+ align:start position:0%
+something that's more complicated and
+ 
+
+ align:start position:0%
+something that's more complicated and
+typically you don't even try you get the
+
+ align:start position:0%
+typically you don't even try you get the
+ 
+
+ align:start position:0%
+typically you don't even try you get the
+statistical software to do it for you
+
+ align:start position:0%
+statistical software to do it for you
+ 
+
+ align:start position:0%
+statistical software to do it for you
+okay so just uh uh let me let me skip a
+
+ align:start position:0%
+okay so just uh uh let me let me skip a
+ 
+
+ align:start position:0%
+okay so just uh uh let me let me skip a
+few lines this is what the table looks
+
+ align:start position:0%
+few lines this is what the table looks
+ 
+
+ align:start position:0%
+few lines this is what the table looks
+like for the com smof test okay so it
+
+ align:start position:0%
+like for the com smof test okay so it
+ 
+
+ align:start position:0%
+like for the com smof test okay so it
+just tells you what is your some number
+
+ align:start position:0%
+just tells you what is your some number
+ 
+
+ align:start position:0%
+just tells you what is your some number
+of observations and then you want Alpha
+
+ align:start position:0%
+of observations and then you want Alpha
+ 
+
+ align:start position:0%
+of observations and then you want Alpha
+to be equal to 5% say let's say you have
+
+ align:start position:0%
+to be equal to 5% say let's say you have
+ 
+
+ align:start position:0%
+to be equal to 5% say let's say you have
+nine observations so if square root of
+
+ align:start position:0%
+nine observations so if square root of
+ 
+
+ align:start position:0%
+nine observations so if square root of
+an absolute value of FN of T minus F of
+
+ align:start position:0%
+an absolute value of FN of T minus F of
+ 
+
+ align:start position:0%
+an absolute value of FN of T minus F of
+T exceeds this thing you
+
+ align:start position:0%
+T exceeds this thing you
+ 
+
+ align:start position:0%
+T exceeds this thing you
+reject
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what's pretty clear from this test is
+
+ align:start position:0%
+so what's pretty clear from this test is
+ 
+
+ align:start position:0%
+so what's pretty clear from this test is
+that it looks very nice and I tell you
+
+ align:start position:0%
+that it looks very nice and I tell you
+ 
+
+ align:start position:0%
+that it looks very nice and I tell you
+this is how you build it but if you
+
+ align:start position:0%
+this is how you build it but if you
+ 
+
+ align:start position:0%
+this is how you build it but if you
+think about it for one second it's
+
+ align:start position:0%
+think about it for one second it's
+ 
+
+ align:start position:0%
+think about it for one second it's
+actually really an annoying thing to
+
+ align:start position:0%
+actually really an annoying thing to
+ 
+
+ align:start position:0%
+actually really an annoying thing to
+build because you have to take the Super
+
+ align:start position:0%
+build because you have to take the Super
+ 
+
+ align:start position:0%
+build because you have to take the Super
+suum over T right this depends on
+
+ align:start position:0%
+suum over T right this depends on
+ 
+
+ align:start position:0%
+suum over T right this depends on
+Computing a supremum which you know in
+
+ align:start position:0%
+Computing a supremum which you know in
+ 
+
+ align:start position:0%
+Computing a supremum which you know in
+practice might be super cumbersome I
+
+ align:start position:0%
+practice might be super cumbersome I
+ 
+
+ align:start position:0%
+practice might be super cumbersome I
+don't want to have to compute this for
+
+ align:start position:0%
+don't want to have to compute this for
+ 
+
+ align:start position:0%
+don't want to have to compute this for
+all values T and then take the maximum
+
+ align:start position:0%
+all values T and then take the maximum
+ 
+
+ align:start position:0%
+all values T and then take the maximum
+of those guys it turns out that it's
+
+ align:start position:0%
+of those guys it turns out that it's
+ 
+
+ align:start position:0%
+of those guys it turns out that it's
+actually quite nice that we don't have
+
+ align:start position:0%
+actually quite nice that we don't have
+ 
+
+ align:start position:0%
+actually quite nice that we don't have
+to actually do this what does the
+
+ align:start position:0%
+to actually do this what does the
+ 
+
+ align:start position:0%
+to actually do this what does the
+empirical distribution function look
+
+ align:start position:0%
+empirical distribution function look
+ 
+
+ align:start position:0%
+empirical distribution function look
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well this thing remember FN of T by
+
+ align:start position:0%
+well this thing remember FN of T by
+ 
+
+ align:start position:0%
+well this thing remember FN of T by
+definition was so let me go to the slide
+
+ align:start position:0%
+definition was so let me go to the slide
+ 
+
+ align:start position:0%
+definition was so let me go to the slide
+that's relevant so FN of T looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so what it means is that when T is
+
+ align:start position:0%
+this so what it means is that when T is
+ 
+
+ align:start position:0%
+this so what it means is that when T is
+between two observations then this guy
+
+ align:start position:0%
+between two observations then this guy
+ 
+
+ align:start position:0%
+between two observations then this guy
+is actually keeping the same value so if
+
+ align:start position:0%
+is actually keeping the same value so if
+ 
+
+ align:start position:0%
+is actually keeping the same value so if
+I put my observations on the real line
+
+ align:start position:0%
+I put my observations on the real line
+ 
+
+ align:start position:0%
+I put my observations on the real line
+here so let's say I have one observation
+
+ align:start position:0%
+here so let's say I have one observation
+ 
+
+ align:start position:0%
+here so let's say I have one observation
+here one observation here one
+
+ align:start position:0%
+here one observation here one
+ 
+
+ align:start position:0%
+here one observation here one
+observation here one observation here
+
+ align:start position:0%
+observation here one observation here
+ 
+
+ align:start position:0%
+observation here one observation here
+and one observation here for Simplicity
+
+ align:start position:0%
+and one observation here for Simplicity
+ 
+
+ align:start position:0%
+and one observation here for Simplicity
+then this is basically up to this
+
+ align:start position:0%
+then this is basically up to this
+ 
+
+ align:start position:0%
+then this is basically up to this
+normalization counting how many
+
+ align:start position:0%
+normalization counting how many
+ 
+
+ align:start position:0%
+normalization counting how many
+observations I have that are less than T
+
+ align:start position:0%
+observations I have that are less than T
+ 
+
+ align:start position:0%
+observations I have that are less than T
+right so since I normalize by N I know
+
+ align:start position:0%
+right so since I normalize by N I know
+ 
+
+ align:start position:0%
+right so since I normalize by N I know
+that the smallest number here is going
+
+ align:start position:0%
+that the smallest number here is going
+ 
+
+ align:start position:0%
+that the smallest number here is going
+to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero and the largest number here is
+
+ align:start position:0%
+zero and the largest number here is
+ 
+
+ align:start position:0%
+zero and the largest number here is
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+one okay so let's say this looks like
+
+ align:start position:0%
+one okay so let's say this looks like
+ 
+
+ align:start position:0%
+one okay so let's say this looks like
+this this is the value
+
+ align:start position:0%
+this this is the value
+ 
+
+ align:start position:0%
+this this is the value
+one okay add the value since I take it
+
+ align:start position:0%
+one okay add the value since I take it
+ 
+
+ align:start position:0%
+one okay add the value since I take it
+less than or equal to when I'm at XI I'm
+
+ align:start position:0%
+less than or equal to when I'm at XI I'm
+ 
+
+ align:start position:0%
+less than or equal to when I'm at XI I'm
+actually counting it so the jump happens
+
+ align:start position:0%
+actually counting it so the jump happens
+ 
+
+ align:start position:0%
+actually counting it so the jump happens
+at x i so that's the first observation
+
+ align:start position:0%
+at x i so that's the first observation
+ 
+
+ align:start position:0%
+at x i so that's the first observation
+and then I jump by how much do I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+jump
+
+ align:start position:0%
+jump
+ 
+
+ align:start position:0%
+jump
+yeah one over n
+
+ align:start position:0%
+yeah one over n
+ 
+
+ align:start position:0%
+yeah one over n
+right okay and then this value belongs
+
+ align:start position:0%
+right okay and then this value belongs
+ 
+
+ align:start position:0%
+right okay and then this value belongs
+to uh to the right and then I do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again I'm going to I I know I'm it's not
+
+ align:start position:0%
+again I'm going to I I know I'm it's not
+ 
+
+ align:start position:0%
+again I'm going to I I know I'm it's not
+going to work out for me but we'll see
+
+ align:start position:0%
+going to work out for me but we'll see
+ 
+
+ align:start position:0%
+going to work out for me but we'll see
+uh that's oh no actually I pretty well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay this is what my cumulative
+
+ align:start position:0%
+uh okay this is what my cumulative
+ 
+
+ align:start position:0%
+uh okay this is what my cumulative
+distribution looks like now if you look
+
+ align:start position:0%
+distribution looks like now if you look
+ 
+
+ align:start position:0%
+distribution looks like now if you look
+on this slide there's this weird
+
+ align:start position:0%
+on this slide there's this weird
+ 
+
+ align:start position:0%
+on this slide there's this weird
+notation where I start putting now my
+
+ align:start position:0%
+notation where I start putting now my
+ 
+
+ align:start position:0%
+notation where I start putting now my
+indices in parenthesis X parenthesis one
+
+ align:start position:0%
+indices in parenthesis X parenthesis one
+ 
+
+ align:start position:0%
+indices in parenthesis X parenthesis one
+exp parenthesis 2 etc those are called
+
+ align:start position:0%
+exp parenthesis 2 etc those are called
+ 
+
+ align:start position:0%
+exp parenthesis 2 etc those are called
+the ordered statistic it's just because
+
+ align:start position:0%
+the ordered statistic it's just because
+ 
+
+ align:start position:0%
+the ordered statistic it's just because
+it might be you know when my data is
+
+ align:start position:0%
+it might be you know when my data is
+ 
+
+ align:start position:0%
+it might be you know when my data is
+given to me I just call the first
+
+ align:start position:0%
+given to me I just call the first
+ 
+
+ align:start position:0%
+given to me I just call the first
+observation the one that's on top of the
+
+ align:start position:0%
+observation the one that's on top of the
+ 
+
+ align:start position:0%
+observation the one that's on top of the
+table but isn't doesn't have to be the
+
+ align:start position:0%
+table but isn't doesn't have to be the
+ 
+
+ align:start position:0%
+table but isn't doesn't have to be the
+smallest value so it might be that this
+
+ align:start position:0%
+smallest value so it might be that this
+ 
+
+ align:start position:0%
+smallest value so it might be that this
+is X1 and that this is X2 then this is
+
+ align:start position:0%
+is X1 and that this is X2 then this is
+ 
+
+ align:start position:0%
+is X1 and that this is X2 then this is
+X3 X4 and X5 right this might be my
+
+ align:start position:0%
+X3 X4 and X5 right this might be my
+ 
+
+ align:start position:0%
+X3 X4 and X5 right this might be my
+observations so what I do is that I
+
+ align:start position:0%
+observations so what I do is that I
+ 
+
+ align:start position:0%
+observations so what I do is that I
+recall them in such a way that this is
+
+ align:start position:0%
+recall them in such a way that this is
+ 
+
+ align:start position:0%
+recall them in such a way that this is
+actually I recall this guy X1 which is
+
+ align:start position:0%
+actually I recall this guy X1 which is
+ 
+
+ align:start position:0%
+actually I recall this guy X1 which is
+just really
+
+ align:start position:0%
+just really
+ 
+
+ align:start position:0%
+just really
+X3 uh this is X2
+
+ align:start position:0%
+X3 uh this is X2
+ 
+
+ align:start position:0%
+X3 uh this is X2
+X3 X4 and X5 these are my reordered
+
+ align:start position:0%
+X3 X4 and X5 these are my reordered
+ 
+
+ align:start position:0%
+X3 X4 and X5 these are my reordered
+observations in such a way that the
+
+ align:start position:0%
+observations in such a way that the
+ 
+
+ align:start position:0%
+observations in such a way that the
+smallest one is indexed by one and the
+
+ align:start position:0%
+smallest one is indexed by one and the
+ 
+
+ align:start position:0%
+smallest one is indexed by one and the
+largest one is indexed by n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now this is actually quite nice
+
+ align:start position:0%
+okay so now this is actually quite nice
+ 
+
+ align:start position:0%
+okay so now this is actually quite nice
+because what I'm trying to do is to find
+
+ align:start position:0%
+because what I'm trying to do is to find
+ 
+
+ align:start position:0%
+because what I'm trying to do is to find
+the largest deviation from this guy to
+
+ align:start position:0%
+the largest deviation from this guy to
+ 
+
+ align:start position:0%
+the largest deviation from this guy to
+the true cumulative distribution
+
+ align:start position:0%
+the true cumulative distribution
+ 
+
+ align:start position:0%
+the true cumulative distribution
+function the true cumulative
+
+ align:start position:0%
+function the true cumulative
+ 
+
+ align:start position:0%
+function the true cumulative
+distribution function let's say it's
+
+ align:start position:0%
+distribution function let's say it's
+ 
+
+ align:start position:0%
+distribution function let's say it's
+gaussian looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this right this is something
+
+ align:start position:0%
+this right this is something
+ 
+
+ align:start position:0%
+this right this is something
+continuous for a symmetric distribution
+
+ align:start position:0%
+continuous for a symmetric distribution
+ 
+
+ align:start position:0%
+continuous for a symmetric distribution
+it crosses this axis at 1 half and
+
+ align:start position:0%
+it crosses this axis at 1 half and
+ 
+
+ align:start position:0%
+it crosses this axis at 1 half and
+that's what it looks like and the cumul
+
+ align:start position:0%
+that's what it looks like and the cumul
+ 
+
+ align:start position:0%
+that's what it looks like and the cumul
+the the com of T is just telling me how
+
+ align:start position:0%
+the the com of T is just telling me how
+ 
+
+ align:start position:0%
+the the com of T is just telling me how
+far do I get those two curves get in the
+
+ align:start position:0%
+far do I get those two curves get in the
+ 
+
+ align:start position:0%
+far do I get those two curves get in the
+worst possible
+
+ align:start position:0%
+worst possible
+ 
+
+ align:start position:0%
+worst possible
+case right so in particular here where
+
+ align:start position:0%
+case right so in particular here where
+ 
+
+ align:start position:0%
+case right so in particular here where
+are they the farthest clearly that's
+
+ align:start position:0%
+are they the farthest clearly that's
+ 
+
+ align:start position:0%
+are they the farthest clearly that's
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+point and so up to resaling this is the
+
+ align:start position:0%
+point and so up to resaling this is the
+ 
+
+ align:start position:0%
+point and so up to resaling this is the
+value I'm going to be interested in
+
+ align:start position:0%
+value I'm going to be interested in
+ 
+
+ align:start position:0%
+value I'm going to be interested in
+that's how they get as far as possible
+
+ align:start position:0%
+that's how they get as far as possible
+ 
+
+ align:start position:0%
+that's how they get as far as possible
+from each
+
+ align:start position:0%
+from each
+ 
+
+ align:start position:0%
+from each
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+here something just happened right the
+
+ align:start position:0%
+here something just happened right the
+ 
+
+ align:start position:0%
+here something just happened right the
+farthest distance that I got was exactly
+
+ align:start position:0%
+farthest distance that I got was exactly
+ 
+
+ align:start position:0%
+farthest distance that I got was exactly
+at one of those
+
+ align:start position:0%
+at one of those
+ 
+
+ align:start position:0%
+at one of those
+dots it turns out this is enough to look
+
+ align:start position:0%
+dots it turns out this is enough to look
+ 
+
+ align:start position:0%
+dots it turns out this is enough to look
+at those dots and the reason is well
+
+ align:start position:0%
+at those dots and the reason is well
+ 
+
+ align:start position:0%
+at those dots and the reason is well
+because after this Dot and until the
+
+ align:start position:0%
+because after this Dot and until the
+ 
+
+ align:start position:0%
+because after this Dot and until the
+next jump this guy does not
+
+ align:start position:0%
+next jump this guy does not
+ 
+
+ align:start position:0%
+next jump this guy does not
+change but this guy
+
+ align:start position:0%
+change but this guy
+ 
+
+ align:start position:0%
+change but this guy
+increases and so the the only point
+
+ align:start position:0%
+increases and so the the only point
+ 
+
+ align:start position:0%
+increases and so the the only point
+where they can be the farthest apart is
+
+ align:start position:0%
+where they can be the farthest apart is
+ 
+
+ align:start position:0%
+where they can be the farthest apart is
+either to the left at one to the left of
+
+ align:start position:0%
+either to the left at one to the left of
+ 
+
+ align:start position:0%
+either to the left at one to the left of
+a jump or to the right of a jump that's
+
+ align:start position:0%
+a jump or to the right of a jump that's
+ 
+
+ align:start position:0%
+a jump or to the right of a jump that's
+the only place where they can be far
+
+ align:start position:0%
+the only place where they can be far
+ 
+
+ align:start position:0%
+the only place where they can be far
+from each other and that means that only
+
+ align:start position:0%
+from each other and that means that only
+ 
+
+ align:start position:0%
+from each other and that means that only
+one observation everybody see SE that
+
+ align:start position:0%
+one observation everybody see SE that
+ 
+
+ align:start position:0%
+one observation everybody see SE that
+the farthest points the points at which
+
+ align:start position:0%
+the farthest points the points at which
+ 
+
+ align:start position:0%
+the farthest points the points at which
+those two curves are the farthest from
+
+ align:start position:0%
+those two curves are the farthest from
+ 
+
+ align:start position:0%
+those two curves are the farthest from
+each other has to be at one of the
+
+ align:start position:0%
+each other has to be at one of the
+ 
+
+ align:start position:0%
+each other has to be at one of the
+observations and so rather than looking
+
+ align:start position:0%
+observations and so rather than looking
+ 
+
+ align:start position:0%
+observations and so rather than looking
+at a soup over all possible T's really
+
+ align:start position:0%
+at a soup over all possible T's really
+ 
+
+ align:start position:0%
+at a soup over all possible T's really
+all I need to do is to look at a maximum
+
+ align:start position:0%
+all I need to do is to look at a maximum
+ 
+
+ align:start position:0%
+all I need to do is to look at a maximum
+only at my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observations right I just need to check
+
+ align:start position:0%
+observations right I just need to check
+ 
+
+ align:start position:0%
+observations right I just need to check
+at each of those points where they're
+
+ align:start position:0%
+at each of those points where they're
+ 
+
+ align:start position:0%
+at each of those points where they're
+far now here notice that you did not
+
+ align:start position:0%
+far now here notice that you did not
+ 
+
+ align:start position:0%
+far now here notice that you did not
+this is not written FN of x
+
+ align:start position:0%
+this is not written FN of x
+ 
+
+ align:start position:0%
+this is not written FN of x
+i the reason is because I actually know
+
+ align:start position:0%
+i the reason is because I actually know
+ 
+
+ align:start position:0%
+i the reason is because I actually know
+what FN of x i is FN of the I order
+
+ align:start position:0%
+what FN of x i is FN of the I order
+ 
+
+ align:start position:0%
+what FN of x i is FN of the I order
+observation is just the number of jumps
+
+ align:start position:0%
+observation is just the number of jumps
+ 
+
+ align:start position:0%
+observation is just the number of jumps
+I've had until this observation so here
+
+ align:start position:0%
+I've had until this observation so here
+ 
+
+ align:start position:0%
+I've had until this observation so here
+I know that the value of FN is 1 over n
+
+ align:start position:0%
+I know that the value of FN is 1 over n
+ 
+
+ align:start position:0%
+I know that the value of FN is 1 over n
+here it's 2 over n 3 over n 4 over n 5
+
+ align:start position:0%
+here it's 2 over n 3 over n 4 over n 5
+ 
+
+ align:start position:0%
+here it's 2 over n 3 over n 4 over n 5
+over n so I know that the values of FN
+
+ align:start position:0%
+over n so I know that the values of FN
+ 
+
+ align:start position:0%
+over n so I know that the values of FN
+at my
+
+ align:start position:0%
+at my
+ 
+
+ align:start position:0%
+at my
+observations and those are actually the
+
+ align:start position:0%
+observations and those are actually the
+ 
+
+ align:start position:0%
+observations and those are actually the
+only values that FN can take are an
+
+ align:start position:0%
+only values that FN can take are an
+ 
+
+ align:start position:0%
+only values that FN can take are an
+integer divided by n and that's why you
+
+ align:start position:0%
+integer divided by n and that's why you
+ 
+
+ align:start position:0%
+integer divided by n and that's why you
+see IUS one / n or I over
+
+ align:start position:0%
+see IUS one / n or I over
+ 
+
+ align:start position:0%
+see IUS one / n or I over
+n this is the difference just before the
+
+ align:start position:0%
+n this is the difference just before the
+ 
+
+ align:start position:0%
+n this is the difference just before the
+jump and this is the difference at the
+
+ align:start position:0%
+jump and this is the difference at the
+ 
+
+ align:start position:0%
+jump and this is the difference at the
+jump okay so here the key message is
+
+ align:start position:0%
+jump okay so here the key message is
+ 
+
+ align:start position:0%
+jump okay so here the key message is
+that this is no longer a supremum of all
+
+ align:start position:0%
+that this is no longer a supremum of all
+ 
+
+ align:start position:0%
+that this is no longer a supremum of all
+T's but it's just a maximum from one to
+
+ align:start position:0%
+T's but it's just a maximum from one to
+ 
+
+ align:start position:0%
+T's but it's just a maximum from one to
+n so I really have only two n values to
+
+ align:start position:0%
+n so I really have only two n values to
+ 
+
+ align:start position:0%
+n so I really have only two n values to
+compute this value and this value for
+
+ align:start position:0%
+compute this value and this value for
+ 
+
+ align:start position:0%
+compute this value and this value for
+each observation that's two n total I
+
+ align:start position:0%
+each observation that's two n total I
+ 
+
+ align:start position:0%
+each observation that's two n total I
+look at the maximum and that's actually
+
+ align:start position:0%
+look at the maximum and that's actually
+ 
+
+ align:start position:0%
+look at the maximum and that's actually
+the value and it's actually equal to TN
+
+ align:start position:0%
+the value and it's actually equal to TN
+ 
+
+ align:start position:0%
+the value and it's actually equal to TN
+those are things it's not an
+
+ align:start position:0%
+those are things it's not an
+ 
+
+ align:start position:0%
+those are things it's not an
+approximation those things are equal
+
+ align:start position:0%
+approximation those things are equal
+ 
+
+ align:start position:0%
+approximation those things are equal
+that's just the only places where those
+
+ align:start position:0%
+that's just the only places where those
+ 
+
+ align:start position:0%
+that's just the only places where those
+guys can be
+
+ align:start position:0%
+guys can be
+ 
+
+ align:start position:0%
+guys can be
+maximum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes oh strictly less powerful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so can you I'm not sure what question
+
+ align:start position:0%
+so so can you I'm not sure what question
+ 
+
+ align:start position:0%
+so so can you I'm not sure what question
+you're asking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so remember here in this test
+
+ align:start position:0%
+yeah yeah so remember here in this test
+ 
+
+ align:start position:0%
+yeah yeah so remember here in this test
+we want to conclude to H zero in the
+
+ align:start position:0%
+we want to conclude to H zero in the
+ 
+
+ align:start position:0%
+we want to conclude to H zero in the
+other test we typically want to conclude
+
+ align:start position:0%
+other test we typically want to conclude
+ 
+
+ align:start position:0%
+other test we typically want to conclude
+to H1 so here we actually don't want
+
+ align:start position:0%
+to H1 so here we actually don't want
+ 
+
+ align:start position:0%
+to H1 so here we actually don't want
+power in a way and uh and you have to
+
+ align:start position:0%
+power in a way and uh and you have to
+ 
+
+ align:start position:0%
+power in a way and uh and you have to
+also assume that doing a test on the
+
+ align:start position:0%
+also assume that doing a test on the
+ 
+
+ align:start position:0%
+also assume that doing a test on the
+mean is probably probably not the only
+
+ align:start position:0%
+mean is probably probably not the only
+ 
+
+ align:start position:0%
+mean is probably probably not the only
+thing you're going to end up doing on
+
+ align:start position:0%
+thing you're going to end up doing on
+ 
+
+ align:start position:0%
+thing you're going to end up doing on
+your data after after you actually
+
+ align:start position:0%
+your data after after you actually
+ 
+
+ align:start position:0%
+your data after after you actually
+established that it's normally
+
+ align:start position:0%
+established that it's normally
+ 
+
+ align:start position:0%
+established that it's normally
+distributed then you have a data set
+
+ align:start position:0%
+distributed then you have a data set
+ 
+
+ align:start position:0%
+distributed then you have a data set
+you've sort of established this normal
+
+ align:start position:0%
+you've sort of established this normal
+ 
+
+ align:start position:0%
+you've sort of established this normal
+distributed and then you can just run
+
+ align:start position:0%
+distributed and then you can just run
+ 
+
+ align:start position:0%
+distributed and then you can just run
+the Arsenal of statistical studies and
+
+ align:start position:0%
+the Arsenal of statistical studies and
+ 
+
+ align:start position:0%
+the Arsenal of statistical studies and
+we're going to see regression and all
+
+ align:start position:0%
+we're going to see regression and all
+ 
+
+ align:start position:0%
+we're going to see regression and all
+sorts of predi predictive things which
+
+ align:start position:0%
+sorts of predi predictive things which
+ 
+
+ align:start position:0%
+sorts of predi predictive things which
+are not just just test if the mean is
+
+ align:start position:0%
+are not just just test if the mean is
+ 
+
+ align:start position:0%
+are not just just test if the mean is
+equal to something maybe you want to
+
+ align:start position:0%
+equal to something maybe you want to
+ 
+
+ align:start position:0%
+equal to something maybe you want to
+build a confidence interval for the mean
+
+ align:start position:0%
+build a confidence interval for the mean
+ 
+
+ align:start position:0%
+build a confidence interval for the mean
+then this is not the confidence interval
+
+ align:start position:0%
+then this is not the confidence interval
+ 
+
+ align:start position:0%
+then this is not the confidence interval
+is not a test right so you're going to
+
+ align:start position:0%
+is not a test right so you're going to
+ 
+
+ align:start position:0%
+is not a test right so you're going to
+have to first test if it's normal and
+
+ align:start position:0%
+have to first test if it's normal and
+ 
+
+ align:start position:0%
+have to first test if it's normal and
+then see if you can actually use the
+
+ align:start position:0%
+then see if you can actually use the
+ 
+
+ align:start position:0%
+then see if you can actually use the
+quantiles of a g industry distribtion or
+
+ align:start position:0%
+quantiles of a g industry distribtion or
+ 
+
+ align:start position:0%
+quantiles of a g industry distribtion or
+t distribution to build this uh uh
+
+ align:start position:0%
+t distribution to build this uh uh
+ 
+
+ align:start position:0%
+t distribution to build this uh uh
+confidence interval so in a way you
+
+ align:start position:0%
+confidence interval so in a way you
+ 
+
+ align:start position:0%
+confidence interval so in a way you
+could should do this as like you know
+
+ align:start position:0%
+could should do this as like you know
+ 
+
+ align:start position:0%
+could should do this as like you know
+the flat fee to enter the Gan world and
+
+ align:start position:0%
+the flat fee to enter the Gan world and
+ 
+
+ align:start position:0%
+the flat fee to enter the Gan world and
+then you can do whatever you want to do
+
+ align:start position:0%
+then you can do whatever you want to do
+ 
+
+ align:start position:0%
+then you can do whatever you want to do
+in the gaan world um we'll see actually
+
+ align:start position:0%
+in the gaan world um we'll see actually
+ 
+
+ align:start position:0%
+in the gaan world um we'll see actually
+that your question goes back to
+
+ align:start position:0%
+that your question goes back to
+ 
+
+ align:start position:0%
+that your question goes back to
+something that's a little more that's a
+
+ align:start position:0%
+something that's a little more that's a
+ 
+
+ align:start position:0%
+something that's a little more that's a
+little important is here I said f0o is
+
+ align:start position:0%
+little important is here I said f0o is
+ 
+
+ align:start position:0%
+little important is here I said f0o is
+fully specified right it's like an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+N15 but I didn't say is it g is it
+
+ align:start position:0%
+N15 but I didn't say is it g is it
+ 
+
+ align:start position:0%
+N15 but I didn't say is it g is it
+normally distributed which is the
+
+ align:start position:0%
+normally distributed which is the
+ 
+
+ align:start position:0%
+normally distributed which is the
+question that everybody asks right
+
+ align:start position:0%
+question that everybody asks right
+ 
+
+ align:start position:0%
+question that everybody asks right
+you're not asking is it this particular
+
+ align:start position:0%
+you're not asking is it this particular
+ 
+
+ align:start position:0%
+you're not asking is it this particular
+normal distribution with this particular
+
+ align:start position:0%
+normal distribution with this particular
+ 
+
+ align:start position:0%
+normal distribution with this particular
+mean and this particular variance so how
+
+ align:start position:0%
+mean and this particular variance so how
+ 
+
+ align:start position:0%
+mean and this particular variance so how
+would you do it in practice well you
+
+ align:start position:0%
+would you do it in practice well you
+ 
+
+ align:start position:0%
+would you do it in practice well you
+would say I'm just going to replace the
+
+ align:start position:0%
+would say I'm just going to replace the
+ 
+
+ align:start position:0%
+would say I'm just going to replace the
+mean by the empirical mean and the
+
+ align:start position:0%
+mean by the empirical mean and the
+ 
+
+ align:start position:0%
+mean by the empirical mean and the
+variance by the empirical variance but
+
+ align:start position:0%
+variance by the empirical variance but
+ 
+
+ align:start position:0%
+variance by the empirical variance but
+by doing that you're making a huge
+
+ align:start position:0%
+by doing that you're making a huge
+ 
+
+ align:start position:0%
+by doing that you're making a huge
+mistake because you're sort of depriving
+
+ align:start position:0%
+mistake because you're sort of depriving
+ 
+
+ align:start position:0%
+mistake because you're sort of depriving
+your test of the possibility to reject
+
+ align:start position:0%
+your test of the possibility to reject
+ 
+
+ align:start position:0%
+your test of the possibility to reject
+the gaan hypothesis just based on the
+
+ align:start position:0%
+the gaan hypothesis just based on the
+ 
+
+ align:start position:0%
+the gaan hypothesis just based on the
+fact that the mean is wrong or the
+
+ align:start position:0%
+fact that the mean is wrong or the
+ 
+
+ align:start position:0%
+fact that the mean is wrong or the
+variance is wrong you've already stuck
+
+ align:start position:0%
+variance is wrong you've already stuck
+ 
+
+ align:start position:0%
+variance is wrong you've already stuck
+to your data pretty well okay and so
+
+ align:start position:0%
+to your data pretty well okay and so
+ 
+
+ align:start position:0%
+to your data pretty well okay and so
+you're sort of like already you know
+
+ align:start position:0%
+you're sort of like already you know
+ 
+
+ align:start position:0%
+you're sort of like already you know
+tilting the game in favor of A Jero big
+
+ align:start position:0%
+tilting the game in favor of A Jero big
+ 
+
+ align:start position:0%
+tilting the game in favor of A Jero big
+time so there's actually a way to
+
+ align:start position:0%
+time so there's actually a way to
+ 
+
+ align:start position:0%
+time so there's actually a way to
+arrange for this
+
+ align:start position:0%
+arrange for this
+ 
+
+ align:start position:0%
+arrange for this
+uh okay so this is about pivotal
+
+ align:start position:0%
+uh okay so this is about pivotal
+ 
+
+ align:start position:0%
+uh okay so this is about pivotal
+statistic we've used this word many time
+
+ align:start position:0%
+statistic we've used this word many time
+ 
+
+ align:start position:0%
+statistic we've used this word many time
+uh um and uh okay so that's how I'm not
+
+ align:start position:0%
+uh um and uh okay so that's how I'm not
+ 
+
+ align:start position:0%
+uh um and uh okay so that's how I'm not
+going to go into this test it's really
+
+ align:start position:0%
+going to go into this test it's really
+ 
+
+ align:start position:0%
+going to go into this test it's really
+this is a recipe on how you would
+
+ align:start position:0%
+this is a recipe on how you would
+ 
+
+ align:start position:0%
+this is a recipe on how you would
+actually build the the table that I
+
+ align:start position:0%
+actually build the the table that I
+ 
+
+ align:start position:0%
+actually build the the table that I
+showed you right this table this is
+
+ align:start position:0%
+showed you right this table this is
+ 
+
+ align:start position:0%
+showed you right this table this is
+basically the recipe on how to build it
+
+ align:start position:0%
+basically the recipe on how to build it
+ 
+
+ align:start position:0%
+basically the recipe on how to build it
+there's another recipe to build which is
+
+ align:start position:0%
+there's another recipe to build which is
+ 
+
+ align:start position:0%
+there's another recipe to build which is
+just open a book at this page right
+
+ align:start position:0%
+just open a book at this page right
+ 
+
+ align:start position:0%
+just open a book at this page right
+that's a little faster uh or use the
+
+ align:start position:0%
+that's a little faster uh or use the
+ 
+
+ align:start position:0%
+that's a little faster uh or use the
+software um I just wanted to show you so
+
+ align:start position:0%
+software um I just wanted to show you so
+ 
+
+ align:start position:0%
+software um I just wanted to show you so
+let's just keep in mind anybody has a
+
+ align:start position:0%
+let's just keep in mind anybody has a
+ 
+
+ align:start position:0%
+let's just keep in mind anybody has a
+good memory let's just keep in mind this
+
+ align:start position:0%
+good memory let's just keep in mind this
+ 
+
+ align:start position:0%
+good memory let's just keep in mind this
+number this is the the uh the the
+
+ align:start position:0%
+number this is the the uh the the
+ 
+
+ align:start position:0%
+number this is the the uh the the
+threshold for the uh kog statistic if I
+
+ align:start position:0%
+threshold for the uh kog statistic if I
+ 
+
+ align:start position:0%
+threshold for the uh kog statistic if I
+have 10 observations and I want to do it
+
+ align:start position:0%
+have 10 observations and I want to do it
+ 
+
+ align:start position:0%
+have 10 observations and I want to do it
+at 5% okay it's about
+
+ align:start position:0%
+at 5% okay it's about
+ 
+
+ align:start position:0%
+at 5% okay it's about
+41% so that's the number that it should
+
+ align:start position:0%
+41% so that's the number that it should
+ 
+
+ align:start position:0%
+41% so that's the number that it should
+be uh larger from so it turns out that
+
+ align:start position:0%
+be uh larger from so it turns out that
+ 
+
+ align:start position:0%
+be uh larger from so it turns out that
+if you want to test test if it's normal
+
+ align:start position:0%
+if you want to test test if it's normal
+ 
+
+ align:start position:0%
+if you want to test test if it's normal
+and not just a specific normal this
+
+ align:start position:0%
+and not just a specific normal this
+ 
+
+ align:start position:0%
+and not just a specific normal this
+number is going to be different do you
+
+ align:start position:0%
+number is going to be different do you
+ 
+
+ align:start position:0%
+number is going to be different do you
+think the number I'm going to read in a
+
+ align:start position:0%
+think the number I'm going to read in a
+ 
+
+ align:start position:0%
+think the number I'm going to read in a
+table that's appropriate for this is
+
+ align:start position:0%
+table that's appropriate for this is
+ 
+
+ align:start position:0%
+table that's appropriate for this is
+going to be larger or smaller who says
+
+ align:start position:0%
+going to be larger or smaller who says
+ 
+
+ align:start position:0%
+going to be larger or smaller who says
+larger so the question is this is the
+
+ align:start position:0%
+larger so the question is this is the
+ 
+
+ align:start position:0%
+larger so the question is this is the
+number I should see if my test was is
+
+ align:start position:0%
+number I should see if my test was is
+ 
+
+ align:start position:0%
+number I should see if my test was is
+X uh say
+
+ align:start position:0%
+X uh say
+ 
+
+ align:start position:0%
+X uh say
+n 05 right that's a specific
+
+ align:start position:0%
+n 05 right that's a specific
+ 
+
+ align:start position:0%
+n 05 right that's a specific
+distribution with a specific F0 right
+
+ align:start position:0%
+distribution with a specific F0 right
+ 
+
+ align:start position:0%
+distribution with a specific F0 right
+so that's the number that's I would
+
+ align:start position:0%
+so that's the number that's I would
+ 
+
+ align:start position:0%
+so that's the number that's I would
+build the Comm mof statistic from this I
+
+ align:start position:0%
+build the Comm mof statistic from this I
+ 
+
+ align:start position:0%
+build the Comm mof statistic from this I
+would perform a test and check if my kov
+
+ align:start position:0%
+would perform a test and check if my kov
+ 
+
+ align:start position:0%
+would perform a test and check if my kov
+mof statistic TN is larger than this
+
+ align:start position:0%
+mof statistic TN is larger than this
+ 
+
+ align:start position:0%
+mof statistic TN is larger than this
+number or not okay if it's larger I'm
+
+ align:start position:0%
+number or not okay if it's larger I'm
+ 
+
+ align:start position:0%
+number or not okay if it's larger I'm
+going to reject now I say actually I
+
+ align:start position:0%
+going to reject now I say actually I
+ 
+
+ align:start position:0%
+going to reject now I say actually I
+don't want to test if H Zer is and Z5
+
+ align:start position:0%
+don't want to test if H Zer is and Z5
+ 
+
+ align:start position:0%
+don't want to test if H Zer is and Z5
+but it's just n mu Sigma squ for
+
+ align:start position:0%
+but it's just n mu Sigma squ for
+ 
+
+ align:start position:0%
+but it's just n mu Sigma squ for
+some mu and sigma squ and if I think I'm
+
+ align:start position:0%
+some mu and sigma squ and if I think I'm
+ 
+
+ align:start position:0%
+some mu and sigma squ and if I think I'm
+just going to plug in mu hat and sigma
+
+ align:start position:0%
+just going to plug in mu hat and sigma
+ 
+
+ align:start position:0%
+just going to plug in mu hat and sigma
+hat into my fzero run the same statistic
+
+ align:start position:0%
+hat into my fzero run the same statistic
+ 
+
+ align:start position:0%
+hat into my fzero run the same statistic
+but compare it to a different number
+
+ align:start position:0%
+but compare it to a different number
+ 
+
+ align:start position:0%
+but compare it to a different number
+should this so the larger the
+
+ align:start position:0%
+should this so the larger the
+ 
+
+ align:start position:0%
+should this so the larger the
+number the more or less likely I am I am
+
+ align:start position:0%
+number the more or less likely I am I am
+ 
+
+ align:start position:0%
+number the more or less likely I am I am
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+reject the less likely I am to reject
+
+ align:start position:0%
+reject the less likely I am to reject
+ 
+
+ align:start position:0%
+reject the less likely I am to reject
+right so if I just use that number I
+
+ align:start position:0%
+right so if I just use that number I
+ 
+
+ align:start position:0%
+right so if I just use that number I
+would let's say this is the a large
+
+ align:start position:0%
+would let's say this is the a large
+ 
+
+ align:start position:0%
+would let's say this is the a large
+number I would be more tempted to say
+
+ align:start position:0%
+number I would be more tempted to say
+ 
+
+ align:start position:0%
+number I would be more tempted to say
+it's Galan now if you look at the table
+
+ align:start position:0%
+it's Galan now if you look at the table
+ 
+
+ align:start position:0%
+it's Galan now if you look at the table
+you would get if you make the
+
+ align:start position:0%
+you would get if you make the
+ 
+
+ align:start position:0%
+you would get if you make the
+appropriate correction at the same
+
+ align:start position:0%
+appropriate correction at the same
+ 
+
+ align:start position:0%
+appropriate correction at the same
+number of observations 10 and the same
+
+ align:start position:0%
+number of observations 10 and the same
+ 
+
+ align:start position:0%
+number of observations 10 and the same
+level you get 25% out the post to 41%
+
+ align:start position:0%
+level you get 25% out the post to 41%
+ 
+
+ align:start position:0%
+level you get 25% out the post to 41%
+that means that you're actually much
+
+ align:start position:0%
+that means that you're actually much
+ 
+
+ align:start position:0%
+that means that you're actually much
+more likely if you use the appropriate
+
+ align:start position:0%
+more likely if you use the appropriate
+ 
+
+ align:start position:0%
+more likely if you use the appropriate
+test to reject the fact that it's normal
+
+ align:start position:0%
+test to reject the fact that it's normal
+ 
+
+ align:start position:0%
+test to reject the fact that it's normal
+which is bad news because that means you
+
+ align:start position:0%
+which is bad news because that means you
+ 
+
+ align:start position:0%
+which is bad news because that means you
+don't have access to the gaussin Arsenal
+
+ align:start position:0%
+don't have access to the gaussin Arsenal
+ 
+
+ align:start position:0%
+don't have access to the gaussin Arsenal
+and nobody wants to do this so actually
+
+ align:start position:0%
+and nobody wants to do this so actually
+ 
+
+ align:start position:0%
+and nobody wants to do this so actually
+this is a mistake that people do a lot
+
+ align:start position:0%
+this is a mistake that people do a lot
+ 
+
+ align:start position:0%
+this is a mistake that people do a lot
+they use the kov smor test to test for
+
+ align:start position:0%
+they use the kov smor test to test for
+ 
+
+ align:start position:0%
+they use the kov smor test to test for
+normality without adjusting for the fact
+
+ align:start position:0%
+normality without adjusting for the fact
+ 
+
+ align:start position:0%
+normality without adjusting for the fact
+that they've plugged in the estimated
+
+ align:start position:0%
+that they've plugged in the estimated
+ 
+
+ align:start position:0%
+that they've plugged in the estimated
+mean and the estimated variance this
+
+ align:start position:0%
+mean and the estimated variance this
+ 
+
+ align:start position:0%
+mean and the estimated variance this
+leads to rejecting less often right I
+
+ align:start position:0%
+leads to rejecting less often right I
+ 
+
+ align:start position:0%
+leads to rejecting less often right I
+mean this is almost half of the number
+
+ align:start position:0%
+mean this is almost half of the number
+ 
+
+ align:start position:0%
+mean this is almost half of the number
+that we
+
+ align:start position:0%
+that we
+ 
+
+ align:start position:0%
+that we
+had and then there can be happy and walk
+
+ align:start position:0%
+had and then there can be happy and walk
+ 
+
+ align:start position:0%
+had and then there can be happy and walk
+home and say well I did the test and it
+
+ align:start position:0%
+home and say well I did the test and it
+ 
+
+ align:start position:0%
+home and say well I did the test and it
+was normal so this is actually a mistake
+
+ align:start position:0%
+was normal so this is actually a mistake
+ 
+
+ align:start position:0%
+was normal so this is actually a mistake
+that I believe that genuinely at least a
+
+ align:start position:0%
+that I believe that genuinely at least a
+ 
+
+ align:start position:0%
+that I believe that genuinely at least a
+quarter of the people do make in purpose
+
+ align:start position:0%
+quarter of the people do make in purpose
+ 
+
+ align:start position:0%
+quarter of the people do make in purpose
+they say well I wanted it to be gaon so
+
+ align:start position:0%
+they say well I wanted it to be gaon so
+ 
+
+ align:start position:0%
+they say well I wanted it to be gaon so
+I'm just going to make my life easier
+
+ align:start position:0%
+I'm just going to make my life easier
+ 
+
+ align:start position:0%
+I'm just going to make my life easier
+all right so um this is the So-Cal kog
+
+ align:start position:0%
+all right so um this is the So-Cal kog
+ 
+
+ align:start position:0%
+all right so um this is the So-Cal kog
+leader force test we'll talk about it
+
+ align:start position:0%
+leader force test we'll talk about it
+ 
+
+ align:start position:0%
+leader force test we'll talk about it
+well not today for sure um there's other
+
+ align:start position:0%
+well not today for sure um there's other
+ 
+
+ align:start position:0%
+well not today for sure um there's other
+uh statistics that you can test that you
+
+ align:start position:0%
+uh statistics that you can test that you
+ 
+
+ align:start position:0%
+uh statistics that you can test that you
+can use and the idea is to say well we
+
+ align:start position:0%
+can use and the idea is to say well we
+ 
+
+ align:start position:0%
+can use and the idea is to say well we
+want to know if the empirical
+
+ align:start position:0%
+want to know if the empirical
+ 
+
+ align:start position:0%
+want to know if the empirical
+distribution function the empirical CDF
+
+ align:start position:0%
+distribution function the empirical CDF
+ 
+
+ align:start position:0%
+distribution function the empirical CDF
+is close to the true CDF the way we did
+
+ align:start position:0%
+is close to the true CDF the way we did
+ 
+
+ align:start position:0%
+is close to the true CDF the way we did
+it is by forming the difference and
+
+ align:start position:0%
+it is by forming the difference and
+ 
+
+ align:start position:0%
+it is by forming the difference and
+looking at the worst possible distance
+
+ align:start position:0%
+looking at the worst possible distance
+ 
+
+ align:start position:0%
+looking at the worst possible distance
+they can be that's called a sub Norm or
+
+ align:start position:0%
+they can be that's called a sub Norm or
+ 
+
+ align:start position:0%
+they can be that's called a sub Norm or
+L Infinity Norm in in functional
+
+ align:start position:0%
+L Infinity Norm in in functional
+ 
+
+ align:start position:0%
+L Infinity Norm in in functional
+analysis so here this is what it looked
+
+ align:start position:0%
+analysis so here this is what it looked
+ 
+
+ align:start position:0%
+analysis so here this is what it looked
+like right the distance between FN and f
+
+ align:start position:0%
+like right the distance between FN and f
+ 
+
+ align:start position:0%
+like right the distance between FN and f
+that we measured was just the supremum
+
+ align:start position:0%
+that we measured was just the supremum
+ 
+
+ align:start position:0%
+that we measured was just the supremum
+distance over all T's that's one way to
+
+ align:start position:0%
+distance over all T's that's one way to
+ 
+
+ align:start position:0%
+distance over all T's that's one way to
+measure distance between two functions
+
+ align:start position:0%
+measure distance between two functions
+ 
+
+ align:start position:0%
+measure distance between two functions
+but there's an infinite way many ways to
+
+ align:start position:0%
+but there's an infinite way many ways to
+ 
+
+ align:start position:0%
+but there's an infinite way many ways to
+measure distance between functions one
+
+ align:start position:0%
+measure distance between functions one
+ 
+
+ align:start position:0%
+measure distance between functions one
+is something we're much more familiar
+
+ align:start position:0%
+is something we're much more familiar
+ 
+
+ align:start position:0%
+is something we're much more familiar
+with which is the square L2
+
+ align:start position:0%
+with which is the square L2
+ 
+
+ align:start position:0%
+with which is the square L2
+Norm this is nice because this has like
+
+ align:start position:0%
+Norm this is nice because this has like
+ 
+
+ align:start position:0%
+Norm this is nice because this has like
+a inner product it has some nice
+
+ align:start position:0%
+a inner product it has some nice
+ 
+
+ align:start position:0%
+a inner product it has some nice
+properties and you could actually just
+
+ align:start position:0%
+properties and you could actually just
+ 
+
+ align:start position:0%
+properties and you could actually just
+rather than taking the soup you could
+
+ align:start position:0%
+rather than taking the soup you could
+ 
+
+ align:start position:0%
+rather than taking the soup you could
+just integrate the square
+
+ align:start position:0%
+just integrate the square
+ 
+
+ align:start position:0%
+just integrate the square
+distance and this is what leads to CR
+
+ align:start position:0%
+distance and this is what leads to CR
+ 
+
+ align:start position:0%
+distance and this is what leads to CR
+irin Miz's
+
+ align:start position:0%
+irin Miz's
+ 
+
+ align:start position:0%
+irin Miz's
+test and then there's another one that
+
+ align:start position:0%
+test and then there's another one that
+ 
+
+ align:start position:0%
+test and then there's another one that
+says well maybe I don't want to
+
+ align:start position:0%
+says well maybe I don't want to
+ 
+
+ align:start position:0%
+says well maybe I don't want to
+integrate without weights maybe I want
+
+ align:start position:0%
+integrate without weights maybe I want
+ 
+
+ align:start position:0%
+integrate without weights maybe I want
+to put weights that account for the
+
+ align:start position:0%
+to put weights that account for the
+ 
+
+ align:start position:0%
+to put weights that account for the
+variance and this guy is called Anderson
+
+ align:start position:0%
+variance and this guy is called Anderson
+ 
+
+ align:start position:0%
+variance and this guy is called Anderson
+darling for each each of this tests you
+
+ align:start position:0%
+darling for each each of this tests you
+ 
+
+ align:start position:0%
+darling for each each of this tests you
+can check that the ASM totic
+
+ align:start position:0%
+can check that the ASM totic
+ 
+
+ align:start position:0%
+can check that the ASM totic
+distribution is going to be pivotal
+
+ align:start position:0%
+distribution is going to be pivotal
+ 
+
+ align:start position:0%
+distribution is going to be pivotal
+which means that there will be a table
+
+ align:start position:0%
+which means that there will be a table
+ 
+
+ align:start position:0%
+which means that there will be a table
+at the back of some book that tells you
+
+ align:start position:0%
+at the back of some book that tells you
+ 
+
+ align:start position:0%
+at the back of some book that tells you
+what the uh uh statistic the the quental
+
+ align:start position:0%
+what the uh uh statistic the the quental
+ 
+
+ align:start position:0%
+what the uh uh statistic the the quental
+of square root of n times this guy are
+
+ align:start position:0%
+of square root of n times this guy are
+ 
+
+ align:start position:0%
+of square root of n times this guy are
+ASM totically basically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah so that's just to show you
+
+ align:start position:0%
+yeah yeah so that's just to show you
+ 
+
+ align:start position:0%
+yeah yeah so that's just to show you
+that ASM totically it's pivotal and I
+
+ align:start position:0%
+that ASM totically it's pivotal and I
+ 
+
+ align:start position:0%
+that ASM totically it's pivotal and I
+can point you to one specific thing but
+
+ align:start position:0%
+can point you to one specific thing but
+ 
+
+ align:start position:0%
+can point you to one specific thing but
+it turns out that this thing is actually
+
+ align:start position:0%
+it turns out that this thing is actually
+ 
+
+ align:start position:0%
+it turns out that this thing is actually
+pivotal for each n and that's why you
+
+ align:start position:0%
+pivotal for each n and that's why you
+ 
+
+ align:start position:0%
+pivotal for each n and that's why you
+have this recipe to construct the entire
+
+ align:start position:0%
+have this recipe to construct the entire
+ 
+
+ align:start position:0%
+have this recipe to construct the entire
+thing because it's actually not true for
+
+ align:start position:0%
+thing because it's actually not true for
+ 
+
+ align:start position:0%
+thing because it's actually not true for
+all possible ends also there's the nend
+
+ align:start position:0%
+all possible ends also there's the nend
+ 
+
+ align:start position:0%
+all possible ends also there's the nend
+that shows up here so um no actually
+
+ align:start position:0%
+that shows up here so um no actually
+ 
+
+ align:start position:0%
+that shows up here so um no actually
+this is something you should have in
+
+ align:start position:0%
+this is something you should have in
+ 
+
+ align:start position:0%
+this is something you should have in
+mind okay so basically uh let me let me
+
+ align:start position:0%
+mind okay so basically uh let me let me
+ 
+
+ align:start position:0%
+mind okay so basically uh let me let me
+uh strike what I just said this thing
+
+ align:start position:0%
+uh strike what I just said this thing
+ 
+
+ align:start position:0%
+uh strike what I just said this thing
+you can actually this distribution will
+
+ align:start position:0%
+you can actually this distribution will
+ 
+
+ align:start position:0%
+you can actually this distribution will
+not depend on
+
+ align:start position:0%
+not depend on
+ 
+
+ align:start position:0%
+not depend on
+f0o for any particular n it's just not
+
+ align:start position:0%
+f0o for any particular n it's just not
+ 
+
+ align:start position:0%
+f0o for any particular n it's just not
+going to be a brown and bridge but a
+
+ align:start position:0%
+going to be a brown and bridge but a
+ 
+
+ align:start position:0%
+going to be a brown and bridge but a
+finite sample approximation of a brown
+
+ align:start position:0%
+finite sample approximation of a brown
+ 
+
+ align:start position:0%
+finite sample approximation of a brown
+and Bridge and you can simulate that
+
+ align:start position:0%
+and Bridge and you can simulate that
+ 
+
+ align:start position:0%
+and Bridge and you can simulate that
+just drawing samples from it building a
+
+ align:start position:0%
+just drawing samples from it building a
+ 
+
+ align:start position:0%
+just drawing samples from it building a
+histogram and constructing the quentes
+
+ align:start position:0%
+histogram and constructing the quentes
+ 
+
+ align:start position:0%
+histogram and constructing the quentes
+for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guy oh there is one that's the table
+
+ align:start position:0%
+guy oh there is one that's the table
+ 
+
+ align:start position:0%
+guy oh there is one that's the table
+right uh maybe uh let's see if we see it
+
+ align:start position:0%
+right uh maybe uh let's see if we see it
+ 
+
+ align:start position:0%
+right uh maybe uh let's see if we see it
+at the bottom of the other
+
+ align:start position:0%
+at the bottom of the other
+ 
+
+ align:start position:0%
+at the bottom of the other
+table yeah see over 40 over 30 so this
+
+ align:start position:0%
+table yeah see over 40 over 30 so this
+ 
+
+ align:start position:0%
+table yeah see over 40 over 30 so this
+is not the kog SM but that's the kog L
+
+ align:start position:0%
+is not the kog SM but that's the kog L
+ 
+
+ align:start position:0%
+is not the kog SM but that's the kog L
+Force those numbers that you see here
+
+ align:start position:0%
+Force those numbers that you see here
+ 
+
+ align:start position:0%
+Force those numbers that you see here
+they're the numbers for the ASM totic
+
+ align:start position:0%
+they're the numbers for the ASM totic
+ 
+
+ align:start position:0%
+they're the numbers for the ASM totic
+thing which is some sort of bar and
+
+ align:start position:0%
+thing which is some sort of bar and
+ 
+
+ align:start position:0%
+thing which is some sort of bar and
+Bridge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so then you won't have this nice
+
+ align:start position:0%
+yeah so then you won't have this nice
+ 
+
+ align:start position:0%
+yeah so then you won't have this nice
+picture right this can happen at any
+
+ align:start position:0%
+picture right this can happen at any
+ 
+
+ align:start position:0%
+picture right this can happen at any
+point because you're going to have
+
+ align:start position:0%
+point because you're going to have
+ 
+
+ align:start position:0%
+point because you're going to have
+discontinuities in F and those things
+
+ align:start position:0%
+discontinuities in F and those things
+ 
+
+ align:start position:0%
+discontinuities in F and those things
+can happen everywhere and
+
+ align:start position:0%
+can happen everywhere and
+ 
+
+ align:start position:0%
+can happen everywhere and
+then Oh you mean the brown and Bridge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah no no no but you still need it you
+
+ align:start position:0%
+yeah no no no but you still need it you
+ 
+
+ align:start position:0%
+yeah no no no but you still need it you
+still need it for so there's there's
+
+ align:start position:0%
+still need it for so there's there's
+ 
+
+ align:start position:0%
+still need it for so there's there's
+some finite sample versions of it that
+
+ align:start position:0%
+some finite sample versions of it that
+ 
+
+ align:start position:0%
+some finite sample versions of it that
+you can use that are slightly more
+
+ align:start position:0%
+you can use that are slightly more
+ 
+
+ align:start position:0%
+you can use that are slightly more
+conservative so which is in way of good
+
+ align:start position:0%
+conservative so which is in way of good
+ 
+
+ align:start position:0%
+conservative so which is in way of good
+news because you're going to conclude
+
+ align:start position:0%
+news because you're going to conclude
+ 
+
+ align:start position:0%
+news because you're going to conclude
+more to H zero and there's some you know
+
+ align:start position:0%
+more to H zero and there's some you know
+ 
+
+ align:start position:0%
+more to H zero and there's some you know
+I forget the name it's uh uh Keir wol
+
+ align:start position:0%
+I forget the name it's uh uh Keir wol
+ 
+
+ align:start position:0%
+I forget the name it's uh uh Keir wol
+ofit keford vetki wol ofit inequality
+
+ align:start position:0%
+ofit keford vetki wol ofit inequality
+ 
+
+ align:start position:0%
+ofit keford vetki wol ofit inequality
+which is basically like hings inequality
+
+ align:start position:0%
+which is basically like hings inequality
+ 
+
+ align:start position:0%
+which is basically like hings inequality
+so it's basically up tobat constants
+
+ align:start position:0%
+so it's basically up tobat constants
+ 
+
+ align:start position:0%
+so it's basically up tobat constants
+telling you the same result as the brown
+
+ align:start position:0%
+telling you the same result as the brown
+ 
+
+ align:start position:0%
+telling you the same result as the brown
+and Bridge result and those are true all
+
+ align:start position:0%
+and Bridge result and those are true all
+ 
+
+ align:start position:0%
+and Bridge result and those are true all
+the time uh but for the exact ASM totic
+
+ align:start position:0%
+the time uh but for the exact ASM totic
+ 
+
+ align:start position:0%
+the time uh but for the exact ASM totic
+distribution you need continuity
+
+ align:start position:0%
+distribution you need continuity
+ 
+
+ align:start position:0%
+distribution you need continuity
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes well if you know what they are you
+
+ align:start position:0%
+yes well if you know what they are you
+ 
+
+ align:start position:0%
+yes well if you know what they are you
+can use kov smof but if you don't know
+
+ align:start position:0%
+can use kov smof but if you don't know
+ 
+
+ align:start position:0%
+can use kov smof but if you don't know
+what they are are you're going to plug
+
+ align:start position:0%
+what they are are you're going to plug
+ 
+
+ align:start position:0%
+what they are are you're going to plug
+in as soon as you're going to estimate
+
+ align:start position:0%
+in as soon as you're going to estimate
+ 
+
+ align:start position:0%
+in as soon as you're going to estimate
+the mean and the variance from the data
+
+ align:start position:0%
+the mean and the variance from the data
+ 
+
+ align:start position:0%
+the mean and the variance from the data
+you're going to you should use the one
+
+ align:start position:0%
+you're going to you should use the one
+ 
+
+ align:start position:0%
+you're going to you should use the one
+we'll see next time which is called kog
+
+ align:start position:0%
+we'll see next time which is called kog
+ 
+
+ align:start position:0%
+we'll see next time which is called kog
+L Force don't have to think about it too
+
+ align:start position:0%
+L Force don't have to think about it too
+ 
+
+ align:start position:0%
+L Force don't have to think about it too
+much we'll talk about it on Thursday
+
+ align:start position:0%
+much we'll talk about it on Thursday
+ 
+
+ align:start position:0%
+much we'll talk about it on Thursday
+yeah any other question so we're out of
+
+ align:start position:0%
+yeah any other question so we're out of
+ 
+
+ align:start position:0%
+yeah any other question so we're out of
+time so uh I think uh we should stop
+
+ align:start position:0%
+time so uh I think uh we should stop
+ 
+
+ align:start position:0%
+time so uh I think uh we should stop
+here and we'll see uh we we'll resume on
+
+ align:start position:0%
+here and we'll see uh we we'll resume on
+ 
+
+ align:start position:0%
+here and we'll see uh we we'll resume on
+Thursday
\ No newline at end of file
diff --git a/aWLS9GE3elo.txt b/aWLS9GE3elo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9beae1713d34e27c6344b169fa5e3698660b8ac1
--- /dev/null
+++ b/aWLS9GE3elo.txt
@@ -0,0 +1,10795 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT opencourseware continue to
+
+ align:start position:0%
+will help MIT opencourseware continue to
+ 
+
+ align:start position:0%
+will help MIT opencourseware continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free to make a donation or to view
+
+ align:start position:0%
+for free to make a donation or to view
+ 
+
+ align:start position:0%
+for free to make a donation or to view
+additional materials from hundreds of
+
+ align:start position:0%
+additional materials from hundreds of
+ 
+
+ align:start position:0%
+additional materials from hundreds of
+MIT courses visit MIT opencourseware at
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ 
+
+ align:start position:0%
+MIT courses visit MIT opencourseware at
+ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I understand just terrific terrific
+
+ align:start position:0%
+I understand just terrific terrific
+ 
+
+ align:start position:0%
+I understand just terrific terrific
+amount of work he was also a tarpa
+
+ align:start position:0%
+amount of work he was also a tarpa
+ 
+
+ align:start position:0%
+amount of work he was also a tarpa
+program manager where he led the effort
+
+ align:start position:0%
+program manager where he led the effort
+ 
+
+ align:start position:0%
+program manager where he led the effort
+that we have studied in the class the
+
+ align:start position:0%
+that we have studied in the class the
+ 
+
+ align:start position:0%
+that we have studied in the class the
+origami lens and many interesting
+
+ align:start position:0%
+origami lens and many interesting
+ 
+
+ align:start position:0%
+origami lens and many interesting
+projects so here today is going to talk
+
+ align:start position:0%
+projects so here today is going to talk
+ 
+
+ align:start position:0%
+projects so here today is going to talk
+about something that hopefully get us
+
+ align:start position:0%
+about something that hopefully get us
+ 
+
+ align:start position:0%
+about something that hopefully get us
+thinking it's just at the right time you
+
+ align:start position:0%
+thinking it's just at the right time you
+ 
+
+ align:start position:0%
+thinking it's just at the right time you
+know it's the middle of the semester and
+
+ align:start position:0%
+know it's the middle of the semester and
+ 
+
+ align:start position:0%
+know it's the middle of the semester and
+we have learned about a lot of ideas
+
+ align:start position:0%
+we have learned about a lot of ideas
+ 
+
+ align:start position:0%
+we have learned about a lot of ideas
+and always enjoyed talking to Ravi about
+
+ align:start position:0%
+and always enjoyed talking to Ravi about
+ 
+
+ align:start position:0%
+and always enjoyed talking to Ravi about
+you know where the field is going and
+
+ align:start position:0%
+you know where the field is going and
+ 
+
+ align:start position:0%
+you know where the field is going and
+how we can how we can how we can kind of
+
+ align:start position:0%
+how we can how we can how we can kind of
+ 
+
+ align:start position:0%
+how we can how we can how we can kind of
+classify and understand the feel itself
+
+ align:start position:0%
+classify and understand the feel itself
+ 
+
+ align:start position:0%
+classify and understand the feel itself
+of computational Imaging and
+
+ align:start position:0%
+of computational Imaging and
+ 
+
+ align:start position:0%
+of computational Imaging and
+computational Camera better so looking
+
+ align:start position:0%
+computational Camera better so looking
+ 
+
+ align:start position:0%
+computational Camera better so looking
+forward to it thank you thanks very much
+
+ align:start position:0%
+forward to it thank you thanks very much
+ 
+
+ align:start position:0%
+forward to it thank you thanks very much
+it's a pleasure to come here and talk
+
+ align:start position:0%
+it's a pleasure to come here and talk
+ 
+
+ align:start position:0%
+it's a pleasure to come here and talk
+about this index all of us love so much
+
+ align:start position:0%
+about this index all of us love so much
+ 
+
+ align:start position:0%
+about this index all of us love so much
+cameras and this I worked a lot on this
+
+ align:start position:0%
+cameras and this I worked a lot on this
+ 
+
+ align:start position:0%
+cameras and this I worked a lot on this
+title cameras we cannot picture so
+
+ align:start position:0%
+title cameras we cannot picture so
+ 
+
+ align:start position:0%
+title cameras we cannot picture so
+anyway I sent the slides to Ramesh ahead
+
+ align:start position:0%
+anyway I sent the slides to Ramesh ahead
+ 
+
+ align:start position:0%
+anyway I sent the slides to Ramesh ahead
+of time to make sure I didn't know of
+
+ align:start position:0%
+of time to make sure I didn't know of
+ 
+
+ align:start position:0%
+of time to make sure I didn't know of
+the how to calibrate where to go
+
+ align:start position:0%
+the how to calibrate where to go
+ 
+
+ align:start position:0%
+the how to calibrate where to go
+but he said that these slides are just
+
+ align:start position:0%
+but he said that these slides are just
+ 
+
+ align:start position:0%
+but he said that these slides are just
+perfect so I trust his judgment and I I
+
+ align:start position:0%
+perfect so I trust his judgment and I I
+ 
+
+ align:start position:0%
+perfect so I trust his judgment and I I
+want it not not just of the seminar or
+
+ align:start position:0%
+want it not not just of the seminar or
+ 
+
+ align:start position:0%
+want it not not just of the seminar or
+lecture but a lot more interactive so we
+
+ align:start position:0%
+lecture but a lot more interactive so we
+ 
+
+ align:start position:0%
+lecture but a lot more interactive so we
+can go through some of these very
+
+ align:start position:0%
+can go through some of these very
+ 
+
+ align:start position:0%
+can go through some of these very
+quickly if I see from your faces that
+
+ align:start position:0%
+quickly if I see from your faces that
+ 
+
+ align:start position:0%
+quickly if I see from your faces that
+you know why is he telling us these
+
+ align:start position:0%
+you know why is he telling us these
+ 
+
+ align:start position:0%
+you know why is he telling us these
+things but
+
+ align:start position:0%
+things but
+ 
+
+ align:start position:0%
+things but
+uh B is as it may so you know history of
+
+ align:start position:0%
+uh B is as it may so you know history of
+ 
+
+ align:start position:0%
+uh B is as it may so you know history of
+camera I think this was meant did more
+
+ align:start position:0%
+camera I think this was meant did more
+ 
+
+ align:start position:0%
+camera I think this was meant did more
+for General audience so I really focused
+
+ align:start position:0%
+for General audience so I really focused
+ 
+
+ align:start position:0%
+for General audience so I really focused
+a lot on history and how we are at a
+
+ align:start position:0%
+a lot on history and how we are at a
+ 
+
+ align:start position:0%
+a lot on history and how we are at a
+dramatic breakpoint how that breakpoint
+
+ align:start position:0%
+dramatic breakpoint how that breakpoint
+ 
+
+ align:start position:0%
+dramatic breakpoint how that breakpoint
+is likely to impact the future and
+
+ align:start position:0%
+is likely to impact the future and
+ 
+
+ align:start position:0%
+is likely to impact the future and
+things like that so
+
+ align:start position:0%
+things like that so
+ 
+
+ align:start position:0%
+things like that so
+interesting historical Milestones that
+
+ align:start position:0%
+interesting historical Milestones that
+ 
+
+ align:start position:0%
+interesting historical Milestones that
+you may or may not have covered in the
+
+ align:start position:0%
+you may or may not have covered in the
+ 
+
+ align:start position:0%
+you may or may not have covered in the
+class but let's let's go with that
+
+ align:start position:0%
+class but let's let's go with that
+ 
+
+ align:start position:0%
+class but let's let's go with that
+but uh this is one thing of course now
+
+ align:start position:0%
+but uh this is one thing of course now
+ 
+
+ align:start position:0%
+but uh this is one thing of course now
+if you need to be told about uh this uh
+
+ align:start position:0%
+if you need to be told about uh this uh
+ 
+
+ align:start position:0%
+if you need to be told about uh this uh
+you all are carrying cameras
+
+ align:start position:0%
+you all are carrying cameras
+ 
+
+ align:start position:0%
+you all are carrying cameras
+that if you lived in London you probably
+
+ align:start position:0%
+that if you lived in London you probably
+ 
+
+ align:start position:0%
+that if you lived in London you probably
+got photographed about 30 to 40 times
+
+ align:start position:0%
+got photographed about 30 to 40 times
+ 
+
+ align:start position:0%
+got photographed about 30 to 40 times
+during a typical work day as you stepped
+
+ align:start position:0%
+during a typical work day as you stepped
+ 
+
+ align:start position:0%
+during a typical work day as you stepped
+outside and all these things I I just
+
+ align:start position:0%
+outside and all these things I I just
+ 
+
+ align:start position:0%
+outside and all these things I I just
+want to point out too I don't know how
+
+ align:start position:0%
+want to point out too I don't know how
+ 
+
+ align:start position:0%
+want to point out too I don't know how
+many of you will sort of know what that
+
+ align:start position:0%
+many of you will sort of know what that
+ 
+
+ align:start position:0%
+many of you will sort of know what that
+image is
+
+ align:start position:0%
+image is
+ 
+
+ align:start position:0%
+image is
+uh in order to know what that image is
+
+ align:start position:0%
+uh in order to know what that image is
+ 
+
+ align:start position:0%
+uh in order to know what that image is
+you need to focus on the date April 19
+
+ align:start position:0%
+you need to focus on the date April 19
+ 
+
+ align:start position:0%
+you need to focus on the date April 19
+1995.
+
+ align:start position:0%
+1995.
+ 
+
+ align:start position:0%
+1995.
+that date has a special significance
+
+ align:start position:0%
+that date has a special significance
+ 
+
+ align:start position:0%
+that date has a special significance
+that was the Oklahoma City bombing and
+
+ align:start position:0%
+that was the Oklahoma City bombing and
+ 
+
+ align:start position:0%
+that was the Oklahoma City bombing and
+this is the truck this is the rider
+
+ align:start position:0%
+this is the truck this is the rider
+ 
+
+ align:start position:0%
+this is the truck this is the rider
+truck that carrying the bomb and this is
+
+ align:start position:0%
+truck that carrying the bomb and this is
+ 
+
+ align:start position:0%
+truck that carrying the bomb and this is
+a picture from a security camera in the
+
+ align:start position:0%
+a picture from a security camera in the
+ 
+
+ align:start position:0%
+a picture from a security camera in the
+bank across the street and this image
+
+ align:start position:0%
+bank across the street and this image
+ 
+
+ align:start position:0%
+bank across the street and this image
+has been used by many many people to
+
+ align:start position:0%
+has been used by many many people to
+ 
+
+ align:start position:0%
+has been used by many many people to
+justify the work on high Dynamic
+
+ align:start position:0%
+justify the work on high Dynamic
+ 
+
+ align:start position:0%
+justify the work on high Dynamic
+limiting everything inside is completely
+
+ align:start position:0%
+limiting everything inside is completely
+ 
+
+ align:start position:0%
+limiting everything inside is completely
+underexposed everything outside is
+
+ align:start position:0%
+underexposed everything outside is
+ 
+
+ align:start position:0%
+underexposed everything outside is
+completely Overexposed as a result this
+
+ align:start position:0%
+completely Overexposed as a result this
+ 
+
+ align:start position:0%
+completely Overexposed as a result this
+image by itself is pretty much useless
+
+ align:start position:0%
+image by itself is pretty much useless
+ 
+
+ align:start position:0%
+image by itself is pretty much useless
+so things come in two sizes too big and
+
+ align:start position:0%
+so things come in two sizes too big and
+ 
+
+ align:start position:0%
+so things come in two sizes too big and
+too small so similarly
+
+ align:start position:0%
+too small so similarly
+ 
+
+ align:start position:0%
+too small so similarly
+this is the thing this this is a very
+
+ align:start position:0%
+this is the thing this this is a very
+ 
+
+ align:start position:0%
+this is the thing this this is a very
+interesting thing and I I also had
+
+ align:start position:0%
+interesting thing and I I also had
+ 
+
+ align:start position:0%
+interesting thing and I I also had
+another image of
+
+ align:start position:0%
+another image of
+ 
+
+ align:start position:0%
+another image of
+somewhere in Iraq and IED going off and
+
+ align:start position:0%
+somewhere in Iraq and IED going off and
+ 
+
+ align:start position:0%
+somewhere in Iraq and IED going off and
+blowing up and some person holding the
+
+ align:start position:0%
+blowing up and some person holding the
+ 
+
+ align:start position:0%
+blowing up and some person holding the
+cell phone and so I'm sure you're aware
+
+ align:start position:0%
+cell phone and so I'm sure you're aware
+ 
+
+ align:start position:0%
+cell phone and so I'm sure you're aware
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+over the last few years any significant
+
+ align:start position:0%
+over the last few years any significant
+ 
+
+ align:start position:0%
+over the last few years any significant
+news event that happened in most places
+
+ align:start position:0%
+news event that happened in most places
+ 
+
+ align:start position:0%
+news event that happened in most places
+around the world the first reports in
+
+ align:start position:0%
+around the world the first reports in
+ 
+
+ align:start position:0%
+around the world the first reports in
+the first images to came out come out of
+
+ align:start position:0%
+the first images to came out come out of
+ 
+
+ align:start position:0%
+the first images to came out come out of
+that yourself on campus so everybody's
+
+ align:start position:0%
+that yourself on campus so everybody's
+ 
+
+ align:start position:0%
+that yourself on campus so everybody's
+reported
+
+ align:start position:0%
+reported
+ 
+
+ align:start position:0%
+reported
+so anyway one of the interesting things
+
+ align:start position:0%
+so anyway one of the interesting things
+ 
+
+ align:start position:0%
+so anyway one of the interesting things
+is uh
+
+ align:start position:0%
+is uh
+ 
+
+ align:start position:0%
+is uh
+uh this business about natural
+
+ align:start position:0%
+uh this business about natural
+ 
+
+ align:start position:0%
+uh this business about natural
+observation
+
+ align:start position:0%
+observation
+ 
+
+ align:start position:0%
+observation
+gaps in the leaves projecting images of
+
+ align:start position:0%
+gaps in the leaves projecting images of
+ 
+
+ align:start position:0%
+gaps in the leaves projecting images of
+a partial solar eclipse so
+
+ align:start position:0%
+a partial solar eclipse so
+ 
+
+ align:start position:0%
+a partial solar eclipse so
+our ancestors must have observed these
+
+ align:start position:0%
+our ancestors must have observed these
+ 
+
+ align:start position:0%
+our ancestors must have observed these
+things and said okay something is going
+
+ align:start position:0%
+things and said okay something is going
+ 
+
+ align:start position:0%
+things and said okay something is going
+on so exactly what is going on and how
+
+ align:start position:0%
+on so exactly what is going on and how
+ 
+
+ align:start position:0%
+on so exactly what is going on and how
+can we replicate it how can we
+
+ align:start position:0%
+can we replicate it how can we
+ 
+
+ align:start position:0%
+can we replicate it how can we
+understand what's going on over there
+
+ align:start position:0%
+understand what's going on over there
+ 
+
+ align:start position:0%
+understand what's going on over there
+this is another very beautiful
+
+ align:start position:0%
+this is another very beautiful
+ 
+
+ align:start position:0%
+this is another very beautiful
+photograph I'm sure
+
+ align:start position:0%
+photograph I'm sure
+ 
+
+ align:start position:0%
+photograph I'm sure
+watercraft acting as a lens forming the
+
+ align:start position:0%
+watercraft acting as a lens forming the
+ 
+
+ align:start position:0%
+watercraft acting as a lens forming the
+image so just before there was any
+
+ align:start position:0%
+image so just before there was any
+ 
+
+ align:start position:0%
+image so just before there was any
+technology before there was even a
+
+ align:start position:0%
+technology before there was even a
+ 
+
+ align:start position:0%
+technology before there was even a
+formal modern scientific process
+
+ align:start position:0%
+formal modern scientific process
+ 
+
+ align:start position:0%
+formal modern scientific process
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+our ancestors couple of thousand years
+
+ align:start position:0%
+our ancestors couple of thousand years
+ 
+
+ align:start position:0%
+our ancestors couple of thousand years
+ago since they didn't have the
+
+ align:start position:0%
+ago since they didn't have the
+ 
+
+ align:start position:0%
+ago since they didn't have the
+distractions of cable TV and cell phones
+
+ align:start position:0%
+distractions of cable TV and cell phones
+ 
+
+ align:start position:0%
+distractions of cable TV and cell phones
+and all that they had a lot of time to
+
+ align:start position:0%
+and all that they had a lot of time to
+ 
+
+ align:start position:0%
+and all that they had a lot of time to
+really very carefully observe nature and
+
+ align:start position:0%
+really very carefully observe nature and
+ 
+
+ align:start position:0%
+really very carefully observe nature and
+observe it over a long period of time
+
+ align:start position:0%
+observe it over a long period of time
+ 
+
+ align:start position:0%
+observe it over a long period of time
+for many different angles so as an
+
+ align:start position:0%
+for many different angles so as an
+ 
+
+ align:start position:0%
+for many different angles so as an
+outcome of this
+
+ align:start position:0%
+outcome of this
+ 
+
+ align:start position:0%
+outcome of this
+was the observation of pinhole images
+
+ align:start position:0%
+was the observation of pinhole images
+ 
+
+ align:start position:0%
+was the observation of pinhole images
+going back several thousand years
+
+ align:start position:0%
+going back several thousand years
+ 
+
+ align:start position:0%
+going back several thousand years
+and I believe I at least I understand
+
+ align:start position:0%
+and I believe I at least I understand
+ 
+
+ align:start position:0%
+and I believe I at least I understand
+that this was the first comprehensive
+
+ align:start position:0%
+that this was the first comprehensive
+ 
+
+ align:start position:0%
+that this was the first comprehensive
+study on Optics al-hazam and
+
+ align:start position:0%
+study on Optics al-hazam and
+ 
+
+ align:start position:0%
+study on Optics al-hazam and
+this is the drawing of a pinhole camera
+
+ align:start position:0%
+this is the drawing of a pinhole camera
+ 
+
+ align:start position:0%
+this is the drawing of a pinhole camera
+I think Ramesh you have probably told
+
+ align:start position:0%
+I think Ramesh you have probably told
+ 
+
+ align:start position:0%
+I think Ramesh you have probably told
+them about the origin of the word
+
+ align:start position:0%
+them about the origin of the word
+ 
+
+ align:start position:0%
+them about the origin of the word
+you yeah I have not oh you have not okay
+
+ align:start position:0%
+you yeah I have not oh you have not okay
+ 
+
+ align:start position:0%
+you yeah I have not oh you have not okay
+um camera the literal meaning of the
+
+ align:start position:0%
+um camera the literal meaning of the
+ 
+
+ align:start position:0%
+um camera the literal meaning of the
+word is room
+
+ align:start position:0%
+word is room
+ 
+
+ align:start position:0%
+word is room
+because the first camera was in need a
+
+ align:start position:0%
+because the first camera was in need a
+ 
+
+ align:start position:0%
+because the first camera was in need a
+room with a pole there and the image
+
+ align:start position:0%
+room with a pole there and the image
+ 
+
+ align:start position:0%
+room with a pole there and the image
+projected back there so you can trace it
+
+ align:start position:0%
+projected back there so you can trace it
+ 
+
+ align:start position:0%
+projected back there so you can trace it
+or something like that
+
+ align:start position:0%
+or something like that
+ 
+
+ align:start position:0%
+or something like that
+now what is interesting is fast forward
+
+ align:start position:0%
+now what is interesting is fast forward
+ 
+
+ align:start position:0%
+now what is interesting is fast forward
+A Thousand Years
+
+ align:start position:0%
+A Thousand Years
+ 
+
+ align:start position:0%
+A Thousand Years
+and the world's largest pinhole camera
+
+ align:start position:0%
+and the world's largest pinhole camera
+ 
+
+ align:start position:0%
+and the world's largest pinhole camera
+was constructed in July 2006. where El
+
+ align:start position:0%
+was constructed in July 2006. where El
+ 
+
+ align:start position:0%
+was constructed in July 2006. where El
+Toro Marine Corps Air Station in Irvine
+
+ align:start position:0%
+Toro Marine Corps Air Station in Irvine
+ 
+
+ align:start position:0%
+Toro Marine Corps Air Station in Irvine
+was decommissioned they wanted to
+
+ align:start position:0%
+was decommissioned they wanted to
+ 
+
+ align:start position:0%
+was decommissioned they wanted to
+preserve it
+
+ align:start position:0%
+preserve it
+ 
+
+ align:start position:0%
+preserve it
+so they took an airplane hangar closed
+
+ align:start position:0%
+so they took an airplane hangar closed
+ 
+
+ align:start position:0%
+so they took an airplane hangar closed
+the door and drilled a hole the size
+
+ align:start position:0%
+the door and drilled a hole the size
+ 
+
+ align:start position:0%
+the door and drilled a hole the size
+about a tennis ball or something and on
+
+ align:start position:0%
+about a tennis ball or something and on
+ 
+
+ align:start position:0%
+about a tennis ball or something and on
+the back side had a photographic film
+
+ align:start position:0%
+the back side had a photographic film
+ 
+
+ align:start position:0%
+the back side had a photographic film
+eight stories tall and one-third the
+
+ align:start position:0%
+eight stories tall and one-third the
+ 
+
+ align:start position:0%
+eight stories tall and one-third the
+length
+
+ align:start position:0%
+length
+ 
+
+ align:start position:0%
+length
+and here it is
+
+ align:start position:0%
+and here it is
+ 
+
+ align:start position:0%
+and here it is
+this is the image of the base upside
+
+ align:start position:0%
+this is the image of the base upside
+ 
+
+ align:start position:0%
+this is the image of the base upside
+down projector on the back wall this is
+
+ align:start position:0%
+down projector on the back wall this is
+ 
+
+ align:start position:0%
+down projector on the back wall this is
+the this is the photographic Emulsion
+
+ align:start position:0%
+the this is the photographic Emulsion
+ 
+
+ align:start position:0%
+the this is the photographic Emulsion
+and there were a lot a lot of numbers as
+
+ align:start position:0%
+and there were a lot a lot of numbers as
+ 
+
+ align:start position:0%
+and there were a lot a lot of numbers as
+to how many gallons of developer
+
+ align:start position:0%
+to how many gallons of developer
+ 
+
+ align:start position:0%
+to how many gallons of developer
+solution they needed and basically throw
+
+ align:start position:0%
+solution they needed and basically throw
+ 
+
+ align:start position:0%
+solution they needed and basically throw
+it over a barrel and take a broom and
+
+ align:start position:0%
+it over a barrel and take a broom and
+ 
+
+ align:start position:0%
+it over a barrel and take a broom and
+spread it over and develop it and I I
+
+ align:start position:0%
+spread it over and develop it and I I
+ 
+
+ align:start position:0%
+spread it over and develop it and I I
+don't know where that image is now I
+
+ align:start position:0%
+don't know where that image is now I
+ 
+
+ align:start position:0%
+don't know where that image is now I
+think it is in California some art
+
+ align:start position:0%
+think it is in California some art
+ 
+
+ align:start position:0%
+think it is in California some art
+museums somewhere in Los Angeles the
+
+ align:start position:0%
+museums somewhere in Los Angeles the
+ 
+
+ align:start position:0%
+museums somewhere in Los Angeles the
+point of that is over a thousand years
+
+ align:start position:0%
+point of that is over a thousand years
+ 
+
+ align:start position:0%
+point of that is over a thousand years
+and exactly the same operating principle
+
+ align:start position:0%
+and exactly the same operating principle
+ 
+
+ align:start position:0%
+and exactly the same operating principle
+it's just the room except a much much
+
+ align:start position:0%
+it's just the room except a much much
+ 
+
+ align:start position:0%
+it's just the room except a much much
+larger room and taking a picture of a
+
+ align:start position:0%
+larger room and taking a picture of a
+ 
+
+ align:start position:0%
+larger room and taking a picture of a
+much much larger area
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in your lifetime
+
+ align:start position:0%
+in your lifetime
+ 
+
+ align:start position:0%
+in your lifetime
+yes indeed
+
+ align:start position:0%
+yes indeed
+ 
+
+ align:start position:0%
+yes indeed
+uh the first Optical instrument is
+
+ align:start position:0%
+uh the first Optical instrument is
+ 
+
+ align:start position:0%
+uh the first Optical instrument is
+spectacles and I think it really the
+
+ align:start position:0%
+spectacles and I think it really the
+ 
+
+ align:start position:0%
+spectacles and I think it really the
+point this is an interesting point
+
+ align:start position:0%
+point this is an interesting point
+ 
+
+ align:start position:0%
+point this is an interesting point
+spectacles of glasses it really is a
+
+ align:start position:0%
+spectacles of glasses it really is a
+ 
+
+ align:start position:0%
+spectacles of glasses it really is a
+mechanical packaging solution so okay so
+
+ align:start position:0%
+mechanical packaging solution so okay so
+ 
+
+ align:start position:0%
+mechanical packaging solution so okay so
+people realize that having these
+
+ align:start position:0%
+people realize that having these
+ 
+
+ align:start position:0%
+people realize that having these
+specifically shaped lenses improves your
+
+ align:start position:0%
+specifically shaped lenses improves your
+ 
+
+ align:start position:0%
+specifically shaped lenses improves your
+vision but how do you do that how do you
+
+ align:start position:0%
+vision but how do you do that how do you
+ 
+
+ align:start position:0%
+vision but how do you do that how do you
+make it convenient for you to wear
+
+ align:start position:0%
+make it convenient for you to wear
+ 
+
+ align:start position:0%
+make it convenient for you to wear
+so people realize you have two years and
+
+ align:start position:0%
+so people realize you have two years and
+ 
+
+ align:start position:0%
+so people realize you have two years and
+they're shaped in this manner and there
+
+ align:start position:0%
+they're shaped in this manner and there
+ 
+
+ align:start position:0%
+they're shaped in this manner and there
+is the bridge of the nose so three point
+
+ align:start position:0%
+is the bridge of the nose so three point
+ 
+
+ align:start position:0%
+is the bridge of the nose so three point
+support like this of course uh then
+
+ align:start position:0%
+support like this of course uh then
+ 
+
+ align:start position:0%
+support like this of course uh then
+there were all the collaborations of the
+
+ align:start position:0%
+there were all the collaborations of the
+ 
+
+ align:start position:0%
+there were all the collaborations of the
+fences uh glasses sitting or the monocle
+
+ align:start position:0%
+fences uh glasses sitting or the monocle
+ 
+
+ align:start position:0%
+fences uh glasses sitting or the monocle
+that you can screw into your aisle but
+
+ align:start position:0%
+that you can screw into your aisle but
+ 
+
+ align:start position:0%
+that you can screw into your aisle but
+but those were but this is basically
+
+ align:start position:0%
+but those were but this is basically
+ 
+
+ align:start position:0%
+but those were but this is basically
+1270 is the
+
+ align:start position:0%
+1270 is the
+ 
+
+ align:start position:0%
+1270 is the
+taking these Optical phenomena and
+
+ align:start position:0%
+taking these Optical phenomena and
+ 
+
+ align:start position:0%
+taking these Optical phenomena and
+constructing a useful instrument that
+
+ align:start position:0%
+constructing a useful instrument that
+ 
+
+ align:start position:0%
+constructing a useful instrument that
+can be portable and that is used
+
+ align:start position:0%
+can be portable and that is used
+ 
+
+ align:start position:0%
+can be portable and that is used
+beyond that the almost a 300 year Gap
+
+ align:start position:0%
+beyond that the almost a 300 year Gap
+ 
+
+ align:start position:0%
+beyond that the almost a 300 year Gap
+between a single lens Optical instrument
+
+ align:start position:0%
+between a single lens Optical instrument
+ 
+
+ align:start position:0%
+between a single lens Optical instrument
+and a compound articles microscope and
+
+ align:start position:0%
+and a compound articles microscope and
+ 
+
+ align:start position:0%
+and a compound articles microscope and
+then telescope and everything they might
+
+ align:start position:0%
+then telescope and everything they might
+ 
+
+ align:start position:0%
+then telescope and everything they might
+have known this is the 400th anniversary
+
+ align:start position:0%
+have known this is the 400th anniversary
+ 
+
+ align:start position:0%
+have known this is the 400th anniversary
+of the Galilean telescope Revolution and
+
+ align:start position:0%
+of the Galilean telescope Revolution and
+ 
+
+ align:start position:0%
+of the Galilean telescope Revolution and
+this is the diaper to multiple lenses
+
+ align:start position:0%
+this is the diaper to multiple lenses
+ 
+
+ align:start position:0%
+this is the diaper to multiple lenses
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+going forward the next history is
+
+ align:start position:0%
+going forward the next history is
+ 
+
+ align:start position:0%
+going forward the next history is
+photography this is the first photograph
+
+ align:start position:0%
+photography this is the first photograph
+ 
+
+ align:start position:0%
+photography this is the first photograph
+ever by deep sea 1827
+
+ align:start position:0%
+ever by deep sea 1827
+ 
+
+ align:start position:0%
+ever by deep sea 1827
+and it's basically the Civil salt
+
+ align:start position:0%
+and it's basically the Civil salt
+ 
+
+ align:start position:0%
+and it's basically the Civil salt
+sensitive media in various forms and it
+
+ align:start position:0%
+sensitive media in various forms and it
+ 
+
+ align:start position:0%
+sensitive media in various forms and it
+just evolved one of the big
+
+ align:start position:0%
+just evolved one of the big
+ 
+
+ align:start position:0%
+just evolved one of the big
+milestone was instead of glass it was
+
+ align:start position:0%
+milestone was instead of glass it was
+ 
+
+ align:start position:0%
+milestone was instead of glass it was
+quoted on the paper and rolled and other
+
+ align:start position:0%
+quoted on the paper and rolled and other
+ 
+
+ align:start position:0%
+quoted on the paper and rolled and other
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+so this is another tidbit
+
+ align:start position:0%
+so this is another tidbit
+ 
+
+ align:start position:0%
+so this is another tidbit
+Eastman Kodak what does Kodak
+
+ align:start position:0%
+Eastman Kodak what does Kodak
+ 
+
+ align:start position:0%
+Eastman Kodak what does Kodak
+what does Kodak mean anybody knows
+
+ align:start position:0%
+what does Kodak mean anybody knows
+ 
+
+ align:start position:0%
+what does Kodak mean anybody knows
+Eastman wanted a world that was a very
+
+ align:start position:0%
+Eastman wanted a world that was a very
+ 
+
+ align:start position:0%
+Eastman wanted a world that was a very
+crisp world
+
+ align:start position:0%
+crisp world
+ 
+
+ align:start position:0%
+crisp world
+and that was very positive
+
+ align:start position:0%
+and that was very positive
+ 
+
+ align:start position:0%
+and that was very positive
+forward-leaning kind of a world
+
+ align:start position:0%
+forward-leaning kind of a world
+ 
+
+ align:start position:0%
+forward-leaning kind of a world
+and so apparently
+
+ align:start position:0%
+and so apparently
+ 
+
+ align:start position:0%
+and so apparently
+correct is the sound that the shutter
+
+ align:start position:0%
+correct is the sound that the shutter
+ 
+
+ align:start position:0%
+correct is the sound that the shutter
+made
+
+ align:start position:0%
+made
+ 
+
+ align:start position:0%
+made
+so it was not George Eastman and his
+
+ align:start position:0%
+so it was not George Eastman and his
+ 
+
+ align:start position:0%
+so it was not George Eastman and his
+colleague
+
+ align:start position:0%
+colleague
+ 
+
+ align:start position:0%
+colleague
+Kodak was named after but the slogan was
+
+ align:start position:0%
+Kodak was named after but the slogan was
+ 
+
+ align:start position:0%
+Kodak was named after but the slogan was
+you push the button and we do the rest
+
+ align:start position:0%
+you push the button and we do the rest
+ 
+
+ align:start position:0%
+you push the button and we do the rest
+and I think one dollar brownie camera if
+
+ align:start position:0%
+and I think one dollar brownie camera if
+ 
+
+ align:start position:0%
+and I think one dollar brownie camera if
+if you put it in historical context that
+
+ align:start position:0%
+if you put it in historical context that
+ 
+
+ align:start position:0%
+if you put it in historical context that
+was around the same time when Model T
+
+ align:start position:0%
+was around the same time when Model T
+ 
+
+ align:start position:0%
+was around the same time when Model T
+maybe few years earlier 10 15 years
+
+ align:start position:0%
+maybe few years earlier 10 15 years
+ 
+
+ align:start position:0%
+maybe few years earlier 10 15 years
+earlier but it's taking essentially
+
+ align:start position:0%
+earlier but it's taking essentially
+ 
+
+ align:start position:0%
+earlier but it's taking essentially
+really high technology and using
+
+ align:start position:0%
+really high technology and using
+ 
+
+ align:start position:0%
+really high technology and using
+some Innovation to bring it down to
+
+ align:start position:0%
+some Innovation to bring it down to
+ 
+
+ align:start position:0%
+some Innovation to bring it down to
+masses so everybody can use it so you
+
+ align:start position:0%
+masses so everybody can use it so you
+ 
+
+ align:start position:0%
+masses so everybody can use it so you
+can say that morality and the brownie
+
+ align:start position:0%
+can say that morality and the brownie
+ 
+
+ align:start position:0%
+can say that morality and the brownie
+camera was the first age of modern
+
+ align:start position:0%
+camera was the first age of modern
+ 
+
+ align:start position:0%
+camera was the first age of modern
+consumer technological culture
+
+ align:start position:0%
+consumer technological culture
+ 
+
+ align:start position:0%
+consumer technological culture
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+modern three color color immersion
+
+ align:start position:0%
+modern three color color immersion
+ 
+
+ align:start position:0%
+modern three color color immersion
+Kodachrome stacked with doping and
+
+ align:start position:0%
+Kodachrome stacked with doping and
+ 
+
+ align:start position:0%
+Kodachrome stacked with doping and
+everything and Polaroid instant camera
+
+ align:start position:0%
+everything and Polaroid instant camera
+ 
+
+ align:start position:0%
+everything and Polaroid instant camera
+of course in 1945 the definition of
+
+ align:start position:0%
+of course in 1945 the definition of
+ 
+
+ align:start position:0%
+of course in 1945 the definition of
+instant was a little bit different 30
+
+ align:start position:0%
+instant was a little bit different 30
+ 
+
+ align:start position:0%
+instant was a little bit different 30
+seconds to two minutes was considered to
+
+ align:start position:0%
+seconds to two minutes was considered to
+ 
+
+ align:start position:0%
+seconds to two minutes was considered to
+be instant
+
+ align:start position:0%
+be instant
+ 
+
+ align:start position:0%
+be instant
+and this I I was really free this of
+
+ align:start position:0%
+and this I I was really free this of
+ 
+
+ align:start position:0%
+and this I I was really free this of
+course I found it on
+
+ align:start position:0%
+course I found it on
+ 
+
+ align:start position:0%
+course I found it on
+Wikipedia But Maxwell whom we don't
+
+ align:start position:0%
+Wikipedia But Maxwell whom we don't
+ 
+
+ align:start position:0%
+Wikipedia But Maxwell whom we don't
+normally associate with doing
+
+ align:start position:0%
+normally associate with doing
+ 
+
+ align:start position:0%
+normally associate with doing
+experimental work but this was the color
+
+ align:start position:0%
+experimental work but this was the color
+ 
+
+ align:start position:0%
+experimental work but this was the color
+photograph you know how it was captured
+
+ align:start position:0%
+photograph you know how it was captured
+ 
+
+ align:start position:0%
+photograph you know how it was captured
+uh three separate exposures and then
+
+ align:start position:0%
+uh three separate exposures and then
+ 
+
+ align:start position:0%
+uh three separate exposures and then
+stack
+
+ align:start position:0%
+stack
+ 
+
+ align:start position:0%
+stack
+three separate films to through the
+
+ align:start position:0%
+three separate films to through the
+ 
+
+ align:start position:0%
+three separate films to through the
+three separate filters but how do we put
+
+ align:start position:0%
+three separate filters but how do we put
+ 
+
+ align:start position:0%
+three separate filters but how do we put
+them together I guess aligned it by hand
+
+ align:start position:0%
+them together I guess aligned it by hand
+ 
+
+ align:start position:0%
+them together I guess aligned it by hand
+after developing it yeah yeah and of
+
+ align:start position:0%
+after developing it yeah yeah and of
+ 
+
+ align:start position:0%
+after developing it yeah yeah and of
+course you know Abraham Lincoln was the
+
+ align:start position:0%
+course you know Abraham Lincoln was the
+ 
+
+ align:start position:0%
+course you know Abraham Lincoln was the
+first president to be photographed so
+
+ align:start position:0%
+first president to be photographed so
+ 
+
+ align:start position:0%
+first president to be photographed so
+and lots of beautiful photographs of uh
+
+ align:start position:0%
+and lots of beautiful photographs of uh
+ 
+
+ align:start position:0%
+and lots of beautiful photographs of uh
+Civil War progress looks too crisp
+
+ align:start position:0%
+Civil War progress looks too crisp
+ 
+
+ align:start position:0%
+Civil War progress looks too crisp
+yeah I I don't know I don't know if it
+
+ align:start position:0%
+yeah I I don't know I don't know if it
+ 
+
+ align:start position:0%
+yeah I I don't know I don't know if it
+was uh subsequently touched up they use
+
+ align:start position:0%
+was uh subsequently touched up they use
+ 
+
+ align:start position:0%
+was uh subsequently touched up they use
+the Whitefield
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+camera was invented back in 1908 so yeah
+
+ align:start position:0%
+camera was invented back in 1908 so yeah
+ 
+
+ align:start position:0%
+camera was invented back in 1908 so yeah
+it looks like it's a long exposure maybe
+
+ align:start position:0%
+it looks like it's a long exposure maybe
+ 
+
+ align:start position:0%
+it looks like it's a long exposure maybe
+because the trees in the background yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all exposures were long I'm sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay another historic Milestone that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so mechanical scanning and all kinds of
+
+ align:start position:0%
+so mechanical scanning and all kinds of
+ 
+
+ align:start position:0%
+so mechanical scanning and all kinds of
+other things CCD uh just I I gave this
+
+ align:start position:0%
+other things CCD uh just I I gave this
+ 
+
+ align:start position:0%
+other things CCD uh just I I gave this
+seminar about
+
+ align:start position:0%
+seminar about
+ 
+
+ align:start position:0%
+seminar about
+a month and a half ago and two weeks
+
+ align:start position:0%
+a month and a half ago and two weeks
+ 
+
+ align:start position:0%
+a month and a half ago and two weeks
+later the CCD Nobel Prize was announced
+
+ align:start position:0%
+later the CCD Nobel Prize was announced
+ 
+
+ align:start position:0%
+later the CCD Nobel Prize was announced
+I I don't know many of you are probably
+
+ align:start position:0%
+I I don't know many of you are probably
+ 
+
+ align:start position:0%
+I I don't know many of you are probably
+aware of the controversy whether these
+
+ align:start position:0%
+aware of the controversy whether these
+ 
+
+ align:start position:0%
+aware of the controversy whether these
+people really deserve the Nobel Prize or
+
+ align:start position:0%
+people really deserve the Nobel Prize or
+ 
+
+ align:start position:0%
+people really deserve the Nobel Prize or
+not because they were working on uh
+
+ align:start position:0%
+not because they were working on uh
+ 
+
+ align:start position:0%
+not because they were working on uh
+shift registered memory and it was
+
+ align:start position:0%
+shift registered memory and it was
+ 
+
+ align:start position:0%
+shift registered memory and it was
+somebody else who said hey you know it's
+
+ align:start position:0%
+somebody else who said hey you know it's
+ 
+
+ align:start position:0%
+somebody else who said hey you know it's
+like sense or whatever anyway but then
+
+ align:start position:0%
+like sense or whatever anyway but then
+ 
+
+ align:start position:0%
+like sense or whatever anyway but then
+most of these things there is always a
+
+ align:start position:0%
+most of these things there is always a
+ 
+
+ align:start position:0%
+most of these things there is always a
+controversy about
+
+ align:start position:0%
+controversy about
+ 
+
+ align:start position:0%
+controversy about
+including MRI and all kinds of other
+
+ align:start position:0%
+including MRI and all kinds of other
+ 
+
+ align:start position:0%
+including MRI and all kinds of other
+things but this is kind of interesting
+
+ align:start position:0%
+things but this is kind of interesting
+ 
+
+ align:start position:0%
+things but this is kind of interesting
+yeah look at this the first Fair Tire
+
+ align:start position:0%
+yeah look at this the first Fair Tire
+ 
+
+ align:start position:0%
+yeah look at this the first Fair Tire
+88 pounds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.01 megapixels 23 seconds
+
+ align:start position:0%
+0.01 megapixels 23 seconds
+ 
+
+ align:start position:0%
+0.01 megapixels 23 seconds
+and actually if you look at the date
+
+ align:start position:0%
+and actually if you look at the date
+ 
+
+ align:start position:0%
+and actually if you look at the date
+December 75 that that's not that far
+
+ align:start position:0%
+December 75 that that's not that far
+ 
+
+ align:start position:0%
+December 75 that that's not that far
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+it's not that far back at all then the
+
+ align:start position:0%
+it's not that far back at all then the
+ 
+
+ align:start position:0%
+it's not that far back at all then the
+subsequent digital camera Sony mavita
+
+ align:start position:0%
+subsequent digital camera Sony mavita
+ 
+
+ align:start position:0%
+subsequent digital camera Sony mavita
+quarter minor pixel DCS 100 one
+
+ align:start position:0%
+quarter minor pixel DCS 100 one
+ 
+
+ align:start position:0%
+quarter minor pixel DCS 100 one
+megapixel twenty thousand dollars
+
+ align:start position:0%
+megapixel twenty thousand dollars
+ 
+
+ align:start position:0%
+megapixel twenty thousand dollars
+and 97 was the first
+
+ align:start position:0%
+and 97 was the first
+ 
+
+ align:start position:0%
+and 97 was the first
+transmission of picture of cell phone
+
+ align:start position:0%
+transmission of picture of cell phone
+ 
+
+ align:start position:0%
+transmission of picture of cell phone
+and cell phone camera and his last one
+
+ align:start position:0%
+and cell phone camera and his last one
+ 
+
+ align:start position:0%
+and cell phone camera and his last one
+is very interesting very recently
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if anybody has film cameras well you
+
+ align:start position:0%
+so if anybody has film cameras well you
+ 
+
+ align:start position:0%
+so if anybody has film cameras well you
+better start stocking up on old film and
+
+ align:start position:0%
+better start stocking up on old film and
+ 
+
+ align:start position:0%
+better start stocking up on old film and
+2006 uh the 10 megapixel cell phone I
+
+ align:start position:0%
+2006 uh the 10 megapixel cell phone I
+ 
+
+ align:start position:0%
+2006 uh the 10 megapixel cell phone I
+think with these 12 pixel cell phone
+
+ align:start position:0%
+think with these 12 pixel cell phone
+ 
+
+ align:start position:0%
+think with these 12 pixel cell phone
+cameras and all that instead of a cell
+
+ align:start position:0%
+cameras and all that instead of a cell
+ 
+
+ align:start position:0%
+cameras and all that instead of a cell
+phone with a camera this is the camera
+
+ align:start position:0%
+phone with a camera this is the camera
+ 
+
+ align:start position:0%
+phone with a camera this is the camera
+with a cell phone so bulk of it is
+
+ align:start position:0%
+with a cell phone so bulk of it is
+ 
+
+ align:start position:0%
+with a cell phone so bulk of it is
+probably with the uptakes and everything
+
+ align:start position:0%
+probably with the uptakes and everything
+ 
+
+ align:start position:0%
+probably with the uptakes and everything
+else Optics most that goes with it
+
+ align:start position:0%
+else Optics most that goes with it
+ 
+
+ align:start position:0%
+else Optics most that goes with it
+uh you have heard of Moore's Law so
+
+ align:start position:0%
+uh you have heard of Moore's Law so
+ 
+
+ align:start position:0%
+uh you have heard of Moore's Law so
+there is something called hindi's law uh
+
+ align:start position:0%
+there is something called hindi's law uh
+ 
+
+ align:start position:0%
+there is something called hindi's law uh
+empirical observation
+
+ align:start position:0%
+empirical observation
+ 
+
+ align:start position:0%
+empirical observation
+how many pixels per dollar and that's of
+
+ align:start position:0%
+how many pixels per dollar and that's of
+ 
+
+ align:start position:0%
+how many pixels per dollar and that's of
+course a large scale and this is a
+
+ align:start position:0%
+course a large scale and this is a
+ 
+
+ align:start position:0%
+course a large scale and this is a
+linear scale in years
+
+ align:start position:0%
+linear scale in years
+ 
+
+ align:start position:0%
+linear scale in years
+from this BCS 460
+
+ align:start position:0%
+from this BCS 460
+ 
+
+ align:start position:0%
+from this BCS 460
+100 pixels per dollar
+
+ align:start position:0%
+100 pixels per dollar
+ 
+
+ align:start position:0%
+100 pixels per dollar
+to all the way here and we will probably
+
+ align:start position:0%
+to all the way here and we will probably
+ 
+
+ align:start position:0%
+to all the way here and we will probably
+I I don't know this is still an old
+
+ align:start position:0%
+I I don't know this is still an old
+ 
+
+ align:start position:0%
+I I don't know this is still an old
+curve uh a megapixel camera I think five
+
+ align:start position:0%
+curve uh a megapixel camera I think five
+ 
+
+ align:start position:0%
+curve uh a megapixel camera I think five
+dollars and I think the goal of many of
+
+ align:start position:0%
+dollars and I think the goal of many of
+ 
+
+ align:start position:0%
+dollars and I think the goal of many of
+these companies is megapixel camera for
+
+ align:start position:0%
+these companies is megapixel camera for
+ 
+
+ align:start position:0%
+these companies is megapixel camera for
+a buck everything the lens the focal
+
+ align:start position:0%
+a buck everything the lens the focal
+ 
+
+ align:start position:0%
+a buck everything the lens the focal
+plane array the PC board and everything
+
+ align:start position:0%
+plane array the PC board and everything
+ 
+
+ align:start position:0%
+plane array the PC board and everything
+ready to plug into it with the wafer
+
+ align:start position:0%
+ready to plug into it with the wafer
+ 
+
+ align:start position:0%
+ready to plug into it with the wafer
+level cameras it's already about a
+
+ align:start position:0%
+level cameras it's already about a
+ 
+
+ align:start position:0%
+level cameras it's already about a
+dollars yeah
+
+ align:start position:0%
+dollars yeah
+ 
+
+ align:start position:0%
+dollars yeah
+so megapixel per dollar so it's already
+
+ align:start position:0%
+so megapixel per dollar so it's already
+ 
+
+ align:start position:0%
+so megapixel per dollar so it's already
+out there somewhere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is sort of the picture gallery
+
+ align:start position:0%
+and this is sort of the picture gallery
+ 
+
+ align:start position:0%
+and this is sort of the picture gallery
+so the mavi card is yes 100 Samsung
+
+ align:start position:0%
+so the mavi card is yes 100 Samsung
+ 
+
+ align:start position:0%
+so the mavi card is yes 100 Samsung
+this is uh the Omni Visions focal
+
+ align:start position:0%
+this is uh the Omni Visions focal
+ 
+
+ align:start position:0%
+this is uh the Omni Visions focal
+planaret 2.1 by 2.3 millimeters
+
+ align:start position:0%
+planaret 2.1 by 2.3 millimeters
+ 
+
+ align:start position:0%
+planaret 2.1 by 2.3 millimeters
+and this is a very interesting thing
+
+ align:start position:0%
+and this is a very interesting thing
+ 
+
+ align:start position:0%
+and this is a very interesting thing
+marigas uh uh for Endoscopy video
+
+ align:start position:0%
+marigas uh uh for Endoscopy video
+ 
+
+ align:start position:0%
+marigas uh uh for Endoscopy video
+endoscopy 1.8 millimeter diameter
+
+ align:start position:0%
+endoscopy 1.8 millimeter diameter
+ 
+
+ align:start position:0%
+endoscopy 1.8 millimeter diameter
+includes lens the focal plane the cable
+
+ align:start position:0%
+includes lens the focal plane the cable
+ 
+
+ align:start position:0%
+includes lens the focal plane the cable
+for Trans sending power sending the
+
+ align:start position:0%
+for Trans sending power sending the
+ 
+
+ align:start position:0%
+for Trans sending power sending the
+signals back
+
+ align:start position:0%
+signals back
+ 
+
+ align:start position:0%
+signals back
+not great resolution
+
+ align:start position:0%
+not great resolution
+ 
+
+ align:start position:0%
+not great resolution
+326 by 382 but if something needs to be
+
+ align:start position:0%
+326 by 382 but if something needs to be
+ 
+
+ align:start position:0%
+326 by 382 but if something needs to be
+stuck inside your body smaller the
+
+ align:start position:0%
+stuck inside your body smaller the
+ 
+
+ align:start position:0%
+stuck inside your body smaller the
+better and 1.8 millimeter which is
+
+ align:start position:0%
+better and 1.8 millimeter which is
+ 
+
+ align:start position:0%
+better and 1.8 millimeter which is
+definitely definitely nice
+
+ align:start position:0%
+definitely definitely nice
+ 
+
+ align:start position:0%
+definitely definitely nice
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this chair is the one that's used in the
+
+ align:start position:0%
+this chair is the one that's used in the
+ 
+
+ align:start position:0%
+this chair is the one that's used in the
+pill camera that you swallow to image
+
+ align:start position:0%
+pill camera that you swallow to image
+ 
+
+ align:start position:0%
+pill camera that you swallow to image
+you are inside
+
+ align:start position:0%
+you are inside
+ 
+
+ align:start position:0%
+you are inside
+ah this is uh I I thought of something
+
+ align:start position:0%
+ah this is uh I I thought of something
+ 
+
+ align:start position:0%
+ah this is uh I I thought of something
+you know the Imaging yeah case study
+
+ align:start position:0%
+you know the Imaging yeah case study
+ 
+
+ align:start position:0%
+you know the Imaging yeah case study
+studying the Inner Space versus stunning
+
+ align:start position:0%
+studying the Inner Space versus stunning
+ 
+
+ align:start position:0%
+studying the Inner Space versus stunning
+the outer space
+
+ align:start position:0%
+the outer space
+ 
+
+ align:start position:0%
+the outer space
+so the camera appeal and the Hubble
+
+ align:start position:0%
+so the camera appeal and the Hubble
+ 
+
+ align:start position:0%
+so the camera appeal and the Hubble
+Space Telescope
+
+ align:start position:0%
+Space Telescope
+ 
+
+ align:start position:0%
+Space Telescope
+so but both are shaped like a pillow
+
+ align:start position:0%
+so but both are shaped like a pillow
+ 
+
+ align:start position:0%
+so but both are shaped like a pillow
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+I mean both are shaped like a pill in
+
+ align:start position:0%
+I mean both are shaped like a pill in
+ 
+
+ align:start position:0%
+I mean both are shaped like a pill in
+the sense this was actually in the
+
+ align:start position:0%
+the sense this was actually in the
+ 
+
+ align:start position:0%
+the sense this was actually in the
+Montage
+
+ align:start position:0%
+Montage
+ 
+
+ align:start position:0%
+Montage
+program that I started at DARPA that
+
+ align:start position:0%
+program that I started at DARPA that
+ 
+
+ align:start position:0%
+program that I started at DARPA that
+that was one of the motivations that
+
+ align:start position:0%
+that was one of the motivations that
+ 
+
+ align:start position:0%
+that was one of the motivations that
+over the past 30 40 years
+
+ align:start position:0%
+over the past 30 40 years
+ 
+
+ align:start position:0%
+over the past 30 40 years
+the displays have become thinner from
+
+ align:start position:0%
+the displays have become thinner from
+ 
+
+ align:start position:0%
+the displays have become thinner from
+bulky CRTs to thin flat panel displays
+
+ align:start position:0%
+bulky CRTs to thin flat panel displays
+ 
+
+ align:start position:0%
+bulky CRTs to thin flat panel displays
+but the cameras the aspect ratio of the
+
+ align:start position:0%
+but the cameras the aspect ratio of the
+ 
+
+ align:start position:0%
+but the cameras the aspect ratio of the
+cameras have not changed in the past
+
+ align:start position:0%
+cameras have not changed in the past
+ 
+
+ align:start position:0%
+cameras have not changed in the past
+however many thousand years they are
+
+ align:start position:0%
+however many thousand years they are
+ 
+
+ align:start position:0%
+however many thousand years they are
+always tube-like and so the goal was can
+
+ align:start position:0%
+always tube-like and so the goal was can
+ 
+
+ align:start position:0%
+always tube-like and so the goal was can
+you squash the camera
+
+ align:start position:0%
+you squash the camera
+ 
+
+ align:start position:0%
+you squash the camera
+can you make a camera
+
+ align:start position:0%
+can you make a camera
+ 
+
+ align:start position:0%
+can you make a camera
+that is five millimeters thick with the
+
+ align:start position:0%
+that is five millimeters thick with the
+ 
+
+ align:start position:0%
+that is five millimeters thick with the
+effective focal length is 50 millimeters
+
+ align:start position:0%
+effective focal length is 50 millimeters
+ 
+
+ align:start position:0%
+effective focal length is 50 millimeters
+and the light Gathering Power also
+
+ align:start position:0%
+and the light Gathering Power also
+ 
+
+ align:start position:0%
+and the light Gathering Power also
+offers and there are various tricks that
+
+ align:start position:0%
+offers and there are various tricks that
+ 
+
+ align:start position:0%
+offers and there are various tricks that
+you can play the origami lunch that you
+
+ align:start position:0%
+you can play the origami lunch that you
+ 
+
+ align:start position:0%
+you can play the origami lunch that you
+probably studied is one of the examples
+
+ align:start position:0%
+probably studied is one of the examples
+ 
+
+ align:start position:0%
+probably studied is one of the examples
+the multi aperture is another example
+
+ align:start position:0%
+the multi aperture is another example
+ 
+
+ align:start position:0%
+the multi aperture is another example
+but one of the things about and I'm not
+
+ align:start position:0%
+but one of the things about and I'm not
+ 
+
+ align:start position:0%
+but one of the things about and I'm not
+sure in this presentation there are the
+
+ align:start position:0%
+sure in this presentation there are the
+ 
+
+ align:start position:0%
+sure in this presentation there are the
+technical details or specifications but
+
+ align:start position:0%
+technical details or specifications but
+ 
+
+ align:start position:0%
+technical details or specifications but
+it's very interesting if you look at the
+
+ align:start position:0%
+it's very interesting if you look at the
+ 
+
+ align:start position:0%
+it's very interesting if you look at the
+specifications of say Hubble a pill
+
+ align:start position:0%
+specifications of say Hubble a pill
+ 
+
+ align:start position:0%
+specifications of say Hubble a pill
+camera or take one of the modern
+
+ align:start position:0%
+camera or take one of the modern
+ 
+
+ align:start position:0%
+camera or take one of the modern
+lithography lenses I don't think I have
+
+ align:start position:0%
+lithography lenses I don't think I have
+ 
+
+ align:start position:0%
+lithography lenses I don't think I have
+a picture of that but the modern
+
+ align:start position:0%
+a picture of that but the modern
+ 
+
+ align:start position:0%
+a picture of that but the modern
+lithography lenses are a Marvel of
+
+ align:start position:0%
+lithography lenses are a Marvel of
+ 
+
+ align:start position:0%
+lithography lenses are a Marvel of
+technology that these things get you you
+
+ align:start position:0%
+technology that these things get you you
+ 
+
+ align:start position:0%
+technology that these things get you you
+remember how much the database several
+
+ align:start position:0%
+remember how much the database several
+ 
+
+ align:start position:0%
+remember how much the database several
+thousand pounds right
+
+ align:start position:0%
+thousand pounds right
+ 
+
+ align:start position:0%
+thousand pounds right
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+obscenely heavy a huge number of
+
+ align:start position:0%
+obscenely heavy a huge number of
+ 
+
+ align:start position:0%
+obscenely heavy a huge number of
+elements in this and cost multiple
+
+ align:start position:0%
+elements in this and cost multiple
+ 
+
+ align:start position:0%
+elements in this and cost multiple
+billion dollars
+
+ align:start position:0%
+billion dollars
+ 
+
+ align:start position:0%
+billion dollars
+and the reason is that it's absolutely
+
+ align:start position:0%
+and the reason is that it's absolutely
+ 
+
+ align:start position:0%
+and the reason is that it's absolutely
+diffraction limited performance over a
+
+ align:start position:0%
+diffraction limited performance over a
+ 
+
+ align:start position:0%
+diffraction limited performance over a
+fairly wide field of view with zero
+
+ align:start position:0%
+fairly wide field of view with zero
+ 
+
+ align:start position:0%
+fairly wide field of view with zero
+Distortion and all the aberrations
+
+ align:start position:0%
+Distortion and all the aberrations
+ 
+
+ align:start position:0%
+Distortion and all the aberrations
+everything correctly so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now multi-scale images broad wide
+
+ align:start position:0%
+okay now multi-scale images broad wide
+ 
+
+ align:start position:0%
+okay now multi-scale images broad wide
+ending now everybody giggle gigapixel
+
+ align:start position:0%
+ending now everybody giggle gigapixel
+ 
+
+ align:start position:0%
+ending now everybody giggle gigapixel
+Imaging since the inauguration it has
+
+ align:start position:0%
+Imaging since the inauguration it has
+ 
+
+ align:start position:0%
+Imaging since the inauguration it has
+really taken off there are so many
+
+ align:start position:0%
+really taken off there are so many
+ 
+
+ align:start position:0%
+really taken off there are so many
+images like that having the white
+
+ align:start position:0%
+images like that having the white
+ 
+
+ align:start position:0%
+images like that having the white
+Panorama and finding the details like
+
+ align:start position:0%
+Panorama and finding the details like
+ 
+
+ align:start position:0%
+Panorama and finding the details like
+over here somewhere
+
+ align:start position:0%
+over here somewhere
+ 
+
+ align:start position:0%
+over here somewhere
+there is an eagle and so
+
+ align:start position:0%
+there is an eagle and so
+ 
+
+ align:start position:0%
+there is an eagle and so
+can we get here from where we are right
+
+ align:start position:0%
+can we get here from where we are right
+ 
+
+ align:start position:0%
+can we get here from where we are right
+now and in a realistic size weight cost
+
+ align:start position:0%
+now and in a realistic size weight cost
+ 
+
+ align:start position:0%
+now and in a realistic size weight cost
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+uh can we get a gigapixel camera
+
+ align:start position:0%
+uh can we get a gigapixel camera
+ 
+
+ align:start position:0%
+uh can we get a gigapixel camera
+can we get a 10 or 100 giga pixel camera
+
+ align:start position:0%
+can we get a 10 or 100 giga pixel camera
+ 
+
+ align:start position:0%
+can we get a 10 or 100 giga pixel camera
+very wide field of view very high
+
+ align:start position:0%
+very wide field of view very high
+ 
+
+ align:start position:0%
+very wide field of view very high
+resolution these are some of the
+
+ align:start position:0%
+resolution these are some of the
+ 
+
+ align:start position:0%
+resolution these are some of the
+challenges that will be addressed and
+
+ align:start position:0%
+challenges that will be addressed and
+ 
+
+ align:start position:0%
+challenges that will be addressed and
+not not doing Brute Force
+
+ align:start position:0%
+not not doing Brute Force
+ 
+
+ align:start position:0%
+not not doing Brute Force
+so it's it's an interesting uh Prospect
+
+ align:start position:0%
+so it's it's an interesting uh Prospect
+ 
+
+ align:start position:0%
+so it's it's an interesting uh Prospect
+and it's an interesting Direction
+
+ align:start position:0%
+and it's an interesting Direction
+ 
+
+ align:start position:0%
+and it's an interesting Direction
+now what do you think these are the
+
+ align:start position:0%
+now what do you think these are the
+ 
+
+ align:start position:0%
+now what do you think these are the
+cameras that individuals will carry or
+
+ align:start position:0%
+cameras that individuals will carry or
+ 
+
+ align:start position:0%
+cameras that individuals will carry or
+this will be installed and then you have
+
+ align:start position:0%
+this will be installed and then you have
+ 
+
+ align:start position:0%
+this will be installed and then you have
+access to it so that you can region of
+
+ align:start position:0%
+access to it so that you can region of
+ 
+
+ align:start position:0%
+access to it so that you can region of
+interest you can you can capture what
+
+ align:start position:0%
+interest you can you can capture what
+ 
+
+ align:start position:0%
+interest you can you can capture what
+you want
+
+ align:start position:0%
+you want
+ 
+
+ align:start position:0%
+you want
+that this is kind of an interesting
+
+ align:start position:0%
+that this is kind of an interesting
+ 
+
+ align:start position:0%
+that this is kind of an interesting
+thing you you can imagine
+
+ align:start position:0%
+thing you you can imagine
+ 
+
+ align:start position:0%
+thing you you can imagine
+uh an individual uh likes uh Special
+
+ align:start position:0%
+uh an individual uh likes uh Special
+ 
+
+ align:start position:0%
+uh an individual uh likes uh Special
+Operation soldiers
+
+ align:start position:0%
+Operation soldiers
+ 
+
+ align:start position:0%
+Operation soldiers
+carrying binoculars like with the
+
+ align:start position:0%
+carrying binoculars like with the
+ 
+
+ align:start position:0%
+carrying binoculars like with the
+standard binocular form factor uh that
+
+ align:start position:0%
+standard binocular form factor uh that
+ 
+
+ align:start position:0%
+standard binocular form factor uh that
+will be equivalent to a gigapixel but
+
+ align:start position:0%
+will be equivalent to a gigapixel but
+ 
+
+ align:start position:0%
+will be equivalent to a gigapixel but
+not there are no gigapixel displays
+
+ align:start position:0%
+not there are no gigapixel displays
+ 
+
+ align:start position:0%
+not there are no gigapixel displays
+human Vision doesn't have the space
+
+ align:start position:0%
+human Vision doesn't have the space
+ 
+
+ align:start position:0%
+human Vision doesn't have the space
+bandwidth for gigapixel So within that
+
+ align:start position:0%
+bandwidth for gigapixel So within that
+ 
+
+ align:start position:0%
+bandwidth for gigapixel So within that
+gigaplex so you should be able to
+
+ align:start position:0%
+gigaplex so you should be able to
+ 
+
+ align:start position:0%
+gigaplex so you should be able to
+fobiate and zoom in and look at the
+
+ align:start position:0%
+fobiate and zoom in and look at the
+ 
+
+ align:start position:0%
+fobiate and zoom in and look at the
+details
+
+ align:start position:0%
+details
+ 
+
+ align:start position:0%
+details
+there is an ongoing DARPA program I
+
+ align:start position:0%
+there is an ongoing DARPA program I
+ 
+
+ align:start position:0%
+there is an ongoing DARPA program I
+don't know what phase it is at
+
+ align:start position:0%
+don't know what phase it is at
+ 
+
+ align:start position:0%
+don't know what phase it is at
+some cognitive technology for Warfighter
+
+ align:start position:0%
+some cognitive technology for Warfighter
+ 
+
+ align:start position:0%
+some cognitive technology for Warfighter
+blah blah it was colloquially called
+
+ align:start position:0%
+blah blah it was colloquially called
+ 
+
+ align:start position:0%
+blah blah it was colloquially called
+Luke's binoculars so in Star Wars look
+
+ align:start position:0%
+Luke's binoculars so in Star Wars look
+ 
+
+ align:start position:0%
+Luke's binoculars so in Star Wars look
+at these binoculars and you're looking
+
+ align:start position:0%
+at these binoculars and you're looking
+ 
+
+ align:start position:0%
+at these binoculars and you're looking
+at it and it would put a cursor that
+
+ align:start position:0%
+at it and it would put a cursor that
+ 
+
+ align:start position:0%
+at it and it would put a cursor that
+alien there or there's that so that that
+
+ align:start position:0%
+alien there or there's that so that that
+ 
+
+ align:start position:0%
+alien there or there's that so that that
+can it was primarily focused on the
+
+ align:start position:0%
+can it was primarily focused on the
+ 
+
+ align:start position:0%
+can it was primarily focused on the
+processing
+
+ align:start position:0%
+processing
+ 
+
+ align:start position:0%
+processing
+based on
+
+ align:start position:0%
+based on
+ 
+
+ align:start position:0%
+based on
+neuromorphic algorithms or something
+
+ align:start position:0%
+neuromorphic algorithms or something
+ 
+
+ align:start position:0%
+neuromorphic algorithms or something
+like that so uh the idea will be if you
+
+ align:start position:0%
+like that so uh the idea will be if you
+ 
+
+ align:start position:0%
+like that so uh the idea will be if you
+can design
+
+ align:start position:0%
+can design
+ 
+
+ align:start position:0%
+can design
+the camera or an Imaging sensor that can
+
+ align:start position:0%
+the camera or an Imaging sensor that can
+ 
+
+ align:start position:0%
+the camera or an Imaging sensor that can
+capture a gigapixel worth of information
+
+ align:start position:0%
+capture a gigapixel worth of information
+ 
+
+ align:start position:0%
+capture a gigapixel worth of information
+and if you have this back end this
+
+ align:start position:0%
+and if you have this back end this
+ 
+
+ align:start position:0%
+and if you have this back end this
+neuromorphically induced processing that
+
+ align:start position:0%
+neuromorphically induced processing that
+ 
+
+ align:start position:0%
+neuromorphically induced processing that
+can cue the soldiers and look here there
+
+ align:start position:0%
+can cue the soldiers and look here there
+ 
+
+ align:start position:0%
+can cue the soldiers and look here there
+and the soldier can learn appropriately
+
+ align:start position:0%
+and the soldier can learn appropriately
+ 
+
+ align:start position:0%
+and the soldier can learn appropriately
+Focus there so that that in terms of
+
+ align:start position:0%
+Focus there so that that in terms of
+ 
+
+ align:start position:0%
+Focus there so that that in terms of
+what kind of things that will be really
+
+ align:start position:0%
+what kind of things that will be really
+ 
+
+ align:start position:0%
+what kind of things that will be really
+useful for Warfighter right now that
+
+ align:start position:0%
+useful for Warfighter right now that
+ 
+
+ align:start position:0%
+useful for Warfighter right now that
+that would be one of the things and then
+
+ align:start position:0%
+that would be one of the things and then
+ 
+
+ align:start position:0%
+that would be one of the things and then
+of course you have platforms at various
+
+ align:start position:0%
+of course you have platforms at various
+ 
+
+ align:start position:0%
+of course you have platforms at various
+levels from micro ulvs with about nine
+
+ align:start position:0%
+levels from micro ulvs with about nine
+ 
+
+ align:start position:0%
+levels from micro ulvs with about nine
+inch wingspan to predators to all the
+
+ align:start position:0%
+inch wingspan to predators to all the
+ 
+
+ align:start position:0%
+inch wingspan to predators to all the
+way space-based energy and the field of
+
+ align:start position:0%
+way space-based energy and the field of
+ 
+
+ align:start position:0%
+way space-based energy and the field of
+view and the pixel resolution
+
+ align:start position:0%
+view and the pixel resolution
+ 
+
+ align:start position:0%
+view and the pixel resolution
+requirements and everything it spans all
+
+ align:start position:0%
+requirements and everything it spans all
+ 
+
+ align:start position:0%
+requirements and everything it spans all
+over the space
+
+ align:start position:0%
+over the space
+ 
+
+ align:start position:0%
+over the space
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm Switching gears a little bit and
+
+ align:start position:0%
+so I'm Switching gears a little bit and
+ 
+
+ align:start position:0%
+so I'm Switching gears a little bit and
+uh previous was sort of uh you you can
+
+ align:start position:0%
+uh previous was sort of uh you you can
+ 
+
+ align:start position:0%
+uh previous was sort of uh you you can
+say an anecdotal or event-based vision
+
+ align:start position:0%
+say an anecdotal or event-based vision
+ 
+
+ align:start position:0%
+say an anecdotal or event-based vision
+of the history now we will go into a
+
+ align:start position:0%
+of the history now we will go into a
+ 
+
+ align:start position:0%
+of the history now we will go into a
+little bit of a technical
+
+ align:start position:0%
+little bit of a technical
+ 
+
+ align:start position:0%
+little bit of a technical
+angle of looking at history
+
+ align:start position:0%
+angle of looking at history
+ 
+
+ align:start position:0%
+angle of looking at history
+so I think for first one of the
+
+ align:start position:0%
+so I think for first one of the
+ 
+
+ align:start position:0%
+so I think for first one of the
+questions and this this sort of also
+
+ align:start position:0%
+questions and this this sort of also
+ 
+
+ align:start position:0%
+questions and this this sort of also
+gets into
+
+ align:start position:0%
+gets into
+ 
+
+ align:start position:0%
+gets into
+where we should be headed anyway
+
+ align:start position:0%
+where we should be headed anyway
+ 
+
+ align:start position:0%
+where we should be headed anyway
+so Imaging sensors or you can say
+
+ align:start position:0%
+so Imaging sensors or you can say
+ 
+
+ align:start position:0%
+so Imaging sensors or you can say
+sensors in general
+
+ align:start position:0%
+sensors in general
+ 
+
+ align:start position:0%
+sensors in general
+why do we do this what it is and why do
+
+ align:start position:0%
+why do we do this what it is and why do
+ 
+
+ align:start position:0%
+why do we do this what it is and why do
+we do this so
+
+ align:start position:0%
+we do this so
+ 
+
+ align:start position:0%
+we do this so
+uh questions we asked and this is
+
+ align:start position:0%
+uh questions we asked and this is
+ 
+
+ align:start position:0%
+uh questions we asked and this is
+something that these are very generic
+
+ align:start position:0%
+something that these are very generic
+ 
+
+ align:start position:0%
+something that these are very generic
+questions and we constantly are asking
+
+ align:start position:0%
+questions and we constantly are asking
+ 
+
+ align:start position:0%
+questions and we constantly are asking
+these questions who what where when
+
+ align:start position:0%
+these questions who what where when
+ 
+
+ align:start position:0%
+these questions who what where when
+that's the sensing front-end part
+
+ align:start position:0%
+that's the sensing front-end part
+ 
+
+ align:start position:0%
+that's the sensing front-end part
+and how and why is the analysis and
+
+ align:start position:0%
+and how and why is the analysis and
+ 
+
+ align:start position:0%
+and how and why is the analysis and
+exploitation part
+
+ align:start position:0%
+exploitation part
+ 
+
+ align:start position:0%
+exploitation part
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+when you reduce it down to its sense
+
+ align:start position:0%
+when you reduce it down to its sense
+ 
+
+ align:start position:0%
+when you reduce it down to its sense
+all we care about is answering these
+
+ align:start position:0%
+all we care about is answering these
+ 
+
+ align:start position:0%
+all we care about is answering these
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+uh when it when it comes to
+
+ align:start position:0%
+uh when it when it comes to
+ 
+
+ align:start position:0%
+uh when it when it comes to
+using Imaging as spatial sensors not
+
+ align:start position:0%
+using Imaging as spatial sensors not
+ 
+
+ align:start position:0%
+using Imaging as spatial sensors not
+Imaging to take photographs of your
+
+ align:start position:0%
+Imaging to take photographs of your
+ 
+
+ align:start position:0%
+Imaging to take photographs of your
+vacation where you can view this and
+
+ align:start position:0%
+vacation where you can view this and
+ 
+
+ align:start position:0%
+vacation where you can view this and
+recapture The Experience that's that's a
+
+ align:start position:0%
+recapture The Experience that's that's a
+ 
+
+ align:start position:0%
+recapture The Experience that's that's a
+different world and in some sense
+
+ align:start position:0%
+different world and in some sense
+ 
+
+ align:start position:0%
+different world and in some sense
+computational photography and
+
+ align:start position:0%
+computational photography and
+ 
+
+ align:start position:0%
+computational photography and
+computational imaging that's what when I
+
+ align:start position:0%
+computational imaging that's what when I
+ 
+
+ align:start position:0%
+computational imaging that's what when I
+say computational Imaging you're looking
+
+ align:start position:0%
+say computational Imaging you're looking
+ 
+
+ align:start position:0%
+say computational Imaging you're looking
+at Imaging you are considering that as a
+
+ align:start position:0%
+at Imaging you are considering that as a
+ 
+
+ align:start position:0%
+at Imaging you are considering that as a
+spatial sensor a spatial sensor Means A
+
+ align:start position:0%
+spatial sensor a spatial sensor Means A
+ 
+
+ align:start position:0%
+spatial sensor a spatial sensor Means A
+system that is designed to answer these
+
+ align:start position:0%
+system that is designed to answer these
+ 
+
+ align:start position:0%
+system that is designed to answer these
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+identifying various constituent elements
+
+ align:start position:0%
+identifying various constituent elements
+ 
+
+ align:start position:0%
+identifying various constituent elements
+in the scene
+
+ align:start position:0%
+in the scene
+ 
+
+ align:start position:0%
+in the scene
+specifying their location and their time
+
+ align:start position:0%
+specifying their location and their time
+ 
+
+ align:start position:0%
+specifying their location and their time
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now within this sense within this
+
+ align:start position:0%
+now within this sense within this
+ 
+
+ align:start position:0%
+now within this sense within this
+particular Realm you have two different
+
+ align:start position:0%
+particular Realm you have two different
+ 
+
+ align:start position:0%
+particular Realm you have two different
+sensory modalities one you can say
+
+ align:start position:0%
+sensory modalities one you can say
+ 
+
+ align:start position:0%
+sensory modalities one you can say
+proximate sensor and the other is
+
+ align:start position:0%
+proximate sensor and the other is
+ 
+
+ align:start position:0%
+proximate sensor and the other is
+standoff sensor so proximate sensor
+
+ align:start position:0%
+standoff sensor so proximate sensor
+ 
+
+ align:start position:0%
+standoff sensor so proximate sensor
+I want to know what is the texture of a
+
+ align:start position:0%
+I want to know what is the texture of a
+ 
+
+ align:start position:0%
+I want to know what is the texture of a
+surface I put my hand as a sense and
+
+ align:start position:0%
+surface I put my hand as a sense and
+ 
+
+ align:start position:0%
+surface I put my hand as a sense and
+move around I say is it rough or smooth
+
+ align:start position:0%
+move around I say is it rough or smooth
+ 
+
+ align:start position:0%
+move around I say is it rough or smooth
+is it uniform what is the granularity in
+
+ align:start position:0%
+is it uniform what is the granularity in
+ 
+
+ align:start position:0%
+is it uniform what is the granularity in
+other words your sensors are specially
+
+ align:start position:0%
+other words your sensors are specially
+ 
+
+ align:start position:0%
+other words your sensors are specially
+collocated
+
+ align:start position:0%
+collocated
+ 
+
+ align:start position:0%
+collocated
+with the object that you are trying to
+
+ align:start position:0%
+with the object that you are trying to
+ 
+
+ align:start position:0%
+with the object that you are trying to
+measure
+
+ align:start position:0%
+measure
+ 
+
+ align:start position:0%
+measure
+and the other thing is your sensors are
+
+ align:start position:0%
+and the other thing is your sensors are
+ 
+
+ align:start position:0%
+and the other thing is your sensors are
+separated by some distance now that
+
+ align:start position:0%
+separated by some distance now that
+ 
+
+ align:start position:0%
+separated by some distance now that
+standoff is a malleable soft concept uh
+
+ align:start position:0%
+standoff is a malleable soft concept uh
+ 
+
+ align:start position:0%
+standoff is a malleable soft concept uh
+say for example take the the
+
+ align:start position:0%
+say for example take the the
+ 
+
+ align:start position:0%
+say for example take the the
+magnetic hard drive disk head
+
+ align:start position:0%
+magnetic hard drive disk head
+ 
+
+ align:start position:0%
+magnetic hard drive disk head
+so for a magnetic storage the heads will
+
+ align:start position:0%
+so for a magnetic storage the heads will
+ 
+
+ align:start position:0%
+so for a magnetic storage the heads will
+be floating I don't know a few microns
+
+ align:start position:0%
+be floating I don't know a few microns
+ 
+
+ align:start position:0%
+be floating I don't know a few microns
+or a few hundred nanometers above the
+
+ align:start position:0%
+or a few hundred nanometers above the
+ 
+
+ align:start position:0%
+or a few hundred nanometers above the
+disc surface so if when you go to the
+
+ align:start position:0%
+disc surface so if when you go to the
+ 
+
+ align:start position:0%
+disc surface so if when you go to the
+optical disks and the optical head is
+
+ align:start position:0%
+optical disks and the optical head is
+ 
+
+ align:start position:0%
+optical disks and the optical head is
+floating two millimeters away from the
+
+ align:start position:0%
+floating two millimeters away from the
+ 
+
+ align:start position:0%
+floating two millimeters away from the
+surface that's a huge distance
+
+ align:start position:0%
+surface that's a huge distance
+ 
+
+ align:start position:0%
+surface that's a huge distance
+so that's a standoff
+
+ align:start position:0%
+so that's a standoff
+ 
+
+ align:start position:0%
+so that's a standoff
+for writing and reading
+
+ align:start position:0%
+for writing and reading
+ 
+
+ align:start position:0%
+for writing and reading
+whereas a standoff if you're talking
+
+ align:start position:0%
+whereas a standoff if you're talking
+ 
+
+ align:start position:0%
+whereas a standoff if you're talking
+about a Hubble Space Telescope that's
+
+ align:start position:0%
+about a Hubble Space Telescope that's
+ 
+
+ align:start position:0%
+about a Hubble Space Telescope that's
+looking at the farthest galaxy in the
+
+ align:start position:0%
+looking at the farthest galaxy in the
+ 
+
+ align:start position:0%
+looking at the farthest galaxy in the
+universe that stand out distance is
+
+ align:start position:0%
+universe that stand out distance is
+ 
+
+ align:start position:0%
+universe that stand out distance is
+however many billion light years away
+
+ align:start position:0%
+however many billion light years away
+ 
+
+ align:start position:0%
+however many billion light years away
+but the point is where you are making
+
+ align:start position:0%
+but the point is where you are making
+ 
+
+ align:start position:0%
+but the point is where you are making
+the measurements is not co-located with
+
+ align:start position:0%
+the measurements is not co-located with
+ 
+
+ align:start position:0%
+the measurements is not co-located with
+what it is that you are trying to
+
+ align:start position:0%
+what it is that you are trying to
+ 
+
+ align:start position:0%
+what it is that you are trying to
+measure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you are doing standoff sensing it has
+
+ align:start position:0%
+if you are doing standoff sensing it has
+ 
+
+ align:start position:0%
+if you are doing standoff sensing it has
+to involve weight propagation no if
+
+ align:start position:0%
+to involve weight propagation no if
+ 
+
+ align:start position:0%
+to involve weight propagation no if
+sounds or buds
+
+ align:start position:0%
+sounds or buds
+ 
+
+ align:start position:0%
+sounds or buds
+and that's almost
+
+ align:start position:0%
+and that's almost
+ 
+
+ align:start position:0%
+and that's almost
+contained in the definition of wave
+
+ align:start position:0%
+contained in the definition of wave
+ 
+
+ align:start position:0%
+contained in the definition of wave
+motion wave is defined as a phenomenon
+
+ align:start position:0%
+motion wave is defined as a phenomenon
+ 
+
+ align:start position:0%
+motion wave is defined as a phenomenon
+that carries energy and information over
+
+ align:start position:0%
+that carries energy and information over
+ 
+
+ align:start position:0%
+that carries energy and information over
+distance without material transport
+
+ align:start position:0%
+distance without material transport
+ 
+
+ align:start position:0%
+distance without material transport
+so that's the difference between a sound
+
+ align:start position:0%
+so that's the difference between a sound
+ 
+
+ align:start position:0%
+so that's the difference between a sound
+wave and wind
+
+ align:start position:0%
+wave and wind
+ 
+
+ align:start position:0%
+wave and wind
+will carry leaves with it sound wave
+
+ align:start position:0%
+will carry leaves with it sound wave
+ 
+
+ align:start position:0%
+will carry leaves with it sound wave
+will not carry leaves with it both
+
+ align:start position:0%
+will not carry leaves with it both
+ 
+
+ align:start position:0%
+will not carry leaves with it both
+involve movement of air molecules but
+
+ align:start position:0%
+involve movement of air molecules but
+ 
+
+ align:start position:0%
+involve movement of air molecules but
+sound wave is capable of carrying energy
+
+ align:start position:0%
+sound wave is capable of carrying energy
+ 
+
+ align:start position:0%
+sound wave is capable of carrying energy
+and information over a distance without
+
+ align:start position:0%
+and information over a distance without
+ 
+
+ align:start position:0%
+and information over a distance without
+a bulk transport and then of course you
+
+ align:start position:0%
+a bulk transport and then of course you
+ 
+
+ align:start position:0%
+a bulk transport and then of course you
+have the electromagnetic values then you
+
+ align:start position:0%
+have the electromagnetic values then you
+ 
+
+ align:start position:0%
+have the electromagnetic values then you
+have seismic waves all kinds of waves
+
+ align:start position:0%
+have seismic waves all kinds of waves
+ 
+
+ align:start position:0%
+have seismic waves all kinds of waves
+but nonetheless wave motion it is at the
+
+ align:start position:0%
+but nonetheless wave motion it is at the
+ 
+
+ align:start position:0%
+but nonetheless wave motion it is at the
+heart of any kind of a standoff sensing
+
+ align:start position:0%
+heart of any kind of a standoff sensing
+ 
+
+ align:start position:0%
+heart of any kind of a standoff sensing
+activity
+
+ align:start position:0%
+activity
+ 
+
+ align:start position:0%
+activity
+so when you have wave
+
+ align:start position:0%
+so when you have wave
+ 
+
+ align:start position:0%
+so when you have wave
+and you have standoff distance
+
+ align:start position:0%
+and you have standoff distance
+ 
+
+ align:start position:0%
+and you have standoff distance
+you have wave propagation that involves
+
+ align:start position:0%
+you have wave propagation that involves
+ 
+
+ align:start position:0%
+you have wave propagation that involves
+diffraction
+
+ align:start position:0%
+diffraction
+ 
+
+ align:start position:0%
+diffraction
+and that diffraction essentially
+
+ align:start position:0%
+and that diffraction essentially
+ 
+
+ align:start position:0%
+and that diffraction essentially
+strangles the spatial organizational
+
+ align:start position:0%
+strangles the spatial organizational
+ 
+
+ align:start position:0%
+strangles the spatial organizational
+segments
+
+ align:start position:0%
+segments
+ 
+
+ align:start position:0%
+segments
+so in other words
+
+ align:start position:0%
+so in other words
+ 
+
+ align:start position:0%
+so in other words
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this particular scene there is ambient
+
+ align:start position:0%
+this particular scene there is ambient
+ 
+
+ align:start position:0%
+this particular scene there is ambient
+light that is reflected of your faces
+
+ align:start position:0%
+light that is reflected of your faces
+ 
+
+ align:start position:0%
+light that is reflected of your faces
+individual spots on your face and so
+
+ align:start position:0%
+individual spots on your face and so
+ 
+
+ align:start position:0%
+individual spots on your face and so
+right there if I put a photo detector
+
+ align:start position:0%
+right there if I put a photo detector
+ 
+
+ align:start position:0%
+right there if I put a photo detector
+and move it around your face it can
+
+ align:start position:0%
+and move it around your face it can
+ 
+
+ align:start position:0%
+and move it around your face it can
+measure the reflectance of the surface
+
+ align:start position:0%
+measure the reflectance of the surface
+ 
+
+ align:start position:0%
+measure the reflectance of the surface
+if I move that photo detector over here
+
+ align:start position:0%
+if I move that photo detector over here
+ 
+
+ align:start position:0%
+if I move that photo detector over here
+and if I put a photographic film or a
+
+ align:start position:0%
+and if I put a photographic film or a
+ 
+
+ align:start position:0%
+and if I put a photographic film or a
+CCD without any Optical element I'm just
+
+ align:start position:0%
+CCD without any Optical element I'm just
+ 
+
+ align:start position:0%
+CCD without any Optical element I'm just
+going to get basically your uniform
+
+ align:start position:0%
+going to get basically your uniform
+ 
+
+ align:start position:0%
+going to get basically your uniform
+exposure all that special organization
+
+ align:start position:0%
+exposure all that special organization
+ 
+
+ align:start position:0%
+exposure all that special organization
+is lost
+
+ align:start position:0%
+is lost
+ 
+
+ align:start position:0%
+is lost
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we effectively
+
+ align:start position:0%
+we effectively
+ 
+
+ align:start position:0%
+we effectively
+when we are doing the
+
+ align:start position:0%
+when we are doing the
+ 
+
+ align:start position:0%
+when we are doing the
+standoff sensing
+
+ align:start position:0%
+standoff sensing
+ 
+
+ align:start position:0%
+standoff sensing
+we have two parts
+
+ align:start position:0%
+we have two parts
+ 
+
+ align:start position:0%
+we have two parts
+one you can call it the source encoding
+
+ align:start position:0%
+one you can call it the source encoding
+ 
+
+ align:start position:0%
+one you can call it the source encoding
+that is the phenomenology
+
+ align:start position:0%
+that is the phenomenology
+ 
+
+ align:start position:0%
+that is the phenomenology
+by which the objects in the scene
+
+ align:start position:0%
+by which the objects in the scene
+ 
+
+ align:start position:0%
+by which the objects in the scene
+impress information about themselves on
+
+ align:start position:0%
+impress information about themselves on
+ 
+
+ align:start position:0%
+impress information about themselves on
+the electromagnetic radiation whether
+
+ align:start position:0%
+the electromagnetic radiation whether
+ 
+
+ align:start position:0%
+the electromagnetic radiation whether
+it's by emission or reflection or
+
+ align:start position:0%
+it's by emission or reflection or
+ 
+
+ align:start position:0%
+it's by emission or reflection or
+absorption or scattering and the full
+
+ align:start position:0%
+absorption or scattering and the full
+ 
+
+ align:start position:0%
+absorption or scattering and the full
+domain of the electromagnetic wavefront
+
+ align:start position:0%
+domain of the electromagnetic wavefront
+ 
+
+ align:start position:0%
+domain of the electromagnetic wavefront
+the amplitude and wavelength and poor
+
+ align:start position:0%
+the amplitude and wavelength and poor
+ 
+
+ align:start position:0%
+the amplitude and wavelength and poor
+rotation and everything is used to
+
+ align:start position:0%
+rotation and everything is used to
+ 
+
+ align:start position:0%
+rotation and everything is used to
+encode that information and the other is
+
+ align:start position:0%
+encode that information and the other is
+ 
+
+ align:start position:0%
+encode that information and the other is
+channel encoding or Channel Distortion
+
+ align:start position:0%
+channel encoding or Channel Distortion
+ 
+
+ align:start position:0%
+channel encoding or Channel Distortion
+that is the result of the propagation of
+
+ align:start position:0%
+that is the result of the propagation of
+ 
+
+ align:start position:0%
+that is the result of the propagation of
+that wave between the objects and your
+
+ align:start position:0%
+that wave between the objects and your
+ 
+
+ align:start position:0%
+that wave between the objects and your
+entrance pupil or where you are entering
+
+ align:start position:0%
+entrance pupil or where you are entering
+ 
+
+ align:start position:0%
+entrance pupil or where you are entering
+so these these are the two things so we
+
+ align:start position:0%
+so these these are the two things so we
+ 
+
+ align:start position:0%
+so these these are the two things so we
+we are when we say about processing we
+
+ align:start position:0%
+we are when we say about processing we
+ 
+
+ align:start position:0%
+we are when we say about processing we
+are talking about removing the channel
+
+ align:start position:0%
+are talking about removing the channel
+ 
+
+ align:start position:0%
+are talking about removing the channel
+Distortion or undoing the effects of
+
+ align:start position:0%
+Distortion or undoing the effects of
+ 
+
+ align:start position:0%
+Distortion or undoing the effects of
+diffraction
+
+ align:start position:0%
+diffraction
+ 
+
+ align:start position:0%
+diffraction
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what are the components of an Imaging
+
+ align:start position:0%
+what are the components of an Imaging
+ 
+
+ align:start position:0%
+what are the components of an Imaging
+sensor and I'm sure you you have done
+
+ align:start position:0%
+sensor and I'm sure you you have done
+ 
+
+ align:start position:0%
+sensor and I'm sure you you have done
+this in this class
+
+ align:start position:0%
+this in this class
+ 
+
+ align:start position:0%
+this in this class
+so there is the front-end element that
+
+ align:start position:0%
+so there is the front-end element that
+ 
+
+ align:start position:0%
+so there is the front-end element that
+operates on the electromagnetic wave
+
+ align:start position:0%
+operates on the electromagnetic wave
+ 
+
+ align:start position:0%
+operates on the electromagnetic wave
+directly when there is the construction
+
+ align:start position:0%
+directly when there is the construction
+ 
+
+ align:start position:0%
+directly when there is the construction
+that takes that electromagnetic energy
+
+ align:start position:0%
+that takes that electromagnetic energy
+ 
+
+ align:start position:0%
+that takes that electromagnetic energy
+and transduces it into some other form
+
+ align:start position:0%
+and transduces it into some other form
+ 
+
+ align:start position:0%
+and transduces it into some other form
+in photographic film it was chemical in
+
+ align:start position:0%
+in photographic film it was chemical in
+ 
+
+ align:start position:0%
+in photographic film it was chemical in
+ccds and CMOS it's the electrical energy
+
+ align:start position:0%
+ccds and CMOS it's the electrical energy
+ 
+
+ align:start position:0%
+ccds and CMOS it's the electrical energy
+and then there is the storage display
+
+ align:start position:0%
+and then there is the storage display
+ 
+
+ align:start position:0%
+and then there is the storage display
+processing and exploitation so these are
+
+ align:start position:0%
+processing and exploitation so these are
+ 
+
+ align:start position:0%
+processing and exploitation so these are
+the three stages
+
+ align:start position:0%
+the three stages
+ 
+
+ align:start position:0%
+the three stages
+and I'm using the code this color is not
+
+ align:start position:0%
+and I'm using the code this color is not
+ 
+
+ align:start position:0%
+and I'm using the code this color is not
+that strong but
+
+ align:start position:0%
+that strong but
+ 
+
+ align:start position:0%
+that strong but
+blue means biology and pink means
+
+ align:start position:0%
+blue means biology and pink means
+ 
+
+ align:start position:0%
+blue means biology and pink means
+technology so in the prehistoric period
+
+ align:start position:0%
+technology so in the prehistoric period
+ 
+
+ align:start position:0%
+technology so in the prehistoric period
+all these elements were biological the
+
+ align:start position:0%
+all these elements were biological the
+ 
+
+ align:start position:0%
+all these elements were biological the
+front end element was the Optics of your
+
+ align:start position:0%
+front end element was the Optics of your
+ 
+
+ align:start position:0%
+front end element was the Optics of your
+eye the transduction was your retina and
+
+ align:start position:0%
+eye the transduction was your retina and
+ 
+
+ align:start position:0%
+eye the transduction was your retina and
+the subsequent processing going into B1
+
+ align:start position:0%
+the subsequent processing going into B1
+ 
+
+ align:start position:0%
+the subsequent processing going into B1
+all the way up to the three frontal
+
+ align:start position:0%
+all the way up to the three frontal
+ 
+
+ align:start position:0%
+all the way up to the three frontal
+cortex where
+
+ align:start position:0%
+cortex where
+ 
+
+ align:start position:0%
+cortex where
+some recognition or some processing
+
+ align:start position:0%
+some recognition or some processing
+ 
+
+ align:start position:0%
+some recognition or some processing
+exploitation took place it was probably
+
+ align:start position:0%
+exploitation took place it was probably
+ 
+
+ align:start position:0%
+exploitation took place it was probably
+before language so we don't know what
+
+ align:start position:0%
+before language so we don't know what
+ 
+
+ align:start position:0%
+before language so we don't know what
+the prehistoric primates
+
+ align:start position:0%
+the prehistoric primates
+ 
+
+ align:start position:0%
+the prehistoric primates
+and what turns they thought so
+
+ align:start position:0%
+and what turns they thought so
+ 
+
+ align:start position:0%
+and what turns they thought so
+then we come forward to prehistoric and
+
+ align:start position:0%
+then we come forward to prehistoric and
+ 
+
+ align:start position:0%
+then we come forward to prehistoric and
+historic period
+
+ align:start position:0%
+historic period
+ 
+
+ align:start position:0%
+historic period
+down to cavings
+
+ align:start position:0%
+down to cavings
+ 
+
+ align:start position:0%
+down to cavings
+so there the storage and display
+
+ align:start position:0%
+so there the storage and display
+ 
+
+ align:start position:0%
+so there the storage and display
+technology in quotes for the interviews
+
+ align:start position:0%
+technology in quotes for the interviews
+ 
+
+ align:start position:0%
+technology in quotes for the interviews
+everything else is still biological but
+
+ align:start position:0%
+everything else is still biological but
+ 
+
+ align:start position:0%
+everything else is still biological but
+capturing and storing that experience
+
+ align:start position:0%
+capturing and storing that experience
+ 
+
+ align:start position:0%
+capturing and storing that experience
+and Beyond this prehistoric and historic
+
+ align:start position:0%
+and Beyond this prehistoric and historic
+ 
+
+ align:start position:0%
+and Beyond this prehistoric and historic
+period you can imagine the technology
+
+ align:start position:0%
+period you can imagine the technology
+ 
+
+ align:start position:0%
+period you can imagine the technology
+getting more sophisticated
+
+ align:start position:0%
+getting more sophisticated
+ 
+
+ align:start position:0%
+getting more sophisticated
+but the principle did not change
+
+ align:start position:0%
+but the principle did not change
+ 
+
+ align:start position:0%
+but the principle did not change
+and it it stayed that way through the
+
+ align:start position:0%
+and it it stayed that way through the
+ 
+
+ align:start position:0%
+and it it stayed that way through the
+prehistoric and historic period
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now as we go forward to pre-industrial
+
+ align:start position:0%
+now as we go forward to pre-industrial
+ 
+
+ align:start position:0%
+now as we go forward to pre-industrial
+period and as I said the optical
+
+ align:start position:0%
+period and as I said the optical
+ 
+
+ align:start position:0%
+period and as I said the optical
+elements were introduced so the Optics
+
+ align:start position:0%
+elements were introduced so the Optics
+ 
+
+ align:start position:0%
+elements were introduced so the Optics
+of the eye or the front end element of
+
+ align:start position:0%
+of the eye or the front end element of
+ 
+
+ align:start position:0%
+of the eye or the front end element of
+the entire sensing chain was augmented
+
+ align:start position:0%
+the entire sensing chain was augmented
+ 
+
+ align:start position:0%
+the entire sensing chain was augmented
+by technology
+
+ align:start position:0%
+by technology
+ 
+
+ align:start position:0%
+by technology
+and what were the consequences you could
+
+ align:start position:0%
+and what were the consequences you could
+ 
+
+ align:start position:0%
+and what were the consequences you could
+see further and you could see smaller
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+industrial period was basically the
+
+ align:start position:0%
+industrial period was basically the
+ 
+
+ align:start position:0%
+industrial period was basically the
+invention of Photography so in addition
+
+ align:start position:0%
+invention of Photography so in addition
+ 
+
+ align:start position:0%
+invention of Photography so in addition
+to the eye
+
+ align:start position:0%
+to the eye
+ 
+
+ align:start position:0%
+to the eye
+the transduction element and the storage
+
+ align:start position:0%
+the transduction element and the storage
+ 
+
+ align:start position:0%
+the transduction element and the storage
+and display element
+
+ align:start position:0%
+and display element
+ 
+
+ align:start position:0%
+and display element
+was now technological
+
+ align:start position:0%
+was now technological
+ 
+
+ align:start position:0%
+was now technological
+what are the consequences
+
+ align:start position:0%
+what are the consequences
+ 
+
+ align:start position:0%
+what are the consequences
+we could expand into invisible Spectrum
+
+ align:start position:0%
+we could expand into invisible Spectrum
+ 
+
+ align:start position:0%
+we could expand into invisible Spectrum
+now one has to remember without
+
+ align:start position:0%
+now one has to remember without
+ 
+
+ align:start position:0%
+now one has to remember without
+photographic film x-rays would never
+
+ align:start position:0%
+photographic film x-rays would never
+ 
+
+ align:start position:0%
+photographic film x-rays would never
+have been invented
+
+ align:start position:0%
+have been invented
+ 
+
+ align:start position:0%
+have been invented
+because rented figured out that there
+
+ align:start position:0%
+because rented figured out that there
+ 
+
+ align:start position:0%
+because rented figured out that there
+was something going on because he had
+
+ align:start position:0%
+was something going on because he had
+ 
+
+ align:start position:0%
+was something going on because he had
+this film that was told in that drawer
+
+ align:start position:0%
+this film that was told in that drawer
+ 
+
+ align:start position:0%
+this film that was told in that drawer
+and it's still something happened it
+
+ align:start position:0%
+and it's still something happened it
+ 
+
+ align:start position:0%
+and it's still something happened it
+exposed so
+
+ align:start position:0%
+exposed so
+ 
+
+ align:start position:0%
+exposed so
+so invisible Spectrum then second thing
+
+ align:start position:0%
+so invisible Spectrum then second thing
+ 
+
+ align:start position:0%
+so invisible Spectrum then second thing
+is time sequence recording
+
+ align:start position:0%
+is time sequence recording
+ 
+
+ align:start position:0%
+is time sequence recording
+allowing the analysis of very fast or
+
+ align:start position:0%
+allowing the analysis of very fast or
+ 
+
+ align:start position:0%
+allowing the analysis of very fast or
+very slow events time lapse photography
+
+ align:start position:0%
+very slow events time lapse photography
+ 
+
+ align:start position:0%
+very slow events time lapse photography
+and other things so detailed study of
+
+ align:start position:0%
+and other things so detailed study of
+ 
+
+ align:start position:0%
+and other things so detailed study of
+motion that went well beyond the human
+
+ align:start position:0%
+motion that went well beyond the human
+ 
+
+ align:start position:0%
+motion that went well beyond the human
+time frame
+
+ align:start position:0%
+time frame
+ 
+
+ align:start position:0%
+time frame
+however
+
+ align:start position:0%
+however
+ 
+
+ align:start position:0%
+however
+everything was still non-real time you
+
+ align:start position:0%
+everything was still non-real time you
+ 
+
+ align:start position:0%
+everything was still non-real time you
+still required chemical processing and
+
+ align:start position:0%
+still required chemical processing and
+ 
+
+ align:start position:0%
+still required chemical processing and
+processing and exploitation was still by
+
+ align:start position:0%
+processing and exploitation was still by
+ 
+
+ align:start position:0%
+processing and exploitation was still by
+human
+
+ align:start position:0%
+human
+ 
+
+ align:start position:0%
+human
+so as we move forward to the modern era
+
+ align:start position:0%
+so as we move forward to the modern era
+ 
+
+ align:start position:0%
+so as we move forward to the modern era
+20th century it really is a revolution
+
+ align:start position:0%
+20th century it really is a revolution
+ 
+
+ align:start position:0%
+20th century it really is a revolution
+in imaging sensors
+
+ align:start position:0%
+in imaging sensors
+ 
+
+ align:start position:0%
+in imaging sensors
+that the processing and exploitation is
+
+ align:start position:0%
+that the processing and exploitation is
+ 
+
+ align:start position:0%
+that the processing and exploitation is
+still primarily by humans but that
+
+ align:start position:0%
+still primarily by humans but that
+ 
+
+ align:start position:0%
+still primarily by humans but that
+slowly is moving into a completely
+
+ align:start position:0%
+slowly is moving into a completely
+ 
+
+ align:start position:0%
+slowly is moving into a completely
+automated image exploitation system and
+
+ align:start position:0%
+automated image exploitation system and
+ 
+
+ align:start position:0%
+automated image exploitation system and
+I just thought this is an interesting
+
+ align:start position:0%
+I just thought this is an interesting
+ 
+
+ align:start position:0%
+I just thought this is an interesting
+example I don't think the PV soccer
+
+ align:start position:0%
+example I don't think the PV soccer
+ 
+
+ align:start position:0%
+example I don't think the PV soccer
+league still has a Gold Line camera or
+
+ align:start position:0%
+league still has a Gold Line camera or
+ 
+
+ align:start position:0%
+league still has a Gold Line camera or
+something to decide whether
+
+ align:start position:0%
+something to decide whether
+ 
+
+ align:start position:0%
+something to decide whether
+somebody was outside or whatever but
+
+ align:start position:0%
+somebody was outside or whatever but
+ 
+
+ align:start position:0%
+somebody was outside or whatever but
+it's really a matter of time so
+
+ align:start position:0%
+it's really a matter of time so
+ 
+
+ align:start position:0%
+it's really a matter of time so
+and why is it a dramatic break from the
+
+ align:start position:0%
+and why is it a dramatic break from the
+ 
+
+ align:start position:0%
+and why is it a dramatic break from the
+past real-time acquisition no chemical
+
+ align:start position:0%
+past real-time acquisition no chemical
+ 
+
+ align:start position:0%
+past real-time acquisition no chemical
+processing
+
+ align:start position:0%
+processing
+ 
+
+ align:start position:0%
+processing
+real-time processing and exploit
+
+ align:start position:0%
+real-time processing and exploit
+ 
+
+ align:start position:0%
+real-time processing and exploit
+scalable manufacturing at least as far
+
+ align:start position:0%
+scalable manufacturing at least as far
+ 
+
+ align:start position:0%
+scalable manufacturing at least as far
+as sensors are presented and now with
+
+ align:start position:0%
+as sensors are presented and now with
+ 
+
+ align:start position:0%
+as sensors are presented and now with
+the wafer level camera and new designs
+
+ align:start position:0%
+the wafer level camera and new designs
+ 
+
+ align:start position:0%
+the wafer level camera and new designs
+for front-end Optical elements that
+
+ align:start position:0%
+for front-end Optical elements that
+ 
+
+ align:start position:0%
+for front-end Optical elements that
+scalable manufacturing is also moving
+
+ align:start position:0%
+scalable manufacturing is also moving
+ 
+
+ align:start position:0%
+scalable manufacturing is also moving
+towards objects
+
+ align:start position:0%
+towards objects
+ 
+
+ align:start position:0%
+towards objects
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+let me see this I don't know did you did
+
+ align:start position:0%
+let me see this I don't know did you did
+ 
+
+ align:start position:0%
+let me see this I don't know did you did
+you show this code in the class no I
+
+ align:start position:0%
+you show this code in the class no I
+ 
+
+ align:start position:0%
+you show this code in the class no I
+haven't okay yes this uh as I was
+
+ align:start position:0%
+haven't okay yes this uh as I was
+ 
+
+ align:start position:0%
+haven't okay yes this uh as I was
+working on some of this presentation
+
+ align:start position:0%
+working on some of this presentation
+ 
+
+ align:start position:0%
+working on some of this presentation
+from this very interesting article from
+
+ align:start position:0%
+from this very interesting article from
+ 
+
+ align:start position:0%
+from this very interesting article from
+Nathan mervold people know about Nathan
+
+ align:start position:0%
+Nathan mervold people know about Nathan
+ 
+
+ align:start position:0%
+Nathan mervold people know about Nathan
+merhold and what is I think he was
+
+ align:start position:0%
+merhold and what is I think he was
+ 
+
+ align:start position:0%
+merhold and what is I think he was
+employee number 15 or something at
+
+ align:start position:0%
+employee number 15 or something at
+ 
+
+ align:start position:0%
+employee number 15 or something at
+Microsoft and from what I understand his
+
+ align:start position:0%
+Microsoft and from what I understand his
+ 
+
+ align:start position:0%
+Microsoft and from what I understand his
+primary contribution to the thing at
+
+ align:start position:0%
+primary contribution to the thing at
+ 
+
+ align:start position:0%
+primary contribution to the thing at
+that time to have a standalone company
+
+ align:start position:0%
+that time to have a standalone company
+ 
+
+ align:start position:0%
+that time to have a standalone company
+that is solely for the purpose of
+
+ align:start position:0%
+that is solely for the purpose of
+ 
+
+ align:start position:0%
+that is solely for the purpose of
+developing system software and making
+
+ align:start position:0%
+developing system software and making
+ 
+
+ align:start position:0%
+developing system software and making
+money on that so his contribution was
+
+ align:start position:0%
+money on that so his contribution was
+ 
+
+ align:start position:0%
+money on that so his contribution was
+the business model for Microsoft
+
+ align:start position:0%
+the business model for Microsoft
+ 
+
+ align:start position:0%
+the business model for Microsoft
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+he is currently
+
+ align:start position:0%
+he is currently
+ 
+
+ align:start position:0%
+he is currently
+either the most famous or most reviled
+
+ align:start position:0%
+either the most famous or most reviled
+ 
+
+ align:start position:0%
+either the most famous or most reviled
+person in Silicon Valley
+
+ align:start position:0%
+person in Silicon Valley
+ 
+
+ align:start position:0%
+person in Silicon Valley
+for having started a company
+
+ align:start position:0%
+for having started a company
+ 
+
+ align:start position:0%
+for having started a company
+intellectual Ventures and again he's
+
+ align:start position:0%
+intellectual Ventures and again he's
+ 
+
+ align:start position:0%
+intellectual Ventures and again he's
+trying to do a business model that a
+
+ align:start position:0%
+trying to do a business model that a
+ 
+
+ align:start position:0%
+trying to do a business model that a
+company can exist solely for the purpose
+
+ align:start position:0%
+company can exist solely for the purpose
+ 
+
+ align:start position:0%
+company can exist solely for the purpose
+of inventing things never
+
+ align:start position:0%
+of inventing things never
+ 
+
+ align:start position:0%
+of inventing things never
+commercializing never productizing but
+
+ align:start position:0%
+commercializing never productizing but
+ 
+
+ align:start position:0%
+commercializing never productizing but
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+filing the patents and sitting on them
+
+ align:start position:0%
+filing the patents and sitting on them
+ 
+
+ align:start position:0%
+filing the patents and sitting on them
+and either licensing it or suing people
+
+ align:start position:0%
+and either licensing it or suing people
+ 
+
+ align:start position:0%
+and either licensing it or suing people
+who they think violated so it's a very
+
+ align:start position:0%
+who they think violated so it's a very
+ 
+
+ align:start position:0%
+who they think violated so it's a very
+interesting business model
+
+ align:start position:0%
+interesting business model
+ 
+
+ align:start position:0%
+interesting business model
+so obviously he knows something about
+
+ align:start position:0%
+so obviously he knows something about
+ 
+
+ align:start position:0%
+so obviously he knows something about
+these things but he made this comment
+
+ align:start position:0%
+these things but he made this comment
+ 
+
+ align:start position:0%
+these things but he made this comment
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+cameras will also change the form they
+
+ align:start position:0%
+cameras will also change the form they
+ 
+
+ align:start position:0%
+cameras will also change the form they
+are film cameras without the film
+
+ align:start position:0%
+are film cameras without the film
+ 
+
+ align:start position:0%
+are film cameras without the film
+basically like the early automobiles
+
+ align:start position:0%
+basically like the early automobiles
+ 
+
+ align:start position:0%
+basically like the early automobiles
+were Horseless carriages
+
+ align:start position:0%
+were Horseless carriages
+ 
+
+ align:start position:0%
+were Horseless carriages
+so his point is that the camera stores
+
+ align:start position:0%
+so his point is that the camera stores
+ 
+
+ align:start position:0%
+so his point is that the camera stores
+in the future will surprise us just as
+
+ align:start position:0%
+in the future will surprise us just as
+ 
+
+ align:start position:0%
+in the future will surprise us just as
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+and I was making this comment to
+
+ align:start position:0%
+and I was making this comment to
+ 
+
+ align:start position:0%
+and I was making this comment to
+somebody say oh what the hell is he
+
+ align:start position:0%
+somebody say oh what the hell is he
+ 
+
+ align:start position:0%
+somebody say oh what the hell is he
+talking about the automobiles are still
+
+ align:start position:0%
+talking about the automobiles are still
+ 
+
+ align:start position:0%
+talking about the automobiles are still
+the same with the 1910 100 years later
+
+ align:start position:0%
+the same with the 1910 100 years later
+ 
+
+ align:start position:0%
+the same with the 1910 100 years later
+nothing has changed it still is internal
+
+ align:start position:0%
+nothing has changed it still is internal
+ 
+
+ align:start position:0%
+nothing has changed it still is internal
+combustion engine and transmission and
+
+ align:start position:0%
+combustion engine and transmission and
+ 
+
+ align:start position:0%
+combustion engine and transmission and
+wheels well yes and no so now we we
+
+ align:start position:0%
+wheels well yes and no so now we we
+ 
+
+ align:start position:0%
+wheels well yes and no so now we we
+thought that we'll take this analogy
+
+ align:start position:0%
+thought that we'll take this analogy
+ 
+
+ align:start position:0%
+thought that we'll take this analogy
+little bit forward
+
+ align:start position:0%
+little bit forward
+ 
+
+ align:start position:0%
+little bit forward
+and say okay so horse-drawn carriage
+
+ align:start position:0%
+and say okay so horse-drawn carriage
+ 
+
+ align:start position:0%
+and say okay so horse-drawn carriage
+Horseless carry to a family station
+
+ align:start position:0%
+Horseless carry to a family station
+ 
+
+ align:start position:0%
+Horseless carry to a family station
+wagon up to here you can say really you
+
+ align:start position:0%
+wagon up to here you can say really you
+ 
+
+ align:start position:0%
+wagon up to here you can say really you
+know it's more sophisticated but nothing
+
+ align:start position:0%
+know it's more sophisticated but nothing
+ 
+
+ align:start position:0%
+know it's more sophisticated but nothing
+has changed but then you say what else
+
+ align:start position:0%
+has changed but then you say what else
+ 
+
+ align:start position:0%
+has changed but then you say what else
+has happened
+
+ align:start position:0%
+has happened
+ 
+
+ align:start position:0%
+has happened
+and you know
+
+ align:start position:0%
+and you know
+ 
+
+ align:start position:0%
+and you know
+Automotives
+
+ align:start position:0%
+Automotives
+ 
+
+ align:start position:0%
+Automotives
+tractors track Parts a tank to that car
+
+ align:start position:0%
+tractors track Parts a tank to that car
+ 
+
+ align:start position:0%
+tractors track Parts a tank to that car
+called Tango that can that's allowed to
+
+ align:start position:0%
+called Tango that can that's allowed to
+ 
+
+ align:start position:0%
+called Tango that can that's allowed to
+split delay and this of course you
+
+ align:start position:0%
+split delay and this of course you
+ 
+
+ align:start position:0%
+split delay and this of course you
+recognize that as Stanley
+
+ align:start position:0%
+recognize that as Stanley
+ 
+
+ align:start position:0%
+recognize that as Stanley
+autonomous vehicle
+
+ align:start position:0%
+autonomous vehicle
+ 
+
+ align:start position:0%
+autonomous vehicle
+so if we say
+
+ align:start position:0%
+so if we say
+ 
+
+ align:start position:0%
+so if we say
+that film cameras film less cameras I I
+
+ align:start position:0%
+that film cameras film less cameras I I
+ 
+
+ align:start position:0%
+that film cameras film less cameras I I
+really love this picture because both of
+
+ align:start position:0%
+really love this picture because both of
+ 
+
+ align:start position:0%
+really love this picture because both of
+them and cameras identical this instead
+
+ align:start position:0%
+them and cameras identical this instead
+ 
+
+ align:start position:0%
+them and cameras identical this instead
+of film back plane that's a CCD
+
+ align:start position:0%
+of film back plane that's a CCD
+ 
+
+ align:start position:0%
+of film back plane that's a CCD
+backplane so where is it going in the
+
+ align:start position:0%
+backplane so where is it going in the
+ 
+
+ align:start position:0%
+backplane so where is it going in the
+future what are the future directions
+
+ align:start position:0%
+future what are the future directions
+ 
+
+ align:start position:0%
+future what are the future directions
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+at least our projection is where it's
+
+ align:start position:0%
+at least our projection is where it's
+ 
+
+ align:start position:0%
+at least our projection is where it's
+going in the future is specialization
+
+ align:start position:0%
+going in the future is specialization
+ 
+
+ align:start position:0%
+going in the future is specialization
+and her Farm
+
+ align:start position:0%
+and her Farm
+ 
+
+ align:start position:0%
+and her Farm
+that the same concept of course there is
+
+ align:start position:0%
+that the same concept of course there is
+ 
+
+ align:start position:0%
+that the same concept of course there is
+some energy source and there is some
+
+ align:start position:0%
+some energy source and there is some
+ 
+
+ align:start position:0%
+some energy source and there is some
+mechanism to convert that energy into
+
+ align:start position:0%
+mechanism to convert that energy into
+ 
+
+ align:start position:0%
+mechanism to convert that energy into
+mechanical motion so in that sense
+
+ align:start position:0%
+mechanical motion so in that sense
+ 
+
+ align:start position:0%
+mechanical motion so in that sense
+nothing has changed
+
+ align:start position:0%
+nothing has changed
+ 
+
+ align:start position:0%
+nothing has changed
+but if you look at this and this and
+
+ align:start position:0%
+but if you look at this and this and
+ 
+
+ align:start position:0%
+but if you look at this and this and
+this and this
+
+ align:start position:0%
+this and this
+ 
+
+ align:start position:0%
+this and this
+each one is designed for a different
+
+ align:start position:0%
+each one is designed for a different
+ 
+
+ align:start position:0%
+each one is designed for a different
+purpose each one is specialized for that
+
+ align:start position:0%
+purpose each one is specialized for that
+ 
+
+ align:start position:0%
+purpose each one is specialized for that
+particular purpose
+
+ align:start position:0%
+particular purpose
+ 
+
+ align:start position:0%
+particular purpose
+so similarly cameras right now a camera
+
+ align:start position:0%
+so similarly cameras right now a camera
+ 
+
+ align:start position:0%
+so similarly cameras right now a camera
+is a camera that takes picture whether
+
+ align:start position:0%
+is a camera that takes picture whether
+ 
+
+ align:start position:0%
+is a camera that takes picture whether
+it's the Hubble or whether it is your
+
+ align:start position:0%
+it's the Hubble or whether it is your
+ 
+
+ align:start position:0%
+it's the Hubble or whether it is your
+cell phone camera or anything or the
+
+ align:start position:0%
+cell phone camera or anything or the
+ 
+
+ align:start position:0%
+cell phone camera or anything or the
+fill camera
+
+ align:start position:0%
+fill camera
+ 
+
+ align:start position:0%
+fill camera
+the structure and function
+
+ align:start position:0%
+the structure and function
+ 
+
+ align:start position:0%
+the structure and function
+so far hasn't changed at all
+
+ align:start position:0%
+so far hasn't changed at all
+ 
+
+ align:start position:0%
+so far hasn't changed at all
+and that is where we feel a dramatic
+
+ align:start position:0%
+and that is where we feel a dramatic
+ 
+
+ align:start position:0%
+and that is where we feel a dramatic
+break
+
+ align:start position:0%
+break
+ 
+
+ align:start position:0%
+break
+uh coming in the future because of the
+
+ align:start position:0%
+uh coming in the future because of the
+ 
+
+ align:start position:0%
+uh coming in the future because of the
+flexibility of the technology because of
+
+ align:start position:0%
+flexibility of the technology because of
+ 
+
+ align:start position:0%
+flexibility of the technology because of
+very specialized applications very
+
+ align:start position:0%
+very specialized applications very
+ 
+
+ align:start position:0%
+very specialized applications very
+specialized constraints for things so
+
+ align:start position:0%
+specialized constraints for things so
+ 
+
+ align:start position:0%
+specialized constraints for things so
+why shouldn't there be uh you can say
+
+ align:start position:0%
+why shouldn't there be uh you can say
+ 
+
+ align:start position:0%
+why shouldn't there be uh you can say
+just like there are Asics application
+
+ align:start position:0%
+just like there are Asics application
+ 
+
+ align:start position:0%
+just like there are Asics application
+specific integrated circuits why
+
+ align:start position:0%
+specific integrated circuits why
+ 
+
+ align:start position:0%
+specific integrated circuits why
+shouldn't there be applications specific
+
+ align:start position:0%
+shouldn't there be applications specific
+ 
+
+ align:start position:0%
+shouldn't there be applications specific
+Imaging systems cases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that an Imaging sensor that
+
+ align:start position:0%
+that an Imaging sensor that
+ 
+
+ align:start position:0%
+that an Imaging sensor that
+besides on its own without any manual
+
+ align:start position:0%
+besides on its own without any manual
+ 
+
+ align:start position:0%
+besides on its own without any manual
+intervention where to focus on how to
+
+ align:start position:0%
+intervention where to focus on how to
+ 
+
+ align:start position:0%
+intervention where to focus on how to
+interrogate the scene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is sort of a reworking the
+
+ align:start position:0%
+and this is sort of a reworking the
+ 
+
+ align:start position:0%
+and this is sort of a reworking the
+biological inspiration it's the cameras
+
+ align:start position:0%
+biological inspiration it's the cameras
+ 
+
+ align:start position:0%
+biological inspiration it's the cameras
+are really replacing the human eye
+
+ align:start position:0%
+are really replacing the human eye
+ 
+
+ align:start position:0%
+are really replacing the human eye
+trying to form a similar kind of
+
+ align:start position:0%
+trying to form a similar kind of
+ 
+
+ align:start position:0%
+trying to form a similar kind of
+representation whereas if you go to the
+
+ align:start position:0%
+representation whereas if you go to the
+ 
+
+ align:start position:0%
+representation whereas if you go to the
+biological world it's a vast array of
+
+ align:start position:0%
+biological world it's a vast array of
+ 
+
+ align:start position:0%
+biological world it's a vast array of
+different types of Imaging sensors it's
+
+ align:start position:0%
+different types of Imaging sensors it's
+ 
+
+ align:start position:0%
+different types of Imaging sensors it's
+probably not even proper to call them
+
+ align:start position:0%
+probably not even proper to call them
+ 
+
+ align:start position:0%
+probably not even proper to call them
+Imaging sensors they are more like
+
+ align:start position:0%
+Imaging sensors they are more like
+ 
+
+ align:start position:0%
+Imaging sensors they are more like
+spatial sensors the most primitive form
+
+ align:start position:0%
+spatial sensors the most primitive form
+ 
+
+ align:start position:0%
+spatial sensors the most primitive form
+an earthworm with a light sensitive skin
+
+ align:start position:0%
+an earthworm with a light sensitive skin
+ 
+
+ align:start position:0%
+an earthworm with a light sensitive skin
+that simply is able to distinguish there
+
+ align:start position:0%
+that simply is able to distinguish there
+ 
+
+ align:start position:0%
+that simply is able to distinguish there
+is more light on this side versus that
+
+ align:start position:0%
+is more light on this side versus that
+ 
+
+ align:start position:0%
+is more light on this side versus that
+side and can steer itself accordingly
+
+ align:start position:0%
+side and can steer itself accordingly
+ 
+
+ align:start position:0%
+side and can steer itself accordingly
+and then variety of techniques for the
+
+ align:start position:0%
+and then variety of techniques for the
+ 
+
+ align:start position:0%
+and then variety of techniques for the
+insects and other creatures
+
+ align:start position:0%
+insects and other creatures
+ 
+
+ align:start position:0%
+insects and other creatures
+and these their spectral response the
+
+ align:start position:0%
+and these their spectral response the
+ 
+
+ align:start position:0%
+and these their spectral response the
+processing the functionality just
+
+ align:start position:0%
+processing the functionality just
+ 
+
+ align:start position:0%
+processing the functionality just
+exquisitely you are for the specific
+
+ align:start position:0%
+exquisitely you are for the specific
+ 
+
+ align:start position:0%
+exquisitely you are for the specific
+evolutionary means of the animal for the
+
+ align:start position:0%
+evolutionary means of the animal for the
+ 
+
+ align:start position:0%
+evolutionary means of the animal for the
+survival
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh I I I don't know if I really I
+
+ align:start position:0%
+and uh I I I don't know if I really I
+ 
+
+ align:start position:0%
+and uh I I I don't know if I really I
+think I I would like to sort of
+
+ align:start position:0%
+think I I would like to sort of
+ 
+
+ align:start position:0%
+think I I would like to sort of
+the Optics is now
+
+ align:start position:0%
+the Optics is now
+ 
+
+ align:start position:0%
+the Optics is now
+getting their molding glass plastic
+
+ align:start position:0%
+getting their molding glass plastic
+ 
+
+ align:start position:0%
+getting their molding glass plastic
+lenses Diamond turning micro fabrication
+
+ align:start position:0%
+lenses Diamond turning micro fabrication
+ 
+
+ align:start position:0%
+lenses Diamond turning micro fabrication
+Vapor scale assembly so the grind and
+
+ align:start position:0%
+Vapor scale assembly so the grind and
+ 
+
+ align:start position:0%
+Vapor scale assembly so the grind and
+polish technique for making Optical
+
+ align:start position:0%
+polish technique for making Optical
+ 
+
+ align:start position:0%
+polish technique for making Optical
+elements it really is
+
+ align:start position:0%
+elements it really is
+ 
+
+ align:start position:0%
+elements it really is
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+relegated to very high quality
+
+ align:start position:0%
+relegated to very high quality
+ 
+
+ align:start position:0%
+relegated to very high quality
+specialized
+
+ align:start position:0%
+specialized
+ 
+
+ align:start position:0%
+specialized
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+processing embedded in the cameras
+
+ align:start position:0%
+processing embedded in the cameras
+ 
+
+ align:start position:0%
+processing embedded in the cameras
+that's the first step right now red eye
+
+ align:start position:0%
+that's the first step right now red eye
+ 
+
+ align:start position:0%
+that's the first step right now red eye
+removal face detection smile detection
+
+ align:start position:0%
+removal face detection smile detection
+ 
+
+ align:start position:0%
+removal face detection smile detection
+and this is of course ramesha
+
+ align:start position:0%
+and this is of course ramesha
+ 
+
+ align:start position:0%
+and this is of course ramesha
+illumination right now he's still using
+
+ align:start position:0%
+illumination right now he's still using
+ 
+
+ align:start position:0%
+illumination right now he's still using
+this dumb flash that is goes so spatial
+
+ align:start position:0%
+this dumb flash that is goes so spatial
+ 
+
+ align:start position:0%
+this dumb flash that is goes so spatial
+temporal coding of Illumination in order
+
+ align:start position:0%
+temporal coding of Illumination in order
+ 
+
+ align:start position:0%
+temporal coding of Illumination in order
+to enhance your ability to extract
+
+ align:start position:0%
+to enhance your ability to extract
+ 
+
+ align:start position:0%
+to enhance your ability to extract
+information from the scene
+
+ align:start position:0%
+information from the scene
+ 
+
+ align:start position:0%
+information from the scene
+different spectral regions for
+
+ align:start position:0%
+different spectral regions for
+ 
+
+ align:start position:0%
+different spectral regions for
+exploiting that information
+
+ align:start position:0%
+exploiting that information
+ 
+
+ align:start position:0%
+exploiting that information
+and this is this is some picture gallery
+
+ align:start position:0%
+and this is this is some picture gallery
+ 
+
+ align:start position:0%
+and this is this is some picture gallery
+of new Optics that's the Kodak micro
+
+ align:start position:0%
+of new Optics that's the Kodak micro
+ 
+
+ align:start position:0%
+of new Optics that's the Kodak micro
+lens array folded Optics
+
+ align:start position:0%
+lens array folded Optics
+ 
+
+ align:start position:0%
+lens array folded Optics
+Diamond Turn Optics and freeform
+
+ align:start position:0%
+Diamond Turn Optics and freeform
+ 
+
+ align:start position:0%
+Diamond Turn Optics and freeform
+multi-scale conformal Optics
+
+ align:start position:0%
+multi-scale conformal Optics
+ 
+
+ align:start position:0%
+multi-scale conformal Optics
+what do you use it for the last one I'm
+
+ align:start position:0%
+what do you use it for the last one I'm
+ 
+
+ align:start position:0%
+what do you use it for the last one I'm
+sorry what is the what's the use of the
+
+ align:start position:0%
+sorry what is the what's the use of the
+ 
+
+ align:start position:0%
+sorry what is the what's the use of the
+last one I don't know if this is very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+this is just a technology that's that's
+
+ align:start position:0%
+this is just a technology that's that's
+ 
+
+ align:start position:0%
+this is just a technology that's that's
+there that you saw the in Charlotte they
+
+ align:start position:0%
+there that you saw the in Charlotte they
+ 
+
+ align:start position:0%
+there that you saw the in Charlotte they
+have this
+
+ align:start position:0%
+have this
+ 
+
+ align:start position:0%
+have this
+they can do this like an edge away
+
+ align:start position:0%
+they can do this like an edge away
+ 
+
+ align:start position:0%
+they can do this like an edge away
+Optics
+
+ align:start position:0%
+Optics
+ 
+
+ align:start position:0%
+Optics
+I think it's a six degrees of freedom
+
+ align:start position:0%
+I think it's a six degrees of freedom
+ 
+
+ align:start position:0%
+I think it's a six degrees of freedom
+machine for turning and then you can do
+
+ align:start position:0%
+machine for turning and then you can do
+ 
+
+ align:start position:0%
+machine for turning and then you can do
+that on a conforming surface
+
+ align:start position:0%
+that on a conforming surface
+ 
+
+ align:start position:0%
+that on a conforming surface
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+these uh
+
+ align:start position:0%
+these uh
+ 
+
+ align:start position:0%
+these uh
+these I think uh just going back to your
+
+ align:start position:0%
+these I think uh just going back to your
+ 
+
+ align:start position:0%
+these I think uh just going back to your
+previous comment yeah uh
+
+ align:start position:0%
+previous comment yeah uh
+ 
+
+ align:start position:0%
+previous comment yeah uh
+so okay everything is moving
+
+ align:start position:0%
+so okay everything is moving
+ 
+
+ align:start position:0%
+so okay everything is moving
+in a direction where things are more
+
+ align:start position:0%
+in a direction where things are more
+ 
+
+ align:start position:0%
+in a direction where things are more
+programmable more specialized uh but in
+
+ align:start position:0%
+programmable more specialized uh but in
+ 
+
+ align:start position:0%
+programmable more specialized uh but in
+the basic laws of physics are not going
+
+ align:start position:0%
+the basic laws of physics are not going
+ 
+
+ align:start position:0%
+the basic laws of physics are not going
+to change we're still going to convert
+
+ align:start position:0%
+to change we're still going to convert
+ 
+
+ align:start position:0%
+to change we're still going to convert
+4000 electrons and and so on and so are
+
+ align:start position:0%
+4000 electrons and and so on and so are
+ 
+
+ align:start position:0%
+4000 electrons and and so on and so are
+there some
+
+ align:start position:0%
+there some
+ 
+
+ align:start position:0%
+there some
+uh you know if you want to build a an
+
+ align:start position:0%
+uh you know if you want to build a an
+ 
+
+ align:start position:0%
+uh you know if you want to build a an
+aircraft you're going to use you know
+
+ align:start position:0%
+aircraft you're going to use you know
+ 
+
+ align:start position:0%
+aircraft you're going to use you know
+Bernoulli principle if you're going to
+
+ align:start position:0%
+Bernoulli principle if you're going to
+ 
+
+ align:start position:0%
+Bernoulli principle if you're going to
+if you're going to build a vehicle it's
+
+ align:start position:0%
+if you're going to build a vehicle it's
+ 
+
+ align:start position:0%
+if you're going to build a vehicle it's
+Newton's third law it's just going to
+
+ align:start position:0%
+Newton's third law it's just going to
+ 
+
+ align:start position:0%
+Newton's third law it's just going to
+use those laws of physics yeah yeah is
+
+ align:start position:0%
+use those laws of physics yeah yeah is
+ 
+
+ align:start position:0%
+use those laws of physics yeah yeah is
+there something fundamental about
+
+ align:start position:0%
+there something fundamental about
+ 
+
+ align:start position:0%
+there something fundamental about
+Imaging
+
+ align:start position:0%
+Imaging
+ 
+
+ align:start position:0%
+Imaging
+that we should be challenging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it should be continued as the same laws
+
+ align:start position:0%
+it should be continued as the same laws
+ 
+
+ align:start position:0%
+it should be continued as the same laws
+of physics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what laws of physics I think it may not
+
+ align:start position:0%
+what laws of physics I think it may not
+ 
+
+ align:start position:0%
+what laws of physics I think it may not
+be like challenging laws of physics but
+
+ align:start position:0%
+be like challenging laws of physics but
+ 
+
+ align:start position:0%
+be like challenging laws of physics but
+what are the laws of physics that we can
+
+ align:start position:0%
+what are the laws of physics that we can
+ 
+
+ align:start position:0%
+what are the laws of physics that we can
+bend or there are various qualifiers so
+
+ align:start position:0%
+bend or there are various qualifiers so
+ 
+
+ align:start position:0%
+bend or there are various qualifiers so
+like you know one of the things yeah
+
+ align:start position:0%
+like you know one of the things yeah
+ 
+
+ align:start position:0%
+like you know one of the things yeah
+resolution is limited by the wavelength
+
+ align:start position:0%
+resolution is limited by the wavelength
+ 
+
+ align:start position:0%
+resolution is limited by the wavelength
+of life
+
+ align:start position:0%
+of life
+ 
+
+ align:start position:0%
+of life
+yes as long as you are in the far field
+
+ align:start position:0%
+yes as long as you are in the far field
+ 
+
+ align:start position:0%
+yes as long as you are in the far field
+regime as long as you are in the linear
+
+ align:start position:0%
+regime as long as you are in the linear
+ 
+
+ align:start position:0%
+regime as long as you are in the linear
+regime you highlight one of these and
+
+ align:start position:0%
+regime you highlight one of these and
+ 
+
+ align:start position:0%
+regime you highlight one of these and
+you can do whatever you want if you are
+
+ align:start position:0%
+you can do whatever you want if you are
+ 
+
+ align:start position:0%
+you can do whatever you want if you are
+proximity near field scanning Optical
+
+ align:start position:0%
+proximity near field scanning Optical
+ 
+
+ align:start position:0%
+proximity near field scanning Optical
+microscope you can get as small as you
+
+ align:start position:0%
+microscope you can get as small as you
+ 
+
+ align:start position:0%
+microscope you can get as small as you
+want but if you have non-linear these
+
+ align:start position:0%
+want but if you have non-linear these
+ 
+
+ align:start position:0%
+want but if you have non-linear these
+microscopes fluorescence microscopes you
+
+ align:start position:0%
+microscopes fluorescence microscopes you
+ 
+
+ align:start position:0%
+microscopes fluorescence microscopes you
+can get 50 nanometer resolution with
+
+ align:start position:0%
+can get 50 nanometer resolution with
+ 
+
+ align:start position:0%
+can get 50 nanometer resolution with
+visible light so uh that that sort of is
+
+ align:start position:0%
+visible light so uh that that sort of is
+ 
+
+ align:start position:0%
+visible light so uh that that sort of is
+some ways in which you can really
+
+ align:start position:0%
+some ways in which you can really
+ 
+
+ align:start position:0%
+some ways in which you can really
+carefully look at what we consider to be
+
+ align:start position:0%
+carefully look at what we consider to be
+ 
+
+ align:start position:0%
+carefully look at what we consider to be
+fundamental limit uh imposed by physics
+
+ align:start position:0%
+fundamental limit uh imposed by physics
+ 
+
+ align:start position:0%
+fundamental limit uh imposed by physics
+and say what is the fine thread and can
+
+ align:start position:0%
+and say what is the fine thread and can
+ 
+
+ align:start position:0%
+and say what is the fine thread and can
+we violate so that that would be very
+
+ align:start position:0%
+we violate so that that would be very
+ 
+
+ align:start position:0%
+we violate so that that would be very
+interesting to look at yeah but I mean
+
+ align:start position:0%
+interesting to look at yeah but I mean
+ 
+
+ align:start position:0%
+interesting to look at yeah but I mean
+can we start using our own bodies as as
+
+ align:start position:0%
+can we start using our own bodies as as
+ 
+
+ align:start position:0%
+can we start using our own bodies as as
+Optics or can we start using uh you know
+
+ align:start position:0%
+Optics or can we start using uh you know
+ 
+
+ align:start position:0%
+Optics or can we start using uh you know
+biological principles to
+
+ align:start position:0%
+biological principles to
+ 
+
+ align:start position:0%
+biological principles to
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+um solve the 5w and one H problems
+
+ align:start position:0%
+um solve the 5w and one H problems
+ 
+
+ align:start position:0%
+um solve the 5w and one H problems
+uh I mean in film the film world we
+
+ align:start position:0%
+uh I mean in film the film world we
+ 
+
+ align:start position:0%
+uh I mean in film the film world we
+actually use the chemistry yeah to solve
+
+ align:start position:0%
+actually use the chemistry yeah to solve
+ 
+
+ align:start position:0%
+actually use the chemistry yeah to solve
+a lot of the problems and now somehow we
+
+ align:start position:0%
+a lot of the problems and now somehow we
+ 
+
+ align:start position:0%
+a lot of the problems and now somehow we
+have forgotten chemistry and we're more
+
+ align:start position:0%
+have forgotten chemistry and we're more
+ 
+
+ align:start position:0%
+have forgotten chemistry and we're more
+into the back to the physics now
+
+ align:start position:0%
+into the back to the physics now
+ 
+
+ align:start position:0%
+into the back to the physics now
+yeah I think I I don't know like one of
+
+ align:start position:0%
+yeah I think I I don't know like one of
+ 
+
+ align:start position:0%
+yeah I think I I don't know like one of
+the things I wonder if can we have a
+
+ align:start position:0%
+the things I wonder if can we have a
+ 
+
+ align:start position:0%
+the things I wonder if can we have a
+three-dimensional detector of it a
+
+ align:start position:0%
+three-dimensional detector of it a
+ 
+
+ align:start position:0%
+three-dimensional detector of it a
+volume detector and if we can store it
+
+ align:start position:0%
+volume detector and if we can store it
+ 
+
+ align:start position:0%
+volume detector and if we can store it
+uh what will it record how will we read
+
+ align:start position:0%
+uh what will it record how will we read
+ 
+
+ align:start position:0%
+uh what will it record how will we read
+it out how will we process it uh some
+
+ align:start position:0%
+it out how will we process it uh some
+ 
+
+ align:start position:0%
+it out how will we process it uh some
+people had talked about uh directly
+
+ align:start position:0%
+people had talked about uh directly
+ 
+
+ align:start position:0%
+people had talked about uh directly
+recording the coherence function instead
+
+ align:start position:0%
+recording the coherence function instead
+ 
+
+ align:start position:0%
+recording the coherence function instead
+of just measuring the intensity right so
+
+ align:start position:0%
+of just measuring the intensity right so
+ 
+
+ align:start position:0%
+of just measuring the intensity right so
+there could be and you you can you can
+
+ align:start position:0%
+there could be and you you can you can
+ 
+
+ align:start position:0%
+there could be and you you can you can
+imagine that now uh of course you know
+
+ align:start position:0%
+imagine that now uh of course you know
+ 
+
+ align:start position:0%
+imagine that now uh of course you know
+you can wave the one say Nano and
+
+ align:start position:0%
+you can wave the one say Nano and
+ 
+
+ align:start position:0%
+you can wave the one say Nano and
+everything goes away
+
+ align:start position:0%
+everything goes away
+ 
+
+ align:start position:0%
+everything goes away
+but to some extent that may be true that
+
+ align:start position:0%
+but to some extent that may be true that
+ 
+
+ align:start position:0%
+but to some extent that may be true that
+if you are if you are able to control
+
+ align:start position:0%
+if you are if you are able to control
+ 
+
+ align:start position:0%
+if you are if you are able to control
+the material at deep deep sub wavelength
+
+ align:start position:0%
+the material at deep deep sub wavelength
+ 
+
+ align:start position:0%
+the material at deep deep sub wavelength
+level you can do some pretty ridiculous
+
+ align:start position:0%
+level you can do some pretty ridiculous
+ 
+
+ align:start position:0%
+level you can do some pretty ridiculous
+things so
+
+ align:start position:0%
+things so
+ 
+
+ align:start position:0%
+things so
+that that that's the direction that we
+
+ align:start position:0%
+that that that's the direction that we
+ 
+
+ align:start position:0%
+that that that's the direction that we
+haven't really explored and another
+
+ align:start position:0%
+haven't really explored and another
+ 
+
+ align:start position:0%
+haven't really explored and another
+another interesting thing is that if you
+
+ align:start position:0%
+another interesting thing is that if you
+ 
+
+ align:start position:0%
+another interesting thing is that if you
+have the ability to manipulate matter
+
+ align:start position:0%
+have the ability to manipulate matter
+ 
+
+ align:start position:0%
+have the ability to manipulate matter
+and control it at Deep sub wavelength
+
+ align:start position:0%
+and control it at Deep sub wavelength
+ 
+
+ align:start position:0%
+and control it at Deep sub wavelength
+level then it's really incumbent on you
+
+ align:start position:0%
+level then it's really incumbent on you
+ 
+
+ align:start position:0%
+level then it's really incumbent on you
+to abandon your other
+
+ align:start position:0%
+to abandon your other
+ 
+
+ align:start position:0%
+to abandon your other
+cherished Notions about oh a spherical
+
+ align:start position:0%
+cherished Notions about oh a spherical
+ 
+
+ align:start position:0%
+cherished Notions about oh a spherical
+lens forming a well-focused image on a
+
+ align:start position:0%
+lens forming a well-focused image on a
+ 
+
+ align:start position:0%
+lens forming a well-focused image on a
+focal plane why are you sticking to that
+
+ align:start position:0%
+focal plane why are you sticking to that
+ 
+
+ align:start position:0%
+focal plane why are you sticking to that
+parallel
+
+ align:start position:0%
+parallel
+ 
+
+ align:start position:0%
+parallel
+so if you really fully want to exploit
+
+ align:start position:0%
+so if you really fully want to exploit
+ 
+
+ align:start position:0%
+so if you really fully want to exploit
+the ability to manipulate the
+
+ align:start position:0%
+the ability to manipulate the
+ 
+
+ align:start position:0%
+the ability to manipulate the
+electromagnetic wavefront in very novel
+
+ align:start position:0%
+electromagnetic wavefront in very novel
+ 
+
+ align:start position:0%
+electromagnetic wavefront in very novel
+ways you're using very novel materials
+
+ align:start position:0%
+ways you're using very novel materials
+ 
+
+ align:start position:0%
+ways you're using very novel materials
+you should also start thinking about
+
+ align:start position:0%
+you should also start thinking about
+ 
+
+ align:start position:0%
+you should also start thinking about
+what are we going to measure and how are
+
+ align:start position:0%
+what are we going to measure and how are
+ 
+
+ align:start position:0%
+what are we going to measure and how are
+we going to measure it
+
+ align:start position:0%
+we going to measure it
+ 
+
+ align:start position:0%
+we going to measure it
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+I don't know if I answered your question
+
+ align:start position:0%
+I don't know if I answered your question
+ 
+
+ align:start position:0%
+I don't know if I answered your question
+yeah I mean it's an open question
+
+ align:start position:0%
+yeah I mean it's an open question
+ 
+
+ align:start position:0%
+yeah I mean it's an open question
+yeah yeah I don't think there's a
+
+ align:start position:0%
+yeah yeah I don't think there's a
+ 
+
+ align:start position:0%
+yeah yeah I don't think there's a
+familiar Direction but I mean the chart
+
+ align:start position:0%
+familiar Direction but I mean the chart
+ 
+
+ align:start position:0%
+familiar Direction but I mean the chart
+that you showed earlier of you know uh
+
+ align:start position:0%
+that you showed earlier of you know uh
+ 
+
+ align:start position:0%
+that you showed earlier of you know uh
+different stages where biological I mean
+
+ align:start position:0%
+different stages where biological I mean
+ 
+
+ align:start position:0%
+different stages where biological I mean
+not knowledgeable but human involved and
+
+ align:start position:0%
+not knowledgeable but human involved and
+ 
+
+ align:start position:0%
+not knowledgeable but human involved and
+there we can more and more technological
+
+ align:start position:0%
+there we can more and more technological
+ 
+
+ align:start position:0%
+there we can more and more technological
+now everything that was blue has become
+
+ align:start position:0%
+now everything that was blue has become
+ 
+
+ align:start position:0%
+now everything that was blue has become
+pink yeah so what's next
+
+ align:start position:0%
+pink yeah so what's next
+ 
+
+ align:start position:0%
+pink yeah so what's next
+I think maybe just what kind of
+
+ align:start position:0%
+I think maybe just what kind of
+ 
+
+ align:start position:0%
+I think maybe just what kind of
+Technologies I mean you you can you can
+
+ align:start position:0%
+Technologies I mean you you can you can
+ 
+
+ align:start position:0%
+Technologies I mean you you can you can
+think of some of the things like uh can
+
+ align:start position:0%
+think of some of the things like uh can
+ 
+
+ align:start position:0%
+think of some of the things like uh can
+we think of self-assembled Imaging
+
+ align:start position:0%
+we think of self-assembled Imaging
+ 
+
+ align:start position:0%
+we think of self-assembled Imaging
+sensors that are not lithographically
+
+ align:start position:0%
+sensors that are not lithographically
+ 
+
+ align:start position:0%
+sensors that are not lithographically
+driven or that is not mechanically
+
+ align:start position:0%
+driven or that is not mechanically
+ 
+
+ align:start position:0%
+driven or that is not mechanically
+assembled
+
+ align:start position:0%
+assembled
+ 
+
+ align:start position:0%
+assembled
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I don't know what else it's like it's
+
+ align:start position:0%
+I don't know what else it's like it's
+ 
+
+ align:start position:0%
+I don't know what else it's like it's
+like the discussion on uh similar like
+
+ align:start position:0%
+like the discussion on uh similar like
+ 
+
+ align:start position:0%
+like the discussion on uh similar like
+it's always easier to say it's coming
+
+ align:start position:0%
+it's always easier to say it's coming
+ 
+
+ align:start position:0%
+it's always easier to say it's coming
+tomorrow but when you go back it seems
+
+ align:start position:0%
+tomorrow but when you go back it seems
+ 
+
+ align:start position:0%
+tomorrow but when you go back it seems
+like you know a lot of stuff has to
+
+ align:start position:0%
+like you know a lot of stuff has to
+ 
+
+ align:start position:0%
+like you know a lot of stuff has to
+happen before
+
+ align:start position:0%
+happen before
+ 
+
+ align:start position:0%
+happen before
+uh before uh before we reach that point
+
+ align:start position:0%
+uh before uh before we reach that point
+ 
+
+ align:start position:0%
+uh before uh before we reach that point
+of uh
+
+ align:start position:0%
+of uh
+ 
+
+ align:start position:0%
+of uh
+and many of the turning points in
+
+ align:start position:0%
+and many of the turning points in
+ 
+
+ align:start position:0%
+and many of the turning points in
+technology are turning points only in
+
+ align:start position:0%
+technology are turning points only in
+ 
+
+ align:start position:0%
+technology are turning points only in
+retrospect yes so you say ah that was
+
+ align:start position:0%
+retrospect yes so you say ah that was
+ 
+
+ align:start position:0%
+retrospect yes so you say ah that was
+the day world changed you didn't realize
+
+ align:start position:0%
+the day world changed you didn't realize
+ 
+
+ align:start position:0%
+the day world changed you didn't realize
+that time I mean like the 40-year
+
+ align:start position:0%
+that time I mean like the 40-year
+ 
+
+ align:start position:0%
+that time I mean like the 40-year
+anniversary of the internet and there
+
+ align:start position:0%
+anniversary of the internet and there
+ 
+
+ align:start position:0%
+anniversary of the internet and there
+was a story about what was the first
+
+ align:start position:0%
+was a story about what was the first
+ 
+
+ align:start position:0%
+was a story about what was the first
+message sent first message was login and
+
+ align:start position:0%
+message sent first message was login and
+ 
+
+ align:start position:0%
+message sent first message was login and
+after log the computer is crashed and
+
+ align:start position:0%
+after log the computer is crashed and
+ 
+
+ align:start position:0%
+after log the computer is crashed and
+they had to reboot and so they asked the
+
+ align:start position:0%
+they had to reboot and so they asked the
+ 
+
+ align:start position:0%
+they had to reboot and so they asked the
+person from UCLA so what did you do
+
+ align:start position:0%
+person from UCLA so what did you do
+ 
+
+ align:start position:0%
+person from UCLA so what did you do
+after you send a message oh I went had a
+
+ align:start position:0%
+after you send a message oh I went had a
+ 
+
+ align:start position:0%
+after you send a message oh I went had a
+burger and went to sleep because I
+
+ align:start position:0%
+burger and went to sleep because I
+ 
+
+ align:start position:0%
+burger and went to sleep because I
+didn't didn't know that that
+
+ align:start position:0%
+didn't didn't know that that
+ 
+
+ align:start position:0%
+didn't didn't know that that
+revolutionized or something it's only in
+
+ align:start position:0%
+revolutionized or something it's only in
+ 
+
+ align:start position:0%
+revolutionized or something it's only in
+retrospect
+
+ align:start position:0%
+retrospect
+ 
+
+ align:start position:0%
+retrospect
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and uh these are these are some
+
+ align:start position:0%
+and uh these are these are some
+ 
+
+ align:start position:0%
+and uh these are these are some
+interesting examples just just to say
+
+ align:start position:0%
+interesting examples just just to say
+ 
+
+ align:start position:0%
+interesting examples just just to say
+application specific Imaging and this is
+
+ align:start position:0%
+application specific Imaging and this is
+ 
+
+ align:start position:0%
+application specific Imaging and this is
+uh one example about from a surgeon in
+
+ align:start position:0%
+uh one example about from a surgeon in
+ 
+
+ align:start position:0%
+uh one example about from a surgeon in
+Naval Medical Center
+
+ align:start position:0%
+Naval Medical Center
+ 
+
+ align:start position:0%
+Naval Medical Center
+they are using the free CCD camera on a
+
+ align:start position:0%
+they are using the free CCD camera on a
+ 
+
+ align:start position:0%
+they are using the free CCD camera on a
+laparoscopic Tower and basically his
+
+ align:start position:0%
+laparoscopic Tower and basically his
+ 
+
+ align:start position:0%
+laparoscopic Tower and basically his
+point is that when you are doing surgery
+
+ align:start position:0%
+point is that when you are doing surgery
+ 
+
+ align:start position:0%
+point is that when you are doing surgery
+it's really important to know which is
+
+ align:start position:0%
+it's really important to know which is
+ 
+
+ align:start position:0%
+it's really important to know which is
+the artery and which is the vein you
+
+ align:start position:0%
+the artery and which is the vein you
+ 
+
+ align:start position:0%
+the artery and which is the vein you
+treat you treat it very differently and
+
+ align:start position:0%
+treat you treat it very differently and
+ 
+
+ align:start position:0%
+treat you treat it very differently and
+you sort of say I mean you know hey
+
+ align:start position:0%
+you sort of say I mean you know hey
+ 
+
+ align:start position:0%
+you sort of say I mean you know hey
+color coding wires unfortunately in the
+
+ align:start position:0%
+color coding wires unfortunately in the
+ 
+
+ align:start position:0%
+color coding wires unfortunately in the
+body it's not that straightforward
+
+ align:start position:0%
+body it's not that straightforward
+ 
+
+ align:start position:0%
+body it's not that straightforward
+so uh taking these three uh colors and
+
+ align:start position:0%
+so uh taking these three uh colors and
+ 
+
+ align:start position:0%
+so uh taking these three uh colors and
+then doing the processing and using many
+
+ align:start position:0%
+then doing the processing and using many
+ 
+
+ align:start position:0%
+then doing the processing and using many
+of the things that you saw here that you
+
+ align:start position:0%
+of the things that you saw here that you
+ 
+
+ align:start position:0%
+of the things that you saw here that you
+you can really a very distinct Spectrum
+
+ align:start position:0%
+you can really a very distinct Spectrum
+ 
+
+ align:start position:0%
+you can really a very distinct Spectrum
+for the hemoglobin and oxygenated and so
+
+ align:start position:0%
+for the hemoglobin and oxygenated and so
+ 
+
+ align:start position:0%
+for the hemoglobin and oxygenated and so
+by doing the processing you create that
+
+ align:start position:0%
+by doing the processing you create that
+ 
+
+ align:start position:0%
+by doing the processing you create that
+map and you project it back
+
+ align:start position:0%
+map and you project it back
+ 
+
+ align:start position:0%
+map and you project it back
+you showed it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the arteries are colored red and so
+
+ align:start position:0%
+and the arteries are colored red and so
+ 
+
+ align:start position:0%
+and the arteries are colored red and so
+now here in this particular case the
+
+ align:start position:0%
+now here in this particular case the
+ 
+
+ align:start position:0%
+now here in this particular case the
+surgeon looks at the Monitor and says Ah
+
+ align:start position:0%
+surgeon looks at the Monitor and says Ah
+ 
+
+ align:start position:0%
+surgeon looks at the Monitor and says Ah
+okay this is the one that I should be
+
+ align:start position:0%
+okay this is the one that I should be
+ 
+
+ align:start position:0%
+okay this is the one that I should be
+careful about or whatever but then
+
+ align:start position:0%
+careful about or whatever but then
+ 
+
+ align:start position:0%
+careful about or whatever but then
+some of the things I I don't know how
+
+ align:start position:0%
+some of the things I I don't know how
+ 
+
+ align:start position:0%
+some of the things I I don't know how
+many of you have seen this thing called
+
+ align:start position:0%
+many of you have seen this thing called
+ 
+
+ align:start position:0%
+many of you have seen this thing called
+rain viewer
+
+ align:start position:0%
+rain viewer
+ 
+
+ align:start position:0%
+rain viewer
+have you seen the problem okay I I don't
+
+ align:start position:0%
+have you seen the problem okay I I don't
+ 
+
+ align:start position:0%
+have you seen the problem okay I I don't
+know if there is a
+
+ align:start position:0%
+know if there is a
+ 
+
+ align:start position:0%
+know if there is a
+wireless connection is uh
+
+ align:start position:0%
+wireless connection is uh
+ 
+
+ align:start position:0%
+wireless connection is uh
+good enough we'll we'll see it might it
+
+ align:start position:0%
+good enough we'll we'll see it might it
+ 
+
+ align:start position:0%
+good enough we'll we'll see it might it
+might be working yeah
+
+ align:start position:0%
+might be working yeah
+ 
+
+ align:start position:0%
+might be working yeah
+we have seen that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know it's uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and if you look at the technology it
+
+ align:start position:0%
+and and if you look at the technology it
+ 
+
+ align:start position:0%
+and and if you look at the technology it
+is just absolutely stupid technology
+
+ align:start position:0%
+is just absolutely stupid technology
+ 
+
+ align:start position:0%
+is just absolutely stupid technology
+it's 780 nanometer light illumination
+
+ align:start position:0%
+it's 780 nanometer light illumination
+ 
+
+ align:start position:0%
+it's 780 nanometer light illumination
+that you do that and that penetrates the
+
+ align:start position:0%
+that you do that and that penetrates the
+ 
+
+ align:start position:0%
+that you do that and that penetrates the
+skin and is absorbed by your blood and
+
+ align:start position:0%
+skin and is absorbed by your blood and
+ 
+
+ align:start position:0%
+skin and is absorbed by your blood and
+so you can see the veins deep inside and
+
+ align:start position:0%
+so you can see the veins deep inside and
+ 
+
+ align:start position:0%
+so you can see the veins deep inside and
+the beauty about this is the camera is
+
+ align:start position:0%
+the beauty about this is the camera is
+ 
+
+ align:start position:0%
+the beauty about this is the camera is
+up there and so is the DLP projector and
+
+ align:start position:0%
+up there and so is the DLP projector and
+ 
+
+ align:start position:0%
+up there and so is the DLP projector and
+the processor basically scales and
+
+ align:start position:0%
+the processor basically scales and
+ 
+
+ align:start position:0%
+the processor basically scales and
+aligns the images so that it is
+
+ align:start position:0%
+aligns the images so that it is
+ 
+
+ align:start position:0%
+aligns the images so that it is
+projected back exactly aligned like that
+
+ align:start position:0%
+projected back exactly aligned like that
+ 
+
+ align:start position:0%
+projected back exactly aligned like that
+and but the use is phenomenal yeah it's
+
+ align:start position:0%
+and but the use is phenomenal yeah it's
+ 
+
+ align:start position:0%
+and but the use is phenomenal yeah it's
+one of the best forms of augmented
+
+ align:start position:0%
+one of the best forms of augmented
+ 
+
+ align:start position:0%
+one of the best forms of augmented
+reality exactly so I'll just show it in
+
+ align:start position:0%
+reality exactly so I'll just show it in
+ 
+
+ align:start position:0%
+reality exactly so I'll just show it in
+my augmented reality uh presentations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and I think the rest of the thing
+
+ align:start position:0%
+yeah and I think the rest of the thing
+ 
+
+ align:start position:0%
+yeah and I think the rest of the thing
+may be uh
+
+ align:start position:0%
+may be uh
+ 
+
+ align:start position:0%
+may be uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+yeah this is uh I was talking to Ramesh
+
+ align:start position:0%
+yeah this is uh I was talking to Ramesh
+ 
+
+ align:start position:0%
+yeah this is uh I was talking to Ramesh
+this is uh Doug Hart's company bronte's
+
+ align:start position:0%
+this is uh Doug Hart's company bronte's
+ 
+
+ align:start position:0%
+this is uh Doug Hart's company bronte's
+technology for the 3D I think you saw it
+
+ align:start position:0%
+technology for the 3D I think you saw it
+ 
+
+ align:start position:0%
+technology for the 3D I think you saw it
+we started you saw that and you know
+
+ align:start position:0%
+we started you saw that and you know
+ 
+
+ align:start position:0%
+we started you saw that and you know
+uh lava chair side oral scanners I think
+
+ align:start position:0%
+uh lava chair side oral scanners I think
+ 
+
+ align:start position:0%
+uh lava chair side oral scanners I think
+that that was a video did you see that
+
+ align:start position:0%
+that that was a video did you see that
+ 
+
+ align:start position:0%
+that that was a video did you see that
+video of the doctor manipulating and uh
+
+ align:start position:0%
+video of the doctor manipulating and uh
+ 
+
+ align:start position:0%
+video of the doctor manipulating and uh
+did you show the video I don't remember
+
+ align:start position:0%
+did you show the video I don't remember
+ 
+
+ align:start position:0%
+did you show the video I don't remember
+pleasure entity
+
+ align:start position:0%
+pleasure entity
+ 
+
+ align:start position:0%
+pleasure entity
+I forget I don't know I think it's it's
+
+ align:start position:0%
+I forget I don't know I think it's it's
+ 
+
+ align:start position:0%
+I forget I don't know I think it's it's
+not that important you you know you know
+
+ align:start position:0%
+not that important you you know you know
+ 
+
+ align:start position:0%
+not that important you you know you know
+what it is yeah but it's amazing how
+
+ align:start position:0%
+what it is yeah but it's amazing how
+ 
+
+ align:start position:0%
+what it is yeah but it's amazing how
+simple it is yeah and
+
+ align:start position:0%
+simple it is yeah and
+ 
+
+ align:start position:0%
+simple it is yeah and
+I think one of the things that maybe the
+
+ align:start position:0%
+I think one of the things that maybe the
+ 
+
+ align:start position:0%
+I think one of the things that maybe the
+and the refocus energy
+
+ align:start position:0%
+and the refocus energy
+ 
+
+ align:start position:0%
+and the refocus energy
+right now know anything more about it
+
+ align:start position:0%
+right now know anything more about it
+ 
+
+ align:start position:0%
+right now know anything more about it
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+in some ways when you talk about
+
+ align:start position:0%
+in some ways when you talk about
+ 
+
+ align:start position:0%
+in some ways when you talk about
+application specific cameras
+
+ align:start position:0%
+application specific cameras
+ 
+
+ align:start position:0%
+application specific cameras
+the key is understanding the nature of
+
+ align:start position:0%
+the key is understanding the nature of
+ 
+
+ align:start position:0%
+the key is understanding the nature of
+the problem and finding the simplest
+
+ align:start position:0%
+the problem and finding the simplest
+ 
+
+ align:start position:0%
+the problem and finding the simplest
+solution to that specific problem
+
+ align:start position:0%
+solution to that specific problem
+ 
+
+ align:start position:0%
+solution to that specific problem
+and well one of the examples you saw
+
+ align:start position:0%
+and well one of the examples you saw
+ 
+
+ align:start position:0%
+and well one of the examples you saw
+that Wayne viewer all of you know the
+
+ align:start position:0%
+that Wayne viewer all of you know the
+ 
+
+ align:start position:0%
+that Wayne viewer all of you know the
+pulse oximeters that is clicked to your
+
+ align:start position:0%
+pulse oximeters that is clicked to your
+ 
+
+ align:start position:0%
+pulse oximeters that is clicked to your
+finger It's relatively new I think maybe
+
+ align:start position:0%
+finger It's relatively new I think maybe
+ 
+
+ align:start position:0%
+finger It's relatively new I think maybe
+20 25 years old
+
+ align:start position:0%
+20 25 years old
+ 
+
+ align:start position:0%
+20 25 years old
+technology if again if you look at the
+
+ align:start position:0%
+technology if again if you look at the
+ 
+
+ align:start position:0%
+technology if again if you look at the
+technology it's absolutely dirt simple
+
+ align:start position:0%
+technology it's absolutely dirt simple
+ 
+
+ align:start position:0%
+technology it's absolutely dirt simple
+technology
+
+ align:start position:0%
+technology
+ 
+
+ align:start position:0%
+technology
+two different LEDs looking at the
+
+ align:start position:0%
+two different LEDs looking at the
+ 
+
+ align:start position:0%
+two different LEDs looking at the
+differential absorption through your
+
+ align:start position:0%
+differential absorption through your
+ 
+
+ align:start position:0%
+differential absorption through your
+finger to measure the oxygenation level
+
+ align:start position:0%
+finger to measure the oxygenation level
+ 
+
+ align:start position:0%
+finger to measure the oxygenation level
+of the blood and before they had to draw
+
+ align:start position:0%
+of the blood and before they had to draw
+ 
+
+ align:start position:0%
+of the blood and before they had to draw
+the blood and send it for analysis and
+
+ align:start position:0%
+the blood and send it for analysis and
+ 
+
+ align:start position:0%
+the blood and send it for analysis and
+by the time it came back maybe bad
+
+ align:start position:0%
+by the time it came back maybe bad
+ 
+
+ align:start position:0%
+by the time it came back maybe bad
+things happen but this one is now you
+
+ align:start position:0%
+things happen but this one is now you
+ 
+
+ align:start position:0%
+things happen but this one is now you
+saw in all the TV shows anywhere that
+
+ align:start position:0%
+saw in all the TV shows anywhere that
+ 
+
+ align:start position:0%
+saw in all the TV shows anywhere that
+the first thing they do is clip this on
+
+ align:start position:0%
+the first thing they do is clip this on
+ 
+
+ align:start position:0%
+the first thing they do is clip this on
+your finger and I don't know how how
+
+ align:start position:0%
+your finger and I don't know how how
+ 
+
+ align:start position:0%
+your finger and I don't know how how
+much it costs it still cost thousand
+
+ align:start position:0%
+much it costs it still cost thousand
+ 
+
+ align:start position:0%
+much it costs it still cost thousand
+dollars I don't know why because
+
+ align:start position:0%
+dollars I don't know why because
+ 
+
+ align:start position:0%
+dollars I don't know why because
+somebody is making a lot of money
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh but but then some of the research
+
+ align:start position:0%
+uh but but then some of the research
+ 
+
+ align:start position:0%
+uh but but then some of the research
+projects that I was involved in
+
+ align:start position:0%
+projects that I was involved in
+ 
+
+ align:start position:0%
+projects that I was involved in
+monitoring I talk about can can you do a
+
+ align:start position:0%
+monitoring I talk about can can you do a
+ 
+
+ align:start position:0%
+monitoring I talk about can can you do a
+special map of oxygenation levels using
+
+ align:start position:0%
+special map of oxygenation levels using
+ 
+
+ align:start position:0%
+special map of oxygenation levels using
+this multi-spectral cameras and then
+
+ align:start position:0%
+this multi-spectral cameras and then
+ 
+
+ align:start position:0%
+this multi-spectral cameras and then
+processing and the doctors got really
+
+ align:start position:0%
+processing and the doctors got really
+ 
+
+ align:start position:0%
+processing and the doctors got really
+excited for applications like uh burn
+
+ align:start position:0%
+excited for applications like uh burn
+ 
+
+ align:start position:0%
+excited for applications like uh burn
+assessment
+
+ align:start position:0%
+assessment
+ 
+
+ align:start position:0%
+assessment
+whether it's a first or second or third
+
+ align:start position:0%
+whether it's a first or second or third
+ 
+
+ align:start position:0%
+whether it's a first or second or third
+degree burn the treatment differs
+
+ align:start position:0%
+degree burn the treatment differs
+ 
+
+ align:start position:0%
+degree burn the treatment differs
+dramatically and instead of relying on
+
+ align:start position:0%
+dramatically and instead of relying on
+ 
+
+ align:start position:0%
+dramatically and instead of relying on
+the doctor's visual assessment of what
+
+ align:start position:0%
+the doctor's visual assessment of what
+ 
+
+ align:start position:0%
+the doctor's visual assessment of what
+degree burn it is if you can take a
+
+ align:start position:0%
+degree burn it is if you can take a
+ 
+
+ align:start position:0%
+degree burn it is if you can take a
+camera that can do that blood
+
+ align:start position:0%
+camera that can do that blood
+ 
+
+ align:start position:0%
+camera that can do that blood
+oxygenation map or if you can map the
+
+ align:start position:0%
+oxygenation map or if you can map the
+ 
+
+ align:start position:0%
+oxygenation map or if you can map the
+retina
+
+ align:start position:0%
+retina
+ 
+
+ align:start position:0%
+retina
+and a lot of the diabetic retinopathy
+
+ align:start position:0%
+and a lot of the diabetic retinopathy
+ 
+
+ align:start position:0%
+and a lot of the diabetic retinopathy
+and other diseases there the precursors
+
+ align:start position:0%
+and other diseases there the precursors
+ 
+
+ align:start position:0%
+and other diseases there the precursors
+are in if what is the oxygenation level
+
+ align:start position:0%
+are in if what is the oxygenation level
+ 
+
+ align:start position:0%
+are in if what is the oxygenation level
+so these kind of things just like the
+
+ align:start position:0%
+so these kind of things just like the
+ 
+
+ align:start position:0%
+so these kind of things just like the
+distinction between arteries and veins
+
+ align:start position:0%
+distinction between arteries and veins
+ 
+
+ align:start position:0%
+distinction between arteries and veins
+or the vein viewer and all that it's not
+
+ align:start position:0%
+or the vein viewer and all that it's not
+ 
+
+ align:start position:0%
+or the vein viewer and all that it's not
+you don't need to invent you
+
+ align:start position:0%
+you don't need to invent you
+ 
+
+ align:start position:0%
+you don't need to invent you
+nanotechnologies or something you need
+
+ align:start position:0%
+nanotechnologies or something you need
+ 
+
+ align:start position:0%
+nanotechnologies or something you need
+to understand in depth what the problem
+
+ align:start position:0%
+to understand in depth what the problem
+ 
+
+ align:start position:0%
+to understand in depth what the problem
+is right and what the human factors is
+
+ align:start position:0%
+is right and what the human factors is
+ 
+
+ align:start position:0%
+is right and what the human factors is
+again this thing came here the cool
+
+ align:start position:0%
+again this thing came here the cool
+ 
+
+ align:start position:0%
+again this thing came here the cool
+thing is not just that IR LED but you
+
+ align:start position:0%
+thing is not just that IR LED but you
+ 
+
+ align:start position:0%
+thing is not just that IR LED but you
+can imagine everything else the same
+
+ align:start position:0%
+can imagine everything else the same
+ 
+
+ align:start position:0%
+can imagine everything else the same
+except that image being shown on TV and
+
+ align:start position:0%
+except that image being shown on TV and
+ 
+
+ align:start position:0%
+except that image being shown on TV and
+it will nowhere be as dramatic if the
+
+ align:start position:0%
+it will nowhere be as dramatic if the
+ 
+
+ align:start position:0%
+it will nowhere be as dramatic if the
+doctor has to manipulate the needle here
+
+ align:start position:0%
+doctor has to manipulate the needle here
+ 
+
+ align:start position:0%
+doctor has to manipulate the needle here
+while looking at the monitor it's a
+
+ align:start position:0%
+while looking at the monitor it's a
+ 
+
+ align:start position:0%
+while looking at the monitor it's a
+human factor it's right there so that
+
+ align:start position:0%
+human factor it's right there so that
+ 
+
+ align:start position:0%
+human factor it's right there so that
+that's really where
+
+ align:start position:0%
+that's really where
+ 
+
+ align:start position:0%
+that's really where
+okay so this is the last slide
+
+ align:start position:0%
+okay so this is the last slide
+ 
+
+ align:start position:0%
+okay so this is the last slide
+so uh just a little bit science fantasy
+
+ align:start position:0%
+so uh just a little bit science fantasy
+ 
+
+ align:start position:0%
+so uh just a little bit science fantasy
+not this facial a personal Imaging
+
+ align:start position:0%
+not this facial a personal Imaging
+ 
+
+ align:start position:0%
+not this facial a personal Imaging
+assistant something that just like you
+
+ align:start position:0%
+assistant something that just like you
+ 
+
+ align:start position:0%
+assistant something that just like you
+carry your pen every day or your wallet
+
+ align:start position:0%
+carry your pen every day or your wallet
+ 
+
+ align:start position:0%
+carry your pen every day or your wallet
+or credit card or your cell phone the
+
+ align:start position:0%
+or credit card or your cell phone the
+ 
+
+ align:start position:0%
+or credit card or your cell phone the
+personal Imaging assistant what all will
+
+ align:start position:0%
+personal Imaging assistant what all will
+ 
+
+ align:start position:0%
+personal Imaging assistant what all will
+it do Healthcare
+
+ align:start position:0%
+it do Healthcare
+ 
+
+ align:start position:0%
+it do Healthcare
+checking for sunburns or if you get
+
+ align:start position:0%
+checking for sunburns or if you get
+ 
+
+ align:start position:0%
+checking for sunburns or if you get
+scraped you know hey is it getting
+
+ align:start position:0%
+scraped you know hey is it getting
+ 
+
+ align:start position:0%
+scraped you know hey is it getting
+infected this wound uh you have an
+
+ align:start position:0%
+infected this wound uh you have an
+ 
+
+ align:start position:0%
+infected this wound uh you have an
+attachment you check the ear infection
+
+ align:start position:0%
+attachment you check the ear infection
+ 
+
+ align:start position:0%
+attachment you check the ear infection
+of your children or whatever look at
+
+ align:start position:0%
+of your children or whatever look at
+ 
+
+ align:start position:0%
+of your children or whatever look at
+your tongue are you getting upset
+
+ align:start position:0%
+your tongue are you getting upset
+ 
+
+ align:start position:0%
+your tongue are you getting upset
+stomach
+
+ align:start position:0%
+stomach
+ 
+
+ align:start position:0%
+stomach
+wardrobe matching of course color and
+
+ align:start position:0%
+wardrobe matching of course color and
+ 
+
+ align:start position:0%
+wardrobe matching of course color and
+styles especially yeah what kind of
+
+ align:start position:0%
+styles especially yeah what kind of
+ 
+
+ align:start position:0%
+styles especially yeah what kind of
+makeup will go with this and other
+
+ align:start position:0%
+makeup will go with this and other
+ 
+
+ align:start position:0%
+makeup will go with this and other
+things hygiene cleanliness and bacteria
+
+ align:start position:0%
+things hygiene cleanliness and bacteria
+ 
+
+ align:start position:0%
+things hygiene cleanliness and bacteria
+water food safety quality for this the
+
+ align:start position:0%
+water food safety quality for this the
+ 
+
+ align:start position:0%
+water food safety quality for this the
+last one it's really sort of getting a
+
+ align:start position:0%
+last one it's really sort of getting a
+ 
+
+ align:start position:0%
+last one it's really sort of getting a
+little bit science fictiony but maybe
+
+ align:start position:0%
+little bit science fictiony but maybe
+ 
+
+ align:start position:0%
+little bit science fictiony but maybe
+not given that Sixth Sense thing so
+
+ align:start position:0%
+not given that Sixth Sense thing so
+ 
+
+ align:start position:0%
+not given that Sixth Sense thing so
+you're wearing these glasses of this
+
+ align:start position:0%
+you're wearing these glasses of this
+ 
+
+ align:start position:0%
+you're wearing these glasses of this
+personal Imaging assistant with the
+
+ align:start position:0%
+personal Imaging assistant with the
+ 
+
+ align:start position:0%
+personal Imaging assistant with the
+headphone when somebody walks hey Ramesh
+
+ align:start position:0%
+headphone when somebody walks hey Ramesh
+ 
+
+ align:start position:0%
+headphone when somebody walks hey Ramesh
+how are you somebody this person you're
+
+ align:start position:0%
+how are you somebody this person you're
+ 
+
+ align:start position:0%
+how are you somebody this person you're
+here that's Prime
+
+ align:start position:0%
+here that's Prime
+ 
+
+ align:start position:0%
+here that's Prime
+so that it's like the politicians who
+
+ align:start position:0%
+so that it's like the politicians who
+ 
+
+ align:start position:0%
+so that it's like the politicians who
+have these assistants at their elbow who
+
+ align:start position:0%
+have these assistants at their elbow who
+ 
+
+ align:start position:0%
+have these assistants at their elbow who
+whisper in there ears to who is the
+
+ align:start position:0%
+whisper in there ears to who is the
+ 
+
+ align:start position:0%
+whisper in there ears to who is the
+person walking in and Discerning move
+
+ align:start position:0%
+person walking in and Discerning move
+ 
+
+ align:start position:0%
+person walking in and Discerning move
+that that's again very science can you
+
+ align:start position:0%
+that that's again very science can you
+ 
+
+ align:start position:0%
+that that's again very science can you
+can the image tell you that
+
+ align:start position:0%
+can the image tell you that
+ 
+
+ align:start position:0%
+can the image tell you that
+this guy is very skeptical he's not
+
+ align:start position:0%
+this guy is very skeptical he's not
+ 
+
+ align:start position:0%
+this guy is very skeptical he's not
+buying anything
+
+ align:start position:0%
+buying anything
+ 
+
+ align:start position:0%
+buying anything
+okay and how it's basically exploit the
+
+ align:start position:0%
+okay and how it's basically exploit the
+ 
+
+ align:start position:0%
+okay and how it's basically exploit the
+electromagnetic domain to the hilt
+
+ align:start position:0%
+electromagnetic domain to the hilt
+ 
+
+ align:start position:0%
+electromagnetic domain to the hilt
+combine the processing right there and
+
+ align:start position:0%
+combine the processing right there and
+ 
+
+ align:start position:0%
+combine the processing right there and
+have an Adaptive
+
+ align:start position:0%
+have an Adaptive
+ 
+
+ align:start position:0%
+have an Adaptive
+uh one one analogy that people may right
+
+ align:start position:0%
+uh one one analogy that people may right
+ 
+
+ align:start position:0%
+uh one one analogy that people may right
+now it's a sensor with a total one
+
+ align:start position:0%
+now it's a sensor with a total one
+ 
+
+ align:start position:0%
+now it's a sensor with a total one
+directional flow of information from the
+
+ align:start position:0%
+directional flow of information from the
+ 
+
+ align:start position:0%
+directional flow of information from the
+sensor to the processor
+
+ align:start position:0%
+sensor to the processor
+ 
+
+ align:start position:0%
+sensor to the processor
+how about going back look I I heard
+
+ align:start position:0%
+how about going back look I I heard
+ 
+
+ align:start position:0%
+how about going back look I I heard
+somewhere about human visual Pathways
+
+ align:start position:0%
+somewhere about human visual Pathways
+ 
+
+ align:start position:0%
+somewhere about human visual Pathways
+from the retina to the lactogeniculate
+
+ align:start position:0%
+from the retina to the lactogeniculate
+ 
+
+ align:start position:0%
+from the retina to the lactogeniculate
+nucleus to E1 and all the inferior
+
+ align:start position:0%
+nucleus to E1 and all the inferior
+ 
+
+ align:start position:0%
+nucleus to E1 and all the inferior
+temporal cortex and all that everybody
+
+ align:start position:0%
+temporal cortex and all that everybody
+ 
+
+ align:start position:0%
+temporal cortex and all that everybody
+analyzes that feed forward and what kind
+
+ align:start position:0%
+analyzes that feed forward and what kind
+ 
+
+ align:start position:0%
+analyzes that feed forward and what kind
+of features are extracted
+
+ align:start position:0%
+of features are extracted
+ 
+
+ align:start position:0%
+of features are extracted
+and I heard that from V1 to LG and there
+
+ align:start position:0%
+and I heard that from V1 to LG and there
+ 
+
+ align:start position:0%
+and I heard that from V1 to LG and there
+is a huge amount of feedback connection
+
+ align:start position:0%
+is a huge amount of feedback connection
+ 
+
+ align:start position:0%
+is a huge amount of feedback connection
+what's the role of that and that's I
+
+ align:start position:0%
+what's the role of that and that's I
+ 
+
+ align:start position:0%
+what's the role of that and that's I
+don't think the neuroscientists know yet
+
+ align:start position:0%
+don't think the neuroscientists know yet
+ 
+
+ align:start position:0%
+don't think the neuroscientists know yet
+but uh that that kind of a thing
+
+ align:start position:0%
+but uh that that kind of a thing
+ 
+
+ align:start position:0%
+but uh that that kind of a thing
+an Imaging sensor that analyzes the
+
+ align:start position:0%
+an Imaging sensor that analyzes the
+ 
+
+ align:start position:0%
+an Imaging sensor that analyzes the
+scene says okay now next I should look
+
+ align:start position:0%
+scene says okay now next I should look
+ 
+
+ align:start position:0%
+scene says okay now next I should look
+in this direction in this Vector domain
+
+ align:start position:0%
+in this direction in this Vector domain
+ 
+
+ align:start position:0%
+in this direction in this Vector domain
+in this place or something and in few of
+
+ align:start position:0%
+in this place or something and in few of
+ 
+
+ align:start position:0%
+in this place or something and in few of
+these adaptive steps
+
+ align:start position:0%
+these adaptive steps
+ 
+
+ align:start position:0%
+these adaptive steps
+can learn a hell of a lot about what is
+
+ align:start position:0%
+can learn a hell of a lot about what is
+ 
+
+ align:start position:0%
+can learn a hell of a lot about what is
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+so last thing unobtrusive or most cohort
+
+ align:start position:0%
+so last thing unobtrusive or most cohort
+ 
+
+ align:start position:0%
+so last thing unobtrusive or most cohort
+form factor and it's literally part of
+
+ align:start position:0%
+form factor and it's literally part of
+ 
+
+ align:start position:0%
+form factor and it's literally part of
+getting dressed it's like carry a wallet
+
+ align:start position:0%
+getting dressed it's like carry a wallet
+ 
+
+ align:start position:0%
+getting dressed it's like carry a wallet
+your cell phone carrier Imaging
+
+ align:start position:0%
+your cell phone carrier Imaging
+ 
+
+ align:start position:0%
+your cell phone carrier Imaging
+assistant that can do all of these
+
+ align:start position:0%
+assistant that can do all of these
+ 
+
+ align:start position:0%
+assistant that can do all of these
+things for you
+
+ align:start position:0%
+things for you
+ 
+
+ align:start position:0%
+things for you
+but what form factor is it in the
+
+ align:start position:0%
+but what form factor is it in the
+ 
+
+ align:start position:0%
+but what form factor is it in the
+clothing or is it is it that's
+
+ align:start position:0%
+clothing or is it is it that's
+ 
+
+ align:start position:0%
+clothing or is it is it that's
+interesting in your eyeglasses I I wear
+
+ align:start position:0%
+interesting in your eyeglasses I I wear
+ 
+
+ align:start position:0%
+interesting in your eyeglasses I I wear
+kind of a product or uh I I was this
+
+ align:start position:0%
+kind of a product or uh I I was this
+ 
+
+ align:start position:0%
+kind of a product or uh I I was this
+morning at miter I was looking at some
+
+ align:start position:0%
+morning at miter I was looking at some
+ 
+
+ align:start position:0%
+morning at miter I was looking at some
+of these
+
+ align:start position:0%
+of these
+ 
+
+ align:start position:0%
+of these
+glossy magazines for Army and all that
+
+ align:start position:0%
+glossy magazines for Army and all that
+ 
+
+ align:start position:0%
+glossy magazines for Army and all that
+and I noticed that all the soldiers in
+
+ align:start position:0%
+and I noticed that all the soldiers in
+ 
+
+ align:start position:0%
+and I noticed that all the soldiers in
+Iraq and Afghanistan their helmet had
+
+ align:start position:0%
+Iraq and Afghanistan their helmet had
+ 
+
+ align:start position:0%
+Iraq and Afghanistan their helmet had
+something there and I asked what is this
+
+ align:start position:0%
+something there and I asked what is this
+ 
+
+ align:start position:0%
+something there and I asked what is this
+they say of course it's a video camera
+
+ align:start position:0%
+they say of course it's a video camera
+ 
+
+ align:start position:0%
+they say of course it's a video camera
+so it's it's part of the standard
+
+ align:start position:0%
+so it's it's part of the standard
+ 
+
+ align:start position:0%
+so it's it's part of the standard
+military equipment
+
+ align:start position:0%
+military equipment
+ 
+
+ align:start position:0%
+military equipment
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+I I don't know how unobtrusive you can
+
+ align:start position:0%
+I I don't know how unobtrusive you can
+ 
+
+ align:start position:0%
+I I don't know how unobtrusive you can
+make it is it in the clothing is it
+
+ align:start position:0%
+make it is it in the clothing is it
+ 
+
+ align:start position:0%
+make it is it in the clothing is it
+something that you clip on your shirt or
+
+ align:start position:0%
+something that you clip on your shirt or
+ 
+
+ align:start position:0%
+something that you clip on your shirt or
+is it here
+
+ align:start position:0%
+is it here
+ 
+
+ align:start position:0%
+is it here
+hey you are in media Labs your favorite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so well that's it thank you all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we can use we can make your slides
+
+ align:start position:0%
+and we can use we can make your slides
+ 
+
+ align:start position:0%
+and we can use we can make your slides
+available yeah
+
+ align:start position:0%
+available yeah
+ 
+
+ align:start position:0%
+available yeah
+can I ask a question yes so there's this
+
+ align:start position:0%
+can I ask a question yes so there's this
+ 
+
+ align:start position:0%
+can I ask a question yes so there's this
+problem environment cakes when you want
+
+ align:start position:0%
+problem environment cakes when you want
+ 
+
+ align:start position:0%
+problem environment cakes when you want
+to capture when you want to recognize a
+
+ align:start position:0%
+to capture when you want to recognize a
+ 
+
+ align:start position:0%
+to capture when you want to recognize a
+person at a distance saying uh maybe and
+
+ align:start position:0%
+person at a distance saying uh maybe and
+ 
+
+ align:start position:0%
+person at a distance saying uh maybe and
+they they are pushing programs of Iris
+
+ align:start position:0%
+they they are pushing programs of Iris
+ 
+
+ align:start position:0%
+they they are pushing programs of Iris
+at a distance or face recognition at a
+
+ align:start position:0%
+at a distance or face recognition at a
+ 
+
+ align:start position:0%
+at a distance or face recognition at a
+distance and Maritime government and
+
+ align:start position:0%
+distance and Maritime government and
+ 
+
+ align:start position:0%
+distance and Maritime government and
+things like that and there are two
+
+ align:start position:0%
+things like that and there are two
+ 
+
+ align:start position:0%
+things like that and there are two
+problems in this one is atmosphere
+
+ align:start position:0%
+problems in this one is atmosphere
+ 
+
+ align:start position:0%
+problems in this one is atmosphere
+between the subject and you and the
+
+ align:start position:0%
+between the subject and you and the
+ 
+
+ align:start position:0%
+between the subject and you and the
+other is subject is uh he does not want
+
+ align:start position:0%
+other is subject is uh he does not want
+ 
+
+ align:start position:0%
+other is subject is uh he does not want
+you to recognize him he's Incorporated
+
+ align:start position:0%
+you to recognize him he's Incorporated
+ 
+
+ align:start position:0%
+you to recognize him he's Incorporated
+uh what would be your ideas in terms of
+
+ align:start position:0%
+uh what would be your ideas in terms of
+ 
+
+ align:start position:0%
+uh what would be your ideas in terms of
+how our image concerns should go to
+
+ align:start position:0%
+how our image concerns should go to
+ 
+
+ align:start position:0%
+how our image concerns should go to
+capture that problem because if we have
+
+ align:start position:0%
+capture that problem because if we have
+ 
+
+ align:start position:0%
+capture that problem because if we have
+a really good image then we can run our
+
+ align:start position:0%
+a really good image then we can run our
+ 
+
+ align:start position:0%
+a really good image then we can run our
+recognition algorithms and then we can
+
+ align:start position:0%
+recognition algorithms and then we can
+ 
+
+ align:start position:0%
+recognition algorithms and then we can
+focus more on recognition aspect rather
+
+ align:start position:0%
+focus more on recognition aspect rather
+ 
+
+ align:start position:0%
+focus more on recognition aspect rather
+than dealing with issues like lower or
+
+ align:start position:0%
+than dealing with issues like lower or
+ 
+
+ align:start position:0%
+than dealing with issues like lower or
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+atmospheric issues and stuff like that
+
+ align:start position:0%
+atmospheric issues and stuff like that
+ 
+
+ align:start position:0%
+atmospheric issues and stuff like that
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+broad question it's also the touches
+
+ align:start position:0%
+broad question it's also the touches
+ 
+
+ align:start position:0%
+broad question it's also the touches
+upon some very sensitive topics as you
+
+ align:start position:0%
+upon some very sensitive topics as you
+ 
+
+ align:start position:0%
+upon some very sensitive topics as you
+can imagine
+
+ align:start position:0%
+can imagine
+ 
+
+ align:start position:0%
+can imagine
+all I can say is that that that program
+
+ align:start position:0%
+all I can say is that that that program
+ 
+
+ align:start position:0%
+all I can say is that that that program
+announcement is public right yeah that
+
+ align:start position:0%
+announcement is public right yeah that
+ 
+
+ align:start position:0%
+announcement is public right yeah that
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh okay
+
+ align:start position:0%
+oh okay
+ 
+
+ align:start position:0%
+oh okay
+there are all kinds of agencies
+
+ align:start position:0%
+there are all kinds of agencies
+ 
+
+ align:start position:0%
+there are all kinds of agencies
+yeah that is a program announcement
+
+ align:start position:0%
+yeah that is a program announcement
+ 
+
+ align:start position:0%
+yeah that is a program announcement
+called best biometric exploitation
+
+ align:start position:0%
+called best biometric exploitation
+ 
+
+ align:start position:0%
+called best biometric exploitation
+essentially but uh biometric
+
+ align:start position:0%
+essentially but uh biometric
+ 
+
+ align:start position:0%
+essentially but uh biometric
+exploitation Science and Technology out
+
+ align:start position:0%
+exploitation Science and Technology out
+ 
+
+ align:start position:0%
+exploitation Science and Technology out
+of this agency called ayalpa
+
+ align:start position:0%
+of this agency called ayalpa
+ 
+
+ align:start position:0%
+of this agency called ayalpa
+intelligence Advanced research project
+
+ align:start position:0%
+intelligence Advanced research project
+ 
+
+ align:start position:0%
+intelligence Advanced research project
+agency
+
+ align:start position:0%
+agency
+ 
+
+ align:start position:0%
+agency
+some multi-dimensional problem and there
+
+ align:start position:0%
+some multi-dimensional problem and there
+ 
+
+ align:start position:0%
+some multi-dimensional problem and there
+are all kinds of ideas that are proposed
+
+ align:start position:0%
+are all kinds of ideas that are proposed
+ 
+
+ align:start position:0%
+are all kinds of ideas that are proposed
+hopefully
+
+ align:start position:0%
+hopefully
+ 
+
+ align:start position:0%
+hopefully
+within few months the contracts will be
+
+ align:start position:0%
+within few months the contracts will be
+ 
+
+ align:start position:0%
+within few months the contracts will be
+awarded we'll find out
+
+ align:start position:0%
+awarded we'll find out
+ 
+
+ align:start position:0%
+awarded we'll find out
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+but I think somehow going beyond that I
+
+ align:start position:0%
+but I think somehow going beyond that I
+ 
+
+ align:start position:0%
+but I think somehow going beyond that I
+think really in imaging senses and this
+
+ align:start position:0%
+think really in imaging senses and this
+ 
+
+ align:start position:0%
+think really in imaging senses and this
+this is a debate that we are constantly
+
+ align:start position:0%
+this is a debate that we are constantly
+ 
+
+ align:start position:0%
+this is a debate that we are constantly
+having
+
+ align:start position:0%
+having
+ 
+
+ align:start position:0%
+having
+is it necessary to form an image
+
+ align:start position:0%
+is it necessary to form an image
+ 
+
+ align:start position:0%
+is it necessary to form an image
+and that that's and if you don't form an
+
+ align:start position:0%
+and that that's and if you don't form an
+ 
+
+ align:start position:0%
+and that that's and if you don't form an
+image if you just map directly into
+
+ align:start position:0%
+image if you just map directly into
+ 
+
+ align:start position:0%
+image if you just map directly into
+features number one can you do that
+
+ align:start position:0%
+features number one can you do that
+ 
+
+ align:start position:0%
+features number one can you do that
+number two should you do that is it
+
+ align:start position:0%
+number two should you do that is it
+ 
+
+ align:start position:0%
+number two should you do that is it
+advantages in some form or fashion
+
+ align:start position:0%
+advantages in some form or fashion
+ 
+
+ align:start position:0%
+advantages in some form or fashion
+that's uh it applies to Biometrics as
+
+ align:start position:0%
+that's uh it applies to Biometrics as
+ 
+
+ align:start position:0%
+that's uh it applies to Biometrics as
+well like right now for Iris recognition
+
+ align:start position:0%
+well like right now for Iris recognition
+ 
+
+ align:start position:0%
+well like right now for Iris recognition
+there is the Dogma algorithm
+
+ align:start position:0%
+there is the Dogma algorithm
+ 
+
+ align:start position:0%
+there is the Dogma algorithm
+that so that is geared upon you sampling
+
+ align:start position:0%
+that so that is geared upon you sampling
+ 
+
+ align:start position:0%
+that so that is geared upon you sampling
+the iris at a certain resolution in a
+
+ align:start position:0%
+the iris at a certain resolution in a
+ 
+
+ align:start position:0%
+the iris at a certain resolution in a
+certain way
+
+ align:start position:0%
+certain way
+ 
+
+ align:start position:0%
+certain way
+but if you tie the front end acquisition
+
+ align:start position:0%
+but if you tie the front end acquisition
+ 
+
+ align:start position:0%
+but if you tie the front end acquisition
+to the exploitation could you get into a
+
+ align:start position:0%
+to the exploitation could you get into a
+ 
+
+ align:start position:0%
+to the exploitation could you get into a
+more robust simpler system
+
+ align:start position:0%
+more robust simpler system
+ 
+
+ align:start position:0%
+more robust simpler system
+that's that's an interesting question
+
+ align:start position:0%
+that's that's an interesting question
+ 
+
+ align:start position:0%
+that's that's an interesting question
+but uh it's a little difficult for
+
+ align:start position:0%
+but uh it's a little difficult for
+ 
+
+ align:start position:0%
+but uh it's a little difficult for
+sponsors to launch in that direction
+
+ align:start position:0%
+sponsors to launch in that direction
+ 
+
+ align:start position:0%
+sponsors to launch in that direction
+because too much risk and if something
+
+ align:start position:0%
+because too much risk and if something
+ 
+
+ align:start position:0%
+because too much risk and if something
+changes on one side the whole
+
+ align:start position:0%
+changes on one side the whole
+ 
+
+ align:start position:0%
+changes on one side the whole
+thing May collapse but that's an
+
+ align:start position:0%
+thing May collapse but that's an
+ 
+
+ align:start position:0%
+thing May collapse but that's an
+interesting problem
+
+ align:start position:0%
+interesting problem
+ 
+
+ align:start position:0%
+interesting problem
+is as long as it's as you continue to
+
+ align:start position:0%
+is as long as it's as you continue to
+ 
+
+ align:start position:0%
+is as long as it's as you continue to
+rely on collecting a high quality image
+
+ align:start position:0%
+rely on collecting a high quality image
+ 
+
+ align:start position:0%
+rely on collecting a high quality image
+to do this I think the period of
+
+ align:start position:0%
+to do this I think the period of
+ 
+
+ align:start position:0%
+to do this I think the period of
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+and the diamond algorithm is a perfect
+
+ align:start position:0%
+and the diamond algorithm is a perfect
+ 
+
+ align:start position:0%
+and the diamond algorithm is a perfect
+example you start out with an image
+
+ align:start position:0%
+example you start out with an image
+ 
+
+ align:start position:0%
+example you start out with an image
+that's several hundred kilobytes and you
+
+ align:start position:0%
+that's several hundred kilobytes and you
+ 
+
+ align:start position:0%
+that's several hundred kilobytes and you
+end up with a template that's a couple
+
+ align:start position:0%
+end up with a template that's a couple
+ 
+
+ align:start position:0%
+end up with a template that's a couple
+hundred bytes right so obviously you
+
+ align:start position:0%
+hundred bytes right so obviously you
+ 
+
+ align:start position:0%
+hundred bytes right so obviously you
+don't need all that data that you
+
+ align:start position:0%
+don't need all that data that you
+ 
+
+ align:start position:0%
+don't need all that data that you
+collected in that high-resolution image
+
+ align:start position:0%
+collected in that high-resolution image
+ 
+
+ align:start position:0%
+collected in that high-resolution image
+to do Irish Red information so
+
+ align:start position:0%
+to do Irish Red information so
+ 
+
+ align:start position:0%
+to do Irish Red information so
+why do you need to start with that image
+
+ align:start position:0%
+why do you need to start with that image
+ 
+
+ align:start position:0%
+why do you need to start with that image
+in the first place
+
+ align:start position:0%
+in the first place
+ 
+
+ align:start position:0%
+in the first place
+and if you could develop a compressed
+
+ align:start position:0%
+and if you could develop a compressed
+ 
+
+ align:start position:0%
+and if you could develop a compressed
+representation if you could uh if you
+
+ align:start position:0%
+representation if you could uh if you
+ 
+
+ align:start position:0%
+representation if you could uh if you
+could sense that compressed
+
+ align:start position:0%
+could sense that compressed
+ 
+
+ align:start position:0%
+could sense that compressed
+representation directly would it lead to
+
+ align:start position:0%
+representation directly would it lead to
+ 
+
+ align:start position:0%
+representation directly would it lead to
+a simpler system would it lead to a
+
+ align:start position:0%
+a simpler system would it lead to a
+ 
+
+ align:start position:0%
+a simpler system would it lead to a
+simpler and moreover system that last
+
+ align:start position:0%
+simpler and moreover system that last
+ 
+
+ align:start position:0%
+simpler and moreover system that last
+question is uh very tricky to answer and
+
+ align:start position:0%
+question is uh very tricky to answer and
+ 
+
+ align:start position:0%
+question is uh very tricky to answer and
+the three of us had wrote when he was
+
+ align:start position:0%
+the three of us had wrote when he was
+ 
+
+ align:start position:0%
+the three of us had wrote when he was
+with us four of us have gone over this
+
+ align:start position:0%
+with us four of us have gone over this
+ 
+
+ align:start position:0%
+with us four of us have gone over this
+over and over and we still haven't come
+
+ align:start position:0%
+over and over and we still haven't come
+ 
+
+ align:start position:0%
+over and over and we still haven't come
+to a conclusion
+
+ align:start position:0%
+to a conclusion
+ 
+
+ align:start position:0%
+to a conclusion
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+sure right so hopefully uh as you
+
+ align:start position:0%
+sure right so hopefully uh as you
+ 
+
+ align:start position:0%
+sure right so hopefully uh as you
+already saw a lot of the a lot of the
+
+ align:start position:0%
+already saw a lot of the a lot of the
+ 
+
+ align:start position:0%
+already saw a lot of the a lot of the
+project plans are also about not yeah
+
+ align:start position:0%
+project plans are also about not yeah
+ 
+
+ align:start position:0%
+project plans are also about not yeah
+not about standard cameras and they're
+
+ align:start position:0%
+not about standard cameras and they're
+ 
+
+ align:start position:0%
+not about standard cameras and they're
+exploiting specialization and autonomy
+
+ align:start position:0%
+exploiting specialization and autonomy
+ 
+
+ align:start position:0%
+exploiting specialization and autonomy
+and trying to change a lot of the rules
+
+ align:start position:0%
+and trying to change a lot of the rules
+ 
+
+ align:start position:0%
+and trying to change a lot of the rules
+here so and as a matter of fact any of
+
+ align:start position:0%
+here so and as a matter of fact any of
+ 
+
+ align:start position:0%
+here so and as a matter of fact any of
+the projects we sort of looked at each
+
+ align:start position:0%
+the projects we sort of looked at each
+ 
+
+ align:start position:0%
+the projects we sort of looked at each
+other and said you know should be
+
+ align:start position:0%
+other and said you know should be
+ 
+
+ align:start position:0%
+other and said you know should be
+talking to these people
+
+ align:start position:0%
+talking to these people
+ 
+
+ align:start position:0%
+talking to these people
+come back and visit yeah exactly you're
+
+ align:start position:0%
+come back and visit yeah exactly you're
+ 
+
+ align:start position:0%
+come back and visit yeah exactly you're
+welcome to sign up as a mentor for the
+
+ align:start position:0%
+welcome to sign up as a mentor for the
+ 
+
+ align:start position:0%
+welcome to sign up as a mentor for the
+class so we have we have several mentors
+
+ align:start position:0%
+class so we have we have several mentors
+ 
+
+ align:start position:0%
+class so we have we have several mentors
+for the class in here welcome to sign up
+
+ align:start position:0%
+for the class in here welcome to sign up
+ 
+
+ align:start position:0%
+for the class in here welcome to sign up
+for that so excellent so next week we
+
+ align:start position:0%
+for that so excellent so next week we
+ 
+
+ align:start position:0%
+for that so excellent so next week we
+have the midterm exam uh it's open book
+
+ align:start position:0%
+have the midterm exam uh it's open book
+ 
+
+ align:start position:0%
+have the midterm exam uh it's open book
+open laptop open internet open
+
+ align:start position:0%
+open laptop open internet open
+ 
+
+ align:start position:0%
+open laptop open internet open
+everything so don't study for it
+
+ align:start position:0%
+everything so don't study for it
+ 
+
+ align:start position:0%
+everything so don't study for it
+and it will be mostly about drawing
+
+ align:start position:0%
+and it will be mostly about drawing
+ 
+
+ align:start position:0%
+and it will be mostly about drawing
+diagrams and explaining things and the
+
+ align:start position:0%
+diagrams and explaining things and the
+ 
+
+ align:start position:0%
+diagrams and explaining things and the
+problems that will make you think
+
+ align:start position:0%
+problems that will make you think
+ 
+
+ align:start position:0%
+problems that will make you think
+um and uh after imagine after that we'll
+
+ align:start position:0%
+um and uh after imagine after that we'll
+ 
+
+ align:start position:0%
+um and uh after imagine after that we'll
+be studying uh animal eyes
+
+ align:start position:0%
+be studying uh animal eyes
+ 
+
+ align:start position:0%
+be studying uh animal eyes
+which is different 13th of November
\ No newline at end of file
diff --git a/b11xP6rhn_I.txt b/b11xP6rhn_I.txt
new file mode 100644
index 0000000000000000000000000000000000000000..814c242ff9efc7b9eb46e8ee4a9345b7e9da7d4e
--- /dev/null
+++ b/b11xP6rhn_I.txt
@@ -0,0 +1,11240 @@
+align:start position:0%
+ 
+the following content is provided by mit
+
+ align:start position:0%
+the following content is provided by mit
+ 
+
+ align:start position:0%
+the following content is provided by mit
+opencourseware under a creative commons
+
+ align:start position:0%
+opencourseware under a creative commons
+ 
+
+ align:start position:0%
+opencourseware under a creative commons
+license
+
+ align:start position:0%
+license
+ 
+
+ align:start position:0%
+license
+additional information about our license
+
+ align:start position:0%
+additional information about our license
+ 
+
+ align:start position:0%
+additional information about our license
+and mit opencourseware in general is
+
+ align:start position:0%
+and mit opencourseware in general is
+ 
+
+ align:start position:0%
+and mit opencourseware in general is
+available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay welcome back one quick announcement
+
+ align:start position:0%
+okay welcome back one quick announcement
+ 
+
+ align:start position:0%
+okay welcome back one quick announcement
+before we get started
+
+ align:start position:0%
+before we get started
+ 
+
+ align:start position:0%
+before we get started
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the uh teaching fellows and i have uh
+
+ align:start position:0%
+the uh teaching fellows and i have uh
+ 
+
+ align:start position:0%
+the uh teaching fellows and i have uh
+in in response to a few gentle inquiries
+
+ align:start position:0%
+in in response to a few gentle inquiries
+ 
+
+ align:start position:0%
+in in response to a few gentle inquiries
+uh have come up with a plan for making
+
+ align:start position:0%
+uh have come up with a plan for making
+ 
+
+ align:start position:0%
+uh have come up with a plan for making
+your problem sets and projects a little
+
+ align:start position:0%
+your problem sets and projects a little
+ 
+
+ align:start position:0%
+your problem sets and projects a little
+bit easier
+
+ align:start position:0%
+bit easier
+ 
+
+ align:start position:0%
+bit easier
+getting some time take a look at the
+
+ align:start position:0%
+getting some time take a look at the
+ 
+
+ align:start position:0%
+getting some time take a look at the
+website and talk to your teaching
+
+ align:start position:0%
+website and talk to your teaching
+ 
+
+ align:start position:0%
+website and talk to your teaching
+fellows but basically problems there
+
+ align:start position:0%
+fellows but basically problems there
+ 
+
+ align:start position:0%
+fellows but basically problems there
+will be no problems at six they'll be
+
+ align:start position:0%
+will be no problems at six they'll be
+ 
+
+ align:start position:0%
+will be no problems at six they'll be
+combined with problem set five
+
+ align:start position:0%
+combined with problem set five
+ 
+
+ align:start position:0%
+combined with problem set five
+and so you'll have a full three weeks
+
+ align:start position:0%
+and so you'll have a full three weeks
+ 
+
+ align:start position:0%
+and so you'll have a full three weeks
+to work on your project tripling your
+
+ align:start position:0%
+to work on your project tripling your
+ 
+
+ align:start position:0%
+to work on your project tripling your
+project time now assuming you haven't
+
+ align:start position:0%
+project time now assuming you haven't
+ 
+
+ align:start position:0%
+project time now assuming you haven't
+done anything so far which hopefully all
+
+ align:start position:0%
+done anything so far which hopefully all
+ 
+
+ align:start position:0%
+done anything so far which hopefully all
+of you have done a lot so far
+
+ align:start position:0%
+of you have done a lot so far
+ 
+
+ align:start position:0%
+of you have done a lot so far
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we were correlating absolute levels of
+
+ align:start position:0%
+we were correlating absolute levels of
+ 
+
+ align:start position:0%
+we were correlating absolute levels of
+messenger rna abundance
+
+ align:start position:0%
+messenger rna abundance
+ 
+
+ align:start position:0%
+messenger rna abundance
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+protein
+
+ align:start position:0%
+protein
+ 
+
+ align:start position:0%
+protein
+messenger rna protein
+
+ align:start position:0%
+messenger rna protein
+ 
+
+ align:start position:0%
+messenger rna protein
+and here the uh this study was subjected
+
+ align:start position:0%
+and here the uh this study was subjected
+ 
+
+ align:start position:0%
+and here the uh this study was subjected
+to a little bit of not not terribly
+
+ align:start position:0%
+to a little bit of not not terribly
+ 
+
+ align:start position:0%
+to a little bit of not not terribly
+controversial critique
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what you're seeing here uh
+
+ align:start position:0%
+what you're seeing here uh
+ 
+
+ align:start position:0%
+what you're seeing here uh
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+at very if you have the very low
+
+ align:start position:0%
+at very if you have the very low
+ 
+
+ align:start position:0%
+at very if you have the very low
+abundance proteins you might have what
+
+ align:start position:0%
+abundance proteins you might have what
+ 
+
+ align:start position:0%
+abundance proteins you might have what
+looks like some correlation then you add
+
+ align:start position:0%
+looks like some correlation then you add
+ 
+
+ align:start position:0%
+looks like some correlation then you add
+a few more low abundance proteins so
+
+ align:start position:0%
+a few more low abundance proteins so
+ 
+
+ align:start position:0%
+a few more low abundance proteins so
+this is just some fluctuation and
+
+ align:start position:0%
+this is just some fluctuation and
+ 
+
+ align:start position:0%
+this is just some fluctuation and
+adding proteins should improve your
+
+ align:start position:0%
+adding proteins should improve your
+ 
+
+ align:start position:0%
+adding proteins should improve your
+correlation coefficient but if they're
+
+ align:start position:0%
+correlation coefficient but if they're
+ 
+
+ align:start position:0%
+correlation coefficient but if they're
+of low uh reliability in either the
+
+ align:start position:0%
+of low uh reliability in either the
+ 
+
+ align:start position:0%
+of low uh reliability in either the
+protein or the messenger rna
+
+ align:start position:0%
+protein or the messenger rna
+ 
+
+ align:start position:0%
+protein or the messenger rna
+scale or if there isn't correlation
+
+ align:start position:0%
+scale or if there isn't correlation
+ 
+
+ align:start position:0%
+scale or if there isn't correlation
+between the two for biological reasons
+
+ align:start position:0%
+between the two for biological reasons
+ 
+
+ align:start position:0%
+between the two for biological reasons
+then your correlation coefficient could
+
+ align:start position:0%
+then your correlation coefficient could
+ 
+
+ align:start position:0%
+then your correlation coefficient could
+drop just at random
+
+ align:start position:0%
+drop just at random
+ 
+
+ align:start position:0%
+drop just at random
+but as you add as you get up to adding
+
+ align:start position:0%
+but as you add as you get up to adding
+ 
+
+ align:start position:0%
+but as you add as you get up to adding
+all the proteins
+
+ align:start position:0%
+all the proteins
+ 
+
+ align:start position:0%
+all the proteins
+you could either be dominated by a few
+
+ align:start position:0%
+you could either be dominated by a few
+ 
+
+ align:start position:0%
+you could either be dominated by a few
+high abundance proteins that fit this
+
+ align:start position:0%
+high abundance proteins that fit this
+ 
+
+ align:start position:0%
+high abundance proteins that fit this
+perfectly the messenger rna protein
+
+ align:start position:0%
+perfectly the messenger rna protein
+ 
+
+ align:start position:0%
+perfectly the messenger rna protein
+abundance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway some of the critiques of this had
+
+ align:start position:0%
+anyway some of the critiques of this had
+ 
+
+ align:start position:0%
+anyway some of the critiques of this had
+to do with
+
+ align:start position:0%
+to do with
+ 
+
+ align:start position:0%
+to do with
+the assumptions underlying the pearson
+
+ align:start position:0%
+the assumptions underlying the pearson
+ 
+
+ align:start position:0%
+the assumptions underlying the pearson
+linear correlation coefficient which in
+
+ align:start position:0%
+linear correlation coefficient which in
+ 
+
+ align:start position:0%
+linear correlation coefficient which in
+calculating the statistical significance
+
+ align:start position:0%
+calculating the statistical significance
+ 
+
+ align:start position:0%
+calculating the statistical significance
+of some of these analyses in the
+
+ align:start position:0%
+of some of these analyses in the
+ 
+
+ align:start position:0%
+of some of these analyses in the
+previous slide
+
+ align:start position:0%
+previous slide
+ 
+
+ align:start position:0%
+previous slide
+make an underlying assumption that you
+
+ align:start position:0%
+make an underlying assumption that you
+ 
+
+ align:start position:0%
+make an underlying assumption that you
+have a normal or gaussian
+
+ align:start position:0%
+have a normal or gaussian
+ 
+
+ align:start position:0%
+have a normal or gaussian
+bell curve
+
+ align:start position:0%
+bell curve
+ 
+
+ align:start position:0%
+bell curve
+and this is you don't need to do this in
+
+ align:start position:0%
+and this is you don't need to do this in
+ 
+
+ align:start position:0%
+and this is you don't need to do this in
+order there are variety of measures of
+
+ align:start position:0%
+order there are variety of measures of
+ 
+
+ align:start position:0%
+order there are variety of measures of
+correlation which do not require this
+
+ align:start position:0%
+correlation which do not require this
+ 
+
+ align:start position:0%
+correlation which do not require this
+parametric assumption
+
+ align:start position:0%
+parametric assumption
+ 
+
+ align:start position:0%
+parametric assumption
+um and there are there there are tests
+
+ align:start position:0%
+um and there are there there are tests
+ 
+
+ align:start position:0%
+um and there are there there are tests
+for the how close to normal a
+
+ align:start position:0%
+for the how close to normal a
+ 
+
+ align:start position:0%
+for the how close to normal a
+distribution is
+
+ align:start position:0%
+distribution is
+ 
+
+ align:start position:0%
+distribution is
+deviations from normality can be of all
+
+ align:start position:0%
+deviations from normality can be of all
+ 
+
+ align:start position:0%
+deviations from normality can be of all
+types for example you can have slightly
+
+ align:start position:0%
+types for example you can have slightly
+ 
+
+ align:start position:0%
+types for example you can have slightly
+flatter or slightly sharper than normal
+
+ align:start position:0%
+flatter or slightly sharper than normal
+ 
+
+ align:start position:0%
+flatter or slightly sharper than normal
+you can have skewed to the left or to
+
+ align:start position:0%
+you can have skewed to the left or to
+ 
+
+ align:start position:0%
+you can have skewed to the left or to
+the right and so forth some of these
+
+ align:start position:0%
+the right and so forth some of these
+ 
+
+ align:start position:0%
+the right and so forth some of these
+like skewing can be corrected by a log
+
+ align:start position:0%
+like skewing can be corrected by a log
+ 
+
+ align:start position:0%
+like skewing can be corrected by a log
+transformation where you simply take the
+
+ align:start position:0%
+transformation where you simply take the
+ 
+
+ align:start position:0%
+transformation where you simply take the
+logarithm or some other transformation
+
+ align:start position:0%
+logarithm or some other transformation
+ 
+
+ align:start position:0%
+logarithm or some other transformation
+and log being by by far the most common
+
+ align:start position:0%
+and log being by by far the most common
+ 
+
+ align:start position:0%
+and log being by by far the most common
+and theoretically justified and now it
+
+ align:start position:0%
+and theoretically justified and now it
+ 
+
+ align:start position:0%
+and theoretically justified and now it
+becomes normal and then you can do a
+
+ align:start position:0%
+becomes normal and then you can do a
+ 
+
+ align:start position:0%
+becomes normal and then you can do a
+statistical test
+
+ align:start position:0%
+statistical test
+ 
+
+ align:start position:0%
+statistical test
+as it turns out this is not a huge
+
+ align:start position:0%
+as it turns out this is not a huge
+ 
+
+ align:start position:0%
+as it turns out this is not a huge
+effect but they use it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in order to develop or to point out that
+
+ align:start position:0%
+in order to develop or to point out that
+ 
+
+ align:start position:0%
+in order to develop or to point out that
+you can when you're testing these
+
+ align:start position:0%
+you can when you're testing these
+ 
+
+ align:start position:0%
+you can when you're testing these
+especially the low abundance
+
+ align:start position:0%
+especially the low abundance
+ 
+
+ align:start position:0%
+especially the low abundance
+into the spectrum
+
+ align:start position:0%
+into the spectrum
+ 
+
+ align:start position:0%
+into the spectrum
+you might want to use a rank test
+
+ align:start position:0%
+you might want to use a rank test
+ 
+
+ align:start position:0%
+you might want to use a rank test
+and a rain test here is illustrated that
+
+ align:start position:0%
+and a rain test here is illustrated that
+ 
+
+ align:start position:0%
+and a rain test here is illustrated that
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take if you have
+
+ align:start position:0%
+take if you have
+ 
+
+ align:start position:0%
+take if you have
+say two columns
+
+ align:start position:0%
+say two columns
+ 
+
+ align:start position:0%
+say two columns
+this is a series of pairs
+
+ align:start position:0%
+this is a series of pairs
+ 
+
+ align:start position:0%
+this is a series of pairs
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+intensities of
+
+ align:start position:0%
+intensities of
+ 
+
+ align:start position:0%
+intensities of
+messenger rna and protein say columns x
+
+ align:start position:0%
+messenger rna and protein say columns x
+ 
+
+ align:start position:0%
+messenger rna and protein say columns x
+and column y
+
+ align:start position:0%
+and column y
+ 
+
+ align:start position:0%
+and column y
+down in the lower right hand corner of
+
+ align:start position:0%
+down in the lower right hand corner of
+ 
+
+ align:start position:0%
+down in the lower right hand corner of
+slide 37
+
+ align:start position:0%
+slide 37
+ 
+
+ align:start position:0%
+slide 37
+and let's say the abundances the
+
+ align:start position:0%
+and let's say the abundances the
+ 
+
+ align:start position:0%
+and let's say the abundances the
+absolute abundances for protein x
+
+ align:start position:0%
+absolute abundances for protein x
+ 
+
+ align:start position:0%
+absolute abundances for protein x
+is one six six six
+
+ align:start position:0%
+is one six six six
+ 
+
+ align:start position:0%
+is one six six six
+and corresponding
+
+ align:start position:0%
+and corresponding
+ 
+
+ align:start position:0%
+and corresponding
+rna y which would be eight
+
+ align:start position:0%
+rna y which would be eight
+ 
+
+ align:start position:0%
+rna y which would be eight
+two three and four
+
+ align:start position:0%
+two three and four
+ 
+
+ align:start position:0%
+two three and four
+now you wanna ask whether they're
+
+ align:start position:0%
+now you wanna ask whether they're
+ 
+
+ align:start position:0%
+now you wanna ask whether they're
+correlated or not and what you do is you
+
+ align:start position:0%
+correlated or not and what you do is you
+ 
+
+ align:start position:0%
+correlated or not and what you do is you
+rank them and so the rank of
+
+ align:start position:0%
+rank them and so the rank of
+ 
+
+ align:start position:0%
+rank them and so the rank of
+x
+
+ align:start position:0%
+x
+ 
+
+ align:start position:0%
+x
+is one three three three here it's high
+
+ align:start position:0%
+is one three three three here it's high
+ 
+
+ align:start position:0%
+is one three three three here it's high
+breaker the way you deal with a tie is
+
+ align:start position:0%
+breaker the way you deal with a tie is
+ 
+
+ align:start position:0%
+breaker the way you deal with a tie is
+you give them all the rank of the middle
+
+ align:start position:0%
+you give them all the rank of the middle
+ 
+
+ align:start position:0%
+you give them all the rank of the middle
+one of the series
+
+ align:start position:0%
+one of the series
+ 
+
+ align:start position:0%
+one of the series
+in the pie
+
+ align:start position:0%
+in the pie
+ 
+
+ align:start position:0%
+in the pie
+and uh you get a rank for y
+
+ align:start position:0%
+and uh you get a rank for y
+ 
+
+ align:start position:0%
+and uh you get a rank for y
+and the total number in this case is
+
+ align:start position:0%
+and the total number in this case is
+ 
+
+ align:start position:0%
+and the total number in this case is
+four and so
+
+ align:start position:0%
+four and so
+ 
+
+ align:start position:0%
+four and so
+when you have these um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the rank tests score is basically the
+
+ align:start position:0%
+the rank tests score is basically the
+ 
+
+ align:start position:0%
+the rank tests score is basically the
+sum of the square of all the differences
+
+ align:start position:0%
+sum of the square of all the differences
+ 
+
+ align:start position:0%
+sum of the square of all the differences
+in rank so the difference in rank here
+
+ align:start position:0%
+in rank so the difference in rank here
+ 
+
+ align:start position:0%
+in rank so the difference in rank here
+would be one minus four
+
+ align:start position:0%
+would be one minus four
+ 
+
+ align:start position:0%
+would be one minus four
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be three three squared you take the sum
+
+ align:start position:0%
+be three three squared you take the sum
+ 
+
+ align:start position:0%
+be three three squared you take the sum
+of all those squares and you plug it
+
+ align:start position:0%
+of all those squares and you plug it
+ 
+
+ align:start position:0%
+of all those squares and you plug it
+into this s which is going to go into a
+
+ align:start position:0%
+into this s which is going to go into a
+ 
+
+ align:start position:0%
+into this s which is going to go into a
+correlation coefficient
+
+ align:start position:0%
+correlation coefficient
+ 
+
+ align:start position:0%
+correlation coefficient
+similar to in values and properties to
+
+ align:start position:0%
+similar to in values and properties to
+ 
+
+ align:start position:0%
+similar to in values and properties to
+the pearson but now i'm not making
+
+ align:start position:0%
+the pearson but now i'm not making
+ 
+
+ align:start position:0%
+the pearson but now i'm not making
+assumptions about the parametrics you're
+
+ align:start position:0%
+assumptions about the parametrics you're
+ 
+
+ align:start position:0%
+assumptions about the parametrics you're
+just talking about ranks it's a
+
+ align:start position:0%
+just talking about ranks it's a
+ 
+
+ align:start position:0%
+just talking about ranks it's a
+non-parametric test
+
+ align:start position:0%
+non-parametric test
+ 
+
+ align:start position:0%
+non-parametric test
+and then the n is the total number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you apply that formula now they
+
+ align:start position:0%
+and you apply that formula now they
+ 
+
+ align:start position:0%
+and you apply that formula now they
+apply that formula so it's exactly the
+
+ align:start position:0%
+apply that formula so it's exactly the
+ 
+
+ align:start position:0%
+apply that formula so it's exactly the
+same data set or very similar actually
+
+ align:start position:0%
+same data set or very similar actually
+ 
+
+ align:start position:0%
+same data set or very similar actually
+data set
+
+ align:start position:0%
+data set
+ 
+
+ align:start position:0%
+data set
+another critique they had was that using
+
+ align:start position:0%
+another critique they had was that using
+ 
+
+ align:start position:0%
+another critique they had was that using
+the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the better measure of the of the
+
+ align:start position:0%
+the better measure of the of the
+ 
+
+ align:start position:0%
+the better measure of the of the
+protein abundance would be
+
+ align:start position:0%
+protein abundance would be
+ 
+
+ align:start position:0%
+protein abundance would be
+using a
+
+ align:start position:0%
+using a
+ 
+
+ align:start position:0%
+using a
+radioactive tracer in the protein and
+
+ align:start position:0%
+radioactive tracer in the protein and
+ 
+
+ align:start position:0%
+radioactive tracer in the protein and
+then measuring quantitatively
+
+ align:start position:0%
+then measuring quantitatively
+ 
+
+ align:start position:0%
+then measuring quantitatively
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+the intensity
+
+ align:start position:0%
+the intensity
+ 
+
+ align:start position:0%
+the intensity
+uh of the of beta particles released
+
+ align:start position:0%
+uh of the of beta particles released
+ 
+
+ align:start position:0%
+uh of the of beta particles released
+from the methionines in the proteins
+
+ align:start position:0%
+from the methionines in the proteins
+ 
+
+ align:start position:0%
+from the methionines in the proteins
+so they uh
+
+ align:start position:0%
+so they uh
+ 
+
+ align:start position:0%
+so they uh
+making that change and comparing it to
+
+ align:start position:0%
+making that change and comparing it to
+ 
+
+ align:start position:0%
+making that change and comparing it to
+the same messenger rna
+
+ align:start position:0%
+the same messenger rna
+ 
+
+ align:start position:0%
+the same messenger rna
+assessment
+
+ align:start position:0%
+assessment
+ 
+
+ align:start position:0%
+assessment
+they got this fairly linear correlation
+
+ align:start position:0%
+they got this fairly linear correlation
+ 
+
+ align:start position:0%
+they got this fairly linear correlation
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+three logs
+
+ align:start position:0%
+three logs
+ 
+
+ align:start position:0%
+three logs
+using the the their
+
+ align:start position:0%
+using the the their
+ 
+
+ align:start position:0%
+using the the their
+the pearson correlation coefficient
+
+ align:start position:0%
+the pearson correlation coefficient
+ 
+
+ align:start position:0%
+the pearson correlation coefficient
+which they didn't entirely approve of
+
+ align:start position:0%
+which they didn't entirely approve of
+ 
+
+ align:start position:0%
+which they didn't entirely approve of
+they got a a 0.76 which is a modest uh
+
+ align:start position:0%
+they got a a 0.76 which is a modest uh
+ 
+
+ align:start position:0%
+they got a a 0.76 which is a modest uh
+it's a significant
+
+ align:start position:0%
+it's a significant
+ 
+
+ align:start position:0%
+it's a significant
+linear trend
+
+ align:start position:0%
+linear trend
+ 
+
+ align:start position:0%
+linear trend
+and using their
+
+ align:start position:0%
+and using their
+ 
+
+ align:start position:0%
+and using their
+rank
+
+ align:start position:0%
+rank
+ 
+
+ align:start position:0%
+rank
+method 0.74 which is basically very
+
+ align:start position:0%
+method 0.74 which is basically very
+ 
+
+ align:start position:0%
+method 0.74 which is basically very
+similar
+
+ align:start position:0%
+similar
+ 
+
+ align:start position:0%
+similar
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and found no significant difference
+
+ align:start position:0%
+and found no significant difference
+ 
+
+ align:start position:0%
+and found no significant difference
+between the top 33 and the bottom 33
+
+ align:start position:0%
+between the top 33 and the bottom 33
+ 
+
+ align:start position:0%
+between the top 33 and the bottom 33
+proteins
+
+ align:start position:0%
+proteins
+ 
+
+ align:start position:0%
+proteins
+undermining the
+
+ align:start position:0%
+undermining the
+ 
+
+ align:start position:0%
+undermining the
+previous claim that there was this that
+
+ align:start position:0%
+previous claim that there was this that
+ 
+
+ align:start position:0%
+previous claim that there was this that
+there was less linearity at one end than
+
+ align:start position:0%
+there was less linearity at one end than
+ 
+
+ align:start position:0%
+there was less linearity at one end than
+another you might a priori expect that
+
+ align:start position:0%
+another you might a priori expect that
+ 
+
+ align:start position:0%
+another you might a priori expect that
+the the least abundant messenger artisan
+
+ align:start position:0%
+the the least abundant messenger artisan
+ 
+
+ align:start position:0%
+the the least abundant messenger artisan
+proteins would have a little bit of
+
+ align:start position:0%
+proteins would have a little bit of
+ 
+
+ align:start position:0%
+proteins would have a little bit of
+either biological or instrumental noise
+
+ align:start position:0%
+either biological or instrumental noise
+ 
+
+ align:start position:0%
+either biological or instrumental noise
+nevertheless this group found that it
+
+ align:start position:0%
+nevertheless this group found that it
+ 
+
+ align:start position:0%
+nevertheless this group found that it
+was a
+
+ align:start position:0%
+was a
+ 
+
+ align:start position:0%
+was a
+good correlation now these two plot the
+
+ align:start position:0%
+good correlation now these two plot the
+ 
+
+ align:start position:0%
+good correlation now these two plot the
+plot in the next slide
+
+ align:start position:0%
+plot in the next slide
+ 
+
+ align:start position:0%
+plot in the next slide
+looks similar but it's but
+
+ align:start position:0%
+looks similar but it's but
+ 
+
+ align:start position:0%
+looks similar but it's but
+it's uh
+
+ align:start position:0%
+it's uh
+ 
+
+ align:start position:0%
+it's uh
+really quite different here
+
+ align:start position:0%
+really quite different here
+ 
+
+ align:start position:0%
+really quite different here
+the y-axis remains
+
+ align:start position:0%
+the y-axis remains
+ 
+
+ align:start position:0%
+the y-axis remains
+the protein abundance measured by this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s35 labeling but now we're getting back
+
+ align:start position:0%
+s35 labeling but now we're getting back
+ 
+
+ align:start position:0%
+s35 labeling but now we're getting back
+to this game of asking
+
+ align:start position:0%
+to this game of asking
+ 
+
+ align:start position:0%
+to this game of asking
+to what extent can we make predictions
+
+ align:start position:0%
+to what extent can we make predictions
+ 
+
+ align:start position:0%
+to what extent can we make predictions
+about the properties of the proteins in
+
+ align:start position:0%
+about the properties of the proteins in
+ 
+
+ align:start position:0%
+about the properties of the proteins in
+this case their abundance based on their
+
+ align:start position:0%
+this case their abundance based on their
+ 
+
+ align:start position:0%
+this case their abundance based on their
+use of the of abundant codons
+
+ align:start position:0%
+use of the of abundant codons
+ 
+
+ align:start position:0%
+use of the of abundant codons
+and a way of quantitating this the codop
+
+ align:start position:0%
+and a way of quantitating this the codop
+ 
+
+ align:start position:0%
+and a way of quantitating this the codop
+added
+
+ align:start position:0%
+added
+ 
+
+ align:start position:0%
+added
+adaptation index
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shown in the lower left part of the
+
+ align:start position:0%
+shown in the lower left part of the
+ 
+
+ align:start position:0%
+shown in the lower left part of the
+slide is you have a
+
+ align:start position:0%
+slide is you have a
+ 
+
+ align:start position:0%
+slide is you have a
+it's a it's the log of the fit and
+
+ align:start position:0%
+it's a it's the log of the fit and
+ 
+
+ align:start position:0%
+it's a it's the log of the fit and
+adaptation index is the sum all the
+
+ align:start position:0%
+adaptation index is the sum all the
+ 
+
+ align:start position:0%
+adaptation index is the sum all the
+frequencies f of i of each of the codons
+
+ align:start position:0%
+frequencies f of i of each of the codons
+ 
+
+ align:start position:0%
+frequencies f of i of each of the codons
+where i is
+
+ align:start position:0%
+where i is
+ 
+
+ align:start position:0%
+where i is
+the 61 non-stop codons out of 64 total
+
+ align:start position:0%
+the 61 non-stop codons out of 64 total
+ 
+
+ align:start position:0%
+the 61 non-stop codons out of 64 total
+and the w sub i
+
+ align:start position:0%
+and the w sub i
+ 
+
+ align:start position:0%
+and the w sub i
+is a weighting factor where it's the
+
+ align:start position:0%
+is a weighting factor where it's the
+ 
+
+ align:start position:0%
+is a weighting factor where it's the
+ratio of the frequency of codon i
+
+ align:start position:0%
+ratio of the frequency of codon i
+ 
+
+ align:start position:0%
+ratio of the frequency of codon i
+let's say a leucine codon there's six
+
+ align:start position:0%
+let's say a leucine codon there's six
+ 
+
+ align:start position:0%
+let's say a leucine codon there's six
+different leucine codons and
+
+ align:start position:0%
+different leucine codons and
+ 
+
+ align:start position:0%
+different leucine codons and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+say the first one the w sub one is going
+
+ align:start position:0%
+say the first one the w sub one is going
+ 
+
+ align:start position:0%
+say the first one the w sub one is going
+to be the ratio of the frequency of that
+
+ align:start position:0%
+to be the ratio of the frequency of that
+ 
+
+ align:start position:0%
+to be the ratio of the frequency of that
+first codon to whichever one happens to
+
+ align:start position:0%
+first codon to whichever one happens to
+ 
+
+ align:start position:0%
+first codon to whichever one happens to
+be the most abundant one could be the
+
+ align:start position:0%
+be the most abundant one could be the
+ 
+
+ align:start position:0%
+be the most abundant one could be the
+first one or it could be one of the
+
+ align:start position:0%
+first one or it could be one of the
+ 
+
+ align:start position:0%
+first one or it could be one of the
+other six
+
+ align:start position:0%
+other six
+ 
+
+ align:start position:0%
+other six
+and so that's the formula that is used
+
+ align:start position:0%
+and so that's the formula that is used
+ 
+
+ align:start position:0%
+and so that's the formula that is used
+and you can see again a nice linear
+
+ align:start position:0%
+and you can see again a nice linear
+ 
+
+ align:start position:0%
+and you can see again a nice linear
+trend where indeed the most abundant
+
+ align:start position:0%
+trend where indeed the most abundant
+ 
+
+ align:start position:0%
+trend where indeed the most abundant
+proteins do
+
+ align:start position:0%
+proteins do
+ 
+
+ align:start position:0%
+proteins do
+tend to use the most abundant codons
+
+ align:start position:0%
+tend to use the most abundant codons
+ 
+
+ align:start position:0%
+tend to use the most abundant codons
+the codons that you find and
+
+ align:start position:0%
+the codons that you find and
+ 
+
+ align:start position:0%
+the codons that you find and
+that are most abundant both transfer rna
+
+ align:start position:0%
+that are most abundant both transfer rna
+ 
+
+ align:start position:0%
+that are most abundant both transfer rna
+level and in usage in abundant proteins
+
+ align:start position:0%
+level and in usage in abundant proteins
+ 
+
+ align:start position:0%
+level and in usage in abundant proteins
+now just as with rnas you can measure
+
+ align:start position:0%
+now just as with rnas you can measure
+ 
+
+ align:start position:0%
+now just as with rnas you can measure
+them on a absolute scale or a ratio
+
+ align:start position:0%
+them on a absolute scale or a ratio
+ 
+
+ align:start position:0%
+them on a absolute scale or a ratio
+scale the advantage of
+
+ align:start position:0%
+scale the advantage of
+ 
+
+ align:start position:0%
+scale the advantage of
+in principle if you have it on an
+
+ align:start position:0%
+in principle if you have it on an
+ 
+
+ align:start position:0%
+in principle if you have it on an
+absolute scale you can always calculate
+
+ align:start position:0%
+absolute scale you can always calculate
+ 
+
+ align:start position:0%
+absolute scale you can always calculate
+ratios from it but not necessarily vice
+
+ align:start position:0%
+ratios from it but not necessarily vice
+ 
+
+ align:start position:0%
+ratios from it but not necessarily vice
+versa you have ratios you can't always
+
+ align:start position:0%
+versa you have ratios you can't always
+ 
+
+ align:start position:0%
+versa you have ratios you can't always
+get to absolute
+
+ align:start position:0%
+get to absolute
+ 
+
+ align:start position:0%
+get to absolute
+that's one advantage to absolute
+
+ align:start position:0%
+that's one advantage to absolute
+ 
+
+ align:start position:0%
+that's one advantage to absolute
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+if you're looking at things like code
+
+ align:start position:0%
+if you're looking at things like code
+ 
+
+ align:start position:0%
+if you're looking at things like code
+and adaptation index or messenger rna or
+
+ align:start position:0%
+and adaptation index or messenger rna or
+ 
+
+ align:start position:0%
+and adaptation index or messenger rna or
+a variety of other um
+
+ align:start position:0%
+a variety of other um
+ 
+
+ align:start position:0%
+a variety of other um
+motivations for you need to do it on the
+
+ align:start position:0%
+motivations for you need to do it on the
+ 
+
+ align:start position:0%
+motivations for you need to do it on the
+absolute scale
+
+ align:start position:0%
+absolute scale
+ 
+
+ align:start position:0%
+absolute scale
+but they're an argument conveyed for
+
+ align:start position:0%
+but they're an argument conveyed for
+ 
+
+ align:start position:0%
+but they're an argument conveyed for
+doing it on a ratio metric or or
+
+ align:start position:0%
+doing it on a ratio metric or or
+ 
+
+ align:start position:0%
+doing it on a ratio metric or or
+relative scale
+
+ align:start position:0%
+relative scale
+ 
+
+ align:start position:0%
+relative scale
+in the sense that you can establish
+
+ align:start position:0%
+in the sense that you can establish
+ 
+
+ align:start position:0%
+in the sense that you can establish
+internal standards which are
+
+ align:start position:0%
+internal standards which are
+ 
+
+ align:start position:0%
+internal standards which are
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+precise
+
+ align:start position:0%
+precise
+ 
+
+ align:start position:0%
+precise
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+really uh eliminate many of the
+
+ align:start position:0%
+really uh eliminate many of the
+ 
+
+ align:start position:0%
+really uh eliminate many of the
+systematic errors that can creep in
+
+ align:start position:0%
+systematic errors that can creep in
+ 
+
+ align:start position:0%
+systematic errors that can creep in
+due to differential ionization in the
+
+ align:start position:0%
+due to differential ionization in the
+ 
+
+ align:start position:0%
+due to differential ionization in the
+case of mass spectrometry and so on
+
+ align:start position:0%
+case of mass spectrometry and so on
+ 
+
+ align:start position:0%
+case of mass spectrometry and so on
+now with
+
+ align:start position:0%
+now with
+ 
+
+ align:start position:0%
+now with
+rna that the way we did this ratio
+
+ align:start position:0%
+rna that the way we did this ratio
+ 
+
+ align:start position:0%
+rna that the way we did this ratio
+testing
+
+ align:start position:0%
+testing
+ 
+
+ align:start position:0%
+testing
+ratio quantitation
+
+ align:start position:0%
+ratio quantitation
+ 
+
+ align:start position:0%
+ratio quantitation
+is we would label
+
+ align:start position:0%
+is we would label
+ 
+
+ align:start position:0%
+is we would label
+one messenger rna
+
+ align:start position:0%
+one messenger rna
+ 
+
+ align:start position:0%
+one messenger rna
+red or site five and the other one green
+
+ align:start position:0%
+red or site five and the other one green
+ 
+
+ align:start position:0%
+red or site five and the other one green
+and uh and then by using uh selective
+
+ align:start position:0%
+and uh and then by using uh selective
+ 
+
+ align:start position:0%
+and uh and then by using uh selective
+filtration in the in the imaging you can
+
+ align:start position:0%
+filtration in the in the imaging you can
+ 
+
+ align:start position:0%
+filtration in the in the imaging you can
+you could get ratios with mass
+
+ align:start position:0%
+you could get ratios with mass
+ 
+
+ align:start position:0%
+you could get ratios with mass
+spectrometry you don't have colors
+
+ align:start position:0%
+spectrometry you don't have colors
+ 
+
+ align:start position:0%
+spectrometry you don't have colors
+but somehow you want to get the same
+
+ align:start position:0%
+but somehow you want to get the same
+ 
+
+ align:start position:0%
+but somehow you want to get the same
+idea across and so what you do is you
+
+ align:start position:0%
+idea across and so what you do is you
+ 
+
+ align:start position:0%
+idea across and so what you do is you
+have masses so what you want to do is
+
+ align:start position:0%
+have masses so what you want to do is
+ 
+
+ align:start position:0%
+have masses so what you want to do is
+encode them in something that will not
+
+ align:start position:0%
+encode them in something that will not
+ 
+
+ align:start position:0%
+encode them in something that will not
+change the chemistry but will change the
+
+ align:start position:0%
+change the chemistry but will change the
+ 
+
+ align:start position:0%
+change the chemistry but will change the
+mass not change the mass too much
+
+ align:start position:0%
+mass not change the mass too much
+ 
+
+ align:start position:0%
+mass not change the mass too much
+because if you change too much you might
+
+ align:start position:0%
+because if you change too much you might
+ 
+
+ align:start position:0%
+because if you change too much you might
+change the chemistry or you might not be
+
+ align:start position:0%
+change the chemistry or you might not be
+ 
+
+ align:start position:0%
+change the chemistry or you might not be
+able to find the shadow peak the second
+
+ align:start position:0%
+able to find the shadow peak the second
+ 
+
+ align:start position:0%
+able to find the shadow peak the second
+peak so basically what we're doing is uh
+
+ align:start position:0%
+peak so basically what we're doing is uh
+ 
+
+ align:start position:0%
+peak so basically what we're doing is uh
+we have a
+
+ align:start position:0%
+we have a
+ 
+
+ align:start position:0%
+we have a
+you want to do is take cell state one
+
+ align:start position:0%
+you want to do is take cell state one
+ 
+
+ align:start position:0%
+you want to do is take cell state one
+label it with the light icat reagent
+
+ align:start position:0%
+label it with the light icat reagent
+ 
+
+ align:start position:0%
+label it with the light icat reagent
+substrate two label it with a heavy
+
+ align:start position:0%
+substrate two label it with a heavy
+ 
+
+ align:start position:0%
+substrate two label it with a heavy
+meaning uh more
+
+ align:start position:0%
+meaning uh more
+ 
+
+ align:start position:0%
+meaning uh more
+neutrons in it
+
+ align:start position:0%
+neutrons in it
+ 
+
+ align:start position:0%
+neutrons in it
+and then mix them together as early as
+
+ align:start position:0%
+and then mix them together as early as
+ 
+
+ align:start position:0%
+and then mix them together as early as
+possible and then all these steps that
+
+ align:start position:0%
+possible and then all these steps that
+ 
+
+ align:start position:0%
+possible and then all these steps that
+could have little systematic errors in
+
+ align:start position:0%
+could have little systematic errors in
+ 
+
+ align:start position:0%
+could have little systematic errors in
+it will be
+
+ align:start position:0%
+it will be
+ 
+
+ align:start position:0%
+it will be
+the errors will be equally
+
+ align:start position:0%
+the errors will be equally
+ 
+
+ align:start position:0%
+the errors will be equally
+distributed to each of the
+
+ align:start position:0%
+distributed to each of the
+ 
+
+ align:start position:0%
+distributed to each of the
+peptides has been labeled and then
+
+ align:start position:0%
+peptides has been labeled and then
+ 
+
+ align:start position:0%
+peptides has been labeled and then
+measure the mass and for each mass
+
+ align:start position:0%
+measure the mass and for each mass
+ 
+
+ align:start position:0%
+measure the mass and for each mass
+you'll have two peaks that are separated
+
+ align:start position:0%
+you'll have two peaks that are separated
+ 
+
+ align:start position:0%
+you'll have two peaks that are separated
+by whatever the difference of mass
+
+ align:start position:0%
+by whatever the difference of mass
+ 
+
+ align:start position:0%
+by whatever the difference of mass
+between the labeling agents so what are
+
+ align:start position:0%
+between the labeling agents so what are
+ 
+
+ align:start position:0%
+between the labeling agents so what are
+the properties that you want of a
+
+ align:start position:0%
+the properties that you want of a
+ 
+
+ align:start position:0%
+the properties that you want of a
+labeling agent one is that it should it
+
+ align:start position:0%
+labeling agent one is that it should it
+ 
+
+ align:start position:0%
+labeling agent one is that it should it
+should react covalently so it will
+
+ align:start position:0%
+should react covalently so it will
+ 
+
+ align:start position:0%
+should react covalently so it will
+survive all these mass
+
+ align:start position:0%
+survive all these mass
+ 
+
+ align:start position:0%
+survive all these mass
+these fractionation steps and mass
+
+ align:start position:0%
+these fractionation steps and mass
+ 
+
+ align:start position:0%
+these fractionation steps and mass
+detection steps so it has to be in this
+
+ align:start position:0%
+detection steps so it has to be in this
+ 
+
+ align:start position:0%
+detection steps so it has to be in this
+case style specific you want you want a
+
+ align:start position:0%
+case style specific you want you want a
+ 
+
+ align:start position:0%
+case style specific you want you want a
+way of pulling out only those peptides
+
+ align:start position:0%
+way of pulling out only those peptides
+ 
+
+ align:start position:0%
+way of pulling out only those peptides
+have been modified all the rest are just
+
+ align:start position:0%
+have been modified all the rest are just
+ 
+
+ align:start position:0%
+have been modified all the rest are just
+going to contaminate your mass
+
+ align:start position:0%
+going to contaminate your mass
+ 
+
+ align:start position:0%
+going to contaminate your mass
+spectrometry
+
+ align:start position:0%
+spectrometry
+ 
+
+ align:start position:0%
+spectrometry
+and in between you want something where
+
+ align:start position:0%
+and in between you want something where
+ 
+
+ align:start position:0%
+and in between you want something where
+you can differentially label heavier
+
+ align:start position:0%
+you can differentially label heavier
+ 
+
+ align:start position:0%
+you can differentially label heavier
+light atoms in the original proof of
+
+ align:start position:0%
+light atoms in the original proof of
+ 
+
+ align:start position:0%
+light atoms in the original proof of
+concept these were done with
+
+ align:start position:0%
+concept these were done with
+ 
+
+ align:start position:0%
+concept these were done with
+hydrogen ion
+
+ align:start position:0%
+hydrogen ion
+ 
+
+ align:start position:0%
+hydrogen ion
+hydrogen atoms versus deuterium they
+
+ align:start position:0%
+hydrogen atoms versus deuterium they
+ 
+
+ align:start position:0%
+hydrogen atoms versus deuterium they
+differ by one atomic mass unit per
+
+ align:start position:0%
+differ by one atomic mass unit per
+ 
+
+ align:start position:0%
+differ by one atomic mass unit per
+position
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+however
+
+ align:start position:0%
+however
+ 
+
+ align:start position:0%
+however
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you will see in the next slide this this
+
+ align:start position:0%
+you will see in the next slide this this
+ 
+
+ align:start position:0%
+you will see in the next slide this this
+has the unfortunate consequence that the
+
+ align:start position:0%
+has the unfortunate consequence that the
+ 
+
+ align:start position:0%
+has the unfortunate consequence that the
+hydrogen and deuterium actually are not
+
+ align:start position:0%
+hydrogen and deuterium actually are not
+ 
+
+ align:start position:0%
+hydrogen and deuterium actually are not
+only mass distinguishable but they also
+
+ align:start position:0%
+only mass distinguishable but they also
+ 
+
+ align:start position:0%
+only mass distinguishable but they also
+have different chemical properties
+
+ align:start position:0%
+have different chemical properties
+ 
+
+ align:start position:0%
+have different chemical properties
+there's a an isotope effect that's
+
+ align:start position:0%
+there's a an isotope effect that's
+ 
+
+ align:start position:0%
+there's a an isotope effect that's
+detectable in a variety of chemistries
+
+ align:start position:0%
+detectable in a variety of chemistries
+ 
+
+ align:start position:0%
+detectable in a variety of chemistries
+including
+
+ align:start position:0%
+including
+ 
+
+ align:start position:0%
+including
+retention time on the um hplc
+
+ align:start position:0%
+retention time on the um hplc
+ 
+
+ align:start position:0%
+retention time on the um hplc
+this has since been upgraded for you
+
+ align:start position:0%
+this has since been upgraded for you
+ 
+
+ align:start position:0%
+this has since been upgraded for you
+having c13 versus c12
+
+ align:start position:0%
+having c13 versus c12
+ 
+
+ align:start position:0%
+having c13 versus c12
+now that's a much more subtle difference
+
+ align:start position:0%
+now that's a much more subtle difference
+ 
+
+ align:start position:0%
+now that's a much more subtle difference
+same mass difference you have nine
+
+ align:start position:0%
+same mass difference you have nine
+ 
+
+ align:start position:0%
+same mass difference you have nine
+different carbon atoms in here and that
+
+ align:start position:0%
+different carbon atoms in here and that
+ 
+
+ align:start position:0%
+different carbon atoms in here and that
+works better
+
+ align:start position:0%
+works better
+ 
+
+ align:start position:0%
+works better
+in addition there's a way that you can
+
+ align:start position:0%
+in addition there's a way that you can
+ 
+
+ align:start position:0%
+in addition there's a way that you can
+cleave off the bias and after it's done
+
+ align:start position:0%
+cleave off the bias and after it's done
+ 
+
+ align:start position:0%
+cleave off the bias and after it's done
+its job where you've with avid and
+
+ align:start position:0%
+its job where you've with avid and
+ 
+
+ align:start position:0%
+its job where you've with avid and
+you've selected all those peptides have
+
+ align:start position:0%
+you've selected all those peptides have
+ 
+
+ align:start position:0%
+you've selected all those peptides have
+been modified and then acid cleave off
+
+ align:start position:0%
+been modified and then acid cleave off
+ 
+
+ align:start position:0%
+been modified and then acid cleave off
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+to clean up the mass effect
+
+ align:start position:0%
+to clean up the mass effect
+ 
+
+ align:start position:0%
+to clean up the mass effect
+so here's an example where you have the
+
+ align:start position:0%
+so here's an example where you have the
+ 
+
+ align:start position:0%
+so here's an example where you have the
+difference in uh m over z
+
+ align:start position:0%
+difference in uh m over z
+ 
+
+ align:start position:0%
+difference in uh m over z
+of four
+
+ align:start position:0%
+of four
+ 
+
+ align:start position:0%
+of four
+m over z units between these heavy and
+
+ align:start position:0%
+m over z units between these heavy and
+ 
+
+ align:start position:0%
+m over z units between these heavy and
+light peaks and uh the ratio of these
+
+ align:start position:0%
+light peaks and uh the ratio of these
+ 
+
+ align:start position:0%
+light peaks and uh the ratio of these
+two is something you can use for every
+
+ align:start position:0%
+two is something you can use for every
+ 
+
+ align:start position:0%
+two is something you can use for every
+essentially every peptide where the the
+
+ align:start position:0%
+essentially every peptide where the the
+ 
+
+ align:start position:0%
+essentially every peptide where the the
+the pair of peaks is in an unflooded
+
+ align:start position:0%
+the pair of peaks is in an unflooded
+ 
+
+ align:start position:0%
+the pair of peaks is in an unflooded
+part of the mass spectrum and here's
+
+ align:start position:0%
+part of the mass spectrum and here's
+ 
+
+ align:start position:0%
+part of the mass spectrum and here's
+evidence where you can see
+
+ align:start position:0%
+evidence where you can see
+ 
+
+ align:start position:0%
+evidence where you can see
+that on retention time and the
+
+ align:start position:0%
+that on retention time and the
+ 
+
+ align:start position:0%
+that on retention time and the
+horizontal axis on the on the left-hand
+
+ align:start position:0%
+horizontal axis on the on the left-hand
+ 
+
+ align:start position:0%
+horizontal axis on the on the left-hand
+side of the slide 41
+
+ align:start position:0%
+side of the slide 41
+ 
+
+ align:start position:0%
+side of the slide 41
+you can see this little red line shows
+
+ align:start position:0%
+you can see this little red line shows
+ 
+
+ align:start position:0%
+you can see this little red line shows
+how the centroids of the set of peaks
+
+ align:start position:0%
+how the centroids of the set of peaks
+ 
+
+ align:start position:0%
+how the centroids of the set of peaks
+should line up and has been displaced
+
+ align:start position:0%
+should line up and has been displaced
+ 
+
+ align:start position:0%
+should line up and has been displaced
+through the chemical effects of that
+
+ align:start position:0%
+through the chemical effects of that
+ 
+
+ align:start position:0%
+through the chemical effects of that
+adding a few neutrons
+
+ align:start position:0%
+adding a few neutrons
+ 
+
+ align:start position:0%
+adding a few neutrons
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the lesson here is that
+
+ align:start position:0%
+the lesson here is that
+ 
+
+ align:start position:0%
+the lesson here is that
+hydrogen and deuterium are not
+
+ align:start position:0%
+hydrogen and deuterium are not
+ 
+
+ align:start position:0%
+hydrogen and deuterium are not
+necessarily chemically identical the the
+
+ align:start position:0%
+necessarily chemically identical the the
+ 
+
+ align:start position:0%
+necessarily chemically identical the the
+conceit of isotopes is that they really
+
+ align:start position:0%
+conceit of isotopes is that they really
+ 
+
+ align:start position:0%
+conceit of isotopes is that they really
+should be
+
+ align:start position:0%
+should be
+ 
+
+ align:start position:0%
+should be
+chemically identical but not
+
+ align:start position:0%
+chemically identical but not
+ 
+
+ align:start position:0%
+chemically identical but not
+but really it's better if you work with
+
+ align:start position:0%
+but really it's better if you work with
+ 
+
+ align:start position:0%
+but really it's better if you work with
+heavier atoms
+
+ align:start position:0%
+heavier atoms
+ 
+
+ align:start position:0%
+heavier atoms
+to introduce neutrons
+
+ align:start position:0%
+to introduce neutrons
+ 
+
+ align:start position:0%
+to introduce neutrons
+now so what can we do with this ratio
+
+ align:start position:0%
+now so what can we do with this ratio
+ 
+
+ align:start position:0%
+now so what can we do with this ratio
+metric
+
+ align:start position:0%
+metric
+ 
+
+ align:start position:0%
+metric
+acid now we're going to just like before
+
+ align:start position:0%
+acid now we're going to just like before
+ 
+
+ align:start position:0%
+acid now we're going to just like before
+we compared
+
+ align:start position:0%
+we compared
+ 
+
+ align:start position:0%
+we compared
+absolute protein levels to absolute rna
+
+ align:start position:0%
+absolute protein levels to absolute rna
+ 
+
+ align:start position:0%
+absolute protein levels to absolute rna
+levels now we're going to measure ratios
+
+ align:start position:0%
+levels now we're going to measure ratios
+ 
+
+ align:start position:0%
+levels now we're going to measure ratios
+and do ratios we have to have two
+
+ align:start position:0%
+and do ratios we have to have two
+ 
+
+ align:start position:0%
+and do ratios we have to have two
+different conditions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so another advantage absolutely
+
+ align:start position:0%
+so another advantage absolutely
+ 
+
+ align:start position:0%
+so another advantage absolutely
+you can do it all under one condition
+
+ align:start position:0%
+you can do it all under one condition
+ 
+
+ align:start position:0%
+you can do it all under one condition
+here the two conditions that were chosen
+
+ align:start position:0%
+here the two conditions that were chosen
+ 
+
+ align:start position:0%
+here the two conditions that were chosen
+for this proof-of-concept experiment
+
+ align:start position:0%
+for this proof-of-concept experiment
+ 
+
+ align:start position:0%
+for this proof-of-concept experiment
+were glucose and galactose plus that is
+
+ align:start position:0%
+were glucose and galactose plus that is
+ 
+
+ align:start position:0%
+were glucose and galactose plus that is
+to say growing at plus and minus lactose
+
+ align:start position:0%
+to say growing at plus and minus lactose
+ 
+
+ align:start position:0%
+to say growing at plus and minus lactose
+glacis is a
+
+ align:start position:0%
+glacis is a
+ 
+
+ align:start position:0%
+glacis is a
+a nice
+
+ align:start position:0%
+a nice
+ 
+
+ align:start position:0%
+a nice
+nicely understood metabolic and
+
+ align:start position:0%
+nicely understood metabolic and
+ 
+
+ align:start position:0%
+nicely understood metabolic and
+regulatory system in yeast
+
+ align:start position:0%
+regulatory system in yeast
+ 
+
+ align:start position:0%
+regulatory system in yeast
+it it fits in with what we know about
+
+ align:start position:0%
+it it fits in with what we know about
+ 
+
+ align:start position:0%
+it it fits in with what we know about
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+central carbon metabolism and induces a
+
+ align:start position:0%
+central carbon metabolism and induces a
+ 
+
+ align:start position:0%
+central carbon metabolism and induces a
+set of genes in blue here that are
+
+ align:start position:0%
+set of genes in blue here that are
+ 
+
+ align:start position:0%
+set of genes in blue here that are
+required for galactose catabolism
+
+ align:start position:0%
+required for galactose catabolism
+ 
+
+ align:start position:0%
+required for galactose catabolism
+to produce energy the most strong ones
+
+ align:start position:0%
+to produce energy the most strong ones
+ 
+
+ align:start position:0%
+to produce energy the most strong ones
+are way off in the upper right hand
+
+ align:start position:0%
+are way off in the upper right hand
+ 
+
+ align:start position:0%
+are way off in the upper right hand
+corner here gal 710
+
+ align:start position:0%
+corner here gal 710
+ 
+
+ align:start position:0%
+corner here gal 710
+and one these are the core
+
+ align:start position:0%
+and one these are the core
+ 
+
+ align:start position:0%
+and one these are the core
+catabolic catabolic enzymes
+
+ align:start position:0%
+catabolic catabolic enzymes
+ 
+
+ align:start position:0%
+catabolic catabolic enzymes
+but almost all of the name blue
+
+ align:start position:0%
+but almost all of the name blue
+ 
+
+ align:start position:0%
+but almost all of the name blue
+triangles have some kind of story like
+
+ align:start position:0%
+triangles have some kind of story like
+ 
+
+ align:start position:0%
+triangles have some kind of story like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and these all in the upper
+
+ align:start position:0%
+and these all in the upper
+ 
+
+ align:start position:0%
+and these all in the upper
+right quadrants
+
+ align:start position:0%
+right quadrants
+ 
+
+ align:start position:0%
+right quadrants
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+high log 10 ratio of expression up to
+
+ align:start position:0%
+high log 10 ratio of expression up to
+ 
+
+ align:start position:0%
+high log 10 ratio of expression up to
+3 logs into the third full induction
+
+ align:start position:0%
+3 logs into the third full induction
+ 
+
+ align:start position:0%
+3 logs into the third full induction
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+similarly
+
+ align:start position:0%
+similarly
+ 
+
+ align:start position:0%
+similarly
+or at the other end of the spectrum in
+
+ align:start position:0%
+or at the other end of the spectrum in
+ 
+
+ align:start position:0%
+or at the other end of the spectrum in
+the lower left-hand quadrant are
+
+ align:start position:0%
+the lower left-hand quadrant are
+ 
+
+ align:start position:0%
+the lower left-hand quadrant are
+respiratory genes
+
+ align:start position:0%
+respiratory genes
+ 
+
+ align:start position:0%
+respiratory genes
+that are involved in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oxidative phosphorylation and these are
+
+ align:start position:0%
+oxidative phosphorylation and these are
+ 
+
+ align:start position:0%
+oxidative phosphorylation and these are
+moderately
+
+ align:start position:0%
+moderately
+ 
+
+ align:start position:0%
+moderately
+depressed under galactose and
+
+ align:start position:0%
+depressed under galactose and
+ 
+
+ align:start position:0%
+depressed under galactose and
+conditions
+
+ align:start position:0%
+conditions
+ 
+
+ align:start position:0%
+conditions
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that's why they're in the lower right
+
+ align:start position:0%
+that's why they're in the lower right
+ 
+
+ align:start position:0%
+that's why they're in the lower right
+hand corner
+
+ align:start position:0%
+hand corner
+ 
+
+ align:start position:0%
+hand corner
+and and then the green ones are are
+
+ align:start position:0%
+and and then the green ones are are
+ 
+
+ align:start position:0%
+and and then the green ones are are
+neither going they're not quite along
+
+ align:start position:0%
+neither going they're not quite along
+ 
+
+ align:start position:0%
+neither going they're not quite along
+this diagonal their their messenger rna
+
+ align:start position:0%
+this diagonal their their messenger rna
+ 
+
+ align:start position:0%
+this diagonal their their messenger rna
+is increased
+
+ align:start position:0%
+is increased
+ 
+
+ align:start position:0%
+is increased
+but their protein expression is not and
+
+ align:start position:0%
+but their protein expression is not and
+ 
+
+ align:start position:0%
+but their protein expression is not and
+these are the ribosomal protein genes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is another phenomenon that's
+
+ align:start position:0%
+and this is another phenomenon that's
+ 
+
+ align:start position:0%
+and this is another phenomenon that's
+that's uh well documented in this system
+
+ align:start position:0%
+that's uh well documented in this system
+ 
+
+ align:start position:0%
+that's uh well documented in this system
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now those are examples of
+
+ align:start position:0%
+now those are examples of
+ 
+
+ align:start position:0%
+now those are examples of
+how you can use absolute and rel and why
+
+ align:start position:0%
+how you can use absolute and rel and why
+ 
+
+ align:start position:0%
+how you can use absolute and rel and why
+you're motivated to use absolute and
+
+ align:start position:0%
+you're motivated to use absolute and
+ 
+
+ align:start position:0%
+you're motivated to use absolute and
+relative measures for proteins and
+
+ align:start position:0%
+relative measures for proteins and
+ 
+
+ align:start position:0%
+relative measures for proteins and
+messenger rnas
+
+ align:start position:0%
+messenger rnas
+ 
+
+ align:start position:0%
+messenger rnas
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+these are all treating as if just like
+
+ align:start position:0%
+these are all treating as if just like
+ 
+
+ align:start position:0%
+these are all treating as if just like
+before i said that messenger rnas we
+
+ align:start position:0%
+before i said that messenger rnas we
+ 
+
+ align:start position:0%
+before i said that messenger rnas we
+might lump all together all splice forms
+
+ align:start position:0%
+might lump all together all splice forms
+ 
+
+ align:start position:0%
+might lump all together all splice forms
+and call that the gene product
+
+ align:start position:0%
+and call that the gene product
+ 
+
+ align:start position:0%
+and call that the gene product
+although you know better and the same
+
+ align:start position:0%
+although you know better and the same
+ 
+
+ align:start position:0%
+although you know better and the same
+thing with proteins you might lump
+
+ align:start position:0%
+thing with proteins you might lump
+ 
+
+ align:start position:0%
+thing with proteins you might lump
+together all the protein splice forms
+
+ align:start position:0%
+together all the protein splice forms
+ 
+
+ align:start position:0%
+together all the protein splice forms
+and and not only that but for a
+
+ align:start position:0%
+and and not only that but for a
+ 
+
+ align:start position:0%
+and and not only that but for a
+particular protein splice form there are
+
+ align:start position:0%
+particular protein splice form there are
+ 
+
+ align:start position:0%
+particular protein splice form there are
+many different post-synthetic
+
+ align:start position:0%
+many different post-synthetic
+ 
+
+ align:start position:0%
+many different post-synthetic
+modifications such as proteolysis
+
+ align:start position:0%
+modifications such as proteolysis
+ 
+
+ align:start position:0%
+modifications such as proteolysis
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+phosphorylation
+
+ align:start position:0%
+phosphorylation
+ 
+
+ align:start position:0%
+phosphorylation
+and so we're going to talk about these
+
+ align:start position:0%
+and so we're going to talk about these
+ 
+
+ align:start position:0%
+and so we're going to talk about these
+modifications very briefly
+
+ align:start position:0%
+modifications very briefly
+ 
+
+ align:start position:0%
+modifications very briefly
+to hopefully wet your appetite for one
+
+ align:start position:0%
+to hopefully wet your appetite for one
+ 
+
+ align:start position:0%
+to hopefully wet your appetite for one
+of the most exciting parts of proteomics
+
+ align:start position:0%
+of the most exciting parts of proteomics
+ 
+
+ align:start position:0%
+of the most exciting parts of proteomics
+and whether it's identification or
+
+ align:start position:0%
+and whether it's identification or
+ 
+
+ align:start position:0%
+and whether it's identification or
+quantitation
+
+ align:start position:0%
+quantitation
+ 
+
+ align:start position:0%
+quantitation
+so we've already mentioned radioisotopic
+
+ align:start position:0%
+so we've already mentioned radioisotopic
+ 
+
+ align:start position:0%
+so we've already mentioned radioisotopic
+labeling as a way of quantitating using
+
+ align:start position:0%
+labeling as a way of quantitating using
+ 
+
+ align:start position:0%
+labeling as a way of quantitating using
+uh various
+
+ align:start position:0%
+uh various
+ 
+
+ align:start position:0%
+uh various
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+radioactive sulfur you can use whether
+
+ align:start position:0%
+radioactive sulfur you can use whether
+ 
+
+ align:start position:0%
+radioactive sulfur you can use whether
+it's stable isotopes or radioactive
+
+ align:start position:0%
+it's stable isotopes or radioactive
+ 
+
+ align:start position:0%
+it's stable isotopes or radioactive
+isotopes you can use these to do pulse
+
+ align:start position:0%
+isotopes you can use these to do pulse
+ 
+
+ align:start position:0%
+isotopes you can use these to do pulse
+labeling to monitor
+
+ align:start position:0%
+labeling to monitor
+ 
+
+ align:start position:0%
+labeling to monitor
+a dynamic process
+
+ align:start position:0%
+a dynamic process
+ 
+
+ align:start position:0%
+a dynamic process
+p32 is a if you're in particular if you
+
+ align:start position:0%
+p32 is a if you're in particular if you
+ 
+
+ align:start position:0%
+p32 is a if you're in particular if you
+want to enrich for the
+
+ align:start position:0%
+want to enrich for the
+ 
+
+ align:start position:0%
+want to enrich for the
+some of the most uh
+
+ align:start position:0%
+some of the most uh
+ 
+
+ align:start position:0%
+some of the most uh
+well-studied and significant
+
+ align:start position:0%
+well-studied and significant
+ 
+
+ align:start position:0%
+well-studied and significant
+post-synthetic modifications involved in
+
+ align:start position:0%
+post-synthetic modifications involved in
+ 
+
+ align:start position:0%
+post-synthetic modifications involved in
+signal transduction
+
+ align:start position:0%
+signal transduction
+ 
+
+ align:start position:0%
+signal transduction
+you can enrich for particular types of
+
+ align:start position:0%
+you can enrich for particular types of
+ 
+
+ align:start position:0%
+you can enrich for particular types of
+amino acids we already showed that the
+
+ align:start position:0%
+amino acids we already showed that the
+ 
+
+ align:start position:0%
+amino acids we already showed that the
+cysteines which is kind of an arbitrary
+
+ align:start position:0%
+cysteines which is kind of an arbitrary
+ 
+
+ align:start position:0%
+cysteines which is kind of an arbitrary
+amino acid chosen for the icat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ratiometric method
+
+ align:start position:0%
+ratiometric method
+ 
+
+ align:start position:0%
+ratiometric method
+that was chosen because it has
+
+ align:start position:0%
+that was chosen because it has
+ 
+
+ align:start position:0%
+that was chosen because it has
+interesting react
+
+ align:start position:0%
+interesting react
+ 
+
+ align:start position:0%
+interesting react
+reactivity not because it's
+
+ align:start position:0%
+reactivity not because it's
+ 
+
+ align:start position:0%
+reactivity not because it's
+intrinsically important
+
+ align:start position:0%
+intrinsically important
+ 
+
+ align:start position:0%
+intrinsically important
+low abundance regulatory molecules
+
+ align:start position:0%
+low abundance regulatory molecules
+ 
+
+ align:start position:0%
+low abundance regulatory molecules
+phosphates on the other hand can be very
+
+ align:start position:0%
+phosphates on the other hand can be very
+ 
+
+ align:start position:0%
+phosphates on the other hand can be very
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+and you might need to enrich because
+
+ align:start position:0%
+and you might need to enrich because
+ 
+
+ align:start position:0%
+and you might need to enrich because
+these important regulatory
+
+ align:start position:0%
+these important regulatory
+ 
+
+ align:start position:0%
+these important regulatory
+phosphorylation sites can get lost in
+
+ align:start position:0%
+phosphorylation sites can get lost in
+ 
+
+ align:start position:0%
+phosphorylation sites can get lost in
+the snow of all the rest of the peptides
+
+ align:start position:0%
+the snow of all the rest of the peptides
+ 
+
+ align:start position:0%
+the snow of all the rest of the peptides
+in the proteome
+
+ align:start position:0%
+in the proteome
+ 
+
+ align:start position:0%
+in the proteome
+this can either be done this enrichment
+
+ align:start position:0%
+this can either be done this enrichment
+ 
+
+ align:start position:0%
+this can either be done this enrichment
+can either be done by immobilized metals
+
+ align:start position:0%
+can either be done by immobilized metals
+ 
+
+ align:start position:0%
+can either be done by immobilized metals
+such as
+
+ align:start position:0%
+such as
+ 
+
+ align:start position:0%
+such as
+iron and
+
+ align:start position:0%
+iron and
+ 
+
+ align:start position:0%
+iron and
+gallium and so forth
+
+ align:start position:0%
+gallium and so forth
+ 
+
+ align:start position:0%
+gallium and so forth
+this is called imac from mobilized metal
+
+ align:start position:0%
+this is called imac from mobilized metal
+ 
+
+ align:start position:0%
+this is called imac from mobilized metal
+affinity chromatography or you can have
+
+ align:start position:0%
+affinity chromatography or you can have
+ 
+
+ align:start position:0%
+affinity chromatography or you can have
+antibodies that are specific particular
+
+ align:start position:0%
+antibodies that are specific particular
+ 
+
+ align:start position:0%
+antibodies that are specific particular
+phosphopeptide
+
+ align:start position:0%
+phosphopeptide
+ 
+
+ align:start position:0%
+phosphopeptide
+particularly fossil amino acids
+
+ align:start position:0%
+particularly fossil amino acids
+ 
+
+ align:start position:0%
+particularly fossil amino acids
+you have electrons for carbohydrates
+
+ align:start position:0%
+you have electrons for carbohydrates
+ 
+
+ align:start position:0%
+you have electrons for carbohydrates
+as front ends for mass spectrometry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+even when we do
+
+ align:start position:0%
+even when we do
+ 
+
+ align:start position:0%
+even when we do
+p32 labeling
+
+ align:start position:0%
+p32 labeling
+ 
+
+ align:start position:0%
+p32 labeling
+metabolically where the p32 will only
+
+ align:start position:0%
+metabolically where the p32 will only
+ 
+
+ align:start position:0%
+metabolically where the p32 will only
+label the subset of the proteins which
+
+ align:start position:0%
+label the subset of the proteins which
+ 
+
+ align:start position:0%
+label the subset of the proteins which
+are phosphorylated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is still the case and that some of
+
+ align:start position:0%
+it is still the case and that some of
+ 
+
+ align:start position:0%
+it is still the case and that some of
+the most interesting regulatory cell
+
+ align:start position:0%
+the most interesting regulatory cell
+ 
+
+ align:start position:0%
+the most interesting regulatory cell
+cycle proteins are not detected above
+
+ align:start position:0%
+cycle proteins are not detected above
+ 
+
+ align:start position:0%
+cycle proteins are not detected above
+background because there are many abrupt
+
+ align:start position:0%
+background because there are many abrupt
+ 
+
+ align:start position:0%
+background because there are many abrupt
+abundant proteins such as ribosomal
+
+ align:start position:0%
+abundant proteins such as ribosomal
+ 
+
+ align:start position:0%
+abundant proteins such as ribosomal
+proteins central carbon metabolic
+
+ align:start position:0%
+proteins central carbon metabolic
+ 
+
+ align:start position:0%
+proteins central carbon metabolic
+enzymes
+
+ align:start position:0%
+enzymes
+ 
+
+ align:start position:0%
+enzymes
+which are needed in high abundance but
+
+ align:start position:0%
+which are needed in high abundance but
+ 
+
+ align:start position:0%
+which are needed in high abundance but
+are also needed need to have
+
+ align:start position:0%
+are also needed need to have
+ 
+
+ align:start position:0%
+are also needed need to have
+phosphorylation
+
+ align:start position:0%
+phosphorylation
+ 
+
+ align:start position:0%
+phosphorylation
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+you get this forest of
+
+ align:start position:0%
+you get this forest of
+ 
+
+ align:start position:0%
+you get this forest of
+phospho proteins
+
+ align:start position:0%
+phospho proteins
+ 
+
+ align:start position:0%
+phospho proteins
+such ribosomal metabolic which make it
+
+ align:start position:0%
+such ribosomal metabolic which make it
+ 
+
+ align:start position:0%
+such ribosomal metabolic which make it
+hard to detect the regulatory ones
+
+ align:start position:0%
+hard to detect the regulatory ones
+ 
+
+ align:start position:0%
+hard to detect the regulatory ones
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+but labeling is not a panacea
+
+ align:start position:0%
+but labeling is not a panacea
+ 
+
+ align:start position:0%
+but labeling is not a panacea
+and we'll come
+
+ align:start position:0%
+and we'll come
+ 
+
+ align:start position:0%
+and we'll come
+i think you'll see as we go through the
+
+ align:start position:0%
+i think you'll see as we go through the
+ 
+
+ align:start position:0%
+i think you'll see as we go through the
+protein modifications in mass
+
+ align:start position:0%
+protein modifications in mass
+ 
+
+ align:start position:0%
+protein modifications in mass
+spectrometry that the multi-dimensional
+
+ align:start position:0%
+spectrometry that the multi-dimensional
+ 
+
+ align:start position:0%
+spectrometry that the multi-dimensional
+purification really is the way that you
+
+ align:start position:0%
+purification really is the way that you
+ 
+
+ align:start position:0%
+purification really is the way that you
+get away from the ribosomal proteins and
+
+ align:start position:0%
+get away from the ribosomal proteins and
+ 
+
+ align:start position:0%
+get away from the ribosomal proteins and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+highly abundant metabolic cookings which
+
+ align:start position:0%
+highly abundant metabolic cookings which
+ 
+
+ align:start position:0%
+highly abundant metabolic cookings which
+are interesting but you need a way of
+
+ align:start position:0%
+are interesting but you need a way of
+ 
+
+ align:start position:0%
+are interesting but you need a way of
+both fitting them and the regulatory
+
+ align:start position:0%
+both fitting them and the regulatory
+ 
+
+ align:start position:0%
+both fitting them and the regulatory
+low-level proteins
+
+ align:start position:0%
+low-level proteins
+ 
+
+ align:start position:0%
+low-level proteins
+here are some examples of natural
+
+ align:start position:0%
+here are some examples of natural
+ 
+
+ align:start position:0%
+here are some examples of natural
+crosslinks you can think of this as a
+
+ align:start position:0%
+crosslinks you can think of this as a
+ 
+
+ align:start position:0%
+crosslinks you can think of this as a
+special class of post-synthetic
+
+ align:start position:0%
+special class of post-synthetic
+ 
+
+ align:start position:0%
+special class of post-synthetic
+modification
+
+ align:start position:0%
+modification
+ 
+
+ align:start position:0%
+modification
+instead of
+
+ align:start position:0%
+instead of
+ 
+
+ align:start position:0%
+instead of
+having a phosphate glomming on you have
+
+ align:start position:0%
+having a phosphate glomming on you have
+ 
+
+ align:start position:0%
+having a phosphate glomming on you have
+two different peptides either
+
+ align:start position:0%
+two different peptides either
+ 
+
+ align:start position:0%
+two different peptides either
+intramolecularly within a protein or
+
+ align:start position:0%
+intramolecularly within a protein or
+ 
+
+ align:start position:0%
+intramolecularly within a protein or
+intermolecularly between proteins and
+
+ align:start position:0%
+intermolecularly between proteins and
+ 
+
+ align:start position:0%
+intermolecularly between proteins and
+you should be highly motivated to study
+
+ align:start position:0%
+you should be highly motivated to study
+ 
+
+ align:start position:0%
+you should be highly motivated to study
+these because they tell you something
+
+ align:start position:0%
+these because they tell you something
+ 
+
+ align:start position:0%
+these because they tell you something
+not only about protein structure
+
+ align:start position:0%
+not only about protein structure
+ 
+
+ align:start position:0%
+not only about protein structure
+three-dimensional structure which is the
+
+ align:start position:0%
+three-dimensional structure which is the
+ 
+
+ align:start position:0%
+three-dimensional structure which is the
+topic last time but protein-protein
+
+ align:start position:0%
+topic last time but protein-protein
+ 
+
+ align:start position:0%
+topic last time but protein-protein
+interactions and not just theoretically
+
+ align:start position:0%
+interactions and not just theoretically
+ 
+
+ align:start position:0%
+interactions and not just theoretically
+what proteins might interact with other
+
+ align:start position:0%
+what proteins might interact with other
+ 
+
+ align:start position:0%
+what proteins might interact with other
+proteins or you know or might bind in
+
+ align:start position:0%
+proteins or you know or might bind in
+ 
+
+ align:start position:0%
+proteins or you know or might bind in
+vitro could be in vitro artifact or in
+
+ align:start position:0%
+vitro could be in vitro artifact or in
+ 
+
+ align:start position:0%
+vitro could be in vitro artifact or in
+yeast in a two hybrid system could be a
+
+ align:start position:0%
+yeast in a two hybrid system could be a
+ 
+
+ align:start position:0%
+yeast in a two hybrid system could be a
+yeast to hybrid artifact
+
+ align:start position:0%
+yeast to hybrid artifact
+ 
+
+ align:start position:0%
+yeast to hybrid artifact
+these are actual covalent
+
+ align:start position:0%
+these are actual covalent
+ 
+
+ align:start position:0%
+these are actual covalent
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+caught in the act in in vivo protein
+
+ align:start position:0%
+caught in the act in in vivo protein
+ 
+
+ align:start position:0%
+caught in the act in in vivo protein
+interactions
+
+ align:start position:0%
+interactions
+ 
+
+ align:start position:0%
+interactions
+and and some of these are you know most
+
+ align:start position:0%
+and and some of these are you know most
+ 
+
+ align:start position:0%
+and and some of these are you know most
+of these are very well documented by far
+
+ align:start position:0%
+of these are very well documented by far
+ 
+
+ align:start position:0%
+of these are very well documented by far
+the most uh
+
+ align:start position:0%
+the most uh
+ 
+
+ align:start position:0%
+the most uh
+common one and of great significance to
+
+ align:start position:0%
+common one and of great significance to
+ 
+
+ align:start position:0%
+common one and of great significance to
+protein
+
+ align:start position:0%
+protein
+ 
+
+ align:start position:0%
+protein
+tertiary stability
+
+ align:start position:0%
+tertiary stability
+ 
+
+ align:start position:0%
+tertiary stability
+uh in the class of proteins which are
+
+ align:start position:0%
+uh in the class of proteins which are
+ 
+
+ align:start position:0%
+uh in the class of proteins which are
+extracellular these include
+
+ align:start position:0%
+extracellular these include
+ 
+
+ align:start position:0%
+extracellular these include
+extracellular domains membrane proteins
+
+ align:start position:0%
+extracellular domains membrane proteins
+ 
+
+ align:start position:0%
+extracellular domains membrane proteins
+and secreted proteins
+
+ align:start position:0%
+and secreted proteins
+ 
+
+ align:start position:0%
+and secreted proteins
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in particular because
+
+ align:start position:0%
+in particular because
+ 
+
+ align:start position:0%
+in particular because
+there the oxidation state is such that
+
+ align:start position:0%
+there the oxidation state is such that
+ 
+
+ align:start position:0%
+there the oxidation state is such that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the the this
+
+ align:start position:0%
+the the this
+ 
+
+ align:start position:0%
+the the this
+sulfur sulfur bond is stable while
+
+ align:start position:0%
+sulfur sulfur bond is stable while
+ 
+
+ align:start position:0%
+sulfur sulfur bond is stable while
+intracellularly tends to be more
+
+ align:start position:0%
+intracellularly tends to be more
+ 
+
+ align:start position:0%
+intracellularly tends to be more
+reducing
+
+ align:start position:0%
+reducing
+ 
+
+ align:start position:0%
+reducing
+atmosphere and so that the these
+
+ align:start position:0%
+atmosphere and so that the these
+ 
+
+ align:start position:0%
+atmosphere and so that the these
+disulfides
+
+ align:start position:0%
+disulfides
+ 
+
+ align:start position:0%
+disulfides
+have trouble forming
+
+ align:start position:0%
+have trouble forming
+ 
+
+ align:start position:0%
+have trouble forming
+collagen has a lysine crosslink
+
+ align:start position:0%
+collagen has a lysine crosslink
+ 
+
+ align:start position:0%
+collagen has a lysine crosslink
+ubiquitin has a c thermos two lysine
+
+ align:start position:0%
+ubiquitin has a c thermos two lysine
+ 
+
+ align:start position:0%
+ubiquitin has a c thermos two lysine
+crosslink fibrin
+
+ align:start position:0%
+crosslink fibrin
+ 
+
+ align:start position:0%
+crosslink fibrin
+involved in blood clotting has a
+
+ align:start position:0%
+involved in blood clotting has a
+ 
+
+ align:start position:0%
+involved in blood clotting has a
+glutamine the lysine and so on
+
+ align:start position:0%
+glutamine the lysine and so on
+ 
+
+ align:start position:0%
+glutamine the lysine and so on
+as your
+
+ align:start position:0%
+as your
+ 
+
+ align:start position:0%
+as your
+some of your proteins age you will find
+
+ align:start position:0%
+some of your proteins age you will find
+ 
+
+ align:start position:0%
+some of your proteins age you will find
+the glucose that's in high
+
+ align:start position:0%
+the glucose that's in high
+ 
+
+ align:start position:0%
+the glucose that's in high
+concentrations in your blood will
+
+ align:start position:0%
+concentrations in your blood will
+ 
+
+ align:start position:0%
+concentrations in your blood will
+glycolate the the lysine residues and
+
+ align:start position:0%
+glycolate the the lysine residues and
+ 
+
+ align:start position:0%
+glycolate the the lysine residues and
+this is um
+
+ align:start position:0%
+this is um
+ 
+
+ align:start position:0%
+this is um
+part of the process by which these
+
+ align:start position:0%
+part of the process by which these
+ 
+
+ align:start position:0%
+part of the process by which these
+proteins are eventually
+
+ align:start position:0%
+proteins are eventually
+ 
+
+ align:start position:0%
+proteins are eventually
+lose their function and are cleared
+
+ align:start position:0%
+lose their function and are cleared
+ 
+
+ align:start position:0%
+lose their function and are cleared
+protein nucleic acid interactions we've
+
+ align:start position:0%
+protein nucleic acid interactions we've
+ 
+
+ align:start position:0%
+protein nucleic acid interactions we've
+been talking about so far non-covalent
+
+ align:start position:0%
+been talking about so far non-covalent
+ 
+
+ align:start position:0%
+been talking about so far non-covalent
+some of them are covalent for example
+
+ align:start position:0%
+some of them are covalent for example
+ 
+
+ align:start position:0%
+some of them are covalent for example
+when you want to prime
+
+ align:start position:0%
+when you want to prime
+ 
+
+ align:start position:0%
+when you want to prime
+de novo
+
+ align:start position:0%
+de novo
+ 
+
+ align:start position:0%
+de novo
+polymer synthesis dna synthesis okay
+
+ align:start position:0%
+polymer synthesis dna synthesis okay
+ 
+
+ align:start position:0%
+polymer synthesis dna synthesis okay
+so what are the consequences for the
+
+ align:start position:0%
+so what are the consequences for the
+ 
+
+ align:start position:0%
+so what are the consequences for the
+mass spec algorithms we've been talking
+
+ align:start position:0%
+mass spec algorithms we've been talking
+ 
+
+ align:start position:0%
+mass spec algorithms we've been talking
+about say de novo sequencing or
+
+ align:start position:0%
+about say de novo sequencing or
+ 
+
+ align:start position:0%
+about say de novo sequencing or
+or finding a peptide spectrum
+
+ align:start position:0%
+or finding a peptide spectrum
+ 
+
+ align:start position:0%
+or finding a peptide spectrum
+in your database
+
+ align:start position:0%
+in your database
+ 
+
+ align:start position:0%
+in your database
+well you can see the masses are going to
+
+ align:start position:0%
+well you can see the masses are going to
+ 
+
+ align:start position:0%
+well you can see the masses are going to
+be fairly straightforward here's some
+
+ align:start position:0%
+be fairly straightforward here's some
+ 
+
+ align:start position:0%
+be fairly straightforward here's some
+examples of masses and some peptides and
+
+ align:start position:0%
+examples of masses and some peptides and
+ 
+
+ align:start position:0%
+examples of masses and some peptides and
+some crosslink peptides on the top
+
+ align:start position:0%
+some crosslink peptides on the top
+ 
+
+ align:start position:0%
+some crosslink peptides on the top
+uh right
+
+ align:start position:0%
+uh right
+ 
+
+ align:start position:0%
+uh right
+you'll see one
+
+ align:start position:0%
+you'll see one
+ 
+
+ align:start position:0%
+you'll see one
+intramolecular cross link between a
+
+ align:start position:0%
+intramolecular cross link between a
+ 
+
+ align:start position:0%
+intramolecular cross link between a
+lysine and a lysine
+
+ align:start position:0%
+lysine and a lysine
+ 
+
+ align:start position:0%
+lysine and a lysine
+and an intermolecular between two
+
+ align:start position:0%
+and an intermolecular between two
+ 
+
+ align:start position:0%
+and an intermolecular between two
+peptides now each of these peptides
+
+ align:start position:0%
+peptides now each of these peptides
+ 
+
+ align:start position:0%
+peptides now each of these peptides
+in this display these are just simple
+
+ align:start position:0%
+in this display these are just simple
+ 
+
+ align:start position:0%
+in this display these are just simple
+masses these are not fragments those are
+
+ align:start position:0%
+masses these are not fragments those are
+ 
+
+ align:start position:0%
+masses these are not fragments those are
+not sub fragments so these expect these
+
+ align:start position:0%
+not sub fragments so these expect these
+ 
+
+ align:start position:0%
+not sub fragments so these expect these
+just be tryptic
+
+ align:start position:0%
+just be tryptic
+ 
+
+ align:start position:0%
+just be tryptic
+products so each of their c-terminals
+
+ align:start position:0%
+products so each of their c-terminals
+ 
+
+ align:start position:0%
+products so each of their c-terminals
+should be either arginine r or lysine k
+
+ align:start position:0%
+should be either arginine r or lysine k
+ 
+
+ align:start position:0%
+should be either arginine r or lysine k
+r k
+
+ align:start position:0%
+r k
+ 
+
+ align:start position:0%
+r k
+r so forth and so you can see this is
+
+ align:start position:0%
+r so forth and so you can see this is
+ 
+
+ align:start position:0%
+r so forth and so you can see this is
+two peptides one ending in r one and the
+
+ align:start position:0%
+two peptides one ending in r one and the
+ 
+
+ align:start position:0%
+two peptides one ending in r one and the
+e k
+
+ align:start position:0%
+e k
+ 
+
+ align:start position:0%
+e k
+so let's look in detail at this that
+
+ align:start position:0%
+so let's look in detail at this that
+ 
+
+ align:start position:0%
+so let's look in detail at this that
+this uh example where you have
+
+ align:start position:0%
+this uh example where you have
+ 
+
+ align:start position:0%
+this uh example where you have
+an intramolecular crosslink and you can
+
+ align:start position:0%
+an intramolecular crosslink and you can
+ 
+
+ align:start position:0%
+an intramolecular crosslink and you can
+see that as uh
+
+ align:start position:0%
+see that as uh
+ 
+
+ align:start position:0%
+see that as uh
+you cleave each of these peptide bonds
+
+ align:start position:0%
+you cleave each of these peptide bonds
+ 
+
+ align:start position:0%
+you cleave each of these peptide bonds
+entering b ions from the internal and y
+
+ align:start position:0%
+entering b ions from the internal and y
+ 
+
+ align:start position:0%
+entering b ions from the internal and y
+ions from the c terminus you'll see that
+
+ align:start position:0%
+ions from the c terminus you'll see that
+ 
+
+ align:start position:0%
+ions from the c terminus you'll see that
+there's a special case in in the region
+
+ align:start position:0%
+there's a special case in in the region
+ 
+
+ align:start position:0%
+there's a special case in in the region
+that's defined between the two
+
+ align:start position:0%
+that's defined between the two
+ 
+
+ align:start position:0%
+that's defined between the two
+cross-links in that any
+
+ align:start position:0%
+cross-links in that any
+ 
+
+ align:start position:0%
+cross-links in that any
+peptide bond cleavage
+
+ align:start position:0%
+peptide bond cleavage
+ 
+
+ align:start position:0%
+peptide bond cleavage
+that might occur in the gas phase when
+
+ align:start position:0%
+that might occur in the gas phase when
+ 
+
+ align:start position:0%
+that might occur in the gas phase when
+colliding with argon some other inert
+
+ align:start position:0%
+colliding with argon some other inert
+ 
+
+ align:start position:0%
+colliding with argon some other inert
+gas
+
+ align:start position:0%
+gas
+ 
+
+ align:start position:0%
+gas
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+will break the chain as usual but the
+
+ align:start position:0%
+will break the chain as usual but the
+ 
+
+ align:start position:0%
+will break the chain as usual but the
+chain won't fall apart because it's got
+
+ align:start position:0%
+chain won't fall apart because it's got
+ 
+
+ align:start position:0%
+chain won't fall apart because it's got
+actually two connections one is through
+
+ align:start position:0%
+actually two connections one is through
+ 
+
+ align:start position:0%
+actually two connections one is through
+the normal peptide bond and the other
+
+ align:start position:0%
+the normal peptide bond and the other
+ 
+
+ align:start position:0%
+the normal peptide bond and the other
+issue is crosslink so cleavage is all
+
+ align:start position:0%
+issue is crosslink so cleavage is all
+ 
+
+ align:start position:0%
+issue is crosslink so cleavage is all
+through in here it takes two hits to get
+
+ align:start position:0%
+through in here it takes two hits to get
+ 
+
+ align:start position:0%
+through in here it takes two hits to get
+separation of these and two hits is on
+
+ align:start position:0%
+separation of these and two hits is on
+ 
+
+ align:start position:0%
+separation of these and two hits is on
+is unlikely and so you'll tend to see
+
+ align:start position:0%
+is unlikely and so you'll tend to see
+ 
+
+ align:start position:0%
+is unlikely and so you'll tend to see
+the b ions and the lions up until right
+
+ align:start position:0%
+the b ions and the lions up until right
+ 
+
+ align:start position:0%
+the b ions and the lions up until right
+up until you hit the first cross-link
+
+ align:start position:0%
+up until you hit the first cross-link
+ 
+
+ align:start position:0%
+up until you hit the first cross-link
+amino acid and then you lose it
+
+ align:start position:0%
+amino acid and then you lose it
+ 
+
+ align:start position:0%
+amino acid and then you lose it
+so that's one of the complications that
+
+ align:start position:0%
+so that's one of the complications that
+ 
+
+ align:start position:0%
+so that's one of the complications that
+you have from crosslinks the other one
+
+ align:start position:0%
+you have from crosslinks the other one
+ 
+
+ align:start position:0%
+you have from crosslinks the other one
+that you have when you have say
+
+ align:start position:0%
+that you have when you have say
+ 
+
+ align:start position:0%
+that you have when you have say
+cross-linking two peptides this might
+
+ align:start position:0%
+cross-linking two peptides this might
+ 
+
+ align:start position:0%
+cross-linking two peptides this might
+occur when you have a interaction
+
+ align:start position:0%
+occur when you have a interaction
+ 
+
+ align:start position:0%
+occur when you have a interaction
+between derivative proteins is you'll
+
+ align:start position:0%
+between derivative proteins is you'll
+ 
+
+ align:start position:0%
+between derivative proteins is you'll
+now have two sets of bi ions and two
+
+ align:start position:0%
+now have two sets of bi ions and two
+ 
+
+ align:start position:0%
+now have two sets of bi ions and two
+sets of y ions as if just having b and y
+
+ align:start position:0%
+sets of y ions as if just having b and y
+ 
+
+ align:start position:0%
+sets of y ions as if just having b and y
+in the same spectrum isn't enough now
+
+ align:start position:0%
+in the same spectrum isn't enough now
+ 
+
+ align:start position:0%
+in the same spectrum isn't enough now
+you've got a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two of each
+
+ align:start position:0%
+two of each
+ 
+
+ align:start position:0%
+two of each
+and even though you don't have this
+
+ align:start position:0%
+and even though you don't have this
+ 
+
+ align:start position:0%
+and even though you don't have this
+cycle to worry about you have a full set
+
+ align:start position:0%
+cycle to worry about you have a full set
+ 
+
+ align:start position:0%
+cycle to worry about you have a full set
+but there is
+
+ align:start position:0%
+but there is
+ 
+
+ align:start position:0%
+but there is
+a uh algorithm
+
+ align:start position:0%
+a uh algorithm
+ 
+
+ align:start position:0%
+a uh algorithm
+that tim chen and others have developed
+
+ align:start position:0%
+that tim chen and others have developed
+ 
+
+ align:start position:0%
+that tim chen and others have developed
+for dealing with that in very clean
+
+ align:start position:0%
+for dealing with that in very clean
+ 
+
+ align:start position:0%
+for dealing with that in very clean
+cases
+
+ align:start position:0%
+cases
+ 
+
+ align:start position:0%
+cases
+and here's an example of
+
+ align:start position:0%
+and here's an example of
+ 
+
+ align:start position:0%
+and here's an example of
+actually using the cross links that you
+
+ align:start position:0%
+actually using the cross links that you
+ 
+
+ align:start position:0%
+actually using the cross links that you
+get from mass spectrometry as a fairly
+
+ align:start position:0%
+get from mass spectrometry as a fairly
+ 
+
+ align:start position:0%
+get from mass spectrometry as a fairly
+inexpensive set of constraints that you
+
+ align:start position:0%
+inexpensive set of constraints that you
+ 
+
+ align:start position:0%
+inexpensive set of constraints that you
+can use for getting distances either
+
+ align:start position:0%
+can use for getting distances either
+ 
+
+ align:start position:0%
+can use for getting distances either
+intramolecularly in this case or
+
+ align:start position:0%
+intramolecularly in this case or
+ 
+
+ align:start position:0%
+intramolecularly in this case or
+conceivably intermolecularly
+
+ align:start position:0%
+conceivably intermolecularly
+ 
+
+ align:start position:0%
+conceivably intermolecularly
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the constraints you can't get any bigger
+
+ align:start position:0%
+the constraints you can't get any bigger
+ 
+
+ align:start position:0%
+the constraints you can't get any bigger
+than the cross-linked distance you know
+
+ align:start position:0%
+than the cross-linked distance you know
+ 
+
+ align:start position:0%
+than the cross-linked distance you know
+the the chemical structure of the
+
+ align:start position:0%
+the the chemical structure of the
+ 
+
+ align:start position:0%
+the the chemical structure of the
+cross-linker and so you can say these
+
+ align:start position:0%
+cross-linker and so you can say these
+ 
+
+ align:start position:0%
+cross-linker and so you can say these
+two amino acids with their side chains
+
+ align:start position:0%
+two amino acids with their side chains
+ 
+
+ align:start position:0%
+two amino acids with their side chains
+and so forth they're reacting have to be
+
+ align:start position:0%
+and so forth they're reacting have to be
+ 
+
+ align:start position:0%
+and so forth they're reacting have to be
+this length or shorter
+
+ align:start position:0%
+this length or shorter
+ 
+
+ align:start position:0%
+this length or shorter
+and that's what these little yellow
+
+ align:start position:0%
+and that's what these little yellow
+ 
+
+ align:start position:0%
+and that's what these little yellow
+lines indicate in this
+
+ align:start position:0%
+lines indicate in this
+ 
+
+ align:start position:0%
+lines indicate in this
+fiberglass growth factor two fgf2
+
+ align:start position:0%
+fiberglass growth factor two fgf2
+ 
+
+ align:start position:0%
+fiberglass growth factor two fgf2
+where the crystal structure of fgf2 is
+
+ align:start position:0%
+where the crystal structure of fgf2 is
+ 
+
+ align:start position:0%
+where the crystal structure of fgf2 is
+known
+
+ align:start position:0%
+known
+ 
+
+ align:start position:0%
+known
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+these constraints will greatly aid your
+
+ align:start position:0%
+these constraints will greatly aid your
+ 
+
+ align:start position:0%
+these constraints will greatly aid your
+ability to find distant homologs or to
+
+ align:start position:0%
+ability to find distant homologs or to
+ 
+
+ align:start position:0%
+ability to find distant homologs or to
+increase the precision of your of your
+
+ align:start position:0%
+increase the precision of your of your
+ 
+
+ align:start position:0%
+increase the precision of your of your
+homology modeling in three dimensions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the shorter your cross-link obviously
+
+ align:start position:0%
+the shorter your cross-link obviously
+ 
+
+ align:start position:0%
+the shorter your cross-link obviously
+the better the the tighter your
+
+ align:start position:0%
+the better the the tighter your
+ 
+
+ align:start position:0%
+the better the the tighter your
+constraints but it might reduce the
+
+ align:start position:0%
+constraints but it might reduce the
+ 
+
+ align:start position:0%
+constraints but it might reduce the
+efficiency of cross-linking if you're
+
+ align:start position:0%
+efficiency of cross-linking if you're
+ 
+
+ align:start position:0%
+efficiency of cross-linking if you're
+doing this as artificial cross-linking
+
+ align:start position:0%
+doing this as artificial cross-linking
+ 
+
+ align:start position:0%
+doing this as artificial cross-linking
+as opposed to if you have a natural
+
+ align:start position:0%
+as opposed to if you have a natural
+ 
+
+ align:start position:0%
+as opposed to if you have a natural
+cross-linking you're basically stuck
+
+ align:start position:0%
+cross-linking you're basically stuck
+ 
+
+ align:start position:0%
+cross-linking you're basically stuck
+with whatever the natural this was a
+
+ align:start position:0%
+with whatever the natural this was a
+ 
+
+ align:start position:0%
+with whatever the natural this was a
+this was artificial cross-linking
+
+ align:start position:0%
+this was artificial cross-linking
+ 
+
+ align:start position:0%
+this was artificial cross-linking
+um with a chemical cross-linker
+
+ align:start position:0%
+um with a chemical cross-linker
+ 
+
+ align:start position:0%
+um with a chemical cross-linker
+bifunctional cross sector that's just a
+
+ align:start position:0%
+bifunctional cross sector that's just a
+ 
+
+ align:start position:0%
+bifunctional cross sector that's just a
+reminder this is not this is a different
+
+ align:start position:0%
+reminder this is not this is a different
+ 
+
+ align:start position:0%
+reminder this is not this is a different
+way of of showing some of the things we
+
+ align:start position:0%
+way of of showing some of the things we
+ 
+
+ align:start position:0%
+way of of showing some of the things we
+had a scatter plot last class which
+
+ align:start position:0%
+had a scatter plot last class which
+ 
+
+ align:start position:0%
+had a scatter plot last class which
+which showed that as you increase the
+
+ align:start position:0%
+which showed that as you increase the
+ 
+
+ align:start position:0%
+which showed that as you increase the
+sequence identity in homology modeling
+
+ align:start position:0%
+sequence identity in homology modeling
+ 
+
+ align:start position:0%
+sequence identity in homology modeling
+up to 100 percent on the vertical axis
+
+ align:start position:0%
+up to 100 percent on the vertical axis
+ 
+
+ align:start position:0%
+up to 100 percent on the vertical axis
+you decrease your uncertainty and this
+
+ align:start position:0%
+you decrease your uncertainty and this
+ 
+
+ align:start position:0%
+you decrease your uncertainty and this
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+root mean square deviation that you get
+
+ align:start position:0%
+root mean square deviation that you get
+ 
+
+ align:start position:0%
+root mean square deviation that you get
+between two structures so if they're if
+
+ align:start position:0%
+between two structures so if they're if
+ 
+
+ align:start position:0%
+between two structures so if they're if
+they're better than eighty percent then
+
+ align:start position:0%
+they're better than eighty percent then
+ 
+
+ align:start position:0%
+they're better than eighty percent then
+you have uh the order of one angstrom
+
+ align:start position:0%
+you have uh the order of one angstrom
+ 
+
+ align:start position:0%
+you have uh the order of one angstrom
+deviation which is quite acceptable for
+
+ align:start position:0%
+deviation which is quite acceptable for
+ 
+
+ align:start position:0%
+deviation which is quite acceptable for
+many purposes
+
+ align:start position:0%
+many purposes
+ 
+
+ align:start position:0%
+many purposes
+now if you want to do threading to very
+
+ align:start position:0%
+now if you want to do threading to very
+ 
+
+ align:start position:0%
+now if you want to do threading to very
+distantly related structures you know
+
+ align:start position:0%
+distantly related structures you know
+ 
+
+ align:start position:0%
+distantly related structures you know
+getting down around 30 percent is
+
+ align:start position:0%
+getting down around 30 percent is
+ 
+
+ align:start position:0%
+getting down around 30 percent is
+getting at 25 percent is getting the
+
+ align:start position:0%
+getting at 25 percent is getting the
+ 
+
+ align:start position:0%
+getting at 25 percent is getting the
+twilight zone where you really can't
+
+ align:start position:0%
+twilight zone where you really can't
+ 
+
+ align:start position:0%
+twilight zone where you really can't
+believe it it's off by
+
+ align:start position:0%
+believe it it's off by
+ 
+
+ align:start position:0%
+believe it it's off by
+too many angstroms
+
+ align:start position:0%
+too many angstroms
+ 
+
+ align:start position:0%
+too many angstroms
+but these constraints in the previous
+
+ align:start position:0%
+but these constraints in the previous
+ 
+
+ align:start position:0%
+but these constraints in the previous
+slide could help you out in either doing
+
+ align:start position:0%
+slide could help you out in either doing
+ 
+
+ align:start position:0%
+slide could help you out in either doing
+the velocity modeling or doing a
+
+ align:start position:0%
+the velocity modeling or doing a
+ 
+
+ align:start position:0%
+the velocity modeling or doing a
+threading where you're searching through
+
+ align:start position:0%
+threading where you're searching through
+ 
+
+ align:start position:0%
+threading where you're searching through
+your favorite sequence through a
+
+ align:start position:0%
+your favorite sequence through a
+ 
+
+ align:start position:0%
+your favorite sequence through a
+database
+
+ align:start position:0%
+database
+ 
+
+ align:start position:0%
+database
+of three-dimensional structures to ask
+
+ align:start position:0%
+of three-dimensional structures to ask
+ 
+
+ align:start position:0%
+of three-dimensional structures to ask
+which three-dimensional structure is
+
+ align:start position:0%
+which three-dimensional structure is
+ 
+
+ align:start position:0%
+which three-dimensional structure is
+closest to now that fgf2 we had two
+
+ align:start position:0%
+closest to now that fgf2 we had two
+ 
+
+ align:start position:0%
+closest to now that fgf2 we had two
+slides back with all those constraints
+
+ align:start position:0%
+slides back with all those constraints
+ 
+
+ align:start position:0%
+slides back with all those constraints
+can be run through this threading
+
+ align:start position:0%
+can be run through this threading
+ 
+
+ align:start position:0%
+can be run through this threading
+algorithm where you run the sequence
+
+ align:start position:0%
+algorithm where you run the sequence
+ 
+
+ align:start position:0%
+algorithm where you run the sequence
+through the database illustrated here
+
+ align:start position:0%
+through the database illustrated here
+ 
+
+ align:start position:0%
+through the database illustrated here
+there's this horizontal then the
+
+ align:start position:0%
+there's this horizontal then the
+ 
+
+ align:start position:0%
+there's this horizontal then the
+various rows of uh different structures
+
+ align:start position:0%
+various rows of uh different structures
+ 
+
+ align:start position:0%
+various rows of uh different structures
+here the full family is in the second
+
+ align:start position:0%
+here the full family is in the second
+ 
+
+ align:start position:0%
+here the full family is in the second
+column from the left
+
+ align:start position:0%
+column from the left
+ 
+
+ align:start position:0%
+column from the left
+the sequence identity of the of our
+
+ align:start position:0%
+the sequence identity of the of our
+ 
+
+ align:start position:0%
+the sequence identity of the of our
+search sequence which is fgf2 against
+
+ align:start position:0%
+search sequence which is fgf2 against
+ 
+
+ align:start position:0%
+search sequence which is fgf2 against
+all the three-dimensional structures the
+
+ align:start position:0%
+all the three-dimensional structures the
+ 
+
+ align:start position:0%
+all the three-dimensional structures the
+percent identity here 98.6 is basically
+
+ align:start position:0%
+percent identity here 98.6 is basically
+ 
+
+ align:start position:0%
+percent identity here 98.6 is basically
+that's the same structure that's the
+
+ align:start position:0%
+that's the same structure that's the
+ 
+
+ align:start position:0%
+that's the same structure that's the
+trivial uh example it's threading rank
+
+ align:start position:0%
+trivial uh example it's threading rank
+ 
+
+ align:start position:0%
+trivial uh example it's threading rank
+is number one as it should be since it's
+
+ align:start position:0%
+is number one as it should be since it's
+ 
+
+ align:start position:0%
+is number one as it should be since it's
+exactly the same structure almost
+
+ align:start position:0%
+exactly the same structure almost
+ 
+
+ align:start position:0%
+exactly the same structure almost
+exactly the same structure the
+
+ align:start position:0%
+exactly the same structure the
+ 
+
+ align:start position:0%
+exactly the same structure the
+constraint error of course is going to
+
+ align:start position:0%
+constraint error of course is going to
+ 
+
+ align:start position:0%
+constraint error of course is going to
+be zero because
+
+ align:start position:0%
+be zero because
+ 
+
+ align:start position:0%
+be zero because
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you know all the
+
+ align:start position:0%
+you know all the
+ 
+
+ align:start position:0%
+you know all the
+three-dimensional structure and all the
+
+ align:start position:0%
+three-dimensional structure and all the
+ 
+
+ align:start position:0%
+three-dimensional structure and all the
+cross-links work to that structure
+
+ align:start position:0%
+cross-links work to that structure
+ 
+
+ align:start position:0%
+cross-links work to that structure
+but an interesting one now this has been
+
+ align:start position:0%
+but an interesting one now this has been
+ 
+
+ align:start position:0%
+but an interesting one now this has been
+ranked by the constraint error not by
+
+ align:start position:0%
+ranked by the constraint error not by
+ 
+
+ align:start position:0%
+ranked by the constraint error not by
+the threading rank
+
+ align:start position:0%
+the threading rank
+ 
+
+ align:start position:0%
+the threading rank
+so and so you can ask
+
+ align:start position:0%
+so and so you can ask
+ 
+
+ align:start position:0%
+so and so you can ask
+does this improve the hits and the next
+
+ align:start position:0%
+does this improve the hits and the next
+ 
+
+ align:start position:0%
+does this improve the hits and the next
+one down is
+
+ align:start position:0%
+one down is
+ 
+
+ align:start position:0%
+one down is
+fgf2 compared to il1 data and they do
+
+ align:start position:0%
+fgf2 compared to il1 data and they do
+ 
+
+ align:start position:0%
+fgf2 compared to il1 data and they do
+have the same fold family we know that
+
+ align:start position:0%
+have the same fold family we know that
+ 
+
+ align:start position:0%
+have the same fold family we know that
+from three dimensional structure and the
+
+ align:start position:0%
+from three dimensional structure and the
+ 
+
+ align:start position:0%
+from three dimensional structure and the
+percent identity is way below the the
+
+ align:start position:0%
+percent identity is way below the the
+ 
+
+ align:start position:0%
+percent identity is way below the the
+usual cutoff where you can't infer from
+
+ align:start position:0%
+usual cutoff where you can't infer from
+ 
+
+ align:start position:0%
+usual cutoff where you can't infer from
+threading or sequencing in fact the
+
+ align:start position:0%
+threading or sequencing in fact the
+ 
+
+ align:start position:0%
+threading or sequencing in fact the
+threading rank is five this is not the
+
+ align:start position:0%
+threading rank is five this is not the
+ 
+
+ align:start position:0%
+threading rank is five this is not the
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+best thread but the constraint arrow is
+
+ align:start position:0%
+best thread but the constraint arrow is
+ 
+
+ align:start position:0%
+best thread but the constraint arrow is
+zero and so if you combine the height
+
+ align:start position:0%
+zero and so if you combine the height
+ 
+
+ align:start position:0%
+zero and so if you combine the height
+the good threading rank and the
+
+ align:start position:0%
+the good threading rank and the
+ 
+
+ align:start position:0%
+the good threading rank and the
+constraint error then you would put this
+
+ align:start position:0%
+constraint error then you would put this
+ 
+
+ align:start position:0%
+constraint error then you would put this
+as your best uh distant homolog 12
+
+ align:start position:0%
+as your best uh distant homolog 12
+ 
+
+ align:start position:0%
+as your best uh distant homolog 12
+13 sequence identity
+
+ align:start position:0%
+13 sequence identity
+ 
+
+ align:start position:0%
+13 sequence identity
+and of course is beating out better
+
+ align:start position:0%
+and of course is beating out better
+ 
+
+ align:start position:0%
+and of course is beating out better
+threading ranks because it has fewer
+
+ align:start position:0%
+threading ranks because it has fewer
+ 
+
+ align:start position:0%
+threading ranks because it has fewer
+constraint errors
+
+ align:start position:0%
+constraint errors
+ 
+
+ align:start position:0%
+constraint errors
+so you can see that how powerful these
+
+ align:start position:0%
+so you can see that how powerful these
+ 
+
+ align:start position:0%
+so you can see that how powerful these
+constraints might be and it's certainly
+
+ align:start position:0%
+constraints might be and it's certainly
+ 
+
+ align:start position:0%
+constraints might be and it's certainly
+uh you know you just need to evaluate
+
+ align:start position:0%
+uh you know you just need to evaluate
+ 
+
+ align:start position:0%
+uh you know you just need to evaluate
+whether just exactly how cost effective
+
+ align:start position:0%
+whether just exactly how cost effective
+ 
+
+ align:start position:0%
+whether just exactly how cost effective
+the mass spectrometry is
+
+ align:start position:0%
+the mass spectrometry is
+ 
+
+ align:start position:0%
+the mass spectrometry is
+now the last topic today
+
+ align:start position:0%
+now the last topic today
+ 
+
+ align:start position:0%
+now the last topic today
+sort of in the realm of protein
+
+ align:start position:0%
+sort of in the realm of protein
+ 
+
+ align:start position:0%
+sort of in the realm of protein
+modifications and interactions are how
+
+ align:start position:0%
+modifications and interactions are how
+ 
+
+ align:start position:0%
+modifications and interactions are how
+we quantitate metabolites now you can
+
+ align:start position:0%
+we quantitate metabolites now you can
+ 
+
+ align:start position:0%
+we quantitate metabolites now you can
+see that we've got some
+
+ align:start position:0%
+see that we've got some
+ 
+
+ align:start position:0%
+see that we've got some
+momentum here on
+
+ align:start position:0%
+momentum here on
+ 
+
+ align:start position:0%
+momentum here on
+quantitative proteins and rnas
+
+ align:start position:0%
+quantitative proteins and rnas
+ 
+
+ align:start position:0%
+quantitative proteins and rnas
+and so what are the issues that are
+
+ align:start position:0%
+and so what are the issues that are
+ 
+
+ align:start position:0%
+and so what are the issues that are
+slightly different from metabolites
+
+ align:start position:0%
+slightly different from metabolites
+ 
+
+ align:start position:0%
+slightly different from metabolites
+and slide 52
+
+ align:start position:0%
+and slide 52
+ 
+
+ align:start position:0%
+and slide 52
+summarizes some of these you have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you break open a cell to isolate
+
+ align:start position:0%
+when you break open a cell to isolate
+ 
+
+ align:start position:0%
+when you break open a cell to isolate
+messenger rna or proteins there is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the rate at which degradative enzymes
+
+ align:start position:0%
+the rate at which degradative enzymes
+ 
+
+ align:start position:0%
+the rate at which degradative enzymes
+act is on the order of
+
+ align:start position:0%
+act is on the order of
+ 
+
+ align:start position:0%
+act is on the order of
+you know seconds
+
+ align:start position:0%
+you know seconds
+ 
+
+ align:start position:0%
+you know seconds
+that's the rate which they go while many
+
+ align:start position:0%
+that's the rate which they go while many
+ 
+
+ align:start position:0%
+that's the rate which they go while many
+of other metabolic processes take on the
+
+ align:start position:0%
+of other metabolic processes take on the
+ 
+
+ align:start position:0%
+of other metabolic processes take on the
+order of milliseconds to microseconds
+
+ align:start position:0%
+order of milliseconds to microseconds
+ 
+
+ align:start position:0%
+order of milliseconds to microseconds
+very rapid kinetics and so as the cell
+
+ align:start position:0%
+very rapid kinetics and so as the cell
+ 
+
+ align:start position:0%
+very rapid kinetics and so as the cell
+starts to get a little bit sick on the
+
+ align:start position:0%
+starts to get a little bit sick on the
+ 
+
+ align:start position:0%
+starts to get a little bit sick on the
+second range
+
+ align:start position:0%
+second range
+ 
+
+ align:start position:0%
+second range
+all these enzymes are rear scrambling
+
+ align:start position:0%
+all these enzymes are rear scrambling
+ 
+
+ align:start position:0%
+all these enzymes are rear scrambling
+the metabolites and concentrations
+
+ align:start position:0%
+the metabolites and concentrations
+ 
+
+ align:start position:0%
+the metabolites and concentrations
+so that you
+
+ align:start position:0%
+so that you
+ 
+
+ align:start position:0%
+so that you
+so you have these rapid changes the
+
+ align:start position:0%
+so you have these rapid changes the
+ 
+
+ align:start position:0%
+so you have these rapid changes the
+detection methods are historically
+
+ align:start position:0%
+detection methods are historically
+ 
+
+ align:start position:0%
+detection methods are historically
+idiosyncratic they might be enzyme
+
+ align:start position:0%
+idiosyncratic they might be enzyme
+ 
+
+ align:start position:0%
+idiosyncratic they might be enzyme
+length where where you'll have in order
+
+ align:start position:0%
+length where where you'll have in order
+ 
+
+ align:start position:0%
+length where where you'll have in order
+to detect the metabolite you have a
+
+ align:start position:0%
+to detect the metabolite you have a
+ 
+
+ align:start position:0%
+to detect the metabolite you have a
+series of enzymes that result in some
+
+ align:start position:0%
+series of enzymes that result in some
+ 
+
+ align:start position:0%
+series of enzymes that result in some
+fluorescent or luminescent assay
+
+ align:start position:0%
+fluorescent or luminescent assay
+ 
+
+ align:start position:0%
+fluorescent or luminescent assay
+or they could be
+
+ align:start position:0%
+or they could be
+ 
+
+ align:start position:0%
+or they could be
+gas chromatography liquid chromatography
+
+ align:start position:0%
+gas chromatography liquid chromatography
+ 
+
+ align:start position:0%
+gas chromatography liquid chromatography
+nmr mass spectrometry and so forth
+
+ align:start position:0%
+nmr mass spectrometry and so forth
+ 
+
+ align:start position:0%
+nmr mass spectrometry and so forth
+the good news is there are usually fewer
+
+ align:start position:0%
+the good news is there are usually fewer
+ 
+
+ align:start position:0%
+the good news is there are usually fewer
+metabolites than there are rnas and
+
+ align:start position:0%
+metabolites than there are rnas and
+ 
+
+ align:start position:0%
+metabolites than there are rnas and
+proteins there could be 30 000 some rnas
+
+ align:start position:0%
+proteins there could be 30 000 some rnas
+ 
+
+ align:start position:0%
+proteins there could be 30 000 some rnas
+and proteins typically only a thousand
+
+ align:start position:0%
+and proteins typically only a thousand
+ 
+
+ align:start position:0%
+and proteins typically only a thousand
+or so metabolites even in the more
+
+ align:start position:0%
+or so metabolites even in the more
+ 
+
+ align:start position:0%
+or so metabolites even in the more
+exotic
+
+ align:start position:0%
+exotic
+ 
+
+ align:start position:0%
+exotic
+metabolically
+
+ align:start position:0%
+metabolically
+ 
+
+ align:start position:0%
+metabolically
+enabled such as e coli
+
+ align:start position:0%
+enabled such as e coli
+ 
+
+ align:start position:0%
+enabled such as e coli
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+uh from their various databases uh
+
+ align:start position:0%
+uh from their various databases uh
+ 
+
+ align:start position:0%
+uh from their various databases uh
+ecocide
+
+ align:start position:0%
+ecocide
+ 
+
+ align:start position:0%
+ecocide
+wit
+
+ align:start position:0%
+wit
+ 
+
+ align:start position:0%
+wit
+keg and so on
+
+ align:start position:0%
+keg and so on
+ 
+
+ align:start position:0%
+keg and so on
+which which
+
+ align:start position:0%
+which which
+ 
+
+ align:start position:0%
+which which
+integrate these
+
+ align:start position:0%
+integrate these
+ 
+
+ align:start position:0%
+integrate these
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+information about metabolites with the
+
+ align:start position:0%
+information about metabolites with the
+ 
+
+ align:start position:0%
+information about metabolites with the
+enzymes that act upon them here we're
+
+ align:start position:0%
+enzymes that act upon them here we're
+ 
+
+ align:start position:0%
+enzymes that act upon them here we're
+just looking at the kind of the sort of
+
+ align:start position:0%
+just looking at the kind of the sort of
+ 
+
+ align:start position:0%
+just looking at the kind of the sort of
+mass range that we have
+
+ align:start position:0%
+mass range that we have
+ 
+
+ align:start position:0%
+mass range that we have
+typical mass range they're they're very
+
+ align:start position:0%
+typical mass range they're they're very
+ 
+
+ align:start position:0%
+typical mass range they're they're very
+small compared to proteins and rnas
+
+ align:start position:0%
+small compared to proteins and rnas
+ 
+
+ align:start position:0%
+small compared to proteins and rnas
+most of them being around 200 atomic
+
+ align:start position:0%
+most of them being around 200 atomic
+ 
+
+ align:start position:0%
+most of them being around 200 atomic
+mass units and many of them having
+
+ align:start position:0%
+mass units and many of them having
+ 
+
+ align:start position:0%
+mass units and many of them having
+absolutely identical mass that is to say
+
+ align:start position:0%
+absolutely identical mass that is to say
+ 
+
+ align:start position:0%
+absolutely identical mass that is to say
+they have atom for atom exactly the same
+
+ align:start position:0%
+they have atom for atom exactly the same
+ 
+
+ align:start position:0%
+they have atom for atom exactly the same
+composition even though it's arranged in
+
+ align:start position:0%
+composition even though it's arranged in
+ 
+
+ align:start position:0%
+composition even though it's arranged in
+three dimensions very differently for
+
+ align:start position:0%
+three dimensions very differently for
+ 
+
+ align:start position:0%
+three dimensions very differently for
+example isoleucine and leucine as their
+
+ align:start position:0%
+example isoleucine and leucine as their
+ 
+
+ align:start position:0%
+example isoleucine and leucine as their
+names might imply
+
+ align:start position:0%
+names might imply
+ 
+
+ align:start position:0%
+names might imply
+have exactly the same mass no matter how
+
+ align:start position:0%
+have exactly the same mass no matter how
+ 
+
+ align:start position:0%
+have exactly the same mass no matter how
+many significant digits you put on them
+
+ align:start position:0%
+many significant digits you put on them
+ 
+
+ align:start position:0%
+many significant digits you put on them
+and this is illustrated by actual data
+
+ align:start position:0%
+and this is illustrated by actual data
+ 
+
+ align:start position:0%
+and this is illustrated by actual data
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+isoleucine and leucine these are hot
+
+ align:start position:0%
+isoleucine and leucine these are hot
+ 
+
+ align:start position:0%
+isoleucine and leucine these are hot
+supposedly highly purified versions uh
+
+ align:start position:0%
+supposedly highly purified versions uh
+ 
+
+ align:start position:0%
+supposedly highly purified versions uh
+commercially available of isoleucine
+
+ align:start position:0%
+commercially available of isoleucine
+ 
+
+ align:start position:0%
+commercially available of isoleucine
+lucy mixed together here and run out in
+
+ align:start position:0%
+lucy mixed together here and run out in
+ 
+
+ align:start position:0%
+lucy mixed together here and run out in
+these two dimensions of mass on the
+
+ align:start position:0%
+these two dimensions of mass on the
+ 
+
+ align:start position:0%
+these two dimensions of mass on the
+horizontal axis and retention time and
+
+ align:start position:0%
+horizontal axis and retention time and
+ 
+
+ align:start position:0%
+horizontal axis and retention time and
+hydrophobic separation now not of
+
+ align:start position:0%
+hydrophobic separation now not of
+ 
+
+ align:start position:0%
+hydrophobic separation now not of
+peptides but of amino acids
+
+ align:start position:0%
+peptides but of amino acids
+ 
+
+ align:start position:0%
+peptides but of amino acids
+metabolites
+
+ align:start position:0%
+metabolites
+ 
+
+ align:start position:0%
+metabolites
+and you can see how that even though
+
+ align:start position:0%
+and you can see how that even though
+ 
+
+ align:start position:0%
+and you can see how that even though
+they are identical in mass
+
+ align:start position:0%
+they are identical in mass
+ 
+
+ align:start position:0%
+they are identical in mass
+as shown in the previous slide around
+
+ align:start position:0%
+as shown in the previous slide around
+ 
+
+ align:start position:0%
+as shown in the previous slide around
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+um they are separable in their
+
+ align:start position:0%
+um they are separable in their
+ 
+
+ align:start position:0%
+um they are separable in their
+by their hydrophobicity
+
+ align:start position:0%
+by their hydrophobicity
+ 
+
+ align:start position:0%
+by their hydrophobicity
+they have the same
+
+ align:start position:0%
+they have the same
+ 
+
+ align:start position:0%
+they have the same
+atomic composition but they are
+
+ align:start position:0%
+atomic composition but they are
+ 
+
+ align:start position:0%
+atomic composition but they are
+separable
+
+ align:start position:0%
+separable
+ 
+
+ align:start position:0%
+separable
+just by this hydrophobic separation and
+
+ align:start position:0%
+just by this hydrophobic separation and
+ 
+
+ align:start position:0%
+just by this hydrophobic separation and
+you can see in the commercial preps
+
+ align:start position:0%
+you can see in the commercial preps
+ 
+
+ align:start position:0%
+you can see in the commercial preps
+there are a variety of contaminated
+
+ align:start position:0%
+there are a variety of contaminated
+ 
+
+ align:start position:0%
+there are a variety of contaminated
+molecules that co-migrate into in the
+
+ align:start position:0%
+molecules that co-migrate into in the
+ 
+
+ align:start position:0%
+molecules that co-migrate into in the
+reverse phase
+
+ align:start position:0%
+reverse phase
+ 
+
+ align:start position:0%
+reverse phase
+dimension presumably because something
+
+ align:start position:0%
+dimension presumably because something
+ 
+
+ align:start position:0%
+dimension presumably because something
+like reverse phase is used for purifying
+
+ align:start position:0%
+like reverse phase is used for purifying
+ 
+
+ align:start position:0%
+like reverse phase is used for purifying
+them commercially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this there are basically three ways
+
+ align:start position:0%
+so this there are basically three ways
+ 
+
+ align:start position:0%
+so this there are basically three ways
+of this of distinguishing
+
+ align:start position:0%
+of this of distinguishing
+ 
+
+ align:start position:0%
+of this of distinguishing
+molecules that have the same mass
+
+ align:start position:0%
+molecules that have the same mass
+ 
+
+ align:start position:0%
+molecules that have the same mass
+the one in the previous slide was
+
+ align:start position:0%
+the one in the previous slide was
+ 
+
+ align:start position:0%
+the one in the previous slide was
+separating them by another property like
+
+ align:start position:0%
+separating them by another property like
+ 
+
+ align:start position:0%
+separating them by another property like
+retention time on a hydrophobic
+
+ align:start position:0%
+retention time on a hydrophobic
+ 
+
+ align:start position:0%
+retention time on a hydrophobic
+properties another one is is secondary
+
+ align:start position:0%
+properties another one is is secondary
+ 
+
+ align:start position:0%
+properties another one is is secondary
+fragmentation just as we could fragment
+
+ align:start position:0%
+fragmentation just as we could fragment
+ 
+
+ align:start position:0%
+fragmentation just as we could fragment
+peptides by collision in the gas phase
+
+ align:start position:0%
+peptides by collision in the gas phase
+ 
+
+ align:start position:0%
+peptides by collision in the gas phase
+with some inert gas we can do this with
+
+ align:start position:0%
+with some inert gas we can do this with
+ 
+
+ align:start position:0%
+with some inert gas we can do this with
+metabolites and so two things that have
+
+ align:start position:0%
+metabolites and so two things that have
+ 
+
+ align:start position:0%
+metabolites and so two things that have
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+mass
+
+ align:start position:0%
+mass
+ 
+
+ align:start position:0%
+mass
+may have a different fragmentation
+
+ align:start position:0%
+may have a different fragmentation
+ 
+
+ align:start position:0%
+may have a different fragmentation
+pattern
+
+ align:start position:0%
+pattern
+ 
+
+ align:start position:0%
+pattern
+and you can see again you can cleave at
+
+ align:start position:0%
+and you can see again you can cleave at
+ 
+
+ align:start position:0%
+and you can see again you can cleave at
+every particular position and here are
+
+ align:start position:0%
+every particular position and here are
+ 
+
+ align:start position:0%
+every particular position and here are
+two different aspects of two different
+
+ align:start position:0%
+two different aspects of two different
+ 
+
+ align:start position:0%
+two different aspects of two different
+labs
+
+ align:start position:0%
+labs
+ 
+
+ align:start position:0%
+labs
+slightly different methodology
+
+ align:start position:0%
+slightly different methodology
+ 
+
+ align:start position:0%
+slightly different methodology
+showing fragmentation in almost every
+
+ align:start position:0%
+showing fragmentation in almost every
+ 
+
+ align:start position:0%
+showing fragmentation in almost every
+carbon bond
+
+ align:start position:0%
+carbon bond
+ 
+
+ align:start position:0%
+carbon bond
+the third method by which you can
+
+ align:start position:0%
+the third method by which you can
+ 
+
+ align:start position:0%
+the third method by which you can
+distinguish
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+compounds that have exactly the same
+
+ align:start position:0%
+compounds that have exactly the same
+ 
+
+ align:start position:0%
+compounds that have exactly the same
+mass in this case this is the most
+
+ align:start position:0%
+mass in this case this is the most
+ 
+
+ align:start position:0%
+mass in this case this is the most
+extreme case these compounds have the
+
+ align:start position:0%
+extreme case these compounds have the
+ 
+
+ align:start position:0%
+extreme case these compounds have the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+have the same mass
+
+ align:start position:0%
+have the same mass
+ 
+
+ align:start position:0%
+have the same mass
+they actually not only have the same
+
+ align:start position:0%
+they actually not only have the same
+ 
+
+ align:start position:0%
+they actually not only have the same
+chemical composition the same atomic
+
+ align:start position:0%
+chemical composition the same atomic
+ 
+
+ align:start position:0%
+chemical composition the same atomic
+composition they actually have the same
+
+ align:start position:0%
+composition they actually have the same
+ 
+
+ align:start position:0%
+composition they actually have the same
+chemical structure their three
+
+ align:start position:0%
+chemical structure their three
+ 
+
+ align:start position:0%
+chemical structure their three
+dimensions are the same their mass is
+
+ align:start position:0%
+dimensions are the same their mass is
+ 
+
+ align:start position:0%
+dimensions are the same their mass is
+the same what it is is this
+
+ align:start position:0%
+the same what it is is this
+ 
+
+ align:start position:0%
+the same what it is is this
+let's let's say the red is the carbon 13
+
+ align:start position:0%
+let's let's say the red is the carbon 13
+ 
+
+ align:start position:0%
+let's let's say the red is the carbon 13
+and the green or the carbon 12 you can
+
+ align:start position:0%
+and the green or the carbon 12 you can
+ 
+
+ align:start position:0%
+and the green or the carbon 12 you can
+have the carbon 13 in different
+
+ align:start position:0%
+have the carbon 13 in different
+ 
+
+ align:start position:0%
+have the carbon 13 in different
+positions on this say this glucose
+
+ align:start position:0%
+positions on this say this glucose
+ 
+
+ align:start position:0%
+positions on this say this glucose
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it has the same three-dimensional
+
+ align:start position:0%
+it has the same three-dimensional
+ 
+
+ align:start position:0%
+it has the same three-dimensional
+structure the same mass it's just you
+
+ align:start position:0%
+structure the same mass it's just you
+ 
+
+ align:start position:0%
+structure the same mass it's just you
+move the position of the c-13 to
+
+ align:start position:0%
+move the position of the c-13 to
+ 
+
+ align:start position:0%
+move the position of the c-13 to
+different positions this is actually an
+
+ align:start position:0%
+different positions this is actually an
+ 
+
+ align:start position:0%
+different positions this is actually an
+interesting case when you have
+
+ align:start position:0%
+interesting case when you have
+ 
+
+ align:start position:0%
+interesting case when you have
+uh natural abundance glucose where you
+
+ align:start position:0%
+uh natural abundance glucose where you
+ 
+
+ align:start position:0%
+uh natural abundance glucose where you
+have c13
+
+ align:start position:0%
+have c13
+ 
+
+ align:start position:0%
+have c13
+trace amounts it can it can
+
+ align:start position:0%
+trace amounts it can it can
+ 
+
+ align:start position:0%
+trace amounts it can it can
+be positioned on various different
+
+ align:start position:0%
+be positioned on various different
+ 
+
+ align:start position:0%
+be positioned on various different
+carbon atoms but you can still tell
+
+ align:start position:0%
+carbon atoms but you can still tell
+ 
+
+ align:start position:0%
+carbon atoms but you can still tell
+where it is by when it when it uh it's
+
+ align:start position:0%
+where it is by when it when it uh it's
+ 
+
+ align:start position:0%
+where it is by when it when it uh it's
+now not broken down in the gas phase by
+
+ align:start position:0%
+now not broken down in the gas phase by
+ 
+
+ align:start position:0%
+now not broken down in the gas phase by
+collision induced dissociation but it's
+
+ align:start position:0%
+collision induced dissociation but it's
+ 
+
+ align:start position:0%
+collision induced dissociation but it's
+broken down in the cell it goes through
+
+ align:start position:0%
+broken down in the cell it goes through
+ 
+
+ align:start position:0%
+broken down in the cell it goes through
+different pathways this is example we're
+
+ align:start position:0%
+different pathways this is example we're
+ 
+
+ align:start position:0%
+different pathways this is example we're
+going to be talking about pathways
+
+ align:start position:0%
+going to be talking about pathways
+ 
+
+ align:start position:0%
+going to be talking about pathways
+uh for the next
+
+ align:start position:0%
+uh for the next
+ 
+
+ align:start position:0%
+uh for the next
+three sessions but here's an example of
+
+ align:start position:0%
+three sessions but here's an example of
+ 
+
+ align:start position:0%
+three sessions but here's an example of
+central carbon metabolism where you
+
+ align:start position:0%
+central carbon metabolism where you
+ 
+
+ align:start position:0%
+central carbon metabolism where you
+start with glucose with the 6-phosphate
+
+ align:start position:0%
+start with glucose with the 6-phosphate
+ 
+
+ align:start position:0%
+start with glucose with the 6-phosphate
+in the upper
+
+ align:start position:0%
+in the upper
+ 
+
+ align:start position:0%
+in the upper
+left-hand corner of this network diagram
+
+ align:start position:0%
+left-hand corner of this network diagram
+ 
+
+ align:start position:0%
+left-hand corner of this network diagram
+and you end up with carbon dioxide down
+
+ align:start position:0%
+and you end up with carbon dioxide down
+ 
+
+ align:start position:0%
+and you end up with carbon dioxide down
+in the lower left
+
+ align:start position:0%
+in the lower left
+ 
+
+ align:start position:0%
+in the lower left
+and it can go through various pathways
+
+ align:start position:0%
+and it can go through various pathways
+ 
+
+ align:start position:0%
+and it can go through various pathways
+through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ribulose or down through
+
+ align:start position:0%
+ribulose or down through
+ 
+
+ align:start position:0%
+ribulose or down through
+three carbons and each of these three
+
+ align:start position:0%
+three carbons and each of these three
+ 
+
+ align:start position:0%
+three carbons and each of these three
+and two carbon breakdown products can
+
+ align:start position:0%
+and two carbon breakdown products can
+ 
+
+ align:start position:0%
+and two carbon breakdown products can
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+the label atom the mass tagged atom in
+
+ align:start position:0%
+the label atom the mass tagged atom in
+ 
+
+ align:start position:0%
+the label atom the mass tagged atom in
+different positions
+
+ align:start position:0%
+different positions
+ 
+
+ align:start position:0%
+different positions
+and as this quote uh the literature
+
+ align:start position:0%
+and as this quote uh the literature
+ 
+
+ align:start position:0%
+and as this quote uh the literature
+points out that when you want to study
+
+ align:start position:0%
+points out that when you want to study
+ 
+
+ align:start position:0%
+points out that when you want to study
+the fluxes through the pathway by
+
+ align:start position:0%
+the fluxes through the pathway by
+ 
+
+ align:start position:0%
+the fluxes through the pathway by
+monitor you can actually do
+
+ align:start position:0%
+monitor you can actually do
+ 
+
+ align:start position:0%
+monitor you can actually do
+a pulse or a stable steady state
+
+ align:start position:0%
+a pulse or a stable steady state
+ 
+
+ align:start position:0%
+a pulse or a stable steady state
+labeling with isotopic labels and you
+
+ align:start position:0%
+labeling with isotopic labels and you
+ 
+
+ align:start position:0%
+labeling with isotopic labels and you
+can monitor the fluxes through these
+
+ align:start position:0%
+can monitor the fluxes through these
+ 
+
+ align:start position:0%
+can monitor the fluxes through these
+pathways but you need to take into
+
+ align:start position:0%
+pathways but you need to take into
+ 
+
+ align:start position:0%
+pathways but you need to take into
+account all the different ways that you
+
+ align:start position:0%
+account all the different ways that you
+ 
+
+ align:start position:0%
+account all the different ways that you
+can go through pathways especially when
+
+ align:start position:0%
+can go through pathways especially when
+ 
+
+ align:start position:0%
+can go through pathways especially when
+you're doing metabolic cycles like the
+
+ align:start position:0%
+you're doing metabolic cycles like the
+ 
+
+ align:start position:0%
+you're doing metabolic cycles like the
+tca cycle or
+
+ align:start position:0%
+tca cycle or
+ 
+
+ align:start position:0%
+tca cycle or
+you have to think think through all the
+
+ align:start position:0%
+you have to think think through all the
+ 
+
+ align:start position:0%
+you have to think think through all the
+multiple terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+in principle that kind of metabolic
+
+ align:start position:0%
+in principle that kind of metabolic
+ 
+
+ align:start position:0%
+in principle that kind of metabolic
+tracing can be done
+
+ align:start position:0%
+tracing can be done
+ 
+
+ align:start position:0%
+tracing can be done
+either with mass spectrometry or with
+
+ align:start position:0%
+either with mass spectrometry or with
+ 
+
+ align:start position:0%
+either with mass spectrometry or with
+nuclear magnetic resonance
+
+ align:start position:0%
+nuclear magnetic resonance
+ 
+
+ align:start position:0%
+nuclear magnetic resonance
+when you do quantitative 2d nuclear
+
+ align:start position:0%
+when you do quantitative 2d nuclear
+ 
+
+ align:start position:0%
+when you do quantitative 2d nuclear
+magnetic resonance you're basically
+
+ align:start position:0%
+magnetic resonance you're basically
+ 
+
+ align:start position:0%
+magnetic resonance you're basically
+looking at the the uh shifts in the
+
+ align:start position:0%
+looking at the the uh shifts in the
+ 
+
+ align:start position:0%
+looking at the the uh shifts in the
+spectral quantities for the
+
+ align:start position:0%
+spectral quantities for the
+ 
+
+ align:start position:0%
+spectral quantities for the
+carbon 13s remember we were talking
+
+ align:start position:0%
+carbon 13s remember we were talking
+ 
+
+ align:start position:0%
+carbon 13s remember we were talking
+about carbon 13 labeling and the the
+
+ align:start position:0%
+about carbon 13 labeling and the the
+ 
+
+ align:start position:0%
+about carbon 13 labeling and the the
+normal most abundant
+
+ align:start position:0%
+normal most abundant
+ 
+
+ align:start position:0%
+normal most abundant
+protons
+
+ align:start position:0%
+protons
+ 
+
+ align:start position:0%
+protons
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+and the chemical shifts here that you
+
+ align:start position:0%
+and the chemical shifts here that you
+ 
+
+ align:start position:0%
+and the chemical shifts here that you
+get are due to the exact chemical
+
+ align:start position:0%
+get are due to the exact chemical
+ 
+
+ align:start position:0%
+get are due to the exact chemical
+environment of this proton or this
+
+ align:start position:0%
+environment of this proton or this
+ 
+
+ align:start position:0%
+environment of this proton or this
+carbon 13
+
+ align:start position:0%
+carbon 13
+ 
+
+ align:start position:0%
+carbon 13
+uh for say the alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for each of these amino acids alpha
+
+ align:start position:0%
+for each of these amino acids alpha
+ 
+
+ align:start position:0%
+for each of these amino acids alpha
+betas and each of these little clusters
+
+ align:start position:0%
+betas and each of these little clusters
+ 
+
+ align:start position:0%
+betas and each of these little clusters
+are schematic for the intensity of of
+
+ align:start position:0%
+are schematic for the intensity of of
+ 
+
+ align:start position:0%
+are schematic for the intensity of of
+this particular
+
+ align:start position:0%
+this particular
+ 
+
+ align:start position:0%
+this particular
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+these particular atoms that you're
+
+ align:start position:0%
+these particular atoms that you're
+ 
+
+ align:start position:0%
+these particular atoms that you're
+monitoring
+
+ align:start position:0%
+monitoring
+ 
+
+ align:start position:0%
+monitoring
+by their isotope effects on the nmr here
+
+ align:start position:0%
+by their isotope effects on the nmr here
+ 
+
+ align:start position:0%
+by their isotope effects on the nmr here
+the the odd number of uh
+
+ align:start position:0%
+the the odd number of uh
+ 
+
+ align:start position:0%
+the the odd number of uh
+nucleons is is critical to the detection
+
+ align:start position:0%
+nucleons is is critical to the detection
+ 
+
+ align:start position:0%
+nucleons is is critical to the detection
+okay so if you know
+
+ align:start position:0%
+okay so if you know
+ 
+
+ align:start position:0%
+okay so if you know
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the structure of the network
+
+ align:start position:0%
+the structure of the network
+ 
+
+ align:start position:0%
+the structure of the network
+then you can use that that knowledge
+
+ align:start position:0%
+then you can use that that knowledge
+ 
+
+ align:start position:0%
+then you can use that that knowledge
+and you know which of these atoms go
+
+ align:start position:0%
+and you know which of these atoms go
+ 
+
+ align:start position:0%
+and you know which of these atoms go
+into which parts then you can use this
+
+ align:start position:0%
+into which parts then you can use this
+ 
+
+ align:start position:0%
+into which parts then you can use this
+to quantitate
+
+ align:start position:0%
+to quantitate
+ 
+
+ align:start position:0%
+to quantitate
+the uh fluxes through any point in the
+
+ align:start position:0%
+the uh fluxes through any point in the
+ 
+
+ align:start position:0%
+the uh fluxes through any point in the
+network on the other hand if you don't
+
+ align:start position:0%
+network on the other hand if you don't
+ 
+
+ align:start position:0%
+network on the other hand if you don't
+if you only know part of the network
+
+ align:start position:0%
+if you only know part of the network
+ 
+
+ align:start position:0%
+if you only know part of the network
+then you can use this way of the
+
+ align:start position:0%
+then you can use this way of the
+ 
+
+ align:start position:0%
+then you can use this way of the
+tracking to slowly piece together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how the network must go
+
+ align:start position:0%
+how the network must go
+ 
+
+ align:start position:0%
+how the network must go
+most of this has been those worked out
+
+ align:start position:0%
+most of this has been those worked out
+ 
+
+ align:start position:0%
+most of this has been those worked out
+well before uh genomics and our current
+
+ align:start position:0%
+well before uh genomics and our current
+ 
+
+ align:start position:0%
+well before uh genomics and our current
+systems biology methods and so there
+
+ align:start position:0%
+systems biology methods and so there
+ 
+
+ align:start position:0%
+systems biology methods and so there
+aren't real algorithms for doing this as
+
+ align:start position:0%
+aren't real algorithms for doing this as
+ 
+
+ align:start position:0%
+aren't real algorithms for doing this as
+far as i know although it certainly is
+
+ align:start position:0%
+far as i know although it certainly is
+ 
+
+ align:start position:0%
+far as i know although it certainly is
+opportunity for doing it now this is
+
+ align:start position:0%
+opportunity for doing it now this is
+ 
+
+ align:start position:0%
+opportunity for doing it now this is
+measuring remember this ratios versus
+
+ align:start position:0%
+measuring remember this ratios versus
+ 
+
+ align:start position:0%
+measuring remember this ratios versus
+absolute amounts this is measuring not
+
+ align:start position:0%
+absolute amounts this is measuring not
+ 
+
+ align:start position:0%
+absolute amounts this is measuring not
+only ratios of metabolite concentrations
+
+ align:start position:0%
+only ratios of metabolite concentrations
+ 
+
+ align:start position:0%
+only ratios of metabolite concentrations
+this is not metallic contributions but
+
+ align:start position:0%
+this is not metallic contributions but
+ 
+
+ align:start position:0%
+this is not metallic contributions but
+fluxes so
+
+ align:start position:0%
+fluxes so
+ 
+
+ align:start position:0%
+fluxes so
+so with metabolites you can measure
+
+ align:start position:0%
+so with metabolites you can measure
+ 
+
+ align:start position:0%
+so with metabolites you can measure
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+concentrations or fluxes absolute or
+
+ align:start position:0%
+concentrations or fluxes absolute or
+ 
+
+ align:start position:0%
+concentrations or fluxes absolute or
+ratios all of all four of those
+
+ align:start position:0%
+ratios all of all four of those
+ 
+
+ align:start position:0%
+ratios all of all four of those
+combinations
+
+ align:start position:0%
+combinations
+ 
+
+ align:start position:0%
+combinations
+now let's say in again in principle if
+
+ align:start position:0%
+now let's say in again in principle if
+ 
+
+ align:start position:0%
+now let's say in again in principle if
+you can measure absolute concentrations
+
+ align:start position:0%
+you can measure absolute concentrations
+ 
+
+ align:start position:0%
+you can measure absolute concentrations
+you can measure ratios
+
+ align:start position:0%
+you can measure ratios
+ 
+
+ align:start position:0%
+you can measure ratios
+and you can measure ratios of fluxes so
+
+ align:start position:0%
+and you can measure ratios of fluxes so
+ 
+
+ align:start position:0%
+and you can measure ratios of fluxes so
+how you measure absolute concentration
+
+ align:start position:0%
+how you measure absolute concentration
+ 
+
+ align:start position:0%
+how you measure absolute concentration
+so remember we said that one of the
+
+ align:start position:0%
+so remember we said that one of the
+ 
+
+ align:start position:0%
+so remember we said that one of the
+problems was that as soon as you start
+
+ align:start position:0%
+problems was that as soon as you start
+ 
+
+ align:start position:0%
+problems was that as soon as you start
+perturbing the cell
+
+ align:start position:0%
+perturbing the cell
+ 
+
+ align:start position:0%
+perturbing the cell
+in microseconds you can get changes but
+
+ align:start position:0%
+in microseconds you can get changes but
+ 
+
+ align:start position:0%
+in microseconds you can get changes but
+one way to do this is without lysing the
+
+ align:start position:0%
+one way to do this is without lysing the
+ 
+
+ align:start position:0%
+one way to do this is without lysing the
+cells you can you can snap freeze the
+
+ align:start position:0%
+cells you can you can snap freeze the
+ 
+
+ align:start position:0%
+cells you can you can snap freeze the
+first yes that
+
+ align:start position:0%
+first yes that
+ 
+
+ align:start position:0%
+first yes that
+snap
+
+ align:start position:0%
+snap
+ 
+
+ align:start position:0%
+snap
+expose them to uh
+
+ align:start position:0%
+expose them to uh
+ 
+
+ align:start position:0%
+expose them to uh
+aqueous methanol and -40 you can wash
+
+ align:start position:0%
+aqueous methanol and -40 you can wash
+ 
+
+ align:start position:0%
+aqueous methanol and -40 you can wash
+them at that it's a liquid and you can
+
+ align:start position:0%
+them at that it's a liquid and you can
+ 
+
+ align:start position:0%
+them at that it's a liquid and you can
+remove the outside metabolites and uh
+
+ align:start position:0%
+remove the outside metabolites and uh
+ 
+
+ align:start position:0%
+remove the outside metabolites and uh
+and there's reason to believe this is
+
+ align:start position:0%
+and there's reason to believe this is
+ 
+
+ align:start position:0%
+and there's reason to believe this is
+the minimally perturbing method of
+
+ align:start position:0%
+the minimally perturbing method of
+ 
+
+ align:start position:0%
+the minimally perturbing method of
+preparing the cells and then you put
+
+ align:start position:0%
+preparing the cells and then you put
+ 
+
+ align:start position:0%
+preparing the cells and then you put
+them in basically boiling alcohol
+
+ align:start position:0%
+them in basically boiling alcohol
+ 
+
+ align:start position:0%
+them in basically boiling alcohol
+and then quantitate with um
+
+ align:start position:0%
+and then quantitate with um
+ 
+
+ align:start position:0%
+and then quantitate with um
+with nmr methods such as the ones we
+
+ align:start position:0%
+with nmr methods such as the ones we
+ 
+
+ align:start position:0%
+with nmr methods such as the ones we
+just talked about
+
+ align:start position:0%
+just talked about
+ 
+
+ align:start position:0%
+just talked about
+getting up to 300 measures
+
+ align:start position:0%
+getting up to 300 measures
+ 
+
+ align:start position:0%
+getting up to 300 measures
+per sample
+
+ align:start position:0%
+per sample
+ 
+
+ align:start position:0%
+per sample
+some examples of some of these internal
+
+ align:start position:0%
+some examples of some of these internal
+ 
+
+ align:start position:0%
+some examples of some of these internal
+metabolite concentrations now remember
+
+ align:start position:0%
+metabolite concentrations now remember
+ 
+
+ align:start position:0%
+metabolite concentrations now remember
+these are not flux ratios but actual
+
+ align:start position:0%
+these are not flux ratios but actual
+ 
+
+ align:start position:0%
+these are not flux ratios but actual
+metabolite concentrations of things like
+
+ align:start position:0%
+metabolite concentrations of things like
+ 
+
+ align:start position:0%
+metabolite concentrations of things like
+glucose 6-phosphate
+
+ align:start position:0%
+glucose 6-phosphate
+ 
+
+ align:start position:0%
+glucose 6-phosphate
+atp ayurvede so on
+
+ align:start position:0%
+atp ayurvede so on
+ 
+
+ align:start position:0%
+atp ayurvede so on
+can be correlated to genomics
+
+ align:start position:0%
+can be correlated to genomics
+ 
+
+ align:start position:0%
+can be correlated to genomics
+by the vehicle of
+
+ align:start position:0%
+by the vehicle of
+ 
+
+ align:start position:0%
+by the vehicle of
+gene knockouts so we have wild type on
+
+ align:start position:0%
+gene knockouts so we have wild type on
+ 
+
+ align:start position:0%
+gene knockouts so we have wild type on
+the top of the far left
+
+ align:start position:0%
+the top of the far left
+ 
+
+ align:start position:0%
+the top of the far left
+followed by a deletion of ho this is a
+
+ align:start position:0%
+followed by a deletion of ho this is a
+ 
+
+ align:start position:0%
+followed by a deletion of ho this is a
+homing endonuclease should have no
+
+ align:start position:0%
+homing endonuclease should have no
+ 
+
+ align:start position:0%
+homing endonuclease should have no
+metabolic consequences so at all this is
+
+ align:start position:0%
+metabolic consequences so at all this is
+ 
+
+ align:start position:0%
+metabolic consequences so at all this is
+used as a control it's a pseudo wild
+
+ align:start position:0%
+used as a control it's a pseudo wild
+ 
+
+ align:start position:0%
+used as a control it's a pseudo wild
+type just shows that the deletion method
+
+ align:start position:0%
+type just shows that the deletion method
+ 
+
+ align:start position:0%
+type just shows that the deletion method
+itself is not changing things
+
+ align:start position:0%
+itself is not changing things
+ 
+
+ align:start position:0%
+itself is not changing things
+the metabolism then as you go further
+
+ align:start position:0%
+the metabolism then as you go further
+ 
+
+ align:start position:0%
+the metabolism then as you go further
+and further down this list you get more
+
+ align:start position:0%
+and further down this list you get more
+ 
+
+ align:start position:0%
+and further down this list you get more
+and more severe
+
+ align:start position:0%
+and more severe
+ 
+
+ align:start position:0%
+and more severe
+expected effects
+
+ align:start position:0%
+expected effects
+ 
+
+ align:start position:0%
+expected effects
+on the ability of the organisms say to
+
+ align:start position:0%
+on the ability of the organisms say to
+ 
+
+ align:start position:0%
+on the ability of the organisms say to
+produce energy as exemplified by atp
+
+ align:start position:0%
+produce energy as exemplified by atp
+ 
+
+ align:start position:0%
+produce energy as exemplified by atp
+production
+
+ align:start position:0%
+production
+ 
+
+ align:start position:0%
+production
+now if you have low atp production that
+
+ align:start position:0%
+now if you have low atp production that
+ 
+
+ align:start position:0%
+now if you have low atp production that
+means you have high residual levels of
+
+ align:start position:0%
+means you have high residual levels of
+ 
+
+ align:start position:0%
+means you have high residual levels of
+adp which is the other end of the energy
+
+ align:start position:0%
+adp which is the other end of the energy
+ 
+
+ align:start position:0%
+adp which is the other end of the energy
+spectrum and so if you look down these
+
+ align:start position:0%
+spectrum and so if you look down these
+ 
+
+ align:start position:0%
+spectrum and so if you look down these
+columns it's a little hard to see with
+
+ align:start position:0%
+columns it's a little hard to see with
+ 
+
+ align:start position:0%
+columns it's a little hard to see with
+all the the clutter that's produced by
+
+ align:start position:0%
+all the the clutter that's produced by
+ 
+
+ align:start position:0%
+all the the clutter that's produced by
+the the standard deviations i wouldn't
+
+ align:start position:0%
+the the standard deviations i wouldn't
+ 
+
+ align:start position:0%
+the the standard deviations i wouldn't
+want them to get rid of those standard
+
+ align:start position:0%
+want them to get rid of those standard
+ 
+
+ align:start position:0%
+want them to get rid of those standard
+deviations it's wonderful but uh anyway
+
+ align:start position:0%
+deviations it's wonderful but uh anyway
+ 
+
+ align:start position:0%
+deviations it's wonderful but uh anyway
+you can summarize this by looking at the
+
+ align:start position:0%
+you can summarize this by looking at the
+ 
+
+ align:start position:0%
+you can summarize this by looking at the
+atp to adp ratio that's a way of you
+
+ align:start position:0%
+atp to adp ratio that's a way of you
+ 
+
+ align:start position:0%
+atp to adp ratio that's a way of you
+don't need ratios for this to work but
+
+ align:start position:0%
+don't need ratios for this to work but
+ 
+
+ align:start position:0%
+don't need ratios for this to work but
+it's a way of accentuating
+
+ align:start position:0%
+it's a way of accentuating
+ 
+
+ align:start position:0%
+it's a way of accentuating
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+balance and so you can see for a while
+
+ align:start position:0%
+balance and so you can see for a while
+ 
+
+ align:start position:0%
+balance and so you can see for a while
+time you have about almost seven is the
+
+ align:start position:0%
+time you have about almost seven is the
+ 
+
+ align:start position:0%
+time you have about almost seven is the
+ratio of atp to adp
+
+ align:start position:0%
+ratio of atp to adp
+ 
+
+ align:start position:0%
+ratio of atp to adp
+highly charged in this high energy state
+
+ align:start position:0%
+highly charged in this high energy state
+ 
+
+ align:start position:0%
+highly charged in this high energy state
+and as you get to these pet mutants
+
+ align:start position:0%
+and as you get to these pet mutants
+ 
+
+ align:start position:0%
+and as you get to these pet mutants
+which are
+
+ align:start position:0%
+which are
+ 
+
+ align:start position:0%
+which are
+mutations in the mitochondrial process
+
+ align:start position:0%
+mutations in the mitochondrial process
+ 
+
+ align:start position:0%
+mutations in the mitochondrial process
+you find the cell is becoming
+
+ align:start position:0%
+you find the cell is becoming
+ 
+
+ align:start position:0%
+you find the cell is becoming
+increasingly ineffective now these were
+
+ align:start position:0%
+increasingly ineffective now these were
+ 
+
+ align:start position:0%
+increasingly ineffective now these were
+all chosen uh because
+
+ align:start position:0%
+all chosen uh because
+ 
+
+ align:start position:0%
+all chosen uh because
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+these were so-called silent mutations
+
+ align:start position:0%
+these were so-called silent mutations
+ 
+
+ align:start position:0%
+these were so-called silent mutations
+that the title of this paper says that
+
+ align:start position:0%
+that the title of this paper says that
+ 
+
+ align:start position:0%
+that the title of this paper says that
+you can get phenotypes by looking at the
+
+ align:start position:0%
+you can get phenotypes by looking at the
+ 
+
+ align:start position:0%
+you can get phenotypes by looking at the
+molecular analysis quantitating the
+
+ align:start position:0%
+molecular analysis quantitating the
+ 
+
+ align:start position:0%
+molecular analysis quantitating the
+whole
+
+ align:start position:0%
+whole
+ 
+
+ align:start position:0%
+whole
+holistically
+
+ align:start position:0%
+holistically
+ 
+
+ align:start position:0%
+holistically
+systematically all the metabolites for
+
+ align:start position:0%
+systematically all the metabolites for
+ 
+
+ align:start position:0%
+systematically all the metabolites for
+things that otherwise have no
+
+ align:start position:0%
+things that otherwise have no
+ 
+
+ align:start position:0%
+things that otherwise have no
+phenotypes
+
+ align:start position:0%
+phenotypes
+ 
+
+ align:start position:0%
+phenotypes
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now this
+
+ align:start position:0%
+now this
+ 
+
+ align:start position:0%
+now this
+representation as you start quantitating
+
+ align:start position:0%
+representation as you start quantitating
+ 
+
+ align:start position:0%
+representation as you start quantitating
+full proteomes proteome interactions
+
+ align:start position:0%
+full proteomes proteome interactions
+ 
+
+ align:start position:0%
+full proteomes proteome interactions
+proteome modifications
+
+ align:start position:0%
+proteome modifications
+ 
+
+ align:start position:0%
+proteome modifications
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+metabolizing their interactions you
+
+ align:start position:0%
+metabolizing their interactions you
+ 
+
+ align:start position:0%
+metabolizing their interactions you
+start wanting to relay this information
+
+ align:start position:0%
+start wanting to relay this information
+ 
+
+ align:start position:0%
+start wanting to relay this information
+summarize this information in the
+
+ align:start position:0%
+summarize this information in the
+ 
+
+ align:start position:0%
+summarize this information in the
+context of models and just this last
+
+ align:start position:0%
+context of models and just this last
+ 
+
+ align:start position:0%
+context of models and just this last
+time the upper left-hand
+
+ align:start position:0%
+time the upper left-hand
+ 
+
+ align:start position:0%
+time the upper left-hand
+portion of this
+
+ align:start position:0%
+portion of this
+ 
+
+ align:start position:0%
+portion of this
+summary
+
+ align:start position:0%
+summary
+ 
+
+ align:start position:0%
+summary
+i emphasize that no model is exact
+
+ align:start position:0%
+i emphasize that no model is exact
+ 
+
+ align:start position:0%
+i emphasize that no model is exact
+sometimes the people working the field
+
+ align:start position:0%
+sometimes the people working the field
+ 
+
+ align:start position:0%
+sometimes the people working the field
+convince themselves is more exact than
+
+ align:start position:0%
+convince themselves is more exact than
+ 
+
+ align:start position:0%
+convince themselves is more exact than
+than lower models
+
+ align:start position:0%
+than lower models
+ 
+
+ align:start position:0%
+than lower models
+but if
+
+ align:start position:0%
+but if
+ 
+
+ align:start position:0%
+but if
+every one of these even the quantum
+
+ align:start position:0%
+every one of these even the quantum
+ 
+
+ align:start position:0%
+every one of these even the quantum
+mechanics is a poor approximation of
+
+ align:start position:0%
+mechanics is a poor approximation of
+ 
+
+ align:start position:0%
+mechanics is a poor approximation of
+electrodynamics and molecular mechanics
+
+ align:start position:0%
+electrodynamics and molecular mechanics
+ 
+
+ align:start position:0%
+electrodynamics and molecular mechanics
+has only spherical atoms represented
+
+ align:start position:0%
+has only spherical atoms represented
+ 
+
+ align:start position:0%
+has only spherical atoms represented
+some of the most challenging uh
+
+ align:start position:0%
+some of the most challenging uh
+ 
+
+ align:start position:0%
+some of the most challenging uh
+cell models involved master equation is
+
+ align:start position:0%
+cell models involved master equation is
+ 
+
+ align:start position:0%
+cell models involved master equation is
+stochastic now we're not talking about
+
+ align:start position:0%
+stochastic now we're not talking about
+ 
+
+ align:start position:0%
+stochastic now we're not talking about
+single atoms anymore we're talking about
+
+ align:start position:0%
+single atoms anymore we're talking about
+ 
+
+ align:start position:0%
+single atoms anymore we're talking about
+single molecules still it's too coarse
+
+ align:start position:0%
+single molecules still it's too coarse
+ 
+
+ align:start position:0%
+single molecules still it's too coarse
+for many uh experiments you can have
+
+ align:start position:0%
+for many uh experiments you can have
+ 
+
+ align:start position:0%
+for many uh experiments you can have
+phonological rates
+
+ align:start position:0%
+phonological rates
+ 
+
+ align:start position:0%
+phonological rates
+such as the ones we've been talking
+
+ align:start position:0%
+such as the ones we've been talking
+ 
+
+ align:start position:0%
+such as the ones we've been talking
+about represented ordinary differential
+
+ align:start position:0%
+about represented ordinary differential
+ 
+
+ align:start position:0%
+about represented ordinary differential
+equations how do you get the parameters
+
+ align:start position:0%
+equations how do you get the parameters
+ 
+
+ align:start position:0%
+equations how do you get the parameters
+that describe
+
+ align:start position:0%
+that describe
+ 
+
+ align:start position:0%
+that describe
+now concentration and time not single
+
+ align:start position:0%
+now concentration and time not single
+ 
+
+ align:start position:0%
+now concentration and time not single
+molecules but sort of
+
+ align:start position:0%
+molecules but sort of
+ 
+
+ align:start position:0%
+molecules but sort of
+treating the them as a bag of you know a
+
+ align:start position:0%
+treating the them as a bag of you know a
+ 
+
+ align:start position:0%
+treating the them as a bag of you know a
+particular part of the cell or the whole
+
+ align:start position:0%
+particular part of the cell or the whole
+ 
+
+ align:start position:0%
+particular part of the cell or the whole
+cell having a bigger concentration of
+
+ align:start position:0%
+cell having a bigger concentration of
+ 
+
+ align:start position:0%
+cell having a bigger concentration of
+molecules
+
+ align:start position:0%
+molecules
+ 
+
+ align:start position:0%
+molecules
+and then we'll go on as as we get into
+
+ align:start position:0%
+and then we'll go on as as we get into
+ 
+
+ align:start position:0%
+and then we'll go on as as we get into
+the network analysis in the next three
+
+ align:start position:0%
+the network analysis in the next three
+ 
+
+ align:start position:0%
+the network analysis in the next three
+lectures we'll talk about some of these
+
+ align:start position:0%
+lectures we'll talk about some of these
+ 
+
+ align:start position:0%
+lectures we'll talk about some of these
+other models
+
+ align:start position:0%
+other models
+ 
+
+ align:start position:0%
+other models
+which have their their rules let's just
+
+ align:start position:0%
+which have their their rules let's just
+ 
+
+ align:start position:0%
+which have their their rules let's just
+get it how would we get
+
+ align:start position:0%
+get it how would we get
+ 
+
+ align:start position:0%
+get it how would we get
+some of the parameters that describe
+
+ align:start position:0%
+some of the parameters that describe
+ 
+
+ align:start position:0%
+some of the parameters that describe
+concentration in time
+
+ align:start position:0%
+concentration in time
+ 
+
+ align:start position:0%
+concentration in time
+and when we talk about the formalism of
+
+ align:start position:0%
+and when we talk about the formalism of
+ 
+
+ align:start position:0%
+and when we talk about the formalism of
+these networks
+
+ align:start position:0%
+these networks
+ 
+
+ align:start position:0%
+these networks
+regulatory networks mainly are about
+
+ align:start position:0%
+regulatory networks mainly are about
+ 
+
+ align:start position:0%
+regulatory networks mainly are about
+binding
+
+ align:start position:0%
+binding
+ 
+
+ align:start position:0%
+binding
+but they intimately connect with
+
+ align:start position:0%
+but they intimately connect with
+ 
+
+ align:start position:0%
+but they intimately connect with
+catalytic networks where you not only
+
+ align:start position:0%
+catalytic networks where you not only
+ 
+
+ align:start position:0%
+catalytic networks where you not only
+bind but you actually change the
+
+ align:start position:0%
+bind but you actually change the
+ 
+
+ align:start position:0%
+bind but you actually change the
+covalent structure of molecules in the
+
+ align:start position:0%
+covalent structure of molecules in the
+ 
+
+ align:start position:0%
+covalent structure of molecules in the
+simplest such case
+
+ align:start position:0%
+simplest such case
+ 
+
+ align:start position:0%
+simplest such case
+single
+
+ align:start position:0%
+single
+ 
+
+ align:start position:0%
+single
+substrate going in single product coming
+
+ align:start position:0%
+substrate going in single product coming
+ 
+
+ align:start position:0%
+substrate going in single product coming
+out is at the top of of this
+
+ align:start position:0%
+out is at the top of of this
+ 
+
+ align:start position:0%
+out is at the top of of this
+slide number 60.
+
+ align:start position:0%
+slide number 60.
+ 
+
+ align:start position:0%
+slide number 60.
+and here you can see that the enzyme e
+
+ align:start position:0%
+and here you can see that the enzyme e
+ 
+
+ align:start position:0%
+and here you can see that the enzyme e
+is typically a protein and or but there
+
+ align:start position:0%
+is typically a protein and or but there
+ 
+
+ align:start position:0%
+is typically a protein and or but there
+are you know rna catalysts and so on um
+
+ align:start position:0%
+are you know rna catalysts and so on um
+ 
+
+ align:start position:0%
+are you know rna catalysts and so on um
+but the but the property that's
+
+ align:start position:0%
+but the but the property that's
+ 
+
+ align:start position:0%
+but the but the property that's
+that's emphasized here is that the
+
+ align:start position:0%
+that's emphasized here is that the
+ 
+
+ align:start position:0%
+that's emphasized here is that the
+enzyme is not consumed as a goes in
+
+ align:start position:0%
+enzyme is not consumed as a goes in
+ 
+
+ align:start position:0%
+enzyme is not consumed as a goes in
+it makes it a covalent change from ea to
+
+ align:start position:0%
+it makes it a covalent change from ea to
+ 
+
+ align:start position:0%
+it makes it a covalent change from ea to
+eb b is released e is recycled b is not
+
+ align:start position:0%
+eb b is released e is recycled b is not
+ 
+
+ align:start position:0%
+eb b is released e is recycled b is not
+consumed by the cycle but a is consumed
+
+ align:start position:0%
+consumed by the cycle but a is consumed
+ 
+
+ align:start position:0%
+consumed by the cycle but a is consumed
+b is produced
+
+ align:start position:0%
+b is produced
+ 
+
+ align:start position:0%
+b is produced
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+but let's look at it in a different
+
+ align:start position:0%
+but let's look at it in a different
+ 
+
+ align:start position:0%
+but let's look at it in a different
+light in a particularly interesting
+
+ align:start position:0%
+light in a particularly interesting
+ 
+
+ align:start position:0%
+light in a particularly interesting
+class of reactions for example those
+
+ align:start position:0%
+class of reactions for example those
+ 
+
+ align:start position:0%
+class of reactions for example those
+involving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+regulatory cascades signal transduction
+
+ align:start position:0%
+regulatory cascades signal transduction
+ 
+
+ align:start position:0%
+regulatory cascades signal transduction
+enzyme modifications
+
+ align:start position:0%
+enzyme modifications
+ 
+
+ align:start position:0%
+enzyme modifications
+here the enzyme now becomes substrate
+
+ align:start position:0%
+here the enzyme now becomes substrate
+ 
+
+ align:start position:0%
+here the enzyme now becomes substrate
+the atp is now no longer cons it
+
+ align:start position:0%
+the atp is now no longer cons it
+ 
+
+ align:start position:0%
+the atp is now no longer cons it
+consumed in the whole cycle atp comes in
+
+ align:start position:0%
+consumed in the whole cycle atp comes in
+ 
+
+ align:start position:0%
+consumed in the whole cycle atp comes in
+modifies the enzyme
+
+ align:start position:0%
+modifies the enzyme
+ 
+
+ align:start position:0%
+modifies the enzyme
+to a enzyme phosphoenzyme and the in a
+
+ align:start position:0%
+to a enzyme phosphoenzyme and the in a
+ 
+
+ align:start position:0%
+to a enzyme phosphoenzyme and the in a
+accompanying reaction regenerates the
+
+ align:start position:0%
+accompanying reaction regenerates the
+ 
+
+ align:start position:0%
+accompanying reaction regenerates the
+atp
+
+ align:start position:0%
+atp
+ 
+
+ align:start position:0%
+atp
+turns the adp back into atp so the atp
+
+ align:start position:0%
+turns the adp back into atp so the atp
+ 
+
+ align:start position:0%
+turns the adp back into atp so the atp
+in a certain sense is catalytic here and
+
+ align:start position:0%
+in a certain sense is catalytic here and
+ 
+
+ align:start position:0%
+in a certain sense is catalytic here and
+now the enzyme is not is consumed
+
+ align:start position:0%
+now the enzyme is not is consumed
+ 
+
+ align:start position:0%
+now the enzyme is not is consumed
+producing a fossil inside so it all
+
+ align:start position:0%
+producing a fossil inside so it all
+ 
+
+ align:start position:0%
+producing a fossil inside so it all
+depends on when you're starting
+
+ align:start position:0%
+depends on when you're starting
+ 
+
+ align:start position:0%
+depends on when you're starting
+constructing these these graphs what is
+
+ align:start position:0%
+constructing these these graphs what is
+ 
+
+ align:start position:0%
+constructing these these graphs what is
+the node whether the node is a
+
+ align:start position:0%
+the node whether the node is a
+ 
+
+ align:start position:0%
+the node whether the node is a
+substrated node as an enzyme depends on
+
+ align:start position:0%
+substrated node as an enzyme depends on
+ 
+
+ align:start position:0%
+substrated node as an enzyme depends on
+on on how you look at it
+
+ align:start position:0%
+on on how you look at it
+ 
+
+ align:start position:0%
+on on how you look at it
+and i do this
+
+ align:start position:0%
+and i do this
+ 
+
+ align:start position:0%
+and i do this
+you know somewhat provocatively so
+
+ align:start position:0%
+you know somewhat provocatively so
+ 
+
+ align:start position:0%
+you know somewhat provocatively so
+you'll think uh about these networks uh
+
+ align:start position:0%
+you'll think uh about these networks uh
+ 
+
+ align:start position:0%
+you'll think uh about these networks uh
+not just this binding but it's catalysis
+
+ align:start position:0%
+not just this binding but it's catalysis
+ 
+
+ align:start position:0%
+not just this binding but it's catalysis
+and not just the enzyme being the
+
+ align:start position:0%
+and not just the enzyme being the
+ 
+
+ align:start position:0%
+and not just the enzyme being the
+catalyst but sometimes the substrates as
+
+ align:start position:0%
+catalyst but sometimes the substrates as
+ 
+
+ align:start position:0%
+catalyst but sometimes the substrates as
+well now this is the simplest case
+
+ align:start position:0%
+well now this is the simplest case
+ 
+
+ align:start position:0%
+well now this is the simplest case
+of measuring kinetics this is not
+
+ align:start position:0%
+of measuring kinetics this is not
+ 
+
+ align:start position:0%
+of measuring kinetics this is not
+equilibrium this is kinetics
+
+ align:start position:0%
+equilibrium this is kinetics
+ 
+
+ align:start position:0%
+equilibrium this is kinetics
+and we're studying the this plot on the
+
+ align:start position:0%
+and we're studying the this plot on the
+ 
+
+ align:start position:0%
+and we're studying the this plot on the
+far left hand side of the fly 61. is as
+
+ align:start position:0%
+far left hand side of the fly 61. is as
+ 
+
+ align:start position:0%
+far left hand side of the fly 61. is as
+in substrate increases the rate of
+
+ align:start position:0%
+in substrate increases the rate of
+ 
+
+ align:start position:0%
+in substrate increases the rate of
+production of product increases
+
+ align:start position:0%
+production of product increases
+ 
+
+ align:start position:0%
+production of product increases
+you can you can start out with with zero
+
+ align:start position:0%
+you can you can start out with with zero
+ 
+
+ align:start position:0%
+you can you can start out with with zero
+product or
+
+ align:start position:0%
+product or
+ 
+
+ align:start position:0%
+product or
+small amounts and it used to be
+
+ align:start position:0%
+small amounts and it used to be
+ 
+
+ align:start position:0%
+small amounts and it used to be
+historically at the bottom
+
+ align:start position:0%
+historically at the bottom
+ 
+
+ align:start position:0%
+historically at the bottom
+you you would require to do the
+
+ align:start position:0%
+you you would require to do the
+ 
+
+ align:start position:0%
+you you would require to do the
+experiment you would require that the
+
+ align:start position:0%
+experiment you would require that the
+ 
+
+ align:start position:0%
+experiment you would require that the
+product be
+
+ align:start position:0%
+product be
+ 
+
+ align:start position:0%
+product be
+be as close to zero as possible you do
+
+ align:start position:0%
+be as close to zero as possible you do
+ 
+
+ align:start position:0%
+be as close to zero as possible you do
+initial rates
+
+ align:start position:0%
+initial rates
+ 
+
+ align:start position:0%
+initial rates
+and you have a simple relationship where
+
+ align:start position:0%
+and you have a simple relationship where
+ 
+
+ align:start position:0%
+and you have a simple relationship where
+the increase in product was a simple
+
+ align:start position:0%
+the increase in product was a simple
+ 
+
+ align:start position:0%
+the increase in product was a simple
+function of
+
+ align:start position:0%
+function of
+ 
+
+ align:start position:0%
+function of
+the one over uh one plus uh reciprocal
+
+ align:start position:0%
+the one over uh one plus uh reciprocal
+ 
+
+ align:start position:0%
+the one over uh one plus uh reciprocal
+of the substrate concentration
+
+ align:start position:0%
+of the substrate concentration
+ 
+
+ align:start position:0%
+of the substrate concentration
+and this as
+
+ align:start position:0%
+and this as
+ 
+
+ align:start position:0%
+and this as
+as the substrate would increase you'd
+
+ align:start position:0%
+as the substrate would increase you'd
+ 
+
+ align:start position:0%
+as the substrate would increase you'd
+eventually saturate the amount of enzyme
+
+ align:start position:0%
+eventually saturate the amount of enzyme
+ 
+
+ align:start position:0%
+eventually saturate the amount of enzyme
+that you have present in the experiment
+
+ align:start position:0%
+that you have present in the experiment
+ 
+
+ align:start position:0%
+that you have present in the experiment
+and that would be the the maximum
+
+ align:start position:0%
+and that would be the the maximum
+ 
+
+ align:start position:0%
+and that would be the the maximum
+velocity for that amount of enzyme or v
+
+ align:start position:0%
+velocity for that amount of enzyme or v
+ 
+
+ align:start position:0%
+velocity for that amount of enzyme or v
+max
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+however if you have a more full equation
+
+ align:start position:0%
+however if you have a more full equation
+ 
+
+ align:start position:0%
+however if you have a more full equation
+where you take into account all the
+
+ align:start position:0%
+where you take into account all the
+ 
+
+ align:start position:0%
+where you take into account all the
+players at least in the simplest system
+
+ align:start position:0%
+players at least in the simplest system
+ 
+
+ align:start position:0%
+players at least in the simplest system
+the the forward velocity dp dt the
+
+ align:start position:0%
+the the forward velocity dp dt the
+ 
+
+ align:start position:0%
+the the forward velocity dp dt the
+derivative of the product concentration
+
+ align:start position:0%
+derivative of the product concentration
+ 
+
+ align:start position:0%
+derivative of the product concentration
+uh as a subjective times might be in
+
+ align:start position:0%
+uh as a subjective times might be in
+ 
+
+ align:start position:0%
+uh as a subjective times might be in
+moles per liter
+
+ align:start position:0%
+moles per liter
+ 
+
+ align:start position:0%
+moles per liter
+it's going to go up with as the
+
+ align:start position:0%
+it's going to go up with as the
+ 
+
+ align:start position:0%
+it's going to go up with as the
+substrate goes up
+
+ align:start position:0%
+substrate goes up
+ 
+
+ align:start position:0%
+substrate goes up
+um more substrate means it'll go faster
+
+ align:start position:0%
+um more substrate means it'll go faster
+ 
+
+ align:start position:0%
+um more substrate means it'll go faster
+in the forward direction towards product
+
+ align:start position:0%
+in the forward direction towards product
+ 
+
+ align:start position:0%
+in the forward direction towards product
+but if you have some product you'll have
+
+ align:start position:0%
+but if you have some product you'll have
+ 
+
+ align:start position:0%
+but if you have some product you'll have
+some product inhibition you'll have a
+
+ align:start position:0%
+some product inhibition you'll have a
+ 
+
+ align:start position:0%
+some product inhibition you'll have a
+tendency to the the
+
+ align:start position:0%
+tendency to the the
+ 
+
+ align:start position:0%
+tendency to the the
+kinetics to go the opposite direction so
+
+ align:start position:0%
+kinetics to go the opposite direction so
+ 
+
+ align:start position:0%
+kinetics to go the opposite direction so
+this is negative as a negative component
+
+ align:start position:0%
+this is negative as a negative component
+ 
+
+ align:start position:0%
+this is negative as a negative component
+with product
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the ks and kp are sometimes called
+
+ align:start position:0%
+the ks and kp are sometimes called
+ 
+
+ align:start position:0%
+the ks and kp are sometimes called
+michaelis constants as the substrate
+
+ align:start position:0%
+michaelis constants as the substrate
+ 
+
+ align:start position:0%
+michaelis constants as the substrate
+gets closer to the michaelis constant uh
+
+ align:start position:0%
+gets closer to the michaelis constant uh
+ 
+
+ align:start position:0%
+gets closer to the michaelis constant uh
+this is basically related to the the
+
+ align:start position:0%
+this is basically related to the the
+ 
+
+ align:start position:0%
+this is basically related to the the
+binding affinity for the substrate and
+
+ align:start position:0%
+binding affinity for the substrate and
+ 
+
+ align:start position:0%
+binding affinity for the substrate and
+that's a natural sort of halfway point
+
+ align:start position:0%
+that's a natural sort of halfway point
+ 
+
+ align:start position:0%
+that's a natural sort of halfway point
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+where the substrate is half half
+
+ align:start position:0%
+where the substrate is half half
+ 
+
+ align:start position:0%
+where the substrate is half half
+saturating is
+
+ align:start position:0%
+saturating is
+ 
+
+ align:start position:0%
+saturating is
+roughly what the ks is all about
+
+ align:start position:0%
+roughly what the ks is all about
+ 
+
+ align:start position:0%
+roughly what the ks is all about
+now let's compare this very simple case
+
+ align:start position:0%
+now let's compare this very simple case
+ 
+
+ align:start position:0%
+now let's compare this very simple case
+we have one substrate producing one
+
+ align:start position:0%
+we have one substrate producing one
+ 
+
+ align:start position:0%
+we have one substrate producing one
+product to a more typical case where you
+
+ align:start position:0%
+product to a more typical case where you
+ 
+
+ align:start position:0%
+product to a more typical case where you
+might have two substrates producing two
+
+ align:start position:0%
+might have two substrates producing two
+ 
+
+ align:start position:0%
+might have two substrates producing two
+products
+
+ align:start position:0%
+products
+ 
+
+ align:start position:0%
+products
+and let's take this out of a real
+
+ align:start position:0%
+and let's take this out of a real
+ 
+
+ align:start position:0%
+and let's take this out of a real
+network we're going to show this real
+
+ align:start position:0%
+network we're going to show this real
+ 
+
+ align:start position:0%
+network we're going to show this real
+network in just a moment and it's all
+
+ align:start position:0%
+network in just a moment and it's all
+ 
+
+ align:start position:0%
+network in just a moment and it's all
+slurry um here you have
+
+ align:start position:0%
+slurry um here you have
+ 
+
+ align:start position:0%
+slurry um here you have
+uh two substrates atp and f6p going to
+
+ align:start position:0%
+uh two substrates atp and f6p going to
+ 
+
+ align:start position:0%
+uh two substrates atp and f6p going to
+two products adp and fdp
+
+ align:start position:0%
+two products adp and fdp
+ 
+
+ align:start position:0%
+two products adp and fdp
+and you've got this this same sort of
+
+ align:start position:0%
+and you've got this this same sort of
+ 
+
+ align:start position:0%
+and you've got this this same sort of
+form where you have a velocity of
+
+ align:start position:0%
+form where you have a velocity of
+ 
+
+ align:start position:0%
+form where you have a velocity of
+produce
+
+ align:start position:0%
+produce
+ 
+
+ align:start position:0%
+produce
+of this reaction
+
+ align:start position:0%
+of this reaction
+ 
+
+ align:start position:0%
+of this reaction
+and it's a function of the reactants f6p
+
+ align:start position:0%
+and it's a function of the reactants f6p
+ 
+
+ align:start position:0%
+and it's a function of the reactants f6p
+and atp
+
+ align:start position:0%
+and atp
+ 
+
+ align:start position:0%
+and atp
+and they you find them in the numerator
+
+ align:start position:0%
+and they you find them in the numerator
+ 
+
+ align:start position:0%
+and they you find them in the numerator
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and you find these michaelis continents
+
+ align:start position:0%
+and you find these michaelis continents
+ 
+
+ align:start position:0%
+and you find these michaelis continents
+in the in the right places
+
+ align:start position:0%
+in the in the right places
+ 
+
+ align:start position:0%
+in the in the right places
+but in addition you find in the
+
+ align:start position:0%
+but in addition you find in the
+ 
+
+ align:start position:0%
+but in addition you find in the
+denominator this curious term that has
+
+ align:start position:0%
+denominator this curious term that has
+ 
+
+ align:start position:0%
+denominator this curious term that has
+these fourth powers we didn't see any
+
+ align:start position:0%
+these fourth powers we didn't see any
+ 
+
+ align:start position:0%
+these fourth powers we didn't see any
+fourth powers in the previous slide
+
+ align:start position:0%
+fourth powers in the previous slide
+ 
+
+ align:start position:0%
+fourth powers in the previous slide
+um why are we getting fourth powers is
+
+ align:start position:0%
+um why are we getting fourth powers is
+ 
+
+ align:start position:0%
+um why are we getting fourth powers is
+because and and and why is amp end here
+
+ align:start position:0%
+because and and and why is amp end here
+ 
+
+ align:start position:0%
+because and and and why is amp end here
+uh it's not even one of the reactions or
+
+ align:start position:0%
+uh it's not even one of the reactions or
+ 
+
+ align:start position:0%
+uh it's not even one of the reactions or
+the products what's going on well this
+
+ align:start position:0%
+the products what's going on well this
+ 
+
+ align:start position:0%
+the products what's going on well this
+is actually a regulatory phenomenon
+
+ align:start position:0%
+is actually a regulatory phenomenon
+ 
+
+ align:start position:0%
+is actually a regulatory phenomenon
+allosteric where you have a second site
+
+ align:start position:0%
+allosteric where you have a second site
+ 
+
+ align:start position:0%
+allosteric where you have a second site
+on the enzyme one side does the
+
+ align:start position:0%
+on the enzyme one side does the
+ 
+
+ align:start position:0%
+on the enzyme one side does the
+catalytic magic and the other one is
+
+ align:start position:0%
+catalytic magic and the other one is
+ 
+
+ align:start position:0%
+catalytic magic and the other one is
+regulated by some for for in the
+
+ align:start position:0%
+regulated by some for for in the
+ 
+
+ align:start position:0%
+regulated by some for for in the
+infinite wisdom of the whole network
+
+ align:start position:0%
+infinite wisdom of the whole network
+ 
+
+ align:start position:0%
+infinite wisdom of the whole network
+is an important feedback so amp is
+
+ align:start position:0%
+is an important feedback so amp is
+ 
+
+ align:start position:0%
+is an important feedback so amp is
+related to adp as a further step and it
+
+ align:start position:0%
+related to adp as a further step and it
+ 
+
+ align:start position:0%
+related to adp as a further step and it
+feeds back on this enzyme as does f6p
+
+ align:start position:0%
+feeds back on this enzyme as does f6p
+ 
+
+ align:start position:0%
+feeds back on this enzyme as does f6p
+and app and so forth so all these and
+
+ align:start position:0%
+and app and so forth so all these and
+ 
+
+ align:start position:0%
+and app and so forth so all these and
+this fourth power just says you want it
+
+ align:start position:0%
+this fourth power just says you want it
+ 
+
+ align:start position:0%
+this fourth power just says you want it
+to be cooperative you want to have a a
+
+ align:start position:0%
+to be cooperative you want to have a a
+ 
+
+ align:start position:0%
+to be cooperative you want to have a a
+non-linear regulation so that's what's
+
+ align:start position:0%
+non-linear regulation so that's what's
+ 
+
+ align:start position:0%
+non-linear regulation so that's what's
+going on in this term and it doesn't
+
+ align:start position:0%
+going on in this term and it doesn't
+ 
+
+ align:start position:0%
+going on in this term and it doesn't
+occur in the whole network we'll show in
+
+ align:start position:0%
+occur in the whole network we'll show in
+ 
+
+ align:start position:0%
+occur in the whole network we'll show in
+the next slide but it does occur at some
+
+ align:start position:0%
+the next slide but it does occur at some
+ 
+
+ align:start position:0%
+the next slide but it does occur at some
+key points like this one where the
+
+ align:start position:0%
+key points like this one where the
+ 
+
+ align:start position:0%
+key points like this one where the
+enzyme has two sites catalytic and
+
+ align:start position:0%
+enzyme has two sites catalytic and
+ 
+
+ align:start position:0%
+enzyme has two sites catalytic and
+regulatory and when you see these terms
+
+ align:start position:0%
+regulatory and when you see these terms
+ 
+
+ align:start position:0%
+regulatory and when you see these terms
+that are greater than linear like fourth
+
+ align:start position:0%
+that are greater than linear like fourth
+ 
+
+ align:start position:0%
+that are greater than linear like fourth
+power that's sometimes referred to the
+
+ align:start position:0%
+power that's sometimes referred to the
+ 
+
+ align:start position:0%
+power that's sometimes referred to the
+hill coefficient and refers to the kind
+
+ align:start position:0%
+hill coefficient and refers to the kind
+ 
+
+ align:start position:0%
+hill coefficient and refers to the kind
+of the steepness of the of the instead
+
+ align:start position:0%
+of the steepness of the of the instead
+ 
+
+ align:start position:0%
+of the steepness of the of the instead
+of having this kind of curve you have
+
+ align:start position:0%
+of having this kind of curve you have
+ 
+
+ align:start position:0%
+of having this kind of curve you have
+this kind of sigmoid curve and the
+
+ align:start position:0%
+this kind of sigmoid curve and the
+ 
+
+ align:start position:0%
+this kind of sigmoid curve and the
+steepness of that is related to that
+
+ align:start position:0%
+steepness of that is related to that
+ 
+
+ align:start position:0%
+steepness of that is related to that
+power
+
+ align:start position:0%
+power
+ 
+
+ align:start position:0%
+power
+now let's look if you compare
+
+ align:start position:0%
+now let's look if you compare
+ 
+
+ align:start position:0%
+now let's look if you compare
+so this little piece this
+
+ align:start position:0%
+so this little piece this
+ 
+
+ align:start position:0%
+so this little piece this
+phosphofructokinase step
+
+ align:start position:0%
+phosphofructokinase step
+ 
+
+ align:start position:0%
+phosphofructokinase step
+is going to be
+
+ align:start position:0%
+is going to be
+ 
+
+ align:start position:0%
+is going to be
+put in context of the entire network in
+
+ align:start position:0%
+put in context of the entire network in
+ 
+
+ align:start position:0%
+put in context of the entire network in
+the red blood cell human red blood cell
+
+ align:start position:0%
+the red blood cell human red blood cell
+ 
+
+ align:start position:0%
+the red blood cell human red blood cell
+right here in the upper left quadrant of
+
+ align:start position:0%
+right here in the upper left quadrant of
+ 
+
+ align:start position:0%
+right here in the upper left quadrant of
+this circle
+
+ align:start position:0%
+this circle
+ 
+
+ align:start position:0%
+this circle
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this is the simplest so that was
+
+ align:start position:0%
+this is the simplest so that was
+ 
+
+ align:start position:0%
+this is the simplest so that was
+this is the simplest metabolic network
+
+ align:start position:0%
+this is the simplest metabolic network
+ 
+
+ align:start position:0%
+this is the simplest metabolic network
+that you'll be talking about this mostly
+
+ align:start position:0%
+that you'll be talking about this mostly
+ 
+
+ align:start position:0%
+that you'll be talking about this mostly
+involves covalent uh
+
+ align:start position:0%
+involves covalent uh
+ 
+
+ align:start position:0%
+involves covalent uh
+transitions or pumping across membranes
+
+ align:start position:0%
+transitions or pumping across membranes
+ 
+
+ align:start position:0%
+transitions or pumping across membranes
+it treats the whole cell as a kind of a
+
+ align:start position:0%
+it treats the whole cell as a kind of a
+ 
+
+ align:start position:0%
+it treats the whole cell as a kind of a
+uniform bag except with a membrane being
+
+ align:start position:0%
+uniform bag except with a membrane being
+ 
+
+ align:start position:0%
+uniform bag except with a membrane being
+a separate compartment and they're
+
+ align:start position:0%
+a separate compartment and they're
+ 
+
+ align:start position:0%
+a separate compartment and they're
+really two objectives of this one is to
+
+ align:start position:0%
+really two objectives of this one is to
+ 
+
+ align:start position:0%
+really two objectives of this one is to
+produce atp
+
+ align:start position:0%
+produce atp
+ 
+
+ align:start position:0%
+produce atp
+so that you can run the pumps to keep
+
+ align:start position:0%
+so that you can run the pumps to keep
+ 
+
+ align:start position:0%
+so that you can run the pumps to keep
+the osmotic pressure constant across the
+
+ align:start position:0%
+the osmotic pressure constant across the
+ 
+
+ align:start position:0%
+the osmotic pressure constant across the
+red blood cell membrane so that it
+
+ align:start position:0%
+red blood cell membrane so that it
+ 
+
+ align:start position:0%
+red blood cell membrane so that it
+maintains its shape
+
+ align:start position:0%
+maintains its shape
+ 
+
+ align:start position:0%
+maintains its shape
+and the other is to maintain the redox
+
+ align:start position:0%
+and the other is to maintain the redox
+ 
+
+ align:start position:0%
+and the other is to maintain the redox
+at the right level so as if so you have
+
+ align:start position:0%
+at the right level so as if so you have
+ 
+
+ align:start position:0%
+at the right level so as if so you have
+a reducing atmosphere uh reducing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the hemoglobin hemoglobin
+
+ align:start position:0%
+the hemoglobin hemoglobin
+ 
+
+ align:start position:0%
+the hemoglobin hemoglobin
+is an intimate contact with oxygen and
+
+ align:start position:0%
+is an intimate contact with oxygen and
+ 
+
+ align:start position:0%
+is an intimate contact with oxygen and
+so there is a certain low level of of
+
+ align:start position:0%
+so there is a certain low level of of
+ 
+
+ align:start position:0%
+so there is a certain low level of of
+oxidation of the iron rather than just
+
+ align:start position:0%
+oxidation of the iron rather than just
+ 
+
+ align:start position:0%
+oxidation of the iron rather than just
+binding to the iron to make
+
+ align:start position:0%
+binding to the iron to make
+ 
+
+ align:start position:0%
+binding to the iron to make
+methemoglobin which is not a good
+
+ align:start position:0%
+methemoglobin which is not a good
+ 
+
+ align:start position:0%
+methemoglobin which is not a good
+physiological state so you want to have
+
+ align:start position:0%
+physiological state so you want to have
+ 
+
+ align:start position:0%
+physiological state so you want to have
+this reducing potential to get it back
+
+ align:start position:0%
+this reducing potential to get it back
+ 
+
+ align:start position:0%
+this reducing potential to get it back
+to the correct oxidation state so it
+
+ align:start position:0%
+to the correct oxidation state so it
+ 
+
+ align:start position:0%
+to the correct oxidation state so it
+will bind oxygen
+
+ align:start position:0%
+will bind oxygen
+ 
+
+ align:start position:0%
+will bind oxygen
+so you have a little bit of purine
+
+ align:start position:0%
+so you have a little bit of purine
+ 
+
+ align:start position:0%
+so you have a little bit of purine
+metabolism here
+
+ align:start position:0%
+metabolism here
+ 
+
+ align:start position:0%
+metabolism here
+quite a bit of metabolism simple
+
+ align:start position:0%
+quite a bit of metabolism simple
+ 
+
+ align:start position:0%
+quite a bit of metabolism simple
+glycolysis
+
+ align:start position:0%
+glycolysis
+ 
+
+ align:start position:0%
+glycolysis
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+oxidative phosphorylation it's just
+
+ align:start position:0%
+oxidative phosphorylation it's just
+ 
+
+ align:start position:0%
+oxidative phosphorylation it's just
+because glycolysis produce reducing
+
+ align:start position:0%
+because glycolysis produce reducing
+ 
+
+ align:start position:0%
+because glycolysis produce reducing
+potential and little atp
+
+ align:start position:0%
+potential and little atp
+ 
+
+ align:start position:0%
+potential and little atp
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+these 40 or so enzymatic reactions can
+
+ align:start position:0%
+these 40 or so enzymatic reactions can
+ 
+
+ align:start position:0%
+these 40 or so enzymatic reactions can
+be modeled with about 200 parameters all
+
+ align:start position:0%
+be modeled with about 200 parameters all
+ 
+
+ align:start position:0%
+be modeled with about 200 parameters all
+these 200 parameters have been measured
+
+ align:start position:0%
+these 200 parameters have been measured
+ 
+
+ align:start position:0%
+these 200 parameters have been measured
+accurately by purifying each of the
+
+ align:start position:0%
+accurately by purifying each of the
+ 
+
+ align:start position:0%
+accurately by purifying each of the
+metabolites and enzymes and this has
+
+ align:start position:0%
+metabolites and enzymes and this has
+ 
+
+ align:start position:0%
+metabolites and enzymes and this has
+been reduced to it ordinary differential
+
+ align:start position:0%
+been reduced to it ordinary differential
+ 
+
+ align:start position:0%
+been reduced to it ordinary differential
+equation model that has been evolving
+
+ align:start position:0%
+equation model that has been evolving
+ 
+
+ align:start position:0%
+equation model that has been evolving
+since the 70s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you if we look up
+
+ align:start position:0%
+if you if we look up
+ 
+
+ align:start position:0%
+if you if we look up
+at the slide 64 at this
+
+ align:start position:0%
+at the slide 64 at this
+ 
+
+ align:start position:0%
+at the slide 64 at this
+phosphofructokinase
+
+ align:start position:0%
+phosphofructokinase
+ 
+
+ align:start position:0%
+phosphofructokinase
+we have the same form that we had a
+
+ align:start position:0%
+we have the same form that we had a
+ 
+
+ align:start position:0%
+we have the same form that we had a
+couple of slides back here's the fourth
+
+ align:start position:0%
+couple of slides back here's the fourth
+ 
+
+ align:start position:0%
+couple of slides back here's the fourth
+power term in the denominator having atp
+
+ align:start position:0%
+power term in the denominator having atp
+ 
+
+ align:start position:0%
+power term in the denominator having atp
+mt as a regulatory molecule and then you
+
+ align:start position:0%
+mt as a regulatory molecule and then you
+ 
+
+ align:start position:0%
+mt as a regulatory molecule and then you
+have the michaelis constants and so
+
+ align:start position:0%
+have the michaelis constants and so
+ 
+
+ align:start position:0%
+have the michaelis constants and so
+forth explicitly stated here
+
+ align:start position:0%
+forth explicitly stated here
+ 
+
+ align:start position:0%
+forth explicitly stated here
+in the numerator for the uh
+
+ align:start position:0%
+in the numerator for the uh
+ 
+
+ align:start position:0%
+in the numerator for the uh
+for the substrates f6p and atp
+
+ align:start position:0%
+for the substrates f6p and atp
+ 
+
+ align:start position:0%
+for the substrates f6p and atp
+and with
+
+ align:start position:0%
+and with
+ 
+
+ align:start position:0%
+and with
+and you have a similar equation for
+
+ align:start position:0%
+and you have a similar equation for
+ 
+
+ align:start position:0%
+and you have a similar equation for
+every single enzyme step in this and
+
+ align:start position:0%
+every single enzyme step in this and
+ 
+
+ align:start position:0%
+every single enzyme step in this and
+that whole network of the red blood cell
+
+ align:start position:0%
+that whole network of the red blood cell
+ 
+
+ align:start position:0%
+that whole network of the red blood cell
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+and uh in green are the are the
+
+ align:start position:0%
+and uh in green are the are the
+ 
+
+ align:start position:0%
+and uh in green are the are the
+concentrations
+
+ align:start position:0%
+concentrations
+ 
+
+ align:start position:0%
+concentrations
+at any given time point is going to be
+
+ align:start position:0%
+at any given time point is going to be
+ 
+
+ align:start position:0%
+at any given time point is going to be
+their dynamic or steady state any given
+
+ align:start position:0%
+their dynamic or steady state any given
+ 
+
+ align:start position:0%
+their dynamic or steady state any given
+time point you'll have a green green for
+
+ align:start position:0%
+time point you'll have a green green for
+ 
+
+ align:start position:0%
+time point you'll have a green green for
+the metabolic concentrations and red for
+
+ align:start position:0%
+the metabolic concentrations and red for
+ 
+
+ align:start position:0%
+the metabolic concentrations and red for
+the fluxes uh indicated by the enzyme
+
+ align:start position:0%
+the fluxes uh indicated by the enzyme
+ 
+
+ align:start position:0%
+the fluxes uh indicated by the enzyme
+names and you can run this as a
+
+ align:start position:0%
+names and you can run this as a
+ 
+
+ align:start position:0%
+names and you can run this as a
+simulation for the red blood cell
+
+ align:start position:0%
+simulation for the red blood cell
+ 
+
+ align:start position:0%
+simulation for the red blood cell
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and see
+
+ align:start position:0%
+and see
+ 
+
+ align:start position:0%
+and see
+all the interesting questions about
+
+ align:start position:0%
+all the interesting questions about
+ 
+
+ align:start position:0%
+all the interesting questions about
+robustness and uh
+
+ align:start position:0%
+robustness and uh
+ 
+
+ align:start position:0%
+robustness and uh
+and optimality and so forth this is this
+
+ align:start position:0%
+and optimality and so forth this is this
+ 
+
+ align:start position:0%
+and optimality and so forth this is this
+is even though this is a very mature
+
+ align:start position:0%
+is even though this is a very mature
+ 
+
+ align:start position:0%
+is even though this is a very mature
+model there still is lots to be done
+
+ align:start position:0%
+model there still is lots to be done
+ 
+
+ align:start position:0%
+model there still is lots to be done
+even in this very simplest system now
+
+ align:start position:0%
+even in this very simplest system now
+ 
+
+ align:start position:0%
+even in this very simplest system now
+we're gonna go on to more complicated
+
+ align:start position:0%
+we're gonna go on to more complicated
+ 
+
+ align:start position:0%
+we're gonna go on to more complicated
+systems in the next three lectures on
+
+ align:start position:0%
+systems in the next three lectures on
+ 
+
+ align:start position:0%
+systems in the next three lectures on
+networks
+
+ align:start position:0%
+networks
+ 
+
+ align:start position:0%
+networks
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but for today we've basically tried to
+
+ align:start position:0%
+but for today we've basically tried to
+ 
+
+ align:start position:0%
+but for today we've basically tried to
+integrate the protein either absolute
+
+ align:start position:0%
+integrate the protein either absolute
+ 
+
+ align:start position:0%
+integrate the protein either absolute
+ratios with rna measurements and with
+
+ align:start position:0%
+ratios with rna measurements and with
+ 
+
+ align:start position:0%
+ratios with rna measurements and with
+metabolite interactions proteins
+
+ align:start position:0%
+metabolite interactions proteins
+ 
+
+ align:start position:0%
+metabolite interactions proteins
+post-synthetic modifications
+
+ align:start position:0%
+post-synthetic modifications
+ 
+
+ align:start position:0%
+post-synthetic modifications
+so until next time thank you very much
\ No newline at end of file
diff --git a/b5H8D_wD2AY.txt b/b5H8D_wD2AY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b18acd7720f58e50662f3256edfd1877261faf54
--- /dev/null
+++ b/b5H8D_wD2AY.txt
@@ -0,0 +1,10075 @@
+align:start position:0%
+ 
+all right let's uh let's start um so
+
+ align:start position:0%
+all right let's uh let's start um so
+ 
+
+ align:start position:0%
+all right let's uh let's start um so
+today I want to talk about uh interest
+
+ align:start position:0%
+today I want to talk about uh interest
+ 
+
+ align:start position:0%
+today I want to talk about uh interest
+rates uh you know if you have followed
+
+ align:start position:0%
+rates uh you know if you have followed
+ 
+
+ align:start position:0%
+rates uh you know if you have followed
+the news there's a lot of debate on
+
+ align:start position:0%
+the news there's a lot of debate on
+ 
+
+ align:start position:0%
+the news there's a lot of debate on
+these days on on on where will the
+
+ align:start position:0%
+these days on on on where will the
+ 
+
+ align:start position:0%
+these days on on on where will the
+interest rate in the US end at the end
+
+ align:start position:0%
+interest rate in the US end at the end
+ 
+
+ align:start position:0%
+interest rate in the US end at the end
+of this Titan tiing tightening
+
+ align:start position:0%
+of this Titan tiing tightening
+ 
+
+ align:start position:0%
+of this Titan tiing tightening
+cycle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and um so I'll show you there has
+
+ align:start position:0%
+uh and um so I'll show you there has
+ 
+
+ align:start position:0%
+uh and um so I'll show you there has
+been a very aggressive monetary policy
+
+ align:start position:0%
+been a very aggressive monetary policy
+ 
+
+ align:start position:0%
+been a very aggressive monetary policy
+trying to fight the inflationary episode
+
+ align:start position:0%
+trying to fight the inflationary episode
+ 
+
+ align:start position:0%
+trying to fight the inflationary episode
+we're going through uh and that's done
+
+ align:start position:0%
+we're going through uh and that's done
+ 
+
+ align:start position:0%
+we're going through uh and that's done
+through interest rates and and the
+
+ align:start position:0%
+through interest rates and and the
+ 
+
+ align:start position:0%
+through interest rates and and the
+question that I want to address today is
+
+ align:start position:0%
+question that I want to address today is
+ 
+
+ align:start position:0%
+question that I want to address today is
+H well how is it that the interest rate
+
+ align:start position:0%
+H well how is it that the interest rate
+ 
+
+ align:start position:0%
+H well how is it that the interest rate
+is determined so when a central bank
+
+ align:start position:0%
+is determined so when a central bank
+ 
+
+ align:start position:0%
+is determined so when a central bank
+decides to hike interest rates how do
+
+ align:start position:0%
+decides to hike interest rates how do
+ 
+
+ align:start position:0%
+decides to hike interest rates how do
+they do that okay and obviously this is
+
+ align:start position:0%
+they do that okay and obviously this is
+ 
+
+ align:start position:0%
+they do that okay and obviously this is
+about financial markets interest rate
+
+ align:start position:0%
+about financial markets interest rate
+ 
+
+ align:start position:0%
+about financial markets interest rate
+are set in financial markets and
+
+ align:start position:0%
+are set in financial markets and
+ 
+
+ align:start position:0%
+are set in financial markets and
+financial markets are very very
+
+ align:start position:0%
+financial markets are very very
+ 
+
+ align:start position:0%
+financial markets are very very
+complicated so we're going to keep it
+
+ align:start position:0%
+complicated so we're going to keep it
+ 
+
+ align:start position:0%
+complicated so we're going to keep it
+very very simple we're want to make
+
+ align:start position:0%
+very very simple we're want to make
+ 
+
+ align:start position:0%
+very very simple we're want to make
+introduce more complexity later on in
+
+ align:start position:0%
+introduce more complexity later on in
+ 
+
+ align:start position:0%
+introduce more complexity later on in
+the course but still we're going to keep
+
+ align:start position:0%
+the course but still we're going to keep
+ 
+
+ align:start position:0%
+the course but still we're going to keep
+it pretty simple because our main
+
+ align:start position:0%
+it pretty simple because our main
+ 
+
+ align:start position:0%
+it pretty simple because our main
+objective in studying Financial Market
+
+ align:start position:0%
+objective in studying Financial Market
+ 
+
+ align:start position:0%
+objective in studying Financial Market
+is really a a to to re to achieve some
+
+ align:start position:0%
+is really a a to to re to achieve some
+ 
+
+ align:start position:0%
+is really a a to to re to achieve some
+sort of understanding of how the
+
+ align:start position:0%
+sort of understanding of how the
+ 
+
+ align:start position:0%
+sort of understanding of how the
+interest rate policy that the Central
+
+ align:start position:0%
+interest rate policy that the Central
+ 
+
+ align:start position:0%
+interest rate policy that the Central
+Bank H controls is is
+
+ align:start position:0%
+Bank H controls is is
+ 
+
+ align:start position:0%
+Bank H controls is is
+determined so before
+
+ align:start position:0%
+determined so before
+ 
+
+ align:start position:0%
+determined so before
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+I I get into specifics so let's let's
+
+ align:start position:0%
+I I get into specifics so let's let's
+ 
+
+ align:start position:0%
+I I get into specifics so let's let's
+see some trivia here who knows who that
+
+ align:start position:0%
+see some trivia here who knows who that
+ 
+
+ align:start position:0%
+see some trivia here who knows who that
+person is
+
+ align:start position:0%
+person is
+ 
+
+ align:start position:0%
+person is
+okay you
+
+ align:start position:0%
+okay you
+ 
+
+ align:start position:0%
+okay you
+Geron Powell exactly and who's Jeron
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Powell the chair of the Federal Reserve
+
+ align:start position:0%
+Powell the chair of the Federal Reserve
+ 
+
+ align:start position:0%
+Powell the chair of the Federal Reserve
+uh system in the US which is the Central
+
+ align:start position:0%
+uh system in the US which is the Central
+ 
+
+ align:start position:0%
+uh system in the US which is the Central
+Bank of the US okay so that's that was
+
+ align:start position:0%
+Bank of the US okay so that's that was
+ 
+
+ align:start position:0%
+Bank of the US okay so that's that was
+an easy one and and every you know if
+
+ align:start position:0%
+an easy one and and every you know if
+ 
+
+ align:start position:0%
+an easy one and and every you know if
+you are into financial markets everyone
+
+ align:start position:0%
+you are into financial markets everyone
+ 
+
+ align:start position:0%
+you are into financial markets everyone
+is worried about what this guy is
+
+ align:start position:0%
+is worried about what this guy is
+ 
+
+ align:start position:0%
+is worried about what this guy is
+thinking and his friends are thinking at
+
+ align:start position:0%
+thinking and his friends are thinking at
+ 
+
+ align:start position:0%
+thinking and his friends are thinking at
+this moment because they determine the
+
+ align:start position:0%
+this moment because they determine the
+ 
+
+ align:start position:0%
+this moment because they determine the
+interest rate how do they do that well
+
+ align:start position:0%
+interest rate how do they do that well
+ 
+
+ align:start position:0%
+interest rate how do they do that well
+that's what we're going to talk about
+
+ align:start position:0%
+that's what we're going to talk about
+ 
+
+ align:start position:0%
+that's what we're going to talk about
+later on a little speaker who is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this no no that's that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cheating katsu WEA he is the next ER
+
+ align:start position:0%
+cheating katsu WEA he is the next ER
+ 
+
+ align:start position:0%
+cheating katsu WEA he is the next ER
+president of the bank of Japan the
+
+ align:start position:0%
+president of the bank of Japan the
+ 
+
+ align:start position:0%
+president of the bank of Japan the
+Central Bank of Japan and an interesting
+
+ align:start position:0%
+Central Bank of Japan and an interesting
+ 
+
+ align:start position:0%
+Central Bank of Japan and an interesting
+there are many interesting things of him
+
+ align:start position:0%
+there are many interesting things of him
+ 
+
+ align:start position:0%
+there are many interesting things of him
+but about him but he's a he's a graduate
+
+ align:start position:0%
+but about him but he's a he's a graduate
+ 
+
+ align:start position:0%
+but about him but he's a he's a graduate
+from our program the PHD
+
+ align:start position:0%
+from our program the PHD
+ 
+
+ align:start position:0%
+from our program the PHD
+program which actually is an incredibly
+
+ align:start position:0%
+program which actually is an incredibly
+ 
+
+ align:start position:0%
+program which actually is an incredibly
+successful program at producing major
+
+ align:start position:0%
+successful program at producing major
+ 
+
+ align:start position:0%
+successful program at producing major
+Central Bankers Ben Bernan is our Alum
+
+ align:start position:0%
+Central Bankers Ben Bernan is our Alum
+ 
+
+ align:start position:0%
+Central Bankers Ben Bernan is our Alum
+Alum that he was
+
+ align:start position:0%
+Alum that he was
+ 
+
+ align:start position:0%
+Alum that he was
+the the chairman of the Central Bank the
+
+ align:start position:0%
+the the chairman of the Central Bank the
+ 
+
+ align:start position:0%
+the the chairman of the Central Bank the
+chair of the Central Bank of the FED
+
+ align:start position:0%
+chair of the Central Bank of the FED
+ 
+
+ align:start position:0%
+chair of the Central Bank of the FED
+during the financial crisis Mario dragi
+
+ align:start position:0%
+during the financial crisis Mario dragi
+ 
+
+ align:start position:0%
+during the financial crisis Mario dragi
+is a one of our graduates Mario dragi
+
+ align:start position:0%
+is a one of our graduates Mario dragi
+ 
+
+ align:start position:0%
+is a one of our graduates Mario dragi
+was the the most successful ER Central
+
+ align:start position:0%
+was the the most successful ER Central
+ 
+
+ align:start position:0%
+was the the most successful ER Central
+Banker in Europe he was the president of
+
+ align:start position:0%
+Banker in Europe he was the president of
+ 
+
+ align:start position:0%
+Banker in Europe he was the president of
+the ECB European Central Bank for many
+
+ align:start position:0%
+the ECB European Central Bank for many
+ 
+
+ align:start position:0%
+the ECB European Central Bank for many
+years and in particular during the
+
+ align:start position:0%
+years and in particular during the
+ 
+
+ align:start position:0%
+years and in particular during the
+Global Financial crisis and the European
+
+ align:start position:0%
+Global Financial crisis and the European
+ 
+
+ align:start position:0%
+Global Financial crisis and the European
+crisis which followed the global
+
+ align:start position:0%
+crisis which followed the global
+ 
+
+ align:start position:0%
+crisis which followed the global
+financial
+
+ align:start position:0%
+financial
+ 
+
+ align:start position:0%
+financial
+crisis uh I mean but you name it Stan
+
+ align:start position:0%
+crisis uh I mean but you name it Stan
+ 
+
+ align:start position:0%
+crisis uh I mean but you name it Stan
+Fisher in the past of the Bank of Israel
+
+ align:start position:0%
+Fisher in the past of the Bank of Israel
+ 
+
+ align:start position:0%
+Fisher in the past of the Bank of Israel
+and nowadays feel low of the the chair
+
+ align:start position:0%
+and nowadays feel low of the the chair
+ 
+
+ align:start position:0%
+and nowadays feel low of the the chair
+of the Reserve Bank of Australia in
+
+ align:start position:0%
+of the Reserve Bank of Australia in
+ 
+
+ align:start position:0%
+of the Reserve Bank of Australia in
+Chile we have had two or three er
+
+ align:start position:0%
+Chile we have had two or three er
+ 
+
+ align:start position:0%
+Chile we have had two or three er
+presents and so on so if you if this is
+
+ align:start position:0%
+presents and so on so if you if this is
+ 
+
+ align:start position:0%
+presents and so on so if you if this is
+your career this is a good program you
+
+ align:start position:0%
+your career this is a good program you
+ 
+
+ align:start position:0%
+your career this is a good program you
+should join our program you may end up
+
+ align:start position:0%
+should join our program you may end up
+ 
+
+ align:start position:0%
+should join our program you may end up
+in a in a good place but that's the the
+
+ align:start position:0%
+in a in a good place but that's the the
+ 
+
+ align:start position:0%
+in a in a good place but that's the the
+next one for Japan
+
+ align:start position:0%
+next one for Japan
+ 
+
+ align:start position:0%
+next one for Japan
+and and Japan is a very interesting
+
+ align:start position:0%
+and and Japan is a very interesting
+ 
+
+ align:start position:0%
+and and Japan is a very interesting
+place from the point of view of monetary
+
+ align:start position:0%
+place from the point of view of monetary
+ 
+
+ align:start position:0%
+place from the point of view of monetary
+policy precisely because they they
+
+ align:start position:0%
+policy precisely because they they
+ 
+
+ align:start position:0%
+policy precisely because they they
+haven't had much space to do
+
+ align:start position:0%
+haven't had much space to do
+ 
+
+ align:start position:0%
+haven't had much space to do
+conventional monetary policy so they
+
+ align:start position:0%
+conventional monetary policy so they
+ 
+
+ align:start position:0%
+conventional monetary policy so they
+have had to do lots of unconventional
+
+ align:start position:0%
+have had to do lots of unconventional
+ 
+
+ align:start position:0%
+have had to do lots of unconventional
+things from the point of view of what a
+
+ align:start position:0%
+things from the point of view of what a
+ 
+
+ align:start position:0%
+things from the point of view of what a
+central bank typically does but today
+
+ align:start position:0%
+central bank typically does but today
+ 
+
+ align:start position:0%
+central bank typically does but today
+we're going to study conventional things
+
+ align:start position:0%
+we're going to study conventional things
+ 
+
+ align:start position:0%
+we're going to study conventional things
+and we'll talk a little bit more about
+
+ align:start position:0%
+and we'll talk a little bit more about
+ 
+
+ align:start position:0%
+and we'll talk a little bit more about
+unconventional things later in the
+
+ align:start position:0%
+unconventional things later in the
+ 
+
+ align:start position:0%
+unconventional things later in the
+course now some institutional knowledge
+
+ align:start position:0%
+course now some institutional knowledge
+ 
+
+ align:start position:0%
+course now some institutional knowledge
+this is the the again in the US the
+
+ align:start position:0%
+this is the the again in the US the
+ 
+
+ align:start position:0%
+this is the the again in the US the
+Central Bank of the US is called called
+
+ align:start position:0%
+Central Bank of the US is called called
+ 
+
+ align:start position:0%
+Central Bank of the US is called called
+the Federal Reserve System and it's a
+
+ align:start position:0%
+the Federal Reserve System and it's a
+ 
+
+ align:start position:0%
+the Federal Reserve System and it's a
+system really H it's a he has a um in um
+
+ align:start position:0%
+system really H it's a he has a um in um
+ 
+
+ align:start position:0%
+system really H it's a he has a um in um
+the Board of Governors which sits in
+
+ align:start position:0%
+the Board of Governors which sits in
+ 
+
+ align:start position:0%
+the Board of Governors which sits in
+Washington
+
+ align:start position:0%
+Washington
+ 
+
+ align:start position:0%
+Washington
+DC um and and there are seven Governors
+
+ align:start position:0%
+DC um and and there are seven Governors
+ 
+
+ align:start position:0%
+DC um and and there are seven Governors
+and the governors are are are nominated
+
+ align:start position:0%
+and the governors are are are nominated
+ 
+
+ align:start position:0%
+and the governors are are are nominated
+by the president and and then confirmed
+
+ align:start position:0%
+by the president and and then confirmed
+ 
+
+ align:start position:0%
+by the president and and then confirmed
+by by the Senate and the president of
+
+ align:start position:0%
+by by the Senate and the president of
+ 
+
+ align:start position:0%
+by by the Senate and the president of
+that board is is H is so the president
+
+ align:start position:0%
+that board is is H is so the president
+ 
+
+ align:start position:0%
+that board is is H is so the president
+of the FED of the FED will be one of
+
+ align:start position:0%
+of the FED of the FED will be one of
+ 
+
+ align:start position:0%
+of the FED of the FED will be one of
+those members okay now on in addition to
+
+ align:start position:0%
+those members okay now on in addition to
+ 
+
+ align:start position:0%
+those members okay now on in addition to
+that the the US has a Federal Reserve
+
+ align:start position:0%
+that the the US has a Federal Reserve
+ 
+
+ align:start position:0%
+that the the US has a Federal Reserve
+Bank system there are seven there are 12
+
+ align:start position:0%
+Bank system there are seven there are 12
+ 
+
+ align:start position:0%
+Bank system there are seven there are 12
+Regional Banks uh there's one in Boston
+
+ align:start position:0%
+Regional Banks uh there's one in Boston
+ 
+
+ align:start position:0%
+Regional Banks uh there's one in Boston
+in fact if you look at the skyline near
+
+ align:start position:0%
+in fact if you look at the skyline near
+ 
+
+ align:start position:0%
+in fact if you look at the skyline near
+the Waterfront there's a building built
+
+ align:start position:0%
+the Waterfront there's a building built
+ 
+
+ align:start position:0%
+the Waterfront there's a building built
+out of recycled aluminum well that's the
+
+ align:start position:0%
+out of recycled aluminum well that's the
+ 
+
+ align:start position:0%
+out of recycled aluminum well that's the
+Reserve Bank of Boston and uh and uh and
+
+ align:start position:0%
+Reserve Bank of Boston and uh and uh and
+ 
+
+ align:start position:0%
+Reserve Bank of Boston and uh and uh and
+of those 12 Regional Banks they
+
+ align:start position:0%
+of those 12 Regional Banks they
+ 
+
+ align:start position:0%
+of those 12 Regional Banks they
+rotate so so policy the interested is
+
+ align:start position:0%
+rotate so so policy the interested is
+ 
+
+ align:start position:0%
+rotate so so policy the interested is
+set into in a committee which is called
+
+ align:start position:0%
+set into in a committee which is called
+ 
+
+ align:start position:0%
+set into in a committee which is called
+the fomc Federal Open Market Committee
+
+ align:start position:0%
+the fomc Federal Open Market Committee
+ 
+
+ align:start position:0%
+the fomc Federal Open Market Committee
+um and and the member of that the voting
+
+ align:start position:0%
+um and and the member of that the voting
+ 
+
+ align:start position:0%
+um and and the member of that the voting
+members of that committee are the the
+
+ align:start position:0%
+members of that committee are the the
+ 
+
+ align:start position:0%
+members of that committee are the the
+seven Governors plus h four out of the
+
+ align:start position:0%
+seven Governors plus h four out of the
+ 
+
+ align:start position:0%
+seven Governors plus h four out of the
+12 and they rotate most of them rotate
+
+ align:start position:0%
+12 and they rotate most of them rotate
+ 
+
+ align:start position:0%
+12 and they rotate most of them rotate
+the the only one I think does not rotate
+
+ align:start position:0%
+the the only one I think does not rotate
+ 
+
+ align:start position:0%
+the the only one I think does not rotate
+is the is the is the president of the of
+
+ align:start position:0%
+is the is the is the president of the of
+ 
+
+ align:start position:0%
+is the is the is the president of the of
+the New York fed because they're so
+
+ align:start position:0%
+the New York fed because they're so
+ 
+
+ align:start position:0%
+the New York fed because they're so
+important because that's a financial
+
+ align:start position:0%
+important because that's a financial
+ 
+
+ align:start position:0%
+important because that's a financial
+heart of the US
+
+ align:start position:0%
+heart of the US
+ 
+
+ align:start position:0%
+heart of the US
+that you certainly want that H ER
+
+ align:start position:0%
+that you certainly want that H ER
+ 
+
+ align:start position:0%
+that you certainly want that H ER
+president to be involved in in interest
+
+ align:start position:0%
+president to be involved in in interest
+ 
+
+ align:start position:0%
+president to be involved in in interest
+rate decisions and it's really the FED
+
+ align:start position:0%
+rate decisions and it's really the FED
+ 
+
+ align:start position:0%
+rate decisions and it's really the FED
+that is in charge of communication with
+
+ align:start position:0%
+that is in charge of communication with
+ 
+
+ align:start position:0%
+that is in charge of communication with
+financial Market which is a huge thing
+
+ align:start position:0%
+financial Market which is a huge thing
+ 
+
+ align:start position:0%
+financial Market which is a huge thing
+for the FED okay they are in New York
+
+ align:start position:0%
+for the FED okay they are in New York
+ 
+
+ align:start position:0%
+for the FED okay they are in New York
+and they're crucial for that okay so
+
+ align:start position:0%
+and they're crucial for that okay so
+ 
+
+ align:start position:0%
+and they're crucial for that okay so
+that's that's that's those are the
+
+ align:start position:0%
+that's that's that's those are the
+ 
+
+ align:start position:0%
+that's that's that's those are the
+people that and in most places around
+
+ align:start position:0%
+people that and in most places around
+ 
+
+ align:start position:0%
+people that and in most places around
+the world you're going to have at least
+
+ align:start position:0%
+the world you're going to have at least
+ 
+
+ align:start position:0%
+the world you're going to have at least
+something equivalent to the the seven
+
+ align:start position:0%
+something equivalent to the the seven
+ 
+
+ align:start position:0%
+something equivalent to the the seven
+governors out there okay most places
+
+ align:start position:0%
+governors out there okay most places
+ 
+
+ align:start position:0%
+governors out there okay most places
+obviously the ECB is different because
+
+ align:start position:0%
+obviously the ECB is different because
+ 
+
+ align:start position:0%
+obviously the ECB is different because
+it's multiple countries so each country
+
+ align:start position:0%
+it's multiple countries so each country
+ 
+
+ align:start position:0%
+it's multiple countries so each country
+sends one member
+
+ align:start position:0%
+sends one member
+ 
+
+ align:start position:0%
+sends one member
+no but but but
+
+ align:start position:0%
+no but but but
+ 
+
+ align:start position:0%
+no but but but
+otherwise um it tends to be like like
+
+ align:start position:0%
+otherwise um it tends to be like like
+ 
+
+ align:start position:0%
+otherwise um it tends to be like like
+the US without the the the regional
+
+ align:start position:0%
+the US without the the the regional
+ 
+
+ align:start position:0%
+the US without the the the regional
+Banks so why do we care about monetary
+
+ align:start position:0%
+Banks so why do we care about monetary
+ 
+
+ align:start position:0%
+Banks so why do we care about monetary
+policy well because I think it's one of
+
+ align:start position:0%
+policy well because I think it's one of
+ 
+
+ align:start position:0%
+policy well because I think it's one of
+the main policy tools you have in the
+
+ align:start position:0%
+the main policy tools you have in the
+ 
+
+ align:start position:0%
+the main policy tools you have in the
+short run remember in this part of the
+
+ align:start position:0%
+short run remember in this part of the
+ 
+
+ align:start position:0%
+short run remember in this part of the
+course we're trying to understand output
+
+ align:start position:0%
+course we're trying to understand output
+ 
+
+ align:start position:0%
+course we're trying to understand output
+in the short ter and one of the main
+
+ align:start position:0%
+in the short ter and one of the main
+ 
+
+ align:start position:0%
+in the short ter and one of the main
+policy levels I mean how can you affect
+
+ align:start position:0%
+policy levels I mean how can you affect
+ 
+
+ align:start position:0%
+policy levels I mean how can you affect
+output is monetary policy which one is
+
+ align:start position:0%
+output is monetary policy which one is
+ 
+
+ align:start position:0%
+output is monetary policy which one is
+the other
+
+ align:start position:0%
+the other
+ 
+
+ align:start position:0%
+the other
+one there are two major ones fiscal
+
+ align:start position:0%
+one there are two major ones fiscal
+ 
+
+ align:start position:0%
+one there are two major ones fiscal
+policy exactly and fiscal policy we did
+
+ align:start position:0%
+policy exactly and fiscal policy we did
+ 
+
+ align:start position:0%
+policy exactly and fiscal policy we did
+look at in the previous lecture remember
+
+ align:start position:0%
+look at in the previous lecture remember
+ 
+
+ align:start position:0%
+look at in the previous lecture remember
+we said an expansionary fiscal policies
+
+ align:start position:0%
+we said an expansionary fiscal policies
+ 
+
+ align:start position:0%
+we said an expansionary fiscal policies
+an increase in G or a decline in t would
+
+ align:start position:0%
+an increase in G or a decline in t would
+ 
+
+ align:start position:0%
+an increase in G or a decline in t would
+lead to an expansion in a great demand
+
+ align:start position:0%
+lead to an expansion in a great demand
+ 
+
+ align:start position:0%
+lead to an expansion in a great demand
+equilibrium output would go out up okay
+
+ align:start position:0%
+equilibrium output would go out up okay
+ 
+
+ align:start position:0%
+equilibrium output would go out up okay
+so fiscal policy is something you always
+
+ align:start position:0%
+so fiscal policy is something you always
+ 
+
+ align:start position:0%
+so fiscal policy is something you always
+use in in in deep recessions
+
+ align:start position:0%
+use in in in deep recessions
+ 
+
+ align:start position:0%
+use in in in deep recessions
+uh but monetary policy is much more
+
+ align:start position:0%
+uh but monetary policy is much more
+ 
+
+ align:start position:0%
+uh but monetary policy is much more
+Nimble is I mean it's a it's a bunch of
+
+ align:start position:0%
+Nimble is I mean it's a it's a bunch of
+ 
+
+ align:start position:0%
+Nimble is I mean it's a it's a bunch of
+people that need to meet and just change
+
+ align:start position:0%
+people that need to meet and just change
+ 
+
+ align:start position:0%
+people that need to meet and just change
+the interest rate anything that is
+
+ align:start position:0%
+the interest rate anything that is
+ 
+
+ align:start position:0%
+the interest rate anything that is
+fiscal there are some automatic
+
+ align:start position:0%
+fiscal there are some automatic
+ 
+
+ align:start position:0%
+fiscal there are some automatic
+stabilizers by the way so automatically
+
+ align:start position:0%
+stabilizers by the way so automatically
+ 
+
+ align:start position:0%
+stabilizers by the way so automatically
+fiscal policy becomes more expansionary
+
+ align:start position:0%
+fiscal policy becomes more expansionary
+ 
+
+ align:start position:0%
+fiscal policy becomes more expansionary
+during recessions and stuff like that
+
+ align:start position:0%
+during recessions and stuff like that
+ 
+
+ align:start position:0%
+during recessions and stuff like that
+but any deviation from the typical
+
+ align:start position:0%
+but any deviation from the typical
+ 
+
+ align:start position:0%
+but any deviation from the typical
+automatic stabilizers require Congress
+
+ align:start position:0%
+automatic stabilizers require Congress
+ 
+
+ align:start position:0%
+automatic stabilizers require Congress
+to approve things it's a long process
+
+ align:start position:0%
+to approve things it's a long process
+ 
+
+ align:start position:0%
+to approve things it's a long process
+and so it's not something that can react
+
+ align:start position:0%
+and so it's not something that can react
+ 
+
+ align:start position:0%
+and so it's not something that can react
+as quickly as monetary policy can okay
+
+ align:start position:0%
+as quickly as monetary policy can okay
+ 
+
+ align:start position:0%
+as quickly as monetary policy can okay
+um so that's what we're going to look
+
+ align:start position:0%
+um so that's what we're going to look
+ 
+
+ align:start position:0%
+um so that's what we're going to look
+that's that's that's that's the reason
+
+ align:start position:0%
+that's that's that's that's the reason
+ 
+
+ align:start position:0%
+that's that's that's that's the reason
+why monetary policy is important for us
+
+ align:start position:0%
+why monetary policy is important for us
+ 
+
+ align:start position:0%
+why monetary policy is important for us
+at this point then there are medium and
+
+ align:start position:0%
+at this point then there are medium and
+ 
+
+ align:start position:0%
+at this point then there are medium and
+long run issues fiscal policies still
+
+ align:start position:0%
+long run issues fiscal policies still
+ 
+
+ align:start position:0%
+long run issues fiscal policies still
+affects equilibrium output in the medium
+
+ align:start position:0%
+affects equilibrium output in the medium
+ 
+
+ align:start position:0%
+affects equilibrium output in the medium
+and long run monetary policies much less
+
+ align:start position:0%
+and long run monetary policies much less
+ 
+
+ align:start position:0%
+and long run monetary policies much less
+effective at that it's very difficult to
+
+ align:start position:0%
+effective at that it's very difficult to
+ 
+
+ align:start position:0%
+effective at that it's very difficult to
+to change sort of equilibrium growth or
+
+ align:start position:0%
+to change sort of equilibrium growth or
+ 
+
+ align:start position:0%
+to change sort of equilibrium growth or
+things like that with monetary policy
+
+ align:start position:0%
+things like that with monetary policy
+ 
+
+ align:start position:0%
+things like that with monetary policy
+it's going to be pretty minor most of
+
+ align:start position:0%
+it's going to be pretty minor most of
+ 
+
+ align:start position:0%
+it's going to be pretty minor most of
+the impact of monetary policy in the
+
+ align:start position:0%
+the impact of monetary policy in the
+ 
+
+ align:start position:0%
+the impact of monetary policy in the
+minum and long run is really on the
+
+ align:start position:0%
+minum and long run is really on the
+ 
+
+ align:start position:0%
+minum and long run is really on the
+price level and inflation more than on
+
+ align:start position:0%
+price level and inflation more than on
+ 
+
+ align:start position:0%
+price level and inflation more than on
+real activity okay but in the short run
+
+ align:start position:0%
+real activity okay but in the short run
+ 
+
+ align:start position:0%
+real activity okay but in the short run
+it's very powerful for reasons that
+
+ align:start position:0%
+it's very powerful for reasons that
+ 
+
+ align:start position:0%
+it's very powerful for reasons that
+we're going to discuss in this and the
+
+ align:start position:0%
+we're going to discuss in this and the
+ 
+
+ align:start position:0%
+we're going to discuss in this and the
+next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lecture okay so as I said well monetary
+
+ align:start position:0%
+lecture okay so as I said well monetary
+ 
+
+ align:start position:0%
+lecture okay so as I said well monetary
+policy acts through financial markets I
+
+ align:start position:0%
+policy acts through financial markets I
+ 
+
+ align:start position:0%
+policy acts through financial markets I
+I think it's a very
+
+ align:start position:0%
+I think it's a very
+ 
+
+ align:start position:0%
+I think it's a very
+interesting part of my research agenda
+
+ align:start position:0%
+interesting part of my research agenda
+ 
+
+ align:start position:0%
+interesting part of my research agenda
+is about that is I think is the central
+
+ align:start position:0%
+is about that is I think is the central
+ 
+
+ align:start position:0%
+is about that is I think is the central
+bank is a very strange institution
+
+ align:start position:0%
+bank is a very strange institution
+ 
+
+ align:start position:0%
+bank is a very strange institution
+because most of its mandate are in terms
+
+ align:start position:0%
+because most of its mandate are in terms
+ 
+
+ align:start position:0%
+because most of its mandate are in terms
+of what happens in the Goods Market says
+
+ align:start position:0%
+of what happens in the Goods Market says
+ 
+
+ align:start position:0%
+of what happens in the Goods Market says
+you know you don't try not to get into
+
+ align:start position:0%
+you know you don't try not to get into
+ 
+
+ align:start position:0%
+you know you don't try not to get into
+recession try to get us out of a
+
+ align:start position:0%
+recession try to get us out of a
+ 
+
+ align:start position:0%
+recession try to get us out of a
+recession and so on but unlike fiscal
+
+ align:start position:0%
+recession and so on but unlike fiscal
+ 
+
+ align:start position:0%
+recession and so on but unlike fiscal
+policy which has tools that are directly
+
+ align:start position:0%
+policy which has tools that are directly
+ 
+
+ align:start position:0%
+policy which has tools that are directly
+aim at the Goods Market remember it's a
+
+ align:start position:0%
+aim at the Goods Market remember it's a
+ 
+
+ align:start position:0%
+aim at the Goods Market remember it's a
+it's a purchases by the government of
+
+ align:start position:0%
+it's a purchases by the government of
+ 
+
+ align:start position:0%
+it's a purchases by the government of
+goods so if there isn't sufficient
+
+ align:start position:0%
+goods so if there isn't sufficient
+ 
+
+ align:start position:0%
+goods so if there isn't sufficient
+demand for goods the fiscal policy the
+
+ align:start position:0%
+demand for goods the fiscal policy the
+ 
+
+ align:start position:0%
+demand for goods the fiscal policy the
+fiscal Authority can go out there and
+
+ align:start position:0%
+fiscal Authority can go out there and
+ 
+
+ align:start position:0%
+fiscal Authority can go out there and
+buy Goods that creates more demand the
+
+ align:start position:0%
+buy Goods that creates more demand the
+ 
+
+ align:start position:0%
+buy Goods that creates more demand the
+the central bank is given the same
+
+ align:start position:0%
+the central bank is given the same
+ 
+
+ align:start position:0%
+the central bank is given the same
+mandate aside from Price stability and
+
+ align:start position:0%
+mandate aside from Price stability and
+ 
+
+ align:start position:0%
+mandate aside from Price stability and
+things like that we're want to worry
+
+ align:start position:0%
+things like that we're want to worry
+ 
+
+ align:start position:0%
+things like that we're want to worry
+about later but it doesn't have any
+
+ align:start position:0%
+about later but it doesn't have any
+ 
+
+ align:start position:0%
+about later but it doesn't have any
+tools the the the central bank if
+
+ align:start position:0%
+tools the the the central bank if
+ 
+
+ align:start position:0%
+tools the the the central bank if
+there's insufficient demand the Central
+
+ align:start position:0%
+there's insufficient demand the Central
+ 
+
+ align:start position:0%
+there's insufficient demand the Central
+Bank cannot go out there and buy
+
+ align:start position:0%
+Bank cannot go out there and buy
+ 
+
+ align:start position:0%
+Bank cannot go out there and buy
+hamburgers right that's fiscal policy
+
+ align:start position:0%
+hamburgers right that's fiscal policy
+ 
+
+ align:start position:0%
+hamburgers right that's fiscal policy
+can do that and expand the demand for
+
+ align:start position:0%
+can do that and expand the demand for
+ 
+
+ align:start position:0%
+can do that and expand the demand for
+hamburgers but not monetary policy what
+
+ align:start position:0%
+hamburgers but not monetary policy what
+ 
+
+ align:start position:0%
+hamburgers but not monetary policy what
+monetary policy can do is by bonds by
+
+ align:start position:0%
+monetary policy can do is by bonds by
+ 
+
+ align:start position:0%
+monetary policy can do is by bonds by
+instruments in the financial markets and
+
+ align:start position:0%
+instruments in the financial markets and
+ 
+
+ align:start position:0%
+instruments in the financial markets and
+through that affects real activity so
+
+ align:start position:0%
+through that affects real activity so
+ 
+
+ align:start position:0%
+through that affects real activity so
+the is it's the fastest policy tool but
+
+ align:start position:0%
+the is it's the fastest policy tool but
+ 
+
+ align:start position:0%
+the is it's the fastest policy tool but
+it's the most indirect in a sense
+
+ align:start position:0%
+it's the most indirect in a sense
+ 
+
+ align:start position:0%
+it's the most indirect in a sense
+because it it it has to go through
+
+ align:start position:0%
+because it it it has to go through
+ 
+
+ align:start position:0%
+because it it it has to go through
+financial market and and and and that CH
+
+ align:start position:0%
+financial market and and and and that CH
+ 
+
+ align:start position:0%
+financial market and and and and that CH
+those channels can be very complex but
+
+ align:start position:0%
+those channels can be very complex but
+ 
+
+ align:start position:0%
+those channels can be very complex but
+obviously we're not in the business of
+
+ align:start position:0%
+obviously we're not in the business of
+ 
+
+ align:start position:0%
+obviously we're not in the business of
+complicating things in this course so
+
+ align:start position:0%
+complicating things in this course so
+ 
+
+ align:start position:0%
+complicating things in this course so
+we're going to make it very very simple
+
+ align:start position:0%
+we're going to make it very very simple
+ 
+
+ align:start position:0%
+we're going to make it very very simple
+we're going to assume that financial
+
+ align:start position:0%
+we're going to assume that financial
+ 
+
+ align:start position:0%
+we're going to assume that financial
+markets only have two instruments
+
+ align:start position:0%
+markets only have two instruments
+ 
+
+ align:start position:0%
+markets only have two instruments
+obviously the huge simplification there
+
+ align:start position:0%
+obviously the huge simplification there
+ 
+
+ align:start position:0%
+obviously the huge simplification there
+are millions of financial instruments
+
+ align:start position:0%
+are millions of financial instruments
+ 
+
+ align:start position:0%
+are millions of financial instruments
+out there but we're going to isolate two
+
+ align:start position:0%
+out there but we're going to isolate two
+ 
+
+ align:start position:0%
+out there but we're going to isolate two
+instruments because this happens to be
+
+ align:start position:0%
+instruments because this happens to be
+ 
+
+ align:start position:0%
+instruments because this happens to be
+the instrument
+
+ align:start position:0%
+the instrument
+ 
+
+ align:start position:0%
+the instrument
+where that that that where the central
+
+ align:start position:0%
+where that that that where the central
+ 
+
+ align:start position:0%
+where that that that where the central
+banks typically participate
+
+ align:start position:0%
+banks typically participate
+ 
+
+ align:start position:0%
+banks typically participate
+they affect all asset prices around but
+
+ align:start position:0%
+they affect all asset prices around but
+ 
+
+ align:start position:0%
+they affect all asset prices around but
+the direct interventions typically
+
+ align:start position:0%
+the direct interventions typically
+ 
+
+ align:start position:0%
+the direct interventions typically
+recently has been a little different but
+
+ align:start position:0%
+recently has been a little different but
+ 
+
+ align:start position:0%
+recently has been a little different but
+typically it's only in this kind of
+
+ align:start position:0%
+typically it's only in this kind of
+ 
+
+ align:start position:0%
+typically it's only in this kind of
+instruments and so we're going to focus
+
+ align:start position:0%
+instruments and so we're going to focus
+ 
+
+ align:start position:0%
+instruments and so we're going to focus
+all of our analysis on on those two
+
+ align:start position:0%
+all of our analysis on on those two
+ 
+
+ align:start position:0%
+all of our analysis on on those two
+instruments for now later on we're going
+
+ align:start position:0%
+instruments for now later on we're going
+ 
+
+ align:start position:0%
+instruments for now later on we're going
+to talk about equity and stuff like that
+
+ align:start position:0%
+to talk about equity and stuff like that
+ 
+
+ align:start position:0%
+to talk about equity and stuff like that
+but but just to isolate the the the how
+
+ align:start position:0%
+but but just to isolate the the the how
+ 
+
+ align:start position:0%
+but but just to isolate the the the how
+monetary policy works is sufficient to
+
+ align:start position:0%
+monetary policy works is sufficient to
+ 
+
+ align:start position:0%
+monetary policy works is sufficient to
+just focus on two financial instruments
+
+ align:start position:0%
+just focus on two financial instruments
+ 
+
+ align:start position:0%
+just focus on two financial instruments
+so we're going to assume that people
+
+ align:start position:0%
+so we're going to assume that people
+ 
+
+ align:start position:0%
+so we're going to assume that people
+have their wealth in only two forms in
+
+ align:start position:0%
+have their wealth in only two forms in
+ 
+
+ align:start position:0%
+have their wealth in only two forms in
+two Financial assets one we're going to
+
+ align:start position:0%
+two Financial assets one we're going to
+ 
+
+ align:start position:0%
+two Financial assets one we're going to
+call it
+
+ align:start position:0%
+call it
+ 
+
+ align:start position:0%
+call it
+money and the other one we want to call
+
+ align:start position:0%
+money and the other one we want to call
+ 
+
+ align:start position:0%
+money and the other one we want to call
+it bonds okay
+
+ align:start position:0%
+it bonds okay
+ 
+
+ align:start position:0%
+it bonds okay
+money the characteristic of money what
+
+ align:start position:0%
+money the characteristic of money what
+ 
+
+ align:start position:0%
+money the characteristic of money what
+we call money there are many definitions
+
+ align:start position:0%
+we call money there are many definitions
+ 
+
+ align:start position:0%
+we call money there are many definitions
+of money M1 M2 M3 M4 but let's keep it
+
+ align:start position:0%
+of money M1 M2 M3 M4 but let's keep it
+ 
+
+ align:start position:0%
+of money M1 M2 M3 M4 but let's keep it
+very simple money essentially means
+
+ align:start position:0%
+very simple money essentially means
+ 
+
+ align:start position:0%
+very simple money essentially means
+something that you can use very easily
+
+ align:start position:0%
+something that you can use very easily
+ 
+
+ align:start position:0%
+something that you can use very easily
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+transactions okay so for example the the
+
+ align:start position:0%
+transactions okay so for example the the
+ 
+
+ align:start position:0%
+transactions okay so for example the the
+most important example of money not the
+
+ align:start position:0%
+most important example of money not the
+ 
+
+ align:start position:0%
+most important example of money not the
+largest but the most important one is
+
+ align:start position:0%
+largest but the most important one is
+ 
+
+ align:start position:0%
+largest but the most important one is
+Cash currency okay you can buy anything
+
+ align:start position:0%
+Cash currency okay you can buy anything
+ 
+
+ align:start position:0%
+Cash currency okay you can buy anything
+with cash there no problem whatsoever
+
+ align:start position:0%
+with cash there no problem whatsoever
+ 
+
+ align:start position:0%
+with cash there no problem whatsoever
+now the the the a characteristic that
+
+ align:start position:0%
+now the the the a characteristic that
+ 
+
+ align:start position:0%
+now the the the a characteristic that
+money typically does not have is that it
+
+ align:start position:0%
+money typically does not have is that it
+ 
+
+ align:start position:0%
+money typically does not have is that it
+doesn't give you any
+
+ align:start position:0%
+doesn't give you any
+ 
+
+ align:start position:0%
+doesn't give you any
+return you don't invest in cash you know
+
+ align:start position:0%
+return you don't invest in cash you know
+ 
+
+ align:start position:0%
+return you don't invest in cash you know
+you have cash because you need to do
+
+ align:start position:0%
+you have cash because you need to do
+ 
+
+ align:start position:0%
+you have cash because you need to do
+transactions but it's not the way you
+
+ align:start position:0%
+transactions but it's not the way you
+ 
+
+ align:start position:0%
+transactions but it's not the way you
+get a return and so money that's what
+
+ align:start position:0%
+get a return and so money that's what
+ 
+
+ align:start position:0%
+get a return and so money that's what
+it's going to mean for us is something
+
+ align:start position:0%
+it's going to mean for us is something
+ 
+
+ align:start position:0%
+it's going to mean for us is something
+that is used in transactions but it pays
+
+ align:start position:0%
+that is used in transactions but it pays
+ 
+
+ align:start position:0%
+that is used in transactions but it pays
+no interest rate no interest there no
+
+ align:start position:0%
+no interest rate no interest there no
+ 
+
+ align:start position:0%
+no interest rate no interest there no
+interest on that a bond is going to be
+
+ align:start position:0%
+interest on that a bond is going to be
+ 
+
+ align:start position:0%
+interest on that a bond is going to be
+the polar opposite it's going to be
+
+ align:start position:0%
+the polar opposite it's going to be
+ 
+
+ align:start position:0%
+the polar opposite it's going to be
+something that pays a positive interest
+
+ align:start position:0%
+something that pays a positive interest
+ 
+
+ align:start position:0%
+something that pays a positive interest
+rate so if you buy a bone for 100 for 95
+
+ align:start position:0%
+rate so if you buy a bone for 100 for 95
+ 
+
+ align:start position:0%
+rate so if you buy a bone for 100 for 95
+you're going to get a 100 a year from
+
+ align:start position:0%
+you're going to get a 100 a year from
+ 
+
+ align:start position:0%
+you're going to get a 100 a year from
+now say so you get something out of that
+
+ align:start position:0%
+now say so you get something out of that
+ 
+
+ align:start position:0%
+now say so you get something out of that
+bone but it's not very useful for
+
+ align:start position:0%
+bone but it's not very useful for
+ 
+
+ align:start position:0%
+bone but it's not very useful for
+transactions I mean you cannot go and
+
+ align:start position:0%
+transactions I mean you cannot go and
+ 
+
+ align:start position:0%
+transactions I mean you cannot go and
+buy your lunch with a bond you get the
+
+ align:start position:0%
+buy your lunch with a bond you get the
+ 
+
+ align:start position:0%
+buy your lunch with a bond you get the
+piece of B for that and and and many
+
+ align:start position:0%
+piece of B for that and and and many
+ 
+
+ align:start position:0%
+piece of B for that and and and many
+things cannot be even even within
+
+ align:start position:0%
+things cannot be even even within
+ 
+
+ align:start position:0%
+things cannot be even even within
+financial markets you cannot buy asset
+
+ align:start position:0%
+financial markets you cannot buy asset
+ 
+
+ align:start position:0%
+financial markets you cannot buy asset
+with asset you have to go through some
+
+ align:start position:0%
+with asset you have to go through some
+ 
+
+ align:start position:0%
+with asset you have to go through some
+process in which you come sell something
+
+ align:start position:0%
+process in which you come sell something
+ 
+
+ align:start position:0%
+process in which you come sell something
+get cash and and with cash you pay for
+
+ align:start position:0%
+get cash and and with cash you pay for
+ 
+
+ align:start position:0%
+get cash and and with cash you pay for
+the other stuff not necessarily cash it
+
+ align:start position:0%
+the other stuff not necessarily cash it
+ 
+
+ align:start position:0%
+the other stuff not necessarily cash it
+could be other forms of money but but
+
+ align:start position:0%
+could be other forms of money but but
+ 
+
+ align:start position:0%
+could be other forms of money but but
+but typically Financial instrument need
+
+ align:start position:0%
+but typically Financial instrument need
+ 
+
+ align:start position:0%
+but typically Financial instrument need
+to be sold before you can buy something
+
+ align:start position:0%
+to be sold before you can buy something
+ 
+
+ align:start position:0%
+to be sold before you can buy something
+else you don't swap them it's not a part
+
+ align:start position:0%
+else you don't swap them it's not a part
+ 
+
+ align:start position:0%
+else you don't swap them it's not a part
+them okay but this is what it means for
+
+ align:start position:0%
+them okay but this is what it means for
+ 
+
+ align:start position:0%
+them okay but this is what it means for
+us so this whenever you see something
+
+ align:start position:0%
+us so this whenever you see something
+ 
+
+ align:start position:0%
+us so this whenever you see something
+like this is always interesting for an
+
+ align:start position:0%
+like this is always interesting for an
+ 
+
+ align:start position:0%
+like this is always interesting for an
+economist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why and any economies micro economies or
+
+ align:start position:0%
+why and any economies micro economies or
+ 
+
+ align:start position:0%
+why and any economies micro economies or
+whatever what what have I done
+
+ align:start position:0%
+whatever what what have I done
+ 
+
+ align:start position:0%
+whatever what what have I done
+there that makes economics is about
+
+ align:start position:0%
+there that makes economics is about
+ 
+
+ align:start position:0%
+there that makes economics is about
+decisions and then it's about
+
+ align:start position:0%
+decisions and then it's about
+ 
+
+ align:start position:0%
+decisions and then it's about
+equilibrium okay it's decisions and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium there's a decision to be
+
+ align:start position:0%
+equilibrium there's a decision to be
+ 
+
+ align:start position:0%
+equilibrium there's a decision to be
+made here there's a tradeoff okay I I
+
+ align:start position:0%
+made here there's a tradeoff okay I I
+ 
+
+ align:start position:0%
+made here there's a tradeoff okay I I
+you know if I need to do lots of
+
+ align:start position:0%
+you know if I need to do lots of
+ 
+
+ align:start position:0%
+you know if I need to do lots of
+transactions I better sort of bias my
+
+ align:start position:0%
+transactions I better sort of bias my
+ 
+
+ align:start position:0%
+transactions I better sort of bias my
+portfolio towards cash towards money if
+
+ align:start position:0%
+portfolio towards cash towards money if
+ 
+
+ align:start position:0%
+portfolio towards cash towards money if
+if I don't need to do lots of
+
+ align:start position:0%
+if I don't need to do lots of
+ 
+
+ align:start position:0%
+if I don't need to do lots of
+transaction then I and the interest rate
+
+ align:start position:0%
+transaction then I and the interest rate
+ 
+
+ align:start position:0%
+transaction then I and the interest rate
+is very high particularly then I this is
+
+ align:start position:0%
+is very high particularly then I this is
+ 
+
+ align:start position:0%
+is very high particularly then I this is
+an issue today today interest rates are
+
+ align:start position:0%
+an issue today today interest rates are
+ 
+
+ align:start position:0%
+an issue today today interest rates are
+very high nobody care about bonds or
+
+ align:start position:0%
+very high nobody care about bonds or
+ 
+
+ align:start position:0%
+very high nobody care about bonds or
+anything you know two years ago when
+
+ align:start position:0%
+anything you know two years ago when
+ 
+
+ align:start position:0%
+anything you know two years ago when
+interest rate was Zero but today
+
+ align:start position:0%
+interest rate was Zero but today
+ 
+
+ align:start position:0%
+interest rate was Zero but today
+interest rate is 5% so it's an issue
+
+ align:start position:0%
+interest rate is 5% so it's an issue
+ 
+
+ align:start position:0%
+interest rate is 5% so it's an issue
+you're not going to if you want to keep
+
+ align:start position:0%
+you're not going to if you want to keep
+ 
+
+ align:start position:0%
+you're not going to if you want to keep
+it in cash you're going to give up a lot
+
+ align:start position:0%
+it in cash you're going to give up a lot
+ 
+
+ align:start position:0%
+it in cash you're going to give up a lot
+of return okay so it's a decision to be
+
+ align:start position:0%
+of return okay so it's a decision to be
+ 
+
+ align:start position:0%
+of return okay so it's a decision to be
+made there a portfolio decision and
+
+ align:start position:0%
+made there a portfolio decision and
+ 
+
+ align:start position:0%
+made there a portfolio decision and
+that's always interesting for
+
+ align:start position:0%
+that's always interesting for
+ 
+
+ align:start position:0%
+that's always interesting for
+economies so let's talk about uh that
+
+ align:start position:0%
+economies so let's talk about uh that
+ 
+
+ align:start position:0%
+economies so let's talk about uh that
+decision and we're going to talk you can
+
+ align:start position:0%
+decision and we're going to talk you can
+ 
+
+ align:start position:0%
+decision and we're going to talk you can
+describe this decision either from the
+
+ align:start position:0%
+describe this decision either from the
+ 
+
+ align:start position:0%
+describe this decision either from the
+side of bonds or from the side of money
+
+ align:start position:0%
+side of bonds or from the side of money
+ 
+
+ align:start position:0%
+side of bonds or from the side of money
+we're going to describe from the side of
+
+ align:start position:0%
+we're going to describe from the side of
+ 
+
+ align:start position:0%
+we're going to describe from the side of
+money because there's a total amount of
+
+ align:start position:0%
+money because there's a total amount of
+ 
+
+ align:start position:0%
+money because there's a total amount of
+wealth and you have to decide what to
+
+ align:start position:0%
+wealth and you have to decide what to
+ 
+
+ align:start position:0%
+wealth and you have to decide what to
+allocate it to so you know it suffices
+
+ align:start position:0%
+allocate it to so you know it suffices
+ 
+
+ align:start position:0%
+allocate it to so you know it suffices
+if I tell you there a total amount of
+
+ align:start position:0%
+if I tell you there a total amount of
+ 
+
+ align:start position:0%
+if I tell you there a total amount of
+wealth and if I tell you how to how much
+
+ align:start position:0%
+wealth and if I tell you how to how much
+ 
+
+ align:start position:0%
+wealth and if I tell you how to how much
+you allocate to money then I'm telling
+
+ align:start position:0%
+you allocate to money then I'm telling
+ 
+
+ align:start position:0%
+you allocate to money then I'm telling
+you implicitly how much you are
+
+ align:start position:0%
+you implicitly how much you are
+ 
+
+ align:start position:0%
+you implicitly how much you are
+allocating to bonds it's a compliment to
+
+ align:start position:0%
+allocating to bonds it's a compliment to
+ 
+
+ align:start position:0%
+allocating to bonds it's a compliment to
+that okay so I can do analysis either
+
+ align:start position:0%
+that okay so I can do analysis either
+ 
+
+ align:start position:0%
+that okay so I can do analysis either
+way but I'm going to do it through money
+
+ align:start position:0%
+way but I'm going to do it through money
+ 
+
+ align:start position:0%
+way but I'm going to do it through money
+which is the way is normally done so
+
+ align:start position:0%
+which is the way is normally done so
+ 
+
+ align:start position:0%
+which is the way is normally done so
+money demand if I plot it in the space
+
+ align:start position:0%
+money demand if I plot it in the space
+ 
+
+ align:start position:0%
+money demand if I plot it in the space
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+M money and the interest rate is a
+
+ align:start position:0%
+M money and the interest rate is a
+ 
+
+ align:start position:0%
+M money and the interest rate is a
+downward sloping
+
+ align:start position:0%
+downward sloping
+ 
+
+ align:start position:0%
+downward sloping
+curve why is it a downward sloping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve the interest rate is higher it
+
+ align:start position:0%
+curve the interest rate is higher it
+ 
+
+ align:start position:0%
+curve the interest rate is higher it
+pays off more to have B your utility
+
+ align:start position:0%
+pays off more to have B your utility
+ 
+
+ align:start position:0%
+pays off more to have B your utility
+should exactly your decision if the
+
+ align:start position:0%
+should exactly your decision if the
+ 
+
+ align:start position:0%
+should exactly your decision if the
+interest rate is very high is to go more
+
+ align:start position:0%
+interest rate is very high is to go more
+ 
+
+ align:start position:0%
+interest rate is very high is to go more
+towards bone the interest is very low I
+
+ align:start position:0%
+towards bone the interest is very low I
+ 
+
+ align:start position:0%
+towards bone the interest is very low I
+don't care too much about bones I'd
+
+ align:start position:0%
+don't care too much about bones I'd
+ 
+
+ align:start position:0%
+don't care too much about bones I'd
+rather keep the thing that helps me
+
+ align:start position:0%
+rather keep the thing that helps me
+ 
+
+ align:start position:0%
+rather keep the thing that helps me
+transact which is money okay and it's
+
+ align:start position:0%
+transact which is money okay and it's
+ 
+
+ align:start position:0%
+transact which is money okay and it's
+interesting because for most of your
+
+ align:start position:0%
+interesting because for most of your
+ 
+
+ align:start position:0%
+interesting because for most of your
+adult life you have Liv in a world in
+
+ align:start position:0%
+adult life you have Liv in a world in
+ 
+
+ align:start position:0%
+adult life you have Liv in a world in
+which that not was not a very
+
+ align:start position:0%
+which that not was not a very
+ 
+
+ align:start position:0%
+which that not was not a very
+interesting decision actually no because
+
+ align:start position:0%
+interesting decision actually no because
+ 
+
+ align:start position:0%
+interesting decision actually no because
+interest were very close to zero now
+
+ align:start position:0%
+interest were very close to zero now
+ 
+
+ align:start position:0%
+interest were very close to zero now
+you're living in a different environment
+
+ align:start position:0%
+you're living in a different environment
+ 
+
+ align:start position:0%
+you're living in a different environment
+interest Are For the First Time sort of
+
+ align:start position:0%
+interest Are For the First Time sort of
+ 
+
+ align:start position:0%
+interest Are For the First Time sort of
+high for you there may a bigger decision
+
+ align:start position:0%
+high for you there may a bigger decision
+ 
+
+ align:start position:0%
+high for you there may a bigger decision
+between invest in equity say and cash
+
+ align:start position:0%
+between invest in equity say and cash
+ 
+
+ align:start position:0%
+between invest in equity say and cash
+but bonds and and and and these are safe
+
+ align:start position:0%
+but bonds and and and and these are safe
+ 
+
+ align:start position:0%
+but bonds and and and and these are safe
+bonds by the way your treasures and
+
+ align:start position:0%
+bonds by the way your treasures and
+ 
+
+ align:start position:0%
+bonds by the way your treasures and
+things like that and money is not
+
+ align:start position:0%
+things like that and money is not
+ 
+
+ align:start position:0%
+things like that and money is not
+something you have to worry
+
+ align:start position:0%
+something you have to worry
+ 
+
+ align:start position:0%
+something you have to worry
+about okay good what I'm saying is
+
+ align:start position:0%
+about okay good what I'm saying is
+ 
+
+ align:start position:0%
+about okay good what I'm saying is
+interest is where around here so you
+
+ align:start position:0%
+interest is where around here so you
+ 
+
+ align:start position:0%
+interest is where around here so you
+we're all in cash one way or the other
+
+ align:start position:0%
+we're all in cash one way or the other
+ 
+
+ align:start position:0%
+we're all in cash one way or the other
+and now interest are a lot High the
+
+ align:start position:0%
+and now interest are a lot High the
+ 
+
+ align:start position:0%
+and now interest are a lot High the
+other thing that so that's a movement
+
+ align:start position:0%
+other thing that so that's a movement
+ 
+
+ align:start position:0%
+other thing that so that's a movement
+along the curve no I'm plotting
+
+ align:start position:0%
+along the curve no I'm plotting
+ 
+
+ align:start position:0%
+along the curve no I'm plotting
+something in the space of interest rate
+
+ align:start position:0%
+something in the space of interest rate
+ 
+
+ align:start position:0%
+something in the space of interest rate
+money and interest rate then when I tell
+
+ align:start position:0%
+money and interest rate then when I tell
+ 
+
+ align:start position:0%
+money and interest rate then when I tell
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+what happens when the inter Rises I'm
+
+ align:start position:0%
+what happens when the inter Rises I'm
+ 
+
+ align:start position:0%
+what happens when the inter Rises I'm
+asking you for a a a movement along the
+
+ align:start position:0%
+asking you for a a a movement along the
+ 
+
+ align:start position:0%
+asking you for a a a movement along the
+curve okay I see so if I raise interest
+
+ align:start position:0%
+curve okay I see so if I raise interest
+ 
+
+ align:start position:0%
+curve okay I see so if I raise interest
+rate I move along the curve up so the
+
+ align:start position:0%
+rate I move along the curve up so the
+ 
+
+ align:start position:0%
+rate I move along the curve up so the
+second thing that we have there is
+
+ align:start position:0%
+second thing that we have there is
+ 
+
+ align:start position:0%
+second thing that we have there is
+argument we have is something that shift
+
+ align:start position:0%
+argument we have is something that shift
+ 
+
+ align:start position:0%
+argument we have is something that shift
+the curve because it's not part of my
+
+ align:start position:0%
+the curve because it's not part of my
+ 
+
+ align:start position:0%
+the curve because it's not part of my
+Axis so so it will shift the curve it's
+
+ align:start position:0%
+Axis so so it will shift the curve it's
+ 
+
+ align:start position:0%
+Axis so so it will shift the curve it's
+a parameter for each of these curves and
+
+ align:start position:0%
+a parameter for each of these curves and
+ 
+
+ align:start position:0%
+a parameter for each of these curves and
+that's nominal income so in particular
+
+ align:start position:0%
+that's nominal income so in particular
+ 
+
+ align:start position:0%
+that's nominal income so in particular
+if nominal income goes
+
+ align:start position:0%
+if nominal income goes
+ 
+
+ align:start position:0%
+if nominal income goes
+up I'm showing you there that money
+
+ align:start position:0%
+up I'm showing you there that money
+ 
+
+ align:start position:0%
+up I'm showing you there that money
+demand goes out meaning for any given
+
+ align:start position:0%
+demand goes out meaning for any given
+ 
+
+ align:start position:0%
+demand goes out meaning for any given
+level of interest rate you're going to
+
+ align:start position:0%
+level of interest rate you're going to
+ 
+
+ align:start position:0%
+level of interest rate you're going to
+demand more
+
+ align:start position:0%
+demand more
+ 
+
+ align:start position:0%
+demand more
+money why do you think that's the case
+
+ align:start position:0%
+money why do you think that's the case
+ 
+
+ align:start position:0%
+money why do you think that's the case
+and again I'm looking here at the
+
+ align:start position:0%
+and again I'm looking here at the
+ 
+
+ align:start position:0%
+and again I'm looking here at the
+aggregate but but it applies to an
+
+ align:start position:0%
+aggregate but but it applies to an
+ 
+
+ align:start position:0%
+aggregate but but it applies to an
+individual as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well so for the same level of wealth now
+
+ align:start position:0%
+well so for the same level of wealth now
+ 
+
+ align:start position:0%
+well so for the same level of wealth now
+nominal GDP is
+
+ align:start position:0%
+nominal GDP is
+ 
+
+ align:start position:0%
+nominal GDP is
+higher remember that nominal GDP is the
+
+ align:start position:0%
+higher remember that nominal GDP is the
+ 
+
+ align:start position:0%
+higher remember that nominal GDP is the
+same as nominal expenditure here okay so
+
+ align:start position:0%
+same as nominal expenditure here okay so
+ 
+
+ align:start position:0%
+same as nominal expenditure here okay so
+if GDP is higher then that means there's
+
+ align:start position:0%
+if GDP is higher then that means there's
+ 
+
+ align:start position:0%
+if GDP is higher then that means there's
+going to be more transactions because
+
+ align:start position:0%
+going to be more transactions because
+ 
+
+ align:start position:0%
+going to be more transactions because
+there's going to be more
+
+ align:start position:0%
+there's going to be more
+ 
+
+ align:start position:0%
+there's going to be more
+expenditure okay and therefore you need
+
+ align:start position:0%
+expenditure okay and therefore you need
+ 
+
+ align:start position:0%
+expenditure okay and therefore you need
+more of the thing that is use useful for
+
+ align:start position:0%
+more of the thing that is use useful for
+ 
+
+ align:start position:0%
+more of the thing that is use useful for
+transactions okay M demand goes up the
+
+ align:start position:0%
+transactions okay M demand goes up the
+ 
+
+ align:start position:0%
+transactions okay M demand goes up the
+second point to highlight is that you
+
+ align:start position:0%
+second point to highlight is that you
+ 
+
+ align:start position:0%
+second point to highlight is that you
+know while in most places I we use why
+
+ align:start position:0%
+know while in most places I we use why
+ 
+
+ align:start position:0%
+know while in most places I we use why
+here I'm using dollar y nominal y why do
+
+ align:start position:0%
+here I'm using dollar y nominal y why do
+ 
+
+ align:start position:0%
+here I'm using dollar y nominal y why do
+you think that's that why why don't I
+
+ align:start position:0%
+you think that's that why why don't I
+ 
+
+ align:start position:0%
+you think that's that why why don't I
+just put there real GDP rather than
+
+ align:start position:0%
+just put there real GDP rather than
+ 
+
+ align:start position:0%
+just put there real GDP rather than
+nominal GDP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+typo let's go in
+
+ align:start position:0%
+typo let's go in
+ 
+
+ align:start position:0%
+typo let's go in
+steps suppose that prices are totally
+
+ align:start position:0%
+steps suppose that prices are totally
+ 
+
+ align:start position:0%
+steps suppose that prices are totally
+fixed and real GDP goes
+
+ align:start position:0%
+fixed and real GDP goes
+ 
+
+ align:start position:0%
+fixed and real GDP goes
+up that means that this economy needs
+
+ align:start position:0%
+up that means that this economy needs
+ 
+
+ align:start position:0%
+up that means that this economy needs
+more transactions because it's going to
+
+ align:start position:0%
+more transactions because it's going to
+ 
+
+ align:start position:0%
+more transactions because it's going to
+be more expenditure there okay so that
+
+ align:start position:0%
+be more expenditure there okay so that
+ 
+
+ align:start position:0%
+be more expenditure there okay so that
+that explains that yeah when real output
+
+ align:start position:0%
+that explains that yeah when real output
+ 
+
+ align:start position:0%
+that explains that yeah when real output
+goes up then money demand goes up when I
+
+ align:start position:0%
+goes up then money demand goes up when I
+ 
+
+ align:start position:0%
+goes up then money demand goes up when I
+say money demand goes up I said for any
+
+ align:start position:0%
+say money demand goes up I said for any
+ 
+
+ align:start position:0%
+say money demand goes up I said for any
+given interest rate we have more money
+
+ align:start position:0%
+given interest rate we have more money
+ 
+
+ align:start position:0%
+given interest rate we have more money
+demand okay now fix real output and I
+
+ align:start position:0%
+demand okay now fix real output and I
+ 
+
+ align:start position:0%
+demand okay now fix real output and I
+tell you suppose that the price of goods
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+doubles do you think you need more money
+
+ align:start position:0%
+doubles do you think you need more money
+ 
+
+ align:start position:0%
+doubles do you think you need more money
+to transact of course because it's the
+
+ align:start position:0%
+to transact of course because it's the
+ 
+
+ align:start position:0%
+to transact of course because it's the
+same it's equivalent now money is
+
+ align:start position:0%
+same it's equivalent now money is
+ 
+
+ align:start position:0%
+same it's equivalent now money is
+dollars I have $10 and now prices are
+
+ align:start position:0%
+dollars I have $10 and now prices are
+ 
+
+ align:start position:0%
+dollars I have $10 and now prices are
+twice what they used to be well I'm
+
+ align:start position:0%
+twice what they used to be well I'm
+ 
+
+ align:start position:0%
+twice what they used to be well I'm
+going to need more dollars to transact
+
+ align:start position:0%
+going to need more dollars to transact
+ 
+
+ align:start position:0%
+going to need more dollars to transact
+okay so that's a reason we have nominal
+
+ align:start position:0%
+okay so that's a reason we have nominal
+ 
+
+ align:start position:0%
+okay so that's a reason we have nominal
+GDP here rather than real GDP
+
+ align:start position:0%
+GDP here rather than real GDP
+ 
+
+ align:start position:0%
+GDP here rather than real GDP
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+good so let's now determine the interest
+
+ align:start position:0%
+good so let's now determine the interest
+ 
+
+ align:start position:0%
+good so let's now determine the interest
+rate and I'm going to do it in the
+
+ align:start position:0%
+rate and I'm going to do it in the
+ 
+
+ align:start position:0%
+rate and I'm going to do it in the
+simplest possible model first and and by
+
+ align:start position:0%
+simplest possible model first and and by
+ 
+
+ align:start position:0%
+simplest possible model first and and by
+simplest I mean here in particular no
+
+ align:start position:0%
+simplest I mean here in particular no
+ 
+
+ align:start position:0%
+simplest I mean here in particular no
+banks no intermediaries okay so there's
+
+ align:start position:0%
+banks no intermediaries okay so there's
+ 
+
+ align:start position:0%
+banks no intermediaries okay so there's
+only Central Bank and and and and and
+
+ align:start position:0%
+only Central Bank and and and and and
+ 
+
+ align:start position:0%
+only Central Bank and and and and and
+people okay so
+
+ align:start position:0%
+people okay so
+ 
+
+ align:start position:0%
+people okay so
+so suppose that the central banks
+
+ align:start position:0%
+so suppose that the central banks
+ 
+
+ align:start position:0%
+so suppose that the central banks
+decides that wants to this is the way
+
+ align:start position:0%
+decides that wants to this is the way
+ 
+
+ align:start position:0%
+decides that wants to this is the way
+monetary policy used to be conducted
+
+ align:start position:0%
+monetary policy used to be conducted
+ 
+
+ align:start position:0%
+monetary policy used to be conducted
+suppose is the size that it wants to
+
+ align:start position:0%
+suppose is the size that it wants to
+ 
+
+ align:start position:0%
+suppose is the size that it wants to
+offer M dollars to the economy and the
+
+ align:start position:0%
+offer M dollars to the economy and the
+ 
+
+ align:start position:0%
+offer M dollars to the economy and the
+central bank is the one that produces
+
+ align:start position:0%
+central bank is the one that produces
+ 
+
+ align:start position:0%
+central bank is the one that produces
+the at this moment which I have no
+
+ align:start position:0%
+the at this moment which I have no
+ 
+
+ align:start position:0%
+the at this moment which I have no
+intermediaries a ER money is really
+
+ align:start position:0%
+intermediaries a ER money is really
+ 
+
+ align:start position:0%
+intermediaries a ER money is really
+currency okay the only one that can
+
+ align:start position:0%
+currency okay the only one that can
+ 
+
+ align:start position:0%
+currency okay the only one that can
+produce currency forget Bitcoin only one
+
+ align:start position:0%
+produce currency forget Bitcoin only one
+ 
+
+ align:start position:0%
+produce currency forget Bitcoin only one
+that can produce currency is the Central
+
+ align:start position:0%
+that can produce currency is the Central
+ 
+
+ align:start position:0%
+that can produce currency is the Central
+Bank okay I mean dollars you can no one
+
+ align:start position:0%
+Bank okay I mean dollars you can no one
+ 
+
+ align:start position:0%
+Bank okay I mean dollars you can no one
+else can produce dollars
+
+ align:start position:0%
+else can produce dollars
+ 
+
+ align:start position:0%
+else can produce dollars
+watch out when we talk about Banks later
+
+ align:start position:0%
+watch out when we talk about Banks later
+ 
+
+ align:start position:0%
+watch out when we talk about Banks later
+on in this economy I'm describing there
+
+ align:start position:0%
+on in this economy I'm describing there
+ 
+
+ align:start position:0%
+on in this economy I'm describing there
+are no banks the only one that can
+
+ align:start position:0%
+are no banks the only one that can
+ 
+
+ align:start position:0%
+are no banks the only one that can
+produce Dollars currency is the Central
+
+ align:start position:0%
+produce Dollars currency is the Central
+ 
+
+ align:start position:0%
+produce Dollars currency is the Central
+Bank any other one that produces dollars
+
+ align:start position:0%
+Bank any other one that produces dollars
+ 
+
+ align:start position:0%
+Bank any other one that produces dollars
+that's illegal okay so it's a central
+
+ align:start position:0%
+that's illegal okay so it's a central
+ 
+
+ align:start position:0%
+that's illegal okay so it's a central
+bank so the central bank can decide how
+
+ align:start position:0%
+bank so the central bank can decide how
+ 
+
+ align:start position:0%
+bank so the central bank can decide how
+much money to
+
+ align:start position:0%
+much money to
+ 
+
+ align:start position:0%
+much money to
+supply and suppose it decides to supply
+
+ align:start position:0%
+supply and suppose it decides to supply
+ 
+
+ align:start position:0%
+supply and suppose it decides to supply
+M that's it it's a
+
+ align:start position:0%
+M that's it it's a
+ 
+
+ align:start position:0%
+M that's it it's a
+decision well what is a now for the
+
+ align:start position:0%
+decision well what is a now for the
+ 
+
+ align:start position:0%
+decision well what is a now for the
+first time I can I can answer the
+
+ align:start position:0%
+first time I can I can answer the
+ 
+
+ align:start position:0%
+first time I can I can answer the
+question is well what the interest rate
+
+ align:start position:0%
+question is well what the interest rate
+ 
+
+ align:start position:0%
+question is well what the interest rate
+in this environment why do I know that
+
+ align:start position:0%
+in this environment why do I know that
+ 
+
+ align:start position:0%
+in this environment why do I know that
+because I have a money supply I have a
+
+ align:start position:0%
+because I have a money supply I have a
+ 
+
+ align:start position:0%
+because I have a money supply I have a
+money demand the intersection at this
+
+ align:start position:0%
+money demand the intersection at this
+ 
+
+ align:start position:0%
+money demand the intersection at this
+level of money supply the equilibrium
+
+ align:start position:0%
+level of money supply the equilibrium
+ 
+
+ align:start position:0%
+level of money supply the equilibrium
+interest rate that is interest is
+
+ align:start position:0%
+interest rate that is interest is
+ 
+
+ align:start position:0%
+interest rate that is interest is
+consistent with money demand equal to
+
+ align:start position:0%
+consistent with money demand equal to
+ 
+
+ align:start position:0%
+consistent with money demand equal to
+money supply is that
+
+ align:start position:0%
+money supply is that
+ 
+
+ align:start position:0%
+money supply is that
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay is it clear so I have my money
+
+ align:start position:0%
+okay is it clear so I have my money
+ 
+
+ align:start position:0%
+okay is it clear so I have my money
+demand and I'm saying the Central Bank
+
+ align:start position:0%
+demand and I'm saying the Central Bank
+ 
+
+ align:start position:0%
+demand and I'm saying the Central Bank
+suppos the Central Bank De size to
+
+ align:start position:0%
+suppos the Central Bank De size to
+ 
+
+ align:start position:0%
+suppos the Central Bank De size to
+supply m well in equilibrium that will
+
+ align:start position:0%
+supply m well in equilibrium that will
+ 
+
+ align:start position:0%
+supply m well in equilibrium that will
+be the interest
+
+ align:start position:0%
+be the interest
+ 
+
+ align:start position:0%
+be the interest
+rate okay that's the way the interest
+
+ align:start position:0%
+rate okay that's the way the interest
+ 
+
+ align:start position:0%
+rate okay that's the way the interest
+rate is
+
+ align:start position:0%
+rate is
+ 
+
+ align:start position:0%
+rate is
+determined
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now suppose that the Central Bank
+
+ align:start position:0%
+now suppose that the Central Bank
+ 
+
+ align:start position:0%
+now suppose that the Central Bank
+increases remember the the goal of this
+
+ align:start position:0%
+increases remember the the goal of this
+ 
+
+ align:start position:0%
+increases remember the the goal of this
+lecture is that we get to understand how
+
+ align:start position:0%
+lecture is that we get to understand how
+ 
+
+ align:start position:0%
+lecture is that we get to understand how
+is that interest rate is deter is
+
+ align:start position:0%
+is that interest rate is deter is
+ 
+
+ align:start position:0%
+is that interest rate is deter is
+determined how is that the fed the
+
+ align:start position:0%
+determined how is that the fed the
+ 
+
+ align:start position:0%
+determined how is that the fed the
+Central Bank determines the interest
+
+ align:start position:0%
+Central Bank determines the interest
+ 
+
+ align:start position:0%
+Central Bank determines the interest
+rate here we said look the Central Bank
+
+ align:start position:0%
+rate here we said look the Central Bank
+ 
+
+ align:start position:0%
+rate here we said look the Central Bank
+decide on certain am amount of money and
+
+ align:start position:0%
+decide on certain am amount of money and
+ 
+
+ align:start position:0%
+decide on certain am amount of money and
+then the market determines what the
+
+ align:start position:0%
+then the market determines what the
+ 
+
+ align:start position:0%
+then the market determines what the
+interest rate
+
+ align:start position:0%
+interest rate
+ 
+
+ align:start position:0%
+interest rate
+is and this is the way monetary policy
+
+ align:start position:0%
+is and this is the way monetary policy
+ 
+
+ align:start position:0%
+is and this is the way monetary policy
+used to be conducted the central banks
+
+ align:start position:0%
+used to be conducted the central banks
+ 
+
+ align:start position:0%
+used to be conducted the central banks
+would typically decide the amount of
+
+ align:start position:0%
+would typically decide the amount of
+ 
+
+ align:start position:0%
+would typically decide the amount of
+money in the system it was called
+
+ align:start position:0%
+money in the system it was called
+ 
+
+ align:start position:0%
+money in the system it was called
+monetary Aggregates the amount of money
+
+ align:start position:0%
+monetary Aggregates the amount of money
+ 
+
+ align:start position:0%
+monetary Aggregates the amount of money
+in the system and then the market would
+
+ align:start position:0%
+in the system and then the market would
+ 
+
+ align:start position:0%
+in the system and then the market would
+determine the interest
+
+ align:start position:0%
+determine the interest
+ 
+
+ align:start position:0%
+determine the interest
+rate it turned out that that was a
+
+ align:start position:0%
+rate it turned out that that was a
+ 
+
+ align:start position:0%
+rate it turned out that that was a
+nightmare and so now that's that's not
+
+ align:start position:0%
+nightmare and so now that's that's not
+ 
+
+ align:start position:0%
+nightmare and so now that's that's not
+what central banks do but and it was a
+
+ align:start position:0%
+what central banks do but and it was a
+ 
+
+ align:start position:0%
+what central banks do but and it was a
+night mayor because this money demand
+
+ align:start position:0%
+night mayor because this money demand
+ 
+
+ align:start position:0%
+night mayor because this money demand
+that looks so peaceful here in practice
+
+ align:start position:0%
+that looks so peaceful here in practice
+ 
+
+ align:start position:0%
+that looks so peaceful here in practice
+is moving around all the time for a
+
+ align:start position:0%
+is moving around all the time for a
+ 
+
+ align:start position:0%
+is moving around all the time for a
+variety of reason you know even holidays
+
+ align:start position:0%
+variety of reason you know even holidays
+ 
+
+ align:start position:0%
+variety of reason you know even holidays
+affect the money demand and all that so
+
+ align:start position:0%
+affect the money demand and all that so
+ 
+
+ align:start position:0%
+affect the money demand and all that so
+so if you fix the monetary Aggregates
+
+ align:start position:0%
+so if you fix the monetary Aggregates
+ 
+
+ align:start position:0%
+so if you fix the monetary Aggregates
+and many the man is moving all over the
+
+ align:start position:0%
+and many the man is moving all over the
+ 
+
+ align:start position:0%
+and many the man is moving all over the
+place what what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happens suppose the Central Bank says
+
+ align:start position:0%
+happens suppose the Central Bank says
+ 
+
+ align:start position:0%
+happens suppose the Central Bank says
+I'm going to offer this amount of M
+
+ align:start position:0%
+I'm going to offer this amount of M
+ 
+
+ align:start position:0%
+I'm going to offer this amount of M
+that's it and now I tell you money the
+
+ align:start position:0%
+that's it and now I tell you money the
+ 
+
+ align:start position:0%
+that's it and now I tell you money the
+money is moving all over the place
+
+ align:start position:0%
+money is moving all over the place
+ 
+
+ align:start position:0%
+money is moving all over the place
+they're weeks that they have you know
+
+ align:start position:0%
+they're weeks that they have you know
+ 
+
+ align:start position:0%
+they're weeks that they have you know
+three days of of weekend that have you
+
+ align:start position:0%
+three days of of weekend that have you
+ 
+
+ align:start position:0%
+three days of of weekend that have you
+know vacations in between or there's a
+
+ align:start position:0%
+know vacations in between or there's a
+ 
+
+ align:start position:0%
+know vacations in between or there's a
+Super Bowl lots of people decide to buy
+
+ align:start position:0%
+Super Bowl lots of people decide to buy
+ 
+
+ align:start position:0%
+Super Bowl lots of people decide to buy
+tickets or whatever or beer so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whatever well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no because when you say shortage I mean
+
+ align:start position:0%
+no because when you say shortage I mean
+ 
+
+ align:start position:0%
+no because when you say shortage I mean
+depends what you mean by shortage but so
+
+ align:start position:0%
+depends what you mean by shortage but so
+ 
+
+ align:start position:0%
+depends what you mean by shortage but so
+so you could be right with that part of
+
+ align:start position:0%
+so you could be right with that part of
+ 
+
+ align:start position:0%
+so you could be right with that part of
+the answer but but when you say exess
+
+ align:start position:0%
+the answer but but when you say exess
+ 
+
+ align:start position:0%
+the answer but but when you say exess
+theand then I have a problem because
+
+ align:start position:0%
+theand then I have a problem because
+ 
+
+ align:start position:0%
+theand then I have a problem because
+that's true only if the interest rate
+
+ align:start position:0%
+that's true only if the interest rate
+ 
+
+ align:start position:0%
+that's true only if the interest rate
+doesn't
+
+ align:start position:0%
+doesn't
+ 
+
+ align:start position:0%
+doesn't
+move but in a in a in a situation you
+
+ align:start position:0%
+move but in a in a in a situation you
+ 
+
+ align:start position:0%
+move but in a in a in a situation you
+could just the Central Bank fix M and
+
+ align:start position:0%
+could just the Central Bank fix M and
+ 
+
+ align:start position:0%
+could just the Central Bank fix M and
+let the market do its thing then the
+
+ align:start position:0%
+let the market do its thing then the
+ 
+
+ align:start position:0%
+let the market do its thing then the
+interest rate will not be fixed and
+
+ align:start position:0%
+interest rate will not be fixed and
+ 
+
+ align:start position:0%
+interest rate will not be fixed and
+that's exactly the problem that the
+
+ align:start position:0%
+that's exactly the problem that the
+ 
+
+ align:start position:0%
+that's exactly the problem that the
+interest rate becomes very very volatile
+
+ align:start position:0%
+interest rate becomes very very volatile
+ 
+
+ align:start position:0%
+interest rate becomes very very volatile
+if you if you do it only only through
+
+ align:start position:0%
+if you if you do it only only through
+ 
+
+ align:start position:0%
+if you if you do it only only through
+through monetary arates because this guy
+
+ align:start position:0%
+through monetary arates because this guy
+ 
+
+ align:start position:0%
+through monetary arates because this guy
+is moving all over the place and so
+
+ align:start position:0%
+is moving all over the place and so
+ 
+
+ align:start position:0%
+is moving all over the place and so
+imagine what happens if this demand
+
+ align:start position:0%
+imagine what happens if this demand
+ 
+
+ align:start position:0%
+imagine what happens if this demand
+shift up then in equilibrium it say goes
+
+ align:start position:0%
+shift up then in equilibrium it say goes
+ 
+
+ align:start position:0%
+shift up then in equilibrium it say goes
+up precisely to avoid your excess demand
+
+ align:start position:0%
+up precisely to avoid your excess demand
+ 
+
+ align:start position:0%
+up precisely to avoid your excess demand
+no because if this thing goes up I have
+
+ align:start position:0%
+no because if this thing goes up I have
+ 
+
+ align:start position:0%
+no because if this thing goes up I have
+an excess demand at that interest rate
+
+ align:start position:0%
+an excess demand at that interest rate
+ 
+
+ align:start position:0%
+an excess demand at that interest rate
+but what happen in equili is the
+
+ align:start position:0%
+but what happen in equili is the
+ 
+
+ align:start position:0%
+but what happen in equili is the
+interest rate will go up and so until
+
+ align:start position:0%
+interest rate will go up and so until
+ 
+
+ align:start position:0%
+interest rate will go up and so until
+the the excess demand
+
+ align:start position:0%
+the the excess demand
+ 
+
+ align:start position:0%
+the the excess demand
+disappears now in in central banks like
+
+ align:start position:0%
+disappears now in in central banks like
+ 
+
+ align:start position:0%
+disappears now in in central banks like
+the US Central Bank the FED they can
+
+ align:start position:0%
+the US Central Bank the FED they can
+ 
+
+ align:start position:0%
+the US Central Bank the FED they can
+control this stuff fairly well many
+
+ align:start position:0%
+control this stuff fairly well many
+ 
+
+ align:start position:0%
+control this stuff fairly well many
+other central banks don't have that if
+
+ align:start position:0%
+other central banks don't have that if
+ 
+
+ align:start position:0%
+other central banks don't have that if
+you look at the at the central at at the
+
+ align:start position:0%
+you look at the at the central at at the
+ 
+
+ align:start position:0%
+you look at the at the central at at the
+Bank of China for example they have lots
+
+ align:start position:0%
+Bank of China for example they have lots
+ 
+
+ align:start position:0%
+Bank of China for example they have lots
+of high frequency movements in interest
+
+ align:start position:0%
+of high frequency movements in interest
+ 
+
+ align:start position:0%
+of high frequency movements in interest
+rate because they not very good at doing
+
+ align:start position:0%
+rate because they not very good at doing
+ 
+
+ align:start position:0%
+rate because they not very good at doing
+this stuff it's it's not that easy to
+
+ align:start position:0%
+this stuff it's it's not that easy to
+ 
+
+ align:start position:0%
+this stuff it's it's not that easy to
+okay to to to control an interest rate
+
+ align:start position:0%
+okay to to to control an interest rate
+ 
+
+ align:start position:0%
+okay to to to control an interest rate
+for example to keep it we but the
+
+ align:start position:0%
+for example to keep it we but the
+ 
+
+ align:start position:0%
+for example to keep it we but the
+Central Bank used to do that that's what
+
+ align:start position:0%
+Central Bank used to do that that's what
+ 
+
+ align:start position:0%
+Central Bank used to do that that's what
+I'm saying used to do that I'm saying in
+
+ align:start position:0%
+I'm saying used to do that I'm saying in
+ 
+
+ align:start position:0%
+I'm saying used to do that I'm saying in
+practice this system wasn't very good
+
+ align:start position:0%
+practice this system wasn't very good
+ 
+
+ align:start position:0%
+practice this system wasn't very good
+because this in practice this the man is
+
+ align:start position:0%
+because this in practice this the man is
+ 
+
+ align:start position:0%
+because this in practice this the man is
+moving around for a lot of EOS syncratic
+
+ align:start position:0%
+moving around for a lot of EOS syncratic
+ 
+
+ align:start position:0%
+moving around for a lot of EOS syncratic
+reasons okay some of them are EOS
+
+ align:start position:0%
+reasons okay some of them are EOS
+ 
+
+ align:start position:0%
+reasons okay some of them are EOS
+syncratic some of them are very
+
+ align:start position:0%
+syncratic some of them are very
+ 
+
+ align:start position:0%
+syncratic some of them are very
+predictable there was a lot of panic
+
+ align:start position:0%
+predictable there was a lot of panic
+ 
+
+ align:start position:0%
+predictable there was a lot of panic
+around the shift of the year 2000 that
+
+ align:start position:0%
+around the shift of the year 2000 that
+ 
+
+ align:start position:0%
+around the shift of the year 2000 that
+the ATMs would stop working and stuff
+
+ align:start position:0%
+the ATMs would stop working and stuff
+ 
+
+ align:start position:0%
+the ATMs would stop working and stuff
+like that so it was a massive increase
+
+ align:start position:0%
+like that so it was a massive increase
+ 
+
+ align:start position:0%
+like that so it was a massive increase
+in money demand because people wanted to
+
+ align:start position:0%
+in money demand because people wanted to
+ 
+
+ align:start position:0%
+in money demand because people wanted to
+have cash just in case ATMs sto working
+
+ align:start position:0%
+have cash just in case ATMs sto working
+ 
+
+ align:start position:0%
+have cash just in case ATMs sto working
+okay and and so there are some are
+
+ align:start position:0%
+okay and and so there are some are
+ 
+
+ align:start position:0%
+okay and and so there are some are
+predictable and so but but you can get
+
+ align:start position:0%
+predictable and so but but you can get
+ 
+
+ align:start position:0%
+predictable and so but but you can get
+very large fluctuations so in practice
+
+ align:start position:0%
+very large fluctuations so in practice
+ 
+
+ align:start position:0%
+very large fluctuations so in practice
+what central banks do nowadays is really
+
+ align:start position:0%
+what central banks do nowadays is really
+ 
+
+ align:start position:0%
+what central banks do nowadays is really
+is they tell you what the interest rate
+
+ align:start position:0%
+is they tell you what the interest rate
+ 
+
+ align:start position:0%
+is they tell you what the interest rate
+is and then they offer whatever M the
+
+ align:start position:0%
+is and then they offer whatever M the
+ 
+
+ align:start position:0%
+is and then they offer whatever M the
+market needs for that interest rate
+
+ align:start position:0%
+market needs for that interest rate
+ 
+
+ align:start position:0%
+market needs for that interest rate
+that's the way modern monetary policy
+
+ align:start position:0%
+that's the way modern monetary policy
+ 
+
+ align:start position:0%
+that's the way modern monetary policy
+works okay I I'll tell you a little bit
+
+ align:start position:0%
+works okay I I'll tell you a little bit
+ 
+
+ align:start position:0%
+works okay I I'll tell you a little bit
+more about that so let's see what
+
+ align:start position:0%
+more about that so let's see what
+ 
+
+ align:start position:0%
+more about that so let's see what
+happens here if if if if
+
+ align:start position:0%
+happens here if if if if
+ 
+
+ align:start position:0%
+happens here if if if if
+uh if the suppose the the Fed
+
+ align:start position:0%
+uh if the suppose the the Fed
+ 
+
+ align:start position:0%
+uh if the suppose the the Fed
+for reasons that you'll understand
+
+ align:start position:0%
+for reasons that you'll understand
+ 
+
+ align:start position:0%
+for reasons that you'll understand
+better in the SEC in the next lecture
+
+ align:start position:0%
+better in the SEC in the next lecture
+ 
+
+ align:start position:0%
+better in the SEC in the next lecture
+suppose the FED decides that they want
+
+ align:start position:0%
+suppose the FED decides that they want
+ 
+
+ align:start position:0%
+suppose the FED decides that they want
+to have an expansionary monetary policy
+
+ align:start position:0%
+to have an expansionary monetary policy
+ 
+
+ align:start position:0%
+to have an expansionary monetary policy
+expansion in monetary policy means it's
+
+ align:start position:0%
+expansion in monetary policy means it's
+ 
+
+ align:start position:0%
+expansion in monetary policy means it's
+going to spand M it was offering certain
+
+ align:start position:0%
+going to spand M it was offering certain
+ 
+
+ align:start position:0%
+going to spand M it was offering certain
+amount of M and now it decides to offer
+
+ align:start position:0%
+amount of M and now it decides to offer
+ 
+
+ align:start position:0%
+amount of M and now it decides to offer
+more of the D so what happens in
+
+ align:start position:0%
+more of the D so what happens in
+ 
+
+ align:start position:0%
+more of the D so what happens in
+equilibrium well we start from an
+
+ align:start position:0%
+equilibrium well we start from an
+ 
+
+ align:start position:0%
+equilibrium well we start from an
+equilibrium here if the interest rate
+
+ align:start position:0%
+equilibrium here if the interest rate
+ 
+
+ align:start position:0%
+equilibrium here if the interest rate
+remains at that level now we have an
+
+ align:start position:0%
+remains at that level now we have an
+ 
+
+ align:start position:0%
+remains at that level now we have an
+excess
+
+ align:start position:0%
+excess
+ 
+
+ align:start position:0%
+excess
+supply of money
+
+ align:start position:0%
+supply of money
+ 
+
+ align:start position:0%
+supply of money
+okay and the only way to restore that
+
+ align:start position:0%
+okay and the only way to restore that
+ 
+
+ align:start position:0%
+okay and the only way to restore that
+equilibrium is by people demanding more
+
+ align:start position:0%
+equilibrium is by people demanding more
+ 
+
+ align:start position:0%
+equilibrium is by people demanding more
+money and how when will people demand
+
+ align:start position:0%
+money and how when will people demand
+ 
+
+ align:start position:0%
+money and how when will people demand
+more money well when the interest rate
+
+ align:start position:0%
+more money well when the interest rate
+ 
+
+ align:start position:0%
+more money well when the interest rate
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+lower okay so excess demand the interest
+
+ align:start position:0%
+lower okay so excess demand the interest
+ 
+
+ align:start position:0%
+lower okay so excess demand the interest
+start declining then demand for money
+
+ align:start position:0%
+start declining then demand for money
+ 
+
+ align:start position:0%
+start declining then demand for money
+starts catching up with a new higher
+
+ align:start position:0%
+starts catching up with a new higher
+ 
+
+ align:start position:0%
+starts catching up with a new higher
+supply of money okay and you end up with
+
+ align:start position:0%
+supply of money okay and you end up with
+ 
+
+ align:start position:0%
+supply of money okay and you end up with
+a lower interest
+
+ align:start position:0%
+a lower interest
+ 
+
+ align:start position:0%
+a lower interest
+rate okay so that's an expansion in
+
+ align:start position:0%
+rate okay so that's an expansion in
+ 
+
+ align:start position:0%
+rate okay so that's an expansion in
+monetary policy an increasing M that
+
+ align:start position:0%
+monetary policy an increasing M that
+ 
+
+ align:start position:0%
+monetary policy an increasing M that
+leads to a decline in the interest rate
+
+ align:start position:0%
+leads to a decline in the interest rate
+ 
+
+ align:start position:0%
+leads to a decline in the interest rate
+again mod than central banks don't tell
+
+ align:start position:0%
+again mod than central banks don't tell
+ 
+
+ align:start position:0%
+again mod than central banks don't tell
+you we're going to increase M by 20%
+
+ align:start position:0%
+you we're going to increase M by 20%
+ 
+
+ align:start position:0%
+you we're going to increase M by 20%
+what they tell you is we're going to cut
+
+ align:start position:0%
+what they tell you is we're going to cut
+ 
+
+ align:start position:0%
+what they tell you is we're going to cut
+interest rate by say 50 basis
+
+ align:start position:0%
+interest rate by say 50 basis
+ 
+
+ align:start position:0%
+interest rate by say 50 basis
+points when they tell you that they're
+
+ align:start position:0%
+points when they tell you that they're
+ 
+
+ align:start position:0%
+points when they tell you that they're
+going to C cut interest in by 50 point
+
+ align:start position:0%
+going to C cut interest in by 50 point
+ 
+
+ align:start position:0%
+going to C cut interest in by 50 point
+they're reading you this
+
+ align:start position:0%
+they're reading you this
+ 
+
+ align:start position:0%
+they're reading you this
+accxes but
+
+ align:start position:0%
+accxes but
+ 
+
+ align:start position:0%
+accxes but
+behind that operation there must have
+
+ align:start position:0%
+behind that operation there must have
+ 
+
+ align:start position:0%
+behind that operation there must have
+been an increase in money
+
+ align:start position:0%
+been an increase in money
+ 
+
+ align:start position:0%
+been an increase in money
+supply and then it comes all the fine
+
+ align:start position:0%
+supply and then it comes all the fine
+ 
+
+ align:start position:0%
+supply and then it comes all the fine
+tuning that that they have to do know so
+
+ align:start position:0%
+tuning that that they have to do know so
+ 
+
+ align:start position:0%
+tuning that that they have to do know so
+so the interestate remains there when
+
+ align:start position:0%
+so the interestate remains there when
+ 
+
+ align:start position:0%
+so the interestate remains there when
+the man is vibrating around that thing
+
+ align:start position:0%
+the man is vibrating around that thing
+ 
+
+ align:start position:0%
+the man is vibrating around that thing
+there but the when we say an
+
+ align:start position:0%
+there but the when we say an
+ 
+
+ align:start position:0%
+there but the when we say an
+expansionary monetary policy we really
+
+ align:start position:0%
+expansionary monetary policy we really
+ 
+
+ align:start position:0%
+expansionary monetary policy we really
+mean cutting interest rates how is the
+
+ align:start position:0%
+mean cutting interest rates how is the
+ 
+
+ align:start position:0%
+mean cutting interest rates how is the
+interest rates cut effectively by
+
+ align:start position:0%
+interest rates cut effectively by
+ 
+
+ align:start position:0%
+interest rates cut effectively by
+increasing the money supply but they
+
+ align:start position:0%
+increasing the money supply but they
+ 
+
+ align:start position:0%
+increasing the money supply but they
+don't tell you that they are doing that
+
+ align:start position:0%
+don't tell you that they are doing that
+ 
+
+ align:start position:0%
+don't tell you that they are doing that
+but that's what they're doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good so nowadays we're in the
+
+ align:start position:0%
+okay good so nowadays we're in the
+ 
+
+ align:start position:0%
+okay good so nowadays we're in the
+opposite process we're moving that way
+
+ align:start position:0%
+opposite process we're moving that way
+ 
+
+ align:start position:0%
+opposite process we're moving that way
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+up but you seen in every single meeting
+
+ align:start position:0%
+up but you seen in every single meeting
+ 
+
+ align:start position:0%
+up but you seen in every single meeting
+now for the last seven minutes or so we
+
+ align:start position:0%
+now for the last seven minutes or so we
+ 
+
+ align:start position:0%
+now for the last seven minutes or so we
+have seen a hike in interest ratees okay
+
+ align:start position:0%
+have seen a hike in interest ratees okay
+ 
+
+ align:start position:0%
+have seen a hike in interest ratees okay
+H well that's they don't tell you that
+
+ align:start position:0%
+H well that's they don't tell you that
+ 
+
+ align:start position:0%
+H well that's they don't tell you that
+but they're saying we're going to cut
+
+ align:start position:0%
+but they're saying we're going to cut
+ 
+
+ align:start position:0%
+but they're saying we're going to cut
+money supply and moving in that
+
+ align:start position:0%
+money supply and moving in that
+ 
+
+ align:start position:0%
+money supply and moving in that
+direction that
+
+ align:start position:0%
+direction that
+ 
+
+ align:start position:0%
+direction that
+direction because if they move in that
+
+ align:start position:0%
+direction because if they move in that
+ 
+
+ align:start position:0%
+direction because if they move in that
+direction then interest rate go
+
+ align:start position:0%
+direction then interest rate go
+ 
+
+ align:start position:0%
+direction then interest rate go
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+clear good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what else shifts uh this is different
+
+ align:start position:0%
+what else shifts uh this is different
+ 
+
+ align:start position:0%
+what else shifts uh this is different
+kind of shift suppose that nominal
+
+ align:start position:0%
+kind of shift suppose that nominal
+ 
+
+ align:start position:0%
+kind of shift suppose that nominal
+income goes up and this is happening all
+
+ align:start position:0%
+income goes up and this is happening all
+ 
+
+ align:start position:0%
+income goes up and this is happening all
+the time nominal income is growing in
+
+ align:start position:0%
+the time nominal income is growing in
+ 
+
+ align:start position:0%
+the time nominal income is growing in
+most economies most of the time unless
+
+ align:start position:0%
+most economies most of the time unless
+ 
+
+ align:start position:0%
+most economies most of the time unless
+you're in a recession nominal income is
+
+ align:start position:0%
+you're in a recession nominal income is
+ 
+
+ align:start position:0%
+you're in a recession nominal income is
+growing it's growing for two reasons one
+
+ align:start position:0%
+growing it's growing for two reasons one
+ 
+
+ align:start position:0%
+growing it's growing for two reasons one
+because we have inflation and the other
+
+ align:start position:0%
+because we have inflation and the other
+ 
+
+ align:start position:0%
+because we have inflation and the other
+one is because real output is growing
+
+ align:start position:0%
+one is because real output is growing
+ 
+
+ align:start position:0%
+one is because real output is growing
+that means that that typically in an
+
+ align:start position:0%
+that means that that typically in an
+ 
+
+ align:start position:0%
+that means that that typically in an
+average year manyy demand is Shifting to
+
+ align:start position:0%
+average year manyy demand is Shifting to
+ 
+
+ align:start position:0%
+average year manyy demand is Shifting to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+right okay
+
+ align:start position:0%
+right okay
+ 
+
+ align:start position:0%
+right okay
+so if money demand shift to the right
+
+ align:start position:0%
+so if money demand shift to the right
+ 
+
+ align:start position:0%
+so if money demand shift to the right
+and money supply does not
+
+ align:start position:0%
+and money supply does not
+ 
+
+ align:start position:0%
+and money supply does not
+change then what happens to the interest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate money demand goes up money supplies
+
+ align:start position:0%
+rate money demand goes up money supplies
+ 
+
+ align:start position:0%
+rate money demand goes up money supplies
+doesn't change what happens to the
+
+ align:start position:0%
+doesn't change what happens to the
+ 
+
+ align:start position:0%
+doesn't change what happens to the
+interest
+
+ align:start position:0%
+interest
+ 
+
+ align:start position:0%
+interest
+rate increases because at this interest
+
+ align:start position:0%
+rate increases because at this interest
+ 
+
+ align:start position:0%
+rate increases because at this interest
+rate here we have an excess demand for
+
+ align:start position:0%
+rate here we have an excess demand for
+ 
+
+ align:start position:0%
+rate here we have an excess demand for
+money so we have to reduce the money
+
+ align:start position:0%
+money so we have to reduce the money
+ 
+
+ align:start position:0%
+money so we have to reduce the money
+demand how do we reduce money Demand by
+
+ align:start position:0%
+demand how do we reduce money Demand by
+ 
+
+ align:start position:0%
+demand how do we reduce money Demand by
+increasing the interest rate
+
+ align:start position:0%
+increasing the interest rate
+ 
+
+ align:start position:0%
+increasing the interest rate
+that's way we so that's yet another
+
+ align:start position:0%
+that's way we so that's yet another
+ 
+
+ align:start position:0%
+that's way we so that's yet another
+reason why why it's not a good idea to
+
+ align:start position:0%
+reason why why it's not a good idea to
+ 
+
+ align:start position:0%
+reason why why it's not a good idea to
+be targeting monetary Aggregates the FED
+
+ align:start position:0%
+be targeting monetary Aggregates the FED
+ 
+
+ align:start position:0%
+be targeting monetary Aggregates the FED
+tells you we we want the interest rate
+
+ align:start position:0%
+tells you we we want the interest rate
+ 
+
+ align:start position:0%
+tells you we we want the interest rate
+at 5% say okay and then the economy will
+
+ align:start position:0%
+at 5% say okay and then the economy will
+ 
+
+ align:start position:0%
+at 5% say okay and then the economy will
+be growing and so on and what the FED
+
+ align:start position:0%
+be growing and so on and what the FED
+ 
+
+ align:start position:0%
+be growing and so on and what the FED
+will be doing is if they want to
+
+ align:start position:0%
+will be doing is if they want to
+ 
+
+ align:start position:0%
+will be doing is if they want to
+maintain the interest rate at 5% well
+
+ align:start position:0%
+maintain the interest rate at 5% well
+ 
+
+ align:start position:0%
+maintain the interest rate at 5% well
+they'll keep expanding M so the interest
+
+ align:start position:0%
+they'll keep expanding M so the interest
+ 
+
+ align:start position:0%
+they'll keep expanding M so the interest
+rate doesn't go up okay that's the way
+
+ align:start position:0%
+rate doesn't go up okay that's the way
+ 
+
+ align:start position:0%
+rate doesn't go up okay that's the way
+normally conduct but if the if the FED
+
+ align:start position:0%
+normally conduct but if the if the FED
+ 
+
+ align:start position:0%
+normally conduct but if the if the FED
+stays sleepy and and and you have an
+
+ align:start position:0%
+stays sleepy and and and you have an
+ 
+
+ align:start position:0%
+stays sleepy and and and you have an
+increasing many demand then then the
+
+ align:start position:0%
+increasing many demand then then the
+ 
+
+ align:start position:0%
+increasing many demand then then the
+interest will tend to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up so I told you that that
+
+ align:start position:0%
+up so I told you that that
+ 
+
+ align:start position:0%
+up so I told you that that
+ER that the central bank is moving M
+
+ align:start position:0%
+ER that the central bank is moving M
+ 
+
+ align:start position:0%
+ER that the central bank is moving M
+increasing them reducing them or
+
+ align:start position:0%
+increasing them reducing them or
+ 
+
+ align:start position:0%
+increasing them reducing them or
+whatever so how do they do
+
+ align:start position:0%
+whatever so how do they do
+ 
+
+ align:start position:0%
+whatever so how do they do
+that I
+
+ align:start position:0%
+that I
+ 
+
+ align:start position:0%
+that I
+mean it's not that they although that
+
+ align:start position:0%
+mean it's not that they although that
+ 
+
+ align:start position:0%
+mean it's not that they although that
+police has been advocated it's not that
+
+ align:start position:0%
+police has been advocated it's not that
+ 
+
+ align:start position:0%
+police has been advocated it's not that
+they go in a helicopter and sort of fly
+
+ align:start position:0%
+they go in a helicopter and sort of fly
+ 
+
+ align:start position:0%
+they go in a helicopter and sort of fly
+bills on top of all of us they don't do
+
+ align:start position:0%
+bills on top of all of us they don't do
+ 
+
+ align:start position:0%
+bills on top of all of us they don't do
+that although again it has been
+
+ align:start position:0%
+that although again it has been
+ 
+
+ align:start position:0%
+that although again it has been
+advocated in extreme cases of recessions
+
+ align:start position:0%
+advocated in extreme cases of recessions
+ 
+
+ align:start position:0%
+advocated in extreme cases of recessions
+and so on and it's called helicopter
+
+ align:start position:0%
+and so on and it's called helicopter
+ 
+
+ align:start position:0%
+and so on and it's called helicopter
+money just give money away okay
+
+ align:start position:0%
+money just give money away okay
+ 
+
+ align:start position:0%
+money just give money away okay
+ER but that's not the way it's normally
+
+ align:start position:0%
+ER but that's not the way it's normally
+ 
+
+ align:start position:0%
+ER but that's not the way it's normally
+done for normal operations is not done
+
+ align:start position:0%
+done for normal operations is not done
+ 
+
+ align:start position:0%
+done for normal operations is not done
+that way so how is it done remember that
+
+ align:start position:0%
+that way so how is it done remember that
+ 
+
+ align:start position:0%
+that way so how is it done remember that
+we have a financial system that is very
+
+ align:start position:0%
+we have a financial system that is very
+ 
+
+ align:start position:0%
+we have a financial system that is very
+simple for now we have money and bonds
+
+ align:start position:0%
+simple for now we have money and bonds
+ 
+
+ align:start position:0%
+simple for now we have money and bonds
+so what the Central Bank does the
+
+ align:start position:0%
+so what the Central Bank does the
+ 
+
+ align:start position:0%
+so what the Central Bank does the
+Central Bank wants to change the
+
+ align:start position:0%
+Central Bank wants to change the
+ 
+
+ align:start position:0%
+Central Bank wants to change the
+portfolio of people that they want
+
+ align:start position:0%
+portfolio of people that they want
+ 
+
+ align:start position:0%
+portfolio of people that they want
+people to have less bonds say and more
+
+ align:start position:0%
+people to have less bonds say and more
+ 
+
+ align:start position:0%
+people to have less bonds say and more
+money that's when that's to ruce the
+
+ align:start position:0%
+money that's when that's to ruce the
+ 
+
+ align:start position:0%
+money that's when that's to ruce the
+interest rate so what the Central Bank
+
+ align:start position:0%
+interest rate so what the Central Bank
+ 
+
+ align:start position:0%
+interest rate so what the Central Bank
+does is goes up there and expansionary
+
+ align:start position:0%
+does is goes up there and expansionary
+ 
+
+ align:start position:0%
+does is goes up there and expansionary
+open market operation open market is
+
+ align:start position:0%
+open market operation open market is
+ 
+
+ align:start position:0%
+open market operation open market is
+because they go into the open market to
+
+ align:start position:0%
+because they go into the open market to
+ 
+
+ align:start position:0%
+because they go into the open market to
+buy bonds okay they as as opposed to an
+
+ align:start position:0%
+buy bonds okay they as as opposed to an
+ 
+
+ align:start position:0%
+buy bonds okay they as as opposed to an
+operation that happens behind doors if
+
+ align:start position:0%
+operation that happens behind doors if
+ 
+
+ align:start position:0%
+operation that happens behind doors if
+the if the FED went directly to the
+
+ align:start position:0%
+the if the FED went directly to the
+ 
+
+ align:start position:0%
+the if the FED went directly to the
+treasury and bought bonds that would not
+
+ align:start position:0%
+treasury and bought bonds that would not
+ 
+
+ align:start position:0%
+treasury and bought bonds that would not
+be an open market operation okay but
+
+ align:start position:0%
+be an open market operation okay but
+ 
+
+ align:start position:0%
+be an open market operation okay but
+what they do is they go to financial
+
+ align:start position:0%
+what they do is they go to financial
+ 
+
+ align:start position:0%
+what they do is they go to financial
+their financial system and they go with
+
+ align:start position:0%
+their financial system and they go with
+ 
+
+ align:start position:0%
+their financial system and they go with
+a big bag of money and say okay we want
+
+ align:start position:0%
+a big bag of money and say okay we want
+ 
+
+ align:start position:0%
+a big bag of money and say okay we want
+bones and so the public sells bones to
+
+ align:start position:0%
+bones and so the public sells bones to
+ 
+
+ align:start position:0%
+bones and so the public sells bones to
+them in exchange for money okay that's
+
+ align:start position:0%
+them in exchange for money okay that's
+ 
+
+ align:start position:0%
+them in exchange for money okay that's
+an expansion in market so what we saw
+
+ align:start position:0%
+an expansion in market so what we saw
+ 
+
+ align:start position:0%
+an expansion in market so what we saw
+that before when M shift to the right
+
+ align:start position:0%
+that before when M shift to the right
+ 
+
+ align:start position:0%
+that before when M shift to the right
+what the central bank really did is went
+
+ align:start position:0%
+what the central bank really did is went
+ 
+
+ align:start position:0%
+what the central bank really did is went
+out there and bought bonds from the
+
+ align:start position:0%
+out there and bought bonds from the
+ 
+
+ align:start position:0%
+out there and bought bonds from the
+public the public sold the
+
+ align:start position:0%
+public the public sold the
+ 
+
+ align:start position:0%
+public the public sold the
+bonds and got the cash okay at some
+
+ align:start position:0%
+bonds and got the cash okay at some
+ 
+
+ align:start position:0%
+bonds and got the cash okay at some
+price people when when I show you
+
+ align:start position:0%
+price people when when I show you
+ 
+
+ align:start position:0%
+price people when when I show you
+equilibrium in the money market that
+
+ align:start position:0%
+equilibrium in the money market that
+ 
+
+ align:start position:0%
+equilibrium in the money market that
+means also an equilibrium in the bond
+
+ align:start position:0%
+means also an equilibrium in the bond
+ 
+
+ align:start position:0%
+means also an equilibrium in the bond
+market necessarily so it has to be that
+
+ align:start position:0%
+market necessarily so it has to be that
+ 
+
+ align:start position:0%
+market necessarily so it has to be that
+the price is right for the for the
+
+ align:start position:0%
+the price is right for the for the
+ 
+
+ align:start position:0%
+the price is right for the for the
+portfolio of individuals a
+
+ align:start position:0%
+portfolio of individuals a
+ 
+
+ align:start position:0%
+portfolio of individuals a
+contractionary open market operation is
+
+ align:start position:0%
+contractionary open market operation is
+ 
+
+ align:start position:0%
+contractionary open market operation is
+the opposite is a central bank goes out
+
+ align:start position:0%
+the opposite is a central bank goes out
+ 
+
+ align:start position:0%
+the opposite is a central bank goes out
+there and sells bonds to the market and
+
+ align:start position:0%
+there and sells bonds to the market and
+ 
+
+ align:start position:0%
+there and sells bonds to the market and
+takes the cash back okay that's a
+
+ align:start position:0%
+takes the cash back okay that's a
+ 
+
+ align:start position:0%
+takes the cash back okay that's a
+contractionary monetary policy so when
+
+ align:start position:0%
+contractionary monetary policy so when
+ 
+
+ align:start position:0%
+contractionary monetary policy so when
+the FED wants to yeah when the FED let
+
+ align:start position:0%
+the FED wants to yeah when the FED let
+ 
+
+ align:start position:0%
+the FED wants to yeah when the FED let
+me justew when the FED wants to cut
+
+ align:start position:0%
+me justew when the FED wants to cut
+ 
+
+ align:start position:0%
+me justew when the FED wants to cut
+interest rate what the FED does is an
+
+ align:start position:0%
+interest rate what the FED does is an
+ 
+
+ align:start position:0%
+interest rate what the FED does is an
+expansion in monetary policy which means
+
+ align:start position:0%
+expansion in monetary policy which means
+ 
+
+ align:start position:0%
+expansion in monetary policy which means
+it goes out there and buys bonds from
+
+ align:start position:0%
+it goes out there and buys bonds from
+ 
+
+ align:start position:0%
+it goes out there and buys bonds from
+the market and gives cash to the market
+
+ align:start position:0%
+the market and gives cash to the market
+ 
+
+ align:start position:0%
+the market and gives cash to the market
+yeah can how can the Central Banking
+
+ align:start position:0%
+yeah can how can the Central Banking
+ 
+
+ align:start position:0%
+yeah can how can the Central Banking
+assistance guarantee that some's apply
+
+ align:start position:0%
+assistance guarantee that some's apply
+ 
+
+ align:start position:0%
+assistance guarantee that some's apply
+their bonds like if they didn't have if
+
+ align:start position:0%
+their bonds like if they didn't have if
+ 
+
+ align:start position:0%
+their bonds like if they didn't have if
+their government didn't have the
+
+ align:start position:0%
+their government didn't have the
+ 
+
+ align:start position:0%
+their government didn't have the
+financial stability I guess the like
+
+ align:start position:0%
+financial stability I guess the like
+ 
+
+ align:start position:0%
+financial stability I guess the like
+United States has how would they
+
+ align:start position:0%
+United States has how would they
+ 
+
+ align:start position:0%
+United States has how would they
+guarantee that these bonds will be worth
+
+ align:start position:0%
+guarantee that these bonds will be worth
+ 
+
+ align:start position:0%
+guarantee that these bonds will be worth
+anything in the long well I mean there's
+
+ align:start position:0%
+anything in the long well I mean there's
+ 
+
+ align:start position:0%
+anything in the long well I mean there's
+you're talking about risk premium and
+
+ align:start position:0%
+you're talking about risk premium and
+ 
+
+ align:start position:0%
+you're talking about risk premium and
+that's a that's
+
+ align:start position:0%
+that's a that's
+ 
+
+ align:start position:0%
+that's a that's
+that's that's an an additional issue
+
+ align:start position:0%
+that's that's an an additional issue
+ 
+
+ align:start position:0%
+that's that's an an additional issue
+typically a a central banks inter
+
+ align:start position:0%
+typically a a central banks inter
+ 
+
+ align:start position:0%
+typically a a central banks inter
+in in in in very short duration bonds so
+
+ align:start position:0%
+in in in in very short duration bonds so
+ 
+
+ align:start position:0%
+in in in in very short duration bonds so
+there it's not the typical bond that is
+
+ align:start position:0%
+there it's not the typical bond that is
+ 
+
+ align:start position:0%
+there it's not the typical bond that is
+risky in many sense it's very very very
+
+ align:start position:0%
+risky in many sense it's very very very
+ 
+
+ align:start position:0%
+risky in many sense it's very very very
+short duration bonds treasuries very
+
+ align:start position:0%
+short duration bonds treasuries very
+ 
+
+ align:start position:0%
+short duration bonds treasuries very
+short duration in fact it's even less
+
+ align:start position:0%
+short duration in fact it's even less
+ 
+
+ align:start position:0%
+short duration in fact it's even less
+nowadays central banks really intervene
+
+ align:start position:0%
+nowadays central banks really intervene
+ 
+
+ align:start position:0%
+nowadays central banks really intervene
+in the in the overnight Market is is but
+
+ align:start position:0%
+in the in the overnight Market is is but
+ 
+
+ align:start position:0%
+in the in the overnight Market is is but
+but you're right that that countries
+
+ align:start position:0%
+but you're right that that countries
+ 
+
+ align:start position:0%
+but you're right that that countries
+that don't have a bond market a
+
+ align:start position:0%
+that don't have a bond market a
+ 
+
+ align:start position:0%
+that don't have a bond market a
+well-developed market have problems with
+
+ align:start position:0%
+well-developed market have problems with
+ 
+
+ align:start position:0%
+well-developed market have problems with
+the management of monetary policy and so
+
+ align:start position:0%
+the management of monetary policy and so
+ 
+
+ align:start position:0%
+the management of monetary policy and so
+on because they have a cretive spread
+
+ align:start position:0%
+on because they have a cretive spread
+ 
+
+ align:start position:0%
+on because they have a cretive spread
+that is moving around around as well but
+
+ align:start position:0%
+that is moving around around as well but
+ 
+
+ align:start position:0%
+that is moving around around as well but
+they tend to focus on the type of
+
+ align:start position:0%
+they tend to focus on the type of
+ 
+
+ align:start position:0%
+they tend to focus on the type of
+instruments that thing becomes very
+
+ align:start position:0%
+instruments that thing becomes very
+ 
+
+ align:start position:0%
+instruments that thing becomes very
+important I mean for Japan even big guys
+
+ align:start position:0%
+important I mean for Japan even big guys
+ 
+
+ align:start position:0%
+important I mean for Japan even big guys
+very big guys now they have an issue
+
+ align:start position:0%
+very big guys now they have an issue
+ 
+
+ align:start position:0%
+very big guys now they have an issue
+because they have been buying bonds very
+
+ align:start position:0%
+because they have been buying bonds very
+ 
+
+ align:start position:0%
+because they have been buying bonds very
+long duration bonds 10 year bonds and
+
+ align:start position:0%
+long duration bonds 10 year bonds and
+ 
+
+ align:start position:0%
+long duration bonds 10 year bonds and
+stuff like that and there it's a little
+
+ align:start position:0%
+stuff like that and there it's a little
+ 
+
+ align:start position:0%
+stuff like that and there it's a little
+trickier Market need to trust you a lot
+
+ align:start position:0%
+trickier Market need to trust you a lot
+ 
+
+ align:start position:0%
+trickier Market need to trust you a lot
+more if you're dealing with 10e things
+
+ align:start position:0%
+more if you're dealing with 10e things
+ 
+
+ align:start position:0%
+more if you're dealing with 10e things
+and you're dealing with a three-month
+
+ align:start position:0%
+and you're dealing with a three-month
+ 
+
+ align:start position:0%
+and you're dealing with a three-month
+Horizons and so
+
+ align:start position:0%
+Horizons and so
+ 
+
+ align:start position:0%
+Horizons and so
+on in other instances a um
+
+ align:start position:0%
+on in other instances a um
+ 
+
+ align:start position:0%
+on in other instances a um
+erh for example Chile has a situation
+
+ align:start position:0%
+erh for example Chile has a situation
+ 
+
+ align:start position:0%
+erh for example Chile has a situation
+like that the Central Bank itself can
+
+ align:start position:0%
+like that the Central Bank itself can
+ 
+
+ align:start position:0%
+like that the Central Bank itself can
+issue bonds and so those are bonds
+
+ align:start position:0%
+issue bonds and so those are bonds
+ 
+
+ align:start position:0%
+issue bonds and so those are bonds
+issued by the central banks and they
+
+ align:start position:0%
+issued by the central banks and they
+ 
+
+ align:start position:0%
+issued by the central banks and they
+tend to be very reliable bonds because
+
+ align:start position:0%
+tend to be very reliable bonds because
+ 
+
+ align:start position:0%
+tend to be very reliable bonds because
+these are bonds that are issuing your
+
+ align:start position:0%
+these are bonds that are issuing your
+ 
+
+ align:start position:0%
+these are bonds that are issuing your
+same currency so you have the currency
+
+ align:start position:0%
+same currency so you have the currency
+ 
+
+ align:start position:0%
+same currency so you have the currency
+to always pay the you can always print
+
+ align:start position:0%
+to always pay the you can always print
+ 
+
+ align:start position:0%
+to always pay the you can always print
+money and pay for those bonds you see so
+
+ align:start position:0%
+money and pay for those bonds you see so
+ 
+
+ align:start position:0%
+money and pay for those bonds you see so
+it rarely happens that there is default
+
+ align:start position:0%
+it rarely happens that there is default
+ 
+
+ align:start position:0%
+it rarely happens that there is default
+on bonds of that kind
+
+ align:start position:0%
+on bonds of that kind
+ 
+
+ align:start position:0%
+on bonds of that kind
+ER the typical bonds government bond
+
+ align:start position:0%
+ER the typical bonds government bond
+ 
+
+ align:start position:0%
+ER the typical bonds government bond
+that defaults is a bond that is issuing
+
+ align:start position:0%
+that defaults is a bond that is issuing
+ 
+
+ align:start position:0%
+that defaults is a bond that is issuing
+a currency different from the one you
+
+ align:start position:0%
+a currency different from the one you
+ 
+
+ align:start position:0%
+a currency different from the one you
+have because then you may not have the
+
+ align:start position:0%
+have because then you may not have the
+ 
+
+ align:start position:0%
+have because then you may not have the
+currency to pay for stu okay and that's
+
+ align:start position:0%
+currency to pay for stu okay and that's
+ 
+
+ align:start position:0%
+currency to pay for stu okay and that's
+the reason em markets run into trouble
+
+ align:start position:0%
+the reason em markets run into trouble
+ 
+
+ align:start position:0%
+the reason em markets run into trouble
+and things of that kind
+
+ align:start position:0%
+and things of that kind
+ 
+
+ align:start position:0%
+and things of that kind
+okay so in terms of the balance sheet of
+
+ align:start position:0%
+okay so in terms of the balance sheet of
+ 
+
+ align:start position:0%
+okay so in terms of the balance sheet of
+the Central Bank how does an open market
+
+ align:start position:0%
+the Central Bank how does an open market
+ 
+
+ align:start position:0%
+the Central Bank how does an open market
+operation look so if you look at the at
+
+ align:start position:0%
+operation look so if you look at the at
+ 
+
+ align:start position:0%
+operation look so if you look at the at
+the balance sheet this is an incredibly
+
+ align:start position:0%
+the balance sheet this is an incredibly
+ 
+
+ align:start position:0%
+the balance sheet this is an incredibly
+simplified version of the balance sheet
+
+ align:start position:0%
+simplified version of the balance sheet
+ 
+
+ align:start position:0%
+simplified version of the balance sheet
+of the of the FED no they have lots of
+
+ align:start position:0%
+of the of the FED no they have lots of
+ 
+
+ align:start position:0%
+of the of the FED no they have lots of
+things some more assets gold and all
+
+ align:start position:0%
+things some more assets gold and all
+ 
+
+ align:start position:0%
+things some more assets gold and all
+sort of stuff but in our simple economy
+
+ align:start position:0%
+sort of stuff but in our simple economy
+ 
+
+ align:start position:0%
+sort of stuff but in our simple economy
+the government the the fed the assets of
+
+ align:start position:0%
+the government the the fed the assets of
+ 
+
+ align:start position:0%
+the government the the fed the assets of
+the feds is they have some bonds it has
+
+ align:start position:0%
+the feds is they have some bonds it has
+ 
+
+ align:start position:0%
+the feds is they have some bonds it has
+already some bonds out there and the
+
+ align:start position:0%
+already some bonds out there and the
+ 
+
+ align:start position:0%
+already some bonds out there and the
+liabilities is the money they issue they
+
+ align:start position:0%
+liabilities is the money they issue they
+ 
+
+ align:start position:0%
+liabilities is the money they issue they
+owe that to people I mean they issue
+
+ align:start position:0%
+owe that to people I mean they issue
+ 
+
+ align:start position:0%
+owe that to people I mean they issue
+currency but you know but but that's
+
+ align:start position:0%
+currency but you know but but that's
+ 
+
+ align:start position:0%
+currency but you know but but that's
+it's a
+
+ align:start position:0%
+it's a
+ 
+
+ align:start position:0%
+it's a
+liability people can do things with can
+
+ align:start position:0%
+liability people can do things with can
+ 
+
+ align:start position:0%
+liability people can do things with can
+buy things with that money and so it's a
+
+ align:start position:0%
+buy things with that money and so it's a
+ 
+
+ align:start position:0%
+buy things with that money and so it's a
+liability so that's the way the balance
+
+ align:start position:0%
+liability so that's the way the balance
+ 
+
+ align:start position:0%
+liability so that's the way the balance
+sheet looks so when when the the FED
+
+ align:start position:0%
+sheet looks so when when the the FED
+ 
+
+ align:start position:0%
+sheet looks so when when the the FED
+decides to do an expansionary open
+
+ align:start position:0%
+decides to do an expansionary open
+ 
+
+ align:start position:0%
+decides to do an expansionary open
+market operation then what it does is it
+
+ align:start position:0%
+market operation then what it does is it
+ 
+
+ align:start position:0%
+market operation then what it does is it
+goes out there it IT issues an say a $1
+
+ align:start position:0%
+goes out there it IT issues an say a $1
+ 
+
+ align:start position:0%
+goes out there it IT issues an say a $1
+million expansionary open market
+
+ align:start position:0%
+million expansionary open market
+ 
+
+ align:start position:0%
+million expansionary open market
+operation they do it in much we get
+
+ align:start position:0%
+operation they do it in much we get
+ 
+
+ align:start position:0%
+operation they do it in much we get
+tickets on this but let's make it simple
+
+ align:start position:0%
+tickets on this but let's make it simple
+ 
+
+ align:start position:0%
+tickets on this but let's make it simple
+$1 million of an expansionary operation
+
+ align:start position:0%
+$1 million of an expansionary operation
+ 
+
+ align:start position:0%
+$1 million of an expansionary operation
+but they go they go out there they they
+
+ align:start position:0%
+but they go they go out there they they
+ 
+
+ align:start position:0%
+but they go they go out there they they
+print a million dollars and they buy a
+
+ align:start position:0%
+print a million dollars and they buy a
+ 
+
+ align:start position:0%
+print a million dollars and they buy a
+million dollars from the market okay and
+
+ align:start position:0%
+million dollars from the market okay and
+ 
+
+ align:start position:0%
+million dollars from the market okay and
+so at the end the balance sheet ends
+
+ align:start position:0%
+so at the end the balance sheet ends
+ 
+
+ align:start position:0%
+so at the end the balance sheet ends
+like it used to be the there's an extra
+
+ align:start position:0%
+like it used to be the there's an extra
+ 
+
+ align:start position:0%
+like it used to be the there's an extra
+$1 million of liabilities because now
+
+ align:start position:0%
+$1 million of liabilities because now
+ 
+
+ align:start position:0%
+$1 million of liabilities because now
+there's a million more of dollars
+
+ align:start position:0%
+there's a million more of dollars
+ 
+
+ align:start position:0%
+there's a million more of dollars
+circulating out there and but but the
+
+ align:start position:0%
+circulating out there and but but the
+ 
+
+ align:start position:0%
+circulating out there and but but the
+against that the Central Bank also has a
+
+ align:start position:0%
+against that the Central Bank also has a
+ 
+
+ align:start position:0%
+against that the Central Bank also has a
+million more of bonds Holdings
+
+ align:start position:0%
+million more of bonds Holdings
+ 
+
+ align:start position:0%
+million more of bonds Holdings
+okay so that's that's what happens with
+
+ align:start position:0%
+okay so that's that's what happens with
+ 
+
+ align:start position:0%
+okay so that's that's what happens with
+when so so when in an expansionary
+
+ align:start position:0%
+when so so when in an expansionary
+ 
+
+ align:start position:0%
+when so so when in an expansionary
+monetary policy the balance sheet of the
+
+ align:start position:0%
+monetary policy the balance sheet of the
+ 
+
+ align:start position:0%
+monetary policy the balance sheet of the
+Central Bank expands both sides expand
+
+ align:start position:0%
+Central Bank expands both sides expand
+ 
+
+ align:start position:0%
+Central Bank expands both sides expand
+by the same amount okay but expands and
+
+ align:start position:0%
+by the same amount okay but expands and
+ 
+
+ align:start position:0%
+by the same amount okay but expands and
+one of the big themes of recent years
+
+ align:start position:0%
+one of the big themes of recent years
+ 
+
+ align:start position:0%
+one of the big themes of recent years
+starting from the global financial
+
+ align:start position:0%
+starting from the global financial
+ 
+
+ align:start position:0%
+starting from the global financial
+crisis is that these balance sheets used
+
+ align:start position:0%
+crisis is that these balance sheets used
+ 
+
+ align:start position:0%
+crisis is that these balance sheets used
+to be small peanuts type things for I
+
+ align:start position:0%
+to be small peanuts type things for I
+ 
+
+ align:start position:0%
+to be small peanuts type things for I
+mean a trillion dollar or something like
+
+ align:start position:0%
+mean a trillion dollar or something like
+ 
+
+ align:start position:0%
+mean a trillion dollar or something like
+that for something like the the US the
+
+ align:start position:0%
+that for something like the the US the
+ 
+
+ align:start position:0%
+that for something like the the US the
+size nowadays they're much much larger
+
+ align:start position:0%
+size nowadays they're much much larger
+ 
+
+ align:start position:0%
+size nowadays they're much much larger
+than that because they have done so many
+
+ align:start position:0%
+than that because they have done so many
+ 
+
+ align:start position:0%
+than that because they have done so many
+operations to first get us out of the
+
+ align:start position:0%
+operations to first get us out of the
+ 
+
+ align:start position:0%
+operations to first get us out of the
+global financial crisis and then to get
+
+ align:start position:0%
+global financial crisis and then to get
+ 
+
+ align:start position:0%
+global financial crisis and then to get
+us out of covid and so on that these
+
+ align:start position:0%
+us out of covid and so on that these
+ 
+
+ align:start position:0%
+us out of covid and so on that these
+balance sheets are
+
+ align:start position:0%
+balance sheets are
+ 
+
+ align:start position:0%
+balance sheets are
+now an order or two orders of magnitude
+
+ align:start position:0%
+now an order or two orders of magnitude
+ 
+
+ align:start position:0%
+now an order or two orders of magnitude
+larger than they used to be
+
+ align:start position:0%
+larger than they used to be
+ 
+
+ align:start position:0%
+larger than they used to be
+okay but be in words they have had to do
+
+ align:start position:0%
+okay but be in words they have had to do
+ 
+
+ align:start position:0%
+okay but be in words they have had to do
+lots of expansionary monetary policy
+
+ align:start position:0%
+lots of expansionary monetary policy
+ 
+
+ align:start position:0%
+lots of expansionary monetary policy
+over the last couple of decades or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so let me talk about a little bit
+
+ align:start position:0%
+so so let me talk about a little bit
+ 
+
+ align:start position:0%
+so so let me talk about a little bit
+about interest rate and bond prices
+
+ align:start position:0%
+about interest rate and bond prices
+ 
+
+ align:start position:0%
+about interest rate and bond prices
+because that's the other side of this
+
+ align:start position:0%
+because that's the other side of this
+ 
+
+ align:start position:0%
+because that's the other side of this
+thing so so what is the connection
+
+ align:start position:0%
+thing so so what is the connection
+ 
+
+ align:start position:0%
+thing so so what is the connection
+because sometimes it's easier to
+
+ align:start position:0%
+because sometimes it's easier to
+ 
+
+ align:start position:0%
+because sometimes it's easier to
+understand things in terms of price in
+
+ align:start position:0%
+understand things in terms of price in
+ 
+
+ align:start position:0%
+understand things in terms of price in
+terms of bonds so suppose a bond pays
+
+ align:start position:0%
+terms of bonds so suppose a bond pays
+ 
+
+ align:start position:0%
+terms of bonds so suppose a bond pays
+$100 a year from now and and no coupon
+
+ align:start position:0%
+$100 a year from now and and no coupon
+ 
+
+ align:start position:0%
+$100 a year from now and and no coupon
+in between so if you buy a bond now for
+
+ align:start position:0%
+in between so if you buy a bond now for
+ 
+
+ align:start position:0%
+in between so if you buy a bond now for
+some price PB you get $100 a year from
+
+ align:start position:0%
+some price PB you get $100 a year from
+ 
+
+ align:start position:0%
+some price PB you get $100 a year from
+now so what is the interest rate of that
+
+ align:start position:0%
+now so what is the interest rate of that
+ 
+
+ align:start position:0%
+now so what is the interest rate of that
+bond that is what is the excess return
+
+ align:start position:0%
+bond that is what is the excess return
+ 
+
+ align:start position:0%
+bond that is what is the excess return
+that you get out of that or the return
+
+ align:start position:0%
+that you get out of that or the return
+ 
+
+ align:start position:0%
+that you get out of that or the return
+you get out of buying that
+
+ align:start position:0%
+you get out of buying that
+ 
+
+ align:start position:0%
+you get out of buying that
+Bond well it's going to be $100 minus
+
+ align:start position:0%
+Bond well it's going to be $100 minus
+ 
+
+ align:start position:0%
+Bond well it's going to be $100 minus
+whatever you pay today say you pay 95
+
+ align:start position:0%
+whatever you pay today say you pay 95
+ 
+
+ align:start position:0%
+whatever you pay today say you pay 95
+then $5 divided by your investment
+
+ align:start position:0%
+then $5 divided by your investment
+ 
+
+ align:start position:0%
+then $5 divided by your investment
+initial investment which was 95 okay so
+
+ align:start position:0%
+initial investment which was 95 okay so
+ 
+
+ align:start position:0%
+initial investment which was 95 okay so
+that's a bond that gives you know a
+
+ align:start position:0%
+that's a bond that gives you know a
+ 
+
+ align:start position:0%
+that's a bond that gives you know a
+little bit more than 5% in a year okay
+
+ align:start position:0%
+little bit more than 5% in a year okay
+ 
+
+ align:start position:0%
+little bit more than 5% in a year okay
+that's a return that's interesting so
+
+ align:start position:0%
+that's a return that's interesting so
+ 
+
+ align:start position:0%
+that's a return that's interesting so
+that's a connection between interest
+
+ align:start position:0%
+that's a connection between interest
+ 
+
+ align:start position:0%
+that's a connection between interest
+rate and prices and notice that this is
+
+ align:start position:0%
+rate and prices and notice that this is
+ 
+
+ align:start position:0%
+rate and prices and notice that this is
+an inverse
+
+ align:start position:0%
+an inverse
+ 
+
+ align:start position:0%
+an inverse
+relation you know when the price of a
+
+ align:start position:0%
+relation you know when the price of a
+ 
+
+ align:start position:0%
+relation you know when the price of a
+bond goes up the interest rate pay goes
+
+ align:start position:0%
+bond goes up the interest rate pay goes
+ 
+
+ align:start position:0%
+bond goes up the interest rate pay goes
+down because you're paying more for the
+
+ align:start position:0%
+down because you're paying more for the
+ 
+
+ align:start position:0%
+down because you're paying more for the
+same principle you're going to get 100
+
+ align:start position:0%
+same principle you're going to get 100
+ 
+
+ align:start position:0%
+same principle you're going to get 100
+but now you're paying more for it well
+
+ align:start position:0%
+but now you're paying more for it well
+ 
+
+ align:start position:0%
+but now you're paying more for it well
+that means the interest rate the return
+
+ align:start position:0%
+that means the interest rate the return
+ 
+
+ align:start position:0%
+that means the interest rate the return
+on that Bond went down
+
+ align:start position:0%
+on that Bond went down
+ 
+
+ align:start position:0%
+on that Bond went down
+okay conversion you can say the other
+
+ align:start position:0%
+okay conversion you can say the other
+ 
+
+ align:start position:0%
+okay conversion you can say the other
+way around the higher is the interest
+
+ align:start position:0%
+way around the higher is the interest
+ 
+
+ align:start position:0%
+way around the higher is the interest
+rate the lower is the price of bond of a
+
+ align:start position:0%
+rate the lower is the price of bond of a
+ 
+
+ align:start position:0%
+rate the lower is the price of bond of a
+bond so for example today the interest
+
+ align:start position:0%
+bond so for example today the interest
+ 
+
+ align:start position:0%
+bond so for example today the interest
+rate is
+
+ align:start position:0%
+rate is
+ 
+
+ align:start position:0%
+rate is
+5% a ER if I want to issue a bond that
+
+ align:start position:0%
+5% a ER if I want to issue a bond that
+ 
+
+ align:start position:0%
+5% a ER if I want to issue a bond that
+doesn't pay any coupon and I'm
+
+ align:start position:0%
+doesn't pay any coupon and I'm
+ 
+
+ align:start position:0%
+doesn't pay any coupon and I'm
+completely safe so I'm the US Treasury
+
+ align:start position:0%
+completely safe so I'm the US Treasury
+ 
+
+ align:start position:0%
+completely safe so I'm the US Treasury
+I'm going to be able to sell that bone
+
+ align:start position:0%
+I'm going to be able to sell that bone
+ 
+
+ align:start position:0%
+I'm going to be able to sell that bone
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+95 two years ago when the interest rate
+
+ align:start position:0%
+95 two years ago when the interest rate
+ 
+
+ align:start position:0%
+95 two years ago when the interest rate
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+Zero the fair would have been able to
+
+ align:start position:0%
+Zero the fair would have been able to
+ 
+
+ align:start position:0%
+Zero the fair would have been able to
+sell that bond for
+
+ align:start position:0%
+sell that bond for
+ 
+
+ align:start position:0%
+sell that bond for
+100 okay
+
+ align:start position:0%
+100 okay
+ 
+
+ align:start position:0%
+100 okay
+so there's an inverse relationship
+
+ align:start position:0%
+so there's an inverse relationship
+ 
+
+ align:start position:0%
+so there's an inverse relationship
+between the interest rate and the price
+
+ align:start position:0%
+between the interest rate and the price
+ 
+
+ align:start position:0%
+between the interest rate and the price
+of bonds and now I can take you back to
+
+ align:start position:0%
+of bonds and now I can take you back to
+ 
+
+ align:start position:0%
+of bonds and now I can take you back to
+my open market operation so remember
+
+ align:start position:0%
+my open market operation so remember
+ 
+
+ align:start position:0%
+my open market operation so remember
+what what I said there's another way of
+
+ align:start position:0%
+what what I said there's another way of
+ 
+
+ align:start position:0%
+what what I said there's another way of
+remembering sort of which way these
+
+ align:start position:0%
+remembering sort of which way these
+ 
+
+ align:start position:0%
+remembering sort of which way these
+signs go remember when you have an
+
+ align:start position:0%
+signs go remember when you have an
+ 
+
+ align:start position:0%
+signs go remember when you have an
+expansionary monetary operation I said
+
+ align:start position:0%
+expansionary monetary operation I said
+ 
+
+ align:start position:0%
+expansionary monetary operation I said
+the FED goes out there with a back of
+
+ align:start position:0%
+the FED goes out there with a back of
+ 
+
+ align:start position:0%
+the FED goes out there with a back of
+money and buys bonds from the market
+
+ align:start position:0%
+money and buys bonds from the market
+ 
+
+ align:start position:0%
+money and buys bonds from the market
+when bonds when you buy something when
+
+ align:start position:0%
+when bonds when you buy something when
+ 
+
+ align:start position:0%
+when bonds when you buy something when
+there's an enormous increase in demand
+
+ align:start position:0%
+there's an enormous increase in demand
+ 
+
+ align:start position:0%
+there's an enormous increase in demand
+for something what do you think happens
+
+ align:start position:0%
+for something what do you think happens
+ 
+
+ align:start position:0%
+for something what do you think happens
+to the price of that something
+
+ align:start position:0%
+to the price of that something
+ 
+
+ align:start position:0%
+to the price of that something
+goes up no for anything cars whatever it
+
+ align:start position:0%
+goes up no for anything cars whatever it
+ 
+
+ align:start position:0%
+goes up no for anything cars whatever it
+is if there's a lot more demand then
+
+ align:start position:0%
+is if there's a lot more demand then
+ 
+
+ align:start position:0%
+is if there's a lot more demand then
+prices will go up and the FED has a lot
+
+ align:start position:0%
+prices will go up and the FED has a lot
+ 
+
+ align:start position:0%
+prices will go up and the FED has a lot
+of cash so he can really buy large
+
+ align:start position:0%
+of cash so he can really buy large
+ 
+
+ align:start position:0%
+of cash so he can really buy large
+amount of bonds and so when the FED goes
+
+ align:start position:0%
+amount of bonds and so when the FED goes
+ 
+
+ align:start position:0%
+amount of bonds and so when the FED goes
+out there and does an expansionary open
+
+ align:start position:0%
+out there and does an expansionary open
+ 
+
+ align:start position:0%
+out there and does an expansionary open
+market operation means it goes out there
+
+ align:start position:0%
+market operation means it goes out there
+ 
+
+ align:start position:0%
+market operation means it goes out there
+and buys a lot of bonds the price of
+
+ align:start position:0%
+and buys a lot of bonds the price of
+ 
+
+ align:start position:0%
+and buys a lot of bonds the price of
+those bonds goes up and made that
+
+ align:start position:0%
+those bonds goes up and made that
+ 
+
+ align:start position:0%
+those bonds goes up and made that
+formula that means the interest rate is
+
+ align:start position:0%
+formula that means the interest rate is
+ 
+
+ align:start position:0%
+formula that means the interest rate is
+going down okay so that's another way of
+
+ align:start position:0%
+going down okay so that's another way of
+ 
+
+ align:start position:0%
+going down okay so that's another way of
+understanding how is it
+
+ align:start position:0%
+understanding how is it
+ 
+
+ align:start position:0%
+understanding how is it
+expansion open market operation lowers
+
+ align:start position:0%
+expansion open market operation lowers
+ 
+
+ align:start position:0%
+expansion open market operation lowers
+the interest rate it's because it raises
+
+ align:start position:0%
+the interest rate it's because it raises
+ 
+
+ align:start position:0%
+the interest rate it's because it raises
+the price of the bonds that is
+
+ align:start position:0%
+the price of the bonds that is
+ 
+
+ align:start position:0%
+the price of the bonds that is
+demanding and when you raise the price
+
+ align:start position:0%
+demanding and when you raise the price
+ 
+
+ align:start position:0%
+demanding and when you raise the price
+of the bonds then the interest rate goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down will I do this to
+
+ align:start position:0%
+down will I do this to
+ 
+
+ align:start position:0%
+down will I do this to
+you well very quickly so really the only
+
+ align:start position:0%
+you well very quickly so really the only
+ 
+
+ align:start position:0%
+you well very quickly so really the only
+thing I really care I want you to
+
+ align:start position:0%
+thing I really care I want you to
+ 
+
+ align:start position:0%
+thing I really care I want you to
+understand what I what I just said well
+
+ align:start position:0%
+understand what I what I just said well
+ 
+
+ align:start position:0%
+understand what I what I just said well
+because we're going to use it
+
+ align:start position:0%
+because we're going to use it
+ 
+
+ align:start position:0%
+because we're going to use it
+I want to you to understand what comes
+
+ align:start position:0%
+I want to you to understand what comes
+ 
+
+ align:start position:0%
+I want to you to understand what comes
+next ideally well but but it's okay if
+
+ align:start position:0%
+next ideally well but but it's okay if
+ 
+
+ align:start position:0%
+next ideally well but but it's okay if
+you don't understand it too well okay
+
+ align:start position:0%
+you don't understand it too well okay
+ 
+
+ align:start position:0%
+you don't understand it too well okay
+and I'm going to tell you when do you
+
+ align:start position:0%
+and I'm going to tell you when do you
+ 
+
+ align:start position:0%
+and I'm going to tell you when do you
+have to start understanding very well
+
+ align:start position:0%
+have to start understanding very well
+ 
+
+ align:start position:0%
+have to start understanding very well
+again okay for now this this is a pie in
+
+ align:start position:0%
+again okay for now this this is a pie in
+ 
+
+ align:start position:0%
+again okay for now this this is a pie in
+qu is what I'm doing here is making
+
+ align:start position:0%
+qu is what I'm doing here is making
+ 
+
+ align:start position:0%
+qu is what I'm doing here is making
+things a little bit more realistic the
+
+ align:start position:0%
+things a little bit more realistic the
+ 
+
+ align:start position:0%
+things a little bit more realistic the
+the message will be similar but it's a
+
+ align:start position:0%
+the message will be similar but it's a
+ 
+
+ align:start position:0%
+the message will be similar but it's a
+little bit more complicated okay and
+
+ align:start position:0%
+little bit more complicated okay and
+ 
+
+ align:start position:0%
+little bit more complicated okay and
+that's the reason sort of
+
+ align:start position:0%
+that's the reason sort of
+ 
+
+ align:start position:0%
+that's the reason sort of
+substantively H um I already told you
+
+ align:start position:0%
+substantively H um I already told you
+ 
+
+ align:start position:0%
+substantively H um I already told you
+what I wanted to tell you
+
+ align:start position:0%
+what I wanted to tell you
+ 
+
+ align:start position:0%
+what I wanted to tell you
+what I'm going to tell you now will give
+
+ align:start position:0%
+what I'm going to tell you now will give
+ 
+
+ align:start position:0%
+what I'm going to tell you now will give
+you a little bit more realism and
+
+ align:start position:0%
+you a little bit more realism and
+ 
+
+ align:start position:0%
+you a little bit more realism and
+therefore will allow you to understand a
+
+ align:start position:0%
+therefore will allow you to understand a
+ 
+
+ align:start position:0%
+therefore will allow you to understand a
+little bit
+
+ align:start position:0%
+little bit
+ 
+
+ align:start position:0%
+little bit
+better a technical description of
+
+ align:start position:0%
+better a technical description of
+ 
+
+ align:start position:0%
+better a technical description of
+monetary policy or something like that
+
+ align:start position:0%
+monetary policy or something like that
+ 
+
+ align:start position:0%
+monetary policy or something like that
+so in
+
+ align:start position:0%
+so in
+ 
+
+ align:start position:0%
+so in
+practice you know in the economy I just
+
+ align:start position:0%
+practice you know in the economy I just
+ 
+
+ align:start position:0%
+practice you know in the economy I just
+describe you had sort of households and
+
+ align:start position:0%
+describe you had sort of households and
+ 
+
+ align:start position:0%
+describe you had sort of households and
+firms and the central bank but in
+
+ align:start position:0%
+firms and the central bank but in
+ 
+
+ align:start position:0%
+firms and the central bank but in
+practice there are lot of financial
+
+ align:start position:0%
+practice there are lot of financial
+ 
+
+ align:start position:0%
+practice there are lot of financial
+intermediaries okay and in financial
+
+ align:start position:0%
+intermediaries okay and in financial
+ 
+
+ align:start position:0%
+intermediaries okay and in financial
+intermed the most prominent of them for
+
+ align:start position:0%
+intermed the most prominent of them for
+ 
+
+ align:start position:0%
+intermed the most prominent of them for
+especially for monetary policy are the
+
+ align:start position:0%
+especially for monetary policy are the
+ 
+
+ align:start position:0%
+especially for monetary policy are the
+banks and there are certain Banks
+
+ align:start position:0%
+banks and there are certain Banks
+ 
+
+ align:start position:0%
+banks and there are certain Banks
+actually they're even more important
+
+ align:start position:0%
+actually they're even more important
+ 
+
+ align:start position:0%
+actually they're even more important
+than others but banks are financially
+
+ align:start position:0%
+than others but banks are financially
+ 
+
+ align:start position:0%
+than others but banks are financially
+intim intimidates they take money from
+
+ align:start position:0%
+intim intimidates they take money from
+ 
+
+ align:start position:0%
+intim intimidates they take money from
+someone or deposit from someone and lend
+
+ align:start position:0%
+someone or deposit from someone and lend
+ 
+
+ align:start position:0%
+someone or deposit from someone and lend
+it to someone else or buy some
+
+ align:start position:0%
+it to someone else or buy some
+ 
+
+ align:start position:0%
+it to someone else or buy some
+instruments okay so so they intermediate
+
+ align:start position:0%
+instruments okay so so they intermediate
+ 
+
+ align:start position:0%
+instruments okay so so they intermediate
+the funds of somebody that wants to save
+
+ align:start position:0%
+the funds of somebody that wants to save
+ 
+
+ align:start position:0%
+the funds of somebody that wants to save
+on in the bank a deposit in a deposit
+
+ align:start position:0%
+on in the bank a deposit in a deposit
+ 
+
+ align:start position:0%
+on in the bank a deposit in a deposit
+account or something and they they lend
+
+ align:start position:0%
+account or something and they they lend
+ 
+
+ align:start position:0%
+account or something and they they lend
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+money effectively in the name of the
+
+ align:start position:0%
+money effectively in the name of the
+ 
+
+ align:start position:0%
+money effectively in the name of the
+other person to H someone else okay so
+
+ align:start position:0%
+other person to H someone else okay so
+ 
+
+ align:start position:0%
+other person to H someone else okay so
+Banks do two things to the model I just
+
+ align:start position:0%
+Banks do two things to the model I just
+ 
+
+ align:start position:0%
+Banks do two things to the model I just
+described the first is that they produce
+
+ align:start position:0%
+described the first is that they produce
+ 
+
+ align:start position:0%
+described the first is that they produce
+money as
+
+ align:start position:0%
+money as
+ 
+
+ align:start position:0%
+money as
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+because ER money is made of currency
+
+ align:start position:0%
+because ER money is made of currency
+ 
+
+ align:start position:0%
+because ER money is made of currency
+which is is issued by the central bank
+
+ align:start position:0%
+which is is issued by the central bank
+ 
+
+ align:start position:0%
+which is is issued by the central bank
+but it's also made of a checkable
+
+ align:start position:0%
+but it's also made of a checkable
+ 
+
+ align:start position:0%
+but it's also made of a checkable
+deposits if you have a a checking
+
+ align:start position:0%
+deposits if you have a a checking
+ 
+
+ align:start position:0%
+deposits if you have a a checking
+account something you can have a debit
+
+ align:start position:0%
+account something you can have a debit
+ 
+
+ align:start position:0%
+account something you can have a debit
+card against or something like that then
+
+ align:start position:0%
+card against or something like that then
+ 
+
+ align:start position:0%
+card against or something like that then
+then that's money for you okay if you
+
+ align:start position:0%
+then that's money for you okay if you
+ 
+
+ align:start position:0%
+then that's money for you okay if you
+deposit in a bank in a checking
+
+ align:start position:0%
+deposit in a bank in a checking
+ 
+
+ align:start position:0%
+deposit in a bank in a checking
+account that's money okay and so when
+
+ align:start position:0%
+account that's money okay and so when
+ 
+
+ align:start position:0%
+account that's money okay and so when
+Banks the liabilities of banks the
+
+ align:start position:0%
+Banks the liabilities of banks the
+ 
+
+ align:start position:0%
+Banks the liabilities of banks the
+deposits is part of money it's something
+
+ align:start position:0%
+deposits is part of money it's something
+ 
+
+ align:start position:0%
+deposits is part of money it's something
+you can use for transactions you can
+
+ align:start position:0%
+you can use for transactions you can
+ 
+
+ align:start position:0%
+you can use for transactions you can
+write checks you can use your debit card
+
+ align:start position:0%
+write checks you can use your debit card
+ 
+
+ align:start position:0%
+write checks you can use your debit card
+and stuff like that okay so that's the
+
+ align:start position:0%
+and stuff like that okay so that's the
+ 
+
+ align:start position:0%
+and stuff like that okay so that's the
+first thing that Banks do okay the other
+
+ align:start position:0%
+first thing that Banks do okay the other
+ 
+
+ align:start position:0%
+first thing that Banks do okay the other
+thing the banks
+
+ align:start position:0%
+thing the banks
+ 
+
+ align:start position:0%
+thing the banks
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+is they themselves have a deposit
+
+ align:start position:0%
+is they themselves have a deposit
+ 
+
+ align:start position:0%
+is they themselves have a deposit
+account at the Central
+
+ align:start position:0%
+account at the Central
+ 
+
+ align:start position:0%
+account at the Central
+Bank okay so they themselves take part
+
+ align:start position:0%
+Bank okay so they themselves take part
+ 
+
+ align:start position:0%
+Bank okay so they themselves take part
+of the deposits they take the deposits
+
+ align:start position:0%
+of the deposits they take the deposits
+ 
+
+ align:start position:0%
+of the deposits they take the deposits
+part of the deposit they lend to other
+
+ align:start position:0%
+part of the deposit they lend to other
+ 
+
+ align:start position:0%
+part of the deposit they lend to other
+people another part they buy financial
+
+ align:start position:0%
+people another part they buy financial
+ 
+
+ align:start position:0%
+people another part they buy financial
+instruments Bond and stuff like that in
+
+ align:start position:0%
+instruments Bond and stuff like that in
+ 
+
+ align:start position:0%
+instruments Bond and stuff like that in
+this economy would be only bonds and the
+
+ align:start position:0%
+this economy would be only bonds and the
+ 
+
+ align:start position:0%
+this economy would be only bonds and the
+other part smaller part 10% or something
+
+ align:start position:0%
+other part smaller part 10% or something
+ 
+
+ align:start position:0%
+other part smaller part 10% or something
+like that they deposit at the central
+
+ align:start position:0%
+like that they deposit at the central
+ 
+
+ align:start position:0%
+like that they deposit at the central
+bank that deposit at the central bank is
+
+ align:start position:0%
+bank that deposit at the central bank is
+ 
+
+ align:start position:0%
+bank that deposit at the central bank is
+called Reserves
+
+ align:start position:0%
+called Reserves
+ 
+
+ align:start position:0%
+called Reserves
+okay so when you he the word reserves of
+
+ align:start position:0%
+okay so when you he the word reserves of
+ 
+
+ align:start position:0%
+okay so when you he the word reserves of
+the banking sector this is the deposits
+
+ align:start position:0%
+the banking sector this is the deposits
+ 
+
+ align:start position:0%
+the banking sector this is the deposits
+of the banks at the Central
+
+ align:start position:0%
+of the banks at the Central
+ 
+
+ align:start position:0%
+of the banks at the Central
+Bank okay and that's that's also
+
+ align:start position:0%
+Bank okay and that's that's also
+ 
+
+ align:start position:0%
+Bank okay and that's that's also
+liability for the Central Bank the
+
+ align:start position:0%
+liability for the Central Bank the
+ 
+
+ align:start position:0%
+liability for the Central Bank the
+central bank is holding that deposit of
+
+ align:start position:0%
+central bank is holding that deposit of
+ 
+
+ align:start position:0%
+central bank is holding that deposit of
+the banks it's not the central bank's
+
+ align:start position:0%
+the banks it's not the central bank's
+ 
+
+ align:start position:0%
+the banks it's not the central bank's
+money it's the it's the bank's money
+
+ align:start position:0%
+money it's the it's the bank's money
+ 
+
+ align:start position:0%
+money it's the it's the bank's money
+okay and they're holding it there it's a
+
+ align:start position:0%
+okay and they're holding it there it's a
+ 
+
+ align:start position:0%
+okay and they're holding it there it's a
+liability as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well so now if you look at how the
+
+ align:start position:0%
+well so now if you look at how the
+ 
+
+ align:start position:0%
+well so now if you look at how the
+balance sheets look
+
+ align:start position:0%
+balance sheets look
+ 
+
+ align:start position:0%
+balance sheets look
+our central bank now has more things he
+
+ align:start position:0%
+our central bank now has more things he
+ 
+
+ align:start position:0%
+our central bank now has more things he
+has assets going to be Bonds in this
+
+ align:start position:0%
+has assets going to be Bonds in this
+ 
+
+ align:start position:0%
+has assets going to be Bonds in this
+economy this only thing you can have but
+
+ align:start position:0%
+economy this only thing you can have but
+ 
+
+ align:start position:0%
+economy this only thing you can have but
+now it will have the currency that had
+
+ align:start position:0%
+now it will have the currency that had
+ 
+
+ align:start position:0%
+now it will have the currency that had
+before and in liabilities but also will
+
+ align:start position:0%
+before and in liabilities but also will
+ 
+
+ align:start position:0%
+before and in liabilities but also will
+have the Reserves the deposits of the
+
+ align:start position:0%
+have the Reserves the deposits of the
+ 
+
+ align:start position:0%
+have the Reserves the deposits of the
+banks themselves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay and this is called this stuff
+
+ align:start position:0%
+okay okay and this is called this stuff
+ 
+
+ align:start position:0%
+okay okay and this is called this stuff
+here is called central bank money in
+
+ align:start position:0%
+here is called central bank money in
+ 
+
+ align:start position:0%
+here is called central bank money in
+contrast it is called Central Bank it
+
+ align:start position:0%
+contrast it is called Central Bank it
+ 
+
+ align:start position:0%
+contrast it is called Central Bank it
+has so many names
+
+ align:start position:0%
+has so many names
+ 
+
+ align:start position:0%
+has so many names
+it's called central bank money high
+
+ align:start position:0%
+it's called central bank money high
+ 
+
+ align:start position:0%
+it's called central bank money high
+power
+
+ align:start position:0%
+power
+ 
+
+ align:start position:0%
+power
+money some other name have some but but
+
+ align:start position:0%
+money some other name have some but but
+ 
+
+ align:start position:0%
+money some other name have some but but
+but he has several names and what is I I
+
+ align:start position:0%
+but he has several names and what is I I
+ 
+
+ align:start position:0%
+but he has several names and what is I I
+like the name central bank money because
+
+ align:start position:0%
+like the name central bank money because
+ 
+
+ align:start position:0%
+like the name central bank money because
+that's in contrast with this kind of
+
+ align:start position:0%
+that's in contrast with this kind of
+ 
+
+ align:start position:0%
+that's in contrast with this kind of
+money it's the money that the banking
+
+ align:start position:0%
+money it's the money that the banking
+ 
+
+ align:start position:0%
+money it's the money that the banking
+sector produces the checkable deposits
+
+ align:start position:0%
+sector produces the checkable deposits
+ 
+
+ align:start position:0%
+sector produces the checkable deposits
+okay so this is the money produced by
+
+ align:start position:0%
+okay so this is the money produced by
+ 
+
+ align:start position:0%
+okay so this is the money produced by
+the central bank and then the and then
+
+ align:start position:0%
+the central bank and then the and then
+ 
+
+ align:start position:0%
+the central bank and then the and then
+through deposits the financial system
+
+ align:start position:0%
+through deposits the financial system
+ 
+
+ align:start position:0%
+through deposits the financial system
+the banks themselves produce more
+
+ align:start position:0%
+the banks themselves produce more
+ 
+
+ align:start position:0%
+the banks themselves produce more
+money so The Total Money in the system
+
+ align:start position:0%
+money so The Total Money in the system
+ 
+
+ align:start position:0%
+money so The Total Money in the system
+is much more than the central bank money
+
+ align:start position:0%
+is much more than the central bank money
+ 
+
+ align:start position:0%
+is much more than the central bank money
+because deposits is a big thing you
+
+ align:start position:0%
+because deposits is a big thing you
+ 
+
+ align:start position:0%
+because deposits is a big thing you
+know this is much larger than that in
+
+ align:start position:0%
+know this is much larger than that in
+ 
+
+ align:start position:0%
+know this is much larger than that in
+practice okay good how does this change
+
+ align:start position:0%
+practice okay good how does this change
+ 
+
+ align:start position:0%
+practice okay good how does this change
+our mold not really much and so so again
+
+ align:start position:0%
+our mold not really much and so so again
+ 
+
+ align:start position:0%
+our mold not really much and so so again
+that's the reason I don't care too much
+
+ align:start position:0%
+that's the reason I don't care too much
+ 
+
+ align:start position:0%
+that's the reason I don't care too much
+if you understand these last two slides
+
+ align:start position:0%
+if you understand these last two slides
+ 
+
+ align:start position:0%
+if you understand these last two slides
+so let me rederive what we
+
+ align:start position:0%
+so let me rederive what we
+ 
+
+ align:start position:0%
+so let me rederive what we
+have with this approach with with this
+
+ align:start position:0%
+have with this approach with with this
+ 
+
+ align:start position:0%
+have with this approach with with this
+this uh extension so money demand is the
+
+ align:start position:0%
+this uh extension so money demand is the
+ 
+
+ align:start position:0%
+this uh extension so money demand is the
+same as it used to be what happens is
+
+ align:start position:0%
+same as it used to be what happens is
+ 
+
+ align:start position:0%
+same as it used to be what happens is
+you're going to demand it in the form of
+
+ align:start position:0%
+you're going to demand it in the form of
+ 
+
+ align:start position:0%
+you're going to demand it in the form of
+currency or checking accounts or
+
+ align:start position:0%
+currency or checking accounts or
+ 
+
+ align:start position:0%
+currency or checking accounts or
+something like that but but the total
+
+ align:start position:0%
+something like that but but the total
+ 
+
+ align:start position:0%
+something like that but but the total
+money demand is exactly as it used to
+
+ align:start position:0%
+money demand is exactly as it used to
+ 
+
+ align:start position:0%
+money demand is exactly as it used to
+be Banks typically hold a share of a and
+
+ align:start position:0%
+be Banks typically hold a share of a and
+ 
+
+ align:start position:0%
+be Banks typically hold a share of a and
+assume for now that there's no currency
+
+ align:start position:0%
+assume for now that there's no currency
+ 
+
+ align:start position:0%
+assume for now that there's no currency
+so everything is check is deposit
+
+ align:start position:0%
+so everything is check is deposit
+ 
+
+ align:start position:0%
+so everything is check is deposit
+otherwise you get a more complicated
+
+ align:start position:0%
+otherwise you get a more complicated
+ 
+
+ align:start position:0%
+otherwise you get a more complicated
+formula okay so no one holds cash which
+
+ align:start position:0%
+formula okay so no one holds cash which
+ 
+
+ align:start position:0%
+formula okay so no one holds cash which
+probably quite realistic nowadays you so
+
+ align:start position:0%
+probably quite realistic nowadays you so
+ 
+
+ align:start position:0%
+probably quite realistic nowadays you so
+everyone has a checking account and
+
+ align:start position:0%
+everyone has a checking account and
+ 
+
+ align:start position:0%
+everyone has a checking account and
+that's it
+
+ align:start position:0%
+that's it
+ 
+
+ align:start position:0%
+that's it
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the banks
+
+ align:start position:0%
+so the banks
+ 
+
+ align:start position:0%
+so the banks
+typically hold for regulatory reasons a
+
+ align:start position:0%
+typically hold for regulatory reasons a
+ 
+
+ align:start position:0%
+typically hold for regulatory reasons a
+share of their Deposit they have a
+
+ align:start position:0%
+share of their Deposit they have a
+ 
+
+ align:start position:0%
+share of their Deposit they have a
+minimum for regulatory reasons a minimum
+
+ align:start position:0%
+minimum for regulatory reasons a minimum
+ 
+
+ align:start position:0%
+minimum for regulatory reasons a minimum
+share of the deposit they have that they
+
+ align:start position:0%
+share of the deposit they have that they
+ 
+
+ align:start position:0%
+share of the deposit they have that they
+need to hold in the form of reserves
+
+ align:start position:0%
+need to hold in the form of reserves
+ 
+
+ align:start position:0%
+need to hold in the form of reserves
+okay and I'm going to call that a fixed
+
+ align:start position:0%
+okay and I'm going to call that a fixed
+ 
+
+ align:start position:0%
+okay and I'm going to call that a fixed
+fraction Theta so if all the money is
+
+ align:start position:0%
+fraction Theta so if all the money is
+ 
+
+ align:start position:0%
+fraction Theta so if all the money is
+held in the form of the deposits then
+
+ align:start position:0%
+held in the form of the deposits then
+ 
+
+ align:start position:0%
+held in the form of the deposits then
+Theta which is a number like 0.1 say
+
+ align:start position:0%
+Theta which is a number like 0.1 say
+ 
+
+ align:start position:0%
+Theta which is a number like 0.1 say
+times the deposits which is money demand
+
+ align:start position:0%
+times the deposits which is money demand
+ 
+
+ align:start position:0%
+times the deposits which is money demand
+is equal to the reserves at the is equal
+
+ align:start position:0%
+is equal to the reserves at the is equal
+ 
+
+ align:start position:0%
+is equal to the reserves at the is equal
+to the central the demand for central
+
+ align:start position:0%
+to the central the demand for central
+ 
+
+ align:start position:0%
+to the central the demand for central
+bank
+
+ align:start position:0%
+bank
+ 
+
+ align:start position:0%
+bank
+money this is the demand for central
+
+ align:start position:0%
+money this is the demand for central
+ 
+
+ align:start position:0%
+money this is the demand for central
+bank money because is this are the N
+
+ align:start position:0%
+bank money because is this are the N
+ 
+
+ align:start position:0%
+bank money because is this are the N
+these are the reserves that the banks
+
+ align:start position:0%
+these are the reserves that the banks
+ 
+
+ align:start position:0%
+these are the reserves that the banks
+want to have at the central bank so the
+
+ align:start position:0%
+want to have at the central bank so the
+ 
+
+ align:start position:0%
+want to have at the central bank so the
+demand they they want to have this
+
+ align:start position:0%
+demand they they want to have this
+ 
+
+ align:start position:0%
+demand they they want to have this
+amount of deposits at the central bank
+
+ align:start position:0%
+amount of deposits at the central bank
+ 
+
+ align:start position:0%
+amount of deposits at the central bank
+this what we call HD it's Theta time m
+
+ align:start position:0%
+this what we call HD it's Theta time m
+ 
+
+ align:start position:0%
+this what we call HD it's Theta time m
+and so now rather than M what the
+
+ align:start position:0%
+and so now rather than M what the
+ 
+
+ align:start position:0%
+and so now rather than M what the
+Central Bank controls really because
+
+ align:start position:0%
+Central Bank controls really because
+ 
+
+ align:start position:0%
+Central Bank controls really because
+it's the only thing can really control
+
+ align:start position:0%
+it's the only thing can really control
+ 
+
+ align:start position:0%
+it's the only thing can really control
+is the money that it issues issues which
+
+ align:start position:0%
+is the money that it issues issues which
+ 
+
+ align:start position:0%
+is the money that it issues issues which
+is the central bank money so R supplying
+
+ align:start position:0%
+is the central bank money so R supplying
+ 
+
+ align:start position:0%
+is the central bank money so R supplying
+M which used to be currency now m is a
+
+ align:start position:0%
+M which used to be currency now m is a
+ 
+
+ align:start position:0%
+M which used to be currency now m is a
+bigger thing because has deposits and
+
+ align:start position:0%
+bigger thing because has deposits and
+ 
+
+ align:start position:0%
+bigger thing because has deposits and
+all sort of stuff but the central bank
+
+ align:start position:0%
+all sort of stuff but the central bank
+ 
+
+ align:start position:0%
+all sort of stuff but the central bank
+is the one that controls how much high
+
+ align:start position:0%
+is the one that controls how much high
+ 
+
+ align:start position:0%
+is the one that controls how much high
+power money how much central bank money
+
+ align:start position:0%
+power money how much central bank money
+ 
+
+ align:start position:0%
+power money how much central bank money
+it issues and we're going to call that
+
+ align:start position:0%
+it issues and we're going to call that
+ 
+
+ align:start position:0%
+it issues and we're going to call that
+H okay so if we go back to my balance
+
+ align:start position:0%
+H okay so if we go back to my balance
+ 
+
+ align:start position:0%
+H okay so if we go back to my balance
+sheet here the Central Bank cannot
+
+ align:start position:0%
+sheet here the Central Bank cannot
+ 
+
+ align:start position:0%
+sheet here the Central Bank cannot
+control total money because it cannot
+
+ align:start position:0%
+control total money because it cannot
+ 
+
+ align:start position:0%
+control total money because it cannot
+control the amount of checkable deposits
+
+ align:start position:0%
+control the amount of checkable deposits
+ 
+
+ align:start position:0%
+control the amount of checkable deposits
+in the economy but it can control this
+
+ align:start position:0%
+in the economy but it can control this
+ 
+
+ align:start position:0%
+in the economy but it can control this
+money here and since we have no currency
+
+ align:start position:0%
+money here and since we have no currency
+ 
+
+ align:start position:0%
+money here and since we have no currency
+my example it really can control how
+
+ align:start position:0%
+my example it really can control how
+ 
+
+ align:start position:0%
+my example it really can control how
+much supply of reserves it can do okay
+
+ align:start position:0%
+much supply of reserves it can do okay
+ 
+
+ align:start position:0%
+much supply of reserves it can do okay
+and so now we have a demand for Reserve
+
+ align:start position:0%
+and so now we have a demand for Reserve
+ 
+
+ align:start position:0%
+and so now we have a demand for Reserve
+which is just proportional to money
+
+ align:start position:0%
+which is just proportional to money
+ 
+
+ align:start position:0%
+which is just proportional to money
+demand equal to some fixed amount H
+
+ align:start position:0%
+demand equal to some fixed amount H
+ 
+
+ align:start position:0%
+demand equal to some fixed amount H
+which is the supply of high power money
+
+ align:start position:0%
+which is the supply of high power money
+ 
+
+ align:start position:0%
+which is the supply of high power money
+by the central bank and then the
+
+ align:start position:0%
+by the central bank and then the
+ 
+
+ align:start position:0%
+by the central bank and then the
+equilibrium looks exactly
+
+ align:start position:0%
+equilibrium looks exactly
+ 
+
+ align:start position:0%
+equilibrium looks exactly
+like before it's going to be some
+
+ align:start position:0%
+like before it's going to be some
+ 
+
+ align:start position:0%
+like before it's going to be some
+remember before we have m equal to
+
+ align:start position:0%
+remember before we have m equal to
+ 
+
+ align:start position:0%
+remember before we have m equal to
+Dollar y i now we're saying it's not M
+
+ align:start position:0%
+Dollar y i now we're saying it's not M
+ 
+
+ align:start position:0%
+Dollar y i now we're saying it's not M
+it's Theta times M really no because
+
+ align:start position:0%
+it's Theta times M really no because
+ 
+
+ align:start position:0%
+it's Theta times M really no because
+it's a fraction only of Total Money okay
+
+ align:start position:0%
+it's a fraction only of Total Money okay
+ 
+
+ align:start position:0%
+it's a fraction only of Total Money okay
+has to be equal to a money demand it's
+
+ align:start position:0%
+has to be equal to a money demand it's
+ 
+
+ align:start position:0%
+has to be equal to a money demand it's
+not Total Money demand it's the money
+
+ align:start position:0%
+not Total Money demand it's the money
+ 
+
+ align:start position:0%
+not Total Money demand it's the money
+demand that ends up being demand for
+
+ align:start position:0%
+demand that ends up being demand for
+ 
+
+ align:start position:0%
+demand that ends up being demand for
+central bank money because Total Money
+
+ align:start position:0%
+central bank money because Total Money
+ 
+
+ align:start position:0%
+central bank money because Total Money
+demand is the checkable checking
+
+ align:start position:0%
+demand is the checkable checking
+ 
+
+ align:start position:0%
+demand is the checkable checking
+account that leads to a demand for
+
+ align:start position:0%
+account that leads to a demand for
+ 
+
+ align:start position:0%
+account that leads to a demand for
+central bank money by the Banks which is
+
+ align:start position:0%
+central bank money by the Banks which is
+ 
+
+ align:start position:0%
+central bank money by the Banks which is
+Theta times those deposits it's not the
+
+ align:start position:0%
+Theta times those deposits it's not the
+ 
+
+ align:start position:0%
+Theta times those deposits it's not the
+full Deposit they don't Deposit they
+
+ align:start position:0%
+full Deposit they don't Deposit they
+ 
+
+ align:start position:0%
+full Deposit they don't Deposit they
+don't take all the deposit and deposit
+
+ align:start position:0%
+don't take all the deposit and deposit
+ 
+
+ align:start position:0%
+don't take all the deposit and deposit
+at Central Bank they say only 10% of
+
+ align:start position:0%
+at Central Bank they say only 10% of
+ 
+
+ align:start position:0%
+at Central Bank they say only 10% of
+those deposit will keep them at the
+
+ align:start position:0%
+those deposit will keep them at the
+ 
+
+ align:start position:0%
+those deposit will keep them at the
+central bank so $100 in deposit if 30 is
+
+ align:start position:0%
+central bank so $100 in deposit if 30 is
+ 
+
+ align:start position:0%
+central bank so $100 in deposit if 30 is
+point1 $100 in deposit leads to a demand
+
+ align:start position:0%
+point1 $100 in deposit leads to a demand
+ 
+
+ align:start position:0%
+point1 $100 in deposit leads to a demand
+for reserves that mean for deposits by
+
+ align:start position:0%
+for reserves that mean for deposits by
+ 
+
+ align:start position:0%
+for reserves that mean for deposits by
+the bank and the Central Bank of
+
+ align:start position:0%
+the bank and the Central Bank of
+ 
+
+ align:start position:0%
+the bank and the Central Bank of
+$10 okay and that is the thing that the
+
+ align:start position:0%
+$10 okay and that is the thing that the
+ 
+
+ align:start position:0%
+$10 okay and that is the thing that the
+central bank can control very well it's
+
+ align:start position:0%
+central bank can control very well it's
+ 
+
+ align:start position:0%
+central bank can control very well it's
+a m the is the demand that comes to me
+
+ align:start position:0%
+a m the is the demand that comes to me
+ 
+
+ align:start position:0%
+a m the is the demand that comes to me
+the central bank is $10 and I decide
+
+ align:start position:0%
+the central bank is $10 and I decide
+ 
+
+ align:start position:0%
+the central bank is $10 and I decide
+whether we do $10 or not you we can do
+
+ align:start position:0%
+whether we do $10 or not you we can do
+ 
+
+ align:start position:0%
+whether we do $10 or not you we can do
+five and then we're going to have the
+
+ align:start position:0%
+five and then we're going to have the
+ 
+
+ align:start position:0%
+five and then we're going to have the
+interest rate sort out five to be in
+
+ align:start position:0%
+interest rate sort out five to be in
+ 
+
+ align:start position:0%
+interest rate sort out five to be in
+equilibrium so it's if if if the banking
+
+ align:start position:0%
+equilibrium so it's if if if the banking
+ 
+
+ align:start position:0%
+equilibrium so it's if if if the banking
+sector wanted 10 and I'm only going to
+
+ align:start position:0%
+sector wanted 10 and I'm only going to
+ 
+
+ align:start position:0%
+sector wanted 10 and I'm only going to
+supply five then something the interest
+
+ align:start position:0%
+supply five then something the interest
+ 
+
+ align:start position:0%
+supply five then something the interest
+rate is going to have to rise so that
+
+ align:start position:0%
+rate is going to have to rise so that
+ 
+
+ align:start position:0%
+rate is going to have to rise so that
+deposits you know decline less demand
+
+ align:start position:0%
+deposits you know decline less demand
+ 
+
+ align:start position:0%
+deposits you know decline less demand
+for money and and the and the final
+
+ align:start position:0%
+for money and and the and the final
+ 
+
+ align:start position:0%
+for money and and the and the final
+demand that gets to me is five not 10
+
+ align:start position:0%
+demand that gets to me is five not 10
+ 
+
+ align:start position:0%
+demand that gets to me is five not 10
+but the mechanism is exactly the same I
+
+ align:start position:0%
+but the mechanism is exactly the same I
+ 
+
+ align:start position:0%
+but the mechanism is exactly the same I
+know this this can be a little confusing
+
+ align:start position:0%
+know this this can be a little confusing
+ 
+
+ align:start position:0%
+know this this can be a little confusing
+but the mechanism exactly the same it's
+
+ align:start position:0%
+but the mechanism exactly the same it's
+ 
+
+ align:start position:0%
+but the mechanism exactly the same it's
+just this just illustrates it makes I
+
+ align:start position:0%
+just this just illustrates it makes I
+ 
+
+ align:start position:0%
+just this just illustrates it makes I
+mean this this is important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it's institutionally important
+
+ align:start position:0%
+because it's institutionally important
+ 
+
+ align:start position:0%
+because it's institutionally important
+more than conceptually important because
+
+ align:start position:0%
+more than conceptually important because
+ 
+
+ align:start position:0%
+more than conceptually important because
+this is the market where really the
+
+ align:start position:0%
+this is the market where really the
+ 
+
+ align:start position:0%
+this is the market where really the
+interest rate is
+
+ align:start position:0%
+interest rate is
+ 
+
+ align:start position:0%
+interest rate is
+set okay so this I'm doing next time
+
+ align:start position:0%
+set okay so this I'm doing next time
+ 
+
+ align:start position:0%
+set okay so this I'm doing next time
+that market the market for reserves
+
+ align:start position:0%
+that market the market for reserves
+ 
+
+ align:start position:0%
+that market the market for reserves
+really because what the banks do is they
+
+ align:start position:0%
+really because what the banks do is they
+ 
+
+ align:start position:0%
+really because what the banks do is they
+want Reserves
+
+ align:start position:0%
+want Reserves
+ 
+
+ align:start position:0%
+want Reserves
+okay deposit at the central bank that
+
+ align:start position:0%
+okay deposit at the central bank that
+ 
+
+ align:start position:0%
+okay deposit at the central bank that
+market for reserves the interest rate in
+
+ align:start position:0%
+market for reserves the interest rate in
+ 
+
+ align:start position:0%
+market for reserves the interest rate in
+that market for reserves is called the
+
+ align:start position:0%
+that market for reserves is called the
+ 
+
+ align:start position:0%
+that market for reserves is called the
+federal funds rate and it's called the
+
+ align:start position:0%
+federal funds rate and it's called the
+ 
+
+ align:start position:0%
+federal funds rate and it's called the
+federal funds rate because the Federal
+
+ align:start position:0%
+federal funds rate because the Federal
+ 
+
+ align:start position:0%
+federal funds rate because the Federal
+Reserves controls that rate so when the
+
+ align:start position:0%
+Reserves controls that rate so when the
+ 
+
+ align:start position:0%
+Reserves controls that rate so when the
+FED when when there is a meeting by the
+
+ align:start position:0%
+FED when when there is a meeting by the
+ 
+
+ align:start position:0%
+FED when when there is a meeting by the
+fed or a policy announcement that tell
+
+ align:start position:0%
+fed or a policy announcement that tell
+ 
+
+ align:start position:0%
+fed or a policy announcement that tell
+you that the the FED has increased the
+
+ align:start position:0%
+you that the the FED has increased the
+ 
+
+ align:start position:0%
+you that the the FED has increased the
+rate by 50 basis points it means it has
+
+ align:start position:0%
+rate by 50 basis points it means it has
+ 
+
+ align:start position:0%
+rate by 50 basis points it means it has
+increased the interest rate in that
+
+ align:start position:0%
+increased the interest rate in that
+ 
+
+ align:start position:0%
+increased the interest rate in that
+market by 50 basis points okay so the
+
+ align:start position:0%
+market by 50 basis points okay so the
+ 
+
+ align:start position:0%
+market by 50 basis points okay so the
+interest rate that the Central Bank
+
+ align:start position:0%
+interest rate that the Central Bank
+ 
+
+ align:start position:0%
+interest rate that the Central Bank
+controls corly is called the federal
+
+ align:start position:0%
+controls corly is called the federal
+ 
+
+ align:start position:0%
+controls corly is called the federal
+funds rate and the federal funds rate is
+
+ align:start position:0%
+funds rate and the federal funds rate is
+ 
+
+ align:start position:0%
+funds rate and the federal funds rate is
+that market is market for reserve for
+
+ align:start position:0%
+that market is market for reserve for
+ 
+
+ align:start position:0%
+that market is market for reserve for
+high power money so all the operations
+
+ align:start position:0%
+high power money so all the operations
+ 
+
+ align:start position:0%
+high power money so all the operations
+happen there they don't participate in
+
+ align:start position:0%
+happen there they don't participate in
+ 
+
+ align:start position:0%
+happen there they don't participate in
+the deposit Market or anything they
+
+ align:start position:0%
+the deposit Market or anything they
+ 
+
+ align:start position:0%
+the deposit Market or anything they
+participate in that market which every
+
+ align:start position:0%
+participate in that market which every
+ 
+
+ align:start position:0%
+participate in that market which every
+night is a is a Hu huge number of
+
+ align:start position:0%
+night is a is a Hu huge number of
+ 
+
+ align:start position:0%
+night is a is a Hu huge number of
+transactions every night because I put
+
+ align:start position:0%
+transactions every night because I put
+ 
+
+ align:start position:0%
+transactions every night because I put
+all the banks together but what happens
+
+ align:start position:0%
+all the banks together but what happens
+ 
+
+ align:start position:0%
+all the banks together but what happens
+every night is some banks have more
+
+ align:start position:0%
+every night is some banks have more
+ 
+
+ align:start position:0%
+every night is some banks have more
+reserves than they need some other banks
+
+ align:start position:0%
+reserves than they need some other banks
+ 
+
+ align:start position:0%
+reserves than they need some other banks
+have less reserves than they need so
+
+ align:start position:0%
+have less reserves than they need so
+ 
+
+ align:start position:0%
+have less reserves than they need so
+they supply and demand within the
+
+ align:start position:0%
+they supply and demand within the
+ 
+
+ align:start position:0%
+they supply and demand within the
+banking sector for for reserves and
+
+ align:start position:0%
+banking sector for for reserves and
+ 
+
+ align:start position:0%
+banking sector for for reserves and
+there's an interest rate that tends to
+
+ align:start position:0%
+there's an interest rate that tends to
+ 
+
+ align:start position:0%
+there's an interest rate that tends to
+equilibrate if too many banks are short
+
+ align:start position:0%
+equilibrate if too many banks are short
+ 
+
+ align:start position:0%
+equilibrate if too many banks are short
+reserves then there's going to be lots
+
+ align:start position:0%
+reserves then there's going to be lots
+ 
+
+ align:start position:0%
+reserves then there's going to be lots
+of demand for reserve and interest rate
+
+ align:start position:0%
+of demand for reserve and interest rate
+ 
+
+ align:start position:0%
+of demand for reserve and interest rate
+is going to tend to go up If the Fed
+
+ align:start position:0%
+is going to tend to go up If the Fed
+ 
+
+ align:start position:0%
+is going to tend to go up If the Fed
+doesn't want that interest rate to go up
+
+ align:start position:0%
+doesn't want that interest rate to go up
+ 
+
+ align:start position:0%
+doesn't want that interest rate to go up
+then what it will do overnight it will
+
+ align:start position:0%
+then what it will do overnight it will
+ 
+
+ align:start position:0%
+then what it will do overnight it will
+go there and inject reserves into the
+
+ align:start position:0%
+go there and inject reserves into the
+ 
+
+ align:start position:0%
+go there and inject reserves into the
+system high power money so the interest
+
+ align:start position:0%
+system high power money so the interest
+ 
+
+ align:start position:0%
+system high power money so the interest
+rate in that market comes down okay and
+
+ align:start position:0%
+rate in that market comes down okay and
+ 
+
+ align:start position:0%
+rate in that market comes down okay and
+that's the way the FED operates that's
+
+ align:start position:0%
+that's the way the FED operates that's
+ 
+
+ align:start position:0%
+that's the way the FED operates that's
+the way it controls it participates in
+
+ align:start position:0%
+the way it controls it participates in
+ 
+
+ align:start position:0%
+the way it controls it participates in
+that market controls the amount of high
+
+ align:start position:0%
+that market controls the amount of high
+ 
+
+ align:start position:0%
+that market controls the amount of high
+power money which regulates the rate in
+
+ align:start position:0%
+power money which regulates the rate in
+ 
+
+ align:start position:0%
+power money which regulates the rate in
+the resarch market and here it's only
+
+ align:start position:0%
+the resarch market and here it's only
+ 
+
+ align:start position:0%
+the resarch market and here it's only
+you know and then so here you have sort
+
+ align:start position:0%
+you know and then so here you have sort
+ 
+
+ align:start position:0%
+you know and then so here you have sort
+of the major Banks participating here
+
+ align:start position:0%
+of the major Banks participating here
+ 
+
+ align:start position:0%
+of the major Banks participating here
+and and and then this leaks into the
+
+ align:start position:0%
+and and and then this leaks into the
+ 
+
+ align:start position:0%
+and and and then this leaks into the
+other interest rates in the economy to
+
+ align:start position:0%
+other interest rates in the economy to
+ 
+
+ align:start position:0%
+other interest rates in the economy to
+into deposit rates to to bond rates and
+
+ align:start position:0%
+into deposit rates to to bond rates and
+ 
+
+ align:start position:0%
+into deposit rates to to bond rates and
+so on but but the real rate they control
+
+ align:start position:0%
+so on but but the real rate they control
+ 
+
+ align:start position:0%
+so on but but the real rate they control
+the rate that they control most directly
+
+ align:start position:0%
+the rate that they control most directly
+ 
+
+ align:start position:0%
+the rate that they control most directly
+is that rate here okay and that's the
+
+ align:start position:0%
+is that rate here okay and that's the
+ 
+
+ align:start position:0%
+is that rate here okay and that's the
+reason I wanted to give you a little bit
+
+ align:start position:0%
+reason I wanted to give you a little bit
+ 
+
+ align:start position:0%
+reason I wanted to give you a little bit
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+institutional I mean to add complexity
+
+ align:start position:0%
+institutional I mean to add complexity
+ 
+
+ align:start position:0%
+institutional I mean to add complexity
+so we could get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to so you could get to this word federal
+
+ align:start position:0%
+to so you could get to this word federal
+ 
+
+ align:start position:0%
+to so you could get to this word federal
+funds rate because that's what you're
+
+ align:start position:0%
+funds rate because that's what you're
+ 
+
+ align:start position:0%
+funds rate because that's what you're
+going to read in the newspapers the FED
+
+ align:start position:0%
+going to read in the newspapers the FED
+ 
+
+ align:start position:0%
+going to read in the newspapers the FED
+increase the federal funds Target is
+
+ align:start position:0%
+increase the federal funds Target is
+ 
+
+ align:start position:0%
+increase the federal funds Target is
+going to say because they target they
+
+ align:start position:0%
+going to say because they target they
+ 
+
+ align:start position:0%
+going to say because they target they
+cannot guarantee it's going to be that
+
+ align:start position:0%
+cannot guarantee it's going to be that
+ 
+
+ align:start position:0%
+cannot guarantee it's going to be that
+they target an interest rate and
+
+ align:start position:0%
+they target an interest rate and
+ 
+
+ align:start position:0%
+they target an interest rate and
+typically they give you a range it's a
+
+ align:start position:0%
+typically they give you a range it's a
+ 
+
+ align:start position:0%
+typically they give you a range it's a
+very narrow range okay you let me just
+
+ align:start position:0%
+very narrow range okay you let me just
+ 
+
+ align:start position:0%
+very narrow range okay you let me just
+conclude by showing you how that rate
+
+ align:start position:0%
+conclude by showing you how that rate
+ 
+
+ align:start position:0%
+conclude by showing you how that rate
+has looked in the US recently okay and I
+
+ align:start position:0%
+has looked in the US recently okay and I
+ 
+
+ align:start position:0%
+has looked in the US recently okay and I
+finish here so here here is before covid
+
+ align:start position:0%
+finish here so here here is before covid
+ 
+
+ align:start position:0%
+finish here so here here is before covid
+okay H the interest rate the Fed was
+
+ align:start position:0%
+okay H the interest rate the Fed was
+ 
+
+ align:start position:0%
+okay H the interest rate the Fed was
+already hik in interest rate it had
+
+ align:start position:0%
+already hik in interest rate it had
+ 
+
+ align:start position:0%
+already hik in interest rate it had
+overdone it there so it was beginning to
+
+ align:start position:0%
+overdone it there so it was beginning to
+ 
+
+ align:start position:0%
+overdone it there so it was beginning to
+lower interest rate and then covid came
+
+ align:start position:0%
+lower interest rate and then covid came
+ 
+
+ align:start position:0%
+lower interest rate and then covid came
+boom and they cut interest rate very
+
+ align:start position:0%
+boom and they cut interest rate very
+ 
+
+ align:start position:0%
+boom and they cut interest rate very
+aggressively the this is the maximum
+
+ align:start position:0%
+aggressively the this is the maximum
+ 
+
+ align:start position:0%
+aggressively the this is the maximum
+they can cut it too and we're going to
+
+ align:start position:0%
+they can cut it too and we're going to
+ 
+
+ align:start position:0%
+they can cut it too and we're going to
+talk about that briefly in the next to
+
+ align:start position:0%
+talk about that briefly in the next to
+ 
+
+ align:start position:0%
+talk about that briefly in the next to
+zero you cannot go below zero you cannot
+
+ align:start position:0%
+zero you cannot go below zero you cannot
+ 
+
+ align:start position:0%
+zero you cannot go below zero you cannot
+pay negative interest rate because then
+
+ align:start position:0%
+pay negative interest rate because then
+ 
+
+ align:start position:0%
+pay negative interest rate because then
+I don't demand money I don't demand
+
+ align:start position:0%
+I don't demand money I don't demand
+ 
+
+ align:start position:0%
+I don't demand money I don't demand
+bonds why should I hold a bond that pays
+
+ align:start position:0%
+bonds why should I hold a bond that pays
+ 
+
+ align:start position:0%
+bonds why should I hold a bond that pays
+me a negative interest rate when cash
+
+ align:start position:0%
+me a negative interest rate when cash
+ 
+
+ align:start position:0%
+me a negative interest rate when cash
+pays zero always zero I can always keep
+
+ align:start position:0%
+pays zero always zero I can always keep
+ 
+
+ align:start position:0%
+pays zero always zero I can always keep
+it under the mattress and and and I
+
+ align:start position:0%
+it under the mattress and and and I
+ 
+
+ align:start position:0%
+it under the mattress and and and I
+don't pay in negative so the interest
+
+ align:start position:0%
+don't pay in negative so the interest
+ 
+
+ align:start position:0%
+don't pay in negative so the interest
+rate the lowest can be zero and you see
+
+ align:start position:0%
+rate the lowest can be zero and you see
+ 
+
+ align:start position:0%
+rate the lowest can be zero and you see
+that they they did the maximum they
+
+ align:start position:0%
+that they they did the maximum they
+ 
+
+ align:start position:0%
+that they they did the maximum they
+could in terms of cutting interest rate
+
+ align:start position:0%
+could in terms of cutting interest rate
+ 
+
+ align:start position:0%
+could in terms of cutting interest rate
+they went to zero effectively zero and
+
+ align:start position:0%
+they went to zero effectively zero and
+ 
+
+ align:start position:0%
+they went to zero effectively zero and
+now they have been trying to catch up
+
+ align:start position:0%
+now they have been trying to catch up
+ 
+
+ align:start position:0%
+now they have been trying to catch up
+because inflation is very high and so
+
+ align:start position:0%
+because inflation is very high and so
+ 
+
+ align:start position:0%
+because inflation is very high and so
+they're trying to to hike interest rate
+
+ align:start position:0%
+they're trying to to hike interest rate
+ 
+
+ align:start position:0%
+they're trying to to hike interest rate
+and you see how what they're doing okay
+
+ align:start position:0%
+and you see how what they're doing okay
+ 
+
+ align:start position:0%
+and you see how what they're doing okay
+well all those interventions happen in
+
+ align:start position:0%
+well all those interventions happen in
+ 
+
+ align:start position:0%
+well all those interventions happen in
+the reserve Market that's what where
+
+ align:start position:0%
+the reserve Market that's what where
+ 
+
+ align:start position:0%
+the reserve Market that's what where
+this is that's the rate is in that
+
+ align:start position:0%
+this is that's the rate is in that
+ 
+
+ align:start position:0%
+this is that's the rate is in that
+market over okay okay so I think we're
+
+ align:start position:0%
+market over okay okay so I think we're
+ 
+
+ align:start position:0%
+market over okay okay so I think we're
+meeting on Tuesday next week uh I think
+
+ align:start position:0%
+meeting on Tuesday next week uh I think
+ 
+
+ align:start position:0%
+meeting on Tuesday next week uh I think
+that's the plan
\ No newline at end of file
diff --git a/bFZ-0FH5hfs.txt b/bFZ-0FH5hfs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9d92db394f888977d27c59a31c70af49f8f64819
--- /dev/null
+++ b/bFZ-0FH5hfs.txt
@@ -0,0 +1,13299 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well actually just do a brief chapter on
+
+ align:start position:0%
+well actually just do a brief chapter on
+ 
+
+ align:start position:0%
+well actually just do a brief chapter on
+Bayesian statistics and there's entire
+
+ align:start position:0%
+Bayesian statistics and there's entire
+ 
+
+ align:start position:0%
+Bayesian statistics and there's entire
+courses on Bayesian statistics there's
+
+ align:start position:0%
+courses on Bayesian statistics there's
+ 
+
+ align:start position:0%
+courses on Bayesian statistics there's
+an entire books on Bayesian statistics
+
+ align:start position:0%
+an entire books on Bayesian statistics
+ 
+
+ align:start position:0%
+an entire books on Bayesian statistics
+this entire careers on Bayesian
+
+ align:start position:0%
+this entire careers on Bayesian
+ 
+
+ align:start position:0%
+this entire careers on Bayesian
+statistics so admittedly I'm not going
+
+ align:start position:0%
+statistics so admittedly I'm not going
+ 
+
+ align:start position:0%
+statistics so admittedly I'm not going
+to be able to do it justice and tell you
+
+ align:start position:0%
+to be able to do it justice and tell you
+ 
+
+ align:start position:0%
+to be able to do it justice and tell you
+all the interesting things that are
+
+ align:start position:0%
+all the interesting things that are
+ 
+
+ align:start position:0%
+all the interesting things that are
+happening in Bayesian statistics but I
+
+ align:start position:0%
+happening in Bayesian statistics but I
+ 
+
+ align:start position:0%
+happening in Bayesian statistics but I
+think it's important as a statistician
+
+ align:start position:0%
+think it's important as a statistician
+ 
+
+ align:start position:0%
+think it's important as a statistician
+to know what it is how it works because
+
+ align:start position:0%
+to know what it is how it works because
+ 
+
+ align:start position:0%
+to know what it is how it works because
+it's actually a weapon of choice for
+
+ align:start position:0%
+it's actually a weapon of choice for
+ 
+
+ align:start position:0%
+it's actually a weapon of choice for
+many practitioners and and because it
+
+ align:start position:0%
+many practitioners and and because it
+ 
+
+ align:start position:0%
+many practitioners and and because it
+allows them to incorporate their
+
+ align:start position:0%
+allows them to incorporate their
+ 
+
+ align:start position:0%
+allows them to incorporate their
+knowledge about a problem in a fairly
+
+ align:start position:0%
+knowledge about a problem in a fairly
+ 
+
+ align:start position:0%
+knowledge about a problem in a fairly
+systematic manner
+
+ align:start position:0%
+systematic manner
+ 
+
+ align:start position:0%
+systematic manner
+so if you look at like say the the
+
+ align:start position:0%
+so if you look at like say the the
+ 
+
+ align:start position:0%
+so if you look at like say the the
+Bayesian statistics literature it's it's
+
+ align:start position:0%
+Bayesian statistics literature it's it's
+ 
+
+ align:start position:0%
+Bayesian statistics literature it's it's
+it's huge and so here I give you you
+
+ align:start position:0%
+it's huge and so here I give you you
+ 
+
+ align:start position:0%
+it's huge and so here I give you you
+know sort of a range of what you can
+
+ align:start position:0%
+know sort of a range of what you can
+ 
+
+ align:start position:0%
+know sort of a range of what you can
+expect to see in Bayesian statistics
+
+ align:start position:0%
+expect to see in Bayesian statistics
+ 
+
+ align:start position:0%
+expect to see in Bayesian statistics
+from your you know second edition of a
+
+ align:start position:0%
+from your you know second edition of a
+ 
+
+ align:start position:0%
+from your you know second edition of a
+traditional book something that involves
+
+ align:start position:0%
+traditional book something that involves
+ 
+
+ align:start position:0%
+traditional book something that involves
+computation some things that involve
+
+ align:start position:0%
+computation some things that involve
+ 
+
+ align:start position:0%
+computation some things that involve
+rethinking and there's a lot of Bayesian
+
+ align:start position:0%
+rethinking and there's a lot of Bayesian
+ 
+
+ align:start position:0%
+rethinking and there's a lot of Bayesian
+thinking there's a lot of things that
+
+ align:start position:0%
+thinking there's a lot of things that
+ 
+
+ align:start position:0%
+thinking there's a lot of things that
+you know talk about sort of like
+
+ align:start position:0%
+you know talk about sort of like
+ 
+
+ align:start position:0%
+you know talk about sort of like
+philosophy of thinking Bayesian this
+
+ align:start position:0%
+philosophy of thinking Bayesian this
+ 
+
+ align:start position:0%
+philosophy of thinking Bayesian this
+book for example seems to be one of them
+
+ align:start position:0%
+book for example seems to be one of them
+ 
+
+ align:start position:0%
+book for example seems to be one of them
+this book is definitely one of them this
+
+ align:start position:0%
+this book is definitely one of them this
+ 
+
+ align:start position:0%
+this book is definitely one of them this
+one represents sort of a wide a broad
+
+ align:start position:0%
+one represents sort of a wide a broad
+ 
+
+ align:start position:0%
+one represents sort of a wide a broad
+literature on Bayesian statistics for
+
+ align:start position:0%
+literature on Bayesian statistics for
+ 
+
+ align:start position:0%
+literature on Bayesian statistics for
+applications for example in social
+
+ align:start position:0%
+applications for example in social
+ 
+
+ align:start position:0%
+applications for example in social
+sciences but even in large scale machine
+
+ align:start position:0%
+sciences but even in large scale machine
+ 
+
+ align:start position:0%
+sciences but even in large scale machine
+learning there's a lot of Bayesian
+
+ align:start position:0%
+learning there's a lot of Bayesian
+ 
+
+ align:start position:0%
+learning there's a lot of Bayesian
+statistics happening particularly using
+
+ align:start position:0%
+statistics happening particularly using
+ 
+
+ align:start position:0%
+statistics happening particularly using
+something called Bayesian and
+
+ align:start position:0%
+something called Bayesian and
+ 
+
+ align:start position:0%
+something called Bayesian and
+parametric's or hierarchical Bayesian
+
+ align:start position:0%
+parametric's or hierarchical Bayesian
+ 
+
+ align:start position:0%
+parametric's or hierarchical Bayesian
+modeling so we do have some experts at
+
+ align:start position:0%
+modeling so we do have some experts at
+ 
+
+ align:start position:0%
+modeling so we do have some experts at
+MIT in the in C cell Tamra Broderick for
+
+ align:start position:0%
+MIT in the in C cell Tamra Broderick for
+ 
+
+ align:start position:0%
+MIT in the in C cell Tamra Broderick for
+example is a person who does quite a bit
+
+ align:start position:0%
+example is a person who does quite a bit
+ 
+
+ align:start position:0%
+example is a person who does quite a bit
+of interesting work on Beijing and
+
+ align:start position:0%
+of interesting work on Beijing and
+ 
+
+ align:start position:0%
+of interesting work on Beijing and
+parametric's and if that's something you
+
+ align:start position:0%
+parametric's and if that's something you
+ 
+
+ align:start position:0%
+parametric's and if that's something you
+want to know more about our duty to go
+
+ align:start position:0%
+want to know more about our duty to go
+ 
+
+ align:start position:0%
+want to know more about our duty to go
+and talk to her so you know before we go
+
+ align:start position:0%
+and talk to her so you know before we go
+ 
+
+ align:start position:0%
+and talk to her so you know before we go
+in those Oh
+
+ align:start position:0%
+in those Oh
+ 
+
+ align:start position:0%
+in those Oh
+or advanced things we need to start with
+
+ align:start position:0%
+or advanced things we need to start with
+ 
+
+ align:start position:0%
+or advanced things we need to start with
+you know what is what is the Bayesian
+
+ align:start position:0%
+you know what is what is the Bayesian
+ 
+
+ align:start position:0%
+you know what is what is the Bayesian
+approach what do what do Beijing's do
+
+ align:start position:0%
+approach what do what do Beijing's do
+ 
+
+ align:start position:0%
+approach what do what do Beijing's do
+and how is it different from what we've
+
+ align:start position:0%
+and how is it different from what we've
+ 
+
+ align:start position:0%
+and how is it different from what we've
+been doing so far so to understand the
+
+ align:start position:0%
+been doing so far so to understand the
+ 
+
+ align:start position:0%
+been doing so far so to understand the
+difference between Beijing's and what
+
+ align:start position:0%
+difference between Beijing's and what
+ 
+
+ align:start position:0%
+difference between Beijing's and what
+we've been doing so far is we need to
+
+ align:start position:0%
+we've been doing so far is we need to
+ 
+
+ align:start position:0%
+we've been doing so far is we need to
+first put a name on what we've been
+
+ align:start position:0%
+first put a name on what we've been
+ 
+
+ align:start position:0%
+first put a name on what we've been
+doing so far it's called frequentist
+
+ align:start position:0%
+doing so far it's called frequentist
+ 
+
+ align:start position:0%
+doing so far it's called frequentist
+statistics so it's usually patient
+
+ align:start position:0%
+statistics so it's usually patient
+ 
+
+ align:start position:0%
+statistics so it's usually patient
+versus frequency statistics I mean by
+
+ align:start position:0%
+versus frequency statistics I mean by
+ 
+
+ align:start position:0%
+versus frequency statistics I mean by
+versus I don't mean that there's
+
+ align:start position:0%
+versus I don't mean that there's
+ 
+
+ align:start position:0%
+versus I don't mean that there's
+naturally in a position to them actually
+
+ align:start position:0%
+naturally in a position to them actually
+ 
+
+ align:start position:0%
+naturally in a position to them actually
+often you will see the same method that
+
+ align:start position:0%
+often you will see the same method that
+ 
+
+ align:start position:0%
+often you will see the same method that
+comes out of both approaches so let's
+
+ align:start position:0%
+comes out of both approaches so let's
+ 
+
+ align:start position:0%
+comes out of both approaches so let's
+see how we did it right the first thing
+
+ align:start position:0%
+see how we did it right the first thing
+ 
+
+ align:start position:0%
+see how we did it right the first thing
+we had data might we observe some data
+
+ align:start position:0%
+we had data might we observe some data
+ 
+
+ align:start position:0%
+we had data might we observe some data
+and we assumed that this data was
+
+ align:start position:0%
+and we assumed that this data was
+ 
+
+ align:start position:0%
+and we assumed that this data was
+generated randomly the reason we did
+
+ align:start position:0%
+generated randomly the reason we did
+ 
+
+ align:start position:0%
+generated randomly the reason we did
+that is that because this would allow us
+
+ align:start position:0%
+that is that because this would allow us
+ 
+
+ align:start position:0%
+that is that because this would allow us
+to leverage tools from probability so
+
+ align:start position:0%
+to leverage tools from probability so
+ 
+
+ align:start position:0%
+to leverage tools from probability so
+let's say by nature measurements you do
+
+ align:start position:0%
+let's say by nature measurements you do
+ 
+
+ align:start position:0%
+let's say by nature measurements you do
+a survey you get some data okay then we
+
+ align:start position:0%
+a survey you get some data okay then we
+ 
+
+ align:start position:0%
+a survey you get some data okay then we
+made some assumptions on the data
+
+ align:start position:0%
+made some assumptions on the data
+ 
+
+ align:start position:0%
+made some assumptions on the data
+generating process for example we assume
+
+ align:start position:0%
+generating process for example we assume
+ 
+
+ align:start position:0%
+generating process for example we assume
+they were AI D that was one of the
+
+ align:start position:0%
+they were AI D that was one of the
+ 
+
+ align:start position:0%
+they were AI D that was one of the
+recurring things sometimes we assume it
+
+ align:start position:0%
+recurring things sometimes we assume it
+ 
+
+ align:start position:0%
+recurring things sometimes we assume it
+was Gaussian if we wanted to you say
+
+ align:start position:0%
+was Gaussian if we wanted to you say
+ 
+
+ align:start position:0%
+was Gaussian if we wanted to you say
+t-test maybe we did some nonparametric
+
+ align:start position:0%
+t-test maybe we did some nonparametric
+ 
+
+ align:start position:0%
+t-test maybe we did some nonparametric
+statistics we assumed it was a smooth
+
+ align:start position:0%
+statistics we assumed it was a smooth
+ 
+
+ align:start position:0%
+statistics we assumed it was a smooth
+function or maybe linear regression
+
+ align:start position:0%
+function or maybe linear regression
+ 
+
+ align:start position:0%
+function or maybe linear regression
+function right so those are our modeling
+
+ align:start position:0%
+function right so those are our modeling
+ 
+
+ align:start position:0%
+function right so those are our modeling
+and this was basically a way to say well
+
+ align:start position:0%
+and this was basically a way to say well
+ 
+
+ align:start position:0%
+and this was basically a way to say well
+we're not going to allow for any
+
+ align:start position:0%
+we're not going to allow for any
+ 
+
+ align:start position:0%
+we're not going to allow for any
+distributions for the data that we have
+
+ align:start position:0%
+distributions for the data that we have
+ 
+
+ align:start position:0%
+distributions for the data that we have
+but maybe a small set of distribution
+
+ align:start position:0%
+but maybe a small set of distribution
+ 
+
+ align:start position:0%
+but maybe a small set of distribution
+that indexed by some small parameters
+
+ align:start position:0%
+that indexed by some small parameters
+ 
+
+ align:start position:0%
+that indexed by some small parameters
+for example or at least you know remove
+
+ align:start position:0%
+for example or at least you know remove
+ 
+
+ align:start position:0%
+for example or at least you know remove
+some of the possibilities otherwise
+
+ align:start position:0%
+some of the possibilities otherwise
+ 
+
+ align:start position:0%
+some of the possibilities otherwise
+there's nothing that could learn and and
+
+ align:start position:0%
+there's nothing that could learn and and
+ 
+
+ align:start position:0%
+there's nothing that could learn and and
+so for example this was associated to
+
+ align:start position:0%
+so for example this was associated to
+ 
+
+ align:start position:0%
+so for example this was associated to
+some parameter of interest state theta
+
+ align:start position:0%
+some parameter of interest state theta
+ 
+
+ align:start position:0%
+some parameter of interest state theta
+or beta in the regression model all
+
+ align:start position:0%
+or beta in the regression model all
+ 
+
+ align:start position:0%
+or beta in the regression model all
+right then we had this unknown problem
+
+ align:start position:0%
+right then we had this unknown problem
+ 
+
+ align:start position:0%
+right then we had this unknown problem
+and this unknown thing a known parameter
+
+ align:start position:0%
+and this unknown thing a known parameter
+ 
+
+ align:start position:0%
+and this unknown thing a known parameter
+in we wanted to find it we wanted to
+
+ align:start position:0%
+in we wanted to find it we wanted to
+ 
+
+ align:start position:0%
+in we wanted to find it we wanted to
+either estimate it or test it or maybe
+
+ align:start position:0%
+either estimate it or test it or maybe
+ 
+
+ align:start position:0%
+either estimate it or test it or maybe
+you find a confidence interval for this
+
+ align:start position:0%
+you find a confidence interval for this
+ 
+
+ align:start position:0%
+you find a confidence interval for this
+object all right so so far I should not
+
+ align:start position:0%
+object all right so so far I should not
+ 
+
+ align:start position:0%
+object all right so so far I should not
+have said anything that's gonna that's
+
+ align:start position:0%
+have said anything that's gonna that's
+ 
+
+ align:start position:0%
+have said anything that's gonna that's
+new but this last sentence is actually
+
+ align:start position:0%
+new but this last sentence is actually
+ 
+
+ align:start position:0%
+new but this last sentence is actually
+what's gonna be different from the the
+
+ align:start position:0%
+what's gonna be different from the the
+ 
+
+ align:start position:0%
+what's gonna be different from the the
+Bayesian part in particular this number
+
+ align:start position:0%
+Bayesian part in particular this number
+ 
+
+ align:start position:0%
+Bayesian part in particular this number
+fix things what it's gonna be changing
+
+ align:start position:0%
+fix things what it's gonna be changing
+ 
+
+ align:start position:0%
+fix things what it's gonna be changing
+alright so in the Bayesian approach we
+
+ align:start position:0%
+alright so in the Bayesian approach we
+ 
+
+ align:start position:0%
+alright so in the Bayesian approach we
+still assume that we observe some random
+
+ align:start position:0%
+still assume that we observe some random
+ 
+
+ align:start position:0%
+still assume that we observe some random
+data but the generating process is
+
+ align:start position:0%
+data but the generating process is
+ 
+
+ align:start position:0%
+data but the generating process is
+slightly different it's sort of a
+
+ align:start position:0%
+slightly different it's sort of a
+ 
+
+ align:start position:0%
+slightly different it's sort of a
+two-layer process and there's one
+
+ align:start position:0%
+two-layer process and there's one
+ 
+
+ align:start position:0%
+two-layer process and there's one
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+that generates the parameter and then
+
+ align:start position:0%
+that generates the parameter and then
+ 
+
+ align:start position:0%
+that generates the parameter and then
+one process that given this parameter
+
+ align:start position:0%
+one process that given this parameter
+ 
+
+ align:start position:0%
+one process that given this parameter
+generates data so what the first layer
+
+ align:start position:0%
+generates data so what the first layer
+ 
+
+ align:start position:0%
+generates data so what the first layer
+does right I mean nobody really believes
+
+ align:start position:0%
+does right I mean nobody really believes
+ 
+
+ align:start position:0%
+does right I mean nobody really believes
+that there's some random process that's
+
+ align:start position:0%
+that there's some random process that's
+ 
+
+ align:start position:0%
+that there's some random process that's
+happening about you know generating what
+
+ align:start position:0%
+happening about you know generating what
+ 
+
+ align:start position:0%
+happening about you know generating what
+is gonna be the true expected number of
+
+ align:start position:0%
+is gonna be the true expected number of
+ 
+
+ align:start position:0%
+is gonna be the true expected number of
+people who turn their head to the right
+
+ align:start position:0%
+people who turn their head to the right
+ 
+
+ align:start position:0%
+people who turn their head to the right
+when they kiss but this is actually
+
+ align:start position:0%
+when they kiss but this is actually
+ 
+
+ align:start position:0%
+when they kiss but this is actually
+gonna be something that brings us some
+
+ align:start position:0%
+gonna be something that brings us some
+ 
+
+ align:start position:0%
+gonna be something that brings us some
+you know easiness rest to incorporate
+
+ align:start position:0%
+you know easiness rest to incorporate
+ 
+
+ align:start position:0%
+you know easiness rest to incorporate
+what we call prior belief right so we'll
+
+ align:start position:0%
+what we call prior belief right so we'll
+ 
+
+ align:start position:0%
+what we call prior belief right so we'll
+see an example in a second but often you
+
+ align:start position:0%
+see an example in a second but often you
+ 
+
+ align:start position:0%
+see an example in a second but often you
+actually have prior belief of what this
+
+ align:start position:0%
+actually have prior belief of what this
+ 
+
+ align:start position:0%
+actually have prior belief of what this
+parameter should be right when we did
+
+ align:start position:0%
+parameter should be right when we did
+ 
+
+ align:start position:0%
+parameter should be right when we did
+say these squares we looked over all of
+
+ align:start position:0%
+say these squares we looked over all of
+ 
+
+ align:start position:0%
+say these squares we looked over all of
+the vectors in all of our to the P
+
+ align:start position:0%
+the vectors in all of our to the P
+ 
+
+ align:start position:0%
+the vectors in all of our to the P
+including the ones that have
+
+ align:start position:0%
+including the ones that have
+ 
+
+ align:start position:0%
+including the ones that have
+coefficients equal to you know fifty
+
+ align:start position:0%
+coefficients equal to you know fifty
+ 
+
+ align:start position:0%
+coefficients equal to you know fifty
+million and so those are things that
+
+ align:start position:0%
+million and so those are things that
+ 
+
+ align:start position:0%
+million and so those are things that
+maybe we might be able to rule out and
+
+ align:start position:0%
+maybe we might be able to rule out and
+ 
+
+ align:start position:0%
+maybe we might be able to rule out and
+maybe we might be able to rule out that
+
+ align:start position:0%
+maybe we might be able to rule out that
+ 
+
+ align:start position:0%
+maybe we might be able to rule out that
+a much smaller scale for example well I
+
+ align:start position:0%
+a much smaller scale for example well I
+ 
+
+ align:start position:0%
+a much smaller scale for example well I
+mean I don't know I'm not an expert on
+
+ align:start position:0%
+mean I don't know I'm not an expert on
+ 
+
+ align:start position:0%
+mean I don't know I'm not an expert on
+on you know turning your head to the
+
+ align:start position:0%
+on you know turning your head to the
+ 
+
+ align:start position:0%
+on you know turning your head to the
+right or to the left but you know maybe
+
+ align:start position:0%
+right or to the left but you know maybe
+ 
+
+ align:start position:0%
+right or to the left but you know maybe
+you can rule out the fact that you know
+
+ align:start position:0%
+you can rule out the fact that you know
+ 
+
+ align:start position:0%
+you can rule out the fact that you know
+almost everybody is turning their head
+
+ align:start position:0%
+almost everybody is turning their head
+ 
+
+ align:start position:0%
+almost everybody is turning their head
+in the same direction or almost
+
+ align:start position:0%
+in the same direction or almost
+ 
+
+ align:start position:0%
+in the same direction or almost
+everybody's turning their head to
+
+ align:start position:0%
+everybody's turning their head to
+ 
+
+ align:start position:0%
+everybody's turning their head to
+another direction so we want to we have
+
+ align:start position:0%
+another direction so we want to we have
+ 
+
+ align:start position:0%
+another direction so we want to we have
+this prior belief and this prior belief
+
+ align:start position:0%
+this prior belief and this prior belief
+ 
+
+ align:start position:0%
+this prior belief and this prior belief
+is going to play say hopefully less and
+
+ align:start position:0%
+is going to play say hopefully less and
+ 
+
+ align:start position:0%
+is going to play say hopefully less and
+less important role as we collect more
+
+ align:start position:0%
+less important role as we collect more
+ 
+
+ align:start position:0%
+less important role as we collect more
+and more data but if we have a smaller
+
+ align:start position:0%
+and more data but if we have a smaller
+ 
+
+ align:start position:0%
+and more data but if we have a smaller
+amount of data we might want to be able
+
+ align:start position:0%
+amount of data we might want to be able
+ 
+
+ align:start position:0%
+amount of data we might want to be able
+to use this information all right
+
+ align:start position:0%
+to use this information all right
+ 
+
+ align:start position:0%
+to use this information all right
+rather than just shooting in the dark
+
+ align:start position:0%
+rather than just shooting in the dark
+ 
+
+ align:start position:0%
+rather than just shooting in the dark
+and so the idea is to have this prior
+
+ align:start position:0%
+and so the idea is to have this prior
+ 
+
+ align:start position:0%
+and so the idea is to have this prior
+belief and then we want to update this
+
+ align:start position:0%
+belief and then we want to update this
+ 
+
+ align:start position:0%
+belief and then we want to update this
+prior belief into it what's called a
+
+ align:start position:0%
+prior belief into it what's called a
+ 
+
+ align:start position:0%
+prior belief into it what's called a
+posterior belief after we've seen some
+
+ align:start position:0%
+posterior belief after we've seen some
+ 
+
+ align:start position:0%
+posterior belief after we've seen some
+data right maybe I believe that you know
+
+ align:start position:0%
+data right maybe I believe that you know
+ 
+
+ align:start position:0%
+data right maybe I believe that you know
+there's something that should be in some
+
+ align:start position:0%
+there's something that should be in some
+ 
+
+ align:start position:0%
+there's something that should be in some
+range but maybe after I see data maybe
+
+ align:start position:0%
+range but maybe after I see data maybe
+ 
+
+ align:start position:0%
+range but maybe after I see data maybe
+it's comforting me in my belief so I'm
+
+ align:start position:0%
+it's comforting me in my belief so I'm
+ 
+
+ align:start position:0%
+it's comforting me in my belief so I'm
+actually having maybe a belief that's
+
+ align:start position:0%
+actually having maybe a belief that's
+ 
+
+ align:start position:0%
+actually having maybe a belief that's
+more so belief and compasses basically
+
+ align:start position:0%
+more so belief and compasses basically
+ 
+
+ align:start position:0%
+more so belief and compasses basically
+what you think and how strongly you
+
+ align:start position:0%
+what you think and how strongly you
+ 
+
+ align:start position:0%
+what you think and how strongly you
+think about it that's what I call belief
+
+ align:start position:0%
+think about it that's what I call belief
+ 
+
+ align:start position:0%
+think about it that's what I call belief
+right so for example if I have a belief
+
+ align:start position:0%
+right so for example if I have a belief
+ 
+
+ align:start position:0%
+right so for example if I have a belief
+about some parameter theta
+
+ align:start position:0%
+about some parameter theta
+ 
+
+ align:start position:0%
+about some parameter theta
+maybe my belief is telling me where
+
+ align:start position:0%
+maybe my belief is telling me where
+ 
+
+ align:start position:0%
+maybe my belief is telling me where
+theta should be and and and how strongly
+
+ align:start position:0%
+theta should be and and and how strongly
+ 
+
+ align:start position:0%
+theta should be and and and how strongly
+I believe in it in the sense that I have
+
+ align:start position:0%
+I believe in it in the sense that I have
+ 
+
+ align:start position:0%
+I believe in it in the sense that I have
+a very narrow region where theta could
+
+ align:start position:0%
+a very narrow region where theta could
+ 
+
+ align:start position:0%
+a very narrow region where theta could
+be all right and so the posterior belief
+
+ align:start position:0%
+be all right and so the posterior belief
+ 
+
+ align:start position:0%
+be all right and so the posterior belief
+says well you see some data and maybe
+
+ align:start position:0%
+says well you see some data and maybe
+ 
+
+ align:start position:0%
+says well you see some data and maybe
+you're more confident or less confident
+
+ align:start position:0%
+you're more confident or less confident
+ 
+
+ align:start position:0%
+you're more confident or less confident
+about what you've seen
+
+ align:start position:0%
+about what you've seen
+ 
+
+ align:start position:0%
+about what you've seen
+you've shifted your belief a little bit
+
+ align:start position:0%
+you've shifted your belief a little bit
+ 
+
+ align:start position:0%
+you've shifted your belief a little bit
+and so that's what we're gonna try to
+
+ align:start position:0%
+and so that's what we're gonna try to
+ 
+
+ align:start position:0%
+and so that's what we're gonna try to
+see and how to do this in a principled
+
+ align:start position:0%
+see and how to do this in a principled
+ 
+
+ align:start position:0%
+see and how to do this in a principled
+manner so of course to understand this
+
+ align:start position:0%
+manner so of course to understand this
+ 
+
+ align:start position:0%
+manner so of course to understand this
+better there's nothing better than an
+
+ align:start position:0%
+better there's nothing better than an
+ 
+
+ align:start position:0%
+better there's nothing better than an
+example so let's talk about and other
+
+ align:start position:0%
+example so let's talk about and other
+ 
+
+ align:start position:0%
+example so let's talk about and other
+stupid statistical question which is
+
+ align:start position:0%
+stupid statistical question which is
+ 
+
+ align:start position:0%
+stupid statistical question which is
+let's try to understand P of course I'm
+
+ align:start position:0%
+let's try to understand P of course I'm
+ 
+
+ align:start position:0%
+let's try to understand P of course I'm
+not going to talk about politics from
+
+ align:start position:0%
+not going to talk about politics from
+ 
+
+ align:start position:0%
+not going to talk about politics from
+now on so there let's talk about P the
+
+ align:start position:0%
+now on so there let's talk about P the
+ 
+
+ align:start position:0%
+now on so there let's talk about P the
+proportion of women in the population
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so what I could do is to
+
+ align:start position:0%
+okay and so what I could do is to
+ 
+
+ align:start position:0%
+okay and so what I could do is to
+collect some data x1 xn and assume that
+
+ align:start position:0%
+collect some data x1 xn and assume that
+ 
+
+ align:start position:0%
+collect some data x1 xn and assume that
+there Burnley with some parameter P
+
+ align:start position:0%
+there Burnley with some parameter P
+ 
+
+ align:start position:0%
+there Burnley with some parameter P
+unknown right so P is in 0 1 ok let's
+
+ align:start position:0%
+unknown right so P is in 0 1 ok let's
+ 
+
+ align:start position:0%
+unknown right so P is in 0 1 ok let's
+assume that those guys are ID so this is
+
+ align:start position:0%
+assume that those guys are ID so this is
+ 
+
+ align:start position:0%
+assume that those guys are ID so this is
+just an indicator for each of my like
+
+ align:start position:0%
+just an indicator for each of my like
+ 
+
+ align:start position:0%
+just an indicator for each of my like
+two data whether the person I randomly
+
+ align:start position:0%
+two data whether the person I randomly
+ 
+
+ align:start position:0%
+two data whether the person I randomly
+sample is a woman I get a wonder if it's
+
+ align:start position:0%
+sample is a woman I get a wonder if it's
+ 
+
+ align:start position:0%
+sample is a woman I get a wonder if it's
+a man I get a 0 okay and so now the
+
+ align:start position:0%
+a man I get a 0 okay and so now the
+ 
+
+ align:start position:0%
+a man I get a 0 okay and so now the
+question is i sample these people
+
+ align:start position:0%
+question is i sample these people
+ 
+
+ align:start position:0%
+question is i sample these people
+randomly I'd you know their their gender
+
+ align:start position:0%
+randomly I'd you know their their gender
+ 
+
+ align:start position:0%
+randomly I'd you know their their gender
+and the frequentist approach was just
+
+ align:start position:0%
+and the frequentist approach was just
+ 
+
+ align:start position:0%
+and the frequentist approach was just
+saying okay let's just estimate P hat
+
+ align:start position:0%
+saying okay let's just estimate P hat
+ 
+
+ align:start position:0%
+saying okay let's just estimate P hat
+being xn bar and then we could do some
+
+ align:start position:0%
+being xn bar and then we could do some
+ 
+
+ align:start position:0%
+being xn bar and then we could do some
+tests right so here there's a test I
+
+ align:start position:0%
+tests right so here there's a test I
+ 
+
+ align:start position:0%
+tests right so here there's a test I
+want to test maybe if P is equal to 0.5
+
+ align:start position:0%
+want to test maybe if P is equal to 0.5
+ 
+
+ align:start position:0%
+want to test maybe if P is equal to 0.5
+or not that sounds like a pretty
+
+ align:start position:0%
+or not that sounds like a pretty
+ 
+
+ align:start position:0%
+or not that sounds like a pretty
+reasonable thing to test and but you
+
+ align:start position:0%
+reasonable thing to test and but you
+ 
+
+ align:start position:0%
+reasonable thing to test and but you
+know we want to also maybe estimate P
+
+ align:start position:0%
+know we want to also maybe estimate P
+ 
+
+ align:start position:0%
+know we want to also maybe estimate P
+but here this is a case where we
+
+ align:start position:0%
+but here this is a case where we
+ 
+
+ align:start position:0%
+but here this is a case where we
+definitely have for our belief of what P
+
+ align:start position:0%
+definitely have for our belief of what P
+ 
+
+ align:start position:0%
+definitely have for our belief of what P
+should be right we are pretty confident
+
+ align:start position:0%
+should be right we are pretty confident
+ 
+
+ align:start position:0%
+should be right we are pretty confident
+that P is not gonna be 0.7 we actually
+
+ align:start position:0%
+that P is not gonna be 0.7 we actually
+ 
+
+ align:start position:0%
+that P is not gonna be 0.7 we actually
+believe that P should be extremely close
+
+ align:start position:0%
+believe that P should be extremely close
+ 
+
+ align:start position:0%
+believe that P should be extremely close
+to 1/2 okay but maybe not exactly maybe
+
+ align:start position:0%
+to 1/2 okay but maybe not exactly maybe
+ 
+
+ align:start position:0%
+to 1/2 okay but maybe not exactly maybe
+I don't know maybe this population is
+
+ align:start position:0%
+I don't know maybe this population is
+ 
+
+ align:start position:0%
+I don't know maybe this population is
+not the population in the world but
+
+ align:start position:0%
+not the population in the world but
+ 
+
+ align:start position:0%
+not the population in the world but
+maybe this is the population of say some
+
+ align:start position:0%
+maybe this is the population of say some
+ 
+
+ align:start position:0%
+maybe this is the population of say some
+college and we want to understand if
+
+ align:start position:0%
+college and we want to understand if
+ 
+
+ align:start position:0%
+college and we want to understand if
+this college has half women or not right
+
+ align:start position:0%
+this college has half women or not right
+ 
+
+ align:start position:0%
+this college has half women or not right
+so maybe we know it's gonna be close to
+
+ align:start position:0%
+so maybe we know it's gonna be close to
+ 
+
+ align:start position:0%
+so maybe we know it's gonna be close to
+1/2 but maybe we're not quite sure and
+
+ align:start position:0%
+1/2 but maybe we're not quite sure and
+ 
+
+ align:start position:0%
+1/2 but maybe we're not quite sure and
+so we're gonna want to integrate that
+
+ align:start position:0%
+so we're gonna want to integrate that
+ 
+
+ align:start position:0%
+so we're gonna want to integrate that
+knowledge all right so I could integrate
+
+ align:start position:0%
+knowledge all right so I could integrate
+ 
+
+ align:start position:0%
+knowledge all right so I could integrate
+it in a blunt manner by saying you know
+
+ align:start position:0%
+it in a blunt manner by saying you know
+ 
+
+ align:start position:0%
+it in a blunt manner by saying you know
+discard the data and say that P
+
+ align:start position:0%
+discard the data and say that P
+ 
+
+ align:start position:0%
+discard the data and say that P
+is equal to 1/2 but maybe that's just a
+
+ align:start position:0%
+is equal to 1/2 but maybe that's just a
+ 
+
+ align:start position:0%
+is equal to 1/2 but maybe that's just a
+little too much so how do I do this
+
+ align:start position:0%
+little too much so how do I do this
+ 
+
+ align:start position:0%
+little too much so how do I do this
+trade-off between you know adding the
+
+ align:start position:0%
+trade-off between you know adding the
+ 
+
+ align:start position:0%
+trade-off between you know adding the
+data and combining it with this prior
+
+ align:start position:0%
+data and combining it with this prior
+ 
+
+ align:start position:0%
+data and combining it with this prior
+knowledge in many ways in many instances
+
+ align:start position:0%
+knowledge in many ways in many instances
+ 
+
+ align:start position:0%
+knowledge in many ways in many instances
+essentially what's going to happen is
+
+ align:start position:0%
+essentially what's going to happen is
+ 
+
+ align:start position:0%
+essentially what's going to happen is
+this this 1/2 is going to act like one
+
+ align:start position:0%
+this this 1/2 is going to act like one
+ 
+
+ align:start position:0%
+this this 1/2 is going to act like one
+new observation essentially so if you
+
+ align:start position:0%
+new observation essentially so if you
+ 
+
+ align:start position:0%
+new observation essentially so if you
+have you know five observations this is
+
+ align:start position:0%
+have you know five observations this is
+ 
+
+ align:start position:0%
+have you know five observations this is
+just the sixth observation which will
+
+ align:start position:0%
+just the sixth observation which will
+ 
+
+ align:start position:0%
+just the sixth observation which will
+play a role if you have a million
+
+ align:start position:0%
+play a role if you have a million
+ 
+
+ align:start position:0%
+play a role if you have a million
+observations you're gonna have a million
+
+ align:start position:0%
+observations you're gonna have a million
+ 
+
+ align:start position:0%
+observations you're gonna have a million
+and one and it's not gonna play so much
+
+ align:start position:0%
+and one and it's not gonna play so much
+ 
+
+ align:start position:0%
+and one and it's not gonna play so much
+of a role that's basically how it goes
+
+ align:start position:0%
+of a role that's basically how it goes
+ 
+
+ align:start position:0%
+of a role that's basically how it goes
+that's basically how it goes but
+
+ align:start position:0%
+that's basically how it goes but
+ 
+
+ align:start position:0%
+that's basically how it goes but
+definitely not always alright because
+
+ align:start position:0%
+definitely not always alright because
+ 
+
+ align:start position:0%
+definitely not always alright because
+we'll see that if I take my prior to be
+
+ align:start position:0%
+we'll see that if I take my prior to be
+ 
+
+ align:start position:0%
+we'll see that if I take my prior to be
+a point myself 1/2 here it's basically
+
+ align:start position:0%
+a point myself 1/2 here it's basically
+ 
+
+ align:start position:0%
+a point myself 1/2 here it's basically
+as if I was recording my data so
+
+ align:start position:0%
+as if I was recording my data so
+ 
+
+ align:start position:0%
+as if I was recording my data so
+essentially there's also your ability to
+
+ align:start position:0%
+essentially there's also your ability to
+ 
+
+ align:start position:0%
+essentially there's also your ability to
+encompass how strongly you believe in
+
+ align:start position:0%
+encompass how strongly you believe in
+ 
+
+ align:start position:0%
+encompass how strongly you believe in
+this prior and if you believe infinitely
+
+ align:start position:0%
+this prior and if you believe infinitely
+ 
+
+ align:start position:0%
+this prior and if you believe infinitely
+more in the prior than you believe in
+
+ align:start position:0%
+more in the prior than you believe in
+ 
+
+ align:start position:0%
+more in the prior than you believe in
+the data you collected then of course
+
+ align:start position:0%
+the data you collected then of course
+ 
+
+ align:start position:0%
+the data you collected then of course
+it's not gonna act like one more
+
+ align:start position:0%
+it's not gonna act like one more
+ 
+
+ align:start position:0%
+it's not gonna act like one more
+observation all right so the Bayesian
+
+ align:start position:0%
+observation all right so the Bayesian
+ 
+
+ align:start position:0%
+observation all right so the Bayesian
+approach is a tool to one include
+
+ align:start position:0%
+approach is a tool to one include
+ 
+
+ align:start position:0%
+approach is a tool to one include
+mathematically or prior and our prior
+
+ align:start position:0%
+mathematically or prior and our prior
+ 
+
+ align:start position:0%
+mathematically or prior and our prior
+belief into statistical procedures right
+
+ align:start position:0%
+belief into statistical procedures right
+ 
+
+ align:start position:0%
+belief into statistical procedures right
+so maybe I have this prior knowledge but
+
+ align:start position:0%
+so maybe I have this prior knowledge but
+ 
+
+ align:start position:0%
+so maybe I have this prior knowledge but
+if I'm a medical doctor it's not clear
+
+ align:start position:0%
+if I'm a medical doctor it's not clear
+ 
+
+ align:start position:0%
+if I'm a medical doctor it's not clear
+to me how I'm gonna turn this into some
+
+ align:start position:0%
+to me how I'm gonna turn this into some
+ 
+
+ align:start position:0%
+to me how I'm gonna turn this into some
+principled way of building estimators
+
+ align:start position:0%
+principled way of building estimators
+ 
+
+ align:start position:0%
+principled way of building estimators
+and of course the second goal is going
+
+ align:start position:0%
+and of course the second goal is going
+ 
+
+ align:start position:0%
+and of course the second goal is going
+to be to a big this prior belief into a
+
+ align:start position:0%
+to be to a big this prior belief into a
+ 
+
+ align:start position:0%
+to be to a big this prior belief into a
+posterior belief by using the data
+
+ align:start position:0%
+posterior belief by using the data
+ 
+
+ align:start position:0%
+posterior belief by using the data
+alright so how do I do this and at some
+
+ align:start position:0%
+alright so how do I do this and at some
+ 
+
+ align:start position:0%
+alright so how do I do this and at some
+point I sort of suggested that there's
+
+ align:start position:0%
+point I sort of suggested that there's
+ 
+
+ align:start position:0%
+point I sort of suggested that there's
+two layers one is where you draw the
+
+ align:start position:0%
+two layers one is where you draw the
+ 
+
+ align:start position:0%
+two layers one is where you draw the
+parameter at random and two once you
+
+ align:start position:0%
+parameter at random and two once you
+ 
+
+ align:start position:0%
+parameter at random and two once you
+have the parameter conditioned on this
+
+ align:start position:0%
+have the parameter conditioned on this
+ 
+
+ align:start position:0%
+have the parameter conditioned on this
+parameter you draw your data nobody
+
+ align:start position:0%
+parameter you draw your data nobody
+ 
+
+ align:start position:0%
+parameter you draw your data nobody
+believes this actually is happening that
+
+ align:start position:0%
+believes this actually is happening that
+ 
+
+ align:start position:0%
+believes this actually is happening that
+nature is just rolling dice for us and
+
+ align:start position:0%
+nature is just rolling dice for us and
+ 
+
+ align:start position:0%
+nature is just rolling dice for us and
+choosing parameters that random but
+
+ align:start position:0%
+choosing parameters that random but
+ 
+
+ align:start position:0%
+choosing parameters that random but
+what's happening is that this idea that
+
+ align:start position:0%
+what's happening is that this idea that
+ 
+
+ align:start position:0%
+what's happening is that this idea that
+the parameter comes from some random
+
+ align:start position:0%
+the parameter comes from some random
+ 
+
+ align:start position:0%
+the parameter comes from some random
+distribution actually captures very well
+
+ align:start position:0%
+distribution actually captures very well
+ 
+
+ align:start position:0%
+distribution actually captures very well
+this idea that how you would encompass
+
+ align:start position:0%
+this idea that how you would encompass
+ 
+
+ align:start position:0%
+this idea that how you would encompass
+your prior right how would you say my
+
+ align:start position:0%
+your prior right how would you say my
+ 
+
+ align:start position:0%
+your prior right how would you say my
+belief is as follows well here's an
+
+ align:start position:0%
+belief is as follows well here's an
+ 
+
+ align:start position:0%
+belief is as follows well here's an
+example about P I'm 90% sure that P is
+
+ align:start position:0%
+example about P I'm 90% sure that P is
+ 
+
+ align:start position:0%
+example about P I'm 90% sure that P is
+between point four and point six
+
+ align:start position:0%
+between point four and point six
+ 
+
+ align:start position:0%
+between point four and point six
+and I'm 95% sure that piece between
+
+ align:start position:0%
+and I'm 95% sure that piece between
+ 
+
+ align:start position:0%
+and I'm 95% sure that piece between
+point three and point eight okay so
+
+ align:start position:0%
+point three and point eight okay so
+ 
+
+ align:start position:0%
+point three and point eight okay so
+essentially I have this possible value
+
+ align:start position:0%
+essentially I have this possible value
+ 
+
+ align:start position:0%
+essentially I have this possible value
+of P and what I know is that there's 95
+
+ align:start position:0%
+of P and what I know is that there's 95
+ 
+
+ align:start position:0%
+of P and what I know is that there's 95
+there's 90 percent here between what did
+
+ align:start position:0%
+there's 90 percent here between what did
+ 
+
+ align:start position:0%
+there's 90 percent here between what did
+I say points
+
+ align:start position:0%
+I say points
+ 
+
+ align:start position:0%
+I say points
+four in point six and then I have point
+
+ align:start position:0%
+four in point six and then I have point
+ 
+
+ align:start position:0%
+four in point six and then I have point
+three and point eight and I know that
+
+ align:start position:0%
+three and point eight and I know that
+ 
+
+ align:start position:0%
+three and point eight and I know that
+I'm 95% sure that I mean here and this
+
+ align:start position:0%
+I'm 95% sure that I mean here and this
+ 
+
+ align:start position:0%
+I'm 95% sure that I mean here and this
+if you remember this sort of looks like
+
+ align:start position:0%
+if you remember this sort of looks like
+ 
+
+ align:start position:0%
+if you remember this sort of looks like
+the kind of pictures that I made when I
+
+ align:start position:0%
+the kind of pictures that I made when I
+ 
+
+ align:start position:0%
+the kind of pictures that I made when I
+had some Gaussian right for example and
+
+ align:start position:0%
+had some Gaussian right for example and
+ 
+
+ align:start position:0%
+had some Gaussian right for example and
+I said oh here we have ninety percent of
+
+ align:start position:0%
+I said oh here we have ninety percent of
+ 
+
+ align:start position:0%
+I said oh here we have ninety percent of
+the observations and here we have 95
+
+ align:start position:0%
+the observations and here we have 95
+ 
+
+ align:start position:0%
+the observations and here we have 95
+percent of the observations so in a way
+
+ align:start position:0%
+percent of the observations so in a way
+ 
+
+ align:start position:0%
+percent of the observations so in a way
+if I were able to tell you all those
+
+ align:start position:0%
+if I were able to tell you all those
+ 
+
+ align:start position:0%
+if I were able to tell you all those
+ranges for all possible values then I
+
+ align:start position:0%
+ranges for all possible values then I
+ 
+
+ align:start position:0%
+ranges for all possible values then I
+would essentially describe a probability
+
+ align:start position:0%
+would essentially describe a probability
+ 
+
+ align:start position:0%
+would essentially describe a probability
+distribution for P and what I'm
+
+ align:start position:0%
+distribution for P and what I'm
+ 
+
+ align:start position:0%
+distribution for P and what I'm
+essentially saying is that P is gonna
+
+ align:start position:0%
+essentially saying is that P is gonna
+ 
+
+ align:start position:0%
+essentially saying is that P is gonna
+have this kind of shape so of course if
+
+ align:start position:0%
+have this kind of shape so of course if
+ 
+
+ align:start position:0%
+have this kind of shape so of course if
+I tell you only to twice this
+
+ align:start position:0%
+I tell you only to twice this
+ 
+
+ align:start position:0%
+I tell you only to twice this
+information that there's ninety percent
+
+ align:start position:0%
+information that there's ninety percent
+ 
+
+ align:start position:0%
+information that there's ninety percent
+I'm here and I'm here between here and
+
+ align:start position:0%
+I'm here and I'm here between here and
+ 
+
+ align:start position:0%
+I'm here and I'm here between here and
+here and 95 percent I'm between here and
+
+ align:start position:0%
+here and 95 percent I'm between here and
+ 
+
+ align:start position:0%
+here and 95 percent I'm between here and
+here then there's many ways I can
+
+ align:start position:0%
+here then there's many ways I can
+ 
+
+ align:start position:0%
+here then there's many ways I can
+accomplish that right I could have
+
+ align:start position:0%
+accomplish that right I could have
+ 
+
+ align:start position:0%
+accomplish that right I could have
+something that looks like this maybe
+
+ align:start position:0%
+something that looks like this maybe
+ 
+
+ align:start position:0%
+something that looks like this maybe
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+I could be really I mean it could be
+
+ align:start position:0%
+I could be really I mean it could be
+ 
+
+ align:start position:0%
+I could be really I mean it could be
+like this I mean there's many ways that
+
+ align:start position:0%
+like this I mean there's many ways that
+ 
+
+ align:start position:0%
+like this I mean there's many ways that
+can have this some of them are
+
+ align:start position:0%
+can have this some of them are
+ 
+
+ align:start position:0%
+can have this some of them are
+definitely gonna be mathematically more
+
+ align:start position:0%
+definitely gonna be mathematically more
+ 
+
+ align:start position:0%
+definitely gonna be mathematically more
+convenient than others and hopefully
+
+ align:start position:0%
+convenient than others and hopefully
+ 
+
+ align:start position:0%
+convenient than others and hopefully
+we're gonna have things that I can
+
+ align:start position:0%
+we're gonna have things that I can
+ 
+
+ align:start position:0%
+we're gonna have things that I can
+parametrize Farewell rather than because
+
+ align:start position:0%
+parametrize Farewell rather than because
+ 
+
+ align:start position:0%
+parametrize Farewell rather than because
+if I tell you this is this guy then
+
+ align:start position:0%
+if I tell you this is this guy then
+ 
+
+ align:start position:0%
+if I tell you this is this guy then
+there's basically 1 2 3 4 5 6 7
+
+ align:start position:0%
+there's basically 1 2 3 4 5 6 7
+ 
+
+ align:start position:0%
+there's basically 1 2 3 4 5 6 7
+parameters right so I probably don't
+
+ align:start position:0%
+parameters right so I probably don't
+ 
+
+ align:start position:0%
+parameters right so I probably don't
+want something that has 7 parameters but
+
+ align:start position:0%
+want something that has 7 parameters but
+ 
+
+ align:start position:0%
+want something that has 7 parameters but
+maybe I can say oh it's a Gaussian and I
+
+ align:start position:0%
+maybe I can say oh it's a Gaussian and I
+ 
+
+ align:start position:0%
+maybe I can say oh it's a Gaussian and I
+all I have to do is to tell you where
+
+ align:start position:0%
+all I have to do is to tell you where
+ 
+
+ align:start position:0%
+all I have to do is to tell you where
+it's centered and what the
+
+ align:start position:0%
+it's centered and what the
+ 
+
+ align:start position:0%
+it's centered and what the
+standardization is ok so the idea of
+
+ align:start position:0%
+standardization is ok so the idea of
+ 
+
+ align:start position:0%
+standardization is ok so the idea of
+using this two layer thing where we
+
+ align:start position:0%
+using this two layer thing where we
+ 
+
+ align:start position:0%
+using this two layer thing where we
+think of the parameter P as being drawn
+
+ align:start position:0%
+think of the parameter P as being drawn
+ 
+
+ align:start position:0%
+think of the parameter P as being drawn
+from some distribution is really just a
+
+ align:start position:0%
+from some distribution is really just a
+ 
+
+ align:start position:0%
+from some distribution is really just a
+way for us to capture this information
+
+ align:start position:0%
+way for us to capture this information
+ 
+
+ align:start position:0%
+way for us to capture this information
+our prior belief being well you know
+
+ align:start position:0%
+our prior belief being well you know
+ 
+
+ align:start position:0%
+our prior belief being well you know
+there's this percentage of change
+
+ align:start position:0%
+there's this percentage of change
+ 
+
+ align:start position:0%
+there's this percentage of change
+that is there but the person has a
+
+ align:start position:0%
+that is there but the person has a
+ 
+
+ align:start position:0%
+that is there but the person has a
+chance I'm not I'm deliberately not
+
+ align:start position:0%
+chance I'm not I'm deliberately not
+ 
+
+ align:start position:0%
+chance I'm not I'm deliberately not
+using probability here it's really right
+
+ align:start position:0%
+using probability here it's really right
+ 
+
+ align:start position:0%
+using probability here it's really right
+so it's really a way to get close to
+
+ align:start position:0%
+so it's really a way to get close to
+ 
+
+ align:start position:0%
+so it's really a way to get close to
+this all right so that's what I say the
+
+ align:start position:0%
+this all right so that's what I say the
+ 
+
+ align:start position:0%
+this all right so that's what I say the
+true parameter is not random but the
+
+ align:start position:0%
+true parameter is not random but the
+ 
+
+ align:start position:0%
+true parameter is not random but the
+Bayesian approach does as if it was
+
+ align:start position:0%
+Bayesian approach does as if it was
+ 
+
+ align:start position:0%
+Bayesian approach does as if it was
+random and then just spits out a
+
+ align:start position:0%
+random and then just spits out a
+ 
+
+ align:start position:0%
+random and then just spits out a
+procedure out of this you know thought
+
+ align:start position:0%
+procedure out of this you know thought
+ 
+
+ align:start position:0%
+procedure out of this you know thought
+process okay this thought experiment so
+
+ align:start position:0%
+process okay this thought experiment so
+ 
+
+ align:start position:0%
+process okay this thought experiment so
+when you practice Bayesian statistics a
+
+ align:start position:0%
+when you practice Bayesian statistics a
+ 
+
+ align:start position:0%
+when you practice Bayesian statistics a
+lot
+
+ align:start position:0%
+lot
+ 
+
+ align:start position:0%
+lot
+you start getting automatisms right so
+
+ align:start position:0%
+you start getting automatisms right so
+ 
+
+ align:start position:0%
+you start getting automatisms right so
+you get like you start getting some
+
+ align:start position:0%
+you get like you start getting some
+ 
+
+ align:start position:0%
+you get like you start getting some
+things that you do without really
+
+ align:start position:0%
+things that you do without really
+ 
+
+ align:start position:0%
+things that you do without really
+thinking about it just like when you're
+
+ align:start position:0%
+thinking about it just like when you're
+ 
+
+ align:start position:0%
+thinking about it just like when you're
+a statistician the first thing you do is
+
+ align:start position:0%
+a statistician the first thing you do is
+ 
+
+ align:start position:0%
+a statistician the first thing you do is
+you know can I think of this data as
+
+ align:start position:0%
+you know can I think of this data as
+ 
+
+ align:start position:0%
+you know can I think of this data as
+being Gaussian for example when you're
+
+ align:start position:0%
+being Gaussian for example when you're
+ 
+
+ align:start position:0%
+being Gaussian for example when you're
+Bayesian you're thinking about okay I
+
+ align:start position:0%
+Bayesian you're thinking about okay I
+ 
+
+ align:start position:0%
+Bayesian you're thinking about okay I
+have a set of parameters right so here I
+
+ align:start position:0%
+have a set of parameters right so here I
+ 
+
+ align:start position:0%
+have a set of parameters right so here I
+can describe my parameter as being theta
+
+ align:start position:0%
+can describe my parameter as being theta
+ 
+
+ align:start position:0%
+can describe my parameter as being theta
+in general in some big space parameters
+
+ align:start position:0%
+in general in some big space parameters
+ 
+
+ align:start position:0%
+in general in some big space parameters
+theta but do you know what it's what
+
+ align:start position:0%
+theta but do you know what it's what
+ 
+
+ align:start position:0%
+theta but do you know what it's what
+spaces did we encounter well we
+
+ align:start position:0%
+spaces did we encounter well we
+ 
+
+ align:start position:0%
+spaces did we encounter well we
+encountered the real line we encountered
+
+ align:start position:0%
+encountered the real line we encountered
+ 
+
+ align:start position:0%
+encountered the real line we encountered
+the interval 0 1 for Bernoulli's and we
+
+ align:start position:0%
+the interval 0 1 for Bernoulli's and we
+ 
+
+ align:start position:0%
+the interval 0 1 for Bernoulli's and we
+encountered maybe some the positive real
+
+ align:start position:0%
+encountered maybe some the positive real
+ 
+
+ align:start position:0%
+encountered maybe some the positive real
+line for exponential distributions etc
+
+ align:start position:0%
+line for exponential distributions etc
+ 
+
+ align:start position:0%
+line for exponential distributions etc
+and so what I'm gonna need to do if I
+
+ align:start position:0%
+and so what I'm gonna need to do if I
+ 
+
+ align:start position:0%
+and so what I'm gonna need to do if I
+want to model some if I want to put some
+
+ align:start position:0%
+want to model some if I want to put some
+ 
+
+ align:start position:0%
+want to model some if I want to put some
+prior on those spaces I'm gonna have to
+
+ align:start position:0%
+prior on those spaces I'm gonna have to
+ 
+
+ align:start position:0%
+prior on those spaces I'm gonna have to
+have a usual set of tools for this guy
+
+ align:start position:0%
+have a usual set of tools for this guy
+ 
+
+ align:start position:0%
+have a usual set of tools for this guy
+usual set of tools for this guy usual
+
+ align:start position:0%
+usual set of tools for this guy usual
+ 
+
+ align:start position:0%
+usual set of tools for this guy usual
+set of two for this guy's and by usual
+
+ align:start position:0%
+set of two for this guy's and by usual
+ 
+
+ align:start position:0%
+set of two for this guy's and by usual
+set of tools I mean I'm gonna have to
+
+ align:start position:0%
+set of tools I mean I'm gonna have to
+ 
+
+ align:start position:0%
+set of tools I mean I'm gonna have to
+have a family of distributions that
+
+ align:start position:0%
+have a family of distributions that
+ 
+
+ align:start position:0%
+have a family of distributions that
+support it on this so in particular this
+
+ align:start position:0%
+support it on this so in particular this
+ 
+
+ align:start position:0%
+support it on this so in particular this
+is the speech in which my parameter that
+
+ align:start position:0%
+is the speech in which my parameter that
+ 
+
+ align:start position:0%
+is the speech in which my parameter that
+I usually denote by P for Bernoulli lips
+
+ align:start position:0%
+I usually denote by P for Bernoulli lips
+ 
+
+ align:start position:0%
+I usually denote by P for Bernoulli lips
+and so what I need is to find a
+
+ align:start position:0%
+and so what I need is to find a
+ 
+
+ align:start position:0%
+and so what I need is to find a
+distribution on the interval 0 1 right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just like this guy the problem with the
+
+ align:start position:0%
+just like this guy the problem with the
+ 
+
+ align:start position:0%
+just like this guy the problem with the
+Gaussian is that it's not on the
+
+ align:start position:0%
+Gaussian is that it's not on the
+ 
+
+ align:start position:0%
+Gaussian is that it's not on the
+interval 0 1 right it's gonna spill out
+
+ align:start position:0%
+interval 0 1 right it's gonna spill out
+ 
+
+ align:start position:0%
+interval 0 1 right it's gonna spill out
+in the end and it's not gonna be
+
+ align:start position:0%
+in the end and it's not gonna be
+ 
+
+ align:start position:0%
+in the end and it's not gonna be
+something that works for me and so the
+
+ align:start position:0%
+something that works for me and so the
+ 
+
+ align:start position:0%
+something that works for me and so the
+question is you know I need to think
+
+ align:start position:0%
+question is you know I need to think
+ 
+
+ align:start position:0%
+question is you know I need to think
+about distributions that are probably
+
+ align:start position:0%
+about distributions that are probably
+ 
+
+ align:start position:0%
+about distributions that are probably
+continuous why would I restrict myself
+
+ align:start position:0%
+continuous why would I restrict myself
+ 
+
+ align:start position:0%
+continuous why would I restrict myself
+to discrete distributions that are
+
+ align:start position:0%
+to discrete distributions that are
+ 
+
+ align:start position:0%
+to discrete distributions that are
+actually convenient and for Burnley one
+
+ align:start position:0%
+actually convenient and for Burnley one
+ 
+
+ align:start position:0%
+actually convenient and for Burnley one
+that's actually basically the
+
+ align:start position:0%
+that's actually basically the
+ 
+
+ align:start position:0%
+that's actually basically the
+main tool that everybody's using is the
+
+ align:start position:0%
+main tool that everybody's using is the
+ 
+
+ align:start position:0%
+main tool that everybody's using is the
+so called beta distribution alright so
+
+ align:start position:0%
+so called beta distribution alright so
+ 
+
+ align:start position:0%
+so called beta distribution alright so
+the beta distribution has two parameters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so X follows a beta with parameters say
+
+ align:start position:0%
+so X follows a beta with parameters say
+ 
+
+ align:start position:0%
+so X follows a beta with parameters say
+a and B if it has a density f of X is
+
+ align:start position:0%
+a and B if it has a density f of X is
+ 
+
+ align:start position:0%
+a and B if it has a density f of X is
+equal to X to the a minus 1 1 minus X to
+
+ align:start position:0%
+equal to X to the a minus 1 1 minus X to
+ 
+
+ align:start position:0%
+equal to X to the a minus 1 1 minus X to
+the B minus 1 if X is in the interval 0
+
+ align:start position:0%
+the B minus 1 if X is in the interval 0
+ 
+
+ align:start position:0%
+the B minus 1 if X is in the interval 0
+1 and 0 for all other X's okay so why is
+
+ align:start position:0%
+1 and 0 for all other X's okay so why is
+ 
+
+ align:start position:0%
+1 and 0 for all other X's okay so why is
+that a good thing well it's a it's a
+
+ align:start position:0%
+that a good thing well it's a it's a
+ 
+
+ align:start position:0%
+that a good thing well it's a it's a
+density that's on the interval 0 1 for
+
+ align:start position:0%
+density that's on the interval 0 1 for
+ 
+
+ align:start position:0%
+density that's on the interval 0 1 for
+sure but now I have these two parameters
+
+ align:start position:0%
+sure but now I have these two parameters
+ 
+
+ align:start position:0%
+sure but now I have these two parameters
+and the set of shapes that I can get by
+
+ align:start position:0%
+and the set of shapes that I can get by
+ 
+
+ align:start position:0%
+and the set of shapes that I can get by
+tweaking those two parameters is
+
+ align:start position:0%
+tweaking those two parameters is
+ 
+
+ align:start position:0%
+tweaking those two parameters is
+incredible okay I mean it's not gonna be
+
+ align:start position:0%
+incredible okay I mean it's not gonna be
+ 
+
+ align:start position:0%
+incredible okay I mean it's not gonna be
+it's gonna be a unimodal distribution
+
+ align:start position:0%
+it's gonna be a unimodal distribution
+ 
+
+ align:start position:0%
+it's gonna be a unimodal distribution
+it's still fairly nice right it's not
+
+ align:start position:0%
+it's still fairly nice right it's not
+ 
+
+ align:start position:0%
+it's still fairly nice right it's not
+gonna be something that goes like this
+
+ align:start position:0%
+gonna be something that goes like this
+ 
+
+ align:start position:0%
+gonna be something that goes like this
+and this because you know if you think
+
+ align:start position:0%
+and this because you know if you think
+ 
+
+ align:start position:0%
+and this because you know if you think
+about this what would it mean if your
+
+ align:start position:0%
+about this what would it mean if your
+ 
+
+ align:start position:0%
+about this what would it mean if your
+prior distribution on the interval 0 1
+
+ align:start position:0%
+prior distribution on the interval 0 1
+ 
+
+ align:start position:0%
+prior distribution on the interval 0 1
+had this shape it would mean that maybe
+
+ align:start position:0%
+had this shape it would mean that maybe
+ 
+
+ align:start position:0%
+had this shape it would mean that maybe
+you think that P is here or maybe you
+
+ align:start position:0%
+you think that P is here or maybe you
+ 
+
+ align:start position:0%
+you think that P is here or maybe you
+think that P is here or maybe you think
+
+ align:start position:0%
+think that P is here or maybe you think
+ 
+
+ align:start position:0%
+think that P is here or maybe you think
+that P is here which essentially mean
+
+ align:start position:0%
+that P is here which essentially mean
+ 
+
+ align:start position:0%
+that P is here which essentially mean
+that you think that P can become can
+
+ align:start position:0%
+that you think that P can become can
+ 
+
+ align:start position:0%
+that you think that P can become can
+come maybe from three different
+
+ align:start position:0%
+come maybe from three different
+ 
+
+ align:start position:0%
+come maybe from three different
+phenomena and there's other models that
+
+ align:start position:0%
+phenomena and there's other models that
+ 
+
+ align:start position:0%
+phenomena and there's other models that
+are called mixtures for that that
+
+ align:start position:0%
+are called mixtures for that that
+ 
+
+ align:start position:0%
+are called mixtures for that that
+directly account for the fact that maybe
+
+ align:start position:0%
+directly account for the fact that maybe
+ 
+
+ align:start position:0%
+directly account for the fact that maybe
+there are several phenomena that are you
+
+ align:start position:0%
+there are several phenomena that are you
+ 
+
+ align:start position:0%
+there are several phenomena that are you
+know aggregated in your data set but if
+
+ align:start position:0%
+know aggregated in your data set but if
+ 
+
+ align:start position:0%
+know aggregated in your data set but if
+you think that your data set is sort of
+
+ align:start position:0%
+you think that your data set is sort of
+ 
+
+ align:start position:0%
+you think that your data set is sort of
+pure and that everything comes from the
+
+ align:start position:0%
+pure and that everything comes from the
+ 
+
+ align:start position:0%
+pure and that everything comes from the
+same phenomenon you want something that
+
+ align:start position:0%
+same phenomenon you want something that
+ 
+
+ align:start position:0%
+same phenomenon you want something that
+looks like maybe like this or maybe
+
+ align:start position:0%
+looks like maybe like this or maybe
+ 
+
+ align:start position:0%
+looks like maybe like this or maybe
+looks like this or maybe is sort of
+
+ align:start position:0%
+looks like this or maybe is sort of
+ 
+
+ align:start position:0%
+looks like this or maybe is sort of
+symmetric you want to get all this stuff
+
+ align:start position:0%
+symmetric you want to get all this stuff
+ 
+
+ align:start position:0%
+symmetric you want to get all this stuff
+right maybe you want something that says
+
+ align:start position:0%
+right maybe you want something that says
+ 
+
+ align:start position:0%
+right maybe you want something that says
+well you know if I'm talking about P
+
+ align:start position:0%
+well you know if I'm talking about P
+ 
+
+ align:start position:0%
+well you know if I'm talking about P
+being the probability of the proportion
+
+ align:start position:0%
+being the probability of the proportion
+ 
+
+ align:start position:0%
+being the probability of the proportion
+of women in the whole world you want
+
+ align:start position:0%
+of women in the whole world you want
+ 
+
+ align:start position:0%
+of women in the whole world you want
+something that's probably really spiked
+
+ align:start position:0%
+something that's probably really spiked
+ 
+
+ align:start position:0%
+something that's probably really spiked
+around 1/2 right
+
+ align:start position:0%
+around 1/2 right
+ 
+
+ align:start position:0%
+around 1/2 right
+most the point mats because you know I
+
+ align:start position:0%
+most the point mats because you know I
+ 
+
+ align:start position:0%
+most the point mats because you know I
+mean okay let's agree that 0.45 is the
+
+ align:start position:0%
+mean okay let's agree that 0.45 is the
+ 
+
+ align:start position:0%
+mean okay let's agree that 0.45 is the
+actual number so you know you want
+
+ align:start position:0%
+actual number so you know you want
+ 
+
+ align:start position:0%
+actual number so you know you want
+something maybe that says okay maybe I'm
+
+ align:start position:0%
+something maybe that says okay maybe I'm
+ 
+
+ align:start position:0%
+something maybe that says okay maybe I'm
+wrong
+
+ align:start position:0%
+wrong
+ 
+
+ align:start position:0%
+wrong
+but I'm sure I'm not gonna be really
+
+ align:start position:0%
+but I'm sure I'm not gonna be really
+ 
+
+ align:start position:0%
+but I'm sure I'm not gonna be really
+that way off and so you want something
+
+ align:start position:0%
+that way off and so you want something
+ 
+
+ align:start position:0%
+that way off and so you want something
+that's really pointy but if it's you
+
+ align:start position:0%
+that's really pointy but if it's you
+ 
+
+ align:start position:0%
+that's really pointy but if it's you
+know something you've never checked
+
+ align:start position:0%
+know something you've never checked
+ 
+
+ align:start position:0%
+know something you've never checked
+right and again I cannot make references
+
+ align:start position:0%
+right and again I cannot make references
+ 
+
+ align:start position:0%
+right and again I cannot make references
+at this point but you know something
+
+ align:start position:0%
+at this point but you know something
+ 
+
+ align:start position:0%
+at this point but you know something
+where you might have some uncertainty
+
+ align:start position:0%
+where you might have some uncertainty
+ 
+
+ align:start position:0%
+where you might have some uncertainty
+then that should be around 1/2 maybe you
+
+ align:start position:0%
+then that should be around 1/2 maybe you
+ 
+
+ align:start position:0%
+then that should be around 1/2 maybe you
+want something that's like a little more
+
+ align:start position:0%
+want something that's like a little more
+ 
+
+ align:start position:0%
+want something that's like a little more
+allows you to say well I think there's
+
+ align:start position:0%
+allows you to say well I think there's
+ 
+
+ align:start position:0%
+allows you to say well I think there's
+more around 1/2 but there's still some
+
+ align:start position:0%
+more around 1/2 but there's still some
+ 
+
+ align:start position:0%
+more around 1/2 but there's still some
+fluctuations that are possible okay and
+
+ align:start position:0%
+fluctuations that are possible okay and
+ 
+
+ align:start position:0%
+fluctuations that are possible okay and
+in particular here I talked about P
+
+ align:start position:0%
+in particular here I talked about P
+ 
+
+ align:start position:0%
+in particular here I talked about P
+where the two parameters a and B are
+
+ align:start position:0%
+where the two parameters a and B are
+ 
+
+ align:start position:0%
+where the two parameters a and B are
+actually the same I call them a when
+
+ align:start position:0%
+actually the same I call them a when
+ 
+
+ align:start position:0%
+actually the same I call them a when
+it's called scale the other one's called
+
+ align:start position:0%
+it's called scale the other one's called
+ 
+
+ align:start position:0%
+it's called scale the other one's called
+shape oh by the way sorry this is not a
+
+ align:start position:0%
+shape oh by the way sorry this is not a
+ 
+
+ align:start position:0%
+shape oh by the way sorry this is not a
+density so it actually has to be
+
+ align:start position:0%
+density so it actually has to be
+ 
+
+ align:start position:0%
+density so it actually has to be
+normalized right when you integrate this
+
+ align:start position:0%
+normalized right when you integrate this
+ 
+
+ align:start position:0%
+normalized right when you integrate this
+guy it's going to be some function that
+
+ align:start position:0%
+guy it's going to be some function that
+ 
+
+ align:start position:0%
+guy it's going to be some function that
+depends on a and B actually depends on
+
+ align:start position:0%
+depends on a and B actually depends on
+ 
+
+ align:start position:0%
+depends on a and B actually depends on
+this function through the beta function
+
+ align:start position:0%
+this function through the beta function
+ 
+
+ align:start position:0%
+this function through the beta function
+right which is this combination of gamma
+
+ align:start position:0%
+right which is this combination of gamma
+ 
+
+ align:start position:0%
+right which is this combination of gamma
+function so that's why it's called beta
+
+ align:start position:0%
+function so that's why it's called beta
+ 
+
+ align:start position:0%
+function so that's why it's called beta
+distribution but that's the definition
+
+ align:start position:0%
+distribution but that's the definition
+ 
+
+ align:start position:0%
+distribution but that's the definition
+of the beta function when you integrate
+
+ align:start position:0%
+of the beta function when you integrate
+ 
+
+ align:start position:0%
+of the beta function when you integrate
+this thing anyway so so I mean you just
+
+ align:start position:0%
+this thing anyway so so I mean you just
+ 
+
+ align:start position:0%
+this thing anyway so so I mean you just
+have to normalize it it's just a number
+
+ align:start position:0%
+have to normalize it it's just a number
+ 
+
+ align:start position:0%
+have to normalize it it's just a number
+that depends on the NB okay so here if
+
+ align:start position:0%
+that depends on the NB okay so here if
+ 
+
+ align:start position:0%
+that depends on the NB okay so here if
+you took if you take a equal to B you
+
+ align:start position:0%
+you took if you take a equal to B you
+ 
+
+ align:start position:0%
+you took if you take a equal to B you
+have something that essentially is
+
+ align:start position:0%
+have something that essentially is
+ 
+
+ align:start position:0%
+have something that essentially is
+symmetric around 1/2 right because what
+
+ align:start position:0%
+symmetric around 1/2 right because what
+ 
+
+ align:start position:0%
+symmetric around 1/2 right because what
+does it look like
+
+ align:start position:0%
+does it look like
+ 
+
+ align:start position:0%
+does it look like
+well it's something so my density f of X
+
+ align:start position:0%
+well it's something so my density f of X
+ 
+
+ align:start position:0%
+well it's something so my density f of X
+is gonna be what is gonna be my constant
+
+ align:start position:0%
+is gonna be what is gonna be my constant
+ 
+
+ align:start position:0%
+is gonna be what is gonna be my constant
+times X times 1 minus X to the a minus 1
+
+ align:start position:0%
+times X times 1 minus X to the a minus 1
+ 
+
+ align:start position:0%
+times X times 1 minus X to the a minus 1
+right and this function x times a minus
+
+ align:start position:0%
+right and this function x times a minus
+ 
+
+ align:start position:0%
+right and this function x times a minus
+1 minus x looks like yes we've drawn it
+
+ align:start position:0%
+1 minus x looks like yes we've drawn it
+ 
+
+ align:start position:0%
+1 minus x looks like yes we've drawn it
+before right that was something that
+
+ align:start position:0%
+before right that was something that
+ 
+
+ align:start position:0%
+before right that was something that
+showed up as being the variance of that
+
+ align:start position:0%
+showed up as being the variance of that
+ 
+
+ align:start position:0%
+showed up as being the variance of that
+was the variance of my burley so we know
+
+ align:start position:0%
+was the variance of my burley so we know
+ 
+
+ align:start position:0%
+was the variance of my burley so we know
+it's something that you know takes its
+
+ align:start position:0%
+it's something that you know takes its
+ 
+
+ align:start position:0%
+it's something that you know takes its
+maximum at 1/2 and now I'm just taking
+
+ align:start position:0%
+maximum at 1/2 and now I'm just taking
+ 
+
+ align:start position:0%
+maximum at 1/2 and now I'm just taking
+your power of this guy so I'm really
+
+ align:start position:0%
+your power of this guy so I'm really
+ 
+
+ align:start position:0%
+your power of this guy so I'm really
+just distorting this thing into some in
+
+ align:start position:0%
+just distorting this thing into some in
+ 
+
+ align:start position:0%
+just distorting this thing into some in
+some fairly symmetric manner okay so the
+
+ align:start position:0%
+some fairly symmetric manner okay so the
+ 
+
+ align:start position:0%
+some fairly symmetric manner okay so the
+the this distribution that we actually
+
+ align:start position:0%
+the this distribution that we actually
+ 
+
+ align:start position:0%
+the this distribution that we actually
+take up for P right so here i assume
+
+ align:start position:0%
+take up for P right so here i assume
+ 
+
+ align:start position:0%
+take up for P right so here i assume
+that pd parameter right I mean notice
+
+ align:start position:0%
+that pd parameter right I mean notice
+ 
+
+ align:start position:0%
+that pd parameter right I mean notice
+this is kind of weird first of all this
+
+ align:start position:0%
+this is kind of weird first of all this
+ 
+
+ align:start position:0%
+this is kind of weird first of all this
+is probably the first time in this
+
+ align:start position:0%
+is probably the first time in this
+ 
+
+ align:start position:0%
+is probably the first time in this
+entire course that we have this has this
+
+ align:start position:0%
+entire course that we have this has this
+ 
+
+ align:start position:0%
+entire course that we have this has this
+something has the distribution when it's
+
+ align:start position:0%
+something has the distribution when it's
+ 
+
+ align:start position:0%
+something has the distribution when it's
+actually a lowercase letter that's
+
+ align:start position:0%
+actually a lowercase letter that's
+ 
+
+ align:start position:0%
+actually a lowercase letter that's
+something you have to deal with because
+
+ align:start position:0%
+something you have to deal with because
+ 
+
+ align:start position:0%
+something you have to deal with because
+we've been using the word case letters
+
+ align:start position:0%
+we've been using the word case letters
+ 
+
+ align:start position:0%
+we've been using the word case letters
+for parameters and now we want them to
+
+ align:start position:0%
+for parameters and now we want them to
+ 
+
+ align:start position:0%
+for parameters and now we want them to
+have a distribution so that's what's
+
+ align:start position:0%
+have a distribution so that's what's
+ 
+
+ align:start position:0%
+have a distribution so that's what's
+gonna happen
+
+ align:start position:0%
+gonna happen
+ 
+
+ align:start position:0%
+gonna happen
+all right then this is called the prior
+
+ align:start position:0%
+all right then this is called the prior
+ 
+
+ align:start position:0%
+all right then this is called the prior
+distribution okay so really I should
+
+ align:start position:0%
+distribution okay so really I should
+ 
+
+ align:start position:0%
+distribution okay so really I should
+write something like f of P is equal to
+
+ align:start position:0%
+write something like f of P is equal to
+ 
+
+ align:start position:0%
+write something like f of P is equal to
+a constant times p1 minus p2 da minus 1
+
+ align:start position:0%
+a constant times p1 minus p2 da minus 1
+ 
+
+ align:start position:0%
+a constant times p1 minus p2 da minus 1
+well no actually I should not because
+
+ align:start position:0%
+well no actually I should not because
+ 
+
+ align:start position:0%
+well no actually I should not because
+then it's confusing
+
+ align:start position:0%
+then it's confusing
+ 
+
+ align:start position:0%
+then it's confusing
+ok so let me not do this one thing in
+
+ align:start position:0%
+ok so let me not do this one thing in
+ 
+
+ align:start position:0%
+ok so let me not do this one thing in
+terms of notation that I'm gonna write
+
+ align:start position:0%
+terms of notation that I'm gonna write
+ 
+
+ align:start position:0%
+terms of notation that I'm gonna write
+I'm gonna write when I have a constant
+
+ align:start position:0%
+I'm gonna write when I have a constant
+ 
+
+ align:start position:0%
+I'm gonna write when I have a constant
+here and I don't want to make it
+
+ align:start position:0%
+here and I don't want to make it
+ 
+
+ align:start position:0%
+here and I don't want to make it
+explicit and we'll see in a second why
+
+ align:start position:0%
+explicit and we'll see in a second why
+ 
+
+ align:start position:0%
+explicit and we'll see in a second why
+they don't need to make it explicit I'm
+
+ align:start position:0%
+they don't need to make it explicit I'm
+ 
+
+ align:start position:0%
+they don't need to make it explicit I'm
+gonna write this as f of X it's
+
+ align:start position:0%
+gonna write this as f of X it's
+ 
+
+ align:start position:0%
+gonna write this as f of X it's
+proportional to X 1 minus X to the minus
+
+ align:start position:0%
+proportional to X 1 minus X to the minus
+ 
+
+ align:start position:0%
+proportional to X 1 minus X to the minus
+1 ok so that's just that's just to say
+
+ align:start position:0%
+1 ok so that's just that's just to say
+ 
+
+ align:start position:0%
+1 ok so that's just that's just to say
+equal to some constant that does not
+
+ align:start position:0%
+equal to some constant that does not
+ 
+
+ align:start position:0%
+equal to some constant that does not
+depend on x times this thing ok so if we
+
+ align:start position:0%
+depend on x times this thing ok so if we
+ 
+
+ align:start position:0%
+depend on x times this thing ok so if we
+continue with our experiment now if P
+
+ align:start position:0%
+continue with our experiment now if P
+ 
+
+ align:start position:0%
+continue with our experiment now if P
+right so that's the experiment where I'm
+
+ align:start position:0%
+right so that's the experiment where I'm
+ 
+
+ align:start position:0%
+right so that's the experiment where I'm
+trying to I'm drawing this data x1 to xn
+
+ align:start position:0%
+trying to I'm drawing this data x1 to xn
+ 
+
+ align:start position:0%
+trying to I'm drawing this data x1 to xn
+which is Bernoulli P if P has some
+
+ align:start position:0%
+which is Bernoulli P if P has some
+ 
+
+ align:start position:0%
+which is Bernoulli P if P has some
+distribution it's not clear what it
+
+ align:start position:0%
+distribution it's not clear what it
+ 
+
+ align:start position:0%
+distribution it's not clear what it
+means to have a burn Allah with some
+
+ align:start position:0%
+means to have a burn Allah with some
+ 
+
+ align:start position:0%
+means to have a burn Allah with some
+random parameter so what I'm gonna do is
+
+ align:start position:0%
+random parameter so what I'm gonna do is
+ 
+
+ align:start position:0%
+random parameter so what I'm gonna do is
+then I'm gonna first draw my P let's say
+
+ align:start position:0%
+then I'm gonna first draw my P let's say
+ 
+
+ align:start position:0%
+then I'm gonna first draw my P let's say
+I get a number point 52 and then I'm
+
+ align:start position:0%
+I get a number point 52 and then I'm
+ 
+
+ align:start position:0%
+I get a number point 52 and then I'm
+gonna draw my data conditionally on P
+
+ align:start position:0%
+gonna draw my data conditionally on P
+ 
+
+ align:start position:0%
+gonna draw my data conditionally on P
+all right so here comes the first and
+
+ align:start position:0%
+all right so here comes the first and
+ 
+
+ align:start position:0%
+all right so here comes the first and
+last flow chart of this class so I'm
+
+ align:start position:0%
+last flow chart of this class so I'm
+ 
+
+ align:start position:0%
+last flow chart of this class so I'm
+gonna first
+
+ align:start position:0%
+gonna first
+ 
+
+ align:start position:0%
+gonna first
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+all right so nature first draws P okay
+
+ align:start position:0%
+all right so nature first draws P okay
+ 
+
+ align:start position:0%
+all right so nature first draws P okay
+so P follows say some beta a a then I
+
+ align:start position:0%
+so P follows say some beta a a then I
+ 
+
+ align:start position:0%
+so P follows say some beta a a then I
+condition on P and then I draw X 1 X n
+
+ align:start position:0%
+condition on P and then I draw X 1 X n
+ 
+
+ align:start position:0%
+condition on P and then I draw X 1 X n
+there are iid there only P everybody
+
+ align:start position:0%
+there are iid there only P everybody
+ 
+
+ align:start position:0%
+there are iid there only P everybody
+understand the process of generating
+
+ align:start position:0%
+understand the process of generating
+ 
+
+ align:start position:0%
+understand the process of generating
+this data all right so you first draw a
+
+ align:start position:0%
+this data all right so you first draw a
+ 
+
+ align:start position:0%
+this data all right so you first draw a
+parameter and then you just flip this
+
+ align:start position:0%
+parameter and then you just flip this
+ 
+
+ align:start position:0%
+parameter and then you just flip this
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+those end by independent biased coins
+
+ align:start position:0%
+those end by independent biased coins
+ 
+
+ align:start position:0%
+those end by independent biased coins
+with this particular P alright so
+
+ align:start position:0%
+with this particular P alright so
+ 
+
+ align:start position:0%
+with this particular P alright so
+there's this like layered thing so now
+
+ align:start position:0%
+there's this like layered thing so now
+ 
+
+ align:start position:0%
+there's this like layered thing so now
+conditionally and P right so here I have
+
+ align:start position:0%
+conditionally and P right so here I have
+ 
+
+ align:start position:0%
+conditionally and P right so here I have
+this prior about P which was the thing
+
+ align:start position:0%
+this prior about P which was the thing
+ 
+
+ align:start position:0%
+this prior about P which was the thing
+so this is just a stop process again
+
+ align:start position:0%
+so this is just a stop process again
+ 
+
+ align:start position:0%
+so this is just a stop process again
+right it's not anything that actually
+
+ align:start position:0%
+right it's not anything that actually
+ 
+
+ align:start position:0%
+right it's not anything that actually
+happens in practice this is my way of
+
+ align:start position:0%
+happens in practice this is my way of
+ 
+
+ align:start position:0%
+happens in practice this is my way of
+thinking about how the data was
+
+ align:start position:0%
+thinking about how the data was
+ 
+
+ align:start position:0%
+thinking about how the data was
+generated and from this I'm gonna try to
+
+ align:start position:0%
+generated and from this I'm gonna try to
+ 
+
+ align:start position:0%
+generated and from this I'm gonna try to
+come up with some procedure just like if
+
+ align:start position:0%
+come up with some procedure just like if
+ 
+
+ align:start position:0%
+come up with some procedure just like if
+your estimator is the average of the
+
+ align:start position:0%
+your estimator is the average of the
+ 
+
+ align:start position:0%
+your estimator is the average of the
+data you don't have to understand
+
+ align:start position:0%
+data you don't have to understand
+ 
+
+ align:start position:0%
+data you don't have to understand
+probability to say that my estimator is
+
+ align:start position:0%
+probability to say that my estimator is
+ 
+
+ align:start position:0%
+probability to say that my estimator is
+the average of the data right I mean
+
+ align:start position:0%
+the average of the data right I mean
+ 
+
+ align:start position:0%
+the average of the data right I mean
+anyone outside this room understand that
+
+ align:start position:0%
+anyone outside this room understand that
+ 
+
+ align:start position:0%
+anyone outside this room understand that
+the average is a good estimator for some
+
+ align:start position:0%
+the average is a good estimator for some
+ 
+
+ align:start position:0%
+the average is a good estimator for some
+you know average behavior and and they
+
+ align:start position:0%
+you know average behavior and and they
+ 
+
+ align:start position:0%
+you know average behavior and and they
+don't need to think of the data as being
+
+ align:start position:0%
+don't need to think of the data as being
+ 
+
+ align:start position:0%
+don't need to think of the data as being
+a random variable etc so same thing
+
+ align:start position:0%
+a random variable etc so same thing
+ 
+
+ align:start position:0%
+a random variable etc so same thing
+basically now we will see I mean
+
+ align:start position:0%
+basically now we will see I mean
+ 
+
+ align:start position:0%
+basically now we will see I mean
+actually we won't but in this case well
+
+ align:start position:0%
+actually we won't but in this case well
+ 
+
+ align:start position:0%
+actually we won't but in this case well
+we will in this case you can see that
+
+ align:start position:0%
+we will in this case you can see that
+ 
+
+ align:start position:0%
+we will in this case you can see that
+essentially the posterior distribution
+
+ align:start position:0%
+essentially the posterior distribution
+ 
+
+ align:start position:0%
+essentially the posterior distribution
+is still a beta all right so what it
+
+ align:start position:0%
+is still a beta all right so what it
+ 
+
+ align:start position:0%
+is still a beta all right so what it
+means is that I had this thing then I
+
+ align:start position:0%
+means is that I had this thing then I
+ 
+
+ align:start position:0%
+means is that I had this thing then I
+observed my data and then I continued
+
+ align:start position:0%
+observed my data and then I continued
+ 
+
+ align:start position:0%
+observed my data and then I continued
+and here I'm gonna update my prior into
+
+ align:start position:0%
+and here I'm gonna update my prior into
+ 
+
+ align:start position:0%
+and here I'm gonna update my prior into
+some posterior distribution PI and here
+
+ align:start position:0%
+some posterior distribution PI and here
+ 
+
+ align:start position:0%
+some posterior distribution PI and here
+this guy is actually also a beta
+
+ align:start position:0%
+this guy is actually also a beta
+ 
+
+ align:start position:0%
+this guy is actually also a beta
+all right so PI now P my posterior
+
+ align:start position:0%
+all right so PI now P my posterior
+ 
+
+ align:start position:0%
+all right so PI now P my posterior
+distribution on P is also a beta
+
+ align:start position:0%
+distribution on P is also a beta
+ 
+
+ align:start position:0%
+distribution on P is also a beta
+distribution with the parameters that
+
+ align:start position:0%
+distribution with the parameters that
+ 
+
+ align:start position:0%
+distribution with the parameters that
+are on this slide and I'll have space to
+
+ align:start position:0%
+are on this slide and I'll have space to
+ 
+
+ align:start position:0%
+are on this slide and I'll have space to
+reproduce them so I start the beginning
+
+ align:start position:0%
+reproduce them so I start the beginning
+ 
+
+ align:start position:0%
+reproduce them so I start the beginning
+of this flow chart as having P which is
+
+ align:start position:0%
+of this flow chart as having P which is
+ 
+
+ align:start position:0%
+of this flow chart as having P which is
+a prior I'm gonna get some observations
+
+ align:start position:0%
+a prior I'm gonna get some observations
+ 
+
+ align:start position:0%
+a prior I'm gonna get some observations
+and then I'm gonna update what my
+
+ align:start position:0%
+and then I'm gonna update what my
+ 
+
+ align:start position:0%
+and then I'm gonna update what my
+posterior is okay so this posterior is
+
+ align:start position:0%
+posterior is okay so this posterior is
+ 
+
+ align:start position:0%
+posterior is okay so this posterior is
+basically something that's in the big in
+
+ align:start position:0%
+basically something that's in the big in
+ 
+
+ align:start position:0%
+basically something that's in the big in
+Bayesian statistics was beautiful is as
+
+ align:start position:0%
+Bayesian statistics was beautiful is as
+ 
+
+ align:start position:0%
+Bayesian statistics was beautiful is as
+soon as you have the distribution it can
+
+ align:start position:0%
+soon as you have the distribution it can
+ 
+
+ align:start position:0%
+soon as you have the distribution it can
+it's essentially capturing all the
+
+ align:start position:0%
+it's essentially capturing all the
+ 
+
+ align:start position:0%
+it's essentially capturing all the
+information about the data that you want
+
+ align:start position:0%
+information about the data that you want
+ 
+
+ align:start position:0%
+information about the data that you want
+for P and it's not just a point right
+
+ align:start position:0%
+for P and it's not just a point right
+ 
+
+ align:start position:0%
+for P and it's not just a point right
+this is not just an average it's
+
+ align:start position:0%
+this is not just an average it's
+ 
+
+ align:start position:0%
+this is not just an average it's
+actually an entire distribution for the
+
+ align:start position:0%
+actually an entire distribution for the
+ 
+
+ align:start position:0%
+actually an entire distribution for the
+possible values of theta and it's not
+
+ align:start position:0%
+possible values of theta and it's not
+ 
+
+ align:start position:0%
+possible values of theta and it's not
+the same thing as saying well you know
+
+ align:start position:0%
+the same thing as saying well you know
+ 
+
+ align:start position:0%
+the same thing as saying well you know
+if theta hat is equal to xn bar in the
+
+ align:start position:0%
+if theta hat is equal to xn bar in the
+ 
+
+ align:start position:0%
+if theta hat is equal to xn bar in the
+gaussian case i know that this is some
+
+ align:start position:0%
+gaussian case i know that this is some
+ 
+
+ align:start position:0%
+gaussian case i know that this is some
+mean mu and then maybe it has variance
+
+ align:start position:0%
+mean mu and then maybe it has variance
+ 
+
+ align:start position:0%
+mean mu and then maybe it has variance
+Sigma squared over n that's not what I
+
+ align:start position:0%
+Sigma squared over n that's not what I
+ 
+
+ align:start position:0%
+Sigma squared over n that's not what I
+mean by this is my posterior
+
+ align:start position:0%
+mean by this is my posterior
+ 
+
+ align:start position:0%
+mean by this is my posterior
+distribution right this is not what I
+
+ align:start position:0%
+distribution right this is not what I
+ 
+
+ align:start position:0%
+distribution right this is not what I
+mean this is gonna come from this guy's
+
+ align:start position:0%
+mean this is gonna come from this guy's
+ 
+
+ align:start position:0%
+mean this is gonna come from this guy's
+right the gaussian thing and the central
+
+ align:start position:0%
+right the gaussian thing and the central
+ 
+
+ align:start position:0%
+right the gaussian thing and the central
+limit theorem but what I mean is this
+
+ align:start position:0%
+limit theorem but what I mean is this
+ 
+
+ align:start position:0%
+limit theorem but what I mean is this
+guy and this came acutally from from the
+
+ align:start position:0%
+guy and this came acutally from from the
+ 
+
+ align:start position:0%
+guy and this came acutally from from the
+prior distribution if I had another
+
+ align:start position:0%
+prior distribution if I had another
+ 
+
+ align:start position:0%
+prior distribution if I had another
+prior I would not necessarily have a
+
+ align:start position:0%
+prior I would not necessarily have a
+ 
+
+ align:start position:0%
+prior I would not necessarily have a
+beta distribution on the output so when
+
+ align:start position:0%
+beta distribution on the output so when
+ 
+
+ align:start position:0%
+beta distribution on the output so when
+I have the same family of distributions
+
+ align:start position:0%
+I have the same family of distributions
+ 
+
+ align:start position:0%
+I have the same family of distributions
+at the beginning and at the end of this
+
+ align:start position:0%
+at the beginning and at the end of this
+ 
+
+ align:start position:0%
+at the beginning and at the end of this
+flowchart I say that beta is a conjugate
+
+ align:start position:0%
+flowchart I say that beta is a conjugate
+ 
+
+ align:start position:0%
+flowchart I say that beta is a conjugate
+prior meaning I get I put in beta as a
+
+ align:start position:0%
+prior meaning I get I put in beta as a
+ 
+
+ align:start position:0%
+prior meaning I get I put in beta as a
+prior and I get betas at but series and
+
+ align:start position:0%
+prior and I get betas at but series and
+ 
+
+ align:start position:0%
+prior and I get betas at but series and
+that's why betas are so popular
+
+ align:start position:0%
+that's why betas are so popular
+ 
+
+ align:start position:0%
+that's why betas are so popular
+conjugate priors are really nice because
+
+ align:start position:0%
+conjugate priors are really nice because
+ 
+
+ align:start position:0%
+conjugate priors are really nice because
+you know that whatever you put in what
+
+ align:start position:0%
+you know that whatever you put in what
+ 
+
+ align:start position:0%
+you know that whatever you put in what
+you're gonna get in the end is a beta so
+
+ align:start position:0%
+you're gonna get in the end is a beta so
+ 
+
+ align:start position:0%
+you're gonna get in the end is a beta so
+all you have to think about is the
+
+ align:start position:0%
+all you have to think about is the
+ 
+
+ align:start position:0%
+all you have to think about is the
+parameters you don't have to check again
+
+ align:start position:0%
+parameters you don't have to check again
+ 
+
+ align:start position:0%
+parameters you don't have to check again
+what the posterior is gonna look like
+
+ align:start position:0%
+what the posterior is gonna look like
+ 
+
+ align:start position:0%
+what the posterior is gonna look like
+what the PDF of this guy is gonna be
+
+ align:start position:0%
+what the PDF of this guy is gonna be
+ 
+
+ align:start position:0%
+what the PDF of this guy is gonna be
+you'll have to think about it you just
+
+ align:start position:0%
+you'll have to think about it you just
+ 
+
+ align:start position:0%
+you'll have to think about it you just
+have to check what the parameters are
+
+ align:start position:0%
+have to check what the parameters are
+ 
+
+ align:start position:0%
+have to check what the parameters are
+and there's families of conjugate priors
+
+ align:start position:0%
+and there's families of conjugate priors
+ 
+
+ align:start position:0%
+and there's families of conjugate priors
+Gaussian gives Gaussian for example
+
+ align:start position:0%
+Gaussian gives Gaussian for example
+ 
+
+ align:start position:0%
+Gaussian gives Gaussian for example
+there's a bunch of them and this is what
+
+ align:start position:0%
+there's a bunch of them and this is what
+ 
+
+ align:start position:0%
+there's a bunch of them and this is what
+drives people to into using specific
+
+ align:start position:0%
+drives people to into using specific
+ 
+
+ align:start position:0%
+drives people to into using specific
+priors as rappers as opposed to other it
+
+ align:start position:0%
+priors as rappers as opposed to other it
+ 
+
+ align:start position:0%
+priors as rappers as opposed to other it
+has nice mathematical properties nobody
+
+ align:start position:0%
+has nice mathematical properties nobody
+ 
+
+ align:start position:0%
+has nice mathematical properties nobody
+believes that the P distribution is it P
+
+ align:start position:0%
+believes that the P distribution is it P
+ 
+
+ align:start position:0%
+believes that the P distribution is it P
+is really distributed according to beta
+
+ align:start position:0%
+is really distributed according to beta
+ 
+
+ align:start position:0%
+is really distributed according to beta
+but it's flexible enough and super
+
+ align:start position:0%
+but it's flexible enough and super
+ 
+
+ align:start position:0%
+but it's flexible enough and super
+convenient mathematical alright so now
+
+ align:start position:0%
+convenient mathematical alright so now
+ 
+
+ align:start position:0%
+convenient mathematical alright so now
+let's see from one second before we
+
+ align:start position:0%
+let's see from one second before we
+ 
+
+ align:start position:0%
+let's see from one second before we
+actually go any further what I did so a
+
+ align:start position:0%
+actually go any further what I did so a
+ 
+
+ align:start position:0%
+actually go any further what I did so a
+and B I didn't mention it a and B are
+
+ align:start position:0%
+and B I didn't mention it a and B are
+ 
+
+ align:start position:0%
+and B I didn't mention it a and B are
+both and here B and B are positive
+
+ align:start position:0%
+both and here B and B are positive
+ 
+
+ align:start position:0%
+both and here B and B are positive
+numbers okay they can be anything
+
+ align:start position:0%
+numbers okay they can be anything
+ 
+
+ align:start position:0%
+numbers okay they can be anything
+positive so here what I did is that I
+
+ align:start position:0%
+positive so here what I did is that I
+ 
+
+ align:start position:0%
+positive so here what I did is that I
+updated a into a plus the sum of my data
+
+ align:start position:0%
+updated a into a plus the sum of my data
+ 
+
+ align:start position:0%
+updated a into a plus the sum of my data
+and B into B plus n minus the sum of my
+
+ align:start position:0%
+and B into B plus n minus the sum of my
+ 
+
+ align:start position:0%
+and B into B plus n minus the sum of my
+data so that's essentially a becomes a
+
+ align:start position:0%
+data so that's essentially a becomes a
+ 
+
+ align:start position:0%
+data so that's essentially a becomes a
+plus the number of ones and B becomes B
+
+ align:start position:0%
+plus the number of ones and B becomes B
+ 
+
+ align:start position:0%
+plus the number of ones and B becomes B
+well that's only when a and I have a na
+
+ align:start position:0%
+well that's only when a and I have a na
+ 
+
+ align:start position:0%
+well that's only when a and I have a na
+right so the first parameters become
+
+ align:start position:0%
+right so the first parameters become
+ 
+
+ align:start position:0%
+right so the first parameters become
+itself plus the number of ones and the
+
+ align:start position:0%
+itself plus the number of ones and the
+ 
+
+ align:start position:0%
+itself plus the number of ones and the
+second one becomes itself plus the
+
+ align:start position:0%
+second one becomes itself plus the
+ 
+
+ align:start position:0%
+second one becomes itself plus the
+number of zeros right and so just as a
+
+ align:start position:0%
+number of zeros right and so just as a
+ 
+
+ align:start position:0%
+number of zeros right and so just as a
+sanity check what does this mean if a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goes to zero what is the beta when a
+
+ align:start position:0%
+goes to zero what is the beta when a
+ 
+
+ align:start position:0%
+goes to zero what is the beta when a
+goes to zero we can actually read this
+
+ align:start position:0%
+goes to zero we can actually read this
+ 
+
+ align:start position:0%
+goes to zero we can actually read this
+from here right right so we had a sorry
+
+ align:start position:0%
+from here right right so we had a sorry
+ 
+
+ align:start position:0%
+from here right right so we had a sorry
+actually let's take a goes to no
+
+ align:start position:0%
+actually let's take a goes to no
+ 
+
+ align:start position:0%
+actually let's take a goes to no
+actually sorry let's just do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's not do this now I'll do it
+
+ align:start position:0%
+okay let's not do this now I'll do it
+ 
+
+ align:start position:0%
+okay let's not do this now I'll do it
+when we talk about not informative prior
+
+ align:start position:0%
+when we talk about not informative prior
+ 
+
+ align:start position:0%
+when we talk about not informative prior
+because it's a it's a little too messy
+
+ align:start position:0%
+because it's a it's a little too messy
+ 
+
+ align:start position:0%
+because it's a it's a little too messy
+yeah okay so how do we do this how did I
+
+ align:start position:0%
+yeah okay so how do we do this how did I
+ 
+
+ align:start position:0%
+yeah okay so how do we do this how did I
+get this posterior distribution given
+
+ align:start position:0%
+get this posterior distribution given
+ 
+
+ align:start position:0%
+get this posterior distribution given
+the prior how do I update this well this
+
+ align:start position:0%
+the prior how do I update this well this
+ 
+
+ align:start position:0%
+the prior how do I update this well this
+is called Bayesian statistics and you've
+
+ align:start position:0%
+is called Bayesian statistics and you've
+ 
+
+ align:start position:0%
+is called Bayesian statistics and you've
+heard this word Bayes before and the way
+
+ align:start position:0%
+heard this word Bayes before and the way
+ 
+
+ align:start position:0%
+heard this word Bayes before and the way
+you've heard it is in the base formula
+
+ align:start position:0%
+you've heard it is in the base formula
+ 
+
+ align:start position:0%
+you've heard it is in the base formula
+right what was the base formula the base
+
+ align:start position:0%
+right what was the base formula the base
+ 
+
+ align:start position:0%
+right what was the base formula the base
+formula was telling you that the
+
+ align:start position:0%
+formula was telling you that the
+ 
+
+ align:start position:0%
+formula was telling you that the
+probability of a given B was equal to
+
+ align:start position:0%
+probability of a given B was equal to
+ 
+
+ align:start position:0%
+probability of a given B was equal to
+something that depended on the
+
+ align:start position:0%
+something that depended on the
+ 
+
+ align:start position:0%
+something that depended on the
+probability of B given a right that's
+
+ align:start position:0%
+probability of B given a right that's
+ 
+
+ align:start position:0%
+probability of B given a right that's
+what it was and III mean you can
+
+ align:start position:0%
+what it was and III mean you can
+ 
+
+ align:start position:0%
+what it was and III mean you can
+actually either remember the formula you
+
+ align:start position:0%
+actually either remember the formula you
+ 
+
+ align:start position:0%
+actually either remember the formula you
+can remember the definition and this is
+
+ align:start position:0%
+can remember the definition and this is
+ 
+
+ align:start position:0%
+can remember the definition and this is
+what P of a and B divided by P of B so
+
+ align:start position:0%
+what P of a and B divided by P of B so
+ 
+
+ align:start position:0%
+what P of a and B divided by P of B so
+this is P of B given a times P of a
+
+ align:start position:0%
+this is P of B given a times P of a
+ 
+
+ align:start position:0%
+this is P of B given a times P of a
+divided by P of B right that's what base
+
+ align:start position:0%
+divided by P of B right that's what base
+ 
+
+ align:start position:0%
+divided by P of B right that's what base
+formula is telling you agree so now what
+
+ align:start position:0%
+formula is telling you agree so now what
+ 
+
+ align:start position:0%
+formula is telling you agree so now what
+I want is to have something that's
+
+ align:start position:0%
+I want is to have something that's
+ 
+
+ align:start position:0%
+I want is to have something that's
+telling me how this is how this is gonna
+
+ align:start position:0%
+telling me how this is how this is gonna
+ 
+
+ align:start position:0%
+telling me how this is how this is gonna
+work okay
+
+ align:start position:0%
+work okay
+ 
+
+ align:start position:0%
+work okay
+so what is gonna play the role of those
+
+ align:start position:0%
+so what is gonna play the role of those
+ 
+
+ align:start position:0%
+so what is gonna play the role of those
+events a and B well one is gonna be what
+
+ align:start position:0%
+events a and B well one is gonna be what
+ 
+
+ align:start position:0%
+events a and B well one is gonna be what
+is the this so this is gonna be the
+
+ align:start position:0%
+is the this so this is gonna be the
+ 
+
+ align:start position:0%
+is the this so this is gonna be the
+distribution of my parameter theta given
+
+ align:start position:0%
+distribution of my parameter theta given
+ 
+
+ align:start position:0%
+distribution of my parameter theta given
+that I see the data and this is gonna
+
+ align:start position:0%
+that I see the data and this is gonna
+ 
+
+ align:start position:0%
+that I see the data and this is gonna
+tell me what is the distribution of the
+
+ align:start position:0%
+tell me what is the distribution of the
+ 
+
+ align:start position:0%
+tell me what is the distribution of the
+data given that I know what my parameter
+
+ align:start position:0%
+data given that I know what my parameter
+ 
+
+ align:start position:0%
+data given that I know what my parameter
+of theta is but that part if this is
+
+ align:start position:0%
+of theta is but that part if this is
+ 
+
+ align:start position:0%
+of theta is but that part if this is
+data and this is the parameter of theta
+
+ align:start position:0%
+data and this is the parameter of theta
+ 
+
+ align:start position:0%
+data and this is the parameter of theta
+this is what we have been all along
+
+ align:start position:0%
+this is what we have been all along
+ 
+
+ align:start position:0%
+this is what we have been all along
+we've been doing all along the
+
+ align:start position:0%
+we've been doing all along the
+ 
+
+ align:start position:0%
+we've been doing all along the
+distribution of the data given the
+
+ align:start position:0%
+distribution of the data given the
+ 
+
+ align:start position:0%
+distribution of the data given the
+parameter here was an iid Bernoulli P I
+
+ align:start position:0%
+parameter here was an iid Bernoulli P I
+ 
+
+ align:start position:0%
+parameter here was an iid Bernoulli P I
+know that I know exactly what their
+
+ align:start position:0%
+know that I know exactly what their
+ 
+
+ align:start position:0%
+know that I know exactly what their
+joint probability mass function is then
+
+ align:start position:0%
+joint probability mass function is then
+ 
+
+ align:start position:0%
+joint probability mass function is then
+that was what so we said that let this
+
+ align:start position:0%
+that was what so we said that let this
+ 
+
+ align:start position:0%
+that was what so we said that let this
+is going to be my data and this is gonna
+
+ align:start position:0%
+is going to be my data and this is gonna
+ 
+
+ align:start position:0%
+is going to be my data and this is gonna
+be my parameter okay so that means that
+
+ align:start position:0%
+be my parameter okay so that means that
+ 
+
+ align:start position:0%
+be my parameter okay so that means that
+this is the probability of my data given
+
+ align:start position:0%
+this is the probability of my data given
+ 
+
+ align:start position:0%
+this is the probability of my data given
+the parameter this is a probability
+
+ align:start position:0%
+the parameter this is a probability
+ 
+
+ align:start position:0%
+the parameter this is a probability
+given the product this is the
+
+ align:start position:0%
+given the product this is the
+ 
+
+ align:start position:0%
+given the product this is the
+probability of the parameter what is
+
+ align:start position:0%
+probability of the parameter what is
+ 
+
+ align:start position:0%
+probability of the parameter what is
+this what did we call this this is the
+
+ align:start position:0%
+this what did we call this this is the
+ 
+
+ align:start position:0%
+this what did we call this this is the
+prior it's just
+
+ align:start position:0%
+prior it's just
+ 
+
+ align:start position:0%
+prior it's just
+distribution of my parameter now what is
+
+ align:start position:0%
+distribution of my parameter now what is
+ 
+
+ align:start position:0%
+distribution of my parameter now what is
+this well this is just a distribution of
+
+ align:start position:0%
+this well this is just a distribution of
+ 
+
+ align:start position:0%
+this well this is just a distribution of
+the data itself alright so this is
+
+ align:start position:0%
+the data itself alright so this is
+ 
+
+ align:start position:0%
+the data itself alright so this is
+essentially the distribution of this if
+
+ align:start position:0%
+essentially the distribution of this if
+ 
+
+ align:start position:0%
+essentially the distribution of this if
+this was indeed a if I mean not
+
+ align:start position:0%
+this was indeed a if I mean not
+ 
+
+ align:start position:0%
+this was indeed a if I mean not
+conditioned on P right so if I don't
+
+ align:start position:0%
+conditioned on P right so if I don't
+ 
+
+ align:start position:0%
+conditioned on P right so if I don't
+condition on P this data is gonna be a
+
+ align:start position:0%
+condition on P this data is gonna be a
+ 
+
+ align:start position:0%
+condition on P this data is gonna be a
+bunch of iid bernly with some parameter
+
+ align:start position:0%
+bunch of iid bernly with some parameter
+ 
+
+ align:start position:0%
+bunch of iid bernly with some parameter
+but the parameter is random right so for
+
+ align:start position:0%
+but the parameter is random right so for
+ 
+
+ align:start position:0%
+but the parameter is random right so for
+different realization of this data set
+
+ align:start position:0%
+different realization of this data set
+ 
+
+ align:start position:0%
+different realization of this data set
+I'm gonna get different parameters for
+
+ align:start position:0%
+I'm gonna get different parameters for
+ 
+
+ align:start position:0%
+I'm gonna get different parameters for
+the Bernoulli and so that leads to some
+
+ align:start position:0%
+the Bernoulli and so that leads to some
+ 
+
+ align:start position:0%
+the Bernoulli and so that leads to some
+sort of you know convolution I mean it's
+
+ align:start position:0%
+sort of you know convolution I mean it's
+ 
+
+ align:start position:0%
+sort of you know convolution I mean it's
+not really convolution in this case but
+
+ align:start position:0%
+not really convolution in this case but
+ 
+
+ align:start position:0%
+not really convolution in this case but
+it's like some sort of composition of
+
+ align:start position:0%
+it's like some sort of composition of
+ 
+
+ align:start position:0%
+it's like some sort of composition of
+distributions right to have the
+
+ align:start position:0%
+distributions right to have the
+ 
+
+ align:start position:0%
+distributions right to have the
+distribution it comes the randomness
+
+ align:start position:0%
+distribution it comes the randomness
+ 
+
+ align:start position:0%
+distribution it comes the randomness
+that comes from here and then the
+
+ align:start position:0%
+that comes from here and then the
+ 
+
+ align:start position:0%
+that comes from here and then the
+randomness that come from realizing the
+
+ align:start position:0%
+randomness that come from realizing the
+ 
+
+ align:start position:0%
+randomness that come from realizing the
+Bernoulli right so that's just a
+
+ align:start position:0%
+Bernoulli right so that's just a
+ 
+
+ align:start position:0%
+Bernoulli right so that's just a
+marginal distribution it's actually
+
+ align:start position:0%
+marginal distribution it's actually
+ 
+
+ align:start position:0%
+marginal distribution it's actually
+might be painful to understand what this
+
+ align:start position:0%
+might be painful to understand what this
+ 
+
+ align:start position:0%
+might be painful to understand what this
+is right I mean in a way it's sort of a
+
+ align:start position:0%
+is right I mean in a way it's sort of a
+ 
+
+ align:start position:0%
+is right I mean in a way it's sort of a
+mixture and it's not super nice but
+
+ align:start position:0%
+mixture and it's not super nice but
+ 
+
+ align:start position:0%
+mixture and it's not super nice but
+we'll see that this actually won't
+
+ align:start position:0%
+we'll see that this actually won't
+ 
+
+ align:start position:0%
+we'll see that this actually won't
+matter for us this is gonna be some
+
+ align:start position:0%
+matter for us this is gonna be some
+ 
+
+ align:start position:0%
+matter for us this is gonna be some
+number it's gonna be there but it won't
+
+ align:start position:0%
+number it's gonna be there but it won't
+ 
+
+ align:start position:0%
+number it's gonna be there but it won't
+matter for us what it is because it
+
+ align:start position:0%
+matter for us what it is because it
+ 
+
+ align:start position:0%
+matter for us what it is because it
+actually does not depend on the
+
+ align:start position:0%
+actually does not depend on the
+ 
+
+ align:start position:0%
+actually does not depend on the
+parameter and that's all that matters to
+
+ align:start position:0%
+parameter and that's all that matters to
+ 
+
+ align:start position:0%
+parameter and that's all that matters to
+us okay
+
+ align:start position:0%
+us okay
+ 
+
+ align:start position:0%
+us okay
+so let's put some names on those things
+
+ align:start position:0%
+so let's put some names on those things
+ 
+
+ align:start position:0%
+so let's put some names on those things
+right I mean this was very informal so
+
+ align:start position:0%
+right I mean this was very informal so
+ 
+
+ align:start position:0%
+right I mean this was very informal so
+let's put some actual names on what we
+
+ align:start position:0%
+let's put some actual names on what we
+ 
+
+ align:start position:0%
+let's put some actual names on what we
+want to call what we call prior so what
+
+ align:start position:0%
+want to call what we call prior so what
+ 
+
+ align:start position:0%
+want to call what we call prior so what
+is the formal definition of a prior what
+
+ align:start position:0%
+is the formal definition of a prior what
+ 
+
+ align:start position:0%
+is the formal definition of a prior what
+is the form of this definition of a
+
+ align:start position:0%
+is the form of this definition of a
+ 
+
+ align:start position:0%
+is the form of this definition of a
+posterior and what are the rules to
+
+ align:start position:0%
+posterior and what are the rules to
+ 
+
+ align:start position:0%
+posterior and what are the rules to
+update it okay so I'm gonna have my data
+
+ align:start position:0%
+update it okay so I'm gonna have my data
+ 
+
+ align:start position:0%
+update it okay so I'm gonna have my data
+which is gonna be x1 xn and so let's say
+
+ align:start position:0%
+which is gonna be x1 xn and so let's say
+ 
+
+ align:start position:0%
+which is gonna be x1 xn and so let's say
+they are iid but they don't actually
+
+ align:start position:0%
+they are iid but they don't actually
+ 
+
+ align:start position:0%
+they are iid but they don't actually
+have two and so I'm gonna have given
+
+ align:start position:0%
+have two and so I'm gonna have given
+ 
+
+ align:start position:0%
+have two and so I'm gonna have given
+theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when I say given it's either given
+
+ align:start position:0%
+and when I say given it's either given
+ 
+
+ align:start position:0%
+and when I say given it's either given
+like I did in the first part of this
+
+ align:start position:0%
+like I did in the first part of this
+ 
+
+ align:start position:0%
+like I did in the first part of this
+class at this course you know previous
+
+ align:start position:0%
+class at this course you know previous
+ 
+
+ align:start position:0%
+class at this course you know previous
+chapters or conditionally on right so
+
+ align:start position:0%
+chapters or conditionally on right so
+ 
+
+ align:start position:0%
+chapters or conditionally on right so
+that's assuring if you're thinking like
+
+ align:start position:0%
+that's assuring if you're thinking like
+ 
+
+ align:start position:0%
+that's assuring if you're thinking like
+a Bayesian that what I really mean is
+
+ align:start position:0%
+a Bayesian that what I really mean is
+ 
+
+ align:start position:0%
+a Bayesian that what I really mean is
+conditionally on this random parameter
+
+ align:start position:0%
+conditionally on this random parameter
+ 
+
+ align:start position:0%
+conditionally on this random parameter
+okay so it's like as if it was a fixed
+
+ align:start position:0%
+okay so it's like as if it was a fixed
+ 
+
+ align:start position:0%
+okay so it's like as if it was a fixed
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+then I'm gonna have they're gonna have
+
+ align:start position:0%
+then I'm gonna have they're gonna have
+ 
+
+ align:start position:0%
+then I'm gonna have they're gonna have
+the distribution x1 xn is gonna have
+
+ align:start position:0%
+the distribution x1 xn is gonna have
+ 
+
+ align:start position:0%
+the distribution x1 xn is gonna have
+some distribution let's say let's assume
+
+ align:start position:0%
+some distribution let's say let's assume
+ 
+
+ align:start position:0%
+some distribution let's say let's assume
+for now it's a PDF PN of X 1 xn okay and
+
+ align:start position:0%
+for now it's a PDF PN of X 1 xn okay and
+ 
+
+ align:start position:0%
+for now it's a PDF PN of X 1 xn okay and
+I'm gonna write theta like this so for
+
+ align:start position:0%
+I'm gonna write theta like this so for
+ 
+
+ align:start position:0%
+I'm gonna write theta like this so for
+example what is this well that's so
+
+ align:start position:0%
+example what is this well that's so
+ 
+
+ align:start position:0%
+example what is this well that's so
+that's it this is a PDF it could be a
+
+ align:start position:0%
+that's it this is a PDF it could be a
+ 
+
+ align:start position:0%
+that's it this is a PDF it could be a
+PMF everything I say I'm gonna think of
+
+ align:start position:0%
+PMF everything I say I'm gonna think of
+ 
+
+ align:start position:0%
+PMF everything I say I'm gonna think of
+them them as being PDFs I'm going to
+
+ align:start position:0%
+them them as being PDFs I'm going to
+ 
+
+ align:start position:0%
+them them as being PDFs I'm going to
+combine PDFs with PDF but I could
+
+ align:start position:0%
+combine PDFs with PDF but I could
+ 
+
+ align:start position:0%
+combine PDFs with PDF but I could
+combine PDF at pmf's PMF with PDFs or
+
+ align:start position:0%
+combine PDF at pmf's PMF with PDFs or
+ 
+
+ align:start position:0%
+combine PDF at pmf's PMF with PDFs or
+PMF with pms okay so everywhere you see
+
+ align:start position:0%
+PMF with pms okay so everywhere you see
+ 
+
+ align:start position:0%
+PMF with pms okay so everywhere you see
+a deed could be an M alright so now I
+
+ align:start position:0%
+a deed could be an M alright so now I
+ 
+
+ align:start position:0%
+a deed could be an M alright so now I
+have those things so what does that mean
+
+ align:start position:0%
+have those things so what does that mean
+ 
+
+ align:start position:0%
+have those things so what does that mean
+so here's some example X 1 xn are iid
+
+ align:start position:0%
+so here's some example X 1 xn are iid
+ 
+
+ align:start position:0%
+so here's some example X 1 xn are iid
+and theta 1 right so now I know exactly
+
+ align:start position:0%
+and theta 1 right so now I know exactly
+ 
+
+ align:start position:0%
+and theta 1 right so now I know exactly
+what the joint PDF of this thing is so
+
+ align:start position:0%
+what the joint PDF of this thing is so
+ 
+
+ align:start position:0%
+what the joint PDF of this thing is so
+it means that P n of X 1 X n given theta
+
+ align:start position:0%
+it means that P n of X 1 X n given theta
+ 
+
+ align:start position:0%
+it means that P n of X 1 X n given theta
+is equal to what well it's like 1 over
+
+ align:start position:0%
+is equal to what well it's like 1 over
+ 
+
+ align:start position:0%
+is equal to what well it's like 1 over
+Sigma root sorry 1 or 2 root 2 pi to the
+
+ align:start position:0%
+Sigma root sorry 1 or 2 root 2 pi to the
+ 
+
+ align:start position:0%
+Sigma root sorry 1 or 2 root 2 pi to the
+power n e to the minus sum from I equal
+
+ align:start position:0%
+power n e to the minus sum from I equal
+ 
+
+ align:start position:0%
+power n e to the minus sum from I equal
+1 to N of X I minus theta squared
+
+ align:start position:0%
+1 to N of X I minus theta squared
+ 
+
+ align:start position:0%
+1 to N of X I minus theta squared
+divided by 2 right so that's just the
+
+ align:start position:0%
+divided by 2 right so that's just the
+ 
+
+ align:start position:0%
+divided by 2 right so that's just the
+Joint Distribution of n iid and theta 1
+
+ align:start position:0%
+Joint Distribution of n iid and theta 1
+ 
+
+ align:start position:0%
+Joint Distribution of n iid and theta 1
+random variables ok so that's my pian
+
+ align:start position:0%
+random variables ok so that's my pian
+ 
+
+ align:start position:0%
+random variables ok so that's my pian
+given theta now this is what we denoted
+
+ align:start position:0%
+given theta now this is what we denoted
+ 
+
+ align:start position:0%
+given theta now this is what we denoted
+by sort of like f sub theta before right
+
+ align:start position:0%
+by sort of like f sub theta before right
+ 
+
+ align:start position:0%
+by sort of like f sub theta before right
+we had this subscript before but now we
+
+ align:start position:0%
+we had this subscript before but now we
+ 
+
+ align:start position:0%
+we had this subscript before but now we
+just put a bar in there because we want
+
+ align:start position:0%
+just put a bar in there because we want
+ 
+
+ align:start position:0%
+just put a bar in there because we want
+to remember that this is actually
+
+ align:start position:0%
+to remember that this is actually
+ 
+
+ align:start position:0%
+to remember that this is actually
+conditioned on theta right but this is
+
+ align:start position:0%
+conditioned on theta right but this is
+ 
+
+ align:start position:0%
+conditioned on theta right but this is
+just notation you should just think of
+
+ align:start position:0%
+just notation you should just think of
+ 
+
+ align:start position:0%
+just notation you should just think of
+this as being just the usual thing that
+
+ align:start position:0%
+this as being just the usual thing that
+ 
+
+ align:start position:0%
+this as being just the usual thing that
+you get from some statistical model all
+
+ align:start position:0%
+you get from some statistical model all
+ 
+
+ align:start position:0%
+you get from some statistical model all
+right so now that's going to be PN and
+
+ align:start position:0%
+right so now that's going to be PN and
+ 
+
+ align:start position:0%
+right so now that's going to be PN and
+here I'm going to assume that theta is
+
+ align:start position:0%
+here I'm going to assume that theta is
+ 
+
+ align:start position:0%
+here I'm going to assume that theta is
+why do I put PI here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so theta has prior distribution pi
+
+ align:start position:0%
+okay so theta has prior distribution pi
+ 
+
+ align:start position:0%
+okay so theta has prior distribution pi
+okay so for example so think of it as
+
+ align:start position:0%
+okay so for example so think of it as
+ 
+
+ align:start position:0%
+okay so for example so think of it as
+either PDF or PMF again so for example
+
+ align:start position:0%
+either PDF or PMF again so for example
+ 
+
+ align:start position:0%
+either PDF or PMF again so for example
+PI of theta was what well it was my it
+
+ align:start position:0%
+PI of theta was what well it was my it
+ 
+
+ align:start position:0%
+PI of theta was what well it was my it
+was some constant times theta to the a
+
+ align:start position:0%
+was some constant times theta to the a
+ 
+
+ align:start position:0%
+was some constant times theta to the a
+minus 1 1 minus theta to the a minus 1
+
+ align:start position:0%
+minus 1 1 minus theta to the a minus 1
+ 
+
+ align:start position:0%
+minus 1 1 minus theta to the a minus 1
+right so it has some prior distribution
+
+ align:start position:0%
+right so it has some prior distribution
+ 
+
+ align:start position:0%
+right so it has some prior distribution
+and that's another PMS so now I'm given
+
+ align:start position:0%
+and that's another PMS so now I'm given
+ 
+
+ align:start position:0%
+and that's another PMS so now I'm given
+the distribution of my X's given theta
+
+ align:start position:0%
+the distribution of my X's given theta
+ 
+
+ align:start position:0%
+the distribution of my X's given theta
+I'm given the distribution of my theta
+
+ align:start position:0%
+I'm given the distribution of my theta
+ 
+
+ align:start position:0%
+I'm given the distribution of my theta
+so I'm given this guy right
+
+ align:start position:0%
+so I'm given this guy right
+ 
+
+ align:start position:0%
+so I'm given this guy right
+that's this guy I'm given that guy which
+
+ align:start position:0%
+that's this guy I'm given that guy which
+ 
+
+ align:start position:0%
+that's this guy I'm given that guy which
+is my pi
+
+ align:start position:0%
+is my pi
+ 
+
+ align:start position:0%
+is my pi
+right so that's my PN of X 1 xn given
+
+ align:start position:0%
+right so that's my PN of X 1 xn given
+ 
+
+ align:start position:0%
+right so that's my PN of X 1 xn given
+theta
+
+ align:start position:0%
+theta
+ 
+
+ align:start position:0%
+theta
+that's my pi of theta and then I have
+
+ align:start position:0%
+that's my pi of theta and then I have
+ 
+
+ align:start position:0%
+that's my pi of theta and then I have
+here just this is what well this is just
+
+ align:start position:0%
+here just this is what well this is just
+ 
+
+ align:start position:0%
+here just this is what well this is just
+the integral of PN X 1 X n times pi of
+
+ align:start position:0%
+the integral of PN X 1 X n times pi of
+ 
+
+ align:start position:0%
+the integral of PN X 1 X n times pi of
+theta D theta right over all possible
+
+ align:start position:0%
+theta D theta right over all possible
+ 
+
+ align:start position:0%
+theta D theta right over all possible
+sets of theta that's just when I
+
+ align:start position:0%
+sets of theta that's just when I
+ 
+
+ align:start position:0%
+sets of theta that's just when I
+integrate out my theta or I compute say
+
+ align:start position:0%
+integrate out my theta or I compute say
+ 
+
+ align:start position:0%
+integrate out my theta or I compute say
+the marginal distribution I get this by
+
+ align:start position:0%
+the marginal distribution I get this by
+ 
+
+ align:start position:0%
+the marginal distribution I get this by
+integrating right that's just basic
+
+ align:start position:0%
+integrating right that's just basic
+ 
+
+ align:start position:0%
+integrating right that's just basic
+probability conditional probabilities
+
+ align:start position:0%
+probability conditional probabilities
+ 
+
+ align:start position:0%
+probability conditional probabilities
+all right then if I had the PMF I would
+
+ align:start position:0%
+all right then if I had the PMF I would
+ 
+
+ align:start position:0%
+all right then if I had the PMF I would
+just sum over the values of Thetas okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now what I want is to find what's
+
+ align:start position:0%
+so now what I want is to find what's
+ 
+
+ align:start position:0%
+so now what I want is to find what's
+called so that's the prior distribution
+
+ align:start position:0%
+called so that's the prior distribution
+ 
+
+ align:start position:0%
+called so that's the prior distribution
+that's the posterior and I want to find
+
+ align:start position:0%
+that's the posterior and I want to find
+ 
+
+ align:start position:0%
+that's the posterior and I want to find
+the posterior distribution so it's cool
+
+ align:start position:0%
+the posterior distribution so it's cool
+ 
+
+ align:start position:0%
+the posterior distribution so it's cool
+it's PI of theta given x1 xn and so if I
+
+ align:start position:0%
+it's PI of theta given x1 xn and so if I
+ 
+
+ align:start position:0%
+it's PI of theta given x1 xn and so if I
+use Bayes rule I know that this is PN of
+
+ align:start position:0%
+use Bayes rule I know that this is PN of
+ 
+
+ align:start position:0%
+use Bayes rule I know that this is PN of
+X 1 xn given theta times PI of theta and
+
+ align:start position:0%
+X 1 xn given theta times PI of theta and
+ 
+
+ align:start position:0%
+X 1 xn given theta times PI of theta and
+then divided by the distribution of
+
+ align:start position:0%
+then divided by the distribution of
+ 
+
+ align:start position:0%
+then divided by the distribution of
+those guys which I will write as
+
+ align:start position:0%
+those guys which I will write as
+ 
+
+ align:start position:0%
+those guys which I will write as
+integral over theta of PN X 1 xn given
+
+ align:start position:0%
+integral over theta of PN X 1 xn given
+ 
+
+ align:start position:0%
+integral over theta of PN X 1 xn given
+theta times Phi of theta and D theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody's with me still so if you're
+
+ align:start position:0%
+everybody's with me still so if you're
+ 
+
+ align:start position:0%
+everybody's with me still so if you're
+not comfortable with this isn't means
+
+ align:start position:0%
+not comfortable with this isn't means
+ 
+
+ align:start position:0%
+not comfortable with this isn't means
+that you probably need to go read your
+
+ align:start position:0%
+that you probably need to go read your
+ 
+
+ align:start position:0%
+that you probably need to go read your
+couple pages on conditional densities
+
+ align:start position:0%
+couple pages on conditional densities
+ 
+
+ align:start position:0%
+couple pages on conditional densities
+and conditional pmfs from your
+
+ align:start position:0%
+and conditional pmfs from your
+ 
+
+ align:start position:0%
+and conditional pmfs from your
+probability class there's really not
+
+ align:start position:0%
+probability class there's really not
+ 
+
+ align:start position:0%
+probability class there's really not
+much there it's just a matter of being
+
+ align:start position:0%
+much there it's just a matter of being
+ 
+
+ align:start position:0%
+much there it's just a matter of being
+able to define those quantities f
+
+ align:start position:0%
+able to define those quantities f
+ 
+
+ align:start position:0%
+able to define those quantities f
+density of X given Y this is just what's
+
+ align:start position:0%
+density of X given Y this is just what's
+ 
+
+ align:start position:0%
+density of X given Y this is just what's
+called a conditional density you need to
+
+ align:start position:0%
+called a conditional density you need to
+ 
+
+ align:start position:0%
+called a conditional density you need to
+understand what this object is and how
+
+ align:start position:0%
+understand what this object is and how
+ 
+
+ align:start position:0%
+understand what this object is and how
+it relates to the Joint Distribution of
+
+ align:start position:0%
+it relates to the Joint Distribution of
+ 
+
+ align:start position:0%
+it relates to the Joint Distribution of
+X and y or maybe the distribution of X
+
+ align:start position:0%
+X and y or maybe the distribution of X
+ 
+
+ align:start position:0%
+X and y or maybe the distribution of X
+for the distribution of Y but it's the
+
+ align:start position:0%
+for the distribution of Y but it's the
+ 
+
+ align:start position:0%
+for the distribution of Y but it's the
+same rules I mean one way to actually
+
+ align:start position:0%
+same rules I mean one way to actually
+ 
+
+ align:start position:0%
+same rules I mean one way to actually
+remember this is this is exactly the
+
+ align:start position:0%
+remember this is this is exactly the
+ 
+
+ align:start position:0%
+remember this is this is exactly the
+same rules as this when you see a bar
+
+ align:start position:0%
+same rules as this when you see a bar
+ 
+
+ align:start position:0%
+same rules as this when you see a bar
+it's the same thing as the probability
+
+ align:start position:0%
+it's the same thing as the probability
+ 
+
+ align:start position:0%
+it's the same thing as the probability
+of this end this guy so for densities
+
+ align:start position:0%
+of this end this guy so for densities
+ 
+
+ align:start position:0%
+of this end this guy so for densities
+it's just a comma divided by the by the
+
+ align:start position:0%
+it's just a comma divided by the by the
+ 
+
+ align:start position:0%
+it's just a comma divided by the by the
+second guy the probability of the second
+
+ align:start position:0%
+second guy the probability of the second
+ 
+
+ align:start position:0%
+second guy the probability of the second
+guy that's it all right so if you
+
+ align:start position:0%
+guy that's it all right so if you
+ 
+
+ align:start position:0%
+guy that's it all right so if you
+remember this you can just do some
+
+ align:start position:0%
+remember this you can just do some
+ 
+
+ align:start position:0%
+remember this you can just do some
+pattern matching and see what I just
+
+ align:start position:0%
+pattern matching and see what I just
+ 
+
+ align:start position:0%
+pattern matching and see what I just
+wrote here okay okay so now I can
+
+ align:start position:0%
+wrote here okay okay so now I can
+ 
+
+ align:start position:0%
+wrote here okay okay so now I can
+compute every single one of these guys
+
+ align:start position:0%
+compute every single one of these guys
+ 
+
+ align:start position:0%
+compute every single one of these guys
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's something I get from my modeling so
+
+ align:start position:0%
+it's something I get from my modeling so
+ 
+
+ align:start position:0%
+it's something I get from my modeling so
+I did not write this it's not written in
+
+ align:start position:0%
+I did not write this it's not written in
+ 
+
+ align:start position:0%
+I did not write this it's not written in
+in the slides but you know I give a name
+
+ align:start position:0%
+in the slides but you know I give a name
+ 
+
+ align:start position:0%
+in the slides but you know I give a name
+to this guy that was my prior
+
+ align:start position:0%
+to this guy that was my prior
+ 
+
+ align:start position:0%
+to this guy that was my prior
+distribution and that was my posterior
+
+ align:start position:0%
+distribution and that was my posterior
+ 
+
+ align:start position:0%
+distribution and that was my posterior
+distribution in the Quran chapter 3
+
+ align:start position:0%
+distribution in the Quran chapter 3
+ 
+
+ align:start position:0%
+distribution in the Quran chapter 3
+maybe what did we call this guy well the
+
+ align:start position:0%
+maybe what did we call this guy well the
+ 
+
+ align:start position:0%
+maybe what did we call this guy well the
+one that does not have a name and that's
+
+ align:start position:0%
+one that does not have a name and that's
+ 
+
+ align:start position:0%
+one that does not have a name and that's
+in the Box this guy how did we call it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is to join distribution of the excise
+
+ align:start position:0%
+it is to join distribution of the excise
+ 
+
+ align:start position:0%
+it is to join distribution of the excise
+and we give you the name
+
+ align:start position:0%
+and we give you the name
+ 
+
+ align:start position:0%
+and we give you the name
+it's the likelihood right this is
+
+ align:start position:0%
+it's the likelihood right this is
+ 
+
+ align:start position:0%
+it's the likelihood right this is
+exactly the likelihood this with the
+
+ align:start position:0%
+exactly the likelihood this with the
+ 
+
+ align:start position:0%
+exactly the likelihood this with the
+likelihood of theta and this is
+
+ align:start position:0%
+likelihood of theta and this is
+ 
+
+ align:start position:0%
+likelihood of theta and this is
+something that's very important to
+
+ align:start position:0%
+something that's very important to
+ 
+
+ align:start position:0%
+something that's very important to
+remember and that really reminds you
+
+ align:start position:0%
+remember and that really reminds you
+ 
+
+ align:start position:0%
+remember and that really reminds you
+that these things are really not that
+
+ align:start position:0%
+that these things are really not that
+ 
+
+ align:start position:0%
+that these things are really not that
+different maximum likelihood estimation
+
+ align:start position:0%
+different maximum likelihood estimation
+ 
+
+ align:start position:0%
+different maximum likelihood estimation
+Bayesian estimation because your
+
+ align:start position:0%
+Bayesian estimation because your
+ 
+
+ align:start position:0%
+Bayesian estimation because your
+posterior is really just your likelihood
+
+ align:start position:0%
+posterior is really just your likelihood
+ 
+
+ align:start position:0%
+posterior is really just your likelihood
+times something that's just putting some
+
+ align:start position:0%
+times something that's just putting some
+ 
+
+ align:start position:0%
+times something that's just putting some
+weights on the Thetas depending on where
+
+ align:start position:0%
+weights on the Thetas depending on where
+ 
+
+ align:start position:0%
+weights on the Thetas depending on where
+you think theta should be all right so
+
+ align:start position:0%
+you think theta should be all right so
+ 
+
+ align:start position:0%
+you think theta should be all right so
+if I had say maximum likelihood
+
+ align:start position:0%
+if I had say maximum likelihood
+ 
+
+ align:start position:0%
+if I had say maximum likelihood
+estimator and my likelihood until I look
+
+ align:start position:0%
+estimator and my likelihood until I look
+ 
+
+ align:start position:0%
+estimator and my likelihood until I look
+like this but my prior and theta looked
+
+ align:start position:0%
+like this but my prior and theta looked
+ 
+
+ align:start position:0%
+like this but my prior and theta looked
+like this I said oh I really want data
+
+ align:start position:0%
+like this I said oh I really want data
+ 
+
+ align:start position:0%
+like this I said oh I really want data
+sort of like this so what's gonna happen
+
+ align:start position:0%
+sort of like this so what's gonna happen
+ 
+
+ align:start position:0%
+sort of like this so what's gonna happen
+is that my I'm gonna turn this into some
+
+ align:start position:0%
+is that my I'm gonna turn this into some
+ 
+
+ align:start position:0%
+is that my I'm gonna turn this into some
+posterior that looks like this okay so
+
+ align:start position:0%
+posterior that looks like this okay so
+ 
+
+ align:start position:0%
+posterior that looks like this okay so
+I'm just really weighting this this
+
+ align:start position:0%
+I'm just really weighting this this
+ 
+
+ align:start position:0%
+I'm just really weighting this this
+posterior this is a constant that does
+
+ align:start position:0%
+posterior this is a constant that does
+ 
+
+ align:start position:0%
+posterior this is a constant that does
+not depend on theta right I agreed I
+
+ align:start position:0%
+not depend on theta right I agreed I
+ 
+
+ align:start position:0%
+not depend on theta right I agreed I
+integrated over theta so theta is going
+
+ align:start position:0%
+integrated over theta so theta is going
+ 
+
+ align:start position:0%
+integrated over theta so theta is going
+so forget about this guy I have
+
+ align:start position:0%
+so forget about this guy I have
+ 
+
+ align:start position:0%
+so forget about this guy I have
+basically that the posterior
+
+ align:start position:0%
+basically that the posterior
+ 
+
+ align:start position:0%
+basically that the posterior
+distribution of to scaling because it
+
+ align:start position:0%
+distribution of to scaling because it
+ 
+
+ align:start position:0%
+distribution of to scaling because it
+has to be a probability density and not
+
+ align:start position:0%
+has to be a probability density and not
+ 
+
+ align:start position:0%
+has to be a probability density and not
+just anything any function that's
+
+ align:start position:0%
+just anything any function that's
+ 
+
+ align:start position:0%
+just anything any function that's
+positive is the product of this guy it's
+
+ align:start position:0%
+positive is the product of this guy it's
+ 
+
+ align:start position:0%
+positive is the product of this guy it's
+a weighted version of my likelihood
+
+ align:start position:0%
+a weighted version of my likelihood
+ 
+
+ align:start position:0%
+a weighted version of my likelihood
+that's all it is
+
+ align:start position:0%
+that's all it is
+ 
+
+ align:start position:0%
+that's all it is
+I'm just waiting the
+
+ align:start position:0%
+I'm just waiting the
+ 
+
+ align:start position:0%
+I'm just waiting the
+hood using my prior belief in theta and
+
+ align:start position:0%
+hood using my prior belief in theta and
+ 
+
+ align:start position:0%
+hood using my prior belief in theta and
+so given this guy a natural estimator if
+
+ align:start position:0%
+so given this guy a natural estimator if
+ 
+
+ align:start position:0%
+so given this guy a natural estimator if
+you follow the maximum likelihood
+
+ align:start position:0%
+you follow the maximum likelihood
+ 
+
+ align:start position:0%
+you follow the maximum likelihood
+principle would be the maximum of this
+
+ align:start position:0%
+principle would be the maximum of this
+ 
+
+ align:start position:0%
+principle would be the maximum of this
+posterior agreed that would basically be
+
+ align:start position:0%
+posterior agreed that would basically be
+ 
+
+ align:start position:0%
+posterior agreed that would basically be
+doing exactly what maximum likelihood
+
+ align:start position:0%
+doing exactly what maximum likelihood
+ 
+
+ align:start position:0%
+doing exactly what maximum likelihood
+estimation is telling you so it turns
+
+ align:start position:0%
+estimation is telling you so it turns
+ 
+
+ align:start position:0%
+estimation is telling you so it turns
+out that you can
+
+ align:start position:0%
+out that you can
+ 
+
+ align:start position:0%
+out that you can
+it's called maximum a-posteriori and I
+
+ align:start position:0%
+it's called maximum a-posteriori and I
+ 
+
+ align:start position:0%
+it's called maximum a-posteriori and I
+won't talk much about this or map so
+
+ align:start position:0%
+won't talk much about this or map so
+ 
+
+ align:start position:0%
+won't talk much about this or map so
+that's maximum a-posteriori so it's just
+
+ align:start position:0%
+that's maximum a-posteriori so it's just
+ 
+
+ align:start position:0%
+that's maximum a-posteriori so it's just
+the theta hat is the org max of pi theta
+
+ align:start position:0%
+the theta hat is the org max of pi theta
+ 
+
+ align:start position:0%
+the theta hat is the org max of pi theta
+given X 1 xn it sounds like it's okay I
+
+ align:start position:0%
+given X 1 xn it sounds like it's okay I
+ 
+
+ align:start position:0%
+given X 1 xn it sounds like it's okay I
+give you a density and you say okay I
+
+ align:start position:0%
+give you a density and you say okay I
+ 
+
+ align:start position:0%
+give you a density and you say okay I
+have a density for all values of my
+
+ align:start position:0%
+have a density for all values of my
+ 
+
+ align:start position:0%
+have a density for all values of my
+parameters you're asking me to summarize
+
+ align:start position:0%
+parameters you're asking me to summarize
+ 
+
+ align:start position:0%
+parameters you're asking me to summarize
+it into one number I'm just gonna take
+
+ align:start position:0%
+it into one number I'm just gonna take
+ 
+
+ align:start position:0%
+it into one number I'm just gonna take
+the most likely number of those guys but
+
+ align:start position:0%
+the most likely number of those guys but
+ 
+
+ align:start position:0%
+the most likely number of those guys but
+you could summarize it otherwise you
+
+ align:start position:0%
+you could summarize it otherwise you
+ 
+
+ align:start position:0%
+you could summarize it otherwise you
+could take the average right you could
+
+ align:start position:0%
+could take the average right you could
+ 
+
+ align:start position:0%
+could take the average right you could
+take the median you could take a bunch
+
+ align:start position:0%
+take the median you could take a bunch
+ 
+
+ align:start position:0%
+take the median you could take a bunch
+of numbers and the beauty of Bayesian
+
+ align:start position:0%
+of numbers and the beauty of Bayesian
+ 
+
+ align:start position:0%
+of numbers and the beauty of Bayesian
+statistics is that you don't have to
+
+ align:start position:0%
+statistics is that you don't have to
+ 
+
+ align:start position:0%
+statistics is that you don't have to
+take any number in particular you have
+
+ align:start position:0%
+take any number in particular you have
+ 
+
+ align:start position:0%
+take any number in particular you have
+an entire posterior distribution this is
+
+ align:start position:0%
+an entire posterior distribution this is
+ 
+
+ align:start position:0%
+an entire posterior distribution this is
+not only telling you where theta is but
+
+ align:start position:0%
+not only telling you where theta is but
+ 
+
+ align:start position:0%
+not only telling you where theta is but
+it's actually telling you the difference
+
+ align:start position:0%
+it's actually telling you the difference
+ 
+
+ align:start position:0%
+it's actually telling you the difference
+if you actually give as a something it
+
+ align:start position:0%
+if you actually give as a something it
+ 
+
+ align:start position:0%
+if you actually give as a something it
+gives you the posterior right so now
+
+ align:start position:0%
+gives you the posterior right so now
+ 
+
+ align:start position:0%
+gives you the posterior right so now
+let's say the theta is a P between 0 & 1
+
+ align:start position:0%
+let's say the theta is a P between 0 & 1
+ 
+
+ align:start position:0%
+let's say the theta is a P between 0 & 1
+if my posterior distribution looks like
+
+ align:start position:0%
+if my posterior distribution looks like
+ 
+
+ align:start position:0%
+if my posterior distribution looks like
+this or if my posterior distribution
+
+ align:start position:0%
+this or if my posterior distribution
+ 
+
+ align:start position:0%
+this or if my posterior distribution
+looked like this then those two guys
+
+ align:start position:0%
+looked like this then those two guys
+ 
+
+ align:start position:0%
+looked like this then those two guys
+have one the same mode right this is the
+
+ align:start position:0%
+have one the same mode right this is the
+ 
+
+ align:start position:0%
+have one the same mode right this is the
+same value and they're symmetric so they
+
+ align:start position:0%
+same value and they're symmetric so they
+ 
+
+ align:start position:0%
+same value and they're symmetric so they
+also have the same mean so these two
+
+ align:start position:0%
+also have the same mean so these two
+ 
+
+ align:start position:0%
+also have the same mean so these two
+posterior distributions give me the same
+
+ align:start position:0%
+posterior distributions give me the same
+ 
+
+ align:start position:0%
+posterior distributions give me the same
+summary into one number however clearly
+
+ align:start position:0%
+summary into one number however clearly
+ 
+
+ align:start position:0%
+summary into one number however clearly
+one is much more confident than the
+
+ align:start position:0%
+one is much more confident than the
+ 
+
+ align:start position:0%
+one is much more confident than the
+other one so I might as well just spit
+
+ align:start position:0%
+other one so I might as well just spit
+ 
+
+ align:start position:0%
+other one so I might as well just spit
+that as a solution okay
+
+ align:start position:0%
+that as a solution okay
+ 
+
+ align:start position:0%
+that as a solution okay
+some people can you can do even better
+
+ align:start position:0%
+some people can you can do even better
+ 
+
+ align:start position:0%
+some people can you can do even better
+people actually do things such as
+
+ align:start position:0%
+people actually do things such as
+ 
+
+ align:start position:0%
+people actually do things such as
+drawing a random number from this
+
+ align:start position:0%
+drawing a random number from this
+ 
+
+ align:start position:0%
+drawing a random number from this
+distribution so this is my number well
+
+ align:start position:0%
+distribution so this is my number well
+ 
+
+ align:start position:0%
+distribution so this is my number well
+that's kind of adventurous but you can
+
+ align:start position:0%
+that's kind of adventurous but you can
+ 
+
+ align:start position:0%
+that's kind of adventurous but you can
+imagine you could do this right all
+
+ align:start position:0%
+imagine you could do this right all
+ 
+
+ align:start position:0%
+imagine you could do this right all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so this is what works that's what we
+
+ align:start position:0%
+so this is what works that's what we
+ 
+
+ align:start position:0%
+so this is what works that's what we
+went through so here is you notice I I
+
+ align:start position:0%
+went through so here is you notice I I
+ 
+
+ align:start position:0%
+went through so here is you notice I I
+don't care so much about this part here
+
+ align:start position:0%
+don't care so much about this part here
+ 
+
+ align:start position:0%
+don't care so much about this part here
+right because it does not depend on
+
+ align:start position:0%
+right because it does not depend on
+ 
+
+ align:start position:0%
+right because it does not depend on
+theta so it's not it's I know that given
+
+ align:start position:0%
+theta so it's not it's I know that given
+ 
+
+ align:start position:0%
+theta so it's not it's I know that given
+the product of those two things this
+
+ align:start position:0%
+the product of those two things this
+ 
+
+ align:start position:0%
+the product of those two things this
+thing is only the constant that I need
+
+ align:start position:0%
+thing is only the constant that I need
+ 
+
+ align:start position:0%
+thing is only the constant that I need
+to device that when I integrate this
+
+ align:start position:0%
+to device that when I integrate this
+ 
+
+ align:start position:0%
+to device that when I integrate this
+thing over theta it integrates to 1
+
+ align:start position:0%
+thing over theta it integrates to 1
+ 
+
+ align:start position:0%
+thing over theta it integrates to 1
+because this has to be a probability
+
+ align:start position:0%
+because this has to be a probability
+ 
+
+ align:start position:0%
+because this has to be a probability
+density on theta so I can write this and
+
+ align:start position:0%
+density on theta so I can write this and
+ 
+
+ align:start position:0%
+density on theta so I can write this and
+just forget about that part and that's
+
+ align:start position:0%
+just forget about that part and that's
+ 
+
+ align:start position:0%
+just forget about that part and that's
+what's really on the on the top of this
+
+ align:start position:0%
+what's really on the on the top of this
+ 
+
+ align:start position:0%
+what's really on the on the top of this
+line okay just this notation this sort
+
+ align:start position:0%
+line okay just this notation this sort
+ 
+
+ align:start position:0%
+line okay just this notation this sort
+of like weird alpha or I don't know
+
+ align:start position:0%
+of like weird alpha or I don't know
+ 
+
+ align:start position:0%
+of like weird alpha or I don't know
+infinity sign crop to the right whatever
+
+ align:start position:0%
+infinity sign crop to the right whatever
+ 
+
+ align:start position:0%
+infinity sign crop to the right whatever
+you want to call this this thing is
+
+ align:start position:0%
+you want to call this this thing is
+ 
+
+ align:start position:0%
+you want to call this this thing is
+actually just really emphasizing the
+
+ align:start position:0%
+actually just really emphasizing the
+ 
+
+ align:start position:0%
+actually just really emphasizing the
+fact that I don't care I write it
+
+ align:start position:0%
+fact that I don't care I write it
+ 
+
+ align:start position:0%
+fact that I don't care I write it
+because I mean yeah I write it because I
+
+ align:start position:0%
+because I mean yeah I write it because I
+ 
+
+ align:start position:0%
+because I mean yeah I write it because I
+can but and you know what it is but you
+
+ align:start position:0%
+can but and you know what it is but you
+ 
+
+ align:start position:0%
+can but and you know what it is but you
+don't actually have to well okay in some
+
+ align:start position:0%
+don't actually have to well okay in some
+ 
+
+ align:start position:0%
+don't actually have to well okay in some
+instances you have to compute the
+
+ align:start position:0%
+instances you have to compute the
+ 
+
+ align:start position:0%
+instances you have to compute the
+integral in some instances you don't
+
+ align:start position:0%
+integral in some instances you don't
+ 
+
+ align:start position:0%
+integral in some instances you don't
+have to compute the integral and a lot
+
+ align:start position:0%
+have to compute the integral and a lot
+ 
+
+ align:start position:0%
+have to compute the integral and a lot
+of Bayesian computation is about saying
+
+ align:start position:0%
+of Bayesian computation is about saying
+ 
+
+ align:start position:0%
+of Bayesian computation is about saying
+okay it's actually really hard to
+
+ align:start position:0%
+okay it's actually really hard to
+ 
+
+ align:start position:0%
+okay it's actually really hard to
+compute this integral so I'd rather not
+
+ align:start position:0%
+compute this integral so I'd rather not
+ 
+
+ align:start position:0%
+compute this integral so I'd rather not
+doing it so let me try to find some
+
+ align:start position:0%
+doing it so let me try to find some
+ 
+
+ align:start position:0%
+doing it so let me try to find some
+methods that allow me to sample from the
+
+ align:start position:0%
+methods that allow me to sample from the
+ 
+
+ align:start position:0%
+methods that allow me to sample from the
+posterior distribution without having to
+
+ align:start position:0%
+posterior distribution without having to
+ 
+
+ align:start position:0%
+posterior distribution without having to
+compute this and that's what's called
+
+ align:start position:0%
+compute this and that's what's called
+ 
+
+ align:start position:0%
+compute this and that's what's called
+Monte Carlo Markov chains or MCMC and
+
+ align:start position:0%
+Monte Carlo Markov chains or MCMC and
+ 
+
+ align:start position:0%
+Monte Carlo Markov chains or MCMC and
+that's exactly what they're doing
+
+ align:start position:0%
+that's exactly what they're doing
+ 
+
+ align:start position:0%
+that's exactly what they're doing
+they're just using only ratios of things
+
+ align:start position:0%
+they're just using only ratios of things
+ 
+
+ align:start position:0%
+they're just using only ratios of things
+like that for different datas and which
+
+ align:start position:0%
+like that for different datas and which
+ 
+
+ align:start position:0%
+like that for different datas and which
+means that if you take ratios the
+
+ align:start position:0%
+means that if you take ratios the
+ 
+
+ align:start position:0%
+means that if you take ratios the
+normalizing constant is going and you
+
+ align:start position:0%
+normalizing constant is going and you
+ 
+
+ align:start position:0%
+normalizing constant is going and you
+don't need to find this integral ok so
+
+ align:start position:0%
+don't need to find this integral ok so
+ 
+
+ align:start position:0%
+don't need to find this integral ok so
+we won't go into those details at all
+
+ align:start position:0%
+we won't go into those details at all
+ 
+
+ align:start position:0%
+we won't go into those details at all
+that would be the purpose of an entire
+
+ align:start position:0%
+that would be the purpose of an entire
+ 
+
+ align:start position:0%
+that would be the purpose of an entire
+course on Bayesian inference actually
+
+ align:start position:0%
+course on Bayesian inference actually
+ 
+
+ align:start position:0%
+course on Bayesian inference actually
+even Bayesian computations would be an
+
+ align:start position:0%
+even Bayesian computations would be an
+ 
+
+ align:start position:0%
+even Bayesian computations would be an
+entire course on its own and there's
+
+ align:start position:0%
+entire course on its own and there's
+ 
+
+ align:start position:0%
+entire course on its own and there's
+some very interesting things that are
+
+ align:start position:0%
+some very interesting things that are
+ 
+
+ align:start position:0%
+some very interesting things that are
+going on there the interface of stats
+
+ align:start position:0%
+going on there the interface of stats
+ 
+
+ align:start position:0%
+going on there the interface of stats
+and computation all right so let's go
+
+ align:start position:0%
+and computation all right so let's go
+ 
+
+ align:start position:0%
+and computation all right so let's go
+back to our example and see if we can
+
+ align:start position:0%
+back to our example and see if we can
+ 
+
+ align:start position:0%
+back to our example and see if we can
+actually compute any of those things
+
+ align:start position:0%
+actually compute any of those things
+ 
+
+ align:start position:0%
+actually compute any of those things
+because it's very nice to give you some
+
+ align:start position:0%
+because it's very nice to give you some
+ 
+
+ align:start position:0%
+because it's very nice to give you some
+data some formulas but you know let's
+
+ align:start position:0%
+data some formulas but you know let's
+ 
+
+ align:start position:0%
+data some formulas but you know let's
+see if we can actually do it all right
+
+ align:start position:0%
+see if we can actually do it all right
+ 
+
+ align:start position:0%
+see if we can actually do it all right
+that in particular can I actually
+
+ align:start position:0%
+that in particular can I actually
+ 
+
+ align:start position:0%
+that in particular can I actually
+recover this claim that the posterior
+
+ align:start position:0%
+recover this claim that the posterior
+ 
+
+ align:start position:0%
+recover this claim that the posterior
+associated to a burn to a beta prior
+
+ align:start position:0%
+associated to a burn to a beta prior
+ 
+
+ align:start position:0%
+associated to a burn to a beta prior
+with Burnley
+
+ align:start position:0%
+with Burnley
+ 
+
+ align:start position:0%
+with Burnley
+likelihood is actually giving me a beta
+
+ align:start position:0%
+likelihood is actually giving me a beta
+ 
+
+ align:start position:0%
+likelihood is actually giving me a beta
+again all right so what was my prior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well it was beta so P was following a
+
+ align:start position:0%
+well it was beta so P was following a
+ 
+
+ align:start position:0%
+well it was beta so P was following a
+beta a a which means that P the density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that was PI of theta well I'm gonna
+
+ align:start position:0%
+so that was PI of theta well I'm gonna
+ 
+
+ align:start position:0%
+so that was PI of theta well I'm gonna
+write it as Phi of Phi of P was
+
+ align:start position:0%
+write it as Phi of Phi of P was
+ 
+
+ align:start position:0%
+write it as Phi of Phi of P was
+proportional to P to the a minus 1 times
+
+ align:start position:0%
+proportional to P to the a minus 1 times
+ 
+
+ align:start position:0%
+proportional to P to the a minus 1 times
+1 minus P to the a minus 1 right so
+
+ align:start position:0%
+1 minus P to the a minus 1 right so
+ 
+
+ align:start position:0%
+1 minus P to the a minus 1 right so
+that's the first ingredient I need to
+
+ align:start position:0%
+that's the first ingredient I need to
+ 
+
+ align:start position:0%
+that's the first ingredient I need to
+compute my posterior I really need only
+
+ align:start position:0%
+compute my posterior I really need only
+ 
+
+ align:start position:0%
+compute my posterior I really need only
+two if I want it about up to constant
+
+ align:start position:0%
+two if I want it about up to constant
+ 
+
+ align:start position:0%
+two if I want it about up to constant
+the second one was PA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we've computed that many times and
+
+ align:start position:0%
+well we've computed that many times and
+ 
+
+ align:start position:0%
+well we've computed that many times and
+we had even a nice compact way of
+
+ align:start position:0%
+we had even a nice compact way of
+ 
+
+ align:start position:0%
+we had even a nice compact way of
+writing it which was that PN of X 1 xn
+
+ align:start position:0%
+writing it which was that PN of X 1 xn
+ 
+
+ align:start position:0%
+writing it which was that PN of X 1 xn
+given a parameter P right so the density
+
+ align:start position:0%
+given a parameter P right so the density
+ 
+
+ align:start position:0%
+given a parameter P right so the density
+the joint density of my data given P
+
+ align:start position:0%
+the joint density of my data given P
+ 
+
+ align:start position:0%
+the joint density of my data given P
+that's my likelihood the likelihood of P
+
+ align:start position:0%
+that's my likelihood the likelihood of P
+ 
+
+ align:start position:0%
+that's my likelihood the likelihood of P
+was what well it was P to the some of
+
+ align:start position:0%
+was what well it was P to the some of
+ 
+
+ align:start position:0%
+was what well it was P to the some of
+the excise 1 minus P to the N minus some
+
+ align:start position:0%
+the excise 1 minus P to the N minus some
+ 
+
+ align:start position:0%
+the excise 1 minus P to the N minus some
+of the excise anybody wants me to parse
+
+ align:start position:0%
+of the excise anybody wants me to parse
+ 
+
+ align:start position:0%
+of the excise anybody wants me to parse
+this more or do you remember seeing that
+
+ align:start position:0%
+this more or do you remember seeing that
+ 
+
+ align:start position:0%
+this more or do you remember seeing that
+from maximum likelihood estimation yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's what conditioning does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so deep I of T is a measure
+
+ align:start position:0%
+okay so deep I of T is a measure
+ 
+
+ align:start position:0%
+okay so deep I of T is a measure
+theoretic notation which I use without
+
+ align:start position:0%
+theoretic notation which I use without
+ 
+
+ align:start position:0%
+theoretic notation which I use without
+thinking and I should not because I can
+
+ align:start position:0%
+thinking and I should not because I can
+ 
+
+ align:start position:0%
+thinking and I should not because I can
+see yeah that's you D PI of T is just a
+
+ align:start position:0%
+see yeah that's you D PI of T is just a
+ 
+
+ align:start position:0%
+see yeah that's you D PI of T is just a
+natural way to say that I integrate
+
+ align:start position:0%
+natural way to say that I integrate
+ 
+
+ align:start position:0%
+natural way to say that I integrate
+against whatever and given for the the
+
+ align:start position:0%
+against whatever and given for the the
+ 
+
+ align:start position:0%
+against whatever and given for the the
+prior of theta in particular if theta is
+
+ align:start position:0%
+prior of theta in particular if theta is
+ 
+
+ align:start position:0%
+prior of theta in particular if theta is
+just the mix of a PDF and a point mass
+
+ align:start position:0%
+just the mix of a PDF and a point mass
+ 
+
+ align:start position:0%
+just the mix of a PDF and a point mass
+right maybe I say that my P takes value
+
+ align:start position:0%
+right maybe I say that my P takes value
+ 
+
+ align:start position:0%
+right maybe I say that my P takes value
+0.5 with probability 0.5 and then is
+
+ align:start position:0%
+0.5 with probability 0.5 and then is
+ 
+
+ align:start position:0%
+0.5 with probability 0.5 and then is
+uniform on the interval with probability
+
+ align:start position:0%
+uniform on the interval with probability
+ 
+
+ align:start position:0%
+uniform on the interval with probability
+0.5 okay so for this I neither have a
+
+ align:start position:0%
+0.5 okay so for this I neither have a
+ 
+
+ align:start position:0%
+0.5 okay so for this I neither have a
+PDF nor a PMF but I can still talk about
+
+ align:start position:0%
+PDF nor a PMF but I can still talk about
+ 
+
+ align:start position:0%
+PDF nor a PMF but I can still talk about
+integrating with respect to this right
+
+ align:start position:0%
+integrating with respect to this right
+ 
+
+ align:start position:0%
+integrating with respect to this right
+it's going to look like if I take a
+
+ align:start position:0%
+it's going to look like if I take a
+ 
+
+ align:start position:0%
+it's going to look like if I take a
+function f of T D PI of T is going to be
+
+ align:start position:0%
+function f of T D PI of T is going to be
+ 
+
+ align:start position:0%
+function f of T D PI of T is going to be
+one-half of F 1/2 right that's the point
+
+ align:start position:0%
+one-half of F 1/2 right that's the point
+ 
+
+ align:start position:0%
+one-half of F 1/2 right that's the point
+mass with probability one half at one
+
+ align:start position:0%
+mass with probability one half at one
+ 
+
+ align:start position:0%
+mass with probability one half at one
+half plus one half of the integral
+
+ align:start position:0%
+half plus one half of the integral
+ 
+
+ align:start position:0%
+half plus one half of the integral
+between 0 and 1 of F of T DT alright so
+
+ align:start position:0%
+between 0 and 1 of F of T DT alright so
+ 
+
+ align:start position:0%
+between 0 and 1 of F of T DT alright so
+this is just a notation which is
+
+ align:start position:0%
+this is just a notation which is
+ 
+
+ align:start position:0%
+this is just a notation which is
+actually internally enough is
+
+ align:start position:0%
+actually internally enough is
+ 
+
+ align:start position:0%
+actually internally enough is
+interchangeable with PI of DT but if you
+
+ align:start position:0%
+interchangeable with PI of DT but if you
+ 
+
+ align:start position:0%
+interchangeable with PI of DT but if you
+have a density it's really just the
+
+ align:start position:0%
+have a density it's really just the
+ 
+
+ align:start position:0%
+have a density it's really just the
+density PI of T DT if I is really a
+
+ align:start position:0%
+density PI of T DT if I is really a
+ 
+
+ align:start position:0%
+density PI of T DT if I is really a
+density but that's when it's when PI is
+
+ align:start position:0%
+density but that's when it's when PI is
+ 
+
+ align:start position:0%
+density but that's when it's when PI is
+a measure in other density but so
+
+ align:start position:0%
+a measure in other density but so
+ 
+
+ align:start position:0%
+a measure in other density but so
+everybody else forget about this I mean
+
+ align:start position:0%
+everybody else forget about this I mean
+ 
+
+ align:start position:0%
+everybody else forget about this I mean
+this is not something you should really
+
+ align:start position:0%
+this is not something you should really
+ 
+
+ align:start position:0%
+this is not something you should really
+worry about at this point this is more
+
+ align:start position:0%
+worry about at this point this is more
+ 
+
+ align:start position:0%
+worry about at this point this is more
+graduate-level probability classes but
+
+ align:start position:0%
+graduate-level probability classes but
+ 
+
+ align:start position:0%
+graduate-level probability classes but
+yet school major theory and that's when
+
+ align:start position:0%
+yet school major theory and that's when
+ 
+
+ align:start position:0%
+yet school major theory and that's when
+you think of PI as being a measure in an
+
+ align:start position:0%
+you think of PI as being a measure in an
+ 
+
+ align:start position:0%
+you think of PI as being a measure in an
+abstract fashion you'll have to worry
+
+ align:start position:0%
+abstract fashion you'll have to worry
+ 
+
+ align:start position:0%
+abstract fashion you'll have to worry
+whether it's a density or not whether it
+
+ align:start position:0%
+whether it's a density or not whether it
+ 
+
+ align:start position:0%
+whether it's a density or not whether it
+has a density even ok
+
+ align:start position:0%
+has a density even ok
+ 
+
+ align:start position:0%
+has a density even ok
+so everybody's okay with this all right
+
+ align:start position:0%
+so everybody's okay with this all right
+ 
+
+ align:start position:0%
+so everybody's okay with this all right
+so now I need to compute my posterior
+
+ align:start position:0%
+so now I need to compute my posterior
+ 
+
+ align:start position:0%
+so now I need to compute my posterior
+and as I said my posterior is really
+
+ align:start position:0%
+and as I said my posterior is really
+ 
+
+ align:start position:0%
+and as I said my posterior is really
+just a product of the likelihood
+
+ align:start position:0%
+just a product of the likelihood
+ 
+
+ align:start position:0%
+just a product of the likelihood
+weighted by the prior right so hopefully
+
+ align:start position:0%
+weighted by the prior right so hopefully
+ 
+
+ align:start position:0%
+weighted by the prior right so hopefully
+by at this stage of your education you
+
+ align:start position:0%
+by at this stage of your education you
+ 
+
+ align:start position:0%
+by at this stage of your education you
+can multiply two functions alright so
+
+ align:start position:0%
+can multiply two functions alright so
+ 
+
+ align:start position:0%
+can multiply two functions alright so
+what's happening is if I multiply this
+
+ align:start position:0%
+what's happening is if I multiply this
+ 
+
+ align:start position:0%
+what's happening is if I multiply this
+guy with this guy well P gets this guy
+
+ align:start position:0%
+guy with this guy well P gets this guy
+ 
+
+ align:start position:0%
+guy with this guy well P gets this guy
+to the power this guy plus this guy and
+
+ align:start position:0%
+to the power this guy plus this guy and
+ 
+
+ align:start position:0%
+to the power this guy plus this guy and
+then 1 minus P gets the power n minus
+
+ align:start position:0%
+then 1 minus P gets the power n minus
+ 
+
+ align:start position:0%
+then 1 minus P gets the power n minus
+some of Excise so this is always from I
+
+ align:start position:0%
+some of Excise so this is always from I
+ 
+
+ align:start position:0%
+some of Excise so this is always from I
+equal 1 to N and then plus a minus 1 as
+
+ align:start position:0%
+equal 1 to N and then plus a minus 1 as
+ 
+
+ align:start position:0%
+equal 1 to N and then plus a minus 1 as
+well okay and this is sorry this is up
+
+ align:start position:0%
+well okay and this is sorry this is up
+ 
+
+ align:start position:0%
+well okay and this is sorry this is up
+to constant because I still need to
+
+ align:start position:0%
+to constant because I still need to
+ 
+
+ align:start position:0%
+to constant because I still need to
+solve this and I could try to do it but
+
+ align:start position:0%
+solve this and I could try to do it but
+ 
+
+ align:start position:0%
+solve this and I could try to do it but
+I really don't have to because I know
+
+ align:start position:0%
+I really don't have to because I know
+ 
+
+ align:start position:0%
+I really don't have to because I know
+that if my density has this form then
+
+ align:start position:0%
+that if my density has this form then
+ 
+
+ align:start position:0%
+that if my density has this form then
+it's a beta distribution and then I can
+
+ align:start position:0%
+it's a beta distribution and then I can
+ 
+
+ align:start position:0%
+it's a beta distribution and then I can
+just go in Wikipedia and see what should
+
+ align:start position:0%
+just go in Wikipedia and see what should
+ 
+
+ align:start position:0%
+just go in Wikipedia and see what should
+be the normalization factor but I know
+
+ align:start position:0%
+be the normalization factor but I know
+ 
+
+ align:start position:0%
+be the normalization factor but I know
+it's going to be a beta distribution
+
+ align:start position:0%
+it's going to be a beta distribution
+ 
+
+ align:start position:0%
+it's going to be a beta distribution
+it's actually the beta with parameter so
+
+ align:start position:0%
+it's actually the beta with parameter so
+ 
+
+ align:start position:0%
+it's actually the beta with parameter so
+this is really my beta with parameter
+
+ align:start position:0%
+this is really my beta with parameter
+ 
+
+ align:start position:0%
+this is really my beta with parameter
+sum of X I I equal 1 to N plus a minus 1
+
+ align:start position:0%
+sum of X I I equal 1 to N plus a minus 1
+ 
+
+ align:start position:0%
+sum of X I I equal 1 to N plus a minus 1
+and then the second parameter is n minus
+
+ align:start position:0%
+and then the second parameter is n minus
+ 
+
+ align:start position:0%
+and then the second parameter is n minus
+sum of the x i's plus a minus 1 ok sorry
+
+ align:start position:0%
+sum of the x i's plus a minus 1 ok sorry
+ 
+
+ align:start position:0%
+sum of the x i's plus a minus 1 ok sorry
+I just wrote what was here Oh what
+
+ align:start position:0%
+I just wrote what was here Oh what
+ 
+
+ align:start position:0%
+I just wrote what was here Oh what
+happened to my 1 oh no sorry sorry sorry
+
+ align:start position:0%
+happened to my 1 oh no sorry sorry sorry
+ 
+
+ align:start position:0%
+happened to my 1 oh no sorry sorry sorry
+beta has the power minus 1 right so
+
+ align:start position:0%
+beta has the power minus 1 right so
+ 
+
+ align:start position:0%
+beta has the power minus 1 right so
+that's that's the parameter of the beta
+
+ align:start position:0%
+that's that's the parameter of the beta
+ 
+
+ align:start position:0%
+that's that's the parameter of the beta
+and this is the parameter of the beta
+
+ align:start position:0%
+and this is the parameter of the beta
+ 
+
+ align:start position:0%
+and this is the parameter of the beta
+right so beta well I don't think it's
+
+ align:start position:0%
+right so beta well I don't think it's
+ 
+
+ align:start position:0%
+right so beta well I don't think it's
+anywhere yeah beta is over there right
+
+ align:start position:0%
+anywhere yeah beta is over there right
+ 
+
+ align:start position:0%
+anywhere yeah beta is over there right
+so I just replaced a by what I see is
+
+ align:start position:0%
+so I just replaced a by what I see is
+ 
+
+ align:start position:0%
+so I just replaced a by what I see is
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+this guy plus this guy in this guy push
+
+ align:start position:0%
+this guy plus this guy in this guy push
+ 
+
+ align:start position:0%
+this guy plus this guy in this guy push
+this guy everybody's comfortable with
+
+ align:start position:0%
+this guy everybody's comfortable with
+ 
+
+ align:start position:0%
+this guy everybody's comfortable with
+this competition all right so we just
+
+ align:start position:0%
+this competition all right so we just
+ 
+
+ align:start position:0%
+this competition all right so we just
+agreed that beta priors for Burnley
+
+ align:start position:0%
+agreed that beta priors for Burnley
+ 
+
+ align:start position:0%
+agreed that beta priors for Burnley
+observations are certainly convenient
+
+ align:start position:0%
+observations are certainly convenient
+ 
+
+ align:start position:0%
+observations are certainly convenient
+right and because they're just
+
+ align:start position:0%
+right and because they're just
+ 
+
+ align:start position:0%
+right and because they're just
+conjugated and we know that's what's
+
+ align:start position:0%
+conjugated and we know that's what's
+ 
+
+ align:start position:0%
+conjugated and we know that's what's
+gonna come out in the end that's gonna
+
+ align:start position:0%
+gonna come out in the end that's gonna
+ 
+
+ align:start position:0%
+gonna come out in the end that's gonna
+be a beta as well so I mean you know I
+
+ align:start position:0%
+be a beta as well so I mean you know I
+ 
+
+ align:start position:0%
+be a beta as well so I mean you know I
+just claimed it was convenient
+
+ align:start position:0%
+just claimed it was convenient
+ 
+
+ align:start position:0%
+just claimed it was convenient
+it was certainly convenient to compute
+
+ align:start position:0%
+it was certainly convenient to compute
+ 
+
+ align:start position:0%
+it was certainly convenient to compute
+this right I mean there was some
+
+ align:start position:0%
+this right I mean there was some
+ 
+
+ align:start position:0%
+this right I mean there was some
+certainly some compatibility when I had
+
+ align:start position:0%
+certainly some compatibility when I had
+ 
+
+ align:start position:0%
+certainly some compatibility when I had
+to multiply this function by that
+
+ align:start position:0%
+to multiply this function by that
+ 
+
+ align:start position:0%
+to multiply this function by that
+function and you can imagine that things
+
+ align:start position:0%
+function and you can imagine that things
+ 
+
+ align:start position:0%
+function and you can imagine that things
+could go much more wrong than just
+
+ align:start position:0%
+could go much more wrong than just
+ 
+
+ align:start position:0%
+could go much more wrong than just
+having P to some power and Peterson
+
+ align:start position:0%
+having P to some power and Peterson
+ 
+
+ align:start position:0%
+having P to some power and Peterson
+power one minus P to some power when I
+
+ align:start position:0%
+power one minus P to some power when I
+ 
+
+ align:start position:0%
+power one minus P to some power when I
+just be to some other power things were
+
+ align:start position:0%
+just be to some other power things were
+ 
+
+ align:start position:0%
+just be to some other power things were
+nice now this is nice but they can also
+
+ align:start position:0%
+nice now this is nice but they can also
+ 
+
+ align:start position:0%
+nice now this is nice but they can also
+question the following things
+
+ align:start position:0%
+question the following things
+ 
+
+ align:start position:0%
+question the following things
+why beta for one I mean the beta tells
+
+ align:start position:0%
+why beta for one I mean the beta tells
+ 
+
+ align:start position:0%
+why beta for one I mean the beta tells
+me something but you know that's
+
+ align:start position:0%
+me something but you know that's
+ 
+
+ align:start position:0%
+me something but you know that's
+convenient but then how do I pick a I
+
+ align:start position:0%
+convenient but then how do I pick a I
+ 
+
+ align:start position:0%
+convenient but then how do I pick a I
+know that a should definitely capture
+
+ align:start position:0%
+know that a should definitely capture
+ 
+
+ align:start position:0%
+know that a should definitely capture
+the fact that I want where I want to
+
+ align:start position:0%
+the fact that I want where I want to
+ 
+
+ align:start position:0%
+the fact that I want where I want to
+have my P most likely located but it
+
+ align:start position:0%
+have my P most likely located but it
+ 
+
+ align:start position:0%
+have my P most likely located but it
+also actually it also captures the
+
+ align:start position:0%
+also actually it also captures the
+ 
+
+ align:start position:0%
+also actually it also captures the
+variance of my beta and so choosing
+
+ align:start position:0%
+variance of my beta and so choosing
+ 
+
+ align:start position:0%
+variance of my beta and so choosing
+different A's is gonna have different
+
+ align:start position:0%
+different A's is gonna have different
+ 
+
+ align:start position:0%
+different A's is gonna have different
+functions if I have a and B if I started
+
+ align:start position:0%
+functions if I have a and B if I started
+ 
+
+ align:start position:0%
+functions if I have a and B if I started
+with the beta with parameter if here I
+
+ align:start position:0%
+with the beta with parameter if here I
+ 
+
+ align:start position:0%
+with the beta with parameter if here I
+started with a B here I would just pick
+
+ align:start position:0%
+started with a B here I would just pick
+ 
+
+ align:start position:0%
+started with a B here I would just pick
+up the be here agreed and that would
+
+ align:start position:0%
+up the be here agreed and that would
+ 
+
+ align:start position:0%
+up the be here agreed and that would
+just be a symmetric but they're gonna
+
+ align:start position:0%
+just be a symmetric but they're gonna
+ 
+
+ align:start position:0%
+just be a symmetric but they're gonna
+capture mean and variance of this thing
+
+ align:start position:0%
+capture mean and variance of this thing
+ 
+
+ align:start position:0%
+capture mean and variance of this thing
+and so how do I pick those guys right I
+
+ align:start position:0%
+and so how do I pick those guys right I
+ 
+
+ align:start position:0%
+and so how do I pick those guys right I
+mean if I'm a doctor and I'm you're
+
+ align:start position:0%
+mean if I'm a doctor and I'm you're
+ 
+
+ align:start position:0%
+mean if I'm a doctor and I'm you're
+asking me what do you think the chances
+
+ align:start position:0%
+asking me what do you think the chances
+ 
+
+ align:start position:0%
+asking me what do you think the chances
+of this drug working and this kind of
+
+ align:start position:0%
+of this drug working and this kind of
+ 
+
+ align:start position:0%
+of this drug working and this kind of
+patients is and I have to say to speed
+
+ align:start position:0%
+patients is and I have to say to speed
+ 
+
+ align:start position:0%
+patients is and I have to say to speed
+up the parameters of a beta for you it
+
+ align:start position:0%
+up the parameters of a beta for you it
+ 
+
+ align:start position:0%
+up the parameters of a beta for you it
+might be a bit of a complicated thing to
+
+ align:start position:0%
+might be a bit of a complicated thing to
+ 
+
+ align:start position:0%
+might be a bit of a complicated thing to
+do so how do you do this especially for
+
+ align:start position:0%
+do so how do you do this especially for
+ 
+
+ align:start position:0%
+do so how do you do this especially for
+problems so by now people have actually
+
+ align:start position:0%
+problems so by now people have actually
+ 
+
+ align:start position:0%
+problems so by now people have actually
+you know found mastered the art of
+
+ align:start position:0%
+you know found mastered the art of
+ 
+
+ align:start position:0%
+you know found mastered the art of
+coming up with you know what how to
+
+ align:start position:0%
+coming up with you know what how to
+ 
+
+ align:start position:0%
+coming up with you know what how to
+formulate those numbers but in new
+
+ align:start position:0%
+formulate those numbers but in new
+ 
+
+ align:start position:0%
+formulate those numbers but in new
+problems that come up how do you do this
+
+ align:start position:0%
+problems that come up how do you do this
+ 
+
+ align:start position:0%
+problems that come up how do you do this
+what do you happens if you want to use
+
+ align:start position:0%
+what do you happens if you want to use
+ 
+
+ align:start position:0%
+what do you happens if you want to use
+Bayesian methods but you actually do not
+
+ align:start position:0%
+Bayesian methods but you actually do not
+ 
+
+ align:start position:0%
+Bayesian methods but you actually do not
+know what you expect to see maybe this
+
+ align:start position:0%
+know what you expect to see maybe this
+ 
+
+ align:start position:0%
+know what you expect to see maybe this
+is the first time you I mean to be fair
+
+ align:start position:0%
+is the first time you I mean to be fair
+ 
+
+ align:start position:0%
+is the first time you I mean to be fair
+before we started this class I hope all
+
+ align:start position:0%
+before we started this class I hope all
+ 
+
+ align:start position:0%
+before we started this class I hope all
+of you had no idea whether people 10th
+
+ align:start position:0%
+of you had no idea whether people 10th
+ 
+
+ align:start position:0%
+of you had no idea whether people 10th
+to bend their head to the right or to
+
+ align:start position:0%
+to bend their head to the right or to
+ 
+
+ align:start position:0%
+to bend their head to the right or to
+the left before kissing because if you
+
+ align:start position:0%
+the left before kissing because if you
+ 
+
+ align:start position:0%
+the left before kissing because if you
+did well you have too much time on your
+
+ align:start position:0%
+did well you have too much time on your
+ 
+
+ align:start position:0%
+did well you have too much time on your
+hand and I should double your homework
+
+ align:start position:0%
+hand and I should double your homework
+ 
+
+ align:start position:0%
+hand and I should double your homework
+and so in this case you have to sort of
+
+ align:start position:0%
+and so in this case you have to sort of
+ 
+
+ align:start position:0%
+and so in this case you have to sort of
+maybe you still want to use the Bayesian
+
+ align:start position:0%
+maybe you still want to use the Bayesian
+ 
+
+ align:start position:0%
+maybe you still want to use the Bayesian
+machinery maybe you just want to do
+
+ align:start position:0%
+machinery maybe you just want to do
+ 
+
+ align:start position:0%
+machinery maybe you just want to do
+something nice it's nice right I mean it
+
+ align:start position:0%
+something nice it's nice right I mean it
+ 
+
+ align:start position:0%
+something nice it's nice right I mean it
+worked out pretty well and so what if
+
+ align:start position:0%
+worked out pretty well and so what if
+ 
+
+ align:start position:0%
+worked out pretty well and so what if
+you want to do well you actually want to
+
+ align:start position:0%
+you want to do well you actually want to
+ 
+
+ align:start position:0%
+you want to do well you actually want to
+use some priors that have no carry no
+
+ align:start position:0%
+use some priors that have no carry no
+ 
+
+ align:start position:0%
+use some priors that have no carry no
+information that basically do not prefer
+
+ align:start position:0%
+information that basically do not prefer
+ 
+
+ align:start position:0%
+information that basically do not prefer
+any theta to another theta now you could
+
+ align:start position:0%
+any theta to another theta now you could
+ 
+
+ align:start position:0%
+any theta to another theta now you could
+read this slide or you could look at
+
+ align:start position:0%
+read this slide or you could look at
+ 
+
+ align:start position:0%
+read this slide or you could look at
+this formula we just said that this pi
+
+ align:start position:0%
+this formula we just said that this pi
+ 
+
+ align:start position:0%
+this formula we just said that this pi
+here was just here to weigh some
+
+ align:start position:0%
+here was just here to weigh some
+ 
+
+ align:start position:0%
+here was just here to weigh some
+theaters more than others depending on
+
+ align:start position:0%
+theaters more than others depending on
+ 
+
+ align:start position:0%
+theaters more than others depending on
+our prior belief if our prior belief
+
+ align:start position:0%
+our prior belief if our prior belief
+ 
+
+ align:start position:0%
+our prior belief if our prior belief
+does not want to put any preference
+
+ align:start position:0%
+does not want to put any preference
+ 
+
+ align:start position:0%
+does not want to put any preference
+towards some Thetas than to others what
+
+ align:start position:0%
+towards some Thetas than to others what
+ 
+
+ align:start position:0%
+towards some Thetas than to others what
+do I do
+
+ align:start position:0%
+do I do
+ 
+
+ align:start position:0%
+do I do
+yeah I remove it and the way to remove
+
+ align:start position:0%
+yeah I remove it and the way to remove
+ 
+
+ align:start position:0%
+yeah I remove it and the way to remove
+something with x is just replace it by
+
+ align:start position:0%
+something with x is just replace it by
+ 
+
+ align:start position:0%
+something with x is just replace it by
+one that's really what we're doing right
+
+ align:start position:0%
+one that's really what we're doing right
+ 
+
+ align:start position:0%
+one that's really what we're doing right
+so if this was a constant and not
+
+ align:start position:0%
+so if this was a constant and not
+ 
+
+ align:start position:0%
+so if this was a constant and not
+depending on theta then that would mean
+
+ align:start position:0%
+depending on theta then that would mean
+ 
+
+ align:start position:0%
+depending on theta then that would mean
+that we're not preferring any theta and
+
+ align:start position:0%
+that we're not preferring any theta and
+ 
+
+ align:start position:0%
+that we're not preferring any theta and
+we're looking sort of the likely I'd add
+
+ align:start position:0%
+we're looking sort of the likely I'd add
+ 
+
+ align:start position:0%
+we're looking sort of the likely I'd add
+the likelihood but not as a function
+
+ align:start position:0%
+the likelihood but not as a function
+ 
+
+ align:start position:0%
+the likelihood but not as a function
+that we're trying to maximize but as a
+
+ align:start position:0%
+that we're trying to maximize but as a
+ 
+
+ align:start position:0%
+that we're trying to maximize but as a
+function that we normalize in such a way
+
+ align:start position:0%
+function that we normalize in such a way
+ 
+
+ align:start position:0%
+function that we normalize in such a way
+that it's actually a distribution so if
+
+ align:start position:0%
+that it's actually a distribution so if
+ 
+
+ align:start position:0%
+that it's actually a distribution so if
+I have Pi which is not here this is
+
+ align:start position:0%
+I have Pi which is not here this is
+ 
+
+ align:start position:0%
+I have Pi which is not here this is
+really just taking the lag field which
+
+ align:start position:0%
+really just taking the lag field which
+ 
+
+ align:start position:0%
+really just taking the lag field which
+is a positive function may not integrate
+
+ align:start position:0%
+is a positive function may not integrate
+ 
+
+ align:start position:0%
+is a positive function may not integrate
+to one so I normalize it so that it
+
+ align:start position:0%
+to one so I normalize it so that it
+ 
+
+ align:start position:0%
+to one so I normalize it so that it
+integrates to 1 and then I just say well
+
+ align:start position:0%
+integrates to 1 and then I just say well
+ 
+
+ align:start position:0%
+integrates to 1 and then I just say well
+this is my posterior distribution now I
+
+ align:start position:0%
+this is my posterior distribution now I
+ 
+
+ align:start position:0%
+this is my posterior distribution now I
+could just maximize this thing and spit
+
+ align:start position:0%
+could just maximize this thing and spit
+ 
+
+ align:start position:0%
+could just maximize this thing and spit
+out my maximum likelihood estimator but
+
+ align:start position:0%
+out my maximum likelihood estimator but
+ 
+
+ align:start position:0%
+out my maximum likelihood estimator but
+now I can also integrate and find what
+
+ align:start position:0%
+now I can also integrate and find what
+ 
+
+ align:start position:0%
+now I can also integrate and find what
+the expectation of this guy is I can
+
+ align:start position:0%
+the expectation of this guy is I can
+ 
+
+ align:start position:0%
+the expectation of this guy is I can
+find what the median if this guy is I
+
+ align:start position:0%
+find what the median if this guy is I
+ 
+
+ align:start position:0%
+find what the median if this guy is I
+can sample data from this guy I can
+
+ align:start position:0%
+can sample data from this guy I can
+ 
+
+ align:start position:0%
+can sample data from this guy I can
+build you know understand what the
+
+ align:start position:0%
+build you know understand what the
+ 
+
+ align:start position:0%
+build you know understand what the
+variance of this guy is which is
+
+ align:start position:0%
+variance of this guy is which is
+ 
+
+ align:start position:0%
+variance of this guy is which is
+something we did not do when we just did
+
+ align:start position:0%
+something we did not do when we just did
+ 
+
+ align:start position:0%
+something we did not do when we just did
+maximum likelihood estimation because
+
+ align:start position:0%
+maximum likelihood estimation because
+ 
+
+ align:start position:0%
+maximum likelihood estimation because
+given a function all we cared about was
+
+ align:start position:0%
+given a function all we cared about was
+ 
+
+ align:start position:0%
+given a function all we cared about was
+the maximum of the arc max of this
+
+ align:start position:0%
+the maximum of the arc max of this
+ 
+
+ align:start position:0%
+the maximum of the arc max of this
+function okay so if you knew this this
+
+ align:start position:0%
+function okay so if you knew this this
+ 
+
+ align:start position:0%
+function okay so if you knew this this
+that priors are called uninformative all
+
+ align:start position:0%
+that priors are called uninformative all
+ 
+
+ align:start position:0%
+that priors are called uninformative all
+right so this is just replacing this
+
+ align:start position:0%
+right so this is just replacing this
+ 
+
+ align:start position:0%
+right so this is just replacing this
+number by one and if I have a or by a
+
+ align:start position:0%
+number by one and if I have a or by a
+ 
+
+ align:start position:0%
+number by one and if I have a or by a
+constant right because it still has to
+
+ align:start position:0%
+constant right because it still has to
+ 
+
+ align:start position:0%
+constant right because it still has to
+be a density and so if I have something
+
+ align:start position:0%
+be a density and so if I have something
+ 
+
+ align:start position:0%
+be a density and so if I have something
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+if I have a ballot said I'm just looking
+
+ align:start position:0%
+if I have a ballot said I'm just looking
+ 
+
+ align:start position:0%
+if I have a ballot said I'm just looking
+for the uniform distribution on this
+
+ align:start position:0%
+for the uniform distribution on this
+ 
+
+ align:start position:0%
+for the uniform distribution on this
+ballot set the one that puts constant 1
+
+ align:start position:0%
+ballot set the one that puts constant 1
+ 
+
+ align:start position:0%
+ballot set the one that puts constant 1
+over the size of this thing but if I
+
+ align:start position:0%
+over the size of this thing but if I
+ 
+
+ align:start position:0%
+over the size of this thing but if I
+have an invalid set what is what is the
+
+ align:start position:0%
+have an invalid set what is what is the
+ 
+
+ align:start position:0%
+have an invalid set what is what is the
+density that takes a constant value on
+
+ align:start position:0%
+density that takes a constant value on
+ 
+
+ align:start position:0%
+density that takes a constant value on
+the entire real line for example what is
+
+ align:start position:0%
+the entire real line for example what is
+ 
+
+ align:start position:0%
+the entire real line for example what is
+this density doesn't exist right I mean
+
+ align:start position:0%
+this density doesn't exist right I mean
+ 
+
+ align:start position:0%
+this density doesn't exist right I mean
+it just doesn't exist I mean you know
+
+ align:start position:0%
+it just doesn't exist I mean you know
+ 
+
+ align:start position:0%
+it just doesn't exist I mean you know
+you the way you can think of it is a
+
+ align:start position:0%
+you the way you can think of it is a
+ 
+
+ align:start position:0%
+you the way you can think of it is a
+Gaussian with the variance going to
+
+ align:start position:0%
+Gaussian with the variance going to
+ 
+
+ align:start position:0%
+Gaussian with the variance going to
+infinity maybe or something like this
+
+ align:start position:0%
+infinity maybe or something like this
+ 
+
+ align:start position:0%
+infinity maybe or something like this
+but you can think of it in many ways you
+
+ align:start position:0%
+but you can think of it in many ways you
+ 
+
+ align:start position:0%
+but you can think of it in many ways you
+can think of the limit of the uniform
+
+ align:start position:0%
+can think of the limit of the uniform
+ 
+
+ align:start position:0%
+can think of the limit of the uniform
+between minus T and T with T going to
+
+ align:start position:0%
+between minus T and T with T going to
+ 
+
+ align:start position:0%
+between minus T and T with T going to
+infinity but this thing is actually zero
+
+ align:start position:0%
+infinity but this thing is actually zero
+ 
+
+ align:start position:0%
+infinity but this thing is actually zero
+right I mean there's there's nothing
+
+ align:start position:0%
+right I mean there's there's nothing
+ 
+
+ align:start position:0%
+right I mean there's there's nothing
+there and so when you're you can
+
+ align:start position:0%
+there and so when you're you can
+ 
+
+ align:start position:0%
+there and so when you're you can
+actually still talk about this right you
+
+ align:start position:0%
+actually still talk about this right you
+ 
+
+ align:start position:0%
+actually still talk about this right you
+could always talk about this thing where
+
+ align:start position:0%
+could always talk about this thing where
+ 
+
+ align:start position:0%
+could always talk about this thing where
+you think of this guy as being a
+
+ align:start position:0%
+you think of this guy as being a
+ 
+
+ align:start position:0%
+you think of this guy as being a
+constant remove this thing from this
+
+ align:start position:0%
+constant remove this thing from this
+ 
+
+ align:start position:0%
+constant remove this thing from this
+equation and just say well my posterior
+
+ align:start position:0%
+equation and just say well my posterior
+ 
+
+ align:start position:0%
+equation and just say well my posterior
+is just the likelihood divided by the
+
+ align:start position:0%
+is just the likelihood divided by the
+ 
+
+ align:start position:0%
+is just the likelihood divided by the
+integral of the likelihood over theta
+
+ align:start position:0%
+integral of the likelihood over theta
+ 
+
+ align:start position:0%
+integral of the likelihood over theta
+and if theta is the entire real line so
+
+ align:start position:0%
+and if theta is the entire real line so
+ 
+
+ align:start position:0%
+and if theta is the entire real line so
+be it as long as this integral converges
+
+ align:start position:0%
+be it as long as this integral converges
+ 
+
+ align:start position:0%
+be it as long as this integral converges
+you can still talk about this stuff and
+
+ align:start position:0%
+you can still talk about this stuff and
+ 
+
+ align:start position:0%
+you can still talk about this stuff and
+so this is what's called an improper
+
+ align:start position:0%
+so this is what's called an improper
+ 
+
+ align:start position:0%
+so this is what's called an improper
+prior right that improper prior is just
+
+ align:start position:0%
+prior right that improper prior is just
+ 
+
+ align:start position:0%
+prior right that improper prior is just
+a down- function the final data but it
+
+ align:start position:0%
+a down- function the final data but it
+ 
+
+ align:start position:0%
+a down- function the final data but it
+does not have to integrate neither to
+
+ align:start position:0%
+does not have to integrate neither to
+ 
+
+ align:start position:0%
+does not have to integrate neither to
+one nor to anything okay it does not
+
+ align:start position:0%
+one nor to anything okay it does not
+ 
+
+ align:start position:0%
+one nor to anything okay it does not
+have to right if I integrate the
+
+ align:start position:0%
+have to right if I integrate the
+ 
+
+ align:start position:0%
+have to right if I integrate the
+function equal to one on the entire real
+
+ align:start position:0%
+function equal to one on the entire real
+ 
+
+ align:start position:0%
+function equal to one on the entire real
+line what do I get infinity right I mean
+
+ align:start position:0%
+line what do I get infinity right I mean
+ 
+
+ align:start position:0%
+line what do I get infinity right I mean
+it's not it's not a proper integral and
+
+ align:start position:0%
+it's not it's not a proper integral and
+ 
+
+ align:start position:0%
+it's not it's not a proper integral and
+so it's not a proper prior it's called
+
+ align:start position:0%
+so it's not a proper prior it's called
+ 
+
+ align:start position:0%
+so it's not a proper prior it's called
+an improper prior and those improper
+
+ align:start position:0%
+an improper prior and those improper
+ 
+
+ align:start position:0%
+an improper prior and those improper
+priors are usually what you see when you
+
+ align:start position:0%
+priors are usually what you see when you
+ 
+
+ align:start position:0%
+priors are usually what you see when you
+start to want non informative priors on
+
+ align:start position:0%
+start to want non informative priors on
+ 
+
+ align:start position:0%
+start to want non informative priors on
+infinite sets Thetas I mean that's just
+
+ align:start position:0%
+infinite sets Thetas I mean that's just
+ 
+
+ align:start position:0%
+infinite sets Thetas I mean that's just
+the nature of it it's just you should
+
+ align:start position:0%
+the nature of it it's just you should
+ 
+
+ align:start position:0%
+the nature of it it's just you should
+think of it as being the uniform prior
+
+ align:start position:0%
+think of it as being the uniform prior
+ 
+
+ align:start position:0%
+think of it as being the uniform prior
+and some infinite the uniform
+
+ align:start position:0%
+and some infinite the uniform
+ 
+
+ align:start position:0%
+and some infinite the uniform
+distribution and some infinite set if
+
+ align:start position:0%
+distribution and some infinite set if
+ 
+
+ align:start position:0%
+distribution and some infinite set if
+that thing were to exist okay so let's
+
+ align:start position:0%
+that thing were to exist okay so let's
+ 
+
+ align:start position:0%
+that thing were to exist okay so let's
+see some examples about non informative
+
+ align:start position:0%
+see some examples about non informative
+ 
+
+ align:start position:0%
+see some examples about non informative
+priors right so if I'm on the uniform if
+
+ align:start position:0%
+priors right so if I'm on the uniform if
+ 
+
+ align:start position:0%
+priors right so if I'm on the uniform if
+I'm on the inter
+
+ align:start position:0%
+I'm on the inter
+ 
+
+ align:start position:0%
+I'm on the inter
+zero-one this is a finite set so I can
+
+ align:start position:0%
+zero-one this is a finite set so I can
+ 
+
+ align:start position:0%
+zero-one this is a finite set so I can
+talk about the uniform prior and the
+
+ align:start position:0%
+talk about the uniform prior and the
+ 
+
+ align:start position:0%
+talk about the uniform prior and the
+interval 0 1 for prouder PE of a
+
+ align:start position:0%
+interval 0 1 for prouder PE of a
+ 
+
+ align:start position:0%
+interval 0 1 for prouder PE of a
+Bernoulli okay and so so if I want to if
+
+ align:start position:0%
+Bernoulli okay and so so if I want to if
+ 
+
+ align:start position:0%
+Bernoulli okay and so so if I want to if
+I want to talk about this then it means
+
+ align:start position:0%
+I want to talk about this then it means
+ 
+
+ align:start position:0%
+I want to talk about this then it means
+that my prior is P follows some uniform
+
+ align:start position:0%
+that my prior is P follows some uniform
+ 
+
+ align:start position:0%
+that my prior is P follows some uniform
+on the interval 0 1 ok so that means
+
+ align:start position:0%
+on the interval 0 1 ok so that means
+ 
+
+ align:start position:0%
+on the interval 0 1 ok so that means
+that the density is well f of X is 1
+
+ align:start position:0%
+that the density is well f of X is 1
+ 
+
+ align:start position:0%
+that the density is well f of X is 1
+if X is in 0 1 and 0 otherwise there's
+
+ align:start position:0%
+if X is in 0 1 and 0 otherwise there's
+ 
+
+ align:start position:0%
+if X is in 0 1 and 0 otherwise there's
+actually not even a normalization this
+
+ align:start position:0%
+actually not even a normalization this
+ 
+
+ align:start position:0%
+actually not even a normalization this
+thing integrates to 1 and so now if I
+
+ align:start position:0%
+thing integrates to 1 and so now if I
+ 
+
+ align:start position:0%
+thing integrates to 1 and so now if I
+look at my likelihood it's still the
+
+ align:start position:0%
+look at my likelihood it's still the
+ 
+
+ align:start position:0%
+look at my likelihood it's still the
+same thing so my posterior becomes theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X 1 X n so that's my posterior I don't
+
+ align:start position:0%
+X 1 X n so that's my posterior I don't
+ 
+
+ align:start position:0%
+X 1 X n so that's my posterior I don't
+write the likelihood again because we
+
+ align:start position:0%
+write the likelihood again because we
+ 
+
+ align:start position:0%
+write the likelihood again because we
+still have it here well we don't have it
+
+ align:start position:0%
+still have it here well we don't have it
+ 
+
+ align:start position:0%
+still have it here well we don't have it
+there anymore is it here how did I just
+
+ align:start position:0%
+there anymore is it here how did I just
+ 
+
+ align:start position:0%
+there anymore is it here how did I just
+do it
+
+ align:start position:0%
+do it
+ 
+
+ align:start position:0%
+do it
+yeah the likelihood is given here all
+
+ align:start position:0%
+yeah the likelihood is given here all
+ 
+
+ align:start position:0%
+yeah the likelihood is given here all
+right so copy-paste over there and so
+
+ align:start position:0%
+right so copy-paste over there and so
+ 
+
+ align:start position:0%
+right so copy-paste over there and so
+the posterior is just this thing times 1
+
+ align:start position:0%
+the posterior is just this thing times 1
+ 
+
+ align:start position:0%
+the posterior is just this thing times 1
+so you will see it in a second so it's P
+
+ align:start position:0%
+so you will see it in a second so it's P
+ 
+
+ align:start position:0%
+so you will see it in a second so it's P
+times the sum to the power some of the
+
+ align:start position:0%
+times the sum to the power some of the
+ 
+
+ align:start position:0%
+times the sum to the power some of the
+excise 1 minus P to the power n minus
+
+ align:start position:0%
+excise 1 minus P to the power n minus
+ 
+
+ align:start position:0%
+excise 1 minus P to the power n minus
+some of the excise and then it's like
+
+ align:start position:0%
+some of the excise and then it's like
+ 
+
+ align:start position:0%
+some of the excise and then it's like
+multiplied by 1 and then divided by this
+
+ align:start position:0%
+multiplied by 1 and then divided by this
+ 
+
+ align:start position:0%
+multiplied by 1 and then divided by this
+integral between 0 and 1 of P some of
+
+ align:start position:0%
+integral between 0 and 1 of P some of
+ 
+
+ align:start position:0%
+integral between 0 and 1 of P some of
+the excise one minus P n minus some of
+
+ align:start position:0%
+the excise one minus P n minus some of
+ 
+
+ align:start position:0%
+the excise one minus P n minus some of
+the excise D P which does not depend on
+
+ align:start position:0%
+the excise D P which does not depend on
+ 
+
+ align:start position:0%
+the excise D P which does not depend on
+P and I really don't care what this
+
+ align:start position:0%
+P and I really don't care what this
+ 
+
+ align:start position:0%
+P and I really don't care what this
+thing actually is okay so now sorry
+
+ align:start position:0%
+thing actually is okay so now sorry
+ 
+
+ align:start position:0%
+thing actually is okay so now sorry
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+prior posterior of C of P and now I can
+
+ align:start position:0%
+prior posterior of C of P and now I can
+ 
+
+ align:start position:0%
+prior posterior of C of P and now I can
+see well what is this well it's actually
+
+ align:start position:0%
+see well what is this well it's actually
+ 
+
+ align:start position:0%
+see well what is this well it's actually
+just the beta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with parameters this guy plus one and
+
+ align:start position:0%
+with parameters this guy plus one and
+ 
+
+ align:start position:0%
+with parameters this guy plus one and
+this guy plus one so I didn't tell you
+
+ align:start position:0%
+this guy plus one so I didn't tell you
+ 
+
+ align:start position:0%
+this guy plus one so I didn't tell you
+what the expectation of a beta was right
+
+ align:start position:0%
+what the expectation of a beta was right
+ 
+
+ align:start position:0%
+what the expectation of a beta was right
+we don't know what the expectation of a
+
+ align:start position:0%
+we don't know what the expectation of a
+ 
+
+ align:start position:0%
+we don't know what the expectation of a
+beta is agreed I mean if I wanted to
+
+ align:start position:0%
+beta is agreed I mean if I wanted to
+ 
+
+ align:start position:0%
+beta is agreed I mean if I wanted to
+find say the expectation of this thing
+
+ align:start position:0%
+find say the expectation of this thing
+ 
+
+ align:start position:0%
+find say the expectation of this thing
+that would be some good estimator we
+
+ align:start position:0%
+that would be some good estimator we
+ 
+
+ align:start position:0%
+that would be some good estimator we
+know that the maximum of this guy what
+
+ align:start position:0%
+know that the maximum of this guy what
+ 
+
+ align:start position:0%
+know that the maximum of this guy what
+is the maximum of this thing oh it's
+
+ align:start position:0%
+is the maximum of this thing oh it's
+ 
+
+ align:start position:0%
+is the maximum of this thing oh it's
+just this thing right I mean it's the
+
+ align:start position:0%
+just this thing right I mean it's the
+ 
+
+ align:start position:0%
+just this thing right I mean it's the
+average of the excise right that's just
+
+ align:start position:0%
+average of the excise right that's just
+ 
+
+ align:start position:0%
+average of the excise right that's just
+the maximum likelihood estimator for
+
+ align:start position:0%
+the maximum likelihood estimator for
+ 
+
+ align:start position:0%
+the maximum likelihood estimator for
+burning we know it's the average do you
+
+ align:start position:0%
+burning we know it's the average do you
+ 
+
+ align:start position:0%
+burning we know it's the average do you
+think if I take the expectation of this
+
+ align:start position:0%
+think if I take the expectation of this
+ 
+
+ align:start position:0%
+think if I take the expectation of this
+thing I'm going to get the average
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so actually I'm not gonna get the
+
+ align:start position:0%
+so actually I'm not gonna get the
+ 
+
+ align:start position:0%
+so actually I'm not gonna get the
+average I'm gonna get this guy plus this
+
+ align:start position:0%
+average I'm gonna get this guy plus this
+ 
+
+ align:start position:0%
+average I'm gonna get this guy plus this
+guy divided by n plus one so I'm gonna
+
+ align:start position:0%
+guy divided by n plus one so I'm gonna
+ 
+
+ align:start position:0%
+guy divided by n plus one so I'm gonna
+do as if I had sorry okay let me not say
+
+ align:start position:0%
+do as if I had sorry okay let me not say
+ 
+
+ align:start position:0%
+do as if I had sorry okay let me not say
+it like that let's look at what this
+
+ align:start position:0%
+it like that let's look at what this
+ 
+
+ align:start position:0%
+it like that let's look at what this
+thing is doing it's looking at the
+
+ align:start position:0%
+thing is doing it's looking at the
+ 
+
+ align:start position:0%
+thing is doing it's looking at the
+number of zeros it's in the number of
+
+ align:start position:0%
+number of zeros it's in the number of
+ 
+
+ align:start position:0%
+number of zeros it's in the number of
+ones and it's adding one and this guy is
+
+ align:start position:0%
+ones and it's adding one and this guy is
+ 
+
+ align:start position:0%
+ones and it's adding one and this guy is
+looking at the number of zeros and it's
+
+ align:start position:0%
+looking at the number of zeros and it's
+ 
+
+ align:start position:0%
+looking at the number of zeros and it's
+adding one okay why is it adding this
+
+ align:start position:0%
+adding one okay why is it adding this
+ 
+
+ align:start position:0%
+adding one okay why is it adding this
+one what's going on here
+
+ align:start position:0%
+one what's going on here
+ 
+
+ align:start position:0%
+one what's going on here
+well what would happen if I had so this
+
+ align:start position:0%
+well what would happen if I had so this
+ 
+
+ align:start position:0%
+well what would happen if I had so this
+actually is going to matter mostly when
+
+ align:start position:0%
+actually is going to matter mostly when
+ 
+
+ align:start position:0%
+actually is going to matter mostly when
+the number of ones is actually zero or
+
+ align:start position:0%
+the number of ones is actually zero or
+ 
+
+ align:start position:0%
+the number of ones is actually zero or
+the number of zeros is zero because what
+
+ align:start position:0%
+the number of zeros is zero because what
+ 
+
+ align:start position:0%
+the number of zeros is zero because what
+it does is just pushes the zero from non
+
+ align:start position:0%
+it does is just pushes the zero from non
+ 
+
+ align:start position:0%
+it does is just pushes the zero from non
+zero and why is that something that this
+
+ align:start position:0%
+zero and why is that something that this
+ 
+
+ align:start position:0%
+zero and why is that something that this
+vision method actually does for you
+
+ align:start position:0%
+vision method actually does for you
+ 
+
+ align:start position:0%
+vision method actually does for you
+automatically is because when we put
+
+ align:start position:0%
+automatically is because when we put
+ 
+
+ align:start position:0%
+automatically is because when we put
+this non-affirmative prior on P which
+
+ align:start position:0%
+this non-affirmative prior on P which
+ 
+
+ align:start position:0%
+this non-affirmative prior on P which
+was uniform on the interval 0 1 in
+
+ align:start position:0%
+was uniform on the interval 0 1 in
+ 
+
+ align:start position:0%
+was uniform on the interval 0 1 in
+particular we know that the probability
+
+ align:start position:0%
+particular we know that the probability
+ 
+
+ align:start position:0%
+particular we know that the probability
+that P is equal to 0 is 0 and the
+
+ align:start position:0%
+that P is equal to 0 is 0 and the
+ 
+
+ align:start position:0%
+that P is equal to 0 is 0 and the
+probability P is equal to 1 is 0 and so
+
+ align:start position:0%
+probability P is equal to 1 is 0 and so
+ 
+
+ align:start position:0%
+probability P is equal to 1 is 0 and so
+the problem is that essentially if I did
+
+ align:start position:0%
+the problem is that essentially if I did
+ 
+
+ align:start position:0%
+the problem is that essentially if I did
+not add this one with some positive
+
+ align:start position:0%
+not add this one with some positive
+ 
+
+ align:start position:0%
+not add this one with some positive
+probability it would be allowed to spit
+
+ align:start position:0%
+probability it would be allowed to spit
+ 
+
+ align:start position:0%
+probability it would be allowed to spit
+out something that actually had had P
+
+ align:start position:0%
+out something that actually had had P
+ 
+
+ align:start position:0%
+out something that actually had had P
+hat which was equal to 0 in the case if
+
+ align:start position:0%
+hat which was equal to 0 in the case if
+ 
+
+ align:start position:0%
+hat which was equal to 0 in the case if
+by chance let's say I have n is equal to
+
+ align:start position:0%
+by chance let's say I have n is equal to
+ 
+
+ align:start position:0%
+by chance let's say I have n is equal to
+3 and I get only 0 0 0 right that could
+
+ align:start position:0%
+3 and I get only 0 0 0 right that could
+ 
+
+ align:start position:0%
+3 and I get only 0 0 0 right that could
+happen with probability 1 over P cubed 1
+
+ align:start position:0%
+happen with probability 1 over P cubed 1
+ 
+
+ align:start position:0%
+happen with probability 1 over P cubed 1
+over 1 minus P Q sorry 1 minus P cube
+
+ align:start position:0%
+over 1 minus P Q sorry 1 minus P cube
+ 
+
+ align:start position:0%
+over 1 minus P Q sorry 1 minus P cube
+then this thing is just gonna not that's
+
+ align:start position:0%
+then this thing is just gonna not that's
+ 
+
+ align:start position:0%
+then this thing is just gonna not that's
+not something that I want and I'm
+
+ align:start position:0%
+not something that I want and I'm
+ 
+
+ align:start position:0%
+not something that I want and I'm
+actually using my prior so my prayer is
+
+ align:start position:0%
+actually using my prior so my prayer is
+ 
+
+ align:start position:0%
+actually using my prior so my prayer is
+not infirmities but somehow it captures
+
+ align:start position:0%
+not infirmities but somehow it captures
+ 
+
+ align:start position:0%
+not infirmities but somehow it captures
+the fact that I don't want to believe
+
+ align:start position:0%
+the fact that I don't want to believe
+ 
+
+ align:start position:0%
+the fact that I don't want to believe
+that P is gonna be either equal to 0 1
+
+ align:start position:0%
+that P is gonna be either equal to 0 1
+ 
+
+ align:start position:0%
+that P is gonna be either equal to 0 1
+okay and so that's sort of taken care of
+
+ align:start position:0%
+okay and so that's sort of taken care of
+ 
+
+ align:start position:0%
+okay and so that's sort of taken care of
+here okay so let's move away a little
+
+ align:start position:0%
+here okay so let's move away a little
+ 
+
+ align:start position:0%
+here okay so let's move away a little
+bit from the birnley example shall we I
+
+ align:start position:0%
+bit from the birnley example shall we I
+ 
+
+ align:start position:0%
+bit from the birnley example shall we I
+mean we think we've seen enough of it
+
+ align:start position:0%
+mean we think we've seen enough of it
+ 
+
+ align:start position:0%
+mean we think we've seen enough of it
+and so let's talk about the Gaussian
+
+ align:start position:0%
+and so let's talk about the Gaussian
+ 
+
+ align:start position:0%
+and so let's talk about the Gaussian
+model right let's say I want to do
+
+ align:start position:0%
+model right let's say I want to do
+ 
+
+ align:start position:0%
+model right let's say I want to do
+Gaussian inference in the in the I want
+
+ align:start position:0%
+Gaussian inference in the in the I want
+ 
+
+ align:start position:0%
+Gaussian inference in the in the I want
+to do inference in a Gaussian model
+
+ align:start position:0%
+to do inference in a Gaussian model
+ 
+
+ align:start position:0%
+to do inference in a Gaussian model
+using Bayesian methods okay so I'm gonna
+
+ align:start position:0%
+using Bayesian methods okay so I'm gonna
+ 
+
+ align:start position:0%
+using Bayesian methods okay so I'm gonna
+actually look at so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what I want is that X I X 1 X n
+
+ align:start position:0%
+okay so what I want is that X I X 1 X n
+ 
+
+ align:start position:0%
+okay so what I want is that X I X 1 X n
+or say and 0 1 idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry theta 1
+
+ align:start position:0%
+sorry theta 1
+ 
+
+ align:start position:0%
+sorry theta 1
+iid conditionally on theta ok so that
+
+ align:start position:0%
+iid conditionally on theta ok so that
+ 
+
+ align:start position:0%
+iid conditionally on theta ok so that
+means that PN of X 1 X n given theta is
+
+ align:start position:0%
+means that PN of X 1 X n given theta is
+ 
+
+ align:start position:0%
+means that PN of X 1 X n given theta is
+equal to well exactly what I wrote
+
+ align:start position:0%
+equal to well exactly what I wrote
+ 
+
+ align:start position:0%
+equal to well exactly what I wrote
+before so 1 square root 2 pi to the N
+
+ align:start position:0%
+before so 1 square root 2 pi to the N
+ 
+
+ align:start position:0%
+before so 1 square root 2 pi to the N
+exponential minus 1/2 sum of X I minus
+
+ align:start position:0%
+exponential minus 1/2 sum of X I minus
+ 
+
+ align:start position:0%
+exponential minus 1/2 sum of X I minus
+theta squared ok so that's just the
+
+ align:start position:0%
+theta squared ok so that's just the
+ 
+
+ align:start position:0%
+theta squared ok so that's just the
+Joint Distribution of my end Gaussian
+
+ align:start position:0%
+Joint Distribution of my end Gaussian
+ 
+
+ align:start position:0%
+Joint Distribution of my end Gaussian
+with mean theta and now the question is
+
+ align:start position:0%
+with mean theta and now the question is
+ 
+
+ align:start position:0%
+with mean theta and now the question is
+what is the posterior distribution okay
+
+ align:start position:0%
+what is the posterior distribution okay
+ 
+
+ align:start position:0%
+what is the posterior distribution okay
+well here I said let's use the
+
+ align:start position:0%
+well here I said let's use the
+ 
+
+ align:start position:0%
+well here I said let's use the
+uninformative prior which is an improper
+
+ align:start position:0%
+uninformative prior which is an improper
+ 
+
+ align:start position:0%
+uninformative prior which is an improper
+prior right it puts weight 1 on every
+
+ align:start position:0%
+prior right it puts weight 1 on every
+ 
+
+ align:start position:0%
+prior right it puts weight 1 on every
+one that's the so-called uniform on the
+
+ align:start position:0%
+one that's the so-called uniform on the
+ 
+
+ align:start position:0%
+one that's the so-called uniform on the
+entire real line so that's certainly not
+
+ align:start position:0%
+entire real line so that's certainly not
+ 
+
+ align:start position:0%
+entire real line so that's certainly not
+a density but I can still just use this
+
+ align:start position:0%
+a density but I can still just use this
+ 
+
+ align:start position:0%
+a density but I can still just use this
+right so all I need to do is to is to
+
+ align:start position:0%
+right so all I need to do is to is to
+ 
+
+ align:start position:0%
+right so all I need to do is to is to
+get this divided by normalizing this
+
+ align:start position:0%
+get this divided by normalizing this
+ 
+
+ align:start position:0%
+get this divided by normalizing this
+thing right so that's what I need to do
+
+ align:start position:0%
+thing right so that's what I need to do
+ 
+
+ align:start position:0%
+thing right so that's what I need to do
+but if I look at this right so
+
+ align:start position:0%
+but if I look at this right so
+ 
+
+ align:start position:0%
+but if I look at this right so
+essentially I want to understand so this
+
+ align:start position:0%
+essentially I want to understand so this
+ 
+
+ align:start position:0%
+essentially I want to understand so this
+is proportional to the exponential minus
+
+ align:start position:0%
+is proportional to the exponential minus
+ 
+
+ align:start position:0%
+is proportional to the exponential minus
+1/2 sum from I equal 1 to N of X I minus
+
+ align:start position:0%
+1/2 sum from I equal 1 to N of X I minus
+ 
+
+ align:start position:0%
+1/2 sum from I equal 1 to N of X I minus
+theta squared and now I want to see this
+
+ align:start position:0%
+theta squared and now I want to see this
+ 
+
+ align:start position:0%
+theta squared and now I want to see this
+thing as a density not on the excise but
+
+ align:start position:0%
+thing as a density not on the excise but
+ 
+
+ align:start position:0%
+thing as a density not on the excise but
+on theta right what I want is a density
+
+ align:start position:0%
+on theta right what I want is a density
+ 
+
+ align:start position:0%
+on theta right what I want is a density
+on theta so it looks like I have chances
+
+ align:start position:0%
+on theta so it looks like I have chances
+ 
+
+ align:start position:0%
+on theta so it looks like I have chances
+of getting something that looks like a
+
+ align:start position:0%
+of getting something that looks like a
+ 
+
+ align:start position:0%
+of getting something that looks like a
+Gaussian but if I really need to have a
+
+ align:start position:0%
+Gaussian but if I really need to have a
+ 
+
+ align:start position:0%
+Gaussian but if I really need to have a
+Gaussian I would need to see minus 1/2
+
+ align:start position:0%
+Gaussian I would need to see minus 1/2
+ 
+
+ align:start position:0%
+Gaussian I would need to see minus 1/2
+and then I would need to see theta minus
+
+ align:start position:0%
+and then I would need to see theta minus
+ 
+
+ align:start position:0%
+and then I would need to see theta minus
+something here ok not just the sum of
+
+ align:start position:0%
+something here ok not just the sum of
+ 
+
+ align:start position:0%
+something here ok not just the sum of
+something minus Thetas so I need to work
+
+ align:start position:0%
+something minus Thetas so I need to work
+ 
+
+ align:start position:0%
+something minus Thetas so I need to work
+a little bit more so I can see what this
+
+ align:start position:0%
+a little bit more so I can see what this
+ 
+
+ align:start position:0%
+a little bit more so I can see what this
+to expand the square here so this thing
+
+ align:start position:0%
+to expand the square here so this thing
+ 
+
+ align:start position:0%
+to expand the square here so this thing
+here is going to be equal to exponential
+
+ align:start position:0%
+here is going to be equal to exponential
+ 
+
+ align:start position:0%
+here is going to be equal to exponential
+minus 1/2 sum from 1 to N of X I squared
+
+ align:start position:0%
+minus 1/2 sum from 1 to N of X I squared
+ 
+
+ align:start position:0%
+minus 1/2 sum from 1 to N of X I squared
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+two x plus theta squared okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+okay and so now basically what I'm gonna
+
+ align:start position:0%
+okay and so now basically what I'm gonna
+ 
+
+ align:start position:0%
+okay and so now basically what I'm gonna
+do is everything remember is up to this
+
+ align:start position:0%
+do is everything remember is up to this
+ 
+
+ align:start position:0%
+do is everything remember is up to this
+little sign right so every time I see a
+
+ align:start position:0%
+little sign right so every time I see a
+ 
+
+ align:start position:0%
+little sign right so every time I see a
+term that does not depend on theta I can
+
+ align:start position:0%
+term that does not depend on theta I can
+ 
+
+ align:start position:0%
+term that does not depend on theta I can
+just push it in there and just make it
+
+ align:start position:0%
+just push it in there and just make it
+ 
+
+ align:start position:0%
+just push it in there and just make it
+disappear agreed okay
+
+ align:start position:0%
+disappear agreed okay
+ 
+
+ align:start position:0%
+disappear agreed okay
+this term here exponential minus 1/2 sum
+
+ align:start position:0%
+this term here exponential minus 1/2 sum
+ 
+
+ align:start position:0%
+this term here exponential minus 1/2 sum
+of X I squared does it depend on theta
+
+ align:start position:0%
+of X I squared does it depend on theta
+ 
+
+ align:start position:0%
+of X I squared does it depend on theta
+no so I'm just pushing it here this guy
+
+ align:start position:0%
+no so I'm just pushing it here this guy
+ 
+
+ align:start position:0%
+no so I'm just pushing it here this guy
+yes and the other one yes so this is
+
+ align:start position:0%
+yes and the other one yes so this is
+ 
+
+ align:start position:0%
+yes and the other one yes so this is
+proportional to exponential X I I'm
+
+ align:start position:0%
+proportional to exponential X I I'm
+ 
+
+ align:start position:0%
+proportional to exponential X I I'm
+sorry some of the X I and then I'm gonna
+
+ align:start position:0%
+sorry some of the X I and then I'm gonna
+ 
+
+ align:start position:0%
+sorry some of the X I and then I'm gonna
+pull out my theta the minus 1/2 cancel
+
+ align:start position:0%
+pull out my theta the minus 1/2 cancel
+ 
+
+ align:start position:0%
+pull out my theta the minus 1/2 cancel
+with the minus 2 and then I have minus
+
+ align:start position:0%
+with the minus 2 and then I have minus
+ 
+
+ align:start position:0%
+with the minus 2 and then I have minus
+1/2 sum from I can 1 to N of theta
+
+ align:start position:0%
+1/2 sum from I can 1 to N of theta
+ 
+
+ align:start position:0%
+1/2 sum from I can 1 to N of theta
+squared right agreed
+
+ align:start position:0%
+squared right agreed
+ 
+
+ align:start position:0%
+squared right agreed
+so now what this thing looks like well
+
+ align:start position:0%
+so now what this thing looks like well
+ 
+
+ align:start position:0%
+so now what this thing looks like well
+this looks very much like some theta
+
+ align:start position:0%
+this looks very much like some theta
+ 
+
+ align:start position:0%
+this looks very much like some theta
+minus something squared this thing here
+
+ align:start position:0%
+minus something squared this thing here
+ 
+
+ align:start position:0%
+minus something squared this thing here
+is really just n over 2 times theta so
+
+ align:start position:0%
+is really just n over 2 times theta so
+ 
+
+ align:start position:0%
+is really just n over 2 times theta so
+sorry times theta squared so now what I
+
+ align:start position:0%
+sorry times theta squared so now what I
+ 
+
+ align:start position:0%
+sorry times theta squared so now what I
+need to do is to write this of the form
+
+ align:start position:0%
+need to do is to write this of the form
+ 
+
+ align:start position:0%
+need to do is to write this of the form
+theta minus something let's call it mu
+
+ align:start position:0%
+theta minus something let's call it mu
+ 
+
+ align:start position:0%
+theta minus something let's call it mu
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+maybe divided by Sigma divided by 2
+
+ align:start position:0%
+maybe divided by Sigma divided by 2
+ 
+
+ align:start position:0%
+maybe divided by Sigma divided by 2
+Sigma squared right
+
+ align:start position:0%
+Sigma squared right
+ 
+
+ align:start position:0%
+Sigma squared right
+I want to turn this into that maybe up
+
+ align:start position:0%
+I want to turn this into that maybe up
+ 
+
+ align:start position:0%
+I want to turn this into that maybe up
+to terms that do not depend on theta
+
+ align:start position:0%
+to terms that do not depend on theta
+ 
+
+ align:start position:0%
+to terms that do not depend on theta
+that's what I'm gonna try to do so
+
+ align:start position:0%
+that's what I'm gonna try to do so
+ 
+
+ align:start position:0%
+that's what I'm gonna try to do so
+that's called completing the square and
+
+ align:start position:0%
+that's called completing the square and
+ 
+
+ align:start position:0%
+that's called completing the square and
+that's some exercise you do you've done
+
+ align:start position:0%
+that's some exercise you do you've done
+ 
+
+ align:start position:0%
+that's some exercise you do you've done
+it probably already in the homework and
+
+ align:start position:0%
+it probably already in the homework and
+ 
+
+ align:start position:0%
+it probably already in the homework and
+that's something you do a lot when you
+
+ align:start position:0%
+that's something you do a lot when you
+ 
+
+ align:start position:0%
+that's something you do a lot when you
+do Bayesian statistics in particular so
+
+ align:start position:0%
+do Bayesian statistics in particular so
+ 
+
+ align:start position:0%
+do Bayesian statistics in particular so
+let's do this well what is gonna be the
+
+ align:start position:0%
+let's do this well what is gonna be the
+ 
+
+ align:start position:0%
+let's do this well what is gonna be the
+leading term where theta squared is
+
+ align:start position:0%
+leading term where theta squared is
+ 
+
+ align:start position:0%
+leading term where theta squared is
+going to be multiplied by this thing so
+
+ align:start position:0%
+going to be multiplied by this thing so
+ 
+
+ align:start position:0%
+going to be multiplied by this thing so
+I'm gonna pull out my n over 2 and then
+
+ align:start position:0%
+I'm gonna pull out my n over 2 and then
+ 
+
+ align:start position:0%
+I'm gonna pull out my n over 2 and then
+I'm gonna write this as theta squared
+
+ align:start position:0%
+I'm gonna write this as theta squared
+ 
+
+ align:start position:0%
+I'm gonna write this as theta squared
+minus and Y sorry minus theta over 2 and
+
+ align:start position:0%
+minus and Y sorry minus theta over 2 and
+ 
+
+ align:start position:0%
+minus and Y sorry minus theta over 2 and
+then I'm gonna write theta square of
+
+ align:start position:0%
+then I'm gonna write theta square of
+ 
+
+ align:start position:0%
+then I'm gonna write theta square of
+theta minus something squared and this
+
+ align:start position:0%
+theta minus something squared and this
+ 
+
+ align:start position:0%
+theta minus something squared and this
+something is going to
+
+ align:start position:0%
+something is going to
+ 
+
+ align:start position:0%
+something is going to
+one half of what I see in the cross
+
+ align:start position:0%
+one half of what I see in the cross
+ 
+
+ align:start position:0%
+one half of what I see in the cross
+product right well I need to actually
+
+ align:start position:0%
+product right well I need to actually
+ 
+
+ align:start position:0%
+product right well I need to actually
+pull this thing out so okay let me write
+
+ align:start position:0%
+pull this thing out so okay let me write
+ 
+
+ align:start position:0%
+pull this thing out so okay let me write
+it like that first so that's theta
+
+ align:start position:0%
+it like that first so that's theta
+ 
+
+ align:start position:0%
+it like that first so that's theta
+squared and then I'm gonna write it as
+
+ align:start position:0%
+squared and then I'm gonna write it as
+ 
+
+ align:start position:0%
+squared and then I'm gonna write it as
+minus two times one over n sum from I
+
+ align:start position:0%
+minus two times one over n sum from I
+ 
+
+ align:start position:0%
+minus two times one over n sum from I
+equal one to n of excise times theta
+
+ align:start position:0%
+equal one to n of excise times theta
+ 
+
+ align:start position:0%
+equal one to n of excise times theta
+right that's exactly just a rewriting of
+
+ align:start position:0%
+right that's exactly just a rewriting of
+ 
+
+ align:start position:0%
+right that's exactly just a rewriting of
+what we had before
+
+ align:start position:0%
+what we had before
+ 
+
+ align:start position:0%
+what we had before
+and that should look much more familiar
+
+ align:start position:0%
+and that should look much more familiar
+ 
+
+ align:start position:0%
+and that should look much more familiar
+x squared minus eight sorry a squared
+
+ align:start position:0%
+x squared minus eight sorry a squared
+ 
+
+ align:start position:0%
+x squared minus eight sorry a squared
+minus two blob a and then I miss
+
+ align:start position:0%
+minus two blob a and then I miss
+ 
+
+ align:start position:0%
+minus two blob a and then I miss
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+so this thing I'm gonna be able to
+
+ align:start position:0%
+so this thing I'm gonna be able to
+ 
+
+ align:start position:0%
+so this thing I'm gonna be able to
+rewrite as theta minus xn bar squared
+
+ align:start position:0%
+rewrite as theta minus xn bar squared
+ 
+
+ align:start position:0%
+rewrite as theta minus xn bar squared
+but then I need to remove the square of
+
+ align:start position:0%
+but then I need to remove the square of
+ 
+
+ align:start position:0%
+but then I need to remove the square of
+xn bar because it's not here okay so I
+
+ align:start position:0%
+xn bar because it's not here okay so I
+ 
+
+ align:start position:0%
+xn bar because it's not here okay so I
+just complete the square and then I
+
+ align:start position:0%
+just complete the square and then I
+ 
+
+ align:start position:0%
+just complete the square and then I
+actually really don't care what this
+
+ align:start position:0%
+actually really don't care what this
+ 
+
+ align:start position:0%
+actually really don't care what this
+thing actually was because it's gonna go
+
+ align:start position:0%
+thing actually was because it's gonna go
+ 
+
+ align:start position:0%
+thing actually was because it's gonna go
+again in the little alpha sign over
+
+ align:start position:0%
+again in the little alpha sign over
+ 
+
+ align:start position:0%
+again in the little alpha sign over
+there so this thing eventually is going
+
+ align:start position:0%
+there so this thing eventually is going
+ 
+
+ align:start position:0%
+there so this thing eventually is going
+to be proportional to exponential of
+
+ align:start position:0%
+to be proportional to exponential of
+ 
+
+ align:start position:0%
+to be proportional to exponential of
+minus n over 2 times theta minus xn bar
+
+ align:start position:0%
+minus n over 2 times theta minus xn bar
+ 
+
+ align:start position:0%
+minus n over 2 times theta minus xn bar
+squared and so we know that if this is a
+
+ align:start position:0%
+squared and so we know that if this is a
+ 
+
+ align:start position:0%
+squared and so we know that if this is a
+density that's proportional to this guy
+
+ align:start position:0%
+density that's proportional to this guy
+ 
+
+ align:start position:0%
+density that's proportional to this guy
+it has to be some N
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with mean xn bar and variance well this
+
+ align:start position:0%
+with mean xn bar and variance well this
+ 
+
+ align:start position:0%
+with mean xn bar and variance well this
+is supposed to be 1 over Sigma squared
+
+ align:start position:0%
+is supposed to be 1 over Sigma squared
+ 
+
+ align:start position:0%
+is supposed to be 1 over Sigma squared
+this guy over here this n so that's
+
+ align:start position:0%
+this guy over here this n so that's
+ 
+
+ align:start position:0%
+this guy over here this n so that's
+really just 1 over n ok so the posterior
+
+ align:start position:0%
+really just 1 over n ok so the posterior
+ 
+
+ align:start position:0%
+really just 1 over n ok so the posterior
+distribution is a Gaussian centered at
+
+ align:start position:0%
+distribution is a Gaussian centered at
+ 
+
+ align:start position:0%
+distribution is a Gaussian centered at
+my the average of my observations and
+
+ align:start position:0%
+my the average of my observations and
+ 
+
+ align:start position:0%
+my the average of my observations and
+with variance 1 over n ok everybody's
+
+ align:start position:0%
+with variance 1 over n ok everybody's
+ 
+
+ align:start position:0%
+with variance 1 over n ok everybody's
+with me so just why I'm saying this I
+
+ align:start position:0%
+with me so just why I'm saying this I
+ 
+
+ align:start position:0%
+with me so just why I'm saying this I
+mean this is what the output of some
+
+ align:start position:0%
+mean this is what the output of some
+ 
+
+ align:start position:0%
+mean this is what the output of some
+computation but it sort of makes sense
+
+ align:start position:0%
+computation but it sort of makes sense
+ 
+
+ align:start position:0%
+computation but it sort of makes sense
+right it's really telling me that the
+
+ align:start position:0%
+right it's really telling me that the
+ 
+
+ align:start position:0%
+right it's really telling me that the
+more observations I have the more
+
+ align:start position:0%
+more observations I have the more
+ 
+
+ align:start position:0%
+more observations I have the more
+concentrated this posterior is
+
+ align:start position:0%
+concentrated this posterior is
+ 
+
+ align:start position:0%
+concentrated this posterior is
+concentrated around what well around
+
+ align:start position:0%
+concentrated around what well around
+ 
+
+ align:start position:0%
+concentrated around what well around
+this xn bar so that looks like something
+
+ align:start position:0%
+this xn bar so that looks like something
+ 
+
+ align:start position:0%
+this xn bar so that looks like something
+we've sort of seen before but it does
+
+ align:start position:0%
+we've sort of seen before but it does
+ 
+
+ align:start position:0%
+we've sort of seen before but it does
+not have the same meaning somehow this
+
+ align:start position:0%
+not have the same meaning somehow this
+ 
+
+ align:start position:0%
+not have the same meaning somehow this
+is really just the posterior
+
+ align:start position:0%
+is really just the posterior
+ 
+
+ align:start position:0%
+is really just the posterior
+distribution and it's not really I mean
+
+ align:start position:0%
+distribution and it's not really I mean
+ 
+
+ align:start position:0%
+distribution and it's not really I mean
+it sort of says it's sort of a sanity
+
+ align:start position:0%
+it sort of says it's sort of a sanity
+ 
+
+ align:start position:0%
+it sort of says it's sort of a sanity
+check that I have this 1 over N when I
+
+ align:start position:0%
+check that I have this 1 over N when I
+ 
+
+ align:start position:0%
+check that I have this 1 over N when I
+have xn bar but it's not the same thing
+
+ align:start position:0%
+have xn bar but it's not the same thing
+ 
+
+ align:start position:0%
+have xn bar but it's not the same thing
+as saying that the variance of xn bar
+
+ align:start position:0%
+as saying that the variance of xn bar
+ 
+
+ align:start position:0%
+as saying that the variance of xn bar
+was 1 over n like we had before ok so as
+
+ align:start position:0%
+was 1 over n like we had before ok so as
+ 
+
+ align:start position:0%
+was 1 over n like we had before ok so as
+an exercise well you probably will have
+
+ align:start position:0%
+an exercise well you probably will have
+ 
+
+ align:start position:0%
+an exercise well you probably will have
+it but I would recommend if you don't
+
+ align:start position:0%
+it but I would recommend if you don't
+ 
+
+ align:start position:0%
+it but I would recommend if you don't
+get it
+
+ align:start position:0%
+get it
+ 
+
+ align:start position:0%
+get it
+just try pi of theta to be equal to some
+
+ align:start position:0%
+just try pi of theta to be equal to some
+ 
+
+ align:start position:0%
+just try pi of theta to be equal to some
+n mu 1 ok so you start so here the prior
+
+ align:start position:0%
+n mu 1 ok so you start so here the prior
+ 
+
+ align:start position:0%
+n mu 1 ok so you start so here the prior
+that we use was completely non
+
+ align:start position:0%
+that we use was completely non
+ 
+
+ align:start position:0%
+that we use was completely non
+informative what happens if i take my
+
+ align:start position:0%
+informative what happens if i take my
+ 
+
+ align:start position:0%
+informative what happens if i take my
+prior to be some Gaussian which is
+
+ align:start position:0%
+prior to be some Gaussian which is
+ 
+
+ align:start position:0%
+prior to be some Gaussian which is
+centered at new and it has the same
+
+ align:start position:0%
+centered at new and it has the same
+ 
+
+ align:start position:0%
+centered at new and it has the same
+variance as the other guys ok so what's
+
+ align:start position:0%
+variance as the other guys ok so what's
+ 
+
+ align:start position:0%
+variance as the other guys ok so what's
+gonna happen here is that we're gonna
+
+ align:start position:0%
+gonna happen here is that we're gonna
+ 
+
+ align:start position:0%
+gonna happen here is that we're gonna
+put a weight and everything that's away
+
+ align:start position:0%
+put a weight and everything that's away
+ 
+
+ align:start position:0%
+put a weight and everything that's away
+from you is gonna actually get less
+
+ align:start position:0%
+from you is gonna actually get less
+ 
+
+ align:start position:0%
+from you is gonna actually get less
+weight right and I want to know how I'm
+
+ align:start position:0%
+weight right and I want to know how I'm
+ 
+
+ align:start position:0%
+weight right and I want to know how I'm
+gonna be updating this prior into a
+
+ align:start position:0%
+gonna be updating this prior into a
+ 
+
+ align:start position:0%
+gonna be updating this prior into a
+posterior so that's right so everybody
+
+ align:start position:0%
+posterior so that's right so everybody
+ 
+
+ align:start position:0%
+posterior so that's right so everybody
+sees what I'm saying here so PI of theta
+
+ align:start position:0%
+sees what I'm saying here so PI of theta
+ 
+
+ align:start position:0%
+sees what I'm saying here so PI of theta
+is just so that means that PI of theta
+
+ align:start position:0%
+is just so that means that PI of theta
+ 
+
+ align:start position:0%
+is just so that means that PI of theta
+has the density proportional to X
+
+ align:start position:0%
+has the density proportional to X
+ 
+
+ align:start position:0%
+has the density proportional to X
+financial minus 1/2 theta minus mu
+
+ align:start position:0%
+financial minus 1/2 theta minus mu
+ 
+
+ align:start position:0%
+financial minus 1/2 theta minus mu
+squared right so I need to multiply my
+
+ align:start position:0%
+squared right so I need to multiply my
+ 
+
+ align:start position:0%
+squared right so I need to multiply my
+my posterior with this and then see what
+
+ align:start position:0%
+my posterior with this and then see what
+ 
+
+ align:start position:0%
+my posterior with this and then see what
+it's like actually gonna be a Gaussian
+
+ align:start position:0%
+it's like actually gonna be a Gaussian
+ 
+
+ align:start position:0%
+it's like actually gonna be a Gaussian
+this is also a conjugate prior it's
+
+ align:start position:0%
+this is also a conjugate prior it's
+ 
+
+ align:start position:0%
+this is also a conjugate prior it's
+gonna spit out another Gaussian you're
+
+ align:start position:0%
+gonna spit out another Gaussian you're
+ 
+
+ align:start position:0%
+gonna spit out another Gaussian you're
+gonna have to complete a square again
+
+ align:start position:0%
+gonna have to complete a square again
+ 
+
+ align:start position:0%
+gonna have to complete a square again
+and just check what it's actually giving
+
+ align:start position:0%
+and just check what it's actually giving
+ 
+
+ align:start position:0%
+and just check what it's actually giving
+you and so spoiler alert it's gonna look
+
+ align:start position:0%
+you and so spoiler alert it's gonna look
+ 
+
+ align:start position:0%
+you and so spoiler alert it's gonna look
+like you get an extra observation which
+
+ align:start position:0%
+like you get an extra observation which
+ 
+
+ align:start position:0%
+like you get an extra observation which
+is actually equal to MU okay so it's
+
+ align:start position:0%
+is actually equal to MU okay so it's
+ 
+
+ align:start position:0%
+is actually equal to MU okay so it's
+gonna it's gonna be the average of n
+
+ align:start position:0%
+gonna it's gonna be the average of n
+ 
+
+ align:start position:0%
+gonna it's gonna be the average of n
+plus 1 observations the first n ones
+
+ align:start position:0%
+plus 1 observations the first n ones
+ 
+
+ align:start position:0%
+plus 1 observations the first n ones
+being x1 to xn in the last one being mu
+
+ align:start position:0%
+being x1 to xn in the last one being mu
+ 
+
+ align:start position:0%
+being x1 to xn in the last one being mu
+and it sort of makes sense okay so
+
+ align:start position:0%
+and it sort of makes sense okay so
+ 
+
+ align:start position:0%
+and it sort of makes sense okay so
+that's actually a fairly simple exercise
+
+ align:start position:0%
+that's actually a fairly simple exercise
+ 
+
+ align:start position:0%
+that's actually a fairly simple exercise
+but before rather than going into more
+
+ align:start position:0%
+but before rather than going into more
+ 
+
+ align:start position:0%
+but before rather than going into more
+computation this is something you can
+
+ align:start position:0%
+computation this is something you can
+ 
+
+ align:start position:0%
+computation this is something you can
+definitely do in your in the comfort of
+
+ align:start position:0%
+definitely do in your in the comfort of
+ 
+
+ align:start position:0%
+definitely do in your in the comfort of
+your room I want to talk about other
+
+ align:start position:0%
+your room I want to talk about other
+ 
+
+ align:start position:0%
+your room I want to talk about other
+types of priors right so the first thing
+
+ align:start position:0%
+types of priors right so the first thing
+ 
+
+ align:start position:0%
+types of priors right so the first thing
+I said is okay all right there's this
+
+ align:start position:0%
+I said is okay all right there's this
+ 
+
+ align:start position:0%
+I said is okay all right there's this
+being a prior that I just pull out of my
+
+ align:start position:0%
+being a prior that I just pull out of my
+ 
+
+ align:start position:0%
+being a prior that I just pull out of my
+hat and that was just convenient then
+
+ align:start position:0%
+hat and that was just convenient then
+ 
+
+ align:start position:0%
+hat and that was just convenient then
+there was this not informative prior and
+
+ align:start position:0%
+there was this not informative prior and
+ 
+
+ align:start position:0%
+there was this not informative prior and
+was convenient great was not informative
+
+ align:start position:0%
+was convenient great was not informative
+ 
+
+ align:start position:0%
+was convenient great was not informative
+so if you don't know anything else maybe
+
+ align:start position:0%
+so if you don't know anything else maybe
+ 
+
+ align:start position:0%
+so if you don't know anything else maybe
+that's what you want to do the question
+
+ align:start position:0%
+that's what you want to do the question
+ 
+
+ align:start position:0%
+that's what you want to do the question
+is are there any other priors that are
+
+ align:start position:0%
+is are there any other priors that are
+ 
+
+ align:start position:0%
+is are there any other priors that are
+sort of principled and generic in the
+
+ align:start position:0%
+sort of principled and generic in the
+ 
+
+ align:start position:0%
+sort of principled and generic in the
+sense that they in uninformative prior
+
+ align:start position:0%
+sense that they in uninformative prior
+ 
+
+ align:start position:0%
+sense that they in uninformative prior
+was generic right I mean it was equal to
+
+ align:start position:0%
+was generic right I mean it was equal to
+ 
+
+ align:start position:0%
+was generic right I mean it was equal to
+one that's as generic as it gets and so
+
+ align:start position:0%
+one that's as generic as it gets and so
+ 
+
+ align:start position:0%
+one that's as generic as it gets and so
+is there anything that's generic as well
+
+ align:start position:0%
+is there anything that's generic as well
+ 
+
+ align:start position:0%
+is there anything that's generic as well
+well there's this priors that are called
+
+ align:start position:0%
+well there's this priors that are called
+ 
+
+ align:start position:0%
+well there's this priors that are called
+Jeffress priors and jeffers prior is a
+
+ align:start position:0%
+Jeffress priors and jeffers prior is a
+ 
+
+ align:start position:0%
+Jeffress priors and jeffers prior is a
+prior which is proportional to square
+
+ align:start position:0%
+prior which is proportional to square
+ 
+
+ align:start position:0%
+prior which is proportional to square
+root of the determinant of the Fisher
+
+ align:start position:0%
+root of the determinant of the Fisher
+ 
+
+ align:start position:0%
+root of the determinant of the Fisher
+information of theta okay and so this is
+
+ align:start position:0%
+information of theta okay and so this is
+ 
+
+ align:start position:0%
+information of theta okay and so this is
+actually kind of a weird thing to do
+
+ align:start position:0%
+actually kind of a weird thing to do
+ 
+
+ align:start position:0%
+actually kind of a weird thing to do
+right it says compute your look at your
+
+ align:start position:0%
+right it says compute your look at your
+ 
+
+ align:start position:0%
+right it says compute your look at your
+model right your model is gonna have a
+
+ align:start position:0%
+model right your model is gonna have a
+ 
+
+ align:start position:0%
+model right your model is gonna have a
+Fisher information let's say it exists
+
+ align:start position:0%
+Fisher information let's say it exists
+ 
+
+ align:start position:0%
+Fisher information let's say it exists
+and because you know we know it does not
+
+ align:start position:0%
+and because you know we know it does not
+ 
+
+ align:start position:0%
+and because you know we know it does not
+always exist for example in the
+
+ align:start position:0%
+always exist for example in the
+ 
+
+ align:start position:0%
+always exist for example in the
+multinomial model we didn't have a
+
+ align:start position:0%
+multinomial model we didn't have a
+ 
+
+ align:start position:0%
+multinomial model we didn't have a
+Fisher information and so the
+
+ align:start position:0%
+Fisher information and so the
+ 
+
+ align:start position:0%
+Fisher information and so the
+determinant of a matrix is somehow
+
+ align:start position:0%
+determinant of a matrix is somehow
+ 
+
+ align:start position:0%
+determinant of a matrix is somehow
+measuring the size of a matrix right and
+
+ align:start position:0%
+measuring the size of a matrix right and
+ 
+
+ align:start position:0%
+measuring the size of a matrix right and
+if you don't trust me just think about
+
+ align:start position:0%
+if you don't trust me just think about
+ 
+
+ align:start position:0%
+if you don't trust me just think about
+the matrix being of size one by one then
+
+ align:start position:0%
+the matrix being of size one by one then
+ 
+
+ align:start position:0%
+the matrix being of size one by one then
+the determinant is just the number that
+
+ align:start position:0%
+the determinant is just the number that
+ 
+
+ align:start position:0%
+the determinant is just the number that
+you have there and so this is really
+
+ align:start position:0%
+you have there and so this is really
+ 
+
+ align:start position:0%
+you have there and so this is really
+something that looks like the Fisher
+
+ align:start position:0%
+something that looks like the Fisher
+ 
+
+ align:start position:0%
+something that looks like the Fisher
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+I mean it's just basically the amount of
+
+ align:start position:0%
+I mean it's just basically the amount of
+ 
+
+ align:start position:0%
+I mean it's just basically the amount of
+information is proportional to the
+
+ align:start position:0%
+information is proportional to the
+ 
+
+ align:start position:0%
+information is proportional to the
+amount of information that you have at a
+
+ align:start position:0%
+amount of information that you have at a
+ 
+
+ align:start position:0%
+amount of information that you have at a
+certain point okay and so what my prior
+
+ align:start position:0%
+certain point okay and so what my prior
+ 
+
+ align:start position:0%
+certain point okay and so what my prior
+is saying it's saying well I want to put
+
+ align:start position:0%
+is saying it's saying well I want to put
+ 
+
+ align:start position:0%
+is saying it's saying well I want to put
+more weights on those Thetas that are
+
+ align:start position:0%
+more weights on those Thetas that are
+ 
+
+ align:start position:0%
+more weights on those Thetas that are
+gonna just like extract more information
+
+ align:start position:0%
+gonna just like extract more information
+ 
+
+ align:start position:0%
+gonna just like extract more information
+from the data okay so you can actually
+
+ align:start position:0%
+from the data okay so you can actually
+ 
+
+ align:start position:0%
+from the data okay so you can actually
+compute those things right so in the
+
+ align:start position:0%
+compute those things right so in the
+ 
+
+ align:start position:0%
+compute those things right so in the
+first example Jefferies Pryor is
+
+ align:start position:0%
+first example Jefferies Pryor is
+ 
+
+ align:start position:0%
+first example Jefferies Pryor is
+something that looks like this right I
+
+ align:start position:0%
+something that looks like this right I
+ 
+
+ align:start position:0%
+something that looks like this right I
+mean in one dimension Fisher information
+
+ align:start position:0%
+mean in one dimension Fisher information
+ 
+
+ align:start position:0%
+mean in one dimension Fisher information
+is essentially one over the variance
+
+ align:start position:0%
+is essentially one over the variance
+ 
+
+ align:start position:0%
+is essentially one over the variance
+right so that's just 1 over the square
+
+ align:start position:0%
+right so that's just 1 over the square
+ 
+
+ align:start position:0%
+right so that's just 1 over the square
+root of the variance because I have the
+
+ align:start position:0%
+root of the variance because I have the
+ 
+
+ align:start position:0%
+root of the variance because I have the
+square root and when I have the uniform
+
+ align:start position:0%
+square root and when I have the uniform
+ 
+
+ align:start position:0%
+square root and when I have the uniform
+sorry the Jeffress prior when i have the
+
+ align:start position:0%
+sorry the Jeffress prior when i have the
+ 
+
+ align:start position:0%
+sorry the Jeffress prior when i have the
+gaussian case right so yeah this is the
+
+ align:start position:0%
+gaussian case right so yeah this is the
+ 
+
+ align:start position:0%
+gaussian case right so yeah this is the
+identity matrix that I would have in the
+
+ align:start position:0%
+identity matrix that I would have in the
+ 
+
+ align:start position:0%
+identity matrix that I would have in the
+gaussian case so the determinant of the
+
+ align:start position:0%
+gaussian case so the determinant of the
+ 
+
+ align:start position:0%
+gaussian case so the determinant of the
+identity is 1 so square root of 1 is 1
+
+ align:start position:0%
+identity is 1 so square root of 1 is 1
+ 
+
+ align:start position:0%
+identity is 1 so square root of 1 is 1
+and so I would basically get 1 that
+
+ align:start position:0%
+and so I would basically get 1 that
+ 
+
+ align:start position:0%
+and so I would basically get 1 that
+gives me my improper prior that I might
+
+ align:start position:0%
+gives me my improper prior that I might
+ 
+
+ align:start position:0%
+gives me my improper prior that I might
+uninformative prior that I had okay so
+
+ align:start position:0%
+uninformative prior that I had okay so
+ 
+
+ align:start position:0%
+uninformative prior that I had okay so
+the uninformative prior 1 is fine I mean
+
+ align:start position:0%
+the uninformative prior 1 is fine I mean
+ 
+
+ align:start position:0%
+the uninformative prior 1 is fine I mean
+you know clearly all the Thetas carry
+
+ align:start position:0%
+you know clearly all the Thetas carry
+ 
+
+ align:start position:0%
+you know clearly all the Thetas carry
+the same information in the Gaussian
+
+ align:start position:0%
+the same information in the Gaussian
+ 
+
+ align:start position:0%
+the same information in the Gaussian
+model right I mean whether I translate
+
+ align:start position:0%
+model right I mean whether I translate
+ 
+
+ align:start position:0%
+model right I mean whether I translate
+it here or here it's pretty clear not
+
+ align:start position:0%
+it here or here it's pretty clear not
+ 
+
+ align:start position:0%
+it here or here it's pretty clear not
+none of them is actually better than the
+
+ align:start position:0%
+none of them is actually better than the
+ 
+
+ align:start position:0%
+none of them is actually better than the
+other but clearly for the Burnham Lee
+
+ align:start position:0%
+other but clearly for the Burnham Lee
+ 
+
+ align:start position:0%
+other but clearly for the Burnham Lee
+case the peas that are closer the piece
+
+ align:start position:0%
+case the peas that are closer the piece
+ 
+
+ align:start position:0%
+case the peas that are closer the piece
+that are closer to the boundary right
+
+ align:start position:0%
+that are closer to the boundary right
+ 
+
+ align:start position:0%
+that are closer to the boundary right
+carry more information right so I sort
+
+ align:start position:0%
+carry more information right so I sort
+ 
+
+ align:start position:0%
+carry more information right so I sort
+of like those guys because they're just
+
+ align:start position:0%
+of like those guys because they're just
+ 
+
+ align:start position:0%
+of like those guys because they're just
+like carry more information so what I do
+
+ align:start position:0%
+like carry more information so what I do
+ 
+
+ align:start position:0%
+like carry more information so what I do
+is that I take this function so P 1
+
+ align:start position:0%
+is that I take this function so P 1
+ 
+
+ align:start position:0%
+is that I take this function so P 1
+minus P remember is something that looks
+
+ align:start position:0%
+minus P remember is something that looks
+ 
+
+ align:start position:0%
+minus P remember is something that looks
+like this on the interval 0 1 0 and 1 so
+
+ align:start position:0%
+like this on the interval 0 1 0 and 1 so
+ 
+
+ align:start position:0%
+like this on the interval 0 1 0 and 1 so
+this guy 1 over square root of P 1 minus
+
+ align:start position:0%
+this guy 1 over square root of P 1 minus
+ 
+
+ align:start position:0%
+this guy 1 over square root of P 1 minus
+P something that looks like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+agreed and so what it's doing is sort of
+
+ align:start position:0%
+agreed and so what it's doing is sort of
+ 
+
+ align:start position:0%
+agreed and so what it's doing is sort of
+like wants to push towards the piece
+
+ align:start position:0%
+like wants to push towards the piece
+ 
+
+ align:start position:0%
+like wants to push towards the piece
+that actually carry more information I
+
+ align:start position:0%
+that actually carry more information I
+ 
+
+ align:start position:0%
+that actually carry more information I
+mean whether you want to bias your data
+
+ align:start position:0%
+mean whether you want to bias your data
+ 
+
+ align:start position:0%
+mean whether you want to bias your data
+that way or not to something you need to
+
+ align:start position:0%
+that way or not to something you need to
+ 
+
+ align:start position:0%
+that way or not to something you need to
+think about right I mean when you put a
+
+ align:start position:0%
+think about right I mean when you put a
+ 
+
+ align:start position:0%
+think about right I mean when you put a
+prior on your data on your parameter
+
+ align:start position:0%
+prior on your data on your parameter
+ 
+
+ align:start position:0%
+prior on your data on your parameter
+you're sort of like biasing towards this
+
+ align:start position:0%
+you're sort of like biasing towards this
+ 
+
+ align:start position:0%
+you're sort of like biasing towards this
+idea your data and maybe you know that's
+
+ align:start position:0%
+idea your data and maybe you know that's
+ 
+
+ align:start position:0%
+idea your data and maybe you know that's
+maybe not such a good idea when you have
+
+ align:start position:0%
+maybe not such a good idea when you have
+ 
+
+ align:start position:0%
+maybe not such a good idea when you have
+when you're you're you have some P
+
+ align:start position:0%
+when you're you're you have some P
+ 
+
+ align:start position:0%
+when you're you're you have some P
+that's actually close to 1/2 for example
+
+ align:start position:0%
+that's actually close to 1/2 for example
+ 
+
+ align:start position:0%
+that's actually close to 1/2 for example
+you're actually saying no I don't want
+
+ align:start position:0%
+you're actually saying no I don't want
+ 
+
+ align:start position:0%
+you're actually saying no I don't want
+to see a PITA
+
+ align:start position:0%
+to see a PITA
+ 
+
+ align:start position:0%
+to see a PITA
+goes to 1/2 just make a decision one way
+
+ align:start position:0%
+goes to 1/2 just make a decision one way
+ 
+
+ align:start position:0%
+goes to 1/2 just make a decision one way
+or another but just make a decision so
+
+ align:start position:0%
+or another but just make a decision so
+ 
+
+ align:start position:0%
+or another but just make a decision so
+it's sort of forcing you to do that okay
+
+ align:start position:0%
+it's sort of forcing you to do that okay
+ 
+
+ align:start position:0%
+it's sort of forcing you to do that okay
+and so Geoffrey's prior so I'm running
+
+ align:start position:0%
+and so Geoffrey's prior so I'm running
+ 
+
+ align:start position:0%
+and so Geoffrey's prior so I'm running
+out of time so I don't want to go into
+
+ align:start position:0%
+out of time so I don't want to go into
+ 
+
+ align:start position:0%
+out of time so I don't want to go into
+too much details but we'll probably stop
+
+ align:start position:0%
+too much details but we'll probably stop
+ 
+
+ align:start position:0%
+too much details but we'll probably stop
+here actually so so Geoffrey's prior
+
+ align:start position:0%
+here actually so so Geoffrey's prior
+ 
+
+ align:start position:0%
+here actually so so Geoffrey's prior
+okay sorry what happened here yeah so
+
+ align:start position:0%
+okay sorry what happened here yeah so
+ 
+
+ align:start position:0%
+okay sorry what happened here yeah so
+Geoffrey's priors have this very nice
+
+ align:start position:0%
+Geoffrey's priors have this very nice
+ 
+
+ align:start position:0%
+Geoffrey's priors have this very nice
+property is that they actually do not
+
+ align:start position:0%
+property is that they actually do not
+ 
+
+ align:start position:0%
+property is that they actually do not
+care about the parameterization of your
+
+ align:start position:0%
+care about the parameterization of your
+ 
+
+ align:start position:0%
+care about the parameterization of your
+space ok so if you actually have P and
+
+ align:start position:0%
+space ok so if you actually have P and
+ 
+
+ align:start position:0%
+space ok so if you actually have P and
+you suddenly decide that P is not the
+
+ align:start position:0%
+you suddenly decide that P is not the
+ 
+
+ align:start position:0%
+you suddenly decide that P is not the
+right parameter for Bo burn Allah but
+
+ align:start position:0%
+right parameter for Bo burn Allah but
+ 
+
+ align:start position:0%
+right parameter for Bo burn Allah but
+it's P squared okay you could decide to
+
+ align:start position:0%
+it's P squared okay you could decide to
+ 
+
+ align:start position:0%
+it's P squared okay you could decide to
+parameterize this by P squared maybe
+
+ align:start position:0%
+parameterize this by P squared maybe
+ 
+
+ align:start position:0%
+parameterize this by P squared maybe
+your doctor is actually much more able
+
+ align:start position:0%
+your doctor is actually much more able
+ 
+
+ align:start position:0%
+your doctor is actually much more able
+to formulate some prior assumption on P
+
+ align:start position:0%
+to formulate some prior assumption on P
+ 
+
+ align:start position:0%
+to formulate some prior assumption on P
+squared rather than P you never know and
+
+ align:start position:0%
+squared rather than P you never know and
+ 
+
+ align:start position:0%
+squared rather than P you never know and
+so what happens is that Jeffrey's priors
+
+ align:start position:0%
+so what happens is that Jeffrey's priors
+ 
+
+ align:start position:0%
+so what happens is that Jeffrey's priors
+are invariant under this and the reason
+
+ align:start position:0%
+are invariant under this and the reason
+ 
+
+ align:start position:0%
+are invariant under this and the reason
+is because well the information carried
+
+ align:start position:0%
+is because well the information carried
+ 
+
+ align:start position:0%
+is because well the information carried
+by P is the same as the information
+
+ align:start position:0%
+by P is the same as the information
+ 
+
+ align:start position:0%
+by P is the same as the information
+carried by P squared somehow right I
+
+ align:start position:0%
+carried by P squared somehow right I
+ 
+
+ align:start position:0%
+carried by P squared somehow right I
+mean those are essentially the same
+
+ align:start position:0%
+mean those are essentially the same
+ 
+
+ align:start position:0%
+mean those are essentially the same
+I mean well yeah they're essentially the
+
+ align:start position:0%
+I mean well yeah they're essentially the
+ 
+
+ align:start position:0%
+I mean well yeah they're essentially the
+same thing and so so I mean you need to
+
+ align:start position:0%
+same thing and so so I mean you need to
+ 
+
+ align:start position:0%
+same thing and so so I mean you need to
+have a one-to-one map right were you
+
+ align:start position:0%
+have a one-to-one map right were you
+ 
+
+ align:start position:0%
+have a one-to-one map right were you
+basically for each parameter before you
+
+ align:start position:0%
+basically for each parameter before you
+ 
+
+ align:start position:0%
+basically for each parameter before you
+have another parameter so let's call ETA
+
+ align:start position:0%
+have another parameter so let's call ETA
+ 
+
+ align:start position:0%
+have another parameter so let's call ETA
+the new parameters then the PDF of so
+
+ align:start position:0%
+the new parameters then the PDF of so
+ 
+
+ align:start position:0%
+the new parameters then the PDF of so
+the PDF of the new prior index by ETA
+
+ align:start position:0%
+the PDF of the new prior index by ETA
+ 
+
+ align:start position:0%
+the PDF of the new prior index by ETA
+this time is actually also Jeffrey's
+
+ align:start position:0%
+this time is actually also Jeffrey's
+ 
+
+ align:start position:0%
+this time is actually also Jeffrey's
+prior but this time the new Fisher
+
+ align:start position:0%
+prior but this time the new Fisher
+ 
+
+ align:start position:0%
+prior but this time the new Fisher
+information is not the Fisher
+
+ align:start position:0%
+information is not the Fisher
+ 
+
+ align:start position:0%
+information is not the Fisher
+information with respect to theta but it
+
+ align:start position:0%
+information with respect to theta but it
+ 
+
+ align:start position:0%
+information with respect to theta but it
+says in the Fisher information this
+
+ align:start position:0%
+says in the Fisher information this
+ 
+
+ align:start position:0%
+says in the Fisher information this
+associated to the statistical model
+
+ align:start position:0%
+associated to the statistical model
+ 
+
+ align:start position:0%
+associated to the statistical model
+indexed by ETA so essentially when you
+
+ align:start position:0%
+indexed by ETA so essentially when you
+ 
+
+ align:start position:0%
+indexed by ETA so essentially when you
+change Geoffrey's prior you still when
+
+ align:start position:0%
+change Geoffrey's prior you still when
+ 
+
+ align:start position:0%
+change Geoffrey's prior you still when
+you change the parameter ization of your
+
+ align:start position:0%
+you change the parameter ization of your
+ 
+
+ align:start position:0%
+you change the parameter ization of your
+model you still get Geoffrey's prior for
+
+ align:start position:0%
+model you still get Geoffrey's prior for
+ 
+
+ align:start position:0%
+model you still get Geoffrey's prior for
+the new parameterization which is in a
+
+ align:start position:0%
+the new parameterization which is in a
+ 
+
+ align:start position:0%
+the new parameterization which is in a
+way a desirable property all right so
+
+ align:start position:0%
+way a desirable property all right so
+ 
+
+ align:start position:0%
+way a desirable property all right so
+that's so Jeffrey's priors just like
+
+ align:start position:0%
+that's so Jeffrey's priors just like
+ 
+
+ align:start position:0%
+that's so Jeffrey's priors just like
+none uninformative priors or priors you
+
+ align:start position:0%
+none uninformative priors or priors you
+ 
+
+ align:start position:0%
+none uninformative priors or priors you
+want to use when you don't when you want
+
+ align:start position:0%
+want to use when you don't when you want
+ 
+
+ align:start position:0%
+want to use when you don't when you want
+a systematic way without really thinking
+
+ align:start position:0%
+a systematic way without really thinking
+ 
+
+ align:start position:0%
+a systematic way without really thinking
+about what to pick for your mouth
+
+ align:start position:0%
+about what to pick for your mouth
+ 
+
+ align:start position:0%
+about what to pick for your mouth
+so well okay I'll finish this next time
+
+ align:start position:0%
+so well okay I'll finish this next time
+ 
+
+ align:start position:0%
+so well okay I'll finish this next time
+and we'll talk about Bayesian confidence
+
+ align:start position:0%
+and we'll talk about Bayesian confidence
+ 
+
+ align:start position:0%
+and we'll talk about Bayesian confidence
+regions will talk about Bayesian
+
+ align:start position:0%
+regions will talk about Bayesian
+ 
+
+ align:start position:0%
+regions will talk about Bayesian
+estimation once I have a purpose here
+
+ align:start position:0%
+estimation once I have a purpose here
+ 
+
+ align:start position:0%
+estimation once I have a purpose here
+what do I get and basically the only
+
+ align:start position:0%
+what do I get and basically the only
+ 
+
+ align:start position:0%
+what do I get and basically the only
+message is going to be that well you
+
+ align:start position:0%
+message is going to be that well you
+ 
+
+ align:start position:0%
+message is going to be that well you
+might want to integrate against the
+
+ align:start position:0%
+might want to integrate against the
+ 
+
+ align:start position:0%
+might want to integrate against the
+posterior find the posterior the
+
+ align:start position:0%
+posterior find the posterior the
+ 
+
+ align:start position:0%
+posterior find the posterior the
+expectation of your posterior
+
+ align:start position:0%
+expectation of your posterior
+ 
+
+ align:start position:0%
+expectation of your posterior
+distribution that's a good point
+
+ align:start position:0%
+distribution that's a good point
+ 
+
+ align:start position:0%
+distribution that's a good point
+estimator for theta and then we'll just
+
+ align:start position:0%
+estimator for theta and then we'll just
+ 
+
+ align:start position:0%
+estimator for theta and then we'll just
+do well just do a couple of computation
+
+ align:start position:0%
+do well just do a couple of computation
+ 
+
+ align:start position:0%
+do well just do a couple of computation
+all right so
\ No newline at end of file
diff --git a/cE6OD7DkCSU.txt b/cE6OD7DkCSU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..aff26cbfda22c7f67e91f9865141eda418ab5ac3
--- /dev/null
+++ b/cE6OD7DkCSU.txt
@@ -0,0 +1,3113 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: So this
+is the outline of
+
+the lecture for today.
+
+So we just need to talk about
+the conditional densities for
+
+Poisson process.
+
+So these are the things that
+we've seen before in previous
+
+sections, so I'm just going to
+give a simple proof for them
+
+and some intuition.
+
+So if you remember the Poisson
+process, this was the famous
+
+figure that we had.
+
+So our time is at zero and
+afterwards zero and then we
+
+had some arrivals.
+
+So our time is then t.
+
+We had N of t arrivals,
+which is equal to n.
+
+This is Sn.
+
+This is the figure
+that we had.
+
+So for the first equation,
+we're looking at--
+
+We want to find the conditional
+distribution of
+
+interval times condition
+and last arrival times.
+
+So first of all, we want to find
+the joint distribution of
+
+the interval arrival
+times and the last
+
+arrival, this equation.
+
+So you know that interval
+arrival times are independent
+
+in the Poisson process, so just
+looking at this thing,
+
+you know that these things are
+independent of each other so
+
+we will have lambda to
+the power of Ne to
+
+the power minus lambda.
+
+And then, this last one
+corresponds to the fact that
+
+xn plus 1 is equal to n plus
+1 minus summation of x.
+
+These two events are equivalent
+to each other, so
+
+this is going to correspond
+to lambda e to the
+
+power of minus lambda.
+
+So we just did it the
+other way, so
+
+it's going to be like--
+
+So you can just get rid of these
+terms and it's going to
+
+be that equation.
+
+So it's very simple, it's
+just the independence of
+
+inter-arrival times.
+
+So you look at the last term as
+the inter-arrival time for
+
+the last arrival, and then
+they're going to be
+
+independent, and the terms kind
+of cancel out and you
+
+have this equation.
+
+So this conditional density
+will be the joint
+
+distribution--
+
+or the distribution of Sn plus
+1, which is like these.
+
+So the joint decision
+will be like this.
+
+So what does the intuition
+behind this mean?
+
+This means that--
+
+you've seen this term before.
+
+This means that we have uniform
+distribution over the
+
+interval of zero to one,
+condition on something.
+
+So previously, what we had was
+the conditional distribution
+
+of arrival times condition on
+the last arrival, so F of s1
+
+and condition on sn plus 1.
+
+But here we have distribution
+of x1 to x and
+
+condition on sn plus 1.
+
+And previously, the constraint
+that we had was like we should
+
+have ordering over the
+arrival times.
+
+So because of this constraint
+we had this n factorial, if
+
+you remember, that order of
+statistics things that you
+
+talked about.
+
+Now here, what we have is
+something like this.
+
+So all the arrival times
+should be positive, and
+
+summation of them should
+be less than t.
+
+Because well, the summation
+of them to n plus 1 is
+
+equal to sn plus 1.
+
+And the last term is positive,
+so this thing should
+
+be less than t.
+
+So these two constraints are
+sort of dual to each other.
+
+So because of this constraint,
+I had some n factorial over
+
+the conditional distribution of
+arrival times, condition on
+
+the last arrival time.
+
+Now, I have inter-arrival
+conditional distribution of
+
+inter-arrival time condition
+on last arrival time and we
+
+should have this n
+factorial here.
+
+The other interesting thing is
+that if I condition it under n
+
+of t, so the number of arrivals
+at time [INAUDIBLE]
+
+t.
+
+The time is going to be very
+similar to the previous one.
+
+Just to prove this thing,
+it's very simple again.
+
+I just wanted to show you--
+
+So what does this thing mean?
+
+This thing means that these are
+the distributions of the
+
+inter-arrival times and the last
+event corresponds to the
+
+fact that xn plus 1 is bigger
+than t minus summation of xi.
+
+Because we have an arrival
+time at [? snn, ?]
+
+and then after that there's
+no arrival.
+
+Because at time nt we
+have n arrivals.
+
+So this corresponds
+to do is thing.
+
+So again, we'll have something
+like lambda n, e
+
+to the power of--
+
+This is for the first event
+and you see that these are
+
+independent because of the
+Poisson properties of the
+
+Poisson process.
+
+And the last term will be--
+
+property of the Poisson
+and a variable bigger
+
+than something is--
+
+Yes, this cancel out.
+
+And then we'll have this term,
+this first n lambda to the
+
+power of n, just forget
+about n plus 1.
+
+And property distribution of n
+of t equal to n is this term
+
+without n plus 1.
+
+So lambda n to the 12, and e
+to the power minus lambda t
+
+over n factorial.
+
+So these terms cancel out and
+we'll have this thing.
+
+So again, we should have these
+constraints that summation of
+
+xk, k equal to 1, n should
+be less than t.
+
+No matter if they are
+conditioning of n of t or sn
+
+plus 1, the last arrival time
+or the number of arrivals at
+
+some time instant, the condition
+of distribution is
+
+uniform subject to
+some constraints.
+
+Is there any questions?
+
+So if you look at the limit, and
+so again, looking at this
+
+figure, you see that this
+corresponds to sn plus 1 and
+
+you see that sn plus
+1 is bigger than t.
+
+So if you take the limit and
+take the t1 going to t, these
+
+two distributions are going
+to be the same.
+
+So t1 corresponds
+to sn plus 1.
+
+t1.
+
+So basically what's it's saying
+is that conditional
+
+distribution of arrival times
+are uniform, independent of
+
+what is going to happen
+in future.
+
+So in future, there might be
+some, I mean, the knowledge
+
+that we have about future could
+be the fact that knowing
+
+what happens in this interval
+or the next arrival is going
+
+to happen at some point, I
+mean, condition on these
+
+things the arrival times are
+going to be uniform.
+
+The other fact is that this
+distribution that I showed
+
+you, they are all symmetric
+with respect to interval
+
+arrival times.
+
+So it doesn't matter, I mean,
+no arrival has more priority
+
+to any other one or they're not
+different to each other.
+
+So if you look at the
+permutation of them, they're
+
+going to be similar.
+
+So now, I want to look at the
+distribution of x1 or s1, they
+
+are equal to each other.
+
+I can easily calculate the
+probability of x1 bigger than
+
+some tau condition, for example,
+n of t is equal to n.
+
+So what is this conditional
+distribution?
+
+So condition on n of t equal
+to n, I know that in this
+
+interval I have n arrivals and
+n inter-arrival times, and I
+
+want to know if x1 is in
+this interval, or s1.
+
+s1 is equal to x1.
+
+And you know that si's
+are also uniform.
+
+So you know that these are
+independent of each other, and
+
+so you can say that the
+probability of this thing is
+
+like this one.
+
+So all of them should
+be bigger than tau.
+
+And since this is symmetric--
+
+so this corresponds to x1.
+
+Since this was--
+
+everything was symmetric for
+all inter-arrival times.
+
+This is also the complimentary
+distribution function for xk.
+
+Is there any questions?
+
+So the other think that are not
+in the slides that I want
+
+to tell you is the conditional
+distribution of
+
+si given n of t.
+
+So I know that there n arrivals
+in this interval, and
+
+I want to see if the i arrival
+is something like this.
+
+So the probability that--
+
+so this even corresponds to
+the fact that there is one
+
+arrival in this interval and i
+minus 1 arrival was here and n
+
+minus i minus 1 arrival
+was here.
+
+Oh, no, sorry, n minus
+i arrival is here.
+
+So the probability of
+having one arrival
+
+here corresponds to--
+
+since arrival times our uniform,
+and I want to have
+
+one arrival in this interval
+like this, and I want to have
+
+i minus arrivals here i minus
+one arrivals here, and n minus
+
+i arrivals here.
+
+So it's like aq binomial
+probability distribution so
+
+out of the n arrival-- n minus
+1 remaining arrivals, I want
+
+to have some of them in
+this interval and
+
+some of them here.
+
+So this is the distribution
+of this thing.
+
+Yeah, so just as a check
+we know that the last
+
+inter-arrival--
+
+last arrival time,
+the distribution
+
+of that thing is--
+
+Here, you just cancel these
+things out, too--
+
+is--
+
+We need to get back to this
+equation, but it's just the
+
+same as this one but you
+let i equal to n.
+
+This is OK?
+
+Just to think i equal to
+n, you get this one.
+
+AUDIENCE: Does this equation
+also apply to i equals
+
+[INAUDIBLE]?
+
+PROFESSOR: Yeah, sure.
+
+Yeah, i equal to 1, we will
+have nt minus tau.
+
+And if you look at this thing,
+so this is a complimentary
+
+distribution function.
+
+You just take to zero
+till you get that.
+
+This is just a check of
+this formulation.
+
+Yeah.
+
+So is there any other
+questions?
+
+Did anybody get why we have
+this kind of formulation?
+
+Is was very simple, it's just
+the combination of a uniform
+
+distribution and a binomial
+distribution.
+
+AUDIENCE: What is tau?
+
+PROFESSOR: Tau is this thing.
+
+Tau is the si.
+
+Change of notation.
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: I said that I want
+one arrival in this interval
+
+and i minus 1 arrival was here
+and n minus i arrival is here.
+
+So I define it, the
+Bernoulli process.
+
+So priority of falling in
+this interval is tau
+
+over t minus tau.
+
+And I say that--
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: OK, so falling in
+this interval in a uniform
+
+distribution corresponds
+to success.
+
+I want, among n minus 1
+arrivals, i minus 1 of them to
+
+be successful and the rest of
+them to be [INAUDIBLE].
+
+[INAUDIBLE]
+
+that one of them should fall
+here and the rest of them
+
+should fall here.
+
+Richard?
+
+AUDIENCE: So that's
+the [INAUDIBLE]?
+
+PROFESSOR: Yeah, you just get
+rid of this dt, that's it.
+
+[? AUDIENCE: Why do ?]
+those stay, n over t.
+
+PROFESSOR: Which one?
+
+AUDIENCE: Can you explain
+again the first term?
+
+The first term there,
+the nd over t?
+
+PROFESSOR: Oh, OK, so I want
+to have one interval
+
+definitely here but among
+n arrivals I want
+
+them to fall here.
+
+So any one of them
+should cancel.
+
+But then i minus 1 of them
+should fall here and n minus i
+
+intervals should fall here.
+
+Any other questions?
+
+It's beautiful, isn't it?
+
+There's a problem.
+
+I studied x1 to xn, but what
+is the distribution of this
+
+remaining part?
+
+So if I condition on n, nt or
+condition on sn plus 1, what
+
+is the distribution of this
+one or this one or doing
+
+distribution off all these?
+
+So this is what we're
+going to look.
+
+So first of all, I do the
+conditioning over sn plus 1,
+
+and I find the distribution
+of--
+
+the distribution of x1 to xn
+condition on sn plus 1, is
+
+there any randomness in
+distribution of xn plus 1?
+
+So this is going to
+be sx plus 1.
+
+So this is going to
+be xn plus 1.
+
+So if I find a distribution of
+x1 to xn condition on this
+
+condition is sn plus 1, it's
+very easy to show that xn plus
+
+1 is equal to sn plus 1.
+
+So there's no randomness here.
+
+But looking at the figure,
+you see that--
+
+and the distributions, you see
+that everything is symmetric.
+
+So I've found the distribution
+x1 to xn and I can find xn
+
+plus 1 easily from them.
+
+But what if I find the
+distribution of x2 to xn plus
+
+1, condition on this thing, and
+then find x1 from them?
+
+So you can say that x1
+is equal to xn minus
+
+1 2 to n plus 1xi.
+
+And then we have
+this solution.
+
+So it seems that there's no
+difference between them and
+
+actually, there's not.
+
+So condition on sn plus 1, we
+have the same distribution for
+
+x1 to xn or x2 to xn plus 1.
+
+But there are only n free
+parameters because the n plus
+
+1's can be calculated
+in your equations.
+
+If you take any n random
+variables out of this n plus 1
+
+random variables, we have
+the same story.
+
+So it's going to be uniform, our
+0 to t for this interval.
+
+So it's symmetric.
+
+Now, the very nice thing is
+about n of t, equal t--
+
+[? so ?] n must be equal to n.
+
+So this is easy because we had
+these equations, but what if I
+
+call this thing xn star of
+n plus 1 and I do the
+
+conditioning over n of t?
+
+So I don't know the arrival time
+for n plus 1's arrival
+
+but I do know the number of
+arrivals at time [INAUDIBLE]
+
+t.
+
+Condition on that, what is the
+distribution for example, for
+
+xn star n plus 1 or x1 to xn?
+
+Again, easily we can say
+that it's the same
+
+story, so it's uniform.
+
+So you can take out of x1 to xn
+and xn star n plus 1, you
+
+can take n off them and find
+the distribution of that.
+
+OK, so the other way to look at
+this is that if I find the
+
+distribution of x1 to xn
+condition on n of t, I will
+
+have the expect that xs star n
+plus 1 is equal to t minus sn,
+
+which is t minus summation
+of x to i.
+
+Can anyone of you see this?
+
+Hope so.
+
+Oh, OK.
+
+So again, if I find the
+distribution of x1 to xn, I
+
+can find sx star n plus
+1 deterministically.
+
+Just as a signage check, you can
+find that f of the star of
+
+x-- oh, sorry, f of x star
+n plus 1 condition on--
+
+So looking at this formulation
+and just replacing everything,
+
+we can't find this thing, and
+you can see that this is
+
+similar to this one again.
+
+So this is the distribution
+for--
+
+well, this is the distribution
+for x1.
+
+So you can find the
+density and this
+
+is going to be density.
+
+So what I'm saying is that
+x1 has the same marginal
+
+distribution as xn
+plus 1 star.
+
+So you can get it with this kind
+of reasoning, saying that
+
+the marginal distribution should
+be the same or looking
+
+at this kind of formulation.
+
+When you have this distribution
+you can find the
+
+distribution of summation of
+xi, i equal to 1 to n.
+
+And then you can find--
+
+So t is determined, so
+you can just replace
+
+everything and find it.
+
+And you can see that these
+two are the same.
+
+AUDIENCE: [INAUDIBLE]
+
+the same distribution
+that is one?
+
+PROFESSOR: Yeah.
+
+Condition on nt [INAUDIBLE].
+
+So everything is symmetric
+and uniform.
+
+But you can only choose n for
+your parameters because the n
+
+plus 1 is a combination
+of the--
+
+Right?
+
+So this is the end of the
+chapter [INAUDIBLE]
+
+for Poisson process, is there
+any problems or any
+
+questions about it?
+
+So let's start the
+Markov chain.
+
+So in this chapter we only talk
+about the finite-state of
+
+Markov chains.
+
+Markov chains are some processes
+that changing
+
+integer-time sense.
+
+So it's like we're quantizing
+time and any kind of change
+
+can happen only in an
+integer-time sense.
+
+And it's different in this way
+from Poisson processes because
+
+we can have the definition of
+Poisson processes for any
+
+continuous time, but Markov
+chains are only defined for
+
+integer-times.
+
+And finite-state Markov chains
+is a Markov chain where states
+
+can be only in a finite set, so
+we usually call it 1 to M,
+
+but you can name it in
+any way you like.
+
+What we are looking for in
+finite-state Markov chains is
+
+the probability distribution of
+the next state conditioned
+
+on whatever [? history ?]
+
+that I have.
+
+So I know that at integer times
+
+there can be some change.
+
+So what is this change?
+
+We model it with the probability
+distribution of
+
+this change corresponding
+to the history.
+
+So we can model any discrete
+integer time
+
+processing this way.
+
+Now, the nice thing about Markov
+chains or homogeneous
+
+Markov chains is that
+this distribution is
+
+equal to these things.
+
+So you see i and j, so i is the
+previous state and j is
+
+the state that I want to go in
+so the distribution of the
+
+next state condition and all
+the history only depends on
+
+the last step.
+
+So even the previous state, the
+new state is independent
+
+of all their earlier things
+that might happen.
+
+So there's a very nice
+way to show it.
+
+So in general, we say
+that xn plus 1 is
+
+independent of xn plus 1.
+
+So if I know the periods--
+
+and these things are true for
+all the possible states.
+
+So whatever the history in the
+earlier process that I had, I
+
+only care about the state that
+I was in in previous time.
+
+And this is going to show me
+what is the distribution of
+
+next state.
+
+So the two important things that
+you can see this in this
+
+formulation is that, first
+of all, this kind of
+
+independence, it is true for
+all i, j, k, m, and so on.
+
+The other thing is that it's
+not time-dependent.
+
+So if I'm in state, the
+probability distribution of my
+
+next state is going to be the
+same if the same thing happens
+
+in 100 years.
+
+So it's not time-dependent.
+
+That's why we call it
+homogeneous Markov chains.
+
+And we can have non-homogeneous
+Markov chains,
+
+but there are not many nice
+results about them.
+
+I mean, we cannot find
+many good things.
+
+And all the information that
+we know to characterize the
+
+Markov chain is this kind
+of distribution.
+
+So we call these things
+transition probabilities.
+
+And something else which is
+called initial probabilities,
+
+which tell me that, at time
+instance 0, what is the
+
+probability distribution
+of the states.
+
+So knowing Markov chains, you
+can find that probability
+
+distribution of x1 is equal to
+probability of x1 condition
+
+and x0 [INAUDIBLE].
+
+So knowing this thing
+and these transition
+
+probabilities, I can kind
+the probability
+
+distribution of x1.
+
+Well, very easily,
+the probability
+
+of xn is equal to--
+
+sorry.
+
+so you can do this thing
+iteratively.
+
+And just knowing the transition
+probabilities and
+
+initial probabilities, you
+can find the probability
+
+distribution of the states at
+any time instant to forever.
+
+Do you see it's very easy?
+
+You just do this thing
+iteratively.
+
+So I talked about the
+independence and initial.
+
+Yeah, so what we do is, we
+characterize the Markov chains
+
+with these set of transition
+probabilities
+
+and the initial state.
+
+And you see that these
+transition probabilities, we
+
+have, well, m times n minus 1,
+free parameters in them,
+
+because the summation of each of
+them should be equal to 1.
+
+So for each initial state, I can
+have a distribution over
+
+the next step.
+
+So I'm going to talk about
+it in the matrix form.
+
+And what we're doing in practice
+usually, we assume
+
+the initial state to be
+a constant state.
+
+So we usually just define a
+state, call it initial state.
+
+Usually, we call it x0.
+
+I mean, it's what's you're going
+to usually see if you
+
+want to study the behavior
+of Markov chains.
+
+So these are the two ways that
+we can visualize the
+
+transition probabilities.
+
+So matrix form is very easy.
+
+So you just look at
+the n probability
+
+distributions that you have.
+
+And with Markov chain with n
+number of states, you will
+
+have n distributions, each of
+them corresponding to the
+
+conditional distribution of next
+step, condition of the
+
+present step equal to i.
+
+So i can be anything.
+
+So this was the thing I was
+saying, the number of free
+
+parameters.
+
+So I have n distribution, and
+each distribution has n minus
+
+1 free parameters, because the
+summation of them should be
+
+equal to 1.
+
+So this is the number of free
+parameters that I have.
+
+So is there any problem
+with the matrix form?
+
+I'm assuming that you've
+all been seeing
+
+this sometime before.
+
+Fine?
+
+So the nice thing about matrix
+form is that you can do many
+
+nice stuff with them.
+
+We can look at the notes for
+them, and we will see these
+
+kinds of properties later.
+
+But you can imagine that just
+looking at the matrix form and
+
+doing some algebra over them,
+we can get very nice results
+
+about the Markov chains.
+
+The other representation of the
+Markov chains is using a
+
+graph, a directed graph in which
+each node corresponds to
+
+a state and each arc, or each
+edge, corresponds to a
+
+transition probability.
+
+And the very important thing
+about graphical model is that
+
+there's a very clear difference
+between 0
+
+transition probabilities
+and non-0 transition
+
+probabilities.
+
+So if there's any possibility
+of going from one state to
+
+another state, we have an
+edge or an arc here.
+
+So probability of 10 to the
+power of minus 5 is
+
+different from 0.
+
+We have an arc in one case and
+no arc in another case,
+
+because there's a chance of
+going from this state to the
+
+next state.
+
+And even then, the probability
+is 10 to the power of minus 5.
+
+And OK, so we can do a lot of
+inference by just looking at
+
+the graphical model.
+
+And it's easier to see some
+properties of the Markov chain
+
+by looking at the graphical
+models.
+
+We will see these properties
+that we can find by looking at
+
+the graphical model.
+
+So this is not really
+
+classification of states, actually.
+
+So there are some definitions,
+very
+
+intuitive definitions here.
+
+So there's something called a
+walk, which says that this is
+
+an ordered string of the nodes,
+where the probability
+
+of going from each node to
+the next one is non-0.
+
+So for example, looking at this
+walk, you can have the
+
+probability of going from 4 to 4
+is positive, 4 to 1, 1 to 2,
+
+2 to 3, and 3, to 2.
+
+So there is no kind of
+constraints in the definition
+
+of the walk.
+
+There should be just positive
+probabilities in going from
+
+one state to the next state.
+
+So we can have repetition.
+
+We can have whatever we like.
+
+And the number of-- well,
+we can find the number
+
+of states for sure.
+
+So what is the maximum number
+of steps in a walk?
+
+Or minimum number?
+
+Minimum number of
+states is two--
+
+[? one. ?]
+
+So what is the maximum
+number of steps?
+
+Well, there's no constraint,
+so it can be anything.
+
+So the next thing that
+we look is a path.
+
+A path is a walk where there
+is no repeated nodes.
+
+So I never go through
+one node twice.
+
+So for example, I have this
+path, 4, 1, 2, 3.
+
+We can see here, 4, 1, 2, 3.
+
+And now we can say, what
+is the maximum number
+
+of steps in a path?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Steps, not states.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: n minus 1, yeah.
+
+Because you cannot go through
+one state twice.
+
+So you have a maximum number
+of steps in n minus 1.
+
+And the cycle is a walk in which
+the first and last node
+
+is repeated.
+
+So first of all, there's not
+a really great difference
+
+between these two cycles,
+so it doesn't
+
+matter where I start.
+
+And we don't care about
+the repetition and
+
+definition of cycle.
+
+Oh, OK.
+
+Yeah, sorry.
+
+No node is repeated.
+
+So sorry, something was wrong.
+
+Yeah, we shouldn't have any
+repetition except for the
+
+first and last nodes.
+
+So the first and last node
+should be the same, but there
+
+shouldn't be any repetition.
+
+So what is the maximum number
+of steps in this case?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: n, yeah, because we
+have an additional step.
+
+Yeah?
+
+AUDIENCE: You said in a path,
+the maximum number of
+
+steps is n minus 1?
+
+PROFESSOR: Yeah.
+
+AUDIENCE: I mean, if you have
+n equals, like, 6, couldn't
+
+there be 1, 2, 3, 4, 5, 6?
+
+PROFESSOR: No, it's the
+steps, not the states.
+
+So if I have path from 1 to
+2, and this is the path.
+
+So there's one step.
+
+Just whenever you're confused,
+make a simple model.
+
+It's going to make everything
+very, very easy.
+
+Any other questions?
+
+So this is another definition.
+
+We say that a node j is
+accessible from i if there is
+
+a walk from i to j.
+
+And by just looking at the
+graphical model, you can
+
+verify the existence of
+this walk very easily.
+
+But the nice thing, again, about
+this thing is what I
+
+emphasized in the
+graphical model.
+
+It talks about if there's any
+positive probability of going
+
+from i to j.
+
+So if j is accessible from i
+and you start at node i,
+
+there's a positive probability
+that you will end in node j
+
+sometime in the future.
+
+There's nothing said about the
+number of steps needed to get
+
+there, or the probability of
+that, except that this
+
+probability is non-0.
+
+It's positive.
+
+So for example, if there's a
+state like k, that we have p
+
+of ik is positive and p of kj is
+positive, then we will have
+
+p of ij [? too ?] is positive.
+
+So we have this kind
+of notation.
+
+I don't have a pointer.
+
+Weird.
+
+So yeah, we have this kind of
+my notation. pijn means that
+
+the probability of going from
+state i to state j in n steps.
+
+And this is exactly
+like n steps.
+
+Actually, this value could
+be different for
+
+different number of n.
+
+For example, if we have a Markov
+chain like this, p of
+
+131 is equal to 0, but
+p of 132 is non-0.
+
+So node j is accessible from i
+if pijn is positive for any n.
+
+So we say that j is not
+accessible from i if this is 0
+
+for all possible n's.
+
+Mercedes?
+
+AUDIENCE: Are those actually
+greater than or equal to?
+
+PROFESSOR: No, greater.
+
+They are always greater
+than or equal to 0.
+
+Probability is always
+non-negative.
+
+So what want is positive
+probability, meaning that
+
+there's a chance that
+I will get there.
+
+I don't care how small this
+chance is, but it
+
+shouldn't be 0.
+
+AUDIENCE: [INAUDIBLE].
+
+So p to ij, though, couldn't it
+be equal to pik, [? pkj? ?]
+
+PROFESSOR: Yeah, exactly.
+
+So in this case, p132 is
+equal to p12, p23,
+
+AUDIENCE: So I guess I'm asking
+if p2ij should be
+
+greater than or equal to pfk.
+
+PROFESSOR: Oh, OK.
+
+No, actually.
+
+You know why?
+
+Because there can exist some
+other state like here.
+
+AUDIENCE: Right.
+
+But if that doesn't exist and
+there's only one path.
+
+PROFESSOR: Yeah, sure.
+
+But there's no guarantee.
+
+What I'm saying is that Pik is
+positive, Pkj is positive.
+
+So this thing is positive,
+but it can be bigger.
+
+In this case, it
+can be bigger.
+
+I don't care about the quantity,
+about the amount of
+
+the probability.
+
+I care about its positiveness,
+it's greater than 0.
+
+I just want it to be non-0.
+
+The other thing is that when we
+look at pijn, I don't care
+
+what kind of walk I have
+between i and j.
+
+It's a walk, so it can have
+repetition, it can have
+
+cycles, or it can
+have anything.
+
+I don't care.
+
+So if you really want to
+calculate pij for n equal to
+
+[INAUDIBLE]
+
+1,000, you should really find
+all possible walks from i to j
+
+and add the probabilities
+to find this value.
+
+And all the walks
+within steps.
+
+Not here.
+
+Let's look at some examples.
+
+So is node 3 accessible
+from node 1?
+
+So you see that there's a
+walk like this, 1, 2, 3.
+
+So there's a positive
+probability of going to state
+
+3 from node 1.
+
+So node 3 is accessible
+from 1.
+
+But if you really want to
+calculate the probability, you
+
+should also look at the fact
+that we can have cycles.
+
+So 1, 2, 3 is a walk.
+
+But 1, 1, 2, 3 is also a walk.
+
+1, 2 3, 2, 3 is also a walk.
+
+You see?
+
+So you have to count all these
+things to find the probability
+
+of p13n for any n.
+
+What about state 5?
+
+So is the node 3 accessible
+from node 5?
+
+You see that it's not.
+
+Actually, if you're going to
+state 5, you never go out.
+
+With [INAUDIBLE]
+
+probability of 1, you
+stay there forever.
+
+So actually, no state except
+state 5 is accessible from 5.
+
+So is node 2 accessible
+from itself?
+
+So accessible means that I
+should have a walk from 2 to 2
+
+in some number of steps.
+
+So you can see that we
+can have 2, 3, 2,
+
+or many other walks.
+
+So it's accessible.
+
+But as you see, node 6 is not
+accessible from itself.
+
+If you are in node 6,
+you always go out.
+
+So it's not accessible.
+
+So let's go back to
+these definitions.
+
+Yeah, this is what I said, and
+I'm emphasizing again.
+
+If you want to say that j is
+not accessible from i, I
+
+should have a pijn equal
+to 0 for all n.
+
+The other thing is that, if
+there's a walk from i to j and
+
+from j to k, we can prove easily
+that there's a walk
+
+from i to k.
+
+So having a walk from i to j
+means that for some n, this
+
+thing is positive.
+
+So this is i to j.
+
+From j to k, this means
+that p of jk, for
+
+some n, this is positive.
+
+So looking at i two k, I can say
+that p of i to k, m plus
+
+n, is greater than.
+
+And I have this thing here
+because of the reason that I
+
+explained right now, because
+there might be other paths
+
+from i to k, except the paths
+going through j, or except the
+
+walks that have n steps to get
+to j and n steps to get to k.
+
+So we know that, well, we can
+concatenate the walks from--
+
+so if there's a walk from i to
+j and j to k, we have a walk
+
+from i to k.
+
+So we say that states i and j
+communicate if there's a walk
+
+from i to j and from j to i.
+
+So it can go back and forth.
+
+So it means that there's
+a cycle from from i
+
+two i or j two j.
+
+This is the implication.
+
+So it's, again, very simple to
+prove that if i communicates
+
+with j and j communicates with
+k, then i communicates with k.
+
+In order to prove that,
+I should assume that i
+
+communicates to j, I need to
+prove that there is a walk
+
+from i to k, and I need to prove
+that there is a walk
+
+from k to i.
+
+So this means that i
+communicates with k.
+
+So these two things can be
+proved easily from the
+
+concatenation of the walks
+and the fact that i and j
+
+communicate and j and
+k communicate.
+
+Now, what I can define
+is something
+
+called a class of states.
+
+So a class is called a non-empty
+set of states, where
+
+all the pairs of states in a
+class communicated with each
+
+other, and none of them
+communicate with any other
+
+state in the Markov chain.
+
+So this is the definition
+of class.
+
+So I just group the pairs that
+can communicate with the state
+
+and just get rid of all those
+who do not communicate to the
+
+[INAUDIBLE].
+
+So for defining a class or for
+finding a class, or for naming
+
+a class, we can have a
+representative state.
+
+So I want to find all the states
+that communicate with
+
+each other in a class.
+
+So I can just pick one of the
+states in this class and find
+
+all the states that communicate
+with this single
+
+state, because if two states
+communicate with one state,
+
+then these two states
+communicate with each other.
+
+And if there's a state that
+doesn't communicate with me,
+
+it doesn't communicate with
+anybody else whom I'm
+
+communicating with.
+
+I'm going to prove it now,
+just in a few moments.
+
+Just, I want to look at
+this figure again.
+
+So first I take state 2 and
+find a class that has this
+
+state in itself.
+
+So you see that in this class,
+we have state 2 on 3, because
+
+there's only a state 3 that
+communicates with 2.
+
+And correspondingly,
+we can have class
+
+having state 4 and 5.
+
+And you see that state 1 is
+communicating with itself, so
+
+it's a class by itself.
+
+But it doesn't communicate
+with anyone else.
+
+So we have this class also.
+
+So next question, why do
+we call C4 a class?
+
+So it doesn't communicate
+with itself.
+
+If you're in state 6, you go out
+of it with probability of
+
+1, eventually.
+
+So why do we call it a class?
+
+Actually, so this is the
+definition of the classes.
+
+But we want to have some very
+nice property of other classes
+
+which says that we can partition
+the states in a
+
+Markov chain by using
+the classes.
+
+So if I don't count this case as
+a class, I cannot partition
+
+it, because partitioning means
+that I should cover the whole
+
+states in the classes.
+
+What I to do is to do some
+kind of partitioning in a
+
+Markov chain that I have, by
+using the classes, so that I
+
+can have a representative
+state for each class.
+
+And this is one way to partition
+the Markov chains.
+
+And why do I say it's
+partitioning?
+
+Well, it's covering the whole
+finite space of the states.
+
+But I need to prove that
+there's no intersection
+
+between classes also.
+
+Why is it like that?
+
+So meaning that I cannot have
+two classes where there is an
+
+intersection between them,
+because if there's an
+
+intersection--
+
+for example, i belongs to
+C1 and i belongs to C2--
+
+it means that i communicates
+with all the states in C1 and
+
+i communicates with
+all states in C2.
+
+So you can say that all states
+in C1 communicate with all
+
+states in C2.
+
+So actually, they should
+be the same.
+
+And there's only these
+states that
+
+communicate with each other.
+
+We have this exclusivity
+that's conditional.
+
+So we can have this kind
+of partitioning.
+
+Is there any question?
+
+Everybody's fine?
+
+So another definition which
+is going to be very, very
+
+important in the future for
+us is the recurrency.
+
+And it's actually very simple.
+
+So a state is called recurrent
+if for all the states that we
+
+have j is accessible to
+i, we also have i is
+
+accessible to j.
+
+So if from some state i, in some
+number of states, I can
+
+go to some state j, I can
+get back to i from
+
+this state for sure.
+
+And this should be
+true for all the
+
+states in a Markov chain.
+
+So if there's a walk from i to
+j, there should be a walk from
+
+j to i, too.
+
+If this is true, then
+i is recurrent.
+
+This is the definition
+of recurrence.
+
+Is it OK?
+
+And if it's not recurrent,
+we call it transient.
+
+And why do we call transient?
+
+I mean, the intuition
+is very nice.
+
+So what is a transient state?
+
+A transient state says that
+there might be some kind of
+
+walk from i to some k.
+
+And then I can't go back.
+
+So there's a positive
+probability that I go out of
+
+state i in some way, in
+some walk, and never
+
+come back to it.
+
+So it's kind of transitional
+behavior.
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: No, no, with
+some probability.
+
+So there exists some
+probability.
+
+There is a positive probability
+that I go out of
+
+it and never come back.
+
+It's enough for definition
+of transience.
+
+So you know why?
+
+Because I have the definition of
+recurrence for all the j's
+
+that are accessible from i.
+
+So with probability 1--
+
+oh, OK, so I cannot say
+with probability 1.
+
+Yeah, I cannot say probability
+of 1 for recurrency.
+
+But for transient behavior,
+there exists some probability.
+
+There's a positive probability
+that I go out
+
+and never come back.
+
+State 1 is transient.
+
+And state 3, is it recurrent
+or transient?
+
+Some idea?
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Transient?
+
+What about state 2?
+
+It's wrong, because there should
+be something going on
+
+[INAUDIBLE].
+
+So now here, it's recurrent.
+
+Good?
+
+Oh yeah, we have
+examples here.
+
+So states 2 and 3 are recurrent,
+because the only
+
+state that I can go out from
+this state is to themselves.
+
+So they are only accessible
+from themselves.
+
+And there's a positive
+probability of going from one
+
+to the other.
+
+So they're recurrent.
+
+But states 4 and 5
+are transient.
+
+And the reason is here, because
+there is a positive
+
+probability that I go out of
+state 4 in that direction and
+
+never come back.
+
+And there's no way
+to come back.
+
+And state 6 and 1 are
+also transient.
+
+State 6 is very, very transient
+because, well, I go
+
+out of it in one step
+and never come back.
+
+And state 1 is also transient,
+because I can go out of it in
+
+this direction and never
+be able to come back.
+
+Do you see?
+
+So this is a very, very, very
+important theorem, which says
+
+that if we have some classes,
+the states in the class are
+
+all recurrent or
+all transient.
+
+This is what we are going to
+use a lot in the future, so
+
+you should remember it.
+
+And the proof is very easy.
+
+So let's assume that state
+i is recurrent.
+
+And let's define Si, all the
+states that communicate with
+
+i, that are accessible from i.
+
+And you know that since i is
+recurrent, being accessible
+
+from i means that i is
+accessible from them.
+
+So if j is accessible from i,
+i is also accessible from j.
+
+So we know that i and j
+communicate with each other if
+
+and only if j is in this set.
+
+So this is a class.
+
+This is the class
+that contains i.
+
+So this is like the class that I
+told you, that we can have a
+
+class where this state
+i is representative.
+
+And actually, any state in a
+class can be representative.
+
+It doesn't matter.
+
+So by just looking at state
+i, I can define a class.
+
+The states that are accessible
+from i-- and actually, this is
+
+the class that contains i.
+
+So let's assume that there's
+a state called k which is
+
+accessible from some j
+which is in this set.
+
+So k is accessible from j, and
+j is accessible from i.
+
+So k is accessible from i.
+
+But k accessible from i
+implies that i is also
+
+accessible from k, because
+i is recurrent.
+
+So you think i is accessible
+from k?
+
+And you know that j is also
+accessible from i because,
+
+well, Si was also a class,
+recurrent class.
+
+So you see that j is
+also recurrent.
+
+So if k is accessible from j,
+then j is also accessible from
+
+k for any k.
+
+So this is the definition
+of recurrency.
+
+So what I want to say is that if
+i is recurrent and it's in
+
+the same class as j, then
+j is recurrent for sure.
+
+And we didn't prove it here,
+but if one of them is
+
+transient, them all of them
+are transient too.
+
+So the proof is very simple.
+
+I proved that if there is any
+state like k that's is
+
+accessible from j, I need
+to prove that j is also
+
+accessible from k.
+
+And I proved it like this.
+
+It's easy.
+
+So the next definition that we
+have is the definition of the
+
+periodic states and classes.
+
+So I told you that the number of
+steps in a walk-- so when I
+
+say that there's a walk from
+some state to the other state,
+
+I didn't specify the number of
+steps needed to get from the
+
+state to another state.
+
+So assuming that there is a
+walk from state i to i,
+
+meaning that i is accessible
+from i, it's not always true.
+
+You might go out of i and
+never come back to it.
+
+So assuming that there's a
+positive probability that we
+
+can go from state i to i, you
+can look at the number of
+
+steps needed for this walk.
+
+And we can find the greatest
+common divisor of
+
+this number of steps.
+
+And it's called the
+period of i.
+
+And if this number is greater
+than 1, then i is
+
+called to be periodic.
+
+And if it's not,
+it's aperiodic.
+
+So the very simple example
+of this thing
+
+is this Markov chain.
+
+So probability of 1,1
+in step is 0.
+
+probability of 1, 1 in two
+steps is positive.
+
+And actually, probability of
+1, 1 for all even number of
+
+steps is positive.
+
+But for all odd number
+of steps, it's 0.
+
+And actually, you can
+prove that 2 is the
+
+greatest common divisor.
+
+So this is the very
+easy example to
+
+show that it's periodic.
+
+So there is a very simple
+thing to check if
+
+something is aperiodic.
+
+But it doesn't tell me--
+
+I mean, if it doesn't exist, we
+don't know its periodicity.
+
+So if there is a walk from state
+1 or state i to itself,
+
+and in this walk, we go from a
+state called, like, j, and
+
+there is a loop here--
+
+so Pjj is positive.
+
+What can we say about the
+periodicity of i?
+
+No, the period is 1.
+
+Yeah, exactly.
+
+So in this case, state i
+is always aperiodic.
+
+So if there's a walk, and in
+this walk, there is a loop, we
+
+always say that.
+
+But if it doesn't exist, can
+we say anything about the
+
+periodicity?
+
+No.
+
+It might be periodic.
+
+It might be aperiodic.
+
+It's just a check.
+
+So whenever you see a loop,
+it's aperiodic.
+
+Whenever you see a loop in the
+walk from i to i, if there's a
+
+loop in the other side of the
+Markov chain, we don't care.
+
+So the definition is fine.
+
+So just looking at this example,
+so if we're going
+
+from state 4 to 4, the number
+of states that we need is,
+
+like, 4, 6, 8.
+
+So 4, 1, 2, 3, 4 is a cycle, or
+is a walk from 4, to 4, and
+
+the number of steps is 4.
+
+4, 5, 6, 7, 8 9, 4
+is another walk.
+
+So this corresponds
+to n equal to 6.
+
+And 4, 1, 2 3, 4, 1, 2, 3,
+4 is another walk which
+
+corresponds to n equal to 8.
+
+So you see that we can go like
+this or this or this.
+
+So these are different n's.
+
+But we see that the greatest
+common divisor is 2.
+
+So the period of state 4 is 2.
+
+For state 7, we have
+this thing.
+
+So the minimum number of steps
+to get from 7 to itself is 6,
+
+and then you can get from
+7 to 7 in 10 steps.
+
+And I hope you see it.
+
+So it's going to be like this.
+
+And so again, the greatest
+common divisor is 2.
+
+So we proved that if one state
+in a class is recurrent, and
+
+then all the states
+are recurrent.
+
+And we said that recurrency
+corresponds to having a cycle,
+
+having a walk from each
+state to itself.
+
+So this is the result, very
+similar to that one, which
+
+says that all the states
+in the same class
+
+have the same period.
+
+And in this example,
+you see it too.
+
+The proof is not very
+complicated, but it takes time
+
+to do that.
+
+So I'm not going to do it.
+
+But it's all nice.
+
+So it's good if you look at
+the text, you'll see that.
+
+AUDIENCE: [INAUDIBLE]
+
+only for recurrent states?
+
+PROFESSOR: Yeah.
+
+For non-recurrent ones, it's--
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: It's 1.
+
+It's aperiodic.
+
+OK, yeah.
+
+Periodicity is only defined for
+recurrent states, yeah.
+
+We have another example here.
+
+I just want to show you.
+
+So I have two recurrent classes
+in this example.
+
+Actually, three.
+
+So one of them is this class.
+
+What is the period for a class
+corresponding to state 1?
+
+It's 1, because I have a loop.
+
+It's very simple.
+
+For any n, there is a positive
+probability.
+
+What is the period for
+this class, states--
+
+containing states 4 and 5?
+
+Look at it.
+
+There is definitely a
+loop in this class.
+
+So it's 1.
+
+No, I said that whenever there
+is a loop, the greatest common
+
+divisor is 1.
+
+So for going from a state 5 to
+5, we can go it in one step,
+
+two step, three step,
+four step, five.
+
+So the greatest common
+divisor is 1.
+
+So here, I showed you that if
+there is a loop, then it's
+
+definitely aperiodic, meaning
+that the greatest common
+
+divisor is 1.
+
+AUDIENCE: [INAUDIBLE] have
+self-transitions [INAUDIBLE]
+
+2?
+
+PROFESSOR: No, I'm talking
+about 4 and 5.
+
+In what?
+
+AUDIENCE: If they didn't
+have self-transitions?
+
+[INAUDIBLE].
+
+PROFESSOR: Oh yeah.
+
+It would be like this one?
+
+AUDIENCE: Yeah, [INAUDIBLE].
+
+PROFESSOR: Yeah, definitely.
+
+So the class containing states
+2 and 3, they are periodic.
+
+AUDIENCE: Oh, wait.
+
+You just said [INAUDIBLE].
+
+PROFESSOR: Oh, OK.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: Yeah, actually,
+we can define
+
+for transient states.
+
+Yeah, for transient classes,
+we can define periodicity,
+
+like this case.
+
+Yeah, why not?
+
+This is another very important
+thing that we can
+
+do in Markov chains.
+
+So I have a class of states
+in a Markov chain,
+
+and they are periodic.
+
+So the period of each state in
+a class is greater than 1.
+
+And you know that all the states
+in a class have the
+
+same period.
+
+So it means that I can partition
+the class into these
+
+subclasses, where
+there is only--
+
+OK, so--
+
+do I have that?
+
+I don't know.
+
+So let's assume that
+d is equal to 3.
+
+And the whole team is the
+class of states that I'm
+
+talking about.
+
+I can partition into three
+classes, in which I only have
+
+transitions from one of these
+to the other one.
+
+So there's no transition in
+this subclass to itself.
+
+And the only transitions
+are from one
+
+class to the next one.
+
+So this is sort of intuitive.
+
+So just looking at three states,
+if the period is 3, I
+
+can partition it in this way.
+
+Or I can have it like two of
+these in this case, where I
+
+have like this.
+
+You see?
+
+So there's a transition from
+this to these two states, and
+
+from these two states to here,
+and from here to here.
+
+But I cannot have any transition
+from here to
+
+itself, or from here to
+here, or here to here.
+
+Just look at the text for the
+proof and illustration.
+
+But there exists this kind
+of partitioning.
+
+You should know that.
+
+Yeah, so if I am in a class, in
+a subclass, the next state
+
+will be in the next subclass,
+for sure.
+
+So I know this subclass
+in [INAUDIBLE].
+
+And in two steps, I will be
+in the other [INAUDIBLE].
+
+So you know that the set of
+classes that I can be in
+
+state, nd plus m.
+
+So the other definition that
+you can say is that, again,
+
+you can choose one of the
+states in a class that I
+
+talked about.
+
+So let's say that I
+choose a state 1.
+
+And I define Sm--
+
+Sm corresponds to
+that subclass--
+
+are all the j's where S1j.
+
+So I told you that I will have
+d classes, I can define each
+
+class like this.
+
+So this is all the possible
+states that I can be in nd
+
+plus m step.
+
+So starting from state 1, in
+nd plus m step, I can be in
+
+set of classes, for some m.
+
+So m can we big.
+
+But anyway, I call this
+the subclass number m.
+
+So let's just talk
+about something.
+
+So I said that in order to
+characterize the Markov
+
+chains, I need to show you the
+initial state or initial state
+
+distribution.
+
+So it can be deterministic,
+like I start from some
+
+specific state all the time,
+or there can be some
+
+distribution, like px0, meaning
+that this is the
+
+distribution that I would have
+at my initial state.
+
+I don't have it here, but using,
+I think, chain rules,
+
+we can easily find a
+distribution of states at each
+
+time instant by having the
+transitional probabilities and
+
+the initial state
+distribution.
+
+I just wrote it for you.
+
+So for characterizing the Markov
+chain, I just need to
+
+tell you the transition
+probabilities
+
+and the initial state.
+
+So a very good question is that,
+is there any kind of
+
+stable behavior when time goes,
+like in very far future?
+
+So I had an example here,
+just looking at here.
+
+So this is a very simple thing
+that I can say about this
+
+Markov chain.
+
+I know that in the very far
+future, there is a 0
+
+probability that
+I'm in state 6.
+
+And you know it why?
+
+Because any time that I am in
+state 6, I will go out of it
+
+with probability 1.
+
+So there's no chance that
+I will be there.
+
+Or I can say that, if I start
+from state 4, in very, very
+
+far future, I will not be in
+state 1, 4, or 5, for sure.
+
+You know why?
+
+Because there is a positive
+probability of going out of
+
+these threes states,
+like here.
+
+And then if I go out of it,
+I can never come back.
+
+So there's a chance of going
+from state 4 to state 2.
+
+And if I ever go there, I
+will never come back.
+
+So these are the statements that
+I can say about the state
+
+of behavior or the very,
+very future behavior
+
+of the Markov chain.
+
+So the question is that, can
+we always say these kind of
+
+statements?
+
+And what kind of statements,
+actually, we can have?
+
+And so you see that, for
+example, for a state six
+
+[INAUDIBLE]
+
+example, I could say that the
+probability of being in state
+
+6 as n goes to infinity is 0.
+
+So can I always have some kind
+of probability distribution
+
+over the states in the future
+as n goes to infinity?
+
+This is a very good question.
+
+And actually, it's related to a
+lot of applications that we
+
+have for Markov chains, like
+the queuing theory.
+
+And you can have queues
+for almost anything.
+
+So one of the most fundamental
+and interesting classes of
+
+states are the states that are
+called ergodic, meaning that
+
+they are recurrent
+and aperiodic.
+
+So if I have a Markov chain that
+has only one class, and
+
+this class is recurrent and
+aperiodic, then we call it a
+
+ergodic Markov chain.
+
+So we had two theorems saying
+that if a state in a class is
+
+recurrent, then all the
+states are recurrent.
+
+And if a state in a class is
+aperiodic, then all the states
+
+are aperiodic.
+
+So we can say that some classes
+are ergodic and some
+
+are not ergodic.
+
+So if the Markov chain has only
+one class, and this class
+
+is aperiodic and recurrent,
+then we call it a ergodic
+
+Markov chain.
+
+And the very important and
+nice property of ergodic
+
+Markov chains is that they
+lose memory as n goes to
+
+infinity, meaning that whatever
+initial distribution
+
+that I have for the initial
+state, I will
+
+lose memory of that.
+
+So whatever state that I start
+in, or whatever distribution
+
+that I start in, after a while,
+for a large enough n,
+
+the distribution of states
+does not depend on that.
+
+So again, looking at that chain
+rule, I could say that I
+
+can find the probability
+distribution of x by looking
+
+at this thing.
+
+And looking at these
+recursively, it all depends on
+
+P of the initial distribution.
+
+And the ergodic Markov chains
+have this property that, after
+
+a while, this distribution
+doesn't depend on initial
+
+distribution anymore.
+
+So they lose memory.
+
+And actually, usually we can
+calculate the stable
+
+distribution.
+
+So this thing goes to a limit
+which is called pj.
+
+So the important thing is that
+it doesn't depend on i.
+
+It doesn't depend
+where i starts.
+
+Eventually, I will converge
+the distribution.
+
+And then this distribution
+doesn't change.
+
+So for a large enough n, I have
+this property for ergodic
+
+Markov chains.
+
+We will have a lot
+to do with these
+
+properties in the future.
+
+So I was saying that this pj,
+pi j, should be positive.
+
+So being in each state has
+a non-0 probability.
+
+The first thing that I need to
+prove is that pijn and is
+
+nonzero for a large enough n for
+all j and all the initial
+
+distributions.
+
+And I want to prove that
+this is true for
+
+ergodic Markov chains.
+
+This is not true, generally.
+
+Well, this is more a
+combinatorial issue, but there
+
+is a theorem here which says
+that for an ergodic Markov
+
+chain, for all n greater than
+this value, I have non-0
+
+probability of going
+from i to j.
+
+So the thing that you should be
+careful here is that, for
+
+all n greater than this value.
+
+So for going from a state 1 to
+1, I can go it in six steps
+
+and 12 steps and so on.
+
+But I cannot go it in
+24 steps, I think.
+
+I cannot go from 1
+to 1 in 25 steps.
+
+But I can go from 1 to 1 in
+26, 27, 28, 29, to 30.
+
+So for n greater than n minus
+1 squared plus 1, I can go
+
+from any state to any state.
+
+So I think this [? bond ?]
+is tied for state 4.
+
+Sorry, maybe what I said
+is true for state 4.
+
+Yeah.
+
+So I'm not going to prove
+this theorem.
+
+Well, actually you don't
+have the proof
+
+in the notes, either.
+
+But yeah, you can look at the
+example and the cases that are
+
+discussed in the notes.
+
+Is there any questions?
+
+Fine?
\ No newline at end of file
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+++ b/cZW2A2z7zcI.txt
@@ -0,0 +1,4595 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the fourth session is to talk about you
+
+ align:start position:0%
+the fourth session is to talk about you
+ 
+
+ align:start position:0%
+the fourth session is to talk about you
+in a facilitative leader role do you
+
+ align:start position:0%
+in a facilitative leader role do you
+ 
+
+ align:start position:0%
+in a facilitative leader role do you
+imagine yourself stepping into a leader
+
+ align:start position:0%
+imagine yourself stepping into a leader
+ 
+
+ align:start position:0%
+imagine yourself stepping into a leader
+role in a public sector do you think you
+
+ align:start position:0%
+role in a public sector do you think you
+ 
+
+ align:start position:0%
+role in a public sector do you think you
+need to develop additional skills or
+
+ align:start position:0%
+need to develop additional skills or
+ 
+
+ align:start position:0%
+need to develop additional skills or
+capabilities before you would do that
+
+ align:start position:0%
+capabilities before you would do that
+ 
+
+ align:start position:0%
+capabilities before you would do that
+that do you know for sure you will never
+
+ align:start position:0%
+that do you know for sure you will never
+ 
+
+ align:start position:0%
+that do you know for sure you will never
+do that I want the discussion to be
+
+ align:start position:0%
+do that I want the discussion to be
+ 
+
+ align:start position:0%
+do that I want the discussion to be
+about each person imagining themselves
+
+ align:start position:0%
+about each person imagining themselves
+ 
+
+ align:start position:0%
+about each person imagining themselves
+yes or no maybe but only if in a
+
+ align:start position:0%
+yes or no maybe but only if in a
+ 
+
+ align:start position:0%
+yes or no maybe but only if in a
+leadership role in the public Arena
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the negotiation field we often teach
+
+ align:start position:0%
+in the negotiation field we often teach
+ 
+
+ align:start position:0%
+in the negotiation field we often teach
+about the need to be able to
+
+ align:start position:0%
+about the need to be able to
+ 
+
+ align:start position:0%
+about the need to be able to
+self-regulate between empathy and
+
+ align:start position:0%
+self-regulate between empathy and
+ 
+
+ align:start position:0%
+self-regulate between empathy and
+assertiveness we make that distinction
+
+ align:start position:0%
+assertiveness we make that distinction
+ 
+
+ align:start position:0%
+assertiveness we make that distinction
+and we make that
+
+ align:start position:0%
+and we make that
+ 
+
+ align:start position:0%
+and we make that
+connection because in most negotiations
+
+ align:start position:0%
+connection because in most negotiations
+ 
+
+ align:start position:0%
+connection because in most negotiations
+we think it's important to hear what the
+
+ align:start position:0%
+we think it's important to hear what the
+ 
+
+ align:start position:0%
+we think it's important to hear what the
+other side's concerns and interests are
+
+ align:start position:0%
+other side's concerns and interests are
+ 
+
+ align:start position:0%
+other side's concerns and interests are
+so that you can find a way of responding
+
+ align:start position:0%
+so that you can find a way of responding
+ 
+
+ align:start position:0%
+so that you can find a way of responding
+to them in exchange for reciprocity but
+
+ align:start position:0%
+to them in exchange for reciprocity but
+ 
+
+ align:start position:0%
+to them in exchange for reciprocity but
+if you can't listened can't hear can't
+
+ align:start position:0%
+if you can't listened can't hear can't
+ 
+
+ align:start position:0%
+if you can't listened can't hear can't
+empathize with their con concerns it's
+
+ align:start position:0%
+empathize with their con concerns it's
+ 
+
+ align:start position:0%
+empathize with their con concerns it's
+unlikely you'll suggest something that
+
+ align:start position:0%
+unlikely you'll suggest something that
+ 
+
+ align:start position:0%
+unlikely you'll suggest something that
+meets their interests meets their needs
+
+ align:start position:0%
+meets their interests meets their needs
+ 
+
+ align:start position:0%
+meets their interests meets their needs
+and yours we tend to think of empathy as
+
+ align:start position:0%
+and yours we tend to think of empathy as
+ 
+
+ align:start position:0%
+and yours we tend to think of empathy as
+something we pour out with people we
+
+ align:start position:0%
+something we pour out with people we
+ 
+
+ align:start position:0%
+something we pour out with people we
+care about but in this leadership SL
+
+ align:start position:0%
+care about but in this leadership SL
+ 
+
+ align:start position:0%
+care about but in this leadership SL
+Neti SL consensus building
+
+ align:start position:0%
+Neti SL consensus building
+ 
+
+ align:start position:0%
+Neti SL consensus building
+context we argue that you need to be
+
+ align:start position:0%
+context we argue that you need to be
+ 
+
+ align:start position:0%
+context we argue that you need to be
+able to up the empathy quotient
+
+ align:start position:0%
+able to up the empathy quotient
+ 
+
+ align:start position:0%
+able to up the empathy quotient
+in order to be able to create enough of
+
+ align:start position:0%
+in order to be able to create enough of
+ 
+
+ align:start position:0%
+in order to be able to create enough of
+a relationship with the others to hear
+
+ align:start position:0%
+a relationship with the others to hear
+ 
+
+ align:start position:0%
+a relationship with the others to hear
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+concerns so that you can construct some
+
+ align:start position:0%
+concerns so that you can construct some
+ 
+
+ align:start position:0%
+concerns so that you can construct some
+proposal that's good for them and great
+
+ align:start position:0%
+proposal that's good for them and great
+ 
+
+ align:start position:0%
+proposal that's good for them and great
+for you and if you can't listen and
+
+ align:start position:0%
+for you and if you can't listen and
+ 
+
+ align:start position:0%
+for you and if you can't listen and
+present yourself in an empathetic way
+
+ align:start position:0%
+present yourself in an empathetic way
+ 
+
+ align:start position:0%
+present yourself in an empathetic way
+you're not likely to find out from them
+
+ align:start position:0%
+you're not likely to find out from them
+ 
+
+ align:start position:0%
+you're not likely to find out from them
+what's really on their mind and what
+
+ align:start position:0%
+what's really on their mind and what
+ 
+
+ align:start position:0%
+what's really on their mind and what
+their most important concerns are so
+
+ align:start position:0%
+their most important concerns are so
+ 
+
+ align:start position:0%
+their most important concerns are so
+there's a constant need to adjust in the
+
+ align:start position:0%
+there's a constant need to adjust in the
+ 
+
+ align:start position:0%
+there's a constant need to adjust in the
+context of the kinds of hypotheticals
+
+ align:start position:0%
+context of the kinds of hypotheticals
+ 
+
+ align:start position:0%
+context of the kinds of hypotheticals
+we've been talking
+
+ align:start position:0%
+we've been talking
+ 
+
+ align:start position:0%
+we've been talking
+about how much empathy you're exhibiting
+
+ align:start position:0%
+about how much empathy you're exhibiting
+ 
+
+ align:start position:0%
+about how much empathy you're exhibiting
+how much empathy you're trying to Jin up
+
+ align:start position:0%
+how much empathy you're trying to Jin up
+ 
+
+ align:start position:0%
+how much empathy you're trying to Jin up
+I'm not talking about play acting I'm
+
+ align:start position:0%
+I'm not talking about play acting I'm
+ 
+
+ align:start position:0%
+I'm not talking about play acting I'm
+talking about serious effort to
+
+ align:start position:0%
+talking about serious effort to
+ 
+
+ align:start position:0%
+talking about serious effort to
+empathize with the concerns of the other
+
+ align:start position:0%
+empathize with the concerns of the other
+ 
+
+ align:start position:0%
+empathize with the concerns of the other
+they'll know if it's not serious and if
+
+ align:start position:0%
+they'll know if it's not serious and if
+ 
+
+ align:start position:0%
+they'll know if it's not serious and if
+it's not serious it won't have the
+
+ align:start position:0%
+it's not serious it won't have the
+ 
+
+ align:start position:0%
+it's not serious it won't have the
+effect you need it to have so how can
+
+ align:start position:0%
+effect you need it to have so how can
+ 
+
+ align:start position:0%
+effect you need it to have so how can
+you you gin up a empathy for someone you
+
+ align:start position:0%
+you you gin up a empathy for someone you
+ 
+
+ align:start position:0%
+you you gin up a empathy for someone you
+disagree with you don't like who you
+
+ align:start position:0%
+disagree with you don't like who you
+ 
+
+ align:start position:0%
+disagree with you don't like who you
+think is evil who stands for bad things
+
+ align:start position:0%
+think is evil who stands for bad things
+ 
+
+ align:start position:0%
+think is evil who stands for bad things
+but I'm saying you have got to find out
+
+ align:start position:0%
+but I'm saying you have got to find out
+ 
+
+ align:start position:0%
+but I'm saying you have got to find out
+what's important to them and you've got
+
+ align:start position:0%
+what's important to them and you've got
+ 
+
+ align:start position:0%
+what's important to them and you've got
+to get them to trust you enough to tell
+
+ align:start position:0%
+to get them to trust you enough to tell
+ 
+
+ align:start position:0%
+to get them to trust you enough to tell
+you what's important to them so that you
+
+ align:start position:0%
+you what's important to them so that you
+ 
+
+ align:start position:0%
+you what's important to them so that you
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+construct
+
+ align:start position:0%
+construct
+ 
+
+ align:start position:0%
+construct
+proposals for the other which could be a
+
+ align:start position:0%
+proposals for the other which could be a
+ 
+
+ align:start position:0%
+proposals for the other which could be a
+group and not just a person and be
+
+ align:start position:0%
+group and not just a person and be
+ 
+
+ align:start position:0%
+group and not just a person and be
+assertive about that at the same time in
+
+ align:start position:0%
+assertive about that at the same time in
+ 
+
+ align:start position:0%
+assertive about that at the same time in
+the same setting in the same
+
+ align:start position:0%
+the same setting in the same
+ 
+
+ align:start position:0%
+the same setting in the same
+interactions in which you have also been
+
+ align:start position:0%
+interactions in which you have also been
+ 
+
+ align:start position:0%
+interactions in which you have also been
+empathetic there's a tension between
+
+ align:start position:0%
+empathetic there's a tension between
+ 
+
+ align:start position:0%
+empathetic there's a tension between
+them but both need to be present there's
+
+ align:start position:0%
+them but both need to be present there's
+ 
+
+ align:start position:0%
+them but both need to be present there's
+a really important distinction between
+
+ align:start position:0%
+a really important distinction between
+ 
+
+ align:start position:0%
+a really important distinction between
+facilitation and mediation I did not
+
+ align:start position:0%
+facilitation and mediation I did not
+ 
+
+ align:start position:0%
+facilitation and mediation I did not
+call this mediating leadership I call
+
+ align:start position:0%
+call this mediating leadership I call
+ 
+
+ align:start position:0%
+call this mediating leadership I call
+this facilitating leadership that's
+
+ align:start position:0%
+this facilitating leadership that's
+ 
+
+ align:start position:0%
+this facilitating leadership that's
+because facilitate ation means something
+
+ align:start position:0%
+because facilitate ation means something
+ 
+
+ align:start position:0%
+because facilitate ation means something
+different from mediation you can't
+
+ align:start position:0%
+different from mediation you can't
+ 
+
+ align:start position:0%
+different from mediation you can't
+mediate unless you can claim and perform
+
+ align:start position:0%
+mediate unless you can claim and perform
+ 
+
+ align:start position:0%
+mediate unless you can claim and perform
+in a neutral way the definition of
+
+ align:start position:0%
+in a neutral way the definition of
+ 
+
+ align:start position:0%
+in a neutral way the definition of
+mediation is neutral nonpartisan now no
+
+ align:start position:0%
+mediation is neutral nonpartisan now no
+ 
+
+ align:start position:0%
+mediation is neutral nonpartisan now no
+human really is neutral ever but in this
+
+ align:start position:0%
+human really is neutral ever but in this
+ 
+
+ align:start position:0%
+human really is neutral ever but in this
+professional role of
+
+ align:start position:0%
+professional role of
+ 
+
+ align:start position:0%
+professional role of
+mediation you have to be accepted as
+
+ align:start position:0%
+mediation you have to be accepted as
+ 
+
+ align:start position:0%
+mediation you have to be accepted as
+nonpartisan by the parties so the
+
+ align:start position:0%
+nonpartisan by the parties so the
+ 
+
+ align:start position:0%
+nonpartisan by the parties so the
+measure of your neutrality is their
+
+ align:start position:0%
+measure of your neutrality is their
+ 
+
+ align:start position:0%
+measure of your neutrality is their
+perception of you and their willingness
+
+ align:start position:0%
+perception of you and their willingness
+ 
+
+ align:start position:0%
+perception of you and their willingness
+to accept the fact you are not there to
+
+ align:start position:0%
+to accept the fact you are not there to
+ 
+
+ align:start position:0%
+to accept the fact you are not there to
+advance one side or the other side or
+
+ align:start position:0%
+advance one side or the other side or
+ 
+
+ align:start position:0%
+advance one side or the other side or
+your own interests because if someone
+
+ align:start position:0%
+your own interests because if someone
+ 
+
+ align:start position:0%
+your own interests because if someone
+thinks I've done something that's
+
+ align:start position:0%
+thinks I've done something that's
+ 
+
+ align:start position:0%
+thinks I've done something that's
+partisan they will tell me to leave so
+
+ align:start position:0%
+partisan they will tell me to leave so
+ 
+
+ align:start position:0%
+partisan they will tell me to leave so
+neutrality goes with mediation
+
+ align:start position:0%
+neutrality goes with mediation
+ 
+
+ align:start position:0%
+neutrality goes with mediation
+facilitation is a skill more than it is
+
+ align:start position:0%
+facilitation is a skill more than it is
+ 
+
+ align:start position:0%
+facilitation is a skill more than it is
+a role you have your own interests you
+
+ align:start position:0%
+a role you have your own interests you
+ 
+
+ align:start position:0%
+a role you have your own interests you
+haven't promised neutrality
+
+ align:start position:0%
+haven't promised neutrality
+ 
+
+ align:start position:0%
+haven't promised neutrality
+to the group but you've promised or
+
+ align:start position:0%
+to the group but you've promised or
+ 
+
+ align:start position:0%
+to the group but you've promised or
+you're offering to
+
+ align:start position:0%
+you're offering to
+ 
+
+ align:start position:0%
+you're offering to
+facilitate a collective effort to deal
+
+ align:start position:0%
+facilitate a collective effort to deal
+ 
+
+ align:start position:0%
+facilitate a collective effort to deal
+with whatever the conflict or the
+
+ align:start position:0%
+with whatever the conflict or the
+ 
+
+ align:start position:0%
+with whatever the conflict or the
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+is sometimes a spoiler will show
+
+ align:start position:0%
+is sometimes a spoiler will show
+ 
+
+ align:start position:0%
+is sometimes a spoiler will show
+themselves and they'll say I don't care
+
+ align:start position:0%
+themselves and they'll say I don't care
+ 
+
+ align:start position:0%
+themselves and they'll say I don't care
+what this process is going to do I can't
+
+ align:start position:0%
+what this process is going to do I can't
+ 
+
+ align:start position:0%
+what this process is going to do I can't
+accept anything less than x and you're
+
+ align:start position:0%
+accept anything less than x and you're
+ 
+
+ align:start position:0%
+accept anything less than x and you're
+trying to have the parties be be
+
+ align:start position:0%
+trying to have the parties be be
+ 
+
+ align:start position:0%
+trying to have the parties be be
+creative and generate new options that
+
+ align:start position:0%
+creative and generate new options that
+ 
+
+ align:start position:0%
+creative and generate new options that
+will meet everybody's interests and this
+
+ align:start position:0%
+will meet everybody's interests and this
+ 
+
+ align:start position:0%
+will meet everybody's interests and this
+person's proposal clearly will make it
+
+ align:start position:0%
+person's proposal clearly will make it
+ 
+
+ align:start position:0%
+person's proposal clearly will make it
+impossible if they won't move off that
+
+ align:start position:0%
+impossible if they won't move off that
+ 
+
+ align:start position:0%
+impossible if they won't move off that
+position we're not going to be part of
+
+ align:start position:0%
+position we're not going to be part of
+ 
+
+ align:start position:0%
+position we're not going to be part of
+any agreement and there's nothing you
+
+ align:start position:0%
+any agreement and there's nothing you
+ 
+
+ align:start position:0%
+any agreement and there's nothing you
+can say there's no song you can sing
+
+ align:start position:0%
+can say there's no song you can sing
+ 
+
+ align:start position:0%
+can say there's no song you can sing
+that's going to get me to agree to
+
+ align:start position:0%
+that's going to get me to agree to
+ 
+
+ align:start position:0%
+that's going to get me to agree to
+something where we don't get this or at
+
+ align:start position:0%
+something where we don't get this or at
+ 
+
+ align:start position:0%
+something where we don't get this or at
+least this and there's a really very
+
+ align:start position:0%
+least this and there's a really very
+ 
+
+ align:start position:0%
+least this and there's a really very
+specific
+
+ align:start position:0%
+specific
+ 
+
+ align:start position:0%
+specific
+maneuver at that moment
+
+ align:start position:0%
+maneuver at that moment
+ 
+
+ align:start position:0%
+maneuver at that moment
+that facilitators and mediators use and
+
+ align:start position:0%
+that facilitators and mediators use and
+ 
+
+ align:start position:0%
+that facilitators and mediators use and
+I can only tell you from my own
+
+ align:start position:0%
+I can only tell you from my own
+ 
+
+ align:start position:0%
+I can only tell you from my own
+experience it stops the flow of the
+
+ align:start position:0%
+experience it stops the flow of the
+ 
+
+ align:start position:0%
+experience it stops the flow of the
+spoilers bad vibrations so when someone
+
+ align:start position:0%
+spoilers bad vibrations so when someone
+ 
+
+ align:start position:0%
+spoilers bad vibrations so when someone
+says if I don't get at least this we're
+
+ align:start position:0%
+says if I don't get at least this we're
+ 
+
+ align:start position:0%
+says if I don't get at least this we're
+out and the facilitator says well before
+
+ align:start position:0%
+out and the facilitator says well before
+ 
+
+ align:start position:0%
+out and the facilitator says well before
+anybody responds you wouldn't want any
+
+ align:start position:0%
+anybody responds you wouldn't want any
+ 
+
+ align:start position:0%
+anybody responds you wouldn't want any
+more than that if I can get the rest of
+
+ align:start position:0%
+more than that if I can get the rest of
+ 
+
+ align:start position:0%
+more than that if I can get the rest of
+this group to do better than that for
+
+ align:start position:0%
+this group to do better than that for
+ 
+
+ align:start position:0%
+this group to do better than that for
+you you you wouldn't want to be part of
+
+ align:start position:0%
+you you you wouldn't want to be part of
+ 
+
+ align:start position:0%
+you you you wouldn't want to be part of
+that conversation you would be amazed at
+
+ align:start position:0%
+that conversation you would be amazed at
+ 
+
+ align:start position:0%
+that conversation you would be amazed at
+the way the facial expressions of people
+
+ align:start position:0%
+the way the facial expressions of people
+ 
+
+ align:start position:0%
+the way the facial expressions of people
+who've built up for a week they're
+
+ align:start position:0%
+who've built up for a week they're
+ 
+
+ align:start position:0%
+who've built up for a week they're
+coming to this meeting and they're going
+
+ align:start position:0%
+coming to this meeting and they're going
+ 
+
+ align:start position:0%
+coming to this meeting and they're going
+to unload and they know everybody's
+
+ align:start position:0%
+to unload and they know everybody's
+ 
+
+ align:start position:0%
+to unload and they know everybody's
+going to be angry at them or hate them
+
+ align:start position:0%
+going to be angry at them or hate them
+ 
+
+ align:start position:0%
+going to be angry at them or hate them
+but they've worked themselves up and we
+
+ align:start position:0%
+but they've worked themselves up and we
+ 
+
+ align:start position:0%
+but they've worked themselves up and we
+have to have this cuz the moment they
+
+ align:start position:0%
+have to have this cuz the moment they
+ 
+
+ align:start position:0%
+have to have this cuz the moment they
+say well no I wouldn't be averse to more
+
+ align:start position:0%
+say well no I wouldn't be averse to more
+ 
+
+ align:start position:0%
+say well no I wouldn't be averse to more
+you say okay good so you need to join
+
+ align:start position:0%
+you say okay good so you need to join
+ 
+
+ align:start position:0%
+you say okay good so you need to join
+the conversation you need to listen to
+
+ align:start position:0%
+the conversation you need to listen to
+ 
+
+ align:start position:0%
+the conversation you need to listen to
+other people's interests we need to see
+
+ align:start position:0%
+other people's interests we need to see
+ 
+
+ align:start position:0%
+other people's interests we need to see
+how much more value we can create and
+
+ align:start position:0%
+how much more value we can create and
+ 
+
+ align:start position:0%
+how much more value we can create and
+then you can make a case for what you
+
+ align:start position:0%
+then you can make a case for what you
+ 
+
+ align:start position:0%
+then you can make a case for what you
+need and let's see if we can't reframe
+
+ align:start position:0%
+need and let's see if we can't reframe
+ 
+
+ align:start position:0%
+need and let's see if we can't reframe
+all of it is around moving them off that
+
+ align:start position:0%
+all of it is around moving them off that
+ 
+
+ align:start position:0%
+all of it is around moving them off that
+position and I'm not suggesting
+
+ align:start position:0%
+position and I'm not suggesting
+ 
+
+ align:start position:0%
+position and I'm not suggesting
+compromise so they got to take a minute
+
+ align:start position:0%
+compromise so they got to take a minute
+ 
+
+ align:start position:0%
+compromise so they got to take a minute
+to process it and then they'll say
+
+ align:start position:0%
+to process it and then they'll say
+ 
+
+ align:start position:0%
+to process it and then they'll say
+something like usually can you guarantee
+
+ align:start position:0%
+something like usually can you guarantee
+ 
+
+ align:start position:0%
+something like usually can you guarantee
+that they'll get me something better
+
+ align:start position:0%
+that they'll get me something better
+ 
+
+ align:start position:0%
+that they'll get me something better
+than that I said we can try I can't
+
+ align:start position:0%
+than that I said we can try I can't
+ 
+
+ align:start position:0%
+than that I said we can try I can't
+guarantee anybody will get anything
+
+ align:start position:0%
+guarantee anybody will get anything
+ 
+
+ align:start position:0%
+guarantee anybody will get anything
+right now but there's a really good
+
+ align:start position:0%
+right now but there's a really good
+ 
+
+ align:start position:0%
+right now but there's a really good
+chance if everybody is
+
+ align:start position:0%
+chance if everybody is
+ 
+
+ align:start position:0%
+chance if everybody is
+negotiating to try to meet their own
+
+ align:start position:0%
+negotiating to try to meet their own
+ 
+
+ align:start position:0%
+negotiating to try to meet their own
+interests and others that we can do that
+
+ align:start position:0%
+interests and others that we can do that
+ 
+
+ align:start position:0%
+interests and others that we can do that
+and they get up and leave because they
+
+ align:start position:0%
+and they get up and leave because they
+ 
+
+ align:start position:0%
+and they get up and leave because they
+don't know what else to do they can't
+
+ align:start position:0%
+don't know what else to do they can't
+ 
+
+ align:start position:0%
+don't know what else to do they can't
+admit that there might be in their
+
+ align:start position:0%
+admit that there might be in their
+ 
+
+ align:start position:0%
+admit that there might be in their
+interest to stay because they've told
+
+ align:start position:0%
+interest to stay because they've told
+ 
+
+ align:start position:0%
+interest to stay because they've told
+their people they were going to come
+
+ align:start position:0%
+their people they were going to come
+ 
+
+ align:start position:0%
+their people they were going to come
+tonight and blast this thing and make
+
+ align:start position:0%
+tonight and blast this thing and make
+ 
+
+ align:start position:0%
+tonight and blast this thing and make
+their position clear and too bad for
+
+ align:start position:0%
+their position clear and too bad for
+ 
+
+ align:start position:0%
+their position clear and too bad for
+everybody else and
+
+ align:start position:0%
+everybody else and
+ 
+
+ align:start position:0%
+everybody else and
+I don't know what they're going to say
+
+ align:start position:0%
+I don't know what they're going to say
+ 
+
+ align:start position:0%
+I don't know what they're going to say
+to their people when they go back
+
+ align:start position:0%
+to their people when they go back
+ 
+
+ align:start position:0%
+to their people when they go back
+they'll have some rationalization but
+
+ align:start position:0%
+they'll have some rationalization but
+ 
+
+ align:start position:0%
+they'll have some rationalization but
+they were so put off by the facilitation
+
+ align:start position:0%
+they were so put off by the facilitation
+ 
+
+ align:start position:0%
+they were so put off by the facilitation
+response that they um they just walked
+
+ align:start position:0%
+response that they um they just walked
+ 
+
+ align:start position:0%
+response that they um they just walked
+away it's not clear they would never
+
+ align:start position:0%
+away it's not clear they would never
+ 
+
+ align:start position:0%
+away it's not clear they would never
+come
+
+ align:start position:0%
+come
+ 
+
+ align:start position:0%
+come
+back if this process is going to go on a
+
+ align:start position:0%
+back if this process is going to go on a
+ 
+
+ align:start position:0%
+back if this process is going to go on a
+while as a facilitator I would certainly
+
+ align:start position:0%
+while as a facilitator I would certainly
+ 
+
+ align:start position:0%
+while as a facilitator I would certainly
+call them after the meeting and say
+
+ align:start position:0%
+call them after the meeting and say
+ 
+
+ align:start position:0%
+call them after the meeting and say
+anything that you can say about whether
+
+ align:start position:0%
+anything that you can say about whether
+ 
+
+ align:start position:0%
+anything that you can say about whether
+you might might rejoin the group you're
+
+ align:start position:0%
+you might might rejoin the group you're
+ 
+
+ align:start position:0%
+you might might rejoin the group you're
+cordially invited to come back to the
+
+ align:start position:0%
+cordially invited to come back to the
+ 
+
+ align:start position:0%
+cordially invited to come back to the
+next meeting no discussion of what
+
+ align:start position:0%
+next meeting no discussion of what
+ 
+
+ align:start position:0%
+next meeting no discussion of what
+happened necessary they sometimes will
+
+ align:start position:0%
+happened necessary they sometimes will
+ 
+
+ align:start position:0%
+happened necessary they sometimes will
+leave and in some instance it's possible
+
+ align:start position:0%
+leave and in some instance it's possible
+ 
+
+ align:start position:0%
+leave and in some instance it's possible
+to bring them back if you can make it
+
+ align:start position:0%
+to bring them back if you can make it
+ 
+
+ align:start position:0%
+to bring them back if you can make it
+not a embarrassing or humiliating
+
+ align:start position:0%
+not a embarrassing or humiliating
+ 
+
+ align:start position:0%
+not a embarrassing or humiliating
+process that's the facilitator's job
+
+ align:start position:0%
+process that's the facilitator's job
+ 
+
+ align:start position:0%
+process that's the facilitator's job
+you're right to be concerned that there
+
+ align:start position:0%
+you're right to be concerned that there
+ 
+
+ align:start position:0%
+you're right to be concerned that there
+might be spoilers your right to be
+
+ align:start position:0%
+might be spoilers your right to be
+ 
+
+ align:start position:0%
+might be spoilers your right to be
+concerned that you're not interested in
+
+ align:start position:0%
+concerned that you're not interested in
+ 
+
+ align:start position:0%
+concerned that you're not interested in
+helping to find some lowest common
+
+ align:start position:0%
+helping to find some lowest common
+ 
+
+ align:start position:0%
+helping to find some lowest common
+denominator compromise that starts with
+
+ align:start position:0%
+denominator compromise that starts with
+ 
+
+ align:start position:0%
+denominator compromise that starts with
+the spoiler dictating the outer limits
+
+ align:start position:0%
+the spoiler dictating the outer limits
+ 
+
+ align:start position:0%
+the spoiler dictating the outer limits
+of what can be produced you don't want
+
+ align:start position:0%
+of what can be produced you don't want
+ 
+
+ align:start position:0%
+of what can be produced you don't want
+to be part of that and I wouldn't either
+
+ align:start position:0%
+to be part of that and I wouldn't either
+ 
+
+ align:start position:0%
+to be part of that and I wouldn't either
+I don't blame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+you a number of people said maybe
+
+ align:start position:0%
+you a number of people said maybe
+ 
+
+ align:start position:0%
+you a number of people said maybe
+someday I might want to be a in a
+
+ align:start position:0%
+someday I might want to be a in a
+ 
+
+ align:start position:0%
+someday I might want to be a in a
+facility of leadership position but um I
+
+ align:start position:0%
+facility of leadership position but um I
+ 
+
+ align:start position:0%
+facility of leadership position but um I
+don't feel like I have the level of
+
+ align:start position:0%
+don't feel like I have the level of
+ 
+
+ align:start position:0%
+don't feel like I have the level of
+self-control or or self-confidence uh to
+
+ align:start position:0%
+self-control or or self-confidence uh to
+ 
+
+ align:start position:0%
+self-control or or self-confidence uh to
+take that role right now maybe there's
+
+ align:start position:0%
+take that role right now maybe there's
+ 
+
+ align:start position:0%
+take that role right now maybe there's
+more things I can learn maybe there's
+
+ align:start position:0%
+more things I can learn maybe there's
+ 
+
+ align:start position:0%
+more things I can learn maybe there's
+more things I can observe but I I don't
+
+ align:start position:0%
+more things I can observe but I I don't
+ 
+
+ align:start position:0%
+more things I can observe but I I don't
+see myself now being able to do that my
+
+ align:start position:0%
+see myself now being able to do that my
+ 
+
+ align:start position:0%
+see myself now being able to do that my
+response is well that's great that you
+
+ align:start position:0%
+response is well that's great that you
+ 
+
+ align:start position:0%
+response is well that's great that you
+have that perspective on yourself
+
+ align:start position:0%
+have that perspective on yourself
+ 
+
+ align:start position:0%
+have that perspective on yourself
+doesn't mean you can and add what skills
+
+ align:start position:0%
+doesn't mean you can and add what skills
+ 
+
+ align:start position:0%
+doesn't mean you can and add what skills
+and competences need to be added doesn't
+
+ align:start position:0%
+and competences need to be added doesn't
+ 
+
+ align:start position:0%
+and competences need to be added doesn't
+mean you have to sign off Forever on the
+
+ align:start position:0%
+mean you have to sign off Forever on the
+ 
+
+ align:start position:0%
+mean you have to sign off Forever on the
+prospect of being in a facilitative
+
+ align:start position:0%
+prospect of being in a facilitative
+ 
+
+ align:start position:0%
+prospect of being in a facilitative
+leadership role there are times in
+
+ align:start position:0%
+leadership role there are times in
+ 
+
+ align:start position:0%
+leadership role there are times in
+people's work life where they're tapped
+
+ align:start position:0%
+people's work life where they're tapped
+ 
+
+ align:start position:0%
+people's work life where they're tapped
+to play a leadership role and they may
+
+ align:start position:0%
+to play a leadership role and they may
+ 
+
+ align:start position:0%
+to play a leadership role and they may
+not think they're ready and they say no
+
+ align:start position:0%
+not think they're ready and they say no
+ 
+
+ align:start position:0%
+not think they're ready and they say no
+I don't see myself doing that that's
+
+ align:start position:0%
+I don't see myself doing that that's
+ 
+
+ align:start position:0%
+I don't see myself doing that that's
+fine if that's not you then that's not
+
+ align:start position:0%
+fine if that's not you then that's not
+ 
+
+ align:start position:0%
+fine if that's not you then that's not
+you I don't I don't see that as a ter
+
+ align:start position:0%
+you I don't I don't see that as a ter
+ 
+
+ align:start position:0%
+you I don't I don't see that as a ter
+able
+
+ align:start position:0%
+able
+ 
+
+ align:start position:0%
+able
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem one person described all of the
+
+ align:start position:0%
+problem one person described all of the
+ 
+
+ align:start position:0%
+problem one person described all of the
+micro skills that I listed for you last
+
+ align:start position:0%
+micro skills that I listed for you last
+ 
+
+ align:start position:0%
+micro skills that I listed for you last
+time as
+
+ align:start position:0%
+time as
+ 
+
+ align:start position:0%
+time as
+values rather than skills as if somehow
+
+ align:start position:0%
+values rather than skills as if somehow
+ 
+
+ align:start position:0%
+values rather than skills as if somehow
+they're about what you believe as
+
+ align:start position:0%
+they're about what you believe as
+ 
+
+ align:start position:0%
+they're about what you believe as
+opposed to what you can do and um these
+
+ align:start position:0%
+opposed to what you can do and um these
+ 
+
+ align:start position:0%
+opposed to what you can do and um these
+are skills
+
+ align:start position:0%
+are skills
+ 
+
+ align:start position:0%
+are skills
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+learned uh you're not necessarily born
+
+ align:start position:0%
+learned uh you're not necessarily born
+ 
+
+ align:start position:0%
+learned uh you're not necessarily born
+with them and they don't come just
+
+ align:start position:0%
+with them and they don't come just
+ 
+
+ align:start position:0%
+with them and they don't come just
+because you've decided you want them uh
+
+ align:start position:0%
+because you've decided you want them uh
+ 
+
+ align:start position:0%
+because you've decided you want them uh
+you have to work to build these micro
+
+ align:start position:0%
+you have to work to build these micro
+ 
+
+ align:start position:0%
+you have to work to build these micro
+skills and the micro skills are give you
+
+ align:start position:0%
+skills and the micro skills are give you
+ 
+
+ align:start position:0%
+skills and the micro skills are give you
+a repertoire I think it's a mistake to
+
+ align:start position:0%
+a repertoire I think it's a mistake to
+ 
+
+ align:start position:0%
+a repertoire I think it's a mistake to
+think of them in the category of values
+
+ align:start position:0%
+think of them in the category of values
+ 
+
+ align:start position:0%
+think of them in the category of values
+if you want to use facilitation in
+
+ align:start position:0%
+if you want to use facilitation in
+ 
+
+ align:start position:0%
+if you want to use facilitation in
+consensus
+
+ align:start position:0%
+consensus
+ 
+
+ align:start position:0%
+consensus
+building that's the set of
+
+ align:start position:0%
+building that's the set of
+ 
+
+ align:start position:0%
+building that's the set of
+skills and you can't just wish it
+
+ align:start position:0%
+skills and you can't just wish it
+ 
+
+ align:start position:0%
+skills and you can't just wish it
+you have to learn it or you have to work
+
+ align:start position:0%
+you have to learn it or you have to work
+ 
+
+ align:start position:0%
+you have to learn it or you have to work
+with someone for a while who is already
+
+ align:start position:0%
+with someone for a while who is already
+ 
+
+ align:start position:0%
+with someone for a while who is already
+more accomplished at it and a sort of
+
+ align:start position:0%
+more accomplished at it and a sort of
+ 
+
+ align:start position:0%
+more accomplished at it and a sort of
+indirectly Apprentice so that you can
+
+ align:start position:0%
+indirectly Apprentice so that you can
+ 
+
+ align:start position:0%
+indirectly Apprentice so that you can
+try it out and then begin to build your
+
+ align:start position:0%
+try it out and then begin to build your
+ 
+
+ align:start position:0%
+try it out and then begin to build your
+self-confidence about being able to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this several people
+
+ align:start position:0%
+this several people
+ 
+
+ align:start position:0%
+this several people
+said while they could see themselves
+
+ align:start position:0%
+said while they could see themselves
+ 
+
+ align:start position:0%
+said while they could see themselves
+becoming facilitative leaders they had
+
+ align:start position:0%
+becoming facilitative leaders they had
+ 
+
+ align:start position:0%
+becoming facilitative leaders they had
+no clear idea right now of how you turn
+
+ align:start position:0%
+no clear idea right now of how you turn
+ 
+
+ align:start position:0%
+no clear idea right now of how you turn
+a confrontation into a collaborative
+
+ align:start position:0%
+a confrontation into a collaborative
+ 
+
+ align:start position:0%
+a confrontation into a collaborative
+problem solving circumstance they don't
+
+ align:start position:0%
+problem solving circumstance they don't
+ 
+
+ align:start position:0%
+problem solving circumstance they don't
+see how you could make it happen and so
+
+ align:start position:0%
+see how you could make it happen and so
+ 
+
+ align:start position:0%
+see how you could make it happen and so
+they're happy to be to see themselves as
+
+ align:start position:0%
+they're happy to be to see themselves as
+ 
+
+ align:start position:0%
+they're happy to be to see themselves as
+facilitative Leaders but if that
+
+ align:start position:0%
+facilitative Leaders but if that
+ 
+
+ align:start position:0%
+facilitative Leaders but if that
+includes transforming a conflict
+
+ align:start position:0%
+includes transforming a conflict
+ 
+
+ align:start position:0%
+includes transforming a conflict
+into a collaborative problem
+
+ align:start position:0%
+into a collaborative problem
+ 
+
+ align:start position:0%
+into a collaborative problem
+solving situation they just didn't think
+
+ align:start position:0%
+solving situation they just didn't think
+ 
+
+ align:start position:0%
+solving situation they just didn't think
+that was possible what I'm going to say
+
+ align:start position:0%
+that was possible what I'm going to say
+ 
+
+ align:start position:0%
+that was possible what I'm going to say
+is true regardless of whether we're in a
+
+ align:start position:0%
+is true regardless of whether we're in a
+ 
+
+ align:start position:0%
+is true regardless of whether we're in a
+leadership context or not I want to take
+
+ align:start position:0%
+leadership context or not I want to take
+ 
+
+ align:start position:0%
+leadership context or not I want to take
+you to the kind of moment that happens
+
+ align:start position:0%
+you to the kind of moment that happens
+ 
+
+ align:start position:0%
+you to the kind of moment that happens
+when everybody shows up with their own
+
+ align:start position:0%
+when everybody shows up with their own
+ 
+
+ align:start position:0%
+when everybody shows up with their own
+ideas about what the right design to
+
+ align:start position:0%
+ideas about what the right design to
+ 
+
+ align:start position:0%
+ideas about what the right design to
+solve a problem would be and you decide
+
+ align:start position:0%
+solve a problem would be and you decide
+ 
+
+ align:start position:0%
+solve a problem would be and you decide
+well let's use the next half hour to
+
+ align:start position:0%
+well let's use the next half hour to
+ 
+
+ align:start position:0%
+well let's use the next half hour to
+brainstorm everybody still came with
+
+ align:start position:0%
+brainstorm everybody still came with
+ 
+
+ align:start position:0%
+brainstorm everybody still came with
+their own idea somebody says let's just
+
+ align:start position:0%
+their own idea somebody says let's just
+ 
+
+ align:start position:0%
+their own idea somebody says let's just
+take the next half hour and engage in
+
+ align:start position:0%
+take the next half hour and engage in
+ 
+
+ align:start position:0%
+take the next half hour and engage in
+brainstorming now anybody who's done
+
+ align:start position:0%
+brainstorming now anybody who's done
+ 
+
+ align:start position:0%
+brainstorming now anybody who's done
+that knows it just a couple of
+
+ align:start position:0%
+that knows it just a couple of
+ 
+
+ align:start position:0%
+that knows it just a couple of
+preconditions for Effective
+
+ align:start position:0%
+preconditions for Effective
+ 
+
+ align:start position:0%
+preconditions for Effective
+brainstorming everybody has to agree
+
+ align:start position:0%
+brainstorming everybody has to agree
+ 
+
+ align:start position:0%
+brainstorming everybody has to agree
+that everything that's said is an idea
+
+ align:start position:0%
+that everything that's said is an idea
+ 
+
+ align:start position:0%
+that everything that's said is an idea
+is a suggestion for this half hour we're
+
+ align:start position:0%
+is a suggestion for this half hour we're
+ 
+
+ align:start position:0%
+is a suggestion for this half hour we're
+going to brainstorm in my practice is a
+
+ align:start position:0%
+going to brainstorm in my practice is a
+ 
+
+ align:start position:0%
+going to brainstorm in my practice is a
+mediator my way of embodying the need to
+
+ align:start position:0%
+mediator my way of embodying the need to
+ 
+
+ align:start position:0%
+mediator my way of embodying the need to
+move that confrontation into problem
+
+ align:start position:0%
+move that confrontation into problem
+ 
+
+ align:start position:0%
+move that confrontation into problem
+solving is often if I'm sitting across
+
+ align:start position:0%
+solving is often if I'm sitting across
+ 
+
+ align:start position:0%
+solving is often if I'm sitting across
+from someone I stand up and I take my
+
+ align:start position:0%
+from someone I stand up and I take my
+ 
+
+ align:start position:0%
+from someone I stand up and I take my
+chair and I put it next to them say
+
+ align:start position:0%
+chair and I put it next to them say
+ 
+
+ align:start position:0%
+chair and I put it next to them say
+let's see how many things we can think
+
+ align:start position:0%
+let's see how many things we can think
+ 
+
+ align:start position:0%
+let's see how many things we can think
+of that we agree on that would be a good
+
+ align:start position:0%
+of that we agree on that would be a good
+ 
+
+ align:start position:0%
+of that we agree on that would be a good
+idea in handling this I'm on your side
+
+ align:start position:0%
+idea in handling this I'm on your side
+ 
+
+ align:start position:0%
+idea in handling this I'm on your side
+is what I'm going and saying I'm trying
+
+ align:start position:0%
+is what I'm going and saying I'm trying
+ 
+
+ align:start position:0%
+is what I'm going and saying I'm trying
+to convert the confrontation into a
+
+ align:start position:0%
+to convert the confrontation into a
+ 
+
+ align:start position:0%
+to convert the confrontation into a
+collaborative moment the idea of talking
+
+ align:start position:0%
+collaborative moment the idea of talking
+ 
+
+ align:start position:0%
+collaborative moment the idea of talking
+about how you're going to talk is
+
+ align:start position:0%
+about how you're going to talk is
+ 
+
+ align:start position:0%
+about how you're going to talk is
+crucial to transforming a conflict into
+
+ align:start position:0%
+crucial to transforming a conflict into
+ 
+
+ align:start position:0%
+crucial to transforming a conflict into
+a collaborative moment I have to build a
+
+ align:start position:0%
+a collaborative moment I have to build a
+ 
+
+ align:start position:0%
+a collaborative moment I have to build a
+different context right in front of us
+
+ align:start position:0%
+different context right in front of us
+ 
+
+ align:start position:0%
+different context right in front of us
+while we're sitting there how can we
+
+ align:start position:0%
+while we're sitting there how can we
+ 
+
+ align:start position:0%
+while we're sitting there how can we
+work together I know everybody's got
+
+ align:start position:0%
+work together I know everybody's got
+ 
+
+ align:start position:0%
+work together I know everybody's got
+their own ideas here and we'll hear
+
+ align:start position:0%
+their own ideas here and we'll hear
+ 
+
+ align:start position:0%
+their own ideas here and we'll hear
+about those but before we do that let's
+
+ align:start position:0%
+about those but before we do that let's
+ 
+
+ align:start position:0%
+about those but before we do that let's
+let's just see what we agree on are good
+
+ align:start position:0%
+let's just see what we agree on are good
+ 
+
+ align:start position:0%
+let's just see what we agree on are good
+ideas relative to solving this problem
+
+ align:start position:0%
+ideas relative to solving this problem
+ 
+
+ align:start position:0%
+ideas relative to solving this problem
+let's brainstorm to brainstorm
+
+ align:start position:0%
+let's brainstorm to brainstorm
+ 
+
+ align:start position:0%
+let's brainstorm to brainstorm
+effectively we need to hold off on
+
+ align:start position:0%
+effectively we need to hold off on
+ 
+
+ align:start position:0%
+effectively we need to hold off on
+negative or evaluative comments we need
+
+ align:start position:0%
+negative or evaluative comments we need
+ 
+
+ align:start position:0%
+negative or evaluative comments we need
+to just put as many thing up there as we
+
+ align:start position:0%
+to just put as many thing up there as we
+ 
+
+ align:start position:0%
+to just put as many thing up there as we
+can there's a time limit for how long
+
+ align:start position:0%
+can there's a time limit for how long
+ 
+
+ align:start position:0%
+can there's a time limit for how long
+we're going to do it nobody's committed
+
+ align:start position:0%
+we're going to do it nobody's committed
+ 
+
+ align:start position:0%
+we're going to do it nobody's committed
+to anything just because they
+
+ align:start position:0%
+to anything just because they
+ 
+
+ align:start position:0%
+to anything just because they
+contributed an idea so don't worry that
+
+ align:start position:0%
+contributed an idea so don't worry that
+ 
+
+ align:start position:0%
+contributed an idea so don't worry that
+you're somehow implicitly committing to
+
+ align:start position:0%
+you're somehow implicitly committing to
+ 
+
+ align:start position:0%
+you're somehow implicitly committing to
+something that you want want to move
+
+ align:start position:0%
+something that you want want to move
+ 
+
+ align:start position:0%
+something that you want want to move
+away from that's about transforming a
+
+ align:start position:0%
+away from that's about transforming a
+ 
+
+ align:start position:0%
+away from that's about transforming a
+built-in conflict to a collaborative
+
+ align:start position:0%
+built-in conflict to a collaborative
+ 
+
+ align:start position:0%
+built-in conflict to a collaborative
+problem solving circumstance doesn't
+
+ align:start position:0%
+problem solving circumstance doesn't
+ 
+
+ align:start position:0%
+problem solving circumstance doesn't
+guarantee agreement but the comments I
+
+ align:start position:0%
+guarantee agreement but the comments I
+ 
+
+ align:start position:0%
+guarantee agreement but the comments I
+was seeing from people is I I just don't
+
+ align:start position:0%
+was seeing from people is I I just don't
+ 
+
+ align:start position:0%
+was seeing from people is I I just don't
+see how I can be in the middle of a
+
+ align:start position:0%
+see how I can be in the middle of a
+ 
+
+ align:start position:0%
+see how I can be in the middle of a
+conflict and be a useful facilitator
+
+ align:start position:0%
+conflict and be a useful facilitator
+ 
+
+ align:start position:0%
+conflict and be a useful facilitator
+you've got to discuss the desire to do
+
+ align:start position:0%
+you've got to discuss the desire to do
+ 
+
+ align:start position:0%
+you've got to discuss the desire to do
+that you've got to set some ground rules
+
+ align:start position:0%
+that you've got to set some ground rules
+ 
+
+ align:start position:0%
+that you've got to set some ground rules
+some people may stay quiet the whole
+
+ align:start position:0%
+some people may stay quiet the whole
+ 
+
+ align:start position:0%
+some people may stay quiet the whole
+brainstorming session CU they can't
+
+ align:start position:0%
+brainstorming session CU they can't
+ 
+
+ align:start position:0%
+brainstorming session CU they can't
+adjust to that they're not flexible
+
+ align:start position:0%
+adjust to that they're not flexible
+ 
+
+ align:start position:0%
+adjust to that they're not flexible
+enough you can facilitate the
+
+ align:start position:0%
+enough you can facilitate the
+ 
+
+ align:start position:0%
+enough you can facilitate the
+transformation of a conflict situation
+
+ align:start position:0%
+transformation of a conflict situation
+ 
+
+ align:start position:0%
+transformation of a conflict situation
+to a joint problem solving situation by
+
+ align:start position:0%
+to a joint problem solving situation by
+ 
+
+ align:start position:0%
+to a joint problem solving situation by
+naming it as the thing you think the
+
+ align:start position:0%
+naming it as the thing you think the
+ 
+
+ align:start position:0%
+naming it as the thing you think the
+group should try for a short time that's
+
+ align:start position:0%
+group should try for a short time that's
+ 
+
+ align:start position:0%
+group should try for a short time that's
+one way of thinking about the
+
+ align:start position:0%
+one way of thinking about the
+ 
+
+ align:start position:0%
+one way of thinking about the
+transformation from a conflict
+
+ align:start position:0%
+transformation from a conflict
+ 
+
+ align:start position:0%
+transformation from a conflict
+situation another is to break up a
+
+ align:start position:0%
+situation another is to break up a
+ 
+
+ align:start position:0%
+situation another is to break up a
+fairly large group into smaller groups
+
+ align:start position:0%
+fairly large group into smaller groups
+ 
+
+ align:start position:0%
+fairly large group into smaller groups
+we work in four groups of three and come
+
+ align:start position:0%
+we work in four groups of three and come
+ 
+
+ align:start position:0%
+we work in four groups of three and come
+up with the criteria for choosing a good
+
+ align:start position:0%
+up with the criteria for choosing a good
+ 
+
+ align:start position:0%
+up with the criteria for choosing a good
+design to solve this problem 10 minutes
+
+ align:start position:0%
+design to solve this problem 10 minutes
+ 
+
+ align:start position:0%
+design to solve this problem 10 minutes
+time's up what did you guys what did you
+
+ align:start position:0%
+time's up what did you guys what did you
+ 
+
+ align:start position:0%
+time's up what did you guys what did you
+what did you what did you it's easier to
+
+ align:start position:0%
+what did you what did you it's easier to
+ 
+
+ align:start position:0%
+what did you what did you it's easier to
+just have to work with three people than
+
+ align:start position:0%
+just have to work with three people than
+ 
+
+ align:start position:0%
+just have to work with three people than
+11 others so we use that as a way of
+
+ align:start position:0%
+11 others so we use that as a way of
+ 
+
+ align:start position:0%
+11 others so we use that as a way of
+buffering the pressures of the conflict
+
+ align:start position:0%
+buffering the pressures of the conflict
+ 
+
+ align:start position:0%
+buffering the pressures of the conflict
+to try to move to transformation you're
+
+ align:start position:0%
+to try to move to transformation you're
+ 
+
+ align:start position:0%
+to try to move to transformation you're
+thinking of a move and are doing it and
+
+ align:start position:0%
+thinking of a move and are doing it and
+ 
+
+ align:start position:0%
+thinking of a move and are doing it and
+you're not worrying about whether people
+
+ align:start position:0%
+you're not worrying about whether people
+ 
+
+ align:start position:0%
+you're not worrying about whether people
+are going to disagree with what you're
+
+ align:start position:0%
+are going to disagree with what you're
+ 
+
+ align:start position:0%
+are going to disagree with what you're
+proposing and you're not worrying about
+
+ align:start position:0%
+proposing and you're not worrying about
+ 
+
+ align:start position:0%
+proposing and you're not worrying about
+whether they're not going to like you
+
+ align:start position:0%
+whether they're not going to like you
+ 
+
+ align:start position:0%
+whether they're not going to like you
+you're just ready to
+
+ align:start position:0%
+you're just ready to
+ 
+
+ align:start position:0%
+you're just ready to
+try some things that will transform the
+
+ align:start position:0%
+try some things that will transform the
+ 
+
+ align:start position:0%
+try some things that will transform the
+context if you don't know how you could
+
+ align:start position:0%
+context if you don't know how you could
+ 
+
+ align:start position:0%
+context if you don't know how you could
+write now be a facilitative leader
+
+ align:start position:0%
+write now be a facilitative leader
+ 
+
+ align:start position:0%
+write now be a facilitative leader
+because you don't know that you could be
+
+ align:start position:0%
+because you don't know that you could be
+ 
+
+ align:start position:0%
+because you don't know that you could be
+comfortable enough in a conflict to help
+
+ align:start position:0%
+comfortable enough in a conflict to help
+ 
+
+ align:start position:0%
+comfortable enough in a conflict to help
+the group transform it um you can learn
+
+ align:start position:0%
+the group transform it um you can learn
+ 
+
+ align:start position:0%
+the group transform it um you can learn
+how to do that but you need some ideas
+
+ align:start position:0%
+how to do that but you need some ideas
+ 
+
+ align:start position:0%
+how to do that but you need some ideas
+to begin to work with last point that
+
+ align:start position:0%
+to begin to work with last point that
+ 
+
+ align:start position:0%
+to begin to work with last point that
+came from two people separately I think
+
+ align:start position:0%
+came from two people separately I think
+ 
+
+ align:start position:0%
+came from two people separately I think
+this whole facilitation thing makes me
+
+ align:start position:0%
+this whole facilitation thing makes me
+ 
+
+ align:start position:0%
+this whole facilitation thing makes me
+look soft I see myself as a principled
+
+ align:start position:0%
+look soft I see myself as a principled
+ 
+
+ align:start position:0%
+look soft I see myself as a principled
+person who doesn't get pushed around
+
+ align:start position:0%
+person who doesn't get pushed around
+ 
+
+ align:start position:0%
+person who doesn't get pushed around
+relative to what I believe is right I
+
+ align:start position:0%
+relative to what I believe is right I
+ 
+
+ align:start position:0%
+relative to what I believe is right I
+believe what I believe I represent the
+
+ align:start position:0%
+believe what I believe I represent the
+ 
+
+ align:start position:0%
+believe what I believe I represent the
+people I work with all I can suggest to
+
+ align:start position:0%
+people I work with all I can suggest to
+ 
+
+ align:start position:0%
+people I work with all I can suggest to
+you is there are other ways of
+
+ align:start position:0%
+you is there are other ways of
+ 
+
+ align:start position:0%
+you is there are other ways of
+accomplishing the goal of getting people
+
+ align:start position:0%
+accomplishing the goal of getting people
+ 
+
+ align:start position:0%
+accomplishing the goal of getting people
+to support what you believe but at their
+
+ align:start position:0%
+to support what you believe but at their
+ 
+
+ align:start position:0%
+to support what you believe but at their
+own
+
+ align:start position:0%
+own
+ 
+
+ align:start position:0%
+own
+volition not because you tell them they
+
+ align:start position:0%
+volition not because you tell them they
+ 
+
+ align:start position:0%
+volition not because you tell them they
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+to and I would argue effective is in the
+
+ align:start position:0%
+to and I would argue effective is in the
+ 
+
+ align:start position:0%
+to and I would argue effective is in the
+middle between soft and hard effective
+
+ align:start position:0%
+middle between soft and hard effective
+ 
+
+ align:start position:0%
+middle between soft and hard effective
+is none of that matters I only care if
+
+ align:start position:0%
+is none of that matters I only care if
+ 
+
+ align:start position:0%
+is none of that matters I only care if
+you perceive me effective in my role as
+
+ align:start position:0%
+you perceive me effective in my role as
+ 
+
+ align:start position:0%
+you perceive me effective in my role as
+helping to get a good outcome for the
+
+ align:start position:0%
+helping to get a good outcome for the
+ 
+
+ align:start position:0%
+helping to get a good outcome for the
+group in which everyone's interests are
+
+ align:start position:0%
+group in which everyone's interests are
+ 
+
+ align:start position:0%
+group in which everyone's interests are
+met when someone says I I don't see
+
+ align:start position:0%
+met when someone says I I don't see
+ 
+
+ align:start position:0%
+met when someone says I I don't see
+being in this kind of leadership role I
+
+ align:start position:0%
+being in this kind of leadership role I
+ 
+
+ align:start position:0%
+being in this kind of leadership role I
+guess they see themselves more as some
+
+ align:start position:0%
+guess they see themselves more as some
+ 
+
+ align:start position:0%
+guess they see themselves more as some
+of our new national
+
+ align:start position:0%
+of our new national
+ 
+
+ align:start position:0%
+of our new national
+leaders where they assume that will tell
+
+ align:start position:0%
+leaders where they assume that will tell
+ 
+
+ align:start position:0%
+leaders where they assume that will tell
+everybody what to do and everyone should
+
+ align:start position:0%
+everybody what to do and everyone should
+ 
+
+ align:start position:0%
+everybody what to do and everyone should
+listen because they are the leader um
+
+ align:start position:0%
+listen because they are the leader um
+ 
+
+ align:start position:0%
+listen because they are the leader um
+that's not the model I'm talking about
+
+ align:start position:0%
+that's not the model I'm talking about
+ 
+
+ align:start position:0%
+that's not the model I'm talking about
+um I don't think the people in that role
+
+ align:start position:0%
+um I don't think the people in that role
+ 
+
+ align:start position:0%
+um I don't think the people in that role
+are going to get very far but we'll see
+
+ align:start position:0%
+are going to get very far but we'll see
+ 
+
+ align:start position:0%
+are going to get very far but we'll see
+in the United States over the next
+
+ align:start position:0%
+in the United States over the next
+ 
+
+ align:start position:0%
+in the United States over the next
+couple of years whether that approach
+
+ align:start position:0%
+couple of years whether that approach
+ 
+
+ align:start position:0%
+couple of years whether that approach
+gets anyone where they want to go
+
+ align:start position:0%
+gets anyone where they want to go
+ 
+
+ align:start position:0%
+gets anyone where they want to go
+someone said it seems like there's lots
+
+ align:start position:0%
+someone said it seems like there's lots
+ 
+
+ align:start position:0%
+someone said it seems like there's lots
+of pre-work needed to be a facilitative
+
+ align:start position:0%
+of pre-work needed to be a facilitative
+ 
+
+ align:start position:0%
+of pre-work needed to be a facilitative
+leader before the Gathering of all the
+
+ align:start position:0%
+leader before the Gathering of all the
+ 
+
+ align:start position:0%
+leader before the Gathering of all the
+parties and the answer to that is
+
+ align:start position:0%
+parties and the answer to that is
+ 
+
+ align:start position:0%
+parties and the answer to that is
+absolutely yes and that's why you work
+
+ align:start position:0%
+absolutely yes and that's why you work
+ 
+
+ align:start position:0%
+absolutely yes and that's why you work
+as a team and that's why you have other
+
+ align:start position:0%
+as a team and that's why you have other
+ 
+
+ align:start position:0%
+as a team and that's why you have other
+people it's not just what you do at the
+
+ align:start position:0%
+people it's not just what you do at the
+ 
+
+ align:start position:0%
+people it's not just what you do at the
+table it's what you do to create the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+table I think one of the
+
+ align:start position:0%
+table I think one of the
+ 
+
+ align:start position:0%
+table I think one of the
+challenges that I can see myself facing
+
+ align:start position:0%
+challenges that I can see myself facing
+ 
+
+ align:start position:0%
+challenges that I can see myself facing
+as a facilitative leader is um ensuring
+
+ align:start position:0%
+as a facilitative leader is um ensuring
+ 
+
+ align:start position:0%
+as a facilitative leader is um ensuring
+that all voices in the room are heard
+
+ align:start position:0%
+that all voices in the room are heard
+ 
+
+ align:start position:0%
+that all voices in the room are heard
+equally while not kind of making it a
+
+ align:start position:0%
+equally while not kind of making it a
+ 
+
+ align:start position:0%
+equally while not kind of making it a
+contrived process like I still want to
+
+ align:start position:0%
+contrived process like I still want to
+ 
+
+ align:start position:0%
+contrived process like I still want to
+like maintain this like Spirit of
+
+ align:start position:0%
+like maintain this like Spirit of
+ 
+
+ align:start position:0%
+like maintain this like Spirit of
+collaboration and people just like
+
+ align:start position:0%
+collaboration and people just like
+ 
+
+ align:start position:0%
+collaboration and people just like
+openly exchanging ideas so do you have
+
+ align:start position:0%
+openly exchanging ideas so do you have
+ 
+
+ align:start position:0%
+openly exchanging ideas so do you have
+some preliminary ideas of how to try
+
+ align:start position:0%
+some preliminary ideas of how to try
+ 
+
+ align:start position:0%
+some preliminary ideas of how to try
+that that's not the
+
+ align:start position:0%
+that that's not the
+ 
+
+ align:start position:0%
+that that's not the
+clunky way proposing different questions
+
+ align:start position:0%
+clunky way proposing different questions
+ 
+
+ align:start position:0%
+clunky way proposing different questions
+maybe other questions that might involve
+
+ align:start position:0%
+maybe other questions that might involve
+ 
+
+ align:start position:0%
+maybe other questions that might involve
+folks who haven't been speaking as much
+
+ align:start position:0%
+folks who haven't been speaking as much
+ 
+
+ align:start position:0%
+folks who haven't been speaking as much
+but yeah I don't know open to any other
+
+ align:start position:0%
+but yeah I don't know open to any other
+ 
+
+ align:start position:0%
+but yeah I don't know open to any other
+ideas too so we're in this context and
+
+ align:start position:0%
+ideas too so we're in this context and
+ 
+
+ align:start position:0%
+ideas too so we're in this context and
+there's several people speaking a lot
+
+ align:start position:0%
+there's several people speaking a lot
+ 
+
+ align:start position:0%
+there's several people speaking a lot
+and there's several people hardly
+
+ align:start position:0%
+and there's several people hardly
+ 
+
+ align:start position:0%
+and there's several people hardly
+speaking and I feel it's my job for
+
+ align:start position:0%
+speaking and I feel it's my job for
+ 
+
+ align:start position:0%
+speaking and I feel it's my job for
+everyone to be heard I'm just repeating
+
+ align:start position:0%
+everyone to be heard I'm just repeating
+ 
+
+ align:start position:0%
+everyone to be heard I'm just repeating
+your premise and I say wait a minute
+
+ align:start position:0%
+your premise and I say wait a minute
+ 
+
+ align:start position:0%
+your premise and I say wait a minute
+wait a minute we've only heard from a
+
+ align:start position:0%
+wait a minute we've only heard from a
+ 
+
+ align:start position:0%
+wait a minute we've only heard from a
+few people
+
+ align:start position:0%
+few people
+ 
+
+ align:start position:0%
+few people
+I really let let's let people who
+
+ align:start position:0%
+I really let let's let people who
+ 
+
+ align:start position:0%
+I really let let's let people who
+haven't spoken yet have the floor so I
+
+ align:start position:0%
+haven't spoken yet have the floor so I
+ 
+
+ align:start position:0%
+haven't spoken yet have the floor so I
+have now empowered those folks and I
+
+ align:start position:0%
+have now empowered those folks and I
+ 
+
+ align:start position:0%
+have now empowered those folks and I
+going to stop anyone who's spoken before
+
+ align:start position:0%
+going to stop anyone who's spoken before
+ 
+
+ align:start position:0%
+going to stop anyone who's spoken before
+from Talking literally that's what my
+
+ align:start position:0%
+from Talking literally that's what my
+ 
+
+ align:start position:0%
+from Talking literally that's what my
+facilitative job is and sometimes that
+
+ align:start position:0%
+facilitative job is and sometimes that
+ 
+
+ align:start position:0%
+facilitative job is and sometimes that
+will make it more
+
+ align:start position:0%
+will make it more
+ 
+
+ align:start position:0%
+will make it more
+comfortable for someone who's been quiet
+
+ align:start position:0%
+comfortable for someone who's been quiet
+ 
+
+ align:start position:0%
+comfortable for someone who's been quiet
+because they don't feel comfortable
+
+ align:start position:0%
+because they don't feel comfortable
+ 
+
+ align:start position:0%
+because they don't feel comfortable
+jumping in when they want to that's one
+
+ align:start position:0%
+jumping in when they want to that's one
+ 
+
+ align:start position:0%
+jumping in when they want to that's one
+idea another idea is to say everyone be
+
+ align:start position:0%
+idea another idea is to say everyone be
+ 
+
+ align:start position:0%
+idea another idea is to say everyone be
+quiet for a few minutes everybody write
+
+ align:start position:0%
+quiet for a few minutes everybody write
+ 
+
+ align:start position:0%
+quiet for a few minutes everybody write
+down two three answers to the question
+
+ align:start position:0%
+down two three answers to the question
+ 
+
+ align:start position:0%
+down two three answers to the question
+that we've been talking about short just
+
+ align:start position:0%
+that we've been talking about short just
+ 
+
+ align:start position:0%
+that we've been talking about short just
+short things I put a lot of people in
+
+ align:start position:0%
+short things I put a lot of people in
+ 
+
+ align:start position:0%
+short things I put a lot of people in
+that situation I haven't singled one
+
+ align:start position:0%
+that situation I haven't singled one
+ 
+
+ align:start position:0%
+that situation I haven't singled one
+person out if I'm not singling someone
+
+ align:start position:0%
+person out if I'm not singling someone
+ 
+
+ align:start position:0%
+person out if I'm not singling someone
+out who's been quiet there's a better
+
+ align:start position:0%
+out who's been quiet there's a better
+ 
+
+ align:start position:0%
+out who's been quiet there's a better
+chance of engaging them a third thing is
+
+ align:start position:0%
+chance of engaging them a third thing is
+ 
+
+ align:start position:0%
+chance of engaging them a third thing is
+to say we've been talking about this for
+
+ align:start position:0%
+to say we've been talking about this for
+ 
+
+ align:start position:0%
+to say we've been talking about this for
+45 minutes um I want to get a sense of
+
+ align:start position:0%
+45 minutes um I want to get a sense of
+ 
+
+ align:start position:0%
+45 minutes um I want to get a sense of
+where the group stands let's just go
+
+ align:start position:0%
+where the group stands let's just go
+ 
+
+ align:start position:0%
+where the group stands let's just go
+around everybody just 30 seconds where
+
+ align:start position:0%
+around everybody just 30 seconds where
+ 
+
+ align:start position:0%
+around everybody just 30 seconds where
+do you stand on this so I am doing
+
+ align:start position:0%
+do you stand on this so I am doing
+ 
+
+ align:start position:0%
+do you stand on this so I am doing
+things to encourage the ones who haven't
+
+ align:start position:0%
+things to encourage the ones who haven't
+ 
+
+ align:start position:0%
+things to encourage the ones who haven't
+spoken I can't make them speak and I do
+
+ align:start position:0%
+spoken I can't make them speak and I do
+ 
+
+ align:start position:0%
+spoken I can't make them speak and I do
+not want to call them and say you
+
+ align:start position:0%
+not want to call them and say you
+ 
+
+ align:start position:0%
+not want to call them and say you
+haven't said anything yet Say Something
+
+ align:start position:0%
+haven't said anything yet Say Something
+ 
+
+ align:start position:0%
+haven't said anything yet Say Something
+There are a whole series of ways you can
+
+ align:start position:0%
+There are a whole series of ways you can
+ 
+
+ align:start position:0%
+There are a whole series of ways you can
+try to do that that I think are better
+
+ align:start position:0%
+try to do that that I think are better
+ 
+
+ align:start position:0%
+try to do that that I think are better
+than either saying well they didn't want
+
+ align:start position:0%
+than either saying well they didn't want
+ 
+
+ align:start position:0%
+than either saying well they didn't want
+to speak they didn't have to speak I
+
+ align:start position:0%
+to speak they didn't have to speak I
+ 
+
+ align:start position:0%
+to speak they didn't have to speak I
+would say that for me the biggest
+
+ align:start position:0%
+would say that for me the biggest
+ 
+
+ align:start position:0%
+would say that for me the biggest
+challenge would be patience and the
+
+ align:start position:0%
+challenge would be patience and the
+ 
+
+ align:start position:0%
+challenge would be patience and the
+management of time I think that
+
+ align:start position:0%
+management of time I think that
+ 
+
+ align:start position:0%
+management of time I think that
+sometimes this kind of discussions when
+
+ align:start position:0%
+sometimes this kind of discussions when
+ 
+
+ align:start position:0%
+sometimes this kind of discussions when
+they don't have like an end time it's
+
+ align:start position:0%
+they don't have like an end time it's
+ 
+
+ align:start position:0%
+they don't have like an end time it's
+really difficult to get people to agree
+
+ align:start position:0%
+really difficult to get people to agree
+ 
+
+ align:start position:0%
+really difficult to get people to agree
+because the discussion can keep going
+
+ align:start position:0%
+because the discussion can keep going
+ 
+
+ align:start position:0%
+because the discussion can keep going
+that's something that I would like
+
+ align:start position:0%
+that's something that I would like
+ 
+
+ align:start position:0%
+that's something that I would like
+struggle with how to manage I think um
+
+ align:start position:0%
+struggle with how to manage I think um
+ 
+
+ align:start position:0%
+struggle with how to manage I think um
+you're right to worry about it I think
+
+ align:start position:0%
+you're right to worry about it I think
+ 
+
+ align:start position:0%
+you're right to worry about it I think
+every facilitator has to worry about
+
+ align:start position:0%
+every facilitator has to worry about
+ 
+
+ align:start position:0%
+every facilitator has to worry about
+managing time their time and the group's
+
+ align:start position:0%
+managing time their time and the group's
+ 
+
+ align:start position:0%
+managing time their time and the group's
+time if I'm entering into that kind of
+
+ align:start position:0%
+time if I'm entering into that kind of
+ 
+
+ align:start position:0%
+time if I'm entering into that kind of
+situation I need another person in the
+
+ align:start position:0%
+situation I need another person in the
+ 
+
+ align:start position:0%
+situation I need another person in the
+group to be timekeeper we could also
+
+ align:start position:0%
+group to be timekeeper we could also
+ 
+
+ align:start position:0%
+group to be timekeeper we could also
+have a ground rule we could say look we
+
+ align:start position:0%
+have a ground rule we could say look we
+ 
+
+ align:start position:0%
+have a ground rule we could say look we
+give everybody 3 minutes for a first
+
+ align:start position:0%
+give everybody 3 minutes for a first
+ 
+
+ align:start position:0%
+give everybody 3 minutes for a first
+statement on anything where you're
+
+ align:start position:0%
+statement on anything where you're
+ 
+
+ align:start position:0%
+statement on anything where you're
+recognized from the queue to speak next
+
+ align:start position:0%
+recognized from the queue to speak next
+ 
+
+ align:start position:0%
+recognized from the queue to speak next
+I can use that as a device for dealing
+
+ align:start position:0%
+I can use that as a device for dealing
+ 
+
+ align:start position:0%
+I can use that as a device for dealing
+with one time problem which is people
+
+ align:start position:0%
+with one time problem which is people
+ 
+
+ align:start position:0%
+with one time problem which is people
+who talk too long I would not start a
+
+ align:start position:0%
+who talk too long I would not start a
+ 
+
+ align:start position:0%
+who talk too long I would not start a
+meeting without an agenda which I sent
+
+ align:start position:0%
+meeting without an agenda which I sent
+ 
+
+ align:start position:0%
+meeting without an agenda which I sent
+out ahead if you have an agenda for any
+
+ align:start position:0%
+out ahead if you have an agenda for any
+ 
+
+ align:start position:0%
+out ahead if you have an agenda for any
+kind of a group you should have time
+
+ align:start position:0%
+kind of a group you should have time
+ 
+
+ align:start position:0%
+kind of a group you should have time
+next to each item including what is the
+
+ align:start position:0%
+next to each item including what is the
+ 
+
+ align:start position:0%
+next to each item including what is the
+ending time but this is about using
+
+ align:start position:0%
+ending time but this is about using
+ 
+
+ align:start position:0%
+ending time but this is about using
+agendas and that's the leaders
+
+ align:start position:0%
+agendas and that's the leaders
+ 
+
+ align:start position:0%
+agendas and that's the leaders
+responsibility tools for time management
+
+ align:start position:0%
+responsibility tools for time management
+ 
+
+ align:start position:0%
+responsibility tools for time management
+for the group not just for for yourself
+
+ align:start position:0%
+for the group not just for for yourself
+ 
+
+ align:start position:0%
+for the group not just for for yourself
+you're not making evaluations about what
+
+ align:start position:0%
+you're not making evaluations about what
+ 
+
+ align:start position:0%
+you're not making evaluations about what
+were the good suggestions and the bad
+
+ align:start position:0%
+were the good suggestions and the bad
+ 
+
+ align:start position:0%
+were the good suggestions and the bad
+suggestions and you're not
+
+ align:start position:0%
+suggestions and you're not
+ 
+
+ align:start position:0%
+suggestions and you're not
+editorializing and leaving something out
+
+ align:start position:0%
+editorializing and leaving something out
+ 
+
+ align:start position:0%
+editorializing and leaving something out
+because you don't agree with it those
+
+ align:start position:0%
+because you don't agree with it those
+ 
+
+ align:start position:0%
+because you don't agree with it those
+are some simple often used tools by
+
+ align:start position:0%
+are some simple often used tools by
+ 
+
+ align:start position:0%
+are some simple often used tools by
+facilitators to deal with the time
+
+ align:start position:0%
+facilitators to deal with the time
+ 
+
+ align:start position:0%
+facilitators to deal with the time
+management problem
+
+ align:start position:0%
+management problem
+ 
+
+ align:start position:0%
+management problem
+main challenge for me personally is how
+
+ align:start position:0%
+main challenge for me personally is how
+ 
+
+ align:start position:0%
+main challenge for me personally is how
+to to deal with people that wants to
+
+ align:start position:0%
+to to deal with people that wants to
+ 
+
+ align:start position:0%
+to to deal with people that wants to
+spoil the process it takes sometimes a
+
+ align:start position:0%
+spoil the process it takes sometimes a
+ 
+
+ align:start position:0%
+spoil the process it takes sometimes a
+lot of
+
+ align:start position:0%
+lot of
+ 
+
+ align:start position:0%
+lot of
+emotional resilience to keep myself in a
+
+ align:start position:0%
+emotional resilience to keep myself in a
+ 
+
+ align:start position:0%
+emotional resilience to keep myself in a
+set of mind that could facilitate the
+
+ align:start position:0%
+set of mind that could facilitate the
+ 
+
+ align:start position:0%
+set of mind that could facilitate the
+processes I think it's a challenge for
+
+ align:start position:0%
+processes I think it's a challenge for
+ 
+
+ align:start position:0%
+processes I think it's a challenge for
+anyone when we are in a process that
+
+ align:start position:0%
+anyone when we are in a process that
+ 
+
+ align:start position:0%
+anyone when we are in a process that
+goes on for a long time which is why um
+
+ align:start position:0%
+goes on for a long time which is why um
+ 
+
+ align:start position:0%
+goes on for a long time which is why um
+most professional facilitators work in
+
+ align:start position:0%
+most professional facilitators work in
+ 
+
+ align:start position:0%
+most professional facilitators work in
+pairs has to be someone that you trust
+
+ align:start position:0%
+pairs has to be someone that you trust
+ 
+
+ align:start position:0%
+pairs has to be someone that you trust
+to be your Alter Ego I'm talking about
+
+ align:start position:0%
+to be your Alter Ego I'm talking about
+ 
+
+ align:start position:0%
+to be your Alter Ego I'm talking about
+someone who can do everything you can do
+
+ align:start position:0%
+someone who can do everything you can do
+ 
+
+ align:start position:0%
+someone who can do everything you can do
+as well as you can do it but you're
+
+ align:start position:0%
+as well as you can do it but you're
+ 
+
+ align:start position:0%
+as well as you can do it but you're
+switching roles in order to let one
+
+ align:start position:0%
+switching roles in order to let one
+ 
+
+ align:start position:0%
+switching roles in order to let one
+person rest and recharge and if people
+
+ align:start position:0%
+person rest and recharge and if people
+ 
+
+ align:start position:0%
+person rest and recharge and if people
+are going to be spoilers and they're
+
+ align:start position:0%
+are going to be spoilers and they're
+ 
+
+ align:start position:0%
+are going to be spoilers and they're
+very good at it I don't have a a a magic
+
+ align:start position:0%
+very good at it I don't have a a a magic
+ 
+
+ align:start position:0%
+very good at it I don't have a a a magic
+solution if I put people on the record
+
+ align:start position:0%
+solution if I put people on the record
+ 
+
+ align:start position:0%
+solution if I put people on the record
+of having to give the reasons for why
+
+ align:start position:0%
+of having to give the reasons for why
+ 
+
+ align:start position:0%
+of having to give the reasons for why
+they're doing something they have to E
+
+ align:start position:0%
+they're doing something they have to E
+ 
+
+ align:start position:0%
+they're doing something they have to E
+either lie but many people won't take
+
+ align:start position:0%
+either lie but many people won't take
+ 
+
+ align:start position:0%
+either lie but many people won't take
+their spoilers role to the point of
+
+ align:start position:0%
+their spoilers role to the point of
+ 
+
+ align:start position:0%
+their spoilers role to the point of
+lying because they know it will ruin
+
+ align:start position:0%
+lying because they know it will ruin
+ 
+
+ align:start position:0%
+lying because they know it will ruin
+their reputation in that context for the
+
+ align:start position:0%
+their reputation in that context for the
+ 
+
+ align:start position:0%
+their reputation in that context for the
+future nobody forgets that that person
+
+ align:start position:0%
+future nobody forgets that that person
+ 
+
+ align:start position:0%
+future nobody forgets that that person
+lied and suddenly the spoiler strategy
+
+ align:start position:0%
+lied and suddenly the spoiler strategy
+ 
+
+ align:start position:0%
+lied and suddenly the spoiler strategy
+Falls away and they become part of the
+
+ align:start position:0%
+Falls away and they become part of the
+ 
+
+ align:start position:0%
+Falls away and they become part of the
+negotiation group a question that I have
+
+ align:start position:0%
+negotiation group a question that I have
+ 
+
+ align:start position:0%
+negotiation group a question that I have
+is like not in the moment of being a
+
+ align:start position:0%
+is like not in the moment of being a
+ 
+
+ align:start position:0%
+is like not in the moment of being a
+facilitator but like communicating that
+
+ align:start position:0%
+facilitator but like communicating that
+ 
+
+ align:start position:0%
+facilitator but like communicating that
+out once the decision has been reached
+
+ align:start position:0%
+out once the decision has been reached
+ 
+
+ align:start position:0%
+out once the decision has been reached
+maintaining like the Vigor of that
+
+ align:start position:0%
+maintaining like the Vigor of that
+ 
+
+ align:start position:0%
+maintaining like the Vigor of that
+decision and seeing it through like how
+
+ align:start position:0%
+decision and seeing it through like how
+ 
+
+ align:start position:0%
+decision and seeing it through like how
+do you kind of like maintain trust in
+
+ align:start position:0%
+do you kind of like maintain trust in
+ 
+
+ align:start position:0%
+do you kind of like maintain trust in
+the process knowing that ultimately like
+
+ align:start position:0%
+the process knowing that ultimately like
+ 
+
+ align:start position:0%
+the process knowing that ultimately like
+you don't have the final say you want to
+
+ align:start position:0%
+you don't have the final say you want to
+ 
+
+ align:start position:0%
+you don't have the final say you want to
+be in charge of a written summary of
+
+ align:start position:0%
+be in charge of a written summary of
+ 
+
+ align:start position:0%
+be in charge of a written summary of
+whatever the key outcome findings
+
+ align:start position:0%
+whatever the key outcome findings
+ 
+
+ align:start position:0%
+whatever the key outcome findings
+agreement is and you want to draft it
+
+ align:start position:0%
+agreement is and you want to draft it
+ 
+
+ align:start position:0%
+agreement is and you want to draft it
+and you want everybody in the group to
+
+ align:start position:0%
+and you want everybody in the group to
+ 
+
+ align:start position:0%
+and you want everybody in the group to
+have a chance to comment on it and if
+
+ align:start position:0%
+have a chance to comment on it and if
+ 
+
+ align:start position:0%
+have a chance to comment on it and if
+there are disagreements you may need to
+
+ align:start position:0%
+there are disagreements you may need to
+ 
+
+ align:start position:0%
+there are disagreements you may need to
+reconvene the parties you can put your
+
+ align:start position:0%
+reconvene the parties you can put your
+ 
+
+ align:start position:0%
+reconvene the parties you can put your
+name as the point of contact not the
+
+ align:start position:0%
+name as the point of contact not the
+ 
+
+ align:start position:0%
+name as the point of contact not the
+author that's the point of contact at
+
+ align:start position:0%
+author that's the point of contact at
+ 
+
+ align:start position:0%
+author that's the point of contact at
+the bottom and you want to give that to
+
+ align:start position:0%
+the bottom and you want to give that to
+ 
+
+ align:start position:0%
+the bottom and you want to give that to
+the mayor and you want to
+
+ align:start position:0%
+the mayor and you want to
+ 
+
+ align:start position:0%
+the mayor and you want to
+say anything not clear in this written
+
+ align:start position:0%
+say anything not clear in this written
+ 
+
+ align:start position:0%
+say anything not clear in this written
+statement this is the group's statement
+
+ align:start position:0%
+statement this is the group's statement
+ 
+
+ align:start position:0%
+statement this is the group's statement
+and then the mayor is going to go say
+
+ align:start position:0%
+and then the mayor is going to go say
+ 
+
+ align:start position:0%
+and then the mayor is going to go say
+whatever the mayor wants but the
+
+ align:start position:0%
+whatever the mayor wants but the
+ 
+
+ align:start position:0%
+whatever the mayor wants but the
+existence of a statement that the whole
+
+ align:start position:0%
+existence of a statement that the whole
+ 
+
+ align:start position:0%
+existence of a statement that the whole
+group had a hand in saying okay to is
+
+ align:start position:0%
+group had a hand in saying okay to is
+ 
+
+ align:start position:0%
+group had a hand in saying okay to is
+the best way of ensuring that what came
+
+ align:start position:0%
+the best way of ensuring that what came
+ 
+
+ align:start position:0%
+the best way of ensuring that what came
+out of the group doesn't go through the
+
+ align:start position:0%
+out of the group doesn't go through the
+ 
+
+ align:start position:0%
+out of the group doesn't go through the
+political meat grinder and come out in
+
+ align:start position:0%
+political meat grinder and come out in
+ 
+
+ align:start position:0%
+political meat grinder and come out in
+unrelated ways the problem is that when
+
+ align:start position:0%
+unrelated ways the problem is that when
+ 
+
+ align:start position:0%
+unrelated ways the problem is that when
+some of the parties become very rigid
+
+ align:start position:0%
+some of the parties become very rigid
+ 
+
+ align:start position:0%
+some of the parties become very rigid
+and uh will not move from their stance
+
+ align:start position:0%
+and uh will not move from their stance
+ 
+
+ align:start position:0%
+and uh will not move from their stance
+what can I do as a facilitative uh
+
+ align:start position:0%
+what can I do as a facilitative uh
+ 
+
+ align:start position:0%
+what can I do as a facilitative uh
+leader my experiences are all based on
+
+ align:start position:0%
+leader my experiences are all based on
+ 
+
+ align:start position:0%
+leader my experiences are all based on
+my government position if I am a
+
+ align:start position:0%
+my government position if I am a
+ 
+
+ align:start position:0%
+my government position if I am a
+facilitative leader with without that
+
+ align:start position:0%
+facilitative leader with without that
+ 
+
+ align:start position:0%
+facilitative leader with without that
+Authority what will be my role some
+
+ align:start position:0%
+Authority what will be my role some
+ 
+
+ align:start position:0%
+Authority what will be my role some
+people in some
+
+ align:start position:0%
+people in some
+ 
+
+ align:start position:0%
+people in some
+countries would not be able to accept
+
+ align:start position:0%
+countries would not be able to accept
+ 
+
+ align:start position:0%
+countries would not be able to accept
+this informal leadership role while they
+
+ align:start position:0%
+this informal leadership role while they
+ 
+
+ align:start position:0%
+this informal leadership role while they
+still held their government appointment
+
+ align:start position:0%
+still held their government appointment
+ 
+
+ align:start position:0%
+still held their government appointment
+not true in the United States not true
+
+ align:start position:0%
+not true in the United States not true
+ 
+
+ align:start position:0%
+not true in the United States not true
+in some countries but is true in some
+
+ align:start position:0%
+in some countries but is true in some
+ 
+
+ align:start position:0%
+in some countries but is true in some
+countries but if that's not the problem
+
+ align:start position:0%
+countries but if that's not the problem
+ 
+
+ align:start position:0%
+countries but if that's not the problem
+if you can do both you have to be really
+
+ align:start position:0%
+if you can do both you have to be really
+ 
+
+ align:start position:0%
+if you can do both you have to be really
+clear with the participants I have this
+
+ align:start position:0%
+clear with the participants I have this
+ 
+
+ align:start position:0%
+clear with the participants I have this
+responsibility and this obligation in
+
+ align:start position:0%
+responsibility and this obligation in
+ 
+
+ align:start position:0%
+responsibility and this obligation in
+the world if there's a point of conflict
+
+ align:start position:0%
+the world if there's a point of conflict
+ 
+
+ align:start position:0%
+the world if there's a point of conflict
+I would have to opt out and you have to
+
+ align:start position:0%
+I would have to opt out and you have to
+ 
+
+ align:start position:0%
+I would have to opt out and you have to
+tell that in one way to the agency you
+
+ align:start position:0%
+tell that in one way to the agency you
+ 
+
+ align:start position:0%
+tell that in one way to the agency you
+work for and you have to say to the
+
+ align:start position:0%
+work for and you have to say to the
+ 
+
+ align:start position:0%
+work for and you have to say to the
+people who still want you to be in this
+
+ align:start position:0%
+people who still want you to be in this
+ 
+
+ align:start position:0%
+people who still want you to be in this
+facilitative leadership role if there
+
+ align:start position:0%
+facilitative leadership role if there
+ 
+
+ align:start position:0%
+facilitative leadership role if there
+comes a conflict I will tell all of you
+
+ align:start position:0%
+comes a conflict I will tell all of you
+ 
+
+ align:start position:0%
+comes a conflict I will tell all of you
+that and I will bow out thank you for
+
+ align:start position:0%
+that and I will bow out thank you for
+ 
+
+ align:start position:0%
+that and I will bow out thank you for
+participating in the four dinner
+
+ align:start position:0%
+participating in the four dinner
+ 
+
+ align:start position:0%
+participating in the four dinner
+discussions we will make this available
+
+ align:start position:0%
+discussions we will make this available
+ 
+
+ align:start position:0%
+discussions we will make this available
+uh hopefully it will be sitting on the
+
+ align:start position:0%
+uh hopefully it will be sitting on the
+ 
+
+ align:start position:0%
+uh hopefully it will be sitting on the
+department's website and I also hope
+
+ align:start position:0%
+department's website and I also hope
+ 
+
+ align:start position:0%
+department's website and I also hope
+that it does lead to the creation of
+
+ align:start position:0%
+that it does lead to the creation of
+ 
+
+ align:start position:0%
+that it does lead to the creation of
+additional courses dealing with
+
+ align:start position:0%
+additional courses dealing with
+ 
+
+ align:start position:0%
+additional courses dealing with
+leadership within the public sector that
+
+ align:start position:0%
+leadership within the public sector that
+ 
+
+ align:start position:0%
+leadership within the public sector that
+DSP takes responsibility for maybe you
+
+ align:start position:0%
+DSP takes responsibility for maybe you
+ 
+
+ align:start position:0%
+DSP takes responsibility for maybe you
+can become a
+
+ align:start position:0%
+can become a
+ 
+
+ align:start position:0%
+can become a
+constituency to ask for something more
+
+ align:start position:0%
+constituency to ask for something more
+ 
+
+ align:start position:0%
+constituency to ask for something more
+on that score and um I'm obviously
+
+ align:start position:0%
+on that score and um I'm obviously
+ 
+
+ align:start position:0%
+on that score and um I'm obviously
+always available to talk with anybody
+
+ align:start position:0%
+always available to talk with anybody
+ 
+
+ align:start position:0%
+always available to talk with anybody
+who wants to pick up on these issues
+
+ align:start position:0%
+who wants to pick up on these issues
+ 
+
+ align:start position:0%
+who wants to pick up on these issues
+oneon-one
+
+ align:start position:0%
+oneon-one
+ 
+
+ align:start position:0%
+oneon-one
+thanks good night
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/cd8lDtAtJbE.txt b/cd8lDtAtJbE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7fbd5eb8752963c441031e21577817366f2676af
--- /dev/null
+++ b/cd8lDtAtJbE.txt
@@ -0,0 +1,10755 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu and I
+
+ align:start position:0%
+ocw.mit.edu and I
+ 
+
+ align:start position:0%
+ocw.mit.edu and I
+have put on the second board just a
+
+ align:start position:0%
+have put on the second board just a
+ 
+
+ align:start position:0%
+have put on the second board just a
+quick review of the key equations
+
+ align:start position:0%
+quick review of the key equations
+ 
+
+ align:start position:0%
+quick review of the key equations
+that we use to do the direct method so
+
+ align:start position:0%
+that we use to do the direct method so
+ 
+
+ align:start position:0%
+that we use to do the direct method so
+straight from Newton Second Law the
+
+ align:start position:0%
+straight from Newton Second Law the
+ 
+
+ align:start position:0%
+straight from Newton Second Law the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+one second one the summation of torqu
+
+ align:start position:0%
+one second one the summation of torqu
+ 
+
+ align:start position:0%
+one second one the summation of torqu
+about some point
+
+ align:start position:0%
+about some point
+ 
+
+ align:start position:0%
+about some point
+a a may be G in which case things
+
+ align:start position:0%
+a a may be G in which case things
+ 
+
+ align:start position:0%
+a a may be G in which case things
+get much simplified G being the center
+
+ align:start position:0%
+get much simplified G being the center
+ 
+
+ align:start position:0%
+get much simplified G being the center
+of mass and if the point a is moving
+
+ align:start position:0%
+of mass and if the point a is moving
+ 
+
+ align:start position:0%
+of mass and if the point a is moving
+then you have this extra term and this
+
+ align:start position:0%
+then you have this extra term and this
+ 
+
+ align:start position:0%
+then you have this extra term and this
+is a new equation over here which I got
+
+ align:start position:0%
+is a new equation over here which I got
+ 
+
+ align:start position:0%
+is a new equation over here which I got
+frustrated with this equation a few days
+
+ align:start position:0%
+frustrated with this equation a few days
+ 
+
+ align:start position:0%
+frustrated with this equation a few days
+ago and derived something which I think
+
+ align:start position:0%
+ago and derived something which I think
+ 
+
+ align:start position:0%
+ago and derived something which I think
+is more is easier to use so I'll do a
+
+ align:start position:0%
+is more is easier to use so I'll do a
+ 
+
+ align:start position:0%
+is more is easier to use so I'll do a
+problem today using that
+
+ align:start position:0%
+problem today using that
+ 
+
+ align:start position:0%
+problem today using that
+expression so I won't talk more about it
+
+ align:start position:0%
+expression so I won't talk more about it
+ 
+
+ align:start position:0%
+expression so I won't talk more about it
+now show it to you in a minute and then
+
+ align:start position:0%
+now show it to you in a minute and then
+ 
+
+ align:start position:0%
+now show it to you in a minute and then
+uh finally it's convenient at times to
+
+ align:start position:0%
+uh finally it's convenient at times to
+ 
+
+ align:start position:0%
+uh finally it's convenient at times to
+express angular momentum with respect to
+
+ align:start position:0%
+express angular momentum with respect to
+ 
+
+ align:start position:0%
+express angular momentum with respect to
+a point a as angular momentum about G
+
+ align:start position:0%
+a point a as angular momentum about G
+ 
+
+ align:start position:0%
+a point a as angular momentum about G
+plus the
+
+ align:start position:0%
+plus the
+ 
+
+ align:start position:0%
+plus the
+position Vector from a to G times the
+
+ align:start position:0%
+position Vector from a to G times the
+ 
+
+ align:start position:0%
+position Vector from a to G times the
+linear momentum so that's kind of the
+
+ align:start position:0%
+linear momentum so that's kind of the
+ 
+
+ align:start position:0%
+linear momentum so that's kind of the
+material covered on the quiz and we're
+
+ align:start position:0%
+material covered on the quiz and we're
+ 
+
+ align:start position:0%
+material covered on the quiz and we're
+going to use these equations I'm going
+
+ align:start position:0%
+going to use these equations I'm going
+ 
+
+ align:start position:0%
+going to use these equations I'm going
+to today what I'm going to do is look at
+
+ align:start position:0%
+to today what I'm going to do is look at
+ 
+
+ align:start position:0%
+to today what I'm going to do is look at
+a few
+
+ align:start position:0%
+a few
+ 
+
+ align:start position:0%
+a few
+problems from the point of from the
+
+ align:start position:0%
+problems from the point of from the
+ 
+
+ align:start position:0%
+problems from the point of from the
+point of view of both equations of
+
+ align:start position:0%
+point of view of both equations of
+ 
+
+ align:start position:0%
+point of view of both equations of
+motion by the direct method and the
+
+ align:start position:0%
+motion by the direct method and the
+ 
+
+ align:start position:0%
+motion by the direct method and the
+lrange method and kind of talk about you
+
+ align:start position:0%
+lrange method and kind of talk about you
+ 
+
+ align:start position:0%
+lrange method and kind of talk about you
+know which one's
+
+ align:start position:0%
+know which one's
+ 
+
+ align:start position:0%
+know which one's
+easier how do you you know when should
+
+ align:start position:0%
+easier how do you you know when should
+ 
+
+ align:start position:0%
+easier how do you you know when should
+you choose this one one to choose that
+
+ align:start position:0%
+you choose this one one to choose that
+ 
+
+ align:start position:0%
+you choose this one one to choose that
+one that's the sort of the nature of
+
+ align:start position:0%
+one that's the sort of the nature of
+ 
+
+ align:start position:0%
+one that's the sort of the nature of
+today's lecture to sort of get you
+
+ align:start position:0%
+today's lecture to sort of get you
+ 
+
+ align:start position:0%
+today's lecture to sort of get you
+prepped for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quiz and a little bit more on
+
+ align:start position:0%
+quiz and a little bit more on
+ 
+
+ align:start position:0%
+quiz and a little bit more on
+generalized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forces you have questions about what's
+
+ align:start position:0%
+forces you have questions about what's
+ 
+
+ align:start position:0%
+forces you have questions about what's
+going to be on the quiz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that last balancing balancing of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotors there's a
+
+ align:start position:0%
+rotors there's a
+ 
+
+ align:start position:0%
+rotors there's a
+rotor anything that we spin about an
+
+ align:start position:0%
+rotor anything that we spin about an
+ 
+
+ align:start position:0%
+rotor anything that we spin about an
+axis you know rigid body spinning about
+
+ align:start position:0%
+axis you know rigid body spinning about
+ 
+
+ align:start position:0%
+axis you know rigid body spinning about
+an axis you can call a rotor of some
+
+ align:start position:0%
+an axis you can call a rotor of some
+ 
+
+ align:start position:0%
+an axis you can call a rotor of some
+kind and balancing is usually on think
+
+ align:start position:0%
+kind and balancing is usually on think
+ 
+
+ align:start position:0%
+kind and balancing is usually on think
+the axes are are fixed and so is this
+
+ align:start position:0%
+the axes are are fixed and so is this
+ 
+
+ align:start position:0%
+the axes are are fixed and so is this
+this is this one this axis passes
+
+ align:start position:0%
+this is this one this axis passes
+ 
+
+ align:start position:0%
+this is this one this axis passes
+through the center of mass so is is this
+
+ align:start position:0%
+through the center of mass so is is this
+ 
+
+ align:start position:0%
+through the center of mass so is is this
+does this rotor is it statically
+
+ align:start position:0%
+does this rotor is it statically
+ 
+
+ align:start position:0%
+does this rotor is it statically
+balanced right is this rotor dynamically
+
+ align:start position:0%
+balanced right is this rotor dynamically
+ 
+
+ align:start position:0%
+balanced right is this rotor dynamically
+balanced would you expect so when this
+
+ align:start position:0%
+balanced would you expect so when this
+ 
+
+ align:start position:0%
+balanced would you expect so when this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+spinning it's its direction of spin is
+
+ align:start position:0%
+spinning it's its direction of spin is
+ 
+
+ align:start position:0%
+spinning it's its direction of spin is
+vertical
+
+ align:start position:0%
+vertical
+ 
+
+ align:start position:0%
+vertical
+right is the direction what direction is
+
+ align:start position:0%
+right is the direction what direction is
+ 
+
+ align:start position:0%
+right is the direction what direction is
+the is the direction of the angular
+
+ align:start position:0%
+the is the direction of the angular
+ 
+
+ align:start position:0%
+the is the direction of the angular
+momentum of this object in the same
+
+ align:start position:0%
+momentum of this object in the same
+ 
+
+ align:start position:0%
+momentum of this object in the same
+direction as the angle of
+
+ align:start position:0%
+direction as the angle of
+ 
+
+ align:start position:0%
+direction as the angle of
+rotation no and so that's and that's an
+
+ align:start position:0%
+rotation no and so that's and that's an
+ 
+
+ align:start position:0%
+rotation no and so that's and that's an
+indic
+
+ align:start position:0%
+indic
+ 
+
+ align:start position:0%
+indic
+of dynamic imbalance the angle of
+
+ align:start position:0%
+of dynamic imbalance the angle of
+ 
+
+ align:start position:0%
+of dynamic imbalance the angle of
+momentum is not in the same direction as
+
+ align:start position:0%
+momentum is not in the same direction as
+ 
+
+ align:start position:0%
+momentum is not in the same direction as
+the angle of rotation right all right
+
+ align:start position:0%
+the angle of rotation right all right
+ 
+
+ align:start position:0%
+the angle of rotation right all right
+and well we're on that subject we'll
+
+ align:start position:0%
+and well we're on that subject we'll
+ 
+
+ align:start position:0%
+and well we're on that subject we'll
+just hit it briefly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here have one other prop I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+need so another rigid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+body and I don't know where G is on this
+
+ align:start position:0%
+body and I don't know where G is on this
+ 
+
+ align:start position:0%
+body and I don't know where G is on this
+rigid body
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so does this is rotating about an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axis is this object statically balanced
+
+ align:start position:0%
+axis is this object statically balanced
+ 
+
+ align:start position:0%
+axis is this object statically balanced
+just from looking just doing this
+
+ align:start position:0%
+just from looking just doing this
+ 
+
+ align:start position:0%
+just from looking just doing this
+experiment we're doing an experiment
+
+ align:start position:0%
+experiment we're doing an experiment
+ 
+
+ align:start position:0%
+experiment we're doing an experiment
+we're sticking this on an axis and we're
+
+ align:start position:0%
+we're sticking this on an axis and we're
+ 
+
+ align:start position:0%
+we're sticking this on an axis and we're
+letting it do its thing and I'm asking
+
+ align:start position:0%
+letting it do its thing and I'm asking
+ 
+
+ align:start position:0%
+letting it do its thing and I'm asking
+you is it statically balanced how do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know down it it would come to a so goes
+
+ align:start position:0%
+know down it it would come to a so goes
+ 
+
+ align:start position:0%
+know down it it would come to a so goes
+to a low point right and that tells you
+
+ align:start position:0%
+to a low point right and that tells you
+ 
+
+ align:start position:0%
+to a low point right and that tells you
+what that about the position of this
+
+ align:start position:0%
+what that about the position of this
+ 
+
+ align:start position:0%
+what that about the position of this
+axis right center of mass has got
+
+ align:start position:0%
+axis right center of mass has got
+ 
+
+ align:start position:0%
+axis right center of mass has got
+gravity puts a force at the center of
+
+ align:start position:0%
+gravity puts a force at the center of
+ 
+
+ align:start position:0%
+gravity puts a force at the center of
+mass creates a torque which brings it to
+
+ align:start position:0%
+mass creates a torque which brings it to
+ 
+
+ align:start position:0%
+mass creates a torque which brings it to
+the low point right does this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+object does this object have a any
+
+ align:start position:0%
+object does this object have a any
+ 
+
+ align:start position:0%
+object does this object have a any
+symmetries that you could point out or
+
+ align:start position:0%
+symmetries that you could point out or
+ 
+
+ align:start position:0%
+symmetries that you could point out or
+in other words could you can you without
+
+ align:start position:0%
+in other words could you can you without
+ 
+
+ align:start position:0%
+in other words could you can you without
+doing any math tell me one principal
+
+ align:start position:0%
+doing any math tell me one principal
+ 
+
+ align:start position:0%
+doing any math tell me one principal
+axis of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+object where the dotted line is
+
+ align:start position:0%
+object where the dotted line is
+ 
+
+ align:start position:0%
+object where the dotted line is
+That's So You see I've got a dotted line
+
+ align:start position:0%
+That's So You see I've got a dotted line
+ 
+
+ align:start position:0%
+That's So You see I've got a dotted line
+around here and that's a plane of what
+
+ align:start position:0%
+around here and that's a plane of what
+ 
+
+ align:start position:0%
+around here and that's a plane of what
+so there's a plane of symmetry cutting
+
+ align:start position:0%
+so there's a plane of symmetry cutting
+ 
+
+ align:start position:0%
+so there's a plane of symmetry cutting
+this thing through here so if you have
+
+ align:start position:0%
+this thing through here so if you have
+ 
+
+ align:start position:0%
+this thing through here so if you have
+if you can identify one plane of
+
+ align:start position:0%
+if you can identify one plane of
+ 
+
+ align:start position:0%
+if you can identify one plane of
+symmetry then where can you tell me that
+
+ align:start position:0%
+symmetry then where can you tell me that
+ 
+
+ align:start position:0%
+symmetry then where can you tell me that
+for sure you know that you can make a
+
+ align:start position:0%
+for sure you know that you can make a
+ 
+
+ align:start position:0%
+for sure you know that you can make a
+principal
+
+ align:start position:0%
+principal
+ 
+
+ align:start position:0%
+principal
+axis he says perpendicular to that plane
+
+ align:start position:0%
+axis he says perpendicular to that plane
+ 
+
+ align:start position:0%
+axis he says perpendicular to that plane
+any place on that plane perpendicular to
+
+ align:start position:0%
+any place on that plane perpendicular to
+ 
+
+ align:start position:0%
+any place on that plane perpendicular to
+it what do you think I mean is so now
+
+ align:start position:0%
+it what do you think I mean is so now
+ 
+
+ align:start position:0%
+it what do you think I mean is so now
+we've identified it has a plane of
+
+ align:start position:0%
+we've identified it has a plane of
+ 
+
+ align:start position:0%
+we've identified it has a plane of
+symmetry and that per an axis
+
+ align:start position:0%
+symmetry and that per an axis
+ 
+
+ align:start position:0%
+symmetry and that per an axis
+perpendicular to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it an axis of symmetry excuse me an axis
+
+ align:start position:0%
+it an axis of symmetry excuse me an axis
+ 
+
+ align:start position:0%
+it an axis of symmetry excuse me an axis
+a principal axis should be perpendicular
+
+ align:start position:0%
+a principal axis should be perpendicular
+ 
+
+ align:start position:0%
+a principal axis should be perpendicular
+to that plane but the question is where
+
+ align:start position:0%
+to that plane but the question is where
+ 
+
+ align:start position:0%
+to that plane but the question is where
+do I put it
+
+ align:start position:0%
+do I put it
+ 
+
+ align:start position:0%
+do I put it
+where perpendicular to that plane can
+
+ align:start position:0%
+where perpendicular to that plane can
+ 
+
+ align:start position:0%
+where perpendicular to that plane can
+this axis be and be a principal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axis she says through G you agree with
+
+ align:start position:0%
+axis she says through G you agree with
+ 
+
+ align:start position:0%
+axis she says through G you agree with
+that okay so certainly through G let's
+
+ align:start position:0%
+that okay so certainly through G let's
+ 
+
+ align:start position:0%
+that okay so certainly through G let's
+say that that really is G and I put it
+
+ align:start position:0%
+say that that really is G and I put it
+ 
+
+ align:start position:0%
+say that that really is G and I put it
+through here and if it was exactly
+
+ align:start position:0%
+through here and if it was exactly
+ 
+
+ align:start position:0%
+through here and if it was exactly
+through G it wouldn't rotate to a low
+
+ align:start position:0%
+through G it wouldn't rotate to a low
+ 
+
+ align:start position:0%
+through G it wouldn't rotate to a low
+spot but it's pretty close it that
+
+ align:start position:0%
+spot but it's pretty close it that
+ 
+
+ align:start position:0%
+spot but it's pretty close it that
+struggles to get there that's definitely
+
+ align:start position:0%
+struggles to get there that's definitely
+ 
+
+ align:start position:0%
+struggles to get there that's definitely
+a axis but are there more this is kind
+
+ align:start position:0%
+a axis but are there more this is kind
+ 
+
+ align:start position:0%
+a axis but are there more this is kind
+of the point real point of the question
+
+ align:start position:0%
+of the point real point of the question
+ 
+
+ align:start position:0%
+of the point real point of the question
+are there other allowable principal axes
+
+ align:start position:0%
+are there other allowable principal axes
+ 
+
+ align:start position:0%
+are there other allowable principal axes
+in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction so we haven't talked about
+
+ align:start position:0%
+direction so we haven't talked about
+ 
+
+ align:start position:0%
+direction so we haven't talked about
+this very much any axis if this is a
+
+ align:start position:0%
+this very much any axis if this is a
+ 
+
+ align:start position:0%
+this very much any axis if this is a
+principal axis any axis parallel to its
+
+ align:start position:0%
+principal axis any axis parallel to its
+ 
+
+ align:start position:0%
+principal axis any axis parallel to its
+a principal
+
+ align:start position:0%
+a principal
+ 
+
+ align:start position:0%
+a principal
+axis it's no longer through G it's no
+
+ align:start position:0%
+axis it's no longer through G it's no
+ 
+
+ align:start position:0%
+axis it's no longer through G it's no
+longer statically balanced about that
+
+ align:start position:0%
+longer statically balanced about that
+ 
+
+ align:start position:0%
+longer statically balanced about that
+point but it's still a principal axis
+
+ align:start position:0%
+point but it's still a principal axis
+ 
+
+ align:start position:0%
+point but it's still a principal axis
+and one one way one measure of whether
+
+ align:start position:0%
+and one one way one measure of whether
+ 
+
+ align:start position:0%
+and one one way one measure of whether
+or not something is a principal axis if
+
+ align:start position:0%
+or not something is a principal axis if
+ 
+
+ align:start position:0%
+or not something is a principal axis if
+if you know the principal axis of an
+
+ align:start position:0%
+if you know the principal axis of an
+ 
+
+ align:start position:0%
+if you know the principal axis of an
+object and you write the mass moment of
+
+ align:start position:0%
+object and you write the mass moment of
+ 
+
+ align:start position:0%
+object and you write the mass moment of
+inertia Matrix of it with respect to G
+
+ align:start position:0%
+inertia Matrix of it with respect to G
+ 
+
+ align:start position:0%
+inertia Matrix of it with respect to G
+what does that Matrix look
+
+ align:start position:0%
+what does that Matrix look
+ 
+
+ align:start position:0%
+what does that Matrix look
+like where does it have zeros and
+
+ align:start position:0%
+like where does it have zeros and
+ 
+
+ align:start position:0%
+like where does it have zeros and
+nonzeros it's a dional it's a diagonal
+
+ align:start position:0%
+nonzeros it's a dional it's a diagonal
+ 
+
+ align:start position:0%
+nonzeros it's a dional it's a diagonal
+matrix if I so if I I about G is
+
+ align:start position:0%
+matrix if I so if I I about G is
+ 
+
+ align:start position:0%
+matrix if I so if I I about G is
+diagonal that means you're computed the
+
+ align:start position:0%
+diagonal that means you're computed the
+ 
+
+ align:start position:0%
+diagonal that means you're computed the
+moment Mass moment properties with
+
+ align:start position:0%
+moment Mass moment properties with
+ 
+
+ align:start position:0%
+moment Mass moment properties with
+respect to three principal axes if it's
+
+ align:start position:0%
+respect to three principal axes if it's
+ 
+
+ align:start position:0%
+respect to three principal axes if it's
+diagonal and I those axes all pass
+
+ align:start position:0%
+diagonal and I those axes all pass
+ 
+
+ align:start position:0%
+diagonal and I those axes all pass
+through G if I now take one of those
+
+ align:start position:0%
+through G if I now take one of those
+ 
+
+ align:start position:0%
+through G if I now take one of those
+axes and say I want to move it over here
+
+ align:start position:0%
+axes and say I want to move it over here
+ 
+
+ align:start position:0%
+axes and say I want to move it over here
+and you
+
+ align:start position:0%
+and you
+ 
+
+ align:start position:0%
+and you
+recomputed the inertia Matrix would it
+
+ align:start position:0%
+recomputed the inertia Matrix would it
+ 
+
+ align:start position:0%
+recomputed the inertia Matrix would it
+still be
+
+ align:start position:0%
+still be
+ 
+
+ align:start position:0%
+still be
+diagonal so you've moved just one
+
+ align:start position:0%
+diagonal so you've moved just one
+ 
+
+ align:start position:0%
+diagonal so you've moved just one
+axis to another spot parallel to its
+
+ align:start position:0%
+axis to another spot parallel to its
+ 
+
+ align:start position:0%
+axis to another spot parallel to its
+original one you know this one is a
+
+ align:start position:0%
+original one you know this one is a
+ 
+
+ align:start position:0%
+original one you know this one is a
+principal axis I'm going to move it
+
+ align:start position:0%
+principal axis I'm going to move it
+ 
+
+ align:start position:0%
+principal axis I'm going to move it
+just parallel only that one axis the
+
+ align:start position:0%
+just parallel only that one axis the
+ 
+
+ align:start position:0%
+just parallel only that one axis the
+other two are staying where they are
+
+ align:start position:0%
+other two are staying where they are
+ 
+
+ align:start position:0%
+other two are staying where they are
+just moved it
+
+ align:start position:0%
+just moved it
+ 
+
+ align:start position:0%
+just moved it
+parallel is that also a principal Axis
+
+ align:start position:0%
+parallel is that also a principal Axis
+ 
+
+ align:start position:0%
+parallel is that also a principal Axis
+or another way of saying it does that
+
+ align:start position:0%
+or another way of saying it does that
+ 
+
+ align:start position:0%
+or another way of saying it does that
+mass Matrix Mass moment inertia Matrix
+
+ align:start position:0%
+mass Matrix Mass moment inertia Matrix
+ 
+
+ align:start position:0%
+mass Matrix Mass moment inertia Matrix
+stay
+
+ align:start position:0%
+stay
+ 
+
+ align:start position:0%
+stay
+diagonal do do any of the terms in it
+
+ align:start position:0%
+diagonal do do any of the terms in it
+ 
+
+ align:start position:0%
+diagonal do do any of the terms in it
+change let's say this is the Z principal
+
+ align:start position:0%
+change let's say this is the Z principal
+ 
+
+ align:start position:0%
+change let's say this is the Z principal
+axis and I move away so now you have the
+
+ align:start position:0%
+axis and I move away so now you have the
+ 
+
+ align:start position:0%
+axis and I move away so now you have the
+this new maximum inertia Matrix
+
+ align:start position:0%
+this new maximum inertia Matrix
+ 
+
+ align:start position:0%
+this new maximum inertia Matrix
+does the I ZZ term
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change Yeah by how
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much and he says ml squ L being what the
+
+ align:start position:0%
+much and he says ml squ L being what the
+ 
+
+ align:start position:0%
+much and he says ml squ L being what the
+length move here and that's this thing
+
+ align:start position:0%
+length move here and that's this thing
+ 
+
+ align:start position:0%
+length move here and that's this thing
+known
+
+ align:start position:0%
+known
+ 
+
+ align:start position:0%
+known
+as parallel axis there right if you move
+
+ align:start position:0%
+as parallel axis there right if you move
+ 
+
+ align:start position:0%
+as parallel axis there right if you move
+one axis this thing is still any axis
+
+ align:start position:0%
+one axis this thing is still any axis
+ 
+
+ align:start position:0%
+one axis this thing is still any axis
+parallel to one of those axes is also
+
+ align:start position:0%
+parallel to one of those axes is also
+ 
+
+ align:start position:0%
+parallel to one of those axes is also
+principal axis so that's a subtle point
+
+ align:start position:0%
+principal axis so that's a subtle point
+ 
+
+ align:start position:0%
+principal axis so that's a subtle point
+we we don't of talk about it but any
+
+ align:start position:0%
+we we don't of talk about it but any
+ 
+
+ align:start position:0%
+we we don't of talk about it but any
+axis parallel to a principal axis is
+
+ align:start position:0%
+axis parallel to a principal axis is
+ 
+
+ align:start position:0%
+axis parallel to a principal axis is
+also a principal axis okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good let's think about a problem we've
+
+ align:start position:0%
+good let's think about a problem we've
+ 
+
+ align:start position:0%
+good let's think about a problem we've
+done this problem before but now we have
+
+ align:start position:0%
+done this problem before but now we have
+ 
+
+ align:start position:0%
+done this problem before but now we have
+all the full tools we have lrange we
+
+ align:start position:0%
+all the full tools we have lrange we
+ 
+
+ align:start position:0%
+all the full tools we have lrange we
+have direct method so that's this
+
+ align:start position:0%
+have direct method so that's this
+ 
+
+ align:start position:0%
+have direct method so that's this
+problem of the we
+
+ align:start position:0%
+problem of the we
+ 
+
+ align:start position:0%
+problem of the we
+on a horizontal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plane kind of a
+
+ align:start position:0%
+plane kind of a
+ 
+
+ align:start position:0%
+plane kind of a
+complicated distribution of mass for
+
+ align:start position:0%
+complicated distribution of mass for
+ 
+
+ align:start position:0%
+complicated distribution of mass for
+which we
+
+ align:start position:0%
+which we
+ 
+
+ align:start position:0%
+which we
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+izz about G is some Mass radius of
+
+ align:start position:0%
+izz about G is some Mass radius of
+ 
+
+ align:start position:0%
+izz about G is some Mass radius of
+gation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared maybe we measured it rather than
+
+ align:start position:0%
+squared maybe we measured it rather than
+ 
+
+ align:start position:0%
+squared maybe we measured it rather than
+computed it so this thing is on a slide
+
+ align:start position:0%
+computed it so this thing is on a slide
+ 
+
+ align:start position:0%
+computed it so this thing is on a slide
+on ice and it
+
+ align:start position:0%
+on ice and it
+ 
+
+ align:start position:0%
+on ice and it
+has cord wrapped around it I'm pulling
+
+ align:start position:0%
+has cord wrapped around it I'm pulling
+ 
+
+ align:start position:0%
+has cord wrapped around it I'm pulling
+with a force F call it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F1 now I'll provide
+
+ align:start position:0%
+F1 now I'll provide
+ 
+
+ align:start position:0%
+F1 now I'll provide
+the inertial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frame and it's got some radius
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bar and will'll say the surface is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frictionless so I don't have a string
+
+ align:start position:0%
+frictionless so I don't have a string
+ 
+
+ align:start position:0%
+frictionless so I don't have a string
+wrapped around but we're really talking
+
+ align:start position:0%
+wrapped around but we're really talking
+ 
+
+ align:start position:0%
+wrapped around but we're really talking
+about this problem I'm pulling on this
+
+ align:start position:0%
+about this problem I'm pulling on this
+ 
+
+ align:start position:0%
+about this problem I'm pulling on this
+string and this thing can slide and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotate so take a sec think about how
+
+ align:start position:0%
+rotate so take a sec think about how
+ 
+
+ align:start position:0%
+rotate so take a sec think about how
+many different ways can you think of
+
+ align:start position:0%
+many different ways can you think of
+ 
+
+ align:start position:0%
+many different ways can you think of
+solving for the equations of motion of
+
+ align:start position:0%
+solving for the equations of motion of
+ 
+
+ align:start position:0%
+solving for the equations of motion of
+this so this is on a quiz I want you to
+
+ align:start position:0%
+this so this is on a quiz I want you to
+ 
+
+ align:start position:0%
+this so this is on a quiz I want you to
+find the equations of
+
+ align:start position:0%
+find the equations of
+ 
+
+ align:start position:0%
+find the equations of
+motion what method would you
+
+ align:start position:0%
+motion what method would you
+ 
+
+ align:start position:0%
+motion what method would you
+use and what's the and then then you're
+
+ align:start position:0%
+use and what's the and then then you're
+ 
+
+ align:start position:0%
+use and what's the and then then you're
+confronted with well I know more than
+
+ align:start position:0%
+confronted with well I know more than
+ 
+
+ align:start position:0%
+confronted with well I know more than
+one method what's the simplest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method and before that you need to
+
+ align:start position:0%
+method and before that you need to
+ 
+
+ align:start position:0%
+method and before that you need to
+decide how many coordinates you're going
+
+ align:start position:0%
+decide how many coordinates you're going
+ 
+
+ align:start position:0%
+decide how many coordinates you're going
+to need how many equations you're going
+
+ align:start position:0%
+to need how many equations you're going
+ 
+
+ align:start position:0%
+to need how many equations you're going
+so let's start there how many
+
+ align:start position:0%
+so let's start there how many
+ 
+
+ align:start position:0%
+so let's start there how many
+independent coordinates do you need to
+
+ align:start position:0%
+independent coordinates do you need to
+ 
+
+ align:start position:0%
+independent coordinates do you need to
+do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem so is so and we'll back up one
+
+ align:start position:0%
+problem so is so and we'll back up one
+ 
+
+ align:start position:0%
+problem so is so and we'll back up one
+more question then is this a planer
+
+ align:start position:0%
+more question then is this a planer
+ 
+
+ align:start position:0%
+more question then is this a planer
+motion
+
+ align:start position:0%
+motion
+ 
+
+ align:start position:0%
+motion
+problem so it's confined to one plane I
+
+ align:start position:0%
+problem so it's confined to one plane I
+ 
+
+ align:start position:0%
+problem so it's confined to one plane I
+see a lot of heads nodding and it
+
+ align:start position:0%
+see a lot of heads nodding and it
+ 
+
+ align:start position:0%
+see a lot of heads nodding and it
+rotates only with one degree of freedom
+
+ align:start position:0%
+rotates only with one degree of freedom
+ 
+
+ align:start position:0%
+rotates only with one degree of freedom
+and rotation axis perpendicular to the
+
+ align:start position:0%
+and rotation axis perpendicular to the
+ 
+
+ align:start position:0%
+and rotation axis perpendicular to the
+plane so this is a planer motion problem
+
+ align:start position:0%
+plane so this is a planer motion problem
+ 
+
+ align:start position:0%
+plane so this is a planer motion problem
+so in general planer motion problems
+
+ align:start position:0%
+so in general planer motion problems
+ 
+
+ align:start position:0%
+so in general planer motion problems
+have how many degrees of freedom per
+
+ align:start position:0%
+have how many degrees of freedom per
+ 
+
+ align:start position:0%
+have how many degrees of freedom per
+rigid body so I see a bunch of Threes
+
+ align:start position:0%
+rigid body so I see a bunch of Threes
+ 
+
+ align:start position:0%
+rigid body so I see a bunch of Threes
+okay does this one have any constraints
+
+ align:start position:0%
+okay does this one have any constraints
+ 
+
+ align:start position:0%
+okay does this one have any constraints
+on those three degrees of freedom so
+
+ align:start position:0%
+on those three degrees of freedom so
+ 
+
+ align:start position:0%
+on those three degrees of freedom so
+this has three degrees of freedom you
+
+ align:start position:0%
+this has three degrees of freedom you
+ 
+
+ align:start position:0%
+this has three degrees of freedom you
+conceivably
+
+ align:start position:0%
+conceivably
+ 
+
+ align:start position:0%
+conceivably
+need three equations of motion okay how
+
+ align:start position:0%
+need three equations of motion okay how
+ 
+
+ align:start position:0%
+need three equations of motion okay how
+now so how can what are the choices for
+
+ align:start position:0%
+now so how can what are the choices for
+ 
+
+ align:start position:0%
+now so how can what are the choices for
+getting
+
+ align:start position:0%
+getting
+ 
+
+ align:start position:0%
+getting
+them what you think about this for a
+
+ align:start position:0%
+them what you think about this for a
+ 
+
+ align:start position:0%
+them what you think about this for a
+minute you decide what way you would do
+
+ align:start position:0%
+minute you decide what way you would do
+ 
+
+ align:start position:0%
+minute you decide what way you would do
+and then let's just kind of take a poll
+
+ align:start position:0%
+and then let's just kind of take a poll
+ 
+
+ align:start position:0%
+and then let's just kind of take a poll
+in a minute you think about it and then
+
+ align:start position:0%
+in a minute you think about it and then
+ 
+
+ align:start position:0%
+in a minute you think about it and then
+let's take a poll for how people would
+
+ align:start position:0%
+let's take a poll for how people would
+ 
+
+ align:start position:0%
+let's take a poll for how people would
+do this problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what's your favorite how would you do
+
+ align:start position:0%
+so what's your favorite how would you do
+ 
+
+ align:start position:0%
+so what's your favorite how would you do
+it direct method he'd use a direct
+
+ align:start position:0%
+it direct method he'd use a direct
+ 
+
+ align:start position:0%
+it direct method he'd use a direct
+method about uh do you need a torque
+
+ align:start position:0%
+method about uh do you need a torque
+ 
+
+ align:start position:0%
+method about uh do you need a torque
+equation about what point he'd use
+
+ align:start position:0%
+equation about what point he'd use
+ 
+
+ align:start position:0%
+equation about what point he'd use
+Center of mass so he'd say direct method
+
+ align:start position:0%
+Center of mass so he'd say direct method
+ 
+
+ align:start position:0%
+Center of mass so he'd say direct method
+and for the torque equation do it about
+
+ align:start position:0%
+and for the torque equation do it about
+ 
+
+ align:start position:0%
+and for the torque equation do it about
+Center Mass anybody have a different way
+
+ align:start position:0%
+Center Mass anybody have a different way
+ 
+
+ align:start position:0%
+Center Mass anybody have a different way
+they would do this
+
+ align:start position:0%
+they would do this
+ 
+
+ align:start position:0%
+they would do this
+problem is there another way to do
+
+ align:start position:0%
+problem is there another way to do
+ 
+
+ align:start position:0%
+problem is there another way to do
+it he wants to do lrange okay everybody
+
+ align:start position:0%
+it he wants to do lrange okay everybody
+ 
+
+ align:start position:0%
+it he wants to do lrange okay everybody
+agree it could be done that way all
+
+ align:start position:0%
+agree it could be done that way all
+ 
+
+ align:start position:0%
+agree it could be done that way all
+right so I agree and Let's do let's
+
+ align:start position:0%
+right so I agree and Let's do let's
+ 
+
+ align:start position:0%
+right so I agree and Let's do let's
+quickly see let's quickly do this
+
+ align:start position:0%
+quickly see let's quickly do this
+ 
+
+ align:start position:0%
+quickly see let's quickly do this
+problem and so direct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method I'm going to make it easy on
+
+ align:start position:0%
+method I'm going to make it easy on
+ 
+
+ align:start position:0%
+method I'm going to make it easy on
+myself here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so the three coordinates you're going
+
+ align:start position:0%
+um so the three coordinates you're going
+ 
+
+ align:start position:0%
+um so the three coordinates you're going
+to need an x a y and a Theta is what
+
+ align:start position:0%
+to need an x a y and a Theta is what
+ 
+
+ align:start position:0%
+to need an x a y and a Theta is what
+I've chosen for the three coordinates to
+
+ align:start position:0%
+I've chosen for the three coordinates to
+ 
+
+ align:start position:0%
+I've chosen for the three coordinates to
+do this direct method and to make it
+
+ align:start position:0%
+do this direct method and to make it
+ 
+
+ align:start position:0%
+do this direct method and to make it
+easy on myself I'm going to align the
+
+ align:start position:0%
+easy on myself I'm going to align the
+ 
+
+ align:start position:0%
+easy on myself I'm going to align the
+force with my coordinates so I'm going
+
+ align:start position:0%
+force with my coordinates so I'm going
+ 
+
+ align:start position:0%
+force with my coordinates so I'm going
+to make essentially make Theta zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so essentially aligning F1 my Force F1
+
+ align:start position:0%
+so essentially aligning F1 my Force F1
+ 
+
+ align:start position:0%
+so essentially aligning F1 my Force F1
+with the x-axis and if I do that then I
+
+ align:start position:0%
+with the x-axis and if I do that then I
+ 
+
+ align:start position:0%
+with the x-axis and if I do that then I
+can say the sum of the forces in the Y
+
+ align:start position:0%
+can say the sum of the forces in the Y
+ 
+
+ align:start position:0%
+can say the sum of the forces in the Y
+the external forces in the y direction
+
+ align:start position:0%
+the external forces in the y direction
+ 
+
+ align:start position:0%
+the external forces in the y direction
+are non-existent zero so that must be m
+
+ align:start position:0%
+are non-existent zero so that must be m
+ 
+
+ align:start position:0%
+are non-existent zero so that must be m
+y dble dot so y dble Dot is zero so we
+
+ align:start position:0%
+y dble dot so y dble Dot is zero so we
+ 
+
+ align:start position:0%
+y dble dot so y dble Dot is zero so we
+that's makes simplifies the problem
+
+ align:start position:0%
+that's makes simplifies the problem
+ 
+
+ align:start position:0%
+that's makes simplifies the problem
+summation of the forces in the X
+
+ align:start position:0%
+summation of the forces in the X
+ 
+
+ align:start position:0%
+summation of the forces in the X
+Direction external forces are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f1i and they must equal to the mass
+
+ align:start position:0%
+f1i and they must equal to the mass
+ 
+
+ align:start position:0%
+f1i and they must equal to the mass
+times the acceleration in the X
+
+ align:start position:0%
+times the acceleration in the X
+ 
+
+ align:start position:0%
+times the acceleration in the X
+Direction and I'm basically done for
+
+ align:start position:0%
+Direction and I'm basically done for
+ 
+
+ align:start position:0%
+Direction and I'm basically done for
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation well so I'm doing this I'm this
+
+ align:start position:0%
+equation well so I'm doing this I'm this
+ 
+
+ align:start position:0%
+equation well so I'm doing this I'm this
+is my inertial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frame is that an inertial frame sure I'm
+
+ align:start position:0%
+frame is that an inertial frame sure I'm
+ 
+
+ align:start position:0%
+frame is that an inertial frame sure I'm
+just now I don't have now I can get I
+
+ align:start position:0%
+just now I don't have now I can get I
+ 
+
+ align:start position:0%
+just now I don't have now I can get I
+don't have to break this Force into
+
+ align:start position:0%
+don't have to break this Force into
+ 
+
+ align:start position:0%
+don't have to break this Force into
+components F1 cosine Theta in the X
+
+ align:start position:0%
+components F1 cosine Theta in the X
+ 
+
+ align:start position:0%
+components F1 cosine Theta in the X
+Direction and f11 sin Theta in the y
+
+ align:start position:0%
+Direction and f11 sin Theta in the y
+ 
+
+ align:start position:0%
+Direction and f11 sin Theta in the y
+direction and get two non get a amount
+
+ align:start position:0%
+direction and get two non get a amount
+ 
+
+ align:start position:0%
+direction and get two non get a amount
+nonzero amount for y dot nonzero amount
+
+ align:start position:0%
+nonzero amount for y dot nonzero amount
+ 
+
+ align:start position:0%
+nonzero amount for y dot nonzero amount
+for x dot I end up with three equations
+
+ align:start position:0%
+for x dot I end up with three equations
+ 
+
+ align:start position:0%
+for x dot I end up with three equations
+I have to work with just by realigning
+
+ align:start position:0%
+I have to work with just by realigning
+ 
+
+ align:start position:0%
+I have to work with just by realigning
+it I can make this problem even
+
+ align:start position:0%
+it I can make this problem even
+ 
+
+ align:start position:0%
+it I can make this problem even
+simpler so just to do it quickly that's
+
+ align:start position:0%
+simpler so just to do it quickly that's
+ 
+
+ align:start position:0%
+simpler so just to do it quickly that's
+what I
+
+ align:start position:0%
+what I
+ 
+
+ align:start position:0%
+what I
+did and finally so I've got two of the
+
+ align:start position:0%
+did and finally so I've got two of the
+ 
+
+ align:start position:0%
+did and finally so I've got two of the
+two of the three equations done and
+
+ align:start position:0%
+two of the three equations done and
+ 
+
+ align:start position:0%
+two of the three equations done and
+finally the uh sum of the torqus about G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we know the angular momentum of this
+
+ align:start position:0%
+and we know the angular momentum of this
+ 
+
+ align:start position:0%
+and we know the angular momentum of this
+would be some
+
+ align:start position:0%
+would be some
+ 
+
+ align:start position:0%
+would be some
+izz G time Omega Z would be the angular
+
+ align:start position:0%
+izz G time Omega Z would be the angular
+ 
+
+ align:start position:0%
+izz G time Omega Z would be the angular
+momentum and it's d d by DT of
+
+ align:start position:0%
+momentum and it's d d by DT of
+ 
+
+ align:start position:0%
+momentum and it's d d by DT of
+that I ZZ about G Omega Z dot which is
+
+ align:start position:0%
+that I ZZ about G Omega Z dot which is
+ 
+
+ align:start position:0%
+that I ZZ about G Omega Z dot which is
+Theta double dot right and what are the
+
+ align:start position:0%
+Theta double dot right and what are the
+ 
+
+ align:start position:0%
+Theta double dot right and what are the
+external torqus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so figure it out what's the external
+
+ align:start position:0%
+so figure it out what's the external
+ 
+
+ align:start position:0%
+so figure it out what's the external
+torque in this problem how what is its
+
+ align:start position:0%
+torque in this problem how what is its
+ 
+
+ align:start position:0%
+torque in this problem how what is its
+size and what's its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction Okay so give somebody give me
+
+ align:start position:0%
+direction Okay so give somebody give me
+ 
+
+ align:start position:0%
+direction Okay so give somebody give me
+uh what's the external
+
+ align:start position:0%
+uh what's the external
+ 
+
+ align:start position:0%
+uh what's the external
+torque with respect to where to start
+
+ align:start position:0%
+torque with respect to where to start
+ 
+
+ align:start position:0%
+torque with respect to where to start
+with so we're summing TS about G the
+
+ align:start position:0%
+with so we're summing TS about G the
+ 
+
+ align:start position:0%
+with so we're summing TS about G the
+center of
+
+ align:start position:0%
+center of
+ 
+
+ align:start position:0%
+center of
+mass R cross F right which comes out in
+
+ align:start position:0%
+mass R cross F right which comes out in
+ 
+
+ align:start position:0%
+mass R cross F right which comes out in
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction K direction right and minus or
+
+ align:start position:0%
+direction K direction right and minus or
+ 
+
+ align:start position:0%
+direction K direction right and minus or
+plus do your right hand rule and notice
+
+ align:start position:0%
+plus do your right hand rule and notice
+ 
+
+ align:start position:0%
+plus do your right hand rule and notice
+I've drawn X and Y such that positive Z
+
+ align:start position:0%
+I've drawn X and Y such that positive Z
+ 
+
+ align:start position:0%
+I've drawn X and Y such that positive Z
+is into the
+
+ align:start position:0%
+is into the
+ 
+
+ align:start position:0%
+is into the
+board pardon so this is positive I did I
+
+ align:start position:0%
+board pardon so this is positive I did I
+ 
+
+ align:start position:0%
+board pardon so this is positive I did I
+put a positive Z into the board on
+
+ align:start position:0%
+put a positive Z into the board on
+ 
+
+ align:start position:0%
+put a positive Z into the board on
+purpose so that this would just work out
+
+ align:start position:0%
+purpose so that this would just work out
+ 
+
+ align:start position:0%
+purpose so that this would just work out
+R fub1 in the K Direction and that's
+
+ align:start position:0%
+R fub1 in the K Direction and that's
+ 
+
+ align:start position:0%
+R fub1 in the K Direction and that's
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+izz Theta oops I ZZ about G Theta double
+
+ align:start position:0%
+izz Theta oops I ZZ about G Theta double
+ 
+
+ align:start position:0%
+izz Theta oops I ZZ about G Theta double
+dot and since it's all with respect to K
+
+ align:start position:0%
+dot and since it's all with respect to K
+ 
+
+ align:start position:0%
+dot and since it's all with respect to K
+you can drop the unit vectors here and
+
+ align:start position:0%
+you can drop the unit vectors here and
+ 
+
+ align:start position:0%
+you can drop the unit vectors here and
+so we have one one
+
+ align:start position:0%
+so we have one one
+ 
+
+ align:start position:0%
+so we have one one
+equation we
+
+ align:start position:0%
+equation we
+ 
+
+ align:start position:0%
+equation we
+have two
+
+ align:start position:0%
+have two
+ 
+
+ align:start position:0%
+have two
+equations and we have three
+
+ align:start position:0%
+equations and we have three
+ 
+
+ align:start position:0%
+equations and we have three
+equations and and that's all we need to
+
+ align:start position:0%
+equations and and that's all we need to
+ 
+
+ align:start position:0%
+equations and and that's all we need to
+complete this is three degrees of
+
+ align:start position:0%
+complete this is three degrees of
+ 
+
+ align:start position:0%
+complete this is three degrees of
+freedom to complete to define the motion
+
+ align:start position:0%
+freedom to complete to define the motion
+ 
+
+ align:start position:0%
+freedom to complete to define the motion
+yep do you want us to have sort of the
+
+ align:start position:0%
+yep do you want us to have sort of the
+ 
+
+ align:start position:0%
+yep do you want us to have sort of the
+trivial case you mean the my DOT equals
+
+ align:start position:0%
+trivial case you mean the my DOT equals
+ 
+
+ align:start position:0%
+trivial case you mean the my DOT equals
+z um well let's let's go let's in
+
+ align:start position:0%
+z um well let's let's go let's in
+ 
+
+ align:start position:0%
+z um well let's let's go let's in
+general you know that's what I started
+
+ align:start position:0%
+general you know that's what I started
+ 
+
+ align:start position:0%
+general you know that's what I started
+this one when I didn't align them then
+
+ align:start position:0%
+this one when I didn't align them then
+ 
+
+ align:start position:0%
+this one when I didn't align them then
+you're forced to use the three right so
+
+ align:start position:0%
+you're forced to use the three right so
+ 
+
+ align:start position:0%
+you're forced to use the three right so
+the only difference between what I did
+
+ align:start position:0%
+the only difference between what I did
+ 
+
+ align:start position:0%
+the only difference between what I did
+and this prob making the problem
+
+ align:start position:0%
+and this prob making the problem
+ 
+
+ align:start position:0%
+and this prob making the problem
+slightly more messy is if I had let
+
+ align:start position:0%
+slightly more messy is if I had let
+ 
+
+ align:start position:0%
+slightly more messy is if I had let
+Theta this angle be other than zero I
+
+ align:start position:0%
+Theta this angle be other than zero I
+ 
+
+ align:start position:0%
+Theta this angle be other than zero I
+would have had to have come up with
+
+ align:start position:0%
+would have had to have come up with
+ 
+
+ align:start position:0%
+would have had to have come up with
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+nonzero acceleration equations right so
+
+ align:start position:0%
+nonzero acceleration equations right so
+ 
+
+ align:start position:0%
+nonzero acceleration equations right so
+I'd say technically or or I'd just say I
+
+ align:start position:0%
+I'd say technically or or I'd just say I
+ 
+
+ align:start position:0%
+I'd say technically or or I'd just say I
+think it's
+
+ align:start position:0%
+think it's
+ 
+
+ align:start position:0%
+think it's
+prudent if you're ever not
+
+ align:start position:0%
+prudent if you're ever not
+ 
+
+ align:start position:0%
+prudent if you're ever not
+sure if you can look at it and by
+
+ align:start position:0%
+sure if you can look at it and by
+ 
+
+ align:start position:0%
+sure if you can look at it and by
+inspection write down my do is zero
+
+ align:start position:0%
+inspection write down my do is zero
+ 
+
+ align:start position:0%
+inspection write down my do is zero
+you've essentially just written an
+
+ align:start position:0%
+you've essentially just written an
+ 
+
+ align:start position:0%
+you've essentially just written an
+equation of motion rather than say let's
+
+ align:start position:0%
+equation of motion rather than say let's
+ 
+
+ align:start position:0%
+equation of motion rather than say let's
+let's ignore it I'd keep it in your I'd
+
+ align:start position:0%
+let's ignore it I'd keep it in your I'd
+ 
+
+ align:start position:0%
+let's ignore it I'd keep it in your I'd
+just put it on the paper my y do equals
+
+ align:start position:0%
+just put it on the paper my y do equals
+ 
+
+ align:start position:0%
+just put it on the paper my y do equals
+z and that's your first trivial equation
+
+ align:start position:0%
+z and that's your first trivial equation
+ 
+
+ align:start position:0%
+z and that's your first trivial equation
+of motion but it is an equation of
+
+ align:start position:0%
+of motion but it is an equation of
+ 
+
+ align:start position:0%
+of motion but it is an equation of
+motion because this body has a true
+
+ align:start position:0%
+motion because this body has a true
+ 
+
+ align:start position:0%
+motion because this body has a true
+degree of freedom in that
+
+ align:start position:0%
+degree of freedom in that
+ 
+
+ align:start position:0%
+degree of freedom in that
+direction that's really the point don't
+
+ align:start position:0%
+direction that's really the point don't
+ 
+
+ align:start position:0%
+direction that's really the point don't
+confuse trivial results because there's
+
+ align:start position:0%
+confuse trivial results because there's
+ 
+
+ align:start position:0%
+confuse trivial results because there's
+no external forces with
+
+ align:start position:0%
+no external forces with
+ 
+
+ align:start position:0%
+no external forces with
+constraints it's unconstrained in the X
+
+ align:start position:0%
+constraints it's unconstrained in the X
+ 
+
+ align:start position:0%
+constraints it's unconstrained in the X
+direction or in the y direction the way
+
+ align:start position:0%
+direction or in the y direction the way
+ 
+
+ align:start position:0%
+direction or in the y direction the way
+I've set it up so I think you're safer
+
+ align:start position:0%
+I've set it up so I think you're safer
+ 
+
+ align:start position:0%
+I've set it up so I think you're safer
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+just if you if it's is just to say the
+
+ align:start position:0%
+just if you if it's is just to say the
+ 
+
+ align:start position:0%
+just if you if it's is just to say the
+torqu or the forces in that direction
+
+ align:start position:0%
+torqu or the forces in that direction
+ 
+
+ align:start position:0%
+torqu or the forces in that direction
+are zero and just write it down okay
+
+ align:start position:0%
+are zero and just write it down okay
+ 
+
+ align:start position:0%
+are zero and just write it down okay
+let's look at this problem from the
+
+ align:start position:0%
+let's look at this problem from the
+ 
+
+ align:start position:0%
+let's look at this problem from the
+point of view of lrange it's also
+
+ align:start position:0%
+point of view of lrange it's also
+ 
+
+ align:start position:0%
+point of view of lrange it's also
+equally simple by L except for
+
+ align:start position:0%
+equally simple by L except for
+ 
+
+ align:start position:0%
+equally simple by L except for
+the um generalized forces actually gr is
+
+ align:start position:0%
+the um generalized forces actually gr is
+ 
+
+ align:start position:0%
+the um generalized forces actually gr is
+harder because you have to think your
+
+ align:start position:0%
+harder because you have to think your
+ 
+
+ align:start position:0%
+harder because you have to think your
+way through the generalized forces in
+
+ align:start position:0%
+way through the generalized forces in
+ 
+
+ align:start position:0%
+way through the generalized forces in
+this problem and I got myself in a
+
+ align:start position:0%
+this problem and I got myself in a
+ 
+
+ align:start position:0%
+this problem and I got myself in a
+pickle with this problem and I spent
+
+ align:start position:0%
+pickle with this problem and I spent
+ 
+
+ align:start position:0%
+pickle with this problem and I spent
+hours trying to figure out a good
+
+ align:start position:0%
+hours trying to figure out a good
+ 
+
+ align:start position:0%
+hours trying to figure out a good
+explanation of a conundrum I ran into
+
+ align:start position:0%
+explanation of a conundrum I ran into
+ 
+
+ align:start position:0%
+explanation of a conundrum I ran into
+with the generalized forces so let's
+
+ align:start position:0%
+with the generalized forces so let's
+ 
+
+ align:start position:0%
+with the generalized forces so let's
+look I'll tell you what that was in a
+
+ align:start position:0%
+look I'll tell you what that was in a
+ 
+
+ align:start position:0%
+look I'll tell you what that was in a
+second let's look at the GR
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you need
+
+ align:start position:0%
+so you need
+ 
+
+ align:start position:0%
+so you need
+T and we're pretty good at this now I
+
+ align:start position:0%
+T and we're pretty good at this now I
+ 
+
+ align:start position:0%
+T and we're pretty good at this now I
+with respect to G ZZ Theta do squ that's
+
+ align:start position:0%
+with respect to G ZZ Theta do squ that's
+ 
+
+ align:start position:0%
+with respect to G ZZ Theta do squ that's
+your rotational kinetic energy 12
+
+ align:start position:0%
+your rotational kinetic energy 12
+ 
+
+ align:start position:0%
+your rotational kinetic energy 12
+m x do 2 + Y do^ 2 your translational of
+
+ align:start position:0%
+m x do 2 + Y do^ 2 your translational of
+ 
+
+ align:start position:0%
+m x do 2 + Y do^ 2 your translational of
+translational kinetic energy associated
+
+ align:start position:0%
+translational kinetic energy associated
+ 
+
+ align:start position:0%
+translational kinetic energy associated
+with the center of mass notice this is
+
+ align:start position:0%
+with the center of mass notice this is
+ 
+
+ align:start position:0%
+with the center of mass notice this is
+with respect to the center of mass
+
+ align:start position:0%
+with respect to the center of mass
+ 
+
+ align:start position:0%
+with respect to the center of mass
+how about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V potential energy in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem any it's all zeros right no
+
+ align:start position:0%
+problem any it's all zeros right no
+ 
+
+ align:start position:0%
+problem any it's all zeros right no
+there's no springs there's no gravity in
+
+ align:start position:0%
+there's no springs there's no gravity in
+ 
+
+ align:start position:0%
+there's no springs there's no gravity in
+this in this plane operating in this
+
+ align:start position:0%
+this in this plane operating in this
+ 
+
+ align:start position:0%
+this in this plane operating in this
+plane so this is zero this this problem
+
+ align:start position:0%
+plane so this is zero this this problem
+ 
+
+ align:start position:0%
+plane so this is zero this this problem
+is going to be particularly simple so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the Theta Direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here this derivative with respect to Q
+
+ align:start position:0%
+here this derivative with respect to Q
+ 
+
+ align:start position:0%
+here this derivative with respect to Q
+dot gives us i z Theta Dot and the time
+
+ align:start position:0%
+dot gives us i z Theta Dot and the time
+ 
+
+ align:start position:0%
+dot gives us i z Theta Dot and the time
+derivative of that I ZZ Theta double
+
+ align:start position:0%
+derivative of that I ZZ Theta double
+ 
+
+ align:start position:0%
+derivative of that I ZZ Theta double
+dot t with respect to to
+
+ align:start position:0%
+dot t with respect to to
+ 
+
+ align:start position:0%
+dot t with respect to to
+Theta
+
+ align:start position:0%
+Theta
+ 
+
+ align:start position:0%
+Theta
+nothing V with respect to Theta nothing
+
+ align:start position:0%
+nothing V with respect to Theta nothing
+ 
+
+ align:start position:0%
+nothing V with respect to Theta nothing
+and on the right hand side we need to
+
+ align:start position:0%
+and on the right hand side we need to
+ 
+
+ align:start position:0%
+and on the right hand side we need to
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+Q Theta
+
+ align:start position:0%
+Q Theta
+ 
+
+ align:start position:0%
+Q Theta
+here and the other equation the
+
+ align:start position:0%
+here and the other equation the
+ 
+
+ align:start position:0%
+here and the other equation the
+we it's the X equation
+
+ align:start position:0%
+we it's the X equation
+ 
+
+ align:start position:0%
+we it's the X equation
+well actually we could have X and Y so
+
+ align:start position:0%
+well actually we could have X and Y so
+ 
+
+ align:start position:0%
+well actually we could have X and Y so
+what about the X equation derivative
+
+ align:start position:0%
+what about the X equation derivative
+ 
+
+ align:start position:0%
+what about the X equation derivative
+with respect to x dot I get an MX dot
+
+ align:start position:0%
+with respect to x dot I get an MX dot
+ 
+
+ align:start position:0%
+with respect to x dot I get an MX dot
+time der of MX double
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dot and with respect to Y the thing
+
+ align:start position:0%
+dot and with respect to Y the thing
+ 
+
+ align:start position:0%
+dot and with respect to Y the thing
+about lrange if you're going to do
+
+ align:start position:0%
+about lrange if you're going to do
+ 
+
+ align:start position:0%
+about lrange if you're going to do
+lrange just do do write down the whole
+
+ align:start position:0%
+lrange just do do write down the whole
+ 
+
+ align:start position:0%
+lrange just do do write down the whole
+expression and just crank it out because
+
+ align:start position:0%
+expression and just crank it out because
+ 
+
+ align:start position:0%
+expression and just crank it out because
+if you say oh well I know this is
+
+ align:start position:0%
+if you say oh well I know this is
+ 
+
+ align:start position:0%
+if you say oh well I know this is
+Trivial then you're actually employing
+
+ align:start position:0%
+Trivial then you're actually employing
+ 
+
+ align:start position:0%
+Trivial then you're actually employing
+some information from the direct method
+
+ align:start position:0%
+some information from the direct method
+ 
+
+ align:start position:0%
+some information from the direct method
+you're saying I know the sum of the
+
+ align:start position:0%
+you're saying I know the sum of the
+ 
+
+ align:start position:0%
+you're saying I know the sum of the
+forces in this direction is zero so when
+
+ align:start position:0%
+forces in this direction is zero so when
+ 
+
+ align:start position:0%
+forces in this direction is zero so when
+you're straight forward straight out
+
+ align:start position:0%
+you're straight forward straight out
+ 
+
+ align:start position:0%
+you're straight forward straight out
+find lrange you can do it without any
+
+ align:start position:0%
+find lrange you can do it without any
+ 
+
+ align:start position:0%
+find lrange you can do it without any
+reference at all to Newton right so in
+
+ align:start position:0%
+reference at all to Newton right so in
+ 
+
+ align:start position:0%
+reference at all to Newton right so in
+this case we just blindly clunk along
+
+ align:start position:0%
+this case we just blindly clunk along
+ 
+
+ align:start position:0%
+this case we just blindly clunk along
+and we say well what's the uh derivative
+
+ align:start position:0%
+and we say well what's the uh derivative
+ 
+
+ align:start position:0%
+and we say well what's the uh derivative
+now with respect to Y dot well I get an
+
+ align:start position:0%
+now with respect to Y dot well I get an
+ 
+
+ align:start position:0%
+now with respect to Y dot well I get an
+m y dot time derivative y dble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dot this derivative would be zero this
+
+ align:start position:0%
+dot this derivative would be zero this
+ 
+
+ align:start position:0%
+dot this derivative would be zero this
+derivative is zero and over here I get
+
+ align:start position:0%
+derivative is zero and over here I get
+ 
+
+ align:start position:0%
+derivative is zero and over here I get
+q y and now I'm left so the left hand
+
+ align:start position:0%
+q y and now I'm left so the left hand
+ 
+
+ align:start position:0%
+q y and now I'm left so the left hand
+side of lrange equations remember you
+
+ align:start position:0%
+side of lrange equations remember you
+ 
+
+ align:start position:0%
+side of lrange equations remember you
+just add these terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together and those these are going to be
+
+ align:start position:0%
+together and those these are going to be
+ 
+
+ align:start position:0%
+together and those these are going to be
+our three equations of motion that
+
+ align:start position:0%
+our three equations of motion that
+ 
+
+ align:start position:0%
+our three equations of motion that
+result and now the remaining work is to
+
+ align:start position:0%
+result and now the remaining work is to
+ 
+
+ align:start position:0%
+result and now the remaining work is to
+get these three generalized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forces
+
+ align:start position:0%
+forces
+ 
+
+ align:start position:0%
+forces
+so let's go back to our
+
+ align:start position:0%
+so let's go back to our
+ 
+
+ align:start position:0%
+so let's go back to our
+picture if we had lined it up like
+
+ align:start position:0%
+picture if we had lined it up like
+ 
+
+ align:start position:0%
+picture if we had lined it up like
+this and now we give it a general a
+
+ align:start position:0%
+this and now we give it a general a
+ 
+
+ align:start position:0%
+this and now we give it a general a
+little virtual displacement Delta Y how
+
+ align:start position:0%
+little virtual displacement Delta Y how
+ 
+
+ align:start position:0%
+little virtual displacement Delta Y how
+much work it's done none and so you read
+
+ align:start position:0%
+much work it's done none and so you read
+ 
+
+ align:start position:0%
+much work it's done none and so you read
+so you just suddenly realize that oh I
+
+ align:start position:0%
+so you just suddenly realize that oh I
+ 
+
+ align:start position:0%
+so you just suddenly realize that oh I
+went to a lot of work for nothing here
+
+ align:start position:0%
+went to a lot of work for nothing here
+ 
+
+ align:start position:0%
+went to a lot of work for nothing here
+this equation is Trivial nothing happens
+
+ align:start position:0%
+this equation is Trivial nothing happens
+ 
+
+ align:start position:0%
+this equation is Trivial nothing happens
+there and so now it's reduced to doing
+
+ align:start position:0%
+there and so now it's reduced to doing
+ 
+
+ align:start position:0%
+there and so now it's reduced to doing
+the QX and q y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just to give us some
+
+ align:start position:0%
+so just to give us some
+ 
+
+ align:start position:0%
+so just to give us some
+practice let's try to let's do Q Theta
+
+ align:start position:0%
+practice let's try to let's do Q Theta
+ 
+
+ align:start position:0%
+practice let's try to let's do Q Theta
+and QX the rigorous kinematic way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to draw the general picture
+
+ align:start position:0%
+I'm going to draw the general picture
+ 
+
+ align:start position:0%
+I'm going to draw the general picture
+here because this is where I got myself
+
+ align:start position:0%
+here because this is where I got myself
+ 
+
+ align:start position:0%
+here because this is where I got myself
+into trouble you know you're working
+
+ align:start position:0%
+into trouble you know you're working
+ 
+
+ align:start position:0%
+into trouble you know you're working
+along with a problem and then something
+
+ align:start position:0%
+along with a problem and then something
+ 
+
+ align:start position:0%
+along with a problem and then something
+doesn't quite work for you well I set
+
+ align:start position:0%
+doesn't quite work for you well I set
+ 
+
+ align:start position:0%
+doesn't quite work for you well I set
+this problem up to do generalized to
+
+ align:start position:0%
+this problem up to do generalized to
+ 
+
+ align:start position:0%
+this problem up to do generalized to
+compute the generalized forces and I set
+
+ align:start position:0%
+compute the generalized forces and I set
+ 
+
+ align:start position:0%
+compute the generalized forces and I set
+it up looking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like set it up like this so that Theta
+
+ align:start position:0%
+like set it up like this so that Theta
+ 
+
+ align:start position:0%
+like set it up like this so that Theta
+is zero
+
+ align:start position:0%
+is zero
+ 
+
+ align:start position:0%
+is zero
+it's lined up like
+
+ align:start position:0%
+it's lined up like
+ 
+
+ align:start position:0%
+it's lined up like
+that and I started thinking about then
+
+ align:start position:0%
+that and I started thinking about then
+ 
+
+ align:start position:0%
+that and I started thinking about then
+generalized my little virtual
+
+ align:start position:0%
+generalized my little virtual
+ 
+
+ align:start position:0%
+generalized my little virtual
+displacements and I got into a
+
+ align:start position:0%
+displacements and I got into a
+ 
+
+ align:start position:0%
+displacements and I got into a
+conceptual problem that I couldn't sort
+
+ align:start position:0%
+conceptual problem that I couldn't sort
+ 
+
+ align:start position:0%
+conceptual problem that I couldn't sort
+out for a while and I'll I I'll work it
+
+ align:start position:0%
+out for a while and I'll I I'll work it
+ 
+
+ align:start position:0%
+out for a while and I'll I I'll work it
+into the explanation
+
+ align:start position:0%
+into the explanation
+ 
+
+ align:start position:0%
+into the explanation
+here so I'm going to set this up more
+
+ align:start position:0%
+here so I'm going to set this up more
+ 
+
+ align:start position:0%
+here so I'm going to set this up more
+generally I have an angle Theta here and
+
+ align:start position:0%
+generally I have an angle Theta here and
+ 
+
+ align:start position:0%
+generally I have an angle Theta here and
+this is my
+
+ align:start position:0%
+this is my
+ 
+
+ align:start position:0%
+this is my
+F1 so to do this by this kinematic way I
+
+ align:start position:0%
+F1 so to do this by this kinematic way I
+ 
+
+ align:start position:0%
+F1 so to do this by this kinematic way I
+need to find a position Vector here's a
+
+ align:start position:0%
+need to find a position Vector here's a
+ 
+
+ align:start position:0%
+need to find a position Vector here's a
+point I'm going to call it D and this is
+
+ align:start position:0%
+point I'm going to call it D and this is
+ 
+
+ align:start position:0%
+point I'm going to call it D and this is
+my point
+
+ align:start position:0%
+my point
+ 
+
+ align:start position:0%
+my point
+G and here's
+
+ align:start position:0%
+G and here's
+ 
+
+ align:start position:0%
+G and here's
+o so I have a position Vector going to
+
+ align:start position:0%
+o so I have a position Vector going to
+ 
+
+ align:start position:0%
+o so I have a position Vector going to
+here it's
+
+ align:start position:0%
+here it's
+ 
+
+ align:start position:0%
+here it's
+RG and a position Vector going to here
+
+ align:start position:0%
+RG and a position Vector going to here
+ 
+
+ align:start position:0%
+RG and a position Vector going to here
+that's R
+
+ align:start position:0%
+that's R
+ 
+
+ align:start position:0%
+that's R
+of D with respect to G and a position
+
+ align:start position:0%
+of D with respect to G and a position
+ 
+
+ align:start position:0%
+of D with respect to G and a position
+Vector from here and that's r d in o and
+
+ align:start position:0%
+Vector from here and that's r d in o and
+ 
+
+ align:start position:0%
+Vector from here and that's r d in o and
+r d in O is RG in o plus r d with
+
+ align:start position:0%
+r d in O is RG in o plus r d with
+ 
+
+ align:start position:0%
+r d in O is RG in o plus r d with
+respect to G I can write that they're
+
+ align:start position:0%
+respect to G I can write that they're
+ 
+
+ align:start position:0%
+respect to G I can write that they're
+vectors okay so I'm going to need those
+
+ align:start position:0%
+vectors okay so I'm going to need those
+ 
+
+ align:start position:0%
+vectors okay so I'm going to need those
+and so what is r g and O well I have
+
+ align:start position:0%
+and so what is r g and O well I have
+ 
+
+ align:start position:0%
+and so what is r g and O well I have
+this coordinate system it's going to be
+
+ align:start position:0%
+this coordinate system it's going to be
+ 
+
+ align:start position:0%
+this coordinate system it's going to be
+some x i + y j in the inertial frame and
+
+ align:start position:0%
+some x i + y j in the inertial frame and
+ 
+
+ align:start position:0%
+some x i + y j in the inertial frame and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+R of D with respect to G I need to have
+
+ align:start position:0%
+R of D with respect to G I need to have
+ 
+
+ align:start position:0%
+R of D with respect to G I need to have
+a uh some kind of coordinate system that
+
+ align:start position:0%
+a uh some kind of coordinate system that
+ 
+
+ align:start position:0%
+a uh some kind of coordinate system that
+rotates with the
+
+ align:start position:0%
+rotates with the
+ 
+
+ align:start position:0%
+rotates with the
+body so I'll call this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y1 and this X1 that's rotating with the
+
+ align:start position:0%
+y1 and this X1 that's rotating with the
+ 
+
+ align:start position:0%
+y1 and this X1 that's rotating with the
+body so now this
+
+ align:start position:0%
+body so now this
+ 
+
+ align:start position:0%
+body so now this
+one down here is minus r in the
+
+ align:start position:0%
+one down here is minus r in the
+ 
+
+ align:start position:0%
+one down here is minus r in the
+J1 Direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the position of this point D
+
+ align:start position:0%
+so that's the position of this point D
+ 
+
+ align:start position:0%
+so that's the position of this point D
+with respect to O written as a sum of
+
+ align:start position:0%
+with respect to O written as a sum of
+ 
+
+ align:start position:0%
+with respect to O written as a sum of
+two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vectors and I'm eventually going to need
+
+ align:start position:0%
+vectors and I'm eventually going to need
+ 
+
+ align:start position:0%
+vectors and I'm eventually going to need
+to be able to express this J J1
+
+ align:start position:0%
+to be able to express this J J1
+ 
+
+ align:start position:0%
+to be able to express this J J1
+in an inertial frame so here's this
+
+ align:start position:0%
+in an inertial frame so here's this
+ 
+
+ align:start position:0%
+in an inertial frame so here's this
+little Vector
+
+ align:start position:0%
+little Vector
+ 
+
+ align:start position:0%
+little Vector
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+J1 and I need its components
+
+ align:start position:0%
+J1 and I need its components
+ 
+
+ align:start position:0%
+J1 and I need its components
+in the J and I
+
+ align:start position:0%
+in the J and I
+ 
+
+ align:start position:0%
+in the J and I
+directions so it's made up of a piece
+
+ align:start position:0%
+directions so it's made up of a piece
+ 
+
+ align:start position:0%
+directions so it's made up of a piece
+like that piece like this
+
+ align:start position:0%
+like that piece like this
+ 
+
+ align:start position:0%
+like that piece like this
+and this angle here is
+
+ align:start position:0%
+and this angle here is
+ 
+
+ align:start position:0%
+and this angle here is
+Theta so little
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A1 so I can convert I can move from this
+
+ align:start position:0%
+A1 so I can convert I can move from this
+ 
+
+ align:start position:0%
+A1 so I can convert I can move from this
+unit Vector system to that one by this
+
+ align:start position:0%
+unit Vector system to that one by this
+ 
+
+ align:start position:0%
+unit Vector system to that one by this
+transformation I'm going to need that in
+
+ align:start position:0%
+transformation I'm going to need that in
+ 
+
+ align:start position:0%
+transformation I'm going to need that in
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minute I'll in it right now so my
+
+ align:start position:0%
+minute I'll in it right now so my
+ 
+
+ align:start position:0%
+minute I'll in it right now so my
+position Vector here is the X components
+
+ align:start position:0%
+position Vector here is the X components
+ 
+
+ align:start position:0%
+position Vector here is the X components
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X can't read my plus I crossed out a
+
+ align:start position:0%
+X can't read my plus I crossed out a
+ 
+
+ align:start position:0%
+X can't read my plus I crossed out a
+plus and a minus I got to sort this out
+
+ align:start position:0%
+plus and a minus I got to sort this out
+ 
+
+ align:start position:0%
+plus and a minus I got to sort this out
+carefully here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right what do you
+
+ align:start position:0%
+right what do you
+ 
+
+ align:start position:0%
+right what do you
+think what have I done
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wrong so this is the plus ey Direction
+
+ align:start position:0%
+wrong so this is the plus ey Direction
+ 
+
+ align:start position:0%
+wrong so this is the plus ey Direction
+this piece here is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so minus s Theta in the I plus cosine
+
+ align:start position:0%
+so minus s Theta in the I plus cosine
+ 
+
+ align:start position:0%
+so minus s Theta in the I plus cosine
+Theta in the J are the components I'm
+
+ align:start position:0%
+Theta in the J are the components I'm
+ 
+
+ align:start position:0%
+Theta in the J are the components I'm
+missing a minus sign there
+
+ align:start position:0%
+missing a minus sign there
+ 
+
+ align:start position:0%
+missing a minus sign there
+okay so I want to collect the I pieces
+
+ align:start position:0%
+okay so I want to collect the I pieces
+ 
+
+ align:start position:0%
+okay so I want to collect the I pieces
+together so I have an X in the I and I
+
+ align:start position:0%
+together so I have an X in the I and I
+ 
+
+ align:start position:0%
+together so I have an X in the I and I
+have a minus r minus sin Theta so plus
+
+ align:start position:0%
+have a minus r minus sin Theta so plus
+ 
+
+ align:start position:0%
+have a minus r minus sin Theta so plus
+r sin Theta this is the I cont
+
+ align:start position:0%
+r sin Theta this is the I cont
+ 
+
+ align:start position:0%
+r sin Theta this is the I cont
+contribution and then over here I have a
+
+ align:start position:0%
+contribution and then over here I have a
+ 
+
+ align:start position:0%
+contribution and then over here I have a
+y and
+
+ align:start position:0%
+y and
+ 
+
+ align:start position:0%
+y and
+a minus r cine Theta in the J so now I
+
+ align:start position:0%
+a minus r cine Theta in the J so now I
+ 
+
+ align:start position:0%
+a minus r cine Theta in the J so now I
+have the uh my this Vector all worked
+
+ align:start position:0%
+have the uh my this Vector all worked
+ 
+
+ align:start position:0%
+have the uh my this Vector all worked
+out in my in my inertial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frame so now I can say that remember
+
+ align:start position:0%
+frame so now I can say that remember
+ 
+
+ align:start position:0%
+frame so now I can say that remember
+q j
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dot Dr this is through a virtual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deflection with for the
+
+ align:start position:0%
+deflection with for the
+ 
+
+ align:start position:0%
+deflection with for the
+jth
+
+ align:start position:0%
+jth
+ 
+
+ align:start position:0%
+jth
+contribution so in this case I'm
+
+ align:start position:0%
+contribution so in this case I'm
+ 
+
+ align:start position:0%
+contribution so in this case I'm
+interested in say the uh one in the
+
+ align:start position:0%
+interested in say the uh one in the
+ 
+
+ align:start position:0%
+interested in say the uh one in the
+which one should we do
+
+ align:start position:0%
+which one should we do
+ 
+
+ align:start position:0%
+which one should we do
+first the X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Direction so this is
+
+ align:start position:0%
+Direction so this is
+ 
+
+ align:start position:0%
+Direction so this is
+F1 in the I Dot
+
+ align:start position:0%
+F1 in the I Dot
+ 
+
+ align:start position:0%
+F1 in the I Dot
+derivative of r d with respect
+
+ align:start position:0%
+derivative of r d with respect
+ 
+
+ align:start position:0%
+derivative of r d with respect
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+X Delta
+
+ align:start position:0%
+X Delta
+ 
+
+ align:start position:0%
+X Delta
+X but now I have an I can work this out
+
+ align:start position:0%
+X but now I have an I can work this out
+ 
+
+ align:start position:0%
+X but now I have an I can work this out
+I can figure this one out directly now
+
+ align:start position:0%
+I can figure this one out directly now
+ 
+
+ align:start position:0%
+I can figure this one out directly now
+because I have an expression
+
+ align:start position:0%
+because I have an expression
+ 
+
+ align:start position:0%
+because I have an expression
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+r that
+
+ align:start position:0%
+r that
+ 
+
+ align:start position:0%
+r that
+Vector in terms of one set of unit
+
+ align:start position:0%
+Vector in terms of one set of unit
+ 
+
+ align:start position:0%
+Vector in terms of one set of unit
+vectors and I can take the derivative
+
+ align:start position:0%
+vectors and I can take the derivative
+ 
+
+ align:start position:0%
+vectors and I can take the derivative
+with respect to
+
+ align:start position:0%
+with respect to
+ 
+
+ align:start position:0%
+with respect to
+X and the only X that shows up here is
+
+ align:start position:0%
+X and the only X that shows up here is
+ 
+
+ align:start position:0%
+X and the only X that shows up here is
+this so the derivative is pretty simple
+
+ align:start position:0%
+this so the derivative is pretty simple
+ 
+
+ align:start position:0%
+this so the derivative is pretty simple
+just one so this is
+
+ align:start position:0%
+just one so this is
+ 
+
+ align:start position:0%
+just one so this is
+F1 I do I Delta X so this tells us that
+
+ align:start position:0%
+F1 I do I Delta X so this tells us that
+ 
+
+ align:start position:0%
+F1 I do I Delta X so this tells us that
+Q x
+
+ align:start position:0%
+Q x
+ 
+
+ align:start position:0%
+Q x
+equals F1 no great surprise we knew the
+
+ align:start position:0%
+equals F1 no great surprise we knew the
+ 
+
+ align:start position:0%
+equals F1 no great surprise we knew the
+answer to that from before and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+oh I made a mistake
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what didn't I I was mixing the two you
+
+ align:start position:0%
+what didn't I I was mixing the two you
+ 
+
+ align:start position:0%
+what didn't I I was mixing the two you
+know I did a simplification when I did
+
+ align:start position:0%
+know I did a simplification when I did
+ 
+
+ align:start position:0%
+know I did a simplification when I did
+the direct one is F1 in the I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Direction so F1 has
+
+ align:start position:0%
+Direction so F1 has
+ 
+
+ align:start position:0%
+Direction so F1 has
+components Vector F1 has magnitude fub1
+
+ align:start position:0%
+components Vector F1 has magnitude fub1
+ 
+
+ align:start position:0%
+components Vector F1 has magnitude fub1
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+uh cine Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+plus sin Theta J and so down here I need
+
+ align:start position:0%
+plus sin Theta J and so down here I need
+ 
+
+ align:start position:0%
+plus sin Theta J and so down here I need
+to put those in and take the dot product
+
+ align:start position:0%
+to put those in and take the dot product
+ 
+
+ align:start position:0%
+to put those in and take the dot product
+so the only dot product that will matter
+
+ align:start position:0%
+so the only dot product that will matter
+ 
+
+ align:start position:0%
+so the only dot product that will matter
+is the I
+
+ align:start position:0%
+is the I
+ 
+
+ align:start position:0%
+is the I
+component this is going to be
+
+ align:start position:0%
+component this is going to be
+ 
+
+ align:start position:0%
+component this is going to be
+fub1 cosine Theta I
+
+ align:start position:0%
+fub1 cosine Theta I
+ 
+
+ align:start position:0%
+fub1 cosine Theta I
+dot this which we know this gives us
+
+ align:start position:0%
+dot this which we know this gives us
+ 
+
+ align:start position:0%
+dot this which we know this gives us
+just an I so I'm leaving out the J piece
+
+ align:start position:0%
+just an I so I'm leaving out the J piece
+ 
+
+ align:start position:0%
+just an I so I'm leaving out the J piece
+so I end up here with F1 cosine
+
+ align:start position:0%
+so I end up here with F1 cosine
+ 
+
+ align:start position:0%
+so I end up here with F1 cosine
+Theta does that look
+
+ align:start position:0%
+Theta does that look
+ 
+
+ align:start position:0%
+Theta does that look
+right so here's your
+
+ align:start position:0%
+right so here's your
+ 
+
+ align:start position:0%
+right so here's your
+Theta here's your this is co F1 cosine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta so if for a coordinate system
+
+ align:start position:0%
+Theta so if for a coordinate system
+ 
+
+ align:start position:0%
+Theta so if for a coordinate system
+that's squared up like this it's only
+
+ align:start position:0%
+that's squared up like this it's only
+ 
+
+ align:start position:0%
+that's squared up like this it's only
+that term is in the F1 Direction and
+
+ align:start position:0%
+that term is in the F1 Direction and
+ 
+
+ align:start position:0%
+that term is in the F1 Direction and
+this this would come out correctly now
+
+ align:start position:0%
+this this would come out correctly now
+ 
+
+ align:start position:0%
+this this would come out correctly now
+and if we let if we now reorient our
+
+ align:start position:0%
+and if we let if we now reorient our
+ 
+
+ align:start position:0%
+and if we let if we now reorient our
+coordinate system so that Theta is
+
+ align:start position:0%
+coordinate system so that Theta is
+ 
+
+ align:start position:0%
+coordinate system so that Theta is
+zero then the this then this would just
+
+ align:start position:0%
+zero then the this then this would just
+ 
+
+ align:start position:0%
+zero then the this then this would just
+turn out to be F1 if you can see that
+
+ align:start position:0%
+turn out to be F1 if you can see that
+ 
+
+ align:start position:0%
+turn out to be F1 if you can see that
+this is F1 cosine Theta without going
+
+ align:start position:0%
+this is F1 cosine Theta without going
+ 
+
+ align:start position:0%
+this is F1 cosine Theta without going
+through all the work what's qy for this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system sure F1 sin
+
+ align:start position:0%
+system sure F1 sin
+ 
+
+ align:start position:0%
+system sure F1 sin
+Theta we won't go through all the work
+
+ align:start position:0%
+Theta we won't go through all the work
+ 
+
+ align:start position:0%
+Theta we won't go through all the work
+but you go through the
+
+ align:start position:0%
+but you go through the
+ 
+
+ align:start position:0%
+but you go through the
+same taking the derivatives in this case
+
+ align:start position:0%
+same taking the derivatives in this case
+ 
+
+ align:start position:0%
+same taking the derivatives in this case
+a derivative of R was back to Y and then
+
+ align:start position:0%
+a derivative of R was back to Y and then
+ 
+
+ align:start position:0%
+a derivative of R was back to Y and then
+dot it with f and you get F1 sin Theta
+
+ align:start position:0%
+dot it with f and you get F1 sin Theta
+ 
+
+ align:start position:0%
+dot it with f and you get F1 sin Theta
+in the J Direction so there's
+
+ align:start position:0%
+in the J Direction so there's
+ 
+
+ align:start position:0%
+in the J Direction so there's
+qy now the problem I ran
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+into conceptually is around this other
+
+ align:start position:0%
+into conceptually is around this other
+ 
+
+ align:start position:0%
+into conceptually is around this other
+piece so Q Theta the virtual work done
+
+ align:start position:0%
+piece so Q Theta the virtual work done
+ 
+
+ align:start position:0%
+piece so Q Theta the virtual work done
+in the Theta direction we know has to do
+
+ align:start position:0%
+in the Theta direction we know has to do
+ 
+
+ align:start position:0%
+in the Theta direction we know has to do
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+rotation and that is going to be some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F1 dot now this is the derivative of r d
+
+ align:start position:0%
+F1 dot now this is the derivative of r d
+ 
+
+ align:start position:0%
+F1 dot now this is the derivative of r d
+with respect to Theta Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta so
+
+ align:start position:0%
+Theta so
+ 
+
+ align:start position:0%
+Theta so
+Rd is here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's indeed a function of theta
+
+ align:start position:0%
+and it's indeed a function of theta
+ 
+
+ align:start position:0%
+and it's indeed a function of theta
+right and so I can take a derivative
+
+ align:start position:0%
+right and so I can take a derivative
+ 
+
+ align:start position:0%
+right and so I can take a derivative
+with respect to Theta and I'll get
+
+ align:start position:0%
+with respect to Theta and I'll get
+ 
+
+ align:start position:0%
+with respect to Theta and I'll get
+derivative of that R sin Theta term and
+
+ align:start position:0%
+derivative of that R sin Theta term and
+ 
+
+ align:start position:0%
+derivative of that R sin Theta term and
+I get a derivative of the r cosine Theta
+
+ align:start position:0%
+I get a derivative of the r cosine Theta
+ 
+
+ align:start position:0%
+I get a derivative of the r cosine Theta
+term but here's how I got myself in
+
+ align:start position:0%
+term but here's how I got myself in
+ 
+
+ align:start position:0%
+term but here's how I got myself in
+trouble it took me and this is the sort
+
+ align:start position:0%
+trouble it took me and this is the sort
+ 
+
+ align:start position:0%
+trouble it took me and this is the sort
+of thing that happens to all of us it
+
+ align:start position:0%
+of thing that happens to all of us it
+ 
+
+ align:start position:0%
+of thing that happens to all of us it
+working a problem throw in a
+
+ align:start position:0%
+working a problem throw in a
+ 
+
+ align:start position:0%
+working a problem throw in a
+simplification and then something
+
+ align:start position:0%
+simplification and then something
+ 
+
+ align:start position:0%
+simplification and then something
+doesn't work well if you had
+
+ align:start position:0%
+doesn't work well if you had
+ 
+
+ align:start position:0%
+doesn't work well if you had
+oriented
+
+ align:start position:0%
+oriented
+ 
+
+ align:start position:0%
+oriented
+the axis initially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that the
+
+ align:start position:0%
+so that the
+ 
+
+ align:start position:0%
+so that the
+force is aligned with X and
+
+ align:start position:0%
+force is aligned with X and
+ 
+
+ align:start position:0%
+force is aligned with X and
+perpendicular to Y then this Theta angle
+
+ align:start position:0%
+perpendicular to Y then this Theta angle
+ 
+
+ align:start position:0%
+perpendicular to Y then this Theta angle
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+right and you don't when you set it up
+
+ align:start position:0%
+right and you don't when you set it up
+ 
+
+ align:start position:0%
+right and you don't when you set it up
+you don't end up with if the cosine of
+
+ align:start position:0%
+you don't end up with if the cosine of
+ 
+
+ align:start position:0%
+you don't end up with if the cosine of
+zero is one and S of 0 is
+
+ align:start position:0%
+zero is one and S of 0 is
+ 
+
+ align:start position:0%
+zero is one and S of 0 is
+0o you don't end up with a cosine and
+
+ align:start position:0%
+0o you don't end up with a cosine and
+ 
+
+ align:start position:0%
+0o you don't end up with a cosine and
+signs in there to take derivatives of
+
+ align:start position:0%
+signs in there to take derivatives of
+ 
+
+ align:start position:0%
+signs in there to take derivatives of
+you just jump to the simplification you
+
+ align:start position:0%
+you just jump to the simplification you
+ 
+
+ align:start position:0%
+you just jump to the simplification you
+just find out that uh you just have
+
+ align:start position:0%
+just find out that uh you just have
+ 
+
+ align:start position:0%
+just find out that uh you just have
+R in the
+
+ align:start position:0%
+R in the
+ 
+
+ align:start position:0%
+R in the
+uh in the J there's no R in
+
+ align:start position:0%
+uh in the J there's no R in
+ 
+
+ align:start position:0%
+uh in the J there's no R in
+the there's no R sin Theta term it's
+
+ align:start position:0%
+the there's no R sin Theta term it's
+ 
+
+ align:start position:0%
+the there's no R sin Theta term it's
+disv vanished on
+
+ align:start position:0%
+disv vanished on
+ 
+
+ align:start position:0%
+disv vanished on
+you and you and now you're need to take
+
+ align:start position:0%
+you and you and now you're need to take
+ 
+
+ align:start position:0%
+you and you and now you're need to take
+that derivative to do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+step you I did kind of looked at that as
+
+ align:start position:0%
+step you I did kind of looked at that as
+ 
+
+ align:start position:0%
+step you I did kind of looked at that as
+huh what have I done wrong well you need
+
+ align:start position:0%
+huh what have I done wrong well you need
+ 
+
+ align:start position:0%
+huh what have I done wrong well you need
+to leave in order to do this method you
+
+ align:start position:0%
+to leave in order to do this method you
+ 
+
+ align:start position:0%
+to leave in order to do this method you
+need to leave it in the sort of General
+
+ align:start position:0%
+need to leave it in the sort of General
+ 
+
+ align:start position:0%
+need to leave it in the sort of General
+formulation and then that Theta be zero
+
+ align:start position:0%
+formulation and then that Theta be zero
+ 
+
+ align:start position:0%
+formulation and then that Theta be zero
+at the end if you want to do that so if
+
+ align:start position:0%
+at the end if you want to do that so if
+ 
+
+ align:start position:0%
+at the end if you want to do that so if
+I had if I if I had then finished
+
+ align:start position:0%
+I had if I if I had then finished
+ 
+
+ align:start position:0%
+I had if I if I had then finished
+it I can do this for this General
+
+ align:start position:0%
+it I can do this for this General
+ 
+
+ align:start position:0%
+it I can do this for this General
+problem and then let Theta go to zero
+
+ align:start position:0%
+problem and then let Theta go to zero
+ 
+
+ align:start position:0%
+problem and then let Theta go to zero
+and the answer will come out all right
+
+ align:start position:0%
+and the answer will come out all right
+ 
+
+ align:start position:0%
+and the answer will come out all right
+so should we do this so this is F1 do
+
+ align:start position:0%
+so should we do this so this is F1 do
+ 
+
+ align:start position:0%
+so should we do this so this is F1 do
+this so F1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dotted with the derivative of r with
+
+ align:start position:0%
+dotted with the derivative of r with
+ 
+
+ align:start position:0%
+dotted with the derivative of r with
+respect to Theta so I
+
+ align:start position:0%
+respect to Theta so I
+ 
+
+ align:start position:0%
+respect to Theta so I
+get an
+
+ align:start position:0%
+get an
+ 
+
+ align:start position:0%
+get an
+R cosine
+
+ align:start position:0%
+R cosine
+ 
+
+ align:start position:0%
+R cosine
+Theta in
+
+ align:start position:0%
+Theta in
+ 
+
+ align:start position:0%
+Theta in
+the I and the derivative of this term
+
+ align:start position:0%
+the I and the derivative of this term
+ 
+
+ align:start position:0%
+the I and the derivative of this term
+derivative of cosine Theta is minus sin
+
+ align:start position:0%
+derivative of cosine Theta is minus sin
+ 
+
+ align:start position:0%
+derivative of cosine Theta is minus sin
+Theta * a minus is a plus
+
+ align:start position:0%
+Theta * a minus is a plus
+ 
+
+ align:start position:0%
+Theta * a minus is a plus
+R sin
+
+ align:start position:0%
+R sin
+ 
+
+ align:start position:0%
+R sin
+Theta in the
+
+ align:start position:0%
+Theta in the
+ 
+
+ align:start position:0%
+Theta in the
+J Delta Theta and I do this dot
+
+ align:start position:0%
+J Delta Theta and I do this dot
+ 
+
+ align:start position:0%
+J Delta Theta and I do this dot
+product so I get the I times the I's and
+
+ align:start position:0%
+product so I get the I times the I's and
+ 
+
+ align:start position:0%
+product so I get the I times the I's and
+the J terms time the J terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it all works out nicely sin squ plus
+
+ align:start position:0%
+and it all works out nicely sin squ plus
+ 
+
+ align:start position:0%
+and it all works out nicely sin squ plus
+cosine squ you get one and you find out
+
+ align:start position:0%
+cosine squ you get one and you find out
+ 
+
+ align:start position:0%
+cosine squ you get one and you find out
+that the torque doesn't care about the
+
+ align:start position:0%
+that the torque doesn't care about the
+ 
+
+ align:start position:0%
+that the torque doesn't care about the
+angle and does that make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sense absolutely I did this on purpose
+
+ align:start position:0%
+sense absolutely I did this on purpose
+ 
+
+ align:start position:0%
+sense absolutely I did this on purpose
+to give us a little more practice using
+
+ align:start position:0%
+to give us a little more practice using
+ 
+
+ align:start position:0%
+to give us a little more practice using
+this kinematic grind it out method but
+
+ align:start position:0%
+this kinematic grind it out method but
+ 
+
+ align:start position:0%
+this kinematic grind it out method but
+but for sure the intuitive method would
+
+ align:start position:0%
+but for sure the intuitive method would
+ 
+
+ align:start position:0%
+but for sure the intuitive method would
+have yielded result a lot faster here
+
+ align:start position:0%
+have yielded result a lot faster here
+ 
+
+ align:start position:0%
+have yielded result a lot faster here
+right we would said let's have a little
+
+ align:start position:0%
+right we would said let's have a little
+ 
+
+ align:start position:0%
+right we would said let's have a little
+uh deflection Delta X what's the virtual
+
+ align:start position:0%
+uh deflection Delta X what's the virtual
+ 
+
+ align:start position:0%
+uh deflection Delta X what's the virtual
+work done well would have been F1 cosine
+
+ align:start position:0%
+work done well would have been F1 cosine
+ 
+
+ align:start position:0%
+work done well would have been F1 cosine
+Theta Delta X it would be Q X Delta
+
+ align:start position:0%
+Theta Delta X it would be Q X Delta
+ 
+
+ align:start position:0%
+Theta Delta X it would be Q X Delta
+Theta Delta X qy Delta y would be fub1
+
+ align:start position:0%
+Theta Delta X qy Delta y would be fub1
+ 
+
+ align:start position:0%
+Theta Delta X qy Delta y would be fub1
+Delta y sin Theta and we're done and the
+
+ align:start position:0%
+Delta y sin Theta and we're done and the
+ 
+
+ align:start position:0%
+Delta y sin Theta and we're done and the
+rotation
+
+ align:start position:0%
+rotation
+ 
+
+ align:start position:0%
+rotation
+one we would have looked at this and
+
+ align:start position:0%
+one we would have looked at this and
+ 
+
+ align:start position:0%
+one we would have looked at this and
+said how much in a little motion Delta
+
+ align:start position:0%
+said how much in a little motion Delta
+ 
+
+ align:start position:0%
+said how much in a little motion Delta
+Theta how much does this move it moves R
+
+ align:start position:0%
+Theta how much does this move it moves R
+ 
+
+ align:start position:0%
+Theta how much does this move it moves R
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+Theta
+
+ align:start position:0%
+Theta
+ 
+
+ align:start position:0%
+Theta
+times crossed with the F that it moves
+
+ align:start position:0%
+times crossed with the F that it moves
+ 
+
+ align:start position:0%
+times crossed with the F that it moves
+through or dot product with that
+
+ align:start position:0%
+through or dot product with that
+ 
+
+ align:start position:0%
+through or dot product with that
+distance would have given you FS1 R
+
+ align:start position:0%
+distance would have given you FS1 R
+ 
+
+ align:start position:0%
+distance would have given you FS1 R
+Delta Theta equal Q Theta Delta Theta so
+
+ align:start position:0%
+Delta Theta equal Q Theta Delta Theta so
+ 
+
+ align:start position:0%
+Delta Theta equal Q Theta Delta Theta so
+what we could have done it in you know a
+
+ align:start position:0%
+what we could have done it in you know a
+ 
+
+ align:start position:0%
+what we could have done it in you know a
+minute
+
+ align:start position:0%
+minute
+ 
+
+ align:start position:0%
+minute
+um and sometimes kind of doing it the
+
+ align:start position:0%
+um and sometimes kind of doing it the
+ 
+
+ align:start position:0%
+um and sometimes kind of doing it the
+hard rigor what it get you in trouble I
+
+ align:start position:0%
+hard rigor what it get you in trouble I
+ 
+
+ align:start position:0%
+hard rigor what it get you in trouble I
+didn't have the S the the cosine thetas
+
+ align:start position:0%
+didn't have the S the the cosine thetas
+ 
+
+ align:start position:0%
+didn't have the S the the cosine thetas
+and S Theta is working out in this and I
+
+ align:start position:0%
+and S Theta is working out in this and I
+ 
+
+ align:start position:0%
+and S Theta is working out in this and I
+couldn't take the derivative I could
+
+ align:start position:0%
+couldn't take the derivative I could
+ 
+
+ align:start position:0%
+couldn't take the derivative I could
+what did I do wrong and I finally
+
+ align:start position:0%
+what did I do wrong and I finally
+ 
+
+ align:start position:0%
+what did I do wrong and I finally
+realized it made the problem too simple
+
+ align:start position:0%
+realized it made the problem too simple
+ 
+
+ align:start position:0%
+realized it made the problem too simple
+simplified it too soon okay so I wanted
+
+ align:start position:0%
+simplified it too soon okay so I wanted
+ 
+
+ align:start position:0%
+simplified it too soon okay so I wanted
+to use this as uh a stepping stone to
+
+ align:start position:0%
+to use this as uh a stepping stone to
+ 
+
+ align:start position:0%
+to use this as uh a stepping stone to
+something I meant to
+
+ align:start position:0%
+something I meant to
+ 
+
+ align:start position:0%
+something I meant to
+cover perhaps weeks ago and there's a
+
+ align:start position:0%
+cover perhaps weeks ago and there's a
+ 
+
+ align:start position:0%
+cover perhaps weeks ago and there's a
+general little lesson that we can learn
+
+ align:start position:0%
+general little lesson that we can learn
+ 
+
+ align:start position:0%
+general little lesson that we can learn
+from this which you've probably been
+
+ align:start position:0%
+from this which you've probably been
+ 
+
+ align:start position:0%
+from this which you've probably been
+taught before but I'm going to remind
+
+ align:start position:0%
+taught before but I'm going to remind
+ 
+
+ align:start position:0%
+taught before but I'm going to remind
+you here's a rigid
+
+ align:start position:0%
+you here's a rigid
+ 
+
+ align:start position:0%
+you here's a rigid
+body got some Center of
+
+ align:start position:0%
+body got some Center of
+ 
+
+ align:start position:0%
+body got some Center of
+mass and I've got a force acting on it
+
+ align:start position:0%
+mass and I've got a force acting on it
+ 
+
+ align:start position:0%
+mass and I've got a force acting on it
+here just some arbitrary position and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+angle so that Force has a line of
+
+ align:start position:0%
+angle so that Force has a line of
+ 
+
+ align:start position:0%
+angle so that Force has a line of
+action and it's per the perpendicular to
+
+ align:start position:0%
+action and it's per the perpendicular to
+ 
+
+ align:start position:0%
+action and it's per the perpendicular to
+that line of action is a distance which
+
+ align:start position:0%
+that line of action is a distance which
+ 
+
+ align:start position:0%
+that line of action is a distance which
+I'll call call D
+
+ align:start position:0%
+I'll call call D
+ 
+
+ align:start position:0%
+I'll call call D
+here and we know that an R cross
+
+ align:start position:0%
+here and we know that an R cross
+ 
+
+ align:start position:0%
+here and we know that an R cross
+F we can this Force exerts a moment
+
+ align:start position:0%
+F we can this Force exerts a moment
+ 
+
+ align:start position:0%
+F we can this Force exerts a moment
+about G that would
+
+ align:start position:0%
+about G that would
+ 
+
+ align:start position:0%
+about G that would
+be R
+
+ align:start position:0%
+be R
+ 
+
+ align:start position:0%
+be R
+cross F where R goes from here to here
+
+ align:start position:0%
+cross F where R goes from here to here
+ 
+
+ align:start position:0%
+cross F where R goes from here to here
+but it that it's only the component
+
+ align:start position:0%
+but it that it's only the component
+ 
+
+ align:start position:0%
+but it that it's only the component
+perpendicular to it so we know that this
+
+ align:start position:0%
+perpendicular to it so we know that this
+ 
+
+ align:start position:0%
+perpendicular to it so we know that this
+is going to create a moment but I want
+
+ align:start position:0%
+is going to create a moment but I want
+ 
+
+ align:start position:0%
+is going to create a moment but I want
+to draw pictures yet here for a moment
+
+ align:start position:0%
+to draw pictures yet here for a moment
+ 
+
+ align:start position:0%
+to draw pictures yet here for a moment
+this diagram is the same as if I could
+
+ align:start position:0%
+this diagram is the same as if I could
+ 
+
+ align:start position:0%
+this diagram is the same as if I could
+draw the same peanut
+
+ align:start position:0%
+draw the same peanut
+ 
+
+ align:start position:0%
+draw the same peanut
+here it's the same as the
+
+ align:start position:0%
+here it's the same as the
+ 
+
+ align:start position:0%
+here it's the same as the
+following a force here that's
+
+ align:start position:0%
+following a force here that's
+ 
+
+ align:start position:0%
+following a force here that's
+F and another Force at G that's F equal
+
+ align:start position:0%
+F and another Force at G that's F equal
+ 
+
+ align:start position:0%
+F and another Force at G that's F equal
+and opposite so it's like adding zero to
+
+ align:start position:0%
+and opposite so it's like adding zero to
+ 
+
+ align:start position:0%
+and opposite so it's like adding zero to
+the problem so I can do that with with
+
+ align:start position:0%
+the problem so I can do that with with
+ 
+
+ align:start position:0%
+the problem so I can do that with with
+impunity and I still have my Force F
+
+ align:start position:0%
+impunity and I still have my Force F
+ 
+
+ align:start position:0%
+impunity and I still have my Force F
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+here so this problem is equal to that
+
+ align:start position:0%
+here so this problem is equal to that
+ 
+
+ align:start position:0%
+here so this problem is equal to that
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so but
+
+ align:start position:0%
+so but
+ 
+
+ align:start position:0%
+so but
+now this force and this force equal an
+
+ align:start position:0%
+now this force and this force equal an
+ 
+
+ align:start position:0%
+now this force and this force equal an
+opposite cancel one another but create
+
+ align:start position:0%
+opposite cancel one another but create
+ 
+
+ align:start position:0%
+opposite cancel one another but create
+what's called a couple a
+
+ align:start position:0%
+what's called a couple a
+ 
+
+ align:start position:0%
+what's called a couple a
+moment that we can compute about my
+
+ align:start position:0%
+moment that we can compute about my
+ 
+
+ align:start position:0%
+moment that we can compute about my
+point G here so these two forces create
+
+ align:start position:0%
+point G here so these two forces create
+ 
+
+ align:start position:0%
+point G here so these two forces create
+just a pure
+
+ align:start position:0%
+just a pure
+ 
+
+ align:start position:0%
+just a pure
+torque
+
+ align:start position:0%
+torque
+ 
+
+ align:start position:0%
+torque
+leaving this as a force they're equal
+
+ align:start position:0%
+leaving this as a force they're equal
+ 
+
+ align:start position:0%
+leaving this as a force they're equal
+opposite so no net force but they create
+
+ align:start position:0%
+opposite so no net force but they create
+ 
+
+ align:start position:0%
+opposite so no net force but they create
+a torque in this direction and there's a
+
+ align:start position:0%
+a torque in this direction and there's a
+ 
+
+ align:start position:0%
+a torque in this direction and there's a
+remaining force on the center of mass so
+
+ align:start position:0%
+remaining force on the center of mass so
+ 
+
+ align:start position:0%
+remaining force on the center of mass so
+this whole
+
+ align:start position:0%
+this whole
+ 
+
+ align:start position:0%
+this whole
+thing is also then equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to the equivalent of a torque around the
+
+ align:start position:0%
+to the equivalent of a torque around the
+ 
+
+ align:start position:0%
+to the equivalent of a torque around the
+center of
+
+ align:start position:0%
+center of
+ 
+
+ align:start position:0%
+center of
+mass and a force applied at the center
+
+ align:start position:0%
+mass and a force applied at the center
+ 
+
+ align:start position:0%
+mass and a force applied at the center
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+mass and in this case the torque would
+
+ align:start position:0%
+mass and in this case the torque would
+ 
+
+ align:start position:0%
+mass and in this case the torque would
+be uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DF this problem is is this problem is
+
+ align:start position:0%
+DF this problem is is this problem is
+ 
+
+ align:start position:0%
+DF this problem is is this problem is
+easier to do if you're trying to compute
+
+ align:start position:0%
+easier to do if you're trying to compute
+ 
+
+ align:start position:0%
+easier to do if you're trying to compute
+generalized forces than the one we
+
+ align:start position:0%
+generalized forces than the one we
+ 
+
+ align:start position:0%
+generalized forces than the one we
+started
+
+ align:start position:0%
+started
+ 
+
+ align:start position:0%
+started
+with because now the position Vector
+
+ align:start position:0%
+with because now the position Vector
+ 
+
+ align:start position:0%
+with because now the position Vector
+that we need goes only to the center of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mass okay so and the general rule for
+
+ align:start position:0%
+mass okay so and the general rule for
+ 
+
+ align:start position:0%
+mass okay so and the general rule for
+this you have a body you have several
+
+ align:start position:0%
+this you have a body you have several
+ 
+
+ align:start position:0%
+this you have a body you have several
+forces fub1 FS2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F3 that's equal
+
+ align:start position:0%
+F3 that's equal
+ 
+
+ align:start position:0%
+F3 that's equal
+to the body with
+
+ align:start position:0%
+to the body with
+ 
+
+ align:start position:0%
+to the body with
+G with a
+
+ align:start position:0%
+G with a
+ 
+
+ align:start position:0%
+G with a
+total F total on it and a moment a
+
+ align:start position:0%
+total F total on it and a moment a
+ 
+
+ align:start position:0%
+total F total on it and a moment a
+torque total and F total it's a vector
+
+ align:start position:0%
+torque total and F total it's a vector
+ 
+
+ align:start position:0%
+torque total and F total it's a vector
+is a summation of the FI
+
+ align:start position:0%
+is a summation of the FI
+ 
+
+ align:start position:0%
+is a summation of the FI
+and T the torque total is the summation
+
+ align:start position:0%
+and T the torque total is the summation
+ 
+
+ align:start position:0%
+and T the torque total is the summation
+of each of these guys here's G this has
+
+ align:start position:0%
+of each of these guys here's G this has
+ 
+
+ align:start position:0%
+of each of these guys here's G this has
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+r one here's an
+
+ align:start position:0%
+r one here's an
+ 
+
+ align:start position:0%
+r one here's an
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+two here's an
+
+ align:start position:0%
+two here's an
+ 
+
+ align:start position:0%
+two here's an
+r i to the I
+
+ align:start position:0%
+r i to the I
+ 
+
+ align:start position:0%
+r i to the I
+force so this is a summation of the r i
+
+ align:start position:0%
+force so this is a summation of the r i
+ 
+
+ align:start position:0%
+force so this is a summation of the r i
+cross f i so if you sum all the forces
+
+ align:start position:0%
+cross f i so if you sum all the forces
+ 
+
+ align:start position:0%
+cross f i so if you sum all the forces
+in Compu the equivalent torque about the
+
+ align:start position:0%
+in Compu the equivalent torque about the
+ 
+
+ align:start position:0%
+in Compu the equivalent torque about the
+center of mass sum all the forces and
+
+ align:start position:0%
+center of mass sum all the forces and
+ 
+
+ align:start position:0%
+center of mass sum all the forces and
+apply it at the center of mass then this
+
+ align:start position:0%
+apply it at the center of mass then this
+ 
+
+ align:start position:0%
+apply it at the center of mass then this
+problem is equal to that
+
+ align:start position:0%
+problem is equal to that
+ 
+
+ align:start position:0%
+problem is equal to that
+problem so they this can come in handy
+
+ align:start position:0%
+problem so they this can come in handy
+ 
+
+ align:start position:0%
+problem so they this can come in handy
+when you're trying to simplify
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems and for this particular problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+draw our hockey
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pack going to put my
+
+ align:start position:0%
+pack going to put my
+ 
+
+ align:start position:0%
+pack going to put my
+force in the simplest Direction here but
+
+ align:start position:0%
+force in the simplest Direction here but
+ 
+
+ align:start position:0%
+force in the simplest Direction here but
+there's my Force this problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal doing the same thing here it's
+
+ align:start position:0%
+is equal doing the same thing here it's
+ 
+
+ align:start position:0%
+is equal doing the same thing here it's
+the same thing as if I had Drew forces
+
+ align:start position:0%
+the same thing as if I had Drew forces
+ 
+
+ align:start position:0%
+the same thing as if I had Drew forces
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and that gives me an equivalent
+
+ align:start position:0%
+this and that gives me an equivalent
+ 
+
+ align:start position:0%
+this and that gives me an equivalent
+problem where I have this couple here
+
+ align:start position:0%
+problem where I have this couple here
+ 
+
+ align:start position:0%
+problem where I have this couple here
+produces a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+torque and there's a net force acting
+
+ align:start position:0%
+torque and there's a net force acting
+ 
+
+ align:start position:0%
+torque and there's a net force acting
+under the center of mass so this problem
+
+ align:start position:0%
+under the center of mass so this problem
+ 
+
+ align:start position:0%
+under the center of mass so this problem
+is equal
+
+ align:start position:0%
+is equal
+ 
+
+ align:start position:0%
+is equal
+to this problem now torque and a force
+
+ align:start position:0%
+to this problem now torque and a force
+ 
+
+ align:start position:0%
+to this problem now torque and a force
+both acting at the center of mass and
+
+ align:start position:0%
+both acting at the center of mass and
+ 
+
+ align:start position:0%
+both acting at the center of mass and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+torque is R F1 in the K and the force is
+
+ align:start position:0%
+torque is R F1 in the K and the force is
+ 
+
+ align:start position:0%
+torque is R F1 in the K and the force is
+just F1 in the
+
+ align:start position:0%
+just F1 in the
+ 
+
+ align:start position:0%
+just F1 in the
+uh positive I
+
+ align:start position:0%
+uh positive I
+ 
+
+ align:start position:0%
+uh positive I
+Direction okay and R but now what is is
+
+ align:start position:0%
+Direction okay and R but now what is is
+ 
+
+ align:start position:0%
+Direction okay and R but now what is is
+the little r Vector if we're going to do
+
+ align:start position:0%
+the little r Vector if we're going to do
+ 
+
+ align:start position:0%
+the little r Vector if we're going to do
+this the kinematic
+
+ align:start position:0%
+this the kinematic
+ 
+
+ align:start position:0%
+this the kinematic
+way from here to G this is R1 I'll call
+
+ align:start position:0%
+way from here to G this is R1 I'll call
+ 
+
+ align:start position:0%
+way from here to G this is R1 I'll call
+it and that's it I only now I have
+
+ align:start position:0%
+it and that's it I only now I have
+ 
+
+ align:start position:0%
+it and that's it I only now I have
+everything acting
+
+ align:start position:0%
+everything acting
+ 
+
+ align:start position:0%
+everything acting
+here and
+
+ align:start position:0%
+here and
+ 
+
+ align:start position:0%
+here and
+QX Delta X is
+
+ align:start position:0%
+QX Delta X is
+ 
+
+ align:start position:0%
+QX Delta X is
+F1
+
+ align:start position:0%
+F1
+ 
+
+ align:start position:0%
+F1
+dot derivative of r with respect to X
+
+ align:start position:0%
+dot derivative of r with respect to X
+ 
+
+ align:start position:0%
+dot derivative of r with respect to X
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+X but R is what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r it's x i + y j and derivative of R1
+
+ align:start position:0%
+r it's x i + y j and derivative of R1
+ 
+
+ align:start position:0%
+r it's x i + y j and derivative of R1
+with respect to X is just one and
+
+ align:start position:0%
+with respect to X is just one and
+ 
+
+ align:start position:0%
+with respect to X is just one and
+derivative of R in the I and derivative
+
+ align:start position:0%
+derivative of R in the I and derivative
+ 
+
+ align:start position:0%
+derivative of R in the I and derivative
+of r with respect to Y is Just J so this
+
+ align:start position:0%
+of r with respect to Y is Just J so this
+ 
+
+ align:start position:0%
+of r with respect to Y is Just J so this
+becomes a trivi
+
+ align:start position:0%
+becomes a trivi
+ 
+
+ align:start position:0%
+becomes a trivi
+calculation fub1 I do I I get QX
+
+ align:start position:0%
+calculation fub1 I do I I get QX
+ 
+
+ align:start position:0%
+calculation fub1 I do I I get QX
+equals F1 Delta X and I get Qi
+
+ align:start position:0%
+equals F1 Delta X and I get Qi
+ 
+
+ align:start position:0%
+equals F1 Delta X and I get Qi
+qy is fub1 which is in the i direction.
+
+ align:start position:0%
+qy is fub1 which is in the i direction.
+ 
+
+ align:start position:0%
+qy is fub1 which is in the i direction.
+j is
+
+ align:start position:0%
+j is
+ 
+
+ align:start position:0%
+j is
+zero and I get Q Theta ah Q Theta now do
+
+ align:start position:0%
+zero and I get Q Theta ah Q Theta now do
+ 
+
+ align:start position:0%
+zero and I get Q Theta ah Q Theta now do
+I use this
+
+ align:start position:0%
+I use this
+ 
+
+ align:start position:0%
+I use this
+expression so I'm not dealing with
+
+ align:start position:0%
+expression so I'm not dealing with
+ 
+
+ align:start position:0%
+expression so I'm not dealing with
+little changes in distance anymore when
+
+ align:start position:0%
+little changes in distance anymore when
+ 
+
+ align:start position:0%
+little changes in distance anymore when
+you can put rotation when you put
+
+ align:start position:0%
+you can put rotation when you put
+ 
+
+ align:start position:0%
+you can put rotation when you put
+moments about centers of mass it's just
+
+ align:start position:0%
+moments about centers of mass it's just
+ 
+
+ align:start position:0%
+moments about centers of mass it's just
+easier this one you call it intuitive
+
+ align:start position:0%
+easier this one you call it intuitive
+ 
+
+ align:start position:0%
+easier this one you call it intuitive
+but this is just going to be uh the sum
+
+ align:start position:0%
+but this is just going to be uh the sum
+ 
+
+ align:start position:0%
+but this is just going to be uh the sum
+Delta Theta is equal to
+
+ align:start position:0%
+Delta Theta is equal to
+ 
+
+ align:start position:0%
+Delta Theta is equal to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+torque total torqu acting at the center
+
+ align:start position:0%
+torque total torqu acting at the center
+ 
+
+ align:start position:0%
+torque total torqu acting at the center
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Mass
+
+ align:start position:0%
+Mass
+ 
+
+ align:start position:0%
+Mass
+DOT Delta Theta and in this case the
+
+ align:start position:0%
+DOT Delta Theta and in this case the
+ 
+
+ align:start position:0%
+DOT Delta Theta and in this case the
+torque is in the K Direction Delta Theta
+
+ align:start position:0%
+torque is in the K Direction Delta Theta
+ 
+
+ align:start position:0%
+torque is in the K Direction Delta Theta
+is the K Direction and this
+
+ align:start position:0%
+is the K Direction and this
+ 
+
+ align:start position:0%
+is the K Direction and this
+is R
+
+ align:start position:0%
+is R
+ 
+
+ align:start position:0%
+is R
+F1 K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do K Delta
+
+ align:start position:0%
+do K Delta
+ 
+
+ align:start position:0%
+do K Delta
+Theta which just gives us r fub1 = q
+
+ align:start position:0%
+Theta which just gives us r fub1 = q
+ 
+
+ align:start position:0%
+Theta which just gives us r fub1 = q
+Theta so the torque equations you can
+
+ align:start position:0%
+Theta so the torque equations you can
+ 
+
+ align:start position:0%
+Theta so the torque equations you can
+write them straight out you don't have
+
+ align:start position:0%
+write them straight out you don't have
+ 
+
+ align:start position:0%
+write them straight out you don't have
+to take derivatives do anything to do
+
+ align:start position:0%
+to take derivatives do anything to do
+ 
+
+ align:start position:0%
+to take derivatives do anything to do
+with change in position it's just a
+
+ align:start position:0%
+with change in position it's just a
+ 
+
+ align:start position:0%
+with change in position it's just a
+little rotation Delta f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it simplifies this problem and
+
+ align:start position:0%
+so it simplifies this problem and
+ 
+
+ align:start position:0%
+so it simplifies this problem and
+actually totally avoids the conundrum I
+
+ align:start position:0%
+actually totally avoids the conundrum I
+ 
+
+ align:start position:0%
+actually totally avoids the conundrum I
+got
+
+ align:start position:0%
+got
+ 
+
+ align:start position:0%
+got
+into I work everything about the center
+
+ align:start position:0%
+into I work everything about the center
+ 
+
+ align:start position:0%
+into I work everything about the center
+of mass of that rigid body the r gets
+
+ align:start position:0%
+of mass of that rigid body the r gets
+ 
+
+ align:start position:0%
+of mass of that rigid body the r gets
+easier the derivatives get easier and
+
+ align:start position:0%
+easier the derivatives get easier and
+ 
+
+ align:start position:0%
+easier the derivatives get easier and
+the torque becomes obvious how it
+
+ align:start position:0%
+the torque becomes obvious how it
+ 
+
+ align:start position:0%
+the torque becomes obvious how it
+applies okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let talk about I have
+
+ align:start position:0%
+let talk about I have
+ 
+
+ align:start position:0%
+let talk about I have
+a pendulum kind of a weird shape
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the pendulum has the following
+
+ align:start position:0%
+but the pendulum has the following
+ 
+
+ align:start position:0%
+but the pendulum has the following
+property so that weird shape that may be
+
+ align:start position:0%
+property so that weird shape that may be
+ 
+
+ align:start position:0%
+property so that weird shape that may be
+this it's got one plane of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetry like this does and I'm going to
+
+ align:start position:0%
+symmetry like this does and I'm going to
+ 
+
+ align:start position:0%
+symmetry like this does and I'm going to
+put what I do with my
+
+ align:start position:0%
+put what I do with my
+ 
+
+ align:start position:0%
+put what I do with my
+axle I'm going to put the axis of
+
+ align:start position:0%
+axle I'm going to put the axis of
+ 
+
+ align:start position:0%
+axle I'm going to put the axis of
+rotation
+
+ align:start position:0%
+rotation
+ 
+
+ align:start position:0%
+rotation
+perpendicular to that plane of symmetry
+
+ align:start position:0%
+perpendicular to that plane of symmetry
+ 
+
+ align:start position:0%
+perpendicular to that plane of symmetry
+somewhere not at G
+
+ align:start position:0%
+somewhere not at G
+ 
+
+ align:start position:0%
+somewhere not at G
+not at the center of mass so just what
+
+ align:start position:0%
+not at the center of mass so just what
+ 
+
+ align:start position:0%
+not at the center of mass so just what
+I've done here I can make so any object
+
+ align:start position:0%
+I've done here I can make so any object
+ 
+
+ align:start position:0%
+I've done here I can make so any object
+that has a plane of
+
+ align:start position:0%
+that has a plane of
+ 
+
+ align:start position:0%
+that has a plane of
+symmetry if
+
+ align:start position:0%
+symmetry if
+ 
+
+ align:start position:0%
+symmetry if
+I have it rotate about an axis that's
+
+ align:start position:0%
+I have it rotate about an axis that's
+ 
+
+ align:start position:0%
+I have it rotate about an axis that's
+perpendicular to that plane of symmetry
+
+ align:start position:0%
+perpendicular to that plane of symmetry
+ 
+
+ align:start position:0%
+perpendicular to that plane of symmetry
+it becomes a simple
+
+ align:start position:0%
+it becomes a simple
+ 
+
+ align:start position:0%
+it becomes a simple
+pendulum and you can write down would by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inspection what the and how so what the
+
+ align:start position:0%
+inspection what the and how so what the
+ 
+
+ align:start position:0%
+inspection what the and how so what the
+equation of motion is so how many
+
+ align:start position:0%
+equation of motion is so how many
+ 
+
+ align:start position:0%
+equation of motion is so how many
+degrees of freedom does this system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have so is it first of all then is it
+
+ align:start position:0%
+have so is it first of all then is it
+ 
+
+ align:start position:0%
+have so is it first of all then is it
+pler motion okay so it has at
+
+ align:start position:0%
+pler motion okay so it has at
+ 
+
+ align:start position:0%
+pler motion okay so it has at
+most three and how many and it has a pin
+
+ align:start position:0%
+most three and how many and it has a pin
+ 
+
+ align:start position:0%
+most three and how many and it has a pin
+through it that doesn't allow it to move
+
+ align:start position:0%
+through it that doesn't allow it to move
+ 
+
+ align:start position:0%
+through it that doesn't allow it to move
+in X or Y how many constraints is that
+
+ align:start position:0%
+in X or Y how many constraints is that
+ 
+
+ align:start position:0%
+in X or Y how many constraints is that
+two so how many how many you got left
+
+ align:start position:0%
+two so how many how many you got left
+ 
+
+ align:start position:0%
+two so how many how many you got left
+one this is a single degree Freedom
+
+ align:start position:0%
+one this is a single degree Freedom
+ 
+
+ align:start position:0%
+one this is a single degree Freedom
+problem and I've chosen to have it move
+
+ align:start position:0%
+problem and I've chosen to have it move
+ 
+
+ align:start position:0%
+problem and I've chosen to have it move
+about an axis that is is this axis a
+
+ align:start position:0%
+about an axis that is is this axis a
+ 
+
+ align:start position:0%
+about an axis that is is this axis a
+principal axis of this body absolutely
+
+ align:start position:0%
+principal axis of this body absolutely
+ 
+
+ align:start position:0%
+principal axis of this body absolutely
+okay and so if I asked you what's the
+
+ align:start position:0%
+okay and so if I asked you what's the
+ 
+
+ align:start position:0%
+okay and so if I asked you what's the
+mass moment of enertia of this if I gave
+
+ align:start position:0%
+mass moment of enertia of this if I gave
+ 
+
+ align:start position:0%
+mass moment of enertia of this if I gave
+you I ZZ about G for this thing and this
+
+ align:start position:0%
+you I ZZ about G for this thing and this
+ 
+
+ align:start position:0%
+you I ZZ about G for this thing and this
+distance what would you tell me the mass
+
+ align:start position:0%
+distance what would you tell me the mass
+ 
+
+ align:start position:0%
+distance what would you tell me the mass
+moment of inertia about the pivot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is I've give give you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this what's the rest of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it not at G got some distance here which
+
+ align:start position:0%
+it not at G got some distance here which
+ 
+
+ align:start position:0%
+it not at G got some distance here which
+you're
+
+ align:start position:0%
+you're
+ 
+
+ align:start position:0%
+you're
+given L we'll call
+
+ align:start position:0%
+given L we'll call
+ 
+
+ align:start position:0%
+given L we'll call
+it okay so parallel axis remember ml s
+
+ align:start position:0%
+it okay so parallel axis remember ml s
+ 
+
+ align:start position:0%
+it okay so parallel axis remember ml s
+so we know that that's true so what's
+
+ align:start position:0%
+so we know that that's true so what's
+ 
+
+ align:start position:0%
+so we know that that's true so what's
+the and the g is over here someplace and
+
+ align:start position:0%
+the and the g is over here someplace and
+ 
+
+ align:start position:0%
+the and the g is over here someplace and
+this is this distance f
+
+ align:start position:0%
+this is this distance f
+ 
+
+ align:start position:0%
+this is this distance f
+and what's the equation of motion for
+
+ align:start position:0%
+and what's the equation of motion for
+ 
+
+ align:start position:0%
+and what's the equation of motion for
+this and it's it's gravity acts no
+
+ align:start position:0%
+this and it's it's gravity acts no
+ 
+
+ align:start position:0%
+this and it's it's gravity acts no
+damping for now what's the equation of
+
+ align:start position:0%
+damping for now what's the equation of
+ 
+
+ align:start position:0%
+damping for now what's the equation of
+motion right off the top of your head
+
+ align:start position:0%
+motion right off the top of your head
+ 
+
+ align:start position:0%
+motion right off the top of your head
+you've done enough of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these I'll give you one minute to think
+
+ align:start position:0%
+these I'll give you one minute to think
+ 
+
+ align:start position:0%
+these I'll give you one minute to think
+about it figure out the equation of
+
+ align:start position:0%
+about it figure out the equation of
+ 
+
+ align:start position:0%
+about it figure out the equation of
+motion for this problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I highly recommend you don't do L
+
+ align:start position:0%
+I highly recommend you don't do L
+ 
+
+ align:start position:0%
+I highly recommend you don't do L
+gr
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay somebody give me their equation or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion so what method do you use would
+
+ align:start position:0%
+motion so what method do you use would
+ 
+
+ align:start position:0%
+motion so what method do you use would
+you choose to use simplest one you could
+
+ align:start position:0%
+you choose to use simplest one you could
+ 
+
+ align:start position:0%
+you choose to use simplest one you could
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+of direct about what
+
+ align:start position:0%
+of direct about what
+ 
+
+ align:start position:0%
+of direct about what
+point about a and what do you say what's
+
+ align:start position:0%
+point about a and what do you say what's
+ 
+
+ align:start position:0%
+point about a and what do you say what's
+the what what equation do you apply
+
+ align:start position:0%
+the what what equation do you apply
+ 
+
+ align:start position:0%
+the what what equation do you apply
+General
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation yeah that'd be the that would
+
+ align:start position:0%
+equation yeah that'd be the that would
+ 
+
+ align:start position:0%
+equation yeah that'd be the that would
+be part of the answer in the equation
+
+ align:start position:0%
+be part of the answer in the equation
+ 
+
+ align:start position:0%
+be part of the answer in the equation
+remember I wrote the list of one two
+
+ align:start position:0%
+remember I wrote the list of one two
+ 
+
+ align:start position:0%
+remember I wrote the list of one two
+three over there which one do you use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just use second just the second one
+
+ align:start position:0%
+just use second just the second one
+ 
+
+ align:start position:0%
+just use second just the second one
+right and the nuisance terms go away
+
+ align:start position:0%
+right and the nuisance terms go away
+ 
+
+ align:start position:0%
+right and the nuisance terms go away
+point a is not moving so sum of the
+
+ align:start position:0%
+point a is not moving so sum of the
+ 
+
+ align:start position:0%
+point a is not moving so sum of the
+torqu is equal to dhdt and it's h with
+
+ align:start position:0%
+torqu is equal to dhdt and it's h with
+ 
+
+ align:start position:0%
+torqu is equal to dhdt and it's h with
+respect to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right d by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT I ZZ with respect to a Theta double
+
+ align:start position:0%
+DT I ZZ with respect to a Theta double
+ 
+
+ align:start position:0%
+DT I ZZ with respect to a Theta double
+dot k equals the sum of the external
+
+ align:start position:0%
+dot k equals the sum of the external
+ 
+
+ align:start position:0%
+dot k equals the sum of the external
+torqus and the rest of the problem is
+
+ align:start position:0%
+torqus and the rest of the problem is
+ 
+
+ align:start position:0%
+torqus and the rest of the problem is
+finding the external torqus what's the
+
+ align:start position:0%
+finding the external torqus what's the
+ 
+
+ align:start position:0%
+finding the external torqus what's the
+free body diagram look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like so here's the object
+
+ align:start position:0%
+like so here's the object
+ 
+
+ align:start position:0%
+like so here's the object
+possibly
+
+ align:start position:0%
+possibly
+ 
+
+ align:start position:0%
+possibly
+a an
+
+ align:start position:0%
+a an
+ 
+
+ align:start position:0%
+a an
+RX and an r
+
+ align:start position:0%
+RX and an r
+ 
+
+ align:start position:0%
+RX and an r
+y and an m
+
+ align:start position:0%
+y and an m
+ 
+
+ align:start position:0%
+y and an m
+g those are your Poss those that's your
+
+ align:start position:0%
+g those are your Poss those that's your
+ 
+
+ align:start position:0%
+g those are your Poss those that's your
+free body diagram right so here's the mg
+
+ align:start position:0%
+free body diagram right so here's the mg
+ 
+
+ align:start position:0%
+free body diagram right so here's the mg
+down what's the torque that that mass
+
+ align:start position:0%
+down what's the torque that that mass
+ 
+
+ align:start position:0%
+down what's the torque that that mass
+that that gravitational force puts on
+
+ align:start position:0%
+that that gravitational force puts on
+ 
+
+ align:start position:0%
+that that gravitational force puts on
+this OB object with respect to point a
+
+ align:start position:0%
+this OB object with respect to point a
+ 
+
+ align:start position:0%
+this OB object with respect to point a
+R cross F
+
+ align:start position:0%
+R cross F
+ 
+
+ align:start position:0%
+R cross F
+right R cross F into the board is that
+
+ align:start position:0%
+right R cross F into the board is that
+ 
+
+ align:start position:0%
+right R cross F into the board is that
+positive or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative and what's the length of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R well from here to here is I guess oh
+
+ align:start position:0%
+R well from here to here is I guess oh
+ 
+
+ align:start position:0%
+R well from here to here is I guess oh
+that's is L so the length of this side
+
+ align:start position:0%
+that's is L so the length of this side
+ 
+
+ align:start position:0%
+that's is L so the length of this side
+of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+triangle L sin
+
+ align:start position:0%
+triangle L sin
+ 
+
+ align:start position:0%
+triangle L sin
+Theta L sin Theta cross
+
+ align:start position:0%
+Theta L sin Theta cross
+ 
+
+ align:start position:0%
+Theta L sin Theta cross
+mg and it is positive or negative what
+
+ align:start position:0%
+mg and it is positive or negative what
+ 
+
+ align:start position:0%
+mg and it is positive or negative what
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+decide looks like
+
+ align:start position:0%
+decide looks like
+ 
+
+ align:start position:0%
+decide looks like
+it's this is positive Theta XY system
+
+ align:start position:0%
+it's this is positive Theta XY system
+ 
+
+ align:start position:0%
+it's this is positive Theta XY system
+that gets
+
+ align:start position:0%
+that gets
+ 
+
+ align:start position:0%
+that gets
+negative minus mg L sin Theta we're done
+
+ align:start position:0%
+negative minus mg L sin Theta we're done
+ 
+
+ align:start position:0%
+negative minus mg L sin Theta we're done
+so generically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is also in the K Direction so
+
+ align:start position:0%
+and this is also in the K Direction so
+ 
+
+ align:start position:0%
+and this is also in the K Direction so
+we can drop the k's now we have our
+
+ align:start position:0%
+we can drop the k's now we have our
+ 
+
+ align:start position:0%
+we can drop the k's now we have our
+equation of motion i z Theta dou dot
+
+ align:start position:0%
+equation of motion i z Theta dou dot
+ 
+
+ align:start position:0%
+equation of motion i z Theta dou dot
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+mg L sin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta
+
+ align:start position:0%
+Theta
+ 
+
+ align:start position:0%
+Theta
+any single degree of Freedom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pendulum made out of a body
+
+ align:start position:0%
+pendulum made out of a body
+ 
+
+ align:start position:0%
+pendulum made out of a body
+rigid body and rotating about an axis
+
+ align:start position:0%
+rigid body and rotating about an axis
+ 
+
+ align:start position:0%
+rigid body and rotating about an axis
+that is a principal
+
+ align:start position:0%
+that is a principal
+ 
+
+ align:start position:0%
+that is a principal
+axis has that equation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion any of
+
+ align:start position:0%
+motion any of
+ 
+
+ align:start position:0%
+motion any of
+them no matter what the shape if you can
+
+ align:start position:0%
+them no matter what the shape if you can
+ 
+
+ align:start position:0%
+them no matter what the shape if you can
+rotate it about a principal axis and not
+
+ align:start position:0%
+rotate it about a principal axis and not
+ 
+
+ align:start position:0%
+rotate it about a principal axis and not
+through G because if if you if you put
+
+ align:start position:0%
+through G because if if you if you put
+ 
+
+ align:start position:0%
+through G because if if you if you put
+what's the natural frequency if you run
+
+ align:start position:0%
+what's the natural frequency if you run
+ 
+
+ align:start position:0%
+what's the natural frequency if you run
+the axis through
+
+ align:start position:0%
+the axis through
+ 
+
+ align:start position:0%
+the axis through
+G what's the
+
+ align:start position:0%
+G what's the
+ 
+
+ align:start position:0%
+G what's the
+torque zero nothing happens
+
+ align:start position:0%
+torque zero nothing happens
+ 
+
+ align:start position:0%
+torque zero nothing happens
+right just doesn't want to do anything
+
+ align:start position:0%
+right just doesn't want to do anything
+ 
+
+ align:start position:0%
+right just doesn't want to do anything
+but as soon as it's not through G then
+
+ align:start position:0%
+but as soon as it's not through G then
+ 
+
+ align:start position:0%
+but as soon as it's not through G then
+the thing will oscillate and that's
+
+ align:start position:0%
+the thing will oscillate and that's
+ 
+
+ align:start position:0%
+the thing will oscillate and that's
+because of the this is now a
+
+ align:start position:0%
+because of the this is now a
+ 
+
+ align:start position:0%
+because of the this is now a
+differential equation I I need to say
+
+ align:start position:0%
+differential equation I I need to say
+ 
+
+ align:start position:0%
+differential equation I I need to say
+equals zero
+
+ align:start position:0%
+equals zero
+ 
+
+ align:start position:0%
+equals zero
+here there's no other forces if you had
+
+ align:start position:0%
+here there's no other forces if you had
+ 
+
+ align:start position:0%
+here there's no other forces if you had
+damping Force then it would show up but
+
+ align:start position:0%
+damping Force then it would show up but
+ 
+
+ align:start position:0%
+damping Force then it would show up but
+this is a generic
+
+ align:start position:0%
+this is a generic
+ 
+
+ align:start position:0%
+this is a generic
+undamped equation of motion for any
+
+ align:start position:0%
+undamped equation of motion for any
+ 
+
+ align:start position:0%
+undamped equation of motion for any
+single degree of Freedom pendulum
+
+ align:start position:0%
+single degree of Freedom pendulum
+ 
+
+ align:start position:0%
+single degree of Freedom pendulum
+rotating about an act one of its
+
+ align:start position:0%
+rotating about an act one of its
+ 
+
+ align:start position:0%
+rotating about an act one of its
+principal axis and if the body you're
+
+ align:start position:0%
+principal axis and if the body you're
+ 
+
+ align:start position:0%
+principal axis and if the body you're
+shown or given has a single plane of
+
+ align:start position:0%
+shown or given has a single plane of
+ 
+
+ align:start position:0%
+shown or given has a single plane of
+symmetry then you can figure out one way
+
+ align:start position:0%
+symmetry then you can figure out one way
+ 
+
+ align:start position:0%
+symmetry then you can figure out one way
+immediately that you know this will that
+
+ align:start position:0%
+immediately that you know this will that
+ 
+
+ align:start position:0%
+immediately that you know this will that
+equation applies any axis perpendicular
+
+ align:start position:0%
+equation applies any axis perpendicular
+ 
+
+ align:start position:0%
+equation applies any axis perpendicular
+to that plane of symmetry is a pendulum
+
+ align:start position:0%
+to that plane of symmetry is a pendulum
+ 
+
+ align:start position:0%
+to that plane of symmetry is a pendulum
+based that equation and the I with
+
+ align:start position:0%
+based that equation and the I with
+ 
+
+ align:start position:0%
+based that equation and the I with
+respect to a you can get from
+
+ align:start position:0%
+respect to a you can get from
+ 
+
+ align:start position:0%
+respect to a you can get from
+simple parallel axis if you're told what
+
+ align:start position:0%
+simple parallel axis if you're told what
+ 
+
+ align:start position:0%
+simple parallel axis if you're told what
+I with respect to G is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions I'm going to put up two
+
+ align:start position:0%
+questions I'm going to put up two
+ 
+
+ align:start position:0%
+questions I'm going to put up two
+additional problems and I'm not going to
+
+ align:start position:0%
+additional problems and I'm not going to
+ 
+
+ align:start position:0%
+additional problems and I'm not going to
+solve them we're going to talk about
+
+ align:start position:0%
+solve them we're going to talk about
+ 
+
+ align:start position:0%
+solve them we're going to talk about
+them you're going to tell me how you
+
+ align:start position:0%
+them you're going to tell me how you
+ 
+
+ align:start position:0%
+them you're going to tell me how you
+would go about doing them and they
+
+ align:start position:0%
+would go about doing them and they
+ 
+
+ align:start position:0%
+would go about doing them and they
+wouldn't be bad problems for you to
+
+ align:start position:0%
+wouldn't be bad problems for you to
+ 
+
+ align:start position:0%
+wouldn't be bad problems for you to
+practice on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you've actually seen both of them
+
+ align:start position:0%
+and you've actually seen both of them
+ 
+
+ align:start position:0%
+and you've actually seen both of them
+before so the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+pulley rotating about a fixed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+axis and this is that thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called Atwoods
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+machine how I draw my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coordinates so I have my
+
+ align:start position:0%
+coordinates so I have my
+ 
+
+ align:start position:0%
+coordinates so I have my
+I ZZ about G is some
+
+ align:start position:0%
+I ZZ about G is some
+ 
+
+ align:start position:0%
+I ZZ about G is some
+M3 Capa squared that's you're given the
+
+ align:start position:0%
+M3 Capa squared that's you're given the
+ 
+
+ align:start position:0%
+M3 Capa squared that's you're given the
+radius of gation of this pulley so
+
+ align:start position:0%
+radius of gation of this pulley so
+ 
+
+ align:start position:0%
+radius of gation of this pulley so
+that's his Mass moment inertia about the
+
+ align:start position:0%
+that's his Mass moment inertia about the
+ 
+
+ align:start position:0%
+that's his Mass moment inertia about the
+Center and you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R you could specify a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta and we have a pair of masses start
+
+ align:start position:0%
+Theta and we have a pair of masses start
+ 
+
+ align:start position:0%
+Theta and we have a pair of masses start
+off like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this M1
+
+ align:start position:0%
+this M1
+ 
+
+ align:start position:0%
+this M1
+M2 and this now so there's I'm going to
+
+ align:start position:0%
+M2 and this now so there's I'm going to
+ 
+
+ align:start position:0%
+M2 and this now so there's I'm going to
+say no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slip this rope goes over the pulley no
+
+ align:start position:0%
+slip this rope goes over the pulley no
+ 
+
+ align:start position:0%
+slip this rope goes over the pulley no
+slip initially stationary I Let Go I
+
+ align:start position:0%
+slip initially stationary I Let Go I
+ 
+
+ align:start position:0%
+slip initially stationary I Let Go I
+want to have I want an equation of
+
+ align:start position:0%
+want to have I want an equation of
+ 
+
+ align:start position:0%
+want to have I want an equation of
+motion for this system so how many is it
+
+ align:start position:0%
+motion for this system so how many is it
+ 
+
+ align:start position:0%
+motion for this system so how many is it
+first of all is it a planer motion
+
+ align:start position:0%
+first of all is it a planer motion
+ 
+
+ align:start position:0%
+first of all is it a planer motion
+problem okay how many rigid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bodies how many potential degrees of
+
+ align:start position:0%
+bodies how many potential degrees of
+ 
+
+ align:start position:0%
+bodies how many potential degrees of
+freedom nine okay how many do you think
+
+ align:start position:0%
+freedom nine okay how many do you think
+ 
+
+ align:start position:0%
+freedom nine okay how many do you think
+they're really are going to end up with
+
+ align:start position:0%
+they're really are going to end up with
+ 
+
+ align:start position:0%
+they're really are going to end up with
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+how many how many how many do you expect
+
+ align:start position:0%
+how many how many how many do you expect
+ 
+
+ align:start position:0%
+how many how many how many do you expect
+to find how many
+
+ align:start position:0%
+to find how many
+ 
+
+ align:start position:0%
+to find how many
+necessary degrees of or coordinates
+
+ align:start position:0%
+necessary degrees of or coordinates
+ 
+
+ align:start position:0%
+necessary degrees of or coordinates
+you're going to need to completely
+
+ align:start position:0%
+you're going to need to completely
+ 
+
+ align:start position:0%
+you're going to need to completely
+describe the motion I see some ones
+
+ align:start position:0%
+describe the motion I see some ones
+ 
+
+ align:start position:0%
+describe the motion I see some ones
+going up everybody believe
+
+ align:start position:0%
+going up everybody believe
+ 
+
+ align:start position:0%
+going up everybody believe
+that lots of constraints we're got we're
+
+ align:start position:0%
+that lots of constraints we're got we're
+ 
+
+ align:start position:0%
+that lots of constraints we're got we're
+not going to let this we're constraining
+
+ align:start position:0%
+not going to let this we're constraining
+ 
+
+ align:start position:0%
+not going to let this we're constraining
+this to move in only allowed it to move
+
+ align:start position:0%
+this to move in only allowed it to move
+ 
+
+ align:start position:0%
+this to move in only allowed it to move
+up and down these can't rotate so
+
+ align:start position:0%
+up and down these can't rotate so
+ 
+
+ align:start position:0%
+up and down these can't rotate so
+there's one for each these can't uh go
+
+ align:start position:0%
+there's one for each these can't uh go
+ 
+
+ align:start position:0%
+there's one for each these can't uh go
+in the this direction so two more this
+
+ align:start position:0%
+in the this direction so two more this
+ 
+
+ align:start position:0%
+in the this direction so two more this
+can only rotate no
+
+ align:start position:0%
+can only rotate no
+ 
+
+ align:start position:0%
+can only rotate no
+translations so you end up you end up
+
+ align:start position:0%
+translations so you end up you end up
+ 
+
+ align:start position:0%
+translations so you end up you end up
+with one and finally there's this no
+
+ align:start position:0%
+with one and finally there's this no
+ 
+
+ align:start position:0%
+with one and finally there's this no
+slip condition which means that R Theta
+
+ align:start position:0%
+slip condition which means that R Theta
+ 
+
+ align:start position:0%
+slip condition which means that R Theta
+equal x and that's one final one that
+
+ align:start position:0%
+equal x and that's one final one that
+ 
+
+ align:start position:0%
+equal x and that's one final one that
+you need to write down okay so if you
+
+ align:start position:0%
+you need to write down okay so if you
+ 
+
+ align:start position:0%
+you need to write down okay so if you
+had that gotten this far find the
+
+ align:start position:0%
+had that gotten this far find the
+ 
+
+ align:start position:0%
+had that gotten this far find the
+equation of motion what method would you
+
+ align:start position:0%
+equation of motion what method would you
+ 
+
+ align:start position:0%
+equation of motion what method would you
+use so your choices are here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and direct method
+
+ align:start position:0%
+and direct method
+ 
+
+ align:start position:0%
+and direct method
+lrange think about it how would you
+
+ align:start position:0%
+lrange think about it how would you
+ 
+
+ align:start position:0%
+lrange think about it how would you
+what's the easiest way for you to do
+
+ align:start position:0%
+what's the easiest way for you to do
+ 
+
+ align:start position:0%
+what's the easiest way for you to do
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem maybe an ancillary question is
+
+ align:start position:0%
+problem maybe an ancillary question is
+ 
+
+ align:start position:0%
+problem maybe an ancillary question is
+how many ways can you think of that you
+
+ align:start position:0%
+how many ways can you think of that you
+ 
+
+ align:start position:0%
+how many ways can you think of that you
+could do this problem how many different
+
+ align:start position:0%
+could do this problem how many different
+ 
+
+ align:start position:0%
+could do this problem how many different
+approaches could you use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how many ways can you how many ways
+
+ align:start position:0%
+so how many ways can you how many ways
+ 
+
+ align:start position:0%
+so how many ways can you how many ways
+can you think of doing this problem
+
+ align:start position:0%
+can you think of doing this problem
+ 
+
+ align:start position:0%
+can you think of doing this problem
+Kristen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I was just picking on her
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but give me the answer
+
+ align:start position:0%
+but give me the answer
+ 
+
+ align:start position:0%
+but give me the answer
+anyway s answer um I think you could do
+
+ align:start position:0%
+anyway s answer um I think you could do
+ 
+
+ align:start position:0%
+anyway s answer um I think you could do
+two but I would choose Lan you would
+
+ align:start position:0%
+two but I would choose Lan you would
+ 
+
+ align:start position:0%
+two but I would choose Lan you would
+want to do it by L Grange how how else
+
+ align:start position:0%
+want to do it by L Grange how how else
+ 
+
+ align:start position:0%
+want to do it by L Grange how how else
+could you do it if you if you did it by
+
+ align:start position:0%
+could you do it if you if you did it by
+ 
+
+ align:start position:0%
+could you do it if you if you did it by
+L Grange got the answer and said I want
+
+ align:start position:0%
+L Grange got the answer and said I want
+ 
+
+ align:start position:0%
+L Grange got the answer and said I want
+to check it what would you do next
+
+ align:start position:0%
+to check it what would you do next
+ 
+
+ align:start position:0%
+to check it what would you do next
+Direct Direct Direct but how where how
+
+ align:start position:0%
+Direct Direct Direct but how where how
+ 
+
+ align:start position:0%
+Direct Direct Direct but how where how
+where would you app fly would you use
+
+ align:start position:0%
+where would you app fly would you use
+ 
+
+ align:start position:0%
+where would you app fly would you use
+torqu would you use forces how would you
+
+ align:start position:0%
+torqu would you use forces how would you
+ 
+
+ align:start position:0%
+torqu would you use forces how would you
+get go about doing this tor about the
+
+ align:start position:0%
+get go about doing this tor about the
+ 
+
+ align:start position:0%
+get go about doing this tor about the
+center of the T about the we did that I
+
+ align:start position:0%
+center of the T about the we did that I
+ 
+
+ align:start position:0%
+center of the T about the we did that I
+mean I work that I actually did this
+
+ align:start position:0%
+mean I work that I actually did this
+ 
+
+ align:start position:0%
+mean I work that I actually did this
+problem by that method uh earlier in the
+
+ align:start position:0%
+problem by that method uh earlier in the
+ 
+
+ align:start position:0%
+problem by that method uh earlier in the
+term tor's about a the the pivot works
+
+ align:start position:0%
+term tor's about a the the pivot works
+ 
+
+ align:start position:0%
+term tor's about a the the pivot works
+fine actually it's pretty it's pretty
+
+ align:start position:0%
+fine actually it's pretty it's pretty
+ 
+
+ align:start position:0%
+fine actually it's pretty it's pretty
+efficient okay so um LR or TS about a
+
+ align:start position:0%
+efficient okay so um LR or TS about a
+ 
+
+ align:start position:0%
+efficient okay so um LR or TS about a
+you only need there's one degree of
+
+ align:start position:0%
+you only need there's one degree of
+ 
+
+ align:start position:0%
+you only need there's one degree of
+Freedom right how many equations do you
+
+ align:start position:0%
+Freedom right how many equations do you
+ 
+
+ align:start position:0%
+Freedom right how many equations do you
+need to right to to you to do this
+
+ align:start position:0%
+need to right to to you to do this
+ 
+
+ align:start position:0%
+need to right to to you to do this
+problem just one so the sum of the
+
+ align:start position:0%
+problem just one so the sum of the
+ 
+
+ align:start position:0%
+problem just one so the sum of the
+torqus about a will give you the answer
+
+ align:start position:0%
+torqus about a will give you the answer
+ 
+
+ align:start position:0%
+torqus about a will give you the answer
+lrange equation will give you the answer
+
+ align:start position:0%
+lrange equation will give you the answer
+ 
+
+ align:start position:0%
+lrange equation will give you the answer
+okay that's a good good problem to go
+
+ align:start position:0%
+okay that's a good good problem to go
+ 
+
+ align:start position:0%
+okay that's a good good problem to go
+practice to practice on uh another
+
+ align:start position:0%
+practice to practice on uh another
+ 
+
+ align:start position:0%
+practice to practice on uh another
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um this is not very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+big is basically this problem this is
+
+ align:start position:0%
+big is basically this problem this is
+ 
+
+ align:start position:0%
+big is basically this problem this is
+just you've seen this I'm sure you've
+
+ align:start position:0%
+just you've seen this I'm sure you've
+ 
+
+ align:start position:0%
+just you've seen this I'm sure you've
+been shown this in physics and stuff
+
+ align:start position:0%
+been shown this in physics and stuff
+ 
+
+ align:start position:0%
+been shown this in physics and stuff
+before this the the falling stick
+
+ align:start position:0%
+before this the the falling stick
+ 
+
+ align:start position:0%
+before this the the falling stick
+problem uh I can't you can't set this up
+
+ align:start position:0%
+problem uh I can't you can't set this up
+ 
+
+ align:start position:0%
+problem uh I can't you can't set this up
+without having some friction so there's
+
+ align:start position:0%
+without having some friction so there's
+ 
+
+ align:start position:0%
+without having some friction so there's
+definitely friction on the table but
+
+ align:start position:0%
+definitely friction on the table but
+ 
+
+ align:start position:0%
+definitely friction on the table but
+until it hits it's doing some things and
+
+ align:start position:0%
+until it hits it's doing some things and
+ 
+
+ align:start position:0%
+until it hits it's doing some things and
+so there's two problems that you could
+
+ align:start position:0%
+so there's two problems that you could
+ 
+
+ align:start position:0%
+so there's two problems that you could
+set up and try to do one is a problem
+
+ align:start position:0%
+set up and try to do one is a problem
+ 
+
+ align:start position:0%
+set up and try to do one is a problem
+with no friction frictionless
+
+ align:start position:0%
+with no friction frictionless
+ 
+
+ align:start position:0%
+with no friction frictionless
+cable and then you could allow friction
+
+ align:start position:0%
+cable and then you could allow friction
+ 
+
+ align:start position:0%
+cable and then you could allow friction
+okay tricky thing about allowing
+
+ align:start position:0%
+okay tricky thing about allowing
+ 
+
+ align:start position:0%
+okay tricky thing about allowing
+friction is do you think that does a
+
+ align:start position:0%
+friction is do you think that does a
+ 
+
+ align:start position:0%
+friction is do you think that does a
+normal force so let's say our usual
+
+ align:start position:0%
+normal force so let's say our usual
+ 
+
+ align:start position:0%
+normal force so let's say our usual
+friction model is the friction force is
+
+ align:start position:0%
+friction model is the friction force is
+ 
+
+ align:start position:0%
+friction model is the friction force is
+Mu * the normal force does the normal
+
+ align:start position:0%
+Mu * the normal force does the normal
+ 
+
+ align:start position:0%
+Mu * the normal force does the normal
+force change with
+
+ align:start position:0%
+force change with
+ 
+
+ align:start position:0%
+force change with
+time in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem so standing up what's the normal
+
+ align:start position:0%
+problem so standing up what's the normal
+ 
+
+ align:start position:0%
+problem so standing up what's the normal
+force mg right but uh and the sum of the
+
+ align:start position:0%
+force mg right but uh and the sum of the
+ 
+
+ align:start position:0%
+force mg right but uh and the sum of the
+forces in the vertical direction is
+
+ align:start position:0%
+forces in the vertical direction is
+ 
+
+ align:start position:0%
+forces in the vertical direction is
+masstimes the acceleration in the
+
+ align:start position:0%
+masstimes the acceleration in the
+ 
+
+ align:start position:0%
+masstimes the acceleration in the
+vertical
+
+ align:start position:0%
+vertical
+ 
+
+ align:start position:0%
+vertical
+Direction and what are the if you draw a
+
+ align:start position:0%
+Direction and what are the if you draw a
+ 
+
+ align:start position:0%
+Direction and what are the if you draw a
+free body diagram of this problem so
+
+ align:start position:0%
+free body diagram of this problem so
+ 
+
+ align:start position:0%
+free body diagram of this problem so
+let's draw it now here's
+
+ align:start position:0%
+let's draw it now here's
+ 
+
+ align:start position:0%
+let's draw it now here's
+my if there's no friction Force I still
+
+ align:start position:0%
+my if there's no friction Force I still
+ 
+
+ align:start position:0%
+my if there's no friction Force I still
+without friction Force I still have a
+
+ align:start position:0%
+without friction Force I still have a
+ 
+
+ align:start position:0%
+without friction Force I still have a
+normal force and I still have mg pulling
+
+ align:start position:0%
+normal force and I still have mg pulling
+ 
+
+ align:start position:0%
+normal force and I still have mg pulling
+down here so the sum of the forces in
+
+ align:start position:0%
+down here so the sum of the forces in
+ 
+
+ align:start position:0%
+down here so the sum of the forces in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+Y certainly have a minus
+
+ align:start position:0%
+Y certainly have a minus
+ 
+
+ align:start position:0%
+Y certainly have a minus
+mg plus n equals the mass time the
+
+ align:start position:0%
+mg plus n equals the mass time the
+ 
+
+ align:start position:0%
+mg plus n equals the mass time the
+acceleration in the y
+
+ align:start position:0%
+acceleration in the y
+ 
+
+ align:start position:0%
+acceleration in the y
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+and if you solve for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n do you then the issue my question is
+
+ align:start position:0%
+n do you then the issue my question is
+ 
+
+ align:start position:0%
+n do you then the issue my question is
+this remain
+
+ align:start position:0%
+this remain
+ 
+
+ align:start position:0%
+this remain
+constant depends on whether or not a y
+
+ align:start position:0%
+constant depends on whether or not a y
+ 
+
+ align:start position:0%
+constant depends on whether or not a y
+remains constant right do you think the
+
+ align:start position:0%
+remains constant right do you think the
+ 
+
+ align:start position:0%
+remains constant right do you think the
+acceleration in the y direction of this
+
+ align:start position:0%
+acceleration in the y direction of this
+ 
+
+ align:start position:0%
+acceleration in the y direction of this
+thing will change as it goes more and
+
+ align:start position:0%
+thing will change as it goes more and
+ 
+
+ align:start position:0%
+thing will change as it goes more and
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+horizontal so here's some notd up and
+
+ align:start position:0%
+horizontal so here's some notd up and
+ 
+
+ align:start position:0%
+horizontal so here's some notd up and
+downs and left and rights I think it's
+
+ align:start position:0%
+downs and left and rights I think it's
+ 
+
+ align:start position:0%
+downs and left and rights I think it's
+going to change for sure you can't
+
+ align:start position:0%
+going to change for sure you can't
+ 
+
+ align:start position:0%
+going to change for sure you can't
+assume that it won't change so you have
+
+ align:start position:0%
+assume that it won't change so you have
+ 
+
+ align:start position:0%
+assume that it won't change so you have
+to assume that it'll change and that
+
+ align:start position:0%
+to assume that it'll change and that
+ 
+
+ align:start position:0%
+to assume that it'll change and that
+means in here this normal force becomes
+
+ align:start position:0%
+means in here this normal force becomes
+ 
+
+ align:start position:0%
+means in here this normal force becomes
+a function of time which makes this
+
+ align:start position:0%
+a function of time which makes this
+ 
+
+ align:start position:0%
+a function of time which makes this
+problem makes certain ways of doing this
+
+ align:start position:0%
+problem makes certain ways of doing this
+ 
+
+ align:start position:0%
+problem makes certain ways of doing this
+problem a little
+
+ align:start position:0%
+problem a little
+ 
+
+ align:start position:0%
+problem a little
+harder so
+
+ align:start position:0%
+harder so
+ 
+
+ align:start position:0%
+harder so
+um how many ways let's say the friction
+
+ align:start position:0%
+um how many ways let's say the friction
+ 
+
+ align:start position:0%
+um how many ways let's say the friction
+let's do
+
+ align:start position:0%
+let's do
+ 
+
+ align:start position:0%
+let's do
+a uh no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+friction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B with friction okay no friction first
+
+ align:start position:0%
+B with friction okay no friction first
+ 
+
+ align:start position:0%
+B with friction okay no friction first
+of all is it a planer motion
+
+ align:start position:0%
+of all is it a planer motion
+ 
+
+ align:start position:0%
+of all is it a planer motion
+problem yep okay we can we can do that
+
+ align:start position:0%
+problem yep okay we can we can do that
+ 
+
+ align:start position:0%
+problem yep okay we can we can do that
+so at most three degrees of freedom how
+
+ align:start position:0%
+so at most three degrees of freedom how
+ 
+
+ align:start position:0%
+so at most three degrees of freedom how
+many does this one have work this one
+
+ align:start position:0%
+many does this one have work this one
+ 
+
+ align:start position:0%
+many does this one have work this one
+out figure out how many degrees of
+
+ align:start position:0%
+out figure out how many degrees of
+ 
+
+ align:start position:0%
+out figure out how many degrees of
+freedom this problem has how many
+
+ align:start position:0%
+freedom this problem has how many
+ 
+
+ align:start position:0%
+freedom this problem has how many
+separate equations do you need to come
+
+ align:start position:0%
+separate equations do you need to come
+ 
+
+ align:start position:0%
+separate equations do you need to come
+up with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you decide what your let's say we're
+
+ align:start position:0%
+so you decide what your let's say we're
+ 
+
+ align:start position:0%
+so you decide what your let's say we're
+going to use lrange what would your
+
+ align:start position:0%
+going to use lrange what would your
+ 
+
+ align:start position:0%
+going to use lrange what would your
+generalized coordinates be to do this
+
+ align:start position:0%
+generalized coordinates be to do this
+ 
+
+ align:start position:0%
+generalized coordinates be to do this
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so problem a no
+
+ align:start position:0%
+so problem a no
+ 
+
+ align:start position:0%
+so problem a no
+friction how many
+
+ align:start position:0%
+friction how many
+ 
+
+ align:start position:0%
+friction how many
+generalized coordinates how many degrees
+
+ align:start position:0%
+generalized coordinates how many degrees
+ 
+
+ align:start position:0%
+generalized coordinates how many degrees
+of freedom how many generalized
+
+ align:start position:0%
+of freedom how many generalized
+ 
+
+ align:start position:0%
+of freedom how many generalized
+coordinates do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+need I heard a
+
+ align:start position:0%
+need I heard a
+ 
+
+ align:start position:0%
+need I heard a
+three I hear one somebody give me two I
+
+ align:start position:0%
+three I hear one somebody give me two I
+ 
+
+ align:start position:0%
+three I hear one somebody give me two I
+got a two all right it's good obviously
+
+ align:start position:0%
+got a two all right it's good obviously
+ 
+
+ align:start position:0%
+got a two all right it's good obviously
+a good question so at most there can be
+
+ align:start position:0%
+a good question so at most there can be
+ 
+
+ align:start position:0%
+a good question so at most there can be
+three because so we've agreed that it's
+
+ align:start position:0%
+three because so we've agreed that it's
+ 
+
+ align:start position:0%
+three because so we've agreed that it's
+planer motion does this problem have any
+
+ align:start position:0%
+planer motion does this problem have any
+ 
+
+ align:start position:0%
+planer motion does this problem have any
+constraints
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where so it can't move in the y
+
+ align:start position:0%
+where so it can't move in the y
+ 
+
+ align:start position:0%
+where so it can't move in the y
+direction okay so if any part of a body
+
+ align:start position:0%
+direction okay so if any part of a body
+ 
+
+ align:start position:0%
+direction okay so if any part of a body
+can't move in in in
+
+ align:start position:0%
+can't move in in in
+ 
+
+ align:start position:0%
+can't move in in in
+translate then there's no translation in
+
+ align:start position:0%
+translate then there's no translation in
+ 
+
+ align:start position:0%
+translate then there's no translation in
+that direction you know pure you know
+
+ align:start position:0%
+that direction you know pure you know
+ 
+
+ align:start position:0%
+that direction you know pure you know
+translation of the body in that
+
+ align:start position:0%
+translation of the body in that
+ 
+
+ align:start position:0%
+translation of the body in that
+direction so There's a constraint in the
+
+ align:start position:0%
+direction so There's a constraint in the
+ 
+
+ align:start position:0%
+direction so There's a constraint in the
+in the Y if we draw a coordinate system
+
+ align:start position:0%
+in the Y if we draw a coordinate system
+ 
+
+ align:start position:0%
+in the Y if we draw a coordinate system
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constraint in the Y true so we're down
+
+ align:start position:0%
+constraint in the Y true so we're down
+ 
+
+ align:start position:0%
+constraint in the Y true so we're down
+to two are there any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constraints no no it's not leaning
+
+ align:start position:0%
+constraints no no it's not leaning
+ 
+
+ align:start position:0%
+constraints no no it's not leaning
+against the wall this is just a stick
+
+ align:start position:0%
+against the wall this is just a stick
+ 
+
+ align:start position:0%
+against the wall this is just a stick
+this this this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem so definitely can't move through
+
+ align:start position:0%
+problem so definitely can't move through
+ 
+
+ align:start position:0%
+problem so definitely can't move through
+the table so it's constrained in y we've
+
+ align:start position:0%
+the table so it's constrained in y we've
+ 
+
+ align:start position:0%
+the table so it's constrained in y we've
+got that so so now that leaves us at
+
+ align:start position:0%
+got that so so now that leaves us at
+ 
+
+ align:start position:0%
+got that so so now that leaves us at
+most
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two are there any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constraints how many say
+
+ align:start position:0%
+constraints how many say
+ 
+
+ align:start position:0%
+constraints how many say
+no how many say yes if you say yes you
+
+ align:start position:0%
+no how many say yes if you say yes you
+ 
+
+ align:start position:0%
+no how many say yes if you say yes you
+got to tell me what it is but I don't
+
+ align:start position:0%
+got to tell me what it is but I don't
+ 
+
+ align:start position:0%
+got to tell me what it is but I don't
+see any others so we're left with two we
+
+ align:start position:0%
+see any others so we're left with two we
+ 
+
+ align:start position:0%
+see any others so we're left with two we
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+two coordinates which what might we pick
+
+ align:start position:0%
+two coordinates which what might we pick
+ 
+
+ align:start position:0%
+two coordinates which what might we pick
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what would you pick you're now
+
+ align:start position:0%
+what would you pick you're now
+ 
+
+ align:start position:0%
+what would you pick you're now
+confronted with this problem do you have
+
+ align:start position:0%
+confronted with this problem do you have
+ 
+
+ align:start position:0%
+confronted with this problem do you have
+rotational if you're going to use a gr
+
+ align:start position:0%
+rotational if you're going to use a gr
+ 
+
+ align:start position:0%
+rotational if you're going to use a gr
+you have rotational kinetic energy in
+
+ align:start position:0%
+you have rotational kinetic energy in
+ 
+
+ align:start position:0%
+you have rotational kinetic energy in
+this problem you're probably going to
+
+ align:start position:0%
+this problem you're probably going to
+ 
+
+ align:start position:0%
+this problem you're probably going to
+need an angular Mo an angle what else
+
+ align:start position:0%
+need an angular Mo an angle what else
+ 
+
+ align:start position:0%
+need an angular Mo an angle what else
+would you need so we're going to need an
+
+ align:start position:0%
+would you need so we're going to need an
+ 
+
+ align:start position:0%
+would you need so we're going to need an
+angle for
+
+ align:start position:0%
+angle for
+ 
+
+ align:start position:0%
+angle for
+sure say again the height of the center
+
+ align:start position:0%
+sure say again the height of the center
+ 
+
+ align:start position:0%
+sure say again the height of the center
+of mass you're going to need the height
+
+ align:start position:0%
+of mass you're going to need the height
+ 
+
+ align:start position:0%
+of mass you're going to need the height
+of the center of mass yeah you're going
+
+ align:start position:0%
+of the center of mass yeah you're going
+ 
+
+ align:start position:0%
+of the center of mass yeah you're going
+to need a potential energy expression
+
+ align:start position:0%
+to need a potential energy expression
+ 
+
+ align:start position:0%
+to need a potential energy expression
+but we've decided that Y is
+
+ align:start position:0%
+but we've decided that Y is
+ 
+
+ align:start position:0%
+but we've decided that Y is
+constrained hm so if you can't have a
+
+ align:start position:0%
+constrained hm so if you can't have a
+ 
+
+ align:start position:0%
+constrained hm so if you can't have a
+Theta and a y let's make this our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta what else is
+
+ align:start position:0%
+Theta what else is
+ 
+
+ align:start position:0%
+Theta what else is
+there X you're going to need an X so
+
+ align:start position:0%
+there X you're going to need an X so
+ 
+
+ align:start position:0%
+there X you're going to need an X so
+let's our generalized coordinates are
+
+ align:start position:0%
+let's our generalized coordinates are
+ 
+
+ align:start position:0%
+let's our generalized coordinates are
+going to be say an X and A Theta and but
+
+ align:start position:0%
+going to be say an X and A Theta and but
+ 
+
+ align:start position:0%
+going to be say an X and A Theta and but
+you do need to be able to write down a
+
+ align:start position:0%
+you do need to be able to write down a
+ 
+
+ align:start position:0%
+you do need to be able to write down a
+potential energy expression and it
+
+ align:start position:0%
+potential energy expression and it
+ 
+
+ align:start position:0%
+potential energy expression and it
+involves Motion in the Y so what do you
+
+ align:start position:0%
+involves Motion in the Y so what do you
+ 
+
+ align:start position:0%
+involves Motion in the Y so what do you
+do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so what's the height of this thing
+
+ align:start position:0%
+right so what's the height of this thing
+ 
+
+ align:start position:0%
+right so what's the height of this thing
+is above the ground is some L over
+
+ align:start position:0%
+is above the ground is some L over
+ 
+
+ align:start position:0%
+is above the ground is some L over
+2 cine Theta = y something like that
+
+ align:start position:0%
+2 cine Theta = y something like that
+ 
+
+ align:start position:0%
+2 cine Theta = y something like that
+right and I might have a depending on
+
+ align:start position:0%
+right and I might have a depending on
+ 
+
+ align:start position:0%
+right and I might have a depending on
+whether you make I haven't thought this
+
+ align:start position:0%
+whether you make I haven't thought this
+ 
+
+ align:start position:0%
+whether you make I haven't thought this
+through whether or not it's XY this way
+
+ align:start position:0%
+through whether or not it's XY this way
+ 
+
+ align:start position:0%
+through whether or not it's XY this way
+or XY that way Theta might be plus or
+
+ align:start position:0%
+or XY that way Theta might be plus or
+ 
+
+ align:start position:0%
+or XY that way Theta might be plus or
+minus this could
+
+ align:start position:0%
+minus this could
+ 
+
+ align:start position:0%
+minus this could
+be there might be a sign in there but
+
+ align:start position:0%
+be there might be a sign in there but
+ 
+
+ align:start position:0%
+be there might be a sign in there but
+basically this is the Theta and Y are
+
+ align:start position:0%
+basically this is the Theta and Y are
+ 
+
+ align:start position:0%
+basically this is the Theta and Y are
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+constrained if you know one you know the
+
+ align:start position:0%
+constrained if you know one you know the
+ 
+
+ align:start position:0%
+constrained if you know one you know the
+other so you do your potential energy
+
+ align:start position:0%
+other so you do your potential energy
+ 
+
+ align:start position:0%
+other so you do your potential energy
+expression this way
+
+ align:start position:0%
+expression this way
+ 
+
+ align:start position:0%
+expression this way
+okay now uh so now you're in front now
+
+ align:start position:0%
+okay now uh so now you're in front now
+ 
+
+ align:start position:0%
+okay now uh so now you're in front now
+you've we've gotten that far we know we
+
+ align:start position:0%
+you've we've gotten that far we know we
+ 
+
+ align:start position:0%
+you've we've gotten that far we know we
+need two two coordinates we're going to
+
+ align:start position:0%
+need two two coordinates we're going to
+ 
+
+ align:start position:0%
+need two two coordinates we're going to
+use x and Theta uh but now you have to
+
+ align:start position:0%
+use x and Theta uh but now you have to
+ 
+
+ align:start position:0%
+use x and Theta uh but now you have to
+decide what method to use direct method
+
+ align:start position:0%
+decide what method to use direct method
+ 
+
+ align:start position:0%
+decide what method to use direct method
+using one of these or lrange what would
+
+ align:start position:0%
+using one of these or lrange what would
+ 
+
+ align:start position:0%
+using one of these or lrange what would
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+do how would you go about so quiz you
+
+ align:start position:0%
+do how would you go about so quiz you
+ 
+
+ align:start position:0%
+do how would you go about so quiz you
+got 20 minutes to finish
+
+ align:start position:0%
+got 20 minutes to finish
+ 
+
+ align:start position:0%
+got 20 minutes to finish
+and you want to do this in the safest
+
+ align:start position:0%
+and you want to do this in the safest
+ 
+
+ align:start position:0%
+and you want to do this in the safest
+quickest possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way what would you try you know this is
+
+ align:start position:0%
+way what would you try you know this is
+ 
+
+ align:start position:0%
+way what would you try you know this is
+you know when this is you know the
+
+ align:start position:0%
+you know when this is you know the
+ 
+
+ align:start position:0%
+you know when this is you know the
+realistic situation right next Tuesday
+
+ align:start position:0%
+realistic situation right next Tuesday
+ 
+
+ align:start position:0%
+realistic situation right next Tuesday
+what do you most what do you trust
+
+ align:start position:0%
+what do you most what do you trust
+ 
+
+ align:start position:0%
+what do you most what do you trust
+yourself to do for the most is probably
+
+ align:start position:0%
+yourself to do for the most is probably
+ 
+
+ align:start position:0%
+yourself to do for the most is probably
+what you ought to do in a quiz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+situation and how many ways can you
+
+ align:start position:0%
+situation and how many ways can you
+ 
+
+ align:start position:0%
+situation and how many ways can you
+think of doing this how many ways could
+
+ align:start position:0%
+think of doing this how many ways could
+ 
+
+ align:start position:0%
+think of doing this how many ways could
+you do this problem
+
+ align:start position:0%
+you do this problem
+ 
+
+ align:start position:0%
+you do this problem
+two two anyway direct and direct what
+
+ align:start position:0%
+two two anyway direct and direct what
+ 
+
+ align:start position:0%
+two two anyway direct and direct what
+where would you use where would you
+
+ align:start position:0%
+where would you use where would you
+ 
+
+ align:start position:0%
+where would you use where would you
+choose to you're going to need a torque
+
+ align:start position:0%
+choose to you're going to need a torque
+ 
+
+ align:start position:0%
+choose to you're going to need a torque
+equation to do this problem if you use
+
+ align:start position:0%
+equation to do this problem if you use
+ 
+
+ align:start position:0%
+equation to do this problem if you use
+direct where would you take your torqus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about think about that where for this
+
+ align:start position:0%
+about think about that where for this
+ 
+
+ align:start position:0%
+about think about that where for this
+problem you're using going direct method
+
+ align:start position:0%
+problem you're using going direct method
+ 
+
+ align:start position:0%
+problem you're using going direct method
+where you going to compute the torqus
+
+ align:start position:0%
+where you going to compute the torqus
+ 
+
+ align:start position:0%
+where you going to compute the torqus
+about what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point so you can do it about that you
+
+ align:start position:0%
+point so you can do it about that you
+ 
+
+ align:start position:0%
+point so you can do it about that you
+can call this point
+
+ align:start position:0%
+can call this point
+ 
+
+ align:start position:0%
+can call this point
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+here yep and what equation would you you
+
+ align:start position:0%
+here yep and what equation would you you
+ 
+
+ align:start position:0%
+here yep and what equation would you you
+now you've got to use that equation
+
+ align:start position:0%
+now you've got to use that equation
+ 
+
+ align:start position:0%
+now you've got to use that equation
+that's got the problematic terms in it
+
+ align:start position:0%
+that's got the problematic terms in it
+ 
+
+ align:start position:0%
+that's got the problematic terms in it
+right and but it's all right you can you
+
+ align:start position:0%
+right and but it's all right you can you
+ 
+
+ align:start position:0%
+right and but it's all right you can you
+can punch those through and do it that
+
+ align:start position:0%
+can punch those through and do it that
+ 
+
+ align:start position:0%
+can punch those through and do it that
+will work and if you use
+
+ align:start position:0%
+will work and if you use
+ 
+
+ align:start position:0%
+will work and if you use
+lrange you've got to be able to figure
+
+ align:start position:0%
+lrange you've got to be able to figure
+ 
+
+ align:start position:0%
+lrange you've got to be able to figure
+out the potential and kinetic energy and
+
+ align:start position:0%
+out the potential and kinetic energy and
+ 
+
+ align:start position:0%
+out the potential and kinetic energy and
+so forth okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so could all of you do this by
+
+ align:start position:0%
+so could all of you do this by
+ 
+
+ align:start position:0%
+so could all of you do this by
+lrange I mean this is a good one to go
+
+ align:start position:0%
+lrange I mean this is a good one to go
+ 
+
+ align:start position:0%
+lrange I mean this is a good one to go
+practice on it's not that hard do it
+
+ align:start position:0%
+practice on it's not that hard do it
+ 
+
+ align:start position:0%
+practice on it's not that hard do it
+it's a good practice
+
+ align:start position:0%
+it's a good practice
+ 
+
+ align:start position:0%
+it's a good practice
+problem now add
+
+ align:start position:0%
+problem now add
+ 
+
+ align:start position:0%
+problem now add
+friction so the B problem it now has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+friction can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you I don't
+
+ align:start position:0%
+you I don't
+ 
+
+ align:start position:0%
+you I don't
+think is is lrange a good choice if it
+
+ align:start position:0%
+think is is lrange a good choice if it
+ 
+
+ align:start position:0%
+think is is lrange a good choice if it
+now has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+friction and I think it's got a
+
+ align:start position:0%
+friction and I think it's got a
+ 
+
+ align:start position:0%
+friction and I think it's got a
+problem and I'd be careful using lrange
+
+ align:start position:0%
+problem and I'd be careful using lrange
+ 
+
+ align:start position:0%
+problem and I'd be careful using lrange
+if it had
+
+ align:start position:0%
+if it had
+ 
+
+ align:start position:0%
+if it had
+friction not that lrange is perfectly
+
+ align:start position:0%
+friction not that lrange is perfectly
+ 
+
+ align:start position:0%
+friction not that lrange is perfectly
+it's not it is certainly valid it's just
+
+ align:start position:0%
+it's not it is certainly valid it's just
+ 
+
+ align:start position:0%
+it's not it is certainly valid it's just
+hard why is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hard yeah well yeah it might be hard to
+
+ align:start position:0%
+hard yeah well yeah it might be hard to
+ 
+
+ align:start position:0%
+hard yeah well yeah it might be hard to
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+what do you need to know to so are there
+
+ align:start position:0%
+what do you need to know to so are there
+ 
+
+ align:start position:0%
+what do you need to know to so are there
+any external non-conservative forces in
+
+ align:start position:0%
+any external non-conservative forces in
+ 
+
+ align:start position:0%
+any external non-conservative forces in
+the problem with friction friction
+
+ align:start position:0%
+the problem with friction friction
+ 
+
+ align:start position:0%
+the problem with friction friction
+friction okay you're going to have to
+
+ align:start position:0%
+friction okay you're going to have to
+ 
+
+ align:start position:0%
+friction okay you're going to have to
+figure out the friction force and to
+
+ align:start position:0%
+figure out the friction force and to
+ 
+
+ align:start position:0%
+figure out the friction force and to
+figure out the friction Force you're
+
+ align:start position:0%
+figure out the friction Force you're
+ 
+
+ align:start position:0%
+figure out the friction Force you're
+going to have to
+
+ align:start position:0%
+going to have to
+ 
+
+ align:start position:0%
+going to have to
+apply direct method no other way you are
+
+ align:start position:0%
+apply direct method no other way you are
+ 
+
+ align:start position:0%
+apply direct method no other way you are
+going to have to apply some direct
+
+ align:start position:0%
+going to have to apply some direct
+ 
+
+ align:start position:0%
+going to have to apply some direct
+method to do this problem no matter
+
+ align:start position:0%
+method to do this problem no matter
+ 
+
+ align:start position:0%
+method to do this problem no matter
+what so you you can't you can't just say
+
+ align:start position:0%
+what so you you can't you can't just say
+ 
+
+ align:start position:0%
+what so you you can't you can't just say
+ah but you can't the gange is not going
+
+ align:start position:0%
+ah but you can't the gange is not going
+ 
+
+ align:start position:0%
+ah but you can't the gange is not going
+to just bail you out and not have to
+
+ align:start position:0%
+to just bail you out and not have to
+ 
+
+ align:start position:0%
+to just bail you out and not have to
+solve some of the fals ma and torque and
+
+ align:start position:0%
+solve some of the fals ma and torque and
+ 
+
+ align:start position:0%
+solve some of the fals ma and torque and
+those sort of things to figure out what
+
+ align:start position:0%
+those sort of things to figure out what
+ 
+
+ align:start position:0%
+those sort of things to figure out what
+friction
+
+ align:start position:0%
+friction
+ 
+
+ align:start position:0%
+friction
+is so there are problems that lrange
+
+ align:start position:0%
+is so there are problems that lrange
+ 
+
+ align:start position:0%
+is so there are problems that lrange
+isn't is isn't all as simple as we
+
+ align:start position:0%
+isn't is isn't all as simple as we
+ 
+
+ align:start position:0%
+isn't is isn't all as simple as we
+sometimes make it out to be all right
+
+ align:start position:0%
+sometimes make it out to be all right
+ 
+
+ align:start position:0%
+sometimes make it out to be all right
+I've run a couple of minutes over thank
+
+ align:start position:0%
+I've run a couple of minutes over thank
+ 
+
+ align:start position:0%
+I've run a couple of minutes over thank
+you we'll see you in class on Tuesday
+
+ align:start position:0%
+you we'll see you in class on Tuesday
+ 
+
+ align:start position:0%
+you we'll see you in class on Tuesday
+we'll do some more review
\ No newline at end of file
diff --git a/cf7JLEqw8Os.txt b/cf7JLEqw8Os.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5b858b790af6b8aee6af86fd1c954651c3e5f868
--- /dev/null
+++ b/cf7JLEqw8Os.txt
@@ -0,0 +1,9475 @@
+align:start position:0%
+ 
+okay why don't we get
+
+ align:start position:0%
+okay why don't we get
+ 
+
+ align:start position:0%
+okay why don't we get
+started so you know we've been talking a
+
+ align:start position:0%
+started so you know we've been talking a
+ 
+
+ align:start position:0%
+started so you know we've been talking a
+bit about magnetics and particularly how
+
+ align:start position:0%
+bit about magnetics and particularly how
+ 
+
+ align:start position:0%
+bit about magnetics and particularly how
+you model magnetics um today I'd like to
+
+ align:start position:0%
+you model magnetics um today I'd like to
+ 
+
+ align:start position:0%
+you model magnetics um today I'd like to
+talk a bit about magnetics
+
+ align:start position:0%
+talk a bit about magnetics
+ 
+
+ align:start position:0%
+talk a bit about magnetics
+loss and we can only really scratch the
+
+ align:start position:0%
+loss and we can only really scratch the
+ 
+
+ align:start position:0%
+loss and we can only really scratch the
+surface
+
+ align:start position:0%
+surface
+ 
+
+ align:start position:0%
+surface
+of this topic I mean it actually takes
+
+ align:start position:0%
+of this topic I mean it actually takes
+ 
+
+ align:start position:0%
+of this topic I mean it actually takes
+up a whole chapter in um principles of
+
+ align:start position:0%
+up a whole chapter in um principles of
+ 
+
+ align:start position:0%
+up a whole chapter in um principles of
+Power Electronics um so beyond what's in
+
+ align:start position:0%
+Power Electronics um so beyond what's in
+ 
+
+ align:start position:0%
+Power Electronics um so beyond what's in
+the the basic magnetics chapter so it's
+
+ align:start position:0%
+the the basic magnetics chapter so it's
+ 
+
+ align:start position:0%
+the the basic magnetics chapter so it's
+a pretty deep topic if you really want
+
+ align:start position:0%
+a pretty deep topic if you really want
+ 
+
+ align:start position:0%
+a pretty deep topic if you really want
+to design very high performance things
+
+ align:start position:0%
+to design very high performance things
+ 
+
+ align:start position:0%
+to design very high performance things
+like how you predict the losses or
+
+ align:start position:0%
+like how you predict the losses or
+ 
+
+ align:start position:0%
+like how you predict the losses or
+calculate the losses and also magnetics
+
+ align:start position:0%
+calculate the losses and also magnetics
+ 
+
+ align:start position:0%
+calculate the losses and also magnetics
+design which is sort of the focus of uh
+
+ align:start position:0%
+design which is sort of the focus of uh
+ 
+
+ align:start position:0%
+design which is sort of the focus of uh
+principles Power Electronics chapter 20
+
+ align:start position:0%
+principles Power Electronics chapter 20
+ 
+
+ align:start position:0%
+principles Power Electronics chapter 20
+is also a pretty extensive topic
+
+ align:start position:0%
+is also a pretty extensive topic
+ 
+
+ align:start position:0%
+is also a pretty extensive topic
+nonetheless you can get pretty far with
+
+ align:start position:0%
+nonetheless you can get pretty far with
+ 
+
+ align:start position:0%
+nonetheless you can get pretty far with
+you know some basic information and we
+
+ align:start position:0%
+you know some basic information and we
+ 
+
+ align:start position:0%
+you know some basic information and we
+put up on the web just some basic
+
+ align:start position:0%
+put up on the web just some basic
+ 
+
+ align:start position:0%
+put up on the web just some basic
+inductor design tips and that should be
+
+ align:start position:0%
+inductor design tips and that should be
+ 
+
+ align:start position:0%
+inductor design tips and that should be
+enough to get you going um in today's
+
+ align:start position:0%
+enough to get you going um in today's
+ 
+
+ align:start position:0%
+enough to get you going um in today's
+lecture I'm going to go into magnetics
+
+ align:start position:0%
+lecture I'm going to go into magnetics
+ 
+
+ align:start position:0%
+lecture I'm going to go into magnetics
+loss
+
+ align:start position:0%
+loss
+ 
+
+ align:start position:0%
+loss
+and I'm going to wave my hands enough
+
+ align:start position:0%
+and I'm going to wave my hands enough
+ 
+
+ align:start position:0%
+and I'm going to wave my hands enough
+that you might start to feel a slight
+
+ align:start position:0%
+that you might start to feel a slight
+ 
+
+ align:start position:0%
+that you might start to feel a slight
+breeze in the sense that
+
+ align:start position:0%
+breeze in the sense that
+ 
+
+ align:start position:0%
+breeze in the sense that
+um I'm not going to jus ify or prove
+
+ align:start position:0%
+um I'm not going to jus ify or prove
+ 
+
+ align:start position:0%
+um I'm not going to jus ify or prove
+anything I say my goal is just to give
+
+ align:start position:0%
+anything I say my goal is just to give
+ 
+
+ align:start position:0%
+anything I say my goal is just to give
+you enough information so that you sort
+
+ align:start position:0%
+you enough information so that you sort
+ 
+
+ align:start position:0%
+you enough information so that you sort
+of know some things that you might look
+
+ align:start position:0%
+of know some things that you might look
+ 
+
+ align:start position:0%
+of know some things that you might look
+out for when you're designing magnetics
+
+ align:start position:0%
+out for when you're designing magnetics
+ 
+
+ align:start position:0%
+out for when you're designing magnetics
+and that's not going to you know the
+
+ align:start position:0%
+and that's not going to you know the
+ 
+
+ align:start position:0%
+and that's not going to you know the
+fact that I'm doing that's not going to
+
+ align:start position:0%
+fact that I'm doing that's not going to
+ 
+
+ align:start position:0%
+fact that I'm doing that's not going to
+prevent you from designing perfectly
+
+ align:start position:0%
+prevent you from designing perfectly
+ 
+
+ align:start position:0%
+prevent you from designing perfectly
+good inductors for your design project
+
+ align:start position:0%
+good inductors for your design project
+ 
+
+ align:start position:0%
+good inductors for your design project
+or or design a perfectly good
+
+ align:start position:0%
+or or design a perfectly good
+ 
+
+ align:start position:0%
+or or design a perfectly good
+Transformer but when you start to really
+
+ align:start position:0%
+Transformer but when you start to really
+ 
+
+ align:start position:0%
+Transformer but when you start to really
+want to push the envelope suddenly you
+
+ align:start position:0%
+want to push the envelope suddenly you
+ 
+
+ align:start position:0%
+want to push the envelope suddenly you
+got to start thinking about these
+
+ align:start position:0%
+got to start thinking about these
+ 
+
+ align:start position:0%
+got to start thinking about these
+effects I'm going to talk about pretty
+
+ align:start position:0%
+effects I'm going to talk about pretty
+ 
+
+ align:start position:0%
+effects I'm going to talk about pretty
+carefully
+
+ align:start position:0%
+carefully
+ 
+
+ align:start position:0%
+carefully
+okay so you know if I'm going to design
+
+ align:start position:0%
+okay so you know if I'm going to design
+ 
+
+ align:start position:0%
+okay so you know if I'm going to design
+a magnetic component
+
+ align:start position:0%
+a magnetic component
+ 
+
+ align:start position:0%
+a magnetic component
+I I really have to think about loss and
+
+ align:start position:0%
+I I really have to think about loss and
+ 
+
+ align:start position:0%
+I I really have to think about loss and
+loss is sort of important for two
+
+ align:start position:0%
+loss is sort of important for two
+ 
+
+ align:start position:0%
+loss is sort of important for two
+reasons if you have bad magnetic
+
+ align:start position:0%
+reasons if you have bad magnetic
+ 
+
+ align:start position:0%
+reasons if you have bad magnetic
+components right they tend to the
+
+ align:start position:0%
+components right they tend to the
+ 
+
+ align:start position:0%
+components right they tend to the
+magnetic components tend to be the
+
+ align:start position:0%
+magnetic components tend to be the
+ 
+
+ align:start position:0%
+magnetic components tend to be the
+dominant source of loss in a converter
+
+ align:start position:0%
+dominant source of loss in a converter
+ 
+
+ align:start position:0%
+dominant source of loss in a converter
+for the most part okay so in a typical
+
+ align:start position:0%
+for the most part okay so in a typical
+ 
+
+ align:start position:0%
+for the most part okay so in a typical
+design if you don't do a good job on the
+
+ align:start position:0%
+design if you don't do a good job on the
+ 
+
+ align:start position:0%
+design if you don't do a good job on the
+magnetics your efficiency is going to
+
+ align:start position:0%
+magnetics your efficiency is going to
+ 
+
+ align:start position:0%
+magnetics your efficiency is going to
+stink okay the second piece of it is is
+
+ align:start position:0%
+stink okay the second piece of it is is
+ 
+
+ align:start position:0%
+stink okay the second piece of it is is
+that what sets the size of the magnetic
+
+ align:start position:0%
+that what sets the size of the magnetic
+ 
+
+ align:start position:0%
+that what sets the size of the magnetic
+component is often the loss so what
+
+ align:start position:0%
+component is often the loss so what
+ 
+
+ align:start position:0%
+component is often the loss so what
+prevents you from making things smaller
+
+ align:start position:0%
+prevents you from making things smaller
+ 
+
+ align:start position:0%
+prevents you from making things smaller
+often is that if you make it too small
+
+ align:start position:0%
+often is that if you make it too small
+ 
+
+ align:start position:0%
+often is that if you make it too small
+it'll get too hot and you'll be out of
+
+ align:start position:0%
+it'll get too hot and you'll be out of
+ 
+
+ align:start position:0%
+it'll get too hot and you'll be out of
+luck okay so thinking about you know
+
+ align:start position:0%
+luck okay so thinking about you know
+ 
+
+ align:start position:0%
+luck okay so thinking about you know
+what are the loss mechanisms and what to
+
+ align:start position:0%
+what are the loss mechanisms and what to
+ 
+
+ align:start position:0%
+what are the loss mechanisms and what to
+watch out for is is what we want to pay
+
+ align:start position:0%
+watch out for is is what we want to pay
+ 
+
+ align:start position:0%
+watch out for is is what we want to pay
+attention to now if I have a typical
+
+ align:start position:0%
+attention to now if I have a typical
+ 
+
+ align:start position:0%
+attention to now if I have a typical
+magnetic component what do I have I have
+
+ align:start position:0%
+magnetic component what do I have I have
+ 
+
+ align:start position:0%
+magnetic component what do I have I have
+a winding and a core usually so the two
+
+ align:start position:0%
+a winding and a core usually so the two
+ 
+
+ align:start position:0%
+a winding and a core usually so the two
+subsets of losses I got to worry about
+
+ align:start position:0%
+subsets of losses I got to worry about
+ 
+
+ align:start position:0%
+subsets of losses I got to worry about
+or one the winding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+loss uh and sometimes this is called
+
+ align:start position:0%
+loss uh and sometimes this is called
+ 
+
+ align:start position:0%
+loss uh and sometimes this is called
+copper loss because most windings are
+
+ align:start position:0%
+copper loss because most windings are
+ 
+
+ align:start position:0%
+copper loss because most windings are
+made of copper you know typically copper
+
+ align:start position:0%
+made of copper you know typically copper
+ 
+
+ align:start position:0%
+made of copper you know typically copper
+wir it's used although aluminum wire is
+
+ align:start position:0%
+wir it's used although aluminum wire is
+ 
+
+ align:start position:0%
+wir it's used although aluminum wire is
+not infrequently used as well especially
+
+ align:start position:0%
+not infrequently used as well especially
+ 
+
+ align:start position:0%
+not infrequently used as well especially
+if you want something that's going to be
+
+ align:start position:0%
+if you want something that's going to be
+ 
+
+ align:start position:0%
+if you want something that's going to be
+very light because aluminum has better
+
+ align:start position:0%
+very light because aluminum has better
+ 
+
+ align:start position:0%
+very light because aluminum has better
+conductivity per unit mass than copper
+
+ align:start position:0%
+conductivity per unit mass than copper
+ 
+
+ align:start position:0%
+conductivity per unit mass than copper
+does uh the second thing is of course
+
+ align:start position:0%
+does uh the second thing is of course
+ 
+
+ align:start position:0%
+does uh the second thing is of course
+core
+
+ align:start position:0%
+core
+ 
+
+ align:start position:0%
+core
+loss okay and so we're going to consider
+
+ align:start position:0%
+loss okay and so we're going to consider
+ 
+
+ align:start position:0%
+loss okay and so we're going to consider
+each of these things today and just give
+
+ align:start position:0%
+each of these things today and just give
+ 
+
+ align:start position:0%
+each of these things today and just give
+you things some things to watch out
+
+ align:start position:0%
+you things some things to watch out
+ 
+
+ align:start position:0%
+you things some things to watch out
+for now at the most basic level if we're
+
+ align:start position:0%
+for now at the most basic level if we're
+ 
+
+ align:start position:0%
+for now at the most basic level if we're
+going to think about uh your winding
+
+ align:start position:0%
+going to think about uh your winding
+ 
+
+ align:start position:0%
+going to think about uh your winding
+loss okay you know you're going to wind
+
+ align:start position:0%
+loss okay you know you're going to wind
+ 
+
+ align:start position:0%
+loss okay you know you're going to wind
+so suppose we're designing inductor
+
+ align:start position:0%
+so suppose we're designing inductor
+ 
+
+ align:start position:0%
+so suppose we're designing inductor
+you're going to wind a bunch of turns
+
+ align:start position:0%
+you're going to wind a bunch of turns
+ 
+
+ align:start position:0%
+you're going to wind a bunch of turns
+typically on a bobin that's going to go
+
+ align:start position:0%
+typically on a bobin that's going to go
+ 
+
+ align:start position:0%
+typically on a bobin that's going to go
+on a core right so just to give you an
+
+ align:start position:0%
+on a core right so just to give you an
+ 
+
+ align:start position:0%
+on a core right so just to give you an
+example if you look at this um in the
+
+ align:start position:0%
+example if you look at this um in the
+ 
+
+ align:start position:0%
+example if you look at this um in the
+top right here right this is sort of a
+
+ align:start position:0%
+top right here right this is sort of a
+ 
+
+ align:start position:0%
+top right here right this is sort of a
+half of a core and then you put two of
+
+ align:start position:0%
+half of a core and then you put two of
+ 
+
+ align:start position:0%
+half of a core and then you put two of
+those half of a cores together and you
+
+ align:start position:0%
+those half of a cores together and you
+ 
+
+ align:start position:0%
+those half of a cores together and you
+might grind the center post to give you
+
+ align:start position:0%
+might grind the center post to give you
+ 
+
+ align:start position:0%
+might grind the center post to give you
+a Gap to store the energy in you would
+
+ align:start position:0%
+a Gap to store the energy in you would
+ 
+
+ align:start position:0%
+a Gap to store the energy in you would
+tend to wind your windings around the
+
+ align:start position:0%
+tend to wind your windings around the
+ 
+
+ align:start position:0%
+tend to wind your windings around the
+center post okay so if you're going to
+
+ align:start position:0%
+center post okay so if you're going to
+ 
+
+ align:start position:0%
+center post okay so if you're going to
+have an inductor you're going to wind it
+
+ align:start position:0%
+have an inductor you're going to wind it
+ 
+
+ align:start position:0%
+have an inductor you're going to wind it
+with some length of wire right so what's
+
+ align:start position:0%
+with some length of wire right so what's
+ 
+
+ align:start position:0%
+with some length of wire right so what's
+it a
+
+ align:start position:0%
+it a
+ 
+
+ align:start position:0%
+it a
+DC right the resistance of the
+
+ align:start position:0%
+DC right the resistance of the
+ 
+
+ align:start position:0%
+DC right the resistance of the
+wire is simply going to be row times the
+
+ align:start position:0%
+wire is simply going to be row times the
+ 
+
+ align:start position:0%
+wire is simply going to be row times the
+length of the wire divided by the area
+
+ align:start position:0%
+length of the wire divided by the area
+ 
+
+ align:start position:0%
+length of the wire divided by the area
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+wire right so you would often pick your
+
+ align:start position:0%
+wire right so you would often pick your
+ 
+
+ align:start position:0%
+wire right so you would often pick your
+wire gauge to give you a certain area
+
+ align:start position:0%
+wire gauge to give you a certain area
+ 
+
+ align:start position:0%
+wire gauge to give you a certain area
+you'll have some length you wind it up
+
+ align:start position:0%
+you'll have some length you wind it up
+ 
+
+ align:start position:0%
+you'll have some length you wind it up
+and resistivity times length over area
+
+ align:start position:0%
+and resistivity times length over area
+ 
+
+ align:start position:0%
+and resistivity times length over area
+is your wire resistance okay one thing
+
+ align:start position:0%
+is your wire resistance okay one thing
+ 
+
+ align:start position:0%
+is your wire resistance okay one thing
+I'll just give you sort of a a heads up
+
+ align:start position:0%
+I'll just give you sort of a a heads up
+ 
+
+ align:start position:0%
+I'll just give you sort of a a heads up
+just to pay attention to is that if you
+
+ align:start position:0%
+just to pay attention to is that if you
+ 
+
+ align:start position:0%
+just to pay attention to is that if you
+think about the resistivity which is you
+
+ align:start position:0%
+think about the resistivity which is you
+ 
+
+ align:start position:0%
+think about the resistivity which is you
+know the resistivity of copper it's
+
+ align:start position:0%
+know the resistivity of copper it's
+ 
+
+ align:start position:0%
+know the resistivity of copper it's
+actually a pretty strong function of
+
+ align:start position:0%
+actually a pretty strong function of
+ 
+
+ align:start position:0%
+actually a pretty strong function of
+temperature if you raise the temperature
+
+ align:start position:0%
+temperature if you raise the temperature
+ 
+
+ align:start position:0%
+temperature if you raise the temperature
+by 100 degrees C which is a lot but not
+
+ align:start position:0%
+by 100 degrees C which is a lot but not
+ 
+
+ align:start position:0%
+by 100 degrees C which is a lot but not
+necessarily unreasonable the resistivity
+
+ align:start position:0%
+necessarily unreasonable the resistivity
+ 
+
+ align:start position:0%
+necessarily unreasonable the resistivity
+of the wire tends to go up by about 40%
+
+ align:start position:0%
+of the wire tends to go up by about 40%
+ 
+
+ align:start position:0%
+of the wire tends to go up by about 40%
+because that's just a characteristic of
+
+ align:start position:0%
+because that's just a characteristic of
+ 
+
+ align:start position:0%
+because that's just a characteristic of
+copper okay so usually you want to use
+
+ align:start position:0%
+copper okay so usually you want to use
+ 
+
+ align:start position:0%
+copper okay so usually you want to use
+the resistivity at whatever the maximum
+
+ align:start position:0%
+the resistivity at whatever the maximum
+ 
+
+ align:start position:0%
+the resistivity at whatever the maximum
+temperature you think your wire is going
+
+ align:start position:0%
+temperature you think your wire is going
+ 
+
+ align:start position:0%
+temperature you think your wire is going
+to get to because that's sort of the
+
+ align:start position:0%
+to get to because that's sort of the
+ 
+
+ align:start position:0%
+to get to because that's sort of the
+worst case and that's going to give you
+
+ align:start position:0%
+worst case and that's going to give you
+ 
+
+ align:start position:0%
+worst case and that's going to give you
+the largest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resistance so then you'd calculate your
+
+ align:start position:0%
+resistance so then you'd calculate your
+ 
+
+ align:start position:0%
+resistance so then you'd calculate your
+loss uh if you're only considering this
+
+ align:start position:0%
+loss uh if you're only considering this
+ 
+
+ align:start position:0%
+loss uh if you're only considering this
+is the DC
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resistance okay and we'll come back to
+
+ align:start position:0%
+resistance okay and we'll come back to
+ 
+
+ align:start position:0%
+resistance okay and we'll come back to
+that right uh Power is just going to be
+
+ align:start position:0%
+that right uh Power is just going to be
+ 
+
+ align:start position:0%
+that right uh Power is just going to be
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+irms squared time r
+
+ align:start position:0%
+irms squared time r
+ 
+
+ align:start position:0%
+irms squared time r
+y okay if the RMS is dominated by the DC
+
+ align:start position:0%
+y okay if the RMS is dominated by the DC
+ 
+
+ align:start position:0%
+y okay if the RMS is dominated by the DC
+component you have almost a current
+
+ align:start position:0%
+component you have almost a current
+ 
+
+ align:start position:0%
+component you have almost a current
+component then RMS is close to IDC and
+
+ align:start position:0%
+component then RMS is close to IDC and
+ 
+
+ align:start position:0%
+component then RMS is close to IDC and
+you might get IDC 2times r y okay so
+
+ align:start position:0%
+you might get IDC 2times r y okay so
+ 
+
+ align:start position:0%
+you might get IDC 2times r y okay so
+pretty straightforward to calculate and
+
+ align:start position:0%
+pretty straightforward to calculate and
+ 
+
+ align:start position:0%
+pretty straightforward to calculate and
+so the CH trade-off you're making is you
+
+ align:start position:0%
+so the CH trade-off you're making is you
+ 
+
+ align:start position:0%
+so the CH trade-off you're making is you
+know how fat do you want the wire to
+
+ align:start position:0%
+know how fat do you want the wire to
+ 
+
+ align:start position:0%
+know how fat do you want the wire to
+be and you know how much length of it
+
+ align:start position:0%
+be and you know how much length of it
+ 
+
+ align:start position:0%
+be and you know how much length of it
+you need to get to get your loss low
+
+ align:start position:0%
+you need to get to get your loss low
+ 
+
+ align:start position:0%
+you need to get to get your loss low
+enough
+
+ align:start position:0%
+enough
+ 
+
+ align:start position:0%
+enough
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um something that does come up is and
+
+ align:start position:0%
+um something that does come up is and
+ 
+
+ align:start position:0%
+um something that does come up is and
+and the reason why I'm talking about
+
+ align:start position:0%
+and the reason why I'm talking about
+ 
+
+ align:start position:0%
+and the reason why I'm talking about
+this wire
+
+ align:start position:0%
+this wire
+ 
+
+ align:start position:0%
+this wire
+area is because you know we're going to
+
+ align:start position:0%
+area is because you know we're going to
+ 
+
+ align:start position:0%
+area is because you know we're going to
+fit our turns you know sort of in this
+
+ align:start position:0%
+fit our turns you know sort of in this
+ 
+
+ align:start position:0%
+fit our turns you know sort of in this
+window right so there's some
+
+ align:start position:0%
+window right so there's some
+ 
+
+ align:start position:0%
+window right so there's some
+cross-sectional area the area of the
+
+ align:start position:0%
+cross-sectional area the area of the
+ 
+
+ align:start position:0%
+cross-sectional area the area of the
+window that you can put your turns of
+
+ align:start position:0%
+window that you can put your turns of
+ 
+
+ align:start position:0%
+window that you can put your turns of
+wire in right and So eventually you can
+
+ align:start position:0%
+wire in right and So eventually you can
+ 
+
+ align:start position:0%
+wire in right and So eventually you can
+only put put so many turns of a certain
+
+ align:start position:0%
+only put put so many turns of a certain
+ 
+
+ align:start position:0%
+only put put so many turns of a certain
+gauge wire before you run out of window
+
+ align:start position:0%
+gauge wire before you run out of window
+ 
+
+ align:start position:0%
+gauge wire before you run out of window
+room right but then you say well I can
+
+ align:start position:0%
+room right but then you say well I can
+ 
+
+ align:start position:0%
+room right but then you say well I can
+use a small wire and put a lot of
+
+ align:start position:0%
+use a small wire and put a lot of
+ 
+
+ align:start position:0%
+use a small wire and put a lot of
+current through it right and yeah maybe
+
+ align:start position:0%
+current through it right and yeah maybe
+ 
+
+ align:start position:0%
+current through it right and yeah maybe
+you can but you got to worry about
+
+ align:start position:0%
+you can but you got to worry about
+ 
+
+ align:start position:0%
+you can but you got to worry about
+overheating things right so something
+
+ align:start position:0%
+overheating things right so something
+ 
+
+ align:start position:0%
+overheating things right so something
+that often comes up when you're doing
+
+ align:start position:0%
+that often comes up when you're doing
+ 
+
+ align:start position:0%
+that often comes up when you're doing
+this is exactly how much current can I
+
+ align:start position:0%
+this is exactly how much current can I
+ 
+
+ align:start position:0%
+this is exactly how much current can I
+put through that piece of wire okay so
+
+ align:start position:0%
+put through that piece of wire okay so
+ 
+
+ align:start position:0%
+put through that piece of wire okay so
+if I wanted to say you know what's the r
+
+ align:start position:0%
+if I wanted to say you know what's the r
+ 
+
+ align:start position:0%
+if I wanted to say you know what's the r
+allowable RMS current maybe that can my
+
+ align:start position:0%
+allowable RMS current maybe that can my
+ 
+
+ align:start position:0%
+allowable RMS current maybe that can my
+wire can carry and that's an interesting
+
+ align:start position:0%
+wire can carry and that's an interesting
+ 
+
+ align:start position:0%
+wire can carry and that's an interesting
+question question because there's not a
+
+ align:start position:0%
+question question because there's not a
+ 
+
+ align:start position:0%
+question question because there's not a
+single answer to that question right
+
+ align:start position:0%
+single answer to that question right
+ 
+
+ align:start position:0%
+single answer to that question right
+it's usually dictated by how hot things
+
+ align:start position:0%
+it's usually dictated by how hot things
+ 
+
+ align:start position:0%
+it's usually dictated by how hot things
+are going to get okay and that in turn
+
+ align:start position:0%
+are going to get okay and that in turn
+ 
+
+ align:start position:0%
+are going to get okay and that in turn
+makes it dependent on heat transfer now
+
+ align:start position:0%
+makes it dependent on heat transfer now
+ 
+
+ align:start position:0%
+makes it dependent on heat transfer now
+we haven't really talked about thermal
+
+ align:start position:0%
+we haven't really talked about thermal
+ 
+
+ align:start position:0%
+we haven't really talked about thermal
+models and heat transfer yet and we will
+
+ align:start position:0%
+models and heat transfer yet and we will
+ 
+
+ align:start position:0%
+models and heat transfer yet and we will
+um but generally people often will work
+
+ align:start position:0%
+um but generally people often will work
+ 
+
+ align:start position:0%
+um but generally people often will work
+by some kind of rule of thumb to start
+
+ align:start position:0%
+by some kind of rule of thumb to start
+ 
+
+ align:start position:0%
+by some kind of rule of thumb to start
+right like in the end you're going to
+
+ align:start position:0%
+right like in the end you're going to
+ 
+
+ align:start position:0%
+right like in the end you're going to
+end up with a design you're going to
+
+ align:start position:0%
+end up with a design you're going to
+ 
+
+ align:start position:0%
+end up with a design you're going to
+find out if it gets too hot or not but
+
+ align:start position:0%
+find out if it gets too hot or not but
+ 
+
+ align:start position:0%
+find out if it gets too hot or not but
+as a place to start start you might take
+
+ align:start position:0%
+as a place to start start you might take
+ 
+
+ align:start position:0%
+as a place to start start you might take
+a guess at the current density
+
+ align:start position:0%
+a guess at the current density
+ 
+
+ align:start position:0%
+a guess at the current density
+J that's an amps per meter squ amps per
+
+ align:start position:0%
+J that's an amps per meter squ amps per
+ 
+
+ align:start position:0%
+J that's an amps per meter squ amps per
+centimeter squared or something right
+
+ align:start position:0%
+centimeter squared or something right
+ 
+
+ align:start position:0%
+centimeter squared or something right
+and the question is um you know how much
+
+ align:start position:0%
+and the question is um you know how much
+ 
+
+ align:start position:0%
+and the question is um you know how much
+current density how many amps per meter
+
+ align:start position:0%
+current density how many amps per meter
+ 
+
+ align:start position:0%
+current density how many amps per meter
+squared can I put my through my wire
+
+ align:start position:0%
+squared can I put my through my wire
+ 
+
+ align:start position:0%
+squared can I put my through my wire
+okay and that number depends on size
+
+ align:start position:0%
+okay and that number depends on size
+ 
+
+ align:start position:0%
+okay and that number depends on size
+right if I have something really big
+
+ align:start position:0%
+right if I have something really big
+ 
+
+ align:start position:0%
+right if I have something really big
+right there's a long distance to get
+
+ align:start position:0%
+right there's a long distance to get
+ 
+
+ align:start position:0%
+right there's a long distance to get
+heat out it has a very high
+
+ align:start position:0%
+heat out it has a very high
+ 
+
+ align:start position:0%
+heat out it has a very high
+volume to surface area ratio right
+
+ align:start position:0%
+volume to surface area ratio right
+ 
+
+ align:start position:0%
+volume to surface area ratio right
+because volume goes as the cube and
+
+ align:start position:0%
+because volume goes as the cube and
+ 
+
+ align:start position:0%
+because volume goes as the cube and
+surface area only goes as the square of
+
+ align:start position:0%
+surface area only goes as the square of
+ 
+
+ align:start position:0%
+surface area only goes as the square of
+linear Dimension right so if you have
+
+ align:start position:0%
+linear Dimension right so if you have
+ 
+
+ align:start position:0%
+linear Dimension right so if you have
+something small it's easy to get heat
+
+ align:start position:0%
+something small it's easy to get heat
+ 
+
+ align:start position:0%
+something small it's easy to get heat
+out of it if you have something big it's
+
+ align:start position:0%
+out of it if you have something big it's
+ 
+
+ align:start position:0%
+out of it if you have something big it's
+hard to get heat out of it so typically
+
+ align:start position:0%
+hard to get heat out of it so typically
+ 
+
+ align:start position:0%
+hard to get heat out of it so typically
+the current densities you can use depend
+
+ align:start position:0%
+the current densities you can use depend
+ 
+
+ align:start position:0%
+the current densities you can use depend
+upon how big the thing you're building
+
+ align:start position:0%
+upon how big the thing you're building
+ 
+
+ align:start position:0%
+upon how big the thing you're building
+is smaller you can use higher current
+
+ align:start position:0%
+is smaller you can use higher current
+ 
+
+ align:start position:0%
+is smaller you can use higher current
+densities a typical
+
+ align:start position:0%
+densities a typical
+ 
+
+ align:start position:0%
+densities a typical
+number might be on the order of 500 amps
+
+ align:start position:0%
+number might be on the order of 500 amps
+ 
+
+ align:start position:0%
+number might be on the order of 500 amps
+per centimeter
+
+ align:start position:0%
+per centimeter
+ 
+
+ align:start position:0%
+per centimeter
+squared we're talking about RMS values
+
+ align:start position:0%
+squared we're talking about RMS values
+ 
+
+ align:start position:0%
+squared we're talking about RMS values
+okay but again it depends on scale this
+
+ align:start position:0%
+okay but again it depends on scale this
+ 
+
+ align:start position:0%
+okay but again it depends on scale this
+chart which I've pulled out of uh
+
+ align:start position:0%
+chart which I've pulled out of uh
+ 
+
+ align:start position:0%
+chart which I've pulled out of uh
+kpvs uh what it shows is if I if I took
+
+ align:start position:0%
+kpvs uh what it shows is if I if I took
+ 
+
+ align:start position:0%
+kpvs uh what it shows is if I if I took
+this kind of core which is known as an
+
+ align:start position:0%
+this kind of core which is known as an
+ 
+
+ align:start position:0%
+this kind of core which is known as an
+RM core rectangular modular
+
+ align:start position:0%
+RM core rectangular modular
+ 
+
+ align:start position:0%
+RM core rectangular modular
+core uh rm4 core is really small rm14
+
+ align:start position:0%
+core uh rm4 core is really small rm14
+ 
+
+ align:start position:0%
+core uh rm4 core is really small rm14
+core is the biggest it's maybe getting
+
+ align:start position:0%
+core is the biggest it's maybe getting
+ 
+
+ align:start position:0%
+core is the biggest it's maybe getting
+close to the size of my fist um and this
+
+ align:start position:0%
+close to the size of my fist um and this
+ 
+
+ align:start position:0%
+close to the size of my fist um and this
+shows if I have
+
+ align:start position:0%
+shows if I have
+ 
+
+ align:start position:0%
+shows if I have
+only winding loss how hot will the thing
+
+ align:start position:0%
+only winding loss how hot will the thing
+ 
+
+ align:start position:0%
+only winding loss how hot will the thing
+get based on measured data and what we
+
+ align:start position:0%
+get based on measured data and what we
+ 
+
+ align:start position:0%
+get based on measured data and what we
+can see is you know maybe you have a few
+
+ align:start position:0%
+can see is you know maybe you have a few
+ 
+
+ align:start position:0%
+can see is you know maybe you have a few
+hundred watts per centimeter squared for
+
+ align:start position:0%
+hundred watts per centimeter squared for
+ 
+
+ align:start position:0%
+hundred watts per centimeter squared for
+a big element and maybe much higher for
+
+ align:start position:0%
+a big element and maybe much higher for
+ 
+
+ align:start position:0%
+a big element and maybe much higher for
+a small element this is for a 25 degre C
+
+ align:start position:0%
+a small element this is for a 25 degre C
+ 
+
+ align:start position:0%
+a small element this is for a 25 degre C
+rise on the one hand maybe you can take
+
+ align:start position:0%
+rise on the one hand maybe you can take
+ 
+
+ align:start position:0%
+rise on the one hand maybe you can take
+more than a 25 degree C rise It's Not
+
+ align:start position:0%
+more than a 25 degree C rise It's Not
+ 
+
+ align:start position:0%
+more than a 25 degree C rise It's Not
+Unusual to have 50 on the other hand you
+
+ align:start position:0%
+Unusual to have 50 on the other hand you
+ 
+
+ align:start position:0%
+Unusual to have 50 on the other hand you
+also have other losses besides the
+
+ align:start position:0%
+also have other losses besides the
+ 
+
+ align:start position:0%
+also have other losses besides the
+winding loss so maybe this is kind of
+
+ align:start position:0%
+winding loss so maybe this is kind of
+ 
+
+ align:start position:0%
+winding loss so maybe this is kind of
+Representative of what might be
+
+ align:start position:0%
+Representative of what might be
+ 
+
+ align:start position:0%
+Representative of what might be
+allowable for current densities and so
+
+ align:start position:0%
+allowable for current densities and so
+ 
+
+ align:start position:0%
+allowable for current densities and so
+you can see my you know my number of
+
+ align:start position:0%
+you can see my you know my number of
+ 
+
+ align:start position:0%
+you can see my you know my number of
+five 100 amp SARS right here so you know
+
+ align:start position:0%
+five 100 amp SARS right here so you know
+ 
+
+ align:start position:0%
+five 100 amp SARS right here so you know
+typically you might start your design
+
+ align:start position:0%
+typically you might start your design
+ 
+
+ align:start position:0%
+typically you might start your design
+off and say you know if it's big maybe
+
+ align:start position:0%
+off and say you know if it's big maybe
+ 
+
+ align:start position:0%
+off and say you know if it's big maybe
+I'll use one or 200 amps centimet
+
+ align:start position:0%
+I'll use one or 200 amps centimet
+ 
+
+ align:start position:0%
+I'll use one or 200 amps centimet
+squared is my guess if it's smaller
+
+ align:start position:0%
+squared is my guess if it's smaller
+ 
+
+ align:start position:0%
+squared is my guess if it's smaller
+maybe I'll go to 500 amps per cenim squ
+
+ align:start position:0%
+maybe I'll go to 500 amps per cenim squ
+ 
+
+ align:start position:0%
+maybe I'll go to 500 amps per cenim squ
+or even a little bit higher and then
+
+ align:start position:0%
+or even a little bit higher and then
+ 
+
+ align:start position:0%
+or even a little bit higher and then
+what's really going to limit me is how
+
+ align:start position:0%
+what's really going to limit me is how
+ 
+
+ align:start position:0%
+what's really going to limit me is how
+hot does the thing
+
+ align:start position:0%
+hot does the thing
+ 
+
+ align:start position:0%
+hot does the thing
+get any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay um that's all well and good and
+
+ align:start position:0%
+okay um that's all well and good and
+ 
+
+ align:start position:0%
+okay um that's all well and good and
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+a basic notion you know here's how I
+
+ align:start position:0%
+a basic notion you know here's how I
+ 
+
+ align:start position:0%
+a basic notion you know here's how I
+calculate my winding loss uh I want to
+
+ align:start position:0%
+calculate my winding loss uh I want to
+ 
+
+ align:start position:0%
+calculate my winding loss uh I want to
+fit a lot of turns in a small
+
+ align:start position:0%
+fit a lot of turns in a small
+ 
+
+ align:start position:0%
+fit a lot of turns in a small
+cross-sectional area so I got to pick an
+
+ align:start position:0%
+cross-sectional area so I got to pick an
+ 
+
+ align:start position:0%
+cross-sectional area so I got to pick an
+a wire and I'm going to be limited by
+
+ align:start position:0%
+a wire and I'm going to be limited by
+ 
+
+ align:start position:0%
+a wire and I'm going to be limited by
+how much current I can carry in that
+
+ align:start position:0%
+how much current I can carry in that
+ 
+
+ align:start position:0%
+how much current I can carry in that
+wire by some number that I make an
+
+ align:start position:0%
+wire by some number that I make an
+ 
+
+ align:start position:0%
+wire by some number that I make an
+estimate at and then go figure out how
+
+ align:start position:0%
+estimate at and then go figure out how
+ 
+
+ align:start position:0%
+estimate at and then go figure out how
+hot it gets
+
+ align:start position:0%
+hot it gets
+ 
+
+ align:start position:0%
+hot it gets
+afterwards
+
+ align:start position:0%
+afterwards
+ 
+
+ align:start position:0%
+afterwards
+um there are however other effects okay
+
+ align:start position:0%
+um there are however other effects okay
+ 
+
+ align:start position:0%
+um there are however other effects okay
+and chief among these is what happens at
+
+ align:start position:0%
+and chief among these is what happens at
+ 
+
+ align:start position:0%
+and chief among these is what happens at
+High
+
+ align:start position:0%
+High
+ 
+
+ align:start position:0%
+High
+frequency so all of this this
+
+ align:start position:0%
+frequency so all of this this
+ 
+
+ align:start position:0%
+frequency so all of this this
+calculation of the resistance is the DC
+
+ align:start position:0%
+calculation of the resistance is the DC
+ 
+
+ align:start position:0%
+calculation of the resistance is the DC
+resistance this is what happens if I put
+
+ align:start position:0%
+resistance this is what happens if I put
+ 
+
+ align:start position:0%
+resistance this is what happens if I put
+a constant current Through the Wire if I
+
+ align:start position:0%
+a constant current Through the Wire if I
+ 
+
+ align:start position:0%
+a constant current Through the Wire if I
+put a current that varies very quickly
+
+ align:start position:0%
+put a current that varies very quickly
+ 
+
+ align:start position:0%
+put a current that varies very quickly
+in time through a big wire what happens
+
+ align:start position:0%
+in time through a big wire what happens
+ 
+
+ align:start position:0%
+in time through a big wire what happens
+is I don't get to use the full wire
+
+ align:start position:0%
+is I don't get to use the full wire
+ 
+
+ align:start position:0%
+is I don't get to use the full wire
+cross-section okay there are two
+
+ align:start position:0%
+cross-section okay there are two
+ 
+
+ align:start position:0%
+cross-section okay there are two
+effects uh one is known as Skin effect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that I'm going to talk about now and
+
+ align:start position:0%
+that I'm going to talk about now and
+ 
+
+ align:start position:0%
+that I'm going to talk about now and
+here's the idea suppose I had some wire
+
+ align:start position:0%
+here's the idea suppose I had some wire
+ 
+
+ align:start position:0%
+here's the idea suppose I had some wire
+okay here's some length of
+
+ align:start position:0%
+okay here's some length of
+ 
+
+ align:start position:0%
+okay here's some length of
+wire and I put some current through it
+
+ align:start position:0%
+wire and I put some current through it
+ 
+
+ align:start position:0%
+wire and I put some current through it
+now at DC what I expect is that current
+
+ align:start position:0%
+now at DC what I expect is that current
+ 
+
+ align:start position:0%
+now at DC what I expect is that current
+if it's going down the wire to kind of
+
+ align:start position:0%
+if it's going down the wire to kind of
+ 
+
+ align:start position:0%
+if it's going down the wire to kind of
+distribute itself evenly across the
+
+ align:start position:0%
+distribute itself evenly across the
+ 
+
+ align:start position:0%
+distribute itself evenly across the
+volume of the wire right evenly across
+
+ align:start position:0%
+volume of the wire right evenly across
+ 
+
+ align:start position:0%
+volume of the wire right evenly across
+the cross-section of the wire and that's
+
+ align:start position:0%
+the cross-section of the wire and that's
+ 
+
+ align:start position:0%
+the cross-section of the wire and that's
+that and that's what you get right the
+
+ align:start position:0%
+that and that's what you get right the
+ 
+
+ align:start position:0%
+that and that's what you get right the
+current will just spread out be carried
+
+ align:start position:0%
+current will just spread out be carried
+ 
+
+ align:start position:0%
+current will just spread out be carried
+evenly everywhere in the wire okay but
+
+ align:start position:0%
+evenly everywhere in the wire okay but
+ 
+
+ align:start position:0%
+evenly everywhere in the wire okay but
+now I have this AC current going into
+
+ align:start position:0%
+now I have this AC current going into
+ 
+
+ align:start position:0%
+now I have this AC current going into
+the wire okay and that AC current
+
+ align:start position:0%
+the wire okay and that AC current
+ 
+
+ align:start position:0%
+the wire okay and that AC current
+develops a magnetic field right so the
+
+ align:start position:0%
+develops a magnetic field right so the
+ 
+
+ align:start position:0%
+develops a magnetic field right so the
+the current that's in the middle of the
+
+ align:start position:0%
+the current that's in the middle of the
+ 
+
+ align:start position:0%
+the current that's in the middle of the
+wire um is going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generate an H field in the wire and
+
+ align:start position:0%
+generate an H field in the wire and
+ 
+
+ align:start position:0%
+generate an H field in the wire and
+hence a b field in the wire and that
+
+ align:start position:0%
+hence a b field in the wire and that
+ 
+
+ align:start position:0%
+hence a b field in the wire and that
+represents magnetic flux being carried
+
+ align:start position:0%
+represents magnetic flux being carried
+ 
+
+ align:start position:0%
+represents magnetic flux being carried
+around inside the
+
+ align:start position:0%
+around inside the
+ 
+
+ align:start position:0%
+around inside the
+wire right but what do we know about
+
+ align:start position:0%
+wire right but what do we know about
+ 
+
+ align:start position:0%
+wire right but what do we know about
+something that generates a
+
+ align:start position:0%
+something that generates a
+ 
+
+ align:start position:0%
+something that generates a
+dbdt a change in magnetic flux density
+
+ align:start position:0%
+dbdt a change in magnetic flux density
+ 
+
+ align:start position:0%
+dbdt a change in magnetic flux density
+We Know by Faraday law that generates a
+
+ align:start position:0%
+We Know by Faraday law that generates a
+ 
+
+ align:start position:0%
+We Know by Faraday law that generates a
+voltage right and that voltage that you
+
+ align:start position:0%
+voltage right and that voltage that you
+ 
+
+ align:start position:0%
+voltage right and that voltage that you
+generate is going to cause essentially
+
+ align:start position:0%
+generate is going to cause essentially
+ 
+
+ align:start position:0%
+generate is going to cause essentially
+Eddy currents to circulate within the
+
+ align:start position:0%
+Eddy currents to circulate within the
+ 
+
+ align:start position:0%
+Eddy currents to circulate within the
+wire and they're going to try to reject
+
+ align:start position:0%
+wire and they're going to try to reject
+ 
+
+ align:start position:0%
+wire and they're going to try to reject
+the change in magnetic flux density in
+
+ align:start position:0%
+the change in magnetic flux density in
+ 
+
+ align:start position:0%
+the change in magnetic flux density in
+The Wire right so what you're going to
+
+ align:start position:0%
+The Wire right so what you're going to
+ 
+
+ align:start position:0%
+The Wire right so what you're going to
+get is induced EDD currents that do
+
+ align:start position:0%
+get is induced EDD currents that do
+ 
+
+ align:start position:0%
+get is induced EDD currents that do
+something like this they're going to
+
+ align:start position:0%
+something like this they're going to
+ 
+
+ align:start position:0%
+something like this they're going to
+come up the wire in the
+
+ align:start position:0%
+come up the wire in the
+ 
+
+ align:start position:0%
+come up the wire in the
+middle and go down the wire on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outside okay and so what's going to
+
+ align:start position:0%
+outside okay and so what's going to
+ 
+
+ align:start position:0%
+outside okay and so what's going to
+happen is in
+
+ align:start position:0%
+happen is in
+ 
+
+ align:start position:0%
+happen is in
+net the current in the middle of the
+
+ align:start position:0%
+net the current in the middle of the
+ 
+
+ align:start position:0%
+net the current in the middle of the
+wire will start to
+
+ align:start position:0%
+wire will start to
+ 
+
+ align:start position:0%
+wire will start to
+cancel okay and so what you will get if
+
+ align:start position:0%
+cancel okay and so what you will get if
+ 
+
+ align:start position:0%
+cancel okay and so what you will get if
+you go to a high enough frequency is
+
+ align:start position:0%
+you go to a high enough frequency is
+ 
+
+ align:start position:0%
+you go to a high enough frequency is
+that the net currents will only be
+
+ align:start position:0%
+that the net currents will only be
+ 
+
+ align:start position:0%
+that the net currents will only be
+carried essentially
+
+ align:start position:0%
+carried essentially
+ 
+
+ align:start position:0%
+carried essentially
+if I if I just said where is the net
+
+ align:start position:0%
+if I if I just said where is the net
+ 
+
+ align:start position:0%
+if I if I just said where is the net
+current will be carried only in a
+
+ align:start position:0%
+current will be carried only in a
+ 
+
+ align:start position:0%
+current will be carried only in a
+band around the surface of the wire
+
+ align:start position:0%
+band around the surface of the wire
+ 
+
+ align:start position:0%
+band around the surface of the wire
+right so instead of getting the full
+
+ align:start position:0%
+right so instead of getting the full
+ 
+
+ align:start position:0%
+right so instead of getting the full
+wire cross-section at high
+
+ align:start position:0%
+wire cross-section at high
+ 
+
+ align:start position:0%
+wire cross-section at high
+frequency you will only get to use the
+
+ align:start position:0%
+frequency you will only get to use the
+ 
+
+ align:start position:0%
+frequency you will only get to use the
+surface of the wire okay that's what's
+
+ align:start position:0%
+surface of the wire okay that's what's
+ 
+
+ align:start position:0%
+surface of the wire okay that's what's
+known as Skin effect why does this
+
+ align:start position:0%
+known as Skin effect why does this
+ 
+
+ align:start position:0%
+known as Skin effect why does this
+happen it happens exactly for these
+
+ align:start position:0%
+happen it happens exactly for these
+ 
+
+ align:start position:0%
+happen it happens exactly for these
+Eddie current reasons to actually solve
+
+ align:start position:0%
+Eddie current reasons to actually solve
+ 
+
+ align:start position:0%
+Eddie current reasons to actually solve
+things you generate what's known as a
+
+ align:start position:0%
+things you generate what's known as a
+ 
+
+ align:start position:0%
+things you generate what's known as a
+magnetic diffusion equation you solve it
+
+ align:start position:0%
+magnetic diffusion equation you solve it
+ 
+
+ align:start position:0%
+magnetic diffusion equation you solve it
+and you can solve for what is the
+
+ align:start position:0%
+and you can solve for what is the
+ 
+
+ align:start position:0%
+and you can solve for what is the
+current density profile going in from
+
+ align:start position:0%
+current density profile going in from
+ 
+
+ align:start position:0%
+current density profile going in from
+the surface of the wire
+
+ align:start position:0%
+the surface of the wire
+ 
+
+ align:start position:0%
+the surface of the wire
+okay um this is kind of annoying right
+
+ align:start position:0%
+okay um this is kind of annoying right
+ 
+
+ align:start position:0%
+okay um this is kind of annoying right
+because you know I got certain amount of
+
+ align:start position:0%
+because you know I got certain amount of
+ 
+
+ align:start position:0%
+because you know I got certain amount of
+wire and I wanted to use it to carry
+
+ align:start position:0%
+wire and I wanted to use it to carry
+ 
+
+ align:start position:0%
+wire and I wanted to use it to carry
+current and now what I'm telling you is
+
+ align:start position:0%
+current and now what I'm telling you is
+ 
+
+ align:start position:0%
+current and now what I'm telling you is
+if the frequency is high enough I don't
+
+ align:start position:0%
+if the frequency is high enough I don't
+ 
+
+ align:start position:0%
+if the frequency is high enough I don't
+get to use all the wire and I've just
+
+ align:start position:0%
+get to use all the wire and I've just
+ 
+
+ align:start position:0%
+get to use all the wire and I've just
+got this dead space in the middle of my
+
+ align:start position:0%
+got this dead space in the middle of my
+ 
+
+ align:start position:0%
+got this dead space in the middle of my
+wire and I'm not getting to use it okay
+
+ align:start position:0%
+wire and I'm not getting to use it okay
+ 
+
+ align:start position:0%
+wire and I'm not getting to use it okay
+well I said that's at high frequency and
+
+ align:start position:0%
+well I said that's at high frequency and
+ 
+
+ align:start position:0%
+well I said that's at high frequency and
+low frequency what do I mean by that
+
+ align:start position:0%
+low frequency what do I mean by that
+ 
+
+ align:start position:0%
+low frequency what do I mean by that
+there's something called The Skin depth
+
+ align:start position:0%
+there's something called The Skin depth
+ 
+
+ align:start position:0%
+there's something called The Skin depth
+which falls out of this analysis I
+
+ align:start position:0%
+which falls out of this analysis I
+ 
+
+ align:start position:0%
+which falls out of this analysis I
+mentioned and the the formula for skin
+
+ align:start position:0%
+mentioned and the the formula for skin
+ 
+
+ align:start position:0%
+mentioned and the the formula for skin
+depth which is written as Delta is uh is
+
+ align:start position:0%
+depth which is written as Delta is uh is
+ 
+
+ align:start position:0%
+depth which is written as Delta is uh is
+equal the square root of the
+
+ align:start position:0%
+equal the square root of the
+ 
+
+ align:start position:0%
+equal the square root of the
+conductivity in this case of the
+
+ align:start position:0%
+conductivity in this case of the
+ 
+
+ align:start position:0%
+conductivity in this case of the
+copper divided by um
+
+ align:start position:0%
+copper divided by um
+ 
+
+ align:start position:0%
+copper divided by um
+pi times the permeability in this case
+
+ align:start position:0%
+pi times the permeability in this case
+ 
+
+ align:start position:0%
+pi times the permeability in this case
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+copper and the
+
+ align:start position:0%
+copper and the
+ 
+
+ align:start position:0%
+copper and the
+frequency okay this skin depth is a
+
+ align:start position:0%
+frequency okay this skin depth is a
+ 
+
+ align:start position:0%
+frequency okay this skin depth is a
+characteristic length that says how
+
+ align:start position:0%
+characteristic length that says how
+ 
+
+ align:start position:0%
+characteristic length that says how
+quickly does the fields and currents
+
+ align:start position:0%
+quickly does the fields and currents
+ 
+
+ align:start position:0%
+quickly does the fields and currents
+fall off inside the wire okay so if you
+
+ align:start position:0%
+fall off inside the wire okay so if you
+ 
+
+ align:start position:0%
+fall off inside the wire okay so if you
+you know take an electromagnetic
+
+ align:start position:0%
+you know take an electromagnetic
+ 
+
+ align:start position:0%
+you know take an electromagnetic
+analysis you've probably done this
+
+ align:start position:0%
+analysis you've probably done this
+ 
+
+ align:start position:0%
+analysis you've probably done this
+analysis before okay but what it says is
+
+ align:start position:0%
+analysis before okay but what it says is
+ 
+
+ align:start position:0%
+analysis before okay but what it says is
+notice that this is a function of
+
+ align:start position:0%
+notice that this is a function of
+ 
+
+ align:start position:0%
+notice that this is a function of
+frequency the skin depth decreases as
+
+ align:start position:0%
+frequency the skin depth decreases as
+ 
+
+ align:start position:0%
+frequency the skin depth decreases as
+one over the square of frequency so so
+
+ align:start position:0%
+one over the square of frequency so so
+ 
+
+ align:start position:0%
+one over the square of frequency so so
+essentially if the skin depths on the
+
+ align:start position:0%
+essentially if the skin depths on the
+ 
+
+ align:start position:0%
+essentially if the skin depths on the
+order of the diameter of my wire yeah I
+
+ align:start position:0%
+order of the diameter of my wire yeah I
+ 
+
+ align:start position:0%
+order of the diameter of my wire yeah I
+pretty much carry it approximately
+
+ align:start position:0%
+pretty much carry it approximately
+ 
+
+ align:start position:0%
+pretty much carry it approximately
+constant across the surface of wire if
+
+ align:start position:0%
+constant across the surface of wire if
+ 
+
+ align:start position:0%
+constant across the surface of wire if
+my skin depth gets small small compared
+
+ align:start position:0%
+my skin depth gets small small compared
+ 
+
+ align:start position:0%
+my skin depth gets small small compared
+to the wire right that's when I'm only
+
+ align:start position:0%
+to the wire right that's when I'm only
+ 
+
+ align:start position:0%
+to the wire right that's when I'm only
+going to carry in the surface and it
+
+ align:start position:0%
+going to carry in the surface and it
+ 
+
+ align:start position:0%
+going to carry in the surface and it
+doesn't it doesn't just you know get
+
+ align:start position:0%
+doesn't it doesn't just you know get
+ 
+
+ align:start position:0%
+doesn't it doesn't just you know get
+carried
+
+ align:start position:0%
+carried
+ 
+
+ align:start position:0%
+carried
+um you know here I'm giving you a a
+
+ align:start position:0%
+um you know here I'm giving you a a
+ 
+
+ align:start position:0%
+um you know here I'm giving you a a
+circular cross-section let's just think
+
+ align:start position:0%
+circular cross-section let's just think
+ 
+
+ align:start position:0%
+circular cross-section let's just think
+of a rectangular crosssection okay and I
+
+ align:start position:0%
+of a rectangular crosssection okay and I
+ 
+
+ align:start position:0%
+of a rectangular crosssection okay and I
+would say okay at
+
+ align:start position:0%
+would say okay at
+ 
+
+ align:start position:0%
+would say okay at
+DC if I looked at the current density
+
+ align:start position:0%
+DC if I looked at the current density
+ 
+
+ align:start position:0%
+DC if I looked at the current density
+versus The Wire Dimension between say
+
+ align:start position:0%
+versus The Wire Dimension between say
+ 
+
+ align:start position:0%
+versus The Wire Dimension between say
+zero and the width of the
+
+ align:start position:0%
+zero and the width of the
+ 
+
+ align:start position:0%
+zero and the width of the
+wire right and I had single sided
+
+ align:start position:0%
+wire right and I had single sided
+ 
+
+ align:start position:0%
+wire right and I had single sided
+conduction which I'll talk about in a
+
+ align:start position:0%
+conduction which I'll talk about in a
+ 
+
+ align:start position:0%
+conduction which I'll talk about in a
+minute at DC what you'd get is sort of a
+
+ align:start position:0%
+minute at DC what you'd get is sort of a
+ 
+
+ align:start position:0%
+minute at DC what you'd get is sort of a
+uniform current density this is sort of
+
+ align:start position:0%
+uniform current density this is sort of
+ 
+
+ align:start position:0%
+uniform current density this is sort of
+J
+
+ align:start position:0%
+J
+ 
+
+ align:start position:0%
+J
+versus the depth into the wire right
+
+ align:start position:0%
+versus the depth into the wire right
+ 
+
+ align:start position:0%
+versus the depth into the wire right
+this is at
+
+ align:start position:0%
+this is at
+ 
+
+ align:start position:0%
+this is at
+DC at high frequency AC what happens is
+
+ align:start position:0%
+DC at high frequency AC what happens is
+ 
+
+ align:start position:0%
+DC at high frequency AC what happens is
+you get a lot of current on the
+
+ align:start position:0%
+you get a lot of current on the
+ 
+
+ align:start position:0%
+you get a lot of current on the
+surface and it falls off in an
+
+ align:start position:0%
+surface and it falls off in an
+ 
+
+ align:start position:0%
+surface and it falls off in an
+exponential
+
+ align:start position:0%
+exponential
+ 
+
+ align:start position:0%
+exponential
+okay and the this goes as sort of e to
+
+ align:start position:0%
+okay and the this goes as sort of e to
+ 
+
+ align:start position:0%
+okay and the this goes as sort of e to
+the - x over Delta right it falls off
+
+ align:start position:0%
+the - x over Delta right it falls off
+ 
+
+ align:start position:0%
+the - x over Delta right it falls off
+exponentially with a length constant
+
+ align:start position:0%
+exponentially with a length constant
+ 
+
+ align:start position:0%
+exponentially with a length constant
+that's the skin
+
+ align:start position:0%
+that's the skin
+ 
+
+ align:start position:0%
+that's the skin
+depth all right so when do you have to
+
+ align:start position:0%
+depth all right so when do you have to
+ 
+
+ align:start position:0%
+depth all right so when do you have to
+worry about this when your wire is on
+
+ align:start position:0%
+worry about this when your wire is on
+ 
+
+ align:start position:0%
+worry about this when your wire is on
+the dimension or or larger significantly
+
+ align:start position:0%
+the dimension or or larger significantly
+ 
+
+ align:start position:0%
+the dimension or or larger significantly
+larger than dimension of the skin depth
+
+ align:start position:0%
+larger than dimension of the skin depth
+ 
+
+ align:start position:0%
+larger than dimension of the skin depth
+so you just calculate the skin depth and
+
+ align:start position:0%
+so you just calculate the skin depth and
+ 
+
+ align:start position:0%
+so you just calculate the skin depth and
+you'll find out if you're going to have
+
+ align:start position:0%
+you'll find out if you're going to have
+ 
+
+ align:start position:0%
+you'll find out if you're going to have
+a lot of skin
+
+ align:start position:0%
+a lot of skin
+ 
+
+ align:start position:0%
+a lot of skin
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+interestingly
+
+ align:start position:0%
+interestingly
+ 
+
+ align:start position:0%
+interestingly
+if if you you have a case where the
+
+ align:start position:0%
+if if you you have a case where the
+ 
+
+ align:start position:0%
+if if you you have a case where the
+width of the wire this is the sort of
+
+ align:start position:0%
+width of the wire this is the sort of
+ 
+
+ align:start position:0%
+width of the wire this is the sort of
+that I'm having a foil where I'm
+
+ align:start position:0%
+that I'm having a foil where I'm
+ 
+
+ align:start position:0%
+that I'm having a foil where I'm
+carrying current into the board now
+
+ align:start position:0%
+carrying current into the board now
+ 
+
+ align:start position:0%
+carrying current into the board now
+right so this is the notion this is a
+
+ align:start position:0%
+right so this is the notion this is a
+ 
+
+ align:start position:0%
+right so this is the notion this is a
+foil going into the board or you can do
+
+ align:start position:0%
+foil going into the board or you can do
+ 
+
+ align:start position:0%
+foil going into the board or you can do
+something similar
+
+ align:start position:0%
+something similar
+ 
+
+ align:start position:0%
+something similar
+here interestingly the loss is exactly
+
+ align:start position:0%
+here interestingly the loss is exactly
+ 
+
+ align:start position:0%
+here interestingly the loss is exactly
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+same in this case as if I carried all
+
+ align:start position:0%
+same in this case as if I carried all
+ 
+
+ align:start position:0%
+same in this case as if I carried all
+the current in one skin depth okay and
+
+ align:start position:0%
+the current in one skin depth okay and
+ 
+
+ align:start position:0%
+the current in one skin depth okay and
+that's it's just an interesting thing
+
+ align:start position:0%
+that's it's just an interesting thing
+ 
+
+ align:start position:0%
+that's it's just an interesting thing
+you can derive so you can kind of think
+
+ align:start position:0%
+you can derive so you can kind of think
+ 
+
+ align:start position:0%
+you can derive so you can kind of think
+about it from a cross-sectional area
+
+ align:start position:0%
+about it from a cross-sectional area
+ 
+
+ align:start position:0%
+about it from a cross-sectional area
+carry capability you can kind of Imagine
+
+ align:start position:0%
+carry capability you can kind of Imagine
+ 
+
+ align:start position:0%
+carry capability you can kind of Imagine
+even though I had you know W of with the
+
+ align:start position:0%
+even though I had you know W of with the
+ 
+
+ align:start position:0%
+even though I had you know W of with the
+wire I can only use perhaps Delta of it
+
+ align:start position:0%
+wire I can only use perhaps Delta of it
+ 
+
+ align:start position:0%
+wire I can only use perhaps Delta of it
+and I can just calculate the AC
+
+ align:start position:0%
+and I can just calculate the AC
+ 
+
+ align:start position:0%
+and I can just calculate the AC
+resistance as if I had a length of had
+
+ align:start position:0%
+resistance as if I had a length of had
+ 
+
+ align:start position:0%
+resistance as if I had a length of had
+the skin depth so I would go back
+
+ align:start position:0%
+the skin depth so I would go back
+ 
+
+ align:start position:0%
+the skin depth so I would go back
+instead of carrying you know having the
+
+ align:start position:0%
+instead of carrying you know having the
+ 
+
+ align:start position:0%
+instead of carrying you know having the
+area of the wire which might be the
+
+ align:start position:0%
+area of the wire which might be the
+ 
+
+ align:start position:0%
+area of the wire which might be the
+height of the wire times the width of
+
+ align:start position:0%
+height of the wire times the width of
+ 
+
+ align:start position:0%
+height of the wire times the width of
+the wire I'd have the height of the wire
+
+ align:start position:0%
+the wire I'd have the height of the wire
+ 
+
+ align:start position:0%
+the wire I'd have the height of the wire
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+Delta or another way to express that is
+
+ align:start position:0%
+Delta or another way to express that is
+ 
+
+ align:start position:0%
+Delta or another way to express that is
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+W is much greater than Delta if the
+
+ align:start position:0%
+W is much greater than Delta if the
+ 
+
+ align:start position:0%
+W is much greater than Delta if the
+width of my wire is much greater than
+
+ align:start position:0%
+width of my wire is much greater than
+ 
+
+ align:start position:0%
+width of my wire is much greater than
+the skin
+
+ align:start position:0%
+the skin
+ 
+
+ align:start position:0%
+the skin
+depth then I can write the AC resistance
+
+ align:start position:0%
+depth then I can write the AC resistance
+ 
+
+ align:start position:0%
+depth then I can write the AC resistance
+as being equal to the DC resistance
+
+ align:start position:0%
+as being equal to the DC resistance
+ 
+
+ align:start position:0%
+as being equal to the DC resistance
+which is what I calculated over there
+
+ align:start position:0%
+which is what I calculated over there
+ 
+
+ align:start position:0%
+which is what I calculated over there
+times um W over Delta right so if my
+
+ align:start position:0%
+times um W over Delta right so if my
+ 
+
+ align:start position:0%
+times um W over Delta right so if my
+width of my wire is 10 skin
+
+ align:start position:0%
+width of my wire is 10 skin
+ 
+
+ align:start position:0%
+width of my wire is 10 skin
+depths my AC resistance is 10x the DC
+
+ align:start position:0%
+depths my AC resistance is 10x the DC
+ 
+
+ align:start position:0%
+depths my AC resistance is 10x the DC
+resistance
+
+ align:start position:0%
+resistance
+ 
+
+ align:start position:0%
+resistance
+and from this my AC resistance sort of
+
+ align:start position:0%
+and from this my AC resistance sort of
+ 
+
+ align:start position:0%
+and from this my AC resistance sort of
+goes up as the square root of the
+
+ align:start position:0%
+goes up as the square root of the
+ 
+
+ align:start position:0%
+goes up as the square root of the
+frequency of what I'm carrying for for
+
+ align:start position:0%
+frequency of what I'm carrying for for
+ 
+
+ align:start position:0%
+frequency of what I'm carrying for for
+when I get into this
+
+ align:start position:0%
+when I get into this
+ 
+
+ align:start position:0%
+when I get into this
+regime any questions about
+
+ align:start position:0%
+regime any questions about
+ 
+
+ align:start position:0%
+regime any questions about
+that this chart
+
+ align:start position:0%
+that this chart
+ 
+
+ align:start position:0%
+that this chart
+here just tends to show this is the
+
+ align:start position:0%
+here just tends to show this is the
+ 
+
+ align:start position:0%
+here just tends to show this is the
+field versus the width so this is
+
+ align:start position:0%
+field versus the width so this is
+ 
+
+ align:start position:0%
+field versus the width so this is
+basically we've got a current Source
+
+ align:start position:0%
+basically we've got a current Source
+ 
+
+ align:start position:0%
+basically we've got a current Source
+coming here and
+
+ align:start position:0%
+coming here and
+ 
+
+ align:start position:0%
+coming here and
+carrying current and then the question
+
+ align:start position:0%
+carrying current and then the question
+ 
+
+ align:start position:0%
+carrying current and then the question
+is where in this conductor is the
+
+ align:start position:0%
+is where in this conductor is the
+ 
+
+ align:start position:0%
+is where in this conductor is the
+current turn this shows the field inside
+
+ align:start position:0%
+current turn this shows the field inside
+ 
+
+ align:start position:0%
+current turn this shows the field inside
+the conductor and then this shows the
+
+ align:start position:0%
+the conductor and then this shows the
+ 
+
+ align:start position:0%
+the conductor and then this shows the
+associated current so if I'm if I have a
+
+ align:start position:0%
+associated current so if I'm if I have a
+ 
+
+ align:start position:0%
+associated current so if I'm if I have a
+width of this conductor that's thin
+
+ align:start position:0%
+width of this conductor that's thin
+ 
+
+ align:start position:0%
+width of this conductor that's thin
+compared to a skin depth or on the order
+
+ align:start position:0%
+compared to a skin depth or on the order
+ 
+
+ align:start position:0%
+compared to a skin depth or on the order
+of a skin depth yeah the current's
+
+ align:start position:0%
+of a skin depth yeah the current's
+ 
+
+ align:start position:0%
+of a skin depth yeah the current's
+almost evenly distributed across but
+
+ align:start position:0%
+almost evenly distributed across but
+ 
+
+ align:start position:0%
+almost evenly distributed across but
+once I turn up the frequency and the
+
+ align:start position:0%
+once I turn up the frequency and the
+ 
+
+ align:start position:0%
+once I turn up the frequency and the
+width is much bigger than the skin depth
+
+ align:start position:0%
+width is much bigger than the skin depth
+ 
+
+ align:start position:0%
+width is much bigger than the skin depth
+the current falls off exponentially from
+
+ align:start position:0%
+the current falls off exponentially from
+ 
+
+ align:start position:0%
+the current falls off exponentially from
+the edge of the conductor where there's
+
+ align:start position:0%
+the edge of the conductor where there's
+ 
+
+ align:start position:0%
+the edge of the conductor where there's
+High field okay so when I say oh why is
+
+ align:start position:0%
+High field okay so when I say oh why is
+ 
+
+ align:start position:0%
+High field okay so when I say oh why is
+it why is the sort of the current
+
+ align:start position:0%
+it why is the sort of the current
+ 
+
+ align:start position:0%
+it why is the sort of the current
+sticking to the surface of the wire
+
+ align:start position:0%
+sticking to the surface of the wire
+ 
+
+ align:start position:0%
+sticking to the surface of the wire
+right the question is does it stick to
+
+ align:start position:0%
+right the question is does it stick to
+ 
+
+ align:start position:0%
+right the question is does it stick to
+this side or does it stick to this side
+
+ align:start position:0%
+this side or does it stick to this side
+ 
+
+ align:start position:0%
+this side or does it stick to this side
+it sticks to whatever side of the
+
+ align:start position:0%
+it sticks to whatever side of the
+ 
+
+ align:start position:0%
+it sticks to whatever side of the
+conductor has high magnetic field
+
+ align:start position:0%
+conductor has high magnetic field
+ 
+
+ align:start position:0%
+conductor has high magnetic field
+imposed on it so the way you would
+
+ align:start position:0%
+imposed on it so the way you would
+ 
+
+ align:start position:0%
+imposed on it so the way you would
+Analyze This is you say okay let me
+
+ align:start position:0%
+Analyze This is you say okay let me
+ 
+
+ align:start position:0%
+Analyze This is you say okay let me
+analyze this where are the magnetic
+
+ align:start position:0%
+analyze this where are the magnetic
+ 
+
+ align:start position:0%
+analyze this where are the magnetic
+fields around the conductor where
+
+ align:start position:0%
+fields around the conductor where
+ 
+
+ align:start position:0%
+fields around the conductor where
+there's High magnetic field that's the
+
+ align:start position:0%
+there's High magnetic field that's the
+ 
+
+ align:start position:0%
+there's High magnetic field that's the
+surface of the conductor to which the
+
+ align:start position:0%
+surface of the conductor to which the
+ 
+
+ align:start position:0%
+surface of the conductor to which the
+the current's going to get
+
+ align:start position:0%
+the current's going to get
+ 
+
+ align:start position:0%
+the current's going to get
+compressed any questions about
+
+ align:start position:0%
+compressed any questions about
+ 
+
+ align:start position:0%
+compressed any questions about
+that now I don't know about you but that
+
+ align:start position:0%
+that now I don't know about you but that
+ 
+
+ align:start position:0%
+that now I don't know about you but that
+kind kind of bends my brain a little bit
+
+ align:start position:0%
+kind kind of bends my brain a little bit
+ 
+
+ align:start position:0%
+kind kind of bends my brain a little bit
+so I thought you know the the nicest
+
+ align:start position:0%
+so I thought you know the the nicest
+ 
+
+ align:start position:0%
+so I thought you know the the nicest
+thing is to actually see this for real
+
+ align:start position:0%
+thing is to actually see this for real
+ 
+
+ align:start position:0%
+thing is to actually see this for real
+and you can see that here the H field
+
+ align:start position:0%
+and you can see that here the H field
+ 
+
+ align:start position:0%
+and you can see that here the H field
+this is the H field and this is the
+
+ align:start position:0%
+this is the H field and this is the
+ 
+
+ align:start position:0%
+this is the H field and this is the
+current density we can't see the current
+
+ align:start position:0%
+current density we can't see the current
+ 
+
+ align:start position:0%
+current density we can't see the current
+density but maybe we can look at how the
+
+ align:start position:0%
+density but maybe we can look at how the
+ 
+
+ align:start position:0%
+density but maybe we can look at how the
+H Fields drop inside the conductor and
+
+ align:start position:0%
+H Fields drop inside the conductor and
+ 
+
+ align:start position:0%
+H Fields drop inside the conductor and
+that will relate to how the the fields
+
+ align:start position:0%
+that will relate to how the the fields
+ 
+
+ align:start position:0%
+that will relate to how the the fields
+uh how the currents distribute inside
+
+ align:start position:0%
+uh how the currents distribute inside
+ 
+
+ align:start position:0%
+uh how the currents distribute inside
+the conductor so to demonstrate this we
+
+ align:start position:0%
+the conductor so to demonstrate this we
+ 
+
+ align:start position:0%
+the conductor so to demonstrate this we
+have uh this
+
+ align:start position:0%
+have uh this
+ 
+
+ align:start position:0%
+have uh this
+giant uh block of aluminum here and the
+
+ align:start position:0%
+giant uh block of aluminum here and the
+ 
+
+ align:start position:0%
+giant uh block of aluminum here and the
+aluminum forms a one turn secondary on
+
+ align:start position:0%
+aluminum forms a one turn secondary on
+ 
+
+ align:start position:0%
+aluminum forms a one turn secondary on
+this Transformer so here you can you
+
+ align:start position:0%
+this Transformer so here you can you
+ 
+
+ align:start position:0%
+this Transformer so here you can you
+might be able to see there's a core here
+
+ align:start position:0%
+might be able to see there's a core here
+ 
+
+ align:start position:0%
+might be able to see there's a core here
+we have a winding over here that we're
+
+ align:start position:0%
+we have a winding over here that we're
+ 
+
+ align:start position:0%
+we have a winding over here that we're
+going to drive but this is one turn
+
+ align:start position:0%
+going to drive but this is one turn
+ 
+
+ align:start position:0%
+going to drive but this is one turn
+around the inside of this Transformer
+
+ align:start position:0%
+around the inside of this Transformer
+ 
+
+ align:start position:0%
+around the inside of this Transformer
+and so we're going to have current
+
+ align:start position:0%
+and so we're going to have current
+ 
+
+ align:start position:0%
+and so we're going to have current
+flowing in there and it's hard for us to
+
+ align:start position:0%
+flowing in there and it's hard for us to
+ 
+
+ align:start position:0%
+flowing in there and it's hard for us to
+measure the current but the current
+
+ align:start position:0%
+measure the current but the current
+ 
+
+ align:start position:0%
+measure the current but the current
+generates magnetic field and so we have
+
+ align:start position:0%
+generates magnetic field and so we have
+ 
+
+ align:start position:0%
+generates magnetic field and so we have
+this magnetic field probe over here and
+
+ align:start position:0%
+this magnetic field probe over here and
+ 
+
+ align:start position:0%
+this magnetic field probe over here and
+we're going to move the magnetic field
+
+ align:start position:0%
+we're going to move the magnetic field
+ 
+
+ align:start position:0%
+we're going to move the magnetic field
+probe right now the end of the probe is
+
+ align:start position:0%
+probe right now the end of the probe is
+ 
+
+ align:start position:0%
+probe right now the end of the probe is
+right on the Inside Edge here okay and
+
+ align:start position:0%
+right on the Inside Edge here okay and
+ 
+
+ align:start position:0%
+right on the Inside Edge here okay and
+we're going to move it about halfway
+
+ align:start position:0%
+we're going to move it about halfway
+ 
+
+ align:start position:0%
+we're going to move it about halfway
+across the block and then we're going to
+
+ align:start position:0%
+across the block and then we're going to
+ 
+
+ align:start position:0%
+across the block and then we're going to
+move it back again now when we move it
+
+ align:start position:0%
+move it back again now when we move it
+ 
+
+ align:start position:0%
+move it back again now when we move it
+uh from The Edge to the middle we're
+
+ align:start position:0%
+uh from The Edge to the middle we're
+ 
+
+ align:start position:0%
+uh from The Edge to the middle we're
+going to excite our Transformer at 60
+
+ align:start position:0%
+going to excite our Transformer at 60
+ 
+
+ align:start position:0%
+going to excite our Transformer at 60
+htz okay so relatively low frequency and
+
+ align:start position:0%
+htz okay so relatively low frequency and
+ 
+
+ align:start position:0%
+htz okay so relatively low frequency and
+so the skin depth will be quite long and
+
+ align:start position:0%
+so the skin depth will be quite long and
+ 
+
+ align:start position:0%
+so the skin depth will be quite long and
+so we should get uh good uh current you
+
+ align:start position:0%
+so we should get uh good uh current you
+ 
+
+ align:start position:0%
+so we should get uh good uh current you
+know in in the block and and we'll see
+
+ align:start position:0%
+know in in the block and and we'll see
+ 
+
+ align:start position:0%
+know in in the block and and we'll see
+that it it goes quite deep into the
+
+ align:start position:0%
+that it it goes quite deep into the
+ 
+
+ align:start position:0%
+that it it goes quite deep into the
+block then when we return we're going to
+
+ align:start position:0%
+block then when we return we're going to
+ 
+
+ align:start position:0%
+block then when we return we're going to
+turn up the frequency to 240 htz okay
+
+ align:start position:0%
+turn up the frequency to 240 htz okay
+ 
+
+ align:start position:0%
+turn up the frequency to 240 htz okay
+and then we're going to see how that
+
+ align:start position:0%
+and then we're going to see how that
+ 
+
+ align:start position:0%
+and then we're going to see how that
+compares to the 60 HZ result so the
+
+ align:start position:0%
+compares to the 60 HZ result so the
+ 
+
+ align:start position:0%
+compares to the 60 HZ result so the
+first time I'm just going to run it so
+
+ align:start position:0%
+first time I'm just going to run it so
+ 
+
+ align:start position:0%
+first time I'm just going to run it so
+that you can just sort of see how the
+
+ align:start position:0%
+that you can just sort of see how the
+ 
+
+ align:start position:0%
+that you can just sort of see how the
+apparatus is working
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I'm using a stepper motor here
+
+ align:start position:0%
+okay so I'm using a stepper motor here
+ 
+
+ align:start position:0%
+okay so I'm using a stepper motor here
+to move the probe uh and so you can see
+
+ align:start position:0%
+to move the probe uh and so you can see
+ 
+
+ align:start position:0%
+to move the probe uh and so you can see
+that it's slowly pulling out okay and
+
+ align:start position:0%
+that it's slowly pulling out okay and
+ 
+
+ align:start position:0%
+that it's slowly pulling out okay and
+then when we get about halfway then it's
+
+ align:start position:0%
+then when we get about halfway then it's
+ 
+
+ align:start position:0%
+then when we get about halfway then it's
+going to go back
+
+ align:start position:0%
+going to go back
+ 
+
+ align:start position:0%
+going to go back
+uh it's changed the frequency at this
+
+ align:start position:0%
+uh it's changed the frequency at this
+ 
+
+ align:start position:0%
+uh it's changed the frequency at this
+point and then it's going to go back in
+
+ align:start position:0%
+point and then it's going to go back in
+ 
+
+ align:start position:0%
+point and then it's going to go back in
+again so now I'll change the display so
+
+ align:start position:0%
+again so now I'll change the display so
+ 
+
+ align:start position:0%
+again so now I'll change the display so
+you could look at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scope takes a takes a second for VGA to
+
+ align:start position:0%
+scope takes a takes a second for VGA to
+ 
+
+ align:start position:0%
+scope takes a takes a second for VGA to
+lock okay so now this is the the uh it's
+
+ align:start position:0%
+lock okay so now this is the the uh it's
+ 
+
+ align:start position:0%
+lock okay so now this is the the uh it's
+the strength of the magnetic field which
+
+ align:start position:0%
+the strength of the magnetic field which
+ 
+
+ align:start position:0%
+the strength of the magnetic field which
+is proportional to the strength of the
+
+ align:start position:0%
+is proportional to the strength of the
+ 
+
+ align:start position:0%
+is proportional to the strength of the
+current as it's going in or it's going
+
+ align:start position:0%
+current as it's going in or it's going
+ 
+
+ align:start position:0%
+current as it's going in or it's going
+from The Edge to the middle okay you can
+
+ align:start position:0%
+from The Edge to the middle okay you can
+ 
+
+ align:start position:0%
+from The Edge to the middle okay you can
+see that the magnitude is going down has
+
+ align:start position:0%
+see that the magnitude is going down has
+ 
+
+ align:start position:0%
+see that the magnitude is going down has
+kind of an exponential look to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it and now it's changed frequency so you
+
+ align:start position:0%
+it and now it's changed frequency so you
+ 
+
+ align:start position:0%
+it and now it's changed frequency so you
+can see that the amplitude is smaller
+
+ align:start position:0%
+can see that the amplitude is smaller
+ 
+
+ align:start position:0%
+can see that the amplitude is smaller
+right away
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I've tried to adjust it so that the
+
+ align:start position:0%
+so I've tried to adjust it so that the
+ 
+
+ align:start position:0%
+so I've tried to adjust it so that the
+two amplitudes are the same at the at
+
+ align:start position:0%
+two amplitudes are the same at the at
+ 
+
+ align:start position:0%
+two amplitudes are the same at the at
+the uh at the outside edge and so you
+
+ align:start position:0%
+the uh at the outside edge and so you
+ 
+
+ align:start position:0%
+the uh at the outside edge and so you
+can sort of see what the relative uh
+
+ align:start position:0%
+can sort of see what the relative uh
+ 
+
+ align:start position:0%
+can sort of see what the relative uh
+distances uh are for the two different
+
+ align:start position:0%
+distances uh are for the two different
+ 
+
+ align:start position:0%
+distances uh are for the two different
+frequencies the green one is 60 htz and
+
+ align:start position:0%
+frequencies the green one is 60 htz and
+ 
+
+ align:start position:0%
+frequencies the green one is 60 htz and
+the yellow one is 240
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Herz okay I'll give you back your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+screen thanks Steve so you could see
+
+ align:start position:0%
+screen thanks Steve so you could see
+ 
+
+ align:start position:0%
+screen thanks Steve so you could see
+that the skin depth that's the
+
+ align:start position:0%
+that the skin depth that's the
+ 
+
+ align:start position:0%
+that the skin depth that's the
+exponential exponential length constant
+
+ align:start position:0%
+exponential exponential length constant
+ 
+
+ align:start position:0%
+exponential exponential length constant
+uh with which things decayed was about a
+
+ align:start position:0%
+uh with which things decayed was about a
+ 
+
+ align:start position:0%
+uh with which things decayed was about a
+factor of two different in those two
+
+ align:start position:0%
+factor of two different in those two
+ 
+
+ align:start position:0%
+factor of two different in those two
+examples because the frequencies were
+
+ align:start position:0%
+examples because the frequencies were
+ 
+
+ align:start position:0%
+examples because the frequencies were
+about a factor of four different okay so
+
+ align:start position:0%
+about a factor of four different okay so
+ 
+
+ align:start position:0%
+about a factor of four different okay so
+what do I hope that you're going to take
+
+ align:start position:0%
+what do I hope that you're going to take
+ 
+
+ align:start position:0%
+what do I hope that you're going to take
+away from that what I hope you're going
+
+ align:start position:0%
+away from that what I hope you're going
+ 
+
+ align:start position:0%
+away from that what I hope you're going
+to take away is you're going to think
+
+ align:start position:0%
+to take away is you're going to think
+ 
+
+ align:start position:0%
+to take away is you're going to think
+when you design something oh if I'm
+
+ align:start position:0%
+when you design something oh if I'm
+ 
+
+ align:start position:0%
+when you design something oh if I'm
+trying to carry
+
+ align:start position:0%
+trying to carry
+ 
+
+ align:start position:0%
+trying to carry
+um high frequency
+
+ align:start position:0%
+um high frequency
+ 
+
+ align:start position:0%
+um high frequency
+currents okay um I bet think about how
+
+ align:start position:0%
+currents okay um I bet think about how
+ 
+
+ align:start position:0%
+currents okay um I bet think about how
+big my conductor is relative to the skin
+
+ align:start position:0%
+big my conductor is relative to the skin
+ 
+
+ align:start position:0%
+big my conductor is relative to the skin
+depth and maybe I can use the DC
+
+ align:start position:0%
+depth and maybe I can use the DC
+ 
+
+ align:start position:0%
+depth and maybe I can use the DC
+resistance or maybe I already figure out
+
+ align:start position:0%
+resistance or maybe I already figure out
+ 
+
+ align:start position:0%
+resistance or maybe I already figure out
+what the um skin depth is and calculate
+
+ align:start position:0%
+what the um skin depth is and calculate
+ 
+
+ align:start position:0%
+what the um skin depth is and calculate
+the AC resistance of my winding okay and
+
+ align:start position:0%
+the AC resistance of my winding okay and
+ 
+
+ align:start position:0%
+the AC resistance of my winding okay and
+by the way I put in the notes this is
+
+ align:start position:0%
+by the way I put in the notes this is
+ 
+
+ align:start position:0%
+by the way I put in the notes this is
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+approximation is for if W is much bigger
+
+ align:start position:0%
+approximation is for if W is much bigger
+ 
+
+ align:start position:0%
+approximation is for if W is much bigger
+than the skin du in the lecture notes I
+
+ align:start position:0%
+than the skin du in the lecture notes I
+ 
+
+ align:start position:0%
+than the skin du in the lecture notes I
+put what the approximation looks like if
+
+ align:start position:0%
+put what the approximation looks like if
+ 
+
+ align:start position:0%
+put what the approximation looks like if
+it's sort of in some intermediate value
+
+ align:start position:0%
+it's sort of in some intermediate value
+ 
+
+ align:start position:0%
+it's sort of in some intermediate value
+so it's not like um you know there's
+
+ align:start position:0%
+so it's not like um you know there's
+ 
+
+ align:start position:0%
+so it's not like um you know there's
+sort of a a frequency dependent AC
+
+ align:start position:0%
+sort of a a frequency dependent AC
+ 
+
+ align:start position:0%
+sort of a a frequency dependent AC
+resistance but it's important because
+
+ align:start position:0%
+resistance but it's important because
+ 
+
+ align:start position:0%
+resistance but it's important because
+sometimes what you can find is you're
+
+ align:start position:0%
+sometimes what you can find is you're
+ 
+
+ align:start position:0%
+sometimes what you can find is you're
+trying to carry large currents at high
+
+ align:start position:0%
+trying to carry large currents at high
+ 
+
+ align:start position:0%
+trying to carry large currents at high
+frequencies you find out that your AC
+
+ align:start position:0%
+frequencies you find out that your AC
+ 
+
+ align:start position:0%
+frequencies you find out that your AC
+resistance is significantly bigger than
+
+ align:start position:0%
+resistance is significantly bigger than
+ 
+
+ align:start position:0%
+resistance is significantly bigger than
+you would have gotten if you just
+
+ align:start position:0%
+you would have gotten if you just
+ 
+
+ align:start position:0%
+you would have gotten if you just
+calculated this
+
+ align:start position:0%
+calculated this
+ 
+
+ align:start position:0%
+calculated this
+value any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that yeah like this instead of having
+
+ align:start position:0%
+that yeah like this instead of having
+ 
+
+ align:start position:0%
+that yeah like this instead of having
+one be conductor par
+
+ align:start position:0%
+one be conductor par
+ 
+
+ align:start position:0%
+one be conductor par
+conductor yes and no
+
+ align:start position:0%
+conductor yes and no
+ 
+
+ align:start position:0%
+conductor yes and no
+um yes you can but you just can't have
+
+ align:start position:0%
+um yes you can but you just can't have
+ 
+
+ align:start position:0%
+um yes you can but you just can't have
+parallel conductors because like indeed
+
+ align:start position:0%
+parallel conductors because like indeed
+ 
+
+ align:start position:0%
+parallel conductors because like indeed
+what is one big conductor except a bunch
+
+ align:start position:0%
+what is one big conductor except a bunch
+ 
+
+ align:start position:0%
+what is one big conductor except a bunch
+of parallel conductors but what you can
+
+ align:start position:0%
+of parallel conductors but what you can
+ 
+
+ align:start position:0%
+of parallel conductors but what you can
+use is something called litz wire and
+
+ align:start position:0%
+use is something called litz wire and
+ 
+
+ align:start position:0%
+use is something called litz wire and
+here's a picture of litz wire so this is
+
+ align:start position:0%
+here's a picture of litz wire so this is
+ 
+
+ align:start position:0%
+here's a picture of litz wire so this is
+a what you do is if you want to carry a
+
+ align:start position:0%
+a what you do is if you want to carry a
+ 
+
+ align:start position:0%
+a what you do is if you want to carry a
+lot of current so you need a lot of
+
+ align:start position:0%
+lot of current so you need a lot of
+ 
+
+ align:start position:0%
+lot of current so you need a lot of
+cross-section but your skin depth is
+
+ align:start position:0%
+cross-section but your skin depth is
+ 
+
+ align:start position:0%
+cross-section but your skin depth is
+small what do you do you get a bunch of
+
+ align:start position:0%
+small what do you do you get a bunch of
+ 
+
+ align:start position:0%
+small what do you do you get a bunch of
+insulated strands so each of these
+
+ align:start position:0%
+insulated strands so each of these
+ 
+
+ align:start position:0%
+insulated strands so each of these
+strands is insulated from one another
+
+ align:start position:0%
+strands is insulated from one another
+ 
+
+ align:start position:0%
+strands is insulated from one another
+but then you can't just parallel them
+
+ align:start position:0%
+but then you can't just parallel them
+ 
+
+ align:start position:0%
+but then you can't just parallel them
+because um of the way the magnetic field
+
+ align:start position:0%
+because um of the way the magnetic field
+ 
+
+ align:start position:0%
+because um of the way the magnetic field
+will behave basically the current will
+
+ align:start position:0%
+will behave basically the current will
+ 
+
+ align:start position:0%
+will behave basically the current will
+still be carried in the outer ones and
+
+ align:start position:0%
+still be carried in the outer ones and
+ 
+
+ align:start position:0%
+still be carried in the outer ones and
+not in the inner ones but what they do
+
+ align:start position:0%
+not in the inner ones but what they do
+ 
+
+ align:start position:0%
+not in the inner ones but what they do
+is they basically weave these windings
+
+ align:start position:0%
+is they basically weave these windings
+ 
+
+ align:start position:0%
+is they basically weave these windings
+together in the simplest thing you can
+
+ align:start position:0%
+together in the simplest thing you can
+ 
+
+ align:start position:0%
+together in the simplest thing you can
+kind of twist it but the key thing is
+
+ align:start position:0%
+kind of twist it but the key thing is
+ 
+
+ align:start position:0%
+kind of twist it but the key thing is
+you want sometimes the conductor is on
+
+ align:start position:0%
+you want sometimes the conductor is on
+ 
+
+ align:start position:0%
+you want sometimes the conductor is on
+the inside and sometimes it's on the
+
+ align:start position:0%
+the inside and sometimes it's on the
+ 
+
+ align:start position:0%
+the inside and sometimes it's on the
+outside so if you imagine that you weave
+
+ align:start position:0%
+outside so if you imagine that you weave
+ 
+
+ align:start position:0%
+outside so if you imagine that you weave
+your windings in a in a pattern called
+
+ align:start position:0%
+your windings in a in a pattern called
+ 
+
+ align:start position:0%
+your windings in a in a pattern called
+litz transposition such that each piece
+
+ align:start position:0%
+litz transposition such that each piece
+ 
+
+ align:start position:0%
+litz transposition such that each piece
+of conductor spends an equal amount of
+
+ align:start position:0%
+of conductor spends an equal amount of
+ 
+
+ align:start position:0%
+of conductor spends an equal amount of
+time on the surface and in the middle
+
+ align:start position:0%
+time on the surface and in the middle
+ 
+
+ align:start position:0%
+time on the surface and in the middle
+and the center then sort of if you want
+
+ align:start position:0%
+and the center then sort of if you want
+ 
+
+ align:start position:0%
+and the center then sort of if you want
+to think about the current doesn't know
+
+ align:start position:0%
+to think about the current doesn't know
+ 
+
+ align:start position:0%
+to think about the current doesn't know
+which way to go they all look equal so
+
+ align:start position:0%
+which way to go they all look equal so
+ 
+
+ align:start position:0%
+which way to go they all look equal so
+it goes through equal through everybody
+
+ align:start position:0%
+it goes through equal through everybody
+ 
+
+ align:start position:0%
+it goes through equal through everybody
+and everybody's happy so you'll see a
+
+ align:start position:0%
+and everybody's happy so you'll see a
+ 
+
+ align:start position:0%
+and everybody's happy so you'll see a
+lot of high frequency designs where
+
+ align:start position:0%
+lot of high frequency designs where
+ 
+
+ align:start position:0%
+lot of high frequency designs where
+you're carrying High currents that will
+
+ align:start position:0%
+you're carrying High currents that will
+ 
+
+ align:start position:0%
+you're carrying High currents that will
+use litz wire as the conductor for
+
+ align:start position:0%
+use litz wire as the conductor for
+ 
+
+ align:start position:0%
+use litz wire as the conductor for
+precisely that purpose and when you want
+
+ align:start position:0%
+precisely that purpose and when you want
+ 
+
+ align:start position:0%
+precisely that purpose and when you want
+to make really big wire you make smaller
+
+ align:start position:0%
+to make really big wire you make smaller
+ 
+
+ align:start position:0%
+to make really big wire you make smaller
+litz bundles and then you know as you
+
+ align:start position:0%
+litz bundles and then you know as you
+ 
+
+ align:start position:0%
+litz bundles and then you know as you
+see down here you weave those together
+
+ align:start position:0%
+see down here you weave those together
+ 
+
+ align:start position:0%
+see down here you weave those together
+or twist those together in order to get
+
+ align:start position:0%
+or twist those together in order to get
+ 
+
+ align:start position:0%
+or twist those together in order to get
+this effect okay and there are papers
+
+ align:start position:0%
+this effect okay and there are papers
+ 
+
+ align:start position:0%
+this effect okay and there are papers
+that show you what well how small do
+
+ align:start position:0%
+that show you what well how small do
+ 
+
+ align:start position:0%
+that show you what well how small do
+your lit bundles have to be but the
+
+ align:start position:0%
+your lit bundles have to be but the
+ 
+
+ align:start position:0%
+your lit bundles have to be but the
+first thing you might think of is all
+
+ align:start position:0%
+first thing you might think of is all
+ 
+
+ align:start position:0%
+first thing you might think of is all
+you're dealing with the skin effect is
+
+ align:start position:0%
+you're dealing with the skin effect is
+ 
+
+ align:start position:0%
+you're dealing with the skin effect is
+you would like your litz wire to have a
+
+ align:start position:0%
+you would like your litz wire to have a
+ 
+
+ align:start position:0%
+you would like your litz wire to have a
+diameter that's on the order of a skin
+
+ align:start position:0%
+diameter that's on the order of a skin
+ 
+
+ align:start position:0%
+diameter that's on the order of a skin
+depth right is a good place to start if
+
+ align:start position:0%
+depth right is a good place to start if
+ 
+
+ align:start position:0%
+depth right is a good place to start if
+all you're thinking about is skin effect
+
+ align:start position:0%
+all you're thinking about is skin effect
+ 
+
+ align:start position:0%
+all you're thinking about is skin effect
+excellent question any other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions so skin effect is a pain but
+
+ align:start position:0%
+questions so skin effect is a pain but
+ 
+
+ align:start position:0%
+questions so skin effect is a pain but
+it turns out that there's something even
+
+ align:start position:0%
+it turns out that there's something even
+ 
+
+ align:start position:0%
+it turns out that there's something even
+worse than skin effect that can occur
+
+ align:start position:0%
+worse than skin effect that can occur
+ 
+
+ align:start position:0%
+worse than skin effect that can occur
+and that's known as proximity effect
+
+ align:start position:0%
+and that's known as proximity effect
+ 
+
+ align:start position:0%
+and that's known as proximity effect
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um what is proximity effect well
+
+ align:start position:0%
+um what is proximity effect well
+ 
+
+ align:start position:0%
+um what is proximity effect well
+proximity effect is when we get Eddie
+
+ align:start position:0%
+proximity effect is when we get Eddie
+ 
+
+ align:start position:0%
+proximity effect is when we get Eddie
+currents in a wire due to fields from
+
+ align:start position:0%
+currents in a wire due to fields from
+ 
+
+ align:start position:0%
+currents in a wire due to fields from
+some other piece of conductor nearby
+
+ align:start position:0%
+some other piece of conductor nearby
+ 
+
+ align:start position:0%
+some other piece of conductor nearby
+right and I'm still generating loss
+
+ align:start position:0%
+right and I'm still generating loss
+ 
+
+ align:start position:0%
+right and I'm still generating loss
+right so imagine that
+
+ align:start position:0%
+right so imagine that
+ 
+
+ align:start position:0%
+right so imagine that
+um and here here's an example imagine I
+
+ align:start position:0%
+um and here here's an example imagine I
+ 
+
+ align:start position:0%
+um and here here's an example imagine I
+have a piece of conductor and maybe this
+
+ align:start position:0%
+have a piece of conductor and maybe this
+ 
+
+ align:start position:0%
+have a piece of conductor and maybe this
+is a foil conductor carrying some
+
+ align:start position:0%
+is a foil conductor carrying some
+ 
+
+ align:start position:0%
+is a foil conductor carrying some
+current right in my in my you know I'm
+
+ align:start position:0%
+current right in my in my you know I'm
+ 
+
+ align:start position:0%
+current right in my in my you know I'm
+carrying current in this direction right
+
+ align:start position:0%
+carrying current in this direction right
+ 
+
+ align:start position:0%
+carrying current in this direction right
+and because of where this conductor is
+
+ align:start position:0%
+and because of where this conductor is
+ 
+
+ align:start position:0%
+and because of where this conductor is
+sitting it's sitting in inside some H
+
+ align:start position:0%
+sitting it's sitting in inside some H
+ 
+
+ align:start position:0%
+sitting it's sitting in inside some H
+field like here right some external H
+
+ align:start position:0%
+field like here right some external H
+ 
+
+ align:start position:0%
+field like here right some external H
+field on each surface and this conductor
+
+ align:start position:0%
+field on each surface and this conductor
+ 
+
+ align:start position:0%
+field on each surface and this conductor
+could be carrying no neet current it's
+
+ align:start position:0%
+could be carrying no neet current it's
+ 
+
+ align:start position:0%
+could be carrying no neet current it's
+just sitting there
+
+ align:start position:0%
+just sitting there
+ 
+
+ align:start position:0%
+just sitting there
+but because of some other current nearby
+
+ align:start position:0%
+but because of some other current nearby
+ 
+
+ align:start position:0%
+but because of some other current nearby
+it has a field on it what should I
+
+ align:start position:0%
+it has a field on it what should I
+ 
+
+ align:start position:0%
+it has a field on it what should I
+affect I'm trying to
+
+ align:start position:0%
+affect I'm trying to
+ 
+
+ align:start position:0%
+affect I'm trying to
+punch H field through the conductor
+
+ align:start position:0%
+punch H field through the conductor
+ 
+
+ align:start position:0%
+punch H field through the conductor
+right and again that's going to generate
+
+ align:start position:0%
+right and again that's going to generate
+ 
+
+ align:start position:0%
+right and again that's going to generate
+some eddy current trying to reject the
+
+ align:start position:0%
+some eddy current trying to reject the
+ 
+
+ align:start position:0%
+some eddy current trying to reject the
+flux from the center right so what
+
+ align:start position:0%
+flux from the center right so what
+ 
+
+ align:start position:0%
+flux from the center right so what
+that's going to do is that's essentially
+
+ align:start position:0%
+that's going to do is that's essentially
+ 
+
+ align:start position:0%
+that's going to do is that's essentially
+going to generate a
+
+ align:start position:0%
+going to generate a
+ 
+
+ align:start position:0%
+going to generate a
+current it's going to generate an eddy
+
+ align:start position:0%
+current it's going to generate an eddy
+ 
+
+ align:start position:0%
+current it's going to generate an eddy
+current that um goes in on this surface
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and comes out on this
+
+ align:start position:0%
+and comes out on this
+ 
+
+ align:start position:0%
+and comes out on this
+surface why because that's going to
+
+ align:start position:0%
+surface why because that's going to
+ 
+
+ align:start position:0%
+surface why because that's going to
+generate you know this is if this is an
+
+ align:start position:0%
+generate you know this is if this is an
+ 
+
+ align:start position:0%
+generate you know this is if this is an
+AC current the dbdt generates these
+
+ align:start position:0%
+AC current the dbdt generates these
+ 
+
+ align:start position:0%
+AC current the dbdt generates these
+circulating currents inside the
+
+ align:start position:0%
+circulating currents inside the
+ 
+
+ align:start position:0%
+circulating currents inside the
+conductor that try to reject the field
+
+ align:start position:0%
+conductor that try to reject the field
+ 
+
+ align:start position:0%
+conductor that try to reject the field
+from the
+
+ align:start position:0%
+from the
+ 
+
+ align:start position:0%
+from the
+center all right here in this plot you
+
+ align:start position:0%
+center all right here in this plot you
+ 
+
+ align:start position:0%
+center all right here in this plot you
+can see these are
+
+ align:start position:0%
+can see these are
+ 
+
+ align:start position:0%
+can see these are
+solutions um here's where I have a piece
+
+ align:start position:0%
+solutions um here's where I have a piece
+ 
+
+ align:start position:0%
+solutions um here's where I have a piece
+of conductor and there's um vertical
+
+ align:start position:0%
+of conductor and there's um vertical
+ 
+
+ align:start position:0%
+of conductor and there's um vertical
+fields on each surface so the conductor
+
+ align:start position:0%
+fields on each surface so the conductor
+ 
+
+ align:start position:0%
+fields on each surface so the conductor
+is not carrying any net current and what
+
+ align:start position:0%
+is not carrying any net current and what
+ 
+
+ align:start position:0%
+is not carrying any net current and what
+we can see is we get Eddy currents that
+
+ align:start position:0%
+we can see is we get Eddy currents that
+ 
+
+ align:start position:0%
+we can see is we get Eddy currents that
+decay away into the middle of the
+
+ align:start position:0%
+decay away into the middle of the
+ 
+
+ align:start position:0%
+decay away into the middle of the
+conductor
+
+ align:start position:0%
+conductor
+ 
+
+ align:start position:0%
+conductor
+um with the same skin death
+
+ align:start position:0%
+um with the same skin death
+ 
+
+ align:start position:0%
+um with the same skin death
+relationship
+
+ align:start position:0%
+relationship
+ 
+
+ align:start position:0%
+relationship
+okay why is proximity effect
+
+ align:start position:0%
+okay why is proximity effect
+ 
+
+ align:start position:0%
+okay why is proximity effect
+particularly bad because I'm inducing
+
+ align:start position:0%
+particularly bad because I'm inducing
+ 
+
+ align:start position:0%
+particularly bad because I'm inducing
+loss in this conductor even though that
+
+ align:start position:0%
+loss in this conductor even though that
+ 
+
+ align:start position:0%
+loss in this conductor even though that
+I'm not getting to use that conductor to
+
+ align:start position:0%
+I'm not getting to use that conductor to
+ 
+
+ align:start position:0%
+I'm not getting to use that conductor to
+really carry any
+
+ align:start position:0%
+really carry any
+ 
+
+ align:start position:0%
+really carry any
+current right well why should I care
+
+ align:start position:0%
+current right well why should I care
+ 
+
+ align:start position:0%
+current right well why should I care
+about this proximity effect because
+
+ align:start position:0%
+about this proximity effect because
+ 
+
+ align:start position:0%
+about this proximity effect because
+imagine I
+
+ align:start position:0%
+imagine I
+ 
+
+ align:start position:0%
+imagine I
+imagine I have some core like a pot core
+
+ align:start position:0%
+imagine I have some core like a pot core
+ 
+
+ align:start position:0%
+imagine I have some core like a pot core
+where I have some Center Post and then I
+
+ align:start position:0%
+where I have some Center Post and then I
+ 
+
+ align:start position:0%
+where I have some Center Post and then I
+have this window where I'm winding
+
+ align:start position:0%
+have this window where I'm winding
+ 
+
+ align:start position:0%
+have this window where I'm winding
+winding uh
+
+ align:start position:0%
+winding uh
+ 
+
+ align:start position:0%
+winding uh
+currents okay so here is my
+
+ align:start position:0%
+currents okay so here is my
+ 
+
+ align:start position:0%
+currents okay so here is my
+core okay so this is I'm looking at a
+
+ align:start position:0%
+core okay so this is I'm looking at a
+ 
+
+ align:start position:0%
+core okay so this is I'm looking at a
+crosssection of the core okay like this
+
+ align:start position:0%
+crosssection of the core okay like this
+ 
+
+ align:start position:0%
+crosssection of the core okay like this
+and suppose this is a
+
+ align:start position:0%
+and suppose this is a
+ 
+
+ align:start position:0%
+and suppose this is a
+Transformer then maybe I wrap my
+
+ align:start position:0%
+Transformer then maybe I wrap my
+ 
+
+ align:start position:0%
+Transformer then maybe I wrap my
+conductor in and back out so maybe I
+
+ align:start position:0%
+conductor in and back out so maybe I
+ 
+
+ align:start position:0%
+conductor in and back out so maybe I
+have you know some set some foil
+
+ align:start position:0%
+have you know some set some foil
+ 
+
+ align:start position:0%
+have you know some set some foil
+conductor or set of wire conductors
+
+ align:start position:0%
+conductor or set of wire conductors
+ 
+
+ align:start position:0%
+conductor or set of wire conductors
+that's going in here and carrying
+
+ align:start position:0%
+that's going in here and carrying
+ 
+
+ align:start position:0%
+that's going in here and carrying
+current in this
+
+ align:start position:0%
+current in this
+ 
+
+ align:start position:0%
+current in this
+way and then it's wrapped around it's
+
+ align:start position:0%
+way and then it's wrapped around it's
+ 
+
+ align:start position:0%
+way and then it's wrapped around it's
+coming out
+
+ align:start position:0%
+coming out
+ 
+
+ align:start position:0%
+coming out
+here right and I have a layer of
+
+ align:start position:0%
+here right and I have a layer of
+ 
+
+ align:start position:0%
+here right and I have a layer of
+that right and maybe I have a second
+
+ align:start position:0%
+that right and maybe I have a second
+ 
+
+ align:start position:0%
+that right and maybe I have a second
+layer right because I'm winding out and
+
+ align:start position:0%
+layer right because I'm winding out and
+ 
+
+ align:start position:0%
+layer right because I'm winding out and
+I have another second
+
+ align:start position:0%
+I have another second
+ 
+
+ align:start position:0%
+I have another second
+layer
+
+ align:start position:0%
+layer
+ 
+
+ align:start position:0%
+layer
+okay going in going in going in going in
+
+ align:start position:0%
+okay going in going in going in going in
+ 
+
+ align:start position:0%
+okay going in going in going in going in
+and coming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out okay it's doing that and maybe over
+
+ align:start position:0%
+out okay it's doing that and maybe over
+ 
+
+ align:start position:0%
+out okay it's doing that and maybe over
+here I have some secondary so maybe the
+
+ align:start position:0%
+here I have some secondary so maybe the
+ 
+
+ align:start position:0%
+here I have some secondary so maybe the
+secondary carries an equal and opposite
+
+ align:start position:0%
+secondary carries an equal and opposite
+ 
+
+ align:start position:0%
+secondary carries an equal and opposite
+current maybe it carries twice as much
+
+ align:start position:0%
+current maybe it carries twice as much
+ 
+
+ align:start position:0%
+current maybe it carries twice as much
+current it's a two to one Transformer so
+
+ align:start position:0%
+current it's a two to one Transformer so
+ 
+
+ align:start position:0%
+current it's a two to one Transformer so
+you know here I have two dots two dots
+
+ align:start position:0%
+you know here I have two dots two dots
+ 
+
+ align:start position:0%
+you know here I have two dots two dots
+coming out two dots coming out two dots
+
+ align:start position:0%
+coming out two dots coming out two dots
+ 
+
+ align:start position:0%
+coming out two dots coming out two dots
+coming out right and same thing on this
+
+ align:start position:0%
+coming out right and same thing on this
+ 
+
+ align:start position:0%
+coming out right and same thing on this
+side it's two dots going in and so forth
+
+ align:start position:0%
+side it's two dots going in and so forth
+ 
+
+ align:start position:0%
+side it's two dots going in and so forth
+okay so I'm plotting sort of the current
+
+ align:start position:0%
+okay so I'm plotting sort of the current
+ 
+
+ align:start position:0%
+okay so I'm plotting sort of the current
+density and these are the net currents
+
+ align:start position:0%
+density and these are the net currents
+ 
+
+ align:start position:0%
+density and these are the net currents
+that are being
+
+ align:start position:0%
+that are being
+ 
+
+ align:start position:0%
+that are being
+carried right so what happens inside my
+
+ align:start position:0%
+carried right so what happens inside my
+ 
+
+ align:start position:0%
+carried right so what happens inside my
+core if this is my core if this is high
+
+ align:start position:0%
+core if this is my core if this is high
+ 
+
+ align:start position:0%
+core if this is my core if this is high
+permeability material there is no h
+
+ align:start position:0%
+permeability material there is no h
+ 
+
+ align:start position:0%
+permeability material there is no h
+field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so if I execute ampers law
+
+ align:start position:0%
+right so if I execute ampers law
+ 
+
+ align:start position:0%
+right so if I execute ampers law
+integral of h. DL around say a loop here
+
+ align:start position:0%
+integral of h. DL around say a loop here
+ 
+
+ align:start position:0%
+integral of h. DL around say a loop here
+the only field that appears is in the
+
+ align:start position:0%
+the only field that appears is in the
+ 
+
+ align:start position:0%
+the only field that appears is in the
+window and what that means is in this
+
+ align:start position:0%
+window and what that means is in this
+ 
+
+ align:start position:0%
+window and what that means is in this
+picture if I plotted the H field I ought
+
+ align:start position:0%
+picture if I plotted the H field I ought
+ 
+
+ align:start position:0%
+picture if I plotted the H field I ought
+to have some H field
+
+ align:start position:0%
+to have some H field
+ 
+
+ align:start position:0%
+to have some H field
+here right that's associated with this
+
+ align:start position:0%
+here right that's associated with this
+ 
+
+ align:start position:0%
+here right that's associated with this
+current from the middle and if I looped
+
+ align:start position:0%
+current from the middle and if I looped
+ 
+
+ align:start position:0%
+current from the middle and if I looped
+around two layers of winding I get two H
+
+ align:start position:0%
+around two layers of winding I get two H
+ 
+
+ align:start position:0%
+around two layers of winding I get two H
+Fields
+
+ align:start position:0%
+Fields
+ 
+
+ align:start position:0%
+Fields
+right and so forth so what's happening
+
+ align:start position:0%
+right and so forth so what's happening
+ 
+
+ align:start position:0%
+right and so forth so what's happening
+is I go across the window I my field
+
+ align:start position:0%
+is I go across the window I my field
+ 
+
+ align:start position:0%
+is I go across the window I my field
+builds up and the first layer I've got
+
+ align:start position:0%
+builds up and the first layer I've got
+ 
+
+ align:start position:0%
+builds up and the first layer I've got
+one unit of H and the second layer I've
+
+ align:start position:0%
+one unit of H and the second layer I've
+ 
+
+ align:start position:0%
+one unit of H and the second layer I've
+got two Unit H if I had three layers I'd
+
+ align:start position:0%
+got two Unit H if I had three layers I'd
+ 
+
+ align:start position:0%
+got two Unit H if I had three layers I'd
+have three units of H right this layer
+
+ align:start position:0%
+have three units of H right this layer
+ 
+
+ align:start position:0%
+have three units of H right this layer
+is only carrying one unit of current but
+
+ align:start position:0%
+is only carrying one unit of current but
+ 
+
+ align:start position:0%
+is only carrying one unit of current but
+you can see that it has an average of
+
+ align:start position:0%
+you can see that it has an average of
+ 
+
+ align:start position:0%
+you can see that it has an average of
+1.5 or it has sort
+
+ align:start position:0%
+1.5 or it has sort
+ 
+
+ align:start position:0%
+1.5 or it has sort
+of it h I'm sorry it it has field that's
+
+ align:start position:0%
+of it h I'm sorry it it has field that's
+ 
+
+ align:start position:0%
+of it h I'm sorry it it has field that's
+imposed on it that's bigger than the net
+
+ align:start position:0%
+imposed on it that's bigger than the net
+ 
+
+ align:start position:0%
+imposed on it that's bigger than the net
+currents
+
+ align:start position:0%
+currents
+ 
+
+ align:start position:0%
+currents
+carrying right so this is an example
+
+ align:start position:0%
+carrying right so this is an example
+ 
+
+ align:start position:0%
+carrying right so this is an example
+where Fields owing to this layer are
+
+ align:start position:0%
+where Fields owing to this layer are
+ 
+
+ align:start position:0%
+where Fields owing to this layer are
+hitting this layer Fields owing from
+
+ align:start position:0%
+hitting this layer Fields owing from
+ 
+
+ align:start position:0%
+hitting this layer Fields owing from
+these two layers would hit the next
+
+ align:start position:0%
+these two layers would hit the next
+ 
+
+ align:start position:0%
+these two layers would hit the next
+layer and what happens is that I've got
+
+ align:start position:0%
+layer and what happens is that I've got
+ 
+
+ align:start position:0%
+layer and what happens is that I've got
+this effect where I'm imposing fields on
+
+ align:start position:0%
+this effect where I'm imposing fields on
+ 
+
+ align:start position:0%
+this effect where I'm imposing fields on
+my conductor and I'm going to get Eddie
+
+ align:start position:0%
+my conductor and I'm going to get Eddie
+ 
+
+ align:start position:0%
+my conductor and I'm going to get Eddie
+currents in the second
+
+ align:start position:0%
+currents in the second
+ 
+
+ align:start position:0%
+currents in the second
+layer that's going to cause
+
+ align:start position:0%
+layer that's going to cause
+ 
+
+ align:start position:0%
+layer that's going to cause
+loss okay and the problem with that is
+
+ align:start position:0%
+loss okay and the problem with that is
+ 
+
+ align:start position:0%
+loss okay and the problem with that is
+especially if I have very many layers of
+
+ align:start position:0%
+especially if I have very many layers of
+ 
+
+ align:start position:0%
+especially if I have very many layers of
+winding and I have very high AC current
+
+ align:start position:0%
+winding and I have very high AC current
+ 
+
+ align:start position:0%
+winding and I have very high AC current
+components I can have that induced loss
+
+ align:start position:0%
+components I can have that induced loss
+ 
+
+ align:start position:0%
+components I can have that induced loss
+gets reflected the way it looks
+
+ align:start position:0%
+gets reflected the way it looks
+ 
+
+ align:start position:0%
+gets reflected the way it looks
+electrically is is a much higher AC
+
+ align:start position:0%
+electrically is is a much higher AC
+ 
+
+ align:start position:0%
+electrically is is a much higher AC
+resistance to the winding so you could
+
+ align:start position:0%
+resistance to the winding so you could
+ 
+
+ align:start position:0%
+resistance to the winding so you could
+calculate you know your wire resistance
+
+ align:start position:0%
+calculate you know your wire resistance
+ 
+
+ align:start position:0%
+calculate you know your wire resistance
+your theoretical wire DC wire resistance
+
+ align:start position:0%
+your theoretical wire DC wire resistance
+ 
+
+ align:start position:0%
+your theoretical wire DC wire resistance
+and say it's 10
+
+ align:start position:0%
+and say it's 10
+ 
+
+ align:start position:0%
+and say it's 10
+milliohms then you could think oh but if
+
+ align:start position:0%
+milliohms then you could think oh but if
+ 
+
+ align:start position:0%
+milliohms then you could think oh but if
+I include skin effect it's 20 or 30
+
+ align:start position:0%
+I include skin effect it's 20 or 30
+ 
+
+ align:start position:0%
+I include skin effect it's 20 or 30
+Milli
+
+ align:start position:0%
+Milli
+ 
+
+ align:start position:0%
+Milli
+ohms because I have a bunch of skin
+
+ align:start position:0%
+ohms because I have a bunch of skin
+ 
+
+ align:start position:0%
+ohms because I have a bunch of skin
+effect and then you figure out what the
+
+ align:start position:0%
+effect and then you figure out what the
+ 
+
+ align:start position:0%
+effect and then you figure out what the
+proximity effect is if you have a bunch
+
+ align:start position:0%
+proximity effect is if you have a bunch
+ 
+
+ align:start position:0%
+proximity effect is if you have a bunch
+of layers and the L can sort of goes the
+
+ align:start position:0%
+of layers and the L can sort of goes the
+ 
+
+ align:start position:0%
+of layers and the L can sort of goes the
+square number of layers you could have
+
+ align:start position:0%
+square number of layers you could have
+ 
+
+ align:start position:0%
+square number of layers you could have
+300 Milli ohms right so where's your DC
+
+ align:start position:0%
+300 Milli ohms right so where's your DC
+ 
+
+ align:start position:0%
+300 Milli ohms right so where's your DC
+resistance might only have been 10 Mill
+
+ align:start position:0%
+resistance might only have been 10 Mill
+ 
+
+ align:start position:0%
+resistance might only have been 10 Mill
+ohms suddenly you got 300 Mill ohms
+
+ align:start position:0%
+ohms suddenly you got 300 Mill ohms
+ 
+
+ align:start position:0%
+ohms suddenly you got 300 Mill ohms
+that's you know a factor of 30 30 times
+
+ align:start position:0%
+that's you know a factor of 30 30 times
+ 
+
+ align:start position:0%
+that's you know a factor of 30 30 times
+the loss you were expecting right so
+
+ align:start position:0%
+the loss you were expecting right so
+ 
+
+ align:start position:0%
+the loss you were expecting right so
+when does this occur this occurs when
+
+ align:start position:0%
+when does this occur this occurs when
+ 
+
+ align:start position:0%
+when does this occur this occurs when
+you have conductors that are large
+
+ align:start position:0%
+you have conductors that are large
+ 
+
+ align:start position:0%
+you have conductors that are large
+compared to a skin
+
+ align:start position:0%
+compared to a skin
+ 
+
+ align:start position:0%
+compared to a skin
+depth or on the order of a skin depth
+
+ align:start position:0%
+depth or on the order of a skin depth
+ 
+
+ align:start position:0%
+depth or on the order of a skin depth
+and when you have many layers of winding
+
+ align:start position:0%
+and when you have many layers of winding
+ 
+
+ align:start position:0%
+and when you have many layers of winding
+such that fields from one winding are
+
+ align:start position:0%
+such that fields from one winding are
+ 
+
+ align:start position:0%
+such that fields from one winding are
+hitting the other if you're designing
+
+ align:start position:0%
+hitting the other if you're designing
+ 
+
+ align:start position:0%
+hitting the other if you're designing
+something that's carrying mostly DC ah
+
+ align:start position:0%
+something that's carrying mostly DC ah
+ 
+
+ align:start position:0%
+something that's carrying mostly DC ah
+don't worry about it if you're designing
+
+ align:start position:0%
+don't worry about it if you're designing
+ 
+
+ align:start position:0%
+don't worry about it if you're designing
+a TR really high frequency Transformer
+
+ align:start position:0%
+a TR really high frequency Transformer
+ 
+
+ align:start position:0%
+a TR really high frequency Transformer
+you might might want to start thinking
+
+ align:start position:0%
+you might might want to start thinking
+ 
+
+ align:start position:0%
+you might might want to start thinking
+about it because it can be a big effect
+
+ align:start position:0%
+about it because it can be a big effect
+ 
+
+ align:start position:0%
+about it because it can be a big effect
+um um and in fact uh what does that say
+
+ align:start position:0%
+um um and in fact uh what does that say
+ 
+
+ align:start position:0%
+um um and in fact uh what does that say
+you should do typically if I said okay
+
+ align:start position:0%
+you should do typically if I said okay
+ 
+
+ align:start position:0%
+you should do typically if I said okay
+because of skin effect I wanted my uh
+
+ align:start position:0%
+because of skin effect I wanted my uh
+ 
+
+ align:start position:0%
+because of skin effect I wanted my uh
+wire to be on the order of a skin depth
+
+ align:start position:0%
+wire to be on the order of a skin depth
+ 
+
+ align:start position:0%
+wire to be on the order of a skin depth
+or thicker or at least my strand
+
+ align:start position:0%
+or thicker or at least my strand
+ 
+
+ align:start position:0%
+or thicker or at least my strand
+diameter for my lips if you include
+
+ align:start position:0%
+diameter for my lips if you include
+ 
+
+ align:start position:0%
+diameter for my lips if you include
+proximity effect very often you want
+
+ align:start position:0%
+proximity effect very often you want
+ 
+
+ align:start position:0%
+proximity effect very often you want
+your skin depth you want your strand
+
+ align:start position:0%
+your skin depth you want your strand
+ 
+
+ align:start position:0%
+your skin depth you want your strand
+diameter or your wire diameter to be
+
+ align:start position:0%
+diameter or your wire diameter to be
+ 
+
+ align:start position:0%
+diameter or your wire diameter to be
+maybe three skin depths right or you get
+
+ align:start position:0%
+maybe three skin depths right or you get
+ 
+
+ align:start position:0%
+maybe three skin depths right or you get
+into this weird cir
+
+ align:start position:0%
+into this weird cir
+ 
+
+ align:start position:0%
+into this weird cir
+situation and and so sometimes that
+
+ align:start position:0%
+situation and and so sometimes that
+ 
+
+ align:start position:0%
+situation and and so sometimes that
+forces you to use really fine wire
+
+ align:start position:0%
+forces you to use really fine wire
+ 
+
+ align:start position:0%
+forces you to use really fine wire
+really small
+
+ align:start position:0%
+really small
+ 
+
+ align:start position:0%
+really small
+um really small
+
+ align:start position:0%
+um really small
+ 
+
+ align:start position:0%
+um really small
+strands even smaller than a skin depth
+
+ align:start position:0%
+strands even smaller than a skin depth
+ 
+
+ align:start position:0%
+strands even smaller than a skin depth
+so I think you know three skin depths
+
+ align:start position:0%
+so I think you know three skin depths
+ 
+
+ align:start position:0%
+so I think you know three skin depths
+might be what You' get if you had a lot
+
+ align:start position:0%
+might be what You' get if you had a lot
+ 
+
+ align:start position:0%
+might be what You' get if you had a lot
+of layers okay so that's just sort of a
+
+ align:start position:0%
+of layers okay so that's just sort of a
+ 
+
+ align:start position:0%
+of layers okay so that's just sort of a
+warning because you can get into this
+
+ align:start position:0%
+warning because you can get into this
+ 
+
+ align:start position:0%
+warning because you can get into this
+weird situation I've been there where
+
+ align:start position:0%
+weird situation I've been there where
+ 
+
+ align:start position:0%
+weird situation I've been there where
+you think oh my conduction loss is too
+
+ align:start position:0%
+you think oh my conduction loss is too
+ 
+
+ align:start position:0%
+you think oh my conduction loss is too
+high I'm measuring it I've got too much
+
+ align:start position:0%
+high I'm measuring it I've got too much
+ 
+
+ align:start position:0%
+high I'm measuring it I've got too much
+resistance so what do what's my natural
+
+ align:start position:0%
+resistance so what do what's my natural
+ 
+
+ align:start position:0%
+resistance so what do what's my natural
+inclination put in more copper use
+
+ align:start position:0%
+inclination put in more copper use
+ 
+
+ align:start position:0%
+inclination put in more copper use
+fatter wire and you find out you put in
+
+ align:start position:0%
+fatter wire and you find out you put in
+ 
+
+ align:start position:0%
+fatter wire and you find out you put in
+fatter wire and the resistance goes
+
+ align:start position:0%
+fatter wire and the resistance goes
+ 
+
+ align:start position:0%
+fatter wire and the resistance goes
+up right and the reason the resistance
+
+ align:start position:0%
+up right and the reason the resistance
+ 
+
+ align:start position:0%
+up right and the reason the resistance
+goes up is because this loss as you make
+
+ align:start position:0%
+goes up is because this loss as you make
+ 
+
+ align:start position:0%
+goes up is because this loss as you make
+this conductor wider there's more room
+
+ align:start position:0%
+this conductor wider there's more room
+ 
+
+ align:start position:0%
+this conductor wider there's more room
+for the Edie currents to circulate
+
+ align:start position:0%
+for the Edie currents to circulate
+ 
+
+ align:start position:0%
+for the Edie currents to circulate
+because of proximity effect if you make
+
+ align:start position:0%
+because of proximity effect if you make
+ 
+
+ align:start position:0%
+because of proximity effect if you make
+the current conductor thinner sort of
+
+ align:start position:0%
+the current conductor thinner sort of
+ 
+
+ align:start position:0%
+the current conductor thinner sort of
+this current going this way and this
+
+ align:start position:0%
+this current going this way and this
+ 
+
+ align:start position:0%
+this current going this way and this
+current coming this back kind of overlap
+
+ align:start position:0%
+current coming this back kind of overlap
+ 
+
+ align:start position:0%
+current coming this back kind of overlap
+and cancel and you get less proximity
+
+ align:start position:0%
+and cancel and you get less proximity
+ 
+
+ align:start position:0%
+and cancel and you get less proximity
+effect loss so sometimes it can be
+
+ align:start position:0%
+effect loss so sometimes it can be
+ 
+
+ align:start position:0%
+effect loss so sometimes it can be
+better to use thinner wire instead of
+
+ align:start position:0%
+better to use thinner wire instead of
+ 
+
+ align:start position:0%
+better to use thinner wire instead of
+thicker get less loss in net okay so
+
+ align:start position:0%
+thicker get less loss in net okay so
+ 
+
+ align:start position:0%
+thicker get less loss in net okay so
+that's just a a heads up about that any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions don't worry about it if you're
+
+ align:start position:0%
+questions don't worry about it if you're
+ 
+
+ align:start position:0%
+questions don't worry about it if you're
+carrying mostly DC it's not a problem
+
+ align:start position:0%
+carrying mostly DC it's not a problem
+ 
+
+ align:start position:0%
+carrying mostly DC it's not a problem
+it's just something for you to know
+
+ align:start position:0%
+it's just something for you to know
+ 
+
+ align:start position:0%
+it's just something for you to know
+about when you start to think about
+
+ align:start position:0%
+about when you start to think about
+ 
+
+ align:start position:0%
+about when you start to think about
+signing really high frequency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things it's a well okay so the skin
+
+ align:start position:0%
+things it's a well okay so the skin
+ 
+
+ align:start position:0%
+things it's a well okay so the skin
+depth at 60 HZ and this depends again on
+
+ align:start position:0%
+depth at 60 HZ and this depends again on
+ 
+
+ align:start position:0%
+depth at 60 HZ and this depends again on
+temperature is on the order of three4 of
+
+ align:start position:0%
+temperature is on the order of three4 of
+ 
+
+ align:start position:0%
+temperature is on the order of three4 of
+a centimeter so if you were talking a
+
+ align:start position:0%
+a centimeter so if you were talking a
+ 
+
+ align:start position:0%
+a centimeter so if you were talking a
+really Mondo like you wanted to carry
+
+ align:start position:0%
+really Mondo like you wanted to carry
+ 
+
+ align:start position:0%
+really Mondo like you wanted to carry
+you know 10,000 amps yeah well then
+
+ align:start position:0%
+you know 10,000 amps yeah well then
+ 
+
+ align:start position:0%
+you know 10,000 amps yeah well then
+you're going to have to Strand and
+
+ align:start position:0%
+you're going to have to Strand and
+ 
+
+ align:start position:0%
+you're going to have to Strand and
+insulate your wire and litz wire and so
+
+ align:start position:0%
+insulate your wire and litz wire and so
+ 
+
+ align:start position:0%
+insulate your wire and litz wire and so
+if you look at things like steamed
+
+ align:start position:0%
+if you look at things like steamed
+ 
+
+ align:start position:0%
+if you look at things like steamed
+herban generators they do use lits their
+
+ align:start position:0%
+herban generators they do use lits their
+ 
+
+ align:start position:0%
+herban generators they do use lits their
+bundles are like this and it's but but
+
+ align:start position:0%
+bundles are like this and it's but but
+ 
+
+ align:start position:0%
+bundles are like this and it's but but
+it's big compressed chunks of copper so
+
+ align:start position:0%
+it's big compressed chunks of copper so
+ 
+
+ align:start position:0%
+it's big compressed chunks of copper so
+this applies at any frequency if you're
+
+ align:start position:0%
+this applies at any frequency if you're
+ 
+
+ align:start position:0%
+this applies at any frequency if you're
+carrying enough current if I'm building
+
+ align:start position:0%
+carrying enough current if I'm building
+ 
+
+ align:start position:0%
+carrying enough current if I'm building
+a 60 HZ Transformer that's carrying an
+
+ align:start position:0%
+a 60 HZ Transformer that's carrying an
+ 
+
+ align:start position:0%
+a 60 HZ Transformer that's carrying an
+amp my conductors are naturally going to
+
+ align:start position:0%
+amp my conductors are naturally going to
+ 
+
+ align:start position:0%
+amp my conductors are naturally going to
+be less much less in the skin depth than
+
+ align:start position:0%
+be less much less in the skin depth than
+ 
+
+ align:start position:0%
+be less much less in the skin depth than
+I wouldn't even think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's winding loss right and
+
+ align:start position:0%
+okay so that's winding loss right and
+ 
+
+ align:start position:0%
+okay so that's winding loss right and
+these are just some things to think
+
+ align:start position:0%
+these are just some things to think
+ 
+
+ align:start position:0%
+these are just some things to think
+about watch out for skin effect and
+
+ align:start position:0%
+about watch out for skin effect and
+ 
+
+ align:start position:0%
+about watch out for skin effect and
+really watch out for proximity effect if
+
+ align:start position:0%
+really watch out for proximity effect if
+ 
+
+ align:start position:0%
+really watch out for proximity effect if
+you're carrying High AC currents the
+
+ align:start position:0%
+you're carrying High AC currents the
+ 
+
+ align:start position:0%
+you're carrying High AC currents the
+other piece of course of any inductor or
+
+ align:start position:0%
+other piece of course of any inductor or
+ 
+
+ align:start position:0%
+other piece of course of any inductor or
+any Transformer is the core
+
+ align:start position:0%
+any Transformer is the core
+ 
+
+ align:start position:0%
+any Transformer is the core
+okay and um ideally a core material is
+
+ align:start position:0%
+okay and um ideally a core material is
+ 
+
+ align:start position:0%
+okay and um ideally a core material is
+lossless right we have always sort of
+
+ align:start position:0%
+lossless right we have always sort of
+ 
+
+ align:start position:0%
+lossless right we have always sort of
+idealized if you will our BH
+
+ align:start position:0%
+idealized if you will our BH
+ 
+
+ align:start position:0%
+idealized if you will our BH
+characteristic of our core to look
+
+ align:start position:0%
+characteristic of our core to look
+ 
+
+ align:start position:0%
+characteristic of our core to look
+something like this right so um I might
+
+ align:start position:0%
+something like this right so um I might
+ 
+
+ align:start position:0%
+something like this right so um I might
+have plotted B versus
+
+ align:start position:0%
+have plotted B versus
+ 
+
+ align:start position:0%
+have plotted B versus
+H right to do something like I have some
+
+ align:start position:0%
+H right to do something like I have some
+ 
+
+ align:start position:0%
+H right to do something like I have some
+ideal you know this is Mu of my core and
+
+ align:start position:0%
+ideal you know this is Mu of my core and
+ 
+
+ align:start position:0%
+ideal you know this is Mu of my core and
+if I get above saturation it starts to
+
+ align:start position:0%
+if I get above saturation it starts to
+ 
+
+ align:start position:0%
+if I get above saturation it starts to
+do something like this and it goes back
+
+ align:start position:0%
+do something like this and it goes back
+ 
+
+ align:start position:0%
+do something like this and it goes back
+to Mu not right so that's that's my
+
+ align:start position:0%
+to Mu not right so that's that's my
+ 
+
+ align:start position:0%
+to Mu not right so that's that's my
+idealization but it actually doesn't
+
+ align:start position:0%
+idealization but it actually doesn't
+ 
+
+ align:start position:0%
+idealization but it actually doesn't
+look like that quite a real core right
+
+ align:start position:0%
+look like that quite a real core right
+ 
+
+ align:start position:0%
+look like that quite a real core right
+so if I just thought suppose I built a
+
+ align:start position:0%
+so if I just thought suppose I built a
+ 
+
+ align:start position:0%
+so if I just thought suppose I built a
+core
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and it had
+
+ align:start position:0%
+okay and it had
+ 
+
+ align:start position:0%
+okay and it had
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+um it had some area of the
+
+ align:start position:0%
+um it had some area of the
+ 
+
+ align:start position:0%
+um it had some area of the
+core it had some U of the core area of
+
+ align:start position:0%
+core it had some U of the core area of
+ 
+
+ align:start position:0%
+core it had some U of the core area of
+the core length of the core right and I
+
+ align:start position:0%
+the core length of the core right and I
+ 
+
+ align:start position:0%
+the core length of the core right and I
+put a winding on it and let me imagine
+
+ align:start position:0%
+put a winding on it and let me imagine
+ 
+
+ align:start position:0%
+put a winding on it and let me imagine
+that my winding has no resistance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right what would the you know what would
+
+ align:start position:0%
+right what would the you know what would
+ 
+
+ align:start position:0%
+right what would the you know what would
+the net power going into the core look
+
+ align:start position:0%
+the net power going into the core look
+ 
+
+ align:start position:0%
+the net power going into the core look
+like or the net
+
+ align:start position:0%
+like or the net
+ 
+
+ align:start position:0%
+like or the net
+energy let's let's calculate the energy
+
+ align:start position:0%
+energy let's let's calculate the energy
+ 
+
+ align:start position:0%
+energy let's let's calculate the energy
+that I'm putting into the core right so
+
+ align:start position:0%
+that I'm putting into the core right so
+ 
+
+ align:start position:0%
+that I'm putting into the core right so
+the input
+
+ align:start position:0%
+the input
+ 
+
+ align:start position:0%
+the input
+energy would be the integral over a
+
+ align:start position:0%
+energy would be the integral over a
+ 
+
+ align:start position:0%
+energy would be the integral over a
+period of V of T time I of T DT right
+
+ align:start position:0%
+period of V of T time I of T DT right
+ 
+
+ align:start position:0%
+period of V of T time I of T DT right
+it's the voltage applied times the
+
+ align:start position:0%
+it's the voltage applied times the
+ 
+
+ align:start position:0%
+it's the voltage applied times the
+current and if there's any loss in this
+
+ align:start position:0%
+current and if there's any loss in this
+ 
+
+ align:start position:0%
+current and if there's any loss in this
+system in the core right
+
+ align:start position:0%
+system in the core right
+ 
+
+ align:start position:0%
+system in the core right
+um I will have an integral of VI that
+
+ align:start position:0%
+um I will have an integral of VI that
+ 
+
+ align:start position:0%
+um I will have an integral of VI that
+would be not zero right ideal inductor
+
+ align:start position:0%
+would be not zero right ideal inductor
+ 
+
+ align:start position:0%
+would be not zero right ideal inductor
+of course that ought to be zero um but
+
+ align:start position:0%
+of course that ought to be zero um but
+ 
+
+ align:start position:0%
+of course that ought to be zero um but
+if I have loss it won't be okay and what
+
+ align:start position:0%
+if I have loss it won't be okay and what
+ 
+
+ align:start position:0%
+if I have loss it won't be okay and what
+does this look like well let me let me
+
+ align:start position:0%
+does this look like well let me let me
+ 
+
+ align:start position:0%
+does this look like well let me let me
+rewrite this in magnetic
+
+ align:start position:0%
+rewrite this in magnetic
+ 
+
+ align:start position:0%
+rewrite this in magnetic
+terms right what is v v is equal to uh
+
+ align:start position:0%
+terms right what is v v is equal to uh
+ 
+
+ align:start position:0%
+terms right what is v v is equal to uh
+n times the area of the core times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dbdt
+
+ align:start position:0%
+dbdt
+ 
+
+ align:start position:0%
+dbdt
+right why because V is D Lambda DT and
+
+ align:start position:0%
+right why because V is D Lambda DT and
+ 
+
+ align:start position:0%
+right why because V is D Lambda DT and
+Lambda is
+
+ align:start position:0%
+Lambda is
+ 
+
+ align:start position:0%
+Lambda is
+nbac so then I have NAC time
+
+ align:start position:0%
+nbac so then I have NAC time
+ 
+
+ align:start position:0%
+nbac so then I have NAC time
+dbdt okay what is the current well keep
+
+ align:start position:0%
+dbdt okay what is the current well keep
+ 
+
+ align:start position:0%
+dbdt okay what is the current well keep
+in mind if I integrated the H of the
+
+ align:start position:0%
+in mind if I integrated the H of the
+ 
+
+ align:start position:0%
+in mind if I integrated the H of the
+core around the length I should have ni
+
+ align:start position:0%
+core around the length I should have ni
+ 
+
+ align:start position:0%
+core around the length I should have ni
+right so what I get is H in the core
+
+ align:start position:0%
+right so what I get is H in the core
+ 
+
+ align:start position:0%
+right so what I get is H in the core
+time the length of the core is equal to
+
+ align:start position:0%
+time the length of the core is equal to
+ 
+
+ align:start position:0%
+time the length of the core is equal to
+ni I right so I ought to be able to
+
+ align:start position:0%
+ni I right so I ought to be able to
+ 
+
+ align:start position:0%
+ni I right so I ought to be able to
+write I is being equal to HC *
+
+ align:start position:0%
+write I is being equal to HC *
+ 
+
+ align:start position:0%
+write I is being equal to HC *
+LC
+
+ align:start position:0%
+LC
+ 
+
+ align:start position:0%
+LC
+n right so then I could write I of t as
+
+ align:start position:0%
+n right so then I could write I of t as
+ 
+
+ align:start position:0%
+n right so then I could write I of t as
+being equal to
+
+ align:start position:0%
+being equal to
+ 
+
+ align:start position:0%
+being equal to
+uh HC * LC ID n
+
+ align:start position:0%
+uh HC * LC ID n
+ 
+
+ align:start position:0%
+uh HC * LC ID n
+DT okay so let me cancel out the NS here
+
+ align:start position:0%
+DT okay so let me cancel out the NS here
+ 
+
+ align:start position:0%
+DT okay so let me cancel out the NS here
+and let me isolate I could I could write
+
+ align:start position:0%
+and let me isolate I could I could write
+ 
+
+ align:start position:0%
+and let me isolate I could I could write
+this as let me take out LC and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+AC the length of the core times area
+
+ align:start position:0%
+AC the length of the core times area
+ 
+
+ align:start position:0%
+AC the length of the core times area
+core this is just the volume of the core
+
+ align:start position:0%
+core this is just the volume of the core
+ 
+
+ align:start position:0%
+core this is just the volume of the core
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+right times the integral of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hdb and I'm going over a cycle so
+
+ align:start position:0%
+hdb and I'm going over a cycle so
+ 
+
+ align:start position:0%
+hdb and I'm going over a cycle so
+presumably B is looping so this
+
+ align:start position:0%
+presumably B is looping so this
+ 
+
+ align:start position:0%
+presumably B is looping so this
+is around a closed cycle all right so
+
+ align:start position:0%
+is around a closed cycle all right so
+ 
+
+ align:start position:0%
+is around a closed cycle all right so
+this is the energy I lose in going
+
+ align:start position:0%
+this is the energy I lose in going
+ 
+
+ align:start position:0%
+this is the energy I lose in going
+in cycling around it's the integral of
+
+ align:start position:0%
+in cycling around it's the integral of
+ 
+
+ align:start position:0%
+in cycling around it's the integral of
+hdb in the
+
+ align:start position:0%
+hdb in the
+ 
+
+ align:start position:0%
+hdb in the
+core and what we will see is that in a
+
+ align:start position:0%
+core and what we will see is that in a
+ 
+
+ align:start position:0%
+core and what we will see is that in a
+real core material you know B and H
+
+ align:start position:0%
+real core material you know B and H
+ 
+
+ align:start position:0%
+real core material you know B and H
+don't quite go up and down proportional
+
+ align:start position:0%
+don't quite go up and down proportional
+ 
+
+ align:start position:0%
+don't quite go up and down proportional
+the one the way this illustrates what
+
+ align:start position:0%
+the one the way this illustrates what
+ 
+
+ align:start position:0%
+the one the way this illustrates what
+you really see is something that does
+
+ align:start position:0%
+you really see is something that does
+ 
+
+ align:start position:0%
+you really see is something that does
+this it goes
+
+ align:start position:0%
+this it goes
+ 
+
+ align:start position:0%
+this it goes
+up and then it comes down with some
+
+ align:start position:0%
+up and then it comes down with some
+ 
+
+ align:start position:0%
+up and then it comes down with some
+slight
+
+ align:start position:0%
+slight
+ 
+
+ align:start position:0%
+slight
+spacing like
+
+ align:start position:0%
+spacing like
+ 
+
+ align:start position:0%
+spacing like
+that okay and if I think about the
+
+ align:start position:0%
+that okay and if I think about the
+ 
+
+ align:start position:0%
+that okay and if I think about the
+integral of hdb that's really this
+
+ align:start position:0%
+integral of hdb that's really this
+ 
+
+ align:start position:0%
+integral of hdb that's really this
+area Okay so H and B really form a
+
+ align:start position:0%
+area Okay so H and B really form a
+ 
+
+ align:start position:0%
+area Okay so H and B really form a
+hysteresis Loop and the area inside that
+
+ align:start position:0%
+hysteresis Loop and the area inside that
+ 
+
+ align:start position:0%
+hysteresis Loop and the area inside that
+hysteresis Loop is the energy I lose in
+
+ align:start position:0%
+hysteresis Loop is the energy I lose in
+ 
+
+ align:start position:0%
+hysteresis Loop is the energy I lose in
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+cycle any questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that this would sort of
+
+ align:start position:0%
+that this would sort of
+ 
+
+ align:start position:0%
+that this would sort of
+suggest
+
+ align:start position:0%
+suggest
+ 
+
+ align:start position:0%
+suggest
+that I lose so much energy per cycle for
+
+ align:start position:0%
+that I lose so much energy per cycle for
+ 
+
+ align:start position:0%
+that I lose so much energy per cycle for
+a given b or H
+
+ align:start position:0%
+a given b or H
+ 
+
+ align:start position:0%
+a given b or H
+swing and if I do it twice as fast I
+
+ align:start position:0%
+swing and if I do it twice as fast I
+ 
+
+ align:start position:0%
+swing and if I do it twice as fast I
+lose twice as much and so forth
+
+ align:start position:0%
+lose twice as much and so forth
+ 
+
+ align:start position:0%
+lose twice as much and so forth
+right um and at low frequencies that's
+
+ align:start position:0%
+right um and at low frequencies that's
+ 
+
+ align:start position:0%
+right um and at low frequencies that's
+kind of true at low enough frequencies
+
+ align:start position:0%
+kind of true at low enough frequencies
+ 
+
+ align:start position:0%
+kind of true at low enough frequencies
+that's kind of true they call this when
+
+ align:start position:0%
+that's kind of true they call this when
+ 
+
+ align:start position:0%
+that's kind of true they call this when
+that's true they call it hysteresis
+
+ align:start position:0%
+that's true they call it hysteresis
+ 
+
+ align:start position:0%
+that's true they call it hysteresis
+loss
+
+ align:start position:0%
+loss
+ 
+
+ align:start position:0%
+loss
+okay um unfortunately when you get
+
+ align:start position:0%
+okay um unfortunately when you get
+ 
+
+ align:start position:0%
+okay um unfortunately when you get
+higher in frequency where does this loss
+
+ align:start position:0%
+higher in frequency where does this loss
+ 
+
+ align:start position:0%
+higher in frequency where does this loss
+come from I should say it's because
+
+ align:start position:0%
+come from I should say it's because
+ 
+
+ align:start position:0%
+come from I should say it's because
+you're doing work to move magnetic
+
+ align:start position:0%
+you're doing work to move magnetic
+ 
+
+ align:start position:0%
+you're doing work to move magnetic
+domains around right they're
+
+ align:start position:0%
+domains around right they're
+ 
+
+ align:start position:0%
+domains around right they're
+mechanically moving around and by the
+
+ align:start position:0%
+mechanically moving around and by the
+ 
+
+ align:start position:0%
+mechanically moving around and by the
+way when the magnetic domains jump they
+
+ align:start position:0%
+way when the magnetic domains jump they
+ 
+
+ align:start position:0%
+way when the magnetic domains jump they
+introduce little Eddy currents in the
+
+ align:start position:0%
+introduce little Eddy currents in the
+ 
+
+ align:start position:0%
+introduce little Eddy currents in the
+material and so that generates loss
+
+ align:start position:0%
+material and so that generates loss
+ 
+
+ align:start position:0%
+material and so that generates loss
+right so you you do have a bunch of loss
+
+ align:start position:0%
+right so you you do have a bunch of loss
+ 
+
+ align:start position:0%
+right so you you do have a bunch of loss
+moving the magnetic domains around and
+
+ align:start position:0%
+moving the magnetic domains around and
+ 
+
+ align:start position:0%
+moving the magnetic domains around and
+hence that appears as sort of this net
+
+ align:start position:0%
+hence that appears as sort of this net
+ 
+
+ align:start position:0%
+hence that appears as sort of this net
+loss that even if you ignored winding
+
+ align:start position:0%
+loss that even if you ignored winding
+ 
+
+ align:start position:0%
+loss that even if you ignored winding
+loss or some additional loss by swinging
+
+ align:start position:0%
+loss or some additional loss by swinging
+ 
+
+ align:start position:0%
+loss or some additional loss by swinging
+AC flux in the core
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this
+
+ align:start position:0%
+okay this
+ 
+
+ align:start position:0%
+okay this
+loss is sometimes called classical
+
+ align:start position:0%
+loss is sometimes called classical
+ 
+
+ align:start position:0%
+loss is sometimes called classical
+hysteresis loss okay um unfortunately
+
+ align:start position:0%
+hysteresis loss okay um unfortunately
+ 
+
+ align:start position:0%
+hysteresis loss okay um unfortunately
+while at low frequencies is sort of
+
+ align:start position:0%
+while at low frequencies is sort of
+ 
+
+ align:start position:0%
+while at low frequencies is sort of
+proportional to frequeny qu when you get
+
+ align:start position:0%
+proportional to frequeny qu when you get
+ 
+
+ align:start position:0%
+proportional to frequeny qu when you get
+up to high frequencies it turns out the
+
+ align:start position:0%
+up to high frequencies it turns out the
+ 
+
+ align:start position:0%
+up to high frequencies it turns out the
+shape of the loop changes so it turns
+
+ align:start position:0%
+shape of the loop changes so it turns
+ 
+
+ align:start position:0%
+shape of the loop changes so it turns
+out that actual loss in many magnetic
+
+ align:start position:0%
+out that actual loss in many magnetic
+ 
+
+ align:start position:0%
+out that actual loss in many magnetic
+materials is not proportional to
+
+ align:start position:0%
+materials is not proportional to
+ 
+
+ align:start position:0%
+materials is not proportional to
+frequency is proportional to something
+
+ align:start position:0%
+frequency is proportional to something
+ 
+
+ align:start position:0%
+frequency is proportional to something
+higher than frequency it just depends on
+
+ align:start position:0%
+higher than frequency it just depends on
+ 
+
+ align:start position:0%
+higher than frequency it just depends on
+the magnetic material so that's one
+
+ align:start position:0%
+the magnetic material so that's one
+ 
+
+ align:start position:0%
+the magnetic material so that's one
+thing you got to keep in mind all right
+
+ align:start position:0%
+thing you got to keep in mind all right
+ 
+
+ align:start position:0%
+thing you got to keep in mind all right
+so people sometimes talk about
+
+ align:start position:0%
+so people sometimes talk about
+ 
+
+ align:start position:0%
+so people sometimes talk about
+hysteresis loss but what this hysteresis
+
+ align:start position:0%
+hysteresis loss but what this hysteresis
+ 
+
+ align:start position:0%
+hysteresis loss but what this hysteresis
+Loop looks like is frequency
+
+ align:start position:0%
+Loop looks like is frequency
+ 
+
+ align:start position:0%
+Loop looks like is frequency
+dependent okay the other thing I would
+
+ align:start position:0%
+dependent okay the other thing I would
+ 
+
+ align:start position:0%
+dependent okay the other thing I would
+say is that for this kind of loss you
+
+ align:start position:0%
+say is that for this kind of loss you
+ 
+
+ align:start position:0%
+say is that for this kind of loss you
+can kind of calculated as loss per unit
+
+ align:start position:0%
+can kind of calculated as loss per unit
+ 
+
+ align:start position:0%
+can kind of calculated as loss per unit
+volume right if I told you the shape of
+
+ align:start position:0%
+volume right if I told you the shape of
+ 
+
+ align:start position:0%
+volume right if I told you the shape of
+the hysteresis Loop and what B you were
+
+ align:start position:0%
+the hysteresis Loop and what B you were
+ 
+
+ align:start position:0%
+the hysteresis Loop and what B you were
+swinging over you could say this
+
+ align:start position:0%
+swinging over you could say this
+ 
+
+ align:start position:0%
+swinging over you could say this
+area times the volume of the core times
+
+ align:start position:0%
+area times the volume of the core times
+ 
+
+ align:start position:0%
+area times the volume of the core times
+the frequency would give
+
+ align:start position:0%
+the frequency would give
+ 
+
+ align:start position:0%
+the frequency would give
+me my power dissipation in the core
+
+ align:start position:0%
+me my power dissipation in the core
+ 
+
+ align:start position:0%
+me my power dissipation in the core
+material make sense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody I should say that this kind of
+
+ align:start position:0%
+everybody I should say that this kind of
+ 
+
+ align:start position:0%
+everybody I should say that this kind of
+loss o to the magnetic is sort of one
+
+ align:start position:0%
+loss o to the magnetic is sort of one
+ 
+
+ align:start position:0%
+loss o to the magnetic is sort of one
+form of loss you can get there are other
+
+ align:start position:0%
+form of loss you can get there are other
+ 
+
+ align:start position:0%
+form of loss you can get there are other
+forms of loss you can get however in
+
+ align:start position:0%
+forms of loss you can get however in
+ 
+
+ align:start position:0%
+forms of loss you can get however in
+core that are not so-called hysteresis
+
+ align:start position:0%
+core that are not so-called hysteresis
+ 
+
+ align:start position:0%
+core that are not so-called hysteresis
+or related loss and one of those is in
+
+ align:start position:0%
+or related loss and one of those is in
+ 
+
+ align:start position:0%
+or related loss and one of those is in
+fact Edie current loss in the
+
+ align:start position:0%
+fact Edie current loss in the
+ 
+
+ align:start position:0%
+fact Edie current loss in the
+core think about this what is this core
+
+ align:start position:0%
+core think about this what is this core
+ 
+
+ align:start position:0%
+core think about this what is this core
+doing if I put a current in here I'm
+
+ align:start position:0%
+doing if I put a current in here I'm
+ 
+
+ align:start position:0%
+doing if I put a current in here I'm
+putting a
+
+ align:start position:0%
+putting a
+ 
+
+ align:start position:0%
+putting a
+flux and a flux density of B through the
+
+ align:start position:0%
+flux and a flux density of B through the
+ 
+
+ align:start position:0%
+flux and a flux density of B through the
+core itself right well at low
+
+ align:start position:0%
+core itself right well at low
+ 
+
+ align:start position:0%
+core itself right well at low
+frequencies especially we often use
+
+ align:start position:0%
+frequencies especially we often use
+ 
+
+ align:start position:0%
+frequencies especially we often use
+conductive magnetic materials right we
+
+ align:start position:0%
+conductive magnetic materials right we
+ 
+
+ align:start position:0%
+conductive magnetic materials right we
+use like steel Steel's pretty conductive
+
+ align:start position:0%
+use like steel Steel's pretty conductive
+ 
+
+ align:start position:0%
+use like steel Steel's pretty conductive
+and so if I look looked at this
+
+ align:start position:0%
+and so if I look looked at this
+ 
+
+ align:start position:0%
+and so if I look looked at this
+crosssection right that I drew here in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+white you know what I would get is I
+
+ align:start position:0%
+white you know what I would get is I
+ 
+
+ align:start position:0%
+white you know what I would get is I
+would have some flux going in like
+
+ align:start position:0%
+would have some flux going in like
+ 
+
+ align:start position:0%
+would have some flux going in like
+this right and what would that do if I
+
+ align:start position:0%
+this right and what would that do if I
+ 
+
+ align:start position:0%
+this right and what would that do if I
+have an AC flux dbdt I'm going to
+
+ align:start position:0%
+have an AC flux dbdt I'm going to
+ 
+
+ align:start position:0%
+have an AC flux dbdt I'm going to
+generate a field inside the conductor um
+
+ align:start position:0%
+generate a field inside the conductor um
+ 
+
+ align:start position:0%
+generate a field inside the conductor um
+that does this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that AC field is then going to
+
+ align:start position:0%
+and that AC field is then going to
+ 
+
+ align:start position:0%
+and that AC field is then going to
+generate Eddie currents which try to to
+
+ align:start position:0%
+generate Eddie currents which try to to
+ 
+
+ align:start position:0%
+generate Eddie currents which try to to
+counteract that and reject the flux in
+
+ align:start position:0%
+counteract that and reject the flux in
+ 
+
+ align:start position:0%
+counteract that and reject the flux in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+core right so in other words the fact
+
+ align:start position:0%
+core right so in other words the fact
+ 
+
+ align:start position:0%
+core right so in other words the fact
+that I'm carrying AC flux through a
+
+ align:start position:0%
+that I'm carrying AC flux through a
+ 
+
+ align:start position:0%
+that I'm carrying AC flux through a
+conductive material means I can get Edie
+
+ align:start position:0%
+conductive material means I can get Edie
+ 
+
+ align:start position:0%
+conductive material means I can get Edie
+currents circulating in the
+
+ align:start position:0%
+currents circulating in the
+ 
+
+ align:start position:0%
+currents circulating in the
+core all right that's kind of um
+
+ align:start position:0%
+core all right that's kind of um
+ 
+
+ align:start position:0%
+core all right that's kind of um
+unfortunate I'm sorry if I put flux in
+
+ align:start position:0%
+unfortunate I'm sorry if I put flux in
+ 
+
+ align:start position:0%
+unfortunate I'm sorry if I put flux in
+the core the Eddy currents are going to
+
+ align:start position:0%
+the core the Eddy currents are going to
+ 
+
+ align:start position:0%
+the core the Eddy currents are going to
+circulate this way right so this is I
+
+ align:start position:0%
+circulate this way right so this is I
+ 
+
+ align:start position:0%
+circulate this way right so this is I
+Eddie when do I start to care about this
+
+ align:start position:0%
+Eddie when do I start to care about this
+ 
+
+ align:start position:0%
+Eddie when do I start to care about this
+Eddie current loss I care about it when
+
+ align:start position:0%
+Eddie current loss I care about it when
+ 
+
+ align:start position:0%
+Eddie current loss I care about it when
+the dimension of the core is on the
+
+ align:start position:0%
+the dimension of the core is on the
+ 
+
+ align:start position:0%
+the dimension of the core is on the
+order of the skin depth right and if I
+
+ align:start position:0%
+order of the skin depth right and if I
+ 
+
+ align:start position:0%
+order of the skin depth right and if I
+get a Core cross-section that's too big
+
+ align:start position:0%
+get a Core cross-section that's too big
+ 
+
+ align:start position:0%
+get a Core cross-section that's too big
+two things happen first I get a lot of
+
+ align:start position:0%
+two things happen first I get a lot of
+ 
+
+ align:start position:0%
+two things happen first I get a lot of
+Eddie current loss and that just
+
+ align:start position:0%
+Eddie current loss and that just
+ 
+
+ align:start position:0%
+Eddie current loss and that just
+manifests itself as uh additional loss
+
+ align:start position:0%
+manifests itself as uh additional loss
+ 
+
+ align:start position:0%
+manifests itself as uh additional loss
+and by the way it scales up with area
+
+ align:start position:0%
+and by the way it scales up with area
+ 
+
+ align:start position:0%
+and by the way it scales up with area
+because I have more room for Eddie
+
+ align:start position:0%
+because I have more room for Eddie
+ 
+
+ align:start position:0%
+because I have more room for Eddie
+currents to run around in so it's not
+
+ align:start position:0%
+currents to run around in so it's not
+ 
+
+ align:start position:0%
+currents to run around in so it's not
+even loss per unit volume get get worse
+
+ align:start position:0%
+even loss per unit volume get get worse
+ 
+
+ align:start position:0%
+even loss per unit volume get get worse
+as the volume as the cross-sectional
+
+ align:start position:0%
+as the volume as the cross-sectional
+ 
+
+ align:start position:0%
+as the volume as the cross-sectional
+area gets bigger um but the other thing
+
+ align:start position:0%
+area gets bigger um but the other thing
+ 
+
+ align:start position:0%
+area gets bigger um but the other thing
+is if it's bad enough it sends a reject
+
+ align:start position:0%
+is if it's bad enough it sends a reject
+ 
+
+ align:start position:0%
+is if it's bad enough it sends a reject
+flux from the center of the core and I
+
+ align:start position:0%
+flux from the center of the core and I
+ 
+
+ align:start position:0%
+flux from the center of the core and I
+don't even you know I might drive up the
+
+ align:start position:0%
+don't even you know I might drive up the
+ 
+
+ align:start position:0%
+don't even you know I might drive up the
+concentrational flux at the edges and
+
+ align:start position:0%
+concentrational flux at the edges and
+ 
+
+ align:start position:0%
+concentrational flux at the edges and
+maybe even saturate
+
+ align:start position:0%
+maybe even saturate
+ 
+
+ align:start position:0%
+maybe even saturate
+it so what do people do about
+
+ align:start position:0%
+it so what do people do about
+ 
+
+ align:start position:0%
+it so what do people do about
+this if you have high frequency
+
+ align:start position:0%
+this if you have high frequency
+ 
+
+ align:start position:0%
+this if you have high frequency
+materials like ferite it turns out
+
+ align:start position:0%
+materials like ferite it turns out
+ 
+
+ align:start position:0%
+materials like ferite it turns out
+they're not very
+
+ align:start position:0%
+they're not very
+ 
+
+ align:start position:0%
+they're not very
+conductive okay so you don't usually
+
+ align:start position:0%
+conductive okay so you don't usually
+ 
+
+ align:start position:0%
+conductive okay so you don't usually
+worry about Edy currents in your loss
+
+ align:start position:0%
+worry about Edy currents in your loss
+ 
+
+ align:start position:0%
+worry about Edy currents in your loss
+unless in your core unless you're really
+
+ align:start position:0%
+unless in your core unless you're really
+ 
+
+ align:start position:0%
+unless in your core unless you're really
+high frequencies but if you're at low
+
+ align:start position:0%
+high frequencies but if you're at low
+ 
+
+ align:start position:0%
+high frequencies but if you're at low
+frequency materials like Steels you do
+
+ align:start position:0%
+frequency materials like Steels you do
+ 
+
+ align:start position:0%
+frequency materials like Steels you do
+have to worry about this how do they fix
+
+ align:start position:0%
+have to worry about this how do they fix
+ 
+
+ align:start position:0%
+have to worry about this how do they fix
+this instead of making one big giant
+
+ align:start position:0%
+this instead of making one big giant
+ 
+
+ align:start position:0%
+this instead of making one big giant
+core cross-sectional area they sort of
+
+ align:start position:0%
+core cross-sectional area they sort of
+ 
+
+ align:start position:0%
+core cross-sectional area they sort of
+take the same trick what they do they
+
+ align:start position:0%
+take the same trick what they do they
+ 
+
+ align:start position:0%
+take the same trick what they do they
+don't need to litz transpose it because
+
+ align:start position:0%
+don't need to litz transpose it because
+ 
+
+ align:start position:0%
+don't need to litz transpose it because
+they're not it's not like they're
+
+ align:start position:0%
+they're not it's not like they're
+ 
+
+ align:start position:0%
+they're not it's not like they're
+carrying current in it what they'll do
+
+ align:start position:0%
+carrying current in it what they'll do
+ 
+
+ align:start position:0%
+carrying current in it what they'll do
+is instead of making a big cross-section
+
+ align:start position:0%
+is instead of making a big cross-section
+ 
+
+ align:start position:0%
+is instead of making a big cross-section
+they'll make this out of little sheets
+
+ align:start position:0%
+they'll make this out of little sheets
+ 
+
+ align:start position:0%
+they'll make this out of little sheets
+like this that are insulated from one
+
+ align:start position:0%
+like this that are insulated from one
+ 
+
+ align:start position:0%
+like this that are insulated from one
+another called
+
+ align:start position:0%
+another called
+ 
+
+ align:start position:0%
+another called
+laminations
+
+ align:start position:0%
+laminations
+ 
+
+ align:start position:0%
+laminations
+right so instead of building up a big
+
+ align:start position:0%
+right so instead of building up a big
+ 
+
+ align:start position:0%
+right so instead of building up a big
+fat piece of steel they'll build it
+
+ align:start position:0%
+fat piece of steel they'll build it
+ 
+
+ align:start position:0%
+fat piece of steel they'll build it
+usually out of stampings and insulate
+
+ align:start position:0%
+usually out of stampings and insulate
+ 
+
+ align:start position:0%
+usually out of stampings and insulate
+them and then stack them up and the nice
+
+ align:start position:0%
+them and then stack them up and the nice
+ 
+
+ align:start position:0%
+them and then stack them up and the nice
+thing about this is instead of this big
+
+ align:start position:0%
+thing about this is instead of this big
+ 
+
+ align:start position:0%
+thing about this is instead of this big
+eddy current being allowed to run around
+
+ align:start position:0%
+eddy current being allowed to run around
+ 
+
+ align:start position:0%
+eddy current being allowed to run around
+this huge Loop and cause lots of loss
+
+ align:start position:0%
+this huge Loop and cause lots of loss
+ 
+
+ align:start position:0%
+this huge Loop and cause lots of loss
+it's being forced to circulate in these
+
+ align:start position:0%
+it's being forced to circulate in these
+ 
+
+ align:start position:0%
+it's being forced to circulate in these
+tiny little areas and as long as these
+
+ align:start position:0%
+tiny little areas and as long as these
+ 
+
+ align:start position:0%
+tiny little areas and as long as these
+laminations are thin compared to a skin
+
+ align:start position:0%
+laminations are thin compared to a skin
+ 
+
+ align:start position:0%
+laminations are thin compared to a skin
+depth the Edie currents more or less
+
+ align:start position:0%
+depth the Edie currents more or less
+ 
+
+ align:start position:0%
+depth the Edie currents more or less
+cancel out and you don't get much Edie
+
+ align:start position:0%
+cancel out and you don't get much Edie
+ 
+
+ align:start position:0%
+cancel out and you don't get much Edie
+current loss so you'll see a lot of 60
+
+ align:start position:0%
+current loss so you'll see a lot of 60
+ 
+
+ align:start position:0%
+current loss so you'll see a lot of 60
+HZ Transformers or electric machines are
+
+ align:start position:0%
+HZ Transformers or electric machines are
+ 
+
+ align:start position:0%
+HZ Transformers or electric machines are
+all built out of laminations how do they
+
+ align:start position:0%
+all built out of laminations how do they
+ 
+
+ align:start position:0%
+all built out of laminations how do they
+size the skin depth of those
+
+ align:start position:0%
+size the skin depth of those
+ 
+
+ align:start position:0%
+size the skin depth of those
+laminations how do they size the
+
+ align:start position:0%
+laminations how do they size the
+ 
+
+ align:start position:0%
+laminations how do they size the
+lamination thickness they ask what the
+
+ align:start position:0%
+lamination thickness they ask what the
+ 
+
+ align:start position:0%
+lamination thickness they ask what the
+skin depth and the steel is they make
+
+ align:start position:0%
+skin depth and the steel is they make
+ 
+
+ align:start position:0%
+skin depth and the steel is they make
+the lamination sort of thin compared to
+
+ align:start position:0%
+the lamination sort of thin compared to
+ 
+
+ align:start position:0%
+the lamination sort of thin compared to
+that any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+um core as being higher
+
+ align:start position:0%
+um core as being higher
+ 
+
+ align:start position:0%
+um core as being higher
+or like is it related to permability or
+
+ align:start position:0%
+or like is it related to permability or
+ 
+
+ align:start position:0%
+or like is it related to permability or
+well it's so what's the yeah it comes
+
+ align:start position:0%
+well it's so what's the yeah it comes
+ 
+
+ align:start position:0%
+well it's so what's the yeah it comes
+down to
+
+ align:start position:0%
+down to
+ 
+
+ align:start position:0%
+down to
+what's the skin depth so if you have
+
+ align:start position:0%
+what's the skin depth so if you have
+ 
+
+ align:start position:0%
+what's the skin depth so if you have
+high permeability the skin depth gets
+
+ align:start position:0%
+high permeability the skin depth gets
+ 
+
+ align:start position:0%
+high permeability the skin depth gets
+small right so you just kind of plunk
+
+ align:start position:0%
+small right so you just kind of plunk
+ 
+
+ align:start position:0%
+small right so you just kind of plunk
+this in and find out you know what is
+
+ align:start position:0%
+this in and find out you know what is
+ 
+
+ align:start position:0%
+this in and find out you know what is
+the dimension that I would care
+
+ align:start position:0%
+the dimension that I would care
+ 
+
+ align:start position:0%
+the dimension that I would care
+about um I should
+
+ align:start position:0%
+about um I should
+ 
+
+ align:start position:0%
+about um I should
+say I can fix Eddie currents just by
+
+ align:start position:0%
+say I can fix Eddie currents just by
+ 
+
+ align:start position:0%
+say I can fix Eddie currents just by
+laminating okay um so then I'm sort of
+
+ align:start position:0%
+laminating okay um so then I'm sort of
+ 
+
+ align:start position:0%
+laminating okay um so then I'm sort of
+left with this kind of hysteresis kind
+
+ align:start position:0%
+left with this kind of hysteresis kind
+ 
+
+ align:start position:0%
+left with this kind of hysteresis kind
+of behavior but I said that fyes is in
+
+ align:start position:0%
+of behavior but I said that fyes is in
+ 
+
+ align:start position:0%
+of behavior but I said that fyes is in
+reality frequency dependent and the
+
+ align:start position:0%
+reality frequency dependent and the
+ 
+
+ align:start position:0%
+reality frequency dependent and the
+truth of the matter is it doesn't it's
+
+ align:start position:0%
+truth of the matter is it doesn't it's
+ 
+
+ align:start position:0%
+truth of the matter is it doesn't it's
+not proportional to frequency uh how do
+
+ align:start position:0%
+not proportional to frequency uh how do
+ 
+
+ align:start position:0%
+not proportional to frequency uh how do
+people treat it they treat it rather
+
+ align:start position:0%
+people treat it they treat it rather
+ 
+
+ align:start position:0%
+people treat it they treat it rather
+empirically what they really do is they
+
+ align:start position:0%
+empirically what they really do is they
+ 
+
+ align:start position:0%
+empirically what they really do is they
+plot loss per unit volume versus flux
+
+ align:start position:0%
+plot loss per unit volume versus flux
+ 
+
+ align:start position:0%
+plot loss per unit volume versus flux
+density at different frequencies and you
+
+ align:start position:0%
+density at different frequencies and you
+ 
+
+ align:start position:0%
+density at different frequencies and you
+might get curves like this you can see
+
+ align:start position:0%
+might get curves like this you can see
+ 
+
+ align:start position:0%
+might get curves like this you can see
+that the loss goes up some you know this
+
+ align:start position:0%
+that the loss goes up some you know this
+ 
+
+ align:start position:0%
+that the loss goes up some you know this
+is a log log plot so it comes up goes up
+
+ align:start position:0%
+is a log log plot so it comes up goes up
+ 
+
+ align:start position:0%
+is a log log plot so it comes up goes up
+with some
+
+ align:start position:0%
+with some
+ 
+
+ align:start position:0%
+with some
+power of the flux density and it also
+
+ align:start position:0%
+power of the flux density and it also
+ 
+
+ align:start position:0%
+power of the flux density and it also
+increases somehow in frequency and they
+
+ align:start position:0%
+increases somehow in frequency and they
+ 
+
+ align:start position:0%
+increases somehow in frequency and they
+model it and they say okay okay the
+
+ align:start position:0%
+model it and they say okay okay the
+ 
+
+ align:start position:0%
+model it and they say okay okay the
+power per unit
+
+ align:start position:0%
+power per unit
+ 
+
+ align:start position:0%
+power per unit
+volume p subv is power per unit volume
+
+ align:start position:0%
+volume p subv is power per unit volume
+ 
+
+ align:start position:0%
+volume p subv is power per unit volume
+is equal to some
+
+ align:start position:0%
+is equal to some
+ 
+
+ align:start position:0%
+is equal to some
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+K times some
+
+ align:start position:0%
+K times some
+ 
+
+ align:start position:0%
+K times some
+frequency to the first Power and some AC
+
+ align:start position:0%
+frequency to the first Power and some AC
+ 
+
+ align:start position:0%
+frequency to the first Power and some AC
+flux density amplitude and this is
+
+ align:start position:0%
+flux density amplitude and this is
+ 
+
+ align:start position:0%
+flux density amplitude and this is
+usually calcul this is only usually
+
+ align:start position:0%
+usually calcul this is only usually
+ 
+
+ align:start position:0%
+usually calcul this is only usually
+measured for sinusoids unfortunately to
+
+ align:start position:0%
+measured for sinusoids unfortunately to
+ 
+
+ align:start position:0%
+measured for sinusoids unfortunately to
+some other power Beta And basically what
+
+ align:start position:0%
+some other power Beta And basically what
+ 
+
+ align:start position:0%
+some other power Beta And basically what
+they do is they'll collect data like
+
+ align:start position:0%
+they do is they'll collect data like
+ 
+
+ align:start position:0%
+they do is they'll collect data like
+that they'll figure out the core loss
+
+ align:start position:0%
+that they'll figure out the core loss
+ 
+
+ align:start position:0%
+that they'll figure out the core loss
+from kind of measurements we're going to
+
+ align:start position:0%
+from kind of measurements we're going to
+ 
+
+ align:start position:0%
+from kind of measurements we're going to
+do show you right now and they'll say k
+
+ align:start position:0%
+do show you right now and they'll say k
+ 
+
+ align:start position:0%
+do show you right now and they'll say k
+Alpha and beta or they'll give you a
+
+ align:start position:0%
+Alpha and beta or they'll give you a
+ 
+
+ align:start position:0%
+Alpha and beta or they'll give you a
+plot and you look at this and say okay
+
+ align:start position:0%
+plot and you look at this and say okay
+ 
+
+ align:start position:0%
+plot and you look at this and say okay
+this is a highfrequency material I'm
+
+ align:start position:0%
+this is a highfrequency material I'm
+ 
+
+ align:start position:0%
+this is a highfrequency material I'm
+going to put 10 millitesla through it
+
+ align:start position:0%
+going to put 10 millitesla through it
+ 
+
+ align:start position:0%
+going to put 10 millitesla through it
+and I'm going to do it at 5 megahertz
+
+ align:start position:0%
+and I'm going to do it at 5 megahertz
+ 
+
+ align:start position:0%
+and I'm going to do it at 5 megahertz
+and I have 500 millatt per centimeter
+
+ align:start position:0%
+and I have 500 millatt per centimeter
+ 
+
+ align:start position:0%
+and I have 500 millatt per centimeter
+cubed and that's how you calculate it
+
+ align:start position:0%
+cubed and that's how you calculate it
+ 
+
+ align:start position:0%
+cubed and that's how you calculate it
+okay so it's very very
+
+ align:start position:0%
+okay so it's very very
+ 
+
+ align:start position:0%
+okay so it's very very
+empirical unlike winding laws where you
+
+ align:start position:0%
+empirical unlike winding laws where you
+ 
+
+ align:start position:0%
+empirical unlike winding laws where you
+can write lots of equations and kind of
+
+ align:start position:0%
+can write lots of equations and kind of
+ 
+
+ align:start position:0%
+can write lots of equations and kind of
+predict it very ly core loss is very
+
+ align:start position:0%
+predict it very ly core loss is very
+ 
+
+ align:start position:0%
+predict it very ly core loss is very
+much determined by measurement it's very
+
+ align:start position:0%
+much determined by measurement it's very
+ 
+
+ align:start position:0%
+much determined by measurement it's very
+hard to link the microscopic Behavior to
+
+ align:start position:0%
+hard to link the microscopic Behavior to
+ 
+
+ align:start position:0%
+hard to link the microscopic Behavior to
+the macroscopic behavior except in
+
+ align:start position:0%
+the macroscopic behavior except in
+ 
+
+ align:start position:0%
+the macroscopic behavior except in
+limited
+
+ align:start position:0%
+limited
+ 
+
+ align:start position:0%
+limited
+circumstances now I'm almost out of time
+
+ align:start position:0%
+circumstances now I'm almost out of time
+ 
+
+ align:start position:0%
+circumstances now I'm almost out of time
+here but what we wanted to show you and
+
+ align:start position:0%
+here but what we wanted to show you and
+ 
+
+ align:start position:0%
+here but what we wanted to show you and
+maybe I will hand this over to
+
+ align:start position:0%
+maybe I will hand this over to
+ 
+
+ align:start position:0%
+maybe I will hand this over to
+Mony so we have an inductor here and I'm
+
+ align:start position:0%
+Mony so we have an inductor here and I'm
+ 
+
+ align:start position:0%
+Mony so we have an inductor here and I'm
+plotting the current through the
+
+ align:start position:0%
+plotting the current through the
+ 
+
+ align:start position:0%
+plotting the current through the
+inductor that's that's proportional to H
+
+ align:start position:0%
+inductor that's that's proportional to H
+ 
+
+ align:start position:0%
+inductor that's that's proportional to H
+and it's on the x- axis and we are also
+
+ align:start position:0%
+and it's on the x- axis and we are also
+ 
+
+ align:start position:0%
+and it's on the x- axis and we are also
+plotting the voltage to the inductor and
+
+ align:start position:0%
+plotting the voltage to the inductor and
+ 
+
+ align:start position:0%
+plotting the voltage to the inductor and
+it's integrating it and it's on the y
+
+ align:start position:0%
+it's integrating it and it's on the y
+ 
+
+ align:start position:0%
+it's integrating it and it's on the y
+axis so we are trying to get the BH cve
+
+ align:start position:0%
+axis so we are trying to get the BH cve
+ 
+
+ align:start position:0%
+axis so we are trying to get the BH cve
+for the code and I'll slowly increase
+
+ align:start position:0%
+for the code and I'll slowly increase
+ 
+
+ align:start position:0%
+for the code and I'll slowly increase
+the current that's being pushed through
+
+ align:start position:0%
+the current that's being pushed through
+ 
+
+ align:start position:0%
+the current that's being pushed through
+the inductor so let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so this is where we can see it
+
+ align:start position:0%
+yeah so this is where we can see it
+ 
+
+ align:start position:0%
+yeah so this is where we can see it
+slightly like reling the saturation of
+
+ align:start position:0%
+slightly like reling the saturation of
+ 
+
+ align:start position:0%
+slightly like reling the saturation of
+the code and this is the VH C
+
+ align:start position:0%
+the code and this is the VH C
+ 
+
+ align:start position:0%
+the code and this is the VH C
+add no so there you can see just based
+
+ align:start position:0%
+add no so there you can see just based
+ 
+
+ align:start position:0%
+add no so there you can see just based
+on the earlier calculation we did
+
+ align:start position:0%
+on the earlier calculation we did
+ 
+
+ align:start position:0%
+on the earlier calculation we did
+there's kind of this hysteresis Loop
+
+ align:start position:0%
+there's kind of this hysteresis Loop
+ 
+
+ align:start position:0%
+there's kind of this hysteresis Loop
+between B and H you would see that it
+
+ align:start position:0%
+between B and H you would see that it
+ 
+
+ align:start position:0%
+between B and H you would see that it
+change change shape versus frequency and
+
+ align:start position:0%
+change change shape versus frequency and
+ 
+
+ align:start position:0%
+change change shape versus frequency and
+from this that's what a real core
+
+ align:start position:0%
+from this that's what a real core
+ 
+
+ align:start position:0%
+from this that's what a real core
+material does looks like even though we
+
+ align:start position:0%
+material does looks like even though we
+ 
+
+ align:start position:0%
+material does looks like even though we
+pretend it doesn't do that so all you
+
+ align:start position:0%
+pretend it doesn't do that so all you
+ 
+
+ align:start position:0%
+pretend it doesn't do that so all you
+got to do is be careful if you're going
+
+ align:start position:0%
+got to do is be careful if you're going
+ 
+
+ align:start position:0%
+got to do is be careful if you're going
+to have a lot of AC flux density
+
+ align:start position:0%
+to have a lot of AC flux density
+ 
+
+ align:start position:0%
+to have a lot of AC flux density
+figure out your loss per unit volum and
+
+ align:start position:0%
+figure out your loss per unit volum and
+ 
+
+ align:start position:0%
+figure out your loss per unit volum and
+use it so that that's my very handwavy
+
+ align:start position:0%
+use it so that that's my very handwavy
+ 
+
+ align:start position:0%
+use it so that that's my very handwavy
+introduction to loss and magnetics I
+
+ align:start position:0%
+introduction to loss and magnetics I
+ 
+
+ align:start position:0%
+introduction to loss and magnetics I
+think it'll be enough to get you through
+
+ align:start position:0%
+think it'll be enough to get you through
+ 
+
+ align:start position:0%
+think it'll be enough to get you through
+to designing some pretty reasonable
+
+ align:start position:0%
+to designing some pretty reasonable
+ 
+
+ align:start position:0%
+to designing some pretty reasonable
+inductors and Transformers and uh we
+
+ align:start position:0%
+inductors and Transformers and uh we
+ 
+
+ align:start position:0%
+inductors and Transformers and uh we
+will pick uh a new topic up next class
+
+ align:start position:0%
+will pick uh a new topic up next class
+ 
+
+ align:start position:0%
+will pick uh a new topic up next class
+so have a great day
\ No newline at end of file
diff --git a/djrhQK-dBx0.txt b/djrhQK-dBx0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..70bc91b1570ea52ab88e64b4e9148ee8dc21627f
--- /dev/null
+++ b/djrhQK-dBx0.txt
@@ -0,0 +1,9387 @@
+align:start position:0%
+ 
+um it's a great pleasure to present um
+
+ align:start position:0%
+um it's a great pleasure to present um
+ 
+
+ align:start position:0%
+um it's a great pleasure to present um
+uh thank you thank you Steve um at this
+
+ align:start position:0%
+uh thank you thank you Steve um at this
+ 
+
+ align:start position:0%
+uh thank you thank you Steve um at this
+conference and it's a great Gathering
+
+ align:start position:0%
+conference and it's a great Gathering
+ 
+
+ align:start position:0%
+conference and it's a great Gathering
+and I I thank Steve um and John because
+
+ align:start position:0%
+and I I thank Steve um and John because
+ 
+
+ align:start position:0%
+and I I thank Steve um and John because
+I feel the fire you know again U the
+
+ align:start position:0%
+I feel the fire you know again U the
+ 
+
+ align:start position:0%
+I feel the fire you know again U the
+Auto ID center went through a period of
+
+ align:start position:0%
+Auto ID center went through a period of
+ 
+
+ align:start position:0%
+Auto ID center went through a period of
+similar uh ignition and it was
+
+ align:start position:0%
+similar uh ignition and it was
+ 
+
+ align:start position:0%
+similar uh ignition and it was
+fascinating it was kind of like uh you
+
+ align:start position:0%
+fascinating it was kind of like uh you
+ 
+
+ align:start position:0%
+fascinating it was kind of like uh you
+know a petri dish where things new life
+
+ align:start position:0%
+know a petri dish where things new life
+ 
+
+ align:start position:0%
+know a petri dish where things new life
+forms were being born and then we moved
+
+ align:start position:0%
+forms were being born and then we moved
+ 
+
+ align:start position:0%
+forms were being born and then we moved
+into the into the execution phase and
+
+ align:start position:0%
+into the into the execution phase and
+ 
+
+ align:start position:0%
+into the into the execution phase and
+APC Global of whom the many
+
+ align:start position:0%
+APC Global of whom the many
+ 
+
+ align:start position:0%
+APC Global of whom the many
+representatives here started excuting uh
+
+ align:start position:0%
+representatives here started excuting uh
+ 
+
+ align:start position:0%
+representatives here started excuting uh
+and meanwhile uh the Auto ID lab you
+
+ align:start position:0%
+and meanwhile uh the Auto ID lab you
+ 
+
+ align:start position:0%
+and meanwhile uh the Auto ID lab you
+know refocuses attentions um on new
+
+ align:start position:0%
+know refocuses attentions um on new
+ 
+
+ align:start position:0%
+know refocuses attentions um on new
+research and we have a family of Auto ID
+
+ align:start position:0%
+research and we have a family of Auto ID
+ 
+
+ align:start position:0%
+research and we have a family of Auto ID
+lab members professors students uh
+
+ align:start position:0%
+lab members professors students uh
+ 
+
+ align:start position:0%
+lab members professors students uh
+colleagues here uh who've kind of
+
+ align:start position:0%
+colleagues here uh who've kind of
+ 
+
+ align:start position:0%
+colleagues here uh who've kind of
+recreated this entire environment and
+
+ align:start position:0%
+recreated this entire environment and
+ 
+
+ align:start position:0%
+recreated this entire environment and
+eler Flash and Jun marai and and John
+
+ align:start position:0%
+eler Flash and Jun marai and and John
+ 
+
+ align:start position:0%
+eler Flash and Jun marai and and John
+Williams and Peter Cole of course who's
+
+ align:start position:0%
+Williams and Peter Cole of course who's
+ 
+
+ align:start position:0%
+Williams and Peter Cole of course who's
+been involved with this for a long time
+
+ align:start position:0%
+been involved with this for a long time
+ 
+
+ align:start position:0%
+been involved with this for a long time
+Dan Engles it's fantastic to see this
+
+ align:start position:0%
+Dan Engles it's fantastic to see this
+ 
+
+ align:start position:0%
+Dan Engles it's fantastic to see this
+all come together again um how uh so uh
+
+ align:start position:0%
+all come together again um how uh so uh
+ 
+
+ align:start position:0%
+all come together again um how uh so uh
+it's a great pleasure it's almost like I
+
+ align:start position:0%
+it's a great pleasure it's almost like I
+ 
+
+ align:start position:0%
+it's a great pleasure it's almost like I
+keep saying this every time I can go to
+
+ align:start position:0%
+keep saying this every time I can go to
+ 
+
+ align:start position:0%
+keep saying this every time I can go to
+a Auto ID event it's like a it's like a
+
+ align:start position:0%
+a Auto ID event it's like a it's like a
+ 
+
+ align:start position:0%
+a Auto ID event it's like a it's like a
+wedding you know it's like going back to
+
+ align:start position:0%
+wedding you know it's like going back to
+ 
+
+ align:start position:0%
+wedding you know it's like going back to
+a family wedding and recognizing all
+
+ align:start position:0%
+a family wedding and recognizing all
+ 
+
+ align:start position:0%
+a family wedding and recognizing all
+your friends um so it's a great pleasure
+
+ align:start position:0%
+your friends um so it's a great pleasure
+ 
+
+ align:start position:0%
+your friends um so it's a great pleasure
+what I thought I would do is talk about
+
+ align:start position:0%
+what I thought I would do is talk about
+ 
+
+ align:start position:0%
+what I thought I would do is talk about
+the future as I see it um and actually
+
+ align:start position:0%
+the future as I see it um and actually
+ 
+
+ align:start position:0%
+the future as I see it um and actually
+funly enough I didn't have to change my
+
+ align:start position:0%
+funly enough I didn't have to change my
+ 
+
+ align:start position:0%
+funly enough I didn't have to change my
+slides from about uh uh seven years ago
+
+ align:start position:0%
+slides from about uh uh seven years ago
+ 
+
+ align:start position:0%
+slides from about uh uh seven years ago
+um and just paint a landscape of what it
+
+ align:start position:0%
+um and just paint a landscape of what it
+ 
+
+ align:start position:0%
+um and just paint a landscape of what it
+is that academics could do research and
+
+ align:start position:0%
+is that academics could do research and
+ 
+
+ align:start position:0%
+is that academics could do research and
+I should tell you a little story when I
+
+ align:start position:0%
+I should tell you a little story when I
+ 
+
+ align:start position:0%
+I should tell you a little story when I
+started this research seven or eight
+
+ align:start position:0%
+started this research seven or eight
+ 
+
+ align:start position:0%
+started this research seven or eight
+years ago David Brock and I actually
+
+ align:start position:0%
+years ago David Brock and I actually
+ 
+
+ align:start position:0%
+years ago David Brock and I actually
+actually David Brock gets a lot of
+
+ align:start position:0%
+actually David Brock gets a lot of
+ 
+
+ align:start position:0%
+actually David Brock gets a lot of
+credit for this uh I wasn't sure that
+
+ align:start position:0%
+credit for this uh I wasn't sure that
+ 
+
+ align:start position:0%
+credit for this uh I wasn't sure that
+you know I was coming up for 10 years I
+
+ align:start position:0%
+you know I was coming up for 10 years I
+ 
+
+ align:start position:0%
+you know I was coming up for 10 years I
+was uh trying to write papers and and
+
+ align:start position:0%
+was uh trying to write papers and and
+ 
+
+ align:start position:0%
+was uh trying to write papers and and
+make an academic field out of this um
+
+ align:start position:0%
+make an academic field out of this um
+ 
+
+ align:start position:0%
+make an academic field out of this um
+and um as many of my former students
+
+ align:start position:0%
+and um as many of my former students
+ 
+
+ align:start position:0%
+and um as many of my former students
+sitting here will tell you I wasn't sure
+
+ align:start position:0%
+sitting here will tell you I wasn't sure
+ 
+
+ align:start position:0%
+sitting here will tell you I wasn't sure
+this would be a tenable topic you know
+
+ align:start position:0%
+this would be a tenable topic you know
+ 
+
+ align:start position:0%
+this would be a tenable topic you know
+could I write papers could this be
+
+ align:start position:0%
+could I write papers could this be
+ 
+
+ align:start position:0%
+could I write papers could this be
+academic is there some real researcher
+
+ align:start position:0%
+academic is there some real researcher
+ 
+
+ align:start position:0%
+academic is there some real researcher
+or am I just slapping tags on things and
+
+ align:start position:0%
+or am I just slapping tags on things and
+ 
+
+ align:start position:0%
+or am I just slapping tags on things and
+you know reading them and feeling good
+
+ align:start position:0%
+you know reading them and feeling good
+ 
+
+ align:start position:0%
+you know reading them and feeling good
+about it right and has all the indust
+
+ align:start position:0%
+about it right and has all the indust
+ 
+
+ align:start position:0%
+about it right and has all the indust
+has all the technology development being
+
+ align:start position:0%
+has all the technology development being
+ 
+
+ align:start position:0%
+has all the technology development being
+done um and uh we we as a group grabbed
+
+ align:start position:0%
+done um and uh we we as a group grabbed
+ 
+
+ align:start position:0%
+done um and uh we we as a group grabbed
+the tiger by the tail and the tiger took
+
+ align:start position:0%
+the tiger by the tail and the tiger took
+ 
+
+ align:start position:0%
+the tiger by the tail and the tiger took
+us to places that we didn't discover uh
+
+ align:start position:0%
+us to places that we didn't discover uh
+ 
+
+ align:start position:0%
+us to places that we didn't discover uh
+we didn't know that even existed you
+
+ align:start position:0%
+we didn't know that even existed you
+ 
+
+ align:start position:0%
+we didn't know that even existed you
+know um and what I discovered in that
+
+ align:start position:0%
+know um and what I discovered in that
+ 
+
+ align:start position:0%
+know um and what I discovered in that
+process and perhaps this applies to
+
+ align:start position:0%
+process and perhaps this applies to
+ 
+
+ align:start position:0%
+process and perhaps this applies to
+other Technologies as well as I think
+
+ align:start position:0%
+other Technologies as well as I think
+ 
+
+ align:start position:0%
+other Technologies as well as I think
+one needs to understand that in any new
+
+ align:start position:0%
+one needs to understand that in any new
+ 
+
+ align:start position:0%
+one needs to understand that in any new
+technology and especially in RFID there
+
+ align:start position:0%
+technology and especially in RFID there
+ 
+
+ align:start position:0%
+technology and especially in RFID there
+are embedded layers of richness uh that
+
+ align:start position:0%
+are embedded layers of richness uh that
+ 
+
+ align:start position:0%
+are embedded layers of richness uh that
+are revealed as you start making things
+
+ align:start position:0%
+are revealed as you start making things
+ 
+
+ align:start position:0%
+are revealed as you start making things
+practical and and the beauty is that
+
+ align:start position:0%
+practical and and the beauty is that
+ 
+
+ align:start position:0%
+practical and and the beauty is that
+they come in different colors it could
+
+ align:start position:0%
+they come in different colors it could
+ 
+
+ align:start position:0%
+they come in different colors it could
+be in in security it me protocols
+
+ align:start position:0%
+be in in security it me protocols
+ 
+
+ align:start position:0%
+be in in security it me protocols
+there's so many areas of richness um
+
+ align:start position:0%
+there's so many areas of richness um
+ 
+
+ align:start position:0%
+there's so many areas of richness um
+that uh that are waiting to be explored
+
+ align:start position:0%
+that uh that are waiting to be explored
+ 
+
+ align:start position:0%
+that uh that are waiting to be explored
+that's the first thing and the second
+
+ align:start position:0%
+that's the first thing and the second
+ 
+
+ align:start position:0%
+that's the first thing and the second
+point I want to make was that we are
+
+ align:start position:0%
+point I want to make was that we are
+ 
+
+ align:start position:0%
+point I want to make was that we are
+very much at the beginning of the
+
+ align:start position:0%
+very much at the beginning of the
+ 
+
+ align:start position:0%
+very much at the beginning of the
+journey and that's kind of where I'll
+
+ align:start position:0%
+journey and that's kind of where I'll
+ 
+
+ align:start position:0%
+journey and that's kind of where I'll
+start so there is a lot of
+
+ align:start position:0%
+start so there is a lot of
+ 
+
+ align:start position:0%
+start so there is a lot of
+self-satisfaction which is I think in
+
+ align:start position:0%
+self-satisfaction which is I think in
+ 
+
+ align:start position:0%
+self-satisfaction which is I think in
+some ways deserved that oh we're there
+
+ align:start position:0%
+some ways deserved that oh we're there
+ 
+
+ align:start position:0%
+some ways deserved that oh we're there
+let's start doing it and that's that's
+
+ align:start position:0%
+let's start doing it and that's that's
+ 
+
+ align:start position:0%
+let's start doing it and that's that's
+great we should be doing it but I have
+
+ align:start position:0%
+great we should be doing it but I have
+ 
+
+ align:start position:0%
+great we should be doing it but I have
+to say that we're very much at the
+
+ align:start position:0%
+to say that we're very much at the
+ 
+
+ align:start position:0%
+to say that we're very much at the
+beginning of this journey thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you sp you we're very much at the
+
+ align:start position:0%
+you sp you we're very much at the
+ 
+
+ align:start position:0%
+you sp you we're very much at the
+beginning of this journey um RFID has
+
+ align:start position:0%
+beginning of this journey um RFID has
+ 
+
+ align:start position:0%
+beginning of this journey um RFID has
+been around for 50 years the Auto ID
+
+ align:start position:0%
+been around for 50 years the Auto ID
+ 
+
+ align:start position:0%
+been around for 50 years the Auto ID
+center is only 8 years old but it would
+
+ align:start position:0%
+center is only 8 years old but it would
+ 
+
+ align:start position:0%
+center is only 8 years old but it would
+be very arrogant for anyone to suggest
+
+ align:start position:0%
+be very arrogant for anyone to suggest
+ 
+
+ align:start position:0%
+be very arrogant for anyone to suggest
+that somehow the research has been done
+
+ align:start position:0%
+that somehow the research has been done
+ 
+
+ align:start position:0%
+that somehow the research has been done
+there's just so much exciting stuff to
+
+ align:start position:0%
+there's just so much exciting stuff to
+ 
+
+ align:start position:0%
+there's just so much exciting stuff to
+be done and um you know if you look at
+
+ align:start position:0%
+be done and um you know if you look at
+ 
+
+ align:start position:0%
+be done and um you know if you look at
+the history right I mean the first
+
+ align:start position:0%
+the history right I mean the first
+ 
+
+ align:start position:0%
+the history right I mean the first
+papers in this uh and I did a reference
+
+ align:start position:0%
+papers in this uh and I did a reference
+ 
+
+ align:start position:0%
+papers in this uh and I did a reference
+search uh by the way there's a wonderful
+
+ align:start position:0%
+search uh by the way there's a wonderful
+ 
+
+ align:start position:0%
+search uh by the way there's a wonderful
+paper called the shrouds of time the
+
+ align:start position:0%
+paper called the shrouds of time the
+ 
+
+ align:start position:0%
+paper called the shrouds of time the
+history of RFID by lant it was published
+
+ align:start position:0%
+history of RFID by lant it was published
+ 
+
+ align:start position:0%
+history of RFID by lant it was published
+as an aim um publication if you do a
+
+ align:start position:0%
+as an aim um publication if you do a
+ 
+
+ align:start position:0%
+as an aim um publication if you do a
+search on Google you will find it uh it
+
+ align:start position:0%
+search on Google you will find it uh it
+ 
+
+ align:start position:0%
+search on Google you will find it uh it
+captures the history very well um but if
+
+ align:start position:0%
+captures the history very well um but if
+ 
+
+ align:start position:0%
+captures the history very well um but if
+you do a reference search the first
+
+ align:start position:0%
+you do a reference search the first
+ 
+
+ align:start position:0%
+you do a reference search the first
+papers came out in 48 Peter Cole who's
+
+ align:start position:0%
+papers came out in 48 Peter Cole who's
+ 
+
+ align:start position:0%
+papers came out in 48 Peter Cole who's
+sitting right up front here was involved
+
+ align:start position:0%
+sitting right up front here was involved
+ 
+
+ align:start position:0%
+sitting right up front here was involved
+in with many of the early mations of
+
+ align:start position:0%
+in with many of the early mations of
+ 
+
+ align:start position:0%
+in with many of the early mations of
+RFID and in the' 70s uh Automotive
+
+ align:start position:0%
+RFID and in the' 70s uh Automotive
+ 
+
+ align:start position:0%
+RFID and in the' 70s uh Automotive
+license plates is that about right Peter
+
+ align:start position:0%
+license plates is that about right Peter
+ 
+
+ align:start position:0%
+license plates is that about right Peter
+is that about the first reference um
+
+ align:start position:0%
+is that about the first reference um
+ 
+
+ align:start position:0%
+is that about the first reference um
+began to appear and then RFID went into
+
+ align:start position:0%
+began to appear and then RFID went into
+ 
+
+ align:start position:0%
+began to appear and then RFID went into
+this this uh this uh you know this
+
+ align:start position:0%
+this this uh this uh you know this
+ 
+
+ align:start position:0%
+this this uh this uh you know this
+highly uh kind of specialized research
+
+ align:start position:0%
+highly uh kind of specialized research
+ 
+
+ align:start position:0%
+highly uh kind of specialized research
+phase uh we as a center started in '98
+
+ align:start position:0%
+phase uh we as a center started in '98
+ 
+
+ align:start position:0%
+phase uh we as a center started in '98
+uh and then we developed standards in
+
+ align:start position:0%
+uh and then we developed standards in
+ 
+
+ align:start position:0%
+uh and then we developed standards in
+2001 we couldn't get the rest of the
+
+ align:start position:0%
+2001 we couldn't get the rest of the
+ 
+
+ align:start position:0%
+2001 we couldn't get the rest of the
+industry to really join us so we bucked
+
+ align:start position:0%
+industry to really join us so we bucked
+ 
+
+ align:start position:0%
+industry to really join us so we bucked
+the trend and developed our own
+
+ align:start position:0%
+the trend and developed our own
+ 
+
+ align:start position:0%
+the trend and developed our own
+protocols with some Innovative startup
+
+ align:start position:0%
+protocols with some Innovative startup
+ 
+
+ align:start position:0%
+protocols with some Innovative startup
+companies like alien technology and
+
+ align:start position:0%
+companies like alien technology and
+ 
+
+ align:start position:0%
+companies like alien technology and
+Matrix and those with the Gen one
+
+ align:start position:0%
+Matrix and those with the Gen one
+ 
+
+ align:start position:0%
+Matrix and those with the Gen one
+protocols and that's how we started
+
+ align:start position:0%
+protocols and that's how we started
+ 
+
+ align:start position:0%
+protocols and that's how we started
+getting the industry going um but the
+
+ align:start position:0%
+getting the industry going um but the
+ 
+
+ align:start position:0%
+getting the industry going um but the
+reason I'm putting that up there is
+
+ align:start position:0%
+reason I'm putting that up there is
+ 
+
+ align:start position:0%
+reason I'm putting that up there is
+that's you know 2000s this is 2006 it's
+
+ align:start position:0%
+that's you know 2000s this is 2006 it's
+ 
+
+ align:start position:0%
+that's you know 2000s this is 2006 it's
+not that long ago and it would be very
+
+ align:start position:0%
+not that long ago and it would be very
+ 
+
+ align:start position:0%
+not that long ago and it would be very
+arrogant for any of us to suggest that
+
+ align:start position:0%
+arrogant for any of us to suggest that
+ 
+
+ align:start position:0%
+arrogant for any of us to suggest that
+somehow in five or six years we figured
+
+ align:start position:0%
+somehow in five or six years we figured
+ 
+
+ align:start position:0%
+somehow in five or six years we figured
+out everything that they needs to you
+
+ align:start position:0%
+out everything that they needs to you
+ 
+
+ align:start position:0%
+out everything that they needs to you
+know one needs to know about RFID um and
+
+ align:start position:0%
+know one needs to know about RFID um and
+ 
+
+ align:start position:0%
+know one needs to know about RFID um and
+the first bulk taging is only a year old
+
+ align:start position:0%
+the first bulk taging is only a year old
+ 
+
+ align:start position:0%
+the first bulk taging is only a year old
+folks really it's only one year old uh
+
+ align:start position:0%
+folks really it's only one year old uh
+ 
+
+ align:start position:0%
+folks really it's only one year old uh
+you know the first mandate really hit in
+
+ align:start position:0%
+you know the first mandate really hit in
+ 
+
+ align:start position:0%
+you know the first mandate really hit in
+early 2005 here we are in January 2006
+
+ align:start position:0%
+early 2005 here we are in January 2006
+ 
+
+ align:start position:0%
+early 2005 here we are in January 2006
+so there's a heck of a lot lot of work
+
+ align:start position:0%
+so there's a heck of a lot lot of work
+ 
+
+ align:start position:0%
+so there's a heck of a lot lot of work
+waiting to be done and what I did seven
+
+ align:start position:0%
+waiting to be done and what I did seven
+ 
+
+ align:start position:0%
+waiting to be done and what I did seven
+or eight years ago is I created a
+
+ align:start position:0%
+or eight years ago is I created a
+ 
+
+ align:start position:0%
+or eight years ago is I created a
+landscape I looked at every research
+
+ align:start position:0%
+landscape I looked at every research
+ 
+
+ align:start position:0%
+landscape I looked at every research
+topic I could possibly do in RFID
+
+ align:start position:0%
+topic I could possibly do in RFID
+ 
+
+ align:start position:0%
+topic I could possibly do in RFID
+because remember I was trying to you
+
+ align:start position:0%
+because remember I was trying to you
+ 
+
+ align:start position:0%
+because remember I was trying to you
+know get tenure write papers and I
+
+ align:start position:0%
+know get tenure write papers and I
+ 
+
+ align:start position:0%
+know get tenure write papers and I
+wanted to create a landscape and
+
+ align:start position:0%
+wanted to create a landscape and
+ 
+
+ align:start position:0%
+wanted to create a landscape and
+actually that hasn't fleshed out very
+
+ align:start position:0%
+actually that hasn't fleshed out very
+ 
+
+ align:start position:0%
+actually that hasn't fleshed out very
+much so I'll put that up now and I'll
+
+ align:start position:0%
+much so I'll put that up now and I'll
+ 
+
+ align:start position:0%
+much so I'll put that up now and I'll
+use that as a theme for the rest of my
+
+ align:start position:0%
+use that as a theme for the rest of my
+ 
+
+ align:start position:0%
+use that as a theme for the rest of my
+talk you can break it up in many ways
+
+ align:start position:0%
+talk you can break it up in many ways
+ 
+
+ align:start position:0%
+talk you can break it up in many ways
+you can look at technology and the
+
+ align:start position:0%
+you can look at technology and the
+ 
+
+ align:start position:0%
+you can look at technology and the
+beauty of RFID is it spans everything
+
+ align:start position:0%
+beauty of RFID is it spans everything
+ 
+
+ align:start position:0%
+beauty of RFID is it spans everything
+from semiconductor Manufacturing ing to
+
+ align:start position:0%
+from semiconductor Manufacturing ing to
+ 
+
+ align:start position:0%
+from semiconductor Manufacturing ing to
+systems research and distributor
+
+ align:start position:0%
+systems research and distributor
+ 
+
+ align:start position:0%
+systems research and distributor
+Discovery and things like that so you
+
+ align:start position:0%
+Discovery and things like that so you
+ 
+
+ align:start position:0%
+Discovery and things like that so you
+have tags you have semiconductors you
+
+ align:start position:0%
+have tags you have semiconductors you
+ 
+
+ align:start position:0%
+have tags you have semiconductors you
+have antenna on tags you have material
+
+ align:start position:0%
+have antenna on tags you have material
+ 
+
+ align:start position:0%
+have antenna on tags you have material
+constants your material properties you
+
+ align:start position:0%
+constants your material properties you
+ 
+
+ align:start position:0%
+constants your material properties you
+have the interconnect between the chip
+
+ align:start position:0%
+have the interconnect between the chip
+ 
+
+ align:start position:0%
+have the interconnect between the chip
+and an antenna by itself is a
+
+ align:start position:0%
+and an antenna by itself is a
+ 
+
+ align:start position:0%
+and an antenna by itself is a
+significant PhD thesis waiting to happen
+
+ align:start position:0%
+significant PhD thesis waiting to happen
+ 
+
+ align:start position:0%
+significant PhD thesis waiting to happen
+right just that right you have um
+
+ align:start position:0%
+right just that right you have um
+ 
+
+ align:start position:0%
+right just that right you have um
+packaging um off the off the tag you
+
+ align:start position:0%
+packaging um off the off the tag you
+ 
+
+ align:start position:0%
+packaging um off the off the tag you
+have you know how how does the tag deal
+
+ align:start position:0%
+have you know how how does the tag deal
+ 
+
+ align:start position:0%
+have you know how how does the tag deal
+with you know reactor packaging we had a
+
+ align:start position:0%
+with you know reactor packaging we had a
+ 
+
+ align:start position:0%
+with you know reactor packaging we had a
+wonderful uh project here that Dan
+
+ align:start position:0%
+wonderful uh project here that Dan
+ 
+
+ align:start position:0%
+wonderful uh project here that Dan
+Engles LED on on tag packaging and
+
+ align:start position:0%
+Engles LED on on tag packaging and
+ 
+
+ align:start position:0%
+Engles LED on on tag packaging and
+performance you have Protocols of course
+
+ align:start position:0%
+performance you have Protocols of course
+ 
+
+ align:start position:0%
+performance you have Protocols of course
+this the Auto ID center did a lot of and
+
+ align:start position:0%
+this the Auto ID center did a lot of and
+ 
+
+ align:start position:0%
+this the Auto ID center did a lot of and
+there a lot of experts here on tag
+
+ align:start position:0%
+there a lot of experts here on tag
+ 
+
+ align:start position:0%
+there a lot of experts here on tag
+protocols uh we're barely scratching the
+
+ align:start position:0%
+protocols uh we're barely scratching the
+ 
+
+ align:start position:0%
+protocols uh we're barely scratching the
+surface of protocols we have gen one
+
+ align:start position:0%
+surface of protocols we have gen one
+ 
+
+ align:start position:0%
+surface of protocols we have gen one
+which is Gen one UHF we have some HF now
+
+ align:start position:0%
+which is Gen one UHF we have some HF now
+ 
+
+ align:start position:0%
+which is Gen one UHF we have some HF now
+we have gen two but then there's Ultra
+
+ align:start position:0%
+we have gen two but then there's Ultra
+ 
+
+ align:start position:0%
+we have gen two but then there's Ultra
+wide band there's all sorts of
+
+ align:start position:0%
+wide band there's all sorts of
+ 
+
+ align:start position:0%
+wide band there's all sorts of
+interesting stuff just waiting to be
+
+ align:start position:0%
+interesting stuff just waiting to be
+ 
+
+ align:start position:0%
+interesting stuff just waiting to be
+done and I'll touch upon it um in in uh
+
+ align:start position:0%
+done and I'll touch upon it um in in uh
+ 
+
+ align:start position:0%
+done and I'll touch upon it um in in uh
+in in the next few slides you have
+
+ align:start position:0%
+in in the next few slides you have
+ 
+
+ align:start position:0%
+in in the next few slides you have
+reader antenna think about this everyone
+
+ align:start position:0%
+reader antenna think about this everyone
+ 
+
+ align:start position:0%
+reader antenna think about this everyone
+thinks of that uh I should say there's a
+
+ align:start position:0%
+thinks of that uh I should say there's a
+ 
+
+ align:start position:0%
+thinks of that uh I should say there's a
+lot of thought that perhaps per you know
+
+ align:start position:0%
+lot of thought that perhaps per you know
+ 
+
+ align:start position:0%
+lot of thought that perhaps per you know
+antenna not not that interesting maybe
+
+ align:start position:0%
+antenna not not that interesting maybe
+ 
+
+ align:start position:0%
+antenna not not that interesting maybe
+there's not so much research there but
+
+ align:start position:0%
+there's not so much research there but
+ 
+
+ align:start position:0%
+there's not so much research there but
+think about it you have miles and miles
+
+ align:start position:0%
+think about it you have miles and miles
+ 
+
+ align:start position:0%
+think about it you have miles and miles
+and miles of store shelves how on Earth
+
+ align:start position:0%
+and miles of store shelves how on Earth
+ 
+
+ align:start position:0%
+and miles of store shelves how on Earth
+are you going to read all the stuff on
+
+ align:start position:0%
+are you going to read all the stuff on
+ 
+
+ align:start position:0%
+are you going to read all the stuff on
+those shelves now initially people are
+
+ align:start position:0%
+those shelves now initially people are
+ 
+
+ align:start position:0%
+those shelves now initially people are
+looking at portal based Solutions you
+
+ align:start position:0%
+looking at portal based Solutions you
+ 
+
+ align:start position:0%
+looking at portal based Solutions you
+put readers in doors but eventually you
+
+ align:start position:0%
+put readers in doors but eventually you
+ 
+
+ align:start position:0%
+put readers in doors but eventually you
+going to want to get realtime inventory
+
+ align:start position:0%
+going to want to get realtime inventory
+ 
+
+ align:start position:0%
+going to want to get realtime inventory
+not based on Transit but on on a real
+
+ align:start position:0%
+not based on Transit but on on a real
+ 
+
+ align:start position:0%
+not based on Transit but on on a real
+integrated measure that is a measure of
+
+ align:start position:0%
+integrated measure that is a measure of
+ 
+
+ align:start position:0%
+integrated measure that is a measure of
+actual inventory how are you going to
+
+ align:start position:0%
+actual inventory how are you going to
+ 
+
+ align:start position:0%
+actual inventory how are you going to
+put readers on these things is it going
+
+ align:start position:0%
+put readers on these things is it going
+ 
+
+ align:start position:0%
+put readers on these things is it going
+to be cheap antenna which Multiplex
+
+ align:start position:0%
+to be cheap antenna which Multiplex
+ 
+
+ align:start position:0%
+to be cheap antenna which Multiplex
+using some sort of you know printed ink
+
+ align:start position:0%
+using some sort of you know printed ink
+ 
+
+ align:start position:0%
+using some sort of you know printed ink
+Multiplex in uh over a cheap Wireless to
+
+ align:start position:0%
+Multiplex in uh over a cheap Wireless to
+ 
+
+ align:start position:0%
+Multiplex in uh over a cheap Wireless to
+a reader is that what's going to happen
+
+ align:start position:0%
+a reader is that what's going to happen
+ 
+
+ align:start position:0%
+a reader is that what's going to happen
+or are we going to in then how do you
+
+ align:start position:0%
+or are we going to in then how do you
+ 
+
+ align:start position:0%
+or are we going to in then how do you
+power if you put readers everywhere how
+
+ align:start position:0%
+power if you put readers everywhere how
+ 
+
+ align:start position:0%
+power if you put readers everywhere how
+do you power them right um walking if
+
+ align:start position:0%
+do you power them right um walking if
+ 
+
+ align:start position:0%
+do you power them right um walking if
+you walk into a retail store and you see
+
+ align:start position:0%
+you walk into a retail store and you see
+ 
+
+ align:start position:0%
+you walk into a retail store and you see
+a display of clothes you will find that
+
+ align:start position:0%
+a display of clothes you will find that
+ 
+
+ align:start position:0%
+a display of clothes you will find that
+the clothes sometimes are right in the
+
+ align:start position:0%
+the clothes sometimes are right in the
+ 
+
+ align:start position:0%
+the clothes sometimes are right in the
+middle of the floor how do you power
+
+ align:start position:0%
+middle of the floor how do you power
+ 
+
+ align:start position:0%
+middle of the floor how do you power
+them is it a battery or do you need to
+
+ align:start position:0%
+them is it a battery or do you need to
+ 
+
+ align:start position:0%
+them is it a battery or do you need to
+run wiring underneath such mundane
+
+ align:start position:0%
+run wiring underneath such mundane
+ 
+
+ align:start position:0%
+run wiring underneath such mundane
+problems power over ethernet is a Hot
+
+ align:start position:0%
+problems power over ethernet is a Hot
+ 
+
+ align:start position:0%
+problems power over ethernet is a Hot
+Topic these days is that a solution I'm
+
+ align:start position:0%
+Topic these days is that a solution I'm
+ 
+
+ align:start position:0%
+Topic these days is that a solution I'm
+I'm sure there are 10 other Solutions we
+
+ align:start position:0%
+I'm sure there are 10 other Solutions we
+ 
+
+ align:start position:0%
+I'm sure there are 10 other Solutions we
+haven't even explored and we there's a
+
+ align:start position:0%
+haven't even explored and we there's a
+ 
+
+ align:start position:0%
+haven't even explored and we there's a
+tendency to kind of take the clich
+
+ align:start position:0%
+tendency to kind of take the clich
+ 
+
+ align:start position:0%
+tendency to kind of take the clich
+solution where something very Innovative
+
+ align:start position:0%
+solution where something very Innovative
+ 
+
+ align:start position:0%
+solution where something very Innovative
+and probably gamechanging is just
+
+ align:start position:0%
+and probably gamechanging is just
+ 
+
+ align:start position:0%
+and probably gamechanging is just
+lurking around the corner so some very
+
+ align:start position:0%
+lurking around the corner so some very
+ 
+
+ align:start position:0%
+lurking around the corner so some very
+interesting Technologies just in these
+
+ align:start position:0%
+interesting Technologies just in these
+ 
+
+ align:start position:0%
+interesting Technologies just in these
+four topics waiting to be researched and
+
+ align:start position:0%
+four topics waiting to be researched and
+ 
+
+ align:start position:0%
+four topics waiting to be researched and
+then there's readers you know um I I we
+
+ align:start position:0%
+then there's readers you know um I I we
+ 
+
+ align:start position:0%
+then there's readers you know um I I we
+predicted some uh 10 8 years ago that
+
+ align:start position:0%
+predicted some uh 10 8 years ago that
+ 
+
+ align:start position:0%
+predicted some uh 10 8 years ago that
+readers would eventually be very
+
+ align:start position:0%
+readers would eventually be very
+ 
+
+ align:start position:0%
+readers would eventually be very
+inexpensive you know hundreds of bucks
+
+ align:start position:0%
+inexpensive you know hundreds of bucks
+ 
+
+ align:start position:0%
+inexpensive you know hundreds of bucks
+they're down to $1,000 now but there's a
+
+ align:start position:0%
+they're down to $1,000 now but there's a
+ 
+
+ align:start position:0%
+they're down to $1,000 now but there's a
+long way to go and the fact of the
+
+ align:start position:0%
+long way to go and the fact of the
+ 
+
+ align:start position:0%
+long way to go and the fact of the
+matter is the electronics invers is not
+
+ align:start position:0%
+matter is the electronics invers is not
+ 
+
+ align:start position:0%
+matter is the electronics invers is not
+that complicated so we have a lot of uh
+
+ align:start position:0%
+that complicated so we have a lot of uh
+ 
+
+ align:start position:0%
+that complicated so we have a lot of uh
+advant enement then there's middleware
+
+ align:start position:0%
+advant enement then there's middleware
+ 
+
+ align:start position:0%
+advant enement then there's middleware
+there's software um there's the actual
+
+ align:start position:0%
+there's software um there's the actual
+ 
+
+ align:start position:0%
+there's software um there's the actual
+middleware you know one of the problems
+
+ align:start position:0%
+middleware you know one of the problems
+ 
+
+ align:start position:0%
+middleware you know one of the problems
+with RFID is that there's a tendency to
+
+ align:start position:0%
+with RFID is that there's a tendency to
+ 
+
+ align:start position:0%
+with RFID is that there's a tendency to
+believe that RFID tags will be read in
+
+ align:start position:0%
+believe that RFID tags will be read in
+ 
+
+ align:start position:0%
+believe that RFID tags will be read in
+the same way the barcodes will be that
+
+ align:start position:0%
+the same way the barcodes will be that
+ 
+
+ align:start position:0%
+the same way the barcodes will be that
+is you read the barcode you know exactly
+
+ align:start position:0%
+is you read the barcode you know exactly
+ 
+
+ align:start position:0%
+is you read the barcode you know exactly
+what's there and you're done the fact of
+
+ align:start position:0%
+what's there and you're done the fact of
+ 
+
+ align:start position:0%
+what's there and you're done the fact of
+the matter is the whole point of RFID is
+
+ align:start position:0%
+the matter is the whole point of RFID is
+ 
+
+ align:start position:0%
+the matter is the whole point of RFID is
+you're reading all the time and you're
+
+ align:start position:0%
+you're reading all the time and you're
+ 
+
+ align:start position:0%
+you're reading all the time and you're
+going to miss a few and missing reads
+
+ align:start position:0%
+going to miss a few and missing reads
+ 
+
+ align:start position:0%
+going to miss a few and missing reads
+results in Phantom inventory especially
+
+ align:start position:0%
+results in Phantom inventory especially
+ 
+
+ align:start position:0%
+results in Phantom inventory especially
+have when you have a throughput model
+
+ align:start position:0%
+have when you have a throughput model
+ 
+
+ align:start position:0%
+have when you have a throughput model
+where you look at things going in and
+
+ align:start position:0%
+where you look at things going in and
+ 
+
+ align:start position:0%
+where you look at things going in and
+out right it results in negative and
+
+ align:start position:0%
+out right it results in negative and
+ 
+
+ align:start position:0%
+out right it results in negative and
+positive Phantom inventory and Phantom
+
+ align:start position:0%
+positive Phantom inventory and Phantom
+ 
+
+ align:start position:0%
+positive Phantom inventory and Phantom
+inventory is going to completely jam up
+
+ align:start position:0%
+inventory is going to completely jam up
+ 
+
+ align:start position:0%
+inventory is going to completely jam up
+any inventory control system any
+
+ align:start position:0%
+any inventory control system any
+ 
+
+ align:start position:0%
+any inventory control system any
+application that you develop so for
+
+ align:start position:0%
+application that you develop so for
+ 
+
+ align:start position:0%
+application that you develop so for
+example let's say we all we all had tags
+
+ align:start position:0%
+example let's say we all we all had tags
+ 
+
+ align:start position:0%
+example let's say we all we all had tags
+and God forbid there was a fire and we
+
+ align:start position:0%
+and God forbid there was a fire and we
+ 
+
+ align:start position:0%
+and God forbid there was a fire and we
+all went out and there were readers of
+
+ align:start position:0%
+all went out and there were readers of
+ 
+
+ align:start position:0%
+all went out and there were readers of
+the doors and the readers of the doors
+
+ align:start position:0%
+the doors and the readers of the doors
+ 
+
+ align:start position:0%
+the doors and the readers of the doors
+missed a few of
+
+ align:start position:0%
+missed a few of
+ 
+
+ align:start position:0%
+missed a few of
+us this room would legitimately claim
+
+ align:start position:0%
+us this room would legitimately claim
+ 
+
+ align:start position:0%
+us this room would legitimately claim
+that those of us that didn't get read
+
+ align:start position:0%
+that those of us that didn't get read
+ 
+
+ align:start position:0%
+that those of us that didn't get read
+are still in this room and it might send
+
+ align:start position:0%
+are still in this room and it might send
+ 
+
+ align:start position:0%
+are still in this room and it might send
+a fireman into this room looking for
+
+ align:start position:0%
+a fireman into this room looking for
+ 
+
+ align:start position:0%
+a fireman into this room looking for
+those people that the reader missed
+
+ align:start position:0%
+those people that the reader missed
+ 
+
+ align:start position:0%
+those people that the reader missed
+now you can see right away now that's a
+
+ align:start position:0%
+now you can see right away now that's a
+ 
+
+ align:start position:0%
+now you can see right away now that's a
+a dramatic example but you can see right
+
+ align:start position:0%
+a dramatic example but you can see right
+ 
+
+ align:start position:0%
+a dramatic example but you can see right
+away that when you're doing inventory
+
+ align:start position:0%
+away that when you're doing inventory
+ 
+
+ align:start position:0%
+away that when you're doing inventory
+control how terribly that could up that
+
+ align:start position:0%
+control how terribly that could up that
+ 
+
+ align:start position:0%
+control how terribly that could up that
+could send an inventory control system
+
+ align:start position:0%
+could send an inventory control system
+ 
+
+ align:start position:0%
+could send an inventory control system
+out of control right how do you manage
+
+ align:start position:0%
+out of control right how do you manage
+ 
+
+ align:start position:0%
+out of control right how do you manage
+things like that well you know what
+
+ align:start position:0%
+things like that well you know what
+ 
+
+ align:start position:0%
+things like that well you know what
+maybe there's a reader on the way out
+
+ align:start position:0%
+maybe there's a reader on the way out
+ 
+
+ align:start position:0%
+maybe there's a reader on the way out
+and that picked me up so you can say
+
+ align:start position:0%
+and that picked me up so you can say
+ 
+
+ align:start position:0%
+and that picked me up so you can say
+listen although this reader didn't pick
+
+ align:start position:0%
+listen although this reader didn't pick
+ 
+
+ align:start position:0%
+listen although this reader didn't pick
+me up a later reader saw me so let's
+
+ align:start position:0%
+me up a later reader saw me so let's
+ 
+
+ align:start position:0%
+me up a later reader saw me so let's
+correct inventory here that's a very
+
+ align:start position:0%
+correct inventory here that's a very
+ 
+
+ align:start position:0%
+correct inventory here that's a very
+deep database concept all right that's
+
+ align:start position:0%
+deep database concept all right that's
+ 
+
+ align:start position:0%
+deep database concept all right that's
+uh it's kind of a generalized predicate
+
+ align:start position:0%
+uh it's kind of a generalized predicate
+ 
+
+ align:start position:0%
+uh it's kind of a generalized predicate
+of consistency that you need to Super
+
+ align:start position:0%
+of consistency that you need to Super
+ 
+
+ align:start position:0%
+of consistency that you need to Super
+impose on top of a database to make sure
+
+ align:start position:0%
+impose on top of a database to make sure
+ 
+
+ align:start position:0%
+impose on top of a database to make sure
+that your data is consistent right there
+
+ align:start position:0%
+that your data is consistent right there
+ 
+
+ align:start position:0%
+that your data is consistent right there
+is a research topic just waiting for
+
+ align:start position:0%
+is a research topic just waiting for
+ 
+
+ align:start position:0%
+is a research topic just waiting for
+someone to look into um and then there's
+
+ align:start position:0%
+someone to look into um and then there's
+ 
+
+ align:start position:0%
+someone to look into um and then there's
+databases there's you know streaming
+
+ align:start position:0%
+databases there's you know streaming
+ 
+
+ align:start position:0%
+databases there's you know streaming
+data right fast and furious how do you
+
+ align:start position:0%
+data right fast and furious how do you
+ 
+
+ align:start position:0%
+data right fast and furious how do you
+handle do joins on streaming data
+
+ align:start position:0%
+handle do joins on streaming data
+ 
+
+ align:start position:0%
+handle do joins on streaming data
+there's actually a lot lot of research
+
+ align:start position:0%
+there's actually a lot lot of research
+ 
+
+ align:start position:0%
+there's actually a lot lot of research
+uh in various computer science
+
+ align:start position:0%
+uh in various computer science
+ 
+
+ align:start position:0%
+uh in various computer science
+departments on that there's Enterprise
+
+ align:start position:0%
+departments on that there's Enterprise
+ 
+
+ align:start position:0%
+departments on that there's Enterprise
+architecture is this going to
+
+ align:start position:0%
+architecture is this going to
+ 
+
+ align:start position:0%
+architecture is this going to
+fundamentally change the way in which we
+
+ align:start position:0%
+fundamentally change the way in which we
+ 
+
+ align:start position:0%
+fundamentally change the way in which we
+do Enterprise architecture you know the
+
+ align:start position:0%
+do Enterprise architecture you know the
+ 
+
+ align:start position:0%
+do Enterprise architecture you know the
+world is built around databases today
+
+ align:start position:0%
+world is built around databases today
+ 
+
+ align:start position:0%
+world is built around databases today
+will we go to fundamentally a new uh
+
+ align:start position:0%
+will we go to fundamentally a new uh
+ 
+
+ align:start position:0%
+will we go to fundamentally a new uh
+Enterprise architecture my own feeling
+
+ align:start position:0%
+Enterprise architecture my own feeling
+ 
+
+ align:start position:0%
+Enterprise architecture my own feeling
+is about 10 years will'll be in new in a
+
+ align:start position:0%
+is about 10 years will'll be in new in a
+ 
+
+ align:start position:0%
+is about 10 years will'll be in new in a
+completely different way of thinking
+
+ align:start position:0%
+completely different way of thinking
+ 
+
+ align:start position:0%
+completely different way of thinking
+about enterprise software systems based
+
+ align:start position:0%
+about enterprise software systems based
+ 
+
+ align:start position:0%
+about enterprise software systems based
+completely on events as opposed to based
+
+ align:start position:0%
+completely on events as opposed to based
+ 
+
+ align:start position:0%
+completely on events as opposed to based
+on databases that's my view uh but I may
+
+ align:start position:0%
+on databases that's my view uh but I may
+ 
+
+ align:start position:0%
+on databases that's my view uh but I may
+be wrong and then there distributed
+
+ align:start position:0%
+be wrong and then there distributed
+ 
+
+ align:start position:0%
+be wrong and then there distributed
+systems Discovery uh we developed
+
+ align:start position:0%
+systems Discovery uh we developed
+ 
+
+ align:start position:0%
+systems Discovery uh we developed
+something called the object name system
+
+ align:start position:0%
+something called the object name system
+ 
+
+ align:start position:0%
+something called the object name system
+if you're familiar with it it's just a
+
+ align:start position:0%
+if you're familiar with it it's just a
+ 
+
+ align:start position:0%
+if you're familiar with it it's just a
+way to find the company that owns a
+
+ align:start position:0%
+way to find the company that owns a
+ 
+
+ align:start position:0%
+way to find the company that owns a
+particular EPC that was a drop in the
+
+ align:start position:0%
+particular EPC that was a drop in the
+ 
+
+ align:start position:0%
+particular EPC that was a drop in the
+bucket already we seeing that that is us
+
+ align:start position:0%
+bucket already we seeing that that is us
+ 
+
+ align:start position:0%
+bucket already we seeing that that is us
+useful but it's 1% of the way to
+
+ align:start position:0%
+useful but it's 1% of the way to
+ 
+
+ align:start position:0%
+useful but it's 1% of the way to
+everything you need to do to really take
+
+ align:start position:0%
+everything you need to do to really take
+ 
+
+ align:start position:0%
+everything you need to do to really take
+advantage of RFID right I can say that
+
+ align:start position:0%
+advantage of RFID right I can say that
+ 
+
+ align:start position:0%
+advantage of RFID right I can say that
+because we I was one of the people who
+
+ align:start position:0%
+because we I was one of the people who
+ 
+
+ align:start position:0%
+because we I was one of the people who
+wrote on it so I can criticize it but I
+
+ align:start position:0%
+wrote on it so I can criticize it but I
+ 
+
+ align:start position:0%
+wrote on it so I can criticize it but I
+think it's very important for an
+
+ align:start position:0%
+think it's very important for an
+ 
+
+ align:start position:0%
+think it's very important for an
+academic Community to point focus on
+
+ align:start position:0%
+academic Community to point focus on
+ 
+
+ align:start position:0%
+academic Community to point focus on
+microscope and critique these things and
+
+ align:start position:0%
+microscope and critique these things and
+ 
+
+ align:start position:0%
+microscope and critique these things and
+start improving on them and it's just
+
+ align:start position:0%
+start improving on them and it's just
+ 
+
+ align:start position:0%
+start improving on them and it's just
+waiting to happen is it going to be I
+
+ align:start position:0%
+waiting to happen is it going to be I
+ 
+
+ align:start position:0%
+waiting to happen is it going to be I
+don't know the semantic web what's it
+
+ align:start position:0%
+don't know the semantic web what's it
+ 
+
+ align:start position:0%
+don't know the semantic web what's it
+going to be right we need to look at
+
+ align:start position:0%
+going to be right we need to look at
+ 
+
+ align:start position:0%
+going to be right we need to look at
+that identity management what's going to
+
+ align:start position:0%
+that identity management what's going to
+ 
+
+ align:start position:0%
+that identity management what's going to
+happen when you have hundreds and
+
+ align:start position:0%
+happen when you have hundreds and
+ 
+
+ align:start position:0%
+happen when you have hundreds and
+hundreds of companies trying to access
+
+ align:start position:0%
+hundreds of companies trying to access
+ 
+
+ align:start position:0%
+hundreds of companies trying to access
+data how do you manage identity is it
+
+ align:start position:0%
+data how do you manage identity is it
+ 
+
+ align:start position:0%
+data how do you manage identity is it
+going to be using Microsoft of passport
+
+ align:start position:0%
+going to be using Microsoft of passport
+ 
+
+ align:start position:0%
+going to be using Microsoft of passport
+is it going to be using something else
+
+ align:start position:0%
+is it going to be using something else
+ 
+
+ align:start position:0%
+is it going to be using something else
+right what are the standards there is it
+
+ align:start position:0%
+right what are the standards there is it
+ 
+
+ align:start position:0%
+right what are the standards there is it
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+Federated
+
+ align:start position:0%
+Federated
+ 
+
+ align:start position:0%
+Federated
+fascinating tens and hundreds of
+
+ align:start position:0%
+fascinating tens and hundreds of
+ 
+
+ align:start position:0%
+fascinating tens and hundreds of
+research topics waiting here the problem
+
+ align:start position:0%
+research topics waiting here the problem
+ 
+
+ align:start position:0%
+research topics waiting here the problem
+will lie in making sure that these
+
+ align:start position:0%
+will lie in making sure that these
+ 
+
+ align:start position:0%
+will lie in making sure that these
+research projects solve the question
+
+ align:start position:0%
+research projects solve the question
+ 
+
+ align:start position:0%
+research projects solve the question
+with a clear understanding of the
+
+ align:start position:0%
+with a clear understanding of the
+ 
+
+ align:start position:0%
+with a clear understanding of the
+application and that is why uh I think
+
+ align:start position:0%
+application and that is why uh I think
+ 
+
+ align:start position:0%
+application and that is why uh I think
+this conference is perfectly timed um
+
+ align:start position:0%
+this conference is perfectly timed um
+ 
+
+ align:start position:0%
+this conference is perfectly timed um
+because the industry is finally looking
+
+ align:start position:0%
+because the industry is finally looking
+ 
+
+ align:start position:0%
+because the industry is finally looking
+at this very seriously you know uh Mike
+
+ align:start position:0%
+at this very seriously you know uh Mike
+ 
+
+ align:start position:0%
+at this very seriously you know uh Mike
+Rose of J&J we were just having
+
+ align:start position:0%
+Rose of J&J we were just having
+ 
+
+ align:start position:0%
+Rose of J&J we were just having
+breakfast this morning and we were
+
+ align:start position:0%
+breakfast this morning and we were
+ 
+
+ align:start position:0%
+breakfast this morning and we were
+talking about you know how the industry
+
+ align:start position:0%
+talking about you know how the industry
+ 
+
+ align:start position:0%
+talking about you know how the industry
+really is struggling with some serious
+
+ align:start position:0%
+really is struggling with some serious
+ 
+
+ align:start position:0%
+really is struggling with some serious
+problems um and you know they have some
+
+ align:start position:0%
+problems um and you know they have some
+ 
+
+ align:start position:0%
+problems um and you know they have some
+experts and they're academic experts and
+
+ align:start position:0%
+experts and they're academic experts and
+ 
+
+ align:start position:0%
+experts and they're academic experts and
+finally now they can be a real
+
+ align:start position:0%
+finally now they can be a real
+ 
+
+ align:start position:0%
+finally now they can be a real
+conversation when we were doing this a
+
+ align:start position:0%
+conversation when we were doing this a
+ 
+
+ align:start position:0%
+conversation when we were doing this a
+few years ago we were making stuff up
+
+ align:start position:0%
+few years ago we were making stuff up
+ 
+
+ align:start position:0%
+few years ago we were making stuff up
+and projecting our industry and hoping
+
+ align:start position:0%
+and projecting our industry and hoping
+ 
+
+ align:start position:0%
+and projecting our industry and hoping
+we were right and by luck dumb luck many
+
+ align:start position:0%
+we were right and by luck dumb luck many
+ 
+
+ align:start position:0%
+we were right and by luck dumb luck many
+ways right we were kind of right and we
+
+ align:start position:0%
+ways right we were kind of right and we
+ 
+
+ align:start position:0%
+ways right we were kind of right and we
+had great guidance from the early
+
+ align:start position:0%
+had great guidance from the early
+ 
+
+ align:start position:0%
+had great guidance from the early
+sponsors the gillet the Jes Walmarts Etc
+
+ align:start position:0%
+sponsors the gillet the Jes Walmarts Etc
+ 
+
+ align:start position:0%
+sponsors the gillet the Jes Walmarts Etc
+targets right but now is a time to have
+
+ align:start position:0%
+targets right but now is a time to have
+ 
+
+ align:start position:0%
+targets right but now is a time to have
+a very high bandwidth conversation
+
+ align:start position:0%
+a very high bandwidth conversation
+ 
+
+ align:start position:0%
+a very high bandwidth conversation
+uh and finally by the way I think that
+
+ align:start position:0%
+uh and finally by the way I think that
+ 
+
+ align:start position:0%
+uh and finally by the way I think that
+RFID is going to change the way our
+
+ align:start position:0%
+RFID is going to change the way our
+ 
+
+ align:start position:0%
+RFID is going to change the way our
+business processes work it's going to
+
+ align:start position:0%
+business processes work it's going to
+ 
+
+ align:start position:0%
+business processes work it's going to
+change the way that you go into a store
+
+ align:start position:0%
+change the way that you go into a store
+ 
+
+ align:start position:0%
+change the way that you go into a store
+and you interact with the store it's
+
+ align:start position:0%
+and you interact with the store it's
+ 
+
+ align:start position:0%
+and you interact with the store it's
+going to change the way a store is
+
+ align:start position:0%
+going to change the way a store is
+ 
+
+ align:start position:0%
+going to change the way a store is
+operated the Machinery is going to
+
+ align:start position:0%
+operated the Machinery is going to
+ 
+
+ align:start position:0%
+operated the Machinery is going to
+change and that to me is a technology
+
+ align:start position:0%
+change and that to me is a technology
+ 
+
+ align:start position:0%
+change and that to me is a technology
+it's not business it's a technology and
+
+ align:start position:0%
+it's not business it's a technology and
+ 
+
+ align:start position:0%
+it's not business it's a technology and
+that that's going to be the most
+
+ align:start position:0%
+that that's going to be the most
+ 
+
+ align:start position:0%
+that that's going to be the most
+fascinating part of all
+
+ align:start position:0%
+fascinating part of all
+ 
+
+ align:start position:0%
+fascinating part of all
+this you can look at applications you
+
+ align:start position:0%
+this you can look at applications you
+ 
+
+ align:start position:0%
+this you can look at applications you
+know the most of the attention's been on
+
+ align:start position:0%
+know the most of the attention's been on
+ 
+
+ align:start position:0%
+know the most of the attention's been on
+supply chain but supply chain is barely
+
+ align:start position:0%
+supply chain but supply chain is barely
+ 
+
+ align:start position:0%
+supply chain but supply chain is barely
+a start um you know we talk about retail
+
+ align:start position:0%
+a start um you know we talk about retail
+ 
+
+ align:start position:0%
+a start um you know we talk about retail
+Healthcare business to business critical
+
+ align:start position:0%
+Healthcare business to business critical
+ 
+
+ align:start position:0%
+Healthcare business to business critical
+Goods we just went through Katrina this
+
+ align:start position:0%
+Goods we just went through Katrina this
+ 
+
+ align:start position:0%
+Goods we just went through Katrina this
+uh in the US and the tsunami and uh and
+
+ align:start position:0%
+uh in the US and the tsunami and uh and
+ 
+
+ align:start position:0%
+uh in the US and the tsunami and uh and
+the earthquake in Pakistan uh what
+
+ align:start position:0%
+the earthquake in Pakistan uh what
+ 
+
+ align:start position:0%
+the earthquake in Pakistan uh what
+happens when the next disaster occurs
+
+ align:start position:0%
+happens when the next disaster occurs
+ 
+
+ align:start position:0%
+happens when the next disaster occurs
+how do we make sure that we route blood
+
+ align:start position:0%
+how do we make sure that we route blood
+ 
+
+ align:start position:0%
+how do we make sure that we route blood
+correctly how do we make sure that if
+
+ align:start position:0%
+correctly how do we make sure that if
+ 
+
+ align:start position:0%
+correctly how do we make sure that if
+there's a bird flu episode somewhere in
+
+ align:start position:0%
+there's a bird flu episode somewhere in
+ 
+
+ align:start position:0%
+there's a bird flu episode somewhere in
+in some town somewhere that we uh route
+
+ align:start position:0%
+in some town somewhere that we uh route
+ 
+
+ align:start position:0%
+in some town somewhere that we uh route
+uh flu vaccines or Tamiflu correctly
+
+ align:start position:0%
+uh flu vaccines or Tamiflu correctly
+ 
+
+ align:start position:0%
+uh flu vaccines or Tamiflu correctly
+these are all again very fundamental
+
+ align:start position:0%
+these are all again very fundamental
+ 
+
+ align:start position:0%
+these are all again very fundamental
+opportunities for our of ID and it
+
+ align:start position:0%
+opportunities for our of ID and it
+ 
+
+ align:start position:0%
+opportunities for our of ID and it
+behooves us to start dealing with these
+
+ align:start position:0%
+behooves us to start dealing with these
+ 
+
+ align:start position:0%
+behooves us to start dealing with these
+things uh in a scientific way and so the
+
+ align:start position:0%
+things uh in a scientific way and so the
+ 
+
+ align:start position:0%
+things uh in a scientific way and so the
+uh very really uh ancient approaches
+
+ align:start position:0%
+uh very really uh ancient approaches
+ 
+
+ align:start position:0%
+uh very really uh ancient approaches
+we're taking to Disaster Recovery with
+
+ align:start position:0%
+we're taking to Disaster Recovery with
+ 
+
+ align:start position:0%
+we're taking to Disaster Recovery with
+RFID we should be able to kind of run
+
+ align:start position:0%
+RFID we should be able to kind of run
+ 
+
+ align:start position:0%
+RFID we should be able to kind of run
+you know you should have a map it's like
+
+ align:start position:0%
+you know you should have a map it's like
+ 
+
+ align:start position:0%
+you know you should have a map it's like
+a weather map of the disaster and where
+
+ align:start position:0%
+a weather map of the disaster and where
+ 
+
+ align:start position:0%
+a weather map of the disaster and where
+your your various you know uh resources
+
+ align:start position:0%
+your your various you know uh resources
+ 
+
+ align:start position:0%
+your your various you know uh resources
+are and how do you map them and you know
+
+ align:start position:0%
+are and how do you map them and you know
+ 
+
+ align:start position:0%
+are and how do you map them and you know
+what what you need where well here's you
+
+ align:start position:0%
+what what you need where well here's you
+ 
+
+ align:start position:0%
+what what you need where well here's you
+know here's where the flooding is we
+
+ align:start position:0%
+know here's where the flooding is we
+ 
+
+ align:start position:0%
+know here's where the flooding is we
+need to send certain equipment here
+
+ align:start position:0%
+need to send certain equipment here
+ 
+
+ align:start position:0%
+need to send certain equipment here
+here's where there's a disease outbreak
+
+ align:start position:0%
+here's where there's a disease outbreak
+ 
+
+ align:start position:0%
+here's where there's a disease outbreak
+we need to send something here we should
+
+ align:start position:0%
+we need to send something here we should
+ 
+
+ align:start position:0%
+we need to send something here we should
+be able to do this in a much more
+
+ align:start position:0%
+be able to do this in a much more
+ 
+
+ align:start position:0%
+be able to do this in a much more
+scientific way and visibility is
+
+ align:start position:0%
+scientific way and visibility is
+ 
+
+ align:start position:0%
+scientific way and visibility is
+key um Steve talked about uh the airline
+
+ align:start position:0%
+key um Steve talked about uh the airline
+ 
+
+ align:start position:0%
+key um Steve talked about uh the airline
+uh the sorry the uh the aircraft
+
+ align:start position:0%
+uh the sorry the uh the aircraft
+ 
+
+ align:start position:0%
+uh the sorry the uh the aircraft
+industry um and what's happening there
+
+ align:start position:0%
+industry um and what's happening there
+ 
+
+ align:start position:0%
+industry um and what's happening there
+is the aircraft industry which is
+
+ align:start position:0%
+is the aircraft industry which is
+ 
+
+ align:start position:0%
+is the aircraft industry which is
+historically been very inefficient I
+
+ align:start position:0%
+historically been very inefficient I
+ 
+
+ align:start position:0%
+historically been very inefficient I
+happen to have studied that in my in a
+
+ align:start position:0%
+happen to have studied that in my in a
+ 
+
+ align:start position:0%
+happen to have studied that in my in a
+past life is again waiting for a
+
+ align:start position:0%
+past life is again waiting for a
+ 
+
+ align:start position:0%
+past life is again waiting for a
+fundamentally new efficient model Boeing
+
+ align:start position:0%
+fundamentally new efficient model Boeing
+ 
+
+ align:start position:0%
+fundamentally new efficient model Boeing
+and Airbus cannot survive the way they
+
+ align:start position:0%
+and Airbus cannot survive the way they
+ 
+
+ align:start position:0%
+and Airbus cannot survive the way they
+have survived with gigantic government
+
+ align:start position:0%
+have survived with gigantic government
+ 
+
+ align:start position:0%
+have survived with gigantic government
+subsidies at some level or the other
+
+ align:start position:0%
+subsidies at some level or the other
+ 
+
+ align:start position:0%
+subsidies at some level or the other
+right and they have done theong right
+
+ align:start position:0%
+right and they have done theong right
+ 
+
+ align:start position:0%
+right and they have done theong right
+thing and they're trying to reengineer
+
+ align:start position:0%
+thing and they're trying to reengineer
+ 
+
+ align:start position:0%
+thing and they're trying to reengineer
+their supply Chains It's very different
+
+ align:start position:0%
+their supply Chains It's very different
+ 
+
+ align:start position:0%
+their supply Chains It's very different
+than even the automotive supply chain
+
+ align:start position:0%
+than even the automotive supply chain
+ 
+
+ align:start position:0%
+than even the automotive supply chain
+because the lots are much smaller and
+
+ align:start position:0%
+because the lots are much smaller and
+ 
+
+ align:start position:0%
+because the lots are much smaller and
+the products are much fewer and they can
+
+ align:start position:0%
+the products are much fewer and they can
+ 
+
+ align:start position:0%
+the products are much fewer and they can
+get a lot more flexibility um and I
+
+ align:start position:0%
+get a lot more flexibility um and I
+ 
+
+ align:start position:0%
+get a lot more flexibility um and I
+think that's a great new opportunity to
+
+ align:start position:0%
+think that's a great new opportunity to
+ 
+
+ align:start position:0%
+think that's a great new opportunity to
+use RFID to get visibility through Just
+
+ align:start position:0%
+use RFID to get visibility through Just
+ 
+
+ align:start position:0%
+use RFID to get visibility through Just
+in Time Manufacturing delivery Etc so
+
+ align:start position:0%
+in Time Manufacturing delivery Etc so
+ 
+
+ align:start position:0%
+in Time Manufacturing delivery Etc so
+again for people who do operations
+
+ align:start position:0%
+again for people who do operations
+ 
+
+ align:start position:0%
+again for people who do operations
+research Tully right fantastic
+
+ align:start position:0%
+research Tully right fantastic
+ 
+
+ align:start position:0%
+research Tully right fantastic
+opportunity there now if you look at
+
+ align:start position:0%
+opportunity there now if you look at
+ 
+
+ align:start position:0%
+opportunity there now if you look at
+just operations uh Factory
+
+ align:start position:0%
+just operations uh Factory
+ 
+
+ align:start position:0%
+just operations uh Factory
+operations uh air bu and and and uh and
+
+ align:start position:0%
+operations uh air bu and and and uh and
+ 
+
+ align:start position:0%
+operations uh air bu and and and uh and
+boing going to do it DC operations Brian
+
+ align:start position:0%
+boing going to do it DC operations Brian
+ 
+
+ align:start position:0%
+boing going to do it DC operations Brian
+subana who's there right there right
+
+ align:start position:0%
+subana who's there right there right
+ 
+
+ align:start position:0%
+subana who's there right there right
+spend a lot a lot of time with jillette
+
+ align:start position:0%
+spend a lot a lot of time with jillette
+ 
+
+ align:start position:0%
+spend a lot a lot of time with jillette
+looking at their DCU operations and it's
+
+ align:start position:0%
+looking at their DCU operations and it's
+ 
+
+ align:start position:0%
+looking at their DCU operations and it's
+such a b you know when we started that
+
+ align:start position:0%
+such a b you know when we started that
+ 
+
+ align:start position:0%
+such a b you know when we started that
+research we thought is this boring I
+
+ align:start position:0%
+research we thought is this boring I
+ 
+
+ align:start position:0%
+research we thought is this boring I
+mean are we going to find something but
+
+ align:start position:0%
+mean are we going to find something but
+ 
+
+ align:start position:0%
+mean are we going to find something but
+when you actually get into it it's
+
+ align:start position:0%
+when you actually get into it it's
+ 
+
+ align:start position:0%
+when you actually get into it it's
+fascinating you start peeling the onion
+
+ align:start position:0%
+fascinating you start peeling the onion
+ 
+
+ align:start position:0%
+fascinating you start peeling the onion
+and you find that there's so many
+
+ align:start position:0%
+and you find that there's so many
+ 
+
+ align:start position:0%
+and you find that there's so many
+opportunities to make DCS this boring
+
+ align:start position:0%
+opportunities to make DCS this boring
+ 
+
+ align:start position:0%
+opportunities to make DCS this boring
+Dusty you know box of a building
+
+ align:start position:0%
+Dusty you know box of a building
+ 
+
+ align:start position:0%
+Dusty you know box of a building
+exciting faster more efficient less aone
+
+ align:start position:0%
+exciting faster more efficient less aone
+ 
+
+ align:start position:0%
+exciting faster more efficient less aone
+and fundamentally you can start reducing
+
+ align:start position:0%
+and fundamentally you can start reducing
+ 
+
+ align:start position:0%
+and fundamentally you can start reducing
+inventories
+
+ align:start position:0%
+inventories
+ 
+
+ align:start position:0%
+inventories
+right um and of course uh you can look
+
+ align:start position:0%
+right um and of course uh you can look
+ 
+
+ align:start position:0%
+right um and of course uh you can look
+at institutions uh hospitals Hospital
+
+ align:start position:0%
+at institutions uh hospitals Hospital
+ 
+
+ align:start position:0%
+at institutions uh hospitals Hospital
+operations a huge opportunity right you
+
+ align:start position:0%
+operations a huge opportunity right you
+ 
+
+ align:start position:0%
+operations a huge opportunity right you
+could there are several PhD Theses
+
+ align:start position:0%
+could there are several PhD Theses
+ 
+
+ align:start position:0%
+could there are several PhD Theses
+probably in looking at the logistics of
+
+ align:start position:0%
+probably in looking at the logistics of
+ 
+
+ align:start position:0%
+probably in looking at the logistics of
+hospitals um and uh you know uh drug
+
+ align:start position:0%
+hospitals um and uh you know uh drug
+ 
+
+ align:start position:0%
+hospitals um and uh you know uh drug
+delivery Mis prescriptions in hospitals
+
+ align:start position:0%
+delivery Mis prescriptions in hospitals
+ 
+
+ align:start position:0%
+delivery Mis prescriptions in hospitals
+I'll talk about that in a second
+
+ align:start position:0%
+I'll talk about that in a second
+ 
+
+ align:start position:0%
+I'll talk about that in a second
+personal systems you know so I can't I
+
+ align:start position:0%
+personal systems you know so I can't I
+ 
+
+ align:start position:0%
+personal systems you know so I can't I
+mean I could barely scratch the surface
+
+ align:start position:0%
+mean I could barely scratch the surface
+ 
+
+ align:start position:0%
+mean I could barely scratch the surface
+of applications and then finally the the
+
+ align:start position:0%
+of applications and then finally the the
+ 
+
+ align:start position:0%
+of applications and then finally the the
+kind of the million dooll question
+
+ align:start position:0%
+kind of the million dooll question
+ 
+
+ align:start position:0%
+kind of the million dooll question
+question for an academic is so what's
+
+ align:start position:0%
+question for an academic is so what's
+ 
+
+ align:start position:0%
+question for an academic is so what's
+the analysis you know where do where are
+
+ align:start position:0%
+the analysis you know where do where are
+ 
+
+ align:start position:0%
+the analysis you know where do where are
+my equations this is all fine right but
+
+ align:start position:0%
+my equations this is all fine right but
+ 
+
+ align:start position:0%
+my equations this is all fine right but
+where are my equations can I write an i
+
+ align:start position:0%
+where are my equations can I write an i
+ 
+
+ align:start position:0%
+where are my equations can I write an i
+journal or an ACM paper on this um and
+
+ align:start position:0%
+journal or an ACM paper on this um and
+ 
+
+ align:start position:0%
+journal or an ACM paper on this um and
+and and uh you know uh VI for the next
+
+ align:start position:0%
+and and uh you know uh VI for the next
+ 
+
+ align:start position:0%
+and and uh you know uh VI for the next
+touring award I actually fundamentally
+
+ align:start position:0%
+touring award I actually fundamentally
+ 
+
+ align:start position:0%
+touring award I actually fundamentally
+think yes there are some fundamental
+
+ align:start position:0%
+think yes there are some fundamental
+ 
+
+ align:start position:0%
+think yes there are some fundamental
+intellectual opportunities at every
+
+ align:start position:0%
+intellectual opportunities at every
+ 
+
+ align:start position:0%
+intellectual opportunities at every
+level um everything from RF systems and
+
+ align:start position:0%
+level um everything from RF systems and
+ 
+
+ align:start position:0%
+level um everything from RF systems and
+Communications many years ago I was
+
+ align:start position:0%
+Communications many years ago I was
+ 
+
+ align:start position:0%
+Communications many years ago I was
+sitting down with Peter and I said Peter
+
+ align:start position:0%
+sitting down with Peter and I said Peter
+ 
+
+ align:start position:0%
+sitting down with Peter and I said Peter
+what what is the fundamental difference
+
+ align:start position:0%
+what what is the fundamental difference
+ 
+
+ align:start position:0%
+what what is the fundamental difference
+between RFID and other communication
+
+ align:start position:0%
+between RFID and other communication
+ 
+
+ align:start position:0%
+between RFID and other communication
+systems and he summarized to me it is
+
+ align:start position:0%
+systems and he summarized to me it is
+ 
+
+ align:start position:0%
+systems and he summarized to me it is
+that in RFID unlike in other
+
+ align:start position:0%
+that in RFID unlike in other
+ 
+
+ align:start position:0%
+that in RFID unlike in other
+communication systems the bandwidths and
+
+ align:start position:0%
+communication systems the bandwidths and
+ 
+
+ align:start position:0%
+communication systems the bandwidths and
+the power are just very different in two
+
+ align:start position:0%
+the power are just very different in two
+ 
+
+ align:start position:0%
+the power are just very different in two
+directions and you want to design
+
+ align:start position:0%
+directions and you want to design
+ 
+
+ align:start position:0%
+directions and you want to design
+protocols that work in these asymmetric
+
+ align:start position:0%
+protocols that work in these asymmetric
+ 
+
+ align:start position:0%
+protocols that work in these asymmetric
+channels it's just very different all
+
+ align:start position:0%
+channels it's just very different all
+ 
+
+ align:start position:0%
+channels it's just very different all
+right Computing Cycles I'll talk about
+
+ align:start position:0%
+right Computing Cycles I'll talk about
+ 
+
+ align:start position:0%
+right Computing Cycles I'll talk about
+that are
+
+ align:start position:0%
+that are
+ 
+
+ align:start position:0%
+that are
+expensive um communication Theory very
+
+ align:start position:0%
+expensive um communication Theory very
+ 
+
+ align:start position:0%
+expensive um communication Theory very
+interesting right all the communication
+
+ align:start position:0%
+interesting right all the communication
+ 
+
+ align:start position:0%
+interesting right all the communication
+Theory you know error correcting codes
+
+ align:start position:0%
+Theory you know error correcting codes
+ 
+
+ align:start position:0%
+Theory you know error correcting codes
+all the stuff doesn't necessarily map to
+
+ align:start position:0%
+all the stuff doesn't necessarily map to
+ 
+
+ align:start position:0%
+all the stuff doesn't necessarily map to
+RFID because RFID is so different um
+
+ align:start position:0%
+RFID because RFID is so different um
+ 
+
+ align:start position:0%
+RFID because RFID is so different um
+System Dynamics security I won't belabor
+
+ align:start position:0%
+System Dynamics security I won't belabor
+ 
+
+ align:start position:0%
+System Dynamics security I won't belabor
+it beautiful challenging frustrating
+
+ align:start position:0%
+it beautiful challenging frustrating
+ 
+
+ align:start position:0%
+it beautiful challenging frustrating
+exciting problems wait to be attacked
+
+ align:start position:0%
+exciting problems wait to be attacked
+ 
+
+ align:start position:0%
+exciting problems wait to be attacked
+and it's great to have this community
+
+ align:start position:0%
+and it's great to have this community
+ 
+
+ align:start position:0%
+and it's great to have this community
+come together and try and think about
+
+ align:start position:0%
+come together and try and think about
+ 
+
+ align:start position:0%
+come together and try and think about
+them the thing that makes RFID special
+
+ align:start position:0%
+them the thing that makes RFID special
+ 
+
+ align:start position:0%
+them the thing that makes RFID special
+is everything is different everything
+
+ align:start position:0%
+is everything is different everything
+ 
+
+ align:start position:0%
+is everything is different everything
+about RFID is different right first of
+
+ align:start position:0%
+about RFID is different right first of
+ 
+
+ align:start position:0%
+about RFID is different right first of
+all power is limited so range is limited
+
+ align:start position:0%
+all power is limited so range is limited
+ 
+
+ align:start position:0%
+all power is limited so range is limited
+right you can't compute because every
+
+ align:start position:0%
+right you can't compute because every
+ 
+
+ align:start position:0%
+right you can't compute because every
+compute cycle sucks up power um you
+
+ align:start position:0%
+compute cycle sucks up power um you
+ 
+
+ align:start position:0%
+compute cycle sucks up power um you
+can't put a lot of memory because every
+
+ align:start position:0%
+can't put a lot of memory because every
+ 
+
+ align:start position:0%
+can't put a lot of memory because every
+comp every piece of memory increases
+
+ align:start position:0%
+comp every piece of memory increases
+ 
+
+ align:start position:0%
+comp every piece of memory increases
+cost and Power cost is an issue so
+
+ align:start position:0%
+cost and Power cost is an issue so
+ 
+
+ align:start position:0%
+cost and Power cost is an issue so
+you're kind of boxed in so it's kind of
+
+ align:start position:0%
+you're kind of boxed in so it's kind of
+ 
+
+ align:start position:0%
+you're kind of boxed in so it's kind of
+like uh you know it's it's you have very
+
+ align:start position:0%
+like uh you know it's it's you have very
+ 
+
+ align:start position:0%
+like uh you know it's it's you have very
+little wiggle room but yet you're trying
+
+ align:start position:0%
+little wiggle room but yet you're trying
+ 
+
+ align:start position:0%
+little wiggle room but yet you're trying
+to do everything now you add to that
+
+ align:start position:0%
+to do everything now you add to that
+ 
+
+ align:start position:0%
+to do everything now you add to that
+bandwidth is limited because you're
+
+ align:start position:0%
+bandwidth is limited because you're
+ 
+
+ align:start position:0%
+bandwidth is limited because you're
+always operating in industrial
+
+ align:start position:0%
+always operating in industrial
+ 
+
+ align:start position:0%
+always operating in industrial
+scientific medical bands or some free
+
+ align:start position:0%
+scientific medical bands or some free
+ 
+
+ align:start position:0%
+scientific medical bands or some free
+band uh at least the general RFID
+
+ align:start position:0%
+band uh at least the general RFID
+ 
+
+ align:start position:0%
+band uh at least the general RFID
+movement it's always going to be in a
+
+ align:start position:0%
+movement it's always going to be in a
+ 
+
+ align:start position:0%
+movement it's always going to be in a
+free band so bandwidth is very limited
+
+ align:start position:0%
+free band so bandwidth is very limited
+ 
+
+ align:start position:0%
+free band so bandwidth is very limited
+you can't do much with this stuff um
+
+ align:start position:0%
+you can't do much with this stuff um
+ 
+
+ align:start position:0%
+you can't do much with this stuff um
+memories at a premium as we discovered
+
+ align:start position:0%
+memories at a premium as we discovered
+ 
+
+ align:start position:0%
+memories at a premium as we discovered
+the Auto ID center you get a lot of data
+
+ align:start position:0%
+the Auto ID center you get a lot of data
+ 
+
+ align:start position:0%
+the Auto ID center you get a lot of data
+from RFID tags but it's very followable
+
+ align:start position:0%
+from RFID tags but it's very followable
+ 
+
+ align:start position:0%
+from RFID tags but it's very followable
+in other words there can be a lot of
+
+ align:start position:0%
+in other words there can be a lot of
+ 
+
+ align:start position:0%
+in other words there can be a lot of
+wrong data like as I said it's not wrong
+
+ align:start position:0%
+wrong data like as I said it's not wrong
+ 
+
+ align:start position:0%
+wrong data like as I said it's not wrong
+in the sense that the read is wrong but
+
+ align:start position:0%
+in the sense that the read is wrong but
+ 
+
+ align:start position:0%
+in the sense that the read is wrong but
+the false negatives that is a misread
+
+ align:start position:0%
+the false negatives that is a misread
+ 
+
+ align:start position:0%
+the false negatives that is a misread
+can manifest itself in ways that can
+
+ align:start position:0%
+can manifest itself in ways that can
+ 
+
+ align:start position:0%
+can manifest itself in ways that can
+screw up your typical
+
+ align:start position:0%
+screw up your typical
+ 
+
+ align:start position:0%
+screw up your typical
+algorithm right so you got to correct
+
+ align:start position:0%
+algorithm right so you got to correct
+ 
+
+ align:start position:0%
+algorithm right so you got to correct
+for that um here's a very interesting
+
+ align:start position:0%
+for that um here's a very interesting
+ 
+
+ align:start position:0%
+for that um here's a very interesting
+one tag connectivity is sporadic that's
+
+ align:start position:0%
+one tag connectivity is sporadic that's
+ 
+
+ align:start position:0%
+one tag connectivity is sporadic that's
+a very subtle one you know even my cell
+
+ align:start position:0%
+a very subtle one you know even my cell
+ 
+
+ align:start position:0%
+a very subtle one you know even my cell
+phone right let us say that Singular
+
+ align:start position:0%
+phone right let us say that Singular
+ 
+
+ align:start position:0%
+phone right let us say that Singular
+Wireless decides that it wants to
+
+ align:start position:0%
+Wireless decides that it wants to
+ 
+
+ align:start position:0%
+Wireless decides that it wants to
+upgrade the firmware on my cellone phone
+
+ align:start position:0%
+upgrade the firmware on my cellone phone
+ 
+
+ align:start position:0%
+upgrade the firmware on my cellone phone
+it can kind of do it because it's got
+
+ align:start position:0%
+it can kind of do it because it's got
+ 
+
+ align:start position:0%
+it can kind of do it because it's got
+you know 80% of the time it's on with an
+
+ align:start position:0%
+you know 80% of the time it's on with an
+ 
+
+ align:start position:0%
+you know 80% of the time it's on with an
+RFID tag you don't know where you're
+
+ align:start position:0%
+RFID tag you don't know where you're
+ 
+
+ align:start position:0%
+RFID tag you don't know where you're
+going to see it next let's say you
+
+ align:start position:0%
+going to see it next let's say you
+ 
+
+ align:start position:0%
+going to see it next let's say you
+wanted to you know write some data to it
+
+ align:start position:0%
+wanted to you know write some data to it
+ 
+
+ align:start position:0%
+wanted to you know write some data to it
+you don't know where you're going to see
+
+ align:start position:0%
+you don't know where you're going to see
+ 
+
+ align:start position:0%
+you don't know where you're going to see
+it next it could be in your company it
+
+ align:start position:0%
+it next it could be in your company it
+ 
+
+ align:start position:0%
+it next it could be in your company it
+could be at MIT it could be at PNG it
+
+ align:start position:0%
+could be at MIT it could be at PNG it
+ 
+
+ align:start position:0%
+could be at MIT it could be at PNG it
+could be at Walmart you don't know when
+
+ align:start position:0%
+could be at Walmart you don't know when
+ 
+
+ align:start position:0%
+could be at Walmart you don't know when
+you're going to see it so what are you
+
+ align:start position:0%
+you're going to see it so what are you
+ 
+
+ align:start position:0%
+you're going to see it so what are you
+going to do preposition all that
+
+ align:start position:0%
+going to do preposition all that
+ 
+
+ align:start position:0%
+going to do preposition all that
+information in every reader on the
+
+ align:start position:0%
+information in every reader on the
+ 
+
+ align:start position:0%
+information in every reader on the
+planet that you want to put on that re
+
+ align:start position:0%
+planet that you want to put on that re
+ 
+
+ align:start position:0%
+planet that you want to put on that re
+on that tag well you couldn't possibly
+
+ align:start position:0%
+on that tag well you couldn't possibly
+ 
+
+ align:start position:0%
+on that tag well you couldn't possibly
+do that either so there's some
+
+ align:start position:0%
+do that either so there's some
+ 
+
+ align:start position:0%
+do that either so there's some
+compromise where you kind of know where
+
+ align:start position:0%
+compromise where you kind of know where
+ 
+
+ align:start position:0%
+compromise where you kind of know where
+where stuff is and you think you're
+
+ align:start position:0%
+where stuff is and you think you're
+ 
+
+ align:start position:0%
+where stuff is and you think you're
+going to see it there and you push the
+
+ align:start position:0%
+going to see it there and you push the
+ 
+
+ align:start position:0%
+going to see it there and you push the
+information there in the hope that when
+
+ align:start position:0%
+information there in the hope that when
+ 
+
+ align:start position:0%
+information there in the hope that when
+it shows up you can push that
+
+ align:start position:0%
+it shows up you can push that
+ 
+
+ align:start position:0%
+it shows up you can push that
+information down that's just a
+
+ align:start position:0%
+information down that's just a
+ 
+
+ align:start position:0%
+information down that's just a
+fundamental distributed computing
+
+ align:start position:0%
+fundamental distributed computing
+ 
+
+ align:start position:0%
+fundamental distributed computing
+challenge
+
+ align:start position:0%
+challenge
+ 
+
+ align:start position:0%
+challenge
+of extremely irritating but yet
+
+ align:start position:0%
+of extremely irritating but yet
+ 
+
+ align:start position:0%
+of extremely irritating but yet
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+magnitude right so tag connectivity
+
+ align:start position:0%
+magnitude right so tag connectivity
+ 
+
+ align:start position:0%
+magnitude right so tag connectivity
+being sporadic kind of compounds
+
+ align:start position:0%
+being sporadic kind of compounds
+ 
+
+ align:start position:0%
+being sporadic kind of compounds
+everything and to add to everything cell
+
+ align:start position:0%
+everything and to add to everything cell
+ 
+
+ align:start position:0%
+everything and to add to everything cell
+phones are targeting a human being
+
+ align:start position:0%
+phones are targeting a human being
+ 
+
+ align:start position:0%
+phones are targeting a human being
+carrying this thing and holding it to
+
+ align:start position:0%
+carrying this thing and holding it to
+ 
+
+ align:start position:0%
+carrying this thing and holding it to
+their ear that's it
+
+ align:start position:0%
+their ear that's it
+ 
+
+ align:start position:0%
+their ear that's it
+tags can show up on products they can
+
+ align:start position:0%
+tags can show up on products they can
+ 
+
+ align:start position:0%
+tags can show up on products they can
+show up on animals right they can show
+
+ align:start position:0%
+show up on animals right they can show
+ 
+
+ align:start position:0%
+show up on animals right they can show
+up on pallets they can show up on metal
+
+ align:start position:0%
+up on pallets they can show up on metal
+ 
+
+ align:start position:0%
+up on pallets they can show up on metal
+containers they can show up inside metal
+
+ align:start position:0%
+containers they can show up inside metal
+ 
+
+ align:start position:0%
+containers they can show up inside metal
+containers right they can have sensors
+
+ align:start position:0%
+containers right they can have sensors
+ 
+
+ align:start position:0%
+containers right they can have sensors
+on them they could be active they could
+
+ align:start position:0%
+on them they could be active they could
+ 
+
+ align:start position:0%
+on them they could be active they could
+be passive so you've got to prepare for
+
+ align:start position:0%
+be passive so you've got to prepare for
+ 
+
+ align:start position:0%
+be passive so you've got to prepare for
+everything so if you have a reader here
+
+ align:start position:0%
+everything so if you have a reader here
+ 
+
+ align:start position:0%
+everything so if you have a reader here
+it's got to be ready to read that
+
+ align:start position:0%
+it's got to be ready to read that
+ 
+
+ align:start position:0%
+it's got to be ready to read that
+passive tag sitting right there and
+
+ align:start position:0%
+passive tag sitting right there and
+ 
+
+ align:start position:0%
+passive tag sitting right there and
+possibly an active tag with a 1 km radi
+
+ align:start position:0%
+possibly an active tag with a 1 km radi
+ 
+
+ align:start position:0%
+possibly an active tag with a 1 km radi
+radius which happens to be in the next
+
+ align:start position:0%
+radius which happens to be in the next
+ 
+
+ align:start position:0%
+radius which happens to be in the next
+building and make sense out of it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's fascinating you think about it and
+
+ align:start position:0%
+it's fascinating you think about it and
+ 
+
+ align:start position:0%
+it's fascinating you think about it and
+these are problems that people are
+
+ align:start position:0%
+these are problems that people are
+ 
+
+ align:start position:0%
+these are problems that people are
+facing today these are not problems I
+
+ align:start position:0%
+facing today these are not problems I
+ 
+
+ align:start position:0%
+facing today these are not problems I
+just made up this is just beginning to
+
+ align:start position:0%
+just made up this is just beginning to
+ 
+
+ align:start position:0%
+just made up this is just beginning to
+happen in real life right and finally
+
+ align:start position:0%
+happen in real life right and finally
+ 
+
+ align:start position:0%
+happen in real life right and finally
+the range of Technologies is
+
+ align:start position:0%
+the range of Technologies is
+ 
+
+ align:start position:0%
+the range of Technologies is
+huge um you will have active tax passive
+
+ align:start position:0%
+huge um you will have active tax passive
+ 
+
+ align:start position:0%
+huge um you will have active tax passive
+tax you're going to have GPS right how
+
+ align:start position:0%
+tax you're going to have GPS right how
+ 
+
+ align:start position:0%
+tax you're going to have GPS right how
+do you interact integrate GPS with these
+
+ align:start position:0%
+do you interact integrate GPS with these
+ 
+
+ align:start position:0%
+do you interact integrate GPS with these
+systems actually by the way it's not bad
+
+ align:start position:0%
+systems actually by the way it's not bad
+ 
+
+ align:start position:0%
+systems actually by the way it's not bad
+news it's all good news and there's all
+
+ align:start position:0%
+news it's all good news and there's all
+ 
+
+ align:start position:0%
+news it's all good news and there's all
+the people are doing these things and
+
+ align:start position:0%
+the people are doing these things and
+ 
+
+ align:start position:0%
+the people are doing these things and
+but there is no cohesive overarching
+
+ align:start position:0%
+but there is no cohesive overarching
+ 
+
+ align:start position:0%
+but there is no cohesive overarching
+thinking pulling it all together um you
+
+ align:start position:0%
+thinking pulling it all together um you
+ 
+
+ align:start position:0%
+thinking pulling it all together um you
+have cellular technology readers inside
+
+ align:start position:0%
+have cellular technology readers inside
+ 
+
+ align:start position:0%
+have cellular technology readers inside
+cell phones right
+
+ align:start position:0%
+cell phones right
+ 
+
+ align:start position:0%
+cell phones right
+fascinating so what I thought I would do
+
+ align:start position:0%
+fascinating so what I thought I would do
+ 
+
+ align:start position:0%
+fascinating so what I thought I would do
+is I'll take this map it's kind of like
+
+ align:start position:0%
+is I'll take this map it's kind of like
+ 
+
+ align:start position:0%
+is I'll take this map it's kind of like
+looking the looking at the planet and
+
+ align:start position:0%
+looking the looking at the planet and
+ 
+
+ align:start position:0%
+looking the looking at the planet and
+spend I don't have very much time but
+
+ align:start position:0%
+spend I don't have very much time but
+ 
+
+ align:start position:0%
+spend I don't have very much time but
+I'd like to borrow down in a few places
+
+ align:start position:0%
+I'd like to borrow down in a few places
+ 
+
+ align:start position:0%
+I'd like to borrow down in a few places
+and just give you a taste of some of the
+
+ align:start position:0%
+and just give you a taste of some of the
+ 
+
+ align:start position:0%
+and just give you a taste of some of the
+research that the Auto ID center did
+
+ align:start position:0%
+research that the Auto ID center did
+ 
+
+ align:start position:0%
+research that the Auto ID center did
+other people did and see how you know I
+
+ align:start position:0%
+other people did and see how you know I
+ 
+
+ align:start position:0%
+other people did and see how you know I
+want to show if you haven't seen this
+
+ align:start position:0%
+want to show if you haven't seen this
+ 
+
+ align:start position:0%
+want to show if you haven't seen this
+give you a sense of how rich it can get
+
+ align:start position:0%
+give you a sense of how rich it can get
+ 
+
+ align:start position:0%
+give you a sense of how rich it can get
+how quickly it can can get rich when you
+
+ align:start position:0%
+how quickly it can can get rich when you
+ 
+
+ align:start position:0%
+how quickly it can can get rich when you
+borrow down so I picked um when I was
+
+ align:start position:0%
+borrow down so I picked um when I was
+ 
+
+ align:start position:0%
+borrow down so I picked um when I was
+making these slides I created this
+
+ align:start position:0%
+making these slides I created this
+ 
+
+ align:start position:0%
+making these slides I created this
+landscape and I said let's look at
+
+ align:start position:0%
+landscape and I said let's look at
+ 
+
+ align:start position:0%
+landscape and I said let's look at
+protocols let's look at RFI protocols
+
+ align:start position:0%
+protocols let's look at RFI protocols
+ 
+
+ align:start position:0%
+protocols let's look at RFI protocols
+how rich can that really be right it was
+
+ align:start position:0%
+how rich can that really be right it was
+ 
+
+ align:start position:0%
+how rich can that really be right it was
+a question I asked myself in 1998 when I
+
+ align:start position:0%
+a question I asked myself in 1998 when I
+ 
+
+ align:start position:0%
+a question I asked myself in 1998 when I
+was deciding for David Brock to get into
+
+ align:start position:0%
+was deciding for David Brock to get into
+ 
+
+ align:start position:0%
+was deciding for David Brock to get into
+this research topic could I write a
+
+ align:start position:0%
+this research topic could I write a
+ 
+
+ align:start position:0%
+this research topic could I write a
+paper here right what I can tell you now
+
+ align:start position:0%
+paper here right what I can tell you now
+ 
+
+ align:start position:0%
+paper here right what I can tell you now
+is there probably a million papers there
+
+ align:start position:0%
+is there probably a million papers there
+ 
+
+ align:start position:0%
+is there probably a million papers there
+at that time I thought there was zero
+
+ align:start position:0%
+at that time I thought there was zero
+ 
+
+ align:start position:0%
+at that time I thought there was zero
+right so when you get into it so let's
+
+ align:start position:0%
+right so when you get into it so let's
+ 
+
+ align:start position:0%
+right so when you get into it so let's
+zoom in what's protocols well it turns
+
+ align:start position:0%
+zoom in what's protocols well it turns
+ 
+
+ align:start position:0%
+zoom in what's protocols well it turns
+out Protocols are not just protocols
+
+ align:start position:0%
+out Protocols are not just protocols
+ 
+
+ align:start position:0%
+out Protocols are not just protocols
+there's a physical layer and there's a
+
+ align:start position:0%
+there's a physical layer and there's a
+ 
+
+ align:start position:0%
+there's a physical layer and there's a
+logical layer in the physical layer
+
+ align:start position:0%
+logical layer in the physical layer
+ 
+
+ align:start position:0%
+logical layer in the physical layer
+there are different frequencies to
+
+ align:start position:0%
+there are different frequencies to
+ 
+
+ align:start position:0%
+there are different frequencies to
+consider uh there are different schemes
+
+ align:start position:0%
+consider uh there are different schemes
+ 
+
+ align:start position:0%
+consider uh there are different schemes
+like IDE band that are popping up to
+
+ align:start position:0%
+like IDE band that are popping up to
+ 
+
+ align:start position:0%
+like IDE band that are popping up to
+consider okay well that's pretty good
+
+ align:start position:0%
+consider okay well that's pretty good
+ 
+
+ align:start position:0%
+consider okay well that's pretty good
+right um and then there's a logical
+
+ align:start position:0%
+right um and then there's a logical
+ 
+
+ align:start position:0%
+right um and then there's a logical
+layer in The Logical layer you need to
+
+ align:start position:0%
+layer in The Logical layer you need to
+ 
+
+ align:start position:0%
+layer in The Logical layer you need to
+look at readers interfering with each
+
+ align:start position:0%
+look at readers interfering with each
+ 
+
+ align:start position:0%
+look at readers interfering with each
+other Dan Engles and I wrote a paper in
+
+ align:start position:0%
+other Dan Engles and I wrote a paper in
+ 
+
+ align:start position:0%
+other Dan Engles and I wrote a paper in
+199 I think on readers interfering and
+
+ align:start position:0%
+199 I think on readers interfering and
+ 
+
+ align:start position:0%
+199 I think on readers interfering and
+we thought it was just spy in the sky
+
+ align:start position:0%
+we thought it was just spy in the sky
+ 
+
+ align:start position:0%
+we thought it was just spy in the sky
+just an intellectual problem we invented
+
+ align:start position:0%
+just an intellectual problem we invented
+ 
+
+ align:start position:0%
+just an intellectual problem we invented
+turns out was it's actually a very
+
+ align:start position:0%
+turns out was it's actually a very
+ 
+
+ align:start position:0%
+turns out was it's actually a very
+serious problem right um so you need to
+
+ align:start position:0%
+serious problem right um so you need to
+ 
+
+ align:start position:0%
+serious problem right um so you need to
+make sure that readers don't interfere
+
+ align:start position:0%
+make sure that readers don't interfere
+ 
+
+ align:start position:0%
+make sure that readers don't interfere
+uh and there are a couple of ways to do
+
+ align:start position:0%
+uh and there are a couple of ways to do
+ 
+
+ align:start position:0%
+uh and there are a couple of ways to do
+that you can make you can do something
+
+ align:start position:0%
+that you can make you can do something
+ 
+
+ align:start position:0%
+that you can make you can do something
+called tag sessions which actually is in
+
+ align:start position:0%
+called tag sessions which actually is in
+ 
+
+ align:start position:0%
+called tag sessions which actually is in
+the Gen 2 protocol um and you can do
+
+ align:start position:0%
+the Gen 2 protocol um and you can do
+ 
+
+ align:start position:0%
+the Gen 2 protocol um and you can do
+something called inband reader
+
+ align:start position:0%
+something called inband reader
+ 
+
+ align:start position:0%
+something called inband reader
+coordination which we couldn't get into
+
+ align:start position:0%
+coordination which we couldn't get into
+ 
+
+ align:start position:0%
+coordination which we couldn't get into
+the Gen 2
+
+ align:start position:0%
+the Gen 2
+ 
+
+ align:start position:0%
+the Gen 2
+protocol but there are other reasons for
+
+ align:start position:0%
+protocol but there are other reasons for
+ 
+
+ align:start position:0%
+protocol but there are other reasons for
+that as well there technical challenges
+
+ align:start position:0%
+that as well there technical challenges
+ 
+
+ align:start position:0%
+that as well there technical challenges
+that need to be addressed to do that
+
+ align:start position:0%
+that need to be addressed to do that
+ 
+
+ align:start position:0%
+that need to be addressed to do that
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+security right how do you make sure that
+
+ align:start position:0%
+security right how do you make sure that
+ 
+
+ align:start position:0%
+security right how do you make sure that
+privacy is protected you
+
+ align:start position:0%
+privacy is protected you
+ 
+
+ align:start position:0%
+privacy is protected you
+know you know someone can't even drop on
+
+ align:start position:0%
+know you know someone can't even drop on
+ 
+
+ align:start position:0%
+know you know someone can't even drop on
+targets
+
+ align:start position:0%
+targets
+ 
+
+ align:start position:0%
+targets
+um you know reads and make sure that you
+
+ align:start position:0%
+um you know reads and make sure that you
+ 
+
+ align:start position:0%
+um you know reads and make sure that you
+know uh and see what inventory they've
+
+ align:start position:0%
+know uh and see what inventory they've
+ 
+
+ align:start position:0%
+know uh and see what inventory they've
+purchased so they can game them right
+
+ align:start position:0%
+purchased so they can game them right
+ 
+
+ align:start position:0%
+purchased so they can game them right
+there's different data types there's the
+
+ align:start position:0%
+there's different data types there's the
+ 
+
+ align:start position:0%
+there's different data types there's the
+EPC there might be sensor data then
+
+ align:start position:0%
+EPC there might be sensor data then
+ 
+
+ align:start position:0%
+EPC there might be sensor data then
+there's Sensors how do you make sure
+
+ align:start position:0%
+there's Sensors how do you make sure
+ 
+
+ align:start position:0%
+there's Sensors how do you make sure
+when you read a tag let's say if it has
+
+ align:start position:0%
+when you read a tag let's say if it has
+ 
+
+ align:start position:0%
+when you read a tag let's say if it has
+a sensor that you know it was a
+
+ align:start position:0%
+a sensor that you know it was a
+ 
+
+ align:start position:0%
+a sensor that you know it was a
+temperature sensor that the data is that
+
+ align:start position:0%
+temperature sensor that the data is that
+ 
+
+ align:start position:0%
+temperature sensor that the data is that
+you know follows the EPC well okay the
+
+ align:start position:0%
+you know follows the EPC well okay the
+ 
+
+ align:start position:0%
+you know follows the EPC well okay the
+temperature that reported is it in
+
+ align:start position:0%
+temperature that reported is it in
+ 
+
+ align:start position:0%
+temperature that reported is it in
+Celsius or is it in
+
+ align:start position:0%
+Celsius or is it in
+ 
+
+ align:start position:0%
+Celsius or is it in
+fit is it a Time series or is it the
+
+ align:start position:0%
+fit is it a Time series or is it the
+ 
+
+ align:start position:0%
+fit is it a Time series or is it the
+temperature taken at that
+
+ align:start position:0%
+temperature taken at that
+ 
+
+ align:start position:0%
+temperature taken at that
+moment if if it's a Time series what
+
+ align:start position:0%
+moment if if it's a Time series what
+ 
+
+ align:start position:0%
+moment if if it's a Time series what
+units we are we using for time is it
+
+ align:start position:0%
+units we are we using for time is it
+ 
+
+ align:start position:0%
+units we are we using for time is it
+compressed then what's a compression
+
+ align:start position:0%
+compressed then what's a compression
+ 
+
+ align:start position:0%
+compressed then what's a compression
+algorithm right isn't that incredible
+
+ align:start position:0%
+algorithm right isn't that incredible
+ 
+
+ align:start position:0%
+algorithm right isn't that incredible
+and then just that question you can go
+
+ align:start position:0%
+and then just that question you can go
+ 
+
+ align:start position:0%
+and then just that question you can go
+on and on well if you're going to
+
+ align:start position:0%
+on and on well if you're going to
+ 
+
+ align:start position:0%
+on and on well if you're going to
+compress it what's the cheapest
+
+ align:start position:0%
+compress it what's the cheapest
+ 
+
+ align:start position:0%
+compress it what's the cheapest
+compression algorithm you can put on a
+
+ align:start position:0%
+compression algorithm you can put on a
+ 
+
+ align:start position:0%
+compression algorithm you can put on a
+lowcost chip which has very little power
+
+ align:start position:0%
+lowcost chip which has very little power
+ 
+
+ align:start position:0%
+lowcost chip which has very little power
+a little bandwidth right and very little
+
+ align:start position:0%
+a little bandwidth right and very little
+ 
+
+ align:start position:0%
+a little bandwidth right and very little
+memory and very little computing
+
+ align:start position:0%
+memory and very little computing
+ 
+
+ align:start position:0%
+memory and very little computing
+power so okay so there are a lot of
+
+ align:start position:0%
+power so okay so there are a lot of
+ 
+
+ align:start position:0%
+power so okay so there are a lot of
+things there so let's focus in a little
+
+ align:start position:0%
+things there so let's focus in a little
+ 
+
+ align:start position:0%
+things there so let's focus in a little
+more so suddenly our protocols is a very
+
+ align:start position:0%
+more so suddenly our protocols is a very
+ 
+
+ align:start position:0%
+more so suddenly our protocols is a very
+rich topic all right let's focus on a
+
+ align:start position:0%
+rich topic all right let's focus on a
+ 
+
+ align:start position:0%
+rich topic all right let's focus on a
+little more let's look at just
+
+ align:start position:0%
+little more let's look at just
+ 
+
+ align:start position:0%
+little more let's look at just
+security just security so this happened
+
+ align:start position:0%
+security just security so this happened
+ 
+
+ align:start position:0%
+security just security so this happened
+to me in 2001 or 2002 was it 2002 when I
+
+ align:start position:0%
+to me in 2001 or 2002 was it 2002 when I
+ 
+
+ align:start position:0%
+to me in 2001 or 2002 was it 2002 when I
+gave a talk in in Ron R group he's a
+
+ align:start position:0%
+gave a talk in in Ron R group he's a
+ 
+
+ align:start position:0%
+gave a talk in in Ron R group he's a
+professor here he's one of the security
+
+ align:start position:0%
+professor here he's one of the security
+ 
+
+ align:start position:0%
+professor here he's one of the security
+gurus at MIT and I went and gave a talk
+
+ align:start position:0%
+gurus at MIT and I went and gave a talk
+ 
+
+ align:start position:0%
+gurus at MIT and I went and gave a talk
+there to about RFID and some early
+
+ align:start position:0%
+there to about RFID and some early
+ 
+
+ align:start position:0%
+there to about RFID and some early
+thinking on security so we dived into it
+
+ align:start position:0%
+thinking on security so we dived into it
+ 
+
+ align:start position:0%
+thinking on security so we dived into it
+all right so let's look at security a
+
+ align:start position:0%
+all right so let's look at security a
+ 
+
+ align:start position:0%
+all right so let's look at security a
+little deeper well you know that's not
+
+ align:start position:0%
+little deeper well you know that's not
+ 
+
+ align:start position:0%
+little deeper well you know that's not
+good enough well if you get into
+
+ align:start position:0%
+good enough well if you get into
+ 
+
+ align:start position:0%
+good enough well if you get into
+security there are layers upon layers
+
+ align:start position:0%
+security there are layers upon layers
+ 
+
+ align:start position:0%
+security there are layers upon layers
+there there's reader to tag security
+
+ align:start position:0%
+there there's reader to tag security
+ 
+
+ align:start position:0%
+there there's reader to tag security
+making sure that the reader toag
+
+ align:start position:0%
+making sure that the reader toag
+ 
+
+ align:start position:0%
+making sure that the reader toag
+communication is made secure and we'll
+
+ align:start position:0%
+communication is made secure and we'll
+ 
+
+ align:start position:0%
+communication is made secure and we'll
+expand on that there making sure the
+
+ align:start position:0%
+expand on that there making sure the
+ 
+
+ align:start position:0%
+expand on that there making sure the
+middleware is secure that is that the
+
+ align:start position:0%
+middleware is secure that is that the
+ 
+
+ align:start position:0%
+middleware is secure that is that the
+middleware talks to the reader in a way
+
+ align:start position:0%
+middleware talks to the reader in a way
+ 
+
+ align:start position:0%
+middleware talks to the reader in a way
+that is secure especially if it's
+
+ align:start position:0%
+that is secure especially if it's
+ 
+
+ align:start position:0%
+that is secure especially if it's
+wireless there's um security between the
+
+ align:start position:0%
+wireless there's um security between the
+ 
+
+ align:start position:0%
+wireless there's um security between the
+middleware and applications sap bound
+
+ align:start position:0%
+middleware and applications sap bound
+ 
+
+ align:start position:0%
+middleware and applications sap bound
+whatever it is there's intercorporation
+
+ align:start position:0%
+whatever it is there's intercorporation
+ 
+
+ align:start position:0%
+whatever it is there's intercorporation
+security right um let us say that you
+
+ align:start position:0%
+security right um let us say that you
+ 
+
+ align:start position:0%
+security right um let us say that you
+have a fridge at home that's reading
+
+ align:start position:0%
+have a fridge at home that's reading
+ 
+
+ align:start position:0%
+have a fridge at home that's reading
+tags inside the fridge and someone is
+
+ align:start position:0%
+tags inside the fridge and someone is
+ 
+
+ align:start position:0%
+tags inside the fridge and someone is
+sitting outside looking at your ownest
+
+ align:start position:0%
+sitting outside looking at your ownest
+ 
+
+ align:start position:0%
+sitting outside looking at your ownest
+hits they can figure out you know sham
+
+ align:start position:0%
+hits they can figure out you know sham
+ 
+
+ align:start position:0%
+hits they can figure out you know sham
+you know he likes uh uh margarine right
+
+ align:start position:0%
+you know he likes uh uh margarine right
+ 
+
+ align:start position:0%
+you know he likes uh uh margarine right
+maybe you're worried about that right so
+
+ align:start position:0%
+maybe you're worried about that right so
+ 
+
+ align:start position:0%
+maybe you're worried about that right so
+that is a very rich problem okay that's
+
+ align:start position:0%
+that is a very rich problem okay that's
+ 
+
+ align:start position:0%
+that is a very rich problem okay that's
+getting too broad so now now we're two
+
+ align:start position:0%
+getting too broad so now now we're two
+ 
+
+ align:start position:0%
+getting too broad so now now we're two
+levels down folks all right let's go
+
+ align:start position:0%
+levels down folks all right let's go
+ 
+
+ align:start position:0%
+levels down folks all right let's go
+let's so that's too much let's look at
+
+ align:start position:0%
+let's so that's too much let's look at
+ 
+
+ align:start position:0%
+let's so that's too much let's look at
+reader tag security guess what that gets
+
+ align:start position:0%
+reader tag security guess what that gets
+ 
+
+ align:start position:0%
+reader tag security guess what that gets
+very interesting too now with three
+
+ align:start position:0%
+very interesting too now with three
+ 
+
+ align:start position:0%
+very interesting too now with three
+levels down right and I thought there
+
+ align:start position:0%
+levels down right and I thought there
+ 
+
+ align:start position:0%
+levels down right and I thought there
+wasn't a paper there in 19 in 2000 2001
+
+ align:start position:0%
+wasn't a paper there in 19 in 2000 2001
+ 
+
+ align:start position:0%
+wasn't a paper there in 19 in 2000 2001
+well there's authenticating the tag
+
+ align:start position:0%
+well there's authenticating the tag
+ 
+
+ align:start position:0%
+well there's authenticating the tag
+what's that authenticating the tag is
+
+ align:start position:0%
+what's that authenticating the tag is
+ 
+
+ align:start position:0%
+what's that authenticating the tag is
+making sure that the tag you read is not
+
+ align:start position:0%
+making sure that the tag you read is not
+ 
+
+ align:start position:0%
+making sure that the tag you read is not
+a spoof tag it is that very tag that J&J
+
+ align:start position:0%
+a spoof tag it is that very tag that J&J
+ 
+
+ align:start position:0%
+a spoof tag it is that very tag that J&J
+put on a J&J product so that you can
+
+ align:start position:0%
+put on a J&J product so that you can
+ 
+
+ align:start position:0%
+put on a J&J product so that you can
+prevent counterfeits and that has
+
+ align:start position:0%
+prevent counterfeits and that has
+ 
+
+ align:start position:0%
+prevent counterfeits and that has
+fundamental business benefits health
+
+ align:start position:0%
+fundamental business benefits health
+ 
+
+ align:start position:0%
+fundamental business benefits health
+benefits social benefits there's
+
+ align:start position:0%
+benefits social benefits there's
+ 
+
+ align:start position:0%
+benefits social benefits there's
+authenticating the reader which is a tag
+
+ align:start position:0%
+authenticating the reader which is a tag
+ 
+
+ align:start position:0%
+authenticating the reader which is a tag
+doesn't respond to a reader if it's not
+
+ align:start position:0%
+doesn't respond to a reader if it's not
+ 
+
+ align:start position:0%
+doesn't respond to a reader if it's not
+the right reader that's
+
+ align:start position:0%
+the right reader that's
+ 
+
+ align:start position:0%
+the right reader that's
+privacy right the cheaper tags passive
+
+ align:start position:0%
+privacy right the cheaper tags passive
+ 
+
+ align:start position:0%
+privacy right the cheaper tags passive
+tags the whole privacy discussion arose
+
+ align:start position:0%
+tags the whole privacy discussion arose
+ 
+
+ align:start position:0%
+tags the whole privacy discussion arose
+because the tag is promiscuous any
+
+ align:start position:0%
+because the tag is promiscuous any
+ 
+
+ align:start position:0%
+because the tag is promiscuous any
+reader can read it so if I have a bottle
+
+ align:start position:0%
+reader can read it so if I have a bottle
+ 
+
+ align:start position:0%
+reader can read it so if I have a bottle
+some medication in my pocket Trevor
+
+ align:start position:0%
+some medication in my pocket Trevor
+ 
+
+ align:start position:0%
+some medication in my pocket Trevor
+could come and read it and I certainly
+
+ align:start position:0%
+could come and read it and I certainly
+ 
+
+ align:start position:0%
+could come and read it and I certainly
+don't want Trevor to know what
+
+ align:start position:0%
+don't want Trevor to know what
+ 
+
+ align:start position:0%
+don't want Trevor to know what
+medication I have in my pocket right but
+
+ align:start position:0%
+medication I have in my pocket right but
+ 
+
+ align:start position:0%
+medication I have in my pocket right but
+if the tag say I will only respond to a
+
+ align:start position:0%
+if the tag say I will only respond to a
+ 
+
+ align:start position:0%
+if the tag say I will only respond to a
+reader that belongs to anyone but Trevor
+
+ align:start position:0%
+reader that belongs to anyone but Trevor
+ 
+
+ align:start position:0%
+reader that belongs to anyone but Trevor
+I'm sorry Trevor right then I am
+
+ align:start position:0%
+I'm sorry Trevor right then I am
+ 
+
+ align:start position:0%
+I'm sorry Trevor right then I am
+protecting my privacy from Trevor right
+
+ align:start position:0%
+protecting my privacy from Trevor right
+ 
+
+ align:start position:0%
+protecting my privacy from Trevor right
+so there's authenticating the reader
+
+ align:start position:0%
+so there's authenticating the reader
+ 
+
+ align:start position:0%
+so there's authenticating the reader
+then I need to prevent Eaves dropping
+
+ align:start position:0%
+then I need to prevent Eaves dropping
+ 
+
+ align:start position:0%
+then I need to prevent Eaves dropping
+which is all right the reader and tag
+
+ align:start position:0%
+which is all right the reader and tag
+ 
+
+ align:start position:0%
+which is all right the reader and tag
+authenticate each other I want to make
+
+ align:start position:0%
+authenticate each other I want to make
+ 
+
+ align:start position:0%
+authenticate each other I want to make
+sure a third party can't listen in and
+
+ align:start position:0%
+sure a third party can't listen in and
+ 
+
+ align:start position:0%
+sure a third party can't listen in and
+figure out what inventories in targets
+
+ align:start position:0%
+figure out what inventories in targets
+ 
+
+ align:start position:0%
+figure out what inventories in targets
+Warehouse oh targets running a back to
+
+ align:start position:0%
+Warehouse oh targets running a back to
+ 
+
+ align:start position:0%
+Warehouse oh targets running a back to
+school promotion I can see that
+
+ align:start position:0%
+school promotion I can see that
+ 
+
+ align:start position:0%
+school promotion I can see that
+I'm you know at Staples I'm going to
+
+ align:start position:0%
+I'm you know at Staples I'm going to
+ 
+
+ align:start position:0%
+I'm you know at Staples I'm going to
+compete with
+
+ align:start position:0%
+compete with
+ 
+
+ align:start position:0%
+compete with
+them right they're going you know a week
+
+ align:start position:0%
+them right they're going you know a week
+ 
+
+ align:start position:0%
+them right they're going you know a week
+early this year so I'm going to go week
+
+ align:start position:0%
+early this year so I'm going to go week
+ 
+
+ align:start position:0%
+early this year so I'm going to go week
+earlier that's actually a big deal for
+
+ align:start position:0%
+earlier that's actually a big deal for
+ 
+
+ align:start position:0%
+earlier that's actually a big deal for
+these guys right there's preventing
+
+ align:start position:0%
+these guys right there's preventing
+ 
+
+ align:start position:0%
+these guys right there's preventing
+tracking which is making sure that I
+
+ align:start position:0%
+tracking which is making sure that I
+ 
+
+ align:start position:0%
+tracking which is making sure that I
+don't know by putting readers at every T
+
+ align:start position:0%
+don't know by putting readers at every T
+ 
+
+ align:start position:0%
+don't know by putting readers at every T
+Station in Boston you know um where you
+
+ align:start position:0%
+Station in Boston you know um where you
+ 
+
+ align:start position:0%
+Station in Boston you know um where you
+know uh you know ex's you know um
+
+ align:start position:0%
+know uh you know ex's you know um
+ 
+
+ align:start position:0%
+know uh you know ex's you know um
+girlfriend or boyfriend lives right and
+
+ align:start position:0%
+girlfriend or boyfriend lives right and
+ 
+
+ align:start position:0%
+girlfriend or boyfriend lives right and
+then how do you personalize everything
+
+ align:start position:0%
+then how do you personalize everything
+ 
+
+ align:start position:0%
+then how do you personalize everything
+when I buy socks and take them home how
+
+ align:start position:0%
+when I buy socks and take them home how
+ 
+
+ align:start position:0%
+when I buy socks and take them home how
+do I make sure that only my reader can
+
+ align:start position:0%
+do I make sure that only my reader can
+ 
+
+ align:start position:0%
+do I make sure that only my reader can
+read my socks and my medicines and if
+
+ align:start position:0%
+read my socks and my medicines and if
+ 
+
+ align:start position:0%
+read my socks and my medicines and if
+someone else tries to read them these
+
+ align:start position:0%
+someone else tries to read them these
+ 
+
+ align:start position:0%
+someone else tries to read them these
+are personalized even the maker of the
+
+ align:start position:0%
+are personalized even the maker of the
+ 
+
+ align:start position:0%
+are personalized even the maker of the
+product couldn't read them anymore
+
+ align:start position:0%
+product couldn't read them anymore
+ 
+
+ align:start position:0%
+product couldn't read them anymore
+that's getting rich right so now we're
+
+ align:start position:0%
+that's getting rich right so now we're
+ 
+
+ align:start position:0%
+that's getting rich right so now we're
+three levels down and again it's turned
+
+ align:start position:0%
+three levels down and again it's turned
+ 
+
+ align:start position:0%
+three levels down and again it's turned
+a really complex problem right and you
+
+ align:start position:0%
+a really complex problem right and you
+ 
+
+ align:start position:0%
+a really complex problem right and you
+know just for the flavor of it let's
+
+ align:start position:0%
+know just for the flavor of it let's
+ 
+
+ align:start position:0%
+know just for the flavor of it let's
+brainstorm it actually gets very
+
+ align:start position:0%
+brainstorm it actually gets very
+ 
+
+ align:start position:0%
+brainstorm it actually gets very
+complicated you know my initial guess I
+
+ align:start position:0%
+complicated you know my initial guess I
+ 
+
+ align:start position:0%
+complicated you know my initial guess I
+had a student called uh Joe Foley we
+
+ align:start position:0%
+had a student called uh Joe Foley we
+ 
+
+ align:start position:0%
+had a student called uh Joe Foley we
+said you know let's just encrypt the
+
+ align:start position:0%
+said you know let's just encrypt the
+ 
+
+ align:start position:0%
+said you know let's just encrypt the
+number on the tag privacy will be taken
+
+ align:start position:0%
+number on the tag privacy will be taken
+ 
+
+ align:start position:0%
+number on the tag privacy will be taken
+care of no just if you just encrypt the
+
+ align:start position:0%
+care of no just if you just encrypt the
+ 
+
+ align:start position:0%
+care of no just if you just encrypt the
+number on the tag and put it on the tag
+
+ align:start position:0%
+number on the tag and put it on the tag
+ 
+
+ align:start position:0%
+number on the tag and put it on the tag
+yeah I can't tell that you have you know
+
+ align:start position:0%
+yeah I can't tell that you have you know
+ 
+
+ align:start position:0%
+yeah I can't tell that you have you know
+Gucci shoes on but I know the number are
+
+ align:start position:0%
+Gucci shoes on but I know the number are
+ 
+
+ align:start position:0%
+Gucci shoes on but I know the number are
+they Gucci bu no I know the number and
+
+ align:start position:0%
+they Gucci bu no I know the number and
+ 
+
+ align:start position:0%
+they Gucci bu no I know the number and
+no I know the number and I can still
+
+ align:start position:0%
+no I know the number and I can still
+ 
+
+ align:start position:0%
+no I know the number and I can still
+track you so it didn't actually solve
+
+ align:start position:0%
+track you so it didn't actually solve
+ 
+
+ align:start position:0%
+track you so it didn't actually solve
+the Privacy problem it solve the privacy
+
+ align:start position:0%
+the Privacy problem it solve the privacy
+ 
+
+ align:start position:0%
+the Privacy problem it solve the privacy
+of the shoes it didn't solve Bernie's
+
+ align:start position:0%
+of the shoes it didn't solve Bernie's
+ 
+
+ align:start position:0%
+of the shoes it didn't solve Bernie's
+privacy problem right not not that easy
+
+ align:start position:0%
+privacy problem right not not that easy
+ 
+
+ align:start position:0%
+privacy problem right not not that easy
+right so that doesn't solve the problem
+
+ align:start position:0%
+right so that doesn't solve the problem
+ 
+
+ align:start position:0%
+right so that doesn't solve the problem
+okay then then we thought ah we got it
+
+ align:start position:0%
+okay then then we thought ah we got it
+ 
+
+ align:start position:0%
+okay then then we thought ah we got it
+let's just kill the number all right
+
+ align:start position:0%
+let's just kill the number all right
+ 
+
+ align:start position:0%
+let's just kill the number all right
+sign I don't know it's that particular
+
+ align:start position:0%
+sign I don't know it's that particular
+ 
+
+ align:start position:0%
+sign I don't know it's that particular
+pair of Gucci shoes I know it's a pair
+
+ align:start position:0%
+pair of Gucci shoes I know it's a pair
+ 
+
+ align:start position:0%
+pair of Gucci shoes I know it's a pair
+of Gucci shoes right and a lot of people
+
+ align:start position:0%
+of Gucci shoes right and a lot of people
+ 
+
+ align:start position:0%
+of Gucci shoes right and a lot of people
+wear Gucci shoes so it's okay but you
+
+ align:start position:0%
+wear Gucci shoes so it's okay but you
+ 
+
+ align:start position:0%
+wear Gucci shoes so it's okay but you
+know what Bernie also has a Rox pen in
+
+ align:start position:0%
+know what Bernie also has a Rox pen in
+ 
+
+ align:start position:0%
+know what Bernie also has a Rox pen in
+his in his pocket I believe um and he
+
+ align:start position:0%
+his in his pocket I believe um and he
+ 
+
+ align:start position:0%
+his in his pocket I believe um and he
+may be the only person in Boston with
+
+ align:start position:0%
+may be the only person in Boston with
+ 
+
+ align:start position:0%
+may be the only person in Boston with
+high probability who has both Gucci
+
+ align:start position:0%
+high probability who has both Gucci
+ 
+
+ align:start position:0%
+high probability who has both Gucci
+shoes and RX pen so by constellation
+
+ align:start position:0%
+shoes and RX pen so by constellation
+ 
+
+ align:start position:0%
+shoes and RX pen so by constellation
+tracking I know him and I can track him
+
+ align:start position:0%
+tracking I know him and I can track him
+ 
+
+ align:start position:0%
+tracking I know him and I can track him
+and maybe you add to that you know some
+
+ align:start position:0%
+and maybe you add to that you know some
+ 
+
+ align:start position:0%
+and maybe you add to that you know some
+particular brand of jacket that's it are
+
+ align:start position:0%
+particular brand of jacket that's it are
+ 
+
+ align:start position:0%
+particular brand of jacket that's it are
+triangulated so again I haven't solve
+
+ align:start position:0%
+triangulated so again I haven't solve
+ 
+
+ align:start position:0%
+triangulated so again I haven't solve
+the problem right I'm just trying to
+
+ align:start position:0%
+the problem right I'm just trying to
+ 
+
+ align:start position:0%
+the problem right I'm just trying to
+give you a sense of it tough problem
+
+ align:start position:0%
+give you a sense of it tough problem
+ 
+
+ align:start position:0%
+give you a sense of it tough problem
+folks we thought we had it wrong right
+
+ align:start position:0%
+folks we thought we had it wrong right
+ 
+
+ align:start position:0%
+folks we thought we had it wrong right
+you you get deeper and deeper right and
+
+ align:start position:0%
+you you get deeper and deeper right and
+ 
+
+ align:start position:0%
+you you get deeper and deeper right and
+then you insist that tag needs to know
+
+ align:start position:0%
+then you insist that tag needs to know
+ 
+
+ align:start position:0%
+then you insist that tag needs to know
+the reader well that means that the tag
+
+ align:start position:0%
+the reader well that means that the tag
+ 
+
+ align:start position:0%
+the reader well that means that the tag
+needs to have the password of every
+
+ align:start position:0%
+needs to have the password of every
+ 
+
+ align:start position:0%
+needs to have the password of every
+reader well that's not a cheap tag right
+
+ align:start position:0%
+reader well that's not a cheap tag right
+ 
+
+ align:start position:0%
+reader well that's not a cheap tag right
+so you know it just you know I won't
+
+ align:start position:0%
+so you know it just you know I won't
+ 
+
+ align:start position:0%
+so you know it just you know I won't
+belabor everything but it just turns
+
+ align:start position:0%
+belabor everything but it just turns
+ 
+
+ align:start position:0%
+belabor everything but it just turns
+into such an interesting problem
+
+ align:start position:0%
+into such an interesting problem
+ 
+
+ align:start position:0%
+into such an interesting problem
+preventing counterfeits right this
+
+ align:start position:0%
+preventing counterfeits right this
+ 
+
+ align:start position:0%
+preventing counterfeits right this
+tradition encryption is expensive
+
+ align:start position:0%
+tradition encryption is expensive
+ 
+
+ align:start position:0%
+tradition encryption is expensive
+there's challenge response uh that means
+
+ align:start position:0%
+there's challenge response uh that means
+ 
+
+ align:start position:0%
+there's challenge response uh that means
+you need to put secrets on every tag
+
+ align:start position:0%
+you need to put secrets on every tag
+ 
+
+ align:start position:0%
+you need to put secrets on every tag
+very rich very rich just waiting for
+
+ align:start position:0%
+very rich very rich just waiting for
+ 
+
+ align:start position:0%
+very rich very rich just waiting for
+someone to go nail these problems now
+
+ align:start position:0%
+someone to go nail these problems now
+ 
+
+ align:start position:0%
+someone to go nail these problems now
+these these we've looked at and then we
+
+ align:start position:0%
+these these we've looked at and then we
+ 
+
+ align:start position:0%
+these these we've looked at and then we
+want to prevent eavesdropping many of
+
+ align:start position:0%
+want to prevent eavesdropping many of
+ 
+
+ align:start position:0%
+want to prevent eavesdropping many of
+these things we've kind of solved but
+
+ align:start position:0%
+these things we've kind of solved but
+ 
+
+ align:start position:0%
+these things we've kind of solved but
+here's the secret right actually we've
+
+ align:start position:0%
+here's the secret right actually we've
+ 
+
+ align:start position:0%
+here's the secret right actually we've
+solved some of these problems in indiv
+
+ align:start position:0%
+solved some of these problems in indiv
+ 
+
+ align:start position:0%
+solved some of these problems in indiv
+individually we have not solved the
+
+ align:start position:0%
+individually we have not solved the
+ 
+
+ align:start position:0%
+individually we have not solved the
+bigger problem of solving of addressing
+
+ align:start position:0%
+bigger problem of solving of addressing
+ 
+
+ align:start position:0%
+bigger problem of solving of addressing
+all these questions we just haven't and
+
+ align:start position:0%
+all these questions we just haven't and
+ 
+
+ align:start position:0%
+all these questions we just haven't and
+right there it's just a huge research
+
+ align:start position:0%
+right there it's just a huge research
+ 
+
+ align:start position:0%
+right there it's just a huge research
+topic waiting to be addressed and for
+
+ align:start position:0%
+topic waiting to be addressed and for
+ 
+
+ align:start position:0%
+topic waiting to be addressed and for
+what it's worth uh Steve Weiss wrote a
+
+ align:start position:0%
+what it's worth uh Steve Weiss wrote a
+ 
+
+ align:start position:0%
+what it's worth uh Steve Weiss wrote a
+beautiful pH Master's thesis on this in
+
+ align:start position:0%
+beautiful pH Master's thesis on this in
+ 
+
+ align:start position:0%
+beautiful pH Master's thesis on this in
+which he provides some solutions and he
+
+ align:start position:0%
+which he provides some solutions and he
+ 
+
+ align:start position:0%
+which he provides some solutions and he
+very explicitly lets out the things we
+
+ align:start position:0%
+very explicitly lets out the things we
+ 
+
+ align:start position:0%
+very explicitly lets out the things we
+couldn't solve but that's a start right
+
+ align:start position:0%
+couldn't solve but that's a start right
+ 
+
+ align:start position:0%
+couldn't solve but that's a start right
+so that's a master's thesis that came
+
+ align:start position:0%
+so that's a master's thesis that came
+ 
+
+ align:start position:0%
+so that's a master's thesis that came
+out of one talk where I was pretty
+
+ align:start position:0%
+out of one talk where I was pretty
+ 
+
+ align:start position:0%
+out of one talk where I was pretty
+pretty much saying there's not much
+
+ align:start position:0%
+pretty much saying there's not much
+ 
+
+ align:start position:0%
+pretty much saying there's not much
+research
+
+ align:start position:0%
+research
+ 
+
+ align:start position:0%
+research
+here right and all that Master's the
+
+ align:start position:0%
+here right and all that Master's the
+ 
+
+ align:start position:0%
+here right and all that Master's the
+this great thesis did was solve a couple
+
+ align:start position:0%
+this great thesis did was solve a couple
+ 
+
+ align:start position:0%
+this great thesis did was solve a couple
+of subp parts and list out about 10
+
+ align:start position:0%
+of subp parts and list out about 10
+ 
+
+ align:start position:0%
+of subp parts and list out about 10
+other problems that we didn't
+
+ align:start position:0%
+other problems that we didn't
+ 
+
+ align:start position:0%
+other problems that we didn't
+solve okay so let's Zoom back up the
+
+ align:start position:0%
+solve okay so let's Zoom back up the
+ 
+
+ align:start position:0%
+solve okay so let's Zoom back up the
+that's that was
+
+ align:start position:0%
+that's that was
+ 
+
+ align:start position:0%
+that's that was
+protocols right one of you know 30
+
+ align:start position:0%
+protocols right one of you know 30
+ 
+
+ align:start position:0%
+protocols right one of you know 30
+things I've listed here and you can look
+
+ align:start position:0%
+things I've listed here and you can look
+ 
+
+ align:start position:0%
+things I've listed here and you can look
+at everything retail right what what are
+
+ align:start position:0%
+at everything retail right what what are
+ 
+
+ align:start position:0%
+at everything retail right what what are
+the opportunities in retail okay let's
+
+ align:start position:0%
+the opportunities in retail okay let's
+ 
+
+ align:start position:0%
+the opportunities in retail okay let's
+zoom in right retail what is retail
+
+ align:start position:0%
+zoom in right retail what is retail
+ 
+
+ align:start position:0%
+zoom in right retail what is retail
+really what is the retail supply chain
+
+ align:start position:0%
+really what is the retail supply chain
+ 
+
+ align:start position:0%
+really what is the retail supply chain
+the retail supply chain is a very
+
+ align:start position:0%
+the retail supply chain is a very
+ 
+
+ align:start position:0%
+the retail supply chain is a very
+interesting thing toothbrushes are made
+
+ align:start position:0%
+interesting thing toothbrushes are made
+ 
+
+ align:start position:0%
+interesting thing toothbrushes are made
+in units of made in units of one you
+
+ align:start position:0%
+in units of made in units of one you
+ 
+
+ align:start position:0%
+in units of made in units of one you
+make one toothbrush at a time okay what
+
+ align:start position:0%
+make one toothbrush at a time okay what
+ 
+
+ align:start position:0%
+make one toothbrush at a time okay what
+happens in the retail supply chain is
+
+ align:start position:0%
+happens in the retail supply chain is
+ 
+
+ align:start position:0%
+happens in the retail supply chain is
+you make one toothbrush at a time you
+
+ align:start position:0%
+you make one toothbrush at a time you
+ 
+
+ align:start position:0%
+you make one toothbrush at a time you
+assemble toothbrushes into cases so you
+
+ align:start position:0%
+assemble toothbrushes into cases so you
+ 
+
+ align:start position:0%
+assemble toothbrushes into cases so you
+have say six toothbrushes in a case you
+
+ align:start position:0%
+have say six toothbrushes in a case you
+ 
+
+ align:start position:0%
+have say six toothbrushes in a case you
+put cases together you make a pallet you
+
+ align:start position:0%
+put cases together you make a pallet you
+ 
+
+ align:start position:0%
+put cases together you make a pallet you
+take pallets together you make container
+
+ align:start position:0%
+take pallets together you make container
+ 
+
+ align:start position:0%
+take pallets together you make container
+you assemble them up so that you can
+
+ align:start position:0%
+you assemble them up so that you can
+ 
+
+ align:start position:0%
+you assemble them up so that you can
+ship them together all right so this is
+
+ align:start position:0%
+ship them together all right so this is
+ 
+
+ align:start position:0%
+ship them together all right so this is
+what the supply chain is then you move
+
+ align:start position:0%
+what the supply chain is then you move
+ 
+
+ align:start position:0%
+what the supply chain is then you move
+them you sort them and you repeat Until
+
+ align:start position:0%
+them you sort them and you repeat Until
+ 
+
+ align:start position:0%
+them you sort them and you repeat Until
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+End aggregate sort transfer aggregate
+
+ align:start position:0%
+End aggregate sort transfer aggregate
+ 
+
+ align:start position:0%
+End aggregate sort transfer aggregate
+deaggregate sort transfer and that's
+
+ align:start position:0%
+deaggregate sort transfer and that's
+ 
+
+ align:start position:0%
+deaggregate sort transfer and that's
+basically a supply chain it's a big
+
+ align:start position:0%
+basically a supply chain it's a big
+ 
+
+ align:start position:0%
+basically a supply chain it's a big
+mixing thing where you make things as
+
+ align:start position:0%
+mixing thing where you make things as
+ 
+
+ align:start position:0%
+mixing thing where you make things as
+one but all of the same kind and that's
+
+ align:start position:0%
+one but all of the same kind and that's
+ 
+
+ align:start position:0%
+one but all of the same kind and that's
+a manufacturer and people walk out with
+
+ align:start position:0%
+a manufacturer and people walk out with
+ 
+
+ align:start position:0%
+a manufacturer and people walk out with
+ones but all of a different kind and
+
+ align:start position:0%
+ones but all of a different kind and
+ 
+
+ align:start position:0%
+ones but all of a different kind and
+that's the consumer and trying to do
+
+ align:start position:0%
+that's the consumer and trying to do
+ 
+
+ align:start position:0%
+that's the consumer and trying to do
+that efficiently is the supply chain in
+
+ align:start position:0%
+that efficiently is the supply chain in
+ 
+
+ align:start position:0%
+that efficiently is the supply chain in
+the retail world as we know it right
+
+ align:start position:0%
+the retail world as we know it right
+ 
+
+ align:start position:0%
+the retail world as we know it right
+this is another fascinating research
+
+ align:start position:0%
+this is another fascinating research
+ 
+
+ align:start position:0%
+this is another fascinating research
+area and this is the one where the
+
+ align:start position:0%
+area and this is the one where the
+ 
+
+ align:start position:0%
+area and this is the one where the
+industry has focused its attention most
+
+ align:start position:0%
+industry has focused its attention most
+ 
+
+ align:start position:0%
+industry has focused its attention most
+immediately because you're trying to do
+
+ align:start position:0%
+immediately because you're trying to do
+ 
+
+ align:start position:0%
+immediately because you're trying to do
+this in a timely fashion with very few
+
+ align:start position:0%
+this in a timely fashion with very few
+ 
+
+ align:start position:0%
+this in a timely fashion with very few
+errors and very little shrinkage well if
+
+ align:start position:0%
+errors and very little shrinkage well if
+ 
+
+ align:start position:0%
+errors and very little shrinkage well if
+you actually look at it in real life it
+
+ align:start position:0%
+you actually look at it in real life it
+ 
+
+ align:start position:0%
+you actually look at it in real life it
+turns out that that process is is ridden
+
+ align:start position:0%
+turns out that that process is is ridden
+ 
+
+ align:start position:0%
+turns out that that process is is ridden
+with errors uh too much that's excess
+
+ align:start position:0%
+with errors uh too much that's excess
+ 
+
+ align:start position:0%
+with errors uh too much that's excess
+inefficiencies losses right uh dilution
+
+ align:start position:0%
+inefficiencies losses right uh dilution
+ 
+
+ align:start position:0%
+inefficiencies losses right uh dilution
+counterfeit uh brand
+
+ align:start position:0%
+counterfeit uh brand
+ 
+
+ align:start position:0%
+counterfeit uh brand
+dilution it's just incredible I mean we
+
+ align:start position:0%
+dilution it's just incredible I mean we
+ 
+
+ align:start position:0%
+dilution it's just incredible I mean we
+waste and and you know you can look at
+
+ align:start position:0%
+waste and and you know you can look at
+ 
+
+ align:start position:0%
+waste and and you know you can look at
+the par the the actual numbers that come
+
+ align:start position:0%
+the par the the actual numbers that come
+ 
+
+ align:start position:0%
+the par the the actual numbers that come
+out we carry something like 30 40% of
+
+ align:start position:0%
+out we carry something like 30 40% of
+ 
+
+ align:start position:0%
+out we carry something like 30 40% of
+inv inventory we shouldn't be carrying
+
+ align:start position:0%
+inv inventory we shouldn't be carrying
+ 
+
+ align:start position:0%
+inv inventory we shouldn't be carrying
+for all that we are 10% out of stock is
+
+ align:start position:0%
+for all that we are 10% out of stock is
+ 
+
+ align:start position:0%
+for all that we are 10% out of stock is
+an industry right and there's some
+
+ align:start position:0%
+an industry right and there's some
+ 
+
+ align:start position:0%
+an industry right and there's some
+fundamental research topics here waiting
+
+ align:start position:0%
+fundamental research topics here waiting
+ 
+
+ align:start position:0%
+fundamental research topics here waiting
+to be addressed and whether they go end
+
+ align:start position:0%
+to be addressed and whether they go end
+ 
+
+ align:start position:0%
+to be addressed and whether they go end
+up being looked at by companies whether
+
+ align:start position:0%
+up being looked at by companies whether
+ 
+
+ align:start position:0%
+up being looked at by companies whether
+they end up being looked at by academics
+
+ align:start position:0%
+they end up being looked at by academics
+ 
+
+ align:start position:0%
+they end up being looked at by academics
+right the fact of the matter is that
+
+ align:start position:0%
+right the fact of the matter is that
+ 
+
+ align:start position:0%
+right the fact of the matter is that
+these are rich research topics waiting
+
+ align:start position:0%
+these are rich research topics waiting
+ 
+
+ align:start position:0%
+these are rich research topics waiting
+for academics to look at now I'll say
+
+ align:start position:0%
+for academics to look at now I'll say
+ 
+
+ align:start position:0%
+for academics to look at now I'll say
+this you can actually map the space out
+
+ align:start position:0%
+this you can actually map the space out
+ 
+
+ align:start position:0%
+this you can actually map the space out
+in many ways uh you can take for example
+
+ align:start position:0%
+in many ways uh you can take for example
+ 
+
+ align:start position:0%
+in many ways uh you can take for example
+the supply chain DC to back room back
+
+ align:start position:0%
+the supply chain DC to back room back
+ 
+
+ align:start position:0%
+the supply chain DC to back room back
+room back room to sales flow sales flow
+
+ align:start position:0%
+room back room to sales flow sales flow
+ 
+
+ align:start position:0%
+room back room to sales flow sales flow
+sales flow to storage and you can look
+
+ align:start position:0%
+sales flow to storage and you can look
+ 
+
+ align:start position:0%
+sales flow to storage and you can look
+at different parameters you can get time
+
+ align:start position:0%
+at different parameters you can get time
+ 
+
+ align:start position:0%
+at different parameters you can get time
+quantities configuration and if you map
+
+ align:start position:0%
+quantities configuration and if you map
+ 
+
+ align:start position:0%
+quantities configuration and if you map
+it out in that way
+
+ align:start position:0%
+it out in that way
+ 
+
+ align:start position:0%
+it out in that way
+in the interest of speed I'll just write
+
+ align:start position:0%
+in the interest of speed I'll just write
+ 
+
+ align:start position:0%
+in the interest of speed I'll just write
+it out I don't expect everyone to see
+
+ align:start position:0%
+it out I don't expect everyone to see
+ 
+
+ align:start position:0%
+it out I don't expect everyone to see
+this but all I'm saying is right there
+
+ align:start position:0%
+this but all I'm saying is right there
+ 
+
+ align:start position:0%
+this but all I'm saying is right there
+in that matric I've captured probably
+
+ align:start position:0%
+in that matric I've captured probably
+ 
+
+ align:start position:0%
+in that matric I've captured probably
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+70% of the problems that most retailers
+
+ align:start position:0%
+70% of the problems that most retailers
+ 
+
+ align:start position:0%
+70% of the problems that most retailers
+looking at they're looking at is my
+
+ align:start position:0%
+looking at they're looking at is my
+ 
+
+ align:start position:0%
+looking at they're looking at is my
+fresh food arriving in a timely fashion
+
+ align:start position:0%
+fresh food arriving in a timely fashion
+ 
+
+ align:start position:0%
+fresh food arriving in a timely fashion
+at um uh the fresh food counter so that
+
+ align:start position:0%
+at um uh the fresh food counter so that
+ 
+
+ align:start position:0%
+at um uh the fresh food counter so that
+when my consumer buys that lce it is
+
+ align:start position:0%
+when my consumer buys that lce it is
+ 
+
+ align:start position:0%
+when my consumer buys that lce it is
+fresh if not where is it LO losing its
+
+ align:start position:0%
+fresh if not where is it LO losing its
+ 
+
+ align:start position:0%
+fresh if not where is it LO losing its
+freshness maybe it's spending too much
+
+ align:start position:0%
+freshness maybe it's spending too much
+ 
+
+ align:start position:0%
+freshness maybe it's spending too much
+time in a DC maybe it's spending too
+
+ align:start position:0%
+time in a DC maybe it's spending too
+ 
+
+ align:start position:0%
+time in a DC maybe it's spending too
+much time in a truck maybe it's not cold
+
+ align:start position:0%
+much time in a truck maybe it's not cold
+ 
+
+ align:start position:0%
+much time in a truck maybe it's not cold
+enough in the truck and so it's losing
+
+ align:start position:0%
+enough in the truck and so it's losing
+ 
+
+ align:start position:0%
+enough in the truck and so it's losing
+freshness and what RFID lets you do is
+
+ align:start position:0%
+freshness and what RFID lets you do is
+ 
+
+ align:start position:0%
+freshness and what RFID lets you do is
+it's kind of like injecting a Dye into
+
+ align:start position:0%
+it's kind of like injecting a Dye into
+ 
+
+ align:start position:0%
+it's kind of like injecting a Dye into
+your bloodstream and know looking to see
+
+ align:start position:0%
+your bloodstream and know looking to see
+ 
+
+ align:start position:0%
+your bloodstream and know looking to see
+how you know the body is operating and
+
+ align:start position:0%
+how you know the body is operating and
+ 
+
+ align:start position:0%
+how you know the body is operating and
+uh it lets you kind of go through all
+
+ align:start position:0%
+uh it lets you kind of go through all
+ 
+
+ align:start position:0%
+uh it lets you kind of go through all
+that and figure out uh how your body is
+
+ align:start position:0%
+that and figure out uh how your body is
+ 
+
+ align:start position:0%
+that and figure out uh how your body is
+doing and if you look at different
+
+ align:start position:0%
+doing and if you look at different
+ 
+
+ align:start position:0%
+doing and if you look at different
+retailers look at for example um Walmart
+
+ align:start position:0%
+retailers look at for example um Walmart
+ 
+
+ align:start position:0%
+retailers look at for example um Walmart
+this is publicly what they've said
+
+ align:start position:0%
+this is publicly what they've said
+ 
+
+ align:start position:0%
+this is publicly what they've said
+they're doing if you look at Best Buy
+
+ align:start position:0%
+they're doing if you look at Best Buy
+ 
+
+ align:start position:0%
+they're doing if you look at Best Buy
+this is what they're going after first
+
+ align:start position:0%
+this is what they're going after first
+ 
+
+ align:start position:0%
+this is what they're going after first
+if you look at um
+
+ align:start position:0%
+if you look at um
+ 
+
+ align:start position:0%
+if you look at um
+Lowe's uh lows is the big uh uh do-
+
+ align:start position:0%
+Lowe's uh lows is the big uh uh do-
+ 
+
+ align:start position:0%
+Lowe's uh lows is the big uh uh do-
+it-yourself store this is what they're
+
+ align:start position:0%
+it-yourself store this is what they're
+ 
+
+ align:start position:0%
+it-yourself store this is what they're
+going after so everyone's looking at a
+
+ align:start position:0%
+going after so everyone's looking at a
+ 
+
+ align:start position:0%
+going after so everyone's looking at a
+differ going after different pieces of
+
+ align:start position:0%
+differ going after different pieces of
+ 
+
+ align:start position:0%
+differ going after different pieces of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+puzzle I have you know lots of examples
+
+ align:start position:0%
+puzzle I have you know lots of examples
+ 
+
+ align:start position:0%
+puzzle I have you know lots of examples
+I I kind of zoom in and look at various
+
+ align:start position:0%
+I I kind of zoom in and look at various
+ 
+
+ align:start position:0%
+I I kind of zoom in and look at various
+examples and in this audience are
+
+ align:start position:0%
+examples and in this audience are
+ 
+
+ align:start position:0%
+examples and in this audience are
+hundreds of other examples where you
+
+ align:start position:0%
+hundreds of other examples where you
+ 
+
+ align:start position:0%
+hundreds of other examples where you
+zoom into this landscape it's kind of
+
+ align:start position:0%
+zoom into this landscape it's kind of
+ 
+
+ align:start position:0%
+zoom into this landscape it's kind of
+like using Google Earth seeing something
+
+ align:start position:0%
+like using Google Earth seeing something
+ 
+
+ align:start position:0%
+like using Google Earth seeing something
+interesting and kind of zooming in
+
+ align:start position:0%
+interesting and kind of zooming in
+ 
+
+ align:start position:0%
+interesting and kind of zooming in
+looking at a map zooming in looking at a
+
+ align:start position:0%
+looking at a map zooming in looking at a
+ 
+
+ align:start position:0%
+looking at a map zooming in looking at a
+house you know you can do that and I
+
+ align:start position:0%
+house you know you can do that and I
+ 
+
+ align:start position:0%
+house you know you can do that and I
+think fundamentally this is what this
+
+ align:start position:0%
+think fundamentally this is what this
+ 
+
+ align:start position:0%
+think fundamentally this is what this
+industry needs and academics are the
+
+ align:start position:0%
+industry needs and academics are the
+ 
+
+ align:start position:0%
+industry needs and academics are the
+microscopes and they're going to figure
+
+ align:start position:0%
+microscopes and they're going to figure
+ 
+
+ align:start position:0%
+microscopes and they're going to figure
+out what the opportunities are and
+
+ align:start position:0%
+out what the opportunities are and
+ 
+
+ align:start position:0%
+out what the opportunities are and
+figure out what the solutions are um in
+
+ align:start position:0%
+figure out what the solutions are um in
+ 
+
+ align:start position:0%
+figure out what the solutions are um in
+the interest of time what I'm going to
+
+ align:start position:0%
+the interest of time what I'm going to
+ 
+
+ align:start position:0%
+the interest of time what I'm going to
+do is I'm going to skip over um most of
+
+ align:start position:0%
+do is I'm going to skip over um most of
+ 
+
+ align:start position:0%
+do is I'm going to skip over um most of
+what I'm what I wanted to say except
+
+ align:start position:0%
+what I'm what I wanted to say except
+ 
+
+ align:start position:0%
+what I'm what I wanted to say except
+this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slide and it say two make two statements
+
+ align:start position:0%
+slide and it say two make two statements
+ 
+
+ align:start position:0%
+slide and it say two make two statements
+and end in about one or two
+
+ align:start position:0%
+and end in about one or two
+ 
+
+ align:start position:0%
+and end in about one or two
+minutes you know when when you have
+
+ align:start position:0%
+minutes you know when when you have
+ 
+
+ align:start position:0%
+minutes you know when when you have
+operations for example actually if you
+
+ align:start position:0%
+operations for example actually if you
+ 
+
+ align:start position:0%
+operations for example actually if you
+can ignore the slide for a second if you
+
+ align:start position:0%
+can ignore the slide for a second if you
+ 
+
+ align:start position:0%
+can ignore the slide for a second if you
+look at factory operations you expect
+
+ align:start position:0%
+look at factory operations you expect
+ 
+
+ align:start position:0%
+look at factory operations you expect
+performance to be tight you know when
+
+ align:start position:0%
+performance to be tight you know when
+ 
+
+ align:start position:0%
+performance to be tight you know when
+you say listen Father's Day is coming
+
+ align:start position:0%
+you say listen Father's Day is coming
+ 
+
+ align:start position:0%
+you say listen Father's Day is coming
+around I want to move inventory out to
+
+ align:start position:0%
+around I want to move inventory out to
+ 
+
+ align:start position:0%
+around I want to move inventory out to
+the store you know shaving blades for
+
+ align:start position:0%
+the store you know shaving blades for
+ 
+
+ align:start position:0%
+the store you know shaving blades for
+Father's Day because there's a big you
+
+ align:start position:0%
+Father's Day because there's a big you
+ 
+
+ align:start position:0%
+Father's Day because there's a big you
+know Gift buying event I want to move it
+
+ align:start position:0%
+know Gift buying event I want to move it
+ 
+
+ align:start position:0%
+know Gift buying event I want to move it
+out two weeks before Father's Day and
+
+ align:start position:0%
+out two weeks before Father's Day and
+ 
+
+ align:start position:0%
+out two weeks before Father's Day and
+then I'll start advertising on TV I'm
+
+ align:start position:0%
+then I'll start advertising on TV I'm
+ 
+
+ align:start position:0%
+then I'll start advertising on TV I'm
+going to spend millions of dollars you
+
+ align:start position:0%
+going to spend millions of dollars you
+ 
+
+ align:start position:0%
+going to spend millions of dollars you
+expect that things will work out quite
+
+ align:start position:0%
+expect that things will work out quite
+ 
+
+ align:start position:0%
+expect that things will work out quite
+well right people will move stuff out
+
+ align:start position:0%
+well right people will move stuff out
+ 
+
+ align:start position:0%
+well right people will move stuff out
+the retail supply chain going to kind of
+
+ align:start position:0%
+the retail supply chain going to kind of
+ 
+
+ align:start position:0%
+the retail supply chain going to kind of
+operate as you expected it and things
+
+ align:start position:0%
+operate as you expected it and things
+ 
+
+ align:start position:0%
+operate as you expected it and things
+will happen as you expect it you can run
+
+ align:start position:0%
+will happen as you expect it you can run
+ 
+
+ align:start position:0%
+will happen as you expect it you can run
+your ads and get a good good you're
+
+ align:start position:0%
+your ads and get a good good you're
+ 
+
+ align:start position:0%
+your ads and get a good good you're
+going to get good efficiency the fact of
+
+ align:start position:0%
+going to get good efficiency the fact of
+ 
+
+ align:start position:0%
+going to get good efficiency the fact of
+the matter is that in many systems where
+
+ align:start position:0%
+the matter is that in many systems where
+ 
+
+ align:start position:0%
+the matter is that in many systems where
+lots of human beings are involved and
+
+ align:start position:0%
+lots of human beings are involved and
+ 
+
+ align:start position:0%
+lots of human beings are involved and
+Retail is one one place and hospitals
+
+ align:start position:0%
+Retail is one one place and hospitals
+ 
+
+ align:start position:0%
+Retail is one one place and hospitals
+are another place if you thought that
+
+ align:start position:0%
+are another place if you thought that
+ 
+
+ align:start position:0%
+are another place if you thought that
+the performance you would get would be
+
+ align:start position:0%
+the performance you would get would be
+ 
+
+ align:start position:0%
+the performance you would get would be
+like that that is a bulk of the product
+
+ align:start position:0%
+like that that is a bulk of the product
+ 
+
+ align:start position:0%
+like that that is a bulk of the product
+would be moved out on the day that you
+
+ align:start position:0%
+would be moved out on the day that you
+ 
+
+ align:start position:0%
+would be moved out on the day that you
+expected it to be moved out you're in
+
+ align:start position:0%
+expected it to be moved out you're in
+ 
+
+ align:start position:0%
+expected it to be moved out you're in
+for a disappointment because really in
+
+ align:start position:0%
+for a disappointment because really in
+ 
+
+ align:start position:0%
+for a disappointment because really in
+most Supply chains performance is
+
+ align:start position:0%
+most Supply chains performance is
+ 
+
+ align:start position:0%
+most Supply chains performance is
+unfortunately despite the best effort
+
+ align:start position:0%
+unfortunately despite the best effort
+ 
+
+ align:start position:0%
+unfortunately despite the best effort
+and these we're talking about the top
+
+ align:start position:0%
+and these we're talking about the top
+ 
+
+ align:start position:0%
+and these we're talking about the top
+corporations on the planet very
+
+ align:start position:0%
+corporations on the planet very
+ 
+
+ align:start position:0%
+corporations on the planet very
+lose right it's if you're familiar with
+
+ align:start position:0%
+lose right it's if you're familiar with
+ 
+
+ align:start position:0%
+lose right it's if you're familiar with
+statistical process control the Six
+
+ align:start position:0%
+statistical process control the Six
+ 
+
+ align:start position:0%
+statistical process control the Six
+Sigma variation the coefficient of
+
+ align:start position:0%
+Sigma variation the coefficient of
+ 
+
+ align:start position:0%
+Sigma variation the coefficient of
+performance of execution in most Supply
+
+ align:start position:0%
+performance of execution in most Supply
+ 
+
+ align:start position:0%
+performance of execution in most Supply
+chains in many endeavors where RFID
+
+ align:start position:0%
+chains in many endeavors where RFID
+ 
+
+ align:start position:0%
+chains in many endeavors where RFID
+would be useful is rather poor in fact
+
+ align:start position:0%
+would be useful is rather poor in fact
+ 
+
+ align:start position:0%
+would be useful is rather poor in fact
+the coefficient of performance for a
+
+ align:start position:0%
+the coefficient of performance for a
+ 
+
+ align:start position:0%
+the coefficient of performance for a
+promotion that I looked at recently is
+
+ align:start position:0%
+promotion that I looked at recently is
+ 
+
+ align:start position:0%
+promotion that I looked at recently is
+something like 0.1 where it should
+
+ align:start position:0%
+something like 0.1 where it should
+ 
+
+ align:start position:0%
+something like 0.1 where it should
+really be
+
+ align:start position:0%
+really be
+ 
+
+ align:start position:0%
+really be
+1.3 okay so if you understand what
+
+ align:start position:0%
+1.3 okay so if you understand what
+ 
+
+ align:start position:0%
+1.3 okay so if you understand what
+statistical process control is just a
+
+ align:start position:0%
+statistical process control is just a
+ 
+
+ align:start position:0%
+statistical process control is just a
+metric I can tell you in a very succinct
+
+ align:start position:0%
+metric I can tell you in a very succinct
+ 
+
+ align:start position:0%
+metric I can tell you in a very succinct
+way there is a whole lot of room for
+
+ align:start position:0%
+way there is a whole lot of room for
+ 
+
+ align:start position:0%
+way there is a whole lot of room for
+improvement in the supply chain to make
+
+ align:start position:0%
+improvement in the supply chain to make
+ 
+
+ align:start position:0%
+improvement in the supply chain to make
+it tighter and that's why people are
+
+ align:start position:0%
+it tighter and that's why people are
+ 
+
+ align:start position:0%
+it tighter and that's why people are
+looking at the supply chain I'll end
+
+ align:start position:0%
+looking at the supply chain I'll end
+ 
+
+ align:start position:0%
+looking at the supply chain I'll end
+with uh this
+
+ align:start position:0%
+with uh this
+ 
+
+ align:start position:0%
+with uh this
+slide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again I just want to point to the bottom
+
+ align:start position:0%
+again I just want to point to the bottom
+ 
+
+ align:start position:0%
+again I just want to point to the bottom
+right there's also a lot of exciting
+
+ align:start position:0%
+right there's also a lot of exciting
+ 
+
+ align:start position:0%
+right there's also a lot of exciting
+stuff on how RFID might fundamentally
+
+ align:start position:0%
+stuff on how RFID might fundamentally
+ 
+
+ align:start position:0%
+stuff on how RFID might fundamentally
+change the supply chain and that's in
+
+ align:start position:0%
+change the supply chain and that's in
+ 
+
+ align:start position:0%
+change the supply chain and that's in
+some ways the most exciting part of all
+
+ align:start position:0%
+some ways the most exciting part of all
+ 
+
+ align:start position:0%
+some ways the most exciting part of all
+this right is it going to change is it
+
+ align:start position:0%
+this right is it going to change is it
+ 
+
+ align:start position:0%
+this right is it going to change is it
+going to make some macroeconomic changes
+
+ align:start position:0%
+going to make some macroeconomic changes
+ 
+
+ align:start position:0%
+going to make some macroeconomic changes
+to the way we operate as an economy
+
+ align:start position:0%
+to the way we operate as an economy
+ 
+
+ align:start position:0%
+to the way we operate as an economy
+right now that's getting a little high
+
+ align:start position:0%
+right now that's getting a little high
+ 
+
+ align:start position:0%
+right now that's getting a little high
+futing and maybe getting a little Beyond
+
+ align:start position:0%
+futing and maybe getting a little Beyond
+ 
+
+ align:start position:0%
+futing and maybe getting a little Beyond
+ourselves but this is academics you know
+
+ align:start position:0%
+ourselves but this is academics you know
+ 
+
+ align:start position:0%
+ourselves but this is academics you know
+this is what we should be doing so I
+
+ align:start position:0%
+this is what we should be doing so I
+ 
+
+ align:start position:0%
+this is what we should be doing so I
+just wanted to say let's fantasize a
+
+ align:start position:0%
+just wanted to say let's fantasize a
+ 
+
+ align:start position:0%
+just wanted to say let's fantasize a
+little bit the opportunities are vast
+
+ align:start position:0%
+little bit the opportunities are vast
+ 
+
+ align:start position:0%
+little bit the opportunities are vast
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+perhaps excuse me perhaps we need to
+
+ align:start position:0%
+perhaps excuse me perhaps we need to
+ 
+
+ align:start position:0%
+perhaps excuse me perhaps we need to
+start also thinking kind of at an
+
+ align:start position:0%
+start also thinking kind of at an
+ 
+
+ align:start position:0%
+start also thinking kind of at an
+aggregate level will retailers finally
+
+ align:start position:0%
+aggregate level will retailers finally
+ 
+
+ align:start position:0%
+aggregate level will retailers finally
+say that listen with RFID we own our own
+
+ align:start position:0%
+say that listen with RFID we own our own
+ 
+
+ align:start position:0%
+say that listen with RFID we own our own
+Supply chains we don't need them anymore
+
+ align:start position:0%
+Supply chains we don't need them anymore
+ 
+
+ align:start position:0%
+Supply chains we don't need them anymore
+because it's not comparative advantage
+
+ align:start position:0%
+because it's not comparative advantage
+ 
+
+ align:start position:0%
+because it's not comparative advantage
+anymore maybe Walmart essentially
+
+ align:start position:0%
+anymore maybe Walmart essentially
+ 
+
+ align:start position:0%
+anymore maybe Walmart essentially
+becomes as some many of you know this uh
+
+ align:start position:0%
+becomes as some many of you know this uh
+ 
+
+ align:start position:0%
+becomes as some many of you know this uh
+essentially just real estate with the
+
+ align:start position:0%
+essentially just real estate with the
+ 
+
+ align:start position:0%
+essentially just real estate with the
+Walmart names on it name on it or Target
+
+ align:start position:0%
+Walmart names on it name on it or Target
+ 
+
+ align:start position:0%
+Walmart names on it name on it or Target
+name on it and all they do is you they
+
+ align:start position:0%
+name on it and all they do is you they
+ 
+
+ align:start position:0%
+name on it and all they do is you they
+own the shells and the products there
+
+ align:start position:0%
+own the shells and the products there
+ 
+
+ align:start position:0%
+own the shells and the products there
+it's like Amazon and you go buy it but
+
+ align:start position:0%
+it's like Amazon and you go buy it but
+ 
+
+ align:start position:0%
+it's like Amazon and you go buy it but
+it's completely up to the supplier to
+
+ align:start position:0%
+it's completely up to the supplier to
+ 
+
+ align:start position:0%
+it's completely up to the supplier to
+stock these shelves that's called paper
+
+ align:start position:0%
+stock these shelves that's called paper
+ 
+
+ align:start position:0%
+stock these shelves that's called paper
+scan for those of you are familiar with
+
+ align:start position:0%
+scan for those of you are familiar with
+ 
+
+ align:start position:0%
+scan for those of you are familiar with
+this maybe that's what will happen right
+
+ align:start position:0%
+this maybe that's what will happen right
+ 
+
+ align:start position:0%
+this maybe that's what will happen right
+maybe what will happen is the supply
+
+ align:start position:0%
+maybe what will happen is the supply
+ 
+
+ align:start position:0%
+maybe what will happen is the supply
+chain goes away and UPS takes over the
+
+ align:start position:0%
+chain goes away and UPS takes over the
+ 
+
+ align:start position:0%
+chain goes away and UPS takes over the
+world or Federal Express and
+
+ align:start position:0%
+world or Federal Express and
+ 
+
+ align:start position:0%
+world or Federal Express and
+essentially uh manufacturers FedEx or
+
+ align:start position:0%
+essentially uh manufacturers FedEx or
+ 
+
+ align:start position:0%
+essentially uh manufacturers FedEx or
+UPS their stuff straight to the Shelf
+
+ align:start position:0%
+UPS their stuff straight to the Shelf
+ 
+
+ align:start position:0%
+UPS their stuff straight to the Shelf
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+it who knows right certainly worth kind
+
+ align:start position:0%
+it who knows right certainly worth kind
+ 
+
+ align:start position:0%
+it who knows right certainly worth kind
+of gaming this and if this community
+
+ align:start position:0%
+of gaming this and if this community
+ 
+
+ align:start position:0%
+of gaming this and if this community
+doesn't who's going to game it but in
+
+ align:start position:0%
+doesn't who's going to game it but in
+ 
+
+ align:start position:0%
+doesn't who's going to game it but in
+fact Brian and I were fantasizing about
+
+ align:start position:0%
+fact Brian and I were fantasizing about
+ 
+
+ align:start position:0%
+fact Brian and I were fantasizing about
+that and we call it the ultimately
+
+ align:start position:0%
+that and we call it the ultimately
+ 
+
+ align:start position:0%
+that and we call it the ultimately
+fragmented supply chain maybe that's
+
+ align:start position:0%
+fragmented supply chain maybe that's
+ 
+
+ align:start position:0%
+fragmented supply chain maybe that's
+where it'll go
+
+ align:start position:0%
+where it'll go
+ 
+
+ align:start position:0%
+where it'll go
+right maybe in the end this might change
+
+ align:start position:0%
+right maybe in the end this might change
+ 
+
+ align:start position:0%
+right maybe in the end this might change
+the way offshoring is working today you
+
+ align:start position:0%
+the way offshoring is working today you
+ 
+
+ align:start position:0%
+the way offshoring is working today you
+know if you're familiar with the Zara
+
+ align:start position:0%
+know if you're familiar with the Zara
+ 
+
+ align:start position:0%
+know if you're familiar with the Zara
+supply chain Zara is a Spanish retailer
+
+ align:start position:0%
+supply chain Zara is a Spanish retailer
+ 
+
+ align:start position:0%
+supply chain Zara is a Spanish retailer
+what they do is that they change they're
+
+ align:start position:0%
+what they do is that they change they're
+ 
+
+ align:start position:0%
+what they do is that they change they're
+very tight in terms of fashion Cycles so
+
+ align:start position:0%
+very tight in terms of fashion Cycles so
+ 
+
+ align:start position:0%
+very tight in terms of fashion Cycles so
+every time you know I suppose Britney
+
+ align:start position:0%
+every time you know I suppose Britney
+ 
+
+ align:start position:0%
+every time you know I suppose Britney
+Spears has a concert within a week they
+
+ align:start position:0%
+Spears has a concert within a week they
+ 
+
+ align:start position:0%
+Spears has a concert within a week they
+have those exact clothes on the market
+
+ align:start position:0%
+have those exact clothes on the market
+ 
+
+ align:start position:0%
+have those exact clothes on the market
+for two weeks and then they're gone so
+
+ align:start position:0%
+for two weeks and then they're gone so
+ 
+
+ align:start position:0%
+for two weeks and then they're gone so
+if you go to Zara right you get exactly
+
+ align:start position:0%
+if you go to Zara right you get exactly
+ 
+
+ align:start position:0%
+if you go to Zara right you get exactly
+what you want right there and because
+
+ align:start position:0%
+what you want right there and because
+ 
+
+ align:start position:0%
+what you want right there and because
+it's so fashionable they're so agile no
+
+ align:start position:0%
+it's so fashionable they're so agile no
+ 
+
+ align:start position:0%
+it's so fashionable they're so agile no
+very few other retailers are able to
+
+ align:start position:0%
+very few other retailers are able to
+ 
+
+ align:start position:0%
+very few other retailers are able to
+compete but the only way they can do
+
+ align:start position:0%
+compete but the only way they can do
+ 
+
+ align:start position:0%
+compete but the only way they can do
+that is not by Manufacturing in Asia
+
+ align:start position:0%
+that is not by Manufacturing in Asia
+ 
+
+ align:start position:0%
+that is not by Manufacturing in Asia
+because the lead times are too long but
+
+ align:start position:0%
+because the lead times are too long but
+ 
+
+ align:start position:0%
+because the lead times are too long but
+by manufacturing
+
+ align:start position:0%
+by manufacturing
+ 
+
+ align:start position:0%
+by manufacturing
+locally right maybe with the visibility
+
+ align:start position:0%
+locally right maybe with the visibility
+ 
+
+ align:start position:0%
+locally right maybe with the visibility
+RFID enables maybe a lot of retailers
+
+ align:start position:0%
+RFID enables maybe a lot of retailers
+ 
+
+ align:start position:0%
+RFID enables maybe a lot of retailers
+can do this sort of thing more
+
+ align:start position:0%
+can do this sort of thing more
+ 
+
+ align:start position:0%
+can do this sort of thing more
+efficiently and maybe it's going to
+
+ align:start position:0%
+efficiently and maybe it's going to
+ 
+
+ align:start position:0%
+efficiently and maybe it's going to
+affect impact the way we do offshoring
+
+ align:start position:0%
+affect impact the way we do offshoring
+ 
+
+ align:start position:0%
+affect impact the way we do offshoring
+you know we talk worried in this country
+
+ align:start position:0%
+you know we talk worried in this country
+ 
+
+ align:start position:0%
+you know we talk worried in this country
+about offshoring I'm sure in other
+
+ align:start position:0%
+about offshoring I'm sure in other
+ 
+
+ align:start position:0%
+about offshoring I'm sure in other
+countries as well maybe some tectonic
+
+ align:start position:0%
+countries as well maybe some tectonic
+ 
+
+ align:start position:0%
+countries as well maybe some tectonic
+changes are awaiting Us in the supply
+
+ align:start position:0%
+changes are awaiting Us in the supply
+ 
+
+ align:start position:0%
+changes are awaiting Us in the supply
+chain and how will our play into that I
+
+ align:start position:0%
+chain and how will our play into that I
+ 
+
+ align:start position:0%
+chain and how will our play into that I
+think it's
+
+ align:start position:0%
+think it's
+ 
+
+ align:start position:0%
+think it's
+worth uh discussing that so I conclude
+
+ align:start position:0%
+worth uh discussing that so I conclude
+ 
+
+ align:start position:0%
+worth uh discussing that so I conclude
+simply by saying that you know obviously
+
+ align:start position:0%
+simply by saying that you know obviously
+ 
+
+ align:start position:0%
+simply by saying that you know obviously
+the first place this technology is going
+
+ align:start position:0%
+the first place this technology is going
+ 
+
+ align:start position:0%
+the first place this technology is going
+to make an impact is by tweaking things
+
+ align:start position:0%
+to make an impact is by tweaking things
+ 
+
+ align:start position:0%
+to make an impact is by tweaking things
+the way they're done today eventually
+
+ align:start position:0%
+the way they're done today eventually
+ 
+
+ align:start position:0%
+the way they're done today eventually
+there might be some Evolution but
+
+ align:start position:0%
+there might be some Evolution but
+ 
+
+ align:start position:0%
+there might be some Evolution but
+fundamentally there's going to be
+
+ align:start position:0%
+fundamentally there's going to be
+ 
+
+ align:start position:0%
+fundamentally there's going to be
+transformation and it's the right end of
+
+ align:start position:0%
+transformation and it's the right end of
+ 
+
+ align:start position:0%
+transformation and it's the right end of
+the spectrum the stuff to the right that
+
+ align:start position:0%
+the spectrum the stuff to the right that
+ 
+
+ align:start position:0%
+the spectrum the stuff to the right that
+this community and no other community
+
+ align:start position:0%
+this community and no other community
+ 
+
+ align:start position:0%
+this community and no other community
+will be able to study and enable and
+
+ align:start position:0%
+will be able to study and enable and
+ 
+
+ align:start position:0%
+will be able to study and enable and
+it's a great pleasure to to address you
+
+ align:start position:0%
+it's a great pleasure to to address you
+ 
+
+ align:start position:0%
+it's a great pleasure to to address you
+uh uh and and fantasize um but um also
+
+ align:start position:0%
+uh uh and and fantasize um but um also
+ 
+
+ align:start position:0%
+uh uh and and fantasize um but um also
+uh look forward to talking to you about
+
+ align:start position:0%
+uh look forward to talking to you about
+ 
+
+ align:start position:0%
+uh look forward to talking to you about
+this and have a wonderful conference and
+
+ align:start position:0%
+this and have a wonderful conference and
+ 
+
+ align:start position:0%
+this and have a wonderful conference and
+thanks for letting me subject you to my
+
+ align:start position:0%
+thanks for letting me subject you to my
+ 
+
+ align:start position:0%
+thanks for letting me subject you to my
+crazy thoughts thank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you so maybe a couple questions for sanj
+
+ align:start position:0%
+you so maybe a couple questions for sanj
+ 
+
+ align:start position:0%
+you so maybe a couple questions for sanj
+while we set up the next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+panel any questions yes so there's a
+
+ align:start position:0%
+panel any questions yes so there's a
+ 
+
+ align:start position:0%
+panel any questions yes so there's a
+million papers to be written how many
+
+ align:start position:0%
+million papers to be written how many
+ 
+
+ align:start position:0%
+million papers to be written how many
+need to be before uh the diffusion curve
+
+ align:start position:0%
+need to be before uh the diffusion curve
+ 
+
+ align:start position:0%
+need to be before uh the diffusion curve
+starts to take off yeah that's a great
+
+ align:start position:0%
+starts to take off yeah that's a great
+ 
+
+ align:start position:0%
+starts to take off yeah that's a great
+question um I think that every uh I
+
+ align:start position:0%
+question um I think that every uh I
+ 
+
+ align:start position:0%
+question um I think that every uh I
+don't know I mean you know I think that
+
+ align:start position:0%
+don't know I mean you know I think that
+ 
+
+ align:start position:0%
+don't know I mean you know I think that
+in every topic there's a kind of every
+
+ align:start position:0%
+in every topic there's a kind of every
+ 
+
+ align:start position:0%
+in every topic there's a kind of every
+new area there's a area of there's a
+
+ align:start position:0%
+new area there's a area of there's a
+ 
+
+ align:start position:0%
+new area there's a area of there's a
+time of freshness where the papers are
+
+ align:start position:0%
+time of freshness where the papers are
+ 
+
+ align:start position:0%
+time of freshness where the papers are
+fresh and different and pretty soon they
+
+ align:start position:0%
+fresh and different and pretty soon they
+ 
+
+ align:start position:0%
+fresh and different and pretty soon they
+start kind of grinding and you know into
+
+ align:start position:0%
+start kind of grinding and you know into
+ 
+
+ align:start position:0%
+start kind of grinding and you know into
+each other it's kind of repetitive right
+
+ align:start position:0%
+each other it's kind of repetitive right
+ 
+
+ align:start position:0%
+each other it's kind of repetitive right
+I think we have ways to go you know if
+
+ align:start position:0%
+I think we have ways to go you know if
+ 
+
+ align:start position:0%
+I think we have ways to go you know if
+you take Wireless you take the internet
+
+ align:start position:0%
+you take Wireless you take the internet
+ 
+
+ align:start position:0%
+you take Wireless you take the internet
+uh you know take Google right Google is
+
+ align:start position:0%
+uh you know take Google right Google is
+ 
+
+ align:start position:0%
+uh you know take Google right Google is
+a research project out of Stanford right
+
+ align:start position:0%
+a research project out of Stanford right
+ 
+
+ align:start position:0%
+a research project out of Stanford right
+where 15 years into it take the internet
+
+ align:start position:0%
+where 15 years into it take the internet
+ 
+
+ align:start position:0%
+where 15 years into it take the internet
+we're 40 years into it right I think we
+
+ align:start position:0%
+we're 40 years into it right I think we
+ 
+
+ align:start position:0%
+we're 40 years into it right I think we
+have ways to go but there's no doubt
+
+ align:start position:0%
+have ways to go but there's no doubt
+ 
+
+ align:start position:0%
+have ways to go but there's no doubt
+that's going to set in I think we need
+
+ align:start position:0%
+that's going to set in I think we need
+ 
+
+ align:start position:0%
+that's going to set in I think we need
+to Be watchful for of that as well right
+
+ align:start position:0%
+to Be watchful for of that as well right
+ 
+
+ align:start position:0%
+to Be watchful for of that as well right
+so I agree so we'll balloon but then
+
+ align:start position:0%
+so I agree so we'll balloon but then
+ 
+
+ align:start position:0%
+so I agree so we'll balloon but then
+eventually we'll kind of kill ourselves
+
+ align:start position:0%
+eventually we'll kind of kill ourselves
+ 
+
+ align:start position:0%
+eventually we'll kind of kill ourselves
+and blur an arrow so that's a great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question how do we facilitate that
+
+ align:start position:0%
+question how do we facilitate that
+ 
+
+ align:start position:0%
+question how do we facilitate that
+commun that the research is being driven
+
+ align:start position:0%
+commun that the research is being driven
+ 
+
+ align:start position:0%
+commun that the research is being driven
+in the direction the business is going I
+
+ align:start position:0%
+in the direction the business is going I
+ 
+
+ align:start position:0%
+in the direction the business is going I
+think it's a great question uh when we
+
+ align:start position:0%
+think it's a great question uh when we
+ 
+
+ align:start position:0%
+think it's a great question uh when we
+started the Auto ID center we basically
+
+ align:start position:0%
+started the Auto ID center we basically
+ 
+
+ align:start position:0%
+started the Auto ID center we basically
+made some stuff up right uh and we went
+
+ align:start position:0%
+made some stuff up right uh and we went
+ 
+
+ align:start position:0%
+made some stuff up right uh and we went
+and just evangelized it and um we were
+
+ align:start position:0%
+and just evangelized it and um we were
+ 
+
+ align:start position:0%
+and just evangelized it and um we were
+we were lucky we had some key end users
+
+ align:start position:0%
+we were lucky we had some key end users
+ 
+
+ align:start position:0%
+we were lucky we had some key end users
+involved very in the very beginning so
+
+ align:start position:0%
+involved very in the very beginning so
+ 
+
+ align:start position:0%
+involved very in the very beginning so
+we weren't completely you know making
+
+ align:start position:0%
+we weren't completely you know making
+ 
+
+ align:start position:0%
+we weren't completely you know making
+stuff up we had some directed things we
+
+ align:start position:0%
+stuff up we had some directed things we
+ 
+
+ align:start position:0%
+stuff up we had some directed things we
+were you know going after and we were
+
+ align:start position:0%
+were you know going after and we were
+ 
+
+ align:start position:0%
+were you know going after and we were
+kind of right it's lucky right but we
+
+ align:start position:0%
+kind of right it's lucky right but we
+ 
+
+ align:start position:0%
+kind of right it's lucky right but we
+can't afford to wait on luck in the
+
+ align:start position:0%
+can't afford to wait on luck in the
+ 
+
+ align:start position:0%
+can't afford to wait on luck in the
+future the good news now is the end
+
+ align:start position:0%
+future the good news now is the end
+ 
+
+ align:start position:0%
+future the good news now is the end
+users really get this in fact in many
+
+ align:start position:0%
+users really get this in fact in many
+ 
+
+ align:start position:0%
+users really get this in fact in many
+ways they get it more than the larger
+
+ align:start position:0%
+ways they get it more than the larger
+ 
+
+ align:start position:0%
+ways they get it more than the larger
+academic Community right uh and we have
+
+ align:start position:0%
+academic Community right uh and we have
+ 
+
+ align:start position:0%
+academic Community right uh and we have
+a lot of end users here so I think that
+
+ align:start position:0%
+a lot of end users here so I think that
+ 
+
+ align:start position:0%
+a lot of end users here so I think that
+it's right the time is now right for
+
+ align:start position:0%
+it's right the time is now right for
+ 
+
+ align:start position:0%
+it's right the time is now right for
+researchers to pick up esoteric topics
+
+ align:start position:0%
+researchers to pick up esoteric topics
+ 
+
+ align:start position:0%
+researchers to pick up esoteric topics
+which also happen to be practical how
+
+ align:start position:0%
+which also happen to be practical how
+ 
+
+ align:start position:0%
+which also happen to be practical how
+rarely does that happen right that
+
+ align:start position:0%
+rarely does that happen right that
+ 
+
+ align:start position:0%
+rarely does that happen right that
+establishing that channel the two needs
+
+ align:start position:0%
+establishing that channel the two needs
+ 
+
+ align:start position:0%
+establishing that channel the two needs
+there two things that happen one the
+
+ align:start position:0%
+there two things that happen one the
+ 
+
+ align:start position:0%
+there two things that happen one the
+people need to be there the good news is
+
+ align:start position:0%
+people need to be there the good news is
+ 
+
+ align:start position:0%
+people need to be there the good news is
+they're there now you know you have Mike
+
+ align:start position:0%
+they're there now you know you have Mike
+ 
+
+ align:start position:0%
+they're there now you know you have Mike
+Rose sitting here you'll have dick cell
+
+ align:start position:0%
+Rose sitting here you'll have dick cell
+ 
+
+ align:start position:0%
+Rose sitting here you'll have dick cell
+you have you know Tim Mill right you
+
+ align:start position:0%
+you have you know Tim Mill right you
+ 
+
+ align:start position:0%
+you have you know Tim Mill right you
+have Richard as why I'm back there right
+
+ align:start position:0%
+have Richard as why I'm back there right
+ 
+
+ align:start position:0%
+have Richard as why I'm back there right
+Le Gillette right so you have people now
+
+ align:start position:0%
+Le Gillette right so you have people now
+ 
+
+ align:start position:0%
+Le Gillette right so you have people now
+willing to have these deep conversations
+
+ align:start position:0%
+willing to have these deep conversations
+ 
+
+ align:start position:0%
+willing to have these deep conversations
+and the very well equipped what's
+
+ align:start position:0%
+and the very well equipped what's
+ 
+
+ align:start position:0%
+and the very well equipped what's
+missing is the medium right I think this
+
+ align:start position:0%
+missing is the medium right I think this
+ 
+
+ align:start position:0%
+missing is the medium right I think this
+is a great medium yeah I mean I think we
+
+ align:start position:0%
+is a great medium yeah I mean I think we
+ 
+
+ align:start position:0%
+is a great medium yeah I mean I think we
+need to have we need to present research
+
+ align:start position:0%
+need to have we need to present research
+ 
+
+ align:start position:0%
+need to have we need to present research
+papers and have AC uh business guys go
+
+ align:start position:0%
+papers and have AC uh business guys go
+ 
+
+ align:start position:0%
+papers and have AC uh business guys go
+that's pointless but this I wish you
+
+ align:start position:0%
+that's pointless but this I wish you
+ 
+
+ align:start position:0%
+that's pointless but this I wish you
+would do you know we're not doing that
+
+ align:start position:0%
+would do you know we're not doing that
+ 
+
+ align:start position:0%
+would do you know we're not doing that
+and as actually I think that applies to
+
+ align:start position:0%
+and as actually I think that applies to
+ 
+
+ align:start position:0%
+and as actually I think that applies to
+all of
+
+ align:start position:0%
+all of
+ 
+
+ align:start position:0%
+all of
+Academia yeah
+
+ align:start position:0%
+Academia yeah
+ 
+
+ align:start position:0%
+Academia yeah
+Chris question research perspective one
+
+ align:start position:0%
+Chris question research perspective one
+ 
+
+ align:start position:0%
+Chris question research perspective one
+channels is that um we all present in
+
+ align:start position:0%
+channels is that um we all present in
+ 
+
+ align:start position:0%
+channels is that um we all present in
+different research communities you know
+
+ align:start position:0%
+different research communities you know
+ 
+
+ align:start position:0%
+different research communities you know
+some Human Action folks you know go to
+
+ align:start position:0%
+some Human Action folks you know go to
+ 
+
+ align:start position:0%
+some Human Action folks you know go to
+the HCI conferences why does
+
+ align:start position:0%
+the HCI conferences why does
+ 
+
+ align:start position:0%
+the HCI conferences why does
+communication guys in rid go somewhere
+
+ align:start position:0%
+communication guys in rid go somewhere
+ 
+
+ align:start position:0%
+communication guys in rid go somewhere
+every single time at least at this stage
+
+ align:start position:0%
+every single time at least at this stage
+ 
+
+ align:start position:0%
+every single time at least at this stage
+we've got the problem that we get to
+
+ align:start position:0%
+we've got the problem that we get to
+ 
+
+ align:start position:0%
+we've got the problem that we get to
+motivate many of the problems that you
+
+ align:start position:0%
+motivate many of the problems that you
+ 
+
+ align:start position:0%
+motivate many of the problems that you
+mention and very practical point you
+
+ align:start position:0%
+mention and very practical point you
+ 
+
+ align:start position:0%
+mention and very practical point you
+know sometimes people in in those
+
+ align:start position:0%
+know sometimes people in in those
+ 
+
+ align:start position:0%
+know sometimes people in in those
+communities not very familiar with those
+
+ align:start position:0%
+communities not very familiar with those
+ 
+
+ align:start position:0%
+communities not very familiar with those
+special challenges of R8 so do you think
+
+ align:start position:0%
+special challenges of R8 so do you think
+ 
+
+ align:start position:0%
+special challenges of R8 so do you think
+that in a couple years time we'll see
+
+ align:start position:0%
+that in a couple years time we'll see
+ 
+
+ align:start position:0%
+that in a couple years time we'll see
+you know a dedicated rid conference that
+
+ align:start position:0%
+you know a dedicated rid conference that
+ 
+
+ align:start position:0%
+you know a dedicated rid conference that
+of covers a range maybe not all but a
+
+ align:start position:0%
+of covers a range maybe not all but a
+ 
+
+ align:start position:0%
+of covers a range maybe not all but a
+range of the issues you mention I think
+
+ align:start position:0%
+range of the issues you mention I think
+ 
+
+ align:start position:0%
+range of the issues you mention I think
+that might happen so I mean I think
+
+ align:start position:0%
+that might happen so I mean I think
+ 
+
+ align:start position:0%
+that might happen so I mean I think
+you're pointing at the deeper problem of
+
+ align:start position:0%
+you're pointing at the deeper problem of
+ 
+
+ align:start position:0%
+you're pointing at the deeper problem of
+systems design right and I first of all
+
+ align:start position:0%
+systems design right and I first of all
+ 
+
+ align:start position:0%
+systems design right and I first of all
+I think we have too many conferen was an
+
+ align:start position:0%
+I think we have too many conferen was an
+ 
+
+ align:start position:0%
+I think we have too many conferen was an
+academic field with they're too sub you
+
+ align:start position:0%
+academic field with they're too sub you
+ 
+
+ align:start position:0%
+academic field with they're too sub you
+know selective and you know only those
+
+ align:start position:0%
+know selective and you know only those
+ 
+
+ align:start position:0%
+know selective and you know only those
+people go to those conferences it's a
+
+ align:start position:0%
+people go to those conferences it's a
+ 
+
+ align:start position:0%
+people go to those conferences it's a
+very nice cozy shelter where you don't
+
+ align:start position:0%
+very nice cozy shelter where you don't
+ 
+
+ align:start position:0%
+very nice cozy shelter where you don't
+really able to talk to the other guys
+
+ align:start position:0%
+really able to talk to the other guys
+ 
+
+ align:start position:0%
+really able to talk to the other guys
+right so I do think that an RFID
+
+ align:start position:0%
+right so I do think that an RFID
+ 
+
+ align:start position:0%
+right so I do think that an RFID
+conference an RFID systems Community
+
+ align:start position:0%
+conference an RFID systems Community
+ 
+
+ align:start position:0%
+conference an RFID systems Community
+will evolve and maybe this is the start
+
+ align:start position:0%
+will evolve and maybe this is the start
+ 
+
+ align:start position:0%
+will evolve and maybe this is the start
+of it which is why I congratulate
+
+ align:start position:0%
+of it which is why I congratulate
+ 
+
+ align:start position:0%
+of it which is why I congratulate
+everyone but I think we also need to
+
+ align:start position:0%
+everyone but I think we also need to
+ 
+
+ align:start position:0%
+everyone but I think we also need to
+watch out that that doesn't become an
+
+ align:start position:0%
+watch out that that doesn't become an
+ 
+
+ align:start position:0%
+watch out that that doesn't become an
+ultra academic conference not connected
+
+ align:start position:0%
+ultra academic conference not connected
+ 
+
+ align:start position:0%
+ultra academic conference not connected
+to reality uh which in itself becomes a
+
+ align:start position:0%
+to reality uh which in itself becomes a
+ 
+
+ align:start position:0%
+to reality uh which in itself becomes a
+kind of this you know mutant animal that
+
+ align:start position:0%
+kind of this you know mutant animal that
+ 
+
+ align:start position:0%
+kind of this you know mutant animal that
+no one's interested in so we need to
+
+ align:start position:0%
+no one's interested in so we need to
+ 
+
+ align:start position:0%
+no one's interested in so we need to
+keep the act the end user Community
+
+ align:start position:0%
+keep the act the end user Community
+ 
+
+ align:start position:0%
+keep the act the end user Community
+involved that's my view anyway and that
+
+ align:start position:0%
+involved that's my view anyway and that
+ 
+
+ align:start position:0%
+involved that's my view anyway and that
+was kind of the ESS as you remember from
+
+ align:start position:0%
+was kind of the ESS as you remember from
+ 
+
+ align:start position:0%
+was kind of the ESS as you remember from
+the Auto ID center so but I hope we can
+
+ align:start position:0%
+the Auto ID center so but I hope we can
+ 
+
+ align:start position:0%
+the Auto ID center so but I hope we can
+do that thank you very much thanks thank
+
+ align:start position:0%
+do that thank you very much thanks thank
+ 
+
+ align:start position:0%
+do that thank you very much thanks thank
+you
\ No newline at end of file
diff --git a/dt4sSAb-7cE.txt b/dt4sSAb-7cE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f7f9d0c9a5385a18f376de020d2bd3b3f73d5af6
--- /dev/null
+++ b/dt4sSAb-7cE.txt
@@ -0,0 +1,1231 @@
+PROFESSOR: OK, well let's move
+on then, and just talk about
+
+the amino acids.
+
+Amino acids side chains.
+
+And you won't have to memorize
+these structures.
+
+We will give you a chart
+if you have a problem.
+
+On the other hand, you need to
+get very familiar with them,
+
+so they're old friends even if
+you can't quite remember how
+
+many methylene are in a chain,
+or something like that.
+
+And you will find that they fall
+into certain categories.
+
+And I'm just going to try and
+give you examples of the major
+
+categories.
+
+There are negatively charged
+side chains.
+
+An example would be amino acids
+known as aspartate, or
+
+Asp, in which the side chain
+which corresponds to the R1 or
+
+to the R2 over there, has a
+methylene group, and then a
+
+carboxyl group.
+
+But at pH sevenish, which is the
+pH that you find inside a
+
+cell, that carboxyl group would
+be deprotonated so it
+
+would have a negative charge.
+
+The other negatively charged
+amino acid is glutamate, which
+
+also, as you'll see has
+a carboxyl group.
+
+There are positively charged
+amino acids.
+
+A good one to illustrate this
+is Lysine, in which there's
+
+four methylene groups,
+and then an amino
+
+group at the end.
+
+However, again, at pH 7, the
+kind of pH that you find
+
+inside the cell, that amino
+group is going to get
+
+protonated.
+
+And so it will have a
+positive charge on.
+
+If you have a Lysine side chain,
+and Arginine, and in
+
+most cases, Histidine, are
+examples of other amino acids
+
+that can have a positively
+charged group.
+
+And why I'm going through all
+of this, I hope, will become
+
+apparent in a few minutes.
+
+Some of the side chains are
+not positive or negative
+
+charged, but rather,
+they're polar.
+
+And we just talked about polar
+bonds the last time, where you
+
+have, the more electronegative
+an atom is, the more greedy it
+
+is for electrons.
+
+And if you recall, if you have
+a carbon carbon bond or a
+
+hydrogen hydrogen bond that's
+nonpolar, and the electrons
+
+were distributed equally, the
+oxygen is greedier for
+
+electrons and so there is a
+little bit of a negative
+
+charge there and a little
+bit of positive
+
+charge on the hydrogen.
+
+Well, that same principle
+applies to
+
+amino acid side chains.
+
+Take, for example, the amino
+acid Serine, which has a
+
+methylene group and then
+a hydroxyl group.
+
+Well, here we are.
+
+There's an OH bond, so there
+will be a little bit of a
+
+negative charge on oxygen with
+a positive charge on there.
+
+There's another alcohol called
+threonine, which also has
+
+hydroxyl groups.
+
+And you can make amides of both
+Aspartate and Glutamate,
+
+to give Asparagine and
+Glutamine, and both of these
+
+are also polar too.
+
+So what I'm hoping you're
+beginning to get a sense of,
+
+you can do an awful lot with
+the properties of a peptide
+
+chain, depending on which
+amino acids you
+
+dangle off the side.
+
+And ultimately, that order of
+amino acids is what's going to
+
+be determined by what's in the
+gene encoding that protein.
+
+Then there are quite a number
+of amino acids side chains
+
+which are hydrophobic.
+
+They're sort of fearing
+water, if you will.
+
+The simplest is Alanine, or Ala,
+which is just a methyl
+
+group, or Leucine, is perhaps,
+a little more obvious because
+
+that's got this.
+
+And you can see that
+that's a kind of--
+
+draw it like that.
+
+This is, very much, a kind of
+structure that's not going to
+
+want to interact with water.
+
+And then, another example would
+be Phenylalanine, or
+
+Phe, and that one is a methylene
+group and, then, a
+
+benzene ring.
+
+So most of you know, have some
+sense of the properties of
+
+benzene, a very, very
+organic solvent.
+
+So here you put a side chain
+like this, it's very much a
+
+residue that doesn't want to
+interact with water anymore
+
+than Benzene wants to
+interact with water.
+
+And then there are three
+special cases.
+
+One of these is Glycine.
+
+In this case, it's
+just a hydrogen.
+
+One of the consequences of that
+is that since it's just a
+
+hydrogen, that's going to be a
+very, very flexible place, if
+
+we have a chain of amino acids
+and there's a Glycine there,
+
+it's going to be very little
+of way of constraints
+
+introduced, either by steric
+constraints or by
+
+interactions.
+
+Another very special one is
+one called Cystine, Cys.
+
+And it's the same idea as
+Cyrine, there's an ethylene.
+
+But instead of having an
+OH, it has an SH group.
+
+And that may not seem to be a
+great consequence, the sulfur
+
+is a little bit larger.
+
+But sulfurs have--
+
+a sulfide group here has a
+sulfhydryl group here has a
+
+very special property, and that
+is, it can oxidatively
+
+dimerize with another
+sulfhydryl.
+
+So if you have a side chain, and
+there's a cystine that has
+
+an SH group, and another, either
+part of the same chain,
+
+or part of the different
+polypeptide chain that also
+
+has a cystine, and they're in an
+oxidizing environment, and
+
+they're also close enough
+together to interact, they can
+
+form a bond like this, which is
+known as a disulfide bond,
+
+and it's the only one of the
+amino acids that's capable of
+
+reaching outside the chain in
+either hooking to a different
+
+part of the chain or to a
+completely different protein.
+
+And in fact, proteins that tend
+to get excreted out into
+
+the media, either by bacteria or
+other things, often have a
+
+lot of disulfide bonds.
+
+Because when you link the
+peptide chains together like
+
+that, it tends to make a very
+tough protein that's hard to
+
+break down and can be
+very, very robust.
+
+And there is one other special
+category of, one other special
+
+amino acid that's known
+as Proline.
+
+You have the alpha carbon atom,
+the carboxyl group, and
+
+then there's the amino
+group here.
+
+But this carbon is linked by
+a little ring with three
+
+methylenes to that amino acid.
+
+Again, this may seem sort of
+an unnecessary detail or
+
+something, but this is the way
+life evolved on earth.
+
+This is an amino acid, but
+because of this ring
+
+structure, this bond is
+not able to rotate.
+
+So wherever a Proline shows up
+in the sequence, it puts some
+
+structural constraints on the
+conformational space that that
+
+chain is capable of getting
+itself into.
+
+So when we study protein
+structure, this is at the
+
+heart of how proteins work,
+we'll spend quite a bit of
+
+time in the ensuing lectures
+talking about the central
+
+dogma and the idea that the
+linear order of the amino
+
+acids, in a protein, is
+determined by the sequence of
+
+the DNA and how that's
+encoded.
+
+But at the end, what you end up
+with is a linear sequence
+
+of amino acids, all joined
+together by peptide bonds.
+
+And there's an incredible
+number of
+
+conformations possible.
+
+These things could go all over
+the place in all kinds of
+
+different ways.
+
+Yet, only one form, in general,
+is the biologically
+
+active conformation or maybe
+there's a couple of them and
+
+it switches back and forth as
+part of a machine action, or
+
+are part of what it does.
+
+But by and large, for every
+protein there'll be one, or
+
+just a couple of
+conformations.
+
+And so understanding proteins,
+what many, many people are
+
+interested in is trying to
+understand how you can get
+
+from that linear sequence
+and determine the three
+
+dimensional structure.
+
+There are techniques, X-ray
+crystallography and NMR
+
+techniques now, which enable
+us to get the structures,
+
+solve the structures
+of proteins.
+
+In fact, there's the structures
+of tens of
+
+thousands of them are
+in a database
+
+called the Protein Database.
+
+And we're going to be talking
+about a little protein viewer
+
+that you'll be using that, in
+fact, once you've used it in
+
+your problem set, you could go
+open the structure of any
+
+protein whose structure has ever
+has been solved, if you
+
+want to do it.
+
+But what we haven't yet figured
+out is a reliable way
+
+of saying, here is a protein
+that consists of a particular
+
+chain of amino acids.
+
+I'm going to predict its three
+dimensional shape.
+
+So we understand parts
+of it, but there's
+
+parts we don't know.
+
+And I'm going to take you
+through the first part of
+
+understanding protein
+structure.
+
+And before we do that, I want to
+just talk about the levels
+
+of protein structure and the
+terms that are used to
+
+describe these.
+
+When people talk about the
+primary structure of a
+
+protein, what they're talking
+about is the sequence of amino
+
+acids, and it's possible I'll
+abbreviate those as AA, at
+
+some point without thinking
+about it.
+
+So just in case I do, that's
+a fairly commonly used
+
+abbreviation for amino acids.
+
+So that simply, Phenylalanine
+joined to a Proline joined to
+
+a Glycine joined to two Cystines
+joined to something
+
+else, but that's not terribly
+useful in terms of telling
+
+what the protein does.
+
+Then there's secondary
+structure.
+
+These are regions of local
+folding and they're driven by,
+
+guess what?
+
+Hydrogen bonds.
+
+And we'll talk about how that
+goes in just a moment.
+
+Then the term, tertiary
+structure, is the term used to
+
+describe the entirety of
+the folded protein.
+
+If I went in and determined
+the structure of a protein
+
+using x-ray crystallography,
+this is what I would see.
+
+It would be the tertiary
+structure.
+
+And there are other forces that
+we haven't discussed yet
+
+that contribute to that
+tertiary structure.
+
+And then, a quaternary structure
+means that there's
+
+more than one polypeptide
+chain.
+
+And it could be as simple as
+an enzyme that's got two
+
+subunits and you've got to have
+them both there in order
+
+for it to work, or as I think
+you're beginning to probably
+
+get the sense from my use of
+the term protein machines,
+
+there are structures that have
+multiple interacting proteins
+
+and have complexities that rival
+some of the mechanical
+
+things that we build
+ourselves.
+
+So the interesting story, a
+little, bit how the insights
+
+into secondary structure
+were first arrived.
+
+Some of you may have heard
+the term Linus Pauling.
+
+He was at Cal Tech, a Nobel
+Prize winner, very, very
+
+influential scientist,
+in a variety of ways.
+
+The key insight that
+Linus Pauling had
+
+came in the late 1940s.
+
+People had been doing X-ray
+crystallography on minerals
+
+and things like that, and the
+basic idea was you had a
+
+crystal of some type, you
+bounced electrons off, you got
+
+a diffraction pattern.
+
+Then you could work backwards
+and figure out the structure
+
+that was generating the
+diffraction pattern.
+
+And that had, then, been
+extended to proteins.
+
+And it was discovered there
+were certain proteins that
+
+would crystallize and you could
+bounce electrons off and
+
+get a diffraction pattern.
+
+And at least a category of these
+proteins, and analysis
+
+of the diffraction pattern
+suggested it was some kind of
+
+helix, and there was a repeating
+element of about 5.4
+
+angstroms, roughly.
+
+And so, Linus Pauling was very
+
+interested in protein structure.
+
+And I think it was in late 1948,
+he was visiting England
+
+and he caught the flu,
+just like some of
+
+you have been catching.
+
+And he spent a few days reading
+detective stories and
+
+then he got bored.
+
+And so he tried to
+take on this--
+
+think about this problem.
+
+While he was lying in bed.
+
+And he made a simplifying
+assumption.
+
+He said let's just forget about
+all the side chains.
+
+Maybe they don't really
+matter in terms
+
+of this basic property.
+
+Maybe it's determined by the
+backbone of the peptide chain.
+
+So he took a strip of paper,
+started pleating it.
+
+And he was a very good chemist,
+so he knew about this
+
+partial double [? blind ?]
+
+character of the peptide bond
+and the constraints that it
+
+put on the structures that
+the protein could take.
+
+And in doing this, he realized
+that if he folded the thing
+
+into a helix, kind of like
+this, into a right handed
+
+helix, that things worked out
+such that the carboxyl group
+
+in the backbone was just
+beautifully positioned to form
+
+hydrogen bond that was on
+one of the nitrogens.
+
+He called this an alpha helix.
+
+There were 3.7 amino
+acids per turn.
+
+And the distance from here to
+here was 5.4 angstroms.
+
+And if we just--
+
+sorry, I meant to put that up
+
+earlier, or did I go backwards?
+
+Anyway, there are all
+the amino acids and
+
+they're in your book.
+
+Here is just the backbone
+of an alpha helix.
+
+And the orangey yellow colored
+bonds are the hydrogen bonds.
+
+And I hope you can see
+how the spiral goes.
+
+And you can also see, as it goes
+by, you can look right
+
+down the hole down the
+middle of the helix.
+
+So let's put on some
+amino acids now.
+
+And again, you'll see, as it
+goes by, you can look right
+
+down the helix.
+
+But you see how the amino acids
+stick out onto the side.
+
+And if you look, for example,
+there is a Phenylalanine and a
+
+Tyrosine, they're aromatic
+groups that are very
+
+hydrophobic.
+
+And up here there's a Lysine,
+so that's this side of the
+
+helix is charged.
+
+That's a glutamate.
+
+So there's a couple of charged
+amino acids on
+
+this side of the helix.
+
+Up here we've got a water hating
+part and somehow this
+
+is, I think, reminding me that
+I left something out.
+
+Let me just fix that
+up while I'm at it.
+
+The other hydrophobic amino
+acids, I forgot to say those
+
+are Isoleucine, Valine,
+Methionine, Tyrosine, and
+
+Tryptophan.
+
+Those are in your book.
+
+Those are other examples of
+hydrophobic amino acids.
+
+But I think, even in this little
+example of an alpha
+
+helix, you can see, depending on
+which amino acid was where,
+
+along that little region of
+alpha helix, it would very
+
+much influence what that
+part of the protein
+
+was capable of doing.
+
+There's a second region of
+secondary structure that's
+
+very important.
+
+It's called a beta sheet.
+
+The one I'm showing you is an
+example of an anti-parallel
+
+beta sheet, although you
+can have parallel
+
+beta sheets as well.
+
+But what I've done here is
+to take one strand of a
+
+polypeptide chain and I've
+written it out this way.
+
+And then I've taken a second--
+
+what has happened?
+
+Oops.
+
+That's interesting.
+
+The stool just broke.
+
+OK.
+
+Fortunately, I noticed.
+
+So what we have here is that the
+possibility for hydrogen
+
+bonding between this hydrogen
+of amino group and this
+
+oxygen, again, so we
+can get hydrogen
+
+bonds formed like this.
+
+And this makes what are called
+a beta sheet structure.
+
+And they can build up as well.
+
+This next one gives-- you can
+see how you can put one beta
+
+sheet on top of another.
+
+And both of these are two
+major types of secondary
+
+structure and the way an alpha
+helix is represented is
+
+something like this.
+
+This would be an alpha helix.
+
+And a beta sheet is written
+as an arrow like that.
+
+And so most proteins tend to
+have structures that consist
+
+of, for example, an alpha helix,
+some kind of turn,
+
+maybe a beta sheet, another
+turn, another beta sheet.
+
+Now maybe a turn, maybe an alpha
+helix going this way,
+
+some combination of regions
+of secondary structure.
+
+And I've got just a couple
+of examples of that.
+
+Here you can see a domain of a
+protein with some beta sheets
+
+in purple, alpha
+helix in green.
+
+Where that's a piece of a
+protein coming from what's
+
+known as the bracket one gene.
+
+Some of you may be aware
+there's a familial
+
+susceptibility to breast cancer
+that was discovered.
+
+It's a complex protein.
+
+Part of it, and a very, very
+important part of it, is this
+
+piece known as the
+BRCT domain.
+
+It's the bracket one c terminal
+domain, consists of
+
+beta sheets alpha helix.
+
+Here's a protein I've already
+shown you the structure of,
+
+but maybe you recognize now,
+that green fluorescent protein
+
+is mostly beta sheets.
+
+It's the only beta sheets
+is going down here.
+
+There's a little bit of an
+alpha helix up there.
+
+And there's a bit of
+one over here?
+
+Here's an example of a protein
+that's mostly alpha helix.
+
+What's this one do?
+
+This is a protein we'll talk
+about when we talk about DNA
+
+replication.
+
+It's involved in recognizing
+mismatches in DNA, for
+
+example, the G improperly got
+paired with the T during DNA
+
+replication.
+
+There's a system comes along and
+repairs those mismatches
+
+gives you another several
+thousandfold increase in
+
+fidelity, and if you mutate it
+in that kind of protein in a
+
+human, you have a familial
+
+susceptibility to colon cancer.
+
+So it doesn't matter what their
+function is, when you
+
+get down to regions of secondary
+structure, you'll
+
+see these recurring things --
+alpha helices, beta sheets.
+
+And if you understand their
+properties, you begin to
+
+understand some of the basic
+structure of forces that are
+
+giving the proteins
+their properties.
+
+That's an enzyme called
+chymotrypsin.
+
+What it does, it's an enzyme
+that catalyzes the cleavage of
+
+peptide bonds in
+other proteins.
+
+But there it is.
+
+Got a lot of alpha helices,
+beta sheets, turns.
+
+You can go on and on.
+
+I just said, one
+more up there.
+
+That's the Ras protein.
+
+That's an oncogene.
+
+Mutate that in a particular
+way, you have a
+
+susceptibility to cancer.
+
+But it doesn't matter, when you
+get down to the protein
+
+structure, most proteins have
+beta sheets, alpha helices.
+
+OK.
+
+Go back to that one
+in a second.
+
+So we have to understand
+the rest of the
+
+structure of proteins.
+
+We have to be able to talk about
+the other forces that
+
+are important for making
+a protein.
+
+And the third force
+is pretty simple.
+
+That's an ionic bond, and it's
+just this simple, that if you
+
+had a peptide chain that had,
+for example, an Aspartate with
+
+a negatively charged amino acid
+on it, and we had, say, a
+
+Lysine, four Methylenes, and the
+NH3 plus that was attached
+
+somewhere else on that
+polypeptide chain, then we can
+
+get an ionic bond, because of
+the attraction between the
+
+negative charge on here and
+a positive charge on that.
+
+So that is one of the things
+that then a force that can
+
+influence the structure
+of proteins.
+
+The next one is a harder
+one to understand.
+
+It's known as the van der
+Waals interaction.
+
+And here's basically what's
+going on is that a non-polar
+
+bond can have a transient
+polarity.
+
+Sorry about this.
+
+And it can induce polarity in
+a nearby non-polar bond, and
+
+that can then give
+an attraction.
+
+These things need to be very
+close together, about 0.2 to
+
+0.4 nanometers apart, the two
+non-polar bonds, in order for
+
+this to happen.
+
+Does anybody remember the length
+of the covalent bond,
+
+the 0.15 to 0.2 nanometers,
+so within one or
+
+two covalent bonds.
+
+They have to be that close.
+
+Their strength is about one
+third, one quarter to one
+
+third, to that of the
+hydrogen bond.
+
+And if you remember, the
+hydrogen bond was about one
+
+twentieth of the force of the
+strength of the hydrogen bond.
+
+But nevertheless, you can have
+a lot of them because, if you
+
+have an extended surface of a
+protein that's very close
+
+together, you can get a lot
+of these van der Waal
+
+interactions.
+
+And I'd always found
+this a somewhat
+
+esoteric kind of force.
+
+But in fact, we're familiar with
+these because that's how
+
+a lizard manages to
+go up a surface.
+
+It uses van der Waals
+interactions.
+
+And as I'll show you in a
+minute, the trick is it's got
+
+little hairs on the bottom of
+its feet that have about a
+
+billion split ends and they're
+so tiny they're able to make
+
+van der Waals interactions
+with the surface.
+
+In a minute, I think there's
+a shot from underneath.
+
+I got these movies from Robert
+Full at Berkeley,
+
+who's worked on these.
+
+You could see the lizard kind
+of peeling its foot off.
+
+And here they've made a little
+robot that can work by van der
+
+Waals forces and it will
+climb up the wall
+
+kind of like a lizard.
+
+And here's what's going on
+at the molecular level.
+
+These are the toe pads on
+a lizard like this.
+
+We're going to be just
+zooming in now.
+
+And you'll see they're covered
+with hairs, and you keep
+
+zooming in more, there's
+more hairs.
+
+And we keep zooming in more,
+get down to a single hair,
+
+there is a 30,000 fold
+magnification.
+
+There's 115,000 magnification.
+
+And in the end, a gecko, such
+as you've got here, has a
+
+billion 0.2 micron tips.
+
+And just to compare it to a
+human hair, over on the edge,
+
+then you can see what the
+gecko hair is like.
+
+It's a very, very fine hair and
+it's able to use van der
+
+Waal interactions to stick
+to the surface.
+
+Bob actually made a Band-Aid
+by collecting this little
+
+hairs out of the thing.
+
+And he made a little joke of
+putting it in a Band-Aid box.
+
+But this is interesting
+because it
+
+isn't affected by water.
+
+You can peel it off.
+
+You can put it back down.
+
+And he thinks there were
+commercial possibilities for
+
+using van der Waals
+interaction.
+
+So, OK, I think we have one more
+force to go, but I think
+
+we will call it a
+day right here.
\ No newline at end of file
diff --git a/e8yvJp0VqtI.txt b/e8yvJp0VqtI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eaecb837f8d7186b9fb149eadccad2d6447b9033
--- /dev/null
+++ b/e8yvJp0VqtI.txt
@@ -0,0 +1,1035 @@
+align:start position:0%
+ 
+in this lecture we'll use a technique
+
+ align:start position:0%
+in this lecture we'll use a technique
+ 
+
+ align:start position:0%
+in this lecture we'll use a technique
+called back of words to build text
+
+ align:start position:0%
+called back of words to build text
+ 
+
+ align:start position:0%
+called back of words to build text
+analytics models fully understanding
+
+ align:start position:0%
+analytics models fully understanding
+ 
+
+ align:start position:0%
+analytics models fully understanding
+text is difficult but bag of words
+
+ align:start position:0%
+text is difficult but bag of words
+ 
+
+ align:start position:0%
+text is difficult but bag of words
+provides a very simple approach it just
+
+ align:start position:0%
+provides a very simple approach it just
+ 
+
+ align:start position:0%
+provides a very simple approach it just
+counts the number of times each word
+
+ align:start position:0%
+counts the number of times each word
+ 
+
+ align:start position:0%
+counts the number of times each word
+appears in the text and uses these
+
+ align:start position:0%
+appears in the text and uses these
+ 
+
+ align:start position:0%
+appears in the text and uses these
+counts as the independent variables for
+
+ align:start position:0%
+counts as the independent variables for
+ 
+
+ align:start position:0%
+counts as the independent variables for
+example in the sentence this course is
+
+ align:start position:0%
+example in the sentence this course is
+ 
+
+ align:start position:0%
+example in the sentence this course is
+great I would recommend this course to
+
+ align:start position:0%
+great I would recommend this course to
+ 
+
+ align:start position:0%
+great I would recommend this course to
+my friends the word this is seen twice
+
+ align:start position:0%
+my friends the word this is seen twice
+ 
+
+ align:start position:0%
+my friends the word this is seen twice
+the word course is seen twice the word
+
+ align:start position:0%
+the word course is seen twice the word
+ 
+
+ align:start position:0%
+the word course is seen twice the word
+great is seen once etc in bag of words
+
+ align:start position:0%
+great is seen once etc in bag of words
+ 
+
+ align:start position:0%
+great is seen once etc in bag of words
+there's one feature for each word this
+
+ align:start position:0%
+there's one feature for each word this
+ 
+
+ align:start position:0%
+there's one feature for each word this
+is a very simple approach but is often
+
+ align:start position:0%
+is a very simple approach but is often
+ 
+
+ align:start position:0%
+is a very simple approach but is often
+very effective - it's used as a baseline
+
+ align:start position:0%
+very effective - it's used as a baseline
+ 
+
+ align:start position:0%
+very effective - it's used as a baseline
+in text analytics projects and for
+
+ align:start position:0%
+in text analytics projects and for
+ 
+
+ align:start position:0%
+in text analytics projects and for
+natural language processing this isn't
+
+ align:start position:0%
+natural language processing this isn't
+ 
+
+ align:start position:0%
+natural language processing this isn't
+the whole story though pre-processing
+
+ align:start position:0%
+the whole story though pre-processing
+ 
+
+ align:start position:0%
+the whole story though pre-processing
+the text can dramatically improve the
+
+ align:start position:0%
+the text can dramatically improve the
+ 
+
+ align:start position:0%
+the text can dramatically improve the
+performance of the bag of words method
+
+ align:start position:0%
+performance of the bag of words method
+ 
+
+ align:start position:0%
+performance of the bag of words method
+one part of pre-processing the text is
+
+ align:start position:0%
+one part of pre-processing the text is
+ 
+
+ align:start position:0%
+one part of pre-processing the text is
+to clean up irregularities text data
+
+ align:start position:0%
+to clean up irregularities text data
+ 
+
+ align:start position:0%
+to clean up irregularities text data
+often has many inconsistencies that will
+
+ align:start position:0%
+often has many inconsistencies that will
+ 
+
+ align:start position:0%
+often has many inconsistencies that will
+cause algorithms trouble
+
+ align:start position:0%
+cause algorithms trouble
+ 
+
+ align:start position:0%
+cause algorithms trouble
+computers are very literal by default
+
+ align:start position:0%
+computers are very literal by default
+ 
+
+ align:start position:0%
+computers are very literal by default
+Apple with just an uppercase a Apple all
+
+ align:start position:0%
+Apple with just an uppercase a Apple all
+ 
+
+ align:start position:0%
+Apple with just an uppercase a Apple all
+in uppercase letters or apple with a
+
+ align:start position:0%
+in uppercase letters or apple with a
+ 
+
+ align:start position:0%
+in uppercase letters or apple with a
+mixture of uppercase and lowercase
+
+ align:start position:0%
+mixture of uppercase and lowercase
+ 
+
+ align:start position:0%
+mixture of uppercase and lowercase
+letters will all be counted separately
+
+ align:start position:0%
+letters will all be counted separately
+ 
+
+ align:start position:0%
+letters will all be counted separately
+we want to change the text so that all
+
+ align:start position:0%
+we want to change the text so that all
+ 
+
+ align:start position:0%
+we want to change the text so that all
+three versions of Apple here will be
+
+ align:start position:0%
+three versions of Apple here will be
+ 
+
+ align:start position:0%
+three versions of Apple here will be
+counted as the same word by either
+
+ align:start position:0%
+counted as the same word by either
+ 
+
+ align:start position:0%
+counted as the same word by either
+changing all words to uppercase or two
+
+ align:start position:0%
+changing all words to uppercase or two
+ 
+
+ align:start position:0%
+changing all words to uppercase or two
+lowercase will typically change all the
+
+ align:start position:0%
+lowercase will typically change all the
+ 
+
+ align:start position:0%
+lowercase will typically change all the
+letters to lowercase so these three
+
+ align:start position:0%
+letters to lowercase so these three
+ 
+
+ align:start position:0%
+letters to lowercase so these three
+versions of Apple will all become Apple
+
+ align:start position:0%
+versions of Apple will all become Apple
+ 
+
+ align:start position:0%
+versions of Apple will all become Apple
+with lowercase letters and will be
+
+ align:start position:0%
+with lowercase letters and will be
+ 
+
+ align:start position:0%
+with lowercase letters and will be
+counted as the same word punctuation can
+
+ align:start position:0%
+counted as the same word punctuation can
+ 
+
+ align:start position:0%
+counted as the same word punctuation can
+also cause problems the basic approach
+
+ align:start position:0%
+also cause problems the basic approach
+ 
+
+ align:start position:0%
+also cause problems the basic approach
+is to deal with this is to remove
+
+ align:start position:0%
+is to deal with this is to remove
+ 
+
+ align:start position:0%
+is to deal with this is to remove
+everything that is in a standard number
+
+ align:start position:0%
+everything that is in a standard number
+ 
+
+ align:start position:0%
+everything that is in a standard number
+or letter however sometimes punctuation
+
+ align:start position:0%
+or letter however sometimes punctuation
+ 
+
+ align:start position:0%
+or letter however sometimes punctuation
+is meaningful in the case of Twitter an
+
+ align:start position:0%
+is meaningful in the case of Twitter an
+ 
+
+ align:start position:0%
+is meaningful in the case of Twitter an
+apple denotes a message to Apple and
+
+ align:start position:0%
+apple denotes a message to Apple and
+ 
+
+ align:start position:0%
+apple denotes a message to Apple and
+hashtag Apple is a message about Apple
+
+ align:start position:0%
+hashtag Apple is a message about Apple
+ 
+
+ align:start position:0%
+hashtag Apple is a message about Apple
+for web addresses the
+
+ align:start position:0%
+for web addresses the
+ 
+
+ align:start position:0%
+for web addresses the
+shishun often defines the web address
+
+ align:start position:0%
+shishun often defines the web address
+ 
+
+ align:start position:0%
+shishun often defines the web address
+for these reasons the removal of
+
+ align:start position:0%
+for these reasons the removal of
+ 
+
+ align:start position:0%
+for these reasons the removal of
+punctuation should be tailored to the
+
+ align:start position:0%
+punctuation should be tailored to the
+ 
+
+ align:start position:0%
+punctuation should be tailored to the
+specific problem in our case we will
+
+ align:start position:0%
+specific problem in our case we will
+ 
+
+ align:start position:0%
+specific problem in our case we will
+remove all punctuation so at Apple Apple
+
+ align:start position:0%
+remove all punctuation so at Apple Apple
+ 
+
+ align:start position:0%
+remove all punctuation so at Apple Apple
+with an exclamation point apple with
+
+ align:start position:0%
+with an exclamation point apple with
+ 
+
+ align:start position:0%
+with an exclamation point apple with
+dashes will all count as just Apple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another pre-processing task we want to
+
+ align:start position:0%
+another pre-processing task we want to
+ 
+
+ align:start position:0%
+another pre-processing task we want to
+do is to remove unhelpful terms many
+
+ align:start position:0%
+do is to remove unhelpful terms many
+ 
+
+ align:start position:0%
+do is to remove unhelpful terms many
+words are frequently used but are only
+
+ align:start position:0%
+words are frequently used but are only
+ 
+
+ align:start position:0%
+words are frequently used but are only
+meaningful in a sentence these are
+
+ align:start position:0%
+meaningful in a sentence these are
+ 
+
+ align:start position:0%
+meaningful in a sentence these are
+called stop words examples are the is at
+
+ align:start position:0%
+called stop words examples are the is at
+ 
+
+ align:start position:0%
+called stop words examples are the is at
+and which it's unlikely that these words
+
+ align:start position:0%
+and which it's unlikely that these words
+ 
+
+ align:start position:0%
+and which it's unlikely that these words
+will improve the machine learning
+
+ align:start position:0%
+will improve the machine learning
+ 
+
+ align:start position:0%
+will improve the machine learning
+prediction quality so we want to remove
+
+ align:start position:0%
+prediction quality so we want to remove
+ 
+
+ align:start position:0%
+prediction quality so we want to remove
+them to reduce the size of the data
+
+ align:start position:0%
+them to reduce the size of the data
+ 
+
+ align:start position:0%
+them to reduce the size of the data
+there are some potential problems of
+
+ align:start position:0%
+there are some potential problems of
+ 
+
+ align:start position:0%
+there are some potential problems of
+this approach sometimes to stop words
+
+ align:start position:0%
+this approach sometimes to stop words
+ 
+
+ align:start position:0%
+this approach sometimes to stop words
+taken together have a very important
+
+ align:start position:0%
+taken together have a very important
+ 
+
+ align:start position:0%
+taken together have a very important
+meaning for example the who which is a
+
+ align:start position:0%
+meaning for example the who which is a
+ 
+
+ align:start position:0%
+meaning for example the who which is a
+combination of two stop words is
+
+ align:start position:0%
+combination of two stop words is
+ 
+
+ align:start position:0%
+combination of two stop words is
+actually the ban the name of the band we
+
+ align:start position:0%
+actually the ban the name of the band we
+ 
+
+ align:start position:0%
+actually the ban the name of the band we
+see on the right here by removing the
+
+ align:start position:0%
+see on the right here by removing the
+ 
+
+ align:start position:0%
+see on the right here by removing the
+stop words we remove both of these words
+
+ align:start position:0%
+stop words we remove both of these words
+ 
+
+ align:start position:0%
+stop words we remove both of these words
+but the who might actually have a
+
+ align:start position:0%
+but the who might actually have a
+ 
+
+ align:start position:0%
+but the who might actually have a
+significant meaning for a prediction
+
+ align:start position:0%
+significant meaning for a prediction
+ 
+
+ align:start position:0%
+significant meaning for a prediction
+task another example is the phrase take
+
+ align:start position:0%
+task another example is the phrase take
+ 
+
+ align:start position:0%
+task another example is the phrase take
+that if we remove the stop words will
+
+ align:start position:0%
+that if we remove the stop words will
+ 
+
+ align:start position:0%
+that if we remove the stop words will
+remove the word that
+
+ align:start position:0%
+remove the word that
+ 
+
+ align:start position:0%
+remove the word that
+so the phrase will just say take it no
+
+ align:start position:0%
+so the phrase will just say take it no
+ 
+
+ align:start position:0%
+so the phrase will just say take it no
+longer has the same meaning as before so
+
+ align:start position:0%
+longer has the same meaning as before so
+ 
+
+ align:start position:0%
+longer has the same meaning as before so
+while removing stop words sometimes is
+
+ align:start position:0%
+while removing stop words sometimes is
+ 
+
+ align:start position:0%
+while removing stop words sometimes is
+not helpful it generally is a very
+
+ align:start position:0%
+not helpful it generally is a very
+ 
+
+ align:start position:0%
+not helpful it generally is a very
+helpful pre-processing step lastly an
+
+ align:start position:0%
+helpful pre-processing step lastly an
+ 
+
+ align:start position:0%
+helpful pre-processing step lastly an
+important pre-processing step is called
+
+ align:start position:0%
+important pre-processing step is called
+ 
+
+ align:start position:0%
+important pre-processing step is called
+stemming this step is motivated by the
+
+ align:start position:0%
+stemming this step is motivated by the
+ 
+
+ align:start position:0%
+stemming this step is motivated by the
+desire to represent words with different
+
+ align:start position:0%
+desire to represent words with different
+ 
+
+ align:start position:0%
+desire to represent words with different
+endings as the same word we probably do
+
+ align:start position:0%
+endings as the same word we probably do
+ 
+
+ align:start position:0%
+endings as the same word we probably do
+not need to draw a distinction between
+
+ align:start position:0%
+not need to draw a distinction between
+ 
+
+ align:start position:0%
+not need to draw a distinction between
+argue argued argues and arguing they
+
+ align:start position:0%
+argue argued argues and arguing they
+ 
+
+ align:start position:0%
+argue argued argues and arguing they
+could all be represented by a common
+
+ align:start position:0%
+could all be represented by a common
+ 
+
+ align:start position:0%
+could all be represented by a common
+stem argue the algorithmic process of
+
+ align:start position:0%
+stem argue the algorithmic process of
+ 
+
+ align:start position:0%
+stem argue the algorithmic process of
+performing this reduction is called
+
+ align:start position:0%
+performing this reduction is called
+ 
+
+ align:start position:0%
+performing this reduction is called
+stemming there are many ways to approach
+
+ align:start position:0%
+stemming there are many ways to approach
+ 
+
+ align:start position:0%
+stemming there are many ways to approach
+the problem one approach is to build a
+
+ align:start position:0%
+the problem one approach is to build a
+ 
+
+ align:start position:0%
+the problem one approach is to build a
+database of words and their stems a pro
+
+ align:start position:0%
+database of words and their stems a pro
+ 
+
+ align:start position:0%
+database of words and their stems a pro
+is that this approach
+
+ align:start position:0%
+is that this approach
+ 
+
+ align:start position:0%
+is that this approach
+handles exceptions very nicely since we
+
+ align:start position:0%
+handles exceptions very nicely since we
+ 
+
+ align:start position:0%
+handles exceptions very nicely since we
+have to find all of the stems however it
+
+ align:start position:0%
+have to find all of the stems however it
+ 
+
+ align:start position:0%
+have to find all of the stems however it
+won't handle new words at all since they
+
+ align:start position:0%
+won't handle new words at all since they
+ 
+
+ align:start position:0%
+won't handle new words at all since they
+are not in the database
+
+ align:start position:0%
+are not in the database
+ 
+
+ align:start position:0%
+are not in the database
+this is especially bad for problems
+
+ align:start position:0%
+this is especially bad for problems
+ 
+
+ align:start position:0%
+this is especially bad for problems
+where we're using data from the internet
+
+ align:start position:0%
+where we're using data from the internet
+ 
+
+ align:start position:0%
+where we're using data from the internet
+since we have no idea what words will be
+
+ align:start position:0%
+since we have no idea what words will be
+ 
+
+ align:start position:0%
+since we have no idea what words will be
+used a different approach is to write a
+
+ align:start position:0%
+used a different approach is to write a
+ 
+
+ align:start position:0%
+used a different approach is to write a
+rule based algorithm in this approach if
+
+ align:start position:0%
+rule based algorithm in this approach if
+ 
+
+ align:start position:0%
+rule based algorithm in this approach if
+a word ends in things like edy ing or ly
+
+ align:start position:0%
+a word ends in things like edy ing or ly
+ 
+
+ align:start position:0%
+a word ends in things like edy ing or ly
+we would remove the ending appro of this
+
+ align:start position:0%
+we would remove the ending appro of this
+ 
+
+ align:start position:0%
+we would remove the ending appro of this
+approach is that it handles new or
+
+ align:start position:0%
+approach is that it handles new or
+ 
+
+ align:start position:0%
+approach is that it handles new or
+unknown words well however there are
+
+ align:start position:0%
+unknown words well however there are
+ 
+
+ align:start position:0%
+unknown words well however there are
+many exceptions and this approach would
+
+ align:start position:0%
+many exceptions and this approach would
+ 
+
+ align:start position:0%
+many exceptions and this approach would
+miss all of these words like child and
+
+ align:start position:0%
+miss all of these words like child and
+ 
+
+ align:start position:0%
+miss all of these words like child and
+children would be considered different
+
+ align:start position:0%
+children would be considered different
+ 
+
+ align:start position:0%
+children would be considered different
+but it would get other plurals like dog
+
+ align:start position:0%
+but it would get other plurals like dog
+ 
+
+ align:start position:0%
+but it would get other plurals like dog
+and dogs the second approach is widely
+
+ align:start position:0%
+and dogs the second approach is widely
+ 
+
+ align:start position:0%
+and dogs the second approach is widely
+popular and is called the porter stemmer
+
+ align:start position:0%
+popular and is called the porter stemmer
+ 
+
+ align:start position:0%
+popular and is called the porter stemmer
+designed by martin porter in 1980 and
+
+ align:start position:0%
+designed by martin porter in 1980 and
+ 
+
+ align:start position:0%
+designed by martin porter in 1980 and
+it's still used today stim words like
+
+ align:start position:0%
+it's still used today stim words like
+ 
+
+ align:start position:0%
+it's still used today stim words like
+this one have been written for many
+
+ align:start position:0%
+this one have been written for many
+ 
+
+ align:start position:0%
+this one have been written for many
+languages other options for stemming
+
+ align:start position:0%
+languages other options for stemming
+ 
+
+ align:start position:0%
+languages other options for stemming
+include machine learning where
+
+ align:start position:0%
+include machine learning where
+ 
+
+ align:start position:0%
+include machine learning where
+algorithms are trained to recognize the
+
+ align:start position:0%
+algorithms are trained to recognize the
+ 
+
+ align:start position:0%
+algorithms are trained to recognize the
+roots of words and combinations of the
+
+ align:start position:0%
+roots of words and combinations of the
+ 
+
+ align:start position:0%
+roots of words and combinations of the
+approaches explained here as a real
+
+ align:start position:0%
+approaches explained here as a real
+ 
+
+ align:start position:0%
+approaches explained here as a real
+example from our data set the phrase by
+
+ align:start position:0%
+example from our data set the phrase by
+ 
+
+ align:start position:0%
+example from our data set the phrase by
+far the best customer care service I
+
+ align:start position:0%
+far the best customer care service I
+ 
+
+ align:start position:0%
+far the best customer care service I
+have ever received has three words that
+
+ align:start position:0%
+have ever received has three words that
+ 
+
+ align:start position:0%
+have ever received has three words that
+would be stemmed customer service and
+
+ align:start position:0%
+would be stemmed customer service and
+ 
+
+ align:start position:0%
+would be stemmed customer service and
+received the ER would be removed in
+
+ align:start position:0%
+received the ER would be removed in
+ 
+
+ align:start position:0%
+received the ER would be removed in
+customer the e would be removed in
+
+ align:start position:0%
+customer the e would be removed in
+ 
+
+ align:start position:0%
+customer the e would be removed in
+service and the IDI would be removed in
+
+ align:start position:0%
+service and the IDI would be removed in
+ 
+
+ align:start position:0%
+service and the IDI would be removed in
+received in the next video we'll see how
+
+ align:start position:0%
+received in the next video we'll see how
+ 
+
+ align:start position:0%
+received in the next video we'll see how
+to run these pre-processing steps in our
\ No newline at end of file
diff --git a/ePH6sgXk9vw.txt b/ePH6sgXk9vw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..060b88138c106ed5f232d7d6de2e777db0633516
--- /dev/null
+++ b/ePH6sgXk9vw.txt
@@ -0,0 +1,403 @@
+align:start position:0%
+ 
+one of the physiological scenarios
+
+ align:start position:0%
+one of the physiological scenarios
+ 
+
+ align:start position:0%
+one of the physiological scenarios
+is probably very common in
+
+ align:start position:0%
+is probably very common in
+ 
+
+ align:start position:0%
+is probably very common in
+you know has to do with diabetes I'm
+
+ align:start position:0%
+you know has to do with diabetes I'm
+ 
+
+ align:start position:0%
+you know has to do with diabetes I'm
+diabetic and my great-grandfather was
+
+ align:start position:0%
+diabetic and my great-grandfather was
+ 
+
+ align:start position:0%
+diabetic and my great-grandfather was
+diabetic his daughter like grandmother
+
+ align:start position:0%
+diabetic his daughter like grandmother
+ 
+
+ align:start position:0%
+diabetic his daughter like grandmother
+was diabetic five of her six sons were
+
+ align:start position:0%
+was diabetic five of her six sons were
+ 
+
+ align:start position:0%
+was diabetic five of her six sons were
+diabetic one of whom was my father
+
+ align:start position:0%
+diabetic one of whom was my father
+ 
+
+ align:start position:0%
+diabetic one of whom was my father
+so you see a very genetic disease here
+
+ align:start position:0%
+so you see a very genetic disease here
+ 
+
+ align:start position:0%
+so you see a very genetic disease here
+okay that's in in my case type to date
+
+ align:start position:0%
+okay that's in in my case type to date
+ 
+
+ align:start position:0%
+okay that's in in my case type to date
+diabetic so you know adult onset
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so my cells are insulin resistant so if
+
+ align:start position:0%
+so my cells are insulin resistant so if
+ 
+
+ align:start position:0%
+so my cells are insulin resistant so if
+I eat a meal that has carbohydrate or
+
+ align:start position:0%
+I eat a meal that has carbohydrate or
+ 
+
+ align:start position:0%
+I eat a meal that has carbohydrate or
+fat in it like pancreas is probably
+
+ align:start position:0%
+fat in it like pancreas is probably
+ 
+
+ align:start position:0%
+fat in it like pancreas is probably
+responding and I probably like my beta
+
+ align:start position:0%
+responding and I probably like my beta
+ 
+
+ align:start position:0%
+responding and I probably like my beta
+cells in my Cantonese are probably ok
+
+ align:start position:0%
+cells in my Cantonese are probably ok
+ 
+
+ align:start position:0%
+cells in my Cantonese are probably ok
+but the insulin just isn't able by
+
+ align:start position:0%
+but the insulin just isn't able by
+ 
+
+ align:start position:0%
+but the insulin just isn't able by
+producing insulin and but the insulin
+
+ align:start position:0%
+producing insulin and but the insulin
+ 
+
+ align:start position:0%
+producing insulin and but the insulin
+just isn't able to signal my cells to be
+
+ align:start position:0%
+just isn't able to signal my cells to be
+ 
+
+ align:start position:0%
+just isn't able to signal my cells to be
+able to take up the glucose as a
+
+ align:start position:0%
+able to take up the glucose as a
+ 
+
+ align:start position:0%
+able to take up the glucose as a
+consequence I'm somewhat in a technical
+
+ align:start position:0%
+consequence I'm somewhat in a technical
+ 
+
+ align:start position:0%
+consequence I'm somewhat in a technical
+state of starvation mic like egde and
+
+ align:start position:0%
+state of starvation mic like egde and
+ 
+
+ align:start position:0%
+state of starvation mic like egde and
+reserves are therefore smaller than
+
+ align:start position:0%
+reserves are therefore smaller than
+ 
+
+ align:start position:0%
+reserves are therefore smaller than
+yours and I can tell this in times for
+
+ align:start position:0%
+yours and I can tell this in times for
+ 
+
+ align:start position:0%
+yours and I can tell this in times for
+example when I was first became diabetic
+
+ align:start position:0%
+example when I was first became diabetic
+ 
+
+ align:start position:0%
+example when I was first became diabetic
+I loved mountain climbing and hiking and
+
+ align:start position:0%
+I loved mountain climbing and hiking and
+ 
+
+ align:start position:0%
+I loved mountain climbing and hiking and
+so on and I that I would go out and I'd
+
+ align:start position:0%
+so on and I that I would go out and I'd
+ 
+
+ align:start position:0%
+so on and I that I would go out and I'd
+be totally exhausted for the first ten
+
+ align:start position:0%
+be totally exhausted for the first ten
+ 
+
+ align:start position:0%
+be totally exhausted for the first ten
+minutes or so and that's because I have
+
+ align:start position:0%
+minutes or so and that's because I have
+ 
+
+ align:start position:0%
+minutes or so and that's because I have
+very small glycogen reserves what I had
+
+ align:start position:0%
+very small glycogen reserves what I had
+ 
+
+ align:start position:0%
+very small glycogen reserves what I had
+to do is this metabolic switch over to
+
+ align:start position:0%
+to do is this metabolic switch over to
+ 
+
+ align:start position:0%
+to do is this metabolic switch over to
+booting up oxidative metabolism of fats
+
+ align:start position:0%
+booting up oxidative metabolism of fats
+ 
+
+ align:start position:0%
+booting up oxidative metabolism of fats
+that all had to be turned on and it's
+
+ align:start position:0%
+that all had to be turned on and it's
+ 
+
+ align:start position:0%
+that all had to be turned on and it's
+hard it's a hard transition but once it
+
+ align:start position:0%
+hard it's a hard transition but once it
+ 
+
+ align:start position:0%
+hard it's a hard transition but once it
+got going as long as I stay aerobic in
+
+ align:start position:0%
+got going as long as I stay aerobic in
+ 
+
+ align:start position:0%
+got going as long as I stay aerobic in
+other words I don't go so fast that I go
+
+ align:start position:0%
+other words I don't go so fast that I go
+ 
+
+ align:start position:0%
+other words I don't go so fast that I go
+anaerobic I can climb forever because if
+
+ align:start position:0%
+anaerobic I can climb forever because if
+ 
+
+ align:start position:0%
+anaerobic I can climb forever because if
+I stay aerobic I've got plenty of fat
+
+ align:start position:0%
+I stay aerobic I've got plenty of fat
+ 
+
+ align:start position:0%
+I stay aerobic I've got plenty of fat
+reserves in fact it's probably a good
+
+ align:start position:0%
+reserves in fact it's probably a good
+ 
+
+ align:start position:0%
+reserves in fact it's probably a good
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+that I'm burning them so I'm just a
+
+ align:start position:0%
+that I'm burning them so I'm just a
+ 
+
+ align:start position:0%
+that I'm burning them so I'm just a
+little bit different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'd like to teach this
+
+ align:start position:0%
+I'd like to teach this
+ 
+
+ align:start position:0%
+I'd like to teach this
+seven in part because I was probably not
+
+ align:start position:0%
+seven in part because I was probably not
+ 
+
+ align:start position:0%
+seven in part because I was probably not
+that many kids in the class you know 100
+
+ align:start position:0%
+that many kids in the class you know 100
+ 
+
+ align:start position:0%
+that many kids in the class you know 100
+hundred and thirty or so students would
+
+ align:start position:0%
+hundred and thirty or so students would
+ 
+
+ align:start position:0%
+hundred and thirty or so students would
+be diabetic but it's about six to eight
+
+ align:start position:0%
+be diabetic but it's about six to eight
+ 
+
+ align:start position:0%
+be diabetic but it's about six to eight
+percent of the population in the United
+
+ align:start position:0%
+percent of the population in the United
+ 
+
+ align:start position:0%
+percent of the population in the United
+States right now and so you know
+
+ align:start position:0%
+States right now and so you know
+ 
+
+ align:start position:0%
+States right now and so you know
+everybody knows someone is diabetic or
+
+ align:start position:0%
+everybody knows someone is diabetic or
+ 
+
+ align:start position:0%
+everybody knows someone is diabetic or
+maybe your parents are and you know what
+
+ align:start position:0%
+maybe your parents are and you know what
+ 
+
+ align:start position:0%
+maybe your parents are and you know what
+are the risk factors so we teach that
\ No newline at end of file
diff --git a/esHLwySu4XU.txt b/esHLwySu4XU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b1c23e12924fffb0f95876acc23dbd95bb38cc27
--- /dev/null
+++ b/esHLwySu4XU.txt
@@ -0,0 +1,243 @@
+align:start position:0%
+ 
+let's look at going between
+
+ align:start position:0%
+let's look at going between
+ 
+
+ align:start position:0%
+let's look at going between
+representations we'll start in the ijk
+
+ align:start position:0%
+representations we'll start in the ijk
+ 
+
+ align:start position:0%
+representations we'll start in the ijk
+representation going to the magnitude
+
+ align:start position:0%
+representation going to the magnitude
+ 
+
+ align:start position:0%
+representation going to the magnitude
+and angle representation so if we have
+
+ align:start position:0%
+and angle representation so if we have
+ 
+
+ align:start position:0%
+and angle representation so if we have
+our vector the arbitrary vector can be
+
+ align:start position:0%
+our vector the arbitrary vector can be
+ 
+
+ align:start position:0%
+our vector the arbitrary vector can be
+written as ax I hat plus a YJ hat in
+
+ align:start position:0%
+written as ax I hat plus a YJ hat in
+ 
+
+ align:start position:0%
+written as ax I hat plus a YJ hat in
+this particular case were given a vector
+
+ align:start position:0%
+this particular case were given a vector
+ 
+
+ align:start position:0%
+this particular case were given a vector
+minus 2 I hat plus 3 J hat I would like
+
+ align:start position:0%
+minus 2 I hat plus 3 J hat I would like
+ 
+
+ align:start position:0%
+minus 2 I hat plus 3 J hat I would like
+to go to the magnitude and angle
+
+ align:start position:0%
+to go to the magnitude and angle
+ 
+
+ align:start position:0%
+to go to the magnitude and angle
+representation so first of all let's
+
+ align:start position:0%
+representation so first of all let's
+ 
+
+ align:start position:0%
+representation so first of all let's
+draw it out on our grid like this and
+
+ align:start position:0%
+draw it out on our grid like this and
+ 
+
+ align:start position:0%
+draw it out on our grid like this and
+let's find the magnitude so the
+
+ align:start position:0%
+let's find the magnitude so the
+ 
+
+ align:start position:0%
+let's find the magnitude so the
+magnitude we can find through the
+
+ align:start position:0%
+magnitude we can find through the
+ 
+
+ align:start position:0%
+magnitude we can find through the
+Pythagorean theorem it's just the square
+
+ align:start position:0%
+Pythagorean theorem it's just the square
+ 
+
+ align:start position:0%
+Pythagorean theorem it's just the square
+root of the X component squared plus the
+
+ align:start position:0%
+root of the X component squared plus the
+ 
+
+ align:start position:0%
+root of the X component squared plus the
+Y component squared and now we can find
+
+ align:start position:0%
+Y component squared and now we can find
+ 
+
+ align:start position:0%
+Y component squared and now we can find
+the angle the angle the tangent of the
+
+ align:start position:0%
+the angle the angle the tangent of the
+ 
+
+ align:start position:0%
+the angle the angle the tangent of the
+angle is just equal to the Y component
+
+ align:start position:0%
+angle is just equal to the Y component
+ 
+
+ align:start position:0%
+angle is just equal to the Y component
+divided by the X component like this and
+
+ align:start position:0%
+divided by the X component like this and
+ 
+
+ align:start position:0%
+divided by the X component like this and
+so in this way we can solve for the
+
+ align:start position:0%
+so in this way we can solve for the
+ 
+
+ align:start position:0%
+so in this way we can solve for the
+angle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let's practice going back the other
+
+ align:start position:0%
+now let's practice going back the other
+ 
+
+ align:start position:0%
+now let's practice going back the other
+way if we're given a vector whose
+
+ align:start position:0%
+way if we're given a vector whose
+ 
+
+ align:start position:0%
+way if we're given a vector whose
+magnitude is two and whose angle from
+
+ align:start position:0%
+magnitude is two and whose angle from
+ 
+
+ align:start position:0%
+magnitude is two and whose angle from
+the x-axis is 30 degrees like this one
+
+ align:start position:0%
+the x-axis is 30 degrees like this one
+ 
+
+ align:start position:0%
+the x-axis is 30 degrees like this one
+here then the X component is just the
+
+ align:start position:0%
+here then the X component is just the
+ 
+
+ align:start position:0%
+here then the X component is just the
+magnitude times the cosine of the angle
+
+ align:start position:0%
+magnitude times the cosine of the angle
+ 
+
+ align:start position:0%
+magnitude times the cosine of the angle
+so two times the cosine of 30 and the Y
+
+ align:start position:0%
+so two times the cosine of 30 and the Y
+ 
+
+ align:start position:0%
+so two times the cosine of 30 and the Y
+component is just the magnitude times
+
+ align:start position:0%
+component is just the magnitude times
+ 
+
+ align:start position:0%
+component is just the magnitude times
+the sine of the angle so two times the
+
+ align:start position:0%
+the sine of the angle so two times the
+ 
+
+ align:start position:0%
+the sine of the angle so two times the
+sine of 30
\ No newline at end of file
diff --git a/euO8bqSW_Ow.txt b/euO8bqSW_Ow.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b4d9f80b1069a5643bff300e4e1d47cd315130e2
--- /dev/null
+++ b/euO8bqSW_Ow.txt
@@ -0,0 +1,4022 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help
+MIT OpenCourseWare
+
+continue to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+INSTRUCTOR: So today, we
+start on project 4, which is,
+
+as you know, the big project.
+
+And Helen is going to do a
+walkthrough of the project,
+
+and the code, and
+the organization,
+
+because this is a pretty
+big sized project.
+
+It's got about
+4,500 lines of code.
+
+And it's not code that is
+kind of like simple code.
+
+It's all content-bearing code.
+
+So I think having a bit
+of an orientation to it,
+
+more than we give for the
+other codes that you work,
+
+on which are pretty
+small, this will be great.
+
+So, Helen, take it away.
+
+HELEN XU: Hi, everyone.
+
+Can you hear me?
+
+Awesome, so today we're going
+to be doing the walkthrough
+
+for the final project.
+
+You can look at the code
+and clone it publicly here.
+
+And please remember to fill up
+your team's by 7:00 PM today,
+
+so we can populate the
+list and get your repos.
+
+Yeah, and if there are
+any issues accessing this,
+
+just let me know.
+
+Or put it on Piazza
+and then we can fix it.
+
+So we just had a
+game of Lesierchess.
+
+But in case you
+missed it, we'll go
+
+into more details about
+what the game actually does.
+
+So first, we're going to
+go through the game rules.
+
+So you saw that there
+are these pieces.
+
+There's these triangles.
+
+And there's kings.
+
+So the triangles are pawns.
+
+And the kings, they
+look like crowns.
+
+And there are two teams.
+
+There's orange and lavender,
+or tangerine and lavender.
+
+And each side starts out with
+seven pawns and one king.
+
+And this is the
+starting position.
+
+So you can see like the
+kings are in the corner.
+
+And they're just lined
+up like in the middle.
+
+And each piece has
+four orientations.
+
+So you can see that the pawn
+is up, down, left, right.
+
+And then the king
+is also like that.
+
+And in general, the game starts
+with tangerine moving first.
+
+And then the play alternates
+between the two players.
+
+Each piece moves the same,
+whether it's king or pawn.
+
+And each turn has two parts.
+
+So you saw the demo.
+
+But you move first.
+
+When you pick one of your
+pieces, and you move first.
+
+And then at the end, your
+King has to fire the laser.
+
+And the laser reflects off
+the long edge of the pawn.
+
+And they'll kill the pawn if
+it shoots the short edges.
+
+And one side wins when
+the king gets shot,
+
+or when the opposing king gets
+shot, whether by themselves
+
+or by your own king.
+
+And so I talked a
+little about moving.
+
+And at the beginning of each
+turn, the player to move
+
+chooses a piece to move.
+
+And you can move your
+King or any of your pawns.
+
+And there are two
+types of moves.
+
+There's basic moves,
+and swat moves.
+
+And basic moves are just,
+basically, shifts or rotations.
+
+So in the example, you can
+rotate 90, 180, or 270 degrees.
+
+So in the top, row
+you just rotate.
+
+This is the example
+of moving a pawn.
+
+So you rotate your pawn.
+
+Or you can move to an
+empty adjacent square.
+
+So those are the
+bottom two rows.
+
+And there are eight adjacent
+squares in this example.
+
+So there are eight shifts.
+
+But there would
+be less than eight
+
+if you were, for example,
+like at the edge of the board.
+
+And on a move, you can
+either shift or rotate.
+
+But you can't do both.
+
+There are also these swap loops.
+
+So if you're adjacent
+to an opposing piece,
+
+you can switch with them.
+
+And then you have to
+make another basic move
+
+after that, that is not a swap.
+
+So, basically, you can either--
+
+and it has to be
+with that same piece
+
+that you just swapped with.
+
+So you just either
+shift or rotate.
+
+Is everyone good on the rules?
+
+Just a couple more things.
+
+So there's this
+Ko rule, which is
+
+from Go, which ensures that
+the game makes progress.
+
+So it makes a move illegal if
+it undoes the opponent's most
+
+recent move by just moving
+back to where you just were.
+
+So this is an example.
+
+Let's say you're tangerine.
+
+And you swapped with the
+purple one right next to you.
+
+And then you shifted
+left and bottom.
+
+And so lavender can
+return by swapping back
+
+with your orange piece,
+and shifting again.
+
+But this is actually,
+illegal because now
+
+you just got to your
+original position.
+
+So you're not allowed to just
+keep cycling back and forth.
+
+And so a draw occurs if there
+have been 50 moves by each side
+
+without a pawn being
+zapped, the same position
+
+repeats itself by
+the side on move,
+
+or the two players
+agree to a draw.
+
+So just kind of like
+in chess, a chess clock
+
+limits the amount of time the
+players have to make a move.
+
+So you can't just keep
+competing indefinitely.
+
+When it's your moves,
+your clock counts down.
+
+When it's your opponent's
+moves, your clock stops.
+
+So it's not counting your time.
+
+And we used Fisher time control.
+
+There's a picture
+of Bobby Fisher, who
+
+made it, up which used an
+initial time budget and a time
+
+increment.
+
+So in this example,
+there's fis60 and 0.5,
+
+which means that,
+in the beginning,
+
+each player has 60 seconds.
+
+And you get to use the 60
+seconds however you want.
+
+And when you end your move,
+you get 0.5 extra seconds.
+
+But the 60 and 0.5
+could be anything.
+
+That's just an example.
+
+So we'll go into an
+example of how you actually
+
+play this game.
+
+For a king to zap
+the enemy king,
+
+it risks opening itself
+to counter-attack.
+
+So look at this example.
+
+And how can tangerine zap
+the lavender pawn in F5,
+
+by moving one of its pieces?
+
+AUDIENCE: [INAUDIBLE]
+
+HELEN XU: Move C4.
+
+AUDIENCE: Tangerine,
+that's lavender.
+
+HELEN XU: You're
+tangerine in this example.
+
+And you're trying to
+zap the one on F5.
+
+Yep?
+
+AUDIENCE: You move the
+tangerine piece at E22 to F1.
+
+HELEN XU: E2 to F1.
+
+Oh, sorry, by zap, it
+means shoot the backside.
+
+That would shoot the long side.
+
+Good point.
+
+Yeah, so you're trying
+to kill the piece on F5.
+
+AUDIENCE: [INAUDIBLE]
+
+HELEN XU: Yeah, exactly.
+
+So in this, you can move
+C2 to B1, as you just said.
+
+And then you draw the path.
+
+And you can see that
+you've just killed--
+
+or if you're tangerine, you've
+just killed the piece at F5.
+
+Now, how can lavender counter?
+
+By counter, we mean
+lavender can win
+
+the game from this position.
+
+AUDIENCE: Is it A4 to A3?
+
+HELEN XU: A4 to A3.
+
+No, I don't think so.
+
+Yep?
+
+AUDIENCE: [INAUDIBLE]
+
+HELEN XU: Sorry, what?
+
+King, like the orange one?
+
+Oh, the lavender one.
+
+You're trying to
+shoot the orange king.
+
+Oh, yes, you're right.
+
+You can, actually.
+
+Yes, good, that's not
+the one that we had,
+
+but apparently
+there are two ways.
+
+Good.
+
+So if you notice
+you could also--
+
+that's another way
+to get that path.
+
+But you can also move
+one of the pawns.
+
+Cool, so this is
+just pointing out
+
+one of the subtleties of
+the game, which is you
+
+should watch out for
+just naively killing
+
+all the pieces you can,
+because that might open you up
+
+to the opponent.
+
+Yeah?
+
+AUDIENCE: [INAUDIBLE]
+
+HELEN XU: Yes, it can
+be from any direction.
+
+But the pawns only
+die if you shoot them
+
+from not on the long edge.
+
+Yep?
+
+AUDIENCE: What if you
+shoot your own block?
+
+HELEN XU: By block,
+you mean your own pawn?
+
+AUDIENCE: Yeah.
+
+HELEN XU: You'll die.
+
+AUDIENCE: Oh.
+
+HELEN XU: Yeah?
+
+AUDIENCE: [INAUDIBLE]
+
+HELEN XU: Yes, but only one
+piece can be on each square.
+
+But you can have
+as many near you.
+
+But do you have a question?
+
+AUDIENCE: Can you make it
+impossible to kill your person?
+
+HELEN XU: Like your King?
+
+Like if you barricaded
+it by pawns.
+
+But then the opponent can
+come in and swap with them,
+
+so it will open your barricade.
+
+AUDIENCE: Can the purple
+king shoot upward?
+
+HELEN XU: If it wanted to.
+
+But then in this example, it
+would shoot up off the board,
+
+and nothing would happen.
+
+Yeah?
+
+AUDIENCE: When you kill
+a pawn, does the laser
+
+stop at the place where
+the pawn is or does it
+
+go through the pawn?
+
+HELEN XU: No, it
+just shoots one.
+
+Good questions.
+
+Everyone good so far?
+
+OK, great.
+
+PROFESSOR: This year,
+it shoots only one.
+
+Last year, it kept shooting.
+
+AUDIENCE: Can the
+king shoot itself?
+
+HELEN XU: Yes.
+
+It should try not
+to, but it can.
+
+So you should be careful.
+
+So moving on-- we use force
+Fosythe-Edwards Notation,
+
+which is a representation of a
+chess position using a string.
+
+So you can see an example
+of the starting position.
+
+And the bottom
+includes the string
+
+that describes the
+starting position.
+
+If you look at the
+representation,
+
+the arrow corresponds
+to one of the rows.
+
+And that points to the substring
+that has a bubble over it.
+
+So in this row, there is
+one purple pawn at B3,
+
+and two orange
+ones at F3 and G3.
+
+So this is row three.
+
+And the slashes separate
+the rows in the string.
+
+And the one represents
+there's an empty space.
+
+And then there's a
+pawn facing southeast.
+
+And then there's three
+empty spaces, and one facing
+
+northwest, and then one
+facing southeast, and then
+
+an empty space.
+
+AUDIENCE: [INAUDIBLE]
+
+HELEN XU: Oh, yeah,
+it's animated.
+
+What do you mean?
+
+Yeah, so at the end of the
+string, there's also a--
+
+it just tells you which
+side's move it is.
+
+So this is the opening position.
+
+But you can use any
+position in this notation.
+
+And this is useful
+for debugging,
+
+because if you, for example,
+you're running a bot,
+
+and it crashes at some position.
+
+And you can get back
+to that position.
+
+You can start up
+the game and just
+
+go there without having to make
+all the moves to get there.
+
+And this is how you
+represent the games.
+
+So each of these is one move.
+
+And the left column
+is tangerine.
+
+And the right
+column is lavender.
+
+And an example,
+you can see E6, E7,
+
+means they moved a
+piece from E6 to E7.
+
+B3L, so you rotated
+the piece on B3 left.
+
+There's D5, E4, F5, which
+means that you swapped.
+
+So your original
+piece was on D5.
+
+You swapped with the one at E4.
+
+And now you moved
+that piece to F5.
+
+So the one that was
+E4 is now on F5.
+
+And the opposing piece is now
+on D5, because you swapped.
+
+You can swap and then rotate.
+
+So instead of just
+having a third square,
+
+you would just have a rotation.
+
+And at the end, you
+could see who won.
+
+So in this one, lavender
+one because it's 0-1.
+
+But 1-0 would mean
+tangerine wins.
+
+And half and half
+would be a draw.
+
+So you can look at the
+logs for your games.
+
+Yes?
+
+AUDIENCE: [INAUDIBLE]
+
+HELEN XU: There's a
+rotate up and rotate down.
+
+AUDIENCE: [INAUDIBLE]
+do a U-turn?
+
+HELEN XU: Oh, is that what U is?
+
+AUDIENCE: Yeah, U-turn.
+
+HELEN XU: Oh I, see because
+there's only three rotations.
+
+Yes, sorry, so left is 90.
+
+Then right is 270.
+
+And U is 180,
+because you flip it.
+
+Is everyone good
+on the notation?
+
+This is just how you
+describe the games,
+
+if you wanted to
+look at your logs,
+
+and if there are some issues.
+
+So you can test your bot with
+other teams in the class,
+
+as well as with staff bots
+on the scrimmage server.
+
+And we have a reference,
+which is here, which
+
+is just the additional release.
+
+But we will be optimizing
+our bots while we're
+
+optimizing your bots.
+
+And we'll release a reference
+plus, and maybe an even better
+
+one later, which you can play
+with on the scrimmage sever.
+
+So I'll just do a
+really quick demo.
+
+So right now, since we haven't
+done the team formation yet,
+
+you are not able
+to log into this.
+
+But once you do your
+team formation, probably
+
+by tomorrow, you'll
+be able to log in.
+
+And, basically, you can see
+the general functionality.
+
+So this updates your
+player, pulls your player
+
+from your repo, whatever's
+on the master branch.
+
+And then right now,
+there's only reference,
+
+and reference plus,
+and reference TAs.
+
+And here's a team
+with me and Jess.
+
+But later on, we'll
+populate this list
+
+with everyone in the class.
+
+And then you can
+challenge anybody else
+
+in the class to see how you do.
+
+You can also challenge us.
+
+So you would just
+pick, for example,
+
+let's say I wanted to
+challenge reference.
+
+And then a hit send challenge.
+
+Now, you can see that there's
+some new matches spawned.
+
+And this is how I look at all
+the matches that I've played.
+
+So each time you
+hit send challenge,
+
+it spawns off two games,
+one where you're tangerine,
+
+and one you're lavender.
+
+So that's how you can watch
+the matches on the scrimmage
+
+server.
+
+Everyone good?
+
+I'm going to move on so
+don't run out of town.
+
+You can watch them later.
+
+And you can even play your own.
+
+OK.
+
+And, in addition to
+the scrimmage server--
+
+so the scrimmage
+server, you can only
+
+spawn off one game at a time.
+
+But you can do more.
+
+And you don't have
+to necessarily do it
+
+on your master branch,
+or against opposing teams
+
+in the class.
+
+So there's something called the
+Cloud autotester, which you can
+
+run by going to your Athena.
+
+And then you type
+in this command.
+
+You do autotest run.
+
+And then you do
+the time control.
+
+And you give it a number of
+games that you want to run.
+
+And then you give it
+a list of binaries.
+
+So I'll go into each of
+these in more detail.
+
+So the time control is just what
+I talked about earlier, which
+
+is if you use Fisher time
+control, these are some set,
+
+preset things.
+
+So you would type in one
+of the preset things.
+
+So you would talk in blitz to
+do 60 and 0.5, for example.
+
+And the number of games is
+just whatever you want to do.
+
+And the list of
+binaries-- so let's
+
+say you had a
+reference invalidation,
+
+and then you made some change.
+
+So I called it
+Lesierchess with changes.
+
+And then you would
+just put those
+
+after the number of games,
+separated by spaces.
+
+And then it would
+upload your binaries,
+
+and play them in the
+cloud auto tester.
+
+And once you submit your
+job, you get a link.
+
+And you follow the
+link in your browser.
+
+And you can view
+the game running.
+
+And then after the
+games are done,
+
+you will get some output saying
+like, which bot, one more?
+
+And how many times have
+won, and some rankings.
+
+Yep?
+
+AUDIENCE: How fast do they run?
+
+HELEN XU: How fast do they run?
+
+AUDIENCE: [INAUDIBLE]
+
+HELEN XU: So it depends on
+how many other games are
+
+queued at the same time.
+
+So if a lot of people
+are running tests,
+
+it might take some time.
+
+But blitz is just how long
+the game itself will take.
+
+And it might take
+longer than 60 seconds,
+
+because if you use less than
+0.5 seconds in your move,
+
+and then you add 0.5 seconds
+at the end of the move,
+
+then you would
+increase your time.
+
+But 60 is just the time control.
+
+Each side starts
+with 60 seconds.
+
+And depending on how they use
+it, they have more or less.
+
+Good question.
+
+Well, I'll keep going.
+
+And if there's time at the end,
+I'll do a demo of this one too.
+
+But it basically looks the
+same as the scrimmage server.
+
+Like, you just watch the
+games in the same way.
+
+So now, I'm going to go into
+the project organization, which
+
+is the organization
+of the directories
+
+that we handed out in this repo.
+
+So there are some directories.
+
+The first one is doc,
+which just includes
+
+the rules and documentation
+for the interface.
+
+There's the auto tester, which
+is the Java local auto tester.
+
+So if the cloud--
+
+we recommend that you run tests
+using the cloud auto tester.
+
+But if there's some small
+change, or if you think that--
+
+if the cue is too long,
+then you can do local tests.
+
+And you can also
+run these overnight.
+
+There's pgnstates, which
+just parses your statistics
+
+from the auto test results,
+like how many times you won,
+
+stuff like that.
+
+There's tests, which is
+how you specify tests.
+
+And I'll go into more detail
+about how you define this.
+
+There's the player, which
+is where you're actually
+
+going to be optimizing.
+
+So player is the
+code that actually
+
+runs the bot to play the game.
+
+And the webgui is a local webgui
+where you can watch the game
+
+and play it.
+
+So in the webgui, you can even
+play it yourself as a human
+
+so you can get a better
+sense of how the game works.
+
+To go into more detail,
+the Java local auto tester
+
+is an auto tester.
+
+You can make your changes, and
+then you can test your changes.
+
+And the test directory, which is
+parallel, holds configurations.
+
+So you can specify the
+number of games and the bots
+
+that you want to use,
+and the time control,
+
+and other things too.
+
+So this an example
+of the configuration
+
+file that you would use
+to run your auto tester.
+
+So this is saying that
+you run it on 12 CPUs.
+
+And book means that
+you're pointing
+
+to open a book, which
+I'll talk about later.
+
+Game rounds is how many games
+you're going to spawn off.
+
+Title is just the title of
+the test that you're running.
+
+And after that, you have
+the player definitions.
+
+So player reference
+is just the binary.
+
+And invoke is the
+path to the binary.
+
+And then fis is
+the time control.
+
+And the next one is
+just a second binary,
+
+if you made a change and
+you want to test them.
+
+Yeah, that's the binary.
+
+To interface with auto
+tester, Lesierchess
+
+uses the universal
+chest interface, or UCI,
+
+which is a communication
+protocol for automatic games.
+
+And you pass information between
+the auto tester and your bot.
+
+And it allows the programmer
+or the auto tester
+
+to enter moves to
+the game engine.
+
+So you could use UCI
+to start up your bot.
+
+And then you type in
+the moves that you
+
+want to make to see the
+changes in the state.
+
+And you could use this to
+debug to get to a state
+
+that you want to look at.
+
+We'll measure the bots
+using Elo ratings.
+
+So Elo is a rating system
+that measures relative skill
+
+level in zero sum games.
+
+The Elo rating depends on the
+Elo rating of your opponents.
+
+And on the bottom, you
+can see an example output.
+
+So I had three binaries.
+
+And I ran about 100 games.
+
+And you can see that
+the Elo of the top one
+
+is much higher than
+the other ones.
+
+And so higher Elo is good.
+
+And we'll be comparing
+the performance.
+
+We'll be comparing the Elo of
+your bot against our reference,
+
+and improved reference
+implementations.
+
+So notice that this
+is not, as before,
+
+just a straight measure of time.
+
+So like before, in
+previous projects,
+
+if you used less time,
+than you would get a higher
+
+grade or better performance.
+
+In general, I'll show
+you a graph later
+
+that actually shows if
+you searched the higher
+
+depth, which means that you
+are faster, you do improve.
+
+But it's not an
+exact correlation.
+
+And you can look at
+the nodes per second
+
+that you search using the UCI.
+
+And just above here, to local
+webgui lets you watch a game,
+
+or play one, without sending
+it to the scrimmage server.
+
+So if you wanted to
+play one as a human,
+
+you would use the local webgui.
+
+And you can run it using
+the commands in the readme.
+
+OK, so is everyone good so far?
+
+Now, I'm going to go into more
+details about how you actually
+
+play the game.
+
+So first, every
+player, or every bot,
+
+needs to generate
+the moves, which
+
+means that once you
+have a position,
+
+you need to look at the
+moves that you can do.
+
+And to do that, you need a
+board representation, which
+
+is to represent what
+pieces are on the board,
+
+and how big the board is,
+and where the pieces are.
+
+And the reference implantation
+uses a 16 by 16 board
+
+to store an 8 by 8 board.
+
+So you can see that the inner
+squares is actually the board.
+
+And the outer dark
+square is sentinels.
+
+So you use sentinels
+to keep track
+
+of when you go off the board.
+
+And then the inner square
+is just the actual board.
+
+We store the position
+using this struct.
+
+So you can see the fields in the
+position, which are the board.
+
+And the array size
+is just representing
+
+the board, plus the sentinels.
+
+And there's the history
+of the position,
+
+which is, how did we get here?
+
+And there's a key, which is
+a hash key for this position.
+
+There is ply, which tells
+you what side it is.
+
+So even means white.
+
+And odd means black.
+
+There is, what was
+the last move that was
+
+made to get to this position?
+
+There's a victim struct,
+which is the pieces destroyed
+
+by when you shot the laser.
+
+And there is the
+location of the kings.
+
+The position struct
+and Lesierchess struct
+
+stores the border
+presentation and other things
+
+that I just went through.
+
+So I talked about this move,
+which means just like a move
+
+that you make for
+one of your pieces.
+
+And I'll go into how
+it's represented.
+
+So right now, we already
+do the packing for you.
+
+So we use 28 bits.
+
+And the first two
+are the piece type.
+
+So there's a number of
+moves that you can make.
+
+And the first two bits
+represents the piece type,
+
+which is empty, pawn,
+king, or invalid.
+
+The orientation of
+the piece, which
+
+is just how you rotated it.
+
+The from square, which is where
+your piece already started.
+
+There's the intermediate
+square, which
+
+is used when you do a swap.
+
+And there's a two square,
+which is the final position
+
+that your piece will end up in.
+
+So if you're not doing a swap,
+then the intermediate and from
+
+should be the same.
+
+But if you are doing
+a swap, then there's
+
+some skipping that happens.
+
+At each turn, you
+need to see what
+
+moves you could possibly make.
+
+And in move gen, which is one
+of the files in the handout,
+
+we generate all the
+moves, given a position,
+
+depending on whose turn it is.
+
+So depending on
+whose turn it is,
+
+you can make different moves.
+
+And in the reference
+implantation,
+
+we iterate through
+the entire board.
+
+And once we find a piece,
+we generate all the moves
+
+from that piece.
+
+You can also debug
+using move generation.
+
+So there's something
+called perft,
+
+which is a debugging
+function that enumerates
+
+all moves at a certain depth.
+
+So use perft to make sure that
+if you make changes to the move
+
+generation that
+you're generating
+
+the same number of moves.
+
+And if you modify
+the move generated,
+
+just make sure that
+it returns the same,
+
+because regardless
+of what optimizations
+
+you do, you still should see the
+same moves from each position
+
+that you can possibly make.
+
+OK, so now that we talked
+about move generation,
+
+I'll talk about how you
+tell that a move is good.
+
+And for that, we use something
+called static evaluation.
+
+So we use static
+evaluation to determine
+
+which positions are
+better than others,
+
+and which moves
+that we should make.
+
+And the function eval,
+which is in eval.c,
+
+generate a score
+based on a position,
+
+using some heuristics.
+
+And at first, we suggest,
+instead of making up
+
+your own heuristics,
+we suggest focusing
+
+on optimizing the existing
+structs and evaluation
+
+heuristics before
+coming up with new ones,
+
+because it's kind of hard
+to come up with new ones.
+
+And there's a lot
+of optimizations
+
+that you can make to
+the existing ones.
+
+So I've just grouped
+these into categories.
+
+So there's a few
+regarding the king.
+
+So there's one
+called KFACE, which
+
+is a bonus for your king
+facing the enemy king.
+
+There's KAGGRESSIVE,
+which gives you
+
+a bonus for if
+your King is closer
+
+to the center of the board.
+
+And there's MOBILITY,
+which counts up, basically,
+
+how many squares around
+your king are free.
+
+You want to be able to
+move your king freely.
+
+And there's some
+regarding pawns.
+
+So there's PCENTRAL, which gives
+you a bonus if your pawns are
+
+in the center of the board.
+
+And there's PBETWEEN, which
+basically draw a bounding box
+
+with both kings at the corner.
+
+And then you count
+how many pawns
+
+are in the center of those.
+
+And then there's points
+based on distance.
+
+So there's LCOVERAGE, which
+means laser coverage, which
+
+is basically you make all
+the possible moves that you
+
+can make from your position.
+
+And then you draw
+the laser path.
+
+And then you do some
+scaling to determine
+
+how well you can
+possibly cover the board,
+
+based on your current position.
+
+So that's basically how you tell
+if a position is good or not,
+
+with these heuristics.
+
+So I'll just go through the
+high level of how you actually
+
+play the game using search.
+
+So at the very
+highest level, there's
+
+something called game
+search trees, which
+
+is we've invented in search.c.
+
+But, basically, this
+is a representation
+
+of how you play the game.
+
+At the top, there's
+an orange square,
+
+which is the orange side,
+which is the opening
+
+position, and then the arrows.
+
+So the top square--
+
+actually, all the nodes
+are positions in the tree.
+
+And you use move generation
+that I just talked about,
+
+to enumerate all the possible
+moves from a single position.
+
+And each edge is a move.
+
+So to get from position
+to position, you do moves.
+
+And you can see that
+circle is the position
+
+after you've made the move.
+
+And you do this tree
+to some depth d.
+
+And then you do static
+evaluation of the leaves.
+
+So this is at a really high
+level how game playing programs
+
+actually play the game.
+
+They enumerate all
+the possible moves.
+
+And then they have a position.
+
+And then they pick which one
+is best, based on evaluation.
+
+But you can see that
+there's a lot of nodes.
+
+Like, if you do this
+naively, there'd
+
+be number of moves raised to
+d, which is a huge number,
+
+and too many to generate.
+
+So we're going to talk about
+how you reduce those later.
+
+There's something that you have
+to do on search series, which
+
+is called Quiescence
+search, which
+
+is if you fix your depth--
+
+let's say you fix depth, and
+then you go down to the leaves,
+
+and you just captured a piece.
+
+But it's dangerous to just
+stop there at fixed depth,
+
+because maybe if you
+searched one level deeper,
+
+you would see that the opponent
+would capture your piece.
+
+And so if you do
+your search, and you
+
+see that you capture
+a piece at the leaves,
+
+or your opponent captures the
+piece at the leaves, we say,
+
+that's not quiet.
+
+And you keep searching
+the tree until there
+
+are no more captures.
+
+So that's called
+Quiescence search,
+
+because you quiet the position.
+
+And that's implemented
+in the search column.
+
+So this is a graph
+that I generated
+
+by doing the reference
+spot to different depths.
+
+And you can see that
+the Elo increases as you
+
+increase the search depth.
+
+So you just search
+the search tree.
+
+And so if you optimize
+your bot to make it faster,
+
+you can search deeper, which
+means that you'll do better.
+
+So next, I'll talk about
+min-max search, which
+
+is a more complex
+version of searching
+
+that can improve the amount
+of nodes you have to evaluate.
+
+So at a high level, there's
+two players, max and min.
+
+And in our example,
+there's orange and purple.
+
+And orange is a square.
+
+And purple is a circle.
+
+And the game trees
+represents all moves
+
+from the current position from
+a given ply, which means depth.
+
+And if the leaves,
+like I said, you
+
+play a static
+evaluation function.
+
+And max chooses the maximum
+score among its children.
+
+And min chooses
+the minimum score.
+
+So one side is
+trying to maximize,
+
+and one side is
+trying to minimize.
+
+To evaluate the
+search try, I'll first
+
+talk about an algorithm
+called alpha beta, which
+
+is that each search from a
+node has a window alpha beta.
+
+And if the value of the
+search falls below alpha,
+
+the move is not good enough,
+and you keep searching.
+
+And if the value falls
+within alpha and beta,
+
+then you increase your alpha,
+which is the lower bound,
+
+and you keep searching,
+because you know
+
+you can do at least that well.
+
+And if the value of the
+search falls above beta,
+
+than you generate a
+beta cut off in return.
+
+Beta basically means one
+side is trying to maximize,
+
+and one side is
+trying to minimize.
+
+So beta is basically
+saying, the opponent
+
+would never let you do that
+move, because it'd be too good.
+
+So you don't need to keep
+searching there, because you're
+
+not going to get there anyway.
+
+So I'll do an example.
+
+Let's say you have this tree.
+
+And if max discovered a
+move that min wouldn't
+
+let you do, because
+it's too good,
+
+then max's other
+children don't need
+
+to be searched, which is
+what a beta cut off is.
+
+So you'd start at the root.
+
+And then you go down to
+the lowest left leaf.
+
+And you see that it's three.
+
+So you propagate three up.
+
+And then you can see
+that in this sub-tree,
+
+you can do at least three.
+
+And then you keep
+searching your children.
+
+And then you see six.
+
+And then you say, OK, now
+you update your alpha value
+
+to be six.
+
+Now, you search four.
+
+But four is worse than six.
+
+So you don't have
+to do anything.
+
+So you first search
+the leftmost subtree.
+
+And then you see the best
+move that you could possibly
+
+make there.
+
+So you propagate
+six up to the root.
+
+And then you search
+your other subtrees.
+
+But now, you have
+this value of six
+
+that you basically use
+in the other subtrees.
+
+So you look at two.
+
+And you see that two
+is less than six.
+
+So you propagate it up.
+
+But now, you look at nine.
+
+And you see that nine
+is greater than six.
+
+So you say that this subtree
+would let purple do nine,
+
+which is greater than six.
+
+And so that would be too good,
+because orange would never
+
+let purple do that well.
+
+So you don't have to
+evaluate five anymore.
+
+So you cut off five.
+
+Does that make sense?
+
+OK, so, basically, now
+you apply the same thing
+
+to the regular subtree.
+
+And you look at seven.
+
+And you see that seven
+is greater than six.
+
+So you propagate that up.
+
+And now you're done, because
+seven is greater than six.
+
+So you don't have to search
+the rest of the subtree.
+
+So that's how you evaluate fewer
+moves than the entire tree.
+
+And there's a theorem
+that says for a game tree
+
+with branching factor b and
+depth d, and alpha beta search
+
+with moves searched
+in best-first order
+
+examines exactly b
+raised to the d over 2,
+
+plus b raised to the d over
+2 minus 1 nodes apply d.
+
+So best first order means that
+you sorted the moves in terms
+
+of your static evaluation.
+
+The naive algorithm
+examines b to the d nodes.
+
+And in the example I did,
+you can see how you prune.
+
+And for the same work, the
+search stuff is doubled.
+
+And for the same depth,
+the work is square rooted.
+
+So this is a huge benefit
+over the naive evaluation.
+
+Is everyone good on alpha beta?
+
+Great, so the code
+is pretty short.
+
+So I'll just go through
+some pseudocode for it.
+
+Basically, the main
+point is that at line 11,
+
+one side is trying to
+minimize and one side
+
+is trying to maximize.
+
+But if you negate, then
+that's just the same
+
+as minimizing and maximizing.
+
+And you get all
+the possible moves
+
+that you could possibly
+make using gen moves.
+
+And you go through
+the entire move list.
+
+And then you make
+each of the children.
+
+And you search for the score.
+
+And then you see whether
+you had a beta cut off.
+
+And then you don't need to
+search the subtree If you did.
+
+So that was basic alpha beta.
+
+And we actually implement a
+variation of alpha beta called
+
+principle variation search.
+
+And the main idea is that you
+assume that the first move is
+
+the best one.
+
+And you run scout search, which
+is also called zero window
+
+search, on the remaining moves
+to verify that they're worse.
+
+So in this example, you,
+again, search the most leftmost
+
+subtree.
+
+And you see that the best you
+can do in the left-most subtree
+
+is three.
+
+And you evaluate the
+ones to the right
+
+of it using scout search,
+which is not a full search.
+
+You're basically
+assuming that you
+
+can do no better than three.
+
+And then now you're kind of
+doing an initial search to see
+
+whether or not that's true.
+
+And see you see that
+some of them are--
+
+the one after that is seven.
+
+The first one after
+that is seven.
+
+And the one after that in
+the other subtree is six.
+
+So then you can prune them,
+because those are better--
+
+because you know
+already in those
+
+subtrees that you can
+do better than three.
+
+So you don't have to
+keep evaluating them.
+
+And you don't have to-- yeah?
+
+AUDIENCE: How do we know
+the score of the subtree
+
+before we evaluate?
+
+How can we prune something?
+
+HELEN XU: So you actually
+had to find seven.
+
+Like, zero and eight are there.
+
+But you haven't found them yet.
+
+So, basically, if you thought
+about doing it serially,
+
+you do the leftmost subtree,
+which has 2, 3, and 0.
+
+And then you would find seven.
+
+And that would be a
+cut off, because seven
+
+is bigger than three.
+
+So you're not actually
+finding zero and eight.
+
+The point is that you
+wouldn't get to that subtree,
+
+because the opponent
+wouldn't let you get there,
+
+because you can do too well.
+
+So they would just not
+let you go down that path.
+
+Like, let's say you were purple,
+and the opponent is orange.
+
+And you want to get 7 and 8.
+
+But the opponent can
+also search that, and see
+
+that you would get 7 and 8.
+
+So they would prefer you to do
+something like two or three.
+
+AUDIENCE: So what
+do you do instead?
+
+HELEN XU: You're not always
+making the best move that you
+
+could possibly do, because--
+
+like, if you just searched
+without this pruning,
+
+and you just picked--
+
+let's say you wanted
+to make the best move.
+
+Like, if you don't take
+into account the opponent,
+
+then you're never
+going to get to there.
+
+So you're basically
+trying to find a move
+
+that the opponent
+would let you get
+
+to that's also good for
+you, because you switch off.
+
+Yes?
+
+AUDIENCE: [INAUDIBLE]
+
+HELEN XU: I guess in this
+example, you're purple.
+
+No, sorry, you're orange,
+because you're cutting off--
+
+no, you're purple,
+because you're
+
+trying to maximize what
+you get at the leaves.
+
+AUDIENCE: [INAUDIBLE]
+
+HELEN XU: Yes.
+
+The main point of-- sorry.
+
+AUDIENCE: Oh.
+
+We're trying to
+minimize the score.
+
+HELEN XU: Yes.
+
+So orange is trying
+to minimize the score.
+
+And purple is trying
+to maximize the score.
+
+AUDIENCE: So we're
+cutting that off,
+
+you're saying you don't need to
+search this because we already
+
+know they're the same here.
+
+So we shouldn't go
+down this path anyway.
+
+HELEN XU: Does anyone
+have questions?
+
+Does that make sense?
+
+Yeah, it's basically
+exactly as you said.
+
+So there's kind of this balance
+between one side trying--
+
+both sides are just
+trying to make--
+
+you're trying to
+make good moves.
+
+But you're also trying
+to make the opponent make
+
+not good moves, if
+that makes sense.
+
+So you're not only
+searching for your maximum.
+
+But you're also searching
+to minimize the opponent.
+
+Good question.
+
+AUDIENCE: [INAUDIBLE]
+
+HELEN XU: Sorry?
+
+AUDIENCE: So we
+don't want to choose
+
+either of those orange ones.
+
+We don't want to let--
+
+I think it's OK.
+
+I think you can move on.
+
+HELEN XU: Oh, OK.
+
+Yes?
+
+AUDIENCE: What if
+you and your opponent
+
+have different reward criteria?
+
+Like, you guys evaluate--
+
+HELEN XU: That's OK.
+
+It's fine.
+
+The actual evaluation,
+like what number
+
+you assign to each position,
+is not exposed to the opponent.
+
+The main point is that, at the
+end of each move, you pick one.
+
+And they can do with
+it what they want.
+
+Like, that may not have
+been the one they picked.
+
+But it's OK.
+
+Sorry, I think you're
+orange in this one,
+
+because the root is orange.
+
+AUDIENCE: [INAUDIBLE]
+
+HELEN XU: So let's start over.
+
+So I think that we are orange.
+
+So remember that
+each edge is a move.
+
+And each node is a position.
+
+And so you're orange.
+
+And you start at the root.
+
+And now you, for example,
+make the move left.
+
+And purple now can make moves
+whatever three after that.
+
+And now, you're orange again.
+
+And then you can make
+moves after that.
+
+And now, you evaluate the
+position after that as a leaf.
+
+And so, basically,
+you're searching
+
+past like the second
+level of orange.
+
+And you are cutting off if you
+see that you would do better,
+
+because you think that
+purple would never
+
+let you get to that
+orange node right above.
+
+Yes?
+
+AUDIENCE: [INAUDIBLE]
+
+HELEN XU: Yeah, I guess
+that's the score that you,
+
+as orange would receive.
+
+Yes?
+
+AUDIENCE: [INAUDIBLE]
+
+HELEN XU: You're
+not trying to give--
+
+it's not so much like you're
+trying to give purple zero,
+
+as you think that purple would
+not give you seven and eight,
+
+because purple would have
+to go down the left subtree
+
+to give you that.
+
+Any other questions?
+
+I'm going to move
+on with the search
+
+then, if there are no questions.
+
+[INTERPOSING VOICES]
+
+HELEN XU: Is everyone good?
+
+Can I keep going?
+
+OK, so just going back to
+principal variations pruning,
+
+the main idea is
+that you go down
+
+the first path on the
+left side, thinking
+
+that that's the best path.
+
+And then you're basically
+doing initial passes
+
+through the trees to make
+sure that your assumption is
+
+correct.
+
+And if they're not
+correct, then you
+
+have to search the
+entire subtree.
+
+But if they are correct,
+then you kind of
+
+fail, you early exit.
+
+So you search down
+the left subtree.
+
+And you find three in
+the leftmost subtree.
+
+And now, you search the
+ones to the right of that.
+
+And those are seven and eight.
+
+So those produce a cutoff,
+because seven and eight
+
+is higher than three.
+
+So you think that
+purple would not
+
+let you get to that subtree.
+
+And now, you do a scout search
+again on the middle subtree.
+
+And then you see that--
+
+you find this first node of
+each one of those subtrees
+
+underneath the middle subtree.
+
+And you see that they're
+all higher than three.
+
+So it turns out that you
+failed to prove that you
+
+can do no better than three.
+
+The main point of
+the scout search
+
+is that you assume that your
+first move that you search
+
+is the best you can do.
+
+And then you do initial passes
+to verify that assumption.
+
+And if you search later
+subtrees, and you find that--
+
+for example, in this
+one in the middle,
+
+they're all higher than threes.
+
+So your assumption is not true.
+
+So now you have to
+do a full search
+
+of that entire middle subtree.
+
+Is that OK?
+
+Are there questions?
+
+So once you find that you
+have to actually search
+
+the middle subtree, you can
+recursively apply scout search.
+
+So you have to search the
+left subtree in the middle.
+
+But now, you apply scout
+search to the lower middle
+
+and the lower right.
+
+And you do a zero
+window search there.
+
+And, again, you assume that
+you can do no better than six.
+
+And now, you're trying
+to verify that you
+
+can do better than six.
+
+But you actually can.
+
+So you have to search them.
+
+And then you apply the same
+thing again to the subtree.
+
+And you see that you
+can do better than six
+
+on the left one.
+
+But you do worse than
+six on the right one.
+
+And you cut off two, because the
+middle subtree already gave you
+
+two.
+
+And so you don't have
+to search that one.
+
+So in this example, there
+were 13 leaves pruned.
+
+And the point of scout
+search is that you
+
+can improve pruning a
+little bit over alpha beta,
+
+and that you process
+most of the game tree
+
+with zero window searches.
+
+The main point is that it
+reduces your work, because you
+
+have to process less.
+
+Questions?
+
+So now we're going to talk
+about-- so I kind of glossed
+
+over how you order the moves.
+
+So the ordering
+determines which order
+
+you explore the subtrees in.
+
+Alpha-beta search and
+principal variation search
+
+depend on putting the
+best moves in the front
+
+to trigger an early cut off.
+
+And the main question
+is, how do we
+
+determine moves,
+which moves are good,
+
+without doing static
+evaluation at every level?
+
+Like, for example, we
+only did static evaluation
+
+with the leaves.
+
+And we can't get
+sortable move list,
+
+which is a function in search.
+
+And sortable move
+lists, kind of talk
+
+about how you
+populate that later.
+
+As I said before, moves are
+represented in 128 bits.
+
+So you can use it in 32.
+
+And to make them sortable,
+you store a sort key
+
+in the upper 32 bits in 64.
+
+And then you sort,
+based on that key.
+
+That make sense?
+
+So I'll just go over some search
+optimizations that you can do.
+
+We actually implement
+these already.
+
+So I'm just going
+to go through them
+
+so it's not super confusing
+when you look at the code.
+
+The most important one is
+called the transposition table.
+
+The main idea in the
+transposition table
+
+is that chess programs often
+encounter the same positions
+
+repeatedly during a search.
+
+And you can store those results
+in a transposition table
+
+to avoid unnecessary
+feature searches.
+
+And I've listed where
+you can find those.
+
+There's something
+called Zobrist hashing,
+
+which is a technique for
+hashing a board position which
+
+you use to index the
+transmission table.
+
+And it's a table of random
+numbers, indexed by piece,
+
+orientation, and square.
+
+So each position
+has a unique hash.
+
+And it produces the
+hash by exporting
+
+all of these random
+numbers together.
+
+And the advantage
+of Zobrist hashing
+
+is that the hash function can
+be updated incrementally, which
+
+is like if you move a
+position-- if you move a piece,
+
+you just xor it out.
+
+And then you xor
+the new one, so you
+
+don't have to recompute
+the hash each time.
+
+So the transposition table
+saves you a lot of work
+
+by preventing you from
+researching things.
+
+And there's also something
+called the killer move table.
+
+So the transposition
+table is like how
+
+you determine how to
+do sorting at things
+
+that are not the leaves, and
+also the killing moves table.
+
+So the killer
+moves people stores
+
+moves that are really good so
+that the opponent wouldn't let
+
+you go down that path,
+so you have to keep
+
+recomputing the same values.
+
+And the table is indexed
+by ply, because you
+
+tend to see the same
+moves at the same depth.
+
+So the killer move table,
+basically, just stores
+
+move that trigger the beta
+cut off before in your search.
+
+There's a best move
+table, which is stored
+
+at the root of the search.
+
+And it is the move that
+got the maximum score
+
+in your evaluation.
+
+And the best move table
+is indexed by color,
+
+piece, square, and orientation.
+
+And there's a history
+table in the code.
+
+So these are all,
+basically, just
+
+things to help you
+optimize your search,
+
+and produce early cut offs.
+
+And there's something called
+null-move pruning, which
+
+tries to reduce your
+search space by first
+
+not moving, and then doing
+a shallower search to see
+
+if this subtree is
+worth further exploring.
+
+Basically, it says,
+don't move, and then do
+
+a little bit of evaluation.
+
+And if you're still
+doing really well,
+
+even if you didn't
+move in the subtree,
+
+then it's not worth exploring,
+because the opponent
+
+would never let you go there,
+because the position is
+
+too good.
+
+There's futility
+pruning, which explores
+
+moves that only have the
+potential to increase alpha.
+
+And it calculates
+that possibility
+
+by adding a futility
+margin, which
+
+is the most you could possibly
+gain from going there, and then
+
+evaluating a little bit.
+
+And if the result does
+not go higher than alpha,
+
+then you skip it,
+because there's
+
+no point in even going
+that way, because it
+
+wouldn't increase your alpha.
+
+There's late move
+reduction, which
+
+is after you order the
+moves at a position,
+
+you explore the-- the-- ones in
+front are likely to be better.
+
+So you explore those
+in higher depth.
+
+And then you explore the ones
+later with shallower depth,
+
+because those are less
+likely to be good.
+
+And some things that
+you can optimize
+
+are implementing a
+better opening book.
+
+I think we have produced
+a very basic opening
+
+book in the handout.
+
+But this is something
+that you can definitely
+
+work on, and make better,
+because it doesn't have
+
+many positions in it right now.
+
+And the main point
+of an opening book
+
+is that you store the positions
+at the beginning of the game
+
+that you've already
+pre-computed.
+
+And that saves time and
+search, and can store results
+
+to a higher depth.
+
+And the KM75 theorem
+implies it's better
+
+to keep separate opening books
+than to keep the same opening
+
+book for both sides.
+
+So opening books
+are really helpful,
+
+because in the beginning,
+there's a huge number of moves
+
+that you could possibly make.
+
+And searching those
+takes a lot of time.
+
+But if you pre-compute them,
+you can save them for later.
+
+And another useful
+table you can keep
+
+is an end game
+database, which is
+
+a table for guiding your chess
+program through the end game.
+
+For end game positions,
+the distance from the end
+
+might be too far
+to search entirely.
+
+So you can pre-compute them.
+
+And then you store who
+will win, and how far you
+
+are from the end of the game.
+
+And we've given you a c file
+that you can implement it in.
+
+OK, so I'll just go
+through some guidelines,
+
+some tips for the project.
+
+I was giving links
+at most of the bottom
+
+of the slides for where you can
+read up more on these topics.
+
+But there's a chess
+programming wiki.
+
+The link is there, which has
+many more pages about reading
+
+about chess playing programs.
+
+Just in general, it's
+a really good idea
+
+to test your code
+often, because it's
+
+easy to make a mistake
+with your optimizations.
+
+And it doesn't appear when
+you search to fixed depth.
+
+So if you start up your
+bot, you can say, like,
+
+search to depth 5, for example.
+
+And then it will tell you like
+how many nodes per seconds
+
+you searched.
+
+And then I'll tell you the best
+move at the end of that search.
+
+But you should test
+full games using
+
+the auto tester, and
+the cloud auto tester,
+
+and the script server,
+just to watch your bot
+
+to make sure that it
+doesn't do anything weird.
+
+And the testing methodology,
+I went through some of it.
+
+There's a webgui.
+
+There's a Java autotester.
+
+There's a cloud autotester.
+
+And you can do node
+counts, which is basically
+
+just counting the number
+of nodes in the tree
+
+that you searched.
+
+And there's function
+comparison testing,
+
+which is, if you
+optimize a function,
+
+you should save the
+old version, and then
+
+just compare the results.
+
+PROFESSOR: Let me make
+a comment about testing.
+
+I can't tell you how
+often in this class
+
+we've had student groups
+who discover that they've
+
+made a whole bunch of changes.
+
+And then there's something
+wrong with their bot.
+
+And they can't get
+back to a stable place
+
+when things were correct.
+
+They discover the problem.
+
+But they've made 30 changes.
+
+And now, which of those 30 is
+responsible for the problem?
+
+So it's really
+important to test,
+
+and have a good
+test infrastructure
+
+for this project.
+
+If you have a really
+good test infrastructure,
+
+it's really easy to be
+innovative in the kinds
+
+of optimizations that
+you do, because then you
+
+know that what you're
+doing is right.
+
+And then you can make
+forward progress.
+
+Otherwise, you'll find yourself
+self debugging like crazy,
+
+and not being able
+to find the bugs.
+
+Some other tips
+are, especially when
+
+we get to the
+parallel part, it's
+
+non-deterministic programming.
+
+And the reason is
+because as you're
+
+executing you're going
+to be looking up things
+
+in transposition table that
+you're going to want to share,
+
+so that if one branch
+discovers a value then
+
+another branch can use that.
+
+So it's really important
+to be able to turn that
+
+off so that you're, for
+example, able to search
+
+without a transposition
+table to get all
+
+the searching stuff right,
+and be able to turn that
+
+on independently.
+
+So that's another really
+important place to do it.
+
+Another thing is that when
+you do timed searches,
+
+the time it takes to do
+the search will vary.
+
+And what you'll end
+up exploring varies.
+
+So as much as possible, you
+wanted to fix depth searches.
+
+Search to five ply
+to test something,
+
+rather than searching
+for a minute,
+
+or whatever the
+amount of time is,
+
+because when you start
+searching for time,
+
+that's, in fact, what you're
+going to end up doing.
+
+But you can't repeat what
+just happened if you end up
+
+searching for that
+amount of time
+
+again, because the machines
+are not deterministic.
+
+And there may be
+something else going
+
+on that causes the amount
+of time to be different.
+
+And so, for example, if
+you're making a change that
+
+doesn't affect the
+logic of the program,
+
+it's just strictly
+an optimization,
+
+you should get exactly
+the same result
+
+if you do a five ply
+search, for example.
+
+Shouldn't have changed
+the five ply search.
+
+Just a five ply search
+should be faster.
+
+And so that's a good
+way-- as much as possible,
+
+you want to check things that
+are deterministic and so forth.
+
+And, really, as I say, I
+can't emphasize this enough,
+
+how having a good
+test infrastructure,
+
+the ability to control
+turn off non-determinism,
+
+the ability to test various
+parts of this program,
+
+this is a pretty
+big piece of code
+
+for a project of this nature.
+
+And you'll feel pretty
+overwhelmed by it
+
+to begin with.
+
+Once you settle,
+you'll discover,
+
+it's this wonderful thing,
+where by the end of the project
+
+everybody feels really confident
+about their ability to handle
+
+a decent sized piece of code.
+
+But when you first get into
+it, it's like, oh my goodness.
+
+There's move ordering.
+
+And there's static evaluation.
+
+And there's the search.
+
+And what's going on with
+that transposition table?
+
+Because every one of
+these things has got
+
+cleverness in it.
+
+OK, so it's really
+hard code to deal with.
+
+But you guys are
+going to just fine.
+
+HELEN XU: So this is the
+eval.c file in the handout.
+
+So this in 32 here is
+the evaluation score.
+
+And the main function
+is called eval.
+
+And it takes in a position.
+
+And it outputs two scores, one
+for white and one for black.
+
+And right now, it does--
+
+I guess it does counts
+of the number of pawns.
+
+OK, so I was talking before
+about, p between and p central,
+
+which are you pawn heuristics.
+
+And so basically,
+right now, it iterates
+
+through the entire board.
+
+You can see for rank and
+file are just row and column.
+
+And it looks at each
+square in the iteration.
+
+And then it looks at the piece
+and the color of the piece.
+
+And based on the type of the
+piece, it does some evaluation.
+
+So if it's a pawn, it
+does the pawn heuristics.
+
+If it's a fits king, it
+does these king heuristics.
+
+And otherwise, or both--
+
+or not otherwise, I guess--
+
+yeah, in both cases it'll do--
+
+this is an old version.
+
+So it's not there anymore.
+
+But this is laser
+coverage, which
+
+we talked about
+earlier, which doesn't
+
+depend on what piece it is.
+
+This is after you iterate
+through the entire board.
+
+And then this isn't
+here anymore either.
+
+But we can look at
+each of these in depth.
+
+So right now, for
+example, there's
+
+p between, which goes
+through every single pawn
+
+in your iteration.
+
+And then it will
+determine whether or not
+
+it's between both kings,
+and the return slide.
+
+So it will add it to the score,
+if you find that it's true.
+
+And there's p central, which
+takes in a rank and a file.
+
+And, basically, it
+increments something,
+
+or it gives you a
+bonus, depending
+
+on how close you are to
+the center of the board.
+
+So look at this.
+
+There's a board with--
+
+and F as your file.
+
+And R is your rank.
+
+PROFESSOR: I think you have
+a slightly older version.
+
+HELEN XU: Potentially.
+
+PROFESSOR: It's
+correct on the screen.
+
+HELEN XU: Is
+correct in this one?
+
+AUDIENCE: Yeah.
+
+HELEN XU: OK, so
+this is just the--
+
+I guess is the most
+updated version.
+
+The first one is p central.
+
+So this just count
+the difference
+
+between where you are and
+the center of the board.
+
+And it gives you some
+bonus, depending on how far
+
+you are from the center.
+
+And this one is between.
+
+Yeah, so this is between, which
+is a helper for p between.
+
+And it tells you
+whether or not your pawn
+
+is in the bounding box
+determined by the kings.
+
+And this one is k face,
+which is given a king,
+
+you look at its orientation.
+
+And then you give it
+a bonus, depending
+
+on which way you're
+facing, and how far you
+
+are from the center, I think--
+
+no, how far you are
+from the opponent.
+
+So f and r where you are.
+
+And now it does the delta
+between you and the opposing
+
+king.
+
+And then you do some scaling,
+depending on which direction
+
+you're facing.
+
+So this is just
+your orientation.
+
+And then this is k
+aggressive, which
+
+gives you a bonus
+for how far you
+
+are from the edge of the board.
+
+So you can see here op square is
+where do the opposing king is.
+
+And delta file and
+delta rank are how far
+
+you are from the opposing king.
+
+And then you add the bonus,
+depending on which case
+
+the deltas fall into.
+
+And this gives you a
+bonus if you're farther
+
+from the edge of the board.
+
+Yeah, and there's
+l coverage, which
+
+is the most complicated
+one, probably.
+
+And, basically, what laser
+coverage does is that,
+
+basically, it takes a position.
+
+And depending on
+what side you are,
+
+it generates all the moves
+that you could possibly
+
+make from that position.
+
+So you generate all
+with color, which
+
+means that, given
+your color, you
+
+generate all the possible
+moves that you can make.
+
+And you get a list of moves.
+
+And you iterate through it.
+
+And then you make each of them.
+
+And you draw a laser path.
+
+And what the laser path
+does is, basically, it
+
+bounces off some pause.
+
+And for each square, you
+increment the distance,
+
+basically, along the path.
+
+And if it takes the
+minimum distance
+
+over all these possible
+paths for each square.
+
+And if it doesn't touch a
+square, then it's just 0.
+
+And it divides it.
+
+I can go into this.
+
+So it draws the path
+through this while true.
+
+Or this is just
+changing the orientation
+
+if you need to
+bounce off a pawn.
+
+But this one is setting the--
+
+you keep a laser map.
+
+And you keep the
+minimum path of a laser
+
+that would possibly touch that.
+
+And, no, this is just
+changing the orientation.
+
+So then you generate this map
+for all the possible moves
+
+that you could do.
+
+And then you do some scaling.
+
+So, depending on the distance
+from the opposing king,
+
+you iterate through
+the entire board.
+
+And you divide the
+minimum distance
+
+by the actual distance
+from the laser.
+
+So the maximum that
+this ratio can be is 1.
+
+And then you multiply it
+by 1 over the distance.
+
+So this one is
+really complicated.
+
+And there's a lot
+to optimize here.
+
+For example, you
+probably don't have
+
+to iterate through
+the entire board
+
+each time, because even
+in eval, like here, you
+
+have to iterate through
+the entire board
+
+to find each piece.
+
+And if you start a
+better representation,
+
+you might not have to do
+that, like if you just
+
+kept track of where
+the pawns were,
+
+because you already keep
+track of the king separately.
+
+So that's one thing you can do.
+
+PROFESSOR: There are
+two basic strategies
+
+for changing the
+representation of the board.
+
+And maybe there are more.
+
+But the two basic
+ones are, instead
+
+of keeping the whole board
+with a piece on each square,
+
+and then having to go and
+search for where the pieces are,
+
+you can keep just a list
+of where the pawns are,
+
+and what the locations
+of the kings are,
+
+so that when you
+want to make a move,
+
+you can just go
+through where they are,
+
+rather than having to search
+through all 64 squares
+
+on the board.
+
+Then the other strategy
+that you can do
+
+is use what's called
+bit boards, where
+
+you have a 64-bit word
+for which, if there's
+
+a pawn in a given
+position, you set that bit.
+
+And so there are different
+ways of representing
+
+things that could possibly be,
+definitely be, more efficient.
+
+But you have some choices there.
+
+And also, one of the
+complexities of this
+
+is that to change
+the representation,
+
+there's going to be
+places in the code you
+
+need to find out where they're
+assuming that things are.
+
+So you say, oh, I'll change
+the board representation.
+
+Oh, I didn't realize
+that over here, there's
+
+another place that it's using
+the board representation,
+
+and so forth.
+
+A good strategy for changing
+board representation
+
+is to actually keep both
+representations around
+
+while you migrate
+functionality from the old one
+
+to the new one.
+
+And then the advantage of
+that is that you can actually
+
+then use assertions
+to say, you know,
+
+the old one and the
+new one are the same.
+
+So implementing conversion
+functions is really good.
+
+For example, if
+you decide you're
+
+going to use a bit
+board representation,
+
+have a function that
+converts the bit board
+
+to the standard board
+so that then you
+
+can compare whether
+you've got the same thing.
+
+And, eventually, you'll
+want to get rid of that.
+
+And, of course, that'll
+slow down you down,
+
+because you're
+doing more things.
+
+But it will allow
+you to get it correct
+
+with a new representation.
+
+And once you've got it correct
+with a new representation
+
+with the old one gone,
+that's when you have a chance
+
+to make things go fast.
+
+But it kind of is taking
+two steps backwards
+
+to take five steps forward.
+
+I say not one step and two
+steps, because really, often,
+
+you really are slowing things
+down considerably in order
+
+to convert from one
+representation to another.
+
+The most important thing is
+you maintain the invariant
+
+of correctness in your code.
+
+You do not want
+to make something
+
+that goes faster, but
+is wrong, and have
+
+to debug the correctness.
+
+You'd much rather ensure
+that things are correct,
+
+are moving to the place
+that you want to do it.
+
+And then you can
+optimize for performance.
+
+So the most important
+thing is keep
+
+that invariant of correctness.
+
+And that's where
+the testing and so
+
+forth comes in, having
+good test infrastructure,
+
+and having assertions
+littered throughout your code.
+
+HELEN XU: And then we can
+go through the [INAUDIBLE]..
+
+Actually, OK, so,
+just as an example
+
+of how you would
+possibly, one way
+
+of determining whether or
+not you state correct--
+
+so this is an example of a
+place where I compiled the code.
+
+See the binary code
+is called Lesierchess.
+
+And if you look at help,
+it gives you some options
+
+for what you can do.
+
+For example, there's display.
+
+And that's the opening position.
+
+And let's say I want to search.
+
+So I do a fixed depth,
+and go depth three.
+
+And it tells me
+the number of nodes
+
+that I searched at each depth.
+
+And so if you make changes,
+if they are deterministic,
+
+these node counts
+should stay the same.
+
+So that's one way of telling.
+
+So you should keep
+track of this,
+
+and make sure that
+they're the same.
+
+And also, you can
+do perft, which
+
+gives you the number of
+possible moves you can make.
+
+And that should be the
+same, no matter what you do.
+
+So that's one way of testing.
+
+There's other ways.
+
+So if you go to higher depth,
+you'll get more node counts.
+
+And here, this is nodes that
+you searched at this depth.
+
+And this is nodes per second.
+
+So you want to make
+this one faster.
+
+So that's how you run the code.
+
+And I was supposed to do a
+demo for the auto tester.
+
+So let's say I wanted to do--
+
+so when I made it, it's in
+a binary called Lesierchess.
+
+And then here, you
+can type in commands.
+
+So you're basically just
+typing commands from this.
+
+Like, you run your binary.
+
+PROFESSOR: This is the UCI
+interface that we talked about.
+
+And in Lesierchess.c is
+the implementation of that.
+
+And so if you want to add your
+commands to it to help debug,
+
+you can enter-- if we
+go into Lesierchess.c,
+
+you can see the table.
+
+What I want to do
+is show the table
+
+of all the options, which is--
+
+there we go, OK.
+
+HELEN XU: This is
+just the heuristics.
+
+PROFESSOR: So these are
+tables of heuristics
+
+and so forth, which
+allow you to set
+
+the values of the
+various things,
+
+and to say, how much
+is this heuristic
+
+worth to the static evaluation?
+
+And through these,
+all these can be
+
+set, so you don't
+have to recompile
+
+the binary if you want to try
+out things with different--
+
+if you want to
+auto test with, let
+
+me count this as worth
+a third of a pawn.
+
+Let me count this as worth
+half a pawn, or whatever.
+
+You can just enter it
+through the UCI interface.
+
+And in the auto tester,
+you can specify that.
+
+So it will just test those
+without you having to recompile
+
+binaries for every one of them.
+
+And so there's a table
+here which basically says,
+
+what's the name
+of the heuristic?
+
+What's the variable
+that is going to be
+
+set what the default value is?
+
+And pawn ev value is
+the value of a pawn.
+
+And if there's any restrictions
+on the range of those values,
+
+what's the smallest it can be?
+
+What's the largest it can be?
+
+So you can edit this
+table, and so forth.
+
+And as I say, you can set it
+through the UCI interface.
+
+So it's really a
+very flexible way
+
+of getting access to
+anything that you want to do.
+
+You can put your own
+commands in there,
+
+including new
+heuristics, or whatever.
+
+And there's some
+things in there.
+
+For example, if we
+go to the other part
+
+where they actually are
+passing the UCI stuff,
+
+so it basically takes it.
+
+It parses it, figures out
+what the command is, and then
+
+implements the command.
+
+So all that kind of stuff,
+you have control over.
+
+So that that will help you in
+choosing to do other things.
+
+So, for example, if you
+search for perft or something
+
+in there--
+
+so if you have
+perft, here's what
+
+the correct outputs should be.
+
+And now, here's the
+code that it executes.
+
+And perft is in
+a different file.
+
+I think it's in the
+move generation file.
+
+HELEN XU: Do I have
+the wrong output?
+
+PROFESSOR: That may be
+for the older game, yeah.
+
+I actually noticed a couple
+of other bugs in there
+
+that hadn't been fixed.
+
+So we will make sure
+that those are--
+
+basically, it's just dead
+code, is what's in there.
+
+We need to clean up
+some of the dead code.
+
+Some of the code
+is from last year.
+
+And we changed the game.
+
+And not all the dead
+code got eliminated.
+
+HELEN XU: That'll be fixed
+for when I make the repost.
+
+PROFESSOR: Yeah.
+
+So we're just
+finishing up some--
+
+right now, I think
+it's all cleanliness.
+
+But if you find any bugs
+like that, let us know.
+
+We'll fix them, and so forth.
+
+Appreciate if you do see
+other inconsistencies,
+
+or what have you.
+
+Good, so great project,
+this is like lots of fun.
+
+Next month is going to be
+lots of fun for all of you.
+
+You may not think it's fun
+every minute of the day.
+
+But you'll have a good time.
+
+It is fun.
\ No newline at end of file
diff --git a/ezBuTFbF5Gs.txt b/ezBuTFbF5Gs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2cd7c7f3609e9ef2b4190416d813259415c9cf30
--- /dev/null
+++ b/ezBuTFbF5Gs.txt
@@ -0,0 +1,3529 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from 100 of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: All right.
+
+So today then we are going
+to talk about eye movement
+
+control.
+
+This is a fact-laden
+set of topics.
+
+We're going to talk about
+the basics of eye movements,
+
+and then we're going to talk
+about the various neural
+
+structures that are involved
+in eye movement control.
+
+The interesting thing about
+studying eye movement control
+
+here, which is very closely,
+obviously related to vision.
+
+It's also very closely related
+to the ocular motor system
+
+because it involves
+moving the eyes.
+
+Now the basic fact is
+that we move our eyes
+
+practically endlessly every day.
+
+We make about three
+saccades a second.
+
+And we make more than
+150,000 saccades every day.
+
+And it's not something
+you ever think about.
+
+Yet every time you
+look at something,
+
+you have to decide as to where
+you're going to look next.
+
+You're not even aware of it.
+
+It just happens automatically.
+
+It's a remarkable system,
+works with incredible rapidity,
+
+and it involves recognizing
+objects out there,
+
+recognizing the visual
+scenes, making a selection,
+
+moving your eye there,
+and you keep doing it,
+
+as I said, three times a second.
+
+So this is, obviously,
+the eye movements
+
+that you make like that, jumping
+from one location to another.
+
+And with each of those eye
+movements, as I've said,
+
+you need to decide where
+are you going to look next.
+
+So that's quite an amazing feat.
+
+And it's not just something
+that we do as humans,
+
+but it's also done
+regularly by animals.
+
+And most of the work
+I will tell you about
+
+has been conducted actually on
+monkeys whose eye movements are
+
+remarkably similar to
+those of our eye movements.
+
+Now let's first of
+all go over what
+
+I'm going to cover in
+the next two sessions.
+
+First of all, before
+I do that, I just
+
+thought I'll show you an
+amusing cartoon from The New
+
+Yorker, which was made
+in 2001 which sort of
+
+puts in a nutshell what
+the nature of all this is.
+
+Here's a cat.
+
+He's going to try to jump
+up there to get the thing.
+
+And so it has to make a decision
+where that thing is in space,
+
+has to make the
+calculations, as to how
+
+to generate the motor
+activities to jump up there.
+
+Now when it comes to
+the eye movements,
+
+you don't have to
+jump up there, but you
+
+have to decide how to
+jump your eye from one
+
+location to the next.
+
+So what we are going
+to try to understand
+
+is what are these
+calculations that we perform
+
+to be able to make accurate
+eye movements from one location
+
+to another.
+
+And what neural structures
+are involved in this,
+
+and what are the various
+rules these neural structures
+
+are involved in to generate
+those eye movements.
+
+Now here are the topics.
+
+First of all,
+we're going to look
+
+at just the basics
+of eye movements.
+
+Then we are going to look
+at the so-called eye plant
+
+and the brain stem
+nuclei, which are
+
+involved in moving
+your eye muscles.
+
+Then, we are going to look at
+an important structure in eye
+
+movement generation which is
+called the superior colliculus
+
+that we hadn't talked about yet.
+
+And then we are going to
+look at the visual input
+
+for saccade generation.
+
+We're going to examine
+what the various types
+
+of retinal ganglion cells do
+to be involved in eye movement
+
+generation.
+
+In particular, we
+are going to look
+
+at the midget and
+the parasol cells.
+
+Then perhaps a little bit today,
+but most of the next time,
+
+we can look at the
+cortical structures
+
+involved in movement control.
+
+Then we're going to look
+at the effects of paired
+
+electrical and
+visual stimulation
+
+because that would give
+us additional insights
+
+about the nature
+of eye movements.
+
+And then we're going
+to look at what
+
+happens when you have various
+deficits in motor control
+
+as a result of having
+lesions in various parts
+
+of the visual and
+ocular motor systems.
+
+And then we're going to look
+at some pharmacological studies
+
+to try to understand what the
+pharmacology is of eye movement
+
+control.
+
+And I should only say visually
+guided eye movement control.
+
+All right.
+
+So let's first start then with
+the basics of eye movements.
+
+We can ask a question,
+why do we move our eyes.
+
+Now you already have the
+answer to the first reason
+
+we do that, which is
+that in the retina,
+
+we have a highly specialized
+system in higher mammals
+
+and humans where there's
+only a very small area
+
+where you have a very high
+density of photoreceptors.
+
+And so to see fine
+detail, you need
+
+to move your eye to
+the location to be
+
+able to analyze it at
+a high level acuity.
+
+So that then involves
+the directive
+
+to acquire objects
+for central viewing.
+
+Because it's the
+central viewing that
+
+allows you to have high acuity.
+
+Now those are
+accomplished predominantly
+
+by saccadic eye movements,
+just like the ones
+
+I had mimicked at
+the very beginning.
+
+You make these very
+rapid eye movements
+
+fro one location to another.
+
+Another important part
+of eye movement control
+
+is that when either your are
+in motion, or whatever you're
+
+looking at, like a
+bird flying in the sky,
+
+to be able to analyze it,
+you track that object.
+
+You make what is called
+smooth pursuit eye movements.
+
+So that is another
+important mechanism
+
+that enables you to analyze
+things accurately in the world.
+
+Now yet another factor is
+that when we move about,
+
+it's important for us
+to be able for our eyes
+
+to be stable with respect
+to the world out there.
+
+And one of the
+mechanisms involved
+
+in that, as we shall see, is
+the accessory optic system--
+
+and that's what you're going to
+be writing a paper about-- that
+
+is involved in controlling
+the eyes involving
+
+both visual stimuli and
+the vestibular system.
+
+So that is what we're
+going to talk about.
+
+Actually that part
+we're probably
+
+going to talk about
+when we-- in the next
+
+to last lecture, not next
+time, but the time after.
+
+We're going to talk about the
+accessory optic system a bit.
+
+All right.
+
+So now then, just
+to reiterate then,
+
+we're talking about
+the vestibular ocular
+
+reflex and the
+accessory optic system.
+
+So now then, people have
+classified eye movements
+
+into some very basic types.
+
+We have so-called conjugate
+eye movements when the two
+
+eyes move in unison, and
+then vergence eye movements
+
+of an object comes close to
+you, it goes away from you,
+
+then the two eyes
+converge or diverge.
+
+And that still has to
+be done to make sure
+
+that the images you
+see in the world
+
+fall upon corresponding
+regions of the two eyes.
+
+Now the conjugate eye movements
+fall into two basic categories.
+
+They're called
+saccadic eye movements,
+
+the ones we have talked
+about already a bit,
+
+and smooth pursuit
+eye movements that
+
+causes us to be
+able to track object
+
+so that we can keep that
+object on the fovea.
+
+Now vergence eye
+movement-- you go back
+
+to that picture I'd shown
+you before in which you have
+
+the horopter or the Vieth-Muller
+circle, if you remember.
+
+If any object is along
+the Vieth-Muller circle,
+
+like going from 1 to 2, say an
+object jumps from here to here,
+
+then when the eyes
+track it, they
+
+follow in corresponding
+points into two retinae.
+
+However, if there is an object
+that falls outside or inside
+
+the Vieth-Muller circle, as
+shown here, then the object,
+
+the second object follows
+an non-corresponding point.
+
+And so therefore you have to
+bring about eye movements that
+
+involved vergence-- either
+divergence or convergence.
+
+For the most part, we
+get, today especially
+
+and the next time
+as well, we're going
+
+to be talking about
+saccadic eye movements.
+
+And then as I said, after
+we have covered movement,
+
+we're going to look
+at the movements that
+
+involve pursuit and vergence.
+
+Let's now take a look
+at a human subject
+
+and see the eye movements
+the subject makes.
+
+I mean, you're
+perfectly aware of it,
+
+but I thought it would be
+fun for you to look at it.
+
+So here's a subject, and he's
+looking at something, right?
+
+And all these eye
+movements obvious there's
+
+nothing moving out
+there, so these are all
+
+saccadic eye movements.
+
+The head is fixed.
+
+And so now once
+you've seen this,
+
+there are a number of questions
+that comes into one's mind.
+
+The first one, on the
+not too scientific end,
+
+is well was that
+a male or female.
+
+Or secondly, what was
+a person looking at?
+
+And then thirdly, way down
+the list you say, but how does
+
+the brain do this.
+
+So let's see if you can
+answer these three questions.
+
+The third one will
+take the two lectures.
+
+But the first and second one
+can be answers fairly quickly.
+
+Was it a male or female?
+
+Anybody want commit themselves?
+
+AUDIENCE: Male, male, male.
+
+PROFESSOR: Male, male, male.
+
+Anybody think it was a female?
+
+You guys are good.
+
+It was a male.
+
+Very good.
+
+All right.
+
+Now the second
+thing, of course, is
+
+what on earth was this
+person looking at.
+
+Now there's no way you could
+glean that until I tell you.
+
+So let me tell you what
+this person is looking at.
+
+And what this person
+looking at is up
+
+picture which is created
+by Rene Magritte.
+
+And actually resides in at
+the National Gallery of Art
+
+in Washington DC.
+
+That's quite an
+interesting painting,
+
+and that's what I'm
+showing it to you.
+
+And it relates closely
+to perception--
+
+the curious aspects of it.
+
+And you can see this doesn't
+make sense quite right.
+
+But it's because
+of that, because
+
+of the puzzling nature
+of this picture that it
+
+is in the fabulous museum.
+
+Because it is so unusual
+and different that it makes
+
+you think.
+
+So anyway, what happens then
+suppose you started here
+
+when picture came
+on, then you're
+
+going to have to
+make a decision where
+
+you're going to look next.
+
+So what would you look at next?
+
+Most, commonly, would look
+at the eyes Of the rider.
+
+Then you would look at
+the eyes of the horse.
+
+And so I look at various
+outstanding features.
+
+Now the way this looks, more or
+less-- looks like in real time,
+
+looks like this.
+
+So that's what this
+person was looking at.
+
+And that makes you
+aware of the fact
+
+that whenever you look at the
+pictures, you look at anything,
+
+you make all these eye movements
+in this very short time for you
+
+to comprehend the scene and to
+understand it in some detail.
+
+When this kind of eye
+movement series is made,
+
+you wonder is this something
+that animals also do.
+
+And the answer is yes.
+
+Monkeys certainly do.
+
+Most mammals do, and even
+birds do this kind of stuff.
+
+So what I want to
+show you next is,
+
+first of all, what the
+pattern of eye movements
+
+is in humans and the
+initial person who
+
+did beautiful work on
+this who's name is Yarbus.
+
+Now this is a famous sculpture.
+
+This sculpture the
+so-called Bust of Nefertiti.
+
+And what Yarbus did is he looked
+at the kinds of eye movements
+
+a person makes when
+they look at this figure
+
+to be to comprehend it.
+
+And you can see
+what is interesting
+
+about this is there is a lot
+of saccades along the edges,
+
+and there's a lot of detail,
+and not too many saccades
+
+made to regions where
+there's smooth areas.
+
+So what Yarbus did, he
+actually published a book
+
+on this analyzing the
+nature of our eye movements
+
+just looking at its
+behavior like this.
+
+Now if you do the same
+thing with monkeys,
+
+they are going to show you that
+monkey, a bunch of monkeys,
+
+they also move their
+eyes just like we do.
+
+They also have foveas, of
+course, as we discussed.
+
+And so as they move around
+and look around in the world,
+
+they make even more eye
+movements than we do.
+
+They're a little bit
+more quick about it,
+
+and so they make many,
+many eye movements
+
+and make about maybe almost
+four saccades a second.
+
+Now to see whether they
+also actually select objects
+
+in a sensible way,
+what you can do
+
+is you can present
+a bunch of displays.
+
+Here is a bunch of round
+ones-- in round locations,
+
+I should say--
+different objects.
+
+And here we have a
+bunch of them arranged
+
+in a rectangular fashion.
+
+Then on the right, with the
+[INAUDIBLE] fixed again,
+
+you see the kinds of eye
+movements the monkey makes.
+
+And what you can readily do,
+even if you didn't see these
+
+here, you can tell
+that there must
+
+be a whole bunch of
+objects at these locations,
+
+including one in the
+center, and here,
+
+that the objects must be-- are
+aligned the way they are there.
+
+So clearly the monkeys
+do the same thing we do.
+
+They tend to look at particular
+objects in the scene,
+
+and make accurate
+saccades to them
+
+to be able to analyze them.
+
+So because of that, it is
+natural to take monkeys
+
+and to study their eye
+movements and to study
+
+the underlying neural mechanisms
+in these animals, which
+
+would then make us more
+capable of understanding
+
+just how the brain
+moves your eyes about.
+
+So now, let us becoming more
+concerned with the neural
+
+mechanisms and the machinery
+involved in eye movement
+
+generation.
+
+And so we are going to
+refer to this as eye plant
+
+and the brain stem
+nuclei, which are
+
+in the mid and lower portions
+of the brain, not in the cortex.
+
+We'll talk about the
+cortical factors later on.
+
+So let's start first of
+all, with the muscles.
+
+Each eye have six
+extraocular muscles,
+
+as they are delineated here.
+
+They're called the superior
+and inferior recti,
+
+the medial and lateral
+recti, and the obliques,
+
+the superior and
+inferior oblique muscles.
+
+Now the remarkable feature
+about these muscles
+
+that renders them
+different from the muscles
+
+that you have in the
+rest of your body
+
+is that the fibers
+of each muscle
+
+run the entire length
+of the muscle itself.
+
+It's not segmented.
+
+Most muscles in the
+body are segmented.
+
+Because of that, they're
+often difficult to understand
+
+the nature of the operation.
+
+But here we have a situation
+that since all the fibers
+
+on the entire length,
+it is a relatively easy
+
+to comprehend the basic
+mechanisms that generate
+
+the eye movements
+at this low level.
+
+The next thing that's
+important to know
+
+is that the eye is a
+balanced structure.
+
+It doesn't have any
+weights anywhere.
+
+And so when you
+move the eyes, it's
+
+not like when you have
+to pick up an object.
+
+If you were to pick
+up a heavy object
+
+and you thought it
+was a feather then
+
+you would practically
+hit yourself in the face.
+
+But if you know what the object
+is, you can correct for the way
+
+you're going to
+lift it, which adds
+
+another huge dimension on
+how you move your body about,
+
+and how you operate
+your muscles.
+
+Luckily when it comes to the
+eyes, that is not a factor.
+
+And because of that,
+it's easier to understand
+
+the way it operates.
+
+So now that you have this,
+the next question one can ask
+
+is how are these
+muscles innervated.
+
+I mean obviously, you have
+to have some nerves that
+
+connect to it that's cause
+the muscles to contract
+
+or to let go.
+
+The way that works is
+that the nerves that
+
+connect to the muscles
+of the eye release
+
+acetylcholine that causes
+the muscle to contract.
+
+OK so that's a basic-- that
+happens everywhere in the body.
+
+So that's very basic.
+
+You already know all that.
+
+But what you probably
+don't know yet
+
+is what are the nuerons--
+where do they come from,
+
+in other words, to
+innervate these muscles.
+
+Well it turns out that there
+are three cranial nerves--
+
+how many cranial nerves
+are there in the brain?
+
+AUDIENCE: 12.
+
+12?
+
+PROFESSOR: 12.
+
+3 of those, believe
+it or not, are
+
+involved in the control
+of eye movement.
+
+And so we can designate that.
+
+We can tell you that
+the lateral rectus
+
+is innervated by
+the abducens nerve.
+
+The abducens nerve comes
+from the abducens nucleus.
+
+The superior oblique
+muscle is innervated
+
+by trochlear nerve, which
+is the fourth cranial nerve.
+
+And the rest of
+them are innervated
+
+by sub-nuclei of the
+third nerve, which
+
+is called the oculomotor nerve.
+
+So we have these three
+oculomotor is a third,
+
+trochlear is the fourth,
+and abducens is the sixth.
+
+So it's these three
+nuclei which-- note again
+
+that the oculomotor
+has sub-nuclei--
+
+that innervate these muscles.
+
+So now that we know
+that, the next question
+
+is how do these neurons
+from these three nuclei
+
+act to do this.
+
+But before I tell
+you that, I want
+
+to make sure that you learn
+what the 12 cranial nuclei are.
+
+What you can do
+here-- and I'm using
+
+a so-called clean
+mnemonic device.
+
+On old Olympus towering
+tops a fat armed girl vends
+
+snowy hops.
+
+That's easy enough to remember.
+
+The first letter
+of each designates
+
+each of the 12 cranial nerves.
+
+So if we then look at
+that, here they are.
+
+The first one is the olfactory
+one, the second is the optic.
+
+Then we have the
+ones in blue here,
+
+which innervate
+the eye muscles--
+
+oculomotor, trochlear, abducens.
+
+And then one important
+ones that you're
+
+going to hear a lot about
+is the auditory one--
+
+that's number eight.
+
+So those are 12 cranial nerves.
+
+And then, you don't
+have to remember this,
+
+it might help to
+know that, of course,
+
+you have a whole bunch
+of spinal nerves as well.
+
+You have 31 of them.
+
+And those 31, of course,
+each doubles-- one
+
+on the left side, one
+on the right side.
+
+You have 8 cervical, 12
+thoracic, 5 lumbar, 5 sacral,
+
+and 1 coccygeal.
+
+Now you don't-- as I say, you
+don't have to remember this.
+
+And I'm not even tell you
+have to remember these.
+
+But it's good to know that.
+
+It's something that you
+can commit to memory,
+
+so that when you go to a
+party and talk to somebody,
+
+you can say, hey, you know
+about the 12 cranial nerves.
+
+And they go, [YAWNS],
+see you later.
+
+All right.
+
+So anyway, we can
+move on now and see
+
+how these neurons that
+innervate the muscles, that
+
+are so often referred to as
+a final common path-- how
+
+they operate.
+
+Actually that underwent
+quite a bit of debate
+
+for a long, long time.
+
+We're not going to go
+into the debate itself,
+
+but I'm just going to
+tell you how it works.
+
+But the fact is
+that these neurons
+
+are involved in generating
+all sorts of eye-- all the eye
+
+movements we talk about,
+meaning smooth pursuit,
+
+meaning maintained eye
+position, and saccade.
+
+And so here's an example.
+
+This show vertical
+eye movements, just
+
+vertical eye movements.
+
+And what you can see here
+is that the more they eye
+
+looks down, like here, the
+more sustained activity
+
+to keep the muscle contracted,
+to keep the eye down.
+
+Now but you also have to
+remember that while this
+
+is happening here,
+the opposite muscle
+
+on top, the superior
+rectus, has to let go.
+
+So there would be no
+activity to contract
+
+the muscle in the superior
+rectus-- no muscle
+
+fibers in the superior rectus.
+
+Secondly, the important
+thing to notice here
+
+is that whenever
+there's a saccade--
+
+saccade, saccade,
+saccade, saccade,
+
+and so on, when there's
+a little saccade,
+
+there's a high frequency burst.
+
+And the high frequency is short.
+
+When you have a big
+saccade, there's
+
+a much longer high
+frequency burst.
+
+And when there's a saccade
+in the opposite direction,
+
+there is a pause.
+
+So what do you think happens
+when there's a pause?
+
+In that case, the superior
+rectus would get a burst
+
+and would contract rapidly to
+get an upward eye movement.
+
+So this muscle will cause
+your downward eye movement,
+
+and the superior rectus records
+an upward movement, of course.
+
+So that is the basic layout.
+
+Now this is schematic, but to
+show you that this is real,
+
+I'm going to show you some
+data here of a monkey doing
+
+the actual eye movements,
+recording from the ocular motor
+
+nucleus.
+
+And in this case again,
+invading the inferior rectus.
+
+And what you can see here
+are a bunch of saccades.
+
+And here the monkey is tracking
+an apple as it moved down.
+
+And what you can
+see-- let's look first
+
+at this at the bottom.
+
+What you can see here is
+that somewhere along the line
+
+here is what the
+monkey's tracking.
+
+This particular neuron
+begins to cut in,
+
+and then gradually
+it increases the rate
+
+of its activity as
+a result of which,
+
+you get smooth
+pursuit eye movements.
+
+Now if you look
+at the upper part,
+
+once again as I've shown you,
+the frequency of activity
+
+is proportional to the angular
+deviation of the eye, this case
+
+because you're talking
+about the inferior rectus,
+
+in the vertical dimension.
+
+And whenever there's
+a saccade downward,
+
+there's a high frequency burst.
+
+And whenever there's a saccade
+upward, there's a pause.
+
+So that is the basic
+nature of this.
+
+And what is so lovely about
+this, is it's like a machine.
+
+This is so lovely
+that if you then
+
+collect data from several cells,
+and here's an example of it,
+
+and you look at the number
+of spikes per second
+
+and the angular
+deviation of the eye,
+
+it shows you that each
+of these four neurons
+
+acts in a linear fashion.
+
+As the eye deviates
+more and more,
+
+the frequency, the activity,
+gradually increases.
+
+This is not saccades, obviously.
+
+This is maintained activity--
+let me go back again--
+
+like here, like here,
+like here, and like here.
+
+So you get this beautiful linear
+function, which again as I've
+
+said, makes it relatively easy
+to understand quantitatively
+
+the process of moving the eyes.
+
+So that is the basic
+mechanism that you
+
+see in the oculomotor nuclei.
+
+And the important thing
+to understand then
+
+is that the activity
+of these neurons
+
+is involved both in
+the making saccades
+
+and in maintaining
+various eye positions.
+
+The reason I emphasize
+this is because maybe
+
+about 30 years ago,
+there was a big debate.
+
+Some people argued,
+and they initially
+
+began to record from
+these oculomotor nuclei
+
+that we have two
+different sets of neurons
+
+in the final common path, one
+of which controls saccades,
+
+and one of which controls
+maintained position,
+
+or smooth pursuit.
+
+But that's not the case.
+
+The case is that
+these neurons do both.
+
+Now why did this
+confusion arise?
+
+Well, it arose
+because it was found
+
+that if you looked at the
+so-called supranuclear
+
+complex, which are neurons which
+are sort of above, if you will,
+
+the oculomotor, trochlear,
+and abducens nuclei,
+
+there are a whole bunch
+of subnuclei there--
+
+we're not going to go
+into details about them.
+
+You don't have to know that.
+
+But at any rate, in
+those nuclei there
+
+are neurons that are
+indeed separately coding
+
+different attributes.
+
+I'm going to show
+this, but before I
+
+do I want to make one
+more important point.
+
+If you take a microelectrode,
+and you put it
+
+in one of these nuclei that
+controls a final common path,
+
+if you stimulate there at a
+high frequency, in this case
+
+500 Hertz, if you increase the
+duration of the stimulation,
+
+you get progressively
+bigger saccades,
+
+Which proves, with
+stimulation that it's indeed
+
+the duration of the high
+frequency burst that defines
+
+the size of the saccade
+that you elicit.
+
+So now we can move on.
+
+And in this case as I say,
+you don't have to know this,
+
+but I want to just
+mention it briefly.
+
+We have a [INAUDIBLE]
+the eye-- the eye muscle.
+
+And then we have, in addition
+to the final common path,
+
+we have a supranuclear complex,
+which have various neuron, some
+
+which pause, in other words,
+that don't cause saccades,
+
+and some which fire
+only to saccades.
+
+I think that's the only
+ones I need to point out.
+
+But at that level,
+they're separate.
+
+But once they come together
+in the oculomotor complex,
+
+then they impinge
+on these neurons
+
+of the final common path that
+carry both of these signals.
+
+So that then is the essence
+of the oculomotor complex
+
+that I want to cover.
+
+And so we can a quick,
+summary diagram here.
+
+We're going to make
+a diagram that's
+
+going to grow over in this
+session and the next one,
+
+and that's going to be
+very complex in the end,
+
+unfortunately.
+
+But here we have the brain
+stem oculomotor complex.
+
+And the way to put
+this-- because you
+
+talk about what kinds of coding
+operations are involved-- this
+
+carries what you're going
+to call a rate code.
+
+The higher the rate, the
+greater the angular deviation
+
+of the eye.
+
+And of course, the longer
+the high frequency burst,
+
+the bigger the saccade.
+
+So that is the
+so-called rate code.
+
+So this is the
+basic layout then.
+
+And of course, if there's
+a lot of activity here,
+
+this muscle is
+going to contract,
+
+the eye is going to
+deviate downward.
+
+At the same time, you're
+going to get a signal
+
+to the upper part
+that's going to let go.
+
+In other words,
+the signal is going
+
+to be terminated
+so that you have
+
+no activity in the upper part,
+so that that muscle can expand.
+
+So that's basically
+it at this point.
+
+And as I say, this will grow,
+and grow, and grow, and grow,
+
+until by the end
+of next time, it's
+
+going to be really complicated.
+
+But that's how the brain works.
+
+It's complicated.
+
+So with that then,
+we are next going
+
+to move to the so-called
+superior colliculus.
+
+Now the first thing I want
+to say about this structure
+
+is that this region of
+the brain-- I'll show you
+
+a picture of it
+in just a minute--
+
+is one that has undergone
+tremendous changes
+
+in the course of evolution.
+
+In more primitive
+animals, like in fish
+
+and in amphibia,
+what you find is
+
+that this structure is the prime
+structure for analyzing vision.
+
+So it does vision
+and then generates
+
+commands of various
+sorts, including
+
+commands to make eye
+movements, or generate
+
+other kinds of movements
+in different animals.
+
+And this is the case
+because in these animals,
+
+there is very little cortex.
+
+But with the process
+of encephalization
+
+more and more of the
+analytical undertakings
+
+the brain was involved in had
+been relegated to the cortex.
+
+And that also meant
+that more and more
+
+of the way we analyze
+vision became more central,
+
+as we have discussed already,
+with cortical mechanisms.
+
+Now to make this
+clear, let me show
+
+you three drawings of a
+so-called toad, a rabbit,
+
+and a monkey.
+
+And what you see
+here, the toad--
+
+here is the superior colliculus.
+
+This structure is
+quite large relative
+
+to the rest of the brain.
+
+Then when you come
+to the rabbit,
+
+there's some degree
+of encephalization.
+
+So this structure
+is much smaller
+
+relative to the
+rest of the brain.
+
+And then when it
+comes to the monkey,
+
+it looks like the superior
+colliculus is actually
+
+quite tiny.
+
+And in monkeys and humans,
+the superior colliculus
+
+is very small.
+
+It's maybe about five or
+six millimeters in diameter.
+
+And yet, it's an extremely
+important structure
+
+and we're going to examine
+just what the structure does.
+
+And later on, we're
+going to examine
+
+what happens if you
+lose that structure.
+
+So now here is a sagittal
+midline section of the monkey.
+
+So you can see this real.
+
+And here we have
+the lunate again.
+
+This is what part
+of the brain here?
+
+This is a cephalic area.
+
+AUDIENCE: [INAUDIBLE].
+
+PROFESSOR: OK, good.
+
+This is area V1 here.
+
+Then if you look down here,
+you see this little bubble
+
+looking thing here?
+
+That's the superior colliculus.
+
+So that is a
+structure that we are
+
+going to look at in some detail.
+
+Now if one enlarges this--
+this in a cat actually--
+
+and one takes a
+coronal cross section
+
+of the superior
+colliculus, they can
+
+see it's a fairly
+complicated structure.
+
+It has several layers.
+
+People have distinguished
+at least seven clear layers.
+
+And you can see
+the upper part here
+
+is often referred to
+as superficial gray.
+
+There are two layers of that.
+
+The very top layer gets an
+input directly from the retina.
+
+The one little
+further down, I'll
+
+elaborate on that in the minute.
+
+It gets input from
+the visual cortex.
+
+And then we have a whole
+bunch of other layers
+
+that we are going to examine in
+some detail in just a minute.
+
+So that's the nature
+of the structure--
+
+the superior colliculus.
+
+And the fact is that in more
+primitive animals, actually,
+
+it is a structure
+with many more layers.
+
+Some of these more
+primitive animals
+
+have as many as 14
+layers in this structure
+
+because it is heavily involved
+in eye movement control,
+
+as well as in the
+analysis of vision.
+
+Now the interesting
+fact about the way
+
+this is laid out in the
+cat, and in higher animals,
+
+and in humans, that most of
+the cells in the various layers
+
+reside in those layers.
+
+They don't talk to
+each other that much.
+
+But they get a lot of input
+from many other structures
+
+that control those layers.
+
+And I'll go into that in
+some detail in a minute.
+
+Now the next important fact
+about the superior colliculus,
+
+which makes it similar to
+lateral geniculate nucleus
+
+in the cortex, is that the
+visual field is laid out
+
+in a topographic manner in
+the superior colliculus.
+
+This is a top view
+of the colliculus.
+
+This is the visual field.
+
+And once again, the
+rule, if you remember,
+
+is that the contralateral
+half of the visual field
+
+is it projects to the
+superior colliculus.
+
+And of course, the opposite then
+is the case for the other side.
+
+And then if you look at the
+nature of the connections,
+
+you find that everything
+that's close to the fovea,
+
+the foveal representation,
+projects to the anterior
+
+level of the
+superior colliculus.
+
+So this is sort of
+the foveal region.
+
+Then the upper
+visual field projects
+
+to the medial portion
+of the colliculus.
+
+The horizontal
+meridian area projects
+
+to the horizontal meridian of
+the colliculus in the back.
+
+And the lower part
+of the visual field
+
+projects to the lateral
+portion of the colliculus.
+
+Now why do I emphasize this?
+
+You will see in just a
+minute why that is important.
+
+It's very important
+for us understand
+
+that there's a lovely
+topographic layout
+
+of the visual field on to
+the superior colliculus.
+
+So now we are going
+to move on and examine
+
+the question of what is
+the nature of the responses
+
+of neurons in the
+superior colliculus.
+
+Now I can tell you right off
+that in the monkey colliculus,
+
+in the cat
+colliculus, the nature
+
+of the responses
+of these neurons
+
+is not particularly interesting.
+
+They're small receptive
+fields, and they
+
+tend to respond
+both to the onset
+
+and the termination
+of a visual stimulus,
+
+meaning that they seem to get
+an input from both on and off.
+
+And then if you make the a
+stimulus progressively larger.
+
+You get an increase
+in responses,
+
+but then once you make it quite
+large, in this case 10 degrees
+
+and 20 degrees, the
+response greatly
+
+declines, which says that
+just like in the retina,
+
+these neurons have
+centers around antagonism.
+
+And they respond
+vigorously to small spots
+
+and very little to large spots.
+
+Now that's a basic layout.
+
+But then if you
+ask the question,
+
+well, are these cells in
+the colliculus orientation
+
+and direction specific?
+
+Are these cells color selective?
+
+For the most part,
+that answer is
+
+no, not entirely, but
+mostly no, meaning
+
+that these cells are not
+that really interesting.
+
+They are very, very, very basic.
+
+So that is the nature
+of the responses
+
+of these neurons in
+the superior colliculus
+
+in the superficial layers.
+
+I've told you that the
+superficial gray, which
+
+consists of two layers,
+the one that that's
+
+a direct input from the
+retina, and the other that
+
+gets an input from
+the cortex, gives you
+
+vigorous visual responses.
+
+But now, when you
+get into the deeper
+
+layers of the colliculus, you
+find something very exciting
+
+an extremely interesting.
+
+And that is sort
+of diagrammed here.
+
+What you have is a
+bunch of eye movements.
+
+And then look at this cell.
+
+This cell responds-- it's the
+same cell throughout-- responds
+
+vigorously to a small saccade.
+
+And this responds well
+before the saccade is made.
+
+That's what happens here.
+
+But then if the monkey
+makes bigger saccades,
+
+and some even in the same
+direction, like these here,
+
+you don't get a response.
+
+So what does that mean?
+
+That's curious.
+
+So what that means is that
+these cells, some have something
+
+to do with eye movements.
+
+This fires vigorously, and
+then eye movement ensues--
+
+fires vigorously and
+eye movement ensues.
+
+Now there's an eye movement
+that ensues here as well,
+
+but there's no saccade.
+
+So how do we explain this?
+
+Well, what you're do in
+these kinds of experiments
+
+then is that you collect
+extensive data to see when
+
+a cell like this fires,
+and when it doesn't fire.
+
+And you can generate a
+response curve, if you will,
+
+or a response diagram
+to see when it fires
+
+and when it doesn't fire.
+
+So now to look at that,
+here's an example of that.
+
+In this case, all
+the white spots
+
+are saccadic eye
+movements generated
+
+from a central point that were
+not preceded by eye move--
+
+saccadic-- by neural responses.
+
+And the red ones
+show the times when
+
+the neurons you're recording
+from, the single cell,
+
+responded vigorously.
+
+So that meant that
+whatever mark you
+
+made a saccade in
+this direction,
+
+there was vigorous
+activity in this neuron,
+
+meaning the neuron had an
+important role in generating
+
+an eye movement, whereas all
+the other saccades did not
+
+generate a responds in
+this particular neuron.
+
+But to make this clear, there
+are many different neurons
+
+in many different parts
+of the colliculus.
+
+And so when you generated
+other eye movements,
+
+other neurons fired.
+
+So how can we analyze
+this in more detail?
+
+Well, the way we can-- let me
+just add one more point here.
+
+This green circle
+here is what we're
+
+going to call the motor field
+of this particular neuron.
+
+So that's a new concept
+for you-- motor field.
+
+These neurons in the
+intermediate and deep layers
+
+of the colliculus
+have motor field
+
+that define the
+size of the saccade.
+
+Now let me say one more
+thing in anticipation--
+
+that if you then study where the
+cells' visual receptive field
+
+is, it's right there relative
+to the central fixation point.
+
+So it means that
+this particular cell
+
+fires when a saccade is
+made into the receptive
+
+field of that neuron.
+
+So how can we verify this
+interesting, clever arrangement
+
+in the superior colliculus?
+
+Well, the way we can do this
+is to instead of recording,
+
+or actually I shouldn't
+say instead, really.
+
+But we can do two things.
+
+We can record and
+see what happens
+
+in different parts
+of the colliculus.
+
+Or we can electrically
+stimulate there.
+
+Well, so here is a schematic.
+
+Here is a colliculus-- this is
+anterior, this is posterior.
+
+So this, obviously,
+if you remember,
+
+this is close to the fovea.
+
+And here is medial
+and here is lateral.
+
+And what we can do
+then, we can see
+
+where the receptive fields
+are of these neurons.
+
+And we can plot them out.
+
+Here are the receptive fields.
+
+Here is number 1,
+close to the fovea,
+
+number 2 is medial is
+up, and lateral is down.
+
+Now that one has done
+this, you can switch over
+
+and you can
+electrically stimulate.
+
+And look what happens.
+
+If you electrically
+stimulate at 1,
+
+you get a saccade that moves
+the eye into the receptive
+
+field of that neuron-- that
+set of neurons, I should say.
+
+Then if you stimulate in 2, you
+get saccades that move it to 2.
+
+And when you simulate in
+3, it moves to location 3.
+
+Now what more do we need to
+verify given this situation?
+
+How can one believe this
+hypothesis, if you will,
+
+at this stage?
+
+What did I tell you about
+when you electrically
+
+stimulate the neurons in
+the final common paths,
+
+back in abducens, in
+the oculomotor nucleus,
+
+for example?
+
+What did I tell you?
+
+That this duration
+of the simulation
+
+define the size of the
+saccade elicited, right?
+
+Now if that's the case,
+if that's were the case,
+
+then this would not mean
+a damn thing, would it?
+
+Because you could take that same
+location and stimulated longer,
+
+and you would get
+a bigger saccade.
+
+So what you need to do?
+
+You need to systematically
+vary the duration
+
+of the high frequency
+burst in the colliculus
+
+to compare it with what
+happens when you stimulate
+
+in the abducens or
+oculomotor nuclei.
+
+OK so let's look at that.
+
+Here is a picture
+I've shown you before.
+
+As we increase the duration
+of the high frequency burst,
+
+you get progressively
+biggest saccades.
+
+So now we do the same
+thing in the colliculus.
+
+And lo and behold, you get
+something totally different
+
+because you have a
+totally different code
+
+in the colliculus.
+
+What you get here
+is that you get
+
+after you exceed a very
+short time-- just 10
+
+milliseconds-- when you
+don't get a saccade.
+
+From 25 to about 120
+milliseconds, you get saccades,
+
+but they're all
+the same size, so
+
+meaning it's where you stimulate
+in the colliculus, not how
+
+long you stimulate.
+
+And then to prove
+this even further,
+
+when you make the stimulation
+much longer than that, you get
+
+a staircase of saccades,
+each reaches the same size.
+
+Now yet another proof here
+is that if you stimulate
+
+an anterior tip
+of the colliculus,
+
+remember where the
+receptive fields are very
+
+close to the foveola, then
+they get a hold array of,
+
+I think there's something like
+14 saccadic eye movements--
+
+bang, bang, bang bang, bang,
+bang-- because the simulation
+
+goes on for a long time.
+
+So each little saccade
+is the same size,
+
+you just get a
+staircase of them.
+
+So that proves that the coding
+operation in the colliculus
+
+is one that defines the
+location of a receptive field,
+
+and when you stimulate
+it, it generates a saccade
+
+that moves the eye into
+that receptive field.
+
+So that then in a
+nutshell tells you
+
+what the basic principle
+is off the functioning
+
+of the colliculus when
+it comes to eye movement.
+
+Namely it says, a
+saccade is generated
+
+by computing the
+size and direction
+
+of the saccadic
+vector needed to null
+
+the retinal error between
+the present and intended eye
+
+positions.
+
+That's just putting it in a
+slightly different way, saying
+
+that, OK, I decide I'm going to
+make a saccade to here-- bang,
+
+like that.
+
+Just a saccade line.
+
+And but you did that you
+had an intended location.
+
+And by making an eye
+movement, you know the error.
+
+Now the colliculus is
+really quite accurate.
+
+You can make saccades
+with very small error.
+
+Usually the error is
+roughly, at most around 10%,
+
+meaning that when you
+make very small saccades,
+
+is almost negligible.
+
+When you make a large saccade,
+then maybe there is an error.
+
+And when that happens,
+sometimes what you have to do
+
+is to make what is called
+the corrective saccade.
+
+So suppose you're looking here
+and an object appears here.
+
+And so you say, I
+intend to go here,
+
+and the colliculus fires in
+that region of the colliculus
+
+to generate an eye movement.
+
+And say the eye
+movement goes to here.
+
+Then what you have to do is
+to make a second saccade,
+
+like that, to correct
+for that little error.
+
+So sometimes when you
+make large eye movements,
+
+indeed, you make a secondary
+saccade for the correction
+
+because your accuracy is
+roughly around 90% correct.
+
+Does everybody so far
+follow the basic principle?
+
+It's very important to
+understand the basic principle
+
+of the operational
+characteristics
+
+of the superior colliculus.
+
+So again to repeat, a
+saccade is generated
+
+by computing the
+size and direction
+
+of the saccadic
+vector needed to know
+
+the retinal error between
+the present and intended eye
+
+position.
+
+And what you have
+in the colliculus
+
+is a cell that is
+being activated
+
+because a target falls into it.
+
+And that activation
+then generates a signal
+
+to the lower parts
+of the colliculus--
+
+we'll talk about that, how that
+is done-- which then results
+
+in a saccadic eye movement
+that nulls that error signal.
+
+Very clever, very
+basic, very beautiful--
+
+and almost computer-like
+at this level.
+
+So what we can do now, we are
+adding the superior colliculus,
+
+the very basics of it
+so far, to this diagram.
+
+And that says that
+the colliculus then
+
+sends a signal to
+the brain stem.
+
+Some of it initially to
+the supranuclear complex,
+
+and then from there
+it sends a signal
+
+to the abducens, or
+oculomotor, or trochlear nuclei
+
+to generate the
+appropriate eye movements.
+
+So that then is
+the very basics of
+
+the operational characteristics
+of the superior colliculus.
+
+Now what we're
+going to do next is
+
+we are going to examine what
+the nature of the visual input
+
+is, predominantly the
+superior colliculus--
+
+not entirely, but heavily--
+to generate a saccadic eye
+
+movement.
+
+So if you remember, I told
+you that in the retina,
+
+we make a major distinction
+between two classes
+
+of retinal ganglion cells--
+the midget and the parasol.
+
+The midget project to
+the parvocellular layers
+
+of the colliculus.
+
+And the parasol cells project
+to the magnocellular layers.
+
+However, it's also been
+found that-- I mentioned
+
+that only briefly,
+that in the retina
+
+there is yet another
+class of cells
+
+it is called-- some
+people have called
+
+it the W cells in the cat.
+
+Other people have called it
+the corneal cellular cells that
+
+reside in the relatively
+small numbers compared
+
+to the other two throughout the
+retina, and project, in part,
+
+to interlaminar layers of the
+lateral geniculate nucleus.
+
+But it's been found that
+they also project heavily
+
+to the superior colliculus.
+
+Now how do we know this?
+
+Well let me tell
+you, it's important
+
+always is to understand the
+experimental procedures.
+
+So let me skip that here.
+
+Just to remind you again
+are the connections.
+
+This I've shown you
+several times before.
+
+So it says here the
+interlaminar layers project
+
+to the upper portions
+of the visual cortex.
+
+But I didn't tell
+you before that
+
+these corneal
+cellular cells also
+
+project to the
+superior colliculus.
+
+So here's the
+superior colliculus.
+
+And here, initially, we
+can ask the question,
+
+what projects look
+to the colliculus.
+
+So how do we find out?
+
+Suppose you are in a laboratory
+where the big question is what
+
+kinds of cells project
+from the retina
+
+to the superior colliculus.
+
+Think about this for a minute.
+
+What kind of experiment
+would you do?
+
+How would you find out?
+
+Well, that's quite an
+interesting question.
+
+And so to understand
+that, I'm going
+
+to tell you about a
+couple of techniques.
+
+One technique would be
+that you could inject--
+
+anatomical technique--
+you would inject
+
+a substance in the colliculus
+that would be then retrogradely
+
+transported to the retina, and
+would light up the cells there.
+
+That's would be one approach.
+
+Another approach is
+that you could actually
+
+record from the retina
+itself with microelectrodes.
+
+And you could electrically
+stimulate the colliculus.
+
+That way we would be
+backdriving cells.
+
+And when you find the
+cell in the retina that
+
+is backdriven from
+the colliculus,
+
+you know that particular cell
+does project to the colliculus.
+
+So that's a very
+strong technique
+
+because that enables you then
+to identify the cell type
+
+and also you could, if you
+do intercellular recording,
+
+to label it.
+
+So they can do the
+same thing also--
+
+because I'm going to talk
+about that as well-- is
+
+to see what happens
+in terms of inputs
+
+to the colliculus
+from the cortex.
+
+So let's talk about
+each of those,
+
+and that'll give us a
+better sense of what
+
+the projections
+are from the retina
+
+and from the cortex
+to the colliculus.
+
+So here's an example
+of how you do it again.
+
+So we are recording
+from the retina here,
+
+or in a different experiment,
+you can record from the cortex.
+
+You can then electrically
+stimulate here.
+
+You can backdrive the
+cells in the retina,
+
+or we can backdrive the
+cells in the visual cortex.
+
+And then once we do so, and
+record it from a single cell,
+
+you can study to
+see what it is like.
+
+So that is the approach.
+
+And if you do that, you come
+up with some very nice answers.
+
+First of all, these
+cells are W-like,
+
+which means that they're like
+the corneal cellular cells
+
+that we have seen the retina.
+
+These are these small
+cells that are not
+
+particularly rapidly
+conducting, obviously
+
+and are not color selective.
+
+And then if we look
+at the cells up here,
+
+we find that all those
+cells are complex cells,
+
+and they all reside
+in layer five.
+
+That's already
+known anatomically
+
+that the cells in
+layer five are the ones
+
+that project-- many
+of them project
+
+to the superior colliculus.
+
+So that then is the
+basic procedure.
+
+So now we can expand on
+this basic procedure.
+
+What we can do here
+is we can record
+
+from the superior colliculus.
+
+And then we can eliminate
+the inputs from the cortex
+
+by cooling it.
+
+That's one approach.
+
+So if you do that, you
+record from a cell here,
+
+you drive it by
+electric stimulation--
+
+by visual stimulation.
+
+We identify that cell
+in V1 by backdriving it.
+
+And then once you cool it,
+cool the visual cortex,
+
+you see what happens to that
+cell in the various layers
+
+of the superior colliculus.
+
+Well when you do that, you get
+a very dramatic and, luckily,
+
+clear cut result.
+
+The result is the following.
+
+If you look at the superficial
+layers of the colliculus,
+
+and look at what happens
+before you cool, when you cool,
+
+and after you cool,
+the cells keep firing.
+
+So in these upper layers
+in superficial gray,
+
+those cells keep firing.
+
+They're not
+interested in anything
+
+that comes down from the cortex.
+
+That's because the
+inputs from the retina
+
+goes to these upper layers
+of the superior colliculus,
+
+and goes predominantly
+to the superficial gray.
+
+However, once you get down
+to the intermediate layers,
+
+and the lower layers
+as well, every time
+
+you cool, the cell stops
+firing, as you can see here.
+
+Which means that these cells
+in the intermediate and lower
+
+layers of the
+colliculus are driven
+
+by the cortical down flow.
+
+They're not driven by the
+direct input from the retina.
+
+So now that we have seen this,
+one can say, OK, that's fine.
+
+But is this really something
+that happens over time,
+
+or is this just
+something peculiar
+
+to the particular
+experiment that's been run?
+
+So what do you do to
+see if this is really
+
+something-- a permanent effect?
+
+Well, what you can do here
+is you can take a monkey,
+
+and you can remove the
+visual cortex on one side,
+
+so the monkey can see fine
+in half the visual field.
+
+And then you can
+record on either side--
+
+the intact side or
+the affected side--
+
+in the superior colliculus.
+
+Everybody follow that?
+
+All right.
+
+So if you do that, what you
+find is this is the intact side,
+
+and this is the side
+where there's no V1.
+
+And this was taken months
+after the area V1 was removed.
+
+And here you see these red spots
+here, and the red spots here?
+
+That spot is the location
+after which you no longer
+
+could drive any cells visually.
+
+So in the intact
+side, you can drive it
+
+to very deep layers
+of the colliculus.
+
+They had responded very
+well to visual stimuli.
+
+But on this side, they
+stopped responding here.
+
+So none of these
+deeper layers could
+
+be activated by visual stimuli
+because those deep layer,
+
+indeed, are driven
+by visual inputs
+
+from the downflow
+from the cortex.
+
+So that then is the
+basic rule of what
+
+has happened in the
+superior colliculus.
+
+All right.
+
+Now let's see-- the next
+big question we can ask
+
+is this downflow
+from the cortex that
+
+drives these important
+intermediate layers, which
+
+are involved in eye movement
+generation, to what degree are
+
+those cortical
+tactile cells driven
+
+by either the parvocellular
+or the magnocellular
+
+layer of cells, meaning
+by the midget cells,
+
+or the parasol cells.
+
+Well how do you do that?
+
+I've already told
+you about experiments
+
+in which what you can do
+is you can put a recording
+
+electrode, in this
+case in the colliculus.
+
+And then you can inactivate
+either the parvocellular
+
+or the magnocellular of the
+lateral geniculate nucleus,
+
+while you record in the
+superior colliculus.
+
+So what happens is that these
+cells then, obviously as shown
+
+here, project to V1, and then
+layer five cells project down.
+
+So what we are going
+to identify then
+
+is what is the nature of
+these cells in layer five
+
+that drive down there.
+
+So first of all,
+what this shows is
+
+that if you record
+from-- in this case,
+
+from two cells in the
+geniculate shown-- sorry,
+
+two cells in the
+colliculus shown,
+
+this is under normal
+conditions, and this
+
+is when the parvocell
+layers are blocked.
+
+Here's another cell--
+normal condition,
+
+and then magnocellular
+layers are blocked.
+
+So this clearly shows-- and
+this was done with dozens,
+
+and dozens, and
+dozens of cells--
+
+that blocking the
+parvocellular layers,
+
+meaning blocking
+the midget system,
+
+had no effect on the cortical
+tactile driving of cells,
+
+whereas magnocellular
+block eliminated it.
+
+So that meant that these
+cells in layer five that
+
+project to the
+superior colliculus
+
+are driven exclusively
+by the parasol system.
+
+And indeed then,
+that was also done--
+
+now let me go back to
+that-- that was also done
+
+in another set of
+experiments showing that
+
+those cells in the
+cortex in layer five,
+
+that you could drive from the
+geniculate by backdriving it
+
+if you then block the
+midget or parasol cells,
+
+those cells would stop firing.
+
+So those were indeed cells
+that were driven exclusively
+
+by the parasol system.
+
+So the parasol system
+plays a very important role
+
+in getting-- in
+driving the colliculus.
+
+But doing it so only through
+the cortex, not directly.
+
+so to then put this in an
+easy to remember the diagram,
+
+is to say that when you come to
+these high level animals, what
+
+happened is that due
+to encephalization,
+
+the cortex gained control
+over the superior colliculus,
+
+except the superficial gray.
+
+Everything else
+in the colliculus
+
+is controlled by the
+cortical downflow.
+
+And that, of course,
+became very important
+
+because when you make a
+decision as to where you're
+
+going to look next, where you're
+going to identify an object,
+
+you have to have information
+from the cortex itself,
+
+which then has to be
+transferred, in this case,
+
+to the colliculus to generate
+the desired eye movement,
+
+so that you can
+analyze in detail
+
+what you want to analyze.
+
+So that then is
+the basic layout.
+
+And so now what we can
+do is we can expand
+
+some more on this diagram,
+namely-- once again,
+
+let's go through all this.
+
+We have the brain stem
+here, which is a rate code.
+
+And then we have a
+superior colliculus.
+
+And that code that we're
+going talk about there,
+
+that I've already
+described, you can
+
+refer to that as
+the vector code.
+
+And then what we
+can see here-- some
+
+of this work I've
+shown you before--
+
+is that we have these three
+systems from the retina
+
+that we talked about now.
+
+The midget, the parasol,
+and the W system,
+
+or the corneal cellular system,
+that goes up the cortex.
+
+And then the downflow
+from V1, we now know,
+
+is driven exclusively, it
+seems, by the parasol system.
+
+However, remember also that
+when we go to higher cortical
+
+areas-- V2, MT, and V4, and so
+on-- these areas, some of them
+
+get a mixed input
+from two systems,
+
+like V4 and the temporal lobe.
+
+And MT, on the other
+hand, is dominated
+
+by inputs from the parasol
+system, but it's not exclusive.
+
+So in the end, the
+colliculus also
+
+gets an input from
+the midget system.
+
+But the heaviest input to it is
+indeed from the parasol system.
+
+So that then is what the diagram
+looks like at this point.
+
+And so what we are
+going to do next time,
+
+we're going to expand on
+this connection in which we
+
+are going to look at
+some other cortical
+
+structures-- namely I've already
+referred to that a few times--
+
+the frontal eye fields
+and the medial eye fields,
+
+which are regions in the cortex
+that control eye movements.
+
+And that's what we're going to
+look at in much more detail.
+
+So now I'm ready to summarize
+what I told you so far.
+
+First of all, there are several
+classes of eye movements
+
+one can distinguish.
+
+Those are vergence eye movements
+and conjugate eye movements.
+
+And the conjugate
+eye movements come
+
+in two major types, which
+we call the smooth pursuit
+
+type and the saccadic type.
+
+Then we're going to
+talk about eye movements
+
+as a result of the 6 extraocular
+muscles that we have.
+
+And important to note that
+these extraocular muscles are
+
+such that the
+fibers in the muscle
+
+run the entire length
+of the muscles.
+
+They're not segmented,
+and that they
+
+are innervated by the
+third, fourth, and sixth
+
+cranial nerves.
+
+Then we say that
+the discharge rate
+
+in neurons of the
+final common path
+
+is proportional to the
+angular deviation of the eye.
+
+Saccade size is a
+function of the duration
+
+of the high frequency
+burst in these neurons.
+
+And if you look it up
+and down eye movements,
+
+as I've shown you, if the
+more the muscles contract that
+
+are the inferior recti, the more
+the idea deviates downwards.
+
+And because it's reciprocal, as
+the eye deviates more and more,
+
+the superior rectus is
+activated less and less.
+
+So we have this
+proportional arrangements.
+
+It's as beautiful as I've shown
+you-- a linear system that
+
+defines very accurately
+the degree of deviation
+
+of the eye as a function
+of the frequency
+
+of the neuronal activity.
+
+Then the superior colliculus
+codes saccadic vectors
+
+whose amplitude and direction is
+laid out in an orderly fashion
+
+and is in register with the
+visual receptive fields.
+
+I told you that in the
+anterior colliculus,
+
+the receptive fields are
+very close to the fovea.
+
+And then you go to the
+back of the colliculus,
+
+the progressively further
+peripheral, and medial is up,
+
+lateral is down.
+
+It's a nice orderly arrangement.
+
+And you have an arrangement
+where the visual receptive
+
+fields and the motor fields are
+in register with each other.
+
+And every time there's activity,
+there's a particular receptive
+
+field location, the
+result is that a saccade
+
+will move the eye into the
+receptive field, thereby
+
+nulling the retinal
+error signal.
+
+And then the retinal input
+to the superior colliculus
+
+comes predominantly
+from w-like cells.
+
+But the cortical downflow from
+V1, which comes from layer 5,
+
+is driven by the parasol system.
+
+But we should not
+neglect the fact--
+
+I'm not sure if you're-- neglect
+the fact that they are other
+
+pathways to which the midget
+system can also make maybe
+
+a more limited contribution
+in generating eye movements.
+
+And as a diagram
+I had shown you,
+
+I demonstrated that
+the superior colliculus
+
+is on the cortical control
+in higher primates.
+
+So that then is the essence of
+what I wanted to cover today.
+
+And then next time, we are going
+to talk about-- let me see,
+
+do I have a--
+we're going to talk
+
+about the cortical areas
+involved in saccadic eye
+
+movements control,
+which we will then
+
+highlight the fact that this
+incessant activity of us moving
+
+the eyes is incredibly
+elaborate and complicated.
+
+There are millions of
+neurons involved in doing it.
+
+And yet, it's such
+an incredible system
+
+that it's something we
+never even think about.
+
+Luckily, it's a kind of system--
+partly because of the fact
+
+that there's no wait
+involved in the muscles,
+
+and that the fibers run
+the entire length of each
+
+of the extraocular muscles-- it
+is a system that one has been
+
+fortunate enough to
+understand reasonably
+
+well in how it
+works in the brain.
+
+So that, in essence, is what
+I wanted to cover today.
+
+If any of you have
+any questions,
+
+anything that-- I know this
+is kind of complicated,
+
+but I hope that
+you will understand
+
+this reasonably well.
+
+And if it's not
+clear to you, I will
+
+be very happy to answer any
+questions that you might have.
+
+Well, I was
+reasonably clear then.
+
+So next time-- here's my
+to-do-- the cortex, heavily.
+
+I will also show you some
+interesting movies about that.
+
+And I think you're
+going to find that it's
+
+a really fascinating story
+of how the cortex has evolved
+
+to generate more and more
+areas that are involved
+
+in an incredible
+number of functions
+
+in the generation of eye
+movements, as well, of course,
+
+as in processing
+visual information.
+
+OK.
+
+Well, thank you very much.
\ No newline at end of file
diff --git a/f2eYLK6TpRs.txt b/f2eYLK6TpRs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dccb56c32f087ac17ba0a30f6a0919e2188eb30e
--- /dev/null
+++ b/f2eYLK6TpRs.txt
@@ -0,0 +1,9131 @@
+align:start position:0%
+ 
+well thanks for coming to this uh first
+
+ align:start position:0%
+well thanks for coming to this uh first
+ 
+
+ align:start position:0%
+well thanks for coming to this uh first
+in the series of lectures so on this
+
+ align:start position:0%
+in the series of lectures so on this
+ 
+
+ align:start position:0%
+in the series of lectures so on this
+board I wrote the title positive
+
+ align:start position:0%
+board I wrote the title positive
+ 
+
+ align:start position:0%
+board I wrote the title positive
+definite matrices and I'll try each time
+
+ align:start position:0%
+definite matrices and I'll try each time
+ 
+
+ align:start position:0%
+definite matrices and I'll try each time
+to uh make a little list of the main
+
+ align:start position:0%
+to uh make a little list of the main
+ 
+
+ align:start position:0%
+to uh make a little list of the main
+topics of the
+
+ align:start position:0%
+topics of the
+ 
+
+ align:start position:0%
+topics of the
+lecture um see if I think about applied
+
+ align:start position:0%
+lecture um see if I think about applied
+ 
+
+ align:start position:0%
+lecture um see if I think about applied
+math
+
+ align:start position:0%
+math
+ 
+
+ align:start position:0%
+math
+generally um there sort of two parts to
+
+ align:start position:0%
+generally um there sort of two parts to
+ 
+
+ align:start position:0%
+generally um there sort of two parts to
+it one is to find the equation in the
+
+ align:start position:0%
+it one is to find the equation in the
+ 
+
+ align:start position:0%
+it one is to find the equation in the
+first place so maybe I put this just
+
+ align:start position:0%
+first place so maybe I put this just
+ 
+
+ align:start position:0%
+first place so maybe I put this just
+over in the corner so part part of
+
+ align:start position:0%
+over in the corner so part part of
+ 
+
+ align:start position:0%
+over in the corner so part part of
+Applied math a big part is to find the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation create the model you could say
+
+ align:start position:0%
+equation create the model you could say
+ 
+
+ align:start position:0%
+equation create the model you could say
+that's the Applied Mathematics and then
+
+ align:start position:0%
+that's the Applied Mathematics and then
+ 
+
+ align:start position:0%
+that's the Applied Mathematics and then
+a second part of it is solving the
+
+ align:start position:0%
+a second part of it is solving the
+ 
+
+ align:start position:0%
+a second part of it is solving the
+equation when we have the
+
+ align:start position:0%
+equation when we have the
+ 
+
+ align:start position:0%
+equation when we have the
+Matrix or the differential equation or
+
+ align:start position:0%
+Matrix or the differential equation or
+ 
+
+ align:start position:0%
+Matrix or the differential equation or
+the integral equation and the problem is
+
+ align:start position:0%
+the integral equation and the problem is
+ 
+
+ align:start position:0%
+the integral equation and the problem is
+how do we solve it
+
+ align:start position:0%
+how do we solve it
+ 
+
+ align:start position:0%
+how do we solve it
+and you could say that's the scientific
+
+ align:start position:0%
+and you could say that's the scientific
+ 
+
+ align:start position:0%
+and you could say that's the scientific
+Computing part so this is really the the
+
+ align:start position:0%
+Computing part so this is really the the
+ 
+
+ align:start position:0%
+Computing part so this is really the the
+twin parts of this
+
+ align:start position:0%
+twin parts of this
+ 
+
+ align:start position:0%
+twin parts of this
+course uh the applied math and the
+
+ align:start position:0%
+course uh the applied math and the
+ 
+
+ align:start position:0%
+course uh the applied math and the
+scientific Computing and uh so I'll go
+
+ align:start position:0%
+scientific Computing and uh so I'll go
+ 
+
+ align:start position:0%
+scientific Computing and uh so I'll go
+back and
+
+ align:start position:0%
+back and
+ 
+
+ align:start position:0%
+back and
+forth uh maybe today I'll start with my
+
+ align:start position:0%
+forth uh maybe today I'll start with my
+ 
+
+ align:start position:0%
+forth uh maybe today I'll start with my
+favorite
+
+ align:start position:0%
+favorite
+ 
+
+ align:start position:0%
+favorite
+matrices which are already here on the
+
+ align:start position:0%
+matrices which are already here on the
+ 
+
+ align:start position:0%
+matrices which are already here on the
+board okay and actually I realized in in
+
+ align:start position:0%
+board okay and actually I realized in in
+ 
+
+ align:start position:0%
+board okay and actually I realized in in
+planning these first lectures that a lot
+
+ align:start position:0%
+planning these first lectures that a lot
+ 
+
+ align:start position:0%
+planning these first lectures that a lot
+that that these these particular
+
+ align:start position:0%
+that that these these particular
+ 
+
+ align:start position:0%
+that that these these particular
+matrices come up so much and illustrate
+
+ align:start position:0%
+matrices come up so much and illustrate
+ 
+
+ align:start position:0%
+matrices come up so much and illustrate
+so much about applied math that uh if we
+
+ align:start position:0%
+so much about applied math that uh if we
+ 
+
+ align:start position:0%
+so much about applied math that uh if we
+kind of get friendly with them uh get to
+
+ align:start position:0%
+kind of get friendly with them uh get to
+ 
+
+ align:start position:0%
+kind of get friendly with them uh get to
+know them uh it's very much worth it
+
+ align:start position:0%
+know them uh it's very much worth it
+ 
+
+ align:start position:0%
+know them uh it's very much worth it
+then we can refer to them as the example
+
+ align:start position:0%
+then we can refer to them as the example
+ 
+
+ align:start position:0%
+then we can refer to them as the example
+that we're familiar with now uh I wrote
+
+ align:start position:0%
+that we're familiar with now uh I wrote
+ 
+
+ align:start position:0%
+that we're familiar with now uh I wrote
+down the 3X3 version and I'm going to
+
+ align:start position:0%
+down the 3X3 version and I'm going to
+ 
+
+ align:start position:0%
+down the 3X3 version and I'm going to
+ask you in a
+
+ align:start position:0%
+ask you in a
+ 
+
+ align:start position:0%
+ask you in a
+minute uh for let's start with
+
+ align:start position:0%
+minute uh for let's start with
+ 
+
+ align:start position:0%
+minute uh for let's start with
+K3 uh for some of its
+
+ align:start position:0%
+K3 uh for some of its
+ 
+
+ align:start position:0%
+K3 uh for some of its
+properties what what do we see in that
+
+ align:start position:0%
+properties what what do we see in that
+ 
+
+ align:start position:0%
+properties what what do we see in that
+Matrix uh but let me emphasize that this
+
+ align:start position:0%
+Matrix uh but let me emphasize that this
+ 
+
+ align:start position:0%
+Matrix uh but let me emphasize that this
+was the 3X3 case but in my in my mind I
+
+ align:start position:0%
+was the 3X3 case but in my in my mind I
+ 
+
+ align:start position:0%
+was the 3X3 case but in my in my mind I
+have a whole family of matrices so what
+
+ align:start position:0%
+have a whole family of matrices so what
+ 
+
+ align:start position:0%
+have a whole family of matrices so what
+would K4 look like K4 would be
+
+ align:start position:0%
+would K4 look like K4 would be
+ 
+
+ align:start position:0%
+would K4 look like K4 would be
+4x4 and it would have twos down the
+
+ align:start position:0%
+4x4 and it would have twos down the
+ 
+
+ align:start position:0%
+4x4 and it would have twos down the
+diagonal main diagonal minus ones above
+
+ align:start position:0%
+diagonal main diagonal minus ones above
+ 
+
+ align:start position:0%
+diagonal main diagonal minus ones above
+and below and otherwise zero
+
+ align:start position:0%
+and below and otherwise zero
+ 
+
+ align:start position:0%
+and below and otherwise zero
+so K 100 we would if we had K 100 we
+
+ align:start position:0%
+so K 100 we would if we had K 100 we
+ 
+
+ align:start position:0%
+so K 100 we would if we had K 100 we
+would really begin to see the structure
+
+ align:start position:0%
+would really begin to see the structure
+ 
+
+ align:start position:0%
+would really begin to see the structure
+of just uh just that 99 and 99 nonzeros
+
+ align:start position:0%
+of just uh just that 99 and 99 nonzeros
+ 
+
+ align:start position:0%
+of just uh just that 99 and 99 nonzeros
+and otherwise zeros now T3 has the same
+
+ align:start position:0%
+and otherwise zeros now T3 has the same
+ 
+
+ align:start position:0%
+and otherwise zeros now T3 has the same
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+except I that t is sort of for top if
+
+ align:start position:0%
+except I that t is sort of for top if
+ 
+
+ align:start position:0%
+except I that t is sort of for top if
+you like uh uh the the top row is
+
+ align:start position:0%
+you like uh uh the the top row is
+ 
+
+ align:start position:0%
+you like uh uh the the top row is
+different and B is for both the both the
+
+ align:start position:0%
+different and B is for both the both the
+ 
+
+ align:start position:0%
+different and B is for both the both the
+top row and the bottom row are are
+
+ align:start position:0%
+top row and the bottom row are are
+ 
+
+ align:start position:0%
+top row and the bottom row are are
+different those would be that the sort
+
+ align:start position:0%
+different those would be that the sort
+ 
+
+ align:start position:0%
+different those would be that the sort
+of the first row and the last row often
+
+ align:start position:0%
+of the first row and the last row often
+ 
+
+ align:start position:0%
+of the first row and the last row often
+reflect boundary conditions in some
+
+ align:start position:0%
+reflect boundary conditions in some
+ 
+
+ align:start position:0%
+reflect boundary conditions in some
+problem so these have different boundary
+
+ align:start position:0%
+problem so these have different boundary
+ 
+
+ align:start position:0%
+problem so these have different boundary
+conditions but otherwise we're seeing
+
+ align:start position:0%
+conditions but otherwise we're seeing
+ 
+
+ align:start position:0%
+conditions but otherwise we're seeing
+the same structure so so one thing you
+
+ align:start position:0%
+the same structure so so one thing you
+ 
+
+ align:start position:0%
+the same structure so so one thing you
+might
+
+ align:start position:0%
+might
+ 
+
+ align:start position:0%
+might
+do uh just to like get the hang of mat
+
+ align:start position:0%
+do uh just to like get the hang of mat
+ 
+
+ align:start position:0%
+do uh just to like get the hang of mat
+lab is create write a write a uh little
+
+ align:start position:0%
+lab is create write a write a uh little
+ 
+
+ align:start position:0%
+lab is create write a write a uh little
+file that would create K of N and T of N
+
+ align:start position:0%
+file that would create K of N and T of N
+ 
+
+ align:start position:0%
+file that would create K of N and T of N
+and B of n uh you know find mat lab
+
+ align:start position:0%
+and B of n uh you know find mat lab
+ 
+
+ align:start position:0%
+and B of n uh you know find mat lab
+commands that will help to do that and
+
+ align:start position:0%
+commands that will help to do that and
+ 
+
+ align:start position:0%
+commands that will help to do that and
+then uh I'll suggest what to do once
+
+ align:start position:0%
+then uh I'll suggest what to do once
+ 
+
+ align:start position:0%
+then uh I'll suggest what to do once
+you've got those matrices okay so can we
+
+ align:start position:0%
+you've got those matrices okay so can we
+ 
+
+ align:start position:0%
+you've got those matrices okay so can we
+just take these matrices then as my
+
+ align:start position:0%
+just take these matrices then as my
+ 
+
+ align:start position:0%
+just take these matrices then as my
+second lecture actually today
+
+ align:start position:0%
+second lecture actually today
+ 
+
+ align:start position:0%
+second lecture actually today
+that's something to be giving you know
+
+ align:start position:0%
+that's something to be giving you know
+ 
+
+ align:start position:0%
+that's something to be giving you know
+so I can usually when I think about the
+
+ align:start position:0%
+so I can usually when I think about the
+ 
+
+ align:start position:0%
+so I can usually when I think about the
+next lecture it's sometime far in the
+
+ align:start position:0%
+next lecture it's sometime far in the
+ 
+
+ align:start position:0%
+next lecture it's sometime far in the
+future and I have time to prepare for it
+
+ align:start position:0%
+future and I have time to prepare for it
+ 
+
+ align:start position:0%
+future and I have time to prepare for it
+but uh uh the second lecture will be
+
+ align:start position:0%
+but uh uh the second lecture will be
+ 
+
+ align:start position:0%
+but uh uh the second lecture will be
+within minutes of the first uh so that
+
+ align:start position:0%
+within minutes of the first uh so that
+ 
+
+ align:start position:0%
+within minutes of the first uh so that
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+discuss um this aspect of where the
+
+ align:start position:0%
+discuss um this aspect of where the
+ 
+
+ align:start position:0%
+discuss um this aspect of where the
+matrices come from right now let's just
+
+ align:start position:0%
+matrices come from right now let's just
+ 
+
+ align:start position:0%
+matrices come from right now let's just
+take them and say what are they like
+
+ align:start position:0%
+take them and say what are they like
+ 
+
+ align:start position:0%
+take them and say what are they like
+what properties do they have cuz they
+
+ align:start position:0%
+what properties do they have cuz they
+ 
+
+ align:start position:0%
+what properties do they have cuz they
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+important okay so and I guess with a
+
+ align:start position:0%
+important okay so and I guess with a
+ 
+
+ align:start position:0%
+important okay so and I guess with a
+microphone you can see that I don't I'm
+
+ align:start position:0%
+microphone you can see that I don't I'm
+ 
+
+ align:start position:0%
+microphone you can see that I don't I'm
+unable to teach without involving the
+
+ align:start position:0%
+unable to teach without involving the
+ 
+
+ align:start position:0%
+unable to teach without involving the
+without getting the class to teach it
+
+ align:start position:0%
+without getting the class to teach it
+ 
+
+ align:start position:0%
+without getting the class to teach it
+teach the course and I just sort of
+
+ align:start position:0%
+teach the course and I just sort of
+ 
+
+ align:start position:0%
+teach the course and I just sort of
+stand back but uh here with the
+
+ align:start position:0%
+stand back but uh here with the
+ 
+
+ align:start position:0%
+stand back but uh here with the
+microphone I have to I'll try to
+
+ align:start position:0%
+microphone I have to I'll try to
+ 
+
+ align:start position:0%
+microphone I have to I'll try to
+remember to repeat uh what you say so
+
+ align:start position:0%
+remember to repeat uh what you say so
+ 
+
+ align:start position:0%
+remember to repeat uh what you say so
+it's permanently so you could say
+
+ align:start position:0%
+it's permanently so you could say
+ 
+
+ align:start position:0%
+it's permanently so you could say
+anything actually I think the mic
+
+ align:start position:0%
+anything actually I think the mic
+ 
+
+ align:start position:0%
+anything actually I think the mic
+doesn't pick you up and then I'll repeat
+
+ align:start position:0%
+doesn't pick you up and then I'll repeat
+ 
+
+ align:start position:0%
+doesn't pick you up and then I'll repeat
+uh okay so tell me some facts about that
+
+ align:start position:0%
+uh okay so tell me some facts about that
+ 
+
+ align:start position:0%
+uh okay so tell me some facts about that
+let's start with that Matrix what are
+
+ align:start position:0%
+let's start with that Matrix what are
+ 
+
+ align:start position:0%
+let's start with that Matrix what are
+some facts about it and I'll just write
+
+ align:start position:0%
+some facts about it and I'll just write
+ 
+
+ align:start position:0%
+some facts about it and I'll just write
+them up as we see any symmetric
+
+ align:start position:0%
+them up as we see any symmetric
+ 
+
+ align:start position:0%
+them up as we see any symmetric
+symmetric that's that's number one
+
+ align:start position:0%
+symmetric that's that's number one
+ 
+
+ align:start position:0%
+symmetric that's that's number one
+that's well that's the key one that's
+
+ align:start position:0%
+that's well that's the key one that's
+ 
+
+ align:start position:0%
+that's well that's the key one that's
+the one I was hoping for so it's a
+
+ align:start position:0%
+the one I was hoping for so it's a
+ 
+
+ align:start position:0%
+the one I was hoping for so it's a
+symmetric Matrix okay what else now I'm
+
+ align:start position:0%
+symmetric Matrix okay what else now I'm
+ 
+
+ align:start position:0%
+symmetric Matrix okay what else now I'm
+thinking about this whole family not
+
+ align:start position:0%
+thinking about this whole family not
+ 
+
+ align:start position:0%
+thinking about this whole family not
+just K3 itself um what other properties
+
+ align:start position:0%
+just K3 itself um what other properties
+ 
+
+ align:start position:0%
+just K3 itself um what other properties
+so that's a key property and how would I
+
+ align:start position:0%
+so that's a key property and how would I
+ 
+
+ align:start position:0%
+so that's a key property and how would I
+write that uh I would write that as k
+
+ align:start position:0%
+write that uh I would write that as k
+ 
+
+ align:start position:0%
+write that uh I would write that as k
+equal K
+
+ align:start position:0%
+equal K
+ 
+
+ align:start position:0%
+equal K
+transpose that'll be my notation for the
+
+ align:start position:0%
+transpose that'll be my notation for the
+ 
+
+ align:start position:0%
+transpose that'll be my notation for the
+transpose of the Matrix mat lab's
+
+ align:start position:0%
+transpose of the Matrix mat lab's
+ 
+
+ align:start position:0%
+transpose of the Matrix mat lab's
+notation would be a prime uh I'll use a
+
+ align:start position:0%
+notation would be a prime uh I'll use a
+ 
+
+ align:start position:0%
+notation would be a prime uh I'll use a
+transpose okay so that's symmetric
+
+ align:start position:0%
+transpose okay so that's symmetric
+ 
+
+ align:start position:0%
+transpose okay so that's symmetric
+matricies show up all the time in
+
+ align:start position:0%
+matricies show up all the time in
+ 
+
+ align:start position:0%
+matricies show up all the time in
+applications and that's we're lucky they
+
+ align:start position:0%
+applications and that's we're lucky they
+ 
+
+ align:start position:0%
+applications and that's we're lucky they
+do okay what other properties of this
+
+ align:start position:0%
+do okay what other properties of this
+ 
+
+ align:start position:0%
+do okay what other properties of this
+family strike you yeah it's not singular
+
+ align:start position:0%
+family strike you yeah it's not singular
+ 
+
+ align:start position:0%
+family strike you yeah it's not singular
+oh well now that's a that's a key
+
+ align:start position:0%
+oh well now that's a that's a key
+ 
+
+ align:start position:0%
+oh well now that's a that's a key
+question uh to decide whether the Matrix
+
+ align:start position:0%
+question uh to decide whether the Matrix
+ 
+
+ align:start position:0%
+question uh to decide whether the Matrix
+has an inverse whether it's non singular
+
+ align:start position:0%
+has an inverse whether it's non singular
+ 
+
+ align:start position:0%
+has an inverse whether it's non singular
+okay I'm going to put that in the sort
+
+ align:start position:0%
+okay I'm going to put that in the sort
+ 
+
+ align:start position:0%
+okay I'm going to put that in the sort
+of more difficult column because you
+
+ align:start position:0%
+of more difficult column because you
+ 
+
+ align:start position:0%
+of more difficult column because you
+can't just glance at a matrix and decide
+
+ align:start position:0%
+can't just glance at a matrix and decide
+ 
+
+ align:start position:0%
+can't just glance at a matrix and decide
+that where we can glance at it and see
+
+ align:start position:0%
+that where we can glance at it and see
+ 
+
+ align:start position:0%
+that where we can glance at it and see
+that it's symmetric so but it's true
+
+ align:start position:0%
+that it's symmetric so but it's true
+ 
+
+ align:start position:0%
+that it's symmetric so but it's true
+that it's non- singular or which is
+
+ align:start position:0%
+that it's non- singular or which is
+ 
+
+ align:start position:0%
+that it's non- singular or which is
+another word
+
+ align:start position:0%
+another word
+ 
+
+ align:start position:0%
+another word
+for uh
+
+ align:start position:0%
+for uh
+ 
+
+ align:start position:0%
+for uh
+invertible so we be interested in what
+
+ align:start position:0%
+invertible so we be interested in what
+ 
+
+ align:start position:0%
+invertible so we be interested in what
+those inverses are and I can do the 3X3
+
+ align:start position:0%
+those inverses are and I can do the 3X3
+ 
+
+ align:start position:0%
+those inverses are and I can do the 3X3
+inverses or I could do two by twos also
+
+ align:start position:0%
+inverses or I could do two by twos also
+ 
+
+ align:start position:0%
+inverses or I could do two by twos also
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+4x4s we'll have fun with okay uh what
+
+ align:start position:0%
+4x4s we'll have fun with okay uh what
+ 
+
+ align:start position:0%
+4x4s we'll have fun with okay uh what
+other properties then so that's a
+
+ align:start position:0%
+other properties then so that's a
+ 
+
+ align:start position:0%
+other properties then so that's a
+property to
+
+ align:start position:0%
+property to
+ 
+
+ align:start position:0%
+property to
+be to be determined so to speak um what
+
+ align:start position:0%
+be to be determined so to speak um what
+ 
+
+ align:start position:0%
+be to be determined so to speak um what
+else about these matrices yeah trional
+
+ align:start position:0%
+else about these matrices yeah trional
+ 
+
+ align:start position:0%
+else about these matrices yeah trional
+triagonal that's another key property of
+
+ align:start position:0%
+triagonal that's another key property of
+ 
+
+ align:start position:0%
+triagonal that's another key property of
+a matrix Tri diagonal
+
+ align:start position:0%
+a matrix Tri diagonal
+ 
+
+ align:start position:0%
+a matrix Tri diagonal
+so uh and everybody sees what that means
+
+ align:start position:0%
+so uh and everybody sees what that means
+ 
+
+ align:start position:0%
+so uh and everybody sees what that means
+so it's a banded Matrix so banded would
+
+ align:start position:0%
+so it's a banded Matrix so banded would
+ 
+
+ align:start position:0%
+so it's a banded Matrix so banded would
+be the general family of matrices that
+
+ align:start position:0%
+be the general family of matrices that
+ 
+
+ align:start position:0%
+be the general family of matrices that
+are kind of close to the
+
+ align:start position:0%
+are kind of close to the
+ 
+
+ align:start position:0%
+are kind of close to the
+diagonal and tri diagonal is really
+
+ align:start position:0%
+diagonal and tri diagonal is really
+ 
+
+ align:start position:0%
+diagonal and tri diagonal is really
+close just the main diagonal and the two
+
+ align:start position:0%
+close just the main diagonal and the two
+ 
+
+ align:start position:0%
+close just the main diagonal and the two
+neighbors okay uh so that what's the
+
+ align:start position:0%
+neighbors okay uh so that what's the
+ 
+
+ align:start position:0%
+neighbors okay uh so that what's the
+consequence of
+
+ align:start position:0%
+consequence of
+ 
+
+ align:start position:0%
+consequence of
+triagonal rough so it means it's lots of
+
+ align:start position:0%
+triagonal rough so it means it's lots of
+ 
+
+ align:start position:0%
+triagonal rough so it means it's lots of
+zeros right in the here I'm only seeing
+
+ align:start position:0%
+zeros right in the here I'm only seeing
+ 
+
+ align:start position:0%
+zeros right in the here I'm only seeing
+those two zeros but um once the family
+
+ align:start position:0%
+those two zeros but um once the family
+ 
+
+ align:start position:0%
+those two zeros but um once the family
+is once we're up to say 100 by 100 or
+
+ align:start position:0%
+is once we're up to say 100 by 100 or
+ 
+
+ align:start position:0%
+is once we're up to say 100 by 100 or
+thousand by thousand now will that
+
+ align:start position:0%
+thousand by thousand now will that
+ 
+
+ align:start position:0%
+thousand by thousand now will that
+Matrix be hard to compute with pretty SP
+
+ align:start position:0%
+Matrix be hard to compute with pretty SP
+ 
+
+ align:start position:0%
+Matrix be hard to compute with pretty SP
+it's extremely sparse that's right
+
+ align:start position:0%
+it's extremely sparse that's right
+ 
+
+ align:start position:0%
+it's extremely sparse that's right
+extremely sparse and extremely
+
+ align:start position:0%
+extremely sparse and extremely
+ 
+
+ align:start position:0%
+extremely sparse and extremely
+structured so actually the Thousand by
+
+ align:start position:0%
+structured so actually the Thousand by
+ 
+
+ align:start position:0%
+structured so actually the Thousand by
+th000 matrix will be total cinch to
+
+ align:start position:0%
+th000 matrix will be total cinch to
+ 
+
+ align:start position:0%
+th000 matrix will be total cinch to
+compute with we can we can uh solve uh
+
+ align:start position:0%
+compute with we can we can uh solve uh
+ 
+
+ align:start position:0%
+compute with we can we can uh solve uh
+linear equations with with a tridiagonal
+
+ align:start position:0%
+linear equations with with a tridiagonal
+ 
+
+ align:start position:0%
+linear equations with with a tridiagonal
+matrix uh very very fast so it's
+
+ align:start position:0%
+matrix uh very very fast so it's
+ 
+
+ align:start position:0%
+matrix uh very very fast so it's
+extremely convenient okay that that's
+
+ align:start position:0%
+extremely convenient okay that that's
+ 
+
+ align:start position:0%
+extremely convenient okay that that's
+good uh any other comment on these
+
+ align:start position:0%
+good uh any other comment on these
+ 
+
+ align:start position:0%
+good uh any other comment on these
+matrices before we uh yeah
+
+ align:start position:0%
+matrices before we uh yeah
+ 
+
+ align:start position:0%
+matrices before we uh yeah
+uh ah yes okay this is great I I'm not
+
+ align:start position:0%
+uh ah yes okay this is great I I'm not
+ 
+
+ align:start position:0%
+uh ah yes okay this is great I I'm not
+going to have to teach this class at all
+
+ align:start position:0%
+going to have to teach this class at all
+ 
+
+ align:start position:0%
+going to have to teach this class at all
+uh uh okay so the Matrix
+
+ align:start position:0%
+uh uh okay so the Matrix
+ 
+
+ align:start position:0%
+uh uh okay so the Matrix
+has constant diagonals so it's not only
+
+ align:start position:0%
+has constant diagonals so it's not only
+ 
+
+ align:start position:0%
+has constant diagonals so it's not only
+Tri diagonal but but there's a certain
+
+ align:start position:0%
+Tri diagonal but but there's a certain
+ 
+
+ align:start position:0%
+Tri diagonal but but there's a certain
+time invariance or shift and variance
+
+ align:start position:0%
+time invariance or shift and variance
+ 
+
+ align:start position:0%
+time invariance or shift and variance
+going on there so can I put constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagonal
+
+ align:start position:0%
+diagonal
+ 
+
+ align:start position:0%
+diagonal
+and because meaning that down each
+
+ align:start position:0%
+and because meaning that down each
+ 
+
+ align:start position:0%
+and because meaning that down each
+diagonal I'm seeing the same number okay
+
+ align:start position:0%
+diagonal I'm seeing the same number okay
+ 
+
+ align:start position:0%
+diagonal I'm seeing the same number okay
+now it's true that I'm not that there's
+
+ align:start position:0%
+now it's true that I'm not that there's
+ 
+
+ align:start position:0%
+now it's true that I'm not that there's
+this little change there so that one is
+
+ align:start position:0%
+this little change there so that one is
+ 
+
+ align:start position:0%
+this little change there so that one is
+not quite constant d diagonal but but uh
+
+ align:start position:0%
+not quite constant d diagonal but but uh
+ 
+
+ align:start position:0%
+not quite constant d diagonal but but uh
+morally speaking uh it's uh it's still
+
+ align:start position:0%
+morally speaking uh it's uh it's still
+ 
+
+ align:start position:0%
+morally speaking uh it's uh it's still
+that way okay so what while we're on
+
+ align:start position:0%
+that way okay so what while we're on
+ 
+
+ align:start position:0%
+that way okay so what while we're on
+that subject of constant diagonal
+
+ align:start position:0%
+that subject of constant diagonal
+ 
+
+ align:start position:0%
+that subject of constant diagonal
+matrices and you use the name
+
+ align:start position:0%
+matrices and you use the name
+ 
+
+ align:start position:0%
+matrices and you use the name
+uh so often they're called after
+
+ align:start position:0%
+uh so often they're called after
+ 
+
+ align:start position:0%
+uh so often they're called after
+tuplets so it's a tlets matrix it's a
+
+ align:start position:0%
+tuplets so it's a tlets matrix it's a
+ 
+
+ align:start position:0%
+tuplets so it's a tlets matrix it's a
+constant diagonal matrix it shows up all
+
+ align:start position:0%
+constant diagonal matrix it shows up all
+ 
+
+ align:start position:0%
+constant diagonal matrix it shows up all
+the time in
+
+ align:start position:0%
+the time in
+ 
+
+ align:start position:0%
+the time in
+filters and uh would have a lot to say
+
+ align:start position:0%
+filters and uh would have a lot to say
+ 
+
+ align:start position:0%
+filters and uh would have a lot to say
+about that uh at at a later point in the
+
+ align:start position:0%
+about that uh at at a later point in the
+ 
+
+ align:start position:0%
+about that uh at at a later point in the
+course uh so so it's I'm seeing this
+
+ align:start position:0%
+course uh so so it's I'm seeing this
+ 
+
+ align:start position:0%
+course uh so so it's I'm seeing this
+minus1 2 minus one pattern and uh and
+
+ align:start position:0%
+minus1 2 minus one pattern and uh and
+ 
+
+ align:start position:0%
+minus1 2 minus one pattern and uh and
+actually maybe even now we can say okay
+
+ align:start position:0%
+actually maybe even now we can say okay
+ 
+
+ align:start position:0%
+actually maybe even now we can say okay
+who
+
+ align:start position:0%
+who
+ 
+
+ align:start position:0%
+who
+knows how do we take advantage of this
+
+ align:start position:0%
+knows how do we take advantage of this
+ 
+
+ align:start position:0%
+knows how do we take advantage of this
+constant diagonal triplets uh perfect uh
+
+ align:start position:0%
+constant diagonal triplets uh perfect uh
+ 
+
+ align:start position:0%
+constant diagonal triplets uh perfect uh
+shift up and down
+
+ align:start position:0%
+shift up and down
+ 
+
+ align:start position:0%
+shift up and down
+property uh well the key is that's where
+
+ align:start position:0%
+property uh well the key is that's where
+ 
+
+ align:start position:0%
+property uh well the key is that's where
+Fier methods are perfect so we for a
+
+ align:start position:0%
+Fier methods are perfect so we for a
+ 
+
+ align:start position:0%
+Fier methods are perfect so we for a
+matrix like that we get into forier
+
+ align:start position:0%
+matrix like that we get into forier
+ 
+
+ align:start position:0%
+matrix like that we get into forier
+analysis move into the Fier domain use
+
+ align:start position:0%
+analysis move into the Fier domain use
+ 
+
+ align:start position:0%
+analysis move into the Fier domain use
+the forier transform
+
+ align:start position:0%
+the forier transform
+ 
+
+ align:start position:0%
+the forier transform
+and just the whole
+
+ align:start position:0%
+and just the whole
+ 
+
+ align:start position:0%
+and just the whole
+problem dealing with these matrices
+
+ align:start position:0%
+problem dealing with these matrices
+ 
+
+ align:start position:0%
+problem dealing with these matrices
+becomes fun when uh you move when you
+
+ align:start position:0%
+becomes fun when uh you move when you
+ 
+
+ align:start position:0%
+becomes fun when uh you move when you
+change to Fier domain okay so that's uh
+
+ align:start position:0%
+change to Fier domain okay so that's uh
+ 
+
+ align:start position:0%
+change to Fier domain okay so that's uh
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+something I mean we can't do everything
+
+ align:start position:0%
+something I mean we can't do everything
+ 
+
+ align:start position:0%
+something I mean we can't do everything
+the very first day so let's leave this
+
+ align:start position:0%
+the very first day so let's leave this
+ 
+
+ align:start position:0%
+the very first day so let's leave this
+topic uh because that's a major part of
+
+ align:start position:0%
+topic uh because that's a major part of
+ 
+
+ align:start position:0%
+topic uh because that's a major part of
+Applied Mathematics uh all that flows
+
+ align:start position:0%
+Applied Mathematics uh all that flows
+ 
+
+ align:start position:0%
+Applied Mathematics uh all that flows
+out of Fier for for a future day okay
+
+ align:start position:0%
+out of Fier for for a future day okay
+ 
+
+ align:start position:0%
+out of Fier for for a future day okay
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+um come to the properties that we we
+
+ align:start position:0%
+um come to the properties that we we
+ 
+
+ align:start position:0%
+um come to the properties that we we
+wrote down that it was invertible but
+
+ align:start position:0%
+wrote down that it was invertible but
+ 
+
+ align:start position:0%
+wrote down that it was invertible but
+how did we know
+
+ align:start position:0%
+how did we know
+ 
+
+ align:start position:0%
+how did we know
+that uh um as I say you can't just look
+
+ align:start position:0%
+that uh um as I say you can't just look
+ 
+
+ align:start position:0%
+that uh um as I say you can't just look
+at a matrix how do you know if a matrix
+
+ align:start position:0%
+at a matrix how do you know if a matrix
+ 
+
+ align:start position:0%
+at a matrix how do you know if a matrix
+is invertible or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not take a well okay so that's one way
+
+ align:start position:0%
+not take a well okay so that's one way
+ 
+
+ align:start position:0%
+not take a well okay so that's one way
+is to take its
+
+ align:start position:0%
+is to take its
+ 
+
+ align:start position:0%
+is to take its
+determinant um yes so determinant is not
+
+ align:start position:0%
+determinant um yes so determinant is not
+ 
+
+ align:start position:0%
+determinant um yes so determinant is not
+zero right
+
+ align:start position:0%
+zero right
+ 
+
+ align:start position:0%
+zero right
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um yes sorry comp right we could we can
+
+ align:start position:0%
+um yes sorry comp right we could we can
+ 
+
+ align:start position:0%
+um yes sorry comp right we could we can
+we can compute with it so somehow
+
+ align:start position:0%
+we can compute with it so somehow
+ 
+
+ align:start position:0%
+we can compute with it so somehow
+well when I say take its determinant I
+
+ align:start position:0%
+well when I say take its determinant I
+ 
+
+ align:start position:0%
+well when I say take its determinant I
+didn't actually say how we would do it
+
+ align:start position:0%
+didn't actually say how we would do it
+ 
+
+ align:start position:0%
+didn't actually say how we would do it
+or how matlb would do it in in the case
+
+ align:start position:0%
+or how matlb would do it in in the case
+ 
+
+ align:start position:0%
+or how matlb would do it in in the case
+of a larger Matrix so uh so let me speak
+
+ align:start position:0%
+of a larger Matrix so uh so let me speak
+ 
+
+ align:start position:0%
+of a larger Matrix so uh so let me speak
+about that aspect uh so
+
+ align:start position:0%
+about that aspect uh so
+ 
+
+ align:start position:0%
+about that aspect uh so
+but well of course another way to show
+
+ align:start position:0%
+but well of course another way to show
+ 
+
+ align:start position:0%
+but well of course another way to show
+that it's invertible is to write down
+
+ align:start position:0%
+that it's invertible is to write down
+ 
+
+ align:start position:0%
+that it's invertible is to write down
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+inverse uh can I uh I left a little
+
+ align:start position:0%
+inverse uh can I uh I left a little
+ 
+
+ align:start position:0%
+inverse uh can I uh I left a little
+space for that you saw that uh so could
+
+ align:start position:0%
+space for that you saw that uh so could
+ 
+
+ align:start position:0%
+space for that you saw that uh so could
+I write down the inverses
+
+ align:start position:0%
+I write down the inverses
+ 
+
+ align:start position:0%
+I write down the inverses
+of these
+
+ align:start position:0%
+of these
+ 
+
+ align:start position:0%
+of these
+matrices uh so I if I put it just
+
+ align:start position:0%
+matrices uh so I if I put it just
+ 
+
+ align:start position:0%
+matrices uh so I if I put it just
+beside uh you could do the
+
+ align:start position:0%
+beside uh you could do the
+ 
+
+ align:start position:0%
+beside uh you could do the
+multiplication and I hope get the
+
+ align:start position:0%
+multiplication and I hope get the
+ 
+
+ align:start position:0%
+multiplication and I hope get the
+identity Matrix okay so
+
+ align:start position:0%
+identity Matrix okay so
+ 
+
+ align:start position:0%
+identity Matrix okay so
+3x3 uh I think that the inverse of this
+
+ align:start position:0%
+3x3 uh I think that the inverse of this
+ 
+
+ align:start position:0%
+3x3 uh I think that the inverse of this
+one is
+
+ align:start position:0%
+one is
+ 
+
+ align:start position:0%
+one is
+three and then
+
+ align:start position:0%
+three and then
+ 
+
+ align:start position:0%
+three and then
+twos and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ones okay uh let me can we just like
+
+ align:start position:0%
+ones okay uh let me can we just like
+ 
+
+ align:start position:0%
+ones okay uh let me can we just like
+check that for a moment so I believe
+
+ align:start position:0%
+check that for a moment so I believe
+ 
+
+ align:start position:0%
+check that for a moment so I believe
+that that this is that this is T3
+
+ align:start position:0%
+that that this is that this is T3
+ 
+
+ align:start position:0%
+that that this is that this is T3
+inverse
+
+ align:start position:0%
+inverse
+ 
+
+ align:start position:0%
+inverse
+there uh does that look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay let's let's just
+
+ align:start position:0%
+right okay let's let's just
+ 
+
+ align:start position:0%
+right okay let's let's just
+uh yeah let's see what what uh what do I
+
+ align:start position:0%
+uh yeah let's see what what uh what do I
+ 
+
+ align:start position:0%
+uh yeah let's see what what uh what do I
+we want to find a pattern and and
+
+ align:start position:0%
+we want to find a pattern and and
+ 
+
+ align:start position:0%
+we want to find a pattern and and
+actually we're this one is I wrote that
+
+ align:start position:0%
+actually we're this one is I wrote that
+ 
+
+ align:start position:0%
+actually we're this one is I wrote that
+one down first because it's uh because
+
+ align:start position:0%
+one down first because it's uh because
+ 
+
+ align:start position:0%
+one down first because it's uh because
+the pattern will be easier to find for
+
+ align:start position:0%
+the pattern will be easier to find for
+ 
+
+ align:start position:0%
+the pattern will be easier to find for
+T3 um somehow let's
+
+ align:start position:0%
+T3 um somehow let's
+ 
+
+ align:start position:0%
+T3 um somehow let's
+see it it's all right it works okay now
+
+ align:start position:0%
+see it it's all right it works okay now
+ 
+
+ align:start position:0%
+see it it's all right it works okay now
+I have to ask you how you checked it I
+
+ align:start position:0%
+I have to ask you how you checked it I
+ 
+
+ align:start position:0%
+I have to ask you how you checked it I
+mean how did you do that matrix
+
+ align:start position:0%
+mean how did you do that matrix
+ 
+
+ align:start position:0%
+mean how did you do that matrix
+multiplication um you probably did rows
+
+ align:start position:0%
+multiplication um you probably did rows
+ 
+
+ align:start position:0%
+multiplication um you probably did rows
+here times columns there
+
+ align:start position:0%
+here times columns there
+ 
+
+ align:start position:0%
+here times columns there
+okay all right fair enough uh yeah
+
+ align:start position:0%
+okay all right fair enough uh yeah
+ 
+
+ align:start position:0%
+okay all right fair enough uh yeah
+actually here's can I just make a
+
+ align:start position:0%
+actually here's can I just make a
+ 
+
+ align:start position:0%
+actually here's can I just make a
+comment on that it's while we're looking
+
+ align:start position:0%
+comment on that it's while we're looking
+ 
+
+ align:start position:0%
+comment on that it's while we're looking
+it because it's terrific to have actual
+
+ align:start position:0%
+it because it's terrific to have actual
+ 
+
+ align:start position:0%
+it because it's terrific to have actual
+numbers okay what I what I mean the
+
+ align:start position:0%
+numbers okay what I what I mean the
+ 
+
+ align:start position:0%
+numbers okay what I what I mean the
+crucial thing in these all these
+
+ align:start position:0%
+crucial thing in these all these
+ 
+
+ align:start position:0%
+crucial thing in these all these
+matrices is this pattern minus1 2
+
+ align:start position:0%
+matrices is this pattern minus1 2
+ 
+
+ align:start position:0%
+matrices is this pattern minus1 2
+minus1 and we're going to recognize that
+
+ align:start position:0%
+minus1 and we're going to recognize that
+ 
+
+ align:start position:0%
+minus1 and we're going to recognize that
+as a as a kind of second difference so
+
+ align:start position:0%
+as a as a kind of second difference so
+ 
+
+ align:start position:0%
+as a as a kind of second difference so
+I'm not surprised if I take what I
+
+ align:start position:0%
+I'm not surprised if I take what I
+ 
+
+ align:start position:0%
+I'm not surprised if I take what I
+notice about that column is that it's
+
+ align:start position:0%
+notice about that column is that it's
+ 
+
+ align:start position:0%
+notice about that column is that it's
+like linear 2 1 and then if I take a
+
+ align:start position:0%
+like linear 2 1 and then if I take a
+ 
+
+ align:start position:0%
+like linear 2 1 and then if I take a
+second difference of a linear thing I
+
+ align:start position:0%
+second difference of a linear thing I
+ 
+
+ align:start position:0%
+second difference of a linear thing I
+expect to get zero just let's just check
+
+ align:start position:0%
+expect to get zero just let's just check
+ 
+
+ align:start position:0%
+expect to get zero just let's just check
+that I do -3 + 4
+
+ align:start position:0%
+that I do -3 + 4
+ 
+
+ align:start position:0%
+that I do -3 + 4
+-1 and If I multiply that row by this
+
+ align:start position:0%
+-1 and If I multiply that row by this
+ 
+
+ align:start position:0%
+-1 and If I multiply that row by this
+one well of course it's linear it's even
+
+ align:start position:0%
+one well of course it's linear it's even
+ 
+
+ align:start position:0%
+one well of course it's linear it's even
+constant so I get min -1 + 2 - one I'm
+
+ align:start position:0%
+constant so I get min -1 + 2 - one I'm
+ 
+
+ align:start position:0%
+constant so I get min -1 + 2 - one I'm
+getting zero and then of course I should
+
+ align:start position:0%
+getting zero and then of course I should
+ 
+
+ align:start position:0%
+getting zero and then of course I should
+check that I got the diagonal right Min
+
+ align:start position:0%
+check that I got the diagonal right Min
+ 
+
+ align:start position:0%
+check that I got the diagonal right Min
+-2 + 4 -1 right that's that leaves one
+
+ align:start position:0%
+-2 + 4 -1 right that's that leaves one
+ 
+
+ align:start position:0%
+-2 + 4 -1 right that's that leaves one
+okay so that is the
+
+ align:start position:0%
+okay so that is the
+ 
+
+ align:start position:0%
+okay so that is the
+inverse for
+
+ align:start position:0%
+inverse for
+ 
+
+ align:start position:0%
+inverse for
+T3 and we could guess okay so math
+
+ align:start position:0%
+T3 and we could guess okay so math
+ 
+
+ align:start position:0%
+T3 and we could guess okay so math
+mathematics is
+
+ align:start position:0%
+mathematics is
+ 
+
+ align:start position:0%
+mathematics is
+often uh I'm going to I think it'll be
+
+ align:start position:0%
+often uh I'm going to I think it'll be
+ 
+
+ align:start position:0%
+often uh I'm going to I think it'll be
+fun to see if we can find the inverses
+
+ align:start position:0%
+fun to see if we can find the inverses
+ 
+
+ align:start position:0%
+fun to see if we can find the inverses
+here and uh by a mixture of guesswork
+
+ align:start position:0%
+here and uh by a mixture of guesswork
+ 
+
+ align:start position:0%
+here and uh by a mixture of guesswork
+and then maybe understanding sort of
+
+ align:start position:0%
+and then maybe understanding sort of
+ 
+
+ align:start position:0%
+and then maybe understanding sort of
+inspired guess and then and then see
+
+ align:start position:0%
+inspired guess and then and then see
+ 
+
+ align:start position:0%
+inspired guess and then and then see
+why okay now can I move to the
+
+ align:start position:0%
+why okay now can I move to the
+ 
+
+ align:start position:0%
+why okay now can I move to the
+inverse with a question
+
+ align:start position:0%
+inverse with a question
+ 
+
+ align:start position:0%
+inverse with a question
+mark of this of this one of this
+
+ align:start position:0%
+mark of this of this one of this
+ 
+
+ align:start position:0%
+mark of this of this one of this
+one what about so this was I wrote down
+
+ align:start position:0%
+one what about so this was I wrote down
+ 
+
+ align:start position:0%
+one what about so this was I wrote down
+the word non- singular because you told
+
+ align:start position:0%
+the word non- singular because you told
+ 
+
+ align:start position:0%
+the word non- singular because you told
+me to but now I'm not so sure about this
+
+ align:start position:0%
+me to but now I'm not so sure about this
+ 
+
+ align:start position:0%
+me to but now I'm not so sure about this
+one I believe what do you think on that
+
+ align:start position:0%
+one I believe what do you think on that
+ 
+
+ align:start position:0%
+one I believe what do you think on that
+yes to zero the row sum to zero right
+
+ align:start position:0%
+yes to zero the row sum to zero right
+ 
+
+ align:start position:0%
+yes to zero the row sum to zero right
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+suspicious in fact that should actually
+
+ align:start position:0%
+suspicious in fact that should actually
+ 
+
+ align:start position:0%
+suspicious in fact that should actually
+tell us that it's not invertible right
+
+ align:start position:0%
+tell us that it's not invertible right
+ 
+
+ align:start position:0%
+tell us that it's not invertible right
+and and what's a good way to to
+
+ align:start position:0%
+and and what's a good way to to
+ 
+
+ align:start position:0%
+and and what's a good way to to
+recognize that a matrix isn't invertible
+
+ align:start position:0%
+recognize that a matrix isn't invertible
+ 
+
+ align:start position:0%
+recognize that a matrix isn't invertible
+well you could say take its
+
+ align:start position:0%
+well you could say take its
+ 
+
+ align:start position:0%
+well you could say take its
+determinant but don't say that
+
+ align:start position:0%
+determinant but don't say that
+ 
+
+ align:start position:0%
+determinant but don't say that
+uh Matt mat lab will take its
+
+ align:start position:0%
+uh Matt mat lab will take its
+ 
+
+ align:start position:0%
+uh Matt mat lab will take its
+determinant and and for 3x3 of course we
+
+ align:start position:0%
+determinant and and for 3x3 of course we
+ 
+
+ align:start position:0%
+determinant and and for 3x3 of course we
+could do it but it's much better to like
+
+ align:start position:0%
+could do it but it's much better to like
+ 
+
+ align:start position:0%
+could do it but it's much better to like
+recognize a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vector that it takes to zero if if we
+
+ align:start position:0%
+vector that it takes to zero if if we
+ 
+
+ align:start position:0%
+vector that it takes to zero if if we
+can find a vector that that it takes to
+
+ align:start position:0%
+can find a vector that that it takes to
+ 
+
+ align:start position:0%
+can find a vector that that it takes to
+zero so so what I'm going to show is B3
+
+ align:start position:0%
+zero so so what I'm going to show is B3
+ 
+
+ align:start position:0%
+zero so so what I'm going to show is B3
+is is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+singular okay and uh so that with this
+
+ align:start position:0%
+singular okay and uh so that with this
+ 
+
+ align:start position:0%
+singular okay and uh so that with this
+with both of these both the first row
+
+ align:start position:0%
+with both of these both the first row
+ 
+
+ align:start position:0%
+with both of these both the first row
+and last row uh altered
+
+ align:start position:0%
+and last row uh altered
+ 
+
+ align:start position:0%
+and last row uh altered
+uh that that brings the Matrix down
+
+ align:start position:0%
+uh that that brings the Matrix down
+ 
+
+ align:start position:0%
+uh that that brings the Matrix down
+those matrices are we'll see positive
+
+ align:start position:0%
+those matrices are we'll see positive
+ 
+
+ align:start position:0%
+those matrices are we'll see positive
+definite this one is dragged down to
+
+ align:start position:0%
+definite this one is dragged down to
+ 
+
+ align:start position:0%
+definite this one is dragged down to
+being only as we'll see positive
+
+ align:start position:0%
+being only as we'll see positive
+ 
+
+ align:start position:0%
+being only as we'll see positive
+semi-definite okay what's the vector
+
+ align:start position:0%
+semi-definite okay what's the vector
+ 
+
+ align:start position:0%
+semi-definite okay what's the vector
+that that's that's knocked out by
+
+ align:start position:0%
+that that's that's knocked out by
+ 
+
+ align:start position:0%
+that that's that's knocked out by
+B3 all ones right the constant Vector
+
+ align:start position:0%
+B3 all ones right the constant Vector
+ 
+
+ align:start position:0%
+B3 all ones right the constant Vector
+right and that's exactly because as you
+
+ align:start position:0%
+right and that's exactly because as you
+ 
+
+ align:start position:0%
+right and that's exactly because as you
+said when the when the row when the row
+
+ align:start position:0%
+said when the when the row when the row
+ 
+
+ align:start position:0%
+said when the when the row when the row
+is add to zero then when I multiply by
+
+ align:start position:0%
+is add to zero then when I multiply by
+ 
+
+ align:start position:0%
+is add to zero then when I multiply by
+all ones then I'm adding up what I'm
+
+ align:start position:0%
+all ones then I'm adding up what I'm
+ 
+
+ align:start position:0%
+all ones then I'm adding up what I'm
+doing is adding up each row and I'm
+
+ align:start position:0%
+doing is adding up each row and I'm
+ 
+
+ align:start position:0%
+doing is adding up each row and I'm
+getting all zeros and do you see that we
+
+ align:start position:0%
+getting all zeros and do you see that we
+ 
+
+ align:start position:0%
+getting all zeros and do you see that we
+have now demonstrated that the Matrix is
+
+ align:start position:0%
+have now demonstrated that the Matrix is
+ 
+
+ align:start position:0%
+have now demonstrated that the Matrix is
+singular it's it has to be a singular
+
+ align:start position:0%
+singular it's it has to be a singular
+ 
+
+ align:start position:0%
+singular it's it has to be a singular
+Matrix if it's taking some Vector to
+
+ align:start position:0%
+Matrix if it's taking some Vector to
+ 
+
+ align:start position:0%
+Matrix if it's taking some Vector to
+zero it it couldn't have an inverse if
+
+ align:start position:0%
+zero it it couldn't have an inverse if
+ 
+
+ align:start position:0%
+zero it it couldn't have an inverse if
+if we have a solution we have a we for
+
+ align:start position:0%
+if we have a solution we have a we for
+ 
+
+ align:start position:0%
+if we have a solution we have a we for
+this B3 we found a vector X that is
+
+ align:start position:0%
+this B3 we found a vector X that is
+ 
+
+ align:start position:0%
+this B3 we found a vector X that is
+completely knocked
+
+ align:start position:0%
+completely knocked
+ 
+
+ align:start position:0%
+completely knocked
+out okay now if there was an inverse we
+
+ align:start position:0%
+out okay now if there was an inverse we
+ 
+
+ align:start position:0%
+out okay now if there was an inverse we
+could multiply that equation by that
+
+ align:start position:0%
+could multiply that equation by that
+ 
+
+ align:start position:0%
+could multiply that equation by that
+inverse and what would we
+
+ align:start position:0%
+inverse and what would we
+ 
+
+ align:start position:0%
+inverse and what would we
+learn we we learn X is zero so it if a
+
+ align:start position:0%
+learn we we learn X is zero so it if a
+ 
+
+ align:start position:0%
+learn we we learn X is zero so it if a
+if a matrix I'm talking about Square
+
+ align:start position:0%
+if a matrix I'm talking about Square
+ 
+
+ align:start position:0%
+if a matrix I'm talking about Square
+matrices here if it has an
+
+ align:start position:0%
+matrices here if it has an
+ 
+
+ align:start position:0%
+matrices here if it has an
+inverse then the only
+
+ align:start position:0%
+inverse then the only
+ 
+
+ align:start position:0%
+inverse then the only
+Vector X that would solve this equation
+
+ align:start position:0%
+Vector X that would solve this equation
+ 
+
+ align:start position:0%
+Vector X that would solve this equation
+would be the zero vector
+
+ align:start position:0%
+would be the zero vector
+ 
+
+ align:start position:0%
+would be the zero vector
+and and that's the case for those two
+
+ align:start position:0%
+and and that's the case for those two
+ 
+
+ align:start position:0%
+and and that's the case for those two
+but here we have an X not the zero
+
+ align:start position:0%
+but here we have an X not the zero
+ 
+
+ align:start position:0%
+but here we have an X not the zero
+Vector that solves the equation so we
+
+ align:start position:0%
+Vector that solves the equation so we
+ 
+
+ align:start position:0%
+Vector that solves the equation so we
+know there's a there there are vectors X
+
+ align:start position:0%
+know there's a there there are vectors X
+ 
+
+ align:start position:0%
+know there's a there there are vectors X
+that are knocked out can I just repeat
+
+ align:start position:0%
+that are knocked out can I just repeat
+ 
+
+ align:start position:0%
+that are knocked out can I just repeat
+that argument from this if there is an
+
+ align:start position:0%
+that argument from this if there is an
+ 
+
+ align:start position:0%
+that argument from this if there is an
+inverse I could multiply by
+
+ align:start position:0%
+inverse I could multiply by
+ 
+
+ align:start position:0%
+inverse I could multiply by
+it and I would learn X was zero so so
+
+ align:start position:0%
+it and I would learn X was zero so so
+ 
+
+ align:start position:0%
+it and I would learn X was zero so so
+having an inverse means the only
+
+ align:start position:0%
+having an inverse means the only
+ 
+
+ align:start position:0%
+having an inverse means the only
+solution so in these cases
+
+ align:start position:0%
+solution so in these cases
+ 
+
+ align:start position:0%
+solution so in these cases
+which which do have inverses the only
+
+ align:start position:0%
+which which do have inverses the only
+ 
+
+ align:start position:0%
+which which do have inverses the only
+solution to t3x equal 0 is the is the
+
+ align:start position:0%
+solution to t3x equal 0 is the is the
+ 
+
+ align:start position:0%
+solution to t3x equal 0 is the is the
+zero Vector but here we have other
+
+ align:start position:0%
+zero Vector but here we have other
+ 
+
+ align:start position:0%
+zero Vector but here we have other
+Solutions in fact while we're at it tell
+
+ align:start position:0%
+Solutions in fact while we're at it tell
+ 
+
+ align:start position:0%
+Solutions in fact while we're at it tell
+me more solutions to b3x equals 0 to
+
+ align:start position:0%
+me more solutions to b3x equals 0 to
+ 
+
+ align:start position:0%
+me more solutions to b3x equals 0 to
+tell me the whole null space of this
+
+ align:start position:0%
+tell me the whole null space of this
+ 
+
+ align:start position:0%
+tell me the whole null space of this
+Matrix so this this x just to use that
+
+ align:start position:0%
+Matrix so this this x just to use that
+ 
+
+ align:start position:0%
+Matrix so this this x just to use that
+word this x is in the null
+
+ align:start position:0%
+word this x is in the null
+ 
+
+ align:start position:0%
+word this x is in the null
+space meaning just what it says of B3
+
+ align:start position:0%
+space meaning just what it says of B3
+ 
+
+ align:start position:0%
+space meaning just what it says of B3
+okay and now tell me another X that's in
+
+ align:start position:0%
+okay and now tell me another X that's in
+ 
+
+ align:start position:0%
+okay and now tell me another X that's in
+the null
+
+ align:start position:0%
+the null
+ 
+
+ align:start position:0%
+the null
+space yeah any constant times it
+
+ align:start position:0%
+space yeah any constant times it
+ 
+
+ align:start position:0%
+space yeah any constant times it
+333 or
+
+ align:start position:0%
+333 or
+ 
+
+ align:start position:0%
+333 or
+666 and in fact that's the whole null
+
+ align:start position:0%
+666 and in fact that's the whole null
+ 
+
+ align:start position:0%
+666 and in fact that's the whole null
+space the the null space is any
+
+ align:start position:0%
+space the the null space is any
+ 
+
+ align:start position:0%
+space the the null space is any
+multiple of that particular Vector X and
+
+ align:start position:0%
+multiple of that particular Vector X and
+ 
+
+ align:start position:0%
+multiple of that particular Vector X and
+uh that that the null space is that line
+
+ align:start position:0%
+uh that that the null space is that line
+ 
+
+ align:start position:0%
+uh that that the null space is that line
+okay one other point actually an
+
+ align:start position:0%
+okay one other point actually an
+ 
+
+ align:start position:0%
+okay one other point actually an
+important point just while we're doing
+
+ align:start position:0%
+important point just while we're doing
+ 
+
+ align:start position:0%
+important point just while we're doing
+matrices how do I multiply a matrix by a
+
+ align:start position:0%
+matrices how do I multiply a matrix by a
+ 
+
+ align:start position:0%
+matrices how do I multiply a matrix by a
+vector what do I what do I see going on
+
+ align:start position:0%
+vector what do I what do I see going on
+ 
+
+ align:start position:0%
+vector what do I what do I see going on
+there I like to
+
+ align:start position:0%
+there I like to
+ 
+
+ align:start position:0%
+there I like to
+multiply by columns a column at a time
+
+ align:start position:0%
+multiply by columns a column at a time
+ 
+
+ align:start position:0%
+multiply by columns a column at a time
+so I see this as that multiplication of
+
+ align:start position:0%
+so I see this as that multiplication of
+ 
+
+ align:start position:0%
+so I see this as that multiplication of
+a matrix by Vector this is how I think
+
+ align:start position:0%
+a matrix by Vector this is how I think
+ 
+
+ align:start position:0%
+a matrix by Vector this is how I think
+of it as 1 times the First Column plus 1
+
+ align:start position:0%
+of it as 1 times the First Column plus 1
+ 
+
+ align:start position:0%
+of it as 1 times the First Column plus 1
+* the second column plus 1 * the third
+
+ align:start position:0%
+* the second column plus 1 * the third
+ 
+
+ align:start position:0%
+* the second column plus 1 * the third
+column so what in this case because it
+
+ align:start position:0%
+column so what in this case because it
+ 
+
+ align:start position:0%
+column so what in this case because it
+happened to be all ones I'm I'm just I'm
+
+ align:start position:0%
+happened to be all ones I'm I'm just I'm
+ 
+
+ align:start position:0%
+happened to be all ones I'm I'm just I'm
+taking the First Column plus the second
+
+ align:start position:0%
+taking the First Column plus the second
+ 
+
+ align:start position:0%
+taking the First Column plus the second
+column plus the third column and then
+
+ align:start position:0%
+column plus the third column and then
+ 
+
+ align:start position:0%
+column plus the third column and then
+getting the answer do you see that I've
+
+ align:start position:0%
+getting the answer do you see that I've
+ 
+
+ align:start position:0%
+getting the answer do you see that I've
+done it like with columns you were
+
+ align:start position:0%
+done it like with columns you were
+ 
+
+ align:start position:0%
+done it like with columns you were
+probably inclined to take that row times
+
+ align:start position:0%
+probably inclined to take that row times
+ 
+
+ align:start position:0%
+probably inclined to take that row times
+this which was a natural thing to do and
+
+ align:start position:0%
+this which was a natural thing to do and
+ 
+
+ align:start position:0%
+this which was a natural thing to do and
+get that zero and then that row times
+
+ align:start position:0%
+get that zero and then that row times
+ 
+
+ align:start position:0%
+get that zero and then that row times
+this and get that zero what I'm saying
+
+ align:start position:0%
+this and get that zero what I'm saying
+ 
+
+ align:start position:0%
+this and get that zero what I'm saying
+is also think about matrix
+
+ align:start position:0%
+is also think about matrix
+ 
+
+ align:start position:0%
+is also think about matrix
+multiplication by columns so one of that
+
+ align:start position:0%
+multiplication by columns so one of that
+ 
+
+ align:start position:0%
+multiplication by columns so one of that
+column one of that column one of that
+
+ align:start position:0%
+column one of that column one of that
+ 
+
+ align:start position:0%
+column one of that column one of that
+column gives the zero column sort of
+
+ align:start position:0%
+column gives the zero column sort of
+ 
+
+ align:start position:0%
+column gives the zero column sort of
+vector at a time okay so that's for B3
+
+ align:start position:0%
+vector at a time okay so that's for B3
+ 
+
+ align:start position:0%
+vector at a time okay so that's for B3
+now it's
+
+ align:start position:0%
+now it's
+ 
+
+ align:start position:0%
+now it's
+uh it's giving us an example of a
+
+ align:start position:0%
+uh it's giving us an example of a
+ 
+
+ align:start position:0%
+uh it's giving us an example of a
+singular
+
+ align:start position:0%
+singular
+ 
+
+ align:start position:0%
+singular
+Matrix now let me come back to these
+
+ align:start position:0%
+Matrix now let me come back to these
+ 
+
+ align:start position:0%
+Matrix now let me come back to these
+non- singular
+
+ align:start position:0%
+non- singular
+ 
+
+ align:start position:0%
+non- singular
+ones okay well my
+
+ align:start position:0%
+ones okay well my
+ 
+
+ align:start position:0%
+ones okay well my
+real challenge is to fill in that space
+
+ align:start position:0%
+real challenge is to fill in that space
+ 
+
+ align:start position:0%
+real challenge is to fill in that space
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+K3 can I tell you what K3 is and then
+
+ align:start position:0%
+K3 can I tell you what K3 is and then
+ 
+
+ align:start position:0%
+K3 can I tell you what K3 is and then
+ask you next week what K4 K3 inverse and
+
+ align:start position:0%
+ask you next week what K4 K3 inverse and
+ 
+
+ align:start position:0%
+ask you next week what K4 K3 inverse and
+and ask you next week what K4 inverse
+
+ align:start position:0%
+and ask you next week what K4 inverse
+ 
+
+ align:start position:0%
+and ask you next week what K4 inverse
+is uh yeah because here's because it
+
+ align:start position:0%
+is uh yeah because here's because it
+ 
+
+ align:start position:0%
+is uh yeah because here's because it
+took me a little while I had a long
+
+ align:start position:0%
+took me a little while I had a long
+ 
+
+ align:start position:0%
+took me a little while I had a long
+flight and I came back with the inverse
+
+ align:start position:0%
+flight and I came back with the inverse
+ 
+
+ align:start position:0%
+flight and I came back with the inverse
+to this Matrix okay so here it is uh
+
+ align:start position:0%
+to this Matrix okay so here it is uh
+ 
+
+ align:start position:0%
+to this Matrix okay so here it is uh
+it's got a factor 1 14 in it so can I
+
+ align:start position:0%
+it's got a factor 1 14 in it so can I
+ 
+
+ align:start position:0%
+it's got a factor 1 14 in it so can I
+just bring that factor out
+
+ align:start position:0%
+just bring that factor out
+ 
+
+ align:start position:0%
+just bring that factor out
+and then I think
+
+ align:start position:0%
+and then I think
+ 
+
+ align:start position:0%
+and then I think
+it's O I think it's
+
+ align:start position:0%
+it's O I think it's
+ 
+
+ align:start position:0%
+it's O I think it's
+three 2 one it sort of starts the same
+
+ align:start position:0%
+three 2 one it sort of starts the same
+ 
+
+ align:start position:0%
+three 2 one it sort of starts the same
+and then I think it's a four in the
+
+ align:start position:0%
+and then I think it's a four in the
+ 
+
+ align:start position:0%
+and then I think it's a four in the
+middle okay can I can I check one or two
+
+ align:start position:0%
+middle okay can I can I check one or two
+ 
+
+ align:start position:0%
+middle okay can I can I check one or two
+cases to see if my memory is reasonable
+
+ align:start position:0%
+cases to see if my memory is reasonable
+ 
+
+ align:start position:0%
+cases to see if my memory is reasonable
+say the first row 6 minus 2 is four and
+
+ align:start position:0%
+say the first row 6 minus 2 is four and
+ 
+
+ align:start position:0%
+say the first row 6 minus 2 is four and
+then when I divide by the four I get one
+
+ align:start position:0%
+then when I divide by the four I get one
+ 
+
+ align:start position:0%
+then when I divide by the four I get one
+correctly
+
+ align:start position:0%
+correctly
+ 
+
+ align:start position:0%
+correctly
+4 - 4 is 0 fine 2 - 2 is zero yeah I
+
+ align:start position:0%
+4 - 4 is 0 fine 2 - 2 is zero yeah I
+ 
+
+ align:start position:0%
+4 - 4 is 0 fine 2 - 2 is zero yeah I
+think that's right so um so that's the
+
+ align:start position:0%
+think that's right so um so that's the
+ 
+
+ align:start position:0%
+think that's right so um so that's the
+inverse and and just while we're on the
+
+ align:start position:0%
+inverse and and just while we're on the
+ 
+
+ align:start position:0%
+inverse and and just while we're on the
+subject where why any idea why why
+
+ align:start position:0%
+subject where why any idea why why
+ 
+
+ align:start position:0%
+subject where why any idea why why
+there's why the denominator is a four
+
+ align:start position:0%
+there's why the denominator is a four
+ 
+
+ align:start position:0%
+there's why the denominator is a four
+there if you do you know about inverses
+
+ align:start position:0%
+there if you do you know about inverses
+ 
+
+ align:start position:0%
+there if you do you know about inverses
+of matrices because there be so there'
+
+ align:start position:0%
+of matrices because there be so there'
+ 
+
+ align:start position:0%
+of matrices because there be so there'
+be some general formula for the inverse
+
+ align:start position:0%
+be some general formula for the inverse
+ 
+
+ align:start position:0%
+be some general formula for the inverse
+of a matrix and what goes in the
+
+ align:start position:0%
+of a matrix and what goes in the
+ 
+
+ align:start position:0%
+of a matrix and what goes in the
+denominator in that formula the
+
+ align:start position:0%
+denominator in that formula the
+ 
+
+ align:start position:0%
+denominator in that formula the
+determinant the determinant right so so
+
+ align:start position:0%
+determinant the determinant right so so
+ 
+
+ align:start position:0%
+determinant the determinant right so so
+four is the determinant of this Matrix
+
+ align:start position:0%
+four is the determinant of this Matrix
+ 
+
+ align:start position:0%
+four is the determinant of this Matrix
+so it's the denominator but then puzzle
+
+ align:start position:0%
+so it's the denominator but then puzzle
+ 
+
+ align:start position:0%
+so it's the denominator but then puzzle
+out the rest of the numbers that's
+
+ align:start position:0%
+out the rest of the numbers that's
+ 
+
+ align:start position:0%
+out the rest of the numbers that's
+that's the key that's the key question
+
+ align:start position:0%
+that's the key that's the key question
+ 
+
+ align:start position:0%
+that's the key that's the key question
+okay this one the determinant happened
+
+ align:start position:0%
+okay this one the determinant happened
+ 
+
+ align:start position:0%
+okay this one the determinant happened
+to be one that's why we didn't notice it
+
+ align:start position:0%
+to be one that's why we didn't notice it
+ 
+
+ align:start position:0%
+to be one that's why we didn't notice it
+in denominator there okay
+
+ align:start position:0%
+in denominator there okay
+ 
+
+ align:start position:0%
+in denominator there okay
+now all right so what do we do with
+
+ align:start position:0%
+now all right so what do we do with
+ 
+
+ align:start position:0%
+now all right so what do we do with
+these matrices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm I'm I'm still in this mode of
+
+ align:start position:0%
+I'm I'm I'm still in this mode of
+ 
+
+ align:start position:0%
+I'm I'm I'm still in this mode of
+solving equations so imagining these
+
+ align:start position:0%
+solving equations so imagining these
+ 
+
+ align:start position:0%
+solving equations so imagining these
+matrices came from somewhere okay so how
+
+ align:start position:0%
+matrices came from somewhere okay so how
+ 
+
+ align:start position:0%
+matrices came from somewhere okay so how
+would I solve let's say so that's the
+
+ align:start position:0%
+would I solve let's say so that's the
+ 
+
+ align:start position:0%
+would I solve let's say so that's the
+inverse and I'll notice that the inverse
+
+ align:start position:0%
+inverse and I'll notice that the inverse
+ 
+
+ align:start position:0%
+inverse and I'll notice that the inverse
+is symmetric too so the inverse is also
+
+ align:start position:0%
+is symmetric too so the inverse is also
+ 
+
+ align:start position:0%
+is symmetric too so the inverse is also
+symmetric but not Tri
+
+ align:start position:0%
+symmetric but not Tri
+ 
+
+ align:start position:0%
+symmetric but not Tri
+diagonal if the inverse is filled up so
+
+ align:start position:0%
+diagonal if the inverse is filled up so
+ 
+
+ align:start position:0%
+diagonal if the inverse is filled up so
+it's not good to work with inverse
+
+ align:start position:0%
+it's not good to work with inverse
+ 
+
+ align:start position:0%
+it's not good to work with inverse
+matrices I
+
+ align:start position:0%
+matrices I
+ 
+
+ align:start position:0%
+matrices I
+uh I would if I have to solve this
+
+ align:start position:0%
+uh I would if I have to solve this
+ 
+
+ align:start position:0%
+uh I would if I have to solve this
+system um so let me now make a little
+
+ align:start position:0%
+system um so let me now make a little
+ 
+
+ align:start position:0%
+system um so let me now make a little
+space to to deal with it suppose I now
+
+ align:start position:0%
+space to to deal with it suppose I now
+ 
+
+ align:start position:0%
+space to to deal with it suppose I now
+want to solve a system K3 u = f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the source of this equation will be
+
+ align:start position:0%
+so the source of this equation will be
+ 
+
+ align:start position:0%
+so the source of this equation will be
+in in lecture two let's take it as it is
+
+ align:start position:0%
+in in lecture two let's take it as it is
+ 
+
+ align:start position:0%
+in in lecture two let's take it as it is
+and and uh figure out how to solve for
+
+ align:start position:0%
+and and uh figure out how to solve for
+ 
+
+ align:start position:0%
+and and uh figure out how to solve for
+it how to solve it okay just so this is
+
+ align:start position:0%
+it how to solve it okay just so this is
+ 
+
+ align:start position:0%
+it how to solve it okay just so this is
+now a quick review of linear algebra
+
+ align:start position:0%
+now a quick review of linear algebra
+ 
+
+ align:start position:0%
+now a quick review of linear algebra
+with apologies to those who um mastered
+
+ align:start position:0%
+with apologies to those who um mastered
+ 
+
+ align:start position:0%
+with apologies to those who um mastered
+the subject completely uh in the summer
+
+ align:start position:0%
+the subject completely uh in the summer
+ 
+
+ align:start position:0%
+the subject completely uh in the summer
+uh this is this is I have
+
+ align:start position:0%
+uh this is this is I have
+ 
+
+ align:start position:0%
+uh this is this is I have
+to where am I
+
+ align:start position:0%
+to where am I
+ 
+
+ align:start position:0%
+to where am I
+headed well I have to talk about solving
+
+ align:start position:0%
+headed well I have to talk about solving
+ 
+
+ align:start position:0%
+headed well I have to talk about solving
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+equations and for one part of this
+
+ align:start position:0%
+equations and for one part of this
+ 
+
+ align:start position:0%
+equations and for one part of this
+lecture I'll actually go through a
+
+ align:start position:0%
+lecture I'll actually go through a
+ 
+
+ align:start position:0%
+lecture I'll actually go through a
+little of the mechanics but of course
+
+ align:start position:0%
+little of the mechanics but of course
+ 
+
+ align:start position:0%
+little of the mechanics but of course
+matlb is going to do the job for us but
+
+ align:start position:0%
+matlb is going to do the job for us but
+ 
+
+ align:start position:0%
+matlb is going to do the job for us but
+in the mechanics so this solving this
+
+ align:start position:0%
+in the mechanics so this solving this
+ 
+
+ align:start position:0%
+in the mechanics so this solving this
+equation by elimination so I'm going to
+
+ align:start position:0%
+equation by elimination so I'm going to
+ 
+
+ align:start position:0%
+equation by elimination so I'm going to
+solve this by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elimination so that means I do a lot of
+
+ align:start position:0%
+elimination so that means I do a lot of
+ 
+
+ align:start position:0%
+elimination so that means I do a lot of
+row operations right I multiply this
+
+ align:start position:0%
+row operations right I multiply this
+ 
+
+ align:start position:0%
+row operations right I multiply this
+row by a suitable multiplier
+
+ align:start position:0%
+row by a suitable multiplier
+ 
+
+ align:start position:0%
+row by a suitable multiplier
+and I use it onto the next row to
+
+ align:start position:0%
+and I use it onto the next row to
+ 
+
+ align:start position:0%
+and I use it onto the next row to
+produce a zero in that spot remember the
+
+ align:start position:0%
+produce a zero in that spot remember the
+ 
+
+ align:start position:0%
+produce a zero in that spot remember the
+key idea of solving equations is to make
+
+ align:start position:0%
+key idea of solving equations is to make
+ 
+
+ align:start position:0%
+key idea of solving equations is to make
+them systematically
+
+ align:start position:0%
+them systematically
+ 
+
+ align:start position:0%
+them systematically
+simpler uh I'll even since space is
+
+ align:start position:0%
+simpler uh I'll even since space is
+ 
+
+ align:start position:0%
+simpler uh I'll even since space is
+getting short let me do 2 by two first
+
+ align:start position:0%
+getting short let me do 2 by two first
+ 
+
+ align:start position:0%
+getting short let me do 2 by two first
+okay so I'll take the 2 by two case Okay
+
+ align:start position:0%
+okay so I'll take the 2 by two case Okay
+ 
+
+ align:start position:0%
+okay so I'll take the 2 by two case Okay
+so so this is just K2
+
+ align:start position:0%
+so so this is just K2
+ 
+
+ align:start position:0%
+so so this is just K2
+now okay and it's got some XY y equals
+
+ align:start position:0%
+now okay and it's got some XY y equals
+ 
+
+ align:start position:0%
+now okay and it's got some XY y equals
+so we take some whatever right hand
+
+ align:start position:0%
+so we take some whatever right hand
+ 
+
+ align:start position:0%
+so we take some whatever right hand
+side
+
+ align:start position:0%
+side
+ 
+
+ align:start position:0%
+side
+F okay so uh equals some right hand side
+
+ align:start position:0%
+F okay so uh equals some right hand side
+ 
+
+ align:start position:0%
+F okay so uh equals some right hand side
+fub1 F2
+
+ align:start position:0%
+fub1 F2
+ 
+
+ align:start position:0%
+fub1 F2
+okay okay H how do you solve a system
+
+ align:start position:0%
+okay okay H how do you solve a system
+ 
+
+ align:start position:0%
+okay okay H how do you solve a system
+like that well elimination is the way to
+
+ align:start position:0%
+like that well elimination is the way to
+ 
+
+ align:start position:0%
+like that well elimination is the way to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+it um so what does elimination mean it
+
+ align:start position:0%
+it um so what does elimination mean it
+ 
+
+ align:start position:0%
+it um so what does elimination mean it
+means that I in words
+
+ align:start position:0%
+means that I in words
+ 
+
+ align:start position:0%
+means that I in words
+I would like to add half of that row to
+
+ align:start position:0%
+I would like to add half of that row to
+ 
+
+ align:start position:0%
+I would like to add half of that row to
+that one right that would be that would
+
+ align:start position:0%
+that one right that would be that would
+ 
+
+ align:start position:0%
+that one right that would be that would
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+produce so elimination
+
+ align:start position:0%
+produce so elimination
+ 
+
+ align:start position:0%
+produce so elimination
+would add half of that row so the first
+
+ align:start position:0%
+would add half of that row so the first
+ 
+
+ align:start position:0%
+would add half of that row so the first
+equation won't change 2 - one will still
+
+ align:start position:0%
+equation won't change 2 - one will still
+ 
+
+ align:start position:0%
+equation won't change 2 - one will still
+multiply XY and still
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+produce
+
+ align:start position:0%
+produce
+ 
+
+ align:start position:0%
+produce
+FS1 but what will be the second equation
+
+ align:start position:0%
+FS1 but what will be the second equation
+ 
+
+ align:start position:0%
+FS1 but what will be the second equation
+after elimination so I'm going to add
+
+ align:start position:0%
+after elimination so I'm going to add
+ 
+
+ align:start position:0%
+after elimination so I'm going to add
+half of that to this in order to produce
+
+ align:start position:0%
+half of that to this in order to produce
+ 
+
+ align:start position:0%
+half of that to this in order to produce
+that zero and then when I add half of
+
+ align:start position:0%
+that zero and then when I add half of
+ 
+
+ align:start position:0%
+that zero and then when I add half of
+that so that's minus a half added to the
+
+ align:start position:0%
+that so that's minus a half added to the
+ 
+
+ align:start position:0%
+that so that's minus a half added to the
+two I'm left with one and a half three
+
+ align:start position:0%
+two I'm left with one and a half three
+ 
+
+ align:start position:0%
+two I'm left with one and a half three
+halves XY and here I have fub1 plus a
+
+ align:start position:0%
+halves XY and here I have fub1 plus a
+ 
+
+ align:start position:0%
+halves XY and here I have fub1 plus a
+half of FS2 oh F sorry F2 is what I had
+
+ align:start position:0%
+half of FS2 oh F sorry F2 is what I had
+ 
+
+ align:start position:0%
+half of FS2 oh F sorry F2 is what I had
+and then I added on half of
+
+ align:start position:0%
+and then I added on half of
+ 
+
+ align:start position:0%
+and then I added on half of
+F1
+
+ align:start position:0%
+F1
+ 
+
+ align:start position:0%
+F1
+okay right
+
+ align:start position:0%
+okay right
+ 
+
+ align:start position:0%
+okay right
+again forgive me for dealing with a 2 by
+
+ align:start position:0%
+again forgive me for dealing with a 2 by
+ 
+
+ align:start position:0%
+again forgive me for dealing with a 2 by
+two system but it's best to see it all
+
+ align:start position:0%
+two system but it's best to see it all
+ 
+
+ align:start position:0%
+two system but it's best to see it all
+clearly see the whole step okay so so we
+
+ align:start position:0%
+clearly see the whole step okay so so we
+ 
+
+ align:start position:0%
+clearly see the whole step okay so so we
+did a
+
+ align:start position:0%
+did a
+ 
+
+ align:start position:0%
+did a
+multiplication and I patiently copied uh
+
+ align:start position:0%
+multiplication and I patiently copied uh
+ 
+
+ align:start position:0%
+multiplication and I patiently copied uh
+the unknown XY but that was a waste of
+
+ align:start position:0%
+the unknown XY but that was a waste of
+ 
+
+ align:start position:0%
+the unknown XY but that was a waste of
+my of time and space and I also followed
+
+ align:start position:0%
+my of time and space and I also followed
+ 
+
+ align:start position:0%
+my of time and space and I also followed
+up on the right hand side I had to do to
+
+ align:start position:0%
+up on the right hand side I had to do to
+ 
+
+ align:start position:0%
+up on the right hand side I had to do to
+the right hand side what I did to the
+
+ align:start position:0%
+the right hand side what I did to the
+ 
+
+ align:start position:0%
+the right hand side what I did to the
+left but the
+
+ align:start position:0%
+left but the
+ 
+
+ align:start position:0%
+left but the
+serious effort the thinking is all in
+
+ align:start position:0%
+serious effort the thinking is all in
+ 
+
+ align:start position:0%
+serious effort the thinking is all in
+the Matrix in going from this Matrix
+
+ align:start position:0%
+the Matrix in going from this Matrix
+ 
+
+ align:start position:0%
+the Matrix in going from this Matrix
+which was our original Matrix
+
+ align:start position:0%
+which was our original Matrix
+ 
+
+ align:start position:0%
+which was our original Matrix
+K to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix which is our Matrix what shall we
+
+ align:start position:0%
+Matrix which is our Matrix what shall we
+ 
+
+ align:start position:0%
+Matrix which is our Matrix what shall we
+call that u u good for upper upper
+
+ align:start position:0%
+call that u u good for upper upper
+ 
+
+ align:start position:0%
+call that u u good for upper upper
+triangular so that's the idea of
+
+ align:start position:0%
+triangular so that's the idea of
+ 
+
+ align:start position:0%
+triangular so that's the idea of
+elimination is start with your Matrix do
+
+ align:start position:0%
+elimination is start with your Matrix do
+ 
+
+ align:start position:0%
+elimination is start with your Matrix do
+these row operations and end up with an
+
+ align:start position:0%
+these row operations and end up with an
+ 
+
+ align:start position:0%
+these row operations and end up with an
+upper triangular Matrix okay
+
+ align:start position:0%
+upper triangular Matrix okay
+ 
+
+ align:start position:0%
+upper triangular Matrix okay
+now okay I can I I better give some
+
+ align:start position:0%
+now okay I can I I better give some
+ 
+
+ align:start position:0%
+now okay I can I I better give some
+names to some of the the numbers that
+
+ align:start position:0%
+names to some of the the numbers that
+ 
+
+ align:start position:0%
+names to some of the the numbers that
+are showing up here this number
+
+ align:start position:0%
+are showing up here this number
+ 
+
+ align:start position:0%
+are showing up here this number
+two is called the first pivot this this
+
+ align:start position:0%
+two is called the first pivot this this
+ 
+
+ align:start position:0%
+two is called the first pivot this this
+is a pivoting step so so of course it
+
+ align:start position:0%
+is a pivoting step so so of course it
+ 
+
+ align:start position:0%
+is a pivoting step so so of course it
+didn't change so it's still there the
+
+ align:start position:0%
+didn't change so it's still there the
+ 
+
+ align:start position:0%
+didn't change so it's still there the
+number two is the first
+
+ align:start position:0%
+number two is the first
+ 
+
+ align:start position:0%
+number two is the first
+pivot then then I use it so I use that
+
+ align:start position:0%
+pivot then then I use it so I use that
+ 
+
+ align:start position:0%
+pivot then then I use it so I use that
+first pivot to clear out the column
+
+ align:start position:0%
+first pivot to clear out the column
+ 
+
+ align:start position:0%
+first pivot to clear out the column
+below it now I'm over here now I use the
+
+ align:start position:0%
+below it now I'm over here now I use the
+ 
+
+ align:start position:0%
+below it now I'm over here now I use the
+second pivot well I don't even actually
+
+ align:start position:0%
+second pivot well I don't even actually
+ 
+
+ align:start position:0%
+second pivot well I don't even actually
+because it's the last pivot I don't have
+
+ align:start position:0%
+because it's the last pivot I don't have
+ 
+
+ align:start position:0%
+because it's the last pivot I don't have
+anything more to do with it but still it
+
+ align:start position:0%
+anything more to do with it but still it
+ 
+
+ align:start position:0%
+anything more to do with it but still it
+counts so the those are the pivots two
+
+ align:start position:0%
+counts so the those are the pivots two
+ 
+
+ align:start position:0%
+counts so the those are the pivots two
+and three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+halves for this Matrix for this for this
+
+ align:start position:0%
+halves for this Matrix for this for this
+ 
+
+ align:start position:0%
+halves for this Matrix for this for this
+2x2 this is K2
+
+ align:start position:0%
+2x2 this is K2
+ 
+
+ align:start position:0%
+2x2 this is K2
+okay okay now what is it I wanted to ask
+
+ align:start position:0%
+okay okay now what is it I wanted to ask
+ 
+
+ align:start position:0%
+okay okay now what is it I wanted to ask
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+K2 well the same questions I asked about
+
+ align:start position:0%
+K2 well the same questions I asked about
+ 
+
+ align:start position:0%
+K2 well the same questions I asked about
+K3 uh now should be easier for K2 first
+
+ align:start position:0%
+K3 uh now should be easier for K2 first
+ 
+
+ align:start position:0%
+K3 uh now should be easier for K2 first
+of all well symmetric K2 was SYM all
+
+ align:start position:0%
+of all well symmetric K2 was SYM all
+ 
+
+ align:start position:0%
+of all well symmetric K2 was SYM all
+these were easy now it's it's these
+
+ align:start position:0%
+these were easy now it's it's these
+ 
+
+ align:start position:0%
+these were easy now it's it's these
+harder questions that I'm I'm interested
+
+ align:start position:0%
+harder questions that I'm I'm interested
+ 
+
+ align:start position:0%
+harder questions that I'm I'm interested
+in is
+
+ align:start position:0%
+in is
+ 
+
+ align:start position:0%
+in is
+K2
+
+ align:start position:0%
+K2
+ 
+
+ align:start position:0%
+K2
+invertible is that Matrix invertible and
+
+ align:start position:0%
+invertible is that Matrix invertible and
+ 
+
+ align:start position:0%
+invertible is that Matrix invertible and
+you're don't not allowed to take its
+
+ align:start position:0%
+you're don't not allowed to take its
+ 
+
+ align:start position:0%
+you're don't not allowed to take its
+determinant uh what
+
+ align:start position:0%
+determinant uh what
+ 
+
+ align:start position:0%
+determinant uh what
+I I claim that I can see from what's
+
+ align:start position:0%
+I I claim that I can see from what's
+ 
+
+ align:start position:0%
+I I claim that I can see from what's
+written on the board that it's
+
+ align:start position:0%
+written on the board that it's
+ 
+
+ align:start position:0%
+written on the board that it's
+invertible because
+
+ align:start position:0%
+invertible because
+ 
+
+ align:start position:0%
+invertible because
+why because once I get here I
+
+ align:start position:0%
+why because once I get here I
+ 
+
+ align:start position:0%
+why because once I get here I
+know no problems I can solve that right
+
+ align:start position:0%
+know no problems I can solve that right
+ 
+
+ align:start position:0%
+know no problems I can solve that right
+when the pivots are not zero that's the
+
+ align:start position:0%
+when the pivots are not zero that's the
+ 
+
+ align:start position:0%
+when the pivots are not zero that's the
+test for invertibility that's matlb test
+
+ align:start position:0%
+test for invertibility that's matlb test
+ 
+
+ align:start position:0%
+test for invertibility that's matlb test
+the pivots so invertible let me let me
+
+ align:start position:0%
+the pivots so invertible let me let me
+ 
+
+ align:start position:0%
+the pivots so invertible let me let me
+write that down invertible means a full
+
+ align:start position:0%
+write that down invertible means a full
+ 
+
+ align:start position:0%
+write that down invertible means a full
+set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pivots non pivots are never zero so so
+
+ align:start position:0%
+pivots non pivots are never zero so so
+ 
+
+ align:start position:0%
+pivots non pivots are never zero so so
+pivots means not zero whereas if I had
+
+ align:start position:0%
+pivots means not zero whereas if I had
+ 
+
+ align:start position:0%
+pivots means not zero whereas if I had
+oh let's see this
+
+ align:start position:0%
+oh let's see this
+ 
+
+ align:start position:0%
+oh let's see this
+one can can you mentally do pivoting for
+
+ align:start position:0%
+one can can you mentally do pivoting for
+ 
+
+ align:start position:0%
+one can can you mentally do pivoting for
+me just while we're we're doing this so
+
+ align:start position:0%
+me just while we're we're doing this so
+ 
+
+ align:start position:0%
+me just while we're we're doing this so
+the what are the pivots of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B3 well the first pivot is a one right
+
+ align:start position:0%
+B3 well the first pivot is a one right
+ 
+
+ align:start position:0%
+B3 well the first pivot is a one right
+right and then what's the second pivot
+
+ align:start position:0%
+right and then what's the second pivot
+ 
+
+ align:start position:0%
+right and then what's the second pivot
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+B3 also oh okay I'll talk faster you're
+
+ align:start position:0%
+B3 also oh okay I'll talk faster you're
+ 
+
+ align:start position:0%
+B3 also oh okay I'll talk faster you're
+giving me answers okay the second pivot
+
+ align:start position:0%
+giving me answers okay the second pivot
+ 
+
+ align:start position:0%
+giving me answers okay the second pivot
+is a one and I believe the third pivot
+
+ align:start position:0%
+is a one and I believe the third pivot
+ 
+
+ align:start position:0%
+is a one and I believe the third pivot
+is a one also in fact I'm sure of it
+
+ align:start position:0%
+is a one also in fact I'm sure of it
+ 
+
+ align:start position:0%
+is a one also in fact I'm sure of it
+because the product of the pivots is
+
+ align:start position:0%
+because the product of the pivots is
+ 
+
+ align:start position:0%
+because the product of the pivots is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+determinant that that I refuse to talk
+
+ align:start position:0%
+determinant that that I refuse to talk
+ 
+
+ align:start position:0%
+determinant that that I refuse to talk
+about uh so and and the determinate am I
+
+ align:start position:0%
+about uh so and and the determinate am I
+ 
+
+ align:start position:0%
+about uh so and and the determinate am I
+looking the right place no I'm looking
+
+ align:start position:0%
+looking the right place no I'm looking
+ 
+
+ align:start position:0%
+looking the right place no I'm looking
+here this is what I should was where I
+
+ align:start position:0%
+here this is what I should was where I
+ 
+
+ align:start position:0%
+here this is what I should was where I
+should looking sorry here the pivots are
+
+ align:start position:0%
+should looking sorry here the pivots are
+ 
+
+ align:start position:0%
+should looking sorry here the pivots are
+one and one and one so let me write
+
+ align:start position:0%
+one and one and one so let me write
+ 
+
+ align:start position:0%
+one and one and one so let me write
+those down I I just believe they're
+
+ align:start position:0%
+those down I I just believe they're
+ 
+
+ align:start position:0%
+those down I I just believe they're
+right and I'll come back to
+
+ align:start position:0%
+right and I'll come back to
+ 
+
+ align:start position:0%
+right and I'll come back to
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay what are the pivots in this one
+
+ align:start position:0%
+okay what are the pivots in this one
+ 
+
+ align:start position:0%
+okay what are the pivots in this one
+yeah let let let me do these pivots all
+
+ align:start position:0%
+yeah let let let me do these pivots all
+ 
+
+ align:start position:0%
+yeah let let let me do these pivots all
+correctly what are the pivots for that
+
+ align:start position:0%
+correctly what are the pivots for that
+ 
+
+ align:start position:0%
+correctly what are the pivots for that
+Matrix well as you said one and then one
+
+ align:start position:0%
+Matrix well as you said one and then one
+ 
+
+ align:start position:0%
+Matrix well as you said one and then one
+and then zero which I don't accept as a
+
+ align:start position:0%
+and then zero which I don't accept as a
+ 
+
+ align:start position:0%
+and then zero which I don't accept as a
+pivot so I'm I'll so the pivots are
+
+ align:start position:0%
+pivot so I'm I'll so the pivots are
+ 
+
+ align:start position:0%
+pivot so I'm I'll so the pivots are
+well I've never figured out how to never
+
+ align:start position:0%
+well I've never figured out how to never
+ 
+
+ align:start position:0%
+well I've never figured out how to never
+tried to do this the pivots are one and
+
+ align:start position:0%
+tried to do this the pivots are one and
+ 
+
+ align:start position:0%
+tried to do this the pivots are one and
+one and I'm unwilling to write zero what
+
+ align:start position:0%
+one and I'm unwilling to write zero what
+ 
+
+ align:start position:0%
+one and I'm unwilling to write zero what
+can I put maybe just a blank or
+
+ align:start position:0%
+can I put maybe just a blank or
+ 
+
+ align:start position:0%
+can I put maybe just a blank or
+something okay because I don't I I won't
+
+ align:start position:0%
+something okay because I don't I I won't
+ 
+
+ align:start position:0%
+something okay because I don't I I won't
+won't call it a pivot if it's zero okay
+
+ align:start position:0%
+won't call it a pivot if it's zero okay
+ 
+
+ align:start position:0%
+won't call it a pivot if it's zero okay
+and now can we do the pivots for this
+
+ align:start position:0%
+and now can we do the pivots for this
+ 
+
+ align:start position:0%
+and now can we do the pivots for this
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+huh well we can start anyway so what's
+
+ align:start position:0%
+huh well we can start anyway so what's
+ 
+
+ align:start position:0%
+huh well we can start anyway so what's
+the first pivot
+
+ align:start position:0%
+the first pivot
+ 
+
+ align:start position:0%
+the first pivot
+two and what's the second
+
+ align:start position:0%
+two and what's the second
+ 
+
+ align:start position:0%
+two and what's the second
+pivot three halves why is
+
+ align:start position:0%
+pivot three halves why is
+ 
+
+ align:start position:0%
+pivot three halves why is
+that well we did it here we got the
+
+ align:start position:0%
+that well we did it here we got the
+ 
+
+ align:start position:0%
+that well we did it here we got the
+three halves here and
+
+ align:start position:0%
+three halves here and
+ 
+
+ align:start position:0%
+three halves here and
+actually this Matrix starts the same
+
+ align:start position:0%
+actually this Matrix starts the same
+ 
+
+ align:start position:0%
+actually this Matrix starts the same
+way so and and when you're finding the
+
+ align:start position:0%
+way so and and when you're finding the
+ 
+
+ align:start position:0%
+way so and and when you're finding the
+pivots if you know if you're looking for
+
+ align:start position:0%
+pivots if you know if you're looking for
+ 
+
+ align:start position:0%
+pivots if you know if you're looking for
+the second pivot all you need to know is
+
+ align:start position:0%
+the second pivot all you need to know is
+ 
+
+ align:start position:0%
+the second pivot all you need to know is
+that part so the second pivot is three
+
+ align:start position:0%
+that part so the second pivot is three
+ 
+
+ align:start position:0%
+that part so the second pivot is three
+halves and actually the next pivot will
+
+ align:start position:0%
+halves and actually the next pivot will
+ 
+
+ align:start position:0%
+halves and actually the next pivot will
+turn out to be
+
+ align:start position:0%
+turn out to be
+ 
+
+ align:start position:0%
+turn out to be
+4/3 and the next pivot after that would
+
+ align:start position:0%
+4/3 and the next pivot after that would
+ 
+
+ align:start position:0%
+4/3 and the next pivot after that would
+be 54s and 6 fifths and so on H have the
+
+ align:start position:0%
+be 54s and 6 fifths and so on H have the
+ 
+
+ align:start position:0%
+be 54s and 6 fifths and so on H have the
+fun of playing with these matrices
+
+ align:start position:0%
+fun of playing with these matrices
+ 
+
+ align:start position:0%
+fun of playing with these matrices
+between now and next Thursday so uh so
+
+ align:start position:0%
+between now and next Thursday so uh so
+ 
+
+ align:start position:0%
+between now and next Thursday so uh so
+the pivots are two for this 3x3 the
+
+ align:start position:0%
+the pivots are two for this 3x3 the
+ 
+
+ align:start position:0%
+the pivots are two for this 3x3 the
+pivots are two and three halves and then
+
+ align:start position:0%
+pivots are two and three halves and then
+ 
+
+ align:start position:0%
+pivots are two and three halves and then
+the next one will be
+
+ align:start position:0%
+the next one will be
+ 
+
+ align:start position:0%
+the next one will be
+4/3 oh I ought to have mentioned where
+
+ align:start position:0%
+4/3 oh I ought to have mentioned where
+ 
+
+ align:start position:0%
+4/3 oh I ought to have mentioned where
+in the book you might look for some some
+
+ align:start position:0%
+in the book you might look for some some
+ 
+
+ align:start position:0%
+in the book you might look for some some
+of this so so today's lecture is is most
+
+ align:start position:0%
+of this so so today's lecture is is most
+ 
+
+ align:start position:0%
+of this so so today's lecture is is most
+closely connected to section
+
+ align:start position:0%
+closely connected to section
+ 
+
+ align:start position:0%
+closely connected to section
+1.2 in the applied math
+
+ align:start position:0%
+1.2 in the applied math
+ 
+
+ align:start position:0%
+1.2 in the applied math
+book but but uh and really what I'm
+
+ align:start position:0%
+book but but uh and really what I'm
+ 
+
+ align:start position:0%
+book but but uh and really what I'm
+guess I'm saying is you might look at
+
+ align:start position:0%
+guess I'm saying is you might look at
+ 
+
+ align:start position:0%
+guess I'm saying is you might look at
+some of the exercises in that section as
+
+ align:start position:0%
+some of the exercises in that section as
+ 
+
+ align:start position:0%
+some of the exercises in that section as
+sort of additional questions about um
+
+ align:start position:0%
+sort of additional questions about um
+ 
+
+ align:start position:0%
+sort of additional questions about um
+this this topic okay now
+
+ align:start position:0%
+this this topic okay now
+ 
+
+ align:start position:0%
+this this topic okay now
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right so we we have the idea of
+
+ align:start position:0%
+right so we we have the idea of
+ 
+
+ align:start position:0%
+right so we we have the idea of
+elimination I want to say one more thing
+
+ align:start position:0%
+elimination I want to say one more thing
+ 
+
+ align:start position:0%
+elimination I want to say one more thing
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elimination um cuz we got from The
+
+ align:start position:0%
+elimination um cuz we got from The
+ 
+
+ align:start position:0%
+elimination um cuz we got from The
+Matrix to the upper triangular one that
+
+ align:start position:0%
+Matrix to the upper triangular one that
+ 
+
+ align:start position:0%
+Matrix to the upper triangular one that
+was no problem Oh but then
+
+ align:start position:0%
+was no problem Oh but then
+ 
+
+ align:start position:0%
+was no problem Oh but then
+then I want to get there with
+
+ align:start position:0%
+then I want to get there with
+ 
+
+ align:start position:0%
+then I want to get there with
+matrices right I I I I can't I mean if
+
+ align:start position:0%
+matrices right I I I I can't I mean if
+ 
+
+ align:start position:0%
+matrices right I I I I can't I mean if
+we a large problem I can't
+
+ align:start position:0%
+we a large problem I can't
+ 
+
+ align:start position:0%
+we a large problem I can't
+like list all the pivoting operations
+
+ align:start position:0%
+like list all the pivoting operations
+ 
+
+ align:start position:0%
+like list all the pivoting operations
+they ought to fit into a matrix there
+
+ align:start position:0%
+they ought to fit into a matrix there
+ 
+
+ align:start position:0%
+they ought to fit into a matrix there
+ought to be some Matrix which we're
+
+ align:start position:0%
+ought to be some Matrix which we're
+ 
+
+ align:start position:0%
+ought to be some Matrix which we're
+multiplying this by to get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so can I can you tell me what that
+
+ align:start position:0%
+that so can I can you tell me what that
+ 
+
+ align:start position:0%
+that so can I can you tell me what that
+so I want to say Okay that was much too
+
+ align:start position:0%
+so I want to say Okay that was much too
+ 
+
+ align:start position:0%
+so I want to say Okay that was much too
+much writing on that line let me start
+
+ align:start position:0%
+much writing on that line let me start
+ 
+
+ align:start position:0%
+much writing on that line let me start
+over and
+
+ align:start position:0%
+over and
+ 
+
+ align:start position:0%
+over and
+just go from the M from the one Matrix
+
+ align:start position:0%
+just go from the M from the one Matrix
+ 
+
+ align:start position:0%
+just go from the M from the one Matrix
+to the other and and not worry about all
+
+ align:start position:0%
+to the other and and not worry about all
+ 
+
+ align:start position:0%
+to the other and and not worry about all
+the about keeping up with the right hand
+
+ align:start position:0%
+the about keeping up with the right hand
+ 
+
+ align:start position:0%
+the about keeping up with the right hand
+side mat lab deals with the rightand
+
+ align:start position:0%
+side mat lab deals with the rightand
+ 
+
+ align:start position:0%
+side mat lab deals with the rightand
+side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+later so I'm getting from this Matrix
+
+ align:start position:0%
+later so I'm getting from this Matrix
+ 
+
+ align:start position:0%
+later so I'm getting from this Matrix
+now what I want to do is multiply by a
+
+ align:start position:0%
+now what I want to do is multiply by a
+ 
+
+ align:start position:0%
+now what I want to do is multiply by a
+suitable Matrix that produces the the
+
+ align:start position:0%
+suitable Matrix that produces the the
+ 
+
+ align:start position:0%
+suitable Matrix that produces the the
+answer leaves the first row
+
+ align:start position:0%
+answer leaves the first row
+ 
+
+ align:start position:0%
+answer leaves the first row
+unchanged tell me what the first row of
+
+ align:start position:0%
+unchanged tell me what the first row of
+ 
+
+ align:start position:0%
+unchanged tell me what the first row of
+this Matrix ought to be
+
+ align:start position:0%
+this Matrix ought to be
+ 
+
+ align:start position:0%
+this Matrix ought to be
+if I if I want to multiply this is my
+
+ align:start position:0%
+if I if I want to multiply this is my
+ 
+
+ align:start position:0%
+if I if I want to multiply this is my
+elimination Matrix you could say this is
+
+ align:start position:0%
+elimination Matrix you could say this is
+ 
+
+ align:start position:0%
+elimination Matrix you could say this is
+my Matrix that that does the step that I
+
+ align:start position:0%
+my Matrix that that does the step that I
+ 
+
+ align:start position:0%
+my Matrix that that does the step that I
+carried out in long hand okay what just
+
+ align:start position:0%
+carried out in long hand okay what just
+ 
+
+ align:start position:0%
+carried out in long hand okay what just
+while we're at it I already you can
+
+ align:start position:0%
+while we're at it I already you can
+ 
+
+ align:start position:0%
+while we're at it I already you can
+already tell me what the first row has
+
+ align:start position:0%
+already tell me what the first row has
+ 
+
+ align:start position:0%
+already tell me what the first row has
+to be and it's one zero because that
+
+ align:start position:0%
+to be and it's one zero because that
+ 
+
+ align:start position:0%
+to be and it's one zero because that
+takes one of that row and zero of that
+
+ align:start position:0%
+takes one of that row and zero of that
+ 
+
+ align:start position:0%
+takes one of that row and zero of that
+row and that's what I want okay now what
+
+ align:start position:0%
+row and that's what I want okay now what
+ 
+
+ align:start position:0%
+row and that's what I want okay now what
+about the second
+
+ align:start position:0%
+about the second
+ 
+
+ align:start position:0%
+about the second
+row okay the second row was what did
+
+ align:start position:0%
+row okay the second row was what did
+ 
+
+ align:start position:0%
+row okay the second row was what did
+what did we do to get the new second row
+
+ align:start position:0%
+what did we do to get the new second row
+ 
+
+ align:start position:0%
+what did we do to get the new second row
+so the new second row was 0 three
+
+ align:start position:0%
+so the new second row was 0 three
+ 
+
+ align:start position:0%
+so the new second row was 0 three
+halves what what did we
+
+ align:start position:0%
+halves what what did we
+ 
+
+ align:start position:0%
+halves what what did we
+do we took half of the first
+
+ align:start position:0%
+do we took half of the first
+ 
+
+ align:start position:0%
+do we took half of the first
+row plus all of the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+row so this is our e or something our
+
+ align:start position:0%
+row so this is our e or something our
+ 
+
+ align:start position:0%
+row so this is our e or something our
+elementary guy who produced uced
+
+ align:start position:0%
+elementary guy who produced uced
+ 
+
+ align:start position:0%
+elementary guy who produced uced
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+okay all right that's okay that's we're
+
+ align:start position:0%
+okay all right that's okay that's we're
+ 
+
+ align:start position:0%
+okay all right that's okay that's we're
+seeing we're seeing at least we're
+
+ align:start position:0%
+seeing we're seeing at least we're
+ 
+
+ align:start position:0%
+seeing we're seeing at least we're
+seeing elimination carried out by a
+
+ align:start position:0%
+seeing elimination carried out by a
+ 
+
+ align:start position:0%
+seeing elimination carried out by a
+matrix I but the the beautiful play the
+
+ align:start position:0%
+matrix I but the the beautiful play the
+ 
+
+ align:start position:0%
+matrix I but the the beautiful play the
+beautiful way to describe this is to put
+
+ align:start position:0%
+beautiful way to describe this is to put
+ 
+
+ align:start position:0%
+beautiful way to describe this is to put
+the E over on the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side and have k equals something so what
+
+ align:start position:0%
+side and have k equals something so what
+ 
+
+ align:start position:0%
+side and have k equals something so what
+I'm what I'm saying here is that the key
+
+ align:start position:0%
+I'm what I'm saying here is that the key
+ 
+
+ align:start position:0%
+I'm what I'm saying here is that the key
+ideas of linear algebra so this is in
+
+ align:start position:0%
+ideas of linear algebra so this is in
+ 
+
+ align:start position:0%
+ideas of linear algebra so this is in
+the solve
+
+ align:start position:0%
+the solve
+ 
+
+ align:start position:0%
+the solve
+part can I tell you linear algebra here
+
+ align:start position:0%
+part can I tell you linear algebra here
+ 
+
+ align:start position:0%
+part can I tell you linear algebra here
+in in in in that small
+
+ align:start position:0%
+in in in in that small
+ 
+
+ align:start position:0%
+in in in in that small
+space um
+
+ align:start position:0%
+space um
+ 
+
+ align:start position:0%
+space um
+so but don't tell anybody it's so simple
+
+ align:start position:0%
+so but don't tell anybody it's so simple
+ 
+
+ align:start position:0%
+so but don't tell anybody it's so simple
+right uh so the key idea of elimination
+
+ align:start position:0%
+right uh so the key idea of elimination
+ 
+
+ align:start position:0%
+right uh so the key idea of elimination
+so everything you do in linear algebra
+
+ align:start position:0%
+so everything you do in linear algebra
+ 
+
+ align:start position:0%
+so everything you do in linear algebra
+all the big operations elimination is
+
+ align:start position:0%
+all the big operations elimination is
+ 
+
+ align:start position:0%
+all the big operations elimination is
+the first one Graham Schmid
+
+ align:start position:0%
+the first one Graham Schmid
+ 
+
+ align:start position:0%
+the first one Graham Schmid
+orthogonalization of vectors is another
+
+ align:start position:0%
+orthogonalization of vectors is another
+ 
+
+ align:start position:0%
+orthogonalization of vectors is another
+one igen values is another one the
+
+ align:start position:0%
+one igen values is another one the
+ 
+
+ align:start position:0%
+one igen values is another one the
+singular value decomposition those are
+
+ align:start position:0%
+singular value decomposition those are
+ 
+
+ align:start position:0%
+singular value decomposition those are
+the big
+
+ align:start position:0%
+the big
+ 
+
+ align:start position:0%
+the big
+four and each of those is described by a
+
+ align:start position:0%
+four and each of those is described by a
+ 
+
+ align:start position:0%
+four and each of those is described by a
+factorization as k equals breaking K
+
+ align:start position:0%
+factorization as k equals breaking K
+ 
+
+ align:start position:0%
+factorization as k equals breaking K
+down into a product of special pieces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm going to speak for the moment
+
+ align:start position:0%
+and I'm going to speak for the moment
+ 
+
+ align:start position:0%
+and I'm going to speak for the moment
+about the elimination form and the usual
+
+ align:start position:0%
+about the elimination form and the usual
+ 
+
+ align:start position:0%
+about the elimination form and the usual
+way you see elimination is as L *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U lower triangular times upper
+
+ align:start position:0%
+U lower triangular times upper
+ 
+
+ align:start position:0%
+U lower triangular times upper
+triangular and let's get let's do that
+
+ align:start position:0%
+triangular and let's get let's do that
+ 
+
+ align:start position:0%
+triangular and let's get let's do that
+so can we get to that do you see what
+
+ align:start position:0%
+so can we get to that do you see what
+ 
+
+ align:start position:0%
+so can we get to that do you see what
+there we have the
+
+ align:start position:0%
+there we have the
+ 
+
+ align:start position:0%
+there we have the
+K and we have the
+
+ align:start position:0%
+K and we have the
+ 
+
+ align:start position:0%
+K and we have the
+U what
+
+ align:start position:0%
+U what
+ 
+
+ align:start position:0%
+U what
+what what isn't ready here is I've got
+
+ align:start position:0%
+what what isn't ready here is I've got
+ 
+
+ align:start position:0%
+what what isn't ready here is I've got
+the E on this side and I'm want to move
+
+ align:start position:0%
+the E on this side and I'm want to move
+ 
+
+ align:start position:0%
+the E on this side and I'm want to move
+it over to be an L on that side is that
+
+ align:start position:0%
+it over to be an L on that side is that
+ 
+
+ align:start position:0%
+it over to be an L on that side is that
+all right so so I'm just going to take
+
+ align:start position:0%
+all right so so I'm just going to take
+ 
+
+ align:start position:0%
+all right so so I'm just going to take
+that and and I'm going to rewrite it I'm
+
+ align:start position:0%
+that and and I'm going to rewrite it I'm
+ 
+
+ align:start position:0%
+that and and I'm going to rewrite it I'm
+with the K alone by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+itself and now what Matrix goes on that
+
+ align:start position:0%
+itself and now what Matrix goes on that
+ 
+
+ align:start position:0%
+itself and now what Matrix goes on that
+side times the
+
+ align:start position:0%
+side times the
+ 
+
+ align:start position:0%
+side times the
+U if you could say
+
+ align:start position:0%
+U if you could say
+ 
+
+ align:start position:0%
+U if you could say
+this this form is like how to undo
+
+ align:start position:0%
+this this form is like how to undo
+ 
+
+ align:start position:0%
+this this form is like how to undo
+elimination how how to reverse starting
+
+ align:start position:0%
+elimination how how to reverse starting
+ 
+
+ align:start position:0%
+elimination how how to reverse starting
+from here what do I do to get back and
+
+ align:start position:0%
+from here what do I do to get back and
+ 
+
+ align:start position:0%
+from here what do I do to get back and
+it just turns out better to have the the
+
+ align:start position:0%
+it just turns out better to have the the
+ 
+
+ align:start position:0%
+it just turns out better to have the the
+all take to have the Matrix on one side
+
+ align:start position:0%
+all take to have the Matrix on one side
+ 
+
+ align:start position:0%
+all take to have the Matrix on one side
+like here and the so what Matrix do I
+
+ align:start position:0%
+like here and the so what Matrix do I
+ 
+
+ align:start position:0%
+like here and the so what Matrix do I
+want in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theree E inverse e inverse that's the
+
+ align:start position:0%
+theree E inverse e inverse that's the
+ 
+
+ align:start position:0%
+theree E inverse e inverse that's the
+key point right CU because here e was
+
+ align:start position:0%
+key point right CU because here e was
+ 
+
+ align:start position:0%
+key point right CU because here e was
+here so if I multiply that through so e
+
+ align:start position:0%
+here so if I multiply that through so e
+ 
+
+ align:start position:0%
+here so if I multiply that through so e
+times this e times the K gave me the U
+
+ align:start position:0%
+times this e times the K gave me the U
+ 
+
+ align:start position:0%
+times this e times the K gave me the U
+If I multiply through by E inverse so if
+
+ align:start position:0%
+If I multiply through by E inverse so if
+ 
+
+ align:start position:0%
+If I multiply through by E inverse so if
+I undo the elimination step that knocks
+
+ align:start position:0%
+I undo the elimination step that knocks
+ 
+
+ align:start position:0%
+I undo the elimination step that knocks
+out the thing and puts it here so the so
+
+ align:start position:0%
+out the thing and puts it here so the so
+ 
+
+ align:start position:0%
+out the thing and puts it here so the so
+what I'm asking you is what's the
+
+ align:start position:0%
+what I'm asking you is what's the
+ 
+
+ align:start position:0%
+what I'm asking you is what's the
+inverse of that
+
+ align:start position:0%
+inverse of that
+ 
+
+ align:start position:0%
+inverse of that
+Matrix and do you know what the inverse
+
+ align:start position:0%
+Matrix and do you know what the inverse
+ 
+
+ align:start position:0%
+Matrix and do you know what the inverse
+of that Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is it's it's yeah it's the same Matrix
+
+ align:start position:0%
+is it's it's yeah it's the same Matrix
+ 
+
+ align:start position:0%
+is it's it's yeah it's the same Matrix
+with a minus there and can we see why
+
+ align:start position:0%
+with a minus there and can we see why
+ 
+
+ align:start position:0%
+with a minus there and can we see why
+that would un we could check that that
+
+ align:start position:0%
+that would un we could check that that
+ 
+
+ align:start position:0%
+that would un we could check that that
+so let me write it down so
+
+ align:start position:0%
+so let me write it down so
+ 
+
+ align:start position:0%
+so let me write it down so
+I'm so it's one Z and it's has a minus a
+
+ align:start position:0%
+I'm so it's one Z and it's has a minus a
+ 
+
+ align:start position:0%
+I'm so it's one Z and it's has a minus a
+half and I claim that this is this is e
+
+ align:start position:0%
+half and I claim that this is this is e
+ 
+
+ align:start position:0%
+half and I claim that this is this is e
+inverse but now I'm going to call it l
+
+ align:start position:0%
+inverse but now I'm going to call it l
+ 
+
+ align:start position:0%
+inverse but now I'm going to call it l
+it's lower triangular and this is the U
+
+ align:start position:0%
+it's lower triangular and this is the U
+ 
+
+ align:start position:0%
+it's lower triangular and this is the U
+and this is of course the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k i I think we it's important to like I
+
+ align:start position:0%
+k i I think we it's important to like I
+ 
+
+ align:start position:0%
+k i I think we it's important to like I
+mean we're covering quite a bit here in
+
+ align:start position:0%
+mean we're covering quite a bit here in
+ 
+
+ align:start position:0%
+mean we're covering quite a bit here in
+in an hour uh but we could do you see
+
+ align:start position:0%
+in an hour uh but we could do you see
+ 
+
+ align:start position:0%
+in an hour uh but we could do you see
+why in words sort of why the inverse
+
+ align:start position:0%
+why in words sort of why the inverse
+ 
+
+ align:start position:0%
+why in words sort of why the inverse
+Matrix the inverse operation should
+
+ align:start position:0%
+Matrix the inverse operation should
+ 
+
+ align:start position:0%
+Matrix the inverse operation should
+be this guy with the sign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+changed I mean as I say I you could
+
+ align:start position:0%
+changed I mean as I say I you could
+ 
+
+ align:start position:0%
+changed I mean as I say I you could
+check that that Matrix times that Matrix
+
+ align:start position:0%
+check that that Matrix times that Matrix
+ 
+
+ align:start position:0%
+check that that Matrix times that Matrix
+gives the identity they they are
+
+ align:start position:0%
+gives the identity they they are
+ 
+
+ align:start position:0%
+gives the identity they they are
+inverses of each other but we added a
+
+ align:start position:0%
+inverses of each other but we added a
+ 
+
+ align:start position:0%
+inverses of each other but we added a
+half and now we take it away good good
+
+ align:start position:0%
+half and now we take it away good good
+ 
+
+ align:start position:0%
+half and now we take it away good good
+good exactly exactly that's that's the
+
+ align:start position:0%
+good exactly exactly that's that's the
+ 
+
+ align:start position:0%
+good exactly exactly that's that's the
+words I'm looking for this step added a
+
+ align:start position:0%
+words I'm looking for this step added a
+ 
+
+ align:start position:0%
+words I'm looking for this step added a
+half of this row to that and so if we
+
+ align:start position:0%
+half of this row to that and so if we
+ 
+
+ align:start position:0%
+half of this row to that and so if we
+want to invert if we want to undo it we
+
+ align:start position:0%
+want to invert if we want to undo it we
+ 
+
+ align:start position:0%
+want to invert if we want to undo it we
+subtract a half of this Row from that
+
+ align:start position:0%
+subtract a half of this Row from that
+ 
+
+ align:start position:0%
+subtract a half of this Row from that
+and then we're back back to where we
+
+ align:start position:0%
+and then we're back back to where we
+ 
+
+ align:start position:0%
+and then we're back back to where we
+were okay so I'm happy to have it on
+
+ align:start position:0%
+were okay so I'm happy to have it on
+ 
+
+ align:start position:0%
+were okay so I'm happy to have it on
+this side actually I'm happy for
+
+ align:start position:0%
+this side actually I'm happy for
+ 
+
+ align:start position:0%
+this side actually I'm happy for
+multiple reasons um
+
+ align:start position:0%
+multiple reasons um
+ 
+
+ align:start position:0%
+multiple reasons um
+this yeah which I'll let me let me uh
+
+ align:start position:0%
+this yeah which I'll let me let me uh
+ 
+
+ align:start position:0%
+this yeah which I'll let me let me uh
+let me just emphasize that this is the
+
+ align:start position:0%
+let me just emphasize that this is the
+ 
+
+ align:start position:0%
+let me just emphasize that this is the
+great place to have it now only one
+
+ align:start position:0%
+great place to have it now only one
+ 
+
+ align:start position:0%
+great place to have it now only one
+thing I'd like to improve here in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lu and that is that I've lost the
+
+ align:start position:0%
+Lu and that is that I've lost the
+ 
+
+ align:start position:0%
+Lu and that is that I've lost the
+Symmetry this was a symmetric Matrix
+
+ align:start position:0%
+Symmetry this was a symmetric Matrix
+ 
+
+ align:start position:0%
+Symmetry this was a symmetric Matrix
+that that's a too important a property
+
+ align:start position:0%
+that that's a too important a property
+ 
+
+ align:start position:0%
+that that's a too important a property
+to to give up
+
+ align:start position:0%
+to to give up
+ 
+
+ align:start position:0%
+to to give up
+on so I would like to my fact
+
+ align:start position:0%
+on so I would like to my fact
+ 
+
+ align:start position:0%
+on so I would like to my fact
+factorization to be somehow a symmetric
+
+ align:start position:0%
+factorization to be somehow a symmetric
+ 
+
+ align:start position:0%
+factorization to be somehow a symmetric
+factorization and uh let me show you one
+
+ align:start position:0%
+factorization and uh let me show you one
+ 
+
+ align:start position:0%
+factorization and uh let me show you one
+way to do that L I'm totally happy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with and now I'm going to factor out of
+
+ align:start position:0%
+with and now I'm going to factor out of
+ 
+
+ align:start position:0%
+with and now I'm going to factor out of
+here a diagonal matrix that just shows
+
+ align:start position:0%
+here a diagonal matrix that just shows
+ 
+
+ align:start position:0%
+here a diagonal matrix that just shows
+the pivots two and three
+
+ align:start position:0%
+the pivots two and three
+ 
+
+ align:start position:0%
+the pivots two and three
+Hales is that all right so that's an
+
+ align:start position:0%
+Hales is that all right so that's an
+ 
+
+ align:start position:0%
+Hales is that all right so that's an
+easy it's nice to have a Diagon
+
+ align:start position:0%
+easy it's nice to have a Diagon
+ 
+
+ align:start position:0%
+easy it's nice to have a Diagon
+Matrix couldn't be better than that and
+
+ align:start position:0%
+Matrix couldn't be better than that and
+ 
+
+ align:start position:0%
+Matrix couldn't be better than that and
+then I've got something left so you see
+
+ align:start position:0%
+then I've got something left so you see
+ 
+
+ align:start position:0%
+then I've got something left so you see
+all I'm doing is I'm taking this Matrix
+
+ align:start position:0%
+all I'm doing is I'm taking this Matrix
+ 
+
+ align:start position:0%
+all I'm doing is I'm taking this Matrix
+and I'm dividing that row by two and I'm
+
+ align:start position:0%
+and I'm dividing that row by two and I'm
+ 
+
+ align:start position:0%
+and I'm dividing that row by two and I'm
+dividing that row by three halves so
+
+ align:start position:0%
+dividing that row by three halves so
+ 
+
+ align:start position:0%
+dividing that row by three halves so
+that I get a simpler so I'll get a
+
+ align:start position:0%
+that I get a simpler so I'll get a
+ 
+
+ align:start position:0%
+that I get a simpler so I'll get a
+matrix that only has ones there and of
+
+ align:start position:0%
+matrix that only has ones there and of
+ 
+
+ align:start position:0%
+matrix that only has ones there and of
+course it's got a zero there and now you
+
+ align:start position:0%
+course it's got a zero there and now you
+ 
+
+ align:start position:0%
+course it's got a zero there and now you
+just tell me what's there and I'm I'm
+
+ align:start position:0%
+just tell me what's there and I'm I'm
+ 
+
+ align:start position:0%
+just tell me what's there and I'm I'm
+really uh pleased
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so what did I do I that row I just
+
+ align:start position:0%
+so so what did I do I that row I just
+ 
+
+ align:start position:0%
+so so what did I do I that row I just
+divided the three halves just came out
+
+ align:start position:0%
+divided the three halves just came out
+ 
+
+ align:start position:0%
+divided the three halves just came out
+so that was fine this row I divided by
+
+ align:start position:0%
+so that was fine this row I divided by
+ 
+
+ align:start position:0%
+so that was fine this row I divided by
+two I divided by the pivot to separate
+
+ align:start position:0%
+two I divided by the pivot to separate
+ 
+
+ align:start position:0%
+two I divided by the pivot to separate
+out the pivot so that left me with a one
+
+ align:start position:0%
+out the pivot so that left me with a one
+ 
+
+ align:start position:0%
+out the pivot so that left me with a one
+on the main diagonal and what's
+
+ align:start position:0%
+on the main diagonal and what's
+ 
+
+ align:start position:0%
+on the main diagonal and what's
+here minus a half right because that two
+
+ align:start position:0%
+here minus a half right because that two
+ 
+
+ align:start position:0%
+here minus a half right because that two
+will multiply minus a half and give me
+
+ align:start position:0%
+will multiply minus a half and give me
+ 
+
+ align:start position:0%
+will multiply minus a half and give me
+the minus one now let me give you a
+
+ align:start position:0%
+the minus one now let me give you a
+ 
+
+ align:start position:0%
+the minus one now let me give you a
+chance to look at that because I'm going
+
+ align:start position:0%
+chance to look at that because I'm going
+ 
+
+ align:start position:0%
+chance to look at that because I'm going
+pretty quickly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the form I won't I have no
+
+ align:start position:0%
+that's the form I won't I have no
+ 
+
+ align:start position:0%
+that's the form I won't I have no
+complaints now that's the form that uh
+
+ align:start position:0%
+complaints now that's the form that uh
+ 
+
+ align:start position:0%
+complaints now that's the form that uh
+that we're shooting for the Matrix has
+
+ align:start position:0%
+that we're shooting for the Matrix has
+ 
+
+ align:start position:0%
+that we're shooting for the Matrix has
+been factored into a lower triangular
+
+ align:start position:0%
+been factored into a lower triangular
+ 
+
+ align:start position:0%
+been factored into a lower triangular
+one that has these multipliers in it a
+
+ align:start position:0%
+one that has these multipliers in it a
+ 
+
+ align:start position:0%
+one that has these multipliers in it a
+diagonal that has the pivots in it and
+
+ align:start position:0%
+diagonal that has the pivots in it and
+ 
+
+ align:start position:0%
+diagonal that has the pivots in it and
+then an upper triangular and what's
+
+ align:start position:0%
+then an upper triangular and what's
+ 
+
+ align:start position:0%
+then an upper triangular and what's
+special about this upper upper
+
+ align:start position:0%
+special about this upper upper
+ 
+
+ align:start position:0%
+special about this upper upper
+triangular guy
+
+ align:start position:0%
+triangular guy
+ 
+
+ align:start position:0%
+triangular guy
+lower it's the transpose of the lower so
+
+ align:start position:0%
+lower it's the transpose of the lower so
+ 
+
+ align:start position:0%
+lower it's the transpose of the lower so
+that this factorization is now
+
+ align:start position:0%
+that this factorization is now
+ 
+
+ align:start position:0%
+that this factorization is now
+symmetrized so to speak we've di pulled
+
+ align:start position:0%
+symmetrized so to speak we've di pulled
+ 
+
+ align:start position:0%
+symmetrized so to speak we've di pulled
+out the diagonal and we were left with
+
+ align:start position:0%
+out the diagonal and we were left with
+ 
+
+ align:start position:0%
+out the diagonal and we were left with
+the transpose of the first
+
+ align:start position:0%
+the transpose of the first
+ 
+
+ align:start position:0%
+the transpose of the first
+factor and that's great I mean that's
+
+ align:start position:0%
+factor and that's great I mean that's
+ 
+
+ align:start position:0%
+factor and that's great I mean that's
+the right way to have a symmetric Matrix
+
+ align:start position:0%
+the right way to have a symmetric Matrix
+ 
+
+ align:start position:0%
+the right way to have a symmetric Matrix
+because a m every L * D in
+
+ align:start position:0%
+because a m every L * D in
+ 
+
+ align:start position:0%
+because a m every L * D in
+fact the next several hours
+
+ align:start position:0%
+fact the next several hours
+ 
+
+ align:start position:0%
+fact the next several hours
+are going to be about products of three
+
+ align:start position:0%
+are going to be about products of three
+ 
+
+ align:start position:0%
+are going to be about products of three
+matrices where the outside factors are
+
+ align:start position:0%
+matrices where the outside factors are
+ 
+
+ align:start position:0%
+matrices where the outside factors are
+transposes of each other
+
+ align:start position:0%
+transposes of each other
+ 
+
+ align:start position:0%
+transposes of each other
+and that's always a symmetric result if
+
+ align:start position:0%
+and that's always a symmetric result if
+ 
+
+ align:start position:0%
+and that's always a symmetric result if
+I take a matrix times something in the
+
+ align:start position:0%
+I take a matrix times something in the
+ 
+
+ align:start position:0%
+I take a matrix times something in the
+middle times the transpose of the
+
+ align:start position:0%
+middle times the transpose of the
+ 
+
+ align:start position:0%
+middle times the transpose of the
+first that has that that Matrix that
+
+ align:start position:0%
+first that has that that Matrix that
+ 
+
+ align:start position:0%
+first that has that that Matrix that
+product is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetric and in this case the factor is
+
+ align:start position:0%
+symmetric and in this case the factor is
+ 
+
+ align:start position:0%
+symmetric and in this case the factor is
+lower triangular that factor is diagonal
+
+ align:start position:0%
+lower triangular that factor is diagonal
+ 
+
+ align:start position:0%
+lower triangular that factor is diagonal
+so on that's great but can we just check
+
+ align:start position:0%
+so on that's great but can we just check
+ 
+
+ align:start position:0%
+so on that's great but can we just check
+can we just see that general fact why do
+
+ align:start position:0%
+can we just see that general fact why do
+ 
+
+ align:start position:0%
+can we just see that general fact why do
+I claim that whatever L and D might
+
+ align:start position:0%
+I claim that whatever L and D might
+ 
+
+ align:start position:0%
+I claim that whatever L and D might
+happen to
+
+ align:start position:0%
+happen to
+ 
+
+ align:start position:0%
+happen to
+be that products of this this triple
+
+ align:start position:0%
+be that products of this this triple
+ 
+
+ align:start position:0%
+be that products of this this triple
+symmetric triple product you could call
+
+ align:start position:0%
+symmetric triple product you could call
+ 
+
+ align:start position:0%
+symmetric triple product you could call
+it produces why is that why is the
+
+ align:start position:0%
+it produces why is that why is the
+ 
+
+ align:start position:0%
+it produces why is that why is the
+result a symmetric Matrix how can I
+
+ align:start position:0%
+result a symmetric Matrix how can I
+ 
+
+ align:start position:0%
+result a symmetric Matrix how can I
+check that that result is a symmetric
+
+ align:start position:0%
+check that that result is a symmetric
+ 
+
+ align:start position:0%
+check that that result is a symmetric
+Matrix it looks kind
+
+ align:start position:0%
+Matrix it looks kind
+ 
+
+ align:start position:0%
+Matrix it looks kind
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+symmetric take its transpose as a very I
+
+ align:start position:0%
+symmetric take its transpose as a very I
+ 
+
+ align:start position:0%
+symmetric take its transpose as a very I
+mean right if we want to know if
+
+ align:start position:0%
+mean right if we want to know if
+ 
+
+ align:start position:0%
+mean right if we want to know if
+something is
+
+ align:start position:0%
+something is
+ 
+
+ align:start position:0%
+something is
+symmetric take its transpose and and see
+
+ align:start position:0%
+symmetric take its transpose and and see
+ 
+
+ align:start position:0%
+symmetric take its transpose and and see
+what if we get it
+
+ align:start position:0%
+what if we get it
+ 
+
+ align:start position:0%
+what if we get it
+again in that case we've got a symmetric
+
+ align:start position:0%
+again in that case we've got a symmetric
+ 
+
+ align:start position:0%
+again in that case we've got a symmetric
+Matrix okay so I take the transpose of
+
+ align:start position:0%
+Matrix okay so I take the transpose of
+ 
+
+ align:start position:0%
+Matrix okay so I take the transpose of
+this thing so this is like offline here
+
+ align:start position:0%
+this thing so this is like offline here
+ 
+
+ align:start position:0%
+this thing so this is like offline here
+because because
+
+ align:start position:0%
+because because
+ 
+
+ align:start position:0%
+because because
+uh uh well or I'll put it in here uh so
+
+ align:start position:0%
+uh uh well or I'll put it in here uh so
+ 
+
+ align:start position:0%
+uh uh well or I'll put it in here uh so
+what is the transpose of this thing so I
+
+ align:start position:0%
+what is the transpose of this thing so I
+ 
+
+ align:start position:0%
+what is the transpose of this thing so I
+have a product of three things and I
+
+ align:start position:0%
+have a product of three things and I
+ 
+
+ align:start position:0%
+have a product of three things and I
+want to transpose it so this is just
+
+ align:start position:0%
+want to transpose it so this is just
+ 
+
+ align:start position:0%
+want to transpose it so this is just
+this is a little check that the result
+
+ align:start position:0%
+this is a little check that the result
+ 
+
+ align:start position:0%
+this is a little check that the result
+is always symmetric and it's okay what
+
+ align:start position:0%
+is always symmetric and it's okay what
+ 
+
+ align:start position:0%
+is always symmetric and it's okay what
+happens when you take the transpose
+
+ align:start position:0%
+happens when you take the transpose
+ 
+
+ align:start position:0%
+happens when you take the transpose
+you've got several things multiplied
+
+ align:start position:0%
+you've got several things multiplied
+ 
+
+ align:start position:0%
+you've got several things multiplied
+together and you take the
+
+ align:start position:0%
+together and you take the
+ 
+
+ align:start position:0%
+together and you take the
+transpose you it's you you take the
+
+ align:start position:0%
+transpose you it's you you take the
+ 
+
+ align:start position:0%
+transpose you it's you you take the
+separate transposes but you reverse the
+
+ align:start position:0%
+separate transposes but you reverse the
+ 
+
+ align:start position:0%
+separate transposes but you reverse the
+order it's like inverses
+
+ align:start position:0%
+order it's like inverses
+ 
+
+ align:start position:0%
+order it's like inverses
+it reverses the order so that means that
+
+ align:start position:0%
+it reverses the order so that means that
+ 
+
+ align:start position:0%
+it reverses the order so that means that
+this last guy comes first L transposed
+
+ align:start position:0%
+this last guy comes first L transposed
+ 
+
+ align:start position:0%
+this last guy comes first L transposed
+transposed then the D
+
+ align:start position:0%
+transposed then the D
+ 
+
+ align:start position:0%
+transposed then the D
+transpose and then the L
+
+ align:start position:0%
+transpose and then the L
+ 
+
+ align:start position:0%
+transpose and then the L
+transpose okay so now did I get back
+
+ align:start position:0%
+transpose okay so now did I get back
+ 
+
+ align:start position:0%
+transpose okay so now did I get back
+what I started
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with well what's L transpose
+
+ align:start position:0%
+with well what's L transpose
+ 
+
+ align:start position:0%
+with well what's L transpose
+transpose it's l because if I flip it
+
+ align:start position:0%
+transpose it's l because if I flip it
+ 
+
+ align:start position:0%
+transpose it's l because if I flip it
+twice I'm back and what oh yeah what is
+
+ align:start position:0%
+twice I'm back and what oh yeah what is
+ 
+
+ align:start position:0%
+twice I'm back and what oh yeah what is
+D trans suppose it is D oh but now I see
+
+ align:start position:0%
+D trans suppose it is D oh but now I see
+ 
+
+ align:start position:0%
+D trans suppose it is D oh but now I see
+I I I misspoke earlier because there is
+
+ align:start position:0%
+I I I misspoke earlier because there is
+ 
+
+ align:start position:0%
+I I I misspoke earlier because there is
+this Center
+
+ align:start position:0%
+this Center
+ 
+
+ align:start position:0%
+this Center
+guy doesn't have to be diagonal here it
+
+ align:start position:0%
+guy doesn't have to be diagonal here it
+ 
+
+ align:start position:0%
+guy doesn't have to be diagonal here it
+is but what does it have to be it better
+
+ align:start position:0%
+is but what does it have to be it better
+ 
+
+ align:start position:0%
+is but what does it have to be it better
+be symmetric because I want D transposed
+
+ align:start position:0%
+be symmetric because I want D transposed
+ 
+
+ align:start position:0%
+be symmetric because I want D transposed
+to be the same as D and then I have a so
+
+ align:start position:0%
+to be the same as D and then I have a so
+ 
+
+ align:start position:0%
+to be the same as D and then I have a so
+this is so all my triple products will
+
+ align:start position:0%
+this is so all my triple products will
+ 
+
+ align:start position:0%
+this is so all my triple products will
+have something and something transpose
+
+ align:start position:0%
+have something and something transpose
+ 
+
+ align:start position:0%
+have something and something transpose
+on the outside side and a symmetric
+
+ align:start position:0%
+on the outside side and a symmetric
+ 
+
+ align:start position:0%
+on the outside side and a symmetric
+Matrix in the middle yeah that's the
+
+ align:start position:0%
+Matrix in the middle yeah that's the
+ 
+
+ align:start position:0%
+Matrix in the middle yeah that's the
+right that's the symmetric form and and
+
+ align:start position:0%
+right that's the symmetric form and and
+ 
+
+ align:start position:0%
+right that's the symmetric form and and
+as I say we we've got symmetric matrices
+
+ align:start position:0%
+as I say we we've got symmetric matrices
+ 
+
+ align:start position:0%
+as I say we we've got symmetric matrices
+are what nature gives us all the time so
+
+ align:start position:0%
+are what nature gives us all the time so
+ 
+
+ align:start position:0%
+are what nature gives us all the time so
+we ought to know what's special about
+
+ align:start position:0%
+we ought to know what's special about
+ 
+
+ align:start position:0%
+we ought to know what's special about
+them okay so now I'm going to
+
+ align:start position:0%
+them okay so now I'm going to
+ 
+
+ align:start position:0%
+them okay so now I'm going to
+introduce the word that's actually the
+
+ align:start position:0%
+introduce the word that's actually the
+ 
+
+ align:start position:0%
+introduce the word that's actually the
+title of this lecture you might have
+
+ align:start position:0%
+title of this lecture you might have
+ 
+
+ align:start position:0%
+title of this lecture you might have
+said when is he going to get to this
+
+ align:start position:0%
+said when is he going to get to this
+ 
+
+ align:start position:0%
+said when is he going to get to this
+this word positive definite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because so that Matrix is symmetric it's
+
+ align:start position:0%
+because so that Matrix is symmetric it's
+ 
+
+ align:start position:0%
+because so that Matrix is symmetric it's
+triagonal it has constant diagonals it's
+
+ align:start position:0%
+triagonal it has constant diagonals it's
+ 
+
+ align:start position:0%
+triagonal it has constant diagonals it's
+tets it's
+
+ align:start position:0%
+tets it's
+ 
+
+ align:start position:0%
+tets it's
+invertible it's invertible because the
+
+ align:start position:0%
+invertible it's invertible because the
+ 
+
+ align:start position:0%
+invertible it's invertible because the
+pivots are not zero we got a full set of
+
+ align:start position:0%
+pivots are not zero we got a full set of
+ 
+
+ align:start position:0%
+pivots are not zero we got a full set of
+pivots but more than that it has this
+
+ align:start position:0%
+pivots but more than that it has this
+ 
+
+ align:start position:0%
+pivots but more than that it has this
+additional
+
+ align:start position:0%
+additional
+ 
+
+ align:start position:0%
+additional
+property that I want to talk about
+
+ align:start position:0%
+property that I want to talk about
+ 
+
+ align:start position:0%
+property that I want to talk about
+because it's such an extra valuable
+
+ align:start position:0%
+because it's such an extra valuable
+ 
+
+ align:start position:0%
+because it's such an extra valuable
+property and that and that is it's
+
+ align:start position:0%
+property and that and that is it's
+ 
+
+ align:start position:0%
+property and that and that is it's
+positive definite so it's non- singular
+
+ align:start position:0%
+positive definite so it's non- singular
+ 
+
+ align:start position:0%
+positive definite so it's non- singular
+let me let me uh make space
+
+ align:start position:0%
+let me let me uh make space
+ 
+
+ align:start position:0%
+let me let me uh make space
+here I don't need this anymore just as
+
+ align:start position:0%
+here I don't need this anymore just as
+ 
+
+ align:start position:0%
+here I don't need this anymore just as
+matlb wouldn't save the E Mad Lab would
+
+ align:start position:0%
+matlb wouldn't save the E Mad Lab would
+ 
+
+ align:start position:0%
+matlb wouldn't save the E Mad Lab would
+create the L as it goes and would
+
+ align:start position:0%
+create the L as it goes and would
+ 
+
+ align:start position:0%
+create the L as it goes and would
+never never even look at the
+
+ align:start position:0%
+never never even look at the
+ 
+
+ align:start position:0%
+never never even look at the
+ease
+
+ align:start position:0%
+ease
+ 
+
+ align:start position:0%
+ease
+okay okay so this is my list of
+
+ align:start position:0%
+okay okay so this is my list of
+ 
+
+ align:start position:0%
+okay okay so this is my list of
+properties I'm going to add one more and
+
+ align:start position:0%
+properties I'm going to add one more and
+ 
+
+ align:start position:0%
+properties I'm going to add one more and
+and that is that it's positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definite okay so that's the the word I
+
+ align:start position:0%
+definite okay so that's the the word I
+ 
+
+ align:start position:0%
+definite okay so that's the the word I
+have to tell you what that means and I I
+
+ align:start position:0%
+have to tell you what that means and I I
+ 
+
+ align:start position:0%
+have to tell you what that means and I I
+I guess I'm my claim is it's really
+
+ align:start position:0%
+I guess I'm my claim is it's really
+ 
+
+ align:start position:0%
+I guess I'm my claim is it's really
+worth
+
+ align:start position:0%
+worth
+ 
+
+ align:start position:0%
+worth
+learning what that what that is
+
+ align:start position:0%
+learning what that what that is
+ 
+
+ align:start position:0%
+learning what that what that is
+about and what are the so how do I
+
+ align:start position:0%
+about and what are the so how do I
+ 
+
+ align:start position:0%
+about and what are the so how do I
+recognize a positive definition Matrix
+
+ align:start position:0%
+recognize a positive definition Matrix
+ 
+
+ align:start position:0%
+recognize a positive definition Matrix
+well several different ways and one way
+
+ align:start position:0%
+well several different ways and one way
+ 
+
+ align:start position:0%
+well several different ways and one way
+to recognize it
+
+ align:start position:0%
+to recognize it
+ 
+
+ align:start position:0%
+to recognize it
+is it has to be
+
+ align:start position:0%
+is it has to be
+ 
+
+ align:start position:0%
+is it has to be
+symmetric I shall I say symmetric
+
+ align:start position:0%
+symmetric I shall I say symmetric
+ 
+
+ align:start position:0%
+symmetric I shall I say symmetric
+because because I'm only interested here
+
+ align:start position:0%
+because because I'm only interested here
+ 
+
+ align:start position:0%
+because because I'm only interested here
+in symmetric matrices but now I'm now I
+
+ align:start position:0%
+in symmetric matrices but now I'm now I
+ 
+
+ align:start position:0%
+in symmetric matrices but now I'm now I
+want to say what's positive about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it and here what's positive about it is
+
+ align:start position:0%
+it and here what's positive about it is
+ 
+
+ align:start position:0%
+it and here what's positive about it is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+pivots so that's the that's one test if
+
+ align:start position:0%
+pivots so that's the that's one test if
+ 
+
+ align:start position:0%
+pivots so that's the that's one test if
+you just give me a Matrix a specific
+
+ align:start position:0%
+you just give me a Matrix a specific
+ 
+
+ align:start position:0%
+you just give me a Matrix a specific
+Matrix like this one or this
+
+ align:start position:0%
+Matrix like this one or this
+ 
+
+ align:start position:0%
+Matrix like this one or this
+one uh so it has a full set it it it's a
+
+ align:start position:0%
+one uh so it has a full set it it it's a
+ 
+
+ align:start position:0%
+one uh so it has a full set it it it's a
+full
+
+ align:start position:0%
+full
+ 
+
+ align:start position:0%
+full
+set or shall I say
+
+ align:start position:0%
+set or shall I say
+ 
+
+ align:start position:0%
+set or shall I say
+N N's always the size of the Matrix n
+
+ align:start position:0%
+N N's always the size of the Matrix n
+ 
+
+ align:start position:0%
+N N's always the size of the Matrix n
+pivots all
+
+ align:start position:0%
+pivots all
+ 
+
+ align:start position:0%
+pivots all
+positive n pivots so I say n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pivots greater than zero all in pivots
+
+ align:start position:0%
+pivots greater than zero all in pivots
+ 
+
+ align:start position:0%
+pivots greater than zero all in pivots
+so let me
+
+ align:start position:0%
+so let me
+ 
+
+ align:start position:0%
+so let me
+all M pivots are positive okay that's
+
+ align:start position:0%
+all M pivots are positive okay that's
+ 
+
+ align:start position:0%
+all M pivots are positive okay that's
+uh that's happens here two and three
+
+ align:start position:0%
+uh that's happens here two and three
+ 
+
+ align:start position:0%
+uh that's happens here two and three
+halves are not only not zero which was
+
+ align:start position:0%
+halves are not only not zero which was
+ 
+
+ align:start position:0%
+halves are not only not zero which was
+the requirement to be invertible but
+
+ align:start position:0%
+the requirement to be invertible but
+ 
+
+ align:start position:0%
+the requirement to be invertible but
+they're positive that's the requirement
+
+ align:start position:0%
+they're positive that's the requirement
+ 
+
+ align:start position:0%
+they're positive that's the requirement
+to be positive definite this guy is
+
+ align:start position:0%
+to be positive definite this guy is
+ 
+
+ align:start position:0%
+to be positive definite this guy is
+positive definite too his pivots are one
+
+ align:start position:0%
+positive definite too his pivots are one
+ 
+
+ align:start position:0%
+positive definite too his pivots are one
+one and
+
+ align:start position:0%
+one and
+ 
+
+ align:start position:0%
+one and
+one okay is this Matrix
+
+ align:start position:0%
+one okay is this Matrix
+ 
+
+ align:start position:0%
+one okay is this Matrix
+positive definite
+
+ align:start position:0%
+positive definite
+ 
+
+ align:start position:0%
+positive definite
+no cuz it hasn't got that third pivot
+
+ align:start position:0%
+no cuz it hasn't got that third pivot
+ 
+
+ align:start position:0%
+no cuz it hasn't got that third pivot
+the other it's
+
+ align:start position:0%
+the other it's
+ 
+
+ align:start position:0%
+the other it's
+true those things are positive but then
+
+ align:start position:0%
+true those things are positive but then
+ 
+
+ align:start position:0%
+true those things are positive but then
+it flakes out at the last minute and the
+
+ align:start position:0%
+it flakes out at the last minute and the
+ 
+
+ align:start position:0%
+it flakes out at the last minute and the
+last pivot isn't there so I would call
+
+ align:start position:0%
+last pivot isn't there so I would call
+ 
+
+ align:start position:0%
+last pivot isn't there so I would call
+that positive semi-definite so
+
+ align:start position:0%
+that positive semi-definite so
+ 
+
+ align:start position:0%
+that positive semi-definite so
+semi-definite means you could like
+
+ align:start position:0%
+semi-definite means you could like
+ 
+
+ align:start position:0%
+semi-definite means you could like
+pivots greater or equal to zero you
+
+ align:start position:0%
+pivots greater or equal to zero you
+ 
+
+ align:start position:0%
+pivots greater or equal to zero you
+could say or something so so this this
+
+ align:start position:0%
+could say or something so so this this
+ 
+
+ align:start position:0%
+could say or something so so this this
+is a great example of the Matrix that's
+
+ align:start position:0%
+is a great example of the Matrix that's
+ 
+
+ align:start position:0%
+is a great example of the Matrix that's
+sort of on the
+
+ align:start position:0%
+sort of on the
+ 
+
+ align:start position:0%
+sort of on the
+borderline it's it's been pushed out of
+
+ align:start position:0%
+borderline it's it's been pushed out of
+ 
+
+ align:start position:0%
+borderline it's it's been pushed out of
+the positive thing but not to the
+
+ align:start position:0%
+the positive thing but not to the
+ 
+
+ align:start position:0%
+the positive thing but not to the
+negative side so it's positive
+
+ align:start position:0%
+negative side so it's positive
+ 
+
+ align:start position:0%
+negative side so it's positive
+semidefinite okay but I'm interested in
+
+ align:start position:0%
+semidefinite okay but I'm interested in
+ 
+
+ align:start position:0%
+semidefinite okay but I'm interested in
+focusing on positive definite here
+
+ align:start position:0%
+focusing on positive definite here
+ 
+
+ align:start position:0%
+focusing on positive definite here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so and and so this is an important idea
+
+ align:start position:0%
+so and and so this is an important idea
+ 
+
+ align:start position:0%
+so and and so this is an important idea
+is it's a it's the best class of
+
+ align:start position:0%
+is it's a it's the best class of
+ 
+
+ align:start position:0%
+is it's a it's the best class of
+matrices you could
+
+ align:start position:0%
+matrices you could
+ 
+
+ align:start position:0%
+matrices you could
+say it's matrices it's the class of
+
+ align:start position:0%
+say it's matrices it's the class of
+ 
+
+ align:start position:0%
+say it's matrices it's the class of
+matrices which fortunately will will see
+
+ align:start position:0%
+matrices which fortunately will will see
+ 
+
+ align:start position:0%
+matrices which fortunately will will see
+a lot
+
+ align:start position:0%
+a lot
+ 
+
+ align:start position:0%
+a lot
+of and can I tell you other ways to
+
+ align:start position:0%
+of and can I tell you other ways to
+ 
+
+ align:start position:0%
+of and can I tell you other ways to
+recognize a positive definite Matrix so
+
+ align:start position:0%
+recognize a positive definite Matrix so
+ 
+
+ align:start position:0%
+recognize a positive definite Matrix so
+it's it's really wonderful
+
+ align:start position:0%
+it's it's really wonderful
+ 
+
+ align:start position:0%
+it's it's really wonderful
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+that all the different pieces of linear
+
+ align:start position:0%
+that all the different pieces of linear
+ 
+
+ align:start position:0%
+that all the different pieces of linear
+algebra come together in this positive
+
+ align:start position:0%
+algebra come together in this positive
+ 
+
+ align:start position:0%
+algebra come together in this positive
+definite idea
+
+ align:start position:0%
+definite idea
+ 
+
+ align:start position:0%
+definite idea
+okay the second piece I'll just
+
+ align:start position:0%
+okay the second piece I'll just
+ 
+
+ align:start position:0%
+okay the second piece I'll just
+say straight out and then leave for the
+
+ align:start position:0%
+say straight out and then leave for the
+ 
+
+ align:start position:0%
+say straight out and then leave for the
+lectures of next week all
+
+ align:start position:0%
+lectures of next week all
+ 
+
+ align:start position:0%
+lectures of next week all
+n igen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+okay so you may well already know about
+
+ align:start position:0%
+okay so you may well already know about
+ 
+
+ align:start position:0%
+okay so you may well already know about
+igen
+
+ align:start position:0%
+igen
+ 
+
+ align:start position:0%
+igen
+values but
+
+ align:start position:0%
+values but
+ 
+
+ align:start position:0%
+values but
+also know that
+
+ align:start position:0%
+also know that
+ 
+
+ align:start position:0%
+also know that
+you you know looking at a
+
+ align:start position:0%
+you you know looking at a
+ 
+
+ align:start position:0%
+you you know looking at a
+matrix it may not be easy to spot its
+
+ align:start position:0%
+matrix it may not be easy to spot its
+ 
+
+ align:start position:0%
+matrix it may not be easy to spot its
+inverse but it sure isn't easy to spot
+
+ align:start position:0%
+inverse but it sure isn't easy to spot
+ 
+
+ align:start position:0%
+inverse but it sure isn't easy to spot
+its IG values I mean that's that's one
+
+ align:start position:0%
+its IG values I mean that's that's one
+ 
+
+ align:start position:0%
+its IG values I mean that's that's one
+step deeper than the inverse definit I
+
+ align:start position:0%
+step deeper than the inverse definit I
+ 
+
+ align:start position:0%
+step deeper than the inverse definit I
+mean a big step deeper so I've written
+
+ align:start position:0%
+mean a big step deeper so I've written
+ 
+
+ align:start position:0%
+mean a big step deeper so I've written
+this here but I haven't said what the I
+
+ align:start position:0%
+this here but I haven't said what the I
+ 
+
+ align:start position:0%
+this here but I haven't said what the I
+values
+
+ align:start position:0%
+values
+ 
+
+ align:start position:0%
+values
+are let's that'll we have to work for
+
+ align:start position:0%
+are let's that'll we have to work for
+ 
+
+ align:start position:0%
+are let's that'll we have to work for
+those okay but it isn't it satisfying
+
+ align:start position:0%
+those okay but it isn't it satisfying
+ 
+
+ align:start position:0%
+those okay but it isn't it satisfying
+that when all the pivots are positive
+
+ align:start position:0%
+that when all the pivots are positive
+ 
+
+ align:start position:0%
+that when all the pivots are positive
+all the Aon values are positive okay and
+
+ align:start position:0%
+all the Aon values are positive okay and
+ 
+
+ align:start position:0%
+all the Aon values are positive okay and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+finally the third thing which is really
+
+ align:start position:0%
+finally the third thing which is really
+ 
+
+ align:start position:0%
+finally the third thing which is really
+the definition so I I it's really the
+
+ align:start position:0%
+the definition so I I it's really the
+ 
+
+ align:start position:0%
+the definition so I I it's really the
+definition of positive
+
+ align:start position:0%
+definition of positive
+ 
+
+ align:start position:0%
+definition of positive
+definite and this is a consequence and
+
+ align:start position:0%
+definite and this is a consequence and
+ 
+
+ align:start position:0%
+definite and this is a consequence and
+this is a consequence but the definition
+
+ align:start position:0%
+this is a consequence but the definition
+ 
+
+ align:start position:0%
+this is a consequence but the definition
+is sort of more uh fundamental
+
+ align:start position:0%
+is sort of more uh fundamental
+ 
+
+ align:start position:0%
+is sort of more uh fundamental
+okay so what am I I'm talking about this
+
+ align:start position:0%
+okay so what am I I'm talking about this
+ 
+
+ align:start position:0%
+okay so what am I I'm talking about this
+Matrix K so my my claim is going to be
+
+ align:start position:0%
+Matrix K so my my claim is going to be
+ 
+
+ align:start position:0%
+Matrix K so my my claim is going to be
+that all this whole family is positive
+
+ align:start position:0%
+that all this whole family is positive
+ 
+
+ align:start position:0%
+that all this whole family is positive
+definite this whole family is positive
+
+ align:start position:0%
+definite this whole family is positive
+ 
+
+ align:start position:0%
+definite this whole family is positive
+definite for whatever size and this
+
+ align:start position:0%
+definite for whatever size and this
+ 
+
+ align:start position:0%
+definite for whatever size and this
+family is positive semi-definite for
+
+ align:start position:0%
+family is positive semi-definite for
+ 
+
+ align:start position:0%
+family is positive semi-definite for
+whatever size we we get down to the very
+
+ align:start position:0%
+whatever size we we get down to the very
+ 
+
+ align:start position:0%
+whatever size we we get down to the very
+last pivot and then it lets us down and
+
+ align:start position:0%
+last pivot and then it lets us down and
+ 
+
+ align:start position:0%
+last pivot and then it lets us down and
+uh we're only semi-definite okay so what
+
+ align:start position:0%
+uh we're only semi-definite okay so what
+ 
+
+ align:start position:0%
+uh we're only semi-definite okay so what
+does positive definite
+
+ align:start position:0%
+does positive definite
+ 
+
+ align:start position:0%
+does positive definite
+mean it means means that if I take my
+
+ align:start position:0%
+mean it means means that if I take my
+ 
+
+ align:start position:0%
+mean it means means that if I take my
+Matrix call call my Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K by the way in the beginning so my my
+
+ align:start position:0%
+K by the way in the beginning so my my
+ 
+
+ align:start position:0%
+K by the way in the beginning so my my
+general rule will
+
+ align:start position:0%
+general rule will
+ 
+
+ align:start position:0%
+general rule will
+be that if I have a specific Matrix in
+
+ align:start position:0%
+be that if I have a specific Matrix in
+ 
+
+ align:start position:0%
+be that if I have a specific Matrix in
+mind like k i I give it a
+
+ align:start position:0%
+mind like k i I give it a
+ 
+
+ align:start position:0%
+mind like k i I give it a
+name or t or
+
+ align:start position:0%
+name or t or
+ 
+
+ align:start position:0%
+name or t or
+B if I can't think of any particular if
+
+ align:start position:0%
+B if I can't think of any particular if
+ 
+
+ align:start position:0%
+B if I can't think of any particular if
+it's just a matrix I'll always call it a
+
+ align:start position:0%
+it's just a matrix I'll always call it a
+ 
+
+ align:start position:0%
+it's just a matrix I'll always call it a
+so a just stands for some Matrix that I
+
+ align:start position:0%
+so a just stands for some Matrix that I
+ 
+
+ align:start position:0%
+so a just stands for some Matrix that I
+that more or less could be anything but
+
+ align:start position:0%
+that more or less could be anything but
+ 
+
+ align:start position:0%
+that more or less could be anything but
+here I'm speaking about a specific
+
+ align:start position:0%
+here I'm speaking about a specific
+ 
+
+ align:start position:0%
+here I'm speaking about a specific
+Matrix this this guy that we're looking
+
+ align:start position:0%
+Matrix this this guy that we're looking
+ 
+
+ align:start position:0%
+Matrix this this guy that we're looking
+at okay now so positive definite means
+
+ align:start position:0%
+at okay now so positive definite means
+ 
+
+ align:start position:0%
+at okay now so positive definite means
+okay if I multiply by X by any Vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X and I multiply on this side by the
+
+ align:start position:0%
+X and I multiply on this side by the
+ 
+
+ align:start position:0%
+X and I multiply on this side by the
+transpose of that Vector
+
+ align:start position:0%
+transpose of that Vector
+ 
+
+ align:start position:0%
+transpose of that Vector
+X okay this is for for any X this is
+
+ align:start position:0%
+X okay this is for for any X this is
+ 
+
+ align:start position:0%
+X okay this is for for any X this is
+any any vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X so I take this 3x3 Matrix I multiply
+
+ align:start position:0%
+X so I take this 3x3 Matrix I multiply
+ 
+
+ align:start position:0%
+X so I take this 3x3 Matrix I multiply
+by any Vector that has three components
+
+ align:start position:0%
+by any Vector that has three components
+ 
+
+ align:start position:0%
+by any Vector that has three components
+and here I'm multiplying so this is like
+
+ align:start position:0%
+and here I'm multiplying so this is like
+ 
+
+ align:start position:0%
+and here I'm multiplying so this is like
+3x one right and what's the shape of X
+
+ align:start position:0%
+3x one right and what's the shape of X
+ 
+
+ align:start position:0%
+3x one right and what's the shape of X
+transpose then 1 by3 and what what have
+
+ align:start position:0%
+transpose then 1 by3 and what what have
+ 
+
+ align:start position:0%
+transpose then 1 by3 and what what have
+I got when I take a 1x3
+
+ align:start position:0%
+I got when I take a 1x3
+ 
+
+ align:start position:0%
+I got when I take a 1x3
+matrix which is just a row time 3x3
+
+ align:start position:0%
+matrix which is just a row time 3x3
+ 
+
+ align:start position:0%
+matrix which is just a row time 3x3
+times 3x
+
+ align:start position:0%
+times 3x
+ 
+
+ align:start position:0%
+times 3x
+1 I've got
+
+ align:start position:0%
+1 I've got
+ 
+
+ align:start position:0%
+1 I've got
+a A 1 by one right one by one a number
+
+ align:start position:0%
+a A 1 by one right one by one a number
+ 
+
+ align:start position:0%
+a A 1 by one right one by one a number
+okay and now everybody's going to tell
+
+ align:start position:0%
+okay and now everybody's going to tell
+ 
+
+ align:start position:0%
+okay and now everybody's going to tell
+me what's the requirement for positive
+
+ align:start position:0%
+me what's the requirement for positive
+ 
+
+ align:start position:0%
+me what's the requirement for positive
+definite it should be positive right
+
+ align:start position:0%
+definite it should be positive right
+ 
+
+ align:start position:0%
+definite it should be positive right
+good as long as X isn't zero so any
+
+ align:start position:0%
+good as long as X isn't zero so any
+ 
+
+ align:start position:0%
+good as long as X isn't zero so any
+Vector X other than zero
+
+ align:start position:0%
+Vector X other than zero
+ 
+
+ align:start position:0%
+Vector X other than zero
+because for the zero Vector obviously
+
+ align:start position:0%
+because for the zero Vector obviously
+ 
+
+ align:start position:0%
+because for the zero Vector obviously
+we're going to get the answer zero but
+
+ align:start position:0%
+we're going to get the answer zero but
+ 
+
+ align:start position:0%
+we're going to get the answer zero but
+every other Vector X is with with that
+
+ align:start position:0%
+every other Vector X is with with that
+ 
+
+ align:start position:0%
+every other Vector X is with with that
+Vector on the right and this and its
+
+ align:start position:0%
+Vector on the right and this and its
+ 
+
+ align:start position:0%
+Vector on the right and this and its
+transpose on the left is gives me a
+
+ align:start position:0%
+transpose on the left is gives me a
+ 
+
+ align:start position:0%
+transpose on the left is gives me a
+positive number well you might
+
+ align:start position:0%
+positive number well you might
+ 
+
+ align:start position:0%
+positive number well you might
+say where did that come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from and the answer is it came from
+
+ align:start position:0%
+from and the answer is it came from
+ 
+
+ align:start position:0%
+from and the answer is it came from
+physics and applications too this
+
+ align:start position:0%
+physics and applications too this
+ 
+
+ align:start position:0%
+physics and applications too this
+expression is an energy that's the
+
+ align:start position:0%
+expression is an energy that's the
+ 
+
+ align:start position:0%
+expression is an energy that's the
+energy associated with the Matrix
+
+ align:start position:0%
+energy associated with the Matrix
+ 
+
+ align:start position:0%
+energy associated with the Matrix
+K sometimes use a factor half beside it
+
+ align:start position:0%
+K sometimes use a factor half beside it
+ 
+
+ align:start position:0%
+K sometimes use a factor half beside it
+often you you remember kinetic energy is
+
+ align:start position:0%
+often you you remember kinetic energy is
+ 
+
+ align:start position:0%
+often you you remember kinetic energy is
+a half masstimes velocity
+
+ align:start position:0%
+a half masstimes velocity
+ 
+
+ align:start position:0%
+a half masstimes velocity
+squared well it's like uh you know
+
+ align:start position:0%
+squared well it's like uh you know
+ 
+
+ align:start position:0%
+squared well it's like uh you know
+there's the mass and there's some
+
+ align:start position:0%
+there's the mass and there's some
+ 
+
+ align:start position:0%
+there's the mass and there's some
+something squared and I could put in the
+
+ align:start position:0%
+something squared and I could put in the
+ 
+
+ align:start position:0%
+something squared and I could put in the
+half or what's potential energy
+
+ align:start position:0%
+half or what's potential energy
+ 
+
+ align:start position:0%
+half or what's potential energy
+potential energy in a spring actually we
+
+ align:start position:0%
+potential energy in a spring actually we
+ 
+
+ align:start position:0%
+potential energy in a spring actually we
+could see that in the in the next hour
+
+ align:start position:0%
+could see that in the in the next hour
+ 
+
+ align:start position:0%
+could see that in the in the next hour
+um the energy in a spring is there's a
+
+ align:start position:0%
+um the energy in a spring is there's a
+ 
+
+ align:start position:0%
+um the energy in a spring is there's a
+constant a spring constant a stiffness
+
+ align:start position:0%
+constant a spring constant a stiffness
+ 
+
+ align:start position:0%
+constant a spring constant a stiffness
+times the stretching
+
+ align:start position:0%
+times the stretching
+ 
+
+ align:start position:0%
+times the stretching
+squared so this is energy this is energy
+
+ align:start position:0%
+squared so this is energy this is energy
+ 
+
+ align:start position:0%
+squared so this is energy this is energy
+in the system that's associated with
+
+ align:start position:0%
+in the system that's associated with
+ 
+
+ align:start position:0%
+in the system that's associated with
+with K which will be we could make an
+
+ align:start position:0%
+with K which will be we could make an
+ 
+
+ align:start position:0%
+with K which will be we could make an
+example with springs and masses so so
+
+ align:start position:0%
+example with springs and masses so so
+ 
+
+ align:start position:0%
+example with springs and masses so so
+that has a meaning is all I'm trying to
+
+ align:start position:0%
+that has a meaning is all I'm trying to
+ 
+
+ align:start position:0%
+that has a meaning is all I'm trying to
+say I can't you you'll see the meaning
+
+ align:start position:0%
+say I can't you you'll see the meaning
+ 
+
+ align:start position:0%
+say I can't you you'll see the meaning
+when we do the applied MTH so that this
+
+ align:start position:0%
+when we do the applied MTH so that this
+ 
+
+ align:start position:0%
+when we do the applied MTH so that this
+lecture again was
+
+ align:start position:0%
+lecture again was
+ 
+
+ align:start position:0%
+lecture again was
+the was the dealing with the Matrix once
+
+ align:start position:0%
+the was the dealing with the Matrix once
+ 
+
+ align:start position:0%
+the was the dealing with the Matrix once
+we once we had it and now I'll take a
+
+ align:start position:0%
+we once we had it and now I'll take a
+ 
+
+ align:start position:0%
+we once we had it and now I'll take a
+break uh after
+
+ align:start position:0%
+break uh after
+ 
+
+ align:start position:0%
+break uh after
+suggesting um saying again what you
+
+ align:start position:0%
+suggesting um saying again what you
+ 
+
+ align:start position:0%
+suggesting um saying again what you
+might want to do
+
+ align:start position:0%
+might want to do
+ 
+
+ align:start position:0%
+might want to do
+um uh between now and next
+
+ align:start position:0%
+um uh between now and next
+ 
+
+ align:start position:0%
+um uh between now and next
+Thursday I really
+
+ align:start position:0%
+Thursday I really
+ 
+
+ align:start position:0%
+Thursday I really
+so one thing would be to get those
+
+ align:start position:0%
+so one thing would be to get those
+ 
+
+ align:start position:0%
+so one thing would be to get those
+inverses and you can probably guess
+
+ align:start position:0%
+inverses and you can probably guess
+ 
+
+ align:start position:0%
+inverses and you can probably guess
+those and you I think you can guess the
+
+ align:start position:0%
+those and you I think you can guess the
+ 
+
+ align:start position:0%
+those and you I think you can guess the
+determinants I mean so first step was
+
+ align:start position:0%
+determinants I mean so first step was
+ 
+
+ align:start position:0%
+determinants I mean so first step was
+create these matrices by mat lab and mat
+
+ align:start position:0%
+create these matrices by mat lab and mat
+ 
+
+ align:start position:0%
+create these matrices by mat lab and mat
+lab compute the determinants and and
+
+ align:start position:0%
+lab compute the determinants and and
+ 
+
+ align:start position:0%
+lab compute the determinants and and
+inverses for say n equal so so my
+
+ align:start position:0%
+inverses for say n equal so so my
+ 
+
+ align:start position:0%
+inverses for say n equal so so my
+homework suggestion is let mat lab do n
+
+ align:start position:0%
+homework suggestion is let mat lab do n
+ 
+
+ align:start position:0%
+homework suggestion is let mat lab do n
+equal 1 2 3 and
+
+ align:start position:0%
+equal 1 2 3 and
+ 
+
+ align:start position:0%
+equal 1 2 3 and
+four and then try to see the
+
+ align:start position:0%
+four and then try to see the
+ 
+
+ align:start position:0%
+four and then try to see the
+pattern and I think you'll see the
+
+ align:start position:0%
+pattern and I think you'll see the
+ 
+
+ align:start position:0%
+pattern and I think you'll see the
+pattern in T3
+
+ align:start position:0%
+pattern in T3
+ 
+
+ align:start position:0%
+pattern in T3
+inverse that challenge my so my
+
+ align:start position:0%
+inverse that challenge my so my
+ 
+
+ align:start position:0%
+inverse that challenge my so my
+challenge problem and and I'm ready for
+
+ align:start position:0%
+challenge problem and and I'm ready for
+ 
+
+ align:start position:0%
+challenge problem and and I'm ready for
+um email on this
+
+ align:start position:0%
+um email on this
+ 
+
+ align:start position:0%
+um email on this
+one um well if you
+
+ align:start position:0%
+one um well if you
+ 
+
+ align:start position:0%
+one um well if you
+succeed uh is find the pattern in the in
+
+ align:start position:0%
+succeed uh is find the pattern in the in
+ 
+
+ align:start position:0%
+succeed uh is find the pattern in the in
+K inverse knen inverse I if anybody
+
+ align:start position:0%
+K inverse knen inverse I if anybody
+ 
+
+ align:start position:0%
+K inverse knen inverse I if anybody
+comes up with a formula for KNN inverse
+
+ align:start position:0%
+comes up with a formula for KNN inverse
+ 
+
+ align:start position:0%
+comes up with a formula for KNN inverse
+I'm impressed let me let me say that the
+
+ align:start position:0%
+I'm impressed let me let me say that the
+ 
+
+ align:start position:0%
+I'm impressed let me let me say that the
+formula should
+
+ align:start position:0%
+formula should
+ 
+
+ align:start position:0%
+formula should
+have if you get a formula for the for
+
+ align:start position:0%
+have if you get a formula for the for
+ 
+
+ align:start position:0%
+have if you get a formula for the for
+the upper half
+
+ align:start position:0%
+the upper half
+ 
+
+ align:start position:0%
+the upper half
+then I'm happy with that right because
+
+ align:start position:0%
+then I'm happy with that right because
+ 
+
+ align:start position:0%
+then I'm happy with that right because
+it's symmetric so I'm prepared to fill
+
+ align:start position:0%
+it's symmetric so I'm prepared to fill
+ 
+
+ align:start position:0%
+it's symmetric so I'm prepared to fill
+in the lower half so if you can uh spot
+
+ align:start position:0%
+in the lower half so if you can uh spot
+ 
+
+ align:start position:0%
+in the lower half so if you can uh spot
+the formula and you you may have to go
+
+ align:start position:0%
+the formula and you you may have to go
+ 
+
+ align:start position:0%
+the formula and you you may have to go
+to certainly have to go to four maybe
+
+ align:start position:0%
+to certainly have to go to four maybe
+ 
+
+ align:start position:0%
+to certainly have to go to four maybe
+the five to even begin to see what up
+
+ align:start position:0%
+the five to even begin to see what up
+ 
+
+ align:start position:0%
+the five to even begin to see what up
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh that so that's certainly a challenge
+
+ align:start position:0%
+uh that so that's certainly a challenge
+ 
+
+ align:start position:0%
+uh that so that's certainly a challenge
+uh problem and then section one two has
+
+ align:start position:0%
+uh problem and then section one two has
+ 
+
+ align:start position:0%
+uh problem and then section one two has
+a lot of uh other uh exercises on those
+
+ align:start position:0%
+a lot of uh other uh exercises on those
+ 
+
+ align:start position:0%
+a lot of uh other uh exercises on those
+topics so I'll stop here as the end of
+
+ align:start position:0%
+topics so I'll stop here as the end of
+ 
+
+ align:start position:0%
+topics so I'll stop here as the end of
+the end of lecture one
\ No newline at end of file
diff --git a/f_BHF-OYwr4.txt b/f_BHF-OYwr4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..18ecf68b364461c0af4c04a1126e3ebf71acf763
--- /dev/null
+++ b/f_BHF-OYwr4.txt
@@ -0,0 +1,1171 @@
+align:start position:0%
+ 
+in this final segment we want to discuss
+
+ align:start position:0%
+in this final segment we want to discuss
+ 
+
+ align:start position:0%
+in this final segment we want to discuss
+an interesting point about linear
+
+ align:start position:0%
+an interesting point about linear
+ 
+
+ align:start position:0%
+an interesting point about linear
+estimators here's what the issue is you
+
+ align:start position:0%
+estimators here's what the issue is you
+ 
+
+ align:start position:0%
+estimators here's what the issue is you
+obtain an observation X on the basis of
+
+ align:start position:0%
+obtain an observation X on the basis of
+ 
+
+ align:start position:0%
+obtain an observation X on the basis of
+which you want to estimate theta but
+
+ align:start position:0%
+which you want to estimate theta but
+ 
+
+ align:start position:0%
+which you want to estimate theta but
+perhaps you measure X on a different
+
+ align:start position:0%
+perhaps you measure X on a different
+ 
+
+ align:start position:0%
+perhaps you measure X on a different
+scale let's say on a cubic scale so that
+
+ align:start position:0%
+scale let's say on a cubic scale so that
+ 
+
+ align:start position:0%
+scale let's say on a cubic scale so that
+what you record actually is X cube so
+
+ align:start position:0%
+what you record actually is X cube so
+ 
+
+ align:start position:0%
+what you record actually is X cube so
+you're faced with two possible
+
+ align:start position:0%
+you're faced with two possible
+ 
+
+ align:start position:0%
+you're faced with two possible
+estimation problems one estimation
+
+ align:start position:0%
+estimation problems one estimation
+ 
+
+ align:start position:0%
+estimation problems one estimation
+problem is to use X to estimate theta
+
+ align:start position:0%
+problem is to use X to estimate theta
+ 
+
+ align:start position:0%
+problem is to use X to estimate theta
+another estimation problem is to use X
+
+ align:start position:0%
+another estimation problem is to use X
+ 
+
+ align:start position:0%
+another estimation problem is to use X
+cube to estimate theta does it make a
+
+ align:start position:0%
+cube to estimate theta does it make a
+ 
+
+ align:start position:0%
+cube to estimate theta does it make a
+difference let us consider the case of
+
+ align:start position:0%
+difference let us consider the case of
+ 
+
+ align:start position:0%
+difference let us consider the case of
+least mean squares estimation without
+
+ align:start position:0%
+least mean squares estimation without
+ 
+
+ align:start position:0%
+least mean squares estimation without
+any linearity constraint if you use X to
+
+ align:start position:0%
+any linearity constraint if you use X to
+ 
+
+ align:start position:0%
+any linearity constraint if you use X to
+estimate theta your estimator is going
+
+ align:start position:0%
+estimate theta your estimator is going
+ 
+
+ align:start position:0%
+estimate theta your estimator is going
+to be this conditional expectation if
+
+ align:start position:0%
+to be this conditional expectation if
+ 
+
+ align:start position:0%
+to be this conditional expectation if
+you use X cube to estimate theta your
+
+ align:start position:0%
+you use X cube to estimate theta your
+ 
+
+ align:start position:0%
+you use X cube to estimate theta your
+estimator will be this conditional
+
+ align:start position:0%
+estimator will be this conditional
+ 
+
+ align:start position:0%
+estimator will be this conditional
+expectation are they different well X
+
+ align:start position:0%
+expectation are they different well X
+ 
+
+ align:start position:0%
+expectation are they different well X
+and X cube carry the same information
+
+ align:start position:0%
+and X cube carry the same information
+ 
+
+ align:start position:0%
+and X cube carry the same information
+about theta in particular the posterior
+
+ align:start position:0%
+about theta in particular the posterior
+ 
+
+ align:start position:0%
+about theta in particular the posterior
+distribution of theta given X is going
+
+ align:start position:0%
+distribution of theta given X is going
+ 
+
+ align:start position:0%
+distribution of theta given X is going
+to be the same as the posterior
+
+ align:start position:0%
+to be the same as the posterior
+ 
+
+ align:start position:0%
+to be the same as the posterior
+distribution of theta given X cube you
+
+ align:start position:0%
+distribution of theta given X cube you
+ 
+
+ align:start position:0%
+distribution of theta given X cube you
+will be getting the same information the
+
+ align:start position:0%
+will be getting the same information the
+ 
+
+ align:start position:0%
+will be getting the same information the
+same knowledge about X and in particular
+
+ align:start position:0%
+same knowledge about X and in particular
+ 
+
+ align:start position:0%
+same knowledge about X and in particular
+if you calculate conditional
+
+ align:start position:0%
+if you calculate conditional
+ 
+
+ align:start position:0%
+if you calculate conditional
+expectations these will also be the same
+
+ align:start position:0%
+expectations these will also be the same
+ 
+
+ align:start position:0%
+expectations these will also be the same
+what about the linear case if we
+
+ align:start position:0%
+what about the linear case if we
+ 
+
+ align:start position:0%
+what about the linear case if we
+restrict to linear estimators then on
+
+ align:start position:0%
+restrict to linear estimators then on
+ 
+
+ align:start position:0%
+restrict to linear estimators then on
+the basis of X you would form a linear
+
+ align:start position:0%
+the basis of X you would form a linear
+ 
+
+ align:start position:0%
+the basis of X you would form a linear
+estimation of this kind but if your
+
+ align:start position:0%
+estimation of this kind but if your
+ 
+
+ align:start position:0%
+estimation of this kind but if your
+observation is in the form of X cube
+
+ align:start position:0%
+observation is in the form of X cube
+ 
+
+ align:start position:0%
+observation is in the form of X cube
+then a linear estimator would form a
+
+ align:start position:0%
+then a linear estimator would form a
+ 
+
+ align:start position:0%
+then a linear estimator would form a
+linear function of X cube so this would
+
+ align:start position:0%
+linear function of X cube so this would
+ 
+
+ align:start position:0%
+linear function of X cube so this would
+be a different kind of estimator we have
+
+ align:start position:0%
+be a different kind of estimator we have
+ 
+
+ align:start position:0%
+be a different kind of estimator we have
+seen a formula on how to obtain the best
+
+ align:start position:0%
+seen a formula on how to obtain the best
+ 
+
+ align:start position:0%
+seen a formula on how to obtain the best
+estimator the best choices of a and B
+
+ align:start position:0%
+estimator the best choices of a and B
+ 
+
+ align:start position:0%
+estimator the best choices of a and B
+for estimators of this kind we can use
+
+ align:start position:0%
+for estimators of this kind we can use
+ 
+
+ align:start position:0%
+for estimators of this kind we can use
+that same formula to obtain the best
+
+ align:start position:0%
+that same formula to obtain the best
+ 
+
+ align:start position:0%
+that same formula to obtain the best
+estimator of that kind it's going to be
+
+ align:start position:0%
+estimator of that kind it's going to be
+ 
+
+ align:start position:0%
+estimator of that kind it's going to be
+of course a different estimator here
+
+ align:start position:0%
+of course a different estimator here
+ 
+
+ align:start position:0%
+of course a different estimator here
+we're optimizing within a different
+
+ align:start position:0%
+we're optimizing within a different
+ 
+
+ align:start position:0%
+we're optimizing within a different
+class which one of the two is better
+
+ align:start position:0%
+class which one of the two is better
+ 
+
+ align:start position:0%
+class which one of the two is better
+well this depends on what you know about
+
+ align:start position:0%
+well this depends on what you know about
+ 
+
+ align:start position:0%
+well this depends on what you know about
+the particular problem at hand if you
+
+ align:start position:0%
+the particular problem at hand if you
+ 
+
+ align:start position:0%
+the particular problem at hand if you
+have some reason to believe or if you
+
+ align:start position:0%
+have some reason to believe or if you
+ 
+
+ align:start position:0%
+have some reason to believe or if you
+know that theta and X are roughly
+
+ align:start position:0%
+know that theta and X are roughly
+ 
+
+ align:start position:0%
+know that theta and X are roughly
+related by some kind of cubic relation
+
+ align:start position:0%
+related by some kind of cubic relation
+ 
+
+ align:start position:0%
+related by some kind of cubic relation
+then perhaps estimators in this class
+
+ align:start position:0%
+then perhaps estimators in this class
+ 
+
+ align:start position:0%
+then perhaps estimators in this class
+are going to perform better than
+
+ align:start position:0%
+are going to perform better than
+ 
+
+ align:start position:0%
+are going to perform better than
+estimators in that class let me also
+
+ align:start position:0%
+estimators in that class let me also
+ 
+
+ align:start position:0%
+estimators in that class let me also
+point out a related issue that would
+
+ align:start position:0%
+point out a related issue that would
+ 
+
+ align:start position:0%
+point out a related issue that would
+come here to find the right choice of a
+
+ align:start position:0%
+come here to find the right choice of a
+ 
+
+ align:start position:0%
+come here to find the right choice of a
+you need to know the covariance between
+
+ align:start position:0%
+you need to know the covariance between
+ 
+
+ align:start position:0%
+you need to know the covariance between
+X and theta that's what the formula
+
+ align:start position:0%
+X and theta that's what the formula
+ 
+
+ align:start position:0%
+X and theta that's what the formula
+tells us about the optimal linear
+
+ align:start position:0%
+tells us about the optimal linear
+ 
+
+ align:start position:0%
+tells us about the optimal linear
+estimator here you would need to know
+
+ align:start position:0%
+estimator here you would need to know
+ 
+
+ align:start position:0%
+estimator here you would need to know
+the covariance between theta and X cube
+
+ align:start position:0%
+the covariance between theta and X cube
+ 
+
+ align:start position:0%
+the covariance between theta and X cube
+in addition the formula requires the
+
+ align:start position:0%
+in addition the formula requires the
+ 
+
+ align:start position:0%
+in addition the formula requires the
+variance of X but here instead of X were
+
+ align:start position:0%
+variance of X but here instead of X were
+ 
+
+ align:start position:0%
+variance of X but here instead of X were
+using X cube so in this case we would
+
+ align:start position:0%
+using X cube so in this case we would
+ 
+
+ align:start position:0%
+using X cube so in this case we would
+need the variance of X cube now this
+
+ align:start position:0%
+need the variance of X cube now this
+ 
+
+ align:start position:0%
+need the variance of X cube now this
+could be more challenging in general the
+
+ align:start position:0%
+could be more challenging in general the
+ 
+
+ align:start position:0%
+could be more challenging in general the
+higher the powers that you have the more
+
+ align:start position:0%
+higher the powers that you have the more
+ 
+
+ align:start position:0%
+higher the powers that you have the more
+difficult these quantities are to
+
+ align:start position:0%
+difficult these quantities are to
+ 
+
+ align:start position:0%
+difficult these quantities are to
+calculate or to know what they are but
+
+ align:start position:0%
+calculate or to know what they are but
+ 
+
+ align:start position:0%
+calculate or to know what they are but
+leaving that issue aside what we have
+
+ align:start position:0%
+leaving that issue aside what we have
+ 
+
+ align:start position:0%
+leaving that issue aside what we have
+here is two alternative choices for the
+
+ align:start position:0%
+here is two alternative choices for the
+ 
+
+ align:start position:0%
+here is two alternative choices for the
+structure of the estimator that we are
+
+ align:start position:0%
+structure of the estimator that we are
+ 
+
+ align:start position:0%
+structure of the estimator that we are
+using now we can push this story further
+
+ align:start position:0%
+using now we can push this story further
+ 
+
+ align:start position:0%
+using now we can push this story further
+instead of considering just estimators
+
+ align:start position:0%
+instead of considering just estimators
+ 
+
+ align:start position:0%
+instead of considering just estimators
+of this kind we might consider as well
+
+ align:start position:0%
+of this kind we might consider as well
+ 
+
+ align:start position:0%
+of this kind we might consider as well
+estimators of this kind is this a linear
+
+ align:start position:0%
+estimators of this kind is this a linear
+ 
+
+ align:start position:0%
+estimators of this kind is this a linear
+estimator we still call it a linear
+
+ align:start position:0%
+estimator we still call it a linear
+ 
+
+ align:start position:0%
+estimator we still call it a linear
+estimator because it is linear in the
+
+ align:start position:0%
+estimator because it is linear in the
+ 
+
+ align:start position:0%
+estimator because it is linear in the
+coefficients that we have to choose on
+
+ align:start position:0%
+coefficients that we have to choose on
+ 
+
+ align:start position:0%
+coefficients that we have to choose on
+how to optimize that's the more
+
+ align:start position:0%
+how to optimize that's the more
+ 
+
+ align:start position:0%
+how to optimize that's the more
+important part it's the linearity in
+
+ align:start position:0%
+important part it's the linearity in
+ 
+
+ align:start position:0%
+important part it's the linearity in
+these coefficients that's important
+
+ align:start position:0%
+these coefficients that's important
+ 
+
+ align:start position:0%
+these coefficients that's important
+rather than the linearity in the axis so
+
+ align:start position:0%
+rather than the linearity in the axis so
+ 
+
+ align:start position:0%
+rather than the linearity in the axis so
+as a function of X is this is nonlinear
+
+ align:start position:0%
+as a function of X is this is nonlinear
+ 
+
+ align:start position:0%
+as a function of X is this is nonlinear
+on the other hand we can think of this X
+
+ align:start position:0%
+on the other hand we can think of this X
+ 
+
+ align:start position:0%
+on the other hand we can think of this X
+as one observation x squared as another
+
+ align:start position:0%
+as one observation x squared as another
+ 
+
+ align:start position:0%
+as one observation x squared as another
+observation X cube as a third
+
+ align:start position:0%
+observation X cube as a third
+ 
+
+ align:start position:0%
+observation X cube as a third
+observation and what we got here is a
+
+ align:start position:0%
+observation and what we got here is a
+ 
+
+ align:start position:0%
+observation and what we got here is a
+linear function of three different
+
+ align:start position:0%
+linear function of three different
+ 
+
+ align:start position:0%
+linear function of three different
+observation
+
+ align:start position:0%
+observation
+ 
+
+ align:start position:0%
+observation
+so we can still pose a least squares
+
+ align:start position:0%
+so we can still pose a least squares
+ 
+
+ align:start position:0%
+so we can still pose a least squares
+problem in which we try to find the best
+
+ align:start position:0%
+problem in which we try to find the best
+ 
+
+ align:start position:0%
+problem in which we try to find the best
+choices for the coefficients a1 a2 and
+
+ align:start position:0%
+choices for the coefficients a1 a2 and
+ 
+
+ align:start position:0%
+choices for the coefficients a1 a2 and
+a3 as well as the coefficient B find
+
+ align:start position:0%
+a3 as well as the coefficient B find
+ 
+
+ align:start position:0%
+a3 as well as the coefficient B find
+those choices that are going to give us
+
+ align:start position:0%
+those choices that are going to give us
+ 
+
+ align:start position:0%
+those choices that are going to give us
+the smallest possible mean squared error
+
+ align:start position:0%
+the smallest possible mean squared error
+ 
+
+ align:start position:0%
+the smallest possible mean squared error
+so we can optimize within this class
+
+ align:start position:0%
+so we can optimize within this class
+ 
+
+ align:start position:0%
+so we can optimize within this class
+within this class of estimators we
+
+ align:start position:0%
+within this class of estimators we
+ 
+
+ align:start position:0%
+within this class of estimators we
+certainly have more flexibility this is
+
+ align:start position:0%
+certainly have more flexibility this is
+ 
+
+ align:start position:0%
+certainly have more flexibility this is
+a more general class of estimators on
+
+ align:start position:0%
+a more general class of estimators on
+ 
+
+ align:start position:0%
+a more general class of estimators on
+either this one or that one
+
+ align:start position:0%
+either this one or that one
+ 
+
+ align:start position:0%
+either this one or that one
+so within this class we should be able
+
+ align:start position:0%
+so within this class we should be able
+ 
+
+ align:start position:0%
+so within this class we should be able
+to do even better on the other hand we
+
+ align:start position:0%
+to do even better on the other hand we
+ 
+
+ align:start position:0%
+to do even better on the other hand we
+will have to pay a price that this is a
+
+ align:start position:0%
+will have to pay a price that this is a
+ 
+
+ align:start position:0%
+will have to pay a price that this is a
+more complex structure it will be more
+
+ align:start position:0%
+more complex structure it will be more
+ 
+
+ align:start position:0%
+more complex structure it will be more
+difficult to find the optimal
+
+ align:start position:0%
+difficult to find the optimal
+ 
+
+ align:start position:0%
+difficult to find the optimal
+coefficients and also we're going to
+
+ align:start position:0%
+coefficients and also we're going to
+ 
+
+ align:start position:0%
+coefficients and also we're going to
+need higher order moments or
+
+ align:start position:0%
+need higher order moments or
+ 
+
+ align:start position:0%
+need higher order moments or
+expectations related to the X's and the
+
+ align:start position:0%
+expectations related to the X's and the
+ 
+
+ align:start position:0%
+expectations related to the X's and the
+Thetas finally there's nothing special
+
+ align:start position:0%
+Thetas finally there's nothing special
+ 
+
+ align:start position:0%
+Thetas finally there's nothing special
+in us using powers of X and using a
+
+ align:start position:0%
+in us using powers of X and using a
+ 
+
+ align:start position:0%
+in us using powers of X and using a
+polynomial we could also look at
+
+ align:start position:0%
+polynomial we could also look at
+ 
+
+ align:start position:0%
+polynomial we could also look at
+estimators that have some other type of
+
+ align:start position:0%
+estimators that have some other type of
+ 
+
+ align:start position:0%
+estimators that have some other type of
+structure for example we might want to
+
+ align:start position:0%
+structure for example we might want to
+ 
+
+ align:start position:0%
+structure for example we might want to
+mix an exponential function in X and the
+
+ align:start position:0%
+mix an exponential function in X and the
+ 
+
+ align:start position:0%
+mix an exponential function in X and the
+logarithmic function of X look at
+
+ align:start position:0%
+logarithmic function of X look at
+ 
+
+ align:start position:0%
+logarithmic function of X look at
+estimators of this form and try to
+
+ align:start position:0%
+estimators of this form and try to
+ 
+
+ align:start position:0%
+estimators of this form and try to
+choose the best one find the best choice
+
+ align:start position:0%
+choose the best one find the best choice
+ 
+
+ align:start position:0%
+choose the best one find the best choice
+of the coefficients again this is
+
+ align:start position:0%
+of the coefficients again this is
+ 
+
+ align:start position:0%
+of the coefficients again this is
+something that is possible and again
+
+ align:start position:0%
+something that is possible and again
+ 
+
+ align:start position:0%
+something that is possible and again
+it's going to boil down to solving a
+
+ align:start position:0%
+it's going to boil down to solving a
+ 
+
+ align:start position:0%
+it's going to boil down to solving a
+system of linear equations in the
+
+ align:start position:0%
+system of linear equations in the
+ 
+
+ align:start position:0%
+system of linear equations in the
+coefficients on the other hand we need
+
+ align:start position:0%
+coefficients on the other hand we need
+ 
+
+ align:start position:0%
+coefficients on the other hand we need
+to know various expectations about X
+
+ align:start position:0%
+to know various expectations about X
+ 
+
+ align:start position:0%
+to know various expectations about X
+that might be difficult to obtain how do
+
+ align:start position:0%
+that might be difficult to obtain how do
+ 
+
+ align:start position:0%
+that might be difficult to obtain how do
+we choose which structure to use should
+
+ align:start position:0%
+we choose which structure to use should
+ 
+
+ align:start position:0%
+we choose which structure to use should
+it be this one this one this one or that
+
+ align:start position:0%
+it be this one this one this one or that
+ 
+
+ align:start position:0%
+it be this one this one this one or that
+one there's a trade-off that more
+
+ align:start position:0%
+one there's a trade-off that more
+ 
+
+ align:start position:0%
+one there's a trade-off that more
+complicated structures introduce more
+
+ align:start position:0%
+complicated structures introduce more
+ 
+
+ align:start position:0%
+complicated structures introduce more
+complexity and make the problem more
+
+ align:start position:0%
+complexity and make the problem more
+ 
+
+ align:start position:0%
+complexity and make the problem more
+difficult but there's also another issue
+
+ align:start position:0%
+difficult but there's also another issue
+ 
+
+ align:start position:0%
+difficult but there's also another issue
+it has to do with what we know about the
+
+ align:start position:0%
+it has to do with what we know about the
+ 
+
+ align:start position:0%
+it has to do with what we know about the
+particular problem at hand if we know or
+
+ align:start position:0%
+particular problem at hand if we know or
+ 
+
+ align:start position:0%
+particular problem at hand if we know or
+have reason to believe that third order
+
+ align:start position:0%
+have reason to believe that third order
+ 
+
+ align:start position:0%
+have reason to believe that third order
+polynomials are going to give us
+
+ align:start position:0%
+polynomials are going to give us
+ 
+
+ align:start position:0%
+polynomials are going to give us
+excellent estimates of theta then we may
+
+ align:start position:0%
+excellent estimates of theta then we may
+ 
+
+ align:start position:0%
+excellent estimates of theta then we may
+want to work with in this class in any
+
+ align:start position:0%
+want to work with in this class in any
+ 
+
+ align:start position:0%
+want to work with in this class in any
+case the moral of the story is that if
+
+ align:start position:0%
+case the moral of the story is that if
+ 
+
+ align:start position:0%
+case the moral of the story is that if
+we are to use the linear estimation
+
+ align:start position:0%
+we are to use the linear estimation
+ 
+
+ align:start position:0%
+we are to use the linear estimation
+methodology we
+
+ align:start position:0%
+methodology we
+ 
+
+ align:start position:0%
+methodology we
+do have some choices linear in what and
+
+ align:start position:0%
+do have some choices linear in what and
+ 
+
+ align:start position:0%
+do have some choices linear in what and
+different choices will give us different
+
+ align:start position:0%
+different choices will give us different
+ 
+
+ align:start position:0%
+different choices will give us different
+performance but this now gets some words
+
+ align:start position:0%
+performance but this now gets some words
+ 
+
+ align:start position:0%
+performance but this now gets some words
+away from the subject of mathematical
+
+ align:start position:0%
+away from the subject of mathematical
+ 
+
+ align:start position:0%
+away from the subject of mathematical
+methodology and it gets closer to the
+
+ align:start position:0%
+methodology and it gets closer to the
+ 
+
+ align:start position:0%
+methodology and it gets closer to the
+art that you need to exercise in any
+
+ align:start position:0%
+art that you need to exercise in any
+ 
+
+ align:start position:0%
+art that you need to exercise in any
+particular problem domain
\ No newline at end of file
diff --git a/fdECxAuBSBU.txt b/fdECxAuBSBU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..164465d84255a11cdd3a9520d73362b3fe82fc28
--- /dev/null
+++ b/fdECxAuBSBU.txt
@@ -0,0 +1,14744 @@
+align:start position:0%
+ 
+all right I think we can go ahead and
+
+ align:start position:0%
+all right I think we can go ahead and
+ 
+
+ align:start position:0%
+all right I think we can go ahead and
+get started I'm going to put this um is
+
+ align:start position:0%
+get started I'm going to put this um is
+ 
+
+ align:start position:0%
+get started I'm going to put this um is
+anybody here I think everybody who's
+
+ align:start position:0%
+anybody here I think everybody who's
+ 
+
+ align:start position:0%
+anybody here I think everybody who's
+here is already signed up uh I'm going
+
+ align:start position:0%
+here is already signed up uh I'm going
+ 
+
+ align:start position:0%
+here is already signed up uh I'm going
+to put the clipboard in the back and
+
+ align:start position:0%
+to put the clipboard in the back and
+ 
+
+ align:start position:0%
+to put the clipboard in the back and
+couple people haven't signed up but I
+
+ align:start position:0%
+couple people haven't signed up but I
+ 
+
+ align:start position:0%
+couple people haven't signed up but I
+want to uh I I've everyone who's signed
+
+ align:start position:0%
+want to uh I I've everyone who's signed
+ 
+
+ align:start position:0%
+want to uh I I've everyone who's signed
+up I've actually approved your topics um
+
+ align:start position:0%
+up I've actually approved your topics um
+ 
+
+ align:start position:0%
+up I've actually approved your topics um
+so but there's a couple people who
+
+ align:start position:0%
+so but there's a couple people who
+ 
+
+ align:start position:0%
+so but there's a couple people who
+haven't filled in their topics so uh
+
+ align:start position:0%
+haven't filled in their topics so uh
+ 
+
+ align:start position:0%
+haven't filled in their topics so uh
+obviously I can't approve them until
+
+ align:start position:0%
+obviously I can't approve them until
+ 
+
+ align:start position:0%
+obviously I can't approve them until
+they're filled in so I'll put this back
+
+ align:start position:0%
+they're filled in so I'll put this back
+ 
+
+ align:start position:0%
+they're filled in so I'll put this back
+here there's two handouts for today the
+
+ align:start position:0%
+here there's two handouts for today the
+ 
+
+ align:start position:0%
+here there's two handouts for today the
+lecture notes and the homework uh your
+
+ align:start position:0%
+lecture notes and the homework uh your
+ 
+
+ align:start position:0%
+lecture notes and the homework uh your
+final homework and I'm I'm handing back
+
+ align:start position:0%
+final homework and I'm I'm handing back
+ 
+
+ align:start position:0%
+final homework and I'm I'm handing back
+um some homework sets that people
+
+ align:start position:0%
+um some homework sets that people
+ 
+
+ align:start position:0%
+um some homework sets that people
+haven't picked up yet they're in the
+
+ align:start position:0%
+haven't picked up yet they're in the
+ 
+
+ align:start position:0%
+haven't picked up yet they're in the
+back okay so let's just take a look at
+
+ align:start position:0%
+back okay so let's just take a look at
+ 
+
+ align:start position:0%
+back okay so let's just take a look at
+where we are schedule-wise so today is
+
+ align:start position:0%
+where we are schedule-wise so today is
+ 
+
+ align:start position:0%
+where we are schedule-wise so today is
+November 9th and um we're on the second
+
+ align:start position:0%
+November 9th and um we're on the second
+ 
+
+ align:start position:0%
+November 9th and um we're on the second
+lecture here on chapter nine so
+
+ align:start position:0%
+lecture here on chapter nine so
+ 
+
+ align:start position:0%
+lecture here on chapter nine so
+hopefully you're reading chapter nine of
+
+ align:start position:0%
+hopefully you're reading chapter nine of
+ 
+
+ align:start position:0%
+hopefully you're reading chapter nine of
+your textbook and uh homework number
+
+ align:start position:0%
+your textbook and uh homework number
+ 
+
+ align:start position:0%
+your textbook and uh homework number
+five I'm handing out today and that's
+
+ align:start position:0%
+five I'm handing out today and that's
+ 
+
+ align:start position:0%
+five I'm handing out today and that's
+your final homework so um uh I think
+
+ align:start position:0%
+your final homework so um uh I think
+ 
+
+ align:start position:0%
+your final homework so um uh I think
+it's an interesting problem set one
+
+ align:start position:0%
+it's an interesting problem set one
+ 
+
+ align:start position:0%
+it's an interesting problem set one
+thing I want to remind you is that there
+
+ align:start position:0%
+thing I want to remind you is that there
+ 
+
+ align:start position:0%
+thing I want to remind you is that there
+is a Part B on the back so don't don't
+
+ align:start position:0%
+is a Part B on the back so don't don't
+ 
+
+ align:start position:0%
+is a Part B on the back so don't don't
+miss Part B on the back side of the
+
+ align:start position:0%
+miss Part B on the back side of the
+ 
+
+ align:start position:0%
+miss Part B on the back side of the
+homework there's three
+
+ align:start position:0%
+homework there's three
+ 
+
+ align:start position:0%
+homework there's three
+problems um and um particularly problem
+
+ align:start position:0%
+problems um and um particularly problem
+ 
+
+ align:start position:0%
+problems um and um particularly problem
+number three I think you'll find
+
+ align:start position:0%
+number three I think you'll find
+ 
+
+ align:start position:0%
+number three I think you'll find
+interesting it's it's about transient
+
+ align:start position:0%
+interesting it's it's about transient
+ 
+
+ align:start position:0%
+interesting it's it's about transient
+enhanced diffusion um part A you''ll be
+
+ align:start position:0%
+enhanced diffusion um part A you''ll be
+ 
+
+ align:start position:0%
+enhanced diffusion um part A you''ll be
+doing some hand calculations of teed uh
+
+ align:start position:0%
+doing some hand calculations of teed uh
+ 
+
+ align:start position:0%
+doing some hand calculations of teed uh
+and using some analytic formulas for
+
+ align:start position:0%
+and using some analytic formulas for
+ 
+
+ align:start position:0%
+and using some analytic formulas for
+iron implant and
+
+ align:start position:0%
+iron implant and
+ 
+
+ align:start position:0%
+iron implant and
+diffusion um and part B which is on the
+
+ align:start position:0%
+diffusion um and part B which is on the
+ 
+
+ align:start position:0%
+diffusion um and part B which is on the
+back side again don't miss that we we'll
+
+ align:start position:0%
+back side again don't miss that we we'll
+ 
+
+ align:start position:0%
+back side again don't miss that we we'll
+uh you'll do some Supreme simulations
+
+ align:start position:0%
+uh you'll do some Supreme simulations
+ 
+
+ align:start position:0%
+uh you'll do some Supreme simulations
+and then compare it to the uh hand
+
+ align:start position:0%
+and then compare it to the uh hand
+ 
+
+ align:start position:0%
+and then compare it to the uh hand
+calculation of the teed and the um other
+
+ align:start position:0%
+calculation of the teed and the um other
+ 
+
+ align:start position:0%
+calculation of the teed and the um other
+thing to mention for me to mention about
+
+ align:start position:0%
+thing to mention for me to mention about
+ 
+
+ align:start position:0%
+thing to mention for me to mention about
+Part B this is the first um homework
+
+ align:start position:0%
+Part B this is the first um homework
+ 
+
+ align:start position:0%
+Part B this is the first um homework
+where you're not given the Supreme code
+
+ align:start position:0%
+where you're not given the Supreme code
+ 
+
+ align:start position:0%
+where you're not given the Supreme code
+you've been given Supreme codes you've
+
+ align:start position:0%
+you've been given Supreme codes you've
+ 
+
+ align:start position:0%
+you've been given Supreme codes you've
+been running all along have been given
+
+ align:start position:0%
+been running all along have been given
+ 
+
+ align:start position:0%
+been running all along have been given
+to you that been written by the TA and
+
+ align:start position:0%
+to you that been written by the TA and
+ 
+
+ align:start position:0%
+to you that been written by the TA and
+you just have to run them um freeb
+
+ align:start position:0%
+you just have to run them um freeb
+ 
+
+ align:start position:0%
+you just have to run them um freeb
+you're actually asked to write the code
+
+ align:start position:0%
+you're actually asked to write the code
+ 
+
+ align:start position:0%
+you're actually asked to write the code
+now what you can do clearly is you've
+
+ align:start position:0%
+now what you can do clearly is you've
+ 
+
+ align:start position:0%
+now what you can do clearly is you've
+been given a lot of codes you can take
+
+ align:start position:0%
+been given a lot of codes you can take
+ 
+
+ align:start position:0%
+been given a lot of codes you can take
+the pro you know the examples of what
+
+ align:start position:0%
+the pro you know the examples of what
+ 
+
+ align:start position:0%
+the pro you know the examples of what
+you've been given as you're starting you
+
+ align:start position:0%
+you've been given as you're starting you
+ 
+
+ align:start position:0%
+you've been given as you're starting you
+don't have to start from scratch you can
+
+ align:start position:0%
+don't have to start from scratch you can
+ 
+
+ align:start position:0%
+don't have to start from scratch you can
+take other files and just modify them
+
+ align:start position:0%
+take other files and just modify them
+ 
+
+ align:start position:0%
+take other files and just modify them
+accordingly it's a relatively simple uh
+
+ align:start position:0%
+accordingly it's a relatively simple uh
+ 
+
+ align:start position:0%
+accordingly it's a relatively simple uh
+simple process but I just wanted to make
+
+ align:start position:0%
+simple process but I just wanted to make
+ 
+
+ align:start position:0%
+simple process but I just wanted to make
+you aware that there is a Part B on the
+
+ align:start position:0%
+you aware that there is a Part B on the
+ 
+
+ align:start position:0%
+you aware that there is a Part B on the
+backside and I think it's you'll be
+
+ align:start position:0%
+backside and I think it's you'll be
+ 
+
+ align:start position:0%
+backside and I think it's you'll be
+problem number three should be an
+
+ align:start position:0%
+problem number three should be an
+ 
+
+ align:start position:0%
+problem number three should be an
+interesting one for
+
+ align:start position:0%
+interesting one for
+ 
+
+ align:start position:0%
+interesting one for
+you uh and as I mentioned that's the
+
+ align:start position:0%
+you uh and as I mentioned that's the
+ 
+
+ align:start position:0%
+you uh and as I mentioned that's the
+last homework for the course the reason
+
+ align:start position:0%
+last homework for the course the reason
+ 
+
+ align:start position:0%
+last homework for the course the reason
+I I I make just the last problem set um
+
+ align:start position:0%
+I I I make just the last problem set um
+ 
+
+ align:start position:0%
+I I I make just the last problem set um
+this one is due on November 18th because
+
+ align:start position:0%
+this one is due on November 18th because
+ 
+
+ align:start position:0%
+this one is due on November 18th because
+I want to give you enough time between
+
+ align:start position:0%
+I want to give you enough time between
+ 
+
+ align:start position:0%
+I want to give you enough time between
+that last problem set so you can get the
+
+ align:start position:0%
+that last problem set so you can get the
+ 
+
+ align:start position:0%
+that last problem set so you can get the
+problems out of out of the way um enough
+
+ align:start position:0%
+problems out of out of the way um enough
+ 
+
+ align:start position:0%
+problems out of out of the way um enough
+time to be working on your uh your final
+
+ align:start position:0%
+time to be working on your uh your final
+ 
+
+ align:start position:0%
+time to be working on your uh your final
+project so that's either the written
+
+ align:start position:0%
+project so that's either the written
+ 
+
+ align:start position:0%
+project so that's either the written
+report or the oral uh or the oral
+
+ align:start position:0%
+report or the oral uh or the oral
+ 
+
+ align:start position:0%
+report or the oral uh or the oral
+presentation um so definitely if you
+
+ align:start position:0%
+presentation um so definitely if you
+ 
+
+ align:start position:0%
+presentation um so definitely if you
+haven't done so uh get started on your
+
+ align:start position:0%
+haven't done so uh get started on your
+ 
+
+ align:start position:0%
+haven't done so uh get started on your
+uh on your project
+
+ align:start position:0%
+uh on your project
+ 
+
+ align:start position:0%
+uh on your project
+soon all right so that's sort of the
+
+ align:start position:0%
+soon all right so that's sort of the
+ 
+
+ align:start position:0%
+soon all right so that's sort of the
+mechanics of where we are and uh let's
+
+ align:start position:0%
+mechanics of where we are and uh let's
+ 
+
+ align:start position:0%
+mechanics of where we are and uh let's
+go on with today's um I'll start with
+
+ align:start position:0%
+go on with today's um I'll start with
+ 
+
+ align:start position:0%
+go on with today's um I'll start with
+today's
+
+ align:start position:0%
+today's
+ 
+
+ align:start position:0%
+today's
+lecture handout this is handout number
+
+ align:start position:0%
+lecture handout this is handout number
+ 
+
+ align:start position:0%
+lecture handout this is handout number
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and this is the second lecture on
+
+ align:start position:0%
+and this is the second lecture on
+ 
+
+ align:start position:0%
+and this is the second lecture on
+chapter nine um chapter nine is about
+
+ align:start position:0%
+chapter nine um chapter nine is about
+ 
+
+ align:start position:0%
+chapter nine um chapter nine is about
+thin film deposition and epitaxy uh last
+
+ align:start position:0%
+thin film deposition and epitaxy uh last
+ 
+
+ align:start position:0%
+thin film deposition and epitaxy uh last
+time we did gave you an introduction we
+
+ align:start position:0%
+time we did gave you an introduction we
+ 
+
+ align:start position:0%
+time we did gave you an introduction we
+developed a very simple model for
+
+ align:start position:0%
+developed a very simple model for
+ 
+
+ align:start position:0%
+developed a very simple model for
+atmospheric uh chemical vapor deposition
+
+ align:start position:0%
+atmospheric uh chemical vapor deposition
+ 
+
+ align:start position:0%
+atmospheric uh chemical vapor deposition
+and remember we had two late rate
+
+ align:start position:0%
+and remember we had two late rate
+ 
+
+ align:start position:0%
+and remember we had two late rate
+limiting uh regimes uh we had a c a
+
+ align:start position:0%
+limiting uh regimes uh we had a c a
+ 
+
+ align:start position:0%
+limiting uh regimes uh we had a c a
+regime of growth where the growth rate
+
+ align:start position:0%
+regime of growth where the growth rate
+ 
+
+ align:start position:0%
+regime of growth where the growth rate
+was determined by the surface reaction
+
+ align:start position:0%
+was determined by the surface reaction
+ 
+
+ align:start position:0%
+was determined by the surface reaction
+rate um and it had a certain activation
+
+ align:start position:0%
+rate um and it had a certain activation
+ 
+
+ align:start position:0%
+rate um and it had a certain activation
+energy depended exponentially on
+
+ align:start position:0%
+energy depended exponentially on
+ 
+
+ align:start position:0%
+energy depended exponentially on
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+and we had another regime where the
+
+ align:start position:0%
+and we had another regime where the
+ 
+
+ align:start position:0%
+and we had another regime where the
+growth rate was determined by mass
+
+ align:start position:0%
+growth rate was determined by mass
+ 
+
+ align:start position:0%
+growth rate was determined by mass
+transport that was the rate limiting
+
+ align:start position:0%
+transport that was the rate limiting
+ 
+
+ align:start position:0%
+transport that was the rate limiting
+step um we also talked about the fact
+
+ align:start position:0%
+step um we also talked about the fact
+ 
+
+ align:start position:0%
+step um we also talked about the fact
+that the mass transport limit regime
+
+ align:start position:0%
+that the mass transport limit regime
+ 
+
+ align:start position:0%
+that the mass transport limit regime
+gives you a very high growth rate this
+
+ align:start position:0%
+gives you a very high growth rate this
+ 
+
+ align:start position:0%
+gives you a very high growth rate this
+tends to be at high temperatures uh
+
+ align:start position:0%
+tends to be at high temperatures uh
+ 
+
+ align:start position:0%
+tends to be at high temperatures uh
+where the surface reaction is fast gives
+
+ align:start position:0%
+where the surface reaction is fast gives
+ 
+
+ align:start position:0%
+where the surface reaction is fast gives
+you a high growth rate it's relatively
+
+ align:start position:0%
+you a high growth rate it's relatively
+ 
+
+ align:start position:0%
+you a high growth rate it's relatively
+independent of
+
+ align:start position:0%
+independent of
+ 
+
+ align:start position:0%
+independent of
+temperature uh in contrast to the the
+
+ align:start position:0%
+temperature uh in contrast to the the
+ 
+
+ align:start position:0%
+temperature uh in contrast to the the
+surface reaction uh control regime but
+
+ align:start position:0%
+surface reaction uh control regime but
+ 
+
+ align:start position:0%
+surface reaction uh control regime but
+it's also sensitive to reactor geometry
+
+ align:start position:0%
+it's also sensitive to reactor geometry
+ 
+
+ align:start position:0%
+it's also sensitive to reactor geometry
+so it depends uh the growth rate and
+
+ align:start position:0%
+so it depends uh the growth rate and
+ 
+
+ align:start position:0%
+so it depends uh the growth rate and
+uniformity depend quite a bit on how um
+
+ align:start position:0%
+uniformity depend quite a bit on how um
+ 
+
+ align:start position:0%
+uniformity depend quite a bit on how um
+the gas flows through the
+
+ align:start position:0%
+the gas flows through the
+ 
+
+ align:start position:0%
+the gas flows through the
+reactor we also introduced this uh this
+
+ align:start position:0%
+reactor we also introduced this uh this
+ 
+
+ align:start position:0%
+reactor we also introduced this uh this
+lpcvd uh which is an acronym that stands
+
+ align:start position:0%
+lpcvd uh which is an acronym that stands
+ 
+
+ align:start position:0%
+lpcvd uh which is an acronym that stands
+for low pressure CBD um and we
+
+ align:start position:0%
+for low pressure CBD um and we
+ 
+
+ align:start position:0%
+for low pressure CBD um and we
+introduced the use of lpcvd in a hot
+
+ align:start position:0%
+introduced the use of lpcvd in a hot
+ 
+
+ align:start position:0%
+introduced the use of lpcvd in a hot
+wall batch reactor which is in just
+
+ align:start position:0%
+wall batch reactor which is in just
+ 
+
+ align:start position:0%
+wall batch reactor which is in just
+about every Fab um that that you'll ever
+
+ align:start position:0%
+about every Fab um that that you'll ever
+ 
+
+ align:start position:0%
+about every Fab um that that you'll ever
+see and and it's used to deposit very
+
+ align:start position:0%
+see and and it's used to deposit very
+ 
+
+ align:start position:0%
+see and and it's used to deposit very
+commonly used film such as polysilicon
+
+ align:start position:0%
+commonly used film such as polysilicon
+ 
+
+ align:start position:0%
+commonly used film such as polysilicon
+for the gate or other applications um
+
+ align:start position:0%
+for the gate or other applications um
+ 
+
+ align:start position:0%
+for the gate or other applications um
+oxide deposited oxide and deposited
+
+ align:start position:0%
+oxide deposited oxide and deposited
+ 
+
+ align:start position:0%
+oxide deposited oxide and deposited
+silicon Nitro so in the next lecture or
+
+ align:start position:0%
+silicon Nitro so in the next lecture or
+ 
+
+ align:start position:0%
+silicon Nitro so in the next lecture or
+two what I want to discuss are um some
+
+ align:start position:0%
+two what I want to discuss are um some
+ 
+
+ align:start position:0%
+two what I want to discuss are um some
+specific examples of CBD so I want to
+
+ align:start position:0%
+specific examples of CBD so I want to
+ 
+
+ align:start position:0%
+specific examples of CBD so I want to
+discuss specifically the uh aspects of
+
+ align:start position:0%
+discuss specifically the uh aspects of
+ 
+
+ align:start position:0%
+discuss specifically the uh aspects of
+the deposition of poly Crystal and
+
+ align:start position:0%
+the deposition of poly Crystal and
+ 
+
+ align:start position:0%
+the deposition of poly Crystal and
+silicon uh deposition of silicon dioxide
+
+ align:start position:0%
+silicon uh deposition of silicon dioxide
+ 
+
+ align:start position:0%
+silicon uh deposition of silicon dioxide
+and um silicon
+
+ align:start position:0%
+and um silicon
+ 
+
+ align:start position:0%
+and um silicon
+nitride uh and also uh what we'll talk
+
+ align:start position:0%
+nitride uh and also uh what we'll talk
+ 
+
+ align:start position:0%
+nitride uh and also uh what we'll talk
+about towards the end of today's lecture
+
+ align:start position:0%
+about towards the end of today's lecture
+ 
+
+ align:start position:0%
+about towards the end of today's lecture
+is um introduction to the basics of
+
+ align:start position:0%
+is um introduction to the basics of
+ 
+
+ align:start position:0%
+is um introduction to the basics of
+physical vapor deposition so we have
+
+ align:start position:0%
+physical vapor deposition so we have
+ 
+
+ align:start position:0%
+physical vapor deposition so we have
+chemical vapor deposition and
+
+ align:start position:0%
+chemical vapor deposition and
+ 
+
+ align:start position:0%
+chemical vapor deposition and
+physical okay okay let's go on to page
+
+ align:start position:0%
+physical okay okay let's go on to page
+ 
+
+ align:start position:0%
+physical okay okay let's go on to page
+number um two uh or slide number two on
+
+ align:start position:0%
+number um two uh or slide number two on
+ 
+
+ align:start position:0%
+number um two uh or slide number two on
+your handout this is just a um a uh a
+
+ align:start position:0%
+your handout this is just a um a uh a
+ 
+
+ align:start position:0%
+your handout this is just a um a uh a
+chart I took right out of your textbook
+
+ align:start position:0%
+chart I took right out of your textbook
+ 
+
+ align:start position:0%
+chart I took right out of your textbook
+on uh in in the section in chapter nine
+
+ align:start position:0%
+on uh in in the section in chapter nine
+ 
+
+ align:start position:0%
+on uh in in the section in chapter nine
+on M manufacturing methods for CBD and
+
+ align:start position:0%
+on M manufacturing methods for CBD and
+ 
+
+ align:start position:0%
+on M manufacturing methods for CBD and
+what it gives you is just some common um
+
+ align:start position:0%
+what it gives you is just some common um
+ 
+
+ align:start position:0%
+what it gives you is just some common um
+thin films that are deposited by CBD I
+
+ align:start position:0%
+thin films that are deposited by CBD I
+ 
+
+ align:start position:0%
+thin films that are deposited by CBD I
+think these are the most common epic
+
+ align:start position:0%
+think these are the most common epic
+ 
+
+ align:start position:0%
+think these are the most common epic
+silicon polysilicon silicon nitride and
+
+ align:start position:0%
+silicon polysilicon silicon nitride and
+ 
+
+ align:start position:0%
+silicon polysilicon silicon nitride and
+sio2 uh it talks about the type of
+
+ align:start position:0%
+sio2 uh it talks about the type of
+ 
+
+ align:start position:0%
+sio2 uh it talks about the type of
+equipment used for example we talked
+
+ align:start position:0%
+equipment used for example we talked
+ 
+
+ align:start position:0%
+equipment used for example we talked
+last time about epitaxial silicon can be
+
+ align:start position:0%
+last time about epitaxial silicon can be
+ 
+
+ align:start position:0%
+last time about epitaxial silicon can be
+either atmospheric or low pressure CBD
+
+ align:start position:0%
+either atmospheric or low pressure CBD
+ 
+
+ align:start position:0%
+either atmospheric or low pressure CBD
+there's actually another type of
+
+ align:start position:0%
+there's actually another type of
+ 
+
+ align:start position:0%
+there's actually another type of
+epitaxial silicon that wasn't listed
+
+ align:start position:0%
+epitaxial silicon that wasn't listed
+ 
+
+ align:start position:0%
+epitaxial silicon that wasn't listed
+here because it's not commonly used in
+
+ align:start position:0%
+here because it's not commonly used in
+ 
+
+ align:start position:0%
+here because it's not commonly used in
+Fabs that much uh but it should be
+
+ align:start position:0%
+Fabs that much uh but it should be
+ 
+
+ align:start position:0%
+Fabs that much uh but it should be
+listed for completeness if you want to
+
+ align:start position:0%
+listed for completeness if you want to
+ 
+
+ align:start position:0%
+listed for completeness if you want to
+put it down uh ultra high vacuum cvd uhv
+
+ align:start position:0%
+put it down uh ultra high vacuum cvd uhv
+ 
+
+ align:start position:0%
+put it down uh ultra high vacuum cvd uhv
+cvd is another U method of of depositing
+
+ align:start position:0%
+cvd is another U method of of depositing
+ 
+
+ align:start position:0%
+cvd is another U method of of depositing
+uh or growing epitaxial
+
+ align:start position:0%
+uh or growing epitaxial
+ 
+
+ align:start position:0%
+uh or growing epitaxial
+silicon um and that wasn't listed in the
+
+ align:start position:0%
+silicon um and that wasn't listed in the
+ 
+
+ align:start position:0%
+silicon um and that wasn't listed in the
+text some typical reactions that we we
+
+ align:start position:0%
+text some typical reactions that we we
+ 
+
+ align:start position:0%
+text some typical reactions that we we
+talked about uh for instance the use of
+
+ align:start position:0%
+talked about uh for instance the use of
+ 
+
+ align:start position:0%
+talked about uh for instance the use of
+silene uh uh to grow epitaxial silicon
+
+ align:start position:0%
+silene uh uh to grow epitaxial silicon
+ 
+
+ align:start position:0%
+silene uh uh to grow epitaxial silicon
+at high temperature the silene
+
+ align:start position:0%
+at high temperature the silene
+ 
+
+ align:start position:0%
+at high temperature the silene
+decomposes into silicon and hydrogen and
+
+ align:start position:0%
+decomposes into silicon and hydrogen and
+ 
+
+ align:start position:0%
+decomposes into silicon and hydrogen and
+evolves hydrogen uh under comments here
+
+ align:start position:0%
+evolves hydrogen uh under comments here
+ 
+
+ align:start position:0%
+evolves hydrogen uh under comments here
+is listed some typical temperature range
+
+ align:start position:0%
+is listed some typical temperature range
+ 
+
+ align:start position:0%
+is listed some typical temperature range
+um here if you're in atmospheric
+
+ align:start position:0%
+um here if you're in atmospheric
+ 
+
+ align:start position:0%
+um here if you're in atmospheric
+pressure cvd you typically don't grow
+
+ align:start position:0%
+pressure cvd you typically don't grow
+ 
+
+ align:start position:0%
+pressure cvd you typically don't grow
+too much below a, maybe 900 degrees
+
+ align:start position:0%
+too much below a, maybe 900 degrees
+ 
+
+ align:start position:0%
+too much below a, maybe 900 degrees
+Centigrade uh much more common these
+
+ align:start position:0%
+Centigrade uh much more common these
+ 
+
+ align:start position:0%
+Centigrade uh much more common these
+days though is reduced pressure um
+
+ align:start position:0%
+days though is reduced pressure um
+ 
+
+ align:start position:0%
+days though is reduced pressure um
+deposition of epitaxial silicon we
+
+ align:start position:0%
+deposition of epitaxial silicon we
+ 
+
+ align:start position:0%
+deposition of epitaxial silicon we
+talked about that here the the
+
+ align:start position:0%
+talked about that here the the
+ 
+
+ align:start position:0%
+talked about that here the the
+deposition temperatures are lowered
+
+ align:start position:0%
+deposition temperatures are lowered
+ 
+
+ align:start position:0%
+deposition temperatures are lowered
+significantly compared to atmospheric
+
+ align:start position:0%
+significantly compared to atmospheric
+ 
+
+ align:start position:0%
+significantly compared to atmospheric
+pressure and people can deposit
+
+ align:start position:0%
+pressure and people can deposit
+ 
+
+ align:start position:0%
+pressure and people can deposit
+epitaxial silicon uh typically all the
+
+ align:start position:0%
+epitaxial silicon uh typically all the
+ 
+
+ align:start position:0%
+epitaxial silicon uh typically all the
+way down to 750 maybe 700 even um in the
+
+ align:start position:0%
+way down to 750 maybe 700 even um in the
+ 
+
+ align:start position:0%
+way down to 750 maybe 700 even um in the
+reduced pressure systems uh besides um
+
+ align:start position:0%
+reduced pressure systems uh besides um
+ 
+
+ align:start position:0%
+reduced pressure systems uh besides um
+siline we also talked about silicon
+
+ align:start position:0%
+siline we also talked about silicon
+ 
+
+ align:start position:0%
+siline we also talked about silicon
+tetrachloride being used also um
+
+ align:start position:0%
+tetrachloride being used also um
+ 
+
+ align:start position:0%
+tetrachloride being used also um
+torosyan shown here and dorosy probably
+
+ align:start position:0%
+torosyan shown here and dorosy probably
+ 
+
+ align:start position:0%
+torosyan shown here and dorosy probably
+one of the most common uh gases so are
+
+ align:start position:0%
+one of the most common uh gases so are
+ 
+
+ align:start position:0%
+one of the most common uh gases so are
+dorosy for for Selective epig growth
+
+ align:start position:0%
+dorosy for for Selective epig growth
+ 
+
+ align:start position:0%
+dorosy for for Selective epig growth
+polysilicon we we mentioned last time
+
+ align:start position:0%
+polysilicon we we mentioned last time
+ 
+
+ align:start position:0%
+polysilicon we we mentioned last time
+it's it's put down in a batch furnace
+
+ align:start position:0%
+it's it's put down in a batch furnace
+ 
+
+ align:start position:0%
+it's it's put down in a batch furnace
+typically uh by lpcvd
+
+ align:start position:0%
+typically uh by lpcvd
+ 
+
+ align:start position:0%
+typically uh by lpcvd
+the the gas reactions and the precursors
+
+ align:start position:0%
+the the gas reactions and the precursors
+ 
+
+ align:start position:0%
+the the gas reactions and the precursors
+are the same typically as used as epita
+
+ align:start position:0%
+are the same typically as used as epita
+ 
+
+ align:start position:0%
+are the same typically as used as epita
+of silicon I would say um that uh silene
+
+ align:start position:0%
+of silicon I would say um that uh silene
+ 
+
+ align:start position:0%
+of silicon I would say um that uh silene
+is really the precursor that people use
+
+ align:start position:0%
+is really the precursor that people use
+ 
+
+ align:start position:0%
+is really the precursor that people use
+for poly Crystal and silicon um
+
+ align:start position:0%
+for poly Crystal and silicon um
+ 
+
+ align:start position:0%
+for poly Crystal and silicon um
+polysilicon is typically put down
+
+ align:start position:0%
+polysilicon is typically put down
+ 
+
+ align:start position:0%
+polysilicon is typically put down
+somewhere in it's pretty tight
+
+ align:start position:0%
+somewhere in it's pretty tight
+ 
+
+ align:start position:0%
+somewhere in it's pretty tight
+temperature range uh 7 575 to 650
+
+ align:start position:0%
+temperature range uh 7 575 to 650
+ 
+
+ align:start position:0%
+temperature range uh 7 575 to 650
+degrees Centigrade um the the morphology
+
+ align:start position:0%
+degrees Centigrade um the the morphology
+ 
+
+ align:start position:0%
+degrees Centigrade um the the morphology
+of the film uh and its grain structure
+
+ align:start position:0%
+of the film uh and its grain structure
+ 
+
+ align:start position:0%
+of the film uh and its grain structure
+and we'll talk about that in this
+
+ align:start position:0%
+and we'll talk about that in this
+ 
+
+ align:start position:0%
+and we'll talk about that in this
+lecture depends on the deposition
+
+ align:start position:0%
+lecture depends on the deposition
+ 
+
+ align:start position:0%
+lecture depends on the deposition
+conditions uh the temperature and the
+
+ align:start position:0%
+conditions uh the temperature and the
+ 
+
+ align:start position:0%
+conditions uh the temperature and the
+doping uh quite a bit so you adjust your
+
+ align:start position:0%
+doping uh quite a bit so you adjust your
+ 
+
+ align:start position:0%
+doping uh quite a bit so you adjust your
+temperature to achieve the type of grain
+
+ align:start position:0%
+temperature to achieve the type of grain
+ 
+
+ align:start position:0%
+temperature to achieve the type of grain
+structure that you need for your
+
+ align:start position:0%
+structure that you need for your
+ 
+
+ align:start position:0%
+structure that you need for your
+application silicon nitride can be put
+
+ align:start position:0%
+application silicon nitride can be put
+ 
+
+ align:start position:0%
+application silicon nitride can be put
+down by a lpcvd process as well as we we
+
+ align:start position:0%
+down by a lpcvd process as well as we we
+ 
+
+ align:start position:0%
+down by a lpcvd process as well as we we
+talked last time about plasma enhanced
+
+ align:start position:0%
+talked last time about plasma enhanced
+ 
+
+ align:start position:0%
+talked last time about plasma enhanced
+CBD and this is becoming more and more
+
+ align:start position:0%
+CBD and this is becoming more and more
+ 
+
+ align:start position:0%
+CBD and this is becoming more and more
+common um for low pressure CBD uh there
+
+ align:start position:0%
+common um for low pressure CBD uh there
+ 
+
+ align:start position:0%
+common um for low pressure CBD uh there
+are two different types of uh reactions
+
+ align:start position:0%
+are two different types of uh reactions
+ 
+
+ align:start position:0%
+are two different types of uh reactions
+that are commonly used uh silene is
+
+ align:start position:0%
+that are commonly used uh silene is
+ 
+
+ align:start position:0%
+that are commonly used uh silene is
+reacted with ammonia to create um
+
+ align:start position:0%
+reacted with ammonia to create um
+ 
+
+ align:start position:0%
+reacted with ammonia to create um
+silicon nitride the other one the most
+
+ align:start position:0%
+silicon nitride the other one the most
+ 
+
+ align:start position:0%
+silicon nitride the other one the most
+common one the one that's used here in
+
+ align:start position:0%
+common one the one that's used here in
+ 
+
+ align:start position:0%
+common one the one that's used here in
+MIT in lpcvd is to use dorosy react that
+
+ align:start position:0%
+MIT in lpcvd is to use dorosy react that
+ 
+
+ align:start position:0%
+MIT in lpcvd is to use dorosy react that
+with ammonia and obtain silicon
+
+ align:start position:0%
+with ammonia and obtain silicon
+ 
+
+ align:start position:0%
+with ammonia and obtain silicon
+nitride this reaction typically goes or
+
+ align:start position:0%
+nitride this reaction typically goes or
+ 
+
+ align:start position:0%
+nitride this reaction typically goes or
+is typically deposited to get reasonable
+
+ align:start position:0%
+is typically deposited to get reasonable
+ 
+
+ align:start position:0%
+is typically deposited to get reasonable
+depth rates at around 800 degrees C so
+
+ align:start position:0%
+depth rates at around 800 degrees C so
+ 
+
+ align:start position:0%
+depth rates at around 800 degrees C so
+lpcvd nitrite is one of those things
+
+ align:start position:0%
+lpcvd nitrite is one of those things
+ 
+
+ align:start position:0%
+lpcvd nitrite is one of those things
+that um it's it's at it's at a
+
+ align:start position:0%
+that um it's it's at it's at a
+ 
+
+ align:start position:0%
+that um it's it's at it's at a
+temperature where we talked about in the
+
+ align:start position:0%
+temperature where we talked about in the
+ 
+
+ align:start position:0%
+temperature where we talked about in the
+last several Tes um t Transit enhanced
+
+ align:start position:0%
+last several Tes um t Transit enhanced
+ 
+
+ align:start position:0%
+last several Tes um t Transit enhanced
+diffusion can be an issue so it's it's
+
+ align:start position:0%
+diffusion can be an issue so it's it's
+ 
+
+ align:start position:0%
+diffusion can be an issue so it's it's
+right in that intermediate temperature
+
+ align:start position:0%
+right in that intermediate temperature
+ 
+
+ align:start position:0%
+right in that intermediate temperature
+range um what what else do people use
+
+ align:start position:0%
+range um what what else do people use
+ 
+
+ align:start position:0%
+range um what what else do people use
+well an alternative uh people sometimes
+
+ align:start position:0%
+well an alternative uh people sometimes
+ 
+
+ align:start position:0%
+well an alternative uh people sometimes
+use is low temperatures plasma enhance
+
+ align:start position:0%
+use is low temperatures plasma enhance
+ 
+
+ align:start position:0%
+use is low temperatures plasma enhance
+cvd for a passivating layer uh doesn't
+
+ align:start position:0%
+cvd for a passivating layer uh doesn't
+ 
+
+ align:start position:0%
+cvd for a passivating layer uh doesn't
+have as good properties as uh or the
+
+ align:start position:0%
+have as good properties as uh or the
+ 
+
+ align:start position:0%
+have as good properties as uh or the
+same properties as LP CBD nitride and
+
+ align:start position:0%
+same properties as LP CBD nitride and
+ 
+
+ align:start position:0%
+same properties as LP CBD nitride and
+I'll talk a little bit more about
+
+ align:start position:0%
+I'll talk a little bit more about
+ 
+
+ align:start position:0%
+I'll talk a little bit more about
+that the last one here probably one of
+
+ align:start position:0%
+that the last one here probably one of
+ 
+
+ align:start position:0%
+that the last one here probably one of
+the most important silicon
+
+ align:start position:0%
+the most important silicon
+ 
+
+ align:start position:0%
+the most important silicon
+dioxide remember ear earlier in the
+
+ align:start position:0%
+dioxide remember ear earlier in the
+ 
+
+ align:start position:0%
+dioxide remember ear earlier in the
+course we talked about growing silicon
+
+ align:start position:0%
+course we talked about growing silicon
+ 
+
+ align:start position:0%
+course we talked about growing silicon
+dioxide well now we're talking about
+
+ align:start position:0%
+dioxide well now we're talking about
+ 
+
+ align:start position:0%
+dioxide well now we're talking about
+depositing it which is quite different
+
+ align:start position:0%
+depositing it which is quite different
+ 
+
+ align:start position:0%
+depositing it which is quite different
+uh we react typically siline uh as a
+
+ align:start position:0%
+uh we react typically siline uh as a
+ 
+
+ align:start position:0%
+uh we react typically siline uh as a
+precursor with oxygen to form sio2 so
+
+ align:start position:0%
+precursor with oxygen to form sio2 so
+ 
+
+ align:start position:0%
+precursor with oxygen to form sio2 so
+that uh you don't have to have silicon
+
+ align:start position:0%
+that uh you don't have to have silicon
+ 
+
+ align:start position:0%
+that uh you don't have to have silicon
+Exposed on the wafer you don't consume
+
+ align:start position:0%
+Exposed on the wafer you don't consume
+ 
+
+ align:start position:0%
+Exposed on the wafer you don't consume
+necessarily much silicon on the wafer
+
+ align:start position:0%
+necessarily much silicon on the wafer
+ 
+
+ align:start position:0%
+necessarily much silicon on the wafer
+this is listed between 200 and 800
+
+ align:start position:0%
+this is listed between 200 and 800
+ 
+
+ align:start position:0%
+this is listed between 200 and 800
+that's pretty pretty wide range the
+
+ align:start position:0%
+that's pretty pretty wide range the
+ 
+
+ align:start position:0%
+that's pretty pretty wide range the
+really the most common is between 200
+
+ align:start position:0%
+really the most common is between 200
+ 
+
+ align:start position:0%
+really the most common is between 200
+and 500 in fact lto is a very common
+
+ align:start position:0%
+and 500 in fact lto is a very common
+ 
+
+ align:start position:0%
+and 500 in fact lto is a very common
+acronym you'll find in the Fab lto is as
+
+ align:start position:0%
+acronym you'll find in the Fab lto is as
+ 
+
+ align:start position:0%
+acronym you'll find in the Fab lto is as
+we call it um typically lto is put down
+
+ align:start position:0%
+we call it um typically lto is put down
+ 
+
+ align:start position:0%
+we call it um typically lto is put down
+uh between 350 and 450 that's really a
+
+ align:start position:0%
+uh between 350 and 450 that's really a
+ 
+
+ align:start position:0%
+uh between 350 and 450 that's really a
+more uh a more reasonable range um in
+
+ align:start position:0%
+more uh a more reasonable range um in
+ 
+
+ align:start position:0%
+more uh a more reasonable range um in
+order to get reasonable properties slow
+
+ align:start position:0%
+order to get reasonable properties slow
+ 
+
+ align:start position:0%
+order to get reasonable properties slow
+uh to reduce the edge rate and things
+
+ align:start position:0%
+uh to reduce the edge rate and things
+ 
+
+ align:start position:0%
+uh to reduce the edge rate and things
+people usually High have to high
+
+ align:start position:0%
+people usually High have to high
+ 
+
+ align:start position:0%
+people usually High have to high
+temperature an Neal lto so they have to
+
+ align:start position:0%
+temperature an Neal lto so they have to
+ 
+
+ align:start position:0%
+temperature an Neal lto so they have to
+what they call densify it uh because
+
+ align:start position:0%
+what they call densify it uh because
+ 
+
+ align:start position:0%
+what they call densify it uh because
+it's non stochiometric
+
+ align:start position:0%
+it's non stochiometric
+ 
+
+ align:start position:0%
+it's non stochiometric
+si2 um in modern Fabs you will also find
+
+ align:start position:0%
+si2 um in modern Fabs you will also find
+ 
+
+ align:start position:0%
+si2 um in modern Fabs you will also find
+a very common process um called teos
+
+ align:start position:0%
+a very common process um called teos
+ 
+
+ align:start position:0%
+a very common process um called teos
+people refer to um lto uh sometimes as
+
+ align:start position:0%
+people refer to um lto uh sometimes as
+ 
+
+ align:start position:0%
+people refer to um lto uh sometimes as
+TS and TS is this uh refers to this
+
+ align:start position:0%
+TS and TS is this uh refers to this
+ 
+
+ align:start position:0%
+TS and TS is this uh refers to this
+particular um uh organic compound and
+
+ align:start position:0%
+particular um uh organic compound and
+ 
+
+ align:start position:0%
+particular um uh organic compound and
+you notice it's a compound that includes
+
+ align:start position:0%
+you notice it's a compound that includes
+ 
+
+ align:start position:0%
+you notice it's a compound that includes
+silicon along with an organic group uh a
+
+ align:start position:0%
+silicon along with an organic group uh a
+ 
+
+ align:start position:0%
+silicon along with an organic group uh a
+c2h5 group you react that with ozone and
+
+ align:start position:0%
+c2h5 group you react that with ozone and
+ 
+
+ align:start position:0%
+c2h5 group you react that with ozone and
+at a very low temperature say 400 or
+
+ align:start position:0%
+at a very low temperature say 400 or
+ 
+
+ align:start position:0%
+at a very low temperature say 400 or
+below you can get um very high depth
+
+ align:start position:0%
+below you can get um very high depth
+ 
+
+ align:start position:0%
+below you can get um very high depth
+rates of
+
+ align:start position:0%
+rates of
+ 
+
+ align:start position:0%
+rates of
+sio2 um and now the only thing about
+
+ align:start position:0%
+sio2 um and now the only thing about
+ 
+
+ align:start position:0%
+sio2 um and now the only thing about
+teos is that you need to be aware of
+
+ align:start position:0%
+teos is that you need to be aware of
+ 
+
+ align:start position:0%
+teos is that you need to be aware of
+what's different is there's an organic
+
+ align:start position:0%
+what's different is there's an organic
+ 
+
+ align:start position:0%
+what's different is there's an organic
+element in the precursor some of which
+
+ align:start position:0%
+element in the precursor some of which
+ 
+
+ align:start position:0%
+element in the precursor some of which
+can potentially be incorporated in the
+
+ align:start position:0%
+can potentially be incorporated in the
+ 
+
+ align:start position:0%
+can potentially be incorporated in the
+film and so teos films may have more
+
+ align:start position:0%
+film and so teos films may have more
+ 
+
+ align:start position:0%
+film and so teos films may have more
+carbon incorporation or carbon
+
+ align:start position:0%
+carbon incorporation or carbon
+ 
+
+ align:start position:0%
+carbon incorporation or carbon
+contamination and their their uh some of
+
+ align:start position:0%
+contamination and their their uh some of
+ 
+
+ align:start position:0%
+contamination and their their uh some of
+their properties will be a little
+
+ align:start position:0%
+their properties will be a little
+ 
+
+ align:start position:0%
+their properties will be a little
+different from lto but Taos is very
+
+ align:start position:0%
+different from lto but Taos is very
+ 
+
+ align:start position:0%
+different from lto but Taos is very
+commonly used uh in Fabs
+
+ align:start position:0%
+commonly used uh in Fabs
+ 
+
+ align:start position:0%
+commonly used uh in Fabs
+today okay so that's just a little uh
+
+ align:start position:0%
+today okay so that's just a little uh
+ 
+
+ align:start position:0%
+today okay so that's just a little uh
+background on the different types of
+
+ align:start position:0%
+background on the different types of
+ 
+
+ align:start position:0%
+background on the different types of
+materials um let's remind ourselves
+
+ align:start position:0%
+materials um let's remind ourselves
+ 
+
+ align:start position:0%
+materials um let's remind ourselves
+about low pressure on here on slide
+
+ align:start position:0%
+about low pressure on here on slide
+ 
+
+ align:start position:0%
+about low pressure on here on slide
+three about low pressure um
+
+ align:start position:0%
+three about low pressure um
+ 
+
+ align:start position:0%
+three about low pressure um
+cvd uh atmospheric pressure systems have
+
+ align:start position:0%
+cvd uh atmospheric pressure systems have
+ 
+
+ align:start position:0%
+cvd uh atmospheric pressure systems have
+some major drawbacks uh for example if
+
+ align:start position:0%
+some major drawbacks uh for example if
+ 
+
+ align:start position:0%
+some major drawbacks uh for example if
+you operate them at high temperature um
+
+ align:start position:0%
+you operate them at high temperature um
+ 
+
+ align:start position:0%
+you operate them at high temperature um
+the gas flow makes a really big
+
+ align:start position:0%
+the gas flow makes a really big
+ 
+
+ align:start position:0%
+the gas flow makes a really big
+difference and they have to be designed
+
+ align:start position:0%
+difference and they have to be designed
+ 
+
+ align:start position:0%
+difference and they have to be designed
+just right you typically need a
+
+ align:start position:0%
+just right you typically need a
+ 
+
+ align:start position:0%
+just right you typically need a
+horizontal configuration as we showed
+
+ align:start position:0%
+horizontal configuration as we showed
+ 
+
+ align:start position:0%
+horizontal configuration as we showed
+last time and you only can really do a
+
+ align:start position:0%
+last time and you only can really do a
+ 
+
+ align:start position:0%
+last time and you only can really do a
+few Wafers at a time in order to get any
+
+ align:start position:0%
+few Wafers at a time in order to get any
+ 
+
+ align:start position:0%
+few Wafers at a time in order to get any
+kind of real uniformity so um
+
+ align:start position:0%
+kind of real uniformity so um
+ 
+
+ align:start position:0%
+kind of real uniformity so um
+atmospheric pressure presss are really
+
+ align:start position:0%
+atmospheric pressure presss are really
+ 
+
+ align:start position:0%
+atmospheric pressure presss are really
+not that commonly used anymore if you
+
+ align:start position:0%
+not that commonly used anymore if you
+ 
+
+ align:start position:0%
+not that commonly used anymore if you
+try to operate them at low te you say
+
+ align:start position:0%
+try to operate them at low te you say
+ 
+
+ align:start position:0%
+try to operate them at low te you say
+okay I'll go to the low temperature
+
+ align:start position:0%
+okay I'll go to the low temperature
+ 
+
+ align:start position:0%
+okay I'll go to the low temperature
+where um there will be surface reaction
+
+ align:start position:0%
+where um there will be surface reaction
+ 
+
+ align:start position:0%
+where um there will be surface reaction
+rate limited um but the deposition rate
+
+ align:start position:0%
+rate limited um but the deposition rate
+ 
+
+ align:start position:0%
+rate limited um but the deposition rate
+goes
+
+ align:start position:0%
+goes
+ 
+
+ align:start position:0%
+goes
+down um uh to quite a bit so there is a
+
+ align:start position:0%
+down um uh to quite a bit so there is a
+ 
+
+ align:start position:0%
+down um uh to quite a bit so there is a
+solution though which is to operate uh
+
+ align:start position:0%
+solution though which is to operate uh
+ 
+
+ align:start position:0%
+solution though which is to operate uh
+the reactor at lower pressures so
+
+ align:start position:0%
+the reactor at lower pressures so
+ 
+
+ align:start position:0%
+the reactor at lower pressures so
+instead of 760 tour you might operate at
+
+ align:start position:0%
+instead of 760 tour you might operate at
+ 
+
+ align:start position:0%
+instead of 760 tour you might operate at
+1 to 10
+
+ align:start position:0%
+1 to 10
+ 
+
+ align:start position:0%
+1 to 10
+tour um now if you go back to the mass
+
+ align:start position:0%
+tour um now if you go back to the mass
+ 
+
+ align:start position:0%
+tour um now if you go back to the mass
+transfer limited regime remember there
+
+ align:start position:0%
+transfer limited regime remember there
+ 
+
+ align:start position:0%
+transfer limited regime remember there
+was a transport coefficient H subg so
+
+ align:start position:0%
+was a transport coefficient H subg so
+ 
+
+ align:start position:0%
+was a transport coefficient H subg so
+this tells you uh this is the the limit
+
+ align:start position:0%
+this tells you uh this is the the limit
+ 
+
+ align:start position:0%
+this tells you uh this is the the limit
+limiting step in getting the gas from
+
+ align:start position:0%
+limiting step in getting the gas from
+ 
+
+ align:start position:0%
+limiting step in getting the gas from
+the main stream of the gas um to diffuse
+
+ align:start position:0%
+the main stream of the gas um to diffuse
+ 
+
+ align:start position:0%
+the main stream of the gas um to diffuse
+through the boundary layer to the
+
+ align:start position:0%
+through the boundary layer to the
+ 
+
+ align:start position:0%
+through the boundary layer to the
+surface where it can react so this mass
+
+ align:start position:0%
+surface where it can react so this mass
+ 
+
+ align:start position:0%
+surface where it can react so this mass
+transport coefficient HG was equal to a
+
+ align:start position:0%
+transport coefficient HG was equal to a
+ 
+
+ align:start position:0%
+transport coefficient HG was equal to a
+diffusivity uh through the boundary
+
+ align:start position:0%
+diffusivity uh through the boundary
+ 
+
+ align:start position:0%
+diffusivity uh through the boundary
+layer divided by the boundary layer
+
+ align:start position:0%
+layer divided by the boundary layer
+ 
+
+ align:start position:0%
+layer divided by the boundary layer
+thickness so Delta here is the boundary
+
+ align:start position:0%
+thickness so Delta here is the boundary
+ 
+
+ align:start position:0%
+thickness so Delta here is the boundary
+layer thickness but you notice the
+
+ align:start position:0%
+layer thickness but you notice the
+ 
+
+ align:start position:0%
+layer thickness but you notice the
+diffusivity of through in the gas phase
+
+ align:start position:0%
+diffusivity of through in the gas phase
+ 
+
+ align:start position:0%
+diffusivity of through in the gas phase
+is proportional to one over the pressure
+
+ align:start position:0%
+is proportional to one over the pressure
+ 
+
+ align:start position:0%
+is proportional to one over the pressure
+one over the total pressure so this is
+
+ align:start position:0%
+one over the total pressure so this is
+ 
+
+ align:start position:0%
+one over the total pressure so this is
+the key um uh leverage that you're going
+
+ align:start position:0%
+the key um uh leverage that you're going
+ 
+
+ align:start position:0%
+the key um uh leverage that you're going
+to use by reducing the
+
+ align:start position:0%
+to use by reducing the
+ 
+
+ align:start position:0%
+to use by reducing the
+pressure so the diffusivity will go up
+
+ align:start position:0%
+pressure so the diffusivity will go up
+ 
+
+ align:start position:0%
+pressure so the diffusivity will go up
+by about 760 times if I go for at
+
+ align:start position:0%
+by about 760 times if I go for at
+ 
+
+ align:start position:0%
+by about 760 times if I go for at
+atmospheric pressure remember
+
+ align:start position:0%
+atmospheric pressure remember
+ 
+
+ align:start position:0%
+atmospheric pressure remember
+atmospheric pressure is 760 T if I go
+
+ align:start position:0%
+atmospheric pressure is 760 T if I go
+ 
+
+ align:start position:0%
+atmospheric pressure is 760 T if I go
+down to one t um this this is going to
+
+ align:start position:0%
+down to one t um this this is going to
+ 
+
+ align:start position:0%
+down to one t um this this is going to
+go up by a 760 um where while the um the
+
+ align:start position:0%
+go up by a 760 um where while the um the
+ 
+
+ align:start position:0%
+go up by a 760 um where while the um the
+boundary layer itself is also um is
+
+ align:start position:0%
+boundary layer itself is also um is
+ 
+
+ align:start position:0%
+boundary layer itself is also um is
+going to increase but not quite as much
+
+ align:start position:0%
+going to increase but not quite as much
+ 
+
+ align:start position:0%
+going to increase but not quite as much
+only seven times so we can get about a
+
+ align:start position:0%
+only seven times so we can get about a
+ 
+
+ align:start position:0%
+only seven times so we can get about a
+factor of 100 in HG uh if I drop the
+
+ align:start position:0%
+factor of 100 in HG uh if I drop the
+ 
+
+ align:start position:0%
+factor of 100 in HG uh if I drop the
+pressure from atmospheric down to
+
+ align:start position:0%
+pressure from atmospheric down to
+ 
+
+ align:start position:0%
+pressure from atmospheric down to
+T um and then the in the one tour regime
+
+ align:start position:0%
+T um and then the in the one tour regime
+ 
+
+ align:start position:0%
+T um and then the in the one tour regime
+uh the transport of reactants from the
+
+ align:start position:0%
+uh the transport of reactants from the
+ 
+
+ align:start position:0%
+uh the transport of reactants from the
+gas phase to the surface through the
+
+ align:start position:0%
+gas phase to the surface through the
+ 
+
+ align:start position:0%
+gas phase to the surface through the
+surface boundary layer is no longer rate
+
+ align:start position:0%
+surface boundary layer is no longer rate
+ 
+
+ align:start position:0%
+surface boundary layer is no longer rate
+limiting so it can really speed uh speed
+
+ align:start position:0%
+limiting so it can really speed uh speed
+ 
+
+ align:start position:0%
+limiting so it can really speed uh speed
+up that
+
+ align:start position:0%
+up that
+ 
+
+ align:start position:0%
+up that
+process in fact we can show this gra
+
+ align:start position:0%
+process in fact we can show this gra
+ 
+
+ align:start position:0%
+process in fact we can show this gra
+let's look at slide number four and you
+
+ align:start position:0%
+let's look at slide number four and you
+ 
+
+ align:start position:0%
+let's look at slide number four and you
+can see this graphically um this is a
+
+ align:start position:0%
+can see this graphically um this is a
+ 
+
+ align:start position:0%
+can see this graphically um this is a
+plot similar to what I showed last time
+
+ align:start position:0%
+plot similar to what I showed last time
+ 
+
+ align:start position:0%
+plot similar to what I showed last time
+it's the growth rate on on a log scale
+
+ align:start position:0%
+it's the growth rate on on a log scale
+ 
+
+ align:start position:0%
+it's the growth rate on on a log scale
+versus one over T so we typically call
+
+ align:start position:0%
+versus one over T so we typically call
+ 
+
+ align:start position:0%
+versus one over T so we typically call
+this an arous plot and um for
+
+ align:start position:0%
+this an arous plot and um for
+ 
+
+ align:start position:0%
+this an arous plot and um for
+atmospheric pressure cvd it's this lower
+
+ align:start position:0%
+atmospheric pressure cvd it's this lower
+ 
+
+ align:start position:0%
+atmospheric pressure cvd it's this lower
+line right here is the net growth rate
+
+ align:start position:0%
+line right here is the net growth rate
+ 
+
+ align:start position:0%
+line right here is the net growth rate
+and at low temperatures here your
+
+ align:start position:0%
+and at low temperatures here your
+ 
+
+ align:start position:0%
+and at low temperatures here your
+surface reaction control but look what
+
+ align:start position:0%
+surface reaction control but look what
+ 
+
+ align:start position:0%
+surface reaction control but look what
+happens you get to certain temperature
+
+ align:start position:0%
+happens you get to certain temperature
+ 
+
+ align:start position:0%
+happens you get to certain temperature
+and there's like a knee in the curve and
+
+ align:start position:0%
+and there's like a knee in the curve and
+ 
+
+ align:start position:0%
+and there's like a knee in the curve and
+it sort of flattens out so at 760 T it
+
+ align:start position:0%
+it sort of flattens out so at 760 T it
+ 
+
+ align:start position:0%
+it sort of flattens out so at 760 T it
+flattens out and you can only get a
+
+ align:start position:0%
+flattens out and you can only get a
+ 
+
+ align:start position:0%
+flattens out and you can only get a
+certain growth growth rate um for
+
+ align:start position:0%
+certain growth growth rate um for
+ 
+
+ align:start position:0%
+certain growth growth rate um for
+atmospheric systems now if I drop the
+
+ align:start position:0%
+atmospheric systems now if I drop the
+ 
+
+ align:start position:0%
+atmospheric systems now if I drop the
+pressure to one tour again I could get
+
+ align:start position:0%
+pressure to one tour again I could get
+ 
+
+ align:start position:0%
+pressure to one tour again I could get
+about a factor of 100 increase remember
+
+ align:start position:0%
+about a factor of 100 increase remember
+ 
+
+ align:start position:0%
+about a factor of 100 increase remember
+this is a log scale so going from here
+
+ align:start position:0%
+this is a log scale so going from here
+ 
+
+ align:start position:0%
+this is a log scale so going from here
+to here doesn't look like much but this
+
+ align:start position:0%
+to here doesn't look like much but this
+ 
+
+ align:start position:0%
+to here doesn't look like much but this
+could be a factor of 10 to 100 in growth
+
+ align:start position:0%
+could be a factor of 10 to 100 in growth
+ 
+
+ align:start position:0%
+could be a factor of 10 to 100 in growth
+rate um at at one
+
+ align:start position:0%
+rate um at at one
+ 
+
+ align:start position:0%
+rate um at at one
+tour because why is this happening
+
+ align:start position:0%
+tour because why is this happening
+ 
+
+ align:start position:0%
+tour because why is this happening
+because the gas Bas diffusion rate
+
+ align:start position:0%
+because the gas Bas diffusion rate
+ 
+
+ align:start position:0%
+because the gas Bas diffusion rate
+through the boundary layer is increasing
+
+ align:start position:0%
+through the boundary layer is increasing
+ 
+
+ align:start position:0%
+through the boundary layer is increasing
+as I drop that that pressure um so I can
+
+ align:start position:0%
+as I drop that that pressure um so I can
+ 
+
+ align:start position:0%
+as I drop that that pressure um so I can
+really um uh up the growth rate by going
+
+ align:start position:0%
+really um uh up the growth rate by going
+ 
+
+ align:start position:0%
+really um uh up the growth rate by going
+to uh low pressure and so that's that's
+
+ align:start position:0%
+to uh low pressure and so that's that's
+ 
+
+ align:start position:0%
+to uh low pressure and so that's that's
+how the two curves notice the two curves
+
+ align:start position:0%
+how the two curves notice the two curves
+ 
+
+ align:start position:0%
+how the two curves notice the two curves
+converge though pretty closely when you
+
+ align:start position:0%
+converge though pretty closely when you
+ 
+
+ align:start position:0%
+converge though pretty closely when you
+get down to low enough temperatures that
+
+ align:start position:0%
+get down to low enough temperatures that
+ 
+
+ align:start position:0%
+get down to low enough temperatures that
+you really are surface reaction
+
+ align:start position:0%
+you really are surface reaction
+ 
+
+ align:start position:0%
+you really are surface reaction
+controlled you can drop the pressure you
+
+ align:start position:0%
+controlled you can drop the pressure you
+ 
+
+ align:start position:0%
+controlled you can drop the pressure you
+know by a factor of a th000 and you only
+
+ align:start position:0%
+know by a factor of a th000 and you only
+ 
+
+ align:start position:0%
+know by a factor of a th000 and you only
+get a very small increase you'll get
+
+ align:start position:0%
+get a very small increase you'll get
+ 
+
+ align:start position:0%
+get a very small increase you'll get
+some increase uh or or some change
+
+ align:start position:0%
+some increase uh or or some change
+ 
+
+ align:start position:0%
+some increase uh or or some change
+rather in the growth rate but not so
+
+ align:start position:0%
+rather in the growth rate but not so
+ 
+
+ align:start position:0%
+rather in the growth rate but not so
+much because the surface reaction rate
+
+ align:start position:0%
+much because the surface reaction rate
+ 
+
+ align:start position:0%
+much because the surface reaction rate
+is Right limiting at that at that
+
+ align:start position:0%
+is Right limiting at that at that
+ 
+
+ align:start position:0%
+is Right limiting at that at that
+temperature so that's one of the big
+
+ align:start position:0%
+temperature so that's one of the big
+ 
+
+ align:start position:0%
+temperature so that's one of the big
+motivations for going to low pressure um
+
+ align:start position:0%
+motivations for going to low pressure um
+ 
+
+ align:start position:0%
+motivations for going to low pressure um
+let's go to let's go to slide uh slide
+
+ align:start position:0%
+let's go to let's go to slide uh slide
+ 
+
+ align:start position:0%
+let's go to let's go to slide uh slide
+number five and we talked about this
+
+ align:start position:0%
+number five and we talked about this
+ 
+
+ align:start position:0%
+number five and we talked about this
+last time but I want to give more detail
+
+ align:start position:0%
+last time but I want to give more detail
+ 
+
+ align:start position:0%
+last time but I want to give more detail
+now on the deposition of polycrystal and
+
+ align:start position:0%
+now on the deposition of polycrystal and
+ 
+
+ align:start position:0%
+now on the deposition of polycrystal and
+silicon we we introduced this sort of U
+
+ align:start position:0%
+silicon we we introduced this sort of U
+ 
+
+ align:start position:0%
+silicon we we introduced this sort of U
+rudimentary reactor this type of setup
+
+ align:start position:0%
+rudimentary reactor this type of setup
+ 
+
+ align:start position:0%
+rudimentary reactor this type of setup
+is found pretty much in every Fab maybe
+
+ align:start position:0%
+is found pretty much in every Fab maybe
+ 
+
+ align:start position:0%
+is found pretty much in every Fab maybe
+slightly different uh configuration but
+
+ align:start position:0%
+slightly different uh configuration but
+ 
+
+ align:start position:0%
+slightly different uh configuration but
+uh it's essentially a hot wall furnace
+
+ align:start position:0%
+uh it's essentially a hot wall furnace
+ 
+
+ align:start position:0%
+uh it's essentially a hot wall furnace
+it's a hot wall furnace and that's
+
+ align:start position:0%
+it's a hot wall furnace and that's
+ 
+
+ align:start position:0%
+it's a hot wall furnace and that's
+resistively heated the Wafers are
+
+ align:start position:0%
+resistively heated the Wafers are
+ 
+
+ align:start position:0%
+resistively heated the Wafers are
+usually put on in quartz boats or or or
+
+ align:start position:0%
+usually put on in quartz boats or or or
+ 
+
+ align:start position:0%
+usually put on in quartz boats or or or
+quartz um quartz wear and they usually
+
+ align:start position:0%
+quartz um quartz wear and they usually
+ 
+
+ align:start position:0%
+quartz um quartz wear and they usually
+stand up together uh very close to each
+
+ align:start position:0%
+stand up together uh very close to each
+ 
+
+ align:start position:0%
+stand up together uh very close to each
+other uh and it's a batch process so you
+
+ align:start position:0%
+other uh and it's a batch process so you
+ 
+
+ align:start position:0%
+other uh and it's a batch process so you
+can get 25 50 maybe 75 wafers in a batch
+
+ align:start position:0%
+can get 25 50 maybe 75 wafers in a batch
+ 
+
+ align:start position:0%
+can get 25 50 maybe 75 wafers in a batch
+quite a few Wafers uh you have some gas
+
+ align:start position:0%
+quite a few Wafers uh you have some gas
+ 
+
+ align:start position:0%
+quite a few Wafers uh you have some gas
+sources consisting of silene and and
+
+ align:start position:0%
+sources consisting of silene and and
+ 
+
+ align:start position:0%
+sources consisting of silene and and
+nitrogen and maybe it doens if you want
+
+ align:start position:0%
+nitrogen and maybe it doens if you want
+ 
+
+ align:start position:0%
+nitrogen and maybe it doens if you want
+it flow into this quartz tube Into The
+
+ align:start position:0%
+it flow into this quartz tube Into The
+ 
+
+ align:start position:0%
+it flow into this quartz tube Into The
+Hot Zone and then there um the pressure
+
+ align:start position:0%
+Hot Zone and then there um the pressure
+ 
+
+ align:start position:0%
+Hot Zone and then there um the pressure
+the low pressure is maintained by a
+
+ align:start position:0%
+the low pressure is maintained by a
+ 
+
+ align:start position:0%
+the low pressure is maintained by a
+vacuum pump so um this is not an open
+
+ align:start position:0%
+vacuum pump so um this is not an open
+ 
+
+ align:start position:0%
+vacuum pump so um this is not an open
+tube furnace the the the um the mouth of
+
+ align:start position:0%
+tube furnace the the the um the mouth of
+ 
+
+ align:start position:0%
+tube furnace the the the um the mouth of
+the Furnace where the Wafers come in and
+
+ align:start position:0%
+the Furnace where the Wafers come in and
+ 
+
+ align:start position:0%
+the Furnace where the Wafers come in and
+out actually is sealed with an O-ring so
+
+ align:start position:0%
+out actually is sealed with an O-ring so
+ 
+
+ align:start position:0%
+out actually is sealed with an O-ring so
+you can you can pull a
+
+ align:start position:0%
+you can you can pull a
+ 
+
+ align:start position:0%
+you can you can pull a
+vacuum um typical depositions uh usually
+
+ align:start position:0%
+vacuum um typical depositions uh usually
+ 
+
+ align:start position:0%
+vacuum um typical depositions uh usually
+um usually poly silicon is deposit on
+
+ align:start position:0%
+um usually poly silicon is deposit on
+ 
+
+ align:start position:0%
+um usually poly silicon is deposit on
+oxide maybe or on an oxide with silicon
+
+ align:start position:0%
+oxide maybe or on an oxide with silicon
+ 
+
+ align:start position:0%
+oxide maybe or on an oxide with silicon
+wind window s uh it's a non-selective
+
+ align:start position:0%
+wind window s uh it's a non-selective
+ 
+
+ align:start position:0%
+wind window s uh it's a non-selective
+process so it it goes over the entire uh
+
+ align:start position:0%
+process so it it goes over the entire uh
+ 
+
+ align:start position:0%
+process so it it goes over the entire uh
+wafer on all structures uh the diluent
+
+ align:start position:0%
+wafer on all structures uh the diluent
+ 
+
+ align:start position:0%
+wafer on all structures uh the diluent
+gas so what what is the usually flow
+
+ align:start position:0%
+gas so what what is the usually flow
+ 
+
+ align:start position:0%
+gas so what what is the usually flow
+sometimes people flow nothing sometimes
+
+ align:start position:0%
+sometimes people flow nothing sometimes
+ 
+
+ align:start position:0%
+sometimes people flow nothing sometimes
+it's just silent flowing in in the tool
+
+ align:start position:0%
+it's just silent flowing in in the tool
+ 
+
+ align:start position:0%
+it's just silent flowing in in the tool
+relatively low sometimes people use a
+
+ align:start position:0%
+relatively low sometimes people use a
+ 
+
+ align:start position:0%
+relatively low sometimes people use a
+carrier gas um such as nitrogen uh
+
+ align:start position:0%
+carrier gas um such as nitrogen uh
+ 
+
+ align:start position:0%
+carrier gas um such as nitrogen uh
+notice that hydrogen is not used
+
+ align:start position:0%
+notice that hydrogen is not used
+ 
+
+ align:start position:0%
+notice that hydrogen is not used
+typically uh and there was a question I
+
+ align:start position:0%
+typically uh and there was a question I
+ 
+
+ align:start position:0%
+typically uh and there was a question I
+believe about this last in the last
+
+ align:start position:0%
+believe about this last in the last
+ 
+
+ align:start position:0%
+believe about this last in the last
+lecture hydrogen is not used because it
+
+ align:start position:0%
+lecture hydrogen is not used because it
+ 
+
+ align:start position:0%
+lecture hydrogen is not used because it
+reduces the growth rate again this is
+
+ align:start position:0%
+reduces the growth rate again this is
+ 
+
+ align:start position:0%
+reduces the growth rate again this is
+the reaction from silene going to solid
+
+ align:start position:0%
+the reaction from silene going to solid
+ 
+
+ align:start position:0%
+the reaction from silene going to solid
+silicon and it evolves hydrogen if you
+
+ align:start position:0%
+silicon and it evolves hydrogen if you
+ 
+
+ align:start position:0%
+silicon and it evolves hydrogen if you
+put hydrogen into the reactor it tends
+
+ align:start position:0%
+put hydrogen into the reactor it tends
+ 
+
+ align:start position:0%
+put hydrogen into the reactor it tends
+to push the reaction backwards and
+
+ align:start position:0%
+to push the reaction backwards and
+ 
+
+ align:start position:0%
+to push the reaction backwards and
+slower the grow uh slow down the growth
+
+ align:start position:0%
+slower the grow uh slow down the growth
+ 
+
+ align:start position:0%
+slower the grow uh slow down the growth
+rate typical pressure for poly depth is
+
+ align:start position:0%
+rate typical pressure for poly depth is
+ 
+
+ align:start position:0%
+rate typical pressure for poly depth is
+about 200 milour maybe up to a t um T is
+
+ align:start position:0%
+about 200 milour maybe up to a t um T is
+ 
+
+ align:start position:0%
+about 200 milour maybe up to a t um T is
+a little bit High uh the low pressure
+
+ align:start position:0%
+a little bit High uh the low pressure
+ 
+
+ align:start position:0%
+a little bit High uh the low pressure
+here in in the hundreds of millor range
+
+ align:start position:0%
+here in in the hundreds of millor range
+ 
+
+ align:start position:0%
+here in in the hundreds of millor range
+improves the film uniformity the film
+
+ align:start position:0%
+improves the film uniformity the film
+ 
+
+ align:start position:0%
+improves the film uniformity the film
+thickness
+
+ align:start position:0%
+thickness
+ 
+
+ align:start position:0%
+thickness
+uniformity and um again the temperature
+
+ align:start position:0%
+uniformity and um again the temperature
+ 
+
+ align:start position:0%
+uniformity and um again the temperature
+range is pretty tight 57 75 to
+
+ align:start position:0%
+range is pretty tight 57 75 to
+ 
+
+ align:start position:0%
+range is pretty tight 57 75 to
+650 uh and an important number to keep
+
+ align:start position:0%
+650 uh and an important number to keep
+ 
+
+ align:start position:0%
+650 uh and an important number to keep
+in your head an important temperature
+
+ align:start position:0%
+in your head an important temperature
+ 
+
+ align:start position:0%
+in your head an important temperature
+for poly silic is 580 that's right
+
+ align:start position:0%
+for poly silic is 580 that's right
+ 
+
+ align:start position:0%
+for poly silic is 580 that's right
+around the uh the amorphous to
+
+ align:start position:0%
+around the uh the amorphous to
+ 
+
+ align:start position:0%
+around the uh the amorphous to
+crystallin phase transition so if you go
+
+ align:start position:0%
+crystallin phase transition so if you go
+ 
+
+ align:start position:0%
+crystallin phase transition so if you go
+below 580 the film is is pretty much
+
+ align:start position:0%
+below 580 the film is is pretty much
+ 
+
+ align:start position:0%
+below 580 the film is is pretty much
+amorphous primarily although it will
+
+ align:start position:0%
+amorphous primarily although it will
+ 
+
+ align:start position:0%
+amorphous primarily although it will
+contain some small poly crystallin or
+
+ align:start position:0%
+contain some small poly crystallin or
+ 
+
+ align:start position:0%
+contain some small poly crystallin or
+crystallites which sometimes people call
+
+ align:start position:0%
+crystallites which sometimes people call
+ 
+
+ align:start position:0%
+crystallites which sometimes people call
+seeds um so 580 is the magic number you
+
+ align:start position:0%
+seeds um so 580 is the magic number you
+ 
+
+ align:start position:0%
+seeds um so 580 is the magic number you
+go down below that you get Amorphis
+
+ align:start position:0%
+go down below that you get Amorphis
+ 
+
+ align:start position:0%
+go down below that you get Amorphis
+material as deposited you go above that
+
+ align:start position:0%
+material as deposited you go above that
+ 
+
+ align:start position:0%
+material as deposited you go above that
+and you get poly crystallin uh
+
+ align:start position:0%
+and you get poly crystallin uh
+ 
+
+ align:start position:0%
+and you get poly crystallin uh
+polycrystal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uteria so if we go on to slide six in
+
+ align:start position:0%
+uteria so if we go on to slide six in
+ 
+
+ align:start position:0%
+uteria so if we go on to slide six in
+fact there are some um pictures of
+
+ align:start position:0%
+fact there are some um pictures of
+ 
+
+ align:start position:0%
+fact there are some um pictures of
+polycrystal and silicon this uh although
+
+ align:start position:0%
+polycrystal and silicon this uh although
+ 
+
+ align:start position:0%
+polycrystal and silicon this uh although
+this is a figure in your text uh in
+
+ align:start position:0%
+this is a figure in your text uh in
+ 
+
+ align:start position:0%
+this is a figure in your text uh in
+chapter 9 figure
+
+ align:start position:0%
+chapter 9 figure
+ 
+
+ align:start position:0%
+chapter 9 figure
+9-32 uh it's actually originally taken
+
+ align:start position:0%
+9-32 uh it's actually originally taken
+ 
+
+ align:start position:0%
+9-32 uh it's actually originally taken
+from Ted Cam's book on polycrystal and
+
+ align:start position:0%
+from Ted Cam's book on polycrystal and
+ 
+
+ align:start position:0%
+from Ted Cam's book on polycrystal and
+silicon so I've given up here on the
+
+ align:start position:0%
+silicon so I've given up here on the
+ 
+
+ align:start position:0%
+silicon so I've given up here on the
+upper left the original reference um of
+
+ align:start position:0%
+upper left the original reference um of
+ 
+
+ align:start position:0%
+upper left the original reference um of
+that uh that that work and there are uh
+
+ align:start position:0%
+that uh that that work and there are uh
+ 
+
+ align:start position:0%
+that uh that that work and there are uh
+these are cross-section tem micrographs
+
+ align:start position:0%
+these are cross-section tem micrographs
+ 
+
+ align:start position:0%
+these are cross-section tem micrographs
+under four four different conditions of
+
+ align:start position:0%
+under four four different conditions of
+ 
+
+ align:start position:0%
+under four four different conditions of
+poly silic put down by low press
+
+ align:start position:0%
+poly silic put down by low press
+ 
+
+ align:start position:0%
+poly silic put down by low press
+CBD uh and this this was all the all
+
+ align:start position:0%
+CBD uh and this this was all the all
+ 
+
+ align:start position:0%
+CBD uh and this this was all the all
+these films were deposited at 625 so
+
+ align:start position:0%
+these films were deposited at 625 so
+ 
+
+ align:start position:0%
+these films were deposited at 625 so
+here's just an example of a
+
+ align:start position:0%
+here's just an example of a
+ 
+
+ align:start position:0%
+here's just an example of a
+cross-section TM of an undoped film and
+
+ align:start position:0%
+cross-section TM of an undoped film and
+ 
+
+ align:start position:0%
+cross-section TM of an undoped film and
+it's a little hard to see that didn't
+
+ align:start position:0%
+it's a little hard to see that didn't
+ 
+
+ align:start position:0%
+it's a little hard to see that didn't
+reproduce that well but you see the very
+
+ align:start position:0%
+reproduce that well but you see the very
+ 
+
+ align:start position:0%
+reproduce that well but you see the very
+columnar grain structure um these dark
+
+ align:start position:0%
+columnar grain structure um these dark
+ 
+
+ align:start position:0%
+columnar grain structure um these dark
+bands uh correspond to Regions where the
+
+ align:start position:0%
+bands uh correspond to Regions where the
+ 
+
+ align:start position:0%
+bands uh correspond to Regions where the
+Electron Beam is defract uh by the
+
+ align:start position:0%
+Electron Beam is defract uh by the
+ 
+
+ align:start position:0%
+Electron Beam is defract uh by the
+different Crystal orientations and and
+
+ align:start position:0%
+different Crystal orientations and and
+ 
+
+ align:start position:0%
+different Crystal orientations and and
+by uh grain
+
+ align:start position:0%
+by uh grain
+ 
+
+ align:start position:0%
+by uh grain
+boundaries um so in undoped film deposit
+
+ align:start position:0%
+boundaries um so in undoped film deposit
+ 
+
+ align:start position:0%
+boundaries um so in undoped film deposit
+of 625 in cross-section looks something
+
+ align:start position:0%
+of 625 in cross-section looks something
+ 
+
+ align:start position:0%
+of 625 in cross-section looks something
+like this a very CER grain structure
+
+ align:start position:0%
+like this a very CER grain structure
+ 
+
+ align:start position:0%
+like this a very CER grain structure
+with relatively small grain
+
+ align:start position:0%
+with relatively small grain
+ 
+
+ align:start position:0%
+with relatively small grain
+size um as deposited if it's heavily
+
+ align:start position:0%
+size um as deposited if it's heavily
+ 
+
+ align:start position:0%
+size um as deposited if it's heavily
+phosphorous dooped again um uh at 625 so
+
+ align:start position:0%
+phosphorous dooped again um uh at 625 so
+ 
+
+ align:start position:0%
+phosphorous dooped again um uh at 625 so
+still at very low temperature but very
+
+ align:start position:0%
+still at very low temperature but very
+ 
+
+ align:start position:0%
+still at very low temperature but very
+heavily phosphorous doped you see lots
+
+ align:start position:0%
+heavily phosphorous doped you see lots
+ 
+
+ align:start position:0%
+heavily phosphorous doped you see lots
+um the grains are more equ aied larger
+
+ align:start position:0%
+um the grains are more equ aied larger
+ 
+
+ align:start position:0%
+um the grains are more equ aied larger
+grain size so phosphorus is is is one of
+
+ align:start position:0%
+grain size so phosphorus is is is one of
+ 
+
+ align:start position:0%
+grain size so phosphorus is is is one of
+those doping uh those dopin that tends
+
+ align:start position:0%
+those doping uh those dopin that tends
+ 
+
+ align:start position:0%
+those doping uh those dopin that tends
+to cause secondary grain growth it
+
+ align:start position:0%
+to cause secondary grain growth it
+ 
+
+ align:start position:0%
+to cause secondary grain growth it
+causes the grains to grow quite large so
+
+ align:start position:0%
+causes the grains to grow quite large so
+ 
+
+ align:start position:0%
+causes the grains to grow quite large so
+you get a very different film morphology
+
+ align:start position:0%
+you get a very different film morphology
+ 
+
+ align:start position:0%
+you get a very different film morphology
+if you deposit it uh in situ uh dope say
+
+ align:start position:0%
+if you deposit it uh in situ uh dope say
+ 
+
+ align:start position:0%
+if you deposit it uh in situ uh dope say
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+phosphine the third one down is the
+
+ align:start position:0%
+phosphine the third one down is the
+ 
+
+ align:start position:0%
+phosphine the third one down is the
+undoped film so if you take film a here
+
+ align:start position:0%
+undoped film so if you take film a here
+ 
+
+ align:start position:0%
+undoped film so if you take film a here
+and heat treat it so you en knal it
+
+ align:start position:0%
+and heat treat it so you en knal it
+ 
+
+ align:start position:0%
+and heat treat it so you en knal it
+afterwards at a th000 degrees um you can
+
+ align:start position:0%
+afterwards at a th000 degrees um you can
+ 
+
+ align:start position:0%
+afterwards at a th000 degrees um you can
+see the grains are still columnar but
+
+ align:start position:0%
+see the grains are still columnar but
+ 
+
+ align:start position:0%
+see the grains are still columnar but
+they've grown see the the average grain
+
+ align:start position:0%
+they've grown see the the average grain
+ 
+
+ align:start position:0%
+they've grown see the the average grain
+size looks larger it's a little bit hard
+
+ align:start position:0%
+size looks larger it's a little bit hard
+ 
+
+ align:start position:0%
+size looks larger it's a little bit hard
+to tell in average grain size in
+
+ align:start position:0%
+to tell in average grain size in
+ 
+
+ align:start position:0%
+to tell in average grain size in
+cross-section you get that impression
+
+ align:start position:0%
+cross-section you get that impression
+ 
+
+ align:start position:0%
+cross-section you get that impression
+but look at look what also what has
+
+ align:start position:0%
+but look at look what also what has
+ 
+
+ align:start position:0%
+but look at look what also what has
+happened to the um surface as the grains
+
+ align:start position:0%
+happened to the um surface as the grains
+ 
+
+ align:start position:0%
+happened to the um surface as the grains
+grow um there's a certain amount of uh
+
+ align:start position:0%
+grow um there's a certain amount of uh
+ 
+
+ align:start position:0%
+grow um there's a certain amount of uh
+um induced surface roughness so that the
+
+ align:start position:0%
+um induced surface roughness so that the
+ 
+
+ align:start position:0%
+um induced surface roughness so that the
+the surface is much rougher um than it
+
+ align:start position:0%
+the surface is much rougher um than it
+ 
+
+ align:start position:0%
+the surface is much rougher um than it
+was in the as deposited case uh it's
+
+ align:start position:0%
+was in the as deposited case uh it's
+ 
+
+ align:start position:0%
+was in the as deposited case uh it's
+typical of course to anal a polysilicon
+
+ align:start position:0%
+typical of course to anal a polysilicon
+ 
+
+ align:start position:0%
+typical of course to anal a polysilicon
+film during the sore strain analing or
+
+ align:start position:0%
+film during the sore strain analing or
+ 
+
+ align:start position:0%
+film during the sore strain analing or
+whatever to activate dopic so that's
+
+ align:start position:0%
+whatever to activate dopic so that's
+ 
+
+ align:start position:0%
+whatever to activate dopic so that's
+this is more like it what it might look
+
+ align:start position:0%
+this is more like it what it might look
+ 
+
+ align:start position:0%
+this is more like it what it might look
+like in in in a gate
+
+ align:start position:0%
+like in in in a gate
+ 
+
+ align:start position:0%
+like in in in a gate
+material and um the last one is one that
+
+ align:start position:0%
+material and um the last one is one that
+ 
+
+ align:start position:0%
+material and um the last one is one that
+was um in such a dope so it's filmed B
+
+ align:start position:0%
+was um in such a dope so it's filmed B
+ 
+
+ align:start position:0%
+was um in such a dope so it's filmed B
+but it was also um analed up at a th000
+
+ align:start position:0%
+but it was also um analed up at a th000
+ 
+
+ align:start position:0%
+but it was also um analed up at a th000
+deg c um so look at the big difference
+
+ align:start position:0%
+deg c um so look at the big difference
+ 
+
+ align:start position:0%
+deg c um so look at the big difference
+both both of these films uh deposit at
+
+ align:start position:0%
+both both of these films uh deposit at
+ 
+
+ align:start position:0%
+both both of these films uh deposit at
+625 and both in at 1,00 C the real big
+
+ align:start position:0%
+625 and both in at 1,00 C the real big
+ 
+
+ align:start position:0%
+625 and both in at 1,00 C the real big
+difference is this film is phosphor
+
+ align:start position:0%
+difference is this film is phosphor
+ 
+
+ align:start position:0%
+difference is this film is phosphor
+stoped very large grains in fact um if
+
+ align:start position:0%
+stoped very large grains in fact um if
+ 
+
+ align:start position:0%
+stoped very large grains in fact um if
+you take a thin film course in Material
+
+ align:start position:0%
+you take a thin film course in Material
+ 
+
+ align:start position:0%
+you take a thin film course in Material
+Science one of Carl Thompson's courses
+
+ align:start position:0%
+Science one of Carl Thompson's courses
+ 
+
+ align:start position:0%
+Science one of Carl Thompson's courses
+or whatever you'll study this um the
+
+ align:start position:0%
+or whatever you'll study this um the
+ 
+
+ align:start position:0%
+or whatever you'll study this um the
+thermodynamics of this much more
+
+ align:start position:0%
+thermodynamics of this much more
+ 
+
+ align:start position:0%
+thermodynamics of this much more
+carefully but basically it turns out
+
+ align:start position:0%
+carefully but basically it turns out
+ 
+
+ align:start position:0%
+carefully but basically it turns out
+that the grains tend to grow laterally
+
+ align:start position:0%
+that the grains tend to grow laterally
+ 
+
+ align:start position:0%
+that the grains tend to grow laterally
+to about the same size as their as their
+
+ align:start position:0%
+to about the same size as their as their
+ 
+
+ align:start position:0%
+to about the same size as their as their
+film as the the thickness of the film so
+
+ align:start position:0%
+film as the the thickness of the film so
+ 
+
+ align:start position:0%
+film as the the thickness of the film so
+the average gr you know the thickness of
+
+ align:start position:0%
+the average gr you know the thickness of
+ 
+
+ align:start position:0%
+the average gr you know the thickness of
+this film is about half Micron the
+
+ align:start position:0%
+this film is about half Micron the
+ 
+
+ align:start position:0%
+this film is about half Micron the
+average grain size ends up being uh in
+
+ align:start position:0%
+average grain size ends up being uh in
+ 
+
+ align:start position:0%
+average grain size ends up being uh in
+these large grain films about half
+
+ align:start position:0%
+these large grain films about half
+ 
+
+ align:start position:0%
+these large grain films about half
+Micron um and so so it's phosphorus the
+
+ align:start position:0%
+Micron um and so so it's phosphorus the
+ 
+
+ align:start position:0%
+Micron um and so so it's phosphorus the
+presence of a dopen really accelerates
+
+ align:start position:0%
+presence of a dopen really accelerates
+ 
+
+ align:start position:0%
+presence of a dopen really accelerates
+um the grain growth and you get a very
+
+ align:start position:0%
+um the grain growth and you get a very
+ 
+
+ align:start position:0%
+um the grain growth and you get a very
+different uh morphology
+
+ align:start position:0%
+different uh morphology
+ 
+
+ align:start position:0%
+different uh morphology
+film okay so uh let's go on to slide uh
+
+ align:start position:0%
+film okay so uh let's go on to slide uh
+ 
+
+ align:start position:0%
+film okay so uh let's go on to slide uh
+seven why do we care about all that why
+
+ align:start position:0%
+seven why do we care about all that why
+ 
+
+ align:start position:0%
+seven why do we care about all that why
+why did we go through all that well the
+
+ align:start position:0%
+why did we go through all that well the
+ 
+
+ align:start position:0%
+why did we go through all that well the
+grain structure as it turns out is
+
+ align:start position:0%
+grain structure as it turns out is
+ 
+
+ align:start position:0%
+grain structure as it turns out is
+critical in determining the properties
+
+ align:start position:0%
+critical in determining the properties
+ 
+
+ align:start position:0%
+critical in determining the properties
+of diffusion of dopus through
+
+ align:start position:0%
+of diffusion of dopus through
+ 
+
+ align:start position:0%
+of diffusion of dopus through
+polycrystal and silicon and also in
+
+ align:start position:0%
+polycrystal and silicon and also in
+ 
+
+ align:start position:0%
+polycrystal and silicon and also in
+determining the final resistivity of the
+
+ align:start position:0%
+determining the final resistivity of the
+ 
+
+ align:start position:0%
+determining the final resistivity of the
+film now uh I don't know if anyone
+
+ align:start position:0%
+film now uh I don't know if anyone
+ 
+
+ align:start position:0%
+film now uh I don't know if anyone
+signed up for it but on the clipboard uh
+
+ align:start position:0%
+signed up for it but on the clipboard uh
+ 
+
+ align:start position:0%
+signed up for it but on the clipboard uh
+one of the topics that you uh I had open
+
+ align:start position:0%
+one of the topics that you uh I had open
+ 
+
+ align:start position:0%
+one of the topics that you uh I had open
+for to do a final report on is diffusion
+
+ align:start position:0%
+for to do a final report on is diffusion
+ 
+
+ align:start position:0%
+for to do a final report on is diffusion
+uh or Andor dopen activation in
+
+ align:start position:0%
+uh or Andor dopen activation in
+ 
+
+ align:start position:0%
+uh or Andor dopen activation in
+polycrystal and silicon I'm not going to
+
+ align:start position:0%
+polycrystal and silicon I'm not going to
+ 
+
+ align:start position:0%
+polycrystal and silicon I'm not going to
+talk about it in great detail in the
+
+ align:start position:0%
+talk about it in great detail in the
+ 
+
+ align:start position:0%
+talk about it in great detail in the
+course diffusion through poly Crystal
+
+ align:start position:0%
+course diffusion through poly Crystal
+ 
+
+ align:start position:0%
+course diffusion through poly Crystal
+and silicon is quite different than what
+
+ align:start position:0%
+and silicon is quite different than what
+ 
+
+ align:start position:0%
+and silicon is quite different than what
+we've talked about diffusion in single
+
+ align:start position:0%
+we've talked about diffusion in single
+ 
+
+ align:start position:0%
+we've talked about diffusion in single
+Crystal silicon because in poly silic
+
+ align:start position:0%
+Crystal silicon because in poly silic
+ 
+
+ align:start position:0%
+Crystal silicon because in poly silic
+the dopin can diffuse along the grain
+
+ align:start position:0%
+the dopin can diffuse along the grain
+ 
+
+ align:start position:0%
+the dopin can diffuse along the grain
+boundaries look at this this is a an
+
+ align:start position:0%
+boundaries look at this this is a an
+ 
+
+ align:start position:0%
+boundaries look at this this is a an
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+uh uh up here in the um labeled B called
+
+ align:start position:0%
+uh uh up here in the um labeled B called
+ 
+
+ align:start position:0%
+uh uh up here in the um labeled B called
+the col migraines the uh the dopant a
+
+ align:start position:0%
+the col migraines the uh the dopant a
+ 
+
+ align:start position:0%
+the col migraines the uh the dopant a
+lot of them like arsenic diffuse very
+
+ align:start position:0%
+lot of them like arsenic diffuse very
+ 
+
+ align:start position:0%
+lot of them like arsenic diffuse very
+rapidly down grain boundaries they can
+
+ align:start position:0%
+rapidly down grain boundaries they can
+ 
+
+ align:start position:0%
+rapidly down grain boundaries they can
+also diffuse more slowly in the grains
+
+ align:start position:0%
+also diffuse more slowly in the grains
+ 
+
+ align:start position:0%
+also diffuse more slowly in the grains
+um so you can imagine that the diffusion
+
+ align:start position:0%
+um so you can imagine that the diffusion
+ 
+
+ align:start position:0%
+um so you can imagine that the diffusion
+of dopin in in this uh Cartoon labeled B
+
+ align:start position:0%
+of dopin in in this uh Cartoon labeled B
+ 
+
+ align:start position:0%
+of dopin in in this uh Cartoon labeled B
+here on the upper left it's going to be
+
+ align:start position:0%
+here on the upper left it's going to be
+ 
+
+ align:start position:0%
+here on the upper left it's going to be
+quite different from the one labeled a a
+
+ align:start position:0%
+quite different from the one labeled a a
+ 
+
+ align:start position:0%
+quite different from the one labeled a a
+you have more random grain structure
+
+ align:start position:0%
+you have more random grain structure
+ 
+
+ align:start position:0%
+you have more random grain structure
+looks more like a a brick wall so the
+
+ align:start position:0%
+looks more like a a brick wall so the
+ 
+
+ align:start position:0%
+looks more like a a brick wall so the
+diffusivity is going to be very
+
+ align:start position:0%
+diffusivity is going to be very
+ 
+
+ align:start position:0%
+diffusivity is going to be very
+different in this structure
+
+ align:start position:0%
+different in this structure
+ 
+
+ align:start position:0%
+different in this structure
+um to get the dopin from down from the
+
+ align:start position:0%
+um to get the dopin from down from the
+ 
+
+ align:start position:0%
+um to get the dopin from down from the
+top down to the bottom um it's going to
+
+ align:start position:0%
+top down to the bottom um it's going to
+ 
+
+ align:start position:0%
+top down to the bottom um it's going to
+be quite different why do we care about
+
+ align:start position:0%
+be quite different why do we care about
+ 
+
+ align:start position:0%
+be quite different why do we care about
+that well polysilicon is the gate
+
+ align:start position:0%
+that well polysilicon is the gate
+ 
+
+ align:start position:0%
+that well polysilicon is the gate
+material right uh in seamoss until we
+
+ align:start position:0%
+material right uh in seamoss until we
+ 
+
+ align:start position:0%
+material right uh in seamoss until we
+get to metal gates of course metal gates
+
+ align:start position:0%
+get to metal gates of course metal gates
+ 
+
+ align:start position:0%
+get to metal gates of course metal gates
+are coming very quickly but for the last
+
+ align:start position:0%
+are coming very quickly but for the last
+ 
+
+ align:start position:0%
+are coming very quickly but for the last
+30 years or 25 years polyan has been the
+
+ align:start position:0%
+30 years or 25 years polyan has been the
+ 
+
+ align:start position:0%
+30 years or 25 years polyan has been the
+gate material uh typically how it's
+
+ align:start position:0%
+gate material uh typically how it's
+ 
+
+ align:start position:0%
+gate material uh typically how it's
+doped is it's put down in an undoped
+
+ align:start position:0%
+doped is it's put down in an undoped
+ 
+
+ align:start position:0%
+doped is it's put down in an undoped
+State and then it's Ina planted in the
+
+ align:start position:0%
+State and then it's Ina planted in the
+ 
+
+ align:start position:0%
+State and then it's Ina planted in the
+nearest surface region and then you do a
+
+ align:start position:0%
+nearest surface region and then you do a
+ 
+
+ align:start position:0%
+nearest surface region and then you do a
+high temperature anal typically during
+
+ align:start position:0%
+high temperature anal typically during
+ 
+
+ align:start position:0%
+high temperature anal typically during
+the s drain andal or maybe a separate
+
+ align:start position:0%
+the s drain andal or maybe a separate
+ 
+
+ align:start position:0%
+the s drain andal or maybe a separate
+one in which you hope that you try to
+
+ align:start position:0%
+one in which you hope that you try to
+ 
+
+ align:start position:0%
+one in which you hope that you try to
+get these dopin down from the surface
+
+ align:start position:0%
+get these dopin down from the surface
+ 
+
+ align:start position:0%
+get these dopin down from the surface
+all the way down to the
+
+ align:start position:0%
+all the way down to the
+ 
+
+ align:start position:0%
+all the way down to the
+interface um with the with the oxide to
+
+ align:start position:0%
+interface um with the with the oxide to
+ 
+
+ align:start position:0%
+interface um with the with the oxide to
+form the gate if I don't get all the
+
+ align:start position:0%
+form the gate if I don't get all the
+ 
+
+ align:start position:0%
+form the gate if I don't get all the
+dopin down there you're in deep trouble
+
+ align:start position:0%
+dopin down there you're in deep trouble
+ 
+
+ align:start position:0%
+dopin down there you're in deep trouble
+we in deep trouble because poly silicon
+
+ align:start position:0%
+we in deep trouble because poly silicon
+ 
+
+ align:start position:0%
+we in deep trouble because poly silicon
+then no longer acts metallic if it's not
+
+ align:start position:0%
+then no longer acts metallic if it's not
+ 
+
+ align:start position:0%
+then no longer acts metallic if it's not
+heavily doped in fact it'll deplete
+
+ align:start position:0%
+heavily doped in fact it'll deplete
+ 
+
+ align:start position:0%
+heavily doped in fact it'll deplete
+under gate bias and you'll end up with
+
+ align:start position:0%
+under gate bias and you'll end up with
+ 
+
+ align:start position:0%
+under gate bias and you'll end up with
+with something called gate depletion and
+
+ align:start position:0%
+with something called gate depletion and
+ 
+
+ align:start position:0%
+with something called gate depletion and
+it will not act as a good metallic like
+
+ align:start position:0%
+it will not act as a good metallic like
+ 
+
+ align:start position:0%
+it will not act as a good metallic like
+electrode so how you put the poly silic
+
+ align:start position:0%
+electrode so how you put the poly silic
+ 
+
+ align:start position:0%
+electrode so how you put the poly silic
+down is very critical because it
+
+ align:start position:0%
+down is very critical because it
+ 
+
+ align:start position:0%
+down is very critical because it
+determines um how the dope it's diffuse
+
+ align:start position:0%
+determines um how the dope it's diffuse
+ 
+
+ align:start position:0%
+determines um how the dope it's diffuse
+through it how well they activate uh so
+
+ align:start position:0%
+through it how well they activate uh so
+ 
+
+ align:start position:0%
+through it how well they activate uh so
+the temperature that you use is uh is is
+
+ align:start position:0%
+the temperature that you use is uh is is
+ 
+
+ align:start position:0%
+the temperature that you use is uh is is
+very important um and here's just an
+
+ align:start position:0%
+very important um and here's just an
+ 
+
+ align:start position:0%
+very important um and here's just an
+example of now this is a planer view so
+
+ align:start position:0%
+example of now this is a planer view so
+ 
+
+ align:start position:0%
+example of now this is a planer view so
+in this case you're looking down on the
+
+ align:start position:0%
+in this case you're looking down on the
+ 
+
+ align:start position:0%
+in this case you're looking down on the
+top of the film again it's transmission
+
+ align:start position:0%
+top of the film again it's transmission
+ 
+
+ align:start position:0%
+top of the film again it's transmission
+electron micrograph but plan view uh
+
+ align:start position:0%
+electron micrograph but plan view uh
+ 
+
+ align:start position:0%
+electron micrograph but plan view uh
+this is about 400 nanometers thick um
+
+ align:start position:0%
+this is about 400 nanometers thick um
+ 
+
+ align:start position:0%
+this is about 400 nanometers thick um
+and these are all phosphorous dope films
+
+ align:start position:0%
+and these are all phosphorous dope films
+ 
+
+ align:start position:0%
+and these are all phosphorous dope films
+again I'm showing the enhancement in the
+
+ align:start position:0%
+again I'm showing the enhancement in the
+ 
+
+ align:start position:0%
+again I'm showing the enhancement in the
+growth rate of the grains with
+
+ align:start position:0%
+growth rate of the grains with
+ 
+
+ align:start position:0%
+growth rate of the grains with
+phosphorus these are all annealed at a
+
+ align:start position:0%
+phosphorus these are all annealed at a
+ 
+
+ align:start position:0%
+phosphorus these are all annealed at a
+th000 this one has an average doping of
+
+ align:start position:0%
+th000 this one has an average doping of
+ 
+
+ align:start position:0%
+th000 this one has an average doping of
+about20 um micrograph B the sample has
+
+ align:start position:0%
+about20 um micrograph B the sample has
+ 
+
+ align:start position:0%
+about20 um micrograph B the sample has
+about 2 and a half E20 and micrograph C
+
+ align:start position:0%
+about 2 and a half E20 and micrograph C
+ 
+
+ align:start position:0%
+about 2 and a half E20 and micrograph C
+is about 7 and a halftimes 10 of 20 you
+
+ align:start position:0%
+is about 7 and a halftimes 10 of 20 you
+ 
+
+ align:start position:0%
+is about 7 and a halftimes 10 of 20 you
+can see how large uh again you have uh
+
+ align:start position:0%
+can see how large uh again you have uh
+ 
+
+ align:start position:0%
+can see how large uh again you have uh
+large grains on the order of half Micron
+
+ align:start position:0%
+large grains on the order of half Micron
+ 
+
+ align:start position:0%
+large grains on the order of half Micron
+to a micron here in grain
+
+ align:start position:0%
+to a micron here in grain
+ 
+
+ align:start position:0%
+to a micron here in grain
+size um so phosphorous doping can really
+
+ align:start position:0%
+size um so phosphorous doping can really
+ 
+
+ align:start position:0%
+size um so phosphorous doping can really
+um accelerate the grain
+
+ align:start position:0%
+um accelerate the grain
+ 
+
+ align:start position:0%
+um accelerate the grain
+growth how about uh on slide eight how
+
+ align:start position:0%
+growth how about uh on slide eight how
+ 
+
+ align:start position:0%
+growth how about uh on slide eight how
+about film resistance ity and besides
+
+ align:start position:0%
+about film resistance ity and besides
+ 
+
+ align:start position:0%
+about film resistance ity and besides
+the fact that so I need to I mentioned
+
+ align:start position:0%
+the fact that so I need to I mentioned
+ 
+
+ align:start position:0%
+the fact that so I need to I mentioned
+to you we need to get the dop that are
+
+ align:start position:0%
+to you we need to get the dop that are
+ 
+
+ align:start position:0%
+to you we need to get the dop that are
+implanted at the top of the poly down to
+
+ align:start position:0%
+implanted at the top of the poly down to
+ 
+
+ align:start position:0%
+implanted at the top of the poly down to
+the gate oxide uh interface otherwise
+
+ align:start position:0%
+the gate oxide uh interface otherwise
+ 
+
+ align:start position:0%
+the gate oxide uh interface otherwise
+we're not going to have a good uh
+
+ align:start position:0%
+we're not going to have a good uh
+ 
+
+ align:start position:0%
+we're not going to have a good uh
+polycrystal electrode going to have gate
+
+ align:start position:0%
+polycrystal electrode going to have gate
+ 
+
+ align:start position:0%
+polycrystal electrode going to have gate
+depletion and your mosfet won't work uh
+
+ align:start position:0%
+depletion and your mosfet won't work uh
+ 
+
+ align:start position:0%
+depletion and your mosfet won't work uh
+but there's other requirements we also
+
+ align:start position:0%
+but there's other requirements we also
+ 
+
+ align:start position:0%
+but there's other requirements we also
+care about the sheet resistance or the
+
+ align:start position:0%
+care about the sheet resistance or the
+ 
+
+ align:start position:0%
+care about the sheet resistance or the
+resistivity of the poly
+
+ align:start position:0%
+resistivity of the poly
+ 
+
+ align:start position:0%
+resistivity of the poly
+itself um uh particularly for uh some
+
+ align:start position:0%
+itself um uh particularly for uh some
+ 
+
+ align:start position:0%
+itself um uh particularly for uh some
+high frequency applications so this this
+
+ align:start position:0%
+high frequency applications so this this
+ 
+
+ align:start position:0%
+high frequency applications so this this
+is a plot I also took from Ted cayman's
+
+ align:start position:0%
+is a plot I also took from Ted cayman's
+ 
+
+ align:start position:0%
+is a plot I also took from Ted cayman's
+book of um resistivity now in ohm
+
+ align:start position:0%
+book of um resistivity now in ohm
+ 
+
+ align:start position:0%
+book of um resistivity now in ohm
+centimeter as a function of dopen
+
+ align:start position:0%
+centimeter as a function of dopen
+ 
+
+ align:start position:0%
+centimeter as a function of dopen
+concentration uh in in polysilicon this
+
+ align:start position:0%
+concentration uh in in polysilicon this
+ 
+
+ align:start position:0%
+concentration uh in in polysilicon this
+is these films were all um Iron
+
+ align:start position:0%
+is these films were all um Iron
+ 
+
+ align:start position:0%
+is these films were all um Iron
+implanted with these dopant uh and in
+
+ align:start position:0%
+implanted with these dopant uh and in
+ 
+
+ align:start position:0%
+implanted with these dopant uh and in
+the Neel at a th000 degrees C U so it
+
+ align:start position:0%
+the Neel at a th000 degrees C U so it
+ 
+
+ align:start position:0%
+the Neel at a th000 degrees C U so it
+gives you a rough idea of what happens
+
+ align:start position:0%
+gives you a rough idea of what happens
+ 
+
+ align:start position:0%
+gives you a rough idea of what happens
+if you were to do a a reasonable uh job
+
+ align:start position:0%
+if you were to do a a reasonable uh job
+ 
+
+ align:start position:0%
+if you were to do a a reasonable uh job
+of ion planning and analing and you can
+
+ align:start position:0%
+of ion planning and analing and you can
+ 
+
+ align:start position:0%
+of ion planning and analing and you can
+see the Boron and the Arsenic
+
+ align:start position:0%
+see the Boron and the Arsenic
+ 
+
+ align:start position:0%
+see the Boron and the Arsenic
+phosphorous they all kind of come down
+
+ align:start position:0%
+phosphorous they all kind of come down
+ 
+
+ align:start position:0%
+phosphorous they all kind of come down
+here um and so as you increase the
+
+ align:start position:0%
+here um and so as you increase the
+ 
+
+ align:start position:0%
+here um and so as you increase the
+doping concentration the recessivity
+
+ align:start position:0%
+doping concentration the recessivity
+ 
+
+ align:start position:0%
+doping concentration the recessivity
+drops but all of a sudden it sort of
+
+ align:start position:0%
+drops but all of a sudden it sort of
+ 
+
+ align:start position:0%
+drops but all of a sudden it sort of
+plateaus out so above about one20 or 2
+
+ align:start position:0%
+plateaus out so above about one20 or 2
+ 
+
+ align:start position:0%
+plateaus out so above about one20 or 2
+E20 Arsenic and Bor do poly they they
+
+ align:start position:0%
+E20 Arsenic and Bor do poly they they
+ 
+
+ align:start position:0%
+E20 Arsenic and Bor do poly they they
+sort of flatten out here um at at a
+
+ align:start position:0%
+sort of flatten out here um at at a
+ 
+
+ align:start position:0%
+sort of flatten out here um at at a
+certain uh resistivity and a couple
+
+ align:start position:0%
+certain uh resistivity and a couple
+ 
+
+ align:start position:0%
+certain uh resistivity and a couple
+hundred uh um micro
+
+ align:start position:0%
+hundred uh um micro
+ 
+
+ align:start position:0%
+hundred uh um micro
+centimeter or a couple thousand I'm
+
+ align:start position:0%
+centimeter or a couple thousand I'm
+ 
+
+ align:start position:0%
+centimeter or a couple thousand I'm
+sorry so this this around 2,000 micro
+
+ align:start position:0%
+sorry so this this around 2,000 micro
+ 
+
+ align:start position:0%
+sorry so this this around 2,000 micro
+centimeter which is still pretty high
+
+ align:start position:0%
+centimeter which is still pretty high
+ 
+
+ align:start position:0%
+centimeter which is still pretty high
+resistivity if you use phosphorus you're
+
+ align:start position:0%
+resistivity if you use phosphorus you're
+ 
+
+ align:start position:0%
+resistivity if you use phosphorus you're
+in a little better shape um you can
+
+ align:start position:0%
+in a little better shape um you can
+ 
+
+ align:start position:0%
+in a little better shape um you can
+continue uh getting the resistivity down
+
+ align:start position:0%
+continue uh getting the resistivity down
+ 
+
+ align:start position:0%
+continue uh getting the resistivity down
+as and it plateaus somewhere above 510
+
+ align:start position:0%
+as and it plateaus somewhere above 510
+ 
+
+ align:start position:0%
+as and it plateaus somewhere above 510
+of a 20 it plateaus around 400 uh micro
+
+ align:start position:0%
+of a 20 it plateaus around 400 uh micro
+ 
+
+ align:start position:0%
+of a 20 it plateaus around 400 uh micro
+ohm centimeter um so if you need to get
+
+ align:start position:0%
+ohm centimeter um so if you need to get
+ 
+
+ align:start position:0%
+ohm centimeter um so if you need to get
+the lowest resistivity phosphorus is um
+
+ align:start position:0%
+the lowest resistivity phosphorus is um
+ 
+
+ align:start position:0%
+the lowest resistivity phosphorus is um
+a good doent to use and it activates um
+
+ align:start position:0%
+a good doent to use and it activates um
+ 
+
+ align:start position:0%
+a good doent to use and it activates um
+pretty well so the conduction mechanism
+
+ align:start position:0%
+pretty well so the conduction mechanism
+ 
+
+ align:start position:0%
+pretty well so the conduction mechanism
+as you can imagine and if you go through
+
+ align:start position:0%
+as you can imagine and if you go through
+ 
+
+ align:start position:0%
+as you can imagine and if you go through
+Ted cayman's book The conduction of of
+
+ align:start position:0%
+Ted cayman's book The conduction of of
+ 
+
+ align:start position:0%
+Ted cayman's book The conduction of of
+current in polycrystal Silicon is going
+
+ align:start position:0%
+current in polycrystal Silicon is going
+ 
+
+ align:start position:0%
+current in polycrystal Silicon is going
+to be very different from that in single
+
+ align:start position:0%
+to be very different from that in single
+ 
+
+ align:start position:0%
+to be very different from that in single
+Crystal because one thing you're going
+
+ align:start position:0%
+Crystal because one thing you're going
+ 
+
+ align:start position:0%
+Crystal because one thing you're going
+through if you go back just go back one
+
+ align:start position:0%
+through if you go back just go back one
+ 
+
+ align:start position:0%
+through if you go back just go back one
+slide you can imagine I'm I'm I've got
+
+ align:start position:0%
+slide you can imagine I'm I'm I've got
+ 
+
+ align:start position:0%
+slide you can imagine I'm I'm I've got
+uh a current passing through either th
+
+ align:start position:0%
+uh a current passing through either th
+ 
+
+ align:start position:0%
+uh a current passing through either th
+this film or this film there are all
+
+ align:start position:0%
+this film or this film there are all
+ 
+
+ align:start position:0%
+this film or this film there are all
+these grain boundaries that the carriers
+
+ align:start position:0%
+these grain boundaries that the carriers
+ 
+
+ align:start position:0%
+these grain boundaries that the carriers
+end up going through uh the grain
+
+ align:start position:0%
+end up going through uh the grain
+ 
+
+ align:start position:0%
+end up going through uh the grain
+boundaries are regions of very imperfect
+
+ align:start position:0%
+boundaries are regions of very imperfect
+ 
+
+ align:start position:0%
+boundaries are regions of very imperfect
+crystall and uh um uh quality you can
+
+ align:start position:0%
+crystall and uh um uh quality you can
+ 
+
+ align:start position:0%
+crystall and uh um uh quality you can
+get scattering off of grain boundaries
+
+ align:start position:0%
+get scattering off of grain boundaries
+ 
+
+ align:start position:0%
+get scattering off of grain boundaries
+uh the scattering rate can depend on the
+
+ align:start position:0%
+uh the scattering rate can depend on the
+ 
+
+ align:start position:0%
+uh the scattering rate can depend on the
+um amount of dopin that segregates the
+
+ align:start position:0%
+um amount of dopin that segregates the
+ 
+
+ align:start position:0%
+um amount of dopin that segregates the
+grain boundary so there's a whole lot of
+
+ align:start position:0%
+grain boundary so there's a whole lot of
+ 
+
+ align:start position:0%
+grain boundary so there's a whole lot of
+information that you really need to
+
+ align:start position:0%
+information that you really need to
+ 
+
+ align:start position:0%
+information that you really need to
+understand if you want to understand the
+
+ align:start position:0%
+understand if you want to understand the
+ 
+
+ align:start position:0%
+understand if you want to understand the
+resistivity um and diffusion of dopin in
+
+ align:start position:0%
+resistivity um and diffusion of dopin in
+ 
+
+ align:start position:0%
+resistivity um and diffusion of dopin in
+polycrystal and silicon we don't have
+
+ align:start position:0%
+polycrystal and silicon we don't have
+ 
+
+ align:start position:0%
+polycrystal and silicon we don't have
+time in this class but I just wanted to
+
+ align:start position:0%
+time in this class but I just wanted to
+ 
+
+ align:start position:0%
+time in this class but I just wanted to
+make you aware um and Ted cayman's book
+
+ align:start position:0%
+make you aware um and Ted cayman's book
+ 
+
+ align:start position:0%
+make you aware um and Ted cayman's book
+is a good reference uh he's got a couple
+
+ align:start position:0%
+is a good reference uh he's got a couple
+ 
+
+ align:start position:0%
+is a good reference uh he's got a couple
+of chapters uh on that topic if you're
+
+ align:start position:0%
+of chapters uh on that topic if you're
+ 
+
+ align:start position:0%
+of chapters uh on that topic if you're
+interested okay so that's poly crystall
+
+ align:start position:0%
+interested okay so that's poly crystall
+ 
+
+ align:start position:0%
+interested okay so that's poly crystall
+and silicon and it's again it's it's
+
+ align:start position:0%
+and silicon and it's again it's it's
+ 
+
+ align:start position:0%
+and silicon and it's again it's it's
+commonly deposited pretty much every Fab
+
+ align:start position:0%
+commonly deposited pretty much every Fab
+ 
+
+ align:start position:0%
+commonly deposited pretty much every Fab
+just by simple low pressure um
+
+ align:start position:0%
+just by simple low pressure um
+ 
+
+ align:start position:0%
+just by simple low pressure um
+cvd um on slide nine now I want to go on
+
+ align:start position:0%
+cvd um on slide nine now I want to go on
+ 
+
+ align:start position:0%
+cvd um on slide nine now I want to go on
+to um plasma enhanced CBD and and just
+
+ align:start position:0%
+to um plasma enhanced CBD and and just
+ 
+
+ align:start position:0%
+to um plasma enhanced CBD and and just
+show you some examples of of those
+
+ align:start position:0%
+show you some examples of of those
+ 
+
+ align:start position:0%
+show you some examples of of those
+reactors and how works and again the
+
+ align:start position:0%
+reactors and how works and again the
+ 
+
+ align:start position:0%
+reactors and how works and again the
+acronym here is pcbd the idea why do I
+
+ align:start position:0%
+acronym here is pcbd the idea why do I
+ 
+
+ align:start position:0%
+acronym here is pcbd the idea why do I
+want to use a
+
+ align:start position:0%
+want to use a
+ 
+
+ align:start position:0%
+want to use a
+plasma why would I want to use a plasma
+
+ align:start position:0%
+plasma why would I want to use a plasma
+ 
+
+ align:start position:0%
+plasma why would I want to use a plasma
+well um we we want to enter we want to
+
+ align:start position:0%
+well um we we want to enter we want to
+ 
+
+ align:start position:0%
+well um we we want to enter we want to
+um uh give to the system some kind of
+
+ align:start position:0%
+um uh give to the system some kind of
+ 
+
+ align:start position:0%
+um uh give to the system some kind of
+non-thermal energy uh which is the
+
+ align:start position:0%
+non-thermal energy uh which is the
+ 
+
+ align:start position:0%
+non-thermal energy uh which is the
+plasma energy in order to enhance the
+
+ align:start position:0%
+plasma energy in order to enhance the
+ 
+
+ align:start position:0%
+plasma energy in order to enhance the
+process so it'll go faster uh at lower
+
+ align:start position:0%
+process so it'll go faster uh at lower
+ 
+
+ align:start position:0%
+process so it'll go faster uh at lower
+temperatures um so we get enhanced dep
+
+ align:start position:0%
+temperatures um so we get enhanced dep
+ 
+
+ align:start position:0%
+temperatures um so we get enhanced dep
+rate at at low temperatures uh and this
+
+ align:start position:0%
+rate at at low temperatures uh and this
+ 
+
+ align:start position:0%
+rate at at low temperatures uh and this
+is a typical sort of reactor if you want
+
+ align:start position:0%
+is a typical sort of reactor if you want
+ 
+
+ align:start position:0%
+is a typical sort of reactor if you want
+a canonical plasma a simple DC pla or
+
+ align:start position:0%
+a canonical plasma a simple DC pla or
+ 
+
+ align:start position:0%
+a canonical plasma a simple DC pla or
+plasma reactor actually it's got an RF
+
+ align:start position:0%
+plasma reactor actually it's got an RF
+ 
+
+ align:start position:0%
+plasma reactor actually it's got an RF
+input here so there are two electrodes
+
+ align:start position:0%
+input here so there are two electrodes
+ 
+
+ align:start position:0%
+input here so there are two electrodes
+one at the top one at the bottom the
+
+ align:start position:0%
+one at the top one at the bottom the
+ 
+
+ align:start position:0%
+one at the top one at the bottom the
+Wafers sit on one of the electrodes um
+
+ align:start position:0%
+Wafers sit on one of the electrodes um
+ 
+
+ align:start position:0%
+Wafers sit on one of the electrodes um
+there is a plasma here in between and
+
+ align:start position:0%
+there is a plasma here in between and
+ 
+
+ align:start position:0%
+there is a plasma here in between and
+this plasma consists of um electrons
+
+ align:start position:0%
+this plasma consists of um electrons
+ 
+
+ align:start position:0%
+this plasma consists of um electrons
+ionized molecules who have neutral uh
+
+ align:start position:0%
+ionized molecules who have neutral uh
+ 
+
+ align:start position:0%
+ionized molecules who have neutral uh
+neutral species neutral molecules
+
+ align:start position:0%
+neutral species neutral molecules
+ 
+
+ align:start position:0%
+neutral species neutral molecules
+neutral and ionized fragments of broken
+
+ align:start position:0%
+neutral and ionized fragments of broken
+ 
+
+ align:start position:0%
+neutral and ionized fragments of broken
+up molecules um excited molecules and
+
+ align:start position:0%
+up molecules um excited molecules and
+ 
+
+ align:start position:0%
+up molecules um excited molecules and
+free radicals so there's a lot of things
+
+ align:start position:0%
+free radicals so there's a lot of things
+ 
+
+ align:start position:0%
+free radicals so there's a lot of things
+present in the plasma that are not there
+
+ align:start position:0%
+present in the plasma that are not there
+ 
+
+ align:start position:0%
+present in the plasma that are not there
+if I'm just flowing siline if I'm
+
+ align:start position:0%
+if I'm just flowing siline if I'm
+ 
+
+ align:start position:0%
+if I'm just flowing siline if I'm
+flowing siline and the Plasma's off what
+
+ align:start position:0%
+flowing siline and the Plasma's off what
+ 
+
+ align:start position:0%
+flowing siline and the Plasma's off what
+do I have in the reactor I have silene
+
+ align:start position:0%
+do I have in the reactor I have silene
+ 
+
+ align:start position:0%
+do I have in the reactor I have silene
+okay but if I'm flowing sine in the
+
+ align:start position:0%
+okay but if I'm flowing sine in the
+ 
+
+ align:start position:0%
+okay but if I'm flowing sine in the
+Plasma's on I can break up this molecule
+
+ align:start position:0%
+Plasma's on I can break up this molecule
+ 
+
+ align:start position:0%
+Plasma's on I can break up this molecule
+into all different uh subcomponents some
+
+ align:start position:0%
+into all different uh subcomponents some
+ 
+
+ align:start position:0%
+into all different uh subcomponents some
+of which are highly reactive um and
+
+ align:start position:0%
+of which are highly reactive um and
+ 
+
+ align:start position:0%
+of which are highly reactive um and
+therefore the deposition rate of the
+
+ align:start position:0%
+therefore the deposition rate of the
+ 
+
+ align:start position:0%
+therefore the deposition rate of the
+surface will be dramatically impacted by
+
+ align:start position:0%
+surface will be dramatically impacted by
+ 
+
+ align:start position:0%
+surface will be dramatically impacted by
+the presence uh of of this plasma so
+
+ align:start position:0%
+the presence uh of of this plasma so
+ 
+
+ align:start position:0%
+the presence uh of of this plasma so
+here's sort of a a canonical uh plasma
+
+ align:start position:0%
+here's sort of a a canonical uh plasma
+ 
+
+ align:start position:0%
+here's sort of a a canonical uh plasma
+system and there is a heer here that
+
+ align:start position:0%
+system and there is a heer here that
+ 
+
+ align:start position:0%
+system and there is a heer here that
+would typically uh because you need to
+
+ align:start position:0%
+would typically uh because you need to
+ 
+
+ align:start position:0%
+would typically uh because you need to
+do this um at a finite temperature it
+
+ align:start position:0%
+do this um at a finite temperature it
+ 
+
+ align:start position:0%
+do this um at a finite temperature it
+would heat the
+
+ align:start position:0%
+would heat the
+ 
+
+ align:start position:0%
+would heat the
+Wafers okay so free radicals I mentioned
+
+ align:start position:0%
+Wafers okay so free radicals I mentioned
+ 
+
+ align:start position:0%
+Wafers okay so free radicals I mentioned
+uh if go on to slide 10 they're they're
+
+ align:start position:0%
+uh if go on to slide 10 they're they're
+ 
+
+ align:start position:0%
+uh if go on to slide 10 they're they're
+really critical free radicals are um
+
+ align:start position:0%
+really critical free radicals are um
+ 
+
+ align:start position:0%
+really critical free radicals are um
+electrically neutral species species
+
+ align:start position:0%
+electrically neutral species species
+ 
+
+ align:start position:0%
+electrically neutral species species
+that have incomplete
+
+ align:start position:0%
+that have incomplete
+ 
+
+ align:start position:0%
+that have incomplete
+bonding uh they're not naturally for
+
+ align:start position:0%
+bonding uh they're not naturally for
+ 
+
+ align:start position:0%
+bonding uh they're not naturally for
+found in nature in this free state
+
+ align:start position:0%
+found in nature in this free state
+ 
+
+ align:start position:0%
+found in nature in this free state
+they're created because they're in a
+
+ align:start position:0%
+they're created because they're in a
+ 
+
+ align:start position:0%
+they're created because they're in a
+plasma and you have energy stripping off
+
+ align:start position:0%
+plasma and you have energy stripping off
+ 
+
+ align:start position:0%
+plasma and you have energy stripping off
+atoms from these molecules and there
+
+ align:start position:0%
+atoms from these molecules and there
+ 
+
+ align:start position:0%
+atoms from these molecules and there
+therefore um they are extremely reactive
+
+ align:start position:0%
+therefore um they are extremely reactive
+ 
+
+ align:start position:0%
+therefore um they are extremely reactive
+and so the deposition rate um uh can be
+
+ align:start position:0%
+and so the deposition rate um uh can be
+ 
+
+ align:start position:0%
+and so the deposition rate um uh can be
+dramatically enhanced so for example
+
+ align:start position:0%
+dramatically enhanced so for example
+ 
+
+ align:start position:0%
+dramatically enhanced so for example
+here's an example of a free radical sio
+
+ align:start position:0%
+here's an example of a free radical sio
+ 
+
+ align:start position:0%
+here's an example of a free radical sio
+um typically uh to be electrically
+
+ align:start position:0%
+um typically uh to be electrically
+ 
+
+ align:start position:0%
+um typically uh to be electrically
+neutral this would be si2 or um s sih3
+
+ align:start position:0%
+neutral this would be si2 or um s sih3
+ 
+
+ align:start position:0%
+neutral this would be si2 or um s sih3
+instead of si4 so you have an extra
+
+ align:start position:0%
+instead of si4 so you have an extra
+ 
+
+ align:start position:0%
+instead of si4 so you have an extra
+unsatisfied uh Bond here on the Silicon
+
+ align:start position:0%
+unsatisfied uh Bond here on the Silicon
+ 
+
+ align:start position:0%
+unsatisfied uh Bond here on the Silicon
+so it's going to be very reactive um
+
+ align:start position:0%
+so it's going to be very reactive um
+ 
+
+ align:start position:0%
+so it's going to be very reactive um
+Florine of in and of itself typically
+
+ align:start position:0%
+Florine of in and of itself typically
+ 
+
+ align:start position:0%
+Florine of in and of itself typically
+Florine is present as F2 but you can
+
+ align:start position:0%
+Florine is present as F2 but you can
+ 
+
+ align:start position:0%
+Florine is present as F2 but you can
+break it up with a plasma to form a lot
+
+ align:start position:0%
+break it up with a plasma to form a lot
+ 
+
+ align:start position:0%
+break it up with a plasma to form a lot
+of free radical uh just free Florine
+
+ align:start position:0%
+of free radical uh just free Florine
+ 
+
+ align:start position:0%
+of free radical uh just free Florine
+which is very
+
+ align:start position:0%
+which is very
+ 
+
+ align:start position:0%
+which is very
+reactive so the net result from this
+
+ align:start position:0%
+reactive so the net result from this
+ 
+
+ align:start position:0%
+reactive so the net result from this
+breaking up uh this
+
+ align:start position:0%
+breaking up uh this
+ 
+
+ align:start position:0%
+breaking up uh this
+fragmentation U the free radicals and
+
+ align:start position:0%
+fragmentation U the free radicals and
+ 
+
+ align:start position:0%
+fragmentation U the free radicals and
+the ion bombardment is that the surface
+
+ align:start position:0%
+the ion bombardment is that the surface
+ 
+
+ align:start position:0%
+the ion bombardment is that the surface
+processes occur at much lower
+
+ align:start position:0%
+processes occur at much lower
+ 
+
+ align:start position:0%
+processes occur at much lower
+temperatures um so for dial electrics
+
+ align:start position:0%
+temperatures um so for dial electrics
+ 
+
+ align:start position:0%
+temperatures um so for dial electrics
+you can do pcbd um typically between 200
+
+ align:start position:0%
+you can do pcbd um typically between 200
+ 
+
+ align:start position:0%
+you can do pcbd um typically between 200
+and and 350 and get very high deposition
+
+ align:start position:0%
+and and 350 and get very high deposition
+ 
+
+ align:start position:0%
+and and 350 and get very high deposition
+rates um this is particularly important
+
+ align:start position:0%
+rates um this is particularly important
+ 
+
+ align:start position:0%
+rates um this is particularly important
+if you're doing a backend process so
+
+ align:start position:0%
+if you're doing a backend process so
+ 
+
+ align:start position:0%
+if you're doing a backend process so
+back in meaning you have some metal on
+
+ align:start position:0%
+back in meaning you have some metal on
+ 
+
+ align:start position:0%
+back in meaning you have some metal on
+the wafer you can't take it above 350
+
+ align:start position:0%
+the wafer you can't take it above 350
+ 
+
+ align:start position:0%
+the wafer you can't take it above 350
+for example well if you want to deposit
+
+ align:start position:0%
+for example well if you want to deposit
+ 
+
+ align:start position:0%
+for example well if you want to deposit
+uh lto you have to go to 400 to get any
+
+ align:start position:0%
+uh lto you have to go to 400 to get any
+ 
+
+ align:start position:0%
+uh lto you have to go to 400 to get any
+kind of reasonable dep rate it's going
+
+ align:start position:0%
+kind of reasonable dep rate it's going
+ 
+
+ align:start position:0%
+kind of reasonable dep rate it's going
+to be difficult so people can use in
+
+ align:start position:0%
+to be difficult so people can use in
+ 
+
+ align:start position:0%
+to be difficult so people can use in
+that case can use a plasma enhanced CBD
+
+ align:start position:0%
+that case can use a plasma enhanced CBD
+ 
+
+ align:start position:0%
+that case can use a plasma enhanced CBD
+to get the depth rate up um uh even if
+
+ align:start position:0%
+to get the depth rate up um uh even if
+ 
+
+ align:start position:0%
+to get the depth rate up um uh even if
+you can't use high temperatures so
+
+ align:start position:0%
+you can't use high temperatures so
+ 
+
+ align:start position:0%
+you can't use high temperatures so
+that's a very common application of pbds
+
+ align:start position:0%
+that's a very common application of pbds
+ 
+
+ align:start position:0%
+that's a very common application of pbds
+in the back
+
+ align:start position:0%
+in the back
+ 
+
+ align:start position:0%
+in the back
+end here we go to slide 11 actually this
+
+ align:start position:0%
+end here we go to slide 11 actually this
+ 
+
+ align:start position:0%
+end here we go to slide 11 actually this
+is a picture of uh an example of a P CBD
+
+ align:start position:0%
+is a picture of uh an example of a P CBD
+ 
+
+ align:start position:0%
+is a picture of uh an example of a P CBD
+deposition tool there's one here at at
+
+ align:start position:0%
+deposition tool there's one here at at
+ 
+
+ align:start position:0%
+deposition tool there's one here at at
+uh in the Microsystems technology lab uh
+
+ align:start position:0%
+uh in the Microsystems technology lab uh
+ 
+
+ align:start position:0%
+uh in the Microsystems technology lab uh
+in building 39 here at MIT it's called
+
+ align:start position:0%
+in building 39 here at MIT it's called
+ 
+
+ align:start position:0%
+in building 39 here at MIT it's called
+it's made by a company called nollet and
+
+ align:start position:0%
+it's made by a company called nollet and
+ 
+
+ align:start position:0%
+it's made by a company called nollet and
+it's called the concept one and on the
+
+ align:start position:0%
+it's called the concept one and on the
+ 
+
+ align:start position:0%
+it's called the concept one and on the
+bottom of the slide I put down the um uh
+
+ align:start position:0%
+bottom of the slide I put down the um uh
+ 
+
+ align:start position:0%
+bottom of the slide I put down the um uh
+the URL where you can go get more
+
+ align:start position:0%
+the URL where you can go get more
+ 
+
+ align:start position:0%
+the URL where you can go get more
+information about that particular piece
+
+ align:start position:0%
+information about that particular piece
+ 
+
+ align:start position:0%
+information about that particular piece
+of equipment how how it works um this is
+
+ align:start position:0%
+of equipment how how it works um this is
+ 
+
+ align:start position:0%
+of equipment how how it works um this is
+a photograph of it on the left uh it's
+
+ align:start position:0%
+a photograph of it on the left uh it's
+ 
+
+ align:start position:0%
+a photograph of it on the left uh it's
+right set up right now processing 6in
+
+ align:start position:0%
+right set up right now processing 6in
+ 
+
+ align:start position:0%
+right set up right now processing 6in
+Wafers look at the interesting thing
+
+ align:start position:0%
+Wafers look at the interesting thing
+ 
+
+ align:start position:0%
+Wafers look at the interesting thing
+about it look at the the depth rate for
+
+ align:start position:0%
+about it look at the the depth rate for
+ 
+
+ align:start position:0%
+about it look at the the depth rate for
+oxide at low temperature um 350 300 it
+
+ align:start position:0%
+oxide at low temperature um 350 300 it
+ 
+
+ align:start position:0%
+oxide at low temperature um 350 300 it
+can put oxide down at a micron per
+
+ align:start position:0%
+can put oxide down at a micron per
+ 
+
+ align:start position:0%
+can put oxide down at a micron per
+minute that's an actually an absolutely
+
+ align:start position:0%
+minute that's an actually an absolutely
+ 
+
+ align:start position:0%
+minute that's an actually an absolutely
+phenomenal um growth rate when you think
+
+ align:start position:0%
+phenomenal um growth rate when you think
+ 
+
+ align:start position:0%
+phenomenal um growth rate when you think
+about it yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question uh well it it if you need if
+
+ align:start position:0%
+question uh well it it if you need if
+ 
+
+ align:start position:0%
+question uh well it it if you need if
+you need uh only a couple thousand Anum
+
+ align:start position:0%
+you need uh only a couple thousand Anum
+ 
+
+ align:start position:0%
+you need uh only a couple thousand Anum
+you don't want to use that but you can
+
+ align:start position:0%
+you don't want to use that but you can
+ 
+
+ align:start position:0%
+you don't want to use that but you can
+slow down the dep rate as well but there
+
+ align:start position:0%
+slow down the dep rate as well but there
+ 
+
+ align:start position:0%
+slow down the dep rate as well but there
+are people PE the kind of people who
+
+ align:start position:0%
+are people PE the kind of people who
+ 
+
+ align:start position:0%
+are people PE the kind of people who
+will be using it uh at this depth rate
+
+ align:start position:0%
+will be using it uh at this depth rate
+ 
+
+ align:start position:0%
+will be using it uh at this depth rate
+might be somebody who wants to put down
+
+ align:start position:0%
+might be somebody who wants to put down
+ 
+
+ align:start position:0%
+might be somebody who wants to put down
+10 microns Maybe they're making a Mims
+
+ align:start position:0%
+10 microns Maybe they're making a Mims
+ 
+
+ align:start position:0%
+10 microns Maybe they're making a Mims
+device so they need they need 10 microns
+
+ align:start position:0%
+device so they need they need 10 microns
+ 
+
+ align:start position:0%
+device so they need they need 10 microns
+to do that by any thermal technique I
+
+ align:start position:0%
+to do that by any thermal technique I
+ 
+
+ align:start position:0%
+to do that by any thermal technique I
+mean you'd be there running the reactor
+
+ align:start position:0%
+mean you'd be there running the reactor
+ 
+
+ align:start position:0%
+mean you'd be there running the reactor
+for days and you'd be you'd be going
+
+ align:start position:0%
+for days and you'd be you'd be going
+ 
+
+ align:start position:0%
+for days and you'd be you'd be going
+through cylinder of cylinder of Silent
+
+ align:start position:0%
+through cylinder of cylinder of Silent
+ 
+
+ align:start position:0%
+through cylinder of cylinder of Silent
+it would be totally uh uh you know
+
+ align:start position:0%
+it would be totally uh uh you know
+ 
+
+ align:start position:0%
+it would be totally uh uh you know
+ridiculous so for people who need the
+
+ align:start position:0%
+ridiculous so for people who need the
+ 
+
+ align:start position:0%
+ridiculous so for people who need the
+thick films this is the way to go you
+
+ align:start position:0%
+thick films this is the way to go you
+ 
+
+ align:start position:0%
+thick films this is the way to go you
+can back off on the depth rate this is
+
+ align:start position:0%
+can back off on the depth rate this is
+ 
+
+ align:start position:0%
+can back off on the depth rate this is
+the highest depth rate you can go slower
+
+ align:start position:0%
+the highest depth rate you can go slower
+ 
+
+ align:start position:0%
+the highest depth rate you can go slower
+than that and people do uh do do that um
+
+ align:start position:0%
+than that and people do uh do do that um
+ 
+
+ align:start position:0%
+than that and people do uh do do that um
+it does more than oxide it can deposit
+
+ align:start position:0%
+it does more than oxide it can deposit
+ 
+
+ align:start position:0%
+it does more than oxide it can deposit
+nitride oxy nitride um and other films
+
+ align:start position:0%
+nitride oxy nitride um and other films
+ 
+
+ align:start position:0%
+nitride oxy nitride um and other films
+uh it's it's an RF plasma um it has an
+
+ align:start position:0%
+uh it's it's an RF plasma um it has an
+ 
+
+ align:start position:0%
+uh it's it's an RF plasma um it has an
+interesting thing it has a multiple
+
+ align:start position:0%
+interesting thing it has a multiple
+ 
+
+ align:start position:0%
+interesting thing it has a multiple
+station uh processing sequence it cycles
+
+ align:start position:0%
+station uh processing sequence it cycles
+ 
+
+ align:start position:0%
+station uh processing sequence it cycles
+each wafer through different dep
+
+ align:start position:0%
+each wafer through different dep
+ 
+
+ align:start position:0%
+each wafer through different dep
+deposition Chambers or stations uh to
+
+ align:start position:0%
+deposition Chambers or stations uh to
+ 
+
+ align:start position:0%
+deposition Chambers or stations uh to
+get an averaging effect so that you get
+
+ align:start position:0%
+get an averaging effect so that you get
+ 
+
+ align:start position:0%
+get an averaging effect so that you get
+better uniformity in in any given tool
+
+ align:start position:0%
+better uniformity in in any given tool
+ 
+
+ align:start position:0%
+better uniformity in in any given tool
+you'll often find if it has multiple
+
+ align:start position:0%
+you'll often find if it has multiple
+ 
+
+ align:start position:0%
+you'll often find if it has multiple
+stations say it has five slots um slot
+
+ align:start position:0%
+stations say it has five slots um slot
+ 
+
+ align:start position:0%
+stations say it has five slots um slot
+one and Slot five never have exactly the
+
+ align:start position:0%
+one and Slot five never have exactly the
+ 
+
+ align:start position:0%
+one and Slot five never have exactly the
+same depth rate and it's always a
+
+ align:start position:0%
+same depth rate and it's always a
+ 
+
+ align:start position:0%
+same depth rate and it's always a
+problem so you put five wafers in wafer
+
+ align:start position:0%
+problem so you put five wafers in wafer
+ 
+
+ align:start position:0%
+problem so you put five wafers in wafer
+one and five come out differently um
+
+ align:start position:0%
+one and five come out differently um
+ 
+
+ align:start position:0%
+one and five come out differently um
+this is a very kind of a um Brute Force
+
+ align:start position:0%
+this is a very kind of a um Brute Force
+ 
+
+ align:start position:0%
+this is a very kind of a um Brute Force
+obvious way to do it what they do is
+
+ align:start position:0%
+obvious way to do it what they do is
+ 
+
+ align:start position:0%
+obvious way to do it what they do is
+instead you take one wafering you cycle
+
+ align:start position:0%
+instead you take one wafering you cycle
+ 
+
+ align:start position:0%
+instead you take one wafering you cycle
+through each all five slots and so one
+
+ align:start position:0%
+through each all five slots and so one
+ 
+
+ align:start position:0%
+through each all five slots and so one
+wafer sees a little bit of all five it
+
+ align:start position:0%
+wafer sees a little bit of all five it
+ 
+
+ align:start position:0%
+wafer sees a little bit of all five it
+kind of averages out the non-uniformity
+
+ align:start position:0%
+kind of averages out the non-uniformity
+ 
+
+ align:start position:0%
+kind of averages out the non-uniformity
+and with a robotic control you can do
+
+ align:start position:0%
+and with a robotic control you can do
+ 
+
+ align:start position:0%
+and with a robotic control you can do
+that kind of thing um uh so anyway this
+
+ align:start position:0%
+that kind of thing um uh so anyway this
+ 
+
+ align:start position:0%
+that kind of thing um uh so anyway this
+is the concept one typically used more
+
+ align:start position:0%
+is the concept one typically used more
+ 
+
+ align:start position:0%
+is the concept one typically used more
+for backend processing you don't see too
+
+ align:start position:0%
+for backend processing you don't see too
+ 
+
+ align:start position:0%
+for backend processing you don't see too
+many people using this um in in the
+
+ align:start position:0%
+many people using this um in in the
+ 
+
+ align:start position:0%
+many people using this um in in the
+front end and why is that why why why is
+
+ align:start position:0%
+front end and why is that why why why is
+ 
+
+ align:start position:0%
+front end and why is that why why why is
+that well the backend has to use it ific
+
+ align:start position:0%
+that well the backend has to use it ific
+ 
+
+ align:start position:0%
+that well the backend has to use it ific
+because you need uh typically uh you
+
+ align:start position:0%
+because you need uh typically uh you
+ 
+
+ align:start position:0%
+because you need uh typically uh you
+need very low temperatures but if you go
+
+ align:start position:0%
+need very low temperatures but if you go
+ 
+
+ align:start position:0%
+need very low temperatures but if you go
+to slide 12 um the characteristics of of
+
+ align:start position:0%
+to slide 12 um the characteristics of of
+ 
+
+ align:start position:0%
+to slide 12 um the characteristics of of
+plasma enhanced CBD deposited films like
+
+ align:start position:0%
+plasma enhanced CBD deposited films like
+ 
+
+ align:start position:0%
+plasma enhanced CBD deposited films like
+oxide or silicon nitride they can be
+
+ align:start position:0%
+oxide or silicon nitride they can be
+ 
+
+ align:start position:0%
+oxide or silicon nitride they can be
+quite different from those that are
+
+ align:start position:0%
+quite different from those that are
+ 
+
+ align:start position:0%
+quite different from those that are
+deposited at higher temperatures by
+
+ align:start position:0%
+deposited at higher temperatures by
+ 
+
+ align:start position:0%
+deposited at higher temperatures by
+lpcvd uh for example very different
+
+ align:start position:0%
+lpcvd uh for example very different
+ 
+
+ align:start position:0%
+lpcvd uh for example very different
+stress very different amounts of stress
+
+ align:start position:0%
+stress very different amounts of stress
+ 
+
+ align:start position:0%
+stress very different amounts of stress
+in pecvd and lpcvd films uh hydrogen
+
+ align:start position:0%
+in pecvd and lpcvd films uh hydrogen
+ 
+
+ align:start position:0%
+in pecvd and lpcvd films uh hydrogen
+content in particular make a note um
+
+ align:start position:0%
+content in particular make a note um
+ 
+
+ align:start position:0%
+content in particular make a note um
+pecvd films tend to be loaded with
+
+ align:start position:0%
+pecvd films tend to be loaded with
+ 
+
+ align:start position:0%
+pecvd films tend to be loaded with
+hydrogen
+
+ align:start position:0%
+hydrogen
+ 
+
+ align:start position:0%
+hydrogen
+um I mean a lot you know could be like
+
+ align:start position:0%
+um I mean a lot you know could be like
+ 
+
+ align:start position:0%
+um I mean a lot you know could be like
+10% hydrogen I mean they're just stuffed
+
+ align:start position:0%
+10% hydrogen I mean they're just stuffed
+ 
+
+ align:start position:0%
+10% hydrogen I mean they're just stuffed
+with hydrogen and that's because a lot
+
+ align:start position:0%
+with hydrogen and that's because a lot
+ 
+
+ align:start position:0%
+with hydrogen and that's because a lot
+of these precursors if you go
+
+ align:start position:0%
+of these precursors if you go
+ 
+
+ align:start position:0%
+of these precursors if you go
+back um look look at some of the
+
+ align:start position:0%
+back um look look at some of the
+ 
+
+ align:start position:0%
+back um look look at some of the
+precursors you might be using um silent
+
+ align:start position:0%
+precursors you might be using um silent
+ 
+
+ align:start position:0%
+precursors you might be using um silent
+uh well a lot of those hydrogens get
+
+ align:start position:0%
+uh well a lot of those hydrogens get
+ 
+
+ align:start position:0%
+uh well a lot of those hydrogens get
+ripped off during the plasma process and
+
+ align:start position:0%
+ripped off during the plasma process and
+ 
+
+ align:start position:0%
+ripped off during the plasma process and
+they get and you're growing so fast they
+
+ align:start position:0%
+they get and you're growing so fast they
+ 
+
+ align:start position:0%
+they get and you're growing so fast they
+can get buried in the film so hydrogen
+
+ align:start position:0%
+can get buried in the film so hydrogen
+ 
+
+ align:start position:0%
+can get buried in the film so hydrogen
+incorporation uh just by sort of
+
+ align:start position:0%
+incorporation uh just by sort of
+ 
+
+ align:start position:0%
+incorporation uh just by sort of
+stuffing it in the film is kind of
+
+ align:start position:0%
+stuffing it in the film is kind of
+ 
+
+ align:start position:0%
+stuffing it in the film is kind of
+common in any low temperature plasma
+
+ align:start position:0%
+common in any low temperature plasma
+ 
+
+ align:start position:0%
+common in any low temperature plasma
+process also that the temperat is low
+
+ align:start position:0%
+process also that the temperat is low
+ 
+
+ align:start position:0%
+process also that the temperat is low
+enough hydrogen gets in the film and it
+
+ align:start position:0%
+enough hydrogen gets in the film and it
+ 
+
+ align:start position:0%
+enough hydrogen gets in the film and it
+just sticks it doesn't evolve at higher
+
+ align:start position:0%
+just sticks it doesn't evolve at higher
+ 
+
+ align:start position:0%
+just sticks it doesn't evolve at higher
+temperatures like lpcvd the sticking
+
+ align:start position:0%
+temperatures like lpcvd the sticking
+ 
+
+ align:start position:0%
+temperatures like lpcvd the sticking
+coefficient of hydrogen on the surface
+
+ align:start position:0%
+coefficient of hydrogen on the surface
+ 
+
+ align:start position:0%
+coefficient of hydrogen on the surface
+is very low so you don't get so much
+
+ align:start position:0%
+is very low so you don't get so much
+ 
+
+ align:start position:0%
+is very low so you don't get so much
+hydrogen hydrogen be less than a percent
+
+ align:start position:0%
+hydrogen hydrogen be less than a percent
+ 
+
+ align:start position:0%
+hydrogen hydrogen be less than a percent
+maybe half a percent or less in an lpcvd
+
+ align:start position:0%
+maybe half a percent or less in an lpcvd
+ 
+
+ align:start position:0%
+maybe half a percent or less in an lpcvd
+film oxide film or nitri film uh whereas
+
+ align:start position:0%
+film oxide film or nitri film uh whereas
+ 
+
+ align:start position:0%
+film oxide film or nitri film uh whereas
+in in in a plasma enhanced film it could
+
+ align:start position:0%
+in in in a plasma enhanced film it could
+ 
+
+ align:start position:0%
+in in in a plasma enhanced film it could
+be 10% have a dramatic effect on the uh
+
+ align:start position:0%
+be 10% have a dramatic effect on the uh
+ 
+
+ align:start position:0%
+be 10% have a dramatic effect on the uh
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+properties and the stochiometry of the
+
+ align:start position:0%
+properties and the stochiometry of the
+ 
+
+ align:start position:0%
+properties and the stochiometry of the
+film it will not necessarily be lto is
+
+ align:start position:0%
+film it will not necessarily be lto is
+ 
+
+ align:start position:0%
+film it will not necessarily be lto is
+not necessarily exactly sio2 it could be
+
+ align:start position:0%
+not necessarily exactly sio2 it could be
+ 
+
+ align:start position:0%
+not necessarily exactly sio2 it could be
+siox X is slightly different um from two
+
+ align:start position:0%
+siox X is slightly different um from two
+ 
+
+ align:start position:0%
+siox X is slightly different um from two
+again because you're not growing it
+
+ align:start position:0%
+again because you're not growing it
+ 
+
+ align:start position:0%
+again because you're not growing it
+thermally you're depositing
+
+ align:start position:0%
+thermally you're depositing
+ 
+
+ align:start position:0%
+thermally you're depositing
+it um so these differences between pecvd
+
+ align:start position:0%
+it um so these differences between pecvd
+ 
+
+ align:start position:0%
+it um so these differences between pecvd
+and lpcvd can affect properties like the
+
+ align:start position:0%
+and lpcvd can affect properties like the
+ 
+
+ align:start position:0%
+and lpcvd can affect properties like the
+film adhesion the presence of pin holes
+
+ align:start position:0%
+film adhesion the presence of pin holes
+ 
+
+ align:start position:0%
+film adhesion the presence of pin holes
+plasma enhanced films tend to have a
+
+ align:start position:0%
+plasma enhanced films tend to have a
+ 
+
+ align:start position:0%
+plasma enhanced films tend to have a
+little more tendency to have pin holes
+
+ align:start position:0%
+little more tendency to have pin holes
+ 
+
+ align:start position:0%
+little more tendency to have pin holes
+because again as as was mentioned I mean
+
+ align:start position:0%
+because again as as was mentioned I mean
+ 
+
+ align:start position:0%
+because again as as was mentioned I mean
+they're going down really fast uh
+
+ align:start position:0%
+they're going down really fast uh
+ 
+
+ align:start position:0%
+they're going down really fast uh
+surface roughness can be different uh a
+
+ align:start position:0%
+surface roughness can be different uh a
+ 
+
+ align:start position:0%
+surface roughness can be different uh a
+very important thing uh is the
+
+ align:start position:0%
+very important thing uh is the
+ 
+
+ align:start position:0%
+very important thing uh is the
+dialectric constant again because the
+
+ align:start position:0%
+dialectric constant again because the
+ 
+
+ align:start position:0%
+dialectric constant again because the
+presence of different impurities will be
+
+ align:start position:0%
+presence of different impurities will be
+ 
+
+ align:start position:0%
+presence of different impurities will be
+quite different for a pcbd so the
+
+ align:start position:0%
+quite different for a pcbd so the
+ 
+
+ align:start position:0%
+quite different for a pcbd so the
+optical property the index of refraction
+
+ align:start position:0%
+optical property the index of refraction
+ 
+
+ align:start position:0%
+optical property the index of refraction
+can be dramatically different uh because
+
+ align:start position:0%
+can be dramatically different uh because
+ 
+
+ align:start position:0%
+can be dramatically different uh because
+of stochiometric differences or because
+
+ align:start position:0%
+of stochiometric differences or because
+ 
+
+ align:start position:0%
+of stochiometric differences or because
+of hydrogen um hydrogen can also be uh
+
+ align:start position:0%
+of hydrogen um hydrogen can also be uh
+ 
+
+ align:start position:0%
+of hydrogen um hydrogen can also be uh
+can uh induce vibrational mode which can
+
+ align:start position:0%
+can uh induce vibrational mode which can
+ 
+
+ align:start position:0%
+can uh induce vibrational mode which can
+absorb light so dielectrics put down by
+
+ align:start position:0%
+absorb light so dielectrics put down by
+ 
+
+ align:start position:0%
+absorb light so dielectrics put down by
+pcvd can have much uh different light
+
+ align:start position:0%
+pcvd can have much uh different light
+ 
+
+ align:start position:0%
+pcvd can have much uh different light
+absorption characteristics and finally
+
+ align:start position:0%
+absorption characteristics and finally
+ 
+
+ align:start position:0%
+absorption characteristics and finally
+the important thing is etch rate the
+
+ align:start position:0%
+the important thing is etch rate the
+ 
+
+ align:start position:0%
+the important thing is etch rate the
+etch rate of a pcvd deposited film will
+
+ align:start position:0%
+etch rate of a pcvd deposited film will
+ 
+
+ align:start position:0%
+etch rate of a pcvd deposited film will
+be quite different from that of an lpcvd
+
+ align:start position:0%
+be quite different from that of an lpcvd
+ 
+
+ align:start position:0%
+be quite different from that of an lpcvd
+film which will be quite different from
+
+ align:start position:0%
+film which will be quite different from
+ 
+
+ align:start position:0%
+film which will be quite different from
+that of a thermaline deposited film so
+
+ align:start position:0%
+that of a thermaline deposited film so
+ 
+
+ align:start position:0%
+that of a thermaline deposited film so
+depending how you put it down you need
+
+ align:start position:0%
+depending how you put it down you need
+ 
+
+ align:start position:0%
+depending how you put it down you need
+to know what the hch rate of oxide is in
+
+ align:start position:0%
+to know what the hch rate of oxide is in
+ 
+
+ align:start position:0%
+to know what the hch rate of oxide is in
+HF or whatever you need to test for
+
+ align:start position:0%
+HF or whatever you need to test for
+ 
+
+ align:start position:0%
+HF or whatever you need to test for
+that okay so that's um that that's sort
+
+ align:start position:0%
+that okay so that's um that that's sort
+ 
+
+ align:start position:0%
+that okay so that's um that that's sort
+of what I wanted to say at this point uh
+
+ align:start position:0%
+of what I wanted to say at this point uh
+ 
+
+ align:start position:0%
+of what I wanted to say at this point uh
+about chemical vapor deposition uh if we
+
+ align:start position:0%
+about chemical vapor deposition uh if we
+ 
+
+ align:start position:0%
+about chemical vapor deposition uh if we
+if we go on to slide 13 um I want to
+
+ align:start position:0%
+if we go on to slide 13 um I want to
+ 
+
+ align:start position:0%
+if we go on to slide 13 um I want to
+move on to uh another topic which is
+
+ align:start position:0%
+move on to uh another topic which is
+ 
+
+ align:start position:0%
+move on to uh another topic which is
+called called physical vapor deposition
+
+ align:start position:0%
+called called physical vapor deposition
+ 
+
+ align:start position:0%
+called called physical vapor deposition
+that's discussed in your text as the
+
+ align:start position:0%
+that's discussed in your text as the
+ 
+
+ align:start position:0%
+that's discussed in your text as the
+name implies it's pretty obvious PVD
+
+ align:start position:0%
+name implies it's pretty obvious PVD
+ 
+
+ align:start position:0%
+name implies it's pretty obvious PVD
+uses physical processes it's not so not
+
+ align:start position:0%
+uses physical processes it's not so not
+ 
+
+ align:start position:0%
+uses physical processes it's not so not
+just chemistry uh to deposit films um uh
+
+ align:start position:0%
+just chemistry uh to deposit films um uh
+ 
+
+ align:start position:0%
+just chemistry uh to deposit films um uh
+in the gas phase and and and to get them
+
+ align:start position:0%
+in the gas phase and and and to get them
+ 
+
+ align:start position:0%
+in the gas phase and and and to get them
+onto the wafer uh the most common and
+
+ align:start position:0%
+onto the wafer uh the most common and
+ 
+
+ align:start position:0%
+onto the wafer uh the most common and
+the most classic uh uh physical process
+
+ align:start position:0%
+the most classic uh uh physical process
+ 
+
+ align:start position:0%
+the most classic uh uh physical process
+and and maybe some of you are familiar
+
+ align:start position:0%
+and and maybe some of you are familiar
+ 
+
+ align:start position:0%
+and and maybe some of you are familiar
+with this is is thermal evaporation this
+
+ align:start position:0%
+with this is is thermal evaporation this
+ 
+
+ align:start position:0%
+with this is is thermal evaporation this
+is pretty much totally physical process
+
+ align:start position:0%
+is pretty much totally physical process
+ 
+
+ align:start position:0%
+is pretty much totally physical process
+there's not a whole lot of chemistry
+
+ align:start position:0%
+there's not a whole lot of chemistry
+ 
+
+ align:start position:0%
+there's not a whole lot of chemistry
+you're not flowing in gases or or or
+
+ align:start position:0%
+you're not flowing in gases or or or
+ 
+
+ align:start position:0%
+you're not flowing in gases or or or
+doing any chemistry you're here's an
+
+ align:start position:0%
+doing any chemistry you're here's an
+ 
+
+ align:start position:0%
+doing any chemistry you're here's an
+example of a bell jar um a large vacuum
+
+ align:start position:0%
+example of a bell jar um a large vacuum
+ 
+
+ align:start position:0%
+example of a bell jar um a large vacuum
+chamber um the uh you heat the source
+
+ align:start position:0%
+chamber um the uh you heat the source
+ 
+
+ align:start position:0%
+chamber um the uh you heat the source
+material there's there's a source
+
+ align:start position:0%
+material there's there's a source
+ 
+
+ align:start position:0%
+material there's there's a source
+material here on a heater um that is
+
+ align:start position:0%
+material here on a heater um that is
+ 
+
+ align:start position:0%
+material here on a heater um that is
+then made molten so it's liquefied and
+
+ align:start position:0%
+then made molten so it's liquefied and
+ 
+
+ align:start position:0%
+then made molten so it's liquefied and
+it literally it it evaporates off it has
+
+ align:start position:0%
+it literally it it evaporates off it has
+ 
+
+ align:start position:0%
+it literally it it evaporates off it has
+a finite vapor pressure it evaporates
+
+ align:start position:0%
+a finite vapor pressure it evaporates
+ 
+
+ align:start position:0%
+a finite vapor pressure it evaporates
+into the vacuum the vacuum pressure is
+
+ align:start position:0%
+into the vacuum the vacuum pressure is
+ 
+
+ align:start position:0%
+into the vacuum the vacuum pressure is
+low enough uh less than 10 Theus 5 T so
+
+ align:start position:0%
+low enough uh less than 10 Theus 5 T so
+ 
+
+ align:start position:0%
+low enough uh less than 10 Theus 5 T so
+that the main free path is quite long so
+
+ align:start position:0%
+that the main free path is quite long so
+ 
+
+ align:start position:0%
+that the main free path is quite long so
+it literally just is like a line of
+
+ align:start position:0%
+it literally just is like a line of
+ 
+
+ align:start position:0%
+it literally just is like a line of
+sight spr spraying paint if you will um
+
+ align:start position:0%
+sight spr spraying paint if you will um
+ 
+
+ align:start position:0%
+sight spr spraying paint if you will um
+where the paint is some Atomic um
+
+ align:start position:0%
+where the paint is some Atomic um
+ 
+
+ align:start position:0%
+where the paint is some Atomic um
+species onto the surface of these
+
+ align:start position:0%
+species onto the surface of these
+ 
+
+ align:start position:0%
+species onto the surface of these
+Wafers um and uh so this is a very
+
+ align:start position:0%
+Wafers um and uh so this is a very
+ 
+
+ align:start position:0%
+Wafers um and uh so this is a very
+common physical process not a whole lot
+
+ align:start position:0%
+common physical process not a whole lot
+ 
+
+ align:start position:0%
+common physical process not a whole lot
+of chemistry involved
+
+ align:start position:0%
+of chemistry involved
+ 
+
+ align:start position:0%
+of chemistry involved
+um in in thermal
+
+ align:start position:0%
+um in in thermal
+ 
+
+ align:start position:0%
+um in in thermal
+evaporation so what are um for thin film
+
+ align:start position:0%
+evaporation so what are um for thin film
+ 
+
+ align:start position:0%
+evaporation so what are um for thin film
+evaporation what are some of the
+
+ align:start position:0%
+evaporation what are some of the
+ 
+
+ align:start position:0%
+evaporation what are some of the
+properties well it's mostly what we call
+
+ align:start position:0%
+properties well it's mostly what we call
+ 
+
+ align:start position:0%
+properties well it's mostly what we call
+line of sight deposition because the
+
+ align:start position:0%
+line of sight deposition because the
+ 
+
+ align:start position:0%
+line of sight deposition because the
+pressure is low so there's not a whole
+
+ align:start position:0%
+pressure is low so there's not a whole
+ 
+
+ align:start position:0%
+pressure is low so there's not a whole
+lot of collisions as let's say I'm
+
+ align:start position:0%
+lot of collisions as let's say I'm
+ 
+
+ align:start position:0%
+lot of collisions as let's say I'm
+evaporating aluminum as this aluminum
+
+ align:start position:0%
+evaporating aluminum as this aluminum
+ 
+
+ align:start position:0%
+evaporating aluminum as this aluminum
+comes off um it has a certain flux um in
+
+ align:start position:0%
+comes off um it has a certain flux um in
+ 
+
+ align:start position:0%
+comes off um it has a certain flux um in
+all directions and pretty much the
+
+ align:start position:0%
+all directions and pretty much the
+ 
+
+ align:start position:0%
+all directions and pretty much the
+aluminum uh atoms find their way
+
+ align:start position:0%
+aluminum uh atoms find their way
+ 
+
+ align:start position:0%
+aluminum uh atoms find their way
+straight to the wafer depend depending
+
+ align:start position:0%
+straight to the wafer depend depending
+ 
+
+ align:start position:0%
+straight to the wafer depend depending
+of course on on the pressure if the
+
+ align:start position:0%
+of course on on the pressure if the
+ 
+
+ align:start position:0%
+of course on on the pressure if the
+pressure is low enough they can get
+
+ align:start position:0%
+pressure is low enough they can get
+ 
+
+ align:start position:0%
+pressure is low enough they can get
+straight to the wafer with very few
+
+ align:start position:0%
+straight to the wafer with very few
+ 
+
+ align:start position:0%
+straight to the wafer with very few
+collisions uh the depth rate the depth
+
+ align:start position:0%
+collisions uh the depth rate the depth
+ 
+
+ align:start position:0%
+collisions uh the depth rate the depth
+position rate is really pretty much
+
+ align:start position:0%
+position rate is really pretty much
+ 
+
+ align:start position:0%
+position rate is really pretty much
+determined by the emitted flux and the
+
+ align:start position:0%
+determined by the emitted flux and the
+ 
+
+ align:start position:0%
+determined by the emitted flux and the
+geometry of the target um so it's much
+
+ align:start position:0%
+geometry of the target um so it's much
+ 
+
+ align:start position:0%
+geometry of the target um so it's much
+less complicated in some ways to
+
+ align:start position:0%
+less complicated in some ways to
+ 
+
+ align:start position:0%
+less complicated in some ways to
+calculate then uh or to model it than it
+
+ align:start position:0%
+calculate then uh or to model it than it
+ 
+
+ align:start position:0%
+calculate then uh or to model it than it
+is in cvd in cvd the de rate well we we
+
+ align:start position:0%
+is in cvd in cvd the de rate well we we
+ 
+
+ align:start position:0%
+is in cvd in cvd the de rate well we we
+had that model as a function of
+
+ align:start position:0%
+had that model as a function of
+ 
+
+ align:start position:0%
+had that model as a function of
+temperature but it's very hard to get an
+
+ align:start position:0%
+temperature but it's very hard to get an
+ 
+
+ align:start position:0%
+temperature but it's very hard to get an
+absolute uh dep rate model you always
+
+ align:start position:0%
+absolute uh dep rate model you always
+ 
+
+ align:start position:0%
+absolute uh dep rate model you always
+have to do fitting in cvd this physical
+
+ align:start position:0%
+have to do fitting in cvd this physical
+ 
+
+ align:start position:0%
+have to do fitting in cvd this physical
+deposition is is uh is is quite a bit
+
+ align:start position:0%
+deposition is is uh is is quite a bit
+ 
+
+ align:start position:0%
+deposition is is uh is is quite a bit
+simpler um this evaporation Source what
+
+ align:start position:0%
+simpler um this evaporation Source what
+ 
+
+ align:start position:0%
+simpler um this evaporation Source what
+is it well it's it's um usually it's a
+
+ align:start position:0%
+is it well it's it's um usually it's a
+ 
+
+ align:start position:0%
+is it well it's it's um usually it's a
+little cup called a crucible that's
+
+ align:start position:0%
+little cup called a crucible that's
+ 
+
+ align:start position:0%
+little cup called a crucible that's
+heated that holds um the the the molten
+
+ align:start position:0%
+heated that holds um the the the molten
+ 
+
+ align:start position:0%
+heated that holds um the the the molten
+liquid uh and there's two ways of moding
+
+ align:start position:0%
+liquid uh and there's two ways of moding
+ 
+
+ align:start position:0%
+liquid uh and there's two ways of moding
+it sometimes if it's small enough
+
+ align:start position:0%
+it sometimes if it's small enough
+ 
+
+ align:start position:0%
+it sometimes if it's small enough
+depending on the geometry it can be
+
+ align:start position:0%
+depending on the geometry it can be
+ 
+
+ align:start position:0%
+depending on the geometry it can be
+modeled as a point source just like you
+
+ align:start position:0%
+modeled as a point source just like you
+ 
+
+ align:start position:0%
+modeled as a point source just like you
+have a point in space that's emitting
+
+ align:start position:0%
+have a point in space that's emitting
+ 
+
+ align:start position:0%
+have a point in space that's emitting
+aluminum atoms or whatever you're trying
+
+ align:start position:0%
+aluminum atoms or whatever you're trying
+ 
+
+ align:start position:0%
+aluminum atoms or whatever you're trying
+to evaporate in all
+
+ align:start position:0%
+to evaporate in all
+ 
+
+ align:start position:0%
+to evaporate in all
+directions sometimes it's it's the cup
+
+ align:start position:0%
+directions sometimes it's it's the cup
+ 
+
+ align:start position:0%
+directions sometimes it's it's the cup
+is large enough then you have to
+
+ align:start position:0%
+is large enough then you have to
+ 
+
+ align:start position:0%
+is large enough then you have to
+actually model as a finite Source a
+
+ align:start position:0%
+actually model as a finite Source a
+ 
+
+ align:start position:0%
+actually model as a finite Source a
+small area surface Source um this is
+
+ align:start position:0%
+small area surface Source um this is
+ 
+
+ align:start position:0%
+small area surface Source um this is
+typically more applicable to evaporation
+
+ align:start position:0%
+typically more applicable to evaporation
+ 
+
+ align:start position:0%
+typically more applicable to evaporation
+systems um and I should mention uh
+
+ align:start position:0%
+systems um and I should mention uh
+ 
+
+ align:start position:0%
+systems um and I should mention uh
+there's a uh the heater here is is just
+
+ align:start position:0%
+there's a uh the heater here is is just
+ 
+
+ align:start position:0%
+there's a uh the heater here is is just
+shown as a little box underneath it
+
+ align:start position:0%
+shown as a little box underneath it
+ 
+
+ align:start position:0%
+shown as a little box underneath it
+there are different types of heaters one
+
+ align:start position:0%
+there are different types of heaters one
+ 
+
+ align:start position:0%
+there are different types of heaters one
+is a very very simple resistor it's just
+
+ align:start position:0%
+is a very very simple resistor it's just
+ 
+
+ align:start position:0%
+is a very very simple resistor it's just
+a piece of of wire of tungsten wire
+
+ align:start position:0%
+a piece of of wire of tungsten wire
+ 
+
+ align:start position:0%
+a piece of of wire of tungsten wire
+that's wrapped up into a filament like
+
+ align:start position:0%
+that's wrapped up into a filament like
+ 
+
+ align:start position:0%
+that's wrapped up into a filament like
+you would have in a light bulb and you
+
+ align:start position:0%
+you would have in a light bulb and you
+ 
+
+ align:start position:0%
+you would have in a light bulb and you
+pass a current through this wire and it
+
+ align:start position:0%
+pass a current through this wire and it
+ 
+
+ align:start position:0%
+pass a current through this wire and it
+gets really hot uh and that will um hate
+
+ align:start position:0%
+gets really hot uh and that will um hate
+ 
+
+ align:start position:0%
+gets really hot uh and that will um hate
+the aluminum or whatever is you're
+
+ align:start position:0%
+the aluminum or whatever is you're
+ 
+
+ align:start position:0%
+the aluminum or whatever is you're
+trying to
+
+ align:start position:0%
+trying to
+ 
+
+ align:start position:0%
+trying to
+evaporate um you can only get so hot
+
+ align:start position:0%
+evaporate um you can only get so hot
+ 
+
+ align:start position:0%
+evaporate um you can only get so hot
+with resistive heaters though so there's
+
+ align:start position:0%
+with resistive heaters though so there's
+ 
+
+ align:start position:0%
+with resistive heaters though so there's
+there's another way of heating up um the
+
+ align:start position:0%
+there's another way of heating up um the
+ 
+
+ align:start position:0%
+there's another way of heating up um the
+material in The Crucible that's to take
+
+ align:start position:0%
+material in The Crucible that's to take
+ 
+
+ align:start position:0%
+material in The Crucible that's to take
+an electron beam and to shoot the
+
+ align:start position:0%
+an electron beam and to shoot the
+ 
+
+ align:start position:0%
+an electron beam and to shoot the
+Electron Beam and to deposit energy by
+
+ align:start position:0%
+Electron Beam and to deposit energy by
+ 
+
+ align:start position:0%
+Electron Beam and to deposit energy by
+the Electron Beam into this um Li into
+
+ align:start position:0%
+the Electron Beam into this um Li into
+ 
+
+ align:start position:0%
+the Electron Beam into this um Li into
+this solid here and and liquefy the
+
+ align:start position:0%
+this solid here and and liquefy the
+ 
+
+ align:start position:0%
+this solid here and and liquefy the
+aluminum or whatever so that's called
+
+ align:start position:0%
+aluminum or whatever so that's called
+ 
+
+ align:start position:0%
+aluminum or whatever so that's called
+ebeam evaporation or Electron Beam
+
+ align:start position:0%
+ebeam evaporation or Electron Beam
+ 
+
+ align:start position:0%
+ebeam evaporation or Electron Beam
+evaporation two different methods of
+
+ align:start position:0%
+evaporation two different methods of
+ 
+
+ align:start position:0%
+evaporation two different methods of
+creating either case you're creating
+
+ align:start position:0%
+creating either case you're creating
+ 
+
+ align:start position:0%
+creating either case you're creating
+molten material that then flashes off uh
+
+ align:start position:0%
+molten material that then flashes off uh
+ 
+
+ align:start position:0%
+molten material that then flashes off uh
+and uh creates an atomic flux and that
+
+ align:start position:0%
+and uh creates an atomic flux and that
+ 
+
+ align:start position:0%
+and uh creates an atomic flux and that
+flux hits the surface of the wafer and
+
+ align:start position:0%
+flux hits the surface of the wafer and
+ 
+
+ align:start position:0%
+flux hits the surface of the wafer and
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deposited so if we go on to slide 15
+
+ align:start position:0%
+deposited so if we go on to slide 15
+ 
+
+ align:start position:0%
+deposited so if we go on to slide 15
+this uh is a picture I took directly out
+
+ align:start position:0%
+this uh is a picture I took directly out
+ 
+
+ align:start position:0%
+this uh is a picture I took directly out
+of your text uh and if you sit down with
+
+ align:start position:0%
+of your text uh and if you sit down with
+ 
+
+ align:start position:0%
+of your text uh and if you sit down with
+it and spend some time um you'll realize
+
+ align:start position:0%
+it and spend some time um you'll realize
+ 
+
+ align:start position:0%
+it and spend some time um you'll realize
+this is primarily uh really just uh
+
+ align:start position:0%
+this is primarily uh really just uh
+ 
+
+ align:start position:0%
+this is primarily uh really just uh
+geometry um so there are two cases case
+
+ align:start position:0%
+geometry um so there are two cases case
+ 
+
+ align:start position:0%
+geometry um so there are two cases case
+a on the left case b on the right case A
+
+ align:start position:0%
+a on the left case b on the right case A
+ 
+
+ align:start position:0%
+a on the left case b on the right case A
+is for what we uh call a point source uh
+
+ align:start position:0%
+is for what we uh call a point source uh
+ 
+
+ align:start position:0%
+is for what we uh call a point source uh
+and case b is for a small planer surface
+
+ align:start position:0%
+and case b is for a small planer surface
+ 
+
+ align:start position:0%
+and case b is for a small planer surface
+source of a finite
+
+ align:start position:0%
+source of a finite
+ 
+
+ align:start position:0%
+source of a finite
+extent so we just look for a minute at
+
+ align:start position:0%
+extent so we just look for a minute at
+ 
+
+ align:start position:0%
+extent so we just look for a minute at
+the point source this is where the
+
+ align:start position:0%
+the point source this is where the
+ 
+
+ align:start position:0%
+the point source this is where the
+source is located um imagine at some
+
+ align:start position:0%
+source is located um imagine at some
+ 
+
+ align:start position:0%
+source is located um imagine at some
+distance away H some perpendicular
+
+ align:start position:0%
+distance away H some perpendicular
+ 
+
+ align:start position:0%
+distance away H some perpendicular
+distance uh H there's a wafer holder
+
+ align:start position:0%
+distance uh H there's a wafer holder
+ 
+
+ align:start position:0%
+distance uh H there's a wafer holder
+with a uh on which you can put
+
+ align:start position:0%
+with a uh on which you can put
+ 
+
+ align:start position:0%
+with a uh on which you can put
+Wafers um and let's say you have your
+
+ align:start position:0%
+Wafers um and let's say you have your
+ 
+
+ align:start position:0%
+Wafers um and let's say you have your
+wafer out here um on this wafer holder
+
+ align:start position:0%
+wafer out here um on this wafer holder
+ 
+
+ align:start position:0%
+wafer out here um on this wafer holder
+uh at a distance L from this point from
+
+ align:start position:0%
+uh at a distance L from this point from
+ 
+
+ align:start position:0%
+uh at a distance L from this point from
+the center this makes a right right
+
+ align:start position:0%
+the center this makes a right right
+ 
+
+ align:start position:0%
+the center this makes a right right
+triangle um so the the uh line h l and R
+
+ align:start position:0%
+triangle um so the the uh line h l and R
+ 
+
+ align:start position:0%
+triangle um so the the uh line h l and R
+three together uh make a right triangle
+
+ align:start position:0%
+three together uh make a right triangle
+ 
+
+ align:start position:0%
+three together uh make a right triangle
+um for the for any of these deposition
+
+ align:start position:0%
+um for the for any of these deposition
+ 
+
+ align:start position:0%
+um for the for any of these deposition
+processes what really counts is the um
+
+ align:start position:0%
+processes what really counts is the um
+ 
+
+ align:start position:0%
+processes what really counts is the um
+perpendicular flux so it' be the the
+
+ align:start position:0%
+perpendicular flux so it' be the the
+ 
+
+ align:start position:0%
+perpendicular flux so it' be the the
+flux you know perpendicular um to the
+
+ align:start position:0%
+flux you know perpendicular um to the
+ 
+
+ align:start position:0%
+flux you know perpendicular um to the
+surface so you need to usually project
+
+ align:start position:0%
+surface so you need to usually project
+ 
+
+ align:start position:0%
+surface so you need to usually project
+this flux onto the surface uh and that's
+
+ align:start position:0%
+this flux onto the surface uh and that's
+ 
+
+ align:start position:0%
+this flux onto the surface uh and that's
+where uh you end up with a cosine Theta
+
+ align:start position:0%
+where uh you end up with a cosine Theta
+ 
+
+ align:start position:0%
+where uh you end up with a cosine Theta
+um kind of dependence of the deposition
+
+ align:start position:0%
+um kind of dependence of the deposition
+ 
+
+ align:start position:0%
+um kind of dependence of the deposition
+rate so anyway we have this point source
+
+ align:start position:0%
+rate so anyway we have this point source
+ 
+
+ align:start position:0%
+rate so anyway we have this point source
+it has a certain
+
+ align:start position:0%
+it has a certain
+ 
+
+ align:start position:0%
+it has a certain
+flux um that it's evaporating um that
+
+ align:start position:0%
+flux um that it's evaporating um that
+ 
+
+ align:start position:0%
+flux um that it's evaporating um that
+it's emitting and that is the rate of
+
+ align:start position:0%
+it's emitting and that is the rate of
+ 
+
+ align:start position:0%
+it's emitting and that is the rate of
+evaporation R evap divided by the solid
+
+ align:start position:0%
+evaporation R evap divided by the solid
+ 
+
+ align:start position:0%
+evaporation R evap divided by the solid
+angle Omega uh time R 2 where is the
+
+ align:start position:0%
+angle Omega uh time R 2 where is the
+ 
+
+ align:start position:0%
+angle Omega uh time R 2 where is the
+distance so if I take my point source I
+
+ align:start position:0%
+distance so if I take my point source I
+ 
+
+ align:start position:0%
+distance so if I take my point source I
+just move it further away the flux at
+
+ align:start position:0%
+just move it further away the flux at
+ 
+
+ align:start position:0%
+just move it further away the flux at
+that surface goes down like 1/ R
+
+ align:start position:0%
+that surface goes down like 1/ R
+ 
+
+ align:start position:0%
+that surface goes down like 1/ R
+2 so you can you can adjust the
+
+ align:start position:0%
+2 so you can you can adjust the
+ 
+
+ align:start position:0%
+2 so you can you can adjust the
+evaporation rate by taking the Wafers
+
+ align:start position:0%
+evaporation rate by taking the Wafers
+ 
+
+ align:start position:0%
+evaporation rate by taking the Wafers
+and moving them further or closer to the
+
+ align:start position:0%
+and moving them further or closer to the
+ 
+
+ align:start position:0%
+and moving them further or closer to the
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+source you can adjust the flux uh I'm
+
+ align:start position:0%
+source you can adjust the flux uh I'm
+ 
+
+ align:start position:0%
+source you can adjust the flux uh I'm
+sorry with the one over R squ this Omega
+
+ align:start position:0%
+sorry with the one over R squ this Omega
+ 
+
+ align:start position:0%
+sorry with the one over R squ this Omega
+is the solid angle over which The Source
+
+ align:start position:0%
+is the solid angle over which The Source
+ 
+
+ align:start position:0%
+is the solid angle over which The Source
+emits um it's equal to 4 Pi uh if if
+
+ align:start position:0%
+emits um it's equal to 4 Pi uh if if
+ 
+
+ align:start position:0%
+emits um it's equal to 4 Pi uh if if
+it's if it's emitting in all
+
+ align:start position:0%
+it's if it's emitting in all
+ 
+
+ align:start position:0%
+it's if it's emitting in all
+directions um and in this deposition
+
+ align:start position:0%
+directions um and in this deposition
+ 
+
+ align:start position:0%
+directions um and in this deposition
+rate term here on my left is this
+
+ align:start position:0%
+rate term here on my left is this
+ 
+
+ align:start position:0%
+rate term here on my left is this
+equation for the velocity the deposition
+
+ align:start position:0%
+equation for the velocity the deposition
+ 
+
+ align:start position:0%
+equation for the velocity the deposition
+rate n is the density of the material
+
+ align:start position:0%
+rate n is the density of the material
+ 
+
+ align:start position:0%
+rate n is the density of the material
+being deposited so here's the here's a
+
+ align:start position:0%
+being deposited so here's the here's a
+ 
+
+ align:start position:0%
+being deposited so here's the here's a
+very simple formula to calculate the
+
+ align:start position:0%
+very simple formula to calculate the
+ 
+
+ align:start position:0%
+very simple formula to calculate the
+deposition rate of your reactor it's the
+
+ align:start position:0%
+deposition rate of your reactor it's the
+ 
+
+ align:start position:0%
+deposition rate of your reactor it's the
+evaporation rate which you'll have to
+
+ align:start position:0%
+evaporation rate which you'll have to
+ 
+
+ align:start position:0%
+evaporation rate which you'll have to
+calculate that depends on the
+
+ align:start position:0%
+calculate that depends on the
+ 
+
+ align:start position:0%
+calculate that depends on the
+temperature and all that um divided by
+
+ align:start position:0%
+temperature and all that um divided by
+ 
+
+ align:start position:0%
+temperature and all that um divided by
+the solid angle times the density over R
+
+ align:start position:0%
+the solid angle times the density over R
+ 
+
+ align:start position:0%
+the solid angle times the density over R
+2 uh and there's a cosine Theta um Theta
+
+ align:start position:0%
+2 uh and there's a cosine Theta um Theta
+ 
+
+ align:start position:0%
+2 uh and there's a cosine Theta um Theta
+sub K here so Theta K here is this this
+
+ align:start position:0%
+sub K here so Theta K here is this this
+ 
+
+ align:start position:0%
+sub K here so Theta K here is this this
+angle um right here um so as I move out
+
+ align:start position:0%
+angle um right here um so as I move out
+ 
+
+ align:start position:0%
+angle um right here um so as I move out
+as I if I take a wafer and move it from
+
+ align:start position:0%
+as I if I take a wafer and move it from
+ 
+
+ align:start position:0%
+as I if I take a wafer and move it from
+right here and I move it along this line
+
+ align:start position:0%
+right here and I move it along this line
+ 
+
+ align:start position:0%
+right here and I move it along this line
+uh the deposition rate is is going to go
+
+ align:start position:0%
+uh the deposition rate is is going to go
+ 
+
+ align:start position:0%
+uh the deposition rate is is going to go
+down according to this cosine uh
+
+ align:start position:0%
+down according to this cosine uh
+ 
+
+ align:start position:0%
+down according to this cosine uh
+function um a small planer surface
+
+ align:start position:0%
+function um a small planer surface
+ 
+
+ align:start position:0%
+function um a small planer surface
+source is slightly different um there
+
+ align:start position:0%
+source is slightly different um there
+ 
+
+ align:start position:0%
+source is slightly different um there
+are two angles involved here uh there is
+
+ align:start position:0%
+are two angles involved here uh there is
+ 
+
+ align:start position:0%
+are two angles involved here uh there is
+this angle here um Theta I uh if that's
+
+ align:start position:0%
+this angle here um Theta I uh if that's
+ 
+
+ align:start position:0%
+this angle here um Theta I uh if that's
+the angle between the perpendicular to
+
+ align:start position:0%
+the angle between the perpendicular to
+ 
+
+ align:start position:0%
+the angle between the perpendicular to
+of the planer source so this planer
+
+ align:start position:0%
+of the planer source so this planer
+ 
+
+ align:start position:0%
+of the planer source so this planer
+Source it's like my my hand it has some
+
+ align:start position:0%
+Source it's like my my hand it has some
+ 
+
+ align:start position:0%
+Source it's like my my hand it has some
+angle that it's making uh Theta I um to
+
+ align:start position:0%
+angle that it's making uh Theta I um to
+ 
+
+ align:start position:0%
+angle that it's making uh Theta I um to
+the the point of evaporation and uh
+
+ align:start position:0%
+the the point of evaporation and uh
+ 
+
+ align:start position:0%
+the the point of evaporation and uh
+there's also the cosine Theta
+
+ align:start position:0%
+there's also the cosine Theta
+ 
+
+ align:start position:0%
+there's also the cosine Theta
+k um so the the key point is this
+
+ align:start position:0%
+k um so the the key point is this
+ 
+
+ align:start position:0%
+k um so the the key point is this
+outward flux FK from a point source p is
+
+ align:start position:0%
+outward flux FK from a point source p is
+ 
+
+ align:start position:0%
+outward flux FK from a point source p is
+independent of theta I um because Theta
+
+ align:start position:0%
+independent of theta I um because Theta
+ 
+
+ align:start position:0%
+independent of theta I um because Theta
+I really equals Theta K in this case um
+
+ align:start position:0%
+I really equals Theta K in this case um
+ 
+
+ align:start position:0%
+I really equals Theta K in this case um
+so it's it's independent of it just is
+
+ align:start position:0%
+so it's it's independent of it just is
+ 
+
+ align:start position:0%
+so it's it's independent of it just is
+emitting a point source emits the same
+
+ align:start position:0%
+emitting a point source emits the same
+ 
+
+ align:start position:0%
+emitting a point source emits the same
+around a sphere in all
+
+ align:start position:0%
+around a sphere in all
+ 
+
+ align:start position:0%
+around a sphere in all
+directions so but the outward flux from
+
+ align:start position:0%
+directions so but the outward flux from
+ 
+
+ align:start position:0%
+directions so but the outward flux from
+the small Source like from my head it
+
+ align:start position:0%
+the small Source like from my head it
+ 
+
+ align:start position:0%
+the small Source like from my head it
+depends on uh some some variable uh it
+
+ align:start position:0%
+depends on uh some some variable uh it
+ 
+
+ align:start position:0%
+depends on uh some some variable uh it
+depends in some way cosine Theta I to
+
+ align:start position:0%
+depends in some way cosine Theta I to
+ 
+
+ align:start position:0%
+depends in some way cosine Theta I to
+the end um where n is going to be a
+
+ align:start position:0%
+the end um where n is going to be a
+ 
+
+ align:start position:0%
+the end um where n is going to be a
+variable you end up uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fitting so let's give uh maybe give you
+
+ align:start position:0%
+fitting so let's give uh maybe give you
+ 
+
+ align:start position:0%
+fitting so let's give uh maybe give you
+an example uh to make that a little bit
+
+ align:start position:0%
+an example uh to make that a little bit
+ 
+
+ align:start position:0%
+an example uh to make that a little bit
+clear on on slide 16 this is a plot of
+
+ align:start position:0%
+clear on on slide 16 this is a plot of
+ 
+
+ align:start position:0%
+clear on on slide 16 this is a plot of
+um exactly that structure here I have a
+
+ align:start position:0%
+um exactly that structure here I have a
+ 
+
+ align:start position:0%
+um exactly that structure here I have a
+substrate and uh I'm looking at uh the
+
+ align:start position:0%
+substrate and uh I'm looking at uh the
+ 
+
+ align:start position:0%
+substrate and uh I'm looking at uh the
+evaporation uh as a the evaporation rate
+
+ align:start position:0%
+evaporation uh as a the evaporation rate
+ 
+
+ align:start position:0%
+evaporation uh as a the evaporation rate
+r or the uh flux the the uh yeah the the
+
+ align:start position:0%
+r or the uh flux the the uh yeah the the
+ 
+
+ align:start position:0%
+r or the uh flux the the uh yeah the the
+surface evaporation rate uh as a
+
+ align:start position:0%
+surface evaporation rate uh as a
+ 
+
+ align:start position:0%
+surface evaporation rate uh as a
+function of um l h so again L is the
+
+ align:start position:0%
+function of um l h so again L is the
+ 
+
+ align:start position:0%
+function of um l h so again L is the
+distance that you go out from being
+
+ align:start position:0%
+distance that you go out from being
+ 
+
+ align:start position:0%
+distance that you go out from being
+directly under the under the source um
+
+ align:start position:0%
+directly under the under the source um
+ 
+
+ align:start position:0%
+directly under the under the source um
+and H is the distance of the substrate
+
+ align:start position:0%
+and H is the distance of the substrate
+ 
+
+ align:start position:0%
+and H is the distance of the substrate
+holder from the source and we just this
+
+ align:start position:0%
+holder from the source and we just this
+ 
+
+ align:start position:0%
+holder from the source and we just this
+r l and H makes this right triangle uh
+
+ align:start position:0%
+r l and H makes this right triangle uh
+ 
+
+ align:start position:0%
+r l and H makes this right triangle uh
+so as a function of L over H you see the
+
+ align:start position:0%
+so as a function of L over H you see the
+ 
+
+ align:start position:0%
+so as a function of L over H you see the
+depth rate can be calculated just
+
+ align:start position:0%
+depth rate can be calculated just
+ 
+
+ align:start position:0%
+depth rate can be calculated just
+according to these two equations um so
+
+ align:start position:0%
+according to these two equations um so
+ 
+
+ align:start position:0%
+according to these two equations um so
+when L equals H here uh you can
+
+ align:start position:0%
+when L equals H here uh you can
+ 
+
+ align:start position:0%
+when L equals H here uh you can
+calculate the relative depth rate um
+
+ align:start position:0%
+calculate the relative depth rate um
+ 
+
+ align:start position:0%
+calculate the relative depth rate um
+compared uh compared to the depth rate
+
+ align:start position:0%
+compared uh compared to the depth rate
+ 
+
+ align:start position:0%
+compared uh compared to the depth rate
+directly perpendicular from the source
+
+ align:start position:0%
+directly perpendicular from the source
+ 
+
+ align:start position:0%
+directly perpendicular from the source
+is down by about um it's like
+
+ align:start position:0%
+is down by about um it's like
+ 
+
+ align:start position:0%
+is down by about um it's like
+30% of what it would be the depth rate
+
+ align:start position:0%
+30% of what it would be the depth rate
+ 
+
+ align:start position:0%
+30% of what it would be the depth rate
+right at this point so you get an idea
+
+ align:start position:0%
+right at this point so you get an idea
+ 
+
+ align:start position:0%
+right at this point so you get an idea
+of what the uniformity will be um along
+
+ align:start position:0%
+of what the uniformity will be um along
+ 
+
+ align:start position:0%
+of what the uniformity will be um along
+this surface uh and there's different
+
+ align:start position:0%
+this surface uh and there's different
+ 
+
+ align:start position:0%
+this surface uh and there's different
+curves the dash line here is for the
+
+ align:start position:0%
+curves the dash line here is for the
+ 
+
+ align:start position:0%
+curves the dash line here is for the
+surface source and the point source is
+
+ align:start position:0%
+surface source and the point source is
+ 
+
+ align:start position:0%
+surface source and the point source is
+the solid line so they have slightly
+
+ align:start position:0%
+the solid line so they have slightly
+ 
+
+ align:start position:0%
+the solid line so they have slightly
+different dependence uh on those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parameters so um if we go on to slide
+
+ align:start position:0%
+parameters so um if we go on to slide
+ 
+
+ align:start position:0%
+parameters so um if we go on to slide
+17 um as I as we mentioned the outward
+
+ align:start position:0%
+17 um as I as we mentioned the outward
+ 
+
+ align:start position:0%
+17 um as I as we mentioned the outward
+flux from a point source p is
+
+ align:start position:0%
+flux from a point source p is
+ 
+
+ align:start position:0%
+flux from a point source p is
+independent of this Theta I whereas from
+
+ align:start position:0%
+independent of this Theta I whereas from
+ 
+
+ align:start position:0%
+independent of this Theta I whereas from
+a small area Source it goes like cosine
+
+ align:start position:0%
+a small area Source it goes like cosine
+ 
+
+ align:start position:0%
+a small area Source it goes like cosine
+Theta I and and in fact if you look at
+
+ align:start position:0%
+Theta I and and in fact if you look at
+ 
+
+ align:start position:0%
+Theta I and and in fact if you look at
+this um I think it becomes more
+
+ align:start position:0%
+this um I think it becomes more
+ 
+
+ align:start position:0%
+this um I think it becomes more
+intuitive if you look at just look at
+
+ align:start position:0%
+intuitive if you look at just look at
+ 
+
+ align:start position:0%
+intuitive if you look at just look at
+this diagram on on slide 17 um look at
+
+ align:start position:0%
+this diagram on on slide 17 um look at
+ 
+
+ align:start position:0%
+this diagram on on slide 17 um look at
+look at diagram a this is I have a point
+
+ align:start position:0%
+look at diagram a this is I have a point
+ 
+
+ align:start position:0%
+look at diagram a this is I have a point
+source right at this point and I'm
+
+ align:start position:0%
+source right at this point and I'm
+ 
+
+ align:start position:0%
+source right at this point and I'm
+assuming that Source has uniform that is
+
+ align:start position:0%
+assuming that Source has uniform that is
+ 
+
+ align:start position:0%
+assuming that Source has uniform that is
+isotropic it's the same in all dire
+
+ align:start position:0%
+isotropic it's the same in all dire
+ 
+
+ align:start position:0%
+isotropic it's the same in all dire
+directions emission from a point source
+
+ align:start position:0%
+directions emission from a point source
+ 
+
+ align:start position:0%
+directions emission from a point source
+so each line um is is the length of a
+
+ align:start position:0%
+so each line um is is the length of a
+ 
+
+ align:start position:0%
+so each line um is is the length of a
+line is meant to represent the flux so
+
+ align:start position:0%
+line is meant to represent the flux so
+ 
+
+ align:start position:0%
+line is meant to represent the flux so
+the flux is the same in all directions
+
+ align:start position:0%
+the flux is the same in all directions
+ 
+
+ align:start position:0%
+the flux is the same in all directions
+so this a very spherically uniform
+
+ align:start position:0%
+so this a very spherically uniform
+ 
+
+ align:start position:0%
+so this a very spherically uniform
+isotropic source that would be like a
+
+ align:start position:0%
+isotropic source that would be like a
+ 
+
+ align:start position:0%
+isotropic source that would be like a
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+source um if you uh look at look at um
+
+ align:start position:0%
+source um if you uh look at look at um
+ 
+
+ align:start position:0%
+source um if you uh look at look at um
+uh number B here uh this is um ideal
+
+ align:start position:0%
+uh number B here uh this is um ideal
+ 
+
+ align:start position:0%
+uh number B here uh this is um ideal
+what they call Ideal coine emission from
+
+ align:start position:0%
+what they call Ideal coine emission from
+ 
+
+ align:start position:0%
+what they call Ideal coine emission from
+a small planer surface source so imagine
+
+ align:start position:0%
+a small planer surface source so imagine
+ 
+
+ align:start position:0%
+a small planer surface source so imagine
+right here at this at this point in
+
+ align:start position:0%
+right here at this at this point in
+ 
+
+ align:start position:0%
+right here at this at this point in
+space I have a planer surface Source the
+
+ align:start position:0%
+space I have a planer surface Source the
+ 
+
+ align:start position:0%
+space I have a planer surface Source the
+flux is largest straight above so
+
+ align:start position:0%
+flux is largest straight above so
+ 
+
+ align:start position:0%
+flux is largest straight above so
+because it's the longest arrow and the
+
+ align:start position:0%
+because it's the longest arrow and the
+ 
+
+ align:start position:0%
+because it's the longest arrow and the
+flux then goes down as you go from here
+
+ align:start position:0%
+flux then goes down as you go from here
+ 
+
+ align:start position:0%
+flux then goes down as you go from here
+to here it goes down like a cosine Theta
+
+ align:start position:0%
+to here it goes down like a cosine Theta
+ 
+
+ align:start position:0%
+to here it goes down like a cosine Theta
+where n equals 1 so the flux is going
+
+ align:start position:0%
+where n equals 1 so the flux is going
+ 
+
+ align:start position:0%
+where n equals 1 so the flux is going
+down um and there also in C there are
+
+ align:start position:0%
+down um and there also in C there are
+ 
+
+ align:start position:0%
+down um and there also in C there are
+non ideal more anisotropic emission from
+
+ align:start position:0%
+non ideal more anisotropic emission from
+ 
+
+ align:start position:0%
+non ideal more anisotropic emission from
+a different type of small planer Source
+
+ align:start position:0%
+a different type of small planer Source
+ 
+
+ align:start position:0%
+a different type of small planer Source
+this is cosine Theta the n in general
+
+ align:start position:0%
+this is cosine Theta the n in general
+ 
+
+ align:start position:0%
+this is cosine Theta the n in general
+where n is some some number um and so
+
+ align:start position:0%
+where n is some some number um and so
+ 
+
+ align:start position:0%
+where n is some some number um and so
+you can see what this means as you're
+
+ align:start position:0%
+you can see what this means as you're
+ 
+
+ align:start position:0%
+you can see what this means as you're
+getting much higher flux going straight
+
+ align:start position:0%
+getting much higher flux going straight
+ 
+
+ align:start position:0%
+getting much higher flux going straight
+above the source than you are going as
+
+ align:start position:0%
+above the source than you are going as
+ 
+
+ align:start position:0%
+above the source than you are going as
+you make an angle with respect to the
+
+ align:start position:0%
+you make an angle with respect to the
+ 
+
+ align:start position:0%
+you make an angle with respect to the
+source so it really depends on how the
+
+ align:start position:0%
+source so it really depends on how the
+ 
+
+ align:start position:0%
+source so it really depends on how the
+source is is um set up why do we care
+
+ align:start position:0%
+source is is um set up why do we care
+ 
+
+ align:start position:0%
+source is is um set up why do we care
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+this well we care because depending on
+
+ align:start position:0%
+this well we care because depending on
+ 
+
+ align:start position:0%
+this well we care because depending on
+the type of source we have to figure out
+
+ align:start position:0%
+the type of source we have to figure out
+ 
+
+ align:start position:0%
+the type of source we have to figure out
+how to place the wafers in the
+
+ align:start position:0%
+how to place the wafers in the
+ 
+
+ align:start position:0%
+how to place the wafers in the
+evaporator so you get the most uniform
+
+ align:start position:0%
+evaporator so you get the most uniform
+ 
+
+ align:start position:0%
+evaporator so you get the most uniform
+thickness across any given wafer or from
+
+ align:start position:0%
+thickness across any given wafer or from
+ 
+
+ align:start position:0%
+thickness across any given wafer or from
+wafer to wafer so uh there are two
+
+ align:start position:0%
+wafer to wafer so uh there are two
+ 
+
+ align:start position:0%
+wafer to wafer so uh there are two
+different places you can place uh in
+
+ align:start position:0%
+different places you can place uh in
+ 
+
+ align:start position:0%
+different places you can place uh in
+common in re in Epi in um in evaporators
+
+ align:start position:0%
+common in re in Epi in um in evaporators
+ 
+
+ align:start position:0%
+common in re in Epi in um in evaporators
+so if you have a point source that
+
+ align:start position:0%
+so if you have a point source that
+ 
+
+ align:start position:0%
+so if you have a point source that
+something something that behaves like an
+
+ align:start position:0%
+something something that behaves like an
+ 
+
+ align:start position:0%
+something something that behaves like an
+ideal point source you typically put it
+
+ align:start position:0%
+ideal point source you typically put it
+ 
+
+ align:start position:0%
+ideal point source you typically put it
+right in the center of the sphere so you
+
+ align:start position:0%
+right in the center of the sphere so you
+ 
+
+ align:start position:0%
+right in the center of the sphere so you
+would put the um evaporation source of
+
+ align:start position:0%
+would put the um evaporation source of
+ 
+
+ align:start position:0%
+would put the um evaporation source of
+platinum or aluminum right here in the
+
+ align:start position:0%
+platinum or aluminum right here in the
+ 
+
+ align:start position:0%
+platinum or aluminum right here in the
+center then you get a uniform flux in
+
+ align:start position:0%
+center then you get a uniform flux in
+ 
+
+ align:start position:0%
+center then you get a uniform flux in
+all directions and you put the Wafers
+
+ align:start position:0%
+all directions and you put the Wafers
+ 
+
+ align:start position:0%
+all directions and you put the Wafers
+along um the the circumference uh facing
+
+ align:start position:0%
+along um the the circumference uh facing
+ 
+
+ align:start position:0%
+along um the the circumference uh facing
+that point
+
+ align:start position:0%
+that point
+ 
+
+ align:start position:0%
+that point
+source so use a spherical waer holder um
+
+ align:start position:0%
+source so use a spherical waer holder um
+ 
+
+ align:start position:0%
+source so use a spherical waer holder um
+if you have a small surface Source you
+
+ align:start position:0%
+if you have a small surface Source you
+ 
+
+ align:start position:0%
+if you have a small surface Source you
+usually put the source on the inside of
+
+ align:start position:0%
+usually put the source on the inside of
+ 
+
+ align:start position:0%
+usually put the source on the inside of
+the sphere right here um and you put the
+
+ align:start position:0%
+the sphere right here um and you put the
+ 
+
+ align:start position:0%
+the sphere right here um and you put the
+Wafers again um uh on on the surface of
+
+ align:start position:0%
+Wafers again um uh on on the surface of
+ 
+
+ align:start position:0%
+Wafers again um uh on on the surface of
+the sphere so this tends putting it here
+
+ align:start position:0%
+the sphere so this tends putting it here
+ 
+
+ align:start position:0%
+the sphere so this tends putting it here
+tends to compensate for the cosine Theta
+
+ align:start position:0%
+tends to compensate for the cosine Theta
+ 
+
+ align:start position:0%
+tends to compensate for the cosine Theta
+to the end because look what happens
+
+ align:start position:0%
+to the end because look what happens
+ 
+
+ align:start position:0%
+to the end because look what happens
+this is my source right here I have the
+
+ align:start position:0%
+this is my source right here I have the
+ 
+
+ align:start position:0%
+this is my source right here I have the
+highest flux according to this diagram I
+
+ align:start position:0%
+highest flux according to this diagram I
+ 
+
+ align:start position:0%
+highest flux according to this diagram I
+have the highest flux straight in front
+
+ align:start position:0%
+have the highest flux straight in front
+ 
+
+ align:start position:0%
+have the highest flux straight in front
+of me that wafer is the furthest away so
+
+ align:start position:0%
+of me that wafer is the furthest away so
+ 
+
+ align:start position:0%
+of me that wafer is the furthest away so
+I have a high flux it's the furthest
+
+ align:start position:0%
+I have a high flux it's the furthest
+ 
+
+ align:start position:0%
+I have a high flux it's the furthest
+distance um that one over R squar
+
+ align:start position:0%
+distance um that one over R squar
+ 
+
+ align:start position:0%
+distance um that one over R squar
+dependence will tend to compensate for
+
+ align:start position:0%
+dependence will tend to compensate for
+ 
+
+ align:start position:0%
+dependence will tend to compensate for
+that higher flux and so you get the same
+
+ align:start position:0%
+that higher flux and so you get the same
+ 
+
+ align:start position:0%
+that higher flux and so you get the same
+depth rate on this wafer as you do on
+
+ align:start position:0%
+depth rate on this wafer as you do on
+ 
+
+ align:start position:0%
+depth rate on this wafer as you do on
+this wafer this wafer has the lower flux
+
+ align:start position:0%
+this wafer this wafer has the lower flux
+ 
+
+ align:start position:0%
+this wafer this wafer has the lower flux
+right it's gone down by cosine Theta but
+
+ align:start position:0%
+right it's gone down by cosine Theta but
+ 
+
+ align:start position:0%
+right it's gone down by cosine Theta but
+on the other hand it's also closer so
+
+ align:start position:0%
+on the other hand it's also closer so
+ 
+
+ align:start position:0%
+on the other hand it's also closer so
+the 1/ r squ dependence will cancel that
+
+ align:start position:0%
+the 1/ r squ dependence will cancel that
+ 
+
+ align:start position:0%
+the 1/ r squ dependence will cancel that
+out so this is typically where you want
+
+ align:start position:0%
+out so this is typically where you want
+ 
+
+ align:start position:0%
+out so this is typically where you want
+to put it um for a surface Source in in
+
+ align:start position:0%
+to put it um for a surface Source in in
+ 
+
+ align:start position:0%
+to put it um for a surface Source in in
+an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evaporator okay a little bit more on
+
+ align:start position:0%
+evaporator okay a little bit more on
+ 
+
+ align:start position:0%
+evaporator okay a little bit more on
+evaporation slide 18 this is an
+
+ align:start position:0%
+evaporation slide 18 this is an
+ 
+
+ align:start position:0%
+evaporation slide 18 this is an
+interesting plot this shows the um vapor
+
+ align:start position:0%
+interesting plot this shows the um vapor
+ 
+
+ align:start position:0%
+interesting plot this shows the um vapor
+pressure in t um as a function of
+
+ align:start position:0%
+pressure in t um as a function of
+ 
+
+ align:start position:0%
+pressure in t um as a function of
+temperature for um a number of different
+
+ align:start position:0%
+temperature for um a number of different
+ 
+
+ align:start position:0%
+temperature for um a number of different
+elements uh remember if I go back to my
+
+ align:start position:0%
+elements uh remember if I go back to my
+ 
+
+ align:start position:0%
+elements uh remember if I go back to my
+flux equation or my my deposition rate
+
+ align:start position:0%
+flux equation or my my deposition rate
+ 
+
+ align:start position:0%
+flux equation or my my deposition rate
+go back going back to slide 15 for a
+
+ align:start position:0%
+go back going back to slide 15 for a
+ 
+
+ align:start position:0%
+go back going back to slide 15 for a
+minute um the flux was directly
+
+ align:start position:0%
+minute um the flux was directly
+ 
+
+ align:start position:0%
+minute um the flux was directly
+proportional to the evaporation rate
+
+ align:start position:0%
+proportional to the evaporation rate
+ 
+
+ align:start position:0%
+proportional to the evaporation rate
+over um uh something time R 2 um so I
+
+ align:start position:0%
+over um uh something time R 2 um so I
+ 
+
+ align:start position:0%
+over um uh something time R 2 um so I
+need to know what the evaporation rate
+
+ align:start position:0%
+need to know what the evaporation rate
+ 
+
+ align:start position:0%
+need to know what the evaporation rate
+is in order to calculate the depth rate
+
+ align:start position:0%
+is in order to calculate the depth rate
+ 
+
+ align:start position:0%
+is in order to calculate the depth rate
+on on the
+
+ align:start position:0%
+on on the
+ 
+
+ align:start position:0%
+on on the
+wafer so again going back to slide 18
+
+ align:start position:0%
+wafer so again going back to slide 18
+ 
+
+ align:start position:0%
+wafer so again going back to slide 18
+this this tells you here I have a
+
+ align:start position:0%
+this this tells you here I have a
+ 
+
+ align:start position:0%
+this this tells you here I have a
+formula here that you can calculate the
+
+ align:start position:0%
+formula here that you can calculate the
+ 
+
+ align:start position:0%
+formula here that you can calculate the
+evaporation rate here uh depending on
+
+ align:start position:0%
+evaporation rate here uh depending on
+ 
+
+ align:start position:0%
+evaporation rate here uh depending on
+this um vapor pressure p so B at the
+
+ align:start position:0%
+this um vapor pressure p so B at the
+ 
+
+ align:start position:0%
+this um vapor pressure p so B at the
+evaporation temperature um so uh the
+
+ align:start position:0%
+evaporation temperature um so uh the
+ 
+
+ align:start position:0%
+evaporation temperature um so uh the
+evaporation rate is is is naturally
+
+ align:start position:0%
+evaporation rate is is is naturally
+ 
+
+ align:start position:0%
+evaporation rate is is is naturally
+proportional to vapor pressure uh of uh
+
+ align:start position:0%
+proportional to vapor pressure uh of uh
+ 
+
+ align:start position:0%
+proportional to vapor pressure uh of uh
+uh at the evaporation temperature so
+
+ align:start position:0%
+uh at the evaporation temperature so
+ 
+
+ align:start position:0%
+uh at the evaporation temperature so
+what you can see is you can just need to
+
+ align:start position:0%
+what you can see is you can just need to
+ 
+
+ align:start position:0%
+what you can see is you can just need to
+depending on the element depending on
+
+ align:start position:0%
+depending on the element depending on
+ 
+
+ align:start position:0%
+depending on the element depending on
+whether you're trying to evaporate
+
+ align:start position:0%
+whether you're trying to evaporate
+ 
+
+ align:start position:0%
+whether you're trying to evaporate
+indium well uh indium you can do that at
+
+ align:start position:0%
+indium well uh indium you can do that at
+ 
+
+ align:start position:0%
+indium well uh indium you can do that at
+pretty low temperatures look at its
+
+ align:start position:0%
+pretty low temperatures look at its
+ 
+
+ align:start position:0%
+pretty low temperatures look at its
+vapor pressure it goes at skyrockets
+
+ align:start position:0%
+vapor pressure it goes at skyrockets
+ 
+
+ align:start position:0%
+vapor pressure it goes at skyrockets
+above about 550 Centigrade if you're
+
+ align:start position:0%
+above about 550 Centigrade if you're
+ 
+
+ align:start position:0%
+above about 550 Centigrade if you're
+trying to evaporate some refractory
+
+ align:start position:0%
+trying to evaporate some refractory
+ 
+
+ align:start position:0%
+trying to evaporate some refractory
+metal for instance miminum or tuxen uh
+
+ align:start position:0%
+metal for instance miminum or tuxen uh
+ 
+
+ align:start position:0%
+metal for instance miminum or tuxen uh
+good luck with the resist heater you'd
+
+ align:start position:0%
+good luck with the resist heater you'd
+ 
+
+ align:start position:0%
+good luck with the resist heater you'd
+have to use an electron beam you have to
+
+ align:start position:0%
+have to use an electron beam you have to
+ 
+
+ align:start position:0%
+have to use an electron beam you have to
+go to very high temperatures to get any
+
+ align:start position:0%
+go to very high temperatures to get any
+ 
+
+ align:start position:0%
+go to very high temperatures to get any
+kind of reasonable vapor pressure um
+
+ align:start position:0%
+kind of reasonable vapor pressure um
+ 
+
+ align:start position:0%
+kind of reasonable vapor pressure um
+here but just about if you can design a
+
+ align:start position:0%
+here but just about if you can design a
+ 
+
+ align:start position:0%
+here but just about if you can design a
+heater an electron beam or a resistance
+
+ align:start position:0%
+heater an electron beam or a resistance
+ 
+
+ align:start position:0%
+heater an electron beam or a resistance
+heater then you can evaporate it that's
+
+ align:start position:0%
+heater then you can evaporate it that's
+ 
+
+ align:start position:0%
+heater then you can evaporate it that's
+the name of the game with evaporation
+
+ align:start position:0%
+the name of the game with evaporation
+ 
+
+ align:start position:0%
+the name of the game with evaporation
+you can evaporate just about any element
+
+ align:start position:0%
+you can evaporate just about any element
+ 
+
+ align:start position:0%
+you can evaporate just about any element
+um so in a thin films lab you can do
+
+ align:start position:0%
+um so in a thin films lab you can do
+ 
+
+ align:start position:0%
+um so in a thin films lab you can do
+just about uh anything um the depth rate
+
+ align:start position:0%
+just about uh anything um the depth rate
+ 
+
+ align:start position:0%
+just about uh anything um the depth rate
+of some elements is going to be very
+
+ align:start position:0%
+of some elements is going to be very
+ 
+
+ align:start position:0%
+of some elements is going to be very
+slow because uh the um the evaporation
+
+ align:start position:0%
+slow because uh the um the evaporation
+ 
+
+ align:start position:0%
+slow because uh the um the evaporation
+rate is low as vapor pressure may be low
+
+ align:start position:0%
+rate is low as vapor pressure may be low
+ 
+
+ align:start position:0%
+rate is low as vapor pressure may be low
+um one thing a good point though is it's
+
+ align:start position:0%
+um one thing a good point though is it's
+ 
+
+ align:start position:0%
+um one thing a good point though is it's
+very difficult to evaporate Alloys or
+
+ align:start position:0%
+very difficult to evaporate Alloys or
+ 
+
+ align:start position:0%
+very difficult to evaporate Alloys or
+compounds as you can see that um
+
+ align:start position:0%
+compounds as you can see that um
+ 
+
+ align:start position:0%
+compounds as you can see that um
+depending on the material between you
+
+ align:start position:0%
+depending on the material between you
+ 
+
+ align:start position:0%
+depending on the material between you
+know aluminum and nickel or chromium and
+
+ align:start position:0%
+know aluminum and nickel or chromium and
+ 
+
+ align:start position:0%
+know aluminum and nickel or chromium and
+nickel or whatever at a given
+
+ align:start position:0%
+nickel or whatever at a given
+ 
+
+ align:start position:0%
+nickel or whatever at a given
+temperature their evaporation their
+
+ align:start position:0%
+temperature their evaporation their
+ 
+
+ align:start position:0%
+temperature their evaporation their
+Vapor pressures vary by orders of
+
+ align:start position:0%
+Vapor pressures vary by orders of
+ 
+
+ align:start position:0%
+Vapor pressures vary by orders of
+magnitude orders of magnitude and so uh
+
+ align:start position:0%
+magnitude orders of magnitude and so uh
+ 
+
+ align:start position:0%
+magnitude orders of magnitude and so uh
+if you had you put in your little
+
+ align:start position:0%
+if you had you put in your little
+ 
+
+ align:start position:0%
+if you had you put in your little
+Crucible you know a little bit of one
+
+ align:start position:0%
+Crucible you know a little bit of one
+ 
+
+ align:start position:0%
+Crucible you know a little bit of one
+element a little bit of another element
+
+ align:start position:0%
+element a little bit of another element
+ 
+
+ align:start position:0%
+element a little bit of another element
+um they're going to come off at very
+
+ align:start position:0%
+um they're going to come off at very
+ 
+
+ align:start position:0%
+um they're going to come off at very
+different rates so trying to evaporate a
+
+ align:start position:0%
+different rates so trying to evaporate a
+ 
+
+ align:start position:0%
+different rates so trying to evaporate a
+compound is tricky you probably need two
+
+ align:start position:0%
+compound is tricky you probably need two
+ 
+
+ align:start position:0%
+compound is tricky you probably need two
+crucibles with their temperatures
+
+ align:start position:0%
+crucibles with their temperatures
+ 
+
+ align:start position:0%
+crucibles with their temperatures
+control electronically very carefully so
+
+ align:start position:0%
+control electronically very carefully so
+ 
+
+ align:start position:0%
+control electronically very carefully so
+that gets a little
+
+ align:start position:0%
+that gets a little
+ 
+
+ align:start position:0%
+that gets a little
+tricky um probably the most important
+
+ align:start position:0%
+tricky um probably the most important
+ 
+
+ align:start position:0%
+tricky um probably the most important
+thing reason why evaporation is not used
+
+ align:start position:0%
+thing reason why evaporation is not used
+ 
+
+ align:start position:0%
+thing reason why evaporation is not used
+in Fabrication in in semiconductor
+
+ align:start position:0%
+in Fabrication in in semiconductor
+ 
+
+ align:start position:0%
+in Fabrication in in semiconductor
+manufacturing anymore uh is the step
+
+ align:start position:0%
+manufacturing anymore uh is the step
+ 
+
+ align:start position:0%
+manufacturing anymore uh is the step
+coverage is very poor um it it's pretty
+
+ align:start position:0%
+coverage is very poor um it it's pretty
+ 
+
+ align:start position:0%
+coverage is very poor um it it's pretty
+much line of sight so if you if you're
+
+ align:start position:0%
+much line of sight so if you if you're
+ 
+
+ align:start position:0%
+much line of sight so if you if you're
+doing a trying to fill a trench for
+
+ align:start position:0%
+doing a trying to fill a trench for
+ 
+
+ align:start position:0%
+doing a trying to fill a trench for
+example in in a here and let's say you
+
+ align:start position:0%
+example in in a here and let's say you
+ 
+
+ align:start position:0%
+example in in a here and let's say you
+uniformly want to deposit the material
+
+ align:start position:0%
+uniformly want to deposit the material
+ 
+
+ align:start position:0%
+uniformly want to deposit the material
+all along the trench um because of
+
+ align:start position:0%
+all along the trench um because of
+ 
+
+ align:start position:0%
+all along the trench um because of
+shadowing effects as the this luminum or
+
+ align:start position:0%
+shadowing effects as the this luminum or
+ 
+
+ align:start position:0%
+shadowing effects as the this luminum or
+whatever it is comes down it's pretty
+
+ align:start position:0%
+whatever it is comes down it's pretty
+ 
+
+ align:start position:0%
+whatever it is comes down it's pretty
+much just going to deposit right here
+
+ align:start position:0%
+much just going to deposit right here
+ 
+
+ align:start position:0%
+much just going to deposit right here
+it's not going to hit the sidewalls um
+
+ align:start position:0%
+it's not going to hit the sidewalls um
+ 
+
+ align:start position:0%
+it's not going to hit the sidewalls um
+so if you need this conformal deposition
+
+ align:start position:0%
+so if you need this conformal deposition
+ 
+
+ align:start position:0%
+so if you need this conformal deposition
+you're not going to be able to get it uh
+
+ align:start position:0%
+you're not going to be able to get it uh
+ 
+
+ align:start position:0%
+you're not going to be able to get it uh
+by um you're going to need to use
+
+ align:start position:0%
+by um you're going to need to use
+ 
+
+ align:start position:0%
+by um you're going to need to use
+sputtering you're not to be able to get
+
+ align:start position:0%
+sputtering you're not to be able to get
+ 
+
+ align:start position:0%
+sputtering you're not to be able to get
+it by
+
+ align:start position:0%
+it by
+ 
+
+ align:start position:0%
+it by
+evaporation there are other reasons it's
+
+ align:start position:0%
+evaporation there are other reasons it's
+ 
+
+ align:start position:0%
+evaporation there are other reasons it's
+it's rarely used not just the line of
+
+ align:start position:0%
+it's rarely used not just the line of
+ 
+
+ align:start position:0%
+it's rarely used not just the line of
+sight but um uh the the evaporate itself
+
+ align:start position:0%
+sight but um uh the the evaporate itself
+ 
+
+ align:start position:0%
+sight but um uh the the evaporate itself
+is very hot a lot of impur when you have
+
+ align:start position:0%
+is very hot a lot of impur when you have
+ 
+
+ align:start position:0%
+is very hot a lot of impur when you have
+a little hot body a hot metal body like
+
+ align:start position:0%
+a little hot body a hot metal body like
+ 
+
+ align:start position:0%
+a little hot body a hot metal body like
+that any impurities on the metal body
+
+ align:start position:0%
+that any impurities on the metal body
+ 
+
+ align:start position:0%
+that any impurities on the metal body
+can end up being put onto your wafer so
+
+ align:start position:0%
+can end up being put onto your wafer so
+ 
+
+ align:start position:0%
+can end up being put onto your wafer so
+it's a little bit tricky to control
+
+ align:start position:0%
+it's a little bit tricky to control
+ 
+
+ align:start position:0%
+it's a little bit tricky to control
+impurities um and the Electron Beam uh
+
+ align:start position:0%
+impurities um and the Electron Beam uh
+ 
+
+ align:start position:0%
+impurities um and the Electron Beam uh
+it itself when it strikes things
+
+ align:start position:0%
+it itself when it strikes things
+ 
+
+ align:start position:0%
+it itself when it strikes things
+remember if you have a high energetic
+
+ align:start position:0%
+remember if you have a high energetic
+ 
+
+ align:start position:0%
+remember if you have a high energetic
+electron striking something you can
+
+ align:start position:0%
+electron striking something you can
+ 
+
+ align:start position:0%
+electron striking something you can
+create x-rays you can create photons
+
+ align:start position:0%
+create x-rays you can create photons
+ 
+
+ align:start position:0%
+create x-rays you can create photons
+that's how x-rays are actually created
+
+ align:start position:0%
+that's how x-rays are actually created
+ 
+
+ align:start position:0%
+that's how x-rays are actually created
+so there is an inadvertent creation of
+
+ align:start position:0%
+so there is an inadvertent creation of
+ 
+
+ align:start position:0%
+so there is an inadvertent creation of
+uh energetic uh material energetic
+
+ align:start position:0%
+uh energetic uh material energetic
+ 
+
+ align:start position:0%
+uh energetic uh material energetic
+things like x-rays uh which can then hit
+
+ align:start position:0%
+things like x-rays uh which can then hit
+ 
+
+ align:start position:0%
+things like x-rays uh which can then hit
+the wafer and and interact uh with the
+
+ align:start position:0%
+the wafer and and interact uh with the
+ 
+
+ align:start position:0%
+the wafer and and interact uh with the
+wafer potentially causing oxide damage
+
+ align:start position:0%
+wafer potentially causing oxide damage
+ 
+
+ align:start position:0%
+wafer potentially causing oxide damage
+and things like that so evaporation is
+
+ align:start position:0%
+and things like that so evaporation is
+ 
+
+ align:start position:0%
+and things like that so evaporation is
+used in mems or maybe in in research
+
+ align:start position:0%
+used in mems or maybe in in research
+ 
+
+ align:start position:0%
+used in mems or maybe in in research
+these days but you don't find it too
+
+ align:start position:0%
+these days but you don't find it too
+ 
+
+ align:start position:0%
+these days but you don't find it too
+much uh in in seamless
+
+ align:start position:0%
+much uh in in seamless
+ 
+
+ align:start position:0%
+much uh in in seamless
+manufacturing what you do find in in uh
+
+ align:start position:0%
+manufacturing what you do find in in uh
+ 
+
+ align:start position:0%
+manufacturing what you do find in in uh
+in MOS manufacturing Fabs today is
+
+ align:start position:0%
+in MOS manufacturing Fabs today is
+ 
+
+ align:start position:0%
+in MOS manufacturing Fabs today is
+sputter
+
+ align:start position:0%
+sputter
+ 
+
+ align:start position:0%
+sputter
+deposition um so we're going to spend
+
+ align:start position:0%
+deposition um so we're going to spend
+ 
+
+ align:start position:0%
+deposition um so we're going to spend
+more time talking about this in in the
+
+ align:start position:0%
+more time talking about this in in the
+ 
+
+ align:start position:0%
+more time talking about this in in the
+PVD area what is sputter di well it this
+
+ align:start position:0%
+PVD area what is sputter di well it this
+ 
+
+ align:start position:0%
+PVD area what is sputter di well it this
+uses a
+
+ align:start position:0%
+uses a
+ 
+
+ align:start position:0%
+uses a
+plasma uh it's different from plasma
+
+ align:start position:0%
+plasma uh it's different from plasma
+ 
+
+ align:start position:0%
+plasma uh it's different from plasma
+enhanc cvd so it's it's it's not so much
+
+ align:start position:0%
+enhanc cvd so it's it's it's not so much
+ 
+
+ align:start position:0%
+enhanc cvd so it's it's it's not so much
+chemical process um you use a plasma but
+
+ align:start position:0%
+chemical process um you use a plasma but
+ 
+
+ align:start position:0%
+chemical process um you use a plasma but
+this time you're physically using the
+
+ align:start position:0%
+this time you're physically using the
+ 
+
+ align:start position:0%
+this time you're physically using the
+plasma to hit a Target and sputter off
+
+ align:start position:0%
+plasma to hit a Target and sputter off
+ 
+
+ align:start position:0%
+plasma to hit a Target and sputter off
+or dislodge atoms uh dislodge atoms and
+
+ align:start position:0%
+or dislodge atoms uh dislodge atoms and
+ 
+
+ align:start position:0%
+or dislodge atoms uh dislodge atoms and
+they will then find their way onto the
+
+ align:start position:0%
+they will then find their way onto the
+ 
+
+ align:start position:0%
+they will then find their way onto the
+waer to form the
+
+ align:start position:0%
+waer to form the
+ 
+
+ align:start position:0%
+waer to form the
+film that's what sputtering is all about
+
+ align:start position:0%
+film that's what sputtering is all about
+ 
+
+ align:start position:0%
+film that's what sputtering is all about
+um sputtering uses higher pressures than
+
+ align:start position:0%
+um sputtering uses higher pressures than
+ 
+
+ align:start position:0%
+um sputtering uses higher pressures than
+evaporation evaporation remember I said
+
+ align:start position:0%
+evaporation evaporation remember I said
+ 
+
+ align:start position:0%
+evaporation evaporation remember I said
+you need to have 10 to Minus 5 at least
+
+ align:start position:0%
+you need to have 10 to Minus 5 at least
+ 
+
+ align:start position:0%
+you need to have 10 to Minus 5 at least
+probably 10 to minus 6 T very few that
+
+ align:start position:0%
+probably 10 to minus 6 T very few that
+ 
+
+ align:start position:0%
+probably 10 to minus 6 T very few that
+way you can evaporate and just not hit
+
+ align:start position:0%
+way you can evaporate and just not hit
+ 
+
+ align:start position:0%
+way you can evaporate and just not hit
+anything as that atom goes to your wafer
+
+ align:start position:0%
+anything as that atom goes to your wafer
+ 
+
+ align:start position:0%
+anything as that atom goes to your wafer
+um higher pressures here we're talking
+
+ align:start position:0%
+um higher pressures here we're talking
+ 
+
+ align:start position:0%
+um higher pressures here we're talking
+about one to 100 um millor so that's 1
+
+ align:start position:0%
+about one to 100 um millor so that's 1
+ 
+
+ align:start position:0%
+about one to 100 um millor so that's 1
+to 10 minus 3 T something in that range
+
+ align:start position:0%
+to 10 minus 3 T something in that range
+ 
+
+ align:start position:0%
+to 10 minus 3 T something in that range
+uh it sputtering is typically better at
+
+ align:start position:0%
+uh it sputtering is typically better at
+ 
+
+ align:start position:0%
+uh it sputtering is typically better at
+depositing an alloy because The Sputter
+
+ align:start position:0%
+depositing an alloy because The Sputter
+ 
+
+ align:start position:0%
+depositing an alloy because The Sputter
+rates vary a little bit with the
+
+ align:start position:0%
+rates vary a little bit with the
+ 
+
+ align:start position:0%
+rates vary a little bit with the
+material but not so with the element but
+
+ align:start position:0%
+material but not so with the element but
+ 
+
+ align:start position:0%
+material but not so with the element but
+not so much um this is an example on
+
+ align:start position:0%
+not so much um this is an example on
+ 
+
+ align:start position:0%
+not so much um this is an example on
+slide 19 a very Elementry DC sputter
+
+ align:start position:0%
+slide 19 a very Elementry DC sputter
+ 
+
+ align:start position:0%
+slide 19 a very Elementry DC sputter
+deposition um I have some sputtering gas
+
+ align:start position:0%
+deposition um I have some sputtering gas
+ 
+
+ align:start position:0%
+deposition um I have some sputtering gas
+that I put in the inlet and and argon is
+
+ align:start position:0%
+that I put in the inlet and and argon is
+ 
+
+ align:start position:0%
+that I put in the inlet and and argon is
+very commonly used and why do we use
+
+ align:start position:0%
+very commonly used and why do we use
+ 
+
+ align:start position:0%
+very commonly used and why do we use
+argon it's inert right it's a noble gas
+
+ align:start position:0%
+argon it's inert right it's a noble gas
+ 
+
+ align:start position:0%
+argon it's inert right it's a noble gas
+it's big it's heavy fat it can it can
+
+ align:start position:0%
+it's big it's heavy fat it can it can
+ 
+
+ align:start position:0%
+it's big it's heavy fat it can it can
+give it enough kinetic energy it can
+
+ align:start position:0%
+give it enough kinetic energy it can
+ 
+
+ align:start position:0%
+give it enough kinetic energy it can
+sputter off uh something off your um
+
+ align:start position:0%
+sputter off uh something off your um
+ 
+
+ align:start position:0%
+sputter off uh something off your um
+your Targo your your target your
+
+ align:start position:0%
+your Targo your your target your
+ 
+
+ align:start position:0%
+your Targo your your target your
+electrode uh whatever the material is
+
+ align:start position:0%
+electrode uh whatever the material is
+ 
+
+ align:start position:0%
+electrode uh whatever the material is
+you're trying to get off so argon is
+
+ align:start position:0%
+you're trying to get off so argon is
+ 
+
+ align:start position:0%
+you're trying to get off so argon is
+commonly used you have uh create this
+
+ align:start position:0%
+commonly used you have uh create this
+ 
+
+ align:start position:0%
+commonly used you have uh create this
+argon glow discharge of this plasma The
+
+ align:start position:0%
+argon glow discharge of this plasma The
+ 
+
+ align:start position:0%
+argon glow discharge of this plasma The
+argon's
+
+ align:start position:0%
+argon's
+ 
+
+ align:start position:0%
+argon's
+Accelerated um uh it's positive so the
+
+ align:start position:0%
+Accelerated um uh it's positive so the
+ 
+
+ align:start position:0%
+Accelerated um uh it's positive so the
+argon's accelerate here towards this
+
+ align:start position:0%
+argon's accelerate here towards this
+ 
+
+ align:start position:0%
+argon's accelerate here towards this
+electrode it knocks off the aluminum or
+
+ align:start position:0%
+electrode it knocks off the aluminum or
+ 
+
+ align:start position:0%
+electrode it knocks off the aluminum or
+whatever which Finds Its way on onto the
+
+ align:start position:0%
+whatever which Finds Its way on onto the
+ 
+
+ align:start position:0%
+whatever which Finds Its way on onto the
+wafer this a common DC sputtering uh
+
+ align:start position:0%
+wafer this a common DC sputtering uh
+ 
+
+ align:start position:0%
+wafer this a common DC sputtering uh
+system which she would use to deposit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Metals um so let's look a little more
+
+ align:start position:0%
+Metals um so let's look a little more
+ 
+
+ align:start position:0%
+Metals um so let's look a little more
+carefully on on uh slide 20 and what
+
+ align:start position:0%
+carefully on on uh slide 20 and what
+ 
+
+ align:start position:0%
+carefully on on uh slide 20 and what
+what the plasma consists of um so this
+
+ align:start position:0%
+what the plasma consists of um so this
+ 
+
+ align:start position:0%
+what the plasma consists of um so this
+again now I've turned the Plasma on its
+
+ align:start position:0%
+again now I've turned the Plasma on its
+ 
+
+ align:start position:0%
+again now I've turned the Plasma on its
+side here um the negative electrode uh
+
+ align:start position:0%
+side here um the negative electrode uh
+ 
+
+ align:start position:0%
+side here um the negative electrode uh
+has a voltage V Sub C the cathode as
+
+ align:start position:0%
+has a voltage V Sub C the cathode as
+ 
+
+ align:start position:0%
+has a voltage V Sub C the cathode as
+it's called Uh the cathode is the target
+
+ align:start position:0%
+it's called Uh the cathode is the target
+ 
+
+ align:start position:0%
+it's called Uh the cathode is the target
+um so this material would be aluminum or
+
+ align:start position:0%
+um so this material would be aluminum or
+ 
+
+ align:start position:0%
+um so this material would be aluminum or
+platinum or whatever it is you're trying
+
+ align:start position:0%
+platinum or whatever it is you're trying
+ 
+
+ align:start position:0%
+platinum or whatever it is you're trying
+to sputter uh on the other side you have
+
+ align:start position:0%
+to sputter uh on the other side you have
+ 
+
+ align:start position:0%
+to sputter uh on the other side you have
+the anode which is in a DC system would
+
+ align:start position:0%
+the anode which is in a DC system would
+ 
+
+ align:start position:0%
+the anode which is in a DC system would
+be grounded and you put your Wafers on
+
+ align:start position:0%
+be grounded and you put your Wafers on
+ 
+
+ align:start position:0%
+be grounded and you put your Wafers on
+the grounded or or on the on the
+
+ align:start position:0%
+the grounded or or on the on the
+ 
+
+ align:start position:0%
+the grounded or or on the on the
+anode the plasma itself uh contains
+
+ align:start position:0%
+anode the plasma itself uh contains
+ 
+
+ align:start position:0%
+anode the plasma itself uh contains
+pretty much it's electrically overall
+
+ align:start position:0%
+pretty much it's electrically overall
+ 
+
+ align:start position:0%
+pretty much it's electrically overall
+neutral so it has equal numbers of
+
+ align:start position:0%
+neutral so it has equal numbers of
+ 
+
+ align:start position:0%
+neutral so it has equal numbers of
+positive uh argon ions so the Argon ends
+
+ align:start position:0%
+positive uh argon ions so the Argon ends
+ 
+
+ align:start position:0%
+positive uh argon ions so the Argon ends
+up being positively ionized and
+
+ align:start position:0%
+up being positively ionized and
+ 
+
+ align:start position:0%
+up being positively ionized and
+electrons that are in the plasma as well
+
+ align:start position:0%
+electrons that are in the plasma as well
+ 
+
+ align:start position:0%
+electrons that are in the plasma as well
+as some neutral argon atoms um and if
+
+ align:start position:0%
+as some neutral argon atoms um and if
+ 
+
+ align:start position:0%
+as some neutral argon atoms um and if
+you take plasma fysic class you can
+
+ align:start position:0%
+you take plasma fysic class you can
+ 
+
+ align:start position:0%
+you take plasma fysic class you can
+explain in more detail but for now you
+
+ align:start position:0%
+explain in more detail but for now you
+ 
+
+ align:start position:0%
+explain in more detail but for now you
+can sort of take this as a given that if
+
+ align:start position:0%
+can sort of take this as a given that if
+ 
+
+ align:start position:0%
+can sort of take this as a given that if
+you plot the voltage here uh in the
+
+ align:start position:0%
+you plot the voltage here uh in the
+ 
+
+ align:start position:0%
+you plot the voltage here uh in the
+plasma as a function of distance from
+
+ align:start position:0%
+plasma as a function of distance from
+ 
+
+ align:start position:0%
+plasma as a function of distance from
+the cathode uh most of the voltage drop
+
+ align:start position:0%
+the cathode uh most of the voltage drop
+ 
+
+ align:start position:0%
+the cathode uh most of the voltage drop
+from here to here uh the plasma is has a
+
+ align:start position:0%
+from here to here uh the plasma is has a
+ 
+
+ align:start position:0%
+from here to here uh the plasma is has a
+positive bias here most of it occurs um
+
+ align:start position:0%
+positive bias here most of it occurs um
+ 
+
+ align:start position:0%
+positive bias here most of it occurs um
+over the cathode sheath so most of of it
+
+ align:start position:0%
+over the cathode sheath so most of of it
+ 
+
+ align:start position:0%
+over the cathode sheath so most of of it
+occurs right here um right near the
+
+ align:start position:0%
+occurs right here um right near the
+ 
+
+ align:start position:0%
+occurs right here um right near the
+cathode so that means that the Argon
+
+ align:start position:0%
+cathode so that means that the Argon
+ 
+
+ align:start position:0%
+cathode so that means that the Argon
+then is can be accelerated in this
+
+ align:start position:0%
+then is can be accelerated in this
+ 
+
+ align:start position:0%
+then is can be accelerated in this
+voltage drop going from here from the
+
+ align:start position:0%
+voltage drop going from here from the
+ 
+
+ align:start position:0%
+voltage drop going from here from the
+center of the plasma here it'll be
+
+ align:start position:0%
+center of the plasma here it'll be
+ 
+
+ align:start position:0%
+center of the plasma here it'll be
+accelerated towards the cathode towards
+
+ align:start position:0%
+accelerated towards the cathode towards
+ 
+
+ align:start position:0%
+accelerated towards the cathode towards
+the aluminum Target whatever it is and
+
+ align:start position:0%
+the aluminum Target whatever it is and
+ 
+
+ align:start position:0%
+the aluminum Target whatever it is and
+then it'll gain enough kinetic energy
+
+ align:start position:0%
+then it'll gain enough kinetic energy
+ 
+
+ align:start position:0%
+then it'll gain enough kinetic energy
+that it can knock off um the Alum the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+aluminum so these positive on on slide
+
+ align:start position:0%
+aluminum so these positive on on slide
+ 
+
+ align:start position:0%
+aluminum so these positive on on slide
+21 these positive argon ions are
+
+ align:start position:0%
+21 these positive argon ions are
+ 
+
+ align:start position:0%
+21 these positive argon ions are
+accelerated by this voltage this voltage
+
+ align:start position:0%
+accelerated by this voltage this voltage
+ 
+
+ align:start position:0%
+accelerated by this voltage this voltage
+drop across these cathode sheath um and
+
+ align:start position:0%
+drop across these cathode sheath um and
+ 
+
+ align:start position:0%
+drop across these cathode sheath um and
+they hit the Target and they sputter off
+
+ align:start position:0%
+they hit the Target and they sputter off
+ 
+
+ align:start position:0%
+they hit the Target and they sputter off
+say aluminum these aluminums now then
+
+ align:start position:0%
+say aluminum these aluminums now then
+ 
+
+ align:start position:0%
+say aluminum these aluminums now then
+travel uh through the plasma and they
+
+ align:start position:0%
+travel uh through the plasma and they
+ 
+
+ align:start position:0%
+travel uh through the plasma and they
+deposit um on the Wafers uh that are
+
+ align:start position:0%
+deposit um on the Wafers uh that are
+ 
+
+ align:start position:0%
+deposit um on the Wafers uh that are
+sitting on the anode
+
+ align:start position:0%
+sitting on the anode
+ 
+
+ align:start position:0%
+sitting on the anode
+um so the this rate what what's what
+
+ align:start position:0%
+um so the this rate what what's what
+ 
+
+ align:start position:0%
+um so the this rate what what's what
+rate limits you here is the sputtering
+
+ align:start position:0%
+rate limits you here is the sputtering
+ 
+
+ align:start position:0%
+rate limits you here is the sputtering
+rate and it depends on the sputtering
+
+ align:start position:0%
+rate and it depends on the sputtering
+ 
+
+ align:start position:0%
+rate and it depends on the sputtering
+yield which we call y That's the number
+
+ align:start position:0%
+yield which we call y That's the number
+ 
+
+ align:start position:0%
+yield which we call y That's the number
+of atoms of aluminum or or the number of
+
+ align:start position:0%
+of atoms of aluminum or or the number of
+ 
+
+ align:start position:0%
+of atoms of aluminum or or the number of
+atoms of a Target that come off uh per
+
+ align:start position:0%
+atoms of a Target that come off uh per
+ 
+
+ align:start position:0%
+atoms of a Target that come off uh per
+incident argon ion so that's the the
+
+ align:start position:0%
+incident argon ion so that's the the
+ 
+
+ align:start position:0%
+incident argon ion so that's the the
+definition of The Sputter yield um so I
+
+ align:start position:0%
+definition of The Sputter yield um so I
+ 
+
+ align:start position:0%
+definition of The Sputter yield um so I
+have a very high sputter yield for every
+
+ align:start position:0%
+have a very high sputter yield for every
+ 
+
+ align:start position:0%
+have a very high sputter yield for every
+argon ion that comes in you'll get an
+
+ align:start position:0%
+argon ion that comes in you'll get an
+ 
+
+ align:start position:0%
+argon ion that comes in you'll get an
+aluminum off that would be um a high
+
+ align:start position:0%
+aluminum off that would be um a high
+ 
+
+ align:start position:0%
+aluminum off that would be um a high
+sputter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yield
+
+ align:start position:0%
+yield
+ 
+
+ align:start position:0%
+yield
+looking at slide 22 The Sputter yield Y
+
+ align:start position:0%
+looking at slide 22 The Sputter yield Y
+ 
+
+ align:start position:0%
+looking at slide 22 The Sputter yield Y
+is h a function of the energy so that'll
+
+ align:start position:0%
+is h a function of the energy so that'll
+ 
+
+ align:start position:0%
+is h a function of the energy so that'll
+be dep dependent on the bias in the
+
+ align:start position:0%
+be dep dependent on the bias in the
+ 
+
+ align:start position:0%
+be dep dependent on the bias in the
+plasma right the voltage drop and it
+
+ align:start position:0%
+plasma right the voltage drop and it
+ 
+
+ align:start position:0%
+plasma right the voltage drop and it
+will be also dependent on the mass of
+
+ align:start position:0%
+will be also dependent on the mass of
+ 
+
+ align:start position:0%
+will be also dependent on the mass of
+the ion uh argon is very commonly used
+
+ align:start position:0%
+the ion uh argon is very commonly used
+ 
+
+ align:start position:0%
+the ion uh argon is very commonly used
+it's very massive and on the target
+
+ align:start position:0%
+it's very massive and on the target
+ 
+
+ align:start position:0%
+it's very massive and on the target
+material it'll also be a function of the
+
+ align:start position:0%
+material it'll also be a function of the
+ 
+
+ align:start position:0%
+material it'll also be a function of the
+incident angle of the Argon coming
+
+ align:start position:0%
+incident angle of the Argon coming
+ 
+
+ align:start position:0%
+incident angle of the Argon coming
+in um why this SP yield doesn't vary
+
+ align:start position:0%
+in um why this SP yield doesn't vary
+ 
+
+ align:start position:0%
+in um why this SP yield doesn't vary
+that much uh uh as not nearly as much as
+
+ align:start position:0%
+that much uh uh as not nearly as much as
+ 
+
+ align:start position:0%
+that much uh uh as not nearly as much as
+the vapor pressure vapor pressure varies
+
+ align:start position:0%
+the vapor pressure vapor pressure varies
+ 
+
+ align:start position:0%
+the vapor pressure vapor pressure varies
+by five or 10 ORS of magnitude
+
+ align:start position:0%
+by five or 10 ORS of magnitude
+ 
+
+ align:start position:0%
+by five or 10 ORS of magnitude
+among the elements that's not the case
+
+ align:start position:0%
+among the elements that's not the case
+ 
+
+ align:start position:0%
+among the elements that's not the case
+with sputter yield uh so it is
+
+ align:start position:0%
+with sputter yield uh so it is
+ 
+
+ align:start position:0%
+with sputter yield uh so it is
+sputtering is pretty good for depositing
+
+ align:start position:0%
+sputtering is pretty good for depositing
+ 
+
+ align:start position:0%
+sputtering is pretty good for depositing
+Alloys this is just a schematic on slide
+
+ align:start position:0%
+Alloys this is just a schematic on slide
+ 
+
+ align:start position:0%
+Alloys this is just a schematic on slide
+22 of what's going on let's say I have
+
+ align:start position:0%
+22 of what's going on let's say I have
+ 
+
+ align:start position:0%
+22 of what's going on let's say I have
+an aluminum Target here and here's my
+
+ align:start position:0%
+an aluminum Target here and here's my
+ 
+
+ align:start position:0%
+an aluminum Target here and here's my
+wafer on the surface and this is the
+
+ align:start position:0%
+wafer on the surface and this is the
+ 
+
+ align:start position:0%
+wafer on the surface and this is the
+cathode sheath of the dark space the
+
+ align:start position:0%
+cathode sheath of the dark space the
+ 
+
+ align:start position:0%
+cathode sheath of the dark space the
+aluminum ions that are in the plasma are
+
+ align:start position:0%
+aluminum ions that are in the plasma are
+ 
+
+ align:start position:0%
+aluminum ions that are in the plasma are
+accelerated towards this negative
+
+ align:start position:0%
+accelerated towards this negative
+ 
+
+ align:start position:0%
+accelerated towards this negative
+electrode they have enough energy that
+
+ align:start position:0%
+electrode they have enough energy that
+ 
+
+ align:start position:0%
+electrode they have enough energy that
+they can knock an Alum I'm sorry the
+
+ align:start position:0%
+they can knock an Alum I'm sorry the
+ 
+
+ align:start position:0%
+they can knock an Alum I'm sorry the
+Argon accelerated they knock an aluminum
+
+ align:start position:0%
+Argon accelerated they knock an aluminum
+ 
+
+ align:start position:0%
+Argon accelerated they knock an aluminum
+off it finds its way down to the wafer
+
+ align:start position:0%
+off it finds its way down to the wafer
+ 
+
+ align:start position:0%
+off it finds its way down to the wafer
+where it's where it may move around a
+
+ align:start position:0%
+where it's where it may move around a
+ 
+
+ align:start position:0%
+where it's where it may move around a
+little bit if the wafer is hot but it's
+
+ align:start position:0%
+little bit if the wafer is hot but it's
+ 
+
+ align:start position:0%
+little bit if the wafer is hot but it's
+pretty much um will stick and and
+
+ align:start position:0%
+pretty much um will stick and and
+ 
+
+ align:start position:0%
+pretty much um will stick and and
+deposit um there are other species of
+
+ align:start position:0%
+deposit um there are other species of
+ 
+
+ align:start position:0%
+deposit um there are other species of
+course around there are um there are
+
+ align:start position:0%
+course around there are um there are
+ 
+
+ align:start position:0%
+course around there are um there are
+electrons in in the glow discharge uh
+
+ align:start position:0%
+electrons in in the glow discharge uh
+ 
+
+ align:start position:0%
+electrons in in the glow discharge uh
+and uh depending on uh what's going on
+
+ align:start position:0%
+and uh depending on uh what's going on
+ 
+
+ align:start position:0%
+and uh depending on uh what's going on
+there may be some um other impurities as
+
+ align:start position:0%
+there may be some um other impurities as
+ 
+
+ align:start position:0%
+there may be some um other impurities as
+well depending on the uh the clemance of
+
+ align:start position:0%
+well depending on the uh the clemance of
+ 
+
+ align:start position:0%
+well depending on the uh the clemance of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+vacuum we go to slide 23 um this just
+
+ align:start position:0%
+vacuum we go to slide 23 um this just
+ 
+
+ align:start position:0%
+vacuum we go to slide 23 um this just
+gives you a a schematic which is
+
+ align:start position:0%
+gives you a a schematic which is
+ 
+
+ align:start position:0%
+gives you a a schematic which is
+supposed to point out that um a
+
+ align:start position:0%
+supposed to point out that um a
+ 
+
+ align:start position:0%
+supposed to point out that um a
+sputtering Target itself is generally
+
+ align:start position:0%
+sputtering Target itself is generally
+ 
+
+ align:start position:0%
+sputtering Target itself is generally
+quite large if you go to buy a target
+
+ align:start position:0%
+quite large if you go to buy a target
+ 
+
+ align:start position:0%
+quite large if you go to buy a target
+for aluminum um it's it can be big you
+
+ align:start position:0%
+for aluminum um it's it can be big you
+ 
+
+ align:start position:0%
+for aluminum um it's it can be big you
+know a couple of feet on a side it will
+
+ align:start position:0%
+know a couple of feet on a side it will
+ 
+
+ align:start position:0%
+know a couple of feet on a side it will
+be much larger than the wafer um and so
+
+ align:start position:0%
+be much larger than the wafer um and so
+ 
+
+ align:start position:0%
+be much larger than the wafer um and so
+because it's so large compared to the
+
+ align:start position:0%
+because it's so large compared to the
+ 
+
+ align:start position:0%
+because it's so large compared to the
+wafer it gives you a wide uh range of
+
+ align:start position:0%
+wafer it gives you a wide uh range of
+ 
+
+ align:start position:0%
+wafer it gives you a wide uh range of
+arrival angles in contrast to a point
+
+ align:start position:0%
+arrival angles in contrast to a point
+ 
+
+ align:start position:0%
+arrival angles in contrast to a point
+source so on the left you can imagine if
+
+ align:start position:0%
+source so on the left you can imagine if
+ 
+
+ align:start position:0%
+source so on the left you can imagine if
+I had a point
+
+ align:start position:0%
+I had a point
+ 
+
+ align:start position:0%
+I had a point
+source um you the arrival angle here is
+
+ align:start position:0%
+source um you the arrival angle here is
+ 
+
+ align:start position:0%
+source um you the arrival angle here is
+you know is is somewhat limited but if I
+
+ align:start position:0%
+you know is is somewhat limited but if I
+ 
+
+ align:start position:0%
+you know is is somewhat limited but if I
+have a source that's really much bigger
+
+ align:start position:0%
+have a source that's really much bigger
+ 
+
+ align:start position:0%
+have a source that's really much bigger
+than the wafer um I get a range W um of
+
+ align:start position:0%
+than the wafer um I get a range W um of
+ 
+
+ align:start position:0%
+than the wafer um I get a range W um of
+arrival angles and I can get uh at any
+
+ align:start position:0%
+arrival angles and I can get uh at any
+ 
+
+ align:start position:0%
+arrival angles and I can get uh at any
+given point I can get pretty good uh
+
+ align:start position:0%
+given point I can get pretty good uh
+ 
+
+ align:start position:0%
+given point I can get pretty good uh
+uniformity reasonably low shadowing
+
+ align:start position:0%
+uniformity reasonably low shadowing
+ 
+
+ align:start position:0%
+uniformity reasonably low shadowing
+effects in the evaporator U there were a
+
+ align:start position:0%
+effects in the evaporator U there were a
+ 
+
+ align:start position:0%
+effects in the evaporator U there were a
+lot of when we talked about thermal
+
+ align:start position:0%
+lot of when we talked about thermal
+ 
+
+ align:start position:0%
+lot of when we talked about thermal
+evaporation you can know if you have a
+
+ align:start position:0%
+evaporation you can know if you have a
+ 
+
+ align:start position:0%
+evaporation you can know if you have a
+step that you're evaporating into or a
+
+ align:start position:0%
+step that you're evaporating into or a
+ 
+
+ align:start position:0%
+step that you're evaporating into or a
+hole you can get shadowing effects
+
+ align:start position:0%
+hole you can get shadowing effects
+ 
+
+ align:start position:0%
+hole you can get shadowing effects
+sputtering doesn't suffer nearly from uh
+
+ align:start position:0%
+sputtering doesn't suffer nearly from uh
+ 
+
+ align:start position:0%
+sputtering doesn't suffer nearly from uh
+those kind of shadowing effects it's not
+
+ align:start position:0%
+those kind of shadowing effects it's not
+ 
+
+ align:start position:0%
+those kind of shadowing effects it's not
+really considered line of sight
+
+ align:start position:0%
+really considered line of sight
+ 
+
+ align:start position:0%
+really considered line of sight
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so let's look at slide
+
+ align:start position:0%
+okay so let's look at slide
+ 
+
+ align:start position:0%
+okay so let's look at slide
+24 I this is just a I just to copy this
+
+ align:start position:0%
+24 I this is just a I just to copy this
+ 
+
+ align:start position:0%
+24 I this is just a I just to copy this
+uh page from this uh text or this book
+
+ align:start position:0%
+uh page from this uh text or this book
+ 
+
+ align:start position:0%
+uh page from this uh text or this book
+called the users's guide to vacuum
+
+ align:start position:0%
+called the users's guide to vacuum
+ 
+
+ align:start position:0%
+called the users's guide to vacuum
+technology by oh handin I just wanted to
+
+ align:start position:0%
+technology by oh handin I just wanted to
+ 
+
+ align:start position:0%
+technology by oh handin I just wanted to
+remind people of an important concept
+
+ align:start position:0%
+remind people of an important concept
+ 
+
+ align:start position:0%
+remind people of an important concept
+when you're talking about these these
+
+ align:start position:0%
+when you're talking about these these
+ 
+
+ align:start position:0%
+when you're talking about these these
+vacuum processes like evaporation and
+
+ align:start position:0%
+vacuum processes like evaporation and
+ 
+
+ align:start position:0%
+vacuum processes like evaporation and
+sputtering um the concept of a mean-free
+
+ align:start position:0%
+sputtering um the concept of a mean-free
+ 
+
+ align:start position:0%
+sputtering um the concept of a mean-free
+path um just just to remind you what
+
+ align:start position:0%
+path um just just to remind you what
+ 
+
+ align:start position:0%
+path um just just to remind you what
+this is if you haven't seen it before
+
+ align:start position:0%
+this is if you haven't seen it before
+ 
+
+ align:start position:0%
+this is if you haven't seen it before
+this mean 3T path here a Lambda uh of a
+
+ align:start position:0%
+this mean 3T path here a Lambda uh of a
+ 
+
+ align:start position:0%
+this mean 3T path here a Lambda uh of a
+particle from the kinetic gas Theory it
+
+ align:start position:0%
+particle from the kinetic gas Theory it
+ 
+
+ align:start position:0%
+particle from the kinetic gas Theory it
+depends on
+
+ align:start position:0%
+depends on
+ 
+
+ align:start position:0%
+depends on
+temperature uh directly proportional to
+
+ align:start position:0%
+temperature uh directly proportional to
+ 
+
+ align:start position:0%
+temperature uh directly proportional to
+the temperature uh and it's inversely
+
+ align:start position:0%
+the temperature uh and it's inversely
+ 
+
+ align:start position:0%
+the temperature uh and it's inversely
+proportional to the pressure um so uh
+
+ align:start position:0%
+proportional to the pressure um so uh
+ 
+
+ align:start position:0%
+proportional to the pressure um so uh
+for example in in just a typical
+
+ align:start position:0%
+for example in in just a typical
+ 
+
+ align:start position:0%
+for example in in just a typical
+sputtering system the pressure let's say
+
+ align:start position:0%
+sputtering system the pressure let's say
+ 
+
+ align:start position:0%
+sputtering system the pressure let's say
+maybe is five millor um so this gives us
+
+ align:start position:0%
+maybe is five millor um so this gives us
+ 
+
+ align:start position:0%
+maybe is five millor um so this gives us
+a mean-free path on the order of a
+
+ align:start position:0%
+a mean-free path on the order of a
+ 
+
+ align:start position:0%
+a mean-free path on the order of a
+centimeter so you can think of these
+
+ align:start position:0%
+centimeter so you can think of these
+ 
+
+ align:start position:0%
+centimeter so you can think of these
+argon atoms or ions moving around uh or
+
+ align:start position:0%
+argon atoms or ions moving around uh or
+ 
+
+ align:start position:0%
+argon atoms or ions moving around uh or
+the aluminum uh moving around in that uh
+
+ align:start position:0%
+the aluminum uh moving around in that uh
+ 
+
+ align:start position:0%
+the aluminum uh moving around in that uh
+five millor system with about every
+
+ align:start position:0%
+five millor system with about every
+ 
+
+ align:start position:0%
+five millor system with about every
+centimeter has a collision um so that's
+
+ align:start position:0%
+centimeter has a collision um so that's
+ 
+
+ align:start position:0%
+centimeter has a collision um so that's
+a lot less than the physical path length
+
+ align:start position:0%
+a lot less than the physical path length
+ 
+
+ align:start position:0%
+a lot less than the physical path length
+because you know sputtering system you
+
+ align:start position:0%
+because you know sputtering system you
+ 
+
+ align:start position:0%
+because you know sputtering system you
+know might be this big so you have your
+
+ align:start position:0%
+know might be this big so you have your
+ 
+
+ align:start position:0%
+know might be this big so you have your
+target up here your Wafers down here has
+
+ align:start position:0%
+target up here your Wafers down here has
+ 
+
+ align:start position:0%
+target up here your Wafers down here has
+to go a lot of centimeters so that atom
+
+ align:start position:0%
+to go a lot of centimeters so that atom
+ 
+
+ align:start position:0%
+to go a lot of centimeters so that atom
+sort of Jiggles around as it and has a
+
+ align:start position:0%
+sort of Jiggles around as it and has a
+ 
+
+ align:start position:0%
+sort of Jiggles around as it and has a
+lot of collisions as it finally gets
+
+ align:start position:0%
+lot of collisions as it finally gets
+ 
+
+ align:start position:0%
+lot of collisions as it finally gets
+come to rest on the surface contrast to
+
+ align:start position:0%
+come to rest on the surface contrast to
+ 
+
+ align:start position:0%
+come to rest on the surface contrast to
+an evaporation could be just as long or
+
+ align:start position:0%
+an evaporation could be just as long or
+ 
+
+ align:start position:0%
+an evaporation could be just as long or
+a longer distance but evaporation is
+
+ align:start position:0%
+a longer distance but evaporation is
+ 
+
+ align:start position:0%
+a longer distance but evaporation is
+line of sight Bingo goes from right from
+
+ align:start position:0%
+line of sight Bingo goes from right from
+ 
+
+ align:start position:0%
+line of sight Bingo goes from right from
+here to here uh I'm at 10us 6 t with no
+
+ align:start position:0%
+here to here uh I'm at 10us 6 t with no
+ 
+
+ align:start position:0%
+here to here uh I'm at 10us 6 t with no
+collisions um so this mean-free path is
+
+ align:start position:0%
+collisions um so this mean-free path is
+ 
+
+ align:start position:0%
+collisions um so this mean-free path is
+is also what determines the the uh
+
+ align:start position:0%
+is also what determines the the uh
+ 
+
+ align:start position:0%
+is also what determines the the uh
+conformality of the deposition um in
+
+ align:start position:0%
+conformality of the deposition um in
+ 
+
+ align:start position:0%
+conformality of the deposition um in
+sputtering and and why how it's
+
+ align:start position:0%
+sputtering and and why how it's
+ 
+
+ align:start position:0%
+sputtering and and why how it's
+different from uh
+
+ align:start position:0%
+different from uh
+ 
+
+ align:start position:0%
+different from uh
+evaporation uh looking at slide slide
+
+ align:start position:0%
+evaporation uh looking at slide slide
+ 
+
+ align:start position:0%
+evaporation uh looking at slide slide
+number 25 here um contrasting two
+
+ align:start position:0%
+number 25 here um contrasting two
+ 
+
+ align:start position:0%
+number 25 here um contrasting two
+different cases on the left uh case A is
+
+ align:start position:0%
+different cases on the left uh case A is
+ 
+
+ align:start position:0%
+different cases on the left uh case A is
+for isotropic flux arrival now I'm
+
+ align:start position:0%
+for isotropic flux arrival now I'm
+ 
+
+ align:start position:0%
+for isotropic flux arrival now I'm
+considering I have my Surface of of a
+
+ align:start position:0%
+considering I have my Surface of of a
+ 
+
+ align:start position:0%
+considering I have my Surface of of a
+wafer and I've got a a flux of things
+
+ align:start position:0%
+wafer and I've got a a flux of things
+ 
+
+ align:start position:0%
+wafer and I've got a a flux of things
+coming in from the sputtering as not
+
+ align:start position:0%
+coming in from the sputtering as not
+ 
+
+ align:start position:0%
+coming in from the sputtering as not
+from a aeration but it's coming in at a
+
+ align:start position:0%
+from a aeration but it's coming in at a
+ 
+
+ align:start position:0%
+from a aeration but it's coming in at a
+certain angular distribution in in the
+
+ align:start position:0%
+certain angular distribution in in the
+ 
+
+ align:start position:0%
+certain angular distribution in in the
+sputtering tool um and so um for if n
+
+ align:start position:0%
+sputtering tool um and so um for if n
+ 
+
+ align:start position:0%
+sputtering tool um and so um for if n
+equals 1 I'll get a cosine Theta a rival
+
+ align:start position:0%
+equals 1 I'll get a cosine Theta a rival
+ 
+
+ align:start position:0%
+equals 1 I'll get a cosine Theta a rival
+angle distribution depending on um you
+
+ align:start position:0%
+angle distribution depending on um you
+ 
+
+ align:start position:0%
+angle distribution depending on um you
+know uh the angle of this
+
+ align:start position:0%
+know uh the angle of this
+ 
+
+ align:start position:0%
+know uh the angle of this
+Source um uh with respect to the the
+
+ align:start position:0%
+Source um uh with respect to the the
+ 
+
+ align:start position:0%
+Source um uh with respect to the the
+normal uh if I have an anisotropic flux
+
+ align:start position:0%
+normal uh if I have an anisotropic flux
+ 
+
+ align:start position:0%
+normal uh if I have an anisotropic flux
+arrival flux n will go up n could be
+
+ align:start position:0%
+arrival flux n will go up n could be
+ 
+
+ align:start position:0%
+arrival flux n will go up n could be
+much greater than one maybe 10 or
+
+ align:start position:0%
+much greater than one maybe 10 or
+ 
+
+ align:start position:0%
+much greater than one maybe 10 or
+something like that and if n is very
+
+ align:start position:0%
+something like that and if n is very
+ 
+
+ align:start position:0%
+something like that and if n is very
+large it means most of the flux is
+
+ align:start position:0%
+large it means most of the flux is
+ 
+
+ align:start position:0%
+large it means most of the flux is
+coming straight down not much of it is
+
+ align:start position:0%
+coming straight down not much of it is
+ 
+
+ align:start position:0%
+coming straight down not much of it is
+coming from wide
+
+ align:start position:0%
+coming from wide
+ 
+
+ align:start position:0%
+coming from wide
+angles um so typically for sputtering we
+
+ align:start position:0%
+angles um so typically for sputtering we
+ 
+
+ align:start position:0%
+angles um so typically for sputtering we
+we also use a cosine Theta the N um and
+
+ align:start position:0%
+we also use a cosine Theta the N um and
+ 
+
+ align:start position:0%
+we also use a cosine Theta the N um and
+it's the normal component of the flux so
+
+ align:start position:0%
+it's the normal component of the flux so
+ 
+
+ align:start position:0%
+it's the normal component of the flux so
+it's the component uh in in the normal
+
+ align:start position:0%
+it's the component uh in in the normal
+ 
+
+ align:start position:0%
+it's the component uh in in the normal
+direction that strikes the surface and
+
+ align:start position:0%
+direction that strikes the surface and
+ 
+
+ align:start position:0%
+direction that strikes the surface and
+determines the depth
+
+ align:start position:0%
+determines the depth
+ 
+
+ align:start position:0%
+determines the depth
+rate so the size and the type of source
+
+ align:start position:0%
+rate so the size and the type of source
+ 
+
+ align:start position:0%
+rate so the size and the type of source
+the geometry of the overall sputtering
+
+ align:start position:0%
+the geometry of the overall sputtering
+ 
+
+ align:start position:0%
+the geometry of the overall sputtering
+system uh the pressure and therefore the
+
+ align:start position:0%
+system uh the pressure and therefore the
+ 
+
+ align:start position:0%
+system uh the pressure and therefore the
+collisions in the gas phase all those
+
+ align:start position:0%
+collisions in the gas phase all those
+ 
+
+ align:start position:0%
+collisions in the gas phase all those
+are important in determining the arrival
+
+ align:start position:0%
+are important in determining the arrival
+ 
+
+ align:start position:0%
+are important in determining the arrival
+angle distribution when determining what
+
+ align:start position:0%
+angle distribution when determining what
+ 
+
+ align:start position:0%
+angle distribution when determining what
+this flux looks like as a function of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theta so that says a little bit about DC
+
+ align:start position:0%
+theta so that says a little bit about DC
+ 
+
+ align:start position:0%
+theta so that says a little bit about DC
+sputtering now you might say well
+
+ align:start position:0%
+sputtering now you might say well
+ 
+
+ align:start position:0%
+sputtering now you might say well
+what um that's fine if the target
+
+ align:start position:0%
+what um that's fine if the target
+ 
+
+ align:start position:0%
+what um that's fine if the target
+electrode is a conductor like uh
+
+ align:start position:0%
+electrode is a conductor like uh
+ 
+
+ align:start position:0%
+electrode is a conductor like uh
+platinum or aluminum or whatever what if
+
+ align:start position:0%
+platinum or aluminum or whatever what if
+ 
+
+ align:start position:0%
+platinum or aluminum or whatever what if
+I want to sputter a dialectric material
+
+ align:start position:0%
+I want to sputter a dialectric material
+ 
+
+ align:start position:0%
+I want to sputter a dialectric material
+it doesn't conduct DC DC current you're
+
+ align:start position:0%
+it doesn't conduct DC DC current you're
+ 
+
+ align:start position:0%
+it doesn't conduct DC DC current you're
+going to have some problems well what
+
+ align:start position:0%
+going to have some problems well what
+ 
+
+ align:start position:0%
+going to have some problems well what
+people do is then they use an RF power
+
+ align:start position:0%
+people do is then they use an RF power
+ 
+
+ align:start position:0%
+people do is then they use an RF power
+uh Source because you know you can
+
+ align:start position:0%
+uh Source because you know you can
+ 
+
+ align:start position:0%
+uh Source because you know you can
+transmit
+
+ align:start position:0%
+transmit
+ 
+
+ align:start position:0%
+transmit
+power through insulators if in an AC
+
+ align:start position:0%
+power through insulators if in an AC
+ 
+
+ align:start position:0%
+power through insulators if in an AC
+sense uh by using RF so uh it looks very
+
+ align:start position:0%
+sense uh by using RF so uh it looks very
+ 
+
+ align:start position:0%
+sense uh by using RF so uh it looks very
+much or somewhat similar to a DC system
+
+ align:start position:0%
+much or somewhat similar to a DC system
+ 
+
+ align:start position:0%
+much or somewhat similar to a DC system
+except now you have um an RF generator
+
+ align:start position:0%
+except now you have um an RF generator
+ 
+
+ align:start position:0%
+except now you have um an RF generator
+and a matching network uh and you put
+
+ align:start position:0%
+and a matching network uh and you put
+ 
+
+ align:start position:0%
+and a matching network uh and you put
+your target or your um electrode up here
+
+ align:start position:0%
+your target or your um electrode up here
+ 
+
+ align:start position:0%
+your target or your um electrode up here
+and you'll notice we'll talk about why
+
+ align:start position:0%
+and you'll notice we'll talk about why
+ 
+
+ align:start position:0%
+and you'll notice we'll talk about why
+this is but it's a smaller area than
+
+ align:start position:0%
+this is but it's a smaller area than
+ 
+
+ align:start position:0%
+this is but it's a smaller area than
+your the um electrode that holds uh the
+
+ align:start position:0%
+your the um electrode that holds uh the
+ 
+
+ align:start position:0%
+your the um electrode that holds uh the
+Wafers again you still bring in argon um
+
+ align:start position:0%
+Wafers again you still bring in argon um
+ 
+
+ align:start position:0%
+Wafers again you still bring in argon um
+the uh and it's accelerated towards this
+
+ align:start position:0%
+the uh and it's accelerated towards this
+ 
+
+ align:start position:0%
+the uh and it's accelerated towards this
+Target and you sputter um you can
+
+ align:start position:0%
+Target and you sputter um you can
+ 
+
+ align:start position:0%
+Target and you sputter um you can
+sputter
+
+ align:start position:0%
+sputter
+ 
+
+ align:start position:0%
+sputter
+dielectrics S2 can be sputtered uh in
+
+ align:start position:0%
+dielectrics S2 can be sputtered uh in
+ 
+
+ align:start position:0%
+dielectrics S2 can be sputtered uh in
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way slide 27 shows an example of um the
+
+ align:start position:0%
+way slide 27 shows an example of um the
+ 
+
+ align:start position:0%
+way slide 27 shows an example of um the
+uh steady state now this is steady state
+
+ align:start position:0%
+uh steady state now this is steady state
+ 
+
+ align:start position:0%
+uh steady state now this is steady state
+voltage distribution in an RF uh
+
+ align:start position:0%
+voltage distribution in an RF uh
+ 
+
+ align:start position:0%
+voltage distribution in an RF uh
+sputtering uh system and uh so it's a
+
+ align:start position:0%
+sputtering uh system and uh so it's a
+ 
+
+ align:start position:0%
+sputtering uh system and uh so it's a
+plot of on a y AIS here is voltage as a
+
+ align:start position:0%
+plot of on a y AIS here is voltage as a
+ 
+
+ align:start position:0%
+plot of on a y AIS here is voltage as a
+function of
+
+ align:start position:0%
+function of
+ 
+
+ align:start position:0%
+function of
+distance and here on the left is the
+
+ align:start position:0%
+distance and here on the left is the
+ 
+
+ align:start position:0%
+distance and here on the left is the
+meant to be the target uh could be um
+
+ align:start position:0%
+meant to be the target uh could be um
+ 
+
+ align:start position:0%
+meant to be the target uh could be um
+sao2 if you're sputtering that and on
+
+ align:start position:0%
+sao2 if you're sputtering that and on
+ 
+
+ align:start position:0%
+sao2 if you're sputtering that and on
+the right is the electrode where you put
+
+ align:start position:0%
+the right is the electrode where you put
+ 
+
+ align:start position:0%
+the right is the electrode where you put
+the uh the wafer and there're two
+
+ align:start position:0%
+the uh the wafer and there're two
+ 
+
+ align:start position:0%
+the uh the wafer and there're two
+different plots here um so uh so well
+
+ align:start position:0%
+different plots here um so uh so well
+ 
+
+ align:start position:0%
+different plots here um so uh so well
+first of all because there's slower
+
+ align:start position:0%
+first of all because there's slower
+ 
+
+ align:start position:0%
+first of all because there's slower
+mobility of the ions the ions are more
+
+ align:start position:0%
+mobility of the ions the ions are more
+ 
+
+ align:start position:0%
+mobility of the ions the ions are more
+massive than the electrons the plasma
+
+ align:start position:0%
+massive than the electrons the plasma
+ 
+
+ align:start position:0%
+massive than the electrons the plasma
+always tends to bias positively with
+
+ align:start position:0%
+always tends to bias positively with
+ 
+
+ align:start position:0%
+always tends to bias positively with
+respect to the the two
+
+ align:start position:0%
+respect to the the two
+ 
+
+ align:start position:0%
+respect to the the two
+electrodes um uh so um so the plasma
+
+ align:start position:0%
+electrodes um uh so um so the plasma
+ 
+
+ align:start position:0%
+electrodes um uh so um so the plasma
+tends to be positively biased uh the the
+
+ align:start position:0%
+tends to be positively biased uh the the
+ 
+
+ align:start position:0%
+tends to be positively biased uh the the
+uh the question is what is you know what
+
+ align:start position:0%
+uh the question is what is you know what
+ 
+
+ align:start position:0%
+uh the question is what is you know what
+is the voltage drop look like as a
+
+ align:start position:0%
+is the voltage drop look like as a
+ 
+
+ align:start position:0%
+is the voltage drop look like as a
+function of the area in these two
+
+ align:start position:0%
+function of the area in these two
+ 
+
+ align:start position:0%
+function of the area in these two
+electrodes so it turns out when the area
+
+ align:start position:0%
+electrodes so it turns out when the area
+ 
+
+ align:start position:0%
+electrodes so it turns out when the area
+of the electrodes is not equal uh the
+
+ align:start position:0%
+of the electrodes is not equal uh the
+ 
+
+ align:start position:0%
+of the electrodes is not equal uh the
+field has to be higher at the smaller
+
+ align:start position:0%
+field has to be higher at the smaller
+ 
+
+ align:start position:0%
+field has to be higher at the smaller
+electrode so this is my small let's say
+
+ align:start position:0%
+electrode so this is my small let's say
+ 
+
+ align:start position:0%
+electrode so this is my small let's say
+if this is the smaller electrode um the
+
+ align:start position:0%
+if this is the smaller electrode um the
+ 
+
+ align:start position:0%
+if this is the smaller electrode um the
+field is higher because there's a higher
+
+ align:start position:0%
+field is higher because there's a higher
+ 
+
+ align:start position:0%
+field is higher because there's a higher
+current density so to maintain overall
+
+ align:start position:0%
+current density so to maintain overall
+ 
+
+ align:start position:0%
+current density so to maintain overall
+current continuity it turns out that
+
+ align:start position:0%
+current continuity it turns out that
+ 
+
+ align:start position:0%
+current continuity it turns out that
+this voltage drop here V
+
+ align:start position:0%
+this voltage drop here V
+ 
+
+ align:start position:0%
+this voltage drop here V
+V1 um uh will be uh related to V2
+
+ align:start position:0%
+V1 um uh will be uh related to V2
+ 
+
+ align:start position:0%
+V1 um uh will be uh related to V2
+uh inversely to the
+
+ align:start position:0%
+uh inversely to the
+ 
+
+ align:start position:0%
+uh inversely to the
+areas um so I can uh if I have equal
+
+ align:start position:0%
+areas um so I can uh if I have equal
+ 
+
+ align:start position:0%
+areas um so I can uh if I have equal
+area electrodes I have the solid line so
+
+ align:start position:0%
+area electrodes I have the solid line so
+ 
+
+ align:start position:0%
+area electrodes I have the solid line so
+there's sort of a drop um the voltage
+
+ align:start position:0%
+there's sort of a drop um the voltage
+ 
+
+ align:start position:0%
+there's sort of a drop um the voltage
+drop on the left and the right is about
+
+ align:start position:0%
+drop on the left and the right is about
+ 
+
+ align:start position:0%
+drop on the left and the right is about
+the same if I make um the area this
+
+ align:start position:0%
+the same if I make um the area this
+ 
+
+ align:start position:0%
+the same if I make um the area this
+electrode where the wafer
+
+ align:start position:0%
+electrode where the wafer
+ 
+
+ align:start position:0%
+electrode where the wafer
+sits uh much larger so by making the
+
+ align:start position:0%
+sits uh much larger so by making the
+ 
+
+ align:start position:0%
+sits uh much larger so by making the
+target electrode smaller in other words
+
+ align:start position:0%
+target electrode smaller in other words
+ 
+
+ align:start position:0%
+target electrode smaller in other words
+a there's a larger voltage drop um near
+
+ align:start position:0%
+a there's a larger voltage drop um near
+ 
+
+ align:start position:0%
+a there's a larger voltage drop um near
+the Target and so all the sputtering
+
+ align:start position:0%
+the Target and so all the sputtering
+ 
+
+ align:start position:0%
+the Target and so all the sputtering
+tends to occur near the target not
+
+ align:start position:0%
+tends to occur near the target not
+ 
+
+ align:start position:0%
+tends to occur near the target not
+during your wafer not to your wafer so
+
+ align:start position:0%
+during your wafer not to your wafer so
+ 
+
+ align:start position:0%
+during your wafer not to your wafer so
+just by um imbalancing the size uh of
+
+ align:start position:0%
+just by um imbalancing the size uh of
+ 
+
+ align:start position:0%
+just by um imbalancing the size uh of
+where of the of where you the electrode
+
+ align:start position:0%
+where of the of where you the electrode
+ 
+
+ align:start position:0%
+where of the of where you the electrode
+where you put the wafer the electrode
+
+ align:start position:0%
+where you put the wafer the electrode
+ 
+
+ align:start position:0%
+where you put the wafer the electrode
+where you do the sputtering you can
+
+ align:start position:0%
+where you do the sputtering you can
+ 
+
+ align:start position:0%
+where you do the sputtering you can
+cause most of the voltage drop to be on
+
+ align:start position:0%
+cause most of the voltage drop to be on
+ 
+
+ align:start position:0%
+cause most of the voltage drop to be on
+this sides uh with a smaller electrode
+
+ align:start position:0%
+this sides uh with a smaller electrode
+ 
+
+ align:start position:0%
+this sides uh with a smaller electrode
+and then that's that's that way you
+
+ align:start position:0%
+and then that's that's that way you
+ 
+
+ align:start position:0%
+and then that's that's that way you
+ensure that you get sputtering uh not of
+
+ align:start position:0%
+ensure that you get sputtering uh not of
+ 
+
+ align:start position:0%
+ensure that you get sputtering uh not of
+your wafer but sputtering of the of the
+
+ align:start position:0%
+your wafer but sputtering of the of the
+ 
+
+ align:start position:0%
+your wafer but sputtering of the of the
+target
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+material um and going on to slide 28 the
+
+ align:start position:0%
+material um and going on to slide 28 the
+ 
+
+ align:start position:0%
+material um and going on to slide 28 the
+other thing you can do you can have a
+
+ align:start position:0%
+other thing you can do you can have a
+ 
+
+ align:start position:0%
+other thing you can do you can have a
+separate RF bias which allows you to um
+
+ align:start position:0%
+separate RF bias which allows you to um
+ 
+
+ align:start position:0%
+separate RF bias which allows you to um
+to uh control the uh voltage drop on on
+
+ align:start position:0%
+to uh control the uh voltage drop on on
+ 
+
+ align:start position:0%
+to uh control the uh voltage drop on on
+on this side uh so you can do a cleaning
+
+ align:start position:0%
+on this side uh so you can do a cleaning
+ 
+
+ align:start position:0%
+on this side uh so you can do a cleaning
+step so you very at the very beginning
+
+ align:start position:0%
+step so you very at the very beginning
+ 
+
+ align:start position:0%
+step so you very at the very beginning
+of sputtering you often want to sputter
+
+ align:start position:0%
+of sputtering you often want to sputter
+ 
+
+ align:start position:0%
+of sputtering you often want to sputter
+a little bit off the way for surface
+
+ align:start position:0%
+a little bit off the way for surface
+ 
+
+ align:start position:0%
+a little bit off the way for surface
+let's say you have um a little bit of
+
+ align:start position:0%
+let's say you have um a little bit of
+ 
+
+ align:start position:0%
+let's say you have um a little bit of
+deposition um or you can also um do a
+
+ align:start position:0%
+deposition um or you can also um do a
+ 
+
+ align:start position:0%
+deposition um or you can also um do a
+bias sputter deposition so um you can
+
+ align:start position:0%
+bias sputter deposition so um you can
+ 
+
+ align:start position:0%
+bias sputter deposition so um you can
+actually have the wafer um be it some f
+
+ align:start position:0%
+actually have the wafer um be it some f
+ 
+
+ align:start position:0%
+actually have the wafer um be it some f
+finite uh finite bias uh to get and this
+
+ align:start position:0%
+finite uh finite bias uh to get and this
+ 
+
+ align:start position:0%
+finite uh finite bias uh to get and this
+ends up giving you more conformal
+
+ align:start position:0%
+ends up giving you more conformal
+ 
+
+ align:start position:0%
+ends up giving you more conformal
+deposition because you can get a more
+
+ align:start position:0%
+deposition because you can get a more
+ 
+
+ align:start position:0%
+deposition because you can get a more
+highly directional uh uh uh sputtering
+
+ align:start position:0%
+highly directional uh uh uh sputtering
+ 
+
+ align:start position:0%
+highly directional uh uh uh sputtering
+uh flux so there are a couple different
+
+ align:start position:0%
+uh flux so there are a couple different
+ 
+
+ align:start position:0%
+uh flux so there are a couple different
+methods in in using sputtering where you
+
+ align:start position:0%
+methods in in using sputtering where you
+ 
+
+ align:start position:0%
+methods in in using sputtering where you
+can control uh the arrival angle um uh
+
+ align:start position:0%
+can control uh the arrival angle um uh
+ 
+
+ align:start position:0%
+can control uh the arrival angle um uh
+with bias sputter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+deposition um okay so the the final
+
+ align:start position:0%
+deposition um okay so the the final
+ 
+
+ align:start position:0%
+deposition um okay so the the final
+technique and that I want to talk about
+
+ align:start position:0%
+technique and that I want to talk about
+ 
+
+ align:start position:0%
+technique and that I want to talk about
+today um for pbd is this ionized sputter
+
+ align:start position:0%
+today um for pbd is this ionized sputter
+ 
+
+ align:start position:0%
+today um for pbd is this ionized sputter
+deposition or highdensity plasma
+
+ align:start position:0%
+deposition or highdensity plasma
+ 
+
+ align:start position:0%
+deposition or highdensity plasma
+sputtering so far let's just make it
+
+ align:start position:0%
+sputtering so far let's just make it
+ 
+
+ align:start position:0%
+sputtering so far let's just make it
+clear what we've been talking about is
+
+ align:start position:0%
+clear what we've been talking about is
+ 
+
+ align:start position:0%
+clear what we've been talking about is
+the Argon has been ionized it's been
+
+ align:start position:0%
+the Argon has been ionized it's been
+ 
+
+ align:start position:0%
+the Argon has been ionized it's been
+accelerated towards the towards the
+
+ align:start position:0%
+accelerated towards the towards the
+ 
+
+ align:start position:0%
+accelerated towards the towards the
+target but the atoms coming off um are
+
+ align:start position:0%
+target but the atoms coming off um are
+ 
+
+ align:start position:0%
+target but the atoms coming off um are
+are pretty much neutral the are aluminum
+
+ align:start position:0%
+are pretty much neutral the are aluminum
+ 
+
+ align:start position:0%
+are pretty much neutral the are aluminum
+coming off or the Platinum or whatever
+
+ align:start position:0%
+coming off or the Platinum or whatever
+ 
+
+ align:start position:0%
+coming off or the Platinum or whatever
+um but in some systems you can arrange
+
+ align:start position:0%
+um but in some systems you can arrange
+ 
+
+ align:start position:0%
+um but in some systems you can arrange
+it that the the positing atoms
+
+ align:start position:0%
+it that the the positing atoms
+ 
+
+ align:start position:0%
+it that the the positing atoms
+themselves are ionized so not just the
+
+ align:start position:0%
+themselves are ionized so not just the
+ 
+
+ align:start position:0%
+themselves are ionized so not just the
+sputtering uh material and so so what
+
+ align:start position:0%
+sputtering uh material and so so what
+ 
+
+ align:start position:0%
+sputtering uh material and so so what
+you do is you uh you place in addition
+
+ align:start position:0%
+you do is you uh you place in addition
+ 
+
+ align:start position:0%
+you do is you uh you place in addition
+to this um these uh uh the Target and
+
+ align:start position:0%
+to this um these uh uh the Target and
+ 
+
+ align:start position:0%
+to this um these uh uh the Target and
+and the substrate that are biased uh
+
+ align:start position:0%
+and the substrate that are biased uh
+ 
+
+ align:start position:0%
+and the substrate that are biased uh
+with some kind of RF you can put an RF
+
+ align:start position:0%
+with some kind of RF you can put an RF
+ 
+
+ align:start position:0%
+with some kind of RF you can put an RF
+coil so now we have two RF surfaces you
+
+ align:start position:0%
+coil so now we have two RF surfaces you
+ 
+
+ align:start position:0%
+coil so now we have two RF surfaces you
+can put an RF coil around um the
+
+ align:start position:0%
+can put an RF coil around um the
+ 
+
+ align:start position:0%
+can put an RF coil around um the
+plasma and that's going to induce
+
+ align:start position:0%
+plasma and that's going to induce
+ 
+
+ align:start position:0%
+plasma and that's going to induce
+collisions in the plasma which is going
+
+ align:start position:0%
+collisions in the plasma which is going
+ 
+
+ align:start position:0%
+collisions in the plasma which is going
+to tend to ionize the aluminum so the
+
+ align:start position:0%
+to tend to ionize the aluminum so the
+ 
+
+ align:start position:0%
+to tend to ionize the aluminum so the
+aluminum comes off neutral but you can
+
+ align:start position:0%
+aluminum comes off neutral but you can
+ 
+
+ align:start position:0%
+aluminum comes off neutral but you can
+ionize it with this inductively coupled
+
+ align:start position:0%
+ionize it with this inductively coupled
+ 
+
+ align:start position:0%
+ionize it with this inductively coupled
+uh antenna essentially so now I have a
+
+ align:start position:0%
+uh antenna essentially so now I have a
+ 
+
+ align:start position:0%
+uh antenna essentially so now I have a
+different situation um I'm I'm using the
+
+ align:start position:0%
+different situation um I'm I'm using the
+ 
+
+ align:start position:0%
+different situation um I'm I'm using the
+uh argon ions to be accelerated towards
+
+ align:start position:0%
+uh argon ions to be accelerated towards
+ 
+
+ align:start position:0%
+uh argon ions to be accelerated towards
+the target get the aluminum off then I
+
+ align:start position:0%
+the target get the aluminum off then I
+ 
+
+ align:start position:0%
+the target get the aluminum off then I
+ionize the aluminum as it comes down uh
+
+ align:start position:0%
+ionize the aluminum as it comes down uh
+ 
+
+ align:start position:0%
+ionize the aluminum as it comes down uh
+why would I want to do that well if I I
+
+ align:start position:0%
+why would I want to do that well if I I
+ 
+
+ align:start position:0%
+why would I want to do that well if I I
+have now ions coming down and if I bias
+
+ align:start position:0%
+have now ions coming down and if I bias
+ 
+
+ align:start position:0%
+have now ions coming down and if I bias
+the substrate um I can get a much
+
+ align:start position:0%
+the substrate um I can get a much
+ 
+
+ align:start position:0%
+the substrate um I can get a much
+narrower um rival angle distribution
+
+ align:start position:0%
+narrower um rival angle distribution
+ 
+
+ align:start position:0%
+narrower um rival angle distribution
+because they're being accelerated
+
+ align:start position:0%
+because they're being accelerated
+ 
+
+ align:start position:0%
+because they're being accelerated
+towards the substrate before they were
+
+ align:start position:0%
+towards the substrate before they were
+ 
+
+ align:start position:0%
+towards the substrate before they were
+just sort of coming down in sort of
+
+ align:start position:0%
+just sort of coming down in sort of
+ 
+
+ align:start position:0%
+just sort of coming down in sort of
+collisions mean-free path and the
+
+ align:start position:0%
+collisions mean-free path and the
+ 
+
+ align:start position:0%
+collisions mean-free path and the
+aluminum was just hitting the surface
+
+ align:start position:0%
+aluminum was just hitting the surface
+ 
+
+ align:start position:0%
+aluminum was just hitting the surface
+but now you can actually accelerate them
+
+ align:start position:0%
+but now you can actually accelerate them
+ 
+
+ align:start position:0%
+but now you can actually accelerate them
+uh towards the substrate maybe you can
+
+ align:start position:0%
+uh towards the substrate maybe you can
+ 
+
+ align:start position:0%
+uh towards the substrate maybe you can
+use this um to fill a deep contact hole
+
+ align:start position:0%
+use this um to fill a deep contact hole
+ 
+
+ align:start position:0%
+use this um to fill a deep contact hole
+here's an example on slide 29 you have a
+
+ align:start position:0%
+here's an example on slide 29 you have a
+ 
+
+ align:start position:0%
+here's an example on slide 29 you have a
+deep hole and look at the schematically
+
+ align:start position:0%
+deep hole and look at the schematically
+ 
+
+ align:start position:0%
+deep hole and look at the schematically
+in in on the right in B the arrival
+
+ align:start position:0%
+in in on the right in B the arrival
+ 
+
+ align:start position:0%
+in in on the right in B the arrival
+angle uh distribution is very narrow
+
+ align:start position:0%
+angle uh distribution is very narrow
+ 
+
+ align:start position:0%
+angle uh distribution is very narrow
+they're pretty much all coming straight
+
+ align:start position:0%
+they're pretty much all coming straight
+ 
+
+ align:start position:0%
+they're pretty much all coming straight
+down compared to here where they're
+
+ align:start position:0%
+down compared to here where they're
+ 
+
+ align:start position:0%
+down compared to here where they're
+coming in different directions so you
+
+ align:start position:0%
+coming in different directions so you
+ 
+
+ align:start position:0%
+coming in different directions so you
+can then adjust in this high density
+
+ align:start position:0%
+can then adjust in this high density
+ 
+
+ align:start position:0%
+can then adjust in this high density
+plasma or um inductively coupled people
+
+ align:start position:0%
+plasma or um inductively coupled people
+ 
+
+ align:start position:0%
+plasma or um inductively coupled people
+sometimes call this ICP sputtering um
+
+ align:start position:0%
+sometimes call this ICP sputtering um
+ 
+
+ align:start position:0%
+sometimes call this ICP sputtering um
+you have another Knob that you can turn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+literally so what are some common PVD
+
+ align:start position:0%
+literally so what are some common PVD
+ 
+
+ align:start position:0%
+literally so what are some common PVD
+films and how are they put down that's
+
+ align:start position:0%
+films and how are they put down that's
+ 
+
+ align:start position:0%
+films and how are they put down that's
+listed on on this chart I took from your
+
+ align:start position:0%
+listed on on this chart I took from your
+ 
+
+ align:start position:0%
+listed on on this chart I took from your
+text here on slide 30 um a littleit them
+
+ align:start position:0%
+text here on slide 30 um a littleit them
+ 
+
+ align:start position:0%
+text here on slide 30 um a littleit them
+um put down in in a number of different
+
+ align:start position:0%
+um put down in in a number of different
+ 
+
+ align:start position:0%
+um put down in in a number of different
+ways um but but sputter deposition is
+
+ align:start position:0%
+ways um but but sputter deposition is
+ 
+
+ align:start position:0%
+ways um but but sputter deposition is
+really the most common the standard
+
+ align:start position:0%
+really the most common the standard
+ 
+
+ align:start position:0%
+really the most common the standard
+deposition of aluminum is is to hold the
+
+ align:start position:0%
+deposition of aluminum is is to hold the
+ 
+
+ align:start position:0%
+deposition of aluminum is is to hold the
+Wafers near to room temperature pretty
+
+ align:start position:0%
+Wafers near to room temperature pretty
+ 
+
+ align:start position:0%
+Wafers near to room temperature pretty
+close to room temperature uh um uh there
+
+ align:start position:0%
+close to room temperature uh um uh there
+ 
+
+ align:start position:0%
+close to room temperature uh um uh there
+are some special sputter deposition
+
+ align:start position:0%
+are some special sputter deposition
+ 
+
+ align:start position:0%
+are some special sputter deposition
+systems where we'll put it down in about
+
+ align:start position:0%
+systems where we'll put it down in about
+ 
+
+ align:start position:0%
+systems where we'll put it down in about
+400 to 500 uh so in other words hot
+
+ align:start position:0%
+400 to 500 uh so in other words hot
+ 
+
+ align:start position:0%
+400 to 500 uh so in other words hot
+aluminum and this is if you need to
+
+ align:start position:0%
+aluminum and this is if you need to
+ 
+
+ align:start position:0%
+aluminum and this is if you need to
+Reflow the aluminum for better step
+
+ align:start position:0%
+Reflow the aluminum for better step
+ 
+
+ align:start position:0%
+Reflow the aluminum for better step
+coverage uh you don't see aluminum
+
+ align:start position:0%
+coverage uh you don't see aluminum
+ 
+
+ align:start position:0%
+coverage uh you don't see aluminum
+deposited by chemical vapor deposition
+
+ align:start position:0%
+deposited by chemical vapor deposition
+ 
+
+ align:start position:0%
+deposited by chemical vapor deposition
+is extremely uh rare um it's it's
+
+ align:start position:0%
+is extremely uh rare um it's it's
+ 
+
+ align:start position:0%
+is extremely uh rare um it's it's
+usually sputtered uh another common very
+
+ align:start position:0%
+usually sputtered uh another common very
+ 
+
+ align:start position:0%
+usually sputtered uh another common very
+common uh material you'll find in Fabs
+
+ align:start position:0%
+common uh material you'll find in Fabs
+ 
+
+ align:start position:0%
+common uh material you'll find in Fabs
+is taii or Tai tungsten this is also
+
+ align:start position:0%
+is taii or Tai tungsten this is also
+ 
+
+ align:start position:0%
+is taii or Tai tungsten this is also
+sputter deposited uh again uh cvd can be
+
+ align:start position:0%
+sputter deposited uh again uh cvd can be
+ 
+
+ align:start position:0%
+sputter deposited uh again uh cvd can be
+very difficult um uh so people will use
+
+ align:start position:0%
+very difficult um uh so people will use
+ 
+
+ align:start position:0%
+very difficult um uh so people will use
+sputtering uh tungsten tungsten is used
+
+ align:start position:0%
+sputtering uh tungsten tungsten is used
+ 
+
+ align:start position:0%
+sputtering uh tungsten tungsten is used
+in to fill plugs it's often put down by
+
+ align:start position:0%
+in to fill plugs it's often put down by
+ 
+
+ align:start position:0%
+in to fill plugs it's often put down by
+low pressure um uh cvd using uh tungsten
+
+ align:start position:0%
+low pressure um uh cvd using uh tungsten
+ 
+
+ align:start position:0%
+low pressure um uh cvd using uh tungsten
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+wf6 uh toxin hexif fluoride um TI
+
+ align:start position:0%
+wf6 uh toxin hexif fluoride um TI
+ 
+
+ align:start position:0%
+wf6 uh toxin hexif fluoride um TI
+silicide can be put down in a couple
+
+ align:start position:0%
+silicide can be put down in a couple
+ 
+
+ align:start position:0%
+silicide can be put down in a couple
+different ways It's usually sputtered
+
+ align:start position:0%
+different ways It's usually sputtered
+ 
+
+ align:start position:0%
+different ways It's usually sputtered
+the titanium is usually sputtered
+
+ align:start position:0%
+the titanium is usually sputtered
+ 
+
+ align:start position:0%
+the titanium is usually sputtered
+initially uh and then it's reacted and
+
+ align:start position:0%
+initially uh and then it's reacted and
+ 
+
+ align:start position:0%
+initially uh and then it's reacted and
+we'll talk a little a bit more in in the
+
+ align:start position:0%
+we'll talk a little a bit more in in the
+ 
+
+ align:start position:0%
+we'll talk a little a bit more in in the
+um I think one of the LA couple last
+
+ align:start position:0%
+um I think one of the LA couple last
+ 
+
+ align:start position:0%
+um I think one of the LA couple last
+couple lectures on how pilicides are
+
+ align:start position:0%
+couple lectures on how pilicides are
+ 
+
+ align:start position:0%
+couple lectures on how pilicides are
+formed uh th
+
+ align:start position:0%
+formed uh th
+ 
+
+ align:start position:0%
+formed uh th
+nitride is also sputter but usually in a
+
+ align:start position:0%
+nitride is also sputter but usually in a
+ 
+
+ align:start position:0%
+nitride is also sputter but usually in a
+nitrogen plasma instead of using inert
+
+ align:start position:0%
+nitrogen plasma instead of using inert
+ 
+
+ align:start position:0%
+nitrogen plasma instead of using inert
+gas like argon use nitrogen which then
+
+ align:start position:0%
+gas like argon use nitrogen which then
+ 
+
+ align:start position:0%
+gas like argon use nitrogen which then
+can um not only knock the titanium off
+
+ align:start position:0%
+can um not only knock the titanium off
+ 
+
+ align:start position:0%
+can um not only knock the titanium off
+but then react with it and then go down
+
+ align:start position:0%
+but then react with it and then go down
+ 
+
+ align:start position:0%
+but then react with it and then go down
+as uh as Ty nitrate so those are some
+
+ align:start position:0%
+as uh as Ty nitrate so those are some
+ 
+
+ align:start position:0%
+as uh as Ty nitrate so those are some
+common um films you'll find in the Fabs
+
+ align:start position:0%
+common um films you'll find in the Fabs
+ 
+
+ align:start position:0%
+common um films you'll find in the Fabs
+um so let me just summarize um that um
+
+ align:start position:0%
+um so let me just summarize um that um
+ 
+
+ align:start position:0%
+um so let me just summarize um that um
+the lpcvd uses low pressures and why do
+
+ align:start position:0%
+the lpcvd uses low pressures and why do
+ 
+
+ align:start position:0%
+the lpcvd uses low pressures and why do
+we do that we want to increase the
+
+ align:start position:0%
+we do that we want to increase the
+ 
+
+ align:start position:0%
+we do that we want to increase the
+diffusion rate through the boundary
+
+ align:start position:0%
+diffusion rate through the boundary
+ 
+
+ align:start position:0%
+diffusion rate through the boundary
+label uh layer so you can get more
+
+ align:start position:0%
+label uh layer so you can get more
+ 
+
+ align:start position:0%
+label uh layer so you can get more
+uniform depth across the
+
+ align:start position:0%
+uniform depth across the
+ 
+
+ align:start position:0%
+uniform depth across the
+wafer even when the Wafers are very
+
+ align:start position:0%
+wafer even when the Wafers are very
+ 
+
+ align:start position:0%
+wafer even when the Wafers are very
+closely packed um so the nice thing
+
+ align:start position:0%
+closely packed um so the nice thing
+ 
+
+ align:start position:0%
+closely packed um so the nice thing
+about lpcvd tubes is you don't have to
+
+ align:start position:0%
+about lpcvd tubes is you don't have to
+ 
+
+ align:start position:0%
+about lpcvd tubes is you don't have to
+worry about how the gas flows you just
+
+ align:start position:0%
+worry about how the gas flows you just
+ 
+
+ align:start position:0%
+worry about how the gas flows you just
+have to get um a very uniform
+
+ align:start position:0%
+have to get um a very uniform
+ 
+
+ align:start position:0%
+have to get um a very uniform
+temperature poly silic is the most
+
+ align:start position:0%
+temperature poly silic is the most
+ 
+
+ align:start position:0%
+temperature poly silic is the most
+commonly uh deposited material by lpcvd
+
+ align:start position:0%
+commonly uh deposited material by lpcvd
+ 
+
+ align:start position:0%
+commonly uh deposited material by lpcvd
+it's the gate in seam loss um we've
+
+ align:start position:0%
+it's the gate in seam loss um we've
+ 
+
+ align:start position:0%
+it's the gate in seam loss um we've
+barely scratched the surface of poly I
+
+ align:start position:0%
+barely scratched the surface of poly I
+ 
+
+ align:start position:0%
+barely scratched the surface of poly I
+think it's a reasonably good topic to do
+
+ align:start position:0%
+think it's a reasonably good topic to do
+ 
+
+ align:start position:0%
+think it's a reasonably good topic to do
+if you want wanted you on one of your
+
+ align:start position:0%
+if you want wanted you on one of your
+ 
+
+ align:start position:0%
+if you want wanted you on one of your
+reports you need to optimize the
+
+ align:start position:0%
+reports you need to optimize the
+ 
+
+ align:start position:0%
+reports you need to optimize the
+temperature and the pressure and and the
+
+ align:start position:0%
+temperature and the pressure and and the
+ 
+
+ align:start position:0%
+temperature and the pressure and and the
+exact conditions to get the right grain
+
+ align:start position:0%
+exact conditions to get the right grain
+ 
+
+ align:start position:0%
+exact conditions to get the right grain
+structure so you can get um diffusion of
+
+ align:start position:0%
+structure so you can get um diffusion of
+ 
+
+ align:start position:0%
+structure so you can get um diffusion of
+dopin properly and good electrical
+
+ align:start position:0%
+dopin properly and good electrical
+ 
+
+ align:start position:0%
+dopin properly and good electrical
+activation in the
+
+ align:start position:0%
+activation in the
+ 
+
+ align:start position:0%
+activation in the
+grains
+
+ align:start position:0%
+grains
+ 
+
+ align:start position:0%
+grains
+um this plasma enhancement can be used
+
+ align:start position:0%
+um this plasma enhancement can be used
+ 
+
+ align:start position:0%
+um this plasma enhancement can be used
+to enhance the depth rate at low
+
+ align:start position:0%
+to enhance the depth rate at low
+ 
+
+ align:start position:0%
+to enhance the depth rate at low
+temperatures uh especially for
+
+ align:start position:0%
+temperatures uh especially for
+ 
+
+ align:start position:0%
+temperatures uh especially for
+dielectrics uh we talked about the
+
+ align:start position:0%
+dielectrics uh we talked about the
+ 
+
+ align:start position:0%
+dielectrics uh we talked about the
+noelis concept one which is an example
+
+ align:start position:0%
+noelis concept one which is an example
+ 
+
+ align:start position:0%
+noelis concept one which is an example
+there are many many examples of pcvd
+
+ align:start position:0%
+there are many many examples of pcvd
+ 
+
+ align:start position:0%
+there are many many examples of pcvd
+systems that are used in Fabs
+
+ align:start position:0%
+systems that are used in Fabs
+ 
+
+ align:start position:0%
+systems that are used in Fabs
+um typically use plasmas when you have a
+
+ align:start position:0%
+um typically use plasmas when you have a
+ 
+
+ align:start position:0%
+um typically use plasmas when you have a
+limited thermal budget or if you happen
+
+ align:start position:0%
+limited thermal budget or if you happen
+ 
+
+ align:start position:0%
+limited thermal budget or if you happen
+to be doing Mims or you have something
+
+ align:start position:0%
+to be doing Mims or you have something
+ 
+
+ align:start position:0%
+to be doing Mims or you have something
+where you really need thick layers and
+
+ align:start position:0%
+where you really need thick layers and
+ 
+
+ align:start position:0%
+where you really need thick layers and
+doing it thermally just doesn't is Not
+
+ align:start position:0%
+doing it thermally just doesn't is Not
+ 
+
+ align:start position:0%
+doing it thermally just doesn't is Not
+Practical um the most commonly used pbd
+
+ align:start position:0%
+Practical um the most commonly used pbd
+ 
+
+ align:start position:0%
+Practical um the most commonly used pbd
+technique is sputtering either DC for um
+
+ align:start position:0%
+technique is sputtering either DC for um
+ 
+
+ align:start position:0%
+technique is sputtering either DC for um
+for metals or
+
+ align:start position:0%
+for metals or
+ 
+
+ align:start position:0%
+for metals or
+RF uh for
+
+ align:start position:0%
+RF uh for
+ 
+
+ align:start position:0%
+RF uh for
+dialectric um in contrast to dep
+
+ align:start position:0%
+dialectric um in contrast to dep
+ 
+
+ align:start position:0%
+dialectric um in contrast to dep
+evaporation you can get very good step
+
+ align:start position:0%
+evaporation you can get very good step
+ 
+
+ align:start position:0%
+evaporation you can get very good step
+coverage um and filling of high aspect
+
+ align:start position:0%
+coverage um and filling of high aspect
+ 
+
+ align:start position:0%
+coverage um and filling of high aspect
+ratio holes um so far we've talked very
+
+ align:start position:0%
+ratio holes um so far we've talked very
+ 
+
+ align:start position:0%
+ratio holes um so far we've talked very
+qualitatively what I want to go through
+
+ align:start position:0%
+qualitatively what I want to go through
+ 
+
+ align:start position:0%
+qualitatively what I want to go through
+next time is um some actual models that
+
+ align:start position:0%
+next time is um some actual models that
+ 
+
+ align:start position:0%
+next time is um some actual models that
+people have developed methodologies for
+
+ align:start position:0%
+people have developed methodologies for
+ 
+
+ align:start position:0%
+people have developed methodologies for
+modeling uh these processes both CBD and
+
+ align:start position:0%
+modeling uh these processes both CBD and
+ 
+
+ align:start position:0%
+modeling uh these processes both CBD and
+uh particularly sputtering and pbd
+
+ align:start position:0%
+uh particularly sputtering and pbd
+ 
+
+ align:start position:0%
+uh particularly sputtering and pbd
+that's all I have if you came in late
+
+ align:start position:0%
+that's all I have if you came in late
+ 
+
+ align:start position:0%
+that's all I have if you came in late
+remind you the homework number five went
+
+ align:start position:0%
+remind you the homework number five went
+ 
+
+ align:start position:0%
+remind you the homework number five went
+out and there's a problem on the back so
+
+ align:start position:0%
+out and there's a problem on the back so
+ 
+
+ align:start position:0%
+out and there's a problem on the back so
+don't miss part uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3B and if you haven't signed up make
+
+ align:start position:0%
+3B and if you haven't signed up make
+ 
+
+ align:start position:0%
+3B and if you haven't signed up make
+sure today is the last day to sign up
+
+ align:start position:0%
+sure today is the last day to sign up
+ 
+
+ align:start position:0%
+sure today is the last day to sign up
+for a topic so I've got the clipboard uh
+
+ align:start position:0%
+for a topic so I've got the clipboard uh
+ 
+
+ align:start position:0%
+for a topic so I've got the clipboard uh
+there in the back
\ No newline at end of file
diff --git a/fppdTndwipg.txt b/fppdTndwipg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9caf0ea0039af813c5fd7870499ee6af88c108b6
--- /dev/null
+++ b/fppdTndwipg.txt
@@ -0,0 +1,955 @@
+align:start position:0%
+ 
+all right cool so projects presentations
+
+ align:start position:0%
+all right cool so projects presentations
+ 
+
+ align:start position:0%
+all right cool so projects presentations
+are gonna happen and we're gonna start
+
+ align:start position:0%
+are gonna happen and we're gonna start
+ 
+
+ align:start position:0%
+are gonna happen and we're gonna start
+with the video games and then we're
+
+ align:start position:0%
+with the video games and then we're
+ 
+
+ align:start position:0%
+with the video games and then we're
+going to take a cool break in the middle
+
+ align:start position:0%
+going to take a cool break in the middle
+ 
+
+ align:start position:0%
+going to take a cool break in the middle
+to play with a collaborative cloud sort
+
+ align:start position:0%
+to play with a collaborative cloud sort
+ 
+
+ align:start position:0%
+to play with a collaborative cloud sort
+crowd-sourced cloud based robot that's
+
+ align:start position:0%
+crowd-sourced cloud based robot that's
+ 
+
+ align:start position:0%
+crowd-sourced cloud based robot that's
+gonna try to follow all of our
+
+ align:start position:0%
+gonna try to follow all of our
+ 
+
+ align:start position:0%
+gonna try to follow all of our
+collective input in order to grab a
+
+ align:start position:0%
+collective input in order to grab a
+ 
+
+ align:start position:0%
+collective input in order to grab a
+piece of paper that Abin off the TA for
+
+ align:start position:0%
+piece of paper that Abin off the TA for
+ 
+
+ align:start position:0%
+piece of paper that Abin off the TA for
+the Arduino class has been building in
+
+ align:start position:0%
+the Arduino class has been building in
+ 
+
+ align:start position:0%
+the Arduino class has been building in
+his free time that's a good embarrassed
+
+ align:start position:0%
+his free time that's a good embarrassed
+ 
+
+ align:start position:0%
+his free time that's a good embarrassed
+face that's so that's a way to model
+
+ align:start position:0%
+face that's so that's a way to model
+ 
+
+ align:start position:0%
+face that's so that's a way to model
+embarrassment I appreciate that because
+
+ align:start position:0%
+embarrassment I appreciate that because
+ 
+
+ align:start position:0%
+embarrassment I appreciate that because
+we're all gonna feel embarrassed when we
+
+ align:start position:0%
+we're all gonna feel embarrassed when we
+ 
+
+ align:start position:0%
+we're all gonna feel embarrassed when we
+present and that's okay I feel
+
+ align:start position:0%
+present and that's okay I feel
+ 
+
+ align:start position:0%
+present and that's okay I feel
+embarrassed right now trying to get your
+
+ align:start position:0%
+embarrassed right now trying to get your
+ 
+
+ align:start position:0%
+embarrassed right now trying to get your
+attention and pull you away from your
+
+ align:start position:0%
+attention and pull you away from your
+ 
+
+ align:start position:0%
+attention and pull you away from your
+projects because I know that that's what
+
+ align:start position:0%
+projects because I know that that's what
+ 
+
+ align:start position:0%
+projects because I know that that's what
+you want to be doing right now so that's
+
+ align:start position:0%
+you want to be doing right now so that's
+ 
+
+ align:start position:0%
+you want to be doing right now so that's
+okay we're all going to feel embarrassed
+
+ align:start position:0%
+okay we're all going to feel embarrassed
+ 
+
+ align:start position:0%
+okay we're all going to feel embarrassed
+but we're going to share and not in
+
+ align:start position:0%
+but we're going to share and not in
+ 
+
+ align:start position:0%
+but we're going to share and not in
+order to impress everyone with how
+
+ align:start position:0%
+order to impress everyone with how
+ 
+
+ align:start position:0%
+order to impress everyone with how
+amazing our project was but to open up a
+
+ align:start position:0%
+amazing our project was but to open up a
+ 
+
+ align:start position:0%
+amazing our project was but to open up a
+dialogue about what we learned and what
+
+ align:start position:0%
+dialogue about what we learned and what
+ 
+
+ align:start position:0%
+dialogue about what we learned and what
+other people can learn from us so the
+
+ align:start position:0%
+other people can learn from us so the
+ 
+
+ align:start position:0%
+other people can learn from us so the
+point of coming up and sharing your
+
+ align:start position:0%
+point of coming up and sharing your
+ 
+
+ align:start position:0%
+point of coming up and sharing your
+presentation is not to get accolades
+
+ align:start position:0%
+presentation is not to get accolades
+ 
+
+ align:start position:0%
+presentation is not to get accolades
+from your friends about how amazingly
+
+ align:start position:0%
+from your friends about how amazingly
+ 
+
+ align:start position:0%
+from your friends about how amazingly
+brilliant you are it's to share
+
+ align:start position:0%
+brilliant you are it's to share
+ 
+
+ align:start position:0%
+brilliant you are it's to share
+something so that if someone's interest
+
+ align:start position:0%
+something so that if someone's interest
+ 
+
+ align:start position:0%
+something so that if someone's interest
+gets piqued they can go oh cool how did
+
+ align:start position:0%
+gets piqued they can go oh cool how did
+ 
+
+ align:start position:0%
+gets piqued they can go oh cool how did
+you do that thing and then you have a
+
+ align:start position:0%
+you do that thing and then you have a
+ 
+
+ align:start position:0%
+you do that thing and then you have a
+chance to teach them about that really
+
+ align:start position:0%
+chance to teach them about that really
+ 
+
+ align:start position:0%
+chance to teach them about that really
+specific thing that you did if you were
+
+ align:start position:0%
+specific thing that you did if you were
+ 
+
+ align:start position:0%
+specific thing that you did if you were
+able to make a really cute thing on the
+
+ align:start position:0%
+able to make a really cute thing on the
+ 
+
+ align:start position:0%
+able to make a really cute thing on the
+screen move or if you're able to make a
+
+ align:start position:0%
+screen move or if you're able to make a
+ 
+
+ align:start position:0%
+screen move or if you're able to make a
+really cool video game work or if you're
+
+ align:start position:0%
+really cool video game work or if you're
+ 
+
+ align:start position:0%
+really cool video game work or if you're
+able to make fun Arduino electronics
+
+ align:start position:0%
+able to make fun Arduino electronics
+ 
+
+ align:start position:0%
+able to make fun Arduino electronics
+projects this is your chance to teach by
+
+ align:start position:0%
+projects this is your chance to teach by
+ 
+
+ align:start position:0%
+projects this is your chance to teach by
+sharing what you do and inviting other
+
+ align:start position:0%
+sharing what you do and inviting other
+ 
+
+ align:start position:0%
+sharing what you do and inviting other
+people to ask questions about it so this
+
+ align:start position:0%
+people to ask questions about it so this
+ 
+
+ align:start position:0%
+people to ask questions about it so this
+is not about impressing each other most
+
+ align:start position:0%
+is not about impressing each other most
+ 
+
+ align:start position:0%
+is not about impressing each other most
+of you will never which what you're
+
+ align:start position:0%
+of you will never which what you're
+ 
+
+ align:start position:0%
+of you will never which what you're
+trying to shift me oh yeah you guys
+
+ align:start position:0%
+trying to shift me oh yeah you guys
+ 
+
+ align:start position:0%
+trying to shift me oh yeah you guys
+thank them most of you won't talk after
+
+ align:start position:0%
+thank them most of you won't talk after
+ 
+
+ align:start position:0%
+thank them most of you won't talk after
+this class so don't worry if you do
+
+ align:start position:0%
+this class so don't worry if you do
+ 
+
+ align:start position:0%
+this class so don't worry if you do
+something embarrassing you won't see
+
+ align:start position:0%
+something embarrassing you won't see
+ 
+
+ align:start position:0%
+something embarrassing you won't see
+most of these people the ones that you
+
+ align:start position:0%
+most of these people the ones that you
+ 
+
+ align:start position:0%
+most of these people the ones that you
+do exchange emails with them and talk to
+
+ align:start position:0%
+do exchange emails with them and talk to
+ 
+
+ align:start position:0%
+do exchange emails with them and talk to
+them after and they're not going to care
+
+ align:start position:0%
+them after and they're not going to care
+ 
+
+ align:start position:0%
+them after and they're not going to care
+if you do something silly up here so I
+
+ align:start position:0%
+if you do something silly up here so I
+ 
+
+ align:start position:0%
+if you do something silly up here so I
+just want to set the expectation that
+
+ align:start position:0%
+just want to set the expectation that
+ 
+
+ align:start position:0%
+just want to set the expectation that
+this is not a competitive presentation
+
+ align:start position:0%
+this is not a competitive presentation
+ 
+
+ align:start position:0%
+this is not a competitive presentation
+environment we're not getting venture
+
+ align:start position:0%
+environment we're not getting venture
+ 
+
+ align:start position:0%
+environment we're not getting venture
+capital there's nothing other than
+
+ align:start position:0%
+capital there's nothing other than
+ 
+
+ align:start position:0%
+capital there's nothing other than
+learning opportunity here as Kyle said
+
+ align:start position:0%
+learning opportunity here as Kyle said
+ 
+
+ align:start position:0%
+learning opportunity here as Kyle said
+we're not competing hopefully you had
+
+ align:start position:0%
+we're not competing hopefully you had
+ 
+
+ align:start position:0%
+we're not competing hopefully you had
+fun and learned something over the last
+
+ align:start position:0%
+fun and learned something over the last
+ 
+
+ align:start position:0%
+fun and learned something over the last
+two weeks that's that's teachers only
+
+ align:start position:0%
+two weeks that's that's teachers only
+ 
+
+ align:start position:0%
+two weeks that's that's teachers only
+goal to let you have fun and learn
+
+ align:start position:0%
+goal to let you have fun and learn
+ 
+
+ align:start position:0%
+goal to let you have fun and learn
+something so yeah I think the point of
+
+ align:start position:0%
+something so yeah I think the point of
+ 
+
+ align:start position:0%
+something so yeah I think the point of
+this two weeks is to like get your feet
+
+ align:start position:0%
+this two weeks is to like get your feet
+ 
+
+ align:start position:0%
+this two weeks is to like get your feet
+wet with Arduino and see what it's like
+
+ align:start position:0%
+wet with Arduino and see what it's like
+ 
+
+ align:start position:0%
+wet with Arduino and see what it's like
+to plan a project and try to build it
+
+ align:start position:0%
+to plan a project and try to build it
+ 
+
+ align:start position:0%
+to plan a project and try to build it
+and then figure out how to do it better
+
+ align:start position:0%
+and then figure out how to do it better
+ 
+
+ align:start position:0%
+and then figure out how to do it better
+next time so that's that's what we do
+
+ align:start position:0%
+next time so that's that's what we do
+ 
+
+ align:start position:0%
+next time so that's that's what we do
+but that said you all your groups did
+
+ align:start position:0%
+but that said you all your groups did
+ 
+
+ align:start position:0%
+but that said you all your groups did
+amazing you did so much work which is
+
+ align:start position:0%
+amazing you did so much work which is
+ 
+
+ align:start position:0%
+amazing you did so much work which is
+awesome and we're all excited to see
+
+ align:start position:0%
+awesome and we're all excited to see
+ 
+
+ align:start position:0%
+awesome and we're all excited to see
+what you have to present thank you all
+
+ align:start position:0%
+what you have to present thank you all
+ 
+
+ align:start position:0%
+what you have to present thank you all
+right yes I'm dying come on in all right
+
+ align:start position:0%
+right yes I'm dying come on in all right
+ 
+
+ align:start position:0%
+right yes I'm dying come on in all right
+so the first presents going let me let
+
+ align:start position:0%
+so the first presents going let me let
+ 
+
+ align:start position:0%
+so the first presents going let me let
+them come up and introduce and so the
+
+ align:start position:0%
+them come up and introduce and so the
+ 
+
+ align:start position:0%
+them come up and introduce and so the
+video game groups when you come up take
+
+ align:start position:0%
+video game groups when you come up take
+ 
+
+ align:start position:0%
+video game groups when you come up take
+the microphone introduce your game demo
+
+ align:start position:0%
+the microphone introduce your game demo
+ 
+
+ align:start position:0%
+the microphone introduce your game demo
+your games or introduce your game talk
+
+ align:start position:0%
+your games or introduce your game talk
+ 
+
+ align:start position:0%
+your games or introduce your game talk
+about anything that you feel inspired to
+
+ align:start position:0%
+about anything that you feel inspired to
+ 
+
+ align:start position:0%
+about anything that you feel inspired to
+talk about if there was a fun
+
+ align:start position:0%
+talk about if there was a fun
+ 
+
+ align:start position:0%
+talk about if there was a fun
+interesting learning experience or if
+
+ align:start position:0%
+interesting learning experience or if
+ 
+
+ align:start position:0%
+interesting learning experience or if
+something got you really excited talk
+
+ align:start position:0%
+something got you really excited talk
+ 
+
+ align:start position:0%
+something got you really excited talk
+about that demo your game and then we're
+
+ align:start position:0%
+about that demo your game and then we're
+ 
+
+ align:start position:0%
+about that demo your game and then we're
+gonna open it up to questions as an
+
+ align:start position:0%
+gonna open it up to questions as an
+ 
+
+ align:start position:0%
+gonna open it up to questions as an
+audience member the best thing that you
+
+ align:start position:0%
+audience member the best thing that you
+ 
+
+ align:start position:0%
+audience member the best thing that you
+can do to support someone who's
+
+ align:start position:0%
+can do to support someone who's
+ 
+
+ align:start position:0%
+can do to support someone who's
+presenting is to make occasional eye
+
+ align:start position:0%
+presenting is to make occasional eye
+ 
+
+ align:start position:0%
+presenting is to make occasional eye
+contact and pay some attention and then
+
+ align:start position:0%
+contact and pay some attention and then
+ 
+
+ align:start position:0%
+contact and pay some attention and then
+at the end be able to ask a question
+
+ align:start position:0%
+at the end be able to ask a question
+ 
+
+ align:start position:0%
+at the end be able to ask a question
+that reflects I know I'm very explicit
+
+ align:start position:0%
+that reflects I know I'm very explicit
+ 
+
+ align:start position:0%
+that reflects I know I'm very explicit
+but if you've been amazed at how many
+
+ align:start position:0%
+but if you've been amazed at how many
+ 
+
+ align:start position:0%
+but if you've been amazed at how many
+people don't make eye contact with the
+
+ align:start position:0%
+people don't make eye contact with the
+ 
+
+ align:start position:0%
+people don't make eye contact with the
+presenters and then ask questions at the
+
+ align:start position:0%
+presenters and then ask questions at the
+ 
+
+ align:start position:0%
+presenters and then ask questions at the
+end which reflects something like that
+
+ align:start position:0%
+end which reflects something like that
+ 
+
+ align:start position:0%
+end which reflects something like that
+looked really cool how did you do that
+
+ align:start position:0%
+looked really cool how did you do that
+ 
+
+ align:start position:0%
+looked really cool how did you do that
+and what you're doing is you're setting
+
+ align:start position:0%
+and what you're doing is you're setting
+ 
+
+ align:start position:0%
+and what you're doing is you're setting
+them up to look smart and share
+
+ align:start position:0%
+them up to look smart and share
+ 
+
+ align:start position:0%
+them up to look smart and share
+something that they're passionate about
+
+ align:start position:0%
+something that they're passionate about
+ 
+
+ align:start position:0%
+something that they're passionate about
+and feel support it and you two will
+
+ align:start position:0%
+and feel support it and you two will
+ 
+
+ align:start position:0%
+and feel support it and you two will
+have your chance to be up here and I
+
+ align:start position:0%
+have your chance to be up here and I
+ 
+
+ align:start position:0%
+have your chance to be up here and I
+guarantee that you will want to have an
+
+ align:start position:0%
+guarantee that you will want to have an
+ 
+
+ align:start position:0%
+guarantee that you will want to have an
+audience that makes eye contact and then
+
+ align:start position:0%
+audience that makes eye contact and then
+ 
+
+ align:start position:0%
+audience that makes eye contact and then
+asks you questions about things that
+
+ align:start position:0%
+asks you questions about things that
+ 
+
+ align:start position:0%
+asks you questions about things that
+were interesting in your project so that
+
+ align:start position:0%
+were interesting in your project so that
+ 
+
+ align:start position:0%
+were interesting in your project so that
+you too can feel supported and
+
+ align:start position:0%
+you too can feel supported and
+ 
+
+ align:start position:0%
+you too can feel supported and
+interesting and like people care about
+
+ align:start position:0%
+interesting and like people care about
+ 
+
+ align:start position:0%
+interesting and like people care about
+what you're doing because a lot of this
+
+ align:start position:0%
+what you're doing because a lot of this
+ 
+
+ align:start position:0%
+what you're doing because a lot of this
+class was two weeks of passion projects
+
+ align:start position:0%
+class was two weeks of passion projects
+ 
+
+ align:start position:0%
+class was two weeks of passion projects
+we don't have a lot of structure because
+
+ align:start position:0%
+we don't have a lot of structure because
+ 
+
+ align:start position:0%
+we don't have a lot of structure because
+I think that you know you're here for
+
+ align:start position:0%
+I think that you know you're here for
+ 
+
+ align:start position:0%
+I think that you know you're here for
+two weeks and you should opt into the
+
+ align:start position:0%
+two weeks and you should opt into the
+ 
+
+ align:start position:0%
+two weeks and you should opt into the
+project that you want to do and you
+
+ align:start position:0%
+project that you want to do and you
+ 
+
+ align:start position:0%
+project that you want to do and you
+should find people that you want to work
+
+ align:start position:0%
+should find people that you want to work
+ 
+
+ align:start position:0%
+should find people that you want to work
+with so a lot of this that work that
+
+ align:start position:0%
+with so a lot of this that work that
+ 
+
+ align:start position:0%
+with so a lot of this that work that
+you've done over the last two weeks
+
+ align:start position:0%
+you've done over the last two weeks
+ 
+
+ align:start position:0%
+you've done over the last two weeks
+represents a personal investment and so
+
+ align:start position:0%
+represents a personal investment and so
+ 
+
+ align:start position:0%
+represents a personal investment and so
+respect that in each other like everyone
+
+ align:start position:0%
+respect that in each other like everyone
+ 
+
+ align:start position:0%
+respect that in each other like everyone
+who's up there up here presenting put a
+
+ align:start position:0%
+who's up there up here presenting put a
+ 
+
+ align:start position:0%
+who's up there up here presenting put a
+lot of their own interest and passion
+
+ align:start position:0%
+lot of their own interest and passion
+ 
+
+ align:start position:0%
+lot of their own interest and passion
+into this so yeah support support
+
+ align:start position:0%
+into this so yeah support support
+ 
+
+ align:start position:0%
+into this so yeah support support
+support all right so first group are you
+
+ align:start position:0%
+support all right so first group are you
+ 
+
+ align:start position:0%
+support all right so first group are you
+ready to present all right here you go
\ No newline at end of file
diff --git a/gH_OmTJ9vQs.txt b/gH_OmTJ9vQs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6660b9634f6fa9b80e194832dcd765aa149dafb2
--- /dev/null
+++ b/gH_OmTJ9vQs.txt
@@ -0,0 +1,1091 @@
+align:start position:0%
+ 
+in this segment we introduce the subject
+
+ align:start position:0%
+in this segment we introduce the subject
+ 
+
+ align:start position:0%
+in this segment we introduce the subject
+of list mean squares estimation but as a
+
+ align:start position:0%
+of list mean squares estimation but as a
+ 
+
+ align:start position:0%
+of list mean squares estimation but as a
+warm-up we will start with a very simple
+
+ align:start position:0%
+warm-up we will start with a very simple
+ 
+
+ align:start position:0%
+warm-up we will start with a very simple
+special case suppose that we have some
+
+ align:start position:0%
+special case suppose that we have some
+ 
+
+ align:start position:0%
+special case suppose that we have some
+random variable that we wish to estimate
+
+ align:start position:0%
+random variable that we wish to estimate
+ 
+
+ align:start position:0%
+random variable that we wish to estimate
+and that we have the probability
+
+ align:start position:0%
+and that we have the probability
+ 
+
+ align:start position:0%
+and that we have the probability
+distribution of this random variable the
+
+ align:start position:0%
+distribution of this random variable the
+ 
+
+ align:start position:0%
+distribution of this random variable the
+probability mass function if it's
+
+ align:start position:0%
+probability mass function if it's
+ 
+
+ align:start position:0%
+probability mass function if it's
+discrete or a probability density
+
+ align:start position:0%
+discrete or a probability density
+ 
+
+ align:start position:0%
+discrete or a probability density
+function if it's continuous as a
+
+ align:start position:0%
+function if it's continuous as a
+ 
+
+ align:start position:0%
+function if it's continuous as a
+concrete instance suppose that our
+
+ align:start position:0%
+concrete instance suppose that our
+ 
+
+ align:start position:0%
+concrete instance suppose that our
+random variable is uniformly distributed
+
+ align:start position:0%
+random variable is uniformly distributed
+ 
+
+ align:start position:0%
+random variable is uniformly distributed
+over a certain interval we would like to
+
+ align:start position:0%
+over a certain interval we would like to
+ 
+
+ align:start position:0%
+over a certain interval we would like to
+estimate this random variable we're
+
+ align:start position:0%
+estimate this random variable we're
+ 
+
+ align:start position:0%
+estimate this random variable we're
+interested in a point estimate
+
+ align:start position:0%
+interested in a point estimate
+ 
+
+ align:start position:0%
+interested in a point estimate
+however we look at the very special case
+
+ align:start position:0%
+however we look at the very special case
+ 
+
+ align:start position:0%
+however we look at the very special case
+where there are no observations
+
+ align:start position:0%
+where there are no observations
+ 
+
+ align:start position:0%
+where there are no observations
+available all that we have is this
+
+ align:start position:0%
+available all that we have is this
+ 
+
+ align:start position:0%
+available all that we have is this
+probability distribution how do we
+
+ align:start position:0%
+probability distribution how do we
+ 
+
+ align:start position:0%
+probability distribution how do we
+estimate this random variable well we
+
+ align:start position:0%
+estimate this random variable well we
+ 
+
+ align:start position:0%
+estimate this random variable well we
+can use the rules that we have already
+
+ align:start position:0%
+can use the rules that we have already
+ 
+
+ align:start position:0%
+can use the rules that we have already
+developed for example the maximum a
+
+ align:start position:0%
+developed for example the maximum a
+ 
+
+ align:start position:0%
+developed for example the maximum a
+posteriori probability rule what would
+
+ align:start position:0%
+posteriori probability rule what would
+ 
+
+ align:start position:0%
+posteriori probability rule what would
+it do in this case since there are no
+
+ align:start position:0%
+it do in this case since there are no
+ 
+
+ align:start position:0%
+it do in this case since there are no
+observations the posterior distribution
+
+ align:start position:0%
+observations the posterior distribution
+ 
+
+ align:start position:0%
+observations the posterior distribution
+of theta is the same as the prior there
+
+ align:start position:0%
+of theta is the same as the prior there
+ 
+
+ align:start position:0%
+of theta is the same as the prior there
+are no observations that would change
+
+ align:start position:0%
+are no observations that would change
+ 
+
+ align:start position:0%
+are no observations that would change
+the prior so we need to find the point
+
+ align:start position:0%
+the prior so we need to find the point
+ 
+
+ align:start position:0%
+the prior so we need to find the point
+at which this distribution is highest
+
+ align:start position:0%
+at which this distribution is highest
+ 
+
+ align:start position:0%
+at which this distribution is highest
+well because this distribution is flat
+
+ align:start position:0%
+well because this distribution is flat
+ 
+
+ align:start position:0%
+well because this distribution is flat
+the map rule does not give us a unique
+
+ align:start position:0%
+the map rule does not give us a unique
+ 
+
+ align:start position:0%
+the map rule does not give us a unique
+answer any value of theta inside the
+
+ align:start position:0%
+answer any value of theta inside the
+ 
+
+ align:start position:0%
+answer any value of theta inside the
+interval from 4 to 10 would be an
+
+ align:start position:0%
+interval from 4 to 10 would be an
+ 
+
+ align:start position:0%
+interval from 4 to 10 would be an
+acceptable answer so any particular
+
+ align:start position:0%
+acceptable answer so any particular
+ 
+
+ align:start position:0%
+acceptable answer so any particular
+estimate in this interval would be fine
+
+ align:start position:0%
+estimate in this interval would be fine
+ 
+
+ align:start position:0%
+estimate in this interval would be fine
+so this rule is not particularly helpful
+
+ align:start position:0%
+so this rule is not particularly helpful
+ 
+
+ align:start position:0%
+so this rule is not particularly helpful
+how about a different estimator we have
+
+ align:start position:0%
+how about a different estimator we have
+ 
+
+ align:start position:0%
+how about a different estimator we have
+seen the conditional expectation
+
+ align:start position:0%
+seen the conditional expectation
+ 
+
+ align:start position:0%
+seen the conditional expectation
+estimator once more in our case since we
+
+ align:start position:0%
+estimator once more in our case since we
+ 
+
+ align:start position:0%
+estimator once more in our case since we
+do not have any observations the
+
+ align:start position:0%
+do not have any observations the
+ 
+
+ align:start position:0%
+do not have any observations the
+conditional expectation is the same as
+
+ align:start position:0%
+conditional expectation is the same as
+ 
+
+ align:start position:0%
+conditional expectation is the same as
+the expectation and for this particular
+
+ align:start position:0%
+the expectation and for this particular
+ 
+
+ align:start position:0%
+the expectation and for this particular
+example it would give us the midpoint of
+
+ align:start position:0%
+example it would give us the midpoint of
+ 
+
+ align:start position:0%
+example it would give us the midpoint of
+the distribution namely an estimate
+
+ align:start position:0%
+the distribution namely an estimate
+ 
+
+ align:start position:0%
+the distribution namely an estimate
+equal to 7 now this rule was
+
+ align:start position:0%
+equal to 7 now this rule was
+ 
+
+ align:start position:0%
+equal to 7 now this rule was
+inconclusive
+
+ align:start position:0%
+inconclusive
+ 
+
+ align:start position:0%
+inconclusive
+this rule gave us a number how can we
+
+ align:start position:0%
+this rule gave us a number how can we
+ 
+
+ align:start position:0%
+this rule gave us a number how can we
+choose and decide that one of these is
+
+ align:start position:0%
+choose and decide that one of these is
+ 
+
+ align:start position:0%
+choose and decide that one of these is
+the right estimate we can do that if we
+
+ align:start position:0%
+the right estimate we can do that if we
+ 
+
+ align:start position:0%
+the right estimate we can do that if we
+introduce a specific performance
+
+ align:start position:0%
+introduce a specific performance
+ 
+
+ align:start position:0%
+introduce a specific performance
+criterion what is it that we wish from
+
+ align:start position:0%
+criterion what is it that we wish from
+ 
+
+ align:start position:0%
+criterion what is it that we wish from
+our estimators
+
+ align:start position:0%
+our estimators
+ 
+
+ align:start position:0%
+our estimators
+and the particular criterion the one
+
+ align:start position:0%
+and the particular criterion the one
+ 
+
+ align:start position:0%
+and the particular criterion the one
+that we will be focusing on is the mean
+
+ align:start position:0%
+that we will be focusing on is the mean
+ 
+
+ align:start position:0%
+that we will be focusing on is the mean
+squared error if you come up with a
+
+ align:start position:0%
+squared error if you come up with a
+ 
+
+ align:start position:0%
+squared error if you come up with a
+certain estimate you look at how far is
+
+ align:start position:0%
+certain estimate you look at how far is
+ 
+
+ align:start position:0%
+certain estimate you look at how far is
+your estimate from the true value that
+
+ align:start position:0%
+your estimate from the true value that
+ 
+
+ align:start position:0%
+your estimate from the true value that
+you are trying to estimate take the
+
+ align:start position:0%
+you are trying to estimate take the
+ 
+
+ align:start position:0%
+you are trying to estimate take the
+square that and average it and this
+
+ align:start position:0%
+square that and average it and this
+ 
+
+ align:start position:0%
+square that and average it and this
+leads us to a formulation who are by we
+
+ align:start position:0%
+leads us to a formulation who are by we
+ 
+
+ align:start position:0%
+leads us to a formulation who are by we
+will try to find an estimate theta hat
+
+ align:start position:0%
+will try to find an estimate theta hat
+ 
+
+ align:start position:0%
+will try to find an estimate theta hat
+that minimizes this mean squared error
+
+ align:start position:0%
+that minimizes this mean squared error
+ 
+
+ align:start position:0%
+that minimizes this mean squared error
+over all possible estimates let us now
+
+ align:start position:0%
+over all possible estimates let us now
+ 
+
+ align:start position:0%
+over all possible estimates let us now
+look at this formulation and see how we
+
+ align:start position:0%
+look at this formulation and see how we
+ 
+
+ align:start position:0%
+look at this formulation and see how we
+can solve it this is a function of a
+
+ align:start position:0%
+can solve it this is a function of a
+ 
+
+ align:start position:0%
+can solve it this is a function of a
+single variable theta hat and we can try
+
+ align:start position:0%
+single variable theta hat and we can try
+ 
+
+ align:start position:0%
+single variable theta hat and we can try
+to minimize it using conventional
+
+ align:start position:0%
+to minimize it using conventional
+ 
+
+ align:start position:0%
+to minimize it using conventional
+methods to carry out this minimization
+
+ align:start position:0%
+methods to carry out this minimization
+ 
+
+ align:start position:0%
+methods to carry out this minimization
+let us first expand this expectation
+
+ align:start position:0%
+let us first expand this expectation
+ 
+
+ align:start position:0%
+let us first expand this expectation
+into a sum of terms we have the expected
+
+ align:start position:0%
+into a sum of terms we have the expected
+ 
+
+ align:start position:0%
+into a sum of terms we have the expected
+value of the square of the random
+
+ align:start position:0%
+value of the square of the random
+ 
+
+ align:start position:0%
+value of the square of the random
+variable then a cross term minus 2 the
+
+ align:start position:0%
+variable then a cross term minus 2 the
+ 
+
+ align:start position:0%
+variable then a cross term minus 2 the
+expected value of theta times theta hat
+
+ align:start position:0%
+expected value of theta times theta hat
+ 
+
+ align:start position:0%
+expected value of theta times theta hat
+however theta hat is a number that we're
+
+ align:start position:0%
+however theta hat is a number that we're
+ 
+
+ align:start position:0%
+however theta hat is a number that we're
+trying to choose it's not random
+
+ align:start position:0%
+trying to choose it's not random
+ 
+
+ align:start position:0%
+trying to choose it's not random
+therefore we can pull it outside the
+
+ align:start position:0%
+therefore we can pull it outside the
+ 
+
+ align:start position:0%
+therefore we can pull it outside the
+expectation and similarly the last term
+
+ align:start position:0%
+expectation and similarly the last term
+ 
+
+ align:start position:0%
+expectation and similarly the last term
+the expected value of theta hat squared
+
+ align:start position:0%
+the expected value of theta hat squared
+ 
+
+ align:start position:0%
+the expected value of theta hat squared
+is just theta hat squared itself this is
+
+ align:start position:0%
+is just theta hat squared itself this is
+ 
+
+ align:start position:0%
+is just theta hat squared itself this is
+what we want to minimize how do we
+
+ align:start position:0%
+what we want to minimize how do we
+ 
+
+ align:start position:0%
+what we want to minimize how do we
+minimize it we take the derivative with
+
+ align:start position:0%
+minimize it we take the derivative with
+ 
+
+ align:start position:0%
+minimize it we take the derivative with
+respect to theta hat and set it to 0 and
+
+ align:start position:0%
+respect to theta hat and set it to 0 and
+ 
+
+ align:start position:0%
+respect to theta hat and set it to 0 and
+this gives us minus 2 the expected value
+
+ align:start position:0%
+this gives us minus 2 the expected value
+ 
+
+ align:start position:0%
+this gives us minus 2 the expected value
+of theta plus twice theta hat equal to 0
+
+ align:start position:0%
+of theta plus twice theta hat equal to 0
+ 
+
+ align:start position:0%
+of theta plus twice theta hat equal to 0
+and when we solve this we find that
+
+ align:start position:0%
+and when we solve this we find that
+ 
+
+ align:start position:0%
+and when we solve this we find that
+theta hat the optimal estimate is equal
+
+ align:start position:0%
+theta hat the optimal estimate is equal
+ 
+
+ align:start position:0%
+theta hat the optimal estimate is equal
+to the expected value of theta so this
+
+ align:start position:0%
+to the expected value of theta so this
+ 
+
+ align:start position:0%
+to the expected value of theta so this
+is the answer to our optimization
+
+ align:start position:0%
+is the answer to our optimization
+ 
+
+ align:start position:0%
+is the answer to our optimization
+problem the optimal estimate according
+
+ align:start position:0%
+problem the optimal estimate according
+ 
+
+ align:start position:0%
+problem the optimal estimate according
+to the least squares criterion is the
+
+ align:start position:0%
+to the least squares criterion is the
+ 
+
+ align:start position:0%
+to the least squares criterion is the
+expected value of the random variable
+
+ align:start position:0%
+expected value of the random variable
+ 
+
+ align:start position:0%
+expected value of the random variable
+now it's interesting to derive this
+
+ align:start position:0%
+now it's interesting to derive this
+ 
+
+ align:start position:0%
+now it's interesting to derive this
+result also in a second way since it is
+
+ align:start position:0%
+result also in a second way since it is
+ 
+
+ align:start position:0%
+result also in a second way since it is
+a quite important than phantom
+
+ align:start position:0%
+a quite important than phantom
+ 
+
+ align:start position:0%
+a quite important than phantom
+the result let us see whether there is a
+
+ align:start position:0%
+the result let us see whether there is a
+ 
+
+ align:start position:0%
+the result let us see whether there is a
+different way of establishing it that
+
+ align:start position:0%
+different way of establishing it that
+ 
+
+ align:start position:0%
+different way of establishing it that
+stays closer to the probabilistic world
+
+ align:start position:0%
+stays closer to the probabilistic world
+ 
+
+ align:start position:0%
+stays closer to the probabilistic world
+rather than the calculus world so let us
+
+ align:start position:0%
+rather than the calculus world so let us
+ 
+
+ align:start position:0%
+rather than the calculus world so let us
+look at this criterion that we have here
+
+ align:start position:0%
+look at this criterion that we have here
+ 
+
+ align:start position:0%
+look at this criterion that we have here
+the expected value of the square of a
+
+ align:start position:0%
+the expected value of the square of a
+ 
+
+ align:start position:0%
+the expected value of the square of a
+random variable is always equal to the
+
+ align:start position:0%
+random variable is always equal to the
+ 
+
+ align:start position:0%
+random variable is always equal to the
+variance of that random variable plus
+
+ align:start position:0%
+variance of that random variable plus
+ 
+
+ align:start position:0%
+variance of that random variable plus
+the expected value of that random
+
+ align:start position:0%
+the expected value of that random
+ 
+
+ align:start position:0%
+the expected value of that random
+variable squared this is what we are
+
+ align:start position:0%
+variable squared this is what we are
+ 
+
+ align:start position:0%
+variable squared this is what we are
+trying to minimize now theta hat is a
+
+ align:start position:0%
+trying to minimize now theta hat is a
+ 
+
+ align:start position:0%
+trying to minimize now theta hat is a
+constant the variance of a random
+
+ align:start position:0%
+constant the variance of a random
+ 
+
+ align:start position:0%
+constant the variance of a random
+variable plus or minus a constant is the
+
+ align:start position:0%
+variable plus or minus a constant is the
+ 
+
+ align:start position:0%
+variable plus or minus a constant is the
+same as the variance of that random
+
+ align:start position:0%
+same as the variance of that random
+ 
+
+ align:start position:0%
+same as the variance of that random
+variable and there is nothing that we
+
+ align:start position:0%
+variable and there is nothing that we
+ 
+
+ align:start position:0%
+variable and there is nothing that we
+can do about this term
+
+ align:start position:0%
+can do about this term
+ 
+
+ align:start position:0%
+can do about this term
+so what we are trying to do is
+
+ align:start position:0%
+so what we are trying to do is
+ 
+
+ align:start position:0%
+so what we are trying to do is
+essentially just try to minimize this
+
+ align:start position:0%
+essentially just try to minimize this
+ 
+
+ align:start position:0%
+essentially just try to minimize this
+term with respect to theta hat now here
+
+ align:start position:0%
+term with respect to theta hat now here
+ 
+
+ align:start position:0%
+term with respect to theta hat now here
+we have the square of something the way
+
+ align:start position:0%
+we have the square of something the way
+ 
+
+ align:start position:0%
+we have the square of something the way
+to minimize this is to try to make this
+
+ align:start position:0%
+to minimize this is to try to make this
+ 
+
+ align:start position:0%
+to minimize this is to try to make this
+quantity as small as possible make it
+
+ align:start position:0%
+quantity as small as possible make it
+ 
+
+ align:start position:0%
+quantity as small as possible make it
+zero if we can well we can make it zero
+
+ align:start position:0%
+zero if we can well we can make it zero
+ 
+
+ align:start position:0%
+zero if we can well we can make it zero
+if we set theta hat equal to the
+
+ align:start position:0%
+if we set theta hat equal to the
+ 
+
+ align:start position:0%
+if we set theta hat equal to the
+expected value of theta so this term
+
+ align:start position:0%
+expected value of theta so this term
+ 
+
+ align:start position:0%
+expected value of theta so this term
+here is minimized when theta hat is
+
+ align:start position:0%
+here is minimized when theta hat is
+ 
+
+ align:start position:0%
+here is minimized when theta hat is
+equal to the expected value of theta it
+
+ align:start position:0%
+equal to the expected value of theta it
+ 
+
+ align:start position:0%
+equal to the expected value of theta it
+is minimized because this is a choice
+
+ align:start position:0%
+is minimized because this is a choice
+ 
+
+ align:start position:0%
+is minimized because this is a choice
+that will make this term equal to 0 so
+
+ align:start position:0%
+that will make this term equal to 0 so
+ 
+
+ align:start position:0%
+that will make this term equal to 0 so
+this was a second derivation of why this
+
+ align:start position:0%
+this was a second derivation of why this
+ 
+
+ align:start position:0%
+this was a second derivation of why this
+is the optimal estimate of theta once we
+
+ align:start position:0%
+is the optimal estimate of theta once we
+ 
+
+ align:start position:0%
+is the optimal estimate of theta once we
+adopt this particular estimate the mean
+
+ align:start position:0%
+adopt this particular estimate the mean
+ 
+
+ align:start position:0%
+adopt this particular estimate the mean
+squared error is going to be equal to
+
+ align:start position:0%
+squared error is going to be equal to
+ 
+
+ align:start position:0%
+squared error is going to be equal to
+this because this is our theta hat and
+
+ align:start position:0%
+this because this is our theta hat and
+ 
+
+ align:start position:0%
+this because this is our theta hat and
+of course we recognize that this is the
+
+ align:start position:0%
+of course we recognize that this is the
+ 
+
+ align:start position:0%
+of course we recognize that this is the
+variance so the variance of theta is the
+
+ align:start position:0%
+variance so the variance of theta is the
+ 
+
+ align:start position:0%
+variance so the variance of theta is the
+least possible value of the mean squared
+
+ align:start position:0%
+least possible value of the mean squared
+ 
+
+ align:start position:0%
+least possible value of the mean squared
+error that we can obtained using any
+
+ align:start position:0%
+error that we can obtained using any
+ 
+
+ align:start position:0%
+error that we can obtained using any
+particular estimate
+
+ align:start position:0%
+particular estimate
+ 
+
+ align:start position:0%
+particular estimate
+and this is our final conclusion and in
+
+ align:start position:0%
+and this is our final conclusion and in
+ 
+
+ align:start position:0%
+and this is our final conclusion and in
+the next segment we will exploit the
+
+ align:start position:0%
+the next segment we will exploit the
+ 
+
+ align:start position:0%
+the next segment we will exploit the
+conclusions that we found here and apply
+
+ align:start position:0%
+conclusions that we found here and apply
+ 
+
+ align:start position:0%
+conclusions that we found here and apply
+them to a more general situation
\ No newline at end of file
diff --git a/gLWtkG2O_vs.txt b/gLWtkG2O_vs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b35ec9bd5637554906df1628b05e41184d8542d0
--- /dev/null
+++ b/gLWtkG2O_vs.txt
@@ -0,0 +1,8826 @@
+align:start position:0%
+ 
+okay welcome everybody wonderful uh warm
+
+ align:start position:0%
+okay welcome everybody wonderful uh warm
+ 
+
+ align:start position:0%
+okay welcome everybody wonderful uh warm
+February Friday here and we're uh
+
+ align:start position:0%
+February Friday here and we're uh
+ 
+
+ align:start position:0%
+February Friday here and we're uh
+continuing with our second topic for the
+
+ align:start position:0%
+continuing with our second topic for the
+ 
+
+ align:start position:0%
+continuing with our second topic for the
+class first one being about um notes
+
+ align:start position:0%
+class first one being about um notes
+ 
+
+ align:start position:0%
+class first one being about um notes
+pitches durations and now we're getting
+
+ align:start position:0%
+pitches durations and now we're getting
+ 
+
+ align:start position:0%
+pitches durations and now we're getting
+to how to represent um bigger music SCH
+
+ align:start position:0%
+to how to represent um bigger music SCH
+ 
+
+ align:start position:0%
+to how to represent um bigger music SCH
+scores
+
+ align:start position:0%
+scores
+ 
+
+ align:start position:0%
+scores
+um I'm going to start though by jumping
+
+ align:start position:0%
+um I'm going to start though by jumping
+ 
+
+ align:start position:0%
+um I'm going to start though by jumping
+back to uh topic one for a second I want
+
+ align:start position:0%
+back to uh topic one for a second I want
+ 
+
+ align:start position:0%
+back to uh topic one for a second I want
+to uh talk through a couple things
+
+ align:start position:0%
+to uh talk through a couple things
+ 
+
+ align:start position:0%
+to uh talk through a couple things
+first great job on pet one uh there I
+
+ align:start position:0%
+first great job on pet one uh there I
+ 
+
+ align:start position:0%
+first great job on pet one uh there I
+can and I can say it's nice when you can
+
+ align:start position:0%
+can and I can say it's nice when you can
+ 
+
+ align:start position:0%
+can and I can say it's nice when you can
+say that to the whole class without
+
+ align:start position:0%
+say that to the whole class without
+ 
+
+ align:start position:0%
+say that to the whole class without
+putting uh for the most part P set one
+
+ align:start position:0%
+putting uh for the most part P set one
+ 
+
+ align:start position:0%
+putting uh for the most part P set one
+was really great no every single P set
+
+ align:start position:0%
+was really great no every single P set
+ 
+
+ align:start position:0%
+was really great no every single P set
+one was was very strong um there when
+
+ align:start position:0%
+one was was very strong um there when
+ 
+
+ align:start position:0%
+one was was very strong um there when
+and that's that's my quick to second
+
+ align:start position:0%
+and that's that's my quick to second
+ 
+
+ align:start position:0%
+and that's that's my quick to second
+overview of having the computer
+
+ align:start position:0%
+overview of having the computer
+ 
+
+ align:start position:0%
+overview of having the computer
+automatically go through and just um
+
+ align:start position:0%
+automatically go through and just um
+ 
+
+ align:start position:0%
+automatically go through and just um
+spit out every error that it detected
+
+ align:start position:0%
+spit out every error that it detected
+ 
+
+ align:start position:0%
+spit out every error that it detected
+and I'll go through it by hand because
+
+ align:start position:0%
+and I'll go through it by hand because
+ 
+
+ align:start position:0%
+and I'll go through it by hand because
+um and figure out places where there
+
+ align:start position:0%
+um and figure out places where there
+ 
+
+ align:start position:0%
+um and figure out places where there
+might be partial credit where a mistake
+
+ align:start position:0%
+might be partial credit where a mistake
+ 
+
+ align:start position:0%
+might be partial credit where a mistake
+early on was causing cascading problems
+
+ align:start position:0%
+early on was causing cascading problems
+ 
+
+ align:start position:0%
+early on was causing cascading problems
+and uh things of that sort but um some
+
+ align:start position:0%
+and uh things of that sort but um some
+ 
+
+ align:start position:0%
+and uh things of that sort but um some
+really really great things happening you
+
+ align:start position:0%
+really really great things happening you
+ 
+
+ align:start position:0%
+really really great things happening you
+guys seem to be uh really strong on um
+
+ align:start position:0%
+guys seem to be uh really strong on um
+ 
+
+ align:start position:0%
+guys seem to be uh really strong on um
+on Pitch names on representation on
+
+ align:start position:0%
+on Pitch names on representation on
+ 
+
+ align:start position:0%
+on Pitch names on representation on
+manipulating transposing some really
+
+ align:start position:0%
+manipulating transposing some really
+ 
+
+ align:start position:0%
+manipulating transposing some really
+really good work with inversions for the
+
+ align:start position:0%
+really good work with inversions for the
+ 
+
+ align:start position:0%
+really good work with inversions for the
+most part which is some of the most
+
+ align:start position:0%
+most part which is some of the most
+ 
+
+ align:start position:0%
+most part which is some of the most
+challenging parts of the problem set and
+
+ align:start position:0%
+challenging parts of the problem set and
+ 
+
+ align:start position:0%
+challenging parts of the problem set and
+um yeah
+
+ align:start position:0%
+um yeah
+ 
+
+ align:start position:0%
+um yeah
+so I'd love to dwell for the next hour
+
+ align:start position:0%
+so I'd love to dwell for the next hour
+ 
+
+ align:start position:0%
+so I'd love to dwell for the next hour
+on everything you all did right uh give
+
+ align:start position:0%
+on everything you all did right uh give
+ 
+
+ align:start position:0%
+on everything you all did right uh give
+yourself thumbs up for that but let's
+
+ align:start position:0%
+yourself thumbs up for that but let's
+ 
+
+ align:start position:0%
+yourself thumbs up for that but let's
+let's talk a little bit on a couple of
+
+ align:start position:0%
+let's talk a little bit on a couple of
+ 
+
+ align:start position:0%
+let's talk a little bit on a couple of
+the things that were challenging on the
+
+ align:start position:0%
+the things that were challenging on the
+ 
+
+ align:start position:0%
+the things that were challenging on the
+problem sets some of them that um you
+
+ align:start position:0%
+problem sets some of them that um you
+ 
+
+ align:start position:0%
+problem sets some of them that um you
+know that maybe I could have done better
+
+ align:start position:0%
+know that maybe I could have done better
+ 
+
+ align:start position:0%
+know that maybe I could have done better
+some of them maybe you we could have
+
+ align:start position:0%
+some of them maybe you we could have
+ 
+
+ align:start position:0%
+some of them maybe you we could have
+just thought that one one little bit
+
+ align:start position:0%
+just thought that one one little bit
+ 
+
+ align:start position:0%
+just thought that one one little bit
+harder let's start with um the concept
+
+ align:start position:0%
+harder let's start with um the concept
+ 
+
+ align:start position:0%
+harder let's start with um the concept
+of pitch class
+
+ align:start position:0%
+of pitch class
+ 
+
+ align:start position:0%
+of pitch class
+um how many pitch classes are there
+
+ align:start position:0%
+um how many pitch classes are there
+ 
+
+ align:start position:0%
+um how many pitch classes are there
+let's shout it out on three one two
+
+ align:start position:0%
+let's shout it out on three one two
+ 
+
+ align:start position:0%
+let's shout it out on three one two
+three 12 12 and they're what 1 to
+
+ align:start position:0%
+three 12 12 and they're what 1 to
+ 
+
+ align:start position:0%
+three 12 12 and they're what 1 to
+12 to 11 0 to 11 great super so we
+
+ align:start position:0%
+12 to 11 0 to 11 great super so we
+ 
+
+ align:start position:0%
+12 to 11 0 to 11 great super so we
+almost all got that so and uh what's
+
+ align:start position:0%
+almost all got that so and uh what's
+ 
+
+ align:start position:0%
+almost all got that so and uh what's
+what's a note that's pitch class zero c
+
+ align:start position:0%
+what's a note that's pitch class zero c
+ 
+
+ align:start position:0%
+what's a note that's pitch class zero c
+c good good
+
+ align:start position:0%
+c good good
+ 
+
+ align:start position:0%
+c good good
+so um let's see see if we know our major
+
+ align:start position:0%
+so um let's see see if we know our major
+ 
+
+ align:start position:0%
+so um let's see see if we know our major
+scales pretty well pitch class uh four e
+
+ align:start position:0%
+scales pretty well pitch class uh four e
+ 
+
+ align:start position:0%
+scales pretty well pitch class uh four e
+e good so four is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e e
+
+ align:start position:0%
+e e
+ 
+
+ align:start position:0%
+e e
+flat
+
+ align:start position:0%
+flat
+ 
+
+ align:start position:0%
+flat
+three e double
+
+ align:start position:0%
+three e double
+ 
+
+ align:start position:0%
+three e double
+flat great triple
+
+ align:start position:0%
+flat great triple
+ 
+
+ align:start position:0%
+flat great triple
+flat quadruple
+
+ align:start position:0%
+flat quadruple
+ 
+
+ align:start position:0%
+flat quadruple
+flat quintuple
+
+ align:start position:0%
+flat quintuple
+ 
+
+ align:start position:0%
+flat quintuple
+flat 11 so this ends up being this was
+
+ align:start position:0%
+flat 11 so this ends up being this was
+ 
+
+ align:start position:0%
+flat 11 so this ends up being this was
+one of the things uh challenge that
+
+ align:start position:0%
+one of the things uh challenge that
+ 
+
+ align:start position:0%
+one of the things uh challenge that
+there's a modulo operator right the you
+
+ align:start position:0%
+there's a modulo operator right the you
+ 
+
+ align:start position:0%
+there's a modulo operator right the you
+know trying to make sure everything is
+
+ align:start position:0%
+know trying to make sure everything is
+ 
+
+ align:start position:0%
+know trying to make sure everything is
+between 0 and 11 at first when you're
+
+ align:start position:0%
+between 0 and 11 at first when you're
+ 
+
+ align:start position:0%
+between 0 and 11 at first when you're
+looking at the names see and so almost
+
+ align:start position:0%
+looking at the names see and so almost
+ 
+
+ align:start position:0%
+looking at the names see and so almost
+everybody somewhere encoded right a a
+
+ align:start position:0%
+everybody somewhere encoded right a a
+ 
+
+ align:start position:0%
+everybody somewhere encoded right a a
+array that looks something like this I
+
+ align:start position:0%
+array that looks something like this I
+ 
+
+ align:start position:0%
+array that looks something like this I
+think 5 S I'm getting this right
+
+ align:start position:0%
+think 5 S I'm getting this right
+ 
+
+ align:start position:0%
+think 5 S I'm getting this right
+91 who did something like that at some
+
+ align:start position:0%
+91 who did something like that at some
+ 
+
+ align:start position:0%
+91 who did something like that at some
+point yeah and then um so if you didn't
+
+ align:start position:0%
+point yeah and then um so if you didn't
+ 
+
+ align:start position:0%
+point yeah and then um so if you didn't
+do that and you encoded all of them then
+
+ align:start position:0%
+do that and you encoded all of them then
+ 
+
+ align:start position:0%
+do that and you encoded all of them then
+the hard part was uh
+
+ align:start position:0%
+the hard part was uh
+ 
+
+ align:start position:0%
+the hard part was uh
+nhar monx yeah if you said that one is C
+
+ align:start position:0%
+nhar monx yeah if you said that one is C
+ 
+
+ align:start position:0%
+nhar monx yeah if you said that one is C
+sh o it's also d flat okay I think I've
+
+ align:start position:0%
+sh o it's also d flat okay I think I've
+ 
+
+ align:start position:0%
+sh o it's also d flat okay I think I've
+got it but it's also you know very very
+
+ align:start position:0%
+got it but it's also you know very very
+ 
+
+ align:start position:0%
+got it but it's also you know very very
+odd notes like um b double sharp oops I
+
+ align:start position:0%
+odd notes like um b double sharp oops I
+ 
+
+ align:start position:0%
+odd notes like um b double sharp oops I
+should do a proper double sharp and not
+
+ align:start position:0%
+should do a proper double sharp and not
+ 
+
+ align:start position:0%
+should do a proper double sharp and not
+a programmer's double sharp right
+
+ align:start position:0%
+a programmer's double sharp right
+ 
+
+ align:start position:0%
+a programmer's double sharp right
+yeah things like that that's correct
+
+ align:start position:0%
+yeah things like that that's correct
+ 
+
+ align:start position:0%
+yeah things like that that's correct
+right yeah um so if you did something
+
+ align:start position:0%
+right yeah um so if you did something
+ 
+
+ align:start position:0%
+right yeah um so if you did something
+like this there's that weird thing that
+
+ align:start position:0%
+like this there's that weird thing that
+ 
+
+ align:start position:0%
+like this there's that weird thing that
+almost that a lot of people um forgot
+
+ align:start position:0%
+almost that a lot of people um forgot
+ 
+
+ align:start position:0%
+almost that a lot of people um forgot
+that when you get your modulo to get
+
+ align:start position:0%
+that when you get your modulo to get
+ 
+
+ align:start position:0%
+that when you get your modulo to get
+everything into 02 4 5 79 11 by
+
+ align:start position:0%
+everything into 02 4 5 79 11 by
+ 
+
+ align:start position:0%
+everything into 02 4 5 79 11 by
+stripping off the accidentals then you
+
+ align:start position:0%
+stripping off the accidentals then you
+ 
+
+ align:start position:0%
+stripping off the accidentals then you
+start adding what is it you subtract one
+
+ align:start position:0%
+start adding what is it you subtract one
+ 
+
+ align:start position:0%
+start adding what is it you subtract one
+for every Flat add one for every sharp
+
+ align:start position:0%
+for every Flat add one for every sharp
+ 
+
+ align:start position:0%
+for every Flat add one for every sharp
+so you can do you can have your computer
+
+ align:start position:0%
+so you can do you can have your computer
+ 
+
+ align:start position:0%
+so you can do you can have your computer
+be very smart at first with things that
+
+ align:start position:0%
+be very smart at first with things that
+ 
+
+ align:start position:0%
+be very smart at first with things that
+um that's a e double sharp my
+
+ align:start position:0%
+um that's a e double sharp my
+ 
+
+ align:start position:0%
+um that's a e double sharp my
+handwriting will get better um uh and
+
+ align:start position:0%
+handwriting will get better um uh and
+ 
+
+ align:start position:0%
+handwriting will get better um uh and
+you can do that but remembering at the
+
+ align:start position:0%
+you can do that but remembering at the
+ 
+
+ align:start position:0%
+you can do that but remembering at the
+end that oh if B is 11 that B Sharp is
+
+ align:start position:0%
+end that oh if B is 11 that B Sharp is
+ 
+
+ align:start position:0%
+end that oh if B is 11 that B Sharp is
+not 11 +
+
+ align:start position:0%
+not 11 +
+ 
+
+ align:start position:0%
+not 11 +
+1 but 11 + 1 what do I want to put after
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that mod 12 yep good
+
+ align:start position:0%
+that mod 12 yep good
+ 
+
+ align:start position:0%
+that mod 12 yep good
+good um so that was that was one thing
+
+ align:start position:0%
+good um so that was that was one thing
+ 
+
+ align:start position:0%
+good um so that was that was one thing
+the other thing that came up quite a bit
+
+ align:start position:0%
+the other thing that came up quite a bit
+ 
+
+ align:start position:0%
+the other thing that came up quite a bit
+and uh you're going to think that this
+
+ align:start position:0%
+and uh you're going to think that this
+ 
+
+ align:start position:0%
+and uh you're going to think that this
+is a like a pretty dirty trick for me
+
+ align:start position:0%
+is a like a pretty dirty trick for me
+ 
+
+ align:start position:0%
+is a like a pretty dirty trick for me
+let's start with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um this is pitch set one this is pitch
+
+ align:start position:0%
+um this is pitch set one this is pitch
+ 
+
+ align:start position:0%
+um this is pitch set one this is pitch
+set two is there a way we uh is there an
+
+ align:start position:0%
+set two is there a way we uh is there an
+ 
+
+ align:start position:0%
+set two is there a way we uh is there an
+axis inversion somewhere that will let
+
+ align:start position:0%
+axis inversion somewhere that will let
+ 
+
+ align:start position:0%
+axis inversion somewhere that will let
+us transform pitch set one to pitch set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 no I'm seeing seeing some some nose
+
+ align:start position:0%
+2 no I'm seeing seeing some some nose
+ 
+
+ align:start position:0%
+2 no I'm seeing seeing some some nose
+Matthew what you you had the first head
+
+ align:start position:0%
+Matthew what you you had the first head
+ 
+
+ align:start position:0%
+Matthew what you you had the first head
+uh shock head head Rock what what how
+
+ align:start position:0%
+uh shock head head Rock what what how
+ 
+
+ align:start position:0%
+uh shock head head Rock what what how
+did you compute that very fast did you
+
+ align:start position:0%
+did you compute that very fast did you
+ 
+
+ align:start position:0%
+did you compute that very fast did you
+try all um all
+
+ align:start position:0%
+try all um all
+ 
+
+ align:start position:0%
+try all um all
+132 possible axes of rotation and saw
+
+ align:start position:0%
+132 possible axes of rotation and saw
+ 
+
+ align:start position:0%
+132 possible axes of rotation and saw
+that there were none uh the way that I
+
+ align:start position:0%
+that there were none uh the way that I
+ 
+
+ align:start position:0%
+that there were none uh the way that I
+did it was I made sure that the
+
+ align:start position:0%
+did it was I made sure that the
+ 
+
+ align:start position:0%
+did it was I made sure that the
+intervals of one were the negatives of
+
+ align:start position:0%
+intervals of one were the negatives of
+ 
+
+ align:start position:0%
+intervals of one were the negatives of
+the intervals of the other great so what
+
+ align:start position:0%
+the intervals of the other great so what
+ 
+
+ align:start position:0%
+the intervals of the other great so what
+when we're talking about the intervals
+
+ align:start position:0%
+when we're talking about the intervals
+ 
+
+ align:start position:0%
+when we're talking about the intervals
+of one intervals pitch set one what's
+
+ align:start position:0%
+of one intervals pitch set one what's
+ 
+
+ align:start position:0%
+of one intervals pitch set one what's
+the interval that we're looking at
+
+ align:start position:0%
+the interval that we're looking at
+ 
+
+ align:start position:0%
+the interval that we're looking at
+here what do we call two and what's the
+
+ align:start position:0%
+here what do we call two and what's the
+ 
+
+ align:start position:0%
+here what do we call two and what's the
+interval here two one if we're thinking
+
+ align:start position:0%
+interval here two one if we're thinking
+ 
+
+ align:start position:0%
+interval here two one if we're thinking
+of chromatic what if we're thinking of
+
+ align:start position:0%
+of chromatic what if we're thinking of
+ 
+
+ align:start position:0%
+of chromatic what if we're thinking of
+it in more of our traditional tonal
+
+ align:start position:0%
+it in more of our traditional tonal
+ 
+
+ align:start position:0%
+it in more of our traditional tonal
+space what do we want to call this
+
+ align:start position:0%
+space what do we want to call this
+ 
+
+ align:start position:0%
+space what do we want to call this
+one what's that whole step whole step
+
+ align:start position:0%
+one what's that whole step whole step
+ 
+
+ align:start position:0%
+one what's that whole step whole step
+good another word for whole step usually
+
+ align:start position:0%
+good another word for whole step usually
+ 
+
+ align:start position:0%
+good another word for whole step usually
+major second good and here half step
+
+ align:start position:0%
+major second good and here half step
+ 
+
+ align:start position:0%
+major second good and here half step
+right or minor minor second good so you
+
+ align:start position:0%
+right or minor minor second good so you
+ 
+
+ align:start position:0%
+right or minor minor second good so you
+knew that you weren't going to be able
+
+ align:start position:0%
+knew that you weren't going to be able
+ 
+
+ align:start position:0%
+knew that you weren't going to be able
+to find that you didn't need to do all
+
+ align:start position:0%
+to find that you didn't need to do all
+ 
+
+ align:start position:0%
+to find that you didn't need to do all
+the computation let's do one that's a
+
+ align:start position:0%
+the computation let's do one that's a
+ 
+
+ align:start position:0%
+the computation let's do one that's a
+little bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+harder is there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something like that and can
+
+ align:start position:0%
+something like that and can
+ 
+
+ align:start position:0%
+something like that and can
+we find some sort of an inversion ex of
+
+ align:start position:0%
+we find some sort of an inversion ex of
+ 
+
+ align:start position:0%
+we find some sort of an inversion ex of
+inversion that allows us to transform it
+
+ align:start position:0%
+inversion that allows us to transform it
+ 
+
+ align:start position:0%
+inversion that allows us to transform it
+into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why it's pretty obvious so go ahead take
+
+ align:start position:0%
+why it's pretty obvious so go ahead take
+ 
+
+ align:start position:0%
+why it's pretty obvious so go ahead take
+always take the easy participation
+
+ align:start position:0%
+always take the easy participation
+ 
+
+ align:start position:0%
+always take the easy participation
+points um when you when you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can one has four notes and the other has
+
+ align:start position:0%
+can one has four notes and the other has
+ 
+
+ align:start position:0%
+can one has four notes and the other has
+one has four notes and the other one has
+
+ align:start position:0%
+one has four notes and the other one has
+ 
+
+ align:start position:0%
+one has four notes and the other one has
+five notes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good uh I believe 15 out of the 17
+
+ align:start position:0%
+good uh I believe 15 out of the 17
+ 
+
+ align:start position:0%
+good uh I believe 15 out of the 17
+problem sets turned in found that to be
+
+ align:start position:0%
+problem sets turned in found that to be
+ 
+
+ align:start position:0%
+problem sets turned in found that to be
+acceptable because you weren't comparing
+
+ align:start position:0%
+acceptable because you weren't comparing
+ 
+
+ align:start position:0%
+acceptable because you weren't comparing
+first the obvious thing that they had to
+
+ align:start position:0%
+first the obvious thing that they had to
+ 
+
+ align:start position:0%
+first the obvious thing that they had to
+have the same number of notes um which
+
+ align:start position:0%
+have the same number of notes um which
+ 
+
+ align:start position:0%
+have the same number of notes um which
+does happen quite often right that
+
+ align:start position:0%
+does happen quite often right that
+ 
+
+ align:start position:0%
+does happen quite often right that
+you're going along and you're thinking
+
+ align:start position:0%
+you're going along and you're thinking
+ 
+
+ align:start position:0%
+you're going along and you're thinking
+of here's a Triad here's a Triad here's
+
+ align:start position:0%
+of here's a Triad here's a Triad here's
+ 
+
+ align:start position:0%
+of here's a Triad here's a Triad here's
+a seventh chord here's a Triad is there
+
+ align:start position:0%
+a seventh chord here's a Triad is there
+ 
+
+ align:start position:0%
+a seventh chord here's a Triad is there
+a way that we can manipulate the first
+
+ align:start position:0%
+a way that we can manipulate the first
+ 
+
+ align:start position:0%
+a way that we can manipulate the first
+Triad to be the second Triad yes is
+
+ align:start position:0%
+Triad to be the second Triad yes is
+ 
+
+ align:start position:0%
+Triad to be the second Triad yes is
+there a way that we can manipulate the
+
+ align:start position:0%
+there a way that we can manipulate the
+ 
+
+ align:start position:0%
+there a way that we can manipulate the
+second Triad to be the um the uh the
+
+ align:start position:0%
+second Triad to be the um the uh the
+ 
+
+ align:start position:0%
+second Triad to be the um the uh the
+seventh chord the four note chord not
+
+ align:start position:0%
+seventh chord the four note chord not
+ 
+
+ align:start position:0%
+seventh chord the four note chord not
+with the tools that we've learned so far
+
+ align:start position:0%
+with the tools that we've learned so far
+ 
+
+ align:start position:0%
+with the tools that we've learned so far
+right so those are some things and a a
+
+ align:start position:0%
+right so those are some things and a a
+ 
+
+ align:start position:0%
+right so those are some things and a a
+very very very small um th this one I
+
+ align:start position:0%
+very very very small um th this one I
+ 
+
+ align:start position:0%
+very very very small um th this one I
+think is important because this will
+
+ align:start position:0%
+think is important because this will
+ 
+
+ align:start position:0%
+think is important because this will
+come up in real music
+
+ align:start position:0%
+come up in real music
+ 
+
+ align:start position:0%
+come up in real music
+everywhere very very very small problem
+
+ align:start position:0%
+everywhere very very very small problem
+ 
+
+ align:start position:0%
+everywhere very very very small problem
+in this one this one you might hate your
+
+ align:start position:0%
+in this one this one you might hate your
+ 
+
+ align:start position:0%
+in this one this one you might hate your
+professor for doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that can p set one be converted to P at
+
+ align:start position:0%
+that can p set one be converted to P at
+ 
+
+ align:start position:0%
+that can p set one be converted to P at
+two by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inversion yes because there's nothing
+
+ align:start position:0%
+inversion yes because there's nothing
+ 
+
+ align:start position:0%
+inversion yes because there's nothing
+here you don't need to do any operation
+
+ align:start position:0%
+here you don't need to do any operation
+ 
+
+ align:start position:0%
+here you don't need to do any operation
+or any operation you do to nothing can
+
+ align:start position:0%
+or any operation you do to nothing can
+ 
+
+ align:start position:0%
+or any operation you do to nothing can
+transform it into this right if you
+
+ align:start position:0%
+transform it into this right if you
+ 
+
+ align:start position:0%
+transform it into this right if you
+think about the reciprocal of or you
+
+ align:start position:0%
+think about the reciprocal of or you
+ 
+
+ align:start position:0%
+think about the reciprocal of or you
+know the Nega negation of an empty set
+
+ align:start position:0%
+know the Nega negation of an empty set
+ 
+
+ align:start position:0%
+know the Nega negation of an empty set
+it'll be sort of the empty set and that
+
+ align:start position:0%
+it'll be sort of the empty set and that
+ 
+
+ align:start position:0%
+it'll be sort of the empty set and that
+that one I think I I put like one on10th
+
+ align:start position:0%
+that one I think I I put like one on10th
+ 
+
+ align:start position:0%
+that one I think I I put like one on10th
+of 1% on because it's it's kind of a a
+
+ align:start position:0%
+of 1% on because it's it's kind of a a
+ 
+
+ align:start position:0%
+of 1% on because it's it's kind of a a
+nasty thing but it was one of the cases
+
+ align:start position:0%
+nasty thing but it was one of the cases
+ 
+
+ align:start position:0%
+nasty thing but it was one of the cases
+where uh unlike the fornote thing where
+
+ align:start position:0%
+where uh unlike the fornote thing where
+ 
+
+ align:start position:0%
+where uh unlike the fornote thing where
+uh a lot of times the pro programs your
+
+ align:start position:0%
+uh a lot of times the pro programs your
+ 
+
+ align:start position:0%
+uh a lot of times the pro programs your
+algorithms were returning the incorrect
+
+ align:start position:0%
+algorithms were returning the incorrect
+ 
+
+ align:start position:0%
+algorithms were returning the incorrect
+answer uh this one was uh causing the
+
+ align:start position:0%
+answer uh this one was uh causing the
+ 
+
+ align:start position:0%
+answer uh this one was uh causing the
+programs to crash quite a bit um couple
+
+ align:start position:0%
+programs to crash quite a bit um couple
+ 
+
+ align:start position:0%
+programs to crash quite a bit um couple
+years ago I I didn't my uh automatic
+
+ align:start position:0%
+years ago I I didn't my uh automatic
+ 
+
+ align:start position:0%
+years ago I I didn't my uh automatic
+assessment system didn't that was I I
+
+ align:start position:0%
+assessment system didn't that was I I
+ 
+
+ align:start position:0%
+assessment system didn't that was I I
+stole it from gozi he's very generous
+
+ align:start position:0%
+stole it from gozi he's very generous
+ 
+
+ align:start position:0%
+stole it from gozi he's very generous
+with that uh did not handle crashes very
+
+ align:start position:0%
+with that uh did not handle crashes very
+ 
+
+ align:start position:0%
+with that uh did not handle crashes very
+well now you know it does so um we'll
+
+ align:start position:0%
+well now you know it does so um we'll
+ 
+
+ align:start position:0%
+well now you know it does so um we'll
+we'll see that
+
+ align:start position:0%
+we'll see that
+ 
+
+ align:start position:0%
+we'll see that
+so that's a big parenthesis around um
+
+ align:start position:0%
+so that's a big parenthesis around um
+ 
+
+ align:start position:0%
+so that's a big parenthesis around um
+the fact that the pets were great we're
+
+ align:start position:0%
+the fact that the pets were great we're
+ 
+
+ align:start position:0%
+the fact that the pets were great we're
+very very strong I think you should all
+
+ align:start position:0%
+very very strong I think you should all
+ 
+
+ align:start position:0%
+very very strong I think you should all
+be uh proud on that but but keep keep
+
+ align:start position:0%
+be uh proud on that but but keep keep
+ 
+
+ align:start position:0%
+be uh proud on that but but keep keep
+thinking of the corner cases uh I
+
+ align:start position:0%
+thinking of the corner cases uh I
+ 
+
+ align:start position:0%
+thinking of the corner cases uh I
+especially liked how many um test cases
+
+ align:start position:0%
+especially liked how many um test cases
+ 
+
+ align:start position:0%
+especially liked how many um test cases
+that I didn't write that I saw I mean I
+
+ align:start position:0%
+that I didn't write that I saw I mean I
+ 
+
+ align:start position:0%
+that I didn't write that I saw I mean I
+was really really fast through the code
+
+ align:start position:0%
+was really really fast through the code
+ 
+
+ align:start position:0%
+was really really fast through the code
+because you all just uh turned it in uh
+
+ align:start position:0%
+because you all just uh turned it in uh
+ 
+
+ align:start position:0%
+because you all just uh turned it in uh
+this morning or late last night but for
+
+ align:start position:0%
+this morning or late last night but for
+ 
+
+ align:start position:0%
+this morning or late last night but for
+the most part but I was I was very
+
+ align:start position:0%
+the most part but I was I was very
+ 
+
+ align:start position:0%
+the most part but I was I was very
+impressed with how how much people were
+
+ align:start position:0%
+impressed with how how much people were
+ 
+
+ align:start position:0%
+impressed with how how much people were
+trying to get at the corner cases and
+
+ align:start position:0%
+trying to get at the corner cases and
+ 
+
+ align:start position:0%
+trying to get at the corner cases and
+things and that's a good thing to um
+
+ align:start position:0%
+things and that's a good thing to um
+ 
+
+ align:start position:0%
+things and that's a good thing to um
+feel free to you know use that kind of
+
+ align:start position:0%
+feel free to you know use that kind of
+ 
+
+ align:start position:0%
+feel free to you know use that kind of
+collaborative discussion and we're going
+
+ align:start position:0%
+collaborative discussion and we're going
+ 
+
+ align:start position:0%
+collaborative discussion and we're going
+to encourage some collaborative
+
+ align:start position:0%
+to encourage some collaborative
+ 
+
+ align:start position:0%
+to encourage some collaborative
+discussion uh in the next problem set
+
+ align:start position:0%
+discussion uh in the next problem set
+ 
+
+ align:start position:0%
+discussion uh in the next problem set
+coming right up there was one other
+
+ align:start position:0%
+coming right up there was one other
+ 
+
+ align:start position:0%
+coming right up there was one other
+thing besides U some reading and video
+
+ align:start position:0%
+thing besides U some reading and video
+ 
+
+ align:start position:0%
+thing besides U some reading and video
+watching um that uh I asked you all to
+
+ align:start position:0%
+watching um that uh I asked you all to
+ 
+
+ align:start position:0%
+watching um that uh I asked you all to
+do and I got some really great answers
+
+ align:start position:0%
+do and I got some really great answers
+ 
+
+ align:start position:0%
+do and I got some really great answers
+and that was talking about um various
+
+ align:start position:0%
+and that was talking about um various
+ 
+
+ align:start position:0%
+and that was talking about um various
+kinds of pitch representations what you
+
+ align:start position:0%
+kinds of pitch representations what you
+ 
+
+ align:start position:0%
+kinds of pitch representations what you
+might do and uh what some of the
+
+ align:start position:0%
+might do and uh what some of the
+ 
+
+ align:start position:0%
+might do and uh what some of the
+stakeholders um might be who who might
+
+ align:start position:0%
+stakeholders um might be who who might
+ 
+
+ align:start position:0%
+stakeholders um might be who who might
+want a particular pitch
+
+ align:start position:0%
+want a particular pitch
+ 
+
+ align:start position:0%
+want a particular pitch
+representation um and that might be
+
+ align:start position:0%
+representation um and that might be
+ 
+
+ align:start position:0%
+representation um and that might be
+different from somebody else so anybody
+
+ align:start position:0%
+different from somebody else so anybody
+ 
+
+ align:start position:0%
+different from somebody else so anybody
+and I read through them I'm going to um
+
+ align:start position:0%
+and I read through them I'm going to um
+ 
+
+ align:start position:0%
+and I read through them I'm going to um
+you know say say some things too
+
+ align:start position:0%
+you know say say some things too
+ 
+
+ align:start position:0%
+you know say say some things too
+especially uh things I found really
+
+ align:start position:0%
+especially uh things I found really
+ 
+
+ align:start position:0%
+especially uh things I found really
+great and um if you know but but anybody
+
+ align:start position:0%
+great and um if you know but but anybody
+ 
+
+ align:start position:0%
+great and um if you know but but anybody
+find anything that you thought was was
+
+ align:start position:0%
+find anything that you thought was was
+ 
+
+ align:start position:0%
+find anything that you thought was was
+interesting to different groups or
+
+ align:start position:0%
+interesting to different groups or
+ 
+
+ align:start position:0%
+interesting to different groups or
+audiences or stakeholders that that
+
+ align:start position:0%
+audiences or stakeholders that that
+ 
+
+ align:start position:0%
+audiences or stakeholders that that
+might prefer very different
+
+ align:start position:0%
+might prefer very different
+ 
+
+ align:start position:0%
+might prefer very different
+representations of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pitches yeah Vanessa I think it's
+
+ align:start position:0%
+pitches yeah Vanessa I think it's
+ 
+
+ align:start position:0%
+pitches yeah Vanessa I think it's
+interesting to think like people that
+
+ align:start position:0%
+interesting to think like people that
+ 
+
+ align:start position:0%
+interesting to think like people that
+are more into like editing and like
+
+ align:start position:0%
+are more into like editing and like
+ 
+
+ align:start position:0%
+are more into like editing and like
+really analyzing sound files might be a
+
+ align:start position:0%
+really analyzing sound files might be a
+ 
+
+ align:start position:0%
+really analyzing sound files might be a
+lot more interested in seeing like
+
+ align:start position:0%
+lot more interested in seeing like
+ 
+
+ align:start position:0%
+lot more interested in seeing like
+frequency values suppos to if you have
+
+ align:start position:0%
+frequency values suppos to if you have
+ 
+
+ align:start position:0%
+frequency values suppos to if you have
+like a musician who's reading sheet
+
+ align:start position:0%
+like a musician who's reading sheet
+ 
+
+ align:start position:0%
+like a musician who's reading sheet
+music they look at a frequency value
+
+ align:start position:0%
+music they look at a frequency value
+ 
+
+ align:start position:0%
+music they look at a frequency value
+doesn't mean anything to them yeah so
+
+ align:start position:0%
+doesn't mean anything to them yeah so
+ 
+
+ align:start position:0%
+doesn't mean anything to them yeah so
+they would want one of and vales to be
+
+ align:start position:0%
+they would want one of and vales to be
+ 
+
+ align:start position:0%
+they would want one of and vales to be
+able to understand what you're talking
+
+ align:start position:0%
+able to understand what you're talking
+ 
+
+ align:start position:0%
+able to understand what you're talking
+about yeah yeah totally nobody nobody's
+
+ align:start position:0%
+about yeah yeah totally nobody nobody's
+ 
+
+ align:start position:0%
+about yeah yeah totally nobody nobody's
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+see and uh I don't know
+
+ align:start position:0%
+see and uh I don't know
+ 
+
+ align:start position:0%
+see and uh I don't know
+59.8 I'm just making these up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+947 82 and be like that's my most
+
+ align:start position:0%
+947 82 and be like that's my most
+ 
+
+ align:start position:0%
+947 82 and be like that's my most
+beautiful chord I just I just love that
+
+ align:start position:0%
+beautiful chord I just I just love that
+ 
+
+ align:start position:0%
+beautiful chord I just I just love that
+it's very hard to do on the guitar but
+
+ align:start position:0%
+it's very hard to do on the guitar but
+ 
+
+ align:start position:0%
+it's very hard to do on the guitar but
+when you get it just right yeah yeah so
+
+ align:start position:0%
+when you get it just right yeah yeah so
+ 
+
+ align:start position:0%
+when you get it just right yeah yeah so
+definitely definitely different
+
+ align:start position:0%
+definitely definitely different
+ 
+
+ align:start position:0%
+definitely definitely different
+stakeholders for different um for
+
+ align:start position:0%
+stakeholders for different um for
+ 
+
+ align:start position:0%
+stakeholders for different um for
+different uh for different places
+
+ align:start position:0%
+different uh for different places
+ 
+
+ align:start position:0%
+different uh for different places
+different agendas good um other um other
+
+ align:start position:0%
+different agendas good um other um other
+ 
+
+ align:start position:0%
+different agendas good um other um other
+C so we have uh people sound editors and
+
+ align:start position:0%
+C so we have uh people sound editors and
+ 
+
+ align:start position:0%
+C so we have uh people sound editors and
+um and musicians and we can refine that
+
+ align:start position:0%
+um and musicians and we can refine that
+ 
+
+ align:start position:0%
+um and musicians and we can refine that
+either way thanks so that was great um
+
+ align:start position:0%
+either way thanks so that was great um
+ 
+
+ align:start position:0%
+either way thanks so that was great um
+anybody else I
+
+ align:start position:0%
+anybody else I
+ 
+
+ align:start position:0%
+anybody else I
+think yeah Matthew some people care
+
+ align:start position:0%
+think yeah Matthew some people care
+ 
+
+ align:start position:0%
+think yeah Matthew some people care
+about anharmonic spelling and for some
+
+ align:start position:0%
+about anharmonic spelling and for some
+ 
+
+ align:start position:0%
+about anharmonic spelling and for some
+people that's just access information
+
+ align:start position:0%
+people that's just access information
+ 
+
+ align:start position:0%
+people that's just access information
+that's useless yes the big fight on N
+
+ align:start position:0%
+that's useless yes the big fight on N
+ 
+
+ align:start position:0%
+that's useless yes the big fight on N
+harmonic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spelling yeah I just um got a bug report
+
+ align:start position:0%
+spelling yeah I just um got a bug report
+ 
+
+ align:start position:0%
+spelling yeah I just um got a bug report
+in music 21 uh on Wednesday that music
+
+ align:start position:0%
+in music 21 uh on Wednesday that music
+ 
+
+ align:start position:0%
+in music 21 uh on Wednesday that music
+21 was not properly calling uh this
+
+ align:start position:0%
+21 was not properly calling uh this
+ 
+
+ align:start position:0%
+21 was not properly calling uh this
+um let see if I can even do it no um
+
+ align:start position:0%
+um let see if I can even do it no um
+ 
+
+ align:start position:0%
+um let see if I can even do it no um
+maybe it was
+
+ align:start position:0%
+maybe it was
+ 
+
+ align:start position:0%
+maybe it was
+here was not properly calling this a
+
+ align:start position:0%
+here was not properly calling this a
+ 
+
+ align:start position:0%
+here was not properly calling this a
+dominant seventh chord I was saying it
+
+ align:start position:0%
+dominant seventh chord I was saying it
+ 
+
+ align:start position:0%
+dominant seventh chord I was saying it
+was something
+
+ align:start position:0%
+was something
+ 
+
+ align:start position:0%
+was something
+else but if we flip
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this here actually maybe I hope I
+
+ align:start position:0%
+this here actually maybe I hope I
+ 
+
+ align:start position:0%
+this here actually maybe I hope I
+actually wrote a dominant seventh sign
+
+ align:start position:0%
+actually wrote a dominant seventh sign
+ 
+
+ align:start position:0%
+actually wrote a dominant seventh sign
+that sounds like a dominant seventh
+
+ align:start position:0%
+that sounds like a dominant seventh
+ 
+
+ align:start position:0%
+that sounds like a dominant seventh
+chord um that's right right not I'm not
+
+ align:start position:0%
+chord um that's right right not I'm not
+ 
+
+ align:start position:0%
+chord um that's right right not I'm not
+too far away from teaching music theory
+
+ align:start position:0%
+too far away from teaching music theory
+ 
+
+ align:start position:0%
+too far away from teaching music theory
+for a year so yeah yeah
+
+ align:start position:0%
+for a year so yeah yeah
+ 
+
+ align:start position:0%
+for a year so yeah yeah
+so I've am a stakeholder in enharmonic
+
+ align:start position:0%
+so I've am a stakeholder in enharmonic
+ 
+
+ align:start position:0%
+so I've am a stakeholder in enharmonic
+spelling the bug report was from
+
+ align:start position:0%
+spelling the bug report was from
+ 
+
+ align:start position:0%
+spelling the bug report was from
+somebody who um wasn't a stakeholder in
+
+ align:start position:0%
+somebody who um wasn't a stakeholder in
+ 
+
+ align:start position:0%
+somebody who um wasn't a stakeholder in
+inharmonic spelling
+
+ align:start position:0%
+inharmonic spelling
+ 
+
+ align:start position:0%
+inharmonic spelling
+great who who might not care about
+
+ align:start position:0%
+great who who might not care about
+ 
+
+ align:start position:0%
+great who who might not care about
+inharmonic spelling yeah go ahead uh we
+
+ align:start position:0%
+inharmonic spelling yeah go ahead uh we
+ 
+
+ align:start position:0%
+inharmonic spelling yeah go ahead uh we
+could say like a guitarist who doesn't
+
+ align:start position:0%
+could say like a guitarist who doesn't
+ 
+
+ align:start position:0%
+could say like a guitarist who doesn't
+know sheet music yeah totally totally or
+
+ align:start position:0%
+know sheet music yeah totally totally or
+ 
+
+ align:start position:0%
+know sheet music yeah totally totally or
+who or who's doesn't who who's TR maybe
+
+ align:start position:0%
+who or who's doesn't who who's TR maybe
+ 
+
+ align:start position:0%
+who or who's doesn't who who's TR maybe
+if they they just be a little more inous
+
+ align:start position:0%
+if they they just be a little more inous
+ 
+
+ align:start position:0%
+if they they just be a little more inous
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+they they know something but it's
+
+ align:start position:0%
+they they know something but it's
+ 
+
+ align:start position:0%
+they they know something but it's
+translating from the sheet into the
+
+ align:start position:0%
+translating from the sheet into the
+ 
+
+ align:start position:0%
+translating from the sheet into the
+tablet or into the position before
+
+ align:start position:0%
+tablet or into the position before
+ 
+
+ align:start position:0%
+tablet or into the position before
+translating to the next stage of mental
+
+ align:start position:0%
+translating to the next stage of mental
+ 
+
+ align:start position:0%
+translating to the next stage of mental
+processing right I mean we do that a lot
+
+ align:start position:0%
+processing right I mean we do that a lot
+ 
+
+ align:start position:0%
+processing right I mean we do that a lot
+people who are native speakers in um in
+
+ align:start position:0%
+people who are native speakers in um in
+ 
+
+ align:start position:0%
+people who are native speakers in um in
+two languages don't translate from one
+
+ align:start position:0%
+two languages don't translate from one
+ 
+
+ align:start position:0%
+two languages don't translate from one
+language to another before there's um um
+
+ align:start position:0%
+language to another before there's um um
+ 
+
+ align:start position:0%
+language to another before there's um um
+before there's you know some kind of
+
+ align:start position:0%
+before there's you know some kind of
+ 
+
+ align:start position:0%
+before there's you know some kind of
+conception whereas when I'm learning a
+
+ align:start position:0%
+conception whereas when I'm learning a
+ 
+
+ align:start position:0%
+conception whereas when I'm learning a
+new language it's always going through
+
+ align:start position:0%
+new language it's always going through
+ 
+
+ align:start position:0%
+new language it's always going through
+English before it has a meaning to me
+
+ align:start position:0%
+English before it has a meaning to me
+ 
+
+ align:start position:0%
+English before it has a meaning to me
+yeah so so that uh somebody who plays
+
+ align:start position:0%
+yeah so so that uh somebody who plays
+ 
+
+ align:start position:0%
+yeah so so that uh somebody who plays
+guitar might be translating what they're
+
+ align:start position:0%
+guitar might be translating what they're
+ 
+
+ align:start position:0%
+guitar might be translating what they're
+saying to a fret position and then
+
+ align:start position:0%
+saying to a fret position and then
+ 
+
+ align:start position:0%
+saying to a fret position and then
+saying Ah that's great you see that uh
+
+ align:start position:0%
+saying Ah that's great you see that uh
+ 
+
+ align:start position:0%
+saying Ah that's great you see that uh
+quite often in um in a lot of fake book
+
+ align:start position:0%
+quite often in um in a lot of fake book
+ 
+
+ align:start position:0%
+quite often in um in a lot of fake book
+scores in things where you'll see um I
+
+ align:start position:0%
+scores in things where you'll see um I
+ 
+
+ align:start position:0%
+scores in things where you'll see um I
+don't know well same same type of thing
+
+ align:start position:0%
+don't know well same same type of thing
+ 
+
+ align:start position:0%
+don't know well same same type of thing
+you'll see like E flat minor on
+
+ align:start position:0%
+you'll see like E flat minor on
+ 
+
+ align:start position:0%
+you'll see like E flat minor on
+something and then you'll read on that
+
+ align:start position:0%
+something and then you'll read on that
+ 
+
+ align:start position:0%
+something and then you'll read on that
+the the chord
+
+ align:start position:0%
+the the chord
+ 
+
+ align:start position:0%
+the the chord
+I think that's right
+
+ align:start position:0%
+I think that's right
+ 
+
+ align:start position:0%
+I think that's right
+um quite often you know or some
+
+ align:start position:0%
+um quite often you know or some
+ 
+
+ align:start position:0%
+um quite often you know or some
+something like that in a melody and well
+
+ align:start position:0%
+something like that in a melody and well
+ 
+
+ align:start position:0%
+something like that in a melody and well
+obviously the that's not but because
+
+ align:start position:0%
+obviously the that's not but because
+ 
+
+ align:start position:0%
+obviously the that's not but because
+it's all about translating it uh first
+
+ align:start position:0%
+it's all about translating it uh first
+ 
+
+ align:start position:0%
+it's all about translating it uh first
+that's good good other
+
+ align:start position:0%
+that's good good other
+ 
+
+ align:start position:0%
+that's good good other
+stakeholders or other interesting people
+
+ align:start position:0%
+stakeholders or other interesting people
+ 
+
+ align:start position:0%
+stakeholders or other interesting people
+who might use pitch in a different
+
+ align:start position:0%
+who might use pitch in a different
+ 
+
+ align:start position:0%
+who might use pitch in a different
+way yeah I've heard there's like people
+
+ align:start position:0%
+way yeah I've heard there's like people
+ 
+
+ align:start position:0%
+way yeah I've heard there's like people
+who like make incredible music but they
+
+ align:start position:0%
+who like make incredible music but they
+ 
+
+ align:start position:0%
+who like make incredible music but they
+don't even know music theory at all it's
+
+ align:start position:0%
+don't even know music theory at all it's
+ 
+
+ align:start position:0%
+don't even know music theory at all it's
+just like yeah know that yeah totally uh
+
+ align:start position:0%
+just like yeah know that yeah totally uh
+ 
+
+ align:start position:0%
+just like yeah know that yeah totally uh
+there's a big um big area now of study
+
+ align:start position:0%
+there's a big um big area now of study
+ 
+
+ align:start position:0%
+there's a big um big area now of study
+on um implied cognitions of music theory
+
+ align:start position:0%
+on um implied cognitions of music theory
+ 
+
+ align:start position:0%
+on um implied cognitions of music theory
+that um the idea being for for some of
+
+ align:start position:0%
+that um the idea being for for some of
+ 
+
+ align:start position:0%
+that um the idea being for for some of
+the people who are working on this um
+
+ align:start position:0%
+the people who are working on this um
+ 
+
+ align:start position:0%
+the people who are working on this um
+that nobody who's making absolutely
+
+ align:start position:0%
+that nobody who's making absolutely
+ 
+
+ align:start position:0%
+that nobody who's making absolutely
+amazing music um has no conception of
+
+ align:start position:0%
+amazing music um has no conception of
+ 
+
+ align:start position:0%
+amazing music um has no conception of
+what they're doing they might not have
+
+ align:start position:0%
+what they're doing they might not have
+ 
+
+ align:start position:0%
+what they're doing they might not have
+the vocabulary to share it with us but
+
+ align:start position:0%
+the vocabulary to share it with us but
+ 
+
+ align:start position:0%
+the vocabulary to share it with us but
+there's some sort of underlying
+
+ align:start position:0%
+there's some sort of underlying
+ 
+
+ align:start position:0%
+there's some sort of underlying
+conception and how do we get at that um
+
+ align:start position:0%
+conception and how do we get at that um
+ 
+
+ align:start position:0%
+conception and how do we get at that um
+one of my colleagues one of your uh
+
+ align:start position:0%
+one of my colleagues one of your uh
+ 
+
+ align:start position:0%
+one of my colleagues one of your uh
+fellow professors you can take a class
+
+ align:start position:0%
+fellow professors you can take a class
+ 
+
+ align:start position:0%
+fellow professors you can take a class
+with Leslie Tilly uh who teaches rhythms
+
+ align:start position:0%
+with Leslie Tilly uh who teaches rhythms
+ 
+
+ align:start position:0%
+with Leslie Tilly uh who teaches rhythms
+of the world and the Bolognese gamon uh
+
+ align:start position:0%
+of the world and the Bolognese gamon uh
+ 
+
+ align:start position:0%
+of the world and the Bolognese gamon uh
+Sor and music of Bali and Indonesia
+
+ align:start position:0%
+Sor and music of Bali and Indonesia
+ 
+
+ align:start position:0%
+Sor and music of Bali and Indonesia
+things she just uh wrote a book that won
+
+ align:start position:0%
+things she just uh wrote a book that won
+ 
+
+ align:start position:0%
+things she just uh wrote a book that won
+um that just won the big big award in
+
+ align:start position:0%
+um that just won the big big award in
+ 
+
+ align:start position:0%
+um that just won the big big award in
+music theory which was on trying to
+
+ align:start position:0%
+music theory which was on trying to
+ 
+
+ align:start position:0%
+music theory which was on trying to
+figure out what the conception of
+
+ align:start position:0%
+figure out what the conception of
+ 
+
+ align:start position:0%
+figure out what the conception of
+Bolognese musicians who play these two
+
+ align:start position:0%
+Bolognese musicians who play these two
+ 
+
+ align:start position:0%
+Bolognese musicians who play these two
+people who play these improvised drum
+
+ align:start position:0%
+people who play these improvised drum
+ 
+
+ align:start position:0%
+people who play these improvised drum
+patterns interlocking at huge super
+
+ align:start position:0%
+patterns interlocking at huge super
+ 
+
+ align:start position:0%
+patterns interlocking at huge super
+super fast intervals but sometimes they
+
+ align:start position:0%
+super fast intervals but sometimes they
+ 
+
+ align:start position:0%
+super fast intervals but sometimes they
+one of them stops a bit and does the
+
+ align:start position:0%
+one of them stops a bit and does the
+ 
+
+ align:start position:0%
+one of them stops a bit and does the
+other one and they you almost almost
+
+ align:start position:0%
+other one and they you almost almost
+ 
+
+ align:start position:0%
+other one and they you almost almost
+never miss and when they do you know
+
+ align:start position:0%
+never miss and when they do you know
+ 
+
+ align:start position:0%
+never miss and when they do you know
+just like a flub note they you know they
+
+ align:start position:0%
+just like a flub note they you know they
+ 
+
+ align:start position:0%
+just like a flub note they you know they
+laugh and say oh oh how do how do we it
+
+ align:start position:0%
+laugh and say oh oh how do how do we it
+ 
+
+ align:start position:0%
+laugh and say oh oh how do how do we it
+up but you know they say and um her book
+
+ align:start position:0%
+up but you know they say and um her book
+ 
+
+ align:start position:0%
+up but you know they say and um her book
+begins with asking people how do you how
+
+ align:start position:0%
+begins with asking people how do you how
+ 
+
+ align:start position:0%
+begins with asking people how do you how
+do you do this and said oh you just play
+
+ align:start position:0%
+do you do this and said oh you just play
+ 
+
+ align:start position:0%
+do you do this and said oh you just play
+whatever you want and so of course she
+
+ align:start position:0%
+whatever you want and so of course she
+ 
+
+ align:start position:0%
+whatever you want and so of course she
+plays no no no not that not and so how
+
+ align:start position:0%
+plays no no no not that not and so how
+ 
+
+ align:start position:0%
+plays no no no not that not and so how
+do you get at the implied uh the implied
+
+ align:start position:0%
+do you get at the implied uh the implied
+ 
+
+ align:start position:0%
+do you get at the implied uh the implied
+music theory conceptions super great uh
+
+ align:start position:0%
+music theory conceptions super great uh
+ 
+
+ align:start position:0%
+music theory conceptions super great uh
+question Jordan I keep saying uh who are
+
+ align:start position:0%
+question Jordan I keep saying uh who are
+ 
+
+ align:start position:0%
+question Jordan I keep saying uh who are
+the people who do this but some people
+
+ align:start position:0%
+the people who do this but some people
+ 
+
+ align:start position:0%
+the people who do this but some people
+uh some people in this class identified
+
+ align:start position:0%
+uh some people in this class identified
+ 
+
+ align:start position:0%
+uh some people in this class identified
+um stakeholders that weren't
+
+ align:start position:0%
+um stakeholders that weren't
+ 
+
+ align:start position:0%
+um stakeholders that weren't
+people one yeah go ahead like do did
+
+ align:start position:0%
+people one yeah go ahead like do did
+ 
+
+ align:start position:0%
+people one yeah go ahead like do did
+digital audio workstations yeah yeah so
+
+ align:start position:0%
+digital audio workstations yeah yeah so
+ 
+
+ align:start position:0%
+digital audio workstations yeah yeah so
+we we can give autonomy to a digital
+
+ align:start position:0%
+we we can give autonomy to a digital
+ 
+
+ align:start position:0%
+we we can give autonomy to a digital
+audio workstation or to a computer in
+
+ align:start position:0%
+audio workstation or to a computer in
+ 
+
+ align:start position:0%
+audio workstation or to a computer in
+general or to uh a neural network um
+
+ align:start position:0%
+general or to uh a neural network um
+ 
+
+ align:start position:0%
+general or to uh a neural network um
+there's been a a lot of talk about
+
+ align:start position:0%
+there's been a a lot of talk about
+ 
+
+ align:start position:0%
+there's been a a lot of talk about
+autonomy and sentience in neuron
+
+ align:start position:0%
+autonomy and sentience in neuron
+ 
+
+ align:start position:0%
+autonomy and sentience in neuron
+networks this week um and
+
+ align:start position:0%
+networks this week um and
+ 
+
+ align:start position:0%
+networks this week um and
+uh and you know so so why not talk about
+
+ align:start position:0%
+uh and you know so so why not talk about
+ 
+
+ align:start position:0%
+uh and you know so so why not talk about
+them as stakeholders what makes it
+
+ align:start position:0%
+them as stakeholders what makes it
+ 
+
+ align:start position:0%
+them as stakeholders what makes it
+easier for a digital audio workstation
+
+ align:start position:0%
+easier for a digital audio workstation
+ 
+
+ align:start position:0%
+easier for a digital audio workstation
+to process pitch probably usually uh
+
+ align:start position:0%
+to process pitch probably usually uh
+ 
+
+ align:start position:0%
+to process pitch probably usually uh
+eliminate enharmonic
+
+ align:start position:0%
+eliminate enharmonic
+ 
+
+ align:start position:0%
+eliminate enharmonic
+spelling helps quite a bit um yeah great
+
+ align:start position:0%
+spelling helps quite a bit um yeah great
+ 
+
+ align:start position:0%
+spelling helps quite a bit um yeah great
+uh anything else that came up that that
+
+ align:start position:0%
+uh anything else that came up that that
+ 
+
+ align:start position:0%
+uh anything else that came up that that
+you found especially if you if you read
+
+ align:start position:0%
+you found especially if you if you read
+ 
+
+ align:start position:0%
+you found especially if you if you read
+something and even you don't remember
+
+ align:start position:0%
+something and even you don't remember
+ 
+
+ align:start position:0%
+something and even you don't remember
+who it was but somebody else's that you
+
+ align:start position:0%
+who it was but somebody else's that you
+ 
+
+ align:start position:0%
+who it was but somebody else's that you
+read and and liked and you thought oh I
+
+ align:start position:0%
+read and and liked and you thought oh I
+ 
+
+ align:start position:0%
+read and and liked and you thought oh I
+wish I had thought of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that ah I'll I'll see it when we go
+
+ align:start position:0%
+that ah I'll I'll see it when we go
+ 
+
+ align:start position:0%
+that ah I'll I'll see it when we go
+through the the sheets and stuff so so
+
+ align:start position:0%
+through the the sheets and stuff so so
+ 
+
+ align:start position:0%
+through the the sheets and stuff so so
+that's that's great that's um mostly
+
+ align:start position:0%
+that's that's great that's um mostly
+ 
+
+ align:start position:0%
+that's that's great that's um mostly
+leaving aside topic one now there's one
+
+ align:start position:0%
+leaving aside topic one now there's one
+ 
+
+ align:start position:0%
+leaving aside topic one now there's one
+more thing in topic one and I've put it
+
+ align:start position:0%
+more thing in topic one and I've put it
+ 
+
+ align:start position:0%
+more thing in topic one and I've put it
+on a video to watch this weekend you
+
+ align:start position:0%
+on a video to watch this weekend you
+ 
+
+ align:start position:0%
+on a video to watch this weekend you
+will have unlocked your first music 21
+
+ align:start position:0%
+will have unlocked your first music 21
+ 
+
+ align:start position:0%
+will have unlocked your first music 21
+module so now in any problem set from
+
+ align:start position:0%
+module so now in any problem set from
+ 
+
+ align:start position:0%
+module so now in any problem set from
+now on it is will be fair game to say
+
+ align:start position:0%
+now on it is will be fair game to say
+ 
+
+ align:start position:0%
+now on it is will be fair game to say
+from music
+
+ align:start position:0%
+from music
+ 
+
+ align:start position:0%
+from music
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+import
+
+ align:start position:0%
+import
+ 
+
+ align:start position:0%
+import
+pitch and the video will go into more
+
+ align:start position:0%
+pitch and the video will go into more
+ 
+
+ align:start position:0%
+pitch and the video will go into more
+detail from this pitch is lowercase in
+
+ align:start position:0%
+detail from this pitch is lowercase in
+ 
+
+ align:start position:0%
+detail from this pitch is lowercase in
+Python what's that
+
+ align:start position:0%
+Python what's that
+ 
+
+ align:start position:0%
+Python what's that
+signify if you're importing science
+
+ align:start position:0%
+signify if you're importing science
+ 
+
+ align:start position:0%
+signify if you're importing science
+lowercase probably
+
+ align:start position:0%
+lowercase probably
+ 
+
+ align:start position:0%
+lowercase probably
+well actually well okay there's a
+
+ align:start position:0%
+well actually well okay there's a
+ 
+
+ align:start position:0%
+well actually well okay there's a
+there's a there's a pitch. capital pitch
+
+ align:start position:0%
+there's a there's a pitch. capital pitch
+ 
+
+ align:start position:0%
+there's a there's a pitch. capital pitch
+what what's the distinction between
+
+ align:start position:0%
+what what's the distinction between
+ 
+
+ align:start position:0%
+what what's the distinction between
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+two in this
+
+ align:start position:0%
+two in this
+ 
+
+ align:start position:0%
+two in this
+case yeah one is like a class one is a
+
+ align:start position:0%
+case yeah one is like a class one is a
+ 
+
+ align:start position:0%
+case yeah one is like a class one is a
+class and the other one is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what a
+
+ align:start position:0%
+what a
+ 
+
+ align:start position:0%
+what a
+folder it acts exactly like a folder
+
+ align:start position:0%
+folder it acts exactly like a folder
+ 
+
+ align:start position:0%
+folder it acts exactly like a folder
+great answer there's specific name that
+
+ align:start position:0%
+great answer there's specific name that
+ 
+
+ align:start position:0%
+great answer there's specific name that
+that's used in yeah Jason mod module yep
+
+ align:start position:0%
+that's used in yeah Jason mod module yep
+ 
+
+ align:start position:0%
+that's used in yeah Jason mod module yep
+so which one's
+
+ align:start position:0%
+so which one's
+ 
+
+ align:start position:0%
+so which one's
+which that one's a class that one's a
+
+ align:start position:0%
+which that one's a class that one's a
+ 
+
+ align:start position:0%
+which that one's a class that one's a
+class I'm I'm I'm very bad at I turn
+
+ align:start position:0%
+class I'm I'm I'm very bad at I turn
+ 
+
+ align:start position:0%
+class I'm I'm I'm very bad at I turn
+around and you're Point capital P is a
+
+ align:start position:0%
+around and you're Point capital P is a
+ 
+
+ align:start position:0%
+around and you're Point capital P is a
+class and lowercase one is the module so
+
+ align:start position:0%
+class and lowercase one is the module so
+ 
+
+ align:start position:0%
+class and lowercase one is the module so
+you have everything
+
+ align:start position:0%
+you have everything
+ 
+
+ align:start position:0%
+you have everything
+module module y everything that's in the
+
+ align:start position:0%
+module module y everything that's in the
+ 
+
+ align:start position:0%
+module module y everything that's in the
+pitch module is done because you will
+
+ align:start position:0%
+pitch module is done because you will
+ 
+
+ align:start position:0%
+pitch module is done because you will
+also find in there things like
+
+ align:start position:0%
+also find in there things like
+ 
+
+ align:start position:0%
+also find in there things like
+accidental which is pretty helpful so a
+
+ align:start position:0%
+accidental which is pretty helpful so a
+ 
+
+ align:start position:0%
+accidental which is pretty helpful so a
+module group together a related set of
+
+ align:start position:0%
+module group together a related set of
+ 
+
+ align:start position:0%
+module group together a related set of
+classes if you yeah sorry just going
+
+ align:start position:0%
+classes if you yeah sorry just going
+ 
+
+ align:start position:0%
+classes if you yeah sorry just going
+back to the umentation thing I was
+
+ align:start position:0%
+back to the umentation thing I was
+ 
+
+ align:start position:0%
+back to the umentation thing I was
+wondering if there are any studies on
+
+ align:start position:0%
+wondering if there are any studies on
+ 
+
+ align:start position:0%
+wondering if there are any studies on
+people who don't have perfect pitch but
+
+ align:start position:0%
+people who don't have perfect pitch but
+ 
+
+ align:start position:0%
+people who don't have perfect pitch but
+only Val pitch like take the same piece
+
+ align:start position:0%
+only Val pitch like take the same piece
+ 
+
+ align:start position:0%
+only Val pitch like take the same piece
+of music and then just transcribe it is
+
+ align:start position:0%
+of music and then just transcribe it is
+ 
+
+ align:start position:0%
+of music and then just transcribe it is
+there any emotional difference like to
+
+ align:start position:0%
+there any emotional difference like to
+ 
+
+ align:start position:0%
+there any emotional difference like to
+the doesn't matter if it's like you know
+
+ align:start position:0%
+the doesn't matter if it's like you know
+ 
+
+ align:start position:0%
+the doesn't matter if it's like you know
+starting on D or starting on F some
+
+ align:start position:0%
+starting on D or starting on F some
+ 
+
+ align:start position:0%
+starting on D or starting on F some
+doesn't have who doesn't have perfect
+
+ align:start position:0%
+doesn't have who doesn't have perfect
+ 
+
+ align:start position:0%
+doesn't have who doesn't have perfect
+pitch uh I'll have to look that up I
+
+ align:start position:0%
+pitch uh I'll have to look that up I
+ 
+
+ align:start position:0%
+pitch uh I'll have to look that up I
+imagine I mean uh the I don't have
+
+ align:start position:0%
+imagine I mean uh the I don't have
+ 
+
+ align:start position:0%
+imagine I mean uh the I don't have
+perfect pitch but uh absolute pitches is
+
+ align:start position:0%
+perfect pitch but uh absolute pitches is
+ 
+
+ align:start position:0%
+perfect pitch but uh absolute pitches is
+the term that we're using more often now
+
+ align:start position:0%
+the term that we're using more often now
+ 
+
+ align:start position:0%
+the term that we're using more often now
+uh I don't have perfect or absolute
+
+ align:start position:0%
+uh I don't have perfect or absolute
+ 
+
+ align:start position:0%
+uh I don't have perfect or absolute
+pitch but um but there's definitely
+
+ align:start position:0%
+pitch but um but there's definitely
+ 
+
+ align:start position:0%
+pitch but um but there's definitely
+pieces that if you play you know some
+
+ align:start position:0%
+pieces that if you play you know some
+ 
+
+ align:start position:0%
+pieces that if you play you know some
+song that I know really well and you
+
+ align:start position:0%
+song that I know really well and you
+ 
+
+ align:start position:0%
+song that I know really well and you
+play it up a half step or up a whole
+
+ align:start position:0%
+play it up a half step or up a whole
+ 
+
+ align:start position:0%
+play it up a half step or up a whole
+step it's going to you impact me now if
+
+ align:start position:0%
+step it's going to you impact me now if
+ 
+
+ align:start position:0%
+step it's going to you impact me now if
+it's a song I don't know I'm not not
+
+ align:start position:0%
+it's a song I don't know I'm not not
+ 
+
+ align:start position:0%
+it's a song I don't know I'm not not
+entirely sure but I'll I'll I'll see um
+
+ align:start position:0%
+entirely sure but I'll I'll I'll see um
+ 
+
+ align:start position:0%
+entirely sure but I'll I'll I'll see um
+let me just make make a note on that um
+
+ align:start position:0%
+let me just make make a note on that um
+ 
+
+ align:start position:0%
+let me just make make a note on that um
+I found in one one unscientific study
+
+ align:start position:0%
+I found in one one unscientific study
+ 
+
+ align:start position:0%
+I found in one one unscientific study
+did that um in uh for a paper I was
+
+ align:start position:0%
+did that um in uh for a paper I was
+ 
+
+ align:start position:0%
+did that um in uh for a paper I was
+working on that there's a particular
+
+ align:start position:0%
+working on that there's a particular
+ 
+
+ align:start position:0%
+working on that there's a particular
+case where um you can uh very strangely
+
+ align:start position:0%
+case where um you can uh very strangely
+ 
+
+ align:start position:0%
+case where um you can uh very strangely
+the rep the number of notes within a
+
+ align:start position:0%
+the rep the number of notes within a
+ 
+
+ align:start position:0%
+the rep the number of notes within a
+repetition of Contour is decreasing but
+
+ align:start position:0%
+repetition of Contour is decreasing but
+ 
+
+ align:start position:0%
+repetition of Contour is decreasing but
+the number of um repetitions of that
+
+ align:start position:0%
+the number of um repetitions of that
+ 
+
+ align:start position:0%
+the number of um repetitions of that
+Contour before something changes is
+
+ align:start position:0%
+Contour before something changes is
+ 
+
+ align:start position:0%
+Contour before something changes is
+increasing so the tempo depending on if
+
+ align:start position:0%
+increasing so the tempo depending on if
+ 
+
+ align:start position:0%
+increasing so the tempo depending on if
+you hear
+
+ align:start position:0%
+you hear
+ 
+
+ align:start position:0%
+you hear
+the harmony or the when the harmony
+
+ align:start position:0%
+the harmony or the when the harmony
+ 
+
+ align:start position:0%
+the harmony or the when the harmony
+changes the harmonic changes as
+
+ align:start position:0%
+changes the harmonic changes as
+ 
+
+ align:start position:0%
+changes the harmonic changes as
+determinant of tempo or if you hear the
+
+ align:start position:0%
+determinant of tempo or if you hear the
+ 
+
+ align:start position:0%
+determinant of tempo or if you hear the
+repetition of Contour as determinant of
+
+ align:start position:0%
+repetition of Contour as determinant of
+ 
+
+ align:start position:0%
+repetition of Contour as determinant of
+tempo you can hear the same piece
+
+ align:start position:0%
+tempo you can hear the same piece
+ 
+
+ align:start position:0%
+tempo you can hear the same piece
+speeding up or slowing down and um a lot
+
+ align:start position:0%
+speeding up or slowing down and um a lot
+ 
+
+ align:start position:0%
+speeding up or slowing down and um a lot
+of people were like oh yeah I I hear
+
+ align:start position:0%
+of people were like oh yeah I I hear
+ 
+
+ align:start position:0%
+of people were like oh yeah I I hear
+this and things but um in that uh
+
+ align:start position:0%
+this and things but um in that uh
+ 
+
+ align:start position:0%
+this and things but um in that uh
+unscientific experiment people with
+
+ align:start position:0%
+unscientific experiment people with
+ 
+
+ align:start position:0%
+unscientific experiment people with
+absolute pit um
+
+ align:start position:0%
+absolute pit um
+ 
+
+ align:start position:0%
+absolute pit um
+said I don't hear repetition of Contour
+
+ align:start position:0%
+said I don't hear repetition of Contour
+ 
+
+ align:start position:0%
+said I don't hear repetition of Contour
+when the notes are different
+
+ align:start position:0%
+when the notes are different
+ 
+
+ align:start position:0%
+when the notes are different
+that that doesn't seem to me a kind of
+
+ align:start position:0%
+that that doesn't seem to me a kind of
+ 
+
+ align:start position:0%
+that that doesn't seem to me a kind of
+repetition so there's there probably
+
+ align:start position:0%
+repetition so there's there probably
+ 
+
+ align:start position:0%
+repetition so there's there probably
+different ways we can do that great
+
+ align:start position:0%
+different ways we can do that great
+ 
+
+ align:start position:0%
+different ways we can do that great
+super great question um we'll put that
+
+ align:start position:0%
+super great question um we'll put that
+ 
+
+ align:start position:0%
+super great question um we'll put that
+aside when we edit it we'll edit that
+
+ align:start position:0%
+aside when we edit it we'll edit that
+ 
+
+ align:start position:0%
+aside when we edit it we'll edit that
+about 10 seconds back and we'll jump
+
+ align:start position:0%
+about 10 seconds back and we'll jump
+ 
+
+ align:start position:0%
+about 10 seconds back and we'll jump
+back to here just for a second U don't
+
+ align:start position:0%
+back to here just for a second U don't
+ 
+
+ align:start position:0%
+back to here just for a second U don't
+don't be afraid of of of doing that if
+
+ align:start position:0%
+don't be afraid of of of doing that if
+ 
+
+ align:start position:0%
+don't be afraid of of of doing that if
+if it's something you know and if if
+
+ align:start position:0%
+if it's something you know and if if
+ 
+
+ align:start position:0%
+if it's something you know and if if
+it's something that I think it's going
+
+ align:start position:0%
+it's something that I think it's going
+ 
+
+ align:start position:0%
+it's something that I think it's going
+to be super confusing to everybody if we
+
+ align:start position:0%
+to be super confusing to everybody if we
+ 
+
+ align:start position:0%
+to be super confusing to everybody if we
+jump back I'll say we'll hold that for a
+
+ align:start position:0%
+jump back I'll say we'll hold that for a
+ 
+
+ align:start position:0%
+jump back I'll say we'll hold that for a
+bit but I think we we can still code
+
+ align:start position:0%
+bit but I think we we can still code
+ 
+
+ align:start position:0%
+bit but I think we we can still code
+switch which we can switch back and
+
+ align:start position:0%
+switch which we can switch back and
+ 
+
+ align:start position:0%
+switch which we can switch back and
+forth between what we were talking about
+
+ align:start position:0%
+forth between what we were talking about
+ 
+
+ align:start position:0%
+forth between what we were talking about
+30 seconds earlier and what we were just
+
+ align:start position:0%
+30 seconds earlier and what we were just
+ 
+
+ align:start position:0%
+30 seconds earlier and what we were just
+talking about right good okay so you're
+
+ align:start position:0%
+talking about right good okay so you're
+ 
+
+ align:start position:0%
+talking about right good okay so you're
+going to be able to import and use
+
+ align:start position:0%
+going to be able to import and use
+ 
+
+ align:start position:0%
+going to be able to import and use
+anything in the pitch module as long as
+
+ align:start position:0%
+anything in the pitch module as long as
+ 
+
+ align:start position:0%
+anything in the pitch module as long as
+it doesn't have the word
+
+ align:start position:0%
+it doesn't have the word
+ 
+
+ align:start position:0%
+it doesn't have the word
+transpose in it somewhere because
+
+ align:start position:0%
+transpose in it somewhere because
+ 
+
+ align:start position:0%
+transpose in it somewhere because
+certain kinds of transposition will be
+
+ align:start position:0%
+certain kinds of transposition will be
+ 
+
+ align:start position:0%
+certain kinds of transposition will be
+uh things for us to work out in the next
+
+ align:start position:0%
+uh things for us to work out in the next
+ 
+
+ align:start position:0%
+uh things for us to work out in the next
+couple problem sets good good so that's
+
+ align:start position:0%
+couple problem sets good good so that's
+ 
+
+ align:start position:0%
+couple problem sets good good so that's
+that's what's coming up and then we'll
+
+ align:start position:0%
+that's what's coming up and then we'll
+ 
+
+ align:start position:0%
+that's what's coming up and then we'll
+be done with with
+
+ align:start position:0%
+be done with with
+ 
+
+ align:start position:0%
+be done with with
+that now uh so last class we were
+
+ align:start position:0%
+that now uh so last class we were
+ 
+
+ align:start position:0%
+that now uh so last class we were
+talking a lot more about moving from the
+
+ align:start position:0%
+talking a lot more about moving from the
+ 
+
+ align:start position:0%
+talking a lot more about moving from the
+representation of individual pitches
+
+ align:start position:0%
+representation of individual pitches
+ 
+
+ align:start position:0%
+representation of individual pitches
+individual notes into larger things we
+
+ align:start position:0%
+individual notes into larger things we
+ 
+
+ align:start position:0%
+individual notes into larger things we
+might call it representation of a score
+
+ align:start position:0%
+might call it representation of a score
+ 
+
+ align:start position:0%
+might call it representation of a score
+or simply representation of Music
+
+ align:start position:0%
+or simply representation of Music
+ 
+
+ align:start position:0%
+or simply representation of Music
+something of that sort I introduced a
+
+ align:start position:0%
+something of that sort I introduced a
+ 
+
+ align:start position:0%
+something of that sort I introduced a
+term that some of you already knew from
+
+ align:start position:0%
+term that some of you already knew from
+ 
+
+ align:start position:0%
+term that some of you already knew from
+other classes uh that come goes back to
+
+ align:start position:0%
+other classes uh that come goes back to
+ 
+
+ align:start position:0%
+other classes uh that come goes back to
+uh philosophy but has a inter Twist of a
+
+ align:start position:0%
+uh philosophy but has a inter Twist of a
+ 
+
+ align:start position:0%
+uh philosophy but has a inter Twist of a
+meaning in um in computer science anyone
+
+ align:start position:0%
+meaning in um in computer science anyone
+ 
+
+ align:start position:0%
+meaning in um in computer science anyone
+remember that term without looking down
+
+ align:start position:0%
+remember that term without looking down
+ 
+
+ align:start position:0%
+remember that term without looking down
+at the outline ony ontology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good and last class we explored um some
+
+ align:start position:0%
+good and last class we explored um some
+ 
+
+ align:start position:0%
+good and last class we explored um some
+of the things in the Phil philosophical
+
+ align:start position:0%
+of the things in the Phil philosophical
+ 
+
+ align:start position:0%
+of the things in the Phil philosophical
+thing definition of essence of of what
+
+ align:start position:0%
+thing definition of essence of of what
+ 
+
+ align:start position:0%
+thing definition of essence of of what
+something is I remember some of the
+
+ align:start position:0%
+something is I remember some of the
+ 
+
+ align:start position:0%
+something is I remember some of the
+things that we we had trouble defining
+
+ align:start position:0%
+things that we we had trouble defining
+ 
+
+ align:start position:0%
+things that we we had trouble defining
+when something ended and became
+
+ align:start position:0%
+when something ended and became
+ 
+
+ align:start position:0%
+when something ended and became
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+else yeah we talked about notes we
+
+ align:start position:0%
+else yeah we talked about notes we
+ 
+
+ align:start position:0%
+else yeah we talked about notes we
+talked about notes that we can't really
+
+ align:start position:0%
+talked about notes that we can't really
+ 
+
+ align:start position:0%
+talked about notes that we can't really
+tell is is this one note is this two
+
+ align:start position:0%
+tell is is this one note is this two
+ 
+
+ align:start position:0%
+tell is is this one note is this two
+notes is this six notes is it Infinity
+
+ align:start position:0%
+notes is this six notes is it Infinity
+ 
+
+ align:start position:0%
+notes is this six notes is it Infinity
+of notes or 14 or um yeah then a larger
+
+ align:start position:0%
+of notes or 14 or um yeah then a larger
+ 
+
+ align:start position:0%
+of notes or 14 or um yeah then a larger
+system um of musical notation remember
+
+ align:start position:0%
+system um of musical notation remember
+ 
+
+ align:start position:0%
+system um of musical notation remember
+we called it used in used in uh one part
+
+ align:start position:0%
+we called it used in used in uh one part
+ 
+
+ align:start position:0%
+we called it used in used in uh one part
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+world yeah common western music common
+
+ align:start position:0%
+world yeah common western music common
+ 
+
+ align:start position:0%
+world yeah common western music common
+western music notation yeah and we had
+
+ align:start position:0%
+western music notation yeah and we had
+ 
+
+ align:start position:0%
+western music notation yeah and we had
+we had some trouble distinguishing when
+
+ align:start position:0%
+we had some trouble distinguishing when
+ 
+
+ align:start position:0%
+we had some trouble distinguishing when
+what was common or what was Western
+
+ align:start position:0%
+what was common or what was Western
+ 
+
+ align:start position:0%
+what was common or what was Western
+about it or I suppose in one case what
+
+ align:start position:0%
+about it or I suppose in one case what
+ 
+
+ align:start position:0%
+about it or I suppose in one case what
+was music about it uh seemed to be um
+
+ align:start position:0%
+was music about it uh seemed to be um
+ 
+
+ align:start position:0%
+was music about it uh seemed to be um
+you know uh on the edge good then we
+
+ align:start position:0%
+you know uh on the edge good then we
+ 
+
+ align:start position:0%
+you know uh on the edge good then we
+also brought up a little bit the
+
+ align:start position:0%
+also brought up a little bit the
+ 
+
+ align:start position:0%
+also brought up a little bit the
+computer science
+
+ align:start position:0%
+computer science
+ 
+
+ align:start position:0%
+computer science
+definition and that's what we're going
+
+ align:start position:0%
+definition and that's what we're going
+ 
+
+ align:start position:0%
+definition and that's what we're going
+to be working looking at a little bit
+
+ align:start position:0%
+to be working looking at a little bit
+ 
+
+ align:start position:0%
+to be working looking at a little bit
+now but always feeling like we want to
+
+ align:start position:0%
+now but always feeling like we want to
+ 
+
+ align:start position:0%
+now but always feeling like we want to
+jump back to the philosophical
+
+ align:start position:0%
+jump back to the philosophical
+ 
+
+ align:start position:0%
+jump back to the philosophical
+definition because we don't want ideas
+
+ align:start position:0%
+definition because we don't want ideas
+ 
+
+ align:start position:0%
+definition because we don't want ideas
+from computer science all always to um
+
+ align:start position:0%
+from computer science all always to um
+ 
+
+ align:start position:0%
+from computer science all always to um
+what what is easy to conceive of we
+
+ align:start position:0%
+what what is easy to conceive of we
+ 
+
+ align:start position:0%
+what what is easy to conceive of we
+don't want that to limit our imagination
+
+ align:start position:0%
+don't want that to limit our imagination
+ 
+
+ align:start position:0%
+don't want that to limit our imagination
+of what we might be able to conceive in
+
+ align:start position:0%
+of what we might be able to conceive in
+ 
+
+ align:start position:0%
+of what we might be able to conceive in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+future so we talked about uh so in the
+
+ align:start position:0%
+future so we talked about uh so in the
+ 
+
+ align:start position:0%
+future so we talked about uh so in the
+computer science definitions uh there
+
+ align:start position:0%
+computer science definitions uh there
+ 
+
+ align:start position:0%
+computer science definitions uh there
+are various ones there's ones that are
+
+ align:start position:0%
+are various ones there's ones that are
+ 
+
+ align:start position:0%
+are various ones there's ones that are
+more formalized there's ones that are
+
+ align:start position:0%
+more formalized there's ones that are
+ 
+
+ align:start position:0%
+more formalized there's ones that are
+less one that I can't of keep in my head
+
+ align:start position:0%
+less one that I can't of keep in my head
+ 
+
+ align:start position:0%
+less one that I can't of keep in my head
+because I can remember it when I come uh
+
+ align:start position:0%
+because I can remember it when I come uh
+ 
+
+ align:start position:0%
+because I can remember it when I come uh
+come up is when we're trying to
+
+ align:start position:0%
+come up is when we're trying to
+ 
+
+ align:start position:0%
+come up is when we're trying to
+represent something like music or you
+
+ align:start position:0%
+represent something like music or you
+ 
+
+ align:start position:0%
+represent something like music or you
+know you can be your ontology of um of a
+
+ align:start position:0%
+know you can be your ontology of um of a
+ 
+
+ align:start position:0%
+know you can be your ontology of um of a
+website or something but when you're
+
+ align:start position:0%
+website or something but when you're
+ 
+
+ align:start position:0%
+website or something but when you're
+trying to think of a particular object
+
+ align:start position:0%
+trying to think of a particular object
+ 
+
+ align:start position:0%
+trying to think of a particular object
+that's either conceptual or or you know
+
+ align:start position:0%
+that's either conceptual or or you know
+ 
+
+ align:start position:0%
+that's either conceptual or or you know
+rified uh really real want to think
+
+ align:start position:0%
+rified uh really real want to think
+ 
+
+ align:start position:0%
+rified uh really real want to think
+about how is it made up of what objects
+
+ align:start position:0%
+about how is it made up of what objects
+ 
+
+ align:start position:0%
+about how is it made up of what objects
+are in
+
+ align:start position:0%
+are in
+ 
+
+ align:start position:0%
+are in
+it what are the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relationships
+
+ align:start position:0%
+relationships
+ 
+
+ align:start position:0%
+relationships
+ships between
+
+ align:start position:0%
+ships between
+ 
+
+ align:start position:0%
+ships between
+objects and what are they called or what
+
+ align:start position:0%
+objects and what are they called or what
+ 
+
+ align:start position:0%
+objects and what are they called or what
+are their names
+
+ align:start position:0%
+are their names
+ 
+
+ align:start position:0%
+are their names
+what was it there was something it was
+
+ align:start position:0%
+what was it there was something it was
+ 
+
+ align:start position:0%
+what was it there was something it was
+like first or second class that we had a
+
+ align:start position:0%
+like first or second class that we had a
+ 
+
+ align:start position:0%
+like first or second class that we had a
+real oh I remember now really hard time
+
+ align:start position:0%
+real oh I remember now really hard time
+ 
+
+ align:start position:0%
+real oh I remember now really hard time
+figuring out the name of it and it had
+
+ align:start position:0%
+figuring out the name of it and it had
+ 
+
+ align:start position:0%
+figuring out the name of it and it had
+to do with the well this is a this is a
+
+ align:start position:0%
+to do with the well this is a this is a
+ 
+
+ align:start position:0%
+to do with the well this is a this is a
+eighth note and this one's a whole note
+
+ align:start position:0%
+eighth note and this one's a whole note
+ 
+
+ align:start position:0%
+eighth note and this one's a whole note
+and so the blank of the note is eighth
+
+ align:start position:0%
+and so the blank of the note is eighth
+ 
+
+ align:start position:0%
+and so the blank of the note is eighth
+the blank of the note is whole what what
+
+ align:start position:0%
+the blank of the note is whole what what
+ 
+
+ align:start position:0%
+the blank of the note is whole what what
+did we what did we come up with we had
+
+ align:start position:0%
+did we what did we come up with we had
+ 
+
+ align:start position:0%
+did we what did we come up with we had
+some the Almond of it yeah we we had the
+
+ align:start position:0%
+some the Almond of it yeah we we had the
+ 
+
+ align:start position:0%
+some the Almond of it yeah we we had the
+um so sometimes sometimes pushing it way
+
+ align:start position:0%
+um so sometimes sometimes pushing it way
+ 
+
+ align:start position:0%
+um so sometimes sometimes pushing it way
+out there can make that um I mean some
+
+ align:start position:0%
+out there can make that um I mean some
+ 
+
+ align:start position:0%
+out there can make that um I mean some
+of you all have taken physics you know
+
+ align:start position:0%
+of you all have taken physics you know
+ 
+
+ align:start position:0%
+of you all have taken physics you know
+that uh probably subatomic particles do
+
+ align:start position:0%
+that uh probably subatomic particles do
+ 
+
+ align:start position:0%
+that uh probably subatomic particles do
+not have a charm a color uh things like
+
+ align:start position:0%
+not have a charm a color uh things like
+ 
+
+ align:start position:0%
+not have a charm a color uh things like
+that but these kinds of names can help
+
+ align:start position:0%
+that but these kinds of names can help
+ 
+
+ align:start position:0%
+that but these kinds of names can help
+us conceive of some property of
+
+ align:start position:0%
+us conceive of some property of
+ 
+
+ align:start position:0%
+us conceive of some property of
+something so we might have the Almond of
+
+ align:start position:0%
+something so we might have the Almond of
+ 
+
+ align:start position:0%
+something so we might have the Almond of
+a note I think I went with something
+
+ align:start position:0%
+a note I think I went with something
+ 
+
+ align:start position:0%
+a note I think I went with something
+very generic the type of the note but uh
+
+ align:start position:0%
+very generic the type of the note but uh
+ 
+
+ align:start position:0%
+very generic the type of the note but uh
+always avoid type if you can come up
+
+ align:start position:0%
+always avoid type if you can come up
+ 
+
+ align:start position:0%
+always avoid type if you can come up
+with something better because a type
+
+ align:start position:0%
+with something better because a type
+ 
+
+ align:start position:0%
+with something better because a type
+it's it's too valuable to use if you can
+
+ align:start position:0%
+it's it's too valuable to use if you can
+ 
+
+ align:start position:0%
+it's it's too valuable to use if you can
+and too generic so good so what are
+
+ align:start position:0%
+and too generic so good so what are
+ 
+
+ align:start position:0%
+and too generic so good so what are
+things and what are they called and I'm
+
+ align:start position:0%
+things and what are they called and I'm
+ 
+
+ align:start position:0%
+things and what are they called and I'm
+spending notice what are the objects
+
+ align:start position:0%
+spending notice what are the objects
+ 
+
+ align:start position:0%
+spending notice what are the objects
+you're going to be thinking about that a
+
+ align:start position:0%
+you're going to be thinking about that a
+ 
+
+ align:start position:0%
+you're going to be thinking about that a
+lot what are the relationships what
+
+ align:start position:0%
+lot what are the relationships what
+ 
+
+ align:start position:0%
+lot what are the relationships what
+you're always going to be thinking about
+
+ align:start position:0%
+you're always going to be thinking about
+ 
+
+ align:start position:0%
+you're always going to be thinking about
+that a lot but the name of something can
+
+ align:start position:0%
+that a lot but the name of something can
+ 
+
+ align:start position:0%
+that a lot but the name of something can
+really really help somebody un somebody
+
+ align:start position:0%
+really really help somebody un somebody
+ 
+
+ align:start position:0%
+really really help somebody un somebody
+else understand how you're conceiving
+
+ align:start position:0%
+else understand how you're conceiving
+ 
+
+ align:start position:0%
+else understand how you're conceiving
+something and it's can be very very hard
+
+ align:start position:0%
+something and it's can be very very hard
+ 
+
+ align:start position:0%
+something and it's can be very very hard
+U some of you have probably heard the
+
+ align:start position:0%
+U some of you have probably heard the
+ 
+
+ align:start position:0%
+U some of you have probably heard the
+computer science joke that there's only
+
+ align:start position:0%
+computer science joke that there's only
+ 
+
+ align:start position:0%
+computer science joke that there's only
+three really difficult things in
+
+ align:start position:0%
+three really difficult things in
+ 
+
+ align:start position:0%
+three really difficult things in
+programming what to name something and
+
+ align:start position:0%
+programming what to name something and
+ 
+
+ align:start position:0%
+programming what to name something and
+off by one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+errors good good good some people hadn't
+
+ align:start position:0%
+errors good good good some people hadn't
+ 
+
+ align:start position:0%
+errors good good good some people hadn't
+heard that and some other people have
+
+ align:start position:0%
+heard that and some other people have
+ 
+
+ align:start position:0%
+heard that and some other people have
+yeah so what is something called and um
+
+ align:start position:0%
+yeah so what is something called and um
+ 
+
+ align:start position:0%
+yeah so what is something called and um
+and that but we're going to jump now to
+
+ align:start position:0%
+and that but we're going to jump now to
+ 
+
+ align:start position:0%
+and that but we're going to jump now to
+what are the relationships between
+
+ align:start position:0%
+what are the relationships between
+ 
+
+ align:start position:0%
+what are the relationships between
+objects um what are some things in music
+
+ align:start position:0%
+objects um what are some things in music
+ 
+
+ align:start position:0%
+objects um what are some things in music
+that we might consider an object let's
+
+ align:start position:0%
+that we might consider an object let's
+ 
+
+ align:start position:0%
+that we might consider an object let's
+just let's let's rapid fire just shout
+
+ align:start position:0%
+just let's let's rapid fire just shout
+ 
+
+ align:start position:0%
+just let's let's rapid fire just shout
+out over each other note note good
+
+ align:start position:0%
+out over each other note note good
+ 
+
+ align:start position:0%
+out over each other note note good
+always take the easy one get the easy
+
+ align:start position:0%
+always take the easy one get the easy
+ 
+
+ align:start position:0%
+always take the easy one get the easy
+participation credit great rest rest I
+
+ align:start position:0%
+participation credit great rest rest I
+ 
+
+ align:start position:0%
+participation credit great rest rest I
+heard yep me measure oo that's good
+
+ align:start position:0%
+heard yep me measure oo that's good
+ 
+
+ align:start position:0%
+heard yep me measure oo that's good
+phrase phrase
+
+ align:start position:0%
+phrase phrase
+ 
+
+ align:start position:0%
+phrase phrase
+ah
+
+ align:start position:0%
+ah
+ 
+
+ align:start position:0%
+ah
+good articulate Artic
+
+ align:start position:0%
+good articulate Artic
+ 
+
+ align:start position:0%
+good articulate Artic
+articulation good let's I'm going to
+
+ align:start position:0%
+articulation good let's I'm going to
+ 
+
+ align:start position:0%
+articulation good let's I'm going to
+stop writing down unless I hear
+
+ align:start position:0%
+stop writing down unless I hear
+ 
+
+ align:start position:0%
+stop writing down unless I hear
+something that I've never never thought
+
+ align:start position:0%
+something that I've never never thought
+ 
+
+ align:start position:0%
+something that I've never never thought
+of and um good what else
+
+ align:start position:0%
+of and um good what else
+ 
+
+ align:start position:0%
+of and um good what else
+there Cliff Cliff good the whole score
+
+ align:start position:0%
+there Cliff Cliff good the whole score
+ 
+
+ align:start position:0%
+there Cliff Cliff good the whole score
+the whole score good the score
+
+ align:start position:0%
+the whole score good the score
+ 
+
+ align:start position:0%
+the whole score good the score
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+dynamic the instrument
+
+ align:start position:0%
+dynamic the instrument
+ 
+
+ align:start position:0%
+dynamic the instrument
+Tempo name of the
+
+ align:start position:0%
+Tempo name of the
+ 
+
+ align:start position:0%
+Tempo name of the
+performer Concert Hall that was P
+
+ align:start position:0%
+performer Concert Hall that was P
+ 
+
+ align:start position:0%
+performer Concert Hall that was P
+performed in maybe maybe not we can we
+
+ align:start position:0%
+performed in maybe maybe not we can we
+ 
+
+ align:start position:0%
+performed in maybe maybe not we can we
+can kind of go but these are things we
+
+ align:start position:0%
+can kind of go but these are things we
+ 
+
+ align:start position:0%
+can kind of go but these are things we
+might represent when we're thinking
+
+ align:start position:0%
+might represent when we're thinking
+ 
+
+ align:start position:0%
+might represent when we're thinking
+about a performance of a music um good
+
+ align:start position:0%
+about a performance of a music um good
+ 
+
+ align:start position:0%
+about a performance of a music um good
+anything else on people's jumping on
+
+ align:start position:0%
+anything else on people's jumping on
+ 
+
+ align:start position:0%
+anything else on people's jumping on
+people's mind Angelica do you have one
+
+ align:start position:0%
+people's mind Angelica do you have one
+ 
+
+ align:start position:0%
+people's mind Angelica do you have one
+that you haven't
+
+ align:start position:0%
+that you haven't
+ 
+
+ align:start position:0%
+that you haven't
+heard beat or something beet oh yeah
+
+ align:start position:0%
+heard beat or something beet oh yeah
+ 
+
+ align:start position:0%
+heard beat or something beet oh yeah
+beat
+
+ align:start position:0%
+beat
+ 
+
+ align:start position:0%
+beat
+see that that's great because that's
+
+ align:start position:0%
+see that that's great because that's
+ 
+
+ align:start position:0%
+see that that's great because that's
+something we don't see on the score but
+
+ align:start position:0%
+something we don't see on the score but
+ 
+
+ align:start position:0%
+something we don't see on the score but
+we're thinking all the time right yeah
+
+ align:start position:0%
+we're thinking all the time right yeah
+ 
+
+ align:start position:0%
+we're thinking all the time right yeah
+tamber good the instrumental
+
+ align:start position:0%
+tamber good the instrumental
+ 
+
+ align:start position:0%
+tamber good the instrumental
+color
+
+ align:start position:0%
+color
+ 
+
+ align:start position:0%
+color
+tamber great so so these are all
+
+ align:start position:0%
+tamber great so so these are all
+ 
+
+ align:start position:0%
+tamber great so so these are all
+different things and um that might we
+
+ align:start position:0%
+different things and um that might we
+ 
+
+ align:start position:0%
+different things and um that might we
+might think of as as objects one of the
+
+ align:start position:0%
+might think of as as objects one of the
+ 
+
+ align:start position:0%
+might think of as as objects one of the
+things and some of them we might not
+
+ align:start position:0%
+things and some of them we might not
+ 
+
+ align:start position:0%
+things and some of them we might not
+represent in every programming language
+
+ align:start position:0%
+represent in every programming language
+ 
+
+ align:start position:0%
+represent in every programming language
+as an actual you know object class
+
+ align:start position:0%
+as an actual you know object class
+ 
+
+ align:start position:0%
+as an actual you know object class
+depending on your programming language
+
+ align:start position:0%
+depending on your programming language
+ 
+
+ align:start position:0%
+depending on your programming language
+but you know there things we can think
+
+ align:start position:0%
+but you know there things we can think
+ 
+
+ align:start position:0%
+but you know there things we can think
+of that have a
+
+ align:start position:0%
+of that have a
+ 
+
+ align:start position:0%
+of that have a
+particular um
+
+ align:start position:0%
+particular um
+ 
+
+ align:start position:0%
+particular um
+nness can you say nness that they act
+
+ align:start position:0%
+nness can you say nness that they act
+ 
+
+ align:start position:0%
+nness can you say nness that they act
+like nouns that they have the essence of
+
+ align:start position:0%
+like nouns that they have the essence of
+ 
+
+ align:start position:0%
+like nouns that they have the essence of
+a noun um as opposed to a verb nobody
+
+ align:start position:0%
+a noun um as opposed to a verb nobody
+ 
+
+ align:start position:0%
+a noun um as opposed to a verb nobody
+said that a fundamental object was
+
+ align:start position:0%
+said that a fundamental object was
+ 
+
+ align:start position:0%
+said that a fundamental object was
+transpose or
+
+ align:start position:0%
+transpose or
+ 
+
+ align:start position:0%
+transpose or
+perform right that that those those
+
+ align:start position:0%
+perform right that that those those
+ 
+
+ align:start position:0%
+perform right that that those those
+verby things so when we want to think of
+
+ align:start position:0%
+verby things so when we want to think of
+ 
+
+ align:start position:0%
+verby things so when we want to think of
+various ways that objects can be related
+
+ align:start position:0%
+various ways that objects can be related
+ 
+
+ align:start position:0%
+various ways that objects can be related
+as any um we talk often about taxonomies
+
+ align:start position:0%
+as any um we talk often about taxonomies
+ 
+
+ align:start position:0%
+as any um we talk often about taxonomies
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+momies any has this come up in anybody
+
+ align:start position:0%
+momies any has this come up in anybody
+ 
+
+ align:start position:0%
+momies any has this come up in anybody
+else's in computer science classes think
+
+ align:start position:0%
+else's in computer science classes think
+ 
+
+ align:start position:0%
+else's in computer science classes think
+doesn't come up in was it 69
+
+ align:start position:0%
+doesn't come up in was it 69
+ 
+
+ align:start position:0%
+doesn't come up in was it 69
+6101 okay good who has but who has heard
+
+ align:start position:0%
+6101 okay good who has but who has heard
+ 
+
+ align:start position:0%
+6101 okay good who has but who has heard
+of a taxonomy in another concept yeah
+
+ align:start position:0%
+of a taxonomy in another concept yeah
+ 
+
+ align:start position:0%
+of a taxonomy in another concept yeah
+yeah K what where have you heard it um
+
+ align:start position:0%
+yeah K what where have you heard it um
+ 
+
+ align:start position:0%
+yeah K what where have you heard it um
+like animals animals Kings play cards on
+
+ align:start position:0%
+like animals animals Kings play cards on
+ 
+
+ align:start position:0%
+like animals animals Kings play cards on
+fat green stools do they still teach
+
+ align:start position:0%
+fat green stools do they still teach
+ 
+
+ align:start position:0%
+fat green stools do they still teach
+that or uh Kingdom film yeah I mean now
+
+ align:start position:0%
+that or uh Kingdom film yeah I mean now
+ 
+
+ align:start position:0%
+that or uh Kingdom film yeah I mean now
+there's all these they keep rearranging
+
+ align:start position:0%
+there's all these they keep rearranging
+ 
+
+ align:start position:0%
+there's all these they keep rearranging
+it right they're keeping sub classes and
+
+ align:start position:0%
+it right they're keeping sub classes and
+ 
+
+ align:start position:0%
+it right they're keeping sub classes and
+super kingdoms and and things like that
+
+ align:start position:0%
+super kingdoms and and things like that
+ 
+
+ align:start position:0%
+super kingdoms and and things like that
+but yeah so we can have a taxonomy that
+
+ align:start position:0%
+but yeah so we can have a taxonomy that
+ 
+
+ align:start position:0%
+but yeah so we can have a taxonomy that
+way so taxonomy is one that we're um
+
+ align:start position:0%
+way so taxonomy is one that we're um
+ 
+
+ align:start position:0%
+way so taxonomy is one that we're um
+we're useful for text on I
+
+ align:start position:0%
+we're useful for text on I
+ 
+
+ align:start position:0%
+we're useful for text on I
+can when you're too close it's hard okay
+
+ align:start position:0%
+can when you're too close it's hard okay
+ 
+
+ align:start position:0%
+can when you're too close it's hard okay
+taxonomy um in this definition in
+
+ align:start position:0%
+taxonomy um in this definition in
+ 
+
+ align:start position:0%
+taxonomy um in this definition in
+ontology it's something is
+
+ align:start position:0%
+ontology it's something is
+ 
+
+ align:start position:0%
+ontology it's something is
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+else so um give the example here that
+
+ align:start position:0%
+else so um give the example here that
+ 
+
+ align:start position:0%
+else so um give the example here that
+um that a a minuette is a
+
+ align:start position:0%
+um that a a minuette is a
+ 
+
+ align:start position:0%
+um that a a minuette is a
+dance um for those who know the minuette
+
+ align:start position:0%
+dance um for those who know the minuette
+ 
+
+ align:start position:0%
+dance um for those who know the minuette
+style in the early 18th century the
+
+ align:start position:0%
+style in the early 18th century the
+ 
+
+ align:start position:0%
+style in the early 18th century the
+minuette is a triple time dance which
+
+ align:start position:0%
+minuette is a triple time dance which
+ 
+
+ align:start position:0%
+minuette is a triple time dance which
+means it is a dance um or it is a um or
+
+ align:start position:0%
+means it is a dance um or it is a um or
+ 
+
+ align:start position:0%
+means it is a dance um or it is a um or
+that I don't know what's what's
+
+ align:start position:0%
+that I don't know what's what's
+ 
+
+ align:start position:0%
+that I don't know what's what's
+something else in in music that is
+
+ align:start position:0%
+something else in in music that is
+ 
+
+ align:start position:0%
+something else in in music that is
+something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else yeah aletto is a Tempo aletto is a
+
+ align:start position:0%
+else yeah aletto is a Tempo aletto is a
+ 
+
+ align:start position:0%
+else yeah aletto is a Tempo aletto is a
+Tempo working good I put up this what
+
+ align:start position:0%
+Tempo working good I put up this what
+ 
+
+ align:start position:0%
+Tempo working good I put up this what
+what do you call this one in this
+
+ align:start position:0%
+what do you call this one in this
+ 
+
+ align:start position:0%
+what do you call this one in this
+context Stato Stato now now you'll
+
+ align:start position:0%
+context Stato Stato now now you'll
+ 
+
+ align:start position:0%
+context Stato Stato now now you'll
+understand when when we do Optical music
+
+ align:start position:0%
+understand when when we do Optical music
+ 
+
+ align:start position:0%
+understand when when we do Optical music
+recognition how the context is so
+
+ align:start position:0%
+recognition how the context is so
+ 
+
+ align:start position:0%
+recognition how the context is so
+important otherwise you'd say
+
+ align:start position:0%
+important otherwise you'd say
+ 
+
+ align:start position:0%
+important otherwise you'd say
+augmentation dot right so staccato is a
+
+ align:start position:0%
+augmentation dot right so staccato is a
+ 
+
+ align:start position:0%
+augmentation dot right so staccato is a
+articul articulation good is there any
+
+ align:start position:0%
+articul articulation good is there any
+ 
+
+ align:start position:0%
+articul articulation good is there any
+higher level thing that we might say it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is musicians probably not but when we're
+
+ align:start position:0%
+is musicians probably not but when we're
+ 
+
+ align:start position:0%
+is musicians probably not but when we're
+thinking of representing for computer
+
+ align:start position:0%
+thinking of representing for computer
+ 
+
+ align:start position:0%
+thinking of representing for computer
+yeah John a half note is a note a half
+
+ align:start position:0%
+yeah John a half note is a note a half
+ 
+
+ align:start position:0%
+yeah John a half note is a note a half
+note is a note good half note is a
+
+ align:start position:0%
+note is a note good half note is a
+ 
+
+ align:start position:0%
+note is a note good half note is a
+note great uh I was just going to go
+
+ align:start position:0%
+note great uh I was just going to go
+ 
+
+ align:start position:0%
+note great uh I was just going to go
+back to the articulations also but we'll
+
+ align:start position:0%
+back to the articulations also but we'll
+ 
+
+ align:start position:0%
+back to the articulations also but we'll
+jump to half note is a note in a second
+
+ align:start position:0%
+jump to half note is a note in a second
+ 
+
+ align:start position:0%
+jump to half note is a note in a second
+because that's a pretty fundamental one
+
+ align:start position:0%
+because that's a pretty fundamental one
+ 
+
+ align:start position:0%
+because that's a pretty fundamental one
+um sometimes with with your own
+
+ align:start position:0%
+um sometimes with with your own
+ 
+
+ align:start position:0%
+um sometimes with with your own
+representations you might think of um
+
+ align:start position:0%
+representations you might think of um
+ 
+
+ align:start position:0%
+representations you might think of um
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+instance is Trill an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+articulation who votes yes who votes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no who votes I I have never thought
+
+ align:start position:0%
+no who votes I I have never thought
+ 
+
+ align:start position:0%
+no who votes I I have never thought
+about this and I hope I never have to
+
+ align:start position:0%
+about this and I hope I never have to
+ 
+
+ align:start position:0%
+about this and I hope I never have to
+think about this again in my life okay
+
+ align:start position:0%
+think about this again in my life okay
+ 
+
+ align:start position:0%
+think about this again in my life okay
+good A lot of people call a tra an
+
+ align:start position:0%
+good A lot of people call a tra an
+ 
+
+ align:start position:0%
+good A lot of people call a tra an
+ornament a turn an ornament something
+
+ align:start position:0%
+ornament a turn an ornament something
+ 
+
+ align:start position:0%
+ornament a turn an ornament something
+like that so you might need what is the
+
+ align:start position:0%
+like that so you might need what is the
+ 
+
+ align:start position:0%
+like that so you might need what is the
+class of but but we know that a Trill is
+
+ align:start position:0%
+class of but but we know that a Trill is
+ 
+
+ align:start position:0%
+class of but but we know that a Trill is
+more related to an accent mark than it
+
+ align:start position:0%
+more related to an accent mark than it
+ 
+
+ align:start position:0%
+more related to an accent mark than it
+is to a half note or to um a jaizelle
+
+ align:start position:0%
+is to a half note or to um a jaizelle
+ 
+
+ align:start position:0%
+is to a half note or to um a jaizelle
+right so so we might think of what's
+
+ align:start position:0%
+right so so we might think of what's
+ 
+
+ align:start position:0%
+right so so we might think of what's
+some some kind of slight just like some
+
+ align:start position:0%
+some some kind of slight just like some
+ 
+
+ align:start position:0%
+some some kind of slight just like some
+kind of slightly bigger thing that holds
+
+ align:start position:0%
+kind of slightly bigger thing that holds
+ 
+
+ align:start position:0%
+kind of slightly bigger thing that holds
+um that holds articulations and
+
+ align:start position:0%
+um that holds articulations and
+ 
+
+ align:start position:0%
+um that holds articulations and
+ornaments what might we call that and
+
+ align:start position:0%
+ornaments what might we call that and
+ 
+
+ align:start position:0%
+ornaments what might we call that and
+when we come up with a name for that
+
+ align:start position:0%
+when we come up with a name for that
+ 
+
+ align:start position:0%
+when we come up with a name for that
+yeah Jason first then modifier a
+
+ align:start position:0%
+yeah Jason first then modifier a
+ 
+
+ align:start position:0%
+yeah Jason first then modifier a
+modifier good that's what a lot of
+
+ align:start position:0%
+modifier good that's what a lot of
+ 
+
+ align:start position:0%
+modifier good that's what a lot of
+people um that's believe what it's
+
+ align:start position:0%
+people um that's believe what it's
+ 
+
+ align:start position:0%
+people um that's believe what it's
+called in the um Vex flow notation
+
+ align:start position:0%
+called in the um Vex flow notation
+ 
+
+ align:start position:0%
+called in the um Vex flow notation
+software so somebody yeah I think maybe
+
+ align:start position:0%
+software so somebody yeah I think maybe
+ 
+
+ align:start position:0%
+software so somebody yeah I think maybe
+you could kind of throw under envelope
+
+ align:start position:0%
+you could kind of throw under envelope
+ 
+
+ align:start position:0%
+you could kind of throw under envelope
+if you're thinking about synthesis
+
+ align:start position:0%
+if you're thinking about synthesis
+ 
+
+ align:start position:0%
+if you're thinking about synthesis
+envelope they
+
+ align:start position:0%
+envelope they
+ 
+
+ align:start position:0%
+envelope they
+on are they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+envelopes they might
+
+ align:start position:0%
+envelopes they might
+ 
+
+ align:start position:0%
+envelopes they might
+be envelope envelope Changers envelope
+
+ align:start position:0%
+be envelope envelope Changers envelope
+ 
+
+ align:start position:0%
+be envelope envelope Changers envelope
+there they in themselves the staccato
+
+ align:start position:0%
+there they in themselves the staccato
+ 
+
+ align:start position:0%
+there they in themselves the staccato
+doesn't does the stado have an envelope
+
+ align:start position:0%
+doesn't does the stado have an envelope
+ 
+
+ align:start position:0%
+doesn't does the stado have an envelope
+maybe it does I'm not I don't work in
+
+ align:start position:0%
+maybe it does I'm not I don't work in
+ 
+
+ align:start position:0%
+maybe it does I'm not I don't work in
+this as much but it's like it's just
+
+ align:start position:0%
+this as much but it's like it's just
+ 
+
+ align:start position:0%
+this as much but it's like it's just
+they attack
+
+ align:start position:0%
+they attack
+ 
+
+ align:start position:0%
+they attack
+the the second thing
+
+ align:start position:0%
+the the second thing
+ 
+
+ align:start position:0%
+the the second thing
+sustain uh attack no attack d k s
+
+ align:start position:0%
+sustain uh attack no attack d k s
+ 
+
+ align:start position:0%
+sustain uh attack no attack d k s
+sustain r residen or release yeah not
+
+ align:start position:0%
+sustain r residen or release yeah not
+ 
+
+ align:start position:0%
+sustain r residen or release yeah not
+this class not not what we're talking
+
+ align:start position:0%
+this class not not what we're talking
+ 
+
+ align:start position:0%
+this class not not what we're talking
+about but some people have that
+
+ align:start position:0%
+about but some people have that
+ 
+
+ align:start position:0%
+about but some people have that
+Knowledge from doing electronic music
+
+ align:start position:0%
+Knowledge from doing electronic music
+ 
+
+ align:start position:0%
+Knowledge from doing electronic music
+things yeah so that so this is something
+
+ align:start position:0%
+things yeah so that so this is something
+ 
+
+ align:start position:0%
+things yeah so that so this is something
+that changes how we attack how we Decay
+
+ align:start position:0%
+that changes how we attack how we Decay
+ 
+
+ align:start position:0%
+that changes how we attack how we Decay
+how we sustain how we release right so
+
+ align:start position:0%
+how we sustain how we release right so
+ 
+
+ align:start position:0%
+how we sustain how we release right so
+so yeah maybe that that is a very good
+
+ align:start position:0%
+so yeah maybe that that is a very good
+ 
+
+ align:start position:0%
+so yeah maybe that that is a very good
+term we're going to be coming up with a
+
+ align:start position:0%
+term we're going to be coming up with a
+ 
+
+ align:start position:0%
+term we're going to be coming up with a
+B bunch of these conceptual grouping
+
+ align:start position:0%
+B bunch of these conceptual grouping
+ 
+
+ align:start position:0%
+B bunch of these conceptual grouping
+things because of um of something that
+
+ align:start position:0%
+things because of um of something that
+ 
+
+ align:start position:0%
+things because of um of something that
+you can do with
+
+ align:start position:0%
+you can do with
+ 
+
+ align:start position:0%
+you can do with
+um with uh with things that are in a
+
+ align:start position:0%
+um with uh with things that are in a
+ 
+
+ align:start position:0%
+um with uh with things that are in a
+taxonomic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relationship and I'll write that out and
+
+ align:start position:0%
+relationship and I'll write that out and
+ 
+
+ align:start position:0%
+relationship and I'll write that out and
+and while while you all think what might
+
+ align:start position:0%
+and while while you all think what might
+ 
+
+ align:start position:0%
+and while while you all think what might
+be in those missing letters uh had a had
+
+ align:start position:0%
+be in those missing letters uh had a had
+ 
+
+ align:start position:0%
+be in those missing letters uh had a had
+a question had a comment on the previous
+
+ align:start position:0%
+a question had a comment on the previous
+ 
+
+ align:start position:0%
+a question had a comment on the previous
+one I say like augmentation there there
+
+ align:start position:0%
+one I say like augmentation there there
+ 
+
+ align:start position:0%
+one I say like augmentation there there
+might be an augmentation or in the case
+
+ align:start position:0%
+might be an augmentation or in the case
+ 
+
+ align:start position:0%
+might be an augmentation or in the case
+of a staccato Maybe a negative
+
+ align:start position:0%
+of a staccato Maybe a negative
+ 
+
+ align:start position:0%
+of a staccato Maybe a negative
+augmentation or something yeah a length
+
+ align:start position:0%
+augmentation or something yeah a length
+ 
+
+ align:start position:0%
+augmentation or something yeah a length
+reducer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good what do you think the that in
+
+ align:start position:0%
+good what do you think the that in
+ 
+
+ align:start position:0%
+good what do you think the that in
+computer speak when we say that
+
+ align:start position:0%
+computer speak when we say that
+ 
+
+ align:start position:0%
+computer speak when we say that
+something is something else we can
+
+ align:start position:0%
+something is something else we can
+ 
+
+ align:start position:0%
+something is something else we can
+represent it
+
+ align:start position:0%
+represent it
+ 
+
+ align:start position:0%
+represent it
+with subclass relationships who uh
+
+ align:start position:0%
+with subclass relationships who uh
+ 
+
+ align:start position:0%
+with subclass relationships who uh
+subclasses is something that comes up
+
+ align:start position:0%
+subclasses is something that comes up
+ 
+
+ align:start position:0%
+subclasses is something that comes up
+I'm 99% sure in the prere for this right
+
+ align:start position:0%
+I'm 99% sure in the prere for this right
+ 
+
+ align:start position:0%
+I'm 99% sure in the prere for this right
+you guys deal with classes and subass
+
+ align:start position:0%
+you guys deal with classes and subass
+ 
+
+ align:start position:0%
+you guys deal with classes and subass
+classes and things so um quite often
+
+ align:start position:0%
+classes and things so um quite often
+ 
+
+ align:start position:0%
+classes and things so um quite often
+there there a bunch of builtin sub
+
+ align:start position:0%
+there there a bunch of builtin sub
+ 
+
+ align:start position:0%
+there there a bunch of builtin sub
+classes in um in Python that you have
+
+ align:start position:0%
+classes in um in Python that you have
+ 
+
+ align:start position:0%
+classes in um in Python that you have
+various um a lot of things are uh that
+
+ align:start position:0%
+various um a lot of things are uh that
+ 
+
+ align:start position:0%
+various um a lot of things are uh that
+we think of things are subclasses of
+
+ align:start position:0%
+we think of things are subclasses of
+ 
+
+ align:start position:0%
+we think of things are subclasses of
+number complex numbers oh yeah we all
+
+ align:start position:0%
+number complex numbers oh yeah we all
+ 
+
+ align:start position:0%
+number complex numbers oh yeah we all
+learned uh taxonomies in in our math
+
+ align:start position:0%
+learned uh taxonomies in in our math
+ 
+
+ align:start position:0%
+learned uh taxonomies in in our math
+classes too right complex numbers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+floats ins
+
+ align:start position:0%
+floats ins
+ 
+
+ align:start position:0%
+floats ins
+things like that and quite often for
+
+ align:start position:0%
+things like that and quite often for
+ 
+
+ align:start position:0%
+things like that and quite often for
+different purposes that's why we thought
+
+ align:start position:0%
+different purposes that's why we thought
+ 
+
+ align:start position:0%
+different purposes that's why we thought
+about stakeholders for different
+
+ align:start position:0%
+about stakeholders for different
+ 
+
+ align:start position:0%
+about stakeholders for different
+purposes different um different sort of
+
+ align:start position:0%
+purposes different um different sort of
+ 
+
+ align:start position:0%
+purposes different um different sort of
+taxonomies can be created right I mean
+
+ align:start position:0%
+taxonomies can be created right I mean
+ 
+
+ align:start position:0%
+taxonomies can be created right I mean
+in certain case you could think um well
+
+ align:start position:0%
+in certain case you could think um well
+ 
+
+ align:start position:0%
+in certain case you could think um well
+in integer is a special kind of float
+
+ align:start position:0%
+in integer is a special kind of float
+ 
+
+ align:start position:0%
+in integer is a special kind of float
+that has nothing past the
+
+ align:start position:0%
+that has nothing past the
+ 
+
+ align:start position:0%
+that has nothing past the
+dot and that's a very great mathematical
+
+ align:start position:0%
+dot and that's a very great mathematical
+ 
+
+ align:start position:0%
+dot and that's a very great mathematical
+way of thinking of an integer if you try
+
+ align:start position:0%
+way of thinking of an integer if you try
+ 
+
+ align:start position:0%
+way of thinking of an integer if you try
+to implement it that way in your
+
+ align:start position:0%
+to implement it that way in your
+ 
+
+ align:start position:0%
+to implement it that way in your
+computer
+
+ align:start position:0%
+computer
+ 
+
+ align:start position:0%
+computer
+programs you got some slowness going
+
+ align:start position:0%
+programs you got some slowness going
+ 
+
+ align:start position:0%
+programs you got some slowness going
+because you have a whole bunch of added
+
+ align:start position:0%
+because you have a whole bunch of added
+ 
+
+ align:start position:0%
+because you have a whole bunch of added
+baggage that you wouldn't need or you
+
+ align:start position:0%
+baggage that you wouldn't need or you
+ 
+
+ align:start position:0%
+baggage that you wouldn't need or you
+could think of if you are uh I don't
+
+ align:start position:0%
+could think of if you are uh I don't
+ 
+
+ align:start position:0%
+could think of if you are uh I don't
+know if you're when you're in third
+
+ align:start position:0%
+know if you're when you're in third
+ 
+
+ align:start position:0%
+know if you're when you're in third
+grade fourth grade when's the first time
+
+ align:start position:0%
+grade fourth grade when's the first time
+ 
+
+ align:start position:0%
+grade fourth grade when's the first time
+we learn about decimals we don't know
+
+ align:start position:0%
+we learn about decimals we don't know
+ 
+
+ align:start position:0%
+we learn about decimals we don't know
+the word in but we know that there are
+
+ align:start position:0%
+the word in but we know that there are
+ 
+
+ align:start position:0%
+the word in but we know that there are
+integers we know that there's five and
+
+ align:start position:0%
+integers we know that there's five and
+ 
+
+ align:start position:0%
+integers we know that there's five and
+seven and things and the first time that
+
+ align:start position:0%
+seven and things and the first time that
+ 
+
+ align:start position:0%
+seven and things and the first time that
+you see
+
+ align:start position:0%
+you see
+ 
+
+ align:start position:0%
+you see
+5.2 you would think oh well this seems
+
+ align:start position:0%
+5.2 you would think oh well this seems
+ 
+
+ align:start position:0%
+5.2 you would think oh well this seems
+to be a subass of this because it's a
+
+ align:start position:0%
+to be a subass of this because it's a
+ 
+
+ align:start position:0%
+to be a subass of this because it's a
+different kind of number so depending on
+
+ align:start position:0%
+different kind of number so depending on
+ 
+
+ align:start position:0%
+different kind of number so depending on
+how our ontology how we're
+
+ align:start position:0%
+how our ontology how we're
+ 
+
+ align:start position:0%
+how our ontology how we're
+conceptualizing the world taxonomies
+
+ align:start position:0%
+conceptualizing the world taxonomies
+ 
+
+ align:start position:0%
+conceptualizing the world taxonomies
+could run in two different
+
+ align:start position:0%
+could run in two different
+ 
+
+ align:start position:0%
+could run in two different
+directions so let's um well we'll get
+
+ align:start position:0%
+directions so let's um well we'll get
+ 
+
+ align:start position:0%
+directions so let's um well we'll get
+back to I just want to make sure that we
+
+ align:start position:0%
+back to I just want to make sure that we
+ 
+
+ align:start position:0%
+back to I just want to make sure that we
+can get through this a certain amount of
+
+ align:start position:0%
+can get through this a certain amount of
+ 
+
+ align:start position:0%
+can get through this a certain amount of
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+um then there's something
+
+ align:start position:0%
+um then there's something
+ 
+
+ align:start position:0%
+um then there's something
+called what did I write it down did I
+
+ align:start position:0%
+called what did I write it down did I
+ 
+
+ align:start position:0%
+called what did I write it down did I
+not write it Y no something called a
+
+ align:start position:0%
+not write it Y no something called a
+ 
+
+ align:start position:0%
+not write it Y no something called a
+momy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+aeronomy something that instead of is
+
+ align:start position:0%
+aeronomy something that instead of is
+ 
+
+ align:start position:0%
+aeronomy something that instead of is
+it's something that something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+has um Michael CER is a human most of
+
+ align:start position:0%
+has um Michael CER is a human most of
+ 
+
+ align:start position:0%
+has um Michael CER is a human most of
+the time and therefore he is an animal
+
+ align:start position:0%
+the time and therefore he is an animal
+ 
+
+ align:start position:0%
+the time and therefore he is an animal
+because all humans are animals therefore
+
+ align:start position:0%
+because all humans are animals therefore
+ 
+
+ align:start position:0%
+because all humans are animals therefore
+he is a living thing or that is because
+
+ align:start position:0%
+he is a living thing or that is because
+ 
+
+ align:start position:0%
+he is a living thing or that is because
+that we can think of that as a
+
+ align:start position:0%
+that we can think of that as a
+ 
+
+ align:start position:0%
+that we can think of that as a
+taxonomy uh Michael is an arm he's
+
+ align:start position:0%
+taxonomy uh Michael is an arm he's
+ 
+
+ align:start position:0%
+taxonomy uh Michael is an arm he's
+actually two arms and he's also two legs
+
+ align:start position:0%
+actually two arms and he's also two legs
+ 
+
+ align:start position:0%
+actually two arms and he's also two legs
+no that doesn't make sense there's a
+
+ align:start position:0%
+no that doesn't make sense there's a
+ 
+
+ align:start position:0%
+no that doesn't make sense there's a
+relationship between my arms and my legs
+
+ align:start position:0%
+relationship between my arms and my legs
+ 
+
+ align:start position:0%
+relationship between my arms and my legs
+and me but it's not the is relationship
+
+ align:start position:0%
+and me but it's not the is relationship
+ 
+
+ align:start position:0%
+and me but it's not the is relationship
+or at least not the way I conceive of it
+
+ align:start position:0%
+or at least not the way I conceive of it
+ 
+
+ align:start position:0%
+or at least not the way I conceive of it
+but it's something that I
+
+ align:start position:0%
+but it's something that I
+ 
+
+ align:start position:0%
+but it's something that I
+have so what is something uh oh sorry I
+
+ align:start position:0%
+have so what is something uh oh sorry I
+ 
+
+ align:start position:0%
+have so what is something uh oh sorry I
+meant to leave up John's great um half
+
+ align:start position:0%
+meant to leave up John's great um half
+ 
+
+ align:start position:0%
+meant to leave up John's great um half
+note is a note thing so a half note is a
+
+ align:start position:0%
+note is a note thing so a half note is a
+ 
+
+ align:start position:0%
+note is a note thing so a half note is a
+note what is something that a half note
+
+ align:start position:0%
+note what is something that a half note
+ 
+
+ align:start position:0%
+note what is something that a half note
+has that it is
+
+ align:start position:0%
+has that it is
+ 
+
+ align:start position:0%
+has that it is
+not uh Jason first almond almond it has
+
+ align:start position:0%
+not uh Jason first almond almond it has
+ 
+
+ align:start position:0%
+not uh Jason first almond almond it has
+almond which we used for the type right
+
+ align:start position:0%
+almond which we used for the type right
+ 
+
+ align:start position:0%
+almond which we used for the type right
+that's the Almond great I'm going to I
+
+ align:start position:0%
+that's the Almond great I'm going to I
+ 
+
+ align:start position:0%
+that's the Almond great I'm going to I
+already have chives as a vocabulary
+
+ align:start position:0%
+already have chives as a vocabulary
+ 
+
+ align:start position:0%
+already have chives as a vocabulary
+later now we have almonds so it has a
+
+ align:start position:0%
+later now we have almonds so it has a
+ 
+
+ align:start position:0%
+later now we have almonds so it has a
+particular type great what else does a
+
+ align:start position:0%
+particular type great what else does a
+ 
+
+ align:start position:0%
+particular type great what else does a
+half note
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have duration duration good might have a
+
+ align:start position:0%
+have duration duration good might have a
+ 
+
+ align:start position:0%
+have duration duration good might have a
+duration um what does an eighth note
+
+ align:start position:0%
+duration um what does an eighth note
+ 
+
+ align:start position:0%
+duration um what does an eighth note
+have that a half note
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lacks flag
+
+ align:start position:0%
+lacks flag
+ 
+
+ align:start position:0%
+lacks flag
+flag call that a
+
+ align:start position:0%
+flag call that a
+ 
+
+ align:start position:0%
+flag call that a
+flag and what might two eighth notes
+
+ align:start position:0%
+flag and what might two eighth notes
+ 
+
+ align:start position:0%
+flag and what might two eighth notes
+have that um one eighth note doesn't and
+
+ align:start position:0%
+have that um one eighth note doesn't and
+ 
+
+ align:start position:0%
+have that um one eighth note doesn't and
+yeah uh bar or what do we call that
+
+ align:start position:0%
+yeah uh bar or what do we call that
+ 
+
+ align:start position:0%
+yeah uh bar or what do we call that
+thing beam good good I'm gonna the
+
+ align:start position:0%
+thing beam good good I'm gonna the
+ 
+
+ align:start position:0%
+thing beam good good I'm gonna the
+center of the room has been really
+
+ align:start position:0%
+center of the room has been really
+ 
+
+ align:start position:0%
+center of the room has been really
+active I'm going to focus over here and
+
+ align:start position:0%
+active I'm going to focus over here and
+ 
+
+ align:start position:0%
+active I'm going to focus over here and
+over here for a little bit for the next
+
+ align:start position:0%
+over here for a little bit for the next
+ 
+
+ align:start position:0%
+over here for a little bit for the next
+couple answers good so it has a beam so
+
+ align:start position:0%
+couple answers good so it has a beam so
+ 
+
+ align:start position:0%
+couple answers good so it has a beam so
+we can think of this um and here's where
+
+ align:start position:0%
+we can think of this um and here's where
+ 
+
+ align:start position:0%
+we can think of this um and here's where
+your conceptions go uh eighth note has a
+
+ align:start position:0%
+your conceptions go uh eighth note has a
+ 
+
+ align:start position:0%
+your conceptions go uh eighth note has a
+beam um 16th Note have a beam or 16th
+
+ align:start position:0%
+beam um 16th Note have a beam or 16th
+ 
+
+ align:start position:0%
+beam um 16th Note have a beam or 16th
+notes have a beam yeah do they have do
+
+ align:start position:0%
+notes have a beam yeah do they have do
+ 
+
+ align:start position:0%
+notes have a beam yeah do they have do
+16th notes have a beam that has two
+
+ align:start position:0%
+16th notes have a beam that has two
+ 
+
+ align:start position:0%
+16th notes have a beam that has two
+lines in it or do 16th notes have two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beams you can imagine you're going to
+
+ align:start position:0%
+beams you can imagine you're going to
+ 
+
+ align:start position:0%
+beams you can imagine you're going to
+encode this very
+
+ align:start position:0%
+encode this very
+ 
+
+ align:start position:0%
+encode this very
+differently if you encode number of
+
+ align:start position:0%
+differently if you encode number of
+ 
+
+ align:start position:0%
+differently if you encode number of
+things and some eighth notes don't have
+
+ align:start position:0%
+things and some eighth notes don't have
+ 
+
+ align:start position:0%
+things and some eighth notes don't have
+beams they have Flags instead um but
+
+ align:start position:0%
+beams they have Flags instead um but
+ 
+
+ align:start position:0%
+beams they have Flags instead um but
+they have the potential for gaining a
+
+ align:start position:0%
+they have the potential for gaining a
+ 
+
+ align:start position:0%
+they have the potential for gaining a
+beam perhaps if we think of um you know
+
+ align:start position:0%
+beam perhaps if we think of um you know
+ 
+
+ align:start position:0%
+beam perhaps if we think of um you know
+Mommy I always want to grow up and be a
+
+ align:start position:0%
+Mommy I always want to grow up and be a
+ 
+
+ align:start position:0%
+Mommy I always want to grow up and be a
+beamed uh eighth note not not a not a
+
+ align:start position:0%
+beamed uh eighth note not not a not a
+ 
+
+ align:start position:0%
+beamed uh eighth note not not a not a
+flaged eighth note so you might you
+
+ align:start position:0%
+flaged eighth note so you might you
+ 
+
+ align:start position:0%
+flaged eighth note so you might you
+might say well we're not going to have
+
+ align:start position:0%
+might say well we're not going to have
+ 
+
+ align:start position:0%
+might say well we're not going to have
+um certain eighth notes that have no uh
+
+ align:start position:0%
+um certain eighth notes that have no uh
+ 
+
+ align:start position:0%
+um certain eighth notes that have no uh
+now now we get to computer speak rather
+
+ align:start position:0%
+now now we get to computer speak rather
+ 
+
+ align:start position:0%
+now now we get to computer speak rather
+than philosophy speak that have no
+
+ align:start position:0%
+than philosophy speak that have no
+ 
+
+ align:start position:0%
+than philosophy speak that have no
+attribute that where a beam could go
+
+ align:start position:0%
+attribute that where a beam could go
+ 
+
+ align:start position:0%
+attribute that where a beam could go
+because that's just silly I don't want
+
+ align:start position:0%
+because that's just silly I don't want
+ 
+
+ align:start position:0%
+because that's just silly I don't want
+to have unbe eighth notes and beamed
+
+ align:start position:0%
+to have unbe eighth notes and beamed
+ 
+
+ align:start position:0%
+to have unbe eighth notes and beamed
+eighth notes maybe as two different
+
+ align:start position:0%
+eighth notes maybe as two different
+ 
+
+ align:start position:0%
+eighth notes maybe as two different
+concepts as two different objects maybe
+
+ align:start position:0%
+concepts as two different objects maybe
+ 
+
+ align:start position:0%
+concepts as two different objects maybe
+you say well I'll have one type of
+
+ align:start position:0%
+you say well I'll have one type of
+ 
+
+ align:start position:0%
+you say well I'll have one type of
+eighth note and it has either has or
+
+ align:start position:0%
+eighth note and it has either has or
+ 
+
+ align:start position:0%
+eighth note and it has either has or
+doesn't have
+
+ align:start position:0%
+doesn't have
+ 
+
+ align:start position:0%
+doesn't have
+beams then in your representation you
+
+ align:start position:0%
+beams then in your representation you
+ 
+
+ align:start position:0%
+beams then in your representation you
+might be asking yourself oops leave that
+
+ align:start position:0%
+might be asking yourself oops leave that
+ 
+
+ align:start position:0%
+might be asking yourself oops leave that
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+
+ align:start position:0%
+up you might be asking yourself does it
+ 
+
+ align:start position:0%
+up you might be asking yourself does it
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+
+ align:start position:0%
+make sense to say that eighth notes 16th
+ 
+
+ align:start position:0%
+make sense to say that eighth notes 16th
+notes 32nd notes 64th notes whatever go
+
+ align:start position:0%
+notes 32nd notes 64th notes whatever go
+ 
+
+ align:start position:0%
+notes 32nd notes 64th notes whatever go
+on to the highest power of two you can
+
+ align:start position:0%
+on to the highest power of two you can
+ 
+
+ align:start position:0%
+on to the highest power of two you can
+think of have beams but quarter notes
+
+ align:start position:0%
+think of have beams but quarter notes
+ 
+
+ align:start position:0%
+think of have beams but quarter notes
+and half notes and whole notes
+
+ align:start position:0%
+and half notes and whole notes
+ 
+
+ align:start position:0%
+and half notes and whole notes
+don't or do we say that whole notes
+
+ align:start position:0%
+don't or do we say that whole notes
+ 
+
+ align:start position:0%
+don't or do we say that whole notes
+notes have the potential to have beams
+
+ align:start position:0%
+notes have the potential to have beams
+ 
+
+ align:start position:0%
+notes have the potential to have beams
+but we you better not put any
+
+ align:start position:0%
+but we you better not put any
+ 
+
+ align:start position:0%
+but we you better not put any
+on I don't know there isn't a correct
+
+ align:start position:0%
+on I don't know there isn't a correct
+ 
+
+ align:start position:0%
+on I don't know there isn't a correct
+answer for that and so sometimes what we
+
+ align:start position:0%
+answer for that and so sometimes what we
+ 
+
+ align:start position:0%
+answer for that and so sometimes what we
+conceive of we I cannot conceive of a
+
+ align:start position:0%
+conceive of we I cannot conceive of a
+ 
+
+ align:start position:0%
+conceive of we I cannot conceive of a
+whole note with Beams I I can conceive
+
+ align:start position:0%
+whole note with Beams I I can conceive
+ 
+
+ align:start position:0%
+whole note with Beams I I can conceive
+of a half note with beams but um you
+
+ align:start position:0%
+of a half note with beams but um you
+ 
+
+ align:start position:0%
+of a half note with beams but um you
+know I can think of it I don't know what
+
+ align:start position:0%
+know I can think of it I don't know what
+ 
+
+ align:start position:0%
+know I can think of it I don't know what
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+means actually it means I tremolos D but
+
+ align:start position:0%
+means actually it means I tremolos D but
+ 
+
+ align:start position:0%
+means actually it means I tremolos D but
+but for but that's something else that's
+
+ align:start position:0%
+but for but that's something else that's
+ 
+
+ align:start position:0%
+but for but that's something else that's
+something maybe that's playing visually
+
+ align:start position:0%
+something maybe that's playing visually
+ 
+
+ align:start position:0%
+something maybe that's playing visually
+that looks just like a beam but means
+
+ align:start position:0%
+that looks just like a beam but means
+ 
+
+ align:start position:0%
+that looks just like a beam but means
+something or maybe it's
+
+ align:start position:0%
+something or maybe it's
+ 
+
+ align:start position:0%
+something or maybe it's
+not um so some of the things that come
+
+ align:start position:0%
+not um so some of the things that come
+ 
+
+ align:start position:0%
+not um so some of the things that come
+up in music musical forms give so a
+
+ align:start position:0%
+up in music musical forms give so a
+ 
+
+ align:start position:0%
+up in music musical forms give so a
+Sonata is a type of musical form it's
+
+ align:start position:0%
+Sonata is a type of musical form it's
+ 
+
+ align:start position:0%
+Sonata is a type of musical form it's
+used quite often in the 18th and 19th
+
+ align:start position:0%
+used quite often in the 18th and 19th
+ 
+
+ align:start position:0%
+used quite often in the 18th and 19th
+century um and it's a musical form that
+
+ align:start position:0%
+century um and it's a musical form that
+ 
+
+ align:start position:0%
+century um and it's a musical form that
+has an exposition the thing close to the
+
+ align:start position:0%
+has an exposition the thing close to the
+ 
+
+ align:start position:0%
+has an exposition the thing close to the
+beginning and the exposition has a first
+
+ align:start position:0%
+beginning and the exposition has a first
+ 
+
+ align:start position:0%
+beginning and the exposition has a first
+theme group and a second theme group and
+
+ align:start position:0%
+theme group and a second theme group and
+ 
+
+ align:start position:0%
+theme group and a second theme group and
+the First theme group has a phrase and
+
+ align:start position:0%
+the First theme group has a phrase and
+ 
+
+ align:start position:0%
+the First theme group has a phrase and
+that phrase
+
+ align:start position:0%
+that phrase
+ 
+
+ align:start position:0%
+that phrase
+has measures and those measures have
+
+ align:start position:0%
+has measures and those measures have
+ 
+
+ align:start position:0%
+has measures and those measures have
+notes perhaps is one way of conceiving
+
+ align:start position:0%
+notes perhaps is one way of conceiving
+ 
+
+ align:start position:0%
+notes perhaps is one way of conceiving
+it it would make much less sense to say
+
+ align:start position:0%
+it it would make much less sense to say
+ 
+
+ align:start position:0%
+it it would make much less sense to say
+um well it has a phrase and a phrase is
+
+ align:start position:0%
+um well it has a phrase and a phrase is
+ 
+
+ align:start position:0%
+um well it has a phrase and a phrase is
+a measure and a measure is a
+
+ align:start position:0%
+a measure and a measure is a
+ 
+
+ align:start position:0%
+a measure and a measure is a
+note right
+
+ align:start position:0%
+note right
+ 
+
+ align:start position:0%
+note right
+so this is going to be part of your um
+
+ align:start position:0%
+so this is going to be part of your um
+ 
+
+ align:start position:0%
+so this is going to be part of your um
+the big part of problem set to in fact
+
+ align:start position:0%
+the big part of problem set to in fact
+ 
+
+ align:start position:0%
+the big part of problem set to in fact
+uh we're going to skip um some other uh
+
+ align:start position:0%
+uh we're going to skip um some other uh
+ 
+
+ align:start position:0%
+uh we're going to skip um some other uh
+things we're just going to do a little
+
+ align:start position:0%
+things we're just going to do a little
+ 
+
+ align:start position:0%
+things we're just going to do a little
+bit of the the cook discussion um and
+
+ align:start position:0%
+bit of the the cook discussion um and
+ 
+
+ align:start position:0%
+bit of the the cook discussion um and
+then um then I want to give you time to
+
+ align:start position:0%
+then um then I want to give you time to
+ 
+
+ align:start position:0%
+then um then I want to give you time to
+start thinking about problem set two uh
+
+ align:start position:0%
+start thinking about problem set two uh
+ 
+
+ align:start position:0%
+start thinking about problem set two uh
+in problem set two you're going to think
+
+ align:start position:0%
+in problem set two you're going to think
+ 
+
+ align:start position:0%
+in problem set two you're going to think
+of a type of music that is not common
+
+ align:start position:0%
+of a type of music that is not common
+ 
+
+ align:start position:0%
+of a type of music that is not common
+western music notation might not even
+
+ align:start position:0%
+western music notation might not even
+ 
+
+ align:start position:0%
+western music notation might not even
+have to be a type of music some people
+
+ align:start position:0%
+have to be a type of music some people
+ 
+
+ align:start position:0%
+have to be a type of music some people
+have done um have done things related to
+
+ align:start position:0%
+have done um have done things related to
+ 
+
+ align:start position:0%
+have done um have done things related to
+music such as there was a chess playing
+
+ align:start position:0%
+music such as there was a chess playing
+ 
+
+ align:start position:0%
+music such as there was a chess playing
+music generating system in the 1960s
+
+ align:start position:0%
+music generating system in the 1960s
+ 
+
+ align:start position:0%
+music generating system in the 1960s
+that somebody uh decided to work on or
+
+ align:start position:0%
+that somebody uh decided to work on or
+ 
+
+ align:start position:0%
+that somebody uh decided to work on or
+it might be the the structure of a
+
+ align:start position:0%
+it might be the the structure of a
+ 
+
+ align:start position:0%
+it might be the the structure of a
+concert or something like that and I
+
+ align:start position:0%
+concert or something like that and I
+ 
+
+ align:start position:0%
+concert or something like that and I
+want you to come up with the kinds of
+
+ align:start position:0%
+want you to come up with the kinds of
+ 
+
+ align:start position:0%
+want you to come up with the kinds of
+what's the taxonomy in the ontology in
+
+ align:start position:0%
+what's the taxonomy in the ontology in
+ 
+
+ align:start position:0%
+what's the taxonomy in the ontology in
+the in the conception of the system how
+
+ align:start position:0%
+the in the conception of the system how
+ 
+
+ align:start position:0%
+the in the conception of the system how
+does this work and what is what are
+
+ align:start position:0%
+does this work and what is what are
+ 
+
+ align:start position:0%
+does this work and what is what are
+these relationships what's the meton uh
+
+ align:start position:0%
+these relationships what's the meton uh
+ 
+
+ align:start position:0%
+these relationships what's the meton uh
+morony and the taxonomy there over the
+
+ align:start position:0%
+morony and the taxonomy there over the
+ 
+
+ align:start position:0%
+morony and the taxonomy there over the
+weekend we're going to be going
+
+ align:start position:0%
+weekend we're going to be going
+ 
+
+ align:start position:0%
+weekend we're going to be going
+through some of the past notational
+
+ align:start position:0%
+through some of the past notational
+ 
+
+ align:start position:0%
+through some of the past notational
+formats for
+
+ align:start position:0%
+formats for
+ 
+
+ align:start position:0%
+formats for
+um western music notation for common
+
+ align:start position:0%
+um western music notation for common
+ 
+
+ align:start position:0%
+um western music notation for common
+western music notation some of the
+
+ align:start position:0%
+western music notation some of the
+ 
+
+ align:start position:0%
+western music notation some of the
+representations the ontologies the file
+
+ align:start position:0%
+representations the ontologies the file
+ 
+
+ align:start position:0%
+representations the ontologies the file
+formats that um that have sort of come
+
+ align:start position:0%
+formats that um that have sort of come
+ 
+
+ align:start position:0%
+formats that um that have sort of come
+up over time um one of the things a lot
+
+ align:start position:0%
+up over time um one of the things a lot
+ 
+
+ align:start position:0%
+up over time um one of the things a lot
+of the pieces the discussions that
+
+ align:start position:0%
+of the pieces the discussions that
+ 
+
+ align:start position:0%
+of the pieces the discussions that
+people were talking about have some
+
+ align:start position:0%
+people were talking about have some
+ 
+
+ align:start position:0%
+people were talking about have some
+connection to Common western music
+
+ align:start position:0%
+connection to Common western music
+ 
+
+ align:start position:0%
+connection to Common western music
+notation things I was hearing but are
+
+ align:start position:0%
+notation things I was hearing but are
+ 
+
+ align:start position:0%
+notation things I was hearing but are
+not themselves common western music
+
+ align:start position:0%
+not themselves common western music
+ 
+
+ align:start position:0%
+not themselves common western music
+notation right they they might have you
+
+ align:start position:0%
+notation right they they might have you
+ 
+
+ align:start position:0%
+notation right they they might have you
+know oh yeah well well the rhythm is the
+
+ align:start position:0%
+know oh yeah well well the rhythm is the
+ 
+
+ align:start position:0%
+know oh yeah well well the rhythm is the
+same as you know but as common western
+
+ align:start position:0%
+same as you know but as common western
+ 
+
+ align:start position:0%
+same as you know but as common western
+music notation but something else
+
+ align:start position:0%
+music notation but something else
+ 
+
+ align:start position:0%
+music notation but something else
+anything that you think um is just part
+
+ align:start position:0%
+anything that you think um is just part
+ 
+
+ align:start position:0%
+anything that you think um is just part
+of common western music notation assume
+
+ align:start position:0%
+of common western music notation assume
+ 
+
+ align:start position:0%
+of common western music notation assume
+that part of the um of the rep of the
+
+ align:start position:0%
+that part of the um of the rep of the
+ 
+
+ align:start position:0%
+that part of the um of the rep of the
+ontology of the file format has already
+
+ align:start position:0%
+ontology of the file format has already
+ 
+
+ align:start position:0%
+ontology of the file format has already
+been solved so you know what saying if
+
+ align:start position:0%
+been solved so you know what saying if
+ 
+
+ align:start position:0%
+been solved so you know what saying if
+it's sort of like you're doing something
+
+ align:start position:0%
+it's sort of like you're doing something
+ 
+
+ align:start position:0%
+it's sort of like you're doing something
+with oh this is a dance Groove and
+
+ align:start position:0%
+with oh this is a dance Groove and
+ 
+
+ align:start position:0%
+with oh this is a dance Groove and
+here's and the Baseline is stored this
+
+ align:start position:0%
+here's and the Baseline is stored this
+ 
+
+ align:start position:0%
+here's and the Baseline is stored this
+way it's it's represented in this way
+
+ align:start position:0%
+way it's it's represented in this way
+ 
+
+ align:start position:0%
+way it's it's represented in this way
+and the notes of the Baseline are just
+
+ align:start position:0%
+and the notes of the Baseline are just
+ 
+
+ align:start position:0%
+and the notes of the Baseline are just
+put stored in you know C CW
+
+ align:start position:0%
+put stored in you know C CW
+ 
+
+ align:start position:0%
+put stored in you know C CW
+um MN or something and or stored somehow
+
+ align:start position:0%
+um MN or something and or stored somehow
+ 
+
+ align:start position:0%
+um MN or something and or stored somehow
+stored in music XML stored something
+
+ align:start position:0%
+stored in music XML stored something
+ 
+
+ align:start position:0%
+stored in music XML stored something
+you'll you'll get some formats and but
+
+ align:start position:0%
+you'll you'll get some formats and but
+ 
+
+ align:start position:0%
+you'll you'll get some formats and but
+don't uh the only the only way that
+
+ align:start position:0%
+don't uh the only the only way that
+ 
+
+ align:start position:0%
+don't uh the only the only way that
+people have uh Gone really wrong on on
+
+ align:start position:0%
+people have uh Gone really wrong on on
+ 
+
+ align:start position:0%
+people have uh Gone really wrong on on
+similar assignments to this in the past
+
+ align:start position:0%
+similar assignments to this in the past
+ 
+
+ align:start position:0%
+similar assignments to this in the past
+is spending too much time thinking about
+
+ align:start position:0%
+is spending too much time thinking about
+ 
+
+ align:start position:0%
+is spending too much time thinking about
+the things that have already been solved
+
+ align:start position:0%
+the things that have already been solved
+ 
+
+ align:start position:0%
+the things that have already been solved
+if you need to your format needs to
+
+ align:start position:0%
+if you need to your format needs to
+ 
+
+ align:start position:0%
+if you need to your format needs to
+encode in images at certain points just
+
+ align:start position:0%
+encode in images at certain points just
+ 
+
+ align:start position:0%
+encode in images at certain points just
+say the jpegs don't invent your entire
+
+ align:start position:0%
+say the jpegs don't invent your entire
+ 
+
+ align:start position:0%
+say the jpegs don't invent your entire
+New Image format don't invent a new you
+
+ align:start position:0%
+New Image format don't invent a new you
+ 
+
+ align:start position:0%
+New Image format don't invent a new you
+know things things that you already know
+
+ align:start position:0%
+know things things that you already know
+ 
+
+ align:start position:0%
+know things things that you already know
+that's have spend your time on
+
+ align:start position:0%
+that's have spend your time on
+ 
+
+ align:start position:0%
+that's have spend your time on
+conceptualizing what hasn't been
+
+ align:start position:0%
+conceptualizing what hasn't been
+ 
+
+ align:start position:0%
+conceptualizing what hasn't been
+conceived
+
+ align:start position:0%
+conceived
+ 
+
+ align:start position:0%
+conceived
+before um I just want to uh point out a
+
+ align:start position:0%
+before um I just want to uh point out a
+ 
+
+ align:start position:0%
+before um I just want to uh point out a
+little bit oh sorry that is completely
+
+ align:start position:0%
+little bit oh sorry that is completely
+ 
+
+ align:start position:0%
+little bit oh sorry that is completely
+illegible always feel free to tell me
+
+ align:start position:0%
+illegible always feel free to tell me
+ 
+
+ align:start position:0%
+illegible always feel free to tell me
+when something is completely illegible
+
+ align:start position:0%
+when something is completely illegible
+ 
+
+ align:start position:0%
+when something is completely illegible
+is that there we go now it's not um
+
+ align:start position:0%
+is that there we go now it's not um
+ 
+
+ align:start position:0%
+is that there we go now it's not um
+we're going to go through this more
+
+ align:start position:0%
+we're going to go through this more
+ 
+
+ align:start position:0%
+we're going to go through this more
+slowly uh I think I I can um can't
+
+ align:start position:0%
+slowly uh I think I I can um can't
+ 
+
+ align:start position:0%
+slowly uh I think I I can um can't
+remember over the weekend or on
+
+ align:start position:0%
+remember over the weekend or on
+ 
+
+ align:start position:0%
+remember over the weekend or on
+Wednesday um I should have my syllabus
+
+ align:start position:0%
+Wednesday um I should have my syllabus
+ 
+
+ align:start position:0%
+Wednesday um I should have my syllabus
+in my head but I write it down so I
+
+ align:start position:0%
+in my head but I write it down so I
+ 
+
+ align:start position:0%
+in my head but I write it down so I
+don't have to memorize it um but we're
+
+ align:start position:0%
+don't have to memorize it um but we're
+ 
+
+ align:start position:0%
+don't have to memorize it um but we're
+going to be going through something
+
+ align:start position:0%
+going to be going through something
+ 
+
+ align:start position:0%
+going to be going through something
+called the Rosetta Stone of digital
+
+ align:start position:0%
+called the Rosetta Stone of digital
+ 
+
+ align:start position:0%
+called the Rosetta Stone of digital
+music representations uh by a really
+
+ align:start position:0%
+music representations uh by a really
+ 
+
+ align:start position:0%
+music representations uh by a really
+really smart guy uh Craig sap who
+
+ align:start position:0%
+really smart guy uh Craig sap who
+ 
+
+ align:start position:0%
+really smart guy uh Craig sap who
+realized um anybody seen uh know what
+
+ align:start position:0%
+realized um anybody seen uh know what
+ 
+
+ align:start position:0%
+realized um anybody seen uh know what
+the Rosetta Stone is it was the same
+
+ align:start position:0%
+the Rosetta Stone is it was the same
+ 
+
+ align:start position:0%
+the Rosetta Stone is it was the same
+text written in three different
+
+ align:start position:0%
+text written in three different
+ 
+
+ align:start position:0%
+text written in three different
+languages uh in especially in Greek and
+
+ align:start position:0%
+languages uh in especially in Greek and
+ 
+
+ align:start position:0%
+languages uh in especially in Greek and
+in ancient um
+
+ align:start position:0%
+in ancient um
+ 
+
+ align:start position:0%
+in ancient um
+hieroglyphics that allowed hieroglyphics
+
+ align:start position:0%
+hieroglyphics that allowed hieroglyphics
+ 
+
+ align:start position:0%
+hieroglyphics that allowed hieroglyphics
+to finally be um finally be decoded
+
+ align:start position:0%
+to finally be um finally be decoded
+ 
+
+ align:start position:0%
+to finally be um finally be decoded
+Craig saps Rosetta Stone takes the exact
+
+ align:start position:0%
+Craig saps Rosetta Stone takes the exact
+ 
+
+ align:start position:0%
+Craig saps Rosetta Stone takes the exact
+same little
+
+ align:start position:0%
+same little
+ 
+
+ align:start position:0%
+same little
+Melody I can go
+
+ align:start position:0%
+Melody I can go
+ 
+
+ align:start position:0%
+Melody I can go
+over what is it
+
+ align:start position:0%
+over what is it
+ 
+
+ align:start position:0%
+over what is it
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um my rhythm was pretty bad on that
+
+ align:start position:0%
+um my rhythm was pretty bad on that
+ 
+
+ align:start position:0%
+um my rhythm was pretty bad on that
+should um but that exact same Melody and
+
+ align:start position:0%
+should um but that exact same Melody and
+ 
+
+ align:start position:0%
+should um but that exact same Melody and
+shows
+
+ align:start position:0%
+shows
+ 
+
+ align:start position:0%
+shows
+how that Melody is encoded in I think he
+
+ align:start position:0%
+how that Melody is encoded in I think he
+ 
+
+ align:start position:0%
+how that Melody is encoded in I think he
+has like 32 on his website I have edited
+
+ align:start position:0%
+has like 32 on his website I have edited
+ 
+
+ align:start position:0%
+has like 32 on his website I have edited
+it down to about eight but so that you
+
+ align:start position:0%
+it down to about eight but so that you
+ 
+
+ align:start position:0%
+it down to about eight but so that you
+can see what different representational
+
+ align:start position:0%
+can see what different representational
+ 
+
+ align:start position:0%
+can see what different representational
+choices people have made and what kinds
+
+ align:start position:0%
+choices people have made and what kinds
+ 
+
+ align:start position:0%
+choices people have made and what kinds
+of ontologies they make um for instance
+
+ align:start position:0%
+of ontologies they make um for instance
+ 
+
+ align:start position:0%
+of ontologies they make um for instance
+I remember in this case
+
+ align:start position:0%
+I remember in this case
+ 
+
+ align:start position:0%
+I remember in this case
+beams are high L things they are
+
+ align:start position:0%
+beams are high L things they are
+ 
+
+ align:start position:0%
+beams are high L things they are
+represented by these braces and so
+
+ align:start position:0%
+represented by these braces and so
+ 
+
+ align:start position:0%
+represented by these braces and so
+therefore they they enclose things beams
+
+ align:start position:0%
+therefore they they enclose things beams
+ 
+
+ align:start position:0%
+therefore they they enclose things beams
+in this case seem to have um a morony
+
+ align:start position:0%
+in this case seem to have um a morony
+ 
+
+ align:start position:0%
+in this case seem to have um a morony
+that beams have
+
+ align:start position:0%
+that beams have
+ 
+
+ align:start position:0%
+that beams have
+notes not notes have beams so we'll try
+
+ align:start position:0%
+notes not notes have beams so we'll try
+ 
+
+ align:start position:0%
+notes not notes have beams so we'll try
+to see some of these things it's another
+
+ align:start position:0%
+to see some of these things it's another
+ 
+
+ align:start position:0%
+to see some of these things it's another
+format uh called ABC one of the ones
+
+ align:start position:0%
+format uh called ABC one of the ones
+ 
+
+ align:start position:0%
+format uh called ABC one of the ones
+still in use even though uh quite a bit
+
+ align:start position:0%
+still in use even though uh quite a bit
+ 
+
+ align:start position:0%
+still in use even though uh quite a bit
+old because it's very very simple we'll
+
+ align:start position:0%
+old because it's very very simple we'll
+ 
+
+ align:start position:0%
+old because it's very very simple we'll
+be looking at these in more detail
+
+ align:start position:0%
+be looking at these in more detail
+ 
+
+ align:start position:0%
+be looking at these in more detail
+various formats that at some point were
+
+ align:start position:0%
+various formats that at some point were
+ 
+
+ align:start position:0%
+various formats that at some point were
+very big B um but have mostly faded this
+
+ align:start position:0%
+very big B um but have mostly faded this
+ 
+
+ align:start position:0%
+very big B um but have mostly faded this
+is one that we saw once before M's data
+
+ align:start position:0%
+is one that we saw once before M's data
+ 
+
+ align:start position:0%
+is one that we saw once before M's data
+where um the Q was quarter and the eight
+
+ align:start position:0%
+where um the Q was quarter and the eight
+ 
+
+ align:start position:0%
+where um the Q was quarter and the eight
+um was a certain number of durations and
+
+ align:start position:0%
+um was a certain number of durations and
+ 
+
+ align:start position:0%
+um was a certain number of durations and
+F5 do you remember that from class or
+
+ align:start position:0%
+F5 do you remember that from class or
+ 
+
+ align:start position:0%
+F5 do you remember that from class or
+two ago yep and we'll see over
+
+ align:start position:0%
+two ago yep and we'll see over
+ 
+
+ align:start position:0%
+two ago yep and we'll see over
+time how the formats have gotten to be a
+
+ align:start position:0%
+time how the formats have gotten to be a
+ 
+
+ align:start position:0%
+time how the formats have gotten to be a
+little bit
+
+ align:start position:0%
+little bit
+ 
+
+ align:start position:0%
+little bit
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+complex here we
+
+ align:start position:0%
+complex here we
+ 
+
+ align:start position:0%
+complex here we
+go this is music XML which we're going
+
+ align:start position:0%
+go this is music XML which we're going
+ 
+
+ align:start position:0%
+go this is music XML which we're going
+to be talking about quite a bit of
+
+ align:start position:0%
+to be talking about quite a bit of
+ 
+
+ align:start position:0%
+to be talking about quite a bit of
+course uh invented by Alum of MIT
+
+ align:start position:0%
+course uh invented by Alum of MIT
+ 
+
+ align:start position:0%
+course uh invented by Alum of MIT
+Michael good and um and one of the great
+
+ align:start position:0%
+Michael good and um and one of the great
+ 
+
+ align:start position:0%
+Michael good and um and one of the great
+formats for representing music notation
+
+ align:start position:0%
+formats for representing music notation
+ 
+
+ align:start position:0%
+formats for representing music notation
+uh the first one with enharmonics that
+
+ align:start position:0%
+uh the first one with enharmonics that
+ 
+
+ align:start position:0%
+uh the first one with enharmonics that
+just was taken and used by almost
+
+ align:start position:0%
+just was taken and used by almost
+ 
+
+ align:start position:0%
+just was taken and used by almost
+everybody's about 20 22 years old a lot
+
+ align:start position:0%
+everybody's about 20 22 years old a lot
+ 
+
+ align:start position:0%
+everybody's about 20 22 years old a lot
+of us thought this is the final format
+
+ align:start position:0%
+of us thought this is the final format
+ 
+
+ align:start position:0%
+of us thought this is the final format
+this is the representation that really
+
+ align:start position:0%
+this is the representation that really
+ 
+
+ align:start position:0%
+this is the representation that really
+really works even if there's some weird
+
+ align:start position:0%
+really works even if there's some weird
+ 
+
+ align:start position:0%
+really works even if there's some weird
+quirks we use it forever and then a
+
+ align:start position:0%
+quirks we use it forever and then a
+ 
+
+ align:start position:0%
+quirks we use it forever and then a
+terrible thing started happening to
+
+ align:start position:0%
+terrible thing started happening to
+ 
+
+ align:start position:0%
+terrible thing started happening to
+music a great and terrible thing started
+
+ align:start position:0%
+music a great and terrible thing started
+ 
+
+ align:start position:0%
+music a great and terrible thing started
+happening to music about uh 10 years ago
+
+ align:start position:0%
+happening to music about uh 10 years ago
+ 
+
+ align:start position:0%
+happening to music about uh 10 years ago
+12 almost 15 years ago but um we started
+
+ align:start position:0%
+12 almost 15 years ago but um we started
+ 
+
+ align:start position:0%
+12 almost 15 years ago but um we started
+looking at music sheet music on various
+
+ align:start position:0%
+looking at music sheet music on various
+ 
+
+ align:start position:0%
+looking at music sheet music on various
+sized screens and therefore where it's
+
+ align:start position:0%
+sized screens and therefore where it's
+ 
+
+ align:start position:0%
+sized screens and therefore where it's
+too the screen is too small to look at a
+
+ align:start position:0%
+too the screen is too small to look at a
+ 
+
+ align:start position:0%
+too the screen is too small to look at a
+whole page at the time or or you turn it
+
+ align:start position:0%
+whole page at the time or or you turn it
+ 
+
+ align:start position:0%
+whole page at the time or or you turn it
+sideways and suddenly your page has
+
+ align:start position:0%
+sideways and suddenly your page has
+ 
+
+ align:start position:0%
+sideways and suddenly your page has
+changed so the notion that music cannot
+
+ align:start position:0%
+changed so the notion that music cannot
+ 
+
+ align:start position:0%
+changed so the notion that music cannot
+just be represented by where is on a
+
+ align:start position:0%
+just be represented by where is on a
+ 
+
+ align:start position:0%
+just be represented by where is on a
+page but has to be able to keep
+
+ align:start position:0%
+page but has to be able to keep
+ 
+
+ align:start position:0%
+page but has to be able to keep
+continuously reflowing has caused um a
+
+ align:start position:0%
+continuously reflowing has caused um a
+ 
+
+ align:start position:0%
+continuously reflowing has caused um a
+big change to people today trying to
+
+ align:start position:0%
+big change to people today trying to
+ 
+
+ align:start position:0%
+big change to people today trying to
+come up with what is the optimal format
+
+ align:start position:0%
+come up with what is the optimal format
+ 
+
+ align:start position:0%
+come up with what is the optimal format
+for representing music whose
+
+ align:start position:0%
+for representing music whose
+ 
+
+ align:start position:0%
+for representing music whose
+presentation might be different for you
+
+ align:start position:0%
+presentation might be different for you
+ 
+
+ align:start position:0%
+presentation might be different for you
+because you have an iPad it might be
+
+ align:start position:0%
+because you have an iPad it might be
+ 
+
+ align:start position:0%
+because you have an iPad it might be
+different over here because you have a
+
+ align:start position:0%
+different over here because you have a
+ 
+
+ align:start position:0%
+different over here because you have a
+15in um Monitor and it might be
+
+ align:start position:0%
+15in um Monitor and it might be
+ 
+
+ align:start position:0%
+15in um Monitor and it might be
+different for somebody else because
+
+ align:start position:0%
+different for somebody else because
+ 
+
+ align:start position:0%
+different for somebody else because
+you've just printed it out in the
+
+ align:start position:0%
+you've just printed it out in the
+ 
+
+ align:start position:0%
+you've just printed it out in the
+oldfashioned way how do we represent
+
+ align:start position:0%
+oldfashioned way how do we represent
+ 
+
+ align:start position:0%
+oldfashioned way how do we represent
+music that way I wanted to point out
+
+ align:start position:0%
+music that way I wanted to point out
+ 
+
+ align:start position:0%
+music that way I wanted to point out
+because um there is a huge debate so
+
+ align:start position:0%
+because um there is a huge debate so
+ 
+
+ align:start position:0%
+because um there is a huge debate so
+there's a big discussion happening right
+
+ align:start position:0%
+there's a big discussion happening right
+ 
+
+ align:start position:0%
+there's a big discussion happening right
+now on what the music notation next
+
+ align:start position:0%
+now on what the music notation next
+ 
+
+ align:start position:0%
+now on what the music notation next
+format will be and exactly how it will
+
+ align:start position:0%
+format will be and exactly how it will
+ 
+
+ align:start position:0%
+format will be and exactly how it will
+what its ontology and morony will be so
+
+ align:start position:0%
+what its ontology and morony will be so
+ 
+
+ align:start position:0%
+what its ontology and morony will be so
+that it survives into the next
+
+ align:start position:0%
+that it survives into the next
+ 
+
+ align:start position:0%
+that it survives into the next
+generation of musical School course and
+
+ align:start position:0%
+generation of musical School course and
+ 
+
+ align:start position:0%
+generation of musical School course and
+people you can see are still right now
+
+ align:start position:0%
+people you can see are still right now
+ 
+
+ align:start position:0%
+people you can see are still right now
+um some idiots sometimes post but um and
+
+ align:start position:0%
+um some idiots sometimes post but um and
+ 
+
+ align:start position:0%
+um some idiots sometimes post but um and
+um and exactly what kind of format uh
+
+ align:start position:0%
+um and exactly what kind of format uh
+ 
+
+ align:start position:0%
+um and exactly what kind of format uh
+what the advantages in terms of space
+
+ align:start position:0%
+what the advantages in terms of space
+ 
+
+ align:start position:0%
+what the advantages in terms of space
+speed various representations are going
+
+ align:start position:0%
+speed various representations are going
+ 
+
+ align:start position:0%
+speed various representations are going
+on and I haven't checked it this morning
+
+ align:start position:0%
+on and I haven't checked it this morning
+ 
+
+ align:start position:0%
+on and I haven't checked it this morning
+but it seems to just still be going on
+
+ align:start position:0%
+but it seems to just still be going on
+ 
+
+ align:start position:0%
+but it seems to just still be going on
+so this is a continuous topic of
+
+ align:start position:0%
+so this is a continuous topic of
+ 
+
+ align:start position:0%
+so this is a continuous topic of
+discussion people are still very
+
+ align:start position:0%
+discussion people are still very
+ 
+
+ align:start position:0%
+discussion people are still very
+interested in What's um in what's
+
+ align:start position:0%
+interested in What's um in what's
+ 
+
+ align:start position:0%
+interested in What's um in what's
+happening what music representations are
+
+ align:start position:0%
+happening what music representations are
+ 
+
+ align:start position:0%
+happening what music representations are
+out there and I'm looking forward to
+
+ align:start position:0%
+out there and I'm looking forward to
+ 
+
+ align:start position:0%
+out there and I'm looking forward to
+five new music representations existing
+
+ align:start position:0%
+five new music representations existing
+ 
+
+ align:start position:0%
+five new music representations existing
+a week from now that don't today thanks
+
+ align:start position:0%
+a week from now that don't today thanks
+ 
+
+ align:start position:0%
+a week from now that don't today thanks
+everybody
\ No newline at end of file
diff --git a/gXJa7YutKfM.txt b/gXJa7YutKfM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ea55004bd461c0fe151e4d6bac1cc1187ed0df0c
--- /dev/null
+++ b/gXJa7YutKfM.txt
@@ -0,0 +1,14331 @@
+align:start position:0%
+ 
+great welcome back everybody um this is
+
+ align:start position:0%
+great welcome back everybody um this is
+ 
+
+ align:start position:0%
+great welcome back everybody um this is
+a part of a pro of the program that I
+
+ align:start position:0%
+a part of a pro of the program that I
+ 
+
+ align:start position:0%
+a part of a pro of the program that I
+have really been looking forward to uh
+
+ align:start position:0%
+have really been looking forward to uh
+ 
+
+ align:start position:0%
+have really been looking forward to uh
+quite a bit as we've been planning this
+
+ align:start position:0%
+quite a bit as we've been planning this
+ 
+
+ align:start position:0%
+quite a bit as we've been planning this
+uh I think it's a really wonderful
+
+ align:start position:0%
+uh I think it's a really wonderful
+ 
+
+ align:start position:0%
+uh I think it's a really wonderful
+wonderful opportunity for all of us uh
+
+ align:start position:0%
+wonderful opportunity for all of us uh
+ 
+
+ align:start position:0%
+wonderful opportunity for all of us uh
+to hear from people who were involved uh
+
+ align:start position:0%
+to hear from people who were involved uh
+ 
+
+ align:start position:0%
+to hear from people who were involved uh
+in mit's decision to undertake its open
+
+ align:start position:0%
+in mit's decision to undertake its open
+ 
+
+ align:start position:0%
+in mit's decision to undertake its open
+courseware project 10 years ago which
+
+ align:start position:0%
+courseware project 10 years ago which
+ 
+
+ align:start position:0%
+courseware project 10 years ago which
+was I think a very different uh world
+
+ align:start position:0%
+was I think a very different uh world
+ 
+
+ align:start position:0%
+was I think a very different uh world
+than uh the world living in today um as
+
+ align:start position:0%
+than uh the world living in today um as
+ 
+
+ align:start position:0%
+than uh the world living in today um as
+we heard from Tim O'Reilly as we heard
+
+ align:start position:0%
+we heard from Tim O'Reilly as we heard
+ 
+
+ align:start position:0%
+we heard from Tim O'Reilly as we heard
+from Susan hawkfield there were many
+
+ align:start position:0%
+from Susan hawkfield there were many
+ 
+
+ align:start position:0%
+from Susan hawkfield there were many
+influences many other movements uh
+
+ align:start position:0%
+influences many other movements uh
+ 
+
+ align:start position:0%
+influences many other movements uh
+toward openness on the internet and so
+
+ align:start position:0%
+toward openness on the internet and so
+ 
+
+ align:start position:0%
+toward openness on the internet and so
+uh this doesn't stand on obviously um
+
+ align:start position:0%
+uh this doesn't stand on obviously um
+ 
+
+ align:start position:0%
+uh this doesn't stand on obviously um
+even within education there were there
+
+ align:start position:0%
+even within education there were there
+ 
+
+ align:start position:0%
+even within education there were there
+were other prominent projects that were
+
+ align:start position:0%
+were other prominent projects that were
+ 
+
+ align:start position:0%
+were other prominent projects that were
+being launched uh webcast Berkeley was
+
+ align:start position:0%
+being launched uh webcast Berkeley was
+ 
+
+ align:start position:0%
+being launched uh webcast Berkeley was
+starting up and connections was starting
+
+ align:start position:0%
+starting up and connections was starting
+ 
+
+ align:start position:0%
+starting up and connections was starting
+up uh Wikipedia even could be considered
+
+ align:start position:0%
+up uh Wikipedia even could be considered
+ 
+
+ align:start position:0%
+up uh Wikipedia even could be considered
+an uh open education Resource as well
+
+ align:start position:0%
+an uh open education Resource as well
+ 
+
+ align:start position:0%
+an uh open education Resource as well
+and I and certainly was getting started
+
+ align:start position:0%
+and I and certainly was getting started
+ 
+
+ align:start position:0%
+and I and certainly was getting started
+about that time um but mit's
+
+ align:start position:0%
+about that time um but mit's
+ 
+
+ align:start position:0%
+about that time um but mit's
+announcement on April 4 2001 is probably
+
+ align:start position:0%
+announcement on April 4 2001 is probably
+ 
+
+ align:start position:0%
+announcement on April 4 2001 is probably
+the clearest starting point we have of
+
+ align:start position:0%
+the clearest starting point we have of
+ 
+
+ align:start position:0%
+the clearest starting point we have of
+the history of uh the open courseware
+
+ align:start position:0%
+the history of uh the open courseware
+ 
+
+ align:start position:0%
+the history of uh the open courseware
+movement at least as uh institutional
+
+ align:start position:0%
+movement at least as uh institutional
+ 
+
+ align:start position:0%
+movement at least as uh institutional
+efforts are concerned and and so we're
+
+ align:start position:0%
+efforts are concerned and and so we're
+ 
+
+ align:start position:0%
+efforts are concerned and and so we're
+starting with that today as the starting
+
+ align:start position:0%
+starting with that today as the starting
+ 
+
+ align:start position:0%
+starting with that today as the starting
+point of our exploration of the history
+
+ align:start position:0%
+point of our exploration of the history
+ 
+
+ align:start position:0%
+point of our exploration of the history
+of the open courseware movement um now
+
+ align:start position:0%
+of the open courseware movement um now
+ 
+
+ align:start position:0%
+of the open courseware movement um now
+in my role at MIT open course whereare
+
+ align:start position:0%
+in my role at MIT open course whereare
+ 
+
+ align:start position:0%
+in my role at MIT open course whereare
+uh I work with the media a lot and so
+
+ align:start position:0%
+uh I work with the media a lot and so
+ 
+
+ align:start position:0%
+uh I work with the media a lot and so
+I've probably told the Genesis story of
+
+ align:start position:0%
+I've probably told the Genesis story of
+ 
+
+ align:start position:0%
+I've probably told the Genesis story of
+open course where more than any other
+
+ align:start position:0%
+open course where more than any other
+ 
+
+ align:start position:0%
+open course where more than any other
+person uh at MIT um but this is really
+
+ align:start position:0%
+person uh at MIT um but this is really
+ 
+
+ align:start position:0%
+person uh at MIT um but this is really
+sort of a unique situation for me
+
+ align:start position:0%
+sort of a unique situation for me
+ 
+
+ align:start position:0%
+sort of a unique situation for me
+because I'm probably the least qualified
+
+ align:start position:0%
+because I'm probably the least qualified
+ 
+
+ align:start position:0%
+because I'm probably the least qualified
+person on the stage right now to be
+
+ align:start position:0%
+person on the stage right now to be
+ 
+
+ align:start position:0%
+person on the stage right now to be
+talking about MIT open courseware um but
+
+ align:start position:0%
+talking about MIT open courseware um but
+ 
+
+ align:start position:0%
+talking about MIT open courseware um but
+I'll go ahead and give the Genesis story
+
+ align:start position:0%
+I'll go ahead and give the Genesis story
+ 
+
+ align:start position:0%
+I'll go ahead and give the Genesis story
+with all of its flaws and and probably
+
+ align:start position:0%
+with all of its flaws and and probably
+ 
+
+ align:start position:0%
+with all of its flaws and and probably
+uh Mis perceptions about how the project
+
+ align:start position:0%
+uh Mis perceptions about how the project
+ 
+
+ align:start position:0%
+uh Mis perceptions about how the project
+got started and then let uh the
+
+ align:start position:0%
+got started and then let uh the
+ 
+
+ align:start position:0%
+got started and then let uh the
+gentleman on the panel correct me as we
+
+ align:start position:0%
+gentleman on the panel correct me as we
+ 
+
+ align:start position:0%
+gentleman on the panel correct me as we
+go along um but the the Legends as it
+
+ align:start position:0%
+go along um but the the Legends as it
+ 
+
+ align:start position:0%
+go along um but the the Legends as it
+was handed down to me was that around
+
+ align:start position:0%
+was handed down to me was that around
+ 
+
+ align:start position:0%
+was handed down to me was that around
+1999 2000 uh MIT was struggling with the
+
+ align:start position:0%
+1999 2000 uh MIT was struggling with the
+ 
+
+ align:start position:0%
+1999 2000 uh MIT was struggling with the
+question of what to do about uh
+
+ align:start position:0%
+question of what to do about uh
+ 
+
+ align:start position:0%
+question of what to do about uh
+educational technology and in particular
+
+ align:start position:0%
+educational technology and in particular
+ 
+
+ align:start position:0%
+educational technology and in particular
+the internet a question that was
+
+ align:start position:0%
+the internet a question that was
+ 
+
+ align:start position:0%
+the internet a question that was
+ultimately handed by the Provost and the
+
+ align:start position:0%
+ultimately handed by the Provost and the
+ 
+
+ align:start position:0%
+ultimately handed by the Provost and the
+president to a committee now one of the
+
+ align:start position:0%
+president to a committee now one of the
+ 
+
+ align:start position:0%
+president to a committee now one of the
+things that I usually leave out of this
+
+ align:start position:0%
+things that I usually leave out of this
+ 
+
+ align:start position:0%
+things that I usually leave out of this
+is there were actually two committees
+
+ align:start position:0%
+is there were actually two committees
+ 
+
+ align:start position:0%
+is there were actually two committees
+involved one was the standing committee
+
+ align:start position:0%
+involved one was the standing committee
+ 
+
+ align:start position:0%
+involved one was the standing committee
+that was formed in
+
+ align:start position:0%
+that was formed in
+ 
+
+ align:start position:0%
+that was formed in
+1999 called the Council on educational
+
+ align:start position:0%
+1999 called the Council on educational
+ 
+
+ align:start position:0%
+1999 called the Council on educational
+technology which still meets today
+
+ align:start position:0%
+technology which still meets today
+ 
+
+ align:start position:0%
+technology which still meets today
+regularly at MIT to advise the provos
+
+ align:start position:0%
+regularly at MIT to advise the provos
+ 
+
+ align:start position:0%
+regularly at MIT to advise the provos
+and the president um that committee
+
+ align:start position:0%
+and the president um that committee
+ 
+
+ align:start position:0%
+and the president um that committee
+handed off a number of different aspects
+
+ align:start position:0%
+handed off a number of different aspects
+ 
+
+ align:start position:0%
+handed off a number of different aspects
+of their charge to sub committees and
+
+ align:start position:0%
+of their charge to sub committees and
+ 
+
+ align:start position:0%
+of their charge to sub committees and
+one of those aspects was distance
+
+ align:start position:0%
+one of those aspects was distance
+ 
+
+ align:start position:0%
+one of those aspects was distance
+learning or the impact of the internet
+
+ align:start position:0%
+learning or the impact of the internet
+ 
+
+ align:start position:0%
+learning or the impact of the internet
+on education and that was handed to a
+
+ align:start position:0%
+on education and that was handed to a
+ 
+
+ align:start position:0%
+on education and that was handed to a
+committee on lifelong learning uh in at
+
+ align:start position:0%
+committee on lifelong learning uh in at
+ 
+
+ align:start position:0%
+committee on lifelong learning uh in at
+the beginning of the summer of the year
+
+ align:start position:0%
+the beginning of the summer of the year
+ 
+
+ align:start position:0%
+the beginning of the summer of the year
+2000 that committee worked throughout
+
+ align:start position:0%
+2000 that committee worked throughout
+ 
+
+ align:start position:0%
+2000 that committee worked throughout
+the summer they brought in boo Allen
+
+ align:start position:0%
+the summer they brought in boo Allen
+ 
+
+ align:start position:0%
+the summer they brought in boo Allen
+they brought in uh some other help and
+
+ align:start position:0%
+they brought in uh some other help and
+ 
+
+ align:start position:0%
+they brought in uh some other help and
+they created a bunch of business models
+
+ align:start position:0%
+they created a bunch of business models
+ 
+
+ align:start position:0%
+they created a bunch of business models
+and they looked at the question of
+
+ align:start position:0%
+and they looked at the question of
+ 
+
+ align:start position:0%
+and they looked at the question of
+online learning distance education and
+
+ align:start position:0%
+online learning distance education and
+ 
+
+ align:start position:0%
+online learning distance education and
+they were really confronted with two
+
+ align:start position:0%
+they were really confronted with two
+ 
+
+ align:start position:0%
+they were really confronted with two
+problems one was they didn't feel like
+
+ align:start position:0%
+problems one was they didn't feel like
+ 
+
+ align:start position:0%
+problems one was they didn't feel like
+it was a very good fit with the MIT
+
+ align:start position:0%
+it was a very good fit with the MIT
+ 
+
+ align:start position:0%
+it was a very good fit with the MIT
+mission to disseminate knowledge and the
+
+ align:start position:0%
+mission to disseminate knowledge and the
+ 
+
+ align:start position:0%
+mission to disseminate knowledge and the
+other was they couldn't figure out a
+
+ align:start position:0%
+other was they couldn't figure out a
+ 
+
+ align:start position:0%
+other was they couldn't figure out a
+good way to make uh the economics of it
+
+ align:start position:0%
+good way to make uh the economics of it
+ 
+
+ align:start position:0%
+good way to make uh the economics of it
+work and so at the end of the summer
+
+ align:start position:0%
+work and so at the end of the summer
+ 
+
+ align:start position:0%
+work and so at the end of the summer
+they were really uh pretty convinced
+
+ align:start position:0%
+they were really uh pretty convinced
+ 
+
+ align:start position:0%
+they were really uh pretty convinced
+that distance learning wasn't the
+
+ align:start position:0%
+that distance learning wasn't the
+ 
+
+ align:start position:0%
+that distance learning wasn't the
+direction to go for MIT but they really
+
+ align:start position:0%
+direction to go for MIT but they really
+ 
+
+ align:start position:0%
+direction to go for MIT but they really
+didn't have a proposal and so at that
+
+ align:start position:0%
+didn't have a proposal and so at that
+ 
+
+ align:start position:0%
+didn't have a proposal and so at that
+point they kind of went back to the
+
+ align:start position:0%
+point they kind of went back to the
+ 
+
+ align:start position:0%
+point they kind of went back to the
+basics of what is the internet good at
+
+ align:start position:0%
+basics of what is the internet good at
+ 
+
+ align:start position:0%
+basics of what is the internet good at
+Distributing content widely and cheaply
+
+ align:start position:0%
+Distributing content widely and cheaply
+ 
+
+ align:start position:0%
+Distributing content widely and cheaply
+and what is MIT good at which is uh
+
+ align:start position:0%
+and what is MIT good at which is uh
+ 
+
+ align:start position:0%
+and what is MIT good at which is uh
+residential education and they combin
+
+ align:start position:0%
+residential education and they combin
+ 
+
+ align:start position:0%
+residential education and they combin
+the two and said why not use the
+
+ align:start position:0%
+the two and said why not use the
+ 
+
+ align:start position:0%
+the two and said why not use the
+internet to distribute the materials we
+
+ align:start position:0%
+internet to distribute the materials we
+ 
+
+ align:start position:0%
+internet to distribute the materials we
+create for our residential experience
+
+ align:start position:0%
+create for our residential experience
+ 
+
+ align:start position:0%
+create for our residential experience
+over openly on the internet and so uh at
+
+ align:start position:0%
+over openly on the internet and so uh at
+ 
+
+ align:start position:0%
+over openly on the internet and so uh at
+least as it was told to me there was a a
+
+ align:start position:0%
+least as it was told to me there was a a
+ 
+
+ align:start position:0%
+least as it was told to me there was a a
+report that was about that thick uh that
+
+ align:start position:0%
+report that was about that thick uh that
+ 
+
+ align:start position:0%
+report that was about that thick uh that
+gave all the reasons why distance
+
+ align:start position:0%
+gave all the reasons why distance
+ 
+
+ align:start position:0%
+gave all the reasons why distance
+learning probably wasn't going to work
+
+ align:start position:0%
+learning probably wasn't going to work
+ 
+
+ align:start position:0%
+learning probably wasn't going to work
+for MIT and on top of it was a one-page
+
+ align:start position:0%
+for MIT and on top of it was a one-page
+ 
+
+ align:start position:0%
+for MIT and on top of it was a one-page
+suggestion that we give away all of our
+
+ align:start position:0%
+suggestion that we give away all of our
+ 
+
+ align:start position:0%
+suggestion that we give away all of our
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+materials so every time I speak to one
+
+ align:start position:0%
+materials so every time I speak to one
+ 
+
+ align:start position:0%
+materials so every time I speak to one
+of the the gentlemen at the table or
+
+ align:start position:0%
+of the the gentlemen at the table or
+ 
+
+ align:start position:0%
+of the the gentlemen at the table or
+anyone else who is involved with uh the
+
+ align:start position:0%
+anyone else who is involved with uh the
+ 
+
+ align:start position:0%
+anyone else who is involved with uh the
+creation of open course where I learned
+
+ align:start position:0%
+creation of open course where I learned
+ 
+
+ align:start position:0%
+creation of open course where I learned
+something new a Nuance about how open
+
+ align:start position:0%
+something new a Nuance about how open
+ 
+
+ align:start position:0%
+something new a Nuance about how open
+courseware came about what the
+
+ align:start position:0%
+courseware came about what the
+ 
+
+ align:start position:0%
+courseware came about what the
+circumstances were like at that point in
+
+ align:start position:0%
+circumstances were like at that point in
+ 
+
+ align:start position:0%
+circumstances were like at that point in
+time uh that helps me uh inform my
+
+ align:start position:0%
+time uh that helps me uh inform my
+ 
+
+ align:start position:0%
+time uh that helps me uh inform my
+thinking about the core challenges that
+
+ align:start position:0%
+thinking about the core challenges that
+ 
+
+ align:start position:0%
+thinking about the core challenges that
+all of us face in our own open course
+
+ align:start position:0%
+all of us face in our own open course
+ 
+
+ align:start position:0%
+all of us face in our own open course
+where how do we get and maintain uh
+
+ align:start position:0%
+where how do we get and maintain uh
+ 
+
+ align:start position:0%
+where how do we get and maintain uh
+buyin from our communities how do we
+
+ align:start position:0%
+buyin from our communities how do we
+ 
+
+ align:start position:0%
+buyin from our communities how do we
+recruit faculty what do you do about the
+
+ align:start position:0%
+recruit faculty what do you do about the
+ 
+
+ align:start position:0%
+recruit faculty what do you do about the
+intellectual property concerns and so
+
+ align:start position:0%
+intellectual property concerns and so
+ 
+
+ align:start position:0%
+intellectual property concerns and so
+I'm pleased to share that opportunity
+
+ align:start position:0%
+I'm pleased to share that opportunity
+ 
+
+ align:start position:0%
+I'm pleased to share that opportunity
+for insight with the rest of the open
+
+ align:start position:0%
+for insight with the rest of the open
+ 
+
+ align:start position:0%
+for insight with the rest of the open
+courseware uh Community we have with us
+
+ align:start position:0%
+courseware uh Community we have with us
+ 
+
+ align:start position:0%
+courseware uh Community we have with us
+today three of The Faculty who were
+
+ align:start position:0%
+today three of The Faculty who were
+ 
+
+ align:start position:0%
+today three of The Faculty who were
+involved in the proposal for open course
+
+ align:start position:0%
+involved in the proposal for open course
+ 
+
+ align:start position:0%
+involved in the proposal for open course
+Weare and three of the administrators
+
+ align:start position:0%
+Weare and three of the administrators
+ 
+
+ align:start position:0%
+Weare and three of the administrators
+who re received and supported that
+
+ align:start position:0%
+who re received and supported that
+ 
+
+ align:start position:0%
+who re received and supported that
+proposal uh the three faculty members
+
+ align:start position:0%
+proposal uh the three faculty members
+ 
+
+ align:start position:0%
+proposal uh the three faculty members
+are all members of our faculty advisory
+
+ align:start position:0%
+are all members of our faculty advisory
+ 
+
+ align:start position:0%
+are all members of our faculty advisory
+committee uh the first Professor Hal
+
+ align:start position:0%
+committee uh the first Professor Hal
+ 
+
+ align:start position:0%
+committee uh the first Professor Hal
+ablon who also at the time of open
+
+ align:start position:0%
+ablon who also at the time of open
+ 
+
+ align:start position:0%
+ablon who also at the time of open
+course where's proposal chair at mit's
+
+ align:start position:0%
+course where's proposal chair at mit's
+ 
+
+ align:start position:0%
+course where's proposal chair at mit's
+Council and educational technology or
+
+ align:start position:0%
+Council and educational technology or
+ 
+
+ align:start position:0%
+Council and educational technology or
+co-chaired as I understand uh Professor
+
+ align:start position:0%
+co-chaired as I understand uh Professor
+ 
+
+ align:start position:0%
+co-chaired as I understand uh Professor
+dick U who uh chaired the committee on
+
+ align:start position:0%
+dick U who uh chaired the committee on
+ 
+
+ align:start position:0%
+dick U who uh chaired the committee on
+lifelong learning the proposed open
+
+ align:start position:0%
+lifelong learning the proposed open
+ 
+
+ align:start position:0%
+lifelong learning the proposed open
+course Weare and Professor shiru M aawa
+
+ align:start position:0%
+course Weare and Professor shiru M aawa
+ 
+
+ align:start position:0%
+course Weare and Professor shiru M aawa
+who uh served on the lifelong learning
+
+ align:start position:0%
+who uh served on the lifelong learning
+ 
+
+ align:start position:0%
+who uh served on the lifelong learning
+committee and is also the chair of our
+
+ align:start position:0%
+committee and is also the chair of our
+ 
+
+ align:start position:0%
+committee and is also the chair of our
+faculty advisory committee in addition
+
+ align:start position:0%
+faculty advisory committee in addition
+ 
+
+ align:start position:0%
+faculty advisory committee in addition
+to that we're very fortunate today to
+
+ align:start position:0%
+to that we're very fortunate today to
+ 
+
+ align:start position:0%
+to that we're very fortunate today to
+have three of the senior administrators
+
+ align:start position:0%
+have three of the senior administrators
+ 
+
+ align:start position:0%
+have three of the senior administrators
+at MIT at the time who are are
+
+ align:start position:0%
+at MIT at the time who are are
+ 
+
+ align:start position:0%
+at MIT at the time who are are
+generously sharing their time uh for
+
+ align:start position:0%
+generously sharing their time uh for
+ 
+
+ align:start position:0%
+generously sharing their time uh for
+this panel uh we're joined by Dr Charles
+
+ align:start position:0%
+this panel uh we're joined by Dr Charles
+ 
+
+ align:start position:0%
+this panel uh we're joined by Dr Charles
+vest who's now the president of the
+
+ align:start position:0%
+vest who's now the president of the
+ 
+
+ align:start position:0%
+vest who's now the president of the
+National Academy of engineering and was
+
+ align:start position:0%
+National Academy of engineering and was
+ 
+
+ align:start position:0%
+National Academy of engineering and was
+at the time the president of MIT Dr
+
+ align:start position:0%
+at the time the president of MIT Dr
+ 
+
+ align:start position:0%
+at the time the president of MIT Dr
+Robert Brown who's currently the
+
+ align:start position:0%
+Robert Brown who's currently the
+ 
+
+ align:start position:0%
+Robert Brown who's currently the
+president of Boston University and was
+
+ align:start position:0%
+president of Boston University and was
+ 
+
+ align:start position:0%
+president of Boston University and was
+the Provost uh at MIT at the time the
+
+ align:start position:0%
+the Provost uh at MIT at the time the
+ 
+
+ align:start position:0%
+the Provost uh at MIT at the time the
+proposal for MIT open course whereare
+
+ align:start position:0%
+proposal for MIT open course whereare
+ 
+
+ align:start position:0%
+proposal for MIT open course whereare
+came out and Dr Lawrence Bako who was
+
+ align:start position:0%
+came out and Dr Lawrence Bako who was
+ 
+
+ align:start position:0%
+came out and Dr Lawrence Bako who was
+Chancellor at MIT at the time of MIT MIT
+
+ align:start position:0%
+Chancellor at MIT at the time of MIT MIT
+ 
+
+ align:start position:0%
+Chancellor at MIT at the time of MIT MIT
+open course where proposal and is
+
+ align:start position:0%
+open course where proposal and is
+ 
+
+ align:start position:0%
+open course where proposal and is
+currently the president of tus
+
+ align:start position:0%
+currently the president of tus
+ 
+
+ align:start position:0%
+currently the president of tus
+University so welcome and thank you all
+
+ align:start position:0%
+University so welcome and thank you all
+ 
+
+ align:start position:0%
+University so welcome and thank you all
+for sharing your time um so having given
+
+ align:start position:0%
+for sharing your time um so having given
+ 
+
+ align:start position:0%
+for sharing your time um so having given
+that uh account of MIT open course
+
+ align:start position:0%
+that uh account of MIT open course
+ 
+
+ align:start position:0%
+that uh account of MIT open course
+where's creation I'm now going to O open
+
+ align:start position:0%
+where's creation I'm now going to O open
+ 
+
+ align:start position:0%
+where's creation I'm now going to O open
+the floor for rebuttal first from from
+
+ align:start position:0%
+the floor for rebuttal first from from
+ 
+
+ align:start position:0%
+the floor for rebuttal first from from
+uh Dr vest by asking what was going
+
+ align:start position:0%
+uh Dr vest by asking what was going
+ 
+
+ align:start position:0%
+uh Dr vest by asking what was going
+through your mind when you first heard
+
+ align:start position:0%
+through your mind when you first heard
+ 
+
+ align:start position:0%
+through your mind when you first heard
+what the proposal was going to be coming
+
+ align:start position:0%
+what the proposal was going to be coming
+ 
+
+ align:start position:0%
+what the proposal was going to be coming
+out of that
+
+ align:start position:0%
+out of that
+ 
+
+ align:start position:0%
+out of that
+committee well thank you very much Steve
+
+ align:start position:0%
+committee well thank you very much Steve
+ 
+
+ align:start position:0%
+committee well thank you very much Steve
+and I'm just can't tell you how thrilled
+
+ align:start position:0%
+and I'm just can't tell you how thrilled
+ 
+
+ align:start position:0%
+and I'm just can't tell you how thrilled
+I am to have this group here and realize
+
+ align:start position:0%
+I am to have this group here and realize
+ 
+
+ align:start position:0%
+I am to have this group here and realize
+we're actually celebrating uh 10 years
+
+ align:start position:0%
+we're actually celebrating uh 10 years
+ 
+
+ align:start position:0%
+we're actually celebrating uh 10 years
+um I I want to take very seriously the
+
+ align:start position:0%
+um I I want to take very seriously the
+ 
+
+ align:start position:0%
+um I I want to take very seriously the
+point of this panel to give historical
+
+ align:start position:0%
+point of this panel to give historical
+ 
+
+ align:start position:0%
+point of this panel to give historical
+perspective so I could invent a very
+
+ align:start position:0%
+perspective so I could invent a very
+ 
+
+ align:start position:0%
+perspective so I could invent a very
+flowery version and a very Visionary
+
+ align:start position:0%
+flowery version and a very Visionary
+ 
+
+ align:start position:0%
+flowery version and a very Visionary
+version of what happened but I want to
+
+ align:start position:0%
+version of what happened but I want to
+ 
+
+ align:start position:0%
+version of what happened but I want to
+tell you what from my point of view
+
+ align:start position:0%
+tell you what from my point of view
+ 
+
+ align:start position:0%
+tell you what from my point of view
+happened and the reason I'm uh so
+
+ align:start position:0%
+happened and the reason I'm uh so
+ 
+
+ align:start position:0%
+happened and the reason I'm uh so
+looking forward to this panel is at long
+
+ align:start position:0%
+looking forward to this panel is at long
+ 
+
+ align:start position:0%
+looking forward to this panel is at long
+last I'll find out what really did
+
+ align:start position:0%
+last I'll find out what really did
+ 
+
+ align:start position:0%
+last I'll find out what really did
+happen 10 years ago what really happened
+
+ align:start position:0%
+happen 10 years ago what really happened
+ 
+
+ align:start position:0%
+happen 10 years ago what really happened
+is it was a
+
+ align:start position:0%
+is it was a
+ 
+
+ align:start position:0%
+is it was a
+joke but um I I want to begin by
+
+ align:start position:0%
+joke but um I I want to begin by
+ 
+
+ align:start position:0%
+joke but um I I want to begin by
+pointing out two big lessons that I take
+
+ align:start position:0%
+pointing out two big lessons that I take
+ 
+
+ align:start position:0%
+pointing out two big lessons that I take
+away from this whole adventure and it is
+
+ align:start position:0%
+away from this whole adventure and it is
+ 
+
+ align:start position:0%
+away from this whole adventure and it is
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+adventure and the first lesson is one
+
+ align:start position:0%
+adventure and the first lesson is one
+ 
+
+ align:start position:0%
+adventure and the first lesson is one
+that it reinforced
+
+ align:start position:0%
+that it reinforced
+ 
+
+ align:start position:0%
+that it reinforced
+dramatically which is that the really
+
+ align:start position:0%
+dramatically which is that the really
+ 
+
+ align:start position:0%
+dramatically which is that the really
+great ideas in the University don't come
+
+ align:start position:0%
+great ideas in the University don't come
+ 
+
+ align:start position:0%
+great ideas in the University don't come
+from the top down they come from The
+
+ align:start position:0%
+from the top down they come from The
+ 
+
+ align:start position:0%
+from the top down they come from The
+Faculty they occasionally come from the
+
+ align:start position:0%
+Faculty they occasionally come from the
+ 
+
+ align:start position:0%
+Faculty they occasionally come from the
+students they sometimes come from the
+
+ align:start position:0%
+students they sometimes come from the
+ 
+
+ align:start position:0%
+students they sometimes come from the
+staff but the key to doing great things
+
+ align:start position:0%
+staff but the key to doing great things
+ 
+
+ align:start position:0%
+staff but the key to doing great things
+is to keeping your ear to the ground and
+
+ align:start position:0%
+is to keeping your ear to the ground and
+ 
+
+ align:start position:0%
+is to keeping your ear to the ground and
+listening because that's where the
+
+ align:start position:0%
+listening because that's where the
+ 
+
+ align:start position:0%
+listening because that's where the
+Innovation creativity generally comes
+
+ align:start position:0%
+Innovation creativity generally comes
+ 
+
+ align:start position:0%
+Innovation creativity generally comes
+from certainly did in this case and the
+
+ align:start position:0%
+from certainly did in this case and the
+ 
+
+ align:start position:0%
+from certainly did in this case and the
+second thing is and it may sound a
+
+ align:start position:0%
+second thing is and it may sound a
+ 
+
+ align:start position:0%
+second thing is and it may sound a
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+polanish but it also taught me in a very
+
+ align:start position:0%
+polanish but it also taught me in a very
+ 
+
+ align:start position:0%
+polanish but it also taught me in a very
+dramatic way that if you have a really
+
+ align:start position:0%
+dramatic way that if you have a really
+ 
+
+ align:start position:0%
+dramatic way that if you have a really
+great idea somehow you're going to find
+
+ align:start position:0%
+great idea somehow you're going to find
+ 
+
+ align:start position:0%
+great idea somehow you're going to find
+the means and in this case the financial
+
+ align:start position:0%
+the means and in this case the financial
+ 
+
+ align:start position:0%
+the means and in this case the financial
+means to accomplish it so with those two
+
+ align:start position:0%
+means to accomplish it so with those two
+ 
+
+ align:start position:0%
+means to accomplish it so with those two
+things in
+
+ align:start position:0%
+things in
+ 
+
+ align:start position:0%
+things in
+mind I want to give you two pieces of
+
+ align:start position:0%
+mind I want to give you two pieces of
+ 
+
+ align:start position:0%
+mind I want to give you two pieces of
+background and then I'll very quickly
+
+ align:start position:0%
+background and then I'll very quickly
+ 
+
+ align:start position:0%
+background and then I'll very quickly
+tell you what my earliest experience was
+
+ align:start position:0%
+tell you what my earliest experience was
+ 
+
+ align:start position:0%
+tell you what my earliest experience was
+uh regarding ocw and its
+
+ align:start position:0%
+uh regarding ocw and its
+ 
+
+ align:start position:0%
+uh regarding ocw and its
+Inception one piece of background is
+
+ align:start position:0%
+Inception one piece of background is
+ 
+
+ align:start position:0%
+Inception one piece of background is
+that uh I went to University and
+
+ align:start position:0%
+that uh I went to University and
+ 
+
+ align:start position:0%
+that uh I went to University and
+graduate school in the very late 50s and
+
+ align:start position:0%
+graduate school in the very late 50s and
+ 
+
+ align:start position:0%
+graduate school in the very late 50s and
+early 60s and uh did my undergraduate
+
+ align:start position:0%
+early 60s and uh did my undergraduate
+ 
+
+ align:start position:0%
+early 60s and uh did my undergraduate
+work in mechanical engineering at West
+
+ align:start position:0%
+work in mechanical engineering at West
+ 
+
+ align:start position:0%
+work in mechanical engineering at West
+Virginia University far removed from MIT
+
+ align:start position:0%
+Virginia University far removed from MIT
+ 
+
+ align:start position:0%
+Virginia University far removed from MIT
+in many ways I did my uh doctoral work
+
+ align:start position:0%
+in many ways I did my uh doctoral work
+ 
+
+ align:start position:0%
+in many ways I did my uh doctoral work
+at the University of Michigan in Ann
+
+ align:start position:0%
+at the University of Michigan in Ann
+ 
+
+ align:start position:0%
+at the University of Michigan in Ann
+Arbor and there was something very
+
+ align:start position:0%
+Arbor and there was something very
+ 
+
+ align:start position:0%
+Arbor and there was something very
+common to those two experiences that was
+
+ align:start position:0%
+common to those two experiences that was
+ 
+
+ align:start position:0%
+common to those two experiences that was
+absolutely what came to mind when I
+
+ align:start position:0%
+absolutely what came to mind when I
+ 
+
+ align:start position:0%
+absolutely what came to mind when I
+first heard the uh idea of
+
+ align:start position:0%
+first heard the uh idea of
+ 
+
+ align:start position:0%
+first heard the uh idea of
+ocw um as most of you perhaps all of you
+
+ align:start position:0%
+ocw um as most of you perhaps all of you
+ 
+
+ align:start position:0%
+ocw um as most of you perhaps all of you
+know and Susan mentioned it I believe
+
+ align:start position:0%
+know and Susan mentioned it I believe
+ 
+
+ align:start position:0%
+know and Susan mentioned it I believe
+this morning um during World War II MIT
+
+ align:start position:0%
+this morning um during World War II MIT
+ 
+
+ align:start position:0%
+this morning um during World War II MIT
+hosted and operated together with the
+
+ align:start position:0%
+hosted and operated together with the
+ 
+
+ align:start position:0%
+hosted and operated together with the
+British the radiation lab to develop the
+
+ align:start position:0%
+British the radiation lab to develop the
+ 
+
+ align:start position:0%
+British the radiation lab to develop the
+British invention of radar into a real
+
+ align:start position:0%
+British invention of radar into a real
+ 
+
+ align:start position:0%
+British invention of radar into a real
+Deployable system that had a whole lot
+
+ align:start position:0%
+Deployable system that had a whole lot
+ 
+
+ align:start position:0%
+Deployable system that had a whole lot
+to do with the Allied victory in World
+
+ align:start position:0%
+to do with the Allied victory in World
+ 
+
+ align:start position:0%
+to do with the Allied victory in World
+War II and when the war was over
+
+ align:start position:0%
+War II and when the war was over
+ 
+
+ align:start position:0%
+War II and when the war was over
+astoundingly the government shut the lab
+
+ align:start position:0%
+astoundingly the government shut the lab
+ 
+
+ align:start position:0%
+astoundingly the government shut the lab
+down we never seem to stop things
+
+ align:start position:0%
+down we never seem to stop things
+ 
+
+ align:start position:0%
+down we never seem to stop things
+anymore but they closed it down and they
+
+ align:start position:0%
+anymore but they closed it down and they
+ 
+
+ align:start position:0%
+anymore but they closed it down and they
+did something really smart they gave
+
+ align:start position:0%
+did something really smart they gave
+ 
+
+ align:start position:0%
+did something really smart they gave
+some of the key people involved 6 months
+
+ align:start position:0%
+some of the key people involved 6 months
+ 
+
+ align:start position:0%
+some of the key people involved 6 months
+to write up what they had learned during
+
+ align:start position:0%
+to write up what they had learned during
+ 
+
+ align:start position:0%
+to write up what they had learned during
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+experience and what this did was create
+
+ align:start position:0%
+experience and what this did was create
+ 
+
+ align:start position:0%
+experience and what this did was create
+a whole new way of
+
+ align:start position:0%
+a whole new way of
+ 
+
+ align:start position:0%
+a whole new way of
+bringing a basis of rational science and
+
+ align:start position:0%
+bringing a basis of rational science and
+ 
+
+ align:start position:0%
+bringing a basis of rational science and
+first principles into how electrical
+
+ align:start position:0%
+first principles into how electrical
+ 
+
+ align:start position:0%
+first principles into how electrical
+engineering and ultimately more broadly
+
+ align:start position:0%
+engineering and ultimately more broadly
+ 
+
+ align:start position:0%
+engineering and ultimately more broadly
+engineering was taught and practice
+
+ align:start position:0%
+engineering was taught and practice
+ 
+
+ align:start position:0%
+engineering was taught and practice
+and this launched something that is is
+
+ align:start position:0%
+and this launched something that is is
+ 
+
+ align:start position:0%
+and this launched something that is is
+known in the in the trade as the
+
+ align:start position:0%
+known in the in the trade as the
+ 
+
+ align:start position:0%
+known in the in the trade as the
+engineering science Revolution and MIT
+
+ align:start position:0%
+engineering science Revolution and MIT
+ 
+
+ align:start position:0%
+engineering science Revolution and MIT
+not solely but certainly was the key to
+
+ align:start position:0%
+not solely but certainly was the key to
+ 
+
+ align:start position:0%
+not solely but certainly was the key to
+this revolution in teaching and learning
+
+ align:start position:0%
+this revolution in teaching and learning
+ 
+
+ align:start position:0%
+this revolution in teaching and learning
+in in Engineering in a very new way and
+
+ align:start position:0%
+in in Engineering in a very new way and
+ 
+
+ align:start position:0%
+in in Engineering in a very new way and
+how did it happen uh students were here
+
+ align:start position:0%
+how did it happen uh students were here
+ 
+
+ align:start position:0%
+how did it happen uh students were here
+earning phds in various fields of
+
+ align:start position:0%
+earning phds in various fields of
+ 
+
+ align:start position:0%
+earning phds in various fields of
+Engineering in a day in which there were
+
+ align:start position:0%
+Engineering in a day in which there were
+ 
+
+ align:start position:0%
+Engineering in a day in which there were
+not many large programs of phds in in
+
+ align:start position:0%
+not many large programs of phds in in
+ 
+
+ align:start position:0%
+not many large programs of phds in in
+engineering and the faculty with the
+
+ align:start position:0%
+engineering and the faculty with the
+ 
+
+ align:start position:0%
+engineering and the faculty with the
+follow on of this work from the rad lab
+
+ align:start position:0%
+follow on of this work from the rad lab
+ 
+
+ align:start position:0%
+follow on of this work from the rad lab
+and so forth were busily creating new
+
+ align:start position:0%
+and so forth were busily creating new
+ 
+
+ align:start position:0%
+and so forth were busily creating new
+ways of teaching bringing first
+
+ align:start position:0%
+ways of teaching bringing first
+ 
+
+ align:start position:0%
+ways of teaching bringing first
+principles of Science in underneath
+
+ align:start position:0%
+principles of Science in underneath
+ 
+
+ align:start position:0%
+principles of Science in underneath
+engineering they were writing notes many
+
+ align:start position:0%
+engineering they were writing notes many
+ 
+
+ align:start position:0%
+engineering they were writing notes many
+of which became uh um ultimately
+
+ align:start position:0%
+of which became uh um ultimately
+ 
+
+ align:start position:0%
+of which became uh um ultimately
+textbooks they were creating uh uh
+
+ align:start position:0%
+textbooks they were creating uh uh
+ 
+
+ align:start position:0%
+textbooks they were creating uh uh
+experiments laboratory experiments for
+
+ align:start position:0%
+experiments laboratory experiments for
+ 
+
+ align:start position:0%
+experiments laboratory experiments for
+teaching and all these guys and I have
+
+ align:start position:0%
+teaching and all these guys and I have
+ 
+
+ align:start position:0%
+teaching and all these guys and I have
+to admit they were mostly guys in those
+
+ align:start position:0%
+to admit they were mostly guys in those
+ 
+
+ align:start position:0%
+to admit they were mostly guys in those
+days
+
+ align:start position:0%
+days
+ 
+
+ align:start position:0%
+days
+uh with their freshly mined phds carried
+
+ align:start position:0%
+uh with their freshly mined phds carried
+ 
+
+ align:start position:0%
+uh with their freshly mined phds carried
+all these notes and they went out around
+
+ align:start position:0%
+all these notes and they went out around
+ 
+
+ align:start position:0%
+all these notes and they went out around
+the country including to places like
+
+ align:start position:0%
+the country including to places like
+ 
+
+ align:start position:0%
+the country including to places like
+West Virginia University and the
+
+ align:start position:0%
+West Virginia University and the
+ 
+
+ align:start position:0%
+West Virginia University and the
+University of Michigan and they used not
+
+ align:start position:0%
+University of Michigan and they used not
+ 
+
+ align:start position:0%
+University of Michigan and they used not
+a final product but they used those
+
+ align:start position:0%
+a final product but they used those
+ 
+
+ align:start position:0%
+a final product but they used those
+notes and started adding to them
+
+ align:start position:0%
+notes and started adding to them
+ 
+
+ align:start position:0%
+notes and started adding to them
+subtracting from them adapting them to
+
+ align:start position:0%
+subtracting from them adapting them to
+ 
+
+ align:start position:0%
+subtracting from them adapting them to
+context and it had a really dramatic
+
+ align:start position:0%
+context and it had a really dramatic
+ 
+
+ align:start position:0%
+context and it had a really dramatic
+impact first of all on me personally but
+
+ align:start position:0%
+impact first of all on me personally but
+ 
+
+ align:start position:0%
+impact first of all on me personally but
+much more importantly on the quality and
+
+ align:start position:0%
+much more importantly on the quality and
+ 
+
+ align:start position:0%
+much more importantly on the quality and
+nature of engineering education across
+
+ align:start position:0%
+nature of engineering education across
+ 
+
+ align:start position:0%
+nature of engineering education across
+across the United
+
+ align:start position:0%
+across the United
+ 
+
+ align:start position:0%
+across the United
+States second piece of background and
+
+ align:start position:0%
+States second piece of background and
+ 
+
+ align:start position:0%
+States second piece of background and
+then I'll pull this together uh many of
+
+ align:start position:0%
+then I'll pull this together uh many of
+ 
+
+ align:start position:0%
+then I'll pull this together uh many of
+you uh here work for various nonprofit
+
+ align:start position:0%
+you uh here work for various nonprofit
+ 
+
+ align:start position:0%
+you uh here work for various nonprofit
+organizations and you all know what
+
+ align:start position:0%
+organizations and you all know what
+ 
+
+ align:start position:0%
+organizations and you all know what
+happens when you propose an idea to a
+
+ align:start position:0%
+happens when you propose an idea to a
+ 
+
+ align:start position:0%
+happens when you propose an idea to a
+foundation you write them a letter or
+
+ align:start position:0%
+foundation you write them a letter or
+ 
+
+ align:start position:0%
+foundation you write them a letter or
+have a conversation and they say that's
+
+ align:start position:0%
+have a conversation and they say that's
+ 
+
+ align:start position:0%
+have a conversation and they say that's
+interesting uh uh how about a little
+
+ align:start position:0%
+interesting uh uh how about a little
+ 
+
+ align:start position:0%
+interesting uh uh how about a little
+pre-proposal and you do a five-page
+
+ align:start position:0%
+pre-proposal and you do a five-page
+ 
+
+ align:start position:0%
+pre-proposal and you do a five-page
+pre-proposal and they come back six
+
+ align:start position:0%
+pre-proposal and they come back six
+ 
+
+ align:start position:0%
+pre-proposal and they come back six
+months later and so well we thought
+
+ align:start position:0%
+months later and so well we thought
+ 
+
+ align:start position:0%
+months later and so well we thought
+about about this we'd like to see the
+
+ align:start position:0%
+about about this we'd like to see the
+ 
+
+ align:start position:0%
+about about this we'd like to see the
+costing and so forth you write a big
+
+ align:start position:0%
+costing and so forth you write a big
+ 
+
+ align:start position:0%
+costing and so forth you write a big
+proposal and after about two years they
+
+ align:start position:0%
+proposal and after about two years they
+ 
+
+ align:start position:0%
+proposal and after about two years they
+say well it's really great idea but I'm
+
+ align:start position:0%
+say well it's really great idea but I'm
+ 
+
+ align:start position:0%
+say well it's really great idea but I'm
+afraid it doesn't fit our mission and
+
+ align:start position:0%
+afraid it doesn't fit our mission and
+ 
+
+ align:start position:0%
+afraid it doesn't fit our mission and
+that's what usually happens to you so so
+
+ align:start position:0%
+that's what usually happens to you so so
+ 
+
+ align:start position:0%
+that's what usually happens to you so so
+bear that in mind so one day and you'll
+
+ align:start position:0%
+bear that in mind so one day and you'll
+ 
+
+ align:start position:0%
+bear that in mind so one day and you'll
+hear more about it uh and Steve was was
+
+ align:start position:0%
+hear more about it uh and Steve was was
+ 
+
+ align:start position:0%
+hear more about it uh and Steve was was
+quite accurate in the uh the role of the
+
+ align:start position:0%
+quite accurate in the uh the role of the
+ 
+
+ align:start position:0%
+quite accurate in the uh the role of the
+Council on engineer on educational
+
+ align:start position:0%
+Council on engineer on educational
+ 
+
+ align:start position:0%
+Council on engineer on educational
+technology and so forth that Bob had
+
+ align:start position:0%
+technology and so forth that Bob had
+ 
+
+ align:start position:0%
+technology and so forth that Bob had
+charged and we'll tell you a lot about
+
+ align:start position:0%
+charged and we'll tell you a lot about
+ 
+
+ align:start position:0%
+charged and we'll tell you a lot about
+one day Bob came into my office and and
+
+ align:start position:0%
+one day Bob came into my office and and
+ 
+
+ align:start position:0%
+one day Bob came into my office and and
+he said uh Chuck the uh uh committee is
+
+ align:start position:0%
+he said uh Chuck the uh uh committee is
+ 
+
+ align:start position:0%
+he said uh Chuck the uh uh committee is
+ready to report out their
+
+ align:start position:0%
+ready to report out their
+ 
+
+ align:start position:0%
+ready to report out their
+recommendation and I told them I'd come
+
+ align:start position:0%
+recommendation and I told them I'd come
+ 
+
+ align:start position:0%
+recommendation and I told them I'd come
+and find out whether you were ready to
+
+ align:start position:0%
+and find out whether you were ready to
+ 
+
+ align:start position:0%
+and find out whether you were ready to
+hear it or not are you sitting down and
+
+ align:start position:0%
+hear it or not are you sitting down and
+ 
+
+ align:start position:0%
+hear it or not are you sitting down and
+I said sure and he said well their
+
+ align:start position:0%
+I said sure and he said well their
+ 
+
+ align:start position:0%
+I said sure and he said well their
+conclusion is we could we should give
+
+ align:start position:0%
+conclusion is we could we should give
+ 
+
+ align:start position:0%
+conclusion is we could we should give
+away all of the course materials at MIT
+
+ align:start position:0%
+away all of the course materials at MIT
+ 
+
+ align:start position:0%
+away all of the course materials at MIT
+on all 2,000 of our subjects on the web
+
+ align:start position:0%
+on all 2,000 of our subjects on the web
+ 
+
+ align:start position:0%
+on all 2,000 of our subjects on the web
+for free for anybody that wants it now
+
+ align:start position:0%
+for free for anybody that wants it now
+ 
+
+ align:start position:0%
+for free for anybody that wants it now
+those of you who have worked with me uh
+
+ align:start position:0%
+those of you who have worked with me uh
+ 
+
+ align:start position:0%
+those of you who have worked with me uh
+uh closely like Bob and Larry and so
+
+ align:start position:0%
+uh closely like Bob and Larry and so
+ 
+
+ align:start position:0%
+uh closely like Bob and Larry and so
+forth no I tend to Maul I've got to hear
+
+ align:start position:0%
+forth no I tend to Maul I've got to hear
+ 
+
+ align:start position:0%
+forth no I tend to Maul I've got to hear
+all sides sit sleep roll around in bed
+
+ align:start position:0%
+all sides sit sleep roll around in bed
+ 
+
+ align:start position:0%
+all sides sit sleep roll around in bed
+wearing about at night but somehow this
+
+ align:start position:0%
+wearing about at night but somehow this
+ 
+
+ align:start position:0%
+wearing about at night but somehow this
+instantly connected in my mind with this
+
+ align:start position:0%
+instantly connected in my mind with this
+ 
+
+ align:start position:0%
+instantly connected in my mind with this
+experience of what MIT had done for
+
+ align:start position:0%
+experience of what MIT had done for
+ 
+
+ align:start position:0%
+experience of what MIT had done for
+engineering education in the late 50s
+
+ align:start position:0%
+engineering education in the late 50s
+ 
+
+ align:start position:0%
+engineering education in the late 50s
+and and through the 60s and I just
+
+ align:start position:0%
+and and through the 60s and I just
+ 
+
+ align:start position:0%
+and and through the 60s and I just
+instantly knew this was a wonderful
+
+ align:start position:0%
+instantly knew this was a wonderful
+ 
+
+ align:start position:0%
+instantly knew this was a wonderful
+elegant idea and I was uh so grateful
+
+ align:start position:0%
+elegant idea and I was uh so grateful
+ 
+
+ align:start position:0%
+elegant idea and I was uh so grateful
+it's nothing I would have ever thought
+
+ align:start position:0%
+it's nothing I would have ever thought
+ 
+
+ align:start position:0%
+it's nothing I would have ever thought
+of I'm I'm quite sure in fact as others
+
+ align:start position:0%
+of I'm I'm quite sure in fact as others
+ 
+
+ align:start position:0%
+of I'm I'm quite sure in fact as others
+will tell you we were really going in
+
+ align:start position:0%
+will tell you we were really going in
+ 
+
+ align:start position:0%
+will tell you we were really going in
+expecting what we probably would do
+
+ align:start position:0%
+expecting what we probably would do
+ 
+
+ align:start position:0%
+expecting what we probably would do
+would be produce Cutting Edge modules
+
+ align:start position:0%
+would be produce Cutting Edge modules
+ 
+
+ align:start position:0%
+would be produce Cutting Edge modules
+that would work with our industry
+
+ align:start position:0%
+that would work with our industry
+ 
+
+ align:start position:0%
+that would work with our industry
+Partners we work with and with very
+
+ align:start position:0%
+Partners we work with and with very
+ 
+
+ align:start position:0%
+Partners we work with and with very
+high-end students and we'd uh uh try to
+
+ align:start position:0%
+high-end students and we'd uh uh try to
+ 
+
+ align:start position:0%
+high-end students and we'd uh uh try to
+make money or at least least cover costs
+
+ align:start position:0%
+make money or at least least cover costs
+ 
+
+ align:start position:0%
+make money or at least least cover costs
+but I just for once in my life
+
+ align:start position:0%
+but I just for once in my life
+ 
+
+ align:start position:0%
+but I just for once in my life
+recognized what a beautiful idea it was
+
+ align:start position:0%
+recognized what a beautiful idea it was
+ 
+
+ align:start position:0%
+recognized what a beautiful idea it was
+and decided I was going to roll up my
+
+ align:start position:0%
+and decided I was going to roll up my
+ 
+
+ align:start position:0%
+and decided I was going to roll up my
+sleeves and and try to help my colleagu
+
+ align:start position:0%
+sleeves and and try to help my colleagu
+ 
+
+ align:start position:0%
+sleeves and and try to help my colleagu
+colleagues realize this wonderful vision
+
+ align:start position:0%
+colleagues realize this wonderful vision
+ 
+
+ align:start position:0%
+colleagues realize this wonderful vision
+and so u i called Bill Bowen who was uh
+
+ align:start position:0%
+and so u i called Bill Bowen who was uh
+ 
+
+ align:start position:0%
+and so u i called Bill Bowen who was uh
+at that time the former president of of
+
+ align:start position:0%
+at that time the former president of of
+ 
+
+ align:start position:0%
+at that time the former president of of
+Princeton University and somebody I just
+
+ align:start position:0%
+Princeton University and somebody I just
+ 
+
+ align:start position:0%
+Princeton University and somebody I just
+enormously admire and he was then the
+
+ align:start position:0%
+enormously admire and he was then the
+ 
+
+ align:start position:0%
+enormously admire and he was then the
+president of the melon foundation so I
+
+ align:start position:0%
+president of the melon foundation so I
+ 
+
+ align:start position:0%
+president of the melon foundation so I
+called up to see if I could get an
+
+ align:start position:0%
+called up to see if I could get an
+ 
+
+ align:start position:0%
+called up to see if I could get an
+appointment because I was going to be in
+
+ align:start position:0%
+appointment because I was going to be in
+ 
+
+ align:start position:0%
+appointment because I was going to be in
+New York for another reason he said my
+
+ align:start position:0%
+New York for another reason he said my
+ 
+
+ align:start position:0%
+New York for another reason he said my
+schedule's busy but we'll have breakfast
+
+ align:start position:0%
+schedule's busy but we'll have breakfast
+ 
+
+ align:start position:0%
+schedule's busy but we'll have breakfast
+together so uh I met bill for breakfast
+
+ align:start position:0%
+together so uh I met bill for breakfast
+ 
+
+ align:start position:0%
+together so uh I met bill for breakfast
+and uh a little place there not too far
+
+ align:start position:0%
+and uh a little place there not too far
+ 
+
+ align:start position:0%
+and uh a little place there not too far
+from melon's offices and I had a
+
+ align:start position:0%
+from melon's offices and I had a
+ 
+
+ align:start position:0%
+from melon's offices and I had a
+Florentine omelet I can still remember
+
+ align:start position:0%
+Florentine omelet I can still remember
+ 
+
+ align:start position:0%
+Florentine omelet I can still remember
+that and I said Bill and of course I'd
+
+ align:start position:0%
+that and I said Bill and of course I'd
+ 
+
+ align:start position:0%
+that and I said Bill and of course I'd
+really rehearsed what I wanted to say to
+
+ align:start position:0%
+really rehearsed what I wanted to say to
+ 
+
+ align:start position:0%
+really rehearsed what I wanted to say to
+him because I knew I didn't have much
+
+ align:start position:0%
+him because I knew I didn't have much
+ 
+
+ align:start position:0%
+him because I knew I didn't have much
+time I said Bill the faculty in MIT have
+
+ align:start position:0%
+time I said Bill the faculty in MIT have
+ 
+
+ align:start position:0%
+time I said Bill the faculty in MIT have
+come up with an extraordinary idea and
+
+ align:start position:0%
+come up with an extraordinary idea and
+ 
+
+ align:start position:0%
+come up with an extraordinary idea and
+because I respect you so much as a
+
+ align:start position:0%
+because I respect you so much as a
+ 
+
+ align:start position:0%
+because I respect you so much as a
+leader in higher education I want to
+
+ align:start position:0%
+leader in higher education I want to
+ 
+
+ align:start position:0%
+leader in higher education I want to
+know first of all do you think it's a
+
+ align:start position:0%
+know first of all do you think it's a
+ 
+
+ align:start position:0%
+know first of all do you think it's a
+good idea and second I want to know if
+
+ align:start position:0%
+good idea and second I want to know if
+ 
+
+ align:start position:0%
+good idea and second I want to know if
+you think it's a good idea do you think
+
+ align:start position:0%
+you think it's a good idea do you think
+ 
+
+ align:start position:0%
+you think it's a good idea do you think
+it's the kind of thing that might appeal
+
+ align:start position:0%
+it's the kind of thing that might appeal
+ 
+
+ align:start position:0%
+it's the kind of thing that might appeal
+to a foundation to support and third if
+
+ align:start position:0%
+to a foundation to support and third if
+ 
+
+ align:start position:0%
+to a foundation to support and third if
+you say the answer to that is yes I'm
+
+ align:start position:0%
+you say the answer to that is yes I'm
+ 
+
+ align:start position:0%
+you say the answer to that is yes I'm
+obviously going to ask you if you think
+
+ align:start position:0%
+obviously going to ask you if you think
+ 
+
+ align:start position:0%
+obviously going to ask you if you think
+the melon Foundation might be interested
+
+ align:start position:0%
+the melon Foundation might be interested
+ 
+
+ align:start position:0%
+the melon Foundation might be interested
+in supporting it and I then kind of laid
+
+ align:start position:0%
+in supporting it and I then kind of laid
+ 
+
+ align:start position:0%
+in supporting it and I then kind of laid
+out in just three or four or five
+
+ align:start position:0%
+out in just three or four or five
+ 
+
+ align:start position:0%
+out in just three or four or five
+sentences the idea and that this could
+
+ align:start position:0%
+sentences the idea and that this could
+ 
+
+ align:start position:0%
+sentences the idea and that this could
+accomplish the kind of things that I'd
+
+ align:start position:0%
+accomplish the kind of things that I'd
+ 
+
+ align:start position:0%
+accomplish the kind of things that I'd
+seen in an earlier age with these notes
+
+ align:start position:0%
+seen in an earlier age with these notes
+ 
+
+ align:start position:0%
+seen in an earlier age with these notes
+and experiments going out around the
+
+ align:start position:0%
+and experiments going out around the
+ 
+
+ align:start position:0%
+and experiments going out around the
+country but we could do it at internet
+
+ align:start position:0%
+country but we could do it at internet
+ 
+
+ align:start position:0%
+country but we could do it at internet
+time remember that was a big phrase
+
+ align:start position:0%
+time remember that was a big phrase
+ 
+
+ align:start position:0%
+time remember that was a big phrase
+those days internet time and we could do
+
+ align:start position:0%
+those days internet time and we could do
+ 
+
+ align:start position:0%
+those days internet time and we could do
+it for the whole world and Bill was
+
+ align:start position:0%
+it for the whole world and Bill was
+ 
+
+ align:start position:0%
+it for the whole world and Bill was
+silent for about half a minute and then
+
+ align:start position:0%
+silent for about half a minute and then
+ 
+
+ align:start position:0%
+silent for about half a minute and then
+he looked at me and he said we're going
+
+ align:start position:0%
+he looked at me and he said we're going
+ 
+
+ align:start position:0%
+he looked at me and he said we're going
+to figure out how to do this he said
+
+ align:start position:0%
+to figure out how to do this he said
+ 
+
+ align:start position:0%
+to figure out how to do this he said
+it's too much for melon but I'll get my
+
+ align:start position:0%
+it's too much for melon but I'll get my
+ 
+
+ align:start position:0%
+it's too much for melon but I'll get my
+board to agree to put some serious
+
+ align:start position:0%
+board to agree to put some serious
+ 
+
+ align:start position:0%
+board to agree to put some serious
+support in and we'll go together to heu
+
+ align:start position:0%
+support in and we'll go together to heu
+ 
+
+ align:start position:0%
+support in and we'll go together to heu
+it and we'll try to get the rest of it
+
+ align:start position:0%
+it and we'll try to get the rest of it
+ 
+
+ align:start position:0%
+it and we'll try to get the rest of it
+so having expected that I was launching
+
+ align:start position:0%
+so having expected that I was launching
+ 
+
+ align:start position:0%
+so having expected that I was launching
+into this two-year uh business uh we got
+
+ align:start position:0%
+into this two-year uh business uh we got
+ 
+
+ align:start position:0%
+into this two-year uh business uh we got
+a wonderful initial response and again
+
+ align:start position:0%
+a wonderful initial response and again
+ 
+
+ align:start position:0%
+a wonderful initial response and again
+uh from a sort of historical perspective
+
+ align:start position:0%
+uh from a sort of historical perspective
+ 
+
+ align:start position:0%
+uh from a sort of historical perspective
+I have to tell you something that I
+
+ align:start position:0%
+I have to tell you something that I
+ 
+
+ align:start position:0%
+I have to tell you something that I
+didn't know at the time I actually
+
+ align:start position:0%
+didn't know at the time I actually
+ 
+
+ align:start position:0%
+didn't know at the time I actually
+didn't know it for about 6 months after
+
+ align:start position:0%
+didn't know it for about 6 months after
+ 
+
+ align:start position:0%
+didn't know it for about 6 months after
+that Bill had just before this given a
+
+ align:start position:0%
+that Bill had just before this given a
+ 
+
+ align:start position:0%
+that Bill had just before this given a
+very prestigious lecture at Oxford
+
+ align:start position:0%
+very prestigious lecture at Oxford
+ 
+
+ align:start position:0%
+very prestigious lecture at Oxford
+University and the subject of his
+
+ align:start position:0%
+University and the subject of his
+ 
+
+ align:start position:0%
+University and the subject of his
+lecture was how are universities going
+
+ align:start position:0%
+lecture was how are universities going
+ 
+
+ align:start position:0%
+lecture was how are universities going
+to use the internet to promulgate their
+
+ align:start position:0%
+to use the internet to promulgate their
+ 
+
+ align:start position:0%
+to use the internet to promulgate their
+knowledge base and so you you know you
+
+ align:start position:0%
+knowledge base and so you you know you
+ 
+
+ align:start position:0%
+knowledge base and so you you know you
+you can never understand all the sort of
+
+ align:start position:0%
+you can never understand all the sort of
+ 
+
+ align:start position:0%
+you can never understand all the sort of
+psychological and and historical things
+
+ align:start position:0%
+psychological and and historical things
+ 
+
+ align:start position:0%
+psychological and and historical things
+that that go into a great great
+
+ align:start position:0%
+that that go into a great great
+ 
+
+ align:start position:0%
+that that go into a great great
+decisions so anyway uh from my
+
+ align:start position:0%
+decisions so anyway uh from my
+ 
+
+ align:start position:0%
+decisions so anyway uh from my
+perspective uh that was the uh the
+
+ align:start position:0%
+perspective uh that was the uh the
+ 
+
+ align:start position:0%
+perspective uh that was the uh the
+beginning of of the launch and the only
+
+ align:start position:0%
+beginning of of the launch and the only
+ 
+
+ align:start position:0%
+beginning of of the launch and the only
+other little anecdote I'll tell you on
+
+ align:start position:0%
+other little anecdote I'll tell you on
+ 
+
+ align:start position:0%
+other little anecdote I'll tell you on
+the funding part is it of course took a
+
+ align:start position:0%
+the funding part is it of course took a
+ 
+
+ align:start position:0%
+the funding part is it of course took a
+while to get this package to go to the
+
+ align:start position:0%
+while to get this package to go to the
+ 
+
+ align:start position:0%
+while to get this package to go to the
+melon Foundation board and uh Hal and
+
+ align:start position:0%
+melon Foundation board and uh Hal and
+ 
+
+ align:start position:0%
+melon Foundation board and uh Hal and
+others uh worked really hard on on
+
+ align:start position:0%
+others uh worked really hard on on
+ 
+
+ align:start position:0%
+others uh worked really hard on on
+getting it right and and building in at
+
+ align:start position:0%
+getting it right and and building in at
+ 
+
+ align:start position:0%
+getting it right and and building in at
+the idea of how we were going to
+
+ align:start position:0%
+the idea of how we were going to
+ 
+
+ align:start position:0%
+the idea of how we were going to
+instrument it and understand what it was
+
+ align:start position:0%
+instrument it and understand what it was
+ 
+
+ align:start position:0%
+instrument it and understand what it was
+doing and so forth and Bill called me
+
+ align:start position:0%
+doing and so forth and Bill called me
+ 
+
+ align:start position:0%
+doing and so forth and Bill called me
+back and I said so how did it go with
+
+ align:start position:0%
+back and I said so how did it go with
+ 
+
+ align:start position:0%
+back and I said so how did it go with
+the board and he said well they had one
+
+ align:start position:0%
+the board and he said well they had one
+ 
+
+ align:start position:0%
+the board and he said well they had one
+big question they want to know is this
+
+ align:start position:0%
+big question they want to know is this
+ 
+
+ align:start position:0%
+big question they want to know is this
+just one of Chuck's crazy ideas or is
+
+ align:start position:0%
+just one of Chuck's crazy ideas or is
+ 
+
+ align:start position:0%
+just one of Chuck's crazy ideas or is
+MIT Roy behind this so
+
+ align:start position:0%
+MIT Roy behind this so
+ 
+
+ align:start position:0%
+MIT Roy behind this so
+so anyway that's just a little bit of an
+
+ align:start position:0%
+so anyway that's just a little bit of an
+ 
+
+ align:start position:0%
+so anyway that's just a little bit of an
+opening but I very much look forward to
+
+ align:start position:0%
+opening but I very much look forward to
+ 
+
+ align:start position:0%
+opening but I very much look forward to
+my colleagues who really launched the
+
+ align:start position:0%
+my colleagues who really launched the
+ 
+
+ align:start position:0%
+my colleagues who really launched the
+the idea and then made it happen what
+
+ align:start position:0%
+the idea and then made it happen what
+ 
+
+ align:start position:0%
+the idea and then made it happen what
+they have to say great thank you U maybe
+
+ align:start position:0%
+they have to say great thank you U maybe
+ 
+
+ align:start position:0%
+they have to say great thank you U maybe
+then a question for Dr Brown uh maybe
+
+ align:start position:0%
+then a question for Dr Brown uh maybe
+ 
+
+ align:start position:0%
+then a question for Dr Brown uh maybe
+you could speak a little bit about uh
+
+ align:start position:0%
+you could speak a little bit about uh
+ 
+
+ align:start position:0%
+you could speak a little bit about uh
+the activities of our peer institutions
+
+ align:start position:0%
+the activities of our peer institutions
+ 
+
+ align:start position:0%
+the activities of our peer institutions
+and what they were doing at the time and
+
+ align:start position:0%
+and what they were doing at the time and
+ 
+
+ align:start position:0%
+and what they were doing at the time and
+how that influenced the thinking of uh
+
+ align:start position:0%
+how that influenced the thinking of uh
+ 
+
+ align:start position:0%
+how that influenced the thinking of uh
+mset as they handed off the charge to
+
+ align:start position:0%
+mset as they handed off the charge to
+ 
+
+ align:start position:0%
+mset as they handed off the charge to
+the committee on lifelong learning thank
+
+ align:start position:0%
+the committee on lifelong learning thank
+ 
+
+ align:start position:0%
+the committee on lifelong learning thank
+you steveen it is really a pleasure to
+
+ align:start position:0%
+you steveen it is really a pleasure to
+ 
+
+ align:start position:0%
+you steveen it is really a pleasure to
+be here this morning and and to
+
+ align:start position:0%
+be here this morning and and to
+ 
+
+ align:start position:0%
+be here this morning and and to
+celebrate the 10th anniversary of ocw I
+
+ align:start position:0%
+celebrate the 10th anniversary of ocw I
+ 
+
+ align:start position:0%
+celebrate the 10th anniversary of ocw I
+can remember times in the beginning of
+
+ align:start position:0%
+can remember times in the beginning of
+ 
+
+ align:start position:0%
+can remember times in the beginning of
+this project where we didn't think we'd
+
+ align:start position:0%
+this project where we didn't think we'd
+ 
+
+ align:start position:0%
+this project where we didn't think we'd
+ever get a first
+
+ align:start position:0%
+ever get a first
+ 
+
+ align:start position:0%
+ever get a first
+anniversary uh but I think it is
+
+ align:start position:0%
+anniversary uh but I think it is
+ 
+
+ align:start position:0%
+anniversary uh but I think it is
+important in in what Chuck said to set a
+
+ align:start position:0%
+important in in what Chuck said to set a
+ 
+
+ align:start position:0%
+important in in what Chuck said to set a
+bit of historical context and and
+
+ align:start position:0%
+bit of historical context and and
+ 
+
+ align:start position:0%
+bit of historical context and and
+although U great ideas like ocw really
+
+ align:start position:0%
+although U great ideas like ocw really
+ 
+
+ align:start position:0%
+although U great ideas like ocw really
+do come from The Faculty the bottom up
+
+ align:start position:0%
+do come from The Faculty the bottom up
+ 
+
+ align:start position:0%
+do come from The Faculty the bottom up
+there was a nugget of an idea that was
+
+ align:start position:0%
+there was a nugget of an idea that was
+ 
+
+ align:start position:0%
+there was a nugget of an idea that was
+actually coming from the top down and
+
+ align:start position:0%
+actually coming from the top down and
+ 
+
+ align:start position:0%
+actually coming from the top down and
+and Chuck played an enormous role here
+
+ align:start position:0%
+and Chuck played an enormous role here
+ 
+
+ align:start position:0%
+and Chuck played an enormous role here
+here and it begins in the summer of
+
+ align:start position:0%
+here and it begins in the summer of
+ 
+
+ align:start position:0%
+here and it begins in the summer of
+1998 when Larry and I had just assumed
+
+ align:start position:0%
+1998 when Larry and I had just assumed
+ 
+
+ align:start position:0%
+1998 when Larry and I had just assumed
+positions uh to work with Chuck in the
+
+ align:start position:0%
+positions uh to work with Chuck in the
+ 
+
+ align:start position:0%
+positions uh to work with Chuck in the
+upper administration at MIT and we sat
+
+ align:start position:0%
+upper administration at MIT and we sat
+ 
+
+ align:start position:0%
+upper administration at MIT and we sat
+down and had a meeting and and we did
+
+ align:start position:0%
+down and had a meeting and and we did
+ 
+
+ align:start position:0%
+down and had a meeting and and we did
+this almost annually uh to kind of chart
+
+ align:start position:0%
+this almost annually uh to kind of chart
+ 
+
+ align:start position:0%
+this almost annually uh to kind of chart
+the course for the next year at a where
+
+ align:start position:0%
+the course for the next year at a where
+ 
+
+ align:start position:0%
+the course for the next year at a where
+are we going to spend our time level
+
+ align:start position:0%
+are we going to spend our time level
+ 
+
+ align:start position:0%
+are we going to spend our time level
+what are the things beside making the
+
+ align:start position:0%
+what are the things beside making the
+ 
+
+ align:start position:0%
+what are the things beside making the
+trains run on time where are we going to
+
+ align:start position:0%
+trains run on time where are we going to
+ 
+
+ align:start position:0%
+trains run on time where are we going to
+spend our time u in the institution try
+
+ align:start position:0%
+spend our time u in the institution try
+ 
+
+ align:start position:0%
+spend our time u in the institution try
+to get mobilization behind concept
+
+ align:start position:0%
+to get mobilization behind concept
+ 
+
+ align:start position:0%
+to get mobilization behind concept
+and it was very clear in
+
+ align:start position:0%
+and it was very clear in
+ 
+
+ align:start position:0%
+and it was very clear in
+1998 that MIT was underinvested in
+
+ align:start position:0%
+1998 that MIT was underinvested in
+ 
+
+ align:start position:0%
+1998 that MIT was underinvested in
+educational technology underinvested in
+
+ align:start position:0%
+educational technology underinvested in
+ 
+
+ align:start position:0%
+educational technology underinvested in
+how we were going to innovate in
+
+ align:start position:0%
+how we were going to innovate in
+ 
+
+ align:start position:0%
+how we were going to innovate in
+education interior internally and
+
+ align:start position:0%
+education interior internally and
+ 
+
+ align:start position:0%
+education interior internally and
+externally and there were questions
+
+ align:start position:0%
+externally and there were questions
+ 
+
+ align:start position:0%
+externally and there were questions
+about were we too stagnant and that we
+
+ align:start position:0%
+about were we too stagnant and that we
+ 
+
+ align:start position:0%
+about were we too stagnant and that we
+would wake up 5 years 10 years down the
+
+ align:start position:0%
+would wake up 5 years 10 years down the
+ 
+
+ align:start position:0%
+would wake up 5 years 10 years down the
+road and be left behind by others
+
+ align:start position:0%
+road and be left behind by others
+ 
+
+ align:start position:0%
+road and be left behind by others
+frankly and there were other things
+
+ align:start position:0%
+frankly and there were other things
+ 
+
+ align:start position:0%
+frankly and there were other things
+going on in the in the universe at that
+
+ align:start position:0%
+going on in the in the universe at that
+ 
+
+ align:start position:0%
+going on in the in the universe at that
+point uh within the 98 99 time frame
+
+ align:start position:0%
+point uh within the 98 99 time frame
+ 
+
+ align:start position:0%
+point uh within the 98 99 time frame
+Cornell launched Morningside Ventures
+
+ align:start position:0%
+Cornell launched Morningside Ventures
+ 
+
+ align:start position:0%
+Cornell launched Morningside Ventures
+which was a for-profit entity that was
+
+ align:start position:0%
+which was a for-profit entity that was
+ 
+
+ align:start position:0%
+which was a for-profit entity that was
+going to uh commercialize content and uh
+
+ align:start position:0%
+going to uh commercialize content and uh
+ 
+
+ align:start position:0%
+going to uh commercialize content and uh
+for Carnell e Carnell was formed Yale
+
+ align:start position:0%
+for Carnell e Carnell was formed Yale
+ 
+
+ align:start position:0%
+for Carnell e Carnell was formed Yale
+started their Alumni network which I
+
+ align:start position:0%
+started their Alumni network which I
+ 
+
+ align:start position:0%
+started their Alumni network which I
+think later Princeton joined and it
+
+ align:start position:0%
+think later Princeton joined and it
+ 
+
+ align:start position:0%
+think later Princeton joined and it
+morphed a few times Oxford Stanford
+
+ align:start position:0%
+morphed a few times Oxford Stanford
+ 
+
+ align:start position:0%
+morphed a few times Oxford Stanford
+Oxford Stanford so there were
+
+ align:start position:0%
+Oxford Stanford so there were
+ 
+
+ align:start position:0%
+Oxford Stanford so there were
+institution starting to mobilize based
+
+ align:start position:0%
+institution starting to mobilize based
+ 
+
+ align:start position:0%
+institution starting to mobilize based
+on the internet and so there was a real
+
+ align:start position:0%
+on the internet and so there was a real
+ 
+
+ align:start position:0%
+on the internet and so there was a real
+question on what the internet in and uh
+
+ align:start position:0%
+question on what the internet in and uh
+ 
+
+ align:start position:0%
+question on what the internet in and uh
+uh distance education in that context
+
+ align:start position:0%
+uh distance education in that context
+ 
+
+ align:start position:0%
+uh distance education in that context
+was going to do to for for uh MIT so
+
+ align:start position:0%
+was going to do to for for uh MIT so
+ 
+
+ align:start position:0%
+was going to do to for for uh MIT so
+after a period of consultation I
+
+ align:start position:0%
+after a period of consultation I
+ 
+
+ align:start position:0%
+after a period of consultation I
+remember talking to how I remember
+
+ align:start position:0%
+remember talking to how I remember
+ 
+
+ align:start position:0%
+remember talking to how I remember
+talking to Steve lman who was running a
+
+ align:start position:0%
+talking to Steve lman who was running a
+ 
+
+ align:start position:0%
+talking to Steve lman who was running a
+center on distance education within MIT
+
+ align:start position:0%
+center on distance education within MIT
+ 
+
+ align:start position:0%
+center on distance education within MIT
+at that point a lot of meetings we
+
+ align:start position:0%
+at that point a lot of meetings we
+ 
+
+ align:start position:0%
+at that point a lot of meetings we
+decided in the spring of 99 to form the
+
+ align:start position:0%
+decided in the spring of 99 to form the
+ 
+
+ align:start position:0%
+decided in the spring of 99 to form the
+Council on educational
+
+ align:start position:0%
+Council on educational
+ 
+
+ align:start position:0%
+Council on educational
+technology with a number of different
+
+ align:start position:0%
+technology with a number of different
+ 
+
+ align:start position:0%
+technology with a number of different
+purposes one is highlighting the demand
+
+ align:start position:0%
+purposes one is highlighting the demand
+ 
+
+ align:start position:0%
+purposes one is highlighting the demand
+for innovating in uh the classroom
+
+ align:start position:0%
+for innovating in uh the classroom
+ 
+
+ align:start position:0%
+for innovating in uh the classroom
+Within the institution and then the
+
+ align:start position:0%
+Within the institution and then the
+ 
+
+ align:start position:0%
+Within the institution and then the
+other uh working groups as Steve has
+
+ align:start position:0%
+other uh working groups as Steve has
+ 
+
+ align:start position:0%
+other uh working groups as Steve has
+said looking at the context for external
+
+ align:start position:0%
+said looking at the context for external
+ 
+
+ align:start position:0%
+said looking at the context for external
+impact both through our lumni and uh in
+
+ align:start position:0%
+impact both through our lumni and uh in
+ 
+
+ align:start position:0%
+impact both through our lumni and uh in
+the larger distance education world uh
+
+ align:start position:0%
+the larger distance education world uh
+ 
+
+ align:start position:0%
+the larger distance education world uh
+Steve laid out kind of the Genesis of
+
+ align:start position:0%
+Steve laid out kind of the Genesis of
+ 
+
+ align:start position:0%
+Steve laid out kind of the Genesis of
+the working groups and how the report
+
+ align:start position:0%
+the working groups and how the report
+ 
+
+ align:start position:0%
+the working groups and how the report
+was formed I the one underpinning I
+
+ align:start position:0%
+was formed I the one underpinning I
+ 
+
+ align:start position:0%
+was formed I the one underpinning I
+would like to keep adding to this is I
+
+ align:start position:0%
+would like to keep adding to this is I
+ 
+
+ align:start position:0%
+would like to keep adding to this is I
+it was one of the really interesting
+
+ align:start position:0%
+it was one of the really interesting
+ 
+
+ align:start position:0%
+it was one of the really interesting
+discussions all through this process is
+
+ align:start position:0%
+discussions all through this process is
+ 
+
+ align:start position:0%
+discussions all through this process is
+how this would change
+
+ align:start position:0%
+how this would change
+ 
+
+ align:start position:0%
+how this would change
+MIT not only giving the content of the
+
+ align:start position:0%
+MIT not only giving the content of the
+ 
+
+ align:start position:0%
+MIT not only giving the content of the
+world not only thinking about the the
+
+ align:start position:0%
+world not only thinking about the the
+ 
+
+ align:start position:0%
+world not only thinking about the the
+consequences as I like to say that
+
+ align:start position:0%
+consequences as I like to say that
+ 
+
+ align:start position:0%
+consequences as I like to say that
+there's a lot more smart people in the
+
+ align:start position:0%
+there's a lot more smart people in the
+ 
+
+ align:start position:0%
+there's a lot more smart people in the
+world than we can admit as students that
+
+ align:start position:0%
+world than we can admit as students that
+ 
+
+ align:start position:0%
+world than we can admit as students that
+there's a but there were other contexts
+
+ align:start position:0%
+there's a but there were other contexts
+ 
+
+ align:start position:0%
+there's a but there were other contexts
+that were going on
+
+ align:start position:0%
+that were going on
+ 
+
+ align:start position:0%
+that were going on
+simultaneously uh at at this at the same
+
+ align:start position:0%
+simultaneously uh at at this at the same
+ 
+
+ align:start position:0%
+simultaneously uh at at this at the same
+time what you you found inside uh MIT in
+
+ align:start position:0%
+time what you you found inside uh MIT in
+ 
+
+ align:start position:0%
+time what you you found inside uh MIT in
+the discussion of ocw is the issue of
+
+ align:start position:0%
+the discussion of ocw is the issue of
+ 
+
+ align:start position:0%
+the discussion of ocw is the issue of
+how would people use classroom time when
+
+ align:start position:0%
+how would people use classroom time when
+ 
+
+ align:start position:0%
+how would people use classroom time when
+all their content was on the
+
+ align:start position:0%
+all their content was on the
+ 
+
+ align:start position:0%
+all their content was on the
+web and and the what I call the great
+
+ align:start position:0%
+web and and the what I call the great
+ 
+
+ align:start position:0%
+web and and the what I call the great
+transference where you take a piece of
+
+ align:start position:0%
+transference where you take a piece of
+ 
+
+ align:start position:0%
+transference where you take a piece of
+chalk and you take your notes and you
+
+ align:start position:0%
+chalk and you take your notes and you
+ 
+
+ align:start position:0%
+chalk and you take your notes and you
+write your notes on the Blackboard and
+
+ align:start position:0%
+write your notes on the Blackboard and
+ 
+
+ align:start position:0%
+write your notes on the Blackboard and
+then they write their notes into their
+
+ align:start position:0%
+then they write their notes into their
+ 
+
+ align:start position:0%
+then they write their notes into their
+notebook which was the classical mode of
+
+ align:start position:0%
+notebook which was the classical mode of
+ 
+
+ align:start position:0%
+notebook which was the classical mode of
+teaching and was still very prevalent in
+
+ align:start position:0%
+teaching and was still very prevalent in
+ 
+
+ align:start position:0%
+teaching and was still very prevalent in
+the year 2000 at MIT what would happen
+
+ align:start position:0%
+the year 2000 at MIT what would happen
+ 
+
+ align:start position:0%
+the year 2000 at MIT what would happen
+if you broke that down if all the
+
+ align:start position:0%
+if you broke that down if all the
+ 
+
+ align:start position:0%
+if you broke that down if all the
+content for all those courses was on the
+
+ align:start position:0%
+content for all those courses was on the
+ 
+
+ align:start position:0%
+content for all those courses was on the
+web what would it mean for the
+
+ align:start position:0%
+web what would it mean for the
+ 
+
+ align:start position:0%
+web what would it mean for the
+discussion between a professor in
+
+ align:start position:0%
+discussion between a professor in
+ 
+
+ align:start position:0%
+discussion between a professor in
+mathematics and a professor in pick your
+
+ align:start position:0%
+mathematics and a professor in pick your
+ 
+
+ align:start position:0%
+mathematics and a professor in pick your
+favorite engineering discipline when
+
+ align:start position:0%
+favorite engineering discipline when
+ 
+
+ align:start position:0%
+favorite engineering discipline when
+they talk about the relevance of the
+
+ align:start position:0%
+they talk about the relevance of the
+ 
+
+ align:start position:0%
+they talk about the relevance of the
+course called differential equations
+
+ align:start position:0%
+course called differential equations
+ 
+
+ align:start position:0%
+course called differential equations
+when the you could the math professor
+
+ align:start position:0%
+when the you could the math professor
+ 
+
+ align:start position:0%
+when the you could the math professor
+could see how the content they were
+
+ align:start position:0%
+could see how the content they were
+ 
+
+ align:start position:0%
+could see how the content they were
+using in differential equation or
+
+ align:start position:0%
+using in differential equation or
+ 
+
+ align:start position:0%
+using in differential equation or
+teaching in differential equations was
+
+ align:start position:0%
+teaching in differential equations was
+ 
+
+ align:start position:0%
+teaching in differential equations was
+being used in chemical engineering or
+
+ align:start position:0%
+being used in chemical engineering or
+ 
+
+ align:start position:0%
+being used in chemical engineering or
+aerospace engineering or chemistry or
+
+ align:start position:0%
+aerospace engineering or chemistry or
+ 
+
+ align:start position:0%
+aerospace engineering or chemistry or
+physics and how the students could go
+
+ align:start position:0%
+physics and how the students could go
+ 
+
+ align:start position:0%
+physics and how the students could go
+see it even if the professor didn't that
+
+ align:start position:0%
+see it even if the professor didn't that
+ 
+
+ align:start position:0%
+see it even if the professor didn't that
+you could link these things back and
+
+ align:start position:0%
+you could link these things back and
+ 
+
+ align:start position:0%
+you could link these things back and
+forth because all the content the way it
+
+ align:start position:0%
+forth because all the content the way it
+ 
+
+ align:start position:0%
+forth because all the content the way it
+was being taught was available
+
+ align:start position:0%
+was being taught was available
+ 
+
+ align:start position:0%
+was being taught was available
+internally I think that those those
+
+ align:start position:0%
+internally I think that those those
+ 
+
+ align:start position:0%
+internally I think that those those
+ideas actually captivated a Fair number
+
+ align:start position:0%
+ideas actually captivated a Fair number
+ 
+
+ align:start position:0%
+ideas actually captivated a Fair number
+of the MIT faculty and brought them into
+
+ align:start position:0%
+of the MIT faculty and brought them into
+ 
+
+ align:start position:0%
+of the MIT faculty and brought them into
+the ocw initiative at the same time um
+
+ align:start position:0%
+the ocw initiative at the same time um
+ 
+
+ align:start position:0%
+the ocw initiative at the same time um
+when when you think about uh whether or
+
+ align:start position:0%
+when when you think about uh whether or
+ 
+
+ align:start position:0%
+when when you think about uh whether or
+not those things have actually occurred
+
+ align:start position:0%
+not those things have actually occurred
+ 
+
+ align:start position:0%
+not those things have actually occurred
+and how an
+
+ align:start position:0%
+and how an
+ 
+
+ align:start position:0%
+and how an
+institution uh changes over time we one
+
+ align:start position:0%
+institution uh changes over time we one
+ 
+
+ align:start position:0%
+institution uh changes over time we one
+of the things we deal with is that these
+
+ align:start position:0%
+of the things we deal with is that these
+ 
+
+ align:start position:0%
+of the things we deal with is that these
+institutions change culturally very very
+
+ align:start position:0%
+institutions change culturally very very
+ 
+
+ align:start position:0%
+institutions change culturally very very
+slowly and I think uh uh that ocw really
+
+ align:start position:0%
+slowly and I think uh uh that ocw really
+ 
+
+ align:start position:0%
+slowly and I think uh uh that ocw really
+marks a revolution in the way they share
+
+ align:start position:0%
+marks a revolution in the way they share
+ 
+
+ align:start position:0%
+marks a revolution in the way they share
+the content in inside in my both
+
+ align:start position:0%
+the content in inside in my both
+ 
+
+ align:start position:0%
+the content in inside in my both
+internally and
+
+ align:start position:0%
+internally and
+ 
+
+ align:start position:0%
+internally and
+externally great thank you very much did
+
+ align:start position:0%
+externally great thank you very much did
+ 
+
+ align:start position:0%
+externally great thank you very much did
+you want to jump in I just wanted to to
+
+ align:start position:0%
+you want to jump in I just wanted to to
+ 
+
+ align:start position:0%
+you want to jump in I just wanted to to
+add that uh you know it's it's easy to
+
+ align:start position:0%
+add that uh you know it's it's easy to
+ 
+
+ align:start position:0%
+add that uh you know it's it's easy to
+sit here with the benefit of 10 years of
+
+ align:start position:0%
+sit here with the benefit of 10 years of
+ 
+
+ align:start position:0%
+sit here with the benefit of 10 years of
+success to look back and and conclude
+
+ align:start position:0%
+success to look back and and conclude
+ 
+
+ align:start position:0%
+success to look back and and conclude
+that uh of course this is this is how it
+
+ align:start position:0%
+that uh of course this is this is how it
+ 
+
+ align:start position:0%
+that uh of course this is this is how it
+was going to turn out but it was also
+
+ align:start position:0%
+was going to turn out but it was also
+ 
+
+ align:start position:0%
+was going to turn out but it was also
+true that there was a fair amount of
+
+ align:start position:0%
+true that there was a fair amount of
+ 
+
+ align:start position:0%
+true that there was a fair amount of
+skepticism on the MIT faculty at the
+
+ align:start position:0%
+skepticism on the MIT faculty at the
+ 
+
+ align:start position:0%
+skepticism on the MIT faculty at the
+time and that there were faculty who
+
+ align:start position:0%
+time and that there were faculty who
+ 
+
+ align:start position:0%
+time and that there were faculty who
+were worried about um I think the the
+
+ align:start position:0%
+were worried about um I think the the
+ 
+
+ align:start position:0%
+were worried about um I think the the
+expra the phrase that that was um that
+
+ align:start position:0%
+expra the phrase that that was um that
+ 
+
+ align:start position:0%
+expra the phrase that that was um that
+was used was an another unfunded mandate
+
+ align:start position:0%
+was used was an another unfunded mandate
+ 
+
+ align:start position:0%
+was used was an another unfunded mandate
+uh that faculty would be required to
+
+ align:start position:0%
+uh that faculty would be required to
+ 
+
+ align:start position:0%
+uh that faculty would be required to
+spend uh considerable amounts of time uh
+
+ align:start position:0%
+spend uh considerable amounts of time uh
+ 
+
+ align:start position:0%
+spend uh considerable amounts of time uh
+putting their content up on the web uh
+
+ align:start position:0%
+putting their content up on the web uh
+ 
+
+ align:start position:0%
+putting their content up on the web uh
+and that this would distract them from
+
+ align:start position:0%
+and that this would distract them from
+ 
+
+ align:start position:0%
+and that this would distract them from
+what they saw as you know the real work
+
+ align:start position:0%
+what they saw as you know the real work
+ 
+
+ align:start position:0%
+what they saw as you know the real work
+of the faculty and again here I want to
+
+ align:start position:0%
+of the faculty and again here I want to
+ 
+
+ align:start position:0%
+of the faculty and again here I want to
+credit my colleagues uh who are sitting
+
+ align:start position:0%
+credit my colleagues uh who are sitting
+ 
+
+ align:start position:0%
+credit my colleagues uh who are sitting
+around me because I think that one of
+
+ align:start position:0%
+around me because I think that one of
+ 
+
+ align:start position:0%
+around me because I think that one of
+the ways in which this worked is uh
+
+ align:start position:0%
+the ways in which this worked is uh
+ 
+
+ align:start position:0%
+the ways in which this worked is uh
+Chuck was successful in getting hulet
+
+ align:start position:0%
+Chuck was successful in getting hulet
+ 
+
+ align:start position:0%
+Chuck was successful in getting hulet
+and melon to put a significant amount of
+
+ align:start position:0%
+and melon to put a significant amount of
+ 
+
+ align:start position:0%
+and melon to put a significant amount of
+money on the table so people understood
+
+ align:start position:0%
+money on the table so people understood
+ 
+
+ align:start position:0%
+money on the table so people understood
+immediately that there would be
+
+ align:start position:0%
+immediately that there would be
+ 
+
+ align:start position:0%
+immediately that there would be
+incremental resources to help folks and
+
+ align:start position:0%
+incremental resources to help folks and
+ 
+
+ align:start position:0%
+incremental resources to help folks and
+then the rest of these guys managed a
+
+ align:start position:0%
+then the rest of these guys managed a
+ 
+
+ align:start position:0%
+then the rest of these guys managed a
+conversation in
+
+ align:start position:0%
+conversation in
+ 
+
+ align:start position:0%
+conversation in
+which people basically put their hands
+
+ align:start position:0%
+which people basically put their hands
+ 
+
+ align:start position:0%
+which people basically put their hands
+up in terms of who was going to be an
+
+ align:start position:0%
+up in terms of who was going to be an
+ 
+
+ align:start position:0%
+up in terms of who was going to be an
+early adopter uh and the strategy that
+
+ align:start position:0%
+early adopter uh and the strategy that
+ 
+
+ align:start position:0%
+early adopter uh and the strategy that
+actually got faculty to understand that
+
+ align:start position:0%
+actually got faculty to understand that
+ 
+
+ align:start position:0%
+actually got faculty to understand that
+it wasn't going to be shoved down their
+
+ align:start position:0%
+it wasn't going to be shoved down their
+ 
+
+ align:start position:0%
+it wasn't going to be shoved down their
+throat that people who wanted to come
+
+ align:start position:0%
+throat that people who wanted to come
+ 
+
+ align:start position:0%
+throat that people who wanted to come
+forward would be helped um and that it
+
+ align:start position:0%
+forward would be helped um and that it
+ 
+
+ align:start position:0%
+forward would be helped um and that it
+created really an existence proof that
+
+ align:start position:0%
+created really an existence proof that
+ 
+
+ align:start position:0%
+created really an existence proof that
+it could be done um and that it it would
+
+ align:start position:0%
+it could be done um and that it it would
+ 
+
+ align:start position:0%
+it could be done um and that it it would
+Aid the faculty in their teaching um and
+
+ align:start position:0%
+Aid the faculty in their teaching um and
+ 
+
+ align:start position:0%
+Aid the faculty in their teaching um and
+in their scholarship uh The Faculty
+
+ align:start position:0%
+in their scholarship uh The Faculty
+ 
+
+ align:start position:0%
+in their scholarship uh The Faculty
+would not be inundated with more work
+
+ align:start position:0%
+would not be inundated with more work
+ 
+
+ align:start position:0%
+would not be inundated with more work
+that would come over the transom from
+
+ align:start position:0%
+that would come over the transom from
+ 
+
+ align:start position:0%
+that would come over the transom from
+the the kids who were you know surfing
+
+ align:start position:0%
+the the kids who were you know surfing
+ 
+
+ align:start position:0%
+the the kids who were you know surfing
+the web and God knows where who who
+
+ align:start position:0%
+the web and God knows where who who
+ 
+
+ align:start position:0%
+the web and God knows where who who
+wanted to communicate directly with
+
+ align:start position:0%
+wanted to communicate directly with
+ 
+
+ align:start position:0%
+wanted to communicate directly with
+faculty with questions about uh
+
+ align:start position:0%
+faculty with questions about uh
+ 
+
+ align:start position:0%
+faculty with questions about uh
+particular assignments I think one
+
+ align:start position:0%
+particular assignments I think one
+ 
+
+ align:start position:0%
+particular assignments I think one
+should not underestimate the impact of
+
+ align:start position:0%
+should not underestimate the impact of
+ 
+
+ align:start position:0%
+should not underestimate the impact of
+of those decisions which I think allowed
+
+ align:start position:0%
+of those decisions which I think allowed
+ 
+
+ align:start position:0%
+of those decisions which I think allowed
+for a roll out and an acceptance within
+
+ align:start position:0%
+for a roll out and an acceptance within
+ 
+
+ align:start position:0%
+for a roll out and an acceptance within
+a faculty that you know there was a fair
+
+ align:start position:0%
+a faculty that you know there was a fair
+ 
+
+ align:start position:0%
+a faculty that you know there was a fair
+amount of skepticism um at the time uh
+
+ align:start position:0%
+amount of skepticism um at the time uh
+ 
+
+ align:start position:0%
+amount of skepticism um at the time uh
+we were talking earlier at times like
+
+ align:start position:0%
+we were talking earlier at times like
+ 
+
+ align:start position:0%
+we were talking earlier at times like
+this I'm reminded of Lenin's comments uh
+
+ align:start position:0%
+this I'm reminded of Lenin's comments uh
+ 
+
+ align:start position:0%
+this I'm reminded of Lenin's comments uh
+comment about
+
+ align:start position:0%
+comment about
+ 
+
+ align:start position:0%
+comment about
+revolutions and I always have to preface
+
+ align:start position:0%
+revolutions and I always have to preface
+ 
+
+ align:start position:0%
+revolutions and I always have to preface
+this by saying I'm talking about
+
+ align:start position:0%
+this by saying I'm talking about
+ 
+
+ align:start position:0%
+this by saying I'm talking about
+Vladimir lennin not John Lennon um and
+
+ align:start position:0%
+Vladimir lennin not John Lennon um and
+ 
+
+ align:start position:0%
+Vladimir lennin not John Lennon um and
+Lennon used to say that before
+
+ align:start position:0%
+Lennon used to say that before
+ 
+
+ align:start position:0%
+Lennon used to say that before
+revolution occurred everybody perceived
+
+ align:start position:0%
+revolution occurred everybody perceived
+ 
+
+ align:start position:0%
+revolution occurred everybody perceived
+that it was impossible uh but after it
+
+ align:start position:0%
+that it was impossible uh but after it
+ 
+
+ align:start position:0%
+that it was impossible uh but after it
+it's it succeeded people concluded of
+
+ align:start position:0%
+it's it succeeded people concluded of
+ 
+
+ align:start position:0%
+it's it succeeded people concluded of
+course it was inevitable and it's easy
+
+ align:start position:0%
+course it was inevitable and it's easy
+ 
+
+ align:start position:0%
+course it was inevitable and it's easy
+to look back and sort of say it was
+
+ align:start position:0%
+to look back and sort of say it was
+ 
+
+ align:start position:0%
+to look back and sort of say it was
+inevitable but you know I think that uh
+
+ align:start position:0%
+inevitable but you know I think that uh
+ 
+
+ align:start position:0%
+inevitable but you know I think that uh
+at least it was it was far from certain
+
+ align:start position:0%
+at least it was it was far from certain
+ 
+
+ align:start position:0%
+at least it was it was far from certain
+that it would turn out this way at least
+
+ align:start position:0%
+that it would turn out this way at least
+ 
+
+ align:start position:0%
+that it would turn out this way at least
+initially great thank you um Professor
+
+ align:start position:0%
+initially great thank you um Professor
+ 
+
+ align:start position:0%
+initially great thank you um Professor
+you maybe you could speak a little bit
+
+ align:start position:0%
+you maybe you could speak a little bit
+ 
+
+ align:start position:0%
+you maybe you could speak a little bit
+about the deliberations of the lifelong
+
+ align:start position:0%
+about the deliberations of the lifelong
+ 
+
+ align:start position:0%
+about the deliberations of the lifelong
+learning committee itself what was the
+
+ align:start position:0%
+learning committee itself what was the
+ 
+
+ align:start position:0%
+learning committee itself what was the
+thinking going in when you got the
+
+ align:start position:0%
+thinking going in when you got the
+ 
+
+ align:start position:0%
+thinking going in when you got the
+charge and how did the discussion
+
+ align:start position:0%
+charge and how did the discussion
+ 
+
+ align:start position:0%
+charge and how did the discussion
+develop over the course of the
+
+ align:start position:0%
+develop over the course of the
+ 
+
+ align:start position:0%
+develop over the course of the
+summer so um when uh Bob fed the
+
+ align:start position:0%
+summer so um when uh Bob fed the
+ 
+
+ align:start position:0%
+summer so um when uh Bob fed the
+committee uh the charge was necessarily
+
+ align:start position:0%
+committee uh the charge was necessarily
+ 
+
+ align:start position:0%
+committee uh the charge was necessarily
+both vague but very directional right
+
+ align:start position:0%
+both vague but very directional right
+ 
+
+ align:start position:0%
+both vague but very directional right
+where should we go vague in the sense
+
+ align:start position:0%
+where should we go vague in the sense
+ 
+
+ align:start position:0%
+where should we go vague in the sense
+you know how would education technology
+
+ align:start position:0%
+you know how would education technology
+ 
+
+ align:start position:0%
+you know how would education technology
+change the way MIT do education position
+
+ align:start position:0%
+change the way MIT do education position
+ 
+
+ align:start position:0%
+change the way MIT do education position
+itself and so on and so forth but other
+
+ align:start position:0%
+itself and so on and so forth but other
+ 
+
+ align:start position:0%
+itself and so on and so forth but other
+than that there really were not any
+
+ align:start position:0%
+than that there really were not any
+ 
+
+ align:start position:0%
+than that there really were not any
+other directions right because you don't
+
+ align:start position:0%
+other directions right because you don't
+ 
+
+ align:start position:0%
+other directions right because you don't
+usually form a committee and tell them
+
+ align:start position:0%
+usually form a committee and tell them
+ 
+
+ align:start position:0%
+usually form a committee and tell them
+what the answer you want to hear right
+
+ align:start position:0%
+what the answer you want to hear right
+ 
+
+ align:start position:0%
+what the answer you want to hear right
+so you just say go figure out and so um
+
+ align:start position:0%
+so you just say go figure out and so um
+ 
+
+ align:start position:0%
+so you just say go figure out and so um
+the committee worked very hard and
+
+ align:start position:0%
+the committee worked very hard and
+ 
+
+ align:start position:0%
+the committee worked very hard and
+basically we were at that time of course
+
+ align:start position:0%
+basically we were at that time of course
+ 
+
+ align:start position:0%
+basically we were at that time of course
+looking at our peers right people who
+
+ align:start position:0%
+looking at our peers right people who
+ 
+
+ align:start position:0%
+looking at our peers right people who
+are ahead uh the charge broadly talk
+
+ align:start position:0%
+are ahead uh the charge broadly talk
+ 
+
+ align:start position:0%
+are ahead uh the charge broadly talk
+about could we do some form of Education
+
+ align:start position:0%
+about could we do some form of Education
+ 
+
+ align:start position:0%
+about could we do some form of Education
+to people who are not on campus you know
+
+ align:start position:0%
+to people who are not on campus you know
+ 
+
+ align:start position:0%
+to people who are not on campus you know
+reaching out to alumni satisfying um
+
+ align:start position:0%
+reaching out to alumni satisfying um
+ 
+
+ align:start position:0%
+reaching out to alumni satisfying um
+some both professional and perhaps sort
+
+ align:start position:0%
+some both professional and perhaps sort
+ 
+
+ align:start position:0%
+some both professional and perhaps sort
+of uh interest driven educational demand
+
+ align:start position:0%
+of uh interest driven educational demand
+ 
+
+ align:start position:0%
+of uh interest driven educational demand
+and so forth and the committee basically
+
+ align:start position:0%
+and so forth and the committee basically
+ 
+
+ align:start position:0%
+and so forth and the committee basically
+was um coming up with a an answer that
+
+ align:start position:0%
+was um coming up with a an answer that
+ 
+
+ align:start position:0%
+was um coming up with a an answer that
+if you think about it would not be very
+
+ align:start position:0%
+if you think about it would not be very
+ 
+
+ align:start position:0%
+if you think about it would not be very
+different from what everybody else had
+
+ align:start position:0%
+different from what everybody else had
+ 
+
+ align:start position:0%
+different from what everybody else had
+already done because that was the the
+
+ align:start position:0%
+already done because that was the the
+ 
+
+ align:start position:0%
+already done because that was the the
+model right and you know we started
+
+ align:start position:0%
+model right and you know we started
+ 
+
+ align:start position:0%
+model right and you know we started
+looking at if we were to offer courses
+
+ align:start position:0%
+looking at if we were to offer courses
+ 
+
+ align:start position:0%
+looking at if we were to offer courses
+what kind of courses um if we were to do
+
+ align:start position:0%
+what kind of courses um if we were to do
+ 
+
+ align:start position:0%
+what kind of courses um if we were to do
+certificates one this and on that and
+
+ align:start position:0%
+certificates one this and on that and
+ 
+
+ align:start position:0%
+certificates one this and on that and
+and so you can imagine that was the sort
+
+ align:start position:0%
+and so you can imagine that was the sort
+ 
+
+ align:start position:0%
+and so you can imagine that was the sort
+of the state of the the committee and I
+
+ align:start position:0%
+of the state of the the committee and I
+ 
+
+ align:start position:0%
+of the state of the the committee and I
+think the the key thought was I think I
+
+ align:start position:0%
+think the the key thought was I think I
+ 
+
+ align:start position:0%
+think the the key thought was I think I
+I want to Echo again uh Chuck's um
+
+ align:start position:0%
+I want to Echo again uh Chuck's um
+ 
+
+ align:start position:0%
+I want to Echo again uh Chuck's um
+earlier sort of a comment about not just
+
+ align:start position:0%
+earlier sort of a comment about not just
+ 
+
+ align:start position:0%
+earlier sort of a comment about not just
+the historical context cirker 19 uh
+
+ align:start position:0%
+the historical context cirker 19 uh
+ 
+
+ align:start position:0%
+the historical context cirker 19 uh
+cirker 2000 but but the historical
+
+ align:start position:0%
+cirker 2000 but but the historical
+ 
+
+ align:start position:0%
+cirker 2000 but but the historical
+context of MIT right there was a sort of
+
+ align:start position:0%
+context of MIT right there was a sort of
+ 
+
+ align:start position:0%
+context of MIT right there was a sort of
+a thought that you know MIT had been
+
+ align:start position:0%
+a thought that you know MIT had been
+ 
+
+ align:start position:0%
+a thought that you know MIT had been
+able to had a much broader impact and
+
+ align:start position:0%
+able to had a much broader impact and
+ 
+
+ align:start position:0%
+able to had a much broader impact and
+influence through its
+
+ align:start position:0%
+influence through its
+ 
+
+ align:start position:0%
+influence through its
+activities uh beyond what a lot of other
+
+ align:start position:0%
+activities uh beyond what a lot of other
+ 
+
+ align:start position:0%
+activities uh beyond what a lot of other
+people are doing right we we somehow
+
+ align:start position:0%
+people are doing right we we somehow
+ 
+
+ align:start position:0%
+people are doing right we we somehow
+were able to do little things that turn
+
+ align:start position:0%
+were able to do little things that turn
+ 
+
+ align:start position:0%
+were able to do little things that turn
+out to be very impactful and so I I
+
+ align:start position:0%
+out to be very impactful and so I I
+ 
+
+ align:start position:0%
+out to be very impactful and so I I
+think at some point uh the thought
+
+ align:start position:0%
+think at some point uh the thought
+ 
+
+ align:start position:0%
+think at some point uh the thought
+basically came down to is there is that
+
+ align:start position:0%
+basically came down to is there is that
+ 
+
+ align:start position:0%
+basically came down to is there is that
+all there is to life perhaps I was just
+
+ align:start position:0%
+all there is to life perhaps I was just
+ 
+
+ align:start position:0%
+all there is to life perhaps I was just
+entering you know midlife crisis or
+
+ align:start position:0%
+entering you know midlife crisis or
+ 
+
+ align:start position:0%
+entering you know midlife crisis or
+something you know this so this question
+
+ align:start position:0%
+something you know this so this question
+ 
+
+ align:start position:0%
+something you know this so this question
+is always on my mind right you know so
+
+ align:start position:0%
+is always on my mind right you know so
+ 
+
+ align:start position:0%
+is always on my mind right you know so
+we were ready to give out a report to to
+
+ align:start position:0%
+we were ready to give out a report to to
+ 
+
+ align:start position:0%
+we were ready to give out a report to to
+to to to Bob and Chu at that time that
+
+ align:start position:0%
+to to to Bob and Chu at that time that
+ 
+
+ align:start position:0%
+to to to Bob and Chu at that time that
+basically says we could do the following
+
+ align:start position:0%
+basically says we could do the following
+ 
+
+ align:start position:0%
+basically says we could do the following
+right and nothing out of the ordinary we
+
+ align:start position:0%
+right and nothing out of the ordinary we
+ 
+
+ align:start position:0%
+right and nothing out of the ordinary we
+could copy fathom.com and do this we
+
+ align:start position:0%
+could copy fathom.com and do this we
+ 
+
+ align:start position:0%
+could copy fathom.com and do this we
+could do that okay and I was ready to
+
+ align:start position:0%
+could do that okay and I was ready to
+ 
+
+ align:start position:0%
+could do that okay and I was ready to
+just sign off cuz the job's done and
+
+ align:start position:0%
+just sign off cuz the job's done and
+ 
+
+ align:start position:0%
+just sign off cuz the job's done and
+that was it and we have some economic
+
+ align:start position:0%
+that was it and we have some economic
+ 
+
+ align:start position:0%
+that was it and we have some economic
+models you could know but against that
+
+ align:start position:0%
+models you could know but against that
+ 
+
+ align:start position:0%
+models you could know but against that
+backdrop of what MIT could be I was very
+
+ align:start position:0%
+backdrop of what MIT could be I was very
+ 
+
+ align:start position:0%
+backdrop of what MIT could be I was very
+unhappy because it's no big deal I mean
+
+ align:start position:0%
+unhappy because it's no big deal I mean
+ 
+
+ align:start position:0%
+unhappy because it's no big deal I mean
+you know frankly we could have guessed
+
+ align:start position:0%
+you know frankly we could have guessed
+ 
+
+ align:start position:0%
+you know frankly we could have guessed
+that answer without doing any of the
+
+ align:start position:0%
+that answer without doing any of the
+ 
+
+ align:start position:0%
+that answer without doing any of the
+work right and so the question I think
+
+ align:start position:0%
+work right and so the question I think
+ 
+
+ align:start position:0%
+work right and so the question I think
+for the committee and for me personally
+
+ align:start position:0%
+for the committee and for me personally
+ 
+
+ align:start position:0%
+for the committee and for me personally
+was could we do something that's a
+
+ align:start position:0%
+was could we do something that's a
+ 
+
+ align:start position:0%
+was could we do something that's a
+little bit more exciting right I mean if
+
+ align:start position:0%
+little bit more exciting right I mean if
+ 
+
+ align:start position:0%
+little bit more exciting right I mean if
+we had gone in there and emulated one of
+
+ align:start position:0%
+we had gone in there and emulated one of
+ 
+
+ align:start position:0%
+we had gone in there and emulated one of
+our peers we might have been you know
+
+ align:start position:0%
+our peers we might have been you know
+ 
+
+ align:start position:0%
+our peers we might have been you know
+the top 15 in doing that kind of stuff
+
+ align:start position:0%
+the top 15 in doing that kind of stuff
+ 
+
+ align:start position:0%
+the top 15 in doing that kind of stuff
+entering maybe top 30 we we were not
+
+ align:start position:0%
+entering maybe top 30 we we were not
+ 
+
+ align:start position:0%
+entering maybe top 30 we we were not
+early uh uh uh movers at all in that in
+
+ align:start position:0%
+early uh uh uh movers at all in that in
+ 
+
+ align:start position:0%
+early uh uh uh movers at all in that in
+that domain which which means we would
+
+ align:start position:0%
+that domain which which means we would
+ 
+
+ align:start position:0%
+that domain which which means we would
+have lost maybe a little bit less money
+
+ align:start position:0%
+have lost maybe a little bit less money
+ 
+
+ align:start position:0%
+have lost maybe a little bit less money
+than they
+
+ align:start position:0%
+than they
+ 
+
+ align:start position:0%
+than they
+did and and and if we were doing it
+
+ align:start position:0%
+did and and and if we were doing it
+ 
+
+ align:start position:0%
+did and and and if we were doing it
+really really well with with our good
+
+ align:start position:0%
+really really well with with our good
+ 
+
+ align:start position:0%
+really really well with with our good
+act together we might have been you know
+
+ align:start position:0%
+act together we might have been you know
+ 
+
+ align:start position:0%
+act together we might have been you know
+within the top 10 after five or eight
+
+ align:start position:0%
+within the top 10 after five or eight
+ 
+
+ align:start position:0%
+within the top 10 after five or eight
+years right and the thought was we
+
+ align:start position:0%
+years right and the thought was we
+ 
+
+ align:start position:0%
+years right and the thought was we
+probably could do better than just being
+
+ align:start position:0%
+probably could do better than just being
+ 
+
+ align:start position:0%
+probably could do better than just being
+the top 10 after killing ourselves right
+
+ align:start position:0%
+the top 10 after killing ourselves right
+ 
+
+ align:start position:0%
+the top 10 after killing ourselves right
+so that was I think the the the the
+
+ align:start position:0%
+so that was I think the the the the
+ 
+
+ align:start position:0%
+so that was I think the the the the
+struggle right at the end of this report
+
+ align:start position:0%
+struggle right at the end of this report
+ 
+
+ align:start position:0%
+struggle right at the end of this report
+and it all happened very quickly and I
+
+ align:start position:0%
+and it all happened very quickly and I
+ 
+
+ align:start position:0%
+and it all happened very quickly and I
+think in hindsight we should give credit
+
+ align:start position:0%
+think in hindsight we should give credit
+ 
+
+ align:start position:0%
+think in hindsight we should give credit
+to to at that time my concern was as as
+
+ align:start position:0%
+to to at that time my concern was as as
+ 
+
+ align:start position:0%
+to to at that time my concern was as as
+Larry pointed out right with the faculty
+
+ align:start position:0%
+Larry pointed out right with the faculty
+ 
+
+ align:start position:0%
+Larry pointed out right with the faculty
+buying right uh another concern and and
+
+ align:start position:0%
+buying right uh another concern and and
+ 
+
+ align:start position:0%
+buying right uh another concern and and
+sorry with no disrespect with the
+
+ align:start position:0%
+sorry with no disrespect with the
+ 
+
+ align:start position:0%
+sorry with no disrespect with the
+leadership uh Buy in right would I get
+
+ align:start position:0%
+leadership uh Buy in right would I get
+ 
+
+ align:start position:0%
+leadership uh Buy in right would I get
+just kicked out of the office right dick
+
+ align:start position:0%
+just kicked out of the office right dick
+ 
+
+ align:start position:0%
+just kicked out of the office right dick
+clear your head you know stop drinking
+
+ align:start position:0%
+clear your head you know stop drinking
+ 
+
+ align:start position:0%
+clear your head you know stop drinking
+and come back okay right um frankly I
+
+ align:start position:0%
+and come back okay right um frankly I
+ 
+
+ align:start position:0%
+and come back okay right um frankly I
+mean I was very worried and so uh people
+
+ align:start position:0%
+mean I was very worried and so uh people
+ 
+
+ align:start position:0%
+mean I was very worried and so uh people
+why we sent Bob in run interference
+
+ align:start position:0%
+why we sent Bob in run interference
+ 
+
+ align:start position:0%
+why we sent Bob in run interference
+people talk about this very big folder
+
+ align:start position:0%
+people talk about this very big folder
+ 
+
+ align:start position:0%
+people talk about this very big folder
+you know this 5in folder it was the
+
+ align:start position:0%
+you know this 5in folder it was the
+ 
+
+ align:start position:0%
+you know this 5in folder it was the
+biggest folder that the coupe carried
+
+ align:start position:0%
+biggest folder that the coupe carried
+ 
+
+ align:start position:0%
+biggest folder that the coupe carried
+okay if it wasn't I would have added
+
+ align:start position:0%
+okay if it wasn't I would have added
+ 
+
+ align:start position:0%
+okay if it wasn't I would have added
+more stuff because the one thing I
+
+ align:start position:0%
+more stuff because the one thing I
+ 
+
+ align:start position:0%
+more stuff because the one thing I
+didn't want and Swit is sort of academic
+
+ align:start position:0%
+didn't want and Swit is sort of academic
+ 
+
+ align:start position:0%
+didn't want and Swit is sort of academic
+um suicide or academic death would be
+
+ align:start position:0%
+um suicide or academic death would be
+ 
+
+ align:start position:0%
+um suicide or academic death would be
+let's study it some more right so I
+
+ align:start position:0%
+let's study it some more right so I
+ 
+
+ align:start position:0%
+let's study it some more right so I
+thought like what and if you mention it
+
+ align:start position:0%
+thought like what and if you mention it
+ 
+
+ align:start position:0%
+thought like what and if you mention it
+I'll would say oh no that's chapter four
+
+ align:start position:0%
+I'll would say oh no that's chapter four
+ 
+
+ align:start position:0%
+I'll would say oh no that's chapter four
+in appendix 5 okay right so we kind of
+
+ align:start position:0%
+in appendix 5 okay right so we kind of
+ 
+
+ align:start position:0%
+in appendix 5 okay right so we kind of
+looked at it so there was a little bit
+
+ align:start position:0%
+looked at it so there was a little bit
+ 
+
+ align:start position:0%
+looked at it so there was a little bit
+of that but but in hindsight I think a
+
+ align:start position:0%
+of that but but in hindsight I think a
+ 
+
+ align:start position:0%
+of that but but in hindsight I think a
+lot of it had to do with with uh who
+
+ align:start position:0%
+lot of it had to do with with uh who
+ 
+
+ align:start position:0%
+lot of it had to do with with uh who
+many of us believe MIT um is or could be
+
+ align:start position:0%
+many of us believe MIT um is or could be
+ 
+
+ align:start position:0%
+many of us believe MIT um is or could be
+uh a sense of sort of dissatisfaction of
+
+ align:start position:0%
+uh a sense of sort of dissatisfaction of
+ 
+
+ align:start position:0%
+uh a sense of sort of dissatisfaction of
+just yet doing something which was
+
+ align:start position:0%
+just yet doing something which was
+ 
+
+ align:start position:0%
+just yet doing something which was
+probably more or less done uh it was
+
+ align:start position:0%
+probably more or less done uh it was
+ 
+
+ align:start position:0%
+probably more or less done uh it was
+based upon that kind of a vision and
+
+ align:start position:0%
+based upon that kind of a vision and
+ 
+
+ align:start position:0%
+based upon that kind of a vision and
+there was also I think um uh thanks to
+
+ align:start position:0%
+there was also I think um uh thanks to
+ 
+
+ align:start position:0%
+there was also I think um uh thanks to
+you know the help with consultants and
+
+ align:start position:0%
+you know the help with consultants and
+ 
+
+ align:start position:0%
+you know the help with consultants and
+so forth bu and others uh it was also a
+
+ align:start position:0%
+so forth bu and others uh it was also a
+ 
+
+ align:start position:0%
+so forth bu and others uh it was also a
+sort of a economic uh business model
+
+ align:start position:0%
+sort of a economic uh business model
+ 
+
+ align:start position:0%
+sort of a economic uh business model
+decision right we we actually did go
+
+ align:start position:0%
+decision right we we actually did go
+ 
+
+ align:start position:0%
+decision right we we actually did go
+through and one of the things I was very
+
+ align:start position:0%
+through and one of the things I was very
+ 
+
+ align:start position:0%
+through and one of the things I was very
+surprised was we thought I actually
+
+ align:start position:0%
+surprised was we thought I actually
+ 
+
+ align:start position:0%
+surprised was we thought I actually
+thought many of these other universities
+
+ align:start position:0%
+thought many of these other universities
+ 
+
+ align:start position:0%
+thought many of these other universities
+doing what they were doing they probably
+
+ align:start position:0%
+doing what they were doing they probably
+ 
+
+ align:start position:0%
+doing what they were doing they probably
+didn't do that economic study I I I I
+
+ align:start position:0%
+didn't do that economic study I I I I
+ 
+
+ align:start position:0%
+didn't do that economic study I I I I
+was surprised that they would invest
+
+ align:start position:0%
+was surprised that they would invest
+ 
+
+ align:start position:0%
+was surprised that they would invest
+millions of dollars without doing that
+
+ align:start position:0%
+millions of dollars without doing that
+ 
+
+ align:start position:0%
+millions of dollars without doing that
+and so in the back of my mind I keep
+
+ align:start position:0%
+and so in the back of my mind I keep
+ 
+
+ align:start position:0%
+and so in the back of my mind I keep
+thinking maybe we missed something and
+
+ align:start position:0%
+thinking maybe we missed something and
+ 
+
+ align:start position:0%
+thinking maybe we missed something and
+they saw but then you know I didn't see
+
+ align:start position:0%
+they saw but then you know I didn't see
+ 
+
+ align:start position:0%
+they saw but then you know I didn't see
+anything else right and that was it so
+
+ align:start position:0%
+anything else right and that was it so
+ 
+
+ align:start position:0%
+anything else right and that was it so
+so there was a bit of an economic
+
+ align:start position:0%
+so there was a bit of an economic
+ 
+
+ align:start position:0%
+so there was a bit of an economic
+business sort of decision but primarily
+
+ align:start position:0%
+business sort of decision but primarily
+ 
+
+ align:start position:0%
+business sort of decision but primarily
+it was thinking that the time is right
+
+ align:start position:0%
+it was thinking that the time is right
+ 
+
+ align:start position:0%
+it was thinking that the time is right
+that MIT could do something um and the
+
+ align:start position:0%
+that MIT could do something um and the
+ 
+
+ align:start position:0%
+that MIT could do something um and the
+rest as they say is you know was just
+
+ align:start position:0%
+rest as they say is you know was just
+ 
+
+ align:start position:0%
+rest as they say is you know was just
+getting it done Larry talked about how
+
+ align:start position:0%
+getting it done Larry talked about how
+ 
+
+ align:start position:0%
+getting it done Larry talked about how
+going to all the faculty and convincing
+
+ align:start position:0%
+going to all the faculty and convincing
+ 
+
+ align:start position:0%
+going to all the faculty and convincing
+them I remember one of the things that I
+
+ align:start position:0%
+them I remember one of the things that I
+ 
+
+ align:start position:0%
+them I remember one of the things that I
+thought there might be a catch was to
+
+ align:start position:0%
+thought there might be a catch was to
+ 
+
+ align:start position:0%
+thought there might be a catch was to
+look at different people that we would
+
+ align:start position:0%
+look at different people that we would
+ 
+
+ align:start position:0%
+look at different people that we would
+have to talk to so the question was what
+
+ align:start position:0%
+have to talk to so the question was what
+ 
+
+ align:start position:0%
+have to talk to so the question was what
+are the benefits and values to MIT from
+
+ align:start position:0%
+are the benefits and values to MIT from
+ 
+
+ align:start position:0%
+are the benefits and values to MIT from
+a from a senior Administration point of
+
+ align:start position:0%
+a from a senior Administration point of
+ 
+
+ align:start position:0%
+a from a senior Administration point of
+view right uh you know Bob had assured
+
+ align:start position:0%
+view right uh you know Bob had assured
+ 
+
+ align:start position:0%
+view right uh you know Bob had assured
+me the need for us to move forward in
+
+ align:start position:0%
+me the need for us to move forward in
+ 
+
+ align:start position:0%
+me the need for us to move forward in
+education technology uh would that help
+
+ align:start position:0%
+education technology uh would that help
+ 
+
+ align:start position:0%
+education technology uh would that help
+answer that question um what are the
+
+ align:start position:0%
+answer that question um what are the
+ 
+
+ align:start position:0%
+answer that question um what are the
+values to The Faculty right I mean are
+
+ align:start position:0%
+values to The Faculty right I mean are
+ 
+
+ align:start position:0%
+values to The Faculty right I mean are
+they not going to publish anymore what
+
+ align:start position:0%
+they not going to publish anymore what
+ 
+
+ align:start position:0%
+they not going to publish anymore what
+are the values to our students and then
+
+ align:start position:0%
+are the values to our students and then
+ 
+
+ align:start position:0%
+are the values to our students and then
+you go beyond what are the value to
+
+ align:start position:0%
+you go beyond what are the value to
+ 
+
+ align:start position:0%
+you go beyond what are the value to
+other universities uh other uh
+
+ align:start position:0%
+other universities uh other uh
+ 
+
+ align:start position:0%
+other universities uh other uh
+educational institutions um domestically
+
+ align:start position:0%
+educational institutions um domestically
+ 
+
+ align:start position:0%
+educational institutions um domestically
+internationally uh what might be the
+
+ align:start position:0%
+internationally uh what might be the
+ 
+
+ align:start position:0%
+internationally uh what might be the
+value to a to a foundation frankly and
+
+ align:start position:0%
+value to a to a foundation frankly and
+ 
+
+ align:start position:0%
+value to a to a foundation frankly and
+why would they right so so I remember
+
+ align:start position:0%
+why would they right so so I remember
+ 
+
+ align:start position:0%
+why would they right so so I remember
+this is a very surprising thing and and
+
+ align:start position:0%
+this is a very surprising thing and and
+ 
+
+ align:start position:0%
+this is a very surprising thing and and
+I remember trying to write a you know
+
+ align:start position:0%
+I remember trying to write a you know
+ 
+
+ align:start position:0%
+I remember trying to write a you know
+Page worth of bullets for each of these
+
+ align:start position:0%
+Page worth of bullets for each of these
+ 
+
+ align:start position:0%
+Page worth of bullets for each of these
+questions and it's very interesting
+
+ align:start position:0%
+questions and it's very interesting
+ 
+
+ align:start position:0%
+questions and it's very interesting
+because at the end I had a story I think
+
+ align:start position:0%
+because at the end I had a story I think
+ 
+
+ align:start position:0%
+because at the end I had a story I think
+to convince everybody right this is one
+
+ align:start position:0%
+to convince everybody right this is one
+ 
+
+ align:start position:0%
+to convince everybody right this is one
+of these ideas that I you know for each
+
+ align:start position:0%
+of these ideas that I you know for each
+ 
+
+ align:start position:0%
+of these ideas that I you know for each
+slide this is the faculty if they asked
+
+ align:start position:0%
+slide this is the faculty if they asked
+ 
+
+ align:start position:0%
+slide this is the faculty if they asked
+this we could say that right and they
+
+ align:start position:0%
+this we could say that right and they
+ 
+
+ align:start position:0%
+this we could say that right and they
+were not like okay let's let's not talk
+
+ align:start position:0%
+were not like okay let's let's not talk
+ 
+
+ align:start position:0%
+were not like okay let's let's not talk
+to this group because they wouldn't be
+
+ align:start position:0%
+to this group because they wouldn't be
+ 
+
+ align:start position:0%
+to this group because they wouldn't be
+able to to buy in right so it was very
+
+ align:start position:0%
+able to to buy in right so it was very
+ 
+
+ align:start position:0%
+able to to buy in right so it was very
+interesting it was one of these things
+
+ align:start position:0%
+interesting it was one of these things
+ 
+
+ align:start position:0%
+interesting it was one of these things
+where once we go through thinking about
+
+ align:start position:0%
+where once we go through thinking about
+ 
+
+ align:start position:0%
+where once we go through thinking about
+it it actually answer a lot of the
+
+ align:start position:0%
+it it actually answer a lot of the
+ 
+
+ align:start position:0%
+it it actually answer a lot of the
+questions that that had been on our mind
+
+ align:start position:0%
+questions that that had been on our mind
+ 
+
+ align:start position:0%
+questions that that had been on our mind
+whether very explicitly or in a very
+
+ align:start position:0%
+whether very explicitly or in a very
+ 
+
+ align:start position:0%
+whether very explicitly or in a very
+subtle way that has been been been we've
+
+ align:start position:0%
+subtle way that has been been been we've
+ 
+
+ align:start position:0%
+subtle way that has been been been we've
+been struggling so so that that was I
+
+ align:start position:0%
+been struggling so so that that was I
+ 
+
+ align:start position:0%
+been struggling so so that that was I
+think the at least my perspective of
+
+ align:start position:0%
+think the at least my perspective of
+ 
+
+ align:start position:0%
+think the at least my perspective of
+what transpired over the summer of 2000
+
+ align:start position:0%
+what transpired over the summer of 2000
+ 
+
+ align:start position:0%
+what transpired over the summer of 2000
+and maybe mainly towards the end of the
+
+ align:start position:0%
+and maybe mainly towards the end of the
+ 
+
+ align:start position:0%
+and maybe mainly towards the end of the
+2000 the last you know two three weeks
+
+ align:start position:0%
+2000 the last you know two three weeks
+ 
+
+ align:start position:0%
+2000 the last you know two three weeks
+of trying to wrap up that that report
+
+ align:start position:0%
+of trying to wrap up that that report
+ 
+
+ align:start position:0%
+of trying to wrap up that that report
+and study great great thank you um
+
+ align:start position:0%
+and study great great thank you um
+ 
+
+ align:start position:0%
+and study great great thank you um
+Professor mwa maybe we could get you to
+
+ align:start position:0%
+Professor mwa maybe we could get you to
+ 
+
+ align:start position:0%
+Professor mwa maybe we could get you to
+comment on what I think is one of the
+
+ align:start position:0%
+comment on what I think is one of the
+ 
+
+ align:start position:0%
+comment on what I think is one of the
+the more extraordinary aspects of The
+
+ align:start position:0%
+the more extraordinary aspects of The
+ 
+
+ align:start position:0%
+the more extraordinary aspects of The
+Proposal uh that Dr vest referred to
+
+ align:start position:0%
+Proposal uh that Dr vest referred to
+ 
+
+ align:start position:0%
+Proposal uh that Dr vest referred to
+earlier which was the commitment to
+
+ align:start position:0%
+earlier which was the commitment to
+ 
+
+ align:start position:0%
+earlier which was the commitment to
+publish all 2,000 uh of mit's courses I
+
+ align:start position:0%
+publish all 2,000 uh of mit's courses I
+ 
+
+ align:start position:0%
+publish all 2,000 uh of mit's courses I
+think it would have been one thing if if
+
+ align:start position:0%
+think it would have been one thing if if
+ 
+
+ align:start position:0%
+think it would have been one thing if if
+the proposal had been to publish you
+
+ align:start position:0%
+the proposal had been to publish you
+ 
+
+ align:start position:0%
+the proposal had been to publish you
+know 20 courses or 50 courses or
+
+ align:start position:0%
+know 20 courses or 50 courses or
+ 
+
+ align:start position:0%
+know 20 courses or 50 courses or
+something but the the proposal that came
+
+ align:start position:0%
+something but the the proposal that came
+ 
+
+ align:start position:0%
+something but the the proposal that came
+out of the committee was all
+
+ align:start position:0%
+out of the committee was all
+ 
+
+ align:start position:0%
+out of the committee was all
+2000 uh you know uh when we proposed
+
+ align:start position:0%
+2000 uh you know uh when we proposed
+ 
+
+ align:start position:0%
+2000 uh you know uh when we proposed
+this to Chuck and Bob uh that we should
+
+ align:start position:0%
+this to Chuck and Bob uh that we should
+ 
+
+ align:start position:0%
+this to Chuck and Bob uh that we should
+give away the course materials from all
+
+ align:start position:0%
+give away the course materials from all
+ 
+
+ align:start position:0%
+give away the course materials from all
+our MIT courses we actually didn't know
+
+ align:start position:0%
+our MIT courses we actually didn't know
+ 
+
+ align:start position:0%
+our MIT courses we actually didn't know
+how many courses we taught you know we
+
+ align:start position:0%
+how many courses we taught you know we
+ 
+
+ align:start position:0%
+how many courses we taught you know we
+have to go back and count uh uh after
+
+ align:start position:0%
+have to go back and count uh uh after
+ 
+
+ align:start position:0%
+have to go back and count uh uh after
+the fact after we uh made the initial
+
+ align:start position:0%
+the fact after we uh made the initial
+ 
+
+ align:start position:0%
+the fact after we uh made the initial
+proposal so uh that's how excited we
+
+ align:start position:0%
+proposal so uh that's how excited we
+ 
+
+ align:start position:0%
+proposal so uh that's how excited we
+were and how uh immediate The Proposal
+
+ align:start position:0%
+were and how uh immediate The Proposal
+ 
+
+ align:start position:0%
+were and how uh immediate The Proposal
+sounded but then there are a lot of
+
+ align:start position:0%
+sounded but then there are a lot of
+ 
+
+ align:start position:0%
+sounded but then there are a lot of
+things that we had to do including
+
+ align:start position:0%
+things that we had to do including
+ 
+
+ align:start position:0%
+things that we had to do including
+counting the number of courses and we
+
+ align:start position:0%
+counting the number of courses and we
+ 
+
+ align:start position:0%
+counting the number of courses and we
+found out that we had 2,000 courses and
+
+ align:start position:0%
+found out that we had 2,000 courses and
+ 
+
+ align:start position:0%
+found out that we had 2,000 courses and
+that was a bit of a a surprise to us
+
+ align:start position:0%
+that was a bit of a a surprise to us
+ 
+
+ align:start position:0%
+that was a bit of a a surprise to us
+that boy we have a big work ahead of us
+
+ align:start position:0%
+that boy we have a big work ahead of us
+ 
+
+ align:start position:0%
+that boy we have a big work ahead of us
+um and so uh there a lot of concerns
+
+ align:start position:0%
+um and so uh there a lot of concerns
+ 
+
+ align:start position:0%
+um and so uh there a lot of concerns
+that came up uh as uh uh as we moved
+
+ align:start position:0%
+that came up uh as uh uh as we moved
+ 
+
+ align:start position:0%
+that came up uh as uh uh as we moved
+into the process of convincing The
+
+ align:start position:0%
+into the process of convincing The
+ 
+
+ align:start position:0%
+into the process of convincing The
+Faculty that uh this is a good idea we
+
+ align:start position:0%
+Faculty that uh this is a good idea we
+ 
+
+ align:start position:0%
+Faculty that uh this is a good idea we
+had a notion that this really fit with
+
+ align:start position:0%
+had a notion that this really fit with
+ 
+
+ align:start position:0%
+had a notion that this really fit with
+the core values of MIT okay I mean Chuck
+
+ align:start position:0%
+the core values of MIT okay I mean Chuck
+ 
+
+ align:start position:0%
+the core values of MIT okay I mean Chuck
+referred to this uh MIT in its mission
+
+ align:start position:0%
+referred to this uh MIT in its mission
+ 
+
+ align:start position:0%
+referred to this uh MIT in its mission
+statement says that MIT is here to
+
+ align:start position:0%
+statement says that MIT is here to
+ 
+
+ align:start position:0%
+statement says that MIT is here to
+generate preserve and disseminate
+
+ align:start position:0%
+generate preserve and disseminate
+ 
+
+ align:start position:0%
+generate preserve and disseminate
+knowledge uh and uh bring that to bear
+
+ align:start position:0%
+knowledge uh and uh bring that to bear
+ 
+
+ align:start position:0%
+knowledge uh and uh bring that to bear
+on the big challenges of the world
+
+ align:start position:0%
+on the big challenges of the world
+ 
+
+ align:start position:0%
+on the big challenges of the world
+that's what the mission statement says
+
+ align:start position:0%
+that's what the mission statement says
+ 
+
+ align:start position:0%
+that's what the mission statement says
+and uh and as faculty we we share that
+
+ align:start position:0%
+and uh and as faculty we we share that
+ 
+
+ align:start position:0%
+and uh and as faculty we we share that
+core value and open coare is another
+
+ align:start position:0%
+core value and open coare is another
+ 
+
+ align:start position:0%
+core value and open coare is another
+implementation of this and we were
+
+ align:start position:0%
+implementation of this and we were
+ 
+
+ align:start position:0%
+implementation of this and we were
+seeing as we talked to the faculty uh
+
+ align:start position:0%
+seeing as we talked to the faculty uh
+ 
+
+ align:start position:0%
+seeing as we talked to the faculty uh
+going into this that the faculty were
+
+ align:start position:0%
+going into this that the faculty were
+ 
+
+ align:start position:0%
+going into this that the faculty were
+talking in this way but uh you know we
+
+ align:start position:0%
+talking in this way but uh you know we
+ 
+
+ align:start position:0%
+talking in this way but uh you know we
+have a thousand faculty members and uh
+
+ align:start position:0%
+have a thousand faculty members and uh
+ 
+
+ align:start position:0%
+have a thousand faculty members and uh
+we had to uh we had to uh convince them
+
+ align:start position:0%
+we had to uh we had to uh convince them
+ 
+
+ align:start position:0%
+we had to uh we had to uh convince them
+and actually took quite bit of work um
+
+ align:start position:0%
+and actually took quite bit of work um
+ 
+
+ align:start position:0%
+and actually took quite bit of work um
+Hal and Dick and Steve lurman others uh
+
+ align:start position:0%
+Hal and Dick and Steve lurman others uh
+ 
+
+ align:start position:0%
+Hal and Dick and Steve lurman others uh
+spent uh I think almost six months uh in
+
+ align:start position:0%
+spent uh I think almost six months uh in
+ 
+
+ align:start position:0%
+spent uh I think almost six months uh in
+in small groups talking with faculty
+
+ align:start position:0%
+in small groups talking with faculty
+ 
+
+ align:start position:0%
+in small groups talking with faculty
+talking with students talking with staff
+
+ align:start position:0%
+talking with students talking with staff
+ 
+
+ align:start position:0%
+talking with students talking with staff
+uh to uh persuade but also to uh
+
+ align:start position:0%
+uh to uh persuade but also to uh
+ 
+
+ align:start position:0%
+uh to uh persuade but also to uh
+dissuade them from uh misunderstandings
+
+ align:start position:0%
+dissuade them from uh misunderstandings
+ 
+
+ align:start position:0%
+dissuade them from uh misunderstandings
+about uh about what this was uh that we
+
+ align:start position:0%
+about uh about what this was uh that we
+ 
+
+ align:start position:0%
+about uh about what this was uh that we
+are not giving away MIT education MIT
+
+ align:start position:0%
+are not giving away MIT education MIT
+ 
+
+ align:start position:0%
+are not giving away MIT education MIT
+education is much bigger than uh the
+
+ align:start position:0%
+education is much bigger than uh the
+ 
+
+ align:start position:0%
+education is much bigger than uh the
+course materials that we were proposing
+
+ align:start position:0%
+course materials that we were proposing
+ 
+
+ align:start position:0%
+course materials that we were proposing
+to give away and it was a mindset that
+
+ align:start position:0%
+to give away and it was a mindset that
+ 
+
+ align:start position:0%
+to give away and it was a mindset that
+we were asking of the faculty uh to to
+
+ align:start position:0%
+we were asking of the faculty uh to to
+ 
+
+ align:start position:0%
+we were asking of the faculty uh to to
+uh to have again tapping into what I
+
+ align:start position:0%
+uh to have again tapping into what I
+ 
+
+ align:start position:0%
+uh to have again tapping into what I
+really believe was this core value the
+
+ align:start position:0%
+really believe was this core value the
+ 
+
+ align:start position:0%
+really believe was this core value the
+MIT has always had from its founding 150
+
+ align:start position:0%
+MIT has always had from its founding 150
+ 
+
+ align:start position:0%
+MIT has always had from its founding 150
+years
+
+ align:start position:0%
+years
+ 
+
+ align:start position:0%
+years
+ago one thing I uh I want to uh uh you
+
+ align:start position:0%
+ago one thing I uh I want to uh uh you
+ 
+
+ align:start position:0%
+ago one thing I uh I want to uh uh you
+know say um Chuck uh said that all good
+
+ align:start position:0%
+know say um Chuck uh said that all good
+ 
+
+ align:start position:0%
+know say um Chuck uh said that all good
+ideas come from The Faculty uh and
+
+ align:start position:0%
+ideas come from The Faculty uh and
+ 
+
+ align:start position:0%
+ideas come from The Faculty uh and
+Grassroots and that's correct and that
+
+ align:start position:0%
+Grassroots and that's correct and that
+ 
+
+ align:start position:0%
+Grassroots and that's correct and that
+good ideas will find a way to uh to get
+
+ align:start position:0%
+good ideas will find a way to uh to get
+ 
+
+ align:start position:0%
+good ideas will find a way to uh to get
+legs but you know there's a difference
+
+ align:start position:0%
+legs but you know there's a difference
+ 
+
+ align:start position:0%
+legs but you know there's a difference
+between having a good idea and having
+
+ align:start position:0%
+between having a good idea and having
+ 
+
+ align:start position:0%
+between having a good idea and having
+the will to uh to implement that idea
+
+ align:start position:0%
+the will to uh to implement that idea
+ 
+
+ align:start position:0%
+the will to uh to implement that idea
+and ocw was the first time that I saw a
+
+ align:start position:0%
+and ocw was the first time that I saw a
+ 
+
+ align:start position:0%
+and ocw was the first time that I saw a
+very clear uh manifestation of academic
+
+ align:start position:0%
+very clear uh manifestation of academic
+ 
+
+ align:start position:0%
+very clear uh manifestation of academic
+leadership uh in the form of Chuck in
+
+ align:start position:0%
+leadership uh in the form of Chuck in
+ 
+
+ align:start position:0%
+leadership uh in the form of Chuck in
+the form of uh Bob and in form of Larry
+
+ align:start position:0%
+the form of uh Bob and in form of Larry
+ 
+
+ align:start position:0%
+the form of uh Bob and in form of Larry
+okay uh you know uh we know that there
+
+ align:start position:0%
+okay uh you know uh we know that there
+ 
+
+ align:start position:0%
+okay uh you know uh we know that there
+there's a president at your institution
+
+ align:start position:0%
+there's a president at your institution
+ 
+
+ align:start position:0%
+there's a president at your institution
+uh but most of the time you don't see
+
+ align:start position:0%
+uh but most of the time you don't see
+ 
+
+ align:start position:0%
+uh but most of the time you don't see
+them you know you figure they in this
+
+ align:start position:0%
+them you know you figure they in this
+ 
+
+ align:start position:0%
+them you know you figure they in this
+mysterious s of secretive room uh doing
+
+ align:start position:0%
+mysterious s of secretive room uh doing
+ 
+
+ align:start position:0%
+mysterious s of secretive room uh doing
+whatever they do you suspect that they
+
+ align:start position:0%
+whatever they do you suspect that they
+ 
+
+ align:start position:0%
+whatever they do you suspect that they
+they drink from Real China as opposed to
+
+ align:start position:0%
+they drink from Real China as opposed to
+ 
+
+ align:start position:0%
+they drink from Real China as opposed to
+paper cups that we drink coffee from but
+
+ align:start position:0%
+paper cups that we drink coffee from but
+ 
+
+ align:start position:0%
+paper cups that we drink coffee from but
+for the most of the time you don't you
+
+ align:start position:0%
+for the most of the time you don't you
+ 
+
+ align:start position:0%
+for the most of the time you don't you
+don't see them and they're not visible
+
+ align:start position:0%
+don't see them and they're not visible
+ 
+
+ align:start position:0%
+don't see them and they're not visible
+to you ocw was uh one uh time when I saw
+
+ align:start position:0%
+to you ocw was uh one uh time when I saw
+ 
+
+ align:start position:0%
+to you ocw was uh one uh time when I saw
+academic leadership in a
+
+ align:start position:0%
+academic leadership in a
+ 
+
+ align:start position:0%
+academic leadership in a
+clear way and that really uh that really
+
+ align:start position:0%
+clear way and that really uh that really
+ 
+
+ align:start position:0%
+clear way and that really uh that really
+worked uh if it were not for Chuck and
+
+ align:start position:0%
+worked uh if it were not for Chuck and
+ 
+
+ align:start position:0%
+worked uh if it were not for Chuck and
+Bob and Larry taking the the leadership
+
+ align:start position:0%
+Bob and Larry taking the the leadership
+ 
+
+ align:start position:0%
+Bob and Larry taking the the leadership
+and bringing us know the will uh not
+
+ align:start position:0%
+and bringing us know the will uh not
+ 
+
+ align:start position:0%
+and bringing us know the will uh not
+just the desire which we had but the
+
+ align:start position:0%
+just the desire which we had but the
+ 
+
+ align:start position:0%
+just the desire which we had but the
+will to do that this uh I don't think
+
+ align:start position:0%
+will to do that this uh I don't think
+ 
+
+ align:start position:0%
+will to do that this uh I don't think
+that we would have been here today so
+
+ align:start position:0%
+that we would have been here today so
+ 
+
+ align:start position:0%
+that we would have been here today so
+great thank you thank you Professor
+
+ align:start position:0%
+great thank you thank you Professor
+ 
+
+ align:start position:0%
+great thank you thank you Professor
+aelson you were involved in a number of
+
+ align:start position:0%
+aelson you were involved in a number of
+ 
+
+ align:start position:0%
+aelson you were involved in a number of
+other uh open efforts around the time of
+
+ align:start position:0%
+other uh open efforts around the time of
+ 
+
+ align:start position:0%
+other uh open efforts around the time of
+The Proposal free software Foundation
+
+ align:start position:0%
+The Proposal free software Foundation
+ 
+
+ align:start position:0%
+The Proposal free software Foundation
+creative comment could you maybe build
+
+ align:start position:0%
+creative comment could you maybe build
+ 
+
+ align:start position:0%
+creative comment could you maybe build
+on timy's comments earlier and and
+
+ align:start position:0%
+on timy's comments earlier and and
+ 
+
+ align:start position:0%
+on timy's comments earlier and and
+provide a little more context around
+
+ align:start position:0%
+provide a little more context around
+ 
+
+ align:start position:0%
+provide a little more context around
+openness at the time or or going
+
+ align:start position:0%
+openness at the time or or going
+ 
+
+ align:start position:0%
+openness at the time or or going
+forward yeah I prepared remarks and then
+
+ align:start position:0%
+forward yeah I prepared remarks and then
+ 
+
+ align:start position:0%
+forward yeah I prepared remarks and then
+what I want to do is rip them up because
+
+ align:start position:0%
+what I want to do is rip them up because
+ 
+
+ align:start position:0%
+what I want to do is rip them up because
+what I really want to do is Riff on what
+
+ align:start position:0%
+what I really want to do is Riff on what
+ 
+
+ align:start position:0%
+what I really want to do is Riff on what
+Tim said because it's made this
+
+ align:start position:0%
+Tim said because it's made this
+ 
+
+ align:start position:0%
+Tim said because it's made this
+incredible complicated picture in my
+
+ align:start position:0%
+incredible complicated picture in my
+ 
+
+ align:start position:0%
+incredible complicated picture in my
+head that has kind of three strands one
+
+ align:start position:0%
+head that has kind of three strands one
+ 
+
+ align:start position:0%
+head that has kind of three strands one
+is what we've been talking about with
+
+ align:start position:0%
+is what we've been talking about with
+ 
+
+ align:start position:0%
+is what we've been talking about with
+open course Weare and let me take a
+
+ align:start position:0%
+open course Weare and let me take a
+ 
+
+ align:start position:0%
+open course Weare and let me take a
+minute to just underline what what chera
+
+ align:start position:0%
+minute to just underline what what chera
+ 
+
+ align:start position:0%
+minute to just underline what what chera
+said people sort of talk about what a
+
+ align:start position:0%
+said people sort of talk about what a
+ 
+
+ align:start position:0%
+said people sort of talk about what a
+what a cool great idea open course where
+
+ align:start position:0%
+what a cool great idea open course where
+ 
+
+ align:start position:0%
+what a cool great idea open course where
+was but the reality is MIT is the kind
+
+ align:start position:0%
+was but the reality is MIT is the kind
+ 
+
+ align:start position:0%
+was but the reality is MIT is the kind
+of place where there are lots and lots
+
+ align:start position:0%
+of place where there are lots and lots
+ 
+
+ align:start position:0%
+of place where there are lots and lots
+of good
+
+ align:start position:0%
+of good
+ 
+
+ align:start position:0%
+of good
+ideas and what it takes is the actual
+
+ align:start position:0%
+ideas and what it takes is the actual
+ 
+
+ align:start position:0%
+ideas and what it takes is the actual
+leadership of the institution to make
+
+ align:start position:0%
+leadership of the institution to make
+ 
+
+ align:start position:0%
+leadership of the institution to make
+the idea happen What Chuck did
+
+ align:start position:0%
+the idea happen What Chuck did
+ 
+
+ align:start position:0%
+the idea happen What Chuck did
+is what you just saw him do which is to
+
+ align:start position:0%
+is what you just saw him do which is to
+ 
+
+ align:start position:0%
+is what you just saw him do which is to
+take that and put in the context of
+
+ align:start position:0%
+take that and put in the context of
+ 
+
+ align:start position:0%
+take that and put in the context of
+what's a university for what's MIT about
+
+ align:start position:0%
+what's a university for what's MIT about
+ 
+
+ align:start position:0%
+what's a university for what's MIT about
+what's mit's Mission Bob was just
+
+ align:start position:0%
+what's mit's Mission Bob was just
+ 
+
+ align:start position:0%
+what's mit's Mission Bob was just
+masterful in orchestrating how this
+
+ align:start position:0%
+masterful in orchestrating how this
+ 
+
+ align:start position:0%
+masterful in orchestrating how this
+whole thing was come to was was to come
+
+ align:start position:0%
+whole thing was come to was was to come
+ 
+
+ align:start position:0%
+whole thing was come to was was to come
+together and Larry who just about a half
+
+ align:start position:0%
+together and Larry who just about a half
+ 
+
+ align:start position:0%
+together and Larry who just about a half
+an hour ago said he didn't do anything
+
+ align:start position:0%
+an hour ago said he didn't do anything
+ 
+
+ align:start position:0%
+an hour ago said he didn't do anything
+did this amazing thing it was after I
+
+ align:start position:0%
+did this amazing thing it was after I
+ 
+
+ align:start position:0%
+did this amazing thing it was after I
+believe your your conversation with bu
+
+ align:start position:0%
+believe your your conversation with bu
+ 
+
+ align:start position:0%
+believe your your conversation with bu
+doen and we knew the funding was there
+
+ align:start position:0%
+doen and we knew the funding was there
+ 
+
+ align:start position:0%
+doen and we knew the funding was there
+and we were kind of ready to go and
+
+ align:start position:0%
+and we were kind of ready to go and
+ 
+
+ align:start position:0%
+and we were kind of ready to go and
+announce this thing Larry said no you
+
+ align:start position:0%
+announce this thing Larry said no you
+ 
+
+ align:start position:0%
+announce this thing Larry said no you
+may not do this until you have gone
+
+ align:start position:0%
+may not do this until you have gone
+ 
+
+ align:start position:0%
+may not do this until you have gone
+around and spoke to every department at
+
+ align:start position:0%
+around and spoke to every department at
+ 
+
+ align:start position:0%
+around and spoke to every department at
+MIT all 23 departments because this has
+
+ align:start position:0%
+MIT all 23 departments because this has
+ 
+
+ align:start position:0%
+MIT all 23 departments because this has
+to be an in initiative of the
+
+ align:start position:0%
+to be an in initiative of the
+ 
+
+ align:start position:0%
+to be an in initiative of the
+faculty and I think that was probably
+
+ align:start position:0%
+faculty and I think that was probably
+ 
+
+ align:start position:0%
+faculty and I think that was probably
+the crucial step in open course for so
+
+ align:start position:0%
+the crucial step in open course for so
+ 
+
+ align:start position:0%
+the crucial step in open course for so
+even today when we talk about ocw we
+
+ align:start position:0%
+even today when we talk about ocw we
+ 
+
+ align:start position:0%
+even today when we talk about ocw we
+talk about it as an initiative of the
+
+ align:start position:0%
+talk about it as an initiative of the
+ 
+
+ align:start position:0%
+talk about it as an initiative of the
+MIT faculty and Larry did that and it
+
+ align:start position:0%
+MIT faculty and Larry did that and it
+ 
+
+ align:start position:0%
+MIT faculty and Larry did that and it
+was amazingly important but
+
+ align:start position:0%
+was amazingly important but
+ 
+
+ align:start position:0%
+was amazingly important but
+let me just again get back to the
+
+ align:start position:0%
+let me just again get back to the
+ 
+
+ align:start position:0%
+let me just again get back to the
+general thing about openness there's an
+
+ align:start position:0%
+general thing about openness there's an
+ 
+
+ align:start position:0%
+general thing about openness there's an
+easy story that we can all tell in
+
+ align:start position:0%
+easy story that we can all tell in
+ 
+
+ align:start position:0%
+easy story that we can all tell in
+hindsight you heard Tim Craft it as
+
+ align:start position:0%
+hindsight you heard Tim Craft it as
+ 
+
+ align:start position:0%
+hindsight you heard Tim Craft it as
+uh we uh we we helped move the notion of
+
+ align:start position:0%
+uh we uh we we helped move the notion of
+ 
+
+ align:start position:0%
+uh we uh we we helped move the notion of
+what a university can do from away from
+
+ align:start position:0%
+what a university can do from away from
+ 
+
+ align:start position:0%
+what a university can do from away from
+uh in Tim's words internet one away from
+
+ align:start position:0%
+uh in Tim's words internet one away from
+ 
+
+ align:start position:0%
+uh in Tim's words internet one away from
+a a publishing model where the value is
+
+ align:start position:0%
+a a publishing model where the value is
+ 
+
+ align:start position:0%
+a a publishing model where the value is
+sitting in this material that the
+
+ align:start position:0%
+sitting in this material that the
+ 
+
+ align:start position:0%
+sitting in this material that the
+faculty make
+
+ align:start position:0%
+faculty make
+ 
+
+ align:start position:0%
+faculty make
+uh Bob Bob mentioned things like the
+
+ align:start position:0%
+uh Bob Bob mentioned things like the
+ 
+
+ align:start position:0%
+uh Bob Bob mentioned things like the
+posy Alliance and EC Cornell and
+
+ align:start position:0%
+posy Alliance and EC Cornell and
+ 
+
+ align:start position:0%
+posy Alliance and EC Cornell and
+Morningside Ventures and sitting in MIT
+
+ align:start position:0%
+Morningside Ventures and sitting in MIT
+ 
+
+ align:start position:0%
+Morningside Ventures and sitting in MIT
+we were getting all these approaches
+
+ align:start position:0%
+we were getting all these approaches
+ 
+
+ align:start position:0%
+we were getting all these approaches
+there are places like caliper learning
+
+ align:start position:0%
+there are places like caliper learning
+ 
+
+ align:start position:0%
+there are places like caliper learning
+and pensari and uh in fact the week we
+
+ align:start position:0%
+and pensari and uh in fact the week we
+ 
+
+ align:start position:0%
+and pensari and uh in fact the week we
+were going to announce ocw we got a
+
+ align:start position:0%
+were going to announce ocw we got a
+ 
+
+ align:start position:0%
+were going to announce ocw we got a
+visit from the executive director of
+
+ align:start position:0%
+visit from the executive director of
+ 
+
+ align:start position:0%
+visit from the executive director of
+fathom which was meant to be the the uh
+
+ align:start position:0%
+fathom which was meant to be the the uh
+ 
+
+ align:start position:0%
+fathom which was meant to be the the uh
+concentrating Market site for higher
+
+ align:start position:0%
+concentrating Market site for higher
+ 
+
+ align:start position:0%
+concentrating Market site for higher
+University educ ational materials and I
+
+ align:start position:0%
+University educ ational materials and I
+ 
+
+ align:start position:0%
+University educ ational materials and I
+remember Larry and I got a visit
+
+ align:start position:0%
+remember Larry and I got a visit
+ 
+
+ align:start position:0%
+remember Larry and I got a visit
+together and we were kind of kind of
+
+ align:start position:0%
+together and we were kind of kind of
+ 
+
+ align:start position:0%
+together and we were kind of kind of
+sitting there politely listening to this
+
+ align:start position:0%
+sitting there politely listening to this
+ 
+
+ align:start position:0%
+sitting there politely listening to this
+conversation saying well GE should we
+
+ align:start position:0%
+conversation saying well GE should we
+ 
+
+ align:start position:0%
+conversation saying well GE should we
+say anything that tomorrow we're about
+
+ align:start position:0%
+say anything that tomorrow we're about
+ 
+
+ align:start position:0%
+say anything that tomorrow we're about
+to announce MIT is about to give it away
+
+ align:start position:0%
+to announce MIT is about to give it away
+ 
+
+ align:start position:0%
+to announce MIT is about to give it away
+for free right R blow up her business
+
+ align:start position:0%
+for free right R blow up her business
+ 
+
+ align:start position:0%
+for free right R blow up her business
+model but that's in some sense an easy
+
+ align:start position:0%
+model but that's in some sense an easy
+ 
+
+ align:start position:0%
+model but that's in some sense an easy
+story
+
+ align:start position:0%
+story
+ 
+
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+say the uh the model by which this goes
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+
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+and I want to I worry a little bit that
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+
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+we're going to take the easy answer so
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+
+ align:start position:0%
+from internet one to internet
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+
+ align:start position:0%
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+2 we've heard we should modularize we
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+
+ align:start position:0%
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+
+ align:start position:0%
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+ align:start position:0%
+and what I want to say is man that is so
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+
+ align:start position:0%
+and what I want to say is man that is so
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+
+ align:start position:0%
+Tim O'Reilly
+ 
+
+ align:start position:0%
+Tim O'Reilly
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+
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+2004 we're beyond that what's the really
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+gutsy thing we could do so it was gutsy
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+
+ align:start position:0%
+in 2000 1999 when Dick thought about it
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+in 2000 1999 when Dick thought about it
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+on on his treadmill right that was a
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+gutsy move what's the gutsy move that
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+gutsy move what's the gutsy move that
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+
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+fits with mit's Mission so there's
+ 
+
+ align:start position:0%
+fits with mit's Mission so there's
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+
+ align:start position:0%
+another thing I want to drop I want to
+ 
+
+ align:start position:0%
+another thing I want to drop I want to
+drop into this which is a book you all
+
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+drop into this which is a book you all
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+
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+drop into this which is a book you all
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+should read which is a book by Douglas
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+
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+Thomas and John cely Brown called the
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+new culture of
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+
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+new culture of
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+learning because you remember what Tim
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+university and this new book by John has
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+
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+so many wonderful books by John has done
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+
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+so many wonderful books by John has done
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+
+ align:start position:0%
+he said look we are no longer in a
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+ align:start position:0%
+he said look we are no longer in a
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+publishing mode about learning we are no
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+
+ align:start position:0%
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+
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+
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+dissemination of information with
+ 
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+
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+is can we craft something not just in
+ 
+
+ align:start position:0%
+is can we craft something not just in
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+
+ align:start position:0%
+MIT but the whole Consortium all of us
+ 
+
+ align:start position:0%
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+ align:start position:0%
+saying what are we really
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+saying what are we really
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+
+ align:start position:0%
+about well if you look at mit's
+ 
+
+ align:start position:0%
+about well if you look at mit's
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+
+ align:start position:0%
+Mission and uh you heard that said a
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+
+ align:start position:0%
+Mission and uh you heard that said a
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+
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+couple of times right MIT is about the
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+couple of times right MIT is about the
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+
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+
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+of wondering suppose we really put it on
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+
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+of wondering suppose we really put it on
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+the line and said what we're going to
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+
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+try to commoditize right now is the
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+
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+try to commoditize right now is the
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+
+ align:start position:0%
+generation of
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+knowledge suppose this is no longer
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+
+ align:start position:0%
+knowledge suppose this is no longer
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+
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+about publishing suppose we are talking
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+
+ align:start position:0%
+about what all of us can do together for
+ 
+
+ align:start position:0%
+about what all of us can do together for
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+
+ align:start position:0%
+the benefit of humanity and actually
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+
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+creating new knowledge what would that
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+
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+be like is that an equivalently crazy
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+
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+idea to what ocw was in in
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+
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+idea to what ocw was in in
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+
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+2201 anyway that's that's sort of what's
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+
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+2201 anyway that's that's sort of what's
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+
+ align:start position:0%
+what's going through head that sort of
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+
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+what's going through head that sort of
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+that challenge can we can we learn how
+ 
+
+ align:start position:0%
+that challenge can we can we learn how
+to do that and uh just just as a bottom
+
+ align:start position:0%
+to do that and uh just just as a bottom
+ 
+
+ align:start position:0%
+to do that and uh just just as a bottom
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+
+ align:start position:0%
+line it this links very much with how
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+
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+line it this links very much with how
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+
+ align:start position:0%
+we're all thinking about the changing in
+ 
+
+ align:start position:0%
+we're all thinking about the changing in
+MIT in fact John and I are going tonight
+
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+MIT in fact John and I are going tonight
+ 
+
+ align:start position:0%
+MIT in fact John and I are going tonight
+tonight to a focus group of MIT
+
+ align:start position:0%
+tonight to a focus group of MIT
+ 
+
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+tonight to a focus group of MIT
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+
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+undergraduates saying what do you think
+ 
+
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+undergraduates saying what do you think
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+
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+MIT could be like with all of these
+ 
+
+ align:start position:0%
+MIT could be like with all of these
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+resources because they're the people who
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+
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+resources because they're the people who
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+
+ align:start position:0%
+are going to tell us Professor you you
+ 
+
+ align:start position:0%
+are going to tell us Professor you you
+want I just want to quickly comment I
+
+ align:start position:0%
+want I just want to quickly comment I
+ 
+
+ align:start position:0%
+want I just want to quickly comment I
+think uh I completely support the the
+
+ align:start position:0%
+think uh I completely support the the
+ 
+
+ align:start position:0%
+think uh I completely support the the
+what's already been said namely open
+
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+what's already been said namely open
+ 
+
+ align:start position:0%
+what's already been said namely open
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+
+ align:start position:0%
+course where is very much a reflection
+ 
+
+ align:start position:0%
+course where is very much a reflection
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+
+ align:start position:0%
+of uh the leadership and the vision and
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+
+ align:start position:0%
+of uh the leadership and the vision and
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+
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+courage gutsiness in many ways of the
+ 
+
+ align:start position:0%
+courage gutsiness in many ways of the
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+
+ align:start position:0%
+senior Administration but one should not
+ 
+
+ align:start position:0%
+senior Administration but one should not
+think of open courseware as a good idea
+
+ align:start position:0%
+think of open courseware as a good idea
+ 
+
+ align:start position:0%
+think of open courseware as a good idea
+and we're going to try to make MIT do it
+
+ align:start position:0%
+and we're going to try to make MIT do it
+ 
+
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+and we're going to try to make MIT do it
+right it really is a reflection of in
+
+ align:start position:0%
+right it really is a reflection of in
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+
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+right it really is a reflection of in
+some sense the the DNA of MIT and it
+
+ align:start position:0%
+some sense the the DNA of MIT and it
+ 
+
+ align:start position:0%
+some sense the the DNA of MIT and it
+working out in an expression right and I
+
+ align:start position:0%
+working out in an expression right and I
+ 
+
+ align:start position:0%
+working out in an expression right and I
+I think it would be uh completely uh
+
+ align:start position:0%
+I think it would be uh completely uh
+ 
+
+ align:start position:0%
+I think it would be uh completely uh
+sort of a Omission on our part not to
+
+ align:start position:0%
+sort of a Omission on our part not to
+ 
+
+ align:start position:0%
+sort of a Omission on our part not to
+point out that open course Weare
+
+ align:start position:0%
+point out that open course Weare
+ 
+
+ align:start position:0%
+point out that open course Weare
+wouldn't have happened if overwhelming
+
+ align:start position:0%
+wouldn't have happened if overwhelming
+ 
+
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+wouldn't have happened if overwhelming
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+
+ align:start position:0%
+majority of MIT faculty did not sign on
+ 
+
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+majority of MIT faculty did not sign on
+right and I just wanted to to say that
+
+ align:start position:0%
+right and I just wanted to to say that
+ 
+
+ align:start position:0%
+right and I just wanted to to say that
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+so it the the way our colleagues think
+ 
+
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+so it the the way our colleagues think
+about education think about making a
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+about education think about making a
+ 
+
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+about education think about making a
+contribution were reflected in open
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+contribution were reflected in open
+ 
+
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+contribution were reflected in open
+course workor right I mean they could
+
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+course workor right I mean they could
+ 
+
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+course workor right I mean they could
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+
+ align:start position:0%
+easily have said I'm busy why I do this
+ 
+
+ align:start position:0%
+easily have said I'm busy why I do this
+it's not part of me right I have a book
+
+ align:start position:0%
+it's not part of me right I have a book
+ 
+
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+it's not part of me right I have a book
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+
+ align:start position:0%
+to write and so I think one of the
+ 
+
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+to write and so I think one of the
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+things that I really think we should
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+things that I really think we should
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+point out and we pause to say and is
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+point out and we pause to say and is
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+that the the open course where is very
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+that the the open course where is very
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+much a reflection of the the the DNA the
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+
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+
+ align:start position:0%
+making an
+ 
+
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+making an
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+
+ align:start position:0%
+impact uh getting what they do uh to be
+ 
+
+ align:start position:0%
+impact uh getting what they do uh to be
+um beneficial to more people and so on
+
+ align:start position:0%
+um beneficial to more people and so on
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+
+ align:start position:0%
+um beneficial to more people and so on
+and so forth then the little ni and dime
+
+ align:start position:0%
+and so forth then the little ni and dime
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+
+ align:start position:0%
+and so forth then the little ni and dime
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+
+ align:start position:0%
+stuff that you sometime get into when
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+
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+stuff that you sometime get into when
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+ align:start position:0%
+you talk to faculty and and I just was I
+ 
+
+ align:start position:0%
+you talk to faculty and and I just was I
+wanted to chime in because I was you
+
+ align:start position:0%
+wanted to chime in because I was you
+ 
+
+ align:start position:0%
+wanted to chime in because I was you
+know reminded Larry uh idea about we
+
+ align:start position:0%
+know reminded Larry uh idea about we
+ 
+
+ align:start position:0%
+know reminded Larry uh idea about we
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+should go talk to different groups and
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+
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+should go talk to different groups and
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+
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+so forth and some of us were very
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+
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+concerned that these conversations would
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+bring out the sort of the the negative
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+
+ align:start position:0%
+bring out the sort of the the negative
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+
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+right and it's a historical fact we have
+ 
+
+ align:start position:0%
+right and it's a historical fact we have
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+you know record of all these
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+you know record of all these
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+conversations
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+conversations
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+
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+overwhelmingly MIT faculty bought in to
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+
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+open course were all within those couple
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+
+ align:start position:0%
+months when we went around and that was
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+ align:start position:0%
+months when we went around and that was
+not something that if you didn't know
+
+ align:start position:0%
+not something that if you didn't know
+ 
+
+ align:start position:0%
+not something that if you didn't know
+MIT you could have guessed right you
+
+ align:start position:0%
+MIT you could have guessed right you
+ 
+
+ align:start position:0%
+MIT you could have guessed right you
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+ align:start position:0%
+could have said this is going to be
+ 
+
+ align:start position:0%
+could have said this is going to be
+treacherous okay we we had very very few
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+ align:start position:0%
+treacherous okay we we had very very few
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+
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+treacherous okay we we had very very few
+actually naysayers I mean countable
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+ align:start position:0%
+actually naysayers I mean countable
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+
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+actually naysayers I mean countable
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+
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+ 
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+people who actually thought it wasn't a
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+great idea but the majority the the
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+
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+extremely supportive I just wanted to to
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+ align:start position:0%
+extremely supportive I just wanted to to
+ 
+
+ align:start position:0%
+extremely supportive I just wanted to to
+put that point I think it's very
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+ align:start position:0%
+put that point I think it's very
+ 
+
+ align:start position:0%
+put that point I think it's very
+important for us to put that yeah I I'd
+
+ align:start position:0%
+important for us to put that yeah I I'd
+ 
+
+ align:start position:0%
+important for us to put that yeah I I'd
+like to actually excuse me pick up on
+
+ align:start position:0%
+like to actually excuse me pick up on
+ 
+
+ align:start position:0%
+like to actually excuse me pick up on
+Dick's last comment and just add three
+
+ align:start position:0%
+Dick's last comment and just add three
+ 
+
+ align:start position:0%
+Dick's last comment and just add three
+little uh things to the flavor of the
+
+ align:start position:0%
+little uh things to the flavor of the
+ 
+
+ align:start position:0%
+little uh things to the flavor of the
+discuss
+
+ align:start position:0%
+discuss
+ 
+
+ align:start position:0%
+discuss
+here uh one is it's interesting of
+
+ align:start position:0%
+here uh one is it's interesting of
+ 
+
+ align:start position:0%
+here uh one is it's interesting of
+course there was some faculty reluctance
+
+ align:start position:0%
+course there was some faculty reluctance
+ 
+
+ align:start position:0%
+course there was some faculty reluctance
+and you've heard the kind of distributed
+
+ align:start position:0%
+and you've heard the kind of distributed
+ 
+
+ align:start position:0%
+and you've heard the kind of distributed
+leadership it took to be sure everybody
+
+ align:start position:0%
+leadership it took to be sure everybody
+ 
+
+ align:start position:0%
+leadership it took to be sure everybody
+had thought it through carefully but
+
+ align:start position:0%
+had thought it through carefully but
+ 
+
+ align:start position:0%
+had thought it through carefully but
+there were three
+
+ align:start position:0%
+there were three
+ 
+
+ align:start position:0%
+there were three
+concerns uh the one we all expected or
+
+ align:start position:0%
+concerns uh the one we all expected or
+ 
+
+ align:start position:0%
+concerns uh the one we all expected or
+at least I did was that people would be
+
+ align:start position:0%
+at least I did was that people would be
+ 
+
+ align:start position:0%
+at least I did was that people would be
+worried about their intellectual
+
+ align:start position:0%
+worried about their intellectual
+ 
+
+ align:start position:0%
+worried about their intellectual
+property and say I'm not going to play
+
+ align:start position:0%
+property and say I'm not going to play
+ 
+
+ align:start position:0%
+property and say I'm not going to play
+ball because I'm going to write a
+
+ align:start position:0%
+ball because I'm going to write a
+ 
+
+ align:start position:0%
+ball because I'm going to write a
+textbook and so forth and so on that
+
+ align:start position:0%
+textbook and so forth and so on that
+ 
+
+ align:start position:0%
+textbook and so forth and so on that
+ended up being in the noise level the
+
+ align:start position:0%
+ended up being in the noise level the
+ 
+
+ align:start position:0%
+ended up being in the noise level the
+two things that there was some serious
+
+ align:start position:0%
+two things that there was some serious
+ 
+
+ align:start position:0%
+two things that there was some serious
+faculty reluctance around I think Larry
+
+ align:start position:0%
+faculty reluctance around I think Larry
+ 
+
+ align:start position:0%
+faculty reluctance around I think Larry
+may have have mentioned one of them was
+
+ align:start position:0%
+may have have mentioned one of them was
+ 
+
+ align:start position:0%
+may have have mentioned one of them was
+this concern that we were going to take
+
+ align:start position:0%
+this concern that we were going to take
+ 
+
+ align:start position:0%
+this concern that we were going to take
+away resources in order to make this
+
+ align:start position:0%
+away resources in order to make this
+ 
+
+ align:start position:0%
+away resources in order to make this
+happen and in particular we had just at
+
+ align:start position:0%
+happen and in particular we had just at
+ 
+
+ align:start position:0%
+happen and in particular we had just at
+this time been fortunate to get this
+
+ align:start position:0%
+this time been fortunate to get this
+ 
+
+ align:start position:0%
+this time been fortunate to get this
+wonderful $10 million endowment from uh
+
+ align:start position:0%
+wonderful $10 million endowment from uh
+ 
+
+ align:start position:0%
+wonderful $10 million endowment from uh
+from uh Britain Alex daroff to fund
+
+ align:start position:0%
+from uh Britain Alex daroff to fund
+ 
+
+ align:start position:0%
+from uh Britain Alex daroff to fund
+exciting educational ideas in the
+
+ align:start position:0%
+exciting educational ideas in the
+ 
+
+ align:start position:0%
+exciting educational ideas in the
+faculty people were really worried we're
+
+ align:start position:0%
+faculty people were really worried we're
+ 
+
+ align:start position:0%
+faculty people were really worried we're
+going to do that but the other one to me
+
+ align:start position:0%
+going to do that but the other one to me
+ 
+
+ align:start position:0%
+going to do that but the other one to me
+is the most interesting there was a
+
+ align:start position:0%
+is the most interesting there was a
+ 
+
+ align:start position:0%
+is the most interesting there was a
+non-trivial amount of the faculty who
+
+ align:start position:0%
+non-trivial amount of the faculty who
+ 
+
+ align:start position:0%
+non-trivial amount of the faculty who
+properly said this is not using Cutting
+
+ align:start position:0%
+properly said this is not using Cutting
+ 
+
+ align:start position:0%
+properly said this is not using Cutting
+Edge technology you know this is kind of
+
+ align:start position:0%
+Edge technology you know this is kind of
+ 
+
+ align:start position:0%
+Edge technology you know this is kind of
+technologically
+
+ align:start position:0%
+technologically
+ 
+
+ align:start position:0%
+technologically
+mundane and we're afraid we're going to
+
+ align:start position:0%
+mundane and we're afraid we're going to
+ 
+
+ align:start position:0%
+mundane and we're afraid we're going to
+put stuff out there that is not going to
+
+ align:start position:0%
+put stuff out there that is not going to
+ 
+
+ align:start position:0%
+put stuff out there that is not going to
+look like it's really high quality and
+
+ align:start position:0%
+look like it's really high quality and
+ 
+
+ align:start position:0%
+look like it's really high quality and
+that to me was a very interesting debate
+
+ align:start position:0%
+that to me was a very interesting debate
+ 
+
+ align:start position:0%
+that to me was a very interesting debate
+because the whole Elegance of this idea
+
+ align:start position:0%
+because the whole Elegance of this idea
+ 
+
+ align:start position:0%
+because the whole Elegance of this idea
+was it used fairly simple technology uh
+
+ align:start position:0%
+was it used fairly simple technology uh
+ 
+
+ align:start position:0%
+was it used fairly simple technology uh
+but but as dick said these were really
+
+ align:start position:0%
+but but as dick said these were really
+ 
+
+ align:start position:0%
+but but as dick said these were really
+relatively modest number of outliers
+
+ align:start position:0%
+relatively modest number of outliers
+ 
+
+ align:start position:0%
+relatively modest number of outliers
+other two points very quickly what was
+
+ align:start position:0%
+other two points very quickly what was
+ 
+
+ align:start position:0%
+other two points very quickly what was
+really unique and I know that both the
+
+ align:start position:0%
+really unique and I know that both the
+ 
+
+ align:start position:0%
+really unique and I know that both the
+melan and hulet Foundations put great
+
+ align:start position:0%
+melan and hulet Foundations put great
+ 
+
+ align:start position:0%
+melan and hulet Foundations put great
+weight on this uh lots of people were
+
+ align:start position:0%
+weight on this uh lots of people were
+ 
+
+ align:start position:0%
+weight on this uh lots of people were
+putting up things on the web and and
+
+ align:start position:0%
+putting up things on the web and and
+ 
+
+ align:start position:0%
+putting up things on the web and and
+lots of individual departments or
+
+ align:start position:0%
+lots of individual departments or
+ 
+
+ align:start position:0%
+lots of individual departments or
+schools were it was the
+
+ align:start position:0%
+schools were it was the
+ 
+
+ align:start position:0%
+schools were it was the
+comprehensiveness literally nobody had
+
+ align:start position:0%
+comprehensiveness literally nobody had
+ 
+
+ align:start position:0%
+comprehensiveness literally nobody had
+come at this in what Larry always so
+
+ align:start position:0%
+come at this in what Larry always so
+ 
+
+ align:start position:0%
+come at this in what Larry always so
+well articulated there's one MIT here
+
+ align:start position:0%
+well articulated there's one MIT here
+ 
+
+ align:start position:0%
+well articulated there's one MIT here
+folks and neither you want the whole
+
+ align:start position:0%
+folks and neither you want the whole
+ 
+
+ align:start position:0%
+folks and neither you want the whole
+thing or you don't get it so a lot of
+
+ align:start position:0%
+thing or you don't get it so a lot of
+ 
+
+ align:start position:0%
+thing or you don't get it so a lot of
+the world expected to see a few physics
+
+ align:start position:0%
+the world expected to see a few physics
+ 
+
+ align:start position:0%
+the world expected to see a few physics
+courses and some we courses some
+
+ align:start position:0%
+courses and some we courses some
+ 
+
+ align:start position:0%
+courses and some we courses some
+computer science but it was that
+
+ align:start position:0%
+computer science but it was that
+ 
+
+ align:start position:0%
+computer science but it was that
+holistic view that's what the foundation
+
+ align:start position:0%
+holistic view that's what the foundation
+ 
+
+ align:start position:0%
+holistic view that's what the foundation
+saw that nobody else was doing and
+
+ align:start position:0%
+saw that nobody else was doing and
+ 
+
+ align:start position:0%
+saw that nobody else was doing and
+finally and uh relevant to both what Tim
+
+ align:start position:0%
+finally and uh relevant to both what Tim
+ 
+
+ align:start position:0%
+finally and uh relevant to both what Tim
+O'Reilly said and what what Hal just
+
+ align:start position:0%
+O'Reilly said and what what Hal just
+ 
+
+ align:start position:0%
+O'Reilly said and what what Hal just
+said I think most of us uh viewed this
+
+ align:start position:0%
+said I think most of us uh viewed this
+ 
+
+ align:start position:0%
+said I think most of us uh viewed this
+as something that was largely a tool for
+
+ align:start position:0%
+as something that was largely a tool for
+ 
+
+ align:start position:0%
+as something that was largely a tool for
+teachers that we were going to give
+
+ align:start position:0%
+teachers that we were going to give
+ 
+
+ align:start position:0%
+teachers that we were going to give
+teachers a way of formatting the
+
+ align:start position:0%
+teachers a way of formatting the
+ 
+
+ align:start position:0%
+teachers a way of formatting the
+education that they provided and of
+
+ align:start position:0%
+education that they provided and of
+ 
+
+ align:start position:0%
+education that they provided and of
+course we've since learned that uh that
+
+ align:start position:0%
+course we've since learned that uh that
+ 
+
+ align:start position:0%
+course we've since learned that uh that
+well over half of the users are actually
+
+ align:start position:0%
+well over half of the users are actually
+ 
+
+ align:start position:0%
+well over half of the users are actually
+self-learners but really wasn't designed
+
+ align:start position:0%
+self-learners but really wasn't designed
+ 
+
+ align:start position:0%
+self-learners but really wasn't designed
+for that
+
+ align:start position:0%
+for that
+ 
+
+ align:start position:0%
+for that
+purpose thank you thank you uh Dr backo
+
+ align:start position:0%
+purpose thank you thank you uh Dr backo
+ 
+
+ align:start position:0%
+purpose thank you thank you uh Dr backo
+or perhaps Dr Brown um you know we've
+
+ align:start position:0%
+or perhaps Dr Brown um you know we've
+ 
+
+ align:start position:0%
+or perhaps Dr Brown um you know we've
+heard a lot about faculty by and getting
+
+ align:start position:0%
+heard a lot about faculty by and getting
+ 
+
+ align:start position:0%
+heard a lot about faculty by and getting
+faculty to participate and the
+
+ align:start position:0%
+faculty to participate and the
+ 
+
+ align:start position:0%
+faculty to participate and the
+importance of that but faculty aren't
+
+ align:start position:0%
+importance of that but faculty aren't
+ 
+
+ align:start position:0%
+importance of that but faculty aren't
+the only constituency certainly at a
+
+ align:start position:0%
+the only constituency certainly at a
+ 
+
+ align:start position:0%
+the only constituency certainly at a
+university and there were other
+
+ align:start position:0%
+university and there were other
+ 
+
+ align:start position:0%
+university and there were other
+constituencies of concern uh were there
+
+ align:start position:0%
+constituencies of concern uh were there
+ 
+
+ align:start position:0%
+constituencies of concern uh were there
+uh issues you faced in in bringing them
+
+ align:start position:0%
+uh issues you faced in in bringing them
+ 
+
+ align:start position:0%
+uh issues you faced in in bringing them
+along as well well you know one of the
+
+ align:start position:0%
+along as well well you know one of the
+ 
+
+ align:start position:0%
+along as well well you know one of the
+many reasons I thought that this was
+
+ align:start position:0%
+many reasons I thought that this was
+ 
+
+ align:start position:0%
+many reasons I thought that this was
+such a a terrific idea is that I think
+
+ align:start position:0%
+such a a terrific idea is that I think
+ 
+
+ align:start position:0%
+such a a terrific idea is that I think
+it was clear to most of us that our
+
+ align:start position:0%
+it was clear to most of us that our
+ 
+
+ align:start position:0%
+it was clear to most of us that our
+students expected to be able to access
+
+ align:start position:0%
+students expected to be able to access
+ 
+
+ align:start position:0%
+students expected to be able to access
+content over the web these were our MIT
+
+ align:start position:0%
+content over the web these were our MIT
+ 
+
+ align:start position:0%
+content over the web these were our MIT
+students students and they were in fact
+
+ align:start position:0%
+students students and they were in fact
+ 
+
+ align:start position:0%
+students students and they were in fact
+some were frustrated that more faculty
+
+ align:start position:0%
+some were frustrated that more faculty
+ 
+
+ align:start position:0%
+some were frustrated that more faculty
+had not in fact made their materials
+
+ align:start position:0%
+had not in fact made their materials
+ 
+
+ align:start position:0%
+had not in fact made their materials
+available um this way and
+
+ align:start position:0%
+available um this way and
+ 
+
+ align:start position:0%
+available um this way and
+so students were I think a natural
+
+ align:start position:0%
+so students were I think a natural
+ 
+
+ align:start position:0%
+so students were I think a natural
+constituency in favor of this uh because
+
+ align:start position:0%
+constituency in favor of this uh because
+ 
+
+ align:start position:0%
+constituency in favor of this uh because
+they were going to be able to have you
+
+ align:start position:0%
+they were going to be able to have you
+ 
+
+ align:start position:0%
+they were going to be able to have you
+know everything up there eventually for
+
+ align:start position:0%
+know everything up there eventually for
+ 
+
+ align:start position:0%
+know everything up there eventually for
+them uh whenever they wanted it so I
+
+ align:start position:0%
+them uh whenever they wanted it so I
+ 
+
+ align:start position:0%
+them uh whenever they wanted it so I
+think that you know I I don't recall any
+
+ align:start position:0%
+think that you know I I don't recall any
+ 
+
+ align:start position:0%
+think that you know I I don't recall any
+um push back on the student side at the
+
+ align:start position:0%
+um push back on the student side at the
+ 
+
+ align:start position:0%
+um push back on the student side at the
+at the time it did engender an
+
+ align:start position:0%
+at the time it did engender an
+ 
+
+ align:start position:0%
+at the time it did engender an
+interesting conversation though which I
+
+ align:start position:0%
+interesting conversation though which I
+ 
+
+ align:start position:0%
+interesting conversation though which I
+think was ultimately very helpful and
+
+ align:start position:0%
+think was ultimately very helpful and
+ 
+
+ align:start position:0%
+think was ultimately very helpful and
+that is um The Faculty spent a fair
+
+ align:start position:0%
+that is um The Faculty spent a fair
+ 
+
+ align:start position:0%
+that is um The Faculty spent a fair
+amount of time saying well you know once
+
+ align:start position:0%
+amount of time saying well you know once
+ 
+
+ align:start position:0%
+amount of time saying well you know once
+we make all of the content available for
+
+ align:start position:0%
+we make all of the content available for
+ 
+
+ align:start position:0%
+we make all of the content available for
+all of our courses um to anybody who
+
+ align:start position:0%
+all of our courses um to anybody who
+ 
+
+ align:start position:0%
+all of our courses um to anybody who
+wants it what then is the value added of
+
+ align:start position:0%
+wants it what then is the value added of
+ 
+
+ align:start position:0%
+wants it what then is the value added of
+the MIT residential experience and so I
+
+ align:start position:0%
+the MIT residential experience and so I
+ 
+
+ align:start position:0%
+the MIT residential experience and so I
+think it caused us to think even harder
+
+ align:start position:0%
+think it caused us to think even harder
+ 
+
+ align:start position:0%
+think it caused us to think even harder
+about that and that was at a time in
+
+ align:start position:0%
+about that and that was at a time in
+ 
+
+ align:start position:0%
+about that and that was at a time in
+which chuck had commissioned a sort of a
+
+ align:start position:0%
+which chuck had commissioned a sort of a
+ 
+
+ align:start position:0%
+which chuck had commissioned a sort of a
+searching look at the MIT undergraduate
+
+ align:start position:0%
+searching look at the MIT undergraduate
+ 
+
+ align:start position:0%
+searching look at the MIT undergraduate
+experience and I think that proved to be
+
+ align:start position:0%
+experience and I think that proved to be
+ 
+
+ align:start position:0%
+experience and I think that proved to be
+I mean one reinforced the other at least
+
+ align:start position:0%
+I mean one reinforced the other at least
+ 
+
+ align:start position:0%
+I mean one reinforced the other at least
+that was my recollection I I I I agree
+
+ align:start position:0%
+that was my recollection I I I I agree
+ 
+
+ align:start position:0%
+that was my recollection I I I I agree
+with Larry I there was a fair amount of
+
+ align:start position:0%
+with Larry I there was a fair amount of
+ 
+
+ align:start position:0%
+with Larry I there was a fair amount of
+noise that Focus back on the Provo
+
+ align:start position:0%
+noise that Focus back on the Provo
+ 
+
+ align:start position:0%
+noise that Focus back on the Provo
+office and I think the president's
+
+ align:start position:0%
+office and I think the president's
+ 
+
+ align:start position:0%
+office and I think the president's
+office coming through from three
+
+ align:start position:0%
+office coming through from three
+ 
+
+ align:start position:0%
+office coming through from three
+constituencies one were the students
+
+ align:start position:0%
+constituencies one were the students
+ 
+
+ align:start position:0%
+constituencies one were the students
+alumni and parents about where we giving
+
+ align:start position:0%
+alumni and parents about where we giving
+ 
+
+ align:start position:0%
+alumni and parents about where we giving
+away what is an MIT education for
+
+ align:start position:0%
+away what is an MIT education for
+ 
+
+ align:start position:0%
+away what is an MIT education for
+free compared to the people who had
+
+ align:start position:0%
+free compared to the people who had
+ 
+
+ align:start position:0%
+free compared to the people who had
+earned it by coming to miip in the
+
+ align:start position:0%
+earned it by coming to miip in the
+ 
+
+ align:start position:0%
+earned it by coming to miip in the
+residential experience and it in it
+
+ align:start position:0%
+residential experience and it in it
+ 
+
+ align:start position:0%
+residential experience and it in it
+forced us into this articulation of what
+
+ align:start position:0%
+forced us into this articulation of what
+ 
+
+ align:start position:0%
+forced us into this articulation of what
+was the value of the residential
+
+ align:start position:0%
+was the value of the residential
+ 
+
+ align:start position:0%
+was the value of the residential
+experience of bringing all of these
+
+ align:start position:0%
+experience of bringing all of these
+ 
+
+ align:start position:0%
+experience of bringing all of these
+people together in a small place uh
+
+ align:start position:0%
+people together in a small place uh
+ 
+
+ align:start position:0%
+people together in a small place uh
+under a fair amount of light and
+
+ align:start position:0%
+under a fair amount of light and
+ 
+
+ align:start position:0%
+under a fair amount of light and
+pressure and heat uh that actually forms
+
+ align:start position:0%
+pressure and heat uh that actually forms
+ 
+
+ align:start position:0%
+pressure and heat uh that actually forms
+the MIT experience and uh I think was
+
+ align:start position:0%
+the MIT experience and uh I think was
+ 
+
+ align:start position:0%
+the MIT experience and uh I think was
+healthy I think there were people even
+
+ align:start position:0%
+healthy I think there were people even
+ 
+
+ align:start position:0%
+healthy I think there were people even
+as we launched that believed at that
+
+ align:start position:0%
+as we launched that believed at that
+ 
+
+ align:start position:0%
+as we launched that believed at that
+point in time we were moving down a road
+
+ align:start position:0%
+point in time we were moving down a road
+ 
+
+ align:start position:0%
+point in time we were moving down a road
+of commoditizing an MIT education what
+
+ align:start position:0%
+of commoditizing an MIT education what
+ 
+
+ align:start position:0%
+of commoditizing an MIT education what
+we thought of as an MIT education
+
+ align:start position:0%
+we thought of as an MIT education
+ 
+
+ align:start position:0%
+we thought of as an MIT education
+although we said that clearly wasn't
+
+ align:start position:0%
+although we said that clearly wasn't
+ 
+
+ align:start position:0%
+although we said that clearly wasn't
+what was going to happen at the end of
+
+ align:start position:0%
+what was going to happen at the end of
+ 
+
+ align:start position:0%
+what was going to happen at the end of
+this and it's interesting now a decade
+
+ align:start position:0%
+this and it's interesting now a decade
+ 
+
+ align:start position:0%
+this and it's interesting now a decade
+later about how the putting the content
+
+ align:start position:0%
+later about how the putting the content
+ 
+
+ align:start position:0%
+later about how the putting the content
+of those courses online has affected
+
+ align:start position:0%
+of those courses online has affected
+ 
+
+ align:start position:0%
+of those courses online has affected
+educationally uh education worldwide but
+
+ align:start position:0%
+educationally uh education worldwide but
+ 
+
+ align:start position:0%
+educationally uh education worldwide but
+I don't think anybody believes we've
+
+ align:start position:0%
+I don't think anybody believes we've
+ 
+
+ align:start position:0%
+I don't think anybody believes we've
+commoditized an MIT educ
+
+ align:start position:0%
+commoditized an MIT educ
+ 
+
+ align:start position:0%
+commoditized an MIT educ
+and you know going back to a comment
+
+ align:start position:0%
+and you know going back to a comment
+ 
+
+ align:start position:0%
+and you know going back to a comment
+that Chuck made earlier it was also very
+
+ align:start position:0%
+that Chuck made earlier it was also very
+ 
+
+ align:start position:0%
+that Chuck made earlier it was also very
+helpful to be able to point out to
+
+ align:start position:0%
+helpful to be able to point out to
+ 
+
+ align:start position:0%
+helpful to be able to point out to
+people that you know most of us grew up
+
+ align:start position:0%
+people that you know most of us grew up
+ 
+
+ align:start position:0%
+people that you know most of us grew up
+taking calculus from a textbook that
+
+ align:start position:0%
+taking calculus from a textbook that
+ 
+
+ align:start position:0%
+taking calculus from a textbook that
+George Thomas wrote um you know um we
+
+ align:start position:0%
+George Thomas wrote um you know um we
+ 
+
+ align:start position:0%
+George Thomas wrote um you know um we
+took physics from pssc physics okay that
+
+ align:start position:0%
+took physics from pssc physics okay that
+ 
+
+ align:start position:0%
+took physics from pssc physics okay that
+originated at MIT uh economics from a
+
+ align:start position:0%
+originated at MIT uh economics from a
+ 
+
+ align:start position:0%
+originated at MIT uh economics from a
+textbook that Paul Samson wrote that MIT
+
+ align:start position:0%
+textbook that Paul Samson wrote that MIT
+ 
+
+ align:start position:0%
+textbook that Paul Samson wrote that MIT
+had been in the business for generations
+
+ align:start position:0%
+had been in the business for generations
+ 
+
+ align:start position:0%
+had been in the business for generations
+of propagating materials um and sending
+
+ align:start position:0%
+of propagating materials um and sending
+ 
+
+ align:start position:0%
+of propagating materials um and sending
+them out into the world and that you
+
+ align:start position:0%
+them out into the world and that you
+ 
+
+ align:start position:0%
+them out into the world and that you
+could have access to those materials
+
+ align:start position:0%
+could have access to those materials
+ 
+
+ align:start position:0%
+could have access to those materials
+anytime you wanted
+
+ align:start position:0%
+anytime you wanted
+ 
+
+ align:start position:0%
+anytime you wanted
+that was not what an MIT education was
+
+ align:start position:0%
+that was not what an MIT education was
+ 
+
+ align:start position:0%
+that was not what an MIT education was
+but it did I I think it was actually
+
+ align:start position:0%
+but it did I I think it was actually
+ 
+
+ align:start position:0%
+but it did I I think it was actually
+very helpful that we had that
+
+ align:start position:0%
+very helpful that we had that
+ 
+
+ align:start position:0%
+very helpful that we had that
+conversation about what is it that's
+
+ align:start position:0%
+conversation about what is it that's
+ 
+
+ align:start position:0%
+conversation about what is it that's
+unique about the residential experience
+
+ align:start position:0%
+unique about the residential experience
+ 
+
+ align:start position:0%
+unique about the residential experience
+and it forced us to be able to
+
+ align:start position:0%
+and it forced us to be able to
+ 
+
+ align:start position:0%
+and it forced us to be able to
+articulate far more sharply than I think
+
+ align:start position:0%
+articulate far more sharply than I think
+ 
+
+ align:start position:0%
+articulate far more sharply than I think
+we otherwise might have have done to
+
+ align:start position:0%
+we otherwise might have have done to
+ 
+
+ align:start position:0%
+we otherwise might have have done to
+others as well as to ourselves what was
+
+ align:start position:0%
+others as well as to ourselves what was
+ 
+
+ align:start position:0%
+others as well as to ourselves what was
+the essence of an MIT education as
+
+ align:start position:0%
+the essence of an MIT education as
+ 
+
+ align:start position:0%
+the essence of an MIT education as
+opposed to MIT content if I remember
+
+ align:start position:0%
+opposed to MIT content if I remember
+ 
+
+ align:start position:0%
+opposed to MIT content if I remember
+Larry was quoted in the new New York
+
+ align:start position:0%
+Larry was quoted in the new New York
+ 
+
+ align:start position:0%
+Larry was quoted in the new New York
+Times is saying an MIT education is not
+
+ align:start position:0%
+Times is saying an MIT education is not
+ 
+
+ align:start position:0%
+Times is saying an MIT education is not
+a box full of
+
+ align:start position:0%
+a box full of
+ 
+
+ align:start position:0%
+a box full of
+books I just want to quickly add a
+
+ align:start position:0%
+books I just want to quickly add a
+ 
+
+ align:start position:0%
+books I just want to quickly add a
+thought which is s of in the same line
+
+ align:start position:0%
+thought which is s of in the same line
+ 
+
+ align:start position:0%
+thought which is s of in the same line
+uh the the idea that if we were to
+
+ align:start position:0%
+uh the the idea that if we were to
+ 
+
+ align:start position:0%
+uh the the idea that if we were to
+publish a lot of this material uh it
+
+ align:start position:0%
+publish a lot of this material uh it
+ 
+
+ align:start position:0%
+publish a lot of this material uh it
+would actually free up our faculty to
+
+ align:start position:0%
+would actually free up our faculty to
+ 
+
+ align:start position:0%
+would actually free up our faculty to
+really teach rather than transferring
+
+ align:start position:0%
+really teach rather than transferring
+ 
+
+ align:start position:0%
+really teach rather than transferring
+information from their notebook to the
+
+ align:start position:0%
+information from their notebook to the
+ 
+
+ align:start position:0%
+information from their notebook to the
+Blackboard and from the Blackboard to
+
+ align:start position:0%
+Blackboard and from the Blackboard to
+ 
+
+ align:start position:0%
+Blackboard and from the Blackboard to
+the students notebook which happens a
+
+ align:start position:0%
+the students notebook which happens a
+ 
+
+ align:start position:0%
+the students notebook which happens a
+lot and there were a few again outlier
+
+ align:start position:0%
+lot and there were a few again outlier
+ 
+
+ align:start position:0%
+lot and there were a few again outlier
+type comments and say what if students
+
+ align:start position:0%
+type comments and say what if students
+ 
+
+ align:start position:0%
+type comments and say what if students
+stud don't come to my classes and that
+
+ align:start position:0%
+stud don't come to my classes and that
+ 
+
+ align:start position:0%
+stud don't come to my classes and that
+and of course that would be the case if
+
+ align:start position:0%
+and of course that would be the case if
+ 
+
+ align:start position:0%
+and of course that would be the case if
+all they were doing was copying uh from
+
+ align:start position:0%
+all they were doing was copying uh from
+ 
+
+ align:start position:0%
+all they were doing was copying uh from
+one place or the other but I think in
+
+ align:start position:0%
+one place or the other but I think in
+ 
+
+ align:start position:0%
+one place or the other but I think in
+the over looking back a bit it it did
+
+ align:start position:0%
+the over looking back a bit it it did
+ 
+
+ align:start position:0%
+the over looking back a bit it it did
+free up a lot of us to use the classroom
+
+ align:start position:0%
+free up a lot of us to use the classroom
+ 
+
+ align:start position:0%
+free up a lot of us to use the classroom
+and their interaction for much better uh
+
+ align:start position:0%
+and their interaction for much better uh
+ 
+
+ align:start position:0%
+and their interaction for much better uh
+purposes uh you know we we became much
+
+ align:start position:0%
+purposes uh you know we we became much
+ 
+
+ align:start position:0%
+purposes uh you know we we became much
+more creative about the time we have
+
+ align:start position:0%
+more creative about the time we have
+ 
+
+ align:start position:0%
+more creative about the time we have
+right uh doing new experiments of uh you
+
+ align:start position:0%
+right uh doing new experiments of uh you
+ 
+
+ align:start position:0%
+right uh doing new experiments of uh you
+know etc etc so I think I think this was
+
+ align:start position:0%
+know etc etc so I think I think this was
+ 
+
+ align:start position:0%
+know etc etc so I think I think this was
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+at in the beginning sort of a push back
+
+ align:start position:0%
+at in the beginning sort of a push back
+ 
+
+ align:start position:0%
+at in the beginning sort of a push back
+but it ended up to be an opportunity
+
+ align:start position:0%
+but it ended up to be an opportunity
+ 
+
+ align:start position:0%
+but it ended up to be an opportunity
+actually for us to do a lot of
+
+ align:start position:0%
+actually for us to do a lot of
+ 
+
+ align:start position:0%
+actually for us to do a lot of
+interesting things and just quickly I
+
+ align:start position:0%
+interesting things and just quickly I
+ 
+
+ align:start position:0%
+interesting things and just quickly I
+think I'm going to give let Bob uh there
+
+ align:start position:0%
+think I'm going to give let Bob uh there
+ 
+
+ align:start position:0%
+think I'm going to give let Bob uh there
+were many other constituents with
+
+ align:start position:0%
+were many other constituents with
+ 
+
+ align:start position:0%
+were many other constituents with
+similar concerns that at the end of the
+
+ align:start position:0%
+similar concerns that at the end of the
+ 
+
+ align:start position:0%
+similar concerns that at the end of the
+day looking back it turned out that
+
+ align:start position:0%
+day looking back it turned out that
+ 
+
+ align:start position:0%
+day looking back it turned out that
+those concerns would be there because it
+
+ align:start position:0%
+those concerns would be there because it
+ 
+
+ align:start position:0%
+those concerns would be there because it
+was something you knew and nobody knew
+
+ align:start position:0%
+was something you knew and nobody knew
+ 
+
+ align:start position:0%
+was something you knew and nobody knew
+what the implications are but many of
+
+ align:start position:0%
+what the implications are but many of
+ 
+
+ align:start position:0%
+what the implications are but many of
+the worries actually did not materialize
+
+ align:start position:0%
+the worries actually did not materialize
+ 
+
+ align:start position:0%
+the worries actually did not materialize
+right so I remember a conversation with
+
+ align:start position:0%
+right so I remember a conversation with
+ 
+
+ align:start position:0%
+right so I remember a conversation with
+our emissions director right and say gee
+
+ align:start position:0%
+our emissions director right and say gee
+ 
+
+ align:start position:0%
+our emissions director right and say gee
+you know these guys could got all our
+
+ align:start position:0%
+you know these guys could got all our
+ 
+
+ align:start position:0%
+you know these guys could got all our
+material our applications numbers would
+
+ align:start position:0%
+material our applications numbers would
+ 
+
+ align:start position:0%
+material our applications numbers would
+would decline right because you know
+
+ align:start position:0%
+would decline right because you know
+ 
+
+ align:start position:0%
+would decline right because you know
+people would say I don't need to come to
+
+ align:start position:0%
+people would say I don't need to come to
+ 
+
+ align:start position:0%
+people would say I don't need to come to
+MIT anymore I could you know look at and
+
+ align:start position:0%
+MIT anymore I could you know look at and
+ 
+
+ align:start position:0%
+MIT anymore I could you know look at and
+of course as you know it that never
+
+ align:start position:0%
+of course as you know it that never
+ 
+
+ align:start position:0%
+of course as you know it that never
+materialized it's quite the contrary in
+
+ align:start position:0%
+materialized it's quite the contrary in
+ 
+
+ align:start position:0%
+materialized it's quite the contrary in
+fact a lot of our high school students
+
+ align:start position:0%
+fact a lot of our high school students
+ 
+
+ align:start position:0%
+fact a lot of our high school students
+who before they came to MIT had already
+
+ align:start position:0%
+who before they came to MIT had already
+ 
+
+ align:start position:0%
+who before they came to MIT had already
+became familiar with the kind of uh
+
+ align:start position:0%
+became familiar with the kind of uh
+ 
+
+ align:start position:0%
+became familiar with the kind of uh
+rigor and excitement MIT would provide
+
+ align:start position:0%
+rigor and excitement MIT would provide
+ 
+
+ align:start position:0%
+rigor and excitement MIT would provide
+through open courseware so when when
+
+ align:start position:0%
+through open courseware so when when
+ 
+
+ align:start position:0%
+through open courseware so when when
+when you have an idea like this there
+
+ align:start position:0%
+when you have an idea like this there
+ 
+
+ align:start position:0%
+when you have an idea like this there
+usually a lot of reasons for concern or
+
+ align:start position:0%
+usually a lot of reasons for concern or
+ 
+
+ align:start position:0%
+usually a lot of reasons for concern or
+push back and but in hindsight many of
+
+ align:start position:0%
+push back and but in hindsight many of
+ 
+
+ align:start position:0%
+push back and but in hindsight many of
+them actually did not did not
+
+ align:start position:0%
+them actually did not did not
+ 
+
+ align:start position:0%
+them actually did not did not
+materialize at all right on maybe even
+
+ align:start position:0%
+materialize at all right on maybe even
+ 
+
+ align:start position:0%
+materialize at all right on maybe even
+on the contrary they they opened us up
+
+ align:start position:0%
+on the contrary they they opened us up
+ 
+
+ align:start position:0%
+on the contrary they they opened us up
+to do to good creative things and good
+
+ align:start position:0%
+to do to good creative things and good
+ 
+
+ align:start position:0%
+to do to good creative things and good
+things yeah well it's interesting re uh
+
+ align:start position:0%
+things yeah well it's interesting re uh
+ 
+
+ align:start position:0%
+things yeah well it's interesting re uh
+recalling those days and thinking about
+
+ align:start position:0%
+recalling those days and thinking about
+ 
+
+ align:start position:0%
+recalling those days and thinking about
+uh a number of us who went Department by
+
+ align:start position:0%
+uh a number of us who went Department by
+ 
+
+ align:start position:0%
+uh a number of us who went Department by
+Department with a canned PowerPoint
+
+ align:start position:0%
+Department with a canned PowerPoint
+ 
+
+ align:start position:0%
+Department with a canned PowerPoint
+presentation talking to the faculty
+
+ align:start position:0%
+presentation talking to the faculty
+ 
+
+ align:start position:0%
+presentation talking to the faculty
+about ocw and I remember one with a very
+
+ align:start position:0%
+about ocw and I remember one with a very
+ 
+
+ align:start position:0%
+about ocw and I remember one with a very
+distinguished uh uh faculty member uh
+
+ align:start position:0%
+distinguished uh uh faculty member uh
+ 
+
+ align:start position:0%
+distinguished uh uh faculty member uh
+very senior faculty member who was uh
+
+ align:start position:0%
+very senior faculty member who was uh
+ 
+
+ align:start position:0%
+very senior faculty member who was uh
+world renowned for what he taught uh had
+
+ align:start position:0%
+world renowned for what he taught uh had
+ 
+
+ align:start position:0%
+world renowned for what he taught uh had
+taught the same subject within MIT for
+
+ align:start position:0%
+taught the same subject within MIT for
+ 
+
+ align:start position:0%
+taught the same subject within MIT for
+about a quarter Century maybe a little
+
+ align:start position:0%
+about a quarter Century maybe a little
+ 
+
+ align:start position:0%
+about a quarter Century maybe a little
+longer and we go through the little dog
+
+ align:start position:0%
+longer and we go through the little dog
+ 
+
+ align:start position:0%
+longer and we go through the little dog
+and pony show and start taking questions
+
+ align:start position:0%
+and pony show and start taking questions
+ 
+
+ align:start position:0%
+and pony show and start taking questions
+and he stands up in the back of the room
+
+ align:start position:0%
+and he stands up in the back of the room
+ 
+
+ align:start position:0%
+and he stands up in the back of the room
+and says I am never doing
+
+ align:start position:0%
+and says I am never doing
+ 
+
+ align:start position:0%
+and says I am never doing
+this and he says I have the set of notes
+
+ align:start position:0%
+this and he says I have the set of notes
+ 
+
+ align:start position:0%
+this and he says I have the set of notes
+from which I teach the class and if I
+
+ align:start position:0%
+from which I teach the class and if I
+ 
+
+ align:start position:0%
+from which I teach the class and if I
+put them on the web I have no idea what
+
+ align:start position:0%
+put them on the web I have no idea what
+ 
+
+ align:start position:0%
+put them on the web I have no idea what
+I would do three hours a week
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and as far as I know he never did put
+
+ align:start position:0%
+and as far as I know he never did put
+ 
+
+ align:start position:0%
+and as far as I know he never did put
+his courses up on ocw I think the course
+
+ align:start position:0%
+his courses up on ocw I think the course
+ 
+
+ align:start position:0%
+his courses up on ocw I think the course
+was then taught by someone else who took
+
+ align:start position:0%
+was then taught by someone else who took
+ 
+
+ align:start position:0%
+was then taught by someone else who took
+his notes and put them up on the
+
+ align:start position:0%
+his notes and put them up on the
+ 
+
+ align:start position:0%
+his notes and put them up on the
+web but uh a much younger person uh but
+
+ align:start position:0%
+web but uh a much younger person uh but
+ 
+
+ align:start position:0%
+web but uh a much younger person uh but
+and we talked about this openly quietly
+
+ align:start position:0%
+and we talked about this openly quietly
+ 
+
+ align:start position:0%
+and we talked about this openly quietly
+among the people who were trying to lead
+
+ align:start position:0%
+among the people who were trying to lead
+ 
+
+ align:start position:0%
+among the people who were trying to lead
+this effort that there would be people
+
+ align:start position:0%
+this effort that there would be people
+ 
+
+ align:start position:0%
+this effort that there would be people
+that generationally would not connect
+
+ align:start position:0%
+that generationally would not connect
+ 
+
+ align:start position:0%
+that generationally would not connect
+with the impact of this on their own
+
+ align:start position:0%
+with the impact of this on their own
+ 
+
+ align:start position:0%
+with the impact of this on their own
+teaching style inside the institution
+
+ align:start position:0%
+teaching style inside the institution
+ 
+
+ align:start position:0%
+teaching style inside the institution
+but we believe this too shall pass there
+
+ align:start position:0%
+but we believe this too shall pass there
+ 
+
+ align:start position:0%
+but we believe this too shall pass there
+was another piece that I want to throw
+
+ align:start position:0%
+was another piece that I want to throw
+ 
+
+ align:start position:0%
+was another piece that I want to throw
+out here that was going on in MIT at the
+
+ align:start position:0%
+out here that was going on in MIT at the
+ 
+
+ align:start position:0%
+out here that was going on in MIT at the
+same time because I these two things did
+
+ align:start position:0%
+same time because I these two things did
+ 
+
+ align:start position:0%
+same time because I these two things did
+get connected MIT launched the Singapore
+
+ align:start position:0%
+get connected MIT launched the Singapore
+ 
+
+ align:start position:0%
+get connected MIT launched the Singapore
+MIT Alliance about the same time that
+
+ align:start position:0%
+MIT Alliance about the same time that
+ 
+
+ align:start position:0%
+MIT Alliance about the same time that
+the ocw discussions were starting and in
+
+ align:start position:0%
+the ocw discussions were starting and in
+ 
+
+ align:start position:0%
+the ocw discussions were starting and in
+the Singapore MIT Alliance we had
+
+ align:start position:0%
+the Singapore MIT Alliance we had
+ 
+
+ align:start position:0%
+the Singapore MIT Alliance we had
+started teaching for the very first time
+
+ align:start position:0%
+started teaching for the very first time
+ 
+
+ align:start position:0%
+started teaching for the very first time
+to a distance ed class simultaneously
+
+ align:start position:0%
+to a distance ed class simultaneously
+ 
+
+ align:start position:0%
+to a distance ed class simultaneously
+with the class at MIT the other room was
+
+ align:start position:0%
+with the class at MIT the other room was
+ 
+
+ align:start position:0%
+with the class at MIT the other room was
+in Singapore using video conferencing
+
+ align:start position:0%
+in Singapore using video conferencing
+ 
+
+ align:start position:0%
+in Singapore using video conferencing
+technology VJ Kumar remembers all of
+
+ align:start position:0%
+technology VJ Kumar remembers all of
+ 
+
+ align:start position:0%
+technology VJ Kumar remembers all of
+this uh teach Sim simulcast teaching
+
+ align:start position:0%
+this uh teach Sim simulcast teaching
+ 
+
+ align:start position:0%
+this uh teach Sim simulcast teaching
+live uh which at that point in 2001 was
+
+ align:start position:0%
+live uh which at that point in 2001 was
+ 
+
+ align:start position:0%
+live uh which at that point in 2001 was
+right at the edge of what the internet
+
+ align:start position:0%
+right at the edge of what the internet
+ 
+
+ align:start position:0%
+right at the edge of what the internet
+could do right at the edge of what we
+
+ align:start position:0%
+could do right at the edge of what we
+ 
+
+ align:start position:0%
+could do right at the edge of what we
+could do technologically and the whole
+
+ align:start position:0%
+could do technologically and the whole
+ 
+
+ align:start position:0%
+could do technologically and the whole
+discussion at that point there was a
+
+ align:start position:0%
+discussion at that point there was a
+ 
+
+ align:start position:0%
+discussion at that point there was a
+discussion was that an MIT
+
+ align:start position:0%
+discussion was that an MIT
+ 
+
+ align:start position:0%
+discussion was that an MIT
+education Could you actually using video
+
+ align:start position:0%
+education Could you actually using video
+ 
+
+ align:start position:0%
+education Could you actually using video
+conferencing technology live 12 at time
+
+ align:start position:0%
+conferencing technology live 12 at time
+ 
+
+ align:start position:0%
+conferencing technology live 12 at time
+zones apart actually teach and these
+
+ align:start position:0%
+zones apart actually teach and these
+ 
+
+ align:start position:0%
+zones apart actually teach and these
+were Master's level subjects and so
+
+ align:start position:0%
+were Master's level subjects and so
+ 
+
+ align:start position:0%
+were Master's level subjects and so
+there was a whole discussion going on
+
+ align:start position:0%
+there was a whole discussion going on
+ 
+
+ align:start position:0%
+there was a whole discussion going on
+and that was a faculty debate that
+
+ align:start position:0%
+and that was a faculty debate that
+ 
+
+ align:start position:0%
+and that was a faculty debate that
+roared for five or six years about
+
+ align:start position:0%
+roared for five or six years about
+ 
+
+ align:start position:0%
+roared for five or six years about
+whether that technology got enough
+
+ align:start position:0%
+whether that technology got enough
+ 
+
+ align:start position:0%
+whether that technology got enough
+classroom context enough interaction
+
+ align:start position:0%
+classroom context enough interaction
+ 
+
+ align:start position:0%
+classroom context enough interaction
+that you believe that you were having an
+
+ align:start position:0%
+that you believe that you were having an
+ 
+
+ align:start position:0%
+that you believe that you were having an
+MIT education so this is something that
+
+ align:start position:0%
+MIT education so this is something that
+ 
+
+ align:start position:0%
+MIT education so this is something that
+I think created ocw was part of this a
+
+ align:start position:0%
+I think created ocw was part of this a
+ 
+
+ align:start position:0%
+I think created ocw was part of this a
+very healthy debate about mit's place in
+
+ align:start position:0%
+very healthy debate about mit's place in
+ 
+
+ align:start position:0%
+very healthy debate about mit's place in
+the world uh in terms of facilitating
+
+ align:start position:0%
+the world uh in terms of facilitating
+ 
+
+ align:start position:0%
+the world uh in terms of facilitating
+higher education
+
+ align:start position:0%
+higher education
+ 
+
+ align:start position:0%
+higher education
+great great thank you well one of the
+
+ align:start position:0%
+great great thank you well one of the
+ 
+
+ align:start position:0%
+great great thank you well one of the
+parts of the the story I don't have to
+
+ align:start position:0%
+parts of the the story I don't have to
+ 
+
+ align:start position:0%
+parts of the the story I don't have to
+tell this audience about because you're
+
+ align:start position:0%
+tell this audience about because you're
+ 
+
+ align:start position:0%
+tell this audience about because you're
+all familiar with it is the fact that I
+
+ align:start position:0%
+all familiar with it is the fact that I
+ 
+
+ align:start position:0%
+all familiar with it is the fact that I
+I think much more quickly than anybody
+
+ align:start position:0%
+I think much more quickly than anybody
+ 
+
+ align:start position:0%
+I think much more quickly than anybody
+here expected MIT started to lose market
+
+ align:start position:0%
+here expected MIT started to lose market
+ 
+
+ align:start position:0%
+here expected MIT started to lose market
+share in the open courseware world the
+
+ align:start position:0%
+share in the open courseware world the
+ 
+
+ align:start position:0%
+share in the open courseware world the
+other universities around the world very
+
+ align:start position:0%
+other universities around the world very
+ 
+
+ align:start position:0%
+other universities around the world very
+rapidly began to join the movement uh to
+
+ align:start position:0%
+rapidly began to join the movement uh to
+ 
+
+ align:start position:0%
+rapidly began to join the movement uh to
+extend the concept of open course where
+
+ align:start position:0%
+extend the concept of open course where
+ 
+
+ align:start position:0%
+extend the concept of open course where
+and and to add their own courses to the
+
+ align:start position:0%
+and and to add their own courses to the
+ 
+
+ align:start position:0%
+and and to add their own courses to the
+point where today we're 2,000 out of the
+
+ align:start position:0%
+point where today we're 2,000 out of the
+ 
+
+ align:start position:0%
+point where today we're 2,000 out of the
+15,000 or so courses that are out there
+
+ align:start position:0%
+15,000 or so courses that are out there
+ 
+
+ align:start position:0%
+15,000 or so courses that are out there
+um professor M aawa you were probably as
+
+ align:start position:0%
+um professor M aawa you were probably as
+ 
+
+ align:start position:0%
+um professor M aawa you were probably as
+deeply involved as anybody in the spread
+
+ align:start position:0%
+deeply involved as anybody in the spread
+ 
+
+ align:start position:0%
+deeply involved as anybody in the spread
+of open course where in the in the early
+
+ align:start position:0%
+of open course where in the in the early
+ 
+
+ align:start position:0%
+of open course where in the in the early
+uh 2000s so would you share a little bit
+
+ align:start position:0%
+uh 2000s so would you share a little bit
+ 
+
+ align:start position:0%
+uh 2000s so would you share a little bit
+of that sure um so it's important to to
+
+ align:start position:0%
+of that sure um so it's important to to
+ 
+
+ align:start position:0%
+of that sure um so it's important to to
+point out and it's uh it's not such a
+
+ align:start position:0%
+point out and it's uh it's not such a
+ 
+
+ align:start position:0%
+point out and it's uh it's not such a
+well-known fact that from the very
+
+ align:start position:0%
+well-known fact that from the very
+ 
+
+ align:start position:0%
+well-known fact that from the very
+beginning in fact in that meeting where
+
+ align:start position:0%
+beginning in fact in that meeting where
+ 
+
+ align:start position:0%
+beginning in fact in that meeting where
+we first talked about the idea of open
+
+ align:start position:0%
+we first talked about the idea of open
+ 
+
+ align:start position:0%
+we first talked about the idea of open
+coare indicus meeting we also said that
+
+ align:start position:0%
+coare indicus meeting we also said that
+ 
+
+ align:start position:0%
+coare indicus meeting we also said that
+if this idea uh takes shape and MIT uh
+
+ align:start position:0%
+if this idea uh takes shape and MIT uh
+ 
+
+ align:start position:0%
+if this idea uh takes shape and MIT uh
+wouldn't it be nice if other
+
+ align:start position:0%
+wouldn't it be nice if other
+ 
+
+ align:start position:0%
+wouldn't it be nice if other
+institutions will embrace the same idea
+
+ align:start position:0%
+institutions will embrace the same idea
+ 
+
+ align:start position:0%
+institutions will embrace the same idea
+and so from the very beginning the seed
+
+ align:start position:0%
+and so from the very beginning the seed
+ 
+
+ align:start position:0%
+and so from the very beginning the seed
+was planted for open coare to go beyond
+
+ align:start position:0%
+was planted for open coare to go beyond
+ 
+
+ align:start position:0%
+was planted for open coare to go beyond
+MIT and I remember I think it was in
+
+ align:start position:0%
+MIT and I remember I think it was in
+ 
+
+ align:start position:0%
+MIT and I remember I think it was in
+2003 that we uh made the first attempt
+
+ align:start position:0%
+2003 that we uh made the first attempt
+ 
+
+ align:start position:0%
+2003 that we uh made the first attempt
+to uh call some of our uh neighbor
+
+ align:start position:0%
+to uh call some of our uh neighbor
+ 
+
+ align:start position:0%
+to uh call some of our uh neighbor
+institutions uh to MIT to show them what
+
+ align:start position:0%
+institutions uh to MIT to show them what
+ 
+
+ align:start position:0%
+institutions uh to MIT to show them what
+we were doing tfts was an early adopter
+
+ align:start position:0%
+we were doing tfts was an early adopter
+ 
+
+ align:start position:0%
+we were doing tfts was an early adopter
+and uh uh and we began the uh the
+
+ align:start position:0%
+and uh uh and we began the uh the
+ 
+
+ align:start position:0%
+and uh uh and we began the uh the
+Journey uh and uh I we weren't sure that
+
+ align:start position:0%
+Journey uh and uh I we weren't sure that
+ 
+
+ align:start position:0%
+Journey uh and uh I we weren't sure that
+it would uh it would succeed because it
+
+ align:start position:0%
+it would uh it would succeed because it
+ 
+
+ align:start position:0%
+it would uh it would succeed because it
+was outside of MIT we had never done
+
+ align:start position:0%
+was outside of MIT we had never done
+ 
+
+ align:start position:0%
+was outside of MIT we had never done
+anything like that and really took the
+
+ align:start position:0%
+anything like that and really took the
+ 
+
+ align:start position:0%
+anything like that and really took the
+will desire and will of people uh around
+
+ align:start position:0%
+will desire and will of people uh around
+ 
+
+ align:start position:0%
+will desire and will of people uh around
+uh around the world uh who saw the uh uh
+
+ align:start position:0%
+uh around the world uh who saw the uh uh
+ 
+
+ align:start position:0%
+uh around the world uh who saw the uh uh
+the advantage and the benefit and the
+
+ align:start position:0%
+the advantage and the benefit and the
+ 
+
+ align:start position:0%
+the advantage and the benefit and the
+attractiveness of this idea and to then
+
+ align:start position:0%
+attractiveness of this idea and to then
+ 
+
+ align:start position:0%
+attractiveness of this idea and to then
+translate it into your own uh Society to
+
+ align:start position:0%
+translate it into your own uh Society to
+ 
+
+ align:start position:0%
+translate it into your own uh Society to
+your own institution to your own culture
+
+ align:start position:0%
+your own institution to your own culture
+ 
+
+ align:start position:0%
+your own institution to your own culture
+uh and so I'm just uh quite frankly
+
+ align:start position:0%
+uh and so I'm just uh quite frankly
+ 
+
+ align:start position:0%
+uh and so I'm just uh quite frankly
+astounded at the the number of people
+
+ align:start position:0%
+astounded at the the number of people
+ 
+
+ align:start position:0%
+astounded at the the number of people
+who are here and remembering back to
+
+ align:start position:0%
+who are here and remembering back to
+ 
+
+ align:start position:0%
+who are here and remembering back to
+2003 when I think there were five or six
+
+ align:start position:0%
+2003 when I think there were five or six
+ 
+
+ align:start position:0%
+2003 when I think there were five or six
+people in the room uh and we really
+
+ align:start position:0%
+people in the room uh and we really
+ 
+
+ align:start position:0%
+people in the room uh and we really
+didn't know whether it would succeed but
+
+ align:start position:0%
+didn't know whether it would succeed but
+ 
+
+ align:start position:0%
+didn't know whether it would succeed but
+you know wherever I went uh to Japan to
+
+ align:start position:0%
+you know wherever I went uh to Japan to
+ 
+
+ align:start position:0%
+you know wherever I went uh to Japan to
+Taiwan to Africa to Europe uh this idea
+
+ align:start position:0%
+Taiwan to Africa to Europe uh this idea
+ 
+
+ align:start position:0%
+Taiwan to Africa to Europe uh this idea
+I mean you you saw the same sort of
+
+ align:start position:0%
+I mean you you saw the same sort of
+ 
+
+ align:start position:0%
+I mean you you saw the same sort of
+Eureka uh as Chuck liked to say the idea
+
+ align:start position:0%
+Eureka uh as Chuck liked to say the idea
+ 
+
+ align:start position:0%
+Eureka uh as Chuck liked to say the idea
+of sharing uh is something that uh uh
+
+ align:start position:0%
+of sharing uh is something that uh uh
+ 
+
+ align:start position:0%
+of sharing uh is something that uh uh
+all of you uh understand at an intuitive
+
+ align:start position:0%
+all of you uh understand at an intuitive
+ 
+
+ align:start position:0%
+all of you uh understand at an intuitive
+level at an emotional level at
+
+ align:start position:0%
+level at an emotional level at
+ 
+
+ align:start position:0%
+level at an emotional level at
+intellectual level um and so uh there
+
+ align:start position:0%
+intellectual level um and so uh there
+ 
+
+ align:start position:0%
+intellectual level um and so uh there
+lots of challenges uh lots of challenges
+
+ align:start position:0%
+lots of challenges uh lots of challenges
+ 
+
+ align:start position:0%
+lots of challenges uh lots of challenges
+as we faced uh 10 years ago and as I
+
+ align:start position:0%
+as we faced uh 10 years ago and as I
+ 
+
+ align:start position:0%
+as we faced uh 10 years ago and as I
+hear from you uh but uh I think that uh
+
+ align:start position:0%
+hear from you uh but uh I think that uh
+ 
+
+ align:start position:0%
+hear from you uh but uh I think that uh
+the fact that now there 15,000 courses
+
+ align:start position:0%
+the fact that now there 15,000 courses
+ 
+
+ align:start position:0%
+the fact that now there 15,000 courses
+and MIT only has 2,000 of them is um
+
+ align:start position:0%
+and MIT only has 2,000 of them is um
+ 
+
+ align:start position:0%
+and MIT only has 2,000 of them is um
+it's a marvelous sign that open coare is
+
+ align:start position:0%
+it's a marvelous sign that open coare is
+ 
+
+ align:start position:0%
+it's a marvelous sign that open coare is
+now Beyond
+
+ align:start position:0%
+now Beyond
+ 
+
+ align:start position:0%
+now Beyond
+MIT I just real quickly I just want to
+
+ align:start position:0%
+MIT I just real quickly I just want to
+ 
+
+ align:start position:0%
+MIT I just real quickly I just want to
+say that this idea that it's not all
+
+ align:start position:0%
+say that this idea that it's not all
+ 
+
+ align:start position:0%
+say that this idea that it's not all
+about MIT but about um a bigger
+
+ align:start position:0%
+about MIT but about um a bigger
+ 
+
+ align:start position:0%
+about MIT but about um a bigger
+community of Institutions doing open
+
+ align:start position:0%
+community of Institutions doing open
+ 
+
+ align:start position:0%
+community of Institutions doing open
+course where was very much on our minds
+
+ align:start position:0%
+course where was very much on our minds
+ 
+
+ align:start position:0%
+course where was very much on our minds
+the at the very very beginning it was
+
+ align:start position:0%
+the at the very very beginning it was
+ 
+
+ align:start position:0%
+the at the very very beginning it was
+not an afterthought so to give you a
+
+ align:start position:0%
+not an afterthought so to give you a
+ 
+
+ align:start position:0%
+not an afterthought so to give you a
+sense there was a debate in the
+
+ align:start position:0%
+sense there was a debate in the
+ 
+
+ align:start position:0%
+sense there was a debate in the
+beginning what to call this thing and
+
+ align:start position:0%
+beginning what to call this thing and
+ 
+
+ align:start position:0%
+beginning what to call this thing and
+there were names like Under the Dome the
+
+ align:start position:0%
+there were names like Under the Dome the
+ 
+
+ align:start position:0%
+there were names like Under the Dome the
+infinite Corridor and so forth and uh I
+
+ align:start position:0%
+infinite Corridor and so forth and uh I
+ 
+
+ align:start position:0%
+infinite Corridor and so forth and uh I
+was among the people who pushed for a
+
+ align:start position:0%
+was among the people who pushed for a
+ 
+
+ align:start position:0%
+was among the people who pushed for a
+name that is not uh primarily reflecting
+
+ align:start position:0%
+name that is not uh primarily reflecting
+ 
+
+ align:start position:0%
+name that is not uh primarily reflecting
+something about MIT and uh someone
+
+ align:start position:0%
+something about MIT and uh someone
+ 
+
+ align:start position:0%
+something about MIT and uh someone
+reminded me that open course whereare at
+
+ align:start position:0%
+reminded me that open course whereare at
+ 
+
+ align:start position:0%
+reminded me that open course whereare at
+that time if you did the um alter Vista
+
+ align:start position:0%
+that time if you did the um alter Vista
+ 
+
+ align:start position:0%
+that time if you did the um alter Vista
+search excuse me uh it would have shown
+
+ align:start position:0%
+search excuse me uh it would have shown
+ 
+
+ align:start position:0%
+search excuse me uh it would have shown
+that open course were referred to like
+
+ align:start position:0%
+that open course were referred to like
+ 
+
+ align:start position:0%
+that open course were referred to like
+you know software that aids in the
+
+ align:start position:0%
+you know software that aids in the
+ 
+
+ align:start position:0%
+you know software that aids in the
+teaching of a class or something and we
+
+ align:start position:0%
+teaching of a class or something and we
+ 
+
+ align:start position:0%
+teaching of a class or something and we
+were pushing for something that's much
+
+ align:start position:0%
+were pushing for something that's much
+ 
+
+ align:start position:0%
+were pushing for something that's much
+more uh able to be uh used by other
+
+ align:start position:0%
+more uh able to be uh used by other
+ 
+
+ align:start position:0%
+more uh able to be uh used by other
+people without necessarily making a part
+
+ align:start position:0%
+people without necessarily making a part
+ 
+
+ align:start position:0%
+people without necessarily making a part
+of MIT so so finally I I had my way and
+
+ align:start position:0%
+of MIT so so finally I I had my way and
+ 
+
+ align:start position:0%
+of MIT so so finally I I had my way and
+we we we went in favor of names the name
+
+ align:start position:0%
+we we we went in favor of names the name
+ 
+
+ align:start position:0%
+we we we went in favor of names the name
+open courseware which is you know it
+
+ align:start position:0%
+open courseware which is you know it
+ 
+
+ align:start position:0%
+open courseware which is you know it
+doesn't mention the Dome infin theard or
+
+ align:start position:0%
+doesn't mention the Dome infin theard or
+ 
+
+ align:start position:0%
+doesn't mention the Dome infin theard or
+Cambridge or 77 Massa or anything like
+
+ align:start position:0%
+Cambridge or 77 Massa or anything like
+ 
+
+ align:start position:0%
+Cambridge or 77 Massa or anything like
+that and I remember also a conversation
+
+ align:start position:0%
+that and I remember also a conversation
+ 
+
+ align:start position:0%
+that and I remember also a conversation
+within this committee there were people
+
+ align:start position:0%
+within this committee there were people
+ 
+
+ align:start position:0%
+within this committee there were people
+who were more understanding of ips and
+
+ align:start position:0%
+who were more understanding of ips and
+ 
+
+ align:start position:0%
+who were more understanding of ips and
+so forth and say should we trademark the
+
+ align:start position:0%
+so forth and say should we trademark the
+ 
+
+ align:start position:0%
+so forth and say should we trademark the
+name and the answer was absolutely not
+
+ align:start position:0%
+name and the answer was absolutely not
+ 
+
+ align:start position:0%
+name and the answer was absolutely not
+okay we would trademark MIT or maybe it
+
+ align:start position:0%
+okay we would trademark MIT or maybe it
+ 
+
+ align:start position:0%
+okay we would trademark MIT or maybe it
+open courseware but open courseware as a
+
+ align:start position:0%
+open courseware but open courseware as a
+ 
+
+ align:start position:0%
+open courseware but open courseware as a
+name we would absolutely refuse to do
+
+ align:start position:0%
+name we would absolutely refuse to do
+ 
+
+ align:start position:0%
+name we would absolutely refuse to do
+that so so I just want to quickly point
+
+ align:start position:0%
+that so so I just want to quickly point
+ 
+
+ align:start position:0%
+that so so I just want to quickly point
+out that it was not something that I
+
+ align:start position:0%
+out that it was not something that I
+ 
+
+ align:start position:0%
+out that it was not something that I
+know after two three years we start
+
+ align:start position:0%
+know after two three years we start
+ 
+
+ align:start position:0%
+know after two three years we start
+thinking maybe we would spread it around
+
+ align:start position:0%
+thinking maybe we would spread it around
+ 
+
+ align:start position:0%
+thinking maybe we would spread it around
+it was very much at the beginning the
+
+ align:start position:0%
+it was very much at the beginning the
+ 
+
+ align:start position:0%
+it was very much at the beginning the
+idea that MIT is but one institution and
+
+ align:start position:0%
+idea that MIT is but one institution and
+ 
+
+ align:start position:0%
+idea that MIT is but one institution and
+a relatively small one at that we don't
+
+ align:start position:0%
+a relatively small one at that we don't
+ 
+
+ align:start position:0%
+a relatively small one at that we don't
+do many fields of disciplines um we're
+
+ align:start position:0%
+do many fields of disciplines um we're
+ 
+
+ align:start position:0%
+do many fields of disciplines um we're
+not we don't even do them not not
+
+ align:start position:0%
+not we don't even do them not not
+ 
+
+ align:start position:0%
+not we don't even do them not not
+necessarily we're good at them and and
+
+ align:start position:0%
+necessarily we're good at them and and
+ 
+
+ align:start position:0%
+necessarily we're good at them and and
+that the idea is that we could maybe
+
+ align:start position:0%
+that the idea is that we could maybe
+ 
+
+ align:start position:0%
+that the idea is that we could maybe
+provide a bit of an example early model
+
+ align:start position:0%
+provide a bit of an example early model
+ 
+
+ align:start position:0%
+provide a bit of an example early model
+and that many others would would join in
+
+ align:start position:0%
+and that many others would would join in
+ 
+
+ align:start position:0%
+and that many others would would join in
+and today I think today it's really
+
+ align:start position:0%
+and today I think today it's really
+ 
+
+ align:start position:0%
+and today I think today it's really
+gratifying to see that many others in
+
+ align:start position:0%
+gratifying to see that many others in
+ 
+
+ align:start position:0%
+gratifying to see that many others in
+fact have joined in and contributed
+
+ align:start position:0%
+fact have joined in and contributed
+ 
+
+ align:start position:0%
+fact have joined in and contributed
+perhaps in in mightier ways than than we
+
+ align:start position:0%
+perhaps in in mightier ways than than we
+ 
+
+ align:start position:0%
+perhaps in in mightier ways than than we
+could have ever imagined great um Dr
+
+ align:start position:0%
+could have ever imagined great um Dr
+ 
+
+ align:start position:0%
+could have ever imagined great um Dr
+backa perhaps you could comment you you
+
+ align:start position:0%
+backa perhaps you could comment you you
+ 
+
+ align:start position:0%
+backa perhaps you could comment you you
+uh left MIT right about the time that
+
+ align:start position:0%
+uh left MIT right about the time that
+ 
+
+ align:start position:0%
+uh left MIT right about the time that
+open course whereare was announced and
+
+ align:start position:0%
+open course whereare was announced and
+ 
+
+ align:start position:0%
+open course whereare was announced and
+moved over to tffs and so you've been
+
+ align:start position:0%
+moved over to tffs and so you've been
+ 
+
+ align:start position:0%
+moved over to tffs and so you've been
+involved in probably the most direct
+
+ align:start position:0%
+involved in probably the most direct
+ 
+
+ align:start position:0%
+involved in probably the most direct
+transplant of the open course sare
+
+ align:start position:0%
+transplant of the open course sare
+ 
+
+ align:start position:0%
+transplant of the open course sare
+concept uh so maybe you could comment a
+
+ align:start position:0%
+concept uh so maybe you could comment a
+ 
+
+ align:start position:0%
+concept uh so maybe you could comment a
+little bit on how
+
+ align:start position:0%
+little bit on how
+ 
+
+ align:start position:0%
+little bit on how
+uh it works in a different academic
+
+ align:start position:0%
+uh it works in a different academic
+ 
+
+ align:start position:0%
+uh it works in a different academic
+environment well it was um I was
+
+ align:start position:0%
+environment well it was um I was
+ 
+
+ align:start position:0%
+environment well it was um I was
+delighted to see when I got to tus that
+
+ align:start position:0%
+delighted to see when I got to tus that
+ 
+
+ align:start position:0%
+delighted to see when I got to tus that
+tus was already thinking along this
+
+ align:start position:0%
+tus was already thinking along this
+ 
+
+ align:start position:0%
+tus was already thinking along this
+lines um we had uh the university before
+
+ align:start position:0%
+lines um we had uh the university before
+ 
+
+ align:start position:0%
+lines um we had uh the university before
+I ever got there um had digitized its
+
+ align:start position:0%
+I ever got there um had digitized its
+ 
+
+ align:start position:0%
+I ever got there um had digitized its
+content in the Health Sciences um one of
+
+ align:start position:0%
+content in the Health Sciences um one of
+ 
+
+ align:start position:0%
+content in the Health Sciences um one of
+the problems traditionally of teaching
+
+ align:start position:0%
+the problems traditionally of teaching
+ 
+
+ align:start position:0%
+the problems traditionally of teaching
+for example medical students is that if
+
+ align:start position:0%
+for example medical students is that if
+ 
+
+ align:start position:0%
+for example medical students is that if
+you know medical students would um often
+
+ align:start position:0%
+you know medical students would um often
+ 
+
+ align:start position:0%
+you know medical students would um often
+have to go literally physically check
+
+ align:start position:0%
+have to go literally physically check
+ 
+
+ align:start position:0%
+have to go literally physically check
+out a group of slots
+
+ align:start position:0%
+out a group of slots
+ 
+
+ align:start position:0%
+out a group of slots
+to look at under a microscope and so
+
+ align:start position:0%
+to look at under a microscope and so
+ 
+
+ align:start position:0%
+to look at under a microscope and so
+years before I got to to TS um TS had
+
+ align:start position:0%
+years before I got to to TS um TS had
+ 
+
+ align:start position:0%
+years before I got to to TS um TS had
+looked at this problem and said you know
+
+ align:start position:0%
+looked at this problem and said you know
+ 
+
+ align:start position:0%
+looked at this problem and said you know
+we should just digitize all this content
+
+ align:start position:0%
+we should just digitize all this content
+ 
+
+ align:start position:0%
+we should just digitize all this content
+and it it had and it created a Content
+
+ align:start position:0%
+and it it had and it created a Content
+ 
+
+ align:start position:0%
+and it it had and it created a Content
+management system for it uh and not just
+
+ align:start position:0%
+management system for it uh and not just
+ 
+
+ align:start position:0%
+management system for it uh and not just
+for for medicine but for dental medicine
+
+ align:start position:0%
+for for medicine but for dental medicine
+ 
+
+ align:start position:0%
+for for medicine but for dental medicine
+for veterinary medicine we also have the
+
+ align:start position:0%
+for veterinary medicine we also have the
+ 
+
+ align:start position:0%
+for veterinary medicine we also have the
+only freestanding School of nutrition in
+
+ align:start position:0%
+only freestanding School of nutrition in
+ 
+
+ align:start position:0%
+only freestanding School of nutrition in
+the United States um at tus and this was
+
+ align:start position:0%
+the United States um at tus and this was
+ 
+
+ align:start position:0%
+the United States um at tus and this was
+it's now currently described as the tus
+
+ align:start position:0%
+it's now currently described as the tus
+ 
+
+ align:start position:0%
+it's now currently described as the tus
+University science science knowledge
+
+ align:start position:0%
+University science science knowledge
+ 
+
+ align:start position:0%
+University science science knowledge
+base and my colleagues who made this
+
+ align:start position:0%
+base and my colleagues who made this
+ 
+
+ align:start position:0%
+base and my colleagues who made this
+happen Mary Lee and Susan Albright and
+
+ align:start position:0%
+happen Mary Lee and Susan Albright and
+ 
+
+ align:start position:0%
+happen Mary Lee and Susan Albright and
+Robin McWilliams are all sitting in this
+
+ align:start position:0%
+Robin McWilliams are all sitting in this
+ 
+
+ align:start position:0%
+Robin McWilliams are all sitting in this
+room and so I discovered this when I
+
+ align:start position:0%
+room and so I discovered this when I
+ 
+
+ align:start position:0%
+room and so I discovered this when I
+came to toughs and it was like my God
+
+ align:start position:0%
+came to toughs and it was like my God
+ 
+
+ align:start position:0%
+came to toughs and it was like my God
+you know I I knew I'd come to the right
+
+ align:start position:0%
+you know I I knew I'd come to the right
+ 
+
+ align:start position:0%
+you know I I knew I'd come to the right
+place at least there were some people
+
+ align:start position:0%
+place at least there were some people
+ 
+
+ align:start position:0%
+place at least there were some people
+thinking along the same lines and so I
+
+ align:start position:0%
+thinking along the same lines and so I
+ 
+
+ align:start position:0%
+thinking along the same lines and so I
+said we should be one of the first
+
+ align:start position:0%
+said we should be one of the first
+ 
+
+ align:start position:0%
+said we should be one of the first
+institutions to join hands with MIT
+
+ align:start position:0%
+institutions to join hands with MIT
+ 
+
+ align:start position:0%
+institutions to join hands with MIT
+because what we we had already made a
+
+ align:start position:0%
+because what we we had already made a
+ 
+
+ align:start position:0%
+because what we we had already made a
+significant investment it was already
+
+ align:start position:0%
+significant investment it was already
+ 
+
+ align:start position:0%
+significant investment it was already
+there and by the way it was perfectly
+
+ align:start position:0%
+there and by the way it was perfectly
+ 
+
+ align:start position:0%
+there and by the way it was perfectly
+comp complimentary to the courses and
+
+ align:start position:0%
+comp complimentary to the courses and
+ 
+
+ align:start position:0%
+comp complimentary to the courses and
+the courseware that MIT had already uh
+
+ align:start position:0%
+the courseware that MIT had already uh
+ 
+
+ align:start position:0%
+the courseware that MIT had already uh
+put up on on ocw so it was it was really
+
+ align:start position:0%
+put up on on ocw so it was it was really
+ 
+
+ align:start position:0%
+put up on on ocw so it was it was really
+a very very easy decision um there was
+
+ align:start position:0%
+a very very easy decision um there was
+ 
+
+ align:start position:0%
+a very very easy decision um there was
+absolutely no issue persuading The
+
+ align:start position:0%
+absolutely no issue persuading The
+ 
+
+ align:start position:0%
+absolutely no issue persuading The
+Faculty because they had already you
+
+ align:start position:0%
+Faculty because they had already you
+ 
+
+ align:start position:0%
+Faculty because they had already you
+know gone through the effort um and the
+
+ align:start position:0%
+know gone through the effort um and the
+ 
+
+ align:start position:0%
+know gone through the effort um and the
+institution had already shared this
+
+ align:start position:0%
+institution had already shared this
+ 
+
+ align:start position:0%
+institution had already shared this
+information uh not with the whole world
+
+ align:start position:0%
+information uh not with the whole world
+ 
+
+ align:start position:0%
+information uh not with the whole world
+but with a number of Institutions who
+
+ align:start position:0%
+but with a number of Institutions who
+ 
+
+ align:start position:0%
+but with a number of Institutions who
+had expressed interest in it so you know
+
+ align:start position:0%
+had expressed interest in it so you know
+ 
+
+ align:start position:0%
+had expressed interest in it so you know
+I just tried not to screw things up um
+
+ align:start position:0%
+I just tried not to screw things up um
+ 
+
+ align:start position:0%
+I just tried not to screw things up um
+and and say yeah let's let's join hands
+
+ align:start position:0%
+and and say yeah let's let's join hands
+ 
+
+ align:start position:0%
+and and say yeah let's let's join hands
+and you know candidly also it was an
+
+ align:start position:0%
+and you know candidly also it was an
+ 
+
+ align:start position:0%
+and you know candidly also it was an
+opportunity for somebody who had
+
+ align:start position:0%
+opportunity for somebody who had
+ 
+
+ align:start position:0%
+opportunity for somebody who had
+literally been raised at MIT to maintain
+
+ align:start position:0%
+literally been raised at MIT to maintain
+ 
+
+ align:start position:0%
+literally been raised at MIT to maintain
+a little bit of a connection to an
+
+ align:start position:0%
+a little bit of a connection to an
+ 
+
+ align:start position:0%
+a little bit of a connection to an
+institution that I am still enormously
+
+ align:start position:0%
+institution that I am still enormously
+ 
+
+ align:start position:0%
+institution that I am still enormously
+fond of great great thank you um
+
+ align:start position:0%
+fond of great great thank you um
+ 
+
+ align:start position:0%
+fond of great great thank you um
+Professor Aon I was going to ask you
+
+ align:start position:0%
+Professor Aon I was going to ask you
+ 
+
+ align:start position:0%
+Professor Aon I was going to ask you
+sort of to to give your thoughts on the
+
+ align:start position:0%
+sort of to to give your thoughts on the
+ 
+
+ align:start position:0%
+sort of to to give your thoughts on the
+future direction of open corser but I
+
+ align:start position:0%
+future direction of open corser but I
+ 
+
+ align:start position:0%
+future direction of open corser but I
+think that was kind of the challenge you
+
+ align:start position:0%
+think that was kind of the challenge you
+ 
+
+ align:start position:0%
+think that was kind of the challenge you
+just just laid out for everybody is to
+
+ align:start position:0%
+just just laid out for everybody is to
+ 
+
+ align:start position:0%
+just just laid out for everybody is to
+is to think about the future Direction
+
+ align:start position:0%
+is to think about the future Direction
+ 
+
+ align:start position:0%
+is to think about the future Direction
+but do you have any closing comments or
+
+ align:start position:0%
+but do you have any closing comments or
+ 
+
+ align:start position:0%
+but do you have any closing comments or
+thoughts on on where we're headed or
+
+ align:start position:0%
+thoughts on on where we're headed or
+ 
+
+ align:start position:0%
+thoughts on on where we're headed or
+what might be next for for open
+
+ align:start position:0%
+what might be next for for open
+ 
+
+ align:start position:0%
+what might be next for for open
+courseware well I I think the the
+
+ align:start position:0%
+courseware well I I think the the
+ 
+
+ align:start position:0%
+courseware well I I think the the
+critical thing is thinking about open
+
+ align:start position:0%
+critical thing is thinking about open
+ 
+
+ align:start position:0%
+critical thing is thinking about open
+courseware and education together what
+
+ align:start position:0%
+courseware and education together what
+ 
+
+ align:start position:0%
+courseware and education together what
+the future of open course the future of
+
+ align:start position:0%
+the future of open course the future of
+ 
+
+ align:start position:0%
+the future of open course the future of
+the University how how all of this plays
+
+ align:start position:0%
+the University how how all of this plays
+ 
+
+ align:start position:0%
+the University how how all of this plays
+how all of this plays together if we're
+
+ align:start position:0%
+how all of this plays together if we're
+ 
+
+ align:start position:0%
+how all of this plays together if we're
+moving to a world that is more
+
+ align:start position:0%
+moving to a world that is more
+ 
+
+ align:start position:0%
+moving to a world that is more
+interactive more modular more
+
+ align:start position:0%
+interactive more modular more
+ 
+
+ align:start position:0%
+interactive more modular more
+participatory more about the generation
+
+ align:start position:0%
+participatory more about the generation
+ 
+
+ align:start position:0%
+participatory more about the generation
+of knowledge how do you
+
+ align:start position:0%
+of knowledge how do you
+ 
+
+ align:start position:0%
+of knowledge how do you
+construct a infrastructure that you can
+
+ align:start position:0%
+construct a infrastructure that you can
+ 
+
+ align:start position:0%
+construct a infrastructure that you can
+share with the world and have an impact
+
+ align:start position:0%
+share with the world and have an impact
+ 
+
+ align:start position:0%
+share with the world and have an impact
+on the world like open course for and at
+
+ align:start position:0%
+on the world like open course for and at
+ 
+
+ align:start position:0%
+on the world like open course for and at
+the same time pull that back into the
+
+ align:start position:0%
+the same time pull that back into the
+ 
+
+ align:start position:0%
+the same time pull that back into the
+university so one of the things
+
+ align:start position:0%
+university so one of the things
+ 
+
+ align:start position:0%
+university so one of the things
+that I remember when we were going
+
+ align:start position:0%
+that I remember when we were going
+ 
+
+ align:start position:0%
+that I remember when we were going
+around talking to the different
+
+ align:start position:0%
+around talking to the different
+ 
+
+ align:start position:0%
+around talking to the different
+departments uh went to one department
+
+ align:start position:0%
+departments uh went to one department
+ 
+
+ align:start position:0%
+departments uh went to one department
+and some faculty members stood up in the
+
+ align:start position:0%
+and some faculty members stood up in the
+ 
+
+ align:start position:0%
+and some faculty members stood up in the
+back room and she said this is great
+
+ align:start position:0%
+back room and she said this is great
+ 
+
+ align:start position:0%
+back room and she said this is great
+I'll be able to find out what the other
+
+ align:start position:0%
+I'll be able to find out what the other
+ 
+
+ align:start position:0%
+I'll be able to find out what the other
+people in this department are
+
+ align:start position:0%
+people in this department are
+ 
+
+ align:start position:0%
+people in this department are
+teaching you have to remember how far
+
+ align:start position:0%
+teaching you have to remember how far
+ 
+
+ align:start position:0%
+teaching you have to remember how far
+we've come that things aren't even
+
+ align:start position:0%
+we've come that things aren't even
+ 
+
+ align:start position:0%
+we've come that things aren't even
+shared across the university we now have
+
+ align:start position:0%
+shared across the university we now have
+ 
+
+ align:start position:0%
+shared across the university we now have
+that idea now the question is can we
+
+ align:start position:0%
+that idea now the question is can we
+ 
+
+ align:start position:0%
+that idea now the question is can we
+take this notion of particip
+
+ align:start position:0%
+take this notion of particip
+ 
+
+ align:start position:0%
+take this notion of particip
+participation can we take this notion of
+
+ align:start position:0%
+participation can we take this notion of
+ 
+
+ align:start position:0%
+participation can we take this notion of
+co-generation of knowledge and instill
+
+ align:start position:0%
+co-generation of knowledge and instill
+ 
+
+ align:start position:0%
+co-generation of knowledge and instill
+that first within the university and
+
+ align:start position:0%
+that first within the university and
+ 
+
+ align:start position:0%
+that first within the university and
+across the university and then across
+
+ align:start position:0%
+across the university and then across
+ 
+
+ align:start position:0%
+across the university and then across
+the world so that's how I think about
+
+ align:start position:0%
+the world so that's how I think about
+ 
+
+ align:start position:0%
+the world so that's how I think about
+the future great great thank you well I
+
+ align:start position:0%
+the future great great thank you well I
+ 
+
+ align:start position:0%
+the future great great thank you well I
+could continue asking questions for
+
+ align:start position:0%
+could continue asking questions for
+ 
+
+ align:start position:0%
+could continue asking questions for
+hours uh with this group but we do have
+
+ align:start position:0%
+hours uh with this group but we do have
+ 
+
+ align:start position:0%
+hours uh with this group but we do have
+a few minutes if there's anyone in the
+
+ align:start position:0%
+a few minutes if there's anyone in the
+ 
+
+ align:start position:0%
+a few minutes if there's anyone in the
+audience who would like to ask a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question one up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here you can see the people from all
+
+ align:start position:0%
+here you can see the people from all
+ 
+
+ align:start position:0%
+here you can see the people from all
+over the world to this conference it
+
+ align:start position:0%
+over the world to this conference it
+ 
+
+ align:start position:0%
+over the world to this conference it
+sent one message to everyone is the
+
+ align:start position:0%
+sent one message to everyone is the
+ 
+
+ align:start position:0%
+sent one message to everyone is the
+I think the whole world appreciate Dr
+
+ align:start position:0%
+I think the whole world appreciate Dr
+ 
+
+ align:start position:0%
+I think the whole world appreciate Dr
+West and
+
+ align:start position:0%
+West and
+ 
+
+ align:start position:0%
+West and
+MIT and then your decision definitely
+
+ align:start position:0%
+MIT and then your decision definitely
+ 
+
+ align:start position:0%
+MIT and then your decision definitely
+bring the what change the world
+
+ align:start position:0%
+bring the what change the world
+ 
+
+ align:start position:0%
+bring the what change the world
+education I think today is from my
+
+ align:start position:0%
+education I think today is from my
+ 
+
+ align:start position:0%
+education I think today is from my
+knowledge here is all the open course
+
+ align:start position:0%
+knowledge here is all the open course
+ 
+
+ align:start position:0%
+knowledge here is all the open course
+are a
+
+ align:start position:0%
+are a
+ 
+
+ align:start position:0%
+are a
+synchronized and our College as is
+
+ align:start position:0%
+synchronized and our College as is
+ 
+
+ align:start position:0%
+synchronized and our College as is
+moving to synchronized open education
+
+ align:start position:0%
+moving to synchronized open education
+ 
+
+ align:start position:0%
+moving to synchronized open education
+that means realtime open education
+
+ align:start position:0%
+that means realtime open education
+ 
+
+ align:start position:0%
+that means realtime open education
+realtime open education and so my
+
+ align:start position:0%
+realtime open education and so my
+ 
+
+ align:start position:0%
+realtime open education and so my
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+is what is the future challenge do you
+
+ align:start position:0%
+is what is the future challenge do you
+ 
+
+ align:start position:0%
+is what is the future challenge do you
+see for the open
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+education
+
+ align:start position:0%
+education
+ 
+
+ align:start position:0%
+education
+wow
+
+ align:start position:0%
+wow
+ 
+
+ align:start position:0%
+wow
+yeah um I mean I suppose I could comment
+
+ align:start position:0%
+yeah um I mean I suppose I could comment
+ 
+
+ align:start position:0%
+yeah um I mean I suppose I could comment
+from my perspective that what what I
+
+ align:start position:0%
+from my perspective that what what I
+ 
+
+ align:start position:0%
+from my perspective that what what I
+think that the uh people involved in
+
+ align:start position:0%
+think that the uh people involved in
+ 
+
+ align:start position:0%
+think that the uh people involved in
+open courseware did when they proposed
+
+ align:start position:0%
+open courseware did when they proposed
+ 
+
+ align:start position:0%
+open courseware did when they proposed
+open courseware was uh simplify the
+
+ align:start position:0%
+open courseware was uh simplify the
+ 
+
+ align:start position:0%
+open courseware was uh simplify the
+question of how to bring education to
+
+ align:start position:0%
+question of how to bring education to
+ 
+
+ align:start position:0%
+question of how to bring education to
+the Internet by only focusing on one
+
+ align:start position:0%
+the Internet by only focusing on one
+ 
+
+ align:start position:0%
+the Internet by only focusing on one
+aspect of Internet that the
+
+ align:start position:0%
+aspect of Internet that the
+ 
+
+ align:start position:0%
+aspect of Internet that the
+of Education the content that's used in
+
+ align:start position:0%
+of Education the content that's used in
+ 
+
+ align:start position:0%
+of Education the content that's used in
+supportive education there are also
+
+ align:start position:0%
+supportive education there are also
+ 
+
+ align:start position:0%
+supportive education there are also
+learning experiences that are created
+
+ align:start position:0%
+learning experiences that are created
+ 
+
+ align:start position:0%
+learning experiences that are created
+around education and assessment uh as
+
+ align:start position:0%
+around education and assessment uh as
+ 
+
+ align:start position:0%
+around education and assessment uh as
+well and the learning experiences and
+
+ align:start position:0%
+well and the learning experiences and
+ 
+
+ align:start position:0%
+well and the learning experiences and
+assessment are much more difficult uh
+
+ align:start position:0%
+assessment are much more difficult uh
+ 
+
+ align:start position:0%
+assessment are much more difficult uh
+problems to tackle than the question of
+
+ align:start position:0%
+problems to tackle than the question of
+ 
+
+ align:start position:0%
+problems to tackle than the question of
+uh just getting the content up and
+
+ align:start position:0%
+uh just getting the content up and
+ 
+
+ align:start position:0%
+uh just getting the content up and
+making it available and so I guess the
+
+ align:start position:0%
+making it available and so I guess the
+ 
+
+ align:start position:0%
+making it available and so I guess the
+the way that I would I would answer that
+
+ align:start position:0%
+the way that I would I would answer that
+ 
+
+ align:start position:0%
+the way that I would I would answer that
+is to say that now we're in a position
+
+ align:start position:0%
+is to say that now we're in a position
+ 
+
+ align:start position:0%
+is to say that now we're in a position
+to start looking at those other two
+
+ align:start position:0%
+to start looking at those other two
+ 
+
+ align:start position:0%
+to start looking at those other two
+challenges can we Foster interaction
+
+ align:start position:0%
+challenges can we Foster interaction
+ 
+
+ align:start position:0%
+challenges can we Foster interaction
+around the open content can we at
+
+ align:start position:0%
+around the open content can we at
+ 
+
+ align:start position:0%
+around the open content can we at
+assessment around open content does
+
+ align:start position:0%
+assessment around open content does
+ 
+
+ align:start position:0%
+assessment around open content does
+anyone
+
+ align:start position:0%
+anyone
+ 
+
+ align:start position:0%
+anyone
+have I'd like to make a comment in
+
+ align:start position:0%
+have I'd like to make a comment in
+ 
+
+ align:start position:0%
+have I'd like to make a comment in
+response it's it's not an answer but I'd
+
+ align:start position:0%
+response it's it's not an answer but I'd
+ 
+
+ align:start position:0%
+response it's it's not an answer but I'd
+like to say why I believe your question
+
+ align:start position:0%
+like to say why I believe your question
+ 
+
+ align:start position:0%
+like to say why I believe your question
+is really profoundly
+
+ align:start position:0%
+is really profoundly
+ 
+
+ align:start position:0%
+is really profoundly
+important um and and let me start here
+
+ align:start position:0%
+important um and and let me start here
+ 
+
+ align:start position:0%
+important um and and let me start here
+in the United States um as you know
+
+ align:start position:0%
+in the United States um as you know
+ 
+
+ align:start position:0%
+in the United States um as you know
+we're facing a lot of economic
+
+ align:start position:0%
+we're facing a lot of economic
+ 
+
+ align:start position:0%
+we're facing a lot of economic
+difficulties if you look across our
+
+ align:start position:0%
+difficulties if you look across our
+ 
+
+ align:start position:0%
+difficulties if you look across our
+public universities
+
+ align:start position:0%
+public universities
+ 
+
+ align:start position:0%
+public universities
+which educate most of the people post uh
+
+ align:start position:0%
+which educate most of the people post uh
+ 
+
+ align:start position:0%
+which educate most of the people post uh
+postsecondary in in this
+
+ align:start position:0%
+postsecondary in in this
+ 
+
+ align:start position:0%
+postsecondary in in this
+country uh there State support has
+
+ align:start position:0%
+country uh there State support has
+ 
+
+ align:start position:0%
+country uh there State support has
+dropped
+
+ align:start position:0%
+dropped
+ 
+
+ align:start position:0%
+dropped
+24% in uh 10
+
+ align:start position:0%
+24% in uh 10
+ 
+
+ align:start position:0%
+24% in uh 10
+years their charges for tuition room
+
+ align:start position:0%
+years their charges for tuition room
+ 
+
+ align:start position:0%
+years their charges for tuition room
+board fees has risen 50 some per in 10
+
+ align:start position:0%
+board fees has risen 50 some per in 10
+ 
+
+ align:start position:0%
+board fees has risen 50 some per in 10
+years we're in an unsustainable system
+
+ align:start position:0%
+years we're in an unsustainable system
+ 
+
+ align:start position:0%
+years we're in an unsustainable system
+but then and that's in America if you
+
+ align:start position:0%
+but then and that's in America if you
+ 
+
+ align:start position:0%
+but then and that's in America if you
+look around the rest of the world
+
+ align:start position:0%
+look around the rest of the world
+ 
+
+ align:start position:0%
+look around the rest of the world
+there's some great news uh the desire
+
+ align:start position:0%
+there's some great news uh the desire
+ 
+
+ align:start position:0%
+there's some great news uh the desire
+and the ability to educate is rising all
+
+ align:start position:0%
+and the ability to educate is rising all
+ 
+
+ align:start position:0%
+and the ability to educate is rising all
+over the world I mean this is looking
+
+ align:start position:0%
+over the world I mean this is looking
+ 
+
+ align:start position:0%
+over the world I mean this is looking
+back 50 years from now this is going to
+
+ align:start position:0%
+back 50 years from now this is going to
+ 
+
+ align:start position:0%
+back 50 years from now this is going to
+be one of the things that will really
+
+ align:start position:0%
+be one of the things that will really
+ 
+
+ align:start position:0%
+be one of the things that will really
+stick out I believe historically the
+
+ align:start position:0%
+stick out I believe historically the
+ 
+
+ align:start position:0%
+stick out I believe historically the
+number of young people being educated to
+
+ align:start position:0%
+number of young people being educated to
+ 
+
+ align:start position:0%
+number of young people being educated to
+new heights so somehow we're going to
+
+ align:start position:0%
+new heights so somehow we're going to
+ 
+
+ align:start position:0%
+new heights so somehow we're going to
+have to deal with this scale and even
+
+ align:start position:0%
+have to deal with this scale and even
+ 
+
+ align:start position:0%
+have to deal with this scale and even
+though I happen to deeply believe in the
+
+ align:start position:0%
+though I happen to deeply believe in the
+ 
+
+ align:start position:0%
+though I happen to deeply believe in the
+role of the more or less traditional
+
+ align:start position:0%
+role of the more or less traditional
+ 
+
+ align:start position:0%
+role of the more or less traditional
+residential un University in
+
+ align:start position:0%
+residential un University in
+ 
+
+ align:start position:0%
+residential un University in
+society there is no answer to this
+
+ align:start position:0%
+society there is no answer to this
+ 
+
+ align:start position:0%
+society there is no answer to this
+question that is not based on technology
+
+ align:start position:0%
+question that is not based on technology
+ 
+
+ align:start position:0%
+question that is not based on technology
+and so I am very hopeful while I don't
+
+ align:start position:0%
+and so I am very hopeful while I don't
+ 
+
+ align:start position:0%
+and so I am very hopeful while I don't
+know the answer and I suspect much of it
+
+ align:start position:0%
+know the answer and I suspect much of it
+ 
+
+ align:start position:0%
+know the answer and I suspect much of it
+is going to be along the lines of what
+
+ align:start position:0%
+is going to be along the lines of what
+ 
+
+ align:start position:0%
+is going to be along the lines of what
+how's saying that Computing and the
+
+ align:start position:0%
+how's saying that Computing and the
+ 
+
+ align:start position:0%
+how's saying that Computing and the
+internet and so forth become knowledge
+
+ align:start position:0%
+internet and so forth become knowledge
+ 
+
+ align:start position:0%
+internet and so forth become knowledge
+generators rather than stores and
+
+ align:start position:0%
+generators rather than stores and
+ 
+
+ align:start position:0%
+generators rather than stores and
+transmitters and picking up as Tim and
+
+ align:start position:0%
+transmitters and picking up as Tim and
+ 
+
+ align:start position:0%
+transmitters and picking up as Tim and
+so many other people have done about uh
+
+ align:start position:0%
+so many other people have done about uh
+ 
+
+ align:start position:0%
+so many other people have done about uh
+how we can sort of IC like engag people
+
+ align:start position:0%
+how we can sort of IC like engag people
+ 
+
+ align:start position:0%
+how we can sort of IC like engag people
+the Futures somewhere in this space but
+
+ align:start position:0%
+the Futures somewhere in this space but
+ 
+
+ align:start position:0%
+the Futures somewhere in this space but
+it's really important that bright people
+
+ align:start position:0%
+it's really important that bright people
+ 
+
+ align:start position:0%
+it's really important that bright people
+like this think about it very
+
+ align:start position:0%
+like this think about it very
+ 
+
+ align:start position:0%
+like this think about it very
+explicitly um I also think it's a great
+
+ align:start position:0%
+explicitly um I also think it's a great
+ 
+
+ align:start position:0%
+explicitly um I also think it's a great
+question uh it uh it's a question
+
+ align:start position:0%
+question uh it uh it's a question
+ 
+
+ align:start position:0%
+question uh it uh it's a question
+actually that I'm thinking about a lot
+
+ align:start position:0%
+actually that I'm thinking about a lot
+ 
+
+ align:start position:0%
+actually that I'm thinking about a lot
+these days because I just started
+
+ align:start position:0%
+these days because I just started
+ 
+
+ align:start position:0%
+these days because I just started
+collaborating with Bill Bowen on a
+
+ align:start position:0%
+collaborating with Bill Bowen on a
+ 
+
+ align:start position:0%
+collaborating with Bill Bowen on a
+research project in which we're taking a
+
+ align:start position:0%
+research project in which we're taking a
+ 
+
+ align:start position:0%
+research project in which we're taking a
+look at some of the obstacles that exist
+
+ align:start position:0%
+look at some of the obstacles that exist
+ 
+
+ align:start position:0%
+look at some of the obstacles that exist
+in incorporating interactive online
+
+ align:start position:0%
+in incorporating interactive online
+ 
+
+ align:start position:0%
+in incorporating interactive online
+online learning locally in large public
+
+ align:start position:0%
+online learning locally in large public
+ 
+
+ align:start position:0%
+online learning locally in large public
+research universities I think the rest
+
+ align:start position:0%
+research universities I think the rest
+ 
+
+ align:start position:0%
+research universities I think the rest
+of the world though has a real
+
+ align:start position:0%
+of the world though has a real
+ 
+
+ align:start position:0%
+of the world though has a real
+opportunity here because uh so many
+
+ align:start position:0%
+opportunity here because uh so many
+ 
+
+ align:start position:0%
+opportunity here because uh so many
+nations are making enormous Investments
+
+ align:start position:0%
+nations are making enormous Investments
+ 
+
+ align:start position:0%
+nations are making enormous Investments
+right now in higher
+
+ align:start position:0%
+right now in higher
+ 
+
+ align:start position:0%
+right now in higher
+education and part of the challenge that
+
+ align:start position:0%
+education and part of the challenge that
+ 
+
+ align:start position:0%
+education and part of the challenge that
+we have in this country is that we have
+
+ align:start position:0%
+we have in this country is that we have
+ 
+
+ align:start position:0%
+we have in this country is that we have
+a higher education system that has
+
+ align:start position:0%
+a higher education system that has
+ 
+
+ align:start position:0%
+a higher education system that has
+evolved um to and you might argue has
+
+ align:start position:0%
+evolved um to and you might argue has
+ 
+
+ align:start position:0%
+evolved um to and you might argue has
+been optimized in a world in which this
+
+ align:start position:0%
+been optimized in a world in which this
+ 
+
+ align:start position:0%
+been optimized in a world in which this
+kind of technology did not EX
+
+ align:start position:0%
+kind of technology did not EX
+ 
+
+ align:start position:0%
+kind of technology did not EX
+exist and one opportunity that exists in
+
+ align:start position:0%
+exist and one opportunity that exists in
+ 
+
+ align:start position:0%
+exist and one opportunity that exists in
+the rest of the world is to think about
+
+ align:start position:0%
+the rest of the world is to think about
+ 
+
+ align:start position:0%
+the rest of the world is to think about
+how as you expand opportunities in
+
+ align:start position:0%
+how as you expand opportunities in
+ 
+
+ align:start position:0%
+how as you expand opportunities in
+higher educ education to not just merely
+
+ align:start position:0%
+higher educ education to not just merely
+ 
+
+ align:start position:0%
+higher educ education to not just merely
+ape what we have done in the US and try
+
+ align:start position:0%
+ape what we have done in the US and try
+ 
+
+ align:start position:0%
+ape what we have done in the US and try
+to replicate the kinds of Institutions
+
+ align:start position:0%
+to replicate the kinds of Institutions
+ 
+
+ align:start position:0%
+to replicate the kinds of Institutions
+as good as they are in the US but to
+
+ align:start position:0%
+as good as they are in the US but to
+ 
+
+ align:start position:0%
+as good as they are in the US but to
+reconceptualize what the infrastructure
+
+ align:start position:0%
+reconceptualize what the infrastructure
+ 
+
+ align:start position:0%
+reconceptualize what the infrastructure
+looks like for higher education
+
+ align:start position:0%
+looks like for higher education
+ 
+
+ align:start position:0%
+looks like for higher education
+elsewhere that is in fact that that leap
+
+ align:start position:0%
+elsewhere that is in fact that that leap
+ 
+
+ align:start position:0%
+elsewhere that is in fact that that leap
+frog past what we're doing here because
+
+ align:start position:0%
+frog past what we're doing here because
+ 
+
+ align:start position:0%
+frog past what we're doing here because
+I think this evolution is going to take
+
+ align:start position:0%
+I think this evolution is going to take
+ 
+
+ align:start position:0%
+I think this evolution is going to take
+a long time before it it seriously
+
+ align:start position:0%
+a long time before it it seriously
+ 
+
+ align:start position:0%
+a long time before it it seriously
+penetrates um in in in US higher
+
+ align:start position:0%
+penetrates um in in in US higher
+ 
+
+ align:start position:0%
+penetrates um in in in US higher
+education and starts to fundamentally
+
+ align:start position:0%
+education and starts to fundamentally
+ 
+
+ align:start position:0%
+education and starts to fundamentally
+replace traditional models of of
+
+ align:start position:0%
+replace traditional models of of
+ 
+
+ align:start position:0%
+replace traditional models of of
+teaching and learning great I think we
+
+ align:start position:0%
+teaching and learning great I think we
+ 
+
+ align:start position:0%
+teaching and learning great I think we
+have time for one
+
+ align:start position:0%
+have time for one
+ 
+
+ align:start position:0%
+have time for one
+more yeah just to qu could could you
+
+ align:start position:0%
+more yeah just to qu could could you
+ 
+
+ align:start position:0%
+more yeah just to qu could could you
+comment on the quality of instruction
+
+ align:start position:0%
+comment on the quality of instruction
+ 
+
+ align:start position:0%
+comment on the quality of instruction
+that uh the impact of this within the
+
+ align:start position:0%
+that uh the impact of this within the
+ 
+
+ align:start position:0%
+that uh the impact of this within the
+institution itself uh what has been the
+
+ align:start position:0%
+institution itself uh what has been the
+ 
+
+ align:start position:0%
+institution itself uh what has been the
+effect of open course were within MIT
+
+ align:start position:0%
+effect of open course were within MIT
+ 
+
+ align:start position:0%
+effect of open course were within MIT
+and toughs and so forth in terms of the
+
+ align:start position:0%
+and toughs and so forth in terms of the
+ 
+
+ align:start position:0%
+and toughs and so forth in terms of the
+learning within the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+institution um I don't think within the
+
+ align:start position:0%
+institution um I don't think within the
+ 
+
+ align:start position:0%
+institution um I don't think within the
+my time in the in the University
+
+ align:start position:0%
+my time in the in the University
+ 
+
+ align:start position:0%
+my time in the in the University
+leadership there was a serious attempt
+
+ align:start position:0%
+leadership there was a serious attempt
+ 
+
+ align:start position:0%
+leadership there was a serious attempt
+to try to assess that that I left in
+
+ align:start position:0%
+to try to assess that that I left in
+ 
+
+ align:start position:0%
+to try to assess that that I left in
+2005 um I'm and I don't know of one
+
+ align:start position:0%
+2005 um I'm and I don't know of one
+ 
+
+ align:start position:0%
+2005 um I'm and I don't know of one
+that's gone on since dick how can you do
+
+ align:start position:0%
+that's gone on since dick how can you do
+ 
+
+ align:start position:0%
+that's gone on since dick how can you do
+you know of one I think the honest
+
+ align:start position:0%
+you know of one I think the honest
+ 
+
+ align:start position:0%
+you know of one I think the honest
+answer is that we're trying a bunch of
+
+ align:start position:0%
+answer is that we're trying a bunch of
+ 
+
+ align:start position:0%
+answer is that we're trying a bunch of
+experiments and they're along the lines
+
+ align:start position:0%
+experiments and they're along the lines
+ 
+
+ align:start position:0%
+experiments and they're along the lines
+of modularity of things that say if
+
+ align:start position:0%
+of modularity of things that say if
+ 
+
+ align:start position:0%
+of modularity of things that say if
+there are if there are pieces of courses
+
+ align:start position:0%
+there are if there are pieces of courses
+ 
+
+ align:start position:0%
+there are if there are pieces of courses
+uh one example is differential equations
+
+ align:start position:0%
+uh one example is differential equations
+ 
+
+ align:start position:0%
+uh one example is differential equations
+that's on open course whereare can other
+
+ align:start position:0%
+that's on open course whereare can other
+ 
+
+ align:start position:0%
+that's on open course whereare can other
+courses take advantage of that material
+
+ align:start position:0%
+courses take advantage of that material
+ 
+
+ align:start position:0%
+courses take advantage of that material
+that's already that's already done
+
+ align:start position:0%
+that's already that's already done
+ 
+
+ align:start position:0%
+that's already that's already done
+there's a easier answer in terms of
+
+ align:start position:0%
+there's a easier answer in terms of
+ 
+
+ align:start position:0%
+there's a easier answer in terms of
+students who want to know should they
+
+ align:start position:0%
+students who want to know should they
+ 
+
+ align:start position:0%
+students who want to know should they
+take a course or should they major in in
+
+ align:start position:0%
+take a course or should they major in in
+ 
+
+ align:start position:0%
+take a course or should they major in in
+some particular in some particular field
+
+ align:start position:0%
+some particular in some particular field
+ 
+
+ align:start position:0%
+some particular in some particular field
+they can go look at the curriculum and
+
+ align:start position:0%
+they can go look at the curriculum and
+ 
+
+ align:start position:0%
+they can go look at the curriculum and
+do that their impacts on the advisers
+
+ align:start position:0%
+do that their impacts on the advisers
+ 
+
+ align:start position:0%
+do that their impacts on the advisers
+but the one thing that hasn't happened
+
+ align:start position:0%
+but the one thing that hasn't happened
+ 
+
+ align:start position:0%
+but the one thing that hasn't happened
+is I don't think open corer has
+
+ align:start position:0%
+is I don't think open corer has
+ 
+
+ align:start position:0%
+is I don't think open corer has
+transformed MIT as much as it's
+
+ align:start position:0%
+transformed MIT as much as it's
+ 
+
+ align:start position:0%
+transformed MIT as much as it's
+transformed the world and that to me I
+
+ align:start position:0%
+transformed the world and that to me I
+ 
+
+ align:start position:0%
+transformed the world and that to me I
+think is the fun one of the fundamental
+
+ align:start position:0%
+think is the fun one of the fundamental
+ 
+
+ align:start position:0%
+think is the fun one of the fundamental
+challenges of open course Ro going
+
+ align:start position:0%
+challenges of open course Ro going
+ 
+
+ align:start position:0%
+challenges of open course Ro going
+forward
\ No newline at end of file
diff --git a/h6Ok8CNVOaE.txt b/h6Ok8CNVOaE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e4674d601370bd38c2625488361eccd373dbb36a
--- /dev/null
+++ b/h6Ok8CNVOaE.txt
@@ -0,0 +1,13955 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so we had a big lecture last
+
+ align:start position:0%
+ocw.mit.edu so we had a big lecture last
+ 
+
+ align:start position:0%
+ocw.mit.edu so we had a big lecture last
+time on perfect
+
+ align:start position:0%
+time on perfect
+ 
+
+ align:start position:0%
+time on perfect
+Insurance uh and implications
+
+ align:start position:0%
+Insurance uh and implications
+ 
+
+ align:start position:0%
+Insurance uh and implications
+for uh targeting and policy uh and
+
+ align:start position:0%
+for uh targeting and policy uh and
+ 
+
+ align:start position:0%
+for uh targeting and policy uh and
+evaluations there's a series of lectures
+
+ align:start position:0%
+evaluations there's a series of lectures
+ 
+
+ align:start position:0%
+evaluations there's a series of lectures
+now that have to do with uh working off
+
+ align:start position:0%
+now that have to do with uh working off
+ 
+
+ align:start position:0%
+now that have to do with uh working off
+of that basic risk sharing framework
+
+ align:start position:0%
+of that basic risk sharing framework
+ 
+
+ align:start position:0%
+of that basic risk sharing framework
+today we're going to talk about the
+
+ align:start position:0%
+today we're going to talk about the
+ 
+
+ align:start position:0%
+today we're going to talk about the
+implications for what we should see in
+
+ align:start position:0%
+implications for what we should see in
+ 
+
+ align:start position:0%
+implications for what we should see in
+rates of return and then next class
+
+ align:start position:0%
+rates of return and then next class
+ 
+
+ align:start position:0%
+rates of return and then next class
+we're going to talk about
+
+ align:start position:0%
+we're going to talk about
+ 
+
+ align:start position:0%
+we're going to talk about
+uh alternative
+
+ align:start position:0%
+uh alternative
+ 
+
+ align:start position:0%
+uh alternative
+models of uh of what we might see in the
+
+ align:start position:0%
+models of uh of what we might see in the
+ 
+
+ align:start position:0%
+models of uh of what we might see in the
+consumption
+
+ align:start position:0%
+consumption
+ 
+
+ align:start position:0%
+consumption
+data uh and then the lecture after that
+
+ align:start position:0%
+data uh and then the lecture after that
+ 
+
+ align:start position:0%
+data uh and then the lecture after that
+we're going to return to the perfect
+
+ align:start position:0%
+we're going to return to the perfect
+ 
+
+ align:start position:0%
+we're going to return to the perfect
+Market model and think about Labor
+
+ align:start position:0%
+Market model and think about Labor
+ 
+
+ align:start position:0%
+Market model and think about Labor
+Supply and then finally we're going to
+
+ align:start position:0%
+Supply and then finally we're going to
+ 
+
+ align:start position:0%
+Supply and then finally we're going to
+get to explicit obstacles to trade I
+
+ align:start position:0%
+get to explicit obstacles to trade I
+ 
+
+ align:start position:0%
+get to explicit obstacles to trade I
+must say that you know rather than put
+
+ align:start position:0%
+must say that you know rather than put
+ 
+
+ align:start position:0%
+must say that you know rather than put
+off the obstacles we've been noting and
+
+ align:start position:0%
+off the obstacles we've been noting and
+ 
+
+ align:start position:0%
+off the obstacles we've been noting and
+even talking about
+
+ align:start position:0%
+even talking about
+ 
+
+ align:start position:0%
+even talking about
+alternative models along the
+
+ align:start position:0%
+alternative models along the
+ 
+
+ align:start position:0%
+alternative models along the
+way uh because these benchmarks are
+
+ align:start position:0%
+way uh because these benchmarks are
+ 
+
+ align:start position:0%
+way uh because these benchmarks are
+sometimes rejected and you're going to
+
+ align:start position:0%
+sometimes rejected and you're going to
+ 
+
+ align:start position:0%
+sometimes rejected and you're going to
+see that a bit today as
+
+ align:start position:0%
+see that a bit today as
+ 
+
+ align:start position:0%
+see that a bit today as
+well uh so
+
+ align:start position:0%
+well uh so
+ 
+
+ align:start position:0%
+well uh so
+this perfect market Standard within
+
+ align:start position:0%
+this perfect market Standard within
+ 
+
+ align:start position:0%
+this perfect market Standard within
+Villages that has to do with uh
+
+ align:start position:0%
+Villages that has to do with uh
+ 
+
+ align:start position:0%
+Villages that has to do with uh
+relatives and Friends interacting with
+
+ align:start position:0%
+relatives and Friends interacting with
+ 
+
+ align:start position:0%
+relatives and Friends interacting with
+each other has implications for how you
+
+ align:start position:0%
+each other has implications for how you
+ 
+
+ align:start position:0%
+each other has implications for how you
+adjust for risk and we're going to do
+
+ align:start position:0%
+adjust for risk and we're going to do
+ 
+
+ align:start position:0%
+adjust for risk and we're going to do
+that with a
+
+ align:start position:0%
+that with a
+ 
+
+ align:start position:0%
+that with a
+vengeance but it will turn out that it
+
+ align:start position:0%
+vengeance but it will turn out that it
+ 
+
+ align:start position:0%
+vengeance but it will turn out that it
+does that framework allows us to
+
+ align:start position:0%
+does that framework allows us to
+ 
+
+ align:start position:0%
+does that framework allows us to
+distinguish aggregate from idiosyncratic
+
+ align:start position:0%
+distinguish aggregate from idiosyncratic
+ 
+
+ align:start position:0%
+distinguish aggregate from idiosyncratic
+risk and uh in the idiosyncratic risk
+
+ align:start position:0%
+risk and uh in the idiosyncratic risk
+ 
+
+ align:start position:0%
+risk and uh in the idiosyncratic risk
+should not
+
+ align:start position:0%
+should not
+ 
+
+ align:start position:0%
+should not
+be showing up in rates of return but it
+
+ align:start position:0%
+be showing up in rates of return but it
+ 
+
+ align:start position:0%
+be showing up in rates of return but it
+does at the
+
+ align:start position:0%
+does at the
+ 
+
+ align:start position:0%
+does at the
+end um and then I'll say a few words
+
+ align:start position:0%
+end um and then I'll say a few words
+ 
+
+ align:start position:0%
+end um and then I'll say a few words
+about what else we know about the tii
+
+ align:start position:0%
+about what else we know about the tii
+ 
+
+ align:start position:0%
+about what else we know about the tii
+data in terms of the decomposition of
+
+ align:start position:0%
+data in terms of the decomposition of
+ 
+
+ align:start position:0%
+data in terms of the decomposition of
+volatility uh linking back to a paper we
+
+ align:start position:0%
+volatility uh linking back to a paper we
+ 
+
+ align:start position:0%
+volatility uh linking back to a paper we
+saw saw the very first
+
+ align:start position:0%
+saw saw the very first
+ 
+
+ align:start position:0%
+saw saw the very first
+lecture uh on
+
+ align:start position:0%
+lecture uh on
+ 
+
+ align:start position:0%
+lecture uh on
+quantifying the growth rates by sector
+
+ align:start position:0%
+quantifying the growth rates by sector
+ 
+
+ align:start position:0%
+quantifying the growth rates by sector
+uh but we're going to do it by wealth at
+
+ align:start position:0%
+uh but we're going to do it by wealth at
+ 
+
+ align:start position:0%
+uh but we're going to do it by wealth at
+least I'll say a few words about it uh
+
+ align:start position:0%
+least I'll say a few words about it uh
+ 
+
+ align:start position:0%
+least I'll say a few words about it uh
+and then I'm going to toward the end of
+
+ align:start position:0%
+and then I'm going to toward the end of
+ 
+
+ align:start position:0%
+and then I'm going to toward the end of
+the class sort
+
+ align:start position:0%
+the class sort
+ 
+
+ align:start position:0%
+the class sort
+of uh return to this idea that either
+
+ align:start position:0%
+of uh return to this idea that either
+ 
+
+ align:start position:0%
+of uh return to this idea that either
+things aren't perfect Andor people are
+
+ align:start position:0%
+things aren't perfect Andor people are
+ 
+
+ align:start position:0%
+things aren't perfect Andor people are
+making mistakes and we'll do that in
+
+ align:start position:0%
+making mistakes and we'll do that in
+ 
+
+ align:start position:0%
+making mistakes and we'll do that in
+some um uh unusual context one that has
+
+ align:start position:0%
+some um uh unusual context one that has
+ 
+
+ align:start position:0%
+some um uh unusual context one that has
+to do with data from Sweden an unusually
+
+ align:start position:0%
+to do with data from Sweden an unusually
+ 
+
+ align:start position:0%
+to do with data from Sweden an unusually
+Rich database from Sweden and another
+
+ align:start position:0%
+Rich database from Sweden and another
+ 
+
+ align:start position:0%
+Rich database from Sweden and another
+that has to do with US
+
+ align:start position:0%
+that has to do with US
+ 
+
+ align:start position:0%
+that has to do with US
+Airlines uh but the basic Frameworks
+
+ align:start position:0%
+Airlines uh but the basic Frameworks
+ 
+
+ align:start position:0%
+Airlines uh but the basic Frameworks
+that are getting used whether in the
+
+ align:start position:0%
+that are getting used whether in the
+ 
+
+ align:start position:0%
+that are getting used whether in the
+developing context or Sweden or uh US
+
+ align:start position:0%
+developing context or Sweden or uh US
+ 
+
+ align:start position:0%
+developing context or Sweden or uh US
+airlines are basically all the same so
+
+ align:start position:0%
+airlines are basically all the same so
+ 
+
+ align:start position:0%
+airlines are basically all the same so
+there's a strong complimentarity across
+
+ align:start position:0%
+there's a strong complimentarity across
+ 
+
+ align:start position:0%
+there's a strong complimentarity across
+these papers this paper with
+
+ align:start position:0%
+these papers this paper with
+ 
+
+ align:start position:0%
+these papers this paper with
+Chris um has been in the works for a
+
+ align:start position:0%
+Chris um has been in the works for a
+ 
+
+ align:start position:0%
+Chris um has been in the works for a
+while but we are now able to use you
+
+ align:start position:0%
+while but we are now able to use you
+ 
+
+ align:start position:0%
+while but we are now able to use you
+know 13 years of monthly data so we are
+
+ align:start position:0%
+know 13 years of monthly data so we are
+ 
+
+ align:start position:0%
+know 13 years of monthly data so we are
+doing better than than before um so we
+
+ align:start position:0%
+doing better than than before um so we
+ 
+
+ align:start position:0%
+doing better than than before um so we
+want to talk about risk and return of
+
+ align:start position:0%
+want to talk about risk and return of
+ 
+
+ align:start position:0%
+want to talk about risk and return of
+productive Assets in developing
+
+ align:start position:0%
+productive Assets in developing
+ 
+
+ align:start position:0%
+productive Assets in developing
+countries uh we already looked at some
+
+ align:start position:0%
+countries uh we already looked at some
+ 
+
+ align:start position:0%
+countries uh we already looked at some
+of the slides showing how rates of
+
+ align:start position:0%
+of the slides showing how rates of
+ 
+
+ align:start position:0%
+of the slides showing how rates of
+return differ a lot across different
+
+ align:start position:0%
+return differ a lot across different
+ 
+
+ align:start position:0%
+return differ a lot across different
+households differ in large part by
+
+ align:start position:0%
+households differ in large part by
+ 
+
+ align:start position:0%
+households differ in large part by
+wealth
+
+ align:start position:0%
+wealth
+ 
+
+ align:start position:0%
+wealth
+and how poor
+
+ align:start position:0%
+and how poor
+ 
+
+ align:start position:0%
+and how poor
+people have relatively High rates of
+
+ align:start position:0%
+people have relatively High rates of
+ 
+
+ align:start position:0%
+people have relatively High rates of
+return and they're saving and they you
+
+ align:start position:0%
+return and they're saving and they you
+ 
+
+ align:start position:0%
+return and they're saving and they you
+know they're accumulating assets and so
+
+ align:start position:0%
+know they're accumulating assets and so
+ 
+
+ align:start position:0%
+know they're accumulating assets and so
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+um another people another way people
+
+ align:start position:0%
+um another people another way people
+ 
+
+ align:start position:0%
+um another people another way people
+look at rates of return is to say you
+
+ align:start position:0%
+look at rates of return is to say you
+ 
+
+ align:start position:0%
+look at rates of return is to say you
+know well some people are more talented
+
+ align:start position:0%
+know well some people are more talented
+ 
+
+ align:start position:0%
+know well some people are more talented
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+others uh so you know if we look at
+
+ align:start position:0%
+others uh so you know if we look at
+ 
+
+ align:start position:0%
+others uh so you know if we look at
+rates of return we get some some notion
+
+ align:start position:0%
+rates of return we get some some notion
+ 
+
+ align:start position:0%
+rates of return we get some some notion
+of underlying prot productivity as in
+
+ align:start position:0%
+of underlying prot productivity as in
+ 
+
+ align:start position:0%
+of underlying prot productivity as in
+tfp and so on we've had many lectures
+
+ align:start position:0%
+tfp and so on we've had many lectures
+ 
+
+ align:start position:0%
+tfp and so on we've had many lectures
+about tfp and coefficients in front
+
+ align:start position:0%
+about tfp and coefficients in front
+ 
+
+ align:start position:0%
+about tfp and coefficients in front
+multiplying in front of production
+
+ align:start position:0%
+multiplying in front of production
+ 
+
+ align:start position:0%
+multiplying in front of production
+functions and so on but correct me if
+
+ align:start position:0%
+functions and so on but correct me if
+ 
+
+ align:start position:0%
+functions and so on but correct me if
+I'm wrong nowhere in any of that stuff
+
+ align:start position:0%
+I'm wrong nowhere in any of that stuff
+ 
+
+ align:start position:0%
+I'm wrong nowhere in any of that stuff
+did we ever adjust for
+
+ align:start position:0%
+did we ever adjust for
+ 
+
+ align:start position:0%
+did we ever adjust for
+risk so what's the intuition for
+
+ align:start position:0%
+risk so what's the intuition for
+ 
+
+ align:start position:0%
+risk so what's the intuition for
+adjusting for
+
+ align:start position:0%
+adjusting for
+ 
+
+ align:start position:0%
+adjusting for
+risk
+
+ align:start position:0%
+risk
+ 
+
+ align:start position:0%
+risk
+well if you want to look at you know
+
+ align:start position:0%
+well if you want to look at you know
+ 
+
+ align:start position:0%
+well if you want to look at you know
+compensating differential
+
+ align:start position:0%
+compensating differential
+ 
+
+ align:start position:0%
+compensating differential
+the higher the risk of a project the
+
+ align:start position:0%
+the higher the risk of a project the
+ 
+
+ align:start position:0%
+the higher the risk of a project the
+higher the rate of return ought to be
+
+ align:start position:0%
+higher the rate of return ought to be
+ 
+
+ align:start position:0%
+higher the rate of return ought to be
+other things equal to compensate for
+
+ align:start position:0%
+other things equal to compensate for
+ 
+
+ align:start position:0%
+other things equal to compensate for
+that risk you know like junk bonds have
+
+ align:start position:0%
+that risk you know like junk bonds have
+ 
+
+ align:start position:0%
+that risk you know like junk bonds have
+higher
+
+ align:start position:0%
+higher
+ 
+
+ align:start position:0%
+higher
+yields and so on and so forth so maybe
+
+ align:start position:0%
+yields and so on and so forth so maybe
+ 
+
+ align:start position:0%
+yields and so on and so forth so maybe
+these guys with seemingly very high
+
+ align:start position:0%
+these guys with seemingly very high
+ 
+
+ align:start position:0%
+these guys with seemingly very high
+rates of return actually are just doing
+
+ align:start position:0%
+rates of return actually are just doing
+ 
+
+ align:start position:0%
+rates of return actually are just doing
+risky
+
+ align:start position:0%
+risky
+ 
+
+ align:start position:0%
+risky
+things and indeed if enough of them do
+
+ align:start position:0%
+things and indeed if enough of them do
+ 
+
+ align:start position:0%
+things and indeed if enough of them do
+risky things then on average some of
+
+ align:start position:0%
+risky things then on average some of
+ 
+
+ align:start position:0%
+risky things then on average some of
+them succeed and maybe that would
+
+ align:start position:0%
+them succeed and maybe that would
+ 
+
+ align:start position:0%
+them succeed and maybe that would
+generate the high rate of return so we
+
+ align:start position:0%
+generate the high rate of return so we
+ 
+
+ align:start position:0%
+generate the high rate of return so we
+really need to think think about how to
+
+ align:start position:0%
+really need to think think about how to
+ 
+
+ align:start position:0%
+really need to think think about how to
+measure the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+risk and we're going to rely on finance
+
+ align:start position:0%
+risk and we're going to rely on finance
+ 
+
+ align:start position:0%
+risk and we're going to rely on finance
+Theory but we're I'll be
+
+ align:start position:0%
+Theory but we're I'll be
+ 
+
+ align:start position:0%
+Theory but we're I'll be
+very careful to sort of build into it
+
+ align:start position:0%
+very careful to sort of build into it
+ 
+
+ align:start position:0%
+very careful to sort of build into it
+the economic models you may learn a
+
+ align:start position:0%
+the economic models you may learn a
+ 
+
+ align:start position:0%
+the economic models you may learn a
+little bit of Finance jargon along the
+
+ align:start position:0%
+little bit of Finance jargon along the
+ 
+
+ align:start position:0%
+little bit of Finance jargon along the
+way U but I'm not going to start with
+
+ align:start position:0%
+way U but I'm not going to start with
+ 
+
+ align:start position:0%
+way U but I'm not going to start with
+that um I'll I'll get you up to speed uh
+
+ align:start position:0%
+that um I'll I'll get you up to speed uh
+ 
+
+ align:start position:0%
+that um I'll I'll get you up to speed uh
+it's really not that hard when you look
+
+ align:start position:0%
+it's really not that hard when you look
+ 
+
+ align:start position:0%
+it's really not that hard when you look
+at the equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equs okay so what do we
+
+ align:start position:0%
+equs okay so what do we
+ 
+
+ align:start position:0%
+equs okay so what do we
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+um we do find
+
+ align:start position:0%
+um we do find
+ 
+
+ align:start position:0%
+um we do find
+uh that higher risk is associated with
+
+ align:start position:0%
+uh that higher risk is associated with
+ 
+
+ align:start position:0%
+uh that higher risk is associated with
+higher rate of return
+
+ align:start position:0%
+higher rate of return
+ 
+
+ align:start position:0%
+higher rate of return
+but but the risk that we're going to be
+
+ align:start position:0%
+but but the risk that we're going to be
+ 
+
+ align:start position:0%
+but but the risk that we're going to be
+concentrating on in the model is not
+
+ align:start position:0%
+concentrating on in the model is not
+ 
+
+ align:start position:0%
+concentrating on in the model is not
+idiosyncratic risk it's Village level
+
+ align:start position:0%
+idiosyncratic risk it's Village level
+ 
+
+ align:start position:0%
+idiosyncratic risk it's Village level
+risk
+
+ align:start position:0%
+risk
+ 
+
+ align:start position:0%
+risk
+so when you think about households
+
+ align:start position:0%
+so when you think about households
+ 
+
+ align:start position:0%
+so when you think about households
+together pooling resources as in a risk
+
+ align:start position:0%
+together pooling resources as in a risk
+ 
+
+ align:start position:0%
+together pooling resources as in a risk
+sharing
+
+ align:start position:0%
+sharing
+ 
+
+ align:start position:0%
+sharing
+Syndicate uh they would care about say
+
+ align:start position:0%
+Syndicate uh they would care about say
+ 
+
+ align:start position:0%
+Syndicate uh they would care about say
+aggregate consumption should move
+
+ align:start position:0%
+aggregate consumption should move
+ 
+
+ align:start position:0%
+aggregate consumption should move
+individual consumption and idiosyncratic
+
+ align:start position:0%
+individual consumption and idiosyncratic
+ 
+
+ align:start position:0%
+individual consumption and idiosyncratic
+income shock should not have an
+
+ align:start position:0%
+income shock should not have an
+ 
+
+ align:start position:0%
+income shock should not have an
+influence on
+
+ align:start position:0%
+influence on
+ 
+
+ align:start position:0%
+influence on
+consumption so when is something really
+
+ align:start position:0%
+consumption so when is something really
+ 
+
+ align:start position:0%
+consumption so when is something really
+valuable it's uh a project is valuable
+
+ align:start position:0%
+valuable it's uh a project is valuable
+ 
+
+ align:start position:0%
+valuable it's uh a project is valuable
+when it has a return which is negatively
+
+ align:start position:0%
+when it has a return which is negatively
+ 
+
+ align:start position:0%
+when it has a return which is negatively
+correlated with the village average
+
+ align:start position:0%
+correlated with the village average
+ 
+
+ align:start position:0%
+correlated with the village average
+return you know so that the resources
+
+ align:start position:0%
+return you know so that the resources
+ 
+
+ align:start position:0%
+return you know so that the resources
+come in when you need it so the quote
+
+ align:start position:0%
+come in when you need it so the quote
+ 
+
+ align:start position:0%
+come in when you need it so the quote
+Market the way the finance guys would
+
+ align:start position:0%
+Market the way the finance guys would
+ 
+
+ align:start position:0%
+Market the way the finance guys would
+use it for us is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+village
+
+ align:start position:0%
+village
+ 
+
+ align:start position:0%
+village
+uh and
+
+ align:start position:0%
+uh and
+ 
+
+ align:start position:0%
+uh and
+indeed the more a household has a return
+
+ align:start position:0%
+indeed the more a household has a return
+ 
+
+ align:start position:0%
+indeed the more a household has a return
+on its projects that are correlated with
+
+ align:start position:0%
+on its projects that are correlated with
+ 
+
+ align:start position:0%
+on its projects that are correlated with
+the village average return the higher is
+
+ align:start position:0%
+the village average return the higher is
+ 
+
+ align:start position:0%
+the village average return the higher is
+going to be the measure
+
+ align:start position:0%
+going to be the measure
+ 
+
+ align:start position:0%
+going to be the measure
+expected or average return on that
+
+ align:start position:0%
+expected or average return on that
+ 
+
+ align:start position:0%
+expected or average return on that
+household's
+
+ align:start position:0%
+household's
+ 
+
+ align:start position:0%
+household's
+assets and we have all kinds of ways of
+
+ align:start position:0%
+assets and we have all kinds of ways of
+ 
+
+ align:start position:0%
+assets and we have all kinds of ways of
+adjusting for human
+
+ align:start position:0%
+adjusting for human
+ 
+
+ align:start position:0%
+adjusting for human
+capital and uh and so on which I'll get
+
+ align:start position:0%
+capital and uh and so on which I'll get
+ 
+
+ align:start position:0%
+capital and uh and so on which I'll get
+into as I said though it does in the end
+
+ align:start position:0%
+into as I said though it does in the end
+ 
+
+ align:start position:0%
+into as I said though it does in the end
+leave some ID idiosyncratic risk and
+
+ align:start position:0%
+leave some ID idiosyncratic risk and
+ 
+
+ align:start position:0%
+leave some ID idiosyncratic risk and
+that's also generating higher expected
+
+ align:start position:0%
+that's also generating higher expected
+ 
+
+ align:start position:0%
+that's also generating higher expected
+returns
+
+ align:start position:0%
+returns
+ 
+
+ align:start position:0%
+returns
+um Aggregate and idiosyncratic risk is
+
+ align:start position:0%
+um Aggregate and idiosyncratic risk is
+ 
+
+ align:start position:0%
+um Aggregate and idiosyncratic risk is
+is negatively correlated with
+
+ align:start position:0%
+is negatively correlated with
+ 
+
+ align:start position:0%
+is negatively correlated with
+age so the older household head
+
+ align:start position:0%
+age so the older household head
+ 
+
+ align:start position:0%
+age so the older household head
+basically the uh quote less risky things
+
+ align:start position:0%
+basically the uh quote less risky things
+ 
+
+ align:start position:0%
+basically the uh quote less risky things
+that they're doing but but both in the
+
+ align:start position:0%
+that they're doing but but both in the
+ 
+
+ align:start position:0%
+that they're doing but but both in the
+idiosyncratic and aggregate sense they
+
+ align:start position:0%
+idiosyncratic and aggregate sense they
+ 
+
+ align:start position:0%
+idiosyncratic and aggregate sense they
+tend to do things which
+
+ align:start position:0%
+tend to do things which
+ 
+
+ align:start position:0%
+tend to do things which
+are less correlated with a village
+
+ align:start position:0%
+are less correlated with a village
+ 
+
+ align:start position:0%
+are less correlated with a village
+average
+
+ align:start position:0%
+average
+ 
+
+ align:start position:0%
+average
+um it's negative with wealth meaning
+
+ align:start position:0%
+um it's negative with wealth meaning
+ 
+
+ align:start position:0%
+um it's negative with wealth meaning
+um the lower Is wealth the higher
+
+ align:start position:0%
+um the lower Is wealth the higher
+ 
+
+ align:start position:0%
+um the lower Is wealth the higher
+both the idiosyncratic and aggregate now
+
+ align:start position:0%
+both the idiosyncratic and aggregate now
+ 
+
+ align:start position:0%
+both the idiosyncratic and aggregate now
+this so this gets us into poor people
+
+ align:start position:0%
+this so this gets us into poor people
+ 
+
+ align:start position:0%
+this so this gets us into poor people
+and how exposed are they to
+
+ align:start position:0%
+and how exposed are they to
+ 
+
+ align:start position:0%
+and how exposed are they to
+risk we've
+
+ align:start position:0%
+risk we've
+ 
+
+ align:start position:0%
+risk we've
+seen a bit of that already in risk and
+
+ align:start position:0%
+seen a bit of that already in risk and
+ 
+
+ align:start position:0%
+seen a bit of that already in risk and
+return in Village India that there are
+
+ align:start position:0%
+return in Village India that there are
+ 
+
+ align:start position:0%
+return in Village India that there are
+some landless labors and labor income
+
+ align:start position:0%
+some landless labors and labor income
+ 
+
+ align:start position:0%
+some landless labors and labor income
+that tends to move consumption around
+
+ align:start position:0%
+that tends to move consumption around
+ 
+
+ align:start position:0%
+that tends to move consumption around
+more this is a bit different way of
+
+ align:start position:0%
+more this is a bit different way of
+ 
+
+ align:start position:0%
+more this is a bit different way of
+measuring it in the sense that we're not
+
+ align:start position:0%
+measuring it in the sense that we're not
+ 
+
+ align:start position:0%
+measuring it in the sense that we're not
+going to look so much at the consumption
+
+ align:start position:0%
+going to look so much at the consumption
+ 
+
+ align:start position:0%
+going to look so much at the consumption
+data we're going to assume everyone is
+
+ align:start position:0%
+data we're going to assume everyone is
+ 
+
+ align:start position:0%
+data we're going to assume everyone is
+in this risk sharing Syndicate but we
+
+ align:start position:0%
+in this risk sharing Syndicate but we
+ 
+
+ align:start position:0%
+in this risk sharing Syndicate but we
+turn around and see what is reflected in
+
+ align:start position:0%
+turn around and see what is reflected in
+ 
+
+ align:start position:0%
+turn around and see what is reflected in
+in rates of
+
+ align:start position:0%
+in rates of
+ 
+
+ align:start position:0%
+in rates of
+return and in particular relatively poor
+
+ align:start position:0%
+return and in particular relatively poor
+ 
+
+ align:start position:0%
+return and in particular relatively poor
+people are more exposed to to risk but
+
+ align:start position:0%
+people are more exposed to to risk but
+ 
+
+ align:start position:0%
+people are more exposed to to risk but
+it's not just their own idiosyncratic
+
+ align:start position:0%
+it's not just their own idiosyncratic
+ 
+
+ align:start position:0%
+it's not just their own idiosyncratic
+risk it's the it's the aggregate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+risk um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh there is a little bit of role for
+
+ align:start position:0%
+uh there is a little bit of role for
+ 
+
+ align:start position:0%
+uh there is a little bit of role for
+education but it's kind of problematic
+
+ align:start position:0%
+education but it's kind of problematic
+ 
+
+ align:start position:0%
+education but it's kind of problematic
+and there's some selection bias that
+
+ align:start position:0%
+and there's some selection bias that
+ 
+
+ align:start position:0%
+and there's some selection bias that
+might might talk about when we get there
+
+ align:start position:0%
+might might talk about when we get there
+ 
+
+ align:start position:0%
+might might talk about when we get there
+uh and then and then this is uh maybe
+
+ align:start position:0%
+uh and then and then this is uh maybe
+ 
+
+ align:start position:0%
+uh and then and then this is uh maybe
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+punchline uh if you want to think about
+
+ align:start position:0%
+punchline uh if you want to think about
+ 
+
+ align:start position:0%
+punchline uh if you want to think about
+Talent then you want to adjust for all
+
+ align:start position:0%
+Talent then you want to adjust for all
+ 
+
+ align:start position:0%
+Talent then you want to adjust for all
+sources of risk and when we do that we
+
+ align:start position:0%
+sources of risk and when we do that we
+ 
+
+ align:start position:0%
+sources of risk and when we do that we
+find who are seemingly the really
+
+ align:start position:0%
+find who are seemingly the really
+ 
+
+ align:start position:0%
+find who are seemingly the really
+productive people in the village and all
+
+ align:start position:0%
+productive people in the village and all
+ 
+
+ align:start position:0%
+productive people in the village and all
+of a sudden it's the higher wealth
+
+ align:start position:0%
+of a sudden it's the higher wealth
+ 
+
+ align:start position:0%
+of a sudden it's the higher wealth
+people who have the higher risk adjusted
+
+ align:start position:0%
+people who have the higher risk adjusted
+ 
+
+ align:start position:0%
+people who have the higher risk adjusted
+rate of return and female headed
+
+ align:start position:0%
+rate of return and female headed
+ 
+
+ align:start position:0%
+rate of return and female headed
+households so relatively wealthy females
+
+ align:start position:0%
+households so relatively wealthy females
+ 
+
+ align:start position:0%
+households so relatively wealthy females
+actually dominate in terms of get
+
+ align:start position:0%
+actually dominate in terms of get
+ 
+
+ align:start position:0%
+actually dominate in terms of get
+getting a higher rate of return so we
+
+ align:start position:0%
+getting a higher rate of return so we
+ 
+
+ align:start position:0%
+getting a higher rate of return so we
+have a basic model uh they're going to
+
+ align:start position:0%
+have a basic model uh they're going to
+ 
+
+ align:start position:0%
+have a basic model uh they're going to
+be J
+
+ align:start position:0%
+be J
+ 
+
+ align:start position:0%
+be J
+households uh and L production
+
+ align:start position:0%
+households uh and L production
+ 
+
+ align:start position:0%
+households uh and L production
+activities each activity uses a you
+
+ align:start position:0%
+activities each activity uses a you
+ 
+
+ align:start position:0%
+activities each activity uses a you
+utilizes Capital as an
+
+ align:start position:0%
+utilizes Capital as an
+ 
+
+ align:start position:0%
+utilizes Capital as an
+input and let's simplify and say all
+
+ align:start position:0%
+input and let's simplify and say all
+ 
+
+ align:start position:0%
+input and let's simplify and say all
+these Technologies produce the same
+
+ align:start position:0%
+these Technologies produce the same
+ 
+
+ align:start position:0%
+these Technologies produce the same
+thing consumption goods and we'll
+
+ align:start position:0%
+thing consumption goods and we'll
+ 
+
+ align:start position:0%
+thing consumption goods and we'll
+simplify further and assume all the
+
+ align:start position:0%
+simplify further and assume all the
+ 
+
+ align:start position:0%
+simplify further and assume all the
+Technologies are linear yeah Matt ask a
+
+ align:start position:0%
+Technologies are linear yeah Matt ask a
+ 
+
+ align:start position:0%
+Technologies are linear yeah Matt ask a
+couple things about the previous so um
+
+ align:start position:0%
+couple things about the previous so um
+ 
+
+ align:start position:0%
+couple things about the previous so um
+are we assuming that first thing is are
+
+ align:start position:0%
+are we assuming that first thing is are
+ 
+
+ align:start position:0%
+are we assuming that first thing is are
+we assuming there no we noar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between so we are again going to
+
+ align:start position:0%
+between so we are again going to
+ 
+
+ align:start position:0%
+between so we are again going to
+take uh a stand on
+
+ align:start position:0%
+take uh a stand on
+ 
+
+ align:start position:0%
+take uh a stand on
+our Baseline and it's actually going to
+
+ align:start position:0%
+our Baseline and it's actually going to
+ 
+
+ align:start position:0%
+our Baseline and it's actually going to
+be all four villages in a province not
+
+ align:start position:0%
+be all four villages in a province not
+ 
+
+ align:start position:0%
+be all four villages in a province not
+just a single Village but then we go
+
+ align:start position:0%
+just a single Village but then we go
+ 
+
+ align:start position:0%
+just a single Village but then we go
+back and check for villages individually
+
+ align:start position:0%
+back and check for villages individually
+ 
+
+ align:start position:0%
+back and check for villages individually
+and we actually go back further and look
+
+ align:start position:0%
+and we actually go back further and look
+ 
+
+ align:start position:0%
+and we actually go back further and look
+one network at a time the basic results
+
+ align:start position:0%
+one network at a time the basic results
+ 
+
+ align:start position:0%
+one network at a time the basic results
+don't change okay um another thing which
+
+ align:start position:0%
+don't change okay um another thing which
+ 
+
+ align:start position:0%
+don't change okay um another thing which
+I don't really understand this um when
+
+ align:start position:0%
+I don't really understand this um when
+ 
+
+ align:start position:0%
+I don't really understand this um when
+we when we have this result that the
+
+ align:start position:0%
+we when we have this result that the
+ 
+
+ align:start position:0%
+we when we have this result that the
+returns returns at lower for those with
+
+ align:start position:0%
+returns returns at lower for those with
+ 
+
+ align:start position:0%
+returns returns at lower for those with
+lower initial wealth how do we think of
+
+ align:start position:0%
+lower initial wealth how do we think of
+ 
+
+ align:start position:0%
+lower initial wealth how do we think of
+that in terms of you know one story is
+
+ align:start position:0%
+that in terms of you know one story is
+ 
+
+ align:start position:0%
+that in terms of you know one story is
+that the people with low initial wealth
+
+ align:start position:0%
+that the people with low initial wealth
+ 
+
+ align:start position:0%
+that the people with low initial wealth
+there are very productive people amongst
+
+ align:start position:0%
+there are very productive people amongst
+ 
+
+ align:start position:0%
+there are very productive people amongst
+them but they're unable to you know get
+
+ align:start position:0%
+them but they're unable to you know get
+ 
+
+ align:start position:0%
+them but they're unable to you know get
+to efficient sze of their business so
+
+ align:start position:0%
+to efficient sze of their business so
+ 
+
+ align:start position:0%
+to efficient sze of their business so
+their marginal returns might be really
+
+ align:start position:0%
+their marginal returns might be really
+ 
+
+ align:start position:0%
+their marginal returns might be really
+high and average as well depending on
+
+ align:start position:0%
+high and average as well depending on
+ 
+
+ align:start position:0%
+high and average as well depending on
+yeah so this paper isn't going to help
+
+ align:start position:0%
+yeah so this paper isn't going to help
+ 
+
+ align:start position:0%
+yeah so this paper isn't going to help
+much with that because we're going to
+
+ align:start position:0%
+much with that because we're going to
+ 
+
+ align:start position:0%
+much with that because we're going to
+assume linear Technologies and margins
+
+ align:start position:0%
+assume linear Technologies and margins
+ 
+
+ align:start position:0%
+assume linear Technologies and margins
+are going to be equal to averages okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh and and in more generally you know
+
+ align:start position:0%
+uh and and in more generally you know
+ 
+
+ align:start position:0%
+uh and and in more generally you know
+wealth is clearly an endogenous variable
+
+ align:start position:0%
+wealth is clearly an endogenous variable
+ 
+
+ align:start position:0%
+wealth is clearly an endogenous variable
+so we're not saying you know high wealth
+
+ align:start position:0%
+so we're not saying you know high wealth
+ 
+
+ align:start position:0%
+so we're not saying you know high wealth
+is causing people to have right I mean
+
+ align:start position:0%
+is causing people to have right I mean
+ 
+
+ align:start position:0%
+is causing people to have right I mean
+it's more likely the other way around
+
+ align:start position:0%
+it's more likely the other way around
+ 
+
+ align:start position:0%
+it's more likely the other way around
+but yeah we've gone through a series of
+
+ align:start position:0%
+but yeah we've gone through a series of
+ 
+
+ align:start position:0%
+but yeah we've gone through a series of
+models where wealth helps overcome
+
+ align:start position:0%
+models where wealth helps overcome
+ 
+
+ align:start position:0%
+models where wealth helps overcome
+constraints the first four lectures were
+
+ align:start position:0%
+constraints the first four lectures were
+ 
+
+ align:start position:0%
+constraints the first four lectures were
+like that um so in a way this is another
+
+ align:start position:0%
+like that um so in a way this is another
+ 
+
+ align:start position:0%
+like that um so in a way this is another
+fact finding Mission but it's not just
+
+ align:start position:0%
+fact finding Mission but it's not just
+ 
+
+ align:start position:0%
+fact finding Mission but it's not just
+data summaries it's looking at the data
+
+ align:start position:0%
+data summaries it's looking at the data
+ 
+
+ align:start position:0%
+data summaries it's looking at the data
+through the lens of the model and you
+
+ align:start position:0%
+through the lens of the model and you
+ 
+
+ align:start position:0%
+through the lens of the model and you
+have to make some assumptions to to do
+
+ align:start position:0%
+have to make some assumptions to to do
+ 
+
+ align:start position:0%
+have to make some assumptions to to do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um okay so we have J production
+
+ align:start position:0%
+um okay so we have J production
+ 
+
+ align:start position:0%
+um okay so we have J production
+activities uh we're going to start the
+
+ align:start position:0%
+activities uh we're going to start the
+ 
+
+ align:start position:0%
+activities uh we're going to start the
+economy off with some aggregate wealth
+
+ align:start position:0%
+economy off with some aggregate wealth
+ 
+
+ align:start position:0%
+economy off with some aggregate wealth
+W and and those are basically the
+
+ align:start position:0%
+W and and those are basically the
+ 
+
+ align:start position:0%
+W and and those are basically the
+projects the assets or the trees if you
+
+ align:start position:0%
+projects the assets or the trees if you
+ 
+
+ align:start position:0%
+projects the assets or the trees if you
+like and uh and those projects are going
+
+ align:start position:0%
+like and uh and those projects are going
+ 
+
+ align:start position:0%
+like and uh and those projects are going
+to have rates to return the
+
+ align:start position:0%
+to have rates to return the
+ 
+
+ align:start position:0%
+to have rates to return the
+fruit uh so at the beginning of the
+
+ align:start position:0%
+fruit uh so at the beginning of the
+ 
+
+ align:start position:0%
+fruit uh so at the beginning of the
+period the the total sort of wealth
+
+ align:start position:0%
+period the the total sort of wealth
+ 
+
+ align:start position:0%
+period the the total sort of wealth
+available is the sum of the the trees
+
+ align:start position:0%
+available is the sum of the the trees
+ 
+
+ align:start position:0%
+available is the sum of the the trees
+and the fruits so this is a standard
+
+ align:start position:0%
+and the fruits so this is a standard
+ 
+
+ align:start position:0%
+and the fruits so this is a standard
+kind of
+
+ align:start position:0%
+kind of
+ 
+
+ align:start position:0%
+kind of
+solo reversible Capital assumption that
+
+ align:start position:0%
+solo reversible Capital assumption that
+ 
+
+ align:start position:0%
+solo reversible Capital assumption that
+the assets can basically be be sold
+
+ align:start position:0%
+the assets can basically be be sold
+ 
+
+ align:start position:0%
+the assets can basically be be sold
+there's no irreversibility you can
+
+ align:start position:0%
+there's no irreversibility you can
+ 
+
+ align:start position:0%
+there's no irreversibility you can
+convert them into consumption if you
+
+ align:start position:0%
+convert them into consumption if you
+ 
+
+ align:start position:0%
+convert them into consumption if you
+choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to uh so we're going to have a social
+
+ align:start position:0%
+to uh so we're going to have a social
+ 
+
+ align:start position:0%
+to uh so we're going to have a social
+planner sort of directing the
+
+ align:start position:0%
+planner sort of directing the
+ 
+
+ align:start position:0%
+planner sort of directing the
+show uh which is not to say this might
+
+ align:start position:0%
+show uh which is not to say this might
+ 
+
+ align:start position:0%
+show uh which is not to say this might
+not decentralize in some way that said I
+
+ align:start position:0%
+not decentralize in some way that said I
+ 
+
+ align:start position:0%
+not decentralize in some way that said I
+want to emphasize it's
+
+ align:start position:0%
+want to emphasize it's
+ 
+
+ align:start position:0%
+want to emphasize it's
+not like Finance in the sense that
+
+ align:start position:0%
+not like Finance in the sense that
+ 
+
+ align:start position:0%
+not like Finance in the sense that
+people participate on the you know New
+
+ align:start position:0%
+people participate on the you know New
+ 
+
+ align:start position:0%
+people participate on the you know New
+York Stock Exchange or the financial
+
+ align:start position:0%
+York Stock Exchange or the financial
+ 
+
+ align:start position:0%
+York Stock Exchange or the financial
+markets and they're buying selling
+
+ align:start position:0%
+markets and they're buying selling
+ 
+
+ align:start position:0%
+markets and they're buying selling
+stocks we don't even have the data of
+
+ align:start position:0%
+stocks we don't even have the data of
+ 
+
+ align:start position:0%
+stocks we don't even have the data of
+all these capital goods that's not the
+
+ align:start position:0%
+all these capital goods that's not the
+ 
+
+ align:start position:0%
+all these capital goods that's not the
+mechanism uh this planner's problem may
+
+ align:start position:0%
+mechanism uh this planner's problem may
+ 
+
+ align:start position:0%
+mechanism uh this planner's problem may
+be decentralized in some way but it's
+
+ align:start position:0%
+be decentralized in some way but it's
+ 
+
+ align:start position:0%
+be decentralized in some way but it's
+just much more straightforward just like
+
+ align:start position:0%
+just much more straightforward just like
+ 
+
+ align:start position:0%
+just much more straightforward just like
+when we did the risk sharing stuff not
+
+ align:start position:0%
+when we did the risk sharing stuff not
+ 
+
+ align:start position:0%
+when we did the risk sharing stuff not
+to necessarily be forced into you know
+
+ align:start position:0%
+to necessarily be forced into you know
+ 
+
+ align:start position:0%
+to necessarily be forced into you know
+some interpretation we're just going to
+
+ align:start position:0%
+some interpretation we're just going to
+ 
+
+ align:start position:0%
+some interpretation we're just going to
+solve the planning problem directly
+
+ align:start position:0%
+solve the planning problem directly
+ 
+
+ align:start position:0%
+solve the planning problem directly
+so somehow or other a household is
+
+ align:start position:0%
+so somehow or other a household is
+ 
+
+ align:start position:0%
+so somehow or other a household is
+assigned household J is
+
+ align:start position:0%
+assigned household J is
+ 
+
+ align:start position:0%
+assigned household J is
+assigned capital and is operating
+
+ align:start position:0%
+assigned capital and is operating
+ 
+
+ align:start position:0%
+assigned capital and is operating
+project type I and this is the net rate
+
+ align:start position:0%
+project type I and this is the net rate
+ 
+
+ align:start position:0%
+project type I and this is the net rate
+of return notice that we allow
+
+ align:start position:0%
+of return notice that we allow
+ 
+
+ align:start position:0%
+of return notice that we allow
+individuals to vary in their rates of
+
+ align:start position:0%
+individuals to vary in their rates of
+ 
+
+ align:start position:0%
+individuals to vary in their rates of
+return the planner could take advantage
+
+ align:start position:0%
+return the planner could take advantage
+ 
+
+ align:start position:0%
+return the planner could take advantage
+if it if it knows that some people are
+
+ align:start position:0%
+if it if it knows that some people are
+ 
+
+ align:start position:0%
+if it if it knows that some people are
+better than other people at doing things
+
+ align:start position:0%
+better than other people at doing things
+ 
+
+ align:start position:0%
+better than other people at doing things
+so we're not just getting rid of talent
+
+ align:start position:0%
+so we're not just getting rid of talent
+ 
+
+ align:start position:0%
+so we're not just getting rid of talent
+we're
+
+ align:start position:0%
+we're
+ 
+
+ align:start position:0%
+we're
+embedding it at some level in these
+
+ align:start position:0%
+embedding it at some level in these
+ 
+
+ align:start position:0%
+embedding it at some level in these
+rates of
+
+ align:start position:0%
+rates of
+ 
+
+ align:start position:0%
+rates of
+return and then they you know they have
+
+ align:start position:0%
+return and then they you know they have
+ 
+
+ align:start position:0%
+return and then they you know they have
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+um the tree and the and the and the
+
+ align:start position:0%
+um the tree and the and the and the
+ 
+
+ align:start position:0%
+um the tree and the and the and the
+fruit that's their starting point and
+
+ align:start position:0%
+fruit that's their starting point and
+ 
+
+ align:start position:0%
+fruit that's their starting point and
+then they get taxes and transfers these
+
+ align:start position:0%
+then they get taxes and transfers these
+ 
+
+ align:start position:0%
+then they get taxes and transfers these
+tows I mean here it's written positive
+
+ align:start position:0%
+tows I mean here it's written positive
+ 
+
+ align:start position:0%
+tows I mean here it's written positive
+as it's as if it's incoming and adds to
+
+ align:start position:0%
+as it's as if it's incoming and adds to
+ 
+
+ align:start position:0%
+as it's as if it's incoming and adds to
+the resources of the household but in
+
+ align:start position:0%
+the resources of the household but in
+ 
+
+ align:start position:0%
+the resources of the household but in
+fact the planner you know like a RIS
+
+ align:start position:0%
+fact the planner you know like a RIS
+ 
+
+ align:start position:0%
+fact the planner you know like a RIS
+sharing group you can give and get and
+
+ align:start position:0%
+sharing group you can give and get and
+ 
+
+ align:start position:0%
+sharing group you can give and get and
+contribute to to the social
+
+ align:start position:0%
+contribute to to the social
+ 
+
+ align:start position:0%
+contribute to to the social
+fund so the planning problem is to
+
+ align:start position:0%
+fund so the planning problem is to
+ 
+
+ align:start position:0%
+fund so the planning problem is to
+maximize discounted weighted expected
+
+ align:start position:0%
+maximize discounted weighted expected
+ 
+
+ align:start position:0%
+maximize discounted weighted expected
+utilities so these these Lambda J
+
+ align:start position:0%
+utilities so these these Lambda J
+ 
+
+ align:start position:0%
+utilities so these these Lambda J
+weights are the par weights for
+
+ align:start position:0%
+weights are the par weights for
+ 
+
+ align:start position:0%
+weights are the par weights for
+households type J they're not
+
+ align:start position:0%
+households type J they're not
+ 
+
+ align:start position:0%
+households type J they're not
+necessarily the same over all the
+
+ align:start position:0%
+necessarily the same over all the
+ 
+
+ align:start position:0%
+necessarily the same over all the
+households and this whole term here is
+
+ align:start position:0%
+households and this whole term here is
+ 
+
+ align:start position:0%
+households and this whole term here is
+the utility function which as noted is
+
+ align:start position:0%
+the utility function which as noted is
+ 
+
+ align:start position:0%
+the utility function which as noted is
+just the return on the trees you know
+
+ align:start position:0%
+just the return on the trees you know
+ 
+
+ align:start position:0%
+just the return on the trees you know
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+um plus these
+
+ align:start position:0%
+um plus these
+ 
+
+ align:start position:0%
+um plus these
+transfers um and then
+
+ align:start position:0%
+transfers um and then
+ 
+
+ align:start position:0%
+transfers um and then
+discounted uh expected return for
+
+ align:start position:0%
+discounted uh expected return for
+ 
+
+ align:start position:0%
+discounted uh expected return for
+tomorrow um
+
+ align:start position:0%
+tomorrow um
+ 
+
+ align:start position:0%
+tomorrow um
+fee I usually right is beta but anyway
+
+ align:start position:0%
+fee I usually right is beta but anyway
+ 
+
+ align:start position:0%
+fee I usually right is beta but anyway
+it's it's a intertemporal discount rate
+
+ align:start position:0%
+it's it's a intertemporal discount rate
+ 
+
+ align:start position:0%
+it's it's a intertemporal discount rate
+uh and so you have the value function
+
+ align:start position:0%
+uh and so you have the value function
+ 
+
+ align:start position:0%
+uh and so you have the value function
+today given wealth today and
+
+ align:start position:0%
+today given wealth today and
+ 
+
+ align:start position:0%
+today given wealth today and
+expected value of wealth tomorrow
+
+ align:start position:0%
+expected value of wealth tomorrow
+ 
+
+ align:start position:0%
+expected value of wealth tomorrow
+wpra and you know wealth today can be
+
+ align:start position:0%
+wpra and you know wealth today can be
+ 
+
+ align:start position:0%
+wpra and you know wealth today can be
+allocated into basically consumption so
+
+ align:start position:0%
+allocated into basically consumption so
+ 
+
+ align:start position:0%
+allocated into basically consumption so
+this is just summing over not only over
+
+ align:start position:0%
+this is just summing over not only over
+ 
+
+ align:start position:0%
+this is just summing over not only over
+all projects for household J but all
+
+ align:start position:0%
+all projects for household J but all
+ 
+
+ align:start position:0%
+all projects for household J but all
+households J so this is again just
+
+ align:start position:0%
+households J so this is again just
+ 
+
+ align:start position:0%
+households J so this is again just
+consumption so consumption plus Capital
+
+ align:start position:0%
+consumption so consumption plus Capital
+ 
+
+ align:start position:0%
+consumption so consumption plus Capital
+allocated tomorrow equals total wealth
+
+ align:start position:0%
+allocated tomorrow equals total wealth
+ 
+
+ align:start position:0%
+allocated tomorrow equals total wealth
+pretty standard kind of
+
+ align:start position:0%
+pretty standard kind of
+ 
+
+ align:start position:0%
+pretty standard kind of
+growth Market
+
+ align:start position:0%
+growth Market
+ 
+
+ align:start position:0%
+growth Market
+structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and you know what is total wealth of
+
+ align:start position:0%
+uh and you know what is total wealth of
+ 
+
+ align:start position:0%
+uh and you know what is total wealth of
+the economy it's basically not only the
+
+ align:start position:0%
+the economy it's basically not only the
+ 
+
+ align:start position:0%
+the economy it's basically not only the
+fruit of the trees but the trees
+
+ align:start position:0%
+fruit of the trees but the trees
+ 
+
+ align:start position:0%
+fruit of the trees but the trees
+themselves
+
+ align:start position:0%
+themselves
+ 
+
+ align:start position:0%
+themselves
+um so you can take this expression and
+
+ align:start position:0%
+um so you can take this expression and
+ 
+
+ align:start position:0%
+um so you can take this expression and
+put it on the right hand side if you
+
+ align:start position:0%
+put it on the right hand side if you
+ 
+
+ align:start position:0%
+put it on the right hand side if you
+want okay they have pre-existing Capital
+
+ align:start position:0%
+want okay they have pre-existing Capital
+ 
+
+ align:start position:0%
+want okay they have pre-existing Capital
+they have the rate of return on that we
+
+ align:start position:0%
+they have the rate of return on that we
+ 
+
+ align:start position:0%
+they have the rate of return on that we
+got total resources available you can
+
+ align:start position:0%
+got total resources available you can
+ 
+
+ align:start position:0%
+got total resources available you can
+allocate it to consumption or set some
+
+ align:start position:0%
+allocate it to consumption or set some
+ 
+
+ align:start position:0%
+allocate it to consumption or set some
+aside to continue the Capital stock for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tomorrow
+
+ align:start position:0%
+tomorrow
+ 
+
+ align:start position:0%
+tomorrow
+uh and so we just substitute in the
+
+ align:start position:0%
+uh and so we just substitute in the
+ 
+
+ align:start position:0%
+uh and so we just substitute in the
+expressions
+
+ align:start position:0%
+expressions
+ 
+
+ align:start position:0%
+expressions
+for uh you know tomorrow's wealth and uh
+
+ align:start position:0%
+for uh you know tomorrow's wealth and uh
+ 
+
+ align:start position:0%
+for uh you know tomorrow's wealth and uh
+and today's well for that matter uh and
+
+ align:start position:0%
+and today's well for that matter uh and
+ 
+
+ align:start position:0%
+and today's well for that matter uh and
+then this oddl looking thing here is
+
+ align:start position:0%
+then this oddl looking thing here is
+ 
+
+ align:start position:0%
+then this oddl looking thing here is
+just a substitution from the previous
+
+ align:start position:0%
+just a substitution from the previous
+ 
+
+ align:start position:0%
+just a substitution from the previous
+equation but there's a a common term on
+
+ align:start position:0%
+equation but there's a a common term on
+ 
+
+ align:start position:0%
+equation but there's a a common term on
+both sides it looks that's why it looks
+
+ align:start position:0%
+both sides it looks that's why it looks
+ 
+
+ align:start position:0%
+both sides it looks that's why it looks
+kind of weird because there's a this is
+
+ align:start position:0%
+kind of weird because there's a this is
+ 
+
+ align:start position:0%
+kind of weird because there's a this is
+really you know 1+ R * K over here but
+
+ align:start position:0%
+really you know 1+ R * K over here but
+ 
+
+ align:start position:0%
+really you know 1+ R * K over here but
+there's also a 1 plus r * K here and the
+
+ align:start position:0%
+there's also a 1 plus r * K here and the
+ 
+
+ align:start position:0%
+there's also a 1 plus r * K here and the
+r k things are canceling out so this
+
+ align:start position:0%
+r k things are canceling out so this
+ 
+
+ align:start position:0%
+r k things are canceling out so this
+this is uh just straightforward algebra
+
+ align:start position:0%
+this is uh just straightforward algebra
+ 
+
+ align:start position:0%
+this is uh just straightforward algebra
+so we're going to maximize this thing by
+
+ align:start position:0%
+so we're going to maximize this thing by
+ 
+
+ align:start position:0%
+so we're going to maximize this thing by
+choosing the transfers to J and the
+
+ align:start position:0%
+choosing the transfers to J and the
+ 
+
+ align:start position:0%
+choosing the transfers to J and the
+assignments of tomorrow's Capital
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stock
+
+ align:start position:0%
+stock
+ 
+
+ align:start position:0%
+stock
+yeah yeah there's no preference shocks
+
+ align:start position:0%
+yeah yeah there's no preference shocks
+ 
+
+ align:start position:0%
+yeah yeah there's no preference shocks
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or don't have to specify
+
+ align:start position:0%
+or don't have to specify
+ 
+
+ align:start position:0%
+or don't have to specify
+yet that's probably a good thing okay so
+
+ align:start position:0%
+yet that's probably a good thing okay so
+ 
+
+ align:start position:0%
+yet that's probably a good thing okay so
+so if you
+
+ align:start position:0%
+so if you
+ 
+
+ align:start position:0%
+so if you
+looked uh we've actually seen this
+
+ align:start position:0%
+looked uh we've actually seen this
+ 
+
+ align:start position:0%
+looked uh we've actually seen this
+before but it's explicit here
+
+ align:start position:0%
+before but it's explicit here
+ 
+
+ align:start position:0%
+before but it's explicit here
+again uh consumption and capital are
+
+ align:start position:0%
+again uh consumption and capital are
+ 
+
+ align:start position:0%
+again uh consumption and capital are
+interrelated through this resource
+
+ align:start position:0%
+interrelated through this resource
+ 
+
+ align:start position:0%
+interrelated through this resource
+constraint so when you take a
+
+ align:start position:0%
+constraint so when you take a
+ 
+
+ align:start position:0%
+constraint so when you take a
+derivative to maximize with respect to
+
+ align:start position:0%
+derivative to maximize with respect to
+ 
+
+ align:start position:0%
+derivative to maximize with respect to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+transfers you know you'll pick up a
+
+ align:start position:0%
+transfers you know you'll pick up a
+ 
+
+ align:start position:0%
+transfers you know you'll pick up a
+derivative in the utility
+
+ align:start position:0%
+derivative in the utility
+ 
+
+ align:start position:0%
+derivative in the utility
+function and uh you know the sum of
+
+ align:start position:0%
+function and uh you know the sum of
+ 
+
+ align:start position:0%
+function and uh you know the sum of
+total transfers is down here in the
+
+ align:start position:0%
+total transfers is down here in the
+ 
+
+ align:start position:0%
+total transfers is down here in the
+resource constraint and there's a lrange
+
+ align:start position:0%
+resource constraint and there's a lrange
+ 
+
+ align:start position:0%
+resource constraint and there's a lrange
+multiplier in front of it right so
+
+ align:start position:0%
+multiplier in front of it right so
+ 
+
+ align:start position:0%
+multiplier in front of it right so
+you're going to get margin weighted
+
+ align:start position:0%
+you're going to get margin weighted
+ 
+
+ align:start position:0%
+you're going to get margin weighted
+margin utility of consumption today
+
+ align:start position:0%
+margin utility of consumption today
+ 
+
+ align:start position:0%
+margin utility of consumption today
+equal to a LR multiplier and when you
+
+ align:start position:0%
+equal to a LR multiplier and when you
+ 
+
+ align:start position:0%
+equal to a LR multiplier and when you
+differentiate with respect
+
+ align:start position:0%
+differentiate with respect
+ 
+
+ align:start position:0%
+differentiate with respect
+to the choice of tomorrow's Capital
+
+ align:start position:0%
+to the choice of tomorrow's Capital
+ 
+
+ align:start position:0%
+to the choice of tomorrow's Capital
+stock K Prime well that's going to enter
+
+ align:start position:0%
+stock K Prime well that's going to enter
+ 
+
+ align:start position:0%
+stock K Prime well that's going to enter
+in tomorrow's value so you'll have a
+
+ align:start position:0%
+in tomorrow's value so you'll have a
+ 
+
+ align:start position:0%
+in tomorrow's value so you'll have a
+derivative of the value
+
+ align:start position:0%
+derivative of the value
+ 
+
+ align:start position:0%
+derivative of the value
+function and then internally this sort
+
+ align:start position:0%
+function and then internally this sort
+ 
+
+ align:start position:0%
+function and then internally this sort
+of rate of
+
+ align:start position:0%
+of rate of
+ 
+
+ align:start position:0%
+of rate of
+return and you know that's also entering
+
+ align:start position:0%
+return and you know that's also entering
+ 
+
+ align:start position:0%
+return and you know that's also entering
+this Prime thing is also entering into
+
+ align:start position:0%
+this Prime thing is also entering into
+ 
+
+ align:start position:0%
+this Prime thing is also entering into
+the the same resource constraint so
+
+ align:start position:0%
+the the same resource constraint so
+ 
+
+ align:start position:0%
+the the same resource constraint so
+you're going to get the same lrange
+
+ align:start position:0%
+you're going to get the same lrange
+ 
+
+ align:start position:0%
+you're going to get the same lrange
+multiplier uh as on consumption and that
+
+ align:start position:0%
+multiplier uh as on consumption and that
+ 
+
+ align:start position:0%
+multiplier uh as on consumption and that
+so here's a summary of those
+
+ align:start position:0%
+so here's a summary of those
+ 
+
+ align:start position:0%
+so here's a summary of those
+words weighted margin utilities are
+
+ align:start position:0%
+words weighted margin utilities are
+ 
+
+ align:start position:0%
+words weighted margin utilities are
+equated across all the households to a
+
+ align:start position:0%
+equated across all the households to a
+ 
+
+ align:start position:0%
+equated across all the households to a
+common contemporaneous lrange
+
+ align:start position:0%
+common contemporaneous lrange
+ 
+
+ align:start position:0%
+common contemporaneous lrange
+multiplier and then this is kind of
+
+ align:start position:0%
+multiplier and then this is kind of
+ 
+
+ align:start position:0%
+multiplier and then this is kind of
+a it's an exactly Oiler equation for
+
+ align:start position:0%
+a it's an exactly Oiler equation for
+ 
+
+ align:start position:0%
+a it's an exactly Oiler equation for
+capital accumulation you know this is
+
+ align:start position:0%
+capital accumulation you know this is
+ 
+
+ align:start position:0%
+capital accumulation you know this is
+the the price of capital today it's how
+
+ align:start position:0%
+the the price of capital today it's how
+ 
+
+ align:start position:0%
+the the price of capital today it's how
+much consumption you're giving up and
+
+ align:start position:0%
+much consumption you're giving up and
+ 
+
+ align:start position:0%
+much consumption you're giving up and
+this is expected discounted value of
+
+ align:start position:0%
+this is expected discounted value of
+ 
+
+ align:start position:0%
+this is expected discounted value of
+having uh Capital tomorrow it's the
+
+ align:start position:0%
+having uh Capital tomorrow it's the
+ 
+
+ align:start position:0%
+having uh Capital tomorrow it's the
+derivative of the value function times
+
+ align:start position:0%
+derivative of the value function times
+ 
+
+ align:start position:0%
+derivative of the value function times
+the rate of return depending on which
+
+ align:start position:0%
+the rate of return depending on which
+ 
+
+ align:start position:0%
+the rate of return depending on which
+project I and J is being chosen note
+
+ align:start position:0%
+project I and J is being chosen note
+ 
+
+ align:start position:0%
+project I and J is being chosen note
+that this is for every
+
+ align:start position:0%
+that this is for every
+ 
+
+ align:start position:0%
+that this is for every
+project uh every Capital stock of type I
+
+ align:start position:0%
+project uh every Capital stock of type I
+ 
+
+ align:start position:0%
+project uh every Capital stock of type I
+for household J
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now so far I've talked about real assets
+
+ align:start position:0%
+now so far I've talked about real assets
+ 
+
+ align:start position:0%
+now so far I've talked about real assets
+but uh it's not too hard and we do
+
+ align:start position:0%
+but uh it's not too hard and we do
+ 
+
+ align:start position:0%
+but uh it's not too hard and we do
+actually allow external borrowing you
+
+ align:start position:0%
+actually allow external borrowing you
+ 
+
+ align:start position:0%
+actually allow external borrowing you
+could imagine a village is able to
+
+ align:start position:0%
+could imagine a village is able to
+ 
+
+ align:start position:0%
+could imagine a village is able to
+borrow in lend or the whole set of four
+
+ align:start position:0%
+borrow in lend or the whole set of four
+ 
+
+ align:start position:0%
+borrow in lend or the whole set of four
+Villages have some relationship with the
+
+ align:start position:0%
+Villages have some relationship with the
+ 
+
+ align:start position:0%
+Villages have some relationship with the
+rest of the external economy that still
+
+ align:start position:0%
+rest of the external economy that still
+ 
+
+ align:start position:0%
+rest of the external economy that still
+leaves this sub
+
+ align:start position:0%
+leaves this sub
+ 
+
+ align:start position:0%
+leaves this sub
+problem uh I mean throwing these things
+
+ align:start position:0%
+problem uh I mean throwing these things
+ 
+
+ align:start position:0%
+problem uh I mean throwing these things
+in might deliver some extra conditions
+
+ align:start position:0%
+in might deliver some extra conditions
+ 
+
+ align:start position:0%
+in might deliver some extra conditions
+that we're ignoring but what we're doing
+
+ align:start position:0%
+that we're ignoring but what we're doing
+ 
+
+ align:start position:0%
+that we're ignoring but what we're doing
+is not inconsistent with having this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation all right
+
+ align:start position:0%
+equation all right
+ 
+
+ align:start position:0%
+equation all right
+so if you just
+
+ align:start position:0%
+so if you just
+ 
+
+ align:start position:0%
+so if you just
+take this one and divide both sides
+
+ align:start position:0%
+take this one and divide both sides
+ 
+
+ align:start position:0%
+take this one and divide both sides
+through by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mu you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+um and then you take the expect
+
+ align:start position:0%
+um and then you take the expect
+ 
+
+ align:start position:0%
+um and then you take the expect
+operator in front of everything
+
+ align:start position:0%
+operator in front of everything
+ 
+
+ align:start position:0%
+operator in front of everything
+including mu even though it's not random
+
+ align:start position:0%
+including mu even though it's not random
+ 
+
+ align:start position:0%
+including mu even though it's not random
+from the point of date
+
+ align:start position:0%
+from the point of date
+ 
+
+ align:start position:0%
+from the point of date
+T and then you can
+
+ align:start position:0%
+T and then you can
+ 
+
+ align:start position:0%
+T and then you can
+rewrite uh this guy here as something
+
+ align:start position:0%
+rewrite uh this guy here as something
+ 
+
+ align:start position:0%
+rewrite uh this guy here as something
+called M or M Prime since in effect it's
+
+ align:start position:0%
+called M or M Prime since in effect it's
+ 
+
+ align:start position:0%
+called M or M Prime since in effect it's
+for tomorrow and this R Prime i j is
+
+ align:start position:0%
+for tomorrow and this R Prime i j is
+ 
+
+ align:start position:0%
+for tomorrow and this R Prime i j is
+basically uh you know capital r is
+
+ align:start position:0%
+basically uh you know capital r is
+ 
+
+ align:start position:0%
+basically uh you know capital r is
+little r 1 plus little r sort of the
+
+ align:start position:0%
+little r 1 plus little r sort of the
+ 
+
+ align:start position:0%
+little r 1 plus little r sort of the
+gross rate of return
+
+ align:start position:0%
+gross rate of return
+ 
+
+ align:start position:0%
+gross rate of return
+okay so this
+
+ align:start position:0%
+okay so this
+ 
+
+ align:start position:0%
+okay so this
+is hopefully not mysterious it's just
+
+ align:start position:0%
+is hopefully not mysterious it's just
+ 
+
+ align:start position:0%
+is hopefully not mysterious it's just
+basically uh a relabeling of variables
+
+ align:start position:0%
+basically uh a relabeling of variables
+ 
+
+ align:start position:0%
+basically uh a relabeling of variables
+and it's like the oiler
+
+ align:start position:0%
+and it's like the oiler
+ 
+
+ align:start position:0%
+and it's like the oiler
+equation but if you want to impress your
+
+ align:start position:0%
+equation but if you want to impress your
+ 
+
+ align:start position:0%
+equation but if you want to impress your
+friends and bewilder your enemies you
+
+ align:start position:0%
+friends and bewilder your enemies you
+ 
+
+ align:start position:0%
+friends and bewilder your enemies you
+call this thing the stochastic discount
+
+ align:start position:0%
+call this thing the stochastic discount
+ 
+
+ align:start position:0%
+call this thing the stochastic discount
+Factor but all all it is is the way
+
+ align:start position:0%
+Factor but all all it is is the way
+ 
+
+ align:start position:0%
+Factor but all all it is is the way
+society as a whole is discounting the
+
+ align:start position:0%
+society as a whole is discounting the
+ 
+
+ align:start position:0%
+society as a whole is discounting the
+future it's tomorrow's
+
+ align:start position:0%
+future it's tomorrow's
+ 
+
+ align:start position:0%
+future it's tomorrow's
+sort of Shadow price of resources
+
+ align:start position:0%
+sort of Shadow price of resources
+ 
+
+ align:start position:0%
+sort of Shadow price of resources
+relative to today's so you're
+
+ align:start position:0%
+relative to today's so you're
+ 
+
+ align:start position:0%
+relative to today's so you're
+discounting tomorrow and it's random
+
+ align:start position:0%
+discounting tomorrow and it's random
+ 
+
+ align:start position:0%
+discounting tomorrow and it's random
+because these rates of return are random
+
+ align:start position:0%
+because these rates of return are random
+ 
+
+ align:start position:0%
+because these rates of return are random
+and so the amount of resources available
+
+ align:start position:0%
+and so the amount of resources available
+ 
+
+ align:start position:0%
+and so the amount of resources available
+in the economy is likely random so it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stochastic there's a danger in talking
+
+ align:start position:0%
+stochastic there's a danger in talking
+ 
+
+ align:start position:0%
+stochastic there's a danger in talking
+to someone about stochastic discount
+
+ align:start position:0%
+to someone about stochastic discount
+ 
+
+ align:start position:0%
+to someone about stochastic discount
+factors because you know you're going to
+
+ align:start position:0%
+factors because you know you're going to
+ 
+
+ align:start position:0%
+factors because you know you're going to
+the ation will keep going and you may
+
+ align:start position:0%
+the ation will keep going and you may
+ 
+
+ align:start position:0%
+the ation will keep going and you may
+learn more or get bewildered but anyway
+
+ align:start position:0%
+learn more or get bewildered but anyway
+ 
+
+ align:start position:0%
+learn more or get bewildered but anyway
+as promised we'll keep track of
+
+ align:start position:0%
+as promised we'll keep track of
+ 
+
+ align:start position:0%
+as promised we'll keep track of
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so it's true for all households all
+
+ align:start position:0%
+um so it's true for all households all
+ 
+
+ align:start position:0%
+um so it's true for all households all
+sectors
+
+ align:start position:0%
+sectors
+ 
+
+ align:start position:0%
+sectors
+and the finance jargon is we just looked
+
+ align:start position:0%
+and the finance jargon is we just looked
+ 
+
+ align:start position:0%
+and the finance jargon is we just looked
+at something called the pricing equation
+
+ align:start position:0%
+at something called the pricing equation
+ 
+
+ align:start position:0%
+at something called the pricing equation
+in the consumption-based asset pricing
+
+ align:start position:0%
+in the consumption-based asset pricing
+ 
+
+ align:start position:0%
+in the consumption-based asset pricing
+world but for us just an Oiler equation
+
+ align:start position:0%
+world but for us just an Oiler equation
+ 
+
+ align:start position:0%
+world but for us just an Oiler equation
+you know holding at say the village or
+
+ align:start position:0%
+you know holding at say the village or
+ 
+
+ align:start position:0%
+you know holding at say the village or
+let's call it Township
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level uh another thing you may or may
+
+ align:start position:0%
+level uh another thing you may or may
+ 
+
+ align:start position:0%
+level uh another thing you may or may
+not know or remember from Finance is you
+
+ align:start position:0%
+not know or remember from Finance is you
+ 
+
+ align:start position:0%
+not know or remember from Finance is you
+can take assets and bundle them right so
+
+ align:start position:0%
+can take assets and bundle them right so
+ 
+
+ align:start position:0%
+can take assets and bundle them right so
+you can have a particular asset held by
+
+ align:start position:0%
+you can have a particular asset held by
+ 
+
+ align:start position:0%
+you can have a particular asset held by
+a particular household a project or you
+
+ align:start position:0%
+a particular household a project or you
+ 
+
+ align:start position:0%
+a particular household a project or you
+could take a collection of assets you
+
+ align:start position:0%
+could take a collection of assets you
+ 
+
+ align:start position:0%
+could take a collection of assets you
+know that that Oiler equation has to
+
+ align:start position:0%
+know that that Oiler equation has to
+ 
+
+ align:start position:0%
+know that that Oiler equation has to
+hold for any asset individual and all
+
+ align:start position:0%
+hold for any asset individual and all
+ 
+
+ align:start position:0%
+hold for any asset individual and all
+assets collectively you can bundle
+
+ align:start position:0%
+assets collectively you can bundle
+ 
+
+ align:start position:0%
+assets collectively you can bundle
+package rebundle any way you want and
+
+ align:start position:0%
+package rebundle any way you want and
+ 
+
+ align:start position:0%
+package rebundle any way you want and
+anything that's actually
+
+ align:start position:0%
+anything that's actually
+ 
+
+ align:start position:0%
+anything that's actually
+held by the way there's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another there're sort of out of
+
+ align:start position:0%
+another there're sort of out of
+ 
+
+ align:start position:0%
+another there're sort of out of
+equilibrium projects we're not seeing
+
+ align:start position:0%
+equilibrium projects we're not seeing
+ 
+
+ align:start position:0%
+equilibrium projects we're not seeing
+they wouldn't satisfy the oiler
+
+ align:start position:0%
+they wouldn't satisfy the oiler
+ 
+
+ align:start position:0%
+they wouldn't satisfy the oiler
+equation you know that they have a low
+
+ align:start position:0%
+equation you know that they have a low
+ 
+
+ align:start position:0%
+equation you know that they have a low
+rate of return relative to the other
+
+ align:start position:0%
+rate of return relative to the other
+ 
+
+ align:start position:0%
+rate of return relative to the other
+ones so we're only seeing these
+
+ align:start position:0%
+ones so we're only seeing these
+ 
+
+ align:start position:0%
+ones so we're only seeing these
+equilibrium ones that the households
+
+ align:start position:0%
+equilibrium ones that the households
+ 
+
+ align:start position:0%
+equilibrium ones that the households
+actually hold and of course we're
+
+ align:start position:0%
+actually hold and of course we're
+ 
+
+ align:start position:0%
+actually hold and of course we're
+looking at the data what they they
+
+ align:start position:0%
+looking at the data what they they
+ 
+
+ align:start position:0%
+looking at the data what they they
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+hold I'm mentioning this bundling
+
+ align:start position:0%
+hold I'm mentioning this bundling
+ 
+
+ align:start position:0%
+hold I'm mentioning this bundling
+because and you'll see it again but we
+
+ align:start position:0%
+because and you'll see it again but we
+ 
+
+ align:start position:0%
+because and you'll see it again but we
+might as well get our minds around it
+
+ align:start position:0%
+might as well get our minds around it
+ 
+
+ align:start position:0%
+might as well get our minds around it
+here we are going to look at a
+
+ align:start position:0%
+here we are going to look at a
+ 
+
+ align:start position:0%
+here we are going to look at a
+households rate of return and typical
+
+ align:start position:0%
+households rate of return and typical
+ 
+
+ align:start position:0%
+households rate of return and typical
+households as you know you've already
+
+ align:start position:0%
+households as you know you've already
+ 
+
+ align:start position:0%
+households as you know you've already
+seen this are doing more than one thing
+
+ align:start position:0%
+seen this are doing more than one thing
+ 
+
+ align:start position:0%
+seen this are doing more than one thing
+they're they you know some of the
+
+ align:start position:0%
+they're they you know some of the
+ 
+
+ align:start position:0%
+they're they you know some of the
+incoming money is from labor Supply they
+
+ align:start position:0%
+incoming money is from labor Supply they
+ 
+
+ align:start position:0%
+incoming money is from labor Supply they
+have crops maybe multiple crops some of
+
+ align:start position:0%
+have crops maybe multiple crops some of
+ 
+
+ align:start position:0%
+have crops maybe multiple crops some of
+them have both that and a business and
+
+ align:start position:0%
+them have both that and a business and
+ 
+
+ align:start position:0%
+them have both that and a business and
+so on uh we try very hard
+
+ align:start position:0%
+so on uh we try very hard
+ 
+
+ align:start position:0%
+so on uh we try very hard
+to assign these assets individually to
+
+ align:start position:0%
+to assign these assets individually to
+ 
+
+ align:start position:0%
+to assign these assets individually to
+particular activities but it's kind of
+
+ align:start position:0%
+particular activities but it's kind of
+ 
+
+ align:start position:0%
+particular activities but it's kind of
+treacherous and we're likely to make
+
+ align:start position:0%
+treacherous and we're likely to make
+ 
+
+ align:start position:0%
+treacherous and we're likely to make
+mistakes what do you do with a pickup
+
+ align:start position:0%
+mistakes what do you do with a pickup
+ 
+
+ align:start position:0%
+mistakes what do you do with a pickup
+truck for example is that just using
+
+ align:start position:0%
+truck for example is that just using
+ 
+
+ align:start position:0%
+truck for example is that just using
+farming or you know they're going to the
+
+ align:start position:0%
+farming or you know they're going to the
+ 
+
+ align:start position:0%
+farming or you know they're going to the
+bank they're taking the kids to school
+
+ align:start position:0%
+bank they're taking the kids to school
+ 
+
+ align:start position:0%
+bank they're taking the kids to school
+and uh so rather than face all of that
+
+ align:start position:0%
+and uh so rather than face all of that
+ 
+
+ align:start position:0%
+and uh so rather than face all of that
+we just aggregate up over all the
+
+ align:start position:0%
+we just aggregate up over all the
+ 
+
+ align:start position:0%
+we just aggregate up over all the
+activities any particular household is
+
+ align:start position:0%
+activities any particular household is
+ 
+
+ align:start position:0%
+activities any particular household is
+doing and call that a collection of
+
+ align:start position:0%
+doing and call that a collection of
+ 
+
+ align:start position:0%
+doing and call that a collection of
+assets and the oiler equation should
+
+ align:start position:0%
+assets and the oiler equation should
+ 
+
+ align:start position:0%
+assets and the oiler equation should
+apply now you remember a little bit of
+
+ align:start position:0%
+apply now you remember a little bit of
+ 
+
+ align:start position:0%
+apply now you remember a little bit of
+your sort
+
+ align:start position:0%
+your sort
+ 
+
+ align:start position:0%
+your sort
+of econometrics with means and variances
+
+ align:start position:0%
+of econometrics with means and variances
+ 
+
+ align:start position:0%
+of econometrics with means and variances
+you know the uh or easy mistakes to make
+
+ align:start position:0%
+you know the uh or easy mistakes to make
+ 
+
+ align:start position:0%
+you know the uh or easy mistakes to make
+the expectation of two random variables
+
+ align:start position:0%
+the expectation of two random variables
+ 
+
+ align:start position:0%
+the expectation of two random variables
+is not just the product of the
+
+ align:start position:0%
+is not just the product of the
+ 
+
+ align:start position:0%
+is not just the product of the
+expectations you you uh you've got to
+
+ align:start position:0%
+expectations you you uh you've got to
+ 
+
+ align:start position:0%
+expectations you you uh you've got to
+adjust for the
+
+ align:start position:0%
+adjust for the
+ 
+
+ align:start position:0%
+adjust for the
+co-variance unless this happens to be
+
+ align:start position:0%
+co-variance unless this happens to be
+ 
+
+ align:start position:0%
+co-variance unless this happens to be
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+that this covariance is going to be
+
+ align:start position:0%
+that this covariance is going to be
+ 
+
+ align:start position:0%
+that this covariance is going to be
+crucial for us because you can see
+
+ align:start position:0%
+crucial for us because you can see
+ 
+
+ align:start position:0%
+crucial for us because you can see
+already it's the covariance
+
+ align:start position:0%
+already it's the covariance
+ 
+
+ align:start position:0%
+already it's the covariance
+between dare I say it the stochastic
+
+ align:start position:0%
+between dare I say it the stochastic
+ 
+
+ align:start position:0%
+between dare I say it the stochastic
+discount factor which you know reflects
+
+ align:start position:0%
+discount factor which you know reflects
+ 
+
+ align:start position:0%
+discount factor which you know reflects
+the community's relative valuation of
+
+ align:start position:0%
+the community's relative valuation of
+ 
+
+ align:start position:0%
+the community's relative valuation of
+resources and the particular return that
+
+ align:start position:0%
+resources and the particular return that
+ 
+
+ align:start position:0%
+resources and the particular return that
+uh on Project I held by household J so
+
+ align:start position:0%
+uh on Project I held by household J so
+ 
+
+ align:start position:0%
+uh on Project I held by household J so
+you know since uh we already had this
+
+ align:start position:0%
+you know since uh we already had this
+ 
+
+ align:start position:0%
+you know since uh we already had this
+equal to one as the oiler equation
+
+ align:start position:0%
+equal to one as the oiler equation
+ 
+
+ align:start position:0%
+equal to one as the oiler equation
+right so now we just sort of substitute
+
+ align:start position:0%
+right so now we just sort of substitute
+ 
+
+ align:start position:0%
+right so now we just sort of substitute
+this stuff
+
+ align:start position:0%
+this stuff
+ 
+
+ align:start position:0%
+this stuff
+into here and we get this and now you
+
+ align:start position:0%
+into here and we get this and now you
+ 
+
+ align:start position:0%
+into here and we get this and now you
+could basically divide through by the
+
+ align:start position:0%
+could basically divide through by the
+ 
+
+ align:start position:0%
+could basically divide through by the
+expectation of M
+
+ align:start position:0%
+expectation of M
+ 
+
+ align:start position:0%
+expectation of M
+Prime uh you're going to get one over
+
+ align:start position:0%
+Prime uh you're going to get one over
+ 
+
+ align:start position:0%
+Prime uh you're going to get one over
+that here get rid of it here get the
+
+ align:start position:0%
+that here get rid of it here get the
+ 
+
+ align:start position:0%
+that here get rid of it here get the
+covariance divided by it
+
+ align:start position:0%
+covariance divided by it
+ 
+
+ align:start position:0%
+covariance divided by it
+here and then you divide and multiply
+
+ align:start position:0%
+here and then you divide and multiply
+ 
+
+ align:start position:0%
+here and then you divide and multiply
+which doesn't do any harm by the
+
+ align:start position:0%
+which doesn't do any harm by the
+ 
+
+ align:start position:0%
+which doesn't do any harm by the
+variance of M Prime
+
+ align:start position:0%
+variance of M Prime
+ 
+
+ align:start position:0%
+variance of M Prime
+Prime and rearrange terms so you get you
+
+ align:start position:0%
+Prime and rearrange terms so you get you
+ 
+
+ align:start position:0%
+Prime and rearrange terms so you get you
+get this
+
+ align:start position:0%
+get this
+ 
+
+ align:start position:0%
+get this
+thing you know so we're finally arriving
+
+ align:start position:0%
+thing you know so we're finally arriving
+ 
+
+ align:start position:0%
+thing you know so we're finally arriving
+at something close to what we want which
+
+ align:start position:0%
+at something close to what we want which
+ 
+
+ align:start position:0%
+at something close to what we want which
+is the the expected rate of
+
+ align:start position:0%
+is the the expected rate of
+ 
+
+ align:start position:0%
+is the the expected rate of
+return which is going to be in the data
+
+ align:start position:0%
+return which is going to be in the data
+ 
+
+ align:start position:0%
+return which is going to be in the data
+the average return for household J over
+
+ align:start position:0%
+the average return for household J over
+ 
+
+ align:start position:0%
+the average return for household J over
+all the time periods I'm not
+
+ align:start position:0%
+all the time periods I'm not
+ 
+
+ align:start position:0%
+all the time periods I'm not
+quite is you know sort of looks like a
+
+ align:start position:0%
+quite is you know sort of looks like a
+ 
+
+ align:start position:0%
+quite is you know sort of looks like a
+linear function something with an
+
+ align:start position:0%
+linear function something with an
+ 
+
+ align:start position:0%
+linear function something with an
+intercept
+
+ align:start position:0%
+intercept
+ 
+
+ align:start position:0%
+intercept
+and then beta
+
+ align:start position:0%
+and then beta
+ 
+
+ align:start position:0%
+and then beta
+Lambda
+
+ align:start position:0%
+Lambda
+ 
+
+ align:start position:0%
+Lambda
+beta and finance guys talk about betas
+
+ align:start position:0%
+beta and finance guys talk about betas
+ 
+
+ align:start position:0%
+beta and finance guys talk about betas
+all the time beta for us just means sort
+
+ align:start position:0%
+all the time beta for us just means sort
+ 
+
+ align:start position:0%
+all the time beta for us just means sort
+of the normalized co-variance
+
+ align:start position:0%
+of the normalized co-variance
+ 
+
+ align:start position:0%
+of the normalized co-variance
+between the Returns
+
+ align:start position:0%
+between the Returns
+ 
+
+ align:start position:0%
+between the Returns
+on i j and the stochastic discount
+
+ align:start position:0%
+on i j and the stochastic discount
+ 
+
+ align:start position:0%
+on i j and the stochastic discount
+factor which I already pointed to above
+
+ align:start position:0%
+factor which I already pointed to above
+ 
+
+ align:start position:0%
+factor which I already pointed to above
+okay it's normalized by the overall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variance so that's kind of the risk
+
+ align:start position:0%
+variance so that's kind of the risk
+ 
+
+ align:start position:0%
+variance so that's kind of the risk
+factor or the quantity of
+
+ align:start position:0%
+factor or the quantity of
+ 
+
+ align:start position:0%
+factor or the quantity of
+risk and this other thing could be
+
+ align:start position:0%
+risk and this other thing could be
+ 
+
+ align:start position:0%
+risk and this other thing could be
+called the price of
+
+ align:start position:0%
+called the price of
+ 
+
+ align:start position:0%
+called the price of
+risk uh but it's nothing other than this
+
+ align:start position:0%
+risk uh but it's nothing other than this
+ 
+
+ align:start position:0%
+risk uh but it's nothing other than this
+it's the variance divided by the
+
+ align:start position:0%
+it's the variance divided by the
+ 
+
+ align:start position:0%
+it's the variance divided by the
+mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um it almost looks like a coefficient of
+
+ align:start position:0%
+um it almost looks like a coefficient of
+ 
+
+ align:start position:0%
+um it almost looks like a coefficient of
+variation you know like Sigma Square
+
+ align:start position:0%
+variation you know like Sigma Square
+ 
+
+ align:start position:0%
+variation you know like Sigma Square
+divided by mu or
+
+ align:start position:0%
+divided by mu or
+ 
+
+ align:start position:0%
+divided by mu or
+something uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that there's a name for it I'll I'll
+
+ align:start position:0%
+and that there's a name for it I'll I'll
+ 
+
+ align:start position:0%
+and that there's a name for it I'll I'll
+tell you what it is in a second um all
+
+ align:start position:0%
+tell you what it is in a second um all
+ 
+
+ align:start position:0%
+tell you what it is in a second um all
+right so this is what I said already
+
+ align:start position:0%
+right so this is what I said already
+ 
+
+ align:start position:0%
+right so this is what I said already
+quantities
+
+ align:start position:0%
+quantities
+ 
+
+ align:start position:0%
+quantities
+prices uh oh and one more thing what was
+
+ align:start position:0%
+prices uh oh and one more thing what was
+ 
+
+ align:start position:0%
+prices uh oh and one more thing what was
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+intercept uh well
+
+ align:start position:0%
+intercept uh well
+ 
+
+ align:start position:0%
+intercept uh well
+basically let's just Define this thing
+
+ align:start position:0%
+basically let's just Define this thing
+ 
+
+ align:start position:0%
+basically let's just Define this thing
+this gamma well was already defined to
+
+ align:start position:0%
+this gamma well was already defined to
+ 
+
+ align:start position:0%
+this gamma well was already defined to
+be one over the expectation of M Prime
+
+ align:start position:0%
+be one over the expectation of M Prime
+ 
+
+ align:start position:0%
+be one over the expectation of M Prime
+but let's call it the risk-free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+return first of all why is there no risk
+
+ align:start position:0%
+return first of all why is there no risk
+ 
+
+ align:start position:0%
+return first of all why is there no risk
+because all the V variability in the
+
+ align:start position:0%
+because all the V variability in the
+ 
+
+ align:start position:0%
+because all the V variability in the
+economy is in M prime or the one that we
+
+ align:start position:0%
+economy is in M prime or the one that we
+ 
+
+ align:start position:0%
+economy is in M prime or the one that we
+care about for that equation and we've
+
+ align:start position:0%
+care about for that equation and we've
+ 
+
+ align:start position:0%
+care about for that equation and we've
+already taken the expectation so there's
+
+ align:start position:0%
+already taken the expectation so there's
+ 
+
+ align:start position:0%
+already taken the expectation so there's
+nothing random left so this is a number
+
+ align:start position:0%
+nothing random left so this is a number
+ 
+
+ align:start position:0%
+nothing random left so this is a number
+it's not something
+
+ align:start position:0%
+it's not something
+ 
+
+ align:start position:0%
+it's not something
+stochastic it should be obvious but I
+
+ align:start position:0%
+stochastic it should be obvious but I
+ 
+
+ align:start position:0%
+stochastic it should be obvious but I
+always do it myself which is take that
+
+ align:start position:0%
+always do it myself which is take that
+ 
+
+ align:start position:0%
+always do it myself which is take that
+to be an asset plug that back into the
+
+ align:start position:0%
+to be an asset plug that back into the
+ 
+
+ align:start position:0%
+to be an asset plug that back into the
+asset Oiler equation that we already
+
+ align:start position:0%
+asset Oiler equation that we already
+ 
+
+ align:start position:0%
+asset Oiler equation that we already
+have and just convince yourself you'll
+
+ align:start position:0%
+have and just convince yourself you'll
+ 
+
+ align:start position:0%
+have and just convince yourself you'll
+that that equation applies for the
+
+ align:start position:0%
+that that equation applies for the
+ 
+
+ align:start position:0%
+that that equation applies for the
+risk-free return and you'll and you will
+
+ align:start position:0%
+risk-free return and you'll and you will
+ 
+
+ align:start position:0%
+risk-free return and you'll and you will
+get you'll get this right back again
+
+ align:start position:0%
+get you'll get this right back again
+ 
+
+ align:start position:0%
+get you'll get this right back again
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um so anyway the point is risk-free
+
+ align:start position:0%
+um so anyway the point is risk-free
+ 
+
+ align:start position:0%
+um so anyway the point is risk-free
+because the covariance of this risk-free
+
+ align:start position:0%
+because the covariance of this risk-free
+ 
+
+ align:start position:0%
+because the covariance of this risk-free
+rate with M Prime is zero by
+
+ align:start position:0%
+rate with M Prime is zero by
+ 
+
+ align:start position:0%
+rate with M Prime is zero by
+Construction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so let's
+
+ align:start position:0%
+uh so let's
+ 
+
+ align:start position:0%
+uh so let's
+just let's just look at this again this
+
+ align:start position:0%
+just let's just look at this again this
+ 
+
+ align:start position:0%
+just let's just look at this again this
+is the rate of
+
+ align:start position:0%
+is the rate of
+ 
+
+ align:start position:0%
+is the rate of
+return of the the mean or average rate
+
+ align:start position:0%
+return of the the mean or average rate
+ 
+
+ align:start position:0%
+return of the the mean or average rate
+of return on Project JJ subtract off the
+
+ align:start position:0%
+of return on Project JJ subtract off the
+ 
+
+ align:start position:0%
+of return on Project JJ subtract off the
+risk-free rate this is the return
+
+ align:start position:0%
+risk-free rate this is the return
+ 
+
+ align:start position:0%
+risk-free rate this is the return
+differential this is how much the you
+
+ align:start position:0%
+differential this is how much the you
+ 
+
+ align:start position:0%
+differential this is how much the you
+know in finance it would be like the
+
+ align:start position:0%
+know in finance it would be like the
+ 
+
+ align:start position:0%
+know in finance it would be like the
+junk bond
+
+ align:start position:0%
+junk bond
+ 
+
+ align:start position:0%
+junk bond
+premium right over and above
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+treasuries and so that that difference
+
+ align:start position:0%
+treasuries and so that that difference
+ 
+
+ align:start position:0%
+treasuries and so that that difference
+is sort of the uh premium that that you
+
+ align:start position:0%
+is sort of the uh premium that that you
+ 
+
+ align:start position:0%
+is sort of the uh premium that that you
+get for holding a risky asset and it's
+
+ align:start position:0%
+get for holding a risky asset and it's
+ 
+
+ align:start position:0%
+get for holding a risky asset and it's
+linearly related to
+
+ align:start position:0%
+linearly related to
+ 
+
+ align:start position:0%
+linearly related to
+uh the covariance of that asset with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+market so again I'm going back and forth
+
+ align:start position:0%
+market so again I'm going back and forth
+ 
+
+ align:start position:0%
+market so again I'm going back and forth
+a bit more with this Finance language
+
+ align:start position:0%
+a bit more with this Finance language
+ 
+
+ align:start position:0%
+a bit more with this Finance language
+but it's just all right off the oiler
+
+ align:start position:0%
+but it's just all right off the oiler
+ 
+
+ align:start position:0%
+but it's just all right off the oiler
+equation this is just
+
+ align:start position:0%
+equation this is just
+ 
+
+ align:start position:0%
+equation this is just
+standard uh sort of
+
+ align:start position:0%
+standard uh sort of
+ 
+
+ align:start position:0%
+standard uh sort of
+manipulation
+
+ align:start position:0%
+manipulation
+ 
+
+ align:start position:0%
+manipulation
+so we can even make it more
+
+ align:start position:0%
+so we can even make it more
+ 
+
+ align:start position:0%
+so we can even make it more
+obvious if you're wondering what M Prime
+
+ align:start position:0%
+obvious if you're wondering what M Prime
+ 
+
+ align:start position:0%
+obvious if you're wondering what M Prime
+really is
+
+ align:start position:0%
+really is
+ 
+
+ align:start position:0%
+really is
+uh let's go with quadratic
+
+ align:start position:0%
+uh let's go with quadratic
+ 
+
+ align:start position:0%
+uh let's go with quadratic
+utility okay so this is the form of
+
+ align:start position:0%
+utility okay so this is the form of
+ 
+
+ align:start position:0%
+utility okay so this is the form of
+it the community's value function as a
+
+ align:start position:0%
+it the community's value function as a
+ 
+
+ align:start position:0%
+it the community's value function as a
+function of wealth is just basically the
+
+ align:start position:0%
+function of wealth is just basically the
+ 
+
+ align:start position:0%
+function of wealth is just basically the
+squar of the difference between wealth
+
+ align:start position:0%
+squar of the difference between wealth
+ 
+
+ align:start position:0%
+squar of the difference between wealth
+and some subsistence
+
+ align:start position:0%
+and some subsistence
+ 
+
+ align:start position:0%
+and some subsistence
+level okay with a coefficient in front
+
+ align:start position:0%
+level okay with a coefficient in front
+ 
+
+ align:start position:0%
+level okay with a coefficient in front
+of it so of course if you take the
+
+ align:start position:0%
+of it so of course if you take the
+ 
+
+ align:start position:0%
+of it so of course if you take the
+derivative of it with respect to W uh
+
+ align:start position:0%
+derivative of it with respect to W uh
+ 
+
+ align:start position:0%
+derivative of it with respect to W uh
+you know the twos cancel out and you get
+
+ align:start position:0%
+you know the twos cancel out and you get
+ 
+
+ align:start position:0%
+you know the twos cancel out and you get
+a to times this difference which is
+
+ align:start position:0%
+a to times this difference which is
+ 
+
+ align:start position:0%
+a to times this difference which is
+Linear by the way that's huge so
+
+ align:start position:0%
+Linear by the way that's huge so
+ 
+
+ align:start position:0%
+Linear by the way that's huge so
+marginal value of wealth is linear in
+
+ align:start position:0%
+marginal value of wealth is linear in
+ 
+
+ align:start position:0%
+marginal value of wealth is linear in
+wealth that's what you get at a
+
+ align:start position:0%
+wealth that's what you get at a
+ 
+
+ align:start position:0%
+wealth that's what you get at a
+quadratic and then you just substitute
+
+ align:start position:0%
+quadratic and then you just substitute
+ 
+
+ align:start position:0%
+quadratic and then you just substitute
+our expression for w Prime
+
+ align:start position:0%
+our expression for w Prime
+ 
+
+ align:start position:0%
+our expression for w Prime
+tomorrow into that
+
+ align:start position:0%
+tomorrow into that
+ 
+
+ align:start position:0%
+tomorrow into that
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+um and do a little
+
+ align:start position:0%
+um and do a little
+ 
+
+ align:start position:0%
+um and do a little
+relabeling so all of a sudden this looks
+
+ align:start position:0%
+relabeling so all of a sudden this looks
+ 
+
+ align:start position:0%
+relabeling so all of a sudden this looks
+like the return on the village average
+
+ align:start position:0%
+like the return on the village average
+ 
+
+ align:start position:0%
+like the return on the village average
+and the village average Capital
+
+ align:start position:0%
+and the village average Capital
+ 
+
+ align:start position:0%
+and the village average Capital
+stock uh okay the village average
+
+ align:start position:0%
+stock uh okay the village average
+ 
+
+ align:start position:0%
+stock uh okay the village average
+Capital stock is the sum of the capital
+
+ align:start position:0%
+Capital stock is the sum of the capital
+ 
+
+ align:start position:0%
+Capital stock is the sum of the capital
+stocks allocated over all the projects
+
+ align:start position:0%
+stocks allocated over all the projects
+ 
+
+ align:start position:0%
+stocks allocated over all the projects
+and all the households as it should be
+
+ align:start position:0%
+and all the households as it should be
+ 
+
+ align:start position:0%
+and all the households as it should be
+to be in total right and then what is
+
+ align:start position:0%
+to be in total right and then what is
+ 
+
+ align:start position:0%
+to be in total right and then what is
+the rate of return on it well basically
+
+ align:start position:0%
+the rate of return on it well basically
+ 
+
+ align:start position:0%
+the rate of return on it well basically
+it's like
+
+ align:start position:0%
+it's like
+ 
+
+ align:start position:0%
+it's like
+a capital weighted
+
+ align:start position:0%
+a capital weighted
+ 
+
+ align:start position:0%
+a capital weighted
+return so you know the total return
+
+ align:start position:0%
+return so you know the total return
+ 
+
+ align:start position:0%
+return so you know the total return
+return is coming from a bunch of
+
+ align:start position:0%
+return is coming from a bunch of
+ 
+
+ align:start position:0%
+return is coming from a bunch of
+individual projects so you just take the
+
+ align:start position:0%
+individual projects so you just take the
+ 
+
+ align:start position:0%
+individual projects so you just take the
+return on all the vi individual projects
+
+ align:start position:0%
+return on all the vi individual projects
+ 
+
+ align:start position:0%
+return on all the vi individual projects
+that weight them by the capital being
+
+ align:start position:0%
+that weight them by the capital being
+ 
+
+ align:start position:0%
+that weight them by the capital being
+allocated to those projects and
+
+ align:start position:0%
+allocated to those projects and
+ 
+
+ align:start position:0%
+allocated to those projects and
+renormalized by the total Capital stock
+
+ align:start position:0%
+renormalized by the total Capital stock
+ 
+
+ align:start position:0%
+renormalized by the total Capital stock
+so it's a portfolio weighted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+return that's just a definition but of
+
+ align:start position:0%
+return that's just a definition but of
+ 
+
+ align:start position:0%
+return that's just a definition but of
+course then it looks like this and you
+
+ align:start position:0%
+course then it looks like this and you
+ 
+
+ align:start position:0%
+course then it looks like this and you
+take this up
+
+ align:start position:0%
+take this up
+ 
+
+ align:start position:0%
+take this up
+here and this here and you realize that
+
+ align:start position:0%
+here and this here and you realize that
+ 
+
+ align:start position:0%
+here and this here and you realize that
+there's canceling and that's why it's
+
+ align:start position:0%
+there's canceling and that's why it's
+ 
+
+ align:start position:0%
+there's canceling and that's why it's
+really just equal to this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so but we'll we'll use this
+
+ align:start position:0%
+so but we'll we'll use this
+ 
+
+ align:start position:0%
+so but we'll we'll use this
+now uh so M Prime which is the
+
+ align:start position:0%
+now uh so M Prime which is the
+ 
+
+ align:start position:0%
+now uh so M Prime which is the
+derivative tomorrow is just this
+
+ align:start position:0%
+derivative tomorrow is just this
+ 
+
+ align:start position:0%
+derivative tomorrow is just this
+thing uh divided by mu remember we have
+
+ align:start position:0%
+thing uh divided by mu remember we have
+ 
+
+ align:start position:0%
+thing uh divided by mu remember we have
+to take the current Shadow price and
+
+ align:start position:0%
+to take the current Shadow price and
+ 
+
+ align:start position:0%
+to take the current Shadow price and
+divide
+
+ align:start position:0%
+divide
+ 
+
+ align:start position:0%
+divide
+through and then by you know this is all
+
+ align:start position:0%
+through and then by you know this is all
+ 
+
+ align:start position:0%
+through and then by you know this is all
+additive and linear so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so we get
+
+ align:start position:0%
+um so we get
+ 
+
+ align:start position:0%
+um so we get
+this and
+
+ align:start position:0%
+this and
+ 
+
+ align:start position:0%
+this and
+now M Prime here looks like this plus
+
+ align:start position:0%
+now M Prime here looks like this plus
+ 
+
+ align:start position:0%
+now M Prime here looks like this plus
+this this looks like a constant term
+
+ align:start position:0%
+this this looks like a constant term
+ 
+
+ align:start position:0%
+this this looks like a constant term
+that doesn't depend on the rate of
+
+ align:start position:0%
+that doesn't depend on the rate of
+ 
+
+ align:start position:0%
+that doesn't depend on the rate of
+return and uh and this is a coefficient
+
+ align:start position:0%
+return and uh and this is a coefficient
+ 
+
+ align:start position:0%
+return and uh and this is a coefficient
+premultiplying the rate of return so
+
+ align:start position:0%
+premultiplying the rate of return so
+ 
+
+ align:start position:0%
+premultiplying the rate of return so
+it's starting to look like
+
+ align:start position:0%
+it's starting to look like
+ 
+
+ align:start position:0%
+it's starting to look like
+uh a pretty convenient equation
+
+ align:start position:0%
+uh a pretty convenient equation
+ 
+
+ align:start position:0%
+uh a pretty convenient equation
+for the stochastic discount factor it's
+
+ align:start position:0%
+for the stochastic discount factor it's
+ 
+
+ align:start position:0%
+for the stochastic discount factor it's
+linear linear in the village rate of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+return and again we have this thing we
+
+ align:start position:0%
+return and again we have this thing we
+ 
+
+ align:start position:0%
+return and again we have this thing we
+already
+
+ align:start position:0%
+already
+ 
+
+ align:start position:0%
+already
+derived which was you know a
+
+ align:start position:0%
+derived which was you know a
+ 
+
+ align:start position:0%
+derived which was you know a
+manipulation of the oiler
+
+ align:start position:0%
+manipulation of the oiler
+ 
+
+ align:start position:0%
+manipulation of the oiler
+equation and everywhere you
+
+ align:start position:0%
+equation and everywhere you
+ 
+
+ align:start position:0%
+equation and everywhere you
+see M Prime you start
+
+ align:start position:0%
+see M Prime you start
+ 
+
+ align:start position:0%
+see M Prime you start
+substituting a minus BR RM Prime and
+
+ align:start position:0%
+substituting a minus BR RM Prime and
+ 
+
+ align:start position:0%
+substituting a minus BR RM Prime and
+then you got to remember certain rules
+
+ align:start position:0%
+then you got to remember certain rules
+ 
+
+ align:start position:0%
+then you got to remember certain rules
+about you know co-variance operators and
+
+ align:start position:0%
+about you know co-variance operators and
+ 
+
+ align:start position:0%
+about you know co-variance operators and
+variance operators you know variance
+
+ align:start position:0%
+variance operators you know variance
+ 
+
+ align:start position:0%
+variance operators you know variance
+operators will Square coefficients in
+
+ align:start position:0%
+operators will Square coefficients in
+ 
+
+ align:start position:0%
+operators will Square coefficients in
+front of them co-variance operators
+
+ align:start position:0%
+front of them co-variance operators
+ 
+
+ align:start position:0%
+front of them co-variance operators
+will bring the coefficient
+
+ align:start position:0%
+will bring the coefficient
+ 
+
+ align:start position:0%
+will bring the coefficient
+outside there's a lot of substitutions
+
+ align:start position:0%
+outside there's a lot of substitutions
+ 
+
+ align:start position:0%
+outside there's a lot of substitutions
+here and the B there's B's and B squares
+
+ align:start position:0%
+here and the B there's B's and B squares
+ 
+
+ align:start position:0%
+here and the B there's B's and B squares
+and they're going to cancel with each
+
+ align:start position:0%
+and they're going to cancel with each
+ 
+
+ align:start position:0%
+and they're going to cancel with each
+other and you end up with this
+
+ align:start position:0%
+other and you end up with this
+ 
+
+ align:start position:0%
+other and you end up with this
+thing okay so this says the expected
+
+ align:start position:0%
+thing okay so this says the expected
+ 
+
+ align:start position:0%
+thing okay so this says the expected
+return or sample average return should
+
+ align:start position:0%
+return or sample average return should
+ 
+
+ align:start position:0%
+return or sample average return should
+just be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um uh the covariance of the return with
+
+ align:start position:0%
+um uh the covariance of the return with
+ 
+
+ align:start position:0%
+um uh the covariance of the return with
+the market with a village average
+
+ align:start position:0%
+the market with a village average
+ 
+
+ align:start position:0%
+the market with a village average
+aggregate by the way we know how to
+
+ align:start position:0%
+aggregate by the way we know how to
+ 
+
+ align:start position:0%
+aggregate by the way we know how to
+construct that because we have it in the
+
+ align:start position:0%
+construct that because we have it in the
+ 
+
+ align:start position:0%
+construct that because we have it in the
+data and we have the variance as
+
+ align:start position:0%
+data and we have the variance as
+ 
+
+ align:start position:0%
+data and we have the variance as
+well and then this is just the sort of
+
+ align:start position:0%
+well and then this is just the sort of
+ 
+
+ align:start position:0%
+well and then this is just the sort of
+coefficient that multiplies it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh that's what I was saying about
+
+ align:start position:0%
+uh that's what I was saying about
+ 
+
+ align:start position:0%
+uh that's what I was saying about
+that coefficient of variation you know
+
+ align:start position:0%
+that coefficient of variation you know
+ 
+
+ align:start position:0%
+that coefficient of variation you know
+it's a variance divided by a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean uh so where have we ended up
+
+ align:start position:0%
+mean uh so where have we ended up
+ 
+
+ align:start position:0%
+mean uh so where have we ended up
+uh well with that quadratic we now have
+
+ align:start position:0%
+uh well with that quadratic we now have
+ 
+
+ align:start position:0%
+uh well with that quadratic we now have
+pretty much an exact expression that the
+
+ align:start position:0%
+pretty much an exact expression that the
+ 
+
+ align:start position:0%
+pretty much an exact expression that the
+expected rate of return on Project I run
+
+ align:start position:0%
+expected rate of return on Project I run
+ 
+
+ align:start position:0%
+expected rate of return on Project I run
+by house J should just be a linear
+
+ align:start position:0%
+by house J should just be a linear
+ 
+
+ align:start position:0%
+by house J should just be a linear
+function with a a constant a common
+
+ align:start position:0%
+function with a a constant a common
+ 
+
+ align:start position:0%
+function with a a constant a common
+constant term that has nothing to do
+
+ align:start position:0%
+constant term that has nothing to do
+ 
+
+ align:start position:0%
+constant term that has nothing to do
+with I and J and then uh the
+
+ align:start position:0%
+with I and J and then uh the
+ 
+
+ align:start position:0%
+with I and J and then uh the
+covariance of that household's return
+
+ align:start position:0%
+covariance of that household's return
+ 
+
+ align:start position:0%
+covariance of that household's return
+with the village average
+
+ align:start position:0%
+with the village average
+ 
+
+ align:start position:0%
+with the village average
+return which is something we can compute
+
+ align:start position:0%
+return which is something we can compute
+ 
+
+ align:start position:0%
+return which is something we can compute
+so you start thinking about this like a
+
+ align:start position:0%
+so you start thinking about this like a
+ 
+
+ align:start position:0%
+so you start thinking about this like a
+regression you know we're g to we'll
+
+ align:start position:0%
+regression you know we're g to we'll
+ 
+
+ align:start position:0%
+regression you know we're g to we'll
+know this from the data we'll know this
+
+ align:start position:0%
+know this from the data we'll know this
+ 
+
+ align:start position:0%
+know this from the data we'll know this
+from the data
+
+ align:start position:0%
+from the data
+ 
+
+ align:start position:0%
+from the data
+I'll tell you how to get it in a minute
+
+ align:start position:0%
+I'll tell you how to get it in a minute
+ 
+
+ align:start position:0%
+I'll tell you how to get it in a minute
+and we'll just estimate Lambda and Gamma
+
+ align:start position:0%
+and we'll just estimate Lambda and Gamma
+ 
+
+ align:start position:0%
+and we'll just estimate Lambda and Gamma
+well not quite gamma we can do something
+
+ align:start position:0%
+well not quite gamma we can do something
+ 
+
+ align:start position:0%
+well not quite gamma we can do something
+special with but that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+idea so I've said this already but it
+
+ align:start position:0%
+idea so I've said this already but it
+ 
+
+ align:start position:0%
+idea so I've said this already but it
+Bears
+
+ align:start position:0%
+Bears
+ 
+
+ align:start position:0%
+Bears
+repeating uh our stuff looks a lot like
+
+ align:start position:0%
+repeating uh our stuff looks a lot like
+ 
+
+ align:start position:0%
+repeating uh our stuff looks a lot like
+this capm but the mechanism is very
+
+ align:start position:0%
+this capm but the mechanism is very
+ 
+
+ align:start position:0%
+this capm but the mechanism is very
+different we do not have households
+
+ align:start position:0%
+different we do not have households
+ 
+
+ align:start position:0%
+different we do not have households
+trading assets that are priced in
+
+ align:start position:0%
+trading assets that are priced in
+ 
+
+ align:start position:0%
+trading assets that are priced in
+centralized
+
+ align:start position:0%
+centralized
+ 
+
+ align:start position:0%
+centralized
+markets we're instead optimally
+
+ align:start position:0%
+markets we're instead optimally
+ 
+
+ align:start position:0%
+markets we're instead optimally
+allocating assets across
+
+ align:start position:0%
+allocating assets across
+ 
+
+ align:start position:0%
+allocating assets across
+households but then not forcing them to
+
+ align:start position:0%
+households but then not forcing them to
+ 
+
+ align:start position:0%
+households but then not forcing them to
+eat the return
+
+ align:start position:0%
+eat the return
+ 
+
+ align:start position:0%
+eat the return
+stream instead they enter into this risk
+
+ align:start position:0%
+stream instead they enter into this risk
+ 
+
+ align:start position:0%
+stream instead they enter into this risk
+Syndicate as if a social planner were
+
+ align:start position:0%
+Syndicate as if a social planner were
+ 
+
+ align:start position:0%
+Syndicate as if a social planner were
+reallocating
+
+ align:start position:0%
+reallocating
+ 
+
+ align:start position:0%
+reallocating
+consumption whereas in finance you kind
+
+ align:start position:0%
+consumption whereas in finance you kind
+ 
+
+ align:start position:0%
+consumption whereas in finance you kind
+of assume you're an investor you know
+
+ align:start position:0%
+of assume you're an investor you know
+ 
+
+ align:start position:0%
+of assume you're an investor you know
+you could do means and variances and
+
+ align:start position:0%
+you could do means and variances and
+ 
+
+ align:start position:0%
+you could do means and variances and
+take some risks on your portfolio and
+
+ align:start position:0%
+take some risks on your portfolio and
+ 
+
+ align:start position:0%
+take some risks on your portfolio and
+then you're going to eat
+
+ align:start position:0%
+then you're going to eat
+ 
+
+ align:start position:0%
+then you're going to eat
+it or at least dynamically you know
+
+ align:start position:0%
+it or at least dynamically you know
+ 
+
+ align:start position:0%
+it or at least dynamically you know
+optimize eat some save some for tomorrow
+
+ align:start position:0%
+optimize eat some save some for tomorrow
+ 
+
+ align:start position:0%
+optimize eat some save some for tomorrow
+but this is very different and and it's
+
+ align:start position:0%
+but this is very different and and it's
+ 
+
+ align:start position:0%
+but this is very different and and it's
+key that they don't have to eat the
+
+ align:start position:0%
+key that they don't have to eat the
+ 
+
+ align:start position:0%
+key that they don't have to eat the
+returns off their Capital stock or make
+
+ align:start position:0%
+returns off their Capital stock or make
+ 
+
+ align:start position:0%
+returns off their Capital stock or make
+their own independent savings
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decisions and you've seen you know last
+
+ align:start position:0%
+decisions and you've seen you know last
+ 
+
+ align:start position:0%
+decisions and you've seen you know last
+time building up to this that households
+
+ align:start position:0%
+time building up to this that households
+ 
+
+ align:start position:0%
+time building up to this that households
+are sharing a lot of risk with each
+
+ align:start position:0%
+are sharing a lot of risk with each
+ 
+
+ align:start position:0%
+are sharing a lot of risk with each
+other and these informal Village money
+
+ align:start position:0%
+other and these informal Village money
+ 
+
+ align:start position:0%
+other and these informal Village money
+market Market are are quite active we
+
+ align:start position:0%
+market Market are are quite active we
+ 
+
+ align:start position:0%
+market Market are are quite active we
+called them a money market last time so
+
+ align:start position:0%
+called them a money market last time so
+ 
+
+ align:start position:0%
+called them a money market last time so
+we've already been using that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+language that's what this slide is
+
+ align:start position:0%
+language that's what this slide is
+ 
+
+ align:start position:0%
+language that's what this slide is
+saying that's just a reminder what we
+
+ align:start position:0%
+saying that's just a reminder what we
+ 
+
+ align:start position:0%
+saying that's just a reminder what we
+talked about last
+
+ align:start position:0%
+talked about last
+ 
+
+ align:start position:0%
+talked about last
+time so data it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+monthly I don't know what they call Four
+
+ align:start position:0%
+monthly I don't know what they call Four
+ 
+
+ align:start position:0%
+monthly I don't know what they call Four
+Villages group together in a
+
+ align:start position:0%
+Villages group together in a
+ 
+
+ align:start position:0%
+Villages group together in a
+tomone so we kind of started adopting
+
+ align:start position:0%
+tomone so we kind of started adopting
+ 
+
+ align:start position:0%
+tomone so we kind of started adopting
+this South Africa language I don't I
+
+ align:start position:0%
+this South Africa language I don't I
+ 
+
+ align:start position:0%
+this South Africa language I don't I
+don't know whether I like it we're
+
+ align:start position:0%
+don't know whether I like it we're
+ 
+
+ align:start position:0%
+don't know whether I like it we're
+calling them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+townships Rural and maybe not that nice
+
+ align:start position:0%
+townships Rural and maybe not that nice
+ 
+
+ align:start position:0%
+townships Rural and maybe not that nice
+place to
+
+ align:start position:0%
+place to
+ 
+
+ align:start position:0%
+place to
+be yeah so Tom bone is tie for you know
+
+ align:start position:0%
+be yeah so Tom bone is tie for you know
+ 
+
+ align:start position:0%
+be yeah so Tom bone is tie for you know
+the fact that we picked for at random in
+
+ align:start position:0%
+the fact that we picked for at random in
+ 
+
+ align:start position:0%
+the fact that we picked for at random in
+this geographic area but no one knows
+
+ align:start position:0%
+this geographic area but no one knows
+ 
+
+ align:start position:0%
+this geographic area but no one knows
+what the tomone is so but clearly
+
+ align:start position:0%
+what the tomone is so but clearly
+ 
+
+ align:start position:0%
+what the tomone is so but clearly
+townships distinguishes it from
+
+ align:start position:0%
+townships distinguishes it from
+ 
+
+ align:start position:0%
+townships distinguishes it from
+Villages it's four four villages in the
+
+ align:start position:0%
+Villages it's four four villages in the
+ 
+
+ align:start position:0%
+Villages it's four four villages in the
+data anyway you know all about the where
+
+ align:start position:0%
+data anyway you know all about the where
+ 
+
+ align:start position:0%
+data anyway you know all about the where
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+located reminder that we started
+
+ align:start position:0%
+located reminder that we started
+ 
+
+ align:start position:0%
+located reminder that we started
+in August of 98 we're going to ignore
+
+ align:start position:0%
+in August of 98 we're going to ignore
+ 
+
+ align:start position:0%
+in August of 98 we're going to ignore
+the first four months basically and uh
+
+ align:start position:0%
+the first four months basically and uh
+ 
+
+ align:start position:0%
+the first four months basically and uh
+and and use the data from 1990 on
+
+ align:start position:0%
+and and use the data from 1990 on
+ 
+
+ align:start position:0%
+and and use the data from 1990 on
+1999 uh we're still we'll still we're
+
+ align:start position:0%
+1999 uh we're still we'll still we're
+ 
+
+ align:start position:0%
+1999 uh we're still we'll still we're
+still out there uh at month
+
+ align:start position:0%
+still out there uh at month
+ 
+
+ align:start position:0%
+still out there uh at month
+174 what we're going to use and Christen
+
+ align:start position:0%
+174 what we're going to use and Christen
+ 
+
+ align:start position:0%
+174 what we're going to use and Christen
+I just pick basically redid this in the
+
+ align:start position:0%
+I just pick basically redid this in the
+ 
+
+ align:start position:0%
+I just pick basically redid this in the
+last few weeks um we're going to use
+
+ align:start position:0%
+last few weeks um we're going to use
+ 
+
+ align:start position:0%
+last few weeks um we're going to use
+month 5 to 160 or basically 156 months
+
+ align:start position:0%
+month 5 to 160 or basically 156 months
+ 
+
+ align:start position:0%
+month 5 to 160 or basically 156 months
+or 13 full years of the
+
+ align:start position:0%
+or 13 full years of the
+ 
+
+ align:start position:0%
+or 13 full years of the
+data at the monthly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level for the 541 households who
+
+ align:start position:0%
+level for the 541 households who
+ 
+
+ align:start position:0%
+level for the 541 households who
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+basically not have not dropped out sort
+
+ align:start position:0%
+basically not have not dropped out sort
+ 
+
+ align:start position:0%
+basically not have not dropped out sort
+of the balanced panel
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now about the
+
+ align:start position:0%
+now about the
+ 
+
+ align:start position:0%
+now about the
+townships Matt
+
+ align:start position:0%
+townships Matt
+ 
+
+ align:start position:0%
+townships Matt
+so how what percentage of households
+
+ align:start position:0%
+so how what percentage of households
+ 
+
+ align:start position:0%
+so how what percentage of households
+have relatives living in the same
+
+ align:start position:0%
+have relatives living in the same
+ 
+
+ align:start position:0%
+have relatives living in the same
+Village uh it's a bit low and only half
+
+ align:start position:0%
+Village uh it's a bit low and only half
+ 
+
+ align:start position:0%
+Village uh it's a bit low and only half
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+chauna uh three quarters in lere and
+
+ align:start position:0%
+chauna uh three quarters in lere and
+ 
+
+ align:start position:0%
+chauna uh three quarters in lere and
+buram is already up to the 80s if not to
+
+ align:start position:0%
+buram is already up to the 80s if not to
+ 
+
+ align:start position:0%
+buram is already up to the 80s if not to
+the 90s but if you go to the township
+
+ align:start position:0%
+the 90s but if you go to the township
+ 
+
+ align:start position:0%
+the 90s but if you go to the township
+level you know then 87 is the really 88
+
+ align:start position:0%
+level you know then 87 is the really 88
+ 
+
+ align:start position:0%
+level you know then 87 is the really 88
+is the lowest percent in other words
+
+ align:start position:0%
+is the lowest percent in other words
+ 
+
+ align:start position:0%
+is the lowest percent in other words
+almost every household has a relative if
+
+ align:start position:0%
+almost every household has a relative if
+ 
+
+ align:start position:0%
+almost every household has a relative if
+not in their own village than in a
+
+ align:start position:0%
+not in their own village than in a
+ 
+
+ align:start position:0%
+not in their own village than in a
+village
+
+ align:start position:0%
+village
+ 
+
+ align:start position:0%
+village
+nearby so you know we stopped kind of
+
+ align:start position:0%
+nearby so you know we stopped kind of
+ 
+
+ align:start position:0%
+nearby so you know we stopped kind of
+looking at networks after this
+
+ align:start position:0%
+looking at networks after this
+ 
+
+ align:start position:0%
+looking at networks after this
+and networks confuse people rightly so
+
+ align:start position:0%
+and networks confuse people rightly so
+ 
+
+ align:start position:0%
+and networks confuse people rightly so
+because who's in it and who isn't and is
+
+ align:start position:0%
+because who's in it and who isn't and is
+ 
+
+ align:start position:0%
+because who's in it and who isn't and is
+there selection biased and so on so you
+
+ align:start position:0%
+there selection biased and so on so you
+ 
+
+ align:start position:0%
+there selection biased and so on so you
+know we just made it easy for ourselves
+
+ align:start position:0%
+know we just made it easy for ourselves
+ 
+
+ align:start position:0%
+know we just made it easy for ourselves
+and say they're all really related to
+
+ align:start position:0%
+and say they're all really related to
+ 
+
+ align:start position:0%
+and say they're all really related to
+each other anyway so let's use the whole
+
+ align:start position:0%
+each other anyway so let's use the whole
+ 
+
+ align:start position:0%
+each other anyway so let's use the whole
+sample
+
+ align:start position:0%
+sample
+ 
+
+ align:start position:0%
+sample
+but I'll show you what we go back and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+check this looks like Risk and return in
+
+ align:start position:0%
+check this looks like Risk and return in
+ 
+
+ align:start position:0%
+check this looks like Risk and return in
+Village India I mean you can see the
+
+ align:start position:0%
+Village India I mean you can see the
+ 
+
+ align:start position:0%
+Village India I mean you can see the
+cultivation activities livestock fish
+
+ align:start position:0%
+cultivation activities livestock fish
+ 
+
+ align:start position:0%
+cultivation activities livestock fish
+shrimp uh wage earning and so
+
+ align:start position:0%
+shrimp uh wage earning and so
+ 
+
+ align:start position:0%
+shrimp uh wage earning and so
+on uh you know wage earning is a bit
+
+ align:start position:0%
+on uh you know wage earning is a bit
+ 
+
+ align:start position:0%
+on uh you know wage earning is a bit
+heavier in the Northeast than in
+
+ align:start position:0%
+heavier in the Northeast than in
+ 
+
+ align:start position:0%
+heavier in the Northeast than in
+chatunga only only Chach s has uh fish
+
+ align:start position:0%
+chatunga only only Chach s has uh fish
+ 
+
+ align:start position:0%
+chatunga only only Chach s has uh fish
+and shrimp sounds like a restaurant I
+
+ align:start position:0%
+and shrimp sounds like a restaurant I
+ 
+
+ align:start position:0%
+and shrimp sounds like a restaurant I
+you know I've already told you though
+
+ align:start position:0%
+you know I've already told you though
+ 
+
+ align:start position:0%
+you know I've already told you though
+that's what you're eating in when you
+
+ align:start position:0%
+that's what you're eating in when you
+ 
+
+ align:start position:0%
+that's what you're eating in when you
+buy shrimp at
+
+ align:start position:0%
+buy shrimp at
+ 
+
+ align:start position:0%
+buy shrimp at
+Costco
+
+ align:start position:0%
+Costco
+ 
+
+ align:start position:0%
+Costco
+um and all the business livestocks
+
+ align:start position:0%
+um and all the business livestocks
+ 
+
+ align:start position:0%
+um and all the business livestocks
+pretty heavy in ly also chachang Sal
+
+ align:start position:0%
+pretty heavy in ly also chachang Sal
+ 
+
+ align:start position:0%
+pretty heavy in ly also chachang Sal
+those are the dairy cattle uh so that's
+
+ align:start position:0%
+those are the dairy cattle uh so that's
+ 
+
+ align:start position:0%
+those are the dairy cattle uh so that's
+just a quick reminder of the quote
+
+ align:start position:0%
+just a quick reminder of the quote
+ 
+
+ align:start position:0%
+just a quick reminder of the quote
+projects my project is a
+
+ align:start position:0%
+projects my project is a
+ 
+
+ align:start position:0%
+projects my project is a
+cow
+
+ align:start position:0%
+cow
+ 
+
+ align:start position:0%
+cow
+Etc it's a cash oh that's terrible uh
+
+ align:start position:0%
+Etc it's a cash oh that's terrible uh
+ 
+
+ align:start position:0%
+Etc it's a cash oh that's terrible uh
+and here's
+
+ align:start position:0%
+and here's
+ 
+
+ align:start position:0%
+and here's
+some just reminder of you know
+
+ align:start position:0%
+some just reminder of you know
+ 
+
+ align:start position:0%
+some just reminder of you know
+descriptive
+
+ align:start position:0%
+descriptive
+ 
+
+ align:start position:0%
+descriptive
+statistics males females education
+
+ align:start position:0%
+statistics males females education
+ 
+
+ align:start position:0%
+statistics males females education
+levels some of this you've seen before
+
+ align:start position:0%
+levels some of this you've seen before
+ 
+
+ align:start position:0%
+levels some of this you've seen before
+income levels assets and
+
+ align:start position:0%
+income levels assets and
+ 
+
+ align:start position:0%
+income levels assets and
+liabilities uh and so
+
+ align:start position:0%
+liabilities uh and so
+ 
+
+ align:start position:0%
+liabilities uh and so
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+um so we're going to use a total return
+
+ align:start position:0%
+um so we're going to use a total return
+ 
+
+ align:start position:0%
+um so we're going to use a total return
+and we're going to include Financial
+
+ align:start position:0%
+and we're going to include Financial
+ 
+
+ align:start position:0%
+and we're going to include Financial
+assets we're not going to
+
+ align:start position:0%
+assets we're not going to
+ 
+
+ align:start position:0%
+assets we're not going to
+separate um by the way it's a bit
+
+ align:start position:0%
+separate um by the way it's a bit
+ 
+
+ align:start position:0%
+separate um by the way it's a bit
+problematic to know what to do with a
+
+ align:start position:0%
+problematic to know what to do with a
+ 
+
+ align:start position:0%
+problematic to know what to do with a
+Sav account it's a financial asset but
+
+ align:start position:0%
+Sav account it's a financial asset but
+ 
+
+ align:start position:0%
+Sav account it's a financial asset but
+on the other hand maybe like inventory
+
+ align:start position:0%
+on the other hand maybe like inventory
+ 
+
+ align:start position:0%
+on the other hand maybe like inventory
+it's kind of contributing to the
+
+ align:start position:0%
+it's kind of contributing to the
+ 
+
+ align:start position:0%
+it's kind of contributing to the
+business and if we didn't have it in
+
+ align:start position:0%
+business and if we didn't have it in
+ 
+
+ align:start position:0%
+business and if we didn't have it in
+there then people would ask so we it
+
+ align:start position:0%
+there then people would ask so we it
+ 
+
+ align:start position:0%
+there then people would ask so we it
+didn't make much difference so we put in
+
+ align:start position:0%
+didn't make much difference so we put in
+ 
+
+ align:start position:0%
+didn't make much difference so we put in
+all the financial assets actually
+
+ align:start position:0%
+all the financial assets actually
+ 
+
+ align:start position:0%
+all the financial assets actually
+subtracted off the debts
+
+ align:start position:0%
+subtracted off the debts
+ 
+
+ align:start position:0%
+subtracted off the debts
+too uh it doesn't it doesn't really
+
+ align:start position:0%
+too uh it doesn't it doesn't really
+ 
+
+ align:start position:0%
+too uh it doesn't it doesn't really
+matter if you want to think about this
+
+ align:start position:0%
+matter if you want to think about this
+ 
+
+ align:start position:0%
+matter if you want to think about this
+as real rates of return you would not be
+
+ align:start position:0%
+as real rates of return you would not be
+ 
+
+ align:start position:0%
+as real rates of return you would not be
+misled
+
+ align:start position:0%
+misled
+ 
+
+ align:start position:0%
+misled
+um in real real
+
+ align:start position:0%
+um in real real
+ 
+
+ align:start position:0%
+um in real real
+projects real people real
+
+ align:start position:0%
+projects real people real
+ 
+
+ align:start position:0%
+projects real people real
+assets okay you know we constructed
+
+ align:start position:0%
+assets okay you know we constructed
+ 
+
+ align:start position:0%
+assets okay you know we constructed
+these Financial accounts this is
+
+ align:start position:0%
+these Financial accounts this is
+ 
+
+ align:start position:0%
+these Financial accounts this is
+problematic we have to sort
+
+ align:start position:0%
+problematic we have to sort
+ 
+
+ align:start position:0%
+problematic we have to sort
+of subtract off the cost of Labor and
+
+ align:start position:0%
+of subtract off the cost of Labor and
+ 
+
+ align:start position:0%
+of subtract off the cost of Labor and
+when it's household
+
+ align:start position:0%
+when it's household
+ 
+
+ align:start position:0%
+when it's household
+labor it's not priced this is probably
+
+ align:start position:0%
+labor it's not priced this is probably
+ 
+
+ align:start position:0%
+labor it's not priced this is probably
+our single biggest problem and when I
+
+ align:start position:0%
+our single biggest problem and when I
+ 
+
+ align:start position:0%
+our single biggest problem and when I
+show you residual rates of return in a
+
+ align:start position:0%
+show you residual rates of return in a
+ 
+
+ align:start position:0%
+show you residual rates of return in a
+minute you'll see some of them are low
+
+ align:start position:0%
+minute you'll see some of them are low
+ 
+
+ align:start position:0%
+minute you'll see some of them are low
+you know we probably subtract it off too
+
+ align:start position:0%
+you know we probably subtract it off too
+ 
+
+ align:start position:0%
+you know we probably subtract it off too
+much but it's very hard to know because
+
+ align:start position:0%
+much but it's very hard to know because
+ 
+
+ align:start position:0%
+much but it's very hard to know because
+we try to grab instruments and adjust
+
+ align:start position:0%
+we try to grab instruments and adjust
+ 
+
+ align:start position:0%
+we try to grab instruments and adjust
+you know but it's pretty it's really
+
+ align:start position:0%
+you know but it's pretty it's really
+ 
+
+ align:start position:0%
+you know but it's pretty it's really
+kind of not terribly
+
+ align:start position:0%
+kind of not terribly
+ 
+
+ align:start position:0%
+kind of not terribly
+compelling you'll see this again when we
+
+ align:start position:0%
+compelling you'll see this again when we
+ 
+
+ align:start position:0%
+compelling you'll see this again when we
+get to the labor paper so we adjust the
+
+ align:start position:0%
+get to the labor paper so we adjust the
+ 
+
+ align:start position:0%
+get to the labor paper so we adjust the
+income we divide by fixed assets that as
+
+ align:start position:0%
+income we divide by fixed assets that as
+ 
+
+ align:start position:0%
+income we divide by fixed assets that as
+you know is rate of return on assets we
+
+ align:start position:0%
+you know is rate of return on assets we
+ 
+
+ align:start position:0%
+you know is rate of return on assets we
+make it real the data is nominal it's
+
+ align:start position:0%
+make it real the data is nominal it's
+ 
+
+ align:start position:0%
+make it real the data is nominal it's
+all measured in tbot so we deflate by
+
+ align:start position:0%
+all measured in tbot so we deflate by
+ 
+
+ align:start position:0%
+all measured in tbot so we deflate by
+Bank of
+
+ align:start position:0%
+Bank of
+ 
+
+ align:start position:0%
+Bank of
+Thailand Regional uh price price
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+changes
+
+ align:start position:0%
+changes
+ 
+
+ align:start position:0%
+changes
+um this is uh the table of the rates of
+
+ align:start position:0%
+um this is uh the table of the rates of
+ 
+
+ align:start position:0%
+um this is uh the table of the rates of
+return
+
+ align:start position:0%
+return
+ 
+
+ align:start position:0%
+return
+uh mean standard deviation and the
+
+ align:start position:0%
+uh mean standard deviation and the
+ 
+
+ align:start position:0%
+uh mean standard deviation and the
+so-called shite so I I forgot to say it
+
+ align:start position:0%
+so-called shite so I I forgot to say it
+ 
+
+ align:start position:0%
+so-called shite so I I forgot to say it
+but that thing I kept saying was sort of
+
+ align:start position:0%
+but that thing I kept saying was sort of
+ 
+
+ align:start position:0%
+but that thing I kept saying was sort of
+like a coefficient of variation
+
+ align:start position:0%
+like a coefficient of variation
+ 
+
+ align:start position:0%
+like a coefficient of variation
+that's like the inverse sharp
+
+ align:start position:0%
+that's like the inverse sharp
+ 
+
+ align:start position:0%
+that's like the inverse sharp
+ratio so you can add that to your
+
+ align:start position:0%
+ratio so you can add that to your
+ 
+
+ align:start position:0%
+ratio so you can add that to your
+vocabulary
+
+ align:start position:0%
+vocabulary
+ 
+
+ align:start position:0%
+vocabulary
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now each household has a sample average
+
+ align:start position:0%
+now each household has a sample average
+ 
+
+ align:start position:0%
+now each household has a sample average
+so you're going to have a mean standard
+
+ align:start position:0%
+so you're going to have a mean standard
+ 
+
+ align:start position:0%
+so you're going to have a mean standard
+deviation etc those statistical moments
+
+ align:start position:0%
+deviation etc those statistical moments
+ 
+
+ align:start position:0%
+deviation etc those statistical moments
+for every single household so you have a
+
+ align:start position:0%
+for every single household so you have a
+ 
+
+ align:start position:0%
+for every single household so you have a
+histogram in the population so you can
+
+ align:start position:0%
+histogram in the population so you can
+ 
+
+ align:start position:0%
+histogram in the population so you can
+look at the medium and mean if you want
+
+ align:start position:0%
+look at the medium and mean if you want
+ 
+
+ align:start position:0%
+look at the medium and mean if you want
+if it's not too confusing or uh you know
+
+ align:start position:0%
+if it's not too confusing or uh you know
+ 
+
+ align:start position:0%
+if it's not too confusing or uh you know
+the 25th and 75th quartiles of rates of
+
+ align:start position:0%
+the 25th and 75th quartiles of rates of
+ 
+
+ align:start position:0%
+the 25th and 75th quartiles of rates of
+return
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you know some of them are high many
+
+ align:start position:0%
+um you know some of them are high many
+ 
+
+ align:start position:0%
+um you know some of them are high many
+of them are not that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+high but in any event these are not
+
+ align:start position:0%
+high but in any event these are not
+ 
+
+ align:start position:0%
+high but in any event these are not
+adjusted at all they're just the crude
+
+ align:start position:0%
+adjusted at all they're just the crude
+ 
+
+ align:start position:0%
+adjusted at all they're just the crude
+rates of return if
+
+ align:start position:0%
+rates of return if
+ 
+
+ align:start position:0%
+rates of return if
+um okay so now we got to decide what to
+
+ align:start position:0%
+um okay so now we got to decide what to
+ 
+
+ align:start position:0%
+um okay so now we got to decide what to
+do with the risk-free
+
+ align:start position:0%
+do with the risk-free
+ 
+
+ align:start position:0%
+do with the risk-free
+rate uh well these are supposed to be
+
+ align:start position:0%
+rate uh well these are supposed to be
+ 
+
+ align:start position:0%
+rate uh well these are supposed to be
+real so we're we're basically going to
+
+ align:start position:0%
+real so we're we're basically going to
+ 
+
+ align:start position:0%
+real so we're we're basically going to
+assume they have something like
+
+ align:start position:0%
+assume they have something like
+ 
+
+ align:start position:0%
+assume they have something like
+inventory that goes up with the price
+
+ align:start position:0%
+inventory that goes up with the price
+ 
+
+ align:start position:0%
+inventory that goes up with the price
+level and there's nothing stochastic
+
+ align:start position:0%
+level and there's nothing stochastic
+ 
+
+ align:start position:0%
+level and there's nothing stochastic
+about it so we're going to assume the
+
+ align:start position:0%
+about it so we're going to assume the
+ 
+
+ align:start position:0%
+about it so we're going to assume the
+real rate of return is zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh now again if we're guessing wrong
+
+ align:start position:0%
+uh now again if we're guessing wrong
+ 
+
+ align:start position:0%
+uh now again if we're guessing wrong
+about this we're going to be guessing
+
+ align:start position:0%
+about this we're going to be guessing
+ 
+
+ align:start position:0%
+about this we're going to be guessing
+wrong about the intercepts because
+
+ align:start position:0%
+wrong about the intercepts because
+ 
+
+ align:start position:0%
+wrong about the intercepts because
+everything we do is you know subtracting
+
+ align:start position:0%
+everything we do is you know subtracting
+ 
+
+ align:start position:0%
+everything we do is you know subtracting
+off
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero but anyway that's what we
+
+ align:start position:0%
+zero but anyway that's what we
+ 
+
+ align:start position:0%
+zero but anyway that's what we
+do the market return is the sort of the
+
+ align:start position:0%
+do the market return is the sort of the
+ 
+
+ align:start position:0%
+do the market return is the sort of the
+average uh Township rate of return you
+
+ align:start position:0%
+average uh Township rate of return you
+ 
+
+ align:start position:0%
+average uh Township rate of return you
+know and again
+
+ align:start position:0%
+know and again
+ 
+
+ align:start position:0%
+know and again
+that's just looking at the income over
+
+ align:start position:0%
+that's just looking at the income over
+ 
+
+ align:start position:0%
+that's just looking at the income over
+all the
+
+ align:start position:0%
+all the
+ 
+
+ align:start position:0%
+all the
+households divided
+
+ align:start position:0%
+households divided
+ 
+
+ align:start position:0%
+households divided
+by all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+assets we're about to run a regression
+
+ align:start position:0%
+assets we're about to run a regression
+ 
+
+ align:start position:0%
+assets we're about to run a regression
+though so we will take out the
+
+ align:start position:0%
+though so we will take out the
+ 
+
+ align:start position:0%
+though so we will take out the
+household's own contribution to the
+
+ align:start position:0%
+household's own contribution to the
+ 
+
+ align:start position:0%
+household's own contribution to the
+Village average it's like a leave out
+
+ align:start position:0%
+Village average it's like a leave out
+ 
+
+ align:start position:0%
+Village average it's like a leave out
+mean so we don't you know bias it in the
+
+ align:start position:0%
+mean so we don't you know bias it in the
+ 
+
+ align:start position:0%
+mean so we don't you know bias it in the
+obvious way yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depreciation is is in here because
+
+ align:start position:0%
+depreciation is is in here because
+ 
+
+ align:start position:0%
+depreciation is is in here because
+depreciation is a uh a cost that we're
+
+ align:start position:0%
+depreciation is a uh a cost that we're
+ 
+
+ align:start position:0%
+depreciation is a uh a cost that we're
+subtracting off in the financial
+
+ align:start position:0%
+subtracting off in the financial
+ 
+
+ align:start position:0%
+subtracting off in the financial
+accounts
+
+ align:start position:0%
+accounts
+ 
+
+ align:start position:0%
+accounts
+uhhuh so the these these numbers are
+
+ align:start position:0%
+uhhuh so the these these numbers are
+ 
+
+ align:start position:0%
+uhhuh so the these these numbers are
+basically coming off of the income as in
+
+ align:start position:0%
+basically coming off of the income as in
+ 
+
+ align:start position:0%
+basically coming off of the income as in
+the income statement and the assets as
+
+ align:start position:0%
+the income statement and the assets as
+ 
+
+ align:start position:0%
+the income statement and the assets as
+in the balance sheet which you've seen
+
+ align:start position:0%
+in the balance sheet which you've seen
+ 
+
+ align:start position:0%
+in the balance sheet which you've seen
+before although it is true that we cover
+
+ align:start position:0%
+before although it is true that we cover
+ 
+
+ align:start position:0%
+before although it is true that we cover
+a lot of ground
+
+ align:start position:0%
+a lot of ground
+ 
+
+ align:start position:0%
+a lot of ground
+so happy to remind you
+
+ align:start position:0%
+so happy to remind you
+ 
+
+ align:start position:0%
+so happy to remind you
+um so how do we get the relationship of
+
+ align:start position:0%
+um so how do we get the relationship of
+ 
+
+ align:start position:0%
+um so how do we get the relationship of
+the households rate of return to the
+
+ align:start position:0%
+the households rate of return to the
+ 
+
+ align:start position:0%
+the households rate of return to the
+Village average we run a
+
+ align:start position:0%
+Village average we run a
+ 
+
+ align:start position:0%
+Village average we run a
+regression we run a regression of the
+
+ align:start position:0%
+regression we run a regression of the
+ 
+
+ align:start position:0%
+regression we run a regression of the
+households over all of its projects
+
+ align:start position:0%
+households over all of its projects
+ 
+
+ align:start position:0%
+households over all of its projects
+households
+
+ align:start position:0%
+households
+ 
+
+ align:start position:0%
+households
+return at dat T but you know there are
+
+ align:start position:0%
+return at dat T but you know there are
+ 
+
+ align:start position:0%
+return at dat T but you know there are
+lots of dates t with all those months
+
+ align:start position:0%
+lots of dates t with all those months
+ 
+
+ align:start position:0%
+lots of dates t with all those months
+more on that in a second regressed
+
+ align:start position:0%
+more on that in a second regressed
+ 
+
+ align:start position:0%
+more on that in a second regressed
+against the village return at day t
+
+ align:start position:0%
+against the village return at day t
+ 
+
+ align:start position:0%
+against the village return at day t
+okay so this beta is just literally the
+
+ align:start position:0%
+okay so this beta is just literally the
+ 
+
+ align:start position:0%
+okay so this beta is just literally the
+regression coefficient that we wanted
+
+ align:start position:0%
+regression coefficient that we wanted
+ 
+
+ align:start position:0%
+regression coefficient that we wanted
+conveniently yes assuming this beta is
+
+ align:start position:0%
+conveniently yes assuming this beta is
+ 
+
+ align:start position:0%
+conveniently yes assuming this beta is
+constant over time uh we're going
+
+ align:start position:0%
+constant over time uh we're going
+ 
+
+ align:start position:0%
+constant over time uh we're going
+to okay so yeah we're there's several
+
+ align:start position:0%
+to okay so yeah we're there's several
+ 
+
+ align:start position:0%
+to okay so yeah we're there's several
+adjustments I think it's on the next
+
+ align:start position:0%
+adjustments I think it's on the next
+ 
+
+ align:start position:0%
+adjustments I think it's on the next
+page but anyway so so actually what
+
+ align:start position:0%
+page but anyway so so actually what
+ 
+
+ align:start position:0%
+page but anyway so so actually what
+we're going to do is do
+
+ align:start position:0%
+we're going to do is do
+ 
+
+ align:start position:0%
+we're going to do is do
+fiveyear
+
+ align:start position:0%
+fiveyear
+ 
+
+ align:start position:0%
+fiveyear
+increments uh you could just take one
+
+ align:start position:0%
+increments uh you could just take one
+ 
+
+ align:start position:0%
+increments uh you could just take one
+household over for all the many you know
+
+ align:start position:0%
+household over for all the many you know
+ 
+
+ align:start position:0%
+household over for all the many you know
+years and
+
+ align:start position:0%
+years and
+ 
+
+ align:start position:0%
+years and
+months and uh and ignore possible shifts
+
+ align:start position:0%
+months and uh and ignore possible shifts
+ 
+
+ align:start position:0%
+months and uh and ignore possible shifts
+in their
+
+ align:start position:0%
+in their
+ 
+
+ align:start position:0%
+in their
+portfolio but like you're saying that
+
+ align:start position:0%
+portfolio but like you're saying that
+ 
+
+ align:start position:0%
+portfolio but like you're saying that
+might be a bad idea so we redid
+
+ align:start position:0%
+might be a bad idea so we redid
+ 
+
+ align:start position:0%
+might be a bad idea so we redid
+it as if you know the household had
+
+ align:start position:0%
+it as if you know the household had
+ 
+
+ align:start position:0%
+it as if you know the household had
+Returns on a portfolio from year 1
+
+ align:start position:0%
+Returns on a portfolio from year 1
+ 
+
+ align:start position:0%
+Returns on a portfolio from year 1
+through five then Returns on a portfolio
+
+ align:start position:0%
+through five then Returns on a portfolio
+ 
+
+ align:start position:0%
+through five then Returns on a portfolio
+from year 2 through six 7 through 8 and
+
+ align:start position:0%
+from year 2 through six 7 through 8 and
+ 
+
+ align:start position:0%
+from year 2 through six 7 through 8 and
+so on all the way through and it turns
+
+ align:start position:0%
+so on all the way through and it turns
+ 
+
+ align:start position:0%
+so on all the way through and it turns
+out that's that idea as many others come
+
+ align:start position:0%
+out that's that idea as many others come
+ 
+
+ align:start position:0%
+out that's that idea as many others come
+from the finance literature so that's
+
+ align:start position:0%
+from the finance literature so that's
+ 
+
+ align:start position:0%
+from the finance literature so that's
+what we're
+
+ align:start position:0%
+what we're
+ 
+
+ align:start position:0%
+what we're
+doing uh the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+adjustment I should have mentioned
+
+ align:start position:0%
+adjustment I should have mentioned
+ 
+
+ align:start position:0%
+adjustment I should have mentioned
+earlier and I didn't but you remember
+
+ align:start position:0%
+earlier and I didn't but you remember
+ 
+
+ align:start position:0%
+earlier and I didn't but you remember
+when we used a quadratic
+
+ align:start position:0%
+when we used a quadratic
+ 
+
+ align:start position:0%
+when we used a quadratic
+utility it was a plus b time something
+
+ align:start position:0%
+utility it was a plus b time something
+ 
+
+ align:start position:0%
+utility it was a plus b time something
+right and there was no t on those things
+
+ align:start position:0%
+right and there was no t on those things
+ 
+
+ align:start position:0%
+right and there was no t on those things
+so it was like the marginal utility of
+
+ align:start position:0%
+so it was like the marginal utility of
+ 
+
+ align:start position:0%
+so it was like the marginal utility of
+wealth you know just depends on wealth
+
+ align:start position:0%
+wealth you know just depends on wealth
+ 
+
+ align:start position:0%
+wealth you know just depends on wealth
+and it doesn't depend on anything else
+
+ align:start position:0%
+and it doesn't depend on anything else
+ 
+
+ align:start position:0%
+and it doesn't depend on anything else
+but in many intertemporal
+
+ align:start position:0%
+but in many intertemporal
+ 
+
+ align:start position:0%
+but in many intertemporal
+models
+
+ align:start position:0%
+models
+ 
+
+ align:start position:0%
+models
+uh those things would be moving
+
+ align:start position:0%
+uh those things would be moving
+ 
+
+ align:start position:0%
+uh those things would be moving
+around so we're I'll tell you about that
+
+ align:start position:0%
+around so we're I'll tell you about that
+ 
+
+ align:start position:0%
+around so we're I'll tell you about that
+adjustment
+
+ align:start position:0%
+adjustment
+ 
+
+ align:start position:0%
+adjustment
+too we actually did it all the different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ways
+
+ align:start position:0%
+ways
+ 
+
+ align:start position:0%
+ways
+so but these are the key steps We Run
+
+ align:start position:0%
+so but these are the key steps We Run
+ 
+
+ align:start position:0%
+so but these are the key steps We Run
+The regression or regressions for each
+
+ align:start position:0%
+The regression or regressions for each
+ 
+
+ align:start position:0%
+The regression or regressions for each
+household um
+
+ align:start position:0%
+household um
+ 
+
+ align:start position:0%
+household um
+and then uh we get the beta for each
+
+ align:start position:0%
+and then uh we get the beta for each
+ 
+
+ align:start position:0%
+and then uh we get the beta for each
+household
+
+ align:start position:0%
+household
+ 
+
+ align:start position:0%
+household
+J and we get the ex the uh the average
+
+ align:start position:0%
+J and we get the ex the uh the average
+ 
+
+ align:start position:0%
+J and we get the ex the uh the average
+return either over all the years or over
+
+ align:start position:0%
+return either over all the years or over
+ 
+
+ align:start position:0%
+return either over all the years or over
+these five year increments and then we
+
+ align:start position:0%
+these five year increments and then we
+ 
+
+ align:start position:0%
+these five year increments and then we
+we run this regression
+
+ align:start position:0%
+we run this regression
+ 
+
+ align:start position:0%
+we run this regression
+essentially with this already coming
+
+ align:start position:0%
+essentially with this already coming
+ 
+
+ align:start position:0%
+essentially with this already coming
+from a previous regression using the
+
+ align:start position:0%
+from a previous regression using the
+ 
+
+ align:start position:0%
+from a previous regression using the
+panel this thing is just a
+
+ align:start position:0%
+panel this thing is just a
+ 
+
+ align:start position:0%
+panel this thing is just a
+cross-sectional regression there's no
+
+ align:start position:0%
+cross-sectional regression there's no
+ 
+
+ align:start position:0%
+cross-sectional regression there's no
+time date here this is the average
+
+ align:start position:0%
+time date here this is the average
+ 
+
+ align:start position:0%
+time date here this is the average
+return this is the extent to which the
+
+ align:start position:0%
+return this is the extent to which the
+ 
+
+ align:start position:0%
+return this is the extent to which the
+village that household's returns are
+
+ align:start position:0%
+village that household's returns are
+ 
+
+ align:start position:0%
+village that household's returns are
+correlated with the village
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+average and we'll get expressions for
+
+ align:start position:0%
+average and we'll get expressions for
+ 
+
+ align:start position:0%
+average and we'll get expressions for
+Lambda Alpha and so on and there are
+
+ align:start position:0%
+Lambda Alpha and so on and there are
+ 
+
+ align:start position:0%
+Lambda Alpha and so on and there are
+restrictions although you no
+
+ align:start position:0%
+restrictions although you no
+ 
+
+ align:start position:0%
+restrictions although you no
+doubt can't remember you know seven and
+
+ align:start position:0%
+doubt can't remember you know seven and
+ 
+
+ align:start position:0%
+doubt can't remember you know seven and
+a half slides back that that this Lambda
+
+ align:start position:0%
+a half slides back that that this Lambda
+ 
+
+ align:start position:0%
+a half slides back that that this Lambda
+ought to be equal to something like the
+
+ align:start position:0%
+ought to be equal to something like the
+ 
+
+ align:start position:0%
+ought to be equal to something like the
+expected market rate of r turn but just
+
+ align:start position:0%
+expected market rate of r turn but just
+ 
+
+ align:start position:0%
+expected market rate of r turn but just
+hit my word for
+
+ align:start position:0%
+hit my word for
+ 
+
+ align:start position:0%
+hit my word for
+it we don't impose that restriction so
+
+ align:start position:0%
+it we don't impose that restriction so
+ 
+
+ align:start position:0%
+it we don't impose that restriction so
+here's the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+result
+
+ align:start position:0%
+result
+ 
+
+ align:start position:0%
+result
+beta is on the right hand side and it's
+
+ align:start position:0%
+beta is on the right hand side and it's
+ 
+
+ align:start position:0%
+beta is on the right hand side and it's
+being regressed against a households
+
+ align:start position:0%
+being regressed against a households
+ 
+
+ align:start position:0%
+being regressed against a households
+mean rate of
+
+ align:start position:0%
+mean rate of
+ 
+
+ align:start position:0%
+mean rate of
+return
+
+ align:start position:0%
+return
+ 
+
+ align:start position:0%
+return
+and three of the four
+
+ align:start position:0%
+and three of the four
+ 
+
+ align:start position:0%
+and three of the four
+provinces it's quite uh quite positive
+
+ align:start position:0%
+provinces it's quite uh quite positive
+ 
+
+ align:start position:0%
+provinces it's quite uh quite positive
+and significant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the only thing in this you know these
+
+ align:start position:0%
+the only thing in this you know these
+ 
+
+ align:start position:0%
+the only thing in this you know these
+are the regression coefficients the
+
+ align:start position:0%
+are the regression coefficients the
+ 
+
+ align:start position:0%
+are the regression coefficients the
+lambas basically and this is the
+
+ align:start position:0%
+lambas basically and this is the
+ 
+
+ align:start position:0%
+lambas basically and this is the
+estimated
+
+ align:start position:0%
+estimated
+ 
+
+ align:start position:0%
+estimated
+constant and uh you know R squares you
+
+ align:start position:0%
+constant and uh you know R squares you
+ 
+
+ align:start position:0%
+constant and uh you know R squares you
+know what it is kind of worth noting
+
+ align:start position:0%
+know what it is kind of worth noting
+ 
+
+ align:start position:0%
+know what it is kind of worth noting
+buam fails and has a very low R
+
+ align:start position:0%
+buam fails and has a very low R
+ 
+
+ align:start position:0%
+buam fails and has a very low R
+square and buam is one of the places
+
+ align:start position:0%
+square and buam is one of the places
+ 
+
+ align:start position:0%
+square and buam is one of the places
+I've mentioned where the Farmland got
+
+ align:start position:0%
+I've mentioned where the Farmland got
+ 
+
+ align:start position:0%
+I've mentioned where the Farmland got
+plowed over with roads and you know the
+
+ align:start position:0%
+plowed over with roads and you know the
+ 
+
+ align:start position:0%
+plowed over with roads and you know the
+town was being built up so there
+
+ align:start position:0%
+town was being built up so there
+ 
+
+ align:start position:0%
+town was being built up so there
+arguably were a lot of changes in
+
+ align:start position:0%
+arguably were a lot of changes in
+ 
+
+ align:start position:0%
+arguably were a lot of changes in
+occupations um we'll try to fix that yes
+
+ align:start position:0%
+occupations um we'll try to fix that yes
+ 
+
+ align:start position:0%
+occupations um we'll try to fix that yes
+so is this for one fiveyear period or is
+
+ align:start position:0%
+so is this for one fiveyear period or is
+ 
+
+ align:start position:0%
+so is this for one fiveyear period or is
+this like an average of the this is
+
+ align:start position:0%
+this like an average of the this is
+ 
+
+ align:start position:0%
+this like an average of the this is
+actually with all of the treating each
+
+ align:start position:0%
+actually with all of the treating each
+ 
+
+ align:start position:0%
+actually with all of the treating each
+household multiple times okay so I think
+
+ align:start position:0%
+household multiple times okay so I think
+ 
+
+ align:start position:0%
+household multiple times okay so I think
+let me just see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no it's not yet so that's like the whole
+
+ align:start position:0%
+no it's not yet so that's like the whole
+ 
+
+ align:start position:0%
+no it's not yet so that's like the whole
+this is the whole thing we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+haveu there some possibility
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we worried quite a bit about you know
+
+ align:start position:0%
+we worried quite a bit about you know
+ 
+
+ align:start position:0%
+we worried quite a bit about you know
+potentially ecometric biases and so on
+
+ align:start position:0%
+potentially ecometric biases and so on
+ 
+
+ align:start position:0%
+potentially ecometric biases and so on
+and so forth then we went back and read
+
+ align:start position:0%
+and so forth then we went back and read
+ 
+
+ align:start position:0%
+and so forth then we went back and read
+the classics in finance F French you
+
+ align:start position:0%
+the classics in finance F French you
+ 
+
+ align:start position:0%
+the classics in finance F French you
+know all these guys and we're doing what
+
+ align:start position:0%
+know all these guys and we're doing what
+ 
+
+ align:start position:0%
+know all these guys and we're doing what
+they're doing so we felt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+better uh
+
+ align:start position:0%
+better uh
+ 
+
+ align:start position:0%
+better uh
+if we regress the errors on the lag
+
+ align:start position:0%
+if we regress the errors on the lag
+ 
+
+ align:start position:0%
+if we regress the errors on the lag
+themselves does it pass a test or is it
+
+ align:start position:0%
+themselves does it pass a test or is it
+ 
+
+ align:start position:0%
+themselves does it pass a test or is it
+oh we haven't yeah we I don't think
+
+ align:start position:0%
+oh we haven't yeah we I don't think
+ 
+
+ align:start position:0%
+oh we haven't yeah we I don't think
+we've looked for autocorrelation and
+
+ align:start position:0%
+we've looked for autocorrelation and
+ 
+
+ align:start position:0%
+we've looked for autocorrelation and
+stuff like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the HH
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Factor okay we we'll check that yes so
+
+ align:start position:0%
+Factor okay we we'll check that yes so
+ 
+
+ align:start position:0%
+Factor okay we we'll check that yes so
+do you think it's worth to just test to
+
+ align:start position:0%
+do you think it's worth to just test to
+ 
+
+ align:start position:0%
+do you think it's worth to just test to
+Joint test RHA J for each household like
+
+ align:start position:0%
+Joint test RHA J for each household like
+ 
+
+ align:start position:0%
+Joint test RHA J for each household like
+the finance guys we're about to show you
+
+ align:start position:0%
+the finance guys we're about to show you
+ 
+
+ align:start position:0%
+the finance guys we're about to show you
+the alas okay I haven't gotten there yet
+
+ align:start position:0%
+the alas okay I haven't gotten there yet
+ 
+
+ align:start position:0%
+the alas okay I haven't gotten there yet
+I'm we we'll see when I get there
+
+ align:start position:0%
+I'm we we'll see when I get there
+ 
+
+ align:start position:0%
+I'm we we'll see when I get there
+whether you have something different in
+
+ align:start position:0%
+whether you have something different in
+ 
+
+ align:start position:0%
+whether you have something different in
+mind
+
+ align:start position:0%
+mind
+ 
+
+ align:start position:0%
+mind
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway oops sorry so if you want to
+
+ align:start position:0%
+anyway oops sorry so if you want to
+ 
+
+ align:start position:0%
+anyway oops sorry so if you want to
+visually see sort of a mean variance
+
+ align:start position:0%
+visually see sort of a mean variance
+ 
+
+ align:start position:0%
+visually see sort of a mean variance
+Frontier uh you know this the beta is
+
+ align:start position:0%
+Frontier uh you know this the beta is
+ 
+
+ align:start position:0%
+Frontier uh you know this the beta is
+down here that's kind of the risk
+
+ align:start position:0%
+down here that's kind of the risk
+ 
+
+ align:start position:0%
+down here that's kind of the risk
+factor if you believe this model and the
+
+ align:start position:0%
+factor if you believe this model and the
+ 
+
+ align:start position:0%
+factor if you believe this model and the
+expected returns are here and you can
+
+ align:start position:0%
+expected returns are here and you can
+ 
+
+ align:start position:0%
+expected returns are here and you can
+see a pretty close
+
+ align:start position:0%
+see a pretty close
+ 
+
+ align:start position:0%
+see a pretty close
+fit now this you know I've shown to the
+
+ align:start position:0%
+fit now this you know I've shown to the
+ 
+
+ align:start position:0%
+fit now this you know I've shown to the
+finance guys you
+
+ align:start position:0%
+finance guys you
+ 
+
+ align:start position:0%
+finance guys you
+know at lunches and things and they're
+
+ align:start position:0%
+know at lunches and things and they're
+ 
+
+ align:start position:0%
+know at lunches and things and they're
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+wow because this this is actually pretty
+
+ align:start position:0%
+wow because this this is actually pretty
+ 
+
+ align:start position:0%
+wow because this this is actually pretty
+good relative to New York financial
+
+ align:start position:0%
+good relative to New York financial
+ 
+
+ align:start position:0%
+good relative to New York financial
+markets um
+
+ align:start position:0%
+markets um
+ 
+
+ align:start position:0%
+markets um
+oh it's an easy target
+
+ align:start position:0%
+oh it's an easy target
+ 
+
+ align:start position:0%
+oh it's an easy target
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh so so far we are showing that uh just
+
+ align:start position:0%
+uh so so far we are showing that uh just
+ 
+
+ align:start position:0%
+uh so so far we are showing that uh just
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+repeat uh when someone has a high return
+
+ align:start position:0%
+repeat uh when someone has a high return
+ 
+
+ align:start position:0%
+repeat uh when someone has a high return
+it's partly not Talent it's just that
+
+ align:start position:0%
+it's partly not Talent it's just that
+ 
+
+ align:start position:0%
+it's partly not Talent it's just that
+it's correlated with the The Village
+
+ align:start position:0%
+it's correlated with the The Village
+ 
+
+ align:start position:0%
+it's correlated with the The Village
+average and and it's it's high because
+
+ align:start position:0%
+average and and it's it's high because
+ 
+
+ align:start position:0%
+average and and it's it's high because
+you need to adjust for the
+
+ align:start position:0%
+you need to adjust for the
+ 
+
+ align:start position:0%
+you need to adjust for the
+risk now we can do this at the Village
+
+ align:start position:0%
+risk now we can do this at the Village
+ 
+
+ align:start position:0%
+risk now we can do this at the Village
+level in which case nine of the 16
+
+ align:start position:0%
+level in which case nine of the 16
+ 
+
+ align:start position:0%
+level in which case nine of the 16
+Villages we're going to have this
+
+ align:start position:0%
+Villages we're going to have this
+ 
+
+ align:start position:0%
+Villages we're going to have this
+positive correlation that the theory
+
+ align:start position:0%
+positive correlation that the theory
+ 
+
+ align:start position:0%
+positive correlation that the theory
+says ought to be there and when you go
+
+ align:start position:0%
+says ought to be there and when you go
+ 
+
+ align:start position:0%
+says ought to be there and when you go
+to the town the
+
+ align:start position:0%
+to the town the
+ 
+
+ align:start position:0%
+to the town the
+uh we go to the network level we have
+
+ align:start position:0%
+uh we go to the network level we have
+ 
+
+ align:start position:0%
+uh we go to the network level we have
+five out of nine
+
+ align:start position:0%
+five out of nine
+ 
+
+ align:start position:0%
+five out of nine
+networks and and I'll show you about the
+
+ align:start position:0%
+networks and and I'll show you about the
+ 
+
+ align:start position:0%
+networks and and I'll show you about the
+adjustments remind you here's a kinship
+
+ align:start position:0%
+adjustments remind you here's a kinship
+ 
+
+ align:start position:0%
+adjustments remind you here's a kinship
+Network you know 206 is married with 207
+
+ align:start position:0%
+Network you know 206 is married with 207
+ 
+
+ align:start position:0%
+Network you know 206 is married with 207
+in some way and 214 has all these so you
+
+ align:start position:0%
+in some way and 214 has all these so you
+ 
+
+ align:start position:0%
+in some way and 214 has all these so you
+know connect literally connect the
+
+ align:start position:0%
+know connect literally connect the
+ 
+
+ align:start position:0%
+know connect literally connect the
+dots here's a big Dynasty down here
+
+ align:start position:0%
+dots here's a big Dynasty down here
+ 
+
+ align:start position:0%
+dots here's a big Dynasty down here
+here's a little Dynasty there another
+
+ align:start position:0%
+here's a little Dynasty there another
+ 
+
+ align:start position:0%
+here's a little Dynasty there another
+little Dynasty there so we went through
+
+ align:start position:0%
+little Dynasty there so we went through
+ 
+
+ align:start position:0%
+little Dynasty there so we went through
+all the villages and sort of and they
+
+ align:start position:0%
+all the villages and sort of and they
+ 
+
+ align:start position:0%
+all the villages and sort of and they
+had to have enough data to do this so we
+
+ align:start position:0%
+had to have enough data to do this so we
+ 
+
+ align:start position:0%
+had to have enough data to do this so we
+ended
+
+ align:start position:0%
+ended
+ 
+
+ align:start position:0%
+ended
+up with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh with networks now some
+
+ align:start position:0%
+uh with networks now some
+ 
+
+ align:start position:0%
+uh with networks now some
+Villages uh have more than one
+
+ align:start position:0%
+Villages uh have more than one
+ 
+
+ align:start position:0%
+Villages uh have more than one
+Etc um so of the nine with enough data
+
+ align:start position:0%
+Etc um so of the nine with enough data
+ 
+
+ align:start position:0%
+Etc um so of the nine with enough data
+you know we picking up the theory doing
+
+ align:start position:0%
+you know we picking up the theory doing
+ 
+
+ align:start position:0%
+you know we picking up the theory doing
+well here and not in some of the other
+
+ align:start position:0%
+well here and not in some of the other
+ 
+
+ align:start position:0%
+well here and not in some of the other
+ones so as I said we get go micro go
+
+ align:start position:0%
+ones so as I said we get go micro go
+ 
+
+ align:start position:0%
+ones so as I said we get go micro go
+macro zooming in and out
+
+ align:start position:0%
+macro zooming in and out
+ 
+
+ align:start position:0%
+macro zooming in and out
+um there's a lot
+
+ align:start position:0%
+um there's a lot
+ 
+
+ align:start position:0%
+um there's a lot
+of explanation of the rate of
+
+ align:start position:0%
+of explanation of the rate of
+ 
+
+ align:start position:0%
+of explanation of the rate of
+return that has to do with a village
+
+ align:start position:0%
+return that has to do with a village
+ 
+
+ align:start position:0%
+return that has to do with a village
+average this is
+
+ align:start position:0%
+average this is
+ 
+
+ align:start position:0%
+average this is
+Villages uh okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this has to do with changing projects
+
+ align:start position:0%
+so this has to do with changing projects
+ 
+
+ align:start position:0%
+so this has to do with changing projects
+basically so it's what I said we use
+
+ align:start position:0%
+basically so it's what I said we use
+ 
+
+ align:start position:0%
+basically so it's what I said we use
+these sort
+
+ align:start position:0%
+these sort
+ 
+
+ align:start position:0%
+these sort
+of 5year intervals and redo
+
+ align:start position:0%
+of 5year intervals and redo
+ 
+
+ align:start position:0%
+of 5year intervals and redo
+it uh and and kind of reassuringly buram
+
+ align:start position:0%
+it uh and and kind of reassuringly buram
+ 
+
+ align:start position:0%
+it uh and and kind of reassuringly buram
+Pops back in there because buram was the
+
+ align:start position:0%
+Pops back in there because buram was the
+ 
+
+ align:start position:0%
+Pops back in there because buram was the
+place for sure that I know that they've
+
+ align:start position:0%
+place for sure that I know that they've
+ 
+
+ align:start position:0%
+place for sure that I know that they've
+switched occupations quite a bit and
+
+ align:start position:0%
+switched occupations quite a bit and
+ 
+
+ align:start position:0%
+switched occupations quite a bit and
+moved from you know lower to higher
+
+ align:start position:0%
+moved from you know lower to higher
+ 
+
+ align:start position:0%
+moved from you know lower to higher
+rates of return so it's kind of
+
+ align:start position:0%
+rates of return so it's kind of
+ 
+
+ align:start position:0%
+rates of return so it's kind of
+reassuring given the previous work to
+
+ align:start position:0%
+reassuring given the previous work to
+ 
+
+ align:start position:0%
+reassuring given the previous work to
+see that this adjustment
+
+ align:start position:0%
+see that this adjustment
+ 
+
+ align:start position:0%
+see that this adjustment
+allows us to
+
+ align:start position:0%
+allows us to
+ 
+
+ align:start position:0%
+allows us to
+recover you know something although the
+
+ align:start position:0%
+recover you know something although the
+ 
+
+ align:start position:0%
+recover you know something although the
+R square is nothing to brag about um but
+
+ align:start position:0%
+R square is nothing to brag about um but
+ 
+
+ align:start position:0%
+R square is nothing to brag about um but
+anyway now another another hard thing
+
+ align:start position:0%
+anyway now another another hard thing
+ 
+
+ align:start position:0%
+anyway now another another hard thing
+easy and hard at the same time is human
+
+ align:start position:0%
+easy and hard at the same time is human
+ 
+
+ align:start position:0%
+easy and hard at the same time is human
+capital not physical
+
+ align:start position:0%
+capital not physical
+ 
+
+ align:start position:0%
+capital not physical
+capital so as you know a lot of these
+
+ align:start position:0%
+capital so as you know a lot of these
+ 
+
+ align:start position:0%
+capital so as you know a lot of these
+households have labors they're earning
+
+ align:start position:0%
+households have labors they're earning
+ 
+
+ align:start position:0%
+households have labors they're earning
+wages and you say well where what's that
+
+ align:start position:0%
+wages and you say well where what's that
+ 
+
+ align:start position:0%
+wages and you say well where what's that
+the the fruit of what tree is that well
+
+ align:start position:0%
+the the fruit of what tree is that well
+ 
+
+ align:start position:0%
+the the fruit of what tree is that well
+the tree is human capital of course you
+
+ align:start position:0%
+the tree is human capital of course you
+ 
+
+ align:start position:0%
+the tree is human capital of course you
+never really see
+
+ align:start position:0%
+never really see
+ 
+
+ align:start position:0%
+never really see
+that you can write Big H and you have
+
+ align:start position:0%
+that you can write Big H and you have
+ 
+
+ align:start position:0%
+that you can write Big H and you have
+the notation for it but what is it
+
+ align:start position:0%
+the notation for it but what is it
+ 
+
+ align:start position:0%
+the notation for it but what is it
+really unfortunately we don't need the
+
+ align:start position:0%
+really unfortunately we don't need the
+ 
+
+ align:start position:0%
+really unfortunately we don't need the
+measure the stock we all we need to do
+
+ align:start position:0%
+measure the stock we all we need to do
+ 
+
+ align:start position:0%
+measure the stock we all we need to do
+is measure the
+
+ align:start position:0%
+is measure the
+ 
+
+ align:start position:0%
+is measure the
+flow so you know so basically it's not
+
+ align:start position:0%
+flow so you know so basically it's not
+ 
+
+ align:start position:0%
+flow so you know so basically it's not
+quite right but largely the uh the
+
+ align:start position:0%
+quite right but largely the uh the
+ 
+
+ align:start position:0%
+quite right but largely the uh the
+return on human capital are the wages
+
+ align:start position:0%
+return on human capital are the wages
+ 
+
+ align:start position:0%
+return on human capital are the wages
+these households are earning and we will
+
+ align:start position:0%
+these households are earning and we will
+ 
+
+ align:start position:0%
+these households are earning and we will
+now put that in the equation as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+yep way I understand this is rather than
+
+ align:start position:0%
+yep way I understand this is rather than
+ 
+
+ align:start position:0%
+yep way I understand this is rather than
+something like still in Talent we saying
+
+ align:start position:0%
+something like still in Talent we saying
+ 
+
+ align:start position:0%
+something like still in Talent we saying
+people are getting different returns
+
+ align:start position:0%
+people are getting different returns
+ 
+
+ align:start position:0%
+people are getting different returns
+because they're somewhere along return
+
+ align:start position:0%
+because they're somewhere along return
+ 
+
+ align:start position:0%
+because they're somewhere along return
+Frontier so once we think of this model
+
+ align:start position:0%
+Frontier so once we think of this model
+ 
+
+ align:start position:0%
+Frontier so once we think of this model
+what like how do we then respond to the
+
+ align:start position:0%
+what like how do we then respond to the
+ 
+
+ align:start position:0%
+what like how do we then respond to the
+big questions of the puzzles of you
+
+ align:start position:0%
+big questions of the puzzles of you
+ 
+
+ align:start position:0%
+big questions of the puzzles of you
+like do we know what well we don't know
+
+ align:start position:0%
+like do we know what well we don't know
+ 
+
+ align:start position:0%
+like do we know what well we don't know
+yet I haven't shown you maybe there's no
+
+ align:start position:0%
+yet I haven't shown you maybe there's no
+ 
+
+ align:start position:0%
+yet I haven't shown you maybe there's no
+puzzle that's the point people aren't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+adjusting but but there still but but
+
+ align:start position:0%
+adjusting but but there still but but
+ 
+
+ align:start position:0%
+adjusting but but there still but but
+anyway not to keep you in suspense it is
+
+ align:start position:0%
+anyway not to keep you in suspense it is
+ 
+
+ align:start position:0%
+anyway not to keep you in suspense it is
+going to turn out that there is a
+
+ align:start position:0%
+going to turn out that there is a
+ 
+
+ align:start position:0%
+going to turn out that there is a
+residual and then we can see what it's
+
+ align:start position:0%
+residual and then we can see what it's
+ 
+
+ align:start position:0%
+residual and then we can see what it's
+related to and I actually said it's
+
+ align:start position:0%
+related to and I actually said it's
+ 
+
+ align:start position:0%
+related to and I actually said it's
+wealthy
+
+ align:start position:0%
+wealthy
+ 
+
+ align:start position:0%
+wealthy
+females who have the high residual rate
+
+ align:start position:0%
+females who have the high residual rate
+ 
+
+ align:start position:0%
+females who have the high residual rate
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+return question given that they're all
+
+ align:start position:0%
+return question given that they're all
+ 
+
+ align:start position:0%
+return question given that they're all
+in that very nice regession line which
+
+ align:start position:0%
+in that very nice regession line which
+ 
+
+ align:start position:0%
+in that very nice regession line which
+ones are where and why and part of the
+
+ align:start position:0%
+ones are where and why and part of the
+ 
+
+ align:start position:0%
+ones are where and why and part of the
+answer might is explained by well
+
+ align:start position:0%
+answer might is explained by well
+ 
+
+ align:start position:0%
+answer might is explained by well
+there's part of it that we're not
+
+ align:start position:0%
+there's part of it that we're not
+ 
+
+ align:start position:0%
+there's part of it that we're not
+explaining
+
+ align:start position:0%
+explaining
+ 
+
+ align:start position:0%
+explaining
+and even in the definition of the model
+
+ align:start position:0%
+and even in the definition of the model
+ 
+
+ align:start position:0%
+and even in the definition of the model
+in the construction of the model and
+
+ align:start position:0%
+in the construction of the model and
+ 
+
+ align:start position:0%
+in the construction of the model and
+another part that's outside the model
+
+ align:start position:0%
+another part that's outside the model
+ 
+
+ align:start position:0%
+another part that's outside the model
+altogether what we're not doing very
+
+ align:start position:0%
+altogether what we're not doing very
+ 
+
+ align:start position:0%
+altogether what we're not doing very
+well is you know why household J is
+
+ align:start position:0%
+well is you know why household J is
+ 
+
+ align:start position:0%
+well is you know why household J is
+running project I and some other
+
+ align:start position:0%
+running project I and some other
+ 
+
+ align:start position:0%
+running project I and some other
+household is not we're just acting like
+
+ align:start position:0%
+household is not we're just acting like
+ 
+
+ align:start position:0%
+household is not we're just acting like
+the social planner new and efficiently
+
+ align:start position:0%
+the social planner new and efficiently
+ 
+
+ align:start position:0%
+the social planner new and efficiently
+allocated projects across
+
+ align:start position:0%
+allocated projects across
+ 
+
+ align:start position:0%
+allocated projects across
+households so that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part is sort of related to the Talon
+
+ align:start position:0%
+part is sort of related to the Talon
+ 
+
+ align:start position:0%
+part is sort of related to the Talon
+thing but we never see it we're not
+
+ align:start position:0%
+thing but we never see it we're not
+ 
+
+ align:start position:0%
+thing but we never see it we're not
+we're not able to we can only look at
+
+ align:start position:0%
+we're not able to we can only look at
+ 
+
+ align:start position:0%
+we're not able to we can only look at
+the residual return which actually ought
+
+ align:start position:0%
+the residual return which actually ought
+ 
+
+ align:start position:0%
+the residual return which actually ought
+to be zero if the model is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+anyway uh
+
+ align:start position:0%
+anyway uh
+ 
+
+ align:start position:0%
+anyway uh
+so another adjustment that I've
+
+ align:start position:0%
+so another adjustment that I've
+ 
+
+ align:start position:0%
+so another adjustment that I've
+mentioned is that you know a plus BW
+
+ align:start position:0%
+mentioned is that you know a plus BW
+ 
+
+ align:start position:0%
+mentioned is that you know a plus BW
+thing and you might want to have time
+
+ align:start position:0%
+thing and you might want to have time
+ 
+
+ align:start position:0%
+thing and you might want to have time
+subscript
+
+ align:start position:0%
+subscript
+ 
+
+ align:start position:0%
+subscript
+so um sorry I'm jumping ahead here's the
+
+ align:start position:0%
+so um sorry I'm jumping ahead here's the
+ 
+
+ align:start position:0%
+so um sorry I'm jumping ahead here's the
+human capital thing so now the rate of
+
+ align:start position:0%
+human capital thing so now the rate of
+ 
+
+ align:start position:0%
+human capital thing so now the rate of
+return is has two factors Allah
+
+ align:start position:0%
+return is has two factors Allah
+ 
+
+ align:start position:0%
+return is has two factors Allah
+basically F French type thing okay one
+
+ align:start position:0%
+basically F French type thing okay one
+ 
+
+ align:start position:0%
+basically F French type thing okay one
+is the physical capital and the other is
+
+ align:start position:0%
+is the physical capital and the other is
+ 
+
+ align:start position:0%
+is the physical capital and the other is
+human capital and uh
+
+ align:start position:0%
+human capital and uh
+ 
+
+ align:start position:0%
+human capital and uh
+and we can figure it try to get both
+
+ align:start position:0%
+and we can figure it try to get both
+ 
+
+ align:start position:0%
+and we can figure it try to get both
+betas another is this uh problem with
+
+ align:start position:0%
+betas another is this uh problem with
+ 
+
+ align:start position:0%
+betas another is this uh problem with
+the varying Shadow prices
+
+ align:start position:0%
+the varying Shadow prices
+ 
+
+ align:start position:0%
+the varying Shadow prices
+um well another way to say this Mew you
+
+ align:start position:0%
+um well another way to say this Mew you
+ 
+
+ align:start position:0%
+um well another way to say this Mew you
+know act like mu was a constant mewt is
+
+ align:start position:0%
+know act like mu was a constant mewt is
+ 
+
+ align:start position:0%
+know act like mu was a constant mewt is
+the value of resources at day
+
+ align:start position:0%
+the value of resources at day
+ 
+
+ align:start position:0%
+the value of resources at day
+T when in the derivation it was always
+
+ align:start position:0%
+T when in the derivation it was always
+ 
+
+ align:start position:0%
+T when in the derivation it was always
+today versus tomorrow and it kind of got
+
+ align:start position:0%
+today versus tomorrow and it kind of got
+ 
+
+ align:start position:0%
+today versus tomorrow and it kind of got
+suppressed but suppose a village has a
+
+ align:start position:0%
+suppressed but suppose a village has a
+ 
+
+ align:start position:0%
+suppressed but suppose a village has a
+run of bad luck like tatring s those
+
+ align:start position:0%
+run of bad luck like tatring s those
+ 
+
+ align:start position:0%
+run of bad luck like tatring s those
+shrimp ponds going bad you know then
+
+ align:start position:0%
+shrimp ponds going bad you know then
+ 
+
+ align:start position:0%
+shrimp ponds going bad you know then
+they have they have less and less income
+
+ align:start position:0%
+they have they have less and less income
+ 
+
+ align:start position:0%
+they have they have less and less income
+so you would think me is going up
+
+ align:start position:0%
+so you would think me is going up
+ 
+
+ align:start position:0%
+so you would think me is going up
+because the marginal value the shadow
+
+ align:start position:0%
+because the marginal value the shadow
+ 
+
+ align:start position:0%
+because the marginal value the shadow
+price is going
+
+ align:start position:0%
+price is going
+ 
+
+ align:start position:0%
+price is going
+up so we really do need to adjust for
+
+ align:start position:0%
+up so we really do need to adjust for
+ 
+
+ align:start position:0%
+up so we really do need to adjust for
+that but there again there's a way to do
+
+ align:start position:0%
+that but there again there's a way to do
+ 
+
+ align:start position:0%
+that but there again there's a way to do
+it it turns out that
+
+ align:start position:0%
+it it turns out that
+ 
+
+ align:start position:0%
+it it turns out that
+that uh that time varying stochastic
+
+ align:start position:0%
+that uh that time varying stochastic
+ 
+
+ align:start position:0%
+that uh that time varying stochastic
+discount factor is related to the
+
+ align:start position:0%
+discount factor is related to the
+ 
+
+ align:start position:0%
+discount factor is related to the
+consumption wealth
+
+ align:start position:0%
+consumption wealth
+ 
+
+ align:start position:0%
+consumption wealth
+ratio and in turn the log consumption
+
+ align:start position:0%
+ratio and in turn the log consumption
+ 
+
+ align:start position:0%
+ratio and in turn the log consumption
+wealth
+
+ align:start position:0%
+wealth
+ 
+
+ align:start position:0%
+wealth
+ratio depends on three factors
+
+ align:start position:0%
+ratio depends on three factors
+ 
+
+ align:start position:0%
+ratio depends on three factors
+consumption physical wealth and uh and
+
+ align:start position:0%
+consumption physical wealth and uh and
+ 
+
+ align:start position:0%
+consumption physical wealth and uh and
+basically labor earnings
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you know rather than getting bogged
+
+ align:start position:0%
+um you know rather than getting bogged
+ 
+
+ align:start position:0%
+um you know rather than getting bogged
+down in the details I think intuitively
+
+ align:start position:0%
+down in the details I think intuitively
+ 
+
+ align:start position:0%
+down in the details I think intuitively
+you could just think well you know
+
+ align:start position:0%
+you could just think well you know
+ 
+
+ align:start position:0%
+you could just think well you know
+there's physical capital so you know
+
+ align:start position:0%
+there's physical capital so you know
+ 
+
+ align:start position:0%
+there's physical capital so you know
+basically the um
+
+ align:start position:0%
+basically the um
+ 
+
+ align:start position:0%
+basically the um
+consumption wealth ratio is kind of
+
+ align:start position:0%
+consumption wealth ratio is kind of
+ 
+
+ align:start position:0%
+consumption wealth ratio is kind of
+picking
+
+ align:start position:0%
+picking
+ 
+
+ align:start position:0%
+picking
+up uh the degree to which they have
+
+ align:start position:0%
+up uh the degree to which they have
+ 
+
+ align:start position:0%
+up uh the degree to which they have
+wealth today relative to consumption so
+
+ align:start position:0%
+wealth today relative to consumption so
+ 
+
+ align:start position:0%
+wealth today relative to consumption so
+that's kind of like an obvious argument
+
+ align:start position:0%
+that's kind of like an obvious argument
+ 
+
+ align:start position:0%
+that's kind of like an obvious argument
+to have in the in today's Shadow price
+
+ align:start position:0%
+to have in the in today's Shadow price
+ 
+
+ align:start position:0%
+to have in the in today's Shadow price
+and these things that determine the
+
+ align:start position:0%
+and these things that determine the
+ 
+
+ align:start position:0%
+and these things that determine the
+consumption wealth or the log
+
+ align:start position:0%
+consumption wealth or the log
+ 
+
+ align:start position:0%
+consumption wealth or the log
+consumption wealth ratio kind of look
+
+ align:start position:0%
+consumption wealth ratio kind of look
+ 
+
+ align:start position:0%
+consumption wealth ratio kind of look
+like the accounting variables that we've
+
+ align:start position:0%
+like the accounting variables that we've
+ 
+
+ align:start position:0%
+like the accounting variables that we've
+had before you know how much are you
+
+ align:start position:0%
+had before you know how much are you
+ 
+
+ align:start position:0%
+had before you know how much are you
+eating again how much is your physical
+
+ align:start position:0%
+eating again how much is your physical
+ 
+
+ align:start position:0%
+eating again how much is your physical
+Capital today and then how much is your
+
+ align:start position:0%
+Capital today and then how much is your
+ 
+
+ align:start position:0%
+Capital today and then how much is your
+is your is your labor earnings okay so
+
+ align:start position:0%
+is your is your labor earnings okay so
+ 
+
+ align:start position:0%
+is your is your labor earnings okay so
+that's kind of the spirit of it and
+
+ align:start position:0%
+that's kind of the spirit of it and
+ 
+
+ align:start position:0%
+that's kind of the spirit of it and
+again do our homework and we can find
+
+ align:start position:0%
+again do our homework and we can find
+ 
+
+ align:start position:0%
+again do our homework and we can find
+this exact derivation in the literature
+
+ align:start position:0%
+this exact derivation in the literature
+ 
+
+ align:start position:0%
+this exact derivation in the literature
+so this consumption asset ratio just
+
+ align:start position:0%
+so this consumption asset ratio just
+ 
+
+ align:start position:0%
+so this consumption asset ratio just
+looks like
+
+ align:start position:0%
+looks like
+ 
+
+ align:start position:0%
+looks like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+um so we we find that in the data by
+
+ align:start position:0%
+um so we we find that in the data by
+ 
+
+ align:start position:0%
+um so we we find that in the data by
+regressing it onto the arguments that I
+
+ align:start position:0%
+regressing it onto the arguments that I
+ 
+
+ align:start position:0%
+regressing it onto the arguments that I
+just mentioned consumption and so on and
+
+ align:start position:0%
+just mentioned consumption and so on and
+ 
+
+ align:start position:0%
+just mentioned consumption and so on and
+then we substitute in that
+
+ align:start position:0%
+then we substitute in that
+ 
+
+ align:start position:0%
+then we substitute in that
+estimated value into the regression that
+
+ align:start position:0%
+estimated value into the regression that
+ 
+
+ align:start position:0%
+estimated value into the regression that
+already was adjusted for human capital
+
+ align:start position:0%
+already was adjusted for human capital
+ 
+
+ align:start position:0%
+already was adjusted for human capital
+so now we just did a double adjustment
+
+ align:start position:0%
+so now we just did a double adjustment
+ 
+
+ align:start position:0%
+so now we just did a double adjustment
+we put human capital in the rate of
+
+ align:start position:0%
+we put human capital in the rate of
+ 
+
+ align:start position:0%
+we put human capital in the rate of
+return on human capital and now we have
+
+ align:start position:0%
+return on human capital and now we have
+ 
+
+ align:start position:0%
+return on human capital and now we have
+extra beta terms that have to do with
+
+ align:start position:0%
+extra beta terms that have to do with
+ 
+
+ align:start position:0%
+extra beta terms that have to do with
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+co-variance uh of those physical and
+
+ align:start position:0%
+co-variance uh of those physical and
+ 
+
+ align:start position:0%
+co-variance uh of those physical and
+human capital returns with this um so
+
+ align:start position:0%
+human capital returns with this um so
+ 
+
+ align:start position:0%
+human capital returns with this um so
+basically we're just interacting we have
+
+ align:start position:0%
+basically we're just interacting we have
+ 
+
+ align:start position:0%
+basically we're just interacting we have
+levels of things and then we're
+
+ align:start position:0%
+levels of things and then we're
+ 
+
+ align:start position:0%
+levels of things and then we're
+interacting it with the rates of
+
+ align:start position:0%
+interacting it with the rates of
+ 
+
+ align:start position:0%
+interacting it with the rates of
+return so we do that we end up with this
+
+ align:start position:0%
+return so we do that we end up with this
+ 
+
+ align:start position:0%
+return so we do that we end up with this
+it's a longer equation and we run it and
+
+ align:start position:0%
+it's a longer equation and we run it and
+ 
+
+ align:start position:0%
+it's a longer equation and we run it and
+we're still
+
+ align:start position:0%
+we're still
+ 
+
+ align:start position:0%
+we're still
+getting you know the beta on physical
+
+ align:start position:0%
+getting you know the beta on physical
+ 
+
+ align:start position:0%
+getting you know the beta on physical
+capital it's quite Hardy it's quite
+
+ align:start position:0%
+capital it's quite Hardy it's quite
+ 
+
+ align:start position:0%
+capital it's quite Hardy it's quite
+robust
+
+ align:start position:0%
+robust
+ 
+
+ align:start position:0%
+robust
+um human
+
+ align:start position:0%
+um human
+ 
+
+ align:start position:0%
+um human
+capital is in there sometimes sometimes
+
+ align:start position:0%
+capital is in there sometimes sometimes
+ 
+
+ align:start position:0%
+capital is in there sometimes sometimes
+not but at least putting it in doesn't
+
+ align:start position:0%
+not but at least putting it in doesn't
+ 
+
+ align:start position:0%
+not but at least putting it in doesn't
+harm this in other words you know as I
+
+ align:start position:0%
+harm this in other words you know as I
+ 
+
+ align:start position:0%
+harm this in other words you know as I
+said we do all the adjustments that we
+
+ align:start position:0%
+said we do all the adjustments that we
+ 
+
+ align:start position:0%
+said we do all the adjustments that we
+can and we still getting getting uh the
+
+ align:start position:0%
+can and we still getting getting uh the
+ 
+
+ align:start position:0%
+can and we still getting getting uh the
+basic result back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out uh now you want to know
+
+ align:start position:0%
+out uh now you want to know
+ 
+
+ align:start position:0%
+out uh now you want to know
+about risk well this is the equation
+
+ align:start position:0%
+about risk well this is the equation
+ 
+
+ align:start position:0%
+about risk well this is the equation
+we're
+
+ align:start position:0%
+we're
+ 
+
+ align:start position:0%
+we're
+running so you know you can do a
+
+ align:start position:0%
+running so you know you can do a
+ 
+
+ align:start position:0%
+running so you know you can do a
+decomposition of variance the total
+
+ align:start position:0%
+decomposition of variance the total
+ 
+
+ align:start position:0%
+decomposition of variance the total
+variance in returns is just the variance
+
+ align:start position:0%
+variance in returns is just the variance
+ 
+
+ align:start position:0%
+variance in returns is just the variance
+having to do with you know the
+
+ align:start position:0%
+having to do with you know the
+ 
+
+ align:start position:0%
+having to do with you know the
+regression times the variant or
+
+ align:start position:0%
+regression times the variant or
+ 
+
+ align:start position:0%
+regression times the variant or
+basically this thing this is the
+
+ align:start position:0%
+basically this thing this is the
+ 
+
+ align:start position:0%
+basically this thing this is the
+contribution of Market risk to the
+
+ align:start position:0%
+contribution of Market risk to the
+ 
+
+ align:start position:0%
+contribution of Market risk to the
+variance of household J and there's a
+
+ align:start position:0%
+variance of household J and there's a
+ 
+
+ align:start position:0%
+variance of household J and there's a
+residual here that we were just chatting
+
+ align:start position:0%
+residual here that we were just chatting
+ 
+
+ align:start position:0%
+residual here that we were just chatting
+about uh so we estimate its variance and
+
+ align:start position:0%
+about uh so we estimate its variance and
+ 
+
+ align:start position:0%
+about uh so we estimate its variance and
+so that's the contribution of os
+
+ align:start position:0%
+so that's the contribution of os
+ 
+
+ align:start position:0%
+so that's the contribution of os
+syncratic risk to the overall variance
+
+ align:start position:0%
+syncratic risk to the overall variance
+ 
+
+ align:start position:0%
+syncratic risk to the overall variance
+so now we have this
+
+ align:start position:0%
+so now we have this
+ 
+
+ align:start position:0%
+so now we have this
+measure finally but note note that it
+
+ align:start position:0%
+measure finally but note note that it
+ 
+
+ align:start position:0%
+measure finally but note note that it
+didn't just come from using the data we
+
+ align:start position:0%
+didn't just come from using the data we
+ 
+
+ align:start position:0%
+didn't just come from using the data we
+used the structure of the model to back
+
+ align:start position:0%
+used the structure of the model to back
+ 
+
+ align:start position:0%
+used the structure of the model to back
+it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh and that idiosyncratic part is
+
+ align:start position:0%
+uh and that idiosyncratic part is
+ 
+
+ align:start position:0%
+uh and that idiosyncratic part is
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+um you know at least half and in many
+
+ align:start position:0%
+um you know at least half and in many
+ 
+
+ align:start position:0%
+um you know at least half and in many
+instances more than quite substantially
+
+ align:start position:0%
+instances more than quite substantially
+ 
+
+ align:start position:0%
+instances more than quite substantially
+more than half of the risk is due to the
+
+ align:start position:0%
+more than half of the risk is due to the
+ 
+
+ align:start position:0%
+more than half of the risk is due to the
+idiosyncratic component rather than the
+
+ align:start position:0%
+idiosyncratic component rather than the
+ 
+
+ align:start position:0%
+idiosyncratic component rather than the
+aggregate now you know one word of
+
+ align:start position:0%
+aggregate now you know one word of
+ 
+
+ align:start position:0%
+aggregate now you know one word of
+caution we still haven't rejected the
+
+ align:start position:0%
+caution we still haven't rejected the
+ 
+
+ align:start position:0%
+caution we still haven't rejected the
+model no one in finance says there
+
+ align:start position:0%
+model no one in finance says there
+ 
+
+ align:start position:0%
+model no one in finance says there
+aren't idiosyn
+
+ align:start position:0%
+aren't idiosyn
+ 
+
+ align:start position:0%
+aren't idiosyn
+Returns the question is whether they're
+
+ align:start position:0%
+Returns the question is whether they're
+ 
+
+ align:start position:0%
+Returns the question is whether they're
+priced if you believe in the capital
+
+ align:start position:0%
+priced if you believe in the capital
+ 
+
+ align:start position:0%
+priced if you believe in the capital
+asset model or the consumption-based you
+
+ align:start position:0%
+asset model or the consumption-based you
+ 
+
+ align:start position:0%
+asset model or the consumption-based you
+know risk sharing model then
+
+ align:start position:0%
+know risk sharing model then
+ 
+
+ align:start position:0%
+know risk sharing model then
+idiosyncratic returns can exist but
+
+ align:start position:0%
+idiosyncratic returns can exist but
+ 
+
+ align:start position:0%
+idiosyncratic returns can exist but
+they're completely
+
+ align:start position:0%
+they're completely
+ 
+
+ align:start position:0%
+they're completely
+pulled
+
+ align:start position:0%
+pulled
+ 
+
+ align:start position:0%
+pulled
+so so this does per se does not reject
+
+ align:start position:0%
+so so this does per se does not reject
+ 
+
+ align:start position:0%
+so so this does per se does not reject
+the model but when
+
+ align:start position:0%
+the model but when
+ 
+
+ align:start position:0%
+the model but when
+we we now stick the variance Sigma Sigma
+
+ align:start position:0%
+we we now stick the variance Sigma Sigma
+ 
+
+ align:start position:0%
+we we now stick the variance Sigma Sigma
+J into the bench Mark model and uh we're
+
+ align:start position:0%
+J into the bench Mark model and uh we're
+ 
+
+ align:start position:0%
+J into the bench Mark model and uh we're
+still doing okay with aggregate risk but
+
+ align:start position:0%
+still doing okay with aggregate risk but
+ 
+
+ align:start position:0%
+still doing okay with aggregate risk but
+but here's the rejection if you like the
+
+ align:start position:0%
+but here's the rejection if you like the
+ 
+
+ align:start position:0%
+but here's the rejection if you like the
+idiosyncratic risk is positively
+
+ align:start position:0%
+idiosyncratic risk is positively
+ 
+
+ align:start position:0%
+idiosyncratic risk is positively
+associated with the expected rate of
+
+ align:start position:0%
+associated with the expected rate of
+ 
+
+ align:start position:0%
+associated with the expected rate of
+return and for all the
+
+ align:start position:0%
+return and for all the
+ 
+
+ align:start position:0%
+return and for all the
+households now you know this is the
+
+ align:start position:0%
+households now you know this is the
+ 
+
+ align:start position:0%
+households now you know this is the
+uh if you like the disappointing part or
+
+ align:start position:0%
+uh if you like the disappointing part or
+ 
+
+ align:start position:0%
+uh if you like the disappointing part or
+the tension you know which is you go to
+
+ align:start position:0%
+the tension you know which is you go to
+ 
+
+ align:start position:0%
+the tension you know which is you go to
+all this work and with a benchmark and
+
+ align:start position:0%
+all this work and with a benchmark and
+ 
+
+ align:start position:0%
+all this work and with a benchmark and
+it seems to to be doing really well but
+
+ align:start position:0%
+it seems to to be doing really well but
+ 
+
+ align:start position:0%
+it seems to to be doing really well but
+there are features of the data against
+
+ align:start position:0%
+there are features of the data against
+ 
+
+ align:start position:0%
+there are features of the data against
+which it's uh it's not you know it's not
+
+ align:start position:0%
+which it's uh it's not you know it's not
+ 
+
+ align:start position:0%
+which it's uh it's not you know it's not
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+um so it's clear that it's not an
+
+ align:start position:0%
+um so it's clear that it's not an
+ 
+
+ align:start position:0%
+um so it's clear that it's not an
+entirely perfect Market's World from the
+
+ align:start position:0%
+entirely perfect Market's World from the
+ 
+
+ align:start position:0%
+entirely perfect Market's World from the
+point of view of the rate of return of
+
+ align:start position:0%
+point of view of the rate of return of
+ 
+
+ align:start position:0%
+point of view of the rate of return of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+assets but is the glass half empty or
+
+ align:start position:0%
+assets but is the glass half empty or
+ 
+
+ align:start position:0%
+assets but is the glass half empty or
+half full because it's also true that a
+
+ align:start position:0%
+half full because it's also true that a
+ 
+
+ align:start position:0%
+half full because it's also true that a
+substantial amount of the rates of
+
+ align:start position:0%
+substantial amount of the rates of
+ 
+
+ align:start position:0%
+substantial amount of the rates of
+return had to do with Market risk
+
+ align:start position:0%
+return had to do with Market risk
+ 
+
+ align:start position:0%
+return had to do with Market risk
+again most development researchers would
+
+ align:start position:0%
+again most development researchers would
+ 
+
+ align:start position:0%
+again most development researchers would
+have ignored that market part I think
+
+ align:start position:0%
+have ignored that market part I think
+ 
+
+ align:start position:0%
+have ignored that market part I think
+it's fair to say even though it's kind
+
+ align:start position:0%
+it's fair to say even though it's kind
+ 
+
+ align:start position:0%
+it's fair to say even though it's kind
+of a natural corollary to rist
+
+ align:start position:0%
+of a natural corollary to rist
+ 
+
+ align:start position:0%
+of a natural corollary to rist
+sharing
+
+ align:start position:0%
+sharing
+ 
+
+ align:start position:0%
+sharing
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so let's go back to these
+
+ align:start position:0%
+uh so let's go back to these
+ 
+
+ align:start position:0%
+uh so let's go back to these
+Alphas um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Jensen talks about having portfolio
+
+ align:start position:0%
+so Jensen talks about having portfolio
+ 
+
+ align:start position:0%
+so Jensen talks about having portfolio
+managers who are somehow smarter or
+
+ align:start position:0%
+managers who are somehow smarter or
+ 
+
+ align:start position:0%
+managers who are somehow smarter or
+better than others and they have
+
+ align:start position:0%
+better than others and they have
+ 
+
+ align:start position:0%
+better than others and they have
+abnormal returns I mean I don't know
+
+ align:start position:0%
+abnormal returns I mean I don't know
+ 
+
+ align:start position:0%
+abnormal returns I mean I don't know
+this is kind of hard for economists it's
+
+ align:start position:0%
+this is kind of hard for economists it's
+ 
+
+ align:start position:0%
+this is kind of hard for economists it's
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+well if you do so well why don't
+
+ align:start position:0%
+well if you do so well why don't
+ 
+
+ align:start position:0%
+well if you do so well why don't
+everyone just go in there you know like
+
+ align:start position:0%
+everyone just go in there you know like
+ 
+
+ align:start position:0%
+everyone just go in there you know like
+I never make money I just don't you know
+
+ align:start position:0%
+I never make money I just don't you know
+ 
+
+ align:start position:0%
+I never make money I just don't you know
+I don't trust my instincts
+
+ align:start position:0%
+I don't trust my instincts
+ 
+
+ align:start position:0%
+I don't trust my instincts
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+um I tell you a story about Walmart so
+
+ align:start position:0%
+um I tell you a story about Walmart so
+ 
+
+ align:start position:0%
+um I tell you a story about Walmart so
+one of my my colleagues who was at
+
+ align:start position:0%
+one of my my colleagues who was at
+ 
+
+ align:start position:0%
+one of my my colleagues who was at
+Chicago a sociologist was in Arkansas
+
+ align:start position:0%
+Chicago a sociologist was in Arkansas
+ 
+
+ align:start position:0%
+Chicago a sociologist was in Arkansas
+and he saw this you know big square flat
+
+ align:start position:0%
+and he saw this you know big square flat
+ 
+
+ align:start position:0%
+and he saw this you know big square flat
+building and uh in Northern Arkansas and
+
+ align:start position:0%
+building and uh in Northern Arkansas and
+ 
+
+ align:start position:0%
+building and uh in Northern Arkansas and
+you know he sort of checked it out and
+
+ align:start position:0%
+you know he sort of checked it out and
+ 
+
+ align:start position:0%
+you know he sort of checked it out and
+wellow this is a really novel way of
+
+ align:start position:0%
+wellow this is a really novel way of
+ 
+
+ align:start position:0%
+wellow this is a really novel way of
+doing business well it turns out to be
+
+ align:start position:0%
+doing business well it turns out to be
+ 
+
+ align:start position:0%
+doing business well it turns out to be
+practically the first branch of Walmart
+
+ align:start position:0%
+practically the first branch of Walmart
+ 
+
+ align:start position:0%
+practically the first branch of Walmart
+and he bought
+
+ align:start position:0%
+and he bought
+ 
+
+ align:start position:0%
+and he bought
+stock he did quite well obiously
+
+ align:start position:0%
+stock he did quite well obiously
+ 
+
+ align:start position:0%
+stock he did quite well obiously
+so anyway so maybe some portfolio
+
+ align:start position:0%
+so anyway so maybe some portfolio
+ 
+
+ align:start position:0%
+so anyway so maybe some portfolio
+managers are better than others maybe
+
+ align:start position:0%
+managers are better than others maybe
+ 
+
+ align:start position:0%
+managers are better than others maybe
+some households are
+
+ align:start position:0%
+some households are
+ 
+
+ align:start position:0%
+some households are
+somehow better than others and uh We've
+
+ align:start position:0%
+somehow better than others and uh We've
+ 
+
+ align:start position:0%
+somehow better than others and uh We've
+now got a way of
+
+ align:start position:0%
+now got a way of
+ 
+
+ align:start position:0%
+now got a way of
+adjusting for um for all those uh risk
+
+ align:start position:0%
+adjusting for um for all those uh risk
+ 
+
+ align:start position:0%
+adjusting for um for all those uh risk
+factors both the
+
+ align:start position:0%
+factors both the
+ 
+
+ align:start position:0%
+factors both the
+idiosyncratic and the aggregate uh by
+
+ align:start position:0%
+idiosyncratic and the aggregate uh by
+ 
+
+ align:start position:0%
+idiosyncratic and the aggregate uh by
+the way you you will be relieved a bit
+
+ align:start position:0%
+the way you you will be relieved a bit
+ 
+
+ align:start position:0%
+the way you you will be relieved a bit
+maybe to know that when we rank order
+
+ align:start position:0%
+maybe to know that when we rank order
+ 
+
+ align:start position:0%
+maybe to know that when we rank order
+the households by the unadjusted rates
+
+ align:start position:0%
+the households by the unadjusted rates
+ 
+
+ align:start position:0%
+the households by the unadjusted rates
+of return and the risk adjusted rates of
+
+ align:start position:0%
+of return and the risk adjusted rates of
+ 
+
+ align:start position:0%
+of return and the risk adjusted rates of
+return the ordering is largely
+
+ align:start position:0%
+return the ordering is largely
+ 
+
+ align:start position:0%
+return the ordering is largely
+preserved but the orders of magnitude
+
+ align:start position:0%
+preserved but the orders of magnitude
+ 
+
+ align:start position:0%
+preserved but the orders of magnitude
+are not the second point is it's not
+
+ align:start position:0%
+are not the second point is it's not
+ 
+
+ align:start position:0%
+are not the second point is it's not
+just completely downshifting the
+
+ align:start position:0%
+just completely downshifting the
+ 
+
+ align:start position:0%
+just completely downshifting the
+distribution after you subtract stuff
+
+ align:start position:0%
+distribution after you subtract stuff
+ 
+
+ align:start position:0%
+distribution after you subtract stuff
+off the tails come in so it has a
+
+ align:start position:0%
+off the tails come in so it has a
+ 
+
+ align:start position:0%
+off the tails come in so it has a
+different level of skewness so it's a
+
+ align:start position:0%
+different level of skewness so it's a
+ 
+
+ align:start position:0%
+different level of skewness so it's a
+it's kind of a
+
+ align:start position:0%
+it's kind of a
+ 
+
+ align:start position:0%
+it's kind of a
+serious filter on the data but some of
+
+ align:start position:0%
+serious filter on the data but some of
+ 
+
+ align:start position:0%
+serious filter on the data but some of
+the earlier
+
+ align:start position:0%
+the earlier
+ 
+
+ align:start position:0%
+the earlier
+results that poor households have high
+
+ align:start position:0%
+results that poor households have high
+ 
+
+ align:start position:0%
+results that poor households have high
+rates of return and reinvest in their
+
+ align:start position:0%
+rates of return and reinvest in their
+ 
+
+ align:start position:0%
+rates of return and reinvest in their
+own projects we're going to rerun those
+
+ align:start position:0%
+own projects we're going to rerun those
+ 
+
+ align:start position:0%
+own projects we're going to rerun those
+but we're pretty confident and those
+
+ align:start position:0%
+but we're pretty confident and those
+ 
+
+ align:start position:0%
+but we're pretty confident and those
+kind of results don't go away and I
+
+ align:start position:0%
+kind of results don't go away and I
+ 
+
+ align:start position:0%
+kind of results don't go away and I
+haven't misled you in the earlier
+
+ align:start position:0%
+haven't misled you in the earlier
+ 
+
+ align:start position:0%
+haven't misled you in the earlier
+lectures
+
+ align:start position:0%
+lectures
+ 
+
+ align:start position:0%
+lectures
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so finally here is running these
+
+ align:start position:0%
+so finally here is running these
+ 
+
+ align:start position:0%
+so finally here is running these
+regressions where we have aggregate risk
+
+ align:start position:0%
+regressions where we have aggregate risk
+ 
+
+ align:start position:0%
+regressions where we have aggregate risk
+also allow idiosyncratic risk where we
+
+ align:start position:0%
+also allow idiosyncratic risk where we
+ 
+
+ align:start position:0%
+also allow idiosyncratic risk where we
+have the betas on you know aggregate
+
+ align:start position:0%
+have the betas on you know aggregate
+ 
+
+ align:start position:0%
+have the betas on you know aggregate
+physical capital and and the
+
+ align:start position:0%
+physical capital and and the
+ 
+
+ align:start position:0%
+physical capital and and the
+coefficients on Sigma so
+
+ align:start position:0%
+coefficients on Sigma so
+ 
+
+ align:start position:0%
+coefficients on Sigma so
+the first two slides I said households
+
+ align:start position:0%
+the first two slides I said households
+ 
+
+ align:start position:0%
+the first two slides I said households
+who are
+
+ align:start position:0%
+who are
+ 
+
+ align:start position:0%
+who are
+older take less take on less risk which
+
+ align:start position:0%
+older take less take on less risk which
+ 
+
+ align:start position:0%
+older take less take on less risk which
+means basically both the idiosyncratic
+
+ align:start position:0%
+means basically both the idiosyncratic
+ 
+
+ align:start position:0%
+means basically both the idiosyncratic
+and aggregate risk factors are
+
+ align:start position:0%
+and aggregate risk factors are
+ 
+
+ align:start position:0%
+and aggregate risk factors are
+negative you might be willing to tell a
+
+ align:start position:0%
+negative you might be willing to tell a
+ 
+
+ align:start position:0%
+negative you might be willing to tell a
+demographic story for that you know well
+
+ align:start position:0%
+demographic story for that you know well
+ 
+
+ align:start position:0%
+demographic story for that you know well
+we don't really have it embedded in the
+
+ align:start position:0%
+we don't really have it embedded in the
+ 
+
+ align:start position:0%
+we don't really have it embedded in the
+model it's more like
+
+ align:start position:0%
+model it's more like
+ 
+
+ align:start position:0%
+model it's more like
+a residual or behavioral thing at this
+
+ align:start position:0%
+a residual or behavioral thing at this
+ 
+
+ align:start position:0%
+a residual or behavioral thing at this
+point because these residuals aren't
+
+ align:start position:0%
+point because these residuals aren't
+ 
+
+ align:start position:0%
+point because these residuals aren't
+supposed to to be there um and here's
+
+ align:start position:0%
+supposed to to be there um and here's
+ 
+
+ align:start position:0%
+supposed to to be there um and here's
+basically the wealth again negative
+
+ align:start position:0%
+basically the wealth again negative
+ 
+
+ align:start position:0%
+basically the wealth again negative
+so um poor people have
+
+ align:start position:0%
+so um poor people have
+ 
+
+ align:start position:0%
+so um poor people have
+higher correlation of their activities
+
+ align:start position:0%
+higher correlation of their activities
+ 
+
+ align:start position:0%
+higher correlation of their activities
+with a village
+
+ align:start position:0%
+with a village
+ 
+
+ align:start position:0%
+with a village
+average and the residual have a higher
+
+ align:start position:0%
+average and the residual have a higher
+ 
+
+ align:start position:0%
+average and the residual have a higher
+residual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variance I'm going to you know come back
+
+ align:start position:0%
+variance I'm going to you know come back
+ 
+
+ align:start position:0%
+variance I'm going to you know come back
+to that poor people seem to be exposed
+
+ align:start position:0%
+to that poor people seem to be exposed
+ 
+
+ align:start position:0%
+to that poor people seem to be exposed
+to a lot of risk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+however if you take out both sources of
+
+ align:start position:0%
+however if you take out both sources of
+ 
+
+ align:start position:0%
+however if you take out both sources of
+risk and regress on demographics and all
+
+ align:start position:0%
+risk and regress on demographics and all
+ 
+
+ align:start position:0%
+risk and regress on demographics and all
+these things you know wealth finally
+
+ align:start position:0%
+these things you know wealth finally
+ 
+
+ align:start position:0%
+these things you know wealth finally
+goes
+
+ align:start position:0%
+goes
+ 
+
+ align:start position:0%
+goes
+positive and
+
+ align:start position:0%
+positive and
+ 
+
+ align:start position:0%
+positive and
+also this is a dummy for male so to
+
+ align:start position:0%
+also this is a dummy for male so to
+ 
+
+ align:start position:0%
+also this is a dummy for male so to
+speak is uh is
+
+ align:start position:0%
+speak is uh is
+ 
+
+ align:start position:0%
+speak is uh is
+negative so the the female headed
+
+ align:start position:0%
+negative so the the female headed
+ 
+
+ align:start position:0%
+negative so the the female headed
+households are and the high wealth
+
+ align:start position:0%
+households are and the high wealth
+ 
+
+ align:start position:0%
+households are and the high wealth
+households are the households with with
+
+ align:start position:0%
+households are the households with with
+ 
+
+ align:start position:0%
+households are the households with with
+the highest sort of residual rates of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+return okay
+
+ align:start position:0%
+return okay
+ 
+
+ align:start position:0%
+return okay
+so now what I I don't have in front of
+
+ align:start position:0%
+so now what I I don't have in front of
+ 
+
+ align:start position:0%
+so now what I I don't have in front of
+me unfortunately we didn't quite get
+
+ align:start position:0%
+me unfortunately we didn't quite get
+ 
+
+ align:start position:0%
+me unfortunately we didn't quite get
+close enough but you may remember that
+
+ align:start position:0%
+close enough but you may remember that
+ 
+
+ align:start position:0%
+close enough but you may remember that
+QJ paper from lecture one on volatility
+
+ align:start position:0%
+QJ paper from lecture one on volatility
+ 
+
+ align:start position:0%
+QJ paper from lecture one on volatility
+you know growth Finance what's related
+
+ align:start position:0%
+you know growth Finance what's related
+ 
+
+ align:start position:0%
+you know growth Finance what's related
+and we said well we got to look at
+
+ align:start position:0%
+and we said well we got to look at
+ 
+
+ align:start position:0%
+and we said well we got to look at
+sectors we got to figure out how much
+
+ align:start position:0%
+sectors we got to figure out how much
+ 
+
+ align:start position:0%
+sectors we got to figure out how much
+each sector is contributing to
+
+ align:start position:0%
+each sector is contributing to
+ 
+
+ align:start position:0%
+each sector is contributing to
+overall change in value added and there
+
+ align:start position:0%
+overall change in value added and there
+ 
+
+ align:start position:0%
+overall change in value added and there
+was some really cool decomposition so
+
+ align:start position:0%
+was some really cool decomposition so
+ 
+
+ align:start position:0%
+was some really cool decomposition so
+we're running that on these tii
+
+ align:start position:0%
+we're running that on these tii
+ 
+
+ align:start position:0%
+we're running that on these tii
+data uh so we can see you
+
+ align:start position:0%
+data uh so we can see you
+ 
+
+ align:start position:0%
+data uh so we can see you
+know at the level of
+
+ align:start position:0%
+know at the level of
+ 
+
+ align:start position:0%
+know at the level of
+income you know how Diversified are
+
+ align:start position:0%
+income you know how Diversified are
+ 
+
+ align:start position:0%
+income you know how Diversified are
+these households it's similar but not
+
+ align:start position:0%
+these households it's similar but not
+ 
+
+ align:start position:0%
+these households it's similar but not
+identical to this capm type approach and
+
+ align:start position:0%
+identical to this capm type approach and
+ 
+
+ align:start position:0%
+identical to this capm type approach and
+so far at least we're getting the same
+
+ align:start position:0%
+so far at least we're getting the same
+ 
+
+ align:start position:0%
+so far at least we're getting the same
+answer that it's the relatively poor
+
+ align:start position:0%
+answer that it's the relatively poor
+ 
+
+ align:start position:0%
+answer that it's the relatively poor
+households who are
+
+ align:start position:0%
+households who are
+ 
+
+ align:start position:0%
+households who are
+specialized and the things they
+
+ align:start position:0%
+specialized and the things they
+ 
+
+ align:start position:0%
+specialized and the things they
+specialize in have high
+
+ align:start position:0%
+specialize in have high
+ 
+
+ align:start position:0%
+specialize in have high
+volatility and
+
+ align:start position:0%
+volatility and
+ 
+
+ align:start position:0%
+volatility and
+uh and so on
+
+ align:start position:0%
+uh and so on
+ 
+
+ align:start position:0%
+uh and so on
+so so poor people seem to be exposed to
+
+ align:start position:0%
+so so poor people seem to be exposed to
+ 
+
+ align:start position:0%
+so so poor people seem to be exposed to
+to risk at least on the income
+
+ align:start position:0%
+to risk at least on the income
+ 
+
+ align:start position:0%
+to risk at least on the income
+side
+
+ align:start position:0%
+side
+ 
+
+ align:start position:0%
+side
+um so here's uh moving to Sweden
+
+ align:start position:0%
+um so here's uh moving to Sweden
+ 
+
+ align:start position:0%
+um so here's uh moving to Sweden
+um more sort of
+
+ align:start position:0%
+um more sort of
+ 
+
+ align:start position:0%
+um more sort of
+standard uh asset
+
+ align:start position:0%
+standard uh asset
+ 
+
+ align:start position:0%
+standard uh asset
+stuff uh which John Campbell and
+
+ align:start position:0%
+stuff uh which John Campbell and
+ 
+
+ align:start position:0%
+stuff uh which John Campbell and
+co-authors have done called down or out
+
+ align:start position:0%
+co-authors have done called down or out
+ 
+
+ align:start position:0%
+co-authors have done called down or out
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh and the and what they're trying to do
+
+ align:start position:0%
+uh and the and what they're trying to do
+ 
+
+ align:start position:0%
+uh and the and what they're trying to do
+is very similar they're trying to look
+
+ align:start position:0%
+is very similar they're trying to look
+ 
+
+ align:start position:0%
+is very similar they're trying to look
+at household
+
+ align:start position:0%
+at household
+ 
+
+ align:start position:0%
+at household
+management uh of financial affairs using
+
+ align:start position:0%
+management uh of financial affairs using
+ 
+
+ align:start position:0%
+management uh of financial affairs using
+measurement in this amazing Swedish
+
+ align:start position:0%
+measurement in this amazing Swedish
+ 
+
+ align:start position:0%
+measurement in this amazing Swedish
+data uh Sweden is you know a socialist
+
+ align:start position:0%
+data uh Sweden is you know a socialist
+ 
+
+ align:start position:0%
+data uh Sweden is you know a socialist
+country largely and they measure
+
+ align:start position:0%
+country largely and they measure
+ 
+
+ align:start position:0%
+country largely and they measure
+everything and everyone has a common ID
+
+ align:start position:0%
+everything and everyone has a common ID
+ 
+
+ align:start position:0%
+everything and everyone has a common ID
+and you know your whole portfolio labor
+
+ align:start position:0%
+and you know your whole portfolio labor
+ 
+
+ align:start position:0%
+and you know your whole portfolio labor
+Supply
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everything so I've
+
+ align:start position:0%
+everything so I've
+ 
+
+ align:start position:0%
+everything so I've
+been collaborating a little bit with a
+
+ align:start position:0%
+been collaborating a little bit with a
+ 
+
+ align:start position:0%
+been collaborating a little bit with a
+Ricks
+
+ align:start position:0%
+Ricks
+ 
+
+ align:start position:0%
+Ricks
+Bank uh largely influenced by you know
+
+ align:start position:0%
+Bank uh largely influenced by you know
+ 
+
+ align:start position:0%
+Bank uh largely influenced by you know
+this paper now unfortunately it takes us
+
+ align:start position:0%
+this paper now unfortunately it takes us
+ 
+
+ align:start position:0%
+this paper now unfortunately it takes us
+away from
+
+ align:start position:0%
+away from
+ 
+
+ align:start position:0%
+away from
+development that's not my point my point
+
+ align:start position:0%
+development that's not my point my point
+ 
+
+ align:start position:0%
+development that's not my point my point
+is the commonality they're going to look
+
+ align:start position:0%
+is the commonality they're going to look
+ 
+
+ align:start position:0%
+is the commonality they're going to look
+at mean variance Frontiers and see what
+
+ align:start position:0%
+at mean variance Frontiers and see what
+ 
+
+ align:start position:0%
+at mean variance Frontiers and see what
+households are doing in particular what
+
+ align:start position:0%
+households are doing in particular what
+ 
+
+ align:start position:0%
+households are doing in particular what
+are the poor people doing or the rich
+
+ align:start position:0%
+are the poor people doing or the rich
+ 
+
+ align:start position:0%
+are the poor people doing or the rich
+ones
+
+ align:start position:0%
+ones
+ 
+
+ align:start position:0%
+ones
+um the focus is a bit different which is
+
+ align:start position:0%
+um the focus is a bit different which is
+ 
+
+ align:start position:0%
+um the focus is a bit different which is
+households can make mistakes in other
+
+ align:start position:0%
+households can make mistakes in other
+ 
+
+ align:start position:0%
+households can make mistakes in other
+words uh let's just assume the model is
+
+ align:start position:0%
+words uh let's just assume the model is
+ 
+
+ align:start position:0%
+words uh let's just assume the model is
+right and you know the mean variance FR
+
+ align:start position:0%
+right and you know the mean variance FR
+ 
+
+ align:start position:0%
+right and you know the mean variance FR
+is what it is and then see households in
+
+ align:start position:0%
+is what it is and then see households in
+ 
+
+ align:start position:0%
+is what it is and then see households in
+the interior who could get less variance
+
+ align:start position:0%
+the interior who could get less variance
+ 
+
+ align:start position:0%
+the interior who could get less variance
+or a higher mean if they only moved to
+
+ align:start position:0%
+or a higher mean if they only moved to
+ 
+
+ align:start position:0%
+or a higher mean if they only moved to
+the frontier
+
+ align:start position:0%
+the frontier
+ 
+
+ align:start position:0%
+the frontier
+and then they look by characteristics
+
+ align:start position:0%
+and then they look by characteristics
+ 
+
+ align:start position:0%
+and then they look by characteristics
+like education wealth and so on to see
+
+ align:start position:0%
+like education wealth and so on to see
+ 
+
+ align:start position:0%
+like education wealth and so on to see
+who is under Diversified those are the
+
+ align:start position:0%
+who is under Diversified those are the
+ 
+
+ align:start position:0%
+who is under Diversified those are the
+down people and who's not participating
+
+ align:start position:0%
+down people and who's not participating
+ 
+
+ align:start position:0%
+down people and who's not participating
+as in the stock market those are the out
+
+ align:start position:0%
+as in the stock market those are the out
+ 
+
+ align:start position:0%
+as in the stock market those are the out
+people and hence the title very clever
+
+ align:start position:0%
+people and hence the title very clever
+ 
+
+ align:start position:0%
+people and hence the title very clever
+down and
+
+ align:start position:0%
+down and
+ 
+
+ align:start position:0%
+down and
+out and they measure the welfare costs
+
+ align:start position:0%
+out and they measure the welfare costs
+ 
+
+ align:start position:0%
+out and they measure the welfare costs
+of those
+
+ align:start position:0%
+of those
+ 
+
+ align:start position:0%
+of those
+deviations as I said they have amazing
+
+ align:start position:0%
+deviations as I said they have amazing
+ 
+
+ align:start position:0%
+deviations as I said they have amazing
+data and here you can see
+
+ align:start position:0%
+data and here you can see
+ 
+
+ align:start position:0%
+data and here you can see
+uh sort of how households manage their
+
+ align:start position:0%
+uh sort of how households manage their
+ 
+
+ align:start position:0%
+uh sort of how households manage their
+growth wealth in
+
+ align:start position:0%
+growth wealth in
+ 
+
+ align:start position:0%
+growth wealth in
+Sweden uh this is the cash oh look at
+
+ align:start position:0%
+Sweden uh this is the cash oh look at
+ 
+
+ align:start position:0%
+Sweden uh this is the cash oh look at
+that poor people have a lot of
+
+ align:start position:0%
+that poor people have a lot of
+ 
+
+ align:start position:0%
+that poor people have a lot of
+cash I think cash just doesn't mean
+
+ align:start position:0%
+cash I think cash just doesn't mean
+ 
+
+ align:start position:0%
+cash I think cash just doesn't mean
+Swedish croner I think it also
+
+ align:start position:0%
+Swedish croner I think it also
+ 
+
+ align:start position:0%
+Swedish croner I think it also
+means uh bank
+
+ align:start position:0%
+means uh bank
+ 
+
+ align:start position:0%
+means uh bank
+accounts
+
+ align:start position:0%
+accounts
+ 
+
+ align:start position:0%
+accounts
+um but stocks poor people don't hold
+
+ align:start position:0%
+um but stocks poor people don't hold
+ 
+
+ align:start position:0%
+um but stocks poor people don't hold
+stocks uh mutual fund has this funny
+
+ align:start position:0%
+stocks uh mutual fund has this funny
+ 
+
+ align:start position:0%
+stocks uh mutual fund has this funny
+hunch now it's interesting that this is
+
+ align:start position:0%
+hunch now it's interesting that this is
+ 
+
+ align:start position:0%
+hunch now it's interesting that this is
+real estate so this is both Financial as
+
+ align:start position:0%
+real estate so this is both Financial as
+ 
+
+ align:start position:0%
+real estate so this is both Financial as
+well as real and on the household side
+
+ align:start position:0%
+well as real and on the household side
+ 
+
+ align:start position:0%
+well as real and on the household side
+you know there are some businesses here
+
+ align:start position:0%
+you know there are some businesses here
+ 
+
+ align:start position:0%
+you know there are some businesses here
+actually but most of these households
+
+ align:start position:0%
+actually but most of these households
+ 
+
+ align:start position:0%
+actually but most of these households
+are salari you know
+
+ align:start position:0%
+are salari you know
+ 
+
+ align:start position:0%
+are salari you know
+employees but they they can hold durable
+
+ align:start position:0%
+employees but they they can hold durable
+ 
+
+ align:start position:0%
+employees but they they can hold durable
+goods in housing if you take the
+
+ align:start position:0%
+goods in housing if you take the
+ 
+
+ align:start position:0%
+goods in housing if you take the
+physical housing wealth out of it then
+
+ align:start position:0%
+physical housing wealth out of it then
+ 
+
+ align:start position:0%
+physical housing wealth out of it then
+the cash thing is still going
+
+ align:start position:0%
+the cash thing is still going
+ 
+
+ align:start position:0%
+the cash thing is still going
+down um
+
+ align:start position:0%
+down um
+ 
+
+ align:start position:0%
+down um
+mutual funds is largely flat except at
+
+ align:start position:0%
+mutual funds is largely flat except at
+ 
+
+ align:start position:0%
+mutual funds is largely flat except at
+the very low and the high end and then
+
+ align:start position:0%
+the very low and the high end and then
+ 
+
+ align:start position:0%
+the very low and the high end and then
+you see this this stock you know it's
+
+ align:start position:0%
+you see this this stock you know it's
+ 
+
+ align:start position:0%
+you see this this stock you know it's
+it's the real it's the 90 percentile up
+
+ align:start position:0%
+it's the real it's the 90 percentile up
+ 
+
+ align:start position:0%
+it's the real it's the 90 percentile up
+are the people who have you know
+
+ align:start position:0%
+are the people who have you know
+ 
+
+ align:start position:0%
+are the people who have you know
+reasonably substantial Holdings in the
+
+ align:start position:0%
+reasonably substantial Holdings in the
+ 
+
+ align:start position:0%
+reasonably substantial Holdings in the
+stocks I ask myself these questions a
+
+ align:start position:0%
+stocks I ask myself these questions a
+ 
+
+ align:start position:0%
+stocks I ask myself these questions a
+lot in Thailand you know sort
+
+ align:start position:0%
+lot in Thailand you know sort
+ 
+
+ align:start position:0%
+lot in Thailand you know sort
+of maybe they shouldn't be investing in
+
+ align:start position:0%
+of maybe they shouldn't be investing in
+ 
+
+ align:start position:0%
+of maybe they shouldn't be investing in
+their own projects maybe they should be
+
+ align:start position:0%
+their own projects maybe they should be
+ 
+
+ align:start position:0%
+their own projects maybe they should be
+invest ing in um Bangkok money market
+
+ align:start position:0%
+invest ing in um Bangkok money market
+ 
+
+ align:start position:0%
+invest ing in um Bangkok money market
+funds safe
+
+ align:start position:0%
+funds safe
+ 
+
+ align:start position:0%
+funds safe
+funds you know we should be sort of
+
+ align:start position:0%
+funds you know we should be sort of
+ 
+
+ align:start position:0%
+funds you know we should be sort of
+looking at the whole mean variance
+
+ align:start position:0%
+looking at the whole mean variance
+ 
+
+ align:start position:0%
+looking at the whole mean variance
+Frontier for these and we are asking
+
+ align:start position:0%
+Frontier for these and we are asking
+ 
+
+ align:start position:0%
+Frontier for these and we are asking
+them now we're actively involved as was
+
+ align:start position:0%
+them now we're actively involved as was
+ 
+
+ align:start position:0%
+them now we're actively involved as was
+on the phone again last night we're
+
+ align:start position:0%
+on the phone again last night we're
+ 
+
+ align:start position:0%
+on the phone again last night we're
+we're about to be asking them a bunch of
+
+ align:start position:0%
+we're about to be asking them a bunch of
+ 
+
+ align:start position:0%
+we're about to be asking them a bunch of
+questions about are they aware of other
+
+ align:start position:0%
+questions about are they aware of other
+ 
+
+ align:start position:0%
+questions about are they aware of other
+assets and you know see if but but in
+
+ align:start position:0%
+assets and you know see if but but in
+ 
+
+ align:start position:0%
+assets and you know see if but but in
+Sweden the point that Campbell is going
+
+ align:start position:0%
+Sweden the point that Campbell is going
+ 
+
+ align:start position:0%
+Sweden the point that Campbell is going
+to make is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you've
+
+ align:start position:0%
+um you've
+ 
+
+ align:start position:0%
+um you've
+got those
+
+ align:start position:0%
+got those
+ 
+
+ align:start position:0%
+got those
+categories and households Can Make
+
+ align:start position:0%
+categories and households Can Make
+ 
+
+ align:start position:0%
+categories and households Can Make
+Mistakes by picking volatile assets
+
+ align:start position:0%
+Mistakes by picking volatile assets
+ 
+
+ align:start position:0%
+Mistakes by picking volatile assets
+holding a concentrated portfolio picking
+
+ align:start position:0%
+holding a concentrated portfolio picking
+ 
+
+ align:start position:0%
+holding a concentrated portfolio picking
+correlated see the the parallel here
+
+ align:start position:0%
+correlated see the the parallel here
+ 
+
+ align:start position:0%
+correlated see the the parallel here
+with what I was saying happens in in the
+
+ align:start position:0%
+with what I was saying happens in in the
+ 
+
+ align:start position:0%
+with what I was saying happens in in the
+Thai villages in terms of relatively
+
+ align:start position:0%
+Thai villages in terms of relatively
+ 
+
+ align:start position:0%
+Thai villages in terms of relatively
+poor people uh not being Diversified and
+
+ align:start position:0%
+poor people uh not being Diversified and
+ 
+
+ align:start position:0%
+poor people uh not being Diversified and
+for some reason doing riskier
+
+ align:start position:0%
+for some reason doing riskier
+ 
+
+ align:start position:0%
+for some reason doing riskier
+things um and there or if if you go in
+
+ align:start position:0%
+things um and there or if if you go in
+ 
+
+ align:start position:0%
+things um and there or if if you go in
+the stock market you could pick your own
+
+ align:start position:0%
+the stock market you could pick your own
+ 
+
+ align:start position:0%
+the stock market you could pick your own
+stocks it's not a particularly clever
+
+ align:start position:0%
+stocks it's not a particularly clever
+ 
+
+ align:start position:0%
+stocks it's not a particularly clever
+thing to do
+
+ align:start position:0%
+thing to do
+ 
+
+ align:start position:0%
+thing to do
+um uh and and this is the picture that
+
+ align:start position:0%
+um uh and and this is the picture that
+ 
+
+ align:start position:0%
+um uh and and this is the picture that
+makes the
+
+ align:start position:0%
+makes the
+ 
+
+ align:start position:0%
+makes the
+paper
+
+ align:start position:0%
+paper
+ 
+
+ align:start position:0%
+paper
+um so here's the sort of mean variance
+
+ align:start position:0%
+um so here's the sort of mean variance
+ 
+
+ align:start position:0%
+um so here's the sort of mean variance
+Frontier standard deviation and means
+
+ align:start position:0%
+Frontier standard deviation and means
+ 
+
+ align:start position:0%
+Frontier standard deviation and means
+here's where they ought to
+
+ align:start position:0%
+here's where they ought to
+ 
+
+ align:start position:0%
+here's where they ought to
+be adjusting or not for international
+
+ align:start position:0%
+be adjusting or not for international
+ 
+
+ align:start position:0%
+be adjusting or not for international
+asset Holdings that's another they do
+
+ align:start position:0%
+asset Holdings that's another they do
+ 
+
+ align:start position:0%
+asset Holdings that's another they do
+both uh but they're basically
+
+ align:start position:0%
+both uh but they're basically
+ 
+
+ align:start position:0%
+both uh but they're basically
+saying
+
+ align:start position:0%
+saying
+ 
+
+ align:start position:0%
+saying
+um you know small guys in some sense are
+
+ align:start position:0%
+um you know small guys in some sense are
+ 
+
+ align:start position:0%
+um you know small guys in some sense are
+unsophisticated and cautious they're
+
+ align:start position:0%
+unsophisticated and cautious they're
+ 
+
+ align:start position:0%
+unsophisticated and cautious they're
+pretty far off the frontier but they
+
+ align:start position:0%
+pretty far off the frontier but they
+ 
+
+ align:start position:0%
+pretty far off the frontier but they
+don't have kind of a lot to
+
+ align:start position:0%
+don't have kind of a lot to
+ 
+
+ align:start position:0%
+don't have kind of a lot to
+lose uh and these these richer guys up
+
+ align:start position:0%
+lose uh and these these richer guys up
+ 
+
+ align:start position:0%
+lose uh and these these richer guys up
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+um you know they're more sophisticated
+
+ align:start position:0%
+um you know they're more sophisticated
+ 
+
+ align:start position:0%
+um you know they're more sophisticated
+their line is quote unquote above this
+
+ align:start position:0%
+their line is quote unquote above this
+ 
+
+ align:start position:0%
+their line is quote unquote above this
+brown one but but their Gap is huge so
+
+ align:start position:0%
+brown one but but their Gap is huge so
+ 
+
+ align:start position:0%
+brown one but but their Gap is huge so
+uh I'll spare you the detail sales when
+
+ align:start position:0%
+uh I'll spare you the detail sales when
+ 
+
+ align:start position:0%
+uh I'll spare you the detail sales when
+they're they're actually measuring the
+
+ align:start position:0%
+they're they're actually measuring the
+ 
+
+ align:start position:0%
+they're they're actually measuring the
+welfare loss and some of these richer
+
+ align:start position:0%
+welfare loss and some of these richer
+ 
+
+ align:start position:0%
+welfare loss and some of these richer
+households are because they are not
+
+ align:start position:0%
+households are because they are not
+ 
+
+ align:start position:0%
+households are because they are not
+diversifying actually have fairly
+
+ align:start position:0%
+diversifying actually have fairly
+ 
+
+ align:start position:0%
+diversifying actually have fairly
+substantial welfare losses now you know
+
+ align:start position:0%
+substantial welfare losses now you know
+ 
+
+ align:start position:0%
+substantial welfare losses now you know
+John goes behavioral in this and maybe
+
+ align:start position:0%
+John goes behavioral in this and maybe
+ 
+
+ align:start position:0%
+John goes behavioral in this and maybe
+rightly so he's saying you know should
+
+ align:start position:0%
+rightly so he's saying you know should
+ 
+
+ align:start position:0%
+rightly so he's saying you know should
+we you know should we really be telling
+
+ align:start position:0%
+we you know should we really be telling
+ 
+
+ align:start position:0%
+we you know should we really be telling
+households in Brazil about uh investing
+
+ align:start position:0%
+households in Brazil about uh investing
+ 
+
+ align:start position:0%
+households in Brazil about uh investing
+in whatever is bedpa can't remember the
+
+ align:start position:0%
+in whatever is bedpa can't remember the
+ 
+
+ align:start position:0%
+in whatever is bedpa can't remember the
+acronym or are they going to make mist
+
+ align:start position:0%
+acronym or are they going to make mist
+ 
+
+ align:start position:0%
+acronym or are they going to make mist
+stes and they're better off not knowing
+
+ align:start position:0%
+stes and they're better off not knowing
+ 
+
+ align:start position:0%
+stes and they're better off not knowing
+there was a
+
+ align:start position:0%
+there was a
+ 
+
+ align:start position:0%
+there was a
+question by the model this is this is
+
+ align:start position:0%
+question by the model this is this is
+ 
+
+ align:start position:0%
+question by the model this is this is
+this takes into account marginal utility
+
+ align:start position:0%
+this takes into account marginal utility
+ 
+
+ align:start position:0%
+this takes into account marginal utility
+of wealth yeah actually I'm sparing you
+
+ align:start position:0%
+of wealth yeah actually I'm sparing you
+ 
+
+ align:start position:0%
+of wealth yeah actually I'm sparing you
+a lot oh I should say this is on the
+
+ align:start position:0%
+a lot oh I should say this is on the
+ 
+
+ align:start position:0%
+a lot oh I should say this is on the
+reading list but I knew I wasn't going
+
+ align:start position:0%
+reading list but I knew I wasn't going
+ 
+
+ align:start position:0%
+reading list but I knew I wasn't going
+to have time to cover it in much detail
+
+ align:start position:0%
+to have time to cover it in much detail
+ 
+
+ align:start position:0%
+to have time to cover it in much detail
+so I picked like six slides but we'll
+
+ align:start position:0%
+so I picked like six slides but we'll
+ 
+
+ align:start position:0%
+so I picked like six slides but we'll
+I'll post the whole paper you don't if
+
+ align:start position:0%
+I'll post the whole paper you don't if
+ 
+
+ align:start position:0%
+I'll post the whole paper you don't if
+you're interested you don't necessarily
+
+ align:start position:0%
+you're interested you don't necessarily
+ 
+
+ align:start position:0%
+you're interested you don't necessarily
+want to or have time to read the whole
+
+ align:start position:0%
+want to or have time to read the whole
+ 
+
+ align:start position:0%
+want to or have time to read the whole
+paper you might as well look at these
+
+ align:start position:0%
+paper you might as well look at these
+ 
+
+ align:start position:0%
+paper you might as well look at these
+lecture notes that I created previously
+
+ align:start position:0%
+lecture notes that I created previously
+ 
+
+ align:start position:0%
+lecture notes that I created previously
+and the same thing for this
+
+ align:start position:0%
+and the same thing for this
+ 
+
+ align:start position:0%
+and the same thing for this
+paper which is adrianos with air Sophie
+
+ align:start position:0%
+paper which is adrianos with air Sophie
+ 
+
+ align:start position:0%
+paper which is adrianos with air Sophie
+Dynamic risk management I've only got a
+
+ align:start position:0%
+Dynamic risk management I've only got a
+ 
+
+ align:start position:0%
+Dynamic risk management I've only got a
+few slides I think I'm going to jump and
+
+ align:start position:0%
+few slides I think I'm going to jump and
+ 
+
+ align:start position:0%
+few slides I think I'm going to jump and
+show you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something Fly
+
+ align:start position:0%
+something Fly
+ 
+
+ align:start position:0%
+something Fly
+Southwest so so this guy's loading that
+
+ align:start position:0%
+Southwest so so this guy's loading that
+ 
+
+ align:start position:0%
+Southwest so so this guy's loading that
+airplane that Capital stock up with this
+
+ align:start position:0%
+airplane that Capital stock up with this
+ 
+
+ align:start position:0%
+airplane that Capital stock up with this
+variable input the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fuel they buy forward
+
+ align:start position:0%
+fuel they buy forward
+ 
+
+ align:start position:0%
+fuel they buy forward
+positions because the price of gasoline
+
+ align:start position:0%
+positions because the price of gasoline
+ 
+
+ align:start position:0%
+positions because the price of gasoline
+moves around a
+
+ align:start position:0%
+moves around a
+ 
+
+ align:start position:0%
+moves around a
+lot so they they basically buy forward
+
+ align:start position:0%
+lot so they they basically buy forward
+ 
+
+ align:start position:0%
+lot so they they basically buy forward
+okay they commit now to buy gasoline at
+
+ align:start position:0%
+okay they commit now to buy gasoline at
+ 
+
+ align:start position:0%
+okay they commit now to buy gasoline at
+a peg future price now what happens if
+
+ align:start position:0%
+a peg future price now what happens if
+ 
+
+ align:start position:0%
+a peg future price now what happens if
+the spot price is lower than that it's
+
+ align:start position:0%
+the spot price is lower than that it's
+ 
+
+ align:start position:0%
+the spot price is lower than that it's
+like oh darn we should have
+
+ align:start position:0%
+like oh darn we should have
+ 
+
+ align:start position:0%
+like oh darn we should have
+waited actually you could reneg on that
+
+ align:start position:0%
+waited actually you could reneg on that
+ 
+
+ align:start position:0%
+waited actually you could reneg on that
+contract and so what do they do with
+
+ align:start position:0%
+contract and so what do they do with
+ 
+
+ align:start position:0%
+contract and so what do they do with
+those things you got to post
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+collateral against these these forward
+
+ align:start position:0%
+collateral against these these forward
+ 
+
+ align:start position:0%
+collateral against these these forward
+gasoline
+
+ align:start position:0%
+gasoline
+ 
+
+ align:start position:0%
+gasoline
+Hedges oh where are we going with this
+
+ align:start position:0%
+Hedges oh where are we going with this
+ 
+
+ align:start position:0%
+Hedges oh where are we going with this
+we're going to get
+
+ align:start position:0%
+we're going to get
+ 
+
+ align:start position:0%
+we're going to get
+to sort of thinking about something that
+
+ align:start position:0%
+to sort of thinking about something that
+ 
+
+ align:start position:0%
+to sort of thinking about something that
+Chris udri was doing in
+
+ align:start position:0%
+Chris udri was doing in
+ 
+
+ align:start position:0%
+Chris udri was doing in
+Ghana okay which
+
+ align:start position:0%
+Ghana okay which
+ 
+
+ align:start position:0%
+Ghana okay which
+is do you want to
+
+ align:start position:0%
+is do you want to
+ 
+
+ align:start position:0%
+is do you want to
+use your your SC scarce
+
+ align:start position:0%
+use your your SC scarce
+ 
+
+ align:start position:0%
+use your your SC scarce
+collateral to borrow and get more
+
+ align:start position:0%
+collateral to borrow and get more
+ 
+
+ align:start position:0%
+collateral to borrow and get more
+aircraft with potentially High rate of
+
+ align:start position:0%
+aircraft with potentially High rate of
+ 
+
+ align:start position:0%
+aircraft with potentially High rate of
+return or do you want to use your scarce
+
+ align:start position:0%
+return or do you want to use your scarce
+ 
+
+ align:start position:0%
+return or do you want to use your scarce
+collateral and tie it up hedging against
+
+ align:start position:0%
+collateral and tie it up hedging against
+ 
+
+ align:start position:0%
+collateral and tie it up hedging against
+future you know states of the world S
+
+ align:start position:0%
+future you know states of the world S
+ 
+
+ align:start position:0%
+future you know states of the world S
+Prime and this paper is about how in
+
+ align:start position:0%
+Prime and this paper is about how in
+ 
+
+ align:start position:0%
+Prime and this paper is about how in
+practice this may not happen now you
+
+ align:start position:0%
+practice this may not happen now you
+ 
+
+ align:start position:0%
+practice this may not happen now you
+know when does it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happen oh where is it it
+
+ align:start position:0%
+happen oh where is it it
+ 
+
+ align:start position:0%
+happen oh where is it it
+happens when the a Airline isn't doing
+
+ align:start position:0%
+happens when the a Airline isn't doing
+ 
+
+ align:start position:0%
+happens when the a Airline isn't doing
+very well so if you think about
+
+ align:start position:0%
+very well so if you think about
+ 
+
+ align:start position:0%
+very well so if you think about
+relatively poor
+
+ align:start position:0%
+relatively poor
+ 
+
+ align:start position:0%
+relatively poor
+households you know it's like oh they're
+
+ align:start position:0%
+households you know it's like oh they're
+ 
+
+ align:start position:0%
+households you know it's like oh they're
+behavioral they're not buying uh
+
+ align:start position:0%
+behavioral they're not buying uh
+ 
+
+ align:start position:0%
+behavioral they're not buying uh
+Insurance what's wrong with them they're
+
+ align:start position:0%
+Insurance what's wrong with them they're
+ 
+
+ align:start position:0%
+Insurance what's wrong with them they're
+they need it most they've got the most
+
+ align:start position:0%
+they need it most they've got the most
+ 
+
+ align:start position:0%
+they need it most they've got the most
+marginal value well no not necessarily
+
+ align:start position:0%
+marginal value well no not necessarily
+ 
+
+ align:start position:0%
+marginal value well no not necessarily
+they may have better use for their
+
+ align:start position:0%
+they may have better use for their
+ 
+
+ align:start position:0%
+they may have better use for their
+existing wealth so this we're getting
+
+ align:start position:0%
+existing wealth so this we're getting
+ 
+
+ align:start position:0%
+existing wealth so this we're getting
+again very explicitly now into obstacles
+
+ align:start position:0%
+again very explicitly now into obstacles
+ 
+
+ align:start position:0%
+again very explicitly now into obstacles
+so when you start writing down model you
+
+ align:start position:0%
+so when you start writing down model you
+ 
+
+ align:start position:0%
+so when you start writing down model you
+know models with obstacles and barriers
+
+ align:start position:0%
+know models with obstacles and barriers
+ 
+
+ align:start position:0%
+know models with obstacles and barriers
+to trade you can get you know at this
+
+ align:start position:0%
+to trade you can get you know at this
+ 
+
+ align:start position:0%
+to trade you can get you know at this
+issue about borrowing to finance
+
+ align:start position:0%
+issue about borrowing to finance
+ 
+
+ align:start position:0%
+issue about borrowing to finance
+projects versus borrowing and maybe so
+
+ align:start position:0%
+projects versus borrowing and maybe so
+ 
+
+ align:start position:0%
+projects versus borrowing and maybe so
+maybe it's still possible that those
+
+ align:start position:0%
+maybe it's still possible that those
+ 
+
+ align:start position:0%
+maybe it's still possible that those
+relatively poor people who seem to be
+
+ align:start position:0%
+relatively poor people who seem to be
+ 
+
+ align:start position:0%
+relatively poor people who seem to be
+doing really risky things and aren't
+
+ align:start position:0%
+doing really risky things and aren't
+ 
+
+ align:start position:0%
+doing really risky things and aren't
+hedged against it maybe there's there's
+
+ align:start position:0%
+hedged against it maybe there's there's
+ 
+
+ align:start position:0%
+hedged against it maybe there's there's
+a reason for that
\ No newline at end of file
diff --git a/hAUFAN8Ceac.txt b/hAUFAN8Ceac.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7baee169b09913e0bdc7e9d85bd0639e573b270c
--- /dev/null
+++ b/hAUFAN8Ceac.txt
@@ -0,0 +1,1259 @@
+align:start position:0%
+ 
+so now we can summarize
+
+ align:start position:0%
+so now we can summarize
+ 
+
+ align:start position:0%
+so now we can summarize
+the safety guideline in a very simple
+
+ align:start position:0%
+the safety guideline in a very simple
+ 
+
+ align:start position:0%
+the safety guideline in a very simple
+formula using the steady state
+
+ align:start position:0%
+formula using the steady state
+ 
+
+ align:start position:0%
+formula using the steady state
+transmission co
+
+ align:start position:0%
+transmission co
+ 
+
+ align:start position:0%
+transmission co
+rate as a more conservative estimate
+
+ align:start position:0%
+rate as a more conservative estimate
+ 
+
+ align:start position:0%
+rate as a more conservative estimate
+than worrying about the transient
+
+ align:start position:0%
+than worrying about the transient
+ 
+
+ align:start position:0%
+than worrying about the transient
+buildup
+
+ align:start position:0%
+buildup
+ 
+
+ align:start position:0%
+buildup
+of aerosols in the room and using the
+
+ align:start position:0%
+of aerosols in the room and using the
+ 
+
+ align:start position:0%
+of aerosols in the room and using the
+simplification of introducing an
+
+ align:start position:0%
+simplification of introducing an
+ 
+
+ align:start position:0%
+simplification of introducing an
+effective
+
+ align:start position:0%
+effective
+ 
+
+ align:start position:0%
+effective
+size for particles r bar that includes
+
+ align:start position:0%
+size for particles r bar that includes
+ 
+
+ align:start position:0%
+size for particles r bar that includes
+and encodes all the information about
+
+ align:start position:0%
+and encodes all the information about
+ 
+
+ align:start position:0%
+and encodes all the information about
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+radius dependent mass penetration factor
+
+ align:start position:0%
+radius dependent mass penetration factor
+ 
+
+ align:start position:0%
+radius dependent mass penetration factor
+sedimentation rate and
+
+ align:start position:0%
+sedimentation rate and
+ 
+
+ align:start position:0%
+sedimentation rate and
+infectivity etc and droplet size
+
+ align:start position:0%
+infectivity etc and droplet size
+ 
+
+ align:start position:0%
+infectivity etc and droplet size
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+and the safety guideline looks like this
+
+ align:start position:0%
+and the safety guideline looks like this
+ 
+
+ align:start position:0%
+and the safety guideline looks like this
+it basically
+
+ align:start position:0%
+it basically
+ 
+
+ align:start position:0%
+it basically
+bounds the cumulative exposure time
+
+ align:start position:0%
+bounds the cumulative exposure time
+ 
+
+ align:start position:0%
+bounds the cumulative exposure time
+which is n minus one the number of
+
+ align:start position:0%
+which is n minus one the number of
+ 
+
+ align:start position:0%
+which is n minus one the number of
+susceptible people when
+
+ align:start position:0%
+susceptible people when
+ 
+
+ align:start position:0%
+susceptible people when
+one person enters a room of occupancy n
+
+ align:start position:0%
+one person enters a room of occupancy n
+ 
+
+ align:start position:0%
+one person enters a room of occupancy n
+uh maximum occupancy and stays
+
+ align:start position:0%
+uh maximum occupancy and stays
+ 
+
+ align:start position:0%
+uh maximum occupancy and stays
+for a time tau and i should mention the
+
+ align:start position:0%
+for a time tau and i should mention the
+ 
+
+ align:start position:0%
+for a time tau and i should mention the
+time tau
+
+ align:start position:0%
+time tau
+ 
+
+ align:start position:0%
+time tau
+does not need to be continuous so if you
+
+ align:start position:0%
+does not need to be continuous so if you
+ 
+
+ align:start position:0%
+does not need to be continuous so if you
+think of say a classroom or an office
+
+ align:start position:0%
+think of say a classroom or an office
+ 
+
+ align:start position:0%
+think of say a classroom or an office
+you would be adding up the time total
+
+ align:start position:0%
+you would be adding up the time total
+ 
+
+ align:start position:0%
+you would be adding up the time total
+time so if this
+
+ align:start position:0%
+time so if this
+ 
+
+ align:start position:0%
+time so if this
+save time is 100 hours and you you have
+
+ align:start position:0%
+save time is 100 hours and you you have
+ 
+
+ align:start position:0%
+save time is 100 hours and you you have
+to spend 10 hours a day
+
+ align:start position:0%
+to spend 10 hours a day
+ 
+
+ align:start position:0%
+to spend 10 hours a day
+you might get 10 days okay according to
+
+ align:start position:0%
+you might get 10 days okay according to
+ 
+
+ align:start position:0%
+you might get 10 days okay according to
+this calculation
+
+ align:start position:0%
+this calculation
+ 
+
+ align:start position:0%
+this calculation
+and so that relationship is plotted as
+
+ align:start position:0%
+and so that relationship is plotted as
+ 
+
+ align:start position:0%
+and so that relationship is plotted as
+this yellow curve
+
+ align:start position:0%
+this yellow curve
+ 
+
+ align:start position:0%
+this yellow curve
+and if you're below that curve you're
+
+ align:start position:0%
+and if you're below that curve you're
+ 
+
+ align:start position:0%
+and if you're below that curve you're
+safe so you have either
+
+ align:start position:0%
+safe so you have either
+ 
+
+ align:start position:0%
+safe so you have either
+smaller time than that or a lower
+
+ align:start position:0%
+smaller time than that or a lower
+ 
+
+ align:start position:0%
+smaller time than that or a lower
+occupancy and that's how you can decide
+
+ align:start position:0%
+occupancy and that's how you can decide
+ 
+
+ align:start position:0%
+occupancy and that's how you can decide
+the safety
+
+ align:start position:0%
+the safety
+ 
+
+ align:start position:0%
+the safety
+again this is the safety exposure
+
+ align:start position:0%
+again this is the safety exposure
+ 
+
+ align:start position:0%
+again this is the safety exposure
+guideline for indoor
+
+ align:start position:0%
+guideline for indoor
+ 
+
+ align:start position:0%
+guideline for indoor
+airborne transmission
+
+ align:start position:0%
+airborne transmission
+ 
+
+ align:start position:0%
+airborne transmission
+and we will talk about other types of
+
+ align:start position:0%
+and we will talk about other types of
+ 
+
+ align:start position:0%
+and we will talk about other types of
+transmission
+
+ align:start position:0%
+transmission
+ 
+
+ align:start position:0%
+transmission
+later what's nice about this formula is
+
+ align:start position:0%
+later what's nice about this formula is
+ 
+
+ align:start position:0%
+later what's nice about this formula is
+it allows you to immediately see the
+
+ align:start position:0%
+it allows you to immediately see the
+ 
+
+ align:start position:0%
+it allows you to immediately see the
+effects of the scaling some of which
+
+ align:start position:0%
+effects of the scaling some of which
+ 
+
+ align:start position:0%
+effects of the scaling some of which
+we've already talked about before
+
+ align:start position:0%
+we've already talked about before
+ 
+
+ align:start position:0%
+we've already talked about before
+so if we would like to move it in this
+
+ align:start position:0%
+so if we would like to move it in this
+ 
+
+ align:start position:0%
+so if we would like to move it in this
+direction obviously we would like
+
+ align:start position:0%
+direction obviously we would like
+ 
+
+ align:start position:0%
+direction obviously we would like
+the curve to be up here somewhere so
+
+ align:start position:0%
+the curve to be up here somewhere so
+ 
+
+ align:start position:0%
+the curve to be up here somewhere so
+this is obviously making the room more
+
+ align:start position:0%
+this is obviously making the room more
+ 
+
+ align:start position:0%
+this is obviously making the room more
+safe if i can push it in this direction
+
+ align:start position:0%
+safe if i can push it in this direction
+ 
+
+ align:start position:0%
+safe if i can push it in this direction
+i can either get more people
+
+ align:start position:0%
+i can either get more people
+ 
+
+ align:start position:0%
+i can either get more people
+or more time or any you know whatever
+
+ align:start position:0%
+or more time or any you know whatever
+ 
+
+ align:start position:0%
+or more time or any you know whatever
+combination of that i'd like
+
+ align:start position:0%
+combination of that i'd like
+ 
+
+ align:start position:0%
+combination of that i'd like
+how can i get there so cq is a
+
+ align:start position:0%
+how can i get there so cq is a
+ 
+
+ align:start position:0%
+how can i get there so cq is a
+disease-specific parameter
+
+ align:start position:0%
+disease-specific parameter
+ 
+
+ align:start position:0%
+disease-specific parameter
+but we will see that cq does depend on
+
+ align:start position:0%
+but we will see that cq does depend on
+ 
+
+ align:start position:0%
+but we will see that cq does depend on
+the type of respiration and activities
+
+ align:start position:0%
+the type of respiration and activities
+ 
+
+ align:start position:0%
+the type of respiration and activities
+such as singing
+
+ align:start position:0%
+such as singing
+ 
+
+ align:start position:0%
+such as singing
+or heavy exercise or loud speaking are
+
+ align:start position:0%
+or heavy exercise or loud speaking are
+ 
+
+ align:start position:0%
+or heavy exercise or loud speaking are
+much worse
+
+ align:start position:0%
+much worse
+ 
+
+ align:start position:0%
+much worse
+than resting or breathing so to get in
+
+ align:start position:0%
+than resting or breathing so to get in
+ 
+
+ align:start position:0%
+than resting or breathing so to get in
+this direction we could do
+
+ align:start position:0%
+this direction we could do
+ 
+
+ align:start position:0%
+this direction we could do
+a smaller cq
+
+ align:start position:0%
+a smaller cq
+ 
+
+ align:start position:0%
+a smaller cq
+which could be resting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+versus speaking or
+
+ align:start position:0%
+versus speaking or
+ 
+
+ align:start position:0%
+versus speaking or
+singing and we'll come back to
+
+ align:start position:0%
+singing and we'll come back to
+ 
+
+ align:start position:0%
+singing and we'll come back to
+characterizing that more carefully so we
+
+ align:start position:0%
+characterizing that more carefully so we
+ 
+
+ align:start position:0%
+characterizing that more carefully so we
+can at least change the type of activity
+
+ align:start position:0%
+can at least change the type of activity
+ 
+
+ align:start position:0%
+can at least change the type of activity
+in the room
+
+ align:start position:0%
+in the room
+ 
+
+ align:start position:0%
+in the room
+well we can uh for physical parameters
+
+ align:start position:0%
+well we can uh for physical parameters
+ 
+
+ align:start position:0%
+well we can uh for physical parameters
+we can increase
+
+ align:start position:0%
+we can increase
+ 
+
+ align:start position:0%
+we can increase
+v the room volume so if you take
+
+ align:start position:0%
+v the room volume so if you take
+ 
+
+ align:start position:0%
+v the room volume so if you take
+everything the same same number of
+
+ align:start position:0%
+everything the same same number of
+ 
+
+ align:start position:0%
+everything the same same number of
+people and you make the room much bigger
+
+ align:start position:0%
+people and you make the room much bigger
+ 
+
+ align:start position:0%
+people and you make the room much bigger
+obviously the air gets more diluted and
+
+ align:start position:0%
+obviously the air gets more diluted and
+ 
+
+ align:start position:0%
+obviously the air gets more diluted and
+hence there's less chance of
+
+ align:start position:0%
+hence there's less chance of
+ 
+
+ align:start position:0%
+hence there's less chance of
+transmission if people are
+
+ align:start position:0%
+transmission if people are
+ 
+
+ align:start position:0%
+transmission if people are
+sort of scattered about the room what
+
+ align:start position:0%
+sort of scattered about the room what
+ 
+
+ align:start position:0%
+sort of scattered about the room what
+else can we do
+
+ align:start position:0%
+else can we do
+ 
+
+ align:start position:0%
+else can we do
+we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can lower qb
+
+ align:start position:0%
+we can lower qb
+ 
+
+ align:start position:0%
+we can lower qb
+which means breathe
+
+ align:start position:0%
+which means breathe
+ 
+
+ align:start position:0%
+which means breathe
+slowly or in a more relaxed way so again
+
+ align:start position:0%
+slowly or in a more relaxed way so again
+ 
+
+ align:start position:0%
+slowly or in a more relaxed way so again
+coming back to the activity in the room
+
+ align:start position:0%
+coming back to the activity in the room
+ 
+
+ align:start position:0%
+coming back to the activity in the room
+if you have heavy physical exercise your
+
+ align:start position:0%
+if you have heavy physical exercise your
+ 
+
+ align:start position:0%
+if you have heavy physical exercise your
+qb might increase although it doesn't
+
+ align:start position:0%
+qb might increase although it doesn't
+ 
+
+ align:start position:0%
+qb might increase although it doesn't
+increase that much
+
+ align:start position:0%
+increase that much
+ 
+
+ align:start position:0%
+increase that much
+resting breathing is around 0.5 meters
+
+ align:start position:0%
+resting breathing is around 0.5 meters
+ 
+
+ align:start position:0%
+resting breathing is around 0.5 meters
+cube per hour
+
+ align:start position:0%
+cube per hour
+ 
+
+ align:start position:0%
+cube per hour
+and even heavy exercise doesn't get much
+
+ align:start position:0%
+and even heavy exercise doesn't get much
+ 
+
+ align:start position:0%
+and even heavy exercise doesn't get much
+higher than about
+
+ align:start position:0%
+higher than about
+ 
+
+ align:start position:0%
+higher than about
+three meters cube per hour and so that's
+
+ align:start position:0%
+three meters cube per hour and so that's
+ 
+
+ align:start position:0%
+three meters cube per hour and so that's
+a total of uh
+
+ align:start position:0%
+a total of uh
+ 
+
+ align:start position:0%
+a total of uh
+a factor of six or so but it comes in
+
+ align:start position:0%
+a factor of six or so but it comes in
+ 
+
+ align:start position:0%
+a factor of six or so but it comes in
+squared so
+
+ align:start position:0%
+squared so
+ 
+
+ align:start position:0%
+squared so
+that could actually be significant so
+
+ align:start position:0%
+that could actually be significant so
+ 
+
+ align:start position:0%
+that could actually be significant so
+definitely heavy exercise is not as good
+
+ align:start position:0%
+definitely heavy exercise is not as good
+ 
+
+ align:start position:0%
+definitely heavy exercise is not as good
+as resting
+
+ align:start position:0%
+as resting
+ 
+
+ align:start position:0%
+as resting
+and what else do we have we have masks
+
+ align:start position:0%
+and what else do we have we have masks
+ 
+
+ align:start position:0%
+and what else do we have we have masks
+well obviously we can
+
+ align:start position:0%
+well obviously we can
+ 
+
+ align:start position:0%
+well obviously we can
+wear masks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that is actually very helpful
+
+ align:start position:0%
+and that is actually very helpful
+ 
+
+ align:start position:0%
+and that is actually very helpful
+because we've already discussed it comes
+
+ align:start position:0%
+because we've already discussed it comes
+ 
+
+ align:start position:0%
+because we've already discussed it comes
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+squared and that is something which is
+
+ align:start position:0%
+squared and that is something which is
+ 
+
+ align:start position:0%
+squared and that is something which is
+sort of very simple fix
+
+ align:start position:0%
+sort of very simple fix
+ 
+
+ align:start position:0%
+sort of very simple fix
+and if the mask penetration factor is uh
+
+ align:start position:0%
+and if the mask penetration factor is uh
+ 
+
+ align:start position:0%
+and if the mask penetration factor is uh
+you know 10 or or even possibly less it
+
+ align:start position:0%
+you know 10 or or even possibly less it
+ 
+
+ align:start position:0%
+you know 10 or or even possibly less it
+comes in squared so that can have a very
+
+ align:start position:0%
+comes in squared so that can have a very
+ 
+
+ align:start position:0%
+comes in squared so that can have a very
+big effect of pushing this over as we
+
+ align:start position:0%
+big effect of pushing this over as we
+ 
+
+ align:start position:0%
+big effect of pushing this over as we
+will see
+
+ align:start position:0%
+will see
+ 
+
+ align:start position:0%
+will see
+so this is basically a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lower p mask
+
+ align:start position:0%
+lower p mask
+ 
+
+ align:start position:0%
+lower p mask
+so when there's no mask pm is equal to
+
+ align:start position:0%
+so when there's no mask pm is equal to
+ 
+
+ align:start position:0%
+so when there's no mask pm is equal to
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+uh finally we also have in lambda c
+
+ align:start position:0%
+uh finally we also have in lambda c
+ 
+
+ align:start position:0%
+uh finally we also have in lambda c
+we have um because we had written that
+
+ align:start position:0%
+we have um because we had written that
+ 
+
+ align:start position:0%
+we have um because we had written that
+out earlier that that also includes
+
+ align:start position:0%
+out earlier that that also includes
+ 
+
+ align:start position:0%
+out earlier that that also includes
+several effects
+
+ align:start position:0%
+several effects
+ 
+
+ align:start position:0%
+several effects
+such as better ventilation um
+
+ align:start position:0%
+such as better ventilation um
+ 
+
+ align:start position:0%
+such as better ventilation um
+so so increase ventilation
+
+ align:start position:0%
+so so increase ventilation
+ 
+
+ align:start position:0%
+so so increase ventilation
+so the flow rate of outside air
+
+ align:start position:0%
+so the flow rate of outside air
+ 
+
+ align:start position:0%
+so the flow rate of outside air
+so the air change rate should be
+
+ align:start position:0%
+so the air change rate should be
+ 
+
+ align:start position:0%
+so the air change rate should be
+increased that gives us a larger lambda
+
+ align:start position:0%
+increased that gives us a larger lambda
+ 
+
+ align:start position:0%
+increased that gives us a larger lambda
+c
+
+ align:start position:0%
+c
+ 
+
+ align:start position:0%
+c
+we can introduce air filtration
+
+ align:start position:0%
+we can introduce air filtration
+ 
+
+ align:start position:0%
+we can introduce air filtration
+and that's sort of buried within lambda
+
+ align:start position:0%
+and that's sort of buried within lambda
+ 
+
+ align:start position:0%
+and that's sort of buried within lambda
+c that's p f lambda f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+although as we discussed earlier because
+
+ align:start position:0%
+although as we discussed earlier because
+ 
+
+ align:start position:0%
+although as we discussed earlier because
+you have to have a certain amount of
+
+ align:start position:0%
+you have to have a certain amount of
+ 
+
+ align:start position:0%
+you have to have a certain amount of
+fresh air coming into the room air
+
+ align:start position:0%
+fresh air coming into the room air
+ 
+
+ align:start position:0%
+fresh air coming into the room air
+filtration doesn't give you as much
+
+ align:start position:0%
+filtration doesn't give you as much
+ 
+
+ align:start position:0%
+filtration doesn't give you as much
+benefit
+
+ align:start position:0%
+benefit
+ 
+
+ align:start position:0%
+benefit
+as you might hope but can still give you
+
+ align:start position:0%
+as you might hope but can still give you
+ 
+
+ align:start position:0%
+as you might hope but can still give you
+you know a factor of
+
+ align:start position:0%
+you know a factor of
+ 
+
+ align:start position:0%
+you know a factor of
+five or something like that if you have
+
+ align:start position:0%
+five or something like that if you have
+ 
+
+ align:start position:0%
+five or something like that if you have
+20 percent outdoor
+
+ align:start position:0%
+20 percent outdoor
+ 
+
+ align:start position:0%
+20 percent outdoor
+fresh air coming in and so those are
+
+ align:start position:0%
+fresh air coming in and so those are
+ 
+
+ align:start position:0%
+fresh air coming in and so those are
+some of the key scalings that we can
+
+ align:start position:0%
+some of the key scalings that we can
+ 
+
+ align:start position:0%
+some of the key scalings that we can
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+and just simply by plugging into a form
+
+ align:start position:0%
+and just simply by plugging into a form
+ 
+
+ align:start position:0%
+and just simply by plugging into a form
+like this we get a sense of how
+
+ align:start position:0%
+like this we get a sense of how
+ 
+
+ align:start position:0%
+like this we get a sense of how
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+mitigation strategies can be compared
+
+ align:start position:0%
+mitigation strategies can be compared
+ 
+
+ align:start position:0%
+mitigation strategies can be compared
+and also how different types of rooms
+
+ align:start position:0%
+and also how different types of rooms
+ 
+
+ align:start position:0%
+and also how different types of rooms
+can be compared in terms of the
+
+ align:start position:0%
+can be compared in terms of the
+ 
+
+ align:start position:0%
+can be compared in terms of the
+occupancy time
+
+ align:start position:0%
+occupancy time
+ 
+
+ align:start position:0%
+occupancy time
+and the number of people that could be
+
+ align:start position:0%
+and the number of people that could be
+ 
+
+ align:start position:0%
+and the number of people that could be
+allowed as a maximum occupancy
+
+ align:start position:0%
+allowed as a maximum occupancy
+ 
+
+ align:start position:0%
+allowed as a maximum occupancy
+and what remains now is to parametrize
+
+ align:start position:0%
+and what remains now is to parametrize
+ 
+
+ align:start position:0%
+and what remains now is to parametrize
+this for covet 19 specifically
+
+ align:start position:0%
+this for covet 19 specifically
+ 
+
+ align:start position:0%
+this for covet 19 specifically
+which boils down to understanding this
+
+ align:start position:0%
+which boils down to understanding this
+ 
+
+ align:start position:0%
+which boils down to understanding this
+parameter cq
\ No newline at end of file
diff --git a/hDwkKrWqdZE.txt b/hDwkKrWqdZE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fb68dc0c6a46191d22662b3e8bb517855cf6f717
--- /dev/null
+++ b/hDwkKrWqdZE.txt
@@ -0,0 +1,8867 @@
+align:start position:0%
+ 
+all right we are going to continue our
+
+ align:start position:0%
+all right we are going to continue our
+ 
+
+ align:start position:0%
+all right we are going to continue our
+discussion of extrema graph theory last
+
+ align:start position:0%
+discussion of extrema graph theory last
+ 
+
+ align:start position:0%
+discussion of extrema graph theory last
+time we discussed what happens when we
+
+ align:start position:0%
+time we discussed what happens when we
+ 
+
+ align:start position:0%
+time we discussed what happens when we
+exclude a triangle or more generally a
+
+ align:start position:0%
+exclude a triangle or more generally a
+ 
+
+ align:start position:0%
+exclude a triangle or more generally a
+creek and we wish to find a graph that
+
+ align:start position:0%
+creek and we wish to find a graph that
+ 
+
+ align:start position:0%
+creek and we wish to find a graph that
+maximizes the number of edges and at the
+
+ align:start position:0%
+maximizes the number of edges and at the
+ 
+
+ align:start position:0%
+maximizes the number of edges and at the
+end of the lecture I stated the theorem
+
+ align:start position:0%
+end of the lecture I stated the theorem
+ 
+
+ align:start position:0%
+end of the lecture I stated the theorem
+of error stone and shamone which which
+
+ align:start position:0%
+of error stone and shamone which which
+ 
+
+ align:start position:0%
+of error stone and shamone which which
+test recall that if you have a fixed H
+
+ align:start position:0%
+test recall that if you have a fixed H
+ 
+
+ align:start position:0%
+test recall that if you have a fixed H
+and I wish to understand the maximum
+
+ align:start position:0%
+and I wish to understand the maximum
+ 
+
+ align:start position:0%
+and I wish to understand the maximum
+number of edges in an N vertex graph
+
+ align:start position:0%
+number of edges in an N vertex graph
+ 
+
+ align:start position:0%
+number of edges in an N vertex graph
+that is H free so remember this
+
+ align:start position:0%
+that is H free so remember this
+ 
+
+ align:start position:0%
+that is H free so remember this
+definition this is the maximum number of
+
+ align:start position:0%
+definition this is the maximum number of
+ 
+
+ align:start position:0%
+definition this is the maximum number of
+edges in an N vertex H free graph so we
+
+ align:start position:0%
+edges in an N vertex H free graph so we
+ 
+
+ align:start position:0%
+edges in an N vertex H free graph so we
+are going to be looking at this quantity
+
+ align:start position:0%
+are going to be looking at this quantity
+ 
+
+ align:start position:0%
+are going to be looking at this quantity
+in the next few lectures
+
+ align:start position:0%
+in the next few lectures
+ 
+
+ align:start position:0%
+in the next few lectures
+so the Adderstone Shmuel image theorem
+
+ align:start position:0%
+so the Adderstone Shmuel image theorem
+ 
+
+ align:start position:0%
+so the Adderstone Shmuel image theorem
+tells us that perhaps quite surprisingly
+
+ align:start position:0%
+tells us that perhaps quite surprisingly
+ 
+
+ align:start position:0%
+tells us that perhaps quite surprisingly
+this quantity is largely governed by the
+
+ align:start position:0%
+this quantity is largely governed by the
+ 
+
+ align:start position:0%
+this quantity is largely governed by the
+chromatic number of H even though H
+
+ align:start position:0%
+chromatic number of H even though H
+ 
+
+ align:start position:0%
+chromatic number of H even though H
+itself might be quite involved so if you
+
+ align:start position:0%
+itself might be quite involved so if you
+ 
+
+ align:start position:0%
+itself might be quite involved so if you
+knew the chromatic number you already
+
+ align:start position:0%
+knew the chromatic number you already
+ 
+
+ align:start position:0%
+knew the chromatic number you already
+know a lot of information about the
+
+ align:start position:0%
+know a lot of information about the
+ 
+
+ align:start position:0%
+know a lot of information about the
+growth rate of this function in
+
+ align:start position:0%
+growth rate of this function in
+ 
+
+ align:start position:0%
+growth rate of this function in
+particular as long as H is not bipartite
+
+ align:start position:0%
+particular as long as H is not bipartite
+ 
+
+ align:start position:0%
+particular as long as H is not bipartite
+so that the chromatic number is at least
+
+ align:start position:0%
+so that the chromatic number is at least
+ 
+
+ align:start position:0%
+so that the chromatic number is at least
+3 we already know the first word
+
+ align:start position:0%
+3 we already know the first word
+ 
+
+ align:start position:0%
+3 we already know the first word
+asymptotics from the error Stoneman
+
+ align:start position:0%
+asymptotics from the error Stoneman
+ 
+
+ align:start position:0%
+asymptotics from the error Stoneman
+image theorem however when H is
+
+ align:start position:0%
+image theorem however when H is
+ 
+
+ align:start position:0%
+image theorem however when H is
+bipartite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that the chromatic number is exactly
+
+ align:start position:0%
+so that the chromatic number is exactly
+ 
+
+ align:start position:0%
+so that the chromatic number is exactly
+two then the theorem tells us only that
+
+ align:start position:0%
+two then the theorem tells us only that
+ 
+
+ align:start position:0%
+two then the theorem tells us only that
+this quantity is little o of N squared
+
+ align:start position:0%
+this quantity is little o of N squared
+ 
+
+ align:start position:0%
+this quantity is little o of N squared
+which is some useful information but it
+
+ align:start position:0%
+which is some useful information but it
+ 
+
+ align:start position:0%
+which is some useful information but it
+doesn't tell us the whole story in the
+
+ align:start position:0%
+doesn't tell us the whole story in the
+ 
+
+ align:start position:0%
+doesn't tell us the whole story in the
+next several lectures I want to explore
+
+ align:start position:0%
+next several lectures I want to explore
+ 
+
+ align:start position:0%
+next several lectures I want to explore
+what more can we say about this quantity
+
+ align:start position:0%
+what more can we say about this quantity
+ 
+
+ align:start position:0%
+what more can we say about this quantity
+here for bipartite graphs H and it turns
+
+ align:start position:0%
+here for bipartite graphs H and it turns
+ 
+
+ align:start position:0%
+here for bipartite graphs H and it turns
+out that there's a lot that we do not
+
+ align:start position:0%
+out that there's a lot that we do not
+ 
+
+ align:start position:0%
+out that there's a lot that we do not
+know there are lots of open problems in
+
+ align:start position:0%
+know there are lots of open problems in
+ 
+
+ align:start position:0%
+know there are lots of open problems in
+this area having to do with trying to
+
+ align:start position:0%
+this area having to do with trying to
+ 
+
+ align:start position:0%
+this area having to do with trying to
+pin down the growth rate of this
+
+ align:start position:0%
+pin down the growth rate of this
+ 
+
+ align:start position:0%
+pin down the growth rate of this
+function in particular for bipartite
+
+ align:start position:0%
+function in particular for bipartite
+ 
+
+ align:start position:0%
+function in particular for bipartite
+graphs there's a bipartite graph that
+
+ align:start position:0%
+graphs there's a bipartite graph that
+ 
+
+ align:start position:0%
+graphs there's a bipartite graph that
+plays a somewhat special role namely the
+
+ align:start position:0%
+plays a somewhat special role namely the
+ 
+
+ align:start position:0%
+plays a somewhat special role namely the
+complete bipartite graph so KST in the
+
+ align:start position:0%
+complete bipartite graph so KST in the
+ 
+
+ align:start position:0%
+complete bipartite graph so KST in the
+complete bipartite graph with s vertices
+
+ align:start position:0%
+complete bipartite graph with s vertices
+ 
+
+ align:start position:0%
+complete bipartite graph with s vertices
+on one side and P vertices on the other
+
+ align:start position:0%
+on one side and P vertices on the other
+ 
+
+ align:start position:0%
+on one side and P vertices on the other
+side so this is a very nice bipartite
+
+ align:start position:0%
+side so this is a very nice bipartite
+ 
+
+ align:start position:0%
+side so this is a very nice bipartite
+graph and just to understand the
+
+ align:start position:0%
+graph and just to understand the
+ 
+
+ align:start position:0%
+graph and just to understand the
+extremal number for this graph is a
+
+ align:start position:0%
+extremal number for this graph is a
+ 
+
+ align:start position:0%
+extremal number for this graph is a
+famous open problem in this area and it
+
+ align:start position:0%
+famous open problem in this area and it
+ 
+
+ align:start position:0%
+famous open problem in this area and it
+has the name of 0 and K which problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is to determine or estimate the
+
+ align:start position:0%
+which is to determine or estimate the
+ 
+
+ align:start position:0%
+which is to determine or estimate the
+extremal numbers for these complete
+
+ align:start position:0%
+extremal numbers for these complete
+ 
+
+ align:start position:0%
+extremal numbers for these complete
+bipartite graphs ok so i'll tell you
+
+ align:start position:0%
+bipartite graphs ok so i'll tell you
+ 
+
+ align:start position:0%
+bipartite graphs ok so i'll tell you
+pretty much all we know about this
+
+ align:start position:0%
+pretty much all we know about this
+ 
+
+ align:start position:0%
+pretty much all we know about this
+problem there are some interesting
+
+ align:start position:0%
+problem there are some interesting
+ 
+
+ align:start position:0%
+problem there are some interesting
+things but we do not know all that much
+
+ align:start position:0%
+things but we do not know all that much
+ 
+
+ align:start position:0%
+things but we do not know all that much
+you know every bipartite graph is a
+
+ align:start position:0%
+you know every bipartite graph is a
+ 
+
+ align:start position:0%
+you know every bipartite graph is a
+subset it's a sub graph of such a
+
+ align:start position:0%
+subset it's a sub graph of such a
+ 
+
+ align:start position:0%
+subset it's a sub graph of such a
+complete bipartite graph so every
+
+ align:start position:0%
+complete bipartite graph so every
+ 
+
+ align:start position:0%
+complete bipartite graph so every
+bipartite h is a soft graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of some KST and we know that if H is a
+
+ align:start position:0%
+of some KST and we know that if H is a
+ 
+
+ align:start position:0%
+of some KST and we know that if H is a
+sub graph of this KST then the extremal
+
+ align:start position:0%
+sub graph of this KST then the extremal
+ 
+
+ align:start position:0%
+sub graph of this KST then the extremal
+number for H if your graph is H free
+
+ align:start position:0%
+number for H if your graph is H free
+ 
+
+ align:start position:0%
+number for H if your graph is H free
+then automatically has to be KST 3 so
+
+ align:start position:0%
+then automatically has to be KST 3 so
+ 
+
+ align:start position:0%
+then automatically has to be KST 3 so
+there's this bound between these two
+
+ align:start position:0%
+there's this bound between these two
+ 
+
+ align:start position:0%
+there's this bound between these two
+extremal numbers so in particular if you
+
+ align:start position:0%
+extremal numbers so in particular if you
+ 
+
+ align:start position:0%
+extremal numbers so in particular if you
+have some upper bound on case T's then
+
+ align:start position:0%
+have some upper bound on case T's then
+ 
+
+ align:start position:0%
+have some upper bound on case T's then
+you have some upper bound on bipartite
+
+ align:start position:0%
+you have some upper bound on bipartite
+ 
+
+ align:start position:0%
+you have some upper bound on bipartite
+graphs although for specific bipartite
+
+ align:start position:0%
+graphs although for specific bipartite
+ 
+
+ align:start position:0%
+graphs although for specific bipartite
+graphs each maybe we can do better than
+
+ align:start position:0%
+graphs each maybe we can do better than
+ 
+
+ align:start position:0%
+graphs each maybe we can do better than
+using the spam and we'll see examples of
+
+ align:start position:0%
+using the spam and we'll see examples of
+ 
+
+ align:start position:0%
+using the spam and we'll see examples of
+that later in the course as well okay so
+
+ align:start position:0%
+that later in the course as well okay so
+ 
+
+ align:start position:0%
+that later in the course as well okay so
+what can we say about the extremal
+
+ align:start position:0%
+what can we say about the extremal
+ 
+
+ align:start position:0%
+what can we say about the extremal
+numbers of these ksps and so the most
+
+ align:start position:0%
+numbers of these ksps and so the most
+ 
+
+ align:start position:0%
+numbers of these ksps and so the most
+important theorem in this area of this
+
+ align:start position:0%
+important theorem in this area of this
+ 
+
+ align:start position:0%
+important theorem in this area of this
+problem is a result due to Kaveri show
+
+ align:start position:0%
+problem is a result due to Kaveri show
+ 
+
+ align:start position:0%
+problem is a result due to Kaveri show
+Shantaram so the kaveri shows Terron
+
+ align:start position:0%
+Shantaram so the kaveri shows Terron
+ 
+
+ align:start position:0%
+Shantaram so the kaveri shows Terron
+theorem tells us that for every fixed
+
+ align:start position:0%
+theorem tells us that for every fixed
+ 
+
+ align:start position:0%
+theorem tells us that for every fixed
+integers s and t as a most t there
+
+ align:start position:0%
+integers s and t as a most t there
+ 
+
+ align:start position:0%
+integers s and t as a most t there
+exists some constant C such that the
+
+ align:start position:0%
+exists some constant C such that the
+ 
+
+ align:start position:0%
+exists some constant C such that the
+extremal number is upper bounded by
+
+ align:start position:0%
+extremal number is upper bounded by
+ 
+
+ align:start position:0%
+extremal number is upper bounded by
+something which is on the order of n to
+
+ align:start position:0%
+something which is on the order of n to
+ 
+
+ align:start position:0%
+something which is on the order of n to
+the 2 minus 1 over s gives you some
+
+ align:start position:0%
+the 2 minus 1 over s gives you some
+ 
+
+ align:start position:0%
+the 2 minus 1 over s gives you some
+upper bound showing you that it has not
+
+ align:start position:0%
+upper bound showing you that it has not
+ 
+
+ align:start position:0%
+upper bound showing you that it has not
+only sub-quadratic but there's a gap
+
+ align:start position:0%
+only sub-quadratic but there's a gap
+ 
+
+ align:start position:0%
+only sub-quadratic but there's a gap
+from 2 in the exponent now in
+
+ align:start position:0%
+from 2 in the exponent now in
+ 
+
+ align:start position:0%
+from 2 in the exponent now in
+combinatorics SS with many fields of
+
+ align:start position:0%
+combinatorics SS with many fields of
+ 
+
+ align:start position:0%
+combinatorics SS with many fields of
+mathematics it can be somewhat
+
+ align:start position:0%
+mathematics it can be somewhat
+ 
+
+ align:start position:0%
+mathematics it can be somewhat
+intimidating to newcomers when you see a
+
+ align:start position:0%
+intimidating to newcomers when you see a
+ 
+
+ align:start position:0%
+intimidating to newcomers when you see a
+lot of names or every germs seems to be
+
+ align:start position:0%
+lot of names or every germs seems to be
+ 
+
+ align:start position:0%
+lot of names or every germs seems to be
+half named after a string of
+
+ align:start position:0%
+half named after a string of
+ 
+
+ align:start position:0%
+half named after a string of
+mathematicians know some of humor
+
+ align:start position:0%
+mathematicians know some of humor
+ 
+
+ align:start position:0%
+mathematicians know some of humor
+I heard of some me not and Aguas and it
+
+ align:start position:0%
+I heard of some me not and Aguas and it
+ 
+
+ align:start position:0%
+I heard of some me not and Aguas and it
+may be difficult to remember who is who
+
+ align:start position:0%
+may be difficult to remember who is who
+ 
+
+ align:start position:0%
+may be difficult to remember who is who
+and what is what
+
+ align:start position:0%
+and what is what
+ 
+
+ align:start position:0%
+and what is what
+I think this term has a very nice way to
+
+ align:start position:0%
+I think this term has a very nice way to
+ 
+
+ align:start position:0%
+I think this term has a very nice way to
+remember which is that it's a term about
+
+ align:start position:0%
+remember which is that it's a term about
+ 
+
+ align:start position:0%
+remember which is that it's a term about
+K STS and this is the KSR T theorem okay
+
+ align:start position:0%
+K STS and this is the KSR T theorem okay
+ 
+
+ align:start position:0%
+K STS and this is the KSR T theorem okay
+all right so this is the KSR T theorem I
+
+ align:start position:0%
+all right so this is the KSR T theorem I
+ 
+
+ align:start position:0%
+all right so this is the KSR T theorem I
+want to begin by showing you how to
+
+ align:start position:0%
+want to begin by showing you how to
+ 
+
+ align:start position:0%
+want to begin by showing you how to
+prove the KS t theorem but the proof is
+
+ align:start position:0%
+prove the KS t theorem but the proof is
+ 
+
+ align:start position:0%
+prove the KS t theorem but the proof is
+we are a nice not too difficult double
+
+ align:start position:0%
+we are a nice not too difficult double
+ 
+
+ align:start position:0%
+we are a nice not too difficult double
+counting argument and then show you some
+
+ align:start position:0%
+counting argument and then show you some
+ 
+
+ align:start position:0%
+counting argument and then show you some
+applications so let's prove this theorem
+
+ align:start position:0%
+applications so let's prove this theorem
+ 
+
+ align:start position:0%
+applications so let's prove this theorem
+and it's by a double counting argument
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are we going to count well let's
+
+ align:start position:0%
+what are we going to count well let's
+ 
+
+ align:start position:0%
+what are we going to count well let's
+start with the object that we're working
+
+ align:start position:0%
+start with the object that we're working
+ 
+
+ align:start position:0%
+start with the object that we're working
+with so there's going to be a graph G
+
+ align:start position:0%
+with so there's going to be a graph G
+ 
+
+ align:start position:0%
+with so there's going to be a graph G
+that has n vertices and edges and KS T 3
+
+ align:start position:0%
+that has n vertices and edges and KS T 3
+ 
+
+ align:start position:0%
+that has n vertices and edges and KS T 3
+and let's count the number of stars K s
+
+ align:start position:0%
+and let's count the number of stars K s
+ 
+
+ align:start position:0%
+and let's count the number of stars K s
+1 in this graph G so we're counting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+configurations like that do an upper
+
+ align:start position:0%
+configurations like that do an upper
+ 
+
+ align:start position:0%
+configurations like that do an upper
+bound and a lower bound on one hand so
+
+ align:start position:0%
+bound and a lower bound on one hand so
+ 
+
+ align:start position:0%
+bound and a lower bound on one hand so
+let's start with the upper bound I want
+
+ align:start position:0%
+let's start with the upper bound I want
+ 
+
+ align:start position:0%
+let's start with the upper bound I want
+hand every subset of s vertices in the
+
+ align:start position:0%
+hand every subset of s vertices in the
+ 
+
+ align:start position:0%
+hand every subset of s vertices in the
+graph G has at most t minus 1 comma
+
+ align:start position:0%
+graph G has at most t minus 1 comma
+ 
+
+ align:start position:0%
+graph G has at most t minus 1 comma
+neighbors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because if they have T common neighbors
+
+ align:start position:0%
+because if they have T common neighbors
+ 
+
+ align:start position:0%
+because if they have T common neighbors
+then you get a KS t so that's one down
+
+ align:start position:0%
+then you get a KS t so that's one down
+ 
+
+ align:start position:0%
+then you get a KS t so that's one down
+on the other hand let's see what happens
+
+ align:start position:0%
+on the other hand let's see what happens
+ 
+
+ align:start position:0%
+on the other hand let's see what happens
+to the number of common neighbors if you
+
+ align:start position:0%
+to the number of common neighbors if you
+ 
+
+ align:start position:0%
+to the number of common neighbors if you
+knew that this graph has a lot of edges
+
+ align:start position:0%
+knew that this graph has a lot of edges
+ 
+
+ align:start position:0%
+knew that this graph has a lot of edges
+so the number of stars well I can
+
+ align:start position:0%
+so the number of stars well I can
+ 
+
+ align:start position:0%
+so the number of stars well I can
+calculate this quantity explicitly by
+
+ align:start position:0%
+calculate this quantity explicitly by
+ 
+
+ align:start position:0%
+calculate this quantity explicitly by
+running over all the vertices of G for
+
+ align:start position:0%
+running over all the vertices of G for
+ 
+
+ align:start position:0%
+running over all the vertices of G for
+each vertex look at its neighborhood and
+
+ align:start position:0%
+each vertex look at its neighborhood and
+ 
+
+ align:start position:0%
+each vertex look at its neighborhood and
+choose s vertices from its neighborhood
+
+ align:start position:0%
+choose s vertices from its neighborhood
+ 
+
+ align:start position:0%
+choose s vertices from its neighborhood
+so for each beep I need to find a sub
+
+ align:start position:0%
+so for each beep I need to find a sub
+ 
+
+ align:start position:0%
+so for each beep I need to find a sub
+set of s vertices from its neighborhood
+
+ align:start position:0%
+set of s vertices from its neighborhood
+ 
+
+ align:start position:0%
+set of s vertices from its neighborhood
+by convexity I can lower bound the sum
+
+ align:start position:0%
+by convexity I can lower bound the sum
+ 
+
+ align:start position:0%
+by convexity I can lower bound the sum
+by the average in some sense because
+
+ align:start position:0%
+by the average in some sense because
+ 
+
+ align:start position:0%
+by the average in some sense because
+okay let me first write down the
+
+ align:start position:0%
+okay let me first write down the
+ 
+
+ align:start position:0%
+okay let me first write down the
+expression so I can do a convex the
+
+ align:start position:0%
+expression so I can do a convex the
+ 
+
+ align:start position:0%
+expression so I can do a convex the
+argument that gives me this lower bound
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I'm using abusing notation somewhat
+
+ align:start position:0%
+here I'm using abusing notation somewhat
+ 
+
+ align:start position:0%
+here I'm using abusing notation somewhat
+and writing binomial coefficients with a
+
+ align:start position:0%
+and writing binomial coefficients with a
+ 
+
+ align:start position:0%
+and writing binomial coefficients with a
+real entry on top where I mean the
+
+ align:start position:0%
+real entry on top where I mean the
+ 
+
+ align:start position:0%
+real entry on top where I mean the
+expression as you would expect treating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sky is a polynomial in X and the key
+
+ align:start position:0%
+the sky is a polynomial in X and the key
+ 
+
+ align:start position:0%
+the sky is a polynomial in X and the key
+fact we're using here is that this
+
+ align:start position:0%
+fact we're using here is that this
+ 
+
+ align:start position:0%
+fact we're using here is that this
+function here is convex for X at least
+
+ align:start position:0%
+function here is convex for X at least
+ 
+
+ align:start position:0%
+function here is convex for X at least
+and minus one so in particular if you
+
+ align:start position:0%
+and minus one so in particular if you
+ 
+
+ align:start position:0%
+and minus one so in particular if you
+think about this function here we have a
+
+ align:start position:0%
+think about this function here we have a
+ 
+
+ align:start position:0%
+think about this function here we have a
+lot of zeros and then it becomes convex
+
+ align:start position:0%
+lot of zeros and then it becomes convex
+ 
+
+ align:start position:0%
+lot of zeros and then it becomes convex
+afterwards so you can even think of
+
+ align:start position:0%
+afterwards so you can even think of
+ 
+
+ align:start position:0%
+afterwards so you can even think of
+extending this function is zero to the
+
+ align:start position:0%
+extending this function is zero to the
+ 
+
+ align:start position:0%
+extending this function is zero to the
+left of em -
+
+ align:start position:0%
+left of em -
+ 
+
+ align:start position:0%
+left of em -
+so this is a convex function and you can
+
+ align:start position:0%
+so this is a convex function and you can
+ 
+
+ align:start position:0%
+so this is a convex function and you can
+apply convexity to reduce this
+
+ align:start position:0%
+apply convexity to reduce this
+ 
+
+ align:start position:0%
+apply convexity to reduce this
+inequality but you know the sum of the
+
+ align:start position:0%
+inequality but you know the sum of the
+ 
+
+ align:start position:0%
+inequality but you know the sum of the
+degrees that's just essentially twice I
+
+ align:start position:0%
+degrees that's just essentially twice I
+ 
+
+ align:start position:0%
+degrees that's just essentially twice I
+mean that is to twice the number of
+
+ align:start position:0%
+mean that is to twice the number of
+ 
+
+ align:start position:0%
+mean that is to twice the number of
+edges so we have this expression right
+
+ align:start position:0%
+edges so we have this expression right
+ 
+
+ align:start position:0%
+edges so we have this expression right
+here so you have an upper bound on the
+
+ align:start position:0%
+here so you have an upper bound on the
+ 
+
+ align:start position:0%
+here so you have an upper bound on the
+number of s stars coming from KST
+
+ align:start position:0%
+number of s stars coming from KST
+ 
+
+ align:start position:0%
+number of s stars coming from KST
+freeness and lower bound on the number
+
+ align:start position:0%
+freeness and lower bound on the number
+ 
+
+ align:start position:0%
+freeness and lower bound on the number
+of s stars coming from just having lots
+
+ align:start position:0%
+of s stars coming from just having lots
+ 
+
+ align:start position:0%
+of s stars coming from just having lots
+of edges and applying convexity okay
+
+ align:start position:0%
+of edges and applying convexity okay
+ 
+
+ align:start position:0%
+of edges and applying convexity okay
+putting these two things together we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find that there's this inequality here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we are thinking of s and TS fixed
+
+ align:start position:0%
+here we are thinking of s and TS fixed
+ 
+
+ align:start position:0%
+here we are thinking of s and TS fixed
+and we are trying to understand how m
+
+ align:start position:0%
+and we are trying to understand how m
+ 
+
+ align:start position:0%
+and we are trying to understand how m
+and n depend on each other as they get
+
+ align:start position:0%
+and n depend on each other as they get
+ 
+
+ align:start position:0%
+and n depend on each other as they get
+large so it will be helpful to use the
+
+ align:start position:0%
+large so it will be helpful to use the
+ 
+
+ align:start position:0%
+large so it will be helpful to use the
+asymptotics that and choose s grows like
+
+ align:start position:0%
+asymptotics that and choose s grows like
+ 
+
+ align:start position:0%
+asymptotics that and choose s grows like
+and to the s divided by s factorial for
+
+ align:start position:0%
+and to the s divided by s factorial for
+ 
+
+ align:start position:0%
+and to the s divided by s factorial for
+fixed s so looking at that expression
+
+ align:start position:0%
+fixed s so looking at that expression
+ 
+
+ align:start position:0%
+fixed s so looking at that expression
+and applying this asymptotics to both
+
+ align:start position:0%
+and applying this asymptotics to both
+ 
+
+ align:start position:0%
+and applying this asymptotics to both
+sides we have this inequality here so
+
+ align:start position:0%
+sides we have this inequality here so
+ 
+
+ align:start position:0%
+sides we have this inequality here so
+I've eliminated s factorial from both
+
+ align:start position:0%
+I've eliminated s factorial from both
+ 
+
+ align:start position:0%
+I've eliminated s factorial from both
+sides okay so now rearrange clean things
+
+ align:start position:0%
+sides okay so now rearrange clean things
+ 
+
+ align:start position:0%
+sides okay so now rearrange clean things
+up we find the following upper bound on
+
+ align:start position:0%
+up we find the following upper bound on
+ 
+
+ align:start position:0%
+up we find the following upper bound on
+M the number of edges in G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's the expression so for fixed
+
+ align:start position:0%
+and that's the expression so for fixed
+ 
+
+ align:start position:0%
+and that's the expression so for fixed
+SNT a gross like n to the 2 minus 1 over
+
+ align:start position:0%
+SNT a gross like n to the 2 minus 1 over
+ 
+
+ align:start position:0%
+SNT a gross like n to the 2 minus 1 over
+s any questions yeah so so the questions
+
+ align:start position:0%
+s any questions yeah so so the questions
+ 
+
+ align:start position:0%
+s any questions yeah so so the questions
+were the right side of inequality which
+
+ align:start position:0%
+were the right side of inequality which
+ 
+
+ align:start position:0%
+were the right side of inequality which
+inequality this one here right so here
+
+ align:start position:0%
+inequality this one here right so here
+ 
+
+ align:start position:0%
+inequality this one here right so here
+we are counting the number of K as once
+
+ align:start position:0%
+we are counting the number of K as once
+ 
+
+ align:start position:0%
+we are counting the number of K as once
+so here I am so upper lower bounding the
+
+ align:start position:0%
+so here I am so upper lower bounding the
+ 
+
+ align:start position:0%
+so here I am so upper lower bounding the
+number of KS once using what we derived
+
+ align:start position:0%
+number of KS once using what we derived
+ 
+
+ align:start position:0%
+number of KS once using what we derived
+earlier yes right the question is do we
+
+ align:start position:0%
+earlier yes right the question is do we
+ 
+
+ align:start position:0%
+earlier yes right the question is do we
+care that s is less than equal to T in
+
+ align:start position:0%
+care that s is less than equal to T in
+ 
+
+ align:start position:0%
+care that s is less than equal to T in
+the argument the argument doesn't care
+
+ align:start position:0%
+the argument the argument doesn't care
+ 
+
+ align:start position:0%
+the argument the argument doesn't care
+but of course if you want the better
+
+ align:start position:0%
+but of course if you want the better
+ 
+
+ align:start position:0%
+but of course if you want the better
+asymptotics for fixed s and T as n gets
+
+ align:start position:0%
+asymptotics for fixed s and T as n gets
+ 
+
+ align:start position:0%
+asymptotics for fixed s and T as n gets
+large you should take s to be less than
+
+ align:start position:0%
+large you should take s to be less than
+ 
+
+ align:start position:0%
+large you should take s to be less than
+equal to T question what happens when T
+
+ align:start position:0%
+equal to T question what happens when T
+ 
+
+ align:start position:0%
+equal to T question what happens when T
+equals to 1 well that's a great question
+
+ align:start position:0%
+equals to 1 well that's a great question
+ 
+
+ align:start position:0%
+equals to 1 well that's a great question
+I'll leave you to think about it if you
+
+ align:start position:0%
+I'll leave you to think about it if you
+ 
+
+ align:start position:0%
+I'll leave you to think about it if you
+have if you know that your graph has
+
+ align:start position:0%
+have if you know that your graph has
+ 
+
+ align:start position:0%
+have if you know that your graph has
+maximum degree at most T what can you
+
+ align:start position:0%
+maximum degree at most T what can you
+ 
+
+ align:start position:0%
+maximum degree at most T what can you
+tell me about a number of edges in the
+
+ align:start position:0%
+tell me about a number of edges in the
+ 
+
+ align:start position:0%
+tell me about a number of edges in the
+graph
+
+ align:start position:0%
+graph
+ 
+
+ align:start position:0%
+graph
+okay any more questions
+
+ align:start position:0%
+okay any more questions
+ 
+
+ align:start position:0%
+okay any more questions
+okay well come back to this theorem in
+
+ align:start position:0%
+okay well come back to this theorem in
+ 
+
+ align:start position:0%
+okay well come back to this theorem in
+fact this will occupy us for at least a
+
+ align:start position:0%
+fact this will occupy us for at least a
+ 
+
+ align:start position:0%
+fact this will occupy us for at least a
+couple of lectures basically it's this
+
+ align:start position:0%
+couple of lectures basically it's this
+ 
+
+ align:start position:0%
+couple of lectures basically it's this
+theorem kite and it is conjectured to be
+
+ align:start position:0%
+theorem kite and it is conjectured to be
+ 
+
+ align:start position:0%
+theorem kite and it is conjectured to be
+although that is a major open problem
+
+ align:start position:0%
+although that is a major open problem
+ 
+
+ align:start position:0%
+although that is a major open problem
+extreme of graph theory
+
+ align:start position:0%
+extreme of graph theory
+ 
+
+ align:start position:0%
+extreme of graph theory
+we only know a small number of values
+
+ align:start position:0%
+we only know a small number of values
+ 
+
+ align:start position:0%
+we only know a small number of values
+well for most values of s and T in
+
+ align:start position:0%
+well for most values of s and T in
+ 
+
+ align:start position:0%
+well for most values of s and T in
+particular one s and P are both equal to
+
+ align:start position:0%
+particular one s and P are both equal to
+ 
+
+ align:start position:0%
+particular one s and P are both equal to
+four we do not know if this bound is
+
+ align:start position:0%
+four we do not know if this bound is
+ 
+
+ align:start position:0%
+four we do not know if this bound is
+tight but there are some values of s and
+
+ align:start position:0%
+tight but there are some values of s and
+ 
+
+ align:start position:0%
+tight but there are some values of s and
+T for which we do know that it is tight
+
+ align:start position:0%
+T for which we do know that it is tight
+ 
+
+ align:start position:0%
+T for which we do know that it is tight
+for example 2 & 2 3 & 3 4 & 7 s and if T
+
+ align:start position:0%
+for example 2 & 2 3 & 3 4 & 7 s and if T
+ 
+
+ align:start position:0%
+for example 2 & 2 3 & 3 4 & 7 s and if T
+is really really large and I will show
+
+ align:start position:0%
+is really really large and I will show
+ 
+
+ align:start position:0%
+is really really large and I will show
+you some constructions later on creating
+
+ align:start position:0%
+you some constructions later on creating
+ 
+
+ align:start position:0%
+you some constructions later on creating
+graphs G that are KST free for those
+
+ align:start position:0%
+graphs G that are KST free for those
+ 
+
+ align:start position:0%
+graphs G that are KST free for those
+parameters that matches this KST bound
+
+ align:start position:0%
+parameters that matches this KST bound
+ 
+
+ align:start position:0%
+parameters that matches this KST bound
+up to a constant factor yes right so the
+
+ align:start position:0%
+up to a constant factor yes right so the
+ 
+
+ align:start position:0%
+up to a constant factor yes right so the
+question is for a fixed value of s is
+
+ align:start position:0%
+question is for a fixed value of s is
+ 
+
+ align:start position:0%
+question is for a fixed value of s is
+there some bound on T for which we get
+
+ align:start position:0%
+there some bound on T for which we get
+ 
+
+ align:start position:0%
+there some bound on T for which we get
+equality cases there is a conjecture
+
+ align:start position:0%
+equality cases there is a conjecture
+ 
+
+ align:start position:0%
+equality cases there is a conjecture
+that this bound is sharp up to a
+
+ align:start position:0%
+that this bound is sharp up to a
+ 
+
+ align:start position:0%
+that this bound is sharp up to a
+constant factor for every s and T but we
+
+ align:start position:0%
+constant factor for every s and T but we
+ 
+
+ align:start position:0%
+constant factor for every s and T but we
+only know how to prove that conjecture
+
+ align:start position:0%
+only know how to prove that conjecture
+ 
+
+ align:start position:0%
+only know how to prove that conjecture
+and I will explain I will tell you much
+
+ align:start position:0%
+and I will explain I will tell you much
+ 
+
+ align:start position:0%
+and I will explain I will tell you much
+more about that later on when P is much
+
+ align:start position:0%
+more about that later on when P is much
+ 
+
+ align:start position:0%
+more about that later on when P is much
+larger compared to s there's there are
+
+ align:start position:0%
+larger compared to s there's there are
+ 
+
+ align:start position:0%
+larger compared to s there's there are
+lots of unexplored territory on this
+
+ align:start position:0%
+lots of unexplored territory on this
+ 
+
+ align:start position:0%
+lots of unexplored territory on this
+problem any more questions ok before
+
+ align:start position:0%
+problem any more questions ok before
+ 
+
+ align:start position:0%
+problem any more questions ok before
+diving into the curve average shorter on
+
+ align:start position:0%
+diving into the curve average shorter on
+ 
+
+ align:start position:0%
+diving into the curve average shorter on
+theorem further I just want to show you
+
+ align:start position:0%
+theorem further I just want to show you
+ 
+
+ align:start position:0%
+theorem further I just want to show you
+some neat applications
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I want to begin with a geometric
+
+ align:start position:0%
+and I want to begin with a geometric
+ 
+
+ align:start position:0%
+and I want to begin with a geometric
+application there's a classic problem
+
+ align:start position:0%
+application there's a classic problem
+ 
+
+ align:start position:0%
+application there's a classic problem
+asked by elders back in the 40s called
+
+ align:start position:0%
+asked by elders back in the 40s called
+ 
+
+ align:start position:0%
+asked by elders back in the 40s called
+the unit distance problem which asks
+
+ align:start position:0%
+the unit distance problem which asks
+ 
+
+ align:start position:0%
+the unit distance problem which asks
+what is the maximum number of unit
+
+ align:start position:0%
+what is the maximum number of unit
+ 
+
+ align:start position:0%
+what is the maximum number of unit
+distances maximum number of unit
+
+ align:start position:0%
+distances maximum number of unit
+ 
+
+ align:start position:0%
+distances maximum number of unit
+distances formed by n points in the
+
+ align:start position:0%
+distances formed by n points in the
+ 
+
+ align:start position:0%
+distances formed by n points in the
+plane let me give you some examples if
+
+ align:start position:0%
+plane let me give you some examples if
+ 
+
+ align:start position:0%
+plane let me give you some examples if
+you have three points you put them in an
+
+ align:start position:0%
+you have three points you put them in an
+ 
+
+ align:start position:0%
+you have three points you put them in an
+equilateral triangle and all three
+
+ align:start position:0%
+equilateral triangle and all three
+ 
+
+ align:start position:0%
+equilateral triangle and all three
+distances are unit great if you have
+
+ align:start position:0%
+distances are unit great if you have
+ 
+
+ align:start position:0%
+distances are unit great if you have
+hope four points you cannot place them
+
+ align:start position:0%
+hope four points you cannot place them
+ 
+
+ align:start position:0%
+hope four points you cannot place them
+so that all 6 distances are units if
+
+ align:start position:0%
+so that all 6 distances are units if
+ 
+
+ align:start position:0%
+so that all 6 distances are units if
+you're staying the plane so the best
+
+ align:start position:0%
+you're staying the plane so the best
+ 
+
+ align:start position:0%
+you're staying the plane so the best
+thing you can do is something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I'm drawing all the edges that
+
+ align:start position:0%
+okay so I'm drawing all the edges that
+ 
+
+ align:start position:0%
+okay so I'm drawing all the edges that
+are unit distances if you have one more
+
+ align:start position:0%
+are unit distances if you have one more
+ 
+
+ align:start position:0%
+are unit distances if you have one more
+point turns out that's the best thing
+
+ align:start position:0%
+point turns out that's the best thing
+ 
+
+ align:start position:0%
+point turns out that's the best thing
+you can do with five points with six
+
+ align:start position:0%
+you can do with five points with six
+ 
+
+ align:start position:0%
+you can do with five points with six
+points there are some more possibilities
+
+ align:start position:0%
+points there are some more possibilities
+ 
+
+ align:start position:0%
+points there are some more possibilities
+let me draw for you some possibilities
+
+ align:start position:0%
+let me draw for you some possibilities
+ 
+
+ align:start position:0%
+let me draw for you some possibilities
+you can extend the previous
+
+ align:start position:0%
+you can extend the previous
+ 
+
+ align:start position:0%
+you can extend the previous
+configuration by adding more triangles
+
+ align:start position:0%
+configuration by adding more triangles
+ 
+
+ align:start position:0%
+configuration by adding more triangles
+and there are many different ways that
+
+ align:start position:0%
+and there are many different ways that
+ 
+
+ align:start position:0%
+and there are many different ways that
+you can attach an extra triangle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's actually one more way to do it
+
+ align:start position:0%
+there's actually one more way to do it
+ 
+
+ align:start position:0%
+there's actually one more way to do it
+with six points namely I can put them
+
+ align:start position:0%
+with six points namely I can put them
+ 
+
+ align:start position:0%
+with six points namely I can put them
+like a projection of a prism so all of
+
+ align:start position:0%
+like a projection of a prism so all of
+ 
+
+ align:start position:0%
+like a projection of a prism so all of
+these configurations have the maximum
+
+ align:start position:0%
+these configurations have the maximum
+ 
+
+ align:start position:0%
+these configurations have the maximum
+number of unit distances obtained if you
+
+ align:start position:0%
+number of unit distances obtained if you
+ 
+
+ align:start position:0%
+number of unit distances obtained if you
+draw six points if you draw seven points
+
+ align:start position:0%
+draw six points if you draw seven points
+ 
+
+ align:start position:0%
+draw six points if you draw seven points
+turns out this is the best way to do it
+
+ align:start position:0%
+turns out this is the best way to do it
+ 
+
+ align:start position:0%
+turns out this is the best way to do it
+okay so you can go on for a while and
+
+ align:start position:0%
+okay so you can go on for a while and
+ 
+
+ align:start position:0%
+okay so you can go on for a while and
+people have okay so you can try to
+
+ align:start position:0%
+people have okay so you can try to
+ 
+
+ align:start position:0%
+people have okay so you can try to
+tabulate for every and what's the
+
+ align:start position:0%
+tabulate for every and what's the
+ 
+
+ align:start position:0%
+tabulate for every and what's the
+maximum number of unit distances you can
+
+ align:start position:0%
+maximum number of unit distances you can
+ 
+
+ align:start position:0%
+maximum number of unit distances you can
+generate having n points in the plane
+
+ align:start position:0%
+generate having n points in the plane
+ 
+
+ align:start position:0%
+generate having n points in the plane
+and the question is what is the answer
+
+ align:start position:0%
+and the question is what is the answer
+ 
+
+ align:start position:0%
+and the question is what is the answer
+for n points and it turns out for this
+
+ align:start position:0%
+for n points and it turns out for this
+ 
+
+ align:start position:0%
+for n points and it turns out for this
+problem and for many problems like it in
+
+ align:start position:0%
+problem and for many problems like it in
+ 
+
+ align:start position:0%
+problem and for many problems like it in
+combinatorics you can have a lot of fun
+
+ align:start position:0%
+combinatorics you can have a lot of fun
+ 
+
+ align:start position:0%
+combinatorics you can have a lot of fun
+with playing with small examples but
+
+ align:start position:0%
+with playing with small examples but
+ 
+
+ align:start position:0%
+with playing with small examples but
+they are often misleading it doesn't
+
+ align:start position:0%
+they are often misleading it doesn't
+ 
+
+ align:start position:0%
+they are often misleading it doesn't
+really tell you what the overall
+
+ align:start position:0%
+really tell you what the overall
+ 
+
+ align:start position:0%
+really tell you what the overall
+structure should be like and it turns
+
+ align:start position:0%
+structure should be like and it turns
+ 
+
+ align:start position:0%
+structure should be like and it turns
+out this is a major open-palm for which
+
+ align:start position:0%
+out this is a major open-palm for which
+ 
+
+ align:start position:0%
+out this is a major open-palm for which
+we do not understand what the structure
+
+ align:start position:0%
+we do not understand what the structure
+ 
+
+ align:start position:0%
+we do not understand what the structure
+is like for large values of n so think
+
+ align:start position:0%
+is like for large values of n so think
+ 
+
+ align:start position:0%
+is like for large values of n so think
+and large what are some possible ways to
+
+ align:start position:0%
+and large what are some possible ways to
+ 
+
+ align:start position:0%
+and large what are some possible ways to
+generate many unit distances yep great
+
+ align:start position:0%
+generate many unit distances yep great
+ 
+
+ align:start position:0%
+generate many unit distances yep great
+so one way is to draw lots of triangles
+
+ align:start position:0%
+so one way is to draw lots of triangles
+ 
+
+ align:start position:0%
+so one way is to draw lots of triangles
+so extend this figure forward okay so
+
+ align:start position:0%
+so extend this figure forward okay so
+ 
+
+ align:start position:0%
+so extend this figure forward okay so
+let's do that well actually let me give
+
+ align:start position:0%
+let's do that well actually let me give
+ 
+
+ align:start position:0%
+let's do that well actually let me give
+you something even simpler to begin with
+
+ align:start position:0%
+you something even simpler to begin with
+ 
+
+ align:start position:0%
+you something even simpler to begin with
+I can just put the endpoints on the line
+
+ align:start position:0%
+I can just put the endpoints on the line
+ 
+
+ align:start position:0%
+I can just put the endpoints on the line
+equal spaced okay I get n minus 1
+
+ align:start position:0%
+equal spaced okay I get n minus 1
+ 
+
+ align:start position:0%
+equal spaced okay I get n minus 1
+distances I minus 1 unit distances if I
+
+ align:start position:0%
+distances I minus 1 unit distances if I
+ 
+
+ align:start position:0%
+distances I minus 1 unit distances if I
+put them like that how many units
+
+ align:start position:0%
+put them like that how many units
+ 
+
+ align:start position:0%
+put them like that how many units
+distances do I get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right two times n minus one so each
+
+ align:start position:0%
+all right two times n minus one so each
+ 
+
+ align:start position:0%
+all right two times n minus one so each
+new point gives you two extra new
+
+ align:start position:0%
+new point gives you two extra new
+ 
+
+ align:start position:0%
+new point gives you two extra new
+distances and you can try to think about
+
+ align:start position:0%
+distances and you can try to think about
+ 
+
+ align:start position:0%
+distances and you can try to think about
+how to do better if you follow that
+
+ align:start position:0%
+how to do better if you follow that
+ 
+
+ align:start position:0%
+how to do better if you follow that
+sequence of examples maybe you're
+
+ align:start position:0%
+sequence of examples maybe you're
+ 
+
+ align:start position:0%
+sequence of examples maybe you're
+limited to such ideas yes you are not
+
+ align:start position:0%
+limited to such ideas yes you are not
+ 
+
+ align:start position:0%
+limited to such ideas yes you are not
+allowed to put in the same points in the
+
+ align:start position:0%
+allowed to put in the same points in the
+ 
+
+ align:start position:0%
+allowed to put in the same points in the
+same place that's a great question but
+
+ align:start position:0%
+same place that's a great question but
+ 
+
+ align:start position:0%
+same place that's a great question but
+you're not allowed to put points in the
+
+ align:start position:0%
+you're not allowed to put points in the
+ 
+
+ align:start position:0%
+you're not allowed to put points in the
+same place yes so so I didn't quite
+
+ align:start position:0%
+same place yes so so I didn't quite
+ 
+
+ align:start position:0%
+same place yes so so I didn't quite
+understand so you say if you put huh yep
+
+ align:start position:0%
+understand so you say if you put huh yep
+ 
+
+ align:start position:0%
+understand so you say if you put huh yep
+ah so you want to take this example and
+
+ align:start position:0%
+ah so you want to take this example and
+ 
+
+ align:start position:0%
+ah so you want to take this example and
+keep translating in some directions I
+
+ align:start position:0%
+keep translating in some directions I
+ 
+
+ align:start position:0%
+keep translating in some directions I
+think you would run out of room pretty
+
+ align:start position:0%
+think you would run out of room pretty
+ 
+
+ align:start position:0%
+think you would run out of room pretty
+quickly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hmm I say you want to take this
+
+ align:start position:0%
+hmm I say you want to take this
+ 
+
+ align:start position:0%
+hmm I say you want to take this
+configuration and translate it in some
+
+ align:start position:0%
+configuration and translate it in some
+ 
+
+ align:start position:0%
+configuration and translate it in some
+unit direction well then you double the
+
+ align:start position:0%
+unit direction well then you double the
+ 
+
+ align:start position:0%
+unit direction well then you double the
+number of points but you don't actually
+
+ align:start position:0%
+number of points but you don't actually
+ 
+
+ align:start position:0%
+number of points but you don't actually
+increase the number of unit distances or
+
+ align:start position:0%
+increase the number of unit distances or
+ 
+
+ align:start position:0%
+increase the number of unit distances or
+that much okay so the suggestion is we
+
+ align:start position:0%
+that much okay so the suggestion is we
+ 
+
+ align:start position:0%
+that much okay so the suggestion is we
+take some configuration we take some
+
+ align:start position:0%
+take some configuration we take some
+ 
+
+ align:start position:0%
+take some configuration we take some
+configuration let's say this graph G and
+
+ align:start position:0%
+configuration let's say this graph G and
+ 
+
+ align:start position:0%
+configuration let's say this graph G and
+I form two copies of G by translating G
+
+ align:start position:0%
+I form two copies of G by translating G
+ 
+
+ align:start position:0%
+I form two copies of G by translating G
+in some unit Direction some generic unit
+
+ align:start position:0%
+in some unit Direction some generic unit
+ 
+
+ align:start position:0%
+in some unit Direction some generic unit
+Direction okay great so what happens to
+
+ align:start position:0%
+Direction okay great so what happens to
+ 
+
+ align:start position:0%
+Direction okay great so what happens to
+the number of vertices so n goes to 2m
+
+ align:start position:0%
+the number of vertices so n goes to 2m
+ 
+
+ align:start position:0%
+the number of vertices so n goes to 2m
+and the number of edges goes from m2 to
+
+ align:start position:0%
+and the number of edges goes from m2 to
+ 
+
+ align:start position:0%
+and the number of edges goes from m2 to
+M plus n all right okay great so if you
+
+ align:start position:0%
+M plus n all right okay great so if you
+ 
+
+ align:start position:0%
+M plus n all right okay great so if you
+do that what do you get and log n okay
+
+ align:start position:0%
+do that what do you get and log n okay
+ 
+
+ align:start position:0%
+do that what do you get and log n okay
+that's much better than before okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good very nice yes
+
+ align:start position:0%
+good very nice yes
+ 
+
+ align:start position:0%
+good very nice yes
+Oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so there are suggestions to start
+
+ align:start position:0%
+right so there are suggestions to start
+ 
+
+ align:start position:0%
+right so there are suggestions to start
+with some graph G and then I'm replacing
+
+ align:start position:0%
+with some graph G and then I'm replacing
+ 
+
+ align:start position:0%
+with some graph G and then I'm replacing
+so let's as an example look at that one
+
+ align:start position:0%
+so let's as an example look at that one
+ 
+
+ align:start position:0%
+so let's as an example look at that one
+and I'm replacing each vertex here by an
+
+ align:start position:0%
+and I'm replacing each vertex here by an
+ 
+
+ align:start position:0%
+and I'm replacing each vertex here by an
+equilateral triangle but I want to
+
+ align:start position:0%
+equilateral triangle but I want to
+ 
+
+ align:start position:0%
+equilateral triangle but I want to
+maintain the same unit distance right so
+
+ align:start position:0%
+maintain the same unit distance right so
+ 
+
+ align:start position:0%
+maintain the same unit distance right so
+the huh it's this similar to taking this
+
+ align:start position:0%
+the huh it's this similar to taking this
+ 
+
+ align:start position:0%
+the huh it's this similar to taking this
+graph G and then translating it in two
+
+ align:start position:0%
+graph G and then translating it in two
+ 
+
+ align:start position:0%
+graph G and then translating it in two
+different directions that form an
+
+ align:start position:0%
+different directions that form an
+ 
+
+ align:start position:0%
+different directions that form an
+equilateral triangle I think it's yeah
+
+ align:start position:0%
+equilateral triangle I think it's yeah
+ 
+
+ align:start position:0%
+equilateral triangle I think it's yeah
+so it's a very similar idea and maybe
+
+ align:start position:0%
+so it's a very similar idea and maybe
+ 
+
+ align:start position:0%
+so it's a very similar idea and maybe
+you do a little bit better in terms of
+
+ align:start position:0%
+you do a little bit better in terms of
+ 
+
+ align:start position:0%
+you do a little bit better in terms of
+constants okay yeah all are great
+
+ align:start position:0%
+constants okay yeah all are great
+ 
+
+ align:start position:0%
+constants okay yeah all are great
+suggestions I'm actually this is this is
+
+ align:start position:0%
+suggestions I'm actually this is this is
+ 
+
+ align:start position:0%
+suggestions I'm actually this is this is
+really nice two times and you want to
+
+ align:start position:0%
+really nice two times and you want to
+ 
+
+ align:start position:0%
+really nice two times and you want to
+make a constant correction okay let me
+
+ align:start position:0%
+make a constant correction okay let me
+ 
+
+ align:start position:0%
+make a constant correction okay let me
+just do that any more suggestions okay
+
+ align:start position:0%
+just do that any more suggestions okay
+ 
+
+ align:start position:0%
+just do that any more suggestions okay
+yeah all of this is really nice so so
+
+ align:start position:0%
+yeah all of this is really nice so so
+ 
+
+ align:start position:0%
+yeah all of this is really nice so so
+let me tell you what is the best
+
+ align:start position:0%
+let me tell you what is the best
+ 
+
+ align:start position:0%
+let me tell you what is the best
+construction that people are aware of
+
+ align:start position:0%
+construction that people are aware of
+ 
+
+ align:start position:0%
+construction that people are aware of
+and this is a construction due to air
+
+ align:start position:0%
+and this is a construction due to air
+ 
+
+ align:start position:0%
+and this is a construction due to air
+dish and the idea is to think big not
+
+ align:start position:0%
+dish and the idea is to think big not
+ 
+
+ align:start position:0%
+dish and the idea is to think big not
+build from small examples so what air
+
+ align:start position:0%
+build from small examples so what air
+ 
+
+ align:start position:0%
+build from small examples so what air
+dash did is to consider a square grid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+root n by root n okay when I see
+
+ align:start position:0%
+root n by root n okay when I see
+ 
+
+ align:start position:0%
+root n by root n okay when I see
+something that's do then it's non
+
+ align:start position:0%
+something that's do then it's non
+ 
+
+ align:start position:0%
+something that's do then it's non
+integer just think round down to the
+
+ align:start position:0%
+integer just think round down to the
+ 
+
+ align:start position:0%
+integer just think round down to the
+lowest to the nearest integer I have a
+
+ align:start position:0%
+lowest to the nearest integer I have a
+ 
+
+ align:start position:0%
+lowest to the nearest integer I have a
+square grid now if you take the these
+
+ align:start position:0%
+square grid now if you take the these
+ 
+
+ align:start position:0%
+square grid now if you take the these
+distances as unit distances okay you get
+
+ align:start position:0%
+distances as unit distances okay you get
+ 
+
+ align:start position:0%
+distances as unit distances okay you get
+something which is linear in n so you
+
+ align:start position:0%
+something which is linear in n so you
+ 
+
+ align:start position:0%
+something which is linear in n so you
+don't gain that much but you can take
+
+ align:start position:0%
+don't gain that much but you can take
+ 
+
+ align:start position:0%
+don't gain that much but you can take
+any specific distance as your unit
+
+ align:start position:0%
+any specific distance as your unit
+ 
+
+ align:start position:0%
+any specific distance as your unit
+distance so what we can do is take a
+
+ align:start position:0%
+distance so what we can do is take a
+ 
+
+ align:start position:0%
+distance so what we can do is take a
+distance that is represented many times
+
+ align:start position:0%
+distance that is represented many times
+ 
+
+ align:start position:0%
+distance that is represented many times
+in this grid so let's take the unit
+
+ align:start position:0%
+in this grid so let's take the unit
+ 
+
+ align:start position:0%
+in this grid so let's take the unit
+distance to be a distance root R where R
+
+ align:start position:0%
+distance to be a distance root R where R
+ 
+
+ align:start position:0%
+distance to be a distance root R where R
+is some integer that can be represented
+
+ align:start position:0%
+is some integer that can be represented
+ 
+
+ align:start position:0%
+is some integer that can be represented
+as a sum of two squares in many
+
+ align:start position:0%
+as a sum of two squares in many
+ 
+
+ align:start position:0%
+as a sum of two squares in many
+different ways so for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can take some are so that it has
+
+ align:start position:0%
+so we can take some are so that it has
+ 
+
+ align:start position:0%
+so we can take some are so that it has
+many appearances and if you know some
+
+ align:start position:0%
+many appearances and if you know some
+ 
+
+ align:start position:0%
+many appearances and if you know some
+elementary number theory then you might
+
+ align:start position:0%
+elementary number theory then you might
+ 
+
+ align:start position:0%
+elementary number theory then you might
+know that the best way to do this is to
+
+ align:start position:0%
+know that the best way to do this is to
+ 
+
+ align:start position:0%
+know that the best way to do this is to
+take R to be a product of primes that
+
+ align:start position:0%
+take R to be a product of primes that
+ 
+
+ align:start position:0%
+take R to be a product of primes that
+are one more form in any case you can do
+
+ align:start position:0%
+are one more form in any case you can do
+ 
+
+ align:start position:0%
+are one more form in any case you can do
+this and you can use some analytic
+
+ align:start position:0%
+this and you can use some analytic
+ 
+
+ align:start position:0%
+this and you can use some analytic
+number theory to calculate if you choose
+
+ align:start position:0%
+number theory to calculate if you choose
+ 
+
+ align:start position:0%
+number theory to calculate if you choose
+the best possible value of R how many
+
+ align:start position:0%
+the best possible value of R how many
+ 
+
+ align:start position:0%
+the best possible value of R how many
+distances do you get so that calculation
+
+ align:start position:0%
+distances do you get so that calculation
+ 
+
+ align:start position:0%
+distances do you get so that calculation
+was done and it turns out you get n
+
+ align:start position:0%
+was done and it turns out you get n
+ 
+
+ align:start position:0%
+was done and it turns out you get n
+raised to the power of 1 plus some
+
+ align:start position:0%
+raised to the power of 1 plus some
+ 
+
+ align:start position:0%
+raised to the power of 1 plus some
+constant C over log log and you know
+
+ align:start position:0%
+constant C over log log and you know
+ 
+
+ align:start position:0%
+constant C over log log and you know
+distances so this is better than the
+
+ align:start position:0%
+distances so this is better than the
+ 
+
+ align:start position:0%
+distances so this is better than the
+constructions we've seen before so what
+
+ align:start position:0%
+constructions we've seen before so what
+ 
+
+ align:start position:0%
+constructions we've seen before so what
+can we say about this problem so this is
+
+ align:start position:0%
+can we say about this problem so this is
+ 
+
+ align:start position:0%
+can we say about this problem so this is
+a construction well then you want to
+
+ align:start position:0%
+a construction well then you want to
+ 
+
+ align:start position:0%
+a construction well then you want to
+understand some upper bounds what can we
+
+ align:start position:0%
+understand some upper bounds what can we
+ 
+
+ align:start position:0%
+understand some upper bounds what can we
+say about upper bounds to this prompt
+
+ align:start position:0%
+say about upper bounds to this prompt
+ 
+
+ align:start position:0%
+say about upper bounds to this prompt
+and let me show you a fairly easy upper
+
+ align:start position:0%
+and let me show you a fairly easy upper
+ 
+
+ align:start position:0%
+and let me show you a fairly easy upper
+bound which can be deduced very quickly
+
+ align:start position:0%
+bound which can be deduced very quickly
+ 
+
+ align:start position:0%
+bound which can be deduced very quickly
+from the curve re shows Toronto that
+
+ align:start position:0%
+from the curve re shows Toronto that
+ 
+
+ align:start position:0%
+from the curve re shows Toronto that
+every set of n points in the plane has a
+
+ align:start position:0%
+every set of n points in the plane has a
+ 
+
+ align:start position:0%
+every set of n points in the plane has a
+most on the order of n to the three
+
+ align:start position:0%
+most on the order of n to the three
+ 
+
+ align:start position:0%
+most on the order of n to the three
+halves
+
+ align:start position:0%
+halves
+ 
+
+ align:start position:0%
+halves
+unit distances so not quite
+
+ align:start position:0%
+unit distances so not quite
+ 
+
+ align:start position:0%
+unit distances so not quite
+this bount but it's some time right so
+
+ align:start position:0%
+this bount but it's some time right so
+ 
+
+ align:start position:0%
+this bount but it's some time right so
+the trivia upper bound is and choose
+
+ align:start position:0%
+the trivia upper bound is and choose
+ 
+
+ align:start position:0%
+the trivia upper bound is and choose
+tube it's much better than a trivial
+
+ align:start position:0%
+tube it's much better than a trivial
+ 
+
+ align:start position:0%
+tube it's much better than a trivial
+upper back so here's the proof so let's
+
+ align:start position:0%
+upper back so here's the proof so let's
+ 
+
+ align:start position:0%
+upper back so here's the proof so let's
+consider the unit distance graph which
+
+ align:start position:0%
+consider the unit distance graph which
+ 
+
+ align:start position:0%
+consider the unit distance graph which
+is basically the graphs I've been
+
+ align:start position:0%
+is basically the graphs I've been
+ 
+
+ align:start position:0%
+is basically the graphs I've been
+drawing where you have the vertices the
+
+ align:start position:0%
+drawing where you have the vertices the
+ 
+
+ align:start position:0%
+drawing where you have the vertices the
+points and I join an edge between two
+
+ align:start position:0%
+points and I join an edge between two
+ 
+
+ align:start position:0%
+points and I join an edge between two
+vertices if and only if their distance
+
+ align:start position:0%
+vertices if and only if their distance
+ 
+
+ align:start position:0%
+vertices if and only if their distance
+is exactly one I claim this graph is k23
+
+ align:start position:0%
+is exactly one I claim this graph is k23
+ 
+
+ align:start position:0%
+is exactly one I claim this graph is k23
+free why is that because if you have two
+
+ align:start position:0%
+free why is that because if you have two
+ 
+
+ align:start position:0%
+free why is that because if you have two
+points what are their common neighbors
+
+ align:start position:0%
+points what are their common neighbors
+ 
+
+ align:start position:0%
+points what are their common neighbors
+their common neighbors must all be a
+
+ align:start position:0%
+their common neighbors must all be a
+ 
+
+ align:start position:0%
+their common neighbors must all be a
+distance one from each of the two points
+
+ align:start position:0%
+distance one from each of the two points
+ 
+
+ align:start position:0%
+distance one from each of the two points
+so they're common neighbors must lie on
+
+ align:start position:0%
+so they're common neighbors must lie on
+ 
+
+ align:start position:0%
+so they're common neighbors must lie on
+the intersections of the unit circles
+
+ align:start position:0%
+the intersections of the unit circles
+ 
+
+ align:start position:0%
+the intersections of the unit circles
+centered at these two points and they
+
+ align:start position:0%
+centered at these two points and they
+ 
+
+ align:start position:0%
+centered at these two points and they
+meet at most two points so it's k23 free
+
+ align:start position:0%
+meet at most two points so it's k23 free
+ 
+
+ align:start position:0%
+meet at most two points so it's k23 free
+therefore the caballos quran theorem
+
+ align:start position:0%
+therefore the caballos quran theorem
+ 
+
+ align:start position:0%
+therefore the caballos quran theorem
+tells us that the number of edges in
+
+ align:start position:0%
+tells us that the number of edges in
+ 
+
+ align:start position:0%
+tells us that the number of edges in
+this Jeep is upper bounded by n to the
+
+ align:start position:0%
+this Jeep is upper bounded by n to the
+ 
+
+ align:start position:0%
+this Jeep is upper bounded by n to the
+three half and that's it it gives you
+
+ align:start position:0%
+three half and that's it it gives you
+ 
+
+ align:start position:0%
+three half and that's it it gives you
+some upper bound any questions
+
+ align:start position:0%
+some upper bound any questions
+ 
+
+ align:start position:0%
+some upper bound any questions
+so it's an application to of Torah shows
+
+ align:start position:0%
+so it's an application to of Torah shows
+ 
+
+ align:start position:0%
+so it's an application to of Torah shows
+Turin where we design a graph there has
+
+ align:start position:0%
+Turin where we design a graph there has
+ 
+
+ align:start position:0%
+Turin where we design a graph there has
+to be K two three free and the extremal
+
+ align:start position:0%
+to be K two three free and the extremal
+ 
+
+ align:start position:0%
+to be K two three free and the extremal
+number tells us some information about
+
+ align:start position:0%
+number tells us some information about
+ 
+
+ align:start position:0%
+number tells us some information about
+this graph what is the best found out we
+
+ align:start position:0%
+this graph what is the best found out we
+ 
+
+ align:start position:0%
+this graph what is the best found out we
+know so it turns out we do know how to
+
+ align:start position:0%
+know so it turns out we do know how to
+ 
+
+ align:start position:0%
+know so it turns out we do know how to
+do a little bit better but not anywhere
+
+ align:start position:0%
+do a little bit better but not anywhere
+ 
+
+ align:start position:0%
+do a little bit better but not anywhere
+close to what we believe to be the truth
+
+ align:start position:0%
+close to what we believe to be the truth
+ 
+
+ align:start position:0%
+close to what we believe to be the truth
+so the current best bound is on the
+
+ align:start position:0%
+so the current best bound is on the
+ 
+
+ align:start position:0%
+so the current best bound is on the
+order of n to the 4/3 and we'll actually
+
+ align:start position:0%
+order of n to the 4/3 and we'll actually
+ 
+
+ align:start position:0%
+order of n to the 4/3 and we'll actually
+see a proof of this later in the course
+
+ align:start position:0%
+see a proof of this later in the course
+ 
+
+ align:start position:0%
+see a proof of this later in the course
+once we've developed something called
+
+ align:start position:0%
+once we've developed something called
+ 
+
+ align:start position:0%
+once we've developed something called
+the crossing numbers inequality so
+
+ align:start position:0%
+the crossing numbers inequality so
+ 
+
+ align:start position:0%
+the crossing numbers inequality so
+there's also a very short very neat
+
+ align:start position:0%
+there's also a very short very neat
+ 
+
+ align:start position:0%
+there's also a very short very neat
+proof
+
+ align:start position:0%
+proof
+ 
+
+ align:start position:0%
+proof
+I want to tell you about another problem
+
+ align:start position:0%
+I want to tell you about another problem
+ 
+
+ align:start position:0%
+I want to tell you about another problem
+which looks superficially similar and
+
+ align:start position:0%
+which looks superficially similar and
+ 
+
+ align:start position:0%
+which looks superficially similar and
+also a really interesting geometric
+
+ align:start position:0%
+also a really interesting geometric
+ 
+
+ align:start position:0%
+also a really interesting geometric
+problem and this is the address distinct
+
+ align:start position:0%
+problem and this is the address distinct
+ 
+
+ align:start position:0%
+problem and this is the address distinct
+distances problem which asks for the
+
+ align:start position:0%
+distances problem which asks for the
+ 
+
+ align:start position:0%
+distances problem which asks for the
+maximum number of distinct distances
+
+ align:start position:0%
+maximum number of distinct distances
+ 
+
+ align:start position:0%
+maximum number of distinct distances
+among end points in the plane so the
+
+ align:start position:0%
+among end points in the plane so the
+ 
+
+ align:start position:0%
+among end points in the plane so the
+minimum thank you the minimum number of
+
+ align:start position:0%
+minimum thank you the minimum number of
+ 
+
+ align:start position:0%
+minimum thank you the minimum number of
+distinct distances as a maximum will be
+
+ align:start position:0%
+distinct distances as a maximum will be
+ 
+
+ align:start position:0%
+distinct distances as a maximum will be
+very easy again you have lots of
+
+ align:start position:0%
+very easy again you have lots of
+ 
+
+ align:start position:0%
+very easy again you have lots of
+examples in fact you can look at
+
+ align:start position:0%
+examples in fact you can look at
+ 
+
+ align:start position:0%
+examples in fact you can look at
+basically all the examples so we've
+
+ align:start position:0%
+basically all the examples so we've
+ 
+
+ align:start position:0%
+basically all the examples so we've
+given earlier I mean these two problems
+
+ align:start position:0%
+given earlier I mean these two problems
+ 
+
+ align:start position:0%
+given earlier I mean these two problems
+are very much related to each other you
+
+ align:start position:0%
+are very much related to each other you
+ 
+
+ align:start position:0%
+are very much related to each other you
+see if you want lots of repeat distances
+
+ align:start position:0%
+see if you want lots of repeat distances
+ 
+
+ align:start position:0%
+see if you want lots of repeat distances
+or if you want
+
+ align:start position:0%
+or if you want
+ 
+
+ align:start position:0%
+or if you want
+very few distinct distances right they
+
+ align:start position:0%
+very few distinct distances right they
+ 
+
+ align:start position:0%
+very few distinct distances right they
+they seem like they're very much related
+
+ align:start position:0%
+they seem like they're very much related
+ 
+
+ align:start position:0%
+they seem like they're very much related
+and of course you can also write down an
+
+ align:start position:0%
+and of course you can also write down an
+ 
+
+ align:start position:0%
+and of course you can also write down an
+inequality that relates the two of them
+
+ align:start position:0%
+inequality that relates the two of them
+ 
+
+ align:start position:0%
+inequality that relates the two of them
+because the number of distinct distances
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is at least and choose two divided by
+
+ align:start position:0%
+is at least and choose two divided by
+ 
+
+ align:start position:0%
+is at least and choose two divided by
+the number of the maximum number of unit
+
+ align:start position:0%
+the number of the maximum number of unit
+ 
+
+ align:start position:0%
+the number of the maximum number of unit
+distances
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in other words the number of distances
+
+ align:start position:0%
+in other words the number of distances
+ 
+
+ align:start position:0%
+in other words the number of distances
+that can be repeated in any single
+
+ align:start position:0%
+that can be repeated in any single
+ 
+
+ align:start position:0%
+that can be repeated in any single
+configuration okay right so each of the
+
+ align:start position:0%
+configuration okay right so each of the
+ 
+
+ align:start position:0%
+configuration okay right so each of the
+examples I just erased so for example if
+
+ align:start position:0%
+examples I just erased so for example if
+ 
+
+ align:start position:0%
+examples I just erased so for example if
+you put points on the line you have n
+
+ align:start position:0%
+you put points on the line you have n
+ 
+
+ align:start position:0%
+you put points on the line you have n
+minus 1 to sting distances and we
+
+ align:start position:0%
+minus 1 to sting distances and we
+ 
+
+ align:start position:0%
+minus 1 to sting distances and we
+already saw the square grid so that
+
+ align:start position:0%
+already saw the square grid so that
+ 
+
+ align:start position:0%
+already saw the square grid so that
+might be a good candidate to look at as
+
+ align:start position:0%
+might be a good candidate to look at as
+ 
+
+ align:start position:0%
+might be a good candidate to look at as
+well and there it takes some more number
+
+ align:start position:0%
+well and there it takes some more number
+ 
+
+ align:start position:0%
+well and there it takes some more number
+theory to figure out how many distinct
+
+ align:start position:0%
+theory to figure out how many distinct
+ 
+
+ align:start position:0%
+theory to figure out how many distinct
+distances are they are and this roughly
+
+ align:start position:0%
+distances are they are and this roughly
+ 
+
+ align:start position:0%
+distances are they are and this roughly
+corresponds to the number of yeah so the
+
+ align:start position:0%
+corresponds to the number of yeah so the
+ 
+
+ align:start position:0%
+corresponds to the number of yeah so the
+the number of integers that can be
+
+ align:start position:0%
+the number of integers that can be
+ 
+
+ align:start position:0%
+the number of integers that can be
+written as a sum of two squares and so
+
+ align:start position:0%
+written as a sum of two squares and so
+ 
+
+ align:start position:0%
+written as a sum of two squares and so
+this has been calculated and the result
+
+ align:start position:0%
+this has been calculated and the result
+ 
+
+ align:start position:0%
+this has been calculated and the result
+is n divided by square root of log n so
+
+ align:start position:0%
+is n divided by square root of log n so
+ 
+
+ align:start position:0%
+is n divided by square root of log n so
+that's the order okay and air -
+
+ align:start position:0%
+that's the order okay and air -
+ 
+
+ align:start position:0%
+that's the order okay and air -
+conjecture that this example should be
+
+ align:start position:0%
+conjecture that this example should be
+ 
+
+ align:start position:0%
+conjecture that this example should be
+more or less the best you can do so
+
+ align:start position:0%
+more or less the best you can do so
+ 
+
+ align:start position:0%
+more or less the best you can do so
+these palms look very similar but
+
+ align:start position:0%
+these palms look very similar but
+ 
+
+ align:start position:0%
+these palms look very similar but
+actually this problem here was solved in
+
+ align:start position:0%
+actually this problem here was solved in
+ 
+
+ align:start position:0%
+actually this problem here was solved in
+a spectacular fashion about a decade ago
+
+ align:start position:0%
+a spectacular fashion about a decade ago
+ 
+
+ align:start position:0%
+a spectacular fashion about a decade ago
+by an important paper of Guth and cats
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Larry goose is in our department and
+
+ align:start position:0%
+so Larry goose is in our department and
+ 
+
+ align:start position:0%
+so Larry goose is in our department and
+they showed that every set of n points
+
+ align:start position:0%
+they showed that every set of n points
+ 
+
+ align:start position:0%
+they showed that every set of n points
+in the plane generates at least on the
+
+ align:start position:0%
+in the plane generates at least on the
+ 
+
+ align:start position:0%
+in the plane generates at least on the
+order of n over log n distinct distances
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so not quite what aired is conjectured
+
+ align:start position:0%
+so not quite what aired is conjectured
+ 
+
+ align:start position:0%
+so not quite what aired is conjectured
+but nearly there and in fact all the
+
+ align:start position:0%
+but nearly there and in fact all the
+ 
+
+ align:start position:0%
+but nearly there and in fact all the
+previous results were much worse so they
+
+ align:start position:0%
+previous results were much worse so they
+ 
+
+ align:start position:0%
+previous results were much worse so they
+were off in the exponent but this one
+
+ align:start position:0%
+were off in the exponent but this one
+ 
+
+ align:start position:0%
+were off in the exponent but this one
+more or less got to the truth so this is
+
+ align:start position:0%
+more or less got to the truth so this is
+ 
+
+ align:start position:0%
+more or less got to the truth so this is
+a very sophisticated result that used
+
+ align:start position:0%
+a very sophisticated result that used
+ 
+
+ align:start position:0%
+a very sophisticated result that used
+lots of amazing techniques ranging from
+
+ align:start position:0%
+lots of amazing techniques ranging from
+ 
+
+ align:start position:0%
+lots of amazing techniques ranging from
+the polynomial method in combinatorics
+
+ align:start position:0%
+the polynomial method in combinatorics
+ 
+
+ align:start position:0%
+the polynomial method in combinatorics
+to some algebraic geometry and that's I
+
+ align:start position:0%
+to some algebraic geometry and that's I
+ 
+
+ align:start position:0%
+to some algebraic geometry and that's I
+just want to mention it for cultural
+
+ align:start position:0%
+just want to mention it for cultural
+ 
+
+ align:start position:0%
+just want to mention it for cultural
+value ok any questions yes yeah so for
+
+ align:start position:0%
+value ok any questions yes yeah so for
+ 
+
+ align:start position:0%
+value ok any questions yes yeah so for
+the unit distance problem and actually
+
+ align:start position:0%
+the unit distance problem and actually
+ 
+
+ align:start position:0%
+the unit distance problem and actually
+for the distinct distances problem the
+
+ align:start position:0%
+for the distinct distances problem the
+ 
+
+ align:start position:0%
+for the distinct distances problem the
+question is what was believed to be the
+
+ align:start position:0%
+question is what was believed to be the
+ 
+
+ align:start position:0%
+question is what was believed to be the
+what is believed to be the bound and
+
+ align:start position:0%
+what is believed to be the bound and
+ 
+
+ align:start position:0%
+what is believed to be the bound and
+that it's the square grid all right so
+
+ align:start position:0%
+that it's the square grid all right so
+ 
+
+ align:start position:0%
+that it's the square grid all right so
+maybe you can do slightly better but it
+
+ align:start position:0%
+maybe you can do slightly better but it
+ 
+
+ align:start position:0%
+maybe you can do slightly better but it
+is conjecture that you cannot do much
+
+ align:start position:0%
+is conjecture that you cannot do much
+ 
+
+ align:start position:0%
+is conjecture that you cannot do much
+better let's say by more than a constant
+
+ align:start position:0%
+better let's say by more than a constant
+ 
+
+ align:start position:0%
+better let's say by more than a constant
+factor compared to the square grid yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry so this is Nets cats he's at
+
+ align:start position:0%
+sorry so this is Nets cats he's at
+ 
+
+ align:start position:0%
+sorry so this is Nets cats he's at
+Caltech okay I want to take a short
+
+ align:start position:0%
+Caltech okay I want to take a short
+ 
+
+ align:start position:0%
+Caltech okay I want to take a short
+break now and when we come back I want
+
+ align:start position:0%
+break now and when we come back I want
+ 
+
+ align:start position:0%
+break now and when we come back I want
+to show you some ways to generate lower
+
+ align:start position:0%
+to show you some ways to generate lower
+ 
+
+ align:start position:0%
+to show you some ways to generate lower
+bounds to the extremal number in the
+
+ align:start position:0%
+bounds to the extremal number in the
+ 
+
+ align:start position:0%
+bounds to the extremal number in the
+kaveri shows tauren theorem we
+
+ align:start position:0%
+kaveri shows tauren theorem we
+ 
+
+ align:start position:0%
+kaveri shows tauren theorem we
+understood some upper bounds for the
+
+ align:start position:0%
+understood some upper bounds for the
+ 
+
+ align:start position:0%
+understood some upper bounds for the
+extremal number so I want to turn our
+
+ align:start position:0%
+extremal number so I want to turn our
+ 
+
+ align:start position:0%
+extremal number so I want to turn our
+attention now to lower bounds which
+
+ align:start position:0%
+attention now to lower bounds which
+ 
+
+ align:start position:0%
+attention now to lower bounds which
+means constructing in some sense graphs
+
+ align:start position:0%
+means constructing in some sense graphs
+ 
+
+ align:start position:0%
+means constructing in some sense graphs
+that have lots of edges at the same time
+
+ align:start position:0%
+that have lots of edges at the same time
+ 
+
+ align:start position:0%
+that have lots of edges at the same time
+being KSP 3 there are many classes of
+
+ align:start position:0%
+being KSP 3 there are many classes of
+ 
+
+ align:start position:0%
+being KSP 3 there are many classes of
+construction so there are several
+
+ align:start position:0%
+construction so there are several
+ 
+
+ align:start position:0%
+construction so there are several
+techniques for doing this and I want to
+
+ align:start position:0%
+techniques for doing this and I want to
+ 
+
+ align:start position:0%
+techniques for doing this and I want to
+introduce you to some of these
+
+ align:start position:0%
+introduce you to some of these
+ 
+
+ align:start position:0%
+introduce you to some of these
+techniques and the first one comes from
+
+ align:start position:0%
+techniques and the first one comes from
+ 
+
+ align:start position:0%
+techniques and the first one comes from
+the probabilistic method where we use a
+
+ align:start position:0%
+the probabilistic method where we use a
+ 
+
+ align:start position:0%
+the probabilistic method where we use a
+randomized construction by taking the
+
+ align:start position:0%
+randomized construction by taking the
+ 
+
+ align:start position:0%
+randomized construction by taking the
+graph at random modifying it a little
+
+ align:start position:0%
+graph at random modifying it a little
+ 
+
+ align:start position:0%
+graph at random modifying it a little
+bit in a way that's to our desire this
+
+ align:start position:0%
+bit in a way that's to our desire this
+ 
+
+ align:start position:0%
+bit in a way that's to our desire this
+method is very powerful it is very
+
+ align:start position:0%
+method is very powerful it is very
+ 
+
+ align:start position:0%
+method is very powerful it is very
+general it is applicable in a lot of
+
+ align:start position:0%
+general it is applicable in a lot of
+ 
+
+ align:start position:0%
+general it is applicable in a lot of
+situations but unfortunately for the
+
+ align:start position:0%
+situations but unfortunately for the
+ 
+
+ align:start position:0%
+situations but unfortunately for the
+problem of getting tight bounds it is
+
+ align:start position:0%
+problem of getting tight bounds it is
+ 
+
+ align:start position:0%
+problem of getting tight bounds it is
+really it really allows you to get tight
+
+ align:start position:0%
+really it really allows you to get tight
+ 
+
+ align:start position:0%
+really it really allows you to get tight
+bounds so it is very robust
+
+ align:start position:0%
+bounds so it is very robust
+ 
+
+ align:start position:0%
+bounds so it is very robust
+but somehow it's often not sharp and
+
+ align:start position:0%
+but somehow it's often not sharp and
+ 
+
+ align:start position:0%
+but somehow it's often not sharp and
+another class of constructions that are
+
+ align:start position:0%
+another class of constructions that are
+ 
+
+ align:start position:0%
+another class of constructions that are
+algebraic all the sharp examples come
+
+ align:start position:0%
+algebraic all the sharp examples come
+ 
+
+ align:start position:0%
+algebraic all the sharp examples come
+from algebraic constructions and there
+
+ align:start position:0%
+from algebraic constructions and there
+ 
+
+ align:start position:0%
+from algebraic constructions and there
+were able to use some nice ideas from
+
+ align:start position:0%
+were able to use some nice ideas from
+ 
+
+ align:start position:0%
+were able to use some nice ideas from
+from algebra from algebraic geometry to
+
+ align:start position:0%
+from algebra from algebraic geometry to
+ 
+
+ align:start position:0%
+from algebra from algebraic geometry to
+get tight constructions and you can
+
+ align:start position:0%
+get tight constructions and you can
+ 
+
+ align:start position:0%
+get tight constructions and you can
+wonder is there some way to combine the
+
+ align:start position:0%
+wonder is there some way to combine the
+ 
+
+ align:start position:0%
+wonder is there some way to combine the
+best of both worlds and it turns out
+
+ align:start position:0%
+best of both worlds and it turns out
+ 
+
+ align:start position:0%
+best of both worlds and it turns out
+this was a important recent development
+
+ align:start position:0%
+this was a important recent development
+ 
+
+ align:start position:0%
+this was a important recent development
+that was found just several years ago
+
+ align:start position:0%
+that was found just several years ago
+ 
+
+ align:start position:0%
+that was found just several years ago
+where one can combine ideas from the two
+
+ align:start position:0%
+where one can combine ideas from the two
+ 
+
+ align:start position:0%
+where one can combine ideas from the two
+and obtain a randomized algebraic
+
+ align:start position:0%
+and obtain a randomized algebraic
+ 
+
+ align:start position:0%
+and obtain a randomized algebraic
+construction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that leads to a new source of
+
+ align:start position:0%
+and that leads to a new source of
+ 
+
+ align:start position:0%
+and that leads to a new source of
+constructions for large H free graphs
+
+ align:start position:0%
+constructions for large H free graphs
+ 
+
+ align:start position:0%
+constructions for large H free graphs
+with many edges okay so the plan is to
+
+ align:start position:0%
+with many edges okay so the plan is to
+ 
+
+ align:start position:0%
+with many edges okay so the plan is to
+show you how these constructions work
+
+ align:start position:0%
+show you how these constructions work
+ 
+
+ align:start position:0%
+show you how these constructions work
+okay first let's begin with random nice
+
+ align:start position:0%
+okay first let's begin with random nice
+ 
+
+ align:start position:0%
+okay first let's begin with random nice
+constructions as I mentioned this
+
+ align:start position:0%
+constructions as I mentioned this
+ 
+
+ align:start position:0%
+constructions as I mentioned this
+construction is very general it's very
+
+ align:start position:0%
+construction is very general it's very
+ 
+
+ align:start position:0%
+construction is very general it's very
+robust and we can use it to obtain H
+
+ align:start position:0%
+robust and we can use it to obtain H
+ 
+
+ align:start position:0%
+robust and we can use it to obtain H
+free graphs for every graph H of course
+
+ align:start position:0%
+free graphs for every graph H of course
+ 
+
+ align:start position:0%
+free graphs for every graph H of course
+when H is not bipartite then we saw from
+
+ align:start position:0%
+when H is not bipartite then we saw from
+ 
+
+ align:start position:0%
+when H is not bipartite then we saw from
+the current graph that that's pretty
+
+ align:start position:0%
+the current graph that that's pretty
+ 
+
+ align:start position:0%
+the current graph that that's pretty
+much the right thing to do so you should
+
+ align:start position:0%
+much the right thing to do so you should
+ 
+
+ align:start position:0%
+much the right thing to do so you should
+think about bipartite graphs H so fix
+
+ align:start position:0%
+think about bipartite graphs H so fix
+ 
+
+ align:start position:0%
+think about bipartite graphs H so fix
+the graph H with at least two edges
+
+ align:start position:0%
+the graph H with at least two edges
+ 
+
+ align:start position:0%
+the graph H with at least two edges
+otherwise prom is trivial the claim is
+
+ align:start position:0%
+otherwise prom is trivial the claim is
+ 
+
+ align:start position:0%
+otherwise prom is trivial the claim is
+that there is some constant C such that
+
+ align:start position:0%
+that there is some constant C such that
+ 
+
+ align:start position:0%
+that there is some constant C such that
+for every n you think of n is being
+
+ align:start position:0%
+for every n you think of n is being
+ 
+
+ align:start position:0%
+for every n you think of n is being
+large there exists an H free graph and
+
+ align:start position:0%
+large there exists an H free graph and
+ 
+
+ align:start position:0%
+large there exists an H free graph and
+vertices and having lots of edges and we
+
+ align:start position:0%
+vertices and having lots of edges and we
+ 
+
+ align:start position:0%
+vertices and having lots of edges and we
+will show that you can obtain the
+
+ align:start position:0%
+will show that you can obtain the
+ 
+
+ align:start position:0%
+will show that you can obtain the
+following number of edges so two -
+
+ align:start position:0%
+following number of edges so two -
+ 
+
+ align:start position:0%
+following number of edges so two -
+number of vertices of H - 2 divided by
+
+ align:start position:0%
+number of vertices of H - 2 divided by
+ 
+
+ align:start position:0%
+number of vertices of H - 2 divided by
+the number of edges of H minus 1 okay
+
+ align:start position:0%
+the number of edges of H minus 1 okay
+ 
+
+ align:start position:0%
+the number of edges of H minus 1 okay
+don't worry about this expression in the
+
+ align:start position:0%
+don't worry about this expression in the
+ 
+
+ align:start position:0%
+don't worry about this expression in the
+exponent it will come out of the proof
+
+ align:start position:0%
+exponent it will come out of the proof
+ 
+
+ align:start position:0%
+exponent it will come out of the proof
+in other words the extremal number is at
+
+ align:start position:0%
+in other words the extremal number is at
+ 
+
+ align:start position:0%
+in other words the extremal number is at
+least this quantity here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right how good this is found some
+
+ align:start position:0%
+all right how good this is found some
+ 
+
+ align:start position:0%
+all right how good this is found some
+scary-looking expression in the exponent
+
+ align:start position:0%
+scary-looking expression in the exponent
+ 
+
+ align:start position:0%
+scary-looking expression in the exponent
+so let me just give you some special
+
+ align:start position:0%
+so let me just give you some special
+ 
+
+ align:start position:0%
+so let me just give you some special
+cases for comparison to the calvario
+
+ align:start position:0%
+cases for comparison to the calvario
+ 
+
+ align:start position:0%
+cases for comparison to the calvario
+Sturm theorem for KS TS the bound this
+
+ align:start position:0%
+Sturm theorem for KS TS the bound this
+ 
+
+ align:start position:0%
+Sturm theorem for KS TS the bound this
+construction gives you a lower bound
+
+ align:start position:0%
+construction gives you a lower bound
+ 
+
+ align:start position:0%
+construction gives you a lower bound
+which is of the form n to the 2 minus s
+
+ align:start position:0%
+which is of the form n to the 2 minus s
+ 
+
+ align:start position:0%
+which is of the form n to the 2 minus s
+plus t minus 2 divided by s t minus 1 so
+
+ align:start position:0%
+plus t minus 2 divided by s t minus 1 so
+ 
+
+ align:start position:0%
+plus t minus 2 divided by s t minus 1 so
+i use this symbol this bigger turtle to
+
+ align:start position:0%
+i use this symbol this bigger turtle to
+ 
+
+ align:start position:0%
+i use this symbol this bigger turtle to
+denote dropping constant factors in
+
+ align:start position:0%
+denote dropping constant factors in
+ 
+
+ align:start position:0%
+denote dropping constant factors in
+particular setting s and P to be the
+
+ align:start position:0%
+particular setting s and P to be the
+ 
+
+ align:start position:0%
+particular setting s and P to be the
+same we find that the KS s extremal
+
+ align:start position:0%
+same we find that the KS s extremal
+ 
+
+ align:start position:0%
+same we find that the KS s extremal
+number is lower bounded by this quantity
+
+ align:start position:0%
+number is lower bounded by this quantity
+ 
+
+ align:start position:0%
+number is lower bounded by this quantity
+here okay so how does that compared to
+
+ align:start position:0%
+here okay so how does that compared to
+ 
+
+ align:start position:0%
+here okay so how does that compared to
+Guevara shows toro in Kavala shows
+
+ align:start position:0%
+Guevara shows toro in Kavala shows
+ 
+
+ align:start position:0%
+Guevara shows toro in Kavala shows
+tauren we saw that KS s is at most 2 to
+
+ align:start position:0%
+tauren we saw that KS s is at most 2 to
+ 
+
+ align:start position:0%
+tauren we saw that KS s is at most 2 to
+the n to the 2 minus 1 over s so there's
+
+ align:start position:0%
+the n to the 2 minus 1 over s so there's
+ 
+
+ align:start position:0%
+the n to the 2 minus 1 over s so there's
+a bit of a gap and in particular even
+
+ align:start position:0%
+a bit of a gap and in particular even
+ 
+
+ align:start position:0%
+a bit of a gap and in particular even
+for 2 & 2 these results tell you a lower
+
+ align:start position:0%
+for 2 & 2 these results tell you a lower
+ 
+
+ align:start position:0%
+for 2 & 2 these results tell you a lower
+bound on the order of n to the 4/3 an
+
+ align:start position:0%
+bound on the order of n to the 4/3 an
+ 
+
+ align:start position:0%
+bound on the order of n to the 4/3 an
+upper bound on the order of 3 hi I'm
+
+ align:start position:0%
+upper bound on the order of 3 hi I'm
+ 
+
+ align:start position:0%
+upper bound on the order of 3 hi I'm
+just doing this explicitly to show you
+
+ align:start position:0%
+just doing this explicitly to show you
+ 
+
+ align:start position:0%
+just doing this explicitly to show you
+that even in sometimes the simplest case
+
+ align:start position:0%
+that even in sometimes the simplest case
+ 
+
+ align:start position:0%
+that even in sometimes the simplest case
+there is a gap between these two bounds
+
+ align:start position:0%
+there is a gap between these two bounds
+ 
+
+ align:start position:0%
+there is a gap between these two bounds
+later on we'll see a construction that
+
+ align:start position:0%
+later on we'll see a construction that
+ 
+
+ align:start position:0%
+later on we'll see a construction that
+shows that the right-hand side is tight
+
+ align:start position:0%
+shows that the right-hand side is tight
+ 
+
+ align:start position:0%
+shows that the right-hand side is tight
+right so this is the truth the
+
+ align:start position:0%
+right so this is the truth the
+ 
+
+ align:start position:0%
+right so this is the truth the
+randomized construction gives you
+
+ align:start position:0%
+randomized construction gives you
+ 
+
+ align:start position:0%
+randomized construction gives you
+something but it doesn't give you the
+
+ align:start position:0%
+something but it doesn't give you the
+ 
+
+ align:start position:0%
+something but it doesn't give you the
+truth on the other hand I want you to
+
+ align:start position:0%
+truth on the other hand I want you to
+ 
+
+ align:start position:0%
+truth on the other hand I want you to
+notice that if he gets very long
+
+ align:start position:0%
+notice that if he gets very long
+ 
+
+ align:start position:0%
+notice that if he gets very long
+as a function of s this exponent here
+
+ align:start position:0%
+as a function of s this exponent here
+ 
+
+ align:start position:0%
+as a function of s this exponent here
+approaches one over s as T goes to
+
+ align:start position:0%
+approaches one over s as T goes to
+ 
+
+ align:start position:0%
+approaches one over s as T goes to
+infinity so for very large values of T
+
+ align:start position:0%
+infinity so for very large values of T
+ 
+
+ align:start position:0%
+infinity so for very large values of T
+at least in the exponent it's not that
+
+ align:start position:0%
+at least in the exponent it's not that
+ 
+
+ align:start position:0%
+at least in the exponent it's not that
+far off although you never get the right
+
+ align:start position:0%
+far off although you never get the right
+ 
+
+ align:start position:0%
+far off although you never get the right
+exponent for any specific SNP okay so
+
+ align:start position:0%
+exponent for any specific SNP okay so
+ 
+
+ align:start position:0%
+exponent for any specific SNP okay so
+this is some limitation of the
+
+ align:start position:0%
+this is some limitation of the
+ 
+
+ align:start position:0%
+this is some limitation of the
+randomized method but I know it's very
+
+ align:start position:0%
+randomized method but I know it's very
+ 
+
+ align:start position:0%
+randomized method but I know it's very
+robust and in fact you can use this
+
+ align:start position:0%
+robust and in fact you can use this
+ 
+
+ align:start position:0%
+robust and in fact you can use this
+result to do to bootstrap it to a
+
+ align:start position:0%
+result to do to bootstrap it to a
+ 
+
+ align:start position:0%
+result to do to bootstrap it to a
+slightly better one for some grass h so
+
+ align:start position:0%
+slightly better one for some grass h so
+ 
+
+ align:start position:0%
+slightly better one for some grass h so
+for example one might do better by
+
+ align:start position:0%
+for example one might do better by
+ 
+
+ align:start position:0%
+for example one might do better by
+replacing this H by a subgraph but
+
+ align:start position:0%
+replacing this H by a subgraph but
+ 
+
+ align:start position:0%
+replacing this H by a subgraph but
+because if you have a subgraph H Prime
+
+ align:start position:0%
+because if you have a subgraph H Prime
+ 
+
+ align:start position:0%
+because if you have a subgraph H Prime
+and you construct your G to be H Prime
+
+ align:start position:0%
+and you construct your G to be H Prime
+ 
+
+ align:start position:0%
+and you construct your G to be H Prime
+free then it is automatically H free but
+
+ align:start position:0%
+free then it is automatically H free but
+ 
+
+ align:start position:0%
+free then it is automatically H free but
+maybe this theorem actually gives you a
+
+ align:start position:0%
+maybe this theorem actually gives you a
+ 
+
+ align:start position:0%
+maybe this theorem actually gives you a
+better construction when restricted to H
+
+ align:start position:0%
+better construction when restricted to H
+ 
+
+ align:start position:0%
+better construction when restricted to H
+Prime and what can you do better well
+
+ align:start position:0%
+Prime and what can you do better well
+ 
+
+ align:start position:0%
+Prime and what can you do better well
+you can do better if H prime is such
+
+ align:start position:0%
+you can do better if H prime is such
+ 
+
+ align:start position:0%
+you can do better if H prime is such
+that whatever the quantity that comes up
+
+ align:start position:0%
+that whatever the quantity that comes up
+ 
+
+ align:start position:0%
+that whatever the quantity that comes up
+in the exponent so let me write it like
+
+ align:start position:0%
+in the exponent so let me write it like
+ 
+
+ align:start position:0%
+in the exponent so let me write it like
+this is superior to the exponent you
+
+ align:start position:0%
+this is superior to the exponent you
+ 
+
+ align:start position:0%
+this is superior to the exponent you
+would obtain by just looking at H so let
+
+ align:start position:0%
+would obtain by just looking at H so let
+ 
+
+ align:start position:0%
+would obtain by just looking at H so let
+me get the name to this notion here so
+
+ align:start position:0%
+me get the name to this notion here so
+ 
+
+ align:start position:0%
+me get the name to this notion here so
+let me call the two density of the graph
+
+ align:start position:0%
+let me call the two density of the graph
+ 
+
+ align:start position:0%
+let me call the two density of the graph
+to be whatever quantity here that would
+
+ align:start position:0%
+to be whatever quantity here that would
+ 
+
+ align:start position:0%
+to be whatever quantity here that would
+be the maximum if you allow to pass down
+
+ align:start position:0%
+be the maximum if you allow to pass down
+ 
+
+ align:start position:0%
+be the maximum if you allow to pass down
+two sub graphs the two density of a
+
+ align:start position:0%
+two sub graphs the two density of a
+ 
+
+ align:start position:0%
+two sub graphs the two density of a
+graph H so to know that in literature
+
+ align:start position:0%
+graph H so to know that in literature
+ 
+
+ align:start position:0%
+graph H so to know that in literature
+often s M sub two to be the maximum
+
+ align:start position:0%
+often s M sub two to be the maximum
+ 
+
+ align:start position:0%
+often s M sub two to be the maximum
+where you allowed
+
+ align:start position:0%
+where you allowed
+ 
+
+ align:start position:0%
+where you allowed
+to look at subgraphs let's say on least
+
+ align:start position:0%
+to look at subgraphs let's say on least
+ 
+
+ align:start position:0%
+to look at subgraphs let's say on least
+three vertices to avoid degeneracies
+
+ align:start position:0%
+three vertices to avoid degeneracies
+ 
+
+ align:start position:0%
+three vertices to avoid degeneracies
+this ratio that comes up in the
+
+ align:start position:0%
+this ratio that comes up in the
+ 
+
+ align:start position:0%
+this ratio that comes up in the
+expressions so then the theorem that
+
+ align:start position:0%
+expressions so then the theorem that
+ 
+
+ align:start position:0%
+expressions so then the theorem that
+construction there implies that the
+
+ align:start position:0%
+construction there implies that the
+ 
+
+ align:start position:0%
+construction there implies that the
+extremal number is at least not just the
+
+ align:start position:0%
+extremal number is at least not just the
+ 
+
+ align:start position:0%
+extremal number is at least not just the
+expression I've written but maybe
+
+ align:start position:0%
+expression I've written but maybe
+ 
+
+ align:start position:0%
+expression I've written but maybe
+sometimes you can do slightly better by
+
+ align:start position:0%
+sometimes you can do slightly better by
+ 
+
+ align:start position:0%
+sometimes you can do slightly better by
+passing to a sub graph so let me give
+
+ align:start position:0%
+passing to a sub graph so let me give
+ 
+
+ align:start position:0%
+passing to a sub graph so let me give
+you a concrete example suppose my H yes
+
+ align:start position:0%
+you a concrete example suppose my H yes
+ 
+
+ align:start position:0%
+you a concrete example suppose my H yes
+this graph here so you can run the
+
+ align:start position:0%
+this graph here so you can run the
+ 
+
+ align:start position:0%
+this graph here so you can run the
+calculation and find what these numbers
+
+ align:start position:0%
+calculation and find what these numbers
+ 
+
+ align:start position:0%
+calculation and find what these numbers
+are so the number of vertices edges and
+
+ align:start position:0%
+are so the number of vertices edges and
+ 
+
+ align:start position:0%
+are so the number of vertices edges and
+this ratio here to be five vertices
+
+ align:start position:0%
+this ratio here to be five vertices
+ 
+
+ align:start position:0%
+this ratio here to be five vertices
+eight edges and 7/3 and the idea here is
+
+ align:start position:0%
+eight edges and 7/3 and the idea here is
+ 
+
+ align:start position:0%
+eight edges and 7/3 and the idea here is
+that it's more helpful or so I want to
+
+ align:start position:0%
+that it's more helpful or so I want to
+ 
+
+ align:start position:0%
+that it's more helpful or so I want to
+create something which is a ch3 but
+
+ align:start position:0%
+create something which is a ch3 but
+ 
+
+ align:start position:0%
+create something which is a ch3 but
+dense things are easier to avoid all
+
+ align:start position:0%
+dense things are easier to avoid all
+ 
+
+ align:start position:0%
+dense things are easier to avoid all
+right so if I have something which is
+
+ align:start position:0%
+right so if I have something which is
+ 
+
+ align:start position:0%
+right so if I have something which is
+some fairly dense core that's easier to
+
+ align:start position:0%
+some fairly dense core that's easier to
+ 
+
+ align:start position:0%
+some fairly dense core that's easier to
+avoid so maybe it's better to instead of
+
+ align:start position:0%
+avoid so maybe it's better to instead of
+ 
+
+ align:start position:0%
+avoid so maybe it's better to instead of
+looking at a whole H look at this k4 so
+
+ align:start position:0%
+looking at a whole H look at this k4 so
+ 
+
+ align:start position:0%
+looking at a whole H look at this k4 so
+if you can avoid k4 of course you avoid
+
+ align:start position:0%
+if you can avoid k4 of course you avoid
+ 
+
+ align:start position:0%
+if you can avoid k4 of course you avoid
+H and maybe it's easier to just avoid k4
+
+ align:start position:0%
+H and maybe it's easier to just avoid k4
+ 
+
+ align:start position:0%
+H and maybe it's easier to just avoid k4
+and not worry about some of the extra
+
+ align:start position:0%
+and not worry about some of the extra
+ 
+
+ align:start position:0%
+and not worry about some of the extra
+decorations so if you look at this H
+
+ align:start position:0%
+decorations so if you look at this H
+ 
+
+ align:start position:0%
+decorations so if you look at this H
+Prime and go through the parameters you
+
+ align:start position:0%
+Prime and go through the parameters you
+ 
+
+ align:start position:0%
+Prime and go through the parameters you
+find that it is like that
+
+ align:start position:0%
+find that it is like that
+ 
+
+ align:start position:0%
+find that it is like that
+and it is somewhat denser in this sense
+
+ align:start position:0%
+and it is somewhat denser in this sense
+ 
+
+ align:start position:0%
+and it is somewhat denser in this sense
+compared to looking at whole graphic so
+
+ align:start position:0%
+compared to looking at whole graphic so
+ 
+
+ align:start position:0%
+compared to looking at whole graphic so
+you can improve on this theorem for some
+
+ align:start position:0%
+you can improve on this theorem for some
+ 
+
+ align:start position:0%
+you can improve on this theorem for some
+graphs H where you can pass to a denser
+
+ align:start position:0%
+graphs H where you can pass to a denser
+ 
+
+ align:start position:0%
+graphs H where you can pass to a denser
+core okay any questions so far
+
+ align:start position:0%
+core okay any questions so far
+ 
+
+ align:start position:0%
+core okay any questions so far
+yes questions why is this measure called
+
+ align:start position:0%
+yes questions why is this measure called
+ 
+
+ align:start position:0%
+yes questions why is this measure called
+the two density so that's a named
+
+ align:start position:0%
+the two density so that's a named
+ 
+
+ align:start position:0%
+the two density so that's a named
+covering literature party has to do with
+
+ align:start position:0%
+covering literature party has to do with
+ 
+
+ align:start position:0%
+covering literature party has to do with
+these extra ratios so there are other
+
+ align:start position:0%
+these extra ratios so there are other
+ 
+
+ align:start position:0%
+these extra ratios so there are other
+notions of densities that actually we'll
+
+ align:start position:0%
+notions of densities that actually we'll
+ 
+
+ align:start position:0%
+notions of densities that actually we'll
+see later on
+
+ align:start position:0%
+see later on
+ 
+
+ align:start position:0%
+see later on
+so this term will only see today so it's
+
+ align:start position:0%
+so this term will only see today so it's
+ 
+
+ align:start position:0%
+so this term will only see today so it's
+more of an ad-hoc term for the purpose
+
+ align:start position:0%
+more of an ad-hoc term for the purpose
+ 
+
+ align:start position:0%
+more of an ad-hoc term for the purpose
+of this course later on we'll see
+
+ align:start position:0%
+of this course later on we'll see
+ 
+
+ align:start position:0%
+of this course later on we'll see
+notions of density that are more
+
+ align:start position:0%
+notions of density that are more
+ 
+
+ align:start position:0%
+notions of density that are more
+relevant for our discussions any more
+
+ align:start position:0%
+relevant for our discussions any more
+ 
+
+ align:start position:0%
+relevant for our discussions any more
+questions okay so let me show you how to
+
+ align:start position:0%
+questions okay so let me show you how to
+ 
+
+ align:start position:0%
+questions okay so let me show you how to
+prove this theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the proof is very intuitive the idea is
+
+ align:start position:0%
+the proof is very intuitive the idea is
+ 
+
+ align:start position:0%
+the proof is very intuitive the idea is
+you take something ID random and then
+
+ align:start position:0%
+you take something ID random and then
+ 
+
+ align:start position:0%
+you take something ID random and then
+you fix it that's it let's consider a
+
+ align:start position:0%
+you fix it that's it let's consider a
+ 
+
+ align:start position:0%
+you fix it that's it let's consider a
+random graph the address when a random
+
+ align:start position:0%
+random graph the address when a random
+ 
+
+ align:start position:0%
+random graph the address when a random
+graph so whenever say random graph I
+
+ align:start position:0%
+graph so whenever say random graph I
+ 
+
+ align:start position:0%
+graph so whenever say random graph I
+almost always refer to this one here and
+
+ align:start position:0%
+almost always refer to this one here and
+ 
+
+ align:start position:0%
+almost always refer to this one here and
+the address when a random graph is
+
+ align:start position:0%
+the address when a random graph is
+ 
+
+ align:start position:0%
+the address when a random graph is
+obtained by considering n vertices and
+
+ align:start position:0%
+obtained by considering n vertices and
+ 
+
+ align:start position:0%
+obtained by considering n vertices and
+each edge each possible edge appearing
+
+ align:start position:0%
+each edge each possible edge appearing
+ 
+
+ align:start position:0%
+each edge each possible edge appearing
+independently and uniformly with
+
+ align:start position:0%
+independently and uniformly with
+ 
+
+ align:start position:0%
+independently and uniformly with
+probability P and we're going to decide
+
+ align:start position:0%
+probability P and we're going to decide
+ 
+
+ align:start position:0%
+probability P and we're going to decide
+this P later on so let me not tell you
+
+ align:start position:0%
+this P later on so let me not tell you
+ 
+
+ align:start position:0%
+this P later on so let me not tell you
+what P is for now I'm interested in
+
+ align:start position:0%
+what P is for now I'm interested in
+ 
+
+ align:start position:0%
+what P is for now I'm interested in
+avoiding H so this random graph might
+
+ align:start position:0%
+avoiding H so this random graph might
+ 
+
+ align:start position:0%
+avoiding H so this random graph might
+have some copies of H let me count the
+
+ align:start position:0%
+have some copies of H let me count the
+ 
+
+ align:start position:0%
+have some copies of H let me count the
+number of copies of H we can compute the
+
+ align:start position:0%
+number of copies of H we can compute the
+ 
+
+ align:start position:0%
+number of copies of H we can compute the
+expected number of copies of H by
+
+ align:start position:0%
+expected number of copies of H by
+ 
+
+ align:start position:0%
+expected number of copies of H by
+linearity of expectations for every
+
+ align:start position:0%
+linearity of expectations for every
+ 
+
+ align:start position:0%
+linearity of expectations for every
+possible placement look at what's the
+
+ align:start position:0%
+possible placement look at what's the
+ 
+
+ align:start position:0%
+possible placement look at what's the
+probability that that placement
+
+ align:start position:0%
+probability that that placement
+ 
+
+ align:start position:0%
+probability that that placement
+generates an H namely look at all
+
+ align:start position:0%
+generates an H namely look at all
+ 
+
+ align:start position:0%
+generates an H namely look at all
+different possibilities for choosing the
+
+ align:start position:0%
+different possibilities for choosing the
+ 
+
+ align:start position:0%
+different possibilities for choosing the
+possible vertices of H I need to divide
+
+ align:start position:0%
+possible vertices of H I need to divide
+ 
+
+ align:start position:0%
+possible vertices of H I need to divide
+it by a factor that accounts for the
+
+ align:start position:0%
+it by a factor that accounts for the
+ 
+
+ align:start position:0%
+it by a factor that accounts for the
+number of automorphisms of age but just
+
+ align:start position:0%
+number of automorphisms of age but just
+ 
+
+ align:start position:0%
+number of automorphisms of age but just
+a constant factor don't worry about it
+
+ align:start position:0%
+a constant factor don't worry about it
+ 
+
+ align:start position:0%
+a constant factor don't worry about it
+and for each of these possible
+
+ align:start position:0%
+and for each of these possible
+ 
+
+ align:start position:0%
+and for each of these possible
+placements H appears with probability
+
+ align:start position:0%
+placements H appears with probability
+ 
+
+ align:start position:0%
+placements H appears with probability
+exactly P - the number of edges of H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just by linearity of expectations and I
+
+ align:start position:0%
+just by linearity of expectations and I
+ 
+
+ align:start position:0%
+just by linearity of expectations and I
+can upper bound this quantity very
+
+ align:start position:0%
+can upper bound this quantity very
+ 
+
+ align:start position:0%
+can upper bound this quantity very
+crudely by e to the number of edges of H
+
+ align:start position:0%
+crudely by e to the number of edges of H
+ 
+
+ align:start position:0%
+crudely by e to the number of edges of H
+times n which is the number of vertices
+
+ align:start position:0%
+times n which is the number of vertices
+ 
+
+ align:start position:0%
+times n which is the number of vertices
+of G raised to number of vertices of H
+
+ align:start position:0%
+of G raised to number of vertices of H
+ 
+
+ align:start position:0%
+of G raised to number of vertices of H
+on the other hand I also want a graph G
+
+ align:start position:0%
+on the other hand I also want a graph G
+ 
+
+ align:start position:0%
+on the other hand I also want a graph G
+that has lost
+
+ align:start position:0%
+that has lost
+ 
+
+ align:start position:0%
+that has lost
+of edges because that's what we're
+
+ align:start position:0%
+of edges because that's what we're
+ 
+
+ align:start position:0%
+of edges because that's what we're
+trying to do or trying to generate a
+
+ align:start position:0%
+trying to do or trying to generate a
+ 
+
+ align:start position:0%
+trying to do or trying to generate a
+graph with lots of eight edges that's h3
+
+ align:start position:0%
+graph with lots of eight edges that's h3
+ 
+
+ align:start position:0%
+graph with lots of eight edges that's h3
+so the number of edges of G that's also
+
+ align:start position:0%
+so the number of edges of G that's also
+ 
+
+ align:start position:0%
+so the number of edges of G that's also
+easy to compute it's a binomial
+
+ align:start position:0%
+easy to compute it's a binomial
+ 
+
+ align:start position:0%
+easy to compute it's a binomial
+distribution and has expectation P times
+
+ align:start position:0%
+distribution and has expectation P times
+ 
+
+ align:start position:0%
+distribution and has expectation P times
+and choose two and basically I want this
+
+ align:start position:0%
+and choose two and basically I want this
+ 
+
+ align:start position:0%
+and choose two and basically I want this
+quantity to be much larger than that
+
+ align:start position:0%
+quantity to be much larger than that
+ 
+
+ align:start position:0%
+quantity to be much larger than that
+quantity so I choose an appropriate P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+namely by comparing these two quantities
+
+ align:start position:0%
+namely by comparing these two quantities
+ 
+
+ align:start position:0%
+namely by comparing these two quantities
+and choose P to be let's say 1/2 the
+
+ align:start position:0%
+and choose P to be let's say 1/2 the
+ 
+
+ align:start position:0%
+and choose P to be let's say 1/2 the
+half is not important times n to the D
+
+ align:start position:0%
+half is not important times n to the D
+ 
+
+ align:start position:0%
+half is not important times n to the D
+of H minus 2 divided by e of H minus 1
+
+ align:start position:0%
+of H minus 2 divided by e of H minus 1
+ 
+
+ align:start position:0%
+of H minus 2 divided by e of H minus 1
+the exponent comes out of comparing
+
+ align:start position:0%
+the exponent comes out of comparing
+ 
+
+ align:start position:0%
+the exponent comes out of comparing
+these two expressions so you see a 1 and
+
+ align:start position:0%
+these two expressions so you see a 1 and
+ 
+
+ align:start position:0%
+these two expressions so you see a 1 and
+a 2 once you have this peep see that the
+
+ align:start position:0%
+a 2 once you have this peep see that the
+ 
+
+ align:start position:0%
+a 2 once you have this peep see that the
+number which is the difference so take
+
+ align:start position:0%
+number which is the difference so take
+ 
+
+ align:start position:0%
+number which is the difference so take
+the number of edges of G minus the
+
+ align:start position:0%
+the number of edges of G minus the
+ 
+
+ align:start position:0%
+the number of edges of G minus the
+number of copies of H I know the
+
+ align:start position:0%
+number of copies of H I know the
+ 
+
+ align:start position:0%
+number of copies of H I know the
+expectation of both I can look at their
+
+ align:start position:0%
+expectation of both I can look at their
+ 
+
+ align:start position:0%
+expectation of both I can look at their
+difference with this value of P we find
+
+ align:start position:0%
+difference with this value of P we find
+ 
+
+ align:start position:0%
+difference with this value of P we find
+that it is at least half of the number
+
+ align:start position:0%
+that it is at least half of the number
+ 
+
+ align:start position:0%
+that it is at least half of the number
+of edges so on expectation you don't
+
+ align:start position:0%
+of edges so on expectation you don't
+ 
+
+ align:start position:0%
+of edges so on expectation you don't
+lose too much so piece chosen so that
+
+ align:start position:0%
+lose too much so piece chosen so that
+ 
+
+ align:start position:0%
+lose too much so piece chosen so that
+this inequality is true right so you set
+
+ align:start position:0%
+this inequality is true right so you set
+ 
+
+ align:start position:0%
+this inequality is true right so you set
+what P is we find that this content here
+
+ align:start position:0%
+what P is we find that this content here
+ 
+
+ align:start position:0%
+what P is we find that this content here
+is at least some constant times n to the
+
+ align:start position:0%
+is at least some constant times n to the
+ 
+
+ align:start position:0%
+is at least some constant times n to the
+2 minus V of H minus 2 divided by P of H
+
+ align:start position:0%
+2 minus V of H minus 2 divided by P of H
+ 
+
+ align:start position:0%
+2 minus V of H minus 2 divided by P of H
+minus 1 we're still working with a
+
+ align:start position:0%
+minus 1 we're still working with a
+ 
+
+ align:start position:0%
+minus 1 we're still working with a
+random graph and we know that this
+
+ align:start position:0%
+random graph and we know that this
+ 
+
+ align:start position:0%
+random graph and we know that this
+quantity here is on expectation at least
+
+ align:start position:0%
+quantity here is on expectation at least
+ 
+
+ align:start position:0%
+quantity here is on expectation at least
+that number not too small
+
+ align:start position:0%
+that number not too small
+ 
+
+ align:start position:0%
+that number not too small
+therefore
+
+ align:start position:0%
+therefore
+ 
+
+ align:start position:0%
+therefore
+there exists some instance in this
+
+ align:start position:0%
+there exists some instance in this
+ 
+
+ align:start position:0%
+there exists some instance in this
+randomness some G such that the quantity
+
+ align:start position:0%
+randomness some G such that the quantity
+ 
+
+ align:start position:0%
+randomness some G such that the quantity
+above for the specific random instance
+
+ align:start position:0%
+above for the specific random instance
+ 
+
+ align:start position:0%
+above for the specific random instance
+is at least its expectation so this
+
+ align:start position:0%
+is at least its expectation so this
+ 
+
+ align:start position:0%
+is at least its expectation so this
+gives us a graph G which on one hand has
+
+ align:start position:0%
+gives us a graph G which on one hand has
+ 
+
+ align:start position:0%
+gives us a graph G which on one hand has
+lots of edges but also has very few
+
+ align:start position:0%
+lots of edges but also has very few
+ 
+
+ align:start position:0%
+lots of edges but also has very few
+copies of H relative to the number of
+
+ align:start position:0%
+copies of H relative to the number of
+ 
+
+ align:start position:0%
+copies of H relative to the number of
+edges so we can now get rid of all the
+
+ align:start position:0%
+edges so we can now get rid of all the
+ 
+
+ align:start position:0%
+edges so we can now get rid of all the
+copies of H by removing one edge from
+
+ align:start position:0%
+copies of H by removing one edge from
+ 
+
+ align:start position:0%
+copies of H by removing one edge from
+each copy of H in G to remove all copies
+
+ align:start position:0%
+each copy of H in G to remove all copies
+ 
+
+ align:start position:0%
+each copy of H in G to remove all copies
+of H and now we obtain an H free graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how many edges are there in this graph
+
+ align:start position:0%
+how many edges are there in this graph
+ 
+
+ align:start position:0%
+how many edges are there in this graph
+but we removed at most one edge for each
+
+ align:start position:0%
+but we removed at most one edge for each
+ 
+
+ align:start position:0%
+but we removed at most one edge for each
+copy of H so the number of edges is at
+
+ align:start position:0%
+copy of H so the number of edges is at
+ 
+
+ align:start position:0%
+copy of H so the number of edges is at
+least this quantity here which is what
+
+ align:start position:0%
+least this quantity here which is what
+ 
+
+ align:start position:0%
+least this quantity here which is what
+we wrote
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's it right so now we've
+
+ align:start position:0%
+and that's it right so now we've
+ 
+
+ align:start position:0%
+and that's it right so now we've
+obtained our graph on n vertices with
+
+ align:start position:0%
+obtained our graph on n vertices with
+ 
+
+ align:start position:0%
+obtained our graph on n vertices with
+lots of edges with the claim bound
+
+ align:start position:0%
+lots of edges with the claim bound
+ 
+
+ align:start position:0%
+lots of edges with the claim bound
+that's a ch3 so this is the
+
+ align:start position:0%
+that's a ch3 so this is the
+ 
+
+ align:start position:0%
+that's a ch3 so this is the
+probabilistic method that you start with
+
+ align:start position:0%
+probabilistic method that you start with
+ 
+
+ align:start position:0%
+probabilistic method that you start with
+something random you try to fix it and
+
+ align:start position:0%
+something random you try to fix it and
+ 
+
+ align:start position:0%
+something random you try to fix it and
+this method sometimes has the name of
+
+ align:start position:0%
+this method sometimes has the name of
+ 
+
+ align:start position:0%
+this method sometimes has the name of
+the alteration method and it has a very
+
+ align:start position:0%
+the alteration method and it has a very
+ 
+
+ align:start position:0%
+the alteration method and it has a very
+important idea and one of the key ideas
+
+ align:start position:0%
+important idea and one of the key ideas
+ 
+
+ align:start position:0%
+important idea and one of the key ideas
+in the probabilistic method which I
+
+ align:start position:0%
+in the probabilistic method which I
+ 
+
+ align:start position:0%
+in the probabilistic method which I
+encourage you to go and learn more about
+
+ align:start position:0%
+encourage you to go and learn more about
+ 
+
+ align:start position:0%
+encourage you to go and learn more about
+will also see this method later on when
+
+ align:start position:0%
+will also see this method later on when
+ 
+
+ align:start position:0%
+will also see this method later on when
+we discuss the randomized algebraic
+
+ align:start position:0%
+we discuss the randomized algebraic
+ 
+
+ align:start position:0%
+we discuss the randomized algebraic
+construction so I mean so questions yeah
+
+ align:start position:0%
+construction so I mean so questions yeah
+ 
+
+ align:start position:0%
+construction so I mean so questions yeah
+the question is one is what do I mean by
+
+ align:start position:0%
+the question is one is what do I mean by
+ 
+
+ align:start position:0%
+the question is one is what do I mean by
+the number of copies of H I mean every
+
+ align:start position:0%
+the number of copies of H I mean every
+ 
+
+ align:start position:0%
+the number of copies of H I mean every
+instance of H you see so they could be
+
+ align:start position:0%
+instance of H you see so they could be
+ 
+
+ align:start position:0%
+instance of H you see so they could be
+intersecting I'm not asking for
+
+ align:start position:0%
+intersecting I'm not asking for
+ 
+
+ align:start position:0%
+intersecting I'm not asking for
+destroying copies yeah so a complete
+
+ align:start position:0%
+destroying copies yeah so a complete
+ 
+
+ align:start position:0%
+destroying copies yeah so a complete
+graph on n vertices has n choose 3
+
+ align:start position:0%
+graph on n vertices has n choose 3
+ 
+
+ align:start position:0%
+graph on n vertices has n choose 3
+triangles any more questions ok so now
+
+ align:start position:0%
+triangles any more questions ok so now
+ 
+
+ align:start position:0%
+triangles any more questions ok so now
+we've seen that the probabilistic method
+
+ align:start position:0%
+we've seen that the probabilistic method
+ 
+
+ align:start position:0%
+we've seen that the probabilistic method
+gives you you know some bound and it's
+
+ align:start position:0%
+gives you you know some bound and it's
+ 
+
+ align:start position:0%
+gives you you know some bound and it's
+not too hard to apply but it doesn't
+
+ align:start position:0%
+not too hard to apply but it doesn't
+ 
+
+ align:start position:0%
+not too hard to apply but it doesn't
+give you the right bound it doesn't give
+
+ align:start position:0%
+give you the right bound it doesn't give
+ 
+
+ align:start position:0%
+give you the right bound it doesn't give
+you the truth so now I want to show you
+
+ align:start position:0%
+you the truth so now I want to show you
+ 
+
+ align:start position:0%
+you the truth so now I want to show you
+a different type of constructions namely
+
+ align:start position:0%
+a different type of constructions namely
+ 
+
+ align:start position:0%
+a different type of constructions namely
+algebraic instructions that do allow you
+
+ align:start position:0%
+algebraic instructions that do allow you
+ 
+
+ align:start position:0%
+algebraic instructions that do allow you
+to get the truth but they work in a only
+
+ align:start position:0%
+to get the truth but they work in a only
+ 
+
+ align:start position:0%
+to get the truth but they work in a only
+a small number of cases so it's more
+
+ align:start position:0%
+a small number of cases so it's more
+ 
+
+ align:start position:0%
+a small number of cases so it's more
+magical but they work better when the
+
+ align:start position:0%
+magical but they work better when the
+ 
+
+ align:start position:0%
+magical but they work better when the
+magic happens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's discuss algebraic constructions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in particular I want to show you how to
+
+ align:start position:0%
+in particular I want to show you how to
+ 
+
+ align:start position:0%
+in particular I want to show you how to
+obtain the tight bound on the extremal
+
+ align:start position:0%
+obtain the tight bound on the extremal
+ 
+
+ align:start position:0%
+obtain the tight bound on the extremal
+number for k2 - namely a four cycle so
+
+ align:start position:0%
+number for k2 - namely a four cycle so
+ 
+
+ align:start position:0%
+number for k2 - namely a four cycle so
+this is a result due to elder's rainy
+
+ align:start position:0%
+this is a result due to elder's rainy
+ 
+
+ align:start position:0%
+this is a result due to elder's rainy
+and shoosh and tells us that the
+
+ align:start position:0%
+and shoosh and tells us that the
+ 
+
+ align:start position:0%
+and shoosh and tells us that the
+extremal number for k2 to is at least
+
+ align:start position:0%
+extremal number for k2 to is at least
+ 
+
+ align:start position:0%
+extremal number for k2 to is at least
+one half basically up to asymptotics
+
+ align:start position:0%
+one half basically up to asymptotics
+ 
+
+ align:start position:0%
+one half basically up to asymptotics
+times n to the three-halves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually if you look at the constant
+
+ align:start position:0%
+actually if you look at the constant
+ 
+
+ align:start position:0%
+actually if you look at the constant
+that came out of the proof of the Cova
+
+ align:start position:0%
+that came out of the proof of the Cova
+ 
+
+ align:start position:0%
+that came out of the proof of the Cova
+shows tour on there it is also one half
+
+ align:start position:0%
+shows tour on there it is also one half
+ 
+
+ align:start position:0%
+shows tour on there it is also one half
+so as a corollary we see that the
+
+ align:start position:0%
+so as a corollary we see that the
+ 
+
+ align:start position:0%
+so as a corollary we see that the
+extremal number it's like that okay so
+
+ align:start position:0%
+extremal number it's like that okay so
+ 
+
+ align:start position:0%
+extremal number it's like that okay so
+this is one of extremely few cases where
+
+ align:start position:0%
+this is one of extremely few cases where
+ 
+
+ align:start position:0%
+this is one of extremely few cases where
+we know the extremal number so well so
+
+ align:start position:0%
+we know the extremal number so well so
+ 
+
+ align:start position:0%
+we know the extremal number so well so
+the constant if you go back to the proof
+
+ align:start position:0%
+the constant if you go back to the proof
+ 
+
+ align:start position:0%
+the constant if you go back to the proof
+of Kovar we chose to round you see that
+
+ align:start position:0%
+of Kovar we chose to round you see that
+ 
+
+ align:start position:0%
+of Kovar we chose to round you see that
+the constant actually there is one half
+
+ align:start position:0%
+the constant actually there is one half
+ 
+
+ align:start position:0%
+the constant actually there is one half
+okay so I want to construct for you a
+
+ align:start position:0%
+okay so I want to construct for you a
+ 
+
+ align:start position:0%
+okay so I want to construct for you a
+graph that has no four cycles and has
+
+ align:start position:0%
+graph that has no four cycles and has
+ 
+
+ align:start position:0%
+graph that has no four cycles and has
+lots of edges so that's the name of the
+
+ align:start position:0%
+lots of edges so that's the name of the
+ 
+
+ align:start position:0%
+lots of edges so that's the name of the
+game and I'll describe this graph for
+
+ align:start position:0%
+game and I'll describe this graph for
+ 
+
+ align:start position:0%
+game and I'll describe this graph for
+you explicitly so this graph has a name
+
+ align:start position:0%
+you explicitly so this graph has a name
+ 
+
+ align:start position:0%
+you explicitly so this graph has a name
+it's called a polarity graph
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's suppose that n is a number such
+
+ align:start position:0%
+let's suppose that n is a number such
+ 
+
+ align:start position:0%
+let's suppose that n is a number such
+that one bigger than this number is a
+
+ align:start position:0%
+that one bigger than this number is a
+ 
+
+ align:start position:0%
+that one bigger than this number is a
+square of a prime so construction will
+
+ align:start position:0%
+square of a prime so construction will
+ 
+
+ align:start position:0%
+square of a prime so construction will
+use some prime some finite fields I'll
+
+ align:start position:0%
+use some prime some finite fields I'll
+ 
+
+ align:start position:0%
+use some prime some finite fields I'll
+explain a bit if n it's not of this form
+
+ align:start position:0%
+explain a bit if n it's not of this form
+ 
+
+ align:start position:0%
+explain a bit if n it's not of this form
+then you can change n to a number very
+
+ align:start position:0%
+then you can change n to a number very
+ 
+
+ align:start position:0%
+then you can change n to a number very
+close to of this form and everything
+
+ align:start position:0%
+close to of this form and everything
+ 
+
+ align:start position:0%
+close to of this form and everything
+will be okay the graph will be
+
+ align:start position:0%
+will be okay the graph will be
+ 
+
+ align:start position:0%
+will be okay the graph will be
+constructed as follows the vertex set
+
+ align:start position:0%
+constructed as follows the vertex set
+ 
+
+ align:start position:0%
+constructed as follows the vertex set
+will be the plane over FP let's remove
+
+ align:start position:0%
+will be the plane over FP let's remove
+ 
+
+ align:start position:0%
+will be the plane over FP let's remove
+the origin so has n points exactly and
+
+ align:start position:0%
+the origin so has n points exactly and
+ 
+
+ align:start position:0%
+the origin so has n points exactly and
+the edges are such that I put an edge
+
+ align:start position:0%
+the edges are such that I put an edge
+ 
+
+ align:start position:0%
+the edges are such that I put an edge
+between X Y and a beam if and only if
+
+ align:start position:0%
+between X Y and a beam if and only if
+ 
+
+ align:start position:0%
+between X Y and a beam if and only if
+the equation ax plus py equals to one
+
+ align:start position:0%
+the equation ax plus py equals to one
+ 
+
+ align:start position:0%
+the equation ax plus py equals to one
+holds and this equation is meant to be
+
+ align:start position:0%
+holds and this equation is meant to be
+ 
+
+ align:start position:0%
+holds and this equation is meant to be
+read in FP so that's the graph that's an
+
+ align:start position:0%
+read in FP so that's the graph that's an
+ 
+
+ align:start position:0%
+read in FP so that's the graph that's an
+explicit description of this graph so I
+
+ align:start position:0%
+explicit description of this graph so I
+ 
+
+ align:start position:0%
+explicit description of this graph so I
+need to show you two things one that has
+
+ align:start position:0%
+need to show you two things one that has
+ 
+
+ align:start position:0%
+need to show you two things one that has
+lots of edges the claim number of edges
+
+ align:start position:0%
+lots of edges the claim number of edges
+ 
+
+ align:start position:0%
+lots of edges the claim number of edges
+and - it has no four cycles ok so let's
+
+ align:start position:0%
+and - it has no four cycles ok so let's
+ 
+
+ align:start position:0%
+and - it has no four cycles ok so let's
+start with not having four cycles so why
+
+ align:start position:0%
+start with not having four cycles so why
+ 
+
+ align:start position:0%
+start with not having four cycles so why
+is it K - 2 3 ok what would a K - to be
+
+ align:start position:0%
+is it K - 2 3 ok what would a K - to be
+ 
+
+ align:start position:0%
+is it K - 2 3 ok what would a K - to be
+so let's consider two points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and I want to understand the number
+
+ align:start position:0%
+so and I want to understand the number
+ 
+
+ align:start position:0%
+so and I want to understand the number
+of common neighbors of these two points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well look at the description for the
+
+ align:start position:0%
+well look at the description for the
+ 
+
+ align:start position:0%
+well look at the description for the
+edges what are the neighbors well the
+
+ align:start position:0%
+edges what are the neighbors well the
+ 
+
+ align:start position:0%
+edges what are the neighbors well the
+neighbors correspond to solutions to
+
+ align:start position:0%
+neighbors correspond to solutions to
+ 
+
+ align:start position:0%
+neighbors correspond to solutions to
+this system of equations and the basic
+
+ align:start position:0%
+this system of equations and the basic
+ 
+
+ align:start position:0%
+this system of equations and the basic
+claim is that there's at most one
+
+ align:start position:0%
+claim is that there's at most one
+ 
+
+ align:start position:0%
+claim is that there's at most one
+solution X Y basic back in linear
+
+ align:start position:0%
+solution X Y basic back in linear
+ 
+
+ align:start position:0%
+solution X Y basic back in linear
+algebra you have to be slightly careful
+
+ align:start position:0%
+algebra you have to be slightly careful
+ 
+
+ align:start position:0%
+algebra you have to be slightly careful
+in case a B is a multiple of a prime B
+
+ align:start position:0%
+in case a B is a multiple of a prime B
+ 
+
+ align:start position:0%
+in case a B is a multiple of a prime B
+prime but actually in that case you have
+
+ align:start position:0%
+prime but actually in that case you have
+ 
+
+ align:start position:0%
+prime but actually in that case you have
+no solutions anyway okay the second
+
+ align:start position:0%
+no solutions anyway okay the second
+ 
+
+ align:start position:0%
+no solutions anyway okay the second
+claim then is that this graph has lots
+
+ align:start position:0%
+claim then is that this graph has lots
+ 
+
+ align:start position:0%
+claim then is that this graph has lots
+of edges well actually that's not too
+
+ align:start position:0%
+of edges well actually that's not too
+ 
+
+ align:start position:0%
+of edges well actually that's not too
+hard to show either so I claim that
+
+ align:start position:0%
+hard to show either so I claim that
+ 
+
+ align:start position:0%
+hard to show either so I claim that
+every vertex has degree
+
+ align:start position:0%
+every vertex has degree
+ 
+
+ align:start position:0%
+every vertex has degree
+okay so what's how many edges come out
+
+ align:start position:0%
+okay so what's how many edges come out
+ 
+
+ align:start position:0%
+okay so what's how many edges come out
+of every vertex I'll give you a a comma
+
+ align:start position:0%
+of every vertex I'll give you a a comma
+ 
+
+ align:start position:0%
+of every vertex I'll give you a a comma
+B so how many x comma y satisfy that
+
+ align:start position:0%
+B so how many x comma y satisfy that
+ 
+
+ align:start position:0%
+B so how many x comma y satisfy that
+equation up there basically for one case
+
+ align:start position:0%
+equation up there basically for one case
+ 
+
+ align:start position:0%
+equation up there basically for one case
+one of X in a and B is nonzero so for
+
+ align:start position:0%
+one of X in a and B is nonzero so for
+ 
+
+ align:start position:0%
+one of X in a and B is nonzero so for
+whatever value off so let's say a is
+
+ align:start position:0%
+whatever value off so let's say a is
+ 
+
+ align:start position:0%
+whatever value off so let's say a is
+nonzero then for whatever value of y you
+
+ align:start position:0%
+nonzero then for whatever value of y you
+ 
+
+ align:start position:0%
+nonzero then for whatever value of y you
+set I can find a unique X that solves
+
+ align:start position:0%
+set I can find a unique X that solves
+ 
+
+ align:start position:0%
+set I can find a unique X that solves
+the equation I have to be slightly
+
+ align:start position:0%
+the equation I have to be slightly
+ 
+
+ align:start position:0%
+the equation I have to be slightly
+careful because I don't allow loops in
+
+ align:start position:0%
+careful because I don't allow loops in
+ 
+
+ align:start position:0%
+careful because I don't allow loops in
+my graph so I might lose one edge
+
+ align:start position:0%
+my graph so I might lose one edge
+ 
+
+ align:start position:0%
+my graph so I might lose one edge
+because of that in any case every vertex
+
+ align:start position:0%
+because of that in any case every vertex
+ 
+
+ align:start position:0%
+because of that in any case every vertex
+has degree exactly key or P minus one so
+
+ align:start position:0%
+has degree exactly key or P minus one so
+ 
+
+ align:start position:0%
+has degree exactly key or P minus one so
+just solve that equation in x and y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the P minus one comes from no loops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+therefore up the number of edges is
+
+ align:start position:0%
+therefore up the number of edges is
+ 
+
+ align:start position:0%
+therefore up the number of edges is
+equal to the claimed belt okay so this
+
+ align:start position:0%
+equal to the claimed belt okay so this
+ 
+
+ align:start position:0%
+equal to the claimed belt okay so this
+finish is the proof in case when n has
+
+ align:start position:0%
+finish is the proof in case when n has
+ 
+
+ align:start position:0%
+finish is the proof in case when n has
+that special number theoretic form but
+
+ align:start position:0%
+that special number theoretic form but
+ 
+
+ align:start position:0%
+that special number theoretic form but
+we can extend to all values of n like
+
+ align:start position:0%
+we can extend to all values of n like
+ 
+
+ align:start position:0%
+we can extend to all values of n like
+this if n doesn't have that form then I
+
+ align:start position:0%
+this if n doesn't have that form then I
+ 
+
+ align:start position:0%
+this if n doesn't have that form then I
+can take a prime P may not necessarily
+
+ align:start position:0%
+can take a prime P may not necessarily
+ 
+
+ align:start position:0%
+can take a prime P may not necessarily
+be exactly satisfying that inequality
+
+ align:start position:0%
+be exactly satisfying that inequality
+ 
+
+ align:start position:0%
+be exactly satisfying that inequality
+but I can always take a prime pretty
+
+ align:start position:0%
+but I can always take a prime pretty
+ 
+
+ align:start position:0%
+but I can always take a prime pretty
+close to it so I can always take a prime
+
+ align:start position:0%
+close to it so I can always take a prime
+ 
+
+ align:start position:0%
+close to it so I can always take a prime
+which is up to a negligible
+
+ align:start position:0%
+which is up to a negligible
+ 
+
+ align:start position:0%
+which is up to a negligible
+multiplicative error what I want and
+
+ align:start position:0%
+multiplicative error what I want and
+ 
+
+ align:start position:0%
+multiplicative error what I want and
+then we use and such that P squared
+
+ align:start position:0%
+then we use and such that P squared
+ 
+
+ align:start position:0%
+then we use and such that P squared
+minus 1 is at most and and use the
+
+ align:start position:0%
+minus 1 is at most and and use the
+ 
+
+ align:start position:0%
+minus 1 is at most and and use the
+compulsion struction and add isolated
+
+ align:start position:0%
+compulsion struction and add isolated
+ 
+
+ align:start position:0%
+compulsion struction and add isolated
+vertices to finish the job to get
+
+ align:start position:0%
+vertices to finish the job to get
+ 
+
+ align:start position:0%
+vertices to finish the job to get
+exactly n vertices and the reason that I
+
+ align:start position:0%
+exactly n vertices and the reason that I
+ 
+
+ align:start position:0%
+exactly n vertices and the reason that I
+can always take a prime very close to it
+
+ align:start position:0%
+can always take a prime very close to it
+ 
+
+ align:start position:0%
+can always take a prime very close to it
+is because there's a theorem in number
+
+ align:start position:0%
+is because there's a theorem in number
+ 
+
+ align:start position:0%
+is because there's a theorem in number
+theory that tells us that and large
+
+ align:start position:0%
+theory that tells us that and large
+ 
+
+ align:start position:0%
+theory that tells us that and large
+enough I can always find the prime which
+
+ align:start position:0%
+enough I can always find the prime which
+ 
+
+ align:start position:0%
+enough I can always find the prime which
+is slightly less than n but no more than
+
+ align:start position:0%
+is slightly less than n but no more than
+ 
+
+ align:start position:0%
+is slightly less than n but no more than
+negligible multiplicative factor off the
+
+ align:start position:0%
+negligible multiplicative factor off the
+ 
+
+ align:start position:0%
+negligible multiplicative factor off the
+best result of this form is just I'm
+
+ align:start position:0%
+best result of this form is just I'm
+ 
+
+ align:start position:0%
+best result of this form is just I'm
+just telling you something number three
+
+ align:start position:0%
+just telling you something number three
+ 
+
+ align:start position:0%
+just telling you something number three
+for cultural reasons so
+
+ align:start position:0%
+for cultural reasons so
+ 
+
+ align:start position:0%
+for cultural reasons so
+best result of the storm is due to Baker
+
+ align:start position:0%
+best result of the storm is due to Baker
+ 
+
+ align:start position:0%
+best result of the storm is due to Baker
+Harmon pence so this is the question
+
+ align:start position:0%
+Harmon pence so this is the question
+ 
+
+ align:start position:0%
+Harmon pence so this is the question
+regarding how large can gaps between
+
+ align:start position:0%
+regarding how large can gaps between
+ 
+
+ align:start position:0%
+regarding how large can gaps between
+prime speed so you might know the the
+
+ align:start position:0%
+prime speed so you might know the the
+ 
+
+ align:start position:0%
+prime speed so you might know the the
+rich later them that he'll see there's
+
+ align:start position:0%
+rich later them that he'll see there's
+ 
+
+ align:start position:0%
+rich later them that he'll see there's
+always a prime between N and 2n so what
+
+ align:start position:0%
+always a prime between N and 2n so what
+ 
+
+ align:start position:0%
+always a prime between N and 2n so what
+about between and an M plus 210 actually
+
+ align:start position:0%
+about between and an M plus 210 actually
+ 
+
+ align:start position:0%
+about between and an M plus 210 actually
+we don't know that right so the best
+
+ align:start position:0%
+we don't know that right so the best
+ 
+
+ align:start position:0%
+we don't know that right so the best
+ways out of the form is that there's
+
+ align:start position:0%
+ways out of the form is that there's
+ 
+
+ align:start position:0%
+ways out of the form is that there's
+always a prime for n sufficiently large
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exist a prime between n - n 2 the
+
+ align:start position:0%
+there exist a prime between n - n 2 the
+ 
+
+ align:start position:0%
+there exist a prime between n - n 2 the
+exponent 0.5 to 5 and n any case this
+
+ align:start position:0%
+exponent 0.5 to 5 and n any case this
+ 
+
+ align:start position:0%
+exponent 0.5 to 5 and n any case this
+number here whatever it is is not all N
+
+ align:start position:0%
+number here whatever it is is not all N
+ 
+
+ align:start position:0%
+number here whatever it is is not all N
+and that's enough for that's enough for
+
+ align:start position:0%
+and that's enough for that's enough for
+ 
+
+ align:start position:0%
+and that's enough for that's enough for
+all purpose okay so it's suffices to
+
+ align:start position:0%
+all purpose okay so it's suffices to
+ 
+
+ align:start position:0%
+all purpose okay so it's suffices to
+look at end of a special number
+
+ align:start position:0%
+look at end of a special number
+ 
+
+ align:start position:0%
+look at end of a special number
+theoretic form that where you're allowed
+
+ align:start position:0%
+theoretic form that where you're allowed
+ 
+
+ align:start position:0%
+theoretic form that where you're allowed
+to use Prime's so that's the
+
+ align:start position:0%
+to use Prime's so that's the
+ 
+
+ align:start position:0%
+to use Prime's so that's the
+construction there let me show you a
+
+ align:start position:0%
+construction there let me show you a
+ 
+
+ align:start position:0%
+construction there let me show you a
+interpretation of that construction
+
+ align:start position:0%
+interpretation of that construction
+ 
+
+ align:start position:0%
+interpretation of that construction
+which i think is maybe helpful to to
+
+ align:start position:0%
+which i think is maybe helpful to to
+ 
+
+ align:start position:0%
+which i think is maybe helpful to to
+think about and that's that you can view
+
+ align:start position:0%
+think about and that's that you can view
+ 
+
+ align:start position:0%
+think about and that's that you can view
+it as the incidence graph between points
+
+ align:start position:0%
+it as the incidence graph between points
+ 
+
+ align:start position:0%
+it as the incidence graph between points
+and lines in projective space in
+
+ align:start position:0%
+and lines in projective space in
+ 
+
+ align:start position:0%
+and lines in projective space in
+projective plane so I start with a
+
+ align:start position:0%
+projective plane so I start with a
+ 
+
+ align:start position:0%
+projective plane so I start with a
+projective plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I can view a bipartite version
+
+ align:start position:0%
+okay so I can view a bipartite version
+ 
+
+ align:start position:0%
+okay so I can view a bipartite version
+of that construction it can be viewed as
+
+ align:start position:0%
+of that construction it can be viewed as
+ 
+
+ align:start position:0%
+of that construction it can be viewed as
+the point line incidence graph of a
+
+ align:start position:0%
+the point line incidence graph of a
+ 
+
+ align:start position:0%
+the point line incidence graph of a
+projective plane over a finite field and
+
+ align:start position:0%
+projective plane over a finite field and
+ 
+
+ align:start position:0%
+projective plane over a finite field and
+by this I mean put as one vertex set the
+
+ align:start position:0%
+by this I mean put as one vertex set the
+ 
+
+ align:start position:0%
+by this I mean put as one vertex set the
+points of the projective plane and on
+
+ align:start position:0%
+points of the projective plane and on
+ 
+
+ align:start position:0%
+points of the projective plane and on
+the other side of lines and I put in an
+
+ align:start position:0%
+the other side of lines and I put in an
+ 
+
+ align:start position:0%
+the other side of lines and I put in an
+edge between a point and a line if and
+
+ align:start position:0%
+edge between a point and a line if and
+ 
+
+ align:start position:0%
+edge between a point and a line if and
+only if the point lies on the line so
+
+ align:start position:0%
+only if the point lies on the line so
+ 
+
+ align:start position:0%
+only if the point lies on the line so
+you can do this more explicitly in
+
+ align:start position:0%
+you can do this more explicitly in
+ 
+
+ align:start position:0%
+you can do this more explicitly in
+coordinates if you view them points and
+
+ align:start position:0%
+coordinates if you view them points and
+ 
+
+ align:start position:0%
+coordinates if you view them points and
+lines as coordinates and so the equation
+
+ align:start position:0%
+lines as coordinates and so the equation
+ 
+
+ align:start position:0%
+lines as coordinates and so the equation
+for getting point to be on the line is
+
+ align:start position:0%
+for getting point to be on the line is
+ 
+
+ align:start position:0%
+for getting point to be on the line is
+like that so now why is there no four
+
+ align:start position:0%
+like that so now why is there no four
+ 
+
+ align:start position:0%
+like that so now why is there no four
+cycle a four cycle would correspond to
+
+ align:start position:0%
+cycle a four cycle would correspond to
+ 
+
+ align:start position:0%
+cycle a four cycle would correspond to
+two points lying on two different lines
+
+ align:start position:0%
+two points lying on two different lines
+ 
+
+ align:start position:0%
+two points lying on two different lines
+which is not possible in this geometry
+
+ align:start position:0%
+which is not possible in this geometry
+ 
+
+ align:start position:0%
+which is not possible in this geometry
+right so that's the reason for for that
+
+ align:start position:0%
+right so that's the reason for for that
+ 
+
+ align:start position:0%
+right so that's the reason for for that
+construction up there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so no two points in two lines okay any
+
+ align:start position:0%
+so no two points in two lines okay any
+ 
+
+ align:start position:0%
+so no two points in two lines okay any
+questions about this polarity
+
+ align:start position:0%
+questions about this polarity
+ 
+
+ align:start position:0%
+questions about this polarity
+constructions yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right questions why is it called a
+
+ align:start position:0%
+right questions why is it called a
+ 
+
+ align:start position:0%
+right questions why is it called a
+polarity construction so it relates
+
+ align:start position:0%
+polarity construction so it relates
+ 
+
+ align:start position:0%
+polarity construction so it relates
+points and their Polar's which are lines
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep okay the question is has to do with
+
+ align:start position:0%
+yep okay the question is has to do with
+ 
+
+ align:start position:0%
+yep okay the question is has to do with
+a number of vertices here it's true here
+
+ align:start position:0%
+a number of vertices here it's true here
+ 
+
+ align:start position:0%
+a number of vertices here it's true here
+I double the number of vertices and so I
+
+ align:start position:0%
+I double the number of vertices and so I
+ 
+
+ align:start position:0%
+I double the number of vertices and so I
+don't get that constant there but what
+
+ align:start position:0%
+don't get that constant there but what
+ 
+
+ align:start position:0%
+don't get that constant there but what
+that graph up there that's not a
+
+ align:start position:0%
+that graph up there that's not a
+ 
+
+ align:start position:0%
+that graph up there that's not a
+bipartite graph it is identifying the
+
+ align:start position:0%
+bipartite graph it is identifying the
+ 
+
+ align:start position:0%
+bipartite graph it is identifying the
+points and the lines and overlaying the
+
+ align:start position:0%
+points and the lines and overlaying the
+ 
+
+ align:start position:0%
+points and the lines and overlaying the
+two parts into one but if you don't care
+
+ align:start position:0%
+two parts into one but if you don't care
+ 
+
+ align:start position:0%
+two parts into one but if you don't care
+about the constants this graph here may
+
+ align:start position:0%
+about the constants this graph here may
+ 
+
+ align:start position:0%
+about the constants this graph here may
+be conceptually easier to think about
+
+ align:start position:0%
+be conceptually easier to think about
+ 
+
+ align:start position:0%
+be conceptually easier to think about
+yes great question can you generalize
+
+ align:start position:0%
+yes great question can you generalize
+ 
+
+ align:start position:0%
+yes great question can you generalize
+this polarity graph to K 3 3 and higher
+
+ align:start position:0%
+this polarity graph to K 3 3 and higher
+ 
+
+ align:start position:0%
+this polarity graph to K 3 3 and higher
+so that's what we're about to do next
+
+ align:start position:0%
+so that's what we're about to do next
+ 
+
+ align:start position:0%
+so that's what we're about to do next
+okay so for K 3 3 what can you do
+
+ align:start position:0%
+okay so for K 3 3 what can you do
+ 
+
+ align:start position:0%
+okay so for K 3 3 what can you do
+so the main observation here is that two
+
+ align:start position:0%
+so the main observation here is that two
+ 
+
+ align:start position:0%
+so the main observation here is that two
+lines intersecting at most one point
+
+ align:start position:0%
+lines intersecting at most one point
+ 
+
+ align:start position:0%
+lines intersecting at most one point
+right but there are other geometric
+
+ align:start position:0%
+right but there are other geometric
+ 
+
+ align:start position:0%
+right but there are other geometric
+facts of that form so we're going to use
+
+ align:start position:0%
+facts of that form so we're going to use
+ 
+
+ align:start position:0%
+facts of that form so we're going to use
+one of them to get a 2/3 free graph and
+
+ align:start position:0%
+one of them to get a 2/3 free graph and
+ 
+
+ align:start position:0%
+one of them to get a 2/3 free graph and
+this construction is due to brown that
+
+ align:start position:0%
+this construction is due to brown that
+ 
+
+ align:start position:0%
+this construction is due to brown that
+the extremal number for K 3 3 is also at
+
+ align:start position:0%
+the extremal number for K 3 3 is also at
+ 
+
+ align:start position:0%
+the extremal number for K 3 3 is also at
+least factor 1/2 minus 2 0 1 times ok so
+
+ align:start position:0%
+least factor 1/2 minus 2 0 1 times ok so
+ 
+
+ align:start position:0%
+least factor 1/2 minus 2 0 1 times ok so
+now what's the exponent what is
+
+ align:start position:0%
+now what's the exponent what is
+ 
+
+ align:start position:0%
+now what's the exponent what is
+predicted by cavora shows Terron is 2
+
+ align:start position:0%
+predicted by cavora shows Terron is 2
+ 
+
+ align:start position:0%
+predicted by cavora shows Terron is 2
+minus 1/3 and brown obtains the correct
+
+ align:start position:0%
+minus 1/3 and brown obtains the correct
+ 
+
+ align:start position:0%
+minus 1/3 and brown obtains the correct
+exponent it turns out this is also the
+
+ align:start position:0%
+exponent it turns out this is also the
+ 
+
+ align:start position:0%
+exponent it turns out this is also the
+right constant this 1/2 although it
+
+ align:start position:0%
+right constant this 1/2 although it
+ 
+
+ align:start position:0%
+right constant this 1/2 although it
+doesn't follow from the khawarij shows
+
+ align:start position:0%
+doesn't follow from the khawarij shows
+ 
+
+ align:start position:0%
+doesn't follow from the khawarij shows
+tour under my stated one needs to do a
+
+ align:start position:0%
+tour under my stated one needs to do a
+ 
+
+ align:start position:0%
+tour under my stated one needs to do a
+little bit extra work but it turns out
+
+ align:start position:0%
+little bit extra work but it turns out
+ 
+
+ align:start position:0%
+little bit extra work but it turns out
+it is true that this is also the correct
+
+ align:start position:0%
+it is true that this is also the correct
+ 
+
+ align:start position:0%
+it is true that this is also the correct
+constant and that's actually pretty much
+
+ align:start position:0%
+constant and that's actually pretty much
+ 
+
+ align:start position:0%
+constant and that's actually pretty much
+all the cases where we know the correct
+
+ align:start position:0%
+all the cases where we know the correct
+ 
+
+ align:start position:0%
+all the cases where we know the correct
+constant and there are other cases where
+
+ align:start position:0%
+constant and there are other cases where
+ 
+
+ align:start position:0%
+constant and there are other cases where
+we know the correct exponent but these
+
+ align:start position:0%
+we know the correct exponent but these
+ 
+
+ align:start position:0%
+we know the correct exponent but these
+things tend to be
+
+ align:start position:0%
+things tend to be
+ 
+
+ align:start position:0%
+things tend to be
+hard to come by okay so let me show you
+
+ align:start position:0%
+hard to come by okay so let me show you
+ 
+
+ align:start position:0%
+hard to come by okay so let me show you
+how to construct the scrap so it's based
+
+ align:start position:0%
+how to construct the scrap so it's based
+ 
+
+ align:start position:0%
+how to construct the scrap so it's based
+on a similar idea as the polarity graph
+
+ align:start position:0%
+on a similar idea as the polarity graph
+ 
+
+ align:start position:0%
+on a similar idea as the polarity graph
+it has some more technicalities so I'm
+
+ align:start position:0%
+it has some more technicalities so I'm
+ 
+
+ align:start position:0%
+it has some more technicalities so I'm
+not going to do the full proof and just
+
+ align:start position:0%
+not going to do the full proof and just
+ 
+
+ align:start position:0%
+not going to do the full proof and just
+give you the sketch as earlier I'm using
+
+ align:start position:0%
+give you the sketch as earlier I'm using
+ 
+
+ align:start position:0%
+give you the sketch as earlier I'm using
+the same trick we can assume that n has
+
+ align:start position:0%
+the same trick we can assume that n has
+ 
+
+ align:start position:0%
+the same trick we can assume that n has
+a special form here let me assume that N
+
+ align:start position:0%
+a special form here let me assume that N
+ 
+
+ align:start position:0%
+a special form here let me assume that N
+is a cube of a prime I'm going to put AZ
+
+ align:start position:0%
+is a cube of a prime I'm going to put AZ
+ 
+
+ align:start position:0%
+is a cube of a prime I'm going to put AZ
+edges so first the vertices of my graph
+
+ align:start position:0%
+edges so first the vertices of my graph
+ 
+
+ align:start position:0%
+edges so first the vertices of my graph
+are going to be points in the earth I'm
+
+ align:start position:0%
+are going to be points in the earth I'm
+ 
+
+ align:start position:0%
+are going to be points in the earth I'm
+playing over FP previously the lines had
+
+ align:start position:0%
+playing over FP previously the lines had
+ 
+
+ align:start position:0%
+playing over FP previously the lines had
+to do was previously the edges had to do
+
+ align:start position:0%
+to do was previously the edges had to do
+ 
+
+ align:start position:0%
+to do was previously the edges had to do
+with lines and now let's use spheres so
+
+ align:start position:0%
+with lines and now let's use spheres so
+ 
+
+ align:start position:0%
+with lines and now let's use spheres so
+the edges had the form where I joined
+
+ align:start position:0%
+the edges had the form where I joined
+ 
+
+ align:start position:0%
+the edges had the form where I joined
+two vertices like this if and only if
+
+ align:start position:0%
+two vertices like this if and only if
+ 
+
+ align:start position:0%
+two vertices like this if and only if
+there it's not really a distance but
+
+ align:start position:0%
+there it's not really a distance but
+ 
+
+ align:start position:0%
+there it's not really a distance but
+it's something that looks like the
+
+ align:start position:0%
+it's something that looks like the
+ 
+
+ align:start position:0%
+it's something that looks like the
+equation of a sphere where u is some
+
+ align:start position:0%
+equation of a sphere where u is some
+ 
+
+ align:start position:0%
+equation of a sphere where u is some
+fixed
+
+ align:start position:0%
+fixed
+ 
+
+ align:start position:0%
+fixed
+nonzero element of FP you may have to be
+
+ align:start position:0%
+nonzero element of FP you may have to be
+ 
+
+ align:start position:0%
+nonzero element of FP you may have to be
+somewhat careful in choosing this you
+
+ align:start position:0%
+somewhat careful in choosing this you
+ 
+
+ align:start position:0%
+somewhat careful in choosing this you
+but let me not worry too much about it
+
+ align:start position:0%
+but let me not worry too much about it
+ 
+
+ align:start position:0%
+but let me not worry too much about it
+so you fix some so-called distance even
+
+ align:start position:0%
+so you fix some so-called distance even
+ 
+
+ align:start position:0%
+so you fix some so-called distance even
+though it's not a distance and I joined
+
+ align:start position:0%
+though it's not a distance and I joined
+ 
+
+ align:start position:0%
+though it's not a distance and I joined
+the vertices whenever they satisfy that
+
+ align:start position:0%
+the vertices whenever they satisfy that
+ 
+
+ align:start position:0%
+the vertices whenever they satisfy that
+equation having that you know not
+
+ align:start position:0%
+equation having that you know not
+ 
+
+ align:start position:0%
+equation having that you know not
+distance okay what's the intuition here
+
+ align:start position:0%
+distance okay what's the intuition here
+ 
+
+ align:start position:0%
+distance okay what's the intuition here
+the intuition is that I want to avoid
+
+ align:start position:0%
+the intuition is that I want to avoid
+ 
+
+ align:start position:0%
+the intuition is that I want to avoid
+okay so how do I know that this graph
+
+ align:start position:0%
+okay so how do I know that this graph
+ 
+
+ align:start position:0%
+okay so how do I know that this graph
+has no k33 well first let's think about
+
+ align:start position:0%
+has no k33 well first let's think about
+ 
+
+ align:start position:0%
+has no k33 well first let's think about
+what happens in real space so intuition
+
+ align:start position:0%
+what happens in real space so intuition
+ 
+
+ align:start position:0%
+what happens in real space so intuition
+in in the real space well here I have
+
+ align:start position:0%
+in in the real space well here I have
+ 
+
+ align:start position:0%
+in in the real space well here I have
+this graph that's let's say the unit
+
+ align:start position:0%
+this graph that's let's say the unit
+ 
+
+ align:start position:0%
+this graph that's let's say the unit
+distance graph in r3 so the neighborhood
+
+ align:start position:0%
+distance graph in r3 so the neighborhood
+ 
+
+ align:start position:0%
+distance graph in r3 so the neighborhood
+of each point is a unit sphere and what
+
+ align:start position:0%
+of each point is a unit sphere and what
+ 
+
+ align:start position:0%
+of each point is a unit sphere and what
+I want to know is that if you have three
+
+ align:start position:0%
+I want to know is that if you have three
+ 
+
+ align:start position:0%
+I want to know is that if you have three
+spheres three units spheres
+
+ align:start position:0%
+spheres three units spheres
+ 
+
+ align:start position:0%
+spheres three units spheres
+how many common intersection points can
+
+ align:start position:0%
+how many common intersection points can
+ 
+
+ align:start position:0%
+how many common intersection points can
+they have two spheres intersect in a
+
+ align:start position:0%
+they have two spheres intersect in a
+ 
+
+ align:start position:0%
+they have two spheres intersect in a
+circle and that circle cannot lie on the
+
+ align:start position:0%
+circle and that circle cannot lie on the
+ 
+
+ align:start position:0%
+circle and that circle cannot lie on the
+third circle that you should think about
+
+ align:start position:0%
+third circle that you should think about
+ 
+
+ align:start position:0%
+third circle that you should think about
+so that circle intersects the third
+
+ align:start position:0%
+so that circle intersects the third
+ 
+
+ align:start position:0%
+so that circle intersects the third
+circle you know most two points so three
+
+ align:start position:0%
+circle you know most two points so three
+ 
+
+ align:start position:0%
+circle you know most two points so three
+units spheres at most two common points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so the unit distance graph in r3 is
+
+ align:start position:0%
+and so the unit distance graph in r3 is
+ 
+
+ align:start position:0%
+and so the unit distance graph in r3 is
+K 3 3 3 that entire argument even though
+
+ align:start position:0%
+K 3 3 3 that entire argument even though
+ 
+
+ align:start position:0%
+K 3 3 3 that entire argument even though
+I expressed it geometrically it's an
+
+ align:start position:0%
+I expressed it geometrically it's an
+ 
+
+ align:start position:0%
+I expressed it geometrically it's an
+algebraic argument you can write down
+
+ align:start position:0%
+algebraic argument you can write down
+ 
+
+ align:start position:0%
+algebraic argument you can write down
+equations on intersections between two
+
+ align:start position:0%
+equations on intersections between two
+ 
+
+ align:start position:0%
+equations on intersections between two
+spheres it's the intersection of the
+
+ align:start position:0%
+spheres it's the intersection of the
+ 
+
+ align:start position:0%
+spheres it's the intersection of the
+sphere with its coaxial plane I have a
+
+ align:start position:0%
+sphere with its coaxial plane I have a
+ 
+
+ align:start position:0%
+sphere with its coaxial plane I have a
+couple of these coaxial planes that get
+
+ align:start position:0%
+couple of these coaxial planes that get
+ 
+
+ align:start position:0%
+couple of these coaxial planes that get
+your coaxial line that line has to
+
+ align:start position:0%
+your coaxial line that line has to
+ 
+
+ align:start position:0%
+your coaxial line that line has to
+intersect the sphere in and most two
+
+ align:start position:0%
+intersect the sphere in and most two
+ 
+
+ align:start position:0%
+intersect the sphere in and most two
+points you should actually do this
+
+ align:start position:0%
+points you should actually do this
+ 
+
+ align:start position:0%
+points you should actually do this
+algebra if you want to do the proof
+
+ align:start position:0%
+algebra if you want to do the proof
+ 
+
+ align:start position:0%
+algebra if you want to do the proof
+because they're funny things that
+
+ align:start position:0%
+because they're funny things that
+ 
+
+ align:start position:0%
+because they're funny things that
+can happen you'll find our fuels for
+
+ align:start position:0%
+can happen you'll find our fuels for
+ 
+
+ align:start position:0%
+can happen you'll find our fuels for
+example maybe the sphere contains the
+
+ align:start position:0%
+example maybe the sphere contains the
+ 
+
+ align:start position:0%
+example maybe the sphere contains the
+line but you choose your parameters
+
+ align:start position:0%
+line but you choose your parameters
+ 
+
+ align:start position:0%
+line but you choose your parameters
+correctly and these things don't happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's the intuition and if you
+
+ align:start position:0%
+and that's the intuition and if you
+ 
+
+ align:start position:0%
+and that's the intuition and if you
+actually work this out you find that
+
+ align:start position:0%
+actually work this out you find that
+ 
+
+ align:start position:0%
+actually work this out you find that
+this graph here is indeed K 3 3 3 ok so
+
+ align:start position:0%
+this graph here is indeed K 3 3 3 ok so
+ 
+
+ align:start position:0%
+this graph here is indeed K 3 3 3 ok so
+I'm skipping the details but you should
+
+ align:start position:0%
+I'm skipping the details but you should
+ 
+
+ align:start position:0%
+I'm skipping the details but you should
+do the algebra if you want to have a
+
+ align:start position:0%
+do the algebra if you want to have a
+ 
+
+ align:start position:0%
+do the algebra if you want to have a
+proof on the other hand it also has lots
+
+ align:start position:0%
+proof on the other hand it also has lots
+ 
+
+ align:start position:0%
+proof on the other hand it also has lots
+of edges and that's basically the same
+
+ align:start position:0%
+of edges and that's basically the same
+ 
+
+ align:start position:0%
+of edges and that's basically the same
+reason as before but I can count the
+
+ align:start position:0%
+reason as before but I can count the
+ 
+
+ align:start position:0%
+reason as before but I can count the
+number of edges by fixing some x y&z and
+
+ align:start position:0%
+number of edges by fixing some x y&z and
+ 
+
+ align:start position:0%
+number of edges by fixing some x y&z and
+look at how many ABC satisfy that
+
+ align:start position:0%
+look at how many ABC satisfy that
+ 
+
+ align:start position:0%
+look at how many ABC satisfy that
+equation and that's again something that
+
+ align:start position:0%
+equation and that's again something that
+ 
+
+ align:start position:0%
+equation and that's again something that
+needs to be checked but point is that
+
+ align:start position:0%
+needs to be checked but point is that
+ 
+
+ align:start position:0%
+needs to be checked but point is that
+this graph so every vertex has either P
+
+ align:start position:0%
+this graph so every vertex has either P
+ 
+
+ align:start position:0%
+this graph so every vertex has either P
+squared ok so it has close to P squared
+
+ align:start position:0%
+squared ok so it has close to P squared
+ 
+
+ align:start position:0%
+squared ok so it has close to P squared
+degree so lots of edges and combining
+
+ align:start position:0%
+degree so lots of edges and combining
+ 
+
+ align:start position:0%
+degree so lots of edges and combining
+with basically the same ideas as before
+
+ align:start position:0%
+with basically the same ideas as before
+ 
+
+ align:start position:0%
+with basically the same ideas as before
+you get the construction any questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ok so where can we go from here to
+
+ align:start position:0%
+ok so where can we go from here to
+ 
+
+ align:start position:0%
+ok so where can we go from here to
+construct the k22 by the way if you
+
+ align:start position:0%
+construct the k22 by the way if you
+ 
+
+ align:start position:0%
+construct the k22 by the way if you
+construct a 2 to 3 the same construction
+
+ align:start position:0%
+construct a 2 to 3 the same construction
+ 
+
+ align:start position:0%
+construct a 2 to 3 the same construction
+works for K to 3 free it's K 2 to 3 then
+
+ align:start position:0%
+works for K to 3 free it's K 2 to 3 then
+ 
+
+ align:start position:0%
+works for K to 3 free it's K 2 to 3 then
+it's also K to 3 free K 2 for free here
+
+ align:start position:0%
+it's also K to 3 free K 2 for free here
+ 
+
+ align:start position:0%
+it's also K to 3 free K 2 for free here
+likewise this is also K 3 for free ok so
+
+ align:start position:0%
+likewise this is also K 3 for free ok so
+ 
+
+ align:start position:0%
+likewise this is also K 3 for free ok so
+now what about higher KS T's and you
+
+ align:start position:0%
+now what about higher KS T's and you
+ 
+
+ align:start position:0%
+now what about higher KS T's and you
+might think well let's take these
+
+ align:start position:0%
+might think well let's take these
+ 
+
+ align:start position:0%
+might think well let's take these
+geometric objects and try to extend them
+
+ align:start position:0%
+geometric objects and try to extend them
+ 
+
+ align:start position:0%
+geometric objects and try to extend them
+further but that actually seems kind of
+
+ align:start position:0%
+further but that actually seems kind of
+ 
+
+ align:start position:0%
+further but that actually seems kind of
+difficult we do not really know how to
+
+ align:start position:0%
+difficult we do not really know how to
+ 
+
+ align:start position:0%
+difficult we do not really know how to
+do it we do not know how to obtain a
+
+ align:start position:0%
+do it we do not know how to obtain a
+ 
+
+ align:start position:0%
+do it we do not know how to obtain a
+construction which is of this form that
+
+ align:start position:0%
+construction which is of this form that
+ 
+
+ align:start position:0%
+construction which is of this form that
+works for K 4
+
+ align:start position:0%
+works for K 4
+ 
+
+ align:start position:0%
+works for K 4
+in fact there even some evidence that
+
+ align:start position:0%
+in fact there even some evidence that
+ 
+
+ align:start position:0%
+in fact there even some evidence that
+that might be impossible as I mentioned
+
+ align:start position:0%
+that might be impossible as I mentioned
+ 
+
+ align:start position:0%
+that might be impossible as I mentioned
+k4 4 is a major open problem it has an
+
+ align:start position:0%
+k4 4 is a major open problem it has an
+ 
+
+ align:start position:0%
+k4 4 is a major open problem it has an
+open problem to determine the order of
+
+ align:start position:0%
+open problem to determine the order of
+ 
+
+ align:start position:0%
+open problem to determine the order of
+the extremal number of k4 for playing
+
+ align:start position:0%
+the extremal number of k4 for playing
+ 
+
+ align:start position:0%
+the extremal number of k4 for playing
+any case this construction this idea of
+
+ align:start position:0%
+any case this construction this idea of
+ 
+
+ align:start position:0%
+any case this construction this idea of
+using algebraic constructions is very
+
+ align:start position:0%
+using algebraic constructions is very
+ 
+
+ align:start position:0%
+using algebraic constructions is very
+enlightening that we should look at ways
+
+ align:start position:0%
+enlightening that we should look at ways
+ 
+
+ align:start position:0%
+enlightening that we should look at ways
+to get large KST free graphs by coming
+
+ align:start position:0%
+to get large KST free graphs by coming
+ 
+
+ align:start position:0%
+to get large KST free graphs by coming
+up with clever algebraic constructions
+
+ align:start position:0%
+up with clever algebraic constructions
+ 
+
+ align:start position:0%
+up with clever algebraic constructions
+and next time I will show you a couple
+
+ align:start position:0%
+and next time I will show you a couple
+ 
+
+ align:start position:0%
+and next time I will show you a couple
+of very nice ideas where you can get you
+
+ align:start position:0%
+of very nice ideas where you can get you
+ 
+
+ align:start position:0%
+of very nice ideas where you can get you
+can come up with a different kind of
+
+ align:start position:0%
+can come up with a different kind of
+ 
+
+ align:start position:0%
+can come up with a different kind of
+algebraic construction which has some
+
+ align:start position:0%
+algebraic construction which has some
+ 
+
+ align:start position:0%
+algebraic construction which has some
+superficial similarities to what we've
+
+ align:start position:0%
+superficial similarities to what we've
+ 
+
+ align:start position:0%
+superficial similarities to what we've
+seen today but that's really of a
+
+ align:start position:0%
+seen today but that's really of a
+ 
+
+ align:start position:0%
+seen today but that's really of a
+different nature so next time we will
+
+ align:start position:0%
+different nature so next time we will
+ 
+
+ align:start position:0%
+different nature so next time we will
+see the following theorem which is
+
+ align:start position:0%
+see the following theorem which is
+ 
+
+ align:start position:0%
+see the following theorem which is
+obtain a sequence of two papers Union of
+
+ align:start position:0%
+obtain a sequence of two papers Union of
+ 
+
+ align:start position:0%
+obtain a sequence of two papers Union of
+authors along colar Brownian double that
+
+ align:start position:0%
+authors along colar Brownian double that
+ 
+
+ align:start position:0%
+authors along colar Brownian double that
+shows that if P is much larger than s so
+
+ align:start position:0%
+shows that if P is much larger than s so
+ 
+
+ align:start position:0%
+shows that if P is much larger than s so
+s minus 1 factorial plus 1 then
+
+ align:start position:0%
+s minus 1 factorial plus 1 then
+ 
+
+ align:start position:0%
+s minus 1 factorial plus 1 then
+the extremal number for KST is on the
+
+ align:start position:0%
+the extremal number for KST is on the
+ 
+
+ align:start position:0%
+the extremal number for KST is on the
+same order as the upper bound determined
+
+ align:start position:0%
+same order as the upper bound determined
+ 
+
+ align:start position:0%
+same order as the upper bound determined
+in the cavalry shows Turin theorem just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to be more explicit about what this s
+
+ align:start position:0%
+to be more explicit about what this s
+ 
+
+ align:start position:0%
+to be more explicit about what this s
+and P are if you plug in what's the
+
+ align:start position:0%
+and P are if you plug in what's the
+ 
+
+ align:start position:0%
+and P are if you plug in what's the
+smallest T that this theorem gives for
+
+ align:start position:0%
+smallest T that this theorem gives for
+ 
+
+ align:start position:0%
+smallest T that this theorem gives for
+various values of s find 2 2 & 3 3 and
+
+ align:start position:0%
+various values of s find 2 2 & 3 3 and
+ 
+
+ align:start position:0%
+various values of s find 2 2 & 3 3 and
+the next one is 4 7 and then it gets
+
+ align:start position:0%
+the next one is 4 7 and then it gets
+ 
+
+ align:start position:0%
+the next one is 4 7 and then it gets
+worse from there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these constructions are based on I
+
+ align:start position:0%
+so these constructions are based on I
+ 
+
+ align:start position:0%
+so these constructions are based on I
+mean there are algebraic instructions
+
+ align:start position:0%
+mean there are algebraic instructions
+ 
+
+ align:start position:0%
+mean there are algebraic instructions
+and so we'll see you next time
\ No newline at end of file
diff --git a/h_LNDKRZ_EI.txt b/h_LNDKRZ_EI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0fd944ba9924b959f3353241ed33144bb5d9d40d
--- /dev/null
+++ b/h_LNDKRZ_EI.txt
@@ -0,0 +1,1920 @@
+align:start position:0%
+ 
+Next we have uh someone very famous. I'm
+
+ align:start position:0%
+Next we have uh someone very famous. I'm
+ 
+
+ align:start position:0%
+Next we have uh someone very famous. I'm
+going to talk him up. He's my former
+
+ align:start position:0%
+going to talk him up. He's my former
+ 
+
+ align:start position:0%
+going to talk him up. He's my former
+boss egg and he's going to present on
+
+ align:start position:0%
+boss egg and he's going to present on
+ 
+
+ align:start position:0%
+boss egg and he's going to present on
+Penn South.
+
+ align:start position:0%
+Penn South.
+ 
+
+ align:start position:0%
+Penn South.
+>> Thank you. I've got a lapel also. Thank
+
+ align:start position:0%
+>> Thank you. I've got a lapel also. Thank
+ 
+
+ align:start position:0%
+>> Thank you. I've got a lapel also. Thank
+you, Nick. And as a matter of fact, Nick
+
+ align:start position:0%
+you, Nick. And as a matter of fact, Nick
+ 
+
+ align:start position:0%
+you, Nick. And as a matter of fact, Nick
+will probably uh recognize some of the
+
+ align:start position:0%
+will probably uh recognize some of the
+ 
+
+ align:start position:0%
+will probably uh recognize some of the
+beginning of my presentation here
+
+ align:start position:0%
+beginning of my presentation here
+ 
+
+ align:start position:0%
+beginning of my presentation here
+because he was involved in one of the
+
+ align:start position:0%
+because he was involved in one of the
+ 
+
+ align:start position:0%
+because he was involved in one of the
+first presentations we did on the Penn
+
+ align:start position:0%
+first presentations we did on the Penn
+ 
+
+ align:start position:0%
+first presentations we did on the Penn
+South community. As a matter of fact,
+
+ align:start position:0%
+South community. As a matter of fact,
+ 
+
+ align:start position:0%
+South community. As a matter of fact,
+was involved in the design and did some
+
+ align:start position:0%
+was involved in the design and did some
+ 
+
+ align:start position:0%
+was involved in the design and did some
+of this 3D modeling. And uh I got to
+
+ align:start position:0%
+of this 3D modeling. And uh I got to
+ 
+
+ align:start position:0%
+of this 3D modeling. And uh I got to
+drop back just a little bit. Um both
+
+ align:start position:0%
+drop back just a little bit. Um both
+ 
+
+ align:start position:0%
+drop back just a little bit. Um both
+Carrie who was on remotely
+
+ align:start position:0%
+Carrie who was on remotely
+ 
+
+ align:start position:0%
+Carrie who was on remotely
+uh Carrie first of all sits on the IATMO
+
+ align:start position:0%
+uh Carrie first of all sits on the IATMO
+ 
+
+ align:start position:0%
+uh Carrie first of all sits on the IATMO
+uniform mechanical code technical
+
+ align:start position:0%
+uniform mechanical code technical
+ 
+
+ align:start position:0%
+uniform mechanical code technical
+committee. In other words, we write
+
+ align:start position:0%
+committee. In other words, we write
+ 
+
+ align:start position:0%
+committee. In other words, we write
+approve and submit the final codes and
+
+ align:start position:0%
+approve and submit the final codes and
+ 
+
+ align:start position:0%
+approve and submit the final codes and
+there is a a geothermal code as of 2024
+
+ align:start position:0%
+there is a a geothermal code as of 2024
+ 
+
+ align:start position:0%
+there is a a geothermal code as of 2024
+and as of 2027 there will be a thermal
+
+ align:start position:0%
+and as of 2027 there will be a thermal
+ 
+
+ align:start position:0%
+and as of 2027 there will be a thermal
+energy network code. Interestingly
+
+ align:start position:0%
+energy network code. Interestingly
+ 
+
+ align:start position:0%
+energy network code. Interestingly
+enough, Mark Mezner C448 is a basis that
+
+ align:start position:0%
+enough, Mark Mezner C448 is a basis that
+ 
+
+ align:start position:0%
+enough, Mark Mezner C448 is a basis that
+we use for a design. So, a lot of that
+
+ align:start position:0%
+we use for a design. So, a lot of that
+ 
+
+ align:start position:0%
+we use for a design. So, a lot of that
+is being adopted perhaps uh completely.
+
+ align:start position:0%
+is being adopted perhaps uh completely.
+ 
+
+ align:start position:0%
+is being adopted perhaps uh completely.
+So, we have so many players in here and
+
+ align:start position:0%
+So, we have so many players in here and
+ 
+
+ align:start position:0%
+So, we have so many players in here and
+I can honestly say everybody in here has
+
+ align:start position:0%
+I can honestly say everybody in here has
+ 
+
+ align:start position:0%
+I can honestly say everybody in here has
+had a great deal to do with what we're
+
+ align:start position:0%
+had a great deal to do with what we're
+ 
+
+ align:start position:0%
+had a great deal to do with what we're
+going to talk about now. Uh now, first
+
+ align:start position:0%
+going to talk about now. Uh now, first
+ 
+
+ align:start position:0%
+going to talk about now. Uh now, first
+of all, this is part of uh pawn
+
+ align:start position:0%
+of all, this is part of uh pawn
+ 
+
+ align:start position:0%
+of all, this is part of uh pawn
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+NAERTA. That's a public opportunity
+
+ align:start position:0%
+NAERTA. That's a public opportunity
+ 
+
+ align:start position:0%
+NAERTA. That's a public opportunity
+notice. Now, what they do is they put
+
+ align:start position:0%
+notice. Now, what they do is they put
+ 
+
+ align:start position:0%
+notice. Now, what they do is they put
+out put these things out and they say,
+
+ align:start position:0%
+out put these things out and they say,
+ 
+
+ align:start position:0%
+out put these things out and they say,
+"We got a problem. Can you come up with
+
+ align:start position:0%
+"We got a problem. Can you come up with
+ 
+
+ align:start position:0%
+"We got a problem. Can you come up with
+a solution?" And if we come up with a
+
+ align:start position:0%
+a solution?" And if we come up with a
+ 
+
+ align:start position:0%
+a solution?" And if we come up with a
+good solution or a problem to fit a
+
+ align:start position:0%
+good solution or a problem to fit a
+ 
+
+ align:start position:0%
+good solution or a problem to fit a
+solution and this was for thermal energy
+
+ align:start position:0%
+solution and this was for thermal energy
+ 
+
+ align:start position:0%
+solution and this was for thermal energy
+networks, they award us funding for
+
+ align:start position:0%
+networks, they award us funding for
+ 
+
+ align:start position:0%
+networks, they award us funding for
+this. So, uh, this one started in 2021.
+
+ align:start position:0%
+this. So, uh, this one started in 2021.
+ 
+
+ align:start position:0%
+this. So, uh, this one started in 2021.
+Actually, Penn South hired Egg Geo
+
+ align:start position:0%
+Actually, Penn South hired Egg Geo
+ 
+
+ align:start position:0%
+Actually, Penn South hired Egg Geo
+before that because they wanted to
+
+ align:start position:0%
+before that because they wanted to
+ 
+
+ align:start position:0%
+before that because they wanted to
+convert their campus to um geothermal.
+
+ align:start position:0%
+convert their campus to um geothermal.
+ 
+
+ align:start position:0%
+convert their campus to um geothermal.
+And the reason why is because they had,
+
+ align:start position:0%
+And the reason why is because they had,
+ 
+
+ align:start position:0%
+And the reason why is because they had,
+let me jump back and make sure I didn't
+
+ align:start position:0%
+let me jump back and make sure I didn't
+ 
+
+ align:start position:0%
+let me jump back and make sure I didn't
+Yeah, it'll cover it in a minute. They
+
+ align:start position:0%
+Yeah, it'll cover it in a minute. They
+ 
+
+ align:start position:0%
+Yeah, it'll cover it in a minute. They
+had this 5 megawatt boiler and in
+
+ align:start position:0%
+had this 5 megawatt boiler and in
+ 
+
+ align:start position:0%
+had this 5 megawatt boiler and in
+addition to that, they generate their
+
+ align:start position:0%
+addition to that, they generate their
+ 
+
+ align:start position:0%
+addition to that, they generate their
+own electricity. And so local law uh 91
+
+ align:start position:0%
+own electricity. And so local law uh 91
+ 
+
+ align:start position:0%
+own electricity. And so local law uh 91
+told them if they didn't fix their
+
+ align:start position:0%
+told them if they didn't fix their
+ 
+
+ align:start position:0%
+told them if they didn't fix their
+carbon emissions by xy year, which keeps
+
+ align:start position:0%
+carbon emissions by xy year, which keeps
+ 
+
+ align:start position:0%
+carbon emissions by xy year, which keeps
+getting extended, they would get fined
+
+ align:start position:0%
+getting extended, they would get fined
+ 
+
+ align:start position:0%
+getting extended, they would get fined
+millions of dollars a year. So New York
+
+ align:start position:0%
+millions of dollars a year. So New York
+ 
+
+ align:start position:0%
+millions of dollars a year. So New York
+City is one of those cities that you you
+
+ align:start position:0%
+City is one of those cities that you you
+ 
+
+ align:start position:0%
+City is one of those cities that you you
+hear about the carrot, you know, the way
+
+ align:start position:0%
+hear about the carrot, you know, the way
+ 
+
+ align:start position:0%
+hear about the carrot, you know, the way
+to get people to do things. They've got
+
+ align:start position:0%
+to get people to do things. They've got
+ 
+
+ align:start position:0%
+to get people to do things. They've got
+the stick. If you have too many carbon
+
+ align:start position:0%
+the stick. If you have too many carbon
+ 
+
+ align:start position:0%
+the stick. If you have too many carbon
+emissions, you will get fined millions
+
+ align:start position:0%
+emissions, you will get fined millions
+ 
+
+ align:start position:0%
+emissions, you will get fined millions
+of dollars a year. So they hired us.
+
+ align:start position:0%
+of dollars a year. So they hired us.
+ 
+
+ align:start position:0%
+of dollars a year. So they hired us.
+They're pretty affluent. uh community,
+
+ align:start position:0%
+They're pretty affluent. uh community,
+ 
+
+ align:start position:0%
+They're pretty affluent. uh community,
+152tory buildings covering five blocks
+
+ align:start position:0%
+152tory buildings covering five blocks
+ 
+
+ align:start position:0%
+152tory buildings covering five blocks
+in downtown Manhattan, home to 2500
+
+ align:start position:0%
+in downtown Manhattan, home to 2500
+ 
+
+ align:start position:0%
+in downtown Manhattan, home to 2500
+families. And they have an 18,800 ton
+
+ align:start position:0%
+families. And they have an 18,800 ton
+ 
+
+ align:start position:0%
+families. And they have an 18,800 ton
+central chiller plant. You can see the
+
+ align:start position:0%
+central chiller plant. You can see the
+ 
+
+ align:start position:0%
+central chiller plant. You can see the
+cooling tower there and a 5 megawatt
+
+ align:start position:0%
+cooling tower there and a 5 megawatt
+ 
+
+ align:start position:0%
+cooling tower there and a 5 megawatt
+central boiler. And sorry about the
+
+ align:start position:0%
+central boiler. And sorry about the
+ 
+
+ align:start position:0%
+central boiler. And sorry about the
+overlap here that happens sometimes in
+
+ align:start position:0%
+overlap here that happens sometimes in
+ 
+
+ align:start position:0%
+overlap here that happens sometimes in
+these, so just look through it. Um,
+
+ align:start position:0%
+these, so just look through it. Um,
+ 
+
+ align:start position:0%
+these, so just look through it. Um,
+local law 38, local law 97. I won't go
+
+ align:start position:0%
+local law 38, local law 97. I won't go
+ 
+
+ align:start position:0%
+local law 38, local law 97. I won't go
+into the details of it, but they needed
+
+ align:start position:0%
+into the details of it, but they needed
+ 
+
+ align:start position:0%
+into the details of it, but they needed
+to get compliant on these. So, they
+
+ align:start position:0%
+to get compliant on these. So, they
+ 
+
+ align:start position:0%
+to get compliant on these. So, they
+hired us and then Nick, when Nick was
+
+ align:start position:0%
+hired us and then Nick, when Nick was
+ 
+
+ align:start position:0%
+hired us and then Nick, when Nick was
+working with us, we put in an
+
+ align:start position:0%
+working with us, we put in an
+ 
+
+ align:start position:0%
+working with us, we put in an
+application for this pond and we were
+
+ align:start position:0%
+application for this pond and we were
+ 
+
+ align:start position:0%
+application for this pond and we were
+awarded this pawn. So, we began to study
+
+ align:start position:0%
+awarded this pawn. So, we began to study
+ 
+
+ align:start position:0%
+awarded this pawn. So, we began to study
+how we could take this community off of
+
+ align:start position:0%
+how we could take this community off of
+ 
+
+ align:start position:0%
+how we could take this community off of
+these boilers and stop the emissions.
+
+ align:start position:0%
+these boilers and stop the emissions.
+ 
+
+ align:start position:0%
+these boilers and stop the emissions.
+There is a New York City tool and I keep
+
+ align:start position:0%
+There is a New York City tool and I keep
+ 
+
+ align:start position:0%
+There is a New York City tool and I keep
+hearing about this with regard to bore
+
+ align:start position:0%
+hearing about this with regard to bore
+ 
+
+ align:start position:0%
+hearing about this with regard to bore
+holes and Brock, you probably know this.
+
+ align:start position:0%
+holes and Brock, you probably know this.
+ 
+
+ align:start position:0%
+holes and Brock, you probably know this.
+You can go on to a tool online and if
+
+ align:start position:0%
+You can go on to a tool online and if
+ 
+
+ align:start position:0%
+You can go on to a tool online and if
+you were to look at the details on these
+
+ align:start position:0%
+you were to look at the details on these
+ 
+
+ align:start position:0%
+you were to look at the details on these
+graphs on the right, it shows you how
+
+ align:start position:0%
+graphs on the right, it shows you how
+ 
+
+ align:start position:0%
+graphs on the right, it shows you how
+many bore holes you need to drill, what
+
+ align:start position:0%
+many bore holes you need to drill, what
+ 
+
+ align:start position:0%
+many bore holes you need to drill, what
+the thermal capacity is under the
+
+ align:start position:0%
+the thermal capacity is under the
+ 
+
+ align:start position:0%
+the thermal capacity is under the
+footprint of that to do a closed loop
+
+ align:start position:0%
+footprint of that to do a closed loop
+ 
+
+ align:start position:0%
+footprint of that to do a closed loop
+system. So, the first thing we did is
+
+ align:start position:0%
+system. So, the first thing we did is
+ 
+
+ align:start position:0%
+system. So, the first thing we did is
+studied that and we got the entire uh
+
+ align:start position:0%
+studied that and we got the entire uh
+ 
+
+ align:start position:0%
+studied that and we got the entire uh
+community involved with that. But then
+
+ align:start position:0%
+community involved with that. But then
+ 
+
+ align:start position:0%
+community involved with that. But then
+we really started looking at this and
+
+ align:start position:0%
+we really started looking at this and
+ 
+
+ align:start position:0%
+we really started looking at this and
+this was not easy. This alone took Nick,
+
+ align:start position:0%
+this was not easy. This alone took Nick,
+ 
+
+ align:start position:0%
+this was not easy. This alone took Nick,
+our operations manager, Justin, uh
+
+ align:start position:0%
+our operations manager, Justin, uh
+ 
+
+ align:start position:0%
+our operations manager, Justin, uh
+myself, my wife used to work with us as
+
+ align:start position:0%
+myself, my wife used to work with us as
+ 
+
+ align:start position:0%
+myself, my wife used to work with us as
+our marketing director, and it we put on
+
+ align:start position:0%
+our marketing director, and it we put on
+ 
+
+ align:start position:0%
+our marketing director, and it we put on
+our combat boots and we went out and we
+
+ align:start position:0%
+our combat boots and we went out and we
+ 
+
+ align:start position:0%
+our combat boots and we went out and we
+beat on doors because we wanted to find
+
+ align:start position:0%
+beat on doors because we wanted to find
+ 
+
+ align:start position:0%
+beat on doors because we wanted to find
+out where to get the energy to do that 5
+
+ align:start position:0%
+out where to get the energy to do that 5
+ 
+
+ align:start position:0%
+out where to get the energy to do that 5
+megawatt load. Well, as it turns out,
+
+ align:start position:0%
+megawatt load. Well, as it turns out,
+ 
+
+ align:start position:0%
+megawatt load. Well, as it turns out,
+this is the US Postal Service across the
+
+ align:start position:0%
+this is the US Postal Service across the
+ 
+
+ align:start position:0%
+this is the US Postal Service across the
+street and we worked with uh couple of
+
+ align:start position:0%
+street and we worked with uh couple of
+ 
+
+ align:start position:0%
+street and we worked with uh couple of
+the um well with first we tried to get
+
+ align:start position:0%
+the um well with first we tried to get
+ 
+
+ align:start position:0%
+the um well with first we tried to get
+with the federal government and then we
+
+ align:start position:0%
+with the federal government and then we
+ 
+
+ align:start position:0%
+with the federal government and then we
+found out we could use a local property
+
+ align:start position:0%
+found out we could use a local property
+ 
+
+ align:start position:0%
+found out we could use a local property
+management company but we got the data
+
+ align:start position:0%
+management company but we got the data
+ 
+
+ align:start position:0%
+management company but we got the data
+on it and they have about 8 megawatts of
+
+ align:start position:0%
+on it and they have about 8 megawatts of
+ 
+
+ align:start position:0%
+on it and they have about 8 megawatts of
+thermal rejection through their cooling
+
+ align:start position:0%
+thermal rejection through their cooling
+ 
+
+ align:start position:0%
+thermal rejection through their cooling
+towers. So we said, "Aha, there may and
+
+ align:start position:0%
+towers. So we said, "Aha, there may and
+ 
+
+ align:start position:0%
+towers. So we said, "Aha, there may and
+it's they have data centers and
+
+ align:start position:0%
+it's they have data centers and
+ 
+
+ align:start position:0%
+it's they have data centers and
+equipment. So they may have it all year
+
+ align:start position:0%
+equipment. So they may have it all year
+ 
+
+ align:start position:0%
+equipment. So they may have it all year
+round." And this particular center uses
+
+ align:start position:0%
+round." And this particular center uses
+ 
+
+ align:start position:0%
+round." And this particular center uses
+this orange building. This is the um
+
+ align:start position:0%
+this orange building. This is the um
+ 
+
+ align:start position:0%
+this orange building. This is the um
+this is the physical plant, the chiller
+
+ align:start position:0%
+this is the physical plant, the chiller
+ 
+
+ align:start position:0%
+this is the physical plant, the chiller
+plant and heating where it provides all
+
+ align:start position:0%
+plant and heating where it provides all
+ 
+
+ align:start position:0%
+plant and heating where it provides all
+the heating for all these buildings. And
+
+ align:start position:0%
+the heating for all these buildings. And
+ 
+
+ align:start position:0%
+the heating for all these buildings. And
+we said, well, if we could get this
+
+ align:start position:0%
+we said, well, if we could get this
+ 
+
+ align:start position:0%
+we said, well, if we could get this
+energy over here, we could maybe even do
+
+ align:start position:0%
+energy over here, we could maybe even do
+ 
+
+ align:start position:0%
+energy over here, we could maybe even do
+the whole thing without a single bore
+
+ align:start position:0%
+the whole thing without a single bore
+ 
+
+ align:start position:0%
+the whole thing without a single bore
+hole. And kind of like what Carrie said
+
+ align:start position:0%
+hole. And kind of like what Carrie said
+ 
+
+ align:start position:0%
+hole. And kind of like what Carrie said
+earlier, you know, that's the whole
+
+ align:start position:0%
+earlier, you know, that's the whole
+ 
+
+ align:start position:0%
+earlier, you know, that's the whole
+point of this. So, we said, "Yeah, let's
+
+ align:start position:0%
+point of this. So, we said, "Yeah, let's
+ 
+
+ align:start position:0%
+point of this. So, we said, "Yeah, let's
+go ahead and look at that." And we went
+
+ align:start position:0%
+go ahead and look at that." And we went
+ 
+
+ align:start position:0%
+go ahead and look at that." And we went
+forward with that. And then we start put
+
+ align:start position:0%
+forward with that. And then we start put
+ 
+
+ align:start position:0%
+forward with that. And then we start put
+on our combat boots and we went out and
+
+ align:start position:0%
+on our combat boots and we went out and
+ 
+
+ align:start position:0%
+on our combat boots and we went out and
+we talked to the State University of New
+
+ align:start position:0%
+we talked to the State University of New
+ 
+
+ align:start position:0%
+we talked to the State University of New
+York. We talked to the public school
+
+ align:start position:0%
+York. We talked to the public school
+ 
+
+ align:start position:0%
+York. We talked to the public school
+over here. We've even got Penn Station
+
+ align:start position:0%
+over here. We've even got Penn Station
+ 
+
+ align:start position:0%
+over here. We've even got Penn Station
+involved now. We're almost all the way
+
+ align:start position:0%
+involved now. We're almost all the way
+ 
+
+ align:start position:0%
+involved now. We're almost all the way
+to uh to the to the Hudson River at this
+
+ align:start position:0%
+to uh to the to the Hudson River at this
+ 
+
+ align:start position:0%
+to uh to the to the Hudson River at this
+point. We may even be able to tap into
+
+ align:start position:0%
+point. We may even be able to tap into
+ 
+
+ align:start position:0%
+point. We may even be able to tap into
+that by the time we're done. At any
+
+ align:start position:0%
+that by the time we're done. At any
+ 
+
+ align:start position:0%
+that by the time we're done. At any
+rate, we went to work on this and uh one
+
+ align:start position:0%
+rate, we went to work on this and uh one
+ 
+
+ align:start position:0%
+rate, we went to work on this and uh one
+of the things you'll you'll know and
+
+ align:start position:0%
+of the things you'll you'll know and
+ 
+
+ align:start position:0%
+of the things you'll you'll know and
+this is the biggest concern we always
+
+ align:start position:0%
+this is the biggest concern we always
+ 
+
+ align:start position:0%
+this is the biggest concern we always
+hear about to go underneath the streets
+
+ align:start position:0%
+hear about to go underneath the streets
+ 
+
+ align:start position:0%
+hear about to go underneath the streets
+of New York is a freaking nightmare.
+
+ align:start position:0%
+of New York is a freaking nightmare.
+ 
+
+ align:start position:0%
+of New York is a freaking nightmare.
+This this when when Nick was there when
+
+ align:start position:0%
+This this when when Nick was there when
+ 
+
+ align:start position:0%
+This this when when Nick was there when
+we presented to KED because KED did a
+
+ align:start position:0%
+we presented to KED because KED did a
+ 
+
+ align:start position:0%
+we presented to KED because KED did a
+lot like Eversource did here. They were
+
+ align:start position:0%
+lot like Eversource did here. They were
+ 
+
+ align:start position:0%
+lot like Eversource did here. They were
+directed by the PSC to do these thermal
+
+ align:start position:0%
+directed by the PSC to do these thermal
+ 
+
+ align:start position:0%
+directed by the PSC to do these thermal
+energy networks. Well, you want to take
+
+ align:start position:0%
+energy networks. Well, you want to take
+ 
+
+ align:start position:0%
+energy networks. Well, you want to take
+any kind of a guess how much this is
+
+ align:start position:0%
+any kind of a guess how much this is
+ 
+
+ align:start position:0%
+any kind of a guess how much this is
+going to cost? Try almost a quarter
+
+ align:start position:0%
+going to cost? Try almost a quarter
+ 
+
+ align:start position:0%
+going to cost? Try almost a quarter
+billion dollars. Okay. So, we went to
+
+ align:start position:0%
+billion dollars. Okay. So, we went to
+ 
+
+ align:start position:0%
+billion dollars. Okay. So, we went to
+Coned and they said if you can get it
+
+ align:start position:0%
+Coned and they said if you can get it
+ 
+
+ align:start position:0%
+Coned and they said if you can get it
+down to 90 million, you can have it. We
+
+ align:start position:0%
+down to 90 million, you can have it. We
+ 
+
+ align:start position:0%
+down to 90 million, you can have it. We
+walked because we weren't going to go
+
+ align:start position:0%
+walked because we weren't going to go
+ 
+
+ align:start position:0%
+walked because we weren't going to go
+cheap and we weren't done with our
+
+ align:start position:0%
+cheap and we weren't done with our
+ 
+
+ align:start position:0%
+cheap and we weren't done with our
+study. We just said no. And Penn South
+
+ align:start position:0%
+study. We just said no. And Penn South
+ 
+
+ align:start position:0%
+study. We just said no. And Penn South
+said we'll do whatever you want to. So,
+
+ align:start position:0%
+said we'll do whatever you want to. So,
+ 
+
+ align:start position:0%
+said we'll do whatever you want to. So,
+we walked and we're finding ways to
+
+ align:start position:0%
+we walked and we're finding ways to
+ 
+
+ align:start position:0%
+we walked and we're finding ways to
+reduce that cost now. Meanwhile, Coned's
+
+ align:start position:0%
+reduce that cost now. Meanwhile, Coned's
+ 
+
+ align:start position:0%
+reduce that cost now. Meanwhile, Coned's
+doing great work. I mean, Greg Mullis
+
+ align:start position:0%
+doing great work. I mean, Greg Mullis
+ 
+
+ align:start position:0%
+doing great work. I mean, Greg Mullis
+and the whole team over there. But we
+
+ align:start position:0%
+and the whole team over there. But we
+ 
+
+ align:start position:0%
+and the whole team over there. But we
+wanted to do this. And part of what a
+
+ align:start position:0%
+wanted to do this. And part of what a
+ 
+
+ align:start position:0%
+wanted to do this. And part of what a
+nice study does is this. This is very
+
+ align:start position:0%
+nice study does is this. This is very
+ 
+
+ align:start position:0%
+nice study does is this. This is very
+important. Nothing moves fast with
+
+ align:start position:0%
+important. Nothing moves fast with
+ 
+
+ align:start position:0%
+important. Nothing moves fast with
+government. You've heard that except I
+
+ align:start position:0%
+government. You've heard that except I
+ 
+
+ align:start position:0%
+government. You've heard that except I
+got to take it back with Eversource and
+
+ align:start position:0%
+got to take it back with Eversource and
+ 
+
+ align:start position:0%
+got to take it back with Eversource and
+heat. It just boom. Before I even knew
+
+ align:start position:0%
+heat. It just boom. Before I even knew
+ 
+
+ align:start position:0%
+heat. It just boom. Before I even knew
+what happened, it was done over here in
+
+ align:start position:0%
+what happened, it was done over here in
+ 
+
+ align:start position:0%
+what happened, it was done over here in
+Frammingham. I can't wait to see that a
+
+ align:start position:0%
+Frammingham. I can't wait to see that a
+ 
+
+ align:start position:0%
+Frammingham. I can't wait to see that a
+week from Saturday after the GR
+
+ align:start position:0%
+week from Saturday after the GR
+ 
+
+ align:start position:0%
+week from Saturday after the GR
+conference. But for us, we were just
+
+ align:start position:0%
+conference. But for us, we were just
+ 
+
+ align:start position:0%
+conference. But for us, we were just
+like, "No, we want to get through this."
+
+ align:start position:0%
+like, "No, we want to get through this."
+ 
+
+ align:start position:0%
+like, "No, we want to get through this."
+Plus, Sue Doherty over at Nightert is
+
+ align:start position:0%
+Plus, Sue Doherty over at Nightert is
+ 
+
+ align:start position:0%
+Plus, Sue Doherty over at Nightert is
+our project manager. And for every
+
+ align:start position:0%
+our project manager. And for every
+ 
+
+ align:start position:0%
+our project manager. And for every
+problem, they ask a hundred questions.
+
+ align:start position:0%
+problem, they ask a hundred questions.
+ 
+
+ align:start position:0%
+problem, they ask a hundred questions.
+They said, "Well, how are you going to
+
+ align:start position:0%
+They said, "Well, how are you going to
+ 
+
+ align:start position:0%
+They said, "Well, how are you going to
+deal with that? How?" Because they don't
+
+ align:start position:0%
+deal with that? How?" Because they don't
+ 
+
+ align:start position:0%
+deal with that? How?" Because they don't
+fund this so that somebody can get
+
+ align:start position:0%
+fund this so that somebody can get
+ 
+
+ align:start position:0%
+fund this so that somebody can get
+something for free. Why do you think
+
+ align:start position:0%
+something for free. Why do you think
+ 
+
+ align:start position:0%
+something for free. Why do you think
+they fund it? So we can clear a path for
+
+ align:start position:0%
+they fund it? So we can clear a path for
+ 
+
+ align:start position:0%
+they fund it? So we can clear a path for
+others to do it. And that's exactly what
+
+ align:start position:0%
+others to do it. And that's exactly what
+ 
+
+ align:start position:0%
+others to do it. And that's exactly what
+we're doing. So the amount of paperwork
+
+ align:start position:0%
+we're doing. So the amount of paperwork
+ 
+
+ align:start position:0%
+we're doing. So the amount of paperwork
+we do to tread the way for others to
+
+ align:start position:0%
+we do to tread the way for others to
+ 
+
+ align:start position:0%
+we do to tread the way for others to
+follow is monstrous. Our uh our hat hats
+
+ align:start position:0%
+follow is monstrous. Our uh our hat hats
+ 
+
+ align:start position:0%
+follow is monstrous. Our uh our hat hats
+off to our engineers and so forth. So we
+
+ align:start position:0%
+off to our engineers and so forth. So we
+ 
+
+ align:start position:0%
+off to our engineers and so forth. So we
+move forward. They did this is a
+
+ align:start position:0%
+move forward. They did this is a
+ 
+
+ align:start position:0%
+move forward. They did this is a
+actually from earlier this month. They
+
+ align:start position:0%
+actually from earlier this month. They
+ 
+
+ align:start position:0%
+actually from earlier this month. They
+turned in task five. We had to model it
+
+ align:start position:0%
+turned in task five. We had to model it
+ 
+
+ align:start position:0%
+turned in task five. We had to model it
+without
+
+ align:start position:0%
+without
+ 
+
+ align:start position:0%
+without
+the post office because what if the post
+
+ align:start position:0%
+the post office because what if the post
+ 
+
+ align:start position:0%
+the post office because what if the post
+office decides to move? they're just
+
+ align:start position:0%
+office decides to move? they're just
+ 
+
+ align:start position:0%
+office decides to move? they're just
+renting the building after all from and
+
+ align:start position:0%
+renting the building after all from and
+ 
+
+ align:start position:0%
+renting the building after all from and
+what if we don't have that 8 megawatt.
+
+ align:start position:0%
+what if we don't have that 8 megawatt.
+ 
+
+ align:start position:0%
+what if we don't have that 8 megawatt.
+So we really had to look at it's kind of
+
+ align:start position:0%
+So we really had to look at it's kind of
+ 
+
+ align:start position:0%
+So we really had to look at it's kind of
+like the backup boiler scenario. So our
+
+ align:start position:0%
+like the backup boiler scenario. So our
+ 
+
+ align:start position:0%
+like the backup boiler scenario. So our
+guys really started looking at it and
+
+ align:start position:0%
+guys really started looking at it and
+ 
+
+ align:start position:0%
+guys really started looking at it and
+they said, "Okay, here's where we can
+
+ align:start position:0%
+they said, "Okay, here's where we can
+ 
+
+ align:start position:0%
+they said, "Okay, here's where we can
+put the closed loop, but we'd have to do
+
+ align:start position:0%
+put the closed loop, but we'd have to do
+ 
+
+ align:start position:0%
+put the closed loop, but we'd have to do
+the advanced boring solution like they
+
+ align:start position:0%
+the advanced boring solution like they
+ 
+
+ align:start position:0%
+the advanced boring solution like they
+did in Frammingham." And so that's
+
+ align:start position:0%
+did in Frammingham." And so that's
+ 
+
+ align:start position:0%
+did in Frammingham." And so that's
+expensive. But we have other
+
+ align:start position:0%
+expensive. But we have other
+ 
+
+ align:start position:0%
+expensive. But we have other
+technologies and that involves aquafer
+
+ align:start position:0%
+technologies and that involves aquafer
+ 
+
+ align:start position:0%
+technologies and that involves aquafer
+coupled. And by the way, this particular
+
+ align:start position:0%
+coupled. And by the way, this particular
+ 
+
+ align:start position:0%
+coupled. And by the way, this particular
+part of Manhattan has a very robust
+
+ align:start position:0%
+part of Manhattan has a very robust
+ 
+
+ align:start position:0%
+part of Manhattan has a very robust
+glacial till aquifer. So we we checked
+
+ align:start position:0%
+glacial till aquifer. So we we checked
+ 
+
+ align:start position:0%
+glacial till aquifer. So we we checked
+that. We got involved with it. We looked
+
+ align:start position:0%
+that. We got involved with it. We looked
+ 
+
+ align:start position:0%
+that. We got involved with it. We looked
+at what's called invective flow. If
+
+ align:start position:0%
+at what's called invective flow. If
+ 
+
+ align:start position:0%
+at what's called invective flow. If
+you've listened to a lot of what we're
+
+ align:start position:0%
+you've listened to a lot of what we're
+ 
+
+ align:start position:0%
+you've listened to a lot of what we're
+talking about doing these flow studies
+
+ align:start position:0%
+talking about doing these flow studies
+ 
+
+ align:start position:0%
+talking about doing these flow studies
+shows how fast when we're extracting
+
+ align:start position:0%
+shows how fast when we're extracting
+ 
+
+ align:start position:0%
+shows how fast when we're extracting
+heat or rejecting heat, it can be
+
+ align:start position:0%
+heat or rejecting heat, it can be
+ 
+
+ align:start position:0%
+heat or rejecting heat, it can be
+restored. Plus, we have to show thermal
+
+ align:start position:0%
+restored. Plus, we have to show thermal
+ 
+
+ align:start position:0%
+restored. Plus, we have to show thermal
+influence to the neighboring properties
+
+ align:start position:0%
+influence to the neighboring properties
+ 
+
+ align:start position:0%
+influence to the neighboring properties
+because in New York, they want to know
+
+ align:start position:0%
+because in New York, they want to know
+ 
+
+ align:start position:0%
+because in New York, they want to know
+what you're doing to everybody's
+
+ align:start position:0%
+what you're doing to everybody's
+ 
+
+ align:start position:0%
+what you're doing to everybody's
+property. So each of these models as
+
+ align:start position:0%
+property. So each of these models as
+ 
+
+ align:start position:0%
+property. So each of these models as
+Nick will tell you or any scientist can
+
+ align:start position:0%
+Nick will tell you or any scientist can
+ 
+
+ align:start position:0%
+Nick will tell you or any scientist can
+take eight to 16 even 40 hours. But we
+
+ align:start position:0%
+take eight to 16 even 40 hours. But we
+ 
+
+ align:start position:0%
+take eight to 16 even 40 hours. But we
+get through this and we look at the
+
+ align:start position:0%
+get through this and we look at the
+ 
+
+ align:start position:0%
+get through this and we look at the
+bottom line is we get a thermal
+
+ align:start position:0%
+bottom line is we get a thermal
+ 
+
+ align:start position:0%
+bottom line is we get a thermal
+influence over 25 years. And I think
+
+ align:start position:0%
+influence over 25 years. And I think
+ 
+
+ align:start position:0%
+influence over 25 years. And I think
+that's the way we're going to go. We're
+
+ align:start position:0%
+that's the way we're going to go. We're
+ 
+
+ align:start position:0%
+that's the way we're going to go. We're
+going to go with uh four doulets and
+
+ align:start position:0%
+going to go with uh four doulets and
+ 
+
+ align:start position:0%
+going to go with uh four doulets and
+we're going to be able to handle the
+
+ align:start position:0%
+we're going to be able to handle the
+ 
+
+ align:start position:0%
+we're going to be able to handle the
+peak. We're still going to need some
+
+ align:start position:0%
+peak. We're still going to need some
+ 
+
+ align:start position:0%
+peak. We're still going to need some
+boilers and so forth, but this is um the
+
+ align:start position:0%
+boilers and so forth, but this is um the
+ 
+
+ align:start position:0%
+boilers and so forth, but this is um the
+Penn South Underground utilities. This
+
+ align:start position:0%
+Penn South Underground utilities. This
+ 
+
+ align:start position:0%
+Penn South Underground utilities. This
+is how it's going to be piped. Uh, and
+
+ align:start position:0%
+is how it's going to be piped. Uh, and
+ 
+
+ align:start position:0%
+is how it's going to be piped. Uh, and
+this is what it looks like. That you've
+
+ align:start position:0%
+this is what it looks like. That you've
+ 
+
+ align:start position:0%
+this is what it looks like. That you've
+heard a lot about from Carrie about um
+
+ align:start position:0%
+heard a lot about from Carrie about um
+ 
+
+ align:start position:0%
+heard a lot about from Carrie about um
+single. These are the singular loops and
+
+ align:start position:0%
+single. These are the singular loops and
+ 
+
+ align:start position:0%
+single. These are the singular loops and
+then there's a transportation loop where
+
+ align:start position:0%
+then there's a transportation loop where
+ 
+
+ align:start position:0%
+then there's a transportation loop where
+they can all as a matter of fact right
+
+ align:start position:0%
+they can all as a matter of fact right
+ 
+
+ align:start position:0%
+they can all as a matter of fact right
+here in Frammingham they have those two
+
+ align:start position:0%
+here in Frammingham they have those two
+ 
+
+ align:start position:0%
+here in Frammingham they have those two
+loops. They'll be able to shed or add
+
+ align:start position:0%
+loops. They'll be able to shed or add
+ 
+
+ align:start position:0%
+loops. They'll be able to shed or add
+load one to another. All of these
+
+ align:start position:0%
+load one to another. All of these
+ 
+
+ align:start position:0%
+load one to another. All of these
+individual loops here will be able to
+
+ align:start position:0%
+individual loops here will be able to
+ 
+
+ align:start position:0%
+individual loops here will be able to
+share energy with one another. And this
+
+ align:start position:0%
+share energy with one another. And this
+ 
+
+ align:start position:0%
+share energy with one another. And this
+is just a picture of the big what we
+
+ align:start position:0%
+is just a picture of the big what we
+ 
+
+ align:start position:0%
+is just a picture of the big what we
+call the transportation loop. What is it
+
+ align:start position:0%
+call the transportation loop. What is it
+ 
+
+ align:start position:0%
+call the transportation loop. What is it
+transporting? It's transporting energy.
+
+ align:start position:0%
+transporting? It's transporting energy.
+ 
+
+ align:start position:0%
+transporting? It's transporting energy.
+It's like
+
+ align:start position:0%
+It's like
+ 
+
+ align:start position:0%
+It's like
+it's like the grid when you take a big
+
+ align:start position:0%
+it's like the grid when you take a big
+ 
+
+ align:start position:0%
+it's like the grid when you take a big
+load from maybe in Texas they need extra
+
+ align:start position:0%
+load from maybe in Texas they need extra
+ 
+
+ align:start position:0%
+load from maybe in Texas they need extra
+electricity and you can get it from
+
+ align:start position:0%
+electricity and you can get it from
+ 
+
+ align:start position:0%
+electricity and you can get it from
+maybe Arizona or something like that in
+
+ align:start position:0%
+maybe Arizona or something like that in
+ 
+
+ align:start position:0%
+maybe Arizona or something like that in
+a much smaller way. That's the way it
+
+ align:start position:0%
+a much smaller way. That's the way it
+ 
+
+ align:start position:0%
+a much smaller way. That's the way it
+works. And that is my presentation.
+
+ align:start position:0%
+works. And that is my presentation.
+ 
+
+ align:start position:0%
+works. And that is my presentation.
+Thank you everybody.
\ No newline at end of file
diff --git a/hbBGpXBf3Ig.txt b/hbBGpXBf3Ig.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a3035606c2cc4784565f04f7a9164bc6460cef39
--- /dev/null
+++ b/hbBGpXBf3Ig.txt
@@ -0,0 +1,4747 @@
+align:start position:0%
+ 
+take it away
+
+ align:start position:0%
+take it away
+ 
+
+ align:start position:0%
+take it away
+great we would like a volunteer and we
+
+ align:start position:0%
+great we would like a volunteer and we
+ 
+
+ align:start position:0%
+great we would like a volunteer and we
+believe we have someone who is
+
+ align:start position:0%
+believe we have someone who is
+ 
+
+ align:start position:0%
+believe we have someone who is
+enthusiastically offered yep
+
+ align:start position:0%
+enthusiastically offered yep
+ 
+
+ align:start position:0%
+enthusiastically offered yep
+uh so we would prefer you not to look at
+
+ align:start position:0%
+uh so we would prefer you not to look at
+ 
+
+ align:start position:0%
+uh so we would prefer you not to look at
+the computer screen okay um and just
+
+ align:start position:0%
+the computer screen okay um and just
+ 
+
+ align:start position:0%
+the computer screen okay um and just
+stand uh
+
+ align:start position:0%
+stand uh
+ 
+
+ align:start position:0%
+stand uh
+yeah the audience would be great try not
+
+ align:start position:0%
+yeah the audience would be great try not
+ 
+
+ align:start position:0%
+yeah the audience would be great try not
+to disconnect the wire okay
+
+ align:start position:0%
+to disconnect the wire okay
+ 
+
+ align:start position:0%
+to disconnect the wire okay
+we apologize this is still very much a
+
+ align:start position:0%
+we apologize this is still very much a
+ 
+
+ align:start position:0%
+we apologize this is still very much a
+prototype i'm glad you picked rondo's
+
+ align:start position:0%
+prototype i'm glad you picked rondo's
+ 
+
+ align:start position:0%
+prototype i'm glad you picked rondo's
+these fit me better
+
+ align:start position:0%
+these fit me better
+ 
+
+ align:start position:0%
+these fit me better
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+um and this may take a moment to plug it
+
+ align:start position:0%
+um and this may take a moment to plug it
+ 
+
+ align:start position:0%
+um and this may take a moment to plug it
+in oh yes
+
+ align:start position:0%
+in oh yes
+ 
+
+ align:start position:0%
+in oh yes
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+um right so as you can tell um this game
+
+ align:start position:0%
+um right so as you can tell um this game
+ 
+
+ align:start position:0%
+um right so as you can tell um this game
+is meant to be played without any visual
+
+ align:start position:0%
+is meant to be played without any visual
+ 
+
+ align:start position:0%
+is meant to be played without any visual
+input in fact um
+
+ align:start position:0%
+input in fact um
+ 
+
+ align:start position:0%
+input in fact um
+do you hear this is the game view
+
+ align:start position:0%
+do you hear this is the game view
+ 
+
+ align:start position:0%
+do you hear this is the game view
+for those that aren't super familiar and
+
+ align:start position:0%
+for those that aren't super familiar and
+ 
+
+ align:start position:0%
+for those that aren't super familiar and
+this is our scene view because we wanted
+
+ align:start position:0%
+this is our scene view because we wanted
+ 
+
+ align:start position:0%
+this is our scene view because we wanted
+you to see what was going on
+
+ align:start position:0%
+you to see what was going on
+ 
+
+ align:start position:0%
+you to see what was going on
+yep so what the phone would show
+
+ align:start position:0%
+yep so what the phone would show
+ 
+
+ align:start position:0%
+yep so what the phone would show
+okay so wait just a moment
+
+ align:start position:0%
+okay so wait just a moment
+ 
+
+ align:start position:0%
+okay so wait just a moment
+uh you should be i'm gonna just check
+
+ align:start position:0%
+uh you should be i'm gonna just check
+ 
+
+ align:start position:0%
+uh you should be i'm gonna just check
+um hold on
+
+ align:start position:0%
+um hold on
+ 
+
+ align:start position:0%
+um hold on
+space forward okay great you're you're
+
+ align:start position:0%
+space forward okay great you're you're
+ 
+
+ align:start position:0%
+space forward okay great you're you're
+calibrated so i turned off the screen so
+
+ align:start position:0%
+calibrated so i turned off the screen so
+ 
+
+ align:start position:0%
+calibrated so i turned off the screen so
+you can see what uh
+
+ align:start position:0%
+you can see what uh
+ 
+
+ align:start position:0%
+you can see what uh
+our play tester is looking at well
+
+ align:start position:0%
+our play tester is looking at well
+ 
+
+ align:start position:0%
+our play tester is looking at well
+facing towards facing towards so yes so
+
+ align:start position:0%
+facing towards facing towards so yes so
+ 
+
+ align:start position:0%
+facing towards facing towards so yes so
+our play testers here's a hay over here
+
+ align:start position:0%
+our play testers here's a hay over here
+ 
+
+ align:start position:0%
+our play testers here's a hay over here
+in this game you move using a head tilt
+
+ align:start position:0%
+in this game you move using a head tilt
+ 
+
+ align:start position:0%
+in this game you move using a head tilt
+so you tilt your head forward or down to
+
+ align:start position:0%
+so you tilt your head forward or down to
+ 
+
+ align:start position:0%
+so you tilt your head forward or down to
+move forward
+
+ align:start position:0%
+move forward
+ 
+
+ align:start position:0%
+move forward
+you tilt your head backwards to move
+
+ align:start position:0%
+you tilt your head backwards to move
+ 
+
+ align:start position:0%
+you tilt your head backwards to move
+backwards
+
+ align:start position:0%
+backwards
+ 
+
+ align:start position:0%
+backwards
+and this is the player so the tl dot is
+
+ align:start position:0%
+and this is the player so the tl dot is
+ 
+
+ align:start position:0%
+and this is the player so the tl dot is
+the player and you can turn to face like
+
+ align:start position:0%
+the player and you can turn to face like
+ 
+
+ align:start position:0%
+the player and you can turn to face like
+the sound source and tilt your head down
+
+ align:start position:0%
+the sound source and tilt your head down
+ 
+
+ align:start position:0%
+the sound source and tilt your head down
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+move towards the sound source if you hit
+
+ align:start position:0%
+move towards the sound source if you hit
+ 
+
+ align:start position:0%
+move towards the sound source if you hit
+a wall you'll go bonk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we still have to work out the balances
+
+ align:start position:0%
+we still have to work out the balances
+ 
+
+ align:start position:0%
+we still have to work out the balances
+between all the sounds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+backwards tilt your head back yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is the over here spatialized uh yes
+
+ align:start position:0%
+is the over here spatialized uh yes
+ 
+
+ align:start position:0%
+is the over here spatialized uh yes
+right yes so behind me how do i go
+
+ align:start position:0%
+right yes so behind me how do i go
+ 
+
+ align:start position:0%
+right yes so behind me how do i go
+backwards uh tilt your head back oh i
+
+ align:start position:0%
+backwards uh tilt your head back oh i
+ 
+
+ align:start position:0%
+backwards uh tilt your head back oh i
+get it oh no not that way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i like the footsteps yes so um
+
+ align:start position:0%
+i like the footsteps yes so um
+ 
+
+ align:start position:0%
+i like the footsteps yes so um
+too far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's asking me what i'm doing
+
+ align:start position:0%
+it's asking me what i'm doing
+ 
+
+ align:start position:0%
+it's asking me what i'm doing
+what are you doing okay this is really
+
+ align:start position:0%
+what are you doing okay this is really
+ 
+
+ align:start position:0%
+what are you doing okay this is really
+hard all right congratulations you found
+
+ align:start position:0%
+hard all right congratulations you found
+ 
+
+ align:start position:0%
+hard all right congratulations you found
+the first one now there's another one
+
+ align:start position:0%
+the first one now there's another one
+ 
+
+ align:start position:0%
+the first one now there's another one
+marker
+
+ align:start position:0%
+marker
+ 
+
+ align:start position:0%
+marker
+oh great yeah so um someone else want to
+
+ align:start position:0%
+oh great yeah so um someone else want to
+ 
+
+ align:start position:0%
+oh great yeah so um someone else want to
+try oh keep going keep going for a
+
+ align:start position:0%
+try oh keep going keep going for a
+ 
+
+ align:start position:0%
+try oh keep going keep going for a
+little longer i'm going i'm doing
+
+ align:start position:0%
+little longer i'm going i'm doing
+ 
+
+ align:start position:0%
+little longer i'm going i'm doing
+something else now yeah you're gonna try
+
+ align:start position:0%
+something else now yeah you're gonna try
+ 
+
+ align:start position:0%
+something else now yeah you're gonna try
+to find the target again
+
+ align:start position:0%
+to find the target again
+ 
+
+ align:start position:0%
+to find the target again
+so this is actually our calibration
+
+ align:start position:0%
+so this is actually our calibration
+ 
+
+ align:start position:0%
+so this is actually our calibration
+level
+
+ align:start position:0%
+level
+ 
+
+ align:start position:0%
+level
+the calibration level is really useful
+
+ align:start position:0%
+the calibration level is really useful
+ 
+
+ align:start position:0%
+the calibration level is really useful
+for giving a frame of reference for
+
+ align:start position:0%
+for giving a frame of reference for
+ 
+
+ align:start position:0%
+for giving a frame of reference for
+distances and how far what the what the
+
+ align:start position:0%
+distances and how far what the what the
+ 
+
+ align:start position:0%
+distances and how far what the what the
+sound is and how it sounds further away
+
+ align:start position:0%
+sound is and how it sounds further away
+ 
+
+ align:start position:0%
+sound is and how it sounds further away
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah so
+
+ align:start position:0%
+yeah so
+ 
+
+ align:start position:0%
+yeah so
+maybe try
+
+ align:start position:0%
+maybe try
+ 
+
+ align:start position:0%
+maybe try
+find one more target and we can move to
+
+ align:start position:0%
+find one more target and we can move to
+ 
+
+ align:start position:0%
+find one more target and we can move to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+level
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is going on
+
+ align:start position:0%
+what is going on
+ 
+
+ align:start position:0%
+what is going on
+okay well
+
+ align:start position:0%
+okay well
+ 
+
+ align:start position:0%
+okay well
+that happens sometimes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no not too far too far
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i can tell it's over here but i don't
+
+ align:start position:0%
+i can tell it's over here but i don't
+ 
+
+ align:start position:0%
+i can tell it's over here but i don't
+know how to get there if you if you
+
+ align:start position:0%
+know how to get there if you if you
+ 
+
+ align:start position:0%
+know how to get there if you if you
+because the
+
+ align:start position:0%
+because the
+ 
+
+ align:start position:0%
+because the
+you can you can turn yourself by the way
+
+ align:start position:0%
+you can you can turn yourself by the way
+ 
+
+ align:start position:0%
+you can you can turn yourself by the way
+you can like rotate
+
+ align:start position:0%
+you can like rotate
+ 
+
+ align:start position:0%
+you can like rotate
+and like you will now face that right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it might be that the sound source is
+
+ align:start position:0%
+it might be that the sound source is
+ 
+
+ align:start position:0%
+it might be that the sound source is
+very close to a wall
+
+ align:start position:0%
+very close to a wall
+ 
+
+ align:start position:0%
+very close to a wall
+that's true
+
+ align:start position:0%
+that's true
+ 
+
+ align:start position:0%
+that's true
+yeah well we don't want to take up too
+
+ align:start position:0%
+yeah well we don't want to take up too
+ 
+
+ align:start position:0%
+yeah well we don't want to take up too
+much time for my presentation
+
+ align:start position:0%
+much time for my presentation
+ 
+
+ align:start position:0%
+much time for my presentation
+it no
+
+ align:start position:0%
+it no
+ 
+
+ align:start position:0%
+it no
+we anticipated people to have
+
+ align:start position:0%
+we anticipated people to have
+ 
+
+ align:start position:0%
+we anticipated people to have
+difficulties here do you want to take a
+
+ align:start position:0%
+difficulties here do you want to take a
+ 
+
+ align:start position:0%
+difficulties here do you want to take a
+look at what the what the game looks
+
+ align:start position:0%
+look at what the what the game looks
+ 
+
+ align:start position:0%
+look at what the what the game looks
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you're the teal player first one was
+
+ align:start position:0%
+so you're the teal player first one was
+ 
+
+ align:start position:0%
+so you're the teal player first one was
+here and then it moved up here
+
+ align:start position:0%
+here and then it moved up here
+ 
+
+ align:start position:0%
+here and then it moved up here
+and it went across here yeah oh it moves
+
+ align:start position:0%
+and it went across here yeah oh it moves
+ 
+
+ align:start position:0%
+and it went across here yeah oh it moves
+it did move
+
+ align:start position:0%
+it did move
+ 
+
+ align:start position:0%
+it did move
+surprise okay
+
+ align:start position:0%
+surprise okay
+ 
+
+ align:start position:0%
+surprise okay
+yeah um great and uh we actually want to
+
+ align:start position:0%
+yeah um great and uh we actually want to
+ 
+
+ align:start position:0%
+yeah um great and uh we actually want to
+showcase one more level this time i'll
+
+ align:start position:0%
+showcase one more level this time i'll
+ 
+
+ align:start position:0%
+showcase one more level this time i'll
+put it on put the glasses on because
+
+ align:start position:0%
+put it on put the glasses on because
+ 
+
+ align:start position:0%
+put it on put the glasses on because
+it's uh unless do you want to try it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nobody's very good at it by the way when
+
+ align:start position:0%
+nobody's very good at it by the way when
+ 
+
+ align:start position:0%
+nobody's very good at it by the way when
+they when they start out but people do
+
+ align:start position:0%
+they when they start out but people do
+ 
+
+ align:start position:0%
+they when they start out but people do
+get used to it yes um as
+
+ align:start position:0%
+get used to it yes um as
+ 
+
+ align:start position:0%
+get used to it yes um as
+oh i'm bonking into a wall fun times so
+
+ align:start position:0%
+oh i'm bonking into a wall fun times so
+ 
+
+ align:start position:0%
+oh i'm bonking into a wall fun times so
+we also want to showcase a little bit of
+
+ align:start position:0%
+we also want to showcase a little bit of
+ 
+
+ align:start position:0%
+we also want to showcase a little bit of
+level two
+
+ align:start position:0%
+level two
+ 
+
+ align:start position:0%
+level two
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+so you've had people go through this
+
+ align:start position:0%
+so you've had people go through this
+ 
+
+ align:start position:0%
+so you've had people go through this
+yes people yeah do they do they
+
+ align:start position:0%
+yes people yeah do they do they
+ 
+
+ align:start position:0%
+yes people yeah do they do they
+recognize the sound behind them versus
+
+ align:start position:0%
+recognize the sound behind them versus
+ 
+
+ align:start position:0%
+recognize the sound behind them versus
+in front of them okay
+
+ align:start position:0%
+in front of them okay
+ 
+
+ align:start position:0%
+in front of them okay
+so this is one of the points we're going
+
+ align:start position:0%
+so this is one of the points we're going
+ 
+
+ align:start position:0%
+so this is one of the points we're going
+to bring up before it's very difficult
+
+ align:start position:0%
+to bring up before it's very difficult
+ 
+
+ align:start position:0%
+to bring up before it's very difficult
+to tell in front or behind but as you
+
+ align:start position:0%
+to tell in front or behind but as you
+ 
+
+ align:start position:0%
+to tell in front or behind but as you
+move you can hear whether you're getting
+
+ align:start position:0%
+move you can hear whether you're getting
+ 
+
+ align:start position:0%
+move you can hear whether you're getting
+closer or further away okay is that done
+
+ align:start position:0%
+closer or further away okay is that done
+ 
+
+ align:start position:0%
+closer or further away okay is that done
+with louder or is that done with some
+
+ align:start position:0%
+with louder or is that done with some
+ 
+
+ align:start position:0%
+with louder or is that done with some
+other sound
+
+ align:start position:0%
+other sound
+ 
+
+ align:start position:0%
+other sound
+oh that's done right so we actually were
+
+ align:start position:0%
+oh that's done right so we actually were
+ 
+
+ align:start position:0%
+oh that's done right so we actually were
+wanting to do something where in when
+
+ align:start position:0%
+wanting to do something where in when
+ 
+
+ align:start position:0%
+wanting to do something where in when
+you're facing it it actually gets a
+
+ align:start position:0%
+you're facing it it actually gets a
+ 
+
+ align:start position:0%
+you're facing it it actually gets a
+little bit louder so you know you're
+
+ align:start position:0%
+little bit louder so you know you're
+ 
+
+ align:start position:0%
+little bit louder so you know you're
+looking in the correct direction
+
+ align:start position:0%
+looking in the correct direction
+ 
+
+ align:start position:0%
+looking in the correct direction
+right now that's not
+
+ align:start position:0%
+right now that's not
+ 
+
+ align:start position:0%
+right now that's not
+uh very dynamic
+
+ align:start position:0%
+uh very dynamic
+ 
+
+ align:start position:0%
+uh very dynamic
+yeah i'm having technical difficulties
+
+ align:start position:0%
+yeah i'm having technical difficulties
+ 
+
+ align:start position:0%
+yeah i'm having technical difficulties
+we'll show off level two later
+
+ align:start position:0%
+we'll show off level two later
+ 
+
+ align:start position:0%
+we'll show off level two later
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well it's it's we have a different
+
+ align:start position:0%
+well it's it's we have a different
+ 
+
+ align:start position:0%
+well it's it's we have a different
+roll-off but we're just using what was
+
+ align:start position:0%
+roll-off but we're just using what was
+ 
+
+ align:start position:0%
+roll-off but we're just using what was
+what unity afforded us
+
+ align:start position:0%
+what unity afforded us
+ 
+
+ align:start position:0%
+what unity afforded us
+unity plus bose ar so
+
+ align:start position:0%
+unity plus bose ar so
+ 
+
+ align:start position:0%
+unity plus bose ar so
+um as you noticed later on like you can
+
+ align:start position:0%
+um as you noticed later on like you can
+ 
+
+ align:start position:0%
+um as you noticed later on like you can
+turn yourself and then move right yes
+
+ align:start position:0%
+turn yourself and then move right yes
+ 
+
+ align:start position:0%
+turn yourself and then move right yes
+okay thank you all for being here this
+
+ align:start position:0%
+okay thank you all for being here this
+ 
+
+ align:start position:0%
+okay thank you all for being here this
+is our presentation for going in blind
+
+ align:start position:0%
+is our presentation for going in blind
+ 
+
+ align:start position:0%
+is our presentation for going in blind
+i'm gwen edgar and this is my teammate
+
+ align:start position:0%
+i'm gwen edgar and this is my teammate
+ 
+
+ align:start position:0%
+i'm gwen edgar and this is my teammate
+rio levine
+
+ align:start position:0%
+rio levine
+ 
+
+ align:start position:0%
+rio levine
+and welcome so first we're gonna start
+
+ align:start position:0%
+and welcome so first we're gonna start
+ 
+
+ align:start position:0%
+and welcome so first we're gonna start
+you off with a background on blind
+
+ align:start position:0%
+you off with a background on blind
+ 
+
+ align:start position:0%
+you off with a background on blind
+gaming right so actually
+
+ align:start position:0%
+gaming right so actually
+ 
+
+ align:start position:0%
+gaming right so actually
+blind gaming has been around basically
+
+ align:start position:0%
+blind gaming has been around basically
+ 
+
+ align:start position:0%
+blind gaming has been around basically
+since video gaming was a thing and when
+
+ align:start position:0%
+since video gaming was a thing and when
+ 
+
+ align:start position:0%
+since video gaming was a thing and when
+i'm talking about blind gaming i mean
+
+ align:start position:0%
+i'm talking about blind gaming i mean
+ 
+
+ align:start position:0%
+i'm talking about blind gaming i mean
+like electronic gaming um so starting in
+
+ align:start position:0%
+like electronic gaming um so starting in
+ 
+
+ align:start position:0%
+like electronic gaming um so starting in
+the 70s atari came out with this game
+
+ align:start position:0%
+the 70s atari came out with this game
+ 
+
+ align:start position:0%
+the 70s atari came out with this game
+called touch me and it had flashing
+
+ align:start position:0%
+called touch me and it had flashing
+ 
+
+ align:start position:0%
+called touch me and it had flashing
+lights and it made noises so it was
+
+ align:start position:0%
+lights and it made noises so it was
+ 
+
+ align:start position:0%
+lights and it made noises so it was
+actually accessible to people who
+
+ align:start position:0%
+actually accessible to people who
+ 
+
+ align:start position:0%
+actually accessible to people who
+couldn't see
+
+ align:start position:0%
+couldn't see
+ 
+
+ align:start position:0%
+couldn't see
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+all of these text-based role-playing
+
+ align:start position:0%
+all of these text-based role-playing
+ 
+
+ align:start position:0%
+all of these text-based role-playing
+games were
+
+ align:start position:0%
+games were
+ 
+
+ align:start position:0%
+games were
+getting popular and if you had a
+
+ align:start position:0%
+getting popular and if you had a
+ 
+
+ align:start position:0%
+getting popular and if you had a
+text-to-speech software
+
+ align:start position:0%
+text-to-speech software
+ 
+
+ align:start position:0%
+text-to-speech software
+a visually impaired player could play
+
+ align:start position:0%
+a visually impaired player could play
+ 
+
+ align:start position:0%
+a visually impaired player could play
+those as well but console games action
+
+ align:start position:0%
+those as well but console games action
+ 
+
+ align:start position:0%
+those as well but console games action
+games were very limited
+
+ align:start position:0%
+games were very limited
+ 
+
+ align:start position:0%
+games were very limited
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+gamers are going to game
+
+ align:start position:0%
+gamers are going to game
+ 
+
+ align:start position:0%
+gamers are going to game
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+blind gamers played video games anyway
+
+ align:start position:0%
+blind gamers played video games anyway
+ 
+
+ align:start position:0%
+blind gamers played video games anyway
+so they could use text text-to-speech
+
+ align:start position:0%
+so they could use text text-to-speech
+ 
+
+ align:start position:0%
+so they could use text text-to-speech
+and just based off of sound cues
+
+ align:start position:0%
+and just based off of sound cues
+ 
+
+ align:start position:0%
+and just based off of sound cues
+navigate through very complex levels
+
+ align:start position:0%
+navigate through very complex levels
+ 
+
+ align:start position:0%
+navigate through very complex levels
+completing games like so 2d punch out
+
+ align:start position:0%
+completing games like so 2d punch out
+ 
+
+ align:start position:0%
+completing games like so 2d punch out
+super mario 64. a blind gamer has even
+
+ align:start position:0%
+super mario 64. a blind gamer has even
+ 
+
+ align:start position:0%
+super mario 64. a blind gamer has even
+completed ocarina of time if you've ever
+
+ align:start position:0%
+completed ocarina of time if you've ever
+ 
+
+ align:start position:0%
+completed ocarina of time if you've ever
+played that game it's crazy
+
+ align:start position:0%
+played that game it's crazy
+ 
+
+ align:start position:0%
+played that game it's crazy
+without visuals
+
+ align:start position:0%
+without visuals
+ 
+
+ align:start position:0%
+without visuals
+even resident evil 4 was accidentally
+
+ align:start position:0%
+even resident evil 4 was accidentally
+ 
+
+ align:start position:0%
+even resident evil 4 was accidentally
+accessible because if you pressed pause
+
+ align:start position:0%
+accessible because if you pressed pause
+ 
+
+ align:start position:0%
+accessible because if you pressed pause
+your character would reorient themselves
+
+ align:start position:0%
+your character would reorient themselves
+ 
+
+ align:start position:0%
+your character would reorient themselves
+to face towards the goal
+
+ align:start position:0%
+to face towards the goal
+ 
+
+ align:start position:0%
+to face towards the goal
+that they were trying to get to
+
+ align:start position:0%
+that they were trying to get to
+ 
+
+ align:start position:0%
+that they were trying to get to
+fighting games like 2d fighting games
+
+ align:start position:0%
+fighting games like 2d fighting games
+ 
+
+ align:start position:0%
+fighting games like 2d fighting games
+are actually pretty accessible because
+
+ align:start position:0%
+are actually pretty accessible because
+ 
+
+ align:start position:0%
+are actually pretty accessible because
+they have binaural sound you can tell
+
+ align:start position:0%
+they have binaural sound you can tell
+ 
+
+ align:start position:0%
+they have binaural sound you can tell
+which side your opponent is on
+
+ align:start position:0%
+which side your opponent is on
+ 
+
+ align:start position:0%
+which side your opponent is on
+so mortal kombat street fighter
+
+ align:start position:0%
+so mortal kombat street fighter
+ 
+
+ align:start position:0%
+so mortal kombat street fighter
+both pretty accessible and blind players
+
+ align:start position:0%
+both pretty accessible and blind players
+ 
+
+ align:start position:0%
+both pretty accessible and blind players
+have even been known to play
+
+ align:start position:0%
+have even been known to play
+ 
+
+ align:start position:0%
+have even been known to play
+uh first person shooters so
+
+ align:start position:0%
+uh first person shooters so
+ 
+
+ align:start position:0%
+uh first person shooters so
+as long as there are enough sound cues
+
+ align:start position:0%
+as long as there are enough sound cues
+ 
+
+ align:start position:0%
+as long as there are enough sound cues
+it seems like
+
+ align:start position:0%
+it seems like
+ 
+
+ align:start position:0%
+it seems like
+blind players can play these games and
+
+ align:start position:0%
+blind players can play these games and
+ 
+
+ align:start position:0%
+blind players can play these games and
+that brings us to
+
+ align:start position:0%
+that brings us to
+ 
+
+ align:start position:0%
+that brings us to
+our audio only platformer which as you
+
+ align:start position:0%
+our audio only platformer which as you
+ 
+
+ align:start position:0%
+our audio only platformer which as you
+can see
+
+ align:start position:0%
+can see
+ 
+
+ align:start position:0%
+can see
+you see nothing
+
+ align:start position:0%
+you see nothing
+ 
+
+ align:start position:0%
+you see nothing
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+you have you have to use uh only audio
+
+ align:start position:0%
+you have you have to use uh only audio
+ 
+
+ align:start position:0%
+you have you have to use uh only audio
+cues to navigate throughout the space
+
+ align:start position:0%
+cues to navigate throughout the space
+ 
+
+ align:start position:0%
+cues to navigate throughout the space
+because it's using a lot of binaural
+
+ align:start position:0%
+because it's using a lot of binaural
+ 
+
+ align:start position:0%
+because it's using a lot of binaural
+inputs so you're able to tell in what
+
+ align:start position:0%
+inputs so you're able to tell in what
+ 
+
+ align:start position:0%
+inputs so you're able to tell in what
+direction different things are
+
+ align:start position:0%
+direction different things are
+ 
+
+ align:start position:0%
+direction different things are
+as you all know we're using the bose
+
+ align:start position:0%
+as you all know we're using the bose
+ 
+
+ align:start position:0%
+as you all know we're using the bose
+glasses for this project
+
+ align:start position:0%
+glasses for this project
+ 
+
+ align:start position:0%
+glasses for this project
+and there are a couple of gestures that
+
+ align:start position:0%
+and there are a couple of gestures that
+ 
+
+ align:start position:0%
+and there are a couple of gestures that
+are automatically integrated such as
+
+ align:start position:0%
+are automatically integrated such as
+ 
+
+ align:start position:0%
+are automatically integrated such as
+nodding your head shaking your head and
+
+ align:start position:0%
+nodding your head shaking your head and
+ 
+
+ align:start position:0%
+nodding your head shaking your head and
+double tapping
+
+ align:start position:0%
+double tapping
+ 
+
+ align:start position:0%
+double tapping
+uh we were exploring uh these different
+
+ align:start position:0%
+uh we were exploring uh these different
+ 
+
+ align:start position:0%
+uh we were exploring uh these different
+things and so first we're trying to do
+
+ align:start position:0%
+things and so first we're trying to do
+ 
+
+ align:start position:0%
+things and so first we're trying to do
+movement with head nods so step step
+
+ align:start position:0%
+movement with head nods so step step
+ 
+
+ align:start position:0%
+movement with head nods so step step
+step step
+
+ align:start position:0%
+step step
+ 
+
+ align:start position:0%
+step step
+and we found this got really tiring
+
+ align:start position:0%
+and we found this got really tiring
+ 
+
+ align:start position:0%
+and we found this got really tiring
+and it's hard to know like were you
+
+ align:start position:0%
+and it's hard to know like were you
+ 
+
+ align:start position:0%
+and it's hard to know like were you
+taking a small step were you taking a
+
+ align:start position:0%
+taking a small step were you taking a
+ 
+
+ align:start position:0%
+taking a small step were you taking a
+big step how far am i going like how do
+
+ align:start position:0%
+big step how far am i going like how do
+ 
+
+ align:start position:0%
+big step how far am i going like how do
+i get through these different types of
+
+ align:start position:0%
+i get through these different types of
+ 
+
+ align:start position:0%
+i get through these different types of
+movements
+
+ align:start position:0%
+movements
+ 
+
+ align:start position:0%
+movements
+so we decided to look at something else
+
+ align:start position:0%
+so we decided to look at something else
+ 
+
+ align:start position:0%
+so we decided to look at something else
+which as you saw you tilt your head down
+
+ align:start position:0%
+which as you saw you tilt your head down
+ 
+
+ align:start position:0%
+which as you saw you tilt your head down
+to move forward if you're looking this
+
+ align:start position:0%
+to move forward if you're looking this
+ 
+
+ align:start position:0%
+to move forward if you're looking this
+way you go this way you tilt your head
+
+ align:start position:0%
+way you go this way you tilt your head
+ 
+
+ align:start position:0%
+way you go this way you tilt your head
+back to go back and this allowed for a
+
+ align:start position:0%
+back to go back and this allowed for a
+ 
+
+ align:start position:0%
+back to go back and this allowed for a
+certain smoothness of walking and the
+
+ align:start position:0%
+certain smoothness of walking and the
+ 
+
+ align:start position:0%
+certain smoothness of walking and the
+step foot you hear footsteps as you like
+
+ align:start position:0%
+step foot you hear footsteps as you like
+ 
+
+ align:start position:0%
+step foot you hear footsteps as you like
+move forward which gives a sense of you
+
+ align:start position:0%
+move forward which gives a sense of you
+ 
+
+ align:start position:0%
+move forward which gives a sense of you
+being in the place and a sense of that
+
+ align:start position:0%
+being in the place and a sense of that
+ 
+
+ align:start position:0%
+being in the place and a sense of that
+movement that you're playing towards
+
+ align:start position:0%
+movement that you're playing towards
+ 
+
+ align:start position:0%
+movement that you're playing towards
+and as you like you turn your head your
+
+ align:start position:0%
+and as you like you turn your head your
+ 
+
+ align:start position:0%
+and as you like you turn your head your
+direction will change you might have
+
+ align:start position:0%
+direction will change you might have
+ 
+
+ align:start position:0%
+direction will change you might have
+seen a couple of times that there was a
+
+ align:start position:0%
+seen a couple of times that there was a
+ 
+
+ align:start position:0%
+seen a couple of times that there was a
+curve happening because of
+
+ align:start position:0%
+curve happening because of
+ 
+
+ align:start position:0%
+curve happening because of
+motions like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so that brings us back
+
+ align:start position:0%
+so so that brings us back
+ 
+
+ align:start position:0%
+so so that brings us back
+to the bose glasses we were using the
+
+ align:start position:0%
+to the bose glasses we were using the
+ 
+
+ align:start position:0%
+to the bose glasses we were using the
+gyroscopes a lot which meant we couldn't
+
+ align:start position:0%
+gyroscopes a lot which meant we couldn't
+ 
+
+ align:start position:0%
+gyroscopes a lot which meant we couldn't
+use the head nod or shake because they
+
+ align:start position:0%
+use the head nod or shake because they
+ 
+
+ align:start position:0%
+use the head nod or shake because they
+were kind of using the same thing and if
+
+ align:start position:0%
+were kind of using the same thing and if
+ 
+
+ align:start position:0%
+were kind of using the same thing and if
+you're trying to move forward you can't
+
+ align:start position:0%
+you're trying to move forward you can't
+ 
+
+ align:start position:0%
+you're trying to move forward you can't
+do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now then those were the sensors so that
+
+ align:start position:0%
+now then those were the sensors so that
+ 
+
+ align:start position:0%
+now then those were the sensors so that
+left us with one thing the double tap
+
+ align:start position:0%
+left us with one thing the double tap
+ 
+
+ align:start position:0%
+left us with one thing the double tap
+now what does any platformer need
+
+ align:start position:0%
+now what does any platformer need
+ 
+
+ align:start position:0%
+now what does any platformer need
+well gwen i think it needs platforms
+
+ align:start position:0%
+well gwen i think it needs platforms
+ 
+
+ align:start position:0%
+well gwen i think it needs platforms
+exactly what do you need for platforms
+
+ align:start position:0%
+exactly what do you need for platforms
+ 
+
+ align:start position:0%
+exactly what do you need for platforms
+jumping
+
+ align:start position:0%
+jumping
+ 
+
+ align:start position:0%
+jumping
+so we decided to move that double tap
+
+ align:start position:0%
+so we decided to move that double tap
+ 
+
+ align:start position:0%
+so we decided to move that double tap
+towards jumping and so we you know we
+
+ align:start position:0%
+towards jumping and so we you know we
+ 
+
+ align:start position:0%
+towards jumping and so we you know we
+were thinking about okay so we're going
+
+ align:start position:0%
+were thinking about okay so we're going
+ 
+
+ align:start position:0%
+were thinking about okay so we're going
+to double tap to jump but we want to
+
+ align:start position:0%
+to double tap to jump but we want to
+ 
+
+ align:start position:0%
+to double tap to jump but we want to
+follow follow the platform but if we're
+
+ align:start position:0%
+follow follow the platform but if we're
+ 
+
+ align:start position:0%
+follow follow the platform but if we're
+looking at a platform up here we might
+
+ align:start position:0%
+looking at a platform up here we might
+ 
+
+ align:start position:0%
+looking at a platform up here we might
+start walking backwards if we're looking
+
+ align:start position:0%
+start walking backwards if we're looking
+ 
+
+ align:start position:0%
+start walking backwards if we're looking
+at a platform down here we might start
+
+ align:start position:0%
+at a platform down here we might start
+ 
+
+ align:start position:0%
+at a platform down here we might start
+walking forwards so you're thinking all
+
+ align:start position:0%
+walking forwards so you're thinking all
+ 
+
+ align:start position:0%
+walking forwards so you're thinking all
+right all right we'll have a jump mode
+
+ align:start position:0%
+right all right we'll have a jump mode
+ 
+
+ align:start position:0%
+right all right we'll have a jump mode
+so you double tap first you enter jump
+
+ align:start position:0%
+so you double tap first you enter jump
+ 
+
+ align:start position:0%
+so you double tap first you enter jump
+mode and then you don't move around so
+
+ align:start position:0%
+mode and then you don't move around so
+ 
+
+ align:start position:0%
+mode and then you don't move around so
+you can like look at all your targets
+
+ align:start position:0%
+you can like look at all your targets
+ 
+
+ align:start position:0%
+you can like look at all your targets
+and not worry about falling over an edge
+
+ align:start position:0%
+and not worry about falling over an edge
+ 
+
+ align:start position:0%
+and not worry about falling over an edge
+or going out of the zone
+
+ align:start position:0%
+or going out of the zone
+ 
+
+ align:start position:0%
+or going out of the zone
+but this got really confusing
+
+ align:start position:0%
+but this got really confusing
+ 
+
+ align:start position:0%
+but this got really confusing
+we had it such that three tap three
+
+ align:start position:0%
+we had it such that three tap three
+ 
+
+ align:start position:0%
+we had it such that three tap three
+missed jumps you'd exit it wasn't
+
+ align:start position:0%
+missed jumps you'd exit it wasn't
+ 
+
+ align:start position:0%
+missed jumps you'd exit it wasn't
+integrated very well it didn't feel very
+
+ align:start position:0%
+integrated very well it didn't feel very
+ 
+
+ align:start position:0%
+integrated very well it didn't feel very
+smooth it was kind of clunky
+
+ align:start position:0%
+smooth it was kind of clunky
+ 
+
+ align:start position:0%
+smooth it was kind of clunky
+people were like why did i stop moving
+
+ align:start position:0%
+people were like why did i stop moving
+ 
+
+ align:start position:0%
+people were like why did i stop moving
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+so i decided to move away from that
+
+ align:start position:0%
+so i decided to move away from that
+ 
+
+ align:start position:0%
+so i decided to move away from that
+instead
+
+ align:start position:0%
+instead
+ 
+
+ align:start position:0%
+instead
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+jumped and what what this really meant
+
+ align:start position:0%
+jumped and what what this really meant
+ 
+
+ align:start position:0%
+jumped and what what this really meant
+was that we could only design levels in
+
+ align:start position:0%
+was that we could only design levels in
+ 
+
+ align:start position:0%
+was that we could only design levels in
+certain ways that
+
+ align:start position:0%
+certain ways that
+ 
+
+ align:start position:0%
+certain ways that
+looking at the platforms would be within
+
+ align:start position:0%
+looking at the platforms would be within
+ 
+
+ align:start position:0%
+looking at the platforms would be within
+your range of motion without trying to
+
+ align:start position:0%
+your range of motion without trying to
+ 
+
+ align:start position:0%
+your range of motion without trying to
+go outside of it anyway like moving
+
+ align:start position:0%
+go outside of it anyway like moving
+ 
+
+ align:start position:0%
+go outside of it anyway like moving
+along with the jumping though even even
+
+ align:start position:0%
+along with the jumping though even even
+ 
+
+ align:start position:0%
+along with the jumping though even even
+more was that if we just tried to apply
+
+ align:start position:0%
+more was that if we just tried to apply
+ 
+
+ align:start position:0%
+more was that if we just tried to apply
+a force the player could go spiraling
+
+ align:start position:0%
+a force the player could go spiraling
+ 
+
+ align:start position:0%
+a force the player could go spiraling
+off into space because they didn't know
+
+ align:start position:0%
+off into space because they didn't know
+ 
+
+ align:start position:0%
+off into space because they didn't know
+that there wasn't something for them to
+
+ align:start position:0%
+that there wasn't something for them to
+ 
+
+ align:start position:0%
+that there wasn't something for them to
+land on
+
+ align:start position:0%
+land on
+ 
+
+ align:start position:0%
+land on
+if we allowed them to jump at any point
+
+ align:start position:0%
+if we allowed them to jump at any point
+ 
+
+ align:start position:0%
+if we allowed them to jump at any point
+they might like jump onto a wall and
+
+ align:start position:0%
+they might like jump onto a wall and
+ 
+
+ align:start position:0%
+they might like jump onto a wall and
+then like fall or go through the wall or
+
+ align:start position:0%
+then like fall or go through the wall or
+ 
+
+ align:start position:0%
+then like fall or go through the wall or
+fall down and they don't know why
+
+ align:start position:0%
+fall down and they don't know why
+ 
+
+ align:start position:0%
+fall down and they don't know why
+they failed
+
+ align:start position:0%
+they failed
+ 
+
+ align:start position:0%
+they failed
+so instead what we did is we allowed
+
+ align:start position:0%
+so instead what we did is we allowed
+ 
+
+ align:start position:0%
+so instead what we did is we allowed
+jumping onto platform so if you're
+
+ align:start position:0%
+jumping onto platform so if you're
+ 
+
+ align:start position:0%
+jumping onto platform so if you're
+looking at a platform you just jump and
+
+ align:start position:0%
+looking at a platform you just jump and
+ 
+
+ align:start position:0%
+looking at a platform you just jump and
+it's all good and if you don't it's like
+
+ align:start position:0%
+it's all good and if you don't it's like
+ 
+
+ align:start position:0%
+it's all good and if you don't it's like
+nope
+
+ align:start position:0%
+nope
+ 
+
+ align:start position:0%
+nope
+and doesn't let you yes
+
+ align:start position:0%
+and doesn't let you yes
+ 
+
+ align:start position:0%
+and doesn't let you yes
+and we found that worked pretty well and
+
+ align:start position:0%
+and we found that worked pretty well and
+ 
+
+ align:start position:0%
+and we found that worked pretty well and
+it didn't upset players it was very
+
+ align:start position:0%
+it didn't upset players it was very
+ 
+
+ align:start position:0%
+it didn't upset players it was very
+important to us yes
+
+ align:start position:0%
+important to us yes
+ 
+
+ align:start position:0%
+important to us yes
+um so okay we've gone over what you can
+
+ align:start position:0%
+um so okay we've gone over what you can
+ 
+
+ align:start position:0%
+um so okay we've gone over what you can
+do within our game here are some of the
+
+ align:start position:0%
+do within our game here are some of the
+ 
+
+ align:start position:0%
+do within our game here are some of the
+challenge we face challenges we've faced
+
+ align:start position:0%
+challenge we face challenges we've faced
+ 
+
+ align:start position:0%
+challenge we face challenges we've faced
+when
+
+ align:start position:0%
+when
+ 
+
+ align:start position:0%
+when
+developing it so far
+
+ align:start position:0%
+developing it so far
+ 
+
+ align:start position:0%
+developing it so far
+first challenge player orientation
+
+ align:start position:0%
+first challenge player orientation
+ 
+
+ align:start position:0%
+first challenge player orientation
+fortunately it worked right off the bat
+
+ align:start position:0%
+fortunately it worked right off the bat
+ 
+
+ align:start position:0%
+fortunately it worked right off the bat
+when we did our demo that's good but in
+
+ align:start position:0%
+when we did our demo that's good but in
+ 
+
+ align:start position:0%
+when we did our demo that's good but in
+general uh if you just start the game
+
+ align:start position:0%
+general uh if you just start the game
+ 
+
+ align:start position:0%
+general uh if you just start the game
+without doing any kind of calibration
+
+ align:start position:0%
+without doing any kind of calibration
+ 
+
+ align:start position:0%
+without doing any kind of calibration
+you're looking in some random direction
+
+ align:start position:0%
+you're looking in some random direction
+ 
+
+ align:start position:0%
+you're looking in some random direction
+so you need to make sure to like
+
+ align:start position:0%
+so you need to make sure to like
+ 
+
+ align:start position:0%
+so you need to make sure to like
+face the player forward and since the
+
+ align:start position:0%
+face the player forward and since the
+ 
+
+ align:start position:0%
+face the player forward and since the
+last time we gave this presentation we
+
+ align:start position:0%
+last time we gave this presentation we
+ 
+
+ align:start position:0%
+last time we gave this presentation we
+found a method that faces you forward
+
+ align:start position:0%
+found a method that faces you forward
+ 
+
+ align:start position:0%
+found a method that faces you forward
+towards the the z-axis
+
+ align:start position:0%
+towards the the z-axis
+ 
+
+ align:start position:0%
+towards the the z-axis
+but there's no way to face and make the
+
+ align:start position:0%
+but there's no way to face and make the
+ 
+
+ align:start position:0%
+but there's no way to face and make the
+default any other direction which is
+
+ align:start position:0%
+default any other direction which is
+ 
+
+ align:start position:0%
+default any other direction which is
+fine we just built all of our levels
+
+ align:start position:0%
+fine we just built all of our levels
+ 
+
+ align:start position:0%
+fine we just built all of our levels
+along the positive z-axis
+
+ align:start position:0%
+along the positive z-axis
+ 
+
+ align:start position:0%
+along the positive z-axis
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+next challenge
+
+ align:start position:0%
+next challenge
+ 
+
+ align:start position:0%
+next challenge
+properties of audio sources and the
+
+ align:start position:0%
+properties of audio sources and the
+ 
+
+ align:start position:0%
+properties of audio sources and the
+placements where we put them this was
+
+ align:start position:0%
+placements where we put them this was
+ 
+
+ align:start position:0%
+placements where we put them this was
+discussed in some of those lectures and
+
+ align:start position:0%
+discussed in some of those lectures and
+ 
+
+ align:start position:0%
+discussed in some of those lectures and
+in some of the psychoacoustics lectures
+
+ align:start position:0%
+in some of the psychoacoustics lectures
+ 
+
+ align:start position:0%
+in some of the psychoacoustics lectures
+that we're talking about but yes forward
+
+ align:start position:0%
+that we're talking about but yes forward
+ 
+
+ align:start position:0%
+that we're talking about but yes forward
+and behind you can't really
+
+ align:start position:0%
+and behind you can't really
+ 
+
+ align:start position:0%
+and behind you can't really
+differentiate so if you're on a platform
+
+ align:start position:0%
+differentiate so if you're on a platform
+ 
+
+ align:start position:0%
+differentiate so if you're on a platform
+and there's something moving behind you
+
+ align:start position:0%
+and there's something moving behind you
+ 
+
+ align:start position:0%
+and there's something moving behind you
+there's some platform moving in front of
+
+ align:start position:0%
+there's some platform moving in front of
+ 
+
+ align:start position:0%
+there's some platform moving in front of
+you you can't really follow either
+
+ align:start position:0%
+you you can't really follow either
+ 
+
+ align:start position:0%
+you you can't really follow either
+platform because there's the you can't
+
+ align:start position:0%
+platform because there's the you can't
+ 
+
+ align:start position:0%
+platform because there's the you can't
+focus on either source they get very
+
+ align:start position:0%
+focus on either source they get very
+ 
+
+ align:start position:0%
+focus on either source they get very
+muddled in your head if it's not clear
+
+ align:start position:0%
+muddled in your head if it's not clear
+ 
+
+ align:start position:0%
+muddled in your head if it's not clear
+the platforms are making sound yes i'm
+
+ align:start position:0%
+the platforms are making sound yes i'm
+ 
+
+ align:start position:0%
+the platforms are making sound yes i'm
+sorry i forgot to mention that the
+
+ align:start position:0%
+sorry i forgot to mention that the
+ 
+
+ align:start position:0%
+sorry i forgot to mention that the
+platforms make sound so you can follow
+
+ align:start position:0%
+platforms make sound so you can follow
+ 
+
+ align:start position:0%
+platforms make sound so you can follow
+them so you know you'll get on the
+
+ align:start position:0%
+them so you know you'll get on the
+ 
+
+ align:start position:0%
+them so you know you'll get on the
+platform we turn the volume down on that
+
+ align:start position:0%
+platform we turn the volume down on that
+ 
+
+ align:start position:0%
+platform we turn the volume down on that
+platform or else it's just overpowering
+
+ align:start position:0%
+platform or else it's just overpowering
+ 
+
+ align:start position:0%
+platform or else it's just overpowering
+when you leave it we turn it off such
+
+ align:start position:0%
+when you leave it we turn it off such
+ 
+
+ align:start position:0%
+when you leave it we turn it off such
+that you can always detect what's in
+
+ align:start position:0%
+that you can always detect what's in
+ 
+
+ align:start position:0%
+that you can always detect what's in
+front of you
+
+ align:start position:0%
+front of you
+ 
+
+ align:start position:0%
+front of you
+and that works really well because the
+
+ align:start position:0%
+and that works really well because the
+ 
+
+ align:start position:0%
+and that works really well because the
+audio that is like moving with you
+
+ align:start position:0%
+audio that is like moving with you
+ 
+
+ align:start position:0%
+audio that is like moving with you
+doesn't bother at all with the um
+
+ align:start position:0%
+doesn't bother at all with the um
+ 
+
+ align:start position:0%
+doesn't bother at all with the um
+with the other moving sources so if
+
+ align:start position:0%
+with the other moving sources so if
+ 
+
+ align:start position:0%
+with the other moving sources so if
+you're on a platform it can still make
+
+ align:start position:0%
+you're on a platform it can still make
+ 
+
+ align:start position:0%
+you're on a platform it can still make
+its noise and you can follow one in
+
+ align:start position:0%
+its noise and you can follow one in
+ 
+
+ align:start position:0%
+its noise and you can follow one in
+front of you
+
+ align:start position:0%
+front of you
+ 
+
+ align:start position:0%
+front of you
+yes and ambient noise also is fine to
+
+ align:start position:0%
+yes and ambient noise also is fine to
+ 
+
+ align:start position:0%
+yes and ambient noise also is fine to
+use
+
+ align:start position:0%
+use
+ 
+
+ align:start position:0%
+use
+but also as discussed you can tell some
+
+ align:start position:0%
+but also as discussed you can tell some
+ 
+
+ align:start position:0%
+but also as discussed you can tell some
+things left or right and you're able to
+
+ align:start position:0%
+things left or right and you're able to
+ 
+
+ align:start position:0%
+things left or right and you're able to
+turn towards those yep
+
+ align:start position:0%
+turn towards those yep
+ 
+
+ align:start position:0%
+turn towards those yep
+limited inputs we were talking about
+
+ align:start position:0%
+limited inputs we were talking about
+ 
+
+ align:start position:0%
+limited inputs we were talking about
+this earlier um in a lot of games you
+
+ align:start position:0%
+this earlier um in a lot of games you
+ 
+
+ align:start position:0%
+this earlier um in a lot of games you
+have keyboards so you can have like
+
+ align:start position:0%
+have keyboards so you can have like
+ 
+
+ align:start position:0%
+have keyboards so you can have like
+special abilities and different modes
+
+ align:start position:0%
+special abilities and different modes
+ 
+
+ align:start position:0%
+special abilities and different modes
+you can enter in a bunch of like menus
+
+ align:start position:0%
+you can enter in a bunch of like menus
+ 
+
+ align:start position:0%
+you can enter in a bunch of like menus
+and whatnot and with this we had the two
+
+ align:start position:0%
+and whatnot and with this we had the two
+ 
+
+ align:start position:0%
+and whatnot and with this we had the two
+and so we were working a lot with those
+
+ align:start position:0%
+and so we were working a lot with those
+ 
+
+ align:start position:0%
+and so we were working a lot with those
+and that was just one of the challenges
+
+ align:start position:0%
+and that was just one of the challenges
+ 
+
+ align:start position:0%
+and that was just one of the challenges
+we faced
+
+ align:start position:0%
+we faced
+ 
+
+ align:start position:0%
+we faced
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+um uh also as you might have noticed uh
+
+ align:start position:0%
+um uh also as you might have noticed uh
+ 
+
+ align:start position:0%
+um uh also as you might have noticed uh
+your method of movement is imprecise you
+
+ align:start position:0%
+your method of movement is imprecise you
+ 
+
+ align:start position:0%
+your method of movement is imprecise you
+don't know where you're going you're not
+
+ align:start position:0%
+don't know where you're going you're not
+ 
+
+ align:start position:0%
+don't know where you're going you're not
+really sure if you're going straight
+
+ align:start position:0%
+really sure if you're going straight
+ 
+
+ align:start position:0%
+really sure if you're going straight
+forward you don't know where exactly how
+
+ align:start position:0%
+forward you don't know where exactly how
+ 
+
+ align:start position:0%
+forward you don't know where exactly how
+far things are away from you you might
+
+ align:start position:0%
+far things are away from you you might
+ 
+
+ align:start position:0%
+far things are away from you you might
+think you're going forward but your head
+
+ align:start position:0%
+think you're going forward but your head
+ 
+
+ align:start position:0%
+think you're going forward but your head
+is tilted the side of it so you're
+
+ align:start position:0%
+is tilted the side of it so you're
+ 
+
+ align:start position:0%
+is tilted the side of it so you're
+actually going in this direction
+
+ align:start position:0%
+actually going in this direction
+ 
+
+ align:start position:0%
+actually going in this direction
+fun thing problems to think about one of
+
+ align:start position:0%
+fun thing problems to think about one of
+ 
+
+ align:start position:0%
+fun thing problems to think about one of
+the first things with this was the
+
+ align:start position:0%
+the first things with this was the
+ 
+
+ align:start position:0%
+the first things with this was the
+platforms because players had a lot of
+
+ align:start position:0%
+platforms because players had a lot of
+ 
+
+ align:start position:0%
+platforms because players had a lot of
+trouble looking exactly where the
+
+ align:start position:0%
+trouble looking exactly where the
+ 
+
+ align:start position:0%
+trouble looking exactly where the
+platform was
+
+ align:start position:0%
+platform was
+ 
+
+ align:start position:0%
+platform was
+we had to make a huge collider so this
+
+ align:start position:0%
+we had to make a huge collider so this
+ 
+
+ align:start position:0%
+we had to make a huge collider so this
+entire green box if you hit if you are
+
+ align:start position:0%
+entire green box if you hit if you are
+ 
+
+ align:start position:0%
+entire green box if you hit if you are
+gazing anywhere inside of it you'll go
+
+ align:start position:0%
+gazing anywhere inside of it you'll go
+ 
+
+ align:start position:0%
+gazing anywhere inside of it you'll go
+to the platform on your jump yes
+
+ align:start position:0%
+to the platform on your jump yes
+ 
+
+ align:start position:0%
+to the platform on your jump yes
+it was almost impossible to hit this
+
+ align:start position:0%
+it was almost impossible to hit this
+ 
+
+ align:start position:0%
+it was almost impossible to hit this
+even when looking at the screen
+
+ align:start position:0%
+even when looking at the screen
+ 
+
+ align:start position:0%
+even when looking at the screen
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+um and in graphic games it's also
+
+ align:start position:0%
+um and in graphic games it's also
+ 
+
+ align:start position:0%
+um and in graphic games it's also
+lenient because you jump and you can
+
+ align:start position:0%
+lenient because you jump and you can
+ 
+
+ align:start position:0%
+lenient because you jump and you can
+like fall onto it you don't have to jump
+
+ align:start position:0%
+like fall onto it you don't have to jump
+ 
+
+ align:start position:0%
+like fall onto it you don't have to jump
+exactly to where it is
+
+ align:start position:0%
+exactly to where it is
+ 
+
+ align:start position:0%
+exactly to where it is
+so it follows and to help with the
+
+ align:start position:0%
+so it follows and to help with the
+ 
+
+ align:start position:0%
+so it follows and to help with the
+imprecise like i think i'm moving
+
+ align:start position:0%
+imprecise like i think i'm moving
+ 
+
+ align:start position:0%
+imprecise like i think i'm moving
+forward but maybe i'm listening to the
+
+ align:start position:0%
+forward but maybe i'm listening to the
+ 
+
+ align:start position:0%
+forward but maybe i'm listening to the
+left or right
+
+ align:start position:0%
+left or right
+ 
+
+ align:start position:0%
+left or right
+we made it so that if you are going fast
+
+ align:start position:0%
+we made it so that if you are going fast
+ 
+
+ align:start position:0%
+we made it so that if you are going fast
+enough and you're within like 15 degrees
+
+ align:start position:0%
+enough and you're within like 15 degrees
+ 
+
+ align:start position:0%
+enough and you're within like 15 degrees
+of forward you will go straight forward
+
+ align:start position:0%
+of forward you will go straight forward
+ 
+
+ align:start position:0%
+of forward you will go straight forward
+on the z axis this made one of our
+
+ align:start position:0%
+on the z axis this made one of our
+ 
+
+ align:start position:0%
+on the z axis this made one of our
+levels which was essentially a very long
+
+ align:start position:0%
+levels which was essentially a very long
+ 
+
+ align:start position:0%
+levels which was essentially a very long
+hallway much more
+
+ align:start position:0%
+hallway much more
+ 
+
+ align:start position:0%
+hallway much more
+much less frustrating i won't say easier
+
+ align:start position:0%
+much less frustrating i won't say easier
+ 
+
+ align:start position:0%
+much less frustrating i won't say easier
+but less frustrating for players because
+
+ align:start position:0%
+but less frustrating for players because
+ 
+
+ align:start position:0%
+but less frustrating for players because
+then they could be like oh i'm actually
+
+ align:start position:0%
+then they could be like oh i'm actually
+ 
+
+ align:start position:0%
+then they could be like oh i'm actually
+going forward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um as mentioned don't use different
+
+ align:start position:0%
+um as mentioned don't use different
+ 
+
+ align:start position:0%
+um as mentioned don't use different
+heights so uh
+
+ align:start position:0%
+heights so uh
+ 
+
+ align:start position:0%
+heights so uh
+right like
+
+ align:start position:0%
+right like
+ 
+
+ align:start position:0%
+right like
+yes so as players were playing more and
+
+ align:start position:0%
+yes so as players were playing more and
+ 
+
+ align:start position:0%
+yes so as players were playing more and
+more they were able to tell they were
+
+ align:start position:0%
+more they were able to tell they were
+ 
+
+ align:start position:0%
+more they were able to tell they were
+able to learn more about the sound and
+
+ align:start position:0%
+able to learn more about the sound and
+ 
+
+ align:start position:0%
+able to learn more about the sound and
+tell where it was but when you're
+
+ align:start position:0%
+tell where it was but when you're
+ 
+
+ align:start position:0%
+tell where it was but when you're
+starting the play
+
+ align:start position:0%
+starting the play
+ 
+
+ align:start position:0%
+starting the play
+it's really difficult to try to detect
+
+ align:start position:0%
+it's really difficult to try to detect
+ 
+
+ align:start position:0%
+it's really difficult to try to detect
+where anything is in this axis and i
+
+ align:start position:0%
+where anything is in this axis and i
+ 
+
+ align:start position:0%
+where anything is in this axis and i
+think that based on our play test many
+
+ align:start position:0%
+think that based on our play test many
+ 
+
+ align:start position:0%
+think that based on our play test many
+players were like in a kind of restful
+
+ align:start position:0%
+players were like in a kind of restful
+ 
+
+ align:start position:0%
+players were like in a kind of restful
+position when trying to follow it
+
+ align:start position:0%
+position when trying to follow it
+ 
+
+ align:start position:0%
+position when trying to follow it
+which meant that
+
+ align:start position:0%
+which meant that
+ 
+
+ align:start position:0%
+which meant that
+they couldn't see anything above them
+
+ align:start position:0%
+they couldn't see anything above them
+ 
+
+ align:start position:0%
+they couldn't see anything above them
+first of all because restful is
+
+ align:start position:0%
+first of all because restful is
+ 
+
+ align:start position:0%
+first of all because restful is
+apparently tilted down a little bit and
+
+ align:start position:0%
+apparently tilted down a little bit and
+ 
+
+ align:start position:0%
+apparently tilted down a little bit and
+not looking forward
+
+ align:start position:0%
+not looking forward
+ 
+
+ align:start position:0%
+not looking forward
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and also that
+
+ align:start position:0%
+and also that
+ 
+
+ align:start position:0%
+and also that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i'm sorry that the we couldn't build
+
+ align:start position:0%
+i'm sorry that the we couldn't build
+ 
+
+ align:start position:0%
+i'm sorry that the we couldn't build
+levels upwards right now so we're trying
+
+ align:start position:0%
+levels upwards right now so we're trying
+ 
+
+ align:start position:0%
+levels upwards right now so we're trying
+to build them straight more straight
+
+ align:start position:0%
+to build them straight more straight
+ 
+
+ align:start position:0%
+to build them straight more straight
+forward so the players were able to jump
+
+ align:start position:0%
+forward so the players were able to jump
+ 
+
+ align:start position:0%
+forward so the players were able to jump
+back and forth
+
+ align:start position:0%
+back and forth
+ 
+
+ align:start position:0%
+back and forth
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+play tests yeah
+
+ align:start position:0%
+play tests yeah
+ 
+
+ align:start position:0%
+play tests yeah
+so on monday i got 11 players to play
+
+ align:start position:0%
+so on monday i got 11 players to play
+ 
+
+ align:start position:0%
+so on monday i got 11 players to play
+test the game on
+
+ align:start position:0%
+test the game on
+ 
+
+ align:start position:0%
+test the game on
+wednesday i got one more player to play
+
+ align:start position:0%
+wednesday i got one more player to play
+ 
+
+ align:start position:0%
+wednesday i got one more player to play
+test um
+
+ align:start position:0%
+test um
+ 
+
+ align:start position:0%
+test um
+based on some of the feedback we got and
+
+ align:start position:0%
+based on some of the feedback we got and
+ 
+
+ align:start position:0%
+based on some of the feedback we got and
+oh by the way
+
+ align:start position:0%
+oh by the way
+ 
+
+ align:start position:0%
+oh by the way
+everyone said that it was an interesting
+
+ align:start position:0%
+everyone said that it was an interesting
+ 
+
+ align:start position:0%
+everyone said that it was an interesting
+experience and some of them even said it
+
+ align:start position:0%
+experience and some of them even said it
+ 
+
+ align:start position:0%
+experience and some of them even said it
+was fun
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a lot of them did say it was fun um
+
+ align:start position:0%
+a lot of them did say it was fun um
+ 
+
+ align:start position:0%
+a lot of them did say it was fun um
+so that's good yeah so one of the first
+
+ align:start position:0%
+so that's good yeah so one of the first
+ 
+
+ align:start position:0%
+so that's good yeah so one of the first
+things that popped up a lot was distance
+
+ align:start position:0%
+things that popped up a lot was distance
+ 
+
+ align:start position:0%
+things that popped up a lot was distance
+detection or radar so you have no idea
+
+ align:start position:0%
+detection or radar so you have no idea
+ 
+
+ align:start position:0%
+detection or radar so you have no idea
+how close you are to the wall you
+
+ align:start position:0%
+how close you are to the wall you
+ 
+
+ align:start position:0%
+how close you are to the wall you
+experience that or you don't know how
+
+ align:start position:0%
+experience that or you don't know how
+ 
+
+ align:start position:0%
+experience that or you don't know how
+close or far something might be we're
+
+ align:start position:0%
+close or far something might be we're
+ 
+
+ align:start position:0%
+close or far something might be we're
+thinking of adding something like
+
+ align:start position:0%
+thinking of adding something like
+ 
+
+ align:start position:0%
+thinking of adding something like
+perhaps you could have something like a
+
+ align:start position:0%
+perhaps you could have something like a
+ 
+
+ align:start position:0%
+perhaps you could have something like a
+cane tapping and like you'll hear
+
+ align:start position:0%
+cane tapping and like you'll hear
+ 
+
+ align:start position:0%
+cane tapping and like you'll hear
+different noises or oh there's a gap
+
+ align:start position:0%
+different noises or oh there's a gap
+ 
+
+ align:start position:0%
+different noises or oh there's a gap
+here and we could take away barriers
+
+ align:start position:0%
+here and we could take away barriers
+ 
+
+ align:start position:0%
+here and we could take away barriers
+around edges with the something like
+
+ align:start position:0%
+around edges with the something like
+ 
+
+ align:start position:0%
+around edges with the something like
+this or something like rear assist
+
+ align:start position:0%
+this or something like rear assist
+ 
+
+ align:start position:0%
+this or something like rear assist
+parking so as you like get close to wall
+
+ align:start position:0%
+parking so as you like get close to wall
+ 
+
+ align:start position:0%
+parking so as you like get close to wall
+goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+frame of reference oh yeah so the first
+
+ align:start position:0%
+frame of reference oh yeah so the first
+ 
+
+ align:start position:0%
+frame of reference oh yeah so the first
+level went through a couple of
+
+ align:start position:0%
+level went through a couple of
+ 
+
+ align:start position:0%
+level went through a couple of
+iterations in our most recent iteration
+
+ align:start position:0%
+iterations in our most recent iteration
+ 
+
+ align:start position:0%
+iterations in our most recent iteration
+you have to find multiple targets before
+
+ align:start position:0%
+you have to find multiple targets before
+ 
+
+ align:start position:0%
+you have to find multiple targets before
+you progress to the next level and this
+
+ align:start position:0%
+you progress to the next level and this
+ 
+
+ align:start position:0%
+you progress to the next level and this
+is to give the player a chance to really
+
+ align:start position:0%
+is to give the player a chance to really
+ 
+
+ align:start position:0%
+is to give the player a chance to really
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+get more in the game understand this is
+
+ align:start position:0%
+get more in the game understand this is
+ 
+
+ align:start position:0%
+get more in the game understand this is
+the target this is the sound the target
+
+ align:start position:0%
+the target this is the sound the target
+ 
+
+ align:start position:0%
+the target this is the sound the target
+makes this is how i locate that sound
+
+ align:start position:0%
+makes this is how i locate that sound
+ 
+
+ align:start position:0%
+makes this is how i locate that sound
+this is how i move forward and moving
+
+ align:start position:0%
+this is how i move forward and moving
+ 
+
+ align:start position:0%
+this is how i move forward and moving
+backwards is also an option
+
+ align:start position:0%
+backwards is also an option
+ 
+
+ align:start position:0%
+backwards is also an option
+the target after after the one that you
+
+ align:start position:0%
+the target after after the one that you
+ 
+
+ align:start position:0%
+the target after after the one that you
+saw was directly behind
+
+ align:start position:0%
+saw was directly behind
+ 
+
+ align:start position:0%
+saw was directly behind
+so the idea was trying to give players
+
+ align:start position:0%
+so the idea was trying to give players
+ 
+
+ align:start position:0%
+so the idea was trying to give players
+that range of motion
+
+ align:start position:0%
+that range of motion
+ 
+
+ align:start position:0%
+that range of motion
+and the noises was i listening to more
+
+ align:start position:0%
+and the noises was i listening to more
+ 
+
+ align:start position:0%
+and the noises was i listening to more
+than one target at the time no no okay
+
+ align:start position:0%
+than one target at the time no no okay
+ 
+
+ align:start position:0%
+than one target at the time no no okay
+target voices
+
+ align:start position:0%
+target voices
+ 
+
+ align:start position:0%
+target voices
+that was just one target it was one
+
+ align:start position:0%
+that was just one target it was one
+ 
+
+ align:start position:0%
+that was just one target it was one
+target yes the target would spawn after
+
+ align:start position:0%
+target yes the target would spawn after
+ 
+
+ align:start position:0%
+target yes the target would spawn after
+the next one was destroyed that last one
+
+ align:start position:0%
+the next one was destroyed that last one
+ 
+
+ align:start position:0%
+the next one was destroyed that last one
+was destroyed
+
+ align:start position:0%
+was destroyed
+ 
+
+ align:start position:0%
+was destroyed
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+yeah so front or behind versus left to
+
+ align:start position:0%
+yeah so front or behind versus left to
+ 
+
+ align:start position:0%
+yeah so front or behind versus left to
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+damage death and other punishments
+
+ align:start position:0%
+damage death and other punishments
+ 
+
+ align:start position:0%
+damage death and other punishments
+so you know we talked about like players
+
+ align:start position:0%
+so you know we talked about like players
+ 
+
+ align:start position:0%
+so you know we talked about like players
+spiraling into the void after they jump
+
+ align:start position:0%
+spiraling into the void after they jump
+ 
+
+ align:start position:0%
+spiraling into the void after they jump
+uh what do you do when a player dies you
+
+ align:start position:0%
+uh what do you do when a player dies you
+ 
+
+ align:start position:0%
+uh what do you do when a player dies you
+put them at the the beginning of the
+
+ align:start position:0%
+put them at the the beginning of the
+ 
+
+ align:start position:0%
+put them at the the beginning of the
+level right
+
+ align:start position:0%
+level right
+ 
+
+ align:start position:0%
+level right
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+this is confusing because players don't
+
+ align:start position:0%
+this is confusing because players don't
+ 
+
+ align:start position:0%
+this is confusing because players don't
+really know why they failed they know
+
+ align:start position:0%
+really know why they failed they know
+ 
+
+ align:start position:0%
+really know why they failed they know
+where they are now yeah because now
+
+ align:start position:0%
+where they are now yeah because now
+ 
+
+ align:start position:0%
+where they are now yeah because now
+you've just moved them without them like
+
+ align:start position:0%
+you've just moved them without them like
+ 
+
+ align:start position:0%
+you've just moved them without them like
+moving themselves so they've completely
+
+ align:start position:0%
+moving themselves so they've completely
+ 
+
+ align:start position:0%
+moving themselves so they've completely
+lost
+
+ align:start position:0%
+lost
+ 
+
+ align:start position:0%
+lost
+where they are so we decided to take out
+
+ align:start position:0%
+where they are so we decided to take out
+ 
+
+ align:start position:0%
+where they are so we decided to take out
+damage and dying and
+
+ align:start position:0%
+damage and dying and
+ 
+
+ align:start position:0%
+damage and dying and
+all of that
+
+ align:start position:0%
+all of that
+ 
+
+ align:start position:0%
+all of that
+we have a level with obstacles in it if
+
+ align:start position:0%
+we have a level with obstacles in it if
+ 
+
+ align:start position:0%
+we have a level with obstacles in it if
+you hit the obstacle you say ouch you
+
+ align:start position:0%
+you hit the obstacle you say ouch you
+ 
+
+ align:start position:0%
+you hit the obstacle you say ouch you
+get pushed back a little bit and this
+
+ align:start position:0%
+get pushed back a little bit and this
+ 
+
+ align:start position:0%
+get pushed back a little bit and this
+doesn't disorient players if players are
+
+ align:start position:0%
+doesn't disorient players if players are
+ 
+
+ align:start position:0%
+doesn't disorient players if players are
+worried about dying they're much more
+
+ align:start position:0%
+worried about dying they're much more
+ 
+
+ align:start position:0%
+worried about dying they're much more
+afraid to like move and explore their
+
+ align:start position:0%
+afraid to like move and explore their
+ 
+
+ align:start position:0%
+afraid to like move and explore their
+world as well so we took that out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+level complexity
+
+ align:start position:0%
+level complexity
+ 
+
+ align:start position:0%
+level complexity
+um as i mentioned during the play tests
+
+ align:start position:0%
+um as i mentioned during the play tests
+ 
+
+ align:start position:0%
+um as i mentioned during the play tests
+uh players were saying that as as they
+
+ align:start position:0%
+uh players were saying that as as they
+ 
+
+ align:start position:0%
+uh players were saying that as as they
+were going through they're getting
+
+ align:start position:0%
+were going through they're getting
+ 
+
+ align:start position:0%
+were going through they're getting
+better at navigating they're feeling
+
+ align:start position:0%
+better at navigating they're feeling
+ 
+
+ align:start position:0%
+better at navigating they're feeling
+more confident and they're getting more
+
+ align:start position:0%
+more confident and they're getting more
+ 
+
+ align:start position:0%
+more confident and they're getting more
+used to the sounds they were hearing uh
+
+ align:start position:0%
+used to the sounds they were hearing uh
+ 
+
+ align:start position:0%
+used to the sounds they were hearing uh
+so they're able to detect different
+
+ align:start position:0%
+so they're able to detect different
+ 
+
+ align:start position:0%
+so they're able to detect different
+noises better and the patterns so we're
+
+ align:start position:0%
+noises better and the patterns so we're
+ 
+
+ align:start position:0%
+noises better and the patterns so we're
+wondering how far we can go with this if
+
+ align:start position:0%
+wondering how far we can go with this if
+ 
+
+ align:start position:0%
+wondering how far we can go with this if
+we have people that know how to play the
+
+ align:start position:0%
+we have people that know how to play the
+ 
+
+ align:start position:0%
+we have people that know how to play the
+game how many levels of complexity can
+
+ align:start position:0%
+game how many levels of complexity can
+ 
+
+ align:start position:0%
+game how many levels of complexity can
+we add can we have a staircase of
+
+ align:start position:0%
+we add can we have a staircase of
+ 
+
+ align:start position:0%
+we add can we have a staircase of
+platforms can we make it so you need to
+
+ align:start position:0%
+platforms can we make it so you need to
+ 
+
+ align:start position:0%
+platforms can we make it so you need to
+navigate almost kind of platforms almost
+
+ align:start position:0%
+navigate almost kind of platforms almost
+ 
+
+ align:start position:0%
+navigate almost kind of platforms almost
+like a maze what can we do with this can
+
+ align:start position:0%
+like a maze what can we do with this can
+ 
+
+ align:start position:0%
+like a maze what can we do with this can
+we have enemies how many enemies what
+
+ align:start position:0%
+we have enemies how many enemies what
+ 
+
+ align:start position:0%
+we have enemies how many enemies what
+kind of things can be used uh so the
+
+ align:start position:0%
+kind of things can be used uh so the
+ 
+
+ align:start position:0%
+kind of things can be used uh so the
+idea is really how complex can these end
+
+ align:start position:0%
+idea is really how complex can these end
+ 
+
+ align:start position:0%
+idea is really how complex can these end
+up being made this was not something
+
+ align:start position:0%
+up being made this was not something
+ 
+
+ align:start position:0%
+up being made this was not something
+that we could follow in the scope of
+
+ align:start position:0%
+that we could follow in the scope of
+ 
+
+ align:start position:0%
+that we could follow in the scope of
+this class but that we would like be
+
+ align:start position:0%
+this class but that we would like be
+ 
+
+ align:start position:0%
+this class but that we would like be
+very interested in pursuing and on
+
+ align:start position:0%
+very interested in pursuing and on
+ 
+
+ align:start position:0%
+very interested in pursuing and on
+average it took players about 10 minutes
+
+ align:start position:0%
+average it took players about 10 minutes
+ 
+
+ align:start position:0%
+average it took players about 10 minutes
+to get through all of the levels that we
+
+ align:start position:0%
+to get through all of the levels that we
+ 
+
+ align:start position:0%
+to get through all of the levels that we
+had the three levels we only saw the
+
+ align:start position:0%
+had the three levels we only saw the
+ 
+
+ align:start position:0%
+had the three levels we only saw the
+first one in this round but there's a
+
+ align:start position:0%
+first one in this round but there's a
+ 
+
+ align:start position:0%
+first one in this round but there's a
+level with a platform and a long hallway
+
+ align:start position:0%
+level with a platform and a long hallway
+ 
+
+ align:start position:0%
+level with a platform and a long hallway
+with swinging blades
+
+ align:start position:0%
+with swinging blades
+ 
+
+ align:start position:0%
+with swinging blades
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+and last level guidelines these are we
+
+ align:start position:0%
+and last level guidelines these are we
+ 
+
+ align:start position:0%
+and last level guidelines these are we
+have three main level guidelines that we
+
+ align:start position:0%
+have three main level guidelines that we
+ 
+
+ align:start position:0%
+have three main level guidelines that we
+want that we take as our contributions
+
+ align:start position:0%
+want that we take as our contributions
+ 
+
+ align:start position:0%
+want that we take as our contributions
+and we want to give to you as main
+
+ align:start position:0%
+and we want to give to you as main
+ 
+
+ align:start position:0%
+and we want to give to you as main
+takeaways from our project
+
+ align:start position:0%
+takeaways from our project
+ 
+
+ align:start position:0%
+takeaways from our project
+the first one being to offer the player
+
+ align:start position:0%
+the first one being to offer the player
+ 
+
+ align:start position:0%
+the first one being to offer the player
+one audio target at a time that can be
+
+ align:start position:0%
+one audio target at a time that can be
+ 
+
+ align:start position:0%
+one audio target at a time that can be
+trying to navigate looking for a source
+
+ align:start position:0%
+trying to navigate looking for a source
+ 
+
+ align:start position:0%
+trying to navigate looking for a source
+that can be trying to jump on the
+
+ align:start position:0%
+that can be trying to jump on the
+ 
+
+ align:start position:0%
+that can be trying to jump on the
+platform that can be trying to find the
+
+ align:start position:0%
+platform that can be trying to find the
+ 
+
+ align:start position:0%
+platform that can be trying to find the
+swinging blade
+
+ align:start position:0%
+swinging blade
+ 
+
+ align:start position:0%
+swinging blade
+after you have gotten past that you can
+
+ align:start position:0%
+after you have gotten past that you can
+ 
+
+ align:start position:0%
+after you have gotten past that you can
+present a new target as long as the old
+
+ align:start position:0%
+present a new target as long as the old
+ 
+
+ align:start position:0%
+present a new target as long as the old
+one has been removed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+always have a linear and flat path to
+
+ align:start position:0%
+always have a linear and flat path to
+ 
+
+ align:start position:0%
+always have a linear and flat path to
+follow at least especially in the
+
+ align:start position:0%
+follow at least especially in the
+ 
+
+ align:start position:0%
+follow at least especially in the
+beginning because you can't really
+
+ align:start position:0%
+beginning because you can't really
+ 
+
+ align:start position:0%
+beginning because you can't really
+detect when something is above or below
+
+ align:start position:0%
+detect when something is above or below
+ 
+
+ align:start position:0%
+detect when something is above or below
+you especially if you haven't heard the
+
+ align:start position:0%
+you especially if you haven't heard the
+ 
+
+ align:start position:0%
+you especially if you haven't heard the
+sound before
+
+ align:start position:0%
+sound before
+ 
+
+ align:start position:0%
+sound before
+so especially with these beginning
+
+ align:start position:0%
+so especially with these beginning
+ 
+
+ align:start position:0%
+so especially with these beginning
+levels make sure things are just
+
+ align:start position:0%
+levels make sure things are just
+ 
+
+ align:start position:0%
+levels make sure things are just
+in front of the player so this doesn't
+
+ align:start position:0%
+in front of the player so this doesn't
+ 
+
+ align:start position:0%
+in front of the player so this doesn't
+mean that you can only move forward in a
+
+ align:start position:0%
+mean that you can only move forward in a
+ 
+
+ align:start position:0%
+mean that you can only move forward in a
+level but it means you need to have a
+
+ align:start position:0%
+level but it means you need to have a
+ 
+
+ align:start position:0%
+level but it means you need to have a
+linear progression path so you can like
+
+ align:start position:0%
+linear progression path so you can like
+ 
+
+ align:start position:0%
+linear progression path so you can like
+you can go backwards you can move around
+
+ align:start position:0%
+you can go backwards you can move around
+ 
+
+ align:start position:0%
+you can go backwards you can move around
+but if you've used an element that needs
+
+ align:start position:0%
+but if you've used an element that needs
+ 
+
+ align:start position:0%
+but if you've used an element that needs
+to go away or else be specifically re
+
+ align:start position:0%
+to go away or else be specifically re
+ 
+
+ align:start position:0%
+to go away or else be specifically re
+specifically brought back for reuse
+
+ align:start position:0%
+specifically brought back for reuse
+ 
+
+ align:start position:0%
+specifically brought back for reuse
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+and third give clear and immediate
+
+ align:start position:0%
+and third give clear and immediate
+ 
+
+ align:start position:0%
+and third give clear and immediate
+feedback when you're looking at
+
+ align:start position:0%
+feedback when you're looking at
+ 
+
+ align:start position:0%
+feedback when you're looking at
+something you're able to see
+
+ align:start position:0%
+something you're able to see
+ 
+
+ align:start position:0%
+something you're able to see
+oh i missed the platformer oh i got hit
+
+ align:start position:0%
+oh i missed the platformer oh i got hit
+ 
+
+ align:start position:0%
+oh i missed the platformer oh i got hit
+by something or oh i didn't make the
+
+ align:start position:0%
+by something or oh i didn't make the
+ 
+
+ align:start position:0%
+by something or oh i didn't make the
+jump or oh i ran to a wall but if you
+
+ align:start position:0%
+jump or oh i ran to a wall but if you
+ 
+
+ align:start position:0%
+jump or oh i ran to a wall but if you
+don't have that immediate feedback here
+
+ align:start position:0%
+don't have that immediate feedback here
+ 
+
+ align:start position:0%
+don't have that immediate feedback here
+people are just like what happened i
+
+ align:start position:0%
+people are just like what happened i
+ 
+
+ align:start position:0%
+people are just like what happened i
+it doesn't sound like anything happened
+
+ align:start position:0%
+it doesn't sound like anything happened
+ 
+
+ align:start position:0%
+it doesn't sound like anything happened
+or oh things sound further away now they
+
+ align:start position:0%
+or oh things sound further away now they
+ 
+
+ align:start position:0%
+or oh things sound further away now they
+don't have a good orientation point so
+
+ align:start position:0%
+don't have a good orientation point so
+ 
+
+ align:start position:0%
+don't have a good orientation point so
+footsteps when you're actually walking
+
+ align:start position:0%
+footsteps when you're actually walking
+ 
+
+ align:start position:0%
+footsteps when you're actually walking
+the nope when you can't jump the bump
+
+ align:start position:0%
+the nope when you can't jump the bump
+ 
+
+ align:start position:0%
+the nope when you can't jump the bump
+against the wall when you hit it we're
+
+ align:start position:0%
+against the wall when you hit it we're
+ 
+
+ align:start position:0%
+against the wall when you hit it we're
+very clear and good ways to give that
+
+ align:start position:0%
+very clear and good ways to give that
+ 
+
+ align:start position:0%
+very clear and good ways to give that
+feedback
+
+ align:start position:0%
+feedback
+ 
+
+ align:start position:0%
+feedback
+and okay well that's our presentation
+
+ align:start position:0%
+and okay well that's our presentation
+ 
+
+ align:start position:0%
+and okay well that's our presentation
+it's our game going in blind yes
+
+ align:start position:0%
+it's our game going in blind yes
+ 
+
+ align:start position:0%
+it's our game going in blind yes
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/hm5zqBPsRJM.txt b/hm5zqBPsRJM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..24192df3b169609347b17c67fc8a720673713e84
--- /dev/null
+++ b/hm5zqBPsRJM.txt
@@ -0,0 +1,9259 @@
+align:start position:0%
+ 
+so today we're gonna talk about social
+
+ align:start position:0%
+so today we're gonna talk about social
+ 
+
+ align:start position:0%
+so today we're gonna talk about social
+insurance so why do we have this thing
+
+ align:start position:0%
+insurance so why do we have this thing
+ 
+
+ align:start position:0%
+insurance so why do we have this thing
+called social insurance let's first talk
+
+ align:start position:0%
+called social insurance let's first talk
+ 
+
+ align:start position:0%
+called social insurance let's first talk
+about what social insurance is and then
+
+ align:start position:0%
+about what social insurance is and then
+ 
+
+ align:start position:0%
+about what social insurance is and then
+ask why we have it okay so basically
+
+ align:start position:0%
+ask why we have it okay so basically
+ 
+
+ align:start position:0%
+ask why we have it okay so basically
+social insurance is government provided
+
+ align:start position:0%
+social insurance is government provided
+ 
+
+ align:start position:0%
+social insurance is government provided
+insurance programs this is the largest
+
+ align:start position:0%
+insurance programs this is the largest
+ 
+
+ align:start position:0%
+insurance programs this is the largest
+single category of government
+
+ align:start position:0%
+single category of government
+ 
+
+ align:start position:0%
+single category of government
+expenditure in the u.s. today is
+
+ align:start position:0%
+expenditure in the u.s. today is
+ 
+
+ align:start position:0%
+expenditure in the u.s. today is
+government provided insurance programs
+
+ align:start position:0%
+government provided insurance programs
+ 
+
+ align:start position:0%
+government provided insurance programs
+now why do we have these well you might
+
+ align:start position:0%
+now why do we have these well you might
+ 
+
+ align:start position:0%
+now why do we have these well you might
+say well we know I have these we learned
+
+ align:start position:0%
+say well we know I have these we learned
+ 
+
+ align:start position:0%
+say well we know I have these we learned
+about uncertainty we already talked
+
+ align:start position:0%
+about uncertainty we already talked
+ 
+
+ align:start position:0%
+about uncertainty we already talked
+about how people dislike uncertainty and
+
+ align:start position:0%
+about how people dislike uncertainty and
+ 
+
+ align:start position:0%
+about how people dislike uncertainty and
+about how as a result insurance is big
+
+ align:start position:0%
+about how as a result insurance is big
+ 
+
+ align:start position:0%
+about how as a result insurance is big
+business in America private insurance
+
+ align:start position:0%
+business in America private insurance
+ 
+
+ align:start position:0%
+business in America private insurance
+for health for auto for life for
+
+ align:start position:0%
+for health for auto for life for
+ 
+
+ align:start position:0%
+for health for auto for life for
+property and casualty adds up to about
+
+ align:start position:0%
+property and casualty adds up to about
+ 
+
+ align:start position:0%
+property and casualty adds up to about
+1.5 trillion dollars every year okay so
+
+ align:start position:0%
+1.5 trillion dollars every year okay so
+ 
+
+ align:start position:0%
+1.5 trillion dollars every year okay so
+we already have big business of private
+
+ align:start position:0%
+we already have big business of private
+ 
+
+ align:start position:0%
+we already have big business of private
+insurance so why is the government need
+
+ align:start position:0%
+insurance so why is the government need
+ 
+
+ align:start position:0%
+insurance so why is the government need
+to get involved I mean after all people
+
+ align:start position:0%
+to get involved I mean after all people
+ 
+
+ align:start position:0%
+to get involved I mean after all people
+want insurance if they're risk-averse we
+
+ align:start position:0%
+want insurance if they're risk-averse we
+ 
+
+ align:start position:0%
+want insurance if they're risk-averse we
+talked about insurance markets can work
+
+ align:start position:0%
+talked about insurance markets can work
+ 
+
+ align:start position:0%
+talked about insurance markets can work
+and as always at economics the question
+
+ align:start position:0%
+and as always at economics the question
+ 
+
+ align:start position:0%
+and as always at economics the question
+is what's wrong with the private market
+
+ align:start position:0%
+is what's wrong with the private market
+ 
+
+ align:start position:0%
+is what's wrong with the private market
+what is the market failure that might
+
+ align:start position:0%
+what is the market failure that might
+ 
+
+ align:start position:0%
+what is the market failure that might
+generate interest in government being
+
+ align:start position:0%
+generate interest in government being
+ 
+
+ align:start position:0%
+generate interest in government being
+involved and the market failure in the
+
+ align:start position:0%
+involved and the market failure in the
+ 
+
+ align:start position:0%
+involved and the market failure in the
+context of insurance is a different kind
+
+ align:start position:0%
+context of insurance is a different kind
+ 
+
+ align:start position:0%
+context of insurance is a different kind
+of market rather we've talked about
+
+ align:start position:0%
+of market rather we've talked about
+ 
+
+ align:start position:0%
+of market rather we've talked about
+we've talked about market failures like
+
+ align:start position:0%
+we've talked about market failures like
+ 
+
+ align:start position:0%
+we've talked about market failures like
+imperfect competition as a market
+
+ align:start position:0%
+imperfect competition as a market
+ 
+
+ align:start position:0%
+imperfect competition as a market
+failure we talked about externalities as
+
+ align:start position:0%
+failure we talked about externalities as
+ 
+
+ align:start position:0%
+failure we talked about externalities as
+a market failure the new kind of market
+
+ align:start position:0%
+a market failure the new kind of market
+ 
+
+ align:start position:0%
+a market failure the new kind of market
+oh you want to talk about today is what
+
+ align:start position:0%
+oh you want to talk about today is what
+ 
+
+ align:start position:0%
+oh you want to talk about today is what
+we call information asymmetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+information asymmetry okay basically
+
+ align:start position:0%
+information asymmetry okay basically
+ 
+
+ align:start position:0%
+information asymmetry okay basically
+which is the difference in the
+
+ align:start position:0%
+which is the difference in the
+ 
+
+ align:start position:0%
+which is the difference in the
+information available to sellers and to
+
+ align:start position:0%
+information available to sellers and to
+ 
+
+ align:start position:0%
+information available to sellers and to
+buyers in a given market so far in this
+
+ align:start position:0%
+buyers in a given market so far in this
+ 
+
+ align:start position:0%
+buyers in a given market so far in this
+course we sort of assumed full
+
+ align:start position:0%
+course we sort of assumed full
+ 
+
+ align:start position:0%
+course we sort of assumed full
+information we've assumed everybody
+
+ align:start position:0%
+information we've assumed everybody
+ 
+
+ align:start position:0%
+information we've assumed everybody
+knows everything we weaken that
+
+ align:start position:0%
+knows everything we weaken that
+ 
+
+ align:start position:0%
+knows everything we weaken that
+assumption a little bit with uncertainty
+
+ align:start position:0%
+assumption a little bit with uncertainty
+ 
+
+ align:start position:0%
+assumption a little bit with uncertainty
+and saying that people don't know
+
+ align:start position:0%
+and saying that people don't know
+ 
+
+ align:start position:0%
+and saying that people don't know
+whether they're gonna be sick or healthy
+
+ align:start position:0%
+whether they're gonna be sick or healthy
+ 
+
+ align:start position:0%
+whether they're gonna be sick or healthy
+but they still knew the probabilities
+
+ align:start position:0%
+but they still knew the probabilities
+ 
+
+ align:start position:0%
+but they still knew the probabilities
+now really get it further by saying he
+
+ align:start position:0%
+now really get it further by saying he
+ 
+
+ align:start position:0%
+now really get it further by saying he
+now knows the information imperfect but
+
+ align:start position:0%
+now knows the information imperfect but
+ 
+
+ align:start position:0%
+now knows the information imperfect but
+different parties in a transaction might
+
+ align:start position:0%
+different parties in a transaction might
+ 
+
+ align:start position:0%
+different parties in a transaction might
+have different levels of information and
+
+ align:start position:0%
+have different levels of information and
+ 
+
+ align:start position:0%
+have different levels of information and
+that's going to turn out to cause market
+
+ align:start position:0%
+that's going to turn out to cause market
+ 
+
+ align:start position:0%
+that's going to turn out to cause market
+failure that information asymmetry will
+
+ align:start position:0%
+failure that information asymmetry will
+ 
+
+ align:start position:0%
+failure that information asymmetry will
+cause market failure now the math here
+
+ align:start position:0%
+cause market failure now the math here
+ 
+
+ align:start position:0%
+cause market failure now the math here
+is quite hard harder than we do in this
+
+ align:start position:0%
+is quite hard harder than we do in this
+ 
+
+ align:start position:0%
+is quite hard harder than we do in this
+class so we'll just sort of do this by
+
+ align:start position:0%
+class so we'll just sort of do this by
+ 
+
+ align:start position:0%
+class so we'll just sort of do this by
+an example or two and the best example
+
+ align:start position:0%
+an example or two and the best example
+ 
+
+ align:start position:0%
+an example or two and the best example
+to start with is the so-called lemons
+
+ align:start position:0%
+to start with is the so-called lemons
+ 
+
+ align:start position:0%
+to start with is the so-called lemons
+problem that was laid out by the Nobel
+
+ align:start position:0%
+problem that was laid out by the Nobel
+ 
+
+ align:start position:0%
+problem that was laid out by the Nobel
+prize-winning economist George Akerlof
+
+ align:start position:0%
+prize-winning economist George Akerlof
+ 
+
+ align:start position:0%
+prize-winning economist George Akerlof
+in 1970 Nobel Prize of economists and a
+
+ align:start position:0%
+in 1970 Nobel Prize of economists and a
+ 
+
+ align:start position:0%
+in 1970 Nobel Prize of economists and a
+husband of former Fed Chairman Janet
+
+ align:start position:0%
+husband of former Fed Chairman Janet
+ 
+
+ align:start position:0%
+husband of former Fed Chairman Janet
+Yellen quite a power couple and um
+
+ align:start position:0%
+Yellen quite a power couple and um
+ 
+
+ align:start position:0%
+Yellen quite a power couple and um
+here's what acryl off laid out he said
+
+ align:start position:0%
+here's what acryl off laid out he said
+ 
+
+ align:start position:0%
+here's what acryl off laid out he said
+let's look at the market for used cars
+
+ align:start position:0%
+let's look at the market for used cars
+ 
+
+ align:start position:0%
+let's look at the market for used cars
+so this tomorrow for used cars as of
+
+ align:start position:0%
+so this tomorrow for used cars as of
+ 
+
+ align:start position:0%
+so this tomorrow for used cars as of
+1970 there was no CARFAX
+
+ align:start position:0%
+1970 there was no CARFAX
+ 
+
+ align:start position:0%
+1970 there was no CARFAX
+there was none as information ok 97 when
+
+ align:start position:0%
+there was none as information ok 97 when
+ 
+
+ align:start position:0%
+there was none as information ok 97 when
+to buy a used car just sort of went and
+
+ align:start position:0%
+to buy a used car just sort of went and
+ 
+
+ align:start position:0%
+to buy a used car just sort of went and
+kicked the tires and decide if you're
+
+ align:start position:0%
+kicked the tires and decide if you're
+ 
+
+ align:start position:0%
+kicked the tires and decide if you're
+gonna buy it ok so this is a classic
+
+ align:start position:0%
+gonna buy it ok so this is a classic
+ 
+
+ align:start position:0%
+gonna buy it ok so this is a classic
+case of an information asymmetry in that
+
+ align:start position:0%
+case of an information asymmetry in that
+ 
+
+ align:start position:0%
+case of an information asymmetry in that
+someone selling a car knows what's wrong
+
+ align:start position:0%
+someone selling a car knows what's wrong
+ 
+
+ align:start position:0%
+someone selling a car knows what's wrong
+with it
+
+ align:start position:0%
+with it
+ 
+
+ align:start position:0%
+with it
+where's the person buying the car
+
+ align:start position:0%
+where's the person buying the car
+ 
+
+ align:start position:0%
+where's the person buying the car
+doesn't okay I'll go illegally would
+
+ align:start position:0%
+doesn't okay I'll go illegally would
+ 
+
+ align:start position:0%
+doesn't okay I'll go illegally would
+sort of kick the tires and hope for the
+
+ align:start position:0%
+sort of kick the tires and hope for the
+ 
+
+ align:start position:0%
+sort of kick the tires and hope for the
+best okay we don't so basically um and
+
+ align:start position:0%
+best okay we don't so basically um and
+ 
+
+ align:start position:0%
+best okay we don't so basically um and
+in particular sellers of cars might be
+
+ align:start position:0%
+in particular sellers of cars might be
+ 
+
+ align:start position:0%
+in particular sellers of cars might be
+selling them because they're not good
+
+ align:start position:0%
+selling them because they're not good
+ 
+
+ align:start position:0%
+selling them because they're not good
+after all why sell a car maybe because
+
+ align:start position:0%
+after all why sell a car maybe because
+ 
+
+ align:start position:0%
+after all why sell a car maybe because
+it's what's called a lemon a lemon is
+
+ align:start position:0%
+it's what's called a lemon a lemon is
+ 
+
+ align:start position:0%
+it's what's called a lemon a lemon is
+something which is a poorly performing
+
+ align:start position:0%
+something which is a poorly performing
+ 
+
+ align:start position:0%
+something which is a poorly performing
+product in this case a car that's got
+
+ align:start position:0%
+product in this case a car that's got
+ 
+
+ align:start position:0%
+product in this case a car that's got
+something wrong with it so when you go
+
+ align:start position:0%
+something wrong with it so when you go
+ 
+
+ align:start position:0%
+something wrong with it so when you go
+to buy a car you're worried you want to
+
+ align:start position:0%
+to buy a car you're worried you want to
+ 
+
+ align:start position:0%
+to buy a car you're worried you want to
+buy a car in the used car market but
+
+ align:start position:0%
+buy a car in the used car market but
+ 
+
+ align:start position:0%
+buy a car in the used car market but
+you're worried why is someone selling
+
+ align:start position:0%
+you're worried why is someone selling
+ 
+
+ align:start position:0%
+you're worried why is someone selling
+this car you should be why is someone
+
+ align:start position:0%
+this car you should be why is someone
+ 
+
+ align:start position:0%
+this car you should be why is someone
+selling this car if it's really in good
+
+ align:start position:0%
+selling this car if it's really in good
+ 
+
+ align:start position:0%
+selling this car if it's really in good
+shape why would they be selling it
+
+ align:start position:0%
+shape why would they be selling it
+ 
+
+ align:start position:0%
+shape why would they be selling it
+therefore as a result Akerlof argued
+
+ align:start position:0%
+therefore as a result Akerlof argued
+ 
+
+ align:start position:0%
+therefore as a result Akerlof argued
+there might be a collapse of the entire
+
+ align:start position:0%
+there might be a collapse of the entire
+ 
+
+ align:start position:0%
+there might be a collapse of the entire
+used car market there might not be
+
+ align:start position:0%
+used car market there might not be
+ 
+
+ align:start position:0%
+used car market there might not be
+transactions that happen they can make
+
+ align:start position:0%
+transactions that happen they can make
+ 
+
+ align:start position:0%
+transactions that happen they can make
+both parties better off remember a
+
+ align:start position:0%
+both parties better off remember a
+ 
+
+ align:start position:0%
+both parties better off remember a
+market failure is whenever the private
+
+ align:start position:0%
+market failure is whenever the private
+ 
+
+ align:start position:0%
+market failure is whenever the private
+market fails to maximize welfare what
+
+ align:start position:0%
+market fails to maximize welfare what
+ 
+
+ align:start position:0%
+market fails to maximize welfare what
+that means is a market failure arises
+
+ align:start position:0%
+that means is a market failure arises
+ 
+
+ align:start position:0%
+that means is a market failure arises
+whatever the private market
+
+ align:start position:0%
+whatever the private market
+ 
+
+ align:start position:0%
+whatever the private market
+does not deliver all transactions that
+
+ align:start position:0%
+does not deliver all transactions that
+ 
+
+ align:start position:0%
+does not deliver all transactions that
+make buyer and seller better off okay
+
+ align:start position:0%
+make buyer and seller better off okay
+ 
+
+ align:start position:0%
+make buyer and seller better off okay
+and here and so let's look an example
+
+ align:start position:0%
+and here and so let's look an example
+ 
+
+ align:start position:0%
+and here and so let's look an example
+this suppose that I have a ten-year-old
+
+ align:start position:0%
+this suppose that I have a ten-year-old
+ 
+
+ align:start position:0%
+this suppose that I have a ten-year-old
+car and I keep it in pristine shape hint
+
+ align:start position:0%
+car and I keep it in pristine shape hint
+ 
+
+ align:start position:0%
+car and I keep it in pristine shape hint
+that's not true for me I'm terrible of
+
+ align:start position:0%
+that's not true for me I'm terrible of
+ 
+
+ align:start position:0%
+that's not true for me I'm terrible of
+course but imagine I was someone who
+
+ align:start position:0%
+course but imagine I was someone who
+ 
+
+ align:start position:0%
+course but imagine I was someone who
+wasn't I kept my ten-year-old car in
+
+ align:start position:0%
+wasn't I kept my ten-year-old car in
+ 
+
+ align:start position:0%
+wasn't I kept my ten-year-old car in
+pristine shape and let's say that a
+
+ align:start position:0%
+pristine shape and let's say that a
+ 
+
+ align:start position:0%
+pristine shape and let's say that a
+ten-year-old car in pristine shape is um
+
+ align:start position:0%
+ten-year-old car in pristine shape is um
+ 
+
+ align:start position:0%
+ten-year-old car in pristine shape is um
+and let's say I'm trying to sell this
+
+ align:start position:0%
+and let's say I'm trying to sell this
+ 
+
+ align:start position:0%
+and let's say I'm trying to sell this
+car and let's say that I would happily
+
+ align:start position:0%
+car and let's say that I would happily
+ 
+
+ align:start position:0%
+car and let's say that I would happily
+take $5,000 for this ten-year-old car
+
+ align:start position:0%
+take $5,000 for this ten-year-old car
+ 
+
+ align:start position:0%
+take $5,000 for this ten-year-old car
+that's in pristine shape so I would be
+
+ align:start position:0%
+that's in pristine shape so I would be
+ 
+
+ align:start position:0%
+that's in pristine shape so I would be
+willing to sell at 5k and let's say that
+
+ align:start position:0%
+willing to sell at 5k and let's say that
+ 
+
+ align:start position:0%
+willing to sell at 5k and let's say that
+you let's say Patricia
+
+ align:start position:0%
+you let's say Patricia
+ 
+
+ align:start position:0%
+you let's say Patricia
+needs that used car and she is willing
+
+ align:start position:0%
+needs that used car and she is willing
+ 
+
+ align:start position:0%
+needs that used car and she is willing
+to buy a car that's in good shape for 6k
+
+ align:start position:0%
+to buy a car that's in good shape for 6k
+ 
+
+ align:start position:0%
+to buy a car that's in good shape for 6k
+so my willingness to willingness to
+
+ align:start position:0%
+so my willingness to willingness to
+ 
+
+ align:start position:0%
+so my willingness to willingness to
+provide willingness to supply is 5k her
+
+ align:start position:0%
+provide willingness to supply is 5k her
+ 
+
+ align:start position:0%
+provide willingness to supply is 5k her
+willingness to pay is 6 K so that is a
+
+ align:start position:0%
+willingness to pay is 6 K so that is a
+ 
+
+ align:start position:0%
+willingness to pay is 6 K so that is a
+transaction that should happen given the
+
+ align:start position:0%
+transaction that should happen given the
+ 
+
+ align:start position:0%
+transaction that should happen given the
+quality of my car given this in good
+
+ align:start position:0%
+quality of my car given this in good
+ 
+
+ align:start position:0%
+quality of my car given this in good
+shape she is willing to pay a thousand
+
+ align:start position:0%
+shape she is willing to pay a thousand
+ 
+
+ align:start position:0%
+shape she is willing to pay a thousand
+dollars more than I'm willing to sell it
+
+ align:start position:0%
+dollars more than I'm willing to sell it
+ 
+
+ align:start position:0%
+dollars more than I'm willing to sell it
+for such transaction should happen it'll
+
+ align:start position:0%
+for such transaction should happen it'll
+ 
+
+ align:start position:0%
+for such transaction should happen it'll
+be welfare maximizing but let's say that
+
+ align:start position:0%
+be welfare maximizing but let's say that
+ 
+
+ align:start position:0%
+be welfare maximizing but let's say that
+most ten-year-old cars are not in good
+
+ align:start position:0%
+most ten-year-old cars are not in good
+ 
+
+ align:start position:0%
+most ten-year-old cars are not in good
+shape
+
+ align:start position:0%
+shape
+ 
+
+ align:start position:0%
+shape
+most ten-year-old cars in fact are in
+
+ align:start position:0%
+most ten-year-old cars in fact are in
+ 
+
+ align:start position:0%
+most ten-year-old cars in fact are in
+kind of crappy shape and in fact the for
+
+ align:start position:0%
+kind of crappy shape and in fact the for
+ 
+
+ align:start position:0%
+kind of crappy shape and in fact the for
+the typical ten-year-old car to get it
+
+ align:start position:0%
+the typical ten-year-old car to get it
+ 
+
+ align:start position:0%
+the typical ten-year-old car to get it
+up and running well you'd have to throw
+
+ align:start position:0%
+up and running well you'd have to throw
+ 
+
+ align:start position:0%
+up and running well you'd have to throw
+$2,000 in once you bought it and
+
+ align:start position:0%
+$2,000 in once you bought it and
+ 
+
+ align:start position:0%
+$2,000 in once you bought it and
+Patricia knows this she knows that for
+
+ align:start position:0%
+Patricia knows this she knows that for
+ 
+
+ align:start position:0%
+Patricia knows this she knows that for
+the typical ten-year-old car she would
+
+ align:start position:0%
+the typical ten-year-old car she would
+ 
+
+ align:start position:0%
+the typical ten-year-old car she would
+have to put two thousand dollars in so
+
+ align:start position:0%
+have to put two thousand dollars in so
+ 
+
+ align:start position:0%
+have to put two thousand dollars in so
+her willingness to pay is not 6 K its
+
+ align:start position:0%
+her willingness to pay is not 6 K its
+ 
+
+ align:start position:0%
+her willingness to pay is not 6 K its
+Forte for an average ten-year-old car
+
+ align:start position:0%
+Forte for an average ten-year-old car
+ 
+
+ align:start position:0%
+Forte for an average ten-year-old car
+now I see the Patricia well that's an
+
+ align:start position:0%
+now I see the Patricia well that's an
+ 
+
+ align:start position:0%
+now I see the Patricia well that's an
+average ten-year-old car but I have a
+
+ align:start position:0%
+average ten-year-old car but I have a
+ 
+
+ align:start position:0%
+average ten-year-old car but I have a
+perfect ten-year-old car you don't need
+
+ align:start position:0%
+perfect ten-year-old car you don't need
+ 
+
+ align:start position:0%
+perfect ten-year-old car you don't need
+to put 2 K into it it's good to go so
+
+ align:start position:0%
+to put 2 K into it it's good to go so
+ 
+
+ align:start position:0%
+to put 2 K into it it's good to go so
+why don't we split the difference will
+
+ align:start position:0%
+why don't we split the difference will
+ 
+
+ align:start position:0%
+why don't we split the difference will
+play 55 K and she says no way you're a
+
+ align:start position:0%
+play 55 K and she says no way you're a
+ 
+
+ align:start position:0%
+play 55 K and she says no way you're a
+damn liar I have no way of knowing your
+
+ align:start position:0%
+damn liar I have no way of knowing your
+ 
+
+ align:start position:0%
+damn liar I have no way of knowing your
+car is better than average all I know is
+
+ align:start position:0%
+car is better than average all I know is
+ 
+
+ align:start position:0%
+car is better than average all I know is
+the average ten-year-old car needs
+
+ align:start position:0%
+the average ten-year-old car needs
+ 
+
+ align:start position:0%
+the average ten-year-old car needs
+$2,000 of work so I'm not gonna pay more
+
+ align:start position:0%
+$2,000 of work so I'm not gonna pay more
+ 
+
+ align:start position:0%
+$2,000 of work so I'm not gonna pay more
+than 4
+
+ align:start position:0%
+than 4
+ 
+
+ align:start position:0%
+than 4
+thousand dollars for your car as the
+
+ align:start position:0%
+thousand dollars for your car as the
+ 
+
+ align:start position:0%
+thousand dollars for your car as the
+result Patricia doesn't buy my car and a
+
+ align:start position:0%
+result Patricia doesn't buy my car and a
+ 
+
+ align:start position:0%
+result Patricia doesn't buy my car and a
+transaction that would have made both
+
+ align:start position:0%
+transaction that would have made both
+ 
+
+ align:start position:0%
+transaction that would have made both
+parties better off does not happen a
+
+ align:start position:0%
+parties better off does not happen a
+ 
+
+ align:start position:0%
+parties better off does not happen a
+transaction where if there was full
+
+ align:start position:0%
+transaction where if there was full
+ 
+
+ align:start position:0%
+transaction where if there was full
+information like we have much more of
+
+ align:start position:0%
+information like we have much more of
+ 
+
+ align:start position:0%
+information like we have much more of
+today where you can get the entire
+
+ align:start position:0%
+today where you can get the entire
+ 
+
+ align:start position:0%
+today where you can get the entire
+record of the car all the crash that's
+
+ align:start position:0%
+record of the car all the crash that's
+ 
+
+ align:start position:0%
+record of the car all the crash that's
+been in how much carrots taken care of
+
+ align:start position:0%
+been in how much carrots taken care of
+ 
+
+ align:start position:0%
+been in how much carrots taken care of
+that problem would go away should go
+
+ align:start position:0%
+that problem would go away should go
+ 
+
+ align:start position:0%
+that problem would go away should go
+away because now pictures you could look
+
+ align:start position:0%
+away because now pictures you could look
+ 
+
+ align:start position:0%
+away because now pictures you could look
+at my car fax and note this is this in
+
+ align:start position:0%
+at my car fax and note this is this in
+ 
+
+ align:start position:0%
+at my car fax and note this is this in
+fact is a pristine car and she's more
+
+ align:start position:0%
+fact is a pristine car and she's more
+ 
+
+ align:start position:0%
+fact is a pristine car and she's more
+willing to pay the six thousand for it
+
+ align:start position:0%
+willing to pay the six thousand for it
+ 
+
+ align:start position:0%
+willing to pay the six thousand for it
+but the bottom line is in this world of
+
+ align:start position:0%
+but the bottom line is in this world of
+ 
+
+ align:start position:0%
+but the bottom line is in this world of
+1970 this was a market failure because
+
+ align:start position:0%
+1970 this was a market failure because
+ 
+
+ align:start position:0%
+1970 this was a market failure because
+they transaction that made both parties
+
+ align:start position:0%
+they transaction that made both parties
+ 
+
+ align:start position:0%
+they transaction that made both parties
+better off did not happen because of
+
+ align:start position:0%
+better off did not happen because of
+ 
+
+ align:start position:0%
+better off did not happen because of
+imperfect information okay
+
+ align:start position:0%
+imperfect information okay
+ 
+
+ align:start position:0%
+imperfect information okay
+the buyer was perfectly happy to buy
+
+ align:start position:0%
+the buyer was perfectly happy to buy
+ 
+
+ align:start position:0%
+the buyer was perfectly happy to buy
+Patricia is perfectly happy to buy my
+
+ align:start position:0%
+Patricia is perfectly happy to buy my
+ 
+
+ align:start position:0%
+Patricia is perfectly happy to buy my
+car but because I had information than
+
+ align:start position:0%
+car but because I had information than
+ 
+
+ align:start position:0%
+car but because I had information than
+she didn't and she was suspicious that I
+
+ align:start position:0%
+she didn't and she was suspicious that I
+ 
+
+ align:start position:0%
+she didn't and she was suspicious that I
+was lying
+
+ align:start position:0%
+was lying
+ 
+
+ align:start position:0%
+was lying
+as a result that transaction didn't
+
+ align:start position:0%
+as a result that transaction didn't
+ 
+
+ align:start position:0%
+as a result that transaction didn't
+happen now questions about that people
+
+ align:start position:0%
+happen now questions about that people
+ 
+
+ align:start position:0%
+happen now questions about that people
+understand it's a market failure okay
+
+ align:start position:0%
+understand it's a market failure okay
+ 
+
+ align:start position:0%
+understand it's a market failure okay
+now we come to insurance the story is
+
+ align:start position:0%
+now we come to insurance the story is
+ 
+
+ align:start position:0%
+now we come to insurance the story is
+flipped now it's not the seller that has
+
+ align:start position:0%
+flipped now it's not the seller that has
+ 
+
+ align:start position:0%
+flipped now it's not the seller that has
+the information
+
+ align:start position:0%
+the information
+ 
+
+ align:start position:0%
+the information
+it's the buyer that has the information
+
+ align:start position:0%
+it's the buyer that has the information
+ 
+
+ align:start position:0%
+it's the buyer that has the information
+in particular when you buy insurance you
+
+ align:start position:0%
+in particular when you buy insurance you
+ 
+
+ align:start position:0%
+in particular when you buy insurance you
+know how healthy you are you know your
+
+ align:start position:0%
+know how healthy you are you know your
+ 
+
+ align:start position:0%
+know how healthy you are you know your
+genetic history you know whether you're
+
+ align:start position:0%
+genetic history you know whether you're
+ 
+
+ align:start position:0%
+genetic history you know whether you're
+a risk taker you know whether you're
+
+ align:start position:0%
+a risk taker you know whether you're
+ 
+
+ align:start position:0%
+a risk taker you know whether you're
+around a lot of snotty kids who might
+
+ align:start position:0%
+around a lot of snotty kids who might
+ 
+
+ align:start position:0%
+around a lot of snotty kids who might
+get you sick you know a lot of stuff
+
+ align:start position:0%
+get you sick you know a lot of stuff
+ 
+
+ align:start position:0%
+get you sick you know a lot of stuff
+about yourself that the insurer doesn't
+
+ align:start position:0%
+about yourself that the insurer doesn't
+ 
+
+ align:start position:0%
+about yourself that the insurer doesn't
+know as a result the information
+
+ align:start position:0%
+know as a result the information
+ 
+
+ align:start position:0%
+know as a result the information
+asymmetry is flipped with insurance the
+
+ align:start position:0%
+asymmetry is flipped with insurance the
+ 
+
+ align:start position:0%
+asymmetry is flipped with insurance the
+insurer is worried that when you come
+
+ align:start position:0%
+insurer is worried that when you come
+ 
+
+ align:start position:0%
+insurer is worried that when you come
+looking for insurance they're worried
+
+ align:start position:0%
+looking for insurance they're worried
+ 
+
+ align:start position:0%
+looking for insurance they're worried
+looking for insurance because you're
+
+ align:start position:0%
+looking for insurance because you're
+ 
+
+ align:start position:0%
+looking for insurance because you're
+sick now you might be looking for sure
+
+ align:start position:0%
+sick now you might be looking for sure
+ 
+
+ align:start position:0%
+sick now you might be looking for sure
+it's cuz you're risk-averse and that's
+
+ align:start position:0%
+it's cuz you're risk-averse and that's
+ 
+
+ align:start position:0%
+it's cuz you're risk-averse and that's
+great for insurers we talked about
+
+ align:start position:0%
+great for insurers we talked about
+ 
+
+ align:start position:0%
+great for insurers we talked about
+insurance how there's essentially a gain
+
+ align:start position:0%
+insurance how there's essentially a gain
+ 
+
+ align:start position:0%
+insurance how there's essentially a gain
+I'm willing to pay a risk premium so
+
+ align:start position:0%
+I'm willing to pay a risk premium so
+ 
+
+ align:start position:0%
+I'm willing to pay a risk premium so
+insurers can make money by selling to me
+
+ align:start position:0%
+insurers can make money by selling to me
+ 
+
+ align:start position:0%
+insurers can make money by selling to me
+but what if I'm not coming to you I'm
+
+ align:start position:0%
+but what if I'm not coming to you I'm
+ 
+
+ align:start position:0%
+but what if I'm not coming to you I'm
+risk averse whatever I'm coming because
+
+ align:start position:0%
+risk averse whatever I'm coming because
+ 
+
+ align:start position:0%
+risk averse whatever I'm coming because
+I'm a huge skydiving fan okay and you
+
+ align:start position:0%
+I'm a huge skydiving fan okay and you
+ 
+
+ align:start position:0%
+I'm a huge skydiving fan okay and you
+don't know that you might be afraid to
+
+ align:start position:0%
+don't know that you might be afraid to
+ 
+
+ align:start position:0%
+don't know that you might be afraid to
+sell me insurance because you might lose
+
+ align:start position:0%
+sell me insurance because you might lose
+ 
+
+ align:start position:0%
+sell me insurance because you might lose
+money on me
+
+ align:start position:0%
+money on me
+ 
+
+ align:start position:0%
+money on me
+okay so let's work out another example
+
+ align:start position:0%
+okay so let's work out another example
+ 
+
+ align:start position:0%
+okay so let's work out another example
+to show this imagine you graduate and
+
+ align:start position:0%
+to show this imagine you graduate and
+ 
+
+ align:start position:0%
+to show this imagine you graduate and
+you decide a great business model is to
+
+ align:start position:0%
+you decide a great business model is to
+ 
+
+ align:start position:0%
+you decide a great business model is to
+offer health insurance to recent MIT
+
+ align:start position:0%
+offer health insurance to recent MIT
+ 
+
+ align:start position:0%
+offer health insurance to recent MIT
+grads
+
+ align:start position:0%
+grads
+ 
+
+ align:start position:0%
+grads
+you say look we're a bunch of kind of
+
+ align:start position:0%
+you say look we're a bunch of kind of
+ 
+
+ align:start position:0%
+you say look we're a bunch of kind of
+careful nerds we're like not going to go
+
+ align:start position:0%
+careful nerds we're like not going to go
+ 
+
+ align:start position:0%
+careful nerds we're like not going to go
+skydiving we're like just gonna sit our
+
+ align:start position:0%
+skydiving we're like just gonna sit our
+ 
+
+ align:start position:0%
+skydiving we're like just gonna sit our
+desks and work maybe there'll be carpal
+
+ align:start position:0%
+desks and work maybe there'll be carpal
+ 
+
+ align:start position:0%
+desks and work maybe there'll be carpal
+tunnel risk but other than that we're
+
+ align:start position:0%
+tunnel risk but other than that we're
+ 
+
+ align:start position:0%
+tunnel risk but other than that we're
+pretty safe bunch so I'm going out for
+
+ align:start position:0%
+pretty safe bunch so I'm going out for
+ 
+
+ align:start position:0%
+pretty safe bunch so I'm going out for
+health insurance a recent MIT grads
+
+ align:start position:0%
+health insurance a recent MIT grads
+ 
+
+ align:start position:0%
+health insurance a recent MIT grads
+because they're a healthy group and
+
+ align:start position:0%
+because they're a healthy group and
+ 
+
+ align:start position:0%
+because they're a healthy group and
+let's say suppose that of every hundred
+
+ align:start position:0%
+let's say suppose that of every hundred
+ 
+
+ align:start position:0%
+let's say suppose that of every hundred
+MIT grads 90 are healthy and 10 are
+
+ align:start position:0%
+MIT grads 90 are healthy and 10 are
+ 
+
+ align:start position:0%
+MIT grads 90 are healthy and 10 are
+sickly let's just suppose you know those
+
+ align:start position:0%
+sickly let's just suppose you know those
+ 
+
+ align:start position:0%
+sickly let's just suppose you know those
+facts you know those facts you've
+
+ align:start position:0%
+facts you know those facts you've
+ 
+
+ align:start position:0%
+facts you know those facts you've
+collected the data to know that on
+
+ align:start position:0%
+collected the data to know that on
+ 
+
+ align:start position:0%
+collected the data to know that on
+average of every hovering hundred grads
+
+ align:start position:0%
+average of every hovering hundred grads
+ 
+
+ align:start position:0%
+average of every hovering hundred grads
+nine you're healthy ten or sickly you
+
+ align:start position:0%
+nine you're healthy ten or sickly you
+ 
+
+ align:start position:0%
+nine you're healthy ten or sickly you
+don't know which are which but you know
+
+ align:start position:0%
+don't know which are which but you know
+ 
+
+ align:start position:0%
+don't know which are which but you know
+the proportions and let's say that with
+
+ align:start position:0%
+the proportions and let's say that with
+ 
+
+ align:start position:0%
+the proportions and let's say that with
+a healthy person over the next year
+
+ align:start position:0%
+a healthy person over the next year
+ 
+
+ align:start position:0%
+a healthy person over the next year
+there's a 10% chance that they will need
+
+ align:start position:0%
+there's a 10% chance that they will need
+ 
+
+ align:start position:0%
+there's a 10% chance that they will need
+that they will encourage that they will
+
+ align:start position:0%
+that they will encourage that they will
+ 
+
+ align:start position:0%
+that they will encourage that they will
+incur a $10,000 charge and a 90% chance
+
+ align:start position:0%
+incur a $10,000 charge and a 90% chance
+ 
+
+ align:start position:0%
+incur a $10,000 charge and a 90% chance
+that they will 90% chance that they'll
+
+ align:start position:0%
+that they will 90% chance that they'll
+ 
+
+ align:start position:0%
+that they will 90% chance that they'll
+have zero costs okay so there's a 10%
+
+ align:start position:0%
+have zero costs okay so there's a 10%
+ 
+
+ align:start position:0%
+have zero costs okay so there's a 10%
+chance fall of a ten thousand dollar
+
+ align:start position:0%
+chance fall of a ten thousand dollar
+ 
+
+ align:start position:0%
+chance fall of a ten thousand dollar
+costs knives a chisel of a zero cost
+
+ align:start position:0%
+costs knives a chisel of a zero cost
+ 
+
+ align:start position:0%
+costs knives a chisel of a zero cost
+okay so your expected cost for assuring
+
+ align:start position:0%
+okay so your expected cost for assuring
+ 
+
+ align:start position:0%
+okay so your expected cost for assuring
+this person is one thousand dollars you
+
+ align:start position:0%
+this person is one thousand dollars you
+ 
+
+ align:start position:0%
+this person is one thousand dollars you
+expect someone like that will cost you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$1,000 now suppose for the sickly guy
+
+ align:start position:0%
+$1,000 now suppose for the sickly guy
+ 
+
+ align:start position:0%
+$1,000 now suppose for the sickly guy
+there's a 50% chance 50% chance that
+
+ align:start position:0%
+there's a 50% chance 50% chance that
+ 
+
+ align:start position:0%
+there's a 50% chance 50% chance that
+they'll cost you 10 K and a 50% chance
+
+ align:start position:0%
+they'll cost you 10 K and a 50% chance
+ 
+
+ align:start position:0%
+they'll cost you 10 K and a 50% chance
+that they'll cost you zero so you
+
+ align:start position:0%
+that they'll cost you zero so you
+ 
+
+ align:start position:0%
+that they'll cost you zero so you
+expected costs for them or the expected
+
+ align:start position:0%
+expected costs for them or the expected
+ 
+
+ align:start position:0%
+expected costs for them or the expected
+cost for this person is $5000 okay do
+
+ align:start position:0%
+cost for this person is $5000 okay do
+ 
+
+ align:start position:0%
+cost for this person is $5000 okay do
+people understand the setup there's two
+
+ align:start position:0%
+people understand the setup there's two
+ 
+
+ align:start position:0%
+people understand the setup there's two
+types I know
+
+ align:start position:0%
+types I know
+ 
+
+ align:start position:0%
+types I know
+these facts but I don't know who's who I
+
+ align:start position:0%
+these facts but I don't know who's who I
+ 
+
+ align:start position:0%
+these facts but I don't know who's who I
+just know these facts okay because I'm
+
+ align:start position:0%
+just know these facts okay because I'm
+ 
+
+ align:start position:0%
+just know these facts okay because I'm
+good at math I've done all the actuarial
+
+ align:start position:0%
+good at math I've done all the actuarial
+ 
+
+ align:start position:0%
+good at math I've done all the actuarial
+calculations okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if everyone buys and now I'm gonna set
+
+ align:start position:0%
+if everyone buys and now I'm gonna set
+ 
+
+ align:start position:0%
+if everyone buys and now I'm gonna set
+my price well I'm gonna do the price I'm
+
+ align:start position:0%
+my price well I'm gonna do the price I'm
+ 
+
+ align:start position:0%
+my price well I'm gonna do the price I'm
+going to say look if everyone by is
+
+ align:start position:0%
+going to say look if everyone by is
+ 
+
+ align:start position:0%
+going to say look if everyone by is
+health insurance then I've got my
+
+ align:start position:0%
+health insurance then I've got my
+ 
+
+ align:start position:0%
+health insurance then I've got my
+expected cost is 0.9 times a thousand
+
+ align:start position:0%
+expected cost is 0.9 times a thousand
+ 
+
+ align:start position:0%
+expected cost is 0.9 times a thousand
+plus 0.1 times 5000 my expected cost is
+
+ align:start position:0%
+plus 0.1 times 5000 my expected cost is
+ 
+
+ align:start position:0%
+plus 0.1 times 5000 my expected cost is
+1,400 so I expect to have to spend
+
+ align:start position:0%
+1,400 so I expect to have to spend
+ 
+
+ align:start position:0%
+1,400 so I expect to have to spend
+fourteen hundred a year in fact on
+
+ align:start position:0%
+fourteen hundred a year in fact on
+ 
+
+ align:start position:0%
+fourteen hundred a year in fact on
+average I'll spend fourteen hundred a
+
+ align:start position:0%
+average I'll spend fourteen hundred a
+ 
+
+ align:start position:0%
+average I'll spend fourteen hundred a
+year okay with large enough samples I
+
+ align:start position:0%
+year okay with large enough samples I
+ 
+
+ align:start position:0%
+year okay with large enough samples I
+can predict that with certainty that if
+
+ align:start position:0%
+can predict that with certainty that if
+ 
+
+ align:start position:0%
+can predict that with certainty that if
+everyone buys insurance I'll spend
+
+ align:start position:0%
+everyone buys insurance I'll spend
+ 
+
+ align:start position:0%
+everyone buys insurance I'll spend
+fourteen hundred dollars a year so let's
+
+ align:start position:0%
+fourteen hundred dollars a year so let's
+ 
+
+ align:start position:0%
+fourteen hundred dollars a year so let's
+say you're risk neutral because you're
+
+ align:start position:0%
+say you're risk neutral because you're
+ 
+
+ align:start position:0%
+say you're risk neutral because you're
+rich and so for 200 you know this is
+
+ align:start position:0%
+rich and so for 200 you know this is
+ 
+
+ align:start position:0%
+rich and so for 200 you know this is
+sort of risk neutral for you so you say
+
+ align:start position:0%
+sort of risk neutral for you so you say
+ 
+
+ align:start position:0%
+sort of risk neutral for you so you say
+look I'll just charge I'll set a premium
+
+ align:start position:0%
+look I'll just charge I'll set a premium
+ 
+
+ align:start position:0%
+look I'll just charge I'll set a premium
+of 1500 and I'll make a hundred dollars
+
+ align:start position:0%
+of 1500 and I'll make a hundred dollars
+ 
+
+ align:start position:0%
+of 1500 and I'll make a hundred dollars
+per person if a hundred will buy that's
+
+ align:start position:0%
+per person if a hundred will buy that's
+ 
+
+ align:start position:0%
+per person if a hundred will buy that's
+$10,000 profit that's pretty good okay
+
+ align:start position:0%
+$10,000 profit that's pretty good okay
+ 
+
+ align:start position:0%
+$10,000 profit that's pretty good okay
+there are thousand kids in a graduating
+
+ align:start position:0%
+there are thousand kids in a graduating
+ 
+
+ align:start position:0%
+there are thousand kids in a graduating
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+it's a thousand kids buy and I make
+
+ align:start position:0%
+it's a thousand kids buy and I make
+ 
+
+ align:start position:0%
+it's a thousand kids buy and I make
+hundreds profit it's at the hundred
+
+ align:start position:0%
+hundreds profit it's at the hundred
+ 
+
+ align:start position:0%
+hundreds profit it's at the hundred
+thousand that's pretty good money for a
+
+ align:start position:0%
+thousand that's pretty good money for a
+ 
+
+ align:start position:0%
+thousand that's pretty good money for a
+year okay now what is wrong with this
+
+ align:start position:0%
+year okay now what is wrong with this
+ 
+
+ align:start position:0%
+year okay now what is wrong with this
+calculation what in fact will happen if
+
+ align:start position:0%
+calculation what in fact will happen if
+ 
+
+ align:start position:0%
+calculation what in fact will happen if
+you sell insurance for fifteen hundred
+
+ align:start position:0%
+you sell insurance for fifteen hundred
+ 
+
+ align:start position:0%
+you sell insurance for fifteen hundred
+dollars
+
+ align:start position:0%
+dollars
+ 
+
+ align:start position:0%
+dollars
+yeah well let's go step by step what
+
+ align:start position:0%
+yeah well let's go step by step what
+ 
+
+ align:start position:0%
+yeah well let's go step by step what
+about sick people if you sell fifteen
+
+ align:start position:0%
+about sick people if you sell fifteen
+ 
+
+ align:start position:0%
+about sick people if you sell fifteen
+hundred dollars what will they do yes so
+
+ align:start position:0%
+hundred dollars what will they do yes so
+ 
+
+ align:start position:0%
+hundred dollars what will they do yes so
+if you set up fifty hundred dollars you
+
+ align:start position:0%
+if you set up fifty hundred dollars you
+ 
+
+ align:start position:0%
+if you set up fifty hundred dollars you
+are certainly going to sell to all the
+
+ align:start position:0%
+are certainly going to sell to all the
+ 
+
+ align:start position:0%
+are certainly going to sell to all the
+sick okay so if you sell for fifteen
+
+ align:start position:0%
+sick okay so if you sell for fifteen
+ 
+
+ align:start position:0%
+sick okay so if you sell for fifteen
+hundred dollars you'll certainly sell to
+
+ align:start position:0%
+hundred dollars you'll certainly sell to
+ 
+
+ align:start position:0%
+hundred dollars you'll certainly sell to
+all the sick what about the healthy what
+
+ align:start position:0%
+all the sick what about the healthy what
+ 
+
+ align:start position:0%
+all the sick what about the healthy what
+will determine whether or not they buy
+
+ align:start position:0%
+will determine whether or not they buy
+ 
+
+ align:start position:0%
+will determine whether or not they buy
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not quite not quite there's another
+
+ align:start position:0%
+not quite not quite there's another
+ 
+
+ align:start position:0%
+not quite not quite there's another
+piece too don't forget what else what
+
+ align:start position:0%
+piece too don't forget what else what
+ 
+
+ align:start position:0%
+piece too don't forget what else what
+else what else is not just expected cost
+
+ align:start position:0%
+else what else is not just expected cost
+ 
+
+ align:start position:0%
+else what else is not just expected cost
+what else version remember there's a
+
+ align:start position:0%
+what else version remember there's a
+ 
+
+ align:start position:0%
+what else version remember there's a
+risk premium that they'll pay so whether
+
+ align:start position:0%
+risk premium that they'll pay so whether
+ 
+
+ align:start position:0%
+risk premium that they'll pay so whether
+that's healthy person will buy or not
+
+ align:start position:0%
+that's healthy person will buy or not
+ 
+
+ align:start position:0%
+that's healthy person will buy or not
+you just expected cost then they
+
+ align:start position:0%
+you just expected cost then they
+ 
+
+ align:start position:0%
+you just expected cost then they
+wouldn't buy it's a thousand dollars
+
+ align:start position:0%
+wouldn't buy it's a thousand dollars
+ 
+
+ align:start position:0%
+wouldn't buy it's a thousand dollars
+expected cost while the 1500 but some
+
+ align:start position:0%
+expected cost while the 1500 but some
+ 
+
+ align:start position:0%
+expected cost while the 1500 but some
+might be risk-averse and buy so let's
+
+ align:start position:0%
+might be risk-averse and buy so let's
+ 
+
+ align:start position:0%
+might be risk-averse and buy so let's
+say let's just say half the guys are
+
+ align:start position:0%
+say let's just say half the guys are
+ 
+
+ align:start position:0%
+say let's just say half the guys are
+risk averse and they they're willing to
+
+ align:start position:0%
+risk averse and they they're willing to
+ 
+
+ align:start position:0%
+risk averse and they they're willing to
+pay 1500 for $1,000 expected cost and a
+
+ align:start position:0%
+pay 1500 for $1,000 expected cost and a
+ 
+
+ align:start position:0%
+pay 1500 for $1,000 expected cost and a
+half arm so let's say you end up selling
+
+ align:start position:0%
+half arm so let's say you end up selling
+ 
+
+ align:start position:0%
+half arm so let's say you end up selling
+to all the sick and half the healthy
+
+ align:start position:0%
+to all the sick and half the healthy
+ 
+
+ align:start position:0%
+to all the sick and half the healthy
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so how much money do you make well you
+
+ align:start position:0%
+so how much money do you make well you
+ 
+
+ align:start position:0%
+so how much money do you make well you
+make you sell with 60 people at $1,500
+
+ align:start position:0%
+make you sell with 60 people at $1,500
+ 
+
+ align:start position:0%
+make you sell with 60 people at $1,500
+each so your revenues are $75,000 right
+
+ align:start position:0%
+each so your revenues are $75,000 right
+ 
+
+ align:start position:0%
+each so your revenues are $75,000 right
+you sell 250 healthy intense ik7 $5,000
+
+ align:start position:0%
+you sell 250 healthy intense ik7 $5,000
+ 
+
+ align:start position:0%
+you sell 250 healthy intense ik7 $5,000
+Remy's what are your costs your costs
+
+ align:start position:0%
+Remy's what are your costs your costs
+ 
+
+ align:start position:0%
+Remy's what are your costs your costs
+are you have 10 people that are cost you
+
+ align:start position:0%
+are you have 10 people that are cost you
+ 
+
+ align:start position:0%
+are you have 10 people that are cost you
+five thousand so it's 50 thousand plus
+
+ align:start position:0%
+five thousand so it's 50 thousand plus
+ 
+
+ align:start position:0%
+five thousand so it's 50 thousand plus
+50 people are going to cost you a
+
+ align:start position:0%
+50 people are going to cost you a
+ 
+
+ align:start position:0%
+50 people are going to cost you a
+thousand plus another 50 thousand equals
+
+ align:start position:0%
+thousand plus another 50 thousand equals
+ 
+
+ align:start position:0%
+thousand plus another 50 thousand equals
+one hundred thousand dollars and you've
+
+ align:start position:0%
+one hundred thousand dollars and you've
+ 
+
+ align:start position:0%
+one hundred thousand dollars and you've
+lost money you priced at above the
+
+ align:start position:0%
+lost money you priced at above the
+ 
+
+ align:start position:0%
+lost money you priced at above the
+expected total and lost money why did
+
+ align:start position:0%
+expected total and lost money why did
+ 
+
+ align:start position:0%
+expected total and lost money why did
+you lose money you lost money because of
+
+ align:start position:0%
+you lose money you lost money because of
+ 
+
+ align:start position:0%
+you lose money you lost money because of
+the problem of adverse selection the
+
+ align:start position:0%
+the problem of adverse selection the
+ 
+
+ align:start position:0%
+the problem of adverse selection the
+problem of we call adverse selection
+
+ align:start position:0%
+problem of we call adverse selection
+ 
+
+ align:start position:0%
+problem of we call adverse selection
+adverse selection is the problem that
+
+ align:start position:0%
+adverse selection is the problem that
+ 
+
+ align:start position:0%
+adverse selection is the problem that
+due to information asymmetries only the
+
+ align:start position:0%
+due to information asymmetries only the
+ 
+
+ align:start position:0%
+due to information asymmetries only the
+worst risks will participate in the
+
+ align:start position:0%
+worst risks will participate in the
+ 
+
+ align:start position:0%
+worst risks will participate in the
+market and that will cost people selling
+
+ align:start position:0%
+market and that will cost people selling
+ 
+
+ align:start position:0%
+market and that will cost people selling
+in the market to lose money or likewise
+
+ align:start position:0%
+in the market to lose money or likewise
+ 
+
+ align:start position:0%
+in the market to lose money or likewise
+here the concern is that only the only
+
+ align:start position:0%
+here the concern is that only the only
+ 
+
+ align:start position:0%
+here the concern is that only the only
+the worst cars will put his fate in the
+
+ align:start position:0%
+the worst cars will put his fate in the
+ 
+
+ align:start position:0%
+the worst cars will put his fate in the
+market and so the people buy cars will
+
+ align:start position:0%
+market and so the people buy cars will
+ 
+
+ align:start position:0%
+market and so the people buy cars will
+be worse off yeah
+
+ align:start position:0%
+be worse off yeah
+ 
+
+ align:start position:0%
+be worse off yeah
+we can make know you sell to you sell
+
+ align:start position:0%
+we can make know you sell to you sell
+ 
+
+ align:start position:0%
+we can make know you sell to you sell
+1500 each and you sell to uh yes you're
+
+ align:start position:0%
+1500 each and you sell to uh yes you're
+ 
+
+ align:start position:0%
+1500 each and you sell to uh yes you're
+right you'd make ninety thousand my bad
+
+ align:start position:0%
+right you'd make ninety thousand my bad
+ 
+
+ align:start position:0%
+right you'd make ninety thousand my bad
+yes fifteen hundred each time sixty
+
+ align:start position:0%
+yes fifteen hundred each time sixty
+ 
+
+ align:start position:0%
+yes fifteen hundred each time sixty
+people's ninety thousand he still lose
+
+ align:start position:0%
+people's ninety thousand he still lose
+ 
+
+ align:start position:0%
+people's ninety thousand he still lose
+money but not as much right okay now
+
+ align:start position:0%
+money but not as much right okay now
+ 
+
+ align:start position:0%
+money but not as much right okay now
+there's no you might say look you're not
+
+ align:start position:0%
+there's no you might say look you're not
+ 
+
+ align:start position:0%
+there's no you might say look you're not
+losing that much easy solution just
+
+ align:start position:0%
+losing that much easy solution just
+ 
+
+ align:start position:0%
+losing that much easy solution just
+raise the price right what if he said
+
+ align:start position:0%
+raise the price right what if he said
+ 
+
+ align:start position:0%
+raise the price right what if he said
+fine let's just raise the price and
+
+ align:start position:0%
+fine let's just raise the price and
+ 
+
+ align:start position:0%
+fine let's just raise the price and
+let's charge two thousand dollars a
+
+ align:start position:0%
+let's charge two thousand dollars a
+ 
+
+ align:start position:0%
+let's charge two thousand dollars a
+person then that would cover right
+
+ align:start position:0%
+person then that would cover right
+ 
+
+ align:start position:0%
+person then that would cover right
+because two thousand dollars a person
+
+ align:start position:0%
+because two thousand dollars a person
+ 
+
+ align:start position:0%
+because two thousand dollars a person
+six who will make one hundred and twenty
+
+ align:start position:0%
+six who will make one hundred and twenty
+ 
+
+ align:start position:0%
+six who will make one hundred and twenty
+thousand the costs are a hundred
+
+ align:start position:0%
+thousand the costs are a hundred
+ 
+
+ align:start position:0%
+thousand the costs are a hundred
+thousand you'd be golden right yeah who
+
+ align:start position:0%
+thousand you'd be golden right yeah who
+ 
+
+ align:start position:0%
+thousand you'd be golden right yeah who
+would you lose not the sick the sick are
+
+ align:start position:0%
+would you lose not the sick the sick are
+ 
+
+ align:start position:0%
+would you lose not the sick the sick are
+delighted by ten thousand but once you
+
+ align:start position:0%
+delighted by ten thousand but once you
+ 
+
+ align:start position:0%
+delighted by ten thousand but once you
+raise the price more healthy people drop
+
+ align:start position:0%
+raise the price more healthy people drop
+ 
+
+ align:start position:0%
+raise the price more healthy people drop
+out because it's higher than the risk
+
+ align:start position:0%
+out because it's higher than the risk
+ 
+
+ align:start position:0%
+out because it's higher than the risk
+premium so what happens is by raising
+
+ align:start position:0%
+premium so what happens is by raising
+ 
+
+ align:start position:0%
+premium so what happens is by raising
+the price you necessarily make money it
+
+ align:start position:0%
+the price you necessarily make money it
+ 
+
+ align:start position:0%
+the price you necessarily make money it
+depends on how many healthy people drop
+
+ align:start position:0%
+depends on how many healthy people drop
+ 
+
+ align:start position:0%
+depends on how many healthy people drop
+out so for example imagine that you
+
+ align:start position:0%
+out so for example imagine that you
+ 
+
+ align:start position:0%
+out so for example imagine that you
+raise it to two thousand dollars but now
+
+ align:start position:0%
+raise it to two thousand dollars but now
+ 
+
+ align:start position:0%
+raise it to two thousand dollars but now
+the number of healthy people that buys
+
+ align:start position:0%
+the number of healthy people that buys
+ 
+
+ align:start position:0%
+the number of healthy people that buys
+drops to 20 from fifty then you lose
+
+ align:start position:0%
+drops to 20 from fifty then you lose
+ 
+
+ align:start position:0%
+drops to 20 from fifty then you lose
+money again so the point is you can
+
+ align:start position:0%
+money again so the point is you can
+ 
+
+ align:start position:0%
+money again so the point is you can
+actually solve this problem just by
+
+ align:start position:0%
+actually solve this problem just by
+ 
+
+ align:start position:0%
+actually solve this problem just by
+raising the price because there's this
+
+ align:start position:0%
+raising the price because there's this
+ 
+
+ align:start position:0%
+raising the price because there's this
+what we call death spiral does this term
+
+ align:start position:0%
+what we call death spiral does this term
+ 
+
+ align:start position:0%
+what we call death spiral does this term
+of call a death spiral which is as you
+
+ align:start position:0%
+of call a death spiral which is as you
+ 
+
+ align:start position:0%
+of call a death spiral which is as you
+raise the price you chase out the
+
+ align:start position:0%
+raise the price you chase out the
+ 
+
+ align:start position:0%
+raise the price you chase out the
+healthier people which means you have to
+
+ align:start position:0%
+healthier people which means you have to
+ 
+
+ align:start position:0%
+healthier people which means you have to
+raise the price more which shakes out
+
+ align:start position:0%
+raise the price more which shakes out
+ 
+
+ align:start position:0%
+raise the price more which shakes out
+even healthier even more healthy people
+
+ align:start position:0%
+even healthier even more healthy people
+ 
+
+ align:start position:0%
+even healthier even more healthy people
+and you end up in this death spiral okay
+
+ align:start position:0%
+and you end up in this death spiral okay
+ 
+
+ align:start position:0%
+and you end up in this death spiral okay
+so that is the problem of that is the
+
+ align:start position:0%
+so that is the problem of that is the
+ 
+
+ align:start position:0%
+so that is the problem of that is the
+problem of adverse selection and that
+
+ align:start position:0%
+problem of adverse selection and that
+ 
+
+ align:start position:0%
+problem of adverse selection and that
+leads you to say you know what I'm not
+
+ align:start position:0%
+leads you to say you know what I'm not
+ 
+
+ align:start position:0%
+leads you to say you know what I'm not
+going to offer this product I can't make
+
+ align:start position:0%
+going to offer this product I can't make
+ 
+
+ align:start position:0%
+going to offer this product I can't make
+money on it because what if I set the
+
+ align:start position:0%
+money on it because what if I set the
+ 
+
+ align:start position:0%
+money on it because what if I set the
+price um whatever price I said I'm gonna
+
+ align:start position:0%
+price um whatever price I said I'm gonna
+ 
+
+ align:start position:0%
+price um whatever price I said I'm gonna
+lose money so I'm not gonna offer the
+
+ align:start position:0%
+lose money so I'm not gonna offer the
+ 
+
+ align:start position:0%
+lose money so I'm not gonna offer the
+product therefore the market has failed
+
+ align:start position:0%
+product therefore the market has failed
+ 
+
+ align:start position:0%
+product therefore the market has failed
+a market that might have existed on
+
+ align:start position:0%
+a market that might have existed on
+ 
+
+ align:start position:0%
+a market that might have existed on
+average this was a market that made
+
+ align:start position:0%
+average this was a market that made
+ 
+
+ align:start position:0%
+average this was a market that made
+people better off but the market that
+
+ align:start position:0%
+people better off but the market that
+ 
+
+ align:start position:0%
+people better off but the market that
+might have existed doesn't does it exist
+
+ align:start position:0%
+might have existed doesn't does it exist
+ 
+
+ align:start position:0%
+might have existed doesn't does it exist
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so if you leave this alone that's
+
+ align:start position:0%
+right so if you leave this alone that's
+ 
+
+ align:start position:0%
+right so if you leave this alone that's
+an excellent point
+
+ align:start position:0%
+an excellent point
+ 
+
+ align:start position:0%
+an excellent point
+watch what should the new equilibrium be
+
+ align:start position:0%
+watch what should the new equilibrium be
+ 
+
+ align:start position:0%
+watch what should the new equilibrium be
+the price brow should continue to you've
+
+ align:start position:0%
+the price brow should continue to you've
+ 
+
+ align:start position:0%
+the price brow should continue to you've
+chased all the healthy people out and
+
+ align:start position:0%
+chased all the healthy people out and
+ 
+
+ align:start position:0%
+chased all the healthy people out and
+then you price but you'd have to price
+
+ align:start position:0%
+then you price but you'd have to price
+ 
+
+ align:start position:0%
+then you price but you'd have to price
+it then at what five thousand plus
+
+ align:start position:0%
+it then at what five thousand plus
+ 
+
+ align:start position:0%
+it then at what five thousand plus
+something so as long as sickly people or
+
+ align:start position:0%
+something so as long as sickly people or
+ 
+
+ align:start position:0%
+something so as long as sickly people or
+risk-averse you could still make money
+
+ align:start position:0%
+risk-averse you could still make money
+ 
+
+ align:start position:0%
+risk-averse you could still make money
+you can still make money if you sold say
+
+ align:start position:0%
+you can still make money if you sold say
+ 
+
+ align:start position:0%
+you can still make money if you sold say
+fifty five hundred with even modest risk
+
+ align:start position:0%
+fifty five hundred with even modest risk
+ 
+
+ align:start position:0%
+fifty five hundred with even modest risk
+aversion why is that still a market
+
+ align:start position:0%
+aversion why is that still a market
+ 
+
+ align:start position:0%
+aversion why is that still a market
+failure well because there's there's all
+
+ align:start position:0%
+failure well because there's there's all
+ 
+
+ align:start position:0%
+failure well because there's there's all
+these healthy people who now can't get
+
+ align:start position:0%
+these healthy people who now can't get
+ 
+
+ align:start position:0%
+these healthy people who now can't get
+health insurance okay so yes it doesn't
+
+ align:start position:0%
+health insurance okay so yes it doesn't
+ 
+
+ align:start position:0%
+health insurance okay so yes it doesn't
+mean the market collapses market
+
+ align:start position:0%
+mean the market collapses market
+ 
+
+ align:start position:0%
+mean the market collapses market
+failures in this looming market collapse
+
+ align:start position:0%
+failures in this looming market collapse
+ 
+
+ align:start position:0%
+failures in this looming market collapse
+it means a reduction in welfare because
+
+ align:start position:0%
+it means a reduction in welfare because
+ 
+
+ align:start position:0%
+it means a reduction in welfare because
+transactions that might make some people
+
+ align:start position:0%
+transactions that might make some people
+ 
+
+ align:start position:0%
+transactions that might make some people
+better off on happening here you might
+
+ align:start position:0%
+better off on happening here you might
+ 
+
+ align:start position:0%
+better off on happening here you might
+be able to offer insurance for healthy
+
+ align:start position:0%
+be able to offer insurance for healthy
+ 
+
+ align:start position:0%
+be able to offer insurance for healthy
+will that makes them better off but
+
+ align:start position:0%
+will that makes them better off but
+ 
+
+ align:start position:0%
+will that makes them better off but
+you're not you're only offering
+
+ align:start position:0%
+you're not you're only offering
+ 
+
+ align:start position:0%
+you're not you're only offering
+insurance for the sick so it's a market
+
+ align:start position:0%
+insurance for the sick so it's a market
+ 
+
+ align:start position:0%
+insurance for the sick so it's a market
+failure because healthy people who might
+
+ align:start position:0%
+failure because healthy people who might
+ 
+
+ align:start position:0%
+failure because healthy people who might
+want the insurance end up being kept out
+
+ align:start position:0%
+want the insurance end up being kept out
+ 
+
+ align:start position:0%
+want the insurance end up being kept out
+of the market by ever selection okay
+
+ align:start position:0%
+of the market by ever selection okay
+ 
+
+ align:start position:0%
+of the market by ever selection okay
+questions about that and that is the
+
+ align:start position:0%
+questions about that and that is the
+ 
+
+ align:start position:0%
+questions about that and that is the
+fundamental market failure we face an
+
+ align:start position:0%
+fundamental market failure we face an
+ 
+
+ align:start position:0%
+fundamental market failure we face an
+insurance market that's why we think
+
+ align:start position:0%
+insurance market that's why we think
+ 
+
+ align:start position:0%
+insurance market that's why we think
+private insurance markets will not
+
+ align:start position:0%
+private insurance markets will not
+ 
+
+ align:start position:0%
+private insurance markets will not
+function well because private insurers
+
+ align:start position:0%
+function well because private insurers
+ 
+
+ align:start position:0%
+function well because private insurers
+in some sense the fundamental problem is
+
+ align:start position:0%
+in some sense the fundamental problem is
+ 
+
+ align:start position:0%
+in some sense the fundamental problem is
+that you're setting one price one price
+
+ align:start position:0%
+that you're setting one price one price
+ 
+
+ align:start position:0%
+that you're setting one price one price
+for multiple products the great case of
+
+ align:start position:0%
+for multiple products the great case of
+ 
+
+ align:start position:0%
+for multiple products the great case of
+average selection is going to buy fruit
+
+ align:start position:0%
+average selection is going to buy fruit
+ 
+
+ align:start position:0%
+average selection is going to buy fruit
+at the beginning versus the end of the
+
+ align:start position:0%
+at the beginning versus the end of the
+ 
+
+ align:start position:0%
+at the beginning versus the end of the
+day what's the difference buy fruit to
+
+ align:start position:0%
+day what's the difference buy fruit to
+ 
+
+ align:start position:0%
+day what's the difference buy fruit to
+begin the end of the day yeah I don't
+
+ align:start position:0%
+begin the end of the day yeah I don't
+ 
+
+ align:start position:0%
+begin the end of the day yeah I don't
+buy a lot of fruit but try to think
+
+ align:start position:0%
+buy a lot of fruit but try to think
+ 
+
+ align:start position:0%
+buy a lot of fruit but try to think
+about it yeah what's left is left
+
+ align:start position:0%
+about it yeah what's left is left
+ 
+
+ align:start position:0%
+about it yeah what's left is left
+because you'll check one price you
+
+ align:start position:0%
+because you'll check one price you
+ 
+
+ align:start position:0%
+because you'll check one price you
+didn't say good apples a dollar at
+
+ align:start position:0%
+didn't say good apples a dollar at
+ 
+
+ align:start position:0%
+didn't say good apples a dollar at
+eighty shitty apples a dollar forty you
+
+ align:start position:0%
+eighty shitty apples a dollar forty you
+ 
+
+ align:start position:0%
+eighty shitty apples a dollar forty you
+said apples one seventy so people come
+
+ align:start position:0%
+said apples one seventy so people come
+ 
+
+ align:start position:0%
+said apples one seventy so people come
+and they buy apples they they go and
+
+ align:start position:0%
+and they buy apples they they go and
+ 
+
+ align:start position:0%
+and they buy apples they they go and
+they feel it you know and they feel
+
+ align:start position:0%
+they feel it you know and they feel
+ 
+
+ align:start position:0%
+they feel it you know and they feel
+around they find the good ones the ones
+
+ align:start position:0%
+around they find the good ones the ones
+ 
+
+ align:start position:0%
+around they find the good ones the ones
+that left or crack okay and that is the
+
+ align:start position:0%
+that left or crack okay and that is the
+ 
+
+ align:start position:0%
+that left or crack okay and that is the
+adverse selection problem now with
+
+ align:start position:0%
+adverse selection problem now with
+ 
+
+ align:start position:0%
+adverse selection problem now with
+apples the markets
+
+ align:start position:0%
+apples the markets
+ 
+
+ align:start position:0%
+apples the markets
+exist why because they charge so much
+
+ align:start position:0%
+exist why because they charge so much
+ 
+
+ align:start position:0%
+exist why because they charge so much
+they can live with a few bad apples
+
+ align:start position:0%
+they can live with a few bad apples
+ 
+
+ align:start position:0%
+they can live with a few bad apples
+being at the bottom so to speak a few
+
+ align:start position:0%
+being at the bottom so to speak a few
+ 
+
+ align:start position:0%
+being at the bottom so to speak a few
+bad apples being at the bottom with
+
+ align:start position:0%
+bad apples being at the bottom with
+ 
+
+ align:start position:0%
+bad apples being at the bottom with
+health insurance if I get one bad risk
+
+ align:start position:0%
+health insurance if I get one bad risk
+ 
+
+ align:start position:0%
+health insurance if I get one bad risk
+someone say who's really really sick and
+
+ align:start position:0%
+someone say who's really really sick and
+ 
+
+ align:start position:0%
+someone say who's really really sick and
+cost a million dollars I go out of
+
+ align:start position:0%
+cost a million dollars I go out of
+ 
+
+ align:start position:0%
+cost a million dollars I go out of
+business so adverse selection may not
+
+ align:start position:0%
+business so adverse selection may not
+ 
+
+ align:start position:0%
+business so adverse selection may not
+destroy markets that doesn't destroy the
+
+ align:start position:0%
+destroy markets that doesn't destroy the
+ 
+
+ align:start position:0%
+destroy markets that doesn't destroy the
+apple market but it can destroy or
+
+ align:start position:0%
+apple market but it can destroy or
+ 
+
+ align:start position:0%
+apple market but it can destroy or
+significantly impede insurance markets
+
+ align:start position:0%
+significantly impede insurance markets
+ 
+
+ align:start position:0%
+significantly impede insurance markets
+okay questions about that yeah we'll
+
+ align:start position:0%
+okay questions about that yeah we'll
+ 
+
+ align:start position:0%
+okay questions about that yeah we'll
+talk about that next lecture we talk
+
+ align:start position:0%
+talk about that next lecture we talk
+ 
+
+ align:start position:0%
+talk about that next lecture we talk
+about health care
+
+ align:start position:0%
+about health care
+ 
+
+ align:start position:0%
+about health care
+so that's separate about the cost of
+
+ align:start position:0%
+so that's separate about the cost of
+ 
+
+ align:start position:0%
+so that's separate about the cost of
+health care this is a reason why
+
+ align:start position:0%
+health care this is a reason why
+ 
+
+ align:start position:0%
+health care this is a reason why
+insurance companies make you felt a lot
+
+ align:start position:0%
+insurance companies make you felt a lot
+ 
+
+ align:start position:0%
+insurance companies make you felt a lot
+of forms before you go in so it's for
+
+ align:start position:0%
+of forms before you go in so it's for
+ 
+
+ align:start position:0%
+of forms before you go in so it's for
+this reason insurance companies are not
+
+ align:start position:0%
+this reason insurance companies are not
+ 
+
+ align:start position:0%
+this reason insurance companies are not
+powerless against this problem they
+
+ align:start position:0%
+powerless against this problem they
+ 
+
+ align:start position:0%
+powerless against this problem they
+could try to collect as much information
+
+ align:start position:0%
+could try to collect as much information
+ 
+
+ align:start position:0%
+could try to collect as much information
+about you as they can as I get more and
+
+ align:start position:0%
+about you as they can as I get more and
+ 
+
+ align:start position:0%
+about you as they can as I get more and
+more information can learn more and more
+
+ align:start position:0%
+more information can learn more and more
+ 
+
+ align:start position:0%
+more information can learn more and more
+who's healthy who's sick then I can
+
+ align:start position:0%
+who's healthy who's sick then I can
+ 
+
+ align:start position:0%
+who's healthy who's sick then I can
+solve this problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah yeah so is it possible so this
+
+ align:start position:0%
+yeah yeah yeah so is it possible so this
+ 
+
+ align:start position:0%
+yeah yeah yeah so is it possible so this
+is a great point it's for next time I'll
+
+ align:start position:0%
+is a great point it's for next time I'll
+ 
+
+ align:start position:0%
+is a great point it's for next time I'll
+talk about it now
+
+ align:start position:0%
+talk about it now
+ 
+
+ align:start position:0%
+talk about it now
+which is in some sense we are eventually
+
+ align:start position:0%
+which is in some sense we are eventually
+ 
+
+ align:start position:0%
+which is in some sense we are eventually
+moving to a point with OB no adverse
+
+ align:start position:0%
+moving to a point with OB no adverse
+ 
+
+ align:start position:0%
+moving to a point with OB no adverse
+selection now you might say in the one
+
+ align:start position:0%
+selection now you might say in the one
+ 
+
+ align:start position:0%
+selection now you might say in the one
+hand that's because último menteur born
+
+ align:start position:0%
+hand that's because último menteur born
+ 
+
+ align:start position:0%
+hand that's because último menteur born
+right well no your genes
+
+ align:start position:0%
+right well no your genes
+ 
+
+ align:start position:0%
+right well no your genes
+well no it's good now we won't know if
+
+ align:start position:0%
+well no it's good now we won't know if
+ 
+
+ align:start position:0%
+well no it's good now we won't know if
+you're a skydiver but well no no
+
+ align:start position:0%
+you're a skydiver but well no no
+ 
+
+ align:start position:0%
+you're a skydiver but well no no
+probably no genes to determine risk
+
+ align:start position:0%
+probably no genes to determine risk
+ 
+
+ align:start position:0%
+probably no genes to determine risk
+taking and we'll charge more for people
+
+ align:start position:0%
+taking and we'll charge more for people
+ 
+
+ align:start position:0%
+taking and we'll charge more for people
+like taking risks
+
+ align:start position:0%
+like taking risks
+ 
+
+ align:start position:0%
+like taking risks
+so the doubt the good news is that then
+
+ align:start position:0%
+so the doubt the good news is that then
+ 
+
+ align:start position:0%
+so the doubt the good news is that then
+I can I can make the market work the bad
+
+ align:start position:0%
+I can I can make the market work the bad
+ 
+
+ align:start position:0%
+I can I can make the market work the bad
+news is in that world how would I set my
+
+ align:start position:0%
+news is in that world how would I set my
+ 
+
+ align:start position:0%
+news is in that world how would I set my
+insurance prices I would charge because
+
+ align:start position:0%
+insurance prices I would charge because
+ 
+
+ align:start position:0%
+insurance prices I would charge because
+what I would do is I'd say your genes
+
+ align:start position:0%
+what I would do is I'd say your genes
+ 
+
+ align:start position:0%
+what I would do is I'd say your genes
+say you're healthy so I want 1,100 bucks
+
+ align:start position:0%
+say you're healthy so I want 1,100 bucks
+ 
+
+ align:start position:0%
+say you're healthy so I want 1,100 bucks
+from you your genes say you're sick so I
+
+ align:start position:0%
+from you your genes say you're sick so I
+ 
+
+ align:start position:0%
+from you your genes say you're sick so I
+want six thousand dollars from you
+
+ align:start position:0%
+want six thousand dollars from you
+ 
+
+ align:start position:0%
+want six thousand dollars from you
+so essentially insurance wouldn't exist
+
+ align:start position:0%
+so essentially insurance wouldn't exist
+ 
+
+ align:start position:0%
+so essentially insurance wouldn't exist
+anymore
+
+ align:start position:0%
+anymore
+ 
+
+ align:start position:0%
+anymore
+there'd be no insurance what is
+
+ align:start position:0%
+there'd be no insurance what is
+ 
+
+ align:start position:0%
+there'd be no insurance what is
+insurance insurance is pooling people
+
+ align:start position:0%
+insurance insurance is pooling people
+ 
+
+ align:start position:0%
+insurance insurance is pooling people
+with different probabilities of adverse
+
+ align:start position:0%
+with different probabilities of adverse
+ 
+
+ align:start position:0%
+with different probabilities of adverse
+events and letting us all benefit for
+
+ align:start position:0%
+events and letting us all benefit for
+ 
+
+ align:start position:0%
+events and letting us all benefit for
+the fact that if it happens to us at
+
+ align:start position:0%
+the fact that if it happens to us at
+ 
+
+ align:start position:0%
+the fact that if it happens to us at
+least we're protected well if you charge
+
+ align:start position:0%
+least we're protected well if you charge
+ 
+
+ align:start position:0%
+least we're protected well if you charge
+me my expected cost I'm no longer
+
+ align:start position:0%
+me my expected cost I'm no longer
+ 
+
+ align:start position:0%
+me my expected cost I'm no longer
+protected so here's the example that
+
+ align:start position:0%
+protected so here's the example that
+ 
+
+ align:start position:0%
+protected so here's the example that
+makes it perfectly clear one of the most
+
+ align:start position:0%
+makes it perfectly clear one of the most
+ 
+
+ align:start position:0%
+makes it perfectly clear one of the most
+famous examples Ken arrow is one of the
+
+ align:start position:0%
+famous examples Ken arrow is one of the
+ 
+
+ align:start position:0%
+famous examples Ken arrow is one of the
+great economists the 20th century died
+
+ align:start position:0%
+great economists the 20th century died
+ 
+
+ align:start position:0%
+great economists the 20th century died
+recently he had his famous Islands
+
+ align:start position:0%
+recently he had his famous Islands
+ 
+
+ align:start position:0%
+recently he had his famous Islands
+example ken arrows Islands examples the
+
+ align:start position:0%
+example ken arrows Islands examples the
+ 
+
+ align:start position:0%
+example ken arrows Islands examples the
+following a measures to island somewhere
+
+ align:start position:0%
+following a measures to island somewhere
+ 
+
+ align:start position:0%
+following a measures to island somewhere
+in the South Pacific that are very small
+
+ align:start position:0%
+in the South Pacific that are very small
+ 
+
+ align:start position:0%
+in the South Pacific that are very small
+that's got one farmer on each and the
+
+ align:start position:0%
+that's got one farmer on each and the
+ 
+
+ align:start position:0%
+that's got one farmer on each and the
+farmers know a hurricane is coming and
+
+ align:start position:0%
+farmers know a hurricane is coming and
+ 
+
+ align:start position:0%
+farmers know a hurricane is coming and
+it's gonna wipe out one of their islands
+
+ align:start position:0%
+it's gonna wipe out one of their islands
+ 
+
+ align:start position:0%
+it's gonna wipe out one of their islands
+but they don't know which there's no
+
+ align:start position:0%
+but they don't know which there's no
+ 
+
+ align:start position:0%
+but they don't know which there's no
+one's gonna get wiped out what will they
+
+ align:start position:0%
+one's gonna get wiped out what will they
+ 
+
+ align:start position:0%
+one's gonna get wiped out what will they
+naturally do they'll naturally get
+
+ align:start position:0%
+naturally do they'll naturally get
+ 
+
+ align:start position:0%
+naturally do they'll naturally get
+together and say look I'll just get it
+
+ align:start position:0%
+together and say look I'll just get it
+ 
+
+ align:start position:0%
+together and say look I'll just get it
+wiped out but let's ensure each other
+
+ align:start position:0%
+wiped out but let's ensure each other
+ 
+
+ align:start position:0%
+wiped out but let's ensure each other
+if I get wiped out you give me a bunch
+
+ align:start position:0%
+if I get wiped out you give me a bunch
+ 
+
+ align:start position:0%
+if I get wiped out you give me a bunch
+of your crop if you get why
+
+ align:start position:0%
+of your crop if you get why
+ 
+
+ align:start position:0%
+of your crop if you get why
+are you into my crop that will improve
+
+ align:start position:0%
+are you into my crop that will improve
+ 
+
+ align:start position:0%
+are you into my crop that will improve
+both our welfare right because getting
+
+ align:start position:0%
+both our welfare right because getting
+ 
+
+ align:start position:0%
+both our welfare right because getting
+wiped out is going to zero you die
+
+ align:start position:0%
+wiped out is going to zero you die
+ 
+
+ align:start position:0%
+wiped out is going to zero you die
+that's a terrible outcome so that will
+
+ align:start position:0%
+that's a terrible outcome so that will
+ 
+
+ align:start position:0%
+that's a terrible outcome so that will
+improve our welfare if we insure each
+
+ align:start position:0%
+improve our welfare if we insure each
+ 
+
+ align:start position:0%
+improve our welfare if we insure each
+other now let's say a weather service
+
+ align:start position:0%
+other now let's say a weather service
+ 
+
+ align:start position:0%
+other now let's say a weather service
+comes along and provides information and
+
+ align:start position:0%
+comes along and provides information and
+ 
+
+ align:start position:0%
+comes along and provides information and
+tells you that farmer aids island is
+
+ align:start position:0%
+tells you that farmer aids island is
+ 
+
+ align:start position:0%
+tells you that farmer aids island is
+getting wiped out in farmer B's islands
+
+ align:start position:0%
+getting wiped out in farmer B's islands
+ 
+
+ align:start position:0%
+getting wiped out in farmer B's islands
+gonna be fine what has happened to
+
+ align:start position:0%
+gonna be fine what has happened to
+ 
+
+ align:start position:0%
+gonna be fine what has happened to
+welfare it's gotten worse
+
+ align:start position:0%
+welfare it's gotten worse
+ 
+
+ align:start position:0%
+welfare it's gotten worse
+why because farmer a goes far beats it
+
+ align:start position:0%
+why because farmer a goes far beats it
+ 
+
+ align:start position:0%
+why because farmer a goes far beats it
+turns out a new wipeout farm B says welp
+
+ align:start position:0%
+turns out a new wipeout farm B says welp
+ 
+
+ align:start position:0%
+turns out a new wipeout farm B says welp
+see ya I'm just gonna keep consuming my
+
+ align:start position:0%
+see ya I'm just gonna keep consuming my
+ 
+
+ align:start position:0%
+see ya I'm just gonna keep consuming my
+high level farmer B is somewhat better
+
+ align:start position:0%
+high level farmer B is somewhat better
+ 
+
+ align:start position:0%
+high level farmer B is somewhat better
+off farmer a is dead okay total social
+
+ align:start position:0%
+off farmer a is dead okay total social
+ 
+
+ align:start position:0%
+off farmer a is dead okay total social
+welfare has fallen because the concavity
+
+ align:start position:0%
+welfare has fallen because the concavity
+ 
+
+ align:start position:0%
+welfare has fallen because the concavity
+because of diminishing marginal 'ti more
+
+ align:start position:0%
+because of diminishing marginal 'ti more
+ 
+
+ align:start position:0%
+because of diminishing marginal 'ti more
+information has made us worse we say is
+
+ align:start position:0%
+information has made us worse we say is
+ 
+
+ align:start position:0%
+information has made us worse we say is
+more is better in economics once you get
+
+ align:start position:0%
+more is better in economics once you get
+ 
+
+ align:start position:0%
+more is better in economics once you get
+topics like this you realize more is not
+
+ align:start position:0%
+topics like this you realize more is not
+ 
+
+ align:start position:0%
+topics like this you realize more is not
+always better more is worse more
+
+ align:start position:0%
+always better more is worse more
+ 
+
+ align:start position:0%
+always better more is worse more
+information has destroyed the insurance
+
+ align:start position:0%
+information has destroyed the insurance
+ 
+
+ align:start position:0%
+information has destroyed the insurance
+market that might function so in fact
+
+ align:start position:0%
+market that might function so in fact
+ 
+
+ align:start position:0%
+market that might function so in fact
+this issue I'm talking about is becoming
+
+ align:start position:0%
+this issue I'm talking about is becoming
+ 
+
+ align:start position:0%
+this issue I'm talking about is becoming
+paramount as we move more and more
+
+ align:start position:0%
+paramount as we move more and more
+ 
+
+ align:start position:0%
+paramount as we move more and more
+towards perfect information environment
+
+ align:start position:0%
+towards perfect information environment
+ 
+
+ align:start position:0%
+towards perfect information environment
+okay so the kind of government Paul sim
+
+ align:start position:0%
+okay so the kind of government Paul sim
+ 
+
+ align:start position:0%
+okay so the kind of government Paul sim
+talk about next become critical as you
+
+ align:start position:0%
+talk about next become critical as you
+ 
+
+ align:start position:0%
+talk about next become critical as you
+move towards that environment but first
+
+ align:start position:0%
+move towards that environment but first
+ 
+
+ align:start position:0%
+move towards that environment but first
+I wanna make sure we lunched into the
+
+ align:start position:0%
+I wanna make sure we lunched into the
+ 
+
+ align:start position:0%
+I wanna make sure we lunched into the
+front why the private markets failed why
+
+ align:start position:0%
+front why the private markets failed why
+ 
+
+ align:start position:0%
+front why the private markets failed why
+it's a failure okay now what can the
+
+ align:start position:0%
+it's a failure okay now what can the
+ 
+
+ align:start position:0%
+it's a failure okay now what can the
+government do about this what are some
+
+ align:start position:0%
+government do about this what are some
+ 
+
+ align:start position:0%
+government do about this what are some
+potential government solutions and we've
+
+ align:start position:0%
+potential government solutions and we've
+ 
+
+ align:start position:0%
+potential government solutions and we've
+tried all these in the US and around the
+
+ align:start position:0%
+tried all these in the US and around the
+ 
+
+ align:start position:0%
+tried all these in the US and around the
+world let's talk about three categories
+
+ align:start position:0%
+world let's talk about three categories
+ 
+
+ align:start position:0%
+world let's talk about three categories
+of government solutions the first is
+
+ align:start position:0%
+of government solutions the first is
+ 
+
+ align:start position:0%
+of government solutions the first is
+subsidization the government could
+
+ align:start position:0%
+subsidization the government could
+ 
+
+ align:start position:0%
+subsidization the government could
+subsidize the purchase of health
+
+ align:start position:0%
+subsidize the purchase of health
+ 
+
+ align:start position:0%
+subsidize the purchase of health
+insurance so for example what if the US
+
+ align:start position:0%
+insurance so for example what if the US
+ 
+
+ align:start position:0%
+insurance so for example what if the US
+government said to all the MIT grads I
+
+ align:start position:0%
+government said to all the MIT grads I
+ 
+
+ align:start position:0%
+government said to all the MIT grads I
+am gonna give you a $400 tax credit that
+
+ align:start position:0%
+am gonna give you a $400 tax credit that
+ 
+
+ align:start position:0%
+am gonna give you a $400 tax credit that
+you can have if or 500 credit if you buy
+
+ align:start position:0%
+you can have if or 500 credit if you buy
+ 
+
+ align:start position:0%
+you can have if or 500 credit if you buy
+health insurance well if there's a $5
+
+ align:start position:0%
+health insurance well if there's a $5
+ 
+
+ align:start position:0%
+health insurance well if there's a $5
+verified by health insurance then what's
+
+ align:start position:0%
+verified by health insurance then what's
+ 
+
+ align:start position:0%
+verified by health insurance then what's
+and I charge $1,500 then what's the
+
+ align:start position:0%
+and I charge $1,500 then what's the
+ 
+
+ align:start position:0%
+and I charge $1,500 then what's the
+effective priced out of the healthy guy
+
+ align:start position:0%
+effective priced out of the healthy guy
+ 
+
+ align:start position:0%
+effective priced out of the healthy guy
+a thousand so he buys even if he's risk
+
+ align:start position:0%
+a thousand so he buys even if he's risk
+ 
+
+ align:start position:0%
+a thousand so he buys even if he's risk
+neutrally by its long as he's a tiny bit
+
+ align:start position:0%
+neutrally by its long as he's a tiny bit
+ 
+
+ align:start position:0%
+neutrally by its long as he's a tiny bit
+risk-averse so I do sell to everyone and
+
+ align:start position:0%
+risk-averse so I do sell to everyone and
+ 
+
+ align:start position:0%
+risk-averse so I do sell to everyone and
+I make my money so one way to solve this
+
+ align:start position:0%
+I make my money so one way to solve this
+ 
+
+ align:start position:0%
+I make my money so one way to solve this
+problem is to basically pay to help
+
+ align:start position:0%
+problem is to basically pay to help
+ 
+
+ align:start position:0%
+problem is to basically pay to help
+people to get into the market they can
+
+ align:start position:0%
+people to get into the market they can
+ 
+
+ align:start position:0%
+people to get into the market they can
+seek the help money to help you
+
+ align:start position:0%
+seek the help money to help you
+ 
+
+ align:start position:0%
+seek the help money to help you
+give it to everyone because you can't
+
+ align:start position:0%
+give it to everyone because you can't
+ 
+
+ align:start position:0%
+give it to everyone because you can't
+tell it was healthy but if you give
+
+ align:start position:0%
+tell it was healthy but if you give
+ 
+
+ align:start position:0%
+tell it was healthy but if you give
+everyone a tax credit then we can bring
+
+ align:start position:0%
+everyone a tax credit then we can bring
+ 
+
+ align:start position:0%
+everyone a tax credit then we can bring
+everyone into the market and solve this
+
+ align:start position:0%
+everyone into the market and solve this
+ 
+
+ align:start position:0%
+everyone into the market and solve this
+problem well in fact we do this in
+
+ align:start position:0%
+problem well in fact we do this in
+ 
+
+ align:start position:0%
+problem well in fact we do this in
+America it's actually perhaps the
+
+ align:start position:0%
+America it's actually perhaps the
+ 
+
+ align:start position:0%
+America it's actually perhaps the
+largest hidden government expenditure in
+
+ align:start position:0%
+largest hidden government expenditure in
+ 
+
+ align:start position:0%
+largest hidden government expenditure in
+our country which is the tax subsidy to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+employer sponsored insurance employer
+
+ align:start position:0%
+employer sponsored insurance employer
+ 
+
+ align:start position:0%
+employer sponsored insurance employer
+health insurance attack subs employer
+
+ align:start position:0%
+health insurance attack subs employer
+ 
+
+ align:start position:0%
+health insurance attack subs employer
+health insurance what I mean by that
+
+ align:start position:0%
+health insurance what I mean by that
+ 
+
+ align:start position:0%
+health insurance what I mean by that
+what a means of following when MIT pays
+
+ align:start position:0%
+what a means of following when MIT pays
+ 
+
+ align:start position:0%
+what a means of following when MIT pays
+me in wages I am taxed on that like the
+
+ align:start position:0%
+me in wages I am taxed on that like the
+ 
+
+ align:start position:0%
+me in wages I am taxed on that like the
+taxation we talked about a couple
+
+ align:start position:0%
+taxation we talked about a couple
+ 
+
+ align:start position:0%
+taxation we talked about a couple
+lectures ago when MIT pays me and health
+
+ align:start position:0%
+lectures ago when MIT pays me and health
+ 
+
+ align:start position:0%
+lectures ago when MIT pays me and health
+insurance I am not taxed on that so what
+
+ align:start position:0%
+insurance I am not taxed on that so what
+ 
+
+ align:start position:0%
+insurance I am not taxed on that so what
+does that mean so if MIT comes to me
+
+ align:start position:0%
+does that mean so if MIT comes to me
+ 
+
+ align:start position:0%
+does that mean so if MIT comes to me
+they say would you like $1,000 race or
+
+ align:start position:0%
+they say would you like $1,000 race or
+ 
+
+ align:start position:0%
+they say would you like $1,000 race or
+$1,000 orthodontia benefits for your
+
+ align:start position:0%
+$1,000 orthodontia benefits for your
+ 
+
+ align:start position:0%
+$1,000 orthodontia benefits for your
+daughter
+
+ align:start position:0%
+daughter
+ 
+
+ align:start position:0%
+daughter
+I say well thousand all the Rays of
+
+ align:start position:0%
+I say well thousand all the Rays of
+ 
+
+ align:start position:0%
+I say well thousand all the Rays of
+today's tax rates I'm gonna take home
+
+ align:start position:0%
+today's tax rates I'm gonna take home
+ 
+
+ align:start position:0%
+today's tax rates I'm gonna take home
+about 550 if you add up all the taxes
+
+ align:start position:0%
+about 550 if you add up all the taxes
+ 
+
+ align:start position:0%
+about 550 if you add up all the taxes
+I'll pay and I'll take them about 550
+
+ align:start position:0%
+I'll pay and I'll take them about 550
+ 
+
+ align:start position:0%
+I'll pay and I'll take them about 550
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+thousand I also don't understand
+
+ align:start position:0%
+thousand I also don't understand
+ 
+
+ align:start position:0%
+thousand I also don't understand
+benefits my daughter I get the whole
+
+ align:start position:0%
+benefits my daughter I get the whole
+ 
+
+ align:start position:0%
+benefits my daughter I get the whole
+thousand so why not so I got these cool
+
+ align:start position:0%
+thousand so why not so I got these cool
+ 
+
+ align:start position:0%
+thousand so why not so I got these cool
+braces they spin and change color and
+
+ align:start position:0%
+braces they spin and change color and
+ 
+
+ align:start position:0%
+braces they spin and change color and
+every two weeks she's in four different
+
+ align:start position:0%
+every two weeks she's in four different
+ 
+
+ align:start position:0%
+every two weeks she's in four different
+kind of braces it's great cuz it's free
+
+ align:start position:0%
+kind of braces it's great cuz it's free
+ 
+
+ align:start position:0%
+kind of braces it's great cuz it's free
+okay so we do subsidize health insurance
+
+ align:start position:0%
+okay so we do subsidize health insurance
+ 
+
+ align:start position:0%
+okay so we do subsidize health insurance
+in America and this amounts to this
+
+ align:start position:0%
+in America and this amounts to this
+ 
+
+ align:start position:0%
+in America and this amounts to this
+program that I just talked about amounts
+
+ align:start position:0%
+program that I just talked about amounts
+ 
+
+ align:start position:0%
+program that I just talked about amounts
+to almost 300 billion dollars per year
+
+ align:start position:0%
+to almost 300 billion dollars per year
+ 
+
+ align:start position:0%
+to almost 300 billion dollars per year
+we spent almost 300 billion dollars per
+
+ align:start position:0%
+we spent almost 300 billion dollars per
+ 
+
+ align:start position:0%
+we spent almost 300 billion dollars per
+year giving a tax break to people to buy
+
+ align:start position:0%
+year giving a tax break to people to buy
+ 
+
+ align:start position:0%
+year giving a tax break to people to buy
+health insurance okay so that's one
+
+ align:start position:0%
+health insurance okay so that's one
+ 
+
+ align:start position:0%
+health insurance okay so that's one
+tactic we take to try to solve this
+
+ align:start position:0%
+tactic we take to try to solve this
+ 
+
+ align:start position:0%
+tactic we take to try to solve this
+problem to get health people into the
+
+ align:start position:0%
+problem to get health people into the
+ 
+
+ align:start position:0%
+problem to get health people into the
+market
+
+ align:start position:0%
+market
+ 
+
+ align:start position:0%
+market
+that's approach one a second approach
+
+ align:start position:0%
+that's approach one a second approach
+ 
+
+ align:start position:0%
+that's approach one a second approach
+one can use to try to get people into
+
+ align:start position:0%
+one can use to try to get people into
+ 
+
+ align:start position:0%
+one can use to try to get people into
+the market is a mandate suppose I just
+
+ align:start position:0%
+the market is a mandate suppose I just
+ 
+
+ align:start position:0%
+the market is a mandate suppose I just
+pass a law that says everyone has to buy
+
+ align:start position:0%
+pass a law that says everyone has to buy
+ 
+
+ align:start position:0%
+pass a law that says everyone has to buy
+health insurance well then I've solved
+
+ align:start position:0%
+health insurance well then I've solved
+ 
+
+ align:start position:0%
+health insurance well then I've solved
+the problem right I know what my
+
+ align:start position:0%
+the problem right I know what my
+ 
+
+ align:start position:0%
+the problem right I know what my
+expected costs are if everyone has to
+
+ align:start position:0%
+expected costs are if everyone has to
+ 
+
+ align:start position:0%
+expected costs are if everyone has to
+buy I know my expected costs are 1,400
+
+ align:start position:0%
+buy I know my expected costs are 1,400
+ 
+
+ align:start position:0%
+buy I know my expected costs are 1,400
+so I know I can make money at 1500 well
+
+ align:start position:0%
+so I know I can make money at 1500 well
+ 
+
+ align:start position:0%
+so I know I can make money at 1500 well
+that's easier one level well they don't
+
+ align:start position:0%
+that's easier one level well they don't
+ 
+
+ align:start position:0%
+that's easier one level well they don't
+have to I don't have to spend I don't
+
+ align:start position:0%
+have to I don't have to spend I don't
+ 
+
+ align:start position:0%
+have to I don't have to spend I don't
+just spend three billion dollars a lot
+
+ align:start position:0%
+just spend three billion dollars a lot
+ 
+
+ align:start position:0%
+just spend three billion dollars a lot
+of money this cost me zero it's harder
+
+ align:start position:0%
+of money this cost me zero it's harder
+ 
+
+ align:start position:0%
+of money this cost me zero it's harder
+another level why what's the problem
+
+ align:start position:0%
+another level why what's the problem
+ 
+
+ align:start position:0%
+another level why what's the problem
+with that solution yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well it may not may not have it that's
+
+ align:start position:0%
+well it may not may not have it that's
+ 
+
+ align:start position:0%
+well it may not may not have it that's
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+what else yeah people are gonna be
+
+ align:start position:0%
+what else yeah people are gonna be
+ 
+
+ align:start position:0%
+what else yeah people are gonna be
+pissed
+
+ align:start position:0%
+pissed
+ 
+
+ align:start position:0%
+pissed
+they're like look if I had chosen not
+
+ align:start position:0%
+they're like look if I had chosen not
+ 
+
+ align:start position:0%
+they're like look if I had chosen not
+you're gonna basically the mandate only
+
+ align:start position:0%
+you're gonna basically the mandate only
+ 
+
+ align:start position:0%
+you're gonna basically the mandate only
+has an effect if it changes people's
+
+ align:start position:0%
+has an effect if it changes people's
+ 
+
+ align:start position:0%
+has an effect if it changes people's
+behavior but chases the behavior you
+
+ align:start position:0%
+behavior but chases the behavior you
+ 
+
+ align:start position:0%
+behavior but chases the behavior you
+mean you're making them do something I
+
+ align:start position:0%
+mean you're making them do something I
+ 
+
+ align:start position:0%
+mean you're making them do something I
+didn't want to do beforehand so the
+
+ align:start position:0%
+didn't want to do beforehand so the
+ 
+
+ align:start position:0%
+didn't want to do beforehand so the
+problem with that the problem with this
+
+ align:start position:0%
+problem with that the problem with this
+ 
+
+ align:start position:0%
+problem with that the problem with this
+is you spend a lot of money problem of
+
+ align:start position:0%
+is you spend a lot of money problem of
+ 
+
+ align:start position:0%
+is you spend a lot of money problem of
+this you piss off healthy people okay
+
+ align:start position:0%
+this you piss off healthy people okay
+ 
+
+ align:start position:0%
+this you piss off healthy people okay
+the third approach we could do okay and
+
+ align:start position:0%
+the third approach we could do okay and
+ 
+
+ align:start position:0%
+the third approach we could do okay and
+there's lots of examples of the mandate
+
+ align:start position:0%
+there's lots of examples of the mandate
+ 
+
+ align:start position:0%
+there's lots of examples of the mandate
+obviously we know about the health
+
+ align:start position:0%
+obviously we know about the health
+ 
+
+ align:start position:0%
+obviously we know about the health
+insurance mandate that was originally
+
+ align:start position:0%
+insurance mandate that was originally
+ 
+
+ align:start position:0%
+insurance mandate that was originally
+part of Obamacare but that's not the
+
+ align:start position:0%
+part of Obamacare but that's not the
+ 
+
+ align:start position:0%
+part of Obamacare but that's not the
+biggest example the biggest example in
+
+ align:start position:0%
+biggest example the biggest example in
+ 
+
+ align:start position:0%
+biggest example the biggest example in
+the u.s. is what's called workers comp
+
+ align:start position:0%
+the u.s. is what's called workers comp
+ 
+
+ align:start position:0%
+the u.s. is what's called workers comp
+insurance which is insurance that you
+
+ align:start position:0%
+insurance which is insurance that you
+ 
+
+ align:start position:0%
+insurance which is insurance that you
+have for on-the-job injuries if you get
+
+ align:start position:0%
+have for on-the-job injuries if you get
+ 
+
+ align:start position:0%
+have for on-the-job injuries if you get
+hurt at work your employer pays money so
+
+ align:start position:0%
+hurt at work your employer pays money so
+ 
+
+ align:start position:0%
+hurt at work your employer pays money so
+that you get reimbursed when you when
+
+ align:start position:0%
+that you get reimbursed when you when
+ 
+
+ align:start position:0%
+that you get reimbursed when you when
+your it pays your medical bills when you
+
+ align:start position:0%
+your it pays your medical bills when you
+ 
+
+ align:start position:0%
+your it pays your medical bills when you
+hurt working gives you partial
+
+ align:start position:0%
+hurt working gives you partial
+ 
+
+ align:start position:0%
+hurt working gives you partial
+replacement of your wages that is
+
+ align:start position:0%
+replacement of your wages that is
+ 
+
+ align:start position:0%
+replacement of your wages that is
+mandated insurance on all employers in
+
+ align:start position:0%
+mandated insurance on all employers in
+ 
+
+ align:start position:0%
+mandated insurance on all employers in
+America except in Texas Texas they can
+
+ align:start position:0%
+America except in Texas Texas they can
+ 
+
+ align:start position:0%
+America except in Texas Texas they can
+choose every other state it's mandated
+
+ align:start position:0%
+choose every other state it's mandated
+ 
+
+ align:start position:0%
+choose every other state it's mandated
+mandated insures that we employ in
+
+ align:start position:0%
+mandated insures that we employ in
+ 
+
+ align:start position:0%
+mandated insures that we employ in
+America they have to buy workers comp so
+
+ align:start position:0%
+America they have to buy workers comp so
+ 
+
+ align:start position:0%
+America they have to buy workers comp so
+we have examples of that and that's at
+
+ align:start position:0%
+we have examples of that and that's at
+ 
+
+ align:start position:0%
+we have examples of that and that's at
+eighty billion dollar a year program
+
+ align:start position:0%
+eighty billion dollar a year program
+ 
+
+ align:start position:0%
+eighty billion dollar a year program
+that's a big deal
+
+ align:start position:0%
+that's a big deal
+ 
+
+ align:start position:0%
+that's a big deal
+finally we could just provide the
+
+ align:start position:0%
+finally we could just provide the
+ 
+
+ align:start position:0%
+finally we could just provide the
+insurance that's actually the most
+
+ align:start position:0%
+insurance that's actually the most
+ 
+
+ align:start position:0%
+insurance that's actually the most
+common thing we do in America
+
+ align:start position:0%
+common thing we do in America
+ 
+
+ align:start position:0%
+common thing we do in America
+Social Security is our program that
+
+ align:start position:0%
+Social Security is our program that
+ 
+
+ align:start position:0%
+Social Security is our program that
+provides insurance for the elderly for
+
+ align:start position:0%
+provides insurance for the elderly for
+ 
+
+ align:start position:0%
+provides insurance for the elderly for
+therefore the costs for survival after
+
+ align:start position:0%
+therefore the costs for survival after
+ 
+
+ align:start position:0%
+therefore the costs for survival after
+retirement Medicare is insurance for the
+
+ align:start position:0%
+retirement Medicare is insurance for the
+ 
+
+ align:start position:0%
+retirement Medicare is insurance for the
+elderly we provide unemployment
+
+ align:start position:0%
+elderly we provide unemployment
+ 
+
+ align:start position:0%
+elderly we provide unemployment
+insurance is that sure as we ride
+
+ align:start position:0%
+insurance is that sure as we ride
+ 
+
+ align:start position:0%
+insurance is that sure as we ride
+against losing your job disability
+
+ align:start position:0%
+against losing your job disability
+ 
+
+ align:start position:0%
+against losing your job disability
+insurance is insurance we provide
+
+ align:start position:0%
+insurance is insurance we provide
+ 
+
+ align:start position:0%
+insurance is insurance we provide
+against having a career-ending
+
+ align:start position:0%
+against having a career-ending
+ 
+
+ align:start position:0%
+against having a career-ending
+disability so this is actually the most
+
+ align:start position:0%
+disability so this is actually the most
+ 
+
+ align:start position:0%
+disability so this is actually the most
+common thing indeed provision of social
+
+ align:start position:0%
+common thing indeed provision of social
+ 
+
+ align:start position:0%
+common thing indeed provision of social
+insurance in America costs almost costs
+
+ align:start position:0%
+insurance in America costs almost costs
+ 
+
+ align:start position:0%
+insurance in America costs almost costs
+more than private insurance so we spent
+
+ align:start position:0%
+more than private insurance so we spent
+ 
+
+ align:start position:0%
+more than private insurance so we spent
+about a trillion and a half on private
+
+ align:start position:0%
+about a trillion and a half on private
+ 
+
+ align:start position:0%
+about a trillion and a half on private
+insurance in America
+
+ align:start position:0%
+insurance in America
+ 
+
+ align:start position:0%
+insurance in America
+social insurance is probably one point
+
+ align:start position:0%
+social insurance is probably one point
+ 
+
+ align:start position:0%
+social insurance is probably one point
+seven to two trillion depending how you
+
+ align:start position:0%
+seven to two trillion depending how you
+ 
+
+ align:start position:0%
+seven to two trillion depending how you
+measure it so actually this is the
+
+ align:start position:0%
+measure it so actually this is the
+ 
+
+ align:start position:0%
+measure it so actually this is the
+biggest thing we do is we just provide
+
+ align:start position:0%
+biggest thing we do is we just provide
+ 
+
+ align:start position:0%
+biggest thing we do is we just provide
+insurance okay
+
+ align:start position:0%
+insurance okay
+ 
+
+ align:start position:0%
+insurance okay
+and that is um and that's a very large
+
+ align:start position:0%
+and that is um and that's a very large
+ 
+
+ align:start position:0%
+and that is um and that's a very large
+that that's a very large solution now
+
+ align:start position:0%
+that that's a very large solution now
+ 
+
+ align:start position:0%
+that that's a very large solution now
+once again what's the problem with this
+
+ align:start position:0%
+once again what's the problem with this
+ 
+
+ align:start position:0%
+once again what's the problem with this
+well you don't make that B help people
+
+ align:start position:0%
+well you don't make that B help people
+ 
+
+ align:start position:0%
+well you don't make that B help people
+unhappy because everyone you just give
+
+ align:start position:0%
+unhappy because everyone you just give
+ 
+
+ align:start position:0%
+unhappy because everyone you just give
+it to them the problem is you have to
+
+ align:start position:0%
+it to them the problem is you have to
+ 
+
+ align:start position:0%
+it to them the problem is you have to
+spend money on this this is one point
+
+ align:start position:0%
+spend money on this this is one point
+ 
+
+ align:start position:0%
+spend money on this this is one point
+seven trillion dollars in taxes we've
+
+ align:start position:0%
+seven trillion dollars in taxes we've
+ 
+
+ align:start position:0%
+seven trillion dollars in taxes we've
+got to raise every year that's that's
+
+ align:start position:0%
+got to raise every year that's that's
+ 
+
+ align:start position:0%
+got to raise every year that's that's
+non-trivial okay so basically each of
+
+ align:start position:0%
+non-trivial okay so basically each of
+ 
+
+ align:start position:0%
+non-trivial okay so basically each of
+these solutions has potential problems
+
+ align:start position:0%
+these solutions has potential problems
+ 
+
+ align:start position:0%
+these solutions has potential problems
+so the adverse selection problem will
+
+ align:start position:0%
+so the adverse selection problem will
+ 
+
+ align:start position:0%
+so the adverse selection problem will
+cause a private market to fail there are
+
+ align:start position:0%
+cause a private market to fail there are
+ 
+
+ align:start position:0%
+cause a private market to fail there are
+potential government solutions but each
+
+ align:start position:0%
+potential government solutions but each
+ 
+
+ align:start position:0%
+potential government solutions but each
+have limitations this one's pretty
+
+ align:start position:0%
+have limitations this one's pretty
+ 
+
+ align:start position:0%
+have limitations this one's pretty
+expensive
+
+ align:start position:0%
+expensive
+ 
+
+ align:start position:0%
+expensive
+this one's super expensive this one
+
+ align:start position:0%
+this one's super expensive this one
+ 
+
+ align:start position:0%
+this one's super expensive this one
+pisses off healthy people okay now
+
+ align:start position:0%
+pisses off healthy people okay now
+ 
+
+ align:start position:0%
+pisses off healthy people okay now
+you'll note the middle one the pissed
+
+ align:start position:0%
+you'll note the middle one the pissed
+ 
+
+ align:start position:0%
+you'll note the middle one the pissed
+off fella feels kind of subtle you don't
+
+ align:start position:0%
+off fella feels kind of subtle you don't
+ 
+
+ align:start position:0%
+off fella feels kind of subtle you don't
+see a lot of health people railing
+
+ align:start position:0%
+see a lot of health people railing
+ 
+
+ align:start position:0%
+see a lot of health people railing
+against mandated version of workers comp
+
+ align:start position:0%
+against mandated version of workers comp
+ 
+
+ align:start position:0%
+against mandated version of workers comp
+like bid against the health insurance
+
+ align:start position:0%
+like bid against the health insurance
+ 
+
+ align:start position:0%
+like bid against the health insurance
+mandate because people don't know okay
+
+ align:start position:0%
+mandate because people don't know okay
+ 
+
+ align:start position:0%
+mandate because people don't know okay
+so it's up says this one's a little bit
+
+ align:start position:0%
+so it's up says this one's a little bit
+ 
+
+ align:start position:0%
+so it's up says this one's a little bit
+subtle okay because people have to know
+
+ align:start position:0%
+subtle okay because people have to know
+ 
+
+ align:start position:0%
+subtle okay because people have to know
+that you're you know basically it's sort
+
+ align:start position:0%
+that you're you know basically it's sort
+ 
+
+ align:start position:0%
+that you're you know basically it's sort
+of crazy that I'm paying taxes every I'm
+
+ align:start position:0%
+of crazy that I'm paying taxes every I'm
+ 
+
+ align:start position:0%
+of crazy that I'm paying taxes every I'm
+never getting hurt at work am I gonna
+
+ align:start position:0%
+never getting hurt at work am I gonna
+ 
+
+ align:start position:0%
+never getting hurt at work am I gonna
+have one I gonna like slip in my desk or
+
+ align:start position:0%
+have one I gonna like slip in my desk or
+ 
+
+ align:start position:0%
+have one I gonna like slip in my desk or
+something never gonna hurt at work but I
+
+ align:start position:0%
+something never gonna hurt at work but I
+ 
+
+ align:start position:0%
+something never gonna hurt at work but I
+pay taxes all the time just in case
+
+ align:start position:0%
+pay taxes all the time just in case
+ 
+
+ align:start position:0%
+pay taxes all the time just in case
+someone else at MIT gets hurt you know
+
+ align:start position:0%
+someone else at MIT gets hurt you know
+ 
+
+ align:start position:0%
+someone else at MIT gets hurt you know
+so when the janitorial staff has a fit
+
+ align:start position:0%
+so when the janitorial staff has a fit
+ 
+
+ align:start position:0%
+so when the janitorial staff has a fit
+as a risk of being hurt I'm paying taxes
+
+ align:start position:0%
+as a risk of being hurt I'm paying taxes
+ 
+
+ align:start position:0%
+as a risk of being hurt I'm paying taxes
+in case the janitor gets hurt I should
+
+ align:start position:0%
+in case the janitor gets hurt I should
+ 
+
+ align:start position:0%
+in case the janitor gets hurt I should
+be upset about that but I'm not and in
+
+ align:start position:0%
+be upset about that but I'm not and in
+ 
+
+ align:start position:0%
+be upset about that but I'm not and in
+subsets it's about kind of what people
+
+ align:start position:0%
+subsets it's about kind of what people
+ 
+
+ align:start position:0%
+subsets it's about kind of what people
+know what they don't okay so that is the
+
+ align:start position:0%
+know what they don't okay so that is the
+ 
+
+ align:start position:0%
+know what they don't okay so that is the
+basic argument for social insurance but
+
+ align:start position:0%
+basic argument for social insurance but
+ 
+
+ align:start position:0%
+basic argument for social insurance but
+would provide social insurance despite
+
+ align:start position:0%
+would provide social insurance despite
+ 
+
+ align:start position:0%
+would provide social insurance despite
+all these problems we enter into a
+
+ align:start position:0%
+all these problems we enter into a
+ 
+
+ align:start position:0%
+all these problems we enter into a
+fundamental trade-off which is let's
+
+ align:start position:0%
+fundamental trade-off which is let's
+ 
+
+ align:start position:0%
+fundamental trade-off which is let's
+decide we've determined some optimal
+
+ align:start position:0%
+decide we've determined some optimal
+ 
+
+ align:start position:0%
+decide we've determined some optimal
+government policy let's decide that the
+
+ align:start position:0%
+government policy let's decide that the
+ 
+
+ align:start position:0%
+government policy let's decide that the
+markets failed so we're gonna do one of
+
+ align:start position:0%
+markets failed so we're gonna do one of
+ 
+
+ align:start position:0%
+markets failed so we're gonna do one of
+these things and so if some kind of
+
+ align:start position:0%
+these things and so if some kind of
+ 
+
+ align:start position:0%
+these things and so if some kind of
+she's in solve the problem the problem
+
+ align:start position:0%
+she's in solve the problem the problem
+ 
+
+ align:start position:0%
+she's in solve the problem the problem
+is that when you insure people for risks
+
+ align:start position:0%
+is that when you insure people for risks
+ 
+
+ align:start position:0%
+is that when you insure people for risks
+you create a new problem called moral
+
+ align:start position:0%
+you create a new problem called moral
+ 
+
+ align:start position:0%
+you create a new problem called moral
+hazard moral hazard moral hazard is
+
+ align:start position:0%
+hazard moral hazard moral hazard is
+ 
+
+ align:start position:0%
+hazard moral hazard moral hazard is
+basically the adverse behavior that is
+
+ align:start position:0%
+basically the adverse behavior that is
+ 
+
+ align:start position:0%
+basically the adverse behavior that is
+encouraged by insurance when you insure
+
+ align:start position:0%
+encouraged by insurance when you insure
+ 
+
+ align:start position:0%
+encouraged by insurance when you insure
+people you encourage adverse behavior so
+
+ align:start position:0%
+people you encourage adverse behavior so
+ 
+
+ align:start position:0%
+people you encourage adverse behavior so
+the classic example this is
+
+ align:start position:0%
+the classic example this is
+ 
+
+ align:start position:0%
+the classic example this is
+if I have health insurance I ride my
+
+ align:start position:0%
+if I have health insurance I ride my
+ 
+
+ align:start position:0%
+if I have health insurance I ride my
+bike less carefully I guess by getting a
+
+ align:start position:0%
+bike less carefully I guess by getting a
+ 
+
+ align:start position:0%
+bike less carefully I guess by getting a
+crash no I'm not crazy I still don't get
+
+ align:start position:0%
+crash no I'm not crazy I still don't get
+ 
+
+ align:start position:0%
+crash no I'm not crazy I still don't get
+in a crash but I'm a little bit less
+
+ align:start position:0%
+in a crash but I'm a little bit less
+ 
+
+ align:start position:0%
+in a crash but I'm a little bit less
+careful because I know I'm insured in
+
+ align:start position:0%
+careful because I know I'm insured in
+ 
+
+ align:start position:0%
+careful because I know I'm insured in
+case I get in a crash if I have fire
+
+ align:start position:0%
+case I get in a crash if I have fire
+ 
+
+ align:start position:0%
+case I get in a crash if I have fire
+insurance I don't buy a fire
+
+ align:start position:0%
+insurance I don't buy a fire
+ 
+
+ align:start position:0%
+insurance I don't buy a fire
+extinguisher for my house because it
+
+ align:start position:0%
+extinguisher for my house because it
+ 
+
+ align:start position:0%
+extinguisher for my house because it
+burns down I just could get the money
+
+ align:start position:0%
+burns down I just could get the money
+ 
+
+ align:start position:0%
+burns down I just could get the money
+back anyway
+
+ align:start position:0%
+back anyway
+ 
+
+ align:start position:0%
+back anyway
+or if workers have insurance against
+
+ align:start position:0%
+or if workers have insurance against
+ 
+
+ align:start position:0%
+or if workers have insurance against
+losing a job that pays them without a
+
+ align:start position:0%
+losing a job that pays them without a
+ 
+
+ align:start position:0%
+losing a job that pays them without a
+work they might search less hard for a
+
+ align:start position:0%
+work they might search less hard for a
+ 
+
+ align:start position:0%
+work they might search less hard for a
+new job right basically if I lose my job
+
+ align:start position:0%
+new job right basically if I lose my job
+ 
+
+ align:start position:0%
+new job right basically if I lose my job
+and I got nothing I'm gonna work my ass
+
+ align:start position:0%
+and I got nothing I'm gonna work my ass
+ 
+
+ align:start position:0%
+and I got nothing I'm gonna work my ass
+off to get a new job if I lose my job
+
+ align:start position:0%
+off to get a new job if I lose my job
+ 
+
+ align:start position:0%
+off to get a new job if I lose my job
+and the government says well for twenty
+
+ align:start position:0%
+and the government says well for twenty
+ 
+
+ align:start position:0%
+and the government says well for twenty
+six weeks we'll give you half your
+
+ align:start position:0%
+six weeks we'll give you half your
+ 
+
+ align:start position:0%
+six weeks we'll give you half your
+salary while you look for a job I'll be
+
+ align:start position:0%
+salary while you look for a job I'll be
+ 
+
+ align:start position:0%
+salary while you look for a job I'll be
+a little bit less rushed okay the
+
+ align:start position:0%
+a little bit less rushed okay the
+ 
+
+ align:start position:0%
+a little bit less rushed okay the
+problem and there's lots of evidence
+
+ align:start position:0%
+problem and there's lots of evidence
+ 
+
+ align:start position:0%
+problem and there's lots of evidence
+that moral hazards the problem it comes
+
+ align:start position:0%
+that moral hazards the problem it comes
+ 
+
+ align:start position:0%
+that moral hazards the problem it comes
+of two types of evidence the first type
+
+ align:start position:0%
+of two types of evidence the first type
+ 
+
+ align:start position:0%
+of two types of evidence the first type
+of evidence is fun anecdotes so the
+
+ align:start position:0%
+of evidence is fun anecdotes so the
+ 
+
+ align:start position:0%
+of evidence is fun anecdotes so the
+greatest best data to a workers
+
+ align:start position:0%
+greatest best data to a workers
+ 
+
+ align:start position:0%
+greatest best data to a workers
+compensation let's take that workers
+
+ align:start position:0%
+compensation let's take that workers
+ 
+
+ align:start position:0%
+compensation let's take that workers
+compensation
+
+ align:start position:0%
+compensation
+ 
+
+ align:start position:0%
+compensation
+it's a program clothes needed lot of
+
+ align:start position:0%
+it's a program clothes needed lot of
+ 
+
+ align:start position:0%
+it's a program clothes needed lot of
+people get hurt at work I don't but lots
+
+ align:start position:0%
+people get hurt at work I don't but lots
+ 
+
+ align:start position:0%
+people get hurt at work I don't but lots
+of people do get hurt at work and so
+
+ align:start position:0%
+of people do get hurt at work and so
+ 
+
+ align:start position:0%
+of people do get hurt at work and so
+it's a sensible social insurance program
+
+ align:start position:0%
+it's a sensible social insurance program
+ 
+
+ align:start position:0%
+it's a sensible social insurance program
+the promise has a huge moral hazard
+
+ align:start position:0%
+the promise has a huge moral hazard
+ 
+
+ align:start position:0%
+the promise has a huge moral hazard
+component and there's fun examples of
+
+ align:start position:0%
+component and there's fun examples of
+ 
+
+ align:start position:0%
+component and there's fun examples of
+this like the the prison guard in
+
+ align:start position:0%
+this like the the prison guard in
+ 
+
+ align:start position:0%
+this like the the prison guard in
+Massachusetts who claimed he got hurt on
+
+ align:start position:0%
+Massachusetts who claimed he got hurt on
+ 
+
+ align:start position:0%
+Massachusetts who claimed he got hurt on
+the job collecting eighty-two thousand
+
+ align:start position:0%
+the job collecting eighty-two thousand
+ 
+
+ align:start position:0%
+the job collecting eighty-two thousand
+dollars in benefits while the whole time
+
+ align:start position:0%
+dollars in benefits while the whole time
+ 
+
+ align:start position:0%
+dollars in benefits while the whole time
+running a karate school and teaching
+
+ align:start position:0%
+running a karate school and teaching
+ 
+
+ align:start position:0%
+running a karate school and teaching
+students karate and finally someone
+
+ align:start position:0%
+students karate and finally someone
+ 
+
+ align:start position:0%
+students karate and finally someone
+noticed online this guy who couldn't
+
+ align:start position:0%
+noticed online this guy who couldn't
+ 
+
+ align:start position:0%
+noticed online this guy who couldn't
+work was running in karate school and
+
+ align:start position:0%
+work was running in karate school and
+ 
+
+ align:start position:0%
+work was running in karate school and
+doing karate kicks and stuff online so
+
+ align:start position:0%
+doing karate kicks and stuff online so
+ 
+
+ align:start position:0%
+doing karate kicks and stuff online so
+there's all sorts of fun examples about
+
+ align:start position:0%
+there's all sorts of fun examples about
+ 
+
+ align:start position:0%
+there's all sorts of fun examples about
+that but more convincing for economists
+
+ align:start position:0%
+that but more convincing for economists
+ 
+
+ align:start position:0%
+that but more convincing for economists
+is statistical evidence and the
+
+ align:start position:0%
+is statistical evidence and the
+ 
+
+ align:start position:0%
+is statistical evidence and the
+statistical evidence is clear that moral
+
+ align:start position:0%
+statistical evidence is clear that moral
+ 
+
+ align:start position:0%
+statistical evidence is clear that moral
+hazards a big problem for example if you
+
+ align:start position:0%
+hazards a big problem for example if you
+ 
+
+ align:start position:0%
+hazards a big problem for example if you
+raise the benefits people get under
+
+ align:start position:0%
+raise the benefits people get under
+ 
+
+ align:start position:0%
+raise the benefits people get under
+workers comp suddenly they become
+
+ align:start position:0%
+workers comp suddenly they become
+ 
+
+ align:start position:0%
+workers comp suddenly they become
+injured more often and stay at work
+
+ align:start position:0%
+injured more often and stay at work
+ 
+
+ align:start position:0%
+injured more often and stay at work
+longer
+
+ align:start position:0%
+longer
+ 
+
+ align:start position:0%
+longer
+there's no reason injuries should be
+
+ align:start position:0%
+there's no reason injuries should be
+ 
+
+ align:start position:0%
+there's no reason injuries should be
+because you got hurt okay so how can it
+
+ align:start position:0%
+because you got hurt okay so how can it
+ 
+
+ align:start position:0%
+because you got hurt okay so how can it
+be that suddenly when a state raises its
+
+ align:start position:0%
+be that suddenly when a state raises its
+ 
+
+ align:start position:0%
+be that suddenly when a state raises its
+benefits suddenly as more injuries well
+
+ align:start position:0%
+benefits suddenly as more injuries well
+ 
+
+ align:start position:0%
+benefits suddenly as more injuries well
+the answer is moral hazard when states
+
+ align:start position:0%
+the answer is moral hazard when states
+ 
+
+ align:start position:0%
+the answer is moral hazard when states
+raise their unemployment insurance
+
+ align:start position:0%
+raise their unemployment insurance
+ 
+
+ align:start position:0%
+raise their unemployment insurance
+benefits more people leave their jobs
+
+ align:start position:0%
+benefits more people leave their jobs
+ 
+
+ align:start position:0%
+benefits more people leave their jobs
+and they stay unemployed longer moral
+
+ align:start position:0%
+and they stay unemployed longer moral
+ 
+
+ align:start position:0%
+and they stay unemployed longer moral
+hazard so the moral has a problem is
+
+ align:start position:0%
+hazard so the moral has a problem is
+ 
+
+ align:start position:0%
+hazard so the moral has a problem is
+real it's that inherent trade-off
+
+ align:start position:0%
+real it's that inherent trade-off
+ 
+
+ align:start position:0%
+real it's that inherent trade-off
+actually not just the public insurance
+
+ align:start position:0%
+actually not just the public insurance
+ 
+
+ align:start position:0%
+actually not just the public insurance
+private insurance - anytime you insure
+
+ align:start position:0%
+private insurance - anytime you insure
+ 
+
+ align:start position:0%
+private insurance - anytime you insure
+people against something bad happens
+
+ align:start position:0%
+people against something bad happens
+ 
+
+ align:start position:0%
+people against something bad happens
+you're providing less than incentive for
+
+ align:start position:0%
+you're providing less than incentive for
+ 
+
+ align:start position:0%
+you're providing less than incentive for
+them to try themselves to avoid that bad
+
+ align:start position:0%
+them to try themselves to avoid that bad
+ 
+
+ align:start position:0%
+them to try themselves to avoid that bad
+thing happening okay
+
+ align:start position:0%
+thing happening okay
+ 
+
+ align:start position:0%
+thing happening okay
+so moral hazard is a real problem and
+
+ align:start position:0%
+so moral hazard is a real problem and
+ 
+
+ align:start position:0%
+so moral hazard is a real problem and
+it's essentially the trade-off on the
+
+ align:start position:0%
+it's essentially the trade-off on the
+ 
+
+ align:start position:0%
+it's essentially the trade-off on the
+one hand we talked about why people like
+
+ align:start position:0%
+one hand we talked about why people like
+ 
+
+ align:start position:0%
+one hand we talked about why people like
+insurance weed locked about why people
+
+ align:start position:0%
+insurance weed locked about why people
+ 
+
+ align:start position:0%
+insurance weed locked about why people
+like private insurance because of risk
+
+ align:start position:0%
+like private insurance because of risk
+ 
+
+ align:start position:0%
+like private insurance because of risk
+aversion we talked about why government
+
+ align:start position:0%
+aversion we talked about why government
+ 
+
+ align:start position:0%
+aversion we talked about why government
+intervention insurance markets is
+
+ align:start position:0%
+intervention insurance markets is
+ 
+
+ align:start position:0%
+intervention insurance markets is
+necessary but that comes with a
+
+ align:start position:0%
+necessary but that comes with a
+ 
+
+ align:start position:0%
+necessary but that comes with a
+trade-off which is the more insurance
+
+ align:start position:0%
+trade-off which is the more insurance
+ 
+
+ align:start position:0%
+trade-off which is the more insurance
+you provide the less people will take
+
+ align:start position:0%
+you provide the less people will take
+ 
+
+ align:start position:0%
+you provide the less people will take
+care of themselves and that's the
+
+ align:start position:0%
+care of themselves and that's the
+ 
+
+ align:start position:0%
+care of themselves and that's the
+trade-off okay now why do we care let's
+
+ align:start position:0%
+trade-off okay now why do we care let's
+ 
+
+ align:start position:0%
+trade-off okay now why do we care let's
+just sit back say okay that's like an
+
+ align:start position:0%
+just sit back say okay that's like an
+ 
+
+ align:start position:0%
+just sit back say okay that's like an
+interesting Kannamma concept but why do
+
+ align:start position:0%
+interesting Kannamma concept but why do
+ 
+
+ align:start position:0%
+interesting Kannamma concept but why do
+I care why don't I care if someone stays
+
+ align:start position:0%
+I care why don't I care if someone stays
+ 
+
+ align:start position:0%
+I care why don't I care if someone stays
+out of work longer or fakes an injury or
+
+ align:start position:0%
+out of work longer or fakes an injury or
+ 
+
+ align:start position:0%
+out of work longer or fakes an injury or
+whatever
+
+ align:start position:0%
+whatever
+ 
+
+ align:start position:0%
+whatever
+why don't I care about this why is this
+
+ align:start position:0%
+why don't I care about this why is this
+ 
+
+ align:start position:0%
+why don't I care about this why is this
+a problem well it's a problem for two
+
+ align:start position:0%
+a problem well it's a problem for two
+ 
+
+ align:start position:0%
+a problem well it's a problem for two
+reasons well there's two costs to moral
+
+ align:start position:0%
+reasons well there's two costs to moral
+ 
+
+ align:start position:0%
+reasons well there's two costs to moral
+hazard the first costume all hazard the
+
+ align:start position:0%
+hazard the first costume all hazard the
+ 
+
+ align:start position:0%
+hazard the first costume all hazard the
+first costume all hazard is lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+efficiency and the best way to see this
+
+ align:start position:0%
+efficiency and the best way to see this
+ 
+
+ align:start position:0%
+efficiency and the best way to see this
+is just to think about the economics of
+
+ align:start position:0%
+is just to think about the economics of
+ 
+
+ align:start position:0%
+is just to think about the economics of
+the consumption leisure trade-off okay
+
+ align:start position:0%
+the consumption leisure trade-off okay
+ 
+
+ align:start position:0%
+the consumption leisure trade-off okay
+think about how I make my decision of
+
+ align:start position:0%
+think about how I make my decision of
+ 
+
+ align:start position:0%
+think about how I make my decision of
+how hard to work okay basically if
+
+ align:start position:0%
+how hard to work okay basically if
+ 
+
+ align:start position:0%
+how hard to work okay basically if
+there's no insurance no social insurance
+
+ align:start position:0%
+there's no insurance no social insurance
+ 
+
+ align:start position:0%
+there's no insurance no social insurance
+no workers comp no employee in sure ins
+
+ align:start position:0%
+no workers comp no employee in sure ins
+ 
+
+ align:start position:0%
+no workers comp no employee in sure ins
+how do I choose how hard to work how do
+
+ align:start position:0%
+how do I choose how hard to work how do
+ 
+
+ align:start position:0%
+how do I choose how hard to work how do
+I choose how hard to work how do I do
+
+ align:start position:0%
+I choose how hard to work how do I do
+ 
+
+ align:start position:0%
+I choose how hard to work how do I do
+that what's a trade-off I consider in
+
+ align:start position:0%
+that what's a trade-off I consider in
+ 
+
+ align:start position:0%
+that what's a trade-off I consider in
+deciding how hard to work yeah
+
+ align:start position:0%
+deciding how hard to work yeah
+ 
+
+ align:start position:0%
+deciding how hard to work yeah
+assumption versus leisure in particular
+
+ align:start position:0%
+assumption versus leisure in particular
+ 
+
+ align:start position:0%
+assumption versus leisure in particular
+I will mix trade them off until the
+
+ align:start position:0%
+I will mix trade them off until the
+ 
+
+ align:start position:0%
+I will mix trade them off until the
+marginal value of the next hour of
+
+ align:start position:0%
+marginal value of the next hour of
+ 
+
+ align:start position:0%
+marginal value of the next hour of
+leisure large Valley sure equals the
+
+ align:start position:0%
+leisure large Valley sure equals the
+ 
+
+ align:start position:0%
+leisure large Valley sure equals the
+wage because the margin by Eve leisure
+
+ align:start position:0%
+wage because the margin by Eve leisure
+ 
+
+ align:start position:0%
+wage because the margin by Eve leisure
+is above the wage I should work less
+
+ align:start position:0%
+is above the wage I should work less
+ 
+
+ align:start position:0%
+is above the wage I should work less
+hard that means I'd rather be at home if
+
+ align:start position:0%
+hard that means I'd rather be at home if
+ 
+
+ align:start position:0%
+hard that means I'd rather be at home if
+the marginalized leisure is below the
+
+ align:start position:0%
+the marginalized leisure is below the
+ 
+
+ align:start position:0%
+the marginalized leisure is below the
+wage that means I'm just wasting my time
+
+ align:start position:0%
+wage that means I'm just wasting my time
+ 
+
+ align:start position:0%
+wage that means I'm just wasting my time
+at home I should work harder so I'll
+
+ align:start position:0%
+at home I should work harder so I'll
+ 
+
+ align:start position:0%
+at home I should work harder so I'll
+continue to trade off work and leisure
+
+ align:start position:0%
+continue to trade off work and leisure
+ 
+
+ align:start position:0%
+continue to trade off work and leisure
+till the next hour of leisure makes me
+
+ align:start position:0%
+till the next hour of leisure makes me
+ 
+
+ align:start position:0%
+till the next hour of leisure makes me
+just as happy as the next hour of
+
+ align:start position:0%
+just as happy as the next hour of
+ 
+
+ align:start position:0%
+just as happy as the next hour of
+working okay and that is the efficient
+
+ align:start position:0%
+working okay and that is the efficient
+ 
+
+ align:start position:0%
+working okay and that is the efficient
+outcome that is the social efficient
+
+ align:start position:0%
+outcome that is the social efficient
+ 
+
+ align:start position:0%
+outcome that is the social efficient
+outcome because leisure is not a social
+
+ align:start position:0%
+outcome because leisure is not a social
+ 
+
+ align:start position:0%
+outcome because leisure is not a social
+bad there's nothing wrong with leisure
+
+ align:start position:0%
+bad there's nothing wrong with leisure
+ 
+
+ align:start position:0%
+bad there's nothing wrong with leisure
+okay people value leisure they should
+
+ align:start position:0%
+okay people value leisure they should
+ 
+
+ align:start position:0%
+okay people value leisure they should
+get to trade
+
+ align:start position:0%
+get to trade
+ 
+
+ align:start position:0%
+get to trade
+the leisure versus what they get from
+
+ align:start position:0%
+the leisure versus what they get from
+ 
+
+ align:start position:0%
+the leisure versus what they get from
+working until they choose the right
+
+ align:start position:0%
+working until they choose the right
+ 
+
+ align:start position:0%
+working until they choose the right
+amount that's what makes society best
+
+ align:start position:0%
+amount that's what makes society best
+ 
+
+ align:start position:0%
+amount that's what makes society best
+off now what happens if I say well if
+
+ align:start position:0%
+off now what happens if I say well if
+ 
+
+ align:start position:0%
+off now what happens if I say well if
+you sit at home you're also going to get
+
+ align:start position:0%
+you sit at home you're also going to get
+ 
+
+ align:start position:0%
+you sit at home you're also going to get
+a check from the government well now
+
+ align:start position:0%
+a check from the government well now
+ 
+
+ align:start position:0%
+a check from the government well now
+what's my new equation well now if I
+
+ align:start position:0%
+what's my new equation well now if I
+ 
+
+ align:start position:0%
+what's my new equation well now if I
+work I still get the wage but what
+
+ align:start position:0%
+work I still get the wage but what
+ 
+
+ align:start position:0%
+work I still get the wage but what
+happens if I sit at home I get the
+
+ align:start position:0%
+happens if I sit at home I get the
+ 
+
+ align:start position:0%
+happens if I sit at home I get the
+marginal value of leisure plus the
+
+ align:start position:0%
+marginal value of leisure plus the
+ 
+
+ align:start position:0%
+marginal value of leisure plus the
+government check so now I sit at home
+
+ align:start position:0%
+government check so now I sit at home
+ 
+
+ align:start position:0%
+government check so now I sit at home
+until this equation is true which means
+
+ align:start position:0%
+until this equation is true which means
+ 
+
+ align:start position:0%
+until this equation is true which means
+that I sit at home until the margin I of
+
+ align:start position:0%
+that I sit at home until the margin I of
+ 
+
+ align:start position:0%
+that I sit at home until the margin I of
+leisure equals the wage minus the
+
+ align:start position:0%
+leisure equals the wage minus the
+ 
+
+ align:start position:0%
+leisure equals the wage minus the
+government transfer that means the
+
+ align:start position:0%
+government transfer that means the
+ 
+
+ align:start position:0%
+government transfer that means the
+moduli of leisure will be lower than it
+
+ align:start position:0%
+moduli of leisure will be lower than it
+ 
+
+ align:start position:0%
+moduli of leisure will be lower than it
+would be without the government transfer
+
+ align:start position:0%
+would be without the government transfer
+ 
+
+ align:start position:0%
+would be without the government transfer
+which means I work what more hard or
+
+ align:start position:0%
+which means I work what more hard or
+ 
+
+ align:start position:0%
+which means I work what more hard or
+less hard if the marginal I of leisure
+
+ align:start position:0%
+less hard if the marginal I of leisure
+ 
+
+ align:start position:0%
+less hard if the marginal I of leisure
+is forced down that means I'm doing what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in return - yeah more leisure because
+
+ align:start position:0%
+so in return - yeah more leisure because
+ 
+
+ align:start position:0%
+so in return - yeah more leisure because
+remember there's diminishing large of
+
+ align:start position:0%
+remember there's diminishing large of
+ 
+
+ align:start position:0%
+remember there's diminishing large of
+ides of everything so I'm taking more
+
+ align:start position:0%
+ides of everything so I'm taking more
+ 
+
+ align:start position:0%
+ides of everything so I'm taking more
+leisure less work so the government is
+
+ align:start position:0%
+leisure less work so the government is
+ 
+
+ align:start position:0%
+leisure less work so the government is
+causing me to work less by essentially
+
+ align:start position:0%
+causing me to work less by essentially
+ 
+
+ align:start position:0%
+causing me to work less by essentially
+saying look I'm gonna reward you more
+
+ align:start position:0%
+saying look I'm gonna reward you more
+ 
+
+ align:start position:0%
+saying look I'm gonna reward you more
+for staying at home what does that do
+
+ align:start position:0%
+for staying at home what does that do
+ 
+
+ align:start position:0%
+for staying at home what does that do
+that means that people work less than is
+
+ align:start position:0%
+that means that people work less than is
+ 
+
+ align:start position:0%
+that means that people work less than is
+socially optimal this is the social
+
+ align:start position:0%
+socially optimal this is the social
+ 
+
+ align:start position:0%
+socially optimal this is the social
+optimum this means people are taking
+
+ align:start position:0%
+optimum this means people are taking
+ 
+
+ align:start position:0%
+optimum this means people are taking
+more leisure and working less than is
+
+ align:start position:0%
+more leisure and working less than is
+ 
+
+ align:start position:0%
+more leisure and working less than is
+socially optimal when people work less
+
+ align:start position:0%
+socially optimal when people work less
+ 
+
+ align:start position:0%
+socially optimal when people work less
+that shifts in the supply curve and
+
+ align:start position:0%
+that shifts in the supply curve and
+ 
+
+ align:start position:0%
+that shifts in the supply curve and
+lower and creates a deadweight loss
+
+ align:start position:0%
+lower and creates a deadweight loss
+ 
+
+ align:start position:0%
+lower and creates a deadweight loss
+social welfare has fallen let's be in
+
+ align:start position:0%
+social welfare has fallen let's be in
+ 
+
+ align:start position:0%
+social welfare has fallen let's be in
+Portland let me remind you it's not
+
+ align:start position:0%
+Portland let me remind you it's not
+ 
+
+ align:start position:0%
+Portland let me remind you it's not
+following because people take some time
+
+ align:start position:0%
+following because people take some time
+ 
+
+ align:start position:0%
+following because people take some time
+off
+
+ align:start position:0%
+off
+ 
+
+ align:start position:0%
+off
+okay many people on the conservative
+
+ align:start position:0%
+okay many people on the conservative
+ 
+
+ align:start position:0%
+okay many people on the conservative
+side inspection will act as if work as a
+
+ align:start position:0%
+side inspection will act as if work as a
+ 
+
+ align:start position:0%
+side inspection will act as if work as a
+virtue work is not a virtue okay the
+
+ align:start position:0%
+virtue work is not a virtue okay the
+ 
+
+ align:start position:0%
+virtue work is not a virtue okay the
+optimal solution is to work until your
+
+ align:start position:0%
+optimal solution is to work until your
+ 
+
+ align:start position:0%
+optimal solution is to work until your
+value of working equals a value of
+
+ align:start position:0%
+value of working equals a value of
+ 
+
+ align:start position:0%
+value of working equals a value of
+leisure if you're someone who has a job
+
+ align:start position:0%
+leisure if you're someone who has a job
+ 
+
+ align:start position:0%
+leisure if you're someone who has a job
+that you hate and doesn't pay well and
+
+ align:start position:0%
+that you hate and doesn't pay well and
+ 
+
+ align:start position:0%
+that you hate and doesn't pay well and
+you love watching TV then you should
+
+ align:start position:0%
+you love watching TV then you should
+ 
+
+ align:start position:0%
+you love watching TV then you should
+work less that's what the UH poem for
+
+ align:start position:0%
+work less that's what the UH poem for
+ 
+
+ align:start position:0%
+work less that's what the UH poem for
+society but you shouldn't work even less
+
+ align:start position:0%
+society but you shouldn't work even less
+ 
+
+ align:start position:0%
+society but you shouldn't work even less
+because the government's paying you to
+
+ align:start position:0%
+because the government's paying you to
+ 
+
+ align:start position:0%
+because the government's paying you to
+stay home that produces efficiency so
+
+ align:start position:0%
+stay home that produces efficiency so
+ 
+
+ align:start position:0%
+stay home that produces efficiency so
+that's the problem of moral hazard is it
+
+ align:start position:0%
+that's the problem of moral hazard is it
+ 
+
+ align:start position:0%
+that's the problem of moral hazard is it
+lowers efficiency
+
+ align:start position:0%
+lowers efficiency
+ 
+
+ align:start position:0%
+lowers efficiency
+there's a second problem of course of
+
+ align:start position:0%
+there's a second problem of course of
+ 
+
+ align:start position:0%
+there's a second problem of course of
+moral hazard which is if you work less
+
+ align:start position:0%
+moral hazard which is if you work less
+ 
+
+ align:start position:0%
+moral hazard which is if you work less
+then we have two taxable who do work
+
+ align:start position:0%
+then we have two taxable who do work
+ 
+
+ align:start position:0%
+then we have two taxable who do work
+more to pay for these programs so it
+
+ align:start position:0%
+more to pay for these programs so it
+ 
+
+ align:start position:0%
+more to pay for these programs so it
+raises taxation raises the required tax
+
+ align:start position:0%
+raises taxation raises the required tax
+ 
+
+ align:start position:0%
+raises taxation raises the required tax
+revenues raises the tax revenues
+
+ align:start position:0%
+revenues raises the tax revenues
+ 
+
+ align:start position:0%
+revenues raises the tax revenues
+required because if you're sitting at
+
+ align:start position:0%
+required because if you're sitting at
+ 
+
+ align:start position:0%
+required because if you're sitting at
+home war I got to make more money to pay
+
+ align:start position:0%
+home war I got to make more money to pay
+ 
+
+ align:start position:0%
+home war I got to make more money to pay
+for you to sit at home and we know
+
+ align:start position:0%
+for you to sit at home and we know
+ 
+
+ align:start position:0%
+for you to sit at home and we know
+taxation also causes deadweight loss so
+
+ align:start position:0%
+taxation also causes deadweight loss so
+ 
+
+ align:start position:0%
+taxation also causes deadweight loss so
+it's a double whammy I caused you to sit
+
+ align:start position:0%
+it's a double whammy I caused you to sit
+ 
+
+ align:start position:0%
+it's a double whammy I caused you to sit
+at home and I caused other people have
+
+ align:start position:0%
+at home and I caused other people have
+ 
+
+ align:start position:0%
+at home and I caused other people have
+to add more taxes to pay for you sit at
+
+ align:start position:0%
+to add more taxes to pay for you sit at
+ 
+
+ align:start position:0%
+to add more taxes to pay for you sit at
+home which causes them to work less -
+
+ align:start position:0%
+home which causes them to work less -
+ 
+
+ align:start position:0%
+home which causes them to work less -
+okay there's a second round effect as a
+
+ align:start position:0%
+okay there's a second round effect as a
+ 
+
+ align:start position:0%
+okay there's a second round effect as a
+result moral hazard causes inefficiency
+
+ align:start position:0%
+result moral hazard causes inefficiency
+ 
+
+ align:start position:0%
+result moral hazard causes inefficiency
+to society and that is the trade-off
+
+ align:start position:0%
+to society and that is the trade-off
+ 
+
+ align:start position:0%
+to society and that is the trade-off
+once again I told you this course is
+
+ align:start position:0%
+once again I told you this course is
+ 
+
+ align:start position:0%
+once again I told you this course is
+annoying we don't give you right answers
+
+ align:start position:0%
+annoying we don't give you right answers
+ 
+
+ align:start position:0%
+annoying we don't give you right answers
+we tell you trade-offs the trade-off
+
+ align:start position:0%
+we tell you trade-offs the trade-off
+ 
+
+ align:start position:0%
+we tell you trade-offs the trade-off
+here is we need programs like
+
+ align:start position:0%
+here is we need programs like
+ 
+
+ align:start position:0%
+here is we need programs like
+unemployment insurance because otherwise
+
+ align:start position:0%
+unemployment insurance because otherwise
+ 
+
+ align:start position:0%
+unemployment insurance because otherwise
+let's take the case of unemployment
+
+ align:start position:0%
+let's take the case of unemployment
+ 
+
+ align:start position:0%
+let's take the case of unemployment
+shows there's one more time imagine is
+
+ align:start position:0%
+shows there's one more time imagine is
+ 
+
+ align:start position:0%
+shows there's one more time imagine is
+no government unemployment insurance and
+
+ align:start position:0%
+no government unemployment insurance and
+ 
+
+ align:start position:0%
+no government unemployment insurance and
+you said that's great I'll offer private
+
+ align:start position:0%
+you said that's great I'll offer private
+ 
+
+ align:start position:0%
+you said that's great I'll offer private
+unemployment insurance well that's not
+
+ align:start position:0%
+unemployment insurance well that's not
+ 
+
+ align:start position:0%
+unemployment insurance well that's not
+going to work why because people know
+
+ align:start position:0%
+going to work why because people know
+ 
+
+ align:start position:0%
+going to work why because people know
+way more than you do about whether
+
+ align:start position:0%
+way more than you do about whether
+ 
+
+ align:start position:0%
+way more than you do about whether
+they're gonna lose their job if you off
+
+ align:start position:0%
+they're gonna lose their job if you off
+ 
+
+ align:start position:0%
+they're gonna lose their job if you off
+tried out for private insurance you'd
+
+ align:start position:0%
+tried out for private insurance you'd
+ 
+
+ align:start position:0%
+tried out for private insurance you'd
+lose your shirt because of adverse
+
+ align:start position:0%
+lose your shirt because of adverse
+ 
+
+ align:start position:0%
+lose your shirt because of adverse
+selection so absent government provided
+
+ align:start position:0%
+selection so absent government provided
+ 
+
+ align:start position:0%
+selection so absent government provided
+unemployment insurance there would be no
+
+ align:start position:0%
+unemployment insurance there would be no
+ 
+
+ align:start position:0%
+unemployment insurance there would be no
+unemployment insurance and that would be
+
+ align:start position:0%
+unemployment insurance and that would be
+ 
+
+ align:start position:0%
+unemployment insurance and that would be
+bad that I mean people we subject to a
+
+ align:start position:0%
+bad that I mean people we subject to a
+ 
+
+ align:start position:0%
+bad that I mean people we subject to a
+risk that would drive their consumption
+
+ align:start position:0%
+risk that would drive their consumption
+ 
+
+ align:start position:0%
+risk that would drive their consumption
+of zero remember most Americans have no
+
+ align:start position:0%
+of zero remember most Americans have no
+ 
+
+ align:start position:0%
+of zero remember most Americans have no
+savings that mean Americans will be
+
+ align:start position:0%
+savings that mean Americans will be
+ 
+
+ align:start position:0%
+savings that mean Americans will be
+chubby too a risk where if they lost
+
+ align:start position:0%
+chubby too a risk where if they lost
+ 
+
+ align:start position:0%
+chubby too a risk where if they lost
+their job they would starve that's a
+
+ align:start position:0%
+their job they would starve that's a
+ 
+
+ align:start position:0%
+their job they would starve that's a
+very bad outcome so it is socially
+
+ align:start position:0%
+very bad outcome so it is socially
+ 
+
+ align:start position:0%
+very bad outcome so it is socially
+valuable to insure against unemployment
+
+ align:start position:0%
+valuable to insure against unemployment
+ 
+
+ align:start position:0%
+valuable to insure against unemployment
+risk the private market can't do it
+
+ align:start position:0%
+risk the private market can't do it
+ 
+
+ align:start position:0%
+risk the private market can't do it
+because of adverse selection therefore
+
+ align:start position:0%
+because of adverse selection therefore
+ 
+
+ align:start position:0%
+because of adverse selection therefore
+there is a compelling case for
+
+ align:start position:0%
+there is a compelling case for
+ 
+
+ align:start position:0%
+there is a compelling case for
+government unemployment insurance but
+
+ align:start position:0%
+government unemployment insurance but
+ 
+
+ align:start position:0%
+government unemployment insurance but
+will it provide unemployment insurance
+
+ align:start position:0%
+will it provide unemployment insurance
+ 
+
+ align:start position:0%
+will it provide unemployment insurance
+it caused people to sit at home extra
+
+ align:start position:0%
+it caused people to sit at home extra
+ 
+
+ align:start position:0%
+it caused people to sit at home extra
+and not work as hard and that's that's
+
+ align:start position:0%
+and not work as hard and that's that's
+ 
+
+ align:start position:0%
+and not work as hard and that's that's
+the sort of chain of logic will teach
+
+ align:start position:0%
+the sort of chain of logic will teach
+ 
+
+ align:start position:0%
+the sort of chain of logic will teach
+you the trade-off what this says is
+
+ align:start position:0%
+you the trade-off what this says is
+ 
+
+ align:start position:0%
+you the trade-off what this says is
+optimal social insurance that in these
+
+ align:start position:0%
+optimal social insurance that in these
+ 
+
+ align:start position:0%
+optimal social insurance that in these
+markets we're gonna want some social
+
+ align:start position:0%
+markets we're gonna want some social
+ 
+
+ align:start position:0%
+markets we're gonna want some social
+insurance but not too much okay we're
+
+ align:start position:0%
+insurance but not too much okay we're
+ 
+
+ align:start position:0%
+insurance but not too much okay we're
+gonna want enough to protect people
+
+ align:start position:0%
+gonna want enough to protect people
+ 
+
+ align:start position:0%
+gonna want enough to protect people
+against starving but not so much that
+
+ align:start position:0%
+against starving but not so much that
+ 
+
+ align:start position:0%
+against starving but not so much that
+cause people sit at home so for example
+
+ align:start position:0%
+cause people sit at home so for example
+ 
+
+ align:start position:0%
+cause people sit at home so for example
+if I told you I'm a setup on
+
+ align:start position:0%
+if I told you I'm a setup on
+ 
+
+ align:start position:0%
+if I told you I'm a setup on
+unemployment insurance program the way
+
+ align:start position:0%
+unemployment insurance program the way
+ 
+
+ align:start position:0%
+unemployment insurance program the way
+it's gonna work is if you lose your job
+
+ align:start position:0%
+it's gonna work is if you lose your job
+ 
+
+ align:start position:0%
+it's gonna work is if you lose your job
+I'm gonna pay your entire wage for as
+
+ align:start position:0%
+I'm gonna pay your entire wage for as
+ 
+
+ align:start position:0%
+I'm gonna pay your entire wage for as
+long as you need until you find a new
+
+ align:start position:0%
+long as you need until you find a new
+ 
+
+ align:start position:0%
+long as you need until you find a new
+job that would not be a good idea okay
+
+ align:start position:0%
+job that would not be a good idea okay
+ 
+
+ align:start position:0%
+job that would not be a good idea okay
+that will cause a huge amount of moral
+
+ align:start position:0%
+that will cause a huge amount of moral
+ 
+
+ align:start position:0%
+that will cause a huge amount of moral
+hazard and remember compare that compare
+
+ align:start position:0%
+hazard and remember compare that compare
+ 
+
+ align:start position:0%
+hazard and remember compare that compare
+that program to one where I'll pay you
+
+ align:start position:0%
+that program to one where I'll pay you
+ 
+
+ align:start position:0%
+that program to one where I'll pay you
+50 percent of your wage you find a new
+
+ align:start position:0%
+50 percent of your wage you find a new
+ 
+
+ align:start position:0%
+50 percent of your wage you find a new
+job well 50 percent it's going from zero
+
+ align:start position:0%
+job well 50 percent it's going from zero
+ 
+
+ align:start position:0%
+job well 50 percent it's going from zero
+to fifty is a zero of your wage to 50
+
+ align:start position:0%
+to fifty is a zero of your wage to 50
+ 
+
+ align:start position:0%
+to fifty is a zero of your wage to 50
+your wage is a huge consumption
+
+ align:start position:0%
+your wage is a huge consumption
+ 
+
+ align:start position:0%
+your wage is a huge consumption
+smoothing benefit you go from starving
+
+ align:start position:0%
+smoothing benefit you go from starving
+ 
+
+ align:start position:0%
+smoothing benefit you go from starving
+to being able to eat decently 5,200 it's
+
+ align:start position:0%
+to being able to eat decently 5,200 it's
+ 
+
+ align:start position:0%
+to being able to eat decently 5,200 it's
+an increase but not as much but 50-100
+
+ align:start position:0%
+an increase but not as much but 50-100
+ 
+
+ align:start position:0%
+an increase but not as much but 50-100
+has a huge moral hazard effect so you
+
+ align:start position:0%
+has a huge moral hazard effect so you
+ 
+
+ align:start position:0%
+has a huge moral hazard effect so you
+can want something more towards the
+
+ align:start position:0%
+can want something more towards the
+ 
+
+ align:start position:0%
+can want something more towards the
+middle where you're getting people away
+
+ align:start position:0%
+middle where you're getting people away
+ 
+
+ align:start position:0%
+middle where you're getting people away
+from starving but not so much that they
+
+ align:start position:0%
+from starving but not so much that they
+ 
+
+ align:start position:0%
+from starving but not so much that they
+don't work okay so that's the trade-off
+
+ align:start position:0%
+don't work okay so that's the trade-off
+ 
+
+ align:start position:0%
+don't work okay so that's the trade-off
+so let's talk about that trade-off in
+
+ align:start position:0%
+so let's talk about that trade-off in
+ 
+
+ align:start position:0%
+so let's talk about that trade-off in
+practice let's talk about the u.s.
+
+ align:start position:0%
+practice let's talk about the u.s.
+ 
+
+ align:start position:0%
+practice let's talk about the u.s.
+Social Security program the Social
+
+ align:start position:0%
+Social Security program the Social
+ 
+
+ align:start position:0%
+Social Security program the Social
+Security program in the US okay
+
+ align:start position:0%
+Security program in the US okay
+ 
+
+ align:start position:0%
+Security program in the US okay
+Social Security is our biggest single
+
+ align:start position:0%
+Social Security is our biggest single
+ 
+
+ align:start position:0%
+Social Security is our biggest single
+social insurance program in the u.s.
+
+ align:start position:0%
+social insurance program in the u.s.
+ 
+
+ align:start position:0%
+social insurance program in the u.s.
+it's currently currently the social
+
+ align:start position:0%
+it's currently currently the social
+ 
+
+ align:start position:0%
+it's currently currently the social
+security progress about eight hundred
+
+ align:start position:0%
+security progress about eight hundred
+ 
+
+ align:start position:0%
+security progress about eight hundred
+billion dollars per year that's real
+
+ align:start position:0%
+billion dollars per year that's real
+ 
+
+ align:start position:0%
+billion dollars per year that's real
+money that's even one Jeff Bezos has
+
+ align:start position:0%
+money that's even one Jeff Bezos has
+ 
+
+ align:start position:0%
+money that's even one Jeff Bezos has
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+eight hundred billion dollars a year
+
+ align:start position:0%
+eight hundred billion dollars a year
+ 
+
+ align:start position:0%
+eight hundred billion dollars a year
+okay that's more than he's worth and
+
+ align:start position:0%
+okay that's more than he's worth and
+ 
+
+ align:start position:0%
+okay that's more than he's worth and
+it's every year okay
+
+ align:start position:0%
+it's every year okay
+ 
+
+ align:start position:0%
+it's every year okay
+what does this program do what this
+
+ align:start position:0%
+what does this program do what this
+ 
+
+ align:start position:0%
+what does this program do what this
+program does in a nutshell is it ensures
+
+ align:start position:0%
+program does in a nutshell is it ensures
+ 
+
+ align:start position:0%
+program does in a nutshell is it ensures
+you against the income loss you're gonna
+
+ align:start position:0%
+you against the income loss you're gonna
+ 
+
+ align:start position:0%
+you against the income loss you're gonna
+face when you retire okay when people
+
+ align:start position:0%
+face when you retire okay when people
+ 
+
+ align:start position:0%
+face when you retire okay when people
+retire they suddenly go from having a
+
+ align:start position:0%
+retire they suddenly go from having a
+ 
+
+ align:start position:0%
+retire they suddenly go from having a
+lot of income to having no income and
+
+ align:start position:0%
+lot of income to having no income and
+ 
+
+ align:start position:0%
+lot of income to having no income and
+basically the idea of Social Security is
+
+ align:start position:0%
+basically the idea of Social Security is
+ 
+
+ align:start position:0%
+basically the idea of Social Security is
+to make sure you don't starve when
+
+ align:start position:0%
+to make sure you don't starve when
+ 
+
+ align:start position:0%
+to make sure you don't starve when
+you're old so the way it works is you
+
+ align:start position:0%
+you're old so the way it works is you
+ 
+
+ align:start position:0%
+you're old so the way it works is you
+pay a tax and if you ever see a line
+
+ align:start position:0%
+pay a tax and if you ever see a line
+ 
+
+ align:start position:0%
+pay a tax and if you ever see a line
+your space that says FICA that's what
+
+ align:start position:0%
+your space that says FICA that's what
+ 
+
+ align:start position:0%
+your space that says FICA that's what
+this is for you pay a fika tax it is
+
+ align:start position:0%
+this is for you pay a fika tax it is
+ 
+
+ align:start position:0%
+this is for you pay a fika tax it is
+twelve point four percent of payroll
+
+ align:start position:0%
+twelve point four percent of payroll
+ 
+
+ align:start position:0%
+twelve point four percent of payroll
+half on you and half on your employer
+
+ align:start position:0%
+half on you and half on your employer
+ 
+
+ align:start position:0%
+half on you and half on your employer
+but it doesn't matter in half so
+
+ align:start position:0%
+but it doesn't matter in half so
+ 
+
+ align:start position:0%
+but it doesn't matter in half so
+employer right because we learn Latin we
+
+ align:start position:0%
+employer right because we learn Latin we
+ 
+
+ align:start position:0%
+employer right because we learn Latin we
+learn two lectures ago it doesn't matter
+
+ align:start position:0%
+learn two lectures ago it doesn't matter
+ 
+
+ align:start position:0%
+learn two lectures ago it doesn't matter
+who pays the tax it's a twelve point
+
+ align:start position:0%
+who pays the tax it's a twelve point
+ 
+
+ align:start position:0%
+who pays the tax it's a twelve point
+four percent tax that's what matters on
+
+ align:start position:0%
+four percent tax that's what matters on
+ 
+
+ align:start position:0%
+four percent tax that's what matters on
+you okay that money then provides that
+
+ align:start position:0%
+you okay that money then provides that
+ 
+
+ align:start position:0%
+you okay that money then provides that
+when you retire starting at age 62 you
+
+ align:start position:0%
+when you retire starting at age 62 you
+ 
+
+ align:start position:0%
+when you retire starting at age 62 you
+get a check from the
+
+ align:start position:0%
+get a check from the
+ 
+
+ align:start position:0%
+get a check from the
+government and you get a check from the
+
+ align:start position:0%
+government and you get a check from the
+ 
+
+ align:start position:0%
+government and you get a check from the
+government that lasts until you die the
+
+ align:start position:0%
+government that lasts until you die the
+ 
+
+ align:start position:0%
+government that lasts until you die the
+check from the government you get is
+
+ align:start position:0%
+check from the government you get is
+ 
+
+ align:start position:0%
+check from the government you get is
+what's called an annuity an annuity is a
+
+ align:start position:0%
+what's called an annuity an annuity is a
+ 
+
+ align:start position:0%
+what's called an annuity an annuity is a
+payment annuities are the opposite of
+
+ align:start position:0%
+payment annuities are the opposite of
+ 
+
+ align:start position:0%
+payment annuities are the opposite of
+life insurance life insurance is money
+
+ align:start position:0%
+life insurance life insurance is money
+ 
+
+ align:start position:0%
+life insurance life insurance is money
+that your family gets when you die
+
+ align:start position:0%
+that your family gets when you die
+ 
+
+ align:start position:0%
+that your family gets when you die
+annuity is that it is a regular payment
+
+ align:start position:0%
+annuity is that it is a regular payment
+ 
+
+ align:start position:0%
+annuity is that it is a regular payment
+you get until you die so the way it
+
+ align:start position:0%
+you get until you die so the way it
+ 
+
+ align:start position:0%
+you get until you die so the way it
+works you pay twelve and a half percent
+
+ align:start position:0%
+works you pay twelve and a half percent
+ 
+
+ align:start position:0%
+works you pay twelve and a half percent
+of your income all the way through your
+
+ align:start position:0%
+of your income all the way through your
+ 
+
+ align:start position:0%
+of your income all the way through your
+working life then we turn 62 or you can
+
+ align:start position:0%
+working life then we turn 62 or you can
+ 
+
+ align:start position:0%
+working life then we turn 62 or you can
+collect it later
+
+ align:start position:0%
+collect it later
+ 
+
+ align:start position:0%
+collect it later
+um you then get a payment for the rest
+
+ align:start position:0%
+um you then get a payment for the rest
+ 
+
+ align:start position:0%
+um you then get a payment for the rest
+of your life okay that payment is
+
+ align:start position:0%
+of your life okay that payment is
+ 
+
+ align:start position:0%
+of your life okay that payment is
+typically about half of what you made
+
+ align:start position:0%
+typically about half of what you made
+ 
+
+ align:start position:0%
+typically about half of what you made
+when you were working but it's very
+
+ align:start position:0%
+when you were working but it's very
+ 
+
+ align:start position:0%
+when you were working but it's very
+progressive in the sense that for
+
+ align:start position:0%
+progressive in the sense that for
+ 
+
+ align:start position:0%
+progressive in the sense that for
+someone who's very poor who has a very
+
+ align:start position:0%
+someone who's very poor who has a very
+ 
+
+ align:start position:0%
+someone who's very poor who has a very
+poor it'll probably more than half of
+
+ align:start position:0%
+poor it'll probably more than half of
+ 
+
+ align:start position:0%
+poor it'll probably more than half of
+what they made for someone who's rich to
+
+ align:start position:0%
+what they made for someone who's rich to
+ 
+
+ align:start position:0%
+what they made for someone who's rich to
+be much less than half of what they made
+
+ align:start position:0%
+be much less than half of what they made
+ 
+
+ align:start position:0%
+be much less than half of what they made
+it's a progressive payment everyone gets
+
+ align:start position:0%
+it's a progressive payment everyone gets
+ 
+
+ align:start position:0%
+it's a progressive payment everyone gets
+it everyone did Social Security but how
+
+ align:start position:0%
+it everyone did Social Security but how
+ 
+
+ align:start position:0%
+it everyone did Social Security but how
+much you get from it depends on your
+
+ align:start position:0%
+much you get from it depends on your
+ 
+
+ align:start position:0%
+much you get from it depends on your
+income the poorer you are the more
+
+ align:start position:0%
+income the poorer you are the more
+ 
+
+ align:start position:0%
+income the poorer you are the more
+generous it is relatively when you
+
+ align:start position:0%
+generous it is relatively when you
+ 
+
+ align:start position:0%
+generous it is relatively when you
+retire
+
+ align:start position:0%
+retire
+ 
+
+ align:start position:0%
+retire
+okay now the F yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's that that's a huge problem it
+
+ align:start position:0%
+that's that that's a huge problem it
+ 
+
+ align:start position:0%
+that's that that's a huge problem it
+sounds like you should definitely be
+
+ align:start position:0%
+sounds like you should definitely be
+ 
+
+ align:start position:0%
+sounds like you should definitely be
+enrolled in 1441 that's a whole half of
+
+ align:start position:0%
+enrolled in 1441 that's a whole half of
+ 
+
+ align:start position:0%
+enrolled in 1441 that's a whole half of
+lecture we spend on that I don't have
+
+ align:start position:0%
+lecture we spend on that I don't have
+ 
+
+ align:start position:0%
+lecture we spend on that I don't have
+time to talk about here but clearly this
+
+ align:start position:0%
+time to talk about here but clearly this
+ 
+
+ align:start position:0%
+time to talk about here but clearly this
+is a huge huge so just to give you a
+
+ align:start position:0%
+is a huge huge so just to give you a
+ 
+
+ align:start position:0%
+is a huge huge so just to give you a
+couple numbers to keep you up at night
+
+ align:start position:0%
+couple numbers to keep you up at night
+ 
+
+ align:start position:0%
+couple numbers to keep you up at night
+okay we all know we're all talking about
+
+ align:start position:0%
+okay we all know we're all talking about
+ 
+
+ align:start position:0%
+okay we all know we're all talking about
+the deficit is 500 billion it's a big
+
+ align:start position:0%
+the deficit is 500 billion it's a big
+ 
+
+ align:start position:0%
+the deficit is 500 billion it's a big
+deal okay if you add ask how much has
+
+ align:start position:0%
+deal okay if you add ask how much has
+ 
+
+ align:start position:0%
+deal okay if you add ask how much has
+America promised to pay to our senior
+
+ align:start position:0%
+America promised to pay to our senior
+ 
+
+ align:start position:0%
+America promised to pay to our senior
+citizens over the foreseeable future -
+
+ align:start position:0%
+citizens over the foreseeable future -
+ 
+
+ align:start position:0%
+citizens over the foreseeable future -
+how much we'll collect in taxes we are
+
+ align:start position:0%
+how much we'll collect in taxes we are
+ 
+
+ align:start position:0%
+how much we'll collect in taxes we are
+currently is the nation seventy five
+
+ align:start position:0%
+currently is the nation seventy five
+ 
+
+ align:start position:0%
+currently is the nation seventy five
+trillion dollars in debt okay it's
+
+ align:start position:0%
+trillion dollars in debt okay it's
+ 
+
+ align:start position:0%
+trillion dollars in debt okay it's
+because of the aging Society and things
+
+ align:start position:0%
+because of the aging Society and things
+ 
+
+ align:start position:0%
+because of the aging Society and things
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+so we've got big problems coming down
+
+ align:start position:0%
+so we've got big problems coming down
+ 
+
+ align:start position:0%
+so we've got big problems coming down
+the road we can talk about that another
+
+ align:start position:0%
+the road we can talk about that another
+ 
+
+ align:start position:0%
+the road we can talk about that another
+time okay but let's focus on the program
+
+ align:start position:0%
+time okay but let's focus on the program
+ 
+
+ align:start position:0%
+time okay but let's focus on the program
+itself at a point in time right now okay
+
+ align:start position:0%
+itself at a point in time right now okay
+ 
+
+ align:start position:0%
+itself at a point in time right now okay
+so basically we see here the moral
+
+ align:start position:0%
+so basically we see here the moral
+ 
+
+ align:start position:0%
+so basically we see here the moral
+hazard trade-off on the one hand we
+
+ align:start position:0%
+hazard trade-off on the one hand we
+ 
+
+ align:start position:0%
+hazard trade-off on the one hand we
+don't be able to starve when they're old
+
+ align:start position:0%
+don't be able to starve when they're old
+ 
+
+ align:start position:0%
+don't be able to starve when they're old
+on the other hand if I pay you once
+
+ align:start position:0%
+on the other hand if I pay you once
+ 
+
+ align:start position:0%
+on the other hand if I pay you once
+you're retired that could cause you to
+
+ align:start position:0%
+you're retired that could cause you to
+ 
+
+ align:start position:0%
+you're retired that could cause you to
+retire if I say once you're retired
+
+ align:start position:0%
+retire if I say once you're retired
+ 
+
+ align:start position:0%
+retire if I say once you're retired
+you're gonna get a check 50 percent of
+
+ align:start position:0%
+you're gonna get a check 50 percent of
+ 
+
+ align:start position:0%
+you're gonna get a check 50 percent of
+your wage you might say well if it's
+
+ align:start position:0%
+your wage you might say well if it's
+ 
+
+ align:start position:0%
+your wage you might say well if it's
+your wage isn't that much but I really
+
+ align:start position:0%
+your wage isn't that much but I really
+ 
+
+ align:start position:0%
+your wage isn't that much but I really
+don't like working in rather just hit
+
+ align:start position:0%
+don't like working in rather just hit
+ 
+
+ align:start position:0%
+don't like working in rather just hit
+the links at 50% of my wage so that's
+
+ align:start position:0%
+the links at 50% of my wage so that's
+ 
+
+ align:start position:0%
+the links at 50% of my wage so that's
+the trade-off okay now how do we think
+
+ align:start position:0%
+the trade-off okay now how do we think
+ 
+
+ align:start position:0%
+the trade-off okay now how do we think
+about evaluating that trade-off well if
+
+ align:start position:0%
+about evaluating that trade-off well if
+ 
+
+ align:start position:0%
+about evaluating that trade-off well if
+I don't that treadeth different
+
+ align:start position:0%
+I don't that treadeth different
+ 
+
+ align:start position:0%
+I don't that treadeth different
+countries think about it differently in
+
+ align:start position:0%
+countries think about it differently in
+ 
+
+ align:start position:0%
+countries think about it differently in
+the u.s. we think about it you know what
+
+ align:start position:0%
+the u.s. we think about it you know what
+ 
+
+ align:start position:0%
+the u.s. we think about it you know what
+I would say is a fairly rational way
+
+ align:start position:0%
+I would say is a fairly rational way
+ 
+
+ align:start position:0%
+I would say is a fairly rational way
+which is let's consider your decision to
+
+ align:start position:0%
+which is let's consider your decision to
+ 
+
+ align:start position:0%
+which is let's consider your decision to
+retire at 62 vs. 63 the way works notice
+
+ align:start position:0%
+retire at 62 vs. 63 the way works notice
+ 
+
+ align:start position:0%
+retire at 62 vs. 63 the way works notice
+we say look if Urich work one year more
+
+ align:start position:0%
+we say look if Urich work one year more
+ 
+
+ align:start position:0%
+we say look if Urich work one year more
+since it's an annuity you will get one
+
+ align:start position:0%
+since it's an annuity you will get one
+ 
+
+ align:start position:0%
+since it's an annuity you will get one
+less year of payment right if you start
+
+ align:start position:0%
+less year of payment right if you start
+ 
+
+ align:start position:0%
+less year of payment right if you start
+at one year later you're gonna die the
+
+ align:start position:0%
+at one year later you're gonna die the
+ 
+
+ align:start position:0%
+at one year later you're gonna die the
+same time you don't when you're less so
+
+ align:start position:0%
+same time you don't when you're less so
+ 
+
+ align:start position:0%
+same time you don't when you're less so
+we do is we pay you more every month
+
+ align:start position:0%
+we do is we pay you more every month
+ 
+
+ align:start position:0%
+we do is we pay you more every month
+indeed for every year you delay you get
+
+ align:start position:0%
+indeed for every year you delay you get
+ 
+
+ align:start position:0%
+indeed for every year you delay you get
+6.7% more every month reflecting the
+
+ align:start position:0%
+6.7% more every month reflecting the
+ 
+
+ align:start position:0%
+6.7% more every month reflecting the
+trade-off that you gonna get it for
+
+ align:start position:0%
+trade-off that you gonna get it for
+ 
+
+ align:start position:0%
+trade-off that you gonna get it for
+shorter period of time and that turns
+
+ align:start position:0%
+shorter period of time and that turns
+ 
+
+ align:start position:0%
+shorter period of time and that turns
+out to be roughly fair given the
+
+ align:start position:0%
+out to be roughly fair given the
+ 
+
+ align:start position:0%
+out to be roughly fair given the
+expected life of Americans that's a
+
+ align:start position:0%
+expected life of Americans that's a
+ 
+
+ align:start position:0%
+expected life of Americans that's a
+roughly fair trade-off okay every year
+
+ align:start position:0%
+roughly fair trade-off okay every year
+ 
+
+ align:start position:0%
+roughly fair trade-off okay every year
+delay gets 6.7% more in Europe they
+
+ align:start position:0%
+delay gets 6.7% more in Europe they
+ 
+
+ align:start position:0%
+delay gets 6.7% more in Europe they
+don't have this so every year you lay
+
+ align:start position:0%
+don't have this so every year you lay
+ 
+
+ align:start position:0%
+don't have this so every year you lay
+you just get less money before you die
+
+ align:start position:0%
+you just get less money before you die
+ 
+
+ align:start position:0%
+you just get less money before you die
+so let's take the example the
+
+ align:start position:0%
+so let's take the example the
+ 
+
+ align:start position:0%
+so let's take the example the
+Netherlands in the Netherlands
+
+ align:start position:0%
+Netherlands in the Netherlands
+ 
+
+ align:start position:0%
+Netherlands in the Netherlands
+you can retire 55 with a benefit that is
+
+ align:start position:0%
+you can retire 55 with a benefit that is
+ 
+
+ align:start position:0%
+you can retire 55 with a benefit that is
+90% of what you mate
+
+ align:start position:0%
+90% of what you mate
+ 
+
+ align:start position:0%
+90% of what you mate
+so if you were in $30,000 you can retire
+
+ align:start position:0%
+so if you were in $30,000 you can retire
+ 
+
+ align:start position:0%
+so if you were in $30,000 you can retire
+55 for the benefit of $27,000 and if you
+
+ align:start position:0%
+55 for the benefit of $27,000 and if you
+ 
+
+ align:start position:0%
+55 for the benefit of $27,000 and if you
+decide to work instead you just forego
+
+ align:start position:0%
+decide to work instead you just forego
+ 
+
+ align:start position:0%
+decide to work instead you just forego
+that $27,000 there's no bump up of your
+
+ align:start position:0%
+that $27,000 there's no bump up of your
+ 
+
+ align:start position:0%
+that $27,000 there's no bump up of your
+benefits that's just one last year of
+
+ align:start position:0%
+benefits that's just one last year of
+ 
+
+ align:start position:0%
+benefits that's just one last year of
+$27,000 you get so what that means if
+
+ align:start position:0%
+$27,000 you get so what that means if
+ 
+
+ align:start position:0%
+$27,000 you get so what that means if
+you're in the Netherlands your choices
+
+ align:start position:0%
+you're in the Netherlands your choices
+ 
+
+ align:start position:0%
+you're in the Netherlands your choices
+work and get 30 or stay at home and get
+
+ align:start position:0%
+work and get 30 or stay at home and get
+ 
+
+ align:start position:0%
+work and get 30 or stay at home and get
+27,000 in other words it's sort of like
+
+ align:start position:0%
+27,000 in other words it's sort of like
+ 
+
+ align:start position:0%
+27,000 in other words it's sort of like
+a 90% tax think about it by working well
+
+ align:start position:0%
+a 90% tax think about it by working well
+ 
+
+ align:start position:0%
+a 90% tax think about it by working well
+stay home I'm only keeping 3,000 or
+
+ align:start position:0%
+stay home I'm only keeping 3,000 or
+ 
+
+ align:start position:0%
+stay home I'm only keeping 3,000 or
+30,000 I made it's basically like a 90
+
+ align:start position:0%
+30,000 I made it's basically like a 90
+ 
+
+ align:start position:0%
+30,000 I made it's basically like a 90
+percent tax but that's not all how do
+
+ align:start position:0%
+percent tax but that's not all how do
+ 
+
+ align:start position:0%
+percent tax but that's not all how do
+they pay for this program well they tax
+
+ align:start position:0%
+they pay for this program well they tax
+ 
+
+ align:start position:0%
+they pay for this program well they tax
+people like Han tax people are home you
+
+ align:start position:0%
+people like Han tax people are home you
+ 
+
+ align:start position:0%
+people like Han tax people are home you
+got tax workers so if you work you also
+
+ align:start position:0%
+got tax workers so if you work you also
+ 
+
+ align:start position:0%
+got tax workers so if you work you also
+have to pay 45% tax to pay for this
+
+ align:start position:0%
+have to pay 45% tax to pay for this
+ 
+
+ align:start position:0%
+have to pay 45% tax to pay for this
+program and lots of other things 45% tax
+
+ align:start position:0%
+program and lots of other things 45% tax
+ 
+
+ align:start position:0%
+program and lots of other things 45% tax
+so you know it's a high tax rate for
+
+ align:start position:0%
+so you know it's a high tax rate for
+ 
+
+ align:start position:0%
+so you know it's a high tax rate for
+everything what that means is if you
+
+ align:start position:0%
+everything what that means is if you
+ 
+
+ align:start position:0%
+everything what that means is if you
+stay at home you get 27,000 if you go to
+
+ align:start position:0%
+stay at home you get 27,000 if you go to
+ 
+
+ align:start position:0%
+stay at home you get 27,000 if you go to
+work you get 30,000 times 1.55 or about
+
+ align:start position:0%
+work you get 30,000 times 1.55 or about
+ 
+
+ align:start position:0%
+work you get 30,000 times 1.55 or about
+our about 18,000 that's one by six one
+
+ align:start position:0%
+our about 18,000 that's one by six one
+ 
+
+ align:start position:0%
+our about 18,000 that's one by six one
+it's sixteen five so your choices stay
+
+ align:start position:0%
+it's sixteen five so your choices stay
+ 
+
+ align:start position:0%
+it's sixteen five so your choices stay
+at home and get 27 work and get sixteen
+
+ align:start position:0%
+at home and get 27 work and get sixteen
+ 
+
+ align:start position:0%
+at home and get 27 work and get sixteen
+five guess what no one works no one over
+
+ align:start position:0%
+five guess what no one works no one over
+ 
+
+ align:start position:0%
+five guess what no one works no one over
+55 Netherlands works like zero okay now
+
+ align:start position:0%
+55 Netherlands works like zero okay now
+ 
+
+ align:start position:0%
+55 Netherlands works like zero okay now
+they might work on the black market and
+
+ align:start position:0%
+they might work on the black market and
+ 
+
+ align:start position:0%
+they might work on the black market and
+wait their report to the government but
+
+ align:start position:0%
+wait their report to the government but
+ 
+
+ align:start position:0%
+wait their report to the government but
+basically they just sort of sit around
+
+ align:start position:0%
+basically they just sort of sit around
+ 
+
+ align:start position:0%
+basically they just sort of sit around
+coffee shops and spend their retirement
+
+ align:start position:0%
+coffee shops and spend their retirement
+ 
+
+ align:start position:0%
+coffee shops and spend their retirement
+money okay so here's a case where
+
+ align:start position:0%
+money okay so here's a case where
+ 
+
+ align:start position:0%
+money okay so here's a case where
+they've made a very different decision
+
+ align:start position:0%
+they've made a very different decision
+ 
+
+ align:start position:0%
+they've made a very different decision
+on how to make this trade-off which is
+
+ align:start position:0%
+on how to make this trade-off which is
+ 
+
+ align:start position:0%
+on how to make this trade-off which is
+you know it's a pretty sweet life for
+
+ align:start position:0%
+you know it's a pretty sweet life for
+ 
+
+ align:start position:0%
+you know it's a pretty sweet life for
+the elderly in the Netherlands okay but
+
+ align:start position:0%
+the elderly in the Netherlands okay but
+ 
+
+ align:start position:0%
+the elderly in the Netherlands okay but
+no one's working over age 55 and that's
+
+ align:start position:0%
+no one's working over age 55 and that's
+ 
+
+ align:start position:0%
+no one's working over age 55 and that's
+a different way to resolve this
+
+ align:start position:0%
+a different way to resolve this
+ 
+
+ align:start position:0%
+a different way to resolve this
+trade-off so basically this illustrates
+
+ align:start position:0%
+trade-off so basically this illustrates
+ 
+
+ align:start position:0%
+trade-off so basically this illustrates
+different design features of the program
+
+ align:start position:0%
+different design features of the program
+ 
+
+ align:start position:0%
+different design features of the program
+what makes the Netherlands program have
+
+ align:start position:0%
+what makes the Netherlands program have
+ 
+
+ align:start position:0%
+what makes the Netherlands program have
+much more moral hazard than the u.s. if
+
+ align:start position:0%
+much more moral hazard than the u.s. if
+ 
+
+ align:start position:0%
+much more moral hazard than the u.s. if
+their benefits are higher and they don't
+
+ align:start position:0%
+their benefits are higher and they don't
+ 
+
+ align:start position:0%
+their benefits are higher and they don't
+increase your benefits if you work more
+
+ align:start position:0%
+increase your benefits if you work more
+ 
+
+ align:start position:0%
+increase your benefits if you work more
+so essentially these are little kind of
+
+ align:start position:0%
+so essentially these are little kind of
+ 
+
+ align:start position:0%
+so essentially these are little kind of
+TWiki details that turn out to matter
+
+ align:start position:0%
+TWiki details that turn out to matter
+ 
+
+ align:start position:0%
+TWiki details that turn out to matter
+enormous lee probably think about the
+
+ align:start position:0%
+enormous lee probably think about the
+ 
+
+ align:start position:0%
+enormous lee probably think about the
+program okay now Oh
+
+ align:start position:0%
+program okay now Oh
+ 
+
+ align:start position:0%
+program okay now Oh
+that interesting that was a lot to put
+
+ align:start position:0%
+that interesting that was a lot to put
+ 
+
+ align:start position:0%
+that interesting that was a lot to put
+in one lecture like I said he finds
+
+ align:start position:0%
+in one lecture like I said he finds
+ 
+
+ align:start position:0%
+in one lecture like I said he finds
+interesting this is a whole third of
+
+ align:start position:0%
+interesting this is a whole third of
+ 
+
+ align:start position:0%
+interesting this is a whole third of
+some third of a semester my class 1441
+
+ align:start position:0%
+some third of a semester my class 1441
+ 
+
+ align:start position:0%
+some third of a semester my class 1441
+so take that we can learn a lot more
+
+ align:start position:0%
+so take that we can learn a lot more
+ 
+
+ align:start position:0%
+so take that we can learn a lot more
+about it
\ No newline at end of file
diff --git a/iBmoqczj7xs.txt b/iBmoqczj7xs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2f8bfc514ddc95268aee35b886a8e4214541190a
--- /dev/null
+++ b/iBmoqczj7xs.txt
@@ -0,0 +1,9986 @@
+align:start position:0%
+ 
+okay today we're going to do our second
+
+ align:start position:0%
+okay today we're going to do our second
+ 
+
+ align:start position:0%
+okay today we're going to do our second
+lecture on
+
+ align:start position:0%
+lecture on
+ 
+
+ align:start position:0%
+lecture on
+monopolies uh remember once again to set
+
+ align:start position:0%
+monopolies uh remember once again to set
+ 
+
+ align:start position:0%
+monopolies uh remember once again to set
+the picture if we want to figure out how
+
+ align:start position:0%
+the picture if we want to figure out how
+ 
+
+ align:start position:0%
+the picture if we want to figure out how
+much producers are going to produce we
+
+ align:start position:0%
+much producers are going to produce we
+ 
+
+ align:start position:0%
+much producers are going to produce we
+need to know what Market structure they
+
+ align:start position:0%
+need to know what Market structure they
+ 
+
+ align:start position:0%
+need to know what Market structure they
+sell into that's the sort of final
+
+ align:start position:0%
+sell into that's the sort of final
+ 
+
+ align:start position:0%
+sell into that's the sort of final
+condition we need to pin down how much
+
+ align:start position:0%
+condition we need to pin down how much
+ 
+
+ align:start position:0%
+condition we need to pin down how much
+producers produce we started with a
+
+ align:start position:0%
+producers produce we started with a
+ 
+
+ align:start position:0%
+producers produce we started with a
+particular Market structure which was
+
+ align:start position:0%
+particular Market structure which was
+ 
+
+ align:start position:0%
+particular Market structure which was
+perfect competition and showed how under
+
+ align:start position:0%
+perfect competition and showed how under
+ 
+
+ align:start position:0%
+perfect competition and showed how under
+perfect competition with price equals
+
+ align:start position:0%
+perfect competition with price equals
+ 
+
+ align:start position:0%
+perfect competition with price equals
+marginal cost we can pin down how much
+
+ align:start position:0%
+marginal cost we can pin down how much
+ 
+
+ align:start position:0%
+marginal cost we can pin down how much
+producers produce we then turned last
+
+ align:start position:0%
+producers produce we then turned last
+ 
+
+ align:start position:0%
+producers produce we then turned last
+lecture to an alternative Market
+
+ align:start position:0%
+lecture to an alternative Market
+ 
+
+ align:start position:0%
+lecture to an alternative Market
+structure really The Other Extreme which
+
+ align:start position:0%
+structure really The Other Extreme which
+ 
+
+ align:start position:0%
+structure really The Other Extreme which
+is Monopoly with only one firm in the
+
+ align:start position:0%
+is Monopoly with only one firm in the
+ 
+
+ align:start position:0%
+is Monopoly with only one firm in the
+market and we showed how that can pin
+
+ align:start position:0%
+market and we showed how that can pin
+ 
+
+ align:start position:0%
+market and we showed how that can pin
+down what producers produce but we also
+
+ align:start position:0%
+down what producers produce but we also
+ 
+
+ align:start position:0%
+down what producers produce but we also
+showed that monopo breaks the link
+
+ align:start position:0%
+showed that monopo breaks the link
+ 
+
+ align:start position:0%
+showed that monopo breaks the link
+between the positive equilibrium outcome
+
+ align:start position:0%
+between the positive equilibrium outcome
+ 
+
+ align:start position:0%
+between the positive equilibrium outcome
+and the normative concept of efficiency
+
+ align:start position:0%
+and the normative concept of efficiency
+ 
+
+ align:start position:0%
+and the normative concept of efficiency
+that we have an equilibrium outcome that
+
+ align:start position:0%
+that we have an equilibrium outcome that
+ 
+
+ align:start position:0%
+that we have an equilibrium outcome that
+unlike with perfect competition is
+
+ align:start position:0%
+unlike with perfect competition is
+ 
+
+ align:start position:0%
+unlike with perfect competition is
+inefficient we create a dead weight loss
+
+ align:start position:0%
+inefficient we create a dead weight loss
+ 
+
+ align:start position:0%
+inefficient we create a dead weight loss
+because monopolists don't sell units
+
+ align:start position:0%
+because monopolists don't sell units
+ 
+
+ align:start position:0%
+because monopolists don't sell units
+that they can produce more cheaply than
+
+ align:start position:0%
+that they can produce more cheaply than
+ 
+
+ align:start position:0%
+that they can produce more cheaply than
+people are willing to pay for them and
+
+ align:start position:0%
+people are willing to pay for them and
+ 
+
+ align:start position:0%
+people are willing to pay for them and
+they don't do that because they don't
+
+ align:start position:0%
+they don't do that because they don't
+ 
+
+ align:start position:0%
+they don't do that because they don't
+want to poison their sales they don't
+
+ align:start position:0%
+want to poison their sales they don't
+ 
+
+ align:start position:0%
+want to poison their sales they don't
+have to lower the price enough to get
+
+ align:start position:0%
+have to lower the price enough to get
+ 
+
+ align:start position:0%
+have to lower the price enough to get
+additional
+
+ align:start position:0%
+additional
+ 
+
+ align:start position:0%
+additional
+sales now what we're going to talk about
+
+ align:start position:0%
+sales now what we're going to talk about
+ 
+
+ align:start position:0%
+sales now what we're going to talk about
+today is a couple topics within Monopoly
+
+ align:start position:0%
+today is a couple topics within Monopoly
+ 
+
+ align:start position:0%
+today is a couple topics within Monopoly
+the first topic we'll talk about is
+
+ align:start position:0%
+the first topic we'll talk about is
+ 
+
+ align:start position:0%
+the first topic we'll talk about is
+where do monopolies come from from so
+
+ align:start position:0%
+where do monopolies come from from so
+ 
+
+ align:start position:0%
+where do monopolies come from from so
+how do monopolies arise or the origin of
+
+ align:start position:0%
+how do monopolies arise or the origin of
+ 
+
+ align:start position:0%
+how do monopolies arise or the origin of
+Monopoly If you're sort of a marble fan
+
+ align:start position:0%
+Monopoly If you're sort of a marble fan
+ 
+
+ align:start position:0%
+Monopoly If you're sort of a marble fan
+well this is our origin
+
+ align:start position:0%
+well this is our origin
+ 
+
+ align:start position:0%
+well this is our origin
+story okay no no radioactive spiders or
+
+ align:start position:0%
+story okay no no radioactive spiders or
+ 
+
+ align:start position:0%
+story okay no no radioactive spiders or
+anything okay but rather we're going to
+
+ align:start position:0%
+anything okay but rather we're going to
+ 
+
+ align:start position:0%
+anything okay but rather we're going to
+talk about markets where Monopoly is
+
+ align:start position:0%
+talk about markets where Monopoly is
+ 
+
+ align:start position:0%
+talk about markets where Monopoly is
+sort of inevitable and natural in
+
+ align:start position:0%
+sort of inevitable and natural in
+ 
+
+ align:start position:0%
+sort of inevitable and natural in
+particular we'll talk about today
+
+ align:start position:0%
+particular we'll talk about today
+ 
+
+ align:start position:0%
+particular we'll talk about today
+natural
+
+ align:start position:0%
+natural
+ 
+
+ align:start position:0%
+natural
+monopolies natural monopolies
+
+ align:start position:0%
+monopolies natural monopolies
+ 
+
+ align:start position:0%
+monopolies natural monopolies
+arise whenever there's a market
+
+ align:start position:0%
+arise whenever there's a market
+ 
+
+ align:start position:0%
+arise whenever there's a market
+where for all relevant
+
+ align:start position:0%
+where for all relevant
+ 
+
+ align:start position:0%
+where for all relevant
+quantities average cost is
+
+ align:start position:0%
+quantities average cost is
+ 
+
+ align:start position:0%
+quantities average cost is
+falling in other words fixed cost is so
+
+ align:start position:0%
+falling in other words fixed cost is so
+ 
+
+ align:start position:0%
+falling in other words fixed cost is so
+large relative to marginal cost you
+
+ align:start position:0%
+large relative to marginal cost you
+ 
+
+ align:start position:0%
+large relative to marginal cost you
+remember our typical average cost curve
+
+ align:start position:0%
+remember our typical average cost curve
+ 
+
+ align:start position:0%
+remember our typical average cost curve
+Falls and then
+
+ align:start position:0%
+Falls and then
+ 
+
+ align:start position:0%
+Falls and then
+Rises we're going to have an example
+
+ align:start position:0%
+Rises we're going to have an example
+ 
+
+ align:start position:0%
+Rises we're going to have an example
+where fixed costs are so large average
+
+ align:start position:0%
+where fixed costs are so large average
+ 
+
+ align:start position:0%
+where fixed costs are so large average
+cost is always falling so for example
+
+ align:start position:0%
+cost is always falling so for example
+ 
+
+ align:start position:0%
+cost is always falling so for example
+the classic example we' use is is like
+
+ align:start position:0%
+the classic example we' use is is like
+ 
+
+ align:start position:0%
+the classic example we' use is is like
+producing Rock from a rock quarry you've
+
+ align:start position:0%
+producing Rock from a rock quarry you've
+ 
+
+ align:start position:0%
+producing Rock from a rock quarry you've
+got to dig up Rock from this rock quarry
+
+ align:start position:0%
+got to dig up Rock from this rock quarry
+ 
+
+ align:start position:0%
+got to dig up Rock from this rock quarry
+it's one resource there's one sort of
+
+ align:start position:0%
+it's one resource there's one sort of
+ 
+
+ align:start position:0%
+it's one resource there's one sort of
+for historical reasons there's one
+
+ align:start position:0%
+for historical reasons there's one
+ 
+
+ align:start position:0%
+for historical reasons there's one
+geological site where we can dig up
+
+ align:start position:0%
+geological site where we can dig up
+ 
+
+ align:start position:0%
+geological site where we can dig up
+Rock okay it's a huge fixed cost finding
+
+ align:start position:0%
+Rock okay it's a huge fixed cost finding
+ 
+
+ align:start position:0%
+Rock okay it's a huge fixed cost finding
+it digging it
+
+ align:start position:0%
+it digging it
+ 
+
+ align:start position:0%
+it digging it
+out but the truth is creating a second
+
+ align:start position:0%
+out but the truth is creating a second
+ 
+
+ align:start position:0%
+out but the truth is creating a second
+Rock cor would be incredible fixed cost
+
+ align:start position:0%
+Rock cor would be incredible fixed cost
+ 
+
+ align:start position:0%
+Rock cor would be incredible fixed cost
+so the fixed cost of doing another one
+
+ align:start position:0%
+so the fixed cost of doing another one
+ 
+
+ align:start position:0%
+so the fixed cost of doing another one
+is small relative to the ongoing
+
+ align:start position:0%
+is small relative to the ongoing
+ 
+
+ align:start position:0%
+is small relative to the ongoing
+marginal cost or more generally this is
+
+ align:start position:0%
+marginal cost or more generally this is
+ 
+
+ align:start position:0%
+marginal cost or more generally this is
+something where basically uh you would
+
+ align:start position:0%
+something where basically uh you would
+ 
+
+ align:start position:0%
+something where basically uh you would
+see this in any sort of
+
+ align:start position:0%
+see this in any sort of
+ 
+
+ align:start position:0%
+see this in any sort of
+utility like delivering water to houses
+
+ align:start position:0%
+utility like delivering water to houses
+ 
+
+ align:start position:0%
+utility like delivering water to houses
+if you deliver water to houses you have
+
+ align:start position:0%
+if you deliver water to houses you have
+ 
+
+ align:start position:0%
+if you deliver water to houses you have
+this incredibly expensive Enterprise of
+
+ align:start position:0%
+this incredibly expensive Enterprise of
+ 
+
+ align:start position:0%
+this incredibly expensive Enterprise of
+laying all the pipes to deliver the
+
+ align:start position:0%
+laying all the pipes to deliver the
+ 
+
+ align:start position:0%
+laying all the pipes to deliver the
+water and then the marginal cost is
+
+ align:start position:0%
+water and then the marginal cost is
+ 
+
+ align:start position:0%
+water and then the marginal cost is
+pretty trivial you just pumped the water
+
+ align:start position:0%
+pretty trivial you just pumped the water
+ 
+
+ align:start position:0%
+pretty trivial you just pumped the water
+through so the fixed costs are so
+
+ align:start position:0%
+through so the fixed costs are so
+ 
+
+ align:start position:0%
+through so the fixed costs are so
+enormous that they're going to dwarf the
+
+ align:start position:0%
+enormous that they're going to dwarf the
+ 
+
+ align:start position:0%
+enormous that they're going to dwarf the
+marginal cost for any relevant
+
+ align:start position:0%
+marginal cost for any relevant
+ 
+
+ align:start position:0%
+marginal cost for any relevant
+quantity and we'll see what that looks
+
+ align:start position:0%
+quantity and we'll see what that looks
+ 
+
+ align:start position:0%
+quantity and we'll see what that looks
+like in figure
+
+ align:start position:0%
+like in figure
+ 
+
+ align:start position:0%
+like in figure
+121 figure 121 is a picture where the
+
+ align:start position:0%
+121 figure 121 is a picture where the
+ 
+
+ align:start position:0%
+121 figure 121 is a picture where the
+average costs are everywhere above the
+
+ align:start position:0%
+average costs are everywhere above the
+ 
+
+ align:start position:0%
+average costs are everywhere above the
+marginal
+
+ align:start position:0%
+marginal
+ 
+
+ align:start position:0%
+marginal
+cost for all relevant quantities now
+
+ align:start position:0%
+cost for all relevant quantities now
+ 
+
+ align:start position:0%
+cost for all relevant quantities now
+it's true could produce enough there's
+
+ align:start position:0%
+it's true could produce enough there's
+ 
+
+ align:start position:0%
+it's true could produce enough there's
+some quantity for which average cost
+
+ align:start position:0%
+some quantity for which average cost
+ 
+
+ align:start position:0%
+some quantity for which average cost
+will fall below marginal cost and start
+
+ align:start position:0%
+will fall below marginal cost and start
+ 
+
+ align:start position:0%
+will fall below marginal cost and start
+to rise again but basically idea is the
+
+ align:start position:0%
+to rise again but basically idea is the
+ 
+
+ align:start position:0%
+to rise again but basically idea is the
+range where average cost is falling
+
+ align:start position:0%
+range where average cost is falling
+ 
+
+ align:start position:0%
+range where average cost is falling
+extends to the entire relevant range not
+
+ align:start position:0%
+extends to the entire relevant range not
+ 
+
+ align:start position:0%
+extends to the entire relevant range not
+just the beginning as in previous
+
+ align:start position:0%
+just the beginning as in previous
+ 
+
+ align:start position:0%
+just the beginning as in previous
+examples why is this cause Monopoly it
+
+ align:start position:0%
+examples why is this cause Monopoly it
+ 
+
+ align:start position:0%
+examples why is this cause Monopoly it
+causes Monopoly because the it creates
+
+ align:start position:0%
+causes Monopoly because the it creates
+ 
+
+ align:start position:0%
+causes Monopoly because the it creates
+such a barrier to entry that no one else
+
+ align:start position:0%
+such a barrier to entry that no one else
+ 
+
+ align:start position:0%
+such a barrier to entry that no one else
+can enter imagine you tried imagine you
+
+ align:start position:0%
+can enter imagine you tried imagine you
+ 
+
+ align:start position:0%
+can enter imagine you tried imagine you
+saw this Market you saw this water
+
+ align:start position:0%
+saw this Market you saw this water
+ 
+
+ align:start position:0%
+saw this Market you saw this water
+utility okay and you said look there's
+
+ align:start position:0%
+utility okay and you said look there's
+ 
+
+ align:start position:0%
+utility okay and you said look there's
+profits be made average costs above
+
+ align:start position:0%
+profits be made average costs above
+ 
+
+ align:start position:0%
+profits be made average costs above
+marginal
+
+ align:start position:0%
+marginal
+ 
+
+ align:start position:0%
+marginal
+cost okay is is is declining above
+
+ align:start position:0%
+cost okay is is is declining above
+ 
+
+ align:start position:0%
+cost okay is is is declining above
+marginal cost there's profits to be made
+
+ align:start position:0%
+marginal cost there's profits to be made
+ 
+
+ align:start position:0%
+marginal cost there's profits to be made
+because average cost is falling I'm
+
+ align:start position:0%
+because average cost is falling I'm
+ 
+
+ align:start position:0%
+because average cost is falling I'm
+going to enter okay what would the
+
+ align:start position:0%
+going to enter okay what would the
+ 
+
+ align:start position:0%
+going to enter okay what would the
+existing firm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do what could the exist the ex existing
+
+ align:start position:0%
+do what could the exist the ex existing
+ 
+
+ align:start position:0%
+do what could the exist the ex existing
+firm that's already invested in the
+
+ align:start position:0%
+firm that's already invested in the
+ 
+
+ align:start position:0%
+firm that's already invested in the
+water pipes you say I'm going to lay a
+
+ align:start position:0%
+water pipes you say I'm going to lay a
+ 
+
+ align:start position:0%
+water pipes you say I'm going to lay a
+whole new set of water pipes and sell
+
+ align:start position:0%
+whole new set of water pipes and sell
+ 
+
+ align:start position:0%
+whole new set of water pipes and sell
+water more cheaply what would they
+
+ align:start position:0%
+water more cheaply what would they
+ 
+
+ align:start position:0%
+water more cheaply what would they
+do what would existing firm do
+
+ align:start position:0%
+do what would existing firm do
+ 
+
+ align:start position:0%
+do what would existing firm do
+well you're an existing firm you've laid
+
+ align:start position:0%
+well you're an existing firm you've laid
+ 
+
+ align:start position:0%
+well you're an existing firm you've laid
+these water pipes you have this graph in
+
+ align:start position:0%
+these water pipes you have this graph in
+ 
+
+ align:start position:0%
+these water pipes you have this graph in
+front of you you're setting your price
+
+ align:start position:0%
+front of you you're setting your price
+ 
+
+ align:start position:0%
+front of you you're setting your price
+at some level well above marginal cost
+
+ align:start position:0%
+at some level well above marginal cost
+ 
+
+ align:start position:0%
+at some level well above marginal cost
+what do you
+
+ align:start position:0%
+what do you
+ 
+
+ align:start position:0%
+what do you
+do yeah lower your price if you lower
+
+ align:start position:0%
+do yeah lower your price if you lower
+ 
+
+ align:start position:0%
+do yeah lower your price if you lower
+your price to marginal cost no firm no
+
+ align:start position:0%
+your price to marginal cost no firm no
+ 
+
+ align:start position:0%
+your price to marginal cost no firm no
+other firm can make money because then
+
+ align:start position:0%
+other firm can make money because then
+ 
+
+ align:start position:0%
+other firm can make money because then
+price is below average cost and you lose
+
+ align:start position:0%
+price is below average cost and you lose
+ 
+
+ align:start position:0%
+price is below average cost and you lose
+money but for you you've already paid
+
+ align:start position:0%
+money but for you you've already paid
+ 
+
+ align:start position:0%
+money but for you you've already paid
+the fixed costs so for you you're still
+
+ align:start position:0%
+the fixed costs so for you you're still
+ 
+
+ align:start position:0%
+the fixed costs so for you you're still
+making money in the marginal unit so
+
+ align:start position:0%
+making money in the marginal unit so
+ 
+
+ align:start position:0%
+making money in the marginal unit so
+yeah the existing fir just lowers its
+
+ align:start position:0%
+yeah the existing fir just lowers its
+ 
+
+ align:start position:0%
+yeah the existing fir just lowers its
+price towards marginal cost below
+
+ align:start position:0%
+price towards marginal cost below
+ 
+
+ align:start position:0%
+price towards marginal cost below
+average cost any other firm looks and
+
+ align:start position:0%
+average cost any other firm looks and
+ 
+
+ align:start position:0%
+average cost any other firm looks and
+says look I can't make back my average
+
+ align:start position:0%
+says look I can't make back my average
+ 
+
+ align:start position:0%
+says look I can't make back my average
+cost I'm not going to enter once you
+
+ align:start position:0%
+cost I'm not going to enter once you
+ 
+
+ align:start position:0%
+cost I'm not going to enter once you
+scare them off you raise your price back
+
+ align:start position:0%
+scare them off you raise your price back
+ 
+
+ align:start position:0%
+scare them off you raise your price back
+up so in a market like this it is
+
+ align:start position:0%
+up so in a market like this it is
+ 
+
+ align:start position:0%
+up so in a market like this it is
+natural it's indeed proper to only have
+
+ align:start position:0%
+natural it's indeed proper to only have
+ 
+
+ align:start position:0%
+natural it's indeed proper to only have
+one firm it makes no sense to have a
+
+ align:start position:0%
+one firm it makes no sense to have a
+ 
+
+ align:start position:0%
+one firm it makes no sense to have a
+second set of pipes going all the way
+
+ align:start position:0%
+second set of pipes going all the way
+ 
+
+ align:start position:0%
+second set of pipes going all the way
+through the town delivering water to
+
+ align:start position:0%
+through the town delivering water to
+ 
+
+ align:start position:0%
+through the town delivering water to
+houses it just makes no sense so in this
+
+ align:start position:0%
+houses it just makes no sense so in this
+ 
+
+ align:start position:0%
+houses it just makes no sense so in this
+case a monopoly is
+
+ align:start position:0%
+case a monopoly is
+ 
+
+ align:start position:0%
+case a monopoly is
+natural and this is basically an example
+
+ align:start position:0%
+natural and this is basically an example
+ 
+
+ align:start position:0%
+natural and this is basically an example
+where a fixed cost
+
+ align:start position:0%
+where a fixed cost
+ 
+
+ align:start position:0%
+where a fixed cost
+creates a barrier to entry the fixed
+
+ align:start position:0%
+creates a barrier to entry the fixed
+ 
+
+ align:start position:0%
+creates a barrier to entry the fixed
+cost is so large that you never enter
+
+ align:start position:0%
+cost is so large that you never enter
+ 
+
+ align:start position:0%
+cost is so large that you never enter
+remember I talked about how we never
+
+ align:start position:0%
+remember I talked about how we never
+ 
+
+ align:start position:0%
+remember I talked about how we never
+have perpect competition because there's
+
+ align:start position:0%
+have perpect competition because there's
+ 
+
+ align:start position:0%
+have perpect competition because there's
+always some slight barried entry someone
+
+ align:start position:0%
+always some slight barried entry someone
+ 
+
+ align:start position:0%
+always some slight barried entry someone
+can beat you up if you try to L sell
+
+ align:start position:0%
+can beat you up if you try to L sell
+ 
+
+ align:start position:0%
+can beat you up if you try to L sell
+additional you know uh little eiel ta
+
+ align:start position:0%
+additional you know uh little eiel ta
+ 
+
+ align:start position:0%
+additional you know uh little eiel ta
+Tower figures or whatever there's always
+
+ align:start position:0%
+Tower figures or whatever there's always
+ 
+
+ align:start position:0%
+Tower figures or whatever there's always
+some fixed always in bar entry here the
+
+ align:start position:0%
+some fixed always in bar entry here the
+ 
+
+ align:start position:0%
+some fixed always in bar entry here the
+bar entry is so large because the nor as
+
+ align:start position:0%
+bar entry is so large because the nor as
+ 
+
+ align:start position:0%
+bar entry is so large because the nor as
+fixed cost basically no one's ever once
+
+ align:start position:0%
+fixed cost basically no one's ever once
+ 
+
+ align:start position:0%
+fixed cost basically no one's ever once
+someone's in no one else is ever going
+
+ align:start position:0%
+someone's in no one else is ever going
+ 
+
+ align:start position:0%
+someone's in no one else is ever going
+to enter and therefore it's a natural
+
+ align:start position:0%
+to enter and therefore it's a natural
+ 
+
+ align:start position:0%
+to enter and therefore it's a natural
+monopoly
+
+ align:start position:0%
+monopoly
+ 
+
+ align:start position:0%
+monopoly
+yeah well with there's nobody delivering
+
+ align:start position:0%
+yeah well with there's nobody delivering
+ 
+
+ align:start position:0%
+yeah well with there's nobody delivering
+water there's money to be made because
+
+ align:start position:0%
+water there's money to be made because
+ 
+
+ align:start position:0%
+water there's money to be made because
+the first room is Monopoly we know
+
+ align:start position:0%
+the first room is Monopoly we know
+ 
+
+ align:start position:0%
+the first room is Monopoly we know
+monopolies make profits so if there's no
+
+ align:start position:0%
+monopolies make profits so if there's no
+ 
+
+ align:start position:0%
+monopolies make profits so if there's no
+one they can come in and lay the pipes
+
+ align:start position:0%
+one they can come in and lay the pipes
+ 
+
+ align:start position:0%
+one they can come in and lay the pipes
+and make and make money now you might
+
+ align:start position:0%
+and make and make money now you might
+ 
+
+ align:start position:0%
+and make and make money now you might
+say how do they know someone else won't
+
+ align:start position:0%
+say how do they know someone else won't
+ 
+
+ align:start position:0%
+say how do they know someone else won't
+come in lay and faster that's an
+
+ align:start position:0%
+come in lay and faster that's an
+ 
+
+ align:start position:0%
+come in lay and faster that's an
+interesting that's exactly the kind of
+
+ align:start position:0%
+interesting that's exactly the kind of
+ 
+
+ align:start position:0%
+interesting that's exactly the kind of
+fun stuff we don't have time to get into
+
+ align:start position:0%
+fun stuff we don't have time to get into
+ 
+
+ align:start position:0%
+fun stuff we don't have time to get into
+in this class but if you take Game
+
+ align:start position:0%
+in this class but if you take Game
+ 
+
+ align:start position:0%
+in this class but if you take Game
+Theory
+
+ align:start position:0%
+Theory
+ 
+
+ align:start position:0%
+Theory
+1412 uh they'll teach you all about how
+
+ align:start position:0%
+1412 uh they'll teach you all about how
+ 
+
+ align:start position:0%
+1412 uh they'll teach you all about how
+we think about these different things
+
+ align:start position:0%
+we think about these different things
+ 
+
+ align:start position:0%
+we think about these different things
+and I'll get into that I'm going to do a
+
+ align:start position:0%
+and I'll get into that I'm going to do a
+ 
+
+ align:start position:0%
+and I'll get into that I'm going to do a
+couple exra in Game Theory but not
+
+ align:start position:0%
+couple exra in Game Theory but not
+ 
+
+ align:start position:0%
+couple exra in Game Theory but not
+nearly enough but think of it as one
+
+ align:start position:0%
+nearly enough but think of it as one
+ 
+
+ align:start position:0%
+nearly enough but think of it as one
+firm just sort of happen to go first and
+
+ align:start position:0%
+firm just sort of happen to go first and
+ 
+
+ align:start position:0%
+firm just sort of happen to go first and
+they own it
+
+ align:start position:0%
+they own it
+ 
+
+ align:start position:0%
+they own it
+okay other
+
+ align:start position:0%
+okay other
+ 
+
+ align:start position:0%
+okay other
+questions so that's one reason One Way
+
+ align:start position:0%
+questions so that's one reason One Way
+ 
+
+ align:start position:0%
+questions so that's one reason One Way
+monopolies can arise another way
+
+ align:start position:0%
+monopolies can arise another way
+ 
+
+ align:start position:0%
+monopolies can arise another way
+monopolies can arise so one way is a
+
+ align:start position:0%
+monopolies can arise so one way is a
+ 
+
+ align:start position:0%
+monopolies can arise so one way is a
+natural monopoly another way monopolies
+
+ align:start position:0%
+natural monopoly another way monopolies
+ 
+
+ align:start position:0%
+natural monopoly another way monopolies
+can arise is the government can create
+
+ align:start position:0%
+can arise is the government can create
+ 
+
+ align:start position:0%
+can arise is the government can create
+monopolies the government can actually
+
+ align:start position:0%
+monopolies the government can actually
+ 
+
+ align:start position:0%
+monopolies the government can actually
+create monopolies one is by actually
+
+ align:start position:0%
+create monopolies one is by actually
+ 
+
+ align:start position:0%
+create monopolies one is by actually
+literally delivering the service so in
+
+ align:start position:0%
+literally delivering the service so in
+ 
+
+ align:start position:0%
+literally delivering the service so in
+most countries when they're young
+
+ align:start position:0%
+most countries when they're young
+ 
+
+ align:start position:0%
+most countries when they're young
+governments do a lot of things we think
+
+ align:start position:0%
+governments do a lot of things we think
+ 
+
+ align:start position:0%
+governments do a lot of things we think
+is private now like they run the
+
+ align:start position:0%
+is private now like they run the
+ 
+
+ align:start position:0%
+is private now like they run the
+airlines they run the steel industry
+
+ align:start position:0%
+airlines they run the steel industry
+ 
+
+ align:start position:0%
+airlines they run the steel industry
+they run the banks and even in mature
+
+ align:start position:0%
+they run the banks and even in mature
+ 
+
+ align:start position:0%
+they run the banks and even in mature
+economies governments still do some
+
+ align:start position:0%
+economies governments still do some
+ 
+
+ align:start position:0%
+economies governments still do some
+services like run the Postal
+
+ align:start position:0%
+services like run the Postal
+ 
+
+ align:start position:0%
+services like run the Postal
+Service there's activities that
+
+ align:start position:0%
+Service there's activities that
+ 
+
+ align:start position:0%
+Service there's activities that
+governments can just do and say we're
+
+ align:start position:0%
+governments can just do and say we're
+ 
+
+ align:start position:0%
+governments can just do and say we're
+goingon to have the Monopoly on them and
+
+ align:start position:0%
+goingon to have the Monopoly on them and
+ 
+
+ align:start position:0%
+goingon to have the Monopoly on them and
+we are going to deliver these Services
+
+ align:start position:0%
+we are going to deliver these Services
+ 
+
+ align:start position:0%
+we are going to deliver these Services
+now as as economies mature typically
+
+ align:start position:0%
+now as as economies mature typically
+ 
+
+ align:start position:0%
+now as as economies mature typically
+those get shifted off to the private
+
+ align:start position:0%
+those get shifted off to the private
+ 
+
+ align:start position:0%
+those get shifted off to the private
+sector okay and we'll we'll come back a
+
+ align:start position:0%
+sector okay and we'll we'll come back a
+ 
+
+ align:start position:0%
+sector okay and we'll we'll come back a
+little bit to that but basically uh that
+
+ align:start position:0%
+little bit to that but basically uh that
+ 
+
+ align:start position:0%
+little bit to that but basically uh that
+is sort of one way the more common way
+
+ align:start position:0%
+is sort of one way the more common way
+ 
+
+ align:start position:0%
+is sort of one way the more common way
+that so one way of government Crea
+
+ align:start position:0%
+that so one way of government Crea
+ 
+
+ align:start position:0%
+that so one way of government Crea
+Monopoly is through
+
+ align:start position:0%
+Monopoly is through
+ 
+
+ align:start position:0%
+Monopoly is through
+delivery but the more common way of
+
+ align:start position:0%
+delivery but the more common way of
+ 
+
+ align:start position:0%
+delivery but the more common way of
+government cre Monopoly is through
+
+ align:start position:0%
+government cre Monopoly is through
+ 
+
+ align:start position:0%
+government cre Monopoly is through
+property rights in particular patents
+
+ align:start position:0%
+property rights in particular patents
+ 
+
+ align:start position:0%
+property rights in particular patents
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+copyrights we talked about copyright
+
+ align:start position:0%
+copyrights we talked about copyright
+ 
+
+ align:start position:0%
+copyrights we talked about copyright
+last time with huckin and Fahrenheit
+
+ align:start position:0%
+last time with huckin and Fahrenheit
+ 
+
+ align:start position:0%
+last time with huckin and Fahrenheit
+451 but a patent is basically an
+
+ align:start position:0%
+451 but a patent is basically an
+ 
+
+ align:start position:0%
+451 but a patent is basically an
+exclusive right to sell a good for some
+
+ align:start position:0%
+exclusive right to sell a good for some
+ 
+
+ align:start position:0%
+exclusive right to sell a good for some
+period of time in the US 17 years
+
+ align:start position:0%
+period of time in the US 17 years
+ 
+
+ align:start position:0%
+period of time in the US 17 years
+typically so the way patent work you
+
+ align:start position:0%
+typically so the way patent work you
+ 
+
+ align:start position:0%
+typically so the way patent work you
+file for a patent if it's granted then
+
+ align:start position:0%
+file for a patent if it's granted then
+ 
+
+ align:start position:0%
+file for a patent if it's granted then
+you are essentially a time limit of
+
+ align:start position:0%
+you are essentially a time limit of
+ 
+
+ align:start position:0%
+you are essentially a time limit of
+Monopoly you have the exclusive right to
+
+ align:start position:0%
+Monopoly you have the exclusive right to
+ 
+
+ align:start position:0%
+Monopoly you have the exclusive right to
+sell that
+
+ align:start position:0%
+sell that
+ 
+
+ align:start position:0%
+sell that
+good so what how do we feel about
+
+ align:start position:0%
+good so what how do we feel about
+ 
+
+ align:start position:0%
+good so what how do we feel about
+patents well in fact there's a good and
+
+ align:start position:0%
+patents well in fact there's a good and
+ 
+
+ align:start position:0%
+patents well in fact there's a good and
+a bad side what's the bad side of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+patents what's the bad side of offering
+
+ align:start position:0%
+patents what's the bad side of offering
+ 
+
+ align:start position:0%
+patents what's the bad side of offering
+patents yeah it's a monopoly you create
+
+ align:start position:0%
+patents yeah it's a monopoly you create
+ 
+
+ align:start position:0%
+patents yeah it's a monopoly you create
+deadweight loss it's inefficient what's
+
+ align:start position:0%
+deadweight loss it's inefficient what's
+ 
+
+ align:start position:0%
+deadweight loss it's inefficient what's
+the good side offering
+
+ align:start position:0%
+the good side offering
+ 
+
+ align:start position:0%
+the good side offering
+patents
+
+ align:start position:0%
+patents
+ 
+
+ align:start position:0%
+patents
+yeah yeah you basically why invent
+
+ align:start position:0%
+yeah yeah you basically why invent
+ 
+
+ align:start position:0%
+yeah yeah you basically why invent
+something if you can't make any money
+
+ align:start position:0%
+something if you can't make any money
+ 
+
+ align:start position:0%
+something if you can't make any money
+off it they create incentives to
+
+ align:start position:0%
+off it they create incentives to
+ 
+
+ align:start position:0%
+off it they create incentives to
+innovate and invent because there's no
+
+ align:start position:0%
+innovate and invent because there's no
+ 
+
+ align:start position:0%
+innovate and invent because there's no
+patents the me you invented something
+
+ align:start position:0%
+patents the me you invented something
+ 
+
+ align:start position:0%
+patents the me you invented something
+someone to just steal it and produce it
+
+ align:start position:0%
+someone to just steal it and produce it
+ 
+
+ align:start position:0%
+someone to just steal it and produce it
+at marginal cost or marginal cost plus
+
+ align:start position:0%
+at marginal cost or marginal cost plus
+ 
+
+ align:start position:0%
+at marginal cost or marginal cost plus
+Epson you wouldn't make any money so why
+
+ align:start position:0%
+Epson you wouldn't make any money so why
+ 
+
+ align:start position:0%
+Epson you wouldn't make any money so why
+put the work in so it's a tradeoff with
+
+ align:start position:0%
+put the work in so it's a tradeoff with
+ 
+
+ align:start position:0%
+put the work in so it's a tradeoff with
+patents between incentives for
+
+ align:start position:0%
+patents between incentives for
+ 
+
+ align:start position:0%
+patents between incentives for
+investment for
+
+ align:start position:0%
+investment for
+ 
+
+ align:start position:0%
+investment for
+Innovation and Monopoly costs to uh
+
+ align:start position:0%
+Innovation and Monopoly costs to uh
+ 
+
+ align:start position:0%
+Innovation and Monopoly costs to uh
+to Consumers so basically the optimal
+
+ align:start position:0%
+to Consumers so basically the optimal
+ 
+
+ align:start position:0%
+to Consumers so basically the optimal
+patent trades off these concerns you
+
+ align:start position:0%
+patent trades off these concerns you
+ 
+
+ align:start position:0%
+patent trades off these concerns you
+want a patent that gives enough rights
+
+ align:start position:0%
+want a patent that gives enough rights
+ 
+
+ align:start position:0%
+want a patent that gives enough rights
+to incent
+
+ align:start position:0%
+to incent
+ 
+
+ align:start position:0%
+to incent
+Innovation and not so much rights that
+
+ align:start position:0%
+Innovation and not so much rights that
+ 
+
+ align:start position:0%
+Innovation and not so much rights that
+you overly hurt
+
+ align:start position:0%
+you overly hurt
+ 
+
+ align:start position:0%
+you overly hurt
+consumers so for example let's take
+
+ align:start position:0%
+consumers so for example let's take
+ 
+
+ align:start position:0%
+consumers so for example let's take
+Pharmaceuticals developing a new drug is
+
+ align:start position:0%
+Pharmaceuticals developing a new drug is
+ 
+
+ align:start position:0%
+Pharmaceuticals developing a new drug is
+incredibly
+
+ align:start position:0%
+incredibly
+ 
+
+ align:start position:0%
+incredibly
+expensive roughly speaking um about one
+
+ align:start position:0%
+expensive roughly speaking um about one
+ 
+
+ align:start position:0%
+expensive roughly speaking um about one
+in every
+
+ align:start position:0%
+in every
+ 
+
+ align:start position:0%
+in every
+10,000 compounds you try is going to end
+
+ align:start position:0%
+10,000 compounds you try is going to end
+ 
+
+ align:start position:0%
+10,000 compounds you try is going to end
+up working in terms of being effective
+
+ align:start position:0%
+up working in terms of being effective
+ 
+
+ align:start position:0%
+up working in terms of being effective
+drug once you have a compound that you
+
+ align:start position:0%
+drug once you have a compound that you
+ 
+
+ align:start position:0%
+drug once you have a compound that you
+think works you do animal testing in
+
+ align:start position:0%
+think works you do animal testing in
+ 
+
+ align:start position:0%
+think works you do animal testing in
+Phase then you have to do three levels
+
+ align:start position:0%
+Phase then you have to do three levels
+ 
+
+ align:start position:0%
+Phase then you have to do three levels
+of human
+
+ align:start position:0%
+of human
+ 
+
+ align:start position:0%
+of human
+testing the best estimates although
+
+ align:start position:0%
+testing the best estimates although
+ 
+
+ align:start position:0%
+testing the best estimates although
+they're rough is that developing a New
+
+ align:start position:0%
+they're rough is that developing a New
+ 
+
+ align:start position:0%
+they're rough is that developing a New
+Drug in the US today costs about2
+
+ align:start position:0%
+Drug in the US today costs about2
+ 
+
+ align:start position:0%
+Drug in the US today costs about2
+billion
+
+ align:start position:0%
+billion
+ 
+
+ align:start position:0%
+billion
+doar about2 billion not not not if you
+
+ align:start position:0%
+doar about2 billion not not not if you
+ 
+
+ align:start position:0%
+doar about2 billion not not not if you
+knew ahead it was going to work but if
+
+ align:start position:0%
+knew ahead it was going to work but if
+ 
+
+ align:start position:0%
+knew ahead it was going to work but if
+you take all the failures along the way
+
+ align:start position:0%
+you take all the failures along the way
+ 
+
+ align:start position:0%
+you take all the failures along the way
+on average by the time you develop the
+
+ align:start position:0%
+on average by the time you develop the
+ 
+
+ align:start position:0%
+on average by the time you develop the
+drug you spent $2 billion that's a lot
+
+ align:start position:0%
+drug you spent $2 billion that's a lot
+ 
+
+ align:start position:0%
+drug you spent $2 billion that's a lot
+of money okay so basically um what we do
+
+ align:start position:0%
+of money okay so basically um what we do
+ 
+
+ align:start position:0%
+of money okay so basically um what we do
+is we give a patent for 17 years and
+
+ align:start position:0%
+is we give a patent for 17 years and
+ 
+
+ align:start position:0%
+is we give a patent for 17 years and
+then when the patent expires other
+
+ align:start position:0%
+then when the patent expires other
+ 
+
+ align:start position:0%
+then when the patent expires other
+companies allowed to enter brce what's
+
+ align:start position:0%
+companies allowed to enter brce what's
+ 
+
+ align:start position:0%
+companies allowed to enter brce what's
+called generic drugs so you have a name
+
+ align:start position:0%
+called generic drugs so you have a name
+ 
+
+ align:start position:0%
+called generic drugs so you have a name
+brand drug you invent it you get 17
+
+ align:start position:0%
+brand drug you invent it you get 17
+ 
+
+ align:start position:0%
+brand drug you invent it you get 17
+years and then after those 17 years
+
+ align:start position:0%
+years and then after those 17 years
+ 
+
+ align:start position:0%
+years and then after those 17 years
+anybody can enter it the formulation
+
+ align:start position:0%
+anybody can enter it the formulation
+ 
+
+ align:start position:0%
+anybody can enter it the formulation
+becomes public and they just produce it
+
+ align:start position:0%
+becomes public and they just produce it
+ 
+
+ align:start position:0%
+becomes public and they just produce it
+at marginal cost and your profits all go
+
+ align:start position:0%
+at marginal cost and your profits all go
+ 
+
+ align:start position:0%
+at marginal cost and your profits all go
+away in theory that's how it works and
+
+ align:start position:0%
+away in theory that's how it works and
+ 
+
+ align:start position:0%
+away in theory that's how it works and
+in theory we'd have an easy solution we
+
+ align:start position:0%
+in theory we'd have an easy solution we
+ 
+
+ align:start position:0%
+in theory we'd have an easy solution we
+just say well well set up an
+
+ align:start position:0%
+just say well well set up an
+ 
+
+ align:start position:0%
+just say well well set up an
+optimization problem where you optimize
+
+ align:start position:0%
+optimization problem where you optimize
+ 
+
+ align:start position:0%
+optimization problem where you optimize
+the incentives to innovate versus the
+
+ align:start position:0%
+the incentives to innovate versus the
+ 
+
+ align:start position:0%
+the incentives to innovate versus the
+losses to Consumers clearly the optim
+
+ align:start position:0%
+losses to Consumers clearly the optim
+ 
+
+ align:start position:0%
+losses to Consumers clearly the optim
+will not be a patent last
+
+ align:start position:0%
+will not be a patent last
+ 
+
+ align:start position:0%
+will not be a patent last
+forever and clearly optim will not be no
+
+ align:start position:0%
+forever and clearly optim will not be no
+ 
+
+ align:start position:0%
+forever and clearly optim will not be no
+patent it'll be somewhere in between who
+
+ align:start position:0%
+patent it'll be somewhere in between who
+ 
+
+ align:start position:0%
+patent it'll be somewhere in between who
+knows the 17 years right but you could
+
+ align:start position:0%
+knows the 17 years right but you could
+ 
+
+ align:start position:0%
+knows the 17 years right but you could
+you could the economics gives the tools
+
+ align:start position:0%
+you could the economics gives the tools
+ 
+
+ align:start position:0%
+you could the economics gives the tools
+to think about this trade-off now right
+
+ align:start position:0%
+to think about this trade-off now right
+ 
+
+ align:start position:0%
+to think about this trade-off now right
+the problem is in practice it doesn't
+
+ align:start position:0%
+the problem is in practice it doesn't
+ 
+
+ align:start position:0%
+the problem is in practice it doesn't
+work that well there's a lot of problems
+
+ align:start position:0%
+work that well there's a lot of problems
+ 
+
+ align:start position:0%
+work that well there's a lot of problems
+with the patent system the first is that
+
+ align:start position:0%
+with the patent system the first is that
+ 
+
+ align:start position:0%
+with the patent system the first is that
+companies have a lot of incentive to
+
+ align:start position:0%
+companies have a lot of incentive to
+ 
+
+ align:start position:0%
+companies have a lot of incentive to
+think up creative ways to effectively
+
+ align:start position:0%
+think up creative ways to effectively
+ 
+
+ align:start position:0%
+think up creative ways to effectively
+extend their
+
+ align:start position:0%
+extend their
+ 
+
+ align:start position:0%
+extend their
+patent okay so for example one thing
+
+ align:start position:0%
+patent okay so for example one thing
+ 
+
+ align:start position:0%
+patent okay so for example one thing
+drug companies will do is do something
+
+ align:start position:0%
+drug companies will do is do something
+ 
+
+ align:start position:0%
+drug companies will do is do something
+called pay for delay let's say I've got
+
+ align:start position:0%
+called pay for delay let's say I've got
+ 
+
+ align:start position:0%
+called pay for delay let's say I've got
+some name Brad brand drug and Pedro is a
+
+ align:start position:0%
+some name Brad brand drug and Pedro is a
+ 
+
+ align:start position:0%
+some name Brad brand drug and Pedro is a
+potential generic uh innovator he wants
+
+ align:start position:0%
+potential generic uh innovator he wants
+ 
+
+ align:start position:0%
+potential generic uh innovator he wants
+to enter and make my drug and I say
+
+ align:start position:0%
+to enter and make my drug and I say
+ 
+
+ align:start position:0%
+to enter and make my drug and I say
+Pedro look I'm making like a billion
+
+ align:start position:0%
+Pedro look I'm making like a billion
+ 
+
+ align:start position:0%
+Pedro look I'm making like a billion
+year on this drug you're a a generate
+
+ align:start position:0%
+year on this drug you're a a generate
+ 
+
+ align:start position:0%
+year on this drug you're a a generate
+guy you're not going to make much money
+
+ align:start position:0%
+guy you're not going to make much money
+ 
+
+ align:start position:0%
+guy you're not going to make much money
+because you're coming in competitive
+
+ align:start position:0%
+because you're coming in competitive
+ 
+
+ align:start position:0%
+because you're coming in competitive
+market I'll pay you $500 million not to
+
+ align:start position:0%
+market I'll pay you $500 million not to
+ 
+
+ align:start position:0%
+market I'll pay you $500 million not to
+come in
+
+ align:start position:0%
+come in
+ 
+
+ align:start position:0%
+come in
+Pat's like great I didn't do I got
+
+ align:start position:0%
+Pat's like great I didn't do I got
+ 
+
+ align:start position:0%
+Pat's like great I didn't do I got
+$500 million I'm still making $500
+
+ align:start position:0%
+$500 million I'm still making $500
+ 
+
+ align:start position:0%
+$500 million I'm still making $500
+million in
+
+ align:start position:0%
+million in
+ 
+
+ align:start position:0%
+million in
+profits so I can effectively extend my
+
+ align:start position:0%
+profits so I can effectively extend my
+ 
+
+ align:start position:0%
+profits so I can effectively extend my
+patent or what I can do is I can tweak
+
+ align:start position:0%
+patent or what I can do is I can tweak
+ 
+
+ align:start position:0%
+patent or what I can do is I can tweak
+the formulation and apply for a new
+
+ align:start position:0%
+the formulation and apply for a new
+ 
+
+ align:start position:0%
+the formulation and apply for a new
+patent so for example insulin is
+
+ align:start position:0%
+patent so for example insulin is
+ 
+
+ align:start position:0%
+patent so for example insulin is
+incredibly cheap to
+
+ align:start position:0%
+incredibly cheap to
+ 
+
+ align:start position:0%
+incredibly cheap to
+make okay and it was invented the
+
+ align:start position:0%
+make okay and it was invented the
+ 
+
+ align:start position:0%
+make okay and it was invented the
+inventors were academics who gave away
+
+ align:start position:0%
+inventors were academics who gave away
+ 
+
+ align:start position:0%
+inventors were academics who gave away
+the patent for a dollar because they
+
+ align:start position:0%
+the patent for a dollar because they
+ 
+
+ align:start position:0%
+the patent for a dollar because they
+wanted to be publicly available but it
+
+ align:start position:0%
+wanted to be publicly available but it
+ 
+
+ align:start position:0%
+wanted to be publicly available but it
+cost a ton of money why because there's
+
+ align:start position:0%
+cost a ton of money why because there's
+ 
+
+ align:start position:0%
+cost a ton of money why because there's
+always Innovations and delivering in
+
+ align:start position:0%
+always Innovations and delivering in
+ 
+
+ align:start position:0%
+always Innovations and delivering in
+that make it a little more efficient a
+
+ align:start position:0%
+that make it a little more efficient a
+ 
+
+ align:start position:0%
+that make it a little more efficient a
+little better now they are true
+
+ align:start position:0%
+little better now they are true
+ 
+
+ align:start position:0%
+little better now they are true
+Innovations but each one extends the
+
+ align:start position:0%
+Innovations but each one extends the
+ 
+
+ align:start position:0%
+Innovations but each one extends the
+patent and makes insulin more expensive
+
+ align:start position:0%
+patent and makes insulin more expensive
+ 
+
+ align:start position:0%
+patent and makes insulin more expensive
+and that trade-off is not really what
+
+ align:start position:0%
+and that trade-off is not really what
+ 
+
+ align:start position:0%
+and that trade-off is not really what
+was what we're that's sort of a
+
+ align:start position:0%
+was what we're that's sort of a
+ 
+
+ align:start position:0%
+was what we're that's sort of a
+different way in the system is supposed
+
+ align:start position:0%
+different way in the system is supposed
+ 
+
+ align:start position:0%
+different way in the system is supposed
+to work so that's one reason this
+
+ align:start position:0%
+to work so that's one reason this
+ 
+
+ align:start position:0%
+to work so that's one reason this
+doesn't work the other reason is that
+
+ align:start position:0%
+doesn't work the other reason is that
+ 
+
+ align:start position:0%
+doesn't work the other reason is that
+generic markets aren't as competitive as
+
+ align:start position:0%
+generic markets aren't as competitive as
+ 
+
+ align:start position:0%
+generic markets aren't as competitive as
+we'd like to think so
+
+ align:start position:0%
+we'd like to think so
+ 
+
+ align:start position:0%
+we'd like to think so
+epipens which are now epinephrine is a
+
+ align:start position:0%
+epipens which are now epinephrine is a
+ 
+
+ align:start position:0%
+epipens which are now epinephrine is a
+generic drug still cost $600
+
+ align:start position:0%
+generic drug still cost $600
+ 
+
+ align:start position:0%
+generic drug still cost $600
+why epens cost $600 because it turns out
+
+ align:start position:0%
+why epens cost $600 because it turns out
+ 
+
+ align:start position:0%
+why epens cost $600 because it turns out
+it's expensive to make an EpiPen the
+
+ align:start position:0%
+it's expensive to make an EpiPen the
+ 
+
+ align:start position:0%
+it's expensive to make an EpiPen the
+delivery device and stuff is expensive
+
+ align:start position:0%
+delivery device and stuff is expensive
+ 
+
+ align:start position:0%
+delivery device and stuff is expensive
+and firms aren't
+
+ align:start position:0%
+and firms aren't
+ 
+
+ align:start position:0%
+and firms aren't
+entering and as we'll talk about
+
+ align:start position:0%
+entering and as we'll talk about
+ 
+
+ align:start position:0%
+entering and as we'll talk about
+starting next lecture unless you have
+
+ align:start position:0%
+starting next lecture unless you have
+ 
+
+ align:start position:0%
+starting next lecture unless you have
+perfect competition there'll be profits
+
+ align:start position:0%
+perfect competition there'll be profits
+ 
+
+ align:start position:0%
+perfect competition there'll be profits
+and there'll be dead weight
+
+ align:start position:0%
+and there'll be dead weight
+ 
+
+ align:start position:0%
+and there'll be dead weight
+loss okay that's the second
+
+ align:start position:0%
+loss okay that's the second
+ 
+
+ align:start position:0%
+loss okay that's the second
+reason a third reason is the biggest
+
+ align:start position:0%
+reason a third reason is the biggest
+ 
+
+ align:start position:0%
+reason a third reason is the biggest
+challenge yet which is for the new class
+
+ align:start position:0%
+challenge yet which is for the new class
+ 
+
+ align:start position:0%
+challenge yet which is for the new class
+of drugs being made called
+
+ align:start position:0%
+of drugs being made called
+ 
+
+ align:start position:0%
+of drugs being made called
+biologics which are not stable small
+
+ align:start position:0%
+biologics which are not stable small
+ 
+
+ align:start position:0%
+biologics which are not stable small
+cell stable large cell I'm sorry drug
+
+ align:start position:0%
+cell stable large cell I'm sorry drug
+ 
+
+ align:start position:0%
+cell stable large cell I'm sorry drug
+development but literally drugs that are
+
+ align:start position:0%
+development but literally drugs that are
+ 
+
+ align:start position:0%
+development but literally drugs that are
+developed and injected and are
+
+ align:start position:0%
+developed and injected and are
+ 
+
+ align:start position:0%
+developed and injected and are
+essentially um formulated they're
+
+ align:start position:0%
+essentially um formulated they're
+ 
+
+ align:start position:0%
+essentially um formulated they're
+biological formulations that are live
+
+ align:start position:0%
+biological formulations that are live
+ 
+
+ align:start position:0%
+biological formulations that are live
+effectively it's hard to make an
+
+ align:start position:0%
+effectively it's hard to make an
+ 
+
+ align:start position:0%
+effectively it's hard to make an
+effective
+
+ align:start position:0%
+effective
+ 
+
+ align:start position:0%
+effective
+generic and so generic composition May
+
+ align:start position:0%
+generic and so generic composition May
+ 
+
+ align:start position:0%
+generic and so generic composition May
+simply not exist for these new biologic
+
+ align:start position:0%
+simply not exist for these new biologic
+ 
+
+ align:start position:0%
+simply not exist for these new biologic
+drugs which is the new class of drugs
+
+ align:start position:0%
+drugs which is the new class of drugs
+ 
+
+ align:start position:0%
+drugs which is the new class of drugs
+which are making incredible uh steps and
+
+ align:start position:0%
+which are making incredible uh steps and
+ 
+
+ align:start position:0%
+which are making incredible uh steps and
+let's be clear the innovation in
+
+ align:start position:0%
+let's be clear the innovation in
+ 
+
+ align:start position:0%
+let's be clear the innovation in
+Pharmaceuticals is
+
+ align:start position:0%
+Pharmaceuticals is
+ 
+
+ align:start position:0%
+Pharmaceuticals is
+unbelievable okay just one example
+
+ align:start position:0%
+unbelievable okay just one example
+ 
+
+ align:start position:0%
+unbelievable okay just one example
+there's a horrible horrible disease
+
+ align:start position:0%
+there's a horrible horrible disease
+ 
+
+ align:start position:0%
+there's a horrible horrible disease
+called spin or muscular
+
+ align:start position:0%
+called spin or muscular
+ 
+
+ align:start position:0%
+called spin or muscular
+atrophy if the baby if your B it's a
+
+ align:start position:0%
+atrophy if the baby if your B it's a
+ 
+
+ align:start position:0%
+atrophy if the baby if your B it's a
+genetic disease purely random if you're
+
+ align:start position:0%
+genetic disease purely random if you're
+ 
+
+ align:start position:0%
+genetic disease purely random if you're
+born with it your life is brutal
+
+ align:start position:0%
+born with it your life is brutal
+ 
+
+ align:start position:0%
+born with it your life is brutal
+miserable and you're dead by two I mean
+
+ align:start position:0%
+miserable and you're dead by two I mean
+ 
+
+ align:start position:0%
+miserable and you're dead by two I mean
+awful can't imagine anything worse as
+
+ align:start position:0%
+awful can't imagine anything worse as
+ 
+
+ align:start position:0%
+awful can't imagine anything worse as
+app parent they've cured it they
+
+ align:start position:0%
+app parent they've cured it they
+ 
+
+ align:start position:0%
+app parent they've cured it they
+developed a miracle cure it's a new
+
+ align:start position:0%
+developed a miracle cure it's a new
+ 
+
+ align:start position:0%
+developed a miracle cure it's a new
+called selling gene therapy would
+
+ align:start position:0%
+called selling gene therapy would
+ 
+
+ align:start position:0%
+called selling gene therapy would
+literally inject a virus in the baby's
+
+ align:start position:0%
+literally inject a virus in the baby's
+ 
+
+ align:start position:0%
+literally inject a virus in the baby's
+body containing a new patched Gene it
+
+ align:start position:0%
+body containing a new patched Gene it
+ 
+
+ align:start position:0%
+body containing a new patched Gene it
+goes through the body and repairs it
+
+ align:start position:0%
+goes through the body and repairs it
+ 
+
+ align:start position:0%
+goes through the body and repairs it
+it's a miracle it's the kind of thing
+
+ align:start position:0%
+it's a miracle it's the kind of thing
+ 
+
+ align:start position:0%
+it's a miracle it's the kind of thing
+you guys are doing here at MIT every day
+
+ align:start position:0%
+you guys are doing here at MIT every day
+ 
+
+ align:start position:0%
+you guys are doing here at MIT every day
+and it's only going to get better this
+
+ align:start position:0%
+and it's only going to get better this
+ 
+
+ align:start position:0%
+and it's only going to get better this
+drug cost $2.1
+
+ align:start position:0%
+drug cost $2.1
+ 
+
+ align:start position:0%
+drug cost $2.1
+million now on the one hand I say $2.1
+
+ align:start position:0%
+million now on the one hand I say $2.1
+ 
+
+ align:start position:0%
+million now on the one hand I say $2.1
+million that's a lot of money on the
+
+ align:start position:0%
+million that's a lot of money on the
+ 
+
+ align:start position:0%
+million that's a lot of money on the
+other hand you're saving a baby's life
+
+ align:start position:0%
+other hand you're saving a baby's life
+ 
+
+ align:start position:0%
+other hand you're saving a baby's life
+you are adding potentially 80 to 100
+
+ align:start position:0%
+you are adding potentially 80 to 100
+ 
+
+ align:start position:0%
+you are adding potentially 80 to 100
+years of life to someone21 million is
+
+ align:start position:0%
+years of life to someone21 million is
+ 
+
+ align:start position:0%
+years of life to someone21 million is
+actually a pretty good deal on the other
+
+ align:start position:0%
+actually a pretty good deal on the other
+ 
+
+ align:start position:0%
+actually a pretty good deal on the other
+hand if we develop drugs for everything
+
+ align:start position:0%
+hand if we develop drugs for everything
+ 
+
+ align:start position:0%
+hand if we develop drugs for everything
+like this we'll bankrupt our country so
+
+ align:start position:0%
+like this we'll bankrupt our country so
+ 
+
+ align:start position:0%
+like this we'll bankrupt our country so
+these are the kind of difficult issues
+
+ align:start position:0%
+these are the kind of difficult issues
+ 
+
+ align:start position:0%
+these are the kind of difficult issues
+we raise in wanting give incenters for
+
+ align:start position:0%
+we raise in wanting give incenters for
+ 
+
+ align:start position:0%
+we raise in wanting give incenters for
+Innovation but also being ultimately
+
+ align:start position:0%
+Innovation but also being ultimately
+ 
+
+ align:start position:0%
+Innovation but also being ultimately
+affordable uh in terms of what consumers
+
+ align:start position:0%
+affordable uh in terms of what consumers
+ 
+
+ align:start position:0%
+affordable uh in terms of what consumers
+need to Consumers need to
+
+ align:start position:0%
+need to Consumers need to
+ 
+
+ align:start position:0%
+need to Consumers need to
+buy okay questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay and this is if this is
+
+ align:start position:0%
+that okay and this is if this is
+ 
+
+ align:start position:0%
+that okay and this is if this is
+something that interests you um this is
+
+ align:start position:0%
+something that interests you um this is
+ 
+
+ align:start position:0%
+something that interests you um this is
+a big debate in the US right now as part
+
+ align:start position:0%
+a big debate in the US right now as part
+ 
+
+ align:start position:0%
+a big debate in the US right now as part
+of President Biden's uh inflation
+
+ align:start position:0%
+of President Biden's uh inflation
+ 
+
+ align:start position:0%
+of President Biden's uh inflation
+reduction act the IRA the government for
+
+ align:start position:0%
+reduction act the IRA the government for
+ 
+
+ align:start position:0%
+reduction act the IRA the government for
+the first time is actually regulating
+
+ align:start position:0%
+the first time is actually regulating
+ 
+
+ align:start position:0%
+the first time is actually regulating
+the price of pharmaceuticals it's
+
+ align:start position:0%
+the price of pharmaceuticals it's
+ 
+
+ align:start position:0%
+the price of pharmaceuticals it's
+actually saying to some Pharmaceuticals
+
+ align:start position:0%
+actually saying to some Pharmaceuticals
+ 
+
+ align:start position:0%
+actually saying to some Pharmaceuticals
+that have competitors look you know
+
+ align:start position:0%
+that have competitors look you know
+ 
+
+ align:start position:0%
+that have competitors look you know
+we're going to regulate your price
+
+ align:start position:0%
+we're going to regulate your price
+ 
+
+ align:start position:0%
+we're going to regulate your price
+because we think you're making too much
+
+ align:start position:0%
+because we think you're making too much
+ 
+
+ align:start position:0%
+because we think you're making too much
+money the government's decide the patent
+
+ align:start position:0%
+money the government's decide the patent
+ 
+
+ align:start position:0%
+money the government's decide the patent
+system isn't working it's out of balance
+
+ align:start position:0%
+system isn't working it's out of balance
+ 
+
+ align:start position:0%
+system isn't working it's out of balance
+and so drug companies are making too
+
+ align:start position:0%
+and so drug companies are making too
+ 
+
+ align:start position:0%
+and so drug companies are making too
+much money and they're regulating prices
+
+ align:start position:0%
+much money and they're regulating prices
+ 
+
+ align:start position:0%
+much money and they're regulating prices
+and that was very controversial and uh a
+
+ align:start position:0%
+and that was very controversial and uh a
+ 
+
+ align:start position:0%
+and that was very controversial and uh a
+significant step forward in how we think
+
+ align:start position:0%
+significant step forward in how we think
+ 
+
+ align:start position:0%
+significant step forward in how we think
+about drug pricing in the US and you can
+
+ align:start position:0%
+about drug pricing in the US and you can
+ 
+
+ align:start position:0%
+about drug pricing in the US and you can
+read more about that if that's something
+
+ align:start position:0%
+read more about that if that's something
+ 
+
+ align:start position:0%
+read more about that if that's something
+that interests you and certainly if you
+
+ align:start position:0%
+that interests you and certainly if you
+ 
+
+ align:start position:0%
+that interests you and certainly if you
+want to go into bi biological
+
+ align:start position:0%
+want to go into bi biological
+ 
+
+ align:start position:0%
+want to go into bi biological
+engineering or or or any of those fields
+
+ align:start position:0%
+engineering or or or any of those fields
+ 
+
+ align:start position:0%
+engineering or or or any of those fields
+this is something important to know
+
+ align:start position:0%
+this is something important to know
+ 
+
+ align:start position:0%
+this is something important to know
+about okay so that's the first topic I
+
+ align:start position:0%
+about okay so that's the first topic I
+ 
+
+ align:start position:0%
+about okay so that's the first topic I
+want to cover where do monopolies come
+
+ align:start position:0%
+want to cover where do monopolies come
+ 
+
+ align:start position:0%
+want to cover where do monopolies come
+from the second topic I want to cover is
+
+ align:start position:0%
+from the second topic I want to cover is
+ 
+
+ align:start position:0%
+from the second topic I want to cover is
+addressing Monopoly because this is
+
+ align:start position:0%
+addressing Monopoly because this is
+ 
+
+ align:start position:0%
+addressing Monopoly because this is
+where things get exciting from my
+
+ align:start position:0%
+where things get exciting from my
+ 
+
+ align:start position:0%
+where things get exciting from my
+perspective I'm a big government liberal
+
+ align:start position:0%
+perspective I'm a big government liberal
+ 
+
+ align:start position:0%
+perspective I'm a big government liberal
+okay I think government can do good
+
+ align:start position:0%
+okay I think government can do good
+ 
+
+ align:start position:0%
+okay I think government can do good
+things yet everything I've taught you in
+
+ align:start position:0%
+things yet everything I've taught you in
+ 
+
+ align:start position:0%
+things yet everything I've taught you in
+this course government's the bad guy
+
+ align:start position:0%
+this course government's the bad guy
+ 
+
+ align:start position:0%
+this course government's the bad guy
+okay I don't like that but that's the
+
+ align:start position:0%
+okay I don't like that but that's the
+ 
+
+ align:start position:0%
+okay I don't like that but that's the
+way Bates economics works and let's be
+
+ align:start position:0%
+way Bates economics works and let's be
+ 
+
+ align:start position:0%
+way Bates economics works and let's be
+clear that that's the proper way to
+
+ align:start position:0%
+clear that that's the proper way to
+ 
+
+ align:start position:0%
+clear that that's the proper way to
+teach the first half of this course the
+
+ align:start position:0%
+teach the first half of this course the
+ 
+
+ align:start position:0%
+teach the first half of this course the
+first fundamental theorem of what for
+
+ align:start position:0%
+first fundamental theorem of what for
+ 
+
+ align:start position:0%
+first fundamental theorem of what for
+economics says government only does bad
+
+ align:start position:0%
+economics says government only does bad
+ 
+
+ align:start position:0%
+economics says government only does bad
+things okay but that's not true in
+
+ align:start position:0%
+things okay but that's not true in
+ 
+
+ align:start position:0%
+things okay but that's not true in
+reality and here's the first case we get
+
+ align:start position:0%
+reality and here's the first case we get
+ 
+
+ align:start position:0%
+reality and here's the first case we get
+to see where government can potentially
+
+ align:start position:0%
+to see where government can potentially
+ 
+
+ align:start position:0%
+to see where government can potentially
+but not obviously make things better and
+
+ align:start position:0%
+but not obviously make things better and
+ 
+
+ align:start position:0%
+but not obviously make things better and
+that is through regulating
+
+ align:start position:0%
+that is through regulating
+ 
+
+ align:start position:0%
+that is through regulating
+monopolies so for example let's go to
+
+ align:start position:0%
+monopolies so for example let's go to
+ 
+
+ align:start position:0%
+monopolies so for example let's go to
+figure
+
+ align:start position:0%
+figure
+ 
+
+ align:start position:0%
+figure
+122 figure 122 is the same figure we
+
+ align:start position:0%
+122 figure 122 is the same figure we
+ 
+
+ align:start position:0%
+122 figure 122 is the same figure we
+ended with last time you've got a
+
+ align:start position:0%
+ended with last time you've got a
+ 
+
+ align:start position:0%
+ended with last time you've got a
+marginal cost curve a demand curve and a
+
+ align:start position:0%
+marginal cost curve a demand curve and a
+ 
+
+ align:start position:0%
+marginal cost curve a demand curve and a
+marginal revenue curve the marginal ring
+
+ align:start position:0%
+marginal revenue curve the marginal ring
+ 
+
+ align:start position:0%
+marginal revenue curve the marginal ring
+curve intersects marginal costs at six
+
+ align:start position:0%
+curve intersects marginal costs at six
+ 
+
+ align:start position:0%
+curve intersects marginal costs at six
+units producing six units you respect
+
+ align:start position:0%
+units producing six units you respect
+ 
+
+ align:start position:0%
+units producing six units you respect
+the demand curve you charge a price of
+
+ align:start position:0%
+the demand curve you charge a price of
+ 
+
+ align:start position:0%
+the demand curve you charge a price of
+18 six units get produced we get a dead
+
+ align:start position:0%
+18 six units get produced we get a dead
+ 
+
+ align:start position:0%
+18 six units get produced we get a dead
+weight loss of C plus
+
+ align:start position:0%
+weight loss of C plus
+ 
+
+ align:start position:0%
+weight loss of C plus
+e so as we said the market outcome is
+
+ align:start position:0%
+e so as we said the market outcome is
+ 
+
+ align:start position:0%
+e so as we said the market outcome is
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+efficient what can the government do
+
+ align:start position:0%
+efficient what can the government do
+ 
+
+ align:start position:0%
+efficient what can the government do
+well what if the government set a price
+
+ align:start position:0%
+well what if the government set a price
+ 
+
+ align:start position:0%
+well what if the government set a price
+ceiling and said we are not going to let
+
+ align:start position:0%
+ceiling and said we are not going to let
+ 
+
+ align:start position:0%
+ceiling and said we are not going to let
+the monopolist charge more than
+
+ align:start position:0%
+the monopolist charge more than
+ 
+
+ align:start position:0%
+the monopolist charge more than
+16 we not going to let the monopolis
+
+ align:start position:0%
+16 we not going to let the monopolis
+ 
+
+ align:start position:0%
+16 we not going to let the monopolis
+charge more than
+
+ align:start position:0%
+charge more than
+ 
+
+ align:start position:0%
+charge more than
+16 well then the new marginal cost curve
+
+ align:start position:0%
+16 well then the new marginal cost curve
+ 
+
+ align:start position:0%
+16 well then the new marginal cost curve
+from for the monopolist the new supply
+
+ align:start position:0%
+from for the monopolist the new supply
+ 
+
+ align:start position:0%
+from for the monopolist the new supply
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+or or the new it's essentially the new
+
+ align:start position:0%
+or or the new it's essentially the new
+ 
+
+ align:start position:0%
+or or the new it's essentially the new
+uh marginal revenue curve I'm sorry the
+
+ align:start position:0%
+uh marginal revenue curve I'm sorry the
+ 
+
+ align:start position:0%
+uh marginal revenue curve I'm sorry the
+new marginal revenue curve becomes the
+
+ align:start position:0%
+new marginal revenue curve becomes the
+ 
+
+ align:start position:0%
+new marginal revenue curve becomes the
+flat line all the way to point e what is
+
+ align:start position:0%
+flat line all the way to point e what is
+ 
+
+ align:start position:0%
+flat line all the way to point e what is
+that e c it should be that intersection
+
+ align:start position:0%
+that e c it should be that intersection
+ 
+
+ align:start position:0%
+that e c it should be that intersection
+of the red and blue lines the flat line
+
+ align:start position:0%
+of the red and blue lines the flat line
+ 
+
+ align:start position:0%
+of the red and blue lines the flat line
+all the point that little e e z I guess
+
+ align:start position:0%
+all the point that little e e z I guess
+ 
+
+ align:start position:0%
+all the point that little e e z I guess
+it looks like it should be EC and then
+
+ align:start position:0%
+it looks like it should be EC and then
+ 
+
+ align:start position:0%
+it looks like it should be EC and then
+it drops the dash line down you go back
+
+ align:start position:0%
+it drops the dash line down you go back
+ 
+
+ align:start position:0%
+it drops the dash line down you go back
+to the old margin Revenue curve so you
+
+ align:start position:0%
+to the old margin Revenue curve so you
+ 
+
+ align:start position:0%
+to the old margin Revenue curve so you
+draw the solid line from the 16 on the
+
+ align:start position:0%
+draw the solid line from the 16 on the
+ 
+
+ align:start position:0%
+draw the solid line from the 16 on the
+y- axis over to the what looks like e0
+
+ align:start position:0%
+y- axis over to the what looks like e0
+ 
+
+ align:start position:0%
+y- axis over to the what looks like e0
+follow that dash line down and then
+
+ align:start position:0%
+follow that dash line down and then
+ 
+
+ align:start position:0%
+follow that dash line down and then
+rejoin the original marginal revenue
+
+ align:start position:0%
+rejoin the original marginal revenue
+ 
+
+ align:start position:0%
+rejoin the original marginal revenue
+curve that's the new marginal revenue
+
+ align:start position:0%
+curve that's the new marginal revenue
+ 
+
+ align:start position:0%
+curve that's the new marginal revenue
+curve why well think about what marginal
+
+ align:start position:0%
+curve why well think about what marginal
+ 
+
+ align:start position:0%
+curve why well think about what marginal
+revenue
+
+ align:start position:0%
+revenue
+ 
+
+ align:start position:0%
+revenue
+is okay if you
+
+ align:start position:0%
+is okay if you
+ 
+
+ align:start position:0%
+is okay if you
+produce remember in the old world if you
+
+ align:start position:0%
+produce remember in the old world if you
+ 
+
+ align:start position:0%
+produce remember in the old world if you
+produce the seventh
+
+ align:start position:0%
+produce the seventh
+ 
+
+ align:start position:0%
+produce the seventh
+unit okay your marginal revenue is your
+
+ align:start position:0%
+unit okay your marginal revenue is your
+ 
+
+ align:start position:0%
+unit okay your marginal revenue is your
+your profits fall because of the
+
+ align:start position:0%
+your profits fall because of the
+ 
+
+ align:start position:0%
+your profits fall because of the
+poisoning effect but now if you produce
+
+ align:start position:0%
+poisoning effect but now if you produce
+ 
+
+ align:start position:0%
+poisoning effect but now if you produce
+the seventh unit you can only charge 16
+
+ align:start position:0%
+the seventh unit you can only charge 16
+ 
+
+ align:start position:0%
+the seventh unit you can only charge 16
+that's the most you can
+
+ align:start position:0%
+that's the most you can
+ 
+
+ align:start position:0%
+that's the most you can
+charge so you might as well produce it
+
+ align:start position:0%
+charge so you might as well produce it
+ 
+
+ align:start position:0%
+charge so you might as well produce it
+at if you can only charge 16 if that's
+
+ align:start position:0%
+at if you can only charge 16 if that's
+ 
+
+ align:start position:0%
+at if you can only charge 16 if that's
+the limit then at that point your your
+
+ align:start position:0%
+the limit then at that point your your
+ 
+
+ align:start position:0%
+the limit then at that point your your
+costs are
+
+ align:start position:0%
+costs are
+ 
+
+ align:start position:0%
+costs are
+below your marginal revenue so you
+
+ align:start position:0%
+below your marginal revenue so you
+ 
+
+ align:start position:0%
+below your marginal revenue so you
+produce in other words the marginal
+
+ align:start position:0%
+produce in other words the marginal
+ 
+
+ align:start position:0%
+produce in other words the marginal
+revenue in the old point when you went
+
+ align:start position:0%
+revenue in the old point when you went
+ 
+
+ align:start position:0%
+revenue in the old point when you went
+to the seventh
+
+ align:start position:0%
+to the seventh
+ 
+
+ align:start position:0%
+to the seventh
+unit marginal cost was above marginal
+
+ align:start position:0%
+unit marginal cost was above marginal
+ 
+
+ align:start position:0%
+unit marginal cost was above marginal
+revenue now going to the seventh unit
+
+ align:start position:0%
+revenue now going to the seventh unit
+ 
+
+ align:start position:0%
+revenue now going to the seventh unit
+it's not because we haven't let you
+
+ align:start position:0%
+it's not because we haven't let you
+ 
+
+ align:start position:0%
+it's not because we haven't let you
+raised your price so the government by
+
+ align:start position:0%
+raised your price so the government by
+ 
+
+ align:start position:0%
+raised your price so the government by
+regulating and saying the price has to
+
+ align:start position:0%
+regulating and saying the price has to
+ 
+
+ align:start position:0%
+regulating and saying the price has to
+be set at 16
+
+ align:start position:0%
+be set at 16
+ 
+
+ align:start position:0%
+be set at 16
+is essentially taking away the poisoning
+
+ align:start position:0%
+is essentially taking away the poisoning
+ 
+
+ align:start position:0%
+is essentially taking away the poisoning
+effect the poisoning effect
+
+ align:start position:0%
+effect the poisoning effect
+ 
+
+ align:start position:0%
+effect the poisoning effect
+arises because if I want to sell one
+
+ align:start position:0%
+arises because if I want to sell one
+ 
+
+ align:start position:0%
+arises because if I want to sell one
+moreon have to lower my price well here
+
+ align:start position:0%
+moreon have to lower my price well here
+ 
+
+ align:start position:0%
+moreon have to lower my price well here
+your price is already low I haven't let
+
+ align:start position:0%
+your price is already low I haven't let
+ 
+
+ align:start position:0%
+your price is already low I haven't let
+you raise your price I haven't let you
+
+ align:start position:0%
+you raise your price I haven't let you
+ 
+
+ align:start position:0%
+you raise your price I haven't let you
+set it at
+
+ align:start position:0%
+set it at
+ 
+
+ align:start position:0%
+set it at
+18 before you didn't want to sell the
+
+ align:start position:0%
+18 before you didn't want to sell the
+ 
+
+ align:start position:0%
+18 before you didn't want to sell the
+seventh unit you lower your price to 17
+
+ align:start position:0%
+seventh unit you lower your price to 17
+ 
+
+ align:start position:0%
+seventh unit you lower your price to 17
+right well now your price is already 16
+
+ align:start position:0%
+right well now your price is already 16
+ 
+
+ align:start position:0%
+right well now your price is already 16
+so why not sell the seventh
+
+ align:start position:0%
+so why not sell the seventh
+ 
+
+ align:start position:0%
+so why not sell the seventh
+Unit 16 is still above marginal cost so
+
+ align:start position:0%
+Unit 16 is still above marginal cost so
+ 
+
+ align:start position:0%
+Unit 16 is still above marginal cost so
+why not do it so essentially the optimal
+
+ align:start position:0%
+why not do it so essentially the optimal
+ 
+
+ align:start position:0%
+why not do it so essentially the optimal
+solution from the monopolis then is to
+
+ align:start position:0%
+solution from the monopolis then is to
+ 
+
+ align:start position:0%
+solution from the monopolis then is to
+sell eight
+
+ align:start position:0%
+sell eight
+ 
+
+ align:start position:0%
+sell eight
+to sell the competitive quantity if you
+
+ align:start position:0%
+to sell the competitive quantity if you
+ 
+
+ align:start position:0%
+to sell the competitive quantity if you
+tell the monopolis they can't charge
+
+ align:start position:0%
+tell the monopolis they can't charge
+ 
+
+ align:start position:0%
+tell the monopolis they can't charge
+more than 16 they have they will they
+
+ align:start position:0%
+more than 16 they have they will they
+ 
+
+ align:start position:0%
+more than 16 they have they will they
+will sell the competitive quantity and
+
+ align:start position:0%
+will sell the competitive quantity and
+ 
+
+ align:start position:0%
+will sell the competitive quantity and
+guess what dead weight loss has gone
+
+ align:start position:0%
+guess what dead weight loss has gone
+ 
+
+ align:start position:0%
+guess what dead weight loss has gone
+away we're now selling the
+
+ align:start position:0%
+away we're now selling the
+ 
+
+ align:start position:0%
+away we're now selling the
+competitive amount and dead weight loss
+
+ align:start position:0%
+competitive amount and dead weight loss
+ 
+
+ align:start position:0%
+competitive amount and dead weight loss
+is going
+
+ align:start position:0%
+is going
+ 
+
+ align:start position:0%
+is going
+away
+
+ align:start position:0%
+away
+ 
+
+ align:start position:0%
+away
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let's think about an example of this
+
+ align:start position:0%
+so let's think about an example of this
+ 
+
+ align:start position:0%
+so let's think about an example of this
+and how the government could make things
+
+ align:start position:0%
+and how the government could make things
+ 
+
+ align:start position:0%
+and how the government could make things
+better okay and let's come to a case of
+
+ align:start position:0%
+better okay and let's come to a case of
+ 
+
+ align:start position:0%
+better okay and let's come to a case of
+a natural monopoly which is
+
+ align:start position:0%
+a natural monopoly which is
+ 
+
+ align:start position:0%
+a natural monopoly which is
+broadband Broadband
+
+ align:start position:0%
+broadband Broadband
+ 
+
+ align:start position:0%
+broadband Broadband
+delivery to deliver Broadband it's not a
+
+ align:start position:0%
+delivery to deliver Broadband it's not a
+ 
+
+ align:start position:0%
+delivery to deliver Broadband it's not a
+fully natural monopoly and that multiple
+
+ align:start position:0%
+fully natural monopoly and that multiple
+ 
+
+ align:start position:0%
+fully natural monopoly and that multiple
+people can lay the lines that come to
+
+ align:start position:0%
+people can lay the lines that come to
+ 
+
+ align:start position:0%
+people can lay the lines that come to
+your house but it's a big fixed cost if
+
+ align:start position:0%
+your house but it's a big fixed cost if
+ 
+
+ align:start position:0%
+your house but it's a big fixed cost if
+you want to set up a Broadband
+
+ align:start position:0%
+you want to set up a Broadband
+ 
+
+ align:start position:0%
+you want to set up a Broadband
+competitor you have to go out and lay a
+
+ align:start position:0%
+competitor you have to go out and lay a
+ 
+
+ align:start position:0%
+competitor you have to go out and lay a
+whole bunch of new fiber cable okay
+
+ align:start position:0%
+whole bunch of new fiber cable okay
+ 
+
+ align:start position:0%
+whole bunch of new fiber cable okay
+that's expensive it's not infinite it's
+
+ align:start position:0%
+that's expensive it's not infinite it's
+ 
+
+ align:start position:0%
+that's expensive it's not infinite it's
+not like a water utility it's doable and
+
+ align:start position:0%
+not like a water utility it's doable and
+ 
+
+ align:start position:0%
+not like a water utility it's doable and
+it happens but it's pretty expensive
+
+ align:start position:0%
+it happens but it's pretty expensive
+ 
+
+ align:start position:0%
+it happens but it's pretty expensive
+competition will be definitely Limited
+
+ align:start position:0%
+competition will be definitely Limited
+ 
+
+ align:start position:0%
+competition will be definitely Limited
+may not be natural monopoly certainly
+
+ align:start position:0%
+may not be natural monopoly certainly
+ 
+
+ align:start position:0%
+may not be natural monopoly certainly
+natural oligopoly you're not going to
+
+ align:start position:0%
+natural oligopoly you're not going to
+ 
+
+ align:start position:0%
+natural oligopoly you're not going to
+have hundreds of firms laying these
+
+ align:start position:0%
+have hundreds of firms laying these
+ 
+
+ align:start position:0%
+have hundreds of firms laying these
+wires getting price making prices
+
+ align:start position:0%
+wires getting price making prices
+ 
+
+ align:start position:0%
+wires getting price making prices
+competitive okay so for example across
+
+ align:start position:0%
+competitive okay so for example across
+ 
+
+ align:start position:0%
+competitive okay so for example across
+20,000 us zip codes
+
+ align:start position:0%
+20,000 us zip codes
+ 
+
+ align:start position:0%
+20,000 us zip codes
+70% have either zero or
+
+ align:start position:0%
+70% have either zero or
+ 
+
+ align:start position:0%
+70% have either zero or
+one option for 25 uh for 25 megabytes
+
+ align:start position:0%
+one option for 25 uh for 25 megabytes
+ 
+
+ align:start position:0%
+one option for 25 uh for 25 megabytes
+per second
+
+ align:start position:0%
+per second
+ 
+
+ align:start position:0%
+per second
+service okay zero or one on is that a
+
+ align:start position:0%
+service okay zero or one on is that a
+ 
+
+ align:start position:0%
+service okay zero or one on is that a
+megabytes per second I say that right I
+
+ align:start position:0%
+megabytes per second I say that right I
+ 
+
+ align:start position:0%
+megabytes per second I say that right I
+think so I hope so Mbps I think I got
+
+ align:start position:0%
+think so I hope so Mbps I think I got
+ 
+
+ align:start position:0%
+think so I hope so Mbps I think I got
+that right uh Z One
+
+ align:start position:0%
+that right uh Z One
+ 
+
+ align:start position:0%
+that right uh Z One
+options okay even at the lowest possible
+
+ align:start position:0%
+options okay even at the lowest possible
+ 
+
+ align:start position:0%
+options okay even at the lowest possible
+speed of internet service only 30% of
+
+ align:start position:0%
+speed of internet service only 30% of
+ 
+
+ align:start position:0%
+speed of internet service only 30% of
+zip codes have more than one option for
+
+ align:start position:0%
+zip codes have more than one option for
+ 
+
+ align:start position:0%
+zip codes have more than one option for
+getting Broadband 30% of America has
+
+ align:start position:0%
+getting Broadband 30% of America has
+ 
+
+ align:start position:0%
+getting Broadband 30% of America has
+only one option for getting their
+
+ align:start position:0%
+only one option for getting their
+ 
+
+ align:start position:0%
+only one option for getting their
+Broadband why because it's a natural
+
+ align:start position:0%
+Broadband why because it's a natural
+ 
+
+ align:start position:0%
+Broadband why because it's a natural
+monopoly in many cases the costs are
+
+ align:start position:0%
+monopoly in many cases the costs are
+ 
+
+ align:start position:0%
+monopoly in many cases the costs are
+really high if you're in some rural town
+
+ align:start position:0%
+really high if you're in some rural town
+ 
+
+ align:start position:0%
+really high if you're in some rural town
+it's not effective to lay a second set
+
+ align:start position:0%
+it's not effective to lay a second set
+ 
+
+ align:start position:0%
+it's not effective to lay a second set
+of wires going to people's
+
+ align:start position:0%
+of wires going to people's
+ 
+
+ align:start position:0%
+of wires going to people's
+houses okay as a result
+
+ align:start position:0%
+houses okay as a result
+ 
+
+ align:start position:0%
+houses okay as a result
+prices are high and there's Monopoly
+
+ align:start position:0%
+prices are high and there's Monopoly
+ 
+
+ align:start position:0%
+prices are high and there's Monopoly
+power now you might say well John and
+
+ align:start position:0%
+power now you might say well John and
+ 
+
+ align:start position:0%
+power now you might say well John and
+the Broadband companies will say well
+
+ align:start position:0%
+the Broadband companies will say well
+ 
+
+ align:start position:0%
+the Broadband companies will say well
+John because they have deep voices John
+
+ align:start position:0%
+John because they have deep voices John
+ 
+
+ align:start position:0%
+John because they have deep voices John
+how do you know we have Monopoly power
+
+ align:start position:0%
+how do you know we have Monopoly power
+ 
+
+ align:start position:0%
+how do you know we have Monopoly power
+just because there's not that many we
+
+ align:start position:0%
+just because there's not that many we
+ 
+
+ align:start position:0%
+just because there's not that many we
+still could be pricing competitively
+
+ align:start position:0%
+still could be pricing competitively
+ 
+
+ align:start position:0%
+still could be pricing competitively
+well economists have developed a very
+
+ align:start position:0%
+well economists have developed a very
+ 
+
+ align:start position:0%
+well economists have developed a very
+clever test fors Monopoly power which is
+
+ align:start position:0%
+clever test fors Monopoly power which is
+ 
+
+ align:start position:0%
+clever test fors Monopoly power which is
+they ask what happens to prices as more
+
+ align:start position:0%
+they ask what happens to prices as more
+ 
+
+ align:start position:0%
+they ask what happens to prices as more
+firms
+
+ align:start position:0%
+firms
+ 
+
+ align:start position:0%
+firms
+enter if a Market's competitive what
+
+ align:start position:0%
+enter if a Market's competitive what
+ 
+
+ align:start position:0%
+enter if a Market's competitive what
+should an additional firm entering do to
+
+ align:start position:0%
+should an additional firm entering do to
+ 
+
+ align:start position:0%
+should an additional firm entering do to
+the price
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no if a Market's perfectly competitive
+
+ align:start position:0%
+no if a Market's perfectly competitive
+ 
+
+ align:start position:0%
+no if a Market's perfectly competitive
+what should additional firm entering doe
+
+ align:start position:0%
+what should additional firm entering doe
+ 
+
+ align:start position:0%
+what should additional firm entering doe
+to the price if it's perfectly
+
+ align:start position:0%
+to the price if it's perfectly
+ 
+
+ align:start position:0%
+to the price if it's perfectly
+competitive price is already set to
+
+ align:start position:0%
+competitive price is already set to
+ 
+
+ align:start position:0%
+competitive price is already set to
+marginal cost it shouldn't do
+
+ align:start position:0%
+marginal cost it shouldn't do
+ 
+
+ align:start position:0%
+marginal cost it shouldn't do
+anything price is already marginal cost
+
+ align:start position:0%
+anything price is already marginal cost
+ 
+
+ align:start position:0%
+anything price is already marginal cost
+so additional firm shouldn't have a
+
+ align:start position:0%
+so additional firm shouldn't have a
+ 
+
+ align:start position:0%
+so additional firm shouldn't have a
+meaningful effect on the price maybe go
+
+ align:start position:0%
+meaningful effect on the price maybe go
+ 
+
+ align:start position:0%
+meaningful effect on the price maybe go
+down a little but not meaningful if it's
+
+ align:start position:0%
+down a little but not meaningful if it's
+ 
+
+ align:start position:0%
+down a little but not meaningful if it's
+a monopoly market and you add a second
+
+ align:start position:0%
+a monopoly market and you add a second
+ 
+
+ align:start position:0%
+a monopoly market and you add a second
+firm price will come down a lot and
+
+ align:start position:0%
+firm price will come down a lot and
+ 
+
+ align:start position:0%
+firm price will come down a lot and
+we'll TR that next next
+
+ align:start position:0%
+we'll TR that next next
+ 
+
+ align:start position:0%
+we'll TR that next next
+lecture so the way to test this is ask
+
+ align:start position:0%
+lecture so the way to test this is ask
+ 
+
+ align:start position:0%
+lecture so the way to test this is ask
+what happens as more firms enter markets
+
+ align:start position:0%
+what happens as more firms enter markets
+ 
+
+ align:start position:0%
+what happens as more firms enter markets
+do prices come down a little
+
+ align:start position:0%
+do prices come down a little
+ 
+
+ align:start position:0%
+do prices come down a little
+or do they come down a
+
+ align:start position:0%
+or do they come down a
+ 
+
+ align:start position:0%
+or do they come down a
+lot and the answer is it comes down a
+
+ align:start position:0%
+lot and the answer is it comes down a
+ 
+
+ align:start position:0%
+lot and the answer is it comes down a
+lot so basically for every um for
+
+ align:start position:0%
+lot so basically for every um for
+ 
+
+ align:start position:0%
+lot so basically for every um for
+gigabyte internet moving from one
+
+ align:start position:0%
+gigabyte internet moving from one
+ 
+
+ align:start position:0%
+gigabyte internet moving from one
+provider to two providers of gigabyte
+
+ align:start position:0%
+provider to two providers of gigabyte
+ 
+
+ align:start position:0%
+provider to two providers of gigabyte
+internet lowers the monthly price by 60
+
+ align:start position:0%
+internet lowers the monthly price by 60
+ 
+
+ align:start position:0%
+internet lowers the monthly price by 60
+bucks a month literally you pay 60 bucks
+
+ align:start position:0%
+bucks a month literally you pay 60 bucks
+ 
+
+ align:start position:0%
+bucks a month literally you pay 60 bucks
+less a month for gigabyte internet when
+
+ align:start position:0%
+less a month for gigabyte internet when
+ 
+
+ align:start position:0%
+less a month for gigabyte internet when
+you get go from one provider to two
+
+ align:start position:0%
+you get go from one provider to two
+ 
+
+ align:start position:0%
+you get go from one provider to two
+provider that is not a competitive
+
+ align:start position:0%
+provider that is not a competitive
+ 
+
+ align:start position:0%
+provider that is not a competitive
+market
+
+ align:start position:0%
+market
+ 
+
+ align:start position:0%
+market
+okay so obviously there are huge
+
+ align:start position:0%
+okay so obviously there are huge
+ 
+
+ align:start position:0%
+okay so obviously there are huge
+Monopoly rents being made in these
+
+ align:start position:0%
+Monopoly rents being made in these
+ 
+
+ align:start position:0%
+Monopoly rents being made in these
+markets so what could we do well the
+
+ align:start position:0%
+markets so what could we do well the
+ 
+
+ align:start position:0%
+markets so what could we do well the
+answer is easy we regulate the
+
+ align:start position:0%
+answer is easy we regulate the
+ 
+
+ align:start position:0%
+answer is easy we regulate the
+price we say look we're going to
+
+ align:start position:0%
+price we say look we're going to
+ 
+
+ align:start position:0%
+price we say look we're going to
+regulate the price at a level you know
+
+ align:start position:0%
+regulate the price at a level you know
+ 
+
+ align:start position:0%
+regulate the price at a level you know
+you can't regulate at truly marginal
+
+ align:start position:0%
+you can't regulate at truly marginal
+ 
+
+ align:start position:0%
+you can't regulate at truly marginal
+cost because then no one will enter it's
+
+ align:start position:0%
+cost because then no one will enter it's
+ 
+
+ align:start position:0%
+cost because then no one will enter it's
+the question I got before why would any
+
+ align:start position:0%
+the question I got before why would any
+ 
+
+ align:start position:0%
+the question I got before why would any
+enter but you say look marginal costs
+
+ align:start position:0%
+enter but you say look marginal costs
+ 
+
+ align:start position:0%
+enter but you say look marginal costs
+this is what we do for example with
+
+ align:start position:0%
+this is what we do for example with
+ 
+
+ align:start position:0%
+this is what we do for example with
+electricity and water those are Public
+
+ align:start position:0%
+electricity and water those are Public
+ 
+
+ align:start position:0%
+electricity and water those are Public
+Utilities the way we regulate we say
+
+ align:start position:0%
+Utilities the way we regulate we say
+ 
+
+ align:start position:0%
+Utilities the way we regulate we say
+look you have an acceptable profit rate
+
+ align:start position:0%
+look you have an acceptable profit rate
+ 
+
+ align:start position:0%
+look you have an acceptable profit rate
+will let you make 10% whatever it is and
+
+ align:start position:0%
+will let you make 10% whatever it is and
+ 
+
+ align:start position:0%
+will let you make 10% whatever it is and
+regulate the price at the marginal cost
+
+ align:start position:0%
+regulate the price at the marginal cost
+ 
+
+ align:start position:0%
+regulate the price at the marginal cost
+plus that profit rate you do the same
+
+ align:start position:0%
+plus that profit rate you do the same
+ 
+
+ align:start position:0%
+plus that profit rate you do the same
+thing with Broadband we already do it we
+
+ align:start position:0%
+thing with Broadband we already do it we
+ 
+
+ align:start position:0%
+thing with Broadband we already do it we
+electricity and water we have plenty of
+
+ align:start position:0%
+electricity and water we have plenty of
+ 
+
+ align:start position:0%
+electricity and water we have plenty of
+electricity and water in the US why not
+
+ align:start position:0%
+electricity and water in the US why not
+ 
+
+ align:start position:0%
+electricity and water in the US why not
+just do the same thing in Broadband
+
+ align:start position:0%
+just do the same thing in Broadband
+ 
+
+ align:start position:0%
+just do the same thing in Broadband
+indeed that's what they do in
+
+ align:start position:0%
+indeed that's what they do in
+ 
+
+ align:start position:0%
+indeed that's what they do in
+Europe in Europe they have quite an
+
+ align:start position:0%
+Europe in Europe they have quite an
+ 
+
+ align:start position:0%
+Europe in Europe they have quite an
+interesting approach they they have a
+
+ align:start position:0%
+interesting approach they they have a
+ 
+
+ align:start position:0%
+interesting approach they they have a
+different they regul the price but
+
+ align:start position:0%
+different they regul the price but
+ 
+
+ align:start position:0%
+different they regul the price but
+actually they do a different kind of
+
+ align:start position:0%
+actually they do a different kind of
+ 
+
+ align:start position:0%
+actually they do a different kind of
+regulation in Europe the public owns the
+
+ align:start position:0%
+regulation in Europe the public owns the
+ 
+
+ align:start position:0%
+regulation in Europe the public owns the
+lines and the companies compete on
+
+ align:start position:0%
+lines and the companies compete on
+ 
+
+ align:start position:0%
+lines and the companies compete on
+sending the signal over the lines
+
+ align:start position:0%
+sending the signal over the lines
+ 
+
+ align:start position:0%
+sending the signal over the lines
+it's kind of a clever approach the fixed
+
+ align:start position:0%
+it's kind of a clever approach the fixed
+ 
+
+ align:start position:0%
+it's kind of a clever approach the fixed
+cost part is laying the lines right the
+
+ align:start position:0%
+cost part is laying the lines right the
+ 
+
+ align:start position:0%
+cost part is laying the lines right the
+marginal cost part is setting the signal
+
+ align:start position:0%
+marginal cost part is setting the signal
+ 
+
+ align:start position:0%
+marginal cost part is setting the signal
+over the lines so the government owns
+
+ align:start position:0%
+over the lines so the government owns
+ 
+
+ align:start position:0%
+over the lines so the government owns
+the lines and companies compete on who
+
+ align:start position:0%
+the lines and companies compete on who
+ 
+
+ align:start position:0%
+the lines and companies compete on who
+sends the signals and Broadband if you
+
+ align:start position:0%
+sends the signals and Broadband if you
+ 
+
+ align:start position:0%
+sends the signals and Broadband if you
+ever been to Europe is incredibly cheap
+
+ align:start position:0%
+ever been to Europe is incredibly cheap
+ 
+
+ align:start position:0%
+ever been to Europe is incredibly cheap
+compared to
+
+ align:start position:0%
+compared to
+ 
+
+ align:start position:0%
+compared to
+here okay that's when way to do it or
+
+ align:start position:0%
+here okay that's when way to do it or
+ 
+
+ align:start position:0%
+here okay that's when way to do it or
+alternatively if we don't like that we
+
+ align:start position:0%
+alternatively if we don't like that we
+ 
+
+ align:start position:0%
+alternatively if we don't like that we
+could just regulate the price so why
+
+ align:start position:0%
+could just regulate the price so why
+ 
+
+ align:start position:0%
+could just regulate the price so why
+don't we just do that why don't we just
+
+ align:start position:0%
+don't we just do that why don't we just
+ 
+
+ align:start position:0%
+don't we just do that why don't we just
+do what figure 122
+
+ align:start position:0%
+do what figure 122
+ 
+
+ align:start position:0%
+do what figure 122
+suggest well the answer is because it
+
+ align:start position:0%
+suggest well the answer is because it
+ 
+
+ align:start position:0%
+suggest well the answer is because it
+turns out to be hard because we don't
+
+ align:start position:0%
+turns out to be hard because we don't
+ 
+
+ align:start position:0%
+turns out to be hard because we don't
+get these handouts in the real world
+
+ align:start position:0%
+get these handouts in the real world
+ 
+
+ align:start position:0%
+get these handouts in the real world
+okay in the real world we have to figure
+
+ align:start position:0%
+okay in the real world we have to figure
+ 
+
+ align:start position:0%
+okay in the real world we have to figure
+out what the competitive price is and
+
+ align:start position:0%
+out what the competitive price is and
+ 
+
+ align:start position:0%
+out what the competitive price is and
+that turns out to be hard it turns out
+
+ align:start position:0%
+that turns out to be hard it turns out
+ 
+
+ align:start position:0%
+that turns out to be hard it turns out
+to be hard because we need to know what
+
+ align:start position:0%
+to be hard because we need to know what
+ 
+
+ align:start position:0%
+to be hard because we need to know what
+demand curves look like and what Supply
+
+ align:start position:0%
+demand curves look like and what Supply
+ 
+
+ align:start position:0%
+demand curves look like and what Supply
+curves look like and both are hard to
+
+ align:start position:0%
+curves look like and both are hard to
+ 
+
+ align:start position:0%
+curves look like and both are hard to
+measure let's start with demand
+
+ align:start position:0%
+measure let's start with demand
+ 
+
+ align:start position:0%
+measure let's start with demand
+curves you might say look it's easy to
+
+ align:start position:0%
+curves you might say look it's easy to
+ 
+
+ align:start position:0%
+curves you might say look it's easy to
+measure a demand curve just ask people
+
+ align:start position:0%
+measure a demand curve just ask people
+ 
+
+ align:start position:0%
+measure a demand curve just ask people
+they're willing us to pay you say
+
+ align:start position:0%
+they're willing us to pay you say
+ 
+
+ align:start position:0%
+they're willing us to pay you say
+literally I go and I do a survey of all
+
+ align:start position:0%
+literally I go and I do a survey of all
+ 
+
+ align:start position:0%
+literally I go and I do a survey of all
+the customers are Bron band I say how
+
+ align:start position:0%
+the customers are Bron band I say how
+ 
+
+ align:start position:0%
+the customers are Bron band I say how
+much you willing to pay for each of
+
+ align:start position:0%
+much you willing to pay for each of
+ 
+
+ align:start position:0%
+much you willing to pay for each of
+these different
+
+ align:start position:0%
+these different
+ 
+
+ align:start position:0%
+these different
+options for broadband and then I
+
+ align:start position:0%
+options for broadband and then I
+ 
+
+ align:start position:0%
+options for broadband and then I
+regulate the price the problem is people
+
+ align:start position:0%
+regulate the price the problem is people
+ 
+
+ align:start position:0%
+regulate the price the problem is people
+have no idea what it's worth to
+
+ align:start position:0%
+have no idea what it's worth to
+ 
+
+ align:start position:0%
+have no idea what it's worth to
+them people don't know when you ask
+
+ align:start position:0%
+them people don't know when you ask
+ 
+
+ align:start position:0%
+them people don't know when you ask
+people with stuff's Worth to them and it
+
+ align:start position:0%
+people with stuff's Worth to them and it
+ 
+
+ align:start position:0%
+people with stuff's Worth to them and it
+is something they buy all the time they
+
+ align:start position:0%
+is something they buy all the time they
+ 
+
+ align:start position:0%
+is something they buy all the time they
+don't know if you ask me what an Apple's
+
+ align:start position:0%
+don't know if you ask me what an Apple's
+ 
+
+ align:start position:0%
+don't know if you ask me what an Apple's
+Worth to I say well I've gone to the
+
+ align:start position:0%
+Worth to I say well I've gone to the
+ 
+
+ align:start position:0%
+Worth to I say well I've gone to the
+store and apple you know Apple cost
+
+ align:start position:0%
+store and apple you know Apple cost
+ 
+
+ align:start position:0%
+store and apple you know Apple cost
+that's about 80 cents or a buck for an
+
+ align:start position:0%
+that's about 80 cents or a buck for an
+ 
+
+ align:start position:0%
+that's about 80 cents or a buck for an
+apple you know for a good apple per
+
+ align:start position:0%
+apple you know for a good apple per
+ 
+
+ align:start position:0%
+apple you know for a good apple per
+pound I can get a sense if you said
+
+ align:start position:0%
+pound I can get a sense if you said
+ 
+
+ align:start position:0%
+pound I can get a sense if you said
+would you pay five bucks for an apple
+
+ align:start position:0%
+would you pay five bucks for an apple
+ 
+
+ align:start position:0%
+would you pay five bucks for an apple
+I'd say no but I don't honestly know I
+
+ align:start position:0%
+I'd say no but I don't honestly know I
+ 
+
+ align:start position:0%
+I'd say no but I don't honestly know I
+mean if you said would you pay $1,000 a
+
+ align:start position:0%
+mean if you said would you pay $1,000 a
+ 
+
+ align:start position:0%
+mean if you said would you pay $1,000 a
+month for internet that's too much and
+
+ align:start position:0%
+month for internet that's too much and
+ 
+
+ align:start position:0%
+month for internet that's too much and
+zero sounds cheap but 60 100 150 I I
+
+ align:start position:0%
+zero sounds cheap but 60 100 150 I I
+ 
+
+ align:start position:0%
+zero sounds cheap but 60 100 150 I I
+have a harder time figuring out what's a
+
+ align:start position:0%
+have a harder time figuring out what's a
+ 
+
+ align:start position:0%
+have a harder time figuring out what's a
+fair price okay this is obviously an
+
+ align:start position:0%
+fair price okay this is obviously an
+ 
+
+ align:start position:0%
+fair price okay this is obviously an
+even bigger problem when you think not
+
+ align:start position:0%
+even bigger problem when you think not
+ 
+
+ align:start position:0%
+even bigger problem when you think not
+just about regulating broad Bend but
+
+ align:start position:0%
+just about regulating broad Bend but
+ 
+
+ align:start position:0%
+just about regulating broad Bend but
+they regulating things like the
+
+ align:start position:0%
+they regulating things like the
+ 
+
+ align:start position:0%
+they regulating things like the
+environment regulating things like U
+
+ align:start position:0%
+environment regulating things like U
+ 
+
+ align:start position:0%
+environment regulating things like U
+stopping oil spills or global warming so
+
+ align:start position:0%
+stopping oil spills or global warming so
+ 
+
+ align:start position:0%
+stopping oil spills or global warming so
+for example if you ask people what
+
+ align:start position:0%
+for example if you ask people what
+ 
+
+ align:start position:0%
+for example if you ask people what
+environmental benefits are worth they
+
+ align:start position:0%
+environmental benefits are worth they
+ 
+
+ align:start position:0%
+environmental benefits are worth they
+have no idea so for example if you ask
+
+ align:start position:0%
+have no idea so for example if you ask
+ 
+
+ align:start position:0%
+have no idea so for example if you ask
+people what it's worth to save the Grand
+
+ align:start position:0%
+people what it's worth to save the Grand
+ 
+
+ align:start position:0%
+people what it's worth to save the Grand
+Canyon and you first ask as a standalone
+
+ align:start position:0%
+Canyon and you first ask as a standalone
+ 
+
+ align:start position:0%
+Canyon and you first ask as a standalone
+question and then separately ask as one
+
+ align:start position:0%
+question and then separately ask as one
+ 
+
+ align:start position:0%
+question and then separately ask as one
+of five questions in the second case
+
+ align:start position:0%
+of five questions in the second case
+ 
+
+ align:start position:0%
+of five questions in the second case
+people give a value that's one as big
+
+ align:start position:0%
+people give a value that's one as big
+ 
+
+ align:start position:0%
+people give a value that's one as big
+shouldn't matter right just your value
+
+ align:start position:0%
+shouldn't matter right just your value
+ 
+
+ align:start position:0%
+shouldn't matter right just your value
+but the problem is they don't know um if
+
+ align:start position:0%
+but the problem is they don't know um if
+ 
+
+ align:start position:0%
+but the problem is they don't know um if
+you ask people how much they'll pay to
+
+ align:start position:0%
+you ask people how much they'll pay to
+ 
+
+ align:start position:0%
+you ask people how much they'll pay to
+save a whale and save a seal if you ask
+
+ align:start position:0%
+save a whale and save a seal if you ask
+ 
+
+ align:start position:0%
+save a whale and save a seal if you ask
+them how they'll pay to to say a to save
+
+ align:start position:0%
+them how they'll pay to to say a to save
+ 
+
+ align:start position:0%
+them how they'll pay to to say a to save
+a whale and save a seal they'll pay $172
+
+ align:start position:0%
+a whale and save a seal they'll pay $172
+ 
+
+ align:start position:0%
+a whale and save a seal they'll pay $172
+to save a whale and $85 save a seal that
+
+ align:start position:0%
+to save a whale and $85 save a seal that
+ 
+
+ align:start position:0%
+to save a whale and $85 save a seal that
+make sense Wells are bigger okay if you
+
+ align:start position:0%
+make sense Wells are bigger okay if you
+ 
+
+ align:start position:0%
+make sense Wells are bigger okay if you
+ask the order reversed
+
+ align:start position:0%
+ask the order reversed
+ 
+
+ align:start position:0%
+ask the order reversed
+and say that um how much save a seal and
+
+ align:start position:0%
+and say that um how much save a seal and
+ 
+
+ align:start position:0%
+and say that um how much save a seal and
+how much save a whale people say they're
+
+ align:start position:0%
+how much save a whale people say they're
+ 
+
+ align:start position:0%
+how much save a whale people say they're
+about worth the
+
+ align:start position:0%
+about worth the
+ 
+
+ align:start position:0%
+about worth the
+same okay um if you ask people how much
+
+ align:start position:0%
+same okay um if you ask people how much
+ 
+
+ align:start position:0%
+same okay um if you ask people how much
+they'll pay to save a thousand birds or
+
+ align:start position:0%
+they'll pay to save a thousand birds or
+ 
+
+ align:start position:0%
+they'll pay to save a thousand birds or
+a million birds or a billion Birds they
+
+ align:start position:0%
+a million birds or a billion Birds they
+ 
+
+ align:start position:0%
+a million birds or a billion Birds they
+give the same answer none of these
+
+ align:start position:0%
+give the same answer none of these
+ 
+
+ align:start position:0%
+give the same answer none of these
+things are consistent with any form of
+
+ align:start position:0%
+things are consistent with any form of
+ 
+
+ align:start position:0%
+things are consistent with any form of
+utility that we write down in this class
+
+ align:start position:0%
+utility that we write down in this class
+ 
+
+ align:start position:0%
+utility that we write down in this class
+people clearly don't know so it's hard
+
+ align:start position:0%
+people clearly don't know so it's hard
+ 
+
+ align:start position:0%
+people clearly don't know so it's hard
+to measure demand it's easy to measure
+
+ align:start position:0%
+to measure demand it's easy to measure
+ 
+
+ align:start position:0%
+to measure demand it's easy to measure
+demand when there's a price signal when
+
+ align:start position:0%
+demand when there's a price signal when
+ 
+
+ align:start position:0%
+demand when there's a price signal when
+you see different prices and you see
+
+ align:start position:0%
+you see different prices and you see
+ 
+
+ align:start position:0%
+you see different prices and you see
+well want different prices but when you
+
+ align:start position:0%
+well want different prices but when you
+ 
+
+ align:start position:0%
+well want different prices but when you
+try to create a new market and you have
+
+ align:start position:0%
+try to create a new market and you have
+ 
+
+ align:start position:0%
+try to create a new market and you have
+to rely on willingness to pay that's
+
+ align:start position:0%
+to rely on willingness to pay that's
+ 
+
+ align:start position:0%
+to rely on willingness to pay that's
+hard that's the first problem demand
+
+ align:start position:0%
+hard that's the first problem demand
+ 
+
+ align:start position:0%
+hard that's the first problem demand
+curves are hard to draw the second
+
+ align:start position:0%
+curves are hard to draw the second
+ 
+
+ align:start position:0%
+curves are hard to draw the second
+problem is Supply curves are hard now
+
+ align:start position:0%
+problem is Supply curves are hard now
+ 
+
+ align:start position:0%
+problem is Supply curves are hard now
+you might say here well it's easy you
+
+ align:start position:0%
+you might say here well it's easy you
+ 
+
+ align:start position:0%
+you might say here well it's easy you
+just go to the firm and you say well
+
+ align:start position:0%
+just go to the firm and you say well
+ 
+
+ align:start position:0%
+just go to the firm and you say well
+give me your marginal
+
+ align:start position:0%
+give me your marginal
+ 
+
+ align:start position:0%
+give me your marginal
+cost and that's great and what does the
+
+ align:start position:0%
+cost and that's great and what does the
+ 
+
+ align:start position:0%
+cost and that's great and what does the
+firm
+
+ align:start position:0%
+firm
+ 
+
+ align:start position:0%
+firm
+say when you say give me Marin cost they
+
+ align:start position:0%
+say when you say give me Marin cost they
+ 
+
+ align:start position:0%
+say when you say give me Marin cost they
+say sure what do they give
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you if you're running a firm what would
+
+ align:start position:0%
+you if you're running a firm what would
+ 
+
+ align:start position:0%
+you if you're running a firm what would
+you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah You' give them the biggest possible
+
+ align:start position:0%
+yeah You' give them the biggest possible
+ 
+
+ align:start position:0%
+yeah You' give them the biggest possible
+margin cost you could ever justify in
+
+ align:start position:0%
+margin cost you could ever justify in
+ 
+
+ align:start position:0%
+margin cost you could ever justify in
+the world remember my story about the SE
+
+ align:start position:0%
+the world remember my story about the SE
+ 
+
+ align:start position:0%
+the world remember my story about the SE
+about the CEO wanted his own plane
+
+ align:start position:0%
+about the CEO wanted his own plane
+ 
+
+ align:start position:0%
+about the CEO wanted his own plane
+that's nothing compared to this okay the
+
+ align:start position:0%
+that's nothing compared to this okay the
+ 
+
+ align:start position:0%
+that's nothing compared to this okay the
+problem is you're trying to regulate an
+
+ align:start position:0%
+problem is you're trying to regulate an
+ 
+
+ align:start position:0%
+problem is you're trying to regulate an
+industry that knows more about itself
+
+ align:start position:0%
+industry that knows more about itself
+ 
+
+ align:start position:0%
+industry that knows more about itself
+than you do so it's hard to know what
+
+ align:start position:0%
+than you do so it's hard to know what
+ 
+
+ align:start position:0%
+than you do so it's hard to know what
+Supply is
+
+ align:start position:0%
+Supply is
+ 
+
+ align:start position:0%
+Supply is
+either so the problem with regulation is
+
+ align:start position:0%
+either so the problem with regulation is
+ 
+
+ align:start position:0%
+either so the problem with regulation is
+that you're you can't just draw these
+
+ align:start position:0%
+that you're you can't just draw these
+ 
+
+ align:start position:0%
+that you're you can't just draw these
+neat diagrams you have to guess at them
+
+ align:start position:0%
+neat diagrams you have to guess at them
+ 
+
+ align:start position:0%
+neat diagrams you have to guess at them
+which is fine except if you get it wrong
+
+ align:start position:0%
+which is fine except if you get it wrong
+ 
+
+ align:start position:0%
+which is fine except if you get it wrong
+you can make things worse take a look at
+
+ align:start position:0%
+you can make things worse take a look at
+ 
+
+ align:start position:0%
+you can make things worse take a look at
+figure
+
+ align:start position:0%
+figure
+ 
+
+ align:start position:0%
+figure
+123 imagine the government
+
+ align:start position:0%
+123 imagine the government
+ 
+
+ align:start position:0%
+123 imagine the government
+decided that it was set the price at 10
+
+ align:start position:0%
+decided that it was set the price at 10
+ 
+
+ align:start position:0%
+decided that it was set the price at 10
+it had some base setting theice it it
+
+ align:start position:0%
+it had some base setting theice it it
+ 
+
+ align:start position:0%
+it had some base setting theice it it
+got its own demand curves Supply curves
+
+ align:start position:0%
+got its own demand curves Supply curves
+ 
+
+ align:start position:0%
+got its own demand curves Supply curves
+it decided 10 was the competitive price
+
+ align:start position:0%
+it decided 10 was the competitive price
+ 
+
+ align:start position:0%
+it decided 10 was the competitive price
+whereas we know the right competitive
+
+ align:start position:0%
+whereas we know the right competitive
+ 
+
+ align:start position:0%
+whereas we know the right competitive
+price is 16 what happens this Market
+
+ align:start position:0%
+price is 16 what happens this Market
+ 
+
+ align:start position:0%
+price is 16 what happens this Market
+sets the price at 10 well at a price of
+
+ align:start position:0%
+sets the price at 10 well at a price of
+ 
+
+ align:start position:0%
+sets the price at 10 well at a price of
+10 the optimal Monopoly choice you
+
+ align:start position:0%
+10 the optimal Monopoly choice you
+ 
+
+ align:start position:0%
+10 the optimal Monopoly choice you
+should solve this for yourself is to
+
+ align:start position:0%
+should solve this for yourself is to
+ 
+
+ align:start position:0%
+should solve this for yourself is to
+produce five
+
+ align:start position:0%
+produce five
+ 
+
+ align:start position:0%
+produce five
+units at a price of 10 well that creates
+
+ align:start position:0%
+units at a price of 10 well that creates
+ 
+
+ align:start position:0%
+units at a price of 10 well that creates
+even bigger dead weight loss than if you
+
+ align:start position:0%
+even bigger dead weight loss than if you
+ 
+
+ align:start position:0%
+even bigger dead weight loss than if you
+just let the Monopoly rip you've lost an
+
+ align:start position:0%
+just let the Monopoly rip you've lost an
+ 
+
+ align:start position:0%
+just let the Monopoly rip you've lost an
+extra that extra shaded
+
+ align:start position:0%
+extra that extra shaded
+ 
+
+ align:start position:0%
+extra that extra shaded
+area Okay from regulating the price at
+
+ align:start position:0%
+area Okay from regulating the price at
+ 
+
+ align:start position:0%
+area Okay from regulating the price at
+10 so the government's made things worse
+
+ align:start position:0%
+10 so the government's made things worse
+ 
+
+ align:start position:0%
+10 so the government's made things worse
+it could be even worse if you're at the
+
+ align:start position:0%
+it could be even worse if you're at the
+ 
+
+ align:start position:0%
+it could be even worse if you're at the
+price low enough you could just kill the
+
+ align:start position:0%
+price low enough you could just kill the
+ 
+
+ align:start position:0%
+price low enough you could just kill the
+industry the industry can say I'm not
+
+ align:start position:0%
+industry the industry can say I'm not
+ 
+
+ align:start position:0%
+industry the industry can say I'm not
+going to form at all because the price
+
+ align:start position:0%
+going to form at all because the price
+ 
+
+ align:start position:0%
+going to form at all because the price
+isn't is too low how would you know the
+
+ align:start position:0%
+isn't is too low how would you know the
+ 
+
+ align:start position:0%
+isn't is too low how would you know the
+industry didn't exist how would you know
+
+ align:start position:0%
+industry didn't exist how would you know
+ 
+
+ align:start position:0%
+industry didn't exist how would you know
+the regulations killed
+
+ align:start position:0%
+the regulations killed
+ 
+
+ align:start position:0%
+the regulations killed
+it okay so
+
+ align:start position:0%
+it okay so
+ 
+
+ align:start position:0%
+it okay so
+basically regulation is tricky there's a
+
+ align:start position:0%
+basically regulation is tricky there's a
+ 
+
+ align:start position:0%
+basically regulation is tricky there's a
+recent research paper I learned about
+
+ align:start position:0%
+recent research paper I learned about
+ 
+
+ align:start position:0%
+recent research paper I learned about
+where someone looked at what happened
+
+ align:start position:0%
+where someone looked at what happened
+ 
+
+ align:start position:0%
+where someone looked at what happened
+when the Food and Drug Administration
+
+ align:start position:0%
+when the Food and Drug Administration
+ 
+
+ align:start position:0%
+when the Food and Drug Administration
+which regulates medical devices loosened
+
+ align:start position:0%
+which regulates medical devices loosened
+ 
+
+ align:start position:0%
+which regulates medical devices loosened
+the regulation categories of medical
+
+ align:start position:0%
+the regulation categories of medical
+ 
+
+ align:start position:0%
+the regulation categories of medical
+devices you want the regular devices
+
+ align:start position:0%
+devices you want the regular devices
+ 
+
+ align:start position:0%
+devices you want the regular devices
+right you want there to be sa you
+
+ align:start position:0%
+right you want there to be sa you
+ 
+
+ align:start position:0%
+right you want there to be sa you
+worried about safety you want some
+
+ align:start position:0%
+worried about safety you want some
+ 
+
+ align:start position:0%
+worried about safety you want some
+regulation when they loosen the
+
+ align:start position:0%
+regulation when they loosen the
+ 
+
+ align:start position:0%
+regulation when they loosen the
+regulations they found Innovation went
+
+ align:start position:0%
+regulations they found Innovation went
+ 
+
+ align:start position:0%
+regulations they found Innovation went
+up a th% and there was no worst safety
+
+ align:start position:0%
+up a th% and there was no worst safety
+ 
+
+ align:start position:0%
+up a th% and there was no worst safety
+clearly they were overregulation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh what the tradeoff is with government
+
+ align:start position:0%
+uh what the tradeoff is with government
+ 
+
+ align:start position:0%
+uh what the tradeoff is with government
+intervention and this is sort of the
+
+ align:start position:0%
+intervention and this is sort of the
+ 
+
+ align:start position:0%
+intervention and this is sort of the
+point of my entire course
+
+ align:start position:0%
+point of my entire course
+ 
+
+ align:start position:0%
+point of my entire course
+1441 which is markets typically feature
+
+ align:start position:0%
+1441 which is markets typically feature
+ 
+
+ align:start position:0%
+1441 which is markets typically feature
+market failure there's honestly truly
+
+ align:start position:0%
+market failure there's honestly truly
+ 
+
+ align:start position:0%
+market failure there's honestly truly
+almost no Market in America doesn't
+
+ align:start position:0%
+almost no Market in America doesn't
+ 
+
+ align:start position:0%
+almost no Market in America doesn't
+feature market failure of some type if
+
+ align:start position:0%
+feature market failure of some type if
+ 
+
+ align:start position:0%
+feature market failure of some type if
+there's a market failure then in theory
+
+ align:start position:0%
+there's a market failure then in theory
+ 
+
+ align:start position:0%
+there's a market failure then in theory
+the government can make it better in
+
+ align:start position:0%
+the government can make it better in
+ 
+
+ align:start position:0%
+the government can make it better in
+practice it's not clear it
+
+ align:start position:0%
+practice it's not clear it
+ 
+
+ align:start position:0%
+practice it's not clear it
+will so the fact there's market failure
+
+ align:start position:0%
+will so the fact there's market failure
+ 
+
+ align:start position:0%
+will so the fact there's market failure
+does not
+
+ align:start position:0%
+does not
+ 
+
+ align:start position:0%
+does not
+justify you saying there that a
+
+ align:start position:0%
+justify you saying there that a
+ 
+
+ align:start position:0%
+justify you saying there that a
+government regulation it better it might
+
+ align:start position:0%
+government regulation it better it might
+ 
+
+ align:start position:0%
+government regulation it better it might
+make it better it justifies considering
+
+ align:start position:0%
+make it better it justifies considering
+ 
+
+ align:start position:0%
+make it better it justifies considering
+the government regulation but you still
+
+ align:start position:0%
+the government regulation but you still
+ 
+
+ align:start position:0%
+the government regulation but you still
+don't know it makes it better until you
+
+ align:start position:0%
+don't know it makes it better until you
+ 
+
+ align:start position:0%
+don't know it makes it better until you
+do the careful empirical
+
+ align:start position:0%
+do the careful empirical
+ 
+
+ align:start position:0%
+do the careful empirical
+analysis okay questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that now let's say you're worried about
+
+ align:start position:0%
+that now let's say you're worried about
+ 
+
+ align:start position:0%
+that now let's say you're worried about
+that and you're worried you say look I'm
+
+ align:start position:0%
+that and you're worried you say look I'm
+ 
+
+ align:start position:0%
+that and you're worried you say look I'm
+really worried about regulating but
+
+ align:start position:0%
+really worried about regulating but
+ 
+
+ align:start position:0%
+really worried about regulating but
+there's this Monopoly and it's consumers
+
+ align:start position:0%
+there's this Monopoly and it's consumers
+ 
+
+ align:start position:0%
+there's this Monopoly and it's consumers
+are losing out and I don't know what to
+
+ align:start position:0%
+are losing out and I don't know what to
+ 
+
+ align:start position:0%
+are losing out and I don't know what to
+do well there's another option
+
+ align:start position:0%
+do well there's another option
+ 
+
+ align:start position:0%
+do well there's another option
+governments have which which is
+
+ align:start position:0%
+governments have which which is
+ 
+
+ align:start position:0%
+governments have which which is
+governments rather than creating an
+
+ align:start position:0%
+governments rather than creating an
+ 
+
+ align:start position:0%
+governments rather than creating an
+creating Monopoly in the way it does up
+
+ align:start position:0%
+creating Monopoly in the way it does up
+ 
+
+ align:start position:0%
+creating Monopoly in the way it does up
+there governments can reduce Monopoly by
+
+ align:start position:0%
+there governments can reduce Monopoly by
+ 
+
+ align:start position:0%
+there governments can reduce Monopoly by
+injecting competition into markets and
+
+ align:start position:0%
+injecting competition into markets and
+ 
+
+ align:start position:0%
+injecting competition into markets and
+there's no better example of that than
+
+ align:start position:0%
+there's no better example of that than
+ 
+
+ align:start position:0%
+there's no better example of that than
+the market for
+
+ align:start position:0%
+the market for
+ 
+
+ align:start position:0%
+the market for
+Education take a look at figure uh
+
+ align:start position:0%
+Education take a look at figure uh
+ 
+
+ align:start position:0%
+Education take a look at figure uh
+124 figure 124 is from my textbook it
+
+ align:start position:0%
+124 figure 124 is from my textbook it
+ 
+
+ align:start position:0%
+124 figure 124 is from my textbook it
+shows educational
+
+ align:start position:0%
+shows educational
+ 
+
+ align:start position:0%
+shows educational
+spending in Blue by each country per
+
+ align:start position:0%
+spending in Blue by each country per
+ 
+
+ align:start position:0%
+spending in Blue by each country per
+student so the US is about
+
+ align:start position:0%
+student so the US is about
+ 
+
+ align:start position:0%
+student so the US is about
+almost 12,000 per student the Czech
+
+ align:start position:0%
+almost 12,000 per student the Czech
+ 
+
+ align:start position:0%
+almost 12,000 per student the Czech
+Republic is about less than 6,000 per
+
+ align:start position:0%
+Republic is about less than 6,000 per
+ 
+
+ align:start position:0%
+Republic is about less than 6,000 per
+student in Orange it shows that
+
+ align:start position:0%
+student in Orange it shows that
+ 
+
+ align:start position:0%
+student in Orange it shows that
+country's performance on an
+
+ align:start position:0%
+country's performance on an
+ 
+
+ align:start position:0%
+country's performance on an
+international math
+
+ align:start position:0%
+international math
+ 
+
+ align:start position:0%
+international math
+exam Czech Republic does better than the
+
+ align:start position:0%
+exam Czech Republic does better than the
+ 
+
+ align:start position:0%
+exam Czech Republic does better than the
+US indeed the US despite spending by far
+
+ align:start position:0%
+US indeed the US despite spending by far
+ 
+
+ align:start position:0%
+US indeed the US despite spending by far
+the most per capita on education it's
+
+ align:start position:0%
+the most per capita on education it's
+ 
+
+ align:start position:0%
+the most per capita on education it's
+pretty mediocre in international
+
+ align:start position:0%
+pretty mediocre in international
+ 
+
+ align:start position:0%
+pretty mediocre in international
+comparisons of Education
+
+ align:start position:0%
+comparisons of Education
+ 
+
+ align:start position:0%
+comparisons of Education
+systems now there's lots of reasons that
+
+ align:start position:0%
+systems now there's lots of reasons that
+ 
+
+ align:start position:0%
+systems now there's lots of reasons that
+could be but clearly our schools are not
+
+ align:start position:0%
+could be but clearly our schools are not
+ 
+
+ align:start position:0%
+could be but clearly our schools are not
+uh getting it done are not
+
+ align:start position:0%
+uh getting it done are not
+ 
+
+ align:start position:0%
+uh getting it done are not
+delivering return for the proper return
+
+ align:start position:0%
+delivering return for the proper return
+ 
+
+ align:start position:0%
+delivering return for the proper return
+for our
+
+ align:start position:0%
+for our
+ 
+
+ align:start position:0%
+for our
+dollar one solution to that is say well
+
+ align:start position:0%
+dollar one solution to that is say well
+ 
+
+ align:start position:0%
+dollar one solution to that is say well
+part of the reason they're not is
+
+ align:start position:0%
+part of the reason they're not is
+ 
+
+ align:start position:0%
+part of the reason they're not is
+because schools are monopolies how many
+
+ align:start position:0%
+because schools are monopolies how many
+ 
+
+ align:start position:0%
+because schools are monopolies how many
+you went to public school how many you
+
+ align:start position:0%
+you went to public school how many you
+ 
+
+ align:start position:0%
+you went to public school how many you
+went to most of you okay public schools
+
+ align:start position:0%
+went to most of you okay public schools
+ 
+
+ align:start position:0%
+went to most of you okay public schools
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+monopolies I live in lexingon my kids if
+
+ align:start position:0%
+monopolies I live in lexingon my kids if
+ 
+
+ align:start position:0%
+monopolies I live in lexingon my kids if
+they want to go public high school go to
+
+ align:start position:0%
+they want to go public high school go to
+ 
+
+ align:start position:0%
+they want to go public high school go to
+lexingon high school it's not like can
+
+ align:start position:0%
+lexingon high school it's not like can
+ 
+
+ align:start position:0%
+lexingon high school it's not like can
+say I'd prefer you know to go to brain
+
+ align:start position:0%
+say I'd prefer you know to go to brain
+ 
+
+ align:start position:0%
+say I'd prefer you know to go to brain
+tree high school instead I don't have
+
+ align:start position:0%
+tree high school instead I don't have
+ 
+
+ align:start position:0%
+tree high school instead I don't have
+that choice I have no choice it's a
+
+ align:start position:0%
+that choice I have no choice it's a
+ 
+
+ align:start position:0%
+that choice I have no choice it's a
+monopoly now in some cities it's not
+
+ align:start position:0%
+monopoly now in some cities it's not
+ 
+
+ align:start position:0%
+monopoly now in some cities it's not
+quite right some cities do have a choice
+
+ align:start position:0%
+quite right some cities do have a choice
+ 
+
+ align:start position:0%
+quite right some cities do have a choice
+of say Elementary School some of you may
+
+ align:start position:0%
+of say Elementary School some of you may
+ 
+
+ align:start position:0%
+of say Elementary School some of you may
+have if you ever grew up you grew up in
+
+ align:start position:0%
+have if you ever grew up you grew up in
+ 
+
+ align:start position:0%
+have if you ever grew up you grew up in
+Chicago or Cambridge or some cities
+
+ align:start position:0%
+Chicago or Cambridge or some cities
+ 
+
+ align:start position:0%
+Chicago or Cambridge or some cities
+where you can choose your elementary
+
+ align:start position:0%
+where you can choose your elementary
+ 
+
+ align:start position:0%
+where you can choose your elementary
+school but typically you can't choose
+
+ align:start position:0%
+school but typically you can't choose
+ 
+
+ align:start position:0%
+school but typically you can't choose
+the choice is not a feature of um of uh
+
+ align:start position:0%
+the choice is not a feature of um of uh
+ 
+
+ align:start position:0%
+the choice is not a feature of um of uh
+Public Schools so the idea is since the
+
+ align:start position:0%
+Public Schools so the idea is since the
+ 
+
+ align:start position:0%
+Public Schools so the idea is since the
+fear is since we've created these
+
+ align:start position:0%
+fear is since we've created these
+ 
+
+ align:start position:0%
+fear is since we've created these
+monopolies have we created inefficient
+
+ align:start position:0%
+monopolies have we created inefficient
+ 
+
+ align:start position:0%
+monopolies have we created inefficient
+schools that not delivering proper
+
+ align:start position:0%
+schools that not delivering proper
+ 
+
+ align:start position:0%
+schools that not delivering proper
+benefits cuz remember I said when
+
+ align:start position:0%
+benefits cuz remember I said when
+ 
+
+ align:start position:0%
+benefits cuz remember I said when
+Monopoly they can make profits well if
+
+ align:start position:0%
+Monopoly they can make profits well if
+ 
+
+ align:start position:0%
+Monopoly they can make profits well if
+it's a monopoly where you can't make
+
+ align:start position:0%
+it's a monopoly where you can't make
+ 
+
+ align:start position:0%
+it's a monopoly where you can't make
+profits but there's no competition the
+
+ align:start position:0%
+profits but there's no competition the
+ 
+
+ align:start position:0%
+profits but there's no competition the
+other way can come out is just not doing
+
+ align:start position:0%
+other way can come out is just not doing
+ 
+
+ align:start position:0%
+other way can come out is just not doing
+a good not being efficient there's no
+
+ align:start position:0%
+a good not being efficient there's no
+ 
+
+ align:start position:0%
+a good not being efficient there's no
+incentive to efficient if you a monopoly
+
+ align:start position:0%
+incentive to efficient if you a monopoly
+ 
+
+ align:start position:0%
+incentive to efficient if you a monopoly
+we could set your
+
+ align:start position:0%
+we could set your
+ 
+
+ align:start position:0%
+we could set your
+price then there's every incentive to be
+
+ align:start position:0%
+price then there's every incentive to be
+ 
+
+ align:start position:0%
+price then there's every incentive to be
+efficient because every dollar
+
+ align:start position:0%
+efficient because every dollar
+ 
+
+ align:start position:0%
+efficient because every dollar
+efficiency gains a dollar profits but
+
+ align:start position:0%
+efficiency gains a dollar profits but
+ 
+
+ align:start position:0%
+efficiency gains a dollar profits but
+imagine your Monopoly that can't set
+
+ align:start position:0%
+imagine your Monopoly that can't set
+ 
+
+ align:start position:0%
+imagine your Monopoly that can't set
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+price why work so hard to be
+
+ align:start position:0%
+price why work so hard to be
+ 
+
+ align:start position:0%
+price why work so hard to be
+efficient right what's the pressure on
+
+ align:start position:0%
+efficient right what's the pressure on
+ 
+
+ align:start position:0%
+efficient right what's the pressure on
+you to do so why not have a slightly
+
+ align:start position:0%
+you to do so why not have a slightly
+ 
+
+ align:start position:0%
+you to do so why not have a slightly
+easier life and that's the concerns
+
+ align:start position:0%
+easier life and that's the concerns
+ 
+
+ align:start position:0%
+easier life and that's the concerns
+happen with schools so that's why
+
+ align:start position:0%
+happen with schools so that's why
+ 
+
+ align:start position:0%
+happen with schools so that's why
+there's a big move introduce competition
+
+ align:start position:0%
+there's a big move introduce competition
+ 
+
+ align:start position:0%
+there's a big move introduce competition
+into the US public school
+
+ align:start position:0%
+into the US public school
+ 
+
+ align:start position:0%
+into the US public school
+system okay one way to do so as I said
+
+ align:start position:0%
+system okay one way to do so as I said
+ 
+
+ align:start position:0%
+system okay one way to do so as I said
+some schools have introduced what we
+
+ align:start position:0%
+some schools have introduced what we
+ 
+
+ align:start position:0%
+some schools have introduced what we
+call public school choice they've
+
+ align:start position:0%
+call public school choice they've
+ 
+
+ align:start position:0%
+call public school choice they've
+allowed students to choose across public
+
+ align:start position:0%
+allowed students to choose across public
+ 
+
+ align:start position:0%
+allowed students to choose across public
+schools and the dollars follow the
+
+ align:start position:0%
+schools and the dollars follow the
+ 
+
+ align:start position:0%
+schools and the dollars follow the
+students so if you're a shitty
+
+ align:start position:0%
+students so if you're a shitty
+ 
+
+ align:start position:0%
+students so if you're a shitty
+Elementary School and folks leave you
+
+ align:start position:0%
+Elementary School and folks leave you
+ 
+
+ align:start position:0%
+Elementary School and folks leave you
+get less money so suddenly it matters
+
+ align:start position:0%
+get less money so suddenly it matters
+ 
+
+ align:start position:0%
+get less money so suddenly it matters
+quality matters for how much money you
+
+ align:start position:0%
+quality matters for how much money you
+ 
+
+ align:start position:0%
+quality matters for how much money you
+have to function and that's uh that's
+
+ align:start position:0%
+have to function and that's uh that's
+ 
+
+ align:start position:0%
+have to function and that's uh that's
+one approach that's been tried generally
+
+ align:start position:0%
+one approach that's been tried generally
+ 
+
+ align:start position:0%
+one approach that's been tried generally
+does not seem to show it has a huge
+
+ align:start position:0%
+does not seem to show it has a huge
+ 
+
+ align:start position:0%
+does not seem to show it has a huge
+effect on student performance
+
+ align:start position:0%
+effect on student performance
+ 
+
+ align:start position:0%
+effect on student performance
+the other approach that's been tried is
+
+ align:start position:0%
+the other approach that's been tried is
+ 
+
+ align:start position:0%
+the other approach that's been tried is
+to set up alternatives to the
+
+ align:start position:0%
+to set up alternatives to the
+ 
+
+ align:start position:0%
+to set up alternatives to the
+traditional public school and the most
+
+ align:start position:0%
+traditional public school and the most
+ 
+
+ align:start position:0%
+traditional public school and the most
+popular those most well known as charter
+
+ align:start position:0%
+popular those most well known as charter
+ 
+
+ align:start position:0%
+popular those most well known as charter
+schools did any goes guys go to Charter
+
+ align:start position:0%
+schools did any goes guys go to Charter
+ 
+
+ align:start position:0%
+schools did any goes guys go to Charter
+School yeah there's uh charter schools
+
+ align:start position:0%
+School yeah there's uh charter schools
+ 
+
+ align:start position:0%
+School yeah there's uh charter schools
+are essentially non-traditional
+
+ align:start position:0%
+are essentially non-traditional
+ 
+
+ align:start position:0%
+are essentially non-traditional
+Alternatives that are publicly funded so
+
+ align:start position:0%
+Alternatives that are publicly funded so
+ 
+
+ align:start position:0%
+Alternatives that are publicly funded so
+idea is you've got your Lex in high
+
+ align:start position:0%
+idea is you've got your Lex in high
+ 
+
+ align:start position:0%
+idea is you've got your Lex in high
+school and you've got your you know
+
+ align:start position:0%
+school and you've got your you know
+ 
+
+ align:start position:0%
+school and you've got your you know
+achievement Academy charter school and
+
+ align:start position:0%
+achievement Academy charter school and
+ 
+
+ align:start position:0%
+achievement Academy charter school and
+that Charter School often they're
+
+ align:start position:0%
+that Charter School often they're
+ 
+
+ align:start position:0%
+that Charter School often they're
+for-profit sometimes they're nonprofit
+
+ align:start position:0%
+for-profit sometimes they're nonprofit
+ 
+
+ align:start position:0%
+for-profit sometimes they're nonprofit
+are essentially Place students can go
+
+ align:start position:0%
+are essentially Place students can go
+ 
+
+ align:start position:0%
+are essentially Place students can go
+they're still funded by the public
+
+ align:start position:0%
+they're still funded by the public
+ 
+
+ align:start position:0%
+they're still funded by the public
+sector but they are not abiding by the
+
+ align:start position:0%
+sector but they are not abiding by the
+ 
+
+ align:start position:0%
+sector but they are not abiding by the
+same set of rules necessarily for
+
+ align:start position:0%
+same set of rules necessarily for
+ 
+
+ align:start position:0%
+same set of rules necessarily for
+instance they don't have to hire
+
+ align:start position:0%
+instance they don't have to hire
+ 
+
+ align:start position:0%
+instance they don't have to hire
+unionized teachers Etc and they provide
+
+ align:start position:0%
+unionized teachers Etc and they provide
+ 
+
+ align:start position:0%
+unionized teachers Etc and they provide
+a competitive alternative and in fact
+
+ align:start position:0%
+a competitive alternative and in fact
+ 
+
+ align:start position:0%
+a competitive alternative and in fact
+charter schools have been shown by my
+
+ align:start position:0%
+charter schools have been shown by my
+ 
+
+ align:start position:0%
+charter schools have been shown by my
+colleagues here MIT who've done the
+
+ align:start position:0%
+colleagues here MIT who've done the
+ 
+
+ align:start position:0%
+colleagues here MIT who've done the
+leading research in the world to be
+
+ align:start position:0%
+leading research in the world to be
+ 
+
+ align:start position:0%
+leading research in the world to be
+generally a very effective alternative
+
+ align:start position:0%
+generally a very effective alternative
+ 
+
+ align:start position:0%
+generally a very effective alternative
+to private to public schools that
+
+ align:start position:0%
+to private to public schools that
+ 
+
+ align:start position:0%
+to private to public schools that
+students who go to Charter School when
+
+ align:start position:0%
+students who go to Charter School when
+ 
+
+ align:start position:0%
+students who go to Charter School when
+you put in a charter school students do
+
+ align:start position:0%
+you put in a charter school students do
+ 
+
+ align:start position:0%
+you put in a charter school students do
+better okay the competition is working
+
+ align:start position:0%
+better okay the competition is working
+ 
+
+ align:start position:0%
+better okay the competition is working
+in the context of Education by having
+
+ align:start position:0%
+in the context of Education by having
+ 
+
+ align:start position:0%
+in the context of Education by having
+these educational
+
+ align:start position:0%
+these educational
+ 
+
+ align:start position:0%
+these educational
+Alternatives so here's the case and in
+
+ align:start position:0%
+Alternatives so here's the case and in
+ 
+
+ align:start position:0%
+Alternatives so here's the case and in
+particular let me say in particular for
+
+ align:start position:0%
+particular let me say in particular for
+ 
+
+ align:start position:0%
+particular let me say in particular for
+disadvantaged students the group that
+
+ align:start position:0%
+disadvantaged students the group that
+ 
+
+ align:start position:0%
+disadvantaged students the group that
+benefits the most from charter schools
+
+ align:start position:0%
+benefits the most from charter schools
+ 
+
+ align:start position:0%
+benefits the most from charter schools
+are minorities under and and low-income
+
+ align:start position:0%
+are minorities under and and low-income
+ 
+
+ align:start position:0%
+are minorities under and and low-income
+students they benefit the most from
+
+ align:start position:0%
+students they benefit the most from
+ 
+
+ align:start position:0%
+students they benefit the most from
+having this alternative so here's an
+
+ align:start position:0%
+having this alternative so here's an
+ 
+
+ align:start position:0%
+having this alternative so here's an
+example of another way governments can
+
+ align:start position:0%
+example of another way governments can
+ 
+
+ align:start position:0%
+example of another way governments can
+try to deal with Market power is by
+
+ align:start position:0%
+try to deal with Market power is by
+ 
+
+ align:start position:0%
+try to deal with Market power is by
+introducing uh introducing
+
+ align:start position:0%
+introducing uh introducing
+ 
+
+ align:start position:0%
+introducing uh introducing
+Alternatives so the bottom line is
+
+ align:start position:0%
+Alternatives so the bottom line is
+ 
+
+ align:start position:0%
+Alternatives so the bottom line is
+governments have the bottom line is
+
+ align:start position:0%
+governments have the bottom line is
+ 
+
+ align:start position:0%
+governments have the bottom line is
+monopolies
+
+ align:start position:0%
+monopolies
+ 
+
+ align:start position:0%
+monopolies
+exist okay governments the fact they
+
+ align:start position:0%
+exist okay governments the fact they
+ 
+
+ align:start position:0%
+exist okay governments the fact they
+exists creates deadweight loss in the
+
+ align:start position:0%
+exists creates deadweight loss in the
+ 
+
+ align:start position:0%
+exists creates deadweight loss in the
+market in fact it's good that they exist
+
+ align:start position:0%
+market in fact it's good that they exist
+ 
+
+ align:start position:0%
+market in fact it's good that they exist
+in many cases like Pharmaceuticals we
+
+ align:start position:0%
+in many cases like Pharmaceuticals we
+ 
+
+ align:start position:0%
+in many cases like Pharmaceuticals we
+want patents but at the same time we
+
+ align:start position:0%
+want patents but at the same time we
+ 
+
+ align:start position:0%
+want patents but at the same time we
+want to figure out the optimal way to
+
+ align:start position:0%
+want to figure out the optimal way to
+ 
+
+ align:start position:0%
+want to figure out the optimal way to
+deliver
+
+ align:start position:0%
+deliver
+ 
+
+ align:start position:0%
+deliver
+Innovation but minimize the loss to
+
+ align:start position:0%
+Innovation but minimize the loss to
+ 
+
+ align:start position:0%
+Innovation but minimize the loss to
+Consumers government regulation is one
+
+ align:start position:0%
+Consumers government regulation is one
+ 
+
+ align:start position:0%
+Consumers government regulation is one
+way to do that okay another way is by
+
+ align:start position:0%
+way to do that okay another way is by
+ 
+
+ align:start position:0%
+way to do that okay another way is by
+increasing competition in the market
+
+ align:start position:0%
+increasing competition in the market
+ 
+
+ align:start position:0%
+increasing competition in the market
+okay questions about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay let's come to the third point
+
+ align:start position:0%
+that okay let's come to the third point
+ 
+
+ align:start position:0%
+that okay let's come to the third point
+I want to talk about which is an
+
+ align:start position:0%
+I want to talk about which is an
+ 
+
+ align:start position:0%
+I want to talk about which is an
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+concept that is sort of starts to lead
+
+ align:start position:0%
+concept that is sort of starts to lead
+ 
+
+ align:start position:0%
+concept that is sort of starts to lead
+us towards a more subtle way of think
+
+ align:start position:0%
+us towards a more subtle way of think
+ 
+
+ align:start position:0%
+us towards a more subtle way of think
+about marks we've thought about two
+
+ align:start position:0%
+about marks we've thought about two
+ 
+
+ align:start position:0%
+about marks we've thought about two
+extremes we've thought about perfect
+
+ align:start position:0%
+extremes we've thought about perfect
+ 
+
+ align:start position:0%
+extremes we've thought about perfect
+competition and Monopoly starting next
+
+ align:start position:0%
+competition and Monopoly starting next
+ 
+
+ align:start position:0%
+competition and Monopoly starting next
+time we're going to start talking more
+
+ align:start position:0%
+time we're going to start talking more
+ 
+
+ align:start position:0%
+time we're going to start talking more
+generally about oligopoly in between
+
+ align:start position:0%
+generally about oligopoly in between
+ 
+
+ align:start position:0%
+generally about oligopoly in between
+cases one sort of Bridge to that is the
+
+ align:start position:0%
+cases one sort of Bridge to that is the
+ 
+
+ align:start position:0%
+cases one sort of Bridge to that is the
+notion of what we call contestable
+
+ align:start position:0%
+notion of what we call contestable
+ 
+
+ align:start position:0%
+notion of what we call contestable
+markets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+contestable
+
+ align:start position:0%
+contestable
+ 
+
+ align:start position:0%
+contestable
+markets a contestable market is one
+
+ align:start position:0%
+markets a contestable market is one
+ 
+
+ align:start position:0%
+markets a contestable market is one
+where there is a monopoly Advantage but
+
+ align:start position:0%
+where there is a monopoly Advantage but
+ 
+
+ align:start position:0%
+where there is a monopoly Advantage but
+it's not so
+
+ align:start position:0%
+it's not so
+ 
+
+ align:start position:0%
+it's not so
+big it's sort of like a natural monopoly
+
+ align:start position:0%
+big it's sort of like a natural monopoly
+ 
+
+ align:start position:0%
+big it's sort of like a natural monopoly
+but with a natural par isn't so large
+
+ align:start position:0%
+but with a natural par isn't so large
+ 
+
+ align:start position:0%
+but with a natural par isn't so large
+with a sunfix costs they're pretty big
+
+ align:start position:0%
+with a sunfix costs they're pretty big
+ 
+
+ align:start position:0%
+with a sunfix costs they're pretty big
+but they're not so big that someone
+
+ align:start position:0%
+but they're not so big that someone
+ 
+
+ align:start position:0%
+but they're not so big that someone
+couldn't enter at some point point the
+
+ align:start position:0%
+couldn't enter at some point point the
+ 
+
+ align:start position:0%
+couldn't enter at some point point the
+idea here is there will be a
+
+ align:start position:0%
+idea here is there will be a
+ 
+
+ align:start position:0%
+idea here is there will be a
+monopoly but it won't make that much
+
+ align:start position:0%
+monopoly but it won't make that much
+ 
+
+ align:start position:0%
+monopoly but it won't make that much
+money the idea is there'll be a monopoly
+
+ align:start position:0%
+money the idea is there'll be a monopoly
+ 
+
+ align:start position:0%
+money the idea is there'll be a monopoly
+but if it tries to set price too high
+
+ align:start position:0%
+but if it tries to set price too high
+ 
+
+ align:start position:0%
+but if it tries to set price too high
+then it will cover fixed cost and firms
+
+ align:start position:0%
+then it will cover fixed cost and firms
+ 
+
+ align:start position:0%
+then it will cover fixed cost and firms
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+enter so monopolies are sort of in a
+
+ align:start position:0%
+enter so monopolies are sort of in a
+ 
+
+ align:start position:0%
+enter so monopolies are sort of in a
+contestable market monopolies have
+
+ align:start position:0%
+contestable market monopolies have
+ 
+
+ align:start position:0%
+contestable market monopolies have
+barriers to entry but they're not so
+
+ align:start position:0%
+barriers to entry but they're not so
+ 
+
+ align:start position:0%
+barriers to entry but they're not so
+big that they can go nuts and charge
+
+ align:start position:0%
+big that they can go nuts and charge
+ 
+
+ align:start position:0%
+big that they can go nuts and charge
+full Monopoly
+
+ align:start position:0%
+full Monopoly
+ 
+
+ align:start position:0%
+full Monopoly
+prices okay and the most famous example
+
+ align:start position:0%
+prices okay and the most famous example
+ 
+
+ align:start position:0%
+prices okay and the most famous example
+of this was in the era of
+
+ align:start position:0%
+of this was in the era of
+ 
+
+ align:start position:0%
+of this was in the era of
+Airlines when I was a
+
+ align:start position:0%
+Airlines when I was a
+ 
+
+ align:start position:0%
+Airlines when I was a
+kid Airlines were a regulated
+
+ align:start position:0%
+kid Airlines were a regulated
+ 
+
+ align:start position:0%
+kid Airlines were a regulated
+Monopoly if you want to fly from A to B
+
+ align:start position:0%
+Monopoly if you want to fly from A to B
+ 
+
+ align:start position:0%
+Monopoly if you want to fly from A to B
+you had to apply to the government they
+
+ align:start position:0%
+you had to apply to the government they
+ 
+
+ align:start position:0%
+you had to apply to the government they
+gave permission to supply from A to B
+
+ align:start position:0%
+gave permission to supply from A to B
+ 
+
+ align:start position:0%
+gave permission to supply from A to B
+and they regulated the price you could
+
+ align:start position:0%
+and they regulated the price you could
+ 
+
+ align:start position:0%
+and they regulated the price you could
+charge
+
+ align:start position:0%
+charge
+ 
+
+ align:start position:0%
+charge
+okay and um in that World um basically
+
+ align:start position:0%
+okay and um in that World um basically
+ 
+
+ align:start position:0%
+okay and um in that World um basically
+the view was governments kind of didn't
+
+ align:start position:0%
+the view was governments kind of didn't
+ 
+
+ align:start position:0%
+the view was governments kind of didn't
+do a very good job and Airlines made a
+
+ align:start position:0%
+do a very good job and Airlines made a
+ 
+
+ align:start position:0%
+do a very good job and Airlines made a
+lot of money the view is governments
+
+ align:start position:0%
+lot of money the view is governments
+ 
+
+ align:start position:0%
+lot of money the view is governments
+because remember the airlines kind of
+
+ align:start position:0%
+because remember the airlines kind of
+ 
+
+ align:start position:0%
+because remember the airlines kind of
+lie about their marginal cost and the
+
+ align:start position:0%
+lie about their marginal cost and the
+ 
+
+ align:start position:0%
+lie about their marginal cost and the
+view was governments were sort of in
+
+ align:start position:0%
+view was governments were sort of in
+ 
+
+ align:start position:0%
+view was governments were sort of in
+their pocket and the government was
+
+ align:start position:0%
+their pocket and the government was
+ 
+
+ align:start position:0%
+their pocket and the government was
+setting prices too highs and making a
+
+ align:start position:0%
+setting prices too highs and making a
+ 
+
+ align:start position:0%
+setting prices too highs and making a
+lot of money and Economist said you know
+
+ align:start position:0%
+lot of money and Economist said you know
+ 
+
+ align:start position:0%
+lot of money and Economist said you know
+what you don't have to regulate this
+
+ align:start position:0%
+what you don't have to regulate this
+ 
+
+ align:start position:0%
+what you don't have to regulate this
+industry yeah it's a natural monopoly
+
+ align:start position:0%
+industry yeah it's a natural monopoly
+ 
+
+ align:start position:0%
+industry yeah it's a natural monopoly
+but it's also a very contestable Market
+
+ align:start position:0%
+but it's also a very contestable Market
+ 
+
+ align:start position:0%
+but it's also a very contestable Market
+okay the fixed costs aren't that fixed
+
+ align:start position:0%
+okay the fixed costs aren't that fixed
+ 
+
+ align:start position:0%
+okay the fixed costs aren't that fixed
+cost aren't that huge because there's
+
+ align:start position:0%
+cost aren't that huge because there's
+ 
+
+ align:start position:0%
+cost aren't that huge because there's
+lots of planes for sale planes that are
+
+ align:start position:0%
+lots of planes for sale planes that are
+ 
+
+ align:start position:0%
+lots of planes for sale planes that are
+a couple years old still work really
+
+ align:start position:0%
+a couple years old still work really
+ 
+
+ align:start position:0%
+a couple years old still work really
+well and other airlines can buy them
+
+ align:start position:0%
+well and other airlines can buy them
+ 
+
+ align:start position:0%
+well and other airlines can buy them
+this is actually not that hard industry
+
+ align:start position:0%
+this is actually not that hard industry
+ 
+
+ align:start position:0%
+this is actually not that hard industry
+to enter I mean it's hard I can't enter
+
+ align:start position:0%
+to enter I mean it's hard I can't enter
+ 
+
+ align:start position:0%
+to enter I mean it's hard I can't enter
+it but it takes you know tens of
+
+ align:start position:0%
+it but it takes you know tens of
+ 
+
+ align:start position:0%
+it but it takes you know tens of
+millions not billions to get into this
+
+ align:start position:0%
+millions not billions to get into this
+ 
+
+ align:start position:0%
+millions not billions to get into this
+industry so actually if we get rid of
+
+ align:start position:0%
+industry so actually if we get rid of
+ 
+
+ align:start position:0%
+industry so actually if we get rid of
+Regulation we can actually do better
+
+ align:start position:0%
+Regulation we can actually do better
+ 
+
+ align:start position:0%
+Regulation we can actually do better
+than if we keep regulation you're in a
+
+ align:start position:0%
+than if we keep regulation you're in a
+ 
+
+ align:start position:0%
+than if we keep regulation you're in a
+case where essentially you're setting
+
+ align:start position:0%
+case where essentially you're setting
+ 
+
+ align:start position:0%
+case where essentially you're setting
+the price so high that if you just let
+
+ align:start position:0%
+the price so high that if you just let
+ 
+
+ align:start position:0%
+the price so high that if you just let
+competition work will do better and
+
+ align:start position:0%
+competition work will do better and
+ 
+
+ align:start position:0%
+competition work will do better and
+economists actually won the day
+
+ align:start position:0%
+economists actually won the day
+ 
+
+ align:start position:0%
+economists actually won the day
+economist convinced the government to
+
+ align:start position:0%
+economist convinced the government to
+ 
+
+ align:start position:0%
+economist convinced the government to
+deregulate the airline
+
+ align:start position:0%
+deregulate the airline
+ 
+
+ align:start position:0%
+deregulate the airline
+industry so what happened three things
+
+ align:start position:0%
+industry so what happened three things
+ 
+
+ align:start position:0%
+industry so what happened three things
+first prices fell enormously economists
+
+ align:start position:0%
+first prices fell enormously economists
+ 
+
+ align:start position:0%
+first prices fell enormously economists
+were right prices fell by about a third
+
+ align:start position:0%
+were right prices fell by about a third
+ 
+
+ align:start position:0%
+were right prices fell by about a third
+the unregulated prices were about
+
+ align:start position:0%
+the unregulated prices were about
+ 
+
+ align:start position:0%
+the unregulated prices were about
+two-thirds of what the regulated prices
+
+ align:start position:0%
+two-thirds of what the regulated prices
+ 
+
+ align:start position:0%
+two-thirds of what the regulated prices
+were because economists were right the
+
+ align:start position:0%
+were because economists were right the
+ 
+
+ align:start position:0%
+were because economists were right the
+government had set the price too high an
+
+ align:start position:0%
+government had set the price too high an
+ 
+
+ align:start position:0%
+government had set the price too high an
+example is that when I was at MIT in the
+
+ align:start position:0%
+example is that when I was at MIT in the
+ 
+
+ align:start position:0%
+example is that when I was at MIT in the
+1980s I would fly home to Newark on
+
+ align:start position:0%
+1980s I would fly home to Newark on
+ 
+
+ align:start position:0%
+1980s I would fly home to Newark on
+people's Express People's Express which
+
+ align:start position:0%
+people's Express People's Express which
+ 
+
+ align:start position:0%
+people's Express People's Express which
+sounds like a communist organization was
+
+ align:start position:0%
+sounds like a communist organization was
+ 
+
+ align:start position:0%
+sounds like a communist organization was
+this new airline that was introduced in
+
+ align:start position:0%
+this new airline that was introduced in
+ 
+
+ align:start position:0%
+this new airline that was introduced in
+the new deregulated Market in 1984 the
+
+ align:start position:0%
+the new deregulated Market in 1984 the
+ 
+
+ align:start position:0%
+the new deregulated Market in 1984 the
+market had only been deregulated about a
+
+ align:start position:0%
+market had only been deregulated about a
+ 
+
+ align:start position:0%
+market had only been deregulated about a
+decade so so this new Airline and I
+
+ align:start position:0%
+decade so so this new Airline and I
+ 
+
+ align:start position:0%
+decade so so this new Airline and I
+would fly from Boston to New York for
+
+ align:start position:0%
+would fly from Boston to New York for
+ 
+
+ align:start position:0%
+would fly from Boston to New York for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+$19.99 okay I mean now it's a few
+
+ align:start position:0%
+$19.99 okay I mean now it's a few
+ 
+
+ align:start position:0%
+$19.99 okay I mean now it's a few
+hundred dollars right it was before that
+
+ align:start position:0%
+hundred dollars right it was before that
+ 
+
+ align:start position:0%
+hundred dollars right it was before that
+Airline also a couple hundred bucks
+
+ align:start position:0%
+Airline also a couple hundred bucks
+ 
+
+ align:start position:0%
+Airline also a couple hundred bucks
+literally didn't even reserve a spot you
+
+ align:start position:0%
+literally didn't even reserve a spot you
+ 
+
+ align:start position:0%
+literally didn't even reserve a spot you
+just literally showed up and lined up
+
+ align:start position:0%
+just literally showed up and lined up
+ 
+
+ align:start position:0%
+just literally showed up and lined up
+when the plane was full they took off I
+
+ align:start position:0%
+when the plane was full they took off I
+ 
+
+ align:start position:0%
+when the plane was full they took off I
+I don't know then they went they came
+
+ align:start position:0%
+I don't know then they went they came
+ 
+
+ align:start position:0%
+I don't know then they went they came
+through with the cart and you paid on
+
+ align:start position:0%
+through with the cart and you paid on
+ 
+
+ align:start position:0%
+through with the cart and you paid on
+the plane I don't know like if you
+
+ align:start position:0%
+the plane I don't know like if you
+ 
+
+ align:start position:0%
+the plane I don't know like if you
+didn't have money they throw you off I
+
+ align:start position:0%
+didn't have money they throw you off I
+ 
+
+ align:start position:0%
+didn't have money they throw you off I
+don't know but like literally it was so
+
+ align:start position:0%
+don't know but like literally it was so
+ 
+
+ align:start position:0%
+don't know but like literally it was so
+cheap to fly prices came way down from
+
+ align:start position:0%
+cheap to fly prices came way down from
+ 
+
+ align:start position:0%
+cheap to fly prices came way down from
+what they used to
+
+ align:start position:0%
+what they used to
+ 
+
+ align:start position:0%
+what they used to
+be the second is the number of routes
+
+ align:start position:0%
+be the second is the number of routes
+ 
+
+ align:start position:0%
+be the second is the number of routes
+that were
+
+ align:start position:0%
+that were
+ 
+
+ align:start position:0%
+that were
+flown went way
+
+ align:start position:0%
+flown went way
+ 
+
+ align:start position:0%
+flown went way
+up because it turns out there were lots
+
+ align:start position:0%
+up because it turns out there were lots
+ 
+
+ align:start position:0%
+up because it turns out there were lots
+of routes that were profitable to fly
+
+ align:start position:0%
+of routes that were profitable to fly
+ 
+
+ align:start position:0%
+of routes that were profitable to fly
+the government wouldn't let happen it
+
+ align:start position:0%
+the government wouldn't let happen it
+ 
+
+ align:start position:0%
+the government wouldn't let happen it
+turned out airlin say well look if you
+
+ align:start position:0%
+turned out airlin say well look if you
+ 
+
+ align:start position:0%
+turned out airlin say well look if you
+let me charge what I want I can figure
+
+ align:start position:0%
+let me charge what I want I can figure
+ 
+
+ align:start position:0%
+let me charge what I want I can figure
+out would make this route profitable so
+
+ align:start position:0%
+out would make this route profitable so
+ 
+
+ align:start position:0%
+out would make this route profitable so
+there's a huge increase in Access huge
+
+ align:start position:0%
+there's a huge increase in Access huge
+ 
+
+ align:start position:0%
+there's a huge increase in Access huge
+increase in where planes went at a much
+
+ align:start position:0%
+increase in where planes went at a much
+ 
+
+ align:start position:0%
+increase in where planes went at a much
+lower
+
+ align:start position:0%
+lower
+ 
+
+ align:start position:0%
+lower
+price third
+
+ align:start position:0%
+price third
+ 
+
+ align:start position:0%
+price third
+effect service
+
+ align:start position:0%
+effect service
+ 
+
+ align:start position:0%
+effect service
+quality
+
+ align:start position:0%
+quality
+ 
+
+ align:start position:0%
+quality
+tanked flying used to be fun when I was
+
+ align:start position:0%
+tanked flying used to be fun when I was
+ 
+
+ align:start position:0%
+tanked flying used to be fun when I was
+a kid everything was free you got in the
+
+ align:start position:0%
+a kid everything was free you got in the
+ 
+
+ align:start position:0%
+a kid everything was free you got in the
+plane free food free booze real
+
+ align:start position:0%
+plane free food free booze real
+ 
+
+ align:start position:0%
+plane free food free booze real
+silverware huge leg room no no charge
+
+ align:start position:0%
+silverware huge leg room no no charge
+ 
+
+ align:start position:0%
+silverware huge leg room no no charge
+for anything free bags okay any of you
+
+ align:start position:0%
+for anything free bags okay any of you
+ 
+
+ align:start position:0%
+for anything free bags okay any of you
+watch Mad Men and watch you know Don Don
+
+ align:start position:0%
+watch Mad Men and watch you know Don Don
+ 
+
+ align:start position:0%
+watch Mad Men and watch you know Don Don
+Draper fly that's what it's like he's
+
+ align:start position:0%
+Draper fly that's what it's like he's
+ 
+
+ align:start position:0%
+Draper fly that's what it's like he's
+not even flying business class in those
+
+ align:start position:0%
+not even flying business class in those
+ 
+
+ align:start position:0%
+not even flying business class in those
+shows it was awesome flying today sucks
+
+ align:start position:0%
+shows it was awesome flying today sucks
+ 
+
+ align:start position:0%
+shows it was awesome flying today sucks
+we all know
+
+ align:start position:0%
+we all know
+ 
+
+ align:start position:0%
+we all know
+that okay so why did that
+
+ align:start position:0%
+that okay so why did that
+ 
+
+ align:start position:0%
+that okay so why did that
+happen why did quality deteriorate so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much but we deregulate Airlines why did
+
+ align:start position:0%
+much but we deregulate Airlines why did
+ 
+
+ align:start position:0%
+much but we deregulate Airlines why did
+quality fall so much yeah actually
+
+ align:start position:0%
+quality fall so much yeah actually
+ 
+
+ align:start position:0%
+quality fall so much yeah actually
+really funny because we're doing a
+
+ align:start position:0%
+really funny because we're doing a
+ 
+
+ align:start position:0%
+really funny because we're doing a
+project in another CL
+
+ align:start position:0%
+project in another CL
+ 
+
+ align:start position:0%
+project in another CL
+okay um long story short like in order
+
+ align:start position:0%
+okay um long story short like in order
+ 
+
+ align:start position:0%
+okay um long story short like in order
+to have such good customer service you
+
+ align:start position:0%
+to have such good customer service you
+ 
+
+ align:start position:0%
+to have such good customer service you
+have to through a lot of employees and
+
+ align:start position:0%
+have to through a lot of employees and
+ 
+
+ align:start position:0%
+have to through a lot of employees and
+so your TR is be really high as a result
+
+ align:start position:0%
+so your TR is be really high as a result
+ 
+
+ align:start position:0%
+so your TR is be really high as a result
+as soon as you start getting market
+
+ align:start position:0%
+as soon as you start getting market
+ 
+
+ align:start position:0%
+as soon as you start getting market
+share for like people's econom
+
+ align:start position:0%
+share for like people's econom
+ 
+
+ align:start position:0%
+share for like people's econom
+people Legacy
+
+ align:start position:0%
+people Legacy
+ 
+
+ align:start position:0%
+people Legacy
+carriers yeah I mean that's a little
+
+ align:start position:0%
+carriers yeah I mean that's a little
+ 
+
+ align:start position:0%
+carriers yeah I mean that's a little
+more detailed answer than I wanted but
+
+ align:start position:0%
+more detailed answer than I wanted but
+ 
+
+ align:start position:0%
+more detailed answer than I wanted but
+basically the bottom line is when you
+
+ align:start position:0%
+basically the bottom line is when you
+ 
+
+ align:start position:0%
+basically the bottom line is when you
+are regulated on
+
+ align:start position:0%
+are regulated on
+ 
+
+ align:start position:0%
+are regulated on
+price but you have different planes
+
+ align:start position:0%
+price but you have different planes
+ 
+
+ align:start position:0%
+price but you have different planes
+flying the same route how do they
+
+ align:start position:0%
+flying the same route how do they
+ 
+
+ align:start position:0%
+flying the same route how do they
+compete on quality right in a in the
+
+ align:start position:0%
+compete on quality right in a in the
+ 
+
+ align:start position:0%
+compete on quality right in a in the
+markets we've discussed so far the only
+
+ align:start position:0%
+markets we've discussed so far the only
+ 
+
+ align:start position:0%
+markets we've discussed so far the only
+way firms can compete is on price but
+
+ align:start position:0%
+way firms can compete is on price but
+ 
+
+ align:start position:0%
+way firms can compete is on price but
+firms compete in reality along multiple
+
+ align:start position:0%
+firms compete in reality along multiple
+ 
+
+ align:start position:0%
+firms compete in reality along multiple
+Dimensions so in the old days if United
+
+ align:start position:0%
+Dimensions so in the old days if United
+ 
+
+ align:start position:0%
+Dimensions so in the old days if United
+America were both flying to
+
+ align:start position:0%
+America were both flying to
+ 
+
+ align:start position:0%
+America were both flying to
+Chicago and they had to charge the same
+
+ align:start position:0%
+Chicago and they had to charge the same
+ 
+
+ align:start position:0%
+Chicago and they had to charge the same
+price how did they get your business by
+
+ align:start position:0%
+price how did they get your business by
+ 
+
+ align:start position:0%
+price how did they get your business by
+being a nicer
+
+ align:start position:0%
+being a nicer
+ 
+
+ align:start position:0%
+being a nicer
+experience now suddenly they can compete
+
+ align:start position:0%
+experience now suddenly they can compete
+ 
+
+ align:start position:0%
+experience now suddenly they can compete
+on price they said we're not going to be
+
+ align:start position:0%
+on price they said we're not going to be
+ 
+
+ align:start position:0%
+on price they said we're not going to be
+nicer experienc anymore it's too
+
+ align:start position:0%
+nicer experienc anymore it's too
+ 
+
+ align:start position:0%
+nicer experienc anymore it's too
+expensive we're just going to charge a
+
+ align:start position:0%
+expensive we're just going to charge a
+ 
+
+ align:start position:0%
+expensive we're just going to charge a
+lower price
+
+ align:start position:0%
+lower price
+ 
+
+ align:start position:0%
+lower price
+now you might say well gee that sucks
+
+ align:start position:0%
+now you might say well gee that sucks
+ 
+
+ align:start position:0%
+now you might say well gee that sucks
+that's a terrible thing it's horrible
+
+ align:start position:0%
+that's a terrible thing it's horrible
+ 
+
+ align:start position:0%
+that's a terrible thing it's horrible
+Airline quality fault why would I tell
+
+ align:start position:0%
+Airline quality fault why would I tell
+ 
+
+ align:start position:0%
+Airline quality fault why would I tell
+you you're wrong why would I tell you
+
+ align:start position:0%
+you you're wrong why would I tell you
+ 
+
+ align:start position:0%
+you you're wrong why would I tell you
+it's good that Airline quality fell why
+
+ align:start position:0%
+it's good that Airline quality fell why
+ 
+
+ align:start position:0%
+it's good that Airline quality fell why
+can I say for sure we're better in a
+
+ align:start position:0%
+can I say for sure we're better in a
+ 
+
+ align:start position:0%
+can I say for sure we're better in a
+world with lower prices and lower
+
+ align:start position:0%
+world with lower prices and lower
+ 
+
+ align:start position:0%
+world with lower prices and lower
+quality than we are than we are in a
+
+ align:start position:0%
+quality than we are than we are in a
+ 
+
+ align:start position:0%
+quality than we are than we are in a
+world with higher price and higher
+
+ align:start position:0%
+world with higher price and higher
+ 
+
+ align:start position:0%
+world with higher price and higher
+quality
+
+ align:start position:0%
+quality
+ 
+
+ align:start position:0%
+quality
+yeah well I I don't know that because
+
+ align:start position:0%
+yeah well I I don't know that because
+ 
+
+ align:start position:0%
+yeah well I I don't know that because
+only because I grew a draft in prices I
+
+ align:start position:0%
+only because I grew a draft in prices I
+ 
+
+ align:start position:0%
+only because I grew a draft in prices I
+didn't draw a draft in
+
+ align:start position:0%
+didn't draw a draft in
+ 
+
+ align:start position:0%
+didn't draw a draft in
+quality I don't know that we got rid of
+
+ align:start position:0%
+quality I don't know that we got rid of
+ 
+
+ align:start position:0%
+quality I don't know that we got rid of
+the Dead weight loss for sure
+
+ align:start position:0%
+the Dead weight loss for sure
+ 
+
+ align:start position:0%
+the Dead weight loss for sure
+but I do know something else what do I
+
+ align:start position:0%
+but I do know something else what do I
+ 
+
+ align:start position:0%
+but I do know something else what do I
+know what fact is true
+
+ align:start position:0%
+know what fact is true
+ 
+
+ align:start position:0%
+know what fact is true
+yeah what's
+
+ align:start position:0%
+yeah what's
+ 
+
+ align:start position:0%
+yeah what's
+that well it's more accessible we flying
+
+ align:start position:0%
+that well it's more accessible we flying
+ 
+
+ align:start position:0%
+that well it's more accessible we flying
+more routes but they're shitty how do I
+
+ align:start position:0%
+more routes but they're shitty how do I
+ 
+
+ align:start position:0%
+more routes but they're shitty how do I
+know people wouldn't
+
+ align:start position:0%
+know people wouldn't
+ 
+
+ align:start position:0%
+know people wouldn't
+rather do something else yeah you can
+
+ align:start position:0%
+rather do something else yeah you can
+ 
+
+ align:start position:0%
+rather do something else yeah you can
+still pay for a better experience so the
+
+ align:start position:0%
+still pay for a better experience so the
+ 
+
+ align:start position:0%
+still pay for a better experience so the
+fact that people are buying a cheaper
+
+ align:start position:0%
+fact that people are buying a cheaper
+ 
+
+ align:start position:0%
+fact that people are buying a cheaper
+ticket yeah because we haven't ruled out
+
+ align:start position:0%
+ticket yeah because we haven't ruled out
+ 
+
+ align:start position:0%
+ticket yeah because we haven't ruled out
+high quality high prices just no one
+
+ align:start position:0%
+high quality high prices just no one
+ 
+
+ align:start position:0%
+high quality high prices just no one
+wants it okay so people who bit
+
+ align:start position:0%
+wants it okay so people who bit
+ 
+
+ align:start position:0%
+wants it okay so people who bit
+about oh flying's terrible they don't
+
+ align:start position:0%
+about oh flying's terrible they don't
+ 
+
+ align:start position:0%
+about oh flying's terrible they don't
+ about the fact it's really cheap
+
+ align:start position:0%
+ about the fact it's really cheap
+ 
+
+ align:start position:0%
+ about the fact it's really cheap
+and if you don't like that fly business
+
+ align:start position:0%
+and if you don't like that fly business
+ 
+
+ align:start position:0%
+and if you don't like that fly business
+class or if you don't like that get
+
+ align:start position:0%
+class or if you don't like that get
+ 
+
+ align:start position:0%
+class or if you don't like that get
+together and form an airline that gives
+
+ align:start position:0%
+together and form an airline that gives
+ 
+
+ align:start position:0%
+together and form an airline that gives
+the old high quality high prices JetBlue
+
+ align:start position:0%
+the old high quality high prices JetBlue
+ 
+
+ align:start position:0%
+the old high quality high prices JetBlue
+sort of tried to do this JetBlue was
+
+ align:start position:0%
+sort of tried to do this JetBlue was
+ 
+
+ align:start position:0%
+sort of tried to do this JetBlue was
+kind of a better experience now that
+
+ align:start position:0%
+kind of a better experience now that
+ 
+
+ align:start position:0%
+kind of a better experience now that
+kind of deteriorated back towards what
+
+ align:start position:0%
+kind of deteriorated back towards what
+ 
+
+ align:start position:0%
+kind of deteriorated back towards what
+the airlines are when jebl started you
+
+ align:start position:0%
+the airlines are when jebl started you
+ 
+
+ align:start position:0%
+the airlines are when jebl started you
+get all these free snacks and stuff
+
+ align:start position:0%
+get all these free snacks and stuff
+ 
+
+ align:start position:0%
+get all these free snacks and stuff
+which no one was doing okay they were
+
+ align:start position:0%
+which no one was doing okay they were
+ 
+
+ align:start position:0%
+which no one was doing okay they were
+trying to do that a little bit but the
+
+ align:start position:0%
+trying to do that a little bit but the
+ 
+
+ align:start position:0%
+trying to do that a little bit but the
+bottom line is if you want to tell me
+
+ align:start position:0%
+bottom line is if you want to tell me
+ 
+
+ align:start position:0%
+bottom line is if you want to tell me
+gee the old world was better I tell you
+
+ align:start position:0%
+gee the old world was better I tell you
+ 
+
+ align:start position:0%
+gee the old world was better I tell you
+fine go back to the old world if it was
+
+ align:start position:0%
+fine go back to the old world if it was
+ 
+
+ align:start position:0%
+fine go back to the old world if it was
+better it should exist it doesn't
+
+ align:start position:0%
+better it should exist it doesn't
+ 
+
+ align:start position:0%
+better it should exist it doesn't
+because while people don't while people
+
+ align:start position:0%
+because while people don't while people
+ 
+
+ align:start position:0%
+because while people don't while people
+may about flying now they they
+
+ align:start position:0%
+may about flying now they they
+ 
+
+ align:start position:0%
+may about flying now they they
+aren't bitching about the prices and
+
+ align:start position:0%
+aren't bitching about the prices and
+ 
+
+ align:start position:0%
+aren't bitching about the prices and
+we're happier and this is the key
+
+ align:start position:0%
+we're happier and this is the key
+ 
+
+ align:start position:0%
+we're happier and this is the key
+concept once again of revealed
+
+ align:start position:0%
+concept once again of revealed
+ 
+
+ align:start position:0%
+concept once again of revealed
+preference this is how economists test
+
+ align:start position:0%
+preference this is how economists test
+ 
+
+ align:start position:0%
+preference this is how economists test
+welfare conclusions we use revealed
+
+ align:start position:0%
+welfare conclusions we use revealed
+ 
+
+ align:start position:0%
+welfare conclusions we use revealed
+preference we've revealed that we'd
+
+ align:start position:0%
+preference we've revealed that we'd
+ 
+
+ align:start position:0%
+preference we've revealed that we'd
+rather have low quality at low prices
+
+ align:start position:0%
+rather have low quality at low prices
+ 
+
+ align:start position:0%
+rather have low quality at low prices
+because it's rewarded in the market new
+
+ align:start position:0%
+because it's rewarded in the market new
+ 
+
+ align:start position:0%
+because it's rewarded in the market new
+lowcost airlines that suck enter all the
+
+ align:start position:0%
+lowcost airlines that suck enter all the
+ 
+
+ align:start position:0%
+lowcost airlines that suck enter all the
+time but high-end Airlines don't so we
+
+ align:start position:0%
+time but high-end Airlines don't so we
+ 
+
+ align:start position:0%
+time but high-end Airlines don't so we
+we want low quality at low prices I we
+
+ align:start position:0%
+we want low quality at low prices I we
+ 
+
+ align:start position:0%
+we want low quality at low prices I we
+i' rather have high quality at low
+
+ align:start position:0%
+i' rather have high quality at low
+ 
+
+ align:start position:0%
+i' rather have high quality at low
+prices but that's not an option okay
+
+ align:start position:0%
+prices but that's not an option okay
+ 
+
+ align:start position:0%
+prices but that's not an option okay
+that's the third thing that happened the
+
+ align:start position:0%
+that's the third thing that happened the
+ 
+
+ align:start position:0%
+that's the third thing that happened the
+fourth thing that happened actually five
+
+ align:start position:0%
+fourth thing that happened actually five
+ 
+
+ align:start position:0%
+fourth thing that happened actually five
+things happened the fourth thing that
+
+ align:start position:0%
+things happened the fourth thing that
+ 
+
+ align:start position:0%
+things happened the fourth thing that
+happened is that safety the other thing
+
+ align:start position:0%
+happened is that safety the other thing
+ 
+
+ align:start position:0%
+happened is that safety the other thing
+you'd be concerned about is well gee now
+
+ align:start position:0%
+you'd be concerned about is well gee now
+ 
+
+ align:start position:0%
+you'd be concerned about is well gee now
+there's no one said it to be safe but in
+
+ align:start position:0%
+there's no one said it to be safe but in
+ 
+
+ align:start position:0%
+there's no one said it to be safe but in
+fact it turns out safety didn't
+
+ align:start position:0%
+fact it turns out safety didn't
+ 
+
+ align:start position:0%
+fact it turns out safety didn't
+change it turns out there's still enough
+
+ align:start position:0%
+change it turns out there's still enough
+ 
+
+ align:start position:0%
+change it turns out there's still enough
+instead of to be safe that it wasn't
+
+ align:start position:0%
+instead of to be safe that it wasn't
+ 
+
+ align:start position:0%
+instead of to be safe that it wasn't
+like the regulation was actually making
+
+ align:start position:0%
+like the regulation was actually making
+ 
+
+ align:start position:0%
+like the regulation was actually making
+flying any safer flying is unbelievable
+
+ align:start position:0%
+flying any safer flying is unbelievable
+ 
+
+ align:start position:0%
+flying any safer flying is unbelievable
+safe it always was it always
+
+ align:start position:0%
+safe it always was it always
+ 
+
+ align:start position:0%
+safe it always was it always
+is so this is all great news Economist
+
+ align:start position:0%
+is so this is all great news Economist
+ 
+
+ align:start position:0%
+is so this is all great news Economist
+for the win except economists got one
+
+ align:start position:0%
+for the win except economists got one
+ 
+
+ align:start position:0%
+for the win except economists got one
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+wrong we got one thing wrong which we
+
+ align:start position:0%
+wrong we got one thing wrong which we
+ 
+
+ align:start position:0%
+wrong we got one thing wrong which we
+missed the fact that while there's not
+
+ align:start position:0%
+missed the fact that while there's not
+ 
+
+ align:start position:0%
+missed the fact that while there's not
+huge barriers to entry in terms of
+
+ align:start position:0%
+huge barriers to entry in terms of
+ 
+
+ align:start position:0%
+huge barriers to entry in terms of
+airplanes there is huge barriers to
+
+ align:start position:0%
+airplanes there is huge barriers to
+ 
+
+ align:start position:0%
+airplanes there is huge barriers to
+entry in terms of what what's the
+
+ align:start position:0%
+entry in terms of what what's the
+ 
+
+ align:start position:0%
+entry in terms of what what's the
+barrier to entry yeah airport
+
+ align:start position:0%
+barrier to entry yeah airport
+ 
+
+ align:start position:0%
+barrier to entry yeah airport
+slots that those are fixed and that it's
+
+ align:start position:0%
+slots that those are fixed and that it's
+ 
+
+ align:start position:0%
+slots that those are fixed and that it's
+incredibly hard to expand an airport it
+
+ align:start position:0%
+incredibly hard to expand an airport it
+ 
+
+ align:start position:0%
+incredibly hard to expand an airport it
+took Logan airport until about 12 years
+
+ align:start position:0%
+took Logan airport until about 12 years
+ 
+
+ align:start position:0%
+took Logan airport until about 12 years
+ago had one Runway at night one runway
+
+ align:start position:0%
+ago had one Runway at night one runway
+ 
+
+ align:start position:0%
+ago had one Runway at night one runway
+in Boston at night think about that for
+
+ align:start position:0%
+in Boston at night think about that for
+ 
+
+ align:start position:0%
+in Boston at night think about that for
+the city of Boston we expanded to two it
+
+ align:start position:0%
+the city of Boston we expanded to two it
+ 
+
+ align:start position:0%
+the city of Boston we expanded to two it
+took 25 years to happen to expand a two
+
+ align:start position:0%
+took 25 years to happen to expand a two
+ 
+
+ align:start position:0%
+took 25 years to happen to expand a two
+runways okay it is very hard to add new
+
+ align:start position:0%
+runways okay it is very hard to add new
+ 
+
+ align:start position:0%
+runways okay it is very hard to add new
+airport slots as a result there is a
+
+ align:start position:0%
+airport slots as a result there is a
+ 
+
+ align:start position:0%
+airport slots as a result there is a
+truly fixed barrier which is Airline
+
+ align:start position:0%
+truly fixed barrier which is Airline
+ 
+
+ align:start position:0%
+truly fixed barrier which is Airline
+slots and as a result competition did
+
+ align:start position:0%
+slots and as a result competition did
+ 
+
+ align:start position:0%
+slots and as a result competition did
+not go up as much as we thought take
+
+ align:start position:0%
+not go up as much as we thought take
+ 
+
+ align:start position:0%
+not go up as much as we thought take
+Minnesota where I had to fly for years
+
+ align:start position:0%
+Minnesota where I had to fly for years
+ 
+
+ align:start position:0%
+Minnesota where I had to fly for years
+to visit my wife's family okay Minnesota
+
+ align:start position:0%
+to visit my wife's family okay Minnesota
+ 
+
+ align:start position:0%
+to visit my wife's family okay Minnesota
+was served almost as a monopoly by what
+
+ align:start position:0%
+was served almost as a monopoly by what
+ 
+
+ align:start position:0%
+was served almost as a monopoly by what
+was called Northwest Airlines in our
+
+ align:start position:0%
+was called Northwest Airlines in our
+ 
+
+ align:start position:0%
+was called Northwest Airlines in our
+part of
+
+ align:start position:0%
+part of
+ 
+
+ align:start position:0%
+part of
+Delta now why didn't the city of mota of
+
+ align:start position:0%
+Delta now why didn't the city of mota of
+ 
+
+ align:start position:0%
+Delta now why didn't the city of mota of
+Minneapolis and Northwest control all
+
+ align:start position:0%
+Minneapolis and Northwest control all
+ 
+
+ align:start position:0%
+Minneapolis and Northwest control all
+the slots at the airport why does it in
+
+ align:start position:0%
+the slots at the airport why does it in
+ 
+
+ align:start position:0%
+the slots at the airport why does it in
+Minneapolis say hey Northwest we're
+
+ align:start position:0%
+Minneapolis say hey Northwest we're
+ 
+
+ align:start position:0%
+Minneapolis say hey Northwest we're
+going to take a a few of your slots and
+
+ align:start position:0%
+going to take a a few of your slots and
+ 
+
+ align:start position:0%
+going to take a a few of your slots and
+allow another airline to come
+
+ align:start position:0%
+allow another airline to come
+ 
+
+ align:start position:0%
+allow another airline to come
+in and create some competition why
+
+ align:start position:0%
+in and create some competition why
+ 
+
+ align:start position:0%
+in and create some competition why
+because Northwest Airlines was
+
+ align:start position:0%
+because Northwest Airlines was
+ 
+
+ align:start position:0%
+because Northwest Airlines was
+headquartered in Minneapolis and said if
+
+ align:start position:0%
+headquartered in Minneapolis and said if
+ 
+
+ align:start position:0%
+headquartered in Minneapolis and said if
+you do that we'll leave and we'll take
+
+ align:start position:0%
+you do that we'll leave and we'll take
+ 
+
+ align:start position:0%
+you do that we'll leave and we'll take
+all our jobs with
+
+ align:start position:0%
+all our jobs with
+ 
+
+ align:start position:0%
+all our jobs with
+us and so essentially uh the city of
+
+ align:start position:0%
+us and so essentially uh the city of
+ 
+
+ align:start position:0%
+us and so essentially uh the city of
+this city of Minneapolis barely let any
+
+ align:start position:0%
+this city of Minneapolis barely let any
+ 
+
+ align:start position:0%
+this city of Minneapolis barely let any
+competition
+
+ align:start position:0%
+competition
+ 
+
+ align:start position:0%
+competition
+in as a result of this ability to sort
+
+ align:start position:0%
+in as a result of this ability to sort
+ 
+
+ align:start position:0%
+in as a result of this ability to sort
+of monopolize slots Airlines set up what
+
+ align:start position:0%
+of monopolize slots Airlines set up what
+ 
+
+ align:start position:0%
+of monopolize slots Airlines set up what
+we call the Hub and spoke
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system which is if you want to fly from
+
+ align:start position:0%
+system which is if you want to fly from
+ 
+
+ align:start position:0%
+system which is if you want to fly from
+A to B you got it on the way stop at C
+
+ align:start position:0%
+A to B you got it on the way stop at C
+ 
+
+ align:start position:0%
+A to B you got it on the way stop at C
+which is their headquarters
+
+ align:start position:0%
+which is their headquarters
+ 
+
+ align:start position:0%
+which is their headquarters
+airport okay so Airlines funneled all
+
+ align:start position:0%
+airport okay so Airlines funneled all
+ 
+
+ align:start position:0%
+airport okay so Airlines funneled all
+their traffic through airports where
+
+ align:start position:0%
+their traffic through airports where
+ 
+
+ align:start position:0%
+their traffic through airports where
+there're sort of
+
+ align:start position:0%
+there're sort of
+ 
+
+ align:start position:0%
+there're sort of
+monopolies and as a result while there's
+
+ align:start position:0%
+monopolies and as a result while there's
+ 
+
+ align:start position:0%
+monopolies and as a result while there's
+much more competition prices did come
+
+ align:start position:0%
+much more competition prices did come
+ 
+
+ align:start position:0%
+much more competition prices did come
+down a third there's much less than we
+
+ align:start position:0%
+down a third there's much less than we
+ 
+
+ align:start position:0%
+down a third there's much less than we
+thought there would
+
+ align:start position:0%
+thought there would
+ 
+
+ align:start position:0%
+thought there would
+be because we missed the fact that the
+
+ align:start position:0%
+be because we missed the fact that the
+ 
+
+ align:start position:0%
+be because we missed the fact that the
+airport slots are truly fixed and aren't
+
+ align:start position:0%
+airport slots are truly fixed and aren't
+ 
+
+ align:start position:0%
+airport slots are truly fixed and aren't
+expanding so there a great lesson in the
+
+ align:start position:0%
+expanding so there a great lesson in the
+ 
+
+ align:start position:0%
+expanding so there a great lesson in the
+power of Economics but even the creative
+
+ align:start position:0%
+power of Economics but even the creative
+ 
+
+ align:start position:0%
+power of Economics but even the creative
+economic aabus can't see the future
+
+ align:start position:0%
+economic aabus can't see the future
+ 
+
+ align:start position:0%
+economic aabus can't see the future
+industry is incredibly creative at
+
+ align:start position:0%
+industry is incredibly creative at
+ 
+
+ align:start position:0%
+industry is incredibly creative at
+maximizing its profits
+
+ align:start position:0%
+maximizing its profits
+ 
+
+ align:start position:0%
+maximizing its profits
+and that they will come up with things
+
+ align:start position:0%
+and that they will come up with things
+ 
+
+ align:start position:0%
+and that they will come up with things
+uh to get around almost any well meaning
+
+ align:start position:0%
+uh to get around almost any well meaning
+ 
+
+ align:start position:0%
+uh to get around almost any well meaning
+government intervention doesn't mean
+
+ align:start position:0%
+government intervention doesn't mean
+ 
+
+ align:start position:0%
+government intervention doesn't mean
+government interventions aren't a good
+
+ align:start position:0%
+government interventions aren't a good
+ 
+
+ align:start position:0%
+government interventions aren't a good
+thing to do doesn't mean we can't do
+
+ align:start position:0%
+thing to do doesn't mean we can't do
+ 
+
+ align:start position:0%
+thing to do doesn't mean we can't do
+more but it does mean we have to
+
+ align:start position:0%
+more but it does mean we have to
+ 
+
+ align:start position:0%
+more but it does mean we have to
+consider we think about projecting the
+
+ align:start position:0%
+consider we think about projecting the
+ 
+
+ align:start position:0%
+consider we think about projecting the
+effects of government interventions how
+
+ align:start position:0%
+effects of government interventions how
+ 
+
+ align:start position:0%
+effects of government interventions how
+industry will respond what we call the
+
+ align:start position:0%
+industry will respond what we call the
+ 
+
+ align:start position:0%
+industry will respond what we call the
+Dynamics we can't just say this is the
+
+ align:start position:0%
+Dynamics we can't just say this is the
+ 
+
+ align:start position:0%
+Dynamics we can't just say this is the
+way the industry works today so it'll
+
+ align:start position:0%
+way the industry works today so it'll
+ 
+
+ align:start position:0%
+way the industry works today so it'll
+always work that way we have to consider
+
+ align:start position:0%
+always work that way we have to consider
+ 
+
+ align:start position:0%
+always work that way we have to consider
+well what are the other angles how's the
+
+ align:start position:0%
+well what are the other angles how's the
+ 
+
+ align:start position:0%
+well what are the other angles how's the
+industry going to respond and that's
+
+ align:start position:0%
+industry going to respond and that's
+ 
+
+ align:start position:0%
+industry going to respond and that's
+once again a big challenge for
+
+ align:start position:0%
+once again a big challenge for
+ 
+
+ align:start position:0%
+once again a big challenge for
+government policy maker is envisioning
+
+ align:start position:0%
+government policy maker is envisioning
+ 
+
+ align:start position:0%
+government policy maker is envisioning
+worlds that might be under your
+
+ align:start position:0%
+worlds that might be under your
+ 
+
+ align:start position:0%
+worlds that might be under your
+regulatory environment not as it is
+
+ align:start position:0%
+regulatory environment not as it is
+ 
+
+ align:start position:0%
+regulatory environment not as it is
+today
\ No newline at end of file
diff --git a/iCexjSqjmDE.txt b/iCexjSqjmDE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..54e400b50ac2d6a34d3b60d9cdcc6a7c9172e431
--- /dev/null
+++ b/iCexjSqjmDE.txt
@@ -0,0 +1,14580 @@
+align:start position:0%
+ 
+the following content is provided by mit
+
+ align:start position:0%
+the following content is provided by mit
+ 
+
+ align:start position:0%
+the following content is provided by mit
+opencourseware under a creative commons
+
+ align:start position:0%
+opencourseware under a creative commons
+ 
+
+ align:start position:0%
+opencourseware under a creative commons
+license
+
+ align:start position:0%
+license
+ 
+
+ align:start position:0%
+license
+additional information about our license
+
+ align:start position:0%
+additional information about our license
+ 
+
+ align:start position:0%
+additional information about our license
+and mit opencourseware in general is
+
+ align:start position:0%
+and mit opencourseware in general is
+ 
+
+ align:start position:0%
+and mit opencourseware in general is
+available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when i was doing my uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when i started my doctoral dissertation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i went in to visit my advisor and i said
+
+ align:start position:0%
+i went in to visit my advisor and i said
+ 
+
+ align:start position:0%
+i went in to visit my advisor and i said
+he laid out
+
+ align:start position:0%
+he laid out
+ 
+
+ align:start position:0%
+he laid out
+uh the problem because it was on a grant
+
+ align:start position:0%
+uh the problem because it was on a grant
+ 
+
+ align:start position:0%
+uh the problem because it was on a grant
+and it was some leeway
+
+ align:start position:0%
+and it was some leeway
+ 
+
+ align:start position:0%
+and it was some leeway
+a lot of leeway
+
+ align:start position:0%
+a lot of leeway
+ 
+
+ align:start position:0%
+a lot of leeway
+and it was on it was on submarines
+
+ align:start position:0%
+and it was on it was on submarines
+ 
+
+ align:start position:0%
+and it was on it was on submarines
+i think i gave you a little
+
+ align:start position:0%
+i think i gave you a little
+ 
+
+ align:start position:0%
+i think i gave you a little
+thing about that and uh
+
+ align:start position:0%
+thing about that and uh
+ 
+
+ align:start position:0%
+thing about that and uh
+so i'd heard a lot of uh
+
+ align:start position:0%
+so i'd heard a lot of uh
+ 
+
+ align:start position:0%
+so i'd heard a lot of uh
+stories about doing dissertations
+
+ align:start position:0%
+stories about doing dissertations
+ 
+
+ align:start position:0%
+stories about doing dissertations
+particularly there was a
+
+ align:start position:0%
+particularly there was a
+ 
+
+ align:start position:0%
+particularly there was a
+it was a guy who was in the department
+
+ align:start position:0%
+it was a guy who was in the department
+ 
+
+ align:start position:0%
+it was a guy who was in the department
+who had been around for
+
+ align:start position:0%
+who had been around for
+ 
+
+ align:start position:0%
+who had been around for
+10 years you know
+
+ align:start position:0%
+10 years you know
+ 
+
+ align:start position:0%
+10 years you know
+so i said
+
+ align:start position:0%
+so i said
+ 
+
+ align:start position:0%
+so i said
+when
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well i finished this dissertation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh i expected him to say when i got
+
+ align:start position:0%
+and uh i expected him to say when i got
+ 
+
+ align:start position:0%
+and uh i expected him to say when i got
+the solution to this problem
+
+ align:start position:0%
+the solution to this problem
+ 
+
+ align:start position:0%
+the solution to this problem
+he didn't say that
+
+ align:start position:0%
+he didn't say that
+ 
+
+ align:start position:0%
+he didn't say that
+he said
+
+ align:start position:0%
+he said
+ 
+
+ align:start position:0%
+he said
+well right now i'm the teacher and
+
+ align:start position:0%
+well right now i'm the teacher and
+ 
+
+ align:start position:0%
+well right now i'm the teacher and
+you're the student
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he said you'll know when you're going to
+
+ align:start position:0%
+he said you'll know when you're going to
+ 
+
+ align:start position:0%
+he said you'll know when you're going to
+finish the dissertation when you become
+
+ align:start position:0%
+finish the dissertation when you become
+ 
+
+ align:start position:0%
+finish the dissertation when you become
+the teacher and i become the student
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in other words
+
+ align:start position:0%
+in other words
+ 
+
+ align:start position:0%
+in other words
+what really what he was really saying
+
+ align:start position:0%
+what really what he was really saying
+ 
+
+ align:start position:0%
+what really what he was really saying
+was when he volunteered to become the
+
+ align:start position:0%
+was when he volunteered to become the
+ 
+
+ align:start position:0%
+was when he volunteered to become the
+student i wasn't going to make you know
+
+ align:start position:0%
+student i wasn't going to make you know
+ 
+
+ align:start position:0%
+student i wasn't going to make you know
+you know when he just sat back and that
+
+ align:start position:0%
+you know when he just sat back and that
+ 
+
+ align:start position:0%
+you know when he just sat back and that
+day came it came all in one
+
+ align:start position:0%
+day came it came all in one
+ 
+
+ align:start position:0%
+day came it came all in one
+in one moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because uh
+
+ align:start position:0%
+because uh
+ 
+
+ align:start position:0%
+because uh
+i had gotten all of these equations but
+
+ align:start position:0%
+i had gotten all of these equations but
+ 
+
+ align:start position:0%
+i had gotten all of these equations but
+i needed one more equation
+
+ align:start position:0%
+i needed one more equation
+ 
+
+ align:start position:0%
+i needed one more equation
+because i i had an extra constraint
+
+ align:start position:0%
+because i i had an extra constraint
+ 
+
+ align:start position:0%
+because i i had an extra constraint
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+and he didn't know where to go with that
+
+ align:start position:0%
+and he didn't know where to go with that
+ 
+
+ align:start position:0%
+and he didn't know where to go with that
+he could get that equation and he had
+
+ align:start position:0%
+he could get that equation and he had
+ 
+
+ align:start position:0%
+he could get that equation and he had
+told me where he thought it came from
+
+ align:start position:0%
+told me where he thought it came from
+ 
+
+ align:start position:0%
+told me where he thought it came from
+and i told him i thought it came from
+
+ align:start position:0%
+and i told him i thought it came from
+ 
+
+ align:start position:0%
+and i told him i thought it came from
+someplace else
+
+ align:start position:0%
+someplace else
+ 
+
+ align:start position:0%
+someplace else
+and so what i did was something that
+
+ align:start position:0%
+and so what i did was something that
+ 
+
+ align:start position:0%
+and so what i did was something that
+graduate students don't normally do i
+
+ align:start position:0%
+graduate students don't normally do i
+ 
+
+ align:start position:0%
+graduate students don't normally do i
+did it both ways
+
+ align:start position:0%
+did it both ways
+ 
+
+ align:start position:0%
+did it both ways
+did it his way
+
+ align:start position:0%
+did it his way
+ 
+
+ align:start position:0%
+did it his way
+and i did it so-called my way
+
+ align:start position:0%
+and i did it so-called my way
+ 
+
+ align:start position:0%
+and i did it so-called my way
+and when i went back i showed him his
+
+ align:start position:0%
+and when i went back i showed him his
+ 
+
+ align:start position:0%
+and when i went back i showed him his
+way and was getting all tangled up
+
+ align:start position:0%
+way and was getting all tangled up
+ 
+
+ align:start position:0%
+way and was getting all tangled up
+looked like it might lead to some place
+
+ align:start position:0%
+looked like it might lead to some place
+ 
+
+ align:start position:0%
+looked like it might lead to some place
+but it just didn't know it wasn't it
+
+ align:start position:0%
+but it just didn't know it wasn't it
+ 
+
+ align:start position:0%
+but it just didn't know it wasn't it
+just it just got tangled up with a lot
+
+ align:start position:0%
+just it just got tangled up with a lot
+ 
+
+ align:start position:0%
+just it just got tangled up with a lot
+of concerns
+
+ align:start position:0%
+of concerns
+ 
+
+ align:start position:0%
+of concerns
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+he said well what do you what do you
+
+ align:start position:0%
+he said well what do you what do you
+ 
+
+ align:start position:0%
+he said well what do you what do you
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+and he said i said but i've got another
+
+ align:start position:0%
+and he said i said but i've got another
+ 
+
+ align:start position:0%
+and he said i said but i've got another
+suggestion
+
+ align:start position:0%
+suggestion
+ 
+
+ align:start position:0%
+suggestion
+so i wrote i made this assumption
+
+ align:start position:0%
+so i wrote i made this assumption
+ 
+
+ align:start position:0%
+so i wrote i made this assumption
+and then he said well are we going to
+
+ align:start position:0%
+and then he said well are we going to
+ 
+
+ align:start position:0%
+and then he said well are we going to
+live with an assumption or can you prove
+
+ align:start position:0%
+live with an assumption or can you prove
+ 
+
+ align:start position:0%
+live with an assumption or can you prove
+this is true i said i can prove it
+
+ align:start position:0%
+this is true i said i can prove it
+ 
+
+ align:start position:0%
+this is true i said i can prove it
+i use geometry to prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+when i did that
+
+ align:start position:0%
+when i did that
+ 
+
+ align:start position:0%
+when i did that
+his whole tone of voice changed instead
+
+ align:start position:0%
+his whole tone of voice changed instead
+ 
+
+ align:start position:0%
+his whole tone of voice changed instead
+of talking to me about what i should be
+
+ align:start position:0%
+of talking to me about what i should be
+ 
+
+ align:start position:0%
+of talking to me about what i should be
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+he asked me what should we be doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i walked out of there and i said i
+
+ align:start position:0%
+and i walked out of there and i said i
+ 
+
+ align:start position:0%
+and i walked out of there and i said i
+got my dissertation well it took another
+
+ align:start position:0%
+got my dissertation well it took another
+ 
+
+ align:start position:0%
+got my dissertation well it took another
+year
+
+ align:start position:0%
+year
+ 
+
+ align:start position:0%
+year
+you know before it was all
+
+ align:start position:0%
+you know before it was all
+ 
+
+ align:start position:0%
+you know before it was all
+done but that might have been in
+
+ align:start position:0%
+done but that might have been in
+ 
+
+ align:start position:0%
+done but that might have been in
+march
+
+ align:start position:0%
+march
+ 
+
+ align:start position:0%
+march
+it was done in november
+
+ align:start position:0%
+it was done in november
+ 
+
+ align:start position:0%
+it was done in november
+at that moment i knew so i'd like to use
+
+ align:start position:0%
+at that moment i knew so i'd like to use
+ 
+
+ align:start position:0%
+at that moment i knew so i'd like to use
+some of that with the class some i want
+
+ align:start position:0%
+some of that with the class some i want
+ 
+
+ align:start position:0%
+some of that with the class some i want
+y'all to turn me around i know next week
+
+ align:start position:0%
+y'all to turn me around i know next week
+ 
+
+ align:start position:0%
+y'all to turn me around i know next week
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+final week of class but that's good uh
+
+ align:start position:0%
+final week of class but that's good uh
+ 
+
+ align:start position:0%
+final week of class but that's good uh
+practice isn't it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+already
+
+ align:start position:0%
+already
+ 
+
+ align:start position:0%
+already
+already
+
+ align:start position:0%
+already
+ 
+
+ align:start position:0%
+already
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh that has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+that's a story that i can tell i'm just
+
+ align:start position:0%
+that's a story that i can tell i'm just
+ 
+
+ align:start position:0%
+that's a story that i can tell i'm just
+trying to think of where to start so i
+
+ align:start position:0%
+trying to think of where to start so i
+ 
+
+ align:start position:0%
+trying to think of where to start so i
+don't take up the whole class people
+
+ align:start position:0%
+don't take up the whole class people
+ 
+
+ align:start position:0%
+don't take up the whole class people
+i want to make five minutes out of it
+
+ align:start position:0%
+i want to make five minutes out of it
+ 
+
+ align:start position:0%
+i want to make five minutes out of it
+right maybe 10 at the most
+
+ align:start position:0%
+right maybe 10 at the most
+ 
+
+ align:start position:0%
+right maybe 10 at the most
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the whole thing started um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't know where the whole thing
+
+ align:start position:0%
+i don't know where the whole thing
+ 
+
+ align:start position:0%
+i don't know where the whole thing
+started
+
+ align:start position:0%
+started
+ 
+
+ align:start position:0%
+started
+but a good place to start is with this
+
+ align:start position:0%
+but a good place to start is with this
+ 
+
+ align:start position:0%
+but a good place to start is with this
+man named joseph campbell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i saw him on the bill moyers program
+
+ align:start position:0%
+and i saw him on the bill moyers program
+ 
+
+ align:start position:0%
+and i saw him on the bill moyers program
+bill moyers had
+
+ align:start position:0%
+bill moyers had
+ 
+
+ align:start position:0%
+bill moyers had
+had this program i forgot the name of
+
+ align:start position:0%
+had this program i forgot the name of
+ 
+
+ align:start position:0%
+had this program i forgot the name of
+but he'd interview these people
+
+ align:start position:0%
+but he'd interview these people
+ 
+
+ align:start position:0%
+but he'd interview these people
+that had something
+
+ align:start position:0%
+that had something
+ 
+
+ align:start position:0%
+that had something
+interesting to say bill moyer's
+
+ align:start position:0%
+interesting to say bill moyer's
+ 
+
+ align:start position:0%
+interesting to say bill moyer's
+background is in divinity i don't know
+
+ align:start position:0%
+background is in divinity i don't know
+ 
+
+ align:start position:0%
+background is in divinity i don't know
+if he's ever been ordained but he has
+
+ align:start position:0%
+if he's ever been ordained but he has
+ 
+
+ align:start position:0%
+if he's ever been ordained but he has
+his doctorate is in divinity
+
+ align:start position:0%
+his doctorate is in divinity
+ 
+
+ align:start position:0%
+his doctorate is in divinity
+so he has an appreciation for
+
+ align:start position:0%
+so he has an appreciation for
+ 
+
+ align:start position:0%
+so he has an appreciation for
+philosophy
+
+ align:start position:0%
+philosophy
+ 
+
+ align:start position:0%
+philosophy
+a deep knowledge of it
+
+ align:start position:0%
+a deep knowledge of it
+ 
+
+ align:start position:0%
+a deep knowledge of it
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+there is an orientation
+
+ align:start position:0%
+there is an orientation
+ 
+
+ align:start position:0%
+there is an orientation
+uh to religion that he had that seemed
+
+ align:start position:0%
+uh to religion that he had that seemed
+ 
+
+ align:start position:0%
+uh to religion that he had that seemed
+to have that uh fit in with with with uh
+
+ align:start position:0%
+to have that uh fit in with with with uh
+ 
+
+ align:start position:0%
+to have that uh fit in with with with uh
+joseph campbell and that was uh
+
+ align:start position:0%
+joseph campbell and that was uh
+ 
+
+ align:start position:0%
+joseph campbell and that was uh
+the notion of uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+allegorical
+
+ align:start position:0%
+allegorical
+ 
+
+ align:start position:0%
+allegorical
+theology
+
+ align:start position:0%
+theology
+ 
+
+ align:start position:0%
+theology
+and that is that what you learn
+
+ align:start position:0%
+and that is that what you learn
+ 
+
+ align:start position:0%
+and that is that what you learn
+is told in a story
+
+ align:start position:0%
+is told in a story
+ 
+
+ align:start position:0%
+is told in a story
+and somehow or another your life story
+
+ align:start position:0%
+and somehow or another your life story
+ 
+
+ align:start position:0%
+and somehow or another your life story
+or the big events in your life
+
+ align:start position:0%
+or the big events in your life
+ 
+
+ align:start position:0%
+or the big events in your life
+will be metaphors of one of those
+
+ align:start position:0%
+will be metaphors of one of those
+ 
+
+ align:start position:0%
+will be metaphors of one of those
+stories
+
+ align:start position:0%
+stories
+ 
+
+ align:start position:0%
+stories
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now they use the same thing in law but
+
+ align:start position:0%
+now they use the same thing in law but
+ 
+
+ align:start position:0%
+now they use the same thing in law but
+they call it by a different name they
+
+ align:start position:0%
+they call it by a different name they
+ 
+
+ align:start position:0%
+they call it by a different name they
+call it uh
+
+ align:start position:0%
+call it uh
+ 
+
+ align:start position:0%
+call it uh
+they call it uh
+
+ align:start position:0%
+they call it uh
+ 
+
+ align:start position:0%
+they call it uh
+what do they call it
+
+ align:start position:0%
+what do they call it
+ 
+
+ align:start position:0%
+what do they call it
+presidents
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when you have a legal case
+
+ align:start position:0%
+so when you have a legal case
+ 
+
+ align:start position:0%
+so when you have a legal case
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a case that you want to prosecute
+
+ align:start position:0%
+a case that you want to prosecute
+ 
+
+ align:start position:0%
+a case that you want to prosecute
+prosecute or defend
+
+ align:start position:0%
+prosecute or defend
+ 
+
+ align:start position:0%
+prosecute or defend
+you go into case history
+
+ align:start position:0%
+you go into case history
+ 
+
+ align:start position:0%
+you go into case history
+and you find one that looks like this
+
+ align:start position:0%
+and you find one that looks like this
+ 
+
+ align:start position:0%
+and you find one that looks like this
+particular case
+
+ align:start position:0%
+particular case
+ 
+
+ align:start position:0%
+particular case
+and then you say well what did the judge
+
+ align:start position:0%
+and then you say well what did the judge
+ 
+
+ align:start position:0%
+and then you say well what did the judge
+how did the judge how did the lawyers
+
+ align:start position:0%
+how did the judge how did the lawyers
+ 
+
+ align:start position:0%
+how did the judge how did the lawyers
+argue the case and what did the judge
+
+ align:start position:0%
+argue the case and what did the judge
+ 
+
+ align:start position:0%
+argue the case and what did the judge
+decide
+
+ align:start position:0%
+decide
+ 
+
+ align:start position:0%
+decide
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+when found guilty of the punishment
+
+ align:start position:0%
+when found guilty of the punishment
+ 
+
+ align:start position:0%
+when found guilty of the punishment
+okay and that's a very interesting
+
+ align:start position:0%
+okay and that's a very interesting
+ 
+
+ align:start position:0%
+okay and that's a very interesting
+question for lawyers
+
+ align:start position:0%
+question for lawyers
+ 
+
+ align:start position:0%
+question for lawyers
+you're remembering the scopes trial
+
+ align:start position:0%
+you're remembering the scopes trial
+ 
+
+ align:start position:0%
+you're remembering the scopes trial
+however so um well i'm going to talk
+
+ align:start position:0%
+however so um well i'm going to talk
+ 
+
+ align:start position:0%
+however so um well i'm going to talk
+about the scope trial for
+
+ align:start position:0%
+about the scope trial for
+ 
+
+ align:start position:0%
+about the scope trial for
+about 20 seconds but the scopes but i'm
+
+ align:start position:0%
+about 20 seconds but the scopes but i'm
+ 
+
+ align:start position:0%
+about 20 seconds but the scopes but i'm
+going to talk about it from the movie
+
+ align:start position:0%
+going to talk about it from the movie
+ 
+
+ align:start position:0%
+going to talk about it from the movie
+uh inherit the wind not from the
+
+ align:start position:0%
+uh inherit the wind not from the
+ 
+
+ align:start position:0%
+uh inherit the wind not from the
+newspapers
+
+ align:start position:0%
+newspapers
+ 
+
+ align:start position:0%
+newspapers
+and from the law courts in the in the
+
+ align:start position:0%
+and from the law courts in the in the
+ 
+
+ align:start position:0%
+and from the law courts in the in the
+movie
+
+ align:start position:0%
+movie
+ 
+
+ align:start position:0%
+movie
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the scopes was found guilty
+
+ align:start position:0%
+the scopes was found guilty
+ 
+
+ align:start position:0%
+the scopes was found guilty
+uh but then the judge said you find him
+
+ align:start position:0%
+uh but then the judge said you find him
+ 
+
+ align:start position:0%
+uh but then the judge said you find him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+uh i i i
+
+ align:start position:0%
+uh i i i
+ 
+
+ align:start position:0%
+uh i i i
+i hope you understand me when i say i
+
+ align:start position:0%
+i hope you understand me when i say i
+ 
+
+ align:start position:0%
+i hope you understand me when i say i
+fell in love with joseph campbell
+
+ align:start position:0%
+fell in love with joseph campbell
+ 
+
+ align:start position:0%
+fell in love with joseph campbell
+not just with what he was saying but the
+
+ align:start position:0%
+not just with what he was saying but the
+ 
+
+ align:start position:0%
+not just with what he was saying but the
+way he said it and all these figures and
+
+ align:start position:0%
+way he said it and all these figures and
+ 
+
+ align:start position:0%
+way he said it and all these figures and
+everything
+
+ align:start position:0%
+everything
+ 
+
+ align:start position:0%
+everything
+and then i got out went out and read
+
+ align:start position:0%
+and then i got out went out and read
+ 
+
+ align:start position:0%
+and then i got out went out and read
+i got the i got the transcript of the um
+
+ align:start position:0%
+i got the i got the transcript of the um
+ 
+
+ align:start position:0%
+i got the i got the transcript of the um
+of the tv program
+
+ align:start position:0%
+of the tv program
+ 
+
+ align:start position:0%
+of the tv program
+then uh
+
+ align:start position:0%
+then uh
+ 
+
+ align:start position:0%
+then uh
+i went out and read four of his books
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then over time i got some videotapes
+
+ align:start position:0%
+and then over time i got some videotapes
+ 
+
+ align:start position:0%
+and then over time i got some videotapes
+some videos of his uh his lectures many
+
+ align:start position:0%
+some videos of his uh his lectures many
+ 
+
+ align:start position:0%
+some videos of his uh his lectures many
+of his lectures have been put on
+
+ align:start position:0%
+of his lectures have been put on
+ 
+
+ align:start position:0%
+of his lectures have been put on
+videotape
+
+ align:start position:0%
+videotape
+ 
+
+ align:start position:0%
+videotape
+so i got about uh
+
+ align:start position:0%
+so i got about uh
+ 
+
+ align:start position:0%
+so i got about uh
+two hours of that
+
+ align:start position:0%
+two hours of that
+ 
+
+ align:start position:0%
+two hours of that
+and sat down with my uh stepson over
+
+ align:start position:0%
+and sat down with my uh stepson over
+ 
+
+ align:start position:0%
+and sat down with my uh stepson over
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay because i was trying to help him
+
+ align:start position:0%
+okay because i was trying to help him
+ 
+
+ align:start position:0%
+okay because i was trying to help him
+with his one of his problems
+
+ align:start position:0%
+with his one of his problems
+ 
+
+ align:start position:0%
+with his one of his problems
+and i used mythology i went out wrote a
+
+ align:start position:0%
+and i used mythology i went out wrote a
+ 
+
+ align:start position:0%
+and i used mythology i went out wrote a
+paper on him
+
+ align:start position:0%
+paper on him
+ 
+
+ align:start position:0%
+paper on him
+now the paper called uh the paper called
+
+ align:start position:0%
+now the paper called uh the paper called
+ 
+
+ align:start position:0%
+now the paper called uh the paper called
+about the about not the concrete symbol
+
+ align:start position:0%
+about the about not the concrete symbol
+ 
+
+ align:start position:0%
+about the about not the concrete symbol
+the one about the oberlin horse
+
+ align:start position:0%
+the one about the oberlin horse
+ 
+
+ align:start position:0%
+the one about the oberlin horse
+i wrote that for him
+
+ align:start position:0%
+i wrote that for him
+ 
+
+ align:start position:0%
+i wrote that for him
+i said this is gonna solve your problem
+
+ align:start position:0%
+i said this is gonna solve your problem
+ 
+
+ align:start position:0%
+i said this is gonna solve your problem
+it didn't
+
+ align:start position:0%
+it didn't
+ 
+
+ align:start position:0%
+it didn't
+but uh
+
+ align:start position:0%
+but uh
+ 
+
+ align:start position:0%
+but uh
+but uh
+
+ align:start position:0%
+but uh
+ 
+
+ align:start position:0%
+but uh
+i think what you'll what you'll see in
+
+ align:start position:0%
+i think what you'll what you'll see in
+ 
+
+ align:start position:0%
+i think what you'll what you'll see in
+this life is that some people
+
+ align:start position:0%
+this life is that some people
+ 
+
+ align:start position:0%
+this life is that some people
+are for example
+
+ align:start position:0%
+are for example
+ 
+
+ align:start position:0%
+are for example
+scientists eight hours a day
+
+ align:start position:0%
+scientists eight hours a day
+ 
+
+ align:start position:0%
+scientists eight hours a day
+after that science didn't mean anything
+
+ align:start position:0%
+after that science didn't mean anything
+ 
+
+ align:start position:0%
+after that science didn't mean anything
+to them
+
+ align:start position:0%
+to them
+ 
+
+ align:start position:0%
+to them
+don't get it wrong they may be the best
+
+ align:start position:0%
+don't get it wrong they may be the best
+ 
+
+ align:start position:0%
+don't get it wrong they may be the best
+some of them may be
+
+ align:start position:0%
+some of them may be
+ 
+
+ align:start position:0%
+some of them may be
+very talented at what they do
+
+ align:start position:0%
+very talented at what they do
+ 
+
+ align:start position:0%
+very talented at what they do
+but um
+
+ align:start position:0%
+but um
+ 
+
+ align:start position:0%
+but um
+i'm what they call a professor 24 hours
+
+ align:start position:0%
+i'm what they call a professor 24 hours
+ 
+
+ align:start position:0%
+i'm what they call a professor 24 hours
+a day i saw the deepest problems in my
+
+ align:start position:0%
+a day i saw the deepest problems in my
+ 
+
+ align:start position:0%
+a day i saw the deepest problems in my
+life by going to the library
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so uh i got i got started with this
+
+ align:start position:0%
+okay so uh i got i got started with this
+ 
+
+ align:start position:0%
+okay so uh i got i got started with this
+whole thing about um
+
+ align:start position:0%
+whole thing about um
+ 
+
+ align:start position:0%
+whole thing about um
+with uh
+
+ align:start position:0%
+with uh
+ 
+
+ align:start position:0%
+with uh
+to answer your question with joseph
+
+ align:start position:0%
+to answer your question with joseph
+ 
+
+ align:start position:0%
+to answer your question with joseph
+campbell
+
+ align:start position:0%
+campbell
+ 
+
+ align:start position:0%
+campbell
+uh that was natural to me because i came
+
+ align:start position:0%
+uh that was natural to me because i came
+ 
+
+ align:start position:0%
+uh that was natural to me because i came
+up in a storytelling family
+
+ align:start position:0%
+up in a storytelling family
+ 
+
+ align:start position:0%
+up in a storytelling family
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+turned off the tv
+
+ align:start position:0%
+turned off the tv
+ 
+
+ align:start position:0%
+turned off the tv
+notice i said tv
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we got our first television in 1948
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we were only two people we were only
+
+ align:start position:0%
+we were only two people we were only
+ 
+
+ align:start position:0%
+we were only two people we were only
+there there were only two families in
+
+ align:start position:0%
+there there were only two families in
+ 
+
+ align:start position:0%
+there there were only two families in
+hickory north carolina that had
+
+ align:start position:0%
+hickory north carolina that had
+ 
+
+ align:start position:0%
+hickory north carolina that had
+television but they had went off
+
+ align:start position:0%
+television but they had went off
+ 
+
+ align:start position:0%
+television but they had went off
+people used the kids used to come over
+
+ align:start position:0%
+people used the kids used to come over
+ 
+
+ align:start position:0%
+people used the kids used to come over
+the television television wasn't on
+
+ align:start position:0%
+the television television wasn't on
+ 
+
+ align:start position:0%
+the television television wasn't on
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+an hour a day
+
+ align:start position:0%
+an hour a day
+ 
+
+ align:start position:0%
+an hour a day
+came on like four o'clock was off at
+
+ align:start position:0%
+came on like four o'clock was off at
+ 
+
+ align:start position:0%
+came on like four o'clock was off at
+five
+
+ align:start position:0%
+five
+ 
+
+ align:start position:0%
+five
+the news was five minutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a tv program a drama was 15.
+
+ align:start position:0%
+a tv program a drama was 15.
+ 
+
+ align:start position:0%
+a tv program a drama was 15.
+uh kids used to come over saturday
+
+ align:start position:0%
+uh kids used to come over saturday
+ 
+
+ align:start position:0%
+uh kids used to come over saturday
+mornings to watch the television my
+
+ align:start position:0%
+mornings to watch the television my
+ 
+
+ align:start position:0%
+mornings to watch the television my
+mother would serve uh popcorn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah uh
+
+ align:start position:0%
+yeah uh
+ 
+
+ align:start position:0%
+yeah uh
+that was down in hickory north carolina
+
+ align:start position:0%
+that was down in hickory north carolina
+ 
+
+ align:start position:0%
+that was down in hickory north carolina
+in 1948
+
+ align:start position:0%
+in 1948
+ 
+
+ align:start position:0%
+in 1948
+uh we turned off but even later in life
+
+ align:start position:0%
+uh we turned off but even later in life
+ 
+
+ align:start position:0%
+uh we turned off but even later in life
+we turned off the television
+
+ align:start position:0%
+we turned off the television
+ 
+
+ align:start position:0%
+we turned off the television
+and our parents would have relatives of
+
+ align:start position:0%
+and our parents would have relatives of
+ 
+
+ align:start position:0%
+and our parents would have relatives of
+friends over and they get to talking
+
+ align:start position:0%
+friends over and they get to talking
+ 
+
+ align:start position:0%
+friends over and they get to talking
+about something and telling and then
+
+ align:start position:0%
+about something and telling and then
+ 
+
+ align:start position:0%
+about something and telling and then
+when they got into the storytelling mode
+
+ align:start position:0%
+when they got into the storytelling mode
+ 
+
+ align:start position:0%
+when they got into the storytelling mode
+they let me and my little brother come
+
+ align:start position:0%
+they let me and my little brother come
+ 
+
+ align:start position:0%
+they let me and my little brother come
+out and we sit on the floor and listen
+
+ align:start position:0%
+out and we sit on the floor and listen
+ 
+
+ align:start position:0%
+out and we sit on the floor and listen
+to him so i came out into a storytelling
+
+ align:start position:0%
+to him so i came out into a storytelling
+ 
+
+ align:start position:0%
+to him so i came out into a storytelling
+mode in the first place so telling
+
+ align:start position:0%
+mode in the first place so telling
+ 
+
+ align:start position:0%
+mode in the first place so telling
+stories so so that so the end of this
+
+ align:start position:0%
+stories so so that so the end of this
+ 
+
+ align:start position:0%
+stories so so that so the end of this
+your question is
+
+ align:start position:0%
+your question is
+ 
+
+ align:start position:0%
+your question is
+that uh i gave a paper at a conference
+
+ align:start position:0%
+that uh i gave a paper at a conference
+ 
+
+ align:start position:0%
+that uh i gave a paper at a conference
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+my thoughts were uh
+
+ align:start position:0%
+my thoughts were uh
+ 
+
+ align:start position:0%
+my thoughts were uh
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+respected to some extent joyed to some
+
+ align:start position:0%
+respected to some extent joyed to some
+ 
+
+ align:start position:0%
+respected to some extent joyed to some
+extent not a whole lot
+
+ align:start position:0%
+extent not a whole lot
+ 
+
+ align:start position:0%
+extent not a whole lot
+uh what i brought to the table was that
+
+ align:start position:0%
+uh what i brought to the table was that
+ 
+
+ align:start position:0%
+uh what i brought to the table was that
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+
+ align:start position:0%
+i was one of the few engineers on the in
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+
+ align:start position:0%
+i was one of the few engineers on the in
+the room when they were talking
+
+ align:start position:0%
+the room when they were talking
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+
+ align:start position:0%
+the room when they were talking
+engineering ethics
+
+ align:start position:0%
+engineering ethics
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+
+ align:start position:0%
+engineering ethics
+uh better stated i was one of the few
+
+ align:start position:0%
+uh better stated i was one of the few
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+
+ align:start position:0%
+uh better stated i was one of the few
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+ align:start position:0%
+engineers who was a
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+
+ align:start position:0%
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+
+ align:start position:0%
+practicing academic academic with a
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+ align:start position:0%
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+ align:start position:0%
+doctor in engineering a lot of more
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+
+ align:start position:0%
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+
+ align:start position:0%
+practicing engineers
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+ align:start position:0%
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+ align:start position:0%
+but i was one of the few so when i gave
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+
+ align:start position:0%
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+ align:start position:0%
+talks people were nice
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+
+ align:start position:0%
+talks people were nice
+one day i gave a talk and i told this
+
+ align:start position:0%
+one day i gave a talk and i told this
+ 
+
+ align:start position:0%
+one day i gave a talk and i told this
+concrete sumo during the whole place
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+published it and got on what they call a
+
+ align:start position:0%
+published it and got on what they call a
+ 
+
+ align:start position:0%
+published it and got on what they call a
+lecture circuit
+
+ align:start position:0%
+lecture circuit
+ 
+
+ align:start position:0%
+lecture circuit
+and i was given lectures around the
+
+ align:start position:0%
+and i was given lectures around the
+ 
+
+ align:start position:0%
+and i was given lectures around the
+country i wasn't making a lot of money
+
+ align:start position:0%
+country i wasn't making a lot of money
+ 
+
+ align:start position:0%
+country i wasn't making a lot of money
+you know some people what was it uh who
+
+ align:start position:0%
+you know some people what was it uh who
+ 
+
+ align:start position:0%
+you know some people what was it uh who
+is it uh
+
+ align:start position:0%
+is it uh
+ 
+
+ align:start position:0%
+is it uh
+colin powell doesn't he charge something
+
+ align:start position:0%
+colin powell doesn't he charge something
+ 
+
+ align:start position:0%
+colin powell doesn't he charge something
+like twenty thousand dollars for a
+
+ align:start position:0%
+like twenty thousand dollars for a
+ 
+
+ align:start position:0%
+like twenty thousand dollars for a
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+i was i was getting fifty dollars
+
+ align:start position:0%
+i was i was getting fifty dollars
+ 
+
+ align:start position:0%
+i was i was getting fifty dollars
+but they would pay my expenses
+
+ align:start position:0%
+but they would pay my expenses
+ 
+
+ align:start position:0%
+but they would pay my expenses
+you know so i went around and got i went
+
+ align:start position:0%
+you know so i went around and got i went
+ 
+
+ align:start position:0%
+you know so i went around and got i went
+on the circuit with it and the story
+
+ align:start position:0%
+on the circuit with it and the story
+ 
+
+ align:start position:0%
+on the circuit with it and the story
+thing just hit
+
+ align:start position:0%
+thing just hit
+ 
+
+ align:start position:0%
+thing just hit
+so i said there it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on thursday um now
+
+ align:start position:0%
+on thursday um now
+ 
+
+ align:start position:0%
+on thursday um now
+as it turns out the human factor has set
+
+ align:start position:0%
+as it turns out the human factor has set
+ 
+
+ align:start position:0%
+as it turns out the human factor has set
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cynthia
+
+ align:start position:0%
+cynthia
+ 
+
+ align:start position:0%
+cynthia
+winston uh
+
+ align:start position:0%
+winston uh
+ 
+
+ align:start position:0%
+winston uh
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+taken a hospital condition
+
+ align:start position:0%
+taken a hospital condition
+ 
+
+ align:start position:0%
+taken a hospital condition
+won't be able to make it
+
+ align:start position:0%
+won't be able to make it
+ 
+
+ align:start position:0%
+won't be able to make it
+i will do my best to cover
+
+ align:start position:0%
+i will do my best to cover
+ 
+
+ align:start position:0%
+i will do my best to cover
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+she was going to cover when i say do my
+
+ align:start position:0%
+she was going to cover when i say do my
+ 
+
+ align:start position:0%
+she was going to cover when i say do my
+best
+
+ align:start position:0%
+best
+ 
+
+ align:start position:0%
+best
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+
+ align:start position:0%
+i am not going to take we were going to
+ 
+
+ align:start position:0%
+i am not going to take we were going to
+have 20 minutes 20 minutes 20 minutes
+
+ align:start position:0%
+have 20 minutes 20 minutes 20 minutes
+ 
+
+ align:start position:0%
+have 20 minutes 20 minutes 20 minutes
+now we're going to have 30 minutes in 30
+
+ align:start position:0%
+now we're going to have 30 minutes in 30
+ 
+
+ align:start position:0%
+now we're going to have 30 minutes in 30
+minutes but i'll take out 10 minutes
+
+ align:start position:0%
+minutes but i'll take out 10 minutes
+ 
+
+ align:start position:0%
+minutes but i'll take out 10 minutes
+give an overview
+
+ align:start position:0%
+give an overview
+ 
+
+ align:start position:0%
+give an overview
+of what she was going to talk about
+
+ align:start position:0%
+of what she was going to talk about
+ 
+
+ align:start position:0%
+of what she was going to talk about
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i have some slides that i really got
+
+ align:start position:0%
+i have some slides that i really got
+ 
+
+ align:start position:0%
+i have some slides that i really got
+from another person
+
+ align:start position:0%
+from another person
+ 
+
+ align:start position:0%
+from another person
+i'll have to get his permission to put
+
+ align:start position:0%
+i'll have to get his permission to put
+ 
+
+ align:start position:0%
+i'll have to get his permission to put
+him up
+
+ align:start position:0%
+him up
+ 
+
+ align:start position:0%
+him up
+but i'll tell you what they are
+
+ align:start position:0%
+but i'll tell you what they are
+ 
+
+ align:start position:0%
+but i'll tell you what they are
+you need to know this is extraordinary
+
+ align:start position:0%
+you need to know this is extraordinary
+ 
+
+ align:start position:0%
+you need to know this is extraordinary
+i'll tell you who he is and where he can
+
+ align:start position:0%
+i'll tell you who he is and where he can
+ 
+
+ align:start position:0%
+i'll tell you who he is and where he can
+be contacted
+
+ align:start position:0%
+be contacted
+ 
+
+ align:start position:0%
+be contacted
+uh his last name is
+
+ align:start position:0%
+uh his last name is
+ 
+
+ align:start position:0%
+uh his last name is
+case beer one word c-a-s-e-b-e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh he holds a rank of major in the
+
+ align:start position:0%
+uh he holds a rank of major in the
+ 
+
+ align:start position:0%
+uh he holds a rank of major in the
+united states air force
+
+ align:start position:0%
+united states air force
+ 
+
+ align:start position:0%
+united states air force
+and my last count was that he was on the
+
+ align:start position:0%
+and my last count was that he was on the
+ 
+
+ align:start position:0%
+and my last count was that he was on the
+faculty at the air force academy
+
+ align:start position:0%
+faculty at the air force academy
+ 
+
+ align:start position:0%
+faculty at the air force academy
+that's what i'm going to try to reach in
+
+ align:start position:0%
+that's what i'm going to try to reach in
+ 
+
+ align:start position:0%
+that's what i'm going to try to reach in
+tonight
+
+ align:start position:0%
+tonight
+ 
+
+ align:start position:0%
+tonight
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i met him here
+
+ align:start position:0%
+i met him here
+ 
+
+ align:start position:0%
+i met him here
+um when i gave my first talk in esd he
+
+ align:start position:0%
+um when i gave my first talk in esd he
+ 
+
+ align:start position:0%
+um when i gave my first talk in esd he
+was there
+
+ align:start position:0%
+was there
+ 
+
+ align:start position:0%
+was there
+and he was there vis because he was a
+
+ align:start position:0%
+and he was there vis because he was a
+ 
+
+ align:start position:0%
+and he was there vis because he was a
+visiting professor up at harvard
+
+ align:start position:0%
+visiting professor up at harvard
+ 
+
+ align:start position:0%
+visiting professor up at harvard
+uh doing
+
+ align:start position:0%
+uh doing
+ 
+
+ align:start position:0%
+uh doing
+okay you ready for this ready for this
+
+ align:start position:0%
+okay you ready for this ready for this
+ 
+
+ align:start position:0%
+okay you ready for this ready for this
+he was doing empirical work on the brain
+
+ align:start position:0%
+he was doing empirical work on the brain
+ 
+
+ align:start position:0%
+he was doing empirical work on the brain
+not the mind on the
+
+ align:start position:0%
+not the mind on the
+ 
+
+ align:start position:0%
+not the mind on the
+brain when it processes stories
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and he's got these slides i could bring
+
+ align:start position:0%
+and he's got these slides i could bring
+ 
+
+ align:start position:0%
+and he's got these slides i could bring
+i've got them right there on my computer
+
+ align:start position:0%
+i've got them right there on my computer
+ 
+
+ align:start position:0%
+i've got them right there on my computer
+today but i do not feel
+
+ align:start position:0%
+today but i do not feel
+ 
+
+ align:start position:0%
+today but i do not feel
+comfortable even showing them to one
+
+ align:start position:0%
+comfortable even showing them to one
+ 
+
+ align:start position:0%
+comfortable even showing them to one
+other person
+
+ align:start position:0%
+other person
+ 
+
+ align:start position:0%
+other person
+because i don't know if he's published
+
+ align:start position:0%
+because i don't know if he's published
+ 
+
+ align:start position:0%
+because i don't know if he's published
+them yet not that i can do anything with
+
+ align:start position:0%
+them yet not that i can do anything with
+ 
+
+ align:start position:0%
+them yet not that i can do anything with
+them not
+
+ align:start position:0%
+them not
+ 
+
+ align:start position:0%
+them not
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+they've got these um
+
+ align:start position:0%
+they've got these um
+ 
+
+ align:start position:0%
+they've got these um
+scans of the brain
+
+ align:start position:0%
+scans of the brain
+ 
+
+ align:start position:0%
+scans of the brain
+and they show the parts of the brain
+
+ align:start position:0%
+and they show the parts of the brain
+ 
+
+ align:start position:0%
+and they show the parts of the brain
+that are active
+
+ align:start position:0%
+that are active
+ 
+
+ align:start position:0%
+that are active
+during storytelling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah and
+
+ align:start position:0%
+yeah and
+ 
+
+ align:start position:0%
+yeah and
+and his area is ethics he's trying to
+
+ align:start position:0%
+and his area is ethics he's trying to
+ 
+
+ align:start position:0%
+and his area is ethics he's trying to
+relate the stories the to the to ethics
+
+ align:start position:0%
+relate the stories the to the to ethics
+ 
+
+ align:start position:0%
+relate the stories the to the to ethics
+he's got his i think his document is
+
+ align:start position:0%
+he's got his i think his document is
+ 
+
+ align:start position:0%
+he's got his i think his document is
+or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no i have to find out you know uh but
+
+ align:start position:0%
+no i have to find out you know uh but
+ 
+
+ align:start position:0%
+no i have to find out you know uh but
+hopefully i'll have enough to say
+
+ align:start position:0%
+hopefully i'll have enough to say
+ 
+
+ align:start position:0%
+hopefully i'll have enough to say
+hopefully i'll get permission from him
+
+ align:start position:0%
+hopefully i'll get permission from him
+ 
+
+ align:start position:0%
+hopefully i'll get permission from him
+tonight
+
+ align:start position:0%
+tonight
+ 
+
+ align:start position:0%
+tonight
+hopefully i'll have enough to say
+
+ align:start position:0%
+hopefully i'll have enough to say
+ 
+
+ align:start position:0%
+hopefully i'll have enough to say
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in plain language i will not attempt to
+
+ align:start position:0%
+in plain language i will not attempt to
+ 
+
+ align:start position:0%
+in plain language i will not attempt to
+be a psychologist but i don't know how
+
+ align:start position:0%
+be a psychologist but i don't know how
+ 
+
+ align:start position:0%
+be a psychologist but i don't know how
+he's gotten into the empirical work
+
+ align:start position:0%
+he's gotten into the empirical work
+ 
+
+ align:start position:0%
+he's gotten into the empirical work
+probably with collaborators
+
+ align:start position:0%
+probably with collaborators
+ 
+
+ align:start position:0%
+probably with collaborators
+but his background he has his background
+
+ align:start position:0%
+but his background he has his background
+ 
+
+ align:start position:0%
+but his background he has his background
+is in ethics and uh
+
+ align:start position:0%
+is in ethics and uh
+ 
+
+ align:start position:0%
+is in ethics and uh
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+it's all empirical he it's incredible
+
+ align:start position:0%
+it's all empirical he it's incredible
+ 
+
+ align:start position:0%
+it's all empirical he it's incredible
+this stuff that he's doing so this this
+
+ align:start position:0%
+this stuff that he's doing so this this
+ 
+
+ align:start position:0%
+this stuff that he's doing so this this
+this business of storytelling
+
+ align:start position:0%
+this business of storytelling
+ 
+
+ align:start position:0%
+this business of storytelling
+um has caught on and i think it caught
+
+ align:start position:0%
+um has caught on and i think it caught
+ 
+
+ align:start position:0%
+um has caught on and i think it caught
+on because
+
+ align:start position:0%
+on because
+ 
+
+ align:start position:0%
+on because
+uh something not totally irrelevant
+
+ align:start position:0%
+uh something not totally irrelevant
+ 
+
+ align:start position:0%
+uh something not totally irrelevant
+i think well what the argument i make i
+
+ align:start position:0%
+i think well what the argument i make i
+ 
+
+ align:start position:0%
+i think well what the argument i make i
+do a historical analysis
+
+ align:start position:0%
+do a historical analysis
+ 
+
+ align:start position:0%
+do a historical analysis
+of all this and what i say is that that
+
+ align:start position:0%
+of all this and what i say is that that
+ 
+
+ align:start position:0%
+of all this and what i say is that that
+the interest really got started with
+
+ align:start position:0%
+the interest really got started with
+ 
+
+ align:start position:0%
+the interest really got started with
+noam chomsky
+
+ align:start position:0%
+noam chomsky
+ 
+
+ align:start position:0%
+noam chomsky
+when noam chomsky said that the brain is
+
+ align:start position:0%
+when noam chomsky said that the brain is
+ 
+
+ align:start position:0%
+when noam chomsky said that the brain is
+wired
+
+ align:start position:0%
+wired
+ 
+
+ align:start position:0%
+wired
+uh for language structures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is that no matter what country
+
+ align:start position:0%
+that is that no matter what country
+ 
+
+ align:start position:0%
+that is that no matter what country
+you're born in
+
+ align:start position:0%
+you're born in
+ 
+
+ align:start position:0%
+you're born in
+no matter what period
+
+ align:start position:0%
+no matter what period
+ 
+
+ align:start position:0%
+no matter what period
+of human development you were born in
+
+ align:start position:0%
+of human development you were born in
+ 
+
+ align:start position:0%
+of human development you were born in
+after we became homo sapiens saving
+
+ align:start position:0%
+after we became homo sapiens saving
+ 
+
+ align:start position:0%
+after we became homo sapiens saving
+that the brain was wired for the same
+
+ align:start position:0%
+that the brain was wired for the same
+ 
+
+ align:start position:0%
+that the brain was wired for the same
+language had the same language
+
+ align:start position:0%
+language had the same language
+ 
+
+ align:start position:0%
+language had the same language
+structures you may learn different
+
+ align:start position:0%
+structures you may learn different
+ 
+
+ align:start position:0%
+structures you may learn different
+languages
+
+ align:start position:0%
+languages
+ 
+
+ align:start position:0%
+languages
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+but but he what and the thing that gets
+
+ align:start position:0%
+but but he what and the thing that gets
+ 
+
+ align:start position:0%
+but but he what and the thing that gets
+the appeal in most people's minds about
+
+ align:start position:0%
+the appeal in most people's minds about
+ 
+
+ align:start position:0%
+the appeal in most people's minds about
+it i think the broad appeal
+
+ align:start position:0%
+it i think the broad appeal
+ 
+
+ align:start position:0%
+it i think the broad appeal
+is that if you really want to teach a
+
+ align:start position:0%
+is that if you really want to teach a
+ 
+
+ align:start position:0%
+is that if you really want to teach a
+child a new line a person to learn a new
+
+ align:start position:0%
+child a new line a person to learn a new
+ 
+
+ align:start position:0%
+child a new line a person to learn a new
+language teach them before their what so
+
+ align:start position:0%
+language teach them before their what so
+ 
+
+ align:start position:0%
+language teach them before their what so
+i'm like six years old they will absorb
+
+ align:start position:0%
+i'm like six years old they will absorb
+ 
+
+ align:start position:0%
+i'm like six years old they will absorb
+it like a sponge
+
+ align:start position:0%
+it like a sponge
+ 
+
+ align:start position:0%
+it like a sponge
+they're not smarter but they're but that
+
+ align:start position:0%
+they're not smarter but they're but that
+ 
+
+ align:start position:0%
+they're not smarter but they're but that
+those structures are not
+
+ align:start position:0%
+those structures are not
+ 
+
+ align:start position:0%
+those structures are not
+cluttered
+
+ align:start position:0%
+cluttered
+ 
+
+ align:start position:0%
+cluttered
+and they can learn more than one
+
+ align:start position:0%
+and they can learn more than one
+ 
+
+ align:start position:0%
+and they can learn more than one
+language i don't understand how that
+
+ align:start position:0%
+language i don't understand how that
+ 
+
+ align:start position:0%
+language i don't understand how that
+goes but gnomes chomsky started this all
+
+ align:start position:0%
+goes but gnomes chomsky started this all
+ 
+
+ align:start position:0%
+goes but gnomes chomsky started this all
+this stuff off
+
+ align:start position:0%
+this stuff off
+ 
+
+ align:start position:0%
+this stuff off
+and so um that a man by the name of
+
+ align:start position:0%
+and so um that a man by the name of
+ 
+
+ align:start position:0%
+and so um that a man by the name of
+bruner
+
+ align:start position:0%
+bruner
+ 
+
+ align:start position:0%
+bruner
+i think it's uh b r u e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n e 1 n e r uh i can check that spelling
+
+ align:start position:0%
+n e 1 n e r uh i can check that spelling
+ 
+
+ align:start position:0%
+n e 1 n e r uh i can check that spelling
+for you i got in my on my computer
+
+ align:start position:0%
+for you i got in my on my computer
+ 
+
+ align:start position:0%
+for you i got in my on my computer
+uh came along and said something that
+
+ align:start position:0%
+uh came along and said something that
+ 
+
+ align:start position:0%
+uh came along and said something that
+had a lot of philosophical import
+
+ align:start position:0%
+had a lot of philosophical import
+ 
+
+ align:start position:0%
+had a lot of philosophical import
+and that was he made a distinction
+
+ align:start position:0%
+and that was he made a distinction
+ 
+
+ align:start position:0%
+and that was he made a distinction
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+understanding and meaning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can understand
+
+ align:start position:0%
+so you can understand
+ 
+
+ align:start position:0%
+so you can understand
+uh what a concept says
+
+ align:start position:0%
+uh what a concept says
+ 
+
+ align:start position:0%
+uh what a concept says
+but you don't get the meaning until the
+
+ align:start position:0%
+but you don't get the meaning until the
+ 
+
+ align:start position:0%
+but you don't get the meaning until the
+concept is put into a story
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the argument and i buy the
+
+ align:start position:0%
+that's the argument and i buy the
+ 
+
+ align:start position:0%
+that's the argument and i buy the
+argument
+
+ align:start position:0%
+argument
+ 
+
+ align:start position:0%
+argument
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the um
+
+ align:start position:0%
+so the um
+ 
+
+ align:start position:0%
+so the um
+notion of storytelling uh
+
+ align:start position:0%
+notion of storytelling uh
+ 
+
+ align:start position:0%
+notion of storytelling uh
+and and as i said storytelling and
+
+ align:start position:0%
+and and as i said storytelling and
+ 
+
+ align:start position:0%
+and and as i said storytelling and
+ethics goes back to plato
+
+ align:start position:0%
+ethics goes back to plato
+ 
+
+ align:start position:0%
+ethics goes back to plato
+all right but it was lost because it got
+
+ align:start position:0%
+all right but it was lost because it got
+ 
+
+ align:start position:0%
+all right but it was lost because it got
+lost in religion
+
+ align:start position:0%
+lost in religion
+ 
+
+ align:start position:0%
+lost in religion
+over the united states and
+
+ align:start position:0%
+over the united states and
+ 
+
+ align:start position:0%
+over the united states and
+and it also got lost because uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now i'm going to make a statement that
+
+ align:start position:0%
+now i'm going to make a statement that
+ 
+
+ align:start position:0%
+now i'm going to make a statement that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i have argued before but never written
+
+ align:start position:0%
+i have argued before but never written
+ 
+
+ align:start position:0%
+i have argued before but never written
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+and never argued um
+
+ align:start position:0%
+and never argued um
+ 
+
+ align:start position:0%
+and never argued um
+uh in a formal setting okay
+
+ align:start position:0%
+uh in a formal setting okay
+ 
+
+ align:start position:0%
+uh in a formal setting okay
+but i can talk to you about what i think
+
+ align:start position:0%
+but i can talk to you about what i think
+ 
+
+ align:start position:0%
+but i can talk to you about what i think
+you can criticize that uh i think that
+
+ align:start position:0%
+you can criticize that uh i think that
+ 
+
+ align:start position:0%
+you can criticize that uh i think that
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+perhaps the main reason it got lost is
+
+ align:start position:0%
+perhaps the main reason it got lost is
+ 
+
+ align:start position:0%
+perhaps the main reason it got lost is
+that it got lost in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in western educational systems
+
+ align:start position:0%
+in western educational systems
+ 
+
+ align:start position:0%
+in western educational systems
+because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you don't have a rigorous
+
+ align:start position:0%
+you don't have a rigorous
+ 
+
+ align:start position:0%
+you don't have a rigorous
+people you don't
+
+ align:start position:0%
+people you don't
+ 
+
+ align:start position:0%
+people you don't
+have you you have there is a rigorous
+
+ align:start position:0%
+have you you have there is a rigorous
+ 
+
+ align:start position:0%
+have you you have there is a rigorous
+method to test
+
+ align:start position:0%
+method to test
+ 
+
+ align:start position:0%
+method to test
+a good story from a bad one
+
+ align:start position:0%
+a good story from a bad one
+ 
+
+ align:start position:0%
+a good story from a bad one
+but not instantaneously not like you can
+
+ align:start position:0%
+but not instantaneously not like you can
+ 
+
+ align:start position:0%
+but not instantaneously not like you can
+put it on a test and i can say yes or no
+
+ align:start position:0%
+put it on a test and i can say yes or no
+ 
+
+ align:start position:0%
+put it on a test and i can say yes or no
+you gotta
+
+ align:start position:0%
+you gotta
+ 
+
+ align:start position:0%
+you gotta
+you know it works itself over time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you go to a drama class
+
+ align:start position:0%
+and if you go to a drama class
+ 
+
+ align:start position:0%
+and if you go to a drama class
+the professor in there will make
+
+ align:start position:0%
+the professor in there will make
+ 
+
+ align:start position:0%
+the professor in there will make
+judgments
+
+ align:start position:0%
+judgments
+ 
+
+ align:start position:0%
+judgments
+this is this story is not not any good
+
+ align:start position:0%
+this is this story is not not any good
+ 
+
+ align:start position:0%
+this is this story is not not any good
+that story is a wonderful story
+
+ align:start position:0%
+that story is a wonderful story
+ 
+
+ align:start position:0%
+that story is a wonderful story
+students don't like them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why isn't this a good story man i've got
+
+ align:start position:0%
+why isn't this a good story man i've got
+ 
+
+ align:start position:0%
+why isn't this a good story man i've got
+all of the
+
+ align:start position:0%
+all of the
+ 
+
+ align:start position:0%
+all of the
+pieces in it that this kid's got
+
+ align:start position:0%
+pieces in it that this kid's got
+ 
+
+ align:start position:0%
+pieces in it that this kid's got
+two years later your story gets a
+
+ align:start position:0%
+two years later your story gets a
+ 
+
+ align:start position:0%
+two years later your story gets a
+pulitzer you know
+
+ align:start position:0%
+pulitzer you know
+ 
+
+ align:start position:0%
+pulitzer you know
+the professor was wrong
+
+ align:start position:0%
+the professor was wrong
+ 
+
+ align:start position:0%
+the professor was wrong
+got nothing to do with anything
+
+ align:start position:0%
+got nothing to do with anything
+ 
+
+ align:start position:0%
+got nothing to do with anything
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+that's a story that's a teaching that's
+
+ align:start position:0%
+that's a story that's a teaching that's
+ 
+
+ align:start position:0%
+that's a story that's a teaching that's
+a teaching uh part of a teaching culture
+
+ align:start position:0%
+a teaching uh part of a teaching culture
+ 
+
+ align:start position:0%
+a teaching uh part of a teaching culture
+that's lost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grade it
+
+ align:start position:0%
+grade it
+ 
+
+ align:start position:0%
+grade it
+degrade it right on the spot
+
+ align:start position:0%
+degrade it right on the spot
+ 
+
+ align:start position:0%
+degrade it right on the spot
+and and
+
+ align:start position:0%
+and and
+ 
+
+ align:start position:0%
+and and
+go ahead
+
+ align:start position:0%
+go ahead
+ 
+
+ align:start position:0%
+go ahead
+no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other students complain to the teachers
+
+ align:start position:0%
+other students complain to the teachers
+ 
+
+ align:start position:0%
+other students complain to the teachers
+i think in recent times since the 60s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i would put it
+
+ align:start position:0%
+i would put it
+ 
+
+ align:start position:0%
+i would put it
+even even more even more precisely i
+
+ align:start position:0%
+even even more even more precisely i
+ 
+
+ align:start position:0%
+even even more even more precisely i
+would i'm going to say that what
+
+ align:start position:0%
+would i'm going to say that what
+ 
+
+ align:start position:0%
+would i'm going to say that what
+happened is students wanted objective
+
+ align:start position:0%
+happened is students wanted objective
+ 
+
+ align:start position:0%
+happened is students wanted objective
+measures of their work
+
+ align:start position:0%
+measures of their work
+ 
+
+ align:start position:0%
+measures of their work
+they don't want subjective measures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did
+
+ align:start position:0%
+did
+ 
+
+ align:start position:0%
+did
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well what i think go ahead no i cut
+
+ align:start position:0%
+well what i think go ahead no i cut
+ 
+
+ align:start position:0%
+well what i think go ahead no i cut
+across because i got excited sorry
+
+ align:start position:0%
+across because i got excited sorry
+ 
+
+ align:start position:0%
+across because i got excited sorry
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're saying that's
+
+ align:start position:0%
+you're saying that's
+ 
+
+ align:start position:0%
+you're saying that's
+that's a shame
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what works is when you know the
+
+ align:start position:0%
+what works is when you know the
+ 
+
+ align:start position:0%
+what works is when you know the
+professor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when the professor says this is no
+
+ align:start position:0%
+and when the professor says this is no
+ 
+
+ align:start position:0%
+and when the professor says this is no
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+you now know that in that professor's
+
+ align:start position:0%
+you now know that in that professor's
+ 
+
+ align:start position:0%
+you now know that in that professor's
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i don't
+
+ align:start position:0%
+i don't
+ 
+
+ align:start position:0%
+i don't
+well i want to say personality but but i
+
+ align:start position:0%
+well i want to say personality but but i
+ 
+
+ align:start position:0%
+well i want to say personality but but i
+want to say in that professor's
+
+ align:start position:0%
+want to say in that professor's
+ 
+
+ align:start position:0%
+want to say in that professor's
+framework
+
+ align:start position:0%
+framework
+ 
+
+ align:start position:0%
+framework
+of understanding the world
+
+ align:start position:0%
+of understanding the world
+ 
+
+ align:start position:0%
+of understanding the world
+that's a good judgment about my work
+
+ align:start position:0%
+that's a good judgment about my work
+ 
+
+ align:start position:0%
+that's a good judgment about my work
+somebody else some other professor would
+
+ align:start position:0%
+somebody else some other professor would
+ 
+
+ align:start position:0%
+somebody else some other professor would
+say something different now i've learned
+
+ align:start position:0%
+say something different now i've learned
+ 
+
+ align:start position:0%
+say something different now i've learned
+how the world operates
+
+ align:start position:0%
+how the world operates
+ 
+
+ align:start position:0%
+how the world operates
+because somebody's going to buy my
+
+ align:start position:0%
+because somebody's going to buy my
+ 
+
+ align:start position:0%
+because somebody's going to buy my
+product somebody else is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah i think that the universal things
+
+ align:start position:0%
+yeah i think that the universal things
+ 
+
+ align:start position:0%
+yeah i think that the universal things
+uh work themselves out over
+
+ align:start position:0%
+uh work themselves out over
+ 
+
+ align:start position:0%
+uh work themselves out over
+generations frankly i don't think it
+
+ align:start position:0%
+generations frankly i don't think it
+ 
+
+ align:start position:0%
+generations frankly i don't think it
+takes time to prove it so per se i think
+
+ align:start position:0%
+takes time to prove it so per se i think
+ 
+
+ align:start position:0%
+takes time to prove it so per se i think
+what you have to be what you have to see
+
+ align:start position:0%
+what you have to be what you have to see
+ 
+
+ align:start position:0%
+what you have to be what you have to see
+is that over space and time and the time
+
+ align:start position:0%
+is that over space and time and the time
+ 
+
+ align:start position:0%
+is that over space and time and the time
+measured in terms of generations
+
+ align:start position:0%
+measured in terms of generations
+ 
+
+ align:start position:0%
+measured in terms of generations
+that the kinds of things that bother
+
+ align:start position:0%
+that the kinds of things that bother
+ 
+
+ align:start position:0%
+that the kinds of things that bother
+some generations
+
+ align:start position:0%
+some generations
+ 
+
+ align:start position:0%
+some generations
+and cause them to criticize this peace
+
+ align:start position:0%
+and cause them to criticize this peace
+ 
+
+ align:start position:0%
+and cause them to criticize this peace
+won't bother the next generation
+
+ align:start position:0%
+won't bother the next generation
+ 
+
+ align:start position:0%
+won't bother the next generation
+but mythology is going to get to every
+
+ align:start position:0%
+but mythology is going to get to every
+ 
+
+ align:start position:0%
+but mythology is going to get to every
+generation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+in one generation uh the greeks don't
+
+ align:start position:0%
+in one generation uh the greeks don't
+ 
+
+ align:start position:0%
+in one generation uh the greeks don't
+like the persians and here comes a piece
+
+ align:start position:0%
+like the persians and here comes a piece
+ 
+
+ align:start position:0%
+like the persians and here comes a piece
+of work out of persia you know
+
+ align:start position:0%
+of work out of persia you know
+ 
+
+ align:start position:0%
+of work out of persia you know
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+somehow another one piece
+
+ align:start position:0%
+somehow another one piece
+ 
+
+ align:start position:0%
+somehow another one piece
+gets the greeks it came out of persia
+
+ align:start position:0%
+gets the greeks it came out of persia
+ 
+
+ align:start position:0%
+gets the greeks it came out of persia
+but they it gets to them then the greeks
+
+ align:start position:0%
+but they it gets to them then the greeks
+ 
+
+ align:start position:0%
+but they it gets to them then the greeks
+produce
+
+ align:start position:0%
+produce
+ 
+
+ align:start position:0%
+produce
+10 generations and the 10th generation
+
+ align:start position:0%
+10 generations and the 10th generation
+ 
+
+ align:start position:0%
+10 generations and the 10th generation
+doesn't care and care anything about
+
+ align:start position:0%
+doesn't care and care anything about
+ 
+
+ align:start position:0%
+doesn't care and care anything about
+persian problems
+
+ align:start position:0%
+persian problems
+ 
+
+ align:start position:0%
+persian problems
+it gets to them too you know so so i
+
+ align:start position:0%
+it gets to them too you know so so i
+ 
+
+ align:start position:0%
+it gets to them too you know so so i
+think that's what um
+
+ align:start position:0%
+think that's what um
+ 
+
+ align:start position:0%
+think that's what um
+there's another there's another art form
+
+ align:start position:0%
+there's another there's another art form
+ 
+
+ align:start position:0%
+there's another there's another art form
+that's like that
+
+ align:start position:0%
+that's like that
+ 
+
+ align:start position:0%
+that's like that
+more precisely is poetry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+portrait
+
+ align:start position:0%
+portrait
+ 
+
+ align:start position:0%
+portrait
+uh and it doesn't have to be uh
+
+ align:start position:0%
+uh and it doesn't have to be uh
+ 
+
+ align:start position:0%
+uh and it doesn't have to be uh
+rhyming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the creatures is nature of the universe
+
+ align:start position:0%
+the creatures is nature of the universe
+ 
+
+ align:start position:0%
+the creatures is nature of the universe
+there's a point
+
+ align:start position:0%
+there's a point
+ 
+
+ align:start position:0%
+there's a point
+the whole thing
+
+ align:start position:0%
+the whole thing
+ 
+
+ align:start position:0%
+the whole thing
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what about the quran
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is it appointment
+
+ align:start position:0%
+is it appointment
+ 
+
+ align:start position:0%
+is it appointment
+the ruby of about cayenne was a point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i wouldn't know because of the only
+
+ align:start position:0%
+i wouldn't know because of the only
+ 
+
+ align:start position:0%
+i wouldn't know because of the only
+parts of the only quran that i know that
+
+ align:start position:0%
+parts of the only quran that i know that
+ 
+
+ align:start position:0%
+parts of the only quran that i know that
+i have read was in english
+
+ align:start position:0%
+i have read was in english
+ 
+
+ align:start position:0%
+i have read was in english
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+but uh
+
+ align:start position:0%
+but uh
+ 
+
+ align:start position:0%
+but uh
+i tell you one of the one one
+
+ align:start position:0%
+i tell you one of the one one
+ 
+
+ align:start position:0%
+i tell you one of the one one
+an illuminating pleasurable experience i
+
+ align:start position:0%
+an illuminating pleasurable experience i
+ 
+
+ align:start position:0%
+an illuminating pleasurable experience i
+had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sitting down in this guy
+
+ align:start position:0%
+sitting down in this guy
+ 
+
+ align:start position:0%
+sitting down in this guy
+sitting down with three people one of
+
+ align:start position:0%
+sitting down with three people one of
+ 
+
+ align:start position:0%
+sitting down with three people one of
+them was from italy this friend of mine
+
+ align:start position:0%
+them was from italy this friend of mine
+ 
+
+ align:start position:0%
+them was from italy this friend of mine
+walked in
+
+ align:start position:0%
+walked in
+ 
+
+ align:start position:0%
+walked in
+i introduced him to this lady
+
+ align:start position:0%
+i introduced him to this lady
+ 
+
+ align:start position:0%
+i introduced him to this lady
+and uh said she was from italy
+
+ align:start position:0%
+and uh said she was from italy
+ 
+
+ align:start position:0%
+and uh said she was from italy
+and this guy says that once a year for
+
+ align:start position:0%
+and this guy says that once a year for
+ 
+
+ align:start position:0%
+and this guy says that once a year for
+the past 20 30 years
+
+ align:start position:0%
+the past 20 30 years
+ 
+
+ align:start position:0%
+the past 20 30 years
+he has gone to um
+
+ align:start position:0%
+he has gone to um
+ 
+
+ align:start position:0%
+he has gone to um
+italy to attend la scala because he
+
+ align:start position:0%
+italy to attend la scala because he
+ 
+
+ align:start position:0%
+italy to attend la scala because he
+loves
+
+ align:start position:0%
+loves
+ 
+
+ align:start position:0%
+loves
+opera he that's he saves and that's what
+
+ align:start position:0%
+opera he that's he saves and that's what
+ 
+
+ align:start position:0%
+opera he that's he saves and that's what
+he does that's his personal thing
+
+ align:start position:0%
+he does that's his personal thing
+ 
+
+ align:start position:0%
+he does that's his personal thing
+and so he's got sat there and read um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dante's um
+
+ align:start position:0%
+dante's um
+ 
+
+ align:start position:0%
+dante's um
+inscription over the right he recited
+
+ align:start position:0%
+inscription over the right he recited
+ 
+
+ align:start position:0%
+inscription over the right he recited
+in italian
+
+ align:start position:0%
+in italian
+ 
+
+ align:start position:0%
+in italian
+dante's uh
+
+ align:start position:0%
+dante's uh
+ 
+
+ align:start position:0%
+dante's uh
+inscription
+
+ align:start position:0%
+inscription
+ 
+
+ align:start position:0%
+inscription
+over the gates of hell
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i didn't understand the word
+
+ align:start position:0%
+i didn't understand the word
+ 
+
+ align:start position:0%
+i didn't understand the word
+i thought that thing was the most
+
+ align:start position:0%
+i thought that thing was the most
+ 
+
+ align:start position:0%
+i thought that thing was the most
+beautiful thing i ever heard
+
+ align:start position:0%
+beautiful thing i ever heard
+ 
+
+ align:start position:0%
+beautiful thing i ever heard
+and i've got the these books that i got
+
+ align:start position:0%
+and i've got the these books that i got
+ 
+
+ align:start position:0%
+and i've got the these books that i got
+a few years ago um i saw him in the in
+
+ align:start position:0%
+a few years ago um i saw him in the in
+ 
+
+ align:start position:0%
+a few years ago um i saw him in the in
+the bookstore
+
+ align:start position:0%
+the bookstore
+ 
+
+ align:start position:0%
+the bookstore
+i saw the first one in the bookstore uh
+
+ align:start position:0%
+i saw the first one in the bookstore uh
+ 
+
+ align:start position:0%
+i saw the first one in the bookstore uh
+maybe five years ago and i got the
+
+ align:start position:0%
+maybe five years ago and i got the
+ 
+
+ align:start position:0%
+maybe five years ago and i got the
+second one
+
+ align:start position:0%
+second one
+ 
+
+ align:start position:0%
+second one
+a couple of months ago volume one volume
+
+ align:start position:0%
+a couple of months ago volume one volume
+ 
+
+ align:start position:0%
+a couple of months ago volume one volume
+two of dante's inferno what they do is
+
+ align:start position:0%
+two of dante's inferno what they do is
+ 
+
+ align:start position:0%
+two of dante's inferno what they do is
+each page when you look when you open
+
+ align:start position:0%
+each page when you look when you open
+ 
+
+ align:start position:0%
+each page when you look when you open
+the book
+
+ align:start position:0%
+the book
+ 
+
+ align:start position:0%
+the book
+the right hand page is written in
+
+ align:start position:0%
+the right hand page is written in
+ 
+
+ align:start position:0%
+the right hand page is written in
+england in english the left hand page is
+
+ align:start position:0%
+england in english the left hand page is
+ 
+
+ align:start position:0%
+england in english the left hand page is
+written in italian
+
+ align:start position:0%
+written in italian
+ 
+
+ align:start position:0%
+written in italian
+and he's got all of the lines numbered
+
+ align:start position:0%
+and he's got all of the lines numbered
+ 
+
+ align:start position:0%
+and he's got all of the lines numbered
+so you can follow them
+
+ align:start position:0%
+so you can follow them
+ 
+
+ align:start position:0%
+so you can follow them
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you look over there and because they use
+
+ align:start position:0%
+you look over there and because they use
+ 
+
+ align:start position:0%
+you look over there and because they use
+the same alphabet
+
+ align:start position:0%
+the same alphabet
+ 
+
+ align:start position:0%
+the same alphabet
+you could
+
+ align:start position:0%
+you could
+ 
+
+ align:start position:0%
+you could
+see the writing
+
+ align:start position:0%
+see the writing
+ 
+
+ align:start position:0%
+see the writing
+and you can call the words you can read
+
+ align:start position:0%
+and you can call the words you can read
+ 
+
+ align:start position:0%
+and you can call the words you can read
+it you cannot i mean i can't understand
+
+ align:start position:0%
+it you cannot i mean i can't understand
+ 
+
+ align:start position:0%
+it you cannot i mean i can't understand
+it but i can certainly read the words
+
+ align:start position:0%
+it but i can certainly read the words
+ 
+
+ align:start position:0%
+it but i can certainly read the words
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and i sit there and listen by saying
+
+ align:start position:0%
+and i sit there and listen by saying
+ 
+
+ align:start position:0%
+and i sit there and listen by saying
+this is beautiful
+
+ align:start position:0%
+this is beautiful
+ 
+
+ align:start position:0%
+this is beautiful
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+it will and and it gets into the brain
+
+ align:start position:0%
+it will and and it gets into the brain
+ 
+
+ align:start position:0%
+it will and and it gets into the brain
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so you can remember it
+
+ align:start position:0%
+so you can remember it
+ 
+
+ align:start position:0%
+so you can remember it
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+that's very important
+
+ align:start position:0%
+that's very important
+ 
+
+ align:start position:0%
+that's very important
+uh another thing is uh now that what
+
+ align:start position:0%
+uh another thing is uh now that what
+ 
+
+ align:start position:0%
+uh another thing is uh now that what
+what people have said
+
+ align:start position:0%
+what people have said
+ 
+
+ align:start position:0%
+what people have said
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+well is a is a
+
+ align:start position:0%
+well is a is a
+ 
+
+ align:start position:0%
+well is a is a
+it's a it's the beginnings of a
+
+ align:start position:0%
+it's a it's the beginnings of a
+ 
+
+ align:start position:0%
+it's a it's the beginnings of a
+scientific perspective that will
+
+ align:start position:0%
+scientific perspective that will
+ 
+
+ align:start position:0%
+scientific perspective that will
+probably work itself out uh in a few
+
+ align:start position:0%
+probably work itself out uh in a few
+ 
+
+ align:start position:0%
+probably work itself out uh in a few
+years
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's got to do with this whole
+
+ align:start position:0%
+and it's got to do with this whole
+ 
+
+ align:start position:0%
+and it's got to do with this whole
+business of what
+
+ align:start position:0%
+business of what
+ 
+
+ align:start position:0%
+business of what
+called prenatal care
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it seemed apparently it is
+
+ align:start position:0%
+and it seemed apparently it is
+ 
+
+ align:start position:0%
+and it seemed apparently it is
+apparently um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mozart's mother
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when she was pregnant with him
+
+ align:start position:0%
+when she was pregnant with him
+ 
+
+ align:start position:0%
+when she was pregnant with him
+used to sit down with
+
+ align:start position:0%
+used to sit down with
+ 
+
+ align:start position:0%
+used to sit down with
+mozart's father who was a musician and
+
+ align:start position:0%
+mozart's father who was a musician and
+ 
+
+ align:start position:0%
+mozart's father who was a musician and
+he would play
+
+ align:start position:0%
+he would play
+ 
+
+ align:start position:0%
+he would play
+to the unborn baby
+
+ align:start position:0%
+to the unborn baby
+ 
+
+ align:start position:0%
+to the unborn baby
+and then up comes mozart okay
+
+ align:start position:0%
+and then up comes mozart okay
+ 
+
+ align:start position:0%
+and then up comes mozart okay
+so but there uh uh there's some there's
+
+ align:start position:0%
+so but there uh uh there's some there's
+ 
+
+ align:start position:0%
+so but there uh uh there's some there's
+some strong evidence that uh
+
+ align:start position:0%
+some strong evidence that uh
+ 
+
+ align:start position:0%
+some strong evidence that uh
+that uh music and and and and
+
+ align:start position:0%
+that uh music and and and and
+ 
+
+ align:start position:0%
+that uh music and and and and
+storytelling
+
+ align:start position:0%
+storytelling
+ 
+
+ align:start position:0%
+storytelling
+uh has some effect on the unborn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's the rhythm of it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how so you asked me how did i get
+
+ align:start position:0%
+so how so you asked me how did i get
+ 
+
+ align:start position:0%
+so how so you asked me how did i get
+involved in the storytelling that's my
+
+ align:start position:0%
+involved in the storytelling that's my
+ 
+
+ align:start position:0%
+involved in the storytelling that's my
+long story that's that's about a third
+
+ align:start position:0%
+long story that's that's about a third
+ 
+
+ align:start position:0%
+long story that's that's about a third
+of it
+
+ align:start position:0%
+of it
+ 
+
+ align:start position:0%
+of it
+but yeah it joseph campbell is right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+i had one other experience
+
+ align:start position:0%
+i had one other experience
+ 
+
+ align:start position:0%
+i had one other experience
+that i want to share with you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about 10 years ago
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+make it 10 make make it 10 years ago
+
+ align:start position:0%
+make it 10 make make it 10 years ago
+ 
+
+ align:start position:0%
+make it 10 make make it 10 years ago
+make it 12 or 15 years ago i can't
+
+ align:start position:0%
+make it 12 or 15 years ago i can't
+ 
+
+ align:start position:0%
+make it 12 or 15 years ago i can't
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+the american association of engineering
+
+ align:start position:0%
+the american association of engineering
+ 
+
+ align:start position:0%
+the american association of engineering
+societies aaes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+got some visitors
+
+ align:start position:0%
+got some visitors
+ 
+
+ align:start position:0%
+got some visitors
+i'll tell you when it was i'll tell you
+
+ align:start position:0%
+i'll tell you when it was i'll tell you
+ 
+
+ align:start position:0%
+i'll tell you when it was i'll tell you
+when it was okay when did the berlin
+
+ align:start position:0%
+when it was okay when did the berlin
+ 
+
+ align:start position:0%
+when it was okay when did the berlin
+wall come down it was a year after that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right it was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ussr
+
+ align:start position:0%
+ussr
+ 
+
+ align:start position:0%
+ussr
+yep keep going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+the wall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's try let's try 92.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it was a year after
+
+ align:start position:0%
+it was a year after
+ 
+
+ align:start position:0%
+it was a year after
+the aas got these visitors from uh
+
+ align:start position:0%
+the aas got these visitors from uh
+ 
+
+ align:start position:0%
+the aas got these visitors from uh
+which was no longer the soviet union
+
+ align:start position:0%
+which was no longer the soviet union
+ 
+
+ align:start position:0%
+which was no longer the soviet union
+from russia
+
+ align:start position:0%
+from russia
+ 
+
+ align:start position:0%
+from russia
+uh and they were philosophers
+
+ align:start position:0%
+uh and they were philosophers
+ 
+
+ align:start position:0%
+uh and they were philosophers
+and they were visiting the united states
+
+ align:start position:0%
+and they were visiting the united states
+ 
+
+ align:start position:0%
+and they were visiting the united states
+and going around
+
+ align:start position:0%
+and going around
+ 
+
+ align:start position:0%
+and going around
+and they were they wanted to talk with
+
+ align:start position:0%
+and they were they wanted to talk with
+ 
+
+ align:start position:0%
+and they were they wanted to talk with
+the ethics committees of the various
+
+ align:start position:0%
+the ethics committees of the various
+ 
+
+ align:start position:0%
+the ethics committees of the various
+engineering societies
+
+ align:start position:0%
+engineering societies
+ 
+
+ align:start position:0%
+engineering societies
+and so i was invited to come down and
+
+ align:start position:0%
+and so i was invited to come down and
+ 
+
+ align:start position:0%
+and so i was invited to come down and
+meet with them when they came to aaes
+
+ align:start position:0%
+meet with them when they came to aaes
+ 
+
+ align:start position:0%
+meet with them when they came to aaes
+i had
+
+ align:start position:0%
+i had
+ 
+
+ align:start position:0%
+i had
+fallen out of favor with him
+
+ align:start position:0%
+fallen out of favor with him
+ 
+
+ align:start position:0%
+fallen out of favor with him
+somehow got partially back
+
+ align:start position:0%
+somehow got partially back
+ 
+
+ align:start position:0%
+somehow got partially back
+and it was a group of about uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+six professors and then some others
+
+ align:start position:0%
+six professors and then some others
+ 
+
+ align:start position:0%
+six professors and then some others
+uh who were with them
+
+ align:start position:0%
+uh who were with them
+ 
+
+ align:start position:0%
+uh who were with them
+and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there was an old person with them
+
+ align:start position:0%
+there was an old person with them
+ 
+
+ align:start position:0%
+there was an old person with them
+and there was this woman who i hesitate
+
+ align:start position:0%
+and there was this woman who i hesitate
+ 
+
+ align:start position:0%
+and there was this woman who i hesitate
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+to say her age is important she was in
+
+ align:start position:0%
+to say her age is important she was in
+ 
+
+ align:start position:0%
+to say her age is important she was in
+early 30s but she spoke english very
+
+ align:start position:0%
+early 30s but she spoke english very
+ 
+
+ align:start position:0%
+early 30s but she spoke english very
+fluently
+
+ align:start position:0%
+fluently
+ 
+
+ align:start position:0%
+fluently
+that's important the old man didn't say
+
+ align:start position:0%
+that's important the old man didn't say
+ 
+
+ align:start position:0%
+that's important the old man didn't say
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+very oh it was very um
+
+ align:start position:0%
+very oh it was very um
+ 
+
+ align:start position:0%
+very oh it was very um
+it looked like a sage very impressive
+
+ align:start position:0%
+it looked like a sage very impressive
+ 
+
+ align:start position:0%
+it looked like a sage very impressive
+looking man
+
+ align:start position:0%
+looking man
+ 
+
+ align:start position:0%
+looking man
+and it was clear somehow when they began
+
+ align:start position:0%
+and it was clear somehow when they began
+ 
+
+ align:start position:0%
+and it was clear somehow when they began
+to talk russian among themselves that uh
+
+ align:start position:0%
+to talk russian among themselves that uh
+ 
+
+ align:start position:0%
+to talk russian among themselves that uh
+he was the leader
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so they opened up the session and uh
+
+ align:start position:0%
+so they opened up the session and uh
+ 
+
+ align:start position:0%
+so they opened up the session and uh
+said one person said that the reason
+
+ align:start position:0%
+said one person said that the reason
+ 
+
+ align:start position:0%
+said one person said that the reason
+that they had uh going on this tour is
+
+ align:start position:0%
+that they had uh going on this tour is
+ 
+
+ align:start position:0%
+that they had uh going on this tour is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+uh it has become very clear that
+
+ align:start position:0%
+uh it has become very clear that
+ 
+
+ align:start position:0%
+uh it has become very clear that
+western culture is going to penetrate
+
+ align:start position:0%
+western culture is going to penetrate
+ 
+
+ align:start position:0%
+western culture is going to penetrate
+russia
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but they don't want the decadence to
+
+ align:start position:0%
+but they don't want the decadence to
+ 
+
+ align:start position:0%
+but they don't want the decadence to
+come along with it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so they want to understand it very
+
+ align:start position:0%
+and so they want to understand it very
+ 
+
+ align:start position:0%
+and so they want to understand it very
+well and go back and craft
+
+ align:start position:0%
+well and go back and craft
+ 
+
+ align:start position:0%
+well and go back and craft
+recre and make sure that their
+
+ align:start position:0%
+recre and make sure that their
+ 
+
+ align:start position:0%
+recre and make sure that their
+universities quote unquote remain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i tell you what's too strong the word
+
+ align:start position:0%
+i tell you what's too strong the word
+ 
+
+ align:start position:0%
+i tell you what's too strong the word
+pure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finer word for me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they want to in other words if there's a
+
+ align:start position:0%
+they want to in other words if there's a
+ 
+
+ align:start position:0%
+they want to in other words if there's a
+price there's a price to pay for
+
+ align:start position:0%
+price there's a price to pay for
+ 
+
+ align:start position:0%
+price there's a price to pay for
+everything they didn't want to pay a big
+
+ align:start position:0%
+everything they didn't want to pay a big
+ 
+
+ align:start position:0%
+everything they didn't want to pay a big
+price for western ethics
+
+ align:start position:0%
+price for western ethics
+ 
+
+ align:start position:0%
+price for western ethics
+the self-interested part
+
+ align:start position:0%
+the self-interested part
+ 
+
+ align:start position:0%
+the self-interested part
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that leads a person to be what they call
+
+ align:start position:0%
+that leads a person to be what they call
+ 
+
+ align:start position:0%
+that leads a person to be what they call
+decadent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+i guess i guess what what i mean is that
+
+ align:start position:0%
+i guess i guess what what i mean is that
+ 
+
+ align:start position:0%
+i guess i guess what what i mean is that
+you that if if you were sitting in that
+
+ align:start position:0%
+you that if if you were sitting in that
+ 
+
+ align:start position:0%
+you that if if you were sitting in that
+room you'd get a different meaning that
+
+ align:start position:0%
+room you'd get a different meaning that
+ 
+
+ align:start position:0%
+room you'd get a different meaning that
+i got so i want you to have enough
+
+ align:start position:0%
+i got so i want you to have enough
+ 
+
+ align:start position:0%
+i got so i want you to have enough
+freedom to say that even if you were
+
+ align:start position:0%
+freedom to say that even if you were
+ 
+
+ align:start position:0%
+freedom to say that even if you were
+there you would interpret what you said
+
+ align:start position:0%
+there you would interpret what you said
+ 
+
+ align:start position:0%
+there you would interpret what you said
+maybe a little bit differently
+
+ align:start position:0%
+maybe a little bit differently
+ 
+
+ align:start position:0%
+maybe a little bit differently
+but uh so so they we had these
+
+ align:start position:0%
+but uh so so they we had these
+ 
+
+ align:start position:0%
+but uh so so they we had these
+discussions
+
+ align:start position:0%
+discussions
+ 
+
+ align:start position:0%
+discussions
+and so the old man is sitting there
+
+ align:start position:0%
+and so the old man is sitting there
+ 
+
+ align:start position:0%
+and so the old man is sitting there
+not saying anything sitting back very
+
+ align:start position:0%
+not saying anything sitting back very
+ 
+
+ align:start position:0%
+not saying anything sitting back very
+wise
+
+ align:start position:0%
+wise
+ 
+
+ align:start position:0%
+wise
+occasionally one of the others would
+
+ align:start position:0%
+occasionally one of the others would
+ 
+
+ align:start position:0%
+occasionally one of the others would
+come back and say something to him in
+
+ align:start position:0%
+come back and say something to him in
+ 
+
+ align:start position:0%
+come back and say something to him in
+russian
+
+ align:start position:0%
+russian
+ 
+
+ align:start position:0%
+russian
+he would say something back
+
+ align:start position:0%
+he would say something back
+ 
+
+ align:start position:0%
+he would say something back
+then they would nod their heads and
+
+ align:start position:0%
+then they would nod their heads and
+ 
+
+ align:start position:0%
+then they would nod their heads and
+come back to the discussion
+
+ align:start position:0%
+come back to the discussion
+ 
+
+ align:start position:0%
+come back to the discussion
+and at
+
+ align:start position:0%
+and at
+ 
+
+ align:start position:0%
+and at
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four-fifths of the way through the
+
+ align:start position:0%
+four-fifths of the way through the
+ 
+
+ align:start position:0%
+four-fifths of the way through the
+discussion
+
+ align:start position:0%
+discussion
+ 
+
+ align:start position:0%
+discussion
+i don't know what it was that i said
+
+ align:start position:0%
+i don't know what it was that i said
+ 
+
+ align:start position:0%
+i don't know what it was that i said
+that man leaned across the table and
+
+ align:start position:0%
+that man leaned across the table and
+ 
+
+ align:start position:0%
+that man leaned across the table and
+started speaking in english
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i had all of the americans sitting
+
+ align:start position:0%
+i had all of the americans sitting
+ 
+
+ align:start position:0%
+i had all of the americans sitting
+around there thinking that he couldn't
+
+ align:start position:0%
+around there thinking that he couldn't
+ 
+
+ align:start position:0%
+around there thinking that he couldn't
+speak any
+
+ align:start position:0%
+speak any
+ 
+
+ align:start position:0%
+speak any
+english and he started speaking in
+
+ align:start position:0%
+english and he started speaking in
+ 
+
+ align:start position:0%
+english and he started speaking in
+english and he answered i had put a
+
+ align:start position:0%
+english and he answered i had put a
+ 
+
+ align:start position:0%
+english and he answered i had put a
+question to them
+
+ align:start position:0%
+question to them
+ 
+
+ align:start position:0%
+question to them
+and he answered the question
+
+ align:start position:0%
+and he answered the question
+ 
+
+ align:start position:0%
+and he answered the question
+by telling the story
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i talked i've talked to other people
+
+ align:start position:0%
+so i talked i've talked to other people
+ 
+
+ align:start position:0%
+so i talked i've talked to other people
+since then and there seems to be a
+
+ align:start position:0%
+since then and there seems to be a
+ 
+
+ align:start position:0%
+since then and there seems to be a
+cultural trait
+
+ align:start position:0%
+cultural trait
+ 
+
+ align:start position:0%
+cultural trait
+outside of the u.s
+
+ align:start position:0%
+outside of the u.s
+ 
+
+ align:start position:0%
+outside of the u.s
+where old people are given the privilege
+
+ align:start position:0%
+where old people are given the privilege
+ 
+
+ align:start position:0%
+where old people are given the privilege
+of answering questions and giving advice
+
+ align:start position:0%
+of answering questions and giving advice
+ 
+
+ align:start position:0%
+of answering questions and giving advice
+by telling a little story
+
+ align:start position:0%
+by telling a little story
+ 
+
+ align:start position:0%
+by telling a little story
+and i'll tell you directly
+
+ align:start position:0%
+and i'll tell you directly
+ 
+
+ align:start position:0%
+and i'll tell you directly
+and you're supposed to think that about
+
+ align:start position:0%
+and you're supposed to think that about
+ 
+
+ align:start position:0%
+and you're supposed to think that about
+that and carry that with you where you
+
+ align:start position:0%
+that and carry that with you where you
+ 
+
+ align:start position:0%
+that and carry that with you where you
+go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is a globalizing world and uh
+
+ align:start position:0%
+so this is a globalizing world and uh
+ 
+
+ align:start position:0%
+so this is a globalizing world and uh
+my instincts tell me that uh if you
+
+ align:start position:0%
+my instincts tell me that uh if you
+ 
+
+ align:start position:0%
+my instincts tell me that uh if you
+develop this allegorical technique
+
+ align:start position:0%
+develop this allegorical technique
+ 
+
+ align:start position:0%
+develop this allegorical technique
+uh that you'll have a lot of listeners
+
+ align:start position:0%
+uh that you'll have a lot of listeners
+ 
+
+ align:start position:0%
+uh that you'll have a lot of listeners
+when you get out of here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thursday
+
+ align:start position:0%
+thursday
+ 
+
+ align:start position:0%
+thursday
+well we're still on thursday right so uh
+
+ align:start position:0%
+well we're still on thursday right so uh
+ 
+
+ align:start position:0%
+well we're still on thursday right so uh
+winston won't be here i'll do something
+
+ align:start position:0%
+winston won't be here i'll do something
+ 
+
+ align:start position:0%
+winston won't be here i'll do something
+uh gabon gayson is supposed to arrive at
+
+ align:start position:0%
+uh gabon gayson is supposed to arrive at
+ 
+
+ align:start position:0%
+uh gabon gayson is supposed to arrive at
+one o'clock
+
+ align:start position:0%
+one o'clock
+ 
+
+ align:start position:0%
+one o'clock
+he's got somebody picking him up i'll be
+
+ align:start position:0%
+he's got somebody picking him up i'll be
+ 
+
+ align:start position:0%
+he's got somebody picking him up i'll be
+talking to him in the office probably
+
+ align:start position:0%
+talking to him in the office probably
+ 
+
+ align:start position:0%
+talking to him in the office probably
+about two or three
+
+ align:start position:0%
+about two or three
+ 
+
+ align:start position:0%
+about two or three
+and uh wednesday he and i will be
+
+ align:start position:0%
+and uh wednesday he and i will be
+ 
+
+ align:start position:0%
+and uh wednesday he and i will be
+crafting out
+
+ align:start position:0%
+crafting out
+ 
+
+ align:start position:0%
+crafting out
+among other things thursday
+
+ align:start position:0%
+among other things thursday
+ 
+
+ align:start position:0%
+among other things thursday
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+uh we agree on the general or what
+
+ align:start position:0%
+uh we agree on the general or what
+ 
+
+ align:start position:0%
+uh we agree on the general or what
+generally you know we talked about in
+
+ align:start position:0%
+generally you know we talked about in
+ 
+
+ align:start position:0%
+generally you know we talked about in
+general
+
+ align:start position:0%
+general
+ 
+
+ align:start position:0%
+general
+uh but he's mainly here
+
+ align:start position:0%
+uh but he's mainly here
+ 
+
+ align:start position:0%
+uh but he's mainly here
+so that we can work on our grant we need
+
+ align:start position:0%
+so that we can work on our grant we need
+ 
+
+ align:start position:0%
+so that we can work on our grant we need
+to work on that on wednesday
+
+ align:start position:0%
+to work on that on wednesday
+ 
+
+ align:start position:0%
+to work on that on wednesday
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+on thursday at
+
+ align:start position:0%
+on thursday at
+ 
+
+ align:start position:0%
+on thursday at
+let's say
+
+ align:start position:0%
+let's say
+ 
+
+ align:start position:0%
+let's say
+10 maybe a few minutes quarter to 10 a
+
+ align:start position:0%
+10 maybe a few minutes quarter to 10 a
+ 
+
+ align:start position:0%
+10 maybe a few minutes quarter to 10 a
+few minutes before
+
+ align:start position:0%
+few minutes before
+ 
+
+ align:start position:0%
+few minutes before
+you're all invited to come to my office
+
+ align:start position:0%
+you're all invited to come to my office
+ 
+
+ align:start position:0%
+you're all invited to come to my office
+there is a style
+
+ align:start position:0%
+there is a style
+ 
+
+ align:start position:0%
+there is a style
+of uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+treating visitors that
+
+ align:start position:0%
+treating visitors that
+ 
+
+ align:start position:0%
+treating visitors that
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+practice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it used to be um
+
+ align:start position:0%
+it used to be um
+ 
+
+ align:start position:0%
+it used to be um
+a big thing at howard i've seen it in
+
+ align:start position:0%
+a big thing at howard i've seen it in
+ 
+
+ align:start position:0%
+a big thing at howard i've seen it in
+other places
+
+ align:start position:0%
+other places
+ 
+
+ align:start position:0%
+other places
+and that is when you get a speaker to
+
+ align:start position:0%
+and that is when you get a speaker to
+ 
+
+ align:start position:0%
+and that is when you get a speaker to
+come to your class
+
+ align:start position:0%
+come to your class
+ 
+
+ align:start position:0%
+come to your class
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you get together with the person or when
+
+ align:start position:0%
+you get together with the person or when
+ 
+
+ align:start position:0%
+you get together with the person or when
+the speaker's giving a talk some
+
+ align:start position:0%
+the speaker's giving a talk some
+ 
+
+ align:start position:0%
+the speaker's giving a talk some
+to your department or whatever you get
+
+ align:start position:0%
+to your department or whatever you get
+ 
+
+ align:start position:0%
+to your department or whatever you get
+together with the personnel a little bit
+
+ align:start position:0%
+together with the personnel a little bit
+ 
+
+ align:start position:0%
+together with the personnel a little bit
+beforehand
+
+ align:start position:0%
+beforehand
+ 
+
+ align:start position:0%
+beforehand
+and some of the people that are going to
+
+ align:start position:0%
+and some of the people that are going to
+ 
+
+ align:start position:0%
+and some of the people that are going to
+be there are there beforehand
+
+ align:start position:0%
+be there are there beforehand
+ 
+
+ align:start position:0%
+be there are there beforehand
+you kind of talk
+
+ align:start position:0%
+you kind of talk
+ 
+
+ align:start position:0%
+you kind of talk
+past some wine around
+
+ align:start position:0%
+past some wine around
+ 
+
+ align:start position:0%
+past some wine around
+i'm not authorized to have wine in e38
+
+ align:start position:0%
+i'm not authorized to have wine in e38
+ 
+
+ align:start position:0%
+i'm not authorized to have wine in e38
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but uh it and then you walk over
+
+ align:start position:0%
+but uh it and then you walk over
+ 
+
+ align:start position:0%
+but uh it and then you walk over
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+okay so um that's what we're going to do
+
+ align:start position:0%
+okay so um that's what we're going to do
+ 
+
+ align:start position:0%
+okay so um that's what we're going to do
+and all you all are invited
+
+ align:start position:0%
+and all you all are invited
+ 
+
+ align:start position:0%
+and all you all are invited
+around tennis
+
+ align:start position:0%
+around tennis
+ 
+
+ align:start position:0%
+around tennis
+uh we're both going to be using
+
+ align:start position:0%
+uh we're both going to be using
+ 
+
+ align:start position:0%
+uh we're both going to be using
+powerpoints out even though that's going
+
+ align:start position:0%
+powerpoints out even though that's going
+ 
+
+ align:start position:0%
+powerpoints out even though that's going
+to be pushing it
+
+ align:start position:0%
+to be pushing it
+ 
+
+ align:start position:0%
+to be pushing it
+i want to get here just as this class is
+
+ align:start position:0%
+i want to get here just as this class is
+ 
+
+ align:start position:0%
+i want to get here just as this class is
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+plugged in everything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+i will open the class up
+
+ align:start position:0%
+i will open the class up
+ 
+
+ align:start position:0%
+i will open the class up
+i don't know how many people are going
+
+ align:start position:0%
+i don't know how many people are going
+ 
+
+ align:start position:0%
+i don't know how many people are going
+to be here with all
+
+ align:start position:0%
+to be here with all
+ 
+
+ align:start position:0%
+to be here with all
+i don't know tony just said that they uh
+
+ align:start position:0%
+i don't know tony just said that they uh
+ 
+
+ align:start position:0%
+i don't know tony just said that they uh
+they've got posters all over the
+
+ align:start position:0%
+they've got posters all over the
+ 
+
+ align:start position:0%
+they've got posters all over the
+university about this thing
+
+ align:start position:0%
+university about this thing
+ 
+
+ align:start position:0%
+university about this thing
+all over the institute and uh i know it
+
+ align:start position:0%
+all over the institute and uh i know it
+ 
+
+ align:start position:0%
+all over the institute and uh i know it
+went out on the web
+
+ align:start position:0%
+went out on the web
+ 
+
+ align:start position:0%
+went out on the web
+mit where
+
+ align:start position:0%
+mit where
+ 
+
+ align:start position:0%
+mit where
+i only got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but since i'm already on copenhagen of
+
+ align:start position:0%
+but since i'm already on copenhagen of
+ 
+
+ align:start position:0%
+but since i'm already on copenhagen of
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+we just have to tell people what you're
+
+ align:start position:0%
+we just have to tell people what you're
+ 
+
+ align:start position:0%
+we just have to tell people what you're
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+in case they want to say something
+
+ align:start position:0%
+in case they want to say something
+ 
+
+ align:start position:0%
+in case they want to say something
+uh the only person i know who know for
+
+ align:start position:0%
+uh the only person i know who know for
+ 
+
+ align:start position:0%
+uh the only person i know who know for
+sure only one person called back said
+
+ align:start position:0%
+sure only one person called back said
+ 
+
+ align:start position:0%
+sure only one person called back said
+that was coming
+
+ align:start position:0%
+that was coming
+ 
+
+ align:start position:0%
+that was coming
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+is um
+
+ align:start position:0%
+is um
+ 
+
+ align:start position:0%
+is um
+a professor
+
+ align:start position:0%
+a professor
+ 
+
+ align:start position:0%
+a professor
+a senior professor actually over brain
+
+ align:start position:0%
+a senior professor actually over brain
+ 
+
+ align:start position:0%
+a senior professor actually over brain
+and cognitive sciences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i will ask you i invited him to come to
+
+ align:start position:0%
+i will ask you i invited him to come to
+ 
+
+ align:start position:0%
+i will ask you i invited him to come to
+my office early
+
+ align:start position:0%
+my office early
+ 
+
+ align:start position:0%
+my office early
+and if he does um
+
+ align:start position:0%
+and if he does um
+ 
+
+ align:start position:0%
+and if he does um
+i'll ask him if he'd be willing to stand
+
+ align:start position:0%
+i'll ask him if he'd be willing to stand
+ 
+
+ align:start position:0%
+i'll ask him if he'd be willing to stand
+by during the q a period
+
+ align:start position:0%
+by during the q a period
+ 
+
+ align:start position:0%
+by during the q a period
+for anything on this business he knows
+
+ align:start position:0%
+for anything on this business he knows
+ 
+
+ align:start position:0%
+for anything on this business he knows
+cynthia winston personally
+
+ align:start position:0%
+cynthia winston personally
+ 
+
+ align:start position:0%
+cynthia winston personally
+so he was really coming to see her
+
+ align:start position:0%
+so he was really coming to see her
+ 
+
+ align:start position:0%
+so he was really coming to see her
+and then i told him that she wouldn't be
+
+ align:start position:0%
+and then i told him that she wouldn't be
+ 
+
+ align:start position:0%
+and then i told him that she wouldn't be
+coming he said he would come anyway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+his name is alan hine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+when we come in i will our call class to
+
+ align:start position:0%
+when we come in i will our call class to
+ 
+
+ align:start position:0%
+when we come in i will our call class to
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+and say what we're going to do that
+
+ align:start position:0%
+and say what we're going to do that
+ 
+
+ align:start position:0%
+and say what we're going to do that
+we've got a panel pres we've got three
+
+ align:start position:0%
+we've got a panel pres we've got three
+ 
+
+ align:start position:0%
+we've got a panel pres we've got three
+presentations two panelists
+
+ align:start position:0%
+presentations two panelists
+ 
+
+ align:start position:0%
+presentations two panelists
+uh one is not able to be with us so one
+
+ align:start position:0%
+uh one is not able to be with us so one
+ 
+
+ align:start position:0%
+uh one is not able to be with us so one
+panelist will give
+
+ align:start position:0%
+panelist will give
+ 
+
+ align:start position:0%
+panelist will give
+some introductory remarks to her
+
+ align:start position:0%
+some introductory remarks to her
+ 
+
+ align:start position:0%
+some introductory remarks to her
+presentation
+
+ align:start position:0%
+presentation
+ 
+
+ align:start position:0%
+presentation
+uh and then i'll say something about the
+
+ align:start position:0%
+uh and then i'll say something about the
+ 
+
+ align:start position:0%
+uh and then i'll say something about the
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+that we have we have two panelists and
+
+ align:start position:0%
+that we have we have two panelists and
+ 
+
+ align:start position:0%
+that we have we have two panelists and
+we have a
+
+ align:start position:0%
+we have a
+ 
+
+ align:start position:0%
+we have a
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a panel chair we have a rapid tour
+
+ align:start position:0%
+a panel chair we have a rapid tour
+ 
+
+ align:start position:0%
+a panel chair we have a rapid tour
+who are students in the class
+
+ align:start position:0%
+who are students in the class
+ 
+
+ align:start position:0%
+who are students in the class
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+then i will introduce the panel chair
+
+ align:start position:0%
+then i will introduce the panel chair
+ 
+
+ align:start position:0%
+then i will introduce the panel chair
+and i will sit down
+
+ align:start position:0%
+and i will sit down
+ 
+
+ align:start position:0%
+and i will sit down
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+looking and we're going to have
+
+ align:start position:0%
+looking and we're going to have
+ 
+
+ align:start position:0%
+looking and we're going to have
+powerpoint so
+
+ align:start position:0%
+powerpoint so
+ 
+
+ align:start position:0%
+powerpoint so
+let's decide now on how we're going to
+
+ align:start position:0%
+let's decide now on how we're going to
+ 
+
+ align:start position:0%
+let's decide now on how we're going to
+sit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normally the panelists face the audience
+
+ align:start position:0%
+normally the panelists face the audience
+ 
+
+ align:start position:0%
+normally the panelists face the audience
+but everybody's going to want to see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the screen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so maybe we should how do you think we
+
+ align:start position:0%
+so maybe we should how do you think we
+ 
+
+ align:start position:0%
+so maybe we should how do you think we
+should do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i want to stand while i speak but when
+
+ align:start position:0%
+i want to stand while i speak but when
+ 
+
+ align:start position:0%
+i want to stand while i speak but when
+i'm not speaking i want to sit and see
+
+ align:start position:0%
+i'm not speaking i want to sit and see
+ 
+
+ align:start position:0%
+i'm not speaking i want to sit and see
+the screen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and look right here at the screen
+
+ align:start position:0%
+and look right here at the screen
+ 
+
+ align:start position:0%
+and look right here at the screen
+okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh that will work uh i just have
+
+ align:start position:0%
+okay uh that will work uh i just have
+ 
+
+ align:start position:0%
+okay uh that will work uh i just have
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+actual concern maybe i should start it
+
+ align:start position:0%
+actual concern maybe i should start it
+ 
+
+ align:start position:0%
+actual concern maybe i should start it
+up at the end of class if i got time
+
+ align:start position:0%
+up at the end of class if i got time
+ 
+
+ align:start position:0%
+up at the end of class if i got time
+i'll put it i have one slot i have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i have i have
+
+ align:start position:0%
+i have i have
+ 
+
+ align:start position:0%
+i have i have
+three slides
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where my picture is not
+
+ align:start position:0%
+where my picture is not
+ 
+
+ align:start position:0%
+where my picture is not
+on the uh powerpoint
+
+ align:start position:0%
+on the uh powerpoint
+ 
+
+ align:start position:0%
+on the uh powerpoint
+as in you know as an insert it is the
+
+ align:start position:0%
+as in you know as an insert it is the
+ 
+
+ align:start position:0%
+as in you know as an insert it is the
+background
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so it's the whole thing and i
+
+ align:start position:0%
+okay so it's the whole thing and i
+ 
+
+ align:start position:0%
+okay so it's the whole thing and i
+wonder if i tried this once before in
+
+ align:start position:0%
+wonder if i tried this once before in
+ 
+
+ align:start position:0%
+wonder if i tried this once before in
+here you couldn't see it too good unless
+
+ align:start position:0%
+here you couldn't see it too good unless
+ 
+
+ align:start position:0%
+here you couldn't see it too good unless
+you said it for you know back
+
+ align:start position:0%
+you said it for you know back
+ 
+
+ align:start position:0%
+you said it for you know back
+but i can't think of a better way to do
+
+ align:start position:0%
+but i can't think of a better way to do
+ 
+
+ align:start position:0%
+but i can't think of a better way to do
+it than to have it as background
+
+ align:start position:0%
+it than to have it as background
+ 
+
+ align:start position:0%
+it than to have it as background
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+why don't we do this
+
+ align:start position:0%
+why don't we do this
+ 
+
+ align:start position:0%
+why don't we do this
+the chair
+
+ align:start position:0%
+the chair
+ 
+
+ align:start position:0%
+the chair
+depending on how many people are here
+
+ align:start position:0%
+depending on how many people are here
+ 
+
+ align:start position:0%
+depending on how many people are here
+will have to make an ad hoc decision
+
+ align:start position:0%
+will have to make an ad hoc decision
+ 
+
+ align:start position:0%
+will have to make an ad hoc decision
+just how to handle it if it doesn't come
+
+ align:start position:0%
+just how to handle it if it doesn't come
+ 
+
+ align:start position:0%
+just how to handle it if it doesn't come
+up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the the chair
+
+ align:start position:0%
+then the the chair
+ 
+
+ align:start position:0%
+then the the chair
+then um i am going to talk i mean uh i'm
+
+ align:start position:0%
+then um i am going to talk i mean uh i'm
+ 
+
+ align:start position:0%
+then um i am going to talk i mean uh i'm
+going to give 10 minutes on
+
+ align:start position:0%
+going to give 10 minutes on
+ 
+
+ align:start position:0%
+going to give 10 minutes on
+narrative
+
+ align:start position:0%
+narrative
+ 
+
+ align:start position:0%
+narrative
+psychology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well now how does the panel chair want
+
+ align:start position:0%
+well now how does the panel chair want
+ 
+
+ align:start position:0%
+well now how does the panel chair want
+to do it
+
+ align:start position:0%
+to do it
+ 
+
+ align:start position:0%
+to do it
+okay the panel chair will say this the
+
+ align:start position:0%
+okay the panel chair will say this the
+ 
+
+ align:start position:0%
+okay the panel chair will say this the
+title of this panel is narrative ethics
+
+ align:start position:0%
+title of this panel is narrative ethics
+ 
+
+ align:start position:0%
+title of this panel is narrative ethics
+and we're pleased to have three
+
+ align:start position:0%
+and we're pleased to have three
+ 
+
+ align:start position:0%
+and we're pleased to have three
+presentations and two speakers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then the panel chair will say uh
+
+ align:start position:0%
+and then the panel chair will say uh
+ 
+
+ align:start position:0%
+and then the panel chair will say uh
+our first speaker
+
+ align:start position:0%
+our first speaker
+ 
+
+ align:start position:0%
+our first speaker
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+couldn't make it with us today
+
+ align:start position:0%
+couldn't make it with us today
+ 
+
+ align:start position:0%
+couldn't make it with us today
+uh don't say couldn't be here today with
+
+ align:start position:0%
+uh don't say couldn't be here today with
+ 
+
+ align:start position:0%
+uh don't say couldn't be here today with
+us today that sounds like she was buried
+
+ align:start position:0%
+us today that sounds like she was buried
+ 
+
+ align:start position:0%
+us today that sounds like she was buried
+i'm just kidding about that but uh you
+
+ align:start position:0%
+i'm just kidding about that but uh you
+ 
+
+ align:start position:0%
+i'm just kidding about that but uh you
+what's what's normal you see you've been
+
+ align:start position:0%
+what's what's normal you see you've been
+ 
+
+ align:start position:0%
+what's what's normal you see you've been
+to these conferences what people
+
+ align:start position:0%
+to these conferences what people
+ 
+
+ align:start position:0%
+to these conferences what people
+normally say um
+
+ align:start position:0%
+normally say um
+ 
+
+ align:start position:0%
+normally say um
+our first panelists sent dr cynthia
+
+ align:start position:0%
+our first panelists sent dr cynthia
+ 
+
+ align:start position:0%
+our first panelists sent dr cynthia
+winston um
+
+ align:start position:0%
+winston um
+ 
+
+ align:start position:0%
+winston um
+uh sends her um
+
+ align:start position:0%
+uh sends her um
+ 
+
+ align:start position:0%
+uh sends her um
+apologies she couldn't be here with us
+
+ align:start position:0%
+apologies she couldn't be here with us
+ 
+
+ align:start position:0%
+apologies she couldn't be here with us
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+she has sent down some things for us to
+
+ align:start position:0%
+she has sent down some things for us to
+ 
+
+ align:start position:0%
+she has sent down some things for us to
+talk about
+
+ align:start position:0%
+talk about
+ 
+
+ align:start position:0%
+talk about
+and uh dr broome will give a 10-minute
+
+ align:start position:0%
+and uh dr broome will give a 10-minute
+ 
+
+ align:start position:0%
+and uh dr broome will give a 10-minute
+presentation we are honored to have
+
+ align:start position:0%
+presentation we are honored to have
+ 
+
+ align:start position:0%
+presentation we are honored to have
+professor uh hine here from brain and
+
+ align:start position:0%
+professor uh hine here from brain and
+ 
+
+ align:start position:0%
+professor uh hine here from brain and
+cognitive sciences here at mit
+
+ align:start position:0%
+cognitive sciences here at mit
+ 
+
+ align:start position:0%
+cognitive sciences here at mit
+uh who's agreed to take on some
+
+ align:start position:0%
+uh who's agreed to take on some
+ 
+
+ align:start position:0%
+uh who's agreed to take on some
+questions and even make some comments
+
+ align:start position:0%
+questions and even make some comments
+ 
+
+ align:start position:0%
+questions and even make some comments
+during the q a period
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so i'll get up and do ten minutes
+
+ align:start position:0%
+and so i'll get up and do ten minutes
+ 
+
+ align:start position:0%
+and so i'll get up and do ten minutes
+uh hopefully i'll have some slash
+
+ align:start position:0%
+uh hopefully i'll have some slash
+ 
+
+ align:start position:0%
+uh hopefully i'll have some slash
+then i sit down
+
+ align:start position:0%
+then i sit down
+ 
+
+ align:start position:0%
+then i sit down
+okay and then
+
+ align:start position:0%
+okay and then
+ 
+
+ align:start position:0%
+okay and then
+on narrative psychology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you will introduce uh dr gabe
+
+ align:start position:0%
+then you will introduce uh dr gabe
+ 
+
+ align:start position:0%
+then you will introduce uh dr gabe
+gabady gazin now that requires some
+
+ align:start position:0%
+gabady gazin now that requires some
+ 
+
+ align:start position:0%
+gabady gazin now that requires some
+effort okay
+
+ align:start position:0%
+effort okay
+ 
+
+ align:start position:0%
+effort okay
+his name
+
+ align:start position:0%
+his name
+ 
+
+ align:start position:0%
+his name
+is nigerian
+
+ align:start position:0%
+is nigerian
+ 
+
+ align:start position:0%
+is nigerian
+g b
+
+ align:start position:0%
+g b
+ 
+
+ align:start position:0%
+g b
+gaba
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+day
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gazing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh ba
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in the uh
+
+ align:start position:0%
+in the uh
+ 
+
+ align:start position:0%
+in the uh
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+20 minutes that we have together before
+
+ align:start position:0%
+20 minutes that we have together before
+ 
+
+ align:start position:0%
+20 minutes that we have together before
+we come over
+
+ align:start position:0%
+we come over
+ 
+
+ align:start position:0%
+we come over
+it's a good time to say how would you
+
+ align:start position:0%
+it's a good time to say how would you
+ 
+
+ align:start position:0%
+it's a good time to say how would you
+like to be introduced
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+many times a person will have
+
+ align:start position:0%
+many times a person will have
+ 
+
+ align:start position:0%
+many times a person will have
+with them a little three by five a card
+
+ align:start position:0%
+with them a little three by five a card
+ 
+
+ align:start position:0%
+with them a little three by five a card
+and have two lines on there
+
+ align:start position:0%
+and have two lines on there
+ 
+
+ align:start position:0%
+and have two lines on there
+for you to use
+
+ align:start position:0%
+for you to use
+ 
+
+ align:start position:0%
+for you to use
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and then he'll get up and do his piece
+
+ align:start position:0%
+and then he'll get up and do his piece
+ 
+
+ align:start position:0%
+and then he'll get up and do his piece
+he will have a powerpoint presentation
+
+ align:start position:0%
+he will have a powerpoint presentation
+ 
+
+ align:start position:0%
+he will have a powerpoint presentation
+which is unusual for philosophers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be prepared for this uh i've seen him
+
+ align:start position:0%
+be prepared for this uh i've seen him
+ 
+
+ align:start position:0%
+be prepared for this uh i've seen him
+give some outstanding i've seen him give
+
+ align:start position:0%
+give some outstanding i've seen him give
+ 
+
+ align:start position:0%
+give some outstanding i've seen him give
+two outstanding talks two talks and both
+
+ align:start position:0%
+two outstanding talks two talks and both
+ 
+
+ align:start position:0%
+two outstanding talks two talks and both
+of them were outstanding okay
+
+ align:start position:0%
+of them were outstanding okay
+ 
+
+ align:start position:0%
+of them were outstanding okay
+uh but he did something that engineers
+
+ align:start position:0%
+uh but he did something that engineers
+ 
+
+ align:start position:0%
+uh but he did something that engineers
+never do
+
+ align:start position:0%
+never do
+ 
+
+ align:start position:0%
+never do
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+of the time philosophers will do it
+
+ align:start position:0%
+of the time philosophers will do it
+ 
+
+ align:start position:0%
+of the time philosophers will do it
+that is read the whole thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the reason is that their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use of the english language is so
+
+ align:start position:0%
+use of the english language is so
+ 
+
+ align:start position:0%
+use of the english language is so
+precise
+
+ align:start position:0%
+precise
+ 
+
+ align:start position:0%
+precise
+that they cannot memorize
+
+ align:start position:0%
+that they cannot memorize
+ 
+
+ align:start position:0%
+that they cannot memorize
+the whole thing and if they're talking
+
+ align:start position:0%
+the whole thing and if they're talking
+ 
+
+ align:start position:0%
+the whole thing and if they're talking
+fluent leisurely
+
+ align:start position:0%
+fluent leisurely
+ 
+
+ align:start position:0%
+fluent leisurely
+get one thing wrong another philosopher
+
+ align:start position:0%
+get one thing wrong another philosopher
+ 
+
+ align:start position:0%
+get one thing wrong another philosopher
+will pick it up
+
+ align:start position:0%
+will pick it up
+ 
+
+ align:start position:0%
+will pick it up
+and crack the whip on them later and so
+
+ align:start position:0%
+and crack the whip on them later and so
+ 
+
+ align:start position:0%
+and crack the whip on them later and so
+they'll read it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+every time every time i've seen an
+
+ align:start position:0%
+every time every time i've seen an
+ 
+
+ align:start position:0%
+every time every time i've seen an
+engineer do that and i've seen it happen
+
+ align:start position:0%
+engineer do that and i've seen it happen
+ 
+
+ align:start position:0%
+engineer do that and i've seen it happen
+a couple of times
+
+ align:start position:0%
+a couple of times
+ 
+
+ align:start position:0%
+a couple of times
+the whole audience we're dead to sleep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+philosophers will sit there and they'll
+
+ align:start position:0%
+philosophers will sit there and they'll
+ 
+
+ align:start position:0%
+philosophers will sit there and they'll
+listen very carefully to every word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i don't know what he's going to do
+
+ align:start position:0%
+so i don't know what he's going to do
+ 
+
+ align:start position:0%
+so i don't know what he's going to do
+with this powerpoint
+
+ align:start position:0%
+with this powerpoint
+ 
+
+ align:start position:0%
+with this powerpoint
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but he will cover two things he will uh
+
+ align:start position:0%
+but he will cover two things he will uh
+ 
+
+ align:start position:0%
+but he will cover two things he will uh
+he will cover
+
+ align:start position:0%
+he will cover
+ 
+
+ align:start position:0%
+he will cover
+he will cover it will be on
+
+ align:start position:0%
+he will cover it will be on
+ 
+
+ align:start position:0%
+he will cover it will be on
+cross-cultural ethics
+
+ align:start position:0%
+cross-cultural ethics
+ 
+
+ align:start position:0%
+cross-cultural ethics
+that's uh pretty much the title
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+he will also talk something about
+
+ align:start position:0%
+he will also talk something about
+ 
+
+ align:start position:0%
+he will also talk something about
+something we did not want to discuss in
+
+ align:start position:0%
+something we did not want to discuss in
+ 
+
+ align:start position:0%
+something we did not want to discuss in
+this class
+
+ align:start position:0%
+this class
+ 
+
+ align:start position:0%
+this class
+as the as the major topic
+
+ align:start position:0%
+as the as the major topic
+ 
+
+ align:start position:0%
+as the as the major topic
+which is bioethics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+i've said before the best way to
+
+ align:start position:0%
+i've said before the best way to
+ 
+
+ align:start position:0%
+i've said before the best way to
+understand what a thing is is to also
+
+ align:start position:0%
+understand what a thing is is to also
+ 
+
+ align:start position:0%
+understand what a thing is is to also
+understand what it is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh remember the uh
+
+ align:start position:0%
+uh remember the uh
+ 
+
+ align:start position:0%
+uh remember the uh
+the monks
+
+ align:start position:0%
+the monks
+ 
+
+ align:start position:0%
+the monks
+in the yellow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the yellow monastery
+
+ align:start position:0%
+and the yellow monastery
+ 
+
+ align:start position:0%
+and the yellow monastery
+they didn't even know what yellow was
+
+ align:start position:0%
+they didn't even know what yellow was
+ 
+
+ align:start position:0%
+they didn't even know what yellow was
+until they saw what it was not
+
+ align:start position:0%
+until they saw what it was not
+ 
+
+ align:start position:0%
+until they saw what it was not
+okay so he'll talk a little bit about
+
+ align:start position:0%
+okay so he'll talk a little bit about
+ 
+
+ align:start position:0%
+okay so he'll talk a little bit about
+bioethics
+
+ align:start position:0%
+bioethics
+ 
+
+ align:start position:0%
+bioethics
+uh i don't know what he's gonna say but
+
+ align:start position:0%
+uh i don't know what he's gonna say but
+ 
+
+ align:start position:0%
+uh i don't know what he's gonna say but
+i know what he said before and i know
+
+ align:start position:0%
+i know what he said before and i know
+ 
+
+ align:start position:0%
+i know what he said before and i know
+what his main
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thrust is and that is that uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+ethics can be universalized over all
+
+ align:start position:0%
+ethics can be universalized over all
+ 
+
+ align:start position:0%
+ethics can be universalized over all
+cultures
+
+ align:start position:0%
+cultures
+ 
+
+ align:start position:0%
+cultures
+and at all points in time
+
+ align:start position:0%
+and at all points in time
+ 
+
+ align:start position:0%
+and at all points in time
+but the um
+
+ align:start position:0%
+but the um
+ 
+
+ align:start position:0%
+but the um
+way people express
+
+ align:start position:0%
+way people express
+ 
+
+ align:start position:0%
+way people express
+ethics difference
+
+ align:start position:0%
+ethics difference
+ 
+
+ align:start position:0%
+ethics difference
+greatly
+
+ align:start position:0%
+greatly
+ 
+
+ align:start position:0%
+greatly
+over all cultures the wrong
+
+ align:start position:0%
+over all cultures the wrong
+ 
+
+ align:start position:0%
+over all cultures the wrong
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+and he's got examples
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+joseph campbell does that too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's what i think is gonna be i
+
+ align:start position:0%
+so that's what i think is gonna be i
+ 
+
+ align:start position:0%
+so that's what i think is gonna be i
+would anticipate is what he's gonna do
+
+ align:start position:0%
+would anticipate is what he's gonna do
+ 
+
+ align:start position:0%
+would anticipate is what he's gonna do
+and we're going to meet this afternoon
+
+ align:start position:0%
+and we're going to meet this afternoon
+ 
+
+ align:start position:0%
+and we're going to meet this afternoon
+and tomorrow and i would not presume
+
+ align:start position:0%
+and tomorrow and i would not presume
+ 
+
+ align:start position:0%
+and tomorrow and i would not presume
+it would not even occur come into my
+
+ align:start position:0%
+it would not even occur come into my
+ 
+
+ align:start position:0%
+it would not even occur come into my
+mind to tell him what to talk about
+
+ align:start position:0%
+mind to tell him what to talk about
+ 
+
+ align:start position:0%
+mind to tell him what to talk about
+he's going to talk about what he wants
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+then he'll sit down
+
+ align:start position:0%
+then he'll sit down
+ 
+
+ align:start position:0%
+then he'll sit down
+maybe a few burning questions
+
+ align:start position:0%
+maybe a few burning questions
+ 
+
+ align:start position:0%
+maybe a few burning questions
+then i'll get up and i'm the title of my
+
+ align:start position:0%
+then i'll get up and i'm the title of my
+ 
+
+ align:start position:0%
+then i'll get up and i'm the title of my
+presentation uh is
+
+ align:start position:0%
+presentation uh is
+ 
+
+ align:start position:0%
+presentation uh is
+the narrative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in engineering ethics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh now um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i want to spend a few minutes today
+
+ align:start position:0%
+i want to spend a few minutes today
+ 
+
+ align:start position:0%
+i want to spend a few minutes today
+before we get out of here depending on
+
+ align:start position:0%
+before we get out of here depending on
+ 
+
+ align:start position:0%
+before we get out of here depending on
+which i want to talk about
+
+ align:start position:0%
+which i want to talk about
+ 
+
+ align:start position:0%
+which i want to talk about
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+on what i want to say
+
+ align:start position:0%
+on what i want to say
+ 
+
+ align:start position:0%
+on what i want to say
+on thursday
+
+ align:start position:0%
+on thursday
+ 
+
+ align:start position:0%
+on thursday
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+because um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't want you to have to listen too
+
+ align:start position:0%
+i don't want you to have to listen too
+ 
+
+ align:start position:0%
+i don't want you to have to listen too
+closely to what i have to say i want you
+
+ align:start position:0%
+closely to what i have to say i want you
+ 
+
+ align:start position:0%
+closely to what i have to say i want you
+to be thinking about you know the rapid
+
+ align:start position:0%
+to be thinking about you know the rapid
+ 
+
+ align:start position:0%
+to be thinking about you know the rapid
+tour kind of stuff and why are you going
+
+ align:start position:0%
+tour kind of stuff and why are you going
+ 
+
+ align:start position:0%
+tour kind of stuff and why are you going
+to ask questions q a
+
+ align:start position:0%
+to ask questions q a
+ 
+
+ align:start position:0%
+to ask questions q a
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+i also want to test it on you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get some feedback but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'd like for you to really have your
+
+ align:start position:0%
+i'd like for you to really have your
+ 
+
+ align:start position:0%
+i'd like for you to really have your
+brains all worked about a gayson has to
+
+ align:start position:0%
+brains all worked about a gayson has to
+ 
+
+ align:start position:0%
+brains all worked about a gayson has to
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+because you've been hearing me all year
+
+ align:start position:0%
+because you've been hearing me all year
+ 
+
+ align:start position:0%
+because you've been hearing me all year
+semester long
+
+ align:start position:0%
+semester long
+ 
+
+ align:start position:0%
+semester long
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we'll have the uh q a
+
+ align:start position:0%
+and then we'll have the uh q a
+ 
+
+ align:start position:0%
+and then we'll have the uh q a
+q a is not exactly what i ever had
+
+ align:start position:0%
+q a is not exactly what i ever had
+ 
+
+ align:start position:0%
+q a is not exactly what i ever had
+people can make comments too
+
+ align:start position:0%
+people can make comments too
+ 
+
+ align:start position:0%
+people can make comments too
+they don't have to phrase them as
+
+ align:start position:0%
+they don't have to phrase them as
+ 
+
+ align:start position:0%
+they don't have to phrase them as
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+but once they've made a comment then the
+
+ align:start position:0%
+but once they've made a comment then the
+ 
+
+ align:start position:0%
+but once they've made a comment then the
+panelists can make a comment on their
+
+ align:start position:0%
+panelists can make a comment on their
+ 
+
+ align:start position:0%
+panelists can make a comment on their
+comment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now and then once that's over then you
+
+ align:start position:0%
+now and then once that's over then you
+ 
+
+ align:start position:0%
+now and then once that's over then you
+thank everybody for coming
+
+ align:start position:0%
+thank everybody for coming
+ 
+
+ align:start position:0%
+thank everybody for coming
+and technically you're supposed to give
+
+ align:start position:0%
+and technically you're supposed to give
+ 
+
+ align:start position:0%
+and technically you're supposed to give
+the class back to me
+
+ align:start position:0%
+the class back to me
+ 
+
+ align:start position:0%
+the class back to me
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+i don't know if there are 30 people in
+
+ align:start position:0%
+i don't know if there are 30 people in
+ 
+
+ align:start position:0%
+i don't know if there are 30 people in
+here and they applaud you know
+
+ align:start position:0%
+here and they applaud you know
+ 
+
+ align:start position:0%
+here and they applaud you know
+for five seconds then the class is over
+
+ align:start position:0%
+for five seconds then the class is over
+ 
+
+ align:start position:0%
+for five seconds then the class is over
+i won't be able to say anything people
+
+ align:start position:0%
+i won't be able to say anything people
+ 
+
+ align:start position:0%
+i won't be able to say anything people
+are walking out and talking
+
+ align:start position:0%
+are walking out and talking
+ 
+
+ align:start position:0%
+are walking out and talking
+but uh
+
+ align:start position:0%
+but uh
+ 
+
+ align:start position:0%
+but uh
+i'm re i have the responsibility for the
+
+ align:start position:0%
+i'm re i have the responsibility for the
+ 
+
+ align:start position:0%
+i'm re i have the responsibility for the
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+i will delegate my authority
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm sorry the repertoire i forgot about
+
+ align:start position:0%
+i'm sorry the repertoire i forgot about
+ 
+
+ align:start position:0%
+i'm sorry the repertoire i forgot about
+the rapporteur
+
+ align:start position:0%
+the rapporteur
+ 
+
+ align:start position:0%
+the rapporteur
+comes up and um
+
+ align:start position:0%
+comes up and um
+ 
+
+ align:start position:0%
+comes up and um
+uh before the q a because the rapture
+
+ align:start position:0%
+uh before the q a because the rapture
+ 
+
+ align:start position:0%
+uh before the q a because the rapture
+will be subject to q a
+
+ align:start position:0%
+will be subject to q a
+ 
+
+ align:start position:0%
+will be subject to q a
+and the rapper tour will spend five
+
+ align:start position:0%
+and the rapper tour will spend five
+ 
+
+ align:start position:0%
+and the rapper tour will spend five
+minutes or so
+
+ align:start position:0%
+minutes or so
+ 
+
+ align:start position:0%
+minutes or so
+talking about what these person said
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and sort of inspiring the audience to
+
+ align:start position:0%
+and sort of inspiring the audience to
+ 
+
+ align:start position:0%
+and sort of inspiring the audience to
+ask certain questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i would like for it to be burning
+
+ align:start position:0%
+i would like for it to be burning
+ 
+
+ align:start position:0%
+i would like for it to be burning
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+so if you got something that can't wait
+
+ align:start position:0%
+so if you got something that can't wait
+ 
+
+ align:start position:0%
+so if you got something that can't wait
+ask it but otherwise save it
+
+ align:start position:0%
+ask it but otherwise save it
+ 
+
+ align:start position:0%
+ask it but otherwise save it
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+now um
+
+ align:start position:0%
+now um
+ 
+
+ align:start position:0%
+now um
+let's talk a little bit about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+skills management and uh
+
+ align:start position:0%
+skills management and uh
+ 
+
+ align:start position:0%
+skills management and uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+in a in a
+
+ align:start position:0%
+in a in a
+ 
+
+ align:start position:0%
+in a in a
+scholarly forum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one day i was uh
+
+ align:start position:0%
+one day i was uh
+ 
+
+ align:start position:0%
+one day i was uh
+chairing a panel
+
+ align:start position:0%
+chairing a panel
+ 
+
+ align:start position:0%
+chairing a panel
+at a conference
+
+ align:start position:0%
+at a conference
+ 
+
+ align:start position:0%
+at a conference
+at johns hopkins
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forgot what the topic was on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the speakers uh was dr rachel
+
+ align:start position:0%
+one of the speakers uh was dr rachel
+ 
+
+ align:start position:0%
+one of the speakers uh was dr rachel
+hollander who just retired
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh this past uh i think february well at
+
+ align:start position:0%
+uh this past uh i think february well at
+ 
+
+ align:start position:0%
+uh this past uh i think february well at
+least put it this way we gave her a
+
+ align:start position:0%
+least put it this way we gave her a
+ 
+
+ align:start position:0%
+least put it this way we gave her a
+retirement party at the aaa's meeting in
+
+ align:start position:0%
+retirement party at the aaa's meeting in
+ 
+
+ align:start position:0%
+retirement party at the aaa's meeting in
+february
+
+ align:start position:0%
+february
+ 
+
+ align:start position:0%
+february
+gave uh
+
+ align:start position:0%
+gave uh
+ 
+
+ align:start position:0%
+gave uh
+and had a um a panel had a panel session
+
+ align:start position:0%
+and had a um a panel had a panel session
+ 
+
+ align:start position:0%
+and had a um a panel had a panel session
+at the conference for her and there was
+
+ align:start position:0%
+at the conference for her and there was
+ 
+
+ align:start position:0%
+at the conference for her and there was
+standing room only in there
+
+ align:start position:0%
+standing room only in there
+ 
+
+ align:start position:0%
+standing room only in there
+she was ahead of the
+
+ align:start position:0%
+she was ahead of the
+ 
+
+ align:start position:0%
+she was ahead of the
+ethics and values program and had been
+
+ align:start position:0%
+ethics and values program and had been
+ 
+
+ align:start position:0%
+ethics and values program and had been
+there like 30 years
+
+ align:start position:0%
+there like 30 years
+ 
+
+ align:start position:0%
+there like 30 years
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+it was
+
+ align:start position:0%
+it was
+ 
+
+ align:start position:0%
+it was
+everybody it was a good it was a good
+
+ align:start position:0%
+everybody it was a good it was a good
+ 
+
+ align:start position:0%
+everybody it was a good it was a good
+attendance in there
+
+ align:start position:0%
+attendance in there
+ 
+
+ align:start position:0%
+attendance in there
+president rensselaer came in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and uh
+
+ align:start position:0%
+uh and uh
+ 
+
+ align:start position:0%
+uh and uh
+i told one story that i had had with her
+
+ align:start position:0%
+i told one story that i had had with her
+ 
+
+ align:start position:0%
+i told one story that i had had with her
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+so we were sort of like roasting her
+
+ align:start position:0%
+so we were sort of like roasting her
+ 
+
+ align:start position:0%
+so we were sort of like roasting her
+and that was the time when i was doing
+
+ align:start position:0%
+and that was the time when i was doing
+ 
+
+ align:start position:0%
+and that was the time when i was doing
+this thing over at hopkins
+
+ align:start position:0%
+this thing over at hopkins
+ 
+
+ align:start position:0%
+this thing over at hopkins
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y'all ever heard of student pug wash
+
+ align:start position:0%
+y'all ever heard of student pug wash
+ 
+
+ align:start position:0%
+y'all ever heard of student pug wash
+well it was a it was an international
+
+ align:start position:0%
+well it was a it was an international
+ 
+
+ align:start position:0%
+well it was a it was an international
+conference of student plug
+
+ align:start position:0%
+conference of student plug
+ 
+
+ align:start position:0%
+conference of student plug
+and we were in a large room
+
+ align:start position:0%
+and we were in a large room
+ 
+
+ align:start position:0%
+and we were in a large room
+and up in the balcony they had you know
+
+ align:start position:0%
+and up in the balcony they had you know
+ 
+
+ align:start position:0%
+and up in the balcony they had you know
+all of this equipment and people up
+
+ align:start position:0%
+all of this equipment and people up
+ 
+
+ align:start position:0%
+all of this equipment and people up
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+that's important okay
+
+ align:start position:0%
+that's important okay
+ 
+
+ align:start position:0%
+that's important okay
+and just before the panel started like
+
+ align:start position:0%
+and just before the panel started like
+ 
+
+ align:start position:0%
+and just before the panel started like
+within a minute
+
+ align:start position:0%
+within a minute
+ 
+
+ align:start position:0%
+within a minute
+the organizers of the conference
+
+ align:start position:0%
+the organizers of the conference
+ 
+
+ align:start position:0%
+the organizers of the conference
+literally ran up on the stage
+
+ align:start position:0%
+literally ran up on the stage
+ 
+
+ align:start position:0%
+literally ran up on the stage
+and corralled me
+
+ align:start position:0%
+and corralled me
+ 
+
+ align:start position:0%
+and corralled me
+and rachelle and said that they um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they used two words infiltrated and
+
+ align:start position:0%
+they used two words infiltrated and
+ 
+
+ align:start position:0%
+they used two words infiltrated and
+attacked
+
+ align:start position:0%
+attacked
+ 
+
+ align:start position:0%
+attacked
+attacked
+
+ align:start position:0%
+attacked
+ 
+
+ align:start position:0%
+attacked
+the audience had been ill infiltrated by
+
+ align:start position:0%
+the audience had been ill infiltrated by
+ 
+
+ align:start position:0%
+the audience had been ill infiltrated by
+what they called lyndon the roosters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that's a um
+
+ align:start position:0%
+that's a um
+ 
+
+ align:start position:0%
+that's a um
+legitimate
+
+ align:start position:0%
+legitimate
+ 
+
+ align:start position:0%
+legitimate
+organization in the united states
+
+ align:start position:0%
+organization in the united states
+ 
+
+ align:start position:0%
+organization in the united states
+mainly of young people lyndon larouche
+
+ align:start position:0%
+mainly of young people lyndon larouche
+ 
+
+ align:start position:0%
+mainly of young people lyndon larouche
+himself is my age
+
+ align:start position:0%
+himself is my age
+ 
+
+ align:start position:0%
+himself is my age
+but um
+
+ align:start position:0%
+but um
+ 
+
+ align:start position:0%
+but um
+i don't know
+
+ align:start position:0%
+i don't know
+ 
+
+ align:start position:0%
+i don't know
+i don't know
+
+ align:start position:0%
+i don't know
+ 
+
+ align:start position:0%
+i don't know
+let's put it this way my my best way of
+
+ align:start position:0%
+let's put it this way my my best way of
+ 
+
+ align:start position:0%
+let's put it this way my my best way of
+describing that organization is
+
+ align:start position:0%
+describing that organization is
+ 
+
+ align:start position:0%
+describing that organization is
+that they have
+
+ align:start position:0%
+that they have
+ 
+
+ align:start position:0%
+that they have
+left wing
+
+ align:start position:0%
+left wing
+ 
+
+ align:start position:0%
+left wing
+positions
+
+ align:start position:0%
+positions
+ 
+
+ align:start position:0%
+positions
+but right wing tactics
+
+ align:start position:0%
+but right wing tactics
+ 
+
+ align:start position:0%
+but right wing tactics
+they'll come in and take over
+
+ align:start position:0%
+they'll come in and take over
+ 
+
+ align:start position:0%
+they'll come in and take over
+your pant your your program
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+have a taste for violence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+look it up on the web
+
+ align:start position:0%
+look it up on the web
+ 
+
+ align:start position:0%
+look it up on the web
+la rush
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you heard of him
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+handing out leaflets
+
+ align:start position:0%
+handing out leaflets
+ 
+
+ align:start position:0%
+handing out leaflets
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+no they'll interrupt you while you're at
+
+ align:start position:0%
+no they'll interrupt you while you're at
+ 
+
+ align:start position:0%
+no they'll interrupt you while you're at
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+if you say something that's out of line
+
+ align:start position:0%
+if you say something that's out of line
+ 
+
+ align:start position:0%
+if you say something that's out of line
+from their program
+
+ align:start position:0%
+from their program
+ 
+
+ align:start position:0%
+from their program
+uh they'll interrupt you while you're at
+
+ align:start position:0%
+uh they'll interrupt you while you're at
+ 
+
+ align:start position:0%
+uh they'll interrupt you while you're at
+it and and take over your program
+
+ align:start position:0%
+it and and take over your program
+ 
+
+ align:start position:0%
+it and and take over your program
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+so i said well there's only two things
+
+ align:start position:0%
+so i said well there's only two things
+ 
+
+ align:start position:0%
+so i said well there's only two things
+we we can do number one this is a
+
+ align:start position:0%
+we we can do number one this is a
+ 
+
+ align:start position:0%
+we we can do number one this is a
+scholarly public
+
+ align:start position:0%
+scholarly public
+ 
+
+ align:start position:0%
+scholarly public
+program we cannot forbid anybody from
+
+ align:start position:0%
+program we cannot forbid anybody from
+ 
+
+ align:start position:0%
+program we cannot forbid anybody from
+speaking
+
+ align:start position:0%
+speaking
+ 
+
+ align:start position:0%
+speaking
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but as chair i can
+
+ align:start position:0%
+but as chair i can
+ 
+
+ align:start position:0%
+but as chair i can
+i i have the
+
+ align:start position:0%
+i i have the
+ 
+
+ align:start position:0%
+i i have the
+parliamentary powers to keep anybody
+
+ align:start position:0%
+parliamentary powers to keep anybody
+ 
+
+ align:start position:0%
+parliamentary powers to keep anybody
+from dominating the program
+
+ align:start position:0%
+from dominating the program
+ 
+
+ align:start position:0%
+from dominating the program
+and if they try to dominate the program
+
+ align:start position:0%
+and if they try to dominate the program
+ 
+
+ align:start position:0%
+and if they try to dominate the program
+i'll make it and
+
+ align:start position:0%
+i'll make it and
+ 
+
+ align:start position:0%
+i'll make it and
+make it a case where they have to get
+
+ align:start position:0%
+make it a case where they have to get
+ 
+
+ align:start position:0%
+make it a case where they have to get
+violent with me to stop me
+
+ align:start position:0%
+violent with me to stop me
+ 
+
+ align:start position:0%
+violent with me to stop me
+and if they get violent with me they'll
+
+ align:start position:0%
+and if they get violent with me they'll
+ 
+
+ align:start position:0%
+and if they get violent with me they'll
+be on
+
+ align:start position:0%
+be on
+ 
+
+ align:start position:0%
+be on
+i point it up there so with all of those
+
+ align:start position:0%
+i point it up there so with all of those
+ 
+
+ align:start position:0%
+i point it up there so with all of those
+cameras i said well i and that's what i
+
+ align:start position:0%
+cameras i said well i and that's what i
+ 
+
+ align:start position:0%
+cameras i said well i and that's what i
+did i announced it right i said i said
+
+ align:start position:0%
+did i announced it right i said i said
+ 
+
+ align:start position:0%
+did i announced it right i said i said
+now if anybody does not want to exp or
+
+ align:start position:0%
+now if anybody does not want to exp or
+ 
+
+ align:start position:0%
+now if anybody does not want to exp or
+they uh
+
+ align:start position:0%
+they uh
+ 
+
+ align:start position:0%
+they uh
+respect uh my um
+
+ align:start position:0%
+respect uh my um
+ 
+
+ align:start position:0%
+respect uh my um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+my uh parliamentary powers
+
+ align:start position:0%
+my uh parliamentary powers
+ 
+
+ align:start position:0%
+my uh parliamentary powers
+then it will be a matter where you have
+
+ align:start position:0%
+then it will be a matter where you have
+ 
+
+ align:start position:0%
+then it will be a matter where you have
+to bring violence to the stage and you
+
+ align:start position:0%
+to bring violence to the stage and you
+ 
+
+ align:start position:0%
+to bring violence to the stage and you
+will be on tape and we will tape you
+
+ align:start position:0%
+will be on tape and we will tape you
+ 
+
+ align:start position:0%
+will be on tape and we will tape you
+right down to the baltimore sun and the
+
+ align:start position:0%
+right down to the baltimore sun and the
+ 
+
+ align:start position:0%
+right down to the baltimore sun and the
+washington post
+
+ align:start position:0%
+washington post
+ 
+
+ align:start position:0%
+washington post
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+well all i'm saying is that i've that um
+
+ align:start position:0%
+well all i'm saying is that i've that um
+ 
+
+ align:start position:0%
+well all i'm saying is that i've that um
+i've seen
+
+ align:start position:0%
+i've seen
+ 
+
+ align:start position:0%
+i've seen
+scholarship
+
+ align:start position:0%
+scholarship
+ 
+
+ align:start position:0%
+scholarship
+at its best i've seen it that is worse
+
+ align:start position:0%
+at its best i've seen it that is worse
+ 
+
+ align:start position:0%
+at its best i've seen it that is worse
+i've seen it
+
+ align:start position:0%
+i've seen it
+ 
+
+ align:start position:0%
+i've seen it
+in cases like this one which was not
+
+ align:start position:0%
+in cases like this one which was not
+ 
+
+ align:start position:0%
+in cases like this one which was not
+necessarily the best but certainly could
+
+ align:start position:0%
+necessarily the best but certainly could
+ 
+
+ align:start position:0%
+necessarily the best but certainly could
+have been the worst and was avoided
+
+ align:start position:0%
+have been the worst and was avoided
+ 
+
+ align:start position:0%
+have been the worst and was avoided
+turned out to be all right they had got
+
+ align:start position:0%
+turned out to be all right they had got
+ 
+
+ align:start position:0%
+turned out to be all right they had got
+up and said what they had to say but
+
+ align:start position:0%
+up and said what they had to say but
+ 
+
+ align:start position:0%
+up and said what they had to say but
+they didn't try to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be belligerent over the
+
+ align:start position:0%
+be belligerent over the
+ 
+
+ align:start position:0%
+be belligerent over the
+thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm saying that um
+
+ align:start position:0%
+so i'm saying that um
+ 
+
+ align:start position:0%
+so i'm saying that um
+when you're chairing a scholarly session
+
+ align:start position:0%
+when you're chairing a scholarly session
+ 
+
+ align:start position:0%
+when you're chairing a scholarly session
+uh attending and sharing a scholarly
+
+ align:start position:0%
+uh attending and sharing a scholarly
+ 
+
+ align:start position:0%
+uh attending and sharing a scholarly
+session
+
+ align:start position:0%
+session
+ 
+
+ align:start position:0%
+session
+that uh everything is not routine all
+
+ align:start position:0%
+that uh everything is not routine all
+ 
+
+ align:start position:0%
+that uh everything is not routine all
+the time everywhere
+
+ align:start position:0%
+the time everywhere
+ 
+
+ align:start position:0%
+the time everywhere
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and that your first obligation is to
+
+ align:start position:0%
+and that your first obligation is to
+ 
+
+ align:start position:0%
+and that your first obligation is to
+good scholarship
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything else
+
+ align:start position:0%
+anything else
+ 
+
+ align:start position:0%
+anything else
+on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so both of you want to be uh chairs and
+
+ align:start position:0%
+so both of you want to be uh chairs and
+ 
+
+ align:start position:0%
+so both of you want to be uh chairs and
+they both want to be rapid tours
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and what about uh charity
+
+ align:start position:0%
+and what about uh charity
+ 
+
+ align:start position:0%
+and what about uh charity
+we're gonna have two chairs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so uh
+
+ align:start position:0%
+all right so uh
+ 
+
+ align:start position:0%
+all right so uh
+then i'll turn over the conference to
+
+ align:start position:0%
+then i'll turn over the conference to
+ 
+
+ align:start position:0%
+then i'll turn over the conference to
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+and you all you manage it from there and
+
+ align:start position:0%
+and you all you manage it from there and
+ 
+
+ align:start position:0%
+and you all you manage it from there and
+then turn it if
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if the
+
+ align:start position:0%
+if the
+ 
+
+ align:start position:0%
+if the
+flow is right you give it back to me at
+
+ align:start position:0%
+flow is right you give it back to me at
+ 
+
+ align:start position:0%
+flow is right you give it back to me at
+the underclass
+
+ align:start position:0%
+the underclass
+ 
+
+ align:start position:0%
+the underclass
+if people are walking out no point
+
+ align:start position:0%
+if people are walking out no point
+ 
+
+ align:start position:0%
+if people are walking out no point
+uh so i i would imagine uh
+
+ align:start position:0%
+uh so i i would imagine uh
+ 
+
+ align:start position:0%
+uh so i i would imagine uh
+i think we can expect a minimum of five
+
+ align:start position:0%
+i think we can expect a minimum of five
+ 
+
+ align:start position:0%
+i think we can expect a minimum of five
+people
+
+ align:start position:0%
+people
+ 
+
+ align:start position:0%
+people
+uh who knows with all of this
+
+ align:start position:0%
+uh who knows with all of this
+ 
+
+ align:start position:0%
+uh who knows with all of this
+advertising what the walk-ins might be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so be prepared for the whole place to be
+
+ align:start position:0%
+so be prepared for the whole place to be
+ 
+
+ align:start position:0%
+so be prepared for the whole place to be
+filled up be prepared for
+
+ align:start position:0%
+filled up be prepared for
+ 
+
+ align:start position:0%
+filled up be prepared for
+by i don't know i haven't figured about
+
+ align:start position:0%
+by i don't know i haven't figured about
+ 
+
+ align:start position:0%
+by i don't know i haven't figured about
+five or six seven people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and that'd be about right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can we uh unless you have some other
+
+ align:start position:0%
+can we uh unless you have some other
+ 
+
+ align:start position:0%
+can we uh unless you have some other
+issues i want to go back to um
+
+ align:start position:0%
+issues i want to go back to um
+ 
+
+ align:start position:0%
+issues i want to go back to um
+vocabulary building
+
+ align:start position:0%
+vocabulary building
+ 
+
+ align:start position:0%
+vocabulary building
+actually not vocabulary building
+
+ align:start position:0%
+actually not vocabulary building
+ 
+
+ align:start position:0%
+actually not vocabulary building
+vocabulary strengthening you already
+
+ align:start position:0%
+vocabulary strengthening you already
+ 
+
+ align:start position:0%
+vocabulary strengthening you already
+have these words and terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's some here are some words and
+
+ align:start position:0%
+here's some here are some words and
+ 
+
+ align:start position:0%
+here's some here are some words and
+terms that i would like to cover
+
+ align:start position:0%
+terms that i would like to cover
+ 
+
+ align:start position:0%
+terms that i would like to cover
+today
+
+ align:start position:0%
+today
+ 
+
+ align:start position:0%
+today
+and in addition to some others
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and
+
+ align:start position:0%
+all right and
+ 
+
+ align:start position:0%
+all right and
+one of them is learning discipline
+
+ align:start position:0%
+one of them is learning discipline
+ 
+
+ align:start position:0%
+one of them is learning discipline
+what do you mean when you say
+
+ align:start position:0%
+what do you mean when you say
+ 
+
+ align:start position:0%
+what do you mean when you say
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+mathematics is a learned discipline
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do you say what do you mean when
+
+ align:start position:0%
+what do you say what do you mean when
+ 
+
+ align:start position:0%
+what do you say what do you mean when
+you say carpentry is not a learning
+
+ align:start position:0%
+you say carpentry is not a learning
+ 
+
+ align:start position:0%
+you say carpentry is not a learning
+discipline
+
+ align:start position:0%
+discipline
+ 
+
+ align:start position:0%
+discipline
+what do you mean by that
+
+ align:start position:0%
+what do you mean by that
+ 
+
+ align:start position:0%
+what do you mean by that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+is engineering i learned at discipline
+
+ align:start position:0%
+is engineering i learned at discipline
+ 
+
+ align:start position:0%
+is engineering i learned at discipline
+is uh esd
+
+ align:start position:0%
+is uh esd
+ 
+
+ align:start position:0%
+is uh esd
+i learned it discipline
+
+ align:start position:0%
+i learned it discipline
+ 
+
+ align:start position:0%
+i learned it discipline
+is education i learned this
+
+ align:start position:0%
+is education i learned this
+ 
+
+ align:start position:0%
+is education i learned this
+itself not what we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does it mean
+
+ align:start position:0%
+what does it mean
+ 
+
+ align:start position:0%
+what does it mean
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does it mean to engage two learning
+
+ align:start position:0%
+what does it mean to engage two learning
+ 
+
+ align:start position:0%
+what does it mean to engage two learning
+disciplines
+
+ align:start position:0%
+disciplines
+ 
+
+ align:start position:0%
+disciplines
+we did go through that a little bit and
+
+ align:start position:0%
+we did go through that a little bit and
+ 
+
+ align:start position:0%
+we did go through that a little bit and
+i'm gonna go through it
+
+ align:start position:0%
+i'm gonna go through it
+ 
+
+ align:start position:0%
+i'm gonna go through it
+on thursday
+
+ align:start position:0%
+on thursday
+ 
+
+ align:start position:0%
+on thursday
+but i really would like to know what it
+
+ align:start position:0%
+but i really would like to know what it
+ 
+
+ align:start position:0%
+but i really would like to know what it
+what does it mean
+
+ align:start position:0%
+what does it mean
+ 
+
+ align:start position:0%
+what does it mean
+to say that ethics is a learning
+
+ align:start position:0%
+to say that ethics is a learning
+ 
+
+ align:start position:0%
+to say that ethics is a learning
+discipline what does it mean to say
+
+ align:start position:0%
+discipline what does it mean to say
+ 
+
+ align:start position:0%
+discipline what does it mean to say
+that engineering is a learned discipline
+
+ align:start position:0%
+that engineering is a learned discipline
+ 
+
+ align:start position:0%
+that engineering is a learned discipline
+can you prove that engineering in fact
+
+ align:start position:0%
+can you prove that engineering in fact
+ 
+
+ align:start position:0%
+can you prove that engineering in fact
+is about this
+
+ align:start position:0%
+is about this
+ 
+
+ align:start position:0%
+is about this
+or does it get all of its
+
+ align:start position:0%
+or does it get all of its
+ 
+
+ align:start position:0%
+or does it get all of its
+first principles from science and math
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is that's it that's the question is
+
+ align:start position:0%
+that is that's it that's the question is
+ 
+
+ align:start position:0%
+that is that's it that's the question is
+debated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we have to define what we mean by
+
+ align:start position:0%
+well we have to define what we mean by
+ 
+
+ align:start position:0%
+well we have to define what we mean by
+learning the first
+
+ align:start position:0%
+learning the first
+ 
+
+ align:start position:0%
+learning the first
+all right so we'll do that i hope yeah i
+
+ align:start position:0%
+all right so we'll do that i hope yeah i
+ 
+
+ align:start position:0%
+all right so we'll do that i hope yeah i
+mean that's what that's why i laid that
+
+ align:start position:0%
+mean that's what that's why i laid that
+ 
+
+ align:start position:0%
+mean that's what that's why i laid that
+one down first um
+
+ align:start position:0%
+one down first um
+ 
+
+ align:start position:0%
+one down first um
+what is what is a profession
+
+ align:start position:0%
+what is what is a profession
+ 
+
+ align:start position:0%
+what is what is a profession
+that's another question
+
+ align:start position:0%
+that's another question
+ 
+
+ align:start position:0%
+that's another question
+what is a profession
+
+ align:start position:0%
+what is a profession
+ 
+
+ align:start position:0%
+what is a profession
+uh and here's a good one for you
+
+ align:start position:0%
+uh and here's a good one for you
+ 
+
+ align:start position:0%
+uh and here's a good one for you
+what does it mean to profess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and after you've got what it means to
+
+ align:start position:0%
+and after you've got what it means to
+ 
+
+ align:start position:0%
+and after you've got what it means to
+profess then tell me what a professor is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one who professes that's what it used to
+
+ align:start position:0%
+one who professes that's what it used to
+ 
+
+ align:start position:0%
+one who professes that's what it used to
+mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some other terms are going to come up oh
+
+ align:start position:0%
+some other terms are going to come up oh
+ 
+
+ align:start position:0%
+some other terms are going to come up oh
+i got a term for you
+
+ align:start position:0%
+i got a term for you
+ 
+
+ align:start position:0%
+i got a term for you
+i was just looking at this uh this
+
+ align:start position:0%
+i was just looking at this uh this
+ 
+
+ align:start position:0%
+i was just looking at this uh this
+morning didn't finish it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+what is it
+
+ align:start position:0%
+what is it
+ 
+
+ align:start position:0%
+what is it
+what is it what does it what does the
+
+ align:start position:0%
+what is it what does it what does the
+ 
+
+ align:start position:0%
+what is it what does it what does the
+word safety mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does the word risk
+
+ align:start position:0%
+what does the word risk
+ 
+
+ align:start position:0%
+what does the word risk
+mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's another word we talked about
+
+ align:start position:0%
+here's another word we talked about
+ 
+
+ align:start position:0%
+here's another word we talked about
+responsibility authority and
+
+ align:start position:0%
+responsibility authority and
+ 
+
+ align:start position:0%
+responsibility authority and
+accountability what about liability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going back to risk
+
+ align:start position:0%
+going back to risk
+ 
+
+ align:start position:0%
+going back to risk
+what is the term risk assessment mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does it mean
+
+ align:start position:0%
+what does it mean
+ 
+
+ align:start position:0%
+what does it mean
+what does acceptable risk mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is it what is an acceptable risk
+
+ align:start position:0%
+what is it what is an acceptable risk
+ 
+
+ align:start position:0%
+what is it what is an acceptable risk
+and what is what does the term
+
+ align:start position:0%
+and what is what does the term
+ 
+
+ align:start position:0%
+and what is what does the term
+risk perception mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it usually means willingness to take the
+
+ align:start position:0%
+it usually means willingness to take the
+ 
+
+ align:start position:0%
+it usually means willingness to take the
+risk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh why don't we go through some of
+
+ align:start position:0%
+okay uh why don't we go through some of
+ 
+
+ align:start position:0%
+okay uh why don't we go through some of
+these terms and words and terms
+
+ align:start position:0%
+these terms and words and terms
+ 
+
+ align:start position:0%
+these terms and words and terms
+start with the first one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+marine addison
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's open this let's have a
+
+ align:start position:0%
+and let's open this let's have a
+ 
+
+ align:start position:0%
+and let's open this let's have a
+discussion first i have
+
+ align:start position:0%
+discussion first i have
+ 
+
+ align:start position:0%
+discussion first i have
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+definitions
+
+ align:start position:0%
+definitions
+ 
+
+ align:start position:0%
+definitions
+for these terms and words
+
+ align:start position:0%
+for these terms and words
+ 
+
+ align:start position:0%
+for these terms and words
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but uh i'd like to have your thoughts
+
+ align:start position:0%
+but uh i'd like to have your thoughts
+ 
+
+ align:start position:0%
+but uh i'd like to have your thoughts
+and feelings about these terms and words
+
+ align:start position:0%
+and feelings about these terms and words
+ 
+
+ align:start position:0%
+and feelings about these terms and words
+we can go back like we did to the web or
+
+ align:start position:0%
+we can go back like we did to the web or
+ 
+
+ align:start position:0%
+we can go back like we did to the web or
+in the dictionary anytime we all classes
+
+ align:start position:0%
+in the dictionary anytime we all classes
+ 
+
+ align:start position:0%
+in the dictionary anytime we all classes
+are open
+
+ align:start position:0%
+are open
+ 
+
+ align:start position:0%
+are open
+for revision of anything that i we have
+
+ align:start position:0%
+for revision of anything that i we have
+ 
+
+ align:start position:0%
+for revision of anything that i we have
+covered before or anything that i have
+
+ align:start position:0%
+covered before or anything that i have
+ 
+
+ align:start position:0%
+covered before or anything that i have
+said before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+feel free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i don't know what i want you to do with
+
+ align:start position:0%
+i don't know what i want you to do with
+ 
+
+ align:start position:0%
+i don't know what i want you to do with
+i want you to feel free
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well you put down some words me let me
+
+ align:start position:0%
+well you put down some words me let me
+ 
+
+ align:start position:0%
+well you put down some words me let me
+now i'm going to ask well you said what
+
+ align:start position:0%
+now i'm going to ask well you said what
+ 
+
+ align:start position:0%
+now i'm going to ask well you said what
+a learning discipline is well i started
+
+ align:start position:0%
+a learning discipline is well i started
+ 
+
+ align:start position:0%
+a learning discipline is well i started
+knowledge
+
+ align:start position:0%
+knowledge
+ 
+
+ align:start position:0%
+knowledge
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+is that definition going to help us
+
+ align:start position:0%
+is that definition going to help us
+ 
+
+ align:start position:0%
+is that definition going to help us
+decide what is not a learned discipline
+
+ align:start position:0%
+decide what is not a learned discipline
+ 
+
+ align:start position:0%
+decide what is not a learned discipline
+or is everything going to qualify if it
+
+ align:start position:0%
+or is everything going to qualify if it
+ 
+
+ align:start position:0%
+or is everything going to qualify if it
+has
+
+ align:start position:0%
+has
+ 
+
+ align:start position:0%
+has
+okay go ahead
+
+ align:start position:0%
+okay go ahead
+ 
+
+ align:start position:0%
+okay go ahead
+i'm thinking about it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then there's
+
+ align:start position:0%
+and then there's
+ 
+
+ align:start position:0%
+and then there's
+a list of characteristics that make
+
+ align:start position:0%
+a list of characteristics that make
+ 
+
+ align:start position:0%
+a list of characteristics that make
+something different you know what you
+
+ align:start position:0%
+something different you know what you
+ 
+
+ align:start position:0%
+something different you know what you
+were suggesting me to say
+
+ align:start position:0%
+were suggesting me to say
+ 
+
+ align:start position:0%
+were suggesting me to say
+without
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so i mean then we could
+
+ align:start position:0%
+okay so i mean then we could
+ 
+
+ align:start position:0%
+okay so i mean then we could
+suppress by
+
+ align:start position:0%
+suppress by
+ 
+
+ align:start position:0%
+suppress by
+what it is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what i like about this is she's got
+
+ align:start position:0%
+and what i like about this is she's got
+ 
+
+ align:start position:0%
+and what i like about this is she's got
+a structured approach
+
+ align:start position:0%
+a structured approach
+ 
+
+ align:start position:0%
+a structured approach
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well first of all
+
+ align:start position:0%
+well first of all
+ 
+
+ align:start position:0%
+well first of all
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's interrogate this
+
+ align:start position:0%
+let's interrogate this
+ 
+
+ align:start position:0%
+let's interrogate this
+i don't and i use the word interrogate
+
+ align:start position:0%
+i don't and i use the word interrogate
+ 
+
+ align:start position:0%
+i don't and i use the word interrogate
+that's what
+
+ align:start position:0%
+that's what
+ 
+
+ align:start position:0%
+that's what
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+let's just interrogate everything that's
+
+ align:start position:0%
+let's just interrogate everything that's
+ 
+
+ align:start position:0%
+let's just interrogate everything that's
+up there
+
+ align:start position:0%
+up there
+ 
+
+ align:start position:0%
+up there
+all right and i'm using the word
+
+ align:start position:0%
+all right and i'm using the word
+ 
+
+ align:start position:0%
+all right and i'm using the word
+interrogate
+
+ align:start position:0%
+interrogate
+ 
+
+ align:start position:0%
+interrogate
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+i don't want to i want to just tell you
+
+ align:start position:0%
+i don't want to i want to just tell you
+ 
+
+ align:start position:0%
+i don't want to i want to just tell you
+that what i come up with in the end that
+
+ align:start position:0%
+that what i come up with in the end that
+ 
+
+ align:start position:0%
+that what i come up with in the end that
+i spent a lot of time on
+
+ align:start position:0%
+i spent a lot of time on
+ 
+
+ align:start position:0%
+i spent a lot of time on
+not necessarily better than what anybody
+
+ align:start position:0%
+not necessarily better than what anybody
+ 
+
+ align:start position:0%
+not necessarily better than what anybody
+else has but it fits into my book okay
+
+ align:start position:0%
+else has but it fits into my book okay
+ 
+
+ align:start position:0%
+else has but it fits into my book okay
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the point that i want to make is
+
+ align:start position:0%
+the point that i want to make is
+ 
+
+ align:start position:0%
+the point that i want to make is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+it's going to look a whole lot like this
+
+ align:start position:0%
+it's going to look a whole lot like this
+ 
+
+ align:start position:0%
+it's going to look a whole lot like this
+so when i interrogate it
+
+ align:start position:0%
+so when i interrogate it
+ 
+
+ align:start position:0%
+so when i interrogate it
+um not trying to tear it down
+
+ align:start position:0%
+um not trying to tear it down
+ 
+
+ align:start position:0%
+um not trying to tear it down
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+let's interrogate it so that we can
+
+ align:start position:0%
+let's interrogate it so that we can
+ 
+
+ align:start position:0%
+let's interrogate it so that we can
+understand it better
+
+ align:start position:0%
+understand it better
+ 
+
+ align:start position:0%
+understand it better
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+abilities
+
+ align:start position:0%
+abilities
+ 
+
+ align:start position:0%
+abilities
+associated with that like you steal
+
+ align:start position:0%
+associated with that like you steal
+ 
+
+ align:start position:0%
+associated with that like you steal
+stuff you can comprehend
+
+ align:start position:0%
+stuff you can comprehend
+ 
+
+ align:start position:0%
+stuff you can comprehend
+you can evaluate you can affect
+
+ align:start position:0%
+you can evaluate you can affect
+ 
+
+ align:start position:0%
+you can evaluate you can affect
+the size
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but maybe you're right maybe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well first of all what a dictionary is
+
+ align:start position:0%
+well first of all what a dictionary is
+ 
+
+ align:start position:0%
+well first of all what a dictionary is
+going to say
+
+ align:start position:0%
+going to say
+ 
+
+ align:start position:0%
+going to say
+i think a dictionary and
+
+ align:start position:0%
+i think a dictionary and
+ 
+
+ align:start position:0%
+i think a dictionary and
+many encyclopedias
+
+ align:start position:0%
+many encyclopedias
+ 
+
+ align:start position:0%
+many encyclopedias
+are going to use are going to base it
+
+ align:start position:0%
+are going to use are going to base it
+ 
+
+ align:start position:0%
+are going to use are going to base it
+start off with it with this term body of
+
+ align:start position:0%
+start off with it with this term body of
+ 
+
+ align:start position:0%
+start off with it with this term body of
+knowledge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well that's the one i want to
+
+ align:start position:0%
+well that's the one i want to
+ 
+
+ align:start position:0%
+well that's the one i want to
+i want to penetrate
+
+ align:start position:0%
+i want to penetrate
+ 
+
+ align:start position:0%
+i want to penetrate
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+we've studied ethics all this semester
+
+ align:start position:0%
+we've studied ethics all this semester
+ 
+
+ align:start position:0%
+we've studied ethics all this semester
+did we produce any knowledge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is ethics about the production of
+
+ align:start position:0%
+is ethics about the production of
+ 
+
+ align:start position:0%
+is ethics about the production of
+knowledge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does ethics have any knowledge in it
+
+ align:start position:0%
+does ethics have any knowledge in it
+ 
+
+ align:start position:0%
+does ethics have any knowledge in it
+that you can't get from someplace else
+
+ align:start position:0%
+that you can't get from someplace else
+ 
+
+ align:start position:0%
+that you can't get from someplace else
+like for example science
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a hard question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it has it means
+
+ align:start position:0%
+it has it means
+ 
+
+ align:start position:0%
+it has it means
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scholar
+
+ align:start position:0%
+scholar
+ 
+
+ align:start position:0%
+scholar
+it ethics knowledge of what other people
+
+ align:start position:0%
+it ethics knowledge of what other people
+ 
+
+ align:start position:0%
+it ethics knowledge of what other people
+have said about out there
+
+ align:start position:0%
+have said about out there
+ 
+
+ align:start position:0%
+have said about out there
+all right now what i want you to do is
+
+ align:start position:0%
+all right now what i want you to do is
+ 
+
+ align:start position:0%
+all right now what i want you to do is
+somewhere above the term body of
+
+ align:start position:0%
+somewhere above the term body of
+ 
+
+ align:start position:0%
+somewhere above the term body of
+knowledge
+
+ align:start position:0%
+knowledge
+ 
+
+ align:start position:0%
+knowledge
+maybe with an arrow i want you to write
+
+ align:start position:0%
+maybe with an arrow i want you to write
+ 
+
+ align:start position:0%
+maybe with an arrow i want you to write
+this man's name
+
+ align:start position:0%
+this man's name
+ 
+
+ align:start position:0%
+this man's name
+his name is bernard
+
+ align:start position:0%
+his name is bernard
+ 
+
+ align:start position:0%
+his name is bernard
+gert g-e-r-t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and he is at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why is this university escaping my mind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in new hampshire
+
+ align:start position:0%
+in new hampshire
+ 
+
+ align:start position:0%
+in new hampshire
+new hampshire yeah
+
+ align:start position:0%
+new hampshire yeah
+ 
+
+ align:start position:0%
+new hampshire yeah
+what university
+
+ align:start position:0%
+what university
+ 
+
+ align:start position:0%
+what university
+dartmouth he said dartmouth
+
+ align:start position:0%
+dartmouth he said dartmouth
+ 
+
+ align:start position:0%
+dartmouth he said dartmouth
+unless he's retired
+
+ align:start position:0%
+unless he's retired
+ 
+
+ align:start position:0%
+unless he's retired
+you know all of my buddies are gone now
+
+ align:start position:0%
+you know all of my buddies are gone now
+ 
+
+ align:start position:0%
+you know all of my buddies are gone now
+uh bert
+
+ align:start position:0%
+uh bert
+ 
+
+ align:start position:0%
+uh bert
+bernard gert wrote a book called he's a
+
+ align:start position:0%
+bernard gert wrote a book called he's a
+ 
+
+ align:start position:0%
+bernard gert wrote a book called he's a
+philosopher and an ethicist he wrote a
+
+ align:start position:0%
+philosopher and an ethicist he wrote a
+ 
+
+ align:start position:0%
+philosopher and an ethicist he wrote a
+book called moral knowledge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he has a view
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that i don't think is uh widely shared
+
+ align:start position:0%
+that i don't think is uh widely shared
+ 
+
+ align:start position:0%
+that i don't think is uh widely shared
+even though his view is is as defensible
+
+ align:start position:0%
+even though his view is is as defensible
+ 
+
+ align:start position:0%
+even though his view is is as defensible
+as anybody else's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because we want to talk about ethics
+
+ align:start position:0%
+because we want to talk about ethics
+ 
+
+ align:start position:0%
+because we want to talk about ethics
+being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+having more to do
+
+ align:start position:0%
+having more to do
+ 
+
+ align:start position:0%
+having more to do
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+value judgments
+
+ align:start position:0%
+value judgments
+ 
+
+ align:start position:0%
+value judgments
+than knowledge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah i guess that's why i added
+
+ align:start position:0%
+yeah i guess that's why i added
+ 
+
+ align:start position:0%
+yeah i guess that's why i added
+abilities because there's
+
+ align:start position:0%
+abilities because there's
+ 
+
+ align:start position:0%
+abilities because there's
+in learning discipline okay there's
+
+ align:start position:0%
+in learning discipline okay there's
+ 
+
+ align:start position:0%
+in learning discipline okay there's
+information you need to have right and
+
+ align:start position:0%
+information you need to have right and
+ 
+
+ align:start position:0%
+information you need to have right and
+then there is
+
+ align:start position:0%
+then there is
+ 
+
+ align:start position:0%
+then there is
+that's the way i think about it like
+
+ align:start position:0%
+that's the way i think about it like
+ 
+
+ align:start position:0%
+that's the way i think about it like
+i've needed to
+
+ align:start position:0%
+i've needed to
+ 
+
+ align:start position:0%
+i've needed to
+understand better vocabulary and like
+
+ align:start position:0%
+understand better vocabulary and like
+ 
+
+ align:start position:0%
+understand better vocabulary and like
+techniques and strategies for looking at
+
+ align:start position:0%
+techniques and strategies for looking at
+ 
+
+ align:start position:0%
+techniques and strategies for looking at
+this around that
+
+ align:start position:0%
+this around that
+ 
+
+ align:start position:0%
+this around that
+and then apply those techniques
+
+ align:start position:0%
+and then apply those techniques
+ 
+
+ align:start position:0%
+and then apply those techniques
+to make values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now most people i think
+
+ align:start position:0%
+now most people i think
+ 
+
+ align:start position:0%
+now most people i think
+when we begin to talk about
+
+ align:start position:0%
+when we begin to talk about
+ 
+
+ align:start position:0%
+when we begin to talk about
+our learning discipline
+
+ align:start position:0%
+our learning discipline
+ 
+
+ align:start position:0%
+our learning discipline
+when i say most people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+most scientists certainly including the
+
+ align:start position:0%
+most scientists certainly including the
+ 
+
+ align:start position:0%
+most scientists certainly including the
+social science
+
+ align:start position:0%
+social science
+ 
+
+ align:start position:0%
+social science
+scientists
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will be happy with that
+
+ align:start position:0%
+will be happy with that
+ 
+
+ align:start position:0%
+will be happy with that
+uh including the mathematician
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the humanists are going to be divided on
+
+ align:start position:0%
+the humanists are going to be divided on
+ 
+
+ align:start position:0%
+the humanists are going to be divided on
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the arts people
+
+ align:start position:0%
+the arts people
+ 
+
+ align:start position:0%
+the arts people
+are going to have a whole lot of trouble
+
+ align:start position:0%
+are going to have a whole lot of trouble
+ 
+
+ align:start position:0%
+are going to have a whole lot of trouble
+with it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+knowledge being the basis of in other
+
+ align:start position:0%
+knowledge being the basis of in other
+ 
+
+ align:start position:0%
+knowledge being the basis of in other
+words
+
+ align:start position:0%
+words
+ 
+
+ align:start position:0%
+words
+they're going to say that music is not
+
+ align:start position:0%
+they're going to say that music is not
+ 
+
+ align:start position:0%
+they're going to say that music is not
+really about knowledge or how you handle
+
+ align:start position:0%
+really about knowledge or how you handle
+ 
+
+ align:start position:0%
+really about knowledge or how you handle
+knowledge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what they come up with in the end is
+
+ align:start position:0%
+now what they come up with in the end is
+ 
+
+ align:start position:0%
+now what they come up with in the end is
+going to be something that you probably
+
+ align:start position:0%
+going to be something that you probably
+ 
+
+ align:start position:0%
+going to be something that you probably
+wouldn't feel comfortable with when i
+
+ align:start position:0%
+wouldn't feel comfortable with when i
+ 
+
+ align:start position:0%
+wouldn't feel comfortable with when i
+say you i mean scientists and engineers
+
+ align:start position:0%
+say you i mean scientists and engineers
+ 
+
+ align:start position:0%
+say you i mean scientists and engineers
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know but uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they are are not going they're going to
+
+ align:start position:0%
+they are are not going they're going to
+ 
+
+ align:start position:0%
+they are are not going they're going to
+say that this whole business of
+
+ align:start position:0%
+say that this whole business of
+ 
+
+ align:start position:0%
+say that this whole business of
+knowledge is overworked
+
+ align:start position:0%
+knowledge is overworked
+ 
+
+ align:start position:0%
+knowledge is overworked
+there are other things that we do with
+
+ align:start position:0%
+there are other things that we do with
+ 
+
+ align:start position:0%
+there are other things that we do with
+our minds other than to produce
+
+ align:start position:0%
+our minds other than to produce
+ 
+
+ align:start position:0%
+our minds other than to produce
+knowledge
+
+ align:start position:0%
+knowledge
+ 
+
+ align:start position:0%
+knowledge
+because and what they'll say is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that our capacities for learning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+include the cognition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay which is
+
+ align:start position:0%
+okay which is
+ 
+
+ align:start position:0%
+okay which is
+our underlying ability
+
+ align:start position:0%
+our underlying ability
+ 
+
+ align:start position:0%
+our underlying ability
+for knowledge under gaining knowledge
+
+ align:start position:0%
+for knowledge under gaining knowledge
+ 
+
+ align:start position:0%
+for knowledge under gaining knowledge
+and making knowledge statements and
+
+ align:start position:0%
+and making knowledge statements and
+ 
+
+ align:start position:0%
+and making knowledge statements and
+justifying knowledge statements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+what will happen before you're done is
+
+ align:start position:0%
+what will happen before you're done is
+ 
+
+ align:start position:0%
+what will happen before you're done is
+that the scientists
+
+ align:start position:0%
+that the scientists
+ 
+
+ align:start position:0%
+that the scientists
+the mathematicians
+
+ align:start position:0%
+the mathematicians
+ 
+
+ align:start position:0%
+the mathematicians
+half the engineering scholars but not
+
+ align:start position:0%
+half the engineering scholars but not
+ 
+
+ align:start position:0%
+half the engineering scholars but not
+all of them
+
+ align:start position:0%
+all of them
+ 
+
+ align:start position:0%
+all of them
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+are going to say well that the cognition
+
+ align:start position:0%
+are going to say well that the cognition
+ 
+
+ align:start position:0%
+are going to say well that the cognition
+is what separates the human being from
+
+ align:start position:0%
+is what separates the human being from
+ 
+
+ align:start position:0%
+is what separates the human being from
+the beast
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+half of the humanists are going to say
+
+ align:start position:0%
+half of the humanists are going to say
+ 
+
+ align:start position:0%
+half of the humanists are going to say
+are going to say go go back to the
+
+ align:start position:0%
+are going to say go go back to the
+ 
+
+ align:start position:0%
+are going to say go go back to the
+psychologist and say well look there's
+
+ align:start position:0%
+psychologist and say well look there's
+ 
+
+ align:start position:0%
+psychologist and say well look there's
+such a thing called the affect
+
+ align:start position:0%
+such a thing called the affect
+ 
+
+ align:start position:0%
+such a thing called the affect
+and out of that is where we get love
+
+ align:start position:0%
+and out of that is where we get love
+ 
+
+ align:start position:0%
+and out of that is where we get love
+and all of these other things
+
+ align:start position:0%
+and all of these other things
+ 
+
+ align:start position:0%
+and all of these other things
+and that's what separates
+
+ align:start position:0%
+and that's what separates
+ 
+
+ align:start position:0%
+and that's what separates
+man from beast
+
+ align:start position:0%
+man from beast
+ 
+
+ align:start position:0%
+man from beast
+[Laughter]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm interrogating
+
+ align:start position:0%
+i'm interrogating
+ 
+
+ align:start position:0%
+i'm interrogating
+i haven't taken a stand yet i will take
+
+ align:start position:0%
+i haven't taken a stand yet i will take
+ 
+
+ align:start position:0%
+i haven't taken a stand yet i will take
+a stand thursday i'm getting ready for
+
+ align:start position:0%
+a stand thursday i'm getting ready for
+ 
+
+ align:start position:0%
+a stand thursday i'm getting ready for
+my stay it looks like we're not going to
+
+ align:start position:0%
+my stay it looks like we're not going to
+ 
+
+ align:start position:0%
+my stay it looks like we're not going to
+have a whole lot of time
+
+ align:start position:0%
+have a whole lot of time
+ 
+
+ align:start position:0%
+have a whole lot of time
+for me to finish it today
+
+ align:start position:0%
+for me to finish it today
+ 
+
+ align:start position:0%
+for me to finish it today
+let me tell you what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wanna i don't know
+
+ align:start position:0%
+wanna i don't know
+ 
+
+ align:start position:0%
+wanna i don't know
+but you're doing so well
+
+ align:start position:0%
+but you're doing so well
+ 
+
+ align:start position:0%
+but you're doing so well
+i know
+
+ align:start position:0%
+i know
+ 
+
+ align:start position:0%
+i know
+well i would like to flush out our
+
+ align:start position:0%
+well i would like to flush out our
+ 
+
+ align:start position:0%
+well i would like to flush out our
+definition a little bit more
+
+ align:start position:0%
+definition a little bit more
+ 
+
+ align:start position:0%
+definition a little bit more
+uh okay here's what i want to say
+
+ align:start position:0%
+uh okay here's what i want to say
+ 
+
+ align:start position:0%
+uh okay here's what i want to say
+here's what i want to say okay why don't
+
+ align:start position:0%
+here's what i want to say okay why don't
+ 
+
+ align:start position:0%
+here's what i want to say okay why don't
+you sit at the edge of the table you may
+
+ align:start position:0%
+you sit at the edge of the table you may
+ 
+
+ align:start position:0%
+you sit at the edge of the table you may
+have to go back to the board nah go do
+
+ align:start position:0%
+have to go back to the board nah go do
+ 
+
+ align:start position:0%
+have to go back to the board nah go do
+what you want to do
+
+ align:start position:0%
+what you want to do
+ 
+
+ align:start position:0%
+what you want to do
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's what i want to say all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i want to say that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are four learning capacities now i
+
+ align:start position:0%
+there are four learning capacities now i
+ 
+
+ align:start position:0%
+there are four learning capacities now i
+have invented none of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and one is our capacity to make
+
+ align:start position:0%
+and one is our capacity to make
+ 
+
+ align:start position:0%
+and one is our capacity to make
+knowledge statements and justify them
+
+ align:start position:0%
+knowledge statements and justify them
+ 
+
+ align:start position:0%
+knowledge statements and justify them
+and we talk about a knowledge statement
+
+ align:start position:0%
+and we talk about a knowledge statement
+ 
+
+ align:start position:0%
+and we talk about a knowledge statement
+what it looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we got another
+
+ align:start position:0%
+we got another
+ 
+
+ align:start position:0%
+we got another
+six minutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+six
+
+ align:start position:0%
+six
+ 
+
+ align:start position:0%
+six
+minutes okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we talked about rational knowledge
+
+ align:start position:0%
+we talked about rational knowledge
+ 
+
+ align:start position:0%
+we talked about rational knowledge
+and logic we talked about empirical
+
+ align:start position:0%
+and logic we talked about empirical
+ 
+
+ align:start position:0%
+and logic we talked about empirical
+knowledge and facts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have another
+
+ align:start position:0%
+we have another
+ 
+
+ align:start position:0%
+we have another
+capacity called the affect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that capacity
+
+ align:start position:0%
+and that capacity
+ 
+
+ align:start position:0%
+and that capacity
+enables us to make value judgments
+
+ align:start position:0%
+enables us to make value judgments
+ 
+
+ align:start position:0%
+enables us to make value judgments
+and to justify them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we not only say
+
+ align:start position:0%
+we not only say
+ 
+
+ align:start position:0%
+we not only say
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+water is a liquid
+
+ align:start position:0%
+water is a liquid
+ 
+
+ align:start position:0%
+water is a liquid
+we are also say able to say something
+
+ align:start position:0%
+we are also say able to say something
+ 
+
+ align:start position:0%
+we are also say able to say something
+very different
+
+ align:start position:0%
+very different
+ 
+
+ align:start position:0%
+very different
+water is good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and when i say water is good now here's
+
+ align:start position:0%
+and when i say water is good now here's
+ 
+
+ align:start position:0%
+and when i say water is good now here's
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+bernard gert would get into discussion
+
+ align:start position:0%
+bernard gert would get into discussion
+ 
+
+ align:start position:0%
+bernard gert would get into discussion
+he's going to say that's a knowledge
+
+ align:start position:0%
+he's going to say that's a knowledge
+ 
+
+ align:start position:0%
+he's going to say that's a knowledge
+statement
+
+ align:start position:0%
+statement
+ 
+
+ align:start position:0%
+statement
+and most people will say that's not a
+
+ align:start position:0%
+and most people will say that's not a
+ 
+
+ align:start position:0%
+and most people will say that's not a
+knowledge date
+
+ align:start position:0%
+knowledge date
+ 
+
+ align:start position:0%
+knowledge date
+got nothing to do with logic got nothing
+
+ align:start position:0%
+got nothing to do with logic got nothing
+ 
+
+ align:start position:0%
+got nothing to do with logic got nothing
+to do with the
+
+ align:start position:0%
+to do with the
+ 
+
+ align:start position:0%
+to do with the
+well it has something indirectly to do
+
+ align:start position:0%
+well it has something indirectly to do
+ 
+
+ align:start position:0%
+well it has something indirectly to do
+with it with a with with an empirical
+
+ align:start position:0%
+with it with a with with an empirical
+ 
+
+ align:start position:0%
+with it with a with with an empirical
+test
+
+ align:start position:0%
+test
+ 
+
+ align:start position:0%
+test
+but that's not the end
+
+ align:start position:0%
+but that's not the end
+ 
+
+ align:start position:0%
+but that's not the end
+okay the end is feeling good
+
+ align:start position:0%
+okay the end is feeling good
+ 
+
+ align:start position:0%
+okay the end is feeling good
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+there's another one
+
+ align:start position:0%
+there's another one
+ 
+
+ align:start position:0%
+there's another one
+the other two have the other two i'd say
+
+ align:start position:0%
+the other two have the other two i'd say
+ 
+
+ align:start position:0%
+the other two have the other two i'd say
+there were four
+
+ align:start position:0%
+there were four
+ 
+
+ align:start position:0%
+there were four
+the other two go together
+
+ align:start position:0%
+the other two go together
+ 
+
+ align:start position:0%
+the other two go together
+i'm gonna go through this on thursday
+
+ align:start position:0%
+i'm gonna go through this on thursday
+ 
+
+ align:start position:0%
+i'm gonna go through this on thursday
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+i'm gonna use the next five minutes to
+
+ align:start position:0%
+i'm gonna use the next five minutes to
+ 
+
+ align:start position:0%
+i'm gonna use the next five minutes to
+get you started because i want you to
+
+ align:start position:0%
+get you started because i want you to
+ 
+
+ align:start position:0%
+get you started because i want you to
+think about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there is such a thing called
+
+ align:start position:0%
+there is such a thing called
+ 
+
+ align:start position:0%
+there is such a thing called
+a commitment pathway
+
+ align:start position:0%
+a commitment pathway
+ 
+
+ align:start position:0%
+a commitment pathway
+i might have
+
+ align:start position:0%
+i might have
+ 
+
+ align:start position:0%
+i might have
+mentioned it before but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the commitment pathway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is from wishes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+wants to intentions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to action
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you get from a wish to a want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with hope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you may wish for a hundred million
+
+ align:start position:0%
+so you may wish for a hundred million
+ 
+
+ align:start position:0%
+so you may wish for a hundred million
+dollars
+
+ align:start position:0%
+dollars
+ 
+
+ align:start position:0%
+dollars
+you start wanting it when you see some
+
+ align:start position:0%
+you start wanting it when you see some
+ 
+
+ align:start position:0%
+you start wanting it when you see some
+possibility of it
+
+ align:start position:0%
+possibility of it
+ 
+
+ align:start position:0%
+possibility of it
+when you've got some hope of getting it
+
+ align:start position:0%
+when you've got some hope of getting it
+ 
+
+ align:start position:0%
+when you've got some hope of getting it
+you go from wants to intentions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with self-esteem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in other words you may want a hundred
+
+ align:start position:0%
+in other words you may want a hundred
+ 
+
+ align:start position:0%
+in other words you may want a hundred
+million dollars
+
+ align:start position:0%
+million dollars
+ 
+
+ align:start position:0%
+million dollars
+but unless you think that you have the
+
+ align:start position:0%
+but unless you think that you have the
+ 
+
+ align:start position:0%
+but unless you think that you have the
+ability to get it
+
+ align:start position:0%
+ability to get it
+ 
+
+ align:start position:0%
+ability to get it
+you won't have the intentions
+
+ align:start position:0%
+you won't have the intentions
+ 
+
+ align:start position:0%
+you won't have the intentions
+to get it
+
+ align:start position:0%
+to get it
+ 
+
+ align:start position:0%
+to get it
+you'll just sit back in pain of wants
+
+ align:start position:0%
+you'll just sit back in pain of wants
+ 
+
+ align:start position:0%
+you'll just sit back in pain of wants
+without intentions
+
+ align:start position:0%
+without intentions
+ 
+
+ align:start position:0%
+without intentions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and then to get from intentions to
+
+ align:start position:0%
+and then to get from intentions to
+ 
+
+ align:start position:0%
+and then to get from intentions to
+action
+
+ align:start position:0%
+action
+ 
+
+ align:start position:0%
+action
+is what
+
+ align:start position:0%
+is what
+ 
+
+ align:start position:0%
+is what
+we call the will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this pathway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+is just as important in life as
+
+ align:start position:0%
+is just as important in life as
+ 
+
+ align:start position:0%
+is just as important in life as
+knowledge and values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as a matter of fact if you read the
+
+ align:start position:0%
+as a matter of fact if you read the
+ 
+
+ align:start position:0%
+as a matter of fact if you read the
+german scholars they will say
+
+ align:start position:0%
+german scholars they will say
+ 
+
+ align:start position:0%
+german scholars they will say
+this is more important
+
+ align:start position:0%
+this is more important
+ 
+
+ align:start position:0%
+this is more important
+than knowledge and values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they'll their starting point for
+
+ align:start position:0%
+and they'll their starting point for
+ 
+
+ align:start position:0%
+and they'll their starting point for
+saying that is
+
+ align:start position:0%
+saying that is
+ 
+
+ align:start position:0%
+saying that is
+if you deprive me of knowledge
+
+ align:start position:0%
+if you deprive me of knowledge
+ 
+
+ align:start position:0%
+if you deprive me of knowledge
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and if i have some conflicting values i
+
+ align:start position:0%
+and if i have some conflicting values i
+ 
+
+ align:start position:0%
+and if i have some conflicting values i
+can still make it in the world
+
+ align:start position:0%
+can still make it in the world
+ 
+
+ align:start position:0%
+can still make it in the world
+if i can prosecute this commitment
+
+ align:start position:0%
+if i can prosecute this commitment
+ 
+
+ align:start position:0%
+if i can prosecute this commitment
+pathway to having my way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you devote scholarship to this
+
+ align:start position:0%
+when you devote scholarship to this
+ 
+
+ align:start position:0%
+when you devote scholarship to this
+commitment pathway
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a word that
+
+ align:start position:0%
+there's a word that
+ 
+
+ align:start position:0%
+there's a word that
+nobody agrees on but everybody will see
+
+ align:start position:0%
+nobody agrees on but everybody will see
+ 
+
+ align:start position:0%
+nobody agrees on but everybody will see
+the point in saying that great
+
+ align:start position:0%
+the point in saying that great
+ 
+
+ align:start position:0%
+the point in saying that great
+scholarship devoted to
+
+ align:start position:0%
+scholarship devoted to
+ 
+
+ align:start position:0%
+scholarship devoted to
+the part of this pathway from wishes to
+
+ align:start position:0%
+the part of this pathway from wishes to
+ 
+
+ align:start position:0%
+the part of this pathway from wishes to
+wants to intentions we can call praxis
+
+ align:start position:0%
+wants to intentions we can call praxis
+ 
+
+ align:start position:0%
+wants to intentions we can call praxis
+p-r-a-x-i-x-s
+
+ align:start position:0%
+p-r-a-x-i-x-s
+ 
+
+ align:start position:0%
+p-r-a-x-i-x-s
+there are other words and then most
+
+ align:start position:0%
+there are other words and then most
+ 
+
+ align:start position:0%
+there are other words and then most
+people have no word for it
+
+ align:start position:0%
+people have no word for it
+ 
+
+ align:start position:0%
+people have no word for it
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and this part from intentions to action
+
+ align:start position:0%
+and this part from intentions to action
+ 
+
+ align:start position:0%
+and this part from intentions to action
+is called practice
+
+ align:start position:0%
+is called practice
+ 
+
+ align:start position:0%
+is called practice
+and few people will disagree with the
+
+ align:start position:0%
+and few people will disagree with the
+ 
+
+ align:start position:0%
+and few people will disagree with the
+use of that word
+
+ align:start position:0%
+use of that word
+ 
+
+ align:start position:0%
+use of that word
+from it from going from intentions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to action
+
+ align:start position:0%
+to action
+ 
+
+ align:start position:0%
+to action
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+and what i want to say then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that underlying praxis is a term i'll
+
+ align:start position:0%
+is that underlying praxis is a term i'll
+ 
+
+ align:start position:0%
+is that underlying praxis is a term i'll
+give you another term
+
+ align:start position:0%
+give you another term
+ 
+
+ align:start position:0%
+give you another term
+just like we have the cognition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called the conation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and underlying all of this practice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's what you call psychomotor skill
+
+ align:start position:0%
+it's what you call psychomotor skill
+ 
+
+ align:start position:0%
+it's what you call psychomotor skill
+psychomotor skill is informed
+
+ align:start position:0%
+psychomotor skill is informed
+ 
+
+ align:start position:0%
+psychomotor skill is informed
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+praxis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as a term used to include all of these
+
+ align:start position:0%
+as a term used to include all of these
+ 
+
+ align:start position:0%
+as a term used to include all of these
+things here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the will
+
+ align:start position:0%
+the will
+ 
+
+ align:start position:0%
+the will
+self-esteem
+
+ align:start position:0%
+self-esteem
+ 
+
+ align:start position:0%
+self-esteem
+uh hope
+
+ align:start position:0%
+uh hope
+ 
+
+ align:start position:0%
+uh hope
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+i'll lay it out more in a chart i guess
+
+ align:start position:0%
+i'll lay it out more in a chart i guess
+ 
+
+ align:start position:0%
+i'll lay it out more in a chart i guess
+better than today but we've got no more
+
+ align:start position:0%
+better than today but we've got no more
+ 
+
+ align:start position:0%
+better than today but we've got no more
+minutes left let me say that let me go
+
+ align:start position:0%
+minutes left let me say that let me go
+ 
+
+ align:start position:0%
+minutes left let me say that let me go
+over time about 30 seconds maybe
+
+ align:start position:0%
+over time about 30 seconds maybe
+ 
+
+ align:start position:0%
+over time about 30 seconds maybe
+because indeed let me just say
+
+ align:start position:0%
+because indeed let me just say
+ 
+
+ align:start position:0%
+because indeed let me just say
+that if you find sciences
+
+ align:start position:0%
+that if you find sciences
+ 
+
+ align:start position:0%
+that if you find sciences
+science
+
+ align:start position:0%
+science
+ 
+
+ align:start position:0%
+science
+the sciences
+
+ align:start position:0%
+the sciences
+ 
+
+ align:start position:0%
+the sciences
+and mathematics
+
+ align:start position:0%
+and mathematics
+ 
+
+ align:start position:0%
+and mathematics
+in the cognitive area with the
+
+ align:start position:0%
+in the cognitive area with the
+ 
+
+ align:start position:0%
+in the cognitive area with the
+production of knowledge and if you say
+
+ align:start position:0%
+production of knowledge and if you say
+ 
+
+ align:start position:0%
+production of knowledge and if you say
+that ethics and the humanities
+
+ align:start position:0%
+that ethics and the humanities
+ 
+
+ align:start position:0%
+that ethics and the humanities
+are in the values area
+
+ align:start position:0%
+are in the values area
+ 
+
+ align:start position:0%
+are in the values area
+with uh
+
+ align:start position:0%
+with uh
+ 
+
+ align:start position:0%
+with uh
+with the
+
+ align:start position:0%
+with the
+ 
+
+ align:start position:0%
+with the
+with the affect
+
+ align:start position:0%
+with the affect
+ 
+
+ align:start position:0%
+with the affect
+you'll find
+
+ align:start position:0%
+you'll find
+ 
+
+ align:start position:0%
+you'll find
+engineering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the performing arts
+
+ align:start position:0%
+the performing arts
+ 
+
+ align:start position:0%
+the performing arts
+over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i have a better definition of the
+
+ align:start position:0%
+i have a better definition of the
+ 
+
+ align:start position:0%
+i have a better definition of the
+various disciplines but you'll be
+
+ align:start position:0%
+various disciplines but you'll be
+ 
+
+ align:start position:0%
+various disciplines but you'll be
+surprised
+
+ align:start position:0%
+surprised
+ 
+
+ align:start position:0%
+surprised
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+miss bethke that it'll look a whole lot
+
+ align:start position:0%
+miss bethke that it'll look a whole lot
+ 
+
+ align:start position:0%
+miss bethke that it'll look a whole lot
+like that
+
+ align:start position:0%
+like that
+ 
+
+ align:start position:0%
+like that
+better to use this structure to get
+
+ align:start position:0%
+better to use this structure to get
+ 
+
+ align:start position:0%
+better to use this structure to get
+it thank you
\ No newline at end of file
diff --git a/iGW0nRbAqEM.txt b/iGW0nRbAqEM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..be46305f73509a37c24928ed02622215e5b207d4
--- /dev/null
+++ b/iGW0nRbAqEM.txt
@@ -0,0 +1,6979 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT open courseware
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT open courseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu I want these these auditory
+
+ align:start position:0%
+ocw.mit.edu I want these these auditory
+ 
+
+ align:start position:0%
+ocw.mit.edu I want these these auditory
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+specializations um I'd like to say just
+
+ align:start position:0%
+specializations um I'd like to say just
+ 
+
+ align:start position:0%
+specializations um I'd like to say just
+a little bit about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh earlier in chapter 6 we talked about
+
+ align:start position:0%
+uh earlier in chapter 6 we talked about
+ 
+
+ align:start position:0%
+uh earlier in chapter 6 we talked about
+the echolocating animals the bats and
+
+ align:start position:0%
+the echolocating animals the bats and
+ 
+
+ align:start position:0%
+the echolocating animals the bats and
+dolphins
+
+ align:start position:0%
+dolphins
+ 
+
+ align:start position:0%
+dolphins
+and it was we pointed out then that they
+
+ align:start position:0%
+and it was we pointed out then that they
+ 
+
+ align:start position:0%
+and it was we pointed out then that they
+have this very large
+
+ align:start position:0%
+have this very large
+ 
+
+ align:start position:0%
+have this very large
+uh auditory midbrain the inferior
+
+ align:start position:0%
+uh auditory midbrain the inferior
+ 
+
+ align:start position:0%
+uh auditory midbrain the inferior
+calculous their animals were the in most
+
+ align:start position:0%
+calculous their animals were the in most
+ 
+
+ align:start position:0%
+calculous their animals were the in most
+animals the rodents we look at in the
+
+ align:start position:0%
+animals the rodents we look at in the
+ 
+
+ align:start position:0%
+animals the rodents we look at in the
+lab the
+
+ align:start position:0%
+lab the
+ 
+
+ align:start position:0%
+lab the
+uh any of the
+
+ align:start position:0%
+uh any of the
+ 
+
+ align:start position:0%
+uh any of the
+primates Superior calculus is much
+
+ align:start position:0%
+primates Superior calculus is much
+ 
+
+ align:start position:0%
+primates Superior calculus is much
+larger than the inferior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculus here are a couple of here's an
+
+ align:start position:0%
+calculus here are a couple of here's an
+ 
+
+ align:start position:0%
+calculus here are a couple of here's an
+one primate the tarsier and here's an
+
+ align:start position:0%
+one primate the tarsier and here's an
+ 
+
+ align:start position:0%
+one primate the tarsier and here's an
+ulate the eex and uh you see the
+
+ align:start position:0%
+ulate the eex and uh you see the
+ 
+
+ align:start position:0%
+ulate the eex and uh you see the
+spiculus being much larger typical for
+
+ align:start position:0%
+spiculus being much larger typical for
+ 
+
+ align:start position:0%
+spiculus being much larger typical for
+an animal dominated by
+
+ align:start position:0%
+an animal dominated by
+ 
+
+ align:start position:0%
+an animal dominated by
+Vision even if they don't have a
+
+ align:start position:0%
+Vision even if they don't have a
+ 
+
+ align:start position:0%
+Vision even if they don't have a
+huge visual C area they will still have
+
+ align:start position:0%
+huge visual C area they will still have
+ 
+
+ align:start position:0%
+huge visual C area they will still have
+a large midbrain area for vision but the
+
+ align:start position:0%
+a large midbrain area for vision but the
+ 
+
+ align:start position:0%
+a large midbrain area for vision but the
+echolocating animals have a much larger
+
+ align:start position:0%
+echolocating animals have a much larger
+ 
+
+ align:start position:0%
+echolocating animals have a much larger
+inferior calculus because some of the
+
+ align:start position:0%
+inferior calculus because some of the
+ 
+
+ align:start position:0%
+inferior calculus because some of the
+processing is is done cortically and the
+
+ align:start position:0%
+processing is is done cortically and the
+ 
+
+ align:start position:0%
+processing is is done cortically and the
+inferior calculus is the major root to
+
+ align:start position:0%
+inferior calculus is the major root to
+ 
+
+ align:start position:0%
+inferior calculus is the major root to
+the uh the auditory
+
+ align:start position:0%
+the uh the auditory
+ 
+
+ align:start position:0%
+the uh the auditory
+Thalamus this is from an early study of
+
+ align:start position:0%
+Thalamus this is from an early study of
+ 
+
+ align:start position:0%
+Thalamus this is from an early study of
+of a bad that uses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+echolocation and uh there is a lot of
+
+ align:start position:0%
+echolocation and uh there is a lot of
+ 
+
+ align:start position:0%
+echolocation and uh there is a lot of
+Cortex devoted to auditory processing
+
+ align:start position:0%
+Cortex devoted to auditory processing
+ 
+
+ align:start position:0%
+Cortex devoted to auditory processing
+and uh early on they they knew the
+
+ align:start position:0%
+and uh early on they they knew the
+ 
+
+ align:start position:0%
+and uh early on they they knew the
+primary area was very
+
+ align:start position:0%
+primary area was very
+ 
+
+ align:start position:0%
+primary area was very
+large um they could map out different
+
+ align:start position:0%
+large um they could map out different
+ 
+
+ align:start position:0%
+large um they could map out different
+frequency representation and there were
+
+ align:start position:0%
+frequency representation and there were
+ 
+
+ align:start position:0%
+frequency representation and there were
+areas like at this point they Suga
+
+ align:start position:0%
+areas like at this point they Suga
+ 
+
+ align:start position:0%
+areas like at this point they Suga
+worked out three different areas where
+
+ align:start position:0%
+worked out three different areas where
+ 
+
+ align:start position:0%
+worked out three different areas where
+the units were responsive to various
+
+ align:start position:0%
+the units were responsive to various
+ 
+
+ align:start position:0%
+the units were responsive to various
+kinds of frequency modulation and then
+
+ align:start position:0%
+kinds of frequency modulation and then
+ 
+
+ align:start position:0%
+kinds of frequency modulation and then
+he continued that work and found areas
+
+ align:start position:0%
+he continued that work and found areas
+ 
+
+ align:start position:0%
+he continued that work and found areas
+or units sensitive to range just how far
+
+ align:start position:0%
+or units sensitive to range just how far
+ 
+
+ align:start position:0%
+or units sensitive to range just how far
+away the animals were uh and to Velocity
+
+ align:start position:0%
+away the animals were uh and to Velocity
+ 
+
+ align:start position:0%
+away the animals were uh and to Velocity
+so they could
+
+ align:start position:0%
+so they could
+ 
+
+ align:start position:0%
+so they could
+detect a number of features of the their
+
+ align:start position:0%
+detect a number of features of the their
+ 
+
+ align:start position:0%
+detect a number of features of the their
+prey that they were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chasing
+
+ align:start position:0%
+chasing
+ 
+
+ align:start position:0%
+chasing
+now if we go to
+
+ align:start position:0%
+now if we go to
+ 
+
+ align:start position:0%
+now if we go to
+birds I'm asking here what is the area
+
+ align:start position:0%
+birds I'm asking here what is the area
+ 
+
+ align:start position:0%
+birds I'm asking here what is the area
+in Birds that's comparable to the
+
+ align:start position:0%
+in Birds that's comparable to the
+ 
+
+ align:start position:0%
+in Birds that's comparable to the
+auditory NE neocortex of a mammal does a
+
+ align:start position:0%
+auditory NE neocortex of a mammal does a
+ 
+
+ align:start position:0%
+auditory NE neocortex of a mammal does a
+bird have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neocortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry what's the
+
+ align:start position:0%
+sorry what's the
+ 
+
+ align:start position:0%
+sorry what's the
+word they have an auditory uh they have
+
+ align:start position:0%
+word they have an auditory uh they have
+ 
+
+ align:start position:0%
+word they have an auditory uh they have
+as areas in the thalamus that
+
+ align:start position:0%
+as areas in the thalamus that
+ 
+
+ align:start position:0%
+as areas in the thalamus that
+receive auditory input just like they
+
+ align:start position:0%
+receive auditory input just like they
+ 
+
+ align:start position:0%
+receive auditory input just like they
+have areas there that receive visual
+
+ align:start position:0%
+have areas there that receive visual
+ 
+
+ align:start position:0%
+have areas there that receive visual
+input where do those areas project
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they do have a kind of visual cortex too
+
+ align:start position:0%
+they do have a kind of visual cortex too
+ 
+
+ align:start position:0%
+they do have a kind of visual cortex too
+but the area their geniculate body
+
+ align:start position:0%
+but the area their geniculate body
+ 
+
+ align:start position:0%
+but the area their geniculate body
+usually isn't called geniculate body
+
+ align:start position:0%
+usually isn't called geniculate body
+ 
+
+ align:start position:0%
+usually isn't called geniculate body
+remember but it's called other things
+
+ align:start position:0%
+remember but it's called other things
+ 
+
+ align:start position:0%
+remember but it's called other things
+but it does project to a cortex like
+
+ align:start position:0%
+but it does project to a cortex like
+ 
+
+ align:start position:0%
+but it does project to a cortex like
+area that that is called the hyper
+
+ align:start position:0%
+area that that is called the hyper
+ 
+
+ align:start position:0%
+area that that is called the hyper
+palum pallum of course is just another
+
+ align:start position:0%
+palum pallum of course is just another
+ 
+
+ align:start position:0%
+palum pallum of course is just another
+name for a cortical region and the hyper
+
+ align:start position:0%
+name for a cortical region and the hyper
+ 
+
+ align:start position:0%
+name for a cortical region and the hyper
+Pali is the most similar to the
+
+ align:start position:0%
+Pali is the most similar to the
+ 
+
+ align:start position:0%
+Pali is the most similar to the
+neocortex of mammals but then
+
+ align:start position:0%
+neocortex of mammals but then
+ 
+
+ align:start position:0%
+neocortex of mammals but then
+they have other nuclei in the thalamus
+
+ align:start position:0%
+they have other nuclei in the thalamus
+ 
+
+ align:start position:0%
+they have other nuclei in the thalamus
+that get input like the lp in mammals or
+
+ align:start position:0%
+that get input like the lp in mammals or
+ 
+
+ align:start position:0%
+that get input like the lp in mammals or
+the medial geniculate body they get
+
+ align:start position:0%
+the medial geniculate body they get
+ 
+
+ align:start position:0%
+the medial geniculate body they get
+input from the
+
+ align:start position:0%
+input from the
+ 
+
+ align:start position:0%
+input from the
+midbrain so in the case of the auditory
+
+ align:start position:0%
+midbrain so in the case of the auditory
+ 
+
+ align:start position:0%
+midbrain so in the case of the auditory
+system they're getting projections from
+
+ align:start position:0%
+system they're getting projections from
+ 
+
+ align:start position:0%
+system they're getting projections from
+the bird's inferior calculous
+
+ align:start position:0%
+the bird's inferior calculous
+ 
+
+ align:start position:0%
+the bird's inferior calculous
+region often again with a different
+
+ align:start position:0%
+region often again with a different
+ 
+
+ align:start position:0%
+region often again with a different
+name
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+here it's in the birds it's usually
+
+ align:start position:0%
+here it's in the birds it's usually
+ 
+
+ align:start position:0%
+here it's in the birds it's usually
+called nucleus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ovoidalis and that projects to this
+
+ align:start position:0%
+ovoidalis and that projects to this
+ 
+
+ align:start position:0%
+ovoidalis and that projects to this
+large region that for many years was
+
+ align:start position:0%
+large region that for many years was
+ 
+
+ align:start position:0%
+large region that for many years was
+called the neostriatum in
+
+ align:start position:0%
+called the neostriatum in
+ 
+
+ align:start position:0%
+called the neostriatum in
+Birds but now we know not only from
+
+ align:start position:0%
+Birds but now we know not only from
+ 
+
+ align:start position:0%
+Birds but now we know not only from
+first from connection data gathered here
+
+ align:start position:0%
+first from connection data gathered here
+ 
+
+ align:start position:0%
+first from connection data gathered here
+at MIT by carton who was working with
+
+ align:start position:0%
+at MIT by carton who was working with
+ 
+
+ align:start position:0%
+at MIT by carton who was working with
+NAA and later in the gene expression
+
+ align:start position:0%
+NAA and later in the gene expression
+ 
+
+ align:start position:0%
+NAA and later in the gene expression
+data we know that that area is not
+
+ align:start position:0%
+data we know that that area is not
+ 
+
+ align:start position:0%
+data we know that that area is not
+striatum uh not equivalent not
+
+ align:start position:0%
+striatum uh not equivalent not
+ 
+
+ align:start position:0%
+striatum uh not equivalent not
+homologous to the striatum of
+
+ align:start position:0%
+homologous to the striatum of
+ 
+
+ align:start position:0%
+homologous to the striatum of
+mammals so it's it's called a nested
+
+ align:start position:0%
+mammals so it's it's called a nested
+ 
+
+ align:start position:0%
+mammals so it's it's called a nested
+pallum or a nidopallium
+
+ align:start position:0%
+pallum or a nidopallium
+ 
+
+ align:start position:0%
+pallum or a nidopallium
+um it is sub cortical if you go by The
+
+ align:start position:0%
+um it is sub cortical if you go by The
+ 
+
+ align:start position:0%
+um it is sub cortical if you go by The
+ventricle Here's Where The ventricle is
+
+ align:start position:0%
+ventricle Here's Where The ventricle is
+ 
+
+ align:start position:0%
+ventricle Here's Where The ventricle is
+along here and that hyper palum is above
+
+ align:start position:0%
+along here and that hyper palum is above
+ 
+
+ align:start position:0%
+along here and that hyper palum is above
+it that would be where
+
+ align:start position:0%
+it that would be where
+ 
+
+ align:start position:0%
+it that would be where
+the the equivalent of the lateral
+
+ align:start position:0%
+the the equivalent of the lateral
+ 
+
+ align:start position:0%
+the the equivalent of the lateral
+geniculate projects for the visual
+
+ align:start position:0%
+geniculate projects for the visual
+ 
+
+ align:start position:0%
+geniculate projects for the visual
+system and a lot of it is Visual and the
+
+ align:start position:0%
+system and a lot of it is Visual and the
+ 
+
+ align:start position:0%
+system and a lot of it is Visual and the
+medial part is
+
+ align:start position:0%
+medial part is
+ 
+
+ align:start position:0%
+medial part is
+hipocampal okay but the auditory region
+
+ align:start position:0%
+hipocampal okay but the auditory region
+ 
+
+ align:start position:0%
+hipocampal okay but the auditory region
+the Nu of the thalamus nucleus ovoidalis
+
+ align:start position:0%
+the Nu of the thalamus nucleus ovoidalis
+ 
+
+ align:start position:0%
+the Nu of the thalamus nucleus ovoidalis
+projects to the nitop palum the medial
+
+ align:start position:0%
+projects to the nitop palum the medial
+ 
+
+ align:start position:0%
+projects to the nitop palum the medial
+part an area we called field
+
+ align:start position:0%
+part an area we called field
+ 
+
+ align:start position:0%
+part an area we called field
+L now the reptiles have something
+
+ align:start position:0%
+L now the reptiles have something
+ 
+
+ align:start position:0%
+L now the reptiles have something
+similar we give the thalamic nucleus
+
+ align:start position:0%
+similar we give the thalamic nucleus
+ 
+
+ align:start position:0%
+similar we give the thalamic nucleus
+that gets auditory input a different
+
+ align:start position:0%
+that gets auditory input a different
+ 
+
+ align:start position:0%
+that gets auditory input a different
+name the
+
+ align:start position:0%
+name the
+ 
+
+ align:start position:0%
+name the
+reunions the medial
+
+ align:start position:0%
+reunions the medial
+ 
+
+ align:start position:0%
+reunions the medial
+reunions it goes to their that large
+
+ align:start position:0%
+reunions it goes to their that large
+ 
+
+ align:start position:0%
+reunions it goes to their that large
+dorsal ventricular
+
+ align:start position:0%
+dorsal ventricular
+ 
+
+ align:start position:0%
+dorsal ventricular
+Ridge and dorsal ventricular Ridge
+
+ align:start position:0%
+Ridge and dorsal ventricular Ridge
+ 
+
+ align:start position:0%
+Ridge and dorsal ventricular Ridge
+becomes nidopallium if it's in bird
+
+ align:start position:0%
+becomes nidopallium if it's in bird
+ 
+
+ align:start position:0%
+becomes nidopallium if it's in bird
+development we keep calling it dorsal
+
+ align:start position:0%
+development we keep calling it dorsal
+ 
+
+ align:start position:0%
+development we keep calling it dorsal
+ventricular rid in the reptiles and they
+
+ align:start position:0%
+ventricular rid in the reptiles and they
+ 
+
+ align:start position:0%
+ventricular rid in the reptiles and they
+have a auditory region just like here
+
+ align:start position:0%
+have a auditory region just like here
+ 
+
+ align:start position:0%
+have a auditory region just like here
+more laterally in this region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right there it gets visual
+
+ align:start position:0%
+right there it gets visual
+ 
+
+ align:start position:0%
+right there it gets visual
+input from a different nucleus in the
+
+ align:start position:0%
+input from a different nucleus in the
+ 
+
+ align:start position:0%
+input from a different nucleus in the
+thalamus a nucleus that gets input from
+
+ align:start position:0%
+thalamus a nucleus that gets input from
+ 
+
+ align:start position:0%
+thalamus a nucleus that gets input from
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+tectum and then of course here's the
+
+ align:start position:0%
+tectum and then of course here's the
+ 
+
+ align:start position:0%
+tectum and then of course here's the
+equivalent circuit in mammals medial
+
+ align:start position:0%
+equivalent circuit in mammals medial
+ 
+
+ align:start position:0%
+equivalent circuit in mammals medial
+genicular body to these auditory
+
+ align:start position:0%
+genicular body to these auditory
+ 
+
+ align:start position:0%
+genicular body to these auditory
+cortical
+
+ align:start position:0%
+cortical
+ 
+
+ align:start position:0%
+cortical
+regions and this is what it looks like
+
+ align:start position:0%
+regions and this is what it looks like
+ 
+
+ align:start position:0%
+regions and this is what it looks like
+this is from an atlas uh by carton
+
+ align:start position:0%
+this is from an atlas uh by carton
+ 
+
+ align:start position:0%
+this is from an atlas uh by carton
+working with Bill
+
+ align:start position:0%
+working with Bill
+ 
+
+ align:start position:0%
+working with Bill
+hodos uh in the late 60s where they and
+
+ align:start position:0%
+hodos uh in the late 60s where they and
+ 
+
+ align:start position:0%
+hodos uh in the late 60s where they and
+they published this Atlas showing the
+
+ align:start position:0%
+they published this Atlas showing the
+ 
+
+ align:start position:0%
+they published this Atlas showing the
+appearance of sections at various levels
+
+ align:start position:0%
+appearance of sections at various levels
+ 
+
+ align:start position:0%
+appearance of sections at various levels
+of the bird brain and you can see just
+
+ align:start position:0%
+of the bird brain and you can see just
+ 
+
+ align:start position:0%
+of the bird brain and you can see just
+looking at the cells here how field L
+
+ align:start position:0%
+looking at the cells here how field L
+ 
+
+ align:start position:0%
+looking at the cells here how field L
+stands out it's got several layers it's
+
+ align:start position:0%
+stands out it's got several layers it's
+ 
+
+ align:start position:0%
+stands out it's got several layers it's
+a little layer down here main layer
+
+ align:start position:0%
+a little layer down here main layer
+ 
+
+ align:start position:0%
+a little layer down here main layer
+there and another more superficial layer
+
+ align:start position:0%
+there and another more superficial layer
+ 
+
+ align:start position:0%
+there and another more superficial layer
+and here's where they we it's
+
+ align:start position:0%
+and here's where they we it's
+ 
+
+ align:start position:0%
+and here's where they we it's
+diagrammed and you can see that's all
+
+ align:start position:0%
+diagrammed and you can see that's all
+ 
+
+ align:start position:0%
+diagrammed and you can see that's all
+below
+
+ align:start position:0%
+below
+ 
+
+ align:start position:0%
+below
+this end brain
+
+ align:start position:0%
+this end brain
+ 
+
+ align:start position:0%
+this end brain
+ventricle and this would be where the
+
+ align:start position:0%
+ventricle and this would be where the
+ 
+
+ align:start position:0%
+ventricle and this would be where the
+hippocampal equivalent is the medial
+
+ align:start position:0%
+hippocampal equivalent is the medial
+ 
+
+ align:start position:0%
+hippocampal equivalent is the medial
+pallum and this whole region in many
+
+ align:start position:0%
+pallum and this whole region in many
+ 
+
+ align:start position:0%
+pallum and this whole region in many
+animals it's just called dorsal cortex
+
+ align:start position:0%
+animals it's just called dorsal cortex
+ 
+
+ align:start position:0%
+animals it's just called dorsal cortex
+but in Birds it's called the
+
+ align:start position:0%
+but in Birds it's called the
+ 
+
+ align:start position:0%
+but in Birds it's called the
+hyperpallium
+
+ align:start position:0%
+hyperpallium
+ 
+
+ align:start position:0%
+hyperpallium
+all right so if you trace the auditory
+
+ align:start position:0%
+all right so if you trace the auditory
+ 
+
+ align:start position:0%
+all right so if you trace the auditory
+pathway from there uh the clear
+
+ align:start position:0%
+pathway from there uh the clear
+ 
+
+ align:start position:0%
+pathway from there uh the clear
+region this is they don't have the
+
+ align:start position:0%
+region this is they don't have the
+ 
+
+ align:start position:0%
+region this is they don't have the
+coiled CIA of mammals but it's instead
+
+ align:start position:0%
+coiled CIA of mammals but it's instead
+ 
+
+ align:start position:0%
+coiled CIA of mammals but it's instead
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+Basler membrane they have a Basler
+
+ align:start position:0%
+Basler membrane they have a Basler
+ 
+
+ align:start position:0%
+Basler membrane they have a Basler
+papilla and uh where the auditory
+
+ align:start position:0%
+papilla and uh where the auditory
+ 
+
+ align:start position:0%
+papilla and uh where the auditory
+receptors uh are in contact with the
+
+ align:start position:0%
+receptors uh are in contact with the
+ 
+
+ align:start position:0%
+receptors uh are in contact with the
+eighth nerve and you can see the eighth
+
+ align:start position:0%
+eighth nerve and you can see the eighth
+ 
+
+ align:start position:0%
+eighth nerve and you can see the eighth
+nerve comes in to contact secondary
+
+ align:start position:0%
+nerve comes in to contact secondary
+ 
+
+ align:start position:0%
+nerve comes in to contact secondary
+sensory cells of the clear nuclei just
+
+ align:start position:0%
+sensory cells of the clear nuclei just
+ 
+
+ align:start position:0%
+sensory cells of the clear nuclei just
+like in mammals we saw that when we
+
+ align:start position:0%
+like in mammals we saw that when we
+ 
+
+ align:start position:0%
+like in mammals we saw that when we
+talked about spatial location remember
+
+ align:start position:0%
+talked about spatial location remember
+ 
+
+ align:start position:0%
+talked about spatial location remember
+for the I showed the
+
+ align:start position:0%
+for the I showed the
+ 
+
+ align:start position:0%
+for the I showed the
+the they're dorsally located uh and the
+
+ align:start position:0%
+the they're dorsally located uh and the
+ 
+
+ align:start position:0%
+the they're dorsally located uh and the
+neurons there project to the inferior
+
+ align:start position:0%
+neurons there project to the inferior
+ 
+
+ align:start position:0%
+neurons there project to the inferior
+calculus of the
+
+ align:start position:0%
+calculus of the
+ 
+
+ align:start position:0%
+calculus of the
+bird it's got a different name the MLD
+
+ align:start position:0%
+bird it's got a different name the MLD
+ 
+
+ align:start position:0%
+bird it's got a different name the MLD
+micus lateralis paror cells okay and
+
+ align:start position:0%
+micus lateralis paror cells okay and
+ 
+
+ align:start position:0%
+micus lateralis paror cells okay and
+that then
+
+ align:start position:0%
+that then
+ 
+
+ align:start position:0%
+that then
+projects to the thalamus nucleus the
+
+ align:start position:0%
+projects to the thalamus nucleus the
+ 
+
+ align:start position:0%
+projects to the thalamus nucleus the
+ovoid nucleus nucleus o do which
+
+ align:start position:0%
+ovoid nucleus nucleus o do which
+ 
+
+ align:start position:0%
+ovoid nucleus nucleus o do which
+projects to field L okay so that's just
+
+ align:start position:0%
+projects to field L okay so that's just
+ 
+
+ align:start position:0%
+projects to field L okay so that's just
+the simplest picture of the auditory
+
+ align:start position:0%
+the simplest picture of the auditory
+ 
+
+ align:start position:0%
+the simplest picture of the auditory
+pathway but you can then follow things
+
+ align:start position:0%
+pathway but you can then follow things
+ 
+
+ align:start position:0%
+pathway but you can then follow things
+from the auditory
+
+ align:start position:0%
+from the auditory
+ 
+
+ align:start position:0%
+from the auditory
+pathway that are involved in controlling
+
+ align:start position:0%
+pathway that are involved in controlling
+ 
+
+ align:start position:0%
+pathway that are involved in controlling
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+vocalizations okay and the most direct
+
+ align:start position:0%
+vocalizations okay and the most direct
+ 
+
+ align:start position:0%
+vocalizations okay and the most direct
+pathway goes from field L to
+
+ align:start position:0%
+pathway goes from field L to
+ 
+
+ align:start position:0%
+pathway goes from field L to
+a so-called higher vocal Center which
+
+ align:start position:0%
+a so-called higher vocal Center which
+ 
+
+ align:start position:0%
+a so-called higher vocal Center which
+then projects to this nucleus robustness
+
+ align:start position:0%
+then projects to this nucleus robustness
+ 
+
+ align:start position:0%
+then projects to this nucleus robustness
+of the arop palum now the arop palum
+
+ align:start position:0%
+of the arop palum now the arop palum
+ 
+
+ align:start position:0%
+of the arop palum now the arop palum
+is an a homologous to the region of
+
+ align:start position:0%
+is an a homologous to the region of
+ 
+
+ align:start position:0%
+is an a homologous to the region of
+mammals remember the amigdala region
+
+ align:start position:0%
+mammals remember the amigdala region
+ 
+
+ align:start position:0%
+mammals remember the amigdala region
+though has many outputs to hypothalamus
+
+ align:start position:0%
+though has many outputs to hypothalamus
+ 
+
+ align:start position:0%
+though has many outputs to hypothalamus
+and to midbrain and in
+
+ align:start position:0%
+and to midbrain and in
+ 
+
+ align:start position:0%
+and to midbrain and in
+Birds this uh nucleus
+
+ align:start position:0%
+Birds this uh nucleus
+ 
+
+ align:start position:0%
+Birds this uh nucleus
+robustus has a direct
+
+ align:start position:0%
+robustus has a direct
+ 
+
+ align:start position:0%
+robustus has a direct
+projection to the hypos nucleus which
+
+ align:start position:0%
+projection to the hypos nucleus which
+ 
+
+ align:start position:0%
+projection to the hypos nucleus which
+part of which controls the sering which
+
+ align:start position:0%
+part of which controls the sering which
+ 
+
+ align:start position:0%
+part of which controls the sering which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+there controls basically the voice box
+
+ align:start position:0%
+there controls basically the voice box
+ 
+
+ align:start position:0%
+there controls basically the voice box
+of the bird controlling his voice
+
+ align:start position:0%
+of the bird controlling his voice
+ 
+
+ align:start position:0%
+of the bird controlling his voice
+localizations together with of course
+
+ align:start position:0%
+localizations together with of course
+ 
+
+ align:start position:0%
+localizations together with of course
+breathing control and then there's a
+
+ align:start position:0%
+breathing control and then there's a
+ 
+
+ align:start position:0%
+breathing control and then there's a
+Less Direct pathway that goes to an
+
+ align:start position:0%
+Less Direct pathway that goes to an
+ 
+
+ align:start position:0%
+Less Direct pathway that goes to an
+outer part of the inferior calculous
+
+ align:start position:0%
+outer part of the inferior calculous
+ 
+
+ align:start position:0%
+outer part of the inferior calculous
+region which then projects to the
+
+ align:start position:0%
+region which then projects to the
+ 
+
+ align:start position:0%
+region which then projects to the
+hypoglossal nucleus and controls the
+
+ align:start position:0%
+hypoglossal nucleus and controls the
+ 
+
+ align:start position:0%
+hypoglossal nucleus and controls the
+searings now there's a Less Direct
+
+ align:start position:0%
+searings now there's a Less Direct
+ 
+
+ align:start position:0%
+searings now there's a Less Direct
+pathway that in many ways is more
+
+ align:start position:0%
+pathway that in many ways is more
+ 
+
+ align:start position:0%
+pathway that in many ways is more
+interesting from field L and the higher
+
+ align:start position:0%
+interesting from field L and the higher
+ 
+
+ align:start position:0%
+interesting from field L and the higher
+vocal Center IT projects to the striatum
+
+ align:start position:0%
+vocal Center IT projects to the striatum
+ 
+
+ align:start position:0%
+vocal Center IT projects to the striatum
+of the bird
+
+ align:start position:0%
+of the bird
+ 
+
+ align:start position:0%
+of the bird
+now we're talking about the real
+
+ align:start position:0%
+now we're talking about the real
+ 
+
+ align:start position:0%
+now we're talking about the real
+striatum
+
+ align:start position:0%
+striatum
+ 
+
+ align:start position:0%
+striatum
+not that is it's equivalent to striatum
+
+ align:start position:0%
+not that is it's equivalent to striatum
+ 
+
+ align:start position:0%
+not that is it's equivalent to striatum
+the dorsal striatum in a
+
+ align:start position:0%
+the dorsal striatum in a
+ 
+
+ align:start position:0%
+the dorsal striatum in a
+mammal and like in mammals the striatum
+
+ align:start position:0%
+mammal and like in mammals the striatum
+ 
+
+ align:start position:0%
+mammal and like in mammals the striatum
+has an output to the
+
+ align:start position:0%
+has an output to the
+ 
+
+ align:start position:0%
+has an output to the
+phalus and the thalamic structure IT
+
+ align:start position:0%
+phalus and the thalamic structure IT
+ 
+
+ align:start position:0%
+phalus and the thalamic structure IT
+projects to then projects back to a
+
+ align:start position:0%
+projects to then projects back to a
+ 
+
+ align:start position:0%
+projects to then projects back to a
+Paleo
+
+ align:start position:0%
+Paleo
+ 
+
+ align:start position:0%
+Paleo
+region it's like a brocas area in
+
+ align:start position:0%
+region it's like a brocas area in
+ 
+
+ align:start position:0%
+region it's like a brocas area in
+mammals that is they're very similar
+
+ align:start position:0%
+mammals that is they're very similar
+ 
+
+ align:start position:0%
+mammals that is they're very similar
+Pathways controlling speech in humans
+
+ align:start position:0%
+Pathways controlling speech in humans
+ 
+
+ align:start position:0%
+Pathways controlling speech in humans
+it's part of the nested
+
+ align:start position:0%
+it's part of the nested
+ 
+
+ align:start position:0%
+it's part of the nested
+pallum remember this more codly the
+
+ align:start position:0%
+pallum remember this more codly the
+ 
+
+ align:start position:0%
+pallum remember this more codly the
+field L the auditory system gets is part
+
+ align:start position:0%
+field L the auditory system gets is part
+ 
+
+ align:start position:0%
+field L the auditory system gets is part
+of that nidopallium well
+
+ align:start position:0%
+of that nidopallium well
+ 
+
+ align:start position:0%
+of that nidopallium well
+roosterly uh this nucleus called Elman
+
+ align:start position:0%
+roosterly uh this nucleus called Elman
+ 
+
+ align:start position:0%
+roosterly uh this nucleus called Elman
+gets is also involved in vocalization
+
+ align:start position:0%
+gets is also involved in vocalization
+ 
+
+ align:start position:0%
+gets is also involved in vocalization
+and in fact this circuit is what's
+
+ align:start position:0%
+and in fact this circuit is what's
+ 
+
+ align:start position:0%
+and in fact this circuit is what's
+involved in male birds learning
+
+ align:start position:0%
+involved in male birds learning
+ 
+
+ align:start position:0%
+involved in male birds learning
+the vocalization of their species and
+
+ align:start position:0%
+the vocalization of their species and
+ 
+
+ align:start position:0%
+the vocalization of their species and
+they learn by imitation of their
+
+ align:start position:0%
+they learn by imitation of their
+ 
+
+ align:start position:0%
+they learn by imitation of their
+listening to their father sing and they
+
+ align:start position:0%
+listening to their father sing and they
+ 
+
+ align:start position:0%
+listening to their father sing and they
+develop if they don't hear that singing
+
+ align:start position:0%
+develop if they don't hear that singing
+ 
+
+ align:start position:0%
+develop if they don't hear that singing
+They Don't develop this complex vocal
+
+ align:start position:0%
+They Don't develop this complex vocal
+ 
+
+ align:start position:0%
+They Don't develop this complex vocal
+repertoire anyway that nucleus projects
+
+ align:start position:0%
+repertoire anyway that nucleus projects
+ 
+
+ align:start position:0%
+repertoire anyway that nucleus projects
+to the robust nucleus which gives rise
+
+ align:start position:0%
+to the robust nucleus which gives rise
+ 
+
+ align:start position:0%
+to the robust nucleus which gives rise
+to those outputs to control the vocal
+
+ align:start position:0%
+to those outputs to control the vocal
+ 
+
+ align:start position:0%
+to those outputs to control the vocal
+system of the bird the sings in the
+
+ align:start position:0%
+system of the bird the sings in the
+ 
+
+ align:start position:0%
+system of the bird the sings in the
+throat
+
+ align:start position:0%
+throat
+ 
+
+ align:start position:0%
+throat
+all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right you learn a lot about that if you
+
+ align:start position:0%
+right you learn a lot about that if you
+ 
+
+ align:start position:0%
+right you learn a lot about that if you
+work with Michael fee in the building
+
+ align:start position:0%
+work with Michael fee in the building
+ 
+
+ align:start position:0%
+work with Michael fee in the building
+and students that work with
+
+ align:start position:0%
+and students that work with
+ 
+
+ align:start position:0%
+and students that work with
+Michael uh probably become pretty
+
+ align:start position:0%
+Michael uh probably become pretty
+ 
+
+ align:start position:0%
+Michael uh probably become pretty
+familiar with that circuit but now I
+
+ align:start position:0%
+familiar with that circuit but now I
+ 
+
+ align:start position:0%
+familiar with that circuit but now I
+want to go through some say a little bit
+
+ align:start position:0%
+want to go through some say a little bit
+ 
+
+ align:start position:0%
+want to go through some say a little bit
+about the forbrain before we become a
+
+ align:start position:0%
+about the forbrain before we become a
+ 
+
+ align:start position:0%
+about the forbrain before we become a
+little more specialized and covering the
+
+ align:start position:0%
+little more specialized and covering the
+ 
+
+ align:start position:0%
+little more specialized and covering the
+for brand we'll be talking about well
+
+ align:start position:0%
+for brand we'll be talking about well
+ 
+
+ align:start position:0%
+for brand we'll be talking about well
+you'll see
+
+ align:start position:0%
+you'll see
+ 
+
+ align:start position:0%
+you'll see
+here we've covered
+
+ align:start position:0%
+here we've covered
+ 
+
+ align:start position:0%
+here we've covered
+now this the first five parts were
+
+ align:start position:0%
+now this the first five parts were
+ 
+
+ align:start position:0%
+now this the first five parts were
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+development and evolution of the brain
+
+ align:start position:0%
+development and evolution of the brain
+ 
+
+ align:start position:0%
+development and evolution of the brain
+explaining the basic organization of the
+
+ align:start position:0%
+explaining the basic organization of the
+ 
+
+ align:start position:0%
+explaining the basic organization of the
+CNS and then we went to specialized
+
+ align:start position:0%
+CNS and then we went to specialized
+ 
+
+ align:start position:0%
+CNS and then we went to specialized
+systems and I began with there were
+
+ align:start position:0%
+systems and I began with there were
+ 
+
+ align:start position:0%
+systems and I began with there were
+three chapters on the motor
+
+ align:start position:0%
+three chapters on the motor
+ 
+
+ align:start position:0%
+three chapters on the motor
+system okay and uh then a single chapter
+
+ align:start position:0%
+system okay and uh then a single chapter
+ 
+
+ align:start position:0%
+system okay and uh then a single chapter
+on brain
+
+ align:start position:0%
+on brain
+ 
+
+ align:start position:0%
+on brain
+States
+
+ align:start position:0%
+States
+ 
+
+ align:start position:0%
+States
+and then sensory systems which should
+
+ align:start position:0%
+and then sensory systems which should
+ 
+
+ align:start position:0%
+and then sensory systems which should
+probably be called special sensory
+
+ align:start position:0%
+probably be called special sensory
+ 
+
+ align:start position:0%
+probably be called special sensory
+because the general sensory some sensory
+
+ align:start position:0%
+because the general sensory some sensory
+ 
+
+ align:start position:0%
+because the general sensory some sensory
+I didn't cover in that special in that
+
+ align:start position:0%
+I didn't cover in that special in that
+ 
+
+ align:start position:0%
+I didn't cover in that special in that
+section because we talked a lot about
+
+ align:start position:0%
+section because we talked a lot about
+ 
+
+ align:start position:0%
+section because we talked a lot about
+somata sensory system in the earlier
+
+ align:start position:0%
+somata sensory system in the earlier
+ 
+
+ align:start position:0%
+somata sensory system in the earlier
+parts of the book so that's when we
+
+ align:start position:0%
+parts of the book so that's when we
+ 
+
+ align:start position:0%
+parts of the book so that's when we
+dealt with gustatory Al Factory Visual
+
+ align:start position:0%
+dealt with gustatory Al Factory Visual
+ 
+
+ align:start position:0%
+dealt with gustatory Al Factory Visual
+and then finally auditory systems so now
+
+ align:start position:0%
+and then finally auditory systems so now
+ 
+
+ align:start position:0%
+and then finally auditory systems so now
+Poe brain Origins and then we talk about
+
+ align:start position:0%
+Poe brain Origins and then we talk about
+ 
+
+ align:start position:0%
+Poe brain Origins and then we talk about
+the lmic system and
+
+ align:start position:0%
+the lmic system and
+ 
+
+ align:start position:0%
+the lmic system and
+hypothalamus that'll be next and then
+
+ align:start position:0%
+hypothalamus that'll be next and then
+ 
+
+ align:start position:0%
+hypothalamus that'll be next and then
+couple chapters on the Corpus trium of
+
+ align:start position:0%
+couple chapters on the Corpus trium of
+ 
+
+ align:start position:0%
+couple chapters on the Corpus trium of
+mammals
+
+ align:start position:0%
+mammals
+ 
+
+ align:start position:0%
+mammals
+primarily and then finally several
+
+ align:start position:0%
+primarily and then finally several
+ 
+
+ align:start position:0%
+primarily and then finally several
+chapters on the
+
+ align:start position:0%
+chapters on the
+ 
+
+ align:start position:0%
+chapters on the
+neocortex
+
+ align:start position:0%
+neocortex
+ 
+
+ align:start position:0%
+neocortex
+so what was most likely the earliest
+
+ align:start position:0%
+so what was most likely the earliest
+ 
+
+ align:start position:0%
+so what was most likely the earliest
+part of the
+
+ align:start position:0%
+part of the
+ 
+
+ align:start position:0%
+part of the
+forbrain you first encountered a
+
+ align:start position:0%
+forbrain you first encountered a
+ 
+
+ align:start position:0%
+forbrain you first encountered a
+forbrain when we talked about anoys a SE
+
+ align:start position:0%
+forbrain when we talked about anoys a SE
+ 
+
+ align:start position:0%
+forbrain when we talked about anoys a SE
+cordate simplest living
+
+ align:start position:0%
+cordate simplest living
+ 
+
+ align:start position:0%
+cordate simplest living
+cordat
+
+ align:start position:0%
+cordat
+ 
+
+ align:start position:0%
+cordat
+and remember he had pigmented cells
+
+ align:start position:0%
+and remember he had pigmented cells
+ 
+
+ align:start position:0%
+and remember he had pigmented cells
+there that respond to light he had
+
+ align:start position:0%
+there that respond to light he had
+ 
+
+ align:start position:0%
+there that respond to light he had
+secretory cells secreting directly into
+
+ align:start position:0%
+secretory cells secreting directly into
+ 
+
+ align:start position:0%
+secretory cells secreting directly into
+the bloodstream of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+animal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry that's an that's a very
+
+ align:start position:0%
+sorry that's an that's a very
+ 
+
+ align:start position:0%
+sorry that's an that's a very
+interesting comment because you would
+
+ align:start position:0%
+interesting comment because you would
+ 
+
+ align:start position:0%
+interesting comment because you would
+think ofaction would probably be the
+
+ align:start position:0%
+think ofaction would probably be the
+ 
+
+ align:start position:0%
+think ofaction would probably be the
+earliest input but in fact we're not
+
+ align:start position:0%
+earliest input but in fact we're not
+ 
+
+ align:start position:0%
+earliest input but in fact we're not
+sure there's old faction in amphioxys
+
+ align:start position:0%
+sure there's old faction in amphioxys
+ 
+
+ align:start position:0%
+sure there's old faction in amphioxys
+but we do know they are those secretory
+
+ align:start position:0%
+but we do know they are those secretory
+ 
+
+ align:start position:0%
+but we do know they are those secretory
+cells and we do know they're getting
+
+ align:start position:0%
+cells and we do know they're getting
+ 
+
+ align:start position:0%
+cells and we do know they're getting
+effects of light through those that
+
+ align:start position:0%
+effects of light through those that
+ 
+
+ align:start position:0%
+effects of light through those that
+pigmented cell region and they have
+
+ align:start position:0%
+pigmented cell region and they have
+ 
+
+ align:start position:0%
+pigmented cell region and they have
+cells that are like retinal gangion
+
+ align:start position:0%
+cells that are like retinal gangion
+ 
+
+ align:start position:0%
+cells that are like retinal gangion
+cells that provide input to the brain
+
+ align:start position:0%
+cells that provide input to the brain
+ 
+
+ align:start position:0%
+cells that provide input to the brain
+now we think the most primitive part is
+
+ align:start position:0%
+now we think the most primitive part is
+ 
+
+ align:start position:0%
+now we think the most primitive part is
+all equivalent to dianon and the gene
+
+ align:start position:0%
+all equivalent to dianon and the gene
+ 
+
+ align:start position:0%
+all equivalent to dianon and the gene
+expression Studies have supported that
+
+ align:start position:0%
+expression Studies have supported that
+ 
+
+ align:start position:0%
+expression Studies have supported that
+it's actually like dianon not like
+
+ align:start position:0%
+it's actually like dianon not like
+ 
+
+ align:start position:0%
+it's actually like dianon not like
+andrain okay so they don't have anything
+
+ align:start position:0%
+andrain okay so they don't have anything
+ 
+
+ align:start position:0%
+andrain okay so they don't have anything
+like cortex they don't appear nothing
+
+ align:start position:0%
+like cortex they don't appear nothing
+ 
+
+ align:start position:0%
+like cortex they don't appear nothing
+for sure uh of
+
+ align:start position:0%
+for sure uh of
+ 
+
+ align:start position:0%
+for sure uh of
+olfaction if they do have any olfaction
+
+ align:start position:0%
+olfaction if they do have any olfaction
+ 
+
+ align:start position:0%
+olfaction if they do have any olfaction
+there are a couple of nerves that they
+
+ align:start position:0%
+there are a couple of nerves that they
+ 
+
+ align:start position:0%
+there are a couple of nerves that they
+don't know much about they one of them
+
+ align:start position:0%
+don't know much about they one of them
+ 
+
+ align:start position:0%
+don't know much about they one of them
+could be equivalent to
+
+ align:start position:0%
+could be equivalent to
+ 
+
+ align:start position:0%
+could be equivalent to
+olfactory but it's going into the the
+
+ align:start position:0%
+olfactory but it's going into the the
+ 
+
+ align:start position:0%
+olfactory but it's going into the the
+equivalent of a tween
+
+ align:start position:0%
+equivalent of a tween
+ 
+
+ align:start position:0%
+equivalent of a tween
+brain so that leads to this next
+
+ align:start position:0%
+brain so that leads to this next
+ 
+
+ align:start position:0%
+brain so that leads to this next
+question what are the cranial nerves
+
+ align:start position:0%
+question what are the cranial nerves
+ 
+
+ align:start position:0%
+question what are the cranial nerves
+that are attached to the forbrain now
+
+ align:start position:0%
+that are attached to the forbrain now
+ 
+
+ align:start position:0%
+that are attached to the forbrain now
+forbrain includes n brain and tween
+
+ align:start position:0%
+forbrain includes n brain and tween
+ 
+
+ align:start position:0%
+forbrain includes n brain and tween
+brain remember so I want all the cranial
+
+ align:start position:0%
+brain remember so I want all the cranial
+ 
+
+ align:start position:0%
+brain remember so I want all the cranial
+nerves that connect
+
+ align:start position:0%
+nerves that connect
+ 
+
+ align:start position:0%
+nerves that connect
+there now one of youve already mentioned
+
+ align:start position:0%
+there now one of youve already mentioned
+ 
+
+ align:start position:0%
+there now one of youve already mentioned
+number one whole faction number
+
+ align:start position:0%
+number one whole faction number
+ 
+
+ align:start position:0%
+number one whole faction number
+two is
+
+ align:start position:0%
+two is
+ 
+
+ align:start position:0%
+two is
+what the optic nerve okay and uh which
+
+ align:start position:0%
+what the optic nerve okay and uh which
+ 
+
+ align:start position:0%
+what the optic nerve okay and uh which
+becomes optic tract so it is a it's a
+
+ align:start position:0%
+becomes optic tract so it is a it's a
+ 
+
+ align:start position:0%
+becomes optic tract so it is a it's a
+CNS tract but we still call it a nerve
+
+ align:start position:0%
+CNS tract but we still call it a nerve
+ 
+
+ align:start position:0%
+CNS tract but we still call it a nerve
+before it gets to the
+
+ align:start position:0%
+before it gets to the
+ 
+
+ align:start position:0%
+before it gets to the
+kism okay so that's two of
+
+ align:start position:0%
+kism okay so that's two of
+ 
+
+ align:start position:0%
+kism okay so that's two of
+them those are the two that are among
+
+ align:start position:0%
+them those are the two that are among
+ 
+
+ align:start position:0%
+them those are the two that are among
+the 12 that we name for the human brain
+
+ align:start position:0%
+the 12 that we name for the human brain
+ 
+
+ align:start position:0%
+the 12 that we name for the human brain
+but there's actually three
+
+ align:start position:0%
+but there's actually three
+ 
+
+ align:start position:0%
+but there's actually three
+others okay and here I list
+
+ align:start position:0%
+others okay and here I list
+ 
+
+ align:start position:0%
+others okay and here I list
+them if you don't have a forbrain he's
+
+ align:start position:0%
+them if you don't have a forbrain he's
+ 
+
+ align:start position:0%
+them if you don't have a forbrain he's
+missing these five
+
+ align:start position:0%
+missing these five
+ 
+
+ align:start position:0%
+missing these five
+nerves nerves one and two but nerve one
+
+ align:start position:0%
+nerves nerves one and two but nerve one
+ 
+
+ align:start position:0%
+nerves nerves one and two but nerve one
+the olfactory nerve could be we could
+
+ align:start position:0%
+the olfactory nerve could be we could
+ 
+
+ align:start position:0%
+the olfactory nerve could be we could
+include the vulon nasal nerve and the
+
+ align:start position:0%
+include the vulon nasal nerve and the
+ 
+
+ align:start position:0%
+include the vulon nasal nerve and the
+terminal
+
+ align:start position:0%
+terminal
+ 
+
+ align:start position:0%
+terminal
+nerve terminal nerve innervates
+
+ align:start position:0%
+nerve terminal nerve innervates
+ 
+
+ align:start position:0%
+nerve terminal nerve innervates
+apparently the nasal septum it's found
+
+ align:start position:0%
+apparently the nasal septum it's found
+ 
+
+ align:start position:0%
+apparently the nasal septum it's found
+in humans at least in most humans
+
+ align:start position:0%
+in humans at least in most humans
+ 
+
+ align:start position:0%
+in humans at least in most humans
+there's some
+
+ align:start position:0%
+there's some
+ 
+
+ align:start position:0%
+there's some
+variability
+
+ align:start position:0%
+variability
+ 
+
+ align:start position:0%
+variability
+uh we think it may respond to ol Factory
+
+ align:start position:0%
+uh we think it may respond to ol Factory
+ 
+
+ align:start position:0%
+uh we think it may respond to ol Factory
+input but even that is not certain okay
+
+ align:start position:0%
+input but even that is not certain okay
+ 
+
+ align:start position:0%
+input but even that is not certain okay
+you will find it in human neuron anatomy
+
+ align:start position:0%
+you will find it in human neuron anatomy
+ 
+
+ align:start position:0%
+you will find it in human neuron anatomy
+books uh vulon nasal though is a the
+
+ align:start position:0%
+books uh vulon nasal though is a the
+ 
+
+ align:start position:0%
+books uh vulon nasal though is a the
+vulon
+
+ align:start position:0%
+vulon
+ 
+
+ align:start position:0%
+vulon
+nasal uh organ is Jacobson's organ it's
+
+ align:start position:0%
+nasal uh organ is Jacobson's organ it's
+ 
+
+ align:start position:0%
+nasal uh organ is Jacobson's organ it's
+it's in the nasal cavity
+
+ align:start position:0%
+it's in the nasal cavity
+ 
+
+ align:start position:0%
+it's in the nasal cavity
+and animals that
+
+ align:start position:0%
+and animals that
+ 
+
+ align:start position:0%
+and animals that
+have this welldeveloped
+
+ align:start position:0%
+have this welldeveloped
+ 
+
+ align:start position:0%
+have this welldeveloped
+have an opening into the roof of the
+
+ align:start position:0%
+have an opening into the roof of the
+ 
+
+ align:start position:0%
+have an opening into the roof of the
+mouth ulad have this very
+
+ align:start position:0%
+mouth ulad have this very
+ 
+
+ align:start position:0%
+mouth ulad have this very
+prominently and
+
+ align:start position:0%
+prominently and
+ 
+
+ align:start position:0%
+prominently and
+uh they for example in mating the male
+
+ align:start position:0%
+uh they for example in mating the male
+ 
+
+ align:start position:0%
+uh they for example in mating the male
+collects urine from the
+
+ align:start position:0%
+collects urine from the
+ 
+
+ align:start position:0%
+collects urine from the
+female brings it into his mouth to that
+
+ align:start position:0%
+female brings it into his mouth to that
+ 
+
+ align:start position:0%
+female brings it into his mouth to that
+organ in the roof of his mouth where
+
+ align:start position:0%
+organ in the roof of his mouth where
+ 
+
+ align:start position:0%
+organ in the roof of his mouth where
+where there are receptors that respond
+
+ align:start position:0%
+where there are receptors that respond
+ 
+
+ align:start position:0%
+where there are receptors that respond
+to Fones that change with the receptive
+
+ align:start position:0%
+to Fones that change with the receptive
+ 
+
+ align:start position:0%
+to Fones that change with the receptive
+state of the
+
+ align:start position:0%
+state of the
+ 
+
+ align:start position:0%
+state of the
+female okay so he can then tell from
+
+ align:start position:0%
+female okay so he can then tell from
+ 
+
+ align:start position:0%
+female okay so he can then tell from
+that preliminary mating
+
+ align:start position:0%
+that preliminary mating
+ 
+
+ align:start position:0%
+that preliminary mating
+action whether she's receptive and
+
+ align:start position:0%
+action whether she's receptive and
+ 
+
+ align:start position:0%
+action whether she's receptive and
+whether can be impregnated at that time
+
+ align:start position:0%
+whether can be impregnated at that time
+ 
+
+ align:start position:0%
+whether can be impregnated at that time
+so it's part of the ritual they go
+
+ align:start position:0%
+so it's part of the ritual they go
+ 
+
+ align:start position:0%
+so it's part of the ritual they go
+through before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mating
+
+ align:start position:0%
+mating
+ 
+
+ align:start position:0%
+mating
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh other animals still collect
+
+ align:start position:0%
+uh other animals still collect
+ 
+
+ align:start position:0%
+uh other animals still collect
+pheromones on their tongue snakes for
+
+ align:start position:0%
+pheromones on their tongue snakes for
+ 
+
+ align:start position:0%
+pheromones on their tongue snakes for
+example you see them flicking out their
+
+ align:start position:0%
+example you see them flicking out their
+ 
+
+ align:start position:0%
+example you see them flicking out their
+tongue they're actually
+
+ align:start position:0%
+tongue they're actually
+ 
+
+ align:start position:0%
+tongue they're actually
+collecting substances from the air and
+
+ align:start position:0%
+collecting substances from the air and
+ 
+
+ align:start position:0%
+collecting substances from the air and
+if that includes pheromones they they
+
+ align:start position:0%
+if that includes pheromones they they
+ 
+
+ align:start position:0%
+if that includes pheromones they they
+bring it to that vasal organ where does
+
+ align:start position:0%
+bring it to that vasal organ where does
+ 
+
+ align:start position:0%
+bring it to that vasal organ where does
+the V nasal organ
+
+ align:start position:0%
+the V nasal organ
+ 
+
+ align:start position:0%
+the V nasal organ
+project the part of the old factory B
+
+ align:start position:0%
+project the part of the old factory B
+ 
+
+ align:start position:0%
+project the part of the old factory B
+remember the there's a main old factory
+
+ align:start position:0%
+remember the there's a main old factory
+ 
+
+ align:start position:0%
+remember the there's a main old factory
+bulb and then there's an accessory
+
+ align:start position:0%
+bulb and then there's an accessory
+ 
+
+ align:start position:0%
+bulb and then there's an accessory
+Factory
+
+ align:start position:0%
+Factory
+ 
+
+ align:start position:0%
+Factory
+bulb
+
+ align:start position:0%
+bulb
+ 
+
+ align:start position:0%
+bulb
+and most mammals have that and it's
+
+ align:start position:0%
+and most mammals have that and it's
+ 
+
+ align:start position:0%
+and most mammals have that and it's
+specializes in responding to pheromones
+
+ align:start position:0%
+specializes in responding to pheromones
+ 
+
+ align:start position:0%
+specializes in responding to pheromones
+that can come in through the old
+
+ align:start position:0%
+that can come in through the old
+ 
+
+ align:start position:0%
+that can come in through the old
+factory epithelium
+
+ align:start position:0%
+factory epithelium
+ 
+
+ align:start position:0%
+factory epithelium
+also not just through vasal organ okay
+
+ align:start position:0%
+also not just through vasal organ okay
+ 
+
+ align:start position:0%
+also not just through vasal organ okay
+and then we have the optic nerve and
+
+ align:start position:0%
+and then we have the optic nerve and
+ 
+
+ align:start position:0%
+and then we have the optic nerve and
+then there's another nerve that responds
+
+ align:start position:0%
+then there's another nerve that responds
+ 
+
+ align:start position:0%
+then there's another nerve that responds
+to brings in information from light
+
+ align:start position:0%
+to brings in information from light
+ 
+
+ align:start position:0%
+to brings in information from light
+the epipal nerve this is the pineal the
+
+ align:start position:0%
+the epipal nerve this is the pineal the
+ 
+
+ align:start position:0%
+the epipal nerve this is the pineal the
+nerve that brings can activate the
+
+ align:start position:0%
+nerve that brings can activate the
+ 
+
+ align:start position:0%
+nerve that brings can activate the
+pineal cells by light and we know that
+
+ align:start position:0%
+pineal cells by light and we know that
+ 
+
+ align:start position:0%
+pineal cells by light and we know that
+about the pineal eye so with animals
+
+ align:start position:0%
+about the pineal eye so with animals
+ 
+
+ align:start position:0%
+about the pineal eye so with animals
+that have a pineal eye on the top of
+
+ align:start position:0%
+that have a pineal eye on the top of
+ 
+
+ align:start position:0%
+that have a pineal eye on the top of
+their head they have a nerve that can
+
+ align:start position:0%
+their head they have a nerve that can
+ 
+
+ align:start position:0%
+their head they have a nerve that can
+that's called the epiphysial
+
+ align:start position:0%
+that's called the epiphysial
+ 
+
+ align:start position:0%
+that's called the epiphysial
+nerve the epiphysis is the name for that
+
+ align:start position:0%
+nerve the epiphysis is the name for that
+ 
+
+ align:start position:0%
+nerve the epiphysis is the name for that
+structure okay so five cranial nerves
+
+ align:start position:0%
+structure okay so five cranial nerves
+ 
+
+ align:start position:0%
+structure okay so five cranial nerves
+but three of them associated with
+
+ align:start position:0%
+but three of them associated with
+ 
+
+ align:start position:0%
+but three of them associated with
+Factory and two of
+
+ align:start position:0%
+Factory and two of
+ 
+
+ align:start position:0%
+Factory and two of
+them responding to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+light okay so if an animal doesn't have
+
+ align:start position:0%
+light okay so if an animal doesn't have
+ 
+
+ align:start position:0%
+light okay so if an animal doesn't have
+a forbrain there's another thing he's
+
+ align:start position:0%
+a forbrain there's another thing he's
+ 
+
+ align:start position:0%
+a forbrain there's another thing he's
+missing he doesn't have control of this
+
+ align:start position:0%
+missing he doesn't have control of this
+ 
+
+ align:start position:0%
+missing he doesn't have control of this
+pit pituitary gland because what
+
+ align:start position:0%
+pit pituitary gland because what
+ 
+
+ align:start position:0%
+pit pituitary gland because what
+controls the pituitary well we're going
+
+ align:start position:0%
+controls the pituitary well we're going
+ 
+
+ align:start position:0%
+controls the pituitary well we're going
+to learn more about that uh after this
+
+ align:start position:0%
+to learn more about that uh after this
+ 
+
+ align:start position:0%
+to learn more about that uh after this
+class we deal with hypothalamus
+
+ align:start position:0%
+class we deal with hypothalamus
+ 
+
+ align:start position:0%
+class we deal with hypothalamus
+specifically but we know the
+
+ align:start position:0%
+specifically but we know the
+ 
+
+ align:start position:0%
+specifically but we know the
+pituitary is connected to the
+
+ align:start position:0%
+pituitary is connected to the
+ 
+
+ align:start position:0%
+pituitary is connected to the
+hypothalamus in a very interesting way
+
+ align:start position:0%
+hypothalamus in a very interesting way
+ 
+
+ align:start position:0%
+hypothalamus in a very interesting way
+that we will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discuss it's possible though to
+
+ align:start position:0%
+discuss it's possible though to
+ 
+
+ align:start position:0%
+discuss it's possible though to
+disconnect the entire forbrain as we
+
+ align:start position:0%
+disconnect the entire forbrain as we
+ 
+
+ align:start position:0%
+disconnect the entire forbrain as we
+learned in I think it was chapter 7 we
+
+ align:start position:0%
+learned in I think it was chapter 7 we
+ 
+
+ align:start position:0%
+learned in I think it was chapter 7 we
+you can disconnect the entire forebrain
+
+ align:start position:0%
+you can disconnect the entire forebrain
+ 
+
+ align:start position:0%
+you can disconnect the entire forebrain
+from the midbrain but you could leave
+
+ align:start position:0%
+from the midbrain but you could leave
+ 
+
+ align:start position:0%
+from the midbrain but you could leave
+the hypothalamus connected to the
+
+ align:start position:0%
+the hypothalamus connected to the
+ 
+
+ align:start position:0%
+the hypothalamus connected to the
+pituitary and if you do so the animal
+
+ align:start position:0%
+pituitary and if you do so the animal
+ 
+
+ align:start position:0%
+pituitary and if you do so the animal
+maintains a lot more function than if
+
+ align:start position:0%
+maintains a lot more function than if
+ 
+
+ align:start position:0%
+maintains a lot more function than if
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+don't because pituitary to function
+
+ align:start position:0%
+don't because pituitary to function
+ 
+
+ align:start position:0%
+don't because pituitary to function
+normally needs the hypothalamus
+
+ align:start position:0%
+normally needs the hypothalamus
+ 
+
+ align:start position:0%
+normally needs the hypothalamus
+attached um and the controls that the
+
+ align:start position:0%
+attached um and the controls that the
+ 
+
+ align:start position:0%
+attached um and the controls that the
+hypothalamus exerts on a pituitary gland
+
+ align:start position:0%
+hypothalamus exerts on a pituitary gland
+ 
+
+ align:start position:0%
+hypothalamus exerts on a pituitary gland
+need to be in
+
+ align:start position:0%
+need to be in
+ 
+
+ align:start position:0%
+need to be in
+taged so in chapter 7 I went through
+
+ align:start position:0%
+taged so in chapter 7 I went through
+ 
+
+ align:start position:0%
+taged so in chapter 7 I went through
+studies where there was
+
+ align:start position:0%
+studies where there was
+ 
+
+ align:start position:0%
+studies where there was
+removal or disconnection of the
+
+ align:start position:0%
+removal or disconnection of the
+ 
+
+ align:start position:0%
+removal or disconnection of the
+forbrain from the midbrain
+
+ align:start position:0%
+forbrain from the midbrain
+ 
+
+ align:start position:0%
+forbrain from the midbrain
+and I said that animals are missing
+
+ align:start position:0%
+and I said that animals are missing
+ 
+
+ align:start position:0%
+and I said that animals are missing
+major components of normal behavior even
+
+ align:start position:0%
+major components of normal behavior even
+ 
+
+ align:start position:0%
+major components of normal behavior even
+if you leave that hypothalamus attached
+
+ align:start position:0%
+if you leave that hypothalamus attached
+ 
+
+ align:start position:0%
+if you leave that hypothalamus attached
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+pituitary so what is missing does
+
+ align:start position:0%
+pituitary so what is missing does
+ 
+
+ align:start position:0%
+pituitary so what is missing does
+anybody remember motiv motivation
+
+ align:start position:0%
+anybody remember motiv motivation
+ 
+
+ align:start position:0%
+anybody remember motiv motivation
+motivated Behavior okay so we called it
+
+ align:start position:0%
+motivated Behavior okay so we called it
+ 
+
+ align:start position:0%
+motivated Behavior okay so we called it
+a pet Behavior you know so if an
+
+ align:start position:0%
+a pet Behavior you know so if an
+ 
+
+ align:start position:0%
+a pet Behavior you know so if an
+animal's hungry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+his behavior that indicates he has an
+
+ align:start position:0%
+his behavior that indicates he has an
+ 
+
+ align:start position:0%
+his behavior that indicates he has an
+appetite for food but you can use that
+
+ align:start position:0%
+appetite for food but you can use that
+ 
+
+ align:start position:0%
+appetite for food but you can use that
+term appetitive behavior for other
+
+ align:start position:0%
+term appetitive behavior for other
+ 
+
+ align:start position:0%
+term appetitive behavior for other
+motivations too for example for thirst
+
+ align:start position:0%
+motivations too for example for thirst
+ 
+
+ align:start position:0%
+motivations too for example for thirst
+ative behavior when an animal's
+
+ align:start position:0%
+ative behavior when an animal's
+ 
+
+ align:start position:0%
+ative behavior when an animal's
+thirsty
+
+ align:start position:0%
+thirsty
+ 
+
+ align:start position:0%
+thirsty
+U Behavior initiated by his motivational
+
+ align:start position:0%
+U Behavior initiated by his motivational
+ 
+
+ align:start position:0%
+U Behavior initiated by his motivational
+system the hypothalamus that centers on
+
+ align:start position:0%
+system the hypothalamus that centers on
+ 
+
+ align:start position:0%
+system the hypothalamus that centers on
+hypothalamus will lead to Locomotion and
+
+ align:start position:0%
+hypothalamus will lead to Locomotion and
+ 
+
+ align:start position:0%
+hypothalamus will lead to Locomotion and
+seeking of
+
+ align:start position:0%
+seeking of
+ 
+
+ align:start position:0%
+seeking of
+water uh you can use the term also for
+
+ align:start position:0%
+water uh you can use the term also for
+ 
+
+ align:start position:0%
+water uh you can use the term also for
+mating behavior for sexual
+
+ align:start position:0%
+mating behavior for sexual
+ 
+
+ align:start position:0%
+mating behavior for sexual
+motivations you can use it for uh rot
+
+ align:start position:0%
+motivations you can use it for uh rot
+ 
+
+ align:start position:0%
+motivations you can use it for uh rot
+tending behaviors if they're raising
+
+ align:start position:0%
+tending behaviors if they're raising
+ 
+
+ align:start position:0%
+tending behaviors if they're raising
+young but there's a lot of other things
+
+ align:start position:0%
+young but there's a lot of other things
+ 
+
+ align:start position:0%
+young but there's a lot of other things
+missing of course that depend on for
+
+ align:start position:0%
+missing of course that depend on for
+ 
+
+ align:start position:0%
+missing of course that depend on for
+brain all the cortical and Corpus statom
+
+ align:start position:0%
+brain all the cortical and Corpus statom
+ 
+
+ align:start position:0%
+brain all the cortical and Corpus statom
+functions and I've listed
+
+ align:start position:0%
+functions and I've listed
+ 
+
+ align:start position:0%
+functions and I've listed
+major forbrain functions all of which
+
+ align:start position:0%
+major forbrain functions all of which
+ 
+
+ align:start position:0%
+major forbrain functions all of which
+we're going to be talking more
+
+ align:start position:0%
+we're going to be talking more
+ 
+
+ align:start position:0%
+we're going to be talking more
+about first of all
+
+ align:start position:0%
+about first of all
+ 
+
+ align:start position:0%
+about first of all
+Acuity animals that develop a large
+
+ align:start position:0%
+Acuity animals that develop a large
+ 
+
+ align:start position:0%
+Acuity animals that develop a large
+forbrain have much better sensory
+
+ align:start position:0%
+forbrain have much better sensory
+ 
+
+ align:start position:0%
+forbrain have much better sensory
+acuity and much better manipulatory
+
+ align:start position:0%
+acuity and much better manipulatory
+ 
+
+ align:start position:0%
+acuity and much better manipulatory
+ability of
+
+ align:start position:0%
+ability of
+ 
+
+ align:start position:0%
+ability of
+their their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limbs but wait a minute does an animal
+
+ align:start position:0%
+limbs but wait a minute does an animal
+ 
+
+ align:start position:0%
+limbs but wait a minute does an animal
+that have a very large optic tectum have
+
+ align:start position:0%
+that have a very large optic tectum have
+ 
+
+ align:start position:0%
+that have a very large optic tectum have
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+Acuity well they do but only
+
+ align:start position:0%
+Acuity well they do but only
+ 
+
+ align:start position:0%
+Acuity well they do but only
+for unlearned
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+behaviors acuity for learn behaviors
+
+ align:start position:0%
+behaviors acuity for learn behaviors
+ 
+
+ align:start position:0%
+behaviors acuity for learn behaviors
+depends on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forbrain and of course humans are so
+
+ align:start position:0%
+forbrain and of course humans are so
+ 
+
+ align:start position:0%
+forbrain and of course humans are so
+dominated by
+
+ align:start position:0%
+dominated by
+ 
+
+ align:start position:0%
+dominated by
+learning that often we're we're pretty
+
+ align:start position:0%
+learning that often we're we're pretty
+ 
+
+ align:start position:0%
+learning that often we're we're pretty
+unaware of the teal be uh controlled
+
+ align:start position:0%
+unaware of the teal be uh controlled
+ 
+
+ align:start position:0%
+unaware of the teal be uh controlled
+Behavior although it exists in primates
+
+ align:start position:0%
+Behavior although it exists in primates
+ 
+
+ align:start position:0%
+Behavior although it exists in primates
+too okay but then other things they lack
+
+ align:start position:0%
+too okay but then other things they lack
+ 
+
+ align:start position:0%
+too okay but then other things they lack
+that you need a forbrain for need an end
+
+ align:start position:0%
+that you need a forbrain for need an end
+ 
+
+ align:start position:0%
+that you need a forbrain for need an end
+brain for lack of
+
+ align:start position:0%
+brain for lack of
+ 
+
+ align:start position:0%
+brain for lack of
+anticipation they're controlled by
+
+ align:start position:0%
+anticipation they're controlled by
+ 
+
+ align:start position:0%
+anticipation they're controlled by
+stimuli coming in but they can't
+
+ align:start position:0%
+stimuli coming in but they can't
+ 
+
+ align:start position:0%
+stimuli coming in but they can't
+anticipate what's going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happen they don't have good spatial
+
+ align:start position:0%
+happen they don't have good spatial
+ 
+
+ align:start position:0%
+happen they don't have good spatial
+memory they don't
+
+ align:start position:0%
+memory they don't
+ 
+
+ align:start position:0%
+memory they don't
+learn the
+
+ align:start position:0%
+learn the
+ 
+
+ align:start position:0%
+learn the
+habits the only learning of the midbrain
+
+ align:start position:0%
+habits the only learning of the midbrain
+ 
+
+ align:start position:0%
+habits the only learning of the midbrain
+and lore structures is very short
+
+ align:start position:0%
+and lore structures is very short
+ 
+
+ align:start position:0%
+and lore structures is very short
+term many Studies have shown
+
+ align:start position:0%
+term many Studies have shown
+ 
+
+ align:start position:0%
+term many Studies have shown
+this long-term memory develop
+
+ align:start position:0%
+this long-term memory develop
+ 
+
+ align:start position:0%
+this long-term memory develop
+veled what we know as long-term memory
+
+ align:start position:0%
+veled what we know as long-term memory
+ 
+
+ align:start position:0%
+veled what we know as long-term memory
+developed out of spatial memory system
+
+ align:start position:0%
+developed out of spatial memory system
+ 
+
+ align:start position:0%
+developed out of spatial memory system
+involving the medial pum or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hippocampus and we know that happen
+
+ align:start position:0%
+hippocampus and we know that happen
+ 
+
+ align:start position:0%
+hippocampus and we know that happen
+learning developed very early in the old
+
+ align:start position:0%
+learning developed very early in the old
+ 
+
+ align:start position:0%
+learning developed very early in the old
+factory system involving the
+
+ align:start position:0%
+factory system involving the
+ 
+
+ align:start position:0%
+factory system involving the
+Statum okay so what do they retain if
+
+ align:start position:0%
+Statum okay so what do they retain if
+ 
+
+ align:start position:0%
+Statum okay so what do they retain if
+they've lost all
+
+ align:start position:0%
+they've lost all
+ 
+
+ align:start position:0%
+they've lost all
+this what can they still
+
+ align:start position:0%
+this what can they still
+ 
+
+ align:start position:0%
+this what can they still
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+they can eat yeah they can eat if you
+
+ align:start position:0%
+they can eat yeah they can eat if you
+ 
+
+ align:start position:0%
+they can eat yeah they can eat if you
+put food in their mouth what do you call
+
+ align:start position:0%
+put food in their mouth what do you call
+ 
+
+ align:start position:0%
+put food in their mouth what do you call
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+eating it you there's a general term we
+
+ align:start position:0%
+eating it you there's a general term we
+ 
+
+ align:start position:0%
+eating it you there's a general term we
+use for all drives for that output sight
+
+ align:start position:0%
+use for all drives for that output sight
+ 
+
+ align:start position:0%
+use for all drives for that output sight
+we call it consummatory Behavior it's
+
+ align:start position:0%
+we call it consummatory Behavior it's
+ 
+
+ align:start position:0%
+we call it consummatory Behavior it's
+very easy to remember for eating because
+
+ align:start position:0%
+very easy to remember for eating because
+ 
+
+ align:start position:0%
+very easy to remember for eating because
+it means consuming the food okay but you
+
+ align:start position:0%
+it means consuming the food okay but you
+ 
+
+ align:start position:0%
+it means consuming the food okay but you
+can refer to consummatory behavior for
+
+ align:start position:0%
+can refer to consummatory behavior for
+ 
+
+ align:start position:0%
+can refer to consummatory behavior for
+thirst going to refer to it for sexual
+
+ align:start position:0%
+thirst going to refer to it for sexual
+ 
+
+ align:start position:0%
+thirst going to refer to it for sexual
+behavior where the consummatory behavior
+
+ align:start position:0%
+behavior where the consummatory behavior
+ 
+
+ align:start position:0%
+behavior where the consummatory behavior
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+mating and so
+
+ align:start position:0%
+mating and so
+ 
+
+ align:start position:0%
+mating and so
+forth so they retain consummatory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Behavior they retain and I've listed
+
+ align:start position:0%
+Behavior they retain and I've listed
+ 
+
+ align:start position:0%
+Behavior they retain and I've listed
+some of those they
+
+ align:start position:0%
+some of those they
+ 
+
+ align:start position:0%
+some of those they
+do have pain lited
+
+ align:start position:0%
+do have pain lited
+ 
+
+ align:start position:0%
+do have pain lited
+aggression so a cat without the
+
+ align:start position:0%
+aggression so a cat without the
+ 
+
+ align:start position:0%
+aggression so a cat without the
+forebrain if you cause him pain like you
+
+ align:start position:0%
+forebrain if you cause him pain like you
+ 
+
+ align:start position:0%
+forebrain if you cause him pain like you
+pull his tail he will strike out you
+
+ align:start position:0%
+pull his tail he will strike out you
+ 
+
+ align:start position:0%
+pull his tail he will strike out you
+just you'll un sheath his claws and
+
+ align:start position:0%
+just you'll un sheath his claws and
+ 
+
+ align:start position:0%
+just you'll un sheath his claws and
+strike out but as soon as you let go
+
+ align:start position:0%
+strike out but as soon as you let go
+ 
+
+ align:start position:0%
+strike out but as soon as you let go
+it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gone so we call it sham rage he acts
+
+ align:start position:0%
+gone so we call it sham rage he acts
+ 
+
+ align:start position:0%
+gone so we call it sham rage he acts
+like he's en raged but it's not
+
+ align:start position:0%
+like he's en raged but it's not
+ 
+
+ align:start position:0%
+like he's en raged but it's not
+enduring as we know what we call rage in
+
+ align:start position:0%
+enduring as we know what we call rage in
+ 
+
+ align:start position:0%
+enduring as we know what we call rage in
+an animal outlasts the stimulus the
+
+ align:start position:0%
+an animal outlasts the stimulus the
+ 
+
+ align:start position:0%
+an animal outlasts the stimulus the
+triggers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it a human can be angry about something
+
+ align:start position:0%
+it a human can be angry about something
+ 
+
+ align:start position:0%
+it a human can be angry about something
+that happened hours
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before he can be angry about something
+
+ align:start position:0%
+before he can be angry about something
+ 
+
+ align:start position:0%
+before he can be angry about something
+he's just thinking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you're going to be angry about some some
+
+ align:start position:0%
+you're going to be angry about some some
+ 
+
+ align:start position:0%
+you're going to be angry about some some
+if you hold a grudge you can be angry
+
+ align:start position:0%
+if you hold a grudge you can be angry
+ 
+
+ align:start position:0%
+if you hold a grudge you can be angry
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+years
+
+ align:start position:0%
+years
+ 
+
+ align:start position:0%
+years
+okay an animal like that retains his
+
+ align:start position:0%
+okay an animal like that retains his
+ 
+
+ align:start position:0%
+okay an animal like that retains his
+sexual postures and
+
+ align:start position:0%
+sexual postures and
+ 
+
+ align:start position:0%
+sexual postures and
+reflexes okay you can stimulate an
+
+ align:start position:0%
+reflexes okay you can stimulate an
+ 
+
+ align:start position:0%
+reflexes okay you can stimulate an
+animal like that like a female cat if
+
+ align:start position:0%
+animal like that like a female cat if
+ 
+
+ align:start position:0%
+animal like that like a female cat if
+she's receptive can stimulate the
+
+ align:start position:0%
+she's receptive can stimulate the
+ 
+
+ align:start position:0%
+she's receptive can stimulate the
+lordosis
+
+ align:start position:0%
+lordosis
+ 
+
+ align:start position:0%
+lordosis
+response okay just by touching her in
+
+ align:start position:0%
+response okay just by touching her in
+ 
+
+ align:start position:0%
+response okay just by touching her in
+the right way okay depending on the
+
+ align:start position:0%
+the right way okay depending on the
+ 
+
+ align:start position:0%
+the right way okay depending on the
+animal they have different regions if
+
+ align:start position:0%
+animal they have different regions if
+ 
+
+ align:start position:0%
+animal they have different regions if
+you give them tactile input they will
+
+ align:start position:0%
+you give them tactile input they will
+ 
+
+ align:start position:0%
+you give them tactile input they will
+assume that receptive posture that's
+
+ align:start position:0%
+assume that receptive posture that's
+ 
+
+ align:start position:0%
+assume that receptive posture that's
+part of
+
+ align:start position:0%
+part of
+ 
+
+ align:start position:0%
+part of
+a you can call it a reflex but it's it's
+
+ align:start position:0%
+a you can call it a reflex but it's it's
+ 
+
+ align:start position:0%
+a you can call it a reflex but it's it's
+a complicated reflex it's part of their
+
+ align:start position:0%
+a complicated reflex it's part of their
+ 
+
+ align:start position:0%
+a complicated reflex it's part of their
+fixed action patterns that they've
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inherited I'm just wondering like how
+
+ align:start position:0%
+inherited I'm just wondering like how
+ 
+
+ align:start position:0%
+inherited I'm just wondering like how
+about like a fear like what of fear like
+
+ align:start position:0%
+about like a fear like what of fear like
+ 
+
+ align:start position:0%
+about like a fear like what of fear like
+what kind of fear like do like do they
+
+ align:start position:0%
+what kind of fear like do like do they
+ 
+
+ align:start position:0%
+what kind of fear like do like do they
+like still retain the Fe
+
+ align:start position:0%
+like still retain the Fe
+ 
+
+ align:start position:0%
+like still retain the Fe
+they they don't
+
+ align:start position:0%
+they they don't
+ 
+
+ align:start position:0%
+they they don't
+remember long time they don't retain the
+
+ align:start position:0%
+remember long time they don't retain the
+ 
+
+ align:start position:0%
+remember long time they don't retain the
+fear and that doesn't last very long you
+
+ align:start position:0%
+fear and that doesn't last very long you
+ 
+
+ align:start position:0%
+fear and that doesn't last very long you
+know but it's all pretty short term you
+
+ align:start position:0%
+know but it's all pretty short term you
+ 
+
+ align:start position:0%
+know but it's all pretty short term you
+know very dependent on the stimulus like
+
+ align:start position:0%
+know very dependent on the stimulus like
+ 
+
+ align:start position:0%
+know very dependent on the stimulus like
+a pigeon will actually fly without a far
+
+ align:start position:0%
+a pigeon will actually fly without a far
+ 
+
+ align:start position:0%
+a pigeon will actually fly without a far
+brain if you've left his optic nerve
+
+ align:start position:0%
+brain if you've left his optic nerve
+ 
+
+ align:start position:0%
+brain if you've left his optic nerve
+attached to the
+
+ align:start position:0%
+attached to the
+ 
+
+ align:start position:0%
+attached to the
+tectum okay because all the stimuli are
+
+ align:start position:0%
+tectum okay because all the stimuli are
+ 
+
+ align:start position:0%
+tectum okay because all the stimuli are
+there if you throw them into the air all
+
+ align:start position:0%
+there if you throw them into the air all
+ 
+
+ align:start position:0%
+there if you throw them into the air all
+the stimuli that's that you listen
+
+ align:start position:0%
+the stimuli that's that you listen
+ 
+
+ align:start position:0%
+the stimuli that's that you listen
+flying are there and he will clap his
+
+ align:start position:0%
+flying are there and he will clap his
+ 
+
+ align:start position:0%
+flying are there and he will clap his
+wings and be able to stay in the air he
+
+ align:start position:0%
+wings and be able to stay in the air he
+ 
+
+ align:start position:0%
+wings and be able to stay in the air he
+will locomote he will fly and he and he
+
+ align:start position:0%
+will locomote he will fly and he and he
+ 
+
+ align:start position:0%
+will locomote he will fly and he and he
+will actually
+
+ align:start position:0%
+will actually
+ 
+
+ align:start position:0%
+will actually
+avoid uh running into things he'll go
+
+ align:start position:0%
+avoid uh running into things he'll go
+ 
+
+ align:start position:0%
+avoid uh running into things he'll go
+around trees he will land
+
+ align:start position:0%
+around trees he will land
+ 
+
+ align:start position:0%
+around trees he will land
+on horizontally placed things land on a
+
+ align:start position:0%
+on horizontally placed things land on a
+ 
+
+ align:start position:0%
+on horizontally placed things land on a
+Surface land on a
+
+ align:start position:0%
+Surface land on a
+ 
+
+ align:start position:0%
+Surface land on a
+limb he won't maintain the motivation
+
+ align:start position:0%
+limb he won't maintain the motivation
+ 
+
+ align:start position:0%
+limb he won't maintain the motivation
+though so once he lands he won't have
+
+ align:start position:0%
+though so once he lands he won't have
+ 
+
+ align:start position:0%
+though so once he lands he won't have
+the incentive to take off again unless
+
+ align:start position:0%
+the incentive to take off again unless
+ 
+
+ align:start position:0%
+the incentive to take off again unless
+something gets blown off the limb then
+
+ align:start position:0%
+something gets blown off the limb then
+ 
+
+ align:start position:0%
+something gets blown off the limb then
+he will start flying again and they will
+
+ align:start position:0%
+he will start flying again and they will
+ 
+
+ align:start position:0%
+he will start flying again and they will
+write themselves if you tip them over
+
+ align:start position:0%
+write themselves if you tip them over
+ 
+
+ align:start position:0%
+write themselves if you tip them over
+they will walk okay but generally they
+
+ align:start position:0%
+they will walk okay but generally they
+ 
+
+ align:start position:0%
+they will walk okay but generally they
+don't initiate much
+
+ align:start position:0%
+don't initiate much
+ 
+
+ align:start position:0%
+don't initiate much
+walking they have to be nudged okay so
+
+ align:start position:0%
+walking they have to be nudged okay so
+ 
+
+ align:start position:0%
+walking they have to be nudged okay so
+let's talk about primitive for brins we
+
+ align:start position:0%
+let's talk about primitive for brins we
+ 
+
+ align:start position:0%
+let's talk about primitive for brins we
+can look at the non-vertebrate cordat
+
+ align:start position:0%
+can look at the non-vertebrate cordat
+ 
+
+ align:start position:0%
+can look at the non-vertebrate cordat
+the invertebrate cordat that will in
+
+ align:start position:0%
+the invertebrate cordat that will in
+ 
+
+ align:start position:0%
+the invertebrate cordat that will in
+that includes
+
+ align:start position:0%
+that includes
+ 
+
+ align:start position:0%
+that includes
+amphioxys we could look
+
+ align:start position:0%
+amphioxys we could look
+ 
+
+ align:start position:0%
+amphioxys we could look
+at the Proto mammals but to do that that
+
+ align:start position:0%
+at the Proto mammals but to do that that
+ 
+
+ align:start position:0%
+at the Proto mammals but to do that that
+animals that led to mammals we can we'd
+
+ align:start position:0%
+animals that led to mammals we can we'd
+ 
+
+ align:start position:0%
+animals that led to mammals we can we'd
+have to use paleontology and look at
+
+ align:start position:0%
+have to use paleontology and look at
+ 
+
+ align:start position:0%
+have to use paleontology and look at
+skulls and that's been done we talked
+
+ align:start position:0%
+skulls and that's been done we talked
+ 
+
+ align:start position:0%
+skulls and that's been done we talked
+about that a little bit in when we
+
+ align:start position:0%
+about that a little bit in when we
+ 
+
+ align:start position:0%
+about that a little bit in when we
+talked about auditory system because
+
+ align:start position:0%
+talked about auditory system because
+ 
+
+ align:start position:0%
+talked about auditory system because
+it's through those studies that we know
+
+ align:start position:0%
+it's through those studies that we know
+ 
+
+ align:start position:0%
+it's through those studies that we know
+about changes in the middle ear bones
+
+ align:start position:0%
+about changes in the middle ear bones
+ 
+
+ align:start position:0%
+about changes in the middle ear bones
+and the bones around the eye which
+
+ align:start position:0%
+and the bones around the eye which
+ 
+
+ align:start position:0%
+and the bones around the eye which
+became reduced in the earliest mammal
+
+ align:start position:0%
+became reduced in the earliest mammal
+ 
+
+ align:start position:0%
+became reduced in the earliest mammal
+and of course we can use comparative
+
+ align:start position:0%
+and of course we can use comparative
+ 
+
+ align:start position:0%
+and of course we can use comparative
+Anatomy to study the brains that is
+
+ align:start position:0%
+Anatomy to study the brains that is
+ 
+
+ align:start position:0%
+Anatomy to study the brains that is
+studies of living animals we can't do
+
+ align:start position:0%
+studies of living animals we can't do
+ 
+
+ align:start position:0%
+studies of living animals we can't do
+comparative Anatomy very much with
+
+ align:start position:0%
+comparative Anatomy very much with
+ 
+
+ align:start position:0%
+comparative Anatomy very much with
+animals where we only have the fossils
+
+ align:start position:0%
+animals where we only have the fossils
+ 
+
+ align:start position:0%
+animals where we only have the fossils
+because brain isn't retained in the
+
+ align:start position:0%
+because brain isn't retained in the
+ 
+
+ align:start position:0%
+because brain isn't retained in the
+fossils and then of course we can study
+
+ align:start position:0%
+fossils and then of course we can study
+ 
+
+ align:start position:0%
+fossils and then of course we can study
+primitive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mammals now we use cladistics to portray
+
+ align:start position:0%
+mammals now we use cladistics to portray
+ 
+
+ align:start position:0%
+mammals now we use cladistics to portray
+these different animals groups and this
+
+ align:start position:0%
+these different animals groups and this
+ 
+
+ align:start position:0%
+these different animals groups and this
+is a typical
+
+ align:start position:0%
+is a typical
+ 
+
+ align:start position:0%
+is a typical
+cladogram of the vertebrates uh drawn
+
+ align:start position:0%
+cladogram of the vertebrates uh drawn
+ 
+
+ align:start position:0%
+cladogram of the vertebrates uh drawn
+by AR Glenn northcut and Glenn northcut
+
+ align:start position:0%
+by AR Glenn northcut and Glenn northcut
+ 
+
+ align:start position:0%
+by AR Glenn northcut and Glenn northcut
+has done a lot of different work in
+
+ align:start position:0%
+has done a lot of different work in
+ 
+
+ align:start position:0%
+has done a lot of different work in
+comparative
+
+ align:start position:0%
+comparative
+ 
+
+ align:start position:0%
+comparative
+neuroanatomy he's a little bit different
+
+ align:start position:0%
+neuroanatomy he's a little bit different
+ 
+
+ align:start position:0%
+neuroanatomy he's a little bit different
+from carton in that he's sort of a
+
+ align:start position:0%
+from carton in that he's sort of a
+ 
+
+ align:start position:0%
+from carton in that he's sort of a
+systematizer whereas carton is a guy who
+
+ align:start position:0%
+systematizer whereas carton is a guy who
+ 
+
+ align:start position:0%
+systematizer whereas carton is a guy who
+studies connections and is interesting
+
+ align:start position:0%
+studies connections and is interesting
+ 
+
+ align:start position:0%
+studies connections and is interesting
+in interested
+
+ align:start position:0%
+in interested
+ 
+
+ align:start position:0%
+in interested
+in what led to what in evolution little
+
+ align:start position:0%
+in what led to what in evolution little
+ 
+
+ align:start position:0%
+in what led to what in evolution little
+a little more like carton carton was
+
+ align:start position:0%
+a little more like carton carton was
+ 
+
+ align:start position:0%
+a little more like carton carton was
+also a student of
+
+ align:start position:0%
+also a student of
+ 
+
+ align:start position:0%
+also a student of
+NAA but northcut and his students have
+
+ align:start position:0%
+NAA but northcut and his students have
+ 
+
+ align:start position:0%
+NAA but northcut and his students have
+done a a lot of contribution
+
+ align:start position:0%
+done a a lot of contribution
+ 
+
+ align:start position:0%
+done a a lot of contribution
+to cladistics in fact northcut was
+
+ align:start position:0%
+to cladistics in fact northcut was
+ 
+
+ align:start position:0%
+to cladistics in fact northcut was
+probably the first neuroanatomist to use
+
+ align:start position:0%
+probably the first neuroanatomist to use
+ 
+
+ align:start position:0%
+probably the first neuroanatomist to use
+this way of
+
+ align:start position:0%
+this way of
+ 
+
+ align:start position:0%
+this way of
+portraying comparing animals what he's
+
+ align:start position:0%
+portraying comparing animals what he's
+ 
+
+ align:start position:0%
+portraying comparing animals what he's
+showing here
+
+ align:start position:0%
+showing here
+ 
+
+ align:start position:0%
+showing here
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+how certain animals blanched branched
+
+ align:start position:0%
+how certain animals blanched branched
+ 
+
+ align:start position:0%
+how certain animals blanched branched
+off from the main vertebrate tree this
+
+ align:start position:0%
+off from the main vertebrate tree this
+ 
+
+ align:start position:0%
+off from the main vertebrate tree this
+is a cordate line
+
+ align:start position:0%
+is a cordate line
+ 
+
+ align:start position:0%
+is a cordate line
+actually like the sea lampy uh
+
+ align:start position:0%
+actually like the sea lampy uh
+ 
+
+ align:start position:0%
+actually like the sea lampy uh
+amphibians well then
+
+ align:start position:0%
+amphibians well then
+ 
+
+ align:start position:0%
+amphibians well then
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+fish and very early the elasmo branches
+
+ align:start position:0%
+fish and very early the elasmo branches
+ 
+
+ align:start position:0%
+fish and very early the elasmo branches
+the carinus fish branched off that
+
+ align:start position:0%
+the carinus fish branched off that
+ 
+
+ align:start position:0%
+the carinus fish branched off that
+includes the sharps sharks the shark
+
+ align:start position:0%
+includes the sharps sharks the shark
+ 
+
+ align:start position:0%
+includes the sharps sharks the shark
+skates and the
+
+ align:start position:0%
+skates and the
+ 
+
+ align:start position:0%
+skates and the
+Rays
+
+ align:start position:0%
+Rays
+ 
+
+ align:start position:0%
+Rays
+uh and then of course later the bony
+
+ align:start position:0%
+uh and then of course later the bony
+ 
+
+ align:start position:0%
+uh and then of course later the bony
+fish so if if you're at the end of an
+
+ align:start position:0%
+fish so if if you're at the end of an
+ 
+
+ align:start position:0%
+fish so if if you're at the end of an
+arrow and he shows a brain of a living
+
+ align:start position:0%
+arrow and he shows a brain of a living
+ 
+
+ align:start position:0%
+arrow and he shows a brain of a living
+animal you're sort of at the where that
+
+ align:start position:0%
+animal you're sort of at the where that
+ 
+
+ align:start position:0%
+animal you're sort of at the where that
+line of evolution is led
+
+ align:start position:0%
+line of evolution is led
+ 
+
+ align:start position:0%
+line of evolution is led
+to and here the Bony vertebrate these
+
+ align:start position:0%
+to and here the Bony vertebrate these
+ 
+
+ align:start position:0%
+to and here the Bony vertebrate these
+are all bony vertebrates you have
+
+ align:start position:0%
+are all bony vertebrates you have
+ 
+
+ align:start position:0%
+are all bony vertebrates you have
+amphibians branching off the
+
+ align:start position:0%
+amphibians branching off the
+ 
+
+ align:start position:0%
+amphibians branching off the
+earliest and then the copses reptiles
+
+ align:start position:0%
+earliest and then the copses reptiles
+ 
+
+ align:start position:0%
+earliest and then the copses reptiles
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+birds but even before they branched off
+
+ align:start position:0%
+birds but even before they branched off
+ 
+
+ align:start position:0%
+birds but even before they branched off
+that line you see the
+
+ align:start position:0%
+that line you see the
+ 
+
+ align:start position:0%
+that line you see the
+mammals okay here's an earli view this
+
+ align:start position:0%
+mammals okay here's an earli view this
+ 
+
+ align:start position:0%
+mammals okay here's an earli view this
+was ludwiig
+
+ align:start position:0%
+was ludwiig
+ 
+
+ align:start position:0%
+was ludwiig
+ainger
+
+ align:start position:0%
+ainger
+ 
+
+ align:start position:0%
+ainger
+1908 and he had a view that can easily
+
+ align:start position:0%
+1908 and he had a view that can easily
+ 
+
+ align:start position:0%
+1908 and he had a view that can easily
+be fitted to the cladogram cladistic
+
+ align:start position:0%
+be fitted to the cladogram cladistic
+ 
+
+ align:start position:0%
+be fitted to the cladogram cladistic
+approach but he
+
+ align:start position:0%
+approach but he
+ 
+
+ align:start position:0%
+approach but he
+didn't use it it was not as we didn't
+
+ align:start position:0%
+didn't use it it was not as we didn't
+ 
+
+ align:start position:0%
+didn't use it it was not as we didn't
+have as many sources of data about
+
+ align:start position:0%
+have as many sources of data about
+ 
+
+ align:start position:0%
+have as many sources of data about
+Evolution then uh so he basically talked
+
+ align:start position:0%
+Evolution then uh so he basically talked
+ 
+
+ align:start position:0%
+Evolution then uh so he basically talked
+about this part that he saw as similar
+
+ align:start position:0%
+about this part that he saw as similar
+ 
+
+ align:start position:0%
+about this part that he saw as similar
+to the neocortex of
+
+ align:start position:0%
+to the neocortex of
+ 
+
+ align:start position:0%
+to the neocortex of
+humans um much smaller in small mammals
+
+ align:start position:0%
+humans um much smaller in small mammals
+ 
+
+ align:start position:0%
+humans um much smaller in small mammals
+like the rabbit
+
+ align:start position:0%
+like the rabbit
+ 
+
+ align:start position:0%
+like the rabbit
+um what he doesn't show here is
+
+ align:start position:0%
+um what he doesn't show here is
+ 
+
+ align:start position:0%
+um what he doesn't show here is
+something major what is the major
+
+ align:start position:0%
+something major what is the major
+ 
+
+ align:start position:0%
+something major what is the major
+difference in that M braan of
+
+ align:start position:0%
+difference in that M braan of
+ 
+
+ align:start position:0%
+difference in that M braan of
+cartilaginous fish and lizards when
+
+ align:start position:0%
+cartilaginous fish and lizards when
+ 
+
+ align:start position:0%
+cartilaginous fish and lizards when
+compared with rabbits and
+
+ align:start position:0%
+compared with rabbits and
+ 
+
+ align:start position:0%
+compared with rabbits and
+humans the
+
+ align:start position:0%
+humans the
+ 
+
+ align:start position:0%
+humans the
+neocortex and that's something the north
+
+ align:start position:0%
+neocortex and that's something the north
+ 
+
+ align:start position:0%
+neocortex and that's something the north
+cut stresses
+
+ align:start position:0%
+cut stresses
+ 
+
+ align:start position:0%
+cut stresses
+okay but what he shows here is the
+
+ align:start position:0%
+okay but what he shows here is the
+ 
+
+ align:start position:0%
+okay but what he shows here is the
+cereal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hemisphere which again we know is
+
+ align:start position:0%
+hemisphere which again we know is
+ 
+
+ align:start position:0%
+hemisphere which again we know is
+different in
+
+ align:start position:0%
+different in
+ 
+
+ align:start position:0%
+different in
+mammals than in all these other animals
+
+ align:start position:0%
+mammals than in all these other animals
+ 
+
+ align:start position:0%
+mammals than in all these other animals
+because only the mammals have the uh
+
+ align:start position:0%
+because only the mammals have the uh
+ 
+
+ align:start position:0%
+because only the mammals have the uh
+have the
+
+ align:start position:0%
+have the
+ 
+
+ align:start position:0%
+have the
+neocortex but if we take a cladogram
+
+ align:start position:0%
+neocortex but if we take a cladogram
+ 
+
+ align:start position:0%
+neocortex but if we take a cladogram
+here and look at the creatures that are
+
+ align:start position:0%
+here and look at the creatures that are
+ 
+
+ align:start position:0%
+here and look at the creatures that are
+still living today that branched off the
+
+ align:start position:0%
+still living today that branched off the
+ 
+
+ align:start position:0%
+still living today that branched off the
+earliest we find these three
+
+ align:start position:0%
+earliest we find these three
+ 
+
+ align:start position:0%
+earliest we find these three
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+amphioxys sea
+
+ align:start position:0%
+amphioxys sea
+ 
+
+ align:start position:0%
+amphioxys sea
+lampy and hag fishes
+
+ align:start position:0%
+lampy and hag fishes
+ 
+
+ align:start position:0%
+lampy and hag fishes
+and we looked at these once before and
+
+ align:start position:0%
+and we looked at these once before and
+ 
+
+ align:start position:0%
+and we looked at these once before and
+you'll just notice very tiny tlon in
+
+ align:start position:0%
+you'll just notice very tiny tlon in
+ 
+
+ align:start position:0%
+you'll just notice very tiny tlon in
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+animals non-existent really in aoys they
+
+ align:start position:0%
+animals non-existent really in aoys they
+ 
+
+ align:start position:0%
+animals non-existent really in aoys they
+just have a diyon like
+
+ align:start position:0%
+just have a diyon like
+ 
+
+ align:start position:0%
+just have a diyon like
+structure uh very tiny smaller than the
+
+ align:start position:0%
+structure uh very tiny smaller than the
+ 
+
+ align:start position:0%
+structure uh very tiny smaller than the
+olfactory bulbs in the sea
+
+ align:start position:0%
+olfactory bulbs in the sea
+ 
+
+ align:start position:0%
+olfactory bulbs in the sea
+lampy and still very very small in the
+
+ align:start position:0%
+lampy and still very very small in the
+ 
+
+ align:start position:0%
+lampy and still very very small in the
+hagfish here's a hag here's a hagfish
+
+ align:start position:0%
+hagfish here's a hag here's a hagfish
+ 
+
+ align:start position:0%
+hagfish here's a hag here's a hagfish
+somewhere
+
+ align:start position:0%
+somewhere
+ 
+
+ align:start position:0%
+somewhere
+here there's the ton sephon there's the
+
+ align:start position:0%
+here there's the ton sephon there's the
+ 
+
+ align:start position:0%
+here there's the ton sephon there's the
+old factory
+
+ align:start position:0%
+old factory
+ 
+
+ align:start position:0%
+old factory
+bulb the whole ton sephon is that much
+
+ align:start position:0%
+bulb the whole ton sephon is that much
+ 
+
+ align:start position:0%
+bulb the whole ton sephon is that much
+not that much bigger than the old
+
+ align:start position:0%
+not that much bigger than the old
+ 
+
+ align:start position:0%
+not that much bigger than the old
+factory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bulb okay and
+
+ align:start position:0%
+bulb okay and
+ 
+
+ align:start position:0%
+bulb okay and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+then I show you here some of the bony
+
+ align:start position:0%
+then I show you here some of the bony
+ 
+
+ align:start position:0%
+then I show you here some of the bony
+fish the marids with a huge
+
+ align:start position:0%
+fish the marids with a huge
+ 
+
+ align:start position:0%
+fish the marids with a huge
+cerebellum a trout with a huge midbrain
+
+ align:start position:0%
+cerebellum a trout with a huge midbrain
+ 
+
+ align:start position:0%
+cerebellum a trout with a huge midbrain
+predatory fish very tiny
+
+ align:start position:0%
+predatory fish very tiny
+ 
+
+ align:start position:0%
+predatory fish very tiny
+tlon here's a bear which is only
+
+ align:start position:0%
+tlon here's a bear which is only
+ 
+
+ align:start position:0%
+tlon here's a bear which is only
+slightly larger
+
+ align:start position:0%
+slightly larger
+ 
+
+ align:start position:0%
+slightly larger
+tlon
+
+ align:start position:0%
+tlon
+ 
+
+ align:start position:0%
+tlon
+okay and here's a question that you
+
+ align:start position:0%
+okay and here's a question that you
+ 
+
+ align:start position:0%
+okay and here's a question that you
+don't see very much but yorg streer
+
+ align:start position:0%
+don't see very much but yorg streer
+ 
+
+ align:start position:0%
+don't see very much but yorg streer
+treats it and so does alma in his book I
+
+ align:start position:0%
+treats it and so does alma in his book I
+ 
+
+ align:start position:0%
+treats it and so does alma in his book I
+say in most cordate groups brain size
+
+ align:start position:0%
+say in most cordate groups brain size
+ 
+
+ align:start position:0%
+say in most cordate groups brain size
+increases in
+
+ align:start position:0%
+increases in
+ 
+
+ align:start position:0%
+increases in
+evolution but in a few groups it
+
+ align:start position:0%
+evolution but in a few groups it
+ 
+
+ align:start position:0%
+evolution but in a few groups it
+decreases so why would it ever decrease
+
+ align:start position:0%
+decreases so why would it ever decrease
+ 
+
+ align:start position:0%
+decreases so why would it ever decrease
+for it to decrease in evolution that
+
+ align:start position:0%
+for it to decrease in evolution that
+ 
+
+ align:start position:0%
+for it to decrease in evolution that
+means there had to be adaptive
+
+ align:start position:0%
+means there had to be adaptive
+ 
+
+ align:start position:0%
+means there had to be adaptive
+reasons why it would decrease in size
+
+ align:start position:0%
+reasons why it would decrease in size
+ 
+
+ align:start position:0%
+reasons why it would decrease in size
+can you think of an Adaptive reason why
+
+ align:start position:0%
+can you think of an Adaptive reason why
+ 
+
+ align:start position:0%
+can you think of an Adaptive reason why
+a brain structure would decrease in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+size and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so even the weight could be a
+
+ align:start position:0%
+this so even the weight could be a
+ 
+
+ align:start position:0%
+this so even the weight could be a
+disadvantage I would say one thing's
+
+ align:start position:0%
+disadvantage I would say one thing's
+ 
+
+ align:start position:0%
+disadvantage I would say one thing's
+even more important and that brain
+
+ align:start position:0%
+even more important and that brain
+ 
+
+ align:start position:0%
+even more important and that brain
+tissue is very demanding in energy
+
+ align:start position:0%
+tissue is very demanding in energy
+ 
+
+ align:start position:0%
+tissue is very demanding in energy
+consumption like our brain is hardly 20%
+
+ align:start position:0%
+consumption like our brain is hardly 20%
+ 
+
+ align:start position:0%
+consumption like our brain is hardly 20%
+of our body weight but it uses 20% % of
+
+ align:start position:0%
+of our body weight but it uses 20% % of
+ 
+
+ align:start position:0%
+of our body weight but it uses 20% % of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay some people get a fever if they
+
+ align:start position:0%
+okay some people get a fever if they
+ 
+
+ align:start position:0%
+okay some people get a fever if they
+think too
+
+ align:start position:0%
+think too
+ 
+
+ align:start position:0%
+think too
+hard sorry couldn't resist that but the
+
+ align:start position:0%
+hard sorry couldn't resist that but the
+ 
+
+ align:start position:0%
+hard sorry couldn't resist that but the
+it actually is uses a lot of
+
+ align:start position:0%
+it actually is uses a lot of
+ 
+
+ align:start position:0%
+it actually is uses a lot of
+energy you can't go without eating too
+
+ align:start position:0%
+energy you can't go without eating too
+ 
+
+ align:start position:0%
+energy you can't go without eating too
+long if you want you're working hard on
+
+ align:start position:0%
+long if you want you're working hard on
+ 
+
+ align:start position:0%
+long if you want you're working hard on
+homework problems okay
+
+ align:start position:0%
+homework problems okay
+ 
+
+ align:start position:0%
+homework problems okay
+uh so it it can decrease because of
+
+ align:start position:0%
+uh so it it can decrease because of
+ 
+
+ align:start position:0%
+uh so it it can decrease because of
+energy demands well why is is that so
+
+ align:start position:0%
+energy demands well why is is that so
+ 
+
+ align:start position:0%
+energy demands well why is is that so
+critical with high energy demands you've
+
+ align:start position:0%
+critical with high energy demands you've
+ 
+
+ align:start position:0%
+critical with high energy demands you've
+got to spend more time getting food
+
+ align:start position:0%
+got to spend more time getting food
+ 
+
+ align:start position:0%
+got to spend more time getting food
+okay and it takes a lot of energy
+
+ align:start position:0%
+okay and it takes a lot of energy
+ 
+
+ align:start position:0%
+okay and it takes a lot of energy
+depending on what you're eating of
+
+ align:start position:0%
+depending on what you're eating of
+ 
+
+ align:start position:0%
+depending on what you're eating of
+course you might be eating a high energy
+
+ align:start position:0%
+course you might be eating a high energy
+ 
+
+ align:start position:0%
+course you might be eating a high energy
+food like eating other
+
+ align:start position:0%
+food like eating other
+ 
+
+ align:start position:0%
+food like eating other
+animals but then it takes energy to
+
+ align:start position:0%
+animals but then it takes energy to
+ 
+
+ align:start position:0%
+animals but then it takes energy to
+digest so that's another big energy
+
+ align:start position:0%
+digest so that's another big energy
+ 
+
+ align:start position:0%
+digest so that's another big energy
+consumer brain
+
+ align:start position:0%
+consumer brain
+ 
+
+ align:start position:0%
+consumer brain
+gut what did humans develop that made
+
+ align:start position:0%
+gut what did humans develop that made
+ 
+
+ align:start position:0%
+gut what did humans develop that made
+possible the much larger brain using a
+
+ align:start position:0%
+possible the much larger brain using a
+ 
+
+ align:start position:0%
+possible the much larger brain using a
+lot more
+
+ align:start position:0%
+lot more
+ 
+
+ align:start position:0%
+lot more
+energy how did humans decrease the
+
+ align:start position:0%
+energy how did humans decrease the
+ 
+
+ align:start position:0%
+energy how did humans decrease the
+demand on their digestive system cing
+
+ align:start position:0%
+demand on their digestive system cing
+ 
+
+ align:start position:0%
+demand on their digestive system cing
+cooking exactly so you see after the
+
+ align:start position:0%
+cooking exactly so you see after the
+ 
+
+ align:start position:0%
+cooking exactly so you see after the
+indications of fire being developed by
+
+ align:start position:0%
+indications of fire being developed by
+ 
+
+ align:start position:0%
+indications of fire being developed by
+humans the last big surge of growth of
+
+ align:start position:0%
+humans the last big surge of growth of
+ 
+
+ align:start position:0%
+humans the last big surge of growth of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+enry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I can't how does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cooking it it requires a lot more energy
+
+ align:start position:0%
+cooking it it requires a lot more energy
+ 
+
+ align:start position:0%
+cooking it it requires a lot more energy
+to digest raw meat than it does cooked
+
+ align:start position:0%
+to digest raw meat than it does cooked
+ 
+
+ align:start position:0%
+to digest raw meat than it does cooked
+meat the energy Alters the
+
+ align:start position:0%
+meat the energy Alters the
+ 
+
+ align:start position:0%
+meat the energy Alters the
+proteins ways that assist their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+digestion this is dealt with in a little
+
+ align:start position:0%
+digestion this is dealt with in a little
+ 
+
+ align:start position:0%
+digestion this is dealt with in a little
+more detail in Almond but you can find
+
+ align:start position:0%
+more detail in Almond but you can find
+ 
+
+ align:start position:0%
+more detail in Almond but you can find
+discussions of it too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+online
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can I can I ask something so I mean from
+
+ align:start position:0%
+can I can I ask something so I mean from
+ 
+
+ align:start position:0%
+can I can I ask something so I mean from
+that like can we say that like the size
+
+ align:start position:0%
+that like can we say that like the size
+ 
+
+ align:start position:0%
+that like can we say that like the size
+of the of a brain
+
+ align:start position:0%
+of the of a brain
+ 
+
+ align:start position:0%
+of the of a brain
+like means you know like it's like it's
+
+ align:start position:0%
+like means you know like it's like it's
+ 
+
+ align:start position:0%
+like means you know like it's like it's
+more smart or something okay you have to
+
+ align:start position:0%
+more smart or something okay you have to
+ 
+
+ align:start position:0%
+more smart or something okay you have to
+add to that that if brain size is
+
+ align:start position:0%
+add to that that if brain size is
+ 
+
+ align:start position:0%
+add to that that if brain size is
+decreasing they must decrease the size
+
+ align:start position:0%
+decreasing they must decrease the size
+ 
+
+ align:start position:0%
+decreasing they must decrease the size
+of something that's not critical for
+
+ align:start position:0%
+of something that's not critical for
+ 
+
+ align:start position:0%
+of something that's not critical for
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+survival you're quite right that we've
+
+ align:start position:0%
+survival you're quite right that we've
+ 
+
+ align:start position:0%
+survival you're quite right that we've
+talked about how the size of a structure
+
+ align:start position:0%
+talked about how the size of a structure
+ 
+
+ align:start position:0%
+talked about how the size of a structure
+increases if there's a lot of neural
+
+ align:start position:0%
+increases if there's a lot of neural
+ 
+
+ align:start position:0%
+increases if there's a lot of neural
+processing going on he needs it for his
+
+ align:start position:0%
+processing going on he needs it for his
+ 
+
+ align:start position:0%
+processing going on he needs it for his
+hunting
+
+ align:start position:0%
+hunting
+ 
+
+ align:start position:0%
+hunting
+Behavior or other things he's
+
+ align:start position:0%
+Behavior or other things he's
+ 
+
+ align:start position:0%
+Behavior or other things he's
+doing you're
+
+ align:start position:0%
+doing you're
+ 
+
+ align:start position:0%
+doing you're
+right let's look at which animals this
+
+ align:start position:0%
+right let's look at which animals this
+ 
+
+ align:start position:0%
+right let's look at which animals this
+these were brain versus body weights of
+
+ align:start position:0%
+these were brain versus body weights of
+ 
+
+ align:start position:0%
+these were brain versus body weights of
+the major animal groups just to remind
+
+ align:start position:0%
+the major animal groups just to remind
+ 
+
+ align:start position:0%
+the major animal groups just to remind
+you where humans
+
+ align:start position:0%
+you where humans
+ 
+
+ align:start position:0%
+you where humans
+are remember it's relative size that
+
+ align:start position:0%
+are remember it's relative size that
+ 
+
+ align:start position:0%
+are remember it's relative size that
+increases this is whale up here this is
+
+ align:start position:0%
+increases this is whale up here this is
+ 
+
+ align:start position:0%
+increases this is whale up here this is
+elephant they have the largest brains
+
+ align:start position:0%
+elephant they have the largest brains
+ 
+
+ align:start position:0%
+elephant they have the largest brains
+humans are here smaller brains but in
+
+ align:start position:0%
+humans are here smaller brains but in
+ 
+
+ align:start position:0%
+humans are here smaller brains but in
+relative to their body weight it's the
+
+ align:start position:0%
+relative to their body weight it's the
+ 
+
+ align:start position:0%
+relative to their body weight it's the
+largest okay and this is a on a
+
+ align:start position:0%
+largest okay and this is a on a
+ 
+
+ align:start position:0%
+largest okay and this is a on a
+cladogram streer Drew this After
+
+ align:start position:0%
+cladogram streer Drew this After
+ 
+
+ align:start position:0%
+cladogram streer Drew this After
+figuring out where the increases in
+
+ align:start position:0%
+figuring out where the increases in
+ 
+
+ align:start position:0%
+figuring out where the increases in
+relative brain size occur where the
+
+ align:start position:0%
+relative brain size occur where the
+ 
+
+ align:start position:0%
+relative brain size occur where the
+decreases occur there's not decreases
+
+ align:start position:0%
+decreases occur there's not decreases
+ 
+
+ align:start position:0%
+decreases occur there's not decreases
+very many places but you see here when
+
+ align:start position:0%
+very many places but you see here when
+ 
+
+ align:start position:0%
+very many places but you see here when
+salamanders evolved there were decreases
+
+ align:start position:0%
+salamanders evolved there were decreases
+ 
+
+ align:start position:0%
+salamanders evolved there were decreases
+in relative
+
+ align:start position:0%
+in relative
+ 
+
+ align:start position:0%
+in relative
+size the eels similar decreases in
+
+ align:start position:0%
+size the eels similar decreases in
+ 
+
+ align:start position:0%
+size the eels similar decreases in
+size all these others the red dots are
+
+ align:start position:0%
+size all these others the red dots are
+ 
+
+ align:start position:0%
+size all these others the red dots are
+for when were marked increases in
+
+ align:start position:0%
+for when were marked increases in
+ 
+
+ align:start position:0%
+for when were marked increases in
+size okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and remember we talked about the very
+
+ align:start position:0%
+so and remember we talked about the very
+ 
+
+ align:start position:0%
+so and remember we talked about the very
+early forbrain and evidence that it's
+
+ align:start position:0%
+early forbrain and evidence that it's
+ 
+
+ align:start position:0%
+early forbrain and evidence that it's
+dominated by old faction I emphasized
+
+ align:start position:0%
+dominated by old faction I emphasized
+ 
+
+ align:start position:0%
+dominated by old faction I emphasized
+that early in the book and I talked
+
+ align:start position:0%
+that early in the book and I talked
+ 
+
+ align:start position:0%
+that early in the book and I talked
+about how old faction dominated the
+
+ align:start position:0%
+about how old faction dominated the
+ 
+
+ align:start position:0%
+about how old faction dominated the
+Primitive in brain we didn't have really
+
+ align:start position:0%
+Primitive in brain we didn't have really
+ 
+
+ align:start position:0%
+Primitive in brain we didn't have really
+good information on that until people
+
+ align:start position:0%
+good information on that until people
+ 
+
+ align:start position:0%
+good information on that until people
+fairly recently studied the olda factory
+
+ align:start position:0%
+fairly recently studied the olda factory
+ 
+
+ align:start position:0%
+fairly recently studied the olda factory
+bulb
+
+ align:start position:0%
+bulb
+ 
+
+ align:start position:0%
+bulb
+projections in
+
+ align:start position:0%
+projections in
+ 
+
+ align:start position:0%
+projections in
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+those two animals that are members of
+
+ align:start position:0%
+those two animals that are members of
+ 
+
+ align:start position:0%
+those two animals that are members of
+the nonbony vertebrates the and that was
+
+ align:start position:0%
+the nonbony vertebrates the and that was
+ 
+
+ align:start position:0%
+the nonbony vertebrates the and that was
+the hag fishes and the Sea lampies
+
+ align:start position:0%
+the hag fishes and the Sea lampies
+ 
+
+ align:start position:0%
+the hag fishes and the Sea lampies
+probably the lamp studies been most
+
+ align:start position:0%
+probably the lamp studies been most
+ 
+
+ align:start position:0%
+probably the lamp studies been most
+interesting cuz the lampies are a little
+
+ align:start position:0%
+interesting cuz the lampies are a little
+ 
+
+ align:start position:0%
+interesting cuz the lampies are a little
+less
+
+ align:start position:0%
+less
+ 
+
+ align:start position:0%
+less
+specialized in the hagfish this is the
+
+ align:start position:0%
+specialized in the hagfish this is the
+ 
+
+ align:start position:0%
+specialized in the hagfish this is the
+hagfish the Pacific
+
+ align:start position:0%
+hagfish the Pacific
+ 
+
+ align:start position:0%
+hagfish the Pacific
+hagfish they injected tracers into the
+
+ align:start position:0%
+hagfish they injected tracers into the
+ 
+
+ align:start position:0%
+hagfish they injected tracers into the
+old factory bulb here this is Bo bulbous
+
+ align:start position:0%
+old factory bulb here this is Bo bulbous
+ 
+
+ align:start position:0%
+old factory bulb here this is Bo bulbous
+old Factoria sorry they lot a lot of
+
+ align:start position:0%
+old Factoria sorry they lot a lot of
+ 
+
+ align:start position:0%
+old Factoria sorry they lot a lot of
+times they like to use the Latin or
+
+ align:start position:0%
+times they like to use the Latin or
+ 
+
+ align:start position:0%
+times they like to use the Latin or
+Greek
+
+ align:start position:0%
+Greek
+ 
+
+ align:start position:0%
+Greek
+names and so they use it here
+
+ align:start position:0%
+names and so they use it here
+ 
+
+ align:start position:0%
+names and so they use it here
+forlon then
+
+ align:start position:0%
+forlon then
+ 
+
+ align:start position:0%
+forlon then
+dianon and what is TM heum believe so
+
+ align:start position:0%
+dianon and what is TM heum believe so
+ 
+
+ align:start position:0%
+dianon and what is TM heum believe so
+mid-brain tectum okay and this is just a
+
+ align:start position:0%
+mid-brain tectum okay and this is just a
+ 
+
+ align:start position:0%
+mid-brain tectum okay and this is just a
+summary of alacer bulb projections in
+
+ align:start position:0%
+summary of alacer bulb projections in
+ 
+
+ align:start position:0%
+summary of alacer bulb projections in
+the hag fish and L PR when compared to
+
+ align:start position:0%
+the hag fish and L PR when compared to
+ 
+
+ align:start position:0%
+the hag fish and L PR when compared to
+amphibians also a pretty primitive the
+
+ align:start position:0%
+amphibians also a pretty primitive the
+ 
+
+ align:start position:0%
+amphibians also a pretty primitive the
+most the most primitive group of
+
+ align:start position:0%
+most the most primitive group of
+ 
+
+ align:start position:0%
+most the most primitive group of
+tetrapods notice that in the hagfish and
+
+ align:start position:0%
+tetrapods notice that in the hagfish and
+ 
+
+ align:start position:0%
+tetrapods notice that in the hagfish and
+also in the lampy the old factory bulb
+
+ align:start position:0%
+also in the lampy the old factory bulb
+ 
+
+ align:start position:0%
+also in the lampy the old factory bulb
+projects to every end brain structure
+
+ align:start position:0%
+projects to every end brain structure
+ 
+
+ align:start position:0%
+projects to every end brain structure
+that's there and some of the tween brain
+
+ align:start position:0%
+that's there and some of the tween brain
+ 
+
+ align:start position:0%
+that's there and some of the tween brain
+structures
+
+ align:start position:0%
+structures
+ 
+
+ align:start position:0%
+structures
+this is a projection to the tween brain
+
+ align:start position:0%
+this is a projection to the tween brain
+ 
+
+ align:start position:0%
+this is a projection to the tween brain
+and some of these structures are tween
+
+ align:start position:0%
+and some of these structures are tween
+ 
+
+ align:start position:0%
+and some of these structures are tween
+brain this is actually Statum
+
+ align:start position:0%
+brain this is actually Statum
+ 
+
+ align:start position:0%
+brain this is actually Statum
+here in the lampri it goes into this
+
+ align:start position:0%
+here in the lampri it goes into this
+ 
+
+ align:start position:0%
+here in the lampri it goes into this
+trium it goes into the medial pallum
+
+ align:start position:0%
+trium it goes into the medial pallum
+ 
+
+ align:start position:0%
+trium it goes into the medial pallum
+here this is a layered structure it's
+
+ align:start position:0%
+here this is a layered structure it's
+ 
+
+ align:start position:0%
+here this is a layered structure it's
+going into one layer and other end brain
+
+ align:start position:0%
+going into one layer and other end brain
+ 
+
+ align:start position:0%
+going into one layer and other end brain
+structures and dellic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+structures but when you get to
+
+ align:start position:0%
+structures but when you get to
+ 
+
+ align:start position:0%
+structures but when you get to
+amphibians you see it it's going to the
+
+ align:start position:0%
+amphibians you see it it's going to the
+ 
+
+ align:start position:0%
+amphibians you see it it's going to the
+medial pum but only the only one edge of
+
+ align:start position:0%
+medial pum but only the only one edge of
+ 
+
+ align:start position:0%
+medial pum but only the only one edge of
+it it's going into the dorsal pum which
+
+ align:start position:0%
+it it's going into the dorsal pum which
+ 
+
+ align:start position:0%
+it it's going into the dorsal pum which
+is like a parahippocampal area in those
+
+ align:start position:0%
+is like a parahippocampal area in those
+ 
+
+ align:start position:0%
+is like a parahippocampal area in those
+animals in that we know it projects into
+
+ align:start position:0%
+animals in that we know it projects into
+ 
+
+ align:start position:0%
+animals in that we know it projects into
+the medial
+
+ align:start position:0%
+the medial
+ 
+
+ align:start position:0%
+the medial
+pum it gets Direct Factory input but
+
+ align:start position:0%
+pum it gets Direct Factory input but
+ 
+
+ align:start position:0%
+pum it gets Direct Factory input but
+only at one Edge and it goes into the
+
+ align:start position:0%
+only at one Edge and it goes into the
+ 
+
+ align:start position:0%
+only at one Edge and it goes into the
+striatum but not throughout the entire
+
+ align:start position:0%
+striatum but not throughout the entire
+ 
+
+ align:start position:0%
+striatum but not throughout the entire
+striatum okay there big areas then that
+
+ align:start position:0%
+striatum okay there big areas then that
+ 
+
+ align:start position:0%
+striatum okay there big areas then that
+don't get old factory bul projections
+
+ align:start position:0%
+don't get old factory bul projections
+ 
+
+ align:start position:0%
+don't get old factory bul projections
+the way they do in the L PRI and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hagfish and it's already 4 I think I
+
+ align:start position:0%
+hagfish and it's already 4 I think I
+ 
+
+ align:start position:0%
+hagfish and it's already 4 I think I
+better stop here and
+
+ align:start position:0%
+better stop here and
+ 
+
+ align:start position:0%
+better stop here and
+uh I think we will finish this and be
+
+ align:start position:0%
+uh I think we will finish this and be
+ 
+
+ align:start position:0%
+uh I think we will finish this and be
+able to start talking about the hype of
+
+ align:start position:0%
+able to start talking about the hype of
+ 
+
+ align:start position:0%
+able to start talking about the hype of
+helness next
+
+ align:start position:0%
+helness next
+ 
+
+ align:start position:0%
+helness next
+time
\ No newline at end of file
diff --git a/iVUsEwSg-lw.txt b/iVUsEwSg-lw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..91a19c8199dfafe9b60d07cdad7e096b010a1d91
--- /dev/null
+++ b/iVUsEwSg-lw.txt
@@ -0,0 +1,7093 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay now where am I with
+
+ align:start position:0%
+ocw.mit.edu okay now where am I with
+ 
+
+ align:start position:0%
+ocw.mit.edu okay now where am I with
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+well last time I spoke
+
+ align:start position:0%
+well last time I spoke
+ 
+
+ align:start position:0%
+well last time I spoke
+about what the situation like as Alpha
+
+ align:start position:0%
+about what the situation like as Alpha
+ 
+
+ align:start position:0%
+about what the situation like as Alpha
+goes to infin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I want to say also a word about more
+
+ align:start position:0%
+and I want to say also a word about more
+ 
+
+ align:start position:0%
+and I want to say also a word about more
+than a word about Alpha going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero um and then the real problems come
+
+ align:start position:0%
+zero um and then the real problems come
+ 
+
+ align:start position:0%
+zero um and then the real problems come
+when Alpha is in between the the real
+
+ align:start position:0%
+when Alpha is in between the the real
+ 
+
+ align:start position:0%
+when Alpha is in between the the real
+problem the the situations these ill
+
+ align:start position:0%
+problem the the situations these ill
+ 
+
+ align:start position:0%
+problem the the situations these ill
+posed problems that come from um inverse
+
+ align:start position:0%
+posed problems that come from um inverse
+ 
+
+ align:start position:0%
+posed problems that come from um inverse
+uh problems trying to find out what
+
+ align:start position:0%
+uh problems trying to find out what
+ 
+
+ align:start position:0%
+uh problems trying to find out what
+inside your brain by taking measurements
+
+ align:start position:0%
+inside your brain by taking measurements
+ 
+
+ align:start position:0%
+inside your brain by taking measurements
+on the at the skull all all sorts of
+
+ align:start position:0%
+on the at the skull all all sorts of
+ 
+
+ align:start position:0%
+on the at the skull all all sorts of
+applications involve uh a a finite Alpha
+
+ align:start position:0%
+applications involve uh a a finite Alpha
+ 
+
+ align:start position:0%
+applications involve uh a a finite Alpha
+and I'm not quite ready to to uh discuss
+
+ align:start position:0%
+and I'm not quite ready to to uh discuss
+ 
+
+ align:start position:0%
+and I'm not quite ready to to uh discuss
+those topics I mean roughly speaking
+
+ align:start position:0%
+those topics I mean roughly speaking
+ 
+
+ align:start position:0%
+those topics I mean roughly speaking
+uh and I'll write down a reminder now
+
+ align:start position:0%
+uh and I'll write down a reminder now
+ 
+
+ align:start position:0%
+uh and I'll write down a reminder now
+what happened when Alpha went to
+
+ align:start position:0%
+what happened when Alpha went to
+ 
+
+ align:start position:0%
+what happened when Alpha went to
+Infinity when Alpha went went to
+
+ align:start position:0%
+Infinity when Alpha went went to
+ 
+
+ align:start position:0%
+Infinity when Alpha went went to
+infinity and enforced this this part
+
+ align:start position:0%
+infinity and enforced this this part
+ 
+
+ align:start position:0%
+infinity and enforced this this part
+became the important part so as Alpha
+
+ align:start position:0%
+became the important part so as Alpha
+ 
+
+ align:start position:0%
+became the important part so as Alpha
+went to Infinity you
+
+ align:start position:0%
+went to Infinity you
+ 
+
+ align:start position:0%
+went to Infinity you
+you the limit was U Infinity so I call
+
+ align:start position:0%
+you the limit was U Infinity so I call
+ 
+
+ align:start position:0%
+you the limit was U Infinity so I call
+it U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinity uh well so U Infinity was a
+
+ align:start position:0%
+Infinity uh well so U Infinity was a
+ 
+
+ align:start position:0%
+Infinity uh well so U Infinity was a
+minimizer of this one U
+
+ align:start position:0%
+minimizer of this one U
+ 
+
+ align:start position:0%
+minimizer of this one U
+Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minimized bu minus d
+
+ align:start position:0%
+minimized bu minus d
+ 
+
+ align:start position:0%
+minimized bu minus d
+squared and in fact in my last uh
+
+ align:start position:0%
+squared and in fact in my last uh
+ 
+
+ align:start position:0%
+squared and in fact in my last uh
+lecture uh I was taking bu equal d as an
+
+ align:start position:0%
+lecture uh I was taking bu equal d as an
+ 
+
+ align:start position:0%
+lecture uh I was taking bu equal d as an
+equation that had Exact Solutions and
+
+ align:start position:0%
+equation that had Exact Solutions and
+ 
+
+ align:start position:0%
+equation that had Exact Solutions and
+saying how did we actually solve bu
+
+ align:start position:0%
+saying how did we actually solve bu
+ 
+
+ align:start position:0%
+saying how did we actually solve bu
+equal D so U Infinity minimizes bu bu
+
+ align:start position:0%
+equal D so U Infinity minimizes bu bu
+ 
+
+ align:start position:0%
+equal D so U Infinity minimizes bu bu
+minus D but that might leave some
+
+ align:start position:0%
+minus D but that might leave some
+ 
+
+ align:start position:0%
+minus D but that might leave some
+Freedom if B doesn't have that many rows
+
+ align:start position:0%
+Freedom if B doesn't have that many rows
+ 
+
+ align:start position:0%
+Freedom if B doesn't have that many rows
+if its rank is not that big then this
+
+ align:start position:0%
+if its rank is not that big then this
+ 
+
+ align:start position:0%
+if its rank is not that big then this
+doesn't finish the job so among these
+
+ align:start position:0%
+doesn't finish the job so among these
+ 
+
+ align:start position:0%
+doesn't finish the job so among these
+then among these if there are if there
+
+ align:start position:0%
+then among these if there are if there
+ 
+
+ align:start position:0%
+then among these if there are if there
+are many and that's what we're
+
+ align:start position:0%
+are many and that's what we're
+ 
+
+ align:start position:0%
+are many and that's what we're
+interested
+
+ align:start position:0%
+interested
+ 
+
+ align:start position:0%
+interested
+in uh you had Infinity that limit will
+
+ align:start position:0%
+in uh you had Infinity that limit will
+ 
+
+ align:start position:0%
+in uh you had Infinity that limit will
+all will minimize the other
+
+ align:start position:0%
+all will minimize the other
+ 
+
+ align:start position:0%
+all will minimize the other
+bit Au U minus B
+
+ align:start position:0%
+bit Au U minus B
+ 
+
+ align:start position:0%
+bit Au U minus B
+squ does that make sense somehow this is
+
+ align:start position:0%
+squ does that make sense somehow this is
+ 
+
+ align:start position:0%
+squ does that make sense somehow this is
+in the problem here for for any finite
+
+ align:start position:0%
+in the problem here for for any finite
+ 
+
+ align:start position:0%
+in the problem here for for any finite
+Alpha as Alpha gets bigger and bigger we
+
+ align:start position:0%
+Alpha as Alpha gets bigger and bigger we
+ 
+
+ align:start position:0%
+Alpha as Alpha gets bigger and bigger we
+push harder and harder on this one so we
+
+ align:start position:0%
+push harder and harder on this one so we
+ 
+
+ align:start position:0%
+push harder and harder on this one so we
+get a one that's a winner for this one
+
+ align:start position:0%
+get a one that's a winner for this one
+ 
+
+ align:start position:0%
+get a one that's a winner for this one
+but the trace of this first part is
+
+ align:start position:0%
+but the trace of this first part is
+ 
+
+ align:start position:0%
+but the trace of this first part is
+still around and if there are many
+
+ align:start position:0%
+still around and if there are many
+ 
+
+ align:start position:0%
+still around and if there are many
+winners then having this first part in
+
+ align:start position:0%
+winners then having this first part in
+ 
+
+ align:start position:0%
+winners then having this first part in
+there will give us the among the winners
+
+ align:start position:0%
+there will give us the among the winners
+ 
+
+ align:start position:0%
+there will give us the among the winners
+the one that does the best on that
+
+ align:start position:0%
+the one that does the best on that
+ 
+
+ align:start position:0%
+the one that does the best on that
+term and small
+
+ align:start position:0%
+term and small
+ 
+
+ align:start position:0%
+term and small
+Alpha going to zero will just be the
+
+ align:start position:0%
+Alpha going to zero will just be the
+ 
+
+ align:start position:0%
+Alpha going to zero will just be the
+opposite right I this finally struck me
+
+ align:start position:0%
+opposite right I this finally struck me
+ 
+
+ align:start position:0%
+opposite right I this finally struck me
+over the weekend you know like I could
+
+ align:start position:0%
+over the weekend you know like I could
+ 
+
+ align:start position:0%
+over the weekend you know like I could
+divide this quantity this whole
+
+ align:start position:0%
+divide this quantity this whole
+ 
+
+ align:start position:0%
+divide this quantity this whole
+expression by Alpha so then I have a one
+
+ align:start position:0%
+expression by Alpha so then I have a one
+ 
+
+ align:start position:0%
+expression by Alpha so then I have a one
+there and a one over Alpha here and now
+
+ align:start position:0%
+there and a one over Alpha here and now
+ 
+
+ align:start position:0%
+there and a one over Alpha here and now
+as Alpha goes to zero this is the big
+
+ align:start position:0%
+as Alpha goes to zero this is the big
+ 
+
+ align:start position:0%
+as Alpha goes to zero this is the big
+term so now you shall I call this u0 to
+
+ align:start position:0%
+term so now you shall I call this u0 to
+ 
+
+ align:start position:0%
+term so now you shall I call this u0 to
+for brilliant notation right this is so
+
+ align:start position:0%
+for brilliant notation right this is so
+ 
+
+ align:start position:0%
+for brilliant notation right this is so
+this this is uh this produces a u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha in that limit it converges to a u
+
+ align:start position:0%
+Alpha in that limit it converges to a u
+ 
+
+ align:start position:0%
+Alpha in that limit it converges to a u
+Infinity that focuses first on this
+
+ align:start position:0%
+Infinity that focuses first on this
+ 
+
+ align:start position:0%
+Infinity that focuses first on this
+problem but in the other limit when
+
+ align:start position:0%
+problem but in the other limit when
+ 
+
+ align:start position:0%
+problem but in the other limit when
+Alpha is going to zero it's this term
+
+ align:start position:0%
+Alpha is going to zero it's this term
+ 
+
+ align:start position:0%
+Alpha is going to zero it's this term
+that's biggest so u0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minimizes Au minus b^
+
+ align:start position:0%
+minimizes Au minus b^
+ 
+
+ align:start position:0%
+minimizes Au minus b^
+2 and if there are many minimizers among
+
+ align:start position:0%
+2 and if there are many minimizers among
+ 
+
+ align:start position:0%
+2 and if there are many minimizers among
+these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well you know what I'm going to write u
+
+ align:start position:0%
+well you know what I'm going to write u
+ 
+
+ align:start position:0%
+well you know what I'm going to write u
+z or I see I put a little hat there did
+
+ align:start position:0%
+z or I see I put a little hat there did
+ 
+
+ align:start position:0%
+z or I see I put a little hat there did
+I I don't know I haven't stayed with
+
+ align:start position:0%
+I I don't know I haven't stayed with
+ 
+
+ align:start position:0%
+I I don't know I haven't stayed with
+these hats very much but maybe
+
+ align:start position:0%
+these hats very much but maybe
+ 
+
+ align:start position:0%
+these hats very much but maybe
+I'll add them uh you hat
+
+ align:start position:0%
+I'll add them uh you hat
+ 
+
+ align:start position:0%
+I'll add them uh you hat
+minimizes the the term that's not so
+
+ align:start position:0%
+minimizes the the term that's not so
+ 
+
+ align:start position:0%
+minimizes the the term that's not so
+important V minus
+
+ align:start position:0%
+important V minus
+ 
+
+ align:start position:0%
+important V minus
+d^2 okay so so today's lecture is still
+
+ align:start position:0%
+d^2 okay so so today's lecture is still
+ 
+
+ align:start position:0%
+d^2 okay so so today's lecture is still
+about these limiting cases
+
+ align:start position:0%
+about these limiting cases
+ 
+
+ align:start position:0%
+about these limiting cases
+as I said
+
+ align:start position:0%
+as I said
+ 
+
+ align:start position:0%
+as I said
+the scientific problems illos
+
+ align:start position:0%
+the scientific problems illos
+ 
+
+ align:start position:0%
+the scientific problems illos
+problems uh especially these inverse
+
+ align:start position:0%
+problems uh especially these inverse
+ 
+
+ align:start position:0%
+problems uh especially these inverse
+problems give situations in which these
+
+ align:start position:0%
+problems give situations in which these
+ 
+
+ align:start position:0%
+problems give situations in which these
+limiting problems are really bad and you
+
+ align:start position:0%
+limiting problems are really bad and you
+ 
+
+ align:start position:0%
+limiting problems are really bad and you
+you don't get to the Limit you don't
+
+ align:start position:0%
+you don't get to the Limit you don't
+ 
+
+ align:start position:0%
+you don't get to the Limit you don't
+want to the whole point is to have a
+
+ align:start position:0%
+want to the whole point is to have a
+ 
+
+ align:start position:0%
+want to the whole point is to have a
+finite
+
+ align:start position:0%
+finite
+ 
+
+ align:start position:0%
+finite
+Alpha uh and but choosing that Alpha
+
+ align:start position:0%
+Alpha uh and but choosing that Alpha
+ 
+
+ align:start position:0%
+Alpha uh and but choosing that Alpha
+correctly is uh is the art let me just
+
+ align:start position:0%
+correctly is uh is the art let me just
+ 
+
+ align:start position:0%
+correctly is uh is the art let me just
+say why the why so I always I'm sort of
+
+ align:start position:0%
+say why the why so I always I'm sort of
+ 
+
+ align:start position:0%
+say why the why so I always I'm sort of
+anticipating what I'm not ready to do
+
+ align:start position:0%
+anticipating what I'm not ready to do
+ 
+
+ align:start position:0%
+anticipating what I'm not ready to do
+properly uh so I I'll say why a finite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha on
+
+ align:start position:0%
+Alpha on
+ 
+
+ align:start position:0%
+Alpha on
+Wednesday why
+
+ align:start position:0%
+Wednesday why
+ 
+
+ align:start position:0%
+Wednesday why
+because noisy data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh even at with because of the noise at
+
+ align:start position:0%
+uh even at with because of the noise at
+ 
+
+ align:start position:0%
+uh even at with because of the noise at
+best uh you is uh
+
+ align:start position:0%
+best uh you is uh
+ 
+
+ align:start position:0%
+best uh you is uh
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+determined because of the
+
+ align:start position:0%
+determined because of the
+ 
+
+ align:start position:0%
+determined because of the
+noise up to some order say order of
+
+ align:start position:0%
+noise up to some order say order of
+ 
+
+ align:start position:0%
+noise up to some order say order of
+let's some some small quantity Delta
+
+ align:start position:0%
+let's some some small quantity Delta
+ 
+
+ align:start position:0%
+let's some some small quantity Delta
+that measures the noise this is like a
+
+ align:start position:0%
+that measures the noise this is like a
+ 
+
+ align:start position:0%
+that measures the noise this is like a
+measure of the noise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then there's no reason to do what we did
+
+ align:start position:0%
+then there's no reason to do what we did
+ 
+
+ align:start position:0%
+then there's no reason to do what we did
+last time like forcing b equal D we
+
+ align:start position:0%
+last time like forcing b equal D we
+ 
+
+ align:start position:0%
+last time like forcing b equal D we
+don't there's no point in forcing bu
+
+ align:start position:0%
+don't there's no point in forcing bu
+ 
+
+ align:start position:0%
+don't there's no point in forcing bu
+equal D if that equation if the D in
+
+ align:start position:0%
+equal D if that equation if the D in
+ 
+
+ align:start position:0%
+equal D if that equation if the D in
+that equation has noise in
+
+ align:start position:0%
+that equation has noise in
+ 
+
+ align:start position:0%
+that equation has noise in
+it then uh pushing it all the way to the
+
+ align:start position:0%
+it then uh pushing it all the way to the
+ 
+
+ align:start position:0%
+it then uh pushing it all the way to the
+limit is uh
+
+ align:start position:0%
+limit is uh
+ 
+
+ align:start position:0%
+limit is uh
+unreasonable and may produce a
+
+ align:start position:0%
+unreasonable and may produce a
+ 
+
+ align:start position:0%
+unreasonable and may produce a
+very uh you know a catastrophic uh
+
+ align:start position:0%
+very uh you know a catastrophic uh
+ 
+
+ align:start position:0%
+very uh you know a catastrophic uh
+illness so uh that's when so it's really
+
+ align:start position:0%
+illness so uh that's when so it's really
+ 
+
+ align:start position:0%
+illness so uh that's when so it's really
+the presence of noise a presence of
+
+ align:start position:0%
+the presence of noise a presence of
+ 
+
+ align:start position:0%
+the presence of noise a presence of
+uncertainty in the first place that says
+
+ align:start position:0%
+uncertainty in the first place that says
+ 
+
+ align:start position:0%
+uncertainty in the first place that says
+Okay um a finite Alpha is fine you're
+
+ align:start position:0%
+Okay um a finite Alpha is fine you're
+ 
+
+ align:start position:0%
+Okay um a finite Alpha is fine you're
+not looking for Perfection what you're
+
+ align:start position:0%
+not looking for Perfection what you're
+ 
+
+ align:start position:0%
+not looking for Perfection what you're
+looking for is some St stability some
+
+ align:start position:0%
+looking for is some St stability some
+ 
+
+ align:start position:0%
+looking for is some St stability some
+control of of uh of on on the stability
+
+ align:start position:0%
+control of of uh of on on the stability
+ 
+
+ align:start position:0%
+control of of uh of on on the stability
+okay right but
+
+ align:start position:0%
+okay right but
+ 
+
+ align:start position:0%
+okay right but
+now so that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Wednesday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today uh let me go I didn't give an
+
+ align:start position:0%
+today uh let me go I didn't give an
+ 
+
+ align:start position:0%
+today uh let me go I didn't give an
+example so today two topics one is an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example with Buu equal D that was last
+
+ align:start position:0%
+example with Buu equal D that was last
+ 
+
+ align:start position:0%
+example with Buu equal D that was last
+lectures and that's the case when Alpha
+
+ align:start position:0%
+lectures and that's the case when Alpha
+ 
+
+ align:start position:0%
+lectures and that's the case when Alpha
+goes to
+
+ align:start position:0%
+goes to
+ 
+
+ align:start position:0%
+goes to
+infinity and then secondly is something
+
+ align:start position:0%
+infinity and then secondly is something
+ 
+
+ align:start position:0%
+infinity and then secondly is something
+called the pseudo inverse you may have
+
+ align:start position:0%
+called the pseudo inverse you may have
+ 
+
+ align:start position:0%
+called the pseudo inverse you may have
+seen that expression the pseudo inverse
+
+ align:start position:0%
+seen that expression the pseudo inverse
+ 
+
+ align:start position:0%
+seen that expression the pseudo inverse
+of a and sometimes it's written a with a
+
+ align:start position:0%
+of a and sometimes it's written a with a
+ 
+
+ align:start position:0%
+of a and sometimes it's written a with a
+dagger or a with a plus
+
+ align:start position:0%
+dagger or a with a plus
+ 
+
+ align:start position:0%
+dagger or a with a plus
+sign and and that is worth knowing about
+
+ align:start position:0%
+sign and and that is worth knowing about
+ 
+
+ align:start position:0%
+sign and and that is worth knowing about
+so this this is a topic in linear
+
+ align:start position:0%
+so this this is a topic in linear
+ 
+
+ align:start position:0%
+so this this is a topic in linear
+algebra it would be in my linear algebra
+
+ align:start position:0%
+algebra it would be in my linear algebra
+ 
+
+ align:start position:0%
+algebra it would be in my linear algebra
+book but it's a topic that never gets
+
+ align:start position:0%
+book but it's a topic that never gets
+ 
+
+ align:start position:0%
+book but it's a topic that never gets
+into the 1806 course CU it's sort of a
+
+ align:start position:0%
+into the 1806 course CU it's sort of a
+ 
+
+ align:start position:0%
+into the 1806 course CU it's sort of a
+little late and that will appear as
+
+ align:start position:0%
+little late and that will appear as
+ 
+
+ align:start position:0%
+little late and that will appear as
+Alpha goes to zero
+
+ align:start position:0%
+Alpha goes to zero
+ 
+
+ align:start position:0%
+Alpha goes to zero
+right so that's what today is about it's
+
+ align:start position:0%
+right so that's what today is about it's
+ 
+
+ align:start position:0%
+right so that's what today is about it's
+it's a it's linear algebra
+
+ align:start position:0%
+it's a it's linear algebra
+ 
+
+ align:start position:0%
+it's a it's linear algebra
+because I'm not ready for the noise yet
+
+ align:start position:0%
+because I'm not ready for the noise yet
+ 
+
+ align:start position:0%
+because I'm not ready for the noise yet
+but it's the noisy data that that uh
+
+ align:start position:0%
+but it's the noisy data that that uh
+ 
+
+ align:start position:0%
+but it's the noisy data that that uh
+that we have in reality and that's why
+
+ align:start position:0%
+that we have in reality and that's why
+ 
+
+ align:start position:0%
+that we have in reality and that's why
+in reality we Alpha will be chosen
+
+ align:start position:0%
+in reality we Alpha will be chosen
+ 
+
+ align:start position:0%
+in reality we Alpha will be chosen
+finite okay so part one then is to do a
+
+ align:start position:0%
+finite okay so part one then is to do a
+ 
+
+ align:start position:0%
+finite okay so part one then is to do a
+very simple example with bu equal D and
+
+ align:start position:0%
+very simple example with bu equal D and
+ 
+
+ align:start position:0%
+very simple example with bu equal D and
+here's the
+
+ align:start position:0%
+here's the
+ 
+
+ align:start position:0%
+here's the
+example okay so this is my sum of
+
+ align:start position:0%
+example okay so this is my sum of
+ 
+
+ align:start position:0%
+example okay so this is my sum of
+squares in which I plan to let Alpha go
+
+ align:start position:0%
+squares in which I plan to let Alpha go
+ 
+
+ align:start position:0%
+squares in which I plan to let Alpha go
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+Infinity so uh so there so a is the
+
+ align:start position:0%
+Infinity so uh so there so a is the
+ 
+
+ align:start position:0%
+Infinity so uh so there so a is the
+identity Matrix and B is zero so that
+
+ align:start position:0%
+identity Matrix and B is zero so that
+ 
+
+ align:start position:0%
+identity Matrix and B is zero so that
+quantity is
+
+ align:start position:0%
+quantity is
+ 
+
+ align:start position:0%
+quantity is
+simple here I have just one equation
+
+ align:start position:0%
+simple here I have just one equation
+ 
+
+ align:start position:0%
+simple here I have just one equation
+so p is 1 P by n is 1 by two I've just
+
+ align:start position:0%
+so p is 1 P by n is 1 by two I've just
+ 
+
+ align:start position:0%
+so p is 1 P by n is 1 by two I've just
+one equation U1 - U2 = 6 and in the
+
+ align:start position:0%
+one equation U1 - U2 = 6 and in the
+ 
+
+ align:start position:0%
+one equation U1 - U2 = 6 and in the
+limit as Alpha goes to Infinity I expect
+
+ align:start position:0%
+limit as Alpha goes to Infinity I expect
+ 
+
+ align:start position:0%
+limit as Alpha goes to Infinity I expect
+to see that that equation is
+
+ align:start position:0%
+to see that that equation is
+ 
+
+ align:start position:0%
+to see that that equation is
+enforced and uh my so there's two ways
+
+ align:start position:0%
+enforced and uh my so there's two ways
+ 
+
+ align:start position:0%
+enforced and uh my so there's two ways
+to do it we can let Alpha go to
+
+ align:start position:0%
+to do it we can let Alpha go to
+ 
+
+ align:start position:0%
+to do it we can let Alpha go to
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+and look at
+
+ align:start position:0%
+and look at
+ 
+
+ align:start position:0%
+and look at
+U Alpha going toward U Infinity maybe
+
+ align:start position:0%
+U Alpha going toward U Infinity maybe
+ 
+
+ align:start position:0%
+U Alpha going toward U Infinity maybe
+with their little
+
+ align:start position:0%
+with their little
+ 
+
+ align:start position:0%
+with their little
+hats or the second method which is the
+
+ align:start position:0%
+hats or the second method which is the
+ 
+
+ align:start position:0%
+hats or the second method which is the
+null space
+
+ align:start position:0%
+null space
+ 
+
+ align:start position:0%
+null space
+method which is what I spoke about last
+
+ align:start position:0%
+method which is what I spoke about last
+ 
+
+ align:start position:0%
+method which is what I spoke about last
+time the null space
+
+ align:start position:0%
+time the null space
+ 
+
+ align:start position:0%
+time the null space
+method solves the constraint bu equal D
+
+ align:start position:0%
+method solves the constraint bu equal D
+ 
+
+ align:start position:0%
+method solves the constraint bu equal D
+which is which is just U1 minus U2 =
+
+ align:start position:0%
+which is which is just U1 minus U2 =
+ 
+
+ align:start position:0%
+which is which is just U1 minus U2 =
+6 okay
+
+ align:start position:0%
+6 okay
+ 
+
+ align:start position:0%
+6 okay
+and that's maybe I'll start with that
+
+ align:start position:0%
+and that's maybe I'll start with that
+ 
+
+ align:start position:0%
+and that's maybe I'll start with that
+one which looks so simple of course just
+
+ align:start position:0%
+one which looks so simple of course just
+ 
+
+ align:start position:0%
+one which looks so simple of course just
+to solve U1 minus U2 = 6 I mean
+
+ align:start position:0%
+to solve U1 minus U2 = 6 I mean
+ 
+
+ align:start position:0%
+to solve U1 minus U2 = 6 I mean
+everybody would say Okay solve it for U2
+
+ align:start position:0%
+everybody would say Okay solve it for U2
+ 
+
+ align:start position:0%
+everybody would say Okay solve it for U2
+= U1 -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+6 so here's the here's the method any
+
+ align:start position:0%
+6 so here's the here's the method any
+ 
+
+ align:start position:0%
+6 so here's the here's the method any
+sensible person would
+
+ align:start position:0%
+sensible person would
+ 
+
+ align:start position:0%
+sensible person would
+use but this course doesn't Okay the the
+
+ align:start position:0%
+use but this course doesn't Okay the the
+ 
+
+ align:start position:0%
+use but this course doesn't Okay the the
+sensible method would be
+
+ align:start position:0%
+sensible method would be
+ 
+
+ align:start position:0%
+sensible method would be
+uh U2 is U1 -
+
+ align:start position:0%
+uh U2 is U1 -
+ 
+
+ align:start position:0%
+uh U2 is U1 -
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+plug that
+
+ align:start position:0%
+plug that
+ 
+
+ align:start position:0%
+plug that
+into the
+
+ align:start position:0%
+into the
+ 
+
+ align:start position:0%
+into the
+squares and
+
+ align:start position:0%
+squares and
+ 
+
+ align:start position:0%
+squares and
+minimize so when I plug this in of
+
+ align:start position:0%
+minimize so when I plug this in of
+ 
+
+ align:start position:0%
+minimize so when I plug this in of
+course this is
+
+ align:start position:0%
+course this is
+ 
+
+ align:start position:0%
+course this is
+exact and this becomes you so I'm
+
+ align:start position:0%
+exact and this becomes you so I'm
+ 
+
+ align:start position:0%
+exact and this becomes you so I'm
+minimizing minimizing U1 2
+
+ align:start position:0%
+minimizing minimizing U1 2
+ 
+
+ align:start position:0%
+minimizing minimizing U1 2
+plus what was it U1 - 6^
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 so that's reduced the
+
+ align:start position:0%
+2 so that's reduced the
+ 
+
+ align:start position:0%
+2 so that's reduced the
+problem to one unknown that's this is
+
+ align:start position:0%
+problem to one unknown that's this is
+ 
+
+ align:start position:0%
+problem to one unknown that's this is
+the null space method the null space
+
+ align:start position:0%
+the null space method the null space
+ 
+
+ align:start position:0%
+the null space method the null space
+method is solve the equation and remove
+
+ align:start position:0%
+method is solve the equation and remove
+ 
+
+ align:start position:0%
+method is solve the equation and remove
+unknowns remove P unknowns coming from
+
+ align:start position:0%
+unknowns remove P unknowns coming from
+ 
+
+ align:start position:0%
+unknowns remove P unknowns coming from
+the P constraints and here there's p is
+
+ align:start position:0%
+the P constraints and here there's p is
+ 
+
+ align:start position:0%
+the P constraints and here there's p is
+one okay and by the way can we just
+
+ align:start position:0%
+one okay and by the way can we just
+ 
+
+ align:start position:0%
+one okay and by the way can we just
+guess or not guess but pretty well be
+
+ align:start position:0%
+guess or not guess but pretty well be
+ 
+
+ align:start position:0%
+guess or not guess but pretty well be
+sure what's the what's the what's the
+
+ align:start position:0%
+sure what's the what's the what's the
+ 
+
+ align:start position:0%
+sure what's the what's the what's the
+minimizer
+
+ align:start position:0%
+minimizer
+ 
+
+ align:start position:0%
+minimizer
+here anybody just tell me what U1 would
+
+ align:start position:0%
+here anybody just tell me what U1 would
+ 
+
+ align:start position:0%
+here anybody just tell me what U1 would
+minimize that make just make a guess
+
+ align:start position:0%
+minimize that make just make a guess
+ 
+
+ align:start position:0%
+minimize that make just make a guess
+maybe uh I'm looking for a number sort
+
+ align:start position:0%
+maybe uh I'm looking for a number sort
+ 
+
+ align:start position:0%
+maybe uh I'm looking for a number sort
+of halfway between zero and six somehow
+
+ align:start position:0%
+of halfway between zero and six somehow
+ 
+
+ align:start position:0%
+of halfway between zero and six somehow
+you I mean you won't be surprised that
+
+ align:start position:0%
+you I mean you won't be surprised that
+ 
+
+ align:start position:0%
+you I mean you won't be surprised that
+that that the U1 is
+
+ align:start position:0%
+that that the U1 is
+ 
+
+ align:start position:0%
+that that the U1 is
+three and then from this equation
+
+ align:start position:0%
+three and then from this equation
+ 
+
+ align:start position:0%
+three and then from this equation
+I should learn that U2 is minus 3 U2 not
+
+ align:start position:0%
+I should learn that U2 is minus 3 U2 not
+ 
+
+ align:start position:0%
+I should learn that U2 is minus 3 U2 not
+yeah U2
+
+ align:start position:0%
+yeah U2
+ 
+
+ align:start position:0%
+yeah U2
+Infinity now I've got too many U to
+
+ align:start position:0%
+Infinity now I've got too many U to
+ 
+
+ align:start position:0%
+Infinity now I've got too many U to
+Infinity is minus 3
+
+ align:start position:0%
+Infinity is minus 3
+ 
+
+ align:start position:0%
+Infinity is minus 3
+anyway simple Calculus if you just set
+
+ align:start position:0%
+anyway simple Calculus if you just set
+ 
+
+ align:start position:0%
+anyway simple Calculus if you just set
+the derivative to zero you'll get three
+
+ align:start position:0%
+the derivative to zero you'll get three
+ 
+
+ align:start position:0%
+the derivative to zero you'll get three
+and then you get minus three for U2 so
+
+ align:start position:0%
+and then you get minus three for U2 so
+ 
+
+ align:start position:0%
+and then you get minus three for U2 so
+that's the null space method except it
+
+ align:start position:0%
+that's the null space method except it
+ 
+
+ align:start position:0%
+that's the null space method except it
+isn't I didn't follow my
+
+ align:start position:0%
+isn't I didn't follow my
+ 
+
+ align:start position:0%
+isn't I didn't follow my
+complicated uh QR
+
+ align:start position:0%
+complicated uh QR
+ 
+
+ align:start position:0%
+complicated uh QR
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+orthogonalization and I just want to do
+
+ align:start position:0%
+orthogonalization and I just want to do
+ 
+
+ align:start position:0%
+orthogonalization and I just want to do
+that quickly to reach the same
+
+ align:start position:0%
+that quickly to reach the same
+ 
+
+ align:start position:0%
+that quickly to reach the same
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+um and and to say why don't I just do
+
+ align:start position:0%
+um and and to say why don't I just do
+ 
+
+ align:start position:0%
+um and and to say why don't I just do
+this anyway this is what this would be
+
+ align:start position:0%
+this anyway this is what this would be
+ 
+
+ align:start position:0%
+this anyway this is what this would be
+the RO this would be the standard method
+
+ align:start position:0%
+the RO this would be the standard method
+ 
+
+ align:start position:0%
+the RO this would be the standard method
+in the first month of linear algebra
+
+ align:start position:0%
+in the first month of linear algebra
+ 
+
+ align:start position:0%
+in the first month of linear algebra
+would be to use the row reduced Echelon
+
+ align:start position:0%
+would be to use the row reduced Echelon
+ 
+
+ align:start position:0%
+would be to use the row reduced Echelon
+form which of course is going to be be
+
+ align:start position:0%
+form which of course is going to be be
+ 
+
+ align:start position:0%
+form which of course is going to be be
+really really simple for this Matrix in
+
+ align:start position:0%
+really really simple for this Matrix in
+ 
+
+ align:start position:0%
+really really simple for this Matrix in
+fact that's already in row reduced
+
+ align:start position:0%
+fact that's already in row reduced
+ 
+
+ align:start position:0%
+fact that's already in row reduced
+Echelon form okay elimination is row
+
+ align:start position:0%
+Echelon form okay elimination is row
+ 
+
+ align:start position:0%
+Echelon form okay elimination is row
+reduction has nothing to do to improve
+
+ align:start position:0%
+reduction has nothing to do to improve
+ 
+
+ align:start position:0%
+reduction has nothing to do to improve
+that and then solve and then plug in and
+
+ align:start position:0%
+that and then solve and then plug in and
+ 
+
+ align:start position:0%
+that and then solve and then plug in and
+go with it okay well the thing is that
+
+ align:start position:0%
+go with it okay well the thing is that
+ 
+
+ align:start position:0%
+go with it okay well the thing is that
+that row reduced Echelon form the stuff
+
+ align:start position:0%
+that row reduced Echelon form the stuff
+ 
+
+ align:start position:0%
+that row reduced Echelon form the stuff
+you teach is not for large systems uh
+
+ align:start position:0%
+you teach is not for large systems uh
+ 
+
+ align:start position:0%
+you teach is not for large systems uh
+guaranteed stable
+
+ align:start position:0%
+guaranteed stable
+ 
+
+ align:start position:0%
+guaranteed stable
+it's it's not numerically stable and the
+
+ align:start position:0%
+it's it's not numerically stable and the
+ 
+
+ align:start position:0%
+it's it's not numerically stable and the
+option of using of
+
+ align:start position:0%
+option of using of
+ 
+
+ align:start position:0%
+option of using of
+orthogonalizing is is the right one to
+
+ align:start position:0%
+orthogonalizing is is the right one to
+ 
+
+ align:start position:0%
+orthogonalizing is is the right one to
+know for a large system so so you you'll
+
+ align:start position:0%
+know for a large system so so you you'll
+ 
+
+ align:start position:0%
+know for a large system so so you you'll
+have to allow me on this really small
+
+ align:start position:0%
+have to allow me on this really small
+ 
+
+ align:start position:0%
+have to allow me on this really small
+example to
+
+ align:start position:0%
+example to
+ 
+
+ align:start position:0%
+example to
+use the method that I described last
+
+ align:start position:0%
+use the method that I described last
+ 
+
+ align:start position:0%
+use the method that I described last
+time and I just want to recap with an
+
+ align:start position:0%
+time and I just want to recap with an
+ 
+
+ align:start position:0%
+time and I just want to recap with an
+example uh on the small system okay so
+
+ align:start position:0%
+example uh on the small system okay so
+ 
+
+ align:start position:0%
+example uh on the small system okay so
+what was that method so this is the null
+
+ align:start position:0%
+what was that method so this is the null
+ 
+
+ align:start position:0%
+what was that method so this is the null
+space method using QR
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now the mat lab command QR so what did
+
+ align:start position:0%
+now the mat lab command QR so what did
+ 
+
+ align:start position:0%
+now the mat lab command QR so what did
+we QR of B Prime do you remember that we
+
+ align:start position:0%
+we QR of B Prime do you remember that we
+ 
+
+ align:start position:0%
+we QR of B Prime do you remember that we
+took the the that's the matlb
+
+ align:start position:0%
+took the the that's the matlb
+ 
+
+ align:start position:0%
+took the the that's the matlb
+command that eventually will or is
+
+ align:start position:0%
+command that eventually will or is
+ 
+
+ align:start position:0%
+command that eventually will or is
+actually already in the notes for this
+
+ align:start position:0%
+actually already in the notes for this
+ 
+
+ align:start position:0%
+actually already in the notes for this
+section and and those notes will get uh
+
+ align:start position:0%
+section and and those notes will get uh
+ 
+
+ align:start position:0%
+section and and those notes will get uh
+updated but that's step one in the
+
+ align:start position:0%
+updated but that's step one in the
+ 
+
+ align:start position:0%
+updated but that's step one in the
+nullspace method QR of B Prime and this
+
+ align:start position:0%
+nullspace method QR of B Prime and this
+ 
+
+ align:start position:0%
+nullspace method QR of B Prime and this
+gives me a chance to say what's up with
+
+ align:start position:0%
+gives me a chance to say what's up with
+ 
+
+ align:start position:0%
+gives me a chance to say what's up with
+this QR
+
+ align:start position:0%
+this QR
+ 
+
+ align:start position:0%
+this QR
+algorithm one I mean after Lu QR is the
+
+ align:start position:0%
+algorithm one I mean after Lu QR is the
+ 
+
+ align:start position:0%
+algorithm one I mean after Lu QR is the
+most important algorithm in matlb and uh
+
+ align:start position:0%
+most important algorithm in matlb and uh
+ 
+
+ align:start position:0%
+most important algorithm in matlb and uh
+so what does it do B Prime the transpose
+
+ align:start position:0%
+so what does it do B Prime the transpose
+ 
+
+ align:start position:0%
+so what does it do B Prime the transpose
+of B is just 1 minus one right
+
+ align:start position:0%
+of B is just 1 minus one right
+ 
+
+ align:start position:0%
+of B is just 1 minus one right
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now what does scram Schmid do to that uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix well the idea of Graham Schmid is
+
+ align:start position:0%
+Matrix well the idea of Graham Schmid is
+ 
+
+ align:start position:0%
+Matrix well the idea of Graham Schmid is
+to produce orthonormal
+
+ align:start position:0%
+to produce orthonormal
+ 
+
+ align:start position:0%
+to produce orthonormal
+columns so the most basic gram Schmid
+
+ align:start position:0%
+columns so the most basic gram Schmid
+ 
+
+ align:start position:0%
+columns so the most basic gram Schmid
+idea would say so what gr what would
+
+ align:start position:0%
+idea would say so what gr what would
+ 
+
+ align:start position:0%
+idea would say so what gr what would
+Graham and Schmidt say they'd say well
+
+ align:start position:0%
+Graham and Schmidt say they'd say well
+ 
+
+ align:start position:0%
+Graham and Schmidt say they'd say well
+we only have one column and all we have
+
+ align:start position:0%
+we only have one column and all we have
+ 
+
+ align:start position:0%
+we only have one column and all we have
+to do is normalize it so the the so
+
+ align:start position:0%
+to do is normalize it so the the so
+ 
+
+ align:start position:0%
+to do is normalize it so the the so
+Graham Schmid would produ would lead
+
+ align:start position:0%
+Graham Schmid would produ would lead
+ 
+
+ align:start position:0%
+Graham Schmid would produ would lead
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+produce uh the
+
+ align:start position:0%
+produce uh the
+ 
+
+ align:start position:0%
+produce uh the
+normalized thing
+
+ align:start position:0%
+normalized thing
+ 
+
+ align:start position:0%
+normalized thing
+times < TK of
+
+ align:start position:0%
+times < TK of
+ 
+
+ align:start position:0%
+times < TK of
+two that would be the Q and this would
+
+ align:start position:0%
+two that would be the Q and this would
+ 
+
+ align:start position:0%
+two that would be the Q and this would
+be the r one by one in Graham
+
+ align:start position:0%
+be the r one by one in Graham
+ 
+
+ align:start position:0%
+be the r one by one in Graham
+Schmid okay but the here's the point
+
+ align:start position:0%
+Schmid okay but the here's the point
+ 
+
+ align:start position:0%
+Schmid okay but the here's the point
+that that the QR
+
+ align:start position:0%
+that that the QR
+ 
+
+ align:start position:0%
+that that the QR
+algorithm in mat lab which no longer
+
+ align:start position:0%
+algorithm in mat lab which no longer
+ 
+
+ align:start position:0%
+algorithm in mat lab which no longer
+uses the gram Schmid idea instead uses a
+
+ align:start position:0%
+uses the gram Schmid idea instead uses a
+ 
+
+ align:start position:0%
+uses the gram Schmid idea instead uses a
+householder idea and one out one nice
+
+ align:start position:0%
+householder idea and one out one nice
+ 
+
+ align:start position:0%
+householder idea and one out one nice
+thing about
+
+ align:start position:0%
+thing about
+ 
+
+ align:start position:0%
+thing about
+this is that it produces not
+
+ align:start position:0%
+this is that it produces not
+ 
+
+ align:start position:0%
+this is that it produces not
+just this
+
+ align:start position:0%
+just this
+ 
+
+ align:start position:0%
+just this
+column but another one it produces a
+
+ align:start position:0%
+column but another one it produces a
+ 
+
+ align:start position:0%
+column but another one it produces a
+column for the of the of the it it
+
+ align:start position:0%
+column for the of the of the it it
+ 
+
+ align:start position:0%
+column for the of the of the it it
+completes the basis to a full
+
+ align:start position:0%
+completes the basis to a full
+ 
+
+ align:start position:0%
+completes the basis to a full
+orthonormal basis so it finds a second
+
+ align:start position:0%
+orthonormal basis so it finds a second
+ 
+
+ align:start position:0%
+orthonormal basis so it finds a second
+Vector so so ordinary Graham Schmidt was
+
+ align:start position:0%
+Vector so so ordinary Graham Schmidt was
+ 
+
+ align:start position:0%
+Vector so so ordinary Graham Schmidt was
+just had one column times one number
+
+ align:start position:0%
+just had one column times one number
+ 
+
+ align:start position:0%
+just had one column times one number
+what QR actually does is ends up with
+
+ align:start position:0%
+what QR actually does is ends up with
+ 
+
+ align:start position:0%
+what QR actually does is ends up with
+two columns and what well everybody can
+
+ align:start position:0%
+two columns and what well everybody can
+ 
+
+ align:start position:0%
+two columns and what well everybody can
+see what the other column in
+
+ align:start position:0%
+see what the other column in
+ 
+
+ align:start position:0%
+see what the other column in
+uh that's that has length one of course
+
+ align:start position:0%
+uh that's that has length one of course
+ 
+
+ align:start position:0%
+uh that's that has length one of course
+and is orthogonal to the First Column
+
+ align:start position:0%
+and is orthogonal to the First Column
+ 
+
+ align:start position:0%
+and is orthogonal to the First Column
+and now that is multiplied
+
+ align:start position:0%
+and now that is multiplied
+ 
+
+ align:start position:0%
+and now that is multiplied
+by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero so this is what QR does
+
+ align:start position:0%
+zero so this is what QR does
+ 
+
+ align:start position:0%
+zero so this is what QR does
+it we we have this 2x1 Matrix It
+
+ align:start position:0%
+it we we have this 2x1 Matrix It
+ 
+
+ align:start position:0%
+it we we have this 2x1 Matrix It
+produces a 2x2 * a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2x1 and you may say it was wasting its
+
+ align:start position:0%
+2x1 and you may say it was wasting its
+ 
+
+ align:start position:0%
+2x1 and you may say it was wasting its
+time because to to find this part
+
+ align:start position:0%
+time because to to find this part
+ 
+
+ align:start position:0%
+time because to to find this part
+because it's multiplied by
+
+ align:start position:0%
+because it's multiplied by
+ 
+
+ align:start position:0%
+because it's multiplied by
+zero but uh but what is what are we
+
+ align:start position:0%
+zero but uh but what is what are we
+ 
+
+ align:start position:0%
+zero but uh but what is what are we
+learning from this Vector from this one
+
+ align:start position:0%
+learning from this Vector from this one
+ 
+
+ align:start position:0%
+learning from this Vector from this one
+one vector or one 1 /un of 2 1un two
+
+ align:start position:0%
+one vector or one 1 /un of 2 1un two
+ 
+
+ align:start position:0%
+one vector or one 1 /un of 2 1un two
+Vector what what good can that do
+
+ align:start position:0%
+Vector what what good can that do
+ 
+
+ align:start position:0%
+Vector what what good can that do
+us it's the null
+
+ align:start position:0%
+us it's the null
+ 
+
+ align:start position:0%
+us it's the null
+space of B so B was 1 minus one so let
+
+ align:start position:0%
+space of B so B was 1 minus one so let
+ 
+
+ align:start position:0%
+space of B so B was 1 minus one so let
+me just so that's the connection with
+
+ align:start position:0%
+me just so that's the connection with
+ 
+
+ align:start position:0%
+me just so that's the connection with
+the null space no space of B if I look
+
+ align:start position:0%
+the null space no space of B if I look
+ 
+
+ align:start position:0%
+the null space no space of B if I look
+to if I look at vectors if there's my
+
+ align:start position:0%
+to if I look at vectors if there's my
+ 
+
+ align:start position:0%
+to if I look at vectors if there's my
+Matrix B and if I'm solving bual D see
+
+ align:start position:0%
+Matrix B and if I'm solving bual D see
+ 
+
+ align:start position:0%
+Matrix B and if I'm solving bual D see
+if I'm solving bu equal d
+
+ align:start position:0%
+if I'm solving bu equal d
+ 
+
+ align:start position:0%
+if I'm solving bu equal d
+then U is U
+
+ align:start position:0%
+then U is U
+ 
+
+ align:start position:0%
+then U is U
+particular and u n space and if I want
+
+ align:start position:0%
+particular and u n space and if I want
+ 
+
+ align:start position:0%
+particular and u n space and if I want
+you null space then that's where this
+
+ align:start position:0%
+you null space then that's where this
+ 
+
+ align:start position:0%
+you null space then that's where this
+and these whatever extra columns this
+
+ align:start position:0%
+and these whatever extra columns this
+ 
+
+ align:start position:0%
+and these whatever extra columns this
+might be P columns and then this would
+
+ align:start position:0%
+might be P columns and then this would
+ 
+
+ align:start position:0%
+might be P columns and then this would
+be n minus P columns that's what that's
+
+ align:start position:0%
+be n minus P columns that's what that's
+ 
+
+ align:start position:0%
+be n minus P columns that's what that's
+good for and of course that column is
+
+ align:start position:0%
+good for and of course that column is
+ 
+
+ align:start position:0%
+good for and of course that column is
+tells me about the null space which for
+
+ align:start position:0%
+tells me about the null space which for
+ 
+
+ align:start position:0%
+tells me about the null space which for
+this Matrix
+
+ align:start position:0%
+this Matrix
+ 
+
+ align:start position:0%
+this Matrix
+is one dimension
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and easy to find okay okay so that that
+
+ align:start position:0%
+and easy to find okay okay so that that
+ 
+
+ align:start position:0%
+and easy to find okay okay so that that
+maybe just to so you know the the
+
+ align:start position:0%
+maybe just to so you know the the
+ 
+
+ align:start position:0%
+maybe just to so you know the the
+difference between Graham Schmidt's QR
+
+ align:start position:0%
+difference between Graham Schmidt's QR
+ 
+
+ align:start position:0%
+difference between Graham Schmidt's QR
+which stops with if you had one column
+
+ align:start position:0%
+which stops with if you had one column
+ 
+
+ align:start position:0%
+which stops with if you had one column
+you end with one column and the mat lab
+
+ align:start position:0%
+you end with one column and the mat lab
+ 
+
+ align:start position:0%
+you end with one column and the mat lab
+householder QR which finds a full Square
+
+ align:start position:0%
+householder QR which finds a full Square
+ 
+
+ align:start position:0%
+householder QR which finds a full Square
+Matrix okay good just good to know and
+
+ align:start position:0%
+Matrix okay good just good to know and
+ 
+
+ align:start position:0%
+Matrix okay good just good to know and
+here we found a use for it
+
+ align:start position:0%
+here we found a use for it
+ 
+
+ align:start position:0%
+here we found a use for it
+okay so then uh um the algorithm that I
+
+ align:start position:0%
+okay so then uh um the algorithm that I
+ 
+
+ align:start position:0%
+okay so then uh um the algorithm that I
+gave last time and I'll give the code in
+
+ align:start position:0%
+gave last time and I'll give the code in
+ 
+
+ align:start position:0%
+gave last time and I'll give the code in
+the notes uh goes through the steps of
+
+ align:start position:0%
+the notes uh goes through the steps of
+ 
+
+ align:start position:0%
+the notes uh goes through the steps of
+finding a u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particular and actually the U particular
+
+ align:start position:0%
+particular and actually the U particular
+ 
+
+ align:start position:0%
+particular and actually the U particular
+that it would find if I is happens to be
+
+ align:start position:0%
+that it would find if I is happens to be
+ 
+
+ align:start position:0%
+that it would find if I is happens to be
+3us
+
+ align:start position:0%
+3us
+ 
+
+ align:start position:0%
+3us
+3 happens to be the actual winner
+
+ align:start position:0%
+3 happens to be the actual winner
+ 
+
+ align:start position:0%
+3 happens to be the actual winner
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the therefore the you no space that that
+
+ align:start position:0%
+the therefore the you no space that that
+ 
+
+ align:start position:0%
+the therefore the you no space that that
+algorithm would find if I if I went
+
+ align:start position:0%
+algorithm would find if I if I went
+ 
+
+ align:start position:0%
+algorithm would find if I if I went
+through all the steps you would see that
+
+ align:start position:0%
+through all the steps you would see that
+ 
+
+ align:start position:0%
+through all the steps you would see that
+because I'm in this very I'm in this
+
+ align:start position:0%
+because I'm in this very I'm in this
+ 
+
+ align:start position:0%
+because I'm in this very I'm in this
+special case of B being zero and so on
+
+ align:start position:0%
+special case of B being zero and so on
+ 
+
+ align:start position:0%
+special case of B being zero and so on
+that the the the vector that it would
+
+ align:start position:0%
+that the the the vector that it would
+ 
+
+ align:start position:0%
+that the the the vector that it would
+choose this is the basis for the null
+
+ align:start position:0%
+choose this is the basis for the null
+ 
+
+ align:start position:0%
+choose this is the basis for the null
+space but it would chose zero of that of
+
+ align:start position:0%
+space but it would chose zero of that of
+ 
+
+ align:start position:0%
+space but it would chose zero of that of
+that basis vector and would come up for
+
+ align:start position:0%
+that basis vector and would come up for
+ 
+
+ align:start position:0%
+that basis vector and would come up for
+that answer okay so that's what the
+
+ align:start position:0%
+that answer okay so that's what the
+ 
+
+ align:start position:0%
+that answer okay so that's what the
+algorithm from last time would have done
+
+ align:start position:0%
+algorithm from last time would have done
+ 
+
+ align:start position:0%
+algorithm from last time would have done
+um to this
+
+ align:start position:0%
+um to this
+ 
+
+ align:start position:0%
+um to this
+problem uh I I also over the weekend uh
+
+ align:start position:0%
+problem uh I I also over the weekend uh
+ 
+
+ align:start position:0%
+problem uh I I also over the weekend uh
+thought okay if it's all
+
+ align:start position:0%
+thought okay if it's all
+ 
+
+ align:start position:0%
+thought okay if it's all
+true I should be able to
+
+ align:start position:0%
+true I should be able to
+ 
+
+ align:start position:0%
+true I should be able to
+to to use my first method the large
+
+ align:start position:0%
+to to use my first method the large
+ 
+
+ align:start position:0%
+to to use my first method the large
+Alpha method and just find the answer to
+
+ align:start position:0%
+Alpha method and just find the answer to
+ 
+
+ align:start position:0%
+Alpha method and just find the answer to
+the original problem and let Alpha go to
+
+ align:start position:0%
+the original problem and let Alpha go to
+ 
+
+ align:start position:0%
+the original problem and let Alpha go to
+Infinity are are you willing to do that
+
+ align:start position:0%
+Infinity are are you willing to do that
+ 
+
+ align:start position:0%
+Infinity are are you willing to do that
+that might take a little more
+
+ align:start position:0%
+that might take a little more
+ 
+
+ align:start position:0%
+that might take a little more
+calculation but let me let me try that
+
+ align:start position:0%
+calculation but let me let me try that
+ 
+
+ align:start position:0%
+calculation but let me let me try that
+I'm hoping you know it it approaches
+
+ align:start position:0%
+I'm hoping you know it it approaches
+ 
+
+ align:start position:0%
+I'm hoping you know it it approaches
+this answer this is the answer I'm I'm
+
+ align:start position:0%
+this answer this is the answer I'm I'm
+ 
+
+ align:start position:0%
+this answer this is the answer I'm I'm
+looking for okay so okay your mind
+
+ align:start position:0%
+looking for okay so okay your mind
+ 
+
+ align:start position:0%
+looking for okay so okay your mind
+just suppose I had to
+
+ align:start position:0%
+just suppose I had to
+ 
+
+ align:start position:0%
+just suppose I had to
+uh do that
+
+ align:start position:0%
+uh do that
+ 
+
+ align:start position:0%
+uh do that
+minimization again now I'm not using the
+
+ align:start position:0%
+minimization again now I'm not using the
+ 
+
+ align:start position:0%
+minimization again now I'm not using the
+null space method so I'm not reducing
+
+ align:start position:0%
+null space method so I'm not reducing
+ 
+
+ align:start position:0%
+null space method so I'm not reducing
+I'm not not getting U2 out of the
+
+ align:start position:0%
+I'm not not getting U2 out of the
+ 
+
+ align:start position:0%
+I'm not not getting U2 out of the
+problem I'm not I'm I'm I'm
+
+ align:start position:0%
+problem I'm not I'm I'm I'm
+ 
+
+ align:start position:0%
+problem I'm not I'm I'm I'm
+uh doing the minimum as it stands and so
+
+ align:start position:0%
+uh doing the minimum as it stands and so
+ 
+
+ align:start position:0%
+uh doing the minimum as it stands and so
+what do I get well I've got two
+
+ align:start position:0%
+what do I get well I've got two
+ 
+
+ align:start position:0%
+what do I get well I've got two
+variables U1 and U2 so I take the
+
+ align:start position:0%
+variables U1 and U2 so I take the
+ 
+
+ align:start position:0%
+variables U1 and U2 so I take the
+derivatives with respect to U1 I I'm
+
+ align:start position:0%
+derivatives with respect to U1 I I'm
+ 
+
+ align:start position:0%
+derivatives with respect to U1 I I'm
+minimizing everybody when I point I'm
+
+ align:start position:0%
+minimizing everybody when I point I'm
+ 
+
+ align:start position:0%
+minimizing everybody when I point I'm
+pointing at that Top Line so it's 2
+
+ align:start position:0%
+pointing at that Top Line so it's 2
+ 
+
+ align:start position:0%
+pointing at that Top Line so it's 2
+U1 and what do I have here two alpha
+
+ align:start position:0%
+U1 and what do I have here two alpha
+ 
+
+ align:start position:0%
+U1 and what do I have here two alpha
+U1 - U2 - 6 is that the equaling zero is
+
+ align:start position:0%
+U1 - U2 - 6 is that the equaling zero is
+ 
+
+ align:start position:0%
+U1 - U2 - 6 is that the equaling zero is
+that did I take the U1 derivative
+
+ align:start position:0%
+that did I take the U1 derivative
+ 
+
+ align:start position:0%
+that did I take the U1 derivative
+correctly now if I take the U2
+
+ align:start position:0%
+correctly now if I take the U2
+ 
+
+ align:start position:0%
+correctly now if I take the U2
+derivative I get two
+
+ align:start position:0%
+derivative I get two
+ 
+
+ align:start position:0%
+derivative I get two
+u2s and now the chain rule is going to
+
+ align:start position:0%
+u2s and now the chain rule is going to
+ 
+
+ align:start position:0%
+u2s and now the chain rule is going to
+give me a minus sign so it would be a
+
+ align:start position:0%
+give me a minus sign so it would be a
+ 
+
+ align:start position:0%
+give me a minus sign so it would be a
+minus 2 Alpha U1 - U2 - 6 = 0 so those
+
+ align:start position:0%
+minus 2 Alpha U1 - U2 - 6 = 0 so those
+ 
+
+ align:start position:0%
+minus 2 Alpha U1 - U2 - 6 = 0 so those
+two equations will determine U1 and U2
+
+ align:start position:0%
+two equations will determine U1 and U2
+ 
+
+ align:start position:0%
+two equations will determine U1 and U2
+for a finite Alpha
+
+ align:start position:0%
+for a finite Alpha
+ 
+
+ align:start position:0%
+for a finite Alpha
+and then I'll let Alpha head to infinity
+
+ align:start position:0%
+and then I'll let Alpha head to infinity
+ 
+
+ align:start position:0%
+and then I'll let Alpha head to infinity
+and see what happens okay first I'll
+
+ align:start position:0%
+and see what happens okay first I'll
+ 
+
+ align:start position:0%
+and see what happens okay first I'll
+multiply by a half and get rid of those
+
+ align:start position:0%
+multiply by a half and get rid of those
+ 
+
+ align:start position:0%
+multiply by a half and get rid of those
+useless twos and then uh
+
+ align:start position:0%
+useless twos and then uh
+ 
+
+ align:start position:0%
+useless twos and then uh
+solve this equation okay so so what do I
+
+ align:start position:0%
+solve this equation okay so so what do I
+ 
+
+ align:start position:0%
+solve this equation okay so so what do I
+have here I've got a
+
+ align:start position:0%
+have here I've got a
+ 
+
+ align:start position:0%
+have here I've got a
+matrix uh U1 is multiplying 1 + Alpha U2
+
+ align:start position:0%
+matrix uh U1 is multiplying 1 + Alpha U2
+ 
+
+ align:start position:0%
+matrix uh U1 is multiplying 1 + Alpha U2
+has a minus
+
+ align:start position:0%
+has a minus
+ 
+
+ align:start position:0%
+has a minus
+Alpha in this line U1 has a minus Alpha
+
+ align:start position:0%
+Alpha in this line U1 has a minus Alpha
+ 
+
+ align:start position:0%
+Alpha in this line U1 has a minus Alpha
+U2 has a
+
+ align:start position:0%
+U2 has a
+ 
+
+ align:start position:0%
+U2 has a
+1 minus - plus Alpha is that am I right
+
+ align:start position:0%
+1 minus - plus Alpha is that am I right
+ 
+
+ align:start position:0%
+1 minus - plus Alpha is that am I right
+times U1
+
+ align:start position:0%
+times U1
+ 
+
+ align:start position:0%
+times U1
+U2 equals what's my right hand side I
+
+ align:start position:0%
+U2 equals what's my right hand side I
+ 
+
+ align:start position:0%
+U2 equals what's my right hand side I
+guess the right hand side has Alphas in
+
+ align:start position:0%
+guess the right hand side has Alphas in
+ 
+
+ align:start position:0%
+guess the right hand side has Alphas in
+it 6
+
+ align:start position:0%
+it 6
+ 
+
+ align:start position:0%
+it 6
+Alpha and minus 6 Alpha I think
+
+ align:start position:0%
+Alpha and minus 6 Alpha I think
+ 
+
+ align:start position:0%
+Alpha and minus 6 Alpha I think
+okay okay two equations two unknown
+
+ align:start position:0%
+okay okay two equations two unknown
+ 
+
+ align:start position:0%
+okay okay two equations two unknown
+that's what that these are the normal
+
+ align:start position:0%
+that's what that these are the normal
+ 
+
+ align:start position:0%
+that's what that these are the normal
+equations for this problem uh written
+
+ align:start position:0%
+equations for this problem uh written
+ 
+
+ align:start position:0%
+equations for this problem uh written
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+explicitly and probably I can find the
+
+ align:start position:0%
+explicitly and probably I can find the
+ 
+
+ align:start position:0%
+explicitly and probably I can find the
+solution and let Alpha go to
+
+ align:start position:0%
+solution and let Alpha go to
+ 
+
+ align:start position:0%
+solution and let Alpha go to
+Infinity you're going to say what are
+
+ align:start position:0%
+Infinity you're going to say what are
+ 
+
+ align:start position:0%
+Infinity you're going to say what are
+you doing PR Strang this this uh
+
+ align:start position:0%
+you doing PR Strang this this uh
+ 
+
+ align:start position:0%
+you doing PR Strang this this uh
+Elementary calculation but there's
+
+ align:start position:0%
+Elementary calculation but there's
+ 
+
+ align:start position:0%
+Elementary calculation but there's
+something sort of satisfying about
+
+ align:start position:0%
+something sort of satisfying about
+ 
+
+ align:start position:0%
+something sort of satisfying about
+seeing a small example actually work at
+
+ align:start position:0%
+seeing a small example actually work at
+ 
+
+ align:start position:0%
+seeing a small example actually work at
+least to me okay so how do I solve those
+
+ align:start position:0%
+least to me okay so how do I solve those
+ 
+
+ align:start position:0%
+least to me okay so how do I solve those
+equations
+
+ align:start position:0%
+equations
+ 
+
+ align:start position:0%
+equations
+well good
+
+ align:start position:0%
+well good
+ 
+
+ align:start position:0%
+well good
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+um should I with a 2X two Matrix can I
+
+ align:start position:0%
+um should I with a 2X two Matrix can I
+ 
+
+ align:start position:0%
+um should I with a 2X two Matrix can I
+do the unforgivable and actually find
+
+ align:start position:0%
+do the unforgivable and actually find
+ 
+
+ align:start position:0%
+do the unforgivable and actually find
+its inverse I mean it's like not allowed
+
+ align:start position:0%
+its inverse I mean it's like not allowed
+ 
+
+ align:start position:0%
+its inverse I mean it's like not allowed
+in in true linear algebra to find the
+
+ align:start position:0%
+in in true linear algebra to find the
+ 
+
+ align:start position:0%
+in in true linear algebra to find the
+inverse but maybe we could do it here uh
+
+ align:start position:0%
+inverse but maybe we could do it here uh
+ 
+
+ align:start position:0%
+inverse but maybe we could do it here uh
+so U1
+
+ align:start position:0%
+so U1
+ 
+
+ align:start position:0%
+so U1
+U2 is going to be the inverse Matrix
+
+ align:start position:0%
+U2 is going to be the inverse Matrix
+ 
+
+ align:start position:0%
+U2 is going to be the inverse Matrix
+which is so my little recipe for finding
+
+ align:start position:0%
+which is so my little recipe for finding
+ 
+
+ align:start position:0%
+which is so my little recipe for finding
+inverses is take the entries this entry
+
+ align:start position:0%
+inverses is take the entries this entry
+ 
+
+ align:start position:0%
+inverses is take the entries this entry
+goes up is up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here that entry goes down there well
+
+ align:start position:0%
+here that entry goes down there well
+ 
+
+ align:start position:0%
+here that entry goes down there well
+couldn't see the difference this entry
+
+ align:start position:0%
+couldn't see the difference this entry
+ 
+
+ align:start position:0%
+couldn't see the difference this entry
+stays the same but CH stays in place
+
+ align:start position:0%
+stays the same but CH stays in place
+ 
+
+ align:start position:0%
+stays the same but CH stays in place
+those change sign and then I have to
+
+ align:start position:0%
+those change sign and then I have to
+ 
+
+ align:start position:0%
+those change sign and then I have to
+divide by the determinant so what was
+
+ align:start position:0%
+divide by the determinant so what was
+ 
+
+ align:start position:0%
+divide by the determinant so what was
+the determinant of this 1+ 2 Alpha +
+
+ align:start position:0%
+the determinant of this 1+ 2 Alpha +
+ 
+
+ align:start position:0%
+the determinant of this 1+ 2 Alpha +
+Alpha 2 - Alpha 2 I get 1 + 2 Alpha and
+
+ align:start position:0%
+Alpha 2 - Alpha 2 I get 1 + 2 Alpha and
+ 
+
+ align:start position:0%
+Alpha 2 - Alpha 2 I get 1 + 2 Alpha and
+that's the inverse Matrix now that's
+
+ align:start position:0%
+that's the inverse Matrix now that's
+ 
+
+ align:start position:0%
+that's the inverse Matrix now that's
+multiplying 6 Alpha and - 6 Alpha okay
+
+ align:start position:0%
+multiplying 6 Alpha and - 6 Alpha okay
+ 
+
+ align:start position:0%
+multiplying 6 Alpha and - 6 Alpha okay
+and if I can do that
+
+ align:start position:0%
+and if I can do that
+ 
+
+ align:start position:0%
+and if I can do that
+multiplication I have well there's this
+
+ align:start position:0%
+multiplication I have well there's this
+ 
+
+ align:start position:0%
+multiplication I have well there's this
+Factor 1 over 1 + 2 Alpha and what do I
+
+ align:start position:0%
+Factor 1 over 1 + 2 Alpha and what do I
+ 
+
+ align:start position:0%
+Factor 1 over 1 + 2 Alpha and what do I
+have 6 Alpha 6 Alpha SAR - 6 Alpha squ I
+
+ align:start position:0%
+have 6 Alpha 6 Alpha SAR - 6 Alpha squ I
+ 
+
+ align:start position:0%
+have 6 Alpha 6 Alpha SAR - 6 Alpha squ I
+think 6
+
+ align:start position:0%
+think 6
+ 
+
+ align:start position:0%
+think 6
+Alpha 6 Alpha 2 - 6 Alpha 2 plus - 6
+
+ align:start position:0%
+Alpha 6 Alpha 2 - 6 Alpha 2 plus - 6
+ 
+
+ align:start position:0%
+Alpha 6 Alpha 2 - 6 Alpha 2 plus - 6
+Alpha I think it's that - 6
+
+ align:start position:0%
+Alpha I think it's that - 6
+ 
+
+ align:start position:0%
+Alpha I think it's that - 6
+Alpha
+
+ align:start position:0%
+Alpha
+ 
+
+ align:start position:0%
+Alpha
+and ready for the great moment let Alpha
+
+ align:start position:0%
+and ready for the great moment let Alpha
+ 
+
+ align:start position:0%
+and ready for the great moment let Alpha
+go
+
+ align:start position:0%
+go
+ 
+
+ align:start position:0%
+go
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+infinity and what do I get as Alpha goes
+
+ align:start position:0%
+infinity and what do I get as Alpha goes
+ 
+
+ align:start position:0%
+infinity and what do I get as Alpha goes
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+Infinity
+
+ align:start position:0%
+Infinity
+ 
+
+ align:start position:0%
+Infinity
+um the the the one becomes insignificant
+
+ align:start position:0%
+um the the the one becomes insignificant
+ 
+
+ align:start position:0%
+um the the the one becomes insignificant
+the alpha cancels the alpha so that's
+
+ align:start position:0%
+the alpha cancels the alpha so that's
+ 
+
+ align:start position:0%
+the alpha cancels the alpha so that's
+approaches 3 - 3
+
+ align:start position:0%
+approaches 3 - 3
+ 
+
+ align:start position:0%
+approaches 3 - 3
+okay so there you see the large Alpha
+
+ align:start position:0%
+okay so there you see the large Alpha
+ 
+
+ align:start position:0%
+okay so there you see the large Alpha
+method in in practice okay and you see
+
+ align:start position:0%
+method in in practice okay and you see
+ 
+
+ align:start position:0%
+method in in practice okay and you see
+what uh
+
+ align:start position:0%
+what uh
+ 
+
+ align:start position:0%
+what uh
+well there's something quite important
+
+ align:start position:0%
+well there's something quite important
+ 
+
+ align:start position:0%
+well there's something quite important
+here something quite important and it's
+
+ align:start position:0%
+here something quite important and it's
+ 
+
+ align:start position:0%
+here something quite important and it's
+connected with the pseudo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse the pseudo
+
+ align:start position:0%
+inverse the pseudo
+ 
+
+ align:start position:0%
+inverse the pseudo
+inverse so now I I want to we got this
+
+ align:start position:0%
+inverse so now I I want to we got this
+ 
+
+ align:start position:0%
+inverse so now I I want to we got this
+answer and what I want to say is that
+
+ align:start position:0%
+answer and what I want to say is that
+ 
+
+ align:start position:0%
+answer and what I want to say is that
+the that the uh Alpha the limiting Alpha
+
+ align:start position:0%
+the that the uh Alpha the limiting Alpha
+ 
+
+ align:start position:0%
+the that the uh Alpha the limiting Alpha
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+has produced the pseudo
+
+ align:start position:0%
+has produced the pseudo
+ 
+
+ align:start position:0%
+has produced the pseudo
+inverse so what so now I have to tell
+
+ align:start position:0%
+inverse so what so now I have to tell
+ 
+
+ align:start position:0%
+inverse so what so now I have to tell
+you about the pseudo inverse and what it
+
+ align:start position:0%
+you about the pseudo inverse and what it
+ 
+
+ align:start position:0%
+you about the pseudo inverse and what it
+means and basically the essential thing
+
+ align:start position:0%
+means and basically the essential thing
+ 
+
+ align:start position:0%
+means and basically the essential thing
+that it means
+
+ align:start position:0%
+that it means
+ 
+
+ align:start position:0%
+that it means
+is the pseudo inverse is gives the
+
+ align:start position:0%
+is the pseudo inverse is gives the
+ 
+
+ align:start position:0%
+is the pseudo inverse is gives the
+solution U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which has no npace
+
+ align:start position:0%
+which has no npace
+ 
+
+ align:start position:0%
+which has no npace
+component that's what the pseudo inverse
+
+ align:start position:0%
+component that's what the pseudo inverse
+ 
+
+ align:start position:0%
+component that's what the pseudo inverse
+is about and I'll draw a picture to say
+
+ align:start position:0%
+is about and I'll draw a picture to say
+ 
+
+ align:start position:0%
+is about and I'll draw a picture to say
+what I'm saying but it's this fact mean
+
+ align:start position:0%
+what I'm saying but it's this fact mean
+ 
+
+ align:start position:0%
+what I'm saying but it's this fact mean
+means that this part which was this
+
+ align:start position:0%
+means that this part which was this
+ 
+
+ align:start position:0%
+means that this part which was this
+number is
+
+ align:start position:0%
+number is
+ 
+
+ align:start position:0%
+number is
+the is the is the output this is this is
+
+ align:start position:0%
+the is the is the output this is this is
+ 
+
+ align:start position:0%
+the is the is the output this is this is
+the pseudo inverse of V applied to 66
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you you see the point B hasn't got an
+
+ align:start position:0%
+you you see the point B hasn't got an
+ 
+
+ align:start position:0%
+you you see the point B hasn't got an
+inverse B is 1 minus
+
+ align:start position:0%
+inverse B is 1 minus
+ 
+
+ align:start position:0%
+inverse B is 1 minus
+one it's a rectangular
+
+ align:start position:0%
+one it's a rectangular
+ 
+
+ align:start position:0%
+one it's a rectangular
+Matrix and uh it's
+
+ align:start position:0%
+Matrix and uh it's
+ 
+
+ align:start position:0%
+Matrix and uh it's
+uh uh it's not invertible in the normal
+
+ align:start position:0%
+uh uh it's not invertible in the normal
+ 
+
+ align:start position:0%
+uh uh it's not invertible in the normal
+sense I can't find a two-sided inverse a
+
+ align:start position:0%
+sense I can't find a two-sided inverse a
+ 
+
+ align:start position:0%
+sense I can't find a two-sided inverse a
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+inverse doesn't exist
+
+ align:start position:0%
+inverse doesn't exist
+ 
+
+ align:start position:0%
+inverse doesn't exist
+but a pseudo inverse counts so so just
+
+ align:start position:0%
+but a pseudo inverse counts so so just
+ 
+
+ align:start position:0%
+but a pseudo inverse counts so so just
+to give the mat matlb as long as I've
+
+ align:start position:0%
+to give the mat matlb as long as I've
+ 
+
+ align:start position:0%
+to give the mat matlb as long as I've
+written a Matlab command here why don't
+
+ align:start position:0%
+written a Matlab command here why don't
+ 
+
+ align:start position:0%
+written a Matlab command here why don't
+I write the mat the other matlb command
+
+ align:start position:0%
+I write the mat the other matlb command
+ 
+
+ align:start position:0%
+I write the mat the other matlb command
+uh U is the pseudo
+
+ align:start position:0%
+uh U is the pseudo
+ 
+
+ align:start position:0%
+uh U is the pseudo
+inverse you remember that pseudo starts
+
+ align:start position:0%
+inverse you remember that pseudo starts
+ 
+
+ align:start position:0%
+inverse you remember that pseudo starts
+with the letter P so p i
+
+ align:start position:0%
+with the letter P so p i
+ 
+
+ align:start position:0%
+with the letter P so p i
+NV of
+
+ align:start position:0%
+NV of
+ 
+
+ align:start position:0%
+NV of
+B multiplying
+
+ align:start position:0%
+B multiplying
+ 
+
+ align:start position:0%
+B multiplying
+d That's the
+
+ align:start position:0%
+d That's the
+ 
+
+ align:start position:0%
+d That's the
+that's the that that's what we got
+
+ align:start position:0%
+that's the that that's what we got
+ 
+
+ align:start position:0%
+that's the that that's what we got
+automatically and it's what we get and
+
+ align:start position:0%
+automatically and it's what we get and
+ 
+
+ align:start position:0%
+automatically and it's what we get and
+the reason we got the pseudo
+
+ align:start position:0%
+the reason we got the pseudo
+ 
+
+ align:start position:0%
+the reason we got the pseudo
+inverse so let me just say what was
+
+ align:start position:0%
+inverse so let me just say what was
+ 
+
+ align:start position:0%
+inverse so let me just say what was
+special here what was special that
+
+ align:start position:0%
+special here what was special that
+ 
+
+ align:start position:0%
+special here what was special that
+produced this pseudo inverse that I'm
+
+ align:start position:0%
+produced this pseudo inverse that I'm
+ 
+
+ align:start position:0%
+produced this pseudo inverse that I'm
+going to speak about more was this
+
+ align:start position:0%
+going to speak about more was this
+ 
+
+ align:start position:0%
+going to speak about more was this
+Choice a equal the identity and b equals
+
+ align:start position:0%
+Choice a equal the identity and b equals
+ 
+
+ align:start position:0%
+Choice a equal the identity and b equals
+zero the the fact that we we just put
+
+ align:start position:0%
+zero the the fact that we we just put
+ 
+
+ align:start position:0%
+zero the the fact that we we just put
+the norm of U2 there
+
+ align:start position:0%
+the norm of U2 there
+ 
+
+ align:start position:0%
+the norm of U2 there
+so this well this is the idea is this
+
+ align:start position:0%
+so this well this is the idea is this
+ 
+
+ align:start position:0%
+so this well this is the idea is this
+produces the pseudo
+
+ align:start position:0%
+produces the pseudo
+ 
+
+ align:start position:0%
+produces the pseudo
+inverse
+
+ align:start position:0%
+inverse
+ 
+
+ align:start position:0%
+inverse
+uh um and and if you like uh yeah so can
+
+ align:start position:0%
+uh um and and if you like uh yeah so can
+ 
+
+ align:start position:0%
+uh um and and if you like uh yeah so can
+I say a little more about the pseudo
+
+ align:start position:0%
+I say a little more about the pseudo
+ 
+
+ align:start position:0%
+I say a little more about the pseudo
+inverse before drawing the picture that
+
+ align:start position:0%
+inverse before drawing the picture that
+ 
+
+ align:start position:0%
+inverse before drawing the picture that
+shows what it's about so I took this
+
+ align:start position:0%
+shows what it's about so I took this
+ 
+
+ align:start position:0%
+shows what it's about so I took this
+thing and let Alpha go to
+
+ align:start position:0%
+thing and let Alpha go to
+ 
+
+ align:start position:0%
+thing and let Alpha go to
+Infinity okay so I could equally well
+
+ align:start position:0%
+Infinity okay so I could equally well
+ 
+
+ align:start position:0%
+Infinity okay so I could equally well
+have divided it by Alpha the whole if I
+
+ align:start position:0%
+have divided it by Alpha the whole if I
+ 
+
+ align:start position:0%
+have divided it by Alpha the whole if I
+divide the whole thing by Alpha that
+
+ align:start position:0%
+divide the whole thing by Alpha that
+ 
+
+ align:start position:0%
+divide the whole thing by Alpha that
+won't
+
+ align:start position:0%
+won't
+ 
+
+ align:start position:0%
+won't
+change the minimizer certainly the same
+
+ align:start position:0%
+change the minimizer certainly the same
+ 
+
+ align:start position:0%
+change the minimizer certainly the same
+use will win and now I see one over Al
+
+ align:start position:0%
+use will win and now I see one over Al
+ 
+
+ align:start position:0%
+use will win and now I see one over Al
+are going to zero and that's where the
+
+ align:start position:0%
+are going to zero and that's where the
+ 
+
+ align:start position:0%
+are going to zero and that's where the
+pseudo inverse is usually seen we we we
+
+ align:start position:0%
+pseudo inverse is usually seen we we we
+ 
+
+ align:start position:0%
+pseudo inverse is usually seen we we we
+take the the given
+
+ align:start position:0%
+take the the given
+ 
+
+ align:start position:0%
+take the the given
+problem which does not completely
+
+ align:start position:0%
+problem which does not completely
+ 
+
+ align:start position:0%
+problem which does not completely
+determine U1 and U2 and we throw in a
+
+ align:start position:0%
+determine U1 and U2 and we throw in a
+ 
+
+ align:start position:0%
+determine U1 and U2 and we throw in a
+small amount of Norm
+
+ align:start position:0%
+small amount of Norm
+ 
+
+ align:start position:0%
+small amount of Norm
+U2 and uh find the minimum for that
+
+ align:start position:0%
+U2 and uh find the minimum for that
+ 
+
+ align:start position:0%
+U2 and uh find the minimum for that
+right so uh
+
+ align:start position:0%
+right so uh
+ 
+
+ align:start position:0%
+right so uh
+yeah let me say it somehow I I take the
+
+ align:start position:0%
+yeah let me say it somehow I I take the
+ 
+
+ align:start position:0%
+yeah let me say it somehow I I take the
+I take the B transpose
+
+ align:start position:0%
+I take the B transpose
+ 
+
+ align:start position:0%
+I take the B transpose
+B plus the one over Alpha I now one over
+
+ align:start position:0%
+B plus the one over Alpha I now one over
+ 
+
+ align:start position:0%
+B plus the one over Alpha I now one over
+alpha alpha is still going to in
+
+ align:start position:0%
+alpha alpha is still going to in
+ 
+
+ align:start position:0%
+alpha alpha is still going to in
+Infinity in my in my in in
+
+ align:start position:0%
+Infinity in my in my in in
+ 
+
+ align:start position:0%
+Infinity in my in my in in
+this lecture so so one over Alpha this
+
+ align:start position:0%
+this lecture so so one over Alpha this
+ 
+
+ align:start position:0%
+this lecture so so one over Alpha this
+is the whole thing is is headed for
+
+ align:start position:0%
+is the whole thing is is headed for
+ 
+
+ align:start position:0%
+is the whole thing is is headed for
+zero times the norm of U ^2 this is the
+
+ align:start position:0%
+zero times the norm of U ^2 this is the
+ 
+
+ align:start position:0%
+zero times the norm of U ^2 this is the
+this is the u12 + U2
+
+ align:start position:0%
+this is the u12 + U2
+ 
+
+ align:start position:0%
+this is the u12 + U2
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+okay and that
+
+ align:start position:0%
+okay and that
+ 
+
+ align:start position:0%
+okay and that
+inverse that quantity inverse approaches
+
+ align:start position:0%
+inverse that quantity inverse approaches
+ 
+
+ align:start position:0%
+inverse that quantity inverse approaches
+the well once I comp the I'm not giving
+
+ align:start position:0%
+the well once I comp the I'm not giving
+ 
+
+ align:start position:0%
+the well once I comp the I'm not giving
+the complete formula but this is what's
+
+ align:start position:0%
+the complete formula but this is what's
+ 
+
+ align:start position:0%
+the complete formula but this is what's
+entering here and it produces leads to
+
+ align:start position:0%
+entering here and it produces leads to
+ 
+
+ align:start position:0%
+entering here and it produces leads to
+so may I say the vague word leads
+
+ align:start position:0%
+so may I say the vague word leads
+ 
+
+ align:start position:0%
+so may I say the vague word leads
+toward the pseudo inverse
+
+ align:start position:0%
+toward the pseudo inverse
+ 
+
+ align:start position:0%
+toward the pseudo inverse
+B+ yeah and I'll do better with that
+
+ align:start position:0%
+B+ yeah and I'll do better with that
+ 
+
+ align:start position:0%
+B+ yeah and I'll do better with that
+okay I I want to go on to the picture
+
+ align:start position:0%
+okay I I want to go on to the picture
+ 
+
+ align:start position:0%
+okay I I want to go on to the picture
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+right do you know the most important
+
+ align:start position:0%
+right do you know the most important
+ 
+
+ align:start position:0%
+right do you know the most important
+picture of linear algebra the whole
+
+ align:start position:0%
+picture of linear algebra the whole
+ 
+
+ align:start position:0%
+picture of linear algebra the whole
+picture of what a matrix is actually
+
+ align:start position:0%
+picture of what a matrix is actually
+ 
+
+ align:start position:0%
+picture of what a matrix is actually
+doing here we have a great example to
+
+ align:start position:0%
+doing here we have a great example to
+ 
+
+ align:start position:0%
+doing here we have a great example to
+draw that picture so this is here's the
+
+ align:start position:0%
+draw that picture so this is here's the
+ 
+
+ align:start position:0%
+draw that picture so this is here's the
+picture that 1806 is it's at the center
+
+ align:start position:0%
+picture that 1806 is it's at the center
+ 
+
+ align:start position:0%
+picture that 1806 is it's at the center
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+1806 for for our 2x1 Matrix so this is
+
+ align:start position:0%
+1806 for for our 2x1 Matrix so this is
+ 
+
+ align:start position:0%
+1806 for for our 2x1 Matrix so this is
+our our Matrix is b = 1 - 1 this is the
+
+ align:start position:0%
+our our Matrix is b = 1 - 1 this is the
+ 
+
+ align:start position:0%
+our our Matrix is b = 1 - 1 this is the
+picture for that Matrix okay so that
+
+ align:start position:0%
+picture for that Matrix okay so that
+ 
+
+ align:start position:0%
+picture for that Matrix okay so that
+Matrix has a row
+
+ align:start position:0%
+Matrix has a row
+ 
+
+ align:start position:0%
+Matrix has a row
+space the row space is the set of all
+
+ align:start position:0%
+space the row space is the set of all
+ 
+
+ align:start position:0%
+space the row space is the set of all
+vectors or or combinations of the rows
+
+ align:start position:0%
+vectors or or combinations of the rows
+ 
+
+ align:start position:0%
+vectors or or combinations of the rows
+but there's only one row so the row
+
+ align:start position:0%
+but there's only one row so the row
+ 
+
+ align:start position:0%
+but there's only one row so the row
+space is only a line I guess it's
+
+ align:start position:0%
+space is only a line I guess it's
+ 
+
+ align:start position:0%
+space is only a line I guess it's
+probably that line so the row
+
+ align:start position:0%
+probably that line so the row
+ 
+
+ align:start position:0%
+probably that line so the row
+space the row space of B of of a matrix
+
+ align:start position:0%
+space the row space of B of of a matrix
+ 
+
+ align:start position:0%
+space the row space of B of of a matrix
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+all multiples of one -
+
+ align:start position:0%
+all multiples of one -
+ 
+
+ align:start position:0%
+all multiples of one -
+one so it's a line let's put the zero
+
+ align:start position:0%
+one so it's a line let's put the zero
+ 
+
+ align:start position:0%
+one so it's a line let's put the zero
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+in okay then the Matrix also has a null
+
+ align:start position:0%
+in okay then the Matrix also has a null
+ 
+
+ align:start position:0%
+in okay then the Matrix also has a null
+space the null space is the of solutions
+
+ align:start position:0%
+space the null space is the of solutions
+ 
+
+ align:start position:0%
+space the null space is the of solutions
+to BX equal 0 it's a
+
+ align:start position:0%
+to BX equal 0 it's a
+ 
+
+ align:start position:0%
+to BX equal 0 it's a
+line in fact it's a perpendicular line
+
+ align:start position:0%
+line in fact it's a perpendicular line
+ 
+
+ align:start position:0%
+line in fact it's a perpendicular line
+so this is the null
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space of B of B and it contains all what
+
+ align:start position:0%
+space of B of B and it contains all what
+ 
+
+ align:start position:0%
+space of B of B and it contains all what
+does it contain all the solutions to BU
+
+ align:start position:0%
+does it contain all the solutions to BU
+ 
+
+ align:start position:0%
+does it contain all the solutions to BU
+equals z which in this case are all
+
+ align:start position:0%
+equals z which in this case are all
+ 
+
+ align:start position:0%
+equals z which in this case are all
+multiples of 1
+
+ align:start position:0%
+multiples of 1
+ 
+
+ align:start position:0%
+multiples of 1
+one and just to come back to my early
+
+ align:start position:0%
+one and just to come back to my early
+ 
+
+ align:start position:0%
+one and just to come back to my early
+comment that's what the QR the sort of
+
+ align:start position:0%
+comment that's what the QR the sort of
+ 
+
+ align:start position:0%
+comment that's what the QR the sort of
+extra half of the QR algorithm is
+
+ align:start position:0%
+extra half of the QR algorithm is
+ 
+
+ align:start position:0%
+extra half of the QR algorithm is
+telling us it's giving us an a beautiful
+
+ align:start position:0%
+telling us it's giving us an a beautiful
+ 
+
+ align:start position:0%
+telling us it's giving us an a beautiful
+basis for the null space and so the the
+
+ align:start position:0%
+basis for the null space and so the the
+ 
+
+ align:start position:0%
+basis for the null space and so the the
+key point is that the null space is
+
+ align:start position:0%
+key point is that the null space is
+ 
+
+ align:start position:0%
+key point is that the null space is
+always perpendicular to the row space
+
+ align:start position:0%
+always perpendicular to the row space
+ 
+
+ align:start position:0%
+always perpendicular to the row space
+which of course we see here this Z is
+
+ align:start position:0%
+which of course we see here this Z is
+ 
+
+ align:start position:0%
+which of course we see here this Z is
+what we had to compute when it was uh
+
+ align:start position:0%
+what we had to compute when it was uh
+ 
+
+ align:start position:0%
+what we had to compute when it was uh
+when there were when there were P
+
+ align:start position:0%
+when there were when there were P
+ 
+
+ align:start position:0%
+when there were when there were P
+components and not just one and now
+
+ align:start position:0%
+components and not just one and now
+ 
+
+ align:start position:0%
+components and not just one and now
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+is uh what let's see what's what's what
+
+ align:start position:0%
+is uh what let's see what's what's what
+ 
+
+ align:start position:0%
+is uh what let's see what's what's what
+else goes into this picture where are
+
+ align:start position:0%
+else goes into this picture where are
+ 
+
+ align:start position:0%
+else goes into this picture where are
+the solutions
+
+ align:start position:0%
+the solutions
+ 
+
+ align:start position:0%
+the solutions
+to my equation bu equal D so my equation
+
+ align:start position:0%
+to my equation bu equal D so my equation
+ 
+
+ align:start position:0%
+to my equation bu equal D so my equation
+was my equation was U1 minus U2 equal a
+
+ align:start position:0%
+was my equation was U1 minus U2 equal a
+ 
+
+ align:start position:0%
+was my equation was U1 minus U2 equal a
+particular number
+
+ align:start position:0%
+particular number
+ 
+
+ align:start position:0%
+particular number
+six and where are the solutions to U1 -
+
+ align:start position:0%
+six and where are the solutions to U1 -
+ 
+
+ align:start position:0%
+six and where are the solutions to U1 -
+U2 =
+
+ align:start position:0%
+U2 =
+ 
+
+ align:start position:0%
+U2 =
+6 okay
+
+ align:start position:0%
+6 okay
+ 
+
+ align:start position:0%
+6 okay
+so so now I want to draw
+
+ align:start position:0%
+so so now I want to draw
+ 
+
+ align:start position:0%
+so so now I want to draw
+the I'll let me draw all where are all
+
+ align:start position:0%
+the I'll let me draw all where are all
+ 
+
+ align:start position:0%
+the I'll let me draw all where are all
+the this is the U1 U2 plane okay so one
+
+ align:start position:0%
+the this is the U1 U2 plane okay so one
+ 
+
+ align:start position:0%
+the this is the U1 U2 plane okay so one
+solution is take c equal to 3 3 minus 3
+
+ align:start position:0%
+solution is take c equal to 3 3 minus 3
+ 
+
+ align:start position:0%
+solution is take c equal to 3 3 minus 3
+three the combination 3 - 3 which is
+
+ align:start position:0%
+three the combination 3 - 3 which is
+ 
+
+ align:start position:0%
+three the combination 3 - 3 which is
+right there is my particular solution
+
+ align:start position:0%
+right there is my particular solution
+ 
+
+ align:start position:0%
+right there is my particular solution
+you particular or or U row space is 3 -
+
+ align:start position:0%
+you particular or or U row space is 3 -
+ 
+
+ align:start position:0%
+you particular or or U row space is 3 -
+3 that solves the
+
+ align:start position:0%
+3 that solves the
+ 
+
+ align:start position:0%
+3 that solves the
+equation and it lies in the row space
+
+ align:start position:0%
+equation and it lies in the row space
+ 
+
+ align:start position:0%
+equation and it lies in the row space
+and now if you understand the whole
+
+ align:start position:0%
+and now if you understand the whole
+ 
+
+ align:start position:0%
+and now if you understand the whole
+point of linear
+
+ align:start position:0%
+point of linear
+ 
+
+ align:start position:0%
+point of linear
+equations where are the rest of the
+
+ align:start position:0%
+equations where are the rest of the
+ 
+
+ align:start position:0%
+equations where are the rest of the
+solutions how do I draw the rest of the
+
+ align:start position:0%
+solutions how do I draw the rest of the
+ 
+
+ align:start position:0%
+solutions how do I draw the rest of the
+solutions
+
+ align:start position:0%
+solutions
+ 
+
+ align:start position:0%
+solutions
+well to a particular solution I add on
+
+ align:start position:0%
+well to a particular solution I add on
+ 
+
+ align:start position:0%
+well to a particular solution I add on
+any null space solution the null space
+
+ align:start position:0%
+any null space solution the null space
+ 
+
+ align:start position:0%
+any null space solution the null space
+Solutions go this way so I add
+
+ align:start position:0%
+Solutions go this way so I add
+ 
+
+ align:start position:0%
+Solutions go this way so I add
+on so this is my whole line of all
+
+ align:start position:0%
+on so this is my whole line of all
+ 
+
+ align:start position:0%
+on so this is my whole line of all
+solutions so this is the line of all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solutions and now the key question is
+
+ align:start position:0%
+solutions and now the key question is
+ 
+
+ align:start position:0%
+solutions and now the key question is
+which solution has is the
+
+ align:start position:0%
+which solution has is the
+ 
+
+ align:start position:0%
+which solution has is the
+smallest when so this is the idea of the
+
+ align:start position:0%
+smallest when so this is the idea of the
+ 
+
+ align:start position:0%
+smallest when so this is the idea of the
+pseudo inverse when there many solutions
+
+ align:start position:0%
+pseudo inverse when there many solutions
+ 
+
+ align:start position:0%
+pseudo inverse when there many solutions
+pick the smallest one pick the shortest
+
+ align:start position:0%
+pick the smallest one pick the shortest
+ 
+
+ align:start position:0%
+pick the smallest one pick the shortest
+one it's the most stable somehow it's
+
+ align:start position:0%
+one it's the most stable somehow it's
+ 
+
+ align:start position:0%
+one it's the most stable somehow it's
+the natural one and which one is
+
+ align:start position:0%
+the natural one and which one is
+ 
+
+ align:start position:0%
+the natural one and which one is
+it okay which so here's the origin what
+
+ align:start position:0%
+it okay which so here's the origin what
+ 
+
+ align:start position:0%
+it okay which so here's the origin what
+point on that line is closest to the
+
+ align:start position:0%
+point on that line is closest to the
+ 
+
+ align:start position:0%
+point on that line is closest to the
+origin what point minimizes u12 plus U2
+
+ align:start position:0%
+origin what point minimizes u12 plus U2
+ 
+
+ align:start position:0%
+origin what point minimizes u12 plus U2
+2 everybody can see this
+
+ align:start position:0%
+2 everybody can see this
+ 
+
+ align:start position:0%
+2 everybody can see this
+guy that minimiz that's the
+
+ align:start position:0%
+guy that minimiz that's the
+ 
+
+ align:start position:0%
+guy that minimiz that's the
+so the pseudo
+
+ align:start position:0%
+so the pseudo
+ 
+
+ align:start position:0%
+so the pseudo
+inverse says wait a minute when you've
+
+ align:start position:0%
+inverse says wait a minute when you've
+ 
+
+ align:start position:0%
+inverse says wait a minute when you've
+got a whole line of solutions just tell
+
+ align:start position:0%
+got a whole line of solutions just tell
+ 
+
+ align:start position:0%
+got a whole line of solutions just tell
+me a good one tell me the special one
+
+ align:start position:0%
+me a good one tell me the special one
+ 
+
+ align:start position:0%
+me a good one tell me the special one
+and the special one is the one in the
+
+ align:start position:0%
+and the special one is the one in the
+ 
+
+ align:start position:0%
+and the special one is the one in the
+row
+
+ align:start position:0%
+row
+ 
+
+ align:start position:0%
+row
+space and that's the one that the pseudo
+
+ align:start position:0%
+space and that's the one that the pseudo
+ 
+
+ align:start position:0%
+space and that's the one that the pseudo
+inverse picks so the pseudo inverse of a
+
+ align:start position:0%
+inverse picks so the pseudo inverse of a
+ 
+
+ align:start position:0%
+inverse picks so the pseudo inverse of a
+matrix so the the the general rule is
+
+ align:start position:0%
+matrix so the the the general rule is
+ 
+
+ align:start position:0%
+matrix so the the the general rule is
+and so part of the lecture was the fact
+
+ align:start position:0%
+and so part of the lecture was the fact
+ 
+
+ align:start position:0%
+and so part of the lecture was the fact
+that as Alpha goes to Infinity in this
+
+ align:start position:0%
+that as Alpha goes to Infinity in this
+ 
+
+ align:start position:0%
+that as Alpha goes to Infinity in this
+problem the pseudo inverse will do it or
+
+ align:start position:0%
+problem the pseudo inverse will do it or
+ 
+
+ align:start position:0%
+problem the pseudo inverse will do it or
+I could say just directly what does the
+
+ align:start position:0%
+I could say just directly what does the
+ 
+
+ align:start position:0%
+I could say just directly what does the
+pseudo inverse do the pseudo
+
+ align:start position:0%
+pseudo inverse do the pseudo
+ 
+
+ align:start position:0%
+pseudo inverse do the pseudo
+inverse uh so so B+ the pseudo inverse
+
+ align:start position:0%
+inverse uh so so B+ the pseudo inverse
+ 
+
+ align:start position:0%
+inverse uh so so B+ the pseudo inverse
+chooses it it it it it it chooses U if
+
+ align:start position:0%
+chooses it it it it it it chooses U if
+ 
+
+ align:start position:0%
+chooses it it it it it it chooses U if
+you like U that's the that's that's
+
+ align:start position:0%
+you like U that's the that's that's
+ 
+
+ align:start position:0%
+you like U that's the that's that's
+that's the that's the B+ that multip the
+
+ align:start position:0%
+that's the that's the B+ that multip the
+ 
+
+ align:start position:0%
+that's the that's the B+ that multip the
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+I can't say B inverse D I mean everybody
+
+ align:start position:0%
+I can't say B inverse D I mean everybody
+ 
+
+ align:start position:0%
+I can't say B inverse D I mean everybody
+knows my equation is Buu equal D so this
+
+ align:start position:0%
+knows my equation is Buu equal D so this
+ 
+
+ align:start position:0%
+knows my equation is Buu equal D so this
+is my equation bu equal
+
+ align:start position:0%
+is my equation bu equal
+ 
+
+ align:start position:0%
+is my equation bu equal
+D and my particular
+
+ align:start position:0%
+D and my particular
+ 
+
+ align:start position:0%
+D and my particular
+solution my pseudo solution my best
+
+ align:start position:0%
+solution my pseudo solution my best
+ 
+
+ align:start position:0%
+solution my pseudo solution my best
+solution is going to be b + D and it's
+
+ align:start position:0%
+solution is going to be b + D and it's
+ 
+
+ align:start position:0%
+solution is going to be b + D and it's
+going to be in the row
+
+ align:start position:0%
+going to be in the row
+ 
+
+ align:start position:0%
+going to be in the row
+space and because it's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smallest solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you meet the idea of pseudo
+
+ align:start position:0%
+so if you meet the idea of pseudo
+ 
+
+ align:start position:0%
+so if you meet the idea of pseudo
+inverses now you know what what it's
+
+ align:start position:0%
+inverses now you know what what it's
+ 
+
+ align:start position:0%
+inverses now you know what what it's
+talking about we've got because we don't
+
+ align:start position:0%
+talking about we've got because we don't
+ 
+
+ align:start position:0%
+talking about we've got because we don't
+have a true inverse we have a whole line
+
+ align:start position:0%
+have a true inverse we have a whole line
+ 
+
+ align:start position:0%
+have a true inverse we have a whole line
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+solutions would we want to pick one and
+
+ align:start position:0%
+solutions would we want to pick one and
+ 
+
+ align:start position:0%
+solutions would we want to pick one and
+the pseudo inverse picks this one it's
+
+ align:start position:0%
+the pseudo inverse picks this one it's
+ 
+
+ align:start position:0%
+the pseudo inverse picks this one it's
+the one in the row space and it's the
+
+ align:start position:0%
+the one in the row space and it's the
+ 
+
+ align:start position:0%
+the one in the row space and it's the
+shortest because these are
+
+ align:start position:0%
+shortest because these are
+ 
+
+ align:start position:0%
+shortest because these are
+orthogonal see because these are
+
+ align:start position:0%
+orthogonal see because these are
+ 
+
+ align:start position:0%
+orthogonal see because these are
+orthogonal the the the U is
+
+ align:start position:0%
+orthogonal the the the U is
+ 
+
+ align:start position:0%
+orthogonal the the the U is
+u+ unu
+
+ align:start position:0%
+u+ unu
+ 
+
+ align:start position:0%
+u+ unu
+n and because those are orthogonal the
+
+ align:start position:0%
+n and because those are orthogonal the
+ 
+
+ align:start position:0%
+n and because those are orthogonal the
+length of u^2 by Pythagoras is the
+
+ align:start position:0%
+length of u^2 by Pythagoras is the
+ 
+
+ align:start position:0%
+length of u^2 by Pythagoras is the
+length of u^ 2 plus the length of UN n^
+
+ align:start position:0%
+length of u^ 2 plus the length of UN n^
+ 
+
+ align:start position:0%
+length of u^ 2 plus the length of UN n^
+2 and which one is
+
+ align:start position:0%
+2 and which one is
+ 
+
+ align:start position:0%
+2 and which one is
+shortest the one that has no
+
+ align:start position:0%
+shortest the one that has no
+ 
+
+ align:start position:0%
+shortest the one that has no
+U that that that orthogonal component
+
+ align:start position:0%
+U that that that orthogonal component
+ 
+
+ align:start position:0%
+U that that that orthogonal component
+might as well be zero if you want the
+
+ align:start position:0%
+might as well be zero if you want the
+ 
+
+ align:start position:0%
+might as well be zero if you want the
+shortest so the so all solutions have
+
+ align:start position:0%
+shortest so the so all solutions have
+ 
+
+ align:start position:0%
+shortest so the so all solutions have
+this and this this is the length of the
+
+ align:start position:0%
+this and this this is the length of the
+ 
+
+ align:start position:0%
+this and this this is the length of the
+shortest one okay so that tells you what
+
+ align:start position:0%
+shortest one okay so that tells you what
+ 
+
+ align:start position:0%
+shortest one okay so that tells you what
+the pseudo inverse is and at least it
+
+ align:start position:0%
+the pseudo inverse is and at least it
+ 
+
+ align:start position:0%
+the pseudo inverse is and at least it
+tells you what it is for a 1x two
+
+ align:start position:0%
+tells you what it is for a 1x two
+ 
+
+ align:start position:0%
+tells you what it is for a 1x two
+Matrix I could yeah let me as long as
+
+ align:start position:0%
+Matrix I could yeah let me as long as
+ 
+
+ align:start position:0%
+Matrix I could yeah let me as long as
+I'm drawing the speaking about the
+
+ align:start position:0%
+I'm drawing the speaking about the
+ 
+
+ align:start position:0%
+I'm drawing the speaking about the
+pseudo inverse let me complete this
+
+ align:start position:0%
+pseudo inverse let me complete this
+ 
+
+ align:start position:0%
+pseudo inverse let me complete this
+thought but you saw the idea of the the
+
+ align:start position:0%
+thought but you saw the idea of the the
+ 
+
+ align:start position:0%
+thought but you saw the idea of the the
+the thought was there there there two
+
+ align:start position:0%
+the thought was there there there two
+ 
+
+ align:start position:0%
+the thought was there there there two
+ways to get it again the null space
+
+ align:start position:0%
+ways to get it again the null space
+ 
+
+ align:start position:0%
+ways to get it again the null space
+method that goes for it directly or the
+
+ align:start position:0%
+method that goes for it directly or the
+ 
+
+ align:start position:0%
+method that goes for it directly or the
+big Alpha method that we checked
+
+ align:start position:0%
+big Alpha method that we checked
+ 
+
+ align:start position:0%
+big Alpha method that we checked
+actually works so that was the point of
+
+ align:start position:0%
+actually works so that was the point of
+ 
+
+ align:start position:0%
+actually works so that was the point of
+this board here that the big Alpha
+
+ align:start position:0%
+this board here that the big Alpha
+ 
+
+ align:start position:0%
+this board here that the big Alpha
+method also produces in the limit as
+
+ align:start position:0%
+method also produces in the limit as
+ 
+
+ align:start position:0%
+method also produces in the limit as
+Alpha goes to Infinity up and then
+
+ align:start position:0%
+Alpha goes to Infinity up and then
+ 
+
+ align:start position:0%
+Alpha goes to Infinity up and then
+there's some little you know there's it
+
+ align:start position:0%
+there's some little you know there's it
+ 
+
+ align:start position:0%
+there's some little you know there's it
+doesn't
+
+ align:start position:0%
+doesn't
+ 
+
+ align:start position:0%
+doesn't
+have if Alpha was a thousand I wouldn't
+
+ align:start position:0%
+have if Alpha was a thousand I wouldn't
+ 
+
+ align:start position:0%
+have if Alpha was a thousand I wouldn't
+get exactly the right answer answer
+
+ align:start position:0%
+get exactly the right answer answer
+ 
+
+ align:start position:0%
+get exactly the right answer answer
+because this would be
+
+ align:start position:0%
+because this would be
+ 
+
+ align:start position:0%
+because this would be
+2001 in the
+
+ align:start position:0%
+2001 in the
+ 
+
+ align:start position:0%
+2001 in the
+denominator but as thousand becomes a
+
+ align:start position:0%
+denominator but as thousand becomes a
+ 
+
+ align:start position:0%
+denominator but as thousand becomes a
+million and Alpha goes to Infinity I get
+
+ align:start position:0%
+million and Alpha goes to Infinity I get
+ 
+
+ align:start position:0%
+million and Alpha goes to Infinity I get
+the exact one okay so oh here I was
+
+ align:start position:0%
+the exact one okay so oh here I was
+ 
+
+ align:start position:0%
+the exact one okay so oh here I was
+going to draw the picture so uh so if I
+
+ align:start position:0%
+going to draw the picture so uh so if I
+ 
+
+ align:start position:0%
+going to draw the picture so uh so if I
+draw a row space can I imagine this is a
+
+ align:start position:0%
+draw a row space can I imagine this is a
+ 
+
+ align:start position:0%
+draw a row space can I imagine this is a
+row
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space whose Dimension is the rank of The
+
+ align:start position:0%
+space whose Dimension is the rank of The
+ 
+
+ align:start position:0%
+space whose Dimension is the rank of The
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+perpendicular to it is a null
+
+ align:start position:0%
+perpendicular to it is a null
+ 
+
+ align:start position:0%
+perpendicular to it is a null
+space whose Dimension
+
+ align:start position:0%
+space whose Dimension
+ 
+
+ align:start position:0%
+space whose Dimension
+is the rest the rank that was the rank
+
+ align:start position:0%
+is the rest the rank that was the rank
+ 
+
+ align:start position:0%
+is the rest the rank that was the rank
+that I always call R then this will have
+
+ align:start position:0%
+that I always call R then this will have
+ 
+
+ align:start position:0%
+that I always call R then this will have
+the dimension n minus r the number
+
+ align:start position:0%
+the dimension n minus r the number
+ 
+
+ align:start position:0%
+the dimension n minus r the number
+of this is exactly these are the two
+
+ align:start position:0%
+of this is exactly these are the two
+ 
+
+ align:start position:0%
+of this is exactly these are the two
+things that
+
+ align:start position:0%
+things that
+ 
+
+ align:start position:0%
+things that
+uh that that mat lab found here
+
+ align:start position:0%
+uh that that mat lab found here
+ 
+
+ align:start position:0%
+uh that that mat lab found here
+these were the r vectors in the row
+
+ align:start position:0%
+these were the r vectors in the row
+ 
+
+ align:start position:0%
+these were the r vectors in the row
+space turned into columns and these were
+
+ align:start position:0%
+space turned into columns and these were
+ 
+
+ align:start position:0%
+space turned into columns and these were
+the N minus r but that was only one
+
+ align:start position:0%
+the N minus r but that was only one
+ 
+
+ align:start position:0%
+the N minus r but that was only one
+vectors in the null space so
+
+ align:start position:0%
+vectors in the null space so
+ 
+
+ align:start position:0%
+vectors in the null space so
+normally we're up in N Dimensions not
+
+ align:start position:0%
+normally we're up in N Dimensions not
+ 
+
+ align:start position:0%
+normally we're up in N Dimensions not
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+two with two Dimensions I just had lines
+
+ align:start position:0%
+two with two Dimensions I just had lines
+ 
+
+ align:start position:0%
+two with two Dimensions I just had lines
+in N Dimensions I have an R dimensional
+
+ align:start position:0%
+in N Dimensions I have an R dimensional
+ 
+
+ align:start position:0%
+in N Dimensions I have an R dimensional
+Subspace perpendicular to an N minus r
+
+ align:start position:0%
+Subspace perpendicular to an N minus r
+ 
+
+ align:start position:0%
+Subspace perpendicular to an N minus r
+dimensional Subspace and now B what does
+
+ align:start position:0%
+dimensional Subspace and now B what does
+ 
+
+ align:start position:0%
+dimensional Subspace and now B what does
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+do okay so suppose I take a vector un n
+
+ align:start position:0%
+do okay so suppose I take a vector un n
+ 
+
+ align:start position:0%
+do okay so suppose I take a vector un n
+in the in the null space of B then B
+
+ align:start position:0%
+in the in the null space of B then B
+ 
+
+ align:start position:0%
+in the in the null space of B then B
+takes it to zero so can I just draw that
+
+ align:start position:0%
+takes it to zero so can I just draw that
+ 
+
+ align:start position:0%
+takes it to zero so can I just draw that
+with an
+
+ align:start position:0%
+with an
+ 
+
+ align:start position:0%
+with an
+arrow this will be zero bu
+
+ align:start position:0%
+arrow this will be zero bu
+ 
+
+ align:start position:0%
+arrow this will be zero bu
+n is zero that's the whole
+
+ align:start position:0%
+n is zero that's the whole
+ 
+
+ align:start position:0%
+n is zero that's the whole
+idea okay but a vector in the row
+
+ align:start position:0%
+idea okay but a vector in the row
+ 
+
+ align:start position:0%
+idea okay but a vector in the row
+space is not taken to zero B will take
+
+ align:start position:0%
+space is not taken to zero B will take
+ 
+
+ align:start position:0%
+space is not taken to zero B will take
+that do into the see I better draw here
+
+ align:start position:0%
+that do into the see I better draw here
+ 
+
+ align:start position:0%
+that do into the see I better draw here
+the column
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B okay which I'm drawing as a Subspace
+
+ align:start position:0%
+B okay which I'm drawing as a Subspace
+ 
+
+ align:start position:0%
+B okay which I'm drawing as a Subspace
+whose Dimension is
+
+ align:start position:0%
+whose Dimension is
+ 
+
+ align:start position:0%
+whose Dimension is
+also also is the same rank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R that's the great fact about m matrices
+
+ align:start position:0%
+R that's the great fact about m matrices
+ 
+
+ align:start position:0%
+R that's the great fact about m matrices
+that the number of independent rows
+
+ align:start position:0%
+that the number of independent rows
+ 
+
+ align:start position:0%
+that the number of independent rows
+equals the number of independent columns
+
+ align:start position:0%
+equals the number of independent columns
+ 
+
+ align:start position:0%
+equals the number of independent columns
+so this guy heads off to
+
+ align:start position:0%
+so this guy heads off to
+ 
+
+ align:start position:0%
+so this guy heads off to
+some b u row
+
+ align:start position:0%
+some b u row
+ 
+
+ align:start position:0%
+some b u row
+space okay and if I complete the picture
+
+ align:start position:0%
+space okay and if I complete the picture
+ 
+
+ align:start position:0%
+space okay and if I complete the picture
+as I really should there's another
+
+ align:start position:0%
+as I really should there's another
+ 
+
+ align:start position:0%
+as I really should there's another
+Subspace over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here which happen to be the zero
+
+ align:start position:0%
+here which happen to be the zero
+ 
+
+ align:start position:0%
+here which happen to be the zero
+Subspace in this example but usually
+
+ align:start position:0%
+Subspace in this example but usually
+ 
+
+ align:start position:0%
+Subspace in this example but usually
+it's here it's the null
+
+ align:start position:0%
+it's here it's the null
+ 
+
+ align:start position:0%
+it's here it's the null
+space of B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transpose in that example B
+
+ align:start position:0%
+transpose in that example B
+ 
+
+ align:start position:0%
+transpose in that example B
+transpose was 1 minus one and that was
+
+ align:start position:0%
+transpose was 1 minus one and that was
+ 
+
+ align:start position:0%
+transpose was 1 minus one and that was
+it's its column was independent so there
+
+ align:start position:0%
+it's its column was independent so there
+ 
+
+ align:start position:0%
+it's its column was independent so there
+was no null space so I had a simple
+
+ align:start position:0%
+was no null space so I had a simple
+ 
+
+ align:start position:0%
+was no null space so I had a simple
+picture and that's why I wanted to draw
+
+ align:start position:0%
+picture and that's why I wanted to draw
+ 
+
+ align:start position:0%
+picture and that's why I wanted to draw
+you a bigger picture with its its
+
+ align:start position:0%
+you a bigger picture with its its
+ 
+
+ align:start position:0%
+you a bigger picture with its its
+Dimension will
+
+ align:start position:0%
+Dimension will
+ 
+
+ align:start position:0%
+Dimension will
+be uh well not n minus r but if if B if
+
+ align:start position:0%
+be uh well not n minus r but if if B if
+ 
+
+ align:start position:0%
+be uh well not n minus r but if if B if
+if B is M byn let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say then it turns out that the this null
+
+ align:start position:0%
+say then it turns out that the this null
+ 
+
+ align:start position:0%
+say then it turns out that the this null
+space will be half Dimension M minus no
+
+ align:start position:0%
+space will be half Dimension M minus no
+ 
+
+ align:start position:0%
+space will be half Dimension M minus no
+problem okay now in the last 3 minutes I
+
+ align:start position:0%
+problem okay now in the last 3 minutes I
+ 
+
+ align:start position:0%
+problem okay now in the last 3 minutes I
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+draw the pseudo
+
+ align:start position:0%
+draw the pseudo
+ 
+
+ align:start position:0%
+draw the pseudo
+inverse so so what I'm saying is that
+
+ align:start position:0%
+inverse so so what I'm saying is that
+ 
+
+ align:start position:0%
+inverse so so what I'm saying is that
+every Matrix B every rectangular Square
+
+ align:start position:0%
+every Matrix B every rectangular Square
+ 
+
+ align:start position:0%
+every Matrix B every rectangular Square
+Matrix B has these four spaces four
+
+ align:start position:0%
+Matrix B has these four spaces four
+ 
+
+ align:start position:0%
+Matrix B has these four spaces four
+fundamental subspaces they've come to be
+
+ align:start position:0%
+fundamental subspaces they've come to be
+ 
+
+ align:start position:0%
+fundamental subspaces they've come to be
+called okay and the null space is the
+
+ align:start position:0%
+called okay and the null space is the
+ 
+
+ align:start position:0%
+called okay and the null space is the
+bunch of is the vectors which B takes to
+
+ align:start position:0%
+bunch of is the vectors which B takes to
+ 
+
+ align:start position:0%
+bunch of is the vectors which B takes to
+zero B takes any Vector into its column
+
+ align:start position:0%
+zero B takes any Vector into its column
+ 
+
+ align:start position:0%
+zero B takes any Vector into its column
+space so now let me just draw what
+
+ align:start position:0%
+space so now let me just draw what
+ 
+
+ align:start position:0%
+space so now let me just draw what
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+to U equal U npace Plus
+
+ align:start position:0%
+to U equal U npace Plus
+ 
+
+ align:start position:0%
+to U equal U npace Plus
+youu row space so this was a guy in the
+
+ align:start position:0%
+youu row space so this was a guy in the
+ 
+
+ align:start position:0%
+youu row space so this was a guy in the
+row
+
+ align:start position:0%
+row
+ 
+
+ align:start position:0%
+row
+space if I act if B what will B do when
+
+ align:start position:0%
+space if I act if B what will B do when
+ 
+
+ align:start position:0%
+space if I act if B what will B do when
+it multiplies this Vector this this
+
+ align:start position:0%
+it multiplies this Vector this this
+ 
+
+ align:start position:0%
+it multiplies this Vector this this
+Vector has a part that's in the null
+
+ align:start position:0%
+Vector has a part that's in the null
+ 
+
+ align:start position:0%
+Vector has a part that's in the null
+space and a part that's in the row space
+
+ align:start position:0%
+space and a part that's in the row space
+ 
+
+ align:start position:0%
+space and a part that's in the row space
+but when I multiply by B what happens to
+
+ align:start position:0%
+but when I multiply by B what happens to
+ 
+
+ align:start position:0%
+but when I multiply by B what happens to
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+part gone when I multiply that by B
+
+ align:start position:0%
+part gone when I multiply that by B
+ 
+
+ align:start position:0%
+part gone when I multiply that by B
+where does it go there so this all these
+
+ align:start position:0%
+where does it go there so this all these
+ 
+
+ align:start position:0%
+where does it go there so this all these
+guys feed into that same point Buu is
+
+ align:start position:0%
+guys feed into that same point Buu is
+ 
+
+ align:start position:0%
+guys feed into that same point Buu is
+also also going
+
+ align:start position:0%
+also also going
+ 
+
+ align:start position:0%
+also also going
+there that's why it's not invertible of
+
+ align:start position:0%
+there that's why it's not invertible of
+ 
+
+ align:start position:0%
+there that's why it's not invertible of
+course that's why it's not invertible I
+
+ align:start position:0%
+course that's why it's not invertible I
+ 
+
+ align:start position:0%
+course that's why it's not invertible I
+here I
+
+ align:start position:0%
+here I
+ 
+
+ align:start position:0%
+here I
+guess uh yeah yeah here here
+
+ align:start position:0%
+guess uh yeah yeah here here
+ 
+
+ align:start position:0%
+guess uh yeah yeah here here
+I'm so so this sorry wait a minute yeah
+
+ align:start position:0%
+I'm so so this sorry wait a minute yeah
+ 
+
+ align:start position:0%
+I'm so so this sorry wait a minute yeah
+this was the null space of B I didn't
+
+ align:start position:0%
+this was the null space of B I didn't
+ 
+
+ align:start position:0%
+this was the null space of B I didn't
+write in what was the null space of okay
+
+ align:start position:0%
+write in what was the null space of okay
+ 
+
+ align:start position:0%
+write in what was the null space of okay
+so the Matrix couldn't be invertible and
+
+ align:start position:0%
+so the Matrix couldn't be invertible and
+ 
+
+ align:start position:0%
+so the Matrix couldn't be invertible and
+actually because it has a null space and
+
+ align:start position:0%
+actually because it has a null space and
+ 
+
+ align:start position:0%
+actually because it has a null space and
+they all send those so what is the
+
+ align:start position:0%
+they all send those so what is the
+ 
+
+ align:start position:0%
+they all send those so what is the
+pseudo inverse finally finally last
+
+ align:start position:0%
+pseudo inverse finally finally last
+ 
+
+ align:start position:0%
+pseudo inverse finally finally last
+moment the pseudo
+
+ align:start position:0%
+moment the pseudo
+ 
+
+ align:start position:0%
+moment the pseudo
+inverse is the matrix it's like an
+
+ align:start position:0%
+inverse is the matrix it's like an
+ 
+
+ align:start position:0%
+inverse is the matrix it's like an
+inverse Matrix that comes backwards
+
+ align:start position:0%
+inverse Matrix that comes backwards
+ 
+
+ align:start position:0%
+inverse Matrix that comes backwards
+right it reverses what B
+
+ align:start position:0%
+right it reverses what B
+ 
+
+ align:start position:0%
+right it reverses what B
+does what it cannot do is reverse stuff
+
+ align:start position:0%
+does what it cannot do is reverse stuff
+ 
+
+ align:start position:0%
+does what it cannot do is reverse stuff
+that's appeared at Z no Matrix could
+
+ align:start position:0%
+that's appeared at Z no Matrix could
+ 
+
+ align:start position:0%
+that's appeared at Z no Matrix could
+send zero back to un right if I multiply
+
+ align:start position:0%
+send zero back to un right if I multiply
+ 
+
+ align:start position:0%
+send zero back to un right if I multiply
+by the zero Vector I'm only going to get
+
+ align:start position:0%
+by the zero Vector I'm only going to get
+ 
+
+ align:start position:0%
+by the zero Vector I'm only going to get
+the zero Vector so the pseudo
+
+ align:start position:0%
+the zero Vector so the pseudo
+ 
+
+ align:start position:0%
+the zero Vector so the pseudo
+inverse has
+
+ align:start position:0%
+inverse has
+ 
+
+ align:start position:0%
+inverse has
+to what it can do is it can send this
+
+ align:start position:0%
+to what it can do is it can send this
+ 
+
+ align:start position:0%
+to what it can do is it can send this
+stuff back to this this is what the
+
+ align:start position:0%
+stuff back to this this is what the
+ 
+
+ align:start position:0%
+stuff back to this this is what the
+pseudo inverse does if I if I had a
+
+ align:start position:0%
+pseudo inverse does if I if I had a
+ 
+
+ align:start position:0%
+pseudo inverse does if I if I had a
+different color chalk I would use it now
+
+ align:start position:0%
+different color chalk I would use it now
+ 
+
+ align:start position:0%
+different color chalk I would use it now
+but let me use two arrows or even
+
+ align:start position:0%
+but let me use two arrows or even
+ 
+
+ align:start position:0%
+but let me use two arrows or even
+three this is what the pseudo inverse
+
+ align:start position:0%
+three this is what the pseudo inverse
+ 
+
+ align:start position:0%
+three this is what the pseudo inverse
+does it takes the column space and sends
+
+ align:start position:0%
+does it takes the column space and sends
+ 
+
+ align:start position:0%
+does it takes the column space and sends
+it back to the row space and and because
+
+ align:start position:0%
+it back to the row space and and because
+ 
+
+ align:start position:0%
+it back to the row space and and because
+these have the same Dimension R the the
+
+ align:start position:0%
+these have the same Dimension R the the
+ 
+
+ align:start position:0%
+these have the same Dimension R the the
+point is inside B is this is this R by R
+
+ align:start position:0%
+point is inside B is this is this R by R
+ 
+
+ align:start position:0%
+point is inside B is this is this R by R
+Matrix that's that's cool it's totally
+
+ align:start position:0%
+Matrix that's that's cool it's totally
+ 
+
+ align:start position:0%
+Matrix that's that's cool it's totally
+invertible and B+ is invert it so from
+
+ align:start position:0%
+invertible and B+ is invert it so from
+ 
+
+ align:start position:0%
+invertible and B+ is invert it so from
+row space to column space goes B
+
+ align:start position:0%
+row space to column space goes B
+ 
+
+ align:start position:0%
+row space to column space goes B
+from column space back to row space
+
+ align:start position:0%
+from column space back to row space
+ 
+
+ align:start position:0%
+from column space back to row space
+comes the pseudo inverse but I can't
+
+ align:start position:0%
+comes the pseudo inverse but I can't
+ 
+
+ align:start position:0%
+comes the pseudo inverse but I can't
+call it a genuine inverse because all
+
+ align:start position:0%
+call it a genuine inverse because all
+ 
+
+ align:start position:0%
+call it a genuine inverse because all
+this stuff including zero the best I can
+
+ align:start position:0%
+this stuff including zero the best I can
+ 
+
+ align:start position:0%
+this stuff including zero the best I can
+do is send those all back to
+
+ align:start position:0%
+do is send those all back to
+ 
+
+ align:start position:0%
+do is send those all back to
+zero there now I've really wiped out
+
+ align:start position:0%
+zero there now I've really wiped out
+ 
+
+ align:start position:0%
+zero there now I've really wiped out
+that figure but I'll put the three
+
+ align:start position:0%
+that figure but I'll put the three
+ 
+
+ align:start position:0%
+that figure but I'll put the three
+arrows there that make it crystal
+
+ align:start position:0%
+arrows there that make it crystal
+ 
+
+ align:start position:0%
+arrows there that make it crystal
+clear so this those three arrows are
+
+ align:start position:0%
+clear so this those three arrows are
+ 
+
+ align:start position:0%
+clear so this those three arrows are
+indicating what the pseudo inverse does
+
+ align:start position:0%
+indicating what the pseudo inverse does
+ 
+
+ align:start position:0%
+indicating what the pseudo inverse does
+it takes
+
+ align:start position:0%
+it takes
+ 
+
+ align:start position:0%
+it takes
+the column space it's its column space
+
+ align:start position:0%
+the column space it's its column space
+ 
+
+ align:start position:0%
+the column space it's its column space
+is the row space the the column space of
+
+ align:start position:0%
+is the row space the the column space of
+ 
+
+ align:start position:0%
+is the row space the the column space of
+B plus is the row space of B you know
+
+ align:start position:0%
+B plus is the row space of B you know
+ 
+
+ align:start position:0%
+B plus is the row space of B you know
+sort of in these two spaces that's where
+
+ align:start position:0%
+sort of in these two spaces that's where
+ 
+
+ align:start position:0%
+sort of in these two spaces that's where
+the pseudo inverse is alive and B kills
+
+ align:start position:0%
+the pseudo inverse is alive and B kills
+ 
+
+ align:start position:0%
+the pseudo inverse is alive and B kills
+the null space and B+ kills the null
+
+ align:start position:0%
+the null space and B+ kills the null
+ 
+
+ align:start position:0%
+the null space and B+ kills the null
+space the other null space the space of
+
+ align:start position:0%
+space the other null space the space of
+ 
+
+ align:start position:0%
+space the other null space the space of
+b transp anyway that pseudo inverse is
+
+ align:start position:0%
+b transp anyway that pseudo inverse is
+ 
+
+ align:start position:0%
+b transp anyway that pseudo inverse is
+is at the center
+
+ align:start position:0%
+is at the center
+ 
+
+ align:start position:0%
+is at the center
+of uh the whole Theory here if I you
+
+ align:start position:0%
+of uh the whole Theory here if I you
+ 
+
+ align:start position:0%
+of uh the whole Theory here if I you
+know when I take out books from the
+
+ align:start position:0%
+know when I take out books from the
+ 
+
+ align:start position:0%
+know when I take out books from the
+library about uh regularizing these
+
+ align:start position:0%
+library about uh regularizing these
+ 
+
+ align:start position:0%
+library about uh regularizing these
+squares they begin by explaining the
+
+ align:start position:0%
+squares they begin by explaining the
+ 
+
+ align:start position:0%
+squares they begin by explaining the
+pseudo
+
+ align:start position:0%
+pseudo
+ 
+
+ align:start position:0%
+pseudo
+inverse which as we've seen is arises as
+
+ align:start position:0%
+inverse which as we've seen is arises as
+ 
+
+ align:start position:0%
+inverse which as we've seen is arises as
+Alpha goes to infinity or zero whichever
+
+ align:start position:0%
+Alpha goes to infinity or zero whichever
+ 
+
+ align:start position:0%
+Alpha goes to infinity or zero whichever
+end we're
+
+ align:start position:0%
+end we're
+ 
+
+ align:start position:0%
+end we're
+at and what I have still to do next time
+
+ align:start position:0%
+at and what I have still to do next time
+ 
+
+ align:start position:0%
+at and what I have still to do next time
+is what happens if I'm not prepared to
+
+ align:start position:0%
+is what happens if I'm not prepared to
+ 
+
+ align:start position:0%
+is what happens if I'm not prepared to
+go all the way to the pseudo inverse
+
+ align:start position:0%
+go all the way to the pseudo inverse
+ 
+
+ align:start position:0%
+go all the way to the pseudo inverse
+because it's it blows up on me and I
+
+ align:start position:0%
+because it's it blows up on me and I
+ 
+
+ align:start position:0%
+because it's it blows up on me and I
+have to and I want a finite Alpha what
+
+ align:start position:0%
+have to and I want a finite Alpha what
+ 
+
+ align:start position:0%
+have to and I want a finite Alpha what
+should that Alpha be and that Alpha will
+
+ align:start position:0%
+should that Alpha be and that Alpha will
+ 
+
+ align:start position:0%
+should that Alpha be and that Alpha will
+be determined by uh as I said by the
+
+ align:start position:0%
+be determined by uh as I said by the
+ 
+
+ align:start position:0%
+be determined by uh as I said by the
+somehow by the noise level in the system
+
+ align:start position:0%
+somehow by the noise level in the system
+ 
+
+ align:start position:0%
+somehow by the noise level in the system
+right and and just to emphasize another
+
+ align:start position:0%
+right and and just to emphasize another
+ 
+
+ align:start position:0%
+right and and just to emphasize another
+example that I'll probably mention you
+
+ align:start position:0%
+example that I'll probably mention you
+ 
+
+ align:start position:0%
+example that I'll probably mention you
+know CT scans MRI all those things that
+
+ align:start position:0%
+know CT scans MRI all those things that
+ 
+
+ align:start position:0%
+know CT scans MRI all those things that
+are trying to
+
+ align:start position:0%
+are trying to
+ 
+
+ align:start position:0%
+are trying to
+reconstruct results from a limited
+
+ align:start position:0%
+reconstruct results from a limited
+ 
+
+ align:start position:0%
+reconstruct results from a limited
+number of measurements measurements that
+
+ align:start position:0%
+number of measurements measurements that
+ 
+
+ align:start position:0%
+number of measurements measurements that
+are not really enough to perfect
+
+ align:start position:0%
+are not really enough to perfect
+ 
+
+ align:start position:0%
+are not really enough to perfect
+reconstruction so this is this is a
+
+ align:start position:0%
+reconstruction so this is this is a
+ 
+
+ align:start position:0%
+reconstruction so this is this is a
+theory of imperfect reconstruction if I
+
+ align:start position:0%
+theory of imperfect reconstruction if I
+ 
+
+ align:start position:0%
+theory of imperfect reconstruction if I
+can if I can invent and
+
+ align:start position:0%
+can if I can invent and
+ 
+
+ align:start position:0%
+can if I can invent and
+expression uh having met perfect
+
+ align:start position:0%
+expression uh having met perfect
+ 
+
+ align:start position:0%
+expression uh having met perfect
+reconstruction in the world of wavelets
+
+ align:start position:0%
+reconstruction in the world of wavelets
+ 
+
+ align:start position:0%
+reconstruction in the world of wavelets
+and Signal processing this is the
+
+ align:start position:0%
+and Signal processing this is the
+ 
+
+ align:start position:0%
+and Signal processing this is the
+subject of imperfect reconstruction and
+
+ align:start position:0%
+subject of imperfect reconstruction and
+ 
+
+ align:start position:0%
+subject of imperfect reconstruction and
+I'll hope to do justice to it on
+
+ align:start position:0%
+I'll hope to do justice to it on
+ 
+
+ align:start position:0%
+I'll hope to do justice to it on
+Wednesday okay thank you
\ No newline at end of file
diff --git a/iYFogDTPlRo.txt b/iYFogDTPlRo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..42ac3870e920f1c0a0003a6d2f9b9d154c5d4ab8
--- /dev/null
+++ b/iYFogDTPlRo.txt
@@ -0,0 +1,1715 @@
+align:start position:0%
+ 
+hi welcome back to recitation I have a
+
+ align:start position:0%
+hi welcome back to recitation I have a
+ 
+
+ align:start position:0%
+hi welcome back to recitation I have a
+nice exercise here for you that tests
+
+ align:start position:0%
+nice exercise here for you that tests
+ 
+
+ align:start position:0%
+nice exercise here for you that tests
+your knowledge of triple integration um
+
+ align:start position:0%
+your knowledge of triple integration um
+ 
+
+ align:start position:0%
+your knowledge of triple integration um
+so in particular I've got for you a
+
+ align:start position:0%
+so in particular I've got for you a
+ 
+
+ align:start position:0%
+so in particular I've got for you a
+cylinder and my cylinder has height H
+
+ align:start position:0%
+cylinder and my cylinder has height H
+ 
+
+ align:start position:0%
+cylinder and my cylinder has height H
+and it has radius B and this is a uh
+
+ align:start position:0%
+and it has radius B and this is a uh
+ 
+
+ align:start position:0%
+and it has radius B and this is a uh
+kind of cylinder I like it's a constant
+
+ align:start position:0%
+kind of cylinder I like it's a constant
+ 
+
+ align:start position:0%
+kind of cylinder I like it's a constant
+density cylinder so its density is is
+
+ align:start position:0%
+density cylinder so its density is is
+ 
+
+ align:start position:0%
+density cylinder so its density is is
+just one every everywhere um so what I'd
+
+ align:start position:0%
+just one every everywhere um so what I'd
+ 
+
+ align:start position:0%
+just one every everywhere um so what I'd
+like you to do is is for this for this
+
+ align:start position:0%
+like you to do is is for this for this
+ 
+
+ align:start position:0%
+like you to do is is for this for this
+cylinder I'd like you to compute its
+
+ align:start position:0%
+cylinder I'd like you to compute its
+ 
+
+ align:start position:0%
+cylinder I'd like you to compute its
+moment of inertia around its Central
+
+ align:start position:0%
+moment of inertia around its Central
+ 
+
+ align:start position:0%
+moment of inertia around its Central
+axis so why don't you pause the video
+
+ align:start position:0%
+axis so why don't you pause the video
+ 
+
+ align:start position:0%
+axis so why don't you pause the video
+have a go at that come back and you can
+
+ align:start position:0%
+have a go at that come back and you can
+ 
+
+ align:start position:0%
+have a go at that come back and you can
+check your work against
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mine hopefully you had some luck working
+
+ align:start position:0%
+mine hopefully you had some luck working
+ 
+
+ align:start position:0%
+mine hopefully you had some luck working
+on this problem let's let's uh talk
+
+ align:start position:0%
+on this problem let's let's uh talk
+ 
+
+ align:start position:0%
+on this problem let's let's uh talk
+about it so the first thing to notice is
+
+ align:start position:0%
+about it so the first thing to notice is
+ 
+
+ align:start position:0%
+about it so the first thing to notice is
+that there aren't any coordinates in
+
+ align:start position:0%
+that there aren't any coordinates in
+ 
+
+ align:start position:0%
+that there aren't any coordinates in
+this problem right I've given you a
+
+ align:start position:0%
+this problem right I've given you a
+ 
+
+ align:start position:0%
+this problem right I've given you a
+cylinder but it's up to you to choose uh
+
+ align:start position:0%
+cylinder but it's up to you to choose uh
+ 
+
+ align:start position:0%
+cylinder but it's up to you to choose uh
+a coordinates a way to arrange their
+
+ align:start position:0%
+a coordinates a way to arrange their
+ 
+
+ align:start position:0%
+a coordinates a way to arrange their
+cylinder in space or a way to arrange
+
+ align:start position:0%
+cylinder in space or a way to arrange
+ 
+
+ align:start position:0%
+cylinder in space or a way to arrange
+your coordinates with respect to your
+
+ align:start position:0%
+your coordinates with respect to your
+ 
+
+ align:start position:0%
+your coordinates with respect to your
+cylinder so a convenient thing to do in
+
+ align:start position:0%
+cylinder so a convenient thing to do in
+ 
+
+ align:start position:0%
+cylinder so a convenient thing to do in
+this case is is going to be you know
+
+ align:start position:0%
+this case is is going to be you know
+ 
+
+ align:start position:0%
+this case is is going to be you know
+we've got we're we're we're working with
+
+ align:start position:0%
+we've got we're we're we're working with
+ 
+
+ align:start position:0%
+we've got we're we're we're working with
+respect to the central axis of the
+
+ align:start position:0%
+respect to the central axis of the
+ 
+
+ align:start position:0%
+respect to the central axis of the
+cylinder so let's make that one of our
+
+ align:start position:0%
+cylinder so let's make that one of our
+ 
+
+ align:start position:0%
+cylinder so let's make that one of our
+axes so in particular why don't we make
+
+ align:start position:0%
+axes so in particular why don't we make
+ 
+
+ align:start position:0%
+axes so in particular why don't we make
+it our z-axis that seems like a a
+
+ align:start position:0%
+it our z-axis that seems like a a
+ 
+
+ align:start position:0%
+it our z-axis that seems like a a
+natural sort of thing to do so let me
+
+ align:start position:0%
+natural sort of thing to do so let me
+ 
+
+ align:start position:0%
+natural sort of thing to do so let me
+try and draw a little picture here so
+
+ align:start position:0%
+try and draw a little picture here so
+ 
+
+ align:start position:0%
+try and draw a little picture here so
+we've got our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cylinder and there it is with our with
+
+ align:start position:0%
+cylinder and there it is with our with
+ 
+
+ align:start position:0%
+cylinder and there it is with our with
+our three coordinate axes okay so I
+
+ align:start position:0%
+our three coordinate axes okay so I
+ 
+
+ align:start position:0%
+our three coordinate axes okay so I
+guess it's got radius B and it's got
+
+ align:start position:0%
+guess it's got radius B and it's got
+ 
+
+ align:start position:0%
+guess it's got radius B and it's got
+height
+
+ align:start position:0%
+height
+ 
+
+ align:start position:0%
+height
+H so now all right so now we've arranged
+
+ align:start position:0%
+H so now all right so now we've arranged
+ 
+
+ align:start position:0%
+H so now all right so now we've arranged
+it now we have coordinates so now um we
+
+ align:start position:0%
+it now we have coordinates so now um we
+ 
+
+ align:start position:0%
+it now we have coordinates so now um we
+want to see what what it is we're trying
+
+ align:start position:0%
+want to see what what it is we're trying
+ 
+
+ align:start position:0%
+want to see what what it is we're trying
+to do with it so we're trying to compute
+
+ align:start position:0%
+to do with it so we're trying to compute
+ 
+
+ align:start position:0%
+to do with it so we're trying to compute
+a moment of inertia so we have to
+
+ align:start position:0%
+a moment of inertia so we have to
+ 
+
+ align:start position:0%
+a moment of inertia so we have to
+remember what a moment of inertia means
+
+ align:start position:0%
+remember what a moment of inertia means
+ 
+
+ align:start position:0%
+remember what a moment of inertia means
+so let me think um so a moment of
+
+ align:start position:0%
+so let me think um so a moment of
+ 
+
+ align:start position:0%
+so let me think um so a moment of
+inertia when you have a when you have a
+
+ align:start position:0%
+inertia when you have a when you have a
+ 
+
+ align:start position:0%
+inertia when you have a when you have a
+solid so your moment of inertia I with
+
+ align:start position:0%
+solid so your moment of inertia I with
+ 
+
+ align:start position:0%
+solid so your moment of inertia I with
+respect to an axis is what you get when
+
+ align:start position:0%
+respect to an axis is what you get when
+ 
+
+ align:start position:0%
+respect to an axis is what you get when
+you take the triple integral so let's
+
+ align:start position:0%
+you take the triple integral so let's
+ 
+
+ align:start position:0%
+you take the triple integral so let's
+say your your
+
+ align:start position:0%
+say your your
+ 
+
+ align:start position:0%
+say your your
+solid is is D your solid D so you take
+
+ align:start position:0%
+solid is is D your solid D so you take
+ 
+
+ align:start position:0%
+solid is is D your solid D so you take
+uh D and you um so you're what you're
+
+ align:start position:0%
+uh D and you um so you're what you're
+ 
+
+ align:start position:0%
+uh D and you um so you're what you're
+take a triple integral over D and you're
+
+ align:start position:0%
+take a triple integral over D and you're
+ 
+
+ align:start position:0%
+take a triple integral over D and you're
+integrating R 2 with respect to the
+
+ align:start position:0%
+integrating R 2 with respect to the
+ 
+
+ align:start position:0%
+integrating R 2 with respect to the
+element of mass okay so r s here this is
+
+ align:start position:0%
+element of mass okay so r s here this is
+ 
+
+ align:start position:0%
+element of mass okay so r s here this is
+the distance from the axis around which
+
+ align:start position:0%
+the distance from the axis around which
+ 
+
+ align:start position:0%
+the distance from the axis around which
+you're Computing the moment of inertia
+
+ align:start position:0%
+you're Computing the moment of inertia
+ 
+
+ align:start position:0%
+you're Computing the moment of inertia
+and in our case so so in any case this
+
+ align:start position:0%
+and in our case so so in any case this
+ 
+
+ align:start position:0%
+and in our case so so in any case this
+little moment of mass is sorry little
+
+ align:start position:0%
+little moment of mass is sorry little
+ 
+
+ align:start position:0%
+little moment of mass is sorry little
+element of mass is density times a
+
+ align:start position:0%
+element of mass is density times a
+ 
+
+ align:start position:0%
+element of mass is density times a
+little element of volume so we can also
+
+ align:start position:0%
+little element of volume so we can also
+ 
+
+ align:start position:0%
+little element of volume so we can also
+write this as the triple integral over
+
+ align:start position:0%
+write this as the triple integral over
+ 
+
+ align:start position:0%
+write this as the triple integral over
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+region of R 2 * Delta *
+
+ align:start position:0%
+region of R 2 * Delta *
+ 
+
+ align:start position:0%
+region of R 2 * Delta *
+DV okay so this is what what this is in
+
+ align:start position:0%
+DV okay so this is what what this is in
+ 
+
+ align:start position:0%
+DV okay so this is what what this is in
+general so now let's think about it in
+
+ align:start position:0%
+general so now let's think about it in
+ 
+
+ align:start position:0%
+general so now let's think about it in
+our case well in our case we've we've
+
+ align:start position:0%
+our case well in our case we've we've
+ 
+
+ align:start position:0%
+our case well in our case we've we've
+cleverly chosen our Central axis to be
+
+ align:start position:0%
+cleverly chosen our Central axis to be
+ 
+
+ align:start position:0%
+cleverly chosen our Central axis to be
+the Z axis so this R is just the
+
+ align:start position:0%
+the Z axis so this R is just the
+ 
+
+ align:start position:0%
+the Z axis so this R is just the
+distance from the
+
+ align:start position:0%
+distance from the
+ 
+
+ align:start position:0%
+distance from the
+z-axis um this uh this I was kind enough
+
+ align:start position:0%
+z-axis um this uh this I was kind enough
+ 
+
+ align:start position:0%
+z-axis um this uh this I was kind enough
+to give you a constant density cylinder
+
+ align:start position:0%
+to give you a constant density cylinder
+ 
+
+ align:start position:0%
+to give you a constant density cylinder
+so this Delta is just one that's going
+
+ align:start position:0%
+so this Delta is just one that's going
+ 
+
+ align:start position:0%
+so this Delta is just one that's going
+to be easy and then we have we have this
+
+ align:start position:0%
+to be easy and then we have we have this
+ 
+
+ align:start position:0%
+to be easy and then we have we have this
+triple integral over the whole cylinder
+
+ align:start position:0%
+triple integral over the whole cylinder
+ 
+
+ align:start position:0%
+triple integral over the whole cylinder
+so we want a triple integral over the
+
+ align:start position:0%
+so we want a triple integral over the
+ 
+
+ align:start position:0%
+so we want a triple integral over the
+whole cylinder of some integram that
+
+ align:start position:0%
+whole cylinder of some integram that
+ 
+
+ align:start position:0%
+whole cylinder of some integram that
+involves R um so a natural sort of situ
+
+ align:start position:0%
+involves R um so a natural sort of situ
+ 
+
+ align:start position:0%
+involves R um so a natural sort of situ
+way to thing to do in this situation a
+
+ align:start position:0%
+way to thing to do in this situation a
+ 
+
+ align:start position:0%
+way to thing to do in this situation a
+natural sort of thing to do when you
+
+ align:start position:0%
+natural sort of thing to do when you
+ 
+
+ align:start position:0%
+natural sort of thing to do when you
+have a a a cylinder or anything that's
+
+ align:start position:0%
+have a a a cylinder or anything that's
+ 
+
+ align:start position:0%
+have a a a cylinder or anything that's
+rotationally symmetric and you have an
+
+ align:start position:0%
+rotationally symmetric and you have an
+ 
+
+ align:start position:0%
+rotationally symmetric and you have an
+integrand that that it behaves nicely
+
+ align:start position:0%
+integrand that that it behaves nicely
+ 
+
+ align:start position:0%
+integrand that that it behaves nicely
+with respect to rotation that can be
+
+ align:start position:0%
+with respect to rotation that can be
+ 
+
+ align:start position:0%
+with respect to rotation that can be
+written easily in terms of r or R and
+
+ align:start position:0%
+written easily in terms of r or R and
+ 
+
+ align:start position:0%
+written easily in terms of r or R and
+Theta is to is to do cylindrical
+
+ align:start position:0%
+Theta is to is to do cylindrical
+ 
+
+ align:start position:0%
+Theta is to is to do cylindrical
+coordinates is to think of cylindrical
+
+ align:start position:0%
+coordinates is to think of cylindrical
+ 
+
+ align:start position:0%
+coordinates is to think of cylindrical
+coordinates um so in our case that means
+
+ align:start position:0%
+coordinates um so in our case that means
+ 
+
+ align:start position:0%
+coordinates um so in our case that means
+we we just need to figure out at this
+
+ align:start position:0%
+we we just need to figure out at this
+ 
+
+ align:start position:0%
+we we just need to figure out at this
+point we need to figure out what how do
+
+ align:start position:0%
+point we need to figure out what how do
+ 
+
+ align:start position:0%
+point we need to figure out what how do
+we integrate over this cylinder in
+
+ align:start position:0%
+we integrate over this cylinder in
+ 
+
+ align:start position:0%
+we integrate over this cylinder in
+cylindrical coordinates now integrating
+
+ align:start position:0%
+cylindrical coordinates now integrating
+ 
+
+ align:start position:0%
+cylindrical coordinates now integrating
+um so okay so let's so let's do it so
+
+ align:start position:0%
+um so okay so let's so let's do it so
+ 
+
+ align:start position:0%
+um so okay so let's so let's do it so
+usually I guess um so in our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case so it doesn't matter too much what
+
+ align:start position:0%
+case so it doesn't matter too much what
+ 
+
+ align:start position:0%
+case so it doesn't matter too much what
+what order we do things and so we need
+
+ align:start position:0%
+what order we do things and so we need
+ 
+
+ align:start position:0%
+what order we do things and so we need
+DV we need to write that in terms of the
+
+ align:start position:0%
+DV we need to write that in terms of the
+ 
+
+ align:start position:0%
+DV we need to write that in terms of the
+the cylindrical coordinates so that's DZ
+
+ align:start position:0%
+the cylindrical coordinates so that's DZ
+ 
+
+ align:start position:0%
+the cylindrical coordinates so that's DZ
+D and D Theta and so we know that DV is
+
+ align:start position:0%
+D and D Theta and so we know that DV is
+ 
+
+ align:start position:0%
+D and D Theta and so we know that DV is
+R DZ d d Theta now you you might want
+
+ align:start position:0%
+R DZ d d Theta now you you might want
+ 
+
+ align:start position:0%
+R DZ d d Theta now you you might want
+some other order there but but that's a
+
+ align:start position:0%
+some other order there but but that's a
+ 
+
+ align:start position:0%
+some other order there but but that's a
+good a nice order it usually is is the
+
+ align:start position:0%
+good a nice order it usually is is the
+ 
+
+ align:start position:0%
+good a nice order it usually is is the
+simplest order to consider um so this
+
+ align:start position:0%
+simplest order to consider um so this
+ 
+
+ align:start position:0%
+simplest order to consider um so this
+moment of inertia in our case is going
+
+ align:start position:0%
+moment of inertia in our case is going
+ 
+
+ align:start position:0%
+moment of inertia in our case is going
+to be this triple
+
+ align:start position:0%
+to be this triple
+ 
+
+ align:start position:0%
+to be this triple
+integral okay so we said r^ 2 Delta R 2
+
+ align:start position:0%
+integral okay so we said r^ 2 Delta R 2
+ 
+
+ align:start position:0%
+integral okay so we said r^ 2 Delta R 2
+time density density is one so that's
+
+ align:start position:0%
+time density density is one so that's
+ 
+
+ align:start position:0%
+time density density is one so that's
+just R 2 and R the distance to the axis
+
+ align:start position:0%
+just R 2 and R the distance to the axis
+ 
+
+ align:start position:0%
+just R 2 and R the distance to the axis
+is R the distance to the z- axis so so
+
+ align:start position:0%
+is R the distance to the z- axis so so
+ 
+
+ align:start position:0%
+is R the distance to the z- axis so so
+that's just R
+
+ align:start position:0%
+that's just R
+ 
+
+ align:start position:0%
+that's just R
+2times okay times R
+
+ align:start position:0%
+2times okay times R
+ 
+
+ align:start position:0%
+2times okay times R
+DZ
+
+ align:start position:0%
+DZ
+ 
+
+ align:start position:0%
+DZ
+Dr D Theta so this is the integral we're
+
+ align:start position:0%
+Dr D Theta so this is the integral we're
+ 
+
+ align:start position:0%
+Dr D Theta so this is the integral we're
+trying to compute but we need bounds
+
+ align:start position:0%
+trying to compute but we need bounds
+ 
+
+ align:start position:0%
+trying to compute but we need bounds
+right it's a it's a triple integral it's
+
+ align:start position:0%
+right it's a it's a triple integral it's
+ 
+
+ align:start position:0%
+right it's a it's a triple integral it's
+a definite integral we need we need to
+
+ align:start position:0%
+a definite integral we need we need to
+ 
+
+ align:start position:0%
+a definite integral we need we need to
+figure out what the bounds are to to
+
+ align:start position:0%
+figure out what the bounds are to to
+ 
+
+ align:start position:0%
+figure out what the bounds are to to
+evaluate it as an iterated integral so
+
+ align:start position:0%
+evaluate it as an iterated integral so
+ 
+
+ align:start position:0%
+evaluate it as an iterated integral so
+let's go look at this little picture we
+
+ align:start position:0%
+let's go look at this little picture we
+ 
+
+ align:start position:0%
+let's go look at this little picture we
+drew so I I I guess I didn't discuss
+
+ align:start position:0%
+drew so I I I guess I didn't discuss
+ 
+
+ align:start position:0%
+drew so I I I guess I didn't discuss
+this but I made a choice just to put the
+
+ align:start position:0%
+this but I made a choice just to put the
+ 
+
+ align:start position:0%
+this but I made a choice just to put the
+bottom of the cylinder in the XY plane
+
+ align:start position:0%
+bottom of the cylinder in the XY plane
+ 
+
+ align:start position:0%
+bottom of the cylinder in the XY plane
+and the top at height H it's not going
+
+ align:start position:0%
+and the top at height H it's not going
+ 
+
+ align:start position:0%
+and the top at height H it's not going
+to matter to you know if I if you had
+
+ align:start position:0%
+to matter to you know if I if you had
+ 
+
+ align:start position:0%
+to matter to you know if I if you had
+made some other choice it would work out
+
+ align:start position:0%
+made some other choice it would work out
+ 
+
+ align:start position:0%
+made some other choice it would work out
+fine um so okay so that means that Z is
+
+ align:start position:0%
+fine um so okay so that means that Z is
+ 
+
+ align:start position:0%
+fine um so okay so that means that Z is
+going from Z to H uh regardless of R and
+
+ align:start position:0%
+going from Z to H uh regardless of R and
+ 
+
+ align:start position:0%
+going from Z to H uh regardless of R and
+Theta okay so Z is going from 0 to H
+
+ align:start position:0%
+Theta okay so Z is going from 0 to H
+ 
+
+ align:start position:0%
+Theta okay so Z is going from 0 to H
+that's nice let's put that over here Z
+
+ align:start position:0%
+that's nice let's put that over here Z
+ 
+
+ align:start position:0%
+that's nice let's put that over here Z
+is the inside one it's going from 0 to H
+
+ align:start position:0%
+is the inside one it's going from 0 to H
+ 
+
+ align:start position:0%
+is the inside one it's going from 0 to H
+okay then R is next well this is also
+
+ align:start position:0%
+okay then R is next well this is also
+ 
+
+ align:start position:0%
+okay then R is next well this is also
+it's a night you know cylinders are
+
+ align:start position:0%
+it's a night you know cylinders are
+ 
+
+ align:start position:0%
+it's a night you know cylinders are
+great for cylindrical coordinates
+
+ align:start position:0%
+great for cylindrical coordinates
+ 
+
+ align:start position:0%
+great for cylindrical coordinates
+shocker right given the name I know um
+
+ align:start position:0%
+shocker right given the name I know um
+ 
+
+ align:start position:0%
+shocker right given the name I know um
+so okay so R is going from zero to
+
+ align:start position:0%
+so okay so R is going from zero to
+ 
+
+ align:start position:0%
+so okay so R is going from zero to
+what's the radius our radius was B so R
+
+ align:start position:0%
+what's the radius our radius was B so R
+ 
+
+ align:start position:0%
+what's the radius our radius was B so R
+goes from Z to B and that's true
+
+ align:start position:0%
+goes from Z to B and that's true
+ 
+
+ align:start position:0%
+goes from Z to B and that's true
+regardless of theta so back over here so
+
+ align:start position:0%
+regardless of theta so back over here so
+ 
+
+ align:start position:0%
+regardless of theta so back over here so
+we have R going from zero to B and Theta
+
+ align:start position:0%
+we have R going from zero to B and Theta
+ 
+
+ align:start position:0%
+we have R going from zero to B and Theta
+is going just going from 0 to 2 pi we're
+
+ align:start position:0%
+is going just going from 0 to 2 pi we're
+ 
+
+ align:start position:0%
+is going just going from 0 to 2 pi we're
+doing a the full rotation all the way
+
+ align:start position:0%
+doing a the full rotation all the way
+ 
+
+ align:start position:0%
+doing a the full rotation all the way
+around the cylinder so this is what our
+
+ align:start position:0%
+around the cylinder so this is what our
+ 
+
+ align:start position:0%
+around the cylinder so this is what our
+moment of inertia is and now we just
+
+ align:start position:0%
+moment of inertia is and now we just
+ 
+
+ align:start position:0%
+moment of inertia is and now we just
+have to compute it so we've got uh our
+
+ align:start position:0%
+have to compute it so we've got uh our
+ 
+
+ align:start position:0%
+have to compute it so we've got uh our
+inner integral here is with ECT to Z so
+
+ align:start position:0%
+inner integral here is with ECT to Z so
+ 
+
+ align:start position:0%
+inner integral here is with ECT to Z so
+the inner
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral is the integral from 0 to H of
+
+ align:start position:0%
+integral is the integral from 0 to H of
+ 
+
+ align:start position:0%
+integral is the integral from 0 to H of
+R cubed DZ and R Cub doesn't have any
+
+ align:start position:0%
+R cubed DZ and R Cub doesn't have any
+ 
+
+ align:start position:0%
+R cubed DZ and R Cub doesn't have any
+Z's in It Fabulous so that's just going
+
+ align:start position:0%
+Z's in It Fabulous so that's just going
+ 
+
+ align:start position:0%
+Z's in It Fabulous so that's just going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+be R cubed Z where Z goes from 0 to H so
+
+ align:start position:0%
+be R cubed Z where Z goes from 0 to H so
+ 
+
+ align:start position:0%
+be R cubed Z where Z goes from 0 to H so
+that's HR cubed minus 0 so HR cubed all
+
+ align:start position:0%
+that's HR cubed minus 0 so HR cubed all
+ 
+
+ align:start position:0%
+that's HR cubed minus 0 so HR cubed all
+right so that's the inner so now let's
+
+ align:start position:0%
+right so that's the inner so now let's
+ 
+
+ align:start position:0%
+right so that's the inner so now let's
+look at the middle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+integral so this is going to be the
+
+ align:start position:0%
+integral so this is going to be the
+ 
+
+ align:start position:0%
+integral so this is going to be the
+integral as it's that's our uh our our R
+
+ align:start position:0%
+integral as it's that's our uh our our R
+ 
+
+ align:start position:0%
+integral as it's that's our uh our our R
+integral so and it's going from zero to
+
+ align:start position:0%
+integral so and it's going from zero to
+ 
+
+ align:start position:0%
+integral so and it's going from zero to
+B and what are we integrating we're
+
+ align:start position:0%
+B and what are we integrating we're
+ 
+
+ align:start position:0%
+B and what are we integrating we're
+integrating the inner integral so the
+
+ align:start position:0%
+integrating the inner integral so the
+ 
+
+ align:start position:0%
+integrating the inner integral so the
+inner integral was HR cubed so we're
+
+ align:start position:0%
+inner integral was HR cubed so we're
+ 
+
+ align:start position:0%
+inner integral was HR cubed so we're
+integrating H R cubed d r from Z to be
+
+ align:start position:0%
+integrating H R cubed d r from Z to be
+ 
+
+ align:start position:0%
+integrating H R cubed d r from Z to be
+all right this is not quite as easy but
+
+ align:start position:0%
+all right this is not quite as easy but
+ 
+
+ align:start position:0%
+all right this is not quite as easy but
+H is a constant we're integrating R cub
+
+ align:start position:0%
+H is a constant we're integrating R cub
+ 
+
+ align:start position:0%
+H is a constant we're integrating R cub
+all right I've done worse you've done
+
+ align:start position:0%
+all right I've done worse you've done
+ 
+
+ align:start position:0%
+all right I've done worse you've done
+worse um so that's going to be HR to 4th
+
+ align:start position:0%
+worse um so that's going to be HR to 4th
+ 
+
+ align:start position:0%
+worse um so that's going to be HR to 4th
+over 4 between 0 and B so okay so that's
+
+ align:start position:0%
+over 4 between 0 and B so okay so that's
+ 
+
+ align:start position:0%
+over 4 between 0 and B so okay so that's
+h b 4 over 4 minus H * 0 4 over 4 so the
+
+ align:start position:0%
+h b 4 over 4 minus H * 0 4 over 4 so the
+ 
+
+ align:start position:0%
+h b 4 over 4 minus H * 0 4 over 4 so the
+second term zero so this is just equal
+
+ align:start position:0%
+second term zero so this is just equal
+ 
+
+ align:start position:0%
+second term zero so this is just equal
+to H * B 4 over 4 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finally we have our outermost integral
+
+ align:start position:0%
+finally we have our outermost integral
+ 
+
+ align:start position:0%
+finally we have our outermost integral
+so what was that integral well that was
+
+ align:start position:0%
+so what was that integral well that was
+ 
+
+ align:start position:0%
+so what was that integral well that was
+the integral from 0 to 2 pi D Theta of
+
+ align:start position:0%
+the integral from 0 to 2 pi D Theta of
+ 
+
+ align:start position:0%
+the integral from 0 to 2 pi D Theta of
+the second integral so this is of the
+
+ align:start position:0%
+the second integral so this is of the
+ 
+
+ align:start position:0%
+the second integral so this is of the
+middle integral so that's the integral
+
+ align:start position:0%
+middle integral so that's the integral
+ 
+
+ align:start position:0%
+middle integral so that's the integral
+from 0 to 2
+
+ align:start position:0%
+from 0 to 2
+ 
+
+ align:start position:0%
+from 0 to 2
+pi D Theta of the middle integral which
+
+ align:start position:0%
+pi D Theta of the middle integral which
+ 
+
+ align:start position:0%
+pi D Theta of the middle integral which
+was h b to 4th over 4 and this is just a
+
+ align:start position:0%
+was h b to 4th over 4 and this is just a
+ 
+
+ align:start position:0%
+was h b to 4th over 4 and this is just a
+constant again great um so this is h b
+
+ align:start position:0%
+constant again great um so this is h b
+ 
+
+ align:start position:0%
+constant again great um so this is h b
+4th over 4 times the okay times 2 pi um
+
+ align:start position:0%
+4th over 4 times the okay times 2 pi um
+ 
+
+ align:start position:0%
+4th over 4 times the okay times 2 pi um
+so it's that's what is that work out to
+
+ align:start position:0%
+so it's that's what is that work out to
+ 
+
+ align:start position:0%
+so it's that's what is that work out to
+that's h b
+
+ align:start position:0%
+that's h b
+ 
+
+ align:start position:0%
+that's h b
+4th
+
+ align:start position:0%
+4th
+ 
+
+ align:start position:0%
+4th
+pi/
+
+ align:start position:0%
+pi/
+ 
+
+ align:start position:0%
+pi/
+2 all right so there you go now um if
+
+ align:start position:0%
+2 all right so there you go now um if
+ 
+
+ align:start position:0%
+2 all right so there you go now um if
+you wanted to you could uh you could
+
+ align:start position:0%
+you wanted to you could uh you could
+ 
+
+ align:start position:0%
+you wanted to you could uh you could
+also rewrite this a little bit because
+
+ align:start position:0%
+also rewrite this a little bit because
+ 
+
+ align:start position:0%
+also rewrite this a little bit because
+you could note that this is pi hb^ s
+
+ align:start position:0%
+you could note that this is pi hb^ s
+ 
+
+ align:start position:0%
+you could note that this is pi hb^ s
+that's your your volume of your of your
+
+ align:start position:0%
+that's your your volume of your of your
+ 
+
+ align:start position:0%
+that's your your volume of your of your
+cylinder and in fact it's not just your
+
+ align:start position:0%
+cylinder and in fact it's not just your
+ 
+
+ align:start position:0%
+cylinder and in fact it's not just your
+volume it's your mass of your cylinder
+
+ align:start position:0%
+volume it's your mass of your cylinder
+ 
+
+ align:start position:0%
+volume it's your mass of your cylinder
+because it had constant density one so
+
+ align:start position:0%
+because it had constant density one so
+ 
+
+ align:start position:0%
+because it had constant density one so
+you also could have written this uh as
+
+ align:start position:0%
+you also could have written this uh as
+ 
+
+ align:start position:0%
+you also could have written this uh as
+mass time a^ 2 / 2 just uh sorry b^2
+
+ align:start position:0%
+mass time a^ 2 / 2 just uh sorry b^2
+ 
+
+ align:start position:0%
+mass time a^ 2 / 2 just uh sorry b^2
+over two don't know where a came from U
+
+ align:start position:0%
+over two don't know where a came from U
+ 
+
+ align:start position:0%
+over two don't know where a came from U
+Mass time B squ so you had you have some
+
+ align:start position:0%
+Mass time B squ so you had you have some
+ 
+
+ align:start position:0%
+Mass time B squ so you had you have some
+other options for how you could write
+
+ align:start position:0%
+other options for how you could write
+ 
+
+ align:start position:0%
+other options for how you could write
+this answer by by using you know
+
+ align:start position:0%
+this answer by by using you know
+ 
+
+ align:start position:0%
+this answer by by using you know
+involving the volume and and mass and so
+
+ align:start position:0%
+involving the volume and and mass and so
+ 
+
+ align:start position:0%
+involving the volume and and mass and so
+on um so let's just recap very quickly
+
+ align:start position:0%
+on um so let's just recap very quickly
+ 
+
+ align:start position:0%
+on um so let's just recap very quickly
+um why we did what we did we had a we
+
+ align:start position:0%
+um why we did what we did we had a we
+ 
+
+ align:start position:0%
+um why we did what we did we had a we
+had a cylinder and so really the the
+
+ align:start position:0%
+had a cylinder and so really the the
+ 
+
+ align:start position:0%
+had a cylinder and so really the the
+given given a cylinder it was a Natural
+
+ align:start position:0%
+given given a cylinder it was a Natural
+ 
+
+ align:start position:0%
+given given a cylinder it was a Natural
+Choice to look at cylindrical
+
+ align:start position:0%
+Choice to look at cylindrical
+ 
+
+ align:start position:0%
+Choice to look at cylindrical
+coordinates and once we had cylindrical
+
+ align:start position:0%
+coordinates and once we had cylindrical
+ 
+
+ align:start position:0%
+coordinates and once we had cylindrical
+coordinates everything was easy so we
+
+ align:start position:0%
+coordinates everything was easy so we
+ 
+
+ align:start position:0%
+coordinates everything was easy so we
+just took our general form of the moment
+
+ align:start position:0%
+just took our general form of the moment
+ 
+
+ align:start position:0%
+just took our general form of the moment
+of inertia took the region in question
+
+ align:start position:0%
+of inertia took the region in question
+ 
+
+ align:start position:0%
+of inertia took the region in question
+in cylindrical coordinates it was very
+
+ align:start position:0%
+in cylindrical coordinates it was very
+ 
+
+ align:start position:0%
+in cylindrical coordinates it was very
+very easy to describe this entire region
+
+ align:start position:0%
+very easy to describe this entire region
+ 
+
+ align:start position:0%
+very easy to describe this entire region
+and then uh our integrals were were
+
+ align:start position:0%
+and then uh our integrals were were
+ 
+
+ align:start position:0%
+and then uh our integrals were were
+pretty easy to compute after we made
+
+ align:start position:0%
+pretty easy to compute after we made
+ 
+
+ align:start position:0%
+pretty easy to compute after we made
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+choice uh after we made that choice they
+
+ align:start position:0%
+choice uh after we made that choice they
+ 
+
+ align:start position:0%
+choice uh after we made that choice they
+were they were nice and easy to compute
+
+ align:start position:0%
+were they were nice and easy to compute
+ 
+
+ align:start position:0%
+were they were nice and easy to compute
+so I'll stop there
\ No newline at end of file
diff --git a/iZPzBHGDsWI.txt b/iZPzBHGDsWI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2fefc85f04c3d9a44946e93cd6ac738685342f65
--- /dev/null
+++ b/iZPzBHGDsWI.txt
@@ -0,0 +1,18688 @@
+align:start position:0%
+ 
+welcome everyone um
+
+ align:start position:0%
+welcome everyone um
+ 
+
+ align:start position:0%
+welcome everyone um
+back to um theory of computation
+
+ align:start position:0%
+back to um theory of computation
+ 
+
+ align:start position:0%
+back to um theory of computation
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we are now at lecture number 15 and
+
+ align:start position:0%
+we are now at lecture number 15 and
+ 
+
+ align:start position:0%
+we are now at lecture number 15 and
+if this is an important
+
+ align:start position:0%
+if this is an important
+ 
+
+ align:start position:0%
+if this is an important
+lecture um well all of our lectures are
+
+ align:start position:0%
+lecture um well all of our lectures are
+ 
+
+ align:start position:0%
+lecture um well all of our lectures are
+important but
+
+ align:start position:0%
+important but
+ 
+
+ align:start position:0%
+important but
+this is i'm going to introduce
+
+ align:start position:0%
+this is i'm going to introduce
+ 
+
+ align:start position:0%
+this is i'm going to introduce
+one of the major topics
+
+ align:start position:0%
+one of the major topics
+ 
+
+ align:start position:0%
+one of the major topics
+that we're going to see
+
+ align:start position:0%
+that we're going to see
+ 
+
+ align:start position:0%
+that we're going to see
+going on in various forms through the
+
+ align:start position:0%
+going on in various forms through the
+ 
+
+ align:start position:0%
+going on in various forms through the
+rest of the semester which is the notion
+
+ align:start position:0%
+rest of the semester which is the notion
+ 
+
+ align:start position:0%
+rest of the semester which is the notion
+of a complete problem in this case it's
+
+ align:start position:0%
+of a complete problem in this case it's
+ 
+
+ align:start position:0%
+of a complete problem in this case it's
+going to be an np complete problem
+
+ align:start position:0%
+going to be an np complete problem
+ 
+
+ align:start position:0%
+going to be an np complete problem
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i think some of you have probably heard
+
+ align:start position:0%
+i think some of you have probably heard
+ 
+
+ align:start position:0%
+i think some of you have probably heard
+of that concept already maybe you've
+
+ align:start position:0%
+of that concept already maybe you've
+ 
+
+ align:start position:0%
+of that concept already maybe you've
+seen it in some courses or other but
+
+ align:start position:0%
+seen it in some courses or other but
+ 
+
+ align:start position:0%
+seen it in some courses or other but
+we're going to do that in a
+
+ align:start position:0%
+we're going to do that in a
+ 
+
+ align:start position:0%
+we're going to do that in a
+in a rather careful and formal way
+
+ align:start position:0%
+in a rather careful and formal way
+ 
+
+ align:start position:0%
+in a rather careful and formal way
+over the next couple of lectures
+
+ align:start position:0%
+over the next couple of lectures
+ 
+
+ align:start position:0%
+over the next couple of lectures
+so we are following up on our
+
+ align:start position:0%
+so we are following up on our
+ 
+
+ align:start position:0%
+so we are following up on our
+previous discussions about complexity
+
+ align:start position:0%
+previous discussions about complexity
+ 
+
+ align:start position:0%
+previous discussions about complexity
+time complexity
+
+ align:start position:0%
+time complexity
+ 
+
+ align:start position:0%
+time complexity
+we defined
+
+ align:start position:0%
+we defined
+ 
+
+ align:start position:0%
+we defined
+the time and non-deterministic time
+
+ align:start position:0%
+the time and non-deterministic time
+ 
+
+ align:start position:0%
+the time and non-deterministic time
+complexity classes as you may remember
+
+ align:start position:0%
+complexity classes as you may remember
+ 
+
+ align:start position:0%
+complexity classes as you may remember
+the classes p and np
+
+ align:start position:0%
+the classes p and np
+ 
+
+ align:start position:0%
+the classes p and np
+talked about the p versus np problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+looked at some interesting algorithm for
+
+ align:start position:0%
+looked at some interesting algorithm for
+ 
+
+ align:start position:0%
+looked at some interesting algorithm for
+showing problems in p called dynamic
+
+ align:start position:0%
+showing problems in p called dynamic
+ 
+
+ align:start position:0%
+showing problems in p called dynamic
+programming
+
+ align:start position:0%
+programming
+ 
+
+ align:start position:0%
+programming
+and we started to move toward our
+
+ align:start position:0%
+and we started to move toward our
+ 
+
+ align:start position:0%
+and we started to move toward our
+discussion of np completeness with the
+
+ align:start position:0%
+discussion of np completeness with the
+ 
+
+ align:start position:0%
+discussion of np completeness with the
+introduction of polynomial time
+
+ align:start position:0%
+introduction of polynomial time
+ 
+
+ align:start position:0%
+introduction of polynomial time
+reducibility
+
+ align:start position:0%
+reducibility
+ 
+
+ align:start position:0%
+reducibility
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+related to some of the earlier
+
+ align:start position:0%
+related to some of the earlier
+ 
+
+ align:start position:0%
+related to some of the earlier
+reducibility notions that we discussed
+
+ align:start position:0%
+reducibility notions that we discussed
+ 
+
+ align:start position:0%
+reducibility notions that we discussed
+in the computability section
+
+ align:start position:0%
+in the computability section
+ 
+
+ align:start position:0%
+in the computability section
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quick review um
+
+ align:start position:0%
+quick review um
+ 
+
+ align:start position:0%
+quick review um
+what it means for one problem to be
+
+ align:start position:0%
+what it means for one problem to be
+ 
+
+ align:start position:0%
+what it means for one problem to be
+polynomial time reducible to another
+
+ align:start position:0%
+polynomial time reducible to another
+ 
+
+ align:start position:0%
+polynomial time reducible to another
+this follows our pattern of
+
+ align:start position:0%
+this follows our pattern of
+ 
+
+ align:start position:0%
+this follows our pattern of
+reducibility concepts where
+
+ align:start position:0%
+reducibility concepts where
+ 
+
+ align:start position:0%
+reducibility concepts where
+um if a problem is reducible to another
+
+ align:start position:0%
+um if a problem is reducible to another
+ 
+
+ align:start position:0%
+um if a problem is reducible to another
+problem and that other problem is
+
+ align:start position:0%
+problem and that other problem is
+ 
+
+ align:start position:0%
+problem and that other problem is
+solvable then the first problem is
+
+ align:start position:0%
+solvable then the first problem is
+ 
+
+ align:start position:0%
+solvable then the first problem is
+solvable so if a problem is reducible to
+
+ align:start position:0%
+solvable so if a problem is reducible to
+ 
+
+ align:start position:0%
+solvable so if a problem is reducible to
+an easy problem that problem becomes
+
+ align:start position:0%
+an easy problem that problem becomes
+ 
+
+ align:start position:0%
+an easy problem that problem becomes
+easy too
+
+ align:start position:0%
+easy too
+ 
+
+ align:start position:0%
+easy too
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+the kind of reduction that we're going
+
+ align:start position:0%
+the kind of reduction that we're going
+ 
+
+ align:start position:0%
+the kind of reduction that we're going
+to be looking at here are the mapping
+
+ align:start position:0%
+to be looking at here are the mapping
+ 
+
+ align:start position:0%
+to be looking at here are the mapping
+reductions but now where the reductions
+
+ align:start position:0%
+reductions but now where the reductions
+ 
+
+ align:start position:0%
+reductions but now where the reductions
+are computable in polynomial time
+
+ align:start position:0%
+are computable in polynomial time
+ 
+
+ align:start position:0%
+are computable in polynomial time
+and so we had this um
+
+ align:start position:0%
+and so we had this um
+ 
+
+ align:start position:0%
+and so we had this um
+result we mentioned last time that if a
+
+ align:start position:0%
+result we mentioned last time that if a
+ 
+
+ align:start position:0%
+result we mentioned last time that if a
+is polynomial time reducible to b and b
+
+ align:start position:0%
+is polynomial time reducible to b and b
+ 
+
+ align:start position:0%
+is polynomial time reducible to b and b
+is in p then a is also in p
+
+ align:start position:0%
+is in p then a is also in p
+ 
+
+ align:start position:0%
+is in p then a is also in p
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so that's going to be um
+
+ align:start position:0%
+so that's going to be um
+ 
+
+ align:start position:0%
+so that's going to be um
+critically important for the
+
+ align:start position:0%
+critically important for the
+ 
+
+ align:start position:0%
+critically important for the
+you know for the
+
+ align:start position:0%
+you know for the
+ 
+
+ align:start position:0%
+you know for the
+for the whole um
+
+ align:start position:0%
+for the whole um
+ 
+
+ align:start position:0%
+for the whole um
+of discussion that's coming
+
+ align:start position:0%
+of discussion that's coming
+ 
+
+ align:start position:0%
+of discussion that's coming
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+our intuition about pnnp um
+
+ align:start position:0%
+our intuition about pnnp um
+ 
+
+ align:start position:0%
+our intuition about pnnp um
+repeating that here um the np problems
+
+ align:start position:0%
+repeating that here um the np problems
+ 
+
+ align:start position:0%
+repeating that here um the np problems
+are the ones where you can verify
+
+ align:start position:0%
+are the ones where you can verify
+ 
+
+ align:start position:0%
+are the ones where you can verify
+membership easily
+
+ align:start position:0%
+membership easily
+ 
+
+ align:start position:0%
+membership easily
+as opposed to
+
+ align:start position:0%
+as opposed to
+ 
+
+ align:start position:0%
+as opposed to
+being able to test membership easily
+
+ align:start position:0%
+being able to test membership easily
+ 
+
+ align:start position:0%
+being able to test membership easily
+those are the problems that are in p the
+
+ align:start position:0%
+those are the problems that are in p the
+ 
+
+ align:start position:0%
+those are the problems that are in p the
+verification typically requires
+
+ align:start position:0%
+verification typically requires
+ 
+
+ align:start position:0%
+verification typically requires
+some kind of a
+
+ align:start position:0%
+some kind of a
+ 
+
+ align:start position:0%
+some kind of a
+certificate
+
+ align:start position:0%
+certificate
+ 
+
+ align:start position:0%
+certificate
+that establishes kind of a proof
+
+ align:start position:0%
+that establishes kind of a proof
+ 
+
+ align:start position:0%
+that establishes kind of a proof
+that the input is a member of that
+
+ align:start position:0%
+that the input is a member of that
+ 
+
+ align:start position:0%
+that the input is a member of that
+language
+
+ align:start position:0%
+language
+ 
+
+ align:start position:0%
+language
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and the
+
+ align:start position:0%
+and the
+ 
+
+ align:start position:0%
+and the
+big question of the field which remains
+
+ align:start position:0%
+big question of the field which remains
+ 
+
+ align:start position:0%
+big question of the field which remains
+an unsolved problem
+
+ align:start position:0%
+an unsolved problem
+ 
+
+ align:start position:0%
+an unsolved problem
+is whether p equals np it's called the p
+
+ align:start position:0%
+is whether p equals np it's called the p
+ 
+
+ align:start position:0%
+is whether p equals np it's called the p
+versus np question
+
+ align:start position:0%
+versus np question
+ 
+
+ align:start position:0%
+versus np question
+and we don't know the answer so whether
+
+ align:start position:0%
+and we don't know the answer so whether
+ 
+
+ align:start position:0%
+and we don't know the answer so whether
+there are problems that are
+
+ align:start position:0%
+there are problems that are
+ 
+
+ align:start position:0%
+there are problems that are
+in np um solvable and nondeterministic
+
+ align:start position:0%
+in np um solvable and nondeterministic
+ 
+
+ align:start position:0%
+in np um solvable and nondeterministic
+polynomial time typically these are
+
+ align:start position:0%
+polynomial time typically these are
+ 
+
+ align:start position:0%
+polynomial time typically these are
+problems that involve searching whether
+
+ align:start position:0%
+problems that involve searching whether
+ 
+
+ align:start position:0%
+problems that involve searching whether
+they can be solved in polynomial time
+
+ align:start position:0%
+they can be solved in polynomial time
+ 
+
+ align:start position:0%
+they can be solved in polynomial time
+typically without the searching um
+
+ align:start position:0%
+typically without the searching um
+ 
+
+ align:start position:0%
+typically without the searching um
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh if p
+
+ align:start position:0%
+uh if p
+ 
+
+ align:start position:0%
+uh if p
+were equal to np then you could always
+
+ align:start position:0%
+were equal to np then you could always
+ 
+
+ align:start position:0%
+were equal to np then you could always
+eliminate searching and a p were
+
+ align:start position:0%
+eliminate searching and a p were
+ 
+
+ align:start position:0%
+eliminate searching and a p were
+different from np then there were cases
+
+ align:start position:0%
+different from np then there were cases
+ 
+
+ align:start position:0%
+different from np then there were cases
+where you need to search um and we don't
+
+ align:start position:0%
+where you need to search um and we don't
+ 
+
+ align:start position:0%
+where you need to search um and we don't
+know the answer to that uh
+
+ align:start position:0%
+know the answer to that uh
+ 
+
+ align:start position:0%
+know the answer to that uh
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+the direction of exploring uh this
+
+ align:start position:0%
+the direction of exploring uh this
+ 
+
+ align:start position:0%
+the direction of exploring uh this
+this question and its ramifications
+
+ align:start position:0%
+this question and its ramifications
+ 
+
+ align:start position:0%
+this question and its ramifications
+we introduced this problem called sat
+
+ align:start position:0%
+we introduced this problem called sat
+ 
+
+ align:start position:0%
+we introduced this problem called sat
+these are the boolean formulas
+
+ align:start position:0%
+these are the boolean formulas
+ 
+
+ align:start position:0%
+these are the boolean formulas
+which have an assignment
+
+ align:start position:0%
+which have an assignment
+ 
+
+ align:start position:0%
+which have an assignment
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+enable that event makes them evaluate to
+
+ align:start position:0%
+enable that event makes them evaluate to
+ 
+
+ align:start position:0%
+enable that event makes them evaluate to
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so we call those satisfiable formulas
+
+ align:start position:0%
+so we call those satisfiable formulas
+ 
+
+ align:start position:0%
+so we call those satisfiable formulas
+and uh we um mentioned but have not yet
+
+ align:start position:0%
+and uh we um mentioned but have not yet
+ 
+
+ align:start position:0%
+and uh we um mentioned but have not yet
+proven and we will not prove until the
+
+ align:start position:0%
+proven and we will not prove until the
+ 
+
+ align:start position:0%
+proven and we will not prove until the
+next lecture on tuesday
+
+ align:start position:0%
+next lecture on tuesday
+ 
+
+ align:start position:0%
+next lecture on tuesday
+that there is this theorem
+
+ align:start position:0%
+that there is this theorem
+ 
+
+ align:start position:0%
+that there is this theorem
+uh kind of a very remarkable theorem
+
+ align:start position:0%
+uh kind of a very remarkable theorem
+ 
+
+ align:start position:0%
+uh kind of a very remarkable theorem
+that says that if you have uh you take
+
+ align:start position:0%
+that says that if you have uh you take
+ 
+
+ align:start position:0%
+that says that if you have uh you take
+the satisfiability problem and if it is
+
+ align:start position:0%
+the satisfiability problem and if it is
+ 
+
+ align:start position:0%
+the satisfiability problem and if it is
+solvable quickly then all of the np
+
+ align:start position:0%
+solvable quickly then all of the np
+ 
+
+ align:start position:0%
+solvable quickly then all of the np
+problems are solvable quickly so if sat
+
+ align:start position:0%
+problems are solvable quickly so if sat
+ 
+
+ align:start position:0%
+problems are solvable quickly so if sat
+is in p then p equals np so in a sense
+
+ align:start position:0%
+is in p then p equals np so in a sense
+ 
+
+ align:start position:0%
+is in p then p equals np so in a sense
+sat is kind of you know the
+
+ align:start position:0%
+sat is kind of you know the
+ 
+
+ align:start position:0%
+sat is kind of you know the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+it's sort of the super
+
+ align:start position:0%
+it's sort of the super
+ 
+
+ align:start position:0%
+it's sort of the super
+np problem in the sense that all of the
+
+ align:start position:0%
+np problem in the sense that all of the
+ 
+
+ align:start position:0%
+np problem in the sense that all of the
+difficulty of any np problem is
+
+ align:start position:0%
+difficulty of any np problem is
+ 
+
+ align:start position:0%
+difficulty of any np problem is
+is embedded within sat so if sat becomes
+
+ align:start position:0%
+is embedded within sat so if sat becomes
+ 
+
+ align:start position:0%
+is embedded within sat so if sat becomes
+easy then all of the other np problems
+
+ align:start position:0%
+easy then all of the other np problems
+ 
+
+ align:start position:0%
+easy then all of the other np problems
+become easy um and we'll eventually
+
+ align:start position:0%
+become easy um and we'll eventually
+ 
+
+ align:start position:0%
+become easy um and we'll eventually
+prove that but right now we're kind of
+
+ align:start position:0%
+prove that but right now we're kind of
+ 
+
+ align:start position:0%
+prove that but right now we're kind of
+setting up
+
+ align:start position:0%
+setting up
+ 
+
+ align:start position:0%
+setting up
+the um terminology to allow us to do
+
+ align:start position:0%
+the um terminology to allow us to do
+ 
+
+ align:start position:0%
+the um terminology to allow us to do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so uh anyway we'll we'll we'll get there
+
+ align:start position:0%
+so uh anyway we'll we'll we'll get there
+ 
+
+ align:start position:0%
+so uh anyway we'll we'll we'll get there
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the the the key ingredient for proving
+
+ align:start position:0%
+the the the key ingredient for proving
+ 
+
+ align:start position:0%
+the the the key ingredient for proving
+this kook 11 theorem is polynomial time
+
+ align:start position:0%
+this kook 11 theorem is polynomial time
+ 
+
+ align:start position:0%
+this kook 11 theorem is polynomial time
+reducibility
+
+ align:start position:0%
+reducibility
+ 
+
+ align:start position:0%
+reducibility
+what we're going to show
+
+ align:start position:0%
+what we're going to show
+ 
+
+ align:start position:0%
+what we're going to show
+is that every problem in np
+
+ align:start position:0%
+is that every problem in np
+ 
+
+ align:start position:0%
+is that every problem in np
+can be polynomial time reduced to set
+
+ align:start position:0%
+can be polynomial time reduced to set
+ 
+
+ align:start position:0%
+can be polynomial time reduced to set
+so every np problem can be converted
+
+ align:start position:0%
+so every np problem can be converted
+ 
+
+ align:start position:0%
+so every np problem can be converted
+into a set problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+working toward that because when you
+
+ align:start position:0%
+working toward that because when you
+ 
+
+ align:start position:0%
+working toward that because when you
+think about it you know there are
+
+ align:start position:0%
+think about it you know there are
+ 
+
+ align:start position:0%
+think about it you know there are
+infinitely many problems in np and
+
+ align:start position:0%
+infinitely many problems in np and
+ 
+
+ align:start position:0%
+infinitely many problems in np and
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+being able to show that all of them
+
+ align:start position:0%
+being able to show that all of them
+ 
+
+ align:start position:0%
+being able to show that all of them
+are reducible to sat as in a sense kind
+
+ align:start position:0%
+are reducible to sat as in a sense kind
+ 
+
+ align:start position:0%
+are reducible to sat as in a sense kind
+of um you have to prove a kind of a
+
+ align:start position:0%
+of um you have to prove a kind of a
+ 
+
+ align:start position:0%
+of um you have to prove a kind of a
+higher level theorem it's not just a
+
+ align:start position:0%
+higher level theorem it's not just a
+ 
+
+ align:start position:0%
+higher level theorem it's not just a
+single reduction we're kind of
+
+ align:start position:0%
+single reduction we're kind of
+ 
+
+ align:start position:0%
+single reduction we're kind of
+exhibiting a schema of reductions which
+
+ align:start position:0%
+exhibiting a schema of reductions which
+ 
+
+ align:start position:0%
+exhibiting a schema of reductions which
+shows that all of these problems can be
+
+ align:start position:0%
+shows that all of these problems can be
+ 
+
+ align:start position:0%
+shows that all of these problems can be
+reduced to set
+
+ align:start position:0%
+reduced to set
+ 
+
+ align:start position:0%
+reduced to set
+um and kind of
+
+ align:start position:0%
+um and kind of
+ 
+
+ align:start position:0%
+um and kind of
+developing
+
+ align:start position:0%
+developing
+ 
+
+ align:start position:0%
+developing
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know our intuition toward that
+
+ align:start position:0%
+you know our intuition toward that
+ 
+
+ align:start position:0%
+you know our intuition toward that
+direction we're going to look at some
+
+ align:start position:0%
+direction we're going to look at some
+ 
+
+ align:start position:0%
+direction we're going to look at some
+specific polynomial time reductions
+
+ align:start position:0%
+specific polynomial time reductions
+ 
+
+ align:start position:0%
+specific polynomial time reductions
+today um
+
+ align:start position:0%
+today um
+ 
+
+ align:start position:0%
+today um
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we'll start out with a reduction between
+
+ align:start position:0%
+we'll start out with a reduction between
+ 
+
+ align:start position:0%
+we'll start out with a reduction between
+two problems we have not yet seen one of
+
+ align:start position:0%
+two problems we have not yet seen one of
+ 
+
+ align:start position:0%
+two problems we have not yet seen one of
+them called threesat and the other one
+
+ align:start position:0%
+them called threesat and the other one
+ 
+
+ align:start position:0%
+them called threesat and the other one
+called clique so on this slide we're
+
+ align:start position:0%
+called clique so on this slide we're
+ 
+
+ align:start position:0%
+called clique so on this slide we're
+going to introduce those two problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so remembering again about boolean
+
+ align:start position:0%
+so remembering again about boolean
+ 
+
+ align:start position:0%
+so remembering again about boolean
+formulas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to consider a special
+
+ align:start position:0%
+we're going to consider a special
+ 
+
+ align:start position:0%
+we're going to consider a special
+class
+
+ align:start position:0%
+class
+ 
+
+ align:start position:0%
+class
+of boolean formulas a restricted form of
+
+ align:start position:0%
+of boolean formulas a restricted form of
+ 
+
+ align:start position:0%
+of boolean formulas a restricted form of
+boolean form formulas called conjunctive
+
+ align:start position:0%
+boolean form formulas called conjunctive
+ 
+
+ align:start position:0%
+boolean form formulas called conjunctive
+normal form
+
+ align:start position:0%
+normal form
+ 
+
+ align:start position:0%
+normal form
+and so this formula here in particular
+
+ align:start position:0%
+and so this formula here in particular
+ 
+
+ align:start position:0%
+and so this formula here in particular
+is in that conjunctive normal form
+
+ align:start position:0%
+is in that conjunctive normal form
+ 
+
+ align:start position:0%
+is in that conjunctive normal form
+um so just remember um i was explaining
+
+ align:start position:0%
+um so just remember um i was explaining
+ 
+
+ align:start position:0%
+um so just remember um i was explaining
+some of this to someone else uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+earlier this morning showing some of
+
+ align:start position:0%
+earlier this morning showing some of
+ 
+
+ align:start position:0%
+earlier this morning showing some of
+these slides and it was pointed out that
+
+ align:start position:0%
+these slides and it was pointed out that
+ 
+
+ align:start position:0%
+these slides and it was pointed out that
+not all of you may have be familiar with
+
+ align:start position:0%
+not all of you may have be familiar with
+ 
+
+ align:start position:0%
+not all of you may have be familiar with
+these um the boolean operations of and
+
+ align:start position:0%
+these um the boolean operations of and
+ 
+
+ align:start position:0%
+these um the boolean operations of and
+and or
+
+ align:start position:0%
+and or
+ 
+
+ align:start position:0%
+and or
+uh so this is the or symbol here
+
+ align:start position:0%
+uh so this is the or symbol here
+ 
+
+ align:start position:0%
+uh so this is the or symbol here
+this is the and symbol here
+
+ align:start position:0%
+this is the and symbol here
+ 
+
+ align:start position:0%
+this is the and symbol here
+you know they operate you know hopefully
+
+ align:start position:0%
+you know they operate you know hopefully
+ 
+
+ align:start position:0%
+you know they operate you know hopefully
+you've seen the just the concept of
+
+ align:start position:0%
+you've seen the just the concept of
+ 
+
+ align:start position:0%
+you've seen the just the concept of
+boolean and or
+
+ align:start position:0%
+boolean and or
+ 
+
+ align:start position:0%
+boolean and or
+or is in a sense a little bit like a
+
+ align:start position:0%
+or is in a sense a little bit like a
+ 
+
+ align:start position:0%
+or is in a sense a little bit like a
+union um and it's like an intersection
+
+ align:start position:0%
+union um and it's like an intersection
+ 
+
+ align:start position:0%
+union um and it's like an intersection
+and the the symbols here are kind of a
+
+ align:start position:0%
+and the the symbols here are kind of a
+ 
+
+ align:start position:0%
+and the the symbols here are kind of a
+little bit similar to the union and
+
+ align:start position:0%
+little bit similar to the union and
+ 
+
+ align:start position:0%
+little bit similar to the union and
+intersections you know the intersection
+
+ align:start position:0%
+intersections you know the intersection
+ 
+
+ align:start position:0%
+intersections you know the intersection
+the union intersection symbols
+
+ align:start position:0%
+the union intersection symbols
+ 
+
+ align:start position:0%
+the union intersection symbols
+themselves like or the v-shaped is a
+
+ align:start position:0%
+themselves like or the v-shaped is a
+ 
+
+ align:start position:0%
+themselves like or the v-shaped is a
+little bit like a
+
+ align:start position:0%
+little bit like a
+ 
+
+ align:start position:0%
+little bit like a
+pointy union symbol and the in the um
+
+ align:start position:0%
+pointy union symbol and the in the um
+ 
+
+ align:start position:0%
+pointy union symbol and the in the um
+upside-down v-shape is a little like a
+
+ align:start position:0%
+upside-down v-shape is a little like a
+ 
+
+ align:start position:0%
+upside-down v-shape is a little like a
+pointy intersection symbol so maybe
+
+ align:start position:0%
+pointy intersection symbol so maybe
+ 
+
+ align:start position:0%
+pointy intersection symbol so maybe
+that's if you haven't seen those seen
+
+ align:start position:0%
+that's if you haven't seen those seen
+ 
+
+ align:start position:0%
+that's if you haven't seen those seen
+that connection before maybe it's
+
+ align:start position:0%
+that connection before maybe it's
+ 
+
+ align:start position:0%
+that connection before maybe it's
+interesting to observe that
+
+ align:start position:0%
+interesting to observe that
+ 
+
+ align:start position:0%
+interesting to observe that
+but anyway um
+
+ align:start position:0%
+but anyway um
+ 
+
+ align:start position:0%
+but anyway um
+what makes this
+
+ align:start position:0%
+what makes this
+ 
+
+ align:start position:0%
+what makes this
+uh formula be in conjunctive normal form
+
+ align:start position:0%
+uh formula be in conjunctive normal form
+ 
+
+ align:start position:0%
+uh formula be in conjunctive normal form
+well the conjunctive normal form
+
+ align:start position:0%
+well the conjunctive normal form
+ 
+
+ align:start position:0%
+well the conjunctive normal form
+formulas
+
+ align:start position:0%
+formulas
+ 
+
+ align:start position:0%
+formulas
+are organized in a certain way they have
+
+ align:start position:0%
+are organized in a certain way they have
+ 
+
+ align:start position:0%
+are organized in a certain way they have
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+these groups called clauses within the
+
+ align:start position:0%
+these groups called clauses within the
+ 
+
+ align:start position:0%
+these groups called clauses within the
+parentheses
+
+ align:start position:0%
+parentheses
+ 
+
+ align:start position:0%
+parentheses
+that are added together that are
+
+ align:start position:0%
+that are added together that are
+ 
+
+ align:start position:0%
+that are added together that are
+connected by these and
+
+ align:start position:0%
+connected by these and
+ 
+
+ align:start position:0%
+connected by these and
+and operations um
+
+ align:start position:0%
+and operations um
+ 
+
+ align:start position:0%
+and operations um
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+within those groups which are called
+
+ align:start position:0%
+within those groups which are called
+ 
+
+ align:start position:0%
+within those groups which are called
+clauses
+
+ align:start position:0%
+clauses
+ 
+
+ align:start position:0%
+clauses
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+elements are
+
+ align:start position:0%
+elements are
+ 
+
+ align:start position:0%
+elements are
+ored together
+
+ align:start position:0%
+ored together
+ 
+
+ align:start position:0%
+ored together
+those elements
+
+ align:start position:0%
+those elements
+ 
+
+ align:start position:0%
+those elements
+are going to be either variables
+
+ align:start position:0%
+are going to be either variables
+ 
+
+ align:start position:0%
+are going to be either variables
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+variables with negation negated
+
+ align:start position:0%
+variables with negation negated
+ 
+
+ align:start position:0%
+variables with negation negated
+variables um
+
+ align:start position:0%
+variables um
+ 
+
+ align:start position:0%
+variables um
+so uh just to repeat that
+
+ align:start position:0%
+so uh just to repeat that
+ 
+
+ align:start position:0%
+so uh just to repeat that
+uh these well i'll just just state those
+
+ align:start position:0%
+uh these well i'll just just state those
+ 
+
+ align:start position:0%
+uh these well i'll just just state those
+those variables or negated variables are
+
+ align:start position:0%
+those variables or negated variables are
+ 
+
+ align:start position:0%
+those variables or negated variables are
+going to be called literals um
+
+ align:start position:0%
+going to be called literals um
+ 
+
+ align:start position:0%
+going to be called literals um
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+ors of a bunch of literals are going to
+
+ align:start position:0%
+ors of a bunch of literals are going to
+ 
+
+ align:start position:0%
+ors of a bunch of literals are going to
+be called clauses
+
+ align:start position:0%
+be called clauses
+ 
+
+ align:start position:0%
+be called clauses
+okay this is just the standard
+
+ align:start position:0%
+okay this is just the standard
+ 
+
+ align:start position:0%
+okay this is just the standard
+terminology in the field
+
+ align:start position:0%
+terminology in the field
+ 
+
+ align:start position:0%
+terminology in the field
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um a literal is a variable or a negated
+
+ align:start position:0%
+um a literal is a variable or a negated
+ 
+
+ align:start position:0%
+um a literal is a variable or a negated
+variable
+
+ align:start position:0%
+variable
+ 
+
+ align:start position:0%
+variable
+and a clause is an or
+
+ align:start position:0%
+and a clause is an or
+ 
+
+ align:start position:0%
+and a clause is an or
+of literals
+
+ align:start position:0%
+of literals
+ 
+
+ align:start position:0%
+of literals
+okay just a definition
+
+ align:start position:0%
+okay just a definition
+ 
+
+ align:start position:0%
+okay just a definition
+all right so we have a bunch of these
+
+ align:start position:0%
+all right so we have a bunch of these
+ 
+
+ align:start position:0%
+all right so we have a bunch of these
+clauses here each of the clauses has an
+
+ align:start position:0%
+clauses here each of the clauses has an
+ 
+
+ align:start position:0%
+clauses here each of the clauses has an
+or of of liter of literals in it
+
+ align:start position:0%
+or of of liter of literals in it
+ 
+
+ align:start position:0%
+or of of liter of literals in it
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+a chomsky
+
+ align:start position:0%
+a chomsky
+ 
+
+ align:start position:0%
+a chomsky
+conjunctive normal form
+
+ align:start position:0%
+conjunctive normal form
+ 
+
+ align:start position:0%
+conjunctive normal form
+uh formula i guess they're both c and
+
+ align:start position:0%
+uh formula i guess they're both c and
+ 
+
+ align:start position:0%
+uh formula i guess they're both c and
+f's but uh
+
+ align:start position:0%
+f's but uh
+ 
+
+ align:start position:0%
+f's but uh
+it's conjunctive normal form formula is
+
+ align:start position:0%
+it's conjunctive normal form formula is
+ 
+
+ align:start position:0%
+it's conjunctive normal form formula is
+one that's written as an and of these
+
+ align:start position:0%
+one that's written as an and of these
+ 
+
+ align:start position:0%
+one that's written as an and of these
+clauses
+
+ align:start position:0%
+clauses
+ 
+
+ align:start position:0%
+clauses
+okay so we take these clauses which
+
+ align:start position:0%
+okay so we take these clauses which
+ 
+
+ align:start position:0%
+okay so we take these clauses which
+themselves are ors we and them together
+
+ align:start position:0%
+themselves are ors we and them together
+ 
+
+ align:start position:0%
+themselves are ors we and them together
+we get a formula that's conjunctive
+
+ align:start position:0%
+we get a formula that's conjunctive
+ 
+
+ align:start position:0%
+we get a formula that's conjunctive
+normal form conjunctive stands for and i
+
+ align:start position:0%
+normal form conjunctive stands for and i
+ 
+
+ align:start position:0%
+normal form conjunctive stands for and i
+think uh conjunction is an and um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then a three
+
+ align:start position:0%
+and then a three
+ 
+
+ align:start position:0%
+and then a three
+cnf
+
+ align:start position:0%
+cnf
+ 
+
+ align:start position:0%
+cnf
+is a cnf where each clause has exactly
+
+ align:start position:0%
+is a cnf where each clause has exactly
+ 
+
+ align:start position:0%
+is a cnf where each clause has exactly
+three literals
+
+ align:start position:0%
+three literals
+ 
+
+ align:start position:0%
+three literals
+so for example this particular
+
+ align:start position:0%
+so for example this particular
+ 
+
+ align:start position:0%
+so for example this particular
+formula is a cnf but it's not a three
+
+ align:start position:0%
+formula is a cnf but it's not a three
+ 
+
+ align:start position:0%
+formula is a cnf but it's not a three
+cnf because it has at least two clauses
+
+ align:start position:0%
+cnf because it has at least two clauses
+ 
+
+ align:start position:0%
+cnf because it has at least two clauses
+which violate the condition of three
+
+ align:start position:0%
+which violate the condition of three
+ 
+
+ align:start position:0%
+which violate the condition of three
+literals per clause this one is okay
+
+ align:start position:0%
+literals per clause this one is okay
+ 
+
+ align:start position:0%
+literals per clause this one is okay
+obviously
+
+ align:start position:0%
+obviously
+ 
+
+ align:start position:0%
+obviously
+this first clause
+
+ align:start position:0%
+this first clause
+ 
+
+ align:start position:0%
+this first clause
+and the three sat problem
+
+ align:start position:0%
+and the three sat problem
+ 
+
+ align:start position:0%
+and the three sat problem
+so this is the first of the two problems
+
+ align:start position:0%
+so this is the first of the two problems
+ 
+
+ align:start position:0%
+so this is the first of the two problems
+we're going to be talking about
+
+ align:start position:0%
+we're going to be talking about
+ 
+
+ align:start position:0%
+we're going to be talking about
+the three sad problem
+
+ align:start position:0%
+the three sad problem
+ 
+
+ align:start position:0%
+the three sad problem
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the satisfiability problem restricted to
+
+ align:start position:0%
+the satisfiability problem restricted to
+ 
+
+ align:start position:0%
+the satisfiability problem restricted to
+these three cnf formulas
+
+ align:start position:0%
+these three cnf formulas
+ 
+
+ align:start position:0%
+these three cnf formulas
+so this is the collection of
+
+ align:start position:0%
+so this is the collection of
+ 
+
+ align:start position:0%
+so this is the collection of
+setup of three cnf formulas which are
+
+ align:start position:0%
+setup of three cnf formulas which are
+ 
+
+ align:start position:0%
+setup of three cnf formulas which are
+satisfiable
+
+ align:start position:0%
+satisfiable
+ 
+
+ align:start position:0%
+satisfiable
+so you can think of it as a kind of a
+
+ align:start position:0%
+so you can think of it as a kind of a
+ 
+
+ align:start position:0%
+so you can think of it as a kind of a
+special case
+
+ align:start position:0%
+special case
+ 
+
+ align:start position:0%
+special case
+of the sat problem where we only care
+
+ align:start position:0%
+of the sat problem where we only care
+ 
+
+ align:start position:0%
+of the sat problem where we only care
+about formulas of the special kind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this being a special case you might
+
+ align:start position:0%
+this being a special case you might
+ 
+
+ align:start position:0%
+this being a special case you might
+imagine that this might be an easier
+
+ align:start position:0%
+imagine that this might be an easier
+ 
+
+ align:start position:0%
+imagine that this might be an easier
+problem to solve but in general it turns
+
+ align:start position:0%
+problem to solve but in general it turns
+ 
+
+ align:start position:0%
+problem to solve but in general it turns
+out not to be as we will see this is
+
+ align:start position:0%
+out not to be as we will see this is
+ 
+
+ align:start position:0%
+out not to be as we will see this is
+just as solving this special case is
+
+ align:start position:0%
+just as solving this special case is
+ 
+
+ align:start position:0%
+just as solving this special case is
+just as har as hard as solving the
+
+ align:start position:0%
+just as har as hard as solving the
+ 
+
+ align:start position:0%
+just as har as hard as solving the
+general case for satisfiability
+
+ align:start position:0%
+general case for satisfiability
+ 
+
+ align:start position:0%
+general case for satisfiability
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+now let's turn to the second
+
+ align:start position:0%
+now let's turn to the second
+ 
+
+ align:start position:0%
+now let's turn to the second
+of these two languages up in the
+
+ align:start position:0%
+of these two languages up in the
+ 
+
+ align:start position:0%
+of these two languages up in the
+headline
+
+ align:start position:0%
+headline
+ 
+
+ align:start position:0%
+headline
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the clique problem
+
+ align:start position:0%
+the clique problem
+ 
+
+ align:start position:0%
+the clique problem
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so for that we gonna turn to graph
+
+ align:start position:0%
+so for that we gonna turn to graph
+ 
+
+ align:start position:0%
+so for that we gonna turn to graph
+theory
+
+ align:start position:0%
+theory
+ 
+
+ align:start position:0%
+theory
+so we're going to consider graphs
+
+ align:start position:0%
+so we're going to consider graphs
+ 
+
+ align:start position:0%
+so we're going to consider graphs
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+points and lines connecting them
+
+ align:start position:0%
+points and lines connecting them
+ 
+
+ align:start position:0%
+points and lines connecting them
+and we will say that a clique
+
+ align:start position:0%
+and we will say that a clique
+ 
+
+ align:start position:0%
+and we will say that a clique
+in a graph
+
+ align:start position:0%
+in a graph
+ 
+
+ align:start position:0%
+in a graph
+is a collection of nodes collection of
+
+ align:start position:0%
+is a collection of nodes collection of
+ 
+
+ align:start position:0%
+is a collection of nodes collection of
+the points that are all pairwise
+
+ align:start position:0%
+the points that are all pairwise
+ 
+
+ align:start position:0%
+the points that are all pairwise
+connected by lines
+
+ align:start position:0%
+connected by lines
+ 
+
+ align:start position:0%
+connected by lines
+and a k click is one where you have case
+
+ align:start position:0%
+and a k click is one where you have case
+ 
+
+ align:start position:0%
+and a k click is one where you have case
+arch nodes
+
+ align:start position:0%
+arch nodes
+ 
+
+ align:start position:0%
+arch nodes
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+here we have a three click four click
+
+ align:start position:0%
+here we have a three click four click
+ 
+
+ align:start position:0%
+here we have a three click four click
+and five click
+
+ align:start position:0%
+and five click
+ 
+
+ align:start position:0%
+and five click
+um and the clique problem
+
+ align:start position:0%
+um and the clique problem
+ 
+
+ align:start position:0%
+um and the clique problem
+is to try to find cliques of a certain
+
+ align:start position:0%
+is to try to find cliques of a certain
+ 
+
+ align:start position:0%
+is to try to find cliques of a certain
+specified size
+
+ align:start position:0%
+specified size
+ 
+
+ align:start position:0%
+specified size
+embedded within a given graph
+
+ align:start position:0%
+embedded within a given graph
+ 
+
+ align:start position:0%
+embedded within a given graph
+so you'd like to know whether you're
+
+ align:start position:0%
+so you'd like to know whether you're
+ 
+
+ align:start position:0%
+so you'd like to know whether you're
+going to be given a graph and it targets
+
+ align:start position:0%
+going to be given a graph and it targets
+ 
+
+ align:start position:0%
+going to be given a graph and it targets
+click-sized k
+
+ align:start position:0%
+click-sized k
+ 
+
+ align:start position:0%
+click-sized k
+and you want to know is there a subset
+
+ align:start position:0%
+and you want to know is there a subset
+ 
+
+ align:start position:0%
+and you want to know is there a subset
+of the nodes in the graph
+
+ align:start position:0%
+of the nodes in the graph
+ 
+
+ align:start position:0%
+of the nodes in the graph
+of size k
+
+ align:start position:0%
+of size k
+ 
+
+ align:start position:0%
+of size k
+that are all connected to one another
+
+ align:start position:0%
+that are all connected to one another
+ 
+
+ align:start position:0%
+that are all connected to one another
+that's the cleat problem
+
+ align:start position:0%
+that's the cleat problem
+ 
+
+ align:start position:0%
+that's the cleat problem
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so obviously
+
+ align:start position:0%
+so obviously
+ 
+
+ align:start position:0%
+so obviously
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the clique problem just as with the
+
+ align:start position:0%
+the clique problem just as with the
+ 
+
+ align:start position:0%
+the clique problem just as with the
+satisfiability problem is a decidable
+
+ align:start position:0%
+satisfiability problem is a decidable
+ 
+
+ align:start position:0%
+satisfiability problem is a decidable
+problem you can just try every possible
+
+ align:start position:0%
+problem you can just try every possible
+ 
+
+ align:start position:0%
+problem you can just try every possible
+subset of k nodes
+
+ align:start position:0%
+subset of k nodes
+ 
+
+ align:start position:0%
+subset of k nodes
+and see whether it constitutes a clique
+
+ align:start position:0%
+and see whether it constitutes a clique
+ 
+
+ align:start position:0%
+and see whether it constitutes a clique
+but that's in general going to be an
+
+ align:start position:0%
+but that's in general going to be an
+ 
+
+ align:start position:0%
+but that's in general going to be an
+exponential algorithm if you have you
+
+ align:start position:0%
+exponential algorithm if you have you
+ 
+
+ align:start position:0%
+exponential algorithm if you have you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+you know k is a large value like it
+
+ align:start position:0%
+you know k is a large value like it
+ 
+
+ align:start position:0%
+you know k is a large value like it
+might be half the size of the graph you
+
+ align:start position:0%
+might be half the size of the graph you
+ 
+
+ align:start position:0%
+might be half the size of the graph you
+might be looking for a very large clique
+
+ align:start position:0%
+might be looking for a very large clique
+ 
+
+ align:start position:0%
+might be looking for a very large clique
+then you have to try
+
+ align:start position:0%
+then you have to try
+ 
+
+ align:start position:0%
+then you have to try
+many many subsets in order to see
+
+ align:start position:0%
+many many subsets in order to see
+ 
+
+ align:start position:0%
+many many subsets in order to see
+whether uh any one of them is a clique
+
+ align:start position:0%
+whether uh any one of them is a clique
+ 
+
+ align:start position:0%
+whether uh any one of them is a clique
+it's also going to be and i hope you get
+
+ align:start position:0%
+it's also going to be and i hope you get
+ 
+
+ align:start position:0%
+it's also going to be and i hope you get
+this intuition this is a problem that's
+
+ align:start position:0%
+this intuition this is a problem that's
+ 
+
+ align:start position:0%
+this intuition this is a problem that's
+in np
+
+ align:start position:0%
+in np
+ 
+
+ align:start position:0%
+in np
+the cleat problem is an np problem
+
+ align:start position:0%
+the cleat problem is an np problem
+ 
+
+ align:start position:0%
+the cleat problem is an np problem
+because you can easily verify
+
+ align:start position:0%
+because you can easily verify
+ 
+
+ align:start position:0%
+because you can easily verify
+that a graph uh has a k click just by
+
+ align:start position:0%
+that a graph uh has a k click just by
+ 
+
+ align:start position:0%
+that a graph uh has a k click just by
+exhibiting the click
+
+ align:start position:0%
+exhibiting the click
+ 
+
+ align:start position:0%
+exhibiting the click
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+now uh
+
+ align:start position:0%
+now uh
+ 
+
+ align:start position:0%
+now uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so the clique language here is you're
+
+ align:start position:0%
+so the clique language here is you're
+ 
+
+ align:start position:0%
+so the clique language here is you're
+given a graph and a k and you want to
+
+ align:start position:0%
+given a graph and a k and you want to
+ 
+
+ align:start position:0%
+given a graph and a k and you want to
+know does the graph contain a cake
+
+ align:start position:0%
+know does the graph contain a cake
+ 
+
+ align:start position:0%
+know does the graph contain a cake
+league um and what we're going to show
+
+ align:start position:0%
+league um and what we're going to show
+ 
+
+ align:start position:0%
+league um and what we're going to show
+is that these two problems are connected
+
+ align:start position:0%
+is that these two problems are connected
+ 
+
+ align:start position:0%
+is that these two problems are connected
+that the three set problem and the cleat
+
+ align:start position:0%
+that the three set problem and the cleat
+ 
+
+ align:start position:0%
+that the three set problem and the cleat
+problem are related in that you can
+
+ align:start position:0%
+problem are related in that you can
+ 
+
+ align:start position:0%
+problem are related in that you can
+reduce in polynomial time three sat to
+
+ align:start position:0%
+reduce in polynomial time three sat to
+ 
+
+ align:start position:0%
+reduce in polynomial time three sat to
+click
+
+ align:start position:0%
+click
+ 
+
+ align:start position:0%
+click
+okay so this is um
+
+ align:start position:0%
+okay so this is um
+ 
+
+ align:start position:0%
+okay so this is um
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+you know just standing back at it
+
+ align:start position:0%
+you know just standing back at it
+ 
+
+ align:start position:0%
+you know just standing back at it
+back for a minute you know that seems
+
+ align:start position:0%
+back for a minute you know that seems
+ 
+
+ align:start position:0%
+back for a minute you know that seems
+kind of surprising there's no real
+
+ align:start position:0%
+kind of surprising there's no real
+ 
+
+ align:start position:0%
+kind of surprising there's no real
+reason
+
+ align:start position:0%
+reason
+ 
+
+ align:start position:0%
+reason
+you know uh obviously anyway no obvious
+
+ align:start position:0%
+you know uh obviously anyway no obvious
+ 
+
+ align:start position:0%
+you know uh obviously anyway no obvious
+reason why there should be a connection
+
+ align:start position:0%
+reason why there should be a connection
+ 
+
+ align:start position:0%
+reason why there should be a connection
+between three sat and click click they
+
+ align:start position:0%
+between three sat and click click they
+ 
+
+ align:start position:0%
+between three sat and click click they
+look very different from one another
+
+ align:start position:0%
+look very different from one another
+ 
+
+ align:start position:0%
+look very different from one another
+but we do give that uh we will give that
+
+ align:start position:0%
+but we do give that uh we will give that
+ 
+
+ align:start position:0%
+but we do give that uh we will give that
+reduction
+
+ align:start position:0%
+reduction
+ 
+
+ align:start position:0%
+reduction
+and um it then that implies that if you
+
+ align:start position:0%
+and um it then that implies that if you
+ 
+
+ align:start position:0%
+and um it then that implies that if you
+can find a way of solving the clique
+
+ align:start position:0%
+can find a way of solving the clique
+ 
+
+ align:start position:0%
+can find a way of solving the clique
+problem quickly that'll give you a way
+
+ align:start position:0%
+problem quickly that'll give you a way
+ 
+
+ align:start position:0%
+problem quickly that'll give you a way
+of solving the the three set problem
+
+ align:start position:0%
+of solving the the three set problem
+ 
+
+ align:start position:0%
+of solving the the three set problem
+quickly
+
+ align:start position:0%
+quickly
+ 
+
+ align:start position:0%
+quickly
+um and that's going to be the whole
+
+ align:start position:0%
+um and that's going to be the whole
+ 
+
+ align:start position:0%
+um and that's going to be the whole
+point of this um
+
+ align:start position:0%
+point of this um
+ 
+
+ align:start position:0%
+point of this um
+so we're going to show this over the
+
+ align:start position:0%
+so we're going to show this over the
+ 
+
+ align:start position:0%
+so we're going to show this over the
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+slide or two um this this polynomial
+
+ align:start position:0%
+slide or two um this this polynomial
+ 
+
+ align:start position:0%
+slide or two um this this polynomial
+time reduction and this is something i'm
+
+ align:start position:0%
+time reduction and this is something i'm
+ 
+
+ align:start position:0%
+time reduction and this is something i'm
+going to walk through it slowly
+
+ align:start position:0%
+going to walk through it slowly
+ 
+
+ align:start position:0%
+going to walk through it slowly
+but this is one where you it's really
+
+ align:start position:0%
+but this is one where you it's really
+ 
+
+ align:start position:0%
+but this is one where you it's really
+important to try to get a sense of how
+
+ align:start position:0%
+important to try to get a sense of how
+ 
+
+ align:start position:0%
+important to try to get a sense of how
+it's working um
+
+ align:start position:0%
+it's working um
+ 
+
+ align:start position:0%
+it's working um
+uh because this is the kind of thing
+
+ align:start position:0%
+uh because this is the kind of thing
+ 
+
+ align:start position:0%
+uh because this is the kind of thing
+that we're going to be doing a lot of
+
+ align:start position:0%
+that we're going to be doing a lot of
+ 
+
+ align:start position:0%
+that we're going to be doing a lot of
+and you're going to be asked to do it
+
+ align:start position:0%
+and you're going to be asked to do it
+ 
+
+ align:start position:0%
+and you're going to be asked to do it
+also on the homework and and possibly on
+
+ align:start position:0%
+also on the homework and and possibly on
+ 
+
+ align:start position:0%
+also on the homework and and possibly on
+the final exam i hate to use that as the
+
+ align:start position:0%
+the final exam i hate to use that as the
+ 
+
+ align:start position:0%
+the final exam i hate to use that as the
+motivating force here but at least it
+
+ align:start position:0%
+motivating force here but at least it
+ 
+
+ align:start position:0%
+motivating force here but at least it
+might be one motivation for some of you
+
+ align:start position:0%
+might be one motivation for some of you
+ 
+
+ align:start position:0%
+might be one motivation for some of you
+that you have to understand how to do uh
+
+ align:start position:0%
+that you have to understand how to do uh
+ 
+
+ align:start position:0%
+that you have to understand how to do uh
+this kind of a reduction
+
+ align:start position:0%
+this kind of a reduction
+ 
+
+ align:start position:0%
+this kind of a reduction
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+you know i i think at a high level
+
+ align:start position:0%
+you know i i think at a high level
+ 
+
+ align:start position:0%
+you know i i think at a high level
+what's going on is we're showing how to
+
+ align:start position:0%
+what's going on is we're showing how to
+ 
+
+ align:start position:0%
+what's going on is we're showing how to
+recode
+
+ align:start position:0%
+recode
+ 
+
+ align:start position:0%
+recode
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+boolean formula satisfiability problem
+
+ align:start position:0%
+boolean formula satisfiability problem
+ 
+
+ align:start position:0%
+boolean formula satisfiability problem
+into the problem of testing whether a
+
+ align:start position:0%
+into the problem of testing whether a
+ 
+
+ align:start position:0%
+into the problem of testing whether a
+graph has a clique
+
+ align:start position:0%
+graph has a clique
+ 
+
+ align:start position:0%
+graph has a clique
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see if we have any questions here
+
+ align:start position:0%
+let's see if we have any questions here
+ 
+
+ align:start position:0%
+let's see if we have any questions here
+that are coming up in the in the chat um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so i this is an interesting
+
+ align:start position:0%
+okay so i this is an interesting
+ 
+
+ align:start position:0%
+okay so i this is an interesting
+question here can we always convert
+
+ align:start position:0%
+question here can we always convert
+ 
+
+ align:start position:0%
+question here can we always convert
+a boolean
+
+ align:start position:0%
+a boolean
+ 
+
+ align:start position:0%
+a boolean
+formula
+
+ align:start position:0%
+formula
+ 
+
+ align:start position:0%
+formula
+into conjunctive into conjunctive normal
+
+ align:start position:0%
+into conjunctive into conjunctive normal
+ 
+
+ align:start position:0%
+into conjunctive into conjunctive normal
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+first of all yes the answer is you can
+
+ align:start position:0%
+first of all yes the answer is you can
+ 
+
+ align:start position:0%
+first of all yes the answer is you can
+always convert a boolean formula into an
+
+ align:start position:0%
+always convert a boolean formula into an
+ 
+
+ align:start position:0%
+always convert a boolean formula into an
+equivalent one in ins into in cnf
+
+ align:start position:0%
+equivalent one in ins into in cnf
+ 
+
+ align:start position:0%
+equivalent one in ins into in cnf
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+in general that might make the formula
+
+ align:start position:0%
+in general that might make the formula
+ 
+
+ align:start position:0%
+in general that might make the formula
+exponentially larger
+
+ align:start position:0%
+exponentially larger
+ 
+
+ align:start position:0%
+exponentially larger
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+just the mere fact that you can convert
+
+ align:start position:0%
+just the mere fact that you can convert
+ 
+
+ align:start position:0%
+just the mere fact that you can convert
+formulas into into conjunctive normal
+
+ align:start position:0%
+formulas into into conjunctive normal
+ 
+
+ align:start position:0%
+formulas into into conjunctive normal
+form doesn't mean
+
+ align:start position:0%
+form doesn't mean
+ 
+
+ align:start position:0%
+form doesn't mean
+that solving um
+
+ align:start position:0%
+that solving um
+ 
+
+ align:start position:0%
+that solving um
+that you know that solving uh
+
+ align:start position:0%
+that you know that solving uh
+ 
+
+ align:start position:0%
+that you know that solving uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+conjunctive normal form uh formulas for
+
+ align:start position:0%
+conjunctive normal form uh formulas for
+ 
+
+ align:start position:0%
+conjunctive normal form uh formulas for
+testing satisfiability of the of the cnf
+
+ align:start position:0%
+testing satisfiability of the of the cnf
+ 
+
+ align:start position:0%
+testing satisfiability of the of the cnf
+formulas is going to be as hard as
+
+ align:start position:0%
+formulas is going to be as hard as
+ 
+
+ align:start position:0%
+formulas is going to be as hard as
+testing the general case because just
+
+ align:start position:0%
+testing the general case because just
+ 
+
+ align:start position:0%
+testing the general case because just
+the conversion might be exponential um
+
+ align:start position:0%
+the conversion might be exponential um
+ 
+
+ align:start position:0%
+the conversion might be exponential um
+there's something more uh more
+
+ align:start position:0%
+there's something more uh more
+ 
+
+ align:start position:0%
+there's something more uh more
+a little bit more complicated going on
+
+ align:start position:0%
+a little bit more complicated going on
+ 
+
+ align:start position:0%
+a little bit more complicated going on
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+than that
+
+ align:start position:0%
+than that
+ 
+
+ align:start position:0%
+than that
+so let's uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let me just see here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh if he is a satisfiable formula which
+
+ align:start position:0%
+uh if he is a satisfiable formula which
+ 
+
+ align:start position:0%
+uh if he is a satisfiable formula which
+is not in cnf can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a similar
+
+ align:start position:0%
+so a similar
+ 
+
+ align:start position:0%
+so a similar
+um you know similar question so the
+
+ align:start position:0%
+um you know similar question so the
+ 
+
+ align:start position:0%
+um you know similar question so the
+questions that i'm getting are about
+
+ align:start position:0%
+questions that i'm getting are about
+ 
+
+ align:start position:0%
+questions that i'm getting are about
+converting formulas uh to cnf um
+
+ align:start position:0%
+converting formulas uh to cnf um
+ 
+
+ align:start position:0%
+converting formulas uh to cnf um
+so yeah you can do it but not in
+
+ align:start position:0%
+so yeah you can do it but not in
+ 
+
+ align:start position:0%
+so yeah you can do it but not in
+polynomial time in general because the
+
+ align:start position:0%
+polynomial time in general because the
+ 
+
+ align:start position:0%
+polynomial time in general because the
+resulting formula you get might be much
+
+ align:start position:0%
+resulting formula you get might be much
+ 
+
+ align:start position:0%
+resulting formula you get might be much
+larger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um if you if you're looking for an
+
+ align:start position:0%
+um if you if you're looking for an
+ 
+
+ align:start position:0%
+um if you if you're looking for an
+equivalent formula if you're not looking
+
+ align:start position:0%
+equivalent formula if you're not looking
+ 
+
+ align:start position:0%
+equivalent formula if you're not looking
+for an equivalent formula then you know
+
+ align:start position:0%
+for an equivalent formula then you know
+ 
+
+ align:start position:0%
+for an equivalent formula then you know
+of course then depending upon what
+
+ align:start position:0%
+of course then depending upon what
+ 
+
+ align:start position:0%
+of course then depending upon what
+you're looking for you might be able to
+
+ align:start position:0%
+you're looking for you might be able to
+ 
+
+ align:start position:0%
+you're looking for you might be able to
+find something smaller
+
+ align:start position:0%
+find something smaller
+ 
+
+ align:start position:0%
+find something smaller
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ah
+
+ align:start position:0%
+ah
+ 
+
+ align:start position:0%
+ah
+this is a this is a i guess a good basic
+
+ align:start position:0%
+this is a this is a i guess a good basic
+ 
+
+ align:start position:0%
+this is a this is a i guess a good basic
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+why is clique in np
+
+ align:start position:0%
+why is clique in np
+ 
+
+ align:start position:0%
+why is clique in np
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+because isn't doesn't verifying that you
+
+ align:start position:0%
+because isn't doesn't verifying that you
+ 
+
+ align:start position:0%
+because isn't doesn't verifying that you
+have a clique require going through all
+
+ align:start position:0%
+have a clique require going through all
+ 
+
+ align:start position:0%
+have a clique require going through all
+the possible cliques
+
+ align:start position:0%
+the possible cliques
+ 
+
+ align:start position:0%
+the possible cliques
+once i
+
+ align:start position:0%
+once i
+ 
+
+ align:start position:0%
+once i
+you have to understand what verifying
+
+ align:start position:0%
+you have to understand what verifying
+ 
+
+ align:start position:0%
+you have to understand what verifying
+means verifying means you can verify
+
+ align:start position:0%
+means verifying means you can verify
+ 
+
+ align:start position:0%
+means verifying means you can verify
+something if you're given a certificate
+
+ align:start position:0%
+something if you're given a certificate
+ 
+
+ align:start position:0%
+something if you're given a certificate
+in the case of a clique
+
+ align:start position:0%
+in the case of a clique
+ 
+
+ align:start position:0%
+in the case of a clique
+the click problem the certificate is the
+
+ align:start position:0%
+the click problem the certificate is the
+ 
+
+ align:start position:0%
+the click problem the certificate is the
+clique
+
+ align:start position:0%
+clique
+ 
+
+ align:start position:0%
+clique
+um so once you have the certificate you
+
+ align:start position:0%
+um so once you have the certificate you
+ 
+
+ align:start position:0%
+um so once you have the certificate you
+can do the verification in polynomial
+
+ align:start position:0%
+can do the verification in polynomial
+ 
+
+ align:start position:0%
+can do the verification in polynomial
+time finding the certificate of course
+
+ align:start position:0%
+time finding the certificate of course
+ 
+
+ align:start position:0%
+time finding the certificate of course
+might be difficult
+
+ align:start position:0%
+might be difficult
+ 
+
+ align:start position:0%
+might be difficult
+so you only think of np in the context
+
+ align:start position:0%
+so you only think of np in the context
+ 
+
+ align:start position:0%
+so you only think of np in the context
+of having that certificate
+
+ align:start position:0%
+of having that certificate
+ 
+
+ align:start position:0%
+of having that certificate
+so in a case for like
+
+ align:start position:0%
+so in a case for like
+ 
+
+ align:start position:0%
+so in a case for like
+compositeness the certificate might be
+
+ align:start position:0%
+compositeness the certificate might be
+ 
+
+ align:start position:0%
+compositeness the certificate might be
+the factor
+
+ align:start position:0%
+the factor
+ 
+
+ align:start position:0%
+the factor
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anyway i hope that's you know it's there
+
+ align:start position:0%
+anyway i hope that's you know it's there
+ 
+
+ align:start position:0%
+anyway i hope that's you know it's there
+there are problems sometimes with what
+
+ align:start position:0%
+there are problems sometimes with what
+ 
+
+ align:start position:0%
+there are problems sometimes with what
+the certificate is is not necessarily
+
+ align:start position:0%
+the certificate is is not necessarily
+ 
+
+ align:start position:0%
+the certificate is is not necessarily
+obvious um but there can be a
+
+ align:start position:0%
+obvious um but there can be a
+ 
+
+ align:start position:0%
+obvious um but there can be a
+certificate um for
+
+ align:start position:0%
+certificate um for
+ 
+
+ align:start position:0%
+certificate um for
+um showing that the
+
+ align:start position:0%
+um showing that the
+ 
+
+ align:start position:0%
+um showing that the
+that the input is in the language but in
+
+ align:start position:0%
+that the input is in the language but in
+ 
+
+ align:start position:0%
+that the input is in the language but in
+the ones that we've done so far maybe
+
+ align:start position:0%
+the ones that we've done so far maybe
+ 
+
+ align:start position:0%
+the ones that we've done so far maybe
+you can argue that this certificate is
+
+ align:start position:0%
+you can argue that this certificate is
+ 
+
+ align:start position:0%
+you can argue that this certificate is
+sort of an obvious thing but it's not
+
+ align:start position:0%
+sort of an obvious thing but it's not
+ 
+
+ align:start position:0%
+sort of an obvious thing but it's not
+always an obvious thing
+
+ align:start position:0%
+always an obvious thing
+ 
+
+ align:start position:0%
+always an obvious thing
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+why don't we move on then
+
+ align:start position:0%
+why don't we move on then
+ 
+
+ align:start position:0%
+why don't we move on then
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so let's see how do we do
+
+ align:start position:0%
+so let's see how do we do
+ 
+
+ align:start position:0%
+so let's see how do we do
+this polynomial time reduction from
+
+ align:start position:0%
+this polynomial time reduction from
+ 
+
+ align:start position:0%
+this polynomial time reduction from
+three sat to click
+
+ align:start position:0%
+three sat to click
+ 
+
+ align:start position:0%
+three sat to click
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+here we go
+
+ align:start position:0%
+here we go
+ 
+
+ align:start position:0%
+here we go
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i'm just going to give a reduction
+
+ align:start position:0%
+so i'm just going to give a reduction
+ 
+
+ align:start position:0%
+so i'm just going to give a reduction
+that's that's that's what the definition
+
+ align:start position:0%
+that's that's that's what the definition
+ 
+
+ align:start position:0%
+that's that's that's what the definition
+means i'm going to give a way of
+
+ align:start position:0%
+means i'm going to give a way of
+ 
+
+ align:start position:0%
+means i'm going to give a way of
+converting
+
+ align:start position:0%
+converting
+ 
+
+ align:start position:0%
+converting
+formulas
+
+ align:start position:0%
+formulas
+ 
+
+ align:start position:0%
+formulas
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+pairs
+
+ align:start position:0%
+pairs
+ 
+
+ align:start position:0%
+pairs
+a g and a k
+
+ align:start position:0%
+a g and a k
+ 
+
+ align:start position:0%
+a g and a k
+where the formula is going to be solid
+
+ align:start position:0%
+where the formula is going to be solid
+ 
+
+ align:start position:0%
+where the formula is going to be solid
+satisfiable if and only if the graph has
+
+ align:start position:0%
+satisfiable if and only if the graph has
+ 
+
+ align:start position:0%
+satisfiable if and only if the graph has
+a k click
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's kind of a little bit do it
+
+ align:start position:0%
+okay so let's kind of a little bit do it
+ 
+
+ align:start position:0%
+okay so let's kind of a little bit do it
+by example
+
+ align:start position:0%
+by example
+ 
+
+ align:start position:0%
+by example
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in order to do that
+
+ align:start position:0%
+in order to do that
+ 
+
+ align:start position:0%
+in order to do that
+so here's going to be a formula now it's
+
+ align:start position:0%
+so here's going to be a formula now it's
+ 
+
+ align:start position:0%
+so here's going to be a formula now it's
+in three cnf that's what i need you know
+
+ align:start position:0%
+in three cnf that's what i need you know
+ 
+
+ align:start position:0%
+in three cnf that's what i need you know
+in order to be doing this reduction i'm
+
+ align:start position:0%
+in order to be doing this reduction i'm
+ 
+
+ align:start position:0%
+in order to be doing this reduction i'm
+converting three cnf formulas into
+
+ align:start position:0%
+converting three cnf formulas into
+ 
+
+ align:start position:0%
+converting three cnf formulas into
+clique problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have to a little bit understand what
+
+ align:start position:0%
+we have to a little bit understand what
+ 
+
+ align:start position:0%
+we have to a little bit understand what
+it means
+
+ align:start position:0%
+it means
+ 
+
+ align:start position:0%
+it means
+when we say
+
+ align:start position:0%
+when we say
+ 
+
+ align:start position:0%
+when we say
+uh we talk about the satisfiability of a
+
+ align:start position:0%
+uh we talk about the satisfiability of a
+ 
+
+ align:start position:0%
+uh we talk about the satisfiability of a
+formula like this because it's going to
+
+ align:start position:0%
+formula like this because it's going to
+ 
+
+ align:start position:0%
+formula like this because it's going to
+be helpful in doing the reduction you
+
+ align:start position:0%
+be helpful in doing the reduction you
+ 
+
+ align:start position:0%
+be helpful in doing the reduction you
+know obviously it's satisfiable means
+
+ align:start position:0%
+know obviously it's satisfiable means
+ 
+
+ align:start position:0%
+know obviously it's satisfiable means
+that the form you can find an assignment
+
+ align:start position:0%
+that the form you can find an assignment
+ 
+
+ align:start position:0%
+that the form you can find an assignment
+of the variables so you're going to set
+
+ align:start position:0%
+of the variables so you're going to set
+ 
+
+ align:start position:0%
+of the variables so you're going to set
+each of these variables a b and c and so
+
+ align:start position:0%
+each of these variables a b and c and so
+ 
+
+ align:start position:0%
+each of these variables a b and c and so
+on to true or false
+
+ align:start position:0%
+on to true or false
+ 
+
+ align:start position:0%
+on to true or false
+and you want to make the whole formula
+
+ align:start position:0%
+and you want to make the whole formula
+ 
+
+ align:start position:0%
+and you want to make the whole formula
+evaluate to true but what does that
+
+ align:start position:0%
+evaluate to true but what does that
+ 
+
+ align:start position:0%
+evaluate to true but what does that
+actually mean
+
+ align:start position:0%
+actually mean
+ 
+
+ align:start position:0%
+actually mean
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+it means that because of the structure
+
+ align:start position:0%
+it means that because of the structure
+ 
+
+ align:start position:0%
+it means that because of the structure
+of the formula
+
+ align:start position:0%
+of the formula
+ 
+
+ align:start position:0%
+of the formula
+that making this formula true
+
+ align:start position:0%
+that making this formula true
+ 
+
+ align:start position:0%
+that making this formula true
+corresponds to making each clause true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+the clauses are all added together so
+
+ align:start position:0%
+the clauses are all added together so
+ 
+
+ align:start position:0%
+the clauses are all added together so
+the only way for the formula to be true
+
+ align:start position:0%
+the only way for the formula to be true
+ 
+
+ align:start position:0%
+the only way for the formula to be true
+is to make each clause true
+
+ align:start position:0%
+is to make each clause true
+ 
+
+ align:start position:0%
+is to make each clause true
+and to make a clause true
+
+ align:start position:0%
+and to make a clause true
+ 
+
+ align:start position:0%
+and to make a clause true
+you have to make at least one of the
+
+ align:start position:0%
+you have to make at least one of the
+ 
+
+ align:start position:0%
+you have to make at least one of the
+literals true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's another way of thinking about
+
+ align:start position:0%
+so it's another way of thinking about
+ 
+
+ align:start position:0%
+so it's another way of thinking about
+uh satisfying this formula
+
+ align:start position:0%
+uh satisfying this formula
+ 
+
+ align:start position:0%
+uh satisfying this formula
+you need satisfying these and a
+
+ align:start position:0%
+you need satisfying these and a
+ 
+
+ align:start position:0%
+you need satisfying these and a
+satisfying assignment
+
+ align:start position:0%
+satisfying assignment
+ 
+
+ align:start position:0%
+satisfying assignment
+makes at least one true literal in every
+
+ align:start position:0%
+makes at least one true literal in every
+ 
+
+ align:start position:0%
+makes at least one true literal in every
+clause
+
+ align:start position:0%
+clause
+ 
+
+ align:start position:0%
+clause
+it's really important to think about it
+
+ align:start position:0%
+it's really important to think about it
+ 
+
+ align:start position:0%
+it's really important to think about it
+that way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because that's what's going to be um
+
+ align:start position:0%
+because that's what's going to be um
+ 
+
+ align:start position:0%
+because that's what's going to be um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+kind of the basis
+
+ align:start position:0%
+kind of the basis
+ 
+
+ align:start position:0%
+kind of the basis
+for doing
+
+ align:start position:0%
+for doing
+ 
+
+ align:start position:0%
+for doing
+this reduction and all of the reductions
+
+ align:start position:0%
+this reduction and all of the reductions
+ 
+
+ align:start position:0%
+this reduction and all of the reductions
+it's kind of what makes three set easy
+
+ align:start position:0%
+it's kind of what makes three set easy
+ 
+
+ align:start position:0%
+it's kind of what makes three set easy
+to think about in terms of its
+
+ align:start position:0%
+to think about in terms of its
+ 
+
+ align:start position:0%
+to think about in terms of its
+satisfiability
+
+ align:start position:0%
+satisfiability
+ 
+
+ align:start position:0%
+satisfiability
+if you had a sort of a general um
+
+ align:start position:0%
+if you had a sort of a general um
+ 
+
+ align:start position:0%
+if you had a sort of a general um
+satisfiability problem and you had a
+
+ align:start position:0%
+satisfiability problem and you had a
+ 
+
+ align:start position:0%
+satisfiability problem and you had a
+satisfiable formula there's no sort of
+
+ align:start position:0%
+satisfiable formula there's no sort of
+ 
+
+ align:start position:0%
+satisfiable formula there's no sort of
+obvious way of sort of seeing what the
+
+ align:start position:0%
+obvious way of sort of seeing what the
+ 
+
+ align:start position:0%
+obvious way of sort of seeing what the
+satisfying assignment looks like but
+
+ align:start position:0%
+satisfying assignment looks like but
+ 
+
+ align:start position:0%
+satisfying assignment looks like but
+here we understand what it looks like it
+
+ align:start position:0%
+here we understand what it looks like it
+ 
+
+ align:start position:0%
+here we understand what it looks like it
+has that very special form
+
+ align:start position:0%
+has that very special form
+ 
+
+ align:start position:0%
+has that very special form
+making one true literal in every clause
+
+ align:start position:0%
+making one true literal in every clause
+ 
+
+ align:start position:0%
+making one true literal in every clause
+at least one true literal in every
+
+ align:start position:0%
+at least one true literal in every
+ 
+
+ align:start position:0%
+at least one true literal in every
+clause
+
+ align:start position:0%
+clause
+ 
+
+ align:start position:0%
+clause
+okay so now we're going to do the
+
+ align:start position:0%
+okay so now we're going to do the
+ 
+
+ align:start position:0%
+okay so now we're going to do the
+reduction so i'm going to take from this
+
+ align:start position:0%
+reduction so i'm going to take from this
+ 
+
+ align:start position:0%
+reduction so i'm going to take from this
+formula you and
+
+ align:start position:0%
+formula you and
+ 
+
+ align:start position:0%
+formula you and
+you have to understand you know i know
+
+ align:start position:0%
+you have to understand you know i know
+ 
+
+ align:start position:0%
+you have to understand you know i know
+for some of you you know you're going to
+
+ align:start position:0%
+for some of you you know you're going to
+ 
+
+ align:start position:0%
+for some of you you know you're going to
+be you know chafing why am i going so
+
+ align:start position:0%
+be you know chafing why am i going so
+ 
+
+ align:start position:0%
+be you know chafing why am i going so
+slowly but i want to make sure that
+
+ align:start position:0%
+slowly but i want to make sure that
+ 
+
+ align:start position:0%
+slowly but i want to make sure that
+we're all together in understanding what
+
+ align:start position:0%
+we're all together in understanding what
+ 
+
+ align:start position:0%
+we're all together in understanding what
+the rules of the game are and what we're
+
+ align:start position:0%
+the rules of the game are and what we're
+ 
+
+ align:start position:0%
+the rules of the game are and what we're
+trying to do
+
+ align:start position:0%
+trying to do
+ 
+
+ align:start position:0%
+trying to do
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're trying to convert
+
+ align:start position:0%
+we're trying to convert
+ 
+
+ align:start position:0%
+we're trying to convert
+this formula into a graph and a number
+
+ align:start position:0%
+this formula into a graph and a number
+ 
+
+ align:start position:0%
+this formula into a graph and a number
+so right now my job is to do this
+
+ align:start position:0%
+so right now my job is to do this
+ 
+
+ align:start position:0%
+so right now my job is to do this
+reduction is to exhibit that graph
+
+ align:start position:0%
+reduction is to exhibit that graph
+ 
+
+ align:start position:0%
+reduction is to exhibit that graph
+okay so i'm going to do that in kind of
+
+ align:start position:0%
+okay so i'm going to do that in kind of
+ 
+
+ align:start position:0%
+okay so i'm going to do that in kind of
+two steps i'll first i'm going to tell
+
+ align:start position:0%
+two steps i'll first i'm going to tell
+ 
+
+ align:start position:0%
+two steps i'll first i'm going to tell
+you what the nodes of the graph are
+
+ align:start position:0%
+you what the nodes of the graph are
+ 
+
+ align:start position:0%
+you what the nodes of the graph are
+then then i'll tell you what the edges
+
+ align:start position:0%
+then then i'll tell you what the edges
+ 
+
+ align:start position:0%
+then then i'll tell you what the edges
+of that graph
+
+ align:start position:0%
+of that graph
+ 
+
+ align:start position:0%
+of that graph
+finally i'll tell you what the number k
+
+ align:start position:0%
+finally i'll tell you what the number k
+ 
+
+ align:start position:0%
+finally i'll tell you what the number k
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the way this polynomial time
+
+ align:start position:0%
+that's the way this polynomial time
+ 
+
+ align:start position:0%
+that's the way this polynomial time
+reduction is going to work
+
+ align:start position:0%
+reduction is going to work
+ 
+
+ align:start position:0%
+reduction is going to work
+and we have to also
+
+ align:start position:0%
+and we have to also
+ 
+
+ align:start position:0%
+and we have to also
+observe at the very end
+
+ align:start position:0%
+observe at the very end
+ 
+
+ align:start position:0%
+observe at the very end
+that the reduction that i'm given giving
+
+ align:start position:0%
+that the reduction that i'm given giving
+ 
+
+ align:start position:0%
+that the reduction that i'm given giving
+you this
+
+ align:start position:0%
+you this
+ 
+
+ align:start position:0%
+you this
+procedure for building this graph can be
+
+ align:start position:0%
+procedure for building this graph can be
+ 
+
+ align:start position:0%
+procedure for building this graph can be
+done in polynomial time but that i think
+
+ align:start position:0%
+done in polynomial time but that i think
+ 
+
+ align:start position:0%
+done in polynomial time but that i think
+you'll see once i'm done that that's
+
+ align:start position:0%
+you'll see once i'm done that that's
+ 
+
+ align:start position:0%
+you'll see once i'm done that that's
+pretty obvious
+
+ align:start position:0%
+pretty obvious
+ 
+
+ align:start position:0%
+pretty obvious
+okay so first as i promised the nodes um
+
+ align:start position:0%
+okay so first as i promised the nodes um
+ 
+
+ align:start position:0%
+okay so first as i promised the nodes um
+so the nodes of this graph are going to
+
+ align:start position:0%
+so the nodes of this graph are going to
+ 
+
+ align:start position:0%
+so the nodes of this graph are going to
+correspond to the literals of the
+
+ align:start position:0%
+correspond to the literals of the
+ 
+
+ align:start position:0%
+correspond to the literals of the
+formula every literal is going to become
+
+ align:start position:0%
+formula every literal is going to become
+ 
+
+ align:start position:0%
+formula every literal is going to become
+a node in the graph and it's going to be
+
+ align:start position:0%
+a node in the graph and it's going to be
+ 
+
+ align:start position:0%
+a node in the graph and it's going to be
+labeled
+
+ align:start position:0%
+labeled
+ 
+
+ align:start position:0%
+labeled
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+the um name of that literal so it's
+
+ align:start position:0%
+the um name of that literal so it's
+ 
+
+ align:start position:0%
+the um name of that literal so it's
+every node is going to be labeled an a
+
+ align:start position:0%
+every node is going to be labeled an a
+ 
+
+ align:start position:0%
+every node is going to be labeled an a
+or b or or c bar
+
+ align:start position:0%
+or b or or c bar
+ 
+
+ align:start position:0%
+or b or or c bar
+and so on so here it goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so those are the nodes
+
+ align:start position:0%
+okay so those are the nodes
+ 
+
+ align:start position:0%
+okay so those are the nodes
+of the graph g
+
+ align:start position:0%
+of the graph g
+ 
+
+ align:start position:0%
+of the graph g
+one for each literal in the formula
+
+ align:start position:0%
+one for each literal in the formula
+ 
+
+ align:start position:0%
+one for each literal in the formula
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+labeled as promised
+
+ align:start position:0%
+labeled as promised
+ 
+
+ align:start position:0%
+labeled as promised
+now i have to tell you what the edges
+
+ align:start position:0%
+now i have to tell you what the edges
+ 
+
+ align:start position:0%
+now i have to tell you what the edges
+look like
+
+ align:start position:0%
+look like
+ 
+
+ align:start position:0%
+look like
+the edges are going to be
+
+ align:start position:0%
+the edges are going to be
+ 
+
+ align:start position:0%
+the edges are going to be
+um i'm going to tell you what the edges
+
+ align:start position:0%
+um i'm going to tell you what the edges
+ 
+
+ align:start position:0%
+um i'm going to tell you what the edges
+are by first telling you what they are
+
+ align:start position:0%
+are by first telling you what they are
+ 
+
+ align:start position:0%
+are by first telling you what they are
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+i'm going to first explain to you what
+
+ align:start position:0%
+i'm going to first explain to you what
+ 
+
+ align:start position:0%
+i'm going to first explain to you what
+the forbidden edges are
+
+ align:start position:0%
+the forbidden edges are
+ 
+
+ align:start position:0%
+the forbidden edges are
+what what edges i'm going to
+
+ align:start position:0%
+what what edges i'm going to
+ 
+
+ align:start position:0%
+what what edges i'm going to
+promise not to include
+
+ align:start position:0%
+promise not to include
+ 
+
+ align:start position:0%
+promise not to include
+and then the ones that i
+
+ align:start position:0%
+and then the ones that i
+ 
+
+ align:start position:0%
+and then the ones that i
+will include are going to be all the
+
+ align:start position:0%
+will include are going to be all the
+ 
+
+ align:start position:0%
+will include are going to be all the
+others
+
+ align:start position:0%
+others
+ 
+
+ align:start position:0%
+others
+okay so what are going to be the
+
+ align:start position:0%
+okay so what are going to be the
+ 
+
+ align:start position:0%
+okay so what are going to be the
+forbidden edges first of all um
+
+ align:start position:0%
+forbidden edges first of all um
+ 
+
+ align:start position:0%
+forbidden edges first of all um
+the the forbidden
+
+ align:start position:0%
+the the forbidden
+ 
+
+ align:start position:0%
+the the forbidden
+edges are going to be of two types one
+
+ align:start position:0%
+edges are going to be of two types one
+ 
+
+ align:start position:0%
+edges are going to be of two types one
+is the edges between nodes
+
+ align:start position:0%
+is the edges between nodes
+ 
+
+ align:start position:0%
+is the edges between nodes
+that come from
+
+ align:start position:0%
+that come from
+ 
+
+ align:start position:0%
+that come from
+literals in the same clause so i would
+
+ align:start position:0%
+literals in the same clause so i would
+ 
+
+ align:start position:0%
+literals in the same clause so i would
+just call that
+
+ align:start position:0%
+just call that
+ 
+
+ align:start position:0%
+just call that
+no edges within a clause
+
+ align:start position:0%
+no edges within a clause
+ 
+
+ align:start position:0%
+no edges within a clause
+okay so for example these three nodes
+
+ align:start position:0%
+okay so for example these three nodes
+ 
+
+ align:start position:0%
+okay so for example these three nodes
+will not be connected to one another and
+
+ align:start position:0%
+will not be connected to one another and
+ 
+
+ align:start position:0%
+will not be connected to one another and
+i'm going to indicate that by writing
+
+ align:start position:0%
+i'm going to indicate that by writing
+ 
+
+ align:start position:0%
+i'm going to indicate that by writing
+red dashed lines which means there's not
+
+ align:start position:0%
+red dashed lines which means there's not
+ 
+
+ align:start position:0%
+red dashed lines which means there's not
+an edge there
+
+ align:start position:0%
+an edge there
+ 
+
+ align:start position:0%
+an edge there
+okay those are those are forbidden from
+
+ align:start position:0%
+okay those are those are forbidden from
+ 
+
+ align:start position:0%
+okay those are those are forbidden from
+having an edge
+
+ align:start position:0%
+having an edge
+ 
+
+ align:start position:0%
+having an edge
+okay so these three have no edge and the
+
+ align:start position:0%
+okay so these three have no edge and the
+ 
+
+ align:start position:0%
+okay so these three have no edge and the
+same thing for every other uh triple of
+
+ align:start position:0%
+same thing for every other uh triple of
+ 
+
+ align:start position:0%
+same thing for every other uh triple of
+three nodes that come from uh clauses
+
+ align:start position:0%
+three nodes that come from uh clauses
+ 
+
+ align:start position:0%
+three nodes that come from uh clauses
+okay those are
+
+ align:start position:0%
+okay those are
+ 
+
+ align:start position:0%
+okay those are
+no edges there
+
+ align:start position:0%
+no edges there
+ 
+
+ align:start position:0%
+no edges there
+and there's one other category of edge
+
+ align:start position:0%
+and there's one other category of edge
+ 
+
+ align:start position:0%
+and there's one other category of edge
+that i'm forbidding
+
+ align:start position:0%
+that i'm forbidding
+ 
+
+ align:start position:0%
+that i'm forbidding
+and that are edges that can
+
+ align:start position:0%
+and that are edges that can
+ 
+
+ align:start position:0%
+and that are edges that can
+that um go between
+
+ align:start position:0%
+that um go between
+ 
+
+ align:start position:0%
+that um go between
+inconsistent labels and the nodes with
+
+ align:start position:0%
+inconsistent labels and the nodes with
+ 
+
+ align:start position:0%
+inconsistent labels and the nodes with
+inconsistent labels so for example
+
+ align:start position:0%
+inconsistent labels so for example
+ 
+
+ align:start position:0%
+inconsistent labels so for example
+between a and a bar those are
+
+ align:start position:0%
+between a and a bar those are
+ 
+
+ align:start position:0%
+between a and a bar those are
+inconsistent
+
+ align:start position:0%
+inconsistent
+ 
+
+ align:start position:0%
+inconsistent
+you know nothing's wrong with a going a
+
+ align:start position:0%
+you know nothing's wrong with a going a
+ 
+
+ align:start position:0%
+you know nothing's wrong with a going a
+to d those are not inconsistent those
+
+ align:start position:0%
+to d those are not inconsistent those
+ 
+
+ align:start position:0%
+to d those are not inconsistent those
+are just different labels or going from
+
+ align:start position:0%
+are just different labels or going from
+ 
+
+ align:start position:0%
+are just different labels or going from
+a to a that's okay
+
+ align:start position:0%
+a to a that's okay
+ 
+
+ align:start position:0%
+a to a that's okay
+but from a to a bar that's that's not
+
+ align:start position:0%
+but from a to a bar that's that's not
+ 
+
+ align:start position:0%
+but from a to a bar that's that's not
+allowed um so that's going to be another
+
+ align:start position:0%
+allowed um so that's going to be another
+ 
+
+ align:start position:0%
+allowed um so that's going to be another
+forbidden edge
+
+ align:start position:0%
+forbidden edge
+ 
+
+ align:start position:0%
+forbidden edge
+or for example a to a bar here
+
+ align:start position:0%
+or for example a to a bar here
+ 
+
+ align:start position:0%
+or for example a to a bar here
+for b a bar to a or for example from
+
+ align:start position:0%
+for b a bar to a or for example from
+ 
+
+ align:start position:0%
+for b a bar to a or for example from
+this c bar to c
+
+ align:start position:0%
+this c bar to c
+ 
+
+ align:start position:0%
+this c bar to c
+forbidden
+
+ align:start position:0%
+forbidden
+ 
+
+ align:start position:0%
+forbidden
+okay so imagine you're going to write
+
+ align:start position:0%
+okay so imagine you're going to write
+ 
+
+ align:start position:0%
+okay so imagine you're going to write
+down all of those forbidden edges and
+
+ align:start position:0%
+down all of those forbidden edges and
+ 
+
+ align:start position:0%
+down all of those forbidden edges and
+then once you've done that
+
+ align:start position:0%
+then once you've done that
+ 
+
+ align:start position:0%
+then once you've done that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+those are all of the the forbidden edges
+
+ align:start position:0%
+those are all of the the forbidden edges
+ 
+
+ align:start position:0%
+those are all of the the forbidden edges
+and then after
+
+ align:start position:0%
+and then after
+ 
+
+ align:start position:0%
+and then after
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+taking those away
+
+ align:start position:0%
+taking those away
+ 
+
+ align:start position:0%
+taking those away
+you're going to be putting in all the
+
+ align:start position:0%
+you're going to be putting in all the
+ 
+
+ align:start position:0%
+you're going to be putting in all the
+other edges possible
+
+ align:start position:0%
+other edges possible
+ 
+
+ align:start position:0%
+other edges possible
+so for example as a let me just uh
+
+ align:start position:0%
+so for example as a let me just uh
+ 
+
+ align:start position:0%
+so for example as a let me just uh
+gray those out so they don't interfere
+
+ align:start position:0%
+gray those out so they don't interfere
+ 
+
+ align:start position:0%
+gray those out so they don't interfere
+with the picture
+
+ align:start position:0%
+with the picture
+ 
+
+ align:start position:0%
+with the picture
+b from a to a to d
+
+ align:start position:0%
+b from a to a to d
+ 
+
+ align:start position:0%
+b from a to a to d
+um there's going to be an edge um
+
+ align:start position:0%
+um there's going to be an edge um
+ 
+
+ align:start position:0%
+um there's going to be an edge um
+because those are not forbid you know a
+
+ align:start position:0%
+because those are not forbid you know a
+ 
+
+ align:start position:0%
+because those are not forbid you know a
+to a not forbidden because
+
+ align:start position:0%
+to a not forbidden because
+ 
+
+ align:start position:0%
+to a not forbidden because
+they they're in different
+
+ align:start position:0%
+they they're in different
+ 
+
+ align:start position:0%
+they they're in different
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+they are in different uh
+
+ align:start position:0%
+they are in different uh
+ 
+
+ align:start position:0%
+they are in different uh
+clauses and they're not inconsistent
+
+ align:start position:0%
+clauses and they're not inconsistent
+ 
+
+ align:start position:0%
+clauses and they're not inconsistent
+they're they're consistent with one
+
+ align:start position:0%
+they're they're consistent with one
+ 
+
+ align:start position:0%
+they're they're consistent with one
+another so here are a whole bunch of
+
+ align:start position:0%
+another so here are a whole bunch of
+ 
+
+ align:start position:0%
+another so here are a whole bunch of
+other i'm not showing them all becomes
+
+ align:start position:0%
+other i'm not showing them all becomes
+ 
+
+ align:start position:0%
+other i'm not showing them all becomes
+very messy but uh here are all the other
+
+ align:start position:0%
+very messy but uh here are all the other
+ 
+
+ align:start position:0%
+very messy but uh here are all the other
+edges between nodes uh which are
+
+ align:start position:0%
+edges between nodes uh which are
+ 
+
+ align:start position:0%
+edges between nodes uh which are
+where there isn't there's
+
+ align:start position:0%
+where there isn't there's
+ 
+
+ align:start position:0%
+where there isn't there's
+no pro
+
+ align:start position:0%
+no pro
+ 
+
+ align:start position:0%
+no pro
+within they're not forbidden
+
+ align:start position:0%
+within they're not forbidden
+ 
+
+ align:start position:0%
+within they're not forbidden
+okay and that's
+
+ align:start position:0%
+okay and that's
+ 
+
+ align:start position:0%
+okay and that's
+that's the graph
+
+ align:start position:0%
+that's the graph
+ 
+
+ align:start position:0%
+that's the graph
+that's g
+
+ align:start position:0%
+that's g
+ 
+
+ align:start position:0%
+that's g
+g is all
+
+ align:start position:0%
+g is all
+ 
+
+ align:start position:0%
+g is all
+those nodes and those edges um which are
+
+ align:start position:0%
+those nodes and those edges um which are
+ 
+
+ align:start position:0%
+those nodes and those edges um which are
+not forbidden
+
+ align:start position:0%
+not forbidden
+ 
+
+ align:start position:0%
+not forbidden
+now i just have to tell you what k a is
+
+ align:start position:0%
+now i just have to tell you what k a is
+ 
+
+ align:start position:0%
+now i just have to tell you what k a is
+k is going to be the number of clauses
+
+ align:start position:0%
+k is going to be the number of clauses
+ 
+
+ align:start position:0%
+k is going to be the number of clauses
+that's going to be the size of the
+
+ align:start position:0%
+that's going to be the size of the
+ 
+
+ align:start position:0%
+that's going to be the size of the
+clique i'm looking for in this graph g
+
+ align:start position:0%
+clique i'm looking for in this graph g
+ 
+
+ align:start position:0%
+clique i'm looking for in this graph g
+that i just spelled out for you
+
+ align:start position:0%
+that i just spelled out for you
+ 
+
+ align:start position:0%
+that i just spelled out for you
+and i'm going to claim
+
+ align:start position:0%
+and i'm going to claim
+ 
+
+ align:start position:0%
+and i'm going to claim
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+this graph here that i just described
+
+ align:start position:0%
+this graph here that i just described
+ 
+
+ align:start position:0%
+this graph here that i just described
+will have a k clique
+
+ align:start position:0%
+will have a k clique
+ 
+
+ align:start position:0%
+will have a k clique
+k is the number of clauses
+
+ align:start position:0%
+k is the number of clauses
+ 
+
+ align:start position:0%
+k is the number of clauses
+exactly when
+
+ align:start position:0%
+exactly when
+ 
+
+ align:start position:0%
+exactly when
+fee was satisfiable
+
+ align:start position:0%
+fee was satisfiable
+ 
+
+ align:start position:0%
+fee was satisfiable
+it's kind of kind of cool you know um if
+
+ align:start position:0%
+it's kind of kind of cool you know um if
+ 
+
+ align:start position:0%
+it's kind of kind of cool you know um if
+he is satisfiable then there will be a
+
+ align:start position:0%
+he is satisfiable then there will be a
+ 
+
+ align:start position:0%
+he is satisfiable then there will be a
+cake leak here
+
+ align:start position:0%
+cake leak here
+ 
+
+ align:start position:0%
+cake leak here
+and if he was not satisfiable okay clean
+
+ align:start position:0%
+and if he was not satisfiable okay clean
+ 
+
+ align:start position:0%
+and if he was not satisfiable okay clean
+so we have to we're gonna prove that as
+
+ align:start position:0%
+so we have to we're gonna prove that as
+ 
+
+ align:start position:0%
+so we have to we're gonna prove that as
+a claim on the next slide
+
+ align:start position:0%
+a claim on the next slide
+ 
+
+ align:start position:0%
+a claim on the next slide
+okay so k is the number of clauses
+
+ align:start position:0%
+okay so k is the number of clauses
+ 
+
+ align:start position:0%
+okay so k is the number of clauses
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+any questions on that on that
+
+ align:start position:0%
+any questions on that on that
+ 
+
+ align:start position:0%
+any questions on that on that
+construction so i've done with the
+
+ align:start position:0%
+construction so i've done with the
+ 
+
+ align:start position:0%
+construction so i've done with the
+construction what's left is to argue why
+
+ align:start position:0%
+construction what's left is to argue why
+ 
+
+ align:start position:0%
+construction what's left is to argue why
+the construction works
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so far so good let's move on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+so here is that very same construction i
+
+ align:start position:0%
+so here is that very same construction i
+ 
+
+ align:start position:0%
+so here is that very same construction i
+eliminated the red uh
+
+ align:start position:0%
+eliminated the red uh
+ 
+
+ align:start position:0%
+eliminated the red uh
+forbidden edges these are the ones that
+
+ align:start position:0%
+forbidden edges these are the ones that
+ 
+
+ align:start position:0%
+forbidden edges these are the ones that
+were remaining
+
+ align:start position:0%
+were remaining
+ 
+
+ align:start position:0%
+were remaining
+plus you know anything else that was not
+
+ align:start position:0%
+plus you know anything else that was not
+ 
+
+ align:start position:0%
+plus you know anything else that was not
+forbidden
+
+ align:start position:0%
+forbidden
+ 
+
+ align:start position:0%
+forbidden
+that was the same formula that i had
+
+ align:start position:0%
+that was the same formula that i had
+ 
+
+ align:start position:0%
+that was the same formula that i had
+from the previous slide
+
+ align:start position:0%
+from the previous slide
+ 
+
+ align:start position:0%
+from the previous slide
+now i'm going to claim that that formula
+
+ align:start position:0%
+now i'm going to claim that that formula
+ 
+
+ align:start position:0%
+now i'm going to claim that that formula
+is satisfiable exactly when g has a k
+
+ align:start position:0%
+is satisfiable exactly when g has a k
+ 
+
+ align:start position:0%
+is satisfiable exactly when g has a k
+click now why in the world is that
+
+ align:start position:0%
+click now why in the world is that
+ 
+
+ align:start position:0%
+click now why in the world is that
+so this is an if and only if it's proved
+
+ align:start position:0%
+so this is an if and only if it's proved
+ 
+
+ align:start position:0%
+so this is an if and only if it's proved
+in both directions
+
+ align:start position:0%
+in both directions
+ 
+
+ align:start position:0%
+in both directions
+and this is going to be the typical kind
+
+ align:start position:0%
+and this is going to be the typical kind
+ 
+
+ align:start position:0%
+and this is going to be the typical kind
+of thing that you're going to want to do
+
+ align:start position:0%
+of thing that you're going to want to do
+ 
+
+ align:start position:0%
+of thing that you're going to want to do
+when you're exhibiting a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you know one of these reductions
+
+ align:start position:0%
+you know one of these reductions
+ 
+
+ align:start position:0%
+you know one of these reductions
+which is you're going to have an
+
+ align:start position:0%
+which is you're going to have an
+ 
+
+ align:start position:0%
+which is you're going to have an
+opportunity to do that um and we'll do
+
+ align:start position:0%
+opportunity to do that um and we'll do
+ 
+
+ align:start position:0%
+opportunity to do that um and we'll do
+do that too
+
+ align:start position:0%
+do that too
+ 
+
+ align:start position:0%
+do that too
+in our examples
+
+ align:start position:0%
+in our examples
+ 
+
+ align:start position:0%
+in our examples
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+uh what i'm what i want to show
+
+ align:start position:0%
+uh what i'm what i want to show
+ 
+
+ align:start position:0%
+uh what i'm what i want to show
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+if fee is satisfiable so let's prove the
+
+ align:start position:0%
+if fee is satisfiable so let's prove the
+ 
+
+ align:start position:0%
+if fee is satisfiable so let's prove the
+forward direction if p is satisfiable
+
+ align:start position:0%
+forward direction if p is satisfiable
+ 
+
+ align:start position:0%
+forward direction if p is satisfiable
+then g has a k click
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so first of all if fee is
+
+ align:start position:0%
+okay so first of all if fee is
+ 
+
+ align:start position:0%
+okay so first of all if fee is
+satisfiable that means it has a
+
+ align:start position:0%
+satisfiable that means it has a
+ 
+
+ align:start position:0%
+satisfiable that means it has a
+satisfying assignment
+
+ align:start position:0%
+satisfying assignment
+ 
+
+ align:start position:0%
+satisfying assignment
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now here's a common confusion i'm not
+
+ align:start position:0%
+now here's a common confusion i'm not
+ 
+
+ align:start position:0%
+now here's a common confusion i'm not
+sure whether it's helpful to
+
+ align:start position:0%
+sure whether it's helpful to
+ 
+
+ align:start position:0%
+sure whether it's helpful to
+sprinkle the confusions in along with
+
+ align:start position:0%
+sprinkle the confusions in along with
+ 
+
+ align:start position:0%
+sprinkle the confusions in along with
+the discussion but
+
+ align:start position:0%
+the discussion but
+ 
+
+ align:start position:0%
+the discussion but
+in case you're worried
+
+ align:start position:0%
+in case you're worried
+ 
+
+ align:start position:0%
+in case you're worried
+you might ask well how do i find that
+
+ align:start position:0%
+you might ask well how do i find that
+ 
+
+ align:start position:0%
+you might ask well how do i find that
+satisfying assignment i thought that was
+
+ align:start position:0%
+satisfying assignment i thought that was
+ 
+
+ align:start position:0%
+satisfying assignment i thought that was
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+exponential
+
+ align:start position:0%
+exponential
+ 
+
+ align:start position:0%
+exponential
+exponentially hard to do
+
+ align:start position:0%
+exponentially hard to do
+ 
+
+ align:start position:0%
+exponentially hard to do
+this is a proof this is not an algorithm
+
+ align:start position:0%
+this is a proof this is not an algorithm
+ 
+
+ align:start position:0%
+this is a proof this is not an algorithm
+okay we're just trying to argue the con
+
+ align:start position:0%
+okay we're just trying to argue the con
+ 
+
+ align:start position:0%
+okay we're just trying to argue the con
+correctness of this construction
+
+ align:start position:0%
+correctness of this construction
+ 
+
+ align:start position:0%
+correctness of this construction
+so there's no longer any concern about
+
+ align:start position:0%
+so there's no longer any concern about
+ 
+
+ align:start position:0%
+so there's no longer any concern about
+how to find an assignment i'm just
+
+ align:start position:0%
+how to find an assignment i'm just
+ 
+
+ align:start position:0%
+how to find an assignment i'm just
+saying if there isn't a sign if there is
+
+ align:start position:0%
+saying if there isn't a sign if there is
+ 
+
+ align:start position:0%
+saying if there isn't a sign if there is
+a satisfying assignment then something
+
+ align:start position:0%
+a satisfying assignment then something
+ 
+
+ align:start position:0%
+a satisfying assignment then something
+will happen something that then then um
+
+ align:start position:0%
+will happen something that then then um
+ 
+
+ align:start position:0%
+will happen something that then then um
+something will happen in particular then
+
+ align:start position:0%
+something will happen in particular then
+ 
+
+ align:start position:0%
+something will happen in particular then
+we will show that g has a cake league
+
+ align:start position:0%
+we will show that g has a cake league
+ 
+
+ align:start position:0%
+we will show that g has a cake league
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's say
+
+ align:start position:0%
+let's say
+ 
+
+ align:start position:0%
+let's say
+fee is satisfiable
+
+ align:start position:0%
+fee is satisfiable
+ 
+
+ align:start position:0%
+fee is satisfiable
+so it has some assignment let's take
+
+ align:start position:0%
+so it has some assignment let's take
+ 
+
+ align:start position:0%
+so it has some assignment let's take
+that satisfying assignment
+
+ align:start position:0%
+that satisfying assignment
+ 
+
+ align:start position:0%
+that satisfying assignment
+and remember
+
+ align:start position:0%
+and remember
+ 
+
+ align:start position:0%
+and remember
+that in any satisfying assignment
+
+ align:start position:0%
+that in any satisfying assignment
+ 
+
+ align:start position:0%
+that in any satisfying assignment
+uh to a formula in cnf
+
+ align:start position:0%
+uh to a formula in cnf
+ 
+
+ align:start position:0%
+uh to a formula in cnf
+that makes at least one literal true in
+
+ align:start position:0%
+that makes at least one literal true in
+ 
+
+ align:start position:0%
+that makes at least one literal true in
+every clause
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's just pick one of those there might
+
+ align:start position:0%
+let's just pick one of those there might
+ 
+
+ align:start position:0%
+let's just pick one of those there might
+be several clauses which have multiple
+
+ align:start position:0%
+be several clauses which have multiple
+ 
+
+ align:start position:0%
+be several clauses which have multiple
+true literals in that case just pick one
+
+ align:start position:0%
+true literals in that case just pick one
+ 
+
+ align:start position:0%
+true literals in that case just pick one
+of them
+
+ align:start position:0%
+of them
+ 
+
+ align:start position:0%
+of them
+arbitrarily
+
+ align:start position:0%
+arbitrarily
+ 
+
+ align:start position:0%
+arbitrarily
+okay so i don't know what the i don't
+
+ align:start position:0%
+okay so i don't know what the i don't
+ 
+
+ align:start position:0%
+okay so i don't know what the i don't
+have this sort of indicated on this
+
+ align:start position:0%
+have this sort of indicated on this
+ 
+
+ align:start position:0%
+have this sort of indicated on this
+diagram here but imagine you know maybe
+
+ align:start position:0%
+diagram here but imagine you know maybe
+ 
+
+ align:start position:0%
+diagram here but imagine you know maybe
+in the very first clause a was true in
+
+ align:start position:0%
+in the very first clause a was true in
+ 
+
+ align:start position:0%
+in the very first clause a was true in
+the second clause b was true in the
+
+ align:start position:0%
+the second clause b was true in the
+ 
+
+ align:start position:0%
+the second clause b was true in the
+third clause
+
+ align:start position:0%
+third clause
+ 
+
+ align:start position:0%
+third clause
+e compliment ebar was true and you know
+
+ align:start position:0%
+e compliment ebar was true and you know
+ 
+
+ align:start position:0%
+e compliment ebar was true and you know
+not not
+
+ align:start position:0%
+not not
+ 
+
+ align:start position:0%
+not not
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+e bar was true which means e itself was
+
+ align:start position:0%
+e bar was true which means e itself was
+ 
+
+ align:start position:0%
+e bar was true which means e itself was
+false but e bar was true and that's the
+
+ align:start position:0%
+false but e bar was true and that's the
+ 
+
+ align:start position:0%
+false but e bar was true and that's the
+way each of those clauses in turn uh got
+
+ align:start position:0%
+way each of those clauses in turn uh got
+ 
+
+ align:start position:0%
+way each of those clauses in turn uh got
+to be true you know in this particular
+
+ align:start position:0%
+to be true you know in this particular
+ 
+
+ align:start position:0%
+to be true you know in this particular
+satisfying assignment
+
+ align:start position:0%
+satisfying assignment
+ 
+
+ align:start position:0%
+satisfying assignment
+because you're going to pick one true
+
+ align:start position:0%
+because you're going to pick one true
+ 
+
+ align:start position:0%
+because you're going to pick one true
+literal in every clause and now
+
+ align:start position:0%
+literal in every clause and now
+ 
+
+ align:start position:0%
+literal in every clause and now
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+that choice
+
+ align:start position:0%
+that choice
+ 
+
+ align:start position:0%
+that choice
+of literals one per clause
+
+ align:start position:0%
+of literals one per clause
+ 
+
+ align:start position:0%
+of literals one per clause
+i'm going to look at the corresponding
+
+ align:start position:0%
+i'm going to look at the corresponding
+ 
+
+ align:start position:0%
+i'm going to look at the corresponding
+nodes in g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'm going to claim
+
+ align:start position:0%
+and i'm going to claim
+ 
+
+ align:start position:0%
+and i'm going to claim
+that those nodes taken together
+
+ align:start position:0%
+that those nodes taken together
+ 
+
+ align:start position:0%
+that those nodes taken together
+form a k click
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so first of all
+
+ align:start position:0%
+okay so first of all
+ 
+
+ align:start position:0%
+okay so first of all
+do they have the right number of nodes
+
+ align:start position:0%
+do they have the right number of nodes
+ 
+
+ align:start position:0%
+do they have the right number of nodes
+well sure because
+
+ align:start position:0%
+well sure because
+ 
+
+ align:start position:0%
+well sure because
+i'm picking one node per click i already
+
+ align:start position:0%
+i'm picking one node per click i already
+ 
+
+ align:start position:0%
+i'm picking one node per click i already
+said k is the number of cliques so i'm
+
+ align:start position:0%
+said k is the number of cliques so i'm
+ 
+
+ align:start position:0%
+said k is the number of cliques so i'm
+getting exactly ka nodes so i have at
+
+ align:start position:0%
+getting exactly ka nodes so i have at
+ 
+
+ align:start position:0%
+getting exactly ka nodes so i have at
+least the right number
+
+ align:start position:0%
+least the right number
+ 
+
+ align:start position:0%
+least the right number
+of nodes but how do i know they're all
+
+ align:start position:0%
+of nodes but how do i know they're all
+ 
+
+ align:start position:0%
+of nodes but how do i know they're all
+connected to one another those nodes uh
+
+ align:start position:0%
+connected to one another those nodes uh
+ 
+
+ align:start position:0%
+connected to one another those nodes uh
+that i just picked
+
+ align:start position:0%
+that i just picked
+ 
+
+ align:start position:0%
+that i just picked
+well they're all connected to each other
+
+ align:start position:0%
+well they're all connected to each other
+ 
+
+ align:start position:0%
+well they're all connected to each other
+because i'm going to say well because
+
+ align:start position:0%
+because i'm going to say well because
+ 
+
+ align:start position:0%
+because i'm going to say well because
+there were no forbidden edges among them
+
+ align:start position:0%
+there were no forbidden edges among them
+ 
+
+ align:start position:0%
+there were no forbidden edges among them
+and remember that we put in all possible
+
+ align:start position:0%
+and remember that we put in all possible
+ 
+
+ align:start position:0%
+and remember that we put in all possible
+edges except for the forbidden ones
+
+ align:start position:0%
+edges except for the forbidden ones
+ 
+
+ align:start position:0%
+edges except for the forbidden ones
+so how do i know there are no forbidden
+
+ align:start position:0%
+so how do i know there are no forbidden
+ 
+
+ align:start position:0%
+so how do i know there are no forbidden
+edges
+
+ align:start position:0%
+edges
+ 
+
+ align:start position:0%
+edges
+well what were the rules for being
+
+ align:start position:0%
+well what were the rules for being
+ 
+
+ align:start position:0%
+well what were the rules for being
+forbidden means they two nodes in the
+
+ align:start position:0%
+forbidden means they two nodes in the
+ 
+
+ align:start position:0%
+forbidden means they two nodes in the
+same clique in the same clause
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well i'm picking one node per clause
+
+ align:start position:0%
+well i'm picking one node per clause
+ 
+
+ align:start position:0%
+well i'm picking one node per clause
+so i can never be having two nodes from
+
+ align:start position:0%
+so i can never be having two nodes from
+ 
+
+ align:start position:0%
+so i can never be having two nodes from
+the same clause so i'm never going to
+
+ align:start position:0%
+the same clause so i'm never going to
+ 
+
+ align:start position:0%
+the same clause so i'm never going to
+run into trouble with uh the first
+
+ align:start position:0%
+run into trouble with uh the first
+ 
+
+ align:start position:0%
+run into trouble with uh the first
+condition of being forbidden so what's
+
+ align:start position:0%
+condition of being forbidden so what's
+ 
+
+ align:start position:0%
+condition of being forbidden so what's
+the second possibility for being
+
+ align:start position:0%
+the second possibility for being
+ 
+
+ align:start position:0%
+the second possibility for being
+forbidden is that i'm picking two nodes
+
+ align:start position:0%
+forbidden is that i'm picking two nodes
+ 
+
+ align:start position:0%
+forbidden is that i'm picking two nodes
+which are inconsistent
+
+ align:start position:0%
+which are inconsistent
+ 
+
+ align:start position:0%
+which are inconsistent
+well how do i know that i didn't end up
+
+ align:start position:0%
+well how do i know that i didn't end up
+ 
+
+ align:start position:0%
+well how do i know that i didn't end up
+with two nodes with inconsistent labels
+
+ align:start position:0%
+with two nodes with inconsistent labels
+ 
+
+ align:start position:0%
+with two nodes with inconsistent labels
+that would be bad because then they
+
+ align:start position:0%
+that would be bad because then they
+ 
+
+ align:start position:0%
+that would be bad because then they
+would have a forbidden edge and what my
+
+ align:start position:0%
+would have a forbidden edge and what my
+ 
+
+ align:start position:0%
+would have a forbidden edge and what my
+result would not be a clique
+
+ align:start position:0%
+result would not be a clique
+ 
+
+ align:start position:0%
+result would not be a clique
+how do i know i didn't end up picking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+in this group i pick a and in this group
+
+ align:start position:0%
+in this group i pick a and in this group
+ 
+
+ align:start position:0%
+in this group i pick a and in this group
+i pick a a bar
+
+ align:start position:0%
+i pick a a bar
+ 
+
+ align:start position:0%
+i pick a a bar
+well because they all came from the same
+
+ align:start position:0%
+well because they all came from the same
+ 
+
+ align:start position:0%
+well because they all came from the same
+assignment
+
+ align:start position:0%
+assignment
+ 
+
+ align:start position:0%
+assignment
+those are all of the true letters they
+
+ align:start position:0%
+those are all of the true letters they
+ 
+
+ align:start position:0%
+those are all of the true letters they
+were all true literals
+
+ align:start position:0%
+were all true literals
+ 
+
+ align:start position:0%
+were all true literals
+in clauses it's not possible that a was
+
+ align:start position:0%
+in clauses it's not possible that a was
+ 
+
+ align:start position:0%
+in clauses it's not possible that a was
+true in this clause and a bar is true in
+
+ align:start position:0%
+true in this clause and a bar is true in
+ 
+
+ align:start position:0%
+true in this clause and a bar is true in
+that clause because if a is true here a
+
+ align:start position:0%
+that clause because if a is true here a
+ 
+
+ align:start position:0%
+that clause because if a is true here a
+bar has got to be false it can't be the
+
+ align:start position:0%
+bar has got to be false it can't be the
+ 
+
+ align:start position:0%
+bar has got to be false it can't be the
+true literal in this clause
+
+ align:start position:0%
+true literal in this clause
+ 
+
+ align:start position:0%
+true literal in this clause
+so i cannot have any inconsistent any
+
+ align:start position:0%
+so i cannot have any inconsistent any
+ 
+
+ align:start position:0%
+so i cannot have any inconsistent any
+inconsistent nodes
+
+ align:start position:0%
+inconsistent nodes
+ 
+
+ align:start position:0%
+inconsistent nodes
+appearing
+
+ align:start position:0%
+appearing
+ 
+
+ align:start position:0%
+appearing
+among the nodes of my clique
+
+ align:start position:0%
+among the nodes of my clique
+ 
+
+ align:start position:0%
+among the nodes of my clique
+and so they're not in the same clause
+
+ align:start position:0%
+and so they're not in the same clause
+ 
+
+ align:start position:0%
+and so they're not in the same clause
+they're not inconsistent so the edge has
+
+ align:start position:0%
+they're not inconsistent so the edge has
+ 
+
+ align:start position:0%
+they're not inconsistent so the edge has
+to be there and that's going to be true
+
+ align:start position:0%
+to be there and that's going to be true
+ 
+
+ align:start position:0%
+to be there and that's going to be true
+for every pair of nodes in that clique
+
+ align:start position:0%
+for every pair of nodes in that clique
+ 
+
+ align:start position:0%
+for every pair of nodes in that clique
+in that in that group of nodes and
+
+ align:start position:0%
+in that in that group of nodes and
+ 
+
+ align:start position:0%
+in that in that group of nodes and
+that's why it's a click
+
+ align:start position:0%
+that's why it's a click
+ 
+
+ align:start position:0%
+that's why it's a click
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so that proves one direction now we stop
+
+ align:start position:0%
+so that proves one direction now we stop
+ 
+
+ align:start position:0%
+so that proves one direction now we stop
+to prove the other direction because we
+
+ align:start position:0%
+to prove the other direction because we
+ 
+
+ align:start position:0%
+to prove the other direction because we
+have to say well if g has a k clique how
+
+ align:start position:0%
+have to say well if g has a k clique how
+ 
+
+ align:start position:0%
+have to say well if g has a k clique how
+do we know that ph is satisfied so
+
+ align:start position:0%
+do we know that ph is satisfied so
+ 
+
+ align:start position:0%
+do we know that ph is satisfied so
+that's the reverse
+
+ align:start position:0%
+that's the reverse
+ 
+
+ align:start position:0%
+that's the reverse
+so let's just take any k clique that's
+
+ align:start position:0%
+so let's just take any k clique that's
+ 
+
+ align:start position:0%
+so let's just take any k clique that's
+in g
+
+ align:start position:0%
+in g
+ 
+
+ align:start position:0%
+in g
+and how do i know i can get from that a
+
+ align:start position:0%
+and how do i know i can get from that a
+ 
+
+ align:start position:0%
+and how do i know i can get from that a
+satisfying assignment to the formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+good um
+
+ align:start position:0%
+good um
+ 
+
+ align:start position:0%
+good um
+getting some good questions here in the
+
+ align:start position:0%
+getting some good questions here in the
+ 
+
+ align:start position:0%
+getting some good questions here in the
+chat but let me just move on
+
+ align:start position:0%
+chat but let me just move on
+ 
+
+ align:start position:0%
+chat but let me just move on
+um take any uh so
+
+ align:start position:0%
+um take any uh so
+ 
+
+ align:start position:0%
+um take any uh so
+proving the reverse
+
+ align:start position:0%
+proving the reverse
+ 
+
+ align:start position:0%
+proving the reverse
+this the reverse direction but we're
+
+ align:start position:0%
+this the reverse direction but we're
+ 
+
+ align:start position:0%
+this the reverse direction but we're
+assuming we have a cake leak to take any
+
+ align:start position:0%
+assuming we have a cake leak to take any
+ 
+
+ align:start position:0%
+assuming we have a cake leak to take any
+such k-click
+
+ align:start position:0%
+such k-click
+ 
+
+ align:start position:0%
+such k-click
+now first of all you observe that it's
+
+ align:start position:0%
+now first of all you observe that it's
+ 
+
+ align:start position:0%
+now first of all you observe that it's
+got to have
+
+ align:start position:0%
+got to have
+ 
+
+ align:start position:0%
+got to have
+one node in every clause
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it can't have two nodes in the same
+
+ align:start position:0%
+it can't have two nodes in the same
+ 
+
+ align:start position:0%
+it can't have two nodes in the same
+clause or zero nodes in in a clause
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first of all it can't have two nodes in
+
+ align:start position:0%
+first of all it can't have two nodes in
+ 
+
+ align:start position:0%
+first of all it can't have two nodes in
+the same clause why well because those
+
+ align:start position:0%
+the same clause why well because those
+ 
+
+ align:start position:0%
+the same clause why well because those
+nodes are never connected to one another
+
+ align:start position:0%
+nodes are never connected to one another
+ 
+
+ align:start position:0%
+nodes are never connected to one another
+so that they cannot be both in the same
+
+ align:start position:0%
+so that they cannot be both in the same
+ 
+
+ align:start position:0%
+so that they cannot be both in the same
+clique because all the nodes in a clique
+
+ align:start position:0%
+clique because all the nodes in a clique
+ 
+
+ align:start position:0%
+clique because all the nodes in a clique
+are connected to one another
+
+ align:start position:0%
+are connected to one another
+ 
+
+ align:start position:0%
+are connected to one another
+um by construction by the way we
+
+ align:start position:0%
+um by construction by the way we
+ 
+
+ align:start position:0%
+um by construction by the way we
+construct a g
+
+ align:start position:0%
+construct a g
+ 
+
+ align:start position:0%
+construct a g
+nodes from the same clause are not
+
+ align:start position:0%
+nodes from the same clause are not
+ 
+
+ align:start position:0%
+nodes from the same clause are not
+connected so they cannot appear in a
+
+ align:start position:0%
+connected so they cannot appear in a
+ 
+
+ align:start position:0%
+connected so they cannot appear in a
+clique together
+
+ align:start position:0%
+clique together
+ 
+
+ align:start position:0%
+clique together
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+there's going to be at most one node
+
+ align:start position:0%
+there's going to be at most one node
+ 
+
+ align:start position:0%
+there's going to be at most one node
+from every clause appearing in this
+
+ align:start position:0%
+from every clause appearing in this
+ 
+
+ align:start position:0%
+from every clause appearing in this
+clique but and but but
+
+ align:start position:0%
+clique but and but but
+ 
+
+ align:start position:0%
+clique but and but but
+appearing in in this clip but we also
+
+ align:start position:0%
+appearing in in this clip but we also
+ 
+
+ align:start position:0%
+appearing in in this clip but we also
+have we know we have k notes
+
+ align:start position:0%
+have we know we have k notes
+ 
+
+ align:start position:0%
+have we know we have k notes
+so that means if there is at most one
+
+ align:start position:0%
+so that means if there is at most one
+ 
+
+ align:start position:0%
+so that means if there is at most one
+per um per clause
+
+ align:start position:0%
+per um per clause
+ 
+
+ align:start position:0%
+per um per clause
+and we only have k clauses that means
+
+ align:start position:0%
+and we only have k clauses that means
+ 
+
+ align:start position:0%
+and we only have k clauses that means
+every clause has got to have one
+
+ align:start position:0%
+every clause has got to have one
+ 
+
+ align:start position:0%
+every clause has got to have one
+you know if some clause is missing or
+
+ align:start position:0%
+you know if some clause is missing or
+ 
+
+ align:start position:0%
+you know if some clause is missing or
+note then there's going to be some other
+
+ align:start position:0%
+note then there's going to be some other
+ 
+
+ align:start position:0%
+note then there's going to be some other
+clause that has two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we know that every um
+
+ align:start position:0%
+so we know that every um
+ 
+
+ align:start position:0%
+so we know that every um
+that this clique that would that g
+
+ align:start position:0%
+that this clique that would that g
+ 
+
+ align:start position:0%
+that this clique that would that g
+has has exactly one node in every clause
+
+ align:start position:0%
+has has exactly one node in every clause
+ 
+
+ align:start position:0%
+has has exactly one node in every clause
+so how do we get from that a satisfying
+
+ align:start position:0%
+so how do we get from that a satisfying
+ 
+
+ align:start position:0%
+so how do we get from that a satisfying
+assignment
+
+ align:start position:0%
+assignment
+ 
+
+ align:start position:0%
+assignment
+so what we're going to do is
+
+ align:start position:0%
+so what we're going to do is
+ 
+
+ align:start position:0%
+so what we're going to do is
+take the current
+
+ align:start position:0%
+take the current
+ 
+
+ align:start position:0%
+take the current
+corresponding literals
+
+ align:start position:0%
+corresponding literals
+ 
+
+ align:start position:0%
+corresponding literals
+that correspond to that one node in the
+
+ align:start position:0%
+that correspond to that one node in the
+ 
+
+ align:start position:0%
+that correspond to that one node in the
+that was in the uh clique
+
+ align:start position:0%
+that was in the uh clique
+ 
+
+ align:start position:0%
+that was in the uh clique
+take those literals and set those
+
+ align:start position:0%
+take those literals and set those
+ 
+
+ align:start position:0%
+take those literals and set those
+literals to be true
+
+ align:start position:0%
+literals to be true
+ 
+
+ align:start position:0%
+literals to be true
+which means setting the variable to be
+
+ align:start position:0%
+which means setting the variable to be
+ 
+
+ align:start position:0%
+which means setting the variable to be
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+um or setting um you know
+
+ align:start position:0%
+um or setting um you know
+ 
+
+ align:start position:0%
+um or setting um you know
+if the literal was a bar then setting a
+
+ align:start position:0%
+if the literal was a bar then setting a
+ 
+
+ align:start position:0%
+if the literal was a bar then setting a
+to be false because you want a bar to be
+
+ align:start position:0%
+to be false because you want a bar to be
+ 
+
+ align:start position:0%
+to be false because you want a bar to be
+true you want to set the literals to be
+
+ align:start position:0%
+true you want to set the literals to be
+ 
+
+ align:start position:0%
+true you want to set the literals to be
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+well now we're setting um there's one
+
+ align:start position:0%
+well now we're setting um there's one
+ 
+
+ align:start position:0%
+well now we're setting um there's one
+note in each clause we're setting one
+
+ align:start position:0%
+note in each clause we're setting one
+ 
+
+ align:start position:0%
+note in each clause we're setting one
+literal uh the corresponding literal
+
+ align:start position:0%
+literal uh the corresponding literal
+ 
+
+ align:start position:0%
+literal uh the corresponding literal
+true so that's going to set one true
+
+ align:start position:0%
+true so that's going to set one true
+ 
+
+ align:start position:0%
+true so that's going to set one true
+literal in every clause
+
+ align:start position:0%
+literal in every clause
+ 
+
+ align:start position:0%
+literal in every clause
+so that means it's going to be
+
+ align:start position:0%
+so that means it's going to be
+ 
+
+ align:start position:0%
+so that means it's going to be
+satisfying there's one thing that one
+
+ align:start position:0%
+satisfying there's one thing that one
+ 
+
+ align:start position:0%
+satisfying there's one thing that one
+has to really to be
+
+ align:start position:0%
+has to really to be
+ 
+
+ align:start position:0%
+has to really to be
+careful here to double check to make
+
+ align:start position:0%
+careful here to double check to make
+ 
+
+ align:start position:0%
+careful here to double check to make
+sure that we're doing this consistently
+
+ align:start position:0%
+sure that we're doing this consistently
+ 
+
+ align:start position:0%
+sure that we're doing this consistently
+that we're not being asked to set you
+
+ align:start position:0%
+that we're not being asked to set you
+ 
+
+ align:start position:0%
+that we're not being asked to set you
+know a
+
+ align:start position:0%
+know a
+ 
+
+ align:start position:0%
+know a
+true and also a bar true because then
+
+ align:start position:0%
+true and also a bar true because then
+ 
+
+ align:start position:0%
+true and also a bar true because then
+that would not be
+
+ align:start position:0%
+that would not be
+ 
+
+ align:start position:0%
+that would not be
+possible
+
+ align:start position:0%
+possible
+ 
+
+ align:start position:0%
+possible
+but a and a bar are not connected
+
+ align:start position:0%
+but a and a bar are not connected
+ 
+
+ align:start position:0%
+but a and a bar are not connected
+so it's we're never going to be trying
+
+ align:start position:0%
+so it's we're never going to be trying
+ 
+
+ align:start position:0%
+so it's we're never going to be trying
+to set both a and a bar true if so we're
+
+ align:start position:0%
+to set both a and a bar true if so we're
+ 
+
+ align:start position:0%
+to set both a and a bar true if so we're
+going to be trying to set a true we're
+
+ align:start position:0%
+going to be trying to set a true we're
+ 
+
+ align:start position:0%
+going to be trying to set a true we're
+never going to try to set a bar true
+
+ align:start position:0%
+never going to try to set a bar true
+ 
+
+ align:start position:0%
+never going to try to set a bar true
+because those are not those a and a bar
+
+ align:start position:0%
+because those are not those a and a bar
+ 
+
+ align:start position:0%
+because those are not those a and a bar
+cannot be in the same clique they're not
+
+ align:start position:0%
+cannot be in the same clique they're not
+ 
+
+ align:start position:0%
+cannot be in the same clique they're not
+connected to each other
+
+ align:start position:0%
+connected to each other
+ 
+
+ align:start position:0%
+connected to each other
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+is the argument um and lastly
+
+ align:start position:0%
+is the argument um and lastly
+ 
+
+ align:start position:0%
+is the argument um and lastly
+i claim we're not going to look at this
+
+ align:start position:0%
+i claim we're not going to look at this
+ 
+
+ align:start position:0%
+i claim we're not going to look at this
+in detail that it's kind of obvious that
+
+ align:start position:0%
+in detail that it's kind of obvious that
+ 
+
+ align:start position:0%
+in detail that it's kind of obvious that
+this reduction can be done in polynomial
+
+ align:start position:0%
+this reduction can be done in polynomial
+ 
+
+ align:start position:0%
+this reduction can be done in polynomial
+time namely if i give you that formula
+
+ align:start position:0%
+time namely if i give you that formula
+ 
+
+ align:start position:0%
+time namely if i give you that formula
+you can write out that graph in
+
+ align:start position:0%
+you can write out that graph in
+ 
+
+ align:start position:0%
+you can write out that graph in
+pretty easily
+
+ align:start position:0%
+pretty easily
+ 
+
+ align:start position:0%
+pretty easily
+there's no hard work to be done in
+
+ align:start position:0%
+there's no hard work to be done in
+ 
+
+ align:start position:0%
+there's no hard work to be done in
+writing out that that graph or counting
+
+ align:start position:0%
+writing out that that graph or counting
+ 
+
+ align:start position:0%
+writing out that that graph or counting
+up the number of clauses
+
+ align:start position:0%
+up the number of clauses
+ 
+
+ align:start position:0%
+up the number of clauses
+so that's that's the proof
+
+ align:start position:0%
+so that's that's the proof
+ 
+
+ align:start position:0%
+so that's that's the proof
+that i can reduce three statically
+
+ align:start position:0%
+that i can reduce three statically
+ 
+
+ align:start position:0%
+that i can reduce three statically
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and it tells you also that if i could
+
+ align:start position:0%
+and it tells you also that if i could
+ 
+
+ align:start position:0%
+and it tells you also that if i could
+solve click quickly
+
+ align:start position:0%
+solve click quickly
+ 
+
+ align:start position:0%
+solve click quickly
+then i can stop threesat quickly
+
+ align:start position:0%
+then i can stop threesat quickly
+ 
+
+ align:start position:0%
+then i can stop threesat quickly
+and this is the whole point
+
+ align:start position:0%
+and this is the whole point
+ 
+
+ align:start position:0%
+and this is the whole point
+because i can convert now clique
+
+ align:start position:0%
+because i can convert now clique
+ 
+
+ align:start position:0%
+because i can convert now clique
+problems to three sat problems
+
+ align:start position:0%
+problems to three sat problems
+ 
+
+ align:start position:0%
+problems to three sat problems
+no
+
+ align:start position:0%
+no
+ 
+
+ align:start position:0%
+no
+no i couldn't i'm sorry i got backwards
+
+ align:start position:0%
+no i couldn't i'm sorry i got backwards
+ 
+
+ align:start position:0%
+no i couldn't i'm sorry i got backwards
+convert three set problems the clique
+
+ align:start position:0%
+convert three set problems the clique
+ 
+
+ align:start position:0%
+convert three set problems the clique
+problem so if i can solve quick click
+
+ align:start position:0%
+problem so if i can solve quick click
+ 
+
+ align:start position:0%
+problem so if i can solve quick click
+easily then i can solve three set easily
+
+ align:start position:0%
+easily then i can solve three set easily
+ 
+
+ align:start position:0%
+easily then i can solve three set easily
+right i just showed a way of converting
+
+ align:start position:0%
+right i just showed a way of converting
+ 
+
+ align:start position:0%
+right i just showed a way of converting
+these formulas to graphs so if that's so
+
+ align:start position:0%
+these formulas to graphs so if that's so
+ 
+
+ align:start position:0%
+these formulas to graphs so if that's so
+that says if i can solve the graphs
+
+ align:start position:0%
+that says if i can solve the graphs
+ 
+
+ align:start position:0%
+that says if i can solve the graphs
+easily then i can solve the formulas
+
+ align:start position:0%
+easily then i can solve the formulas
+ 
+
+ align:start position:0%
+easily then i can solve the formulas
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+why don't we uh turn to some oh question
+
+ align:start position:0%
+why don't we uh turn to some oh question
+ 
+
+ align:start position:0%
+why don't we uh turn to some oh question
+checking but you know we can also
+
+ align:start position:0%
+checking but you know we can also
+ 
+
+ align:start position:0%
+checking but you know we can also
+um why don't i i'll launch a check-in
+
+ align:start position:0%
+um why don't i i'll launch a check-in
+ 
+
+ align:start position:0%
+um why don't i i'll launch a check-in
+but we'll
+
+ align:start position:0%
+but we'll
+ 
+
+ align:start position:0%
+but we'll
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+let's just see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm seeing many many questions here
+
+ align:start position:0%
+i'm seeing many many questions here
+ 
+
+ align:start position:0%
+i'm seeing many many questions here
+which are actually what my check-in is
+
+ align:start position:0%
+which are actually what my check-in is
+ 
+
+ align:start position:0%
+which are actually what my check-in is
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll turn it back to you guys uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where did we use the fact
+
+ align:start position:0%
+where did we use the fact
+ 
+
+ align:start position:0%
+where did we use the fact
+um that we have
+
+ align:start position:0%
+um that we have
+ 
+
+ align:start position:0%
+um that we have
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+uh literals per clause what does this
+
+ align:start position:0%
+uh literals per clause what does this
+ 
+
+ align:start position:0%
+uh literals per clause what does this
+thing just work even if we had any
+
+ align:start position:0%
+thing just work even if we had any
+ 
+
+ align:start position:0%
+thing just work even if we had any
+number of literals per clause
+
+ align:start position:0%
+number of literals per clause
+ 
+
+ align:start position:0%
+number of literals per clause
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+what do you think
+
+ align:start position:0%
+what do you think
+ 
+
+ align:start position:0%
+what do you think
+we're having a
+
+ align:start position:0%
+we're having a
+ 
+
+ align:start position:0%
+we're having a
+we've got a tight race here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hmm uh
+
+ align:start position:0%
+hmm uh
+ 
+
+ align:start position:0%
+hmm uh
+truth is losing out unfortunately
+
+ align:start position:0%
+truth is losing out unfortunately
+ 
+
+ align:start position:0%
+truth is losing out unfortunately
+all right oh it's really close but still
+
+ align:start position:0%
+all right oh it's really close but still
+ 
+
+ align:start position:0%
+all right oh it's really close but still
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one more okay it's neck and neck
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay almost done
+
+ align:start position:0%
+okay almost done
+ 
+
+ align:start position:0%
+okay almost done
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are we done here okay that's it
+
+ align:start position:0%
+are we done here okay that's it
+ 
+
+ align:start position:0%
+are we done here okay that's it
+uh ending polling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+truth is
+
+ align:start position:0%
+truth is
+ 
+
+ align:start position:0%
+truth is
+thank god
+
+ align:start position:0%
+thank god
+ 
+
+ align:start position:0%
+thank god
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah it works for any size clause we
+
+ align:start position:0%
+yeah it works for any size clause we
+ 
+
+ align:start position:0%
+yeah it works for any size clause we
+didn't use the fact that it's a three c
+
+ align:start position:0%
+didn't use the fact that it's a three c
+ 
+
+ align:start position:0%
+didn't use the fact that it's a three c
+and f it could have been any number here
+
+ align:start position:0%
+and f it could have been any number here
+ 
+
+ align:start position:0%
+and f it could have been any number here
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so it's well we've got a i guess it's a
+
+ align:start position:0%
+so it's well we've got a i guess it's a
+ 
+
+ align:start position:0%
+so it's well we've got a i guess it's a
+plural plurality here though that not a
+
+ align:start position:0%
+plural plurality here though that not a
+ 
+
+ align:start position:0%
+plural plurality here though that not a
+majority um
+
+ align:start position:0%
+majority um
+ 
+
+ align:start position:0%
+majority um
+no we didn't where did we use three in
+
+ align:start position:0%
+no we didn't where did we use three in
+ 
+
+ align:start position:0%
+no we didn't where did we use three in
+any of these argument i didn't mention
+
+ align:start position:0%
+any of these argument i didn't mention
+ 
+
+ align:start position:0%
+any of these argument i didn't mention
+it maybe you were imagining that that is
+
+ align:start position:0%
+it maybe you were imagining that that is
+ 
+
+ align:start position:0%
+it maybe you were imagining that that is
+going to be part of it but three does
+
+ align:start position:0%
+going to be part of it but three does
+ 
+
+ align:start position:0%
+going to be part of it but three does
+not come into this at this discussion at
+
+ align:start position:0%
+not come into this at this discussion at
+ 
+
+ align:start position:0%
+not come into this at this discussion at
+all if you think about how it's why it's
+
+ align:start position:0%
+all if you think about how it's why it's
+ 
+
+ align:start position:0%
+all if you think about how it's why it's
+working
+
+ align:start position:0%
+working
+ 
+
+ align:start position:0%
+working
+um even if we had you know one of these
+
+ align:start position:0%
+um even if we had you know one of these
+ 
+
+ align:start position:0%
+um even if we had you know one of these
+clauses had 10 literals in it
+
+ align:start position:0%
+clauses had 10 literals in it
+ 
+
+ align:start position:0%
+clauses had 10 literals in it
+as long as k is the number of clauses
+
+ align:start position:0%
+as long as k is the number of clauses
+ 
+
+ align:start position:0%
+as long as k is the number of clauses
+and we don't connect
+
+ align:start position:0%
+and we don't connect
+ 
+
+ align:start position:0%
+and we don't connect
+any variables any literals internal to a
+
+ align:start position:0%
+any variables any literals internal to a
+ 
+
+ align:start position:0%
+any variables any literals internal to a
+clause
+
+ align:start position:0%
+clause
+ 
+
+ align:start position:0%
+clause
+this whole argument is going to still
+
+ align:start position:0%
+this whole argument is going to still
+ 
+
+ align:start position:0%
+this whole argument is going to still
+work so please check that make sure you
+
+ align:start position:0%
+work so please check that make sure you
+ 
+
+ align:start position:0%
+work so please check that make sure you
+understand what's going on because i can
+
+ align:start position:0%
+understand what's going on because i can
+ 
+
+ align:start position:0%
+understand what's going on because i can
+see that a good chunk of you
+
+ align:start position:0%
+see that a good chunk of you
+ 
+
+ align:start position:0%
+see that a good chunk of you
+have not got this right
+
+ align:start position:0%
+have not got this right
+ 
+
+ align:start position:0%
+have not got this right
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so i got a good question here uh what
+
+ align:start position:0%
+uh so i got a good question here uh what
+ 
+
+ align:start position:0%
+uh so i got a good question here uh what
+if it's only just one big clause so it's
+
+ align:start position:0%
+if it's only just one big clause so it's
+ 
+
+ align:start position:0%
+if it's only just one big clause so it's
+like the whole formula is just one big
+
+ align:start position:0%
+like the whole formula is just one big
+ 
+
+ align:start position:0%
+like the whole formula is just one big
+war so what does happen in that case
+
+ align:start position:0%
+war so what does happen in that case
+ 
+
+ align:start position:0%
+war so what does happen in that case
+good question so in that case um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so the you know suppose has one big
+
+ align:start position:0%
+so the you know suppose has one big
+ 
+
+ align:start position:0%
+so the you know suppose has one big
+clause with a hundred literals
+
+ align:start position:0%
+clause with a hundred literals
+ 
+
+ align:start position:0%
+clause with a hundred literals
+that's the whole formula it's just a big
+
+ align:start position:0%
+that's the whole formula it's just a big
+ 
+
+ align:start position:0%
+that's the whole formula it's just a big
+war so we know the formula is going to
+
+ align:start position:0%
+war so we know the formula is going to
+ 
+
+ align:start position:0%
+war so we know the formula is going to
+be satisfiable by the way obviously um
+
+ align:start position:0%
+be satisfiable by the way obviously um
+ 
+
+ align:start position:0%
+be satisfiable by the way obviously um
+so if you look at the corresponding g
+
+ align:start position:0%
+so if you look at the corresponding g
+ 
+
+ align:start position:0%
+so if you look at the corresponding g
+it's going to have 100 nodes because
+
+ align:start position:0%
+it's going to have 100 nodes because
+ 
+
+ align:start position:0%
+it's going to have 100 nodes because
+there's one for every literal um
+
+ align:start position:0%
+there's one for every literal um
+ 
+
+ align:start position:0%
+there's one for every literal um
+none of them are going to be connected
+
+ align:start position:0%
+none of them are going to be connected
+ 
+
+ align:start position:0%
+none of them are going to be connected
+to each other because they're all in the
+
+ align:start position:0%
+to each other because they're all in the
+ 
+
+ align:start position:0%
+to each other because they're all in the
+same clause
+
+ align:start position:0%
+same clause
+ 
+
+ align:start position:0%
+same clause
+um so it looks like we're going to be in
+
+ align:start position:0%
+um so it looks like we're going to be in
+ 
+
+ align:start position:0%
+um so it looks like we're going to be in
+tough shape trying to find a clique
+
+ align:start position:0%
+tough shape trying to find a clique
+ 
+
+ align:start position:0%
+tough shape trying to find a clique
+there because there's no edges at all
+
+ align:start position:0%
+there because there's no edges at all
+ 
+
+ align:start position:0%
+there because there's no edges at all
+everything's forbidden but what is k
+
+ align:start position:0%
+everything's forbidden but what is k
+ 
+
+ align:start position:0%
+everything's forbidden but what is k
+k is going to be 1 in that case because
+
+ align:start position:0%
+k is going to be 1 in that case because
+ 
+
+ align:start position:0%
+k is going to be 1 in that case because
+there's only one clause
+
+ align:start position:0%
+there's only one clause
+ 
+
+ align:start position:0%
+there's only one clause
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+kind of a degenerate case but a clique
+
+ align:start position:0%
+kind of a degenerate case but a clique
+ 
+
+ align:start position:0%
+kind of a degenerate case but a clique
+with just one
+
+ align:start position:0%
+with just one
+ 
+
+ align:start position:0%
+with just one
+you know just a single node
+
+ align:start position:0%
+you know just a single node
+ 
+
+ align:start position:0%
+you know just a single node
+is it counts as a one clique
+
+ align:start position:0%
+is it counts as a one clique
+ 
+
+ align:start position:0%
+is it counts as a one clique
+because it's just one node there's no
+
+ align:start position:0%
+because it's just one node there's no
+ 
+
+ align:start position:0%
+because it's just one node there's no
+need for any edges at all it still
+
+ align:start position:0%
+need for any edges at all it still
+ 
+
+ align:start position:0%
+need for any edges at all it still
+counts as a clique so it'll still it'll
+
+ align:start position:0%
+counts as a clique so it'll still it'll
+ 
+
+ align:start position:0%
+counts as a clique so it'll still it'll
+still work out um
+
+ align:start position:0%
+still work out um
+ 
+
+ align:start position:0%
+still work out um
+uh let's see what else here uh that was
+
+ align:start position:0%
+uh let's see what else here uh that was
+ 
+
+ align:start position:0%
+uh let's see what else here uh that was
+kind of a fun question that you asked me
+
+ align:start position:0%
+kind of a fun question that you asked me
+ 
+
+ align:start position:0%
+kind of a fun question that you asked me
+thank you um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh there are a lot of questions um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i think we're actually pretty near the
+
+ align:start position:0%
+i think we're actually pretty near the
+ 
+
+ align:start position:0%
+i think we're actually pretty near the
+break also we'll just see
+
+ align:start position:0%
+break also we'll just see
+ 
+
+ align:start position:0%
+break also we'll just see
+yeah um
+
+ align:start position:0%
+yeah um
+ 
+
+ align:start position:0%
+yeah um
+so why don't i um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+many many questions here uh
+
+ align:start position:0%
+many many questions here uh
+ 
+
+ align:start position:0%
+many many questions here uh
+so i i think i'm gonna start start the
+
+ align:start position:0%
+so i i think i'm gonna start start the
+ 
+
+ align:start position:0%
+so i i think i'm gonna start start the
+clock going down for our um our coffee
+
+ align:start position:0%
+clock going down for our um our coffee
+ 
+
+ align:start position:0%
+clock going down for our um our coffee
+break and um
+
+ align:start position:0%
+break and um
+ 
+
+ align:start position:0%
+break and um
+and i will take some of these questions
+
+ align:start position:0%
+and i will take some of these questions
+ 
+
+ align:start position:0%
+and i will take some of these questions
+i'll try to answer some of these
+
+ align:start position:0%
+i'll try to answer some of these
+ 
+
+ align:start position:0%
+i'll try to answer some of these
+questions oops
+
+ align:start position:0%
+questions oops
+ 
+
+ align:start position:0%
+questions oops
+um try to answer some of these questions
+
+ align:start position:0%
+um try to answer some of these questions
+ 
+
+ align:start position:0%
+um try to answer some of these questions
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+afterward
+
+ align:start position:0%
+afterward
+ 
+
+ align:start position:0%
+afterward
+uh all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so i got a question about
+
+ align:start position:0%
+so i got a question about
+ 
+
+ align:start position:0%
+so i got a question about
+making sure why nodes don't have
+
+ align:start position:0%
+making sure why nodes don't have
+ 
+
+ align:start position:0%
+making sure why nodes don't have
+inconsistent labels if i understand the
+
+ align:start position:0%
+inconsistent labels if i understand the
+ 
+
+ align:start position:0%
+inconsistent labels if i understand the
+question correctly
+
+ align:start position:0%
+question correctly
+ 
+
+ align:start position:0%
+question correctly
+um so these would be nodes
+
+ align:start position:0%
+um so these would be nodes
+ 
+
+ align:start position:0%
+um so these would be nodes
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so i never put edges between nodes with
+
+ align:start position:0%
+so i never put edges between nodes with
+ 
+
+ align:start position:0%
+so i never put edges between nodes with
+inconsistent labels that's the rule
+
+ align:start position:0%
+inconsistent labels that's the rule
+ 
+
+ align:start position:0%
+inconsistent labels that's the rule
+that's my construction i get to i get to
+
+ align:start position:0%
+that's my construction i get to i get to
+ 
+
+ align:start position:0%
+that's my construction i get to i get to
+say how the construction works so those
+
+ align:start position:0%
+say how the construction works so those
+ 
+
+ align:start position:0%
+say how the construction works so those
+two nodes with inconsistent labels can
+
+ align:start position:0%
+two nodes with inconsistent labels can
+ 
+
+ align:start position:0%
+two nodes with inconsistent labels can
+never be in the same clique
+
+ align:start position:0%
+never be in the same clique
+ 
+
+ align:start position:0%
+never be in the same clique
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+there's no edge between them
+
+ align:start position:0%
+there's no edge between them
+ 
+
+ align:start position:0%
+there's no edge between them
+so i'm not sure that answered the
+
+ align:start position:0%
+so i'm not sure that answered the
+ 
+
+ align:start position:0%
+so i'm not sure that answered the
+question there but that was uh
+
+ align:start position:0%
+question there but that was uh
+ 
+
+ align:start position:0%
+question there but that was uh
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let's see
+
+ align:start position:0%
+let's see
+ 
+
+ align:start position:0%
+let's see
+so getting another question here
+
+ align:start position:0%
+so getting another question here
+ 
+
+ align:start position:0%
+so getting another question here
+since any boolean formula can be
+
+ align:start position:0%
+since any boolean formula can be
+ 
+
+ align:start position:0%
+since any boolean formula can be
+converted to cnf
+
+ align:start position:0%
+converted to cnf
+ 
+
+ align:start position:0%
+converted to cnf
+does that mean um is sat polynomial time
+
+ align:start position:0%
+does that mean um is sat polynomial time
+ 
+
+ align:start position:0%
+does that mean um is sat polynomial time
+reducible to clique as well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+monomial time reducible to clique but
+
+ align:start position:0%
+monomial time reducible to clique but
+ 
+
+ align:start position:0%
+monomial time reducible to clique but
+not for the reason that any boolean
+
+ align:start position:0%
+not for the reason that any boolean
+ 
+
+ align:start position:0%
+not for the reason that any boolean
+formula can be converted to c and f
+
+ align:start position:0%
+formula can be converted to c and f
+ 
+
+ align:start position:0%
+formula can be converted to c and f
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+that conversion
+
+ align:start position:0%
+that conversion
+ 
+
+ align:start position:0%
+that conversion
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+is going to be an exponential conversion
+
+ align:start position:0%
+is going to be an exponential conversion
+ 
+
+ align:start position:0%
+is going to be an exponential conversion
+in general the conversion to c and f so
+
+ align:start position:0%
+in general the conversion to c and f so
+ 
+
+ align:start position:0%
+in general the conversion to c and f so
+you have to be careful about what we
+
+ align:start position:0%
+you have to be careful about what we
+ 
+
+ align:start position:0%
+you have to be careful about what we
+mean by converting a formula to cnf
+
+ align:start position:0%
+mean by converting a formula to cnf
+ 
+
+ align:start position:0%
+mean by converting a formula to cnf
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh so also getting questions what
+
+ align:start position:0%
+uh so also getting questions what
+ 
+
+ align:start position:0%
+uh so also getting questions what
+happens in the case of one set well we
+
+ align:start position:0%
+happens in the case of one set well we
+ 
+
+ align:start position:0%
+happens in the case of one set well we
+didn't really talk about one set
+
+ align:start position:0%
+didn't really talk about one set
+ 
+
+ align:start position:0%
+didn't really talk about one set
+uh suppose or i guess so the question is
+
+ align:start position:0%
+uh suppose or i guess so the question is
+ 
+
+ align:start position:0%
+uh suppose or i guess so the question is
+suppose there's only a single
+
+ align:start position:0%
+suppose there's only a single
+ 
+
+ align:start position:0%
+suppose there's only a single
+literal per clause
+
+ align:start position:0%
+literal per clause
+ 
+
+ align:start position:0%
+literal per clause
+that's an interesting another
+
+ align:start position:0%
+that's an interesting another
+ 
+
+ align:start position:0%
+that's an interesting another
+sort of edge case here what happens
+
+ align:start position:0%
+sort of edge case here what happens
+ 
+
+ align:start position:0%
+sort of edge case here what happens
+under those circumstances
+
+ align:start position:0%
+under those circumstances
+ 
+
+ align:start position:0%
+under those circumstances
+so um there's only a single literal per
+
+ align:start position:0%
+so um there's only a single literal per
+ 
+
+ align:start position:0%
+so um there's only a single literal per
+clause um
+
+ align:start position:0%
+clause um
+ 
+
+ align:start position:0%
+clause um
+uh so you have to work out what happens
+
+ align:start position:0%
+uh so you have to work out what happens
+ 
+
+ align:start position:0%
+uh so you have to work out what happens
+but in that case
+
+ align:start position:0%
+but in that case
+ 
+
+ align:start position:0%
+but in that case
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all the clauses just have one literal in
+
+ align:start position:0%
+all the clauses just have one literal in
+ 
+
+ align:start position:0%
+all the clauses just have one literal in
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+and now they have um
+
+ align:start position:0%
+and now they have um
+ 
+
+ align:start position:0%
+and now they have um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the only way
+
+ align:start position:0%
+the only way
+ 
+
+ align:start position:0%
+the only way
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+if you think about what is a when you
+
+ align:start position:0%
+if you think about what is a when you
+ 
+
+ align:start position:0%
+if you think about what is a when you
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+one cnf so there's only um
+
+ align:start position:0%
+one cnf so there's only um
+ 
+
+ align:start position:0%
+one cnf so there's only um
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+literal per clause the only way that can
+
+ align:start position:0%
+literal per clause the only way that can
+ 
+
+ align:start position:0%
+literal per clause the only way that can
+be satisfiable is you have to make each
+
+ align:start position:0%
+be satisfiable is you have to make each
+ 
+
+ align:start position:0%
+be satisfiable is you have to make each
+literal true because there's no warring
+
+ align:start position:0%
+literal true because there's no warring
+ 
+
+ align:start position:0%
+literal true because there's no warring
+anymore so every literal has to be true
+
+ align:start position:0%
+anymore so every literal has to be true
+ 
+
+ align:start position:0%
+anymore so every literal has to be true
+in the assignment so that means you can
+
+ align:start position:0%
+in the assignment so that means you can
+ 
+
+ align:start position:0%
+in the assignment so that means you can
+never have inconsistent literals um and
+
+ align:start position:0%
+never have inconsistent literals um and
+ 
+
+ align:start position:0%
+never have inconsistent literals um and
+that's the only case when you would not
+
+ align:start position:0%
+that's the only case when you would not
+ 
+
+ align:start position:0%
+that's the only case when you would not
+have an edge because you're not the
+
+ align:start position:0%
+have an edge because you're not the
+ 
+
+ align:start position:0%
+have an edge because you're not the
+forbidden is the forbidden condition
+
+ align:start position:0%
+forbidden is the forbidden condition
+ 
+
+ align:start position:0%
+forbidden is the forbidden condition
+won't happen because you don't have more
+
+ align:start position:0%
+won't happen because you don't have more
+ 
+
+ align:start position:0%
+won't happen because you don't have more
+than one uh node per per clause every
+
+ align:start position:0%
+than one uh node per per clause every
+ 
+
+ align:start position:0%
+than one uh node per per clause every
+clause is going to have just a single
+
+ align:start position:0%
+clause is going to have just a single
+ 
+
+ align:start position:0%
+clause is going to have just a single
+node in it uh so
+
+ align:start position:0%
+node in it uh so
+ 
+
+ align:start position:0%
+node in it uh so
+it really comes down to whether or not
+
+ align:start position:0%
+it really comes down to whether or not
+ 
+
+ align:start position:0%
+it really comes down to whether or not
+you have an inconsistently labeled um
+
+ align:start position:0%
+you have an inconsistently labeled um
+ 
+
+ align:start position:0%
+you have an inconsistently labeled um
+inconsistent clauses
+
+ align:start position:0%
+inconsistent clauses
+ 
+
+ align:start position:0%
+inconsistent clauses
+i i didn't explain that super well but
+
+ align:start position:0%
+i i didn't explain that super well but
+ 
+
+ align:start position:0%
+i i didn't explain that super well but
+it's the
+
+ align:start position:0%
+it's the
+ 
+
+ align:start position:0%
+it's the
+the argument still works there you
+
+ align:start position:0%
+the argument still works there you
+ 
+
+ align:start position:0%
+the argument still works there you
+should check it for yourself
+
+ align:start position:0%
+should check it for yourself
+ 
+
+ align:start position:0%
+should check it for yourself
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so this is a basic question how do we
+
+ align:start position:0%
+so this is a basic question how do we
+ 
+
+ align:start position:0%
+so this is a basic question how do we
+see that f is polynomial time
+
+ align:start position:0%
+see that f is polynomial time
+ 
+
+ align:start position:0%
+see that f is polynomial time
+i i'm not sure i want to expend a lot of
+
+ align:start position:0%
+i i'm not sure i want to expend a lot of
+ 
+
+ align:start position:0%
+i i'm not sure i want to expend a lot of
+you know a lot of discussion on that
+
+ align:start position:0%
+you know a lot of discussion on that
+ 
+
+ align:start position:0%
+you know a lot of discussion on that
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+the the conversion from the formula
+
+ align:start position:0%
+the the conversion from the formula
+ 
+
+ align:start position:0%
+the the conversion from the formula
+to the graph
+
+ align:start position:0%
+to the graph
+ 
+
+ align:start position:0%
+to the graph
+is kind of a one-to-one
+
+ align:start position:0%
+is kind of a one-to-one
+ 
+
+ align:start position:0%
+is kind of a one-to-one
+you know every no every uh literal
+
+ align:start position:0%
+you know every no every uh literal
+ 
+
+ align:start position:0%
+you know every no every uh literal
+becomes a node
+
+ align:start position:0%
+becomes a node
+ 
+
+ align:start position:0%
+becomes a node
+um the rule for when edges are present
+
+ align:start position:0%
+um the rule for when edges are present
+ 
+
+ align:start position:0%
+um the rule for when edges are present
+it's a very simple rule so i guess i
+
+ align:start position:0%
+it's a very simple rule so i guess i
+ 
+
+ align:start position:0%
+it's a very simple rule so i guess i
+would argue
+
+ align:start position:0%
+would argue
+ 
+
+ align:start position:0%
+would argue
+i'm not sure what what more to say it
+
+ align:start position:0%
+i'm not sure what what more to say it
+ 
+
+ align:start position:0%
+i'm not sure what what more to say it
+seems pretty clear that the
+
+ align:start position:0%
+seems pretty clear that the
+ 
+
+ align:start position:0%
+seems pretty clear that the
+conversion that reduction is polynomial
+
+ align:start position:0%
+conversion that reduction is polynomial
+ 
+
+ align:start position:0%
+conversion that reduction is polynomial
+time computable i mean if you wrote a
+
+ align:start position:0%
+time computable i mean if you wrote a
+ 
+
+ align:start position:0%
+time computable i mean if you wrote a
+program to do that it would operate very
+
+ align:start position:0%
+program to do that it would operate very
+ 
+
+ align:start position:0%
+program to do that it would operate very
+quickly
+
+ align:start position:0%
+quickly
+ 
+
+ align:start position:0%
+quickly
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+is it possible for g to have a k plus n
+
+ align:start position:0%
+is it possible for g to have a k plus n
+ 
+
+ align:start position:0%
+is it possible for g to have a k plus n
+clique where n is greater than zero and
+
+ align:start position:0%
+clique where n is greater than zero and
+ 
+
+ align:start position:0%
+clique where n is greater than zero and
+does that matter
+
+ align:start position:0%
+does that matter
+ 
+
+ align:start position:0%
+does that matter
+now if you think about it
+
+ align:start position:0%
+now if you think about it
+ 
+
+ align:start position:0%
+now if you think about it
+the biggest possible clique that this
+
+ align:start position:0%
+the biggest possible clique that this
+ 
+
+ align:start position:0%
+the biggest possible clique that this
+graph g could have is k
+
+ align:start position:0%
+graph g could have is k
+ 
+
+ align:start position:0%
+graph g could have is k
+it could never have more than
+
+ align:start position:0%
+it could never have more than
+ 
+
+ align:start position:0%
+it could never have more than
+uh uh you know a bigger clique because
+
+ align:start position:0%
+uh uh you know a bigger clique because
+ 
+
+ align:start position:0%
+uh uh you know a bigger clique because
+two nodes in the same uh clause are
+
+ align:start position:0%
+two nodes in the same uh clause are
+ 
+
+ align:start position:0%
+two nodes in the same uh clause are
+never connected
+
+ align:start position:0%
+never connected
+ 
+
+ align:start position:0%
+never connected
+you only have k clauses
+
+ align:start position:0%
+you only have k clauses
+ 
+
+ align:start position:0%
+you only have k clauses
+so the answer is no you cannot have a
+
+ align:start position:0%
+so the answer is no you cannot have a
+ 
+
+ align:start position:0%
+so the answer is no you cannot have a
+bigger
+
+ align:start position:0%
+bigger
+ 
+
+ align:start position:0%
+bigger
+a bigger than a k click it's just not
+
+ align:start position:0%
+a bigger than a k click it's just not
+ 
+
+ align:start position:0%
+a bigger than a k click it's just not
+going to happen
+
+ align:start position:0%
+going to happen
+ 
+
+ align:start position:0%
+going to happen
+does each clause need to have the same
+
+ align:start position:0%
+does each clause need to have the same
+ 
+
+ align:start position:0%
+does each clause need to have the same
+number of literals i don't see why
+
+ align:start position:0%
+number of literals i don't see why
+ 
+
+ align:start position:0%
+number of literals i don't see why
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+so question is why are we worrying about
+
+ align:start position:0%
+so question is why are we worrying about
+ 
+
+ align:start position:0%
+so question is why are we worrying about
+threesat um
+
+ align:start position:0%
+threesat um
+ 
+
+ align:start position:0%
+threesat um
+since it didn't seem to matter here
+
+ align:start position:0%
+since it didn't seem to matter here
+ 
+
+ align:start position:0%
+since it didn't seem to matter here
+there are other examples where it does
+
+ align:start position:0%
+there are other examples where it does
+ 
+
+ align:start position:0%
+there are other examples where it does
+matter i i i'm actually not sure if
+
+ align:start position:0%
+matter i i i'm actually not sure if
+ 
+
+ align:start position:0%
+matter i i i'm actually not sure if
+we'll see one or not but um there there
+
+ align:start position:0%
+we'll see one or not but um there there
+ 
+
+ align:start position:0%
+we'll see one or not but um there there
+are cases where it does matter
+
+ align:start position:0%
+are cases where it does matter
+ 
+
+ align:start position:0%
+are cases where it does matter
+um let me just see if there's any quick
+
+ align:start position:0%
+um let me just see if there's any quick
+ 
+
+ align:start position:0%
+um let me just see if there's any quick
+questions here
+
+ align:start position:0%
+questions here
+ 
+
+ align:start position:0%
+questions here
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somebody's saying doesn't does
+
+ align:start position:0%
+somebody's saying doesn't does
+ 
+
+ align:start position:0%
+somebody's saying doesn't does
+do we have to worry about there being a
+
+ align:start position:0%
+do we have to worry about there being a
+ 
+
+ align:start position:0%
+do we have to worry about there being a
+polynomial number of literals
+
+ align:start position:0%
+polynomial number of literals
+ 
+
+ align:start position:0%
+polynomial number of literals
+so you have to think about what you what
+
+ align:start position:0%
+so you have to think about what you what
+ 
+
+ align:start position:0%
+so you have to think about what you what
+that question means the size of the
+
+ align:start position:0%
+that question means the size of the
+ 
+
+ align:start position:0%
+that question means the size of the
+input which includes all of the literals
+
+ align:start position:0%
+input which includes all of the literals
+ 
+
+ align:start position:0%
+input which includes all of the literals
+is n
+
+ align:start position:0%
+is n
+ 
+
+ align:start position:0%
+is n
+so there's going to be at most n
+
+ align:start position:0%
+so there's going to be at most n
+ 
+
+ align:start position:0%
+so there's going to be at most n
+literals
+
+ align:start position:0%
+literals
+ 
+
+ align:start position:0%
+literals
+um because that's the size of the input
+
+ align:start position:0%
+um because that's the size of the input
+ 
+
+ align:start position:0%
+um because that's the size of the input
+uh the i mean
+
+ align:start position:0%
+uh the i mean
+ 
+
+ align:start position:0%
+uh the i mean
+at most uh and literals appearing so
+
+ align:start position:0%
+at most uh and literals appearing so
+ 
+
+ align:start position:0%
+at most uh and literals appearing so
+you don't have to worry about that being
+
+ align:start position:0%
+you don't have to worry about that being
+ 
+
+ align:start position:0%
+you don't have to worry about that being
+polynomial because by the way we're
+
+ align:start position:0%
+polynomial because by the way we're
+ 
+
+ align:start position:0%
+polynomial because by the way we're
+we're defining the size of the input is
+
+ align:start position:0%
+we're defining the size of the input is
+ 
+
+ align:start position:0%
+we're defining the size of the input is
+going to be at most n literals
+
+ align:start position:0%
+going to be at most n literals
+ 
+
+ align:start position:0%
+going to be at most n literals
+i hope that's clear
+
+ align:start position:0%
+i hope that's clear
+ 
+
+ align:start position:0%
+i hope that's clear
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+when we talk about power
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is a good question when we
+
+ align:start position:0%
+okay so this is a good question when we
+ 
+
+ align:start position:0%
+okay so this is a good question when we
+talk about polynomial time
+
+ align:start position:0%
+talk about polynomial time
+ 
+
+ align:start position:0%
+talk about polynomial time
+it's polynomial in the representation of
+
+ align:start position:0%
+it's polynomial in the representation of
+ 
+
+ align:start position:0%
+it's polynomial in the representation of
+of the input which is if you want to
+
+ align:start position:0%
+of the input which is if you want to
+ 
+
+ align:start position:0%
+of the input which is if you want to
+think about it in terms of bits that's
+
+ align:start position:0%
+think about it in terms of bits that's
+ 
+
+ align:start position:0%
+think about it in terms of bits that's
+fine or whatever it's not going to
+
+ align:start position:0%
+fine or whatever it's not going to
+ 
+
+ align:start position:0%
+fine or whatever it's not going to
+matter if you use some larger alphabet
+
+ align:start position:0%
+matter if you use some larger alphabet
+ 
+
+ align:start position:0%
+matter if you use some larger alphabet
+but the number of symbols you need you
+
+ align:start position:0%
+but the number of symbols you need you
+ 
+
+ align:start position:0%
+but the number of symbols you need you
+know in your fixed size alphabet the
+
+ align:start position:0%
+know in your fixed size alphabet the
+ 
+
+ align:start position:0%
+know in your fixed size alphabet the
+number of symbols you need to write down
+
+ align:start position:0%
+number of symbols you need to write down
+ 
+
+ align:start position:0%
+number of symbols you need to write down
+that input in whatever your reasonable
+
+ align:start position:0%
+that input in whatever your reasonable
+ 
+
+ align:start position:0%
+that input in whatever your reasonable
+encoding is is going to be n and it's
+
+ align:start position:0%
+encoding is is going to be n and it's
+ 
+
+ align:start position:0%
+encoding is is going to be n and it's
+going to be polynomial in n polynomial
+
+ align:start position:0%
+going to be polynomial in n polynomial
+ 
+
+ align:start position:0%
+going to be polynomial in n polynomial
+in that
+
+ align:start position:0%
+in that
+ 
+
+ align:start position:0%
+in that
+length of the input
+
+ align:start position:0%
+length of the input
+ 
+
+ align:start position:0%
+length of the input
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so another question is does sat reduce
+
+ align:start position:0%
+so another question is does sat reduce
+ 
+
+ align:start position:0%
+so another question is does sat reduce
+the three set yes we that we will see um
+
+ align:start position:0%
+the three set yes we that we will see um
+ 
+
+ align:start position:0%
+the three set yes we that we will see um
+sat actually does polynomial time reduce
+
+ align:start position:0%
+sat actually does polynomial time reduce
+ 
+
+ align:start position:0%
+sat actually does polynomial time reduce
+the three set not by converting to an
+
+ align:start position:0%
+the three set not by converting to an
+ 
+
+ align:start position:0%
+the three set not by converting to an
+equivalent formula but by some more uh
+
+ align:start position:0%
+equivalent formula but by some more uh
+ 
+
+ align:start position:0%
+equivalent formula but by some more uh
+somewhat more involved argument uh than
+
+ align:start position:0%
+somewhat more involved argument uh than
+ 
+
+ align:start position:0%
+somewhat more involved argument uh than
+that okay why don't we move on some of
+
+ align:start position:0%
+that okay why don't we move on some of
+ 
+
+ align:start position:0%
+that okay why don't we move on some of
+these are going to come out anyway in
+
+ align:start position:0%
+these are going to come out anyway in
+ 
+
+ align:start position:0%
+these are going to come out anyway in
+the lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now let's talk about mp
+
+ align:start position:0%
+okay so now let's talk about mp
+ 
+
+ align:start position:0%
+okay so now let's talk about mp
+completeness because we've kind of set
+
+ align:start position:0%
+completeness because we've kind of set
+ 
+
+ align:start position:0%
+completeness because we've kind of set
+things up we're not going to prove that
+
+ align:start position:0%
+things up we're not going to prove that
+ 
+
+ align:start position:0%
+things up we're not going to prove that
+you know the basic theorem the cook 11
+
+ align:start position:0%
+you know the basic theorem the cook 11
+ 
+
+ align:start position:0%
+you know the basic theorem the cook 11
+theorem about mp completeness but at
+
+ align:start position:0%
+theorem about mp completeness but at
+ 
+
+ align:start position:0%
+theorem about mp completeness but at
+least we'll be able to make the
+
+ align:start position:0%
+least we'll be able to make the
+ 
+
+ align:start position:0%
+least we'll be able to make the
+definition
+
+ align:start position:0%
+definition
+ 
+
+ align:start position:0%
+definition
+okay here's our definition you know what
+
+ align:start position:0%
+okay here's our definition you know what
+ 
+
+ align:start position:0%
+okay here's our definition you know what
+it means for a problem to be in be
+
+ align:start position:0%
+it means for a problem to be in be
+ 
+
+ align:start position:0%
+it means for a problem to be in be
+complete
+
+ align:start position:0%
+complete
+ 
+
+ align:start position:0%
+complete
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a language
+
+ align:start position:0%
+so a language
+ 
+
+ align:start position:0%
+so a language
+b is called np complete
+
+ align:start position:0%
+b is called np complete
+ 
+
+ align:start position:0%
+b is called np complete
+if it has two properties
+
+ align:start position:0%
+if it has two properties
+ 
+
+ align:start position:0%
+if it has two properties
+number one is that has to be a member of
+
+ align:start position:0%
+number one is that has to be a member of
+ 
+
+ align:start position:0%
+number one is that has to be a member of
+np
+
+ align:start position:0%
+np
+ 
+
+ align:start position:0%
+np
+and number two
+
+ align:start position:0%
+and number two
+ 
+
+ align:start position:0%
+and number two
+every language in np has the polynomial
+
+ align:start position:0%
+every language in np has the polynomial
+ 
+
+ align:start position:0%
+every language in np has the polynomial
+time reduced to that
+
+ align:start position:0%
+time reduced to that
+ 
+
+ align:start position:0%
+time reduced to that
+to that language to that np complete
+
+ align:start position:0%
+to that language to that np complete
+ 
+
+ align:start position:0%
+to that language to that np complete
+language in order for it to be np
+
+ align:start position:0%
+language in order for it to be np
+ 
+
+ align:start position:0%
+language in order for it to be np
+complete
+
+ align:start position:0%
+complete
+ 
+
+ align:start position:0%
+complete
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+simple picture
+
+ align:start position:0%
+simple picture
+ 
+
+ align:start position:0%
+simple picture
+has to be in nnp
+
+ align:start position:0%
+has to be in nnp
+ 
+
+ align:start position:0%
+has to be in nnp
+and everything in np reduces to it
+
+ align:start position:0%
+and everything in np reduces to it
+ 
+
+ align:start position:0%
+and everything in np reduces to it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and so that's kind of the magical
+
+ align:start position:0%
+and so that's kind of the magical
+ 
+
+ align:start position:0%
+and so that's kind of the magical
+property that we claimed that that sat
+
+ align:start position:0%
+property that we claimed that that sat
+ 
+
+ align:start position:0%
+property that we claimed that that sat
+has sat for for one thing is obviously
+
+ align:start position:0%
+has sat for for one thing is obviously
+ 
+
+ align:start position:0%
+has sat for for one thing is obviously
+in np
+
+ align:start position:0%
+in np
+ 
+
+ align:start position:0%
+in np
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+as we
+
+ align:start position:0%
+as we
+ 
+
+ align:start position:0%
+as we
+the cook 11 theorem shows
+
+ align:start position:0%
+the cook 11 theorem shows
+ 
+
+ align:start position:0%
+the cook 11 theorem shows
+or will show
+
+ align:start position:0%
+or will show
+ 
+
+ align:start position:0%
+or will show
+everything in npe is reducible to sat so
+
+ align:start position:0%
+everything in npe is reducible to sat so
+ 
+
+ align:start position:0%
+everything in npe is reducible to sat so
+that's going to be our first example of
+
+ align:start position:0%
+that's going to be our first example of
+ 
+
+ align:start position:0%
+that's going to be our first example of
+an np complete problem
+
+ align:start position:0%
+an np complete problem
+ 
+
+ align:start position:0%
+an np complete problem
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so now
+
+ align:start position:0%
+uh so now
+ 
+
+ align:start position:0%
+uh so now
+uh and we're going to get what we
+
+ align:start position:0%
+uh and we're going to get what we
+ 
+
+ align:start position:0%
+uh and we're going to get what we
+claimed also for sat that if sat or any
+
+ align:start position:0%
+claimed also for sat that if sat or any
+ 
+
+ align:start position:0%
+claimed also for sat that if sat or any
+other np-complete problem
+
+ align:start position:0%
+other np-complete problem
+ 
+
+ align:start position:0%
+other np-complete problem
+turns out to be solvable in polynomial
+
+ align:start position:0%
+turns out to be solvable in polynomial
+ 
+
+ align:start position:0%
+turns out to be solvable in polynomial
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+then every np problem is solvable in
+
+ align:start position:0%
+then every np problem is solvable in
+ 
+
+ align:start position:0%
+then every np problem is solvable in
+polynomial time and and that's immediate
+
+ align:start position:0%
+polynomial time and and that's immediate
+ 
+
+ align:start position:0%
+polynomial time and and that's immediate
+because everything is reducible in
+
+ align:start position:0%
+because everything is reducible in
+ 
+
+ align:start position:0%
+because everything is reducible in
+polynomial time to the np complete
+
+ align:start position:0%
+polynomial time to the np complete
+ 
+
+ align:start position:0%
+polynomial time to the np complete
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+so if you can do it easily you can do
+
+ align:start position:0%
+so if you can do it easily you can do
+ 
+
+ align:start position:0%
+so if you can do it easily you can do
+everything easily just by going through
+
+ align:start position:0%
+everything easily just by going through
+ 
+
+ align:start position:0%
+everything easily just by going through
+the reduction
+
+ align:start position:0%
+the reduction
+ 
+
+ align:start position:0%
+the reduction
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the quick level theorem as i
+
+ align:start position:0%
+so the quick level theorem as i
+ 
+
+ align:start position:0%
+so the quick level theorem as i
+mentioned is that sad is np-complete
+
+ align:start position:0%
+mentioned is that sad is np-complete
+ 
+
+ align:start position:0%
+mentioned is that sad is np-complete
+and we're going to actually prove it
+
+ align:start position:0%
+and we're going to actually prove it
+ 
+
+ align:start position:0%
+and we're going to actually prove it
+next lecture but let's assume for the
+
+ align:start position:0%
+next lecture but let's assume for the
+ 
+
+ align:start position:0%
+next lecture but let's assume for the
+remainder of this lecture that we know
+
+ align:start position:0%
+remainder of this lecture that we know
+ 
+
+ align:start position:0%
+remainder of this lecture that we know
+it to be true because so i'll use the
+
+ align:start position:0%
+it to be true because so i'll use the
+ 
+
+ align:start position:0%
+it to be true because so i'll use the
+terminology of problems being np
+
+ align:start position:0%
+terminology of problems being np
+ 
+
+ align:start position:0%
+terminology of problems being np
+complete uh assuming that we know um
+
+ align:start position:0%
+complete uh assuming that we know um
+ 
+
+ align:start position:0%
+complete uh assuming that we know um
+that we have uh sat as empty complete
+
+ align:start position:0%
+that we have uh sat as empty complete
+ 
+
+ align:start position:0%
+that we have uh sat as empty complete
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we're gonna we're gonna be
+
+ align:start position:0%
+so we're gonna we're gonna be
+ 
+
+ align:start position:0%
+so we're gonna we're gonna be
+using some of the things that were
+
+ align:start position:0%
+using some of the things that were
+ 
+
+ align:start position:0%
+using some of the things that were
+proving next lecture uh just
+
+ align:start position:0%
+proving next lecture uh just
+ 
+
+ align:start position:0%
+proving next lecture uh just
+in the terminology that we're going to
+
+ align:start position:0%
+in the terminology that we're going to
+ 
+
+ align:start position:0%
+in the terminology that we're going to
+be talking today
+
+ align:start position:0%
+be talking today
+ 
+
+ align:start position:0%
+be talking today
+okay so here's the picture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the class np
+
+ align:start position:0%
+here's the class np
+ 
+
+ align:start position:0%
+here's the class np
+and everything in np
+
+ align:start position:0%
+and everything in np
+ 
+
+ align:start position:0%
+and everything in np
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+polynomial time reducible to set
+
+ align:start position:0%
+polynomial time reducible to set
+ 
+
+ align:start position:0%
+polynomial time reducible to set
+sat itself is a member of np but i
+
+ align:start position:0%
+sat itself is a member of np but i
+ 
+
+ align:start position:0%
+sat itself is a member of np but i
+didn't want to show it that way because
+
+ align:start position:0%
+didn't want to show it that way because
+ 
+
+ align:start position:0%
+didn't want to show it that way because
+it makes the picture kind of hard to uh
+
+ align:start position:0%
+it makes the picture kind of hard to uh
+ 
+
+ align:start position:0%
+it makes the picture kind of hard to uh
+hard to uh
+
+ align:start position:0%
+hard to uh
+ 
+
+ align:start position:0%
+hard to uh
+hard to display
+
+ align:start position:0%
+hard to display
+ 
+
+ align:start position:0%
+hard to display
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+just from the perspective of the
+
+ align:start position:0%
+just from the perspective of the
+ 
+
+ align:start position:0%
+just from the perspective of the
+reduction everything in np is polynomial
+
+ align:start position:0%
+reduction everything in np is polynomial
+ 
+
+ align:start position:0%
+reduction everything in np is polynomial
+time reducible to sad we'll show that
+
+ align:start position:0%
+time reducible to sad we'll show that
+ 
+
+ align:start position:0%
+time reducible to sad we'll show that
+next lecture
+
+ align:start position:0%
+next lecture
+ 
+
+ align:start position:0%
+next lecture
+another thing that we'll show next
+
+ align:start position:0%
+another thing that we'll show next
+ 
+
+ align:start position:0%
+another thing that we'll show next
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+is that sat in turn is polynomial time
+
+ align:start position:0%
+is that sat in turn is polynomial time
+ 
+
+ align:start position:0%
+is that sat in turn is polynomial time
+reducible to three sat so
+
+ align:start position:0%
+reducible to three sat so
+ 
+
+ align:start position:0%
+reducible to three sat so
+three stat as you remember are just
+
+ align:start position:0%
+three stat as you remember are just
+ 
+
+ align:start position:0%
+three stat as you remember are just
+those problems that are in conjunction
+
+ align:start position:0%
+those problems that are in conjunction
+ 
+
+ align:start position:0%
+those problems that are in conjunction
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+are in three c and f
+
+ align:start position:0%
+are in three c and f
+ 
+
+ align:start position:0%
+are in three c and f
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+what we showed today is that three set
+
+ align:start position:0%
+what we showed today is that three set
+ 
+
+ align:start position:0%
+what we showed today is that three set
+is polynomial time reducible to clique
+
+ align:start position:0%
+is polynomial time reducible to clique
+ 
+
+ align:start position:0%
+is polynomial time reducible to clique
+so now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+taking the assumption that sat is np
+
+ align:start position:0%
+taking the assumption that sat is np
+ 
+
+ align:start position:0%
+taking the assumption that sat is np
+complete
+
+ align:start position:0%
+complete
+ 
+
+ align:start position:0%
+complete
+so everything is polynomial time
+
+ align:start position:0%
+so everything is polynomial time
+ 
+
+ align:start position:0%
+so everything is polynomial time
+reducible to sat which is in turn
+
+ align:start position:0%
+reducible to sat which is in turn
+ 
+
+ align:start position:0%
+reducible to sat which is in turn
+polynomial time reducible to three sat
+
+ align:start position:0%
+polynomial time reducible to three sat
+ 
+
+ align:start position:0%
+polynomial time reducible to three sat
+in in turn reducible to click
+
+ align:start position:0%
+in in turn reducible to click
+ 
+
+ align:start position:0%
+in in turn reducible to click
+these reductions as we've seen before
+
+ align:start position:0%
+these reductions as we've seen before
+ 
+
+ align:start position:0%
+these reductions as we've seen before
+composed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you can just reply apply one reduction
+
+ align:start position:0%
+you can just reply apply one reduction
+ 
+
+ align:start position:0%
+you can just reply apply one reduction
+function after the next
+
+ align:start position:0%
+function after the next
+ 
+
+ align:start position:0%
+function after the next
+if each one each one individually is
+
+ align:start position:0%
+if each one each one individually is
+ 
+
+ align:start position:0%
+if each one each one individually is
+polynomial the whole thing as a
+
+ align:start position:0%
+polynomial the whole thing as a
+ 
+
+ align:start position:0%
+polynomial the whole thing as a
+combination is going to be polynomial so
+
+ align:start position:0%
+combination is going to be polynomial so
+ 
+
+ align:start position:0%
+combination is going to be polynomial so
+now we know that three sat is going to
+
+ align:start position:0%
+now we know that three sat is going to
+ 
+
+ align:start position:0%
+now we know that three sat is going to
+be also np complete because
+
+ align:start position:0%
+be also np complete because
+ 
+
+ align:start position:0%
+be also np complete because
+we can reduce anything in np to stat and
+
+ align:start position:0%
+we can reduce anything in np to stat and
+ 
+
+ align:start position:0%
+we can reduce anything in np to stat and
+then to three set and then we get a
+
+ align:start position:0%
+then to three set and then we get a
+ 
+
+ align:start position:0%
+then to three set and then we get a
+reduction directly to three sat by
+
+ align:start position:0%
+reduction directly to three sat by
+ 
+
+ align:start position:0%
+reduction directly to three sat by
+composing those two reductions and then
+
+ align:start position:0%
+composing those two reductions and then
+ 
+
+ align:start position:0%
+composing those two reductions and then
+furthermore at the clique so now we
+
+ align:start position:0%
+furthermore at the clique so now we
+ 
+
+ align:start position:0%
+furthermore at the clique so now we
+uh have several np complete problems and
+
+ align:start position:0%
+uh have several np complete problems and
+ 
+
+ align:start position:0%
+uh have several np complete problems and
+moving beyond that
+
+ align:start position:0%
+moving beyond that
+ 
+
+ align:start position:0%
+moving beyond that
+we have the hand path problem which we
+
+ align:start position:0%
+we have the hand path problem which we
+ 
+
+ align:start position:0%
+we have the hand path problem which we
+are going to talk about next and we'll
+
+ align:start position:0%
+are going to talk about next and we'll
+ 
+
+ align:start position:0%
+are going to talk about next and we'll
+show another
+
+ align:start position:0%
+show another
+ 
+
+ align:start position:0%
+show another
+reduction um
+
+ align:start position:0%
+reduction um
+ 
+
+ align:start position:0%
+reduction um
+in addition to the one we just showed to
+
+ align:start position:0%
+in addition to the one we just showed to
+ 
+
+ align:start position:0%
+in addition to the one we just showed to
+click now one going from three set to
+
+ align:start position:0%
+click now one going from three set to
+ 
+
+ align:start position:0%
+click now one going from three set to
+hand
+
+ align:start position:0%
+hand
+ 
+
+ align:start position:0%
+hand
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay uh so in general
+
+ align:start position:0%
+okay uh so in general
+ 
+
+ align:start position:0%
+okay uh so in general
+i think the the the the take away
+
+ align:start position:0%
+i think the the the the take away
+ 
+
+ align:start position:0%
+i think the the the the take away
+message is that to show some language as
+
+ align:start position:0%
+message is that to show some language as
+ 
+
+ align:start position:0%
+message is that to show some language as
+np complete you want to show that three
+
+ align:start position:0%
+np complete you want to show that three
+ 
+
+ align:start position:0%
+np complete you want to show that three
+sat is polynomial time reducible to it
+
+ align:start position:0%
+sat is polynomial time reducible to it
+ 
+
+ align:start position:0%
+sat is polynomial time reducible to it
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+some good questions coming in i'll try
+
+ align:start position:0%
+some good questions coming in i'll try
+ 
+
+ align:start position:0%
+some good questions coming in i'll try
+to answer those so you're going to
+
+ align:start position:0%
+to answer those so you're going to
+ 
+
+ align:start position:0%
+to answer those so you're going to
+retake
+
+ align:start position:0%
+retake
+ 
+
+ align:start position:0%
+retake
+3sat and reduced to c that's the sort of
+
+ align:start position:0%
+3sat and reduced to c that's the sort of
+ 
+
+ align:start position:0%
+3sat and reduced to c that's the sort of
+the most typical case
+
+ align:start position:0%
+the most typical case
+ 
+
+ align:start position:0%
+the most typical case
+or you might have there's going to be
+
+ align:start position:0%
+or you might have there's going to be
+ 
+
+ align:start position:0%
+or you might have there's going to be
+other examples too we might start with
+
+ align:start position:0%
+other examples too we might start with
+ 
+
+ align:start position:0%
+other examples too we might start with
+another problem that you've already
+
+ align:start position:0%
+another problem that you've already
+ 
+
+ align:start position:0%
+another problem that you've already
+shown to be np complete and read and
+
+ align:start position:0%
+shown to be np complete and read and
+ 
+
+ align:start position:0%
+shown to be np complete and read and
+reduce it to your language so it doesn't
+
+ align:start position:0%
+reduce it to your language so it doesn't
+ 
+
+ align:start position:0%
+reduce it to your language so it doesn't
+have to start with reset
+
+ align:start position:0%
+have to start with reset
+ 
+
+ align:start position:0%
+have to start with reset
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+often it does
+
+ align:start position:0%
+often it does
+ 
+
+ align:start position:0%
+often it does
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay why do we why is this concept
+
+ align:start position:0%
+okay why do we why is this concept
+ 
+
+ align:start position:0%
+okay why do we why is this concept
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+so i would say there are two reasons um
+
+ align:start position:0%
+so i would say there are two reasons um
+ 
+
+ align:start position:0%
+so i would say there are two reasons um
+and this is going to get a little bit at
+
+ align:start position:0%
+and this is going to get a little bit at
+ 
+
+ align:start position:0%
+and this is going to get a little bit at
+the uh some of the chat questions um
+
+ align:start position:0%
+the uh some of the chat questions um
+ 
+
+ align:start position:0%
+the uh some of the chat questions um
+first of all
+
+ align:start position:0%
+first of all
+ 
+
+ align:start position:0%
+first of all
+if you're faced with some copy new
+
+ align:start position:0%
+if you're faced with some copy new
+ 
+
+ align:start position:0%
+if you're faced with some copy new
+computational problem you've got some
+
+ align:start position:0%
+computational problem you've got some
+ 
+
+ align:start position:0%
+computational problem you've got some
+robotics problem
+
+ align:start position:0%
+robotics problem
+ 
+
+ align:start position:0%
+robotics problem
+um that you want to solve in your thesis
+
+ align:start position:0%
+um that you want to solve in your thesis
+ 
+
+ align:start position:0%
+um that you want to solve in your thesis
+and you need to some algorithm about
+
+ align:start position:0%
+and you need to some algorithm about
+ 
+
+ align:start position:0%
+and you need to some algorithm about
+whether the robot arm can do such and
+
+ align:start position:0%
+whether the robot arm can do such and
+ 
+
+ align:start position:0%
+whether the robot arm can do such and
+move in a certain such a way and involve
+
+ align:start position:0%
+move in a certain such a way and involve
+ 
+
+ align:start position:0%
+move in a certain such a way and involve
+searching you know possibly searching
+
+ align:start position:0%
+searching you know possibly searching
+ 
+
+ align:start position:0%
+searching you know possibly searching
+through a space of different kinds of
+
+ align:start position:0%
+through a space of different kinds of
+ 
+
+ align:start position:0%
+through a space of different kinds of
+motions and you want to know you know i
+
+ align:start position:0%
+motions and you want to know you know i
+ 
+
+ align:start position:0%
+motions and you want to know you know i
+need a either i'd like to have a i like
+
+ align:start position:0%
+need a either i'd like to have a i like
+ 
+
+ align:start position:0%
+need a either i'd like to have a i like
+to find a polynomial algorithm to solve
+
+ align:start position:0%
+to find a polynomial algorithm to solve
+ 
+
+ align:start position:0%
+to find a polynomial algorithm to solve
+that problem
+
+ align:start position:0%
+that problem
+ 
+
+ align:start position:0%
+that problem
+i'm using this as an example because
+
+ align:start position:0%
+i'm using this as an example because
+ 
+
+ align:start position:0%
+i'm using this as an example because
+this actually did happen to one of the
+
+ align:start position:0%
+this actually did happen to one of the
+ 
+
+ align:start position:0%
+this actually did happen to one of the
+former students from this class who was
+
+ align:start position:0%
+former students from this class who was
+ 
+
+ align:start position:0%
+former students from this class who was
+working in robotics and they actually
+
+ align:start position:0%
+working in robotics and they actually
+ 
+
+ align:start position:0%
+working in robotics and they actually
+end up proving that the problem that
+
+ align:start position:0%
+end up proving that the problem that
+ 
+
+ align:start position:0%
+end up proving that the problem that
+they were trying to solve is np complete
+
+ align:start position:0%
+they were trying to solve is np complete
+ 
+
+ align:start position:0%
+they were trying to solve is np complete
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+that's useful information because even
+
+ align:start position:0%
+that's useful information because even
+ 
+
+ align:start position:0%
+that's useful information because even
+though knowing a problem is np complete
+
+ align:start position:0%
+though knowing a problem is np complete
+ 
+
+ align:start position:0%
+though knowing a problem is np complete
+doesn't guarantee that it's not in p
+
+ align:start position:0%
+doesn't guarantee that it's not in p
+ 
+
+ align:start position:0%
+doesn't guarantee that it's not in p
+because conceivably p equals np
+
+ align:start position:0%
+because conceivably p equals np
+ 
+
+ align:start position:0%
+because conceivably p equals np
+what it does tell you that if you show
+
+ align:start position:0%
+what it does tell you that if you show
+ 
+
+ align:start position:0%
+what it does tell you that if you show
+if you have a problem that's np complete
+
+ align:start position:0%
+if you have a problem that's np complete
+ 
+
+ align:start position:0%
+if you have a problem that's np complete
+and it does turn out to be in p
+
+ align:start position:0%
+and it does turn out to be in p
+ 
+
+ align:start position:0%
+and it does turn out to be in p
+then all then p equals np so the tremend
+
+ align:start position:0%
+then all then p equals np so the tremend
+ 
+
+ align:start position:0%
+then all then p equals np so the tremend
+would be tremendous surprising
+
+ align:start position:0%
+would be tremendous surprising
+ 
+
+ align:start position:0%
+would be tremendous surprising
+consequences
+
+ align:start position:0%
+consequences
+ 
+
+ align:start position:0%
+consequences
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+of your problem if it was known to be
+
+ align:start position:0%
+of your problem if it was known to be
+ 
+
+ align:start position:0%
+of your problem if it was known to be
+np-complete ending up in p so generally
+
+ align:start position:0%
+np-complete ending up in p so generally
+ 
+
+ align:start position:0%
+np-complete ending up in p so generally
+people take a proof of np completeness
+
+ align:start position:0%
+people take a proof of np completeness
+ 
+
+ align:start position:0%
+people take a proof of np completeness
+as powerful evidence that the problem is
+
+ align:start position:0%
+as powerful evidence that the problem is
+ 
+
+ align:start position:0%
+as powerful evidence that the problem is
+not in p even though it's not quite a
+
+ align:start position:0%
+not in p even though it's not quite a
+ 
+
+ align:start position:0%
+not in p even though it's not quite a
+proof
+
+ align:start position:0%
+proof
+ 
+
+ align:start position:0%
+proof
+it's powerful evidence that it's not in
+
+ align:start position:0%
+it's powerful evidence that it's not in
+ 
+
+ align:start position:0%
+it's powerful evidence that it's not in
+p and so you might as well give up
+
+ align:start position:0%
+p and so you might as well give up
+ 
+
+ align:start position:0%
+p and so you might as well give up
+working on trying to find a polynomial
+
+ align:start position:0%
+working on trying to find a polynomial
+ 
+
+ align:start position:0%
+working on trying to find a polynomial
+algorithm for it because if you do
+
+ align:start position:0%
+algorithm for it because if you do
+ 
+
+ align:start position:0%
+algorithm for it because if you do
+you know you don't have to worry about
+
+ align:start position:0%
+you know you don't have to worry about
+ 
+
+ align:start position:0%
+you know you don't have to worry about
+robotics anymore you're going to you
+
+ align:start position:0%
+robotics anymore you're going to you
+ 
+
+ align:start position:0%
+robotics anymore you're going to you
+know become famous as a complexity
+
+ align:start position:0%
+know become famous as a complexity
+ 
+
+ align:start position:0%
+know become famous as a complexity
+theory person um
+
+ align:start position:0%
+theory person um
+ 
+
+ align:start position:0%
+theory person um
+so i wouldn't worry about so if you show
+
+ align:start position:0%
+so i wouldn't worry about so if you show
+ 
+
+ align:start position:0%
+so i wouldn't worry about so if you show
+problems np complete you can pretty much
+
+ align:start position:0%
+problems np complete you can pretty much
+ 
+
+ align:start position:0%
+problems np complete you can pretty much
+assume it's almost certainly not in p um
+
+ align:start position:0%
+assume it's almost certainly not in p um
+ 
+
+ align:start position:0%
+assume it's almost certainly not in p um
+now there's another reason related to
+
+ align:start position:0%
+now there's another reason related to
+ 
+
+ align:start position:0%
+now there's another reason related to
+the to the for the theorists uh to be
+
+ align:start position:0%
+the to the for the theorists uh to be
+ 
+
+ align:start position:0%
+the to the for the theorists uh to be
+care about mp completeness and that is
+
+ align:start position:0%
+care about mp completeness and that is
+ 
+
+ align:start position:0%
+care about mp completeness and that is
+if you're trying to prove p is different
+
+ align:start position:0%
+if you're trying to prove p is different
+ 
+
+ align:start position:0%
+if you're trying to prove p is different
+from np or p equals np as one of the
+
+ align:start position:0%
+from np or p equals np as one of the
+ 
+
+ align:start position:0%
+from np or p equals np as one of the
+chat questions is raising um
+
+ align:start position:0%
+chat questions is raising um
+ 
+
+ align:start position:0%
+chat questions is raising um
+you know the problem you know
+
+ align:start position:0%
+you know the problem you know
+ 
+
+ align:start position:0%
+you know the problem you know
+in order to prove p different from np
+
+ align:start position:0%
+in order to prove p different from np
+ 
+
+ align:start position:0%
+in order to prove p different from np
+you know the most likely approach is you
+
+ align:start position:0%
+you know the most likely approach is you
+ 
+
+ align:start position:0%
+you know the most likely approach is you
+pick some p problem in np and show it's
+
+ align:start position:0%
+pick some p problem in np and show it's
+ 
+
+ align:start position:0%
+pick some p problem in np and show it's
+not in p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's what it would mean for them
+
+ align:start position:0%
+right that's what it would mean for them
+ 
+
+ align:start position:0%
+right that's what it would mean for them
+to be different you're going to pick
+
+ align:start position:0%
+to be different you're going to pick
+ 
+
+ align:start position:0%
+to be different you're going to pick
+some np problem and show it's not not a
+
+ align:start position:0%
+some np problem and show it's not not a
+ 
+
+ align:start position:0%
+some np problem and show it's not not a
+p problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+one thing would be terrible
+
+ align:start position:0%
+one thing would be terrible
+ 
+
+ align:start position:0%
+one thing would be terrible
+is possibly p is different from np and
+
+ align:start position:0%
+is possibly p is different from np and
+ 
+
+ align:start position:0%
+is possibly p is different from np and
+you pick the wrong problem
+
+ align:start position:0%
+you pick the wrong problem
+ 
+
+ align:start position:0%
+you pick the wrong problem
+like suppose i'd spent all my time
+
+ align:start position:0%
+like suppose i'd spent all my time
+ 
+
+ align:start position:0%
+like suppose i'd spent all my time
+trying to show
+
+ align:start position:0%
+trying to show
+ 
+
+ align:start position:0%
+trying to show
+you know back
+
+ align:start position:0%
+you know back
+ 
+
+ align:start position:0%
+you know back
+20 years ago i'm working really hard
+
+ align:start position:0%
+20 years ago i'm working really hard
+ 
+
+ align:start position:0%
+20 years ago i'm working really hard
+trying to show composites
+
+ align:start position:0%
+trying to show composites
+ 
+
+ align:start position:0%
+trying to show composites
+is not in pain
+
+ align:start position:0%
+is not in pain
+ 
+
+ align:start position:0%
+is not in pain
+which is would have been perfectly
+
+ align:start position:0%
+which is would have been perfectly
+ 
+
+ align:start position:0%
+which is would have been perfectly
+reasonable to do
+
+ align:start position:0%
+reasonable to do
+ 
+
+ align:start position:0%
+reasonable to do
+because composites is an np and was not
+
+ align:start position:0%
+because composites is an np and was not
+ 
+
+ align:start position:0%
+because composites is an np and was not
+known to be in p 20 years ago
+
+ align:start position:0%
+known to be in p 20 years ago
+ 
+
+ align:start position:0%
+known to be in p 20 years ago
+um and then i invested tons of effort to
+
+ align:start position:0%
+um and then i invested tons of effort to
+ 
+
+ align:start position:0%
+um and then i invested tons of effort to
+try to prove because you know i like
+
+ align:start position:0%
+try to prove because you know i like
+ 
+
+ align:start position:0%
+try to prove because you know i like
+number theory or god knows what to prove
+
+ align:start position:0%
+number theory or god knows what to prove
+ 
+
+ align:start position:0%
+number theory or god knows what to prove
+that composites is not in p
+
+ align:start position:0%
+that composites is not in p
+ 
+
+ align:start position:0%
+that composites is not in p
+and then it turns out composites wasn't
+
+ align:start position:0%
+and then it turns out composites wasn't
+ 
+
+ align:start position:0%
+and then it turns out composites wasn't
+in p it was the wrong problem to pick
+
+ align:start position:0%
+in p it was the wrong problem to pick
+ 
+
+ align:start position:0%
+in p it was the wrong problem to pick
+even though p might be different from np
+
+ align:start position:0%
+even though p might be different from np
+ 
+
+ align:start position:0%
+even though p might be different from np
+but what np completeness guarantees is
+
+ align:start position:0%
+but what np completeness guarantees is
+ 
+
+ align:start position:0%
+but what np completeness guarantees is
+that if you work on a problem which is
+
+ align:start position:0%
+that if you work on a problem which is
+ 
+
+ align:start position:0%
+that if you work on a problem which is
+np-complete you could you can't pick the
+
+ align:start position:0%
+np-complete you could you can't pick the
+ 
+
+ align:start position:0%
+np-complete you could you can't pick the
+wrong problem because if any problem is
+
+ align:start position:0%
+wrong problem because if any problem is
+ 
+
+ align:start position:0%
+wrong problem because if any problem is
+in np and not in p an np complete
+
+ align:start position:0%
+in np and not in p an np complete
+ 
+
+ align:start position:0%
+in np and not in p an np complete
+problem is going to be an example of
+
+ align:start position:0%
+problem is going to be an example of
+ 
+
+ align:start position:0%
+problem is going to be an example of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+right because if the np complete problem
+
+ align:start position:0%
+right because if the np complete problem
+ 
+
+ align:start position:0%
+right because if the np complete problem
+is in p everything in np is in p
+
+ align:start position:0%
+is in p everything in np is in p
+ 
+
+ align:start position:0%
+is in p everything in np is in p
+so if np is different from p you know
+
+ align:start position:0%
+so if np is different from p you know
+ 
+
+ align:start position:0%
+so if np is different from p you know
+the complete problems are not in p so
+
+ align:start position:0%
+the complete problems are not in p so
+ 
+
+ align:start position:0%
+the complete problems are not in p so
+you might as well work on one of those
+
+ align:start position:0%
+you might as well work on one of those
+ 
+
+ align:start position:0%
+you might as well work on one of those
+so those are two
+
+ align:start position:0%
+so those are two
+ 
+
+ align:start position:0%
+so those are two
+ways in which np completeness and has
+
+ align:start position:0%
+ways in which np completeness and has
+ 
+
+ align:start position:0%
+ways in which np completeness and has
+turned out to be is an important concept
+
+ align:start position:0%
+turned out to be is an important concept
+ 
+
+ align:start position:0%
+turned out to be is an important concept
+okay so here's a check-in um
+
+ align:start position:0%
+okay so here's a check-in um
+ 
+
+ align:start position:0%
+okay so here's a check-in um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+again this
+
+ align:start position:0%
+again this
+ 
+
+ align:start position:0%
+again this
+you guys are kind of getting maybe
+
+ align:start position:0%
+you guys are kind of getting maybe
+ 
+
+ align:start position:0%
+you guys are kind of getting maybe
+you're getting
+
+ align:start position:0%
+you're getting
+ 
+
+ align:start position:0%
+you're getting
+started to think the way i think you get
+
+ align:start position:0%
+started to think the way i think you get
+ 
+
+ align:start position:0%
+started to think the way i think you get
+is some at least one of you would ask
+
+ align:start position:0%
+is some at least one of you would ask
+ 
+
+ align:start position:0%
+is some at least one of you would ask
+this question in the chat
+
+ align:start position:0%
+this question in the chat
+ 
+
+ align:start position:0%
+this question in the chat
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+which language that we've probably seen
+
+ align:start position:0%
+which language that we've probably seen
+ 
+
+ align:start position:0%
+which language that we've probably seen
+is most analogous to sat
+
+ align:start position:0%
+is most analogous to sat
+ 
+
+ align:start position:0%
+is most analogous to sat
+okay atm etm
+
+ align:start position:0%
+okay atm etm
+ 
+
+ align:start position:0%
+okay atm etm
+or zero to the k1 to the k
+
+ align:start position:0%
+or zero to the k1 to the k
+ 
+
+ align:start position:0%
+or zero to the k1 to the k
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+obviously this is maybe subjective you
+
+ align:start position:0%
+obviously this is maybe subjective you
+ 
+
+ align:start position:0%
+obviously this is maybe subjective you
+may have your own interpretation of what
+
+ align:start position:0%
+may have your own interpretation of what
+ 
+
+ align:start position:0%
+may have your own interpretation of what
+that means
+
+ align:start position:0%
+that means
+ 
+
+ align:start position:0%
+that means
+this in a sense perhaps no right answer
+
+ align:start position:0%
+this in a sense perhaps no right answer
+ 
+
+ align:start position:0%
+this in a sense perhaps no right answer
+but what do you think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+okay that's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um i don't know i don't know how in the
+
+ align:start position:0%
+um i don't know i don't know how in the
+ 
+
+ align:start position:0%
+um i don't know i don't know how in the
+world that you could see this problem is
+
+ align:start position:0%
+world that you could see this problem is
+ 
+
+ align:start position:0%
+world that you could see this problem is
+analogous to to zero to the k1 to the k
+
+ align:start position:0%
+analogous to to zero to the k1 to the k
+ 
+
+ align:start position:0%
+analogous to to zero to the k1 to the k
+but okay um
+
+ align:start position:0%
+but okay um
+ 
+
+ align:start position:0%
+but okay um
+i'm sure you have your reason
+
+ align:start position:0%
+i'm sure you have your reason
+ 
+
+ align:start position:0%
+i'm sure you have your reason
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yes this is a lot like eight
+
+ align:start position:0%
+yes this is a lot like eight
+ 
+
+ align:start position:0%
+yes this is a lot like eight
+atm why
+
+ align:start position:0%
+atm why
+ 
+
+ align:start position:0%
+atm why
+well because for one thing we showed in
+
+ align:start position:0%
+well because for one thing we showed in
+ 
+
+ align:start position:0%
+well because for one thing we showed in
+a homework problem
+
+ align:start position:0%
+a homework problem
+ 
+
+ align:start position:0%
+a homework problem
+that all
+
+ align:start position:0%
+that all
+ 
+
+ align:start position:0%
+that all
+um touring recognizable languages are
+
+ align:start position:0%
+um touring recognizable languages are
+ 
+
+ align:start position:0%
+um touring recognizable languages are
+reducible to atm mapping reducible to
+
+ align:start position:0%
+reducible to atm mapping reducible to
+ 
+
+ align:start position:0%
+reducible to atm mapping reducible to
+atm so that's a little bit like the
+
+ align:start position:0%
+atm so that's a little bit like the
+ 
+
+ align:start position:0%
+atm so that's a little bit like the
+notion of completeness
+
+ align:start position:0%
+notion of completeness
+ 
+
+ align:start position:0%
+notion of completeness
+that we have for satisfiability
+
+ align:start position:0%
+that we have for satisfiability
+ 
+
+ align:start position:0%
+that we have for satisfiability
+um because all np problems are going to
+
+ align:start position:0%
+um because all np problems are going to
+ 
+
+ align:start position:0%
+um because all np problems are going to
+be reducible to sad
+
+ align:start position:0%
+be reducible to sad
+ 
+
+ align:start position:0%
+be reducible to sad
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and the other thing too is that once we
+
+ align:start position:0%
+and the other thing too is that once we
+ 
+
+ align:start position:0%
+and the other thing too is that once we
+start once we
+
+ align:start position:0%
+start once we
+ 
+
+ align:start position:0%
+start once we
+uh we started we want to show other
+
+ align:start position:0%
+uh we started we want to show other
+ 
+
+ align:start position:0%
+uh we started we want to show other
+problems are undecidable we reduced atm
+
+ align:start position:0%
+problems are undecidable we reduced atm
+ 
+
+ align:start position:0%
+problems are undecidable we reduced atm
+to them and that's also very similar
+
+ align:start position:0%
+to them and that's also very similar
+ 
+
+ align:start position:0%
+to them and that's also very similar
+we're going to be reducing sat or
+
+ align:start position:0%
+we're going to be reducing sat or
+ 
+
+ align:start position:0%
+we're going to be reducing sat or
+threesat
+
+ align:start position:0%
+threesat
+ 
+
+ align:start position:0%
+threesat
+so it's indirectly from sat to other
+
+ align:start position:0%
+so it's indirectly from sat to other
+ 
+
+ align:start position:0%
+so it's indirectly from sat to other
+problems in order to show that they're
+
+ align:start position:0%
+problems in order to show that they're
+ 
+
+ align:start position:0%
+problems in order to show that they're
+np complete so that they're hard they're
+
+ align:start position:0%
+np complete so that they're hard they're
+ 
+
+ align:start position:0%
+np complete so that they're hard they're
+they're that they're hard in a sense
+
+ align:start position:0%
+they're that they're hard in a sense
+ 
+
+ align:start position:0%
+they're that they're hard in a sense
+and so uh in kind of both those ways
+
+ align:start position:0%
+and so uh in kind of both those ways
+ 
+
+ align:start position:0%
+and so uh in kind of both those ways
+atm and sat are kind of playing similar
+
+ align:start position:0%
+atm and sat are kind of playing similar
+ 
+
+ align:start position:0%
+atm and sat are kind of playing similar
+roles one key difference however
+
+ align:start position:0%
+roles one key difference however
+ 
+
+ align:start position:0%
+roles one key difference however
+between atm and sat is in the for atm we
+
+ align:start position:0%
+between atm and sat is in the for atm we
+ 
+
+ align:start position:0%
+between atm and sat is in the for atm we
+can prove
+
+ align:start position:0%
+can prove
+ 
+
+ align:start position:0%
+can prove
+that it's undecidable
+
+ align:start position:0%
+that it's undecidable
+ 
+
+ align:start position:0%
+that it's undecidable
+but for sat we don't know how to prove
+
+ align:start position:0%
+but for sat we don't know how to prove
+ 
+
+ align:start position:0%
+but for sat we don't know how to prove
+it's outside of p
+
+ align:start position:0%
+it's outside of p
+ 
+
+ align:start position:0%
+it's outside of p
+that would those would be the analogous
+
+ align:start position:0%
+that would those would be the analogous
+ 
+
+ align:start position:0%
+that would those would be the analogous
+situations
+
+ align:start position:0%
+situations
+ 
+
+ align:start position:0%
+situations
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh so
+
+ align:start position:0%
+uh so
+ 
+
+ align:start position:0%
+uh so
+the the story for sat which is kind of
+
+ align:start position:0%
+the the story for sat which is kind of
+ 
+
+ align:start position:0%
+the the story for sat which is kind of
+easily solved by a diagonalization
+
+ align:start position:0%
+easily solved by a diagonalization
+ 
+
+ align:start position:0%
+easily solved by a diagonalization
+argument for atm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's reasons to believe that we will
+
+ align:start position:0%
+there's reasons to believe that we will
+ 
+
+ align:start position:0%
+there's reasons to believe that we will
+see later that diagonalization is not
+
+ align:start position:0%
+see later that diagonalization is not
+ 
+
+ align:start position:0%
+see later that diagonalization is not
+going to work to prove sat
+
+ align:start position:0%
+going to work to prove sat
+ 
+
+ align:start position:0%
+going to work to prove sat
+outside of p
+
+ align:start position:0%
+outside of p
+ 
+
+ align:start position:0%
+outside of p
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+besides that we don't really have any
+
+ align:start position:0%
+besides that we don't really have any
+ 
+
+ align:start position:0%
+besides that we don't really have any
+good methods
+
+ align:start position:0%
+good methods
+ 
+
+ align:start position:0%
+good methods
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh anyway
+
+ align:start position:0%
+uh anyway
+ 
+
+ align:start position:0%
+uh anyway
+uh let's move on
+
+ align:start position:0%
+uh let's move on
+ 
+
+ align:start position:0%
+uh let's move on
+why is etm less analogous
+
+ align:start position:0%
+why is etm less analogous
+ 
+
+ align:start position:0%
+why is etm less analogous
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i know because atm was the first problem
+
+ align:start position:0%
+i know because atm was the first problem
+ 
+
+ align:start position:0%
+i know because atm was the first problem
+we showed undecidable and sad is kind of
+
+ align:start position:0%
+we showed undecidable and sad is kind of
+ 
+
+ align:start position:0%
+we showed undecidable and sad is kind of
+the first problem that we're going to be
+
+ align:start position:0%
+the first problem that we're going to be
+ 
+
+ align:start position:0%
+the first problem that we're going to be
+showing np complete
+
+ align:start position:0%
+showing np complete
+ 
+
+ align:start position:0%
+showing np complete
+i guess that would be my answer
+
+ align:start position:0%
+i guess that would be my answer
+ 
+
+ align:start position:0%
+i guess that would be my answer
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay let's continue so let's show now
+
+ align:start position:0%
+okay let's continue so let's show now
+ 
+
+ align:start position:0%
+okay let's continue so let's show now
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+handpath is np-complete assuming that we
+
+ align:start position:0%
+handpath is np-complete assuming that we
+ 
+
+ align:start position:0%
+handpath is np-complete assuming that we
+know sat
+
+ align:start position:0%
+know sat
+ 
+
+ align:start position:0%
+know sat
+or threesat is np complete
+
+ align:start position:0%
+or threesat is np complete
+ 
+
+ align:start position:0%
+or threesat is np complete
+okay so we're going to give a reduction
+
+ align:start position:0%
+okay so we're going to give a reduction
+ 
+
+ align:start position:0%
+okay so we're going to give a reduction
+from 3sat to handpath that that
+
+ align:start position:0%
+from 3sat to handpath that that
+ 
+
+ align:start position:0%
+from 3sat to handpath that that
+that that's what that's what this is
+
+ align:start position:0%
+that that's what that's what this is
+ 
+
+ align:start position:0%
+that that's what that's what this is
+about it's just like what we did for
+
+ align:start position:0%
+about it's just like what we did for
+ 
+
+ align:start position:0%
+about it's just like what we did for
+clique but now for him path um
+
+ align:start position:0%
+clique but now for him path um
+ 
+
+ align:start position:0%
+clique but now for him path um
+and and this is going to be very typical
+
+ align:start position:0%
+and and this is going to be very typical
+ 
+
+ align:start position:0%
+and and this is going to be very typical
+in in these reductions typically what
+
+ align:start position:0%
+in in these reductions typically what
+ 
+
+ align:start position:0%
+in in these reductions typically what
+happens
+
+ align:start position:0%
+happens
+ 
+
+ align:start position:0%
+happens
+is that you're trying to simulate
+
+ align:start position:0%
+is that you're trying to simulate
+ 
+
+ align:start position:0%
+is that you're trying to simulate
+a formula
+
+ align:start position:0%
+a formula
+ 
+
+ align:start position:0%
+a formula
+use you know a boolean formula for
+
+ align:start position:0%
+use you know a boolean formula for
+ 
+
+ align:start position:0%
+use you know a boolean formula for
+satisfiability
+
+ align:start position:0%
+satisfiability
+ 
+
+ align:start position:0%
+satisfiability
+from the satisfiability perspective
+
+ align:start position:0%
+from the satisfiability perspective
+ 
+
+ align:start position:0%
+from the satisfiability perspective
+you're trying to simulate that formula
+
+ align:start position:0%
+you're trying to simulate that formula
+ 
+
+ align:start position:0%
+you're trying to simulate that formula
+with some sort of structures
+
+ align:start position:0%
+with some sort of structures
+ 
+
+ align:start position:0%
+with some sort of structures
+inside the target language which would
+
+ align:start position:0%
+inside the target language which would
+ 
+
+ align:start position:0%
+inside the target language which would
+be hand path
+
+ align:start position:0%
+be hand path
+ 
+
+ align:start position:0%
+be hand path
+and so what the lingo that
+
+ align:start position:0%
+and so what the lingo that
+ 
+
+ align:start position:0%
+and so what the lingo that
+people use is that you're going to build
+
+ align:start position:0%
+people use is that you're going to build
+ 
+
+ align:start position:0%
+people use is that you're going to build
+gadgets to simulate the structures in
+
+ align:start position:0%
+gadgets to simulate the structures in
+ 
+
+ align:start position:0%
+gadgets to simulate the structures in
+the formula namely
+
+ align:start position:0%
+the formula namely
+ 
+
+ align:start position:0%
+the formula namely
+the variables the literals and the and
+
+ align:start position:0%
+the variables the literals and the and
+ 
+
+ align:start position:0%
+the variables the literals and the and
+the clauses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay these are going to be substructures
+
+ align:start position:0%
+okay these are going to be substructures
+ 
+
+ align:start position:0%
+okay these are going to be substructures
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+either you know the graph in this case
+
+ align:start position:0%
+either you know the graph in this case
+ 
+
+ align:start position:0%
+either you know the graph in this case
+that you're that you're building um
+
+ align:start position:0%
+that you're that you're building um
+ 
+
+ align:start position:0%
+that you're that you're building um
+we'll see what that means so let's take
+
+ align:start position:0%
+we'll see what that means so let's take
+ 
+
+ align:start position:0%
+we'll see what that means so let's take
+a formula here
+
+ align:start position:0%
+a formula here
+ 
+
+ align:start position:0%
+a formula here
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+uh let's again try to imagine how we
+
+ align:start position:0%
+uh let's again try to imagine how we
+ 
+
+ align:start position:0%
+uh let's again try to imagine how we
+would reduce that
+
+ align:start position:0%
+would reduce that
+ 
+
+ align:start position:0%
+would reduce that
+to the hand path problem so the
+
+ align:start position:0%
+to the hand path problem so the
+ 
+
+ align:start position:0%
+to the hand path problem so the
+reduction would produce
+
+ align:start position:0%
+reduction would produce
+ 
+
+ align:start position:0%
+reduction would produce
+a graph no it would produce a hand path
+
+ align:start position:0%
+a graph no it would produce a hand path
+ 
+
+ align:start position:0%
+a graph no it would produce a hand path
+instance so a g s and t want to know is
+
+ align:start position:0%
+instance so a g s and t want to know is
+ 
+
+ align:start position:0%
+instance so a g s and t want to know is
+there a hamiltonian path from s to t in
+
+ align:start position:0%
+there a hamiltonian path from s to t in
+ 
+
+ align:start position:0%
+there a hamiltonian path from s to t in
+the graph
+
+ align:start position:0%
+the graph
+ 
+
+ align:start position:0%
+the graph
+and this is going to be not the whole
+
+ align:start position:0%
+and this is going to be not the whole
+ 
+
+ align:start position:0%
+and this is going to be not the whole
+graph but this is going to be a
+
+ align:start position:0%
+graph but this is going to be a
+ 
+
+ align:start position:0%
+graph but this is going to be a
+substructure in that graph the next
+
+ align:start position:0%
+substructure in that graph the next
+ 
+
+ align:start position:0%
+substructure in that graph the next
+slide is going to have the global
+
+ align:start position:0%
+slide is going to have the global
+ 
+
+ align:start position:0%
+slide is going to have the global
+structure of the graph graph
+
+ align:start position:0%
+structure of the graph graph
+ 
+
+ align:start position:0%
+structure of the graph graph
+but here this is going to be a key
+
+ align:start position:0%
+but here this is going to be a key
+ 
+
+ align:start position:0%
+but here this is going to be a key
+element and it's we're going to call
+
+ align:start position:0%
+element and it's we're going to call
+ 
+
+ align:start position:0%
+element and it's we're going to call
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the variable gadget
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what does it look like i don't know
+
+ align:start position:0%
+okay what does it look like i don't know
+ 
+
+ align:start position:0%
+okay what does it look like i don't know
+if you can see it on your um
+
+ align:start position:0%
+if you can see it on your um
+ 
+
+ align:start position:0%
+if you can see it on your um
+clearly enough but these
+
+ align:start position:0%
+clearly enough but these
+ 
+
+ align:start position:0%
+clearly enough but these
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edges so there are four outside notes
+
+ align:start position:0%
+edges so there are four outside notes
+ 
+
+ align:start position:0%
+edges so there are four outside notes
+here the edges connecting them are all
+
+ align:start position:0%
+here the edges connecting them are all
+ 
+
+ align:start position:0%
+here the edges connecting them are all
+kind of pointed downward
+
+ align:start position:0%
+kind of pointed downward
+ 
+
+ align:start position:0%
+kind of pointed downward
+and then there are these horizontal
+
+ align:start position:0%
+and then there are these horizontal
+ 
+
+ align:start position:0%
+and then there are these horizontal
+nodes here
+
+ align:start position:0%
+nodes here
+ 
+
+ align:start position:0%
+nodes here
+and there are edges connecting them both
+
+ align:start position:0%
+and there are edges connecting them both
+ 
+
+ align:start position:0%
+and there are edges connecting them both
+left to right and right to left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay there's a row of these horizontal
+
+ align:start position:0%
+okay there's a row of these horizontal
+ 
+
+ align:start position:0%
+okay there's a row of these horizontal
+nodes okay so you get the picture of
+
+ align:start position:0%
+nodes okay so you get the picture of
+ 
+
+ align:start position:0%
+nodes okay so you get the picture of
+what this looks like
+
+ align:start position:0%
+what this looks like
+ 
+
+ align:start position:0%
+what this looks like
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you have to look carefully to see the
+
+ align:start position:0%
+you have to look carefully to see the
+ 
+
+ align:start position:0%
+you have to look carefully to see the
+arrowheads i
+
+ align:start position:0%
+arrowheads i
+ 
+
+ align:start position:0%
+arrowheads i
+maybe should have made those a little
+
+ align:start position:0%
+maybe should have made those a little
+ 
+
+ align:start position:0%
+maybe should have made those a little
+bigger
+
+ align:start position:0%
+bigger
+ 
+
+ align:start position:0%
+bigger
+okay so now um
+
+ align:start position:0%
+okay so now um
+ 
+
+ align:start position:0%
+okay so now um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+whoops
+
+ align:start position:0%
+whoops
+ 
+
+ align:start position:0%
+whoops
+let me let me just see so now if we're
+
+ align:start position:0%
+let me let me just see so now if we're
+ 
+
+ align:start position:0%
+let me let me just see so now if we're
+trying to get from this node to that
+
+ align:start position:0%
+trying to get from this node to that
+ 
+
+ align:start position:0%
+trying to get from this node to that
+node imagine now you're trying to build
+
+ align:start position:0%
+node imagine now you're trying to build
+ 
+
+ align:start position:0%
+node imagine now you're trying to build
+a hamiltonian path
+
+ align:start position:0%
+a hamiltonian path
+ 
+
+ align:start position:0%
+a hamiltonian path
+because this is going to be a part
+
+ align:start position:0%
+because this is going to be a part
+ 
+
+ align:start position:0%
+because this is going to be a part
+of that graph g
+
+ align:start position:0%
+of that graph g
+ 
+
+ align:start position:0%
+of that graph g
+that i'm constructing
+
+ align:start position:0%
+that i'm constructing
+ 
+
+ align:start position:0%
+that i'm constructing
+now remember for them there to be a
+
+ align:start position:0%
+now remember for them there to be a
+ 
+
+ align:start position:0%
+now remember for them there to be a
+hamiltonian graph
+
+ align:start position:0%
+hamiltonian graph
+ 
+
+ align:start position:0%
+hamiltonian graph
+that means you have to go through every
+
+ align:start position:0%
+that means you have to go through every
+ 
+
+ align:start position:0%
+that means you have to go through every
+node
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the graph so if i want to get from s
+
+ align:start position:0%
+in the graph so if i want to get from s
+ 
+
+ align:start position:0%
+in the graph so if i want to get from s
+to t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the only way i'm going to be able to to
+
+ align:start position:0%
+the only way i'm going to be able to to
+ 
+
+ align:start position:0%
+the only way i'm going to be able to to
+go to hit these
+
+ align:start position:0%
+go to hit these
+ 
+
+ align:start position:0%
+go to hit these
+horizontal nodes here
+
+ align:start position:0%
+horizontal nodes here
+ 
+
+ align:start position:0%
+horizontal nodes here
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+by picking them up
+
+ align:start position:0%
+by picking them up
+ 
+
+ align:start position:0%
+by picking them up
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+as i go from s to t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the only possibility is if you think
+
+ align:start position:0%
+so the only possibility is if you think
+ 
+
+ align:start position:0%
+so the only possibility is if you think
+about it is it would be for the
+
+ align:start position:0%
+about it is it would be for the
+ 
+
+ align:start position:0%
+about it is it would be for the
+sequence to go like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you could if that comes through for
+
+ align:start position:0%
+if you could if that comes through for
+ 
+
+ align:start position:0%
+if you could if that comes through for
+you so the the path would go from s to
+
+ align:start position:0%
+you so the the path would go from s to
+ 
+
+ align:start position:0%
+you so the the path would go from s to
+this node and then through
+
+ align:start position:0%
+this node and then through
+ 
+
+ align:start position:0%
+this node and then through
+these hops of
+
+ align:start position:0%
+these hops of
+ 
+
+ align:start position:0%
+these hops of
+along these horizontal nodes and then
+
+ align:start position:0%
+along these horizontal nodes and then
+ 
+
+ align:start position:0%
+along these horizontal nodes and then
+down to the bottom node here
+
+ align:start position:0%
+down to the bottom node here
+ 
+
+ align:start position:0%
+down to the bottom node here
+okay so that's one way
+
+ align:start position:0%
+okay so that's one way
+ 
+
+ align:start position:0%
+okay so that's one way
+that you can get from here down to there
+
+ align:start position:0%
+that you can get from here down to there
+ 
+
+ align:start position:0%
+that you can get from here down to there
+and pick up all the other nodes along
+
+ align:start position:0%
+and pick up all the other nodes along
+ 
+
+ align:start position:0%
+and pick up all the other nodes along
+the way which is they're not going to
+
+ align:start position:0%
+the way which is they're not going to
+ 
+
+ align:start position:0%
+the way which is they're not going to
+have any other possibility possible ways
+
+ align:start position:0%
+have any other possibility possible ways
+ 
+
+ align:start position:0%
+have any other possibility possible ways
+of getting to them
+
+ align:start position:0%
+of getting to them
+ 
+
+ align:start position:0%
+of getting to them
+so i'm going to call that a zigzag
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay but there's another way to get from
+
+ align:start position:0%
+okay but there's another way to get from
+ 
+
+ align:start position:0%
+okay but there's another way to get from
+s to the bottom node
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay which is going to be by doing sort
+
+ align:start position:0%
+okay which is going to be by doing sort
+ 
+
+ align:start position:0%
+okay which is going to be by doing sort
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+dual going to the right then going out
+
+ align:start position:0%
+dual going to the right then going out
+ 
+
+ align:start position:0%
+dual going to the right then going out
+to the left and then down to the bottom
+
+ align:start position:0%
+to the left and then down to the bottom
+ 
+
+ align:start position:0%
+to the left and then down to the bottom
+i'm going to call that
+
+ align:start position:0%
+i'm going to call that
+ 
+
+ align:start position:0%
+i'm going to call that
+a zigzig
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh with a little kind of little
+
+ align:start position:0%
+and uh with a little kind of little
+ 
+
+ align:start position:0%
+and uh with a little kind of little
+diagram here just to summarize what it
+
+ align:start position:0%
+diagram here just to summarize what it
+ 
+
+ align:start position:0%
+diagram here just to summarize what it
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+and this is the this is the classic
+
+ align:start position:0%
+and this is the this is the classic
+ 
+
+ align:start position:0%
+and this is the this is the classic
+thing for a variable gadget
+
+ align:start position:0%
+thing for a variable gadget
+ 
+
+ align:start position:0%
+thing for a variable gadget
+because it's a structure
+
+ align:start position:0%
+because it's a structure
+ 
+
+ align:start position:0%
+because it's a structure
+that when you're trying to think about
+
+ align:start position:0%
+that when you're trying to think about
+ 
+
+ align:start position:0%
+that when you're trying to think about
+how the object that you're
+
+ align:start position:0%
+how the object that you're
+ 
+
+ align:start position:0%
+how the object that you're
+asking whether it exists or not the
+
+ align:start position:0%
+asking whether it exists or not the
+ 
+
+ align:start position:0%
+asking whether it exists or not the
+hamiltonian path how it relates to that
+
+ align:start position:0%
+hamiltonian path how it relates to that
+ 
+
+ align:start position:0%
+hamiltonian path how it relates to that
+object it's going to have two
+
+ align:start position:0%
+object it's going to have two
+ 
+
+ align:start position:0%
+object it's going to have two
+possibilities which are going to
+
+ align:start position:0%
+possibilities which are going to
+ 
+
+ align:start position:0%
+possibilities which are going to
+correspond to the variable variable
+
+ align:start position:0%
+correspond to the variable variable
+ 
+
+ align:start position:0%
+correspond to the variable variable
+being set true or false in the formula
+
+ align:start position:0%
+being set true or false in the formula
+ 
+
+ align:start position:0%
+being set true or false in the formula
+so we're showing how to
+
+ align:start position:0%
+so we're showing how to
+ 
+
+ align:start position:0%
+so we're showing how to
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+you know the simulate the variable
+
+ align:start position:0%
+you know the simulate the variable
+ 
+
+ align:start position:0%
+you know the simulate the variable
+in this hand path instance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so setting the variable is going to
+
+ align:start position:0%
+so setting the variable is going to
+ 
+
+ align:start position:0%
+so setting the variable is going to
+correspond to
+
+ align:start position:0%
+correspond to
+ 
+
+ align:start position:0%
+correspond to
+to to
+
+ align:start position:0%
+to to
+ 
+
+ align:start position:0%
+to to
+to constructing the path
+
+ align:start position:0%
+to constructing the path
+ 
+
+ align:start position:0%
+to constructing the path
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now we also have to make sure not only
+
+ align:start position:0%
+now we also have to make sure not only
+ 
+
+ align:start position:0%
+now we also have to make sure not only
+that the variable gets set to true or
+
+ align:start position:0%
+that the variable gets set to true or
+ 
+
+ align:start position:0%
+that the variable gets set to true or
+false but that it gets a set to true and
+
+ align:start position:0%
+false but that it gets a set to true and
+ 
+
+ align:start position:0%
+false but that it gets a set to true and
+false in a way that makes this a
+
+ align:start position:0%
+false in a way that makes this a
+ 
+
+ align:start position:0%
+false in a way that makes this a
+satisfying assignment namely that we get
+
+ align:start position:0%
+satisfying assignment namely that we get
+ 
+
+ align:start position:0%
+satisfying assignment namely that we get
+one true literal in every clause
+
+ align:start position:0%
+one true literal in every clause
+ 
+
+ align:start position:0%
+one true literal in every clause
+so i'm going to add another gadget here
+
+ align:start position:0%
+so i'm going to add another gadget here
+ 
+
+ align:start position:0%
+so i'm going to add another gadget here
+called a clause gadget
+
+ align:start position:0%
+called a clause gadget
+ 
+
+ align:start position:0%
+called a clause gadget
+which is just a single node
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and visiting that node here
+
+ align:start position:0%
+and visiting that node here
+ 
+
+ align:start position:0%
+and visiting that node here
+is going to correspond to
+
+ align:start position:0%
+is going to correspond to
+ 
+
+ align:start position:0%
+is going to correspond to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+satisfying that clause to having a true
+
+ align:start position:0%
+satisfying that clause to having a true
+ 
+
+ align:start position:0%
+satisfying that clause to having a true
+literal in that clause
+
+ align:start position:0%
+literal in that clause
+ 
+
+ align:start position:0%
+literal in that clause
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and now how am i going to get i'm going
+
+ align:start position:0%
+and now how am i going to get i'm going
+ 
+
+ align:start position:0%
+and now how am i going to get i'm going
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+have it enable
+
+ align:start position:0%
+have it enable
+ 
+
+ align:start position:0%
+have it enable
+a detour
+
+ align:start position:0%
+a detour
+ 
+
+ align:start position:0%
+a detour
+from these horizontal nodes out to this
+
+ align:start position:0%
+from these horizontal nodes out to this
+ 
+
+ align:start position:0%
+from these horizontal nodes out to this
+clause gadget
+
+ align:start position:0%
+clause gadget
+ 
+
+ align:start position:0%
+clause gadget
+so here it is here's that detour
+
+ align:start position:0%
+so here it is here's that detour
+ 
+
+ align:start position:0%
+so here it is here's that detour
+as i'm going from left to right
+
+ align:start position:0%
+as i'm going from left to right
+ 
+
+ align:start position:0%
+as i'm going from left to right
+i can instead of jump doing a single
+
+ align:start position:0%
+i can instead of jump doing a single
+ 
+
+ align:start position:0%
+i can instead of jump doing a single
+jump here i could branch out and visit
+
+ align:start position:0%
+jump here i could branch out and visit
+ 
+
+ align:start position:0%
+jump here i could branch out and visit
+that clause node
+
+ align:start position:0%
+that clause node
+ 
+
+ align:start position:0%
+that clause node
+and then come back and pick up my left
+
+ align:start position:0%
+and then come back and pick up my left
+ 
+
+ align:start position:0%
+and then come back and pick up my left
+to right
+
+ align:start position:0%
+to right
+ 
+
+ align:start position:0%
+to right
+uh path as as i was doing before
+
+ align:start position:0%
+uh path as as i was doing before
+ 
+
+ align:start position:0%
+uh path as as i was doing before
+you realize what i'm trying what's
+
+ align:start position:0%
+you realize what i'm trying what's
+ 
+
+ align:start position:0%
+you realize what i'm trying what's
+i hope you're seeing the big picture
+
+ align:start position:0%
+i hope you're seeing the big picture
+ 
+
+ align:start position:0%
+i hope you're seeing the big picture
+because this has to be a hamiltonian
+
+ align:start position:0%
+because this has to be a hamiltonian
+ 
+
+ align:start position:0%
+because this has to be a hamiltonian
+path it has to hit every node that's one
+
+ align:start position:0%
+path it has to hit every node that's one
+ 
+
+ align:start position:0%
+path it has to hit every node that's one
+of the requirements so i've got a this
+
+ align:start position:0%
+of the requirements so i've got a this
+ 
+
+ align:start position:0%
+of the requirements so i've got a this
+is going to be one of the nodes in my
+
+ align:start position:0%
+is going to be one of the nodes in my
+ 
+
+ align:start position:0%
+is going to be one of the nodes in my
+graph it's the path has got to hit that
+
+ align:start position:0%
+graph it's the path has got to hit that
+ 
+
+ align:start position:0%
+graph it's the path has got to hit that
+node the only way it's going to be able
+
+ align:start position:0%
+node the only way it's going to be able
+ 
+
+ align:start position:0%
+node the only way it's going to be able
+to hit that node
+
+ align:start position:0%
+to hit that node
+ 
+
+ align:start position:0%
+to hit that node
+is by taking a detour off of this
+
+ align:start position:0%
+is by taking a detour off of this
+ 
+
+ align:start position:0%
+is by taking a detour off of this
+uh horizontal path here
+
+ align:start position:0%
+uh horizontal path here
+ 
+
+ align:start position:0%
+uh horizontal path here
+but notice and this is the this is the
+
+ align:start position:0%
+but notice and this is the this is the
+ 
+
+ align:start position:0%
+but notice and this is the this is the
+key
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i'm doing a zigzag
+
+ align:start position:0%
+if i'm doing a zigzag
+ 
+
+ align:start position:0%
+if i'm doing a zigzag
+then i can make the detour and visit
+
+ align:start position:0%
+then i can make the detour and visit
+ 
+
+ align:start position:0%
+then i can make the detour and visit
+that clause gadget that clause node
+
+ align:start position:0%
+that clause gadget that clause node
+ 
+
+ align:start position:0%
+that clause gadget that clause node
+but if i'm doing a zag zig
+
+ align:start position:0%
+but if i'm doing a zag zig
+ 
+
+ align:start position:0%
+but if i'm doing a zag zig
+the way this detour is structured does
+
+ align:start position:0%
+the way this detour is structured does
+ 
+
+ align:start position:0%
+the way this detour is structured does
+not allow me
+
+ align:start position:0%
+not allow me
+ 
+
+ align:start position:0%
+not allow me
+to visit that node
+
+ align:start position:0%
+to visit that node
+ 
+
+ align:start position:0%
+to visit that node
+because if i'm going from right to left
+
+ align:start position:0%
+because if i'm going from right to left
+ 
+
+ align:start position:0%
+because if i'm going from right to left
+here by the time i get to
+
+ align:start position:0%
+here by the time i get to
+ 
+
+ align:start position:0%
+here by the time i get to
+to this outgoing edge
+
+ align:start position:0%
+to this outgoing edge
+ 
+
+ align:start position:0%
+to this outgoing edge
+now i come want to come back
+
+ align:start position:0%
+now i come want to come back
+ 
+
+ align:start position:0%
+now i come want to come back
+that note has already been taken
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it only works if i'm going zag zig from
+
+ align:start position:0%
+it only works if i'm going zag zig from
+ 
+
+ align:start position:0%
+it only works if i'm going zag zig from
+going from right to left
+
+ align:start position:0%
+going from right to left
+ 
+
+ align:start position:0%
+going from right to left
+the left to right if i'm going from left
+
+ align:start position:0%
+the left to right if i'm going from left
+ 
+
+ align:start position:0%
+the left to right if i'm going from left
+to right then i can do it for going
+
+ align:start position:0%
+to right then i can do it for going
+ 
+
+ align:start position:0%
+to right then i can do it for going
+right to left no
+
+ align:start position:0%
+right to left no
+ 
+
+ align:start position:0%
+right to left no
+so this is going to correspond if you
+
+ align:start position:0%
+so this is going to correspond if you
+ 
+
+ align:start position:0%
+so this is going to correspond if you
+think of left the left to right
+
+ align:start position:0%
+think of left the left to right
+ 
+
+ align:start position:0%
+think of left the left to right
+direction as true that's going to
+
+ align:start position:0%
+direction as true that's going to
+ 
+
+ align:start position:0%
+direction as true that's going to
+correspond to that variable appearing in
+
+ align:start position:0%
+correspond to that variable appearing in
+ 
+
+ align:start position:0%
+correspond to that variable appearing in
+the positive way in that clause um but
+
+ align:start position:0%
+the positive way in that clause um but
+ 
+
+ align:start position:0%
+the positive way in that clause um but
+not in the negative way the negative way
+
+ align:start position:0%
+not in the negative way the negative way
+ 
+
+ align:start position:0%
+not in the negative way the negative way
+i would reverse
+
+ align:start position:0%
+i would reverse
+ 
+
+ align:start position:0%
+i would reverse
+the in and out
+
+ align:start position:0%
+the in and out
+ 
+
+ align:start position:0%
+the in and out
+of the dot of the detour
+
+ align:start position:0%
+of the dot of the detour
+ 
+
+ align:start position:0%
+of the dot of the detour
+flip that around
+
+ align:start position:0%
+flip that around
+ 
+
+ align:start position:0%
+flip that around
+so now i could only do the detail detour
+
+ align:start position:0%
+so now i could only do the detail detour
+ 
+
+ align:start position:0%
+so now i could only do the detail detour
+when i'm going right to left instead of
+
+ align:start position:0%
+when i'm going right to left instead of
+ 
+
+ align:start position:0%
+when i'm going right to left instead of
+left to right i hope you get the picture
+
+ align:start position:0%
+left to right i hope you get the picture
+ 
+
+ align:start position:0%
+left to right i hope you get the picture
+this is how the structure is working now
+
+ align:start position:0%
+this is how the structure is working now
+ 
+
+ align:start position:0%
+this is how the structure is working now
+what's only left me to do is put it all
+
+ align:start position:0%
+what's only left me to do is put it all
+ 
+
+ align:start position:0%
+what's only left me to do is put it all
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+this slide contains the guts um of
+
+ align:start position:0%
+this slide contains the guts um of
+ 
+
+ align:start position:0%
+this slide contains the guts um of
+what's happening
+
+ align:start position:0%
+what's happening
+ 
+
+ align:start position:0%
+what's happening
+um so you wanna is is there any question
+
+ align:start position:0%
+um so you wanna is is there any question
+ 
+
+ align:start position:0%
+um so you wanna is is there any question
+that i can answer for you
+
+ align:start position:0%
+that i can answer for you
+ 
+
+ align:start position:0%
+that i can answer for you
+um on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's move on to the next slide and then
+
+ align:start position:0%
+let's move on to the next slide and then
+ 
+
+ align:start position:0%
+let's move on to the next slide and then
+as questions come up you can be typing
+
+ align:start position:0%
+as questions come up you can be typing
+ 
+
+ align:start position:0%
+as questions come up you can be typing
+them in we can maybe answer it there
+
+ align:start position:0%
+them in we can maybe answer it there
+ 
+
+ align:start position:0%
+them in we can maybe answer it there
+okay so here is the big picture
+
+ align:start position:0%
+okay so here is the big picture
+ 
+
+ align:start position:0%
+okay so here is the big picture
+so imagine we have
+
+ align:start position:0%
+so imagine we have
+ 
+
+ align:start position:0%
+so imagine we have
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+formula
+
+ align:start position:0%
+formula
+ 
+
+ align:start position:0%
+formula
+that we started we're reducing that
+
+ align:start position:0%
+that we started we're reducing that
+ 
+
+ align:start position:0%
+that we started we're reducing that
+formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+and let's say it has m variables and k
+
+ align:start position:0%
+and let's say it has m variables and k
+ 
+
+ align:start position:0%
+and let's say it has m variables and k
+clauses
+
+ align:start position:0%
+clauses
+ 
+
+ align:start position:0%
+clauses
+i'm going to call them clause c1 c2 up
+
+ align:start position:0%
+i'm going to call them clause c1 c2 up
+ 
+
+ align:start position:0%
+i'm going to call them clause c1 c2 up
+to ck here the m variables appearing
+
+ align:start position:0%
+to ck here the m variables appearing
+ 
+
+ align:start position:0%
+to ck here the m variables appearing
+either
+
+ align:start position:0%
+either
+ 
+
+ align:start position:0%
+either
+positively or
+
+ align:start position:0%
+positively or
+ 
+
+ align:start position:0%
+positively or
+negated in that formula
+
+ align:start position:0%
+negated in that formula
+ 
+
+ align:start position:0%
+negated in that formula
+and this is the way the global structure
+
+ align:start position:0%
+and this is the way the global structure
+ 
+
+ align:start position:0%
+and this is the way the global structure
+of g is going to look like now i'm
+
+ align:start position:0%
+of g is going to look like now i'm
+ 
+
+ align:start position:0%
+of g is going to look like now i'm
+getting a question here what do those
+
+ align:start position:0%
+getting a question here what do those
+ 
+
+ align:start position:0%
+getting a question here what do those
+horizontal nodes what role do they play
+
+ align:start position:0%
+horizontal nodes what role do they play
+ 
+
+ align:start position:0%
+horizontal nodes what role do they play
+there those nodes are there to allow me
+
+ align:start position:0%
+there those nodes are there to allow me
+ 
+
+ align:start position:0%
+there those nodes are there to allow me
+to visit
+
+ align:start position:0%
+to visit
+ 
+
+ align:start position:0%
+to visit
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+clause
+
+ align:start position:0%
+clause
+ 
+
+ align:start position:0%
+clause
+nodes
+
+ align:start position:0%
+nodes
+ 
+
+ align:start position:0%
+nodes
+the the nodes which represent the clause
+
+ align:start position:0%
+the the nodes which represent the clause
+ 
+
+ align:start position:0%
+the the nodes which represent the clause
+gadgets which i'm going to place over
+
+ align:start position:0%
+gadgets which i'm going to place over
+ 
+
+ align:start position:0%
+gadgets which i'm going to place over
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so imag so here here is that
+
+ align:start position:0%
+so imag so here here is that
+ 
+
+ align:start position:0%
+so imag so here here is that
+um here is i mean this is almost a hole
+
+ align:start position:0%
+um here is i mean this is almost a hole
+ 
+
+ align:start position:0%
+um here is i mean this is almost a hole
+of g that i'm just missing uh some a few
+
+ align:start position:0%
+of g that i'm just missing uh some a few
+ 
+
+ align:start position:0%
+of g that i'm just missing uh some a few
+edges but these are all the nodes of g
+
+ align:start position:0%
+edges but these are all the nodes of g
+ 
+
+ align:start position:0%
+edges but these are all the nodes of g
+so remember i'm trying to find out is
+
+ align:start position:0%
+so remember i'm trying to find out is
+ 
+
+ align:start position:0%
+so remember i'm trying to find out is
+there a hamiltonian path from s to t
+
+ align:start position:0%
+there a hamiltonian path from s to t
+ 
+
+ align:start position:0%
+there a hamiltonian path from s to t
+now if i didn't have to worry about the
+
+ align:start position:0%
+now if i didn't have to worry about the
+ 
+
+ align:start position:0%
+now if i didn't have to worry about the
+these c nodes
+
+ align:start position:0%
+these c nodes
+ 
+
+ align:start position:0%
+these c nodes
+the answer would be just yes
+
+ align:start position:0%
+the answer would be just yes
+ 
+
+ align:start position:0%
+the answer would be just yes
+in fact there would be many hamiltonian
+
+ align:start position:0%
+in fact there would be many hamiltonian
+ 
+
+ align:start position:0%
+in fact there would be many hamiltonian
+pairs from s to t because i can do a
+
+ align:start position:0%
+pairs from s to t because i can do a
+ 
+
+ align:start position:0%
+pairs from s to t because i can do a
+zigzag or zx zig through each of these
+
+ align:start position:0%
+zigzag or zx zig through each of these
+ 
+
+ align:start position:0%
+zigzag or zx zig through each of these
+uh variable gadgets and i would take me
+
+ align:start position:0%
+uh variable gadgets and i would take me
+ 
+
+ align:start position:0%
+uh variable gadgets and i would take me
+from s to t and i'd be good
+
+ align:start position:0%
+from s to t and i'd be good
+ 
+
+ align:start position:0%
+from s to t and i'd be good
+it's just these c nodes these nodes
+
+ align:start position:0%
+it's just these c nodes these nodes
+ 
+
+ align:start position:0%
+it's just these c nodes these nodes
+these ci nodes
+
+ align:start position:0%
+these ci nodes
+ 
+
+ align:start position:0%
+these ci nodes
+you know i have to hit them too
+
+ align:start position:0%
+you know i have to hit them too
+ 
+
+ align:start position:0%
+you know i have to hit them too
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+they're going to be
+
+ align:start position:0%
+they're going to be
+ 
+
+ align:start position:0%
+they're going to be
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+visiting them is going to be enabled by
+
+ align:start position:0%
+visiting them is going to be enabled by
+ 
+
+ align:start position:0%
+visiting them is going to be enabled by
+detours from here so
+
+ align:start position:0%
+detours from here so
+ 
+
+ align:start position:0%
+detours from here so
+let me just try to show you what that
+
+ align:start position:0%
+let me just try to show you what that
+ 
+
+ align:start position:0%
+let me just try to show you what that
+looks like so i'm going to magnify
+
+ align:start position:0%
+looks like so i'm going to magnify
+ 
+
+ align:start position:0%
+looks like so i'm going to magnify
+little pieces here
+
+ align:start position:0%
+little pieces here
+ 
+
+ align:start position:0%
+little pieces here
+uh from from these gadgets here and show
+
+ align:start position:0%
+uh from from these gadgets here and show
+ 
+
+ align:start position:0%
+uh from from these gadgets here and show
+you how these guys are connected up
+
+ align:start position:0%
+you how these guys are connected up
+ 
+
+ align:start position:0%
+you how these guys are connected up
+so here is the x1 gadget
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so x1 appears positively in c1
+
+ align:start position:0%
+so x1 appears positively in c1
+ 
+
+ align:start position:0%
+so x1 appears positively in c1
+right here's x1 and c1 and so that means
+
+ align:start position:0%
+right here's x1 and c1 and so that means
+ 
+
+ align:start position:0%
+right here's x1 and c1 and so that means
+when i'm going left to right i'm going
+
+ align:start position:0%
+when i'm going left to right i'm going
+ 
+
+ align:start position:0%
+when i'm going left to right i'm going
+to be a possibility of visiting c1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but now let's look what happens with um
+
+ align:start position:0%
+but now let's look what happens with um
+ 
+
+ align:start position:0%
+but now let's look what happens with um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which was the next one i met i i had
+
+ align:start position:0%
+which was the next one i met i i had
+ 
+
+ align:start position:0%
+which was the next one i met i i had
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so the next one is oh yeah so that's so
+
+ align:start position:0%
+so the next one is oh yeah so that's so
+ 
+
+ align:start position:0%
+so the next one is oh yeah so that's so
+x1 appears positively in c1 and that's
+
+ align:start position:0%
+x1 appears positively in c1 and that's
+ 
+
+ align:start position:0%
+x1 appears positively in c1 and that's
+why i have the connection like this uh
+
+ align:start position:0%
+why i have the connection like this uh
+ 
+
+ align:start position:0%
+why i have the connection like this uh
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+x1 appears negated in c2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i only want to do enable the detour
+
+ align:start position:0%
+so i only want to do enable the detour
+ 
+
+ align:start position:0%
+so i only want to do enable the detour
+to visit c2 when i'm going right to left
+
+ align:start position:0%
+to visit c2 when i'm going right to left
+ 
+
+ align:start position:0%
+to visit c2 when i'm going right to left
+as opposed to left to right
+
+ align:start position:0%
+as opposed to left to right
+ 
+
+ align:start position:0%
+as opposed to left to right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+set of
+
+ align:start position:0%
+set of
+ 
+
+ align:start position:0%
+set of
+horizontal nodes is only going to allow
+
+ align:start position:0%
+horizontal nodes is only going to allow
+ 
+
+ align:start position:0%
+horizontal nodes is only going to allow
+me to take a detour either out to c1
+
+ align:start position:0%
+me to take a detour either out to c1
+ 
+
+ align:start position:0%
+me to take a detour either out to c1
+or out to c2 but not to both
+
+ align:start position:0%
+or out to c2 but not to both
+ 
+
+ align:start position:0%
+or out to c2 but not to both
+because the hamiltonian path is either
+
+ align:start position:0%
+because the hamiltonian path is either
+ 
+
+ align:start position:0%
+because the hamiltonian path is either
+going to go left to right or right to
+
+ align:start position:0%
+going to go left to right or right to
+ 
+
+ align:start position:0%
+going to go left to right or right to
+left it can't do both
+
+ align:start position:0%
+left it can't do both
+ 
+
+ align:start position:0%
+left it can't do both
+when it's going through x the x one uh
+
+ align:start position:0%
+when it's going through x the x one uh
+ 
+
+ align:start position:0%
+when it's going through x the x one uh
+gadget
+
+ align:start position:0%
+gadget
+ 
+
+ align:start position:0%
+gadget
+okay you need to
+
+ align:start position:0%
+okay you need to
+ 
+
+ align:start position:0%
+okay you need to
+didn't kind of you have to i'll try to
+
+ align:start position:0%
+didn't kind of you have to i'll try to
+ 
+
+ align:start position:0%
+didn't kind of you have to i'll try to
+help you through it but you have to try
+
+ align:start position:0%
+help you through it but you have to try
+ 
+
+ align:start position:0%
+help you through it but you have to try
+to think about why it's working
+
+ align:start position:0%
+to think about why it's working
+ 
+
+ align:start position:0%
+to think about why it's working
+so what let's think again together
+
+ align:start position:0%
+so what let's think again together
+ 
+
+ align:start position:0%
+so what let's think again together
+so x2
+
+ align:start position:0%
+so x2
+ 
+
+ align:start position:0%
+so x2
+also appears in c1
+
+ align:start position:0%
+also appears in c1
+ 
+
+ align:start position:0%
+also appears in c1
+but now it appears negated so i'm going
+
+ align:start position:0%
+but now it appears negated so i'm going
+ 
+
+ align:start position:0%
+but now it appears negated so i'm going
+to have edges from this x2
+
+ align:start position:0%
+to have edges from this x2
+ 
+
+ align:start position:0%
+to have edges from this x2
+gadget
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whoops
+
+ align:start position:0%
+whoops
+ 
+
+ align:start position:0%
+whoops
+x the x2 gadget
+
+ align:start position:0%
+x the x2 gadget
+ 
+
+ align:start position:0%
+x the x2 gadget
+but now look at the look at how i've
+
+ align:start position:0%
+but now look at the look at how i've
+ 
+
+ align:start position:0%
+but now look at the look at how i've
+i've arranged that detour you know i can
+
+ align:start position:0%
+i've arranged that detour you know i can
+ 
+
+ align:start position:0%
+i've arranged that detour you know i can
+leave on the left leftward side and
+
+ align:start position:0%
+leave on the left leftward side and
+ 
+
+ align:start position:0%
+leave on the left leftward side and
+return on the rightward side
+
+ align:start position:0%
+return on the rightward side
+ 
+
+ align:start position:0%
+return on the rightward side
+um which means
+
+ align:start position:0%
+um which means
+ 
+
+ align:start position:0%
+um which means
+i can only
+
+ align:start position:0%
+i can only
+ 
+
+ align:start position:0%
+i can only
+do that detour when i'm going right to
+
+ align:start position:0%
+do that detour when i'm going right to
+ 
+
+ align:start position:0%
+do that detour when i'm going right to
+left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+and that's because x2 is negated in c1
+
+ align:start position:0%
+and that's because x2 is negated in c1
+ 
+
+ align:start position:0%
+and that's because x2 is negated in c1
+okay so there's
+
+ align:start position:0%
+okay so there's
+ 
+
+ align:start position:0%
+okay so there's
+maybe it's a lot here if you're if
+
+ align:start position:0%
+maybe it's a lot here if you're if
+ 
+
+ align:start position:0%
+maybe it's a lot here if you're if
+you're not quite getting it but
+
+ align:start position:0%
+you're not quite getting it but
+ 
+
+ align:start position:0%
+you're not quite getting it but
+the point is let's say try to quickly
+
+ align:start position:0%
+the point is let's say try to quickly
+ 
+
+ align:start position:0%
+the point is let's say try to quickly
+prove so that's the whole construction
+
+ align:start position:0%
+prove so that's the whole construction
+ 
+
+ align:start position:0%
+prove so that's the whole construction
+you just do that for every single
+
+ align:start position:0%
+you just do that for every single
+ 
+
+ align:start position:0%
+you just do that for every single
+appearance of a literal
+
+ align:start position:0%
+appearance of a literal
+ 
+
+ align:start position:0%
+appearance of a literal
+in a clause you're going to add these
+
+ align:start position:0%
+in a clause you're going to add these
+ 
+
+ align:start position:0%
+in a clause you're going to add these
+detours which allow you possibly to go
+
+ align:start position:0%
+detours which allow you possibly to go
+ 
+
+ align:start position:0%
+detours which allow you possibly to go
+visit
+
+ align:start position:0%
+visit
+ 
+
+ align:start position:0%
+visit
+the uh the clause
+
+ align:start position:0%
+the uh the clause
+ 
+
+ align:start position:0%
+the uh the clause
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so the forward direction is
+
+ align:start position:0%
+so the forward direction is
+ 
+
+ align:start position:0%
+so the forward direction is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+why is this true so you take any
+
+ align:start position:0%
+why is this true so you take any
+ 
+
+ align:start position:0%
+why is this true so you take any
+satisfying assignment as i suggested
+
+ align:start position:0%
+satisfying assignment as i suggested
+ 
+
+ align:start position:0%
+satisfying assignment as i suggested
+you make the corresponding zigzags or
+
+ align:start position:0%
+you make the corresponding zigzags or
+ 
+
+ align:start position:0%
+you make the corresponding zigzags or
+zag zigs through the variable gadgets
+
+ align:start position:0%
+zag zigs through the variable gadgets
+ 
+
+ align:start position:0%
+zag zigs through the variable gadgets
+from s to t and then take the detours to
+
+ align:start position:0%
+from s to t and then take the detours to
+ 
+
+ align:start position:0%
+from s to t and then take the detours to
+visit the cloud the clause nodes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the reverse direction actually is
+
+ align:start position:0%
+the reverse direction actually is
+ 
+
+ align:start position:0%
+the reverse direction actually is
+slightly trickier we're not gonna have
+
+ align:start position:0%
+slightly trickier we're not gonna have
+ 
+
+ align:start position:0%
+slightly trickier we're not gonna have
+time to go through the subtlety of it
+
+ align:start position:0%
+time to go through the subtlety of it
+ 
+
+ align:start position:0%
+time to go through the subtlety of it
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but uh
+
+ align:start position:0%
+but uh
+ 
+
+ align:start position:0%
+but uh
+what you want to make sure here
+
+ align:start position:0%
+what you want to make sure here
+ 
+
+ align:start position:0%
+what you want to make sure here
+is that you don't have a kind of a a
+
+ align:start position:0%
+is that you don't have a kind of a a
+ 
+
+ align:start position:0%
+is that you don't have a kind of a a
+weird path
+
+ align:start position:0%
+weird path
+ 
+
+ align:start position:0%
+weird path
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+occurring because i'm going to start
+
+ align:start position:0%
+occurring because i'm going to start
+ 
+
+ align:start position:0%
+occurring because i'm going to start
+with a hamiltonian path now and build an
+
+ align:start position:0%
+with a hamiltonian path now and build an
+ 
+
+ align:start position:0%
+with a hamiltonian path now and build an
+assignment
+
+ align:start position:0%
+assignment
+ 
+
+ align:start position:0%
+assignment
+uh and what we want to make sure that
+
+ align:start position:0%
+uh and what we want to make sure that
+ 
+
+ align:start position:0%
+uh and what we want to make sure that
+the the path that i'm constructing
+
+ align:start position:0%
+the the path that i'm constructing
+ 
+
+ align:start position:0%
+the the path that i'm constructing
+doesn't
+
+ align:start position:0%
+doesn't
+ 
+
+ align:start position:0%
+doesn't
+go from one from this
+
+ align:start position:0%
+go from one from this
+ 
+
+ align:start position:0%
+go from one from this
+horizontal nodes
+
+ align:start position:0%
+horizontal nodes
+ 
+
+ align:start position:0%
+horizontal nodes
+to a
+
+ align:start position:0%
+to a
+ 
+
+ align:start position:0%
+to a
+clause node and then back to somebody
+
+ align:start position:0%
+clause node and then back to somebody
+ 
+
+ align:start position:0%
+clause node and then back to somebody
+else's horizontal nodes um and
+
+ align:start position:0%
+else's horizontal nodes um and
+ 
+
+ align:start position:0%
+else's horizontal nodes um and
+is kind of a hodgepodge of things which
+
+ align:start position:0%
+is kind of a hodgepodge of things which
+ 
+
+ align:start position:0%
+is kind of a hodgepodge of things which
+don't make any sense in trying to
+
+ align:start position:0%
+don't make any sense in trying to
+ 
+
+ align:start position:0%
+don't make any sense in trying to
+reconstruct a satisfying assignment what
+
+ align:start position:0%
+reconstruct a satisfying assignment what
+ 
+
+ align:start position:0%
+reconstruct a satisfying assignment what
+you what you really want to have happen
+
+ align:start position:0%
+you what you really want to have happen
+ 
+
+ align:start position:0%
+you what you really want to have happen
+is the hamiltonian path should have
+
+ align:start position:0%
+is the hamiltonian path should have
+ 
+
+ align:start position:0%
+is the hamiltonian path should have
+clear zigzags and zag zigs that allow
+
+ align:start position:0%
+clear zigzags and zag zigs that allow
+ 
+
+ align:start position:0%
+clear zigzags and zag zigs that allow
+you to decide
+
+ align:start position:0%
+you to decide
+ 
+
+ align:start position:0%
+you to decide
+how to set the variables
+
+ align:start position:0%
+how to set the variables
+ 
+
+ align:start position:0%
+how to set the variables
+and so that's the role of these little
+
+ align:start position:0%
+and so that's the role of these little
+ 
+
+ align:start position:0%
+and so that's the role of these little
+nodes here these are spacers
+
+ align:start position:0%
+nodes here these are spacers
+ 
+
+ align:start position:0%
+nodes here these are spacers
+that separate the detours from one
+
+ align:start position:0%
+that separate the detours from one
+ 
+
+ align:start position:0%
+that separate the detours from one
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+and that force
+
+ align:start position:0%
+and that force
+ 
+
+ align:start position:0%
+and that force
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a visit to the
+
+ align:start position:0%
+a visit to the
+ 
+
+ align:start position:0%
+a visit to the
+clause node to come back
+
+ align:start position:0%
+clause node to come back
+ 
+
+ align:start position:0%
+clause node to come back
+to the same
+
+ align:start position:0%
+to the same
+ 
+
+ align:start position:0%
+to the same
+uh place from which it left
+
+ align:start position:0%
+uh place from which it left
+ 
+
+ align:start position:0%
+uh place from which it left
+otherwise you would never be able to
+
+ align:start position:0%
+otherwise you would never be able to
+ 
+
+ align:start position:0%
+otherwise you would never be able to
+visit those uh
+
+ align:start position:0%
+visit those uh
+ 
+
+ align:start position:0%
+visit those uh
+spacer notes
+
+ align:start position:0%
+spacer notes
+ 
+
+ align:start position:0%
+spacer notes
+you have to look in the book for that uh
+
+ align:start position:0%
+you have to look in the book for that uh
+ 
+
+ align:start position:0%
+you have to look in the book for that uh
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+there is a little bit of a detail that
+
+ align:start position:0%
+there is a little bit of a detail that
+ 
+
+ align:start position:0%
+there is a little bit of a detail that
+you have to go through you have to show
+
+ align:start position:0%
+you have to go through you have to show
+ 
+
+ align:start position:0%
+you have to go through you have to show
+it must be zig zags and zig zag zigs
+
+ align:start position:0%
+it must be zig zags and zig zag zigs
+ 
+
+ align:start position:0%
+it must be zig zags and zig zag zigs
+and then you get the corresponding truth
+
+ align:start position:0%
+and then you get the corresponding truth
+ 
+
+ align:start position:0%
+and then you get the corresponding truth
+assignment and the most satisfied fee uh
+
+ align:start position:0%
+assignment and the most satisfied fee uh
+ 
+
+ align:start position:0%
+assignment and the most satisfied fee uh
+for all paths
+
+ align:start position:0%
+for all paths
+ 
+
+ align:start position:0%
+for all paths
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+let's uh again the reduction is
+
+ align:start position:0%
+let's uh again the reduction is
+ 
+
+ align:start position:0%
+let's uh again the reduction is
+polynomial time computable i'm not going
+
+ align:start position:0%
+polynomial time computable i'm not going
+ 
+
+ align:start position:0%
+polynomial time computable i'm not going
+to say more about that we're kind of a
+
+ align:start position:0%
+to say more about that we're kind of a
+ 
+
+ align:start position:0%
+to say more about that we're kind of a
+little bit low on time
+
+ align:start position:0%
+little bit low on time
+ 
+
+ align:start position:0%
+little bit low on time
+um last check in
+
+ align:start position:0%
+um last check in
+ 
+
+ align:start position:0%
+um last check in
+would this construction still work if g
+
+ align:start position:0%
+would this construction still work if g
+ 
+
+ align:start position:0%
+would this construction still work if g
+was undirected
+
+ align:start position:0%
+was undirected
+ 
+
+ align:start position:0%
+was undirected
+suppose
+
+ align:start position:0%
+suppose
+ 
+
+ align:start position:0%
+suppose
+i just eliminated all the directions
+
+ align:start position:0%
+i just eliminated all the directions
+ 
+
+ align:start position:0%
+i just eliminated all the directions
+from the from the edges
+
+ align:start position:0%
+from the from the edges
+ 
+
+ align:start position:0%
+from the from the edges
+uh made them lines instead of arrows
+
+ align:start position:0%
+uh made them lines instead of arrows
+ 
+
+ align:start position:0%
+uh made them lines instead of arrows
+would that now show that the undirected
+
+ align:start position:0%
+would that now show that the undirected
+ 
+
+ align:start position:0%
+would that now show that the undirected
+hamiltonian path problem is np-complete
+
+ align:start position:0%
+hamiltonian path problem is np-complete
+ 
+
+ align:start position:0%
+hamiltonian path problem is np-complete
+let me see
+
+ align:start position:0%
+let me see
+ 
+
+ align:start position:0%
+let me see
+what do this
+
+ align:start position:0%
+what do this
+ 
+
+ align:start position:0%
+what do this
+okay what do the c nodes represent here
+
+ align:start position:0%
+okay what do the c nodes represent here
+ 
+
+ align:start position:0%
+okay what do the c nodes represent here
+there's one c node for every clause
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there are k clauses
+
+ align:start position:0%
+so there are k clauses
+ 
+
+ align:start position:0%
+so there are k clauses
+named one c one to ck
+
+ align:start position:0%
+named one c one to ck
+ 
+
+ align:start position:0%
+named one c one to ck
+and there are k
+
+ align:start position:0%
+and there are k
+ 
+
+ align:start position:0%
+and there are k
+c nodes these are the so called clause
+
+ align:start position:0%
+c nodes these are the so called clause
+ 
+
+ align:start position:0%
+c nodes these are the so called clause
+gadgets
+
+ align:start position:0%
+gadgets
+ 
+
+ align:start position:0%
+gadgets
+which are going to force
+
+ align:start position:0%
+which are going to force
+ 
+
+ align:start position:0%
+which are going to force
+there to be one true literal
+
+ align:start position:0%
+there to be one true literal
+ 
+
+ align:start position:0%
+there to be one true literal
+um in every clause
+
+ align:start position:0%
+um in every clause
+ 
+
+ align:start position:0%
+um in every clause
+for the satisfying assignment
+
+ align:start position:0%
+for the satisfying assignment
+ 
+
+ align:start position:0%
+for the satisfying assignment
+you know it's uh
+
+ align:start position:0%
+you know it's uh
+ 
+
+ align:start position:0%
+you know it's uh
+you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you have to look at it or or maybe we
+
+ align:start position:0%
+you have to look at it or or maybe we
+ 
+
+ align:start position:0%
+you have to look at it or or maybe we
+can spend a little bit more time
+
+ align:start position:0%
+can spend a little bit more time
+ 
+
+ align:start position:0%
+can spend a little bit more time
+explaining it but uh that's what that's
+
+ align:start position:0%
+explaining it but uh that's what that's
+ 
+
+ align:start position:0%
+explaining it but uh that's what that's
+what the purpose is
+
+ align:start position:0%
+what the purpose is
+ 
+
+ align:start position:0%
+what the purpose is
+um does that mean we need only
+
+ align:start position:0%
+um does that mean we need only
+ 
+
+ align:start position:0%
+um does that mean we need only
+does that mean we need only two
+
+ align:start position:0%
+does that mean we need only two
+ 
+
+ align:start position:0%
+does that mean we need only two
+inside nodes
+
+ align:start position:0%
+inside nodes
+ 
+
+ align:start position:0%
+inside nodes
+uh do we know that so the
+
+ align:start position:0%
+uh do we know that so the
+ 
+
+ align:start position:0%
+uh do we know that so the
+the horizontal nodes do we only need two
+
+ align:start position:0%
+the horizontal nodes do we only need two
+ 
+
+ align:start position:0%
+the horizontal nodes do we only need two
+of them
+
+ align:start position:0%
+of them
+ 
+
+ align:start position:0%
+of them
+you won't be able to reuse the reuse
+
+ align:start position:0%
+you won't be able to reuse the reuse
+ 
+
+ align:start position:0%
+you won't be able to reuse the reuse
+these nodes for multiple detours for one
+
+ align:start position:0%
+these nodes for multiple detours for one
+ 
+
+ align:start position:0%
+these nodes for multiple detours for one
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+you know once you've gone to a detour
+
+ align:start position:0%
+you know once you've gone to a detour
+ 
+
+ align:start position:0%
+you know once you've gone to a detour
+you come back to the node next over and
+
+ align:start position:0%
+you come back to the node next over and
+ 
+
+ align:start position:0%
+you come back to the node next over and
+so you better not overlay multiple
+
+ align:start position:0%
+so you better not overlay multiple
+ 
+
+ align:start position:0%
+so you better not overlay multiple
+detours
+
+ align:start position:0%
+detours
+ 
+
+ align:start position:0%
+detours
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+also you need to keep them separated
+
+ align:start position:0%
+also you need to keep them separated
+ 
+
+ align:start position:0%
+also you need to keep them separated
+from each other don't forget and this
+
+ align:start position:0%
+from each other don't forget and this
+ 
+
+ align:start position:0%
+from each other don't forget and this
+node x1 can appear in many many
+
+ align:start position:0%
+node x1 can appear in many many
+ 
+
+ align:start position:0%
+node x1 can appear in many many
+different clauses
+
+ align:start position:0%
+different clauses
+ 
+
+ align:start position:0%
+different clauses
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you would need to have um
+
+ align:start position:0%
+you would need to have um
+ 
+
+ align:start position:0%
+you would need to have um
+possibly many
+
+ align:start position:0%
+possibly many
+ 
+
+ align:start position:0%
+possibly many
+of these horizontal nodes
+
+ align:start position:0%
+of these horizontal nodes
+ 
+
+ align:start position:0%
+of these horizontal nodes
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so some now says 2k inside nodes would
+
+ align:start position:0%
+so some now says 2k inside nodes would
+ 
+
+ align:start position:0%
+so some now says 2k inside nodes would
+suffice
+
+ align:start position:0%
+suffice
+ 
+
+ align:start position:0%
+suffice
+probably 2k i would say 3k just to be
+
+ align:start position:0%
+probably 2k i would say 3k just to be
+ 
+
+ align:start position:0%
+probably 2k i would say 3k just to be
+safe for the spacer nodes um you need to
+
+ align:start position:0%
+safe for the spacer nodes um you need to
+ 
+
+ align:start position:0%
+safe for the spacer nodes um you need to
+look at carefully at the argument which
+
+ align:start position:0%
+look at carefully at the argument which
+ 
+
+ align:start position:0%
+look at carefully at the argument which
+is laid out in the textbook um you may
+
+ align:start position:0%
+is laid out in the textbook um you may
+ 
+
+ align:start position:0%
+is laid out in the textbook um you may
+not actually need the spacer nodes but
+
+ align:start position:0%
+not actually need the spacer nodes but
+ 
+
+ align:start position:0%
+not actually need the spacer nodes but
+then it makes the argument just more
+
+ align:start position:0%
+then it makes the argument just more
+ 
+
+ align:start position:0%
+then it makes the argument just more
+more ugly so the way the construction is
+
+ align:start position:0%
+more ugly so the way the construction is
+ 
+
+ align:start position:0%
+more ugly so the way the construction is
+done is you have three k
+
+ align:start position:0%
+done is you have three k
+ 
+
+ align:start position:0%
+done is you have three k
+inside notes um that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh again several questions like
+
+ align:start position:0%
+okay uh again several questions like
+ 
+
+ align:start position:0%
+okay uh again several questions like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the graph would start looking messy if
+
+ align:start position:0%
+the graph would start looking messy if
+ 
+
+ align:start position:0%
+the graph would start looking messy if
+x9 was in c c1
+
+ align:start position:0%
+x9 was in c c1
+ 
+
+ align:start position:0%
+x9 was in c c1
+yeah if x9 down here was in c1 yeah i
+
+ align:start position:0%
+yeah if x9 down here was in c1 yeah i
+ 
+
+ align:start position:0%
+yeah if x9 down here was in c1 yeah i
+would
+
+ align:start position:0%
+would
+ 
+
+ align:start position:0%
+would
+it'd be messy it's okay my c is allowed
+
+ align:start position:0%
+it'd be messy it's okay my c is allowed
+ 
+
+ align:start position:0%
+it'd be messy it's okay my c is allowed
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+all right i think we're let's end the
+
+ align:start position:0%
+all right i think we're let's end the
+ 
+
+ align:start position:0%
+all right i think we're let's end the
+polling you all are you all in
+
+ align:start position:0%
+polling you all are you all in
+ 
+
+ align:start position:0%
+polling you all are you all in
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+share results
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+the answer is no
+
+ align:start position:0%
+the answer is no
+ 
+
+ align:start position:0%
+the answer is no
+uh the construction depends on this
+
+ align:start position:0%
+uh the construction depends on this
+ 
+
+ align:start position:0%
+uh the construction depends on this
+being directed i mean you can see that
+
+ align:start position:0%
+being directed i mean you can see that
+ 
+
+ align:start position:0%
+being directed i mean you can see that
+all over the place but for one thing
+
+ align:start position:0%
+all over the place but for one thing
+ 
+
+ align:start position:0%
+all over the place but for one thing
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you know the whole point of these
+
+ align:start position:0%
+you know the whole point of these
+ 
+
+ align:start position:0%
+you know the whole point of these
+detours is the directions of the of the
+
+ align:start position:0%
+detours is the directions of the of the
+ 
+
+ align:start position:0%
+detours is the directions of the of the
+um edges and so
+
+ align:start position:0%
+um edges and so
+ 
+
+ align:start position:0%
+um edges and so
+without that
+
+ align:start position:0%
+without that
+ 
+
+ align:start position:0%
+without that
+the the this construction me is is going
+
+ align:start position:0%
+the the this construction me is is going
+ 
+
+ align:start position:0%
+the the this construction me is is going
+to be just a bunch of
+
+ align:start position:0%
+to be just a bunch of
+ 
+
+ align:start position:0%
+to be just a bunch of
+you know not going to mean anything it's
+
+ align:start position:0%
+you know not going to mean anything it's
+ 
+
+ align:start position:0%
+you know not going to mean anything it's
+not going to prove anything it's
+
+ align:start position:0%
+not going to prove anything it's
+ 
+
+ align:start position:0%
+not going to prove anything it's
+probably always going to be have a have
+
+ align:start position:0%
+probably always going to be have a have
+ 
+
+ align:start position:0%
+probably always going to be have a have
+a hamiltonian path without the
+
+ align:start position:0%
+a hamiltonian path without the
+ 
+
+ align:start position:0%
+a hamiltonian path without the
+directions um
+
+ align:start position:0%
+directions um
+ 
+
+ align:start position:0%
+directions um
+so i think we're kind of out of time um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+a quick review um these are the topics
+
+ align:start position:0%
+a quick review um these are the topics
+ 
+
+ align:start position:0%
+a quick review um these are the topics
+we've covered i think we're out of time
+
+ align:start position:0%
+we've covered i think we're out of time
+ 
+
+ align:start position:0%
+we've covered i think we're out of time
+so i should let you go
+
+ align:start position:0%
+so i should let you go
+ 
+
+ align:start position:0%
+so i should let you go
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but i'll stick around for a few minutes
+
+ align:start position:0%
+but i'll stick around for a few minutes
+ 
+
+ align:start position:0%
+but i'll stick around for a few minutes
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+in case any of you have any questions
+
+ align:start position:0%
+in case any of you have any questions
+ 
+
+ align:start position:0%
+in case any of you have any questions
+but i need to run off it for myself for
+
+ align:start position:0%
+but i need to run off it for myself for
+ 
+
+ align:start position:0%
+but i need to run off it for myself for
+another meeting so i don't have much
+
+ align:start position:0%
+another meeting so i don't have much
+ 
+
+ align:start position:0%
+another meeting so i don't have much
+that much time
+
+ align:start position:0%
+that much time
+ 
+
+ align:start position:0%
+that much time
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+clarify my comment about picking the
+
+ align:start position:0%
+clarify my comment about picking the
+ 
+
+ align:start position:0%
+clarify my comment about picking the
+wrong problem to tackle p versus np
+
+ align:start position:0%
+wrong problem to tackle p versus np
+ 
+
+ align:start position:0%
+wrong problem to tackle p versus np
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+when i use composites as an example
+
+ align:start position:0%
+when i use composites as an example
+ 
+
+ align:start position:0%
+when i use composites as an example
+you know if i worked hard to prove that
+
+ align:start position:0%
+you know if i worked hard to prove that
+ 
+
+ align:start position:0%
+you know if i worked hard to prove that
+composites is not in p as a way of
+
+ align:start position:0%
+composites is not in p as a way of
+ 
+
+ align:start position:0%
+composites is not in p as a way of
+proving that there is some np language
+
+ align:start position:0%
+proving that there is some np language
+ 
+
+ align:start position:0%
+proving that there is some np language
+which is not in p
+
+ align:start position:0%
+which is not in p
+ 
+
+ align:start position:0%
+which is not in p
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that would that would have been a
+
+ align:start position:0%
+that would that would have been a
+ 
+
+ align:start position:0%
+that would that would have been a
+mistake because composites is in p
+
+ align:start position:0%
+mistake because composites is in p
+ 
+
+ align:start position:0%
+mistake because composites is in p
+that would be just i would would have
+
+ align:start position:0%
+that would be just i would would have
+ 
+
+ align:start position:0%
+that would be just i would would have
+been working hard to prove something
+
+ align:start position:0%
+been working hard to prove something
+ 
+
+ align:start position:0%
+been working hard to prove something
+which we now know was false
+
+ align:start position:0%
+which we now know was false
+ 
+
+ align:start position:0%
+which we now know was false
+so we don't want to spend time
+
+ align:start position:0%
+so we don't want to spend time
+ 
+
+ align:start position:0%
+so we don't want to spend time
+working on the wrong language
+
+ align:start position:0%
+working on the wrong language
+ 
+
+ align:start position:0%
+working on the wrong language
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know but the nice thing about np
+
+ align:start position:0%
+you know but the nice thing about np
+ 
+
+ align:start position:0%
+you know but the nice thing about np
+complete languages is that we have a
+
+ align:start position:0%
+complete languages is that we have a
+ 
+
+ align:start position:0%
+complete languages is that we have a
+guarantee
+
+ align:start position:0%
+guarantee
+ 
+
+ align:start position:0%
+guarantee
+that if p is different from np that that
+
+ align:start position:0%
+that if p is different from np that that
+ 
+
+ align:start position:0%
+that if p is different from np that that
+language is not in p
+
+ align:start position:0%
+language is not in p
+ 
+
+ align:start position:0%
+language is not in p
+are there problems that are not in p
+
+ align:start position:0%
+are there problems that are not in p
+ 
+
+ align:start position:0%
+are there problems that are not in p
+that are in np but are not np complete
+
+ align:start position:0%
+that are in np but are not np complete
+ 
+
+ align:start position:0%
+that are in np but are not np complete
+oh that's a good question
+
+ align:start position:0%
+oh that's a good question
+ 
+
+ align:start position:0%
+oh that's a good question
+are there
+
+ align:start position:0%
+are there
+ 
+
+ align:start position:0%
+are there
+problems in between
+
+ align:start position:0%
+problems in between
+ 
+
+ align:start position:0%
+problems in between
+uh p and np complete so np complete is
+
+ align:start position:0%
+uh p and np complete so np complete is
+ 
+
+ align:start position:0%
+uh p and np complete so np complete is
+sort of like the hardest problems in np
+
+ align:start position:0%
+sort of like the hardest problems in np
+ 
+
+ align:start position:0%
+sort of like the hardest problems in np
+and the p problems are obviously the
+
+ align:start position:0%
+and the p problems are obviously the
+ 
+
+ align:start position:0%
+and the p problems are obviously the
+easy problems that are in np and how
+
+ align:start position:0%
+easy problems that are in np and how
+ 
+
+ align:start position:0%
+easy problems that are in np and how
+about is everything either np complete
+
+ align:start position:0%
+about is everything either np complete
+ 
+
+ align:start position:0%
+about is everything either np complete
+or mp
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for one thing there are problems
+
+ align:start position:0%
+so for one thing there are problems
+ 
+
+ align:start position:0%
+so for one thing there are problems
+that are not known to be in either
+
+ align:start position:0%
+that are not known to be in either
+ 
+
+ align:start position:0%
+that are not known to be in either
+category
+
+ align:start position:0%
+category
+ 
+
+ align:start position:0%
+category
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+uh so we'll discuss some of those in due
+
+ align:start position:0%
+uh so we'll discuss some of those in due
+ 
+
+ align:start position:0%
+uh so we'll discuss some of those in due
+course but one of them is like the graph
+
+ align:start position:0%
+course but one of them is like the graph
+ 
+
+ align:start position:0%
+course but one of them is like the graph
+isomorphism problem testing two graphs
+
+ align:start position:0%
+isomorphism problem testing two graphs
+ 
+
+ align:start position:0%
+isomorphism problem testing two graphs
+if they're really just permutations of
+
+ align:start position:0%
+if they're really just permutations of
+ 
+
+ align:start position:0%
+if they're really just permutations of
+one another it's clearly a problem in np
+
+ align:start position:0%
+one another it's clearly a problem in np
+ 
+
+ align:start position:0%
+one another it's clearly a problem in np
+but not known to bnp um so there are
+
+ align:start position:0%
+but not known to bnp um so there are
+ 
+
+ align:start position:0%
+but not known to bnp um so there are
+problems that are
+
+ align:start position:0%
+problems that are
+ 
+
+ align:start position:0%
+problems that are
+not known to be either np complete or in
+
+ align:start position:0%
+not known to be either np complete or in
+ 
+
+ align:start position:0%
+not known to be either np complete or in
+p so there are problems that might be in
+
+ align:start position:0%
+p so there are problems that might be in
+ 
+
+ align:start position:0%
+p so there are problems that might be in
+between um
+
+ align:start position:0%
+between um
+ 
+
+ align:start position:0%
+between um
+but then there's another theorem out
+
+ align:start position:0%
+but then there's another theorem out
+ 
+
+ align:start position:0%
+but then there's another theorem out
+there which says that if you if you
+
+ align:start position:0%
+there which says that if you if you
+ 
+
+ align:start position:0%
+there which says that if you if you
+assume that p is different from np then
+
+ align:start position:0%
+assume that p is different from np then
+ 
+
+ align:start position:0%
+assume that p is different from np then
+you can construct
+
+ align:start position:0%
+you can construct
+ 
+
+ align:start position:0%
+you can construct
+problems which are in between which are
+
+ align:start position:0%
+problems which are in between which are
+ 
+
+ align:start position:0%
+problems which are in between which are
+neither np complete nor in p they're np
+
+ align:start position:0%
+neither np complete nor in p they're np
+ 
+
+ align:start position:0%
+neither np complete nor in p they're np
+problems but they're not empty complete
+
+ align:start position:0%
+problems but they're not empty complete
+ 
+
+ align:start position:0%
+problems but they're not empty complete
+not in p um so
+
+ align:start position:0%
+not in p um so
+ 
+
+ align:start position:0%
+not in p um so
+uh those problems themselves are perhaps
+
+ align:start position:0%
+uh those problems themselves are perhaps
+ 
+
+ align:start position:0%
+uh those problems themselves are perhaps
+somewhat artificial but they at least
+
+ align:start position:0%
+somewhat artificial but they at least
+ 
+
+ align:start position:0%
+somewhat artificial but they at least
+prove the point that it is possible to
+
+ align:start position:0%
+prove the point that it is possible to
+ 
+
+ align:start position:0%
+prove the point that it is possible to
+have these intermediate problems
+
+ align:start position:0%
+have these intermediate problems
+ 
+
+ align:start position:0%
+have these intermediate problems
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so somebody's asking isn't factorization
+
+ align:start position:0%
+so somebody's asking isn't factorization
+ 
+
+ align:start position:0%
+so somebody's asking isn't factorization
+one not no you know we
+
+ align:start position:0%
+one not no you know we
+ 
+
+ align:start position:0%
+one not no you know we
+for the case of factorization
+
+ align:start position:0%
+for the case of factorization
+ 
+
+ align:start position:0%
+for the case of factorization
+um or you have to make sure to make a
+
+ align:start position:0%
+um or you have to make sure to make a
+ 
+
+ align:start position:0%
+um or you have to make sure to make a
+language out of that by the way um
+
+ align:start position:0%
+language out of that by the way um
+ 
+
+ align:start position:0%
+language out of that by the way um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it's a um
+
+ align:start position:0%
+it's a um
+ 
+
+ align:start position:0%
+it's a um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+stuff because factorization is a
+
+ align:start position:0%
+stuff because factorization is a
+ 
+
+ align:start position:0%
+stuff because factorization is a
+function so we won't really want to be
+
+ align:start position:0%
+function so we won't really want to be
+ 
+
+ align:start position:0%
+function so we won't really want to be
+talking about languages as kind of as
+
+ align:start position:0%
+talking about languages as kind of as
+ 
+
+ align:start position:0%
+talking about languages as kind of as
+the homework suggests
+
+ align:start position:0%
+the homework suggests
+ 
+
+ align:start position:0%
+the homework suggests
+np and p are classes of languages but
+
+ align:start position:0%
+np and p are classes of languages but
+ 
+
+ align:start position:0%
+np and p are classes of languages but
+okay that's a separate separate note
+
+ align:start position:0%
+okay that's a separate separate note
+ 
+
+ align:start position:0%
+okay that's a separate separate note
+there factorization um
+
+ align:start position:0%
+there factorization um
+ 
+
+ align:start position:0%
+there factorization um
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+uh not no
+
+ align:start position:0%
+uh not no
+ 
+
+ align:start position:0%
+uh not no
+it could factorization could be in p and
+
+ align:start position:0%
+it could factorization could be in p and
+ 
+
+ align:start position:0%
+it could factorization could be in p and
+it could be np-complete
+
+ align:start position:0%
+it could be np-complete
+ 
+
+ align:start position:0%
+it could be np-complete
+you know both of those are not ruled out
+
+ align:start position:0%
+you know both of those are not ruled out
+ 
+
+ align:start position:0%
+you know both of those are not ruled out
+so uh you know i think most people would
+
+ align:start position:0%
+so uh you know i think most people would
+ 
+
+ align:start position:0%
+so uh you know i think most people would
+probably venture to guess that it's it's
+
+ align:start position:0%
+probably venture to guess that it's it's
+ 
+
+ align:start position:0%
+probably venture to guess that it's it's
+a problem that's in the in between state
+
+ align:start position:0%
+a problem that's in the in between state
+ 
+
+ align:start position:0%
+a problem that's in the in between state
+that's neither p nor mp complete but not
+
+ align:start position:0%
+that's neither p nor mp complete but not
+ 
+
+ align:start position:0%
+that's neither p nor mp complete but not
+known
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh do we
+
+ align:start position:0%
+uh do we
+ 
+
+ align:start position:0%
+uh do we
+who who first thought of this reduction
+
+ align:start position:0%
+who who first thought of this reduction
+ 
+
+ align:start position:0%
+who who first thought of this reduction
+from three set to hand path it's so
+
+ align:start position:0%
+from three set to hand path it's so
+ 
+
+ align:start position:0%
+from three set to hand path it's so
+clever
+
+ align:start position:0%
+clever
+ 
+
+ align:start position:0%
+clever
+well it wasn't me uh
+
+ align:start position:0%
+well it wasn't me uh
+ 
+
+ align:start position:0%
+well it wasn't me uh
+i believe that uh reduction from
+
+ align:start position:0%
+i believe that uh reduction from
+ 
+
+ align:start position:0%
+i believe that uh reduction from
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i think that is due to dick carp
+
+ align:start position:0%
+i think that is due to dick carp
+ 
+
+ align:start position:0%
+i think that is due to dick carp
+who was one of my professors at berkeley
+
+ align:start position:0%
+who was one of my professors at berkeley
+ 
+
+ align:start position:0%
+who was one of my professors at berkeley
+where i was a graduate student he that
+
+ align:start position:0%
+where i was a graduate student he that
+ 
+
+ align:start position:0%
+where i was a graduate student he that
+was done before i got there it was
+
+ align:start position:0%
+was done before i got there it was
+ 
+
+ align:start position:0%
+was done before i got there it was
+around 1971 um when so there were two
+
+ align:start position:0%
+around 1971 um when so there were two
+ 
+
+ align:start position:0%
+around 1971 um when so there were two
+famous papers there's the cook paper
+
+ align:start position:0%
+famous papers there's the cook paper
+ 
+
+ align:start position:0%
+famous papers there's the cook paper
+there's also the lemon paper that was in
+
+ align:start position:0%
+there's also the lemon paper that was in
+ 
+
+ align:start position:0%
+there's also the lemon paper that was in
+russian that took a while for people to
+
+ align:start position:0%
+russian that took a while for people to
+ 
+
+ align:start position:0%
+russian that took a while for people to
+discover out here in the west but
+
+ align:start position:0%
+discover out here in the west but
+ 
+
+ align:start position:0%
+discover out here in the west but
+the cook paper was 1971 and very quickly
+
+ align:start position:0%
+the cook paper was 1971 and very quickly
+ 
+
+ align:start position:0%
+the cook paper was 1971 and very quickly
+followed after he just showed sat as np
+
+ align:start position:0%
+followed after he just showed sat as np
+ 
+
+ align:start position:0%
+followed after he just showed sat as np
+complete
+
+ align:start position:0%
+complete
+ 
+
+ align:start position:0%
+complete
+but uh after that uh carp
+
+ align:start position:0%
+but uh after that uh carp
+ 
+
+ align:start position:0%
+but uh after that uh carp
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+he
+
+ align:start position:0%
+he
+ 
+
+ align:start position:0%
+he
+he had a paper called reducibility among
+
+ align:start position:0%
+he had a paper called reducibility among
+ 
+
+ align:start position:0%
+he had a paper called reducibility among
+combinatorial problems and he had a list
+
+ align:start position:0%
+combinatorial problems and he had a list
+ 
+
+ align:start position:0%
+combinatorial problems and he had a list
+of about 20 problems that he showed were
+
+ align:start position:0%
+of about 20 problems that he showed were
+ 
+
+ align:start position:0%
+of about 20 problems that he showed were
+np complete
+
+ align:start position:0%
+np complete
+ 
+
+ align:start position:0%
+np complete
+by reduction from sad um
+
+ align:start position:0%
+by reduction from sad um
+ 
+
+ align:start position:0%
+by reduction from sad um
+include clique include handpath and a
+
+ align:start position:0%
+include clique include handpath and a
+ 
+
+ align:start position:0%
+include clique include handpath and a
+bunch of other things um
+
+ align:start position:0%
+bunch of other things um
+ 
+
+ align:start position:0%
+bunch of other things um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+and that's was also a very famous uh
+
+ align:start position:0%
+and that's was also a very famous uh
+ 
+
+ align:start position:0%
+and that's was also a very famous uh
+very famous paper um both of those were
+
+ align:start position:0%
+very famous paper um both of those were
+ 
+
+ align:start position:0%
+very famous paper um both of those were
+people who often talk about cook carp as
+
+ align:start position:0%
+people who often talk about cook carp as
+ 
+
+ align:start position:0%
+people who often talk about cook carp as
+sort of together they
+
+ align:start position:0%
+sort of together they
+ 
+
+ align:start position:0%
+sort of together they
+uh they they they really sort of
+
+ align:start position:0%
+uh they they they really sort of
+ 
+
+ align:start position:0%
+uh they they they really sort of
+show the importance of np completeness
+
+ align:start position:0%
+show the importance of np completeness
+ 
+
+ align:start position:0%
+show the importance of np completeness
+and exist and no whole notion of np
+
+ align:start position:0%
+and exist and no whole notion of np
+ 
+
+ align:start position:0%
+and exist and no whole notion of np
+completeness
+
+ align:start position:0%
+completeness
+ 
+
+ align:start position:0%
+completeness
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah 21 problems so
+
+ align:start position:0%
+yeah 21 problems so
+ 
+
+ align:start position:0%
+yeah 21 problems so
+yeah so car proof 21 problems wouldn't
+
+ align:start position:0%
+yeah so car proof 21 problems wouldn't
+ 
+
+ align:start position:0%
+yeah so car proof 21 problems wouldn't
+be complete in 1972
+
+ align:start position:0%
+be complete in 1972
+ 
+
+ align:start position:0%
+be complete in 1972
+um so that was shortly after coke showed
+
+ align:start position:0%
+um so that was shortly after coke showed
+ 
+
+ align:start position:0%
+um so that was shortly after coke showed
+that sat was mp complete
+
+ align:start position:0%
+that sat was mp complete
+ 
+
+ align:start position:0%
+that sat was mp complete
+um incidentally i think the terminology
+
+ align:start position:0%
+um incidentally i think the terminology
+ 
+
+ align:start position:0%
+um incidentally i think the terminology
+np complete wasn't around uh
+
+ align:start position:0%
+np complete wasn't around uh
+ 
+
+ align:start position:0%
+np complete wasn't around uh
+uh until a little later
+
+ align:start position:0%
+uh until a little later
+ 
+
+ align:start position:0%
+uh until a little later
+and that might have been might be due to
+
+ align:start position:0%
+and that might have been might be due to
+ 
+
+ align:start position:0%
+and that might have been might be due to
+knuth
+
+ align:start position:0%
+knuth
+ 
+
+ align:start position:0%
+knuth
+i'm not sure i remember he did a big
+
+ align:start position:0%
+i'm not sure i remember he did a big
+ 
+
+ align:start position:0%
+i'm not sure i remember he did a big
+poll
+
+ align:start position:0%
+poll
+ 
+
+ align:start position:0%
+poll
+of people about what should be the right
+
+ align:start position:0%
+of people about what should be the right
+ 
+
+ align:start position:0%
+of people about what should be the right
+language to use for the for that term
+
+ align:start position:0%
+language to use for the for that term
+ 
+
+ align:start position:0%
+language to use for the for that term
+and i think he came up with it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+all right i'm gonna head off guys nice
+
+ align:start position:0%
+all right i'm gonna head off guys nice
+ 
+
+ align:start position:0%
+all right i'm gonna head off guys nice
+uh seeing you all uh so until uh
+
+ align:start position:0%
+uh seeing you all uh so until uh
+ 
+
+ align:start position:0%
+uh seeing you all uh so until uh
+thursday oh until tuesday uh bye-bye
\ No newline at end of file
diff --git a/j9DVXVwVyc4.txt b/j9DVXVwVyc4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e7f8408576f549eed06839743b5041fca946238a
--- /dev/null
+++ b/j9DVXVwVyc4.txt
@@ -0,0 +1,813 @@
+The following content is
+provided under a Creative
+
+Commons License.
+
+Your support will help MIT Open
+Courseware continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT Open Courseware at
+
+ocw.mit.edu.
+
+Hi.
+
+I'm Brian.
+
+We're going to be going over
+problem number 13 of the fall
+
+2009 final exam.
+
+I like to think of the theme of
+this problem as polymers.
+
+So that's the overarching
+concept.
+
+But I'm going to give you some
+things I think are important
+
+to review and to know before
+actually meaningfully
+
+attempting this problem.
+
+So there's three things that I
+that I sort of thought were
+
+very important.
+
+The first one is polymerization
+processes.
+
+So we learned in class and in
+the book as well that there's
+
+two ways that we've covered that
+you can create a polymer.
+
+And that is through either
+addition polymerization or
+
+condensation polymerization.
+
+And I'll talk about that
+more in a second.
+
+The second thing you want to
+know is basically molecular
+
+weight and how it applies
+to polymers.
+
+And you want to know about
+elastomers for this problem.
+
+If you don't know about
+elastomers then you'll have
+
+trouble with the last
+part of the problem.
+
+So that's kind of what
+I would review.
+
+And then once you've got that
+under your belt give the
+
+problem a try.
+
+So we're going to go
+and we're going to
+
+start the problem now.
+
+We're given in the problem the
+6-aminohexanoic acid, which
+
+I've drawn here.
+
+And we're also given at the
+beginning of the problem the
+
+structure of nylon 6.
+
+This is the actual reaction
+that's used to create nylon.
+
+So what I'm going to do is
+I'm going to show you--
+
+or ask the question of how
+do we create nylon from
+
+6-aminohexanoic acid.
+
+And that's actually going to
+answer part A and part B to
+
+this problem.
+
+So to create a polymer--
+
+in this case we're talking about
+the polymer nylon 6--
+
+you actually have to add
+together many mers.
+
+So merge is the term we used
+to denote the single unit
+
+which is repeated n times
+to create the poly mer--
+
+polymer.
+
+So in this case the mer, the
+individual unit of nylon 6, is
+
+6-aminohexanoic acid.
+
+And that's this.
+
+That's the same thing
+right there.
+
+So we're going to add these
+together and we're going to
+
+start creating our long
+chain of nylon 6.
+
+Remember, nylon 6 a polymer is
+a really, really long chain.
+
+Think of it as spaghetti,
+very long spaghetti.
+
+It isn't just two molecules
+that react.
+
+So let's just start somewhere.
+
+It's got to begin somewhere.
+
+You have to have two molecules
+at some point in the beginning
+
+reacting with each other.
+
+So let's look at our
+two molecules of
+
+6-aminohexanoic acid--
+
+I have to keep looking back
+at how to say that--
+
+so let's take a look and we have
+to think about now our
+
+two possible processes or routes
+towards polymerization.
+
+There's addition and there's
+condensation.
+
+Now addition, as you probably
+read and heard, requires there
+
+to be a double bond present
+between two carbon atoms. The
+
+reason for this is because
+usually have a free radical
+
+coming in, which will
+then initiate.
+
+That's why oftentimes the free
+radical molecule or free
+
+radical provider is called
+the initiator.
+
+You need an initiator to come
+in to break that double bond
+
+and then create another
+free radical.
+
+Which then lets the process
+continue along in
+
+a chain like that.
+
+If we look at our molecule here,
+we don't actually have
+
+any double bonds between two
+carbon atoms. We have a double
+
+bond with an oxygen but that's
+not sufficient for an
+
+addition-type reaction.
+
+For a condensation reaction,
+what that basically implies is
+
+two mer units, or two things
+coming together to react and
+
+they give off a byproduct.
+
+So that's how I remember
+condensation, very often the
+
+byproduct is water.
+
+You can have other byproducts,
+like HCl or any other sort of
+
+small molecules can
+be given off.
+
+But most times what we'll see
+in 3091 will be water given
+
+off in condensation, so it's
+sort of intuitive to call it
+
+condensation.
+
+In this problem, if we look at
+this, we have a molecule that
+
+has the Hs on one side and has
+Os on the other side, we can
+
+actually almost see this
+immediately as being a
+
+condensation reaction.
+
+What's going to happen is we're
+going to have this O
+
+reacting with the positive
+end of this
+
+molecule, which has Hs.
+
+And we're going to have an H2O
+liberated and given off.
+
+We're going to have the
+new molecule formed.
+
+Let me draw the molecule
+for you.
+
+Let me write it out.
+
+So we've just begun forming
+our polymer and this is a
+
+polymer which has an n of 2.
+
+It has 2 mer units
+building it.
+
+Notice I've kept
+the ends here.
+
+The positive and the
+negative here.
+
+In reality what's going to
+happen is we have a big vat of
+
+this 6-aminohexanoic
+acid and they're
+
+going to keep reacting.
+
+So we might have another one of
+these molecules float over
+
+and react with this O.
+
+Or conversely, we could have
+another one of these molecules
+
+come over and react
+with the H.
+
+So this thing is going
+to keep building.
+
+And the way these polymerization
+processes begin
+
+is the control of some parameter
+of the system.
+
+It could be temperature,
+pressure you can add something
+
+in to sort of initiate it.
+
+But that's how this
+is going to start.
+
+So we've actually sort of
+answered part a and b.
+
+We've come to the conclusion
+that this is obviously a
+
+condensation reaction.
+
+Because we're going
+to give off--
+
+I left that out there, see
+if you guys caught it--
+
+H2O.
+
+So we're losing this O and
+two of these Hs and
+
+we're forming water.
+
+And that's the byproduct.
+
+And a byproduct immediately
+should tell you we've got
+
+condensation going on.
+
+So condensation polymerization,
+part A.
+
+Part B, we've actually already
+done to sort of logic out the
+
+answer to part A.
+
+This is the answer to part B.
+
+Part B is just the reaction.
+
+I'll read it very
+specifically.
+
+Write the reaction that converts
+two molecules of
+
+6-aminohexanoic acid into
+a dimer of nylon 6.
+
+So we have two molecules
+forming the dimer.
+
+You are going to have trimer,
+and it goes on and on.
+
+The most common mistake on this
+problem was to give us
+
+the full repeating units.
+
+Let me just show you what
+that would look like.
+
+And then we'll move on
+with the problem.
+
+So the most common mistake on
+this problem was to not have
+
+these end units.
+
+And instead say, oh it's created
+this huge, long chain.
+
+So I'm going to write
+it as follows.
+
+And this is the symbol to
+imply that it repeats.
+
+Likewise over here.
+
+So people would give us this.
+
+And that's not correct.
+
+And the reason that's a problem
+is because not only do
+
+you lose points on this
+part, you also lose
+
+points on the next part.
+
+So part C is now asking us to
+calculate the molecular weight
+
+of a molecule given
+a certain n.
+
+n is the degree of
+polymerization.
+
+So in this case, n equals
+2, we've got a dimer.
+
+In part C, we have n equals--
+
+surprisingly--
+
+3,091 You'll see that's a
+recurring theme in this class.
+
+So we have n equals 3,091 And
+the question is, how do we
+
+approach the molecular
+weight problem?
+
+Well we're told that we have
+3,091 one of these mer units
+
+making up this polymer chain.
+
+So let me just write
+this down.
+
+We're going to form
+an equation.
+
+If we take the mass of the full
+chain and divide it by
+
+the mass of a single mer unit
+we should be able to extract
+
+the number of units
+in the chain.
+
+So let me write that
+out for you.
+
+So the total molecular weight
+of the molecule, divided by
+
+the weight of a particular
+mer unit.
+
+OK so we're going to
+put that as mer.
+
+And so this is easy.
+
+Let's first identify what
+our mer unit is.
+
+And this is why it was easy get
+
+tripped up on this problem.
+
+Because if you made a mistake
+on the part B, you have
+
+trouble on part C.
+
+What is our mer unit?
+
+So in our mer unit, what we're
+talking about is a chain which
+
+has 3,091 of these linked
+pieces here.
+
+So let's look at this.
+
+What do we have?
+
+Here's our mer unit.
+
+Let me circle it.
+
+We have 6 carbons.
+
+We have 11 hydrogens,
+1 nitrogen and 1
+
+oxygen in this mer unit.
+
+We're not going to take the
+full, complete end unit.
+
+We're not counting this O.
+
+We're not counting those 2 Hs.
+
+We're dropping off 18 grams
+per reaction into water.
+
+So this is our mere unit.
+
+Let's calculate the mass
+of our mer unit.
+
+So it's going to be--
+
+let me write this here--
+
+we're looking for molecular
+weight.
+
+We're going to divide that by
+the mass of the mer unit.
+
+Let me just write out the full
+line of what it would be.
+
+Approximately 6 times
+12 plus 11 times 1.
+
+So this is 6 carbons, times
+the mass of carbon.
+
+11 hydrogens times the
+mass of hydrogen.
+
+We're going to have 1 oxygen
+times the mass of oxygen.
+
+And we're going to have
+the nitrogen as well.
+
+So let me add that down here.
+
+1 nitrogen times the
+mass of nitrogen.
+
+I rounded.
+
+That's OK.
+
+As long as you get
+the idea right.
+
+So now we can easily
+just solve for
+
+the molecular weight.
+
+And we'll find that molecular
+weight in this problem will be
+
+equal to 3.5 times 10 to the
+fifth grams per mole.
+
+There's another way to do
+this problem, actually.
+
+And what you can do is you
+can calculate n times
+
+the number of this--
+
+this particular molecule--
+
+and you can subtract
+off 3,090 orders.
+
+18 grams. 3,090 times
+eighteen.
+
+You subtract that off.
+
+Think about a little bit why
+it's 3,090 and not 3,091.
+
+So that's just maybe a
+brain teaser for you.
+
+That is the answer to part C.
+
+And now part D asks us if we're
+able to convert this
+
+into an elastomer.
+
+So this is where it's really
+required that you understand
+
+what an elastomer is and what
+that implies and what the
+
+structure looks like.
+
+So an elastomer--
+
+and I sort of paraphrased this
+from the book and added my own
+
+thing to it-- is basically a
+randomly oriented amorphous
+
+polymer with some cross-linking
+such that you
+
+have the ability to move the
+chains but not slide them
+
+completely over each other.
+
+So in order to have an elastomer
+you must have
+
+cross-linking.
+
+In order to have cross-linking,
+
+what must you have?
+
+Well from lecture and from
+the book we know that to
+
+cross-link you must have double
+bonds in your carbons.
+
+So you must have 2 carbons--
+
+going back over here--
+
+which are double-bonded
+together.
+
+And why is that?
+
+Because what happens is those
+double bonds will be broken by
+
+some initiator element-- many
+times we'll have sulfur--
+
+will come in, break the double
+bond and then you'll have
+
+links forming between things.
+
+So let me actually give you
+real-life example of this so
+
+you can see what I'm
+talking about.
+
+We're going to show disulfide
+bridges bounding and creating
+
+cross-links in a molecule.
+
+Something we're very familiar
+with is rubber.
+
+And we're also very familiar
+with car tires.
+
+The big difference between
+those two things is that
+
+rubber has vulcanized Which
+means we're actually putting
+
+sulphur into it to create a
+different type of polymer.
+
+We're looking at a cross-linked,
+much stronger
+
+rubber which we use
+on our car tires.
+
+So polyisoprene looks
+something like this.
+
+You should be familiar with
+this notation by now.
+
+We have this denotes
+it repeats.
+
+We have our double
+bonds, we have
+
+our carbons and hydrogens.
+
+This is polyisoprene.
+
+And this is what we're
+going to add sulphur
+
+to vulcanize rubber.
+
+We're going to create
+vulcanized rubber.
+
+sulphur generally actually
+looks, it's a ring of 8
+
+sulphur atoms. We'll then
+add it to rubber,
+
+maybe heat it up mixed.
+
+And you'll make what you're
+used to on car tires.
+
+So what's actually happening
+here is that you can see we
+
+have this double bond
+between carbons.
+
+The sulphur's going to come in,
+it's going to react with
+
+this double bond, and is
+actually going to pull it off.
+
+And it might form a
+chain like that.
+
+And then this sulfur will then
+connect to another one of
+
+these polyisoprene molecules
+that was
+
+originally double bonded.
+
+And I'm not going to draw
+the rest of it out.
+
+And it's going to react, kill
+this double bond, and it's
+
+going to connect it.
+
+So basically what's happened
+in this process of forming
+
+sulfide bridges is you've got
+this polymer, polyisoprene,
+
+connecting to this polymer,
+polyisoprene, and you have
+
+cross-linking going on.
+
+And that's what we would need
+to have in our case for the
+
+nylon 6 in order to get an
+elastomer, And because nylon
+
+6, because our mer unit,
+6-aminohexanoic acid doesn't
+
+have double bonds, we
+can't break them.
+
+We can't network.
+
+We can't cross-link.
+
+And therefore we can't
+make an elastomer.
+
+So the answer to
+this problem--
+
+in a very long-winded manner--
+
+is no.
+
+You cannot create an elastomer
+given that mer unit.
\ No newline at end of file
diff --git a/j9twDytNikc.txt b/j9twDytNikc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..42da707d7fecf04179e54797d0e82715b8ded0b0
--- /dev/null
+++ b/j9twDytNikc.txt
@@ -0,0 +1,179 @@
+align:start position:0%
+ 
+so um for the cooking assignments they
+
+ align:start position:0%
+so um for the cooking assignments they
+ 
+
+ align:start position:0%
+so um for the cooking assignments they
+had to reproduce something that we had
+
+ align:start position:0%
+had to reproduce something that we had
+ 
+
+ align:start position:0%
+had to reproduce something that we had
+cooked in the previous class and um well
+
+ align:start position:0%
+cooked in the previous class and um well
+ 
+
+ align:start position:0%
+cooked in the previous class and um well
+since for every class we were cooking a
+
+ align:start position:0%
+since for every class we were cooking a
+ 
+
+ align:start position:0%
+since for every class we were cooking a
+variety of dishes then it was up to them
+
+ align:start position:0%
+variety of dishes then it was up to them
+ 
+
+ align:start position:0%
+variety of dishes then it was up to them
+to decide whether they wanted to cook
+
+ align:start position:0%
+to decide whether they wanted to cook
+ 
+
+ align:start position:0%
+to decide whether they wanted to cook
+for example risotto with mushroom or
+
+ align:start position:0%
+for example risotto with mushroom or
+ 
+
+ align:start position:0%
+for example risotto with mushroom or
+risoto with zafferano with saffron or
+
+ align:start position:0%
+risoto with zafferano with saffron or
+ 
+
+ align:start position:0%
+risoto with zafferano with saffron or
+risoto with zucchini I let them that I
+
+ align:start position:0%
+risoto with zucchini I let them that I
+ 
+
+ align:start position:0%
+risoto with zucchini I let them that I
+left them to make the choice but then
+
+ align:start position:0%
+left them to make the choice but then
+ 
+
+ align:start position:0%
+left them to make the choice but then
+the idea was to repeat the dish that we
+
+ align:start position:0%
+the idea was to repeat the dish that we
+ 
+
+ align:start position:0%
+the idea was to repeat the dish that we
+had done on the Thursday before because
+
+ align:start position:0%
+had done on the Thursday before because
+ 
+
+ align:start position:0%
+had done on the Thursday before because
+um it's very difficult if you cook in a
+
+ align:start position:0%
+um it's very difficult if you cook in a
+ 
+
+ align:start position:0%
+um it's very difficult if you cook in a
+group and if there is somebody
+
+ align:start position:0%
+group and if there is somebody
+ 
+
+ align:start position:0%
+group and if there is somebody
+supervising and then when you are on
+
+ align:start position:0%
+supervising and then when you are on
+ 
+
+ align:start position:0%
+supervising and then when you are on
+your own maybe you realize oh that step
+
+ align:start position:0%
+your own maybe you realize oh that step
+ 
+
+ align:start position:0%
+your own maybe you realize oh that step
+is not so clear and it reinforces what
+
+ align:start position:0%
+is not so clear and it reinforces what
+ 
+
+ align:start position:0%
+is not so clear and it reinforces what
+they have been learning the same I mean
+
+ align:start position:0%
+they have been learning the same I mean
+ 
+
+ align:start position:0%
+they have been learning the same I mean
+the idea of the kitchen assignment is
+
+ align:start position:0%
+the idea of the kitchen assignment is
+ 
+
+ align:start position:0%
+the idea of the kitchen assignment is
+the same idea um behind a written
+
+ align:start position:0%
+the same idea um behind a written
+ 
+
+ align:start position:0%
+the same idea um behind a written
+assignment a grammar assignment you want
+
+ align:start position:0%
+assignment a grammar assignment you want
+ 
+
+ align:start position:0%
+assignment a grammar assignment you want
+to reinforce what has been learned
+
+ align:start position:0%
+to reinforce what has been learned
+ 
+
+ align:start position:0%
+to reinforce what has been learned
+before
\ No newline at end of file
diff --git a/jJX_1zT73U0.txt b/jJX_1zT73U0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5af538d81290eff0e55a851dd470cdc5b6e8328c
--- /dev/null
+++ b/jJX_1zT73U0.txt
@@ -0,0 +1,14899 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu
+
+ align:start position:0%
+ocw.mit.edu
+ 
+
+ align:start position:0%
+ocw.mit.edu
+um so it's a beautiful recording okay so
+
+ align:start position:0%
+um so it's a beautiful recording okay so
+ 
+
+ align:start position:0%
+um so it's a beautiful recording okay so
+uh to get started um question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from last time so Barton covered for me
+
+ align:start position:0%
+from last time so Barton covered for me
+ 
+
+ align:start position:0%
+from last time so Barton covered for me
+last time I I fled I was out of town um
+
+ align:start position:0%
+last time I I fled I was out of town um
+ 
+
+ align:start position:0%
+last time I I fled I was out of town um
+I was at a math conference it was pretty
+
+ align:start position:0%
+I was at a math conference it was pretty
+ 
+
+ align:start position:0%
+I was at a math conference it was pretty
+surreal questions
+
+ align:start position:0%
+surreal questions
+ 
+
+ align:start position:0%
+surreal questions
+yes about the exam yes absolutely so um
+
+ align:start position:0%
+yes about the exam yes absolutely so um
+ 
+
+ align:start position:0%
+yes about the exam yes absolutely so um
+the exam uh is as you all know on
+
+ align:start position:0%
+the exam uh is as you all know on
+ 
+
+ align:start position:0%
+the exam uh is as you all know on
+Thursday uh weekend so on Tuesday we
+
+ align:start position:0%
+Thursday uh weekend so on Tuesday we
+ 
+
+ align:start position:0%
+Thursday uh weekend so on Tuesday we
+will have a lecture the material Tuesday
+
+ align:start position:0%
+will have a lecture the material Tuesday
+ 
+
+ align:start position:0%
+will have a lecture the material Tuesday
+will not be covered uh on the exam the
+
+ align:start position:0%
+will not be covered uh on the exam the
+ 
+
+ align:start position:0%
+will not be covered uh on the exam the
+exam will be a review of everything
+
+ align:start position:0%
+exam will be a review of everything
+ 
+
+ align:start position:0%
+exam will be a review of everything
+through today's lecture including the
+
+ align:start position:0%
+through today's lecture including the
+ 
+
+ align:start position:0%
+through today's lecture including the
+problem set which for some technical
+
+ align:start position:0%
+problem set which for some technical
+ 
+
+ align:start position:0%
+problem set which for some technical
+reason I don't know why it didn't get
+
+ align:start position:0%
+reason I don't know why it didn't get
+ 
+
+ align:start position:0%
+reason I don't know why it didn't get
+posted but it should be up after lecture
+
+ align:start position:0%
+posted but it should be up after lecture
+ 
+
+ align:start position:0%
+posted but it should be up after lecture
+today um the exam will be a a
+
+ align:start position:0%
+today um the exam will be a a
+ 
+
+ align:start position:0%
+today um the exam will be a a
+combination of short questions and uh
+
+ align:start position:0%
+combination of short questions and uh
+ 
+
+ align:start position:0%
+combination of short questions and uh
+computations uh it will not focus on an
+
+ align:start position:0%
+computations uh it will not focus on an
+ 
+
+ align:start position:0%
+computations uh it will not focus on an
+enormous number of computations it will
+
+ align:start position:0%
+enormous number of computations it will
+ 
+
+ align:start position:0%
+enormous number of computations it will
+focus more on conceptual things but
+
+ align:start position:0%
+focus more on conceptual things but
+ 
+
+ align:start position:0%
+focus more on conceptual things but
+there will be a few calculations uh on
+
+ align:start position:0%
+there will be a few calculations uh on
+ 
+
+ align:start position:0%
+there will be a few calculations uh on
+the exam um and I will post some
+
+ align:start position:0%
+the exam um and I will post some
+ 
+
+ align:start position:0%
+the exam um and I will post some
+practice problems uh over the next
+
+ align:start position:0%
+practice problems uh over the next
+ 
+
+ align:start position:0%
+practice problems uh over the next
+couple of days um have a problem you you
+
+ align:start position:0%
+couple of days um have a problem you you
+ 
+
+ align:start position:0%
+couple of days um have a problem you you
+do have a problem due Tuesday and that
+
+ align:start position:0%
+do have a problem due Tuesday and that
+ 
+
+ align:start position:0%
+do have a problem due Tuesday and that
+is part of your preparation for the exam
+
+ align:start position:0%
+is part of your preparation for the exam
+ 
+
+ align:start position:0%
+is part of your preparation for the exam
+here's a basic strategy for exams for
+
+ align:start position:0%
+here's a basic strategy for exams for
+ 
+
+ align:start position:0%
+here's a basic strategy for exams for
+this class anything that's on a problem
+
+ align:start position:0%
+this class anything that's on a problem
+ 
+
+ align:start position:0%
+this class anything that's on a problem
+set is fair game anything that's not
+
+ align:start position:0%
+set is fair game anything that's not
+ 
+
+ align:start position:0%
+set is fair game anything that's not
+covered on a problem set is not going to
+
+ align:start position:0%
+covered on a problem set is not going to
+ 
+
+ align:start position:0%
+covered on a problem set is not going to
+be fair game if you haven't seen a
+
+ align:start position:0%
+be fair game if you haven't seen a
+ 
+
+ align:start position:0%
+be fair game if you haven't seen a
+problem on it broadly construed then
+
+ align:start position:0%
+problem on it broadly construed then
+ 
+
+ align:start position:0%
+problem on it broadly construed then
+then you won't you know I won't test you
+
+ align:start position:0%
+then you won't you know I won't test you
+ 
+
+ align:start position:0%
+then you won't you know I won't test you
+on a topic you haven't done problems on
+
+ align:start position:0%
+on a topic you haven't done problems on
+ 
+
+ align:start position:0%
+on a topic you haven't done problems on
+before um but I will take problems and
+
+ align:start position:0%
+before um but I will take problems and
+ 
+
+ align:start position:0%
+before um but I will take problems and
+ideas that you've studied before and
+
+ align:start position:0%
+ideas that you've studied before and
+ 
+
+ align:start position:0%
+ideas that you've studied before and
+spin them slightly differently to make
+
+ align:start position:0%
+spin them slightly differently to make
+ 
+
+ align:start position:0%
+spin them slightly differently to make
+you think through them in real time on
+
+ align:start position:0%
+you think through them in real time on
+ 
+
+ align:start position:0%
+you think through them in real time on
+the exam Okay so
+
+ align:start position:0%
+the exam Okay so
+ 
+
+ align:start position:0%
+the exam Okay so
+the purpose from my point of view the
+
+ align:start position:0%
+the purpose from my point of view the
+ 
+
+ align:start position:0%
+the purpose from my point of view the
+purpose of these exams is not to give
+
+ align:start position:0%
+purpose of these exams is not to give
+ 
+
+ align:start position:0%
+purpose of these exams is not to give
+you a grade I don't care about the grade
+
+ align:start position:0%
+you a grade I don't care about the grade
+ 
+
+ align:start position:0%
+you a grade I don't care about the grade
+the purpose of these exams is to give
+
+ align:start position:0%
+the purpose of these exams is to give
+ 
+
+ align:start position:0%
+the purpose of these exams is to give
+you feedback on your understanding okay
+
+ align:start position:0%
+you feedback on your understanding okay
+ 
+
+ align:start position:0%
+you feedback on your understanding okay
+it's very easy to slip through quantum
+
+ align:start position:0%
+it's very easy to slip through quantum
+ 
+
+ align:start position:0%
+it's very easy to slip through quantum
+mechanics and think like oh yeah I
+
+ align:start position:0%
+mechanics and think like oh yeah I
+ 
+
+ align:start position:0%
+mechanics and think like oh yeah I
+totally I got this this is fine but it's
+
+ align:start position:0%
+totally I got this this is fine but it's
+ 
+
+ align:start position:0%
+totally I got this this is fine but it's
+uh it's not always uh it's not always an
+
+ align:start position:0%
+uh it's not always uh it's not always an
+ 
+
+ align:start position:0%
+uh it's not always uh it's not always an
+accurate read so that's the point um did
+
+ align:start position:0%
+accurate read so that's the point um did
+ 
+
+ align:start position:0%
+accurate read so that's the point um did
+that answer your question okay other
+
+ align:start position:0%
+that answer your question okay other
+ 
+
+ align:start position:0%
+that answer your question okay other
+questions exam yeah uh about the
+
+ align:start position:0%
+questions exam yeah uh about the
+ 
+
+ align:start position:0%
+questions exam yeah uh about the
+harmonic oscillator actually EXC um when
+
+ align:start position:0%
+harmonic oscillator actually EXC um when
+ 
+
+ align:start position:0%
+harmonic oscillator actually EXC um when
+we solve it Tuesday using the series
+
+ align:start position:0%
+we solve it Tuesday using the series
+ 
+
+ align:start position:0%
+we solve it Tuesday using the series
+method yes um so there are two solutions
+
+ align:start position:0%
+method yes um so there are two solutions
+ 
+
+ align:start position:0%
+method yes um so there are two solutions
+techn right the even solution and the
+
+ align:start position:0%
+techn right the even solution and the
+ 
+
+ align:start position:0%
+techn right the even solution and the
+odd term solution good so did boundary
+
+ align:start position:0%
+odd term solution good so did boundary
+ 
+
+ align:start position:0%
+odd term solution good so did boundary
+conditions Force the other one to be
+
+ align:start position:0%
+conditions Force the other one to be
+ 
+
+ align:start position:0%
+conditions Force the other one to be
+completely zero like the coefficient in
+
+ align:start position:0%
+completely zero like the coefficient in
+ 
+
+ align:start position:0%
+completely zero like the coefficient in
+front of it so like there's like an a
+
+ align:start position:0%
+front of it so like there's like an a
+ 
+
+ align:start position:0%
+front of it so like there's like an a
+zero term which determines all the other
+
+ align:start position:0%
+zero term which determines all the other
+ 
+
+ align:start position:0%
+zero term which determines all the other
+ones yes um but there there's like an a
+
+ align:start position:0%
+ones yes um but there there's like an a
+ 
+
+ align:start position:0%
+ones yes um but there there's like an a
+zero term and an A1 term for the evens
+
+ align:start position:0%
+zero term and an A1 term for the evens
+ 
+
+ align:start position:0%
+zero term and an A1 term for the evens
+and odds so did the other one just have
+
+ align:start position:0%
+and odds so did the other one just have
+ 
+
+ align:start position:0%
+and odds so did the other one just have
+to be zero this is a really good
+
+ align:start position:0%
+to be zero this is a really good
+ 
+
+ align:start position:0%
+to be zero this is a really good
+question so this is an excellent
+
+ align:start position:0%
+question so this is an excellent
+ 
+
+ align:start position:0%
+question so this is an excellent
+question let me ask the question
+
+ align:start position:0%
+question let me ask the question
+ 
+
+ align:start position:0%
+question let me ask the question
+slightly differently and tell me if this
+
+ align:start position:0%
+slightly differently and tell me if this
+ 
+
+ align:start position:0%
+slightly differently and tell me if this
+is the same question when we wrote down
+
+ align:start position:0%
+is the same question when we wrote down
+ 
+
+ align:start position:0%
+is the same question when we wrote down
+our differential equation so last time
+
+ align:start position:0%
+our differential equation so last time
+ 
+
+ align:start position:0%
+our differential equation so last time
+we did the harmonic oscillator and uh
+
+ align:start position:0%
+we did the harmonic oscillator and uh
+ 
+
+ align:start position:0%
+we did the harmonic oscillator and uh
+Barton gave you the Brute Force strategy
+
+ align:start position:0%
+Barton gave you the Brute Force strategy
+ 
+
+ align:start position:0%
+Barton gave you the Brute Force strategy
+for the harmonic oscillator we want to
+
+ align:start position:0%
+for the harmonic oscillator we want to
+ 
+
+ align:start position:0%
+for the harmonic oscillator we want to
+find the energy igen states because
+
+ align:start position:0%
+find the energy igen states because
+ 
+
+ align:start position:0%
+find the energy igen states because
+that's what we do to solve the the star
+
+ align:start position:0%
+that's what we do to solve the the star
+ 
+
+ align:start position:0%
+that's what we do to solve the the star
+equation and to we turn that into a
+
+ align:start position:0%
+equation and to we turn that into a
+ 
+
+ align:start position:0%
+equation and to we turn that into a
+differential equation and we solve this
+
+ align:start position:0%
+differential equation and we solve this
+ 
+
+ align:start position:0%
+differential equation and we solve this
+differential equation by doing an ASM
+
+ align:start position:0%
+differential equation by doing an ASM
+ 
+
+ align:start position:0%
+differential equation by doing an ASM
+totic analysis and then a series
+
+ align:start position:0%
+totic analysis and then a series
+ 
+
+ align:start position:0%
+totic analysis and then a series
+expansion right now this is a second
+
+ align:start position:0%
+expansion right now this is a second
+ 
+
+ align:start position:0%
+expansion right now this is a second
+order differential equation everyone
+
+ align:start position:0%
+order differential equation everyone
+ 
+
+ align:start position:0%
+order differential equation everyone
+agree with that it's a second order
+
+ align:start position:0%
+agree with that it's a second order
+ 
+
+ align:start position:0%
+agree with that it's a second order
+differential equation
+
+ align:start position:0%
+differential equation
+ 
+
+ align:start position:0%
+differential equation
+however uh in our series expansion we
+
+ align:start position:0%
+however uh in our series expansion we
+ 
+
+ align:start position:0%
+however uh in our series expansion we
+ended up with uh one integration
+
+ align:start position:0%
+ended up with uh one integration
+ 
+
+ align:start position:0%
+ended up with uh one integration
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+two how does that work how can it be
+
+ align:start position:0%
+two how does that work how can it be
+ 
+
+ align:start position:0%
+two how does that work how can it be
+that there was only one integration
+
+ align:start position:0%
+that there was only one integration
+ 
+
+ align:start position:0%
+that there was only one integration
+constant not two it's a second order
+
+ align:start position:0%
+constant not two it's a second order
+ 
+
+ align:start position:0%
+constant not two it's a second order
+differential equation right is this your
+
+ align:start position:0%
+differential equation right is this your
+ 
+
+ align:start position:0%
+differential equation right is this your
+question okay and this is an excellent
+
+ align:start position:0%
+question okay and this is an excellent
+ 
+
+ align:start position:0%
+question okay and this is an excellent
+question because it must be two true
+
+ align:start position:0%
+question because it must be two true
+ 
+
+ align:start position:0%
+question because it must be two true
+that there are two solutions it cannot
+
+ align:start position:0%
+that there are two solutions it cannot
+ 
+
+ align:start position:0%
+that there are two solutions it cannot
+be that there is just one solution it's
+
+ align:start position:0%
+be that there is just one solution it's
+ 
+
+ align:start position:0%
+be that there is just one solution it's
+a second order differential equation
+
+ align:start position:0%
+a second order differential equation
+ 
+
+ align:start position:0%
+a second order differential equation
+there existence and uniqueness theorems
+
+ align:start position:0%
+there existence and uniqueness theorems
+ 
+
+ align:start position:0%
+there existence and uniqueness theorems
+which tell us there are two integration
+
+ align:start position:0%
+which tell us there are two integration
+ 
+
+ align:start position:0%
+which tell us there are two integration
+constants okay so how can it possibly be
+
+ align:start position:0%
+constants okay so how can it possibly be
+ 
+
+ align:start position:0%
+constants okay so how can it possibly be
+that there was only one well some we did
+
+ align:start position:0%
+that there was only one well some we did
+ 
+
+ align:start position:0%
+that there was only one well some we did
+something rather subtle in that series
+
+ align:start position:0%
+something rather subtle in that series
+ 
+
+ align:start position:0%
+something rather subtle in that series
+expansion in order to for that series
+
+ align:start position:0%
+expansion in order to for that series
+ 
+
+ align:start position:0%
+expansion in order to for that series
+expansion there was a critical moment
+
+ align:start position:0%
+expansion there was a critical moment
+ 
+
+ align:start position:0%
+expansion there was a critical moment
+which I'm not going to go through but
+
+ align:start position:0%
+which I'm not going to go through but
+ 
+
+ align:start position:0%
+which I'm not going to go through but
+you can come to my office hours again
+
+ align:start position:0%
+you can come to my office hours again
+ 
+
+ align:start position:0%
+you can come to my office hours again
+but just look through the notes there's
+
+ align:start position:0%
+but just look through the notes there's
+ 
+
+ align:start position:0%
+but just look through the notes there's
+an important moment in the notes when we
+
+ align:start position:0%
+an important moment in the notes when we
+ 
+
+ align:start position:0%
+an important moment in the notes when we
+say aha these terms matter but what we
+
+ align:start position:0%
+say aha these terms matter but what we
+ 
+
+ align:start position:0%
+say aha these terms matter but what we
+did is we
+
+ align:start position:0%
+did is we
+ 
+
+ align:start position:0%
+did is we
+suppressed a singular solution there's a
+
+ align:start position:0%
+suppressed a singular solution there's a
+ 
+
+ align:start position:0%
+suppressed a singular solution there's a
+solution of that differential equation
+
+ align:start position:0%
+solution of that differential equation
+ 
+
+ align:start position:0%
+solution of that differential equation
+which is not well behaved which is not
+
+ align:start position:0%
+which is not well behaved which is not
+ 
+
+ align:start position:0%
+which is not well behaved which is not
+smooth and in particular which diverges
+
+ align:start position:0%
+smooth and in particular which diverges
+ 
+
+ align:start position:0%
+smooth and in particular which diverges
+okay and we already did from the ASM
+
+ align:start position:0%
+okay and we already did from the ASM
+ 
+
+ align:start position:0%
+okay and we already did from the ASM
+totic analysis we already fixed that the
+
+ align:start position:0%
+totic analysis we already fixed that the
+ 
+
+ align:start position:0%
+totic analysis we already fixed that the
+ASM totic Behavior was exponentially
+
+ align:start position:0%
+ASM totic Behavior was exponentially
+ 
+
+ align:start position:0%
+ASM totic Behavior was exponentially
+falling but there's a second solution
+
+ align:start position:0%
+falling but there's a second solution
+ 
+
+ align:start position:0%
+falling but there's a second solution
+which is exponentially growing
+
+ align:start position:0%
+which is exponentially growing
+ 
+
+ align:start position:0%
+which is exponentially growing
+so what we did remember how we did this
+
+ align:start position:0%
+so what we did remember how we did this
+ 
+
+ align:start position:0%
+so what we did remember how we did this
+this story we took our wave function and
+
+ align:start position:0%
+this story we took our wave function and
+ 
+
+ align:start position:0%
+this story we took our wave function and
+we said okay look we're going to pull
+
+ align:start position:0%
+we said okay look we're going to pull
+ 
+
+ align:start position:0%
+we said okay look we're going to pull
+off we're going to first do ASM totic
+
+ align:start position:0%
+off we're going to first do ASM totic
+ 
+
+ align:start position:0%
+off we're going to first do ASM totic
+analysis an ASM totic analysis tells us
+
+ align:start position:0%
+analysis an ASM totic analysis tells us
+ 
+
+ align:start position:0%
+analysis an ASM totic analysis tells us
+that either we have exponentially
+
+ align:start position:0%
+that either we have exponentially
+ 
+
+ align:start position:0%
+that either we have exponentially
+growing or exponentially shrinking
+
+ align:start position:0%
+growing or exponentially shrinking
+ 
+
+ align:start position:0%
+growing or exponentially shrinking
+Solutions let's pick the exponentially
+
+ align:start position:0%
+Solutions let's pick the exponentially
+ 
+
+ align:start position:0%
+Solutions let's pick the exponentially
+shrinking Solutions so s e is equal to
+
+ align:start position:0%
+shrinking Solutions so s e is equal to
+ 
+
+ align:start position:0%
+shrinking Solutions so s e is equal to
+eus x 2 a^ 2^ 2 times some I don't
+
+ align:start position:0%
+eus x 2 a^ 2^ 2 times some I don't
+ 
+
+ align:start position:0%
+eus x 2 a^ 2^ 2 times some I don't
+remember what Bon called it I'll call it
+
+ align:start position:0%
+remember what Bon called it I'll call it
+ 
+
+ align:start position:0%
+remember what Bon called it I'll call it
+U of X so um so we've extracted because
+
+ align:start position:0%
+U of X so um so we've extracted because
+ 
+
+ align:start position:0%
+U of X so um so we've extracted because
+we know that ASM totically it takes this
+
+ align:start position:0%
+we know that ASM totically it takes this
+ 
+
+ align:start position:0%
+we know that ASM totically it takes this
+form well it could also take the other
+
+ align:start position:0%
+form well it could also take the other
+ 
+
+ align:start position:0%
+form well it could also take the other
+form it could be e to the plus which
+
+ align:start position:0%
+form it could be e to the plus which
+ 
+
+ align:start position:0%
+form it could be e to the plus which
+would be bad not normalizable we've
+
+ align:start position:0%
+would be bad not normalizable we've
+ 
+
+ align:start position:0%
+would be bad not normalizable we've
+extracted that then we write down the
+
+ align:start position:0%
+extracted that then we write down the
+ 
+
+ align:start position:0%
+extracted that then we write down the
+differential equation for U and then we
+
+ align:start position:0%
+differential equation for U and then we
+ 
+
+ align:start position:0%
+differential equation for U and then we
+solve that differential equation by
+
+ align:start position:0%
+solve that differential equation by
+ 
+
+ align:start position:0%
+solve that differential equation by
+series analysis yeah
+
+ align:start position:0%
+series analysis yeah
+ 
+
+ align:start position:0%
+series analysis yeah
+however if this is if I have a second or
+
+ align:start position:0%
+however if this is if I have a second or
+ 
+
+ align:start position:0%
+however if this is if I have a second or
+differential equation for
+
+ align:start position:0%
+differential equation for
+ 
+
+ align:start position:0%
+differential equation for
+fi this change of variables doesn't
+
+ align:start position:0%
+fi this change of variables doesn't
+ 
+
+ align:start position:0%
+fi this change of variables doesn't
+change the fact that it's a second order
+
+ align:start position:0%
+change the fact that it's a second order
+ 
+
+ align:start position:0%
+change the fact that it's a second order
+differential equation for you right
+
+ align:start position:0%
+differential equation for you right
+ 
+
+ align:start position:0%
+differential equation for you right
+there's still two solutions for you one
+
+ align:start position:0%
+there's still two solutions for you one
+ 
+
+ align:start position:0%
+there's still two solutions for you one
+of those Solutions will be the solution
+
+ align:start position:0%
+of those Solutions will be the solution
+ 
+
+ align:start position:0%
+of those Solutions will be the solution
+of the equation that has this ASM totic
+
+ align:start position:0%
+of the equation that has this ASM totic
+ 
+
+ align:start position:0%
+of the equation that has this ASM totic
+form but the other solution will be one
+
+ align:start position:0%
+form but the other solution will be one
+ 
+
+ align:start position:0%
+form but the other solution will be one
+that has an e to the plus x^2 over a^2
+
+ align:start position:0%
+that has an e to the plus x^2 over a^2
+ 
+
+ align:start position:0%
+that has an e to the plus x^2 over a^2
+so that it cancels off this leading
+
+ align:start position:0%
+so that it cancels off this leading
+ 
+
+ align:start position:0%
+so that it cancels off this leading
+factor and gives me the exponentially
+
+ align:start position:0%
+factor and gives me the exponentially
+ 
+
+ align:start position:0%
+factor and gives me the exponentially
+growing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution everyone cool with
+
+ align:start position:0%
+solution everyone cool with
+ 
+
+ align:start position:0%
+solution everyone cool with
+that so in that series analysis there's
+
+ align:start position:0%
+that so in that series analysis there's
+ 
+
+ align:start position:0%
+that so in that series analysis there's
+a sort of a subtle moment where you
+
+ align:start position:0%
+a sort of a subtle moment where you
+ 
+
+ align:start position:0%
+a sort of a subtle moment where you
+impose that you have a the convergent
+
+ align:start position:0%
+impose that you have a the convergent
+ 
+
+ align:start position:0%
+impose that you have a the convergent
+solution so the answer of why did we get
+
+ align:start position:0%
+solution so the answer of why did we get
+ 
+
+ align:start position:0%
+solution so the answer of why did we get
+a first order relation is that we we
+
+ align:start position:0%
+a first order relation is that we we
+ 
+
+ align:start position:0%
+a first order relation is that we we
+very carefully um although it may not
+
+ align:start position:0%
+very carefully um although it may not
+ 
+
+ align:start position:0%
+very carefully um although it may not
+have been totally obvious but um when
+
+ align:start position:0%
+have been totally obvious but um when
+ 
+
+ align:start position:0%
+have been totally obvious but um when
+doing this calculation one carefully
+
+ align:start position:0%
+doing this calculation one carefully
+ 
+
+ align:start position:0%
+doing this calculation one carefully
+chooses the convergent solution that
+
+ align:start position:0%
+chooses the convergent solution that
+ 
+
+ align:start position:0%
+chooses the convergent solution that
+doesn't uh have this this function
+
+ align:start position:0%
+doesn't uh have this this function
+ 
+
+ align:start position:0%
+doesn't uh have this this function
+blowing up so as to overwhelm the
+
+ align:start position:0%
+blowing up so as to overwhelm the
+ 
+
+ align:start position:0%
+blowing up so as to overwhelm the
+envelope did that answer your question
+
+ align:start position:0%
+envelope did that answer your question
+ 
+
+ align:start position:0%
+envelope did that answer your question
+great okay it's a very good question
+
+ align:start position:0%
+great okay it's a very good question
+ 
+
+ align:start position:0%
+great okay it's a very good question
+this is an important subtlety that comes
+
+ align:start position:0%
+this is an important subtlety that comes
+ 
+
+ align:start position:0%
+this is an important subtlety that comes
+up all over the place when you do ASM
+
+ align:start position:0%
+up all over the place when you do ASM
+ 
+
+ align:start position:0%
+up all over the place when you do ASM
+totic analysis um I speak for my heart
+
+ align:start position:0%
+totic analysis um I speak for my heart
+ 
+
+ align:start position:0%
+totic analysis um I speak for my heart
+it it's an important thing the research
+
+ align:start position:0%
+it it's an important thing the research
+ 
+
+ align:start position:0%
+it it's an important thing the research
+that I'm doing right now getting these
+
+ align:start position:0%
+that I'm doing right now getting these
+ 
+
+ align:start position:0%
+that I'm doing right now getting these
+sorts of of uh subtleties right is is it
+
+ align:start position:0%
+sorts of of uh subtleties right is is it
+ 
+
+ align:start position:0%
+sorts of of uh subtleties right is is it
+can be very confusing it's important to
+
+ align:start position:0%
+can be very confusing it's important to
+ 
+
+ align:start position:0%
+can be very confusing it's important to
+think carefully through them so it's a
+
+ align:start position:0%
+think carefully through them so it's a
+ 
+
+ align:start position:0%
+think carefully through them so it's a
+very good question other questions
+
+ align:start position:0%
+very good question other questions
+ 
+
+ align:start position:0%
+very good question other questions
+before we move on
+
+ align:start position:0%
+before we move on
+ 
+
+ align:start position:0%
+before we move on
+okay so um I'm going to erase this
+
+ align:start position:0%
+okay so um I'm going to erase this
+ 
+
+ align:start position:0%
+okay so um I'm going to erase this
+because it's not directly germine but it
+
+ align:start position:0%
+because it's not directly germine but it
+ 
+
+ align:start position:0%
+because it's not directly germine but it
+is great okay so so one of the lessons
+
+ align:start position:0%
+is great okay so so one of the lessons
+ 
+
+ align:start position:0%
+is great okay so so one of the lessons
+of this Brute Force analysis was that we
+
+ align:start position:0%
+of this Brute Force analysis was that we
+ 
+
+ align:start position:0%
+of this Brute Force analysis was that we
+constructed the Spectrum I.E the set of
+
+ align:start position:0%
+constructed the Spectrum I.E the set of
+ 
+
+ align:start position:0%
+constructed the Spectrum I.E the set of
+energy igen values allowed for the
+
+ align:start position:0%
+energy igen values allowed for the
+ 
+
+ align:start position:0%
+energy igen values allowed for the
+harmonic oscillator the quantum Quantum
+
+ align:start position:0%
+harmonic oscillator the quantum Quantum
+ 
+
+ align:start position:0%
+harmonic oscillator the quantum Quantum
+harmonic oscillator and we constructed
+
+ align:start position:0%
+harmonic oscillator and we constructed
+ 
+
+ align:start position:0%
+harmonic oscillator and we constructed
+the wave functions we constructed the
+
+ align:start position:0%
+the wave functions we constructed the
+ 
+
+ align:start position:0%
+the wave functions we constructed the
+wave functions by solving the
+
+ align:start position:0%
+wave functions by solving the
+ 
+
+ align:start position:0%
+wave functions by solving the
+differential equation through ASM totic
+
+ align:start position:0%
+differential equation through ASM totic
+ 
+
+ align:start position:0%
+differential equation through ASM totic
+analysis which gave us the gaussian
+
+ align:start position:0%
+analysis which gave us the gaussian
+ 
+
+ align:start position:0%
+analysis which gave us the gaussian
+envelope and series expansion which gave
+
+ align:start position:0%
+envelope and series expansion which gave
+ 
+
+ align:start position:0%
+envelope and series expansion which gave
+us the
+
+ align:start position:0%
+us the
+ 
+
+ align:start position:0%
+us the
+pooms and then there's some
+
+ align:start position:0%
+pooms and then there's some
+ 
+
+ align:start position:0%
+pooms and then there's some
+normalization
+
+ align:start position:0%
+normalization
+ 
+
+ align:start position:0%
+normalization
+coefficient and then we got the energy
+
+ align:start position:0%
+coefficient and then we got the energy
+ 
+
+ align:start position:0%
+coefficient and then we got the energy
+values by asking when does this series
+
+ align:start position:0%
+values by asking when does this series
+ 
+
+ align:start position:0%
+values by asking when does this series
+expansion converge when does it in fact
+
+ align:start position:0%
+expansion converge when does it in fact
+ 
+
+ align:start position:0%
+expansion converge when does it in fact
+truncate terminate so that we can write
+
+ align:start position:0%
+truncate terminate so that we can write
+ 
+
+ align:start position:0%
+truncate terminate so that we can write
+down an answer um and that was what gave
+
+ align:start position:0%
+down an answer um and that was what gave
+ 
+
+ align:start position:0%
+down an answer um and that was what gave
+us these discrete values but fine we can
+
+ align:start position:0%
+us these discrete values but fine we can
+ 
+
+ align:start position:0%
+us these discrete values but fine we can
+see that it would be discret values
+
+ align:start position:0%
+see that it would be discret values
+ 
+
+ align:start position:0%
+see that it would be discret values
+we're cool with that in fact Barton went
+
+ align:start position:0%
+we're cool with that in fact Barton went
+ 
+
+ align:start position:0%
+we're cool with that in fact Barton went
+through the discussion of the node
+
+ align:start position:0%
+through the discussion of the node
+ 
+
+ align:start position:0%
+through the discussion of the node
+theorem and and the lack of of uh of of
+
+ align:start position:0%
+theorem and and the lack of of uh of of
+ 
+
+ align:start position:0%
+theorem and and the lack of of uh of of
+um degeneracy in one-dimensional quantum
+
+ align:start position:0%
+um degeneracy in one-dimensional quantum
+ 
+
+ align:start position:0%
+um degeneracy in one-dimensional quantum
+mechanics so it's reasonable that we'd
+
+ align:start position:0%
+mechanics so it's reasonable that we'd
+ 
+
+ align:start position:0%
+mechanics so it's reasonable that we'd
+get a bunch of discreet energy igen
+
+ align:start position:0%
+get a bunch of discreet energy igen
+ 
+
+ align:start position:0%
+get a bunch of discreet energy igen
+values as we've talked about now for two
+
+ align:start position:0%
+values as we've talked about now for two
+ 
+
+ align:start position:0%
+values as we've talked about now for two
+lectures however there's a surprise here
+
+ align:start position:0%
+lectures however there's a surprise here
+ 
+
+ align:start position:0%
+lectures however there's a surprise here
+which is that these aren't just discreet
+
+ align:start position:0%
+which is that these aren't just discreet
+ 
+
+ align:start position:0%
+which is that these aren't just discreet
+they're evenly spaced we get a tower
+
+ align:start position:0%
+they're evenly spaced we get a tower
+ 
+
+ align:start position:0%
+they're evenly spaced we get a tower
+starting with the lowest possible energy
+
+ align:start position:0%
+starting with the lowest possible energy
+ 
+
+ align:start position:0%
+starting with the lowest possible energy
+corresponding to a sorry e zero starting
+
+ align:start position:0%
+corresponding to a sorry e zero starting
+ 
+
+ align:start position:0%
+corresponding to a sorry e zero starting
+with the lowest possible energy uh which
+
+ align:start position:0%
+with the lowest possible energy uh which
+ 
+
+ align:start position:0%
+with the lowest possible energy uh which
+is greater than zero uh and a
+
+ align:start position:0%
+is greater than zero uh and a
+ 
+
+ align:start position:0%
+is greater than zero uh and a
+corresponding ground state wave
+
+ align:start position:0%
+corresponding ground state wave
+ 
+
+ align:start position:0%
+corresponding ground state wave
+function and then we have a whole bunch
+
+ align:start position:0%
+function and then we have a whole bunch
+ 
+
+ align:start position:0%
+function and then we have a whole bunch
+of other states F1 f 2 53 54 labeled by
+
+ align:start position:0%
+of other states F1 f 2 53 54 labeled by
+ 
+
+ align:start position:0%
+of other states F1 f 2 53 54 labeled by
+their energies
+
+ align:start position:0%
+their energies
+ 
+
+ align:start position:0%
+their energies
+where the energies are evenly
+
+ align:start position:0%
+where the energies are evenly
+ 
+
+ align:start position:0%
+where the energies are evenly
+spaced yeah they needed to be discreet
+
+ align:start position:0%
+spaced yeah they needed to be discreet
+ 
+
+ align:start position:0%
+spaced yeah they needed to be discreet
+because these are bound
+
+ align:start position:0%
+because these are bound
+ 
+
+ align:start position:0%
+because these are bound
+States but evenly spaced is a surprise
+
+ align:start position:0%
+States but evenly spaced is a surprise
+ 
+
+ align:start position:0%
+States but evenly spaced is a surprise
+so why are they evenly spaced anyone
+
+ align:start position:0%
+so why are they evenly spaced anyone
+ 
+
+ align:start position:0%
+so why are they evenly spaced anyone
+based on last lectures
+
+ align:start position:0%
+based on last lectures
+ 
+
+ align:start position:0%
+based on last lectures
+analysis yeah you don't have a good
+
+ align:start position:0%
+analysis yeah you don't have a good
+ 
+
+ align:start position:0%
+analysis yeah you don't have a good
+answer to that from last lecture's
+
+ align:start position:0%
+answer to that from last lecture's
+ 
+
+ align:start position:0%
+answer to that from last lecture's
+analysis one of the one of the Mysteries
+
+ align:start position:0%
+analysis one of the one of the Mysteries
+ 
+
+ align:start position:0%
+analysis one of the one of the Mysteries
+that comes out of the Brute Force
+
+ align:start position:0%
+that comes out of the Brute Force
+ 
+
+ align:start position:0%
+that comes out of the Brute Force
+analysis when you take a differential
+
+ align:start position:0%
+analysis when you take a differential
+ 
+
+ align:start position:0%
+analysis when you take a differential
+equation you just beat the you know crap
+
+ align:start position:0%
+equation you just beat the you know crap
+ 
+
+ align:start position:0%
+equation you just beat the you know crap
+out of it with a stick by solving it
+
+ align:start position:0%
+out of it with a stick by solving it
+ 
+
+ align:start position:0%
+out of it with a stick by solving it
+with differential equ strategies like
+
+ align:start position:0%
+with differential equ strategies like
+ 
+
+ align:start position:0%
+with differential equ strategies like
+this you don't necessarily get uh some
+
+ align:start position:0%
+this you don't necessarily get uh some
+ 
+
+ align:start position:0%
+this you don't necessarily get uh some
+of the more subtle structure one of the
+
+ align:start position:0%
+of the more subtle structure one of the
+ 
+
+ align:start position:0%
+of the more subtle structure one of the
+goals of today's lecture is going to be
+
+ align:start position:0%
+goals of today's lecture is going to be
+ 
+
+ align:start position:0%
+goals of today's lecture is going to be
+to explain why we get this structure why
+
+ align:start position:0%
+to explain why we get this structure why
+ 
+
+ align:start position:0%
+to explain why we get this structure why
+just from the physics or the problem the
+
+ align:start position:0%
+just from the physics or the problem the
+ 
+
+ align:start position:0%
+just from the physics or the problem the
+underling physics should you know that
+
+ align:start position:0%
+underling physics should you know that
+ 
+
+ align:start position:0%
+underling physics should you know that
+the system is going to have evenly space
+
+ align:start position:0%
+the system is going to have evenly space
+ 
+
+ align:start position:0%
+the system is going to have evenly space
+Dion values what's the structure and
+
+ align:start position:0%
+Dion values what's the structure and
+ 
+
+ align:start position:0%
+Dion values what's the structure and
+secondly I want to show you a way of
+
+ align:start position:0%
+secondly I want to show you a way of
+ 
+
+ align:start position:0%
+secondly I want to show you a way of
+repeating this calculation without doing
+
+ align:start position:0%
+repeating this calculation without doing
+ 
+
+ align:start position:0%
+repeating this calculation without doing
+the Brute Force analysis that reveals
+
+ align:start position:0%
+the Brute Force analysis that reveals
+ 
+
+ align:start position:0%
+the Brute Force analysis that reveals
+some of that more fine grained structure
+
+ align:start position:0%
+some of that more fine grained structure
+ 
+
+ align:start position:0%
+some of that more fine grained structure
+of the problem and this is going to turn
+
+ align:start position:0%
+of the problem and this is going to turn
+ 
+
+ align:start position:0%
+of the problem and this is going to turn
+out to be uh one of the canonical Moves
+
+ align:start position:0%
+out to be uh one of the canonical Moves
+ 
+
+ align:start position:0%
+out to be uh one of the canonical Moves
+In in the analysis of quantum mechanical
+
+ align:start position:0%
+In in the analysis of quantum mechanical
+ 
+
+ align:start position:0%
+In in the analysis of quantum mechanical
+systems so from quantum mechanics to
+
+ align:start position:0%
+systems so from quantum mechanics to
+ 
+
+ align:start position:0%
+systems so from quantum mechanics to
+Quantum field Theory this is a basic
+
+ align:start position:0%
+Quantum field Theory this is a basic
+ 
+
+ align:start position:0%
+Quantum field Theory this is a basic
+series of of logical moves um what I'm
+
+ align:start position:0%
+series of of logical moves um what I'm
+ 
+
+ align:start position:0%
+series of of logical moves um what I'm
+going to do today also has uh an
+
+ align:start position:0%
+going to do today also has uh an
+ 
+
+ align:start position:0%
+going to do today also has uh an
+independent life in mathematics um uh in
+
+ align:start position:0%
+independent life in mathematics um uh in
+ 
+
+ align:start position:0%
+independent life in mathematics um uh in
+algebra uh and that will be something
+
+ align:start position:0%
+algebra uh and that will be something
+ 
+
+ align:start position:0%
+algebra uh and that will be something
+you'll study in more detail on 805 but I
+
+ align:start position:0%
+you'll study in more detail on 805 but I
+ 
+
+ align:start position:0%
+you'll study in more detail on 805 but I
+would encourage you to ask your
+
+ align:start position:0%
+would encourage you to ask your
+ 
+
+ align:start position:0%
+would encourage you to ask your
+recitation instructors uh about it or me
+
+ align:start position:0%
+recitation instructors uh about it or me
+ 
+
+ align:start position:0%
+recitation instructors uh about it or me
+in office hours
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so our goal is to understand that
+
+ align:start position:0%
+okay so our goal is to understand that
+ 
+
+ align:start position:0%
+okay so our goal is to understand that
+even spacing
+
+ align:start position:0%
+even spacing
+ 
+
+ align:start position:0%
+even spacing
+and also to rederive these results
+
+ align:start position:0%
+and also to rederive these results
+ 
+
+ align:start position:0%
+and also to rederive these results
+without the sort of
+
+ align:start position:0%
+without the sort of
+ 
+
+ align:start position:0%
+without the sort of
+brutal uh direct assault methods we used
+
+ align:start position:0%
+brutal uh direct assault methods we used
+ 
+
+ align:start position:0%
+brutal uh direct assault methods we used
+last time so what I'm going to tell you
+
+ align:start position:0%
+last time so what I'm going to tell you
+ 
+
+ align:start position:0%
+last time so what I'm going to tell you
+about today is something called the
+
+ align:start position:0%
+about today is something called the
+ 
+
+ align:start position:0%
+about today is something called the
+operator method it usually goes under
+
+ align:start position:0%
+operator method it usually goes under
+ 
+
+ align:start position:0%
+operator method it usually goes under
+the name of the operator method
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so to get us started let's go back to
+
+ align:start position:0%
+so to get us started let's go back to
+ 
+
+ align:start position:0%
+so to get us started let's go back to
+look at the energy operator for um for
+
+ align:start position:0%
+look at the energy operator for um for
+ 
+
+ align:start position:0%
+look at the energy operator for um for
+the harmonic oor which is what at the
+
+ align:start position:0%
+the harmonic oor which is what at the
+ 
+
+ align:start position:0%
+the harmonic oor which is what at the
+end of the day we want to
+
+ align:start position:0%
+end of the day we want to
+ 
+
+ align:start position:0%
+end of the day we want to
+solve 2 M plus M Omega 2 upon 2
+
+ align:start position:0%
+solve 2 M plus M Omega 2 upon 2
+ 
+
+ align:start position:0%
+solve 2 M plus M Omega 2 upon 2
+x^2 right and this is the operator that
+
+ align:start position:0%
+x^2 right and this is the operator that
+ 
+
+ align:start position:0%
+x^2 right and this is the operator that
+we want to whose Z values we want to
+
+ align:start position:0%
+we want to whose Z values we want to
+ 
+
+ align:start position:0%
+we want to whose Z values we want to
+construct whose Z functions we want to
+
+ align:start position:0%
+construct whose Z functions we want to
+ 
+
+ align:start position:0%
+construct whose Z functions we want to
+construct before we do anything else we
+
+ align:start position:0%
+construct before we do anything else we
+ 
+
+ align:start position:0%
+construct before we do anything else we
+should do dimensional analysis first
+
+ align:start position:0%
+should do dimensional analysis first
+ 
+
+ align:start position:0%
+should do dimensional analysis first
+thing you do when you look at a problem
+
+ align:start position:0%
+thing you do when you look at a problem
+ 
+
+ align:start position:0%
+thing you do when you look at a problem
+is do some dimensional analysis identify
+
+ align:start position:0%
+is do some dimensional analysis identify
+ 
+
+ align:start position:0%
+is do some dimensional analysis identify
+the s scales and make things to the
+
+ align:start position:0%
+the s scales and make things to the
+ 
+
+ align:start position:0%
+the s scales and make things to the
+degree possible dimensionless your life
+
+ align:start position:0%
+degree possible dimensionless your life
+ 
+
+ align:start position:0%
+degree possible dimensionless your life
+will be better so what are the
+
+ align:start position:0%
+will be better so what are the
+ 
+
+ align:start position:0%
+will be better so what are the
+parameters we have available to us we
+
+ align:start position:0%
+parameters we have available to us we
+ 
+
+ align:start position:0%
+parameters we have available to us we
+have uh H because it's quantum mechanics
+
+ align:start position:0%
+have uh H because it's quantum mechanics
+ 
+
+ align:start position:0%
+have uh H because it's quantum mechanics
+we have M because we have a particle of
+
+ align:start position:0%
+we have M because we have a particle of
+ 
+
+ align:start position:0%
+we have M because we have a particle of
+mass m we have omega because this
+
+ align:start position:0%
+mass m we have omega because this
+ 
+
+ align:start position:0%
+mass m we have omega because this
+potential has a characteristic frequency
+
+ align:start position:0%
+potential has a characteristic frequency
+ 
+
+ align:start position:0%
+potential has a characteristic frequency
+Omega what other parameters do we have
+
+ align:start position:0%
+Omega what other parameters do we have
+ 
+
+ align:start position:0%
+Omega what other parameters do we have
+available to us well we have C that's
+
+ align:start position:0%
+available to us well we have C that's
+ 
+
+ align:start position:0%
+available to us well we have C that's
+available to us but is it
+
+ align:start position:0%
+available to us but is it
+ 
+
+ align:start position:0%
+available to us but is it
+relevant No it should no if you get an
+
+ align:start position:0%
+relevant No it should no if you get an
+ 
+
+ align:start position:0%
+relevant No it should no if you get an
+answer that depends on the speed of
+
+ align:start position:0%
+answer that depends on the speed of
+ 
+
+ align:start position:0%
+answer that depends on the speed of
+light you've made some horrible mistake
+
+ align:start position:0%
+light you've made some horrible mistake
+ 
+
+ align:start position:0%
+light you've made some horrible mistake
+right so not there what about the number
+
+ align:start position:0%
+right so not there what about the number
+ 
+
+ align:start position:0%
+right so not there what about the number
+of students in 804
+
+ align:start position:0%
+of students in 804
+ 
+
+ align:start position:0%
+of students in 804
+no there are an infinite number of
+
+ align:start position:0%
+no there are an infinite number of
+ 
+
+ align:start position:0%
+no there are an infinite number of
+parameters that don't matter to this
+
+ align:start position:0%
+parameters that don't matter to this
+ 
+
+ align:start position:0%
+parameters that don't matter to this
+problem what you want to know is when
+
+ align:start position:0%
+problem what you want to know is when
+ 
+
+ align:start position:0%
+problem what you want to know is when
+you do dimensional analysis what
+
+ align:start position:0%
+you do dimensional analysis what
+ 
+
+ align:start position:0%
+you do dimensional analysis what
+parameters matter for the problem what
+
+ align:start position:0%
+parameters matter for the problem what
+ 
+
+ align:start position:0%
+parameters matter for the problem what
+parameters could possibly appear in the
+
+ align:start position:0%
+parameters could possibly appear in the
+ 
+
+ align:start position:0%
+parameters could possibly appear in the
+answer and that's it there are no other
+
+ align:start position:0%
+answer and that's it there are no other
+ 
+
+ align:start position:0%
+answer and that's it there are no other
+parameters in this
+
+ align:start position:0%
+parameters in this
+ 
+
+ align:start position:0%
+parameters in this
+problem yeah so that's the full set of
+
+ align:start position:0%
+problem yeah so that's the full set of
+ 
+
+ align:start position:0%
+problem yeah so that's the full set of
+parameters available to us this has
+
+ align:start position:0%
+parameters available to us this has
+ 
+
+ align:start position:0%
+parameters available to us this has
+dimensions of momentum times length this
+
+ align:start position:0%
+dimensions of momentum times length this
+ 
+
+ align:start position:0%
+dimensions of momentum times length this
+has momentum dimensions of mass and this
+
+ align:start position:0%
+has momentum dimensions of mass and this
+ 
+
+ align:start position:0%
+has momentum dimensions of mass and this
+has dimensions of one Upon a Time and so
+
+ align:start position:0%
+has dimensions of one Upon a Time and so
+ 
+
+ align:start position:0%
+has dimensions of one Upon a Time and so
+what characteristic scales can we build
+
+ align:start position:0%
+what characteristic scales can we build
+ 
+
+ align:start position:0%
+what characteristic scales can we build
+using these three parameters well
+
+ align:start position:0%
+using these three parameters well
+ 
+
+ align:start position:0%
+using these three parameters well
+this is a momentum times a a length if
+
+ align:start position:0%
+this is a momentum times a a length if
+ 
+
+ align:start position:0%
+this is a momentum times a a length if
+we multiply by a mass that's momentum
+
+ align:start position:0%
+we multiply by a mass that's momentum
+ 
+
+ align:start position:0%
+we multiply by a mass that's momentum
+time mass time x which is almost
+
+ align:start position:0%
+time mass time x which is almost
+ 
+
+ align:start position:0%
+time mass time x which is almost
+momentum again we need a velocity not a
+
+ align:start position:0%
+momentum again we need a velocity not a
+ 
+
+ align:start position:0%
+momentum again we need a velocity not a
+position but we have one over time so if
+
+ align:start position:0%
+position but we have one over time so if
+ 
+
+ align:start position:0%
+position but we have one over time so if
+we take H bar time M
+
+ align:start position:0%
+we take H bar time M
+ 
+
+ align:start position:0%
+we take H bar time M
+Omega so that's PX * m/ T that has units
+
+ align:start position:0%
+Omega so that's PX * m/ T that has units
+ 
+
+ align:start position:0%
+Omega so that's PX * m/ T that has units
+of momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared okay and similarly this is
+
+ align:start position:0%
+squared okay and similarly this is
+ 
+
+ align:start position:0%
+squared okay and similarly this is
+momentum which is X which is length mass
+
+ align:start position:0%
+momentum which is X which is length mass
+ 
+
+ align:start position:0%
+momentum which is X which is length mass
+over time I can divide by mass divide by
+
+ align:start position:0%
+over time I can divide by mass divide by
+ 
+
+ align:start position:0%
+over time I can divide by mass divide by
+frequency or multiply by time so H bar
+
+ align:start position:0%
+frequency or multiply by time so H bar
+ 
+
+ align:start position:0%
+frequency or multiply by time so H bar
+upon M
+
+ align:start position:0%
+upon M
+ 
+
+ align:start position:0%
+upon M
+Omega uh and this is going to have units
+
+ align:start position:0%
+Omega uh and this is going to have units
+ 
+
+ align:start position:0%
+Omega uh and this is going to have units
+of length
+
+ align:start position:0%
+of length
+ 
+
+ align:start position:0%
+of length
+squared okay and with a little bit of
+
+ align:start position:0%
+squared okay and with a little bit of
+ 
+
+ align:start position:0%
+squared okay and with a little bit of
+foresight from factors of two I'm going
+
+ align:start position:0%
+foresight from factors of two I'm going
+ 
+
+ align:start position:0%
+foresight from factors of two I'm going
+to Define we use these to Define two
+
+ align:start position:0%
+to Define we use these to Define two
+ 
+
+ align:start position:0%
+to Define we use these to Define two
+length scales X knot is equal to uh H
+
+ align:start position:0%
+length scales X knot is equal to uh H
+ 
+
+ align:start position:0%
+length scales X knot is equal to uh H
+bar oh I want to be careful to get my
+
+ align:start position:0%
+bar oh I want to be careful to get my
+ 
+
+ align:start position:0%
+bar oh I want to be careful to get my
+coefficients yeah I always put the two
+
+ align:start position:0%
+coefficients yeah I always put the two
+ 
+
+ align:start position:0%
+coefficients yeah I always put the two
+in the wrong place so 2 H bar upon M
+
+ align:start position:0%
+in the wrong place so 2 H bar upon M
+ 
+
+ align:start position:0%
+in the wrong place so 2 H bar upon M
+Omega square root and I'm going to
+
+ align:start position:0%
+Omega square root and I'm going to
+ 
+
+ align:start position:0%
+Omega square root and I'm going to
+Define
+
+ align:start position:0%
+Define
+ 
+
+ align:start position:0%
+Define
+p is equal to squ < TK of 2 H time M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Omega okay so here's my claim my claim
+
+ align:start position:0%
+Omega okay so here's my claim my claim
+ 
+
+ align:start position:0%
+Omega okay so here's my claim my claim
+is at the end of the day the Salient
+
+ align:start position:0%
+is at the end of the day the Salient
+ 
+
+ align:start position:0%
+is at the end of the day the Salient
+length scales for this problem should be
+
+ align:start position:0%
+length scales for this problem should be
+ 
+
+ align:start position:0%
+length scales for this problem should be
+integers or dimensionless numbers times
+
+ align:start position:0%
+integers or dimensionless numbers times
+ 
+
+ align:start position:0%
+integers or dimensionless numbers times
+this length scale and saling momentum
+
+ align:start position:0%
+this length scale and saling momentum
+ 
+
+ align:start position:0%
+this length scale and saling momentum
+scale should be this scale okay just
+
+ align:start position:0%
+scale should be this scale okay just
+ 
+
+ align:start position:0%
+scale should be this scale okay just
+from dimensional analysis so if someone
+
+ align:start position:0%
+from dimensional analysis so if someone
+ 
+
+ align:start position:0%
+from dimensional analysis so if someone
+at this point says what do you think is
+
+ align:start position:0%
+at this point says what do you think is
+ 
+
+ align:start position:0%
+at this point says what do you think is
+the typical scale what is the typical
+
+ align:start position:0%
+the typical scale what is the typical
+ 
+
+ align:start position:0%
+the typical scale what is the typical
+size uh of the ground state wave
+
+ align:start position:0%
+size uh of the ground state wave
+ 
+
+ align:start position:0%
+size uh of the ground state wave
+function the typical um length scale
+
+ align:start position:0%
+function the typical um length scale
+ 
+
+ align:start position:0%
+function the typical um length scale
+over which the wave function is not
+
+ align:start position:0%
+over which the wave function is not
+ 
+
+ align:start position:0%
+over which the wave function is not
+zero well that can't possibly be the
+
+ align:start position:0%
+zero well that can't possibly be the
+ 
+
+ align:start position:0%
+zero well that can't possibly be the
+size of manhan it's not the signs of a
+
+ align:start position:0%
+size of manhan it's not the signs of a
+ 
+
+ align:start position:0%
+size of manhan it's not the signs of a
+proton there's only one link scale s to
+
+ align:start position:0%
+proton there's only one link scale s to
+ 
+
+ align:start position:0%
+proton there's only one link scale s to
+the system it should be of Order X knot
+
+ align:start position:0%
+the system it should be of Order X knot
+ 
+
+ align:start position:0%
+the system it should be of Order X knot
+always start with dimensional analysis
+
+ align:start position:0%
+always start with dimensional analysis
+ 
+
+ align:start position:0%
+always start with dimensional analysis
+always okay so with that we can rewrite
+
+ align:start position:0%
+always okay so with that we can rewrite
+ 
+
+ align:start position:0%
+always okay so with that we can rewrite
+this energy oh sorry and there's one
+
+ align:start position:0%
+this energy oh sorry and there's one
+ 
+
+ align:start position:0%
+this energy oh sorry and there's one
+last energy uh we we can write an
+
+ align:start position:0%
+last energy uh we we can write an
+ 
+
+ align:start position:0%
+last energy uh we we can write an
+energy thing with energy um which is
+
+ align:start position:0%
+energy thing with energy um which is
+ 
+
+ align:start position:0%
+energy thing with energy um which is
+equal to H Omega an this times times uh
+
+ align:start position:0%
+equal to H Omega an this times times uh
+ 
+
+ align:start position:0%
+equal to H Omega an this times times uh
+a frequency gives us um uh an
+
+ align:start position:0%
+a frequency gives us um uh an
+ 
+
+ align:start position:0%
+a frequency gives us um uh an
+energy okay
+
+ align:start position:0%
+energy okay
+ 
+
+ align:start position:0%
+energy okay
+so we can rewrite this this energy
+
+ align:start position:0%
+so we can rewrite this this energy
+ 
+
+ align:start position:0%
+so we can rewrite this this energy
+operator as H Omega
+
+ align:start position:0%
+operator as H Omega
+ 
+
+ align:start position:0%
+operator as H Omega
+times p^2 over P so this has units of
+
+ align:start position:0%
+times p^2 over P so this has units of
+ 
+
+ align:start position:0%
+times p^2 over P so this has units of
+energy so everything in here must be
+
+ align:start position:0%
+energy so everything in here must be
+ 
+
+ align:start position:0%
+energy so everything in here must be
+dimensionless and it turns out to be p^2
+
+ align:start position:0%
+dimensionless and it turns out to be p^2
+ 
+
+ align:start position:0%
+dimensionless and it turns out to be p^2
+over p^ S Plus X operator squar over x^
+
+ align:start position:0%
+over p^ S Plus X operator squar over x^
+ 
+
+ align:start position:0%
+over p^ S Plus X operator squar over x^
+squ so that that's
+
+ align:start position:0%
+squ so that that's
+ 
+
+ align:start position:0%
+squ so that that's
+convenient so this has nothing to do
+
+ align:start position:0%
+convenient so this has nothing to do
+ 
+
+ align:start position:0%
+convenient so this has nothing to do
+with the operator method this is just
+
+ align:start position:0%
+with the operator method this is just
+ 
+
+ align:start position:0%
+with the operator method this is just
+being
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reasonable
+
+ align:start position:0%
+reasonable
+ 
+
+ align:start position:0%
+reasonable
+okay quick note thing to note uh X knot
+
+ align:start position:0%
+okay quick note thing to note uh X knot
+ 
+
+ align:start position:0%
+okay quick note thing to note uh X knot
+time P
+
+ align:start position:0%
+time P
+ 
+
+ align:start position:0%
+time P
+KN is just the M omegas cancel so we get
+
+ align:start position:0%
+KN is just the M omegas cancel so we get
+ 
+
+ align:start position:0%
+KN is just the M omegas cancel so we get
+< tk2 H bar s to H bar okay
+
+ align:start position:0%
+< tk2 H bar s to H bar okay
+ 
+
+ align:start position:0%
+< tk2 H bar s to H bar okay
+so little tricks like that are useful to
+
+ align:start position:0%
+so little tricks like that are useful to
+ 
+
+ align:start position:0%
+so little tricks like that are useful to
+keep track of as you go
+
+ align:start position:0%
+keep track of as you go
+ 
+
+ align:start position:0%
+keep track of as you go
+okay so we're interested in this
+
+ align:start position:0%
+okay so we're interested in this
+ 
+
+ align:start position:0%
+okay so we're interested in this
+operator we're interested in this energy
+
+ align:start position:0%
+operator we're interested in this energy
+ 
+
+ align:start position:0%
+operator we're interested in this energy
+operator and it has a nice form it's a
+
+ align:start position:0%
+operator and it has a nice form it's a
+ 
+
+ align:start position:0%
+operator and it has a nice form it's a
+sum of squares and when you see the sum
+
+ align:start position:0%
+sum of squares and when you see the sum
+ 
+
+ align:start position:0%
+sum of squares and when you see the sum
+of squares a very tempting thing to do
+
+ align:start position:0%
+of squares a very tempting thing to do
+ 
+
+ align:start position:0%
+of squares a very tempting thing to do
+is to factor it so for example if I have
+
+ align:start position:0%
+is to factor it so for example if I have
+ 
+
+ align:start position:0%
+is to factor it so for example if I have
+two classical numbers c^2 plus
+
+ align:start position:0%
+two classical numbers c^2 plus
+ 
+
+ align:start position:0%
+two classical numbers c^2 plus
+d^2 the mathematician in me screams out
+
+ align:start position:0%
+d^2 the mathematician in me screams out
+ 
+
+ align:start position:0%
+d^2 the mathematician in me screams out
+to write C minus ID time C plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ID I have factored this and that's
+
+ align:start position:0%
+ID I have factored this and that's
+ 
+
+ align:start position:0%
+ID I have factored this and that's
+usually a step in the right direction
+
+ align:start position:0%
+usually a step in the right direction
+ 
+
+ align:start position:0%
+usually a step in the right direction
+and is this true well yes it's true c^2
+
+ align:start position:0%
+and is this true well yes it's true c^2
+ 
+
+ align:start position:0%
+and is this true well yes it's true c^2
+plus d^2 and the cross terms cancel okay
+
+ align:start position:0%
+plus d^2 and the cross terms cancel okay
+ 
+
+ align:start position:0%
+plus d^2 and the cross terms cancel okay
+that's great four complex numbers or
+
+ align:start position:0%
+that's great four complex numbers or
+ 
+
+ align:start position:0%
+that's great four complex numbers or
+four C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers now is this true for operators
+
+ align:start position:0%
+numbers now is this true for operators
+ 
+
+ align:start position:0%
+numbers now is this true for operators
+can I do this for operators here we have
+
+ align:start position:0%
+can I do this for operators here we have
+ 
+
+ align:start position:0%
+can I do this for operators here we have
+the energy operator as a sum of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squares well let's try
+
+ align:start position:0%
+squares well let's try
+ 
+
+ align:start position:0%
+squares well let's try
+it I'd like to write that in terms of X
+
+ align:start position:0%
+it I'd like to write that in terms of X
+ 
+
+ align:start position:0%
+it I'd like to write that in terms of X
+and P so what about WR
+
+ align:start position:0%
+and P so what about WR
+ 
+
+ align:start position:0%
+and P so what about WR
+is um is so what about writing the
+
+ align:start position:0%
+is um is so what about writing the
+ 
+
+ align:start position:0%
+is um is so what about writing the
+quantity um x minus i p over X over
+
+ align:start position:0%
+quantity um x minus i p over X over
+ 
+
+ align:start position:0%
+quantity um x minus i p over X over
+P operator time X over X Plus IP over P
+
+ align:start position:0%
+P operator time X over X Plus IP over P
+ 
+
+ align:start position:0%
+P operator time X over X Plus IP over P
+KN okay so we can compute this this is
+
+ align:start position:0%
+KN okay so we can compute this this is
+ 
+
+ align:start position:0%
+KN okay so we can compute this this is
+easy so the first term gives us the X
+
+ align:start position:0%
+easy so the first term gives us the X
+ 
+
+ align:start position:0%
+easy so the first term gives us the X
+squ over x^
+
+ align:start position:0%
+squ over x^
+ 
+
+ align:start position:0%
+squ over x^
+squ that last term gives us the I's
+
+ align:start position:0%
+squ that last term gives us the I's
+ 
+
+ align:start position:0%
+squ that last term gives us the I's
+cancel we get p squ over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P Squared but then there are cross terms
+
+ align:start position:0%
+P Squared but then there are cross terms
+ 
+
+ align:start position:0%
+P Squared but then there are cross terms
+we have an x p and an minus PX with an
+
+ align:start position:0%
+we have an x p and an minus PX with an
+ 
+
+ align:start position:0%
+we have an x p and an minus PX with an
+overall I so plus I * x
+
+ align:start position:0%
+overall I so plus I * x
+ 
+
+ align:start position:0%
+overall I so plus I * x
+p uh over x * P so x * P however is 2 H
+
+ align:start position:0%
+p uh over x * P so x * P however is 2 H
+ 
+
+ align:start position:0%
+p uh over x * P so x * P however is 2 H
+bar so that's over 2 H
+
+ align:start position:0%
+bar so that's over 2 H
+ 
+
+ align:start position:0%
+bar so that's over 2 H
+bar okay and then we have the other term
+
+ align:start position:0%
+bar okay and then we have the other term
+ 
+
+ align:start position:0%
+bar okay and then we have the other term
+minus PX same thing so I can write that
+
+ align:start position:0%
+minus PX same thing so I can write that
+ 
+
+ align:start position:0%
+minus PX same thing so I can write that
+as the commutator XP
+
+ align:start position:0%
+as the commutator XP
+ 
+
+ align:start position:0%
+as the commutator XP
+minus PX everyone cool with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that unfortunately this is not what we
+
+ align:start position:0%
+that unfortunately this is not what we
+ 
+
+ align:start position:0%
+that unfortunately this is not what we
+wanted we wanted just p^2 plus x^2 and
+
+ align:start position:0%
+wanted we wanted just p^2 plus x^2 and
+ 
+
+ align:start position:0%
+wanted we wanted just p^2 plus x^2 and
+what we got instead was P S Plus x s
+
+ align:start position:0%
+what we got instead was P S Plus x s
+ 
+
+ align:start position:0%
+what we got instead was P S Plus x s
+close plus a commutator happily this
+
+ align:start position:0%
+close plus a commutator happily this
+ 
+
+ align:start position:0%
+close plus a commutator happily this
+commutator is simple what's the
+
+ align:start position:0%
+commutator is simple what's the
+ 
+
+ align:start position:0%
+commutator is simple what's the
+commutator of X with P yeah exactly
+
+ align:start position:0%
+commutator of X with P yeah exactly
+ 
+
+ align:start position:0%
+commutator of X with P yeah exactly
+Commit This to Memory okay this is this
+
+ align:start position:0%
+Commit This to Memory okay this is this
+ 
+
+ align:start position:0%
+Commit This to Memory okay this is this
+is your
+
+ align:start position:0%
+is your
+ 
+
+ align:start position:0%
+is your
+friend okay so this is just IH bar so
+
+ align:start position:0%
+friend okay so this is just IH bar so
+ 
+
+ align:start position:0%
+friend okay so this is just IH bar so
+this is equal to ditto plus ditto Plus
+
+ align:start position:0%
+this is equal to ditto plus ditto Plus
+ 
+
+ align:start position:0%
+this is equal to ditto plus ditto Plus
+ihar
+
+ align:start position:0%
+ihar
+ 
+
+ align:start position:0%
+ihar
+the I whoops uh somewhere I got a minus
+
+ align:start position:0%
+the I whoops uh somewhere I got a minus
+ 
+
+ align:start position:0%
+the I whoops uh somewhere I got a minus
+sign where did I get my minus sign wrong
+
+ align:start position:0%
+sign where did I get my minus sign wrong
+ 
+
+ align:start position:0%
+sign where did I get my minus sign wrong
+x with
+
+ align:start position:0%
+x with
+ 
+
+ align:start position:0%
+x with
+IP oh no good this is good okay so x
+
+ align:start position:0%
+IP oh no good this is good okay so x
+ 
+
+ align:start position:0%
+IP oh no good this is good okay so x
+with p is I so we get an IH bar no no I
+
+ align:start position:0%
+with p is I so we get an IH bar no no I
+ 
+
+ align:start position:0%
+with p is I so we get an IH bar no no I
+really did screw up the sign how did I
+
+ align:start position:0%
+really did screw up the sign how did I
+ 
+
+ align:start position:0%
+really did screw up the sign how did I
+screw up the
+
+ align:start position:0%
+screw up the
+ 
+
+ align:start position:0%
+screw up the
+sign oh no I
+
+ align:start position:0%
+sign oh no I
+ 
+
+ align:start position:0%
+sign oh no I
+didn't wait oh of course no no no good
+
+ align:start position:0%
+didn't wait oh of course no no no good
+ 
+
+ align:start position:0%
+didn't wait oh of course no no no good
+good good good sorry sorry trust your
+
+ align:start position:0%
+good good good sorry sorry trust your
+ 
+
+ align:start position:0%
+good good good sorry sorry trust your
+calculation not your memory okay so the
+
+ align:start position:0%
+calculation not your memory okay so the
+ 
+
+ align:start position:0%
+calculation not your memory okay so the
+calculation gave us this so what does
+
+ align:start position:0%
+calculation gave us this so what does
+ 
+
+ align:start position:0%
+calculation gave us this so what does
+this give us we give us IH bar so plus
+
+ align:start position:0%
+this give us we give us IH bar so plus
+ 
+
+ align:start position:0%
+this give us we give us IH bar so plus
+but the I bar * I is going to give me a
+
+ align:start position:0%
+but the I bar * I is going to give me a
+ 
+
+ align:start position:0%
+but the I bar * I is going to give me a
+minus and the H bar is going to cancel
+
+ align:start position:0%
+minus and the H bar is going to cancel
+ 
+
+ align:start position:0%
+minus and the H bar is going to cancel
+because I've got an H bar from here and
+
+ align:start position:0%
+because I've got an H bar from here and
+ 
+
+ align:start position:0%
+because I've got an H bar from here and
+an H bar in the denominator minus
+
+ align:start position:0%
+an H bar in the denominator minus
+ 
+
+ align:start position:0%
+an H bar in the denominator minus
+12 so this quantity is equal to the
+
+ align:start position:0%
+12 so this quantity is equal to the
+ 
+
+ align:start position:0%
+12 so this quantity is equal to the
+quantity we wanted minus
+
+ align:start position:0%
+quantity we wanted minus
+ 
+
+ align:start position:0%
+quantity we wanted minus
+12 and what is the quantity we wanted X
+
+ align:start position:0%
+12 and what is the quantity we wanted X
+ 
+
+ align:start position:0%
+12 and what is the quantity we wanted X
+squ plus p^
+
+ align:start position:0%
+squ plus p^
+ 
+
+ align:start position:0%
+squ plus p^
+squ this
+
+ align:start position:0%
+squ this
+ 
+
+ align:start position:0%
+squ this
+guy so putting that all together we can
+
+ align:start position:0%
+guy so putting that all together we can
+ 
+
+ align:start position:0%
+guy so putting that all together we can
+write that the energy
+
+ align:start position:0%
+write that the energy
+ 
+
+ align:start position:0%
+write that the energy
+operator which was equal to um uh H bar
+
+ align:start position:0%
+operator which was equal to um uh H bar
+ 
+
+ align:start position:0%
+operator which was equal to um uh H bar
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+times the quantity we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wanted right is equal to well the
+
+ align:start position:0%
+wanted right is equal to well the
+ 
+
+ align:start position:0%
+wanted right is equal to well the
+quantity we wanted is this quantity plus
+
+ align:start position:0%
+quantity we wanted is this quantity plus
+ 
+
+ align:start position:0%
+quantity we wanted is this quantity plus
+12 H bar Omega times um I'll write this
+
+ align:start position:0%
+12 H bar Omega times um I'll write this
+ 
+
+ align:start position:0%
+12 H bar Omega times um I'll write this
+as uh X over X Plus i p over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p x over X oops over xot minus uh Plus i
+
+ align:start position:0%
+p x over X oops over xot minus uh Plus i
+ 
+
+ align:start position:0%
+p x over X oops over xot minus uh Plus i
+p over
+
+ align:start position:0%
+p over
+ 
+
+ align:start position:0%
+p over
+P hat hat hat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus2 every go with that so it almost
+
+ align:start position:0%
+plus2 every go with that so it almost
+ 
+
+ align:start position:0%
+plus2 every go with that so it almost
+worked we can almost
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Factor so at this point it's tempting to
+
+ align:start position:0%
+Factor so at this point it's tempting to
+ 
+
+ align:start position:0%
+Factor so at this point it's tempting to
+say well that isn't really much an
+
+ align:start position:0%
+say well that isn't really much an
+ 
+
+ align:start position:0%
+say well that isn't really much an
+improvement you've just made it uglier
+
+ align:start position:0%
+improvement you've just made it uglier
+ 
+
+ align:start position:0%
+improvement you've just made it uglier
+but consider the
+
+ align:start position:0%
+but consider the
+ 
+
+ align:start position:0%
+but consider the
+following and just trust me on this one
+
+ align:start position:0%
+following and just trust me on this one
+ 
+
+ align:start position:0%
+following and just trust me on this one
+that this is not a stupid thing to do
+
+ align:start position:0%
+that this is not a stupid thing to do
+ 
+
+ align:start position:0%
+that this is not a stupid thing to do
+oops that's a stupid symbol to write
+
+ align:start position:0%
+oops that's a stupid symbol to write
+ 
+
+ align:start position:0%
+oops that's a stupid symbol to write
+though so let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+define an operator called a which is
+
+ align:start position:0%
+define an operator called a which is
+ 
+
+ align:start position:0%
+define an operator called a which is
+equal to X over
+
+ align:start position:0%
+equal to X over
+ 
+
+ align:start position:0%
+equal to X over
+xot uh plus I P over
+
+ align:start position:0%
+xot uh plus I P over
+ 
+
+ align:start position:0%
+xot uh plus I P over
+p and an operator which I will call a
+
+ align:start position:0%
+p and an operator which I will call a
+ 
+
+ align:start position:0%
+p and an operator which I will call a
+dagger is that a dagger I see before me
+
+ align:start position:0%
+dagger is that a dagger I see before me
+ 
+
+ align:start position:0%
+dagger is that a dagger I see before me
+um X sorry over x minus i p over P KN um
+
+ align:start position:0%
+um X sorry over x minus i p over P KN um
+ 
+
+ align:start position:0%
+um X sorry over x minus i p over P KN um
+uh Hamlet quotes are harder um
+
+ align:start position:0%
+uh Hamlet quotes are harder um
+ 
+
+ align:start position:0%
+uh Hamlet quotes are harder um
+so this is a dagger um and we can now
+
+ align:start position:0%
+so this is a dagger um and we can now
+ 
+
+ align:start position:0%
+so this is a dagger um and we can now
+write the energy operator for the
+
+ align:start position:0%
+write the energy operator for the
+ 
+
+ align:start position:0%
+write the energy operator for the
+harmonic oscillator is equal to H Omega
+
+ align:start position:0%
+harmonic oscillator is equal to H Omega
+ 
+
+ align:start position:0%
+harmonic oscillator is equal to H Omega
+time a dagger
+
+ align:start position:0%
+time a dagger
+ 
+
+ align:start position:0%
+time a dagger
+a plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+12 everyone cool with
+
+ align:start position:0%
+12 everyone cool with
+ 
+
+ align:start position:0%
+12 everyone cool with
+that now this should look suggestive you
+
+ align:start position:0%
+that now this should look suggestive you
+ 
+
+ align:start position:0%
+that now this should look suggestive you
+should say aha this looks like each part
+
+ align:start position:0%
+should say aha this looks like each part
+ 
+
+ align:start position:0%
+should say aha this looks like each part
+mea something plus2 that sure looks
+
+ align:start position:0%
+mea something plus2 that sure looks
+ 
+
+ align:start position:0%
+mea something plus2 that sure looks
+familiar from our Brute Force
+
+ align:start position:0%
+familiar from our Brute Force
+ 
+
+ align:start position:0%
+familiar from our Brute Force
+calculation but okay that familiar it is
+
+ align:start position:0%
+calculation but okay that familiar it is
+ 
+
+ align:start position:0%
+calculation but okay that familiar it is
+not an answer to the question uh
+
+ align:start position:0%
+not an answer to the question uh
+ 
+
+ align:start position:0%
+not an answer to the question uh
+meanwhile you should say something like
+
+ align:start position:0%
+meanwhile you should say something like
+ 
+
+ align:start position:0%
+meanwhile you should say something like
+this look this looks kind of like the
+
+ align:start position:0%
+this look this looks kind of like the
+ 
+
+ align:start position:0%
+this look this looks kind of like the
+complex conjugate of this guy right
+
+ align:start position:0%
+complex conjugate of this guy right
+ 
+
+ align:start position:0%
+complex conjugate of this guy right
+because we you know there's an i and you
+
+ align:start position:0%
+because we you know there's an i and you
+ 
+
+ align:start position:0%
+because we you know there's an i and you
+change a sign of the I but what is a
+
+ align:start position:0%
+change a sign of the I but what is a
+ 
+
+ align:start position:0%
+change a sign of the I but what is a
+complex conjugate of an operator what
+
+ align:start position:0%
+complex conjugate of an operator what
+ 
+
+ align:start position:0%
+complex conjugate of an operator what
+does that
+
+ align:start position:0%
+does that
+ 
+
+ align:start position:0%
+does that
+mean an operator is like take a vector
+
+ align:start position:0%
+mean an operator is like take a vector
+ 
+
+ align:start position:0%
+mean an operator is like take a vector
+rotate what is a complex conjugation of
+
+ align:start position:0%
+rotate what is a complex conjugation of
+ 
+
+ align:start position:0%
+rotate what is a complex conjugation of
+that I don't I mean I don't know so we
+
+ align:start position:0%
+that I don't I mean I don't know so we
+ 
+
+ align:start position:0%
+that I don't I mean I don't know so we
+have to Define
+
+ align:start position:0%
+have to Define
+ 
+
+ align:start position:0%
+have to Define
+that okay so I'm now going to start with
+
+ align:start position:0%
+that okay so I'm now going to start with
+ 
+
+ align:start position:0%
+that okay so I'm now going to start with
+this a quick math aside
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and morally this is about what is the
+
+ align:start position:0%
+and morally this is about what is the
+ 
+
+ align:start position:0%
+and morally this is about what is the
+complex conjugate of an operator but
+
+ align:start position:0%
+complex conjugate of an operator but
+ 
+
+ align:start position:0%
+complex conjugate of an operator but
+before I move on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+okay so here's a mathematical uh series
+
+ align:start position:0%
+okay so here's a mathematical uh series
+ 
+
+ align:start position:0%
+okay so here's a mathematical uh series
+of of facts and claims so given so I
+
+ align:start position:0%
+of of facts and claims so given so I
+ 
+
+ align:start position:0%
+of of facts and claims so given so I
+claim the following
+
+ align:start position:0%
+claim the following
+ 
+
+ align:start position:0%
+claim the following
+given any linear operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+build there's a natural way to build
+
+ align:start position:0%
+build there's a natural way to build
+ 
+
+ align:start position:0%
+build there's a natural way to build
+without making any additional
+
+ align:start position:0%
+without making any additional
+ 
+
+ align:start position:0%
+without making any additional
+assumptions or any additional
+
+ align:start position:0%
+assumptions or any additional
+ 
+
+ align:start position:0%
+assumptions or any additional
+ingredients we can build another
+
+ align:start position:0%
+ingredients we can build another
+ 
+
+ align:start position:0%
+ingredients we can build another
+operator OD dagger hat
+
+ align:start position:0%
+operator OD dagger hat
+ 
+
+ align:start position:0%
+operator OD dagger hat
+hat in the following way consider um the
+
+ align:start position:0%
+hat in the following way consider um the
+ 
+
+ align:start position:0%
+hat in the following way consider um the
+inner product of f with G or the the
+
+ align:start position:0%
+inner product of f with G or the the
+ 
+
+ align:start position:0%
+inner product of f with G or the the
+bracket of f with G so integral DX of f
+
+ align:start position:0%
+bracket of f with G so integral DX of f
+ 
+
+ align:start position:0%
+bracket of f with G so integral DX of f
+complex conjugate G okay now consider
+
+ align:start position:0%
+complex conjugate G okay now consider
+ 
+
+ align:start position:0%
+complex conjugate G okay now consider
+the the the function we're taking here
+
+ align:start position:0%
+the the the function we're taking here
+ 
+
+ align:start position:0%
+the the the function we're taking here
+is actually the operator we have on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G I'm going to Define my op so is a
+
+ align:start position:0%
+G I'm going to Define my op so is a
+ 
+
+ align:start position:0%
+G I'm going to Define my op so is a
+perfectly good thing what this
+
+ align:start position:0%
+perfectly good thing what this
+ 
+
+ align:start position:0%
+perfectly good thing what this
+expression says is take your function G
+
+ align:start position:0%
+expression says is take your function G
+ 
+
+ align:start position:0%
+expression says is take your function G
+act on it with the operator o multiply
+
+ align:start position:0%
+act on it with the operator o multiply
+ 
+
+ align:start position:0%
+act on it with the operator o multiply
+by F complex conjugate take the integral
+
+ align:start position:0%
+by F complex conjugate take the integral
+ 
+
+ align:start position:0%
+by F complex conjugate take the integral
+this is what we would have done if we
+
+ align:start position:0%
+this is what we would have done if we
+ 
+
+ align:start position:0%
+this is what we would have done if we
+had taken the inner product of f with
+
+ align:start position:0%
+had taken the inner product of f with
+ 
+
+ align:start position:0%
+had taken the inner product of f with
+the state we get by or the function we
+
+ align:start position:0%
+the state we get by or the function we
+ 
+
+ align:start position:0%
+the state we get by or the function we
+get by taking o and acting on the
+
+ align:start position:0%
+get by taking o and acting on the
+ 
+
+ align:start position:0%
+get by taking o and acting on the
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G so now here's the thing what we want
+
+ align:start position:0%
+G so now here's the thing what we want
+ 
+
+ align:start position:0%
+G so now here's the thing what we want
+just in a side what we want to do is
+
+ align:start position:0%
+just in a side what we want to do is
+ 
+
+ align:start position:0%
+just in a side what we want to do is
+Define a new operator and here's how I'm
+
+ align:start position:0%
+Define a new operator and here's how I'm
+ 
+
+ align:start position:0%
+Define a new operator and here's how I'm
+going to Define it I'm Define it by
+
+ align:start position:0%
+going to Define it I'm Define it by
+ 
+
+ align:start position:0%
+going to Define it I'm Define it by
+choosing how it acts I'm going to tell
+
+ align:start position:0%
+choosing how it acts I'm going to tell
+ 
+
+ align:start position:0%
+choosing how it acts I'm going to tell
+you exactly how it acts and then we'll
+
+ align:start position:0%
+you exactly how it acts and then we'll
+ 
+
+ align:start position:0%
+you exactly how it acts and then we'll
+Define the operator so this operator o
+
+ align:start position:0%
+Define the operator so this operator o
+ 
+
+ align:start position:0%
+Define the operator so this operator o
+with a
+
+ align:start position:0%
+with a
+ 
+
+ align:start position:0%
+with a
+dagger called the ad joint is defined in
+
+ align:start position:0%
+dagger called the ad joint is defined in
+ 
+
+ align:start position:0%
+dagger called the ad joint is defined in
+the following way this is whatever
+
+ align:start position:0%
+the following way this is whatever
+ 
+
+ align:start position:0%
+the following way this is whatever
+operator you need such that the
+
+ align:start position:0%
+operator you need such that the
+ 
+
+ align:start position:0%
+operator you need such that the
+integral uh gives you such that the
+
+ align:start position:0%
+integral uh gives you such that the
+ 
+
+ align:start position:0%
+integral uh gives you such that the
+following is true integral DX uh o on F
+
+ align:start position:0%
+following is true integral DX uh o on F
+ 
+
+ align:start position:0%
+following is true integral DX uh o on F
+complex conjugate G
+
+ align:start position:0%
+complex conjugate G
+ 
+
+ align:start position:0%
+complex conjugate G
+okay so this is the definition of this
+
+ align:start position:0%
+okay so this is the definition of this
+ 
+
+ align:start position:0%
+okay so this is the definition of this
+dagger action the adjoint
+
+ align:start position:0%
+dagger action the adjoint
+ 
+
+ align:start position:0%
+dagger action the adjoint
+action okay so o
+
+ align:start position:0%
+action okay so o
+ 
+
+ align:start position:0%
+action okay so o
+dagger is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+adjoint and sometimes it's called the
+
+ align:start position:0%
+adjoint and sometimes it's called the
+ 
+
+ align:start position:0%
+adjoint and sometimes it's called the
+herian adjoint uh all occasionally say
+
+ align:start position:0%
+herian adjoint uh all occasionally say
+ 
+
+ align:start position:0%
+herian adjoint uh all occasionally say
+Hermes occasionally not with no
+
+ align:start position:0%
+Hermes occasionally not with no
+ 
+
+ align:start position:0%
+Hermes occasionally not with no
+particular uh or order to it um so what
+
+ align:start position:0%
+particular uh or order to it um so what
+ 
+
+ align:start position:0%
+particular uh or order to it um so what
+does this
+
+ align:start position:0%
+does this
+ 
+
+ align:start position:0%
+does this
+mean this means that the whatever o OD
+
+ align:start position:0%
+mean this means that the whatever o OD
+ 
+
+ align:start position:0%
+mean this means that the whatever o OD
+dagger is it's that operator that when
+
+ align:start position:0%
+dagger is it's that operator that when
+ 
+
+ align:start position:0%
+dagger is it's that operator that when
+acting on G and then taking the inter
+
+ align:start position:0%
+acting on G and then taking the inter
+ 
+
+ align:start position:0%
+acting on G and then taking the inter
+prodct with f gives me the same answer
+
+ align:start position:0%
+prodct with f gives me the same answer
+ 
+
+ align:start position:0%
+prodct with f gives me the same answer
+as taking my original operator and
+
+ align:start position:0%
+as taking my original operator and
+ 
+
+ align:start position:0%
+as taking my original operator and
+acting on F and taking the in product
+
+ align:start position:0%
+acting on F and taking the in product
+ 
+
+ align:start position:0%
+acting on F and taking the in product
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool so we know how if we know what our
+
+ align:start position:0%
+cool so we know how if we know what our
+ 
+
+ align:start position:0%
+cool so we know how if we know what our
+operator o is the challenge now is going
+
+ align:start position:0%
+operator o is the challenge now is going
+ 
+
+ align:start position:0%
+operator o is the challenge now is going
+to be to figure out what must this OD
+
+ align:start position:0%
+to be to figure out what must this OD
+ 
+
+ align:start position:0%
+to be to figure out what must this OD
+dagger operator be such that this
+
+ align:start position:0%
+dagger operator be such that this
+ 
+
+ align:start position:0%
+dagger operator be such that this
+expression is true that's going to be my
+
+ align:start position:0%
+expression is true that's going to be my
+ 
+
+ align:start position:0%
+expression is true that's going to be my
+definition of the
+
+ align:start position:0%
+definition of the
+ 
+
+ align:start position:0%
+definition of the
+Adent cool so I'm going to do a bunch of
+
+ align:start position:0%
+Adent cool so I'm going to do a bunch of
+ 
+
+ align:start position:0%
+Adent cool so I'm going to do a bunch of
+examples I'm going to walk through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay
+
+ align:start position:0%
+this okay
+ 
+
+ align:start position:0%
+this okay
+so the mathematical definition is that
+
+ align:start position:0%
+so the mathematical definition is that
+ 
+
+ align:start position:0%
+so the mathematical definition is that
+an operator o defined in this fashion is
+
+ align:start position:0%
+an operator o defined in this fashion is
+ 
+
+ align:start position:0%
+an operator o defined in this fashion is
+the herian ad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+joint of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+O Okay so that's the mathematical
+
+ align:start position:0%
+O Okay so that's the mathematical
+ 
+
+ align:start position:0%
+O Okay so that's the mathematical
+definition well that's our version of
+
+ align:start position:0%
+definition well that's our version of
+ 
+
+ align:start position:0%
+definition well that's our version of
+the mathematical
+
+ align:start position:0%
+the mathematical
+ 
+
+ align:start position:0%
+the mathematical
+definition I just came back from a math
+
+ align:start position:0%
+definition I just came back from a math
+ 
+
+ align:start position:0%
+definition I just came back from a math
+conference so I'm particularly chased at
+
+ align:start position:0%
+conference so I'm particularly chased at
+ 
+
+ align:start position:0%
+conference so I'm particularly chased at
+the moment to be careful
+
+ align:start position:0%
+the moment to be careful
+ 
+
+ align:start position:0%
+the moment to be careful
+um Okay so here so let's do some quick
+
+ align:start position:0%
+um Okay so here so let's do some quick
+ 
+
+ align:start position:0%
+um Okay so here so let's do some quick
+examples example one uh what's the
+
+ align:start position:0%
+examples example one uh what's the
+ 
+
+ align:start position:0%
+examples example one uh what's the
+suppose uh C is a complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number I claim a number is also an
+
+ align:start position:0%
+number I claim a number is also an
+ 
+
+ align:start position:0%
+number I claim a number is also an
+operator it acts by multiplication the
+
+ align:start position:0%
+operator it acts by multiplication the
+ 
+
+ align:start position:0%
+operator it acts by multiplication the
+number seven is an operator because it
+
+ align:start position:0%
+number seven is an operator because it
+ 
+
+ align:start position:0%
+number seven is an operator because it
+takes a vector and it gives you seven
+
+ align:start position:0%
+takes a vector and it gives you seven
+ 
+
+ align:start position:0%
+takes a vector and it gives you seven
+times that Vector okay so this uh this
+
+ align:start position:0%
+times that Vector okay so this uh this
+ 
+
+ align:start position:0%
+times that Vector okay so this uh this
+number is a particularly simple kind of
+
+ align:start position:0%
+number is a particularly simple kind of
+ 
+
+ align:start position:0%
+number is a particularly simple kind of
+operator uh and what C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+joint okay well we can do that that's
+
+ align:start position:0%
+joint okay well we can do that that's
+ 
+
+ align:start position:0%
+joint okay well we can do that that's
+easy so C adjoint is going to be defined
+
+ align:start position:0%
+easy so C adjoint is going to be defined
+ 
+
+ align:start position:0%
+easy so C adjoint is going to be defined
+in the following way it's integral DX uh
+
+ align:start position:0%
+in the following way it's integral DX uh
+ 
+
+ align:start position:0%
+in the following way it's integral DX uh
+F star of c adjoint g is equal to the
+
+ align:start position:0%
+F star of c adjoint g is equal to the
+ 
+
+ align:start position:0%
+F star of c adjoint g is equal to the
+integral DX of C on F complex conjugate
+
+ align:start position:0%
+integral DX of C on F complex conjugate
+ 
+
+ align:start position:0%
+integral DX of C on F complex conjugate
+time G but what is
+
+ align:start position:0%
+time G but what is
+ 
+
+ align:start position:0%
+time G but what is
+this well C is just a number so when we
+
+ align:start position:0%
+this well C is just a number so when we
+ 
+
+ align:start position:0%
+this well C is just a number so when we
+take its complex conjugate we can just
+
+ align:start position:0%
+take its complex conjugate we can just
+ 
+
+ align:start position:0%
+take its complex conjugate we can just
+pull it out so this is equal to the
+
+ align:start position:0%
+pull it out so this is equal to the
+ 
+
+ align:start position:0%
+pull it out so this is equal to the
+integral DX C complex conjugate fstar
+
+ align:start position:0%
+integral DX C complex conjugate fstar
+ 
+
+ align:start position:0%
+integral DX C complex conjugate fstar
+G but I'm now going to rewrite this
+
+ align:start position:0%
+G but I'm now going to rewrite this
+ 
+
+ align:start position:0%
+G but I'm now going to rewrite this
+using the awesome power of reordering
+
+ align:start position:0%
+using the awesome power of reordering
+ 
+
+ align:start position:0%
+using the awesome power of reordering
+multiplication as C star G and I'm going
+
+ align:start position:0%
+multiplication as C star G and I'm going
+ 
+
+ align:start position:0%
+multiplication as C star G and I'm going
+to put parentheses around this because
+
+ align:start position:0%
+to put parentheses around this because
+ 
+
+ align:start position:0%
+to put parentheses around this because
+it seems like fun so now we have this
+
+ align:start position:0%
+it seems like fun so now we have this
+ 
+
+ align:start position:0%
+it seems like fun so now we have this
+nice expression the integral DX of f c
+
+ align:start position:0%
+nice expression the integral DX of f c
+ 
+
+ align:start position:0%
+nice expression the integral DX of f c
+adint g is equal to the integral DX of
+
+ align:start position:0%
+adint g is equal to the integral DX of
+ 
+
+ align:start position:0%
+adint g is equal to the integral DX of
+f c star g c complex conjugate G but
+
+ align:start position:0%
+f c star g c complex conjugate G but
+ 
+
+ align:start position:0%
+f c star g c complex conjugate G but
+notice that this must be true for all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F it's true for all because I made no
+
+ align:start position:0%
+F it's true for all because I made no
+ 
+
+ align:start position:0%
+F it's true for all because I made no
+assumption about what f and g are true
+
+ align:start position:0%
+assumption about what f and g are true
+ 
+
+ align:start position:0%
+assumption about what f and g are true
+for for all
+
+ align:start position:0%
+for for all
+ 
+
+ align:start position:0%
+for for all
+f and g and therefore the adjoint of a
+
+ align:start position:0%
+f and g and therefore the adjoint of a
+ 
+
+ align:start position:0%
+f and g and therefore the adjoint of a
+complex number is its complex
+
+ align:start position:0%
+complex number is its complex
+ 
+
+ align:start position:0%
+complex number is its complex
+conjugate okay and this is the basic
+
+ align:start position:0%
+conjugate okay and this is the basic
+ 
+
+ align:start position:0%
+conjugate okay and this is the basic
+strategy for determining the complex the
+
+ align:start position:0%
+strategy for determining the complex the
+ 
+
+ align:start position:0%
+strategy for determining the complex the
+adjoint of any operator we're going to
+
+ align:start position:0%
+adjoint of any operator we're going to
+ 
+
+ align:start position:0%
+adjoint of any operator we're going to
+play this exactly this sort of game
+
+ align:start position:0%
+play this exactly this sort of game
+ 
+
+ align:start position:0%
+play this exactly this sort of game
+we'll put the adjoint in here we'll use
+
+ align:start position:0%
+we'll put the adjoint in here we'll use
+ 
+
+ align:start position:0%
+we'll put the adjoint in here we'll use
+the definition of the adjoint and then
+
+ align:start position:0%
+the definition of the adjoint and then
+ 
+
+ align:start position:0%
+the definition of the adjoint and then
+we'll do whatever minations are
+
+ align:start position:0%
+we'll do whatever minations are
+ 
+
+ align:start position:0%
+we'll do whatever minations are
+necessary to rewrite this as some
+
+ align:start position:0%
+necessary to rewrite this as some
+ 
+
+ align:start position:0%
+necessary to rewrite this as some
+operator acting on the first Factor cool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay let's do it for a more
+
+ align:start position:0%
+questions okay let's do it for a more
+ 
+
+ align:start position:0%
+questions okay let's do it for a more
+interesting operator so by the way uh to
+
+ align:start position:0%
+interesting operator so by the way uh to
+ 
+
+ align:start position:0%
+interesting operator so by the way uh to
+check at home and I think this might be
+
+ align:start position:0%
+check at home and I think this might be
+ 
+
+ align:start position:0%
+check at home and I think this might be
+on your problem set um but I don't
+
+ align:start position:0%
+on your problem set um but I don't
+ 
+
+ align:start position:0%
+on your problem set um but I don't
+remember if it's on or not so if it's
+
+ align:start position:0%
+remember if it's on or not so if it's
+ 
+
+ align:start position:0%
+remember if it's on or not so if it's
+not check this for yourself check that
+
+ align:start position:0%
+not check this for yourself check that
+ 
+
+ align:start position:0%
+not check this for yourself check that
+the adjoint of the adjoint is equal to
+
+ align:start position:0%
+the adjoint of the adjoint is equal to
+ 
+
+ align:start position:0%
+the adjoint of the adjoint is equal to
+the operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+itself that's an easy thing to check
+
+ align:start position:0%
+itself that's an easy thing to check
+ 
+
+ align:start position:0%
+itself that's an easy thing to check
+okay so next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example what
+
+ align:start position:0%
+example what
+ 
+
+ align:start position:0%
+example what
+is the adjoint of the operator derived
+
+ align:start position:0%
+is the adjoint of the operator derived
+ 
+
+ align:start position:0%
+is the adjoint of the operator derived
+with respect to
+
+ align:start position:0%
+with respect to
+ 
+
+ align:start position:0%
+with respect to
+X consider the operator which is just
+
+ align:start position:0%
+X consider the operator which is just
+ 
+
+ align:start position:0%
+X consider the operator which is just
+derivative with respect to X and I want
+
+ align:start position:0%
+derivative with respect to X and I want
+ 
+
+ align:start position:0%
+derivative with respect to X and I want
+to know what is the adint of this
+
+ align:start position:0%
+to know what is the adint of this
+ 
+
+ align:start position:0%
+to know what is the adint of this
+Beast okay so how do we do
+
+ align:start position:0%
+Beast okay so how do we do
+ 
+
+ align:start position:0%
+Beast okay so how do we do
+this same logic as before whatever the
+
+ align:start position:0%
+this same logic as before whatever the
+ 
+
+ align:start position:0%
+this same logic as before whatever the
+operator is it's defined in the
+
+ align:start position:0%
+operator is it's defined in the
+ 
+
+ align:start position:0%
+operator is it's defined in the
+following way integral DX F complex
+
+ align:start position:0%
+following way integral DX F complex
+ 
+
+ align:start position:0%
+following way integral DX F complex
+conjugate on DX dagger on G
+
+ align:start position:0%
+conjugate on DX dagger on G
+ 
+
+ align:start position:0%
+conjugate on DX dagger on G
+this is equal to the integral DX of are
+
+ align:start position:0%
+this is equal to the integral DX of are
+ 
+
+ align:start position:0%
+this is equal to the integral DX of are
+you on time good um integral DX of um
+
+ align:start position:0%
+you on time good um integral DX of um
+ 
+
+ align:start position:0%
+you on time good um integral DX of um
+DX F complex conjugate on
+
+ align:start position:0%
+DX F complex conjugate on
+ 
+
+ align:start position:0%
+DX F complex conjugate on
+G now what we want is we want to turn
+
+ align:start position:0%
+G now what we want is we want to turn
+ 
+
+ align:start position:0%
+G now what we want is we want to turn
+this into an expression where the
+
+ align:start position:0%
+this into an expression where the
+ 
+
+ align:start position:0%
+this into an expression where the
+operator is acting on G just our
+
+ align:start position:0%
+operator is acting on G just our
+ 
+
+ align:start position:0%
+operator is acting on G just our
+familiar operator
+
+ align:start position:0%
+familiar operator
+ 
+
+ align:start position:0%
+familiar operator
+DDX so how do I get the DDX oh by the
+
+ align:start position:0%
+DDX so how do I get the DDX oh by the
+ 
+
+ align:start position:0%
+DDX so how do I get the DDX oh by the
+way I so how do I get the DDX over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here I need to do two things first
+
+ align:start position:0%
+here I need to do two things first
+ 
+
+ align:start position:0%
+here I need to do two things first
+what's the complex con of the derivative
+
+ align:start position:0%
+what's the complex con of the derivative
+ 
+
+ align:start position:0%
+what's the complex con of the derivative
+respect to X of a complex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function and my D has indigestion um so
+
+ align:start position:0%
+function and my D has indigestion um so
+ 
+
+ align:start position:0%
+function and my D has indigestion um so
+this is integral DX derivative with
+
+ align:start position:0%
+this is integral DX derivative with
+ 
+
+ align:start position:0%
+this is integral DX derivative with
+respect to X of f complex conjugate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G and now I can I want this operator I
+
+ align:start position:0%
+G and now I can I want this operator I
+ 
+
+ align:start position:0%
+G and now I can I want this operator I
+want derivative acting on G that's the
+
+ align:start position:0%
+want derivative acting on G that's the
+ 
+
+ align:start position:0%
+want derivative acting on G that's the
+definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because I want to know what is
+
+ align:start position:0%
+right because I want to know what is
+ 
+
+ align:start position:0%
+right because I want to know what is
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+operator and so I'm going to do
+
+ align:start position:0%
+operator and so I'm going to do
+ 
+
+ align:start position:0%
+operator and so I'm going to do
+integration by
+
+ align:start position:0%
+integration by
+ 
+
+ align:start position:0%
+integration by
+parts so this is equal to the integral
+
+ align:start position:0%
+parts so this is equal to the integral
+ 
+
+ align:start position:0%
+parts so this is equal to the integral
+DX when I integrate by Parts I get an F
+
+ align:start position:0%
+DX when I integrate by Parts I get an F
+ 
+
+ align:start position:0%
+DX when I integrate by Parts I get an F
+complex conjugate and then a overall
+
+ align:start position:0%
+complex conjugate and then a overall
+ 
+
+ align:start position:0%
+complex conjugate and then a overall
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+sign from the integration by parts minus
+
+ align:start position:0%
+sign from the integration by parts minus
+ 
+
+ align:start position:0%
+sign from the integration by parts minus
+F complex conjugate DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G did I was I telling you the truth or
+
+ align:start position:0%
+G did I was I telling you the truth or
+ 
+
+ align:start position:0%
+G did I was I telling you the truth or
+did I lie to you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay keep thinking about
+
+ align:start position:0%
+okay keep thinking about
+ 
+
+ align:start position:0%
+okay keep thinking about
+that and this is equal to well the
+
+ align:start position:0%
+that and this is equal to well the
+ 
+
+ align:start position:0%
+that and this is equal to well the
+integral of DX F complex conjugate of
+
+ align:start position:0%
+integral of DX F complex conjugate of
+ 
+
+ align:start position:0%
+integral of DX F complex conjugate of
+minus the derivative respect to X acting
+
+ align:start position:0%
+minus the derivative respect to X acting
+ 
+
+ align:start position:0%
+minus the derivative respect to X acting
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+G everyone cool with that but if you
+
+ align:start position:0%
+G everyone cool with that but if you
+ 
+
+ align:start position:0%
+G everyone cool with that but if you
+look at these
+
+ align:start position:0%
+look at these
+ 
+
+ align:start position:0%
+look at these
+equalities DX adint acting on G is equal
+
+ align:start position:0%
+equalities DX adint acting on G is equal
+ 
+
+ align:start position:0%
+equalities DX adint acting on G is equal
+is the same as minus DX acting on G so
+
+ align:start position:0%
+is the same as minus DX acting on G so
+ 
+
+ align:start position:0%
+is the same as minus DX acting on G so
+this tells me that the adint of DX is
+
+ align:start position:0%
+this tells me that the adint of DX is
+ 
+
+ align:start position:0%
+this tells me that the adint of DX is
+equal to minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX yeah are you assuming that your
+
+ align:start position:0%
+DX yeah are you assuming that your
+ 
+
+ align:start position:0%
+DX yeah are you assuming that your
+surface terms vanish thank you I lied to
+
+ align:start position:0%
+surface terms vanish thank you I lied to
+ 
+
+ align:start position:0%
+surface terms vanish thank you I lied to
+you so I assumed in this that my Surface
+
+ align:start position:0%
+you so I assumed in this that my Surface
+ 
+
+ align:start position:0%
+you so I assumed in this that my Surface
+terms vanished I did a variation by
+
+ align:start position:0%
+terms vanished I did a variation by
+ 
+
+ align:start position:0%
+terms vanished I did a variation by
+parts and that that leaves me with a
+
+ align:start position:0%
+parts and that that leaves me with a
+ 
+
+ align:start position:0%
+parts and that that leaves me with a
+total derivative right and that total
+
+ align:start position:0%
+total derivative right and that total
+ 
+
+ align:start position:0%
+total derivative right and that total
+derivative gives me a boundary term
+
+ align:start position:0%
+derivative gives me a boundary term
+ 
+
+ align:start position:0%
+derivative gives me a boundary term
+remember how integration by parts Works
+
+ align:start position:0%
+remember how integration by parts Works
+ 
+
+ align:start position:0%
+remember how integration by parts Works
+integration by parts says the integral
+
+ align:start position:0%
+integration by parts says the integral
+ 
+
+ align:start position:0%
+integration by parts says the integral
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+dxb is equal to the integral of well a
+
+ align:start position:0%
+dxb is equal to the integral of well a
+ 
+
+ align:start position:0%
+dxb is equal to the integral of well a
+dxb can be written as um derivative
+
+ align:start position:0%
+dxb can be written as um derivative
+ 
+
+ align:start position:0%
+dxb can be written as um derivative
+respect to X of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a uh minus um so uh minus B uh
+
+ align:start position:0%
+a uh minus um so uh minus B uh
+ 
+
+ align:start position:0%
+a uh minus um so uh minus B uh
+derivative with respect to X of a right
+
+ align:start position:0%
+derivative with respect to X of a right
+ 
+
+ align:start position:0%
+derivative with respect to X of a right
+because this is a prime B plus b prime a
+
+ align:start position:0%
+because this is a prime B plus b prime a
+ 
+
+ align:start position:0%
+because this is a prime B plus b prime a
+here we have a prime so we just subtract
+
+ align:start position:0%
+here we have a prime so we just subtract
+ 
+
+ align:start position:0%
+here we have a prime so we just subtract
+off the appropriate term but this is a
+
+ align:start position:0%
+off the appropriate term but this is a
+ 
+
+ align:start position:0%
+off the appropriate term but this is a
+total derivative so it only gives us a
+
+ align:start position:0%
+total derivative so it only gives us a
+ 
+
+ align:start position:0%
+total derivative so it only gives us a
+boundary term so this integral is equal
+
+ align:start position:0%
+boundary term so this integral is equal
+ 
+
+ align:start position:0%
+boundary term so this integral is equal
+to can move the integral minus the
+
+ align:start position:0%
+to can move the integral minus the
+ 
+
+ align:start position:0%
+to can move the integral minus the
+integral over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the integral and the derivative because
+
+ align:start position:0%
+the integral and the derivative because
+ 
+
+ align:start position:0%
+the integral and the derivative because
+an integral is nothing but an
+
+ align:start position:0%
+an integral is nothing but an
+ 
+
+ align:start position:0%
+an integral is nothing but an
+anti-derivative the integral and the
+
+ align:start position:0%
+anti-derivative the integral and the
+ 
+
+ align:start position:0%
+anti-derivative the integral and the
+derivative cancel leaving us with a
+
+ align:start position:0%
+derivative cancel leaving us with a
+ 
+
+ align:start position:0%
+derivative cancel leaving us with a
+boundary terms and in this case it's
+
+ align:start position:0%
+boundary terms and in this case it's
+ 
+
+ align:start position:0%
+boundary terms and in this case it's
+from our boundaries which are plus INF
+
+ align:start position:0%
+from our boundaries which are plus INF
+ 
+
+ align:start position:0%
+from our boundaries which are plus INF
+or sorry minus infinity to plus infinity
+
+ align:start position:0%
+or sorry minus infinity to plus infinity
+ 
+
+ align:start position:0%
+or sorry minus infinity to plus infinity
+minus infinity and plus
+
+ align:start position:0%
+minus infinity and plus
+ 
+
+ align:start position:0%
+minus infinity and plus
+infinity now this tells us something
+
+ align:start position:0%
+infinity now this tells us something
+ 
+
+ align:start position:0%
+infinity now this tells us something
+very important and I'm not going to
+
+ align:start position:0%
+very important and I'm not going to
+ 
+
+ align:start position:0%
+very important and I'm not going to
+speak about this in detail but I
+
+ align:start position:0%
+speak about this in detail but I
+ 
+
+ align:start position:0%
+speak about this in detail but I
+encourage the recitation instructors who
+
+ align:start position:0%
+encourage the recitation instructors who
+ 
+
+ align:start position:0%
+encourage the recitation instructors who
+might happen to be here to think to
+
+ align:start position:0%
+might happen to be here to think to
+ 
+
+ align:start position:0%
+might happen to be here to think to
+mention this in recitation um and I
+
+ align:start position:0%
+mention this in recitation um and I
+ 
+
+ align:start position:0%
+mention this in recitation um and I
+encourage you all to think about it
+
+ align:start position:0%
+encourage you all to think about it
+ 
+
+ align:start position:0%
+encourage you all to think about it
+when I if I ask you what is the adjoint
+
+ align:start position:0%
+when I if I ask you what is the adjoint
+ 
+
+ align:start position:0%
+when I if I ask you what is the adjoint
+of the derivative operator acting on the
+
+ align:start position:0%
+of the derivative operator acting on the
+ 
+
+ align:start position:0%
+of the derivative operator acting on the
+space of functions which are
+
+ align:start position:0%
+space of functions which are
+ 
+
+ align:start position:0%
+space of functions which are
+normalizable so that they vanish at
+
+ align:start position:0%
+normalizable so that they vanish at
+ 
+
+ align:start position:0%
+normalizable so that they vanish at
+Infinity what is the adjoint of the
+
+ align:start position:0%
+Infinity what is the adjoint of the
+ 
+
+ align:start position:0%
+Infinity what is the adjoint of the
+derivative operator acting on the space
+
+ align:start position:0%
+derivative operator acting on the space
+ 
+
+ align:start position:0%
+derivative operator acting on the space
+of functions which is normalizable at
+
+ align:start position:0%
+of functions which is normalizable at
+ 
+
+ align:start position:0%
+of functions which is normalizable at
+Infinity we just derive the answer
+
+ align:start position:0%
+Infinity we just derive the answer
+ 
+
+ align:start position:0%
+Infinity we just derive the answer
+because we assumed that these surface
+
+ align:start position:0%
+because we assumed that these surface
+ 
+
+ align:start position:0%
+because we assumed that these surface
+terms
+
+ align:start position:0%
+terms
+ 
+
+ align:start position:0%
+terms
+vanished right because our wave
+
+ align:start position:0%
+vanished right because our wave
+ 
+
+ align:start position:0%
+vanished right because our wave
+functions f and g vanish at Infinity
+
+ align:start position:0%
+functions f and g vanish at Infinity
+ 
+
+ align:start position:0%
+functions f and g vanish at Infinity
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+normalizable however if I had asked you
+
+ align:start position:0%
+normalizable however if I had asked you
+ 
+
+ align:start position:0%
+normalizable however if I had asked you
+a slightly different question if I had
+
+ align:start position:0%
+a slightly different question if I had
+ 
+
+ align:start position:0%
+a slightly different question if I had
+asked you what's the adint of the
+
+ align:start position:0%
+asked you what's the adint of the
+ 
+
+ align:start position:0%
+asked you what's the adint of the
+derivative operator acting on a
+
+ align:start position:0%
+derivative operator acting on a
+ 
+
+ align:start position:0%
+derivative operator acting on a
+different set of functions the set of
+
+ align:start position:0%
+different set of functions the set of
+ 
+
+ align:start position:0%
+different set of functions the set of
+functions that don't necessarily vanish
+
+ align:start position:0%
+functions that don't necessarily vanish
+ 
+
+ align:start position:0%
+functions that don't necessarily vanish
+at Infinity including sinusoids that go
+
+ align:start position:0%
+at Infinity including sinusoids that go
+ 
+
+ align:start position:0%
+at Infinity including sinusoids that go
+off to infinity and don't vanish is this
+
+ align:start position:0%
+off to infinity and don't vanish is this
+ 
+
+ align:start position:0%
+off to infinity and don't vanish is this
+the correct
+
+ align:start position:0%
+the correct
+ 
+
+ align:start position:0%
+the correct
+answer no this would not be the correct
+
+ align:start position:0%
+answer no this would not be the correct
+ 
+
+ align:start position:0%
+answer no this would not be the correct
+answer because they're boundary terms so
+
+ align:start position:0%
+answer because they're boundary terms so
+ 
+
+ align:start position:0%
+answer because they're boundary terms so
+the point I'm making here first off
+
+ align:start position:0%
+the point I'm making here first off
+ 
+
+ align:start position:0%
+the point I'm making here first off
+we're always in physics we're always
+
+ align:start position:0%
+we're always in physics we're always
+ 
+
+ align:start position:0%
+we're always in physics we're always
+going to be talking about normalizable
+
+ align:start position:0%
+going to be talking about normalizable
+ 
+
+ align:start position:0%
+going to be talking about normalizable
+Beast so at the end of the day the
+
+ align:start position:0%
+Beast so at the end of the day the
+ 
+
+ align:start position:0%
+Beast so at the end of the day the
+physical objects we care about are in a
+
+ align:start position:0%
+physical objects we care about are in a
+ 
+
+ align:start position:0%
+physical objects we care about are in a
+room they are not off Infinity so
+
+ align:start position:0%
+room they are not off Infinity so
+ 
+
+ align:start position:0%
+room they are not off Infinity so
+everything is going to be normal ible
+
+ align:start position:0%
+everything is going to be normal ible
+ 
+
+ align:start position:0%
+everything is going to be normal ible
+that is how the world Works however
+
+ align:start position:0%
+that is how the world Works however
+ 
+
+ align:start position:0%
+that is how the world Works however
+you've got to be careful in making these
+
+ align:start position:0%
+you've got to be careful in making these
+ 
+
+ align:start position:0%
+you've got to be careful in making these
+sorts of arguments and realize that when
+
+ align:start position:0%
+sorts of arguments and realize that when
+ 
+
+ align:start position:0%
+sorts of arguments and realize that when
+I ask you what is the derivative what is
+
+ align:start position:0%
+I ask you what is the derivative what is
+ 
+
+ align:start position:0%
+I ask you what is the derivative what is
+the adint of this operator I need to I
+
+ align:start position:0%
+the adint of this operator I need to I
+ 
+
+ align:start position:0%
+the adint of this operator I need to I
+need to uh say something more precise I
+
+ align:start position:0%
+need to uh say something more precise I
+ 
+
+ align:start position:0%
+need to uh say something more precise I
+need to say what's the adint of the
+
+ align:start position:0%
+need to say what's the adint of the
+ 
+
+ align:start position:0%
+need to say what's the adint of the
+derivative uh acting when this operator
+
+ align:start position:0%
+derivative uh acting when this operator
+ 
+
+ align:start position:0%
+derivative uh acting when this operator
+is understood as acting on some
+
+ align:start position:0%
+is understood as acting on some
+ 
+
+ align:start position:0%
+is understood as acting on some
+particular set of functions acting on
+
+ align:start position:0%
+particular set of functions acting on
+ 
+
+ align:start position:0%
+particular set of functions acting on
+normalizable functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so anyway I'll leave that aside as
+
+ align:start position:0%
+good so anyway I'll leave that aside as
+ 
+
+ align:start position:0%
+good so anyway I'll leave that aside as
+a something to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ponder okay but with that technical
+
+ align:start position:0%
+ponder okay but with that technical
+ 
+
+ align:start position:0%
+ponder okay but with that technical
+detail aside as long as we're talking
+
+ align:start position:0%
+detail aside as long as we're talking
+ 
+
+ align:start position:0%
+detail aside as long as we're talking
+about normalizable functions so these
+
+ align:start position:0%
+about normalizable functions so these
+ 
+
+ align:start position:0%
+about normalizable functions so these
+boundary terms from the integration by
+
+ align:start position:0%
+boundary terms from the integration by
+ 
+
+ align:start position:0%
+boundary terms from the integration by
+parts cancel the ad joint to the
+
+ align:start position:0%
+parts cancel the ad joint to the
+ 
+
+ align:start position:0%
+parts cancel the ad joint to the
+derivative operator is minus the
+
+ align:start position:0%
+derivative operator is minus the
+ 
+
+ align:start position:0%
+derivative operator is minus the
+derivative operator
+
+ align:start position:0%
+derivative operator
+ 
+
+ align:start position:0%
+derivative operator
+cool okay let's do another example um
+
+ align:start position:0%
+cool okay let's do another example um
+ 
+
+ align:start position:0%
+cool okay let's do another example um
+and where do I want to do
+
+ align:start position:0%
+and where do I want to do
+ 
+
+ align:start position:0%
+and where do I want to do
+this yeah I'll do it here so another
+
+ align:start position:0%
+this yeah I'll do it here so another
+ 
+
+ align:start position:0%
+this yeah I'll do it here so another
+example actually
+
+ align:start position:0%
+example actually
+ 
+
+ align:start position:0%
+example actually
+no ow I will do it here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we got another example which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+three uh what's the adjoint of the
+
+ align:start position:0%
+three uh what's the adjoint of the
+ 
+
+ align:start position:0%
+three uh what's the adjoint of the
+position operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay take two minutes do this on a piece
+
+ align:start position:0%
+okay take two minutes do this on a piece
+ 
+
+ align:start position:0%
+okay take two minutes do this on a piece
+of paper in front of
+
+ align:start position:0%
+of paper in front of
+ 
+
+ align:start position:0%
+of paper in front of
+you I'm not going to call on you so you
+
+ align:start position:0%
+you I'm not going to call on you so you
+ 
+
+ align:start position:0%
+you I'm not going to call on you so you
+can raise your hand if you okay um chat
+
+ align:start position:0%
+can raise your hand if you okay um chat
+ 
+
+ align:start position:0%
+can raise your hand if you okay um chat
+with the person next to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you I mean chat about physics right just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not what's your
+
+ align:start position:0%
+not what's your
+ 
+
+ align:start position:0%
+not what's your
+uh okay how come
+
+ align:start position:0%
+uh okay how come
+ 
+
+ align:start position:0%
+uh okay how come
+because it seems
+
+ align:start position:0%
+because it seems
+ 
+
+ align:start position:0%
+because it seems
+parsimonious yeah I it's good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+intuition explain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explain okay so how do we go about doing
+
+ align:start position:0%
+explain okay so how do we go about doing
+ 
+
+ align:start position:0%
+explain okay so how do we go about doing
+this we go about solving this
+
+ align:start position:0%
+this we go about solving this
+ 
+
+ align:start position:0%
+this we go about solving this
+problem by
+
+ align:start position:0%
+problem by
+ 
+
+ align:start position:0%
+problem by
+using the definition of the adjoint so
+
+ align:start position:0%
+using the definition of the adjoint so
+ 
+
+ align:start position:0%
+using the definition of the adjoint so
+what is X adjoint it's that operator
+
+ align:start position:0%
+what is X adjoint it's that operator
+ 
+
+ align:start position:0%
+what is X adjoint it's that operator
+such that the following is true such
+
+ align:start position:0%
+such that the following is true such
+ 
+
+ align:start position:0%
+such that the following is true such
+that the integral DX of
+
+ align:start position:0%
+that the integral DX of
+ 
+
+ align:start position:0%
+that the integral DX of
+um of f complex conjugate with X dagger
+
+ align:start position:0%
+um of f complex conjugate with X dagger
+ 
+
+ align:start position:0%
+um of f complex conjugate with X dagger
+acting on G is equal to the integral DX
+
+ align:start position:0%
+acting on G is equal to the integral DX
+ 
+
+ align:start position:0%
+acting on G is equal to the integral DX
+of what I get by taking the complex
+
+ align:start position:0%
+of what I get by taking the complex
+ 
+
+ align:start position:0%
+of what I get by taking the complex
+conjugate of taking X and acting on F
+
+ align:start position:0%
+conjugate of taking X and acting on F
+ 
+
+ align:start position:0%
+conjugate of taking X and acting on F
+and then integrating this against G but
+
+ align:start position:0%
+and then integrating this against G but
+ 
+
+ align:start position:0%
+and then integrating this against G but
+now we can use the action of X and say
+
+ align:start position:0%
+now we can use the action of X and say
+ 
+
+ align:start position:0%
+now we can use the action of X and say
+that this is equal to the integral DX of
+
+ align:start position:0%
+that this is equal to the integral DX of
+ 
+
+ align:start position:0%
+that this is equal to the integral DX of
+x f complex conjugate G but here's the
+
+ align:start position:0%
+x f complex conjugate G but here's the
+ 
+
+ align:start position:0%
+x f complex conjugate G but here's the
+nice thing what is the complex conjugate
+
+ align:start position:0%
+nice thing what is the complex conjugate
+ 
+
+ align:start position:0%
+nice thing what is the complex conjugate
+of X time a complex function of F X is
+
+ align:start position:0%
+of X time a complex function of F X is
+ 
+
+ align:start position:0%
+of X time a complex function of F X is
+real right positions are real so that's
+
+ align:start position:0%
+real right positions are real so that's
+ 
+
+ align:start position:0%
+real right positions are real so that's
+just x a complex conjugate of f so that
+
+ align:start position:0%
+just x a complex conjugate of f so that
+ 
+
+ align:start position:0%
+just x a complex conjugate of f so that
+was the essential move there and now we
+
+ align:start position:0%
+was the essential move there and now we
+ 
+
+ align:start position:0%
+was the essential move there and now we
+can rewrite this as equal the integral
+
+ align:start position:0%
+can rewrite this as equal the integral
+ 
+
+ align:start position:0%
+can rewrite this as equal the integral
+of f complex conjugate
+
+ align:start position:0%
+of f complex conjugate
+ 
+
+ align:start position:0%
+of f complex conjugate
+XG and now eyeballing this x dagger is
+
+ align:start position:0%
+XG and now eyeballing this x dagger is
+ 
+
+ align:start position:0%
+XG and now eyeballing this x dagger is
+that operator which acts by acting by
+
+ align:start position:0%
+that operator which acts by acting by
+ 
+
+ align:start position:0%
+that operator which acts by acting by
+multiplying with X Little
+
+ align:start position:0%
+multiplying with X Little
+ 
+
+ align:start position:0%
+multiplying with X Little
+X therefore the adjoint of the operator
+
+ align:start position:0%
+X therefore the adjoint of the operator
+ 
+
+ align:start position:0%
+X therefore the adjoint of the operator
+X is equal to the same
+
+ align:start position:0%
+X is equal to the same
+ 
+
+ align:start position:0%
+X is equal to the same
+operator X is equal to its own adjoint
+
+ align:start position:0%
+operator X is equal to its own adjoint
+ 
+
+ align:start position:0%
+operator X is equal to its own adjoint
+Okay cool so we've just learned a couple
+
+ align:start position:0%
+Okay cool so we've just learned a couple
+ 
+
+ align:start position:0%
+Okay cool so we've just learned a couple
+of really nice things so the first is um
+
+ align:start position:0%
+of really nice things so the first is um
+ 
+
+ align:start position:0%
+of really nice things so the first is um
+we're want to do this yeah good so we've
+
+ align:start position:0%
+we're want to do this yeah good so we've
+ 
+
+ align:start position:0%
+we're want to do this yeah good so we've
+learned a couple of nice
+
+ align:start position:0%
+learned a couple of nice
+ 
+
+ align:start position:0%
+learned a couple of nice
+things and I want to encode them in the
+
+ align:start position:0%
+things and I want to encode them in the
+ 
+
+ align:start position:0%
+things and I want to encode them in the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+definition
+
+ align:start position:0%
+definition
+ 
+
+ align:start position:0%
+definition
+definition an operator which I will call
+
+ align:start position:0%
+definition an operator which I will call
+ 
+
+ align:start position:0%
+definition an operator which I will call
+O whose adjoint is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+O So an operator whose adjoint is equal
+
+ align:start position:0%
+O So an operator whose adjoint is equal
+ 
+
+ align:start position:0%
+O So an operator whose adjoint is equal
+to itself
+
+ align:start position:0%
+to itself
+ 
+
+ align:start position:0%
+to itself
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+called is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hermes okay so an operator which is
+
+ align:start position:0%
+Hermes okay so an operator which is
+ 
+
+ align:start position:0%
+Hermes okay so an operator which is
+equal to its own Adine is called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+herian and so I want to note a couple of
+
+ align:start position:0%
+herian and so I want to note a couple of
+ 
+
+ align:start position:0%
+herian and so I want to note a couple of
+nice examples of that so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+note um a an a a
+
+ align:start position:0%
+note um a an a a
+ 
+
+ align:start position:0%
+note um a an a a
+number a number which is
+
+ align:start position:0%
+number a number which is
+ 
+
+ align:start position:0%
+number a number which is
+herian is what
+
+ align:start position:0%
+herian is what
+ 
+
+ align:start position:0%
+herian is what
+real right an
+
+ align:start position:0%
+real right an
+ 
+
+ align:start position:0%
+real right an
+operator we found an operator which is
+
+ align:start position:0%
+operator we found an operator which is
+ 
+
+ align:start position:0%
+operator we found an operator which is
+equal to its own ad joint X dagger is
+
+ align:start position:0%
+equal to its own ad joint X dagger is
+ 
+
+ align:start position:0%
+equal to its own ad joint X dagger is
+equal to X and what can you say about
+
+ align:start position:0%
+equal to X and what can you say about
+ 
+
+ align:start position:0%
+equal to X and what can you say about
+the igen values of this operator they're
+
+ align:start position:0%
+the igen values of this operator they're
+ 
+
+ align:start position:0%
+the igen values of this operator they're
+real we use that in the proof actually
+
+ align:start position:0%
+real we use that in the proof actually
+ 
+
+ align:start position:0%
+real we use that in the proof actually
+so this is real I will call an operator
+
+ align:start position:0%
+so this is real I will call an operator
+ 
+
+ align:start position:0%
+so this is real I will call an operator
+real if it's herian and here's a fact a
+
+ align:start position:0%
+real if it's herian and here's a fact a
+ 
+
+ align:start position:0%
+real if it's herian and here's a fact a
+mathematical fact which is that any
+
+ align:start position:0%
+mathematical fact which is that any
+ 
+
+ align:start position:0%
+mathematical fact which is that any
+operator which is herian has all real I
+
+ align:start position:0%
+operator which is herian has all real I
+ 
+
+ align:start position:0%
+operator which is herian has all real I
+values so this is really I I'll se it as
+
+ align:start position:0%
+values so this is really I I'll se it as
+ 
+
+ align:start position:0%
+values so this is really I I'll se it as
+a but it's just a fact for
+
+ align:start position:0%
+a but it's just a fact for
+ 
+
+ align:start position:0%
+a but it's just a fact for
+us um o has
+
+ align:start position:0%
+us um o has
+ 
+
+ align:start position:0%
+us um o has
+all oh good has all real IG
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yeah uh is it if and only no it's not if
+
+ align:start position:0%
+yeah uh is it if and only no it's not if
+ 
+
+ align:start position:0%
+yeah uh is it if and only no it's not if
+it's um
+
+ align:start position:0%
+it's um
+ 
+
+ align:start position:0%
+it's um
+uh uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see um so if you have all real
+
+ align:start position:0%
+let's see um so if you have all real
+ 
+
+ align:start position:0%
+let's see um so if you have all real
+igen values um it does not imply that
+
+ align:start position:0%
+igen values um it does not imply that
+ 
+
+ align:start position:0%
+igen values um it does not imply that
+you're herion however if you have all
+
+ align:start position:0%
+you're herion however if you have all
+ 
+
+ align:start position:0%
+you're herion however if you have all
+real I values and you can be
+
+ align:start position:0%
+real I values and you can be
+ 
+
+ align:start position:0%
+real I values and you can be
+diagonalized it does imply so let me
+
+ align:start position:0%
+diagonalized it does imply so let me
+ 
+
+ align:start position:0%
+diagonalized it does imply so let me
+give you an example so consider the
+
+ align:start position:0%
+give you an example so consider the
+ 
+
+ align:start position:0%
+give you an example so consider the
+following uh
+
+ align:start position:0%
+following uh
+ 
+
+ align:start position:0%
+following uh
+operator um rotations we've done this
+
+ align:start position:0%
+operator um rotations we've done this
+ 
+
+ align:start position:0%
+operator um rotations we've done this
+many times rotation in real
+
+ align:start position:0%
+many times rotation in real
+ 
+
+ align:start position:0%
+many times rotation in real
+threedimensional space of a vector
+
+ align:start position:0%
+threedimensional space of a vector
+ 
+
+ align:start position:0%
+threedimensional space of a vector
+around the vertical axis okay it has one
+
+ align:start position:0%
+around the vertical axis okay it has one
+ 
+
+ align:start position:0%
+around the vertical axis okay it has one
+IG Vector right which is the vertical
+
+ align:start position:0%
+IG Vector right which is the vertical
+ 
+
+ align:start position:0%
+IG Vector right which is the vertical
+vector and the IG value is
+
+ align:start position:0%
+vector and the IG value is
+ 
+
+ align:start position:0%
+vector and the IG value is
+is one so it's real right but that's not
+
+ align:start position:0%
+is one so it's real right but that's not
+ 
+
+ align:start position:0%
+is one so it's real right but that's not
+enough to make it herian because there's
+
+ align:start position:0%
+enough to make it herian because there's
+ 
+
+ align:start position:0%
+enough to make it herian because there's
+another fact that we haven't got to yet
+
+ align:start position:0%
+another fact that we haven't got to yet
+ 
+
+ align:start position:0%
+another fact that we haven't got to yet
+with herian operators which is going to
+
+ align:start position:0%
+with herian operators which is going to
+ 
+
+ align:start position:0%
+with herian operators which is going to
+tell us that a herian operator has as
+
+ align:start position:0%
+tell us that a herian operator has as
+ 
+
+ align:start position:0%
+tell us that a herian operator has as
+many igen vectors as there are
+
+ align:start position:0%
+many igen vectors as there are
+ 
+
+ align:start position:0%
+many igen vectors as there are
+dimensions in the space okay IE that the
+
+ align:start position:0%
+dimensions in the space okay IE that the
+ 
+
+ align:start position:0%
+dimensions in the space okay IE that the
+IG vectors form a basis but there's only
+
+ align:start position:0%
+IG vectors form a basis but there's only
+ 
+
+ align:start position:0%
+IG vectors form a basis but there's only
+one IG Vector for this guy even though
+
+ align:start position:0%
+one IG Vector for this guy even though
+ 
+
+ align:start position:0%
+one IG Vector for this guy even though
+we're in a threedimensional vector space
+
+ align:start position:0%
+we're in a threedimensional vector space
+ 
+
+ align:start position:0%
+we're in a threedimensional vector space
+so this operator Rotation by an angle
+
+ align:start position:0%
+so this operator Rotation by an angle
+ 
+
+ align:start position:0%
+so this operator Rotation by an angle
+Theta is not herian even though it does
+
+ align:start position:0%
+Theta is not herian even though it does
+ 
+
+ align:start position:0%
+Theta is not herian even though it does
+have its only I value is in fact real
+
+ align:start position:0%
+have its only I value is in fact real
+ 
+
+ align:start position:0%
+have its only I value is in fact real
+okay so it's not only if if you are
+
+ align:start position:0%
+okay so it's not only if if you are
+ 
+
+ align:start position:0%
+okay so it's not only if if you are
+herian your I values are all real and
+
+ align:start position:0%
+herian your I values are all real and
+ 
+
+ align:start position:0%
+herian your I values are all real and
+you'll prove this on a problem
+
+ align:start position:0%
+you'll prove this on a problem
+ 
+
+ align:start position:0%
+you'll prove this on a problem
+set yeah if you're herian are your um
+
+ align:start position:0%
+set yeah if you're herian are your um
+ 
+
+ align:start position:0%
+set yeah if you're herian are your um
+are your Ion functions
+
+ align:start position:0%
+are your Ion functions
+ 
+
+ align:start position:0%
+are your Ion functions
+normal uh uh not necessarily but they
+
+ align:start position:0%
+normal uh uh not necessarily but they
+ 
+
+ align:start position:0%
+normal uh uh not necessarily but they
+can be made normal we'll talk about this
+
+ align:start position:0%
+can be made normal we'll talk about this
+ 
+
+ align:start position:0%
+can be made normal we'll talk about this
+in more detail
+
+ align:start position:0%
+in more detail
+ 
+
+ align:start position:0%
+in more detail
+later okay so if that's so let's do a
+
+ align:start position:0%
+later okay so if that's so let's do a
+ 
+
+ align:start position:0%
+later okay so if that's so let's do a
+quick check um last example and I'm not
+
+ align:start position:0%
+quick check um last example and I'm not
+ 
+
+ align:start position:0%
+quick check um last example and I'm not
+actually going to go through this in
+
+ align:start position:0%
+actually going to go through this in
+ 
+
+ align:start position:0%
+actually going to go through this in
+detail um but what about P what about
+
+ align:start position:0%
+detail um but what about P what about
+ 
+
+ align:start position:0%
+detail um but what about P what about
+momentum operator first off do you think
+
+ align:start position:0%
+momentum operator first off do you think
+ 
+
+ align:start position:0%
+momentum operator first off do you think
+the momentum is
+
+ align:start position:0%
+the momentum is
+ 
+
+ align:start position:0%
+the momentum is
+real it sure would be nice right because
+
+ align:start position:0%
+real it sure would be nice right because
+ 
+
+ align:start position:0%
+real it sure would be nice right because
+it's it's Ting values are the observable
+
+ align:start position:0%
+it's it's Ting values are the observable
+ 
+
+ align:start position:0%
+it's it's Ting values are the observable
+values of momentum and so its I Val
+
+ align:start position:0%
+values of momentum and so its I Val
+ 
+
+ align:start position:0%
+values of momentum and so its I Val
+should all be real does that make it
+
+ align:start position:0%
+should all be real does that make it
+ 
+
+ align:start position:0%
+should all be real does that make it
+herian not necessarily but let's check
+
+ align:start position:0%
+herian not necessarily but let's check
+ 
+
+ align:start position:0%
+herian not necessarily but let's check
+so what is the the adjoint of P well
+
+ align:start position:0%
+so what is the the adjoint of P well
+ 
+
+ align:start position:0%
+so what is the the adjoint of P well
+this actually we can do very easily and
+
+ align:start position:0%
+this actually we can do very easily and
+ 
+
+ align:start position:0%
+this actually we can do very easily and
+I'm not going to go through an elaborate
+
+ align:start position:0%
+I'm not going to go through an elaborate
+ 
+
+ align:start position:0%
+I'm not going to go through an elaborate
+argument I'm just going to not the
+
+ align:start position:0%
+argument I'm just going to not the
+ 
+
+ align:start position:0%
+argument I'm just going to not the
+following p is equal to um H bar upon I
+
+ align:start position:0%
+following p is equal to um H bar upon I
+ 
+
+ align:start position:0%
+following p is equal to um H bar upon I
+or sorry I upon yeah H bar upon I
+
+ align:start position:0%
+or sorry I upon yeah H bar upon I
+ 
+
+ align:start position:0%
+or sorry I upon yeah H bar upon I
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+DDX
+
+ align:start position:0%
+DDX
+ 
+
+ align:start position:0%
+DDX
+right and this is an operator and this
+
+ align:start position:0%
+right and this is an operator and this
+ 
+
+ align:start position:0%
+right and this is an operator and this
+is an operator so what's the adjoint of
+
+ align:start position:0%
+is an operator so what's the adjoint of
+ 
+
+ align:start position:0%
+is an operator so what's the adjoint of
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+operator well this under an adjoint gets
+
+ align:start position:0%
+operator well this under an adjoint gets
+ 
+
+ align:start position:0%
+operator well this under an adjoint gets
+a minus sign right it's itself up to a
+
+ align:start position:0%
+a minus sign right it's itself up to a
+ 
+
+ align:start position:0%
+a minus sign right it's itself up to a
+minus sign so is the derivative
+
+ align:start position:0%
+minus sign so is the derivative
+ 
+
+ align:start position:0%
+minus sign so is the derivative
+herian no it's in fact what we call anti
+
+ align:start position:0%
+herian no it's in fact what we call anti
+ 
+
+ align:start position:0%
+herian no it's in fact what we call anti
+herian its adjoint is minus itself okay
+
+ align:start position:0%
+herian its adjoint is minus itself okay
+ 
+
+ align:start position:0%
+herian its adjoint is minus itself okay
+what about I what's its
+
+ align:start position:0%
+what about I what's its
+ 
+
+ align:start position:0%
+what about I what's its
+adjoint minus I sweet so this has an
+
+ align:start position:0%
+adjoint minus I sweet so this has an
+ 
+
+ align:start position:0%
+adjoint minus I sweet so this has an
+Adent picks up a minus this has an
+
+ align:start position:0%
+Adent picks up a minus this has an
+ 
+
+ align:start position:0%
+Adent picks up a minus this has an
+adject pi picks up a minus the minus is
+
+ align:start position:0%
+adject pi picks up a minus the minus is
+ 
+
+ align:start position:0%
+adject pi picks up a minus the minus is
+cancel p adjoint is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p so p is in fact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+teration okay and here's a stronger
+
+ align:start position:0%
+teration okay and here's a stronger
+ 
+
+ align:start position:0%
+teration okay and here's a stronger
+physical fact so now we've seen that
+
+ align:start position:0%
+physical fact so now we've seen that
+ 
+
+ align:start position:0%
+physical fact so now we've seen that
+each of the operators we built uh is is
+
+ align:start position:0%
+each of the operators we built uh is is
+ 
+
+ align:start position:0%
+each of the operators we built uh is is
+X and P each of the operators that we've
+
+ align:start position:0%
+X and P each of the operators that we've
+ 
+
+ align:start position:0%
+X and P each of the operators that we've
+we've looked at so far is uh herian
+
+ align:start position:0%
+we've looked at so far is uh herian
+ 
+
+ align:start position:0%
+we've looked at so far is uh herian
+those that correspond to physical
+
+ align:start position:0%
+those that correspond to physical
+ 
+
+ align:start position:0%
+those that correspond to physical
+observables uh here's a physical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fact all the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observables you measure with
+
+ align:start position:0%
+observables you measure with
+ 
+
+ align:start position:0%
+observables you measure with
+sticks are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+real and the corresponding statement is
+
+ align:start position:0%
+real and the corresponding statement is
+ 
+
+ align:start position:0%
+real and the corresponding statement is
+that all
+
+ align:start position:0%
+that all
+ 
+
+ align:start position:0%
+that all
+operators corresponding
+
+ align:start position:0%
+operators corresponding
+ 
+
+ align:start position:0%
+operators corresponding
+to uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observables all operators must be herian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um to the postulate that says
+
+ align:start position:0%
+um to the postulate that says
+ 
+
+ align:start position:0%
+um to the postulate that says
+observables are represented by operators
+
+ align:start position:0%
+observables are represented by operators
+ 
+
+ align:start position:0%
+observables are represented by operators
+should be adjoined the word heran
+
+ align:start position:0%
+should be adjoined the word heran
+ 
+
+ align:start position:0%
+should be adjoined the word heran
+observables are represented in quantum
+
+ align:start position:0%
+observables are represented in quantum
+ 
+
+ align:start position:0%
+observables are represented in quantum
+mechanics by herian
+
+ align:start position:0%
+mechanics by herian
+ 
+
+ align:start position:0%
+mechanics by herian
+operators which are operators that have
+
+ align:start position:0%
+operators which are operators that have
+ 
+
+ align:start position:0%
+operators which are operators that have
+a number of nice properties including
+
+ align:start position:0%
+a number of nice properties including
+ 
+
+ align:start position:0%
+a number of nice properties including
+they have all real igen values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool
+
+ align:start position:0%
+cool
+ 
+
+ align:start position:0%
+cool
+okay questions yeah so if it has to be
+
+ align:start position:0%
+okay questions yeah so if it has to be
+ 
+
+ align:start position:0%
+okay questions yeah so if it has to be
+herian and not just have like real IG
+
+ align:start position:0%
+herian and not just have like real IG
+ 
+
+ align:start position:0%
+herian and not just have like real IG
+values does that mean the IG values
+
+ align:start position:0%
+values does that mean the IG values
+ 
+
+ align:start position:0%
+values does that mean the IG values
+always need to form some kind of bases
+
+ align:start position:0%
+always need to form some kind of bases
+ 
+
+ align:start position:0%
+always need to form some kind of bases
+yeah the IG vectors will yeah yeah we're
+
+ align:start position:0%
+yeah the IG vectors will yeah yeah we're
+ 
+
+ align:start position:0%
+yeah the IG vectors will yeah yeah we're
+going to so so this is connected to the
+
+ align:start position:0%
+going to so so this is connected to the
+ 
+
+ align:start position:0%
+going to so so this is connected to the
+fact we've already seen if you take an
+
+ align:start position:0%
+fact we've already seen if you take an
+ 
+
+ align:start position:0%
+fact we've already seen if you take an
+arbitrary wave function you can expand
+
+ align:start position:0%
+arbitrary wave function you can expand
+ 
+
+ align:start position:0%
+arbitrary wave function you can expand
+it in states with definite momentum
+
+ align:start position:0%
+it in states with definite momentum
+ 
+
+ align:start position:0%
+it in states with definite momentum
+right as a superp position you can also
+
+ align:start position:0%
+right as a superp position you can also
+ 
+
+ align:start position:0%
+right as a superp position you can also
+expand it as a as a set of in a set of
+
+ align:start position:0%
+expand it as a as a set of in a set of
+ 
+
+ align:start position:0%
+expand it as a as a set of in a set of
+states of definite energy or of definite
+
+ align:start position:0%
+states of definite energy or of definite
+ 
+
+ align:start position:0%
+states of definite energy or of definite
+position anytime you have a herian
+
+ align:start position:0%
+position anytime you have a herian
+ 
+
+ align:start position:0%
+position anytime you have a herian
+operator it's ve its igen
+
+ align:start position:0%
+operator it's ve its igen
+ 
+
+ align:start position:0%
+operator it's ve its igen
+vectors suffice to to expand any
+
+ align:start position:0%
+vectors suffice to to expand any
+ 
+
+ align:start position:0%
+vectors suffice to to expand any
+function okay they provide a basis for
+
+ align:start position:0%
+function okay they provide a basis for
+ 
+
+ align:start position:0%
+function okay they provide a basis for
+representing any function
+
+ align:start position:0%
+representing any function
+ 
+
+ align:start position:0%
+representing any function
+okay so that was the that's the end of
+
+ align:start position:0%
+okay so that was the that's the end of
+ 
+
+ align:start position:0%
+okay so that was the that's the end of
+the mathematical assign let's get back
+
+ align:start position:0%
+the mathematical assign let's get back
+ 
+
+ align:start position:0%
+the mathematical assign let's get back
+to this physical
+
+ align:start position:0%
+to this physical
+ 
+
+ align:start position:0%
+to this physical
+point so we've defined this operator a
+
+ align:start position:0%
+point so we've defined this operator a
+ 
+
+ align:start position:0%
+point so we've defined this operator a
+and this other operator a dagger and
+
+ align:start position:0%
+and this other operator a dagger and
+ 
+
+ align:start position:0%
+and this other operator a dagger and
+here's my question first is a
+
+ align:start position:0%
+here's my question first is a
+ 
+
+ align:start position:0%
+here's my question first is a
+Herm no it's at that's hermion that's
+
+ align:start position:0%
+Herm no it's at that's hermion that's
+ 
+
+ align:start position:0%
+Herm no it's at that's hermion that's
+hermion but there's an I that I will
+
+ align:start position:0%
+hermion but there's an I that I will
+ 
+
+ align:start position:0%
+hermion but there's an I that I will
+pick up a minus sign when we do the
+
+ align:start position:0%
+pick up a minus sign when we do the
+ 
+
+ align:start position:0%
+pick up a minus sign when we do the
+complex conjugation um oh look so sure
+
+ align:start position:0%
+complex conjugation um oh look so sure
+ 
+
+ align:start position:0%
+complex conjugation um oh look so sure
+was fortuitous that I called this a
+
+ align:start position:0%
+was fortuitous that I called this a
+ 
+
+ align:start position:0%
+was fortuitous that I called this a
+dagger since this is equal to a
+
+ align:start position:0%
+dagger since this is equal to a
+ 
+
+ align:start position:0%
+dagger since this is equal to a
+dagger yeah okay so this is the adjoint
+
+ align:start position:0%
+dagger yeah okay so this is the adjoint
+ 
+
+ align:start position:0%
+dagger yeah okay so this is the adjoint
+of a so this tells you immediately tells
+
+ align:start position:0%
+of a so this tells you immediately tells
+ 
+
+ align:start position:0%
+of a so this tells you immediately tells
+you something interesting X and P are
+
+ align:start position:0%
+you something interesting X and P are
+ 
+
+ align:start position:0%
+you something interesting X and P are
+both observables does a correspond to an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observable is it a is it
+
+ align:start position:0%
+observable is it a is it
+ 
+
+ align:start position:0%
+observable is it a is it
+herian we every observable is associated
+
+ align:start position:0%
+herian we every observable is associated
+ 
+
+ align:start position:0%
+herian we every observable is associated
+to a herian operator this is not herian
+
+ align:start position:0%
+to a herian operator this is not herian
+ 
+
+ align:start position:0%
+to a herian operator this is not herian
+so a does not represent an observable
+
+ align:start position:0%
+so a does not represent an observable
+ 
+
+ align:start position:0%
+so a does not represent an observable
+operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and I have I will post notes on the
+
+ align:start position:0%
+okay and I have I will post notes on the
+ 
+
+ align:start position:0%
+okay and I have I will post notes on the
+web page which give us a somewhat
+
+ align:start position:0%
+web page which give us a somewhat
+ 
+
+ align:start position:0%
+web page which give us a somewhat
+lengthy discussion or might be in one of
+
+ align:start position:0%
+lengthy discussion or might be in one of
+ 
+
+ align:start position:0%
+lengthy discussion or might be in one of
+the solutions somewhat lengthy
+
+ align:start position:0%
+the solutions somewhat lengthy
+ 
+
+ align:start position:0%
+the solutions somewhat lengthy
+discussion of what it means for a and a
+
+ align:start position:0%
+discussion of what it means for a and a
+ 
+
+ align:start position:0%
+discussion of what it means for a and a
+dagger to not be observable we you'll
+
+ align:start position:0%
+dagger to not be observable we you'll
+ 
+
+ align:start position:0%
+dagger to not be observable we you'll
+you'll get more discussion of that there
+
+ align:start position:0%
+you'll get more discussion of that there
+ 
+
+ align:start position:0%
+you'll get more discussion of that there
+so meanwhile if a is non observable it's
+
+ align:start position:0%
+so meanwhile if a is non observable it's
+ 
+
+ align:start position:0%
+so meanwhile if a is non observable it's
+not herian does it have real igen
+
+ align:start position:0%
+not herian does it have real igen
+ 
+
+ align:start position:0%
+not herian does it have real igen
+values well here's an important thing I
+
+ align:start position:0%
+values well here's an important thing I
+ 
+
+ align:start position:0%
+values well here's an important thing I
+said if your Hermes and all the I values
+
+ align:start position:0%
+said if your Hermes and all the I values
+ 
+
+ align:start position:0%
+said if your Hermes and all the I values
+are real
+
+ align:start position:0%
+are real
+ 
+
+ align:start position:0%
+are real
+if you're not heran that doesn't tell
+
+ align:start position:0%
+if you're not heran that doesn't tell
+ 
+
+ align:start position:0%
+if you're not heran that doesn't tell
+you you can't have any real igen values
+
+ align:start position:0%
+you you can't have any real igen values
+ 
+
+ align:start position:0%
+you you can't have any real igen values
+it just says that I haven't guaranteed
+
+ align:start position:0%
+it just says that I haven't guaranteed
+ 
+
+ align:start position:0%
+it just says that I haven't guaranteed
+for you that all the igen values are
+
+ align:start position:0%
+for you that all the igen values are
+ 
+
+ align:start position:0%
+for you that all the igen values are
+real okay so what we will Discover at
+
+ align:start position:0%
+real okay so what we will Discover at
+ 
+
+ align:start position:0%
+real okay so what we will Discover at
+towards the end of the course when we
+
+ align:start position:0%
+towards the end of the course when we
+ 
+
+ align:start position:0%
+towards the end of the course when we
+talk about something called coherent
+
+ align:start position:0%
+talk about something called coherent
+ 
+
+ align:start position:0%
+talk about something called coherent
+States is that in fact a does have a
+
+ align:start position:0%
+States is that in fact a does have a
+ 
+
+ align:start position:0%
+States is that in fact a does have a
+nice set of igen vectors they're very
+
+ align:start position:0%
+nice set of igen vectors they're very
+ 
+
+ align:start position:0%
+nice set of igen vectors they're very
+nice they're great we use them for
+
+ align:start position:0%
+nice they're great we use them for
+ 
+
+ align:start position:0%
+nice they're great we use them for
+lasers okay they're very useful and
+
+ align:start position:0%
+lasers okay they're very useful and
+ 
+
+ align:start position:0%
+lasers okay they're very useful and
+they're called coherent States but their
+
+ align:start position:0%
+they're called coherent States but their
+ 
+
+ align:start position:0%
+they're called coherent States but their
+IG vectors or their IG values are not in
+
+ align:start position:0%
+IG vectors or their IG values are not in
+ 
+
+ align:start position:0%
+IG vectors or their IG values are not in
+general real they're generically complex
+
+ align:start position:0%
+general real they're generically complex
+ 
+
+ align:start position:0%
+general real they're generically complex
+numbers okay so are they things you can
+
+ align:start position:0%
+numbers okay so are they things you can
+ 
+
+ align:start position:0%
+numbers okay so are they things you can
+measure not directly um there related to
+
+ align:start position:0%
+measure not directly um there related to
+ 
+
+ align:start position:0%
+measure not directly um there related to
+things you can measure though in some
+
+ align:start position:0%
+things you can measure though in some
+ 
+
+ align:start position:0%
+things you can measure though in some
+pretty nice
+
+ align:start position:0%
+pretty nice
+ 
+
+ align:start position:0%
+pretty nice
+ways
+
+ align:start position:0%
+ways
+ 
+
+ align:start position:0%
+ways
+okay so why are we bothering with these
+
+ align:start position:0%
+okay so why are we bothering with these
+ 
+
+ align:start position:0%
+okay so why are we bothering with these
+guys if they're not
+
+ align:start position:0%
+guys if they're not
+ 
+
+ align:start position:0%
+guys if they're not
+observable you know
+
+ align:start position:0%
+observable you know
+ 
+
+ align:start position:0%
+observable you know
+yeah yeah good excellent that's really
+
+ align:start position:0%
+yeah yeah good excellent that's really
+ 
+
+ align:start position:0%
+yeah yeah good excellent that's really
+good so two things about it so one thing
+
+ align:start position:0%
+good so two things about it so one thing
+ 
+
+ align:start position:0%
+good so two things about it so one thing
+is um this form for the energy operator
+
+ align:start position:0%
+is um this form for the energy operator
+ 
+
+ align:start position:0%
+is um this form for the energy operator
+is particularly simple we see the one
+
+ align:start position:0%
+is particularly simple we see the one
+ 
+
+ align:start position:0%
+is particularly simple we see the one
+half this looks suggestive from before
+
+ align:start position:0%
+half this looks suggestive from before
+ 
+
+ align:start position:0%
+half this looks suggestive from before
+but it it makes it obvious that e is
+
+ align:start position:0%
+but it it makes it obvious that e is
+ 
+
+ align:start position:0%
+but it it makes it obvious that e is
+herian and that may not be obvious to
+
+ align:start position:0%
+herian and that may not be obvious to
+ 
+
+ align:start position:0%
+herian and that may not be obvious to
+you guys so just check so something
+
+ align:start position:0%
+you guys so just check so something
+ 
+
+ align:start position:0%
+you guys so just check so something
+here's something that you'll show on the
+
+ align:start position:0%
+here's something that you'll show on the
+ 
+
+ align:start position:0%
+here's something that you'll show on the
+problem set um AB adint is equal to B
+
+ align:start position:0%
+problem set um AB adint is equal to B
+ 
+
+ align:start position:0%
+problem set um AB adint is equal to B
+adint A adint the order matters these
+
+ align:start position:0%
+adint A adint the order matters these
+ 
+
+ align:start position:0%
+adint A adint the order matters these
+are operators and so if we take the
+
+ align:start position:0%
+are operators and so if we take the
+ 
+
+ align:start position:0%
+are operators and so if we take the
+adint of this what's this going to give
+
+ align:start position:0%
+adint of this what's this going to give
+ 
+
+ align:start position:0%
+adint of this what's this going to give
+us well we change the order so it's
+
+ align:start position:0%
+us well we change the order so it's
+ 
+
+ align:start position:0%
+us well we change the order so it's
+going to be a dagger and then we take
+
+ align:start position:0%
+going to be a dagger and then we take
+ 
+
+ align:start position:0%
+going to be a dagger and then we take
+the dagger of both of them a a dagger so
+
+ align:start position:0%
+the dagger of both of them a a dagger so
+ 
+
+ align:start position:0%
+the dagger of both of them a a dagger so
+this is self this is self adjoint or
+
+ align:start position:0%
+this is self this is self adjoint or
+ 
+
+ align:start position:0%
+this is self this is self adjoint or
+herian so that's good of course we
+
+ align:start position:0%
+herian so that's good of course we
+ 
+
+ align:start position:0%
+herian so that's good of course we
+already knew that because we could have
+
+ align:start position:0%
+already knew that because we could have
+ 
+
+ align:start position:0%
+already knew that because we could have
+written in terms of X and P but this is
+
+ align:start position:0%
+written in terms of X and P but this is
+ 
+
+ align:start position:0%
+written in terms of X and P but this is
+somehow simpler and it in particular
+
+ align:start position:0%
+somehow simpler and it in particular
+ 
+
+ align:start position:0%
+somehow simpler and it in particular
+emphasizes the form of the capitulates
+
+ align:start position:0%
+emphasizes the form of the capitulates
+ 
+
+ align:start position:0%
+emphasizes the form of the capitulates
+the form of the energy values so indeed
+
+ align:start position:0%
+the form of the energy values so indeed
+ 
+
+ align:start position:0%
+the form of the energy values so indeed
+the form why else would we care about a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dagger okay now this is a good moment
+
+ align:start position:0%
+dagger okay now this is a good moment
+ 
+
+ align:start position:0%
+dagger okay now this is a good moment
+here's the second reason so the first
+
+ align:start position:0%
+here's the second reason so the first
+ 
+
+ align:start position:0%
+here's the second reason so the first
+reason you care is the sort of
+
+ align:start position:0%
+reason you care is the sort of
+ 
+
+ align:start position:0%
+reason you care is the sort of
+structural similarity and and and the
+
+ align:start position:0%
+structural similarity and and and the
+ 
+
+ align:start position:0%
+structural similarity and and and the
+fact that it's sort of nicely hermi in a
+
+ align:start position:0%
+fact that it's sort of nicely hermi in a
+ 
+
+ align:start position:0%
+fact that it's sort of nicely hermi in a
+different way here's the key thing
+
+ align:start position:0%
+different way here's the key thing
+ 
+
+ align:start position:0%
+different way here's the key thing
+key okay a and a dagger satisfy the
+
+ align:start position:0%
+key okay a and a dagger satisfy the
+ 
+
+ align:start position:0%
+key okay a and a dagger satisfy the
+simplest commutation relation in the
+
+ align:start position:0%
+simplest commutation relation in the
+ 
+
+ align:start position:0%
+simplest commutation relation in the
+world well the second simplest the
+
+ align:start position:0%
+world well the second simplest the
+ 
+
+ align:start position:0%
+world well the second simplest the
+simplest is that it's zero on the right
+
+ align:start position:0%
+simplest is that it's zero on the right
+ 
+
+ align:start position:0%
+simplest is that it's zero on the right
+hand side but the simplest not trivial
+
+ align:start position:0%
+hand side but the simplest not trivial
+ 
+
+ align:start position:0%
+hand side but the simplest not trivial
+computation relation a with a
+
+ align:start position:0%
+computation relation a with a
+ 
+
+ align:start position:0%
+computation relation a with a
+dagger is equal
+
+ align:start position:0%
+dagger is equal
+ 
+
+ align:start position:0%
+dagger is equal
+to so what is a dagger equal to well we
+
+ align:start position:0%
+to so what is a dagger equal to well we
+ 
+
+ align:start position:0%
+to so what is a dagger equal to well we
+just take the definition let's put this
+
+ align:start position:0%
+just take the definition let's put this
+ 
+
+ align:start position:0%
+just take the definition let's put this
+in so this is uh x uh over X knot uh
+
+ align:start position:0%
+in so this is uh x uh over X knot uh
+ 
+
+ align:start position:0%
+in so this is uh x uh over X knot uh
+plus I P over
+
+ align:start position:0%
+plus I P over
+ 
+
+ align:start position:0%
+plus I P over
+p uh comma uh X over x minus i p over
+
+ align:start position:0%
+p uh comma uh X over x minus i p over
+ 
+
+ align:start position:0%
+p uh comma uh X over x minus i p over
+P hat hat hat hat bracket bracket good
+
+ align:start position:0%
+P hat hat hat hat bracket bracket good
+ 
+
+ align:start position:0%
+P hat hat hat hat bracket bracket good
+so here there going to be four uh there
+
+ align:start position:0%
+so here there going to be four uh there
+ 
+
+ align:start position:0%
+so here there going to be four uh there
+going to be four terms there's x
+
+ align:start position:0%
+going to be four terms there's x
+ 
+
+ align:start position:0%
+going to be four terms there's x
+commutator x what is
+
+ align:start position:0%
+commutator x what is
+ 
+
+ align:start position:0%
+commutator x what is
+that what is the commutator of an
+
+ align:start position:0%
+that what is the commutator of an
+ 
+
+ align:start position:0%
+that what is the commutator of an
+operator with
+
+ align:start position:0%
+operator with
+ 
+
+ align:start position:0%
+operator with
+itself zero because remember the
+
+ align:start position:0%
+itself zero because remember the
+ 
+
+ align:start position:0%
+itself zero because remember the
+definition of the commutator is uh a uh
+
+ align:start position:0%
+definition of the commutator is uh a uh
+ 
+
+ align:start position:0%
+definition of the commutator is uh a uh
+B is a minus b a so a with a is equal to
+
+ align:start position:0%
+B is a minus b a so a with a is equal to
+ 
+
+ align:start position:0%
+B is a minus b a so a with a is equal to
+a a minus a
+
+ align:start position:0%
+a a minus a
+ 
+
+ align:start position:0%
+a a minus a
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+and I mean you have no options there
+
+ align:start position:0%
+and I mean you have no options there
+ 
+
+ align:start position:0%
+and I mean you have no options there
+that's zero so x with X is zero p with p
+
+ align:start position:0%
+that's zero so x with X is zero p with p
+ 
+
+ align:start position:0%
+that's zero so x with X is zero p with p
+is zero so the only terms that matter
+
+ align:start position:0%
+is zero so the only terms that matter
+ 
+
+ align:start position:0%
+is zero so the only terms that matter
+are the cross terms we have an X with p
+
+ align:start position:0%
+are the cross terms we have an X with p
+ 
+
+ align:start position:0%
+are the cross terms we have an X with p
+and notice that's going to be times a
+
+ align:start position:0%
+and notice that's going to be times a
+ 
+
+ align:start position:0%
+and notice that's going to be times a
+minus I with p and X knot and then we
+
+ align:start position:0%
+minus I with p and X knot and then we
+ 
+
+ align:start position:0%
+minus I with p and X knot and then we
+have another term which is p with X
+
+ align:start position:0%
+have another term which is p with X
+ 
+
+ align:start position:0%
+have another term which is p with X
+which is i p over X knot so you change
+
+ align:start position:0%
+which is i p over X knot so you change
+ 
+
+ align:start position:0%
+which is i p over X knot so you change
+the order and you change the sign but if
+
+ align:start position:0%
+the order and you change the sign but if
+ 
+
+ align:start position:0%
+the order and you change the sign but if
+you change the order of a commutator you
+
+ align:start position:0%
+you change the order of a commutator you
+ 
+
+ align:start position:0%
+you change the order of a commutator you
+change the side so we can put them both
+
+ align:start position:0%
+change the side so we can put them both
+ 
+
+ align:start position:0%
+change the side so we can put them both
+in the same order well let me just write
+
+ align:start position:0%
+in the same order well let me just write
+ 
+
+ align:start position:0%
+in the same order well let me just write
+this out so this is I over x p so this
+
+ align:start position:0%
+this out so this is I over x p so this
+ 
+
+ align:start position:0%
+this out so this is I over x p so this
+guy minus I over X x p but x p is equal
+
+ align:start position:0%
+guy minus I over X x p but x p is equal
+ 
+
+ align:start position:0%
+guy minus I over X x p but x p is equal
+to 2 H bar as we checked before uh this
+
+ align:start position:0%
+to 2 H bar as we checked before uh this
+ 
+
+ align:start position:0%
+to 2 H bar as we checked before uh this
+was x with
+
+ align:start position:0%
+was x with
+ 
+
+ align:start position:0%
+was x with
+p uh and then the second term was uh um
+
+ align:start position:0%
+p uh and then the second term was uh um
+ 
+
+ align:start position:0%
+p uh and then the second term was uh um
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+I again over x p which is 2 H bar uh p
+
+ align:start position:0%
+I again over x p which is 2 H bar uh p
+ 
+
+ align:start position:0%
+I again over x p which is 2 H bar uh p
+with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X this x with p is equal
+
+ align:start position:0%
+X this x with p is equal
+ 
+
+ align:start position:0%
+X this x with p is equal
+to IH bar so the H bar cancels the I
+
+ align:start position:0%
+to IH bar so the H bar cancels the I
+ 
+
+ align:start position:0%
+to IH bar so the H bar cancels the I
+gives me a
+
+ align:start position:0%
+gives me a
+ 
+
+ align:start position:0%
+gives me a
+plus one and and P with X gives me minus
+
+ align:start position:0%
+plus one and and P with X gives me minus
+ 
+
+ align:start position:0%
+plus one and and P with X gives me minus
+I bar so the H bar and the minus I gives
+
+ align:start position:0%
+I bar so the H bar and the minus I gives
+ 
+
+ align:start position:0%
+I bar so the H bar and the minus I gives
+me a plus
+
+ align:start position:0%
+me a plus
+ 
+
+ align:start position:0%
+me a plus
+one well that's nice this is equal to
+
+ align:start position:0%
+one well that's nice this is equal to
+ 
+
+ align:start position:0%
+one well that's nice this is equal to
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+so plus
+
+ align:start position:0%
+so plus
+ 
+
+ align:start position:0%
+so plus
+12 uh
+
+ align:start position:0%
+12 uh
+ 
+
+ align:start position:0%
+12 uh
+therefore a with a
+
+ align:start position:0%
+therefore a with a
+ 
+
+ align:start position:0%
+therefore a with a
+dagger is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one as advertised that is about as
+
+ align:start position:0%
+one as advertised that is about as
+ 
+
+ align:start position:0%
+one as advertised that is about as
+simple as a
+
+ align:start position:0%
+simple as a
+ 
+
+ align:start position:0%
+simple as a
+get notice a couple of other commutators
+
+ align:start position:0%
+get notice a couple of other commutators
+ 
+
+ align:start position:0%
+get notice a couple of other commutators
+that follow from
+
+ align:start position:0%
+that follow from
+ 
+
+ align:start position:0%
+that follow from
+this a diager with
+
+ align:start position:0%
+this a diager with
+ 
+
+ align:start position:0%
+this a diager with
+a is equal
+
+ align:start position:0%
+a is equal
+ 
+
+ align:start position:0%
+a is equal
+to minus one we just Chang the order and
+
+ align:start position:0%
+to minus one we just Chang the order and
+ 
+
+ align:start position:0%
+to minus one we just Chang the order and
+that's just an overall minus sign and a
+
+ align:start position:0%
+that's just an overall minus sign and a
+ 
+
+ align:start position:0%
+that's just an overall minus sign and a
+with a is what zero a dger with a dger
+
+ align:start position:0%
+with a is what zero a dger with a dger
+ 
+
+ align:start position:0%
+with a is what zero a dger with a dger
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+okay so we are now going to
+
+ align:start position:0%
+okay so we are now going to
+ 
+
+ align:start position:0%
+okay so we are now going to
+use we are now going to use this
+
+ align:start position:0%
+use we are now going to use this
+ 
+
+ align:start position:0%
+use we are now going to use this
+commutation relation to totally crush
+
+ align:start position:0%
+commutation relation to totally crush
+ 
+
+ align:start position:0%
+commutation relation to totally crush
+the problem into submission it's going
+
+ align:start position:0%
+the problem into submission it's going
+ 
+
+ align:start position:0%
+the problem into submission it's going
+to be weeping before us like the Romans
+
+ align:start position:0%
+to be weeping before us like the Romans
+ 
+
+ align:start position:0%
+to be weeping before us like the Romans
+in front of the vizago it's going to be
+
+ align:start position:0%
+in front of the vizago it's going to be
+ 
+
+ align:start position:0%
+in front of the vizago it's going to be
+dramatic okay so
+
+ align:start position:0%
+dramatic okay so
+ 
+
+ align:start position:0%
+dramatic okay so
+let's let's check so let's combine the
+
+ align:start position:0%
+let's let's check so let's combine the
+ 
+
+ align:start position:0%
+let's let's check so let's combine the
+the two things so we had the first thing
+
+ align:start position:0%
+the two things so we had the first thing
+ 
+
+ align:start position:0%
+the two things so we had the first thing
+is that the form is simple the second is
+
+ align:start position:0%
+is that the form is simple the second is
+ 
+
+ align:start position:0%
+is that the form is simple the second is
+that the commutator is simple let's
+
+ align:start position:0%
+that the commutator is simple let's
+ 
+
+ align:start position:0%
+that the commutator is simple let's
+combine these together and really milk
+
+ align:start position:0%
+combine these together and really milk
+ 
+
+ align:start position:0%
+combine these together and really milk
+the system for what it's got and to do
+
+ align:start position:0%
+the system for what it's got and to do
+ 
+
+ align:start position:0%
+the system for what it's got and to do
+that I need two more commutators
+
+ align:start position:0%
+that I need two more commutators
+ 
+
+ align:start position:0%
+that I need two more commutators
+okay and the lesson of this series of
+
+ align:start position:0%
+okay and the lesson of this series of
+ 
+
+ align:start position:0%
+okay and the lesson of this series of
+machinations it's very tempting to look
+
+ align:start position:0%
+machinations it's very tempting to look
+ 
+
+ align:start position:0%
+machinations it's very tempting to look
+at this and be like why are you doing
+
+ align:start position:0%
+at this and be like why are you doing
+ 
+
+ align:start position:0%
+at this and be like why are you doing
+this and the reason is I want to
+
+ align:start position:0%
+this and the reason is I want to
+ 
+
+ align:start position:0%
+this and the reason is I want to
+encourage you to to I want to encourage
+
+ align:start position:0%
+encourage you to to I want to encourage
+ 
+
+ align:start position:0%
+encourage you to to I want to encourage
+you to see the power of these
+
+ align:start position:0%
+you to see the power of these
+ 
+
+ align:start position:0%
+you to see the power of these
+commutation relations they're telling
+
+ align:start position:0%
+commutation relations they're telling
+ 
+
+ align:start position:0%
+commutation relations they're telling
+you a tremendous amount about the system
+
+ align:start position:0%
+you a tremendous amount about the system
+ 
+
+ align:start position:0%
+you a tremendous amount about the system
+so we're going through and doing some
+
+ align:start position:0%
+so we're going through and doing some
+ 
+
+ align:start position:0%
+so we're going through and doing some
+relatively simple calculations we're
+
+ align:start position:0%
+relatively simple calculations we're
+ 
+
+ align:start position:0%
+relatively simple calculations we're
+just Computing commutators we're
+
+ align:start position:0%
+just Computing commutators we're
+ 
+
+ align:start position:0%
+just Computing commutators we're
+following our noes and we're going to
+
+ align:start position:0%
+following our noes and we're going to
+ 
+
+ align:start position:0%
+following our noes and we're going to
+derive something
+
+ align:start position:0%
+derive something
+ 
+
+ align:start position:0%
+derive something
+awesome so bear so don't just bear with
+
+ align:start position:0%
+awesome so bear so don't just bear with
+ 
+
+ align:start position:0%
+awesome so bear so don't just bear with
+it learn from this that there's
+
+ align:start position:0%
+it learn from this that there's
+ 
+
+ align:start position:0%
+it learn from this that there's
+something very useful and Powerful about
+
+ align:start position:0%
+something very useful and Powerful about
+ 
+
+ align:start position:0%
+something very useful and Powerful about
+commutation relations you'll see that at
+
+ align:start position:0%
+commutation relations you'll see that at
+ 
+
+ align:start position:0%
+commutation relations you'll see that at
+the end but I want you to hold on to the
+
+ align:start position:0%
+the end but I want you to hold on to the
+ 
+
+ align:start position:0%
+the end but I want you to hold on to the
+slight awkwardness right now that it's
+
+ align:start position:0%
+slight awkwardness right now that it's
+ 
+
+ align:start position:0%
+slight awkwardness right now that it's
+not totally obvious beforehand where
+
+ align:start position:0%
+not totally obvious beforehand where
+ 
+
+ align:start position:0%
+not totally obvious beforehand where
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+going so what is e with a well that's
+
+ align:start position:0%
+going so what is e with a well that's
+ 
+
+ align:start position:0%
+going so what is e with a well that's
+easy it's the H bar Omega a diager a uh
+
+ align:start position:0%
+easy it's the H bar Omega a diager a uh
+ 
+
+ align:start position:0%
+easy it's the H bar Omega a diager a uh
+plus one2 so the one/ half what's one/
+
+ align:start position:0%
+plus one2 so the one/ half what's one/
+ 
+
+ align:start position:0%
+plus one2 so the one/ half what's one/
+half commutator with an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator zero because any number
+
+ align:start position:0%
+operator zero because any number
+ 
+
+ align:start position:0%
+operator zero because any number
+commutes with an operator 1/ half
+
+ align:start position:0%
+commutes with an operator 1/ half
+ 
+
+ align:start position:0%
+commutes with an operator 1/ half
+operator is operator one2 it's just a
+
+ align:start position:0%
+operator is operator one2 it's just a
+ 
+
+ align:start position:0%
+operator is operator one2 it's just a
+constant the that term is gone so the
+
+ align:start position:0%
+constant the that term is gone so the
+ 
+
+ align:start position:0%
+constant the that term is gone so the
+only thing that's left over is H bar
+
+ align:start position:0%
+only thing that's left over is H bar
+ 
+
+ align:start position:0%
+only thing that's left over is H bar
+Omega a DI
+
+ align:start position:0%
+Omega a DI
+ 
+
+ align:start position:0%
+Omega a DI
+a with a now the H bar Omega is just a
+
+ align:start position:0%
+a with a now the H bar Omega is just a
+ 
+
+ align:start position:0%
+a with a now the H bar Omega is just a
+constant it's going to pull out no
+
+ align:start position:0%
+constant it's going to pull out no
+ 
+
+ align:start position:0%
+constant it's going to pull out no
+matter which term we're looking at so I
+
+ align:start position:0%
+matter which term we're looking at so I
+ 
+
+ align:start position:0%
+matter which term we're looking at so I
+can write I can just pull that factor
+
+ align:start position:0%
+can write I can just pull that factor
+ 
+
+ align:start position:0%
+can write I can just pull that factor
+out okay so this is equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to H bar
+
+ align:start position:0%
+to H bar
+ 
+
+ align:start position:0%
+to H bar
+Omega times a d a a minus a a dger
+
+ align:start position:0%
+Omega times a d a a minus a a dger
+ 
+
+ align:start position:0%
+Omega times a d a a minus a a dger
+a but this is equal to H bar Omega well
+
+ align:start position:0%
+a but this is equal to H bar Omega well
+ 
+
+ align:start position:0%
+a but this is equal to H bar Omega well
+that's a dagger a a a a dagger a we can
+
+ align:start position:0%
+that's a dagger a a a a dagger a we can
+ 
+
+ align:start position:0%
+that's a dagger a a a a dagger a we can
+just pull out the A on the right um a
+
+ align:start position:0%
+just pull out the A on the right um a
+ 
+
+ align:start position:0%
+just pull out the A on the right um a
+dagger a minus a a dagger
+
+ align:start position:0%
+dagger a minus a a dagger
+ 
+
+ align:start position:0%
+dagger a minus a a dagger
+a but that's equal to H bar Omega well a
+
+ align:start position:0%
+a but that's equal to H bar Omega well a
+ 
+
+ align:start position:0%
+a but that's equal to H bar Omega well a
+dagger with a is equal
+
+ align:start position:0%
+dagger with a is equal
+ 
+
+ align:start position:0%
+dagger with a is equal
+to a diager with a minus one is equal to
+
+ align:start position:0%
+to a diager with a minus one is equal to
+ 
+
+ align:start position:0%
+to a diager with a minus one is equal to
+minus H Omega and we have this a left
+
+ align:start position:0%
+minus H Omega and we have this a left
+ 
+
+ align:start position:0%
+minus H Omega and we have this a left
+over a so e with
+
+ align:start position:0%
+over a so e with
+ 
+
+ align:start position:0%
+over a so e with
+a is equal to minus a well that's
+
+ align:start position:0%
+a is equal to minus a well that's
+ 
+
+ align:start position:0%
+a is equal to minus a well that's
+interesting now the second commutator
+
+ align:start position:0%
+interesting now the second commutator
+ 
+
+ align:start position:0%
+interesting now the second commutator
+I'm not going to do it e with a
+
+ align:start position:0%
+I'm not going to do it e with a
+ 
+
+ align:start position:0%
+I'm not going to do it e with a
+dagger is going to be equal to well it's
+
+ align:start position:0%
+dagger is going to be equal to well it's
+ 
+
+ align:start position:0%
+dagger is going to be equal to well it's
+just eyeball what's going to happen this
+
+ align:start position:0%
+just eyeball what's going to happen this
+ 
+
+ align:start position:0%
+just eyeball what's going to happen this
+going to be uh a dagger so we're going
+
+ align:start position:0%
+going to be uh a dagger so we're going
+ 
+
+ align:start position:0%
+going to be uh a dagger so we're going
+to have a dagger a dagger minus a dagger
+
+ align:start position:0%
+to have a dagger a dagger minus a dagger
+ 
+
+ align:start position:0%
+to have a dagger a dagger minus a dagger
+a dagger a so we're going have an a
+
+ align:start position:0%
+a dagger a so we're going have an a
+ 
+
+ align:start position:0%
+a dagger a so we're going have an a
+dagger in front and then a
+
+ align:start position:0%
+dagger in front and then a
+ 
+
+ align:start position:0%
+dagger in front and then a
+dagger so all we're going to get is a
+
+ align:start position:0%
+dagger so all we're going to get is a
+ 
+
+ align:start position:0%
+dagger so all we're going to get is a
+sign and it's going to be a dagger plus
+
+ align:start position:0%
+sign and it's going to be a dagger plus
+ 
+
+ align:start position:0%
+sign and it's going to be a dagger plus
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dagger I should have written that in the
+
+ align:start position:0%
+dagger I should have written that in the
+ 
+
+ align:start position:0%
+dagger I should have written that in the
+center
+
+ align:start position:0%
+center
+ 
+
+ align:start position:0%
+center
+okay everyone cool with that yeah
+
+ align:start position:0%
+okay everyone cool with that yeah
+ 
+
+ align:start position:0%
+okay everyone cool with that yeah
+oh shoot thank you ah H bar Omega thank
+
+ align:start position:0%
+oh shoot thank you ah H bar Omega thank
+ 
+
+ align:start position:0%
+oh shoot thank you ah H bar Omega thank
+you we would have misruled the Galaxy so
+
+ align:start position:0%
+you we would have misruled the Galaxy so
+ 
+
+ align:start position:0%
+you we would have misruled the Galaxy so
+uh uh okay good other
+
+ align:start position:0%
+uh uh okay good other
+ 
+
+ align:start position:0%
+uh uh okay good other
+questions okay you don't notice you
+
+ align:start position:0%
+questions okay you don't notice you
+ 
+
+ align:start position:0%
+questions okay you don't notice you
+haven't noticed yet but we just won we
+
+ align:start position:0%
+haven't noticed yet but we just won we
+ 
+
+ align:start position:0%
+haven't noticed yet but we just won we
+just totally solved the problem and
+
+ align:start position:0%
+just totally solved the problem and
+ 
+
+ align:start position:0%
+just totally solved the problem and
+here's why once you see this anytime you
+
+ align:start position:0%
+here's why once you see this anytime you
+ 
+
+ align:start position:0%
+here's why once you see this anytime you
+see this anytime you see this commut wow
+
+ align:start position:0%
+see this anytime you see this commut wow
+ 
+
+ align:start position:0%
+see this anytime you see this commut wow
+I'm far anytime you see this commutator
+
+ align:start position:0%
+I'm far anytime you see this commutator
+ 
+
+ align:start position:0%
+I'm far anytime you see this commutator
+an operator with an a is equal to plus a
+
+ align:start position:0%
+an operator with an a is equal to plus a
+ 
+
+ align:start position:0%
+an operator with an a is equal to plus a
+times some constant anytime you see this
+
+ align:start position:0%
+times some constant anytime you see this
+ 
+
+ align:start position:0%
+times some constant anytime you see this
+cheer okay and here's why yeah right
+
+ align:start position:0%
+cheer okay and here's why yeah right
+ 
+
+ align:start position:0%
+cheer okay and here's why yeah right
+exactly now you know um so so here's why
+
+ align:start position:0%
+exactly now you know um so so here's why
+ 
+
+ align:start position:0%
+exactly now you know um so so here's why
+here's why you should cheer because you
+
+ align:start position:0%
+here's why you should cheer because you
+ 
+
+ align:start position:0%
+here's why you should cheer because you
+no longer have to solve any problems you
+
+ align:start position:0%
+no longer have to solve any problems you
+ 
+
+ align:start position:0%
+no longer have to solve any problems you
+no longer have to solve any differential
+
+ align:start position:0%
+no longer have to solve any differential
+ 
+
+ align:start position:0%
+no longer have to solve any differential
+equations you can simply write down the
+
+ align:start position:0%
+equations you can simply write down the
+ 
+
+ align:start position:0%
+equations you can simply write down the
+problem and let's see that you can just
+
+ align:start position:0%
+problem and let's see that you can just
+ 
+
+ align:start position:0%
+problem and let's see that you can just
+write down the answer so
+
+ align:start position:0%
+write down the answer so
+ 
+
+ align:start position:0%
+write down the answer so
+suppose suppose we already happen to
+
+ align:start position:0%
+suppose suppose we already happen to
+ 
+
+ align:start position:0%
+suppose suppose we already happen to
+have access know here in my sleeve I
+
+ align:start position:0%
+have access know here in my sleeve I
+ 
+
+ align:start position:0%
+have access know here in my sleeve I
+have access to an igen function of the
+
+ align:start position:0%
+have access to an igen function of the
+ 
+
+ align:start position:0%
+have access to an igen function of the
+energy operator e on f e is equal to e f
+
+ align:start position:0%
+energy operator e on f e is equal to e f
+ 
+
+ align:start position:0%
+energy operator e on f e is equal to e f
+e suppose I have this guy
+
+ align:start position:0%
+e suppose I have this guy
+ 
+
+ align:start position:0%
+e suppose I have this guy
+cool check this out
+
+ align:start position:0%
+cool check this out
+ 
+
+ align:start position:0%
+cool check this out
+consider a new state s which is equal to
+
+ align:start position:0%
+consider a new state s which is equal to
+ 
+
+ align:start position:0%
+consider a new state s which is equal to
+a do I which do I want to do first it
+
+ align:start position:0%
+a do I which do I want to do first it
+ 
+
+ align:start position:0%
+a do I which do I want to do first it
+doesn't really matter but let's do a
+
+ align:start position:0%
+doesn't really matter but let's do a
+ 
+
+ align:start position:0%
+doesn't really matter but let's do a
+consider s is equal to a on f
+
+ align:start position:0%
+consider s is equal to a on f
+ 
+
+ align:start position:0%
+consider s is equal to a on f
+e okay consider what can you say about
+
+ align:start position:0%
+e okay consider what can you say about
+ 
+
+ align:start position:0%
+e okay consider what can you say about
+this state well it's the state you get
+
+ align:start position:0%
+this state well it's the state you get
+ 
+
+ align:start position:0%
+this state well it's the state you get
+by taking this wave function and acting
+
+ align:start position:0%
+by taking this wave function and acting
+ 
+
+ align:start position:0%
+by taking this wave function and acting
+with a not terribly Illuminating however
+
+ align:start position:0%
+with a not terribly Illuminating however
+ 
+
+ align:start position:0%
+with a not terribly Illuminating however
+e on S is equal to what maybe this has
+
+ align:start position:0%
+e on S is equal to what maybe this has
+ 
+
+ align:start position:0%
+e on S is equal to what maybe this has
+some nice property underacting with
+
+ align:start position:0%
+some nice property underacting with
+ 
+
+ align:start position:0%
+some nice property underacting with
+e this is equal to e on a with f e now
+
+ align:start position:0%
+e this is equal to e on a with f e now
+ 
+
+ align:start position:0%
+e this is equal to e on a with f e now
+this is tantalizing because at this
+
+ align:start position:0%
+this is tantalizing because at this
+ 
+
+ align:start position:0%
+this is tantalizing because at this
+point it's very look that e it really
+
+ align:start position:0%
+point it's very look that e it really
+ 
+
+ align:start position:0%
+point it's very look that e it really
+wants to hit this F right it just really
+
+ align:start position:0%
+wants to hit this F right it just really
+ 
+
+ align:start position:0%
+wants to hit this F right it just really
+wants to there's an e it wants to pull
+
+ align:start position:0%
+wants to there's an e it wants to pull
+ 
+
+ align:start position:0%
+wants to there's an e it wants to pull
+out it'll be great the problem is that
+
+ align:start position:0%
+out it'll be great the problem is that
+ 
+
+ align:start position:0%
+out it'll be great the problem is that
+not there there's an A in the way and so
+
+ align:start position:0%
+not there there's an A in the way and so
+ 
+
+ align:start position:0%
+not there there's an A in the way and so
+at this point we add zero okay this is a
+
+ align:start position:0%
+at this point we add zero okay this is a
+ 
+
+ align:start position:0%
+at this point we add zero okay this is a
+very powerful technique this is equal to
+
+ align:start position:0%
+very powerful technique this is equal to
+ 
+
+ align:start position:0%
+very powerful technique this is equal to
+E A minus a oops e plus a
+
+ align:start position:0%
+E A minus a oops e plus a
+ 
+
+ align:start position:0%
+E A minus a oops e plus a
+e okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F okay but that has a nice expression
+
+ align:start position:0%
+F okay but that has a nice expression
+ 
+
+ align:start position:0%
+F okay but that has a nice expression
+this is equal to E A minus AE that's the
+
+ align:start position:0%
+this is equal to E A minus AE that's the
+ 
+
+ align:start position:0%
+this is equal to E A minus AE that's the
+commutator of e with
+
+ align:start position:0%
+commutator of e with
+ 
+
+ align:start position:0%
+commutator of e with
+a uh plus a
+
+ align:start position:0%
+a uh plus a
+ 
+
+ align:start position:0%
+a uh plus a
+well what's E acting on f e well
+
+ align:start position:0%
+well what's E acting on f e well
+ 
+
+ align:start position:0%
+well what's E acting on f e well
+actually let me just leave this as AE so
+
+ align:start position:0%
+actually let me just leave this as AE so
+ 
+
+ align:start position:0%
+actually let me just leave this as AE so
+what have we done here before we
+
+ align:start position:0%
+what have we done here before we
+ 
+
+ align:start position:0%
+what have we done here before we
+actually act fight what we've done is
+
+ align:start position:0%
+actually act fight what we've done is
+ 
+
+ align:start position:0%
+actually act fight what we've done is
+something called commuting an operator
+
+ align:start position:0%
+something called commuting an operator
+ 
+
+ align:start position:0%
+something called commuting an operator
+through so what do I mean by commuting
+
+ align:start position:0%
+through so what do I mean by commuting
+ 
+
+ align:start position:0%
+through so what do I mean by commuting
+an operator through if we have an
+
+ align:start position:0%
+an operator through if we have an
+ 
+
+ align:start position:0%
+an operator through if we have an
+operator a and an operator B and an and
+
+ align:start position:0%
+operator a and an operator B and an and
+ 
+
+ align:start position:0%
+operator a and an operator B and an and
+a state F and I want a to act on F I can
+
+ align:start position:0%
+a state F and I want a to act on F I can
+ 
+
+ align:start position:0%
+a state F and I want a to act on F I can
+always write this as this is equal to um
+
+ align:start position:0%
+always write this as this is equal to um
+ 
+
+ align:start position:0%
+always write this as this is equal to um
+the commutator of a with B plus ba
+
+ align:start position:0%
+the commutator of a with B plus ba
+ 
+
+ align:start position:0%
+the commutator of a with B plus ba
+acting on F so this lets me act a on F
+
+ align:start position:0%
+acting on F so this lets me act a on F
+ 
+
+ align:start position:0%
+acting on F so this lets me act a on F
+directly without B but I have to know
+
+ align:start position:0%
+directly without B but I have to know
+ 
+
+ align:start position:0%
+directly without B but I have to know
+what the commutator of these two
+
+ align:start position:0%
+what the commutator of these two
+ 
+
+ align:start position:0%
+what the commutator of these two
+operators is so if I know what the
+
+ align:start position:0%
+operators is so if I know what the
+ 
+
+ align:start position:0%
+operators is so if I know what the
+commutator is I can do this I can
+
+ align:start position:0%
+commutator is I can do this I can
+ 
+
+ align:start position:0%
+commutator is I can do this I can
+simplify this is called when one does
+
+ align:start position:0%
+simplify this is called when one does
+ 
+
+ align:start position:0%
+simplify this is called when one does
+this when one takes a and replaces it by
+
+ align:start position:0%
+this when one takes a and replaces it by
+ 
+
+ align:start position:0%
+this when one takes a and replaces it by
+the commutator of a with B plus ba
+
+ align:start position:0%
+the commutator of a with B plus ba
+ 
+
+ align:start position:0%
+the commutator of a with B plus ba
+changing the order the the phrase that
+
+ align:start position:0%
+changing the order the the phrase that
+ 
+
+ align:start position:0%
+changing the order the the phrase that
+one uses is I have commuted a through b
+
+ align:start position:0%
+one uses is I have commuted a through b
+ 
+
+ align:start position:0%
+one uses is I have commuted a through b
+okay and commuting operators through
+
+ align:start position:0%
+okay and commuting operators through
+ 
+
+ align:start position:0%
+okay and commuting operators through
+each other is an extraordinarily useful
+
+ align:start position:0%
+each other is an extraordinarily useful
+ 
+
+ align:start position:0%
+each other is an extraordinarily useful
+tool useful technique now let's see why
+
+ align:start position:0%
+tool useful technique now let's see why
+ 
+
+ align:start position:0%
+tool useful technique now let's see why
+so here what's the commutator of e with
+
+ align:start position:0%
+so here what's the commutator of e with
+ 
+
+ align:start position:0%
+so here what's the commutator of e with
+a oh we just did that it's minus H Omega
+
+ align:start position:0%
+a oh we just did that it's minus H Omega
+ 
+
+ align:start position:0%
+a oh we just did that it's minus H Omega
+a and what's a e on f
+
+ align:start position:0%
+a and what's a e on f
+ 
+
+ align:start position:0%
+a and what's a e on f
+e what's E on f
+
+ align:start position:0%
+e what's E on f
+ 
+
+ align:start position:0%
+e what's E on f
+e e right exactly uh plus uh e uh a on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fi and now we're cooking with gas
+
+ align:start position:0%
+fi and now we're cooking with gas
+ 
+
+ align:start position:0%
+fi and now we're cooking with gas
+because this is equal to H minus H bar
+
+ align:start position:0%
+because this is equal to H minus H bar
+ 
+
+ align:start position:0%
+because this is equal to H minus H bar
+Omega a plus E A I'm going to pull out
+
+ align:start position:0%
+Omega a plus E A I'm going to pull out
+ 
+
+ align:start position:0%
+Omega a plus E A I'm going to pull out
+this common factor of e of a okay so if
+
+ align:start position:0%
+this common factor of e of a okay so if
+ 
+
+ align:start position:0%
+this common factor of e of a okay so if
+I pull out that common factor of
+
+ align:start position:0%
+I pull out that common factor of
+ 
+
+ align:start position:0%
+I pull out that common factor of
+a plus
+
+ align:start position:0%
+a plus
+ 
+
+ align:start position:0%
+a plus
+e a f e and now I'm going to just
+
+ align:start position:0%
+e a f e and now I'm going to just
+ 
+
+ align:start position:0%
+e a f e and now I'm going to just
+slightly write this instead of e or
+
+ align:start position:0%
+slightly write this instead of e or
+ 
+
+ align:start position:0%
+slightly write this instead of e or
+minus H bar Omega plus e I'm going write
+
+ align:start position:0%
+minus H bar Omega plus e I'm going write
+ 
+
+ align:start position:0%
+minus H bar Omega plus e I'm going write
+this as e minus H bar Omega I just
+
+ align:start position:0%
+this as e minus H bar Omega I just
+ 
+
+ align:start position:0%
+this as e minus H bar Omega I just
+literally changing the order of the
+
+ align:start position:0%
+literally changing the order of the
+ 
+
+ align:start position:0%
+literally changing the order of the
+algebra e minus H
+
+ align:start position:0%
+algebra e minus H
+ 
+
+ align:start position:0%
+algebra e minus H
+Omega and what is a
+
+ align:start position:0%
+Omega and what is a
+ 
+
+ align:start position:0%
+Omega and what is a
+e s that was the original state we
+
+ align:start position:0%
+e s that was the original state we
+ 
+
+ align:start position:0%
+e s that was the original state we
+started with
+
+ align:start position:0%
+started with
+ 
+
+ align:start position:0%
+started with
+s well that's cool if I have a state
+
+ align:start position:0%
+s well that's cool if I have a state
+ 
+
+ align:start position:0%
+s well that's cool if I have a state
+with energy e and I act on it with the
+
+ align:start position:0%
+with energy e and I act on it with the
+ 
+
+ align:start position:0%
+with energy e and I act on it with the
+operator
+
+ align:start position:0%
+operator
+ 
+
+ align:start position:0%
+operator
+a I get a new state Sai which is also an
+
+ align:start position:0%
+a I get a new state Sai which is also an
+ 
+
+ align:start position:0%
+a I get a new state Sai which is also an
+IG state of the energy
+
+ align:start position:0%
+IG state of the energy
+ 
+
+ align:start position:0%
+IG state of the energy
+operator but with a slightly different
+
+ align:start position:0%
+operator but with a slightly different
+ 
+
+ align:start position:0%
+operator but with a slightly different
+energy IG value the igen value is now
+
+ align:start position:0%
+energy IG value the igen value is now
+ 
+
+ align:start position:0%
+energy IG value the igen value is now
+decreased by H bar
+
+ align:start position:0%
+decreased by H bar
+ 
+
+ align:start position:0%
+decreased by H bar
+Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cool and that is what we
+
+ align:start position:0%
+cool and that is what we
+ 
+
+ align:start position:0%
+cool and that is what we
+wanted let's explore the consequences of
+
+ align:start position:0%
+wanted let's explore the consequences of
+ 
+
+ align:start position:0%
+wanted let's explore the consequences of
+this so if we have a state with with I
+
+ align:start position:0%
+this so if we have a state with with I
+ 
+
+ align:start position:0%
+this so if we have a state with with I
+value e we have f e such that e on f e
+
+ align:start position:0%
+value e we have f e such that e on f e
+ 
+
+ align:start position:0%
+value e we have f e such that e on f e
+is equal to e f e then the state a f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e has I
+
+ align:start position:0%
+e has I
+ 
+
+ align:start position:0%
+e has I
+value as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy I
+
+ align:start position:0%
+energy I
+ 
+
+ align:start position:0%
+energy I
+value e minus H bar Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I could call
+
+ align:start position:0%
+so I could call
+ 
+
+ align:start position:0%
+so I could call
+S uh uh I could just call this F sub e
+
+ align:start position:0%
+S uh uh I could just call this F sub e
+ 
+
+ align:start position:0%
+S uh uh I could just call this F sub e
+minus H Omega it's an igen value igen
+
+ align:start position:0%
+minus H Omega it's an igen value igen
+ 
+
+ align:start position:0%
+minus H Omega it's an igen value igen
+function of the energy operator the
+
+ align:start position:0%
+function of the energy operator the
+ 
+
+ align:start position:0%
+function of the energy operator the
+value e minus H Omega agreed do I know
+
+ align:start position:0%
+value e minus H Omega agreed do I know
+ 
+
+ align:start position:0%
+value e minus H Omega agreed do I know
+that this is in fact properly
+
+ align:start position:0%
+that this is in fact properly
+ 
+
+ align:start position:0%
+that this is in fact properly
+normalized no because 12 times it would
+
+ align:start position:0%
+normalized no because 12 times it would
+ 
+
+ align:start position:0%
+normalized no because 12 times it would
+also be a perfectly good igen function
+
+ align:start position:0%
+also be a perfectly good igen function
+ 
+
+ align:start position:0%
+also be a perfectly good igen function
+of the energy operator so this is
+
+ align:start position:0%
+of the energy operator so this is
+ 
+
+ align:start position:0%
+of the energy operator so this is
+proportional to the properly normalized
+
+ align:start position:0%
+proportional to the properly normalized
+ 
+
+ align:start position:0%
+proportional to the properly normalized
+guy with some at the moment unknown
+
+ align:start position:0%
+guy with some at the moment unknown
+ 
+
+ align:start position:0%
+guy with some at the moment unknown
+constant coefficient normalization
+
+ align:start position:0%
+constant coefficient normalization
+ 
+
+ align:start position:0%
+constant coefficient normalization
+everyone cool with that so now let's
+
+ align:start position:0%
+everyone cool with that so now let's
+ 
+
+ align:start position:0%
+everyone cool with that so now let's
+think about what this tells us this
+
+ align:start position:0%
+think about what this tells us this
+ 
+
+ align:start position:0%
+think about what this tells us this
+tells us if we have a state f e which I
+
+ align:start position:0%
+tells us if we have a state f e which I
+ 
+
+ align:start position:0%
+tells us if we have a state f e which I
+will denote its energy by this level
+
+ align:start position:0%
+will denote its energy by this level
+ 
+
+ align:start position:0%
+will denote its energy by this level
+then if I act on it with a f e I get
+
+ align:start position:0%
+then if I act on it with a f e I get
+ 
+
+ align:start position:0%
+then if I act on it with a f e I get
+another state where the energy instead
+
+ align:start position:0%
+another state where the energy instead
+ 
+
+ align:start position:0%
+another state where the energy instead
+of being e is equal to eus H bar Omega
+
+ align:start position:0%
+of being e is equal to eus H bar Omega
+ 
+
+ align:start position:0%
+of being e is equal to eus H bar Omega
+so this distance in energy is H bar
+
+ align:start position:0%
+so this distance in energy is H bar
+ 
+
+ align:start position:0%
+so this distance in energy is H bar
+Omega cool let me do it again let's act
+
+ align:start position:0%
+Omega cool let me do it again let's act
+ 
+
+ align:start position:0%
+Omega cool let me do it again let's act
+a on F by exactly the same argument if I
+
+ align:start position:0%
+a on F by exactly the same argument if I
+ 
+
+ align:start position:0%
+a on F by exactly the same argument if I
+make S is equal to a on a
+
+ align:start position:0%
+make S is equal to a on a
+ 
+
+ align:start position:0%
+make S is equal to a on a
+f a s f i get another state again
+
+ align:start position:0%
+f a s f i get another state again
+ 
+
+ align:start position:0%
+f a s f i get another state again
+separated by H bar
+
+ align:start position:0%
+separated by H bar
+ 
+
+ align:start position:0%
+separated by H bar
+Omega e minus 2 H
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Omega Turtles all the way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down everyone cool with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that let's do a slightly different
+
+ align:start position:0%
+that let's do a slightly different
+ 
+
+ align:start position:0%
+that let's do a slightly different
+calcul
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay but before we do that so I want
+
+ align:start position:0%
+so okay but before we do that so I want
+ 
+
+ align:start position:0%
+so okay but before we do that so I want
+to give a a
+
+ align:start position:0%
+to give a a
+ 
+
+ align:start position:0%
+to give a a
+name okay a does something really cool
+
+ align:start position:0%
+name okay a does something really cool
+ 
+
+ align:start position:0%
+name okay a does something really cool
+when you take the state f e that has
+
+ align:start position:0%
+when you take the state f e that has
+ 
+
+ align:start position:0%
+when you take the state f e that has
+definite energy e it's an energy
+
+ align:start position:0%
+definite energy e it's an energy
+ 
+
+ align:start position:0%
+definite energy e it's an energy
+function and you act on it with a what
+
+ align:start position:0%
+function and you act on it with a what
+ 
+
+ align:start position:0%
+function and you act on it with a what
+happens it lowers the energy by H bar
+
+ align:start position:0%
+happens it lowers the energy by H bar
+ 
+
+ align:start position:0%
+happens it lowers the energy by H bar
+Omega so I'm going to call a the
+
+ align:start position:0%
+Omega so I'm going to call a the
+ 
+
+ align:start position:0%
+Omega so I'm going to call a the
+lowering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator because what it does is it
+
+ align:start position:0%
+operator because what it does is it
+ 
+
+ align:start position:0%
+operator because what it does is it
+takes a state with f e with energy value
+
+ align:start position:0%
+takes a state with f e with energy value
+ 
+
+ align:start position:0%
+takes a state with f e with energy value
+e to a state with energy eus H Omega and
+
+ align:start position:0%
+e to a state with energy eus H Omega and
+ 
+
+ align:start position:0%
+e to a state with energy eus H Omega and
+I can just keep doing this as many times
+
+ align:start position:0%
+I can just keep doing this as many times
+ 
+
+ align:start position:0%
+I can just keep doing this as many times
+as I like and I build a tower yes you
+
+ align:start position:0%
+as I like and I build a tower yes you
+ 
+
+ align:start position:0%
+as I like and I build a tower yes you
+the ground state ah very good question
+
+ align:start position:0%
+the ground state ah very good question
+ 
+
+ align:start position:0%
+the ground state ah very good question
+we hold on to that for a
+
+ align:start position:0%
+we hold on to that for a
+ 
+
+ align:start position:0%
+we hold on to that for a
+second we'll come back to that in just a
+
+ align:start position:0%
+second we'll come back to that in just a
+ 
+
+ align:start position:0%
+second we'll come back to that in just a
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+okay so this seems to build for me a
+
+ align:start position:0%
+okay so this seems to build for me a
+ 
+
+ align:start position:0%
+okay so this seems to build for me a
+ladder
+
+ align:start position:0%
+ladder
+ 
+
+ align:start position:0%
+ladder
+downwards everyone cool with that but we
+
+ align:start position:0%
+downwards everyone cool with that but we
+ 
+
+ align:start position:0%
+downwards everyone cool with that but we
+could have done the same thing with a
+
+ align:start position:0%
+could have done the same thing with a
+ 
+
+ align:start position:0%
+could have done the same thing with a
+dagger and how does a story change what
+
+ align:start position:0%
+dagger and how does a story change what
+ 
+
+ align:start position:0%
+dagger and how does a story change what
+happens if we take a dagger instead of a
+
+ align:start position:0%
+happens if we take a dagger instead of a
+ 
+
+ align:start position:0%
+happens if we take a dagger instead of a
+well let's go through every step here so
+
+ align:start position:0%
+well let's go through every step here so
+ 
+
+ align:start position:0%
+well let's go through every step here so
+this is going to be e on a dagger
+
+ align:start position:0%
+this is going to be e on a dagger
+ 
+
+ align:start position:0%
+this is going to be e on a dagger
+and now we have e a dagger a dagger e a
+
+ align:start position:0%
+and now we have e a dagger a dagger e a
+ 
+
+ align:start position:0%
+and now we have e a dagger a dagger e a
+dagger what's e with a
+
+ align:start position:0%
+dagger what's e with a
+ 
+
+ align:start position:0%
+dagger what's e with a
+dagger a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dagger e with a dagger is equal to same
+
+ align:start position:0%
+dagger e with a dagger is equal to same
+ 
+
+ align:start position:0%
+dagger e with a dagger is equal to same
+thing but with a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus and again s same thing because the
+
+ align:start position:0%
+plus and again s same thing because the
+ 
+
+ align:start position:0%
+plus and again s same thing because the
+a dagger factors
+
+ align:start position:0%
+a dagger factors
+ 
+
+ align:start position:0%
+a dagger factors
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so we go down by acting with
+
+ align:start position:0%
+so we go down by acting with
+ 
+
+ align:start position:0%
+so we go down by acting with
+a we go up by acting with a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dagger and again the spacing is H bar
+
+ align:start position:0%
+dagger and again the spacing is H bar
+ 
+
+ align:start position:0%
+dagger and again the spacing is H bar
+Omega and we go up by acting with a
+
+ align:start position:0%
+Omega and we go up by acting with a
+ 
+
+ align:start position:0%
+Omega and we go up by acting with a
+dagger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again so a and a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dagger a and a dagger are called the
+
+ align:start position:0%
+dagger a and a dagger are called the
+ 
+
+ align:start position:0%
+dagger a and a dagger are called the
+raising and lowering operators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+dagger the raising
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator a dagger f
+
+ align:start position:0%
+operator a dagger f
+ 
+
+ align:start position:0%
+operator a dagger f
+e plus h bar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+what that lets us do is build a tower of
+
+ align:start position:0%
+what that lets us do is build a tower of
+ 
+
+ align:start position:0%
+what that lets us do is build a tower of
+States an infinite Tower of States we're
+
+ align:start position:0%
+States an infinite Tower of States we're
+ 
+
+ align:start position:0%
+States an infinite Tower of States we're
+given a state we can walk up this ladder
+
+ align:start position:0%
+given a state we can walk up this ladder
+ 
+
+ align:start position:0%
+given a state we can walk up this ladder
+with the raising operator and we can
+
+ align:start position:0%
+with the raising operator and we can
+ 
+
+ align:start position:0%
+with the raising operator and we can
+walk down it by the lowering
+
+ align:start position:0%
+walk down it by the lowering
+ 
+
+ align:start position:0%
+walk down it by the lowering
+operator so now I ask you the question
+
+ align:start position:0%
+operator so now I ask you the question
+ 
+
+ align:start position:0%
+operator so now I ask you the question
+why is this ladder evenly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spaced there's one equation on the board
+
+ align:start position:0%
+spaced there's one equation on the board
+ 
+
+ align:start position:0%
+spaced there's one equation on the board
+that you can point to well I guess two
+
+ align:start position:0%
+that you can point to well I guess two
+ 
+
+ align:start position:0%
+that you can point to well I guess two
+technically there are two equations on
+
+ align:start position:0%
+technically there are two equations on
+ 
+
+ align:start position:0%
+technically there are two equations on
+the board that you could point to that
+
+ align:start position:0%
+the board that you could point to that
+ 
+
+ align:start position:0%
+the board that you could point to that
+suffice to immediately answer the
+
+ align:start position:0%
+suffice to immediately answer the
+ 
+
+ align:start position:0%
+suffice to immediately answer the
+question why is the power of energy
+
+ align:start position:0%
+question why is the power of energy
+ 
+
+ align:start position:0%
+question why is the power of energy
+states evenly
+
+ align:start position:0%
+states evenly
+ 
+
+ align:start position:0%
+states evenly
+spaced what is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation yeah those
+
+ align:start position:0%
+equation yeah those
+ 
+
+ align:start position:0%
+equation yeah those
+commutators these commutators are all we
+
+ align:start position:0%
+commutators these commutators are all we
+ 
+
+ align:start position:0%
+commutators these commutators are all we
+needed we didn't need to know anything
+
+ align:start position:0%
+needed we didn't need to know anything
+ 
+
+ align:start position:0%
+needed we didn't need to know anything
+else we didn't even need to know what
+
+ align:start position:0%
+else we didn't even need to know what
+ 
+
+ align:start position:0%
+else we didn't even need to know what
+the potential was right if I just told
+
+ align:start position:0%
+the potential was right if I just told
+ 
+
+ align:start position:0%
+the potential was right if I just told
+you there's an energy operator e and
+
+ align:start position:0%
+you there's an energy operator e and
+ 
+
+ align:start position:0%
+you there's an energy operator e and
+there's an operator a that you can build
+
+ align:start position:0%
+there's an operator a that you can build
+ 
+
+ align:start position:0%
+there's an operator a that you can build
+out of the observables of the system
+
+ align:start position:0%
+out of the observables of the system
+ 
+
+ align:start position:0%
+out of the observables of the system
+such that you have this computation
+
+ align:start position:0%
+such that you have this computation
+ 
+
+ align:start position:0%
+such that you have this computation
+relation what do you immediately know
+
+ align:start position:0%
+relation what do you immediately know
+ 
+
+ align:start position:0%
+relation what do you immediately know
+you immediately know that you get a
+
+ align:start position:0%
+you immediately know that you get a
+ 
+
+ align:start position:0%
+you immediately know that you get a
+tower of operators because you can act
+
+ align:start position:0%
+tower of operators because you can act
+ 
+
+ align:start position:0%
+tower of operators because you can act
+with a and raise the energy by a finite
+
+ align:start position:0%
+with a and raise the energy by a finite
+ 
+
+ align:start position:0%
+with a and raise the energy by a finite
+amount which is the coefficient of that
+
+ align:start position:0%
+amount which is the coefficient of that
+ 
+
+ align:start position:0%
+amount which is the coefficient of that
+a in the
+
+ align:start position:0%
+a in the
+ 
+
+ align:start position:0%
+a in the
+commutator
+
+ align:start position:0%
+commutator
+ 
+
+ align:start position:0%
+commutator
+yeah this didn't have to be the quantum
+
+ align:start position:0%
+yeah this didn't have to be the quantum
+ 
+
+ align:start position:0%
+yeah this didn't have to be the quantum
+mechanics of the harmonic oscillator at
+
+ align:start position:0%
+mechanics of the harmonic oscillator at
+ 
+
+ align:start position:0%
+mechanics of the harmonic oscillator at
+this point we just needed this
+
+ align:start position:0%
+this point we just needed this
+ 
+
+ align:start position:0%
+this point we just needed this
+commutator relation e with a e with a
+
+ align:start position:0%
+commutator relation e with a e with a
+ 
+
+ align:start position:0%
+commutator relation e with a e with a
+dagger and one of the totally awesome
+
+ align:start position:0%
+dagger and one of the totally awesome
+ 
+
+ align:start position:0%
+dagger and one of the totally awesome
+things is how often this shows up if you
+
+ align:start position:0%
+things is how often this shows up if you
+ 
+
+ align:start position:0%
+things is how often this shows up if you
+take a bunch of electrons and you put
+
+ align:start position:0%
+take a bunch of electrons and you put
+ 
+
+ align:start position:0%
+take a bunch of electrons and you put
+them in a magnetic field okay bunch of
+
+ align:start position:0%
+them in a magnetic field okay bunch of
+ 
+
+ align:start position:0%
+them in a magnetic field okay bunch of
+electrons magnetic very strong magnetic
+
+ align:start position:0%
+electrons magnetic very strong magnetic
+ 
+
+ align:start position:0%
+electrons magnetic very strong magnetic
+field what you discover is the quantum
+
+ align:start position:0%
+field what you discover is the quantum
+ 
+
+ align:start position:0%
+field what you discover is the quantum
+mechanics of those guys has nothing to
+
+ align:start position:0%
+mechanics of those guys has nothing to
+ 
+
+ align:start position:0%
+mechanics of those guys has nothing to
+do with a harmonic oscillator on the
+
+ align:start position:0%
+do with a harmonic oscillator on the
+ 
+
+ align:start position:0%
+do with a harmonic oscillator on the
+face of it magnetic field it's Laurent
+
+ align:start position:0%
+face of it magnetic field it's Laurent
+ 
+
+ align:start position:0%
+face of it magnetic field it's Laurent
+Force law the whole thing what you
+
+ align:start position:0%
+Force law the whole thing what you
+ 
+
+ align:start position:0%
+Force law the whole thing what you
+discover is there's an operator which
+
+ align:start position:0%
+discover is there's an operator which
+ 
+
+ align:start position:0%
+discover is there's an operator which
+isn't usually called a but you know it
+
+ align:start position:0%
+isn't usually called a but you know it
+ 
+
+ align:start position:0%
+isn't usually called a but you know it
+depends on which book you use it's n or
+
+ align:start position:0%
+depends on which book you use it's n or
+ 
+
+ align:start position:0%
+depends on which book you use it's n or
+M or L there's an operator that commutes
+
+ align:start position:0%
+M or L there's an operator that commutes
+ 
+
+ align:start position:0%
+M or L there's an operator that commutes
+with the energy operator in precisely
+
+ align:start position:0%
+with the energy operator in precisely
+ 
+
+ align:start position:0%
+with the energy operator in precisely
+this fashion which tells you that the
+
+ align:start position:0%
+this fashion which tells you that the
+ 
+
+ align:start position:0%
+this fashion which tells you that the
+energy ion
+
+ align:start position:0%
+energy ion
+ 
+
+ align:start position:0%
+energy ion
+States live in a ladder they're called
+
+ align:start position:0%
+States live in a ladder they're called
+ 
+
+ align:start position:0%
+States live in a ladder they're called
+Lando levels this turns out to be very
+
+ align:start position:0%
+Lando levels this turns out to be very
+ 
+
+ align:start position:0%
+Lando levels this turns out to be very
+useful any of you who are doing a urop
+
+ align:start position:0%
+useful any of you who are doing a urop
+ 
+
+ align:start position:0%
+useful any of you who are doing a urop
+in a lab that has you know graphine or
+
+ align:start position:0%
+in a lab that has you know graphine or
+ 
+
+ align:start position:0%
+in a lab that has you know graphine or
+any material really with the magnetic
+
+ align:start position:0%
+any material really with the magnetic
+ 
+
+ align:start position:0%
+any material really with the magnetic
+field then this matters so this
+
+ align:start position:0%
+field then this matters so this
+ 
+
+ align:start position:0%
+field then this matters so this
+commutator encodes an enormous amount of
+
+ align:start position:0%
+commutator encodes an enormous amount of
+ 
+
+ align:start position:0%
+commutator encodes an enormous amount of
+the structure of the energy IG values
+
+ align:start position:0%
+the structure of the energy IG values
+ 
+
+ align:start position:0%
+the structure of the energy IG values
+and the trick for us was showing that we
+
+ align:start position:0%
+and the trick for us was showing that we
+ 
+
+ align:start position:0%
+and the trick for us was showing that we
+could write the harmonic oscillator
+
+ align:start position:0%
+could write the harmonic oscillator
+ 
+
+ align:start position:0%
+could write the harmonic oscillator
+energy operator in terms of operators
+
+ align:start position:0%
+energy operator in terms of operators
+ 
+
+ align:start position:0%
+energy operator in terms of operators
+that commute in this
+
+ align:start position:0%
+that commute in this
+ 
+
+ align:start position:0%
+that commute in this
+fashion
+
+ align:start position:0%
+fashion
+ 
+
+ align:start position:0%
+fashion
+yeah so what we're going to run into
+
+ align:start position:0%
+yeah so what we're going to run into
+ 
+
+ align:start position:0%
+yeah so what we're going to run into
+this structure over and over again this
+
+ align:start position:0%
+this structure over and over again this
+ 
+
+ align:start position:0%
+this structure over and over again this
+operator commutes with this one to the
+
+ align:start position:0%
+operator commutes with this one to the
+ 
+
+ align:start position:0%
+operator commutes with this one to the
+same operator times a constant that
+
+ align:start position:0%
+same operator times a constant that
+ 
+
+ align:start position:0%
+same operator times a constant that
+tells you you have a ladder we're going
+
+ align:start position:0%
+tells you you have a ladder we're going
+ 
+
+ align:start position:0%
+tells you you have a ladder we're going
+to run into that over and over again
+
+ align:start position:0%
+to run into that over and over again
+ 
+
+ align:start position:0%
+to run into that over and over again
+when we talk about about land levels if
+
+ align:start position:0%
+when we talk about about land levels if
+ 
+
+ align:start position:0%
+when we talk about about land levels if
+we get there when we talk about angular
+
+ align:start position:0%
+we get there when we talk about angular
+ 
+
+ align:start position:0%
+we get there when we talk about angular
+momentum we'll get the same thing when
+
+ align:start position:0%
+momentum we'll get the same thing when
+ 
+
+ align:start position:0%
+momentum we'll get the same thing when
+we talk about the harmonic oscillator
+
+ align:start position:0%
+we talk about the harmonic oscillator
+ 
+
+ align:start position:0%
+we talk about the harmonic oscillator
+we'll get the same thing all sorry the
+
+ align:start position:0%
+we'll get the same thing all sorry the
+ 
+
+ align:start position:0%
+we'll get the same thing all sorry the
+the hydrogen uh system we'll get the
+
+ align:start position:0%
+the hydrogen uh system we'll get the
+ 
+
+ align:start position:0%
+the hydrogen uh system we'll get the
+same thing okay
+
+ align:start position:0%
+same thing okay
+ 
+
+ align:start position:0%
+same thing okay
+so second question does this ladder
+
+ align:start position:0%
+so second question does this ladder
+ 
+
+ align:start position:0%
+so second question does this ladder
+extend infinitely
+
+ align:start position:0%
+extend infinitely
+ 
+
+ align:start position:0%
+extend infinitely
+up yeah why not can it extend infinitely
+
+ align:start position:0%
+up yeah why not can it extend infinitely
+ 
+
+ align:start position:0%
+up yeah why not can it extend infinitely
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+why well okay people are saying ground
+
+ align:start position:0%
+why well okay people are saying ground
+ 
+
+ align:start position:0%
+why well okay people are saying ground
+state well we know that from The Brute
+
+ align:start position:0%
+state well we know that from The Brute
+ 
+
+ align:start position:0%
+state well we know that from The Brute
+Force calculation but without the Brute
+
+ align:start position:0%
+Force calculation but without the Brute
+ 
+
+ align:start position:0%
+Force calculation but without the Brute
+Force calculation can this ladder extend
+
+ align:start position:0%
+Force calculation can this ladder extend
+ 
+
+ align:start position:0%
+Force calculation can this ladder extend
+infinitely
+
+ align:start position:0%
+infinitely
+ 
+
+ align:start position:0%
+infinitely
+down you can't go under the minimum
+
+ align:start position:0%
+down you can't go under the minimum
+ 
+
+ align:start position:0%
+down you can't go under the minimum
+brilliant okay good and as you'll prove
+
+ align:start position:0%
+brilliant okay good and as you'll prove
+ 
+
+ align:start position:0%
+brilliant okay good and as you'll prove
+on the problem set you can't make the
+
+ align:start position:0%
+on the problem set you can't make the
+ 
+
+ align:start position:0%
+on the problem set you can't make the
+energy arbitrarily negative but let me
+
+ align:start position:0%
+energy arbitrarily negative but let me
+ 
+
+ align:start position:0%
+energy arbitrarily negative but let me
+make that let me make that sharp I don't
+
+ align:start position:0%
+make that let me make that sharp I don't
+ 
+
+ align:start position:0%
+make that let me make that sharp I don't
+want to I don't want to appeal to
+
+ align:start position:0%
+want to I don't want to appeal to
+ 
+
+ align:start position:0%
+want to I don't want to appeal to
+something we haven't
+
+ align:start position:0%
+something we haven't
+ 
+
+ align:start position:0%
+something we haven't
+proved proven uh let me show you that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concretely the energy expectation
+
+ align:start position:0%
+concretely the energy expectation
+ 
+
+ align:start position:0%
+concretely the energy expectation
+value in some state in any state right
+
+ align:start position:0%
+value in some state in any state right
+ 
+
+ align:start position:0%
+value in some state in any state right
+the energy expectation value can be
+
+ align:start position:0%
+the energy expectation value can be
+ 
+
+ align:start position:0%
+the energy expectation value can be
+written as the integral of f complex
+
+ align:start position:0%
+written as the integral of f complex
+ 
+
+ align:start position:0%
+written as the integral of f complex
+conjugate let's say in the state f i com
+
+ align:start position:0%
+conjugate let's say in the state f i com
+ 
+
+ align:start position:0%
+conjugate let's say in the state f i com
+conjugate e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f but I can write this as the integral
+
+ align:start position:0%
+f but I can write this as the integral
+ 
+
+ align:start position:0%
+f but I can write this as the integral
+and let's say
+
+ align:start position:0%
+and let's say
+ 
+
+ align:start position:0%
+and let's say
+DX integral DX um let's just put in uh
+
+ align:start position:0%
+DX integral DX um let's just put in uh
+ 
+
+ align:start position:0%
+DX integral DX um let's just put in uh
+what the energy operator looks like so
+
+ align:start position:0%
+what the energy operator looks like so
+ 
+
+ align:start position:0%
+what the energy operator looks like so
+slda we can take the 4 a transform right
+
+ align:start position:0%
+slda we can take the 4 a transform right
+ 
+
+ align:start position:0%
+slda we can take the 4 a transform right
+the ca of P p^2 upon 2 m oops DP for the
+
+ align:start position:0%
+the ca of P p^2 upon 2 m oops DP for the
+ 
+
+ align:start position:0%
+the ca of P p^2 upon 2 m oops DP for the
+F for the kinetic energy term plus the
+
+ align:start position:0%
+F for the kinetic energy term plus the
+ 
+
+ align:start position:0%
+F for the kinetic energy term plus the
+integral and now I'm using the harmonic
+
+ align:start position:0%
+integral and now I'm using the harmonic
+ 
+
+ align:start position:0%
+integral and now I'm using the harmonic
+conator plus the integral DX of s of x
+
+ align:start position:0%
+conator plus the integral DX of s of x
+ 
+
+ align:start position:0%
+conator plus the integral DX of s of x
+Norm
+
+ align:start position:0%
+Norm
+ 
+
+ align:start position:0%
+Norm
+squ Norm s uh M Omega 2 upon
+
+ align:start position:0%
+squ Norm s uh M Omega 2 upon
+ 
+
+ align:start position:0%
+squ Norm s uh M Omega 2 upon
+2x^2 okay little bit of a quick move
+
+ align:start position:0%
+2x^2 okay little bit of a quick move
+ 
+
+ align:start position:0%
+2x^2 okay little bit of a quick move
+there doing the 4A transform for the
+
+ align:start position:0%
+there doing the 4A transform for the
+ 
+
+ align:start position:0%
+there doing the 4A transform for the
+momentum term and not doing the 4
+
+ align:start position:0%
+momentum term and not doing the 4
+ 
+
+ align:start position:0%
+momentum term and not doing the 4
+transform but it's okay they're separate
+
+ align:start position:0%
+transform but it's okay they're separate
+ 
+
+ align:start position:0%
+transform but it's okay they're separate
+integrals I can do this and The crucial
+
+ align:start position:0%
+integrals I can do this and The crucial
+ 
+
+ align:start position:0%
+integrals I can do this and The crucial
+thing here is this is positive definite
+
+ align:start position:0%
+thing here is this is positive definite
+ 
+
+ align:start position:0%
+thing here is this is positive definite
+this is positive definite positive
+
+ align:start position:0%
+this is positive definite positive
+ 
+
+ align:start position:0%
+this is positive definite positive
+definite positive definite all these
+
+ align:start position:0%
+definite positive definite all these
+ 
+
+ align:start position:0%
+definite positive definite all these
+terms are strictly positive this must be
+
+ align:start position:0%
+terms are strictly positive this must be
+ 
+
+ align:start position:0%
+terms are strictly positive this must be
+greater than or equal to zero it can
+
+ align:start position:0%
+greater than or equal to zero it can
+ 
+
+ align:start position:0%
+greater than or equal to zero it can
+never be
+
+ align:start position:0%
+never be
+ 
+
+ align:start position:0%
+never be
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+yeah so what that tells us is there must
+
+ align:start position:0%
+yeah so what that tells us is there must
+ 
+
+ align:start position:0%
+yeah so what that tells us is there must
+be a minimum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e there must be an a minimum energy and
+
+ align:start position:0%
+e there must be an a minimum energy and
+ 
+
+ align:start position:0%
+e there must be an a minimum energy and
+I will call it minimum e
+
+ align:start position:0%
+I will call it minimum e
+ 
+
+ align:start position:0%
+I will call it minimum e
+not okay we can't lower the tower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forever so what is that how is this
+
+ align:start position:0%
+forever so what is that how is this
+ 
+
+ align:start position:0%
+forever so what is that how is this
+possible how is it possible that look on
+
+ align:start position:0%
+possible how is it possible that look on
+ 
+
+ align:start position:0%
+possible how is it possible that look on
+the one hand if we want if we have a
+
+ align:start position:0%
+the one hand if we want if we have a
+ 
+
+ align:start position:0%
+the one hand if we want if we have a
+state we can always build a lower energy
+
+ align:start position:0%
+state we can always build a lower energy
+ 
+
+ align:start position:0%
+state we can always build a lower energy
+state by acting with the lowering
+
+ align:start position:0%
+state by acting with the lowering
+ 
+
+ align:start position:0%
+state by acting with the lowering
+operator a and yet this is telling me
+
+ align:start position:0%
+operator a and yet this is telling me
+ 
+
+ align:start position:0%
+operator a and yet this is telling me
+that I can't
+
+ align:start position:0%
+that I can't
+ 
+
+ align:start position:0%
+that I can't
+there must be a last one where I can't
+
+ align:start position:0%
+there must be a last one where I can't
+ 
+
+ align:start position:0%
+there must be a last one where I can't
+lower it anymore so what reaches out of
+
+ align:start position:0%
+lower it anymore so what reaches out of
+ 
+
+ align:start position:0%
+lower it anymore so what reaches out of
+the chalkboard and stops me from acting
+
+ align:start position:0%
+the chalkboard and stops me from acting
+ 
+
+ align:start position:0%
+the chalkboard and stops me from acting
+with a
+
+ align:start position:0%
+with a
+ 
+
+ align:start position:0%
+with a
+again how can it possibly be true that a
+
+ align:start position:0%
+again how can it possibly be true that a
+ 
+
+ align:start position:0%
+again how can it possibly be true that a
+always lowers the I function but there's
+
+ align:start position:0%
+always lowers the I function but there's
+ 
+
+ align:start position:0%
+always lowers the I function but there's
+a least one that can't be lowered any
+
+ align:start position:0%
+a least one that can't be lowered any
+ 
+
+ align:start position:0%
+a least one that can't be lowered any
+further N normalizable is a good guess
+
+ align:start position:0%
+further N normalizable is a good guess
+ 
+
+ align:start position:0%
+further N normalizable is a good guess
+very good guess not not the case because
+
+ align:start position:0%
+very good guess not not the case because
+ 
+
+ align:start position:0%
+very good guess not not the case because
+at this point we from this argument we
+
+ align:start position:0%
+at this point we from this argument we
+ 
+
+ align:start position:0%
+at this point we from this argument we
+don't even use wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+functions uh that would be bad yes
+
+ align:start position:0%
+functions uh that would be bad yes
+ 
+
+ align:start position:0%
+functions uh that would be bad yes
+exactly so that would be bad but that
+
+ align:start position:0%
+exactly so that would be bad but that
+ 
+
+ align:start position:0%
+exactly so that would be bad but that
+doesn't what I mean that's just saying
+
+ align:start position:0%
+doesn't what I mean that's just saying
+ 
+
+ align:start position:0%
+doesn't what I mean that's just saying
+that there's an inconsistency here so
+
+ align:start position:0%
+that there's an inconsistency here so
+ 
+
+ align:start position:0%
+that there's an inconsistency here so
+I'm going to come back to your your
+
+ align:start position:0%
+I'm going to come back to your your
+ 
+
+ align:start position:0%
+I'm going to come back to your your
+answer non-normalizable it's correct but
+
+ align:start position:0%
+answer non-normalizable it's correct but
+ 
+
+ align:start position:0%
+answer non-normalizable it's correct but
+in a sneaky way here's the way it's not
+
+ align:start position:0%
+in a sneaky way here's the way it's not
+ 
+
+ align:start position:0%
+in a sneaky way here's the way it's not
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+Sneaky consider a state a on fi let's
+
+ align:start position:0%
+Sneaky consider a state a on fi let's
+ 
+
+ align:start position:0%
+Sneaky consider a state a on fi let's
+say this is the lowest State okay the
+
+ align:start position:0%
+say this is the lowest State okay the
+ 
+
+ align:start position:0%
+say this is the lowest State okay the
+lowest possible state it must be true
+
+ align:start position:0%
+lowest possible state it must be true
+ 
+
+ align:start position:0%
+lowest possible state it must be true
+that the resulting state is not F minus
+
+ align:start position:0%
+that the resulting state is not F minus
+ 
+
+ align:start position:0%
+that the resulting state is not F minus
+H bar Omega there can't be any such
+
+ align:start position:0%
+H bar Omega there can't be any such
+ 
+
+ align:start position:0%
+H bar Omega there can't be any such
+State and how can that be that can be if
+
+ align:start position:0%
+State and how can that be that can be if
+ 
+
+ align:start position:0%
+State and how can that be that can be if
+true if it's zero
+
+ align:start position:0%
+true if it's zero
+ 
+
+ align:start position:0%
+true if it's zero
+so if the lowering operator acts on some
+
+ align:start position:0%
+so if the lowering operator acts on some
+ 
+
+ align:start position:0%
+so if the lowering operator acts on some
+State and gives me zero well okay that's
+
+ align:start position:0%
+State and gives me zero well okay that's
+ 
+
+ align:start position:0%
+State and gives me zero well okay that's
+a that's a an igen state but it's a
+
+ align:start position:0%
+a that's a an igen state but it's a
+ 
+
+ align:start position:0%
+a that's a an igen state but it's a
+stupid IG state it doesn't it's not
+
+ align:start position:0%
+stupid IG state it doesn't it's not
+ 
+
+ align:start position:0%
+stupid IG state it doesn't it's not
+normalizable it can't be used to
+
+ align:start position:0%
+normalizable it can't be used to
+ 
+
+ align:start position:0%
+normalizable it can't be used to
+describe any real physical object
+
+ align:start position:0%
+describe any real physical object
+ 
+
+ align:start position:0%
+describe any real physical object
+because where is it well it's nowhere
+
+ align:start position:0%
+because where is it well it's nowhere
+ 
+
+ align:start position:0%
+because where is it well it's nowhere
+the probability density to find it
+
+ align:start position:0%
+the probability density to find it
+ 
+
+ align:start position:0%
+the probability density to find it
+anywhere is nowhere nothing
+
+ align:start position:0%
+anywhere is nowhere nothing
+ 
+
+ align:start position:0%
+anywhere is nowhere nothing
+zero so the way that this this Tower
+
+ align:start position:0%
+zero so the way that this this Tower
+ 
+
+ align:start position:0%
+zero so the way that this this Tower
+terminates is by having a last state
+
+ align:start position:0%
+terminates is by having a last state
+ 
+
+ align:start position:0%
+terminates is by having a last state
+which we'll call pH
+
+ align:start position:0%
+which we'll call pH
+ 
+
+ align:start position:0%
+which we'll call pH
+Z such that lowering it gives me zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not the state called zero which I would
+
+ align:start position:0%
+not the state called zero which I would
+ 
+
+ align:start position:0%
+not the state called zero which I would
+call this but actually the function zero
+
+ align:start position:0%
+call this but actually the function zero
+ 
+
+ align:start position:0%
+call this but actually the function zero
+which is not normalizable which is not a
+
+ align:start position:0%
+which is not normalizable which is not a
+ 
+
+ align:start position:0%
+which is not normalizable which is not a
+good State okay so there's a minimum e
+
+ align:start position:0%
+good State okay so there's a minimum e
+ 
+
+ align:start position:0%
+good State okay so there's a minimum e
+not and associated with
+
+ align:start position:0%
+not and associated with
+ 
+
+ align:start position:0%
+not and associated with
+that is a lowest energy I State called
+
+ align:start position:0%
+that is a lowest energy I State called
+ 
+
+ align:start position:0%
+that is a lowest energy I State called
+the ground
+
+ align:start position:0%
+the ground
+ 
+
+ align:start position:0%
+the ground
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+now can the energy get arbitrarily large
+
+ align:start position:0%
+now can the energy get arbitrarily large
+ 
+
+ align:start position:0%
+now can the energy get arbitrarily large
+sure that's a positive definite thing
+
+ align:start position:0%
+sure that's a positive definite thing
+ 
+
+ align:start position:0%
+sure that's a positive definite thing
+and this could get as large as you like
+
+ align:start position:0%
+and this could get as large as you like
+ 
+
+ align:start position:0%
+and this could get as large as you like
+so there's no problem with the energy I
+
+ align:start position:0%
+so there's no problem with the energy I
+ 
+
+ align:start position:0%
+so there's no problem with the energy I
+values getting arbitrarily large we can
+
+ align:start position:0%
+values getting arbitrarily large we can
+ 
+
+ align:start position:0%
+values getting arbitrarily large we can
+just keep raising and raising and
+
+ align:start position:0%
+just keep raising and raising and
+ 
+
+ align:start position:0%
+just keep raising and raising and
+raising I mention that because later on
+
+ align:start position:0%
+raising I mention that because later on
+ 
+
+ align:start position:0%
+raising I mention that because later on
+in the semester we will find a system
+
+ align:start position:0%
+in the semester we will find a system
+ 
+
+ align:start position:0%
+in the semester we will find a system
+with exactly that commutation relation
+
+ align:start position:0%
+with exactly that commutation relation
+ 
+
+ align:start position:0%
+with exactly that commutation relation
+precisely that commutation relation
+
+ align:start position:0%
+precisely that commutation relation
+ 
+
+ align:start position:0%
+precisely that commutation relation
+where there will be a minimum and a
+
+ align:start position:0%
+where there will be a minimum and a
+ 
+
+ align:start position:0%
+where there will be a minimum and a
+maximum okay so the commutation relation
+
+ align:start position:0%
+maximum okay so the commutation relation
+ 
+
+ align:start position:0%
+maximum okay so the commutation relation
+is a good start but it doesn't tell you
+
+ align:start position:0%
+is a good start but it doesn't tell you
+ 
+
+ align:start position:0%
+is a good start but it doesn't tell you
+anything we have to add in some Physics
+
+ align:start position:0%
+anything we have to add in some Physics
+ 
+
+ align:start position:0%
+anything we have to add in some Physics
+like the energy operator bounded below
+
+ align:start position:0%
+like the energy operator bounded below
+ 
+
+ align:start position:0%
+like the energy operator bounded below
+for the harmonic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oscillator questions at this point yeah
+
+ align:start position:0%
+oscillator questions at this point yeah
+ 
+
+ align:start position:0%
+oscillator questions at this point yeah
+so you so you basically have shown that
+
+ align:start position:0%
+so you so you basically have shown that
+ 
+
+ align:start position:0%
+so you so you basically have shown that
+this ladder has to exist particular
+
+ align:start position:0%
+this ladder has to exist particular
+ 
+
+ align:start position:0%
+this ladder has to exist particular
+energy IEM say that I can kind of
+
+ align:start position:0%
+energy IEM say that I can kind of
+ 
+
+ align:start position:0%
+energy IEM say that I can kind of
+construct a letter how do I know that I
+
+ align:start position:0%
+construct a letter how do I know that I
+ 
+
+ align:start position:0%
+construct a letter how do I know that I
+can't like construct other intersec
+
+ align:start position:0%
+can't like construct other intersec
+ 
+
+ align:start position:0%
+can't like construct other intersec
+letters yeah that's an excellent
+
+ align:start position:0%
+letters yeah that's an excellent
+ 
+
+ align:start position:0%
+letters yeah that's an excellent
+question so when I remember vividly when
+
+ align:start position:0%
+question so when I remember vividly when
+ 
+
+ align:start position:0%
+question so when I remember vividly when
+I saw this lecture in 143a and that
+
+ align:start position:0%
+I saw this lecture in 143a and that
+ 
+
+ align:start position:0%
+I saw this lecture in 143a and that
+question plagued me and foolishly I
+
+ align:start position:0%
+question plagued me and foolishly I
+ 
+
+ align:start position:0%
+question plagued me and foolishly I
+didn't ask it um so here's the question
+
+ align:start position:0%
+didn't ask it um so here's the question
+ 
+
+ align:start position:0%
+didn't ask it um so here's the question
+the question is look you found a bunch
+
+ align:start position:0%
+the question is look you found a bunch
+ 
+
+ align:start position:0%
+the question is look you found a bunch
+of States how do you know that's all of
+
+ align:start position:0%
+of States how do you know that's all of
+ 
+
+ align:start position:0%
+of States how do you know that's all of
+them okay how do you know that's all of
+
+ align:start position:0%
+them okay how do you know that's all of
+ 
+
+ align:start position:0%
+them okay how do you know that's all of
+them so let's think through that that's
+
+ align:start position:0%
+them so let's think through that that's
+ 
+
+ align:start position:0%
+them so let's think through that that's
+a very good question I'm not going to
+
+ align:start position:0%
+a very good question I'm not going to
+ 
+
+ align:start position:0%
+a very good question I'm not going to
+worry about normalization but there's a
+
+ align:start position:0%
+worry about normalization but there's a
+ 
+
+ align:start position:0%
+worry about normalization but there's a
+discussion of normalization in the notes
+
+ align:start position:0%
+discussion of normalization in the notes
+ 
+
+ align:start position:0%
+discussion of normalization in the notes
+um how do I know that's all of
+
+ align:start position:0%
+um how do I know that's all of
+ 
+
+ align:start position:0%
+um how do I know that's all of
+them so yeah that's a little bit tricky
+
+ align:start position:0%
+them so yeah that's a little bit tricky
+ 
+
+ align:start position:0%
+them so yeah that's a little bit tricky
+so let's think through
+
+ align:start position:0%
+so let's think through
+ 
+
+ align:start position:0%
+so let's think through
+it imagine it's not all of them in
+
+ align:start position:0%
+it imagine it's not all of them in
+ 
+
+ align:start position:0%
+it imagine it's not all of them in
+particular what would that mean in order
+
+ align:start position:0%
+particular what would that mean in order
+ 
+
+ align:start position:0%
+particular what would that mean in order
+for there to be more States than the
+
+ align:start position:0%
+for there to be more States than the
+ 
+
+ align:start position:0%
+for there to be more States than the
+ones that we've written down there must
+
+ align:start position:0%
+ones that we've written down there must
+ 
+
+ align:start position:0%
+ones that we've written down there must
+be states that are not on that Tower and
+
+ align:start position:0%
+be states that are not on that Tower and
+ 
+
+ align:start position:0%
+be states that are not on that Tower and
+how can we Poss wow this thing is
+
+ align:start position:0%
+how can we Poss wow this thing is
+ 
+
+ align:start position:0%
+how can we Poss wow this thing is
+totally falling apart how do we do that
+
+ align:start position:0%
+totally falling apart how do we do that
+ 
+
+ align:start position:0%
+totally falling apart how do we do that
+how is that possible so there are two
+
+ align:start position:0%
+how is that possible so there are two
+ 
+
+ align:start position:0%
+how is that possible so there are two
+ways to do it there are two ways to do
+
+ align:start position:0%
+ways to do it there are two ways to do
+ 
+
+ align:start position:0%
+ways to do it there are two ways to do
+it so here's my tower of States okay
+
+ align:start position:0%
+it so here's my tower of States okay
+ 
+
+ align:start position:0%
+it so here's my tower of States okay
+there's my Tower of states and I'll call
+
+ align:start position:0%
+there's my Tower of states and I'll call
+ 
+
+ align:start position:0%
+there's my Tower of states and I'll call
+this one 5 Z okay and so I raise with a
+
+ align:start position:0%
+this one 5 Z okay and so I raise with a
+ 
+
+ align:start position:0%
+this one 5 Z okay and so I raise with a
+dagger and I lower with
+
+ align:start position:0%
+dagger and I lower with
+ 
+
+ align:start position:0%
+dagger and I lower with
+a so how could it be that I miss some
+
+ align:start position:0%
+a so how could it be that I miss some
+ 
+
+ align:start position:0%
+a so how could it be that I miss some
+states well there are two ways to do it
+
+ align:start position:0%
+states well there are two ways to do it
+ 
+
+ align:start position:0%
+states well there are two ways to do it
+one is there could be extra states that
+
+ align:start position:0%
+one is there could be extra states that
+ 
+
+ align:start position:0%
+one is there could be extra states that
+are in between right so let's say that
+
+ align:start position:0%
+are in between right so let's say that
+ 
+
+ align:start position:0%
+are in between right so let's say that
+there's one extra State that's in
+
+ align:start position:0%
+there's one extra State that's in
+ 
+
+ align:start position:0%
+there's one extra State that's in
+between these two okay just imagine
+
+ align:start position:0%
+between these two okay just imagine
+ 
+
+ align:start position:0%
+between these two okay just imagine
+that's true if there is such a state by
+
+ align:start position:0%
+that's true if there is such a state by
+ 
+
+ align:start position:0%
+that's true if there is such a state by
+that commutation relation there must be
+
+ align:start position:0%
+that commutation relation there must be
+ 
+
+ align:start position:0%
+that commutation relation there must be
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+Tower right so there must be this State
+
+ align:start position:0%
+Tower right so there must be this State
+ 
+
+ align:start position:0%
+Tower right so there must be this State
+and there must be this state and there
+
+ align:start position:0%
+and there must be this state and there
+ 
+
+ align:start position:0%
+and there must be this state and there
+must be this state and there must be
+
+ align:start position:0%
+must be this state and there must be
+ 
+
+ align:start position:0%
+must be this state and there must be
+this state yeah okay so so that's good
+
+ align:start position:0%
+this state yeah okay so so that's good
+ 
+
+ align:start position:0%
+this state yeah okay so so that's good
+so far but what happens well a on this
+
+ align:start position:0%
+so far but what happens well a on this
+ 
+
+ align:start position:0%
+so far but what happens well a on this
+guy gave me zero right so a on F not was
+
+ align:start position:0%
+guy gave me zero right so a on F not was
+ 
+
+ align:start position:0%
+guy gave me zero right so a on F not was
+zero and this is going to be some fi
+
+ align:start position:0%
+zero and this is going to be some fi
+ 
+
+ align:start position:0%
+zero and this is going to be some fi
+Tilda um knot suppose that this Tower
+
+ align:start position:0%
+Tilda um knot suppose that this Tower
+ 
+
+ align:start position:0%
+Tilda um knot suppose that this Tower
+ends okay and now you have you have to
+
+ align:start position:0%
+ends okay and now you have you have to
+ 
+
+ align:start position:0%
+ends okay and now you have you have to
+ask the question can there be two
+
+ align:start position:0%
+ask the question can there be two
+ 
+
+ align:start position:0%
+ask the question can there be two
+different states with two different
+
+ align:start position:0%
+different states with two different
+ 
+
+ align:start position:0%
+different states with two different
+energies with a can there be two
+
+ align:start position:0%
+energies with a can there be two
+ 
+
+ align:start position:0%
+energies with a can there be two
+different states that are annihilated by
+
+ align:start position:0%
+different states that are annihilated by
+ 
+
+ align:start position:0%
+different states that are annihilated by
+a not well let's check what must be true
+
+ align:start position:0%
+a not well let's check what must be true
+ 
+
+ align:start position:0%
+a not well let's check what must be true
+of any state annihilated by a well let's
+
+ align:start position:0%
+of any state annihilated by a well let's
+ 
+
+ align:start position:0%
+of any state annihilated by a well let's
+write the energy operator uh acting on
+
+ align:start position:0%
+write the energy operator uh acting on
+ 
+
+ align:start position:0%
+write the energy operator uh acting on
+that state what's the energy of that
+
+ align:start position:0%
+that state what's the energy of that
+ 
+
+ align:start position:0%
+that state what's the energy of that
+state energy on 5 Z is equal to H Omega
+
+ align:start position:0%
+state energy on 5 Z is equal to H Omega
+ 
+
+ align:start position:0%
+state energy on 5 Z is equal to H Omega
+this is a very good question so let's
+
+ align:start position:0%
+this is a very good question so let's
+ 
+
+ align:start position:0%
+this is a very good question so let's
+let's go through it so it's equal to H
+
+ align:start position:0%
+let's go through it so it's equal to H
+ 
+
+ align:start position:0%
+let's go through it so it's equal to H
+bar Omega time a diag A plus
+
+ align:start position:0%
+bar Omega time a diag A plus
+ 
+
+ align:start position:0%
+bar Omega time a diag A plus
+12 on f z okay but what can you say
+
+ align:start position:0%
+12 on f z okay but what can you say
+ 
+
+ align:start position:0%
+12 on f z okay but what can you say
+about this well a annihilates F0 it
+
+ align:start position:0%
+about this well a annihilates F0 it
+ 
+
+ align:start position:0%
+about this well a annihilates F0 it
+gives us zero so in addition to a being
+
+ align:start position:0%
+gives us zero so in addition to a being
+ 
+
+ align:start position:0%
+gives us zero so in addition to a being
+called the lowering operator it's also
+
+ align:start position:0%
+called the lowering operator it's also
+ 
+
+ align:start position:0%
+called the lowering operator it's also
+called the annihilation
+
+ align:start position:0%
+called the annihilation
+ 
+
+ align:start position:0%
+called the annihilation
+operator I don't know we're brutal in
+
+ align:start position:0%
+operator I don't know we're brutal in
+ 
+
+ align:start position:0%
+operator I don't know we're brutal in
+warlike species um so this is equal to H
+
+ align:start position:0%
+warlike species um so this is equal to H
+ 
+
+ align:start position:0%
+warlike species um so this is equal to H
+this term kills again with the kills um
+
+ align:start position:0%
+this term kills again with the kills um
+ 
+
+ align:start position:0%
+this term kills again with the kills um
+and gives me a one half left over one
+
+ align:start position:0%
+and gives me a one half left over one
+ 
+
+ align:start position:0%
+and gives me a one half left over one
+half H bar Omega 5 Z so the ground state
+
+ align:start position:0%
+half H bar Omega 5 Z so the ground state
+ 
+
+ align:start position:0%
+half H bar Omega 5 Z so the ground state
+any state any state annihilated by
+
+ align:start position:0%
+any state any state annihilated by
+ 
+
+ align:start position:0%
+any state any state annihilated by
+a must have the same
+
+ align:start position:0%
+a must have the same
+ 
+
+ align:start position:0%
+a must have the same
+energy yeah the only way you can be
+
+ align:start position:0%
+energy yeah the only way you can be
+ 
+
+ align:start position:0%
+energy yeah the only way you can be
+annihilated by a is if your energy is
+
+ align:start position:0%
+annihilated by a is if your energy is
+ 
+
+ align:start position:0%
+annihilated by a is if your energy is
+this cool so what does it tell you about
+
+ align:start position:0%
+this cool so what does it tell you about
+ 
+
+ align:start position:0%
+this cool so what does it tell you about
+this second ladder of hidden states that
+
+ align:start position:0%
+this second ladder of hidden states that
+ 
+
+ align:start position:0%
+this second ladder of hidden states that
+we missed it's got to be degenerate
+
+ align:start position:0%
+we missed it's got to be degenerate
+ 
+
+ align:start position:0%
+we missed it's got to be degenerate
+right it's got to have the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energies yeah I drew that really badly
+
+ align:start position:0%
+energies yeah I drew that really badly
+ 
+
+ align:start position:0%
+energies yeah I drew that really badly
+didn't I those are evenly spaced um so
+
+ align:start position:0%
+didn't I those are evenly spaced um so
+ 
+
+ align:start position:0%
+didn't I those are evenly spaced um so
+so it's got to be degenerate however
+
+ align:start position:0%
+so it's got to be degenerate however
+ 
+
+ align:start position:0%
+so it's got to be degenerate however
+Barton proved for you the node theorem
+
+ align:start position:0%
+Barton proved for you the node theorem
+ 
+
+ align:start position:0%
+Barton proved for you the node theorem
+last time right he gave you my uh spread
+
+ align:start position:0%
+last time right he gave you my uh spread
+ 
+
+ align:start position:0%
+last time right he gave you my uh spread
+argument for the for the node theorem in
+
+ align:start position:0%
+argument for the for the node theorem in
+ 
+
+ align:start position:0%
+argument for the for the node theorem in
+particular one of the consequences of
+
+ align:start position:0%
+particular one of the consequences of
+ 
+
+ align:start position:0%
+particular one of the consequences of
+that is that in a system with boun stat
+
+ align:start position:0%
+that is that in a system with boun stat
+ 
+
+ align:start position:0%
+that is that in a system with boun stat
+in a system with a potential that goes
+
+ align:start position:0%
+in a system with a potential that goes
+ 
+
+ align:start position:0%
+in a system with a potential that goes
+up you can never have degeneracies in
+
+ align:start position:0%
+up you can never have degeneracies in
+ 
+
+ align:start position:0%
+up you can never have degeneracies in
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+dimension we're not going to prove that
+
+ align:start position:0%
+dimension we're not going to prove that
+ 
+
+ align:start position:0%
+dimension we're not going to prove that
+carefully in in here but it's it's
+
+ align:start position:0%
+carefully in in here but it's it's
+ 
+
+ align:start position:0%
+carefully in in here but it's it's
+relatively easy to prove in fact if you
+
+ align:start position:0%
+relatively easy to prove in fact if you
+ 
+
+ align:start position:0%
+relatively easy to prove in fact if you
+come to my office hours I'll prove it
+
+ align:start position:0%
+come to my office hours I'll prove it
+ 
+
+ align:start position:0%
+come to my office hours I'll prove it
+for you it takes three minutes but I
+
+ align:start position:0%
+for you it takes three minutes but I
+ 
+
+ align:start position:0%
+for you it takes three minutes but I
+don't want to set up the math right now
+
+ align:start position:0%
+don't want to set up the math right now
+ 
+
+ align:start position:0%
+don't want to set up the math right now
+so um how many people know with the Ron
+
+ align:start position:0%
+so um how many people know with the Ron
+ 
+
+ align:start position:0%
+so um how many people know with the Ron
+skin if I say
+
+ align:start position:0%
+skin if I say
+ 
+
+ align:start position:0%
+skin if I say
+wrong that's awesome okay so I leave it
+
+ align:start position:0%
+wrong that's awesome okay so I leave it
+ 
+
+ align:start position:0%
+wrong that's awesome okay so I leave it
+to you as an exercise to use the Ron
+
+ align:start position:0%
+to you as an exercise to use the Ron
+ 
+
+ align:start position:0%
+to you as an exercise to use the Ron
+skin to show that there cannot be
+
+ align:start position:0%
+skin to show that there cannot be
+ 
+
+ align:start position:0%
+skin to show that there cannot be
+degeneracies in one dimension which is
+
+ align:start position:0%
+degeneracies in one dimension which is
+ 
+
+ align:start position:0%
+degeneracies in one dimension which is
+cool um anyway so um the Ronin for the
+
+ align:start position:0%
+cool um anyway so um the Ronin for the
+ 
+
+ align:start position:0%
+cool um anyway so um the Ronin for the
+differential equation which is the
+
+ align:start position:0%
+differential equation which is the
+ 
+
+ align:start position:0%
+differential equation which is the
+energy value equation so there can be no
+
+ align:start position:0%
+energy value equation so there can be no
+ 
+
+ align:start position:0%
+energy value equation so there can be no
+degeneracies in one-dimensional
+
+ align:start position:0%
+degeneracies in one-dimensional
+ 
+
+ align:start position:0%
+degeneracies in one-dimensional
+potentials with bound
+
+ align:start position:0%
+potentials with bound
+ 
+
+ align:start position:0%
+potentials with bound
+States so what we've just shown is that
+
+ align:start position:0%
+States so what we've just shown is that
+ 
+
+ align:start position:0%
+States so what we've just shown is that
+the only way that there can be extra
+
+ align:start position:0%
+the only way that there can be extra
+ 
+
+ align:start position:0%
+the only way that there can be extra
+states that we missed is if there's a
+
+ align:start position:0%
+states that we missed is if there's a
+ 
+
+ align:start position:0%
+states that we missed is if there's a
+tower with exactly identical energies
+
+ align:start position:0%
+tower with exactly identical energies
+ 
+
+ align:start position:0%
+tower with exactly identical energies
+all the way up but if they have exactly
+
+ align:start position:0%
+all the way up but if they have exactly
+ 
+
+ align:start position:0%
+all the way up but if they have exactly
+identical energy that means there's
+
+ align:start position:0%
+identical energy that means there's
+ 
+
+ align:start position:0%
+identical energy that means there's
+degenerate but we can prove that there
+
+ align:start position:0%
+degenerate but we can prove that there
+ 
+
+ align:start position:0%
+degenerate but we can prove that there
+can't be degeneracies in 1D so can there
+
+ align:start position:0%
+can't be degeneracies in 1D so can there
+ 
+
+ align:start position:0%
+can't be degeneracies in 1D so can there
+be an extra Tower States we missed no
+
+ align:start position:0%
+be an extra Tower States we missed no
+ 
+
+ align:start position:0%
+be an extra Tower States we missed no
+can we have missed any
+
+ align:start position:0%
+can we have missed any
+ 
+
+ align:start position:0%
+can we have missed any
+states no those are all the states there
+
+ align:start position:0%
+states no those are all the states there
+ 
+
+ align:start position:0%
+states no those are all the states there
+are and we've done it without ever
+
+ align:start position:0%
+are and we've done it without ever
+ 
+
+ align:start position:0%
+are and we've done it without ever
+solving a differential equation just by
+
+ align:start position:0%
+solving a differential equation just by
+ 
+
+ align:start position:0%
+solving a differential equation just by
+using that commutation relation now at
+
+ align:start position:0%
+using that commutation relation now at
+ 
+
+ align:start position:0%
+using that commutation relation now at
+this point it's very tempting to say
+
+ align:start position:0%
+this point it's very tempting to say
+ 
+
+ align:start position:0%
+this point it's very tempting to say
+like that was just sort of Magical
+
+ align:start position:0%
+like that was just sort of Magical
+ 
+
+ align:start position:0%
+like that was just sort of Magical
+Mystery stuff but what we really did
+
+ align:start position:0%
+Mystery stuff but what we really did
+ 
+
+ align:start position:0%
+Mystery stuff but what we really did
+last time was very honest we wrote down
+
+ align:start position:0%
+last time was very honest we wrote down
+ 
+
+ align:start position:0%
+last time was very honest we wrote down
+a differential equation we found the
+
+ align:start position:0%
+a differential equation we found the
+ 
+
+ align:start position:0%
+a differential equation we found the
+solution and we got the wave functions
+
+ align:start position:0%
+solution and we got the wave functions
+ 
+
+ align:start position:0%
+solution and we got the wave functions
+so you know Professor Adams you just
+
+ align:start position:0%
+so you know Professor Adams you just
+ 
+
+ align:start position:0%
+so you know Professor Adams you just
+monkeyed around at the chalkboard with
+
+ align:start position:0%
+monkeyed around at the chalkboard with
+ 
+
+ align:start position:0%
+monkeyed around at the chalkboard with
+commutators for a while but what are the
+
+ align:start position:0%
+commutators for a while but what are the
+ 
+
+ align:start position:0%
+commutators for a while but what are the
+damn wave functions right
+
+ align:start position:0%
+damn wave functions right
+ 
+
+ align:start position:0%
+damn wave functions right
+so we already have the answer this is
+
+ align:start position:0%
+so we already have the answer this is
+ 
+
+ align:start position:0%
+so we already have the answer this is
+really quite nice last time we solved
+
+ align:start position:0%
+really quite nice last time we solved
+ 
+
+ align:start position:0%
+really quite nice last time we solved
+that differential equation right and we
+
+ align:start position:0%
+that differential equation right and we
+ 
+
+ align:start position:0%
+that differential equation right and we
+had to solve that differential equation
+
+ align:start position:0%
+had to solve that differential equation
+ 
+
+ align:start position:0%
+had to solve that differential equation
+many many times different levels
+
+ align:start position:0%
+many many times different levels
+ 
+
+ align:start position:0%
+many many times different levels
+and but now we have a very nice thing we
+
+ align:start position:0%
+and but now we have a very nice thing we
+ 
+
+ align:start position:0%
+and but now we have a very nice thing we
+can do what's true of the ground
+
+ align:start position:0%
+can do what's true of the ground
+ 
+
+ align:start position:0%
+can do what's true of the ground
+state well the ground state is
+
+ align:start position:0%
+state well the ground state is
+ 
+
+ align:start position:0%
+state well the ground state is
+annihilated by the lowering operator so
+
+ align:start position:0%
+annihilated by the lowering operator so
+ 
+
+ align:start position:0%
+annihilated by the lowering operator so
+that means that a acting on f z of X is
+
+ align:start position:0%
+that means that a acting on f z of X is
+ 
+
+ align:start position:0%
+that means that a acting on f z of X is
+equal to zero but a has a nice
+
+ align:start position:0%
+equal to zero but a has a nice
+ 
+
+ align:start position:0%
+equal to zero but a has a nice
+expression which oh unfortunately I
+
+ align:start position:0%
+expression which oh unfortunately I
+ 
+
+ align:start position:0%
+expression which oh unfortunately I
+erased sorry about that so um a has a
+
+ align:start position:0%
+erased sorry about that so um a has a
+ 
+
+ align:start position:0%
+erased sorry about that so um a has a
+nice expression a is equal to X
+
+ align:start position:0%
+nice expression a is equal to X
+ 
+
+ align:start position:0%
+nice expression a is equal to X
+xot Plus i p over P right and so if you
+
+ align:start position:0%
+xot Plus i p over P right and so if you
+ 
+
+ align:start position:0%
+xot Plus i p over P right and so if you
+write that out and multiply by uh some
+
+ align:start position:0%
+write that out and multiply by uh some
+ 
+
+ align:start position:0%
+write that out and multiply by uh some
+appropriate constants um this
+
+ align:start position:0%
+appropriate constants um this
+ 
+
+ align:start position:0%
+appropriate constants um this
+differential this becomes the following
+
+ align:start position:0%
+differential this becomes the following
+ 
+
+ align:start position:0%
+differential this becomes the following
+differenti equation well the x is just
+
+ align:start position:0%
+differenti equation well the x is just
+ 
+
+ align:start position:0%
+differenti equation well the x is just
+multiplied by X and the p is take a
+
+ align:start position:0%
+multiplied by X and the p is take a
+ 
+
+ align:start position:0%
+multiplied by X and the p is take a
+derivative with respect to X multipli by
+
+ align:start position:0%
+derivative with respect to X multipli by
+ 
+
+ align:start position:0%
+derivative with respect to X multipli by
+H bar upon I and multiplying by I over H
+
+ align:start position:0%
+H bar upon I and multiplying by I over H
+ 
+
+ align:start position:0%
+H bar upon I and multiplying by I over H
+bar to get that equation this gives us
+
+ align:start position:0%
+bar to get that equation this gives us
+ 
+
+ align:start position:0%
+bar to get that equation this gives us
+DX plus p over um H uh X knot whoops P
+
+ align:start position:0%
+DX plus p over um H uh X knot whoops P
+ 
+
+ align:start position:0%
+DX plus p over um H uh X knot whoops P
+KN sorry that shouldn't be an I that
+
+ align:start position:0%
+KN sorry that shouldn't be an I that
+ 
+
+ align:start position:0%
+KN sorry that shouldn't be an I that
+should be p P good um X on F0 is equal
+
+ align:start position:0%
+should be p P good um X on F0 is equal
+ 
+
+ align:start position:0%
+should be p P good um X on F0 is equal
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Z and you solved this last time when you
+
+ align:start position:0%
+Z and you solved this last time when you
+ 
+
+ align:start position:0%
+Z and you solved this last time when you
+did the ASM totic
+
+ align:start position:0%
+did the ASM totic
+ 
+
+ align:start position:0%
+did the ASM totic
+analysis right this is actually a
+
+ align:start position:0%
+analysis right this is actually a
+ 
+
+ align:start position:0%
+analysis right this is actually a
+ridiculously easy equation it's a first
+
+ align:start position:0%
+ridiculously easy equation it's a first
+ 
+
+ align:start position:0%
+ridiculously easy equation it's a first
+order differential equation there's one
+
+ align:start position:0%
+order differential equation there's one
+ 
+
+ align:start position:0%
+order differential equation there's one
+normalization or there's one integration
+
+ align:start position:0%
+normalization or there's one integration
+ 
+
+ align:start position:0%
+normalization or there's one integration
+constant that's going to be the overall
+
+ align:start position:0%
+constant that's going to be the overall
+ 
+
+ align:start position:0%
+constant that's going to be the overall
+normalization and so the form is
+
+ align:start position:0%
+normalization and so the form is
+ 
+
+ align:start position:0%
+normalization and so the form is
+completely fixed first order
+
+ align:start position:0%
+completely fixed first order
+ 
+
+ align:start position:0%
+completely fixed first order
+differential equation so what's the
+
+ align:start position:0%
+differential equation so what's the
+ 
+
+ align:start position:0%
+differential equation so what's the
+solution of this guy it's a gaan and
+
+ align:start position:0%
+solution of this guy it's a gaan and
+ 
+
+ align:start position:0%
+solution of this guy it's a gaan and
+what's the width of that gaan we look at
+
+ align:start position:0%
+what's the width of that gaan we look at
+ 
+
+ align:start position:0%
+what's the width of that gaan we look at
+p H bar x p over H bar well we know that
+
+ align:start position:0%
+p H bar x p over H bar well we know that
+ 
+
+ align:start position:0%
+p H bar x p over H bar well we know that
+P time xot is twice H right so if I
+
+ align:start position:0%
+P time xot is twice H right so if I
+ 
+
+ align:start position:0%
+P time xot is twice H right so if I
+multiply by X on the top and bottom get
+
+ align:start position:0%
+multiply by X on the top and bottom get
+ 
+
+ align:start position:0%
+multiply by X on the top and bottom get
+two H bar the H bars cancel so this
+
+ align:start position:0%
+two H bar the H bars cancel so this
+ 
+
+ align:start position:0%
+two H bar the H bars cancel so this
+gives me 2 upon x^
+
+ align:start position:0%
+gives me 2 upon x^
+ 
+
+ align:start position:0%
+gives me 2 upon x^
+squ okay remember I said it would be
+
+ align:start position:0%
+squ okay remember I said it would be
+ 
+
+ align:start position:0%
+squ okay remember I said it would be
+useful to remember that P KN time xot is
+
+ align:start position:0%
+useful to remember that P KN time xot is
+ 
+
+ align:start position:0%
+useful to remember that P KN time xot is
+2 H bar it's useful um so it gives us
+
+ align:start position:0%
+2 H bar it's useful um so it gives us
+ 
+
+ align:start position:0%
+2 H bar it's useful um so it gives us
+this and so the result is that F not is
+
+ align:start position:0%
+this and so the result is that F not is
+ 
+
+ align:start position:0%
+this and so the result is that F not is
+equal to up to an overall normalization
+
+ align:start position:0%
+equal to up to an overall normalization
+ 
+
+ align:start position:0%
+equal to up to an overall normalization
+coefficient e to the minus x^2 over X
+
+ align:start position:0%
+coefficient e to the minus x^2 over X
+ 
+
+ align:start position:0%
+coefficient e to the minus x^2 over X
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+squ
+
+ align:start position:0%
+squ
+ 
+
+ align:start position:0%
+squ
+solid okay so there we've solved that
+
+ align:start position:0%
+solid okay so there we've solved that
+ 
+
+ align:start position:0%
+solid okay so there we've solved that
+differential equation it's the easiest
+
+ align:start position:0%
+differential equation it's the easiest
+ 
+
+ align:start position:0%
+differential equation it's the easiest
+second easiest differential equation
+
+ align:start position:0%
+second easiest differential equation
+ 
+
+ align:start position:0%
+second easiest differential equation
+it's a first order differential equation
+
+ align:start position:0%
+it's a first order differential equation
+ 
+
+ align:start position:0%
+it's a first order differential equation
+with a linear term rather than a
+
+ align:start position:0%
+with a linear term rather than a
+ 
+
+ align:start position:0%
+with a linear term rather than a
+constant we get a gaussian and now now
+
+ align:start position:0%
+constant we get a gaussian and now now
+ 
+
+ align:start position:0%
+constant we get a gaussian and now now
+that we've got this guy look do you
+
+ align:start position:0%
+that we've got this guy look do you
+ 
+
+ align:start position:0%
+that we've got this guy look do you
+remember the third hermit polinomial
+
+ align:start position:0%
+remember the third hermit polinomial
+ 
+
+ align:start position:0%
+remember the third hermit polinomial
+because you know if you want we know
+
+ align:start position:0%
+because you know if you want we know
+ 
+
+ align:start position:0%
+because you know if you want we know
+that the the third excited state is
+
+ align:start position:0%
+that the the third excited state is
+ 
+
+ align:start position:0%
+that the the third excited state is
+given by H3 times this uh gaussian right
+
+ align:start position:0%
+given by H3 times this uh gaussian right
+ 
+
+ align:start position:0%
+given by H3 times this uh gaussian right
+do you remember it off the top of your
+
+ align:start position:0%
+do you remember it off the top of your
+ 
+
+ align:start position:0%
+do you remember it off the top of your
+head here's how you solve what it is how
+
+ align:start position:0%
+head here's how you solve what it is how
+ 
+
+ align:start position:0%
+head here's how you solve what it is how
+do we get 53 first of how do we get 51
+
+ align:start position:0%
+do we get 53 first of how do we get 51
+ 
+
+ align:start position:0%
+do we get 53 first of how do we get 51
+how do we get the next state in the
+
+ align:start position:0%
+how do we get the next state in the
+ 
+
+ align:start position:0%
+how do we get the next state in the
+ladder how do we get the wave function
+
+ align:start position:0%
+ladder how do we get the wave function
+ 
+
+ align:start position:0%
+ladder how do we get the wave function
+raising operator but what is the raising
+
+ align:start position:0%
+raising operator but what is the raising
+ 
+
+ align:start position:0%
+raising operator but what is the raising
+operator oh it's the differential
+
+ align:start position:0%
+operator oh it's the differential
+ 
+
+ align:start position:0%
+operator oh it's the differential
+operator I take with okay but if I had a
+
+ align:start position:0%
+operator I take with okay but if I had a
+ 
+
+ align:start position:0%
+operator I take with okay but if I had a
+dagger it's just going to change the
+
+ align:start position:0%
+dagger it's just going to change the
+ 
+
+ align:start position:0%
+dagger it's just going to change the
+sign here so now how do I get F1 F1 is
+
+ align:start position:0%
+sign here so now how do I get F1 F1 is
+ 
+
+ align:start position:0%
+sign here so now how do I get F1 F1 is
+equal to up to some
+
+ align:start position:0%
+equal to up to some
+ 
+
+ align:start position:0%
+equal to up to some
+normalization okay DX minus 2x^ 2
+
+ align:start position:0%
+normalization okay DX minus 2x^ 2
+ 
+
+ align:start position:0%
+normalization okay DX minus 2x^ 2
+x 5
+
+ align:start position:0%
+x 5
+ 
+
+ align:start position:0%
+x 5
+Z cool so now do I have to solve a
+
+ align:start position:0%
+Z cool so now do I have to solve a
+ 
+
+ align:start position:0%
+Z cool so now do I have to solve a
+differential equation to get the higher
+
+ align:start position:0%
+differential equation to get the higher
+ 
+
+ align:start position:0%
+differential equation to get the higher
+States no I take derivatives and
+
+ align:start position:0%
+States no I take derivatives and
+ 
+
+ align:start position:0%
+States no I take derivatives and
+multiply by
+
+ align:start position:0%
+multiply by
+ 
+
+ align:start position:0%
+multiply by
+constants okay so to get the Herm third
+
+ align:start position:0%
+constants okay so to get the Herm third
+ 
+
+ align:start position:0%
+constants okay so to get the Herm third
+Herm polinomial what do you do you do
+
+ align:start position:0%
+Herm polinomial what do you do you do
+ 
+
+ align:start position:0%
+Herm polinomial what do you do you do
+this three
+
+ align:start position:0%
+this three
+ 
+
+ align:start position:0%
+this three
+times this is actually an extremely
+
+ align:start position:0%
+times this is actually an extremely
+ 
+
+ align:start position:0%
+times this is actually an extremely
+efficient way it's related to something
+
+ align:start position:0%
+efficient way it's related to something
+ 
+
+ align:start position:0%
+efficient way it's related to something
+called a generating functional extremely
+
+ align:start position:0%
+called a generating functional extremely
+ 
+
+ align:start position:0%
+called a generating functional extremely
+efficient way to write down the hermet
+
+ align:start position:0%
+efficient way to write down the hermet
+ 
+
+ align:start position:0%
+efficient way to write down the hermet
+pols they're the things that you get by
+
+ align:start position:0%
+pols they're the things that you get by
+ 
+
+ align:start position:0%
+pols they're the things that you get by
+acting on this with this operator as
+
+ align:start position:0%
+acting on this with this operator as
+ 
+
+ align:start position:0%
+acting on this with this operator as
+many times as you want that is a nice
+
+ align:start position:0%
+many times as you want that is a nice
+ 
+
+ align:start position:0%
+many times as you want that is a nice
+formal definition of the Herm pooms the
+
+ align:start position:0%
+formal definition of the Herm pooms the
+ 
+
+ align:start position:0%
+formal definition of the Herm pooms the
+upshot of all of this is the following
+
+ align:start position:0%
+upshot of all of this is the following
+ 
+
+ align:start position:0%
+upshot of all of this is the following
+the upshot of of all this is that we've
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derived we've derived that without ever
+
+ align:start position:0%
+derived we've derived that without ever
+ 
+
+ align:start position:0%
+derived we've derived that without ever
+solving the differential equation the
+
+ align:start position:0%
+solving the differential equation the
+ 
+
+ align:start position:0%
+solving the differential equation the
+Spectrum just from that commutation
+
+ align:start position:0%
+Spectrum just from that commutation
+ 
+
+ align:start position:0%
+Spectrum just from that commutation
+relation just from that commutation
+
+ align:start position:0%
+relation just from that commutation
+ 
+
+ align:start position:0%
+relation just from that commutation
+relation I cannot emphasize this
+
+ align:start position:0%
+relation I cannot emphasize this
+ 
+
+ align:start position:0%
+relation I cannot emphasize this
+strongly enough just from the
+
+ align:start position:0%
+strongly enough just from the
+ 
+
+ align:start position:0%
+strongly enough just from the
+commutation relation EA is minus a time
+
+ align:start position:0%
+commutation relation EA is minus a time
+ 
+
+ align:start position:0%
+commutation relation EA is minus a time
+a constant and EA dagger is a dagger
+
+ align:start position:0%
+a constant and EA dagger is a dagger
+ 
+
+ align:start position:0%
+a constant and EA dagger is a dagger
+times a constant we derive that the the
+
+ align:start position:0%
+times a constant we derive that the the
+ 
+
+ align:start position:0%
+times a constant we derive that the the
+energy ion States come in a tower you
+
+ align:start position:0%
+energy ion States come in a tower you
+ 
+
+ align:start position:0%
+energy ion States come in a tower you
+can move along this Tower by raising
+
+ align:start position:0%
+can move along this Tower by raising
+ 
+
+ align:start position:0%
+can move along this Tower by raising
+with a raising operator lowering with
+
+ align:start position:0%
+with a raising operator lowering with
+ 
+
+ align:start position:0%
+with a raising operator lowering with
+the lowering operator you can construct
+
+ align:start position:0%
+the lowering operator you can construct
+ 
+
+ align:start position:0%
+the lowering operator you can construct
+the ground state by building that simple
+
+ align:start position:0%
+the ground state by building that simple
+ 
+
+ align:start position:0%
+the ground state by building that simple
+op wave function which is annihilated by
+
+ align:start position:0%
+op wave function which is annihilated by
+ 
+
+ align:start position:0%
+op wave function which is annihilated by
+the lowering operator you can build all
+
+ align:start position:0%
+the lowering operator you can build all
+ 
+
+ align:start position:0%
+the lowering operator you can build all
+the other states by raising them which
+
+ align:start position:0%
+the other states by raising them which
+ 
+
+ align:start position:0%
+the other states by raising them which
+is just taking derivatives instead of
+
+ align:start position:0%
+is just taking derivatives instead of
+ 
+
+ align:start position:0%
+is just taking derivatives instead of
+solving differential equations which is
+
+ align:start position:0%
+solving differential equations which is
+ 
+
+ align:start position:0%
+solving differential equations which is
+hard and all of this came from this
+
+ align:start position:0%
+hard and all of this came from this
+ 
+
+ align:start position:0%
+hard and all of this came from this
+commutation relation and since we are
+
+ align:start position:0%
+commutation relation and since we are
+ 
+
+ align:start position:0%
+commutation relation and since we are
+going to see this over and over again
+
+ align:start position:0%
+going to see this over and over again
+ 
+
+ align:start position:0%
+going to see this over and over again
+and you will see this depending on how
+
+ align:start position:0%
+and you will see this depending on how
+ 
+
+ align:start position:0%
+and you will see this depending on how
+far you take physics you will see this
+
+ align:start position:0%
+far you take physics you will see this
+ 
+
+ align:start position:0%
+far you take physics you will see this
+in 05 you will see this in 06 you will
+
+ align:start position:0%
+in 05 you will see this in 06 you will
+ 
+
+ align:start position:0%
+in 05 you will see this in 06 you will
+see this in Quantum field Theory this
+
+ align:start position:0%
+see this in Quantum field Theory this
+ 
+
+ align:start position:0%
+see this in Quantum field Theory this
+shows up everywhere it's absolutely at
+
+ align:start position:0%
+shows up everywhere it's absolutely at
+ 
+
+ align:start position:0%
+shows up everywhere it's absolutely at
+the core of how we organize the degrees
+
+ align:start position:0%
+the core of how we organize the degrees
+ 
+
+ align:start position:0%
+the core of how we organize the degrees
+of freedom uh this structure is
+
+ align:start position:0%
+of freedom uh this structure is
+ 
+
+ align:start position:0%
+of freedom uh this structure is
+something you should see and declare
+
+ align:start position:0%
+something you should see and declare
+ 
+
+ align:start position:0%
+something you should see and declare
+Victory upon seeing you should see this
+
+ align:start position:0%
+Victory upon seeing you should see this
+ 
+
+ align:start position:0%
+Victory upon seeing you should see this
+and immediately say I know the answer
+
+ align:start position:0%
+and immediately say I know the answer
+ 
+
+ align:start position:0%
+and immediately say I know the answer
+and I can write it down
+
+ align:start position:0%
+and I can write it down
+ 
+
+ align:start position:0%
+and I can write it down
+okay in the next lecture we're going to
+
+ align:start position:0%
+okay in the next lecture we're going to
+ 
+
+ align:start position:0%
+okay in the next lecture we're going to
+do a review which is going to introduce
+
+ align:start position:0%
+do a review which is going to introduce
+ 
+
+ align:start position:0%
+do a review which is going to introduce
+a slightly more formal presentation of
+
+ align:start position:0%
+a slightly more formal presentation of
+ 
+
+ align:start position:0%
+a slightly more formal presentation of
+all of these ideas that's not going to
+
+ align:start position:0%
+all of these ideas that's not going to
+ 
+
+ align:start position:0%
+all of these ideas that's not going to
+be material covered on the exam but it's
+
+ align:start position:0%
+be material covered on the exam but it's
+ 
+
+ align:start position:0%
+be material covered on the exam but it's
+going to help you with the exam which
+
+ align:start position:0%
+going to help you with the exam which
+ 
+
+ align:start position:0%
+going to help you with the exam which
+will be on Thursday see you Tuesday
\ No newline at end of file
diff --git a/jOl7xci58e8.txt b/jOl7xci58e8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f19fe1beee153f0d75f7c44b3f4ca6b91d7f81a3
--- /dev/null
+++ b/jOl7xci58e8.txt
@@ -0,0 +1,795 @@
+align:start position:0%
+ 
+an artificial dialectric made from an
+
+ align:start position:0%
+an artificial dialectric made from an
+ 
+
+ align:start position:0%
+an artificial dialectric made from an
+array of conducting spheres demonstrates
+
+ align:start position:0%
+array of conducting spheres demonstrates
+ 
+
+ align:start position:0%
+array of conducting spheres demonstrates
+how polarization of media gives rise to
+
+ align:start position:0%
+how polarization of media gives rise to
+ 
+
+ align:start position:0%
+how polarization of media gives rise to
+the properties of a linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dialectric when the region between
+
+ align:start position:0%
+dialectric when the region between
+ 
+
+ align:start position:0%
+dialectric when the region between
+electrodes is filled with a dialectric
+
+ align:start position:0%
+electrodes is filled with a dialectric
+ 
+
+ align:start position:0%
+electrodes is filled with a dialectric
+material the capacitance is
+
+ align:start position:0%
+material the capacitance is
+ 
+
+ align:start position:0%
+material the capacitance is
+increased this increase is due to
+
+ align:start position:0%
+increased this increase is due to
+ 
+
+ align:start position:0%
+increased this increase is due to
+polarization of molecules of the
+
+ align:start position:0%
+polarization of molecules of the
+ 
+
+ align:start position:0%
+polarization of molecules of the
+material
+
+ align:start position:0%
+material
+ 
+
+ align:start position:0%
+material
+we form an appreciation for how this
+
+ align:start position:0%
+we form an appreciation for how this
+ 
+
+ align:start position:0%
+we form an appreciation for how this
+happens by replacing the molecules with
+
+ align:start position:0%
+happens by replacing the molecules with
+ 
+
+ align:start position:0%
+happens by replacing the molecules with
+microscopic spheres suspended in
+
+ align:start position:0%
+microscopic spheres suspended in
+ 
+
+ align:start position:0%
+microscopic spheres suspended in
+air this artificial dialectric is
+
+ align:start position:0%
+air this artificial dialectric is
+ 
+
+ align:start position:0%
+air this artificial dialectric is
+composed of what we can think of as
+
+ align:start position:0%
+composed of what we can think of as
+ 
+
+ align:start position:0%
+composed of what we can think of as
+molecules that are actually essentially
+
+ align:start position:0%
+molecules that are actually essentially
+ 
+
+ align:start position:0%
+molecules that are actually essentially
+perfectly conducting
+
+ align:start position:0%
+perfectly conducting
+ 
+
+ align:start position:0%
+perfectly conducting
+spheres each has radius
+
+ align:start position:0%
+spheres each has radius
+ 
+
+ align:start position:0%
+spheres each has radius
+R and they're in a cubic array with
+
+ align:start position:0%
+R and they're in a cubic array with
+ 
+
+ align:start position:0%
+R and they're in a cubic array with
+spacing s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+application of voltage to the electrodes
+
+ align:start position:0%
+application of voltage to the electrodes
+ 
+
+ align:start position:0%
+application of voltage to the electrodes
+results in the Spheres acquiring
+
+ align:start position:0%
+results in the Spheres acquiring
+ 
+
+ align:start position:0%
+results in the Spheres acquiring
+positive and negative surface charges on
+
+ align:start position:0%
+positive and negative surface charges on
+ 
+
+ align:start position:0%
+positive and negative surface charges on
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+poles in addition to the uniform field
+
+ align:start position:0%
+poles in addition to the uniform field
+ 
+
+ align:start position:0%
+poles in addition to the uniform field
+due to the applied voltage the field
+
+ align:start position:0%
+due to the applied voltage the field
+ 
+
+ align:start position:0%
+due to the applied voltage the field
+outside the sphere is also includes the
+
+ align:start position:0%
+outside the sphere is also includes the
+ 
+
+ align:start position:0%
+outside the sphere is also includes the
+dipole fields from the array of
+
+ align:start position:0%
+dipole fields from the array of
+ 
+
+ align:start position:0%
+dipole fields from the array of
+spheres the Spheres like the molecules
+
+ align:start position:0%
+spheres the Spheres like the molecules
+ 
+
+ align:start position:0%
+spheres the Spheres like the molecules
+of a material are polarized by an
+
+ align:start position:0%
+of a material are polarized by an
+ 
+
+ align:start position:0%
+of a material are polarized by an
+applied
+
+ align:start position:0%
+applied
+ 
+
+ align:start position:0%
+applied
+field the artificial dialectric is
+
+ align:start position:0%
+field the artificial dialectric is
+ 
+
+ align:start position:0%
+field the artificial dialectric is
+composed of an array of pingpong balls
+
+ align:start position:0%
+composed of an array of pingpong balls
+ 
+
+ align:start position:0%
+composed of an array of pingpong balls
+with conducting
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Coatings we're going to measure the
+
+ align:start position:0%
+Coatings we're going to measure the
+ 
+
+ align:start position:0%
+Coatings we're going to measure the
+effective primitivity by measuring the
+
+ align:start position:0%
+effective primitivity by measuring the
+ 
+
+ align:start position:0%
+effective primitivity by measuring the
+change in capacitance as the array is
+
+ align:start position:0%
+change in capacitance as the array is
+ 
+
+ align:start position:0%
+change in capacitance as the array is
+placed between the plates of this plain
+
+ align:start position:0%
+placed between the plates of this plain
+ 
+
+ align:start position:0%
+placed between the plates of this plain
+parallel plate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacitor the cage is grounded for
+
+ align:start position:0%
+capacitor the cage is grounded for
+ 
+
+ align:start position:0%
+capacitor the cage is grounded for
+shielding and to keep us from touching
+
+ align:start position:0%
+shielding and to keep us from touching
+ 
+
+ align:start position:0%
+shielding and to keep us from touching
+the bottom
+
+ align:start position:0%
+the bottom
+ 
+
+ align:start position:0%
+the bottom
+electrode it's driven to 400 volts RMS
+
+ align:start position:0%
+electrode it's driven to 400 volts RMS
+ 
+
+ align:start position:0%
+electrode it's driven to 400 volts RMS
+at 250 Hertz by this
+
+ align:start position:0%
+at 250 Hertz by this
+ 
+
+ align:start position:0%
+at 250 Hertz by this
+Transformer which is itself driven by an
+
+ align:start position:0%
+Transformer which is itself driven by an
+ 
+
+ align:start position:0%
+Transformer which is itself driven by an
+oscillator and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amplifier here's the top
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electrode to avoid fringing effects only
+
+ align:start position:0%
+electrode to avoid fringing effects only
+ 
+
+ align:start position:0%
+electrode to avoid fringing effects only
+the charge induced on this Central
+
+ align:start position:0%
+the charge induced on this Central
+ 
+
+ align:start position:0%
+the charge induced on this Central
+section will be measured when we measure
+
+ align:start position:0%
+section will be measured when we measure
+ 
+
+ align:start position:0%
+section will be measured when we measure
+the capacitance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's how the dialectric is inserted
+
+ align:start position:0%
+here's how the dialectric is inserted
+ 
+
+ align:start position:0%
+here's how the dialectric is inserted
+between the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plates before balancing the bridge we
+
+ align:start position:0%
+plates before balancing the bridge we
+ 
+
+ align:start position:0%
+plates before balancing the bridge we
+remove the array of ping pong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+balls we've already set the driving
+
+ align:start position:0%
+balls we've already set the driving
+ 
+
+ align:start position:0%
+balls we've already set the driving
+voltage to about 400 volts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+RMS here are the resistors in the two
+
+ align:start position:0%
+RMS here are the resistors in the two
+ 
+
+ align:start position:0%
+RMS here are the resistors in the two
+upper legs of the bridge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they Shunk the scope differential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amplifier so the scope signal is the
+
+ align:start position:0%
+amplifier so the scope signal is the
+ 
+
+ align:start position:0%
+amplifier so the scope signal is the
+voltage V Sub
+
+ align:start position:0%
+voltage V Sub
+ 
+
+ align:start position:0%
+voltage V Sub
+0 the balancing capacitance C2 is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here this is the capacitor
+
+ align:start position:0%
+here this is the capacitor
+ 
+
+ align:start position:0%
+here this is the capacitor
+C1 which is there for fine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tuning we can balance the signal with
+
+ align:start position:0%
+tuning we can balance the signal with
+ 
+
+ align:start position:0%
+tuning we can balance the signal with
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacitor so we tune C2 to null the
+
+ align:start position:0%
+capacitor so we tune C2 to null the
+ 
+
+ align:start position:0%
+capacitor so we tune C2 to null the
+bridge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+voltage and C1 to fine-tune the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+null we're ready to insert the
+
+ align:start position:0%
+null we're ready to insert the
+ 
+
+ align:start position:0%
+null we're ready to insert the
+artificial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dialectric as the array is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inserted the bridge becomes
+
+ align:start position:0%
+inserted the bridge becomes
+ 
+
+ align:start position:0%
+inserted the bridge becomes
+unbalanced indicating that the
+
+ align:start position:0%
+unbalanced indicating that the
+ 
+
+ align:start position:0%
+unbalanced indicating that the
+capacitance is
+
+ align:start position:0%
+capacitance is
+ 
+
+ align:start position:0%
+capacitance is
+changed we measure a voltage of 135
+
+ align:start position:0%
+changed we measure a voltage of 135
+ 
+
+ align:start position:0%
+changed we measure a voltage of 135
+molts
+
+ align:start position:0%
+molts
+ 
+
+ align:start position:0%
+molts
+Peak remember what we predicted was a
+
+ align:start position:0%
+Peak remember what we predicted was a
+ 
+
+ align:start position:0%
+Peak remember what we predicted was a
+change of 133 molts Peak
+
+ align:start position:0%
+change of 133 molts Peak
+ 
+
+ align:start position:0%
+change of 133 molts Peak
+the agreement is perhaps better than we
+
+ align:start position:0%
+the agreement is perhaps better than we
+ 
+
+ align:start position:0%
+the agreement is perhaps better than we
+should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expect has the capacitance actually been
+
+ align:start position:0%
+expect has the capacitance actually been
+ 
+
+ align:start position:0%
+expect has the capacitance actually been
+increased by the insertion of the
+
+ align:start position:0%
+increased by the insertion of the
+ 
+
+ align:start position:0%
+increased by the insertion of the
+Spheres let's try the experiment
+
+ align:start position:0%
+Spheres let's try the experiment
+ 
+
+ align:start position:0%
+Spheres let's try the experiment
+again we can see that it has by looking
+
+ align:start position:0%
+again we can see that it has by looking
+ 
+
+ align:start position:0%
+again we can see that it has by looking
+at the balancing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capacitor here the array is out and we
+
+ align:start position:0%
+capacitor here the array is out and we
+ 
+
+ align:start position:0%
+capacitor here the array is out and we
+balance the capacitor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we insert the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+array note the position of the tuning
+
+ align:start position:0%
+array note the position of the tuning
+ 
+
+ align:start position:0%
+array note the position of the tuning
+capacitor
+
+ align:start position:0%
+capacitor
+ 
+
+ align:start position:0%
+capacitor
+plates if the capacitance has been
+
+ align:start position:0%
+plates if the capacitance has been
+ 
+
+ align:start position:0%
+plates if the capacitance has been
+increased to balance the bridge the knob
+
+ align:start position:0%
+increased to balance the bridge the knob
+ 
+
+ align:start position:0%
+increased to balance the bridge the knob
+must be turned so that they have greater
+
+ align:start position:0%
+must be turned so that they have greater
+ 
+
+ align:start position:0%
+must be turned so that they have greater
+area of overlap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the balancing capacitance is
+
+ align:start position:0%
+the balancing capacitance is
+ 
+
+ align:start position:0%
+the balancing capacitance is
+increased so the artificial dialectric
+
+ align:start position:0%
+increased so the artificial dialectric
+ 
+
+ align:start position:0%
+increased so the artificial dialectric
+doeses increase the capacitance of the
+
+ align:start position:0%
+doeses increase the capacitance of the
+ 
+
+ align:start position:0%
+doeses increase the capacitance of the
+plain parallel capacitor
\ No newline at end of file
diff --git a/ja56bJ8ogUw.txt b/ja56bJ8ogUw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dc0e8585fdeda5a20d16dc4f478e68c37871d8cb
--- /dev/null
+++ b/ja56bJ8ogUw.txt
@@ -0,0 +1,11579 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay so um welcome back
+
+ align:start position:0%
+ocw.mit.edu okay so um welcome back
+ 
+
+ align:start position:0%
+ocw.mit.edu okay so um welcome back
+uh we talked last time about the problem
+
+ align:start position:0%
+uh we talked last time about the problem
+ 
+
+ align:start position:0%
+uh we talked last time about the problem
+um of
+
+ align:start position:0%
+um of
+ 
+
+ align:start position:0%
+um of
+policy evaluation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right which was given I'm executing some
+
+ align:start position:0%
+right which was given I'm executing some
+ 
+
+ align:start position:0%
+right which was given I'm executing some
+policy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pi
+
+ align:start position:0%
+Pi
+ 
+
+ align:start position:0%
+Pi
+estimate the cost to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go right and we showed that it was sort
+
+ align:start position:0%
+go right and we showed that it was sort
+ 
+
+ align:start position:0%
+go right and we showed that it was sort
+of trivial to do if you have a
+
+ align:start position:0%
+of trivial to do if you have a
+ 
+
+ align:start position:0%
+of trivial to do if you have a
+model and um if you don't have a
+
+ align:start position:0%
+model and um if you don't have a
+ 
+
+ align:start position:0%
+model and um if you don't have a
+model you can still do it with sort of
+
+ align:start position:0%
+model you can still do it with sort of
+ 
+
+ align:start position:0%
+model you can still do it with sort of
+the temporal difference
+
+ align:start position:0%
+the temporal difference
+ 
+
+ align:start position:0%
+the temporal difference
+learning class of Al
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algorithms which is TD which is in the
+
+ align:start position:0%
+algorithms which is TD which is in the
+ 
+
+ align:start position:0%
+algorithms which is TD which is in the
+title there okay and the temporal
+
+ align:start position:0%
+title there okay and the temporal
+ 
+
+ align:start position:0%
+title there okay and the temporal
+difference learning the TD Lambda in
+
+ align:start position:0%
+difference learning the TD Lambda in
+ 
+
+ align:start position:0%
+difference learning the TD Lambda in
+particular was nice because it
+
+ align:start position:0%
+particular was nice because it
+ 
+
+ align:start position:0%
+particular was nice because it
+encapsulated all the algorithms we
+
+ align:start position:0%
+encapsulated all the algorithms we
+ 
+
+ align:start position:0%
+encapsulated all the algorithms we
+talked about last time um TD if Lambda
+
+ align:start position:0%
+talked about last time um TD if Lambda
+ 
+
+ align:start position:0%
+talked about last time um TD if Lambda
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+zero was essentially the one-step
+
+ align:start position:0%
+zero was essentially the one-step
+ 
+
+ align:start position:0%
+zero was essentially the one-step
+bootstrapping idea we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+said where you
+
+ align:start position:0%
+said where you
+ 
+
+ align:start position:0%
+said where you
+use your current cost plus your expected
+
+ align:start position:0%
+use your current cost plus your expected
+ 
+
+ align:start position:0%
+use your current cost plus your expected
+value of all future costs um as your new
+
+ align:start position:0%
+value of all future costs um as your new
+ 
+
+ align:start position:0%
+value of all future costs um as your new
+estimate of this and the other the
+
+ align:start position:0%
+estimate of this and the other the
+ 
+
+ align:start position:0%
+estimate of this and the other the
+limiting the other limiting case was td1
+
+ align:start position:0%
+limiting the other limiting case was td1
+ 
+
+ align:start position:0%
+limiting the other limiting case was td1
+which resulted in just Monte Carlo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evaluation and what I said quickly at
+
+ align:start position:0%
+evaluation and what I said quickly at
+ 
+
+ align:start position:0%
+evaluation and what I said quickly at
+the end of class is that um we spent all
+
+ align:start position:0%
+the end of class is that um we spent all
+ 
+
+ align:start position:0%
+the end of class is that um we spent all
+our time last time on um doing temporal
+
+ align:start position:0%
+our time last time on um doing temporal
+ 
+
+ align:start position:0%
+our time last time on um doing temporal
+difference learning just on the
+
+ align:start position:0%
+difference learning just on the
+ 
+
+ align:start position:0%
+difference learning just on the
+representation of doing solving a Markov
+
+ align:start position:0%
+representation of doing solving a Markov
+ 
+
+ align:start position:0%
+representation of doing solving a Markov
+chain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right we did it for discrete State
+
+ align:start position:0%
+right we did it for discrete State
+ 
+
+ align:start position:0%
+right we did it for discrete State
+discreet action discret time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and it's known that these algorithms
+
+ align:start position:0%
+um and it's known that these algorithms
+ 
+
+ align:start position:0%
+um and it's known that these algorithms
+converge to the correct estimate if you
+
+ align:start position:0%
+converge to the correct estimate if you
+ 
+
+ align:start position:0%
+converge to the correct estimate if you
+run enough times and your Markov chain
+
+ align:start position:0%
+run enough times and your Markov chain
+ 
+
+ align:start position:0%
+run enough times and your Markov chain
+is orotic if you visit all states at all
+
+ align:start position:0%
+is orotic if you visit all states at all
+ 
+
+ align:start position:0%
+is orotic if you visit all states at all
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+okay but that's pretty limiting because
+
+ align:start position:0%
+okay but that's pretty limiting because
+ 
+
+ align:start position:0%
+okay but that's pretty limiting because
+um in order to do a Markoff chain
+
+ align:start position:0%
+um in order to do a Markoff chain
+ 
+
+ align:start position:0%
+um in order to do a Markoff chain
+analysis of even an acrobot or something
+
+ align:start position:0%
+analysis of even an acrobot or something
+ 
+
+ align:start position:0%
+analysis of even an acrobot or something
+you have to discretize four state
+
+ align:start position:0%
+you have to discretize four state
+ 
+
+ align:start position:0%
+you have to discretize four state
+variables right Theta Theta dot Theta 1
+
+ align:start position:0%
+variables right Theta Theta dot Theta 1
+ 
+
+ align:start position:0%
+variables right Theta Theta dot Theta 1
+Theta 2 Theta 1 do theta 2 dot let's say
+
+ align:start position:0%
+Theta 2 Theta 1 do theta 2 dot let's say
+ 
+
+ align:start position:0%
+Theta 2 Theta 1 do theta 2 dot let's say
+you do 25 I mean things get big fast be
+
+ align:start position:0%
+you do 25 I mean things get big fast be
+ 
+
+ align:start position:0%
+you do 25 I mean things get big fast be
+the 25 to the fourth power if you put 25
+
+ align:start position:0%
+the 25 to the fourth power if you put 25
+ 
+
+ align:start position:0%
+the 25 to the fourth power if you put 25
+bins in each um
+
+ align:start position:0%
+bins in each um
+ 
+
+ align:start position:0%
+bins in each um
+in each Dimension and that's not very
+
+ align:start position:0%
+in each Dimension and that's not very
+ 
+
+ align:start position:0%
+in each Dimension and that's not very
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+so um so today we want to make the tools
+
+ align:start position:0%
+so um so today we want to make the tools
+ 
+
+ align:start position:0%
+so um so today we want to make the tools
+more relevant more powerful by breaking
+
+ align:start position:0%
+more relevant more powerful by breaking
+ 
+
+ align:start position:0%
+more relevant more powerful by breaking
+this assumption that we're in a Markov
+
+ align:start position:0%
+this assumption that we're in a Markov
+ 
+
+ align:start position:0%
+this assumption that we're in a Markov
+chain where we've discretized everything
+
+ align:start position:0%
+chain where we've discretized everything
+ 
+
+ align:start position:0%
+chain where we've discretized everything
+and try to do more General try to do
+
+ align:start position:0%
+and try to do more General try to do
+ 
+
+ align:start position:0%
+and try to do more General try to do
+temporal difference learning on a more
+
+ align:start position:0%
+temporal difference learning on a more
+ 
+
+ align:start position:0%
+temporal difference learning on a more
+General class of functions that are more
+
+ align:start position:0%
+General class of functions that are more
+ 
+
+ align:start position:0%
+General class of functions that are more
+natively continuous okay so we're going
+
+ align:start position:0%
+natively continuous okay so we're going
+ 
+
+ align:start position:0%
+natively continuous okay so we're going
+to do it with function
+
+ align:start position:0%
+to do it with function
+ 
+
+ align:start position:0%
+to do it with function
+approximation now to get there John did
+
+ align:start position:0%
+approximation now to get there John did
+ 
+
+ align:start position:0%
+approximation now to get there John did
+a little bit of function approximation
+
+ align:start position:0%
+a little bit of function approximation
+ 
+
+ align:start position:0%
+a little bit of function approximation
+in the reinforce lectures so I want to
+
+ align:start position:0%
+in the reinforce lectures so I want to
+ 
+
+ align:start position:0%
+in the reinforce lectures so I want to
+basically pick up on the examples the
+
+ align:start position:0%
+basically pick up on the examples the
+ 
+
+ align:start position:0%
+basically pick up on the examples the
+kind of examples he was showing you and
+
+ align:start position:0%
+kind of examples he was showing you and
+ 
+
+ align:start position:0%
+kind of examples he was showing you and
+do a quick sort of Crash Course on least
+
+ align:start position:0%
+do a quick sort of Crash Course on least
+ 
+
+ align:start position:0%
+do a quick sort of Crash Course on least
+squares function approximation just um
+
+ align:start position:0%
+squares function approximation just um
+ 
+
+ align:start position:0%
+squares function approximation just um
+to make sure that people are sort of
+
+ align:start position:0%
+to make sure that people are sort of
+ 
+
+ align:start position:0%
+to make sure that people are sort of
+comfortable with that and we'll we'll
+
+ align:start position:0%
+comfortable with that and we'll we'll
+ 
+
+ align:start position:0%
+comfortable with that and we'll we'll
+build on that
+
+ align:start position:0%
+build on that
+ 
+
+ align:start position:0%
+build on that
+quickly okay
+
+ align:start position:0%
+quickly okay
+ 
+
+ align:start position:0%
+quickly okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let's talk a little bit
+
+ align:start position:0%
+um let's talk a little bit
+ 
+
+ align:start position:0%
+um let's talk a little bit
+about least squares function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximation okay
+
+ align:start position:0%
+approximation okay
+ 
+
+ align:start position:0%
+approximation okay
+so the canonical example which is the
+
+ align:start position:0%
+so the canonical example which is the
+ 
+
+ align:start position:0%
+so the canonical example which is the
+same thing that John showed you in class
+
+ align:start position:0%
+same thing that John showed you in class
+ 
+
+ align:start position:0%
+same thing that John showed you in class
+is we want to
+
+ align:start position:0%
+is we want to
+ 
+
+ align:start position:0%
+is we want to
+approximate we want to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+estimate some function some unknown
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function that takes input X and spits
+
+ align:start position:0%
+function that takes input X and spits
+ 
+
+ align:start position:0%
+function that takes input X and spits
+out output
+
+ align:start position:0%
+out output
+ 
+
+ align:start position:0%
+out output
+y right and you're
+
+ align:start position:0%
+y right and you're
+ 
+
+ align:start position:0%
+y right and you're
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+um input output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which I we could write something like
+
+ align:start position:0%
+which I we could write something like
+ 
+
+ align:start position:0%
+which I we could write something like
+you're given pairs of data
+
+ align:start position:0%
+you're given pairs of data
+ 
+
+ align:start position:0%
+you're given pairs of data
+um samples of the input and output so
+
+ align:start position:0%
+um samples of the input and output so
+ 
+
+ align:start position:0%
+um samples of the input and output so
+you're allowed to query the function
+
+ align:start position:0%
+you're allowed to query the function
+ 
+
+ align:start position:0%
+you're allowed to query the function
+given this input what output um should
+
+ align:start position:0%
+given this input what output um should
+ 
+
+ align:start position:0%
+given this input what output um should
+you do in the basic case it's you're
+
+ align:start position:0%
+you do in the basic case it's you're
+ 
+
+ align:start position:0%
+you do in the basic case it's you're
+you're doing this passively someone just
+
+ align:start position:0%
+you're doing this passively someone just
+ 
+
+ align:start position:0%
+you're doing this passively someone just
+gives you a data set and you're supposed
+
+ align:start position:0%
+gives you a data set and you're supposed
+ 
+
+ align:start position:0%
+gives you a data set and you're supposed
+to then do your best job at
+
+ align:start position:0%
+to then do your best job at
+ 
+
+ align:start position:0%
+to then do your best job at
+reconstructing F okay there are
+
+ align:start position:0%
+reconstructing F okay there are
+ 
+
+ align:start position:0%
+reconstructing F okay there are
+interesting cases that people look at
+
+ align:start position:0%
+interesting cases that people look at
+ 
+
+ align:start position:0%
+interesting cases that people look at
+where you're if you're allowed to choose
+
+ align:start position:0%
+where you're if you're allowed to choose
+ 
+
+ align:start position:0%
+where you're if you're allowed to choose
+this then how do you do how do you
+
+ align:start position:0%
+this then how do you do how do you
+ 
+
+ align:start position:0%
+this then how do you do how do you
+actively interrogate the system how do
+
+ align:start position:0%
+actively interrogate the system how do
+ 
+
+ align:start position:0%
+actively interrogate the system how do
+you pick the X's to get the most
+
+ align:start position:0%
+you pick the X's to get the most
+ 
+
+ align:start position:0%
+you pick the X's to get the most
+information out but in the simple case
+
+ align:start position:0%
+information out but in the simple case
+ 
+
+ align:start position:0%
+information out but in the simple case
+let's just say you're given a collection
+
+ align:start position:0%
+let's just say you're given a collection
+ 
+
+ align:start position:0%
+let's just say you're given a collection
+of input output data and you want to
+
+ align:start position:0%
+of input output data and you want to
+ 
+
+ align:start position:0%
+of input output data and you want to
+estimate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F so um the standard way to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is to write down um there are many
+
+ align:start position:0%
+this is to write down um there are many
+ 
+
+ align:start position:0%
+this is to write down um there are many
+cost functions you you could use but the
+
+ align:start position:0%
+cost functions you you could use but the
+ 
+
+ align:start position:0%
+cost functions you you could use but the
+um the one most people use is to write
+
+ align:start position:0%
+um the one most people use is to write
+ 
+
+ align:start position:0%
+um the one most people use is to write
+down a least squares cost
+
+ align:start position:0%
+down a least squares cost
+ 
+
+ align:start position:0%
+down a least squares cost
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+where we're going to try to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um try to
+
+ align:start position:0%
+um try to
+ 
+
+ align:start position:0%
+um try to
+find um a
+
+ align:start position:0%
+find um a
+ 
+
+ align:start position:0%
+find um a
+model where y hat is some f of let's say
+
+ align:start position:0%
+model where y hat is some f of let's say
+ 
+
+ align:start position:0%
+model where y hat is some f of let's say
+it depends on parameter Vector Alpha
+
+ align:start position:0%
+it depends on parameter Vector Alpha
+ 
+
+ align:start position:0%
+it depends on parameter Vector Alpha
+half of
+
+ align:start position:0%
+half of
+ 
+
+ align:start position:0%
+half of
+X okay just like in the policy gradient
+
+ align:start position:0%
+X okay just like in the policy gradient
+ 
+
+ align:start position:0%
+X okay just like in the policy gradient
+kind of case I'm going to write down a
+
+ align:start position:0%
+kind of case I'm going to write down a
+ 
+
+ align:start position:0%
+kind of case I'm going to write down a
+set of
+
+ align:start position:0%
+set of
+ 
+
+ align:start position:0%
+set of
+functions where the actual function sort
+
+ align:start position:0%
+functions where the actual function sort
+ 
+
+ align:start position:0%
+functions where the actual function sort
+of depends on both Alpha and X but we
+
+ align:start position:0%
+of depends on both Alpha and X but we
+ 
+
+ align:start position:0%
+of depends on both Alpha and X but we
+can think of it as taking X as input and
+
+ align:start position:0%
+can think of it as taking X as input and
+ 
+
+ align:start position:0%
+can think of it as taking X as input and
+generating an estimate y hat okay and
+
+ align:start position:0%
+generating an estimate y hat okay and
+ 
+
+ align:start position:0%
+generating an estimate y hat okay and
+you can formulate the problem with the
+
+ align:start position:0%
+you can formulate the problem with the
+ 
+
+ align:start position:0%
+you can formulate the problem with the
+least squares
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+metric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where you want to minimize over Alpha
+
+ align:start position:0%
+where you want to minimize over Alpha
+ 
+
+ align:start position:0%
+where you want to minimize over Alpha
+um the squared error over my data minus
+
+ align:start position:0%
+um the squared error over my data minus
+ 
+
+ align:start position:0%
+um the squared error over my data minus
+my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+estimator actually have the estimator
+
+ align:start position:0%
+estimator actually have the estimator
+ 
+
+ align:start position:0%
+estimator actually have the estimator
+here no big deal but just to keep it
+
+ align:start position:0%
+here no big deal but just to keep it
+ 
+
+ align:start position:0%
+here no big deal but just to keep it
+consistent with
+
+ align:start position:0%
+consistent with
+ 
+
+ align:start position:0%
+consistent with
+my chicken scratch
+
+ align:start position:0%
+my chicken scratch
+ 
+
+ align:start position:0%
+my chicken scratch
+notes okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so if we can write down a class of
+
+ align:start position:0%
+um so if we can write down a class of
+ 
+
+ align:start position:0%
+um so if we can write down a class of
+functions we want to search over then we
+
+ align:start position:0%
+functions we want to search over then we
+ 
+
+ align:start position:0%
+functions we want to search over then we
+can turn it into the standard
+
+ align:start position:0%
+can turn it into the standard
+ 
+
+ align:start position:0%
+can turn it into the standard
+optimization we've been doing throughout
+
+ align:start position:0%
+optimization we've been doing throughout
+ 
+
+ align:start position:0%
+optimization we've been doing throughout
+where we just try to find um the
+
+ align:start position:0%
+where we just try to find um the
+ 
+
+ align:start position:0%
+where we just try to find um the
+parameter Vector Alpha which makes our
+
+ align:start position:0%
+parameter Vector Alpha which makes our
+ 
+
+ align:start position:0%
+parameter Vector Alpha which makes our
+estimates as close as possible in a
+
+ align:start position:0%
+estimates as close as possible in a
+ 
+
+ align:start position:0%
+estimates as close as possible in a
+least squared sense to the the actual
+
+ align:start position:0%
+least squared sense to the the actual
+ 
+
+ align:start position:0%
+least squared sense to the the actual
+data yeah or Y hat here
+
+ align:start position:0%
+data yeah or Y hat here
+ 
+
+ align:start position:0%
+data yeah or Y hat here
+is fat Alpha XI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay so why do we care about doing
+
+ align:start position:0%
+yeah okay so why do we care about doing
+ 
+
+ align:start position:0%
+yeah okay so why do we care about doing
+that the the the methods used to you
+
+ align:start position:0%
+that the the the methods used to you
+ 
+
+ align:start position:0%
+that the the the methods used to you
+already know optimization methods we
+
+ align:start position:0%
+already know optimization methods we
+ 
+
+ align:start position:0%
+already know optimization methods we
+know a lot of ways that we could
+
+ align:start position:0%
+know a lot of ways that we could
+ 
+
+ align:start position:0%
+know a lot of ways that we could
+potentially try to solve this
+
+ align:start position:0%
+potentially try to solve this
+ 
+
+ align:start position:0%
+potentially try to solve this
+um so for instance we could take the
+
+ align:start position:0%
+um so for instance we could take the
+ 
+
+ align:start position:0%
+um so for instance we could take the
+gradient of this with respect to Alpha
+
+ align:start position:0%
+gradient of this with respect to Alpha
+ 
+
+ align:start position:0%
+gradient of this with respect to Alpha
+and do gradient descent which is exactly
+
+ align:start position:0%
+and do gradient descent which is exactly
+ 
+
+ align:start position:0%
+and do gradient descent which is exactly
+what John was doing in the reinforced
+
+ align:start position:0%
+what John was doing in the reinforced
+ 
+
+ align:start position:0%
+what John was doing in the reinforced
+case except the gradient was not
+
+ align:start position:0%
+case except the gradient was not
+ 
+
+ align:start position:0%
+case except the gradient was not
+calculated explicitly it was estimated
+
+ align:start position:0%
+calculated explicitly it was estimated
+ 
+
+ align:start position:0%
+calculated explicitly it was estimated
+by sampling in the reinforced case
+
+ align:start position:0%
+by sampling in the reinforced case
+ 
+
+ align:start position:0%
+by sampling in the reinforced case
+right and in general there's there's
+
+ align:start position:0%
+right and in general there's there's
+ 
+
+ align:start position:0%
+right and in general there's there's
+some cases there are some classes of
+
+ align:start position:0%
+some cases there are some classes of
+ 
+
+ align:start position:0%
+some cases there are some classes of
+functions that we can choose and I'll
+
+ align:start position:0%
+functions that we can choose and I'll
+ 
+
+ align:start position:0%
+functions that we can choose and I'll
+make this more graphical and explicit in
+
+ align:start position:0%
+make this more graphical and explicit in
+ 
+
+ align:start position:0%
+make this more graphical and explicit in
+a second where you can just Solve IT
+
+ align:start position:0%
+a second where you can just Solve IT
+ 
+
+ align:start position:0%
+a second where you can just Solve IT
+analytically right same way in in the
+
+ align:start position:0%
+analytically right same way in in the
+ 
+
+ align:start position:0%
+analytically right same way in in the
+optimal control derivations um there
+
+ align:start position:0%
+optimal control derivations um there
+ 
+
+ align:start position:0%
+optimal control derivations um there
+were some 's that we could just derive
+
+ align:start position:0%
+were some 's that we could just derive
+ 
+
+ align:start position:0%
+were some 's that we could just derive
+analytically and some that we had to do
+
+ align:start position:0%
+analytically and some that we had to do
+ 
+
+ align:start position:0%
+analytically and some that we had to do
+gradient descent
+
+ align:start position:0%
+gradient descent
+ 
+
+ align:start position:0%
+gradient descent
+for so let's dig in now and get more
+
+ align:start position:0%
+for so let's dig in now and get more
+ 
+
+ align:start position:0%
+for so let's dig in now and get more
+specific and say what kind
+
+ align:start position:0%
+specific and say what kind
+ 
+
+ align:start position:0%
+specific and say what kind
+of models do we want to use as
+
+ align:start position:0%
+of models do we want to use as
+ 
+
+ align:start position:0%
+of models do we want to use as
+candidates for these functions we're
+
+ align:start position:0%
+candidates for these functions we're
+ 
+
+ align:start position:0%
+candidates for these functions we're
+trying to fit right what how would we
+
+ align:start position:0%
+trying to fit right what how would we
+ 
+
+ align:start position:0%
+trying to fit right what how would we
+write down an F hat which depends on
+
+ align:start position:0%
+write down an F hat which depends on
+ 
+
+ align:start position:0%
+write down an F hat which depends on
+both Alpha and X okay the the literature
+
+ align:start position:0%
+both Alpha and X okay the the literature
+ 
+
+ align:start position:0%
+both Alpha and X okay the the literature
+is just filled with people's different
+
+ align:start position:0%
+is just filled with people's different
+ 
+
+ align:start position:0%
+is just filled with people's different
+models that they do this one of the most
+
+ align:start position:0%
+models that they do this one of the most
+ 
+
+ align:start position:0%
+models that they do this one of the most
+popular ones of let's say 20 years ago
+
+ align:start position:0%
+popular ones of let's say 20 years ago
+ 
+
+ align:start position:0%
+popular ones of let's say 20 years ago
+which actually are still popular today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um may we call them function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+classes one of them is neural networks
+
+ align:start position:0%
+classes one of them is neural networks
+ 
+
+ align:start position:0%
+classes one of them is neural networks
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a lot of people believe that a good
+
+ align:start position:0%
+so a lot of people believe that a good
+ 
+
+ align:start position:0%
+so a lot of people believe that a good
+way to write down an arbitrary
+
+ align:start position:0%
+way to write down an arbitrary
+ 
+
+ align:start position:0%
+way to write down an arbitrary
+function is to
+
+ align:start position:0%
+function is to
+ 
+
+ align:start position:0%
+function is to
+um take your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inputs and try to do something that sort
+
+ align:start position:0%
+inputs and try to do something that sort
+ 
+
+ align:start position:0%
+inputs and try to do something that sort
+of models a neuron it adds things up
+
+ align:start position:0%
+of models a neuron it adds things up
+ 
+
+ align:start position:0%
+of models a neuron it adds things up
+adds up the different inputs and then
+
+ align:start position:0%
+adds up the different inputs and then
+ 
+
+ align:start position:0%
+adds up the different inputs and then
+goes through um a sigmoidal function
+
+ align:start position:0%
+goes through um a sigmoidal function
+ 
+
+ align:start position:0%
+goes through um a sigmoidal function
+and gives you an output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+y maybe just because that's what the
+
+ align:start position:0%
+y maybe just because that's what the
+ 
+
+ align:start position:0%
+y maybe just because that's what the
+brain sort of does um maybe because
+
+ align:start position:0%
+brain sort of does um maybe because
+ 
+
+ align:start position:0%
+brain sort of does um maybe because
+there's a lot of success stories from it
+
+ align:start position:0%
+there's a lot of success stories from it
+ 
+
+ align:start position:0%
+there's a lot of success stories from it
+um but a lot of people do this right and
+
+ align:start position:0%
+um but a lot of people do this right and
+ 
+
+ align:start position:0%
+um but a lot of people do this right and
+moreover this is sort of the
+
+ align:start position:0%
+moreover this is sort of the
+ 
+
+ align:start position:0%
+moreover this is sort of the
+single
+
+ align:start position:0%
+single
+ 
+
+ align:start position:0%
+single
+layer
+
+ align:start position:0%
+layer
+ 
+
+ align:start position:0%
+layer
+um neural
+
+ align:start position:0%
+um neural
+ 
+
+ align:start position:0%
+um neural
+network
+
+ align:start position:0%
+network
+ 
+
+ align:start position:0%
+network
+if you have lots of different sort
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+functions and they potentially add up to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instance
+
+ align:start position:0%
+instance
+ 
+
+ align:start position:0%
+instance
+okay and the parameters now are the
+
+ align:start position:0%
+okay and the parameters now are the
+ 
+
+ align:start position:0%
+okay and the parameters now are the
+weights of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+connection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so your
+
+ align:start position:0%
+right so your
+ 
+
+ align:start position:0%
+right so your
+function might be some some squashing
+
+ align:start position:0%
+function might be some some squashing
+ 
+
+ align:start position:0%
+function might be some some squashing
+function this this nonlinear
+
+ align:start position:0%
+function this this nonlinear
+ 
+
+ align:start position:0%
+function this this nonlinear
+function times a weighted combin
+
+ align:start position:0%
+function times a weighted combin
+ 
+
+ align:start position:0%
+function times a weighted combin
+combination of the
+
+ align:start position:0%
+combination of the
+ 
+
+ align:start position:0%
+combination of the
+inputs potentially plus some baseline or
+
+ align:start position:0%
+inputs potentially plus some baseline or
+ 
+
+ align:start position:0%
+inputs potentially plus some baseline or
+something like
+
+ align:start position:0%
+something like
+ 
+
+ align:start position:0%
+something like
+this where this is a tan
+
+ align:start position:0%
+this where this is a tan
+ 
+
+ align:start position:0%
+this where this is a tan
+or some function like that that does a
+
+ align:start position:0%
+or some function like that that does a
+ 
+
+ align:start position:0%
+or some function like that that does a
+sigmoid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and if you do this then you can
+
+ align:start position:0%
+okay and if you do this then you can
+ 
+
+ align:start position:0%
+okay and if you do this then you can
+stack things up and make multiple layer
+
+ align:start position:0%
+stack things up and make multiple layer
+ 
+
+ align:start position:0%
+stack things up and make multiple layer
+neural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+networks and people believe and people
+
+ align:start position:0%
+networks and people believe and people
+ 
+
+ align:start position:0%
+networks and people believe and people
+certainly in the 80s very strongly
+
+ align:start position:0%
+certainly in the 80s very strongly
+ 
+
+ align:start position:0%
+certainly in the 80s very strongly
+believed that um that this is a
+
+ align:start position:0%
+believed that um that this is a
+ 
+
+ align:start position:0%
+believed that um that this is a
+representative class of functions that
+
+ align:start position:0%
+representative class of functions that
+ 
+
+ align:start position:0%
+representative class of functions that
+um that maybe looked a little bit like
+
+ align:start position:0%
+um that maybe looked a little bit like
+ 
+
+ align:start position:0%
+um that maybe looked a little bit like
+what was going on in the
+
+ align:start position:0%
+what was going on in the
+ 
+
+ align:start position:0%
+what was going on in the
+brain and people know that if I have um
+
+ align:start position:0%
+brain and people know that if I have um
+ 
+
+ align:start position:0%
+brain and people know that if I have um
+it's a general function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximator if I have enough of these
+
+ align:start position:0%
+approximator if I have enough of these
+ 
+
+ align:start position:0%
+approximator if I have enough of these
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+neurons and enough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+layers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I can represent any function
+
+ align:start position:0%
+then I can represent any function
+ 
+
+ align:start position:0%
+then I can represent any function
+arbitrarily
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finally so it's kind of a cool result
+
+ align:start position:0%
+finally so it's kind of a cool result
+ 
+
+ align:start position:0%
+finally so it's kind of a cool result
+say using this thing that looks like a
+
+ align:start position:0%
+say using this thing that looks like a
+ 
+
+ align:start position:0%
+say using this thing that looks like a
+the brain if I stack up these these
+
+ align:start position:0%
+the brain if I stack up these these
+ 
+
+ align:start position:0%
+the brain if I stack up these these
+elements then I can represent any
+
+ align:start position:0%
+elements then I can represent any
+ 
+
+ align:start position:0%
+elements then I can represent any
+function with enough
+
+ align:start position:0%
+function with enough
+ 
+
+ align:start position:0%
+function with enough
+neurons and if I want to solve a least
+
+ align:start position:0%
+neurons and if I want to solve a least
+ 
+
+ align:start position:0%
+neurons and if I want to solve a least
+squares optimization problem to make the
+
+ align:start position:0%
+squares optimization problem to make the
+ 
+
+ align:start position:0%
+squares optimization problem to make the
+input and output of this neural network
+
+ align:start position:0%
+input and output of this neural network
+ 
+
+ align:start position:0%
+input and output of this neural network
+work the same that I can just solve this
+
+ align:start position:0%
+work the same that I can just solve this
+ 
+
+ align:start position:0%
+work the same that I can just solve this
+optimization problem with with gradient
+
+ align:start position:0%
+optimization problem with with gradient
+ 
+
+ align:start position:0%
+optimization problem with with gradient
+descent and that's roughly what
+
+ align:start position:0%
+descent and that's roughly what
+ 
+
+ align:start position:0%
+descent and that's roughly what
+everybody did in the 80s I guess that's
+
+ align:start position:0%
+everybody did in the 80s I guess that's
+ 
+
+ align:start position:0%
+everybody did in the 80s I guess that's
+not quite fair but
+
+ align:start position:0%
+not quite fair but
+ 
+
+ align:start position:0%
+not quite fair but
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and it works actually that's you know
+
+ align:start position:0%
+and it works actually that's you know
+ 
+
+ align:start position:0%
+and it works actually that's you know
+people still use these today to to um do
+
+ align:start position:0%
+people still use these today to to um do
+ 
+
+ align:start position:0%
+people still use these today to to um do
+face recognizers right and they they use
+
+ align:start position:0%
+face recognizers right and they they use
+ 
+
+ align:start position:0%
+face recognizers right and they they use
+it to to
+
+ align:start position:0%
+it to to
+ 
+
+ align:start position:0%
+it to to
+um Yan laon down at NYU has got this uh
+
+ align:start position:0%
+um Yan laon down at NYU has got this uh
+ 
+
+ align:start position:0%
+um Yan laon down at NYU has got this uh
+this text recognizer that they use
+
+ align:start position:0%
+this text recognizer that they use
+ 
+
+ align:start position:0%
+this text recognizer that they use
+actually to scan to read checks at the
+
+ align:start position:0%
+actually to scan to read checks at the
+ 
+
+ align:start position:0%
+actually to scan to read checks at the
+bank right they that's still neural
+
+ align:start position:0%
+bank right they that's still neural
+ 
+
+ align:start position:0%
+bank right they that's still neural
+network based okay a lot of people got a
+
+ align:start position:0%
+network based okay a lot of people got a
+ 
+
+ align:start position:0%
+network based okay a lot of people got a
+lot of things to work with these neural
+
+ align:start position:0%
+lot of things to work with these neural
+ 
+
+ align:start position:0%
+lot of things to work with these neural
+networks Jerry Taro in the optimal
+
+ align:start position:0%
+networks Jerry Taro in the optimal
+ 
+
+ align:start position:0%
+networks Jerry Taro in the optimal
+control sense got the TD gam the the the
+
+ align:start position:0%
+control sense got the TD gam the the the
+ 
+
+ align:start position:0%
+control sense got the TD gam the the the
+reinforcement learning system that
+
+ align:start position:0%
+reinforcement learning system that
+ 
+
+ align:start position:0%
+reinforcement learning system that
+played gamon where the the board
+
+ align:start position:0%
+played gamon where the the board
+ 
+
+ align:start position:0%
+played gamon where the the board
+configurations were put in as inputs to
+
+ align:start position:0%
+configurations were put in as inputs to
+ 
+
+ align:start position:0%
+configurations were put in as inputs to
+the neural network and the output was
+
+ align:start position:0%
+the neural network and the output was
+ 
+
+ align:start position:0%
+the neural network and the output was
+what move you should take and he got
+
+ align:start position:0%
+what move you should take and he got
+ 
+
+ align:start position:0%
+what move you should take and he got
+that to work right and there's actually
+
+ align:start position:0%
+that to work right and there's actually
+ 
+
+ align:start position:0%
+that to work right and there's actually
+there was a value function that came out
+
+ align:start position:0%
+there was a value function that came out
+ 
+
+ align:start position:0%
+there was a value function that came out
+he would even explicitly estimate the
+
+ align:start position:0%
+he would even explicitly estimate the
+ 
+
+ align:start position:0%
+he would even explicitly estimate the
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+function but today this is sort of a
+
+ align:start position:0%
+function but today this is sort of a
+ 
+
+ align:start position:0%
+function but today this is sort of a
+straw man because I don't like neural
+
+ align:start position:0%
+straw man because I don't like neural
+ 
+
+ align:start position:0%
+straw man because I don't like neural
+networks they're um they're not a
+
+ align:start position:0%
+networks they're um they're not a
+ 
+
+ align:start position:0%
+networks they're um they're not a
+particularly nice uh lease squares thing
+
+ align:start position:0%
+particularly nice uh lease squares thing
+ 
+
+ align:start position:0%
+particularly nice uh lease squares thing
+to optimize um we can do better these
+
+ align:start position:0%
+to optimize um we can do better these
+ 
+
+ align:start position:0%
+to optimize um we can do better these
+days I just wanted to put it up there as
+
+ align:start position:0%
+days I just wanted to put it up there as
+ 
+
+ align:start position:0%
+days I just wanted to put it up there as
+a important element of the class but not
+
+ align:start position:0%
+a important element of the class but not
+ 
+
+ align:start position:0%
+a important element of the class but not
+one we'll tend to use
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay if you care about least squares
+
+ align:start position:0%
+okay if you care about least squares
+ 
+
+ align:start position:0%
+okay if you care about least squares
+function approximation there are a lot
+
+ align:start position:0%
+function approximation there are a lot
+ 
+
+ align:start position:0%
+function approximation there are a lot
+of other choices you can have for your
+
+ align:start position:0%
+of other choices you can have for your
+ 
+
+ align:start position:0%
+of other choices you can have for your
+function f which would which you can
+
+ align:start position:0%
+function f which would which you can
+ 
+
+ align:start position:0%
+function f which would which you can
+parameterize by Alpha which Maps X to y
+
+ align:start position:0%
+parameterize by Alpha which Maps X to y
+ 
+
+ align:start position:0%
+parameterize by Alpha which Maps X to y
+a lot of choices okay um the ones that
+
+ align:start position:0%
+a lot of choices okay um the ones that
+ 
+
+ align:start position:0%
+a lot of choices okay um the ones that
+people in reinforcement learning tend to
+
+ align:start position:0%
+people in reinforcement learning tend to
+ 
+
+ align:start position:0%
+people in reinforcement learning tend to
+use most effectively are the the linear
+
+ align:start position:0%
+use most effectively are the the linear
+ 
+
+ align:start position:0%
+use most effectively are the the linear
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximators okay um linear here
+
+ align:start position:0%
+approximators okay um linear here
+ 
+
+ align:start position:0%
+approximators okay um linear here
+meaning that they're linear in the
+
+ align:start position:0%
+meaning that they're linear in the
+ 
+
+ align:start position:0%
+meaning that they're linear in the
+parameters but not necessarily linear in
+
+ align:start position:0%
+parameters but not necessarily linear in
+ 
+
+ align:start position:0%
+parameters but not necessarily linear in
+the output so let me so um I want y i
+
+ align:start position:0%
+the output so let me so um I want y i
+ 
+
+ align:start position:0%
+the output so let me so um I want y i
+hat to
+
+ align:start position:0%
+hat to
+ 
+
+ align:start position:0%
+hat to
+be um some linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+combination of potentially nonlinear
+
+ align:start position:0%
+combination of potentially nonlinear
+ 
+
+ align:start position:0%
+combination of potentially nonlinear
+basis
+
+ align:start position:0%
+basis
+ 
+
+ align:start position:0%
+basis
+functions of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+XI
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the neural networks had the
+
+ align:start position:0%
+okay so the neural networks had the
+ 
+
+ align:start position:0%
+okay so the neural networks had the
+problem that um they were Rich because
+
+ align:start position:0%
+problem that um they were Rich because
+ 
+
+ align:start position:0%
+problem that um they were Rich because
+they have nonlinearities in them and if
+
+ align:start position:0%
+they have nonlinearities in them and if
+ 
+
+ align:start position:0%
+they have nonlinearities in them and if
+you stack Cascade nonlinearities you can
+
+ align:start position:0%
+you stack Cascade nonlinearities you can
+ 
+
+ align:start position:0%
+you stack Cascade nonlinearities you can
+get arbitrarily Rich things but the
+
+ align:start position:0%
+get arbitrarily Rich things but the
+ 
+
+ align:start position:0%
+get arbitrarily Rich things but the
+parameters that change the function are
+
+ align:start position:0%
+parameters that change the function are
+ 
+
+ align:start position:0%
+parameters that change the function are
+buried deep inside the nonlinearities
+
+ align:start position:0%
+buried deep inside the nonlinearities
+ 
+
+ align:start position:0%
+buried deep inside the nonlinearities
+okay it turns out if you come up with
+
+ align:start position:0%
+okay it turns out if you come up with
+ 
+
+ align:start position:0%
+okay it turns out if you come up with
+policy and function classes um that can
+
+ align:start position:0%
+policy and function classes um that can
+ 
+
+ align:start position:0%
+policy and function classes um that can
+represent your problem nicely where the
+
+ align:start position:0%
+represent your problem nicely where the
+ 
+
+ align:start position:0%
+represent your problem nicely where the
+the parameters are all at the output
+
+ align:start position:0%
+the parameters are all at the output
+ 
+
+ align:start position:0%
+the parameters are all at the output
+then life gets a lot better okay why
+
+ align:start position:0%
+then life gets a lot better okay why
+ 
+
+ align:start position:0%
+then life gets a lot better okay why
+does life get a lot better well because
+
+ align:start position:0%
+does life get a lot better well because
+ 
+
+ align:start position:0%
+does life get a lot better well because
+now I can take this um least squares
+
+ align:start position:0%
+now I can take this um least squares
+ 
+
+ align:start position:0%
+now I can take this um least squares
+metric and solve it explicitly for Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I can there's two things I can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+represent um arbitrary nonlinear
+
+ align:start position:0%
+represent um arbitrary nonlinear
+ 
+
+ align:start position:0%
+represent um arbitrary nonlinear
+functions if I have the right basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um also
+
+ align:start position:0%
+um also
+ 
+
+ align:start position:0%
+um also
+compute
+
+ align:start position:0%
+compute
+ 
+
+ align:start position:0%
+compute
+Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explicitly don't have to do gradient
+
+ align:start position:0%
+explicitly don't have to do gradient
+ 
+
+ align:start position:0%
+explicitly don't have to do gradient
+descent I can just find the
+
+ align:start position:0%
+descent I can just find the
+ 
+
+ align:start position:0%
+descent I can just find the
+optimum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just to see how that goes you can
+
+ align:start position:0%
+just to see how that goes you can
+ 
+
+ align:start position:0%
+just to see how that goes you can
+probably see it but it's so simple we'll
+
+ align:start position:0%
+probably see it but it's so simple we'll
+ 
+
+ align:start position:0%
+probably see it but it's so simple we'll
+write it out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here if I want to minimize that squared
+
+ align:start position:0%
+here if I want to minimize that squared
+ 
+
+ align:start position:0%
+here if I want to minimize that squared
+error if I
+
+ align:start position:0%
+error if I
+ 
+
+ align:start position:0%
+error if I
+minimize over
+
+ align:start position:0%
+minimize over
+ 
+
+ align:start position:0%
+minimize over
+Alpha um sum over
+
+ align:start position:0%
+Alpha um sum over
+ 
+
+ align:start position:0%
+Alpha um sum over
+I of
+
+ align:start position:0%
+I of
+ 
+
+ align:start position:0%
+I of
+Yi
+
+ align:start position:0%
+Yi
+ 
+
+ align:start position:0%
+Yi
+minus Alpha transpose I'll write the
+
+ align:start position:0%
+minus Alpha transpose I'll write the
+ 
+
+ align:start position:0%
+minus Alpha transpose I'll write the
+vector form of that
+
+ align:start position:0%
+vector form of that
+ 
+
+ align:start position:0%
+vector form of that
+V of x
+
+ align:start position:0%
+V of x
+ 
+
+ align:start position:0%
+V of x
+i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared I can write
+
+ align:start position:0%
+squared I can write
+ 
+
+ align:start position:0%
+squared I can write
+um I could write this even more Vector
+
+ align:start position:0%
+um I could write this even more Vector
+ 
+
+ align:start position:0%
+um I could write this even more Vector
+form if I choose Big Y to be y
+
+ align:start position:0%
+form if I choose Big Y to be y
+ 
+
+ align:start position:0%
+form if I choose Big Y to be y
+um if I if I put these things into a big
+
+ align:start position:0%
+um if I if I put these things into a big
+ 
+
+ align:start position:0%
+um if I if I put these things into a big
+vector and big
+
+ align:start position:0%
+vector and big
+ 
+
+ align:start position:0%
+vector and big
+Fe is uh in the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction then I can write this guy as
+
+ align:start position:0%
+direction then I can write this guy as
+ 
+
+ align:start position:0%
+direction then I can write this guy as
+men over
+
+ align:start position:0%
+men over
+ 
+
+ align:start position:0%
+men over
+Alpha
+
+ align:start position:0%
+Alpha
+ 
+
+ align:start position:0%
+Alpha
+Yus the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you take the gradient with respect to
+
+ align:start position:0%
+if you take the gradient with respect to
+ 
+
+ align:start position:0%
+if you take the gradient with respect to
+Alpha what do you get you get Negative V
+
+ align:start position:0%
+Alpha what do you get you get Negative V
+ 
+
+ align:start position:0%
+Alpha what do you get you get Negative V
+transpose Yus V Alpha equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero assuming that this thing is well
+
+ align:start position:0%
+zero assuming that this thing is well
+ 
+
+ align:start position:0%
+zero assuming that this thing is well
+behaved then you can just say Alpha
+
+ align:start position:0%
+behaved then you can just say Alpha
+ 
+
+ align:start position:0%
+behaved then you can just say Alpha
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very straightforward least squares um
+
+ align:start position:0%
+very straightforward least squares um
+ 
+
+ align:start position:0%
+very straightforward least squares um
+estimation with linear approximators but
+
+ align:start position:0%
+estimation with linear approximators but
+ 
+
+ align:start position:0%
+estimation with linear approximators but
+let me now convince you just how rich
+
+ align:start position:0%
+let me now convince you just how rich
+ 
+
+ align:start position:0%
+let me now convince you just how rich
+that class of functions is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay here's the game um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's some function that exists this
+
+ align:start position:0%
+there's some function that exists this
+ 
+
+ align:start position:0%
+there's some function that exists this
+is my actual F okay I don't know it my
+
+ align:start position:0%
+is my actual F okay I don't know it my
+ 
+
+ align:start position:0%
+is my actual F okay I don't know it my
+algorithm that I'm about to do doesn't
+
+ align:start position:0%
+algorithm that I'm about to do doesn't
+ 
+
+ align:start position:0%
+algorithm that I'm about to do doesn't
+know it but that's the original F I'm
+
+ align:start position:0%
+know it but that's the original F I'm
+ 
+
+ align:start position:0%
+know it but that's the original F I'm
+trying to estimate okay and let's say I
+
+ align:start position:0%
+trying to estimate okay and let's say I
+ 
+
+ align:start position:0%
+trying to estimate okay and let's say I
+don't get to experience F but I get to
+
+ align:start position:0%
+don't get to experience F but I get to
+ 
+
+ align:start position:0%
+don't get to experience F but I get to
+exper I get to sample from F and every
+
+ align:start position:0%
+exper I get to sample from F and every
+ 
+
+ align:start position:0%
+exper I get to sample from F and every
+time I sample from F I get some noise
+
+ align:start position:0%
+time I sample from F I get some noise
+ 
+
+ align:start position:0%
+time I sample from F I get some noise
+right then maybe my data my input output
+
+ align:start position:0%
+right then maybe my data my input output
+ 
+
+ align:start position:0%
+right then maybe my data my input output
+data might look something like this this
+
+ align:start position:0%
+data might look something like this this
+ 
+
+ align:start position:0%
+data might look something like this this
+is just um I took I took a bunch of
+
+ align:start position:0%
+is just um I took I took a bunch of
+ 
+
+ align:start position:0%
+is just um I took I took a bunch of
+random X's I evaluated what the that
+
+ align:start position:0%
+random X's I evaluated what the that
+ 
+
+ align:start position:0%
+random X's I evaluated what the that
+function was and I added a little bit of
+
+ align:start position:0%
+function was and I added a little bit of
+ 
+
+ align:start position:0%
+function was and I added a little bit of
+random noise to it okay now the question
+
+ align:start position:0%
+random noise to it okay now the question
+ 
+
+ align:start position:0%
+random noise to it okay now the question
+is if I just have those red data points
+
+ align:start position:0%
+is if I just have those red data points
+ 
+
+ align:start position:0%
+is if I just have those red data points
+as input output data can I come up with
+
+ align:start position:0%
+as input output data can I come up with
+ 
+
+ align:start position:0%
+as input output data can I come up with
+an
+
+ align:start position:0%
+an
+ 
+
+ align:start position:0%
+an
+estimate in f f hat which re reproduces
+
+ align:start position:0%
+estimate in f f hat which re reproduces
+ 
+
+ align:start position:0%
+estimate in f f hat which re reproduces
+the original half and that's not many
+
+ align:start position:0%
+the original half and that's not many
+ 
+
+ align:start position:0%
+the original half and that's not many
+data points right okay I could do it
+
+ align:start position:0%
+data points right okay I could do it
+ 
+
+ align:start position:0%
+data points right okay I could do it
+with a neural network but I'm just
+
+ align:start position:0%
+with a neural network but I'm just
+ 
+
+ align:start position:0%
+with a neural network but I'm just
+without telling you all the details it's
+
+ align:start position:0%
+without telling you all the details it's
+ 
+
+ align:start position:0%
+without telling you all the details it's
+just it's not quite as elegant we did it
+
+ align:start position:0%
+just it's not quite as elegant we did it
+ 
+
+ align:start position:0%
+just it's not quite as elegant we did it
+with reinforce it took a little bit of
+
+ align:start position:0%
+with reinforce it took a little bit of
+ 
+
+ align:start position:0%
+with reinforce it took a little bit of
+convergence um if we do it with a linear
+
+ align:start position:0%
+convergence um if we do it with a linear
+ 
+
+ align:start position:0%
+convergence um if we do it with a linear
+function approximator we can do it just
+
+ align:start position:0%
+function approximator we can do it just
+ 
+
+ align:start position:0%
+function approximator we can do it just
+in one shot just like
+
+ align:start position:0%
+in one shot just like
+ 
+
+ align:start position:0%
+in one shot just like
+that the first trick though is we have
+
+ align:start position:0%
+that the first trick though is we have
+ 
+
+ align:start position:0%
+that the first trick though is we have
+to pick our bases set fee okay you've
+
+ align:start position:0%
+to pick our bases set fee okay you've
+ 
+
+ align:start position:0%
+to pick our bases set fee okay you've
+got lots of choices with fee
+
+ align:start position:0%
+got lots of choices with fee
+ 
+
+ align:start position:0%
+got lots of choices with fee
+um some of the common ones let's see
+
+ align:start position:0%
+um some of the common ones let's see
+ 
+
+ align:start position:0%
+um some of the common ones let's see
+what I'll let me do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one common one is radial basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+functions okay where you assume f of x
+
+ align:start position:0%
+functions okay where you assume f of x
+ 
+
+ align:start position:0%
+functions okay where you assume f of x
+is just some gaussian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the I of X is just a gaussian function
+
+ align:start position:0%
+the I of X is just a gaussian function
+ 
+
+ align:start position:0%
+the I of X is just a gaussian function
+it doesn't really have to it doesn't the
+
+ align:start position:0%
+it doesn't really have to it doesn't the
+ 
+
+ align:start position:0%
+it doesn't really have to it doesn't the
+nor the normalization doesn't matter x -
+
+ align:start position:0%
+nor the normalization doesn't matter x -
+ 
+
+ align:start position:0%
+nor the normalization doesn't matter x -
+Mi
+
+ align:start position:0%
+Mi
+ 
+
+ align:start position:0%
+Mi
+I um squared to Sigma
+
+ align:start position:0%
+I um squared to Sigma
+ 
+
+ align:start position:0%
+I um squared to Sigma
+I where each it's just a collection of
+
+ align:start position:0%
+I where each it's just a collection of
+ 
+
+ align:start position:0%
+I where each it's just a collection of
+gaussians where the means are different
+
+ align:start position:0%
+gaussians where the means are different
+ 
+
+ align:start position:0%
+gaussians where the means are different
+for every basis function okay the V the
+
+ align:start position:0%
+for every basis function okay the V the
+ 
+
+ align:start position:0%
+for every basis function okay the V the
+variances could be different too it
+
+ align:start position:0%
+variances could be different too it
+ 
+
+ align:start position:0%
+variances could be different too it
+doesn't matter
+
+ align:start position:0%
+doesn't matter
+ 
+
+ align:start position:0%
+doesn't matter
+um so that might look like this if I
+
+ align:start position:0%
+um so that might look like this if I
+ 
+
+ align:start position:0%
+um so that might look like this if I
+made 10 different basis functions for
+
+ align:start position:0%
+made 10 different basis functions for
+ 
+
+ align:start position:0%
+made 10 different basis functions for
+this problem and I centered them at
+
+ align:start position:0%
+this problem and I centered them at
+ 
+
+ align:start position:0%
+this problem and I centered them at
+evenly across my the space that I
+
+ align:start position:0%
+evenly across my the space that I
+ 
+
+ align:start position:0%
+evenly across my the space that I
+sampled for then that would be look like
+
+ align:start position:0%
+sampled for then that would be look like
+ 
+
+ align:start position:0%
+sampled for then that would be look like
+a reasonable basis set for function
+
+ align:start position:0%
+a reasonable basis set for function
+ 
+
+ align:start position:0%
+a reasonable basis set for function
+approximation okay and then the question
+
+ align:start position:0%
+approximation okay and then the question
+ 
+
+ align:start position:0%
+approximation okay and then the question
+is can I take a linear combination of
+
+ align:start position:0%
+is can I take a linear combination of
+ 
+
+ align:start position:0%
+is can I take a linear combination of
+that 10 gaussians and turn it into a
+
+ align:start position:0%
+that 10 gaussians and turn it into a
+ 
+
+ align:start position:0%
+that 10 gaussians and turn it into a
+pretty good estimate of the original
+
+ align:start position:0%
+pretty good estimate of the original
+ 
+
+ align:start position:0%
+pretty good estimate of the original
+function just from looking at the red
+
+ align:start position:0%
+function just from looking at the red
+ 
+
+ align:start position:0%
+function just from looking at the red
+points okay if I plug this equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in then I can get a waiting on each of
+
+ align:start position:0%
+in then I can get a waiting on each of
+ 
+
+ align:start position:0%
+in then I can get a waiting on each of
+those individual fees Alpha I is the
+
+ align:start position:0%
+those individual fees Alpha I is the
+ 
+
+ align:start position:0%
+those individual fees Alpha I is the
+weight on
+
+ align:start position:0%
+weight on
+ 
+
+ align:start position:0%
+weight on
+fi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right I'll do that with another click
+
+ align:start position:0%
+right I'll do that with another click
+ 
+
+ align:start position:0%
+right I'll do that with another click
+here and it turns out it said in order
+
+ align:start position:0%
+here and it turns out it said in order
+ 
+
+ align:start position:0%
+here and it turns out it said in order
+to represent this function that one that
+
+ align:start position:0%
+to represent this function that one that
+ 
+
+ align:start position:0%
+to represent this function that one that
+was centered around zero had better have
+
+ align:start position:0%
+was centered around zero had better have
+ 
+
+ align:start position:0%
+was centered around zero had better have
+some negative value the one that was
+
+ align:start position:0%
+some negative value the one that was
+ 
+
+ align:start position:0%
+some negative value the one that was
+centered around one's got a pretty big
+
+ align:start position:0%
+centered around one's got a pretty big
+ 
+
+ align:start position:0%
+centered around one's got a pretty big
+positive value this one's got a pretty
+
+ align:start position:0%
+positive value this one's got a pretty
+ 
+
+ align:start position:0%
+positive value this one's got a pretty
+big positive value and so on so you can
+
+ align:start position:0%
+big positive value and so on so you can
+ 
+
+ align:start position:0%
+big positive value and so on so you can
+see that all the same gaussin are there
+
+ align:start position:0%
+see that all the same gaussin are there
+ 
+
+ align:start position:0%
+see that all the same gaussin are there
+they're just weighted by a different
+
+ align:start position:0%
+they're just weighted by a different
+ 
+
+ align:start position:0%
+they're just weighted by a different
+amount okay and if you sum all those up
+
+ align:start position:0%
+amount okay and if you sum all those up
+ 
+
+ align:start position:0%
+amount okay and if you sum all those up
+to estimate y then what do you
+
+ align:start position:0%
+to estimate y then what do you
+ 
+
+ align:start position:0%
+to estimate y then what do you
+get pretty good right it's pretty sparse
+
+ align:start position:0%
+get pretty good right it's pretty sparse
+ 
+
+ align:start position:0%
+get pretty good right it's pretty sparse
+set of data points pretty sparse set of
+
+ align:start position:0%
+set of data points pretty sparse set of
+ 
+
+ align:start position:0%
+set of data points pretty sparse set of
+basis functions get a really nice
+
+ align:start position:0%
+basis functions get a really nice
+ 
+
+ align:start position:0%
+basis functions get a really nice
+accurate in one shot no gradient to
+
+ align:start position:0%
+accurate in one shot no gradient to
+ 
+
+ align:start position:0%
+accurate in one shot no gradient to
+Senter or anything this is consistent
+
+ align:start position:0%
+Senter or anything this is consistent
+ 
+
+ align:start position:0%
+Senter or anything this is consistent
+with what John and I've been saying is
+
+ align:start position:0%
+with what John and I've been saying is
+ 
+
+ align:start position:0%
+with what John and I've been saying is
+don't do reinforce unless you have to
+
+ align:start position:0%
+don't do reinforce unless you have to
+ 
+
+ align:start position:0%
+don't do reinforce unless you have to
+because if you know the function and you
+
+ align:start position:0%
+because if you know the function and you
+ 
+
+ align:start position:0%
+because if you know the function and you
+can sample from the function you can
+
+ align:start position:0%
+can sample from the function you can
+ 
+
+ align:start position:0%
+can sample from the function you can
+just explicitly get
+
+ align:start position:0%
+just explicitly get
+ 
+
+ align:start position:0%
+just explicitly get
+it okay um the bicentric interpolators
+
+ align:start position:0%
+it okay um the bicentric interpolators
+ 
+
+ align:start position:0%
+it okay um the bicentric interpolators
+that we talked about
+
+ align:start position:0%
+that we talked about
+ 
+
+ align:start position:0%
+that we talked about
+before remember we interpolated between
+
+ align:start position:0%
+before remember we interpolated between
+ 
+
+ align:start position:0%
+before remember we interpolated between
+elements of the grid with the bicentric
+
+ align:start position:0%
+elements of the grid with the bicentric
+ 
+
+ align:start position:0%
+elements of the grid with the bicentric
+interpolators those are um linear
+
+ align:start position:0%
+interpolators those are um linear
+ 
+
+ align:start position:0%
+interpolators those are um linear
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximators right where it turns out
+
+ align:start position:0%
+approximators right where it turns out
+ 
+
+ align:start position:0%
+approximators right where it turns out
+the uh
+
+ align:start position:0%
+the uh
+ 
+
+ align:start position:0%
+the uh
+you can think of that as having linear
+
+ align:start position:0%
+you can think of that as having linear
+ 
+
+ align:start position:0%
+you can think of that as having linear
+um or nonlinear basis functions which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have something like
+
+ align:start position:0%
+have something like
+ 
+
+ align:start position:0%
+have something like
+this um the whole thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rectified essentially if I if I plot it
+
+ align:start position:0%
+rectified essentially if I if I plot it
+ 
+
+ align:start position:0%
+rectified essentially if I if I plot it
+in um in 2D
+
+ align:start position:0%
+in um in 2D
+ 
+
+ align:start position:0%
+in um in 2D
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then if I turn
+
+ align:start position:0%
+then if I turn
+ 
+
+ align:start position:0%
+then if I turn
+my radial basis functions off into my
+
+ align:start position:0%
+my radial basis functions off into my
+ 
+
+ align:start position:0%
+my radial basis functions off into my
+ber Centric interpolators and I run that
+
+ align:start position:0%
+ber Centric interpolators and I run that
+ 
+
+ align:start position:0%
+ber Centric interpolators and I run that
+same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+demo the bicentric interpolators are
+
+ align:start position:0%
+demo the bicentric interpolators are
+ 
+
+ align:start position:0%
+demo the bicentric interpolators are
+going to look like that okay if I want
+
+ align:start position:0%
+going to look like that okay if I want
+ 
+
+ align:start position:0%
+going to look like that okay if I want
+to linearly interpolate between all
+
+ align:start position:0%
+to linearly interpolate between all
+ 
+
+ align:start position:0%
+to linearly interpolate between all
+these neighboring points one way to view
+
+ align:start position:0%
+these neighboring points one way to view
+ 
+
+ align:start position:0%
+these neighboring points one way to view
+it is I as I take my my distance between
+
+ align:start position:0%
+it is I as I take my my distance between
+ 
+
+ align:start position:0%
+it is I as I take my my distance between
+the points I interpolate another way to
+
+ align:start position:0%
+the points I interpolate another way to
+ 
+
+ align:start position:0%
+the points I interpolate another way to
+view that is actually those are basis
+
+ align:start position:0%
+view that is actually those are basis
+ 
+
+ align:start position:0%
+view that is actually those are basis
+functions that look like
+
+ align:start position:0%
+functions that look like
+ 
+
+ align:start position:0%
+functions that look like
+T and the same thing's true in 2D
+
+ align:start position:0%
+T and the same thing's true in 2D
+ 
+
+ align:start position:0%
+T and the same thing's true in 2D
+they're they're 2d1
+
+ align:start position:0%
+they're they're 2d1
+ 
+
+ align:start position:0%
+they're they're 2d1
+okay it's the opposite way to think
+
+ align:start position:0%
+okay it's the opposite way to think
+ 
+
+ align:start position:0%
+okay it's the opposite way to think
+about it but those bar Centric
+
+ align:start position:0%
+about it but those bar Centric
+ 
+
+ align:start position:0%
+about it but those bar Centric
+interpolators we've been using the whole
+
+ align:start position:0%
+interpolators we've been using the whole
+ 
+
+ align:start position:0%
+interpolators we've been using the whole
+time are exactly um linear basis
+
+ align:start position:0%
+time are exactly um linear basis
+ 
+
+ align:start position:0%
+time are exactly um linear basis
+functions and again I can sum these guys
+
+ align:start position:0%
+functions and again I can sum these guys
+ 
+
+ align:start position:0%
+functions and again I can sum these guys
+up and I can make an approximation of
+
+ align:start position:0%
+up and I can make an approximation of
+ 
+
+ align:start position:0%
+up and I can make an approximation of
+the um the original nonlinear function
+
+ align:start position:0%
+the um the original nonlinear function
+ 
+
+ align:start position:0%
+the um the original nonlinear function
+this will of course it's got to be
+
+ align:start position:0%
+this will of course it's got to be
+ 
+
+ align:start position:0%
+this will of course it's got to be
+piecewise linear but it's okay it did a
+
+ align:start position:0%
+piecewise linear but it's okay it did a
+ 
+
+ align:start position:0%
+piecewise linear but it's okay it did a
+pretty good job considering it's
+
+ align:start position:0%
+pretty good job considering it's
+ 
+
+ align:start position:0%
+pretty good job considering it's
+piecewise linear and it's not a
+
+ align:start position:0%
+piecewise linear and it's not a
+ 
+
+ align:start position:0%
+piecewise linear and it's not a
+piecewise linear thing it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+estimating okay you could do
+
+ align:start position:0%
+estimating okay you could do
+ 
+
+ align:start position:0%
+estimating okay you could do
+um you could do basis functions um based
+
+ align:start position:0%
+um you could do basis functions um based
+ 
+
+ align:start position:0%
+um you could do basis functions um based
+on fora decompositions for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you could do
+
+ align:start position:0%
+you could do
+ 
+
+ align:start position:0%
+you could do
+polom basis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+functions right where the I of
+
+ align:start position:0%
+functions right where the I of
+ 
+
+ align:start position:0%
+functions right where the I of
+X is uh x to the i- one let's say
+
+ align:start position:0%
+X is uh x to the i- one let's say
+ 
+
+ align:start position:0%
+X is uh x to the i- one let's say
+something like that all these things
+
+ align:start position:0%
+something like that all these things
+ 
+
+ align:start position:0%
+something like that all these things
+work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do the 4A one
+
+ align:start position:0%
+do the 4A one
+ 
+
+ align:start position:0%
+do the 4A one
+here same function noisy data there's a
+
+ align:start position:0%
+here same function noisy data there's a
+ 
+
+ align:start position:0%
+here same function noisy data there's a
+forier basis over you know spatial
+
+ align:start position:0%
+forier basis over you know spatial
+ 
+
+ align:start position:0%
+forier basis over you know spatial
+forier um basis I can add those up I get
+
+ align:start position:0%
+forier um basis I can add those up I get
+ 
+
+ align:start position:0%
+forier um basis I can add those up I get
+very large coefficients these are you
+
+ align:start position:0%
+very large coefficients these are you
+ 
+
+ align:start position:0%
+very large coefficients these are you
+know these tend to cancel themselves out
+
+ align:start position:0%
+know these tend to cancel themselves out
+ 
+
+ align:start position:0%
+know these tend to cancel themselves out
+a lot but still I get a pretty nice
+
+ align:start position:0%
+a lot but still I get a pretty nice
+ 
+
+ align:start position:0%
+a lot but still I get a pretty nice
+representation okay so this idea of
+
+ align:start position:0%
+representation okay so this idea of
+ 
+
+ align:start position:0%
+representation okay so this idea of
+using linear function
+
+ align:start position:0%
+using linear function
+ 
+
+ align:start position:0%
+using linear function
+approximators
+
+ align:start position:0%
+approximators
+ 
+
+ align:start position:0%
+approximators
+and um and then linear least Square
+
+ align:start position:0%
+and um and then linear least Square
+ 
+
+ align:start position:0%
+and um and then linear least Square
+exact least Square solution is a very
+
+ align:start position:0%
+exact least Square solution is a very
+ 
+
+ align:start position:0%
+exact least Square solution is a very
+powerful idea you can represent very
+
+ align:start position:0%
+powerful idea you can represent very
+ 
+
+ align:start position:0%
+powerful idea you can represent very
+complicated functions potentially with
+
+ align:start position:0%
+complicated functions potentially with
+ 
+
+ align:start position:0%
+complicated functions potentially with
+this this was not the way people tended
+
+ align:start position:0%
+this this was not the way people tended
+ 
+
+ align:start position:0%
+this this was not the way people tended
+to do things 15 20 years ago it really
+
+ align:start position:0%
+to do things 15 20 years ago it really
+ 
+
+ align:start position:0%
+to do things 15 20 years ago it really
+tends to be the way things do people do
+
+ align:start position:0%
+tends to be the way things do people do
+ 
+
+ align:start position:0%
+tends to be the way things do people do
+things now in fact um so machine
+
+ align:start position:0%
+things now in fact um so machine
+ 
+
+ align:start position:0%
+things now in fact um so machine
+learning sort of got in this kick in
+
+ align:start position:0%
+learning sort of got in this kick in
+ 
+
+ align:start position:0%
+learning sort of got in this kick in
+statistical learning theory people talk
+
+ align:start position:0%
+statistical learning theory people talk
+ 
+
+ align:start position:0%
+statistical learning theory people talk
+about kernel methods and you might you
+
+ align:start position:0%
+about kernel methods and you might you
+ 
+
+ align:start position:0%
+about kernel methods and you might you
+might have know these I mean essential
+
+ align:start position:0%
+might have know these I mean essential
+ 
+
+ align:start position:0%
+might have know these I mean essential
+idea is is so um there's two problems I
+
+ align:start position:0%
+idea is is so um there's two problems I
+ 
+
+ align:start position:0%
+idea is is so um there's two problems I
+didn't I didn't say it but
+
+ align:start position:0%
+didn't I didn't say it but
+ 
+
+ align:start position:0%
+didn't I didn't say it but
+um sometimes people uh are trying to
+
+ align:start position:0%
+um sometimes people uh are trying to
+ 
+
+ align:start position:0%
+um sometimes people uh are trying to
+estimate uh scalar continuous valued
+
+ align:start position:0%
+estimate uh scalar continuous valued
+ 
+
+ align:start position:0%
+estimate uh scalar continuous valued
+outputs sometimes people are trying to
+
+ align:start position:0%
+outputs sometimes people are trying to
+ 
+
+ align:start position:0%
+outputs sometimes people are trying to
+do Boolean outputs they would call that
+
+ align:start position:0%
+do Boolean outputs they would call that
+ 
+
+ align:start position:0%
+do Boolean outputs they would call that
+a classification problem there's
+
+ align:start position:0%
+a classification problem there's
+ 
+
+ align:start position:0%
+a classification problem there's
+different forms of this problem but in
+
+ align:start position:0%
+different forms of this problem but in
+ 
+
+ align:start position:0%
+different forms of this problem but in
+in machine learning people realize that
+
+ align:start position:0%
+in machine learning people realize that
+ 
+
+ align:start position:0%
+in machine learning people realize that
+um you can often take a fairly
+
+ align:start position:0%
+um you can often take a fairly
+ 
+
+ align:start position:0%
+um you can often take a fairly
+low-dimensional problem blow it up into
+
+ align:start position:0%
+low-dimensional problem blow it up into
+ 
+
+ align:start position:0%
+low-dimensional problem blow it up into
+a very high dimensional space right
+
+ align:start position:0%
+a very high dimensional space right
+ 
+
+ align:start position:0%
+a very high dimensional space right
+using lots of basis functions for
+
+ align:start position:0%
+using lots of basis functions for
+ 
+
+ align:start position:0%
+using lots of basis functions for
+instance lots of Kernel functions okay
+
+ align:start position:0%
+instance lots of Kernel functions okay
+ 
+
+ align:start position:0%
+instance lots of Kernel functions okay
+and then do linearly
+
+ align:start position:0%
+and then do linearly
+ 
+
+ align:start position:0%
+and then do linearly
+squares in the high dimensional space
+
+ align:start position:0%
+squares in the high dimensional space
+ 
+
+ align:start position:0%
+squares in the high dimensional space
+and that works a lot better than doing
+
+ align:start position:0%
+and that works a lot better than doing
+ 
+
+ align:start position:0%
+and that works a lot better than doing
+some sort of nonlinear gradient descent
+
+ align:start position:0%
+some sort of nonlinear gradient descent
+ 
+
+ align:start position:0%
+some sort of nonlinear gradient descent
+based estimation in the low dimensional
+
+ align:start position:0%
+based estimation in the low dimensional
+ 
+
+ align:start position:0%
+based estimation in the low dimensional
+space okay so that's really a trend that
+
+ align:start position:0%
+space okay so that's really a trend that
+ 
+
+ align:start position:0%
+space okay so that's really a trend that
+happened in in machine learning and
+
+ align:start position:0%
+happened in in machine learning and
+ 
+
+ align:start position:0%
+happened in in machine learning and
+reinforcement learning it's it's the
+
+ align:start position:0%
+reinforcement learning it's it's the
+ 
+
+ align:start position:0%
+reinforcement learning it's it's the
+norm because essentially when we have
+
+ align:start position:0%
+norm because essentially when we have
+ 
+
+ align:start position:0%
+norm because essentially when we have
+linear function approximators we have
+
+ align:start position:0%
+linear function approximators we have
+ 
+
+ align:start position:0%
+linear function approximators we have
+some proofs that our optimal control
+
+ align:start position:0%
+some proofs that our optimal control
+ 
+
+ align:start position:0%
+some proofs that our optimal control
+algorithms are going to converge when we
+
+ align:start position:0%
+algorithms are going to converge when we
+ 
+
+ align:start position:0%
+algorithms are going to converge when we
+don't we have almost nothing in fact we
+
+ align:start position:0%
+don't we have almost nothing in fact we
+ 
+
+ align:start position:0%
+don't we have almost nothing in fact we
+have in the more nonlinear function
+
+ align:start position:0%
+have in the more nonlinear function
+ 
+
+ align:start position:0%
+have in the more nonlinear function
+approximator case uh we have lots of
+
+ align:start position:0%
+approximator case uh we have lots of
+ 
+
+ align:start position:0%
+approximator case uh we have lots of
+examples where things like TD TD on a
+
+ align:start position:0%
+examples where things like TD TD on a
+ 
+
+ align:start position:0%
+examples where things like TD TD on a
+function approximator just don't
+
+ align:start position:0%
+function approximator just don't
+ 
+
+ align:start position:0%
+function approximator just don't
+converge there's simple examples where
+
+ align:start position:0%
+converge there's simple examples where
+ 
+
+ align:start position:0%
+converge there's simple examples where
+they do exactly the wrong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing good so um just to convince you of
+
+ align:start position:0%
+thing good so um just to convince you of
+ 
+
+ align:start position:0%
+thing good so um just to convince you of
+one more basis function that is is more
+
+ align:start position:0%
+one more basis function that is is more
+ 
+
+ align:start position:0%
+one more basis function that is is more
+relevant to this class that was just the
+
+ align:start position:0%
+relevant to this class that was just the
+ 
+
+ align:start position:0%
+relevant to this class that was just the
+crash course for people who haven't seen
+
+ align:start position:0%
+crash course for people who haven't seen
+ 
+
+ align:start position:0%
+crash course for people who haven't seen
+um function
+
+ align:start position:0%
+um function
+ 
+
+ align:start position:0%
+um function
+approximators let me give you another
+
+ align:start position:0%
+approximators let me give you another
+ 
+
+ align:start position:0%
+approximators let me give you another
+example from system
+
+ align:start position:0%
+example from system
+ 
+
+ align:start position:0%
+example from system
+identification
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nonlinear system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identification as a linear or as a least
+
+ align:start position:0%
+identification as a linear or as a least
+ 
+
+ align:start position:0%
+identification as a linear or as a least
+squares um problem with linear function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximation so let's say we've got
+
+ align:start position:0%
+approximation so let's say we've got
+ 
+
+ align:start position:0%
+approximation so let's say we've got
+our equations of motion which come from
+
+ align:start position:0%
+our equations of motion which come from
+ 
+
+ align:start position:0%
+our equations of motion which come from
+this it's been a little while since I
+
+ align:start position:0%
+this it's been a little while since I
+ 
+
+ align:start position:0%
+this it's been a little while since I
+wrote These equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+jeez let's say it's for the pendulum or
+
+ align:start position:0%
+jeez let's say it's for the pendulum or
+ 
+
+ align:start position:0%
+jeez let's say it's for the pendulum or
+for the acrobot you name it um and let's
+
+ align:start position:0%
+for the acrobot you name it um and let's
+ 
+
+ align:start position:0%
+for the acrobot you name it um and let's
+say we know the form of the equation but
+
+ align:start position:0%
+say we know the form of the equation but
+ 
+
+ align:start position:0%
+say we know the form of the equation but
+we don't know the parameters we don't
+
+ align:start position:0%
+we don't know the parameters we don't
+ 
+
+ align:start position:0%
+we don't know the parameters we don't
+know how much the masses are how long
+
+ align:start position:0%
+know how much the masses are how long
+ 
+
+ align:start position:0%
+know how much the masses are how long
+the link lengths are normally you can
+
+ align:start position:0%
+the link lengths are normally you can
+ 
+
+ align:start position:0%
+the link lengths are normally you can
+measure those but inertias things like
+
+ align:start position:0%
+measure those but inertias things like
+ 
+
+ align:start position:0%
+measure those but inertias things like
+that these can be harder to get
+
+ align:start position:0%
+that these can be harder to get
+ 
+
+ align:start position:0%
+that these can be harder to get
+right so we could for instance run a
+
+ align:start position:0%
+right so we could for instance run a
+ 
+
+ align:start position:0%
+right so we could for instance run a
+bunch of
+
+ align:start position:0%
+bunch of
+ 
+
+ align:start position:0%
+bunch of
+trials with some dumb open loop
+
+ align:start position:0%
+trials with some dumb open loop
+ 
+
+ align:start position:0%
+trials with some dumb open loop
+controller just pick you randomly let's
+
+ align:start position:0%
+controller just pick you randomly let's
+ 
+
+ align:start position:0%
+controller just pick you randomly let's
+say and and make the acrobot flail
+
+ align:start position:0%
+say and and make the acrobot flail
+ 
+
+ align:start position:0%
+say and and make the acrobot flail
+around a little
+
+ align:start position:0%
+around a little
+ 
+
+ align:start position:0%
+around a little
+bit and collect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data that looked like this right Q um Q
+
+ align:start position:0%
+data that looked like this right Q um Q
+ 
+
+ align:start position:0%
+data that looked like this right Q um Q
+dot even Q double dot and
+
+ align:start position:0%
+dot even Q double dot and
+ 
+
+ align:start position:0%
+dot even Q double dot and
+U at every instant in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time and this is going to be exactly
+
+ align:start position:0%
+time and this is going to be exactly
+ 
+
+ align:start position:0%
+time and this is going to be exactly
+like our input output
+
+ align:start position:0%
+like our input output
+ 
+
+ align:start position:0%
+like our input output
+data in our least squares formulation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and here's the very amazing
+
+ align:start position:0%
+okay and here's the very amazing
+ 
+
+ align:start position:0%
+okay and here's the very amazing
+observation this one really really
+
+ align:start position:0%
+observation this one really really
+ 
+
+ align:start position:0%
+observation this one really really
+surprised me when I first got it the
+
+ align:start position:0%
+surprised me when I first got it the
+ 
+
+ align:start position:0%
+surprised me when I first got it the
+manipulator equations for random robot
+
+ align:start position:0%
+manipulator equations for random robot
+ 
+
+ align:start position:0%
+manipulator equations for random robot
+arms okay they're actually linear in
+
+ align:start position:0%
+arms okay they're actually linear in
+ 
+
+ align:start position:0%
+arms okay they're actually linear in
+their parameters very nonlinear
+
+ align:start position:0%
+their parameters very nonlinear
+ 
+
+ align:start position:0%
+their parameters very nonlinear
+functions they do very complicated
+
+ align:start position:0%
+functions they do very complicated
+ 
+
+ align:start position:0%
+functions they do very complicated
+Dynamics but they tend to be for most
+
+ align:start position:0%
+Dynamics but they tend to be for most
+ 
+
+ align:start position:0%
+Dynamics but they tend to be for most
+sort of robot manipulators yeah uh
+
+ align:start position:0%
+sort of robot manipulators yeah uh
+ 
+
+ align:start position:0%
+sort of robot manipulators yeah uh
+robotic arms on the factory floor
+
+ align:start position:0%
+robotic arms on the factory floor
+ 
+
+ align:start position:0%
+robotic arms on the factory floor
+walking robots things like that um those
+
+ align:start position:0%
+walking robots things like that um those
+ 
+
+ align:start position:0%
+walking robots things like that um those
+equations actually turn out to be linear
+
+ align:start position:0%
+equations actually turn out to be linear
+ 
+
+ align:start position:0%
+equations actually turn out to be linear
+in the parameters they're not linear in
+
+ align:start position:0%
+in the parameters they're not linear in
+ 
+
+ align:start position:0%
+in the parameters they're not linear in
+but they're linear in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parameters
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right take the simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pendulum
+
+ align:start position:0%
+pendulum
+ 
+
+ align:start position:0%
+pendulum
+I can rewrite this
+
+ align:start position:0%
+I can rewrite this
+ 
+
+ align:start position:0%
+I can rewrite this
+Dynamics as Alpha
+
+ align:start position:0%
+Dynamics as Alpha
+ 
+
+ align:start position:0%
+Dynamics as Alpha
+transpose
+
+ align:start position:0%
+transpose
+ 
+
+ align:start position:0%
+transpose
+time Theta double dot Theta dot s of
+
+ align:start position:0%
+time Theta double dot Theta dot s of
+ 
+
+ align:start position:0%
+time Theta double dot Theta dot s of
+theta equals
+
+ align:start position:0%
+theta equals
+ 
+
+ align:start position:0%
+theta equals
+U where Alpha
+
+ align:start position:0%
+U where Alpha
+ 
+
+ align:start position:0%
+U where Alpha
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+i b and mgl
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now you after you think about it a
+
+ align:start position:0%
+okay now you after you think about it a
+ 
+
+ align:start position:0%
+okay now you after you think about it a
+little bit it turns out to be not all
+
+ align:start position:0%
+little bit it turns out to be not all
+ 
+
+ align:start position:0%
+little bit it turns out to be not all
+that surprising in all our robot
+
+ align:start position:0%
+that surprising in all our robot
+ 
+
+ align:start position:0%
+that surprising in all our robot
+manipulators you see s thetas everywhere
+
+ align:start position:0%
+manipulators you see s thetas everywhere
+ 
+
+ align:start position:0%
+manipulators you see s thetas everywhere
+you see um sin squar thetas you see sin
+
+ align:start position:0%
+you see um sin squar thetas you see sin
+ 
+
+ align:start position:0%
+you see um sin squar thetas you see sin
+cosin you see all these things you never
+
+ align:start position:0%
+cosin you see all these things you never
+ 
+
+ align:start position:0%
+cosin you see all these things you never
+see s l Theta or something like
+
+ align:start position:0%
+see s l Theta or something like
+ 
+
+ align:start position:0%
+see s l Theta or something like
+that okay it turns out in these problems
+
+ align:start position:0%
+that okay it turns out in these problems
+ 
+
+ align:start position:0%
+that okay it turns out in these problems
+that the parameters don't end up inside
+
+ align:start position:0%
+that the parameters don't end up inside
+ 
+
+ align:start position:0%
+that the parameters don't end up inside
+your nonlinearities
+
+ align:start position:0%
+your nonlinearities
+ 
+
+ align:start position:0%
+your nonlinearities
+yeah isn't it still not linear because
+
+ align:start position:0%
+yeah isn't it still not linear because
+ 
+
+ align:start position:0%
+yeah isn't it still not linear because
+the parameters are multip together okay
+
+ align:start position:0%
+the parameters are multip together okay
+ 
+
+ align:start position:0%
+the parameters are multip together okay
+good so so it's it's not linear in every
+
+ align:start position:0%
+good so so it's it's not linear in every
+ 
+
+ align:start position:0%
+good so so it's it's not linear in every
+individual uh parameter but I can get um
+
+ align:start position:0%
+individual uh parameter but I can get um
+ 
+
+ align:start position:0%
+individual uh parameter but I can get um
+I can reestimate this as a linear
+
+ align:start position:0%
+I can reestimate this as a linear
+ 
+
+ align:start position:0%
+I can reestimate this as a linear
+optimization so so that's exactly right
+
+ align:start position:0%
+optimization so so that's exactly right
+ 
+
+ align:start position:0%
+optimization so so that's exactly right
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so sometimes you have to setle settle
+
+ align:start position:0%
+so sometimes you have to setle settle
+ 
+
+ align:start position:0%
+so sometimes you have to setle settle
+for um groups of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+parameters but those groups of
+
+ align:start position:0%
+parameters but those groups of
+ 
+
+ align:start position:0%
+parameters but those groups of
+parameters are always enough to rewrite
+
+ align:start position:0%
+parameters are always enough to rewrite
+ 
+
+ align:start position:0%
+parameters are always enough to rewrite
+your initial
+
+ align:start position:0%
+your initial
+ 
+
+ align:start position:0%
+your initial
+Dynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so that actually makes it
+
+ align:start position:0%
+okay okay so that actually makes it
+ 
+
+ align:start position:0%
+okay okay so that actually makes it
+sound like sis IDE is easy for if we
+
+ align:start position:0%
+sound like sis IDE is easy for if we
+ 
+
+ align:start position:0%
+sound like sis IDE is easy for if we
+have a complicated robot yeah says
+
+ align:start position:0%
+have a complicated robot yeah says
+ 
+
+ align:start position:0%
+have a complicated robot yeah says
+Michael who's been doing it for the last
+
+ align:start position:0%
+Michael who's been doing it for the last
+ 
+
+ align:start position:0%
+Michael who's been doing it for the last
+three months six months maybe I don't
+
+ align:start position:0%
+three months six months maybe I don't
+ 
+
+ align:start position:0%
+three months six months maybe I don't
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+uh he just shot daggers at me there
+
+ align:start position:0%
+uh he just shot daggers at me there
+ 
+
+ align:start position:0%
+uh he just shot daggers at me there
+um yeah so CIS ID should be easy for for
+
+ align:start position:0%
+um yeah so CIS ID should be easy for for
+ 
+
+ align:start position:0%
+um yeah so CIS ID should be easy for for
+uh robots that are well behaved it turns
+
+ align:start position:0%
+uh robots that are well behaved it turns
+ 
+
+ align:start position:0%
+uh robots that are well behaved it turns
+out if you have saturations in your
+
+ align:start position:0%
+out if you have saturations in your
+ 
+
+ align:start position:0%
+out if you have saturations in your
+motor and stuff like that it gets more
+
+ align:start position:0%
+motor and stuff like that it gets more
+ 
+
+ align:start position:0%
+motor and stuff like that it gets more
+complicated Michael could tell you all
+
+ align:start position:0%
+complicated Michael could tell you all
+ 
+
+ align:start position:0%
+complicated Michael could tell you all
+about it um but if I have a simulation
+
+ align:start position:0%
+about it um but if I have a simulation
+ 
+
+ align:start position:0%
+about it um but if I have a simulation
+of a pendulum let's say uh then it
+
+ align:start position:0%
+of a pendulum let's say uh then it
+ 
+
+ align:start position:0%
+of a pendulum let's say uh then it
+should be trivial and it is Trivial so
+
+ align:start position:0%
+should be trivial and it is Trivial so
+ 
+
+ align:start position:0%
+should be trivial and it is Trivial so
+let me just uh show you that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it turns out it's exactly the same
+
+ align:start position:0%
+it turns out it's exactly the same
+ 
+
+ align:start position:0%
+it turns out it's exactly the same
+linear function approximation this is my
+
+ align:start position:0%
+linear function approximation this is my
+ 
+
+ align:start position:0%
+linear function approximation this is my
+basis functions right these are my fees
+
+ align:start position:0%
+basis functions right these are my fees
+ 
+
+ align:start position:0%
+basis functions right these are my fees
+I've got three basis functions one is
+
+ align:start position:0%
+I've got three basis functions one is
+ 
+
+ align:start position:0%
+I've got three basis functions one is
+Theta double dot one is Theta dot one is
+
+ align:start position:0%
+Theta double dot one is Theta dot one is
+ 
+
+ align:start position:0%
+Theta double dot one is Theta dot one is
+sin Theta these are my coefficients
+
+ align:start position:0%
+sin Theta these are my coefficients
+ 
+
+ align:start position:0%
+sin Theta these are my coefficients
+Alpha and how how am I going to do it
+
+ align:start position:0%
+Alpha and how how am I going to do it
+ 
+
+ align:start position:0%
+Alpha and how how am I going to do it
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+um uh where is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+this ID
+
+ align:start position:0%
+this ID
+ 
+
+ align:start position:0%
+this ID
+yeah just a few lines there of mat lab
+
+ align:start position:0%
+yeah just a few lines there of mat lab
+ 
+
+ align:start position:0%
+yeah just a few lines there of mat lab
+code and that's includes running the
+
+ align:start position:0%
+code and that's includes running the
+ 
+
+ align:start position:0%
+code and that's includes running the
+tests
+
+ align:start position:0%
+tests
+ 
+
+ align:start position:0%
+tests
+okay so most of this is just setting up
+
+ align:start position:0%
+okay so most of this is just setting up
+ 
+
+ align:start position:0%
+okay so most of this is just setting up
+my uh my simulator I'm going to
+
+ align:start position:0%
+my uh my simulator I'm going to
+ 
+
+ align:start position:0%
+my uh my simulator I'm going to
+pick um some small random
+
+ align:start position:0%
+pick um some small random
+ 
+
+ align:start position:0%
+pick um some small random
+actions
+
+ align:start position:0%
+actions
+ 
+
+ align:start position:0%
+actions
+um a random tape of torqux to play out
+
+ align:start position:0%
+um a random tape of torqux to play out
+ 
+
+ align:start position:0%
+um a random tape of torqux to play out
+I'm going to pick some random initial
+
+ align:start position:0%
+I'm going to pick some random initial
+ 
+
+ align:start position:0%
+I'm going to pick some random initial
+condition I'm going to run my um control
+
+ align:start position:0%
+condition I'm going to run my um control
+ 
+
+ align:start position:0%
+condition I'm going to run my um control
+system with just uh making that that
+
+ align:start position:0%
+system with just uh making that that
+ 
+
+ align:start position:0%
+system with just uh making that that
+tape um a zero order hold on that
+
+ align:start position:0%
+tape um a zero order hold on that
+ 
+
+ align:start position:0%
+tape um a zero order hold on that
+tape okay and I'm going to collect the
+
+ align:start position:0%
+tape okay and I'm going to collect the
+ 
+
+ align:start position:0%
+tape okay and I'm going to collect the
+time x torque and x dot that came out of
+
+ align:start position:0%
+time x torque and x dot that came out of
+ 
+
+ align:start position:0%
+time x torque and x dot that came out of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+simulation and do exactly the math I
+
+ align:start position:0%
+simulation and do exactly the math I
+ 
+
+ align:start position:0%
+simulation and do exactly the math I
+showed you over here where Alpha is i b
+
+ align:start position:0%
+showed you over here where Alpha is i b
+ 
+
+ align:start position:0%
+showed you over here where Alpha is i b
+mgl in here in this case it's the
+
+ align:start position:0%
+mgl in here in this case it's the
+ 
+
+ align:start position:0%
+mgl in here in this case it's the
+location of the center of mass and do
+
+ align:start position:0%
+location of the center of mass and do
+ 
+
+ align:start position:0%
+location of the center of mass and do
+my optimization like that and Watch What
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Happens uh what's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+called okay so I start from random
+
+ align:start position:0%
+called okay so I start from random
+ 
+
+ align:start position:0%
+called okay so I start from random
+initial conditions I small play a small
+
+ align:start position:0%
+initial conditions I small play a small
+ 
+
+ align:start position:0%
+initial conditions I small play a small
+random tape for 10 seconds out okay the
+
+ align:start position:0%
+random tape for 10 seconds out okay the
+ 
+
+ align:start position:0%
+random tape for 10 seconds out okay the
+actual parameters that I um started with
+
+ align:start position:0%
+actual parameters that I um started with
+ 
+
+ align:start position:0%
+actual parameters that I um started with
+were this the ones that are estimated
+
+ align:start position:0%
+were this the ones that are estimated
+ 
+
+ align:start position:0%
+were this the ones that are estimated
+after 10 seconds of running my
+
+ align:start position:0%
+after 10 seconds of running my
+ 
+
+ align:start position:0%
+after 10 seconds of running my
+simulation and doing least squares are
+
+ align:start position:0%
+simulation and doing least squares are
+ 
+
+ align:start position:0%
+simulation and doing least squares are
+that it's pretty good right and that was
+
+ align:start position:0%
+that it's pretty good right and that was
+ 
+
+ align:start position:0%
+that it's pretty good right and that was
+corrupted by noise and not a lot of
+
+ align:start position:0%
+corrupted by noise and not a lot of
+ 
+
+ align:start position:0%
+corrupted by noise and not a lot of
+noise I guess but
+
+ align:start position:0%
+noise I guess but
+ 
+
+ align:start position:0%
+noise I guess but
+noise
+
+ align:start position:0%
+noise
+ 
+
+ align:start position:0%
+noise
+um it's easy system identification is
+
+ align:start position:0%
+um it's easy system identification is
+ 
+
+ align:start position:0%
+um it's easy system identification is
+easy right it's actually a very very
+
+ align:start position:0%
+easy right it's actually a very very
+ 
+
+ align:start position:0%
+easy right it's actually a very very
+powerful observation that you can do
+
+ align:start position:0%
+powerful observation that you can do
+ 
+
+ align:start position:0%
+powerful observation that you can do
+system identification for these really
+
+ align:start position:0%
+system identification for these really
+ 
+
+ align:start position:0%
+system identification for these really
+hard systems just as a l linear function
+
+ align:start position:0%
+hard systems just as a l linear function
+ 
+
+ align:start position:0%
+hard systems just as a l linear function
+approximation task one shot that's what
+
+ align:start position:0%
+approximation task one shot that's what
+ 
+
+ align:start position:0%
+approximation task one shot that's what
+makes adaptive control tick on a lot of
+
+ align:start position:0%
+makes adaptive control tick on a lot of
+ 
+
+ align:start position:0%
+makes adaptive control tick on a lot of
+these manipulators right it's a very
+
+ align:start position:0%
+these manipulators right it's a very
+ 
+
+ align:start position:0%
+these manipulators right it's a very
+fundamental
+
+ align:start position:0%
+fundamental
+ 
+
+ align:start position:0%
+fundamental
+observation what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would okay it's not going to work as
+
+ align:start position:0%
+would okay it's not going to work as
+ 
+
+ align:start position:0%
+would okay it's not going to work as
+well but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's running some random initial tape
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here um it's not catastrophically bad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually small exactly that that one
+
+ align:start position:0%
+actually small exactly that that one
+ 
+
+ align:start position:0%
+actually small exactly that that one
+happened to be a small angle right let's
+
+ align:start position:0%
+happened to be a small angle right let's
+ 
+
+ align:start position:0%
+happened to be a small angle right let's
+see if I get come
+
+ align:start position:0%
+see if I get come
+ 
+
+ align:start position:0%
+see if I get come
+on that's it's a bigger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one that's worse
+
+ align:start position:0%
+one that's worse
+ 
+
+ align:start position:0%
+one that's worse
+yeah there's another way I can break it
+
+ align:start position:0%
+yeah there's another way I can break it
+ 
+
+ align:start position:0%
+yeah there's another way I can break it
+just to anticipate here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let me put it back before I forget
+
+ align:start position:0%
+um let me put it back before I forget
+ 
+
+ align:start position:0%
+um let me put it back before I forget
+this a sign here
+
+ align:start position:0%
+this a sign here
+ 
+
+ align:start position:0%
+this a sign here
+right um what if I don't put enough
+
+ align:start position:0%
+right um what if I don't put enough
+ 
+
+ align:start position:0%
+right um what if I don't put enough
+control torque in okay I put a note to
+
+ align:start position:0%
+control torque in okay I put a note to
+ 
+
+ align:start position:0%
+control torque in okay I put a note to
+myself if I if I make a 0.1 here then
+
+ align:start position:0%
+myself if I if I make a 0.1 here then
+ 
+
+ align:start position:0%
+myself if I if I make a 0.1 here then
+suddenly I'm not putting in very much
+
+ align:start position:0%
+suddenly I'm not putting in very much
+ 
+
+ align:start position:0%
+suddenly I'm not putting in very much
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+torque and why could that be a
+
+ align:start position:0%
+torque and why could that be a
+ 
+
+ align:start position:0%
+torque and why could that be a
+problem what's
+
+ align:start position:0%
+problem what's
+ 
+
+ align:start position:0%
+problem what's
+that yeah I'm sort of not exactly I'm
+
+ align:start position:0%
+that yeah I'm sort of not exactly I'm
+ 
+
+ align:start position:0%
+that yeah I'm sort of not exactly I'm
+not simulating the system beyond the
+
+ align:start position:0%
+not simulating the system beyond the
+ 
+
+ align:start position:0%
+not simulating the system beyond the
+noise that I've added uh and that can
+
+ align:start position:0%
+noise that I've added uh and that can
+ 
+
+ align:start position:0%
+noise that I've added uh and that can
+break things let's see
+
+ align:start position:0%
+break things let's see
+ 
+
+ align:start position:0%
+break things let's see
+so now it's pretty much just falling
+
+ align:start position:0%
+so now it's pretty much just falling
+ 
+
+ align:start position:0%
+so now it's pretty much just falling
+almost as a um passive pendulum and that
+
+ align:start position:0%
+almost as a um passive pendulum and that
+ 
+
+ align:start position:0%
+almost as a um passive pendulum and that
+breaks things more although this is a
+
+ align:start position:0%
+breaks things more although this is a
+ 
+
+ align:start position:0%
+breaks things more although this is a
+pretty easy problem that doesn't
+
+ align:start position:0%
+pretty easy problem that doesn't
+ 
+
+ align:start position:0%
+pretty easy problem that doesn't
+horribly break
+
+ align:start position:0%
+horribly break
+ 
+
+ align:start position:0%
+horribly break
+anything okay that same code could have
+
+ align:start position:0%
+anything okay that same code could have
+ 
+
+ align:start position:0%
+anything okay that same code could have
+run for the acrobot right it couldn't
+
+ align:start position:0%
+run for the acrobot right it couldn't
+ 
+
+ align:start position:0%
+run for the acrobot right it couldn't
+have R run for sort of one of our um
+
+ align:start position:0%
+have R run for sort of one of our um
+ 
+
+ align:start position:0%
+have R run for sort of one of our um
+airplanes because the aerodynamics tends
+
+ align:start position:0%
+airplanes because the aerodynamics tends
+ 
+
+ align:start position:0%
+airplanes because the aerodynamics tends
+to not be linear in the parameters but
+
+ align:start position:0%
+to not be linear in the parameters but
+ 
+
+ align:start position:0%
+to not be linear in the parameters but
+rigid body Dynamics tend to be linear in
+
+ align:start position:0%
+rigid body Dynamics tend to be linear in
+ 
+
+ align:start position:0%
+rigid body Dynamics tend to be linear in
+the parameters
+
+ align:start position:0%
+the parameters
+ 
+
+ align:start position:0%
+the parameters
+right doing it on the acrobots a little
+
+ align:start position:0%
+right doing it on the acrobots a little
+ 
+
+ align:start position:0%
+right doing it on the acrobots a little
+bit harder because you have to be more
+
+ align:start position:0%
+bit harder because you have to be more
+ 
+
+ align:start position:0%
+bit harder because you have to be more
+clever in stimulating all the Dynamics
+
+ align:start position:0%
+clever in stimulating all the Dynamics
+ 
+
+ align:start position:0%
+clever in stimulating all the Dynamics
+with your one actuator so there are a
+
+ align:start position:0%
+with your one actuator so there are a
+ 
+
+ align:start position:0%
+with your one actuator so there are a
+lot of good problems left in system
+
+ align:start position:0%
+lot of good problems left in system
+ 
+
+ align:start position:0%
+lot of good problems left in system
+identification designing sufficiently
+
+ align:start position:0%
+identification designing sufficiently
+ 
+
+ align:start position:0%
+identification designing sufficiently
+Rich inputs to stimulate all your
+
+ align:start position:0%
+Rich inputs to stimulate all your
+ 
+
+ align:start position:0%
+Rich inputs to stimulate all your
+Dynamics is one of the big
+
+ align:start position:0%
+Dynamics is one of the big
+ 
+
+ align:start position:0%
+Dynamics is one of the big
+ones
+
+ align:start position:0%
+ones
+ 
+
+ align:start position:0%
+ones
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but function approximation and least
+
+ align:start position:0%
+but function approximation and least
+ 
+
+ align:start position:0%
+but function approximation and least
+squares is basically what you need to do
+
+ align:start position:0%
+squares is basically what you need to do
+ 
+
+ align:start position:0%
+squares is basically what you need to do
+to do function to do system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identification so if you have like for
+
+ align:start position:0%
+identification so if you have like for
+ 
+
+ align:start position:0%
+identification so if you have like for
+example Y and then presumably you have
+
+ align:start position:0%
+example Y and then presumably you have
+ 
+
+ align:start position:0%
+example Y and then presumably you have
+likeus G as one of the one of the parts
+
+ align:start position:0%
+likeus G as one of the one of the parts
+ 
+
+ align:start position:0%
+likeus G as one of the one of the parts
+in your equations so if you want to get
+
+ align:start position:0%
+in your equations so if you want to get
+ 
+
+ align:start position:0%
+in your equations so if you want to get
+something good you should put that as
+
+ align:start position:0%
+something good you should put that as
+ 
+
+ align:start position:0%
+something good you should put that as
+one of the features right have S Alpha
+
+ align:start position:0%
+one of the features right have S Alpha
+ 
+
+ align:start position:0%
+one of the features right have S Alpha
+minus gamma there and then there's
+
+ align:start position:0%
+minus gamma there and then there's
+ 
+
+ align:start position:0%
+minus gamma there and then there's
+always a step where you have to look at
+
+ align:start position:0%
+always a step where you have to look at
+ 
+
+ align:start position:0%
+always a step where you have to look at
+your equations and pull out the proper
+
+ align:start position:0%
+your equations and pull out the proper
+ 
+
+ align:start position:0%
+your equations and pull out the proper
+basis function to describe that that
+
+ align:start position:0%
+basis function to describe that that
+ 
+
+ align:start position:0%
+basis function to describe that that
+class of systems absolutely so if if
+
+ align:start position:0%
+class of systems absolutely so if if
+ 
+
+ align:start position:0%
+class of systems absolutely so if if
+there's a s Theta 1us Theta 2 floating
+
+ align:start position:0%
+there's a s Theta 1us Theta 2 floating
+ 
+
+ align:start position:0%
+there's a s Theta 1us Theta 2 floating
+around in there it should be in one of
+
+ align:start position:0%
+around in there it should be in one of
+ 
+
+ align:start position:0%
+around in there it should be in one of
+your basis as one of your basis elements
+
+ align:start position:0%
+your basis as one of your basis elements
+ 
+
+ align:start position:0%
+your basis as one of your basis elements
+if you want to do this with a system you
+
+ align:start position:0%
+if you want to do this with a system you
+ 
+
+ align:start position:0%
+if you want to do this with a system you
+don't
+
+ align:start position:0%
+don't
+ 
+
+ align:start position:0%
+don't
+have you think that it's linear but you
+
+ align:start position:0%
+have you think that it's linear but you
+ 
+
+ align:start position:0%
+have you think that it's linear but you
+don't know the ination for
+
+ align:start position:0%
+don't know the ination for
+ 
+
+ align:start position:0%
+don't know the ination for
+good then maybe you should do radial
+
+ align:start position:0%
+good then maybe you should do radial
+ 
+
+ align:start position:0%
+good then maybe you should do radial
+basis functions or pols or some other
+
+ align:start position:0%
+basis functions or pols or some other
+ 
+
+ align:start position:0%
+basis functions or pols or some other
+basis set I think a more common thing
+
+ align:start position:0%
+basis set I think a more common thing
+ 
+
+ align:start position:0%
+basis set I think a more common thing
+would be um imagine there's something
+
+ align:start position:0%
+would be um imagine there's something
+ 
+
+ align:start position:0%
+would be um imagine there's something
+I'm not modeling well in my pendulum
+
+ align:start position:0%
+I'm not modeling well in my pendulum
+ 
+
+ align:start position:0%
+I'm not modeling well in my pendulum
+let's say there's some nonlinear
+
+ align:start position:0%
+let's say there's some nonlinear
+ 
+
+ align:start position:0%
+let's say there's some nonlinear
+friction in the joints or something like
+
+ align:start position:0%
+friction in the joints or something like
+ 
+
+ align:start position:0%
+friction in the joints or something like
+that a common thing that people would do
+
+ align:start position:0%
+that a common thing that people would do
+ 
+
+ align:start position:0%
+that a common thing that people would do
+would be to to add in here some slop
+
+ align:start position:0%
+would be to to add in here some slop
+ 
+
+ align:start position:0%
+would be to to add in here some slop
+terms let's say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um radial basis functions or something
+
+ align:start position:0%
+um radial basis functions or something
+ 
+
+ align:start position:0%
+um radial basis functions or something
+just my standard linear function
+
+ align:start position:0%
+just my standard linear function
+ 
+
+ align:start position:0%
+just my standard linear function
+approximator and do
+
+ align:start position:0%
+approximator and do
+ 
+
+ align:start position:0%
+approximator and do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay and then now you've just added more
+
+ align:start position:0%
+okay and then now you've just added more
+ 
+
+ align:start position:0%
+okay and then now you've just added more
+representational power to this you've
+
+ align:start position:0%
+representational power to this you've
+ 
+
+ align:start position:0%
+representational power to this you've
+given the basis functions which you
+
+ align:start position:0%
+given the basis functions which you
+ 
+
+ align:start position:0%
+given the basis functions which you
+believe to be true right but you also
+
+ align:start position:0%
+believe to be true right but you also
+ 
+
+ align:start position:0%
+believe to be true right but you also
+add in some slop terms right and this is
+
+ align:start position:0%
+add in some slop terms right and this is
+ 
+
+ align:start position:0%
+add in some slop terms right and this is
+I mean so slotin certainly teaches this
+
+ align:start position:0%
+I mean so slotin certainly teaches this
+ 
+
+ align:start position:0%
+I mean so slotin certainly teaches this
+and does this in his robots right for
+
+ align:start position:0%
+and does this in his robots right for
+ 
+
+ align:start position:0%
+and does this in his robots right for
+his adaptive controller he puts those in
+
+ align:start position:0%
+his adaptive controller he puts those in
+ 
+
+ align:start position:0%
+his adaptive controller he puts those in
+to capture the terms that he didn't
+
+ align:start position:0%
+to capture the terms that he didn't
+ 
+
+ align:start position:0%
+to capture the terms that he didn't
+expect to show up yeah um how does this
+
+ align:start position:0%
+expect to show up yeah um how does this
+ 
+
+ align:start position:0%
+expect to show up yeah um how does this
+work for things that aren't really
+
+ align:start position:0%
+work for things that aren't really
+ 
+
+ align:start position:0%
+work for things that aren't really
+smooth like sometimes stick slip can
+
+ align:start position:0%
+smooth like sometimes stick slip can
+ 
+
+ align:start position:0%
+smooth like sometimes stick slip can
+kind of seems
+
+ align:start position:0%
+kind of seems
+ 
+
+ align:start position:0%
+kind of seems
+like plotted it's not really continuous
+
+ align:start position:0%
+like plotted it's not really continuous
+ 
+
+ align:start position:0%
+like plotted it's not really continuous
+function so um continuous doesn't matter
+
+ align:start position:0%
+function so um continuous doesn't matter
+ 
+
+ align:start position:0%
+function so um continuous doesn't matter
+right it's you could if you're if you're
+
+ align:start position:0%
+right it's you could if you're if you're
+ 
+
+ align:start position:0%
+right it's you could if you're if you're
+trying to fit a continuous basis set to
+
+ align:start position:0%
+trying to fit a continuous basis set to
+ 
+
+ align:start position:0%
+trying to fit a continuous basis set to
+a discontinuous function then it'll only
+
+ align:start position:0%
+a discontinuous function then it'll only
+ 
+
+ align:start position:0%
+a discontinuous function then it'll only
+only do as well as it can in at least
+
+ align:start position:0%
+only do as well as it can in at least
+ 
+
+ align:start position:0%
+only do as well as it can in at least
+Square sent but um but you can represent
+
+ align:start position:0%
+Square sent but um but you can represent
+ 
+
+ align:start position:0%
+Square sent but um but you can represent
+arbitrary static functions of you know
+
+ align:start position:0%
+arbitrary static functions of you know
+ 
+
+ align:start position:0%
+arbitrary static functions of you know
+if it's a function of X then it should
+
+ align:start position:0%
+if it's a function of X then it should
+ 
+
+ align:start position:0%
+if it's a function of X then it should
+be right I think the more common problem
+
+ align:start position:0%
+be right I think the more common problem
+ 
+
+ align:start position:0%
+be right I think the more common problem
+maybe in a stick SLP kind of model is
+
+ align:start position:0%
+maybe in a stick SLP kind of model is
+ 
+
+ align:start position:0%
+maybe in a stick SLP kind of model is
+that there's hidden State okay for
+
+ align:start position:0%
+that there's hidden State okay for
+ 
+
+ align:start position:0%
+that there's hidden State okay for
+instance right maybe you don't know
+
+ align:start position:0%
+instance right maybe you don't know
+ 
+
+ align:start position:0%
+instance right maybe you don't know
+exactly what the state of the system is
+
+ align:start position:0%
+exactly what the state of the system is
+ 
+
+ align:start position:0%
+exactly what the state of the system is
+because there's some
+
+ align:start position:0%
+because there's some
+ 
+
+ align:start position:0%
+because there's some
+other and then you'd have to estimate
+
+ align:start position:0%
+other and then you'd have to estimate
+ 
+
+ align:start position:0%
+other and then you'd have to estimate
+that to put it into your basis
+
+ align:start position:0%
+that to put it into your basis
+ 
+
+ align:start position:0%
+that to put it into your basis
+set okay people feel okay with least
+
+ align:start position:0%
+set okay people feel okay with least
+ 
+
+ align:start position:0%
+set okay people feel okay with least
+squares estimation
+
+ align:start position:0%
+squares estimation
+ 
+
+ align:start position:0%
+squares estimation
+yeah good now let's see if we can put it
+
+ align:start position:0%
+yeah good now let's see if we can put it
+ 
+
+ align:start position:0%
+yeah good now let's see if we can put it
+to use to do what we promised at the
+
+ align:start position:0%
+to use to do what we promised at the
+ 
+
+ align:start position:0%
+to use to do what we promised at the
+beginning which is temporal difference
+
+ align:start position:0%
+beginning which is temporal difference
+ 
+
+ align:start position:0%
+beginning which is temporal difference
+learning it's gone isn't
+
+ align:start position:0%
+learning it's gone isn't
+ 
+
+ align:start position:0%
+learning it's gone isn't
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if you remember and I hope the
+
+ align:start position:0%
+okay so if you remember and I hope the
+ 
+
+ align:start position:0%
+okay so if you remember and I hope the
+impression came across when I was
+
+ align:start position:0%
+impression came across when I was
+ 
+
+ align:start position:0%
+impression came across when I was
+talking about temporal difference
+
+ align:start position:0%
+talking about temporal difference
+ 
+
+ align:start position:0%
+talking about temporal difference
+learning that
+
+ align:start position:0%
+learning that
+ 
+
+ align:start position:0%
+learning that
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we made a pretty complicated
+
+ align:start position:0%
+we made a pretty complicated
+ 
+
+ align:start position:0%
+we made a pretty complicated
+update which was this um sort of
+
+ align:start position:0%
+update which was this um sort of
+ 
+
+ align:start position:0%
+update which was this um sort of
+weighted sum of of one step two step
+
+ align:start position:0%
+weighted sum of of one step two step
+ 
+
+ align:start position:0%
+weighted sum of of one step two step
+three step endep
+
+ align:start position:0%
+three step endep
+ 
+
+ align:start position:0%
+three step endep
+returns with a sort of through some
+
+ align:start position:0%
+returns with a sort of through some
+ 
+
+ align:start position:0%
+returns with a sort of through some
+algebraic trick and that's really
+
+ align:start position:0%
+algebraic trick and that's really
+ 
+
+ align:start position:0%
+algebraic trick and that's really
+probably the right way to think about it
+
+ align:start position:0%
+probably the right way to think about it
+ 
+
+ align:start position:0%
+probably the right way to think about it
+through some algebraic trick you could
+
+ align:start position:0%
+through some algebraic trick you could
+ 
+
+ align:start position:0%
+through some algebraic trick you could
+do it with a very simple algorithm so
+
+ align:start position:0%
+do it with a very simple algorithm so
+ 
+
+ align:start position:0%
+do it with a very simple algorithm so
+let me just remind you the that that
+
+ align:start position:0%
+let me just remind you the that that
+ 
+
+ align:start position:0%
+let me just remind you the that that
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if you remember the the picture
+
+ align:start position:0%
+okay so if you remember the the picture
+ 
+
+ align:start position:0%
+okay so if you remember the the picture
+we had last time was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that I've got some markof
+
+ align:start position:0%
+that I've got some markof
+ 
+
+ align:start position:0%
+that I've got some markof
+chain that I'm moving around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay as I'm walking around this Markov
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chain I'm trying to every time I visit a
+
+ align:start position:0%
+chain I'm trying to every time I visit a
+ 
+
+ align:start position:0%
+chain I'm trying to every time I visit a
+state I want to update my estimate of
+
+ align:start position:0%
+state I want to update my estimate of
+ 
+
+ align:start position:0%
+state I want to update my estimate of
+the cost to go from being in that state
+
+ align:start position:0%
+the cost to go from being in that state
+ 
+
+ align:start position:0%
+the cost to go from being in that state
+right and I can do it with this sort of
+
+ align:start position:0%
+right and I can do it with this sort of
+ 
+
+ align:start position:0%
+right and I can do it with this sort of
+very simple
+
+ align:start position:0%
+very simple
+ 
+
+ align:start position:0%
+very simple
+algorithm which keep keeps a decaying
+
+ align:start position:0%
+algorithm which keep keeps a decaying
+ 
+
+ align:start position:0%
+algorithm which keep keeps a decaying
+eligibility trace on each
+
+ align:start position:0%
+eligibility trace on each
+ 
+
+ align:start position:0%
+eligibility trace on each
+node every time I visit this node it
+
+ align:start position:0%
+node every time I visit this node it
+ 
+
+ align:start position:0%
+node every time I visit this node it
+goes up and then it starts decaying
+
+ align:start position:0%
+goes up and then it starts decaying
+ 
+
+ align:start position:0%
+goes up and then it starts decaying
+until the next time I visit and it goes
+
+ align:start position:0%
+until the next time I visit and it goes
+ 
+
+ align:start position:0%
+until the next time I visit and it goes
+up okay the rate at which it decays is
+
+ align:start position:0%
+up okay the rate at which it decays is
+ 
+
+ align:start position:0%
+up okay the rate at which it decays is
+given by the discount factor in my
+
+ align:start position:0%
+given by the discount factor in my
+ 
+
+ align:start position:0%
+given by the discount factor in my
+optimal control problem and the Lambda
+
+ align:start position:0%
+optimal control problem and the Lambda
+ 
+
+ align:start position:0%
+optimal control problem and the Lambda
+which is um the weight the amount that I
+
+ align:start position:0%
+which is um the weight the amount that I
+ 
+
+ align:start position:0%
+which is um the weight the amount that I
+want to weight Monte Carlo long-term
+
+ align:start position:0%
+want to weight Monte Carlo long-term
+ 
+
+ align:start position:0%
+want to weight Monte Carlo long-term
+evaluations versus short-term
+
+ align:start position:0%
+evaluations versus short-term
+ 
+
+ align:start position:0%
+evaluations versus short-term
+evaluations right if Lambda is one I'm
+
+ align:start position:0%
+evaluations right if Lambda is one I'm
+ 
+
+ align:start position:0%
+evaluations right if Lambda is one I'm
+going to let that settle much more
+
+ align:start position:0%
+going to let that settle much more
+ 
+
+ align:start position:0%
+going to let that settle much more
+slowly and it's going to be making very
+
+ align:start position:0%
+slowly and it's going to be making very
+ 
+
+ align:start position:0%
+slowly and it's going to be making very
+long-term updates and if it Lambda is is
+
+ align:start position:0%
+long-term updates and if it Lambda is is
+ 
+
+ align:start position:0%
+long-term updates and if it Lambda is is
+zero then it's just going to make it
+
+ align:start position:0%
+zero then it's just going to make it
+ 
+
+ align:start position:0%
+zero then it's just going to make it
+update based on the one-step
+
+ align:start position:0%
+update based on the one-step
+ 
+
+ align:start position:0%
+update based on the one-step
+prediction okay if I carry around this
+
+ align:start position:0%
+prediction okay if I carry around this
+ 
+
+ align:start position:0%
+prediction okay if I carry around this
+eligibility trace this would be EI as a
+
+ align:start position:0%
+eligibility trace this would be EI as a
+ 
+
+ align:start position:0%
+eligibility trace this would be EI as a
+function of time for every
+
+ align:start position:0%
+function of time for every
+ 
+
+ align:start position:0%
+function of time for every
+I and I do this very simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+update then there's this interpretation
+
+ align:start position:0%
+update then there's this interpretation
+ 
+
+ align:start position:0%
+update then there's this interpretation
+that J hat is doing something between
+
+ align:start position:0%
+that J hat is doing something between
+ 
+
+ align:start position:0%
+that J hat is doing something between
+Monte Carlo and one step bootstrapping
+
+ align:start position:0%
+Monte Carlo and one step bootstrapping
+ 
+
+ align:start position:0%
+Monte Carlo and one step bootstrapping
+depending on what um what Lambda you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so let's say we don't have a
+
+ align:start position:0%
+right okay so let's say we don't have a
+ 
+
+ align:start position:0%
+right okay so let's say we don't have a
+discre a discret state and Action System
+
+ align:start position:0%
+discre a discret state and Action System
+ 
+
+ align:start position:0%
+discre a discret state and Action System
+but we now have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um let's say our Barry Centric
+
+ align:start position:0%
+um let's say our Barry Centric
+ 
+
+ align:start position:0%
+um let's say our Barry Centric
+interpolators on a pendulum or something
+
+ align:start position:0%
+interpolators on a pendulum or something
+ 
+
+ align:start position:0%
+interpolators on a pendulum or something
+like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and let's say I take a trajectory
+
+ align:start position:0%
+right and let's say I take a trajectory
+ 
+
+ align:start position:0%
+right and let's say I take a trajectory
+through here that like that was a bad
+
+ align:start position:0%
+through here that like that was a bad
+ 
+
+ align:start position:0%
+through here that like that was a bad
+trajectory for a phase space
+
+ align:start position:0%
+trajectory for a phase space
+ 
+
+ align:start position:0%
+trajectory for a phase space
+but I take some trajectory through my
+
+ align:start position:0%
+but I take some trajectory through my
+ 
+
+ align:start position:0%
+but I take some trajectory through my
+state space
+
+ align:start position:0%
+state space
+ 
+
+ align:start position:0%
+state space
+okay let's say I'm willing to discre
+
+ align:start position:0%
+okay let's say I'm willing to discre
+ 
+
+ align:start position:0%
+okay let's say I'm willing to discre
+discretize the system in time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+still and let's say my Value Estimate is
+
+ align:start position:0%
+still and let's say my Value Estimate is
+ 
+
+ align:start position:0%
+still and let's say my Value Estimate is
+a linear function approximator which is
+
+ align:start position:0%
+a linear function approximator which is
+ 
+
+ align:start position:0%
+a linear function approximator which is
+this Berry Centric
+
+ align:start position:0%
+this Berry Centric
+ 
+
+ align:start position:0%
+this Berry Centric
+grid okay so at every Point
+
+ align:start position:0%
+grid okay so at every Point
+ 
+
+ align:start position:0%
+grid okay so at every Point
+here right I'm going to say J hat is
+
+ align:start position:0%
+here right I'm going to say J hat is
+ 
+
+ align:start position:0%
+here right I'm going to say J hat is
+just a weighted combination of the four
+
+ align:start position:0%
+just a weighted combination of the four
+ 
+
+ align:start position:0%
+just a weighted combination of the four
+neighboring points weighted by the
+
+ align:start position:0%
+neighboring points weighted by the
+ 
+
+ align:start position:0%
+neighboring points weighted by the
+distance right
+
+ align:start position:0%
+distance right
+ 
+
+ align:start position:0%
+distance right
+like I said that actually is
+
+ align:start position:0%
+like I said that actually is
+ 
+
+ align:start position:0%
+like I said that actually is
+exactly of the form where I've got a
+
+ align:start position:0%
+exactly of the form where I've got a
+ 
+
+ align:start position:0%
+exactly of the form where I've got a
+scalar
+
+ align:start position:0%
+scalar
+ 
+
+ align:start position:0%
+scalar
+output and I've just got you could think
+
+ align:start position:0%
+output and I've just got you could think
+ 
+
+ align:start position:0%
+output and I've just got you could think
+of this as being a
+
+ align:start position:0%
+of this as being a
+ 
+
+ align:start position:0%
+of this as being a
+tent this this value this um being a
+
+ align:start position:0%
+tent this this value this um being a
+ 
+
+ align:start position:0%
+tent this this value this um being a
+basis function which has a sort of a
+
+ align:start position:0%
+basis function which has a sort of a
+ 
+
+ align:start position:0%
+basis function which has a sort of a
+tent of region of applicability right
+
+ align:start position:0%
+tent of region of applicability right
+ 
+
+ align:start position:0%
+tent of region of applicability right
+here and added with this one that has a
+
+ align:start position:0%
+here and added with this one that has a
+ 
+
+ align:start position:0%
+here and added with this one that has a
+tent of applicability here and at every
+
+ align:start position:0%
+tent of applicability here and at every
+ 
+
+ align:start position:0%
+tent of applicability here and at every
+Point there's a at every Crosshair
+
+ align:start position:0%
+Point there's a at every Crosshair
+ 
+
+ align:start position:0%
+Point there's a at every Crosshair
+there's a there's a basis function that
+
+ align:start position:0%
+there's a there's a basis function that
+ 
+
+ align:start position:0%
+there's a there's a basis function that
+looks like a tent did you get that out
+
+ align:start position:0%
+looks like a tent did you get that out
+ 
+
+ align:start position:0%
+looks like a tent did you get that out
+of the previous one the previous
+
+ align:start position:0%
+of the previous one the previous
+ 
+
+ align:start position:0%
+of the previous one the previous
+picture right linearly interpolating
+
+ align:start position:0%
+picture right linearly interpolating
+ 
+
+ align:start position:0%
+picture right linearly interpolating
+between those four points is the same as
+
+ align:start position:0%
+between those four points is the same as
+ 
+
+ align:start position:0%
+between those four points is the same as
+saying I've got four basis functions
+
+ align:start position:0%
+saying I've got four basis functions
+ 
+
+ align:start position:0%
+saying I've got four basis functions
+that are active and each of them
+
+ align:start position:0%
+that are active and each of them
+ 
+
+ align:start position:0%
+that are active and each of them
+contributes in a way that diminishes
+
+ align:start position:0%
+contributes in a way that diminishes
+ 
+
+ align:start position:0%
+contributes in a way that diminishes
+from the point of their point of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attack okay so now I've got a linear
+
+ align:start position:0%
+attack okay so now I've got a linear
+ 
+
+ align:start position:0%
+attack okay so now I've got a linear
+function approximator trying to estimate
+
+ align:start position:0%
+function approximator trying to estimate
+ 
+
+ align:start position:0%
+function approximator trying to estimate
+J hat so how could I possibly um do T
+
+ align:start position:0%
+J hat so how could I possibly um do T
+ 
+
+ align:start position:0%
+J hat so how could I possibly um do T
+temporal difference learning yeah John
+
+ align:start position:0%
+temporal difference learning yeah John
+ 
+
+ align:start position:0%
+temporal difference learning yeah John
+is that volumetric interpolation barric
+
+ align:start position:0%
+is that volumetric interpolation barric
+ 
+
+ align:start position:0%
+is that volumetric interpolation barric
+has small okay good so you can do
+
+ align:start position:0%
+has small okay good so you can do
+ 
+
+ align:start position:0%
+has small okay good so you can do
+barycentric in in three or four actually
+
+ align:start position:0%
+barycentric in in three or four actually
+ 
+
+ align:start position:0%
+barycentric in in three or four actually
+here you have this would be you'd have
+
+ align:start position:0%
+here you have this would be you'd have
+ 
+
+ align:start position:0%
+here you have this would be you'd have
+three points though
+
+ align:start position:0%
+three points though
+ 
+
+ align:start position:0%
+three points though
+right this would still be called
+
+ align:start position:0%
+right this would still be called
+ 
+
+ align:start position:0%
+right this would still be called
+bicentric but it's true the ber Centric
+
+ align:start position:0%
+bicentric but it's true the ber Centric
+ 
+
+ align:start position:0%
+bicentric but it's true the ber Centric
+we did in before was was just you take
+
+ align:start position:0%
+we did in before was was just you take
+ 
+
+ align:start position:0%
+we did in before was was just you take
+the neighboring three
+
+ align:start position:0%
+the neighboring three
+ 
+
+ align:start position:0%
+the neighboring three
+points it's true so actually bicentric
+
+ align:start position:0%
+points it's true so actually bicentric
+ 
+
+ align:start position:0%
+points it's true so actually bicentric
+you can do bicentric with the three
+
+ align:start position:0%
+you can do bicentric with the three
+ 
+
+ align:start position:0%
+you can do bicentric with the three
+neighboring points or the four
+
+ align:start position:0%
+neighboring points or the four
+ 
+
+ align:start position:0%
+neighboring points or the four
+neighboring points or whatever that the
+
+ align:start position:0%
+neighboring points or whatever that the
+ 
+
+ align:start position:0%
+neighboring points or whatever that the
+volumetric is actually also called is
+
+ align:start position:0%
+volumetric is actually also called is
+ 
+
+ align:start position:0%
+volumetric is actually also called is
+also a bicentric interpolator but but
+
+ align:start position:0%
+also a bicentric interpolator but but
+ 
+
+ align:start position:0%
+also a bicentric interpolator but but
+you're right I should have been more
+
+ align:start position:0%
+you're right I should have been more
+ 
+
+ align:start position:0%
+you're right I should have been more
+careful the the way we did bicentric
+
+ align:start position:0%
+careful the the way we did bicentric
+ 
+
+ align:start position:0%
+careful the the way we did bicentric
+before is we took the three uh closest
+
+ align:start position:0%
+before is we took the three uh closest
+ 
+
+ align:start position:0%
+before is we took the three uh closest
+points not the
+
+ align:start position:0%
+points not the
+ 
+
+ align:start position:0%
+points not the
+four right taking the four is also a
+
+ align:start position:0%
+four right taking the four is also a
+ 
+
+ align:start position:0%
+four right taking the four is also a
+good interpolator it also is a called a
+
+ align:start position:0%
+good interpolator it also is a called a
+ 
+
+ align:start position:0%
+good interpolator it also is a called a
+bicentric interpolator actually right
+
+ align:start position:0%
+bicentric interpolator actually right
+ 
+
+ align:start position:0%
+bicentric interpolator actually right
+and the question is just whether how it
+
+ align:start position:0%
+and the question is just whether how it
+ 
+
+ align:start position:0%
+and the question is just whether how it
+grows with State most people use the
+
+ align:start position:0%
+grows with State most people use the
+ 
+
+ align:start position:0%
+grows with State most people use the
+three closest closest points because
+
+ align:start position:0%
+three closest closest points because
+ 
+
+ align:start position:0%
+three closest closest points because
+then in higher Dimensions it's always n
+
+ align:start position:0%
+then in higher Dimensions it's always n
+ 
+
+ align:start position:0%
+then in higher Dimensions it's always n
+plus one points instead of the powers of
+
+ align:start position:0%
+plus one points instead of the powers of
+ 
+
+ align:start position:0%
+plus one points instead of the powers of
+n you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good thank you okay
+
+ align:start position:0%
+good thank you okay
+ 
+
+ align:start position:0%
+good thank you okay
+so um so I guess then the domain of
+
+ align:start position:0%
+so um so I guess then the domain of
+ 
+
+ align:start position:0%
+so um so I guess then the domain of
+Attraction is more like that or
+
+ align:start position:0%
+Attraction is more like that or
+ 
+
+ align:start position:0%
+Attraction is more like that or
+something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right for every for every cross here
+
+ align:start position:0%
+right for every for every cross here
+ 
+
+ align:start position:0%
+right for every for every cross here
+there's a if you're doing the the
+
+ align:start position:0%
+there's a if you're doing the the
+ 
+
+ align:start position:0%
+there's a if you're doing the the
+triangle interpolation then it's it's
+
+ align:start position:0%
+triangle interpolation then it's it's
+ 
+
+ align:start position:0%
+triangle interpolation then it's it's
+more like
+
+ align:start position:0%
+more like
+ 
+
+ align:start position:0%
+more like
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+yeah so what do you think so how can we
+
+ align:start position:0%
+yeah so what do you think so how can we
+ 
+
+ align:start position:0%
+yeah so what do you think so how can we
+make an analogy between going through
+
+ align:start position:0%
+make an analogy between going through
+ 
+
+ align:start position:0%
+make an analogy between going through
+discret States and in increasing
+
+ align:start position:0%
+discret States and in increasing
+ 
+
+ align:start position:0%
+discret States and in increasing
+eligibility right this eligibility is
+
+ align:start position:0%
+eligibility right this eligibility is
+ 
+
+ align:start position:0%
+eligibility right this eligibility is
+really I just need to remember that that
+
+ align:start position:0%
+really I just need to remember that that
+ 
+
+ align:start position:0%
+really I just need to remember that that
+state was relevant in my in my history
+
+ align:start position:0%
+state was relevant in my in my history
+ 
+
+ align:start position:0%
+state was relevant in my in my history
+of of costs
+
+ align:start position:0%
+of of costs
+ 
+
+ align:start position:0%
+of of costs
+right is can you think of an analogy of
+
+ align:start position:0%
+right is can you think of an analogy of
+ 
+
+ align:start position:0%
+right is can you think of an analogy of
+how this function approximator might
+
+ align:start position:0%
+how this function approximator might
+ 
+
+ align:start position:0%
+how this function approximator might
+play into those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equations what I want to get
+
+ align:start position:0%
+equations what I want to get
+ 
+
+ align:start position:0%
+equations what I want to get
+to with function
+
+ align:start position:0%
+to with function
+ 
+
+ align:start position:0%
+to with function
+approximation I want to get an
+
+ align:start position:0%
+approximation I want to get an
+ 
+
+ align:start position:0%
+approximation I want to get an
+update for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that has the same sort of form instead
+
+ align:start position:0%
+that has the same sort of form instead
+ 
+
+ align:start position:0%
+that has the same sort of form instead
+of this J remember was in the money in
+
+ align:start position:0%
+of this J remember was in the money in
+ 
+
+ align:start position:0%
+of this J remember was in the money in
+the Markov chain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case that's a that's a vector J
+
+ align:start position:0%
+case that's a that's a vector J
+ 
+
+ align:start position:0%
+case that's a that's a vector J
+right where each element of the vector
+
+ align:start position:0%
+right where each element of the vector
+ 
+
+ align:start position:0%
+right where each element of the vector
+was the the cost to go estimate for the
+
+ align:start position:0%
+was the the cost to go estimate for the
+ 
+
+ align:start position:0%
+was the the cost to go estimate for the
+I node right now my f my function
+
+ align:start position:0%
+I node right now my f my function
+ 
+
+ align:start position:0%
+I node right now my f my function
+approximator is again I'm trying to
+
+ align:start position:0%
+approximator is again I'm trying to
+ 
+
+ align:start position:0%
+approximator is again I'm trying to
+estimate Vector Alpha but the
+
+ align:start position:0%
+estimate Vector Alpha but the
+ 
+
+ align:start position:0%
+estimate Vector Alpha but the
+um but each Alpha could potentially
+
+ align:start position:0%
+um but each Alpha could potentially
+ 
+
+ align:start position:0%
+um but each Alpha could potentially
+affect my estimate at multiple States
+
+ align:start position:0%
+affect my estimate at multiple States
+ 
+
+ align:start position:0%
+affect my estimate at multiple States
+right that's the power of function
+
+ align:start position:0%
+right that's the power of function
+ 
+
+ align:start position:0%
+right that's the power of function
+approximator is you don't have to
+
+ align:start position:0%
+approximator is you don't have to
+ 
+
+ align:start position:0%
+approximator is you don't have to
+consider every Point individually you
+
+ align:start position:0%
+consider every Point individually you
+ 
+
+ align:start position:0%
+consider every Point individually you
+have you get some
+
+ align:start position:0%
+have you get some
+ 
+
+ align:start position:0%
+have you get some
+generalization that one parameter
+
+ align:start position:0%
+generalization that one parameter
+ 
+
+ align:start position:0%
+generalization that one parameter
+affects multiple
+
+ align:start position:0%
+affects multiple
+ 
+
+ align:start position:0%
+affects multiple
+outputs okay so what could possibly make
+
+ align:start position:0%
+outputs okay so what could possibly make
+ 
+
+ align:start position:0%
+outputs okay so what could possibly make
+this tick how would you do function
+
+ align:start position:0%
+this tick how would you do function
+ 
+
+ align:start position:0%
+this tick how would you do function
+approximator temporal difference
+
+ align:start position:0%
+approximator temporal difference
+ 
+
+ align:start position:0%
+approximator temporal difference
+learning with function approximator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah we basically doing basis function
+
+ align:start position:0%
+yeah we basically doing basis function
+ 
+
+ align:start position:0%
+yeah we basically doing basis function
+that delt at every good point so we can
+
+ align:start position:0%
+that delt at every good point so we can
+ 
+
+ align:start position:0%
+that delt at every good point so we can
+break J hat up
+
+ align:start position:0%
+break J hat up
+ 
+
+ align:start position:0%
+break J hat up
+into something that is actually
+
+ align:start position:0%
+into something that is actually
+ 
+
+ align:start position:0%
+into something that is actually
+based on these other basis
+
+ align:start position:0%
+based on these other basis
+ 
+
+ align:start position:0%
+based on these other basis
+functions so this should be whatever we
+
+ align:start position:0%
+functions so this should be whatever we
+ 
+
+ align:start position:0%
+functions so this should be whatever we
+come up with this should hopefully be
+
+ align:start position:0%
+come up with this should hopefully be
+ 
+
+ align:start position:0%
+come up with this should hopefully be
+the limiting uh case where if my basis
+
+ align:start position:0%
+the limiting uh case where if my basis
+ 
+
+ align:start position:0%
+the limiting uh case where if my basis
+function was Delta functions you'd like
+
+ align:start position:0%
+function was Delta functions you'd like
+ 
+
+ align:start position:0%
+function was Delta functions you'd like
+to get back to
+
+ align:start position:0%
+to get back to
+ 
+
+ align:start position:0%
+to get back to
+that I think that's unfortunately going
+
+ align:start position:0%
+that I think that's unfortunately going
+ 
+
+ align:start position:0%
+that I think that's unfortunately going
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+a u no no well it just happens I'm going
+
+ align:start position:0%
+a u no no well it just happens I'm going
+ 
+
+ align:start position:0%
+a u no no well it just happens I'm going
+to be taking gradients so uh but but
+
+ align:start position:0%
+to be taking gradients so uh but but
+ 
+
+ align:start position:0%
+to be taking gradients so uh but but
+yeah no that's very that's a very nice
+
+ align:start position:0%
+yeah no that's very that's a very nice
+ 
+
+ align:start position:0%
+yeah no that's very that's a very nice
+observation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually what's that but I think you
+
+ align:start position:0%
+actually what's that but I think you
+ 
+
+ align:start position:0%
+actually what's that but I think you
+can't take because that's discreet Delta
+
+ align:start position:0%
+can't take because that's discreet Delta
+ 
+
+ align:start position:0%
+can't take because that's discreet Delta
+so exactly
+
+ align:start position:0%
+so exactly
+ 
+
+ align:start position:0%
+so exactly
+yeah Del function he meant like infity
+
+ align:start position:0%
+yeah Del function he meant like infity
+ 
+
+ align:start position:0%
+yeah Del function he meant like infity
+or that's what John was pointing out so
+
+ align:start position:0%
+or that's what John was pointing out so
+ 
+
+ align:start position:0%
+or that's what John was pointing out so
+so he thinks it's going to be a chronic
+
+ align:start position:0%
+so he thinks it's going to be a chronic
+ 
+
+ align:start position:0%
+so he thinks it's going to be a chronic
+or Delta because it's it's going to have
+
+ align:start position:0%
+or Delta because it's it's going to have
+ 
+
+ align:start position:0%
+or Delta because it's it's going to have
+I guess it could be one yeah so if it is
+
+ align:start position:0%
+I guess it could be one yeah so if it is
+ 
+
+ align:start position:0%
+I guess it could be one yeah so if it is
+one it's actually it would be mapping
+
+ align:start position:0%
+one it's actually it would be mapping
+ 
+
+ align:start position:0%
+one it's actually it would be mapping
+from representation function
+
+ align:start position:0%
+from representation function
+ 
+
+ align:start position:0%
+from representation function
+approximation y but having features that
+
+ align:start position:0%
+approximation y but having features that
+ 
+
+ align:start position:0%
+approximation y but having features that
+just one no I think that's I think it's
+
+ align:start position:0%
+just one no I think that's I think it's
+ 
+
+ align:start position:0%
+just one no I think that's I think it's
+a very nice observation the the if we
+
+ align:start position:0%
+a very nice observation the the if we
+ 
+
+ align:start position:0%
+a very nice observation the the if we
+think of each feature as having height
+
+ align:start position:0%
+think of each feature as having height
+ 
+
+ align:start position:0%
+think of each feature as having height
+one here and
+
+ align:start position:0%
+one here and
+ 
+
+ align:start position:0%
+one here and
+domain nothing right then that should be
+
+ align:start position:0%
+domain nothing right then that should be
+ 
+
+ align:start position:0%
+domain nothing right then that should be
+the limiting case where we get our
+
+ align:start position:0%
+the limiting case where we get our
+ 
+
+ align:start position:0%
+the limiting case where we get our
+markof chain I think that's
+
+ align:start position:0%
+markof chain I think that's
+ 
+
+ align:start position:0%
+markof chain I think that's
+right so if you just change to taking at
+
+ align:start position:0%
+right so if you just change to taking at
+ 
+
+ align:start position:0%
+right so if you just change to taking at
+each step of weed sum of of nodes
+
+ align:start position:0%
+each step of weed sum of of nodes
+ 
+
+ align:start position:0%
+each step of weed sum of of nodes
+mapping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so yeah I mean
+
+ align:start position:0%
+that so yeah I mean
+ 
+
+ align:start position:0%
+that so yeah I mean
+that's that's effectively right so um
+
+ align:start position:0%
+that's that's effectively right so um
+ 
+
+ align:start position:0%
+that's that's effectively right so um
+the way that the way that you can do it
+
+ align:start position:0%
+the way that the way that you can do it
+ 
+
+ align:start position:0%
+the way that the way that you can do it
+turns out to be a little bit again a
+
+ align:start position:0%
+turns out to be a little bit again a
+ 
+
+ align:start position:0%
+turns out to be a little bit again a
+little bit nice and magical okay so it
+
+ align:start position:0%
+little bit nice and magical okay so it
+ 
+
+ align:start position:0%
+little bit nice and magical okay so it
+turns out so so there's there's a couple
+
+ align:start position:0%
+turns out so so there's there's a couple
+ 
+
+ align:start position:0%
+turns out so so there's there's a couple
+ways to think about this one of them is
+
+ align:start position:0%
+ways to think about this one of them is
+ 
+
+ align:start position:0%
+ways to think about this one of them is
+um when I'm going through the Markov
+
+ align:start position:0%
+um when I'm going through the Markov
+ 
+
+ align:start position:0%
+um when I'm going through the Markov
+chain right every time I get here I'm
+
+ align:start position:0%
+chain right every time I get here I'm
+ 
+
+ align:start position:0%
+chain right every time I get here I'm
+going to think forward about I'm going
+
+ align:start position:0%
+going to think forward about I'm going
+ 
+
+ align:start position:0%
+going to think forward about I'm going
+to do a one-step prediction I'm going to
+
+ align:start position:0%
+to do a one-step prediction I'm going to
+ 
+
+ align:start position:0%
+to do a one-step prediction I'm going to
+do a two-step prediction I'm going to do
+
+ align:start position:0%
+do a two-step prediction I'm going to do
+ 
+
+ align:start position:0%
+do a two-step prediction I'm going to do
+a three-step pred prediction and what
+
+ align:start position:0%
+a three-step pred prediction and what
+ 
+
+ align:start position:0%
+a three-step pred prediction and what
+happens is that these eligibility traces
+
+ align:start position:0%
+happens is that these eligibility traces
+ 
+
+ align:start position:0%
+happens is that these eligibility traces
+are just this trick which makes all that
+
+ align:start position:0%
+are just this trick which makes all that
+ 
+
+ align:start position:0%
+are just this trick which makes all that
+work if I just remember where I've been
+
+ align:start position:0%
+work if I just remember where I've been
+ 
+
+ align:start position:0%
+work if I just remember where I've been
+then I can make an update which is the
+
+ align:start position:0%
+then I can make an update which is the
+ 
+
+ align:start position:0%
+then I can make an update which is the
+same as looking forward instead I'm
+
+ align:start position:0%
+same as looking forward instead I'm
+ 
+
+ align:start position:0%
+same as looking forward instead I'm
+looking back in time with my eligibility
+
+ align:start position:0%
+looking back in time with my eligibility
+ 
+
+ align:start position:0%
+looking back in time with my eligibility
+traces in the function approximator case
+
+ align:start position:0%
+traces in the function approximator case
+ 
+
+ align:start position:0%
+traces in the function approximator case
+doing exactly what you said turns out to
+
+ align:start position:0%
+doing exactly what you said turns out to
+ 
+
+ align:start position:0%
+doing exactly what you said turns out to
+be equivalent to remembering how
+
+ align:start position:0%
+be equivalent to remembering how
+ 
+
+ align:start position:0%
+be equivalent to remembering how
+important that parameter Alpha I was in
+
+ align:start position:0%
+important that parameter Alpha I was in
+ 
+
+ align:start position:0%
+important that parameter Alpha I was in
+your recent
+
+ align:start position:0%
+your recent
+ 
+
+ align:start position:0%
+your recent
+history
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay does that make
+
+ align:start position:0%
+okay does that make
+ 
+
+ align:start position:0%
+okay does that make
+sense if I remember how the the the
+
+ align:start position:0%
+sense if I remember how the the the
+ 
+
+ align:start position:0%
+sense if I remember how the the the
+contribution that Alpha made Alpha say
+
+ align:start position:0%
+contribution that Alpha made Alpha say
+ 
+
+ align:start position:0%
+contribution that Alpha made Alpha say
+one of the elements of alpha alpha alpha
+
+ align:start position:0%
+one of the elements of alpha alpha alpha
+ 
+
+ align:start position:0%
+one of the elements of alpha alpha alpha
+I Alpha J made in my recent
+
+ align:start position:0%
+I Alpha J made in my recent
+ 
+
+ align:start position:0%
+I Alpha J made in my recent
+history then I can update
+
+ align:start position:0%
+history then I can update
+ 
+
+ align:start position:0%
+history then I can update
+Alpha in the same sort of trick that
+
+ align:start position:0%
+Alpha in the same sort of trick that
+ 
+
+ align:start position:0%
+Alpha in the same sort of trick that
+this eligibility Trace worked on
+
+ align:start position:0%
+this eligibility Trace worked on
+ 
+
+ align:start position:0%
+this eligibility Trace worked on
+for you do some kind of decaying
+
+ align:start position:0%
+for you do some kind of decaying
+ 
+
+ align:start position:0%
+for you do some kind of decaying
+exponential yeah yeah that's kind of
+
+ align:start position:0%
+exponential yeah yeah that's kind of
+ 
+
+ align:start position:0%
+exponential yeah yeah that's kind of
+what it's doing there this is exactly
+
+ align:start position:0%
+what it's doing there this is exactly
+ 
+
+ align:start position:0%
+what it's doing there this is exactly
+what it's doing
+
+ align:start position:0%
+what it's doing
+ 
+
+ align:start position:0%
+what it's doing
+here in here we had the special case
+
+ align:start position:0%
+here in here we had the special case
+ 
+
+ align:start position:0%
+here in here we had the special case
+where when I visited the state I got a
+
+ align:start position:0%
+where when I visited the state I got a
+ 
+
+ align:start position:0%
+where when I visited the state I got a
+one when I didn't visit it I get here I
+
+ align:start position:0%
+one when I didn't visit it I get here I
+ 
+
+ align:start position:0%
+one when I didn't visit it I get here I
+got nothing and just decayed and what
+
+ align:start position:0%
+got nothing and just decayed and what
+ 
+
+ align:start position:0%
+got nothing and just decayed and what
+we're going to get now is an eligibility
+
+ align:start position:0%
+we're going to get now is an eligibility
+ 
+
+ align:start position:0%
+we're going to get now is an eligibility
+trace on
+
+ align:start position:0%
+trace on
+ 
+
+ align:start position:0%
+trace on
+Alpha do you have it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah excellent so the eligibility Trace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+changes
+
+ align:start position:0%
+changes
+ 
+
+ align:start position:0%
+changes
+Perfect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right gamma it's going to do a um a
+
+ align:start position:0%
+Right gamma it's going to do a um a
+ 
+
+ align:start position:0%
+Right gamma it's going to do a um a
+decaying exponential still right you
+
+ align:start position:0%
+decaying exponential still right you
+ 
+
+ align:start position:0%
+decaying exponential still right you
+want to forget things this thing is now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+right the the new eligibility Trace here
+
+ align:start position:0%
+right the the new eligibility Trace here
+ 
+
+ align:start position:0%
+right the the new eligibility Trace here
+is the same size as Alpha not the number
+
+ align:start position:0%
+is the same size as Alpha not the number
+ 
+
+ align:start position:0%
+is the same size as Alpha not the number
+of nodes in the
+
+ align:start position:0%
+of nodes in the
+ 
+
+ align:start position:0%
+of nodes in the
+system and the the amount that I'm going
+
+ align:start position:0%
+system and the the amount that I'm going
+ 
+
+ align:start position:0%
+system and the the amount that I'm going
+to credit each Alpha
+
+ align:start position:0%
+to credit each Alpha
+ 
+
+ align:start position:0%
+to credit each Alpha
+with is the gradient of my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+estimate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+does that sort of make sense yeah in the
+
+ align:start position:0%
+does that sort of make sense yeah in the
+ 
+
+ align:start position:0%
+does that sort of make sense yeah in the
+case of linear function
+
+ align:start position:0%
+case of linear function
+ 
+
+ align:start position:0%
+case of linear function
+approximators the gradient of
+
+ align:start position:0%
+approximators the gradient of
+ 
+
+ align:start position:0%
+approximators the gradient of
+this is just f of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x partial J partial Alpha just gets rid
+
+ align:start position:0%
+x partial J partial Alpha just gets rid
+ 
+
+ align:start position:0%
+x partial J partial Alpha just gets rid
+of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha okay so I remember the the
+
+ align:start position:0%
+Alpha okay so I remember the the
+ 
+
+ align:start position:0%
+Alpha okay so I remember the the
+relative contribution of each of my
+
+ align:start position:0%
+relative contribution of each of my
+ 
+
+ align:start position:0%
+relative contribution of each of my
+Alphas in the recent past and then based
+
+ align:start position:0%
+Alphas in the recent past and then based
+ 
+
+ align:start position:0%
+Alphas in the recent past and then based
+on this E I make the same update that I
+
+ align:start position:0%
+on this E I make the same update that I
+ 
+
+ align:start position:0%
+on this E I make the same update that I
+did before just copy this down but my
+
+ align:start position:0%
+did before just copy this down but my
+ 
+
+ align:start position:0%
+did before just copy this down but my
+e is now um the eligibility on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B which is what was that yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that um is an intuitively
+
+ align:start position:0%
+okay so that um is an intuitively
+ 
+
+ align:start position:0%
+okay so that um is an intuitively
+correct algorithm I think right so it
+
+ align:start position:0%
+correct algorithm I think right so it
+ 
+
+ align:start position:0%
+correct algorithm I think right so it
+seems pretty natural using the the sort
+
+ align:start position:0%
+seems pretty natural using the the sort
+ 
+
+ align:start position:0%
+seems pretty natural using the the sort
+of um eligibility argument that this
+
+ align:start position:0%
+of um eligibility argument that this
+ 
+
+ align:start position:0%
+of um eligibility argument that this
+could work proving that it works is
+
+ align:start position:0%
+could work proving that it works is
+ 
+
+ align:start position:0%
+could work proving that it works is
+turns out to be a pain it's not actually
+
+ align:start position:0%
+turns out to be a pain it's not actually
+ 
+
+ align:start position:0%
+turns out to be a pain it's not actually
+um an update like we would normally
+
+ align:start position:0%
+um an update like we would normally
+ 
+
+ align:start position:0%
+um an update like we would normally
+have um there's a special okay so so in
+
+ align:start position:0%
+have um there's a special okay so so in
+ 
+
+ align:start position:0%
+have um there's a special okay so so in
+one case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um when Lambda equal
+
+ align:start position:0%
+um when Lambda equal
+ 
+
+ align:start position:0%
+um when Lambda equal
+1 then you can actually
+
+ align:start position:0%
+1 then you can actually
+ 
+
+ align:start position:0%
+1 then you can actually
+show that this TD
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+update with linear function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximation um is doing gradient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ascent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the difference between my um J Lambda
+
+ align:start position:0%
+on the difference between my um J Lambda
+ 
+
+ align:start position:0%
+on the difference between my um J Lambda
+what I call J Lambda and
+
+ align:start position:0%
+what I call J Lambda and
+ 
+
+ align:start position:0%
+what I call J Lambda and
+my other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J
+
+ align:start position:0%
+J
+ 
+
+ align:start position:0%
+J
+squared okay so in the Lambda versus one
+
+ align:start position:0%
+squared okay so in the Lambda versus one
+ 
+
+ align:start position:0%
+squared okay so in the Lambda versus one
+case it actually is doing gradient
+
+ align:start position:0%
+case it actually is doing gradient
+ 
+
+ align:start position:0%
+case it actually is doing gradient
+descent on the um
+
+ align:start position:0%
+descent on the um
+ 
+
+ align:start position:0%
+descent on the um
+on the sort of the Monte Carlo error in
+
+ align:start position:0%
+on the sort of the Monte Carlo error in
+ 
+
+ align:start position:0%
+on the sort of the Monte Carlo error in
+every other setting of Lambda the
+
+ align:start position:0%
+every other setting of Lambda the
+ 
+
+ align:start position:0%
+every other setting of Lambda the
+algorithm is sort of not a standard
+
+ align:start position:0%
+algorithm is sort of not a standard
+ 
+
+ align:start position:0%
+algorithm is sort of not a standard
+optimization framework of going down in
+
+ align:start position:0%
+optimization framework of going down in
+ 
+
+ align:start position:0%
+optimization framework of going down in
+some steepest descent kind of approach
+
+ align:start position:0%
+some steepest descent kind of approach
+ 
+
+ align:start position:0%
+some steepest descent kind of approach
+but it tends in some cases it works
+
+ align:start position:0%
+but it tends in some cases it works
+ 
+
+ align:start position:0%
+but it tends in some cases it works
+faster because it uses previous
+
+ align:start position:0%
+faster because it uses previous
+ 
+
+ align:start position:0%
+faster because it uses previous
+information in a in a heris sort of way
+
+ align:start position:0%
+information in a in a heris sort of way
+ 
+
+ align:start position:0%
+information in a in a heris sort of way
+but it does it very effectively and
+
+ align:start position:0%
+but it does it very effectively and
+ 
+
+ align:start position:0%
+but it does it very effectively and
+people have done the work in fact the
+
+ align:start position:0%
+people have done the work in fact the
+ 
+
+ align:start position:0%
+people have done the work in fact the
+work was done upstairs by SAS and Van
+
+ align:start position:0%
+work was done upstairs by SAS and Van
+ 
+
+ align:start position:0%
+work was done upstairs by SAS and Van
+Roy in '97 or something like that this
+
+ align:start position:0%
+Roy in '97 or something like that this
+ 
+
+ align:start position:0%
+Roy in '97 or something like that this
+to prove that for all lambdas between 0
+
+ align:start position:0%
+to prove that for all lambdas between 0
+ 
+
+ align:start position:0%
+to prove that for all lambdas between 0
+and 1 and linear function
+
+ align:start position:0%
+and 1 and linear function
+ 
+
+ align:start position:0%
+and 1 and linear function
+approximators that this update will go
+
+ align:start position:0%
+approximators that this update will go
+ 
+
+ align:start position:0%
+approximators that this update will go
+to the True Value Estimate as your
+
+ align:start position:0%
+to the True Value Estimate as your
+ 
+
+ align:start position:0%
+to the True Value Estimate as your
+system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+runs
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um they
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+I guess different L would converge to
+
+ align:start position:0%
+I guess different L would converge to
+ 
+
+ align:start position:0%
+I guess different L would converge to
+different results and lals one only
+
+ align:start position:0%
+different results and lals one only
+ 
+
+ align:start position:0%
+different results and lals one only
+converges to the actual thing that
+
+ align:start position:0%
+converges to the actual thing that
+ 
+
+ align:start position:0%
+converges to the actual thing that
+you're looking for but as you start
+
+ align:start position:0%
+you're looking for but as you start
+ 
+
+ align:start position:0%
+you're looking for but as you start
+varrying L you conver to different
+
+ align:start position:0%
+varrying L you conver to different
+ 
+
+ align:start position:0%
+varrying L you conver to different
+things but it's still converging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mind that's possible
+
+ align:start position:0%
+mind that's possible
+ 
+
+ align:start position:0%
+mind that's possible
+but I I mean what's your value F correct
+
+ align:start position:0%
+but I I mean what's your value F correct
+ 
+
+ align:start position:0%
+but I I mean what's your value F correct
+doesn't the Lambda not matter anymore
+
+ align:start position:0%
+doesn't the Lambda not matter anymore
+ 
+
+ align:start position:0%
+doesn't the Lambda not matter anymore
+to the Future yeah the only stationary
+
+ align:start position:0%
+to the Future yeah the only stationary
+ 
+
+ align:start position:0%
+to the Future yeah the only stationary
+point should be the
+
+ align:start position:0%
+point should be the
+ 
+
+ align:start position:0%
+point should be the
+true um cost to go function so if it
+
+ align:start position:0%
+true um cost to go function so if it
+ 
+
+ align:start position:0%
+true um cost to go function so if it
+converges I'd be surprised if that's
+
+ align:start position:0%
+converges I'd be surprised if that's
+ 
+
+ align:start position:0%
+converges I'd be surprised if that's
+true he I mean Alor has done this stuff
+
+ align:start position:0%
+true he I mean Alor has done this stuff
+ 
+
+ align:start position:0%
+true he I mean Alor has done this stuff
+so you might know it better than I do
+
+ align:start position:0%
+so you might know it better than I do
+ 
+
+ align:start position:0%
+so you might know it better than I do
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+um I I was under the impression it
+
+ align:start position:0%
+um I I was under the impression it
+ 
+
+ align:start position:0%
+um I I was under the impression it
+converges to the True Value
+
+ align:start position:0%
+converges to the True Value
+ 
+
+ align:start position:0%
+converges to the True Value
+Estimate there's I mean there's a yeah
+
+ align:start position:0%
+Estimate there's I mean there's a yeah
+ 
+
+ align:start position:0%
+Estimate there's I mean there's a yeah
+it's all based on these contraction
+
+ align:start position:0%
+it's all based on these contraction
+ 
+
+ align:start position:0%
+it's all based on these contraction
+mappings right and I think the
+
+ align:start position:0%
+mappings right and I think the
+ 
+
+ align:start position:0%
+mappings right and I think the
+stationary point of the raction is the
+
+ align:start position:0%
+stationary point of the raction is the
+ 
+
+ align:start position:0%
+stationary point of the raction is the
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+value mhm if you find out differently
+
+ align:start position:0%
+value mhm if you find out differently
+ 
+
+ align:start position:0%
+value mhm if you find out differently
+then tell us next class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definitely
+
+ align:start position:0%
+definitely
+ 
+
+ align:start position:0%
+definitely
+okay so what just happened so um I made
+
+ align:start position:0%
+okay so what just happened so um I made
+ 
+
+ align:start position:0%
+okay so what just happened so um I made
+a trivial change to the algorithm in
+
+ align:start position:0%
+a trivial change to the algorithm in
+ 
+
+ align:start position:0%
+a trivial change to the algorithm in
+fact in some ways it looks almost easier
+
+ align:start position:0%
+fact in some ways it looks almost easier
+ 
+
+ align:start position:0%
+fact in some ways it looks almost easier
+um it's one less line uh and it now
+
+ align:start position:0%
+um it's one less line uh and it now
+ 
+
+ align:start position:0%
+um it's one less line uh and it now
+suddenly works with linear function
+
+ align:start position:0%
+suddenly works with linear function
+ 
+
+ align:start position:0%
+suddenly works with linear function
+approximators so I don't have to feel
+
+ align:start position:0%
+approximators so I don't have to feel
+ 
+
+ align:start position:0%
+approximators so I don't have to feel
+like I discretize my States space I can
+
+ align:start position:0%
+like I discretize my States space I can
+ 
+
+ align:start position:0%
+like I discretize my States space I can
+cover my state space with radial basis
+
+ align:start position:0%
+cover my state space with radial basis
+ 
+
+ align:start position:0%
+cover my state space with radial basis
+functions that might be as painful by
+
+ align:start position:0%
+functions that might be as painful by
+ 
+
+ align:start position:0%
+functions that might be as painful by
+the way as discretizing the state space
+
+ align:start position:0%
+the way as discretizing the state space
+ 
+
+ align:start position:0%
+the way as discretizing the state space
+if you have to put a lot of radial basis
+
+ align:start position:0%
+if you have to put a lot of radial basis
+ 
+
+ align:start position:0%
+if you have to put a lot of radial basis
+functions down but I could also do it
+
+ align:start position:0%
+functions down but I could also do it
+ 
+
+ align:start position:0%
+functions down but I could also do it
+with more complicated I could do it with
+
+ align:start position:0%
+with more complicated I could do it with
+ 
+
+ align:start position:0%
+with more complicated I could do it with
+pols I could do it with fora bases and
+
+ align:start position:0%
+pols I could do it with fora bases and
+ 
+
+ align:start position:0%
+pols I could do it with fora bases and
+and um potentially things that that work
+
+ align:start position:0%
+and um potentially things that that work
+ 
+
+ align:start position:0%
+and um potentially things that that work
+over with less basis functions over a
+
+ align:start position:0%
+over with less basis functions over a
+ 
+
+ align:start position:0%
+over with less basis functions over a
+very large domain and now suddenly the
+
+ align:start position:0%
+very large domain and now suddenly the
+ 
+
+ align:start position:0%
+very large domain and now suddenly the
+tools scale up to little bit higher
+
+ align:start position:0%
+tools scale up to little bit higher
+ 
+
+ align:start position:0%
+tools scale up to little bit higher
+dimensional systems as high as you can
+
+ align:start position:0%
+dimensional systems as high as you can
+ 
+
+ align:start position:0%
+dimensional systems as high as you can
+imagine as as creative as your basis set
+
+ align:start position:0%
+imagine as as creative as your basis set
+ 
+
+ align:start position:0%
+imagine as as creative as your basis set
+allows you to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be the complaint about these algorithms
+
+ align:start position:0%
+be the complaint about these algorithms
+ 
+
+ align:start position:0%
+be the complaint about these algorithms
+is that they're inefficient in their use
+
+ align:start position:0%
+is that they're inefficient in their use
+ 
+
+ align:start position:0%
+is that they're inefficient in their use
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data so if you think certainly in our
+
+ align:start position:0%
+data so if you think certainly in our
+ 
+
+ align:start position:0%
+data so if you think certainly in our
+when we're shooting
+
+ align:start position:0%
+when we're shooting
+ 
+
+ align:start position:0%
+when we're shooting
+planes uh and they break it's or if
+
+ align:start position:0%
+planes uh and they break it's or if
+ 
+
+ align:start position:0%
+planes uh and they break it's or if
+we're using a walking robot and you know
+
+ align:start position:0%
+we're using a walking robot and you know
+ 
+
+ align:start position:0%
+we're using a walking robot and you know
+it falls down a lot then every piece of
+
+ align:start position:0%
+it falls down a lot then every piece of
+ 
+
+ align:start position:0%
+it falls down a lot then every piece of
+data should be treated uh with reverence
+
+ align:start position:0%
+data should be treated uh with reverence
+ 
+
+ align:start position:0%
+data should be treated uh with reverence
+right this is hard-earned data um these
+
+ align:start position:0%
+right this is hard-earned data um these
+ 
+
+ align:start position:0%
+right this is hard-earned data um these
+algorithms as written like this
+
+ align:start position:0%
+algorithms as written like this
+ 
+
+ align:start position:0%
+algorithms as written like this
+basically every time they visit the data
+
+ align:start position:0%
+basically every time they visit the data
+ 
+
+ align:start position:0%
+basically every time they visit the data
+they make some small incremental
+
+ align:start position:0%
+they make some small incremental
+ 
+
+ align:start position:0%
+they make some small incremental
+update right and then throw it away and
+
+ align:start position:0%
+update right and then throw it away and
+ 
+
+ align:start position:0%
+update right and then throw it away and
+keep moving and so by no means are they
+
+ align:start position:0%
+keep moving and so by no means are they
+ 
+
+ align:start position:0%
+keep moving and so by no means are they
+efficient in data they are efficient
+
+ align:start position:0%
+efficient in data they are efficient
+ 
+
+ align:start position:0%
+efficient in data they are efficient
+only in the sense that they they use
+
+ align:start position:0%
+only in the sense that they they use
+ 
+
+ align:start position:0%
+only in the sense that they they use
+previous estimates of J
+
+ align:start position:0%
+previous estimates of J
+ 
+
+ align:start position:0%
+previous estimates of J
+hat um to bootstrap but they
+
+ align:start position:0%
+hat um to bootstrap but they
+ 
+
+ align:start position:0%
+hat um to bootstrap but they
+you know there's no sense of memory
+
+ align:start position:0%
+you know there's no sense of memory
+ 
+
+ align:start position:0%
+you know there's no sense of memory
+remembering all your data and reusing it
+
+ align:start position:0%
+remembering all your data and reusing it
+ 
+
+ align:start position:0%
+remembering all your data and reusing it
+so some people have thought about uh
+
+ align:start position:0%
+so some people have thought about uh
+ 
+
+ align:start position:0%
+so some people have thought about uh
+replaying trajectories so if you store
+
+ align:start position:0%
+replaying trajectories so if you store
+ 
+
+ align:start position:0%
+replaying trajectories so if you store
+all your trajectories let's say let's
+
+ align:start position:0%
+all your trajectories let's say let's
+ 
+
+ align:start position:0%
+all your trajectories let's say let's
+say I ran my my plane 10 times well I'll
+
+ align:start position:0%
+say I ran my my plane 10 times well I'll
+ 
+
+ align:start position:0%
+say I ran my my plane 10 times well I'll
+remember all that data and I'll just run
+
+ align:start position:0%
+remember all that data and I'll just run
+ 
+
+ align:start position:0%
+remember all that data and I'll just run
+the TD update over and over again over
+
+ align:start position:0%
+the TD update over and over again over
+ 
+
+ align:start position:0%
+the TD update over and over again over
+those same 10
+
+ align:start position:0%
+those same 10
+ 
+
+ align:start position:0%
+those same 10
+trajectories that's a reasonable thing
+
+ align:start position:0%
+trajectories that's a reasonable thing
+ 
+
+ align:start position:0%
+trajectories that's a reasonable thing
+to do but again with linear function
+
+ align:start position:0%
+to do but again with linear function
+ 
+
+ align:start position:0%
+to do but again with linear function
+approximators you can do better right
+
+ align:start position:0%
+approximators you can do better right
+ 
+
+ align:start position:0%
+approximators you can do better right
+you can do lstd least squares temporal
+
+ align:start position:0%
+you can do lstd least squares temporal
+ 
+
+ align:start position:0%
+you can do lstd least squares temporal
+difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+learning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is least squares temporal
+
+ align:start position:0%
+this is least squares temporal
+ 
+
+ align:start position:0%
+this is least squares temporal
+difference learning yeah I get
+
+ align:start position:0%
+difference learning yeah I get
+ 
+
+ align:start position:0%
+difference learning yeah I get
+it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a basic the argument basically goes
+
+ align:start position:0%
+and a basic the argument basically goes
+ 
+
+ align:start position:0%
+and a basic the argument basically goes
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so in in um in learning there's
+
+ align:start position:0%
+this so in in um in learning there's
+ 
+
+ align:start position:0%
+this so in in um in learning there's
+always a difference they people like to
+
+ align:start position:0%
+always a difference they people like to
+ 
+
+ align:start position:0%
+always a difference they people like to
+distinguish between online versus batch
+
+ align:start position:0%
+distinguish between online versus batch
+ 
+
+ align:start position:0%
+distinguish between online versus batch
+updates so the online this is an onlight
+
+ align:start position:0%
+updates so the online this is an onlight
+ 
+
+ align:start position:0%
+updates so the online this is an onlight
+update I took my piece of data in I
+
+ align:start position:0%
+update I took my piece of data in I
+ 
+
+ align:start position:0%
+update I took my piece of data in I
+immediately changed Alpha and then I
+
+ align:start position:0%
+immediately changed Alpha and then I
+ 
+
+ align:start position:0%
+immediately changed Alpha and then I
+spat it out right um You can imagine a
+
+ align:start position:0%
+spat it out right um You can imagine a
+ 
+
+ align:start position:0%
+spat it out right um You can imagine a
+batch update which collected a bunch of
+
+ align:start position:0%
+batch update which collected a bunch of
+ 
+
+ align:start position:0%
+batch update which collected a bunch of
+these trajectories let's say ran a whole
+
+ align:start position:0%
+these trajectories let's say ran a whole
+ 
+
+ align:start position:0%
+these trajectories let's say ran a whole
+trajectory with the plane stop now
+
+ align:start position:0%
+trajectory with the plane stop now
+ 
+
+ align:start position:0%
+trajectory with the plane stop now
+process that trajectory make us make a
+
+ align:start position:0%
+process that trajectory make us make a
+ 
+
+ align:start position:0%
+process that trajectory make us make a
+change in Alpha and then repeat so
+
+ align:start position:0%
+change in Alpha and then repeat so
+ 
+
+ align:start position:0%
+change in Alpha and then repeat so
+instead of doing it at every single time
+
+ align:start position:0%
+instead of doing it at every single time
+ 
+
+ align:start position:0%
+instead of doing it at every single time
+step let's clect a little bit of data
+
+ align:start position:0%
+step let's clect a little bit of data
+ 
+
+ align:start position:0%
+step let's clect a little bit of data
+and then make an update okay so let's
+
+ align:start position:0%
+and then make an update okay so let's
+ 
+
+ align:start position:0%
+and then make an update okay so let's
+just write down what a batch update
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um the batch update
+
+ align:start position:0%
+um the batch update
+ 
+
+ align:start position:0%
+um the batch update
+um for for this system if I ran a
+
+ align:start position:0%
+um for for this system if I ran a
+ 
+
+ align:start position:0%
+um for for this system if I ran a
+trajectory and then made an update
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that update would look like this just
+
+ align:start position:0%
+um that update would look like this just
+ 
+
+ align:start position:0%
+um that update would look like this just
+by applying that rule a bunch of times
+
+ align:start position:0%
+by applying that rule a bunch of times
+ 
+
+ align:start position:0%
+by applying that rule a bunch of times
+but without changing Alpha in between
+
+ align:start position:0%
+but without changing Alpha in between
+ 
+
+ align:start position:0%
+but without changing Alpha in between
+right so I'm going to I'm another way to
+
+ align:start position:0%
+right so I'm going to I'm another way to
+ 
+
+ align:start position:0%
+right so I'm going to I'm another way to
+say it is I'm going to
+
+ align:start position:0%
+say it is I'm going to
+ 
+
+ align:start position:0%
+say it is I'm going to
+I'm going to hold Alpha fixed collect up
+
+ align:start position:0%
+I'm going to hold Alpha fixed collect up
+ 
+
+ align:start position:0%
+I'm going to hold Alpha fixed collect up
+all the changes I want to make at Alpha
+
+ align:start position:0%
+all the changes I want to make at Alpha
+ 
+
+ align:start position:0%
+all the changes I want to make at Alpha
+and then at the end of The Run make one
+
+ align:start position:0%
+and then at the end of The Run make one
+ 
+
+ align:start position:0%
+and then at the end of The Run make one
+change to Alpha okay um well then that
+
+ align:start position:0%
+change to Alpha okay um well then that
+ 
+
+ align:start position:0%
+change to Alpha okay um well then that
+change if you do it in this in the batch
+
+ align:start position:0%
+change if you do it in this in the batch
+ 
+
+ align:start position:0%
+change if you do it in this in the batch
+mode is U just going to be a sum of all
+
+ align:start position:0%
+mode is U just going to be a sum of all
+ 
+
+ align:start position:0%
+mode is U just going to be a sum of all
+these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guys that's a scaler times a vector so I
+
+ align:start position:0%
+guys that's a scaler times a vector so I
+ 
+
+ align:start position:0%
+guys that's a scaler times a vector so I
+can reord reorder it without any pain
+
+ align:start position:0%
+can reord reorder it without any pain
+ 
+
+ align:start position:0%
+can reord reorder it without any pain
+oops I got to put that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inside right the intermediate step
+
+ align:start position:0%
+inside right the intermediate step
+ 
+
+ align:start position:0%
+inside right the intermediate step
+here J Alpha i k + 1 minus
+
+ align:start position:0%
+here J Alpha i k + 1 minus
+ 
+
+ align:start position:0%
+here J Alpha i k + 1 minus
+J
+
+ align:start position:0%
+J
+ 
+
+ align:start position:0%
+J
+Alpha ik
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K you agree with that that's the batch
+
+ align:start position:0%
+K you agree with that that's the batch
+ 
+
+ align:start position:0%
+K you agree with that that's the batch
+update of
+
+ align:start position:0%
+update of
+ 
+
+ align:start position:0%
+update of
+that I just collect them all up I sum
+
+ align:start position:0%
+that I just collect them all up I sum
+ 
+
+ align:start position:0%
+that I just collect them all up I sum
+them over K here my all my time steps
+
+ align:start position:0%
+them over K here my all my time steps
+ 
+
+ align:start position:0%
+them over K here my all my time steps
+that's what my update's going to look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I write this a little bit if I break
+
+ align:start position:0%
+if I write this a little bit if I break
+ 
+
+ align:start position:0%
+if I write this a little bit if I break
+into this
+
+ align:start position:0%
+into this
+ 
+
+ align:start position:0%
+into this
+um my my function approximator there I
+
+ align:start position:0%
+um my my function approximator there I
+ 
+
+ align:start position:0%
+um my my function approximator there I
+can write it like this jump over
+
+ align:start position:0%
+can write it like this jump over
+ 
+
+ align:start position:0%
+can write it like this jump over
+K oh boy I forgot my EK over
+
+ align:start position:0%
+K oh boy I forgot my EK over
+ 
+
+ align:start position:0%
+K oh boy I forgot my EK over
+here sorry about that there's an EK
+
+ align:start position:0%
+here sorry about that there's an EK
+ 
+
+ align:start position:0%
+here sorry about that there's an EK
+there too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right J is just f * Alpha so I'm going
+
+ align:start position:0%
+right J is just f * Alpha so I'm going
+ 
+
+ align:start position:0%
+right J is just f * Alpha so I'm going
+to break into
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that if I collect those
+
+ align:start position:0%
+that if I collect those
+ 
+
+ align:start position:0%
+that if I collect those
+terms then I
+
+ align:start position:0%
+terms then I
+ 
+
+ align:start position:0%
+terms then I
+get something we can think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha where this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is B and this guy
+
+ align:start position:0%
+is B and this guy
+ 
+
+ align:start position:0%
+is B and this guy
+here is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a in other words the long-term behavior
+
+ align:start position:0%
+a in other words the long-term behavior
+ 
+
+ align:start position:0%
+a in other words the long-term behavior
+of the system if I if I if I collect the
+
+ align:start position:0%
+of the system if I if I if I collect the
+ 
+
+ align:start position:0%
+of the system if I if I if I collect the
+updates and then make them like
+
+ align:start position:0%
+updates and then make them like
+ 
+
+ align:start position:0%
+updates and then make them like
+this well this looks like a low pass
+
+ align:start position:0%
+this well this looks like a low pass
+ 
+
+ align:start position:0%
+this well this looks like a low pass
+filter really that's going to this
+
+ align:start position:0%
+filter really that's going to this
+ 
+
+ align:start position:0%
+filter really that's going to this
+solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's in the steady
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state is uh Alpha equal a inverse B
+
+ align:start position:0%
+state is uh Alpha equal a inverse B
+ 
+
+ align:start position:0%
+state is uh Alpha equal a inverse B
+where you do that inverse carefully SVD
+
+ align:start position:0%
+where you do that inverse carefully SVD
+ 
+
+ align:start position:0%
+where you do that inverse carefully SVD
+or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that observation led to this
+
+ align:start position:0%
+okay so that observation led to this
+ 
+
+ align:start position:0%
+okay so that observation led to this
+least squares temporal difference
+
+ align:start position:0%
+least squares temporal difference
+ 
+
+ align:start position:0%
+least squares temporal difference
+learning algorithm which said instead of
+
+ align:start position:0%
+learning algorithm which said instead of
+ 
+
+ align:start position:0%
+learning algorithm which said instead of
+chewing up every piece of every data
+
+ align:start position:0%
+chewing up every piece of every data
+ 
+
+ align:start position:0%
+chewing up every piece of every data
+point and spitting it out remember
+
+ align:start position:0%
+point and spitting it out remember
+ 
+
+ align:start position:0%
+point and spitting it out remember
+everything that you have experienced in
+
+ align:start position:0%
+everything that you have experienced in
+ 
+
+ align:start position:0%
+everything that you have experienced in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+past and do go instead of doing this
+
+ align:start position:0%
+past and do go instead of doing this
+ 
+
+ align:start position:0%
+past and do go instead of doing this
+sort of incremental step that goes
+
+ align:start position:0%
+sort of incremental step that goes
+ 
+
+ align:start position:0%
+sort of incremental step that goes
+Epsilon towards the steady state you can
+
+ align:start position:0%
+Epsilon towards the steady state you can
+ 
+
+ align:start position:0%
+Epsilon towards the steady state you can
+solve for that steady state every time
+
+ align:start position:0%
+solve for that steady state every time
+ 
+
+ align:start position:0%
+solve for that steady state every time
+you have if you've collect b and a you
+
+ align:start position:0%
+you have if you've collect b and a you
+ 
+
+ align:start position:0%
+you have if you've collect b and a you
+can just collect that with a bunch of
+
+ align:start position:0%
+can just collect that with a bunch of
+ 
+
+ align:start position:0%
+can just collect that with a bunch of
+data go ahead and jump right to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution so
+
+ align:start position:0%
+solution so
+ 
+
+ align:start position:0%
+solution so
+lstd which I think a lot of people would
+
+ align:start position:0%
+lstd which I think a lot of people would
+ 
+
+ align:start position:0%
+lstd which I think a lot of people would
+consider the state-of-the-art in in if
+
+ align:start position:0%
+consider the state-of-the-art in in if
+ 
+
+ align:start position:0%
+consider the state-of-the-art in in if
+you just want to do policy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evaluation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+build up b and a as you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+run compute Alpha is a inverse B
+
+ align:start position:0%
+run compute Alpha is a inverse B
+ 
+
+ align:start position:0%
+run compute Alpha is a inverse B
+whenever you need a new estimate of
+
+ align:start position:0%
+whenever you need a new estimate of
+ 
+
+ align:start position:0%
+whenever you need a new estimate of
+alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay why do you want to do
+
+ align:start position:0%
+okay why do you want to do
+ 
+
+ align:start position:0%
+okay why do you want to do
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's more efficient with your data you
+
+ align:start position:0%
+it's more efficient with your data you
+ 
+
+ align:start position:0%
+it's more efficient with your data you
+remember and replay Your Bass your last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data
+
+ align:start position:0%
+data
+ 
+
+ align:start position:0%
+data
+seamlessly you don't have to guess some
+
+ align:start position:0%
+seamlessly you don't have to guess some
+ 
+
+ align:start position:0%
+seamlessly you don't have to guess some
+silly learning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate and it doesn't even depend on your
+
+ align:start position:0%
+rate and it doesn't even depend on your
+ 
+
+ align:start position:0%
+rate and it doesn't even depend on your
+initial conditions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anymore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your initial guess at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alpha okay so if I went to go and do if
+
+ align:start position:0%
+Alpha okay so if I went to go and do if
+ 
+
+ align:start position:0%
+Alpha okay so if I went to go and do if
+I if I were were given a um a robot
+
+ align:start position:0%
+I if I were were given a um a robot
+ 
+
+ align:start position:0%
+I if I were were given a um a robot
+that's currently performing some
+
+ align:start position:0%
+that's currently performing some
+ 
+
+ align:start position:0%
+that's currently performing some
+feedback
+
+ align:start position:0%
+feedback
+ 
+
+ align:start position:0%
+feedback
+controller let's say it's stochastic
+
+ align:start position:0%
+controller let's say it's stochastic
+ 
+
+ align:start position:0%
+controller let's say it's stochastic
+it's um stochastic system there's noise
+
+ align:start position:0%
+it's um stochastic system there's noise
+ 
+
+ align:start position:0%
+it's um stochastic system there's noise
+and everything like that and I wanted to
+
+ align:start position:0%
+and everything like that and I wanted to
+ 
+
+ align:start position:0%
+and everything like that and I wanted to
+just evaluate how well it performed on
+
+ align:start position:0%
+just evaluate how well it performed on
+ 
+
+ align:start position:0%
+just evaluate how well it performed on
+this cost function some cost function
+
+ align:start position:0%
+this cost function some cost function
+ 
+
+ align:start position:0%
+this cost function some cost function
+that someone gave me if you know Harry S
+
+ align:start position:0%
+that someone gave me if you know Harry S
+ 
+
+ align:start position:0%
+that someone gave me if you know Harry S
+say I got this robot I've got I wanted
+
+ align:start position:0%
+say I got this robot I've got I wanted
+ 
+
+ align:start position:0%
+say I got this robot I've got I wanted
+it to optimize this cost function how's
+
+ align:start position:0%
+it to optimize this cost function how's
+ 
+
+ align:start position:0%
+it to optimize this cost function how's
+it doing tell me how it's doing I would
+
+ align:start position:0%
+it doing tell me how it's doing I would
+ 
+
+ align:start position:0%
+it doing tell me how it's doing I would
+look at that um um I look at the state
+
+ align:start position:0%
+look at that um um I look at the state
+ 
+
+ align:start position:0%
+look at that um um I look at the state
+space I'd try to come up with a linear
+
+ align:start position:0%
+space I'd try to come up with a linear
+ 
+
+ align:start position:0%
+space I'd try to come up with a linear
+tiling of Bas of radial basis functions
+
+ align:start position:0%
+tiling of Bas of radial basis functions
+ 
+
+ align:start position:0%
+tiling of Bas of radial basis functions
+or some linear function approximator
+
+ align:start position:0%
+or some linear function approximator
+ 
+
+ align:start position:0%
+or some linear function approximator
+over that state space and I'd start
+
+ align:start position:0%
+over that state space and I'd start
+ 
+
+ align:start position:0%
+over that state space and I'd start
+running trials and I'd keep those
+
+ align:start position:0%
+running trials and I'd keep those
+ 
+
+ align:start position:0%
+running trials and I'd keep those
+trials and store
+
+ align:start position:0%
+trials and store
+ 
+
+ align:start position:0%
+trials and store
+up these matrices and do a least squares
+
+ align:start position:0%
+up these matrices and do a least squares
+ 
+
+ align:start position:0%
+up these matrices and do a least squares
+teal difference update and that this
+
+ align:start position:0%
+teal difference update and that this
+ 
+
+ align:start position:0%
+teal difference update and that this
+result basically tells me that it's
+
+ align:start position:0%
+result basically tells me that it's
+ 
+
+ align:start position:0%
+result basically tells me that it's
+going to do the same thing as the
+
+ align:start position:0%
+going to do the same thing as the
+ 
+
+ align:start position:0%
+going to do the same thing as the
+TD it's going to do it potentially more
+
+ align:start position:0%
+TD it's going to do it potentially more
+ 
+
+ align:start position:0%
+TD it's going to do it potentially more
+effectively because it's more efficient
+
+ align:start position:0%
+effectively because it's more efficient
+ 
+
+ align:start position:0%
+effectively because it's more efficient
+with data and it's going to do it
+
+ align:start position:0%
+with data and it's going to do it
+ 
+
+ align:start position:0%
+with data and it's going to do it
+without having to guess without having
+
+ align:start position:0%
+without having to guess without having
+ 
+
+ align:start position:0%
+without having to guess without having
+to guess initial um vector or having
+
+ align:start position:0%
+to guess initial um vector or having
+ 
+
+ align:start position:0%
+to guess initial um vector or having
+some learning rate do do you actually
+
+ align:start position:0%
+some learning rate do do you actually
+ 
+
+ align:start position:0%
+some learning rate do do you actually
+have to define the length of an episode
+
+ align:start position:0%
+have to define the length of an episode
+ 
+
+ align:start position:0%
+have to define the length of an episode
+for example if it's a periodic system
+
+ align:start position:0%
+for example if it's a periodic system
+ 
+
+ align:start position:0%
+for example if it's a periodic system
+like a walking system how do you
+
+ align:start position:0%
+like a walking system how do you
+ 
+
+ align:start position:0%
+like a walking system how do you
+DET so
+
+ align:start position:0%
+DET so
+ 
+
+ align:start position:0%
+DET so
+um that's really good so um so Al bores
+
+ align:start position:0%
+um that's really good so um so Al bores
+ 
+
+ align:start position:0%
+um that's really good so um so Al bores
+here has actually written a paper on
+
+ align:start position:0%
+here has actually written a paper on
+ 
+
+ align:start position:0%
+here has actually written a paper on
+incremental
+
+ align:start position:0%
+incremental
+ 
+
+ align:start position:0%
+incremental
+lstd so you might you might think that
+
+ align:start position:0%
+lstd so you might you might think that
+ 
+
+ align:start position:0%
+lstd so you might you might think that
+doing that update is um is expensive and
+
+ align:start position:0%
+doing that update is um is expensive and
+ 
+
+ align:start position:0%
+doing that update is um is expensive and
+it can be if you just naively do that
+
+ align:start position:0%
+it can be if you just naively do that
+ 
+
+ align:start position:0%
+it can be if you just naively do that
+but you can do recursively squares and
+
+ align:start position:0%
+but you can do recursively squares and
+ 
+
+ align:start position:0%
+but you can do recursively squares and
+you can sort of make a a cheaper online
+
+ align:start position:0%
+you can sort of make a a cheaper online
+ 
+
+ align:start position:0%
+you can sort of make a a cheaper online
+update to try to do this to make this a
+
+ align:start position:0%
+update to try to do this to make this a
+ 
+
+ align:start position:0%
+update to try to do this to make this a
+constant update of alpha if you choose
+
+ align:start position:0%
+constant update of alpha if you choose
+ 
+
+ align:start position:0%
+constant update of alpha if you choose
+to update Alpha on every step which you
+
+ align:start position:0%
+to update Alpha on every step which you
+ 
+
+ align:start position:0%
+to update Alpha on every step which you
+could choose to do and maybe you would
+
+ align:start position:0%
+could choose to do and maybe you would
+ 
+
+ align:start position:0%
+could choose to do and maybe you would
+choose to do in a non-episodic task or
+
+ align:start position:0%
+choose to do in a non-episodic task or
+ 
+
+ align:start position:0%
+choose to do in a non-episodic task or
+maybe in Walking you do it once per step
+
+ align:start position:0%
+maybe in Walking you do it once per step
+ 
+
+ align:start position:0%
+maybe in Walking you do it once per step
+or whatever then you can do it nicely
+
+ align:start position:0%
+or whatever then you can do it nicely
+ 
+
+ align:start position:0%
+or whatever then you can do it nicely
+with an incremental lstd and you can
+
+ align:start position:0%
+with an incremental lstd and you can
+ 
+
+ align:start position:0%
+with an incremental lstd and you can
+look at elor's paper to figure out how
+
+ align:start position:0%
+look at elor's paper to figure out how
+ 
+
+ align:start position:0%
+look at elor's paper to figure out how
+to do that which is an approximation of
+
+ align:start position:0%
+to do that which is an approximation of
+ 
+
+ align:start position:0%
+to do that which is an approximation of
+the true lstd but a pretty good one in
+
+ align:start position:0%
+the true lstd but a pretty good one in
+ 
+
+ align:start position:0%
+the true lstd but a pretty good one in
+your experiments right and much more
+
+ align:start position:0%
+your experiments right and much more
+ 
+
+ align:start position:0%
+your experiments right and much more
+efficient right
+
+ align:start position:0%
+efficient right
+ 
+
+ align:start position:0%
+efficient right
+um yeah or or there's a lot of I mean I
+
+ align:start position:0%
+um yeah or or there's a lot of I mean I
+ 
+
+ align:start position:0%
+um yeah or or there's a lot of I mean I
+think in Walking it turns out I would do
+
+ align:start position:0%
+think in Walking it turns out I would do
+ 
+
+ align:start position:0%
+think in Walking it turns out I would do
+it probably once per step or something
+
+ align:start position:0%
+it probably once per step or something
+ 
+
+ align:start position:0%
+it probably once per step or something
+there's natural
+
+ align:start position:0%
+there's natural
+ 
+
+ align:start position:0%
+there's natural
+discretizations but there's nothing to
+
+ align:start position:0%
+discretizations but there's nothing to
+ 
+
+ align:start position:0%
+discretizations but there's nothing to
+say if you have the computational
+
+ align:start position:0%
+say if you have the computational
+ 
+
+ align:start position:0%
+say if you have the computational
+horsepower you couldn't just do this
+
+ align:start position:0%
+horsepower you couldn't just do this
+ 
+
+ align:start position:0%
+horsepower you couldn't just do this
+every step
+
+ align:start position:0%
+every step
+ 
+
+ align:start position:0%
+every step
+too it's just more expensive than doing
+
+ align:start position:0%
+too it's just more expensive than doing
+ 
+
+ align:start position:0%
+too it's just more expensive than doing
+an incremental
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+version okay so function approximation
+
+ align:start position:0%
+version okay so function approximation
+ 
+
+ align:start position:0%
+version okay so function approximation
+is very powerful this is what's going to
+
+ align:start position:0%
+is very powerful this is what's going to
+ 
+
+ align:start position:0%
+is very powerful this is what's going to
+take our tabular based ideas and their
+
+ align:start position:0%
+take our tabular based ideas and their
+ 
+
+ align:start position:0%
+take our tabular based ideas and their
+Markoff chain ideas and make them scale
+
+ align:start position:0%
+Markoff chain ideas and make them scale
+ 
+
+ align:start position:0%
+Markoff chain ideas and make them scale
+to the the real world this is the first
+
+ align:start position:0%
+to the the real world this is the first
+ 
+
+ align:start position:0%
+to the the real world this is the first
+year I tried to I did function
+
+ align:start position:0%
+year I tried to I did function
+ 
+
+ align:start position:0%
+year I tried to I did function
+approximation first in the temporal
+
+ align:start position:0%
+approximation first in the temporal
+ 
+
+ align:start position:0%
+approximation first in the temporal
+difference learning case but of course
+
+ align:start position:0%
+difference learning case but of course
+ 
+
+ align:start position:0%
+difference learning case but of course
+it's relevant for the policy gradient
+
+ align:start position:0%
+it's relevant for the policy gradient
+ 
+
+ align:start position:0%
+it's relevant for the policy gradient
+world too right
+
+ align:start position:0%
+world too right
+ 
+
+ align:start position:0%
+world too right
+John showed you different function
+
+ align:start position:0%
+John showed you different function
+ 
+
+ align:start position:0%
+John showed you different function
+approximators that was were doing
+
+ align:start position:0%
+approximators that was were doing
+ 
+
+ align:start position:0%
+approximators that was were doing
+reinforce um if instead of
+
+ align:start position:0%
+reinforce um if instead of
+ 
+
+ align:start position:0%
+reinforce um if instead of
+parameterizing my value function as a
+
+ align:start position:0%
+parameterizing my value function as a
+ 
+
+ align:start position:0%
+parameterizing my value function as a
+function approximator I could have also
+
+ align:start position:0%
+function approximator I could have also
+ 
+
+ align:start position:0%
+function approximator I could have also
+just directly parameterized my feedback
+
+ align:start position:0%
+just directly parameterized my feedback
+ 
+
+ align:start position:0%
+just directly parameterized my feedback
+controller as a value function and done
+
+ align:start position:0%
+controller as a value function and done
+ 
+
+ align:start position:0%
+controller as a value function and done
+gradient descent if I had a model or
+
+ align:start position:0%
+gradient descent if I had a model or
+ 
+
+ align:start position:0%
+gradient descent if I had a model or
+reinforce if I didn't have a model
+
+ align:start position:0%
+reinforce if I didn't have a model
+ 
+
+ align:start position:0%
+reinforce if I didn't have a model
+OKAY function approximation is supposed
+
+ align:start position:0%
+OKAY function approximation is supposed
+ 
+
+ align:start position:0%
+OKAY function approximation is supposed
+to be the savior of reinforcement
+
+ align:start position:0%
+to be the savior of reinforcement
+ 
+
+ align:start position:0%
+to be the savior of reinforcement
+learning the problem is there's limited
+
+ align:start position:0%
+learning the problem is there's limited
+ 
+
+ align:start position:0%
+learning the problem is there's limited
+results I mean the linear function
+
+ align:start position:0%
+results I mean the linear function
+ 
+
+ align:start position:0%
+results I mean the linear function
+approximation is really only the case we
+
+ align:start position:0%
+approximation is really only the case we
+ 
+
+ align:start position:0%
+approximation is really only the case we
+have strong results for most of these
+
+ align:start position:0%
+have strong results for most of these
+ 
+
+ align:start position:0%
+have strong results for most of these
+cases so um so I'm going to talk about
+
+ align:start position:0%
+cases so um so I'm going to talk about
+ 
+
+ align:start position:0%
+cases so um so I'm going to talk about
+doing the policy stuff with function
+
+ align:start position:0%
+doing the policy stuff with function
+ 
+
+ align:start position:0%
+doing the policy stuff with function
+approximation on Thursday and then it
+
+ align:start position:0%
+approximation on Thursday and then it
+ 
+
+ align:start position:0%
+approximation on Thursday and then it
+culminates in actor critic where you do
+
+ align:start position:0%
+culminates in actor critic where you do
+ 
+
+ align:start position:0%
+culminates in actor critic where you do
+both function approximation in the in
+
+ align:start position:0%
+both function approximation in the in
+ 
+
+ align:start position:0%
+both function approximation in the in
+the policy and the value function
+
+ align:start position:0%
+the policy and the value function
+ 
+
+ align:start position:0%
+the policy and the value function
+simultaneously and that'll happen
+
+ align:start position:0%
+simultaneously and that'll happen
+ 
+
+ align:start position:0%
+simultaneously and that'll happen
+sometime next
+
+ align:start position:0%
+sometime next
+ 
+
+ align:start position:0%
+sometime next
+week excellent I'll see you next week
\ No newline at end of file
diff --git a/kLqduWF6GXE.txt b/kLqduWF6GXE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f63689148edae253561a46864084dbe39b59dba1
--- /dev/null
+++ b/kLqduWF6GXE.txt
@@ -0,0 +1,8515 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu thermodynamics all right
+
+ align:start position:0%
+ocw.mit.edu thermodynamics all right
+ 
+
+ align:start position:0%
+ocw.mit.edu thermodynamics all right
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+start
+
+ align:start position:0%
+start
+ 
+
+ align:start position:0%
+start
+thermodynamics is the science
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of the flow of heat so Thermo is
+
+ align:start position:0%
+of the flow of heat so Thermo is
+ 
+
+ align:start position:0%
+of the flow of heat so Thermo is
+heat and Dynamics is the motion
+
+ align:start position:0%
+heat and Dynamics is the motion
+ 
+
+ align:start position:0%
+heat and Dynamics is the motion
+of thermodynamics was
+
+ align:start position:0%
+of thermodynamics was
+ 
+
+ align:start position:0%
+of thermodynamics was
+developed uh largely beginning in the
+
+ align:start position:0%
+developed uh largely beginning in the
+ 
+
+ align:start position:0%
+developed uh largely beginning in the
+1800s at the time of the Industrial
+
+ align:start position:0%
+1800s at the time of the Industrial
+ 
+
+ align:start position:0%
+1800s at the time of the Industrial
+Revolution it's a Taming of the of Steel
+
+ align:start position:0%
+Revolution it's a Taming of the of Steel
+ 
+
+ align:start position:0%
+Revolution it's a Taming of the of Steel
+the beginning of
+
+ align:start position:0%
+the beginning of
+ 
+
+ align:start position:0%
+the beginning of
+generating uh Power by burning fossil
+
+ align:start position:0%
+generating uh Power by burning fossil
+ 
+
+ align:start position:0%
+generating uh Power by burning fossil
+fuels uh the beginning of the problems
+
+ align:start position:0%
+fuels uh the beginning of the problems
+ 
+
+ align:start position:0%
+fuels uh the beginning of the problems
+with CO2 in the atmosphere global
+
+ align:start position:0%
+with CO2 in the atmosphere global
+ 
+
+ align:start position:0%
+with CO2 in the atmosphere global
+warming in fact it's interesting to note
+
+ align:start position:0%
+warming in fact it's interesting to note
+ 
+
+ align:start position:0%
+warming in fact it's interesting to note
+that the first
+
+ align:start position:0%
+that the first
+ 
+
+ align:start position:0%
+that the first
+calculation on um the impact of
+
+ align:start position:0%
+calculation on um the impact of
+ 
+
+ align:start position:0%
+calculation on um the impact of
+CO2 on climate was done in the late
+
+ align:start position:0%
+CO2 on climate was done in the late
+ 
+
+ align:start position:0%
+CO2 on climate was done in the late
+1800s by
+
+ align:start position:0%
+1800s by
+ 
+
+ align:start position:0%
+1800s by
+arenus beginning of
+
+ align:start position:0%
+arenus beginning of
+ 
+
+ align:start position:0%
+arenus beginning of
+the generation of power moving heat from
+
+ align:start position:0%
+the generation of power moving heat from
+ 
+
+ align:start position:0%
+the generation of power moving heat from
+fossil fuels to generating energy
+
+ align:start position:0%
+fossil fuels to generating energy
+ 
+
+ align:start position:0%
+fossil fuels to generating energy
+locomotives Etc
+
+ align:start position:0%
+locomotives Etc
+ 
+
+ align:start position:0%
+locomotives Etc
+so he calculated what would happen to
+
+ align:start position:0%
+so he calculated what would happen to
+ 
+
+ align:start position:0%
+so he calculated what would happen to
+this Burning of fossil fuels
+
+ align:start position:0%
+this Burning of fossil fuels
+ 
+
+ align:start position:0%
+this Burning of fossil fuels
+and um he decided in has calculation he
+
+ align:start position:0%
+and um he decided in has calculation he
+ 
+
+ align:start position:0%
+and um he decided in has calculation he
+basically got the calculation right by
+
+ align:start position:0%
+basically got the calculation right by
+ 
+
+ align:start position:0%
+basically got the calculation right by
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+way but he came out that in 2,000 years
+
+ align:start position:0%
+way but he came out that in 2,000 years
+ 
+
+ align:start position:0%
+way but he came out that in 2,000 years
+from the time that he did the
+
+ align:start position:0%
+from the time that he did the
+ 
+
+ align:start position:0%
+from the time that he did the
+calculations humans would be in
+
+ align:start position:0%
+calculations humans would be in
+ 
+
+ align:start position:0%
+calculations humans would be in
+trouble well since this calculation
+
+ align:start position:0%
+trouble well since this calculation
+ 
+
+ align:start position:0%
+trouble well since this calculation
+we've had an exponential growth in the
+
+ align:start position:0%
+we've had an exponential growth in the
+ 
+
+ align:start position:0%
+we've had an exponential growth in the
+amount of CO2 and if you go through the
+
+ align:start position:0%
+amount of CO2 and if you go through the
+ 
+
+ align:start position:0%
+amount of CO2 and if you go through the
+calculations of people have done these
+
+ align:start position:0%
+calculations of people have done these
+ 
+
+ align:start position:0%
+calculations of people have done these
+calculations throughout time since
+
+ align:start position:0%
+calculations throughout time since
+ 
+
+ align:start position:0%
+calculations throughout time since
+serenus the time that we're in trouble
+
+ align:start position:0%
+serenus the time that we're in trouble
+ 
+
+ align:start position:0%
+serenus the time that we're in trouble
+2,000 years and the calculation has gone
+
+ align:start position:0%
+2,000 years and the calculation has gone
+ 
+
+ align:start position:0%
+2,000 years and the calculation has gone
+like this and so now
+
+ align:start position:0%
+like this and so now
+ 
+
+ align:start position:0%
+like this and so now
+we're now we're really in
+
+ align:start position:0%
+we're now we're really in
+ 
+
+ align:start position:0%
+we're now we're really in
+trouble that's a for a different
+
+ align:start position:0%
+trouble that's a for a different
+ 
+
+ align:start position:0%
+trouble that's a for a different
+lecture so anyway thermodynamics dates
+
+ align:start position:0%
+lecture so anyway thermodynamics dates
+ 
+
+ align:start position:0%
+lecture so anyway thermodynamics dates
+from the same period as as as as getting
+
+ align:start position:0%
+from the same period as as as as getting
+ 
+
+ align:start position:0%
+from the same period as as as as getting
+fossil fuels out of the
+
+ align:start position:0%
+fossil fuels out of the
+ 
+
+ align:start position:0%
+fossil fuels out of the
+ground it's Universal turns out
+
+ align:start position:0%
+ground it's Universal turns out
+ 
+
+ align:start position:0%
+ground it's Universal turns out
+everything around us moves energy around
+
+ align:start position:0%
+everything around us moves energy around
+ 
+
+ align:start position:0%
+everything around us moves energy around
+in one way or the other if you're a
+
+ align:start position:0%
+in one way or the other if you're a
+ 
+
+ align:start position:0%
+in one way or the other if you're a
+biological system you're burning
+
+ align:start position:0%
+biological system you're burning
+ 
+
+ align:start position:0%
+biological system you're burning
+calories burning ATP you're creating
+
+ align:start position:0%
+calories burning ATP you're creating
+ 
+
+ align:start position:0%
+calories burning ATP you're creating
+heat if you're warm-blooded animal you
+
+ align:start position:0%
+heat if you're warm-blooded animal you
+ 
+
+ align:start position:0%
+heat if you're warm-blooded animal you
+you need energy to move your arms around
+
+ align:start position:0%
+you need energy to move your arms around
+ 
+
+ align:start position:0%
+you need energy to move your arms around
+and move around mechanical systems
+
+ align:start position:0%
+and move around mechanical systems
+ 
+
+ align:start position:0%
+and move around mechanical systems
+obviously cars boats
+
+ align:start position:0%
+obviously cars boats
+ 
+
+ align:start position:0%
+obviously cars boats
+Etc and even in astrophysics when you
+
+ align:start position:0%
+Etc and even in astrophysics when you
+ 
+
+ align:start position:0%
+Etc and even in astrophysics when you
+talk about stars black holes Etc you're
+
+ align:start position:0%
+talk about stars black holes Etc you're
+ 
+
+ align:start position:0%
+talk about stars black holes Etc you're
+moving energy around you're moving heat
+
+ align:start position:0%
+moving energy around you're moving heat
+ 
+
+ align:start position:0%
+moving energy around you're moving heat
+around and you're changing matter
+
+ align:start position:0%
+around and you're changing matter
+ 
+
+ align:start position:0%
+around and you're changing matter
+through uh
+
+ align:start position:0%
+through uh
+ 
+
+ align:start position:0%
+through uh
+thermodynamics and the concepts of
+
+ align:start position:0%
+thermodynamics and the concepts of
+ 
+
+ align:start position:0%
+thermodynamics and the concepts of
+thermodynamics have even been applied to
+
+ align:start position:0%
+thermodynamics have even been applied to
+ 
+
+ align:start position:0%
+thermodynamics have even been applied to
+economics systems out of equilibrium
+
+ align:start position:0%
+economics systems out of equilibrium
+ 
+
+ align:start position:0%
+economics systems out of equilibrium
+like big companies like it's like Enron
+
+ align:start position:0%
+like big companies like it's like Enron
+ 
+
+ align:start position:0%
+like big companies like it's like Enron
+you know completely out of equilibrium
+
+ align:start position:0%
+you know completely out of equilibrium
+ 
+
+ align:start position:0%
+you know completely out of equilibrium
+Crash and Burn right it's can apply
+
+ align:start position:0%
+Crash and Burn right it's can apply
+ 
+
+ align:start position:0%
+Crash and Burn right it's can apply
+thermodynamic or non-equilibrium
+
+ align:start position:0%
+thermodynamic or non-equilibrium
+ 
+
+ align:start position:0%
+thermodynamic or non-equilibrium
+thermodynamics to to
+
+ align:start position:0%
+thermodynamics to to
+ 
+
+ align:start position:0%
+thermodynamics to to
+economics it was developed before people
+
+ align:start position:0%
+economics it was developed before people
+ 
+
+ align:start position:0%
+economics it was developed before people
+knew about atoms and molecules so it's a
+
+ align:start position:0%
+knew about atoms and molecules so it's a
+ 
+
+ align:start position:0%
+knew about atoms and molecules so it's a
+science that based on macroscopic
+
+ align:start position:0%
+science that based on macroscopic
+ 
+
+ align:start position:0%
+science that based on macroscopic
+properties of
+
+ align:start position:0%
+properties of
+ 
+
+ align:start position:0%
+properties of
+matter since then since we know about
+
+ align:start position:0%
+matter since then since we know about
+ 
+
+ align:start position:0%
+matter since then since we know about
+atoms and molecules now we can
+
+ align:start position:0%
+atoms and molecules now we can
+ 
+
+ align:start position:0%
+atoms and molecules now we can
+rationalize the concepts of
+
+ align:start position:0%
+rationalize the concepts of
+ 
+
+ align:start position:0%
+rationalize the concepts of
+thermodynamics using microscopic
+
+ align:start position:0%
+thermodynamics using microscopic
+ 
+
+ align:start position:0%
+thermodynamics using microscopic
+properties and if you are going to take
+
+ align:start position:0%
+properties and if you are going to take
+ 
+
+ align:start position:0%
+properties and if you are going to take
+562 that's what you learn about you
+
+ align:start position:0%
+562 that's what you learn about you
+ 
+
+ align:start position:0%
+562 that's what you learn about you
+learn about statistical mechanics and
+
+ align:start position:0%
+learn about statistical mechanics and
+ 
+
+ align:start position:0%
+learn about statistical mechanics and
+how the atomistic concepts rationalize
+
+ align:start position:0%
+how the atomistic concepts rationalize
+ 
+
+ align:start position:0%
+how the atomistic concepts rationalize
+thermodynamics it doesn't prove
+
+ align:start position:0%
+thermodynamics it doesn't prove
+ 
+
+ align:start position:0%
+thermodynamics it doesn't prove
+it uh but it helps to getting more
+
+ align:start position:0%
+it uh but it helps to getting more
+ 
+
+ align:start position:0%
+it uh but it helps to getting more
+intuition about U the consequences of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thermodynamics so it applies to
+
+ align:start position:0%
+thermodynamics so it applies to
+ 
+
+ align:start position:0%
+thermodynamics so it applies to
+macroscopic systems that are in
+
+ align:start position:0%
+macroscopic systems that are in
+ 
+
+ align:start position:0%
+macroscopic systems that are in
+equilibrium and how to go from one
+
+ align:start position:0%
+equilibrium and how to go from one
+ 
+
+ align:start position:0%
+equilibrium and how to go from one
+equilibrium state to another poan
+
+ align:start position:0%
+equilibrium state to another poan
+ 
+
+ align:start position:0%
+equilibrium state to another poan
+State and it's entirely empirical in its
+
+ align:start position:0%
+State and it's entirely empirical in its
+ 
+
+ align:start position:0%
+State and it's entirely empirical in its
+foundation people have done experiments
+
+ align:start position:0%
+foundation people have done experiments
+ 
+
+ align:start position:0%
+foundation people have done experiments
+Through the Ages and they've accumulated
+
+ align:start position:0%
+Through the Ages and they've accumulated
+ 
+
+ align:start position:0%
+Through the Ages and they've accumulated
+the knowledge from these experiments and
+
+ align:start position:0%
+the knowledge from these experiments and
+ 
+
+ align:start position:0%
+the knowledge from these experiments and
+they've synthesized these experiments
+
+ align:start position:0%
+they've synthesized these experiments
+ 
+
+ align:start position:0%
+they've synthesized these experiments
+into a few basic empirical rules
+
+ align:start position:0%
+into a few basic empirical rules
+ 
+
+ align:start position:0%
+into a few basic empirical rules
+empirical laws which are the laws of
+
+ align:start position:0%
+empirical laws which are the laws of
+ 
+
+ align:start position:0%
+empirical laws which are the laws of
+thermodynamics and then they've taken
+
+ align:start position:0%
+thermodynamics and then they've taken
+ 
+
+ align:start position:0%
+thermodynamics and then they've taken
+these laws and added a a structure of
+
+ align:start position:0%
+these laws and added a a structure of
+ 
+
+ align:start position:0%
+these laws and added a a structure of
+math upon it to build this edifice which
+
+ align:start position:0%
+math upon it to build this edifice which
+ 
+
+ align:start position:0%
+math upon it to build this edifice which
+is very solid edifice of thermodynamics
+
+ align:start position:0%
+is very solid edifice of thermodynamics
+ 
+
+ align:start position:0%
+is very solid edifice of thermodynamics
+as a science of equilibrium
+
+ align:start position:0%
+as a science of equilibrium
+ 
+
+ align:start position:0%
+as a science of equilibrium
+systems so these empirical observations
+
+ align:start position:0%
+systems so these empirical observations
+ 
+
+ align:start position:0%
+systems so these empirical observations
+then are U summarized into four
+
+ align:start position:0%
+then are U summarized into four
+ 
+
+ align:start position:0%
+then are U summarized into four
+laws okay so um these laws are they're
+
+ align:start position:0%
+laws okay so um these laws are they're
+ 
+
+ align:start position:0%
+laws okay so um these laws are they're
+really deep pillars they're they're not
+
+ align:start position:0%
+really deep pillars they're they're not
+ 
+
+ align:start position:0%
+really deep pillars they're they're not
+proven but they're not wrong they're
+
+ align:start position:0%
+proven but they're not wrong they're
+ 
+
+ align:start position:0%
+proven but they're not wrong they're
+very unlikely to be
+
+ align:start position:0%
+very unlikely to be
+ 
+
+ align:start position:0%
+very unlikely to be
+wrong let's just go through these laws
+
+ align:start position:0%
+wrong let's just go through these laws
+ 
+
+ align:start position:0%
+wrong let's just go through these laws
+okay very quickly there's a zero
+
+ align:start position:0%
+okay very quickly there's a zero
+ 
+
+ align:start position:0%
+okay very quickly there's a zero
+law the zero law every one of these laws
+
+ align:start position:0%
+law the zero law every one of these laws
+ 
+
+ align:start position:0%
+law the zero law every one of these laws
+basically defines a quantity in
+
+ align:start position:0%
+basically defines a quantity in
+ 
+
+ align:start position:0%
+basically defines a quantity in
+thermodynamics and then defines a
+
+ align:start position:0%
+thermodynamics and then defines a
+ 
+
+ align:start position:0%
+thermodynamics and then defines a
+concept the zero law defines temperature
+
+ align:start position:0%
+concept the zero law defines temperature
+ 
+
+ align:start position:0%
+concept the zero law defines temperature
+that's a fairly Common
+
+ align:start position:0%
+that's a fairly Common
+ 
+
+ align:start position:0%
+that's a fairly Common
+Sense idea but it's important to Define
+
+ align:start position:0%
+Sense idea but it's important to Define
+ 
+
+ align:start position:0%
+Sense idea but it's important to Define
+it and I call that the common sense law
+
+ align:start position:0%
+it and I call that the common sense law
+ 
+
+ align:start position:0%
+it and I call that the common sense law
+okay so this is the common sense law
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first
+
+ align:start position:0%
+the first
+ 
+
+ align:start position:0%
+the first
+law ends up uh defining
+
+ align:start position:0%
+law ends up uh defining
+ 
+
+ align:start position:0%
+law ends up uh defining
+energy which we're going to call
+
+ align:start position:0%
+energy which we're going to call
+ 
+
+ align:start position:0%
+energy which we're going to call
+you and um the concept of energy
+
+ align:start position:0%
+you and um the concept of energy
+ 
+
+ align:start position:0%
+you and um the concept of energy
+conservation energy can't be lost or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gained and I'm going to call this the
+
+ align:start position:0%
+gained and I'm going to call this the
+ 
+
+ align:start position:0%
+gained and I'm going to call this the
+you can break even law you can
+
+ align:start position:0%
+you can break even law you can
+ 
+
+ align:start position:0%
+you can break even law you can
+break even you don't lose
+
+ align:start position:0%
+break even you don't lose
+ 
+
+ align:start position:0%
+break even you don't lose
+energy you can't gain energy energ you
+
+ align:start position:0%
+energy you can't gain energy energ you
+ 
+
+ align:start position:0%
+energy you can't gain energy energ you
+break
+
+ align:start position:0%
+break
+ 
+
+ align:start position:0%
+break
+even the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+law is going to Define
+
+ align:start position:0%
+law is going to Define
+ 
+
+ align:start position:0%
+law is going to Define
+entropy and it's going to tell us about
+
+ align:start position:0%
+entropy and it's going to tell us about
+ 
+
+ align:start position:0%
+entropy and it's going to tell us about
+the direction of time something that
+
+ align:start position:0%
+the direction of time something that
+ 
+
+ align:start position:0%
+the direction of time something that
+conceptually we clearly understand but
+
+ align:start position:0%
+conceptually we clearly understand but
+ 
+
+ align:start position:0%
+conceptually we clearly understand but
+it's going to put a mathematical
+
+ align:start position:0%
+it's going to put a mathematical
+ 
+
+ align:start position:0%
+it's going to put a mathematical
+foundation on which way does time go
+
+ align:start position:0%
+foundation on which way does time go
+ 
+
+ align:start position:0%
+foundation on which way does time go
+clearly if I take a chalk like this one
+
+ align:start position:0%
+clearly if I take a chalk like this one
+ 
+
+ align:start position:0%
+clearly if I take a chalk like this one
+here and I throw it on the ground and it
+
+ align:start position:0%
+here and I throw it on the ground and it
+ 
+
+ align:start position:0%
+here and I throw it on the ground and it
+breaks in little pieces if I run the
+
+ align:start position:0%
+breaks in little pieces if I run the
+ 
+
+ align:start position:0%
+breaks in little pieces if I run the
+movie backwards that doesn't make sense
+
+ align:start position:0%
+movie backwards that doesn't make sense
+ 
+
+ align:start position:0%
+movie backwards that doesn't make sense
+right we have a concept of time going
+
+ align:start position:0%
+right we have a concept of time going
+ 
+
+ align:start position:0%
+right we have a concept of time going
+forward in a particular way how does
+
+ align:start position:0%
+forward in a particular way how does
+ 
+
+ align:start position:0%
+forward in a particular way how does
+entropy play into that concept of
+
+ align:start position:0%
+entropy play into that concept of
+ 
+
+ align:start position:0%
+entropy play into that concept of
+time and I'm going to call this the um
+
+ align:start position:0%
+time and I'm going to call this the um
+ 
+
+ align:start position:0%
+time and I'm going to call this the um
+you can break
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+even at 0 degrees Kelvin law okay you
+
+ align:start position:0%
+even at 0 degrees Kelvin law okay you
+ 
+
+ align:start position:0%
+even at 0 degrees Kelvin law okay you
+can only do it at 0 degrees
+
+ align:start position:0%
+can only do it at 0 degrees
+ 
+
+ align:start position:0%
+can only do it at 0 degrees
+Kelvin the third
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+law is going to give a numerical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+entropy and the third law is going to be
+
+ align:start position:0%
+entropy and the third law is going to be
+ 
+
+ align:start position:0%
+entropy and the third law is going to be
+the depressing one and it's going to say
+
+ align:start position:0%
+the depressing one and it's going to say
+ 
+
+ align:start position:0%
+the depressing one and it's going to say
+you can't get to 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degrees okay these laws are universally
+
+ align:start position:0%
+degrees okay these laws are universally
+ 
+
+ align:start position:0%
+degrees okay these laws are universally
+valid they cannot be circumvented
+
+ align:start position:0%
+valid they cannot be circumvented
+ 
+
+ align:start position:0%
+valid they cannot be circumvented
+certainly people have tried to do that
+
+ align:start position:0%
+certainly people have tried to do that
+ 
+
+ align:start position:0%
+certainly people have tried to do that
+and every year there's a newspaper story
+
+ align:start position:0%
+and every year there's a newspaper story
+ 
+
+ align:start position:0%
+and every year there's a newspaper story
+in Wall Street Journal or New York Times
+
+ align:start position:0%
+in Wall Street Journal or New York Times
+ 
+
+ align:start position:0%
+in Wall Street Journal or New York Times
+about somebody that has invented a
+
+ align:start position:0%
+about somebody that has invented a
+ 
+
+ align:start position:0%
+about somebody that has invented a
+device that somehow goes around the
+
+ align:start position:0%
+device that somehow goes around the
+ 
+
+ align:start position:0%
+device that somehow goes around the
+second law and makes more energy than it
+
+ align:start position:0%
+second law and makes more energy than it
+ 
+
+ align:start position:0%
+second law and makes more energy than it
+creates and this is going to be well
+
+ align:start position:0%
+creates and this is going to be well
+ 
+
+ align:start position:0%
+creates and this is going to be well
+first of all for the investors this is
+
+ align:start position:0%
+first of all for the investors this is
+ 
+
+ align:start position:0%
+first of all for the investors this is
+going to make them very very rich and
+
+ align:start position:0%
+going to make them very very rich and
+ 
+
+ align:start position:0%
+going to make them very very rich and
+for the rest of us it's going to be
+
+ align:start position:0%
+for the rest of us it's going to be
+ 
+
+ align:start position:0%
+for the rest of us it's going to be
+wonderful and they go through these
+
+ align:start position:0%
+wonderful and they go through these
+ 
+
+ align:start position:0%
+wonderful and they go through these
+arguments and they find Venture money to
+
+ align:start position:0%
+arguments and they find Venture money to
+ 
+
+ align:start position:0%
+arguments and they find Venture money to
+fund the company and they get very
+
+ align:start position:0%
+fund the company and they get very
+ 
+
+ align:start position:0%
+fund the company and they get very
+famous people to endorse them
+
+ align:start position:0%
+famous people to endorse them
+ 
+
+ align:start position:0%
+famous people to endorse them
+Etc but you guys know because you have
+
+ align:start position:0%
+Etc but you guys know because you have
+ 
+
+ align:start position:0%
+Etc but you guys know because you have
+MIT degrees and
+
+ align:start position:0%
+MIT degrees and
+ 
+
+ align:start position:0%
+MIT degrees and
+you later and you've taken 560 that that
+
+ align:start position:0%
+you later and you've taken 560 that that
+ 
+
+ align:start position:0%
+you later and you've taken 560 that that
+can't be the case and you're not going
+
+ align:start position:0%
+can't be the case and you're not going
+ 
+
+ align:start position:0%
+can't be the case and you're not going
+to get fooled into investing money into
+
+ align:start position:0%
+to get fooled into investing money into
+ 
+
+ align:start position:0%
+to get fooled into investing money into
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+companies but it's amazing that every
+
+ align:start position:0%
+companies but it's amazing that every
+ 
+
+ align:start position:0%
+companies but it's amazing that every
+year you find somebody coming up with a
+
+ align:start position:0%
+year you find somebody coming up with a
+ 
+
+ align:start position:0%
+year you find somebody coming up with a
+way of going around the second law and
+
+ align:start position:0%
+way of going around the second law and
+ 
+
+ align:start position:0%
+way of going around the second law and
+somehow convincing people who are very
+
+ align:start position:0%
+somehow convincing people who are very
+ 
+
+ align:start position:0%
+somehow convincing people who are very
+smart that this will work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so Thermo in is also a big tease as you
+
+ align:start position:0%
+so Thermo in is also a big tease as you
+ 
+
+ align:start position:0%
+so Thermo in is also a big tease as you
+can see from my descriptions of these
+
+ align:start position:0%
+can see from my descriptions of these
+ 
+
+ align:start position:0%
+can see from my descriptions of these
+laws here it makes you believe
+
+ align:start position:0%
+laws here it makes you believe
+ 
+
+ align:start position:0%
+laws here it makes you believe
+initially and the feasibility of perfect
+
+ align:start position:0%
+initially and the feasibility of perfect
+ 
+
+ align:start position:0%
+initially and the feasibility of perfect
+efficiency right the the first law um
+
+ align:start position:0%
+efficiency right the the first law um
+ 
+
+ align:start position:0%
+efficiency right the the first law um
+the first law is very upbeat it talks
+
+ align:start position:0%
+the first law is very upbeat it talks
+ 
+
+ align:start position:0%
+the first law is very upbeat it talks
+about the conservation of energy energy
+
+ align:start position:0%
+about the conservation of energy energy
+ 
+
+ align:start position:0%
+about the conservation of energy energy
+is is conserved in all of its forms you
+
+ align:start position:0%
+is is conserved in all of its forms you
+ 
+
+ align:start position:0%
+is is conserved in all of its forms you
+can take heat energy and convert it to
+
+ align:start position:0%
+can take heat energy and convert it to
+ 
+
+ align:start position:0%
+can take heat energy and convert it to
+work energy and vice versa and it
+
+ align:start position:0%
+work energy and vice versa and it
+ 
+
+ align:start position:0%
+work energy and vice versa and it
+doesn't say anything about that you have
+
+ align:start position:0%
+doesn't say anything about that you have
+ 
+
+ align:start position:0%
+doesn't say anything about that you have
+to waste heat if you're going to
+
+ align:start position:0%
+to waste heat if you're going to
+ 
+
+ align:start position:0%
+to waste heat if you're going to
+transform heat into work it just says
+
+ align:start position:0%
+transform heat into work it just says
+ 
+
+ align:start position:0%
+transform heat into work it just says
+it's energy it's all the same thing
+
+ align:start position:0%
+it's energy it's all the same thing
+ 
+
+ align:start position:0%
+it's energy it's all the same thing
+right so you could break even if you
+
+ align:start position:0%
+right so you could break even if you
+ 
+
+ align:start position:0%
+right so you could break even if you
+were very clever about it and that's
+
+ align:start position:0%
+were very clever about it and that's
+ 
+
+ align:start position:0%
+were very clever about it and that's
+that's pretty neat so in a sense it says
+
+ align:start position:0%
+that's pretty neat so in a sense it says
+ 
+
+ align:start position:0%
+that's pretty neat so in a sense it says
+you know if you wanted to build a boat
+
+ align:start position:0%
+you know if you wanted to build a boat
+ 
+
+ align:start position:0%
+you know if you wanted to build a boat
+that took energy out of the air out the
+
+ align:start position:0%
+that took energy out of the air out the
+ 
+
+ align:start position:0%
+that took energy out of the air out the
+warmth of the air to sale around the
+
+ align:start position:0%
+warmth of the air to sale around the
+ 
+
+ align:start position:0%
+warmth of the air to sale around the
+world you can do
+
+ align:start position:0%
+world you can do
+ 
+
+ align:start position:0%
+world you can do
+that right and then the second law comes
+
+ align:start position:0%
+that right and then the second law comes
+ 
+
+ align:start position:0%
+that right and then the second law comes
+in and says
+
+ align:start position:0%
+in and says
+ 
+
+ align:start position:0%
+in and says
+well that's not quite right right the
+
+ align:start position:0%
+well that's not quite right right the
+ 
+
+ align:start position:0%
+well that's not quite right right the
+second law says yeah energy is pretty
+
+ align:start position:0%
+second law says yeah energy is pretty
+ 
+
+ align:start position:0%
+second law says yeah energy is pretty
+much the same in all its form but if you
+
+ align:start position:0%
+much the same in all its form but if you
+ 
+
+ align:start position:0%
+much the same in all its form but if you
+want to convert one form of energy into
+
+ align:start position:0%
+want to convert one form of energy into
+ 
+
+ align:start position:0%
+want to convert one form of energy into
+another if you want to con convert
+
+ align:start position:0%
+another if you want to con convert
+ 
+
+ align:start position:0%
+another if you want to con convert
+work uh heat into work with 100%
+
+ align:start position:0%
+work uh heat into work with 100%
+ 
+
+ align:start position:0%
+work uh heat into work with 100%
+efficiency you got to go down to 0
+
+ align:start position:0%
+efficiency you got to go down to 0
+ 
+
+ align:start position:0%
+efficiency you got to go down to 0
+degrees Kelvin to absolute zero if you
+
+ align:start position:0%
+degrees Kelvin to absolute zero if you
+ 
+
+ align:start position:0%
+degrees Kelvin to absolute zero if you
+want to do that otherwise you're going
+
+ align:start position:0%
+want to do that otherwise you're going
+ 
+
+ align:start position:0%
+want to do that otherwise you're going
+to waste some
+
+ align:start position:0%
+to waste some
+ 
+
+ align:start position:0%
+to waste some
+some of that heat somewhere along the
+
+ align:start position:0%
+some of that heat somewhere along the
+ 
+
+ align:start position:0%
+some of that heat somewhere along the
+way some of that
+
+ align:start position:0%
+way some of that
+ 
+
+ align:start position:0%
+way some of that
+energy okay so all right so you can't
+
+ align:start position:0%
+energy okay so all right so you can't
+ 
+
+ align:start position:0%
+energy okay so all right so you can't
+get perfect efficiency but at least if
+
+ align:start position:0%
+get perfect efficiency but at least if
+ 
+
+ align:start position:0%
+get perfect efficiency but at least if
+you were able to go to Z degrees Kelvin
+
+ align:start position:0%
+you were able to go to Z degrees Kelvin
+ 
+
+ align:start position:0%
+you were able to go to Z degrees Kelvin
+then you'd be all set right you just got
+
+ align:start position:0%
+then you'd be all set right you just got
+ 
+
+ align:start position:0%
+then you'd be all set right you just got
+to find a good refrigerator on your on
+
+ align:start position:0%
+to find a good refrigerator on your on
+ 
+
+ align:start position:0%
+to find a good refrigerator on your on
+your on your boat and then you can still
+
+ align:start position:0%
+your on your boat and then you can still
+ 
+
+ align:start position:0%
+your on your boat and then you can still
+go around the world then the third law
+
+ align:start position:0%
+go around the world then the third law
+ 
+
+ align:start position:0%
+go around the world then the third law
+comes in and that's the depressing part
+
+ align:start position:0%
+comes in and that's the depressing part
+ 
+
+ align:start position:0%
+comes in and that's the depressing part
+here it says well it's true if you could
+
+ align:start position:0%
+here it says well it's true if you could
+ 
+
+ align:start position:0%
+here it says well it's true if you could
+get a 0 degrees Kelvin you'd get perfect
+
+ align:start position:0%
+get a 0 degrees Kelvin you'd get perfect
+ 
+
+ align:start position:0%
+get a 0 degrees Kelvin you'd get perfect
+efficiency but you can't get to 0
+
+ align:start position:0%
+efficiency but you can't get to 0
+ 
+
+ align:start position:0%
+efficiency but you can't get to 0
+degrees
+
+ align:start position:0%
+degrees
+ 
+
+ align:start position:0%
+degrees
+Kelvin you
+
+ align:start position:0%
+Kelvin you
+ 
+
+ align:start position:0%
+Kelvin you
+can't even if you have an infinite
+
+ align:start position:0%
+can't even if you have an infinite
+ 
+
+ align:start position:0%
+can't even if you have an infinite
+amount of resources you can't get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+okay any questions so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far so thermodynamics based on these
+
+ align:start position:0%
+far so thermodynamics based on these
+ 
+
+ align:start position:0%
+far so thermodynamics based on these
+four laws now requires an edifice and
+
+ align:start position:0%
+four laws now requires an edifice and
+ 
+
+ align:start position:0%
+four laws now requires an edifice and
+it's very it's a very mature science and
+
+ align:start position:0%
+it's very it's a very mature science and
+ 
+
+ align:start position:0%
+it's very it's a very mature science and
+it requires that we Define things
+
+ align:start position:0%
+it requires that we Define things
+ 
+
+ align:start position:0%
+it requires that we Define things
+carefully so we're going to spend a
+
+ align:start position:0%
+carefully so we're going to spend a
+ 
+
+ align:start position:0%
+carefully so we're going to spend a
+little bit of time making sure we Define
+
+ align:start position:0%
+little bit of time making sure we Define
+ 
+
+ align:start position:0%
+little bit of time making sure we Define
+our our Concepts and our words and what
+
+ align:start position:0%
+our our Concepts and our words and what
+ 
+
+ align:start position:0%
+our our Concepts and our words and what
+you'll find that when you do problem
+
+ align:start position:0%
+you'll find that when you do problem
+ 
+
+ align:start position:0%
+you'll find that when you do problem
+sets especially at the
+
+ align:start position:0%
+sets especially at the
+ 
+
+ align:start position:0%
+sets especially at the
+beginning
+
+ align:start position:0%
+beginning
+ 
+
+ align:start position:0%
+beginning
+very uh understanding The
+
+ align:start position:0%
+very uh understanding The
+ 
+
+ align:start position:0%
+very uh understanding The
+Words and the conditions of the problem
+
+ align:start position:0%
+Words and the conditions of the problem
+ 
+
+ align:start position:0%
+Words and the conditions of the problem
+sets
+
+ align:start position:0%
+sets
+ 
+
+ align:start position:0%
+sets
+is most of the way into solving the
+
+ align:start position:0%
+is most of the way into solving the
+ 
+
+ align:start position:0%
+is most of the way into solving the
+problem okay so we're going to talk
+
+ align:start position:0%
+problem okay so we're going to talk
+ 
+
+ align:start position:0%
+problem okay so we're going to talk
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+things like
+
+ align:start position:0%
+things like
+ 
+
+ align:start position:0%
+things like
+systems okay the
+
+ align:start position:0%
+systems okay the
+ 
+
+ align:start position:0%
+systems okay the
+system it's that part of the universe
+
+ align:start position:0%
+system it's that part of the universe
+ 
+
+ align:start position:0%
+system it's that part of the universe
+that we're studying these are going to
+
+ align:start position:0%
+that we're studying these are going to
+ 
+
+ align:start position:0%
+that we're studying these are going to
+be fairly Common Sense definitions but
+
+ align:start position:0%
+be fairly Common Sense definitions but
+ 
+
+ align:start position:0%
+be fairly Common Sense definitions but
+they're important and when you get to a
+
+ align:start position:0%
+they're important and when you get to a
+ 
+
+ align:start position:0%
+they're important and when you get to a
+problem set really nailing down what the
+
+ align:start position:0%
+problem set really nailing down what the
+ 
+
+ align:start position:0%
+problem set really nailing down what the
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+is not more not or less in terms of the
+
+ align:start position:0%
+is not more not or less in terms of the
+ 
+
+ align:start position:0%
+is not more not or less in terms of the
+amount of stuff that's part of the
+
+ align:start position:0%
+amount of stuff that's part of the
+ 
+
+ align:start position:0%
+amount of stuff that's part of the
+system it's going to be often very
+
+ align:start position:0%
+system it's going to be often very
+ 
+
+ align:start position:0%
+system it's going to be often very
+crucial okay so you've got the system
+
+ align:start position:0%
+crucial okay so you've got the system
+ 
+
+ align:start position:0%
+crucial okay so you've got the system
+for instance it could be a person I'm
+
+ align:start position:0%
+for instance it could be a person I'm
+ 
+
+ align:start position:0%
+for instance it could be a person I'm
+the system I could be a system it could
+
+ align:start position:0%
+the system I could be a system it could
+ 
+
+ align:start position:0%
+the system I could be a system it could
+be a a hot coffee and a thermos okay so
+
+ align:start position:0%
+be a a hot coffee and a thermos okay so
+ 
+
+ align:start position:0%
+be a a hot coffee and a thermos okay so
+the coffee and the milk and whatever
+
+ align:start position:0%
+the coffee and the milk and whatever
+ 
+
+ align:start position:0%
+the coffee and the milk and whatever
+else you like in your coffee would be
+
+ align:start position:0%
+else you like in your coffee would be
+ 
+
+ align:start position:0%
+else you like in your coffee would be
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+system a glass of water with ice in it
+
+ align:start position:0%
+system a glass of water with ice in it
+ 
+
+ align:start position:0%
+system a glass of water with ice in it
+it's fine system a volume of air in a
+
+ align:start position:0%
+it's fine system a volume of air in a
+ 
+
+ align:start position:0%
+it's fine system a volume of air in a
+part of a room take a four liters on
+
+ align:start position:0%
+part of a room take a four liters on
+ 
+
+ align:start position:0%
+part of a room take a four liters on
+this corner of the room that's my
+
+ align:start position:0%
+this corner of the room that's my
+ 
+
+ align:start position:0%
+this corner of the room that's my
+system then
+
+ align:start position:0%
+system then
+ 
+
+ align:start position:0%
+system then
+um after you define what your system
+
+ align:start position:0%
+um after you define what your system
+ 
+
+ align:start position:0%
+um after you define what your system
+is whatever is left
+
+ align:start position:0%
+is whatever is left
+ 
+
+ align:start position:0%
+is whatever is left
+over of the universe is the surroundings
+
+ align:start position:0%
+over of the universe is the surroundings
+ 
+
+ align:start position:0%
+over of the universe is the surroundings
+so if I'm the system then everything
+
+ align:start position:0%
+so if I'm the system then everything
+ 
+
+ align:start position:0%
+so if I'm the system then everything
+else is the surroundings you are my
+
+ align:start position:0%
+else is the surroundings you are my
+ 
+
+ align:start position:0%
+else is the surroundings you are my
+surroundings Saturn is my surroundings
+
+ align:start position:0%
+surroundings Saturn is my surroundings
+ 
+
+ align:start position:0%
+surroundings Saturn is my surroundings
+right as far as you can go in the
+
+ align:start position:0%
+right as far as you can go in the
+ 
+
+ align:start position:0%
+right as far as you can go in the
+universe that's part of the
+
+ align:start position:0%
+universe that's part of the
+ 
+
+ align:start position:0%
+universe that's part of the
+surroundings and then between the system
+
+ align:start position:0%
+surroundings and then between the system
+ 
+
+ align:start position:0%
+surroundings and then between the system
+and the surroundings is the
+
+ align:start position:0%
+and the surroundings is the
+ 
+
+ align:start position:0%
+and the surroundings is the
+boundary and the boundary is is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Surface that's uh real like the outside
+
+ align:start position:0%
+Surface that's uh real like the outside
+ 
+
+ align:start position:0%
+Surface that's uh real like the outside
+of my skin or the inner wall
+
+ align:start position:0%
+of my skin or the inner wall
+ 
+
+ align:start position:0%
+of my skin or the inner wall
+of the thermos that has the coffee in
+
+ align:start position:0%
+of the thermos that has the coffee in
+ 
+
+ align:start position:0%
+of the thermos that has the coffee in
+it or could be an imaginary boundary for
+
+ align:start position:0%
+it or could be an imaginary boundary for
+ 
+
+ align:start position:0%
+it or could be an imaginary boundary for
+instance I can imagine that there's a a
+
+ align:start position:0%
+instance I can imagine that there's a a
+ 
+
+ align:start position:0%
+instance I can imagine that there's a a
+boundary that surrounds the four lers of
+
+ align:start position:0%
+boundary that surrounds the four lers of
+ 
+
+ align:start position:0%
+boundary that surrounds the four lers of
+air that's sitting in the corner there
+
+ align:start position:0%
+air that's sitting in the corner there
+ 
+
+ align:start position:0%
+air that's sitting in the corner there
+it doesn't have to be a real container
+
+ align:start position:0%
+it doesn't have to be a real container
+ 
+
+ align:start position:0%
+it doesn't have to be a real container
+to contain it it's just an imaginary
+
+ align:start position:0%
+to contain it it's just an imaginary
+ 
+
+ align:start position:0%
+to contain it it's just an imaginary
+boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there and where you place that boundary
+
+ align:start position:0%
+there and where you place that boundary
+ 
+
+ align:start position:0%
+there and where you place that boundary
+becomes important so for instance for
+
+ align:start position:0%
+becomes important so for instance for
+ 
+
+ align:start position:0%
+becomes important so for instance for
+the uh the thermos with the coffee in it
+
+ align:start position:0%
+the uh the thermos with the coffee in it
+ 
+
+ align:start position:0%
+the uh the thermos with the coffee in it
+if you place the bound be in the inside
+
+ align:start position:0%
+if you place the bound be in the inside
+ 
+
+ align:start position:0%
+if you place the bound be in the inside
+wall of the glass or the outside wall of
+
+ align:start position:0%
+wall of the glass or the outside wall of
+ 
+
+ align:start position:0%
+wall of the glass or the outside wall of
+the glass and the inside of the thermos
+
+ align:start position:0%
+the glass and the inside of the thermos
+ 
+
+ align:start position:0%
+the glass and the inside of the thermos
+that makes a difference different heat
+
+ align:start position:0%
+that makes a difference different heat
+ 
+
+ align:start position:0%
+that makes a difference different heat
+capacity Etc so this becomes where
+
+ align:start position:0%
+capacity Etc so this becomes where
+ 
+
+ align:start position:0%
+capacity Etc so this becomes where
+defining the system and the boundaries
+
+ align:start position:0%
+defining the system and the boundaries
+ 
+
+ align:start position:0%
+defining the system and the boundaries
+and everything becomes important got to
+
+ align:start position:0%
+and everything becomes important got to
+ 
+
+ align:start position:0%
+and everything becomes important got to
+place the boundary at exactly the right
+
+ align:start position:0%
+place the boundary at exactly the right
+ 
+
+ align:start position:0%
+place the boundary at exactly the right
+place otherwise you've got a bit too
+
+ align:start position:0%
+place otherwise you've got a bit too
+ 
+
+ align:start position:0%
+place otherwise you've got a bit too
+much in your system or a bit too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+little okay more definitions the
+
+ align:start position:0%
+little okay more definitions the
+ 
+
+ align:start position:0%
+little okay more definitions the
+system can be an open
+
+ align:start position:0%
+system can be an open
+ 
+
+ align:start position:0%
+system can be an open
+system or it can
+
+ align:start position:0%
+system or it can
+ 
+
+ align:start position:0%
+system or it can
+be a closed system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system or can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+isolated the definitions are also
+
+ align:start position:0%
+isolated the definitions are also
+ 
+
+ align:start position:0%
+isolated the definitions are also
+important here okay an open
+
+ align:start position:0%
+important here okay an open
+ 
+
+ align:start position:0%
+important here okay an open
+system as the name describes allows mass
+
+ align:start position:0%
+system as the name describes allows mass
+ 
+
+ align:start position:0%
+system as the name describes allows mass
+and energy to freely flow through the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+boundary mass and
+
+ align:start position:0%
+boundary mass and
+ 
+
+ align:start position:0%
+boundary mass and
+energy flow through boundary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay mass and energy I'm an open
+
+ align:start position:0%
+okay mass and energy I'm an open
+ 
+
+ align:start position:0%
+okay mass and energy I'm an open
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+right water vapor goes through my skin
+
+ align:start position:0%
+right water vapor goes through my skin
+ 
+
+ align:start position:0%
+right water vapor goes through my skin
+I'm
+
+ align:start position:0%
+I'm
+ 
+
+ align:start position:0%
+I'm
+hot compared to the air of the
+
+ align:start position:0%
+hot compared to the air of the
+ 
+
+ align:start position:0%
+hot compared to the air of the
+room or cold if I'm somewhere that's
+
+ align:start position:0%
+room or cold if I'm somewhere that's
+ 
+
+ align:start position:0%
+room or cold if I'm somewhere that's
+warm so energy can go back and forth the
+
+ align:start position:0%
+warm so energy can go back and forth the
+ 
+
+ align:start position:0%
+warm so energy can go back and forth the
+thermos
+
+ align:start position:0%
+thermos
+ 
+
+ align:start position:0%
+thermos
+with a lid on top is not an open system
+
+ align:start position:0%
+with a lid on top is not an open system
+ 
+
+ align:start position:0%
+with a lid on top is not an open system
+hopefully your coffee is going to stay
+
+ align:start position:0%
+hopefully your coffee is going to stay
+ 
+
+ align:start position:0%
+hopefully your coffee is going to stay
+warm or hot in the thermos right it's
+
+ align:start position:0%
+warm or hot in the thermos right it's
+ 
+
+ align:start position:0%
+warm or hot in the thermos right it's
+not going to get out so the thermos is
+
+ align:start position:0%
+not going to get out so the thermos is
+ 
+
+ align:start position:0%
+not going to get out so the thermos is
+not an open system in fact the thermos
+
+ align:start position:0%
+not an open system in fact the thermos
+ 
+
+ align:start position:0%
+not an open system in fact the thermos
+is an isolated
+
+ align:start position:0%
+is an isolated
+ 
+
+ align:start position:0%
+is an isolated
+system the isol isolated system is the
+
+ align:start position:0%
+system the isol isolated system is the
+ 
+
+ align:start position:0%
+system the isol isolated system is the
+opposite of the open system no mass and
+
+ align:start position:0%
+opposite of the open system no mass and
+ 
+
+ align:start position:0%
+opposite of the open system no mass and
+no energy can flow through the
+
+ align:start position:0%
+no energy can flow through the
+ 
+
+ align:start position:0%
+no energy can flow through the
+boundary the closed
+
+ align:start position:0%
+boundary the closed
+ 
+
+ align:start position:0%
+boundary the closed
+system allows energy to transfer through
+
+ align:start position:0%
+system allows energy to transfer through
+ 
+
+ align:start position:0%
+system allows energy to transfer through
+the boundary but not mass so a CL system
+
+ align:start position:0%
+the boundary but not mass so a CL system
+ 
+
+ align:start position:0%
+the boundary but not mass so a CL system
+would be for instance a glass of ice
+
+ align:start position:0%
+would be for instance a glass of ice
+ 
+
+ align:start position:0%
+would be for instance a glass of ice
+water with an ice cube in it with a lid
+
+ align:start position:0%
+water with an ice cube in it with a lid
+ 
+
+ align:start position:0%
+water with an ice cube in it with a lid
+on top right the glass is not very
+
+ align:start position:0%
+on top right the glass is not very
+ 
+
+ align:start position:0%
+on top right the glass is not very
+insulating energy can flow across the
+
+ align:start position:0%
+insulating energy can flow across the
+ 
+
+ align:start position:0%
+insulating energy can flow across the
+glass but I put a lid on top and so the
+
+ align:start position:0%
+glass but I put a lid on top and so the
+ 
+
+ align:start position:0%
+glass but I put a lid on top and so the
+water can't get out that's a close
+
+ align:start position:0%
+water can't get out that's a close
+ 
+
+ align:start position:0%
+water can't get out that's a close
+system and you goes through the boundary
+
+ align:start position:0%
+system and you goes through the boundary
+ 
+
+ align:start position:0%
+system and you goes through the boundary
+but nothing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else okay important definitions even
+
+ align:start position:0%
+else okay important definitions even
+ 
+
+ align:start position:0%
+else okay important definitions even
+though they may sound really kind of
+
+ align:start position:0%
+though they may sound really kind of
+ 
+
+ align:start position:0%
+though they may sound really kind of
+dumb all right but they're really
+
+ align:start position:0%
+dumb all right but they're really
+ 
+
+ align:start position:0%
+dumb all right but they're really
+important because when you get the
+
+ align:start position:0%
+important because when you get the
+ 
+
+ align:start position:0%
+important because when you get the
+problem figuring out whether you have an
+
+ align:start position:0%
+problem figuring out whether you have an
+ 
+
+ align:start position:0%
+problem figuring out whether you have an
+open closed or isolated system what's
+
+ align:start position:0%
+open closed or isolated system what's
+ 
+
+ align:start position:0%
+open closed or isolated system what's
+the surroundings what's the boundary
+
+ align:start position:0%
+the surroundings what's the boundary
+ 
+
+ align:start position:0%
+the surroundings what's the boundary
+what is the
+
+ align:start position:0%
+what is the
+ 
+
+ align:start position:0%
+what is the
+system that's the first thing to make
+
+ align:start position:0%
+system that's the first thing to make
+ 
+
+ align:start position:0%
+system that's the first thing to make
+sure that is clear if it's not clear the
+
+ align:start position:0%
+sure that is clear if it's not clear the
+ 
+
+ align:start position:0%
+sure that is clear if it's not clear the
+problem is going to be impossible to
+
+ align:start position:0%
+problem is going to be impossible to
+ 
+
+ align:start position:0%
+problem is going to be impossible to
+solve and that's also how people you
+
+ align:start position:0%
+solve and that's also how people you
+ 
+
+ align:start position:0%
+solve and that's also how people you
+know find ways to break the second law
+
+ align:start position:0%
+know find ways to break the second law
+ 
+
+ align:start position:0%
+know find ways to break the second law
+it's because somehow they've messed up
+
+ align:start position:0%
+it's because somehow they've messed up
+ 
+
+ align:start position:0%
+it's because somehow they've messed up
+on what their system
+
+ align:start position:0%
+on what their system
+ 
+
+ align:start position:0%
+on what their system
+is right and they've included too much
+
+ align:start position:0%
+is right and they've included too much
+ 
+
+ align:start position:0%
+is right and they've included too much
+or too little in the system and it looks
+
+ align:start position:0%
+or too little in the system and it looks
+ 
+
+ align:start position:0%
+or too little in the system and it looks
+to them that that the second law is
+
+ align:start position:0%
+to them that that the second law is
+ 
+
+ align:start position:0%
+to them that that the second law is
+broken and they've created more energy
+
+ align:start position:0%
+broken and they've created more energy
+ 
+
+ align:start position:0%
+broken and they've created more energy
+than than uh than it's been brought
+
+ align:start position:0%
+than than uh than it's been brought
+ 
+
+ align:start position:0%
+than than uh than it's been brought
+in that's usually the
+
+ align:start position:0%
+in that's usually the
+ 
+
+ align:start position:0%
+in that's usually the
+case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay let's keep going um so
+
+ align:start position:0%
+questions okay let's keep going um so
+ 
+
+ align:start position:0%
+questions okay let's keep going um so
+now that we've got a system we've got to
+
+ align:start position:0%
+now that we've got a system we've got to
+ 
+
+ align:start position:0%
+now that we've got a system we've got to
+describe
+
+ align:start position:0%
+describe
+ 
+
+ align:start position:0%
+describe
+it so let's describe the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now it turns out that
+
+ align:start position:0%
+now it turns out that
+ 
+
+ align:start position:0%
+now it turns out that
+um when you're talking about macroscopic
+
+ align:start position:0%
+um when you're talking about macroscopic
+ 
+
+ align:start position:0%
+um when you're talking about macroscopic
+properties of
+
+ align:start position:0%
+properties of
+ 
+
+ align:start position:0%
+properties of
+matter you don't need very many
+
+ align:start position:0%
+matter you don't need very many
+ 
+
+ align:start position:0%
+matter you don't need very many
+variables to describe a system
+
+ align:start position:0%
+variables to describe a system
+ 
+
+ align:start position:0%
+variables to describe a system
+completely
+
+ align:start position:0%
+completely
+ 
+
+ align:start position:0%
+completely
+thermodynamically you just need a few
+
+ align:start position:0%
+thermodynamically you just need a few
+ 
+
+ align:start position:0%
+thermodynamically you just need a few
+macroscopic variables that are very
+
+ align:start position:0%
+macroscopic variables that are very
+ 
+
+ align:start position:0%
+macroscopic variables that are very
+familiar to you like the pressure the
+
+ align:start position:0%
+familiar to you like the pressure the
+ 
+
+ align:start position:0%
+familiar to you like the pressure the
+temperature the volume the number of
+
+ align:start position:0%
+temperature the volume the number of
+ 
+
+ align:start position:0%
+temperature the volume the number of
+moles of each
+
+ align:start position:0%
+moles of each
+ 
+
+ align:start position:0%
+moles of each
+component the mass of the
+
+ align:start position:0%
+component the mass of the
+ 
+
+ align:start position:0%
+component the mass of the
+system if you've got a magnetic field
+
+ align:start position:0%
+system if you've got a magnetic field
+ 
+
+ align:start position:0%
+system if you've got a magnetic field
+maybe the magnetic susceptibility the
+
+ align:start position:0%
+maybe the magnetic susceptibility the
+ 
+
+ align:start position:0%
+maybe the magnetic susceptibility the
+electric field we're not going to worry
+
+ align:start position:0%
+electric field we're not going to worry
+ 
+
+ align:start position:0%
+electric field we're not going to worry
+about these mag magnetic fields or
+
+ align:start position:0%
+about these mag magnetic fields or
+ 
+
+ align:start position:0%
+about these mag magnetic fields or
+electric fields in this class so pretty
+
+ align:start position:0%
+electric fields in this class so pretty
+ 
+
+ align:start position:0%
+electric fields in this class so pretty
+much we're going to focus on this set of
+
+ align:start position:0%
+much we're going to focus on this set of
+ 
+
+ align:start position:0%
+much we're going to focus on this set of
+variables
+
+ align:start position:0%
+variables
+ 
+
+ align:start position:0%
+variables
+here you're going to have to know when
+
+ align:start position:0%
+here you're going to have to know when
+ 
+
+ align:start position:0%
+here you're going to have to know when
+you describe the system if your system
+
+ align:start position:0%
+you describe the system if your system
+ 
+
+ align:start position:0%
+you describe the system if your system
+is homogeneous like your coffee with
+
+ align:start position:0%
+is homogeneous like your coffee with
+ 
+
+ align:start position:0%
+is homogeneous like your coffee with
+milk in it or heterogeneous like water
+
+ align:start position:0%
+milk in it or heterogeneous like water
+ 
+
+ align:start position:0%
+milk in it or heterogeneous like water
+with an ice cube in it so heterogeneous
+
+ align:start position:0%
+with an ice cube in it so heterogeneous
+ 
+
+ align:start position:0%
+with an ice cube in it so heterogeneous
+means that you've got different phases
+
+ align:start position:0%
+means that you've got different phases
+ 
+
+ align:start position:0%
+means that you've got different phases
+in your system I'm a heterogeneous
+
+ align:start position:0%
+in your system I'm a heterogeneous
+ 
+
+ align:start position:0%
+in your system I'm a heterogeneous
+system soft stuff heart stuff liquid
+
+ align:start position:0%
+system soft stuff heart stuff liquid
+ 
+
+ align:start position:0%
+system soft stuff heart stuff liquid
+stuff the coffee is homogeneous even
+
+ align:start position:0%
+stuff the coffee is homogeneous even
+ 
+
+ align:start position:0%
+stuff the coffee is homogeneous even
+though it's made up of many
+
+ align:start position:0%
+though it's made up of many
+ 
+
+ align:start position:0%
+though it's made up of many
+components many different kinds of
+
+ align:start position:0%
+components many different kinds of
+ 
+
+ align:start position:0%
+components many different kinds of
+molecules make up your coffee there's
+
+ align:start position:0%
+molecules make up your coffee there's
+ 
+
+ align:start position:0%
+molecules make up your coffee there's
+the water molecules the flavor molecules
+
+ align:start position:0%
+the water molecules the flavor molecules
+ 
+
+ align:start position:0%
+the water molecules the flavor molecules
+the milk proteins Etc but it's all mixed
+
+ align:start position:0%
+the milk proteins Etc but it's all mixed
+ 
+
+ align:start position:0%
+the milk proteins Etc but it's all mixed
+up together in a homogeneous macroscopic
+
+ align:start position:0%
+up together in a homogeneous macroscopic
+ 
+
+ align:start position:0%
+up together in a homogeneous macroscopic
+fashion if you drill down at the level
+
+ align:start position:0%
+fashion if you drill down at the level
+ 
+
+ align:start position:0%
+fashion if you drill down at the level
+of molecules you'd see that it's not
+
+ align:start position:0%
+of molecules you'd see that it's not
+ 
+
+ align:start position:0%
+of molecules you'd see that it's not
+homogeneous but thermodynamics takes a
+
+ align:start position:0%
+homogeneous but thermodynamics takes a
+ 
+
+ align:start position:0%
+homogeneous but thermodynamics takes a
+bird's eye view looks pretty uniform
+
+ align:start position:0%
+bird's eye view looks pretty uniform
+ 
+
+ align:start position:0%
+bird's eye view looks pretty uniform
+okay so that's a genous system one
+
+ align:start position:0%
+okay so that's a genous system one
+ 
+
+ align:start position:0%
+okay so that's a genous system one
+phase you have to know if your system is
+
+ align:start position:0%
+phase you have to know if your system is
+ 
+
+ align:start position:0%
+phase you have to know if your system is
+an equilibrium
+
+ align:start position:0%
+an equilibrium
+ 
+
+ align:start position:0%
+an equilibrium
+system uh or not if it's an equilibrium
+
+ align:start position:0%
+system uh or not if it's an equilibrium
+ 
+
+ align:start position:0%
+system uh or not if it's an equilibrium
+system then thermodynamics can describe
+
+ align:start position:0%
+system then thermodynamics can describe
+ 
+
+ align:start position:0%
+system then thermodynamics can describe
+it if it's not then you're going to have
+
+ align:start position:0%
+it if it's not then you're going to have
+ 
+
+ align:start position:0%
+it if it's not then you're going to have
+trouble describing it using
+
+ align:start position:0%
+trouble describing it using
+ 
+
+ align:start position:0%
+trouble describing it using
+thermodynamic properties thermodynamics
+
+ align:start position:0%
+thermodynamic properties thermodynamics
+ 
+
+ align:start position:0%
+thermodynamic properties thermodynamics
+is talks about equilibrium systems and
+
+ align:start position:0%
+is talks about equilibrium systems and
+ 
+
+ align:start position:0%
+is talks about equilibrium systems and
+how to go from one state of equilibrium
+
+ align:start position:0%
+how to go from one state of equilibrium
+ 
+
+ align:start position:0%
+how to go from one state of equilibrium
+to another state of
+
+ align:start position:0%
+to another state of
+ 
+
+ align:start position:0%
+to another state of
+equilibrium and what does equilibrium
+
+ align:start position:0%
+equilibrium and what does equilibrium
+ 
+
+ align:start position:0%
+equilibrium and what does equilibrium
+mean it means that the properties of the
+
+ align:start position:0%
+mean it means that the properties of the
+ 
+
+ align:start position:0%
+mean it means that the properties of the
+system the properties that describe the
+
+ align:start position:0%
+system the properties that describe the
+ 
+
+ align:start position:0%
+system the properties that describe the
+system don't change in time or in space
+
+ align:start position:0%
+system don't change in time or in space
+ 
+
+ align:start position:0%
+system don't change in time or in space
+so if I've got a a gas in a container
+
+ align:start position:0%
+so if I've got a a gas in a container
+ 
+
+ align:start position:0%
+so if I've got a a gas in a container
+the pressure of the gas has to be the
+
+ align:start position:0%
+the pressure of the gas has to be the
+ 
+
+ align:start position:0%
+the pressure of the gas has to be the
+same everywhere in the container
+
+ align:start position:0%
+same everywhere in the container
+ 
+
+ align:start position:0%
+same everywhere in the container
+otherwise it's not in equilibrium right
+
+ align:start position:0%
+otherwise it's not in equilibrium right
+ 
+
+ align:start position:0%
+otherwise it's not in equilibrium right
+if I place my container of gas on the
+
+ align:start position:0%
+if I place my container of gas on the
+ 
+
+ align:start position:0%
+if I place my container of gas on the
+table here and I come back an hour later
+
+ align:start position:0%
+table here and I come back an hour later
+ 
+
+ align:start position:0%
+table here and I come back an hour later
+the pressure needs to be the same when I
+
+ align:start position:0%
+the pressure needs to be the same when I
+ 
+
+ align:start position:0%
+the pressure needs to be the same when I
+come back otherwise it's not in
+
+ align:start position:0%
+come back otherwise it's not in
+ 
+
+ align:start position:0%
+come back otherwise it's not in
+equilibrium so it only talks about
+
+ align:start position:0%
+equilibrium so it only talks about
+ 
+
+ align:start position:0%
+equilibrium so it only talks about
+equilibrium systems
+
+ align:start position:0%
+equilibrium systems
+ 
+
+ align:start position:0%
+equilibrium systems
+what else do you need to know you need
+
+ align:start position:0%
+what else do you need to know you need
+ 
+
+ align:start position:0%
+what else do you need to know you need
+so you need to know the variables you
+
+ align:start position:0%
+so you need to know the variables you
+ 
+
+ align:start position:0%
+so you need to know the variables you
+need to know if it's heterogeneous or
+
+ align:start position:0%
+need to know if it's heterogeneous or
+ 
+
+ align:start position:0%
+need to know if it's heterogeneous or
+homogeneous you need to know if it's an
+
+ align:start position:0%
+homogeneous you need to know if it's an
+ 
+
+ align:start position:0%
+homogeneous you need to know if it's an
+equilibrium and you also need to know
+
+ align:start position:0%
+equilibrium and you also need to know
+ 
+
+ align:start position:0%
+equilibrium and you also need to know
+how many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+components you have in your system
+
+ align:start position:0%
+components you have in your system
+ 
+
+ align:start position:0%
+components you have in your system
+so a glass of ice water with an ice cube
+
+ align:start position:0%
+so a glass of ice water with an ice cube
+ 
+
+ align:start position:0%
+so a glass of ice water with an ice cube
+in it which is a heterogeneous system
+
+ align:start position:0%
+in it which is a heterogeneous system
+ 
+
+ align:start position:0%
+in it which is a heterogeneous system
+has only one component which is water
+
+ align:start position:0%
+has only one component which is water
+ 
+
+ align:start position:0%
+has only one component which is water
+H2O two phases but one component
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh latte which is a homogeneous system
+
+ align:start position:0%
+uh latte which is a homogeneous system
+ 
+
+ align:start position:0%
+uh latte which is a homogeneous system
+has a very very large number of
+
+ align:start position:0%
+has a very very large number of
+ 
+
+ align:start position:0%
+has a very very large number of
+components to it right all the
+
+ align:start position:0%
+components to it right all the
+ 
+
+ align:start position:0%
+components to it right all the
+components that make up the milk all the
+
+ align:start position:0%
+components that make up the milk all the
+ 
+
+ align:start position:0%
+components that make up the milk all the
+components that make up the coffee and
+
+ align:start position:0%
+components that make up the coffee and
+ 
+
+ align:start position:0%
+components that make up the coffee and
+all the impurities Etc cadmium heavy
+
+ align:start position:0%
+all the impurities Etc cadmium heavy
+ 
+
+ align:start position:0%
+all the impurities Etc cadmium heavy
+metals arene whatever they are in your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coffee okay any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions all right so we've described
+
+ align:start position:0%
+questions all right so we've described
+ 
+
+ align:start position:0%
+questions all right so we've described
+the system
+
+ align:start position:0%
+the system
+ 
+
+ align:start position:0%
+the system
+with these properties now these
+
+ align:start position:0%
+with these properties now these
+ 
+
+ align:start position:0%
+with these properties now these
+properties come in two flavors you have
+
+ align:start position:0%
+properties come in two flavors you have
+ 
+
+ align:start position:0%
+properties come in two flavors you have
+extensive
+
+ align:start position:0%
+extensive
+ 
+
+ align:start position:0%
+extensive
+properties and intensive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+properties the extensive properties are
+
+ align:start position:0%
+properties the extensive properties are
+ 
+
+ align:start position:0%
+properties the extensive properties are
+the ones that scale with the size of the
+
+ align:start position:0%
+the ones that scale with the size of the
+ 
+
+ align:start position:0%
+the ones that scale with the size of the
+system if you double this system they
+
+ align:start position:0%
+system if you double this system they
+ 
+
+ align:start position:0%
+system if you double this system they
+double in in their numerical number for
+
+ align:start position:0%
+double in in their numerical number for
+ 
+
+ align:start position:0%
+double in in their numerical number for
+instance the volume you double the
+
+ align:start position:0%
+instance the volume you double the
+ 
+
+ align:start position:0%
+instance the volume you double the
+volume you double v doubles right I mean
+
+ align:start position:0%
+volume you double v doubles right I mean
+ 
+
+ align:start position:0%
+volume you double v doubles right I mean
+that's obvious the mass if you double
+
+ align:start position:0%
+that's obvious the mass if you double
+ 
+
+ align:start position:0%
+that's obvious the mass if you double
+the amount of stuff the mass will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+double intensive properties don't care
+
+ align:start position:0%
+double intensive properties don't care
+ 
+
+ align:start position:0%
+double intensive properties don't care
+about the scale of your
+
+ align:start position:0%
+about the scale of your
+ 
+
+ align:start position:0%
+about the scale of your
+system if you double everything in the
+
+ align:start position:0%
+system if you double everything in the
+ 
+
+ align:start position:0%
+system if you double everything in the
+system the temperature is not going to
+
+ align:start position:0%
+system the temperature is not going to
+ 
+
+ align:start position:0%
+system the temperature is not going to
+change it's not going to double
+
+ align:start position:0%
+change it's not going to double
+ 
+
+ align:start position:0%
+change it's not going to double
+temperature stays the same so
+
+ align:start position:0%
+temperature stays the same so
+ 
+
+ align:start position:0%
+temperature stays the same so
+temperature is intensive and you can
+
+ align:start position:0%
+temperature is intensive and you can
+ 
+
+ align:start position:0%
+temperature is intensive and you can
+make intensive properties out of the
+
+ align:start position:0%
+make intensive properties out of the
+ 
+
+ align:start position:0%
+make intensive properties out of the
+extensive properties by dividing by the
+
+ align:start position:0%
+extensive properties by dividing by the
+ 
+
+ align:start position:0%
+extensive properties by dividing by the
+number of moles in the
+
+ align:start position:0%
+number of moles in the
+ 
+
+ align:start position:0%
+number of moles in the
+system so I can make a quantity that
+
+ align:start position:0%
+system so I can make a quantity that
+ 
+
+ align:start position:0%
+system so I can make a quantity that
+I'll call V bar which is the m volume
+
+ align:start position:0%
+I'll call V bar which is the m volume
+ 
+
+ align:start position:0%
+I'll call V bar which is the m volume
+the volume of one Mo of of a component
+
+ align:start position:0%
+the volume of one Mo of of a component
+ 
+
+ align:start position:0%
+the volume of one Mo of of a component
+in my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system and that becomes an intensive
+
+ align:start position:0%
+system and that becomes an intensive
+ 
+
+ align:start position:0%
+system and that becomes an intensive
+quantity a volume which is an intensive
+
+ align:start position:0%
+quantity a volume which is an intensive
+ 
+
+ align:start position:0%
+quantity a volume which is an intensive
+volume the volumes per mole of of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stuff okay so as I mentioned
+
+ align:start position:0%
+stuff okay so as I mentioned
+ 
+
+ align:start position:0%
+stuff okay so as I mentioned
+thermodynamics is is the science of
+
+ align:start position:0%
+thermodynamics is is the science of
+ 
+
+ align:start position:0%
+thermodynamics is is the science of
+equilibrium systems and um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we need it you need it also describes
+
+ align:start position:0%
+so we need it you need it also describes
+ 
+
+ align:start position:0%
+so we need it you need it also describes
+the evolution of one equilibrium to one
+
+ align:start position:0%
+the evolution of one equilibrium to one
+ 
+
+ align:start position:0%
+the evolution of one equilibrium to one
+another equilibrium how do we go from
+
+ align:start position:0%
+another equilibrium how do we go from
+ 
+
+ align:start position:0%
+another equilibrium how do we go from
+one to the other and so the set of
+
+ align:start position:0%
+one to the other and so the set of
+ 
+
+ align:start position:0%
+one to the other and so the set of
+properties that describes the system uh
+
+ align:start position:0%
+properties that describes the system uh
+ 
+
+ align:start position:0%
+properties that describes the system uh
+in equilibrium doesn't change okay so
+
+ align:start position:0%
+in equilibrium doesn't change okay so
+ 
+
+ align:start position:0%
+in equilibrium doesn't change okay so
+these unchanging properties that
+
+ align:start position:0%
+these unchanging properties that
+ 
+
+ align:start position:0%
+these unchanging properties that
+describe the state of the equilibrium
+
+ align:start position:0%
+describe the state of the equilibrium
+ 
+
+ align:start position:0%
+describe the state of the equilibrium
+state of the system uh are called State
+
+ align:start position:0%
+state of the system uh are called State
+ 
+
+ align:start position:0%
+state of the system uh are called State
+variables
+
+ align:start position:0%
+variables
+ 
+
+ align:start position:0%
+variables
+okay so the state
+
+ align:start position:0%
+okay so the state
+ 
+
+ align:start position:0%
+okay so the state
+State
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variables describe the equilibrium State
+
+ align:start position:0%
+variables describe the equilibrium State
+ 
+
+ align:start position:0%
+variables describe the equilibrium State
+and they don't care about how the state
+
+ align:start position:0%
+and they don't care about how the state
+ 
+
+ align:start position:0%
+and they don't care about how the state
+got to where it is they don't care about
+
+ align:start position:0%
+got to where it is they don't care about
+ 
+
+ align:start position:0%
+got to where it is they don't care about
+the history of the state they just know
+
+ align:start position:0%
+the history of the state they just know
+ 
+
+ align:start position:0%
+the history of the state they just know
+that if you have water at 0 degrees CSUS
+
+ align:start position:0%
+that if you have water at 0 degrees CSUS
+ 
+
+ align:start position:0%
+that if you have water at 0 degrees CSUS
+with ice in it that you can Define it as
+
+ align:start position:0%
+with ice in it that you can Define it as
+ 
+
+ align:start position:0%
+with ice in it that you can Define it as
+a heterogeneous system with a certain uh
+
+ align:start position:0%
+a heterogeneous system with a certain uh
+ 
+
+ align:start position:0%
+a heterogeneous system with a certain uh
+certain density for the water or certain
+
+ align:start position:0%
+certain density for the water or certain
+ 
+
+ align:start position:0%
+certain density for the water or certain
+density for the ice etc etc okay doesn't
+
+ align:start position:0%
+density for the ice etc etc okay doesn't
+ 
+
+ align:start position:0%
+density for the ice etc etc okay doesn't
+care how you got there we're going to
+
+ align:start position:0%
+care how you got there we're going to
+ 
+
+ align:start position:0%
+care how you got there we're going to
+find other properties that do care about
+
+ align:start position:0%
+find other properties that do care about
+ 
+
+ align:start position:0%
+find other properties that do care about
+the history of the system like work that
+
+ align:start position:0%
+the history of the system like work that
+ 
+
+ align:start position:0%
+the history of the system like work that
+you put in a system or heat that you put
+
+ align:start position:0%
+you put in a system or heat that you put
+ 
+
+ align:start position:0%
+you put in a system or heat that you put
+in a system or some other variables but
+
+ align:start position:0%
+in a system or some other variables but
+ 
+
+ align:start position:0%
+in a system or some other variables but
+you can't use those to define the
+
+ align:start position:0%
+you can't use those to define the
+ 
+
+ align:start position:0%
+you can't use those to define the
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+State you can only use the state
+
+ align:start position:0%
+State you can only use the state
+ 
+
+ align:start position:0%
+State you can only use the state
+variables independent of
+
+ align:start position:0%
+variables independent of
+ 
+
+ align:start position:0%
+variables independent of
+history and it turns out that for a one
+
+ align:start position:0%
+history and it turns out that for a one
+ 
+
+ align:start position:0%
+history and it turns out that for a one
+component system one component meaning
+
+ align:start position:0%
+component system one component meaning
+ 
+
+ align:start position:0%
+component system one component meaning
+one kind of molecule in the system
+
+ align:start position:0%
+one kind of molecule in the system
+ 
+
+ align:start position:0%
+one kind of molecule in the system
+uh all that you need to know to describe
+
+ align:start position:0%
+uh all that you need to know to describe
+ 
+
+ align:start position:0%
+uh all that you need to know to describe
+the system is the number of
+
+ align:start position:0%
+the system is the number of
+ 
+
+ align:start position:0%
+the system is the number of
+moles for one component
+
+ align:start position:0%
+moles for one component
+ 
+
+ align:start position:0%
+moles for one component
+system and to describe one phase in that
+
+ align:start position:0%
+system and to describe one phase in that
+ 
+
+ align:start position:0%
+system and to describe one phase in that
+system one component homogeneous system
+
+ align:start position:0%
+system one component homogeneous system
+ 
+
+ align:start position:0%
+system one component homogeneous system
+you need
+
+ align:start position:0%
+you need
+ 
+
+ align:start position:0%
+you need
+n and two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+variables for instance the pressure and
+
+ align:start position:0%
+variables for instance the pressure and
+ 
+
+ align:start position:0%
+variables for instance the pressure and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+temperature okay or the volume and the
+
+ align:start position:0%
+temperature okay or the volume and the
+ 
+
+ align:start position:0%
+temperature okay or the volume and the
+pressure if you have the number of moles
+
+ align:start position:0%
+pressure if you have the number of moles
+ 
+
+ align:start position:0%
+pressure if you have the number of moles
+and two intensive
+
+ align:start position:0%
+and two intensive
+ 
+
+ align:start position:0%
+and two intensive
+variables then you know everything there
+
+ align:start position:0%
+variables then you know everything there
+ 
+
+ align:start position:0%
+variables then you know everything there
+is to know about the
+
+ align:start position:0%
+is to know about the
+ 
+
+ align:start position:0%
+is to know about the
+system by the equilibrium state of that
+
+ align:start position:0%
+system by the equilibrium state of that
+ 
+
+ align:start position:0%
+system by the equilibrium state of that
+system there are hundreds of of
+
+ align:start position:0%
+system there are hundreds of of
+ 
+
+ align:start position:0%
+system there are hundreds of of
+quantities that you can calculate and
+
+ align:start position:0%
+quantities that you can calculate and
+ 
+
+ align:start position:0%
+quantities that you can calculate and
+measure that are interesting and
+
+ align:start position:0%
+measure that are interesting and
+ 
+
+ align:start position:0%
+measure that are interesting and
+important properties and all you need is
+
+ align:start position:0%
+important properties and all you need is
+ 
+
+ align:start position:0%
+important properties and all you need is
+just a few variables to get everything
+
+ align:start position:0%
+just a few variables to get everything
+ 
+
+ align:start position:0%
+just a few variables to get everything
+out and that's really the power of
+
+ align:start position:0%
+out and that's really the power of
+ 
+
+ align:start position:0%
+out and that's really the power of
+thermodynamics is that it takes so
+
+ align:start position:0%
+thermodynamics is that it takes so
+ 
+
+ align:start position:0%
+thermodynamics is that it takes so
+little information
+
+ align:start position:0%
+little information
+ 
+
+ align:start position:0%
+little information
+to get so much information out so little
+
+ align:start position:0%
+to get so much information out so little
+ 
+
+ align:start position:0%
+to get so much information out so little
+data to get a lot of predictive
+
+ align:start position:0%
+data to get a lot of predictive
+ 
+
+ align:start position:0%
+data to get a lot of predictive
+information
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+notes okay so um as we're going on with
+
+ align:start position:0%
+notes okay so um as we're going on with
+ 
+
+ align:start position:0%
+notes okay so um as we're going on with
+our definitions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um we can summarize a lot of these
+
+ align:start position:0%
+um we can summarize a lot of these
+ 
+
+ align:start position:0%
+um we can summarize a lot of these
+definitions into a
+
+ align:start position:0%
+definitions into a
+ 
+
+ align:start position:0%
+definitions into a
+notation a chemical notation that that
+
+ align:start position:0%
+notation a chemical notation that that
+ 
+
+ align:start position:0%
+notation a chemical notation that that
+will be very important and um so for
+
+ align:start position:0%
+will be very important and um so for
+ 
+
+ align:start position:0%
+will be very important and um so for
+instance if I'm talking about three
+
+ align:start position:0%
+instance if I'm talking about three
+ 
+
+ align:start position:0%
+instance if I'm talking about three
+moles of hydrogen at one bar 100 degrees
+
+ align:start position:0%
+moles of hydrogen at one bar 100 degrees
+ 
+
+ align:start position:0%
+moles of hydrogen at one bar 100 degrees
+C I'm not going to write given three
+
+ align:start position:0%
+C I'm not going to write given three
+ 
+
+ align:start position:0%
+C I'm not going to write given three
+moles of hydrogen at one bar and 3
+
+ align:start position:0%
+moles of hydrogen at one bar and 3
+ 
+
+ align:start position:0%
+moles of hydrogen at one bar and 3
+degrees blah blah blah right I'm going
+
+ align:start position:0%
+degrees blah blah blah right I'm going
+ 
+
+ align:start position:0%
+degrees blah blah blah right I'm going
+to write it in a compact notation I'm
+
+ align:start position:0%
+to write it in a compact notation I'm
+ 
+
+ align:start position:0%
+to write it in a compact notation I'm
+going to write it like this three moles
+
+ align:start position:0%
+going to write it like this three moles
+ 
+
+ align:start position:0%
+going to write it like this three moles
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+hydrogen which is a gas one
+
+ align:start position:0%
+hydrogen which is a gas one
+ 
+
+ align:start position:0%
+hydrogen which is a gas one
+bar 100° C okay this notation gives you
+
+ align:start position:0%
+bar 100° C okay this notation gives you
+ 
+
+ align:start position:0%
+bar 100° C okay this notation gives you
+everything you need to know about the
+
+ align:start position:0%
+everything you need to know about the
+ 
+
+ align:start position:0%
+everything you need to know about the
+system tells you the number of moles
+
+ align:start position:0%
+system tells you the number of moles
+ 
+
+ align:start position:0%
+system tells you the number of moles
+tells you the phase tells you what kind
+
+ align:start position:0%
+tells you the phase tells you what kind
+ 
+
+ align:start position:0%
+tells you the phase tells you what kind
+of molecule it is and gives you two
+
+ align:start position:0%
+of molecule it is and gives you two
+ 
+
+ align:start position:0%
+of molecule it is and gives you two
+variables that are State variables you
+
+ align:start position:0%
+variables that are State variables you
+ 
+
+ align:start position:0%
+variables that are State variables you
+could have the volume on the temperature
+
+ align:start position:0%
+could have the volume on the temperature
+ 
+
+ align:start position:0%
+could have the volume on the temperature
+you could have the volume and the
+
+ align:start position:0%
+you could have the volume and the
+ 
+
+ align:start position:0%
+you could have the volume and the
+pressure but this tells you everything I
+
+ align:start position:0%
+pressure but this tells you everything I
+ 
+
+ align:start position:0%
+pressure but this tells you everything I
+don't need to write it out in words and
+
+ align:start position:0%
+don't need to write it out in words and
+ 
+
+ align:start position:0%
+don't need to write it out in words and
+then if I want to U tell you about a
+
+ align:start position:0%
+then if I want to U tell you about a
+ 
+
+ align:start position:0%
+then if I want to U tell you about a
+change of state or a let's let's first
+
+ align:start position:0%
+change of state or a let's let's first
+ 
+
+ align:start position:0%
+change of state or a let's let's first
+start with a mixture suppose that I
+
+ align:start position:0%
+start with a mixture suppose that I
+ 
+
+ align:start position:0%
+start with a mixture suppose that I
+wanted that I give you a mixture
+
+ align:start position:0%
+wanted that I give you a mixture
+ 
+
+ align:start position:0%
+wanted that I give you a mixture
+like this is a homogeneous system with
+
+ align:start position:0%
+like this is a homogeneous system with
+ 
+
+ align:start position:0%
+like this is a homogeneous system with
+two components like five moles of H2O
+
+ align:start position:0%
+two components like five moles of H2O
+ 
+
+ align:start position:0%
+two components like five moles of H2O
+which is a liquid at one
+
+ align:start position:0%
+which is a liquid at one
+ 
+
+ align:start position:0%
+which is a liquid at one
+bar 25° C
+
+ align:start position:0%
+bar 25° C
+ 
+
+ align:start position:0%
+bar 25° C
+plus 5 moles of
+
+ align:start position:0%
+plus 5 moles of
+ 
+
+ align:start position:0%
+plus 5 moles of
+ch3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ch2 which is a liquid at one
+
+ align:start position:0%
+ch2 which is a liquid at one
+ 
+
+ align:start position:0%
+ch2 which is a liquid at one
+bar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+25° okay this describes rough something
+
+ align:start position:0%
+25° okay this describes rough something
+ 
+
+ align:start position:0%
+25° okay this describes rough something
+that is fairly common place it's a 100
+
+ align:start position:0%
+that is fairly common place it's a 100
+ 
+
+ align:start position:0%
+that is fairly common place it's a 100
+Proof vodka right half water half
+
+ align:start position:0%
+Proof vodka right half water half
+ 
+
+ align:start position:0%
+Proof vodka right half water half
+ethanol that describes that macroscopic
+
+ align:start position:0%
+ethanol that describes that macroscopic
+ 
+
+ align:start position:0%
+ethanol that describes that macroscopic
+system okay you're missing out the
+
+ align:start position:0%
+system okay you're missing out the
+ 
+
+ align:start position:0%
+system okay you're missing out the
+impurities all the little flavor
+
+ align:start position:0%
+impurities all the little flavor
+ 
+
+ align:start position:0%
+impurities all the little flavor
+molecules that go into it but basically
+
+ align:start position:0%
+molecules that go into it but basically
+ 
+
+ align:start position:0%
+molecules that go into it but basically
+that's that's the hom homogeneous system
+
+ align:start position:0%
+that's that's the hom homogeneous system
+ 
+
+ align:start position:0%
+that's that's the hom homogeneous system
+here described two component homogeneous
+
+ align:start position:0%
+here described two component homogeneous
+ 
+
+ align:start position:0%
+here described two component homogeneous
+system then you can do all sorts of
+
+ align:start position:0%
+system then you can do all sorts of
+ 
+
+ align:start position:0%
+system then you can do all sorts of
+predictive uh uh stuff with that system
+
+ align:start position:0%
+predictive uh uh stuff with that system
+ 
+
+ align:start position:0%
+predictive uh uh stuff with that system
+all right that's the equilibrium system
+
+ align:start position:0%
+all right that's the equilibrium system
+ 
+
+ align:start position:0%
+all right that's the equilibrium system
+now we want to show a notation how do we
+
+ align:start position:0%
+now we want to show a notation how do we
+ 
+
+ align:start position:0%
+now we want to show a notation how do we
+go from one equilibrium State like this
+
+ align:start position:0%
+go from one equilibrium State like this
+ 
+
+ align:start position:0%
+go from one equilibrium State like this
+describes to another equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state so we take our two equilibrium
+
+ align:start position:0%
+state so we take our two equilibrium
+ 
+
+ align:start position:0%
+state so we take our two equilibrium
+States and we just put an equal sign
+
+ align:start position:0%
+States and we just put an equal sign
+ 
+
+ align:start position:0%
+States and we just put an equal sign
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+them and the equal sign
+
+ align:start position:0%
+them and the equal sign
+ 
+
+ align:start position:0%
+them and the equal sign
+means take go from one to the other so
+
+ align:start position:0%
+means take go from one to the other so
+ 
+
+ align:start position:0%
+means take go from one to the other so
+if we took three moles of our three of
+
+ align:start position:0%
+if we took three moles of our three of
+ 
+
+ align:start position:0%
+if we took three moles of our three of
+hydrogen which is a gas at 5
+
+ align:start position:0%
+hydrogen which is a gas at 5
+ 
+
+ align:start position:0%
+hydrogen which is a gas at 5
+bar and 100° cus and which is a nice
+
+ align:start position:0%
+bar and 100° cus and which is a nice
+ 
+
+ align:start position:0%
+bar and 100° cus and which is a nice
+equilibrium State here and we say all
+
+ align:start position:0%
+equilibrium State here and we say all
+ 
+
+ align:start position:0%
+equilibrium State here and we say all
+right now we're going to change the
+
+ align:start position:0%
+right now we're going to change the
+ 
+
+ align:start position:0%
+right now we're going to change the
+equilibrium state to something new we're
+
+ align:start position:0%
+equilibrium state to something new we're
+ 
+
+ align:start position:0%
+equilibrium state to something new we're
+going to do
+
+ align:start position:0%
+going to do
+ 
+
+ align:start position:0%
+going to do
+um an expansion let's say all right
+
+ align:start position:0%
+um an expansion let's say all right
+ 
+
+ align:start position:0%
+um an expansion let's say all right
+we're going to drop the the pressure the
+
+ align:start position:0%
+we're going to drop the the pressure the
+ 
+
+ align:start position:0%
+we're going to drop the the pressure the
+volume is going to go up I don't need to
+
+ align:start position:0%
+volume is going to go up I don't need to
+ 
+
+ align:start position:0%
+volume is going to go up I don't need to
+tell you the volume here because you've
+
+ align:start position:0%
+tell you the volume here because you've
+ 
+
+ align:start position:0%
+tell you the volume here because you've
+got enough information to calculate the
+
+ align:start position:0%
+got enough information to calculate the
+ 
+
+ align:start position:0%
+got enough information to calculate the
+volume the number of moles stays the
+
+ align:start position:0%
+volume the number of moles stays the
+ 
+
+ align:start position:0%
+volume the number of moles stays the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+close system gas doesn't come out stays
+
+ align:start position:0%
+close system gas doesn't come out stays
+ 
+
+ align:start position:0%
+close system gas doesn't come out stays
+a gas but now the pressure is less the
+
+ align:start position:0%
+a gas but now the pressure is less the
+ 
+
+ align:start position:0%
+a gas but now the pressure is less the
+temperature is
+
+ align:start position:0%
+temperature is
+ 
+
+ align:start position:0%
+temperature is
+less I've done some sort of expansion on
+
+ align:start position:0%
+less I've done some sort of expansion on
+ 
+
+ align:start position:0%
+less I've done some sort of expansion on
+this I've gone from one equilibrium
+
+ align:start position:0%
+this I've gone from one equilibrium
+ 
+
+ align:start position:0%
+this I've gone from one equilibrium
+state to another equilibrium and the
+
+ align:start position:0%
+state to another equilibrium and the
+ 
+
+ align:start position:0%
+state to another equilibrium and the
+equal sign means you go from this state
+
+ align:start position:0%
+equal sign means you go from this state
+ 
+
+ align:start position:0%
+equal sign means you go from this state
+to that state it's not a chemical
+
+ align:start position:0%
+to that state it's not a chemical
+ 
+
+ align:start position:0%
+to that state it's not a chemical
+reaction right that's why we don't have
+
+ align:start position:0%
+reaction right that's why we don't have
+ 
+
+ align:start position:0%
+reaction right that's why we don't have
+an arrow here because we could go back
+
+ align:start position:0%
+an arrow here because we could go back
+ 
+
+ align:start position:0%
+an arrow here because we could go back
+this way too can go back and forth
+
+ align:start position:0%
+this way too can go back and forth
+ 
+
+ align:start position:0%
+this way too can go back and forth
+between these two kilog states they're
+
+ align:start position:0%
+between these two kilog states they're
+ 
+
+ align:start position:0%
+between these two kilog states they're
+connected this means they're connected
+
+ align:start position:0%
+connected this means they're connected
+ 
+
+ align:start position:0%
+connected this means they're connected
+and when when I put this I have to tell
+
+ align:start position:0%
+and when when I put this I have to tell
+ 
+
+ align:start position:0%
+and when when I put this I have to tell
+you how they are connected I have to
+
+ align:start position:0%
+you how they are connected I have to
+ 
+
+ align:start position:0%
+you how they are connected I have to
+tell you the path if you're going to
+
+ align:start position:0%
+tell you the path if you're going to
+ 
+
+ align:start position:0%
+tell you the path if you're going to
+solve a problem for instance you want to
+
+ align:start position:0%
+solve a problem for instance you want to
+ 
+
+ align:start position:0%
+solve a problem for instance you want to
+know how much energy you're going to get
+
+ align:start position:0%
+know how much energy you're going to get
+ 
+
+ align:start position:0%
+know how much energy you're going to get
+out from doing this expansion right how
+
+ align:start position:0%
+out from doing this expansion right how
+ 
+
+ align:start position:0%
+out from doing this expansion right how
+much energy are you going to get out and
+
+ align:start position:0%
+much energy are you going to get out and
+ 
+
+ align:start position:0%
+much energy are you going to get out and
+how far are you going to be able to
+
+ align:start position:0%
+how far are you going to be able to
+ 
+
+ align:start position:0%
+how far are you going to be able to
+drive the car with this expansion let's
+
+ align:start position:0%
+drive the car with this expansion let's
+ 
+
+ align:start position:0%
+drive the car with this expansion let's
+say let's say that's the problem right
+
+ align:start position:0%
+say let's say that's the problem right
+ 
+
+ align:start position:0%
+say let's say that's the problem right
+so I need to tell you how you're doing
+
+ align:start position:0%
+so I need to tell you how you're doing
+ 
+
+ align:start position:0%
+so I need to tell you how you're doing
+the expansion because that's going to
+
+ align:start position:0%
+the expansion because that's going to
+ 
+
+ align:start position:0%
+the expansion because that's going to
+tell you how much energy you're wasting
+
+ align:start position:0%
+tell you how much energy you're wasting
+ 
+
+ align:start position:0%
+tell you how much energy you're wasting
+during that expansion goes back to the
+
+ align:start position:0%
+during that expansion goes back to the
+ 
+
+ align:start position:0%
+during that expansion goes back to the
+second law right nothing is efficient
+
+ align:start position:0%
+second law right nothing is efficient
+ 
+
+ align:start position:0%
+second law right nothing is efficient
+you're always wasting energy into heat
+
+ align:start position:0%
+you're always wasting energy into heat
+ 
+
+ align:start position:0%
+you're always wasting energy into heat
+somewhere when you do a change that
+
+ align:start position:0%
+somewhere when you do a change that
+ 
+
+ align:start position:0%
+somewhere when you do a change that
+involves a mechanical
+
+ align:start position:0%
+involves a mechanical
+ 
+
+ align:start position:0%
+involves a mechanical
+change all right so I need to tell you
+
+ align:start position:0%
+change all right so I need to tell you
+ 
+
+ align:start position:0%
+change all right so I need to tell you
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+path when I go from one state to the
+
+ align:start position:0%
+path when I go from one state to the
+ 
+
+ align:start position:0%
+path when I go from one state to the
+other and the path is going to be the
+
+ align:start position:0%
+other and the path is going to be the
+ 
+
+ align:start position:0%
+other and the path is going to be the
+sequence intermediate States going from
+
+ align:start position:0%
+sequence intermediate States going from
+ 
+
+ align:start position:0%
+sequence intermediate States going from
+the initial state to the final state so
+
+ align:start position:0%
+the initial state to the final state so
+ 
+
+ align:start position:0%
+the initial state to the final state so
+for instance if I draw a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+graph of pressure on one axis and
+
+ align:start position:0%
+graph of pressure on one axis and
+ 
+
+ align:start position:0%
+graph of pressure on one axis and
+temperature on the other axis my initial
+
+ align:start position:0%
+temperature on the other axis my initial
+ 
+
+ align:start position:0%
+temperature on the other axis my initial
+state is at a temperature of
+
+ align:start position:0%
+state is at a temperature of
+ 
+
+ align:start position:0%
+state is at a temperature of
+100°
+
+ align:start position:0%
+100°
+ 
+
+ align:start position:0%
+100°
+celi and 5 bar my final state is 50° C
+
+ align:start position:0%
+celi and 5 bar my final state is 50° C
+ 
+
+ align:start position:0%
+celi and 5 bar my final state is 50° C
+and one
+
+ align:start position:0%
+and one
+ 
+
+ align:start position:0%
+and one
+bar so I could have a uh two steps in my
+
+ align:start position:0%
+bar so I could have a uh two steps in my
+ 
+
+ align:start position:0%
+bar so I could have a uh two steps in my
+path I could decide first of all to keep
+
+ align:start position:0%
+path I could decide first of all to keep
+ 
+
+ align:start position:0%
+path I could decide first of all to keep
+the pressure
+
+ align:start position:0%
+the pressure
+ 
+
+ align:start position:0%
+the pressure
+constant and lower the
+
+ align:start position:0%
+constant and lower the
+ 
+
+ align:start position:0%
+constant and lower the
+pressure when I get to 50 degrees C I
+
+ align:start position:0%
+pressure when I get to 50 degrees C I
+ 
+
+ align:start position:0%
+pressure when I get to 50 degrees C I
+could choose to keep the temperature
+
+ align:start position:0%
+could choose to keep the temperature
+ 
+
+ align:start position:0%
+could choose to keep the temperature
+constant and lower the pressure I'm
+
+ align:start position:0%
+constant and lower the pressure I'm
+ 
+
+ align:start position:0%
+constant and lower the pressure I'm
+sorry my first step would be to keep the
+
+ align:start position:0%
+sorry my first step would be to keep the
+ 
+
+ align:start position:0%
+sorry my first step would be to keep the
+pressure constant lower the temperature
+
+ align:start position:0%
+pressure constant lower the temperature
+ 
+
+ align:start position:0%
+pressure constant lower the temperature
+then I lower the pressure keeping the
+
+ align:start position:0%
+then I lower the pressure keeping the
+ 
+
+ align:start position:0%
+then I lower the pressure keeping the
+temperature constant so there's my
+
+ align:start position:0%
+temperature constant so there's my
+ 
+
+ align:start position:0%
+temperature constant so there's my
+intermediate State here this is one of
+
+ align:start position:0%
+intermediate State here this is one of
+ 
+
+ align:start position:0%
+intermediate State here this is one of
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+paths there's an infinite number of
+
+ align:start position:0%
+paths there's an infinite number of
+ 
+
+ align:start position:0%
+paths there's an infinite number of
+paths you could take you could take a
+
+ align:start position:0%
+paths you could take you could take a
+ 
+
+ align:start position:0%
+paths you could take you could take a
+continuous path where you have an
+
+ align:start position:0%
+continuous path where you have an
+ 
+
+ align:start position:0%
+continuous path where you have an
+infinite number of
+
+ align:start position:0%
+infinite number of
+ 
+
+ align:start position:0%
+infinite number of
+equilibrium points in between the two a
+
+ align:start position:0%
+equilibrium points in between the two a
+ 
+
+ align:start position:0%
+equilibrium points in between the two a
+smooth path where you drop the pressure
+
+ align:start position:0%
+smooth path where you drop the pressure
+ 
+
+ align:start position:0%
+smooth path where you drop the pressure
+and the temperature simultaneously in
+
+ align:start position:0%
+and the temperature simultaneously in
+ 
+
+ align:start position:0%
+and the temperature simultaneously in
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+increments right so when you do a
+
+ align:start position:0%
+increments right so when you do a
+ 
+
+ align:start position:0%
+increments right so when you do a
+problem the path is going to turned out
+
+ align:start position:0%
+problem the path is going to turned out
+ 
+
+ align:start position:0%
+problem the path is going to turned out
+to be extremely important how do you get
+
+ align:start position:0%
+to be extremely important how do you get
+ 
+
+ align:start position:0%
+to be extremely important how do you get
+from the initial
+
+ align:start position:0%
+from the initial
+ 
+
+ align:start position:0%
+from the initial
+state to the final State Define the
+
+ align:start position:0%
+state to the final State Define the
+ 
+
+ align:start position:0%
+state to the final State Define the
+initial State Define the final State
+
+ align:start position:0%
+initial State Define the final State
+ 
+
+ align:start position:0%
+initial State Define the final State
+Define the path get all these really
+
+ align:start position:0%
+Define the path get all these really
+ 
+
+ align:start position:0%
+Define the path get all these really
+clear and you basically solve the
+
+ align:start position:0%
+clear and you basically solve the
+ 
+
+ align:start position:0%
+clear and you basically solve the
+problem you got to spend the time to
+
+ align:start position:0%
+problem you got to spend the time to
+ 
+
+ align:start position:0%
+problem you got to spend the time to
+make sure that everything is well
+
+ align:start position:0%
+make sure that everything is well
+ 
+
+ align:start position:0%
+make sure that everything is well
+defined before you start trying to work
+
+ align:start position:0%
+defined before you start trying to work
+ 
+
+ align:start position:0%
+defined before you start trying to work
+out these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problems okay more about the path there
+
+ align:start position:0%
+problems okay more about the path there
+ 
+
+ align:start position:0%
+problems okay more about the path there
+there are a couple ways you could go
+
+ align:start position:0%
+there are a couple ways you could go
+ 
+
+ align:start position:0%
+there are a couple ways you could go
+through that
+
+ align:start position:0%
+through that
+ 
+
+ align:start position:0%
+through that
+path if I look at this smooth path here
+
+ align:start position:0%
+path if I look at this smooth path here
+ 
+
+ align:start position:0%
+path if I look at this smooth path here
+I could have that path be very slow and
+
+ align:start position:0%
+I could have that path be very slow and
+ 
+
+ align:start position:0%
+I could have that path be very slow and
+steady so that at every point of the
+
+ align:start position:0%
+steady so that at every point of the
+ 
+
+ align:start position:0%
+steady so that at every point of the
+along the way my gas is in equilibrium
+
+ align:start position:0%
+along the way my gas is in equilibrium
+ 
+
+ align:start position:0%
+along the way my gas is in equilibrium
+so I've got this this piston here it's
+
+ align:start position:0%
+so I've got this this piston here it's
+ 
+
+ align:start position:0%
+so I've got this this piston here it's
+compressed and I slowly slowly increase
+
+ align:start position:0%
+compressed and I slowly slowly increase
+ 
+
+ align:start position:0%
+compressed and I slowly slowly increase
+the volume drop the
+
+ align:start position:0%
+the volume drop the
+ 
+
+ align:start position:0%
+the volume drop the
+temperature I can go back the gas is in
+
+ align:start position:0%
+temperature I can go back the gas is in
+ 
+
+ align:start position:0%
+temperature I can go back the gas is in
+equilibrium at every point of the way
+
+ align:start position:0%
+equilibrium at every point of the way
+ 
+
+ align:start position:0%
+equilibrium at every point of the way
+it's called
+
+ align:start position:0%
+it's called
+ 
+
+ align:start position:0%
+it's called
+it that's a reversible path I can
+
+ align:start position:0%
+it that's a reversible path I can
+ 
+
+ align:start position:0%
+it that's a reversible path I can
+reverse the process I expand it and I
+
+ align:start position:0%
+reverse the process I expand it and I
+ 
+
+ align:start position:0%
+reverse the process I expand it and I
+reverse it no problem so I could have a
+
+ align:start position:0%
+reverse it no problem so I could have a
+ 
+
+ align:start position:0%
+reverse it no problem so I could have a
+reversible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+path or I take my my
+
+ align:start position:0%
+path or I take my my
+ 
+
+ align:start position:0%
+path or I take my my
+gas and instead of slowly slowly raising
+
+ align:start position:0%
+gas and instead of slowly slowly raising
+ 
+
+ align:start position:0%
+gas and instead of slowly slowly raising
+it dropping the pressure I I go from
+
+ align:start position:0%
+it dropping the pressure I I go from
+ 
+
+ align:start position:0%
+it dropping the pressure I I go from
+Five Bar to one bar are extremely fast
+
+ align:start position:0%
+Five Bar to one bar are extremely fast
+ 
+
+ align:start position:0%
+Five Bar to one bar are extremely fast
+right what happens to my gas inside well
+
+ align:start position:0%
+right what happens to my gas inside well
+ 
+
+ align:start position:0%
+right what happens to my gas inside well
+my gas inside is going to be very
+
+ align:start position:0%
+my gas inside is going to be very
+ 
+
+ align:start position:0%
+my gas inside is going to be very
+unhappy it's not going to stay in
+
+ align:start position:0%
+unhappy it's not going to stay in
+ 
+
+ align:start position:0%
+unhappy it's not going to stay in
+equilibrium parts of the system are
+
+ align:start position:0%
+equilibrium parts of the system are
+ 
+
+ align:start position:0%
+equilibrium parts of the system are
+going to be at Five Bar parts of it are
+
+ align:start position:0%
+going to be at Five Bar parts of it are
+ 
+
+ align:start position:0%
+going to be at Five Bar parts of it are
+one bar parts of it may be even at Zero
+
+ align:start position:0%
+one bar parts of it may be even at Zero
+ 
+
+ align:start position:0%
+one bar parts of it may be even at Zero
+Bar if I go really fast I'm going to
+
+ align:start position:0%
+Bar if I go really fast I'm going to
+ 
+
+ align:start position:0%
+Bar if I go really fast I'm going to
+create a vacuum so the system will not
+
+ align:start position:0%
+create a vacuum so the system will not
+ 
+
+ align:start position:0%
+create a vacuum so the system will not
+be described by a single state variable
+
+ align:start position:0%
+be described by a single state variable
+ 
+
+ align:start position:0%
+be described by a single state variable
+during the during the path right if I
+
+ align:start position:0%
+during the during the path right if I
+ 
+
+ align:start position:0%
+during the during the path right if I
+look at different points in my container
+
+ align:start position:0%
+look at different points in my container
+ 
+
+ align:start position:0%
+look at different points in my container
+during that path path I'm going to have
+
+ align:start position:0%
+during that path path I'm going to have
+ 
+
+ align:start position:0%
+during that path path I'm going to have
+to use a different value of pressure or
+
+ align:start position:0%
+to use a different value of pressure or
+ 
+
+ align:start position:0%
+to use a different value of pressure or
+different value of temperature at
+
+ align:start position:0%
+different value of temperature at
+ 
+
+ align:start position:0%
+different value of temperature at
+different points of the path of the
+
+ align:start position:0%
+different points of the path of the
+ 
+
+ align:start position:0%
+different points of the path of the
+container that's not an equilibrium
+
+ align:start position:0%
+container that's not an equilibrium
+ 
+
+ align:start position:0%
+container that's not an equilibrium
+State and that process turns out then to
+
+ align:start position:0%
+State and that process turns out then to
+ 
+
+ align:start position:0%
+State and that process turns out then to
+be an irreversible process do it very
+
+ align:start position:0%
+be an irreversible process do it very
+ 
+
+ align:start position:0%
+be an irreversible process do it very
+quickly now to reverse it and get back
+
+ align:start position:0%
+quickly now to reverse it and get back
+ 
+
+ align:start position:0%
+quickly now to reverse it and get back
+to the initial point is going to require
+
+ align:start position:0%
+to the initial point is going to require
+ 
+
+ align:start position:0%
+to the initial point is going to require
+some input from outside uh like heat or
+
+ align:start position:0%
+some input from outside uh like heat or
+ 
+
+ align:start position:0%
+some input from outside uh like heat or
+extra work or extra heat or something
+
+ align:start position:0%
+extra work or extra heat or something
+ 
+
+ align:start position:0%
+extra work or extra heat or something
+because you've done an irreversible
+
+ align:start position:0%
+because you've done an irreversible
+ 
+
+ align:start position:0%
+because you've done an irreversible
+process you've wasted a lot of of of
+
+ align:start position:0%
+process you've wasted a lot of of of
+ 
+
+ align:start position:0%
+process you've wasted a lot of of of
+energy in in in doing that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process okay you have to tell them tell
+
+ align:start position:0%
+process okay you have to tell them tell
+ 
+
+ align:start position:0%
+process okay you have to tell them tell
+us whether I have to tell you whether
+
+ align:start position:0%
+us whether I have to tell you whether
+ 
+
+ align:start position:0%
+us whether I have to tell you whether
+the path is uh reversible or
+
+ align:start position:0%
+the path is uh reversible or
+ 
+
+ align:start position:0%
+the path is uh reversible or
+irreversible and the irreversible path
+
+ align:start position:0%
+irreversible and the irreversible path
+ 
+
+ align:start position:0%
+irreversible and the irreversible path
+also defines the direction of time right
+
+ align:start position:0%
+also defines the direction of time right
+ 
+
+ align:start position:0%
+also defines the direction of time right
+you can only have an irreversable path
+
+ align:start position:0%
+you can only have an irreversable path
+ 
+
+ align:start position:0%
+you can only have an irreversable path
+go one way in time not the other way
+
+ align:start position:0%
+go one way in time not the other way
+ 
+
+ align:start position:0%
+go one way in time not the other way
+chalk breaks irreversibly and you can't
+
+ align:start position:0%
+chalk breaks irreversibly and you can't
+ 
+
+ align:start position:0%
+chalk breaks irreversibly and you can't
+put it back together so easily you got
+
+ align:start position:0%
+put it back together so easily you got
+ 
+
+ align:start position:0%
+put it back together so easily you got
+to pretty much take that ch and make a
+
+ align:start position:0%
+to pretty much take that ch and make a
+ 
+
+ align:start position:0%
+to pretty much take that ch and make a
+slurry out of it put water and dry it
+
+ align:start position:0%
+slurry out of it put water and dry it
+ 
+
+ align:start position:0%
+slurry out of it put water and dry it
+back up put it in a mold and then you
+
+ align:start position:0%
+back up put it in a mold and then you
+ 
+
+ align:start position:0%
+back up put it in a mold and then you
+can have a chalk again right but you
+
+ align:start position:0%
+can have a chalk again right but you
+ 
+
+ align:start position:0%
+can have a chalk again right but you
+can't just glue it back together that
+
+ align:start position:0%
+can't just glue it back together that
+ 
+
+ align:start position:0%
+can't just glue it back together that
+would not be the same state as what you
+
+ align:start position:0%
+would not be the same state as what you
+ 
+
+ align:start position:0%
+would not be the same state as what you
+started out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with and then there are a bunch of words
+
+ align:start position:0%
+with and then there are a bunch of words
+ 
+
+ align:start position:0%
+with and then there are a bunch of words
+that describe these paths words like
+
+ align:start position:0%
+that describe these paths words like
+ 
+
+ align:start position:0%
+that describe these paths words like
+adiabatic which you'll be very familiar
+
+ align:start position:0%
+adiabatic which you'll be very familiar
+ 
+
+ align:start position:0%
+adiabatic which you'll be very familiar
+with adiabatic means that there's no
+
+ align:start position:0%
+with adiabatic means that there's no
+ 
+
+ align:start position:0%
+with adiabatic means that there's no
+heat transfer between the system and the
+
+ align:start position:0%
+heat transfer between the system and the
+ 
+
+ align:start position:0%
+heat transfer between the system and the
+surrounding the boundary is impervious
+
+ align:start position:0%
+surrounding the boundary is impervious
+ 
+
+ align:start position:0%
+surrounding the boundary is impervious
+to transfer of heat like a thermos
+
+ align:start position:0%
+to transfer of heat like a thermos
+ 
+
+ align:start position:0%
+to transfer of heat like a thermos
+anything that happens inside of the
+
+ align:start position:0%
+anything that happens inside of the
+ 
+
+ align:start position:0%
+anything that happens inside of the
+thermos is an adiabatic change because
+
+ align:start position:0%
+thermos is an adiabatic change because
+ 
+
+ align:start position:0%
+thermos is an adiabatic change because
+the thermos has no connection in terms
+
+ align:start position:0%
+the thermos has no connection in terms
+ 
+
+ align:start position:0%
+the thermos has no connection in terms
+of energy to the outside world there's
+
+ align:start position:0%
+of energy to the outside world there's
+ 
+
+ align:start position:0%
+of energy to the outside world there's
+no heat that can go through the walls of
+
+ align:start position:0%
+no heat that can go through the walls of
+ 
+
+ align:start position:0%
+no heat that can go through the walls of
+the thermos whereas like isobaric means
+
+ align:start position:0%
+the thermos whereas like isobaric means
+ 
+
+ align:start position:0%
+the thermos whereas like isobaric means
+constant pressure so this path right
+
+ align:start position:0%
+constant pressure so this path right
+ 
+
+ align:start position:0%
+constant pressure so this path right
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+from this top red path is an isobaric
+
+ align:start position:0%
+from this top red path is an isobaric
+ 
+
+ align:start position:0%
+from this top red path is an isobaric
+process right constant temperature means
+
+ align:start position:0%
+process right constant temperature means
+ 
+
+ align:start position:0%
+process right constant temperature means
+isothermal so the this part here is an
+
+ align:start position:0%
+isothermal so the this part here is an
+ 
+
+ align:start position:0%
+isothermal so the this part here is an
+isothermal process so the going from
+
+ align:start position:0%
+isothermal process so the going from
+ 
+
+ align:start position:0%
+isothermal process so the going from
+initial to final uh state state Ates
+
+ align:start position:0%
+initial to final uh state state Ates
+ 
+
+ align:start position:0%
+initial to final uh state state Ates
+with a red path you start with an
+
+ align:start position:0%
+with a red path you start with an
+ 
+
+ align:start position:0%
+with a red path you start with an
+isobaric process and you end with an
+
+ align:start position:0%
+isobaric process and you end with an
+ 
+
+ align:start position:0%
+isobaric process and you end with an
+isothermal process again these are words
+
+ align:start position:0%
+isothermal process again these are words
+ 
+
+ align:start position:0%
+isothermal process again these are words
+that are very meaningful when you read
+
+ align:start position:0%
+that are very meaningful when you read
+ 
+
+ align:start position:0%
+that are very meaningful when you read
+the text of of a problem or of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process any questions before we get to
+
+ align:start position:0%
+process any questions before we get to
+ 
+
+ align:start position:0%
+process any questions before we get to
+the zero
+
+ align:start position:0%
+the zero
+ 
+
+ align:start position:0%
+the zero
+flaw pretty much done with our
+
+ align:start position:0%
+flaw pretty much done with our
+ 
+
+ align:start position:0%
+flaw pretty much done with our
+definitions here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes agatic can be either reversible or
+
+ align:start position:0%
+yes agatic can be either reversible or
+ 
+
+ align:start position:0%
+yes agatic can be either reversible or
+not and we're going to do that probably
+
+ align:start position:0%
+not and we're going to do that probably
+ 
+
+ align:start position:0%
+not and we're going to do that probably
+next next time or two
+
+ align:start position:0%
+next next time or two
+ 
+
+ align:start position:0%
+next next time or two
+times any other questions yes is there a
+
+ align:start position:0%
+times any other questions yes is there a
+ 
+
+ align:start position:0%
+times any other questions yes is there a
+boundary between reversible and
+
+ align:start position:0%
+boundary between reversible and
+ 
+
+ align:start position:0%
+boundary between reversible and
+irreversible a boundary between
+
+ align:start position:0%
+irreversible a boundary between
+ 
+
+ align:start position:0%
+irreversible a boundary between
+reversible and
+
+ align:start position:0%
+reversible and
+ 
+
+ align:start position:0%
+reversible and
+irreversible like uh something is almost
+
+ align:start position:0%
+irreversible like uh something is almost
+ 
+
+ align:start position:0%
+irreversible like uh something is almost
+reversible and almost
+
+ align:start position:0%
+reversible and almost
+ 
+
+ align:start position:0%
+reversible and almost
+irreversible no pretty much things are
+
+ align:start position:0%
+irreversible no pretty much things are
+ 
+
+ align:start position:0%
+irreversible no pretty much things are
+either reversible or
+
+ align:start position:0%
+either reversible or
+ 
+
+ align:start position:0%
+either reversible or
+irreversible uh now in in practice it
+
+ align:start position:0%
+irreversible uh now in in practice it
+ 
+
+ align:start position:0%
+irreversible uh now in in practice it
+depends on how good your measurement is
+
+ align:start position:0%
+depends on how good your measurement is
+ 
+
+ align:start position:0%
+depends on how good your measurement is
+right um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and probably also in practice nothing is
+
+ align:start position:0%
+and probably also in practice nothing is
+ 
+
+ align:start position:0%
+and probably also in practice nothing is
+truly
+
+ align:start position:0%
+truly
+ 
+
+ align:start position:0%
+truly
+reversible right so uh it depends on
+
+ align:start position:0%
+reversible right so uh it depends on
+ 
+
+ align:start position:0%
+reversible right so uh it depends on
+your error bar in a sense
+
+ align:start position:0%
+your error bar in a sense
+ 
+
+ align:start position:0%
+your error bar in a sense
+right it depends on what you define
+
+ align:start position:0%
+right it depends on what you define
+ 
+
+ align:start position:0%
+right it depends on what you define
+exactly defining your system becomes a
+
+ align:start position:0%
+exactly defining your system becomes a
+ 
+
+ align:start position:0%
+exactly defining your system becomes a
+great area but it should be pretty clear
+
+ align:start position:0%
+great area but it should be pretty clear
+ 
+
+ align:start position:0%
+great area but it should be pretty clear
+if you can treat something as reversible
+
+ align:start position:0%
+if you can treat something as reversible
+ 
+
+ align:start position:0%
+if you can treat something as reversible
+or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+irreversible questions other questions
+
+ align:start position:0%
+irreversible questions other questions
+ 
+
+ align:start position:0%
+irreversible questions other questions
+it's a it's a good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question okay so the zero law we're
+
+ align:start position:0%
+question okay so the zero law we're
+ 
+
+ align:start position:0%
+question okay so the zero law we're
+going to go through the laws now the
+
+ align:start position:0%
+going to go through the laws now the
+ 
+
+ align:start position:0%
+going to go through the laws now the
+zeroth law talks about defining
+
+ align:start position:0%
+zeroth law talks about defining
+ 
+
+ align:start position:0%
+zeroth law talks about defining
+temperature and it's um it's the common
+
+ align:start position:0%
+temperature and it's um it's the common
+ 
+
+ align:start position:0%
+temperature and it's um it's the common
+sense law you all know how when
+
+ align:start position:0%
+sense law you all know how when
+ 
+
+ align:start position:0%
+sense law you all know how when
+something is hot it's high it's got a
+
+ align:start position:0%
+something is hot it's high it's got a
+ 
+
+ align:start position:0%
+something is hot it's high it's got a
+higher temperature than when something
+
+ align:start position:0%
+higher temperature than when something
+ 
+
+ align:start position:0%
+higher temperature than when something
+is cold but it's important to
+
+ align:start position:0%
+is cold but it's important to
+ 
+
+ align:start position:0%
+is cold but it's important to
+Define define that and Define something
+
+ align:start position:0%
+Define define that and Define something
+ 
+
+ align:start position:0%
+Define define that and Define something
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+thermometer so what do you know what's
+
+ align:start position:0%
+thermometer so what do you know what's
+ 
+
+ align:start position:0%
+thermometer so what do you know what's
+the empirical information that everybody
+
+ align:start position:0%
+the empirical information that everybody
+ 
+
+ align:start position:0%
+the empirical information that everybody
+knows everybody knows that if you take
+
+ align:start position:0%
+knows everybody knows that if you take
+ 
+
+ align:start position:0%
+knows everybody knows that if you take
+something which is
+
+ align:start position:0%
+something which is
+ 
+
+ align:start position:0%
+something which is
+hot and something which is
+
+ align:start position:0%
+hot and something which is
+ 
+
+ align:start position:0%
+hot and something which is
+cold and you bring them
+
+ align:start position:0%
+cold and you bring them
+ 
+
+ align:start position:0%
+cold and you bring them
+together make them touch that heat is
+
+ align:start position:0%
+together make them touch that heat is
+ 
+
+ align:start position:0%
+together make them touch that heat is
+going to flow from the
+
+ align:start position:0%
+going to flow from the
+ 
+
+ align:start position:0%
+going to flow from the
+cold from the hot to the cold right I
+
+ align:start position:0%
+cold from the hot to the cold right I
+ 
+
+ align:start position:0%
+cold from the hot to the cold right I
+make them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+touch and he flows from hot to cold
+
+ align:start position:0%
+touch and he flows from hot to cold
+ 
+
+ align:start position:0%
+touch and he flows from hot to cold
+that's common sense this is
+
+ align:start position:0%
+that's common sense this is
+ 
+
+ align:start position:0%
+that's common sense this is
+part of your DNA right and then the
+
+ align:start position:0%
+part of your DNA right and then the
+ 
+
+ align:start position:0%
+part of your DNA right and then the
+final product is an
+
+ align:start position:0%
+final product is an
+ 
+
+ align:start position:0%
+final product is an
+object
+
+ align:start position:0%
+object
+ 
+
+ align:start position:0%
+object
+AB which ends up at a at a temperature
+
+ align:start position:0%
+AB which ends up at a at a temperature
+ 
+
+ align:start position:0%
+AB which ends up at a at a temperature
+or Warmness which is in between the hot
+
+ align:start position:0%
+or Warmness which is in between the hot
+ 
+
+ align:start position:0%
+or Warmness which is in between the hot
+and the cold so this turns out to be
+
+ align:start position:0%
+and the cold so this turns out to be
+ 
+
+ align:start position:0%
+and the cold so this turns out to be
+warm right you get to a new equilibrium
+
+ align:start position:0%
+warm right you get to a new equilibrium
+ 
+
+ align:start position:0%
+warm right you get to a new equilibrium
+state which is in between what this was
+
+ align:start position:0%
+state which is in between what this was
+ 
+
+ align:start position:0%
+state which is in between what this was
+and what a and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bware so um then how do you know that
+
+ align:start position:0%
+bware so um then how do you know that
+ 
+
+ align:start position:0%
+bware so um then how do you know that
+that it that it's
+
+ align:start position:0%
+that it that it's
+ 
+
+ align:start position:0%
+that it that it's
+changed temperature or that heat has
+
+ align:start position:0%
+changed temperature or that heat has
+ 
+
+ align:start position:0%
+changed temperature or that heat has
+flowed from A to B practically speaking
+
+ align:start position:0%
+flowed from A to B practically speaking
+ 
+
+ align:start position:0%
+flowed from A to B practically speaking
+you need some sort of of property that's
+
+ align:start position:0%
+you need some sort of of property that's
+ 
+
+ align:start position:0%
+you need some sort of of property that's
+changing as heat is Flowing for instance
+
+ align:start position:0%
+changing as heat is Flowing for instance
+ 
+
+ align:start position:0%
+changing as heat is Flowing for instance
+um if a were
+
+ align:start position:0%
+um if a were
+ 
+
+ align:start position:0%
+um if a were
+metallic you could measure the
+
+ align:start position:0%
+metallic you could measure the
+ 
+
+ align:start position:0%
+metallic you could measure the
+conductivity of a or the resistivity and
+
+ align:start position:0%
+conductivity of a or the resistivity and
+ 
+
+ align:start position:0%
+conductivity of a or the resistivity and
+at heat as heat flows out of a into B
+
+ align:start position:0%
+at heat as heat flows out of a into B
+ 
+
+ align:start position:0%
+at heat as heat flows out of a into B
+the resistivity of a would
+
+ align:start position:0%
+the resistivity of a would
+ 
+
+ align:start position:0%
+the resistivity of a would
+change right or you could have something
+
+ align:start position:0%
+change right or you could have something
+ 
+
+ align:start position:0%
+change right or you could have something
+that's colorometric that changes color
+
+ align:start position:0%
+that's colorometric that changes color
+ 
+
+ align:start position:0%
+that's colorometric that changes color
+when when it's colder right and so you
+
+ align:start position:0%
+when when it's colder right and so you
+ 
+
+ align:start position:0%
+when when it's colder right and so you
+could see the heat flowing as a changes
+
+ align:start position:0%
+could see the heat flowing as a changes
+ 
+
+ align:start position:0%
+could see the heat flowing as a changes
+color or B changes color as he flows
+
+ align:start position:0%
+color or B changes color as he flows
+ 
+
+ align:start position:0%
+color or B changes color as he flows
+into B so you need some sort of property
+
+ align:start position:0%
+into B so you need some sort of property
+ 
+
+ align:start position:0%
+into B so you need some sort of property
+some of something you can see something
+
+ align:start position:0%
+some of something you can see something
+ 
+
+ align:start position:0%
+some of something you can see something
+you can measure that tells you uh that
+
+ align:start position:0%
+you can measure that tells you uh that
+ 
+
+ align:start position:0%
+you can measure that tells you uh that
+heat has flowed now if you have three
+
+ align:start position:0%
+heat has flowed now if you have three
+ 
+
+ align:start position:0%
+heat has flowed now if you have three
+objects if you have a b and c
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you bring them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together and a is the hottest B is the
+
+ align:start position:0%
+together and a is the hottest B is the
+ 
+
+ align:start position:0%
+together and a is the hottest B is the
+medium one and C is the coldest so from
+
+ align:start position:0%
+medium one and C is the coldest so from
+ 
+
+ align:start position:0%
+medium one and C is the coldest so from
+hottest to coldest a b c if you bring
+
+ align:start position:0%
+hottest to coldest a b c if you bring
+ 
+
+ align:start position:0%
+hottest to coldest a b c if you bring
+them together and make them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+touch you know intuitively
+
+ align:start position:0%
+touch you know intuitively
+ 
+
+ align:start position:0%
+touch you know intuitively
+that heat will not
+
+ align:start position:0%
+that heat will not
+ 
+
+ align:start position:0%
+that heat will not
+flow like this right you know that's not
+
+ align:start position:0%
+flow like this right you know that's not
+ 
+
+ align:start position:0%
+flow like this right you know that's not
+going to happen you know that what will
+
+ align:start position:0%
+going to happen you know that what will
+ 
+
+ align:start position:0%
+going to happen you know that what will
+happen is that heat will flow from A to
+
+ align:start position:0%
+happen is that heat will flow from A to
+ 
+
+ align:start position:0%
+happen is that heat will flow from A to
+B from B to C and from a to
+
+ align:start position:0%
+B from B to C and from a to
+ 
+
+ align:start position:0%
+B from B to C and from a to
+c that's common sense you know that
+
+ align:start position:0%
+c that's common sense you know that
+ 
+
+ align:start position:0%
+c that's common sense you know that
+right and the other way and the circle
+
+ align:start position:0%
+right and the other way and the circle
+ 
+
+ align:start position:0%
+right and the other way and the circle
+will never happen that would that would
+
+ align:start position:0%
+will never happen that would that would
+ 
+
+ align:start position:0%
+will never happen that would that would
+give rise to a perpetual motion machine
+
+ align:start position:0%
+give rise to a perpetual motion machine
+ 
+
+ align:start position:0%
+give rise to a perpetual motion machine
+breaking of the second
+
+ align:start position:0%
+breaking of the second
+ 
+
+ align:start position:0%
+breaking of the second
+law can't
+
+ align:start position:0%
+law can't
+ 
+
+ align:start position:0%
+law can't
+happen but that's that's an empirical
+
+ align:start position:0%
+happen but that's that's an empirical
+ 
+
+ align:start position:0%
+happen but that's that's an empirical
+observation that he flows in this
+
+ align:start position:0%
+observation that he flows in this
+ 
+
+ align:start position:0%
+observation that he flows in this
+direction and and that's the zero flaw
+
+ align:start position:0%
+direction and and that's the zero flaw
+ 
+
+ align:start position:0%
+direction and and that's the zero flaw
+thermodynamic it's pretty simple right
+
+ align:start position:0%
+thermodynamic it's pretty simple right
+ 
+
+ align:start position:0%
+thermodynamic it's pretty simple right
+the zero flaw says that if a and
+
+ align:start position:0%
+the zero flaw says that if a and
+ 
+
+ align:start position:0%
+the zero flaw says that if a and
+b it doesn't exactly say that but it
+
+ align:start position:0%
+b it doesn't exactly say that but it
+ 
+
+ align:start position:0%
+b it doesn't exactly say that but it
+implies this right it says that if a and
+
+ align:start position:0%
+implies this right it says that if a and
+ 
+
+ align:start position:0%
+implies this right it says that if a and
+b are in thermal equilibrium if these
+
+ align:start position:0%
+b are in thermal equilibrium if these
+ 
+
+ align:start position:0%
+b are in thermal equilibrium if these
+two are in thermal equilibrium meaning
+
+ align:start position:0%
+two are in thermal equilibrium meaning
+ 
+
+ align:start position:0%
+two are in thermal equilibrium meaning
+that there's no heat that flows between
+
+ align:start position:0%
+that there's no heat that flows between
+ 
+
+ align:start position:0%
+that there's no heat that flows between
+them so that's the definition of thermal
+
+ align:start position:0%
+them so that's the definition of thermal
+ 
+
+ align:start position:0%
+them so that's the definition of thermal
+equilibrium no heat flows between them
+
+ align:start position:0%
+equilibrium no heat flows between them
+ 
+
+ align:start position:0%
+equilibrium no heat flows between them
+if these two are in thermal equilibrium
+
+ align:start position:0%
+if these two are in thermal equilibrium
+ 
+
+ align:start position:0%
+if these two are in thermal equilibrium
+and these two are in Thal equilibrium
+
+ align:start position:0%
+and these two are in Thal equilibrium
+ 
+
+ align:start position:0%
+and these two are in Thal equilibrium
+then a and c will always be will also be
+
+ align:start position:0%
+then a and c will always be will also be
+ 
+
+ align:start position:0%
+then a and c will always be will also be
+in thermal
+
+ align:start position:0%
+in thermal
+ 
+
+ align:start position:0%
+in thermal
+equilibrium but if there's no heat
+
+ align:start position:0%
+equilibrium but if there's no heat
+ 
+
+ align:start position:0%
+equilibrium but if there's no heat
+flowing between these two and no heat
+
+ align:start position:0%
+flowing between these two and no heat
+ 
+
+ align:start position:0%
+flowing between these two and no heat
+flowing between these two then you can't
+
+ align:start position:0%
+flowing between these two then you can't
+ 
+
+ align:start position:0%
+flowing between these two then you can't
+have heat flowing between these
+
+ align:start position:0%
+have heat flowing between these
+ 
+
+ align:start position:0%
+have heat flowing between these
+two so if I get rid of these arrows
+
+ align:start position:0%
+two so if I get rid of these arrows
+ 
+
+ align:start position:0%
+two so if I get rid of these arrows
+there's no heat flowing because they're
+
+ align:start position:0%
+there's no heat flowing because they're
+ 
+
+ align:start position:0%
+there's no heat flowing because they're
+in thermal equilibrium then I can't have
+
+ align:start position:0%
+in thermal equilibrium then I can't have
+ 
+
+ align:start position:0%
+in thermal equilibrium then I can't have
+an arrow here that's what a zero FL
+
+ align:start position:0%
+an arrow here that's what a zero FL
+ 
+
+ align:start position:0%
+an arrow here that's what a zero FL
+says they're all the same temperature
+
+ align:start position:0%
+says they're all the same temperature
+ 
+
+ align:start position:0%
+says they're all the same temperature
+that's what it says if two objects are
+
+ align:start position:0%
+that's what it says if two objects are
+ 
+
+ align:start position:0%
+that's what it says if two objects are
+in the same temperature temperature and
+
+ align:start position:0%
+in the same temperature temperature and
+ 
+
+ align:start position:0%
+in the same temperature temperature and
+two other objects have the same
+
+ align:start position:0%
+two other objects have the same
+ 
+
+ align:start position:0%
+two other objects have the same
+temperature then all three must have the
+
+ align:start position:0%
+temperature then all three must have the
+ 
+
+ align:start position:0%
+temperature then all three must have the
+same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temperature that sounds pretty silly but
+
+ align:start position:0%
+temperature that sounds pretty silly but
+ 
+
+ align:start position:0%
+temperature that sounds pretty silly but
+it's really important because it allows
+
+ align:start position:0%
+it's really important because it allows
+ 
+
+ align:start position:0%
+it's really important because it allows
+you to define a
+
+ align:start position:0%
+you to define a
+ 
+
+ align:start position:0%
+you to define a
+thermometer and
+
+ align:start position:0%
+thermometer and
+ 
+
+ align:start position:0%
+thermometer and
+temperature okay because now you can say
+
+ align:start position:0%
+temperature okay because now you can say
+ 
+
+ align:start position:0%
+temperature okay because now you can say
+all right well
+
+ align:start position:0%
+all right well
+ 
+
+ align:start position:0%
+all right well
+now B can be my thermometer I have two
+
+ align:start position:0%
+now B can be my thermometer I have two
+ 
+
+ align:start position:0%
+now B can be my thermometer I have two
+objects I have an object which is in
+
+ align:start position:0%
+objects I have an object which is in
+ 
+
+ align:start position:0%
+objects I have an object which is in
+Madagascar and an object which is in
+
+ align:start position:0%
+Madagascar and an object which is in
+ 
+
+ align:start position:0%
+Madagascar and an object which is in
+Boston
+
+ align:start position:0%
+Boston
+ 
+
+ align:start position:0%
+Boston
+right and I want to know are they the
+
+ align:start position:0%
+right and I want to know are they the
+ 
+
+ align:start position:0%
+right and I want to know are they the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+temperature so I comment with a third
+
+ align:start position:0%
+temperature so I comment with a third
+ 
+
+ align:start position:0%
+temperature so I comment with a third
+object B I go to Madagascar I put B in
+
+ align:start position:0%
+object B I go to Madagascar I put B in
+ 
+
+ align:start position:0%
+object B I go to Madagascar I put B in
+contact with
+
+ align:start position:0%
+contact with
+ 
+
+ align:start position:0%
+contact with
+a then I insulate everything you know
+
+ align:start position:0%
+a then I insulate everything you know
+ 
+
+ align:start position:0%
+a then I insulate everything you know
+take it away make see if there's any
+
+ align:start position:0%
+take it away make see if there's any
+ 
+
+ align:start position:0%
+take it away make see if there's any
+heat flow let's say there's no heat flow
+
+ align:start position:0%
+heat flow let's say there's no heat flow
+ 
+
+ align:start position:0%
+heat flow let's say there's no heat flow
+okay then I insulate it and back get
+
+ align:start position:0%
+okay then I insulate it and back get
+ 
+
+ align:start position:0%
+okay then I insulate it and back get
+back on the plane to Boston and go back
+
+ align:start position:0%
+back on the plane to Boston and go back
+ 
+
+ align:start position:0%
+back on the plane to Boston and go back
+and touch B with C if there's no heat
+
+ align:start position:0%
+and touch B with C if there's no heat
+ 
+
+ align:start position:0%
+and touch B with C if there's no heat
+flow between B and C then I can say all
+
+ align:start position:0%
+flow between B and C then I can say all
+ 
+
+ align:start position:0%
+flow between B and C then I can say all
+right A and C were the same temperature
+
+ align:start position:0%
+right A and C were the same temperature
+ 
+
+ align:start position:0%
+right A and C were the same temperature
+B is my thermometer that tells me that A
+
+ align:start position:0%
+B is my thermometer that tells me that A
+ 
+
+ align:start position:0%
+B is my thermometer that tells me that A
+and C are the same temperature and
+
+ align:start position:0%
+and C are the same temperature and
+ 
+
+ align:start position:0%
+and C are the same temperature and
+there's a certain property associated
+
+ align:start position:0%
+there's a certain property associated
+ 
+
+ align:start position:0%
+there's a certain property associated
+with heat flow with b and it didn't
+
+ align:start position:0%
+with heat flow with b and it didn't
+ 
+
+ align:start position:0%
+with heat flow with b and it didn't
+change right and that property could be
+
+ align:start position:0%
+change right and that property could be
+ 
+
+ align:start position:0%
+change right and that property could be
+color it could be resistivity could be a
+
+ align:start position:0%
+color it could be resistivity could be a
+ 
+
+ align:start position:0%
+color it could be resistivity could be a
+lot of different things could be
+
+ align:start position:0%
+lot of different things could be
+ 
+
+ align:start position:0%
+lot of different things could be
+volume and the temperature then is
+
+ align:start position:0%
+volume and the temperature then is
+ 
+
+ align:start position:0%
+volume and the temperature then is
+associated with that property and if it
+
+ align:start position:0%
+associated with that property and if it
+ 
+
+ align:start position:0%
+associated with that property and if it
+had changed then the temperature between
+
+ align:start position:0%
+had changed then the temperature between
+ 
+
+ align:start position:0%
+had changed then the temperature between
+those two would have changed in a very
+
+ align:start position:0%
+those two would have changed in a very
+ 
+
+ align:start position:0%
+those two would have changed in a very
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+way so Theos slw then allows you to
+
+ align:start position:0%
+way so Theos slw then allows you to
+ 
+
+ align:start position:0%
+way so Theos slw then allows you to
+define the concept of
+
+ align:start position:0%
+define the concept of
+ 
+
+ align:start position:0%
+define the concept of
+temperature and the measurement of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+temperature through a
+
+ align:start position:0%
+temperature through a
+ 
+
+ align:start position:0%
+temperature through a
+thermometer okay let's very briefly go
+
+ align:start position:0%
+thermometer okay let's very briefly go
+ 
+
+ align:start position:0%
+thermometer okay let's very briefly go
+through stuff that you've learned before
+
+ align:start position:0%
+through stuff that you've learned before
+ 
+
+ align:start position:0%
+through stuff that you've learned before
+so now you you have this object which is
+
+ align:start position:0%
+so now you you have this object which is
+ 
+
+ align:start position:0%
+so now you you have this object which is
+going to tell you whether other things
+
+ align:start position:0%
+going to tell you whether other things
+ 
+
+ align:start position:0%
+going to tell you whether other things
+are in thermo not what do you need for
+
+ align:start position:0%
+are in thermo not what do you need for
+ 
+
+ align:start position:0%
+are in thermo not what do you need for
+that object you need
+
+ align:start position:0%
+that object you need
+ 
+
+ align:start position:0%
+that object you need
+um you need that object to be a
+
+ align:start position:0%
+um you need that object to be a
+ 
+
+ align:start position:0%
+um you need that object to be a
+substance to have to be something so the
+
+ align:start position:0%
+substance to have to be something so the
+ 
+
+ align:start position:0%
+substance to have to be something so the
+active part of the thermometer could be
+
+ align:start position:0%
+active part of the thermometer could be
+ 
+
+ align:start position:0%
+active part of the thermometer could be
+could be water could be alcohol Mercury
+
+ align:start position:0%
+could be water could be alcohol Mercury
+ 
+
+ align:start position:0%
+could be water could be alcohol Mercury
+could be a piece of
+
+ align:start position:0%
+could be a piece of
+ 
+
+ align:start position:0%
+could be a piece of
+metal you need a substance and then that
+
+ align:start position:0%
+metal you need a substance and then that
+ 
+
+ align:start position:0%
+metal you need a substance and then that
+substance has to have a property that
+
+ align:start position:0%
+substance has to have a property that
+ 
+
+ align:start position:0%
+substance has to have a property that
+changes depending on the heat flow I.E
+
+ align:start position:0%
+changes depending on the heat flow I.E
+ 
+
+ align:start position:0%
+changes depending on the heat flow I.E
+depending on whether it's it sensing
+
+ align:start position:0%
+depending on whether it's it sensing
+ 
+
+ align:start position:0%
+depending on whether it's it sensing
+that it's the same temperature or a
+
+ align:start position:0%
+that it's the same temperature or a
+ 
+
+ align:start position:0%
+that it's the same temperature or a
+different temperature than something
+
+ align:start position:0%
+different temperature than something
+ 
+
+ align:start position:0%
+different temperature than something
+else and that property uh could be the
+
+ align:start position:0%
+else and that property uh could be the
+ 
+
+ align:start position:0%
+else and that property uh could be the
+volume like if you have a mercury
+
+ align:start position:0%
+volume like if you have a mercury
+ 
+
+ align:start position:0%
+volume like if you have a mercury
+thermometer volume of the Mercury could
+
+ align:start position:0%
+thermometer volume of the Mercury could
+ 
+
+ align:start position:0%
+thermometer volume of the Mercury could
+be temperature could be resistivity if
+
+ align:start position:0%
+be temperature could be resistivity if
+ 
+
+ align:start position:0%
+be temperature could be resistivity if
+you have a a um a thermal
+
+ align:start position:0%
+you have a a um a thermal
+ 
+
+ align:start position:0%
+you have a a um a thermal
+couple um could be the
+
+ align:start position:0%
+couple um could be the
+ 
+
+ align:start position:0%
+couple um could be the
+pressure all right so now you have an
+
+ align:start position:0%
+pressure all right so now you have an
+ 
+
+ align:start position:0%
+pressure all right so now you have an
+object you've got a property that
+
+ align:start position:0%
+object you've got a property that
+ 
+
+ align:start position:0%
+object you've got a property that
+changes depending on the heat flow he's
+
+ align:start position:0%
+changes depending on the heat flow he's
+ 
+
+ align:start position:0%
+changes depending on the heat flow he's
+going to tell you about the temperature
+
+ align:start position:0%
+going to tell you about the temperature
+ 
+
+ align:start position:0%
+going to tell you about the temperature
+now you need to define a temperature
+
+ align:start position:0%
+now you need to define a temperature
+ 
+
+ align:start position:0%
+now you need to define a temperature
+scale so you need some reference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points to be able to tell you okay this
+
+ align:start position:0%
+points to be able to tell you okay this
+ 
+
+ align:start position:0%
+points to be able to tell you okay this
+temperature is 550
+
+ align:start position:0%
+temperature is 550
+ 
+
+ align:start position:0%
+temperature is 550
+de Smith whatever right so you assign
+
+ align:start position:0%
+de Smith whatever right so you assign
+ 
+
+ align:start position:0%
+de Smith whatever right so you assign
+values to very specific states of matter
+
+ align:start position:0%
+values to very specific states of matter
+ 
+
+ align:start position:0%
+values to very specific states of matter
+and and call those the reference points
+
+ align:start position:0%
+and and call those the reference points
+ 
+
+ align:start position:0%
+and and call those the reference points
+for your temperature for instance
+
+ align:start position:0%
+for your temperature for instance
+ 
+
+ align:start position:0%
+for your temperature for instance
+freezing of water or boiling of water
+
+ align:start position:0%
+freezing of water or boiling of water
+ 
+
+ align:start position:0%
+freezing of water or boiling of water
+this the standard ones and then an
+
+ align:start position:0%
+this the standard ones and then an
+ 
+
+ align:start position:0%
+this the standard ones and then an
+interpolation scheme how do you you you
+
+ align:start position:0%
+interpolation scheme how do you you you
+ 
+
+ align:start position:0%
+interpolation scheme how do you you you
+need a functional form that connects the
+
+ align:start position:0%
+need a functional form that connects the
+ 
+
+ align:start position:0%
+need a functional form that connects the
+value at one state of matter the
+
+ align:start position:0%
+value at one state of matter the
+ 
+
+ align:start position:0%
+value at one state of matter the
+freezing point of water to another phase
+
+ align:start position:0%
+freezing point of water to another phase
+ 
+
+ align:start position:0%
+freezing point of water to another phase
+change the boiling corn of water you can
+
+ align:start position:0%
+change the boiling corn of water you can
+ 
+
+ align:start position:0%
+change the boiling corn of water you can
+choose a a linear interpolation or
+
+ align:start position:0%
+choose a a linear interpolation or
+ 
+
+ align:start position:0%
+choose a a linear interpolation or
+quadratic but you've got to choose
+
+ align:start position:0%
+quadratic but you've got to choose
+ 
+
+ align:start position:0%
+quadratic but you've got to choose
+it and it turns out not to be so easy
+
+ align:start position:0%
+it and it turns out not to be so easy
+ 
+
+ align:start position:0%
+it and it turns out not to be so easy
+and if you go back in the 1800s when
+
+ align:start position:0%
+and if you go back in the 1800s when
+ 
+
+ align:start position:0%
+and if you go back in the 1800s when
+thermodynamics were starting there were
+
+ align:start position:0%
+thermodynamics were starting there were
+ 
+
+ align:start position:0%
+thermodynamics were starting there were
+a zillion different temperature scales
+
+ align:start position:0%
+a zillion different temperature scales
+ 
+
+ align:start position:0%
+a zillion different temperature scales
+everybody had their own favorite
+
+ align:start position:0%
+everybody had their own favorite
+ 
+
+ align:start position:0%
+everybody had their own favorite
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+scales the the one that we're most
+
+ align:start position:0%
+scales the the one that we're most
+ 
+
+ align:start position:0%
+scales the the one that we're most
+familiar with is the Centigrade or
+
+ align:start position:0%
+familiar with is the Centigrade or
+ 
+
+ align:start position:0%
+familiar with is the Centigrade or
+Celsius scale with Mercury was the
+
+ align:start position:0%
+Celsius scale with Mercury was the
+ 
+
+ align:start position:0%
+Celsius scale with Mercury was the
+substance and the volume of Mercury is
+
+ align:start position:0%
+substance and the volume of Mercury is
+ 
+
+ align:start position:0%
+substance and the volume of Mercury is
+the property the reference points are
+
+ align:start position:0%
+the property the reference points are
+ 
+
+ align:start position:0%
+the property the reference points are
+water freezing or boiling and the
+
+ align:start position:0%
+water freezing or boiling and the
+ 
+
+ align:start position:0%
+water freezing or boiling and the
+interpolation is linear then that
+
+ align:start position:0%
+interpolation is linear then that
+ 
+
+ align:start position:0%
+interpolation is linear then that
+morphed into the Calvin scale as we're
+
+ align:start position:0%
+morphed into the Calvin scale as we're
+ 
+
+ align:start position:0%
+morphed into the Calvin scale as we're
+going to see later the Fahrenheit scale
+
+ align:start position:0%
+going to see later the Fahrenheit scale
+ 
+
+ align:start position:0%
+going to see later the Fahrenheit scale
+is is an interesting scale turns out the
+
+ align:start position:0%
+is is an interesting scale turns out the
+ 
+
+ align:start position:0%
+is is an interesting scale turns out the
+US and Jamaica are the only two places
+
+ align:start position:0%
+US and Jamaica are the only two places
+ 
+
+ align:start position:0%
+US and Jamaica are the only two places
+on Earth now that used the Fahrenheit
+
+ align:start position:0%
+on Earth now that used the Fahrenheit
+ 
+
+ align:start position:0%
+on Earth now that used the Fahrenheit
+scale Mr
+
+ align:start position:0%
+scale Mr
+ 
+
+ align:start position:0%
+scale Mr
+Fahrenheit Daniel Gabriel Fahrenheit was
+
+ align:start position:0%
+Fahrenheit Daniel Gabriel Fahrenheit was
+ 
+
+ align:start position:0%
+Fahrenheit Daniel Gabriel Fahrenheit was
+a German instrument
+
+ align:start position:0%
+a German instrument
+ 
+
+ align:start position:0%
+a German instrument
+maker and um the way he came up with his
+
+ align:start position:0%
+maker and um the way he came up with his
+ 
+
+ align:start position:0%
+maker and um the way he came up with his
+scale was actually he borrowed um the
+
+ align:start position:0%
+scale was actually he borrowed um the
+ 
+
+ align:start position:0%
+scale was actually he borrowed um the
+RoR scale which came before him the RoR
+
+ align:start position:0%
+RoR scale which came before him the RoR
+ 
+
+ align:start position:0%
+RoR scale which came before him the RoR
+scale was RoR was a Dane and he defined
+
+ align:start position:0%
+scale was RoR was a Dane and he defined
+ 
+
+ align:start position:0%
+scale was RoR was a Dane and he defined
+freezing of water a 7 and a half degrees
+
+ align:start position:0%
+freezing of water a 7 and a half degrees
+ 
+
+ align:start position:0%
+freezing of water a 7 and a half degrees
+RoR and um 22.5 degrees RoR as blood War
+
+ align:start position:0%
+RoR and um 22.5 degrees RoR as blood War
+ 
+
+ align:start position:0%
+RoR and um 22.5 degrees RoR as blood War
+that was his definition all right two
+
+ align:start position:0%
+that was his definition all right two
+ 
+
+ align:start position:0%
+that was his definition all right two
+substances blood water two reference
+
+ align:start position:0%
+substances blood water two reference
+ 
+
+ align:start position:0%
+substances blood water two reference
+points freezing and blood warm in your
+
+ align:start position:0%
+points freezing and blood warm in your
+ 
+
+ align:start position:0%
+points freezing and blood warm in your
+human body a linear interpolation
+
+ align:start position:0%
+human body a linear interpolation
+ 
+
+ align:start position:0%
+human body a linear interpolation
+between the two and then some numbers
+
+ align:start position:0%
+between the two and then some numbers
+ 
+
+ align:start position:0%
+between the two and then some numbers
+associated with them TW 7 and a half and
+
+ align:start position:0%
+associated with them TW 7 and a half and
+ 
+
+ align:start position:0%
+associated with them TW 7 and a half and
+22 and A2 why did he choose 7 and a half
+
+ align:start position:0%
+22 and A2 why did he choose 7 and a half
+ 
+
+ align:start position:0%
+22 and A2 why did he choose 7 and a half
+as the freezing point of water because
+
+ align:start position:0%
+as the freezing point of water because
+ 
+
+ align:start position:0%
+as the freezing point of water because
+he thought that would be big enough that
+
+ align:start position:0%
+he thought that would be big enough that
+ 
+
+ align:start position:0%
+he thought that would be big enough that
+in Denmark temperature wouldn't go below
+
+ align:start position:0%
+in Denmark temperature wouldn't go below
+ 
+
+ align:start position:0%
+in Denmark temperature wouldn't go below
+zero that's how you pick seven and a
+
+ align:start position:0%
+zero that's how you pick seven and a
+ 
+
+ align:start position:0%
+zero that's how you pick seven and a
+half why not right didn't want to use
+
+ align:start position:0%
+half why not right didn't want to use
+ 
+
+ align:start position:0%
+half why not right didn't want to use
+negative numbers to measure temperature
+
+ align:start position:0%
+negative numbers to measure temperature
+ 
+
+ align:start position:0%
+negative numbers to measure temperature
+in Denmark outside well Fahrenheit came
+
+ align:start position:0%
+in Denmark outside well Fahrenheit came
+ 
+
+ align:start position:0%
+in Denmark outside well Fahrenheit came
+along and thought you know 7 and a half
+
+ align:start position:0%
+along and thought you know 7 and a half
+ 
+
+ align:start position:0%
+along and thought you know 7 and a half
+that's kind of silly 22 and a half
+
+ align:start position:0%
+that's kind of silly 22 and a half
+ 
+
+ align:start position:0%
+that's kind of silly 22 and a half
+that's kind of silly so let's multiply
+
+ align:start position:0%
+that's kind of silly so let's multiply
+ 
+
+ align:start position:0%
+that's kind of silly so let's multiply
+everything by
+
+ align:start position:0%
+everything by
+ 
+
+ align:start position:0%
+everything by
+four all right then becomes I think it
+
+ align:start position:0%
+four all right then becomes I think it
+ 
+
+ align:start position:0%
+four all right then becomes I think it
+becomes 90 and uh 30 degrees for the
+
+ align:start position:0%
+becomes 90 and uh 30 degrees for the
+ 
+
+ align:start position:0%
+becomes 90 and uh 30 degrees for the
+freezing of water and 22 and a half time
+
+ align:start position:0%
+freezing of water and 22 and a half time
+ 
+
+ align:start position:0%
+freezing of water and 22 and a half time
+4 which I I don't know what it is 100 or
+
+ align:start position:0%
+4 which I I don't know what it is 100 or
+ 
+
+ align:start position:0%
+4 which I I don't know what it is 100 or
+something no was 92 or 990 I
+
+ align:start position:0%
+something no was 92 or 990 I
+ 
+
+ align:start position:0%
+something no was 92 or 990 I
+think and then for some reason that
+
+ align:start position:0%
+think and then for some reason that
+ 
+
+ align:start position:0%
+think and then for some reason that
+nobody understands he decided to
+
+ align:start position:0%
+nobody understands he decided to
+ 
+
+ align:start position:0%
+nobody understands he decided to
+multiply Again by
+
+ align:start position:0%
+multiply Again by
+ 
+
+ align:start position:0%
+multiply Again by
+165s and that's how we get 32 for
+
+ align:start position:0%
+165s and that's how we get 32 for
+ 
+
+ align:start position:0%
+165s and that's how we get 32 for
+freezing of water and 96 in his words
+
+ align:start position:0%
+freezing of water and 96 in his words
+ 
+
+ align:start position:0%
+freezing of water and 96 in his words
+for the temperature in the mouth or
+
+ align:start position:0%
+for the temperature in the mouth or
+ 
+
+ align:start position:0%
+for the temperature in the mouth or
+underneath the armpit of a living man in
+
+ align:start position:0%
+underneath the armpit of a living man in
+ 
+
+ align:start position:0%
+underneath the armpit of a living man in
+good health what a great temperature
+
+ align:start position:0%
+good health what a great temperature
+ 
+
+ align:start position:0%
+good health what a great temperature
+scale right turns that 96 wasn't quite
+
+ align:start position:0%
+scale right turns that 96 wasn't quite
+ 
+
+ align:start position:0%
+scale right turns that 96 wasn't quite
+right then he interpolated and found
+
+ align:start position:0%
+right then he interpolated and found
+ 
+
+ align:start position:0%
+right then he interpolated and found
+well water boy is at 212 but you know
+
+ align:start position:0%
+well water boy is at 212 but you know
+ 
+
+ align:start position:0%
+well water boy is at 212 but you know
+his experiment wasn't so great and you
+
+ align:start position:0%
+his experiment wasn't so great and you
+ 
+
+ align:start position:0%
+his experiment wasn't so great and you
+know maybe he had a fever when he did
+
+ align:start position:0%
+know maybe he had a fever when he did
+ 
+
+ align:start position:0%
+know maybe he had a fever when he did
+the reference point that 96 whatever
+
+ align:start position:0%
+the reference point that 96 whatever
+ 
+
+ align:start position:0%
+the reference point that 96 whatever
+turns out that it's not 96 to be in good
+
+ align:start position:0%
+turns out that it's not 96 to be in good
+ 
+
+ align:start position:0%
+turns out that it's not 96 to be in good
+health it's
+
+ align:start position:0%
+health it's
+ 
+
+ align:start position:0%
+health it's
+98.6 whatever that's how we got to the
+
+ align:start position:0%
+98.6 whatever that's how we got to the
+ 
+
+ align:start position:0%
+98.6 whatever that's how we got to the
+Fahrenheit
+
+ align:start position:0%
+Fahrenheit
+ 
+
+ align:start position:0%
+Fahrenheit
+scale all right next time we're going to
+
+ align:start position:0%
+scale all right next time we're going to
+ 
+
+ align:start position:0%
+scale all right next time we're going to
+talk about a much better scale which is
+
+ align:start position:0%
+talk about a much better scale which is
+ 
+
+ align:start position:0%
+talk about a much better scale which is
+the ideal gas thermometer and how we get
+
+ align:start position:0%
+the ideal gas thermometer and how we get
+ 
+
+ align:start position:0%
+the ideal gas thermometer and how we get
+to the Calin scale
\ No newline at end of file
diff --git a/kP_1zySn3Rw.txt b/kP_1zySn3Rw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..afb49bfadd113190e5814585c71cf7aad741c06c
--- /dev/null
+++ b/kP_1zySn3Rw.txt
@@ -0,0 +1,683 @@
+align:start position:0%
+ 
+a lights game where basically if you tap
+
+ align:start position:0%
+a lights game where basically if you tap
+ 
+
+ align:start position:0%
+a lights game where basically if you tap
+on the red light you against you
+
+ align:start position:0%
+on the red light you against you
+ 
+
+ align:start position:0%
+on the red light you against you
+increase the score and each time you top
+
+ align:start position:0%
+increase the score and each time you top
+ 
+
+ align:start position:0%
+increase the score and each time you top
+correctly
+
+ align:start position:0%
+correctly
+ 
+
+ align:start position:0%
+correctly
+it keeps switching in between and so the
+
+ align:start position:0%
+it keeps switching in between and so the
+ 
+
+ align:start position:0%
+it keeps switching in between and so the
+original concept for this game was a
+
+ align:start position:0%
+original concept for this game was a
+ 
+
+ align:start position:0%
+original concept for this game was a
+kind of a game sort of like the target
+
+ align:start position:0%
+kind of a game sort of like the target
+ 
+
+ align:start position:0%
+kind of a game sort of like the target
+or Dance Dance Revolution where you have
+
+ align:start position:0%
+or Dance Dance Revolution where you have
+ 
+
+ align:start position:0%
+or Dance Dance Revolution where you have
+the music sync with the lights are your
+
+ align:start position:0%
+the music sync with the lights are your
+ 
+
+ align:start position:0%
+the music sync with the lights are your
+topping on in rhythm and if you get them
+
+ align:start position:0%
+topping on in rhythm and if you get them
+ 
+
+ align:start position:0%
+topping on in rhythm and if you get them
+in rhythm and like at the right time
+
+ align:start position:0%
+in rhythm and like at the right time
+ 
+
+ align:start position:0%
+in rhythm and like at the right time
+right buttons that's when you get the
+
+ align:start position:0%
+right buttons that's when you get the
+ 
+
+ align:start position:0%
+right buttons that's when you get the
+highest score but we were having a lot
+
+ align:start position:0%
+highest score but we were having a lot
+ 
+
+ align:start position:0%
+highest score but we were having a lot
+of issues with regards to just taking
+
+ align:start position:0%
+of issues with regards to just taking
+ 
+
+ align:start position:0%
+of issues with regards to just taking
+this hardware and software set up so we
+
+ align:start position:0%
+this hardware and software set up so we
+ 
+
+ align:start position:0%
+this hardware and software set up so we
+decide there's a normal scope of the
+
+ align:start position:0%
+decide there's a normal scope of the
+ 
+
+ align:start position:0%
+decide there's a normal scope of the
+project it's not much but in theory we
+
+ align:start position:0%
+project it's not much but in theory we
+ 
+
+ align:start position:0%
+project it's not much but in theory we
+could apply this very easily into that
+
+ align:start position:0%
+could apply this very easily into that
+ 
+
+ align:start position:0%
+could apply this very easily into that
+type of project so yeah so basically
+
+ align:start position:0%
+type of project so yeah so basically
+ 
+
+ align:start position:0%
+type of project so yeah so basically
+what the components we have here are we
+
+ align:start position:0%
+what the components we have here are we
+ 
+
+ align:start position:0%
+what the components we have here are we
+have capacitive sensors so they suggest
+
+ align:start position:0%
+have capacitive sensors so they suggest
+ 
+
+ align:start position:0%
+have capacitive sensors so they suggest
+a wire where you just touch it just
+
+ align:start position:0%
+a wire where you just touch it just
+ 
+
+ align:start position:0%
+a wire where you just touch it just
+changes the confidence of the circuit so
+
+ align:start position:0%
+changes the confidence of the circuit so
+ 
+
+ align:start position:0%
+changes the confidence of the circuit so
+you can just register that they're
+
+ align:start position:0%
+you can just register that they're
+ 
+
+ align:start position:0%
+you can just register that they're
+pretty they're pretty receptive pretty
+
+ align:start position:0%
+pretty they're pretty receptive pretty
+ 
+
+ align:start position:0%
+pretty they're pretty receptive pretty
+with up there a border you can drain
+
+ align:start position:0%
+with up there a border you can drain
+ 
+
+ align:start position:0%
+with up there a border you can drain
+borders you have the ability to project
+
+ align:start position:0%
+borders you have the ability to project
+ 
+
+ align:start position:0%
+borders you have the ability to project
+and you know is going to go here here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah you follow the orange when you see
+
+ align:start position:0%
+yeah you follow the orange when you see
+ 
+
+ align:start position:0%
+yeah you follow the orange when you see
+that one is what becomes red next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+I realize that upon making this that
+
+ align:start position:0%
+I realize that upon making this that
+ 
+
+ align:start position:0%
+I realize that upon making this that
+actually having an LED set up farther
+
+ align:start position:0%
+actually having an LED set up farther
+ 
+
+ align:start position:0%
+actually having an LED set up farther
+away from the acrylic covering actually
+
+ align:start position:0%
+away from the acrylic covering actually
+ 
+
+ align:start position:0%
+away from the acrylic covering actually
+makes the squares seem brighter light
+
+ align:start position:0%
+makes the squares seem brighter light
+ 
+
+ align:start position:0%
+makes the squares seem brighter light
+kind of diffuses as opposed to being
+
+ align:start position:0%
+kind of diffuses as opposed to being
+ 
+
+ align:start position:0%
+kind of diffuses as opposed to being
+right next to acrylic where you just see
+
+ align:start position:0%
+right next to acrylic where you just see
+ 
+
+ align:start position:0%
+right next to acrylic where you just see
+that leaky but if you back off you
+
+ align:start position:0%
+that leaky but if you back off you
+ 
+
+ align:start position:0%
+that leaky but if you back off you
+actually get a lot more illumination one
+
+ align:start position:0%
+actually get a lot more illumination one
+ 
+
+ align:start position:0%
+actually get a lot more illumination one
+of the cool lessons yeah we would love
+
+ align:start position:0%
+of the cool lessons yeah we would love
+ 
+
+ align:start position:0%
+of the cool lessons yeah we would love
+to give a lot of credit to Tay he was
+
+ align:start position:0%
+to give a lot of credit to Tay he was
+ 
+
+ align:start position:0%
+to give a lot of credit to Tay he was
+the guy that I group who made this
+
+ align:start position:0%
+the guy that I group who made this
+ 
+
+ align:start position:0%
+the guy that I group who made this
+acrylic with like a laser printer I am
+
+ align:start position:0%
+acrylic with like a laser printer I am
+ 
+
+ align:start position:0%
+acrylic with like a laser printer I am
+put the wood so that like each of the
+
+ align:start position:0%
+put the wood so that like each of the
+ 
+
+ align:start position:0%
+put the wood so that like each of the
+squares are in their own places just
+
+ align:start position:0%
+squares are in their own places just
+ 
+
+ align:start position:0%
+squares are in their own places just
+made this beautiful set of Portuguese
+
+ align:start position:0%
+made this beautiful set of Portuguese
+ 
+
+ align:start position:0%
+made this beautiful set of Portuguese
+not here today and do a lot of the
+
+ align:start position:0%
+not here today and do a lot of the
+ 
+
+ align:start position:0%
+not here today and do a lot of the
+soldiering but there's a lot of these
+
+ align:start position:0%
+soldiering but there's a lot of these
+ 
+
+ align:start position:0%
+soldiering but there's a lot of these
+are really cool also there's they sell
+
+ align:start position:0%
+are really cool also there's they sell
+ 
+
+ align:start position:0%
+are really cool also there's they sell
+LEDs these LEDs were actually one series
+
+ align:start position:0%
+LEDs these LEDs were actually one series
+ 
+
+ align:start position:0%
+LEDs these LEDs were actually one series
+of LEDs on the strip so there's like 100
+
+ align:start position:0%
+of LEDs on the strip so there's like 100
+ 
+
+ align:start position:0%
+of LEDs on the strip so there's like 100
+to 50 LEDs on a couple meters of on a
+
+ align:start position:0%
+to 50 LEDs on a couple meters of on a
+ 
+
+ align:start position:0%
+to 50 LEDs on a couple meters of on a
+spool and you can actually control each
+
+ align:start position:0%
+spool and you can actually control each
+ 
+
+ align:start position:0%
+spool and you can actually control each
+one individually with our Arduino just
+
+ align:start position:0%
+one individually with our Arduino just
+ 
+
+ align:start position:0%
+one individually with our Arduino just
+be careful not to power all of them
+
+ align:start position:0%
+be careful not to power all of them
+ 
+
+ align:start position:0%
+be careful not to power all of them
+actually pass a lot of current through
+
+ align:start position:0%
+actually pass a lot of current through
+ 
+
+ align:start position:0%
+actually pass a lot of current through
+your theme probably
+
+ align:start position:0%
+your theme probably
+ 
+
+ align:start position:0%
+your theme probably
+davender USB
+
+ align:start position:0%
+davender USB
+ 
+
+ align:start position:0%
+davender USB
+one of the things that we learned about
+
+ align:start position:0%
+one of the things that we learned about
+ 
+
+ align:start position:0%
+one of the things that we learned about
+wiring and knowing how much parents
+
+ align:start position:0%
+wiring and knowing how much parents
+ 
+
+ align:start position:0%
+wiring and knowing how much parents
+going through luckily we learned
+
+ align:start position:0%
+going through luckily we learned
+ 
+
+ align:start position:0%
+going through luckily we learned
+Christina USD or know what we leave this
+
+ align:start position:0%
+Christina USD or know what we leave this
+ 
+
+ align:start position:0%
+Christina USD or know what we leave this
+know like we had drew up the magic line
+
+ align:start position:0%
+know like we had drew up the magic line
+ 
+
+ align:start position:0%
+know like we had drew up the magic line
+of code which allows you to just gotta
+
+ align:start position:0%
+of code which allows you to just gotta
+ 
+
+ align:start position:0%
+of code which allows you to just gotta
+admit the total amount of crap you're
+
+ align:start position:0%
+admit the total amount of crap you're
+ 
+
+ align:start position:0%
+admit the total amount of crap you're
+putting out soon if you ask you to draw
+
+ align:start position:0%
+putting out soon if you ask you to draw
+ 
+
+ align:start position:0%
+putting out soon if you ask you to draw
+a ton of crap you just get dim LEDs
+
+ align:start position:0%
+a ton of crap you just get dim LEDs
+ 
+
+ align:start position:0%
+a ton of crap you just get dim LEDs
+we're actually warned but a minute
+
+ align:start position:0%
+we're actually warned but a minute
+ 
+
+ align:start position:0%
+we're actually warned but a minute
+before we're gonna try a lot well
+
+ align:start position:0%
+before we're gonna try a lot well
+ 
+
+ align:start position:0%
+before we're gonna try a lot well
+firstly
+
+ align:start position:0%
+firstly
+ 
+
+ align:start position:0%
+firstly
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+that was about the right summer and you
+
+ align:start position:0%
+that was about the right summer and you
+ 
+
+ align:start position:0%
+that was about the right summer and you
+will maybe attempt to continue to add
+
+ align:start position:0%
+will maybe attempt to continue to add
+ 
+
+ align:start position:0%
+will maybe attempt to continue to add
+more features including timings to get
+
+ align:start position:0%
+more features including timings to get
+ 
+
+ align:start position:0%
+more features including timings to get
+worse points for hitting it in the
+
+ align:start position:0%
+worse points for hitting it in the
+ 
+
+ align:start position:0%
+worse points for hitting it in the
+rhythm with legs or music we originally
+
+ align:start position:0%
+rhythm with legs or music we originally
+ 
+
+ align:start position:0%
+rhythm with legs or music we originally
+would include smoking process process
+
+ align:start position:0%
+would include smoking process process
+ 
+
+ align:start position:0%
+would include smoking process process
+include that the other you know team had
+
+ align:start position:0%
+include that the other you know team had
+ 
+
+ align:start position:0%
+include that the other you know team had
+last time to make some life that
+
+ align:start position:0%
+last time to make some life that
+ 
+
+ align:start position:0%
+last time to make some life that
+flatulence seemed to be with the music
+
+ align:start position:0%
+flatulence seemed to be with the music
+ 
+
+ align:start position:0%
+flatulence seemed to be with the music
+would due to technical difficulties with
+
+ align:start position:0%
+would due to technical difficulties with
+ 
+
+ align:start position:0%
+would due to technical difficulties with
+wiring capacity etc that's not be named
+
+ align:start position:0%
+wiring capacity etc that's not be named
+ 
+
+ align:start position:0%
+wiring capacity etc that's not be named
+later birth yeah so that's our project
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+yeah you mentioned that that relic piece
+
+ align:start position:0%
+yeah you mentioned that that relic piece
+ 
+
+ align:start position:0%
+yeah you mentioned that that relic piece
+was printed
\ No newline at end of file
diff --git a/kk55qwgSXcA.txt b/kk55qwgSXcA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4abee0cfb551d6fa547885d4fd5af3596a57f6f5
--- /dev/null
+++ b/kk55qwgSXcA.txt
@@ -0,0 +1,211 @@
+align:start position:0%
+ 
+hi everybody clock
+
+ align:start position:0%
+hi everybody clock
+ 
+
+ align:start position:0%
+hi everybody clock
+or for an IR light so we just have to
+
+ align:start position:0%
+or for an IR light so we just have to
+ 
+
+ align:start position:0%
+or for an IR light so we just have to
+bite down onto one so if you go you want
+
+ align:start position:0%
+bite down onto one so if you go you want
+ 
+
+ align:start position:0%
+bite down onto one so if you go you want
+to unlock this remotely you hit the
+
+ align:start position:0%
+to unlock this remotely you hit the
+ 
+
+ align:start position:0%
+to unlock this remotely you hit the
+wrong button like you might nothing's
+
+ align:start position:0%
+wrong button like you might nothing's
+ 
+
+ align:start position:0%
+wrong button like you might nothing's
+going to happen but if you want to
+
+ align:start position:0%
+going to happen but if you want to
+ 
+
+ align:start position:0%
+going to happen but if you want to
+actually unlock it aim the light goes on
+
+ align:start position:0%
+actually unlock it aim the light goes on
+ 
+
+ align:start position:0%
+actually unlock it aim the light goes on
+so you can see and now you unlock your
+
+ align:start position:0%
+so you can see and now you unlock your
+ 
+
+ align:start position:0%
+so you can see and now you unlock your
+life
+
+ align:start position:0%
+life
+ 
+
+ align:start position:0%
+life
+lock it back up light goes off Daniel
+
+ align:start position:0%
+lock it back up light goes off Daniel
+ 
+
+ align:start position:0%
+lock it back up light goes off Daniel
+and the other buttons are kind of
+
+ align:start position:0%
+and the other buttons are kind of
+ 
+
+ align:start position:0%
+and the other buttons are kind of
+reminiscent if someone uses a different
+
+ align:start position:0%
+reminiscent if someone uses a different
+ 
+
+ align:start position:0%
+reminiscent if someone uses a different
+key or different remote control it's not
+
+ align:start position:0%
+key or different remote control it's not
+ 
+
+ align:start position:0%
+key or different remote control it's not
+the right one nothing else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so if we program it program there's any
+
+ align:start position:0%
+so if we program it program there's any
+ 
+
+ align:start position:0%
+so if we program it program there's any
+IRS favor yeah
+
+ align:start position:0%
+IRS favor yeah
+ 
+
+ align:start position:0%
+IRS favor yeah
+so there's specific libraries streets
+
+ align:start position:0%
+so there's specific libraries streets
+ 
+
+ align:start position:0%
+so there's specific libraries streets
+remote and as long as you have that
+
+ align:start position:0%
+remote and as long as you have that
+ 
+
+ align:start position:0%
+remote and as long as you have that
+library install it all understand the
+
+ align:start position:0%
+library install it all understand the
+ 
+
+ align:start position:0%
+library install it all understand the
+exactly the easiest way to figure out
+
+ align:start position:0%
+exactly the easiest way to figure out
+ 
+
+ align:start position:0%
+exactly the easiest way to figure out
+what the hex code is is just shining it
+
+ align:start position:0%
+what the hex code is is just shining it
+ 
+
+ align:start position:0%
+what the hex code is is just shining it
+on putting on the serial monitor and
+
+ align:start position:0%
+on putting on the serial monitor and
+ 
+
+ align:start position:0%
+on putting on the serial monitor and
+figuring out what the hex code is we
+
+ align:start position:0%
+figuring out what the hex code is we
+ 
+
+ align:start position:0%
+figuring out what the hex code is we
+also built a emitter but it wasn't as
+
+ align:start position:0%
+also built a emitter but it wasn't as
+ 
+
+ align:start position:0%
+also built a emitter but it wasn't as
+nice so we just decided to go with the
+
+ align:start position:0%
+nice so we just decided to go with the
+ 
+
+ align:start position:0%
+nice so we just decided to go with the
+preset remote
\ No newline at end of file
diff --git a/klz2SdQorbA.txt b/klz2SdQorbA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4bc1732ab25685a06ab05815894641f3f27a6387
--- /dev/null
+++ b/klz2SdQorbA.txt
@@ -0,0 +1,3906 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality, educational
+
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: So today, we're
+showing just a very short
+
+video I just wanted
+you to hear.
+
+And we're going to be talking
+about Pratham today.
+
+We've had a very long
+relationship with Pratham over
+
+the years, we being J-PAL.
+
+That is me and Professor
+Banerjee and
+
+several graduate students.
+
+And one of the leaders of is
+this person, Rukmini Banerji
+
+And it's sort of useful
+to hear this.
+
+It's a very short segment where
+she explains a little
+
+bit what she sees the education
+problem being about.
+
+And then we'll take
+it from there.
+
+[VIDEO WITHHELD]
+
+PROFESSOR: So I kind of wanted
+to take one lecture to go in
+
+detail to all of our work with
+Pratham, not only because I
+
+think Pratham is an amazing
+organization, but also because
+
+it will expose you to how we
+learn about the problem, how
+
+we build from one evolution to
+the next, one project to the
+
+next, how one project is
+bringing some more questions
+
+then we started with, and how
+the next project tries to get
+
+at these questions, also how the
+partnership with the local
+
+partners develops and
+works and all that.
+
+And to this, we are going to be
+talking about this quality
+
+problem, where we are trying
+to address the basic point
+
+that she makes.
+
+Kids are in school.
+
+At the moment, she talked at the
+Clinton Global initiative,
+
+that was 90%.
+
+But the enrollment rates
+are even higher
+
+now, close to 100%.
+
+In some districts, it's more
+than 100%, because some of the
+
+five-year-olds also go to
+school, because that's kind of
+
+a convenient way to
+get babysitting.
+
+But despite that, the
+achievement is low.
+
+She did point out the results
+from the ASER survey.
+
+So every year, since 2005,
+Pratham puts together teams of
+
+people, local people,
+who go from local
+
+universities, et cetera.
+
+And they go in every single
+district in India.
+
+How many districts did she
+say there was in India?
+
+She mentioned it
+at some point.
+
+You see that everything
+[INAUDIBLE]
+
+if you are listening
+to the video.
+
+She said it at some point, how
+many district they work in and
+
+how many districts they have.
+
+If I'm not mistaken, she said
+something like 600.
+
+So they are sending people to
+every district in India, teams
+
+of college students, local
+volunteers, et cetera.
+
+They have a sampling.
+
+Of course they don't go
+to every village.
+
+But they do a sample
+in each district.
+
+And they administer a very
+simple test of reading skills
+
+and math skills.
+
+So the reading skill test
+looks like a page.
+
+On the left side, you have
+a very simple story.
+
+Like she said, I go to school.
+
+My brother goes to school.
+
+We like going to school.
+
+On the right side, you will
+have single words and then
+
+single letters.
+
+First, you start the child
+with a very simple story.
+
+If they can do that, you bring
+them to a slightly longer
+
+story and try to measure
+their comprehension.
+
+If they come to the very simple
+story, you ask them to
+
+read a word.
+
+If they can't read a word, you
+ask them to read a letter.
+
+So you, in this way, classify
+your child as a nothing
+
+reader, a letter reader, a word
+reader, a small paragraph
+
+reader, or a story reader.
+
+And the simple, small paragraph
+reader is what you
+
+should be able to do at the
+end of the first grade.
+
+And what they find is, on
+average, in 2005, that about
+
+35,000 children, aged 7 to 14,
+most of them are in school and
+
+could not read a grade 1
+paragraph and 60% could not
+
+read a grade 2 story.
+
+So these are numbers on one
+of the ASER survey.
+
+So blue is better in the maps
+I'm going to show you.
+
+And this is the fraction of kids
+who are out of school.
+
+And so that's quite a blue map,
+because there are not
+
+very many kids who are
+out of school.
+
+And the colors here
+are the same.
+
+This is now the reading
+ability.
+
+This is the fraction of
+kids who can read a
+
+standard one text.
+
+So it is the fraction of kids
+who can read or understand one
+
+text among the kids who
+are enrolled in
+
+standard three to five.
+
+So among children who are
+enrolled in standard three to
+
+five, how many of them can read
+this grade one paragraph?
+
+And you can see that
+now we have a lot
+
+of red in this card.
+
+The red is a bit distributed
+in different places, but
+
+mostly it's quite red.
+
+If you know India, does this map
+look like what you would
+
+expect for any social indicator
+within India?
+
+For anyone who knew India or
+about India, because this is a
+
+question that you might not
+know the answer to.
+
+So it doesn't really, because
+the folklore in India-- and if
+
+you look at immunization, that's
+really what you get--
+
+is that sort of the bad states
+are these ones, Uttar Pradesh,
+
+Bihar, Rajasthan, Jharkhand.
+
+These are what they call the
+BIMARU state, Bihar,
+
+Rajasthan, Uttar Pradesh.
+
+This is like where you have a
+lot of boys and not very many
+
+girls, suggesting infanticide
+or selective abortion.
+
+This is where you have very
+low immunization rate, bad
+
+outcomes, of course,
+as I mentioned.
+
+And these are the good states,
+Andhra Pradesh, Karnataka,
+
+Tamil Nadu, Kerala.
+
+Kerala is, in particular, one of
+Amartya Sen and John Rawls'
+
+favorite states for its
+successful education.
+
+Kerala does well here, almost
+everyone can read.
+
+But what is surprising is
+you have Tamil Nadu.
+
+They're very proud
+of themselves.
+
+A lot of the kids are in
+school, et cetera.
+
+It's very red.
+
+Less than half the kids enrolled
+in [INAUDIBLE] three
+
+to five cannot read
+a sentence.
+
+So that upset the government
+of Tamil Nadu a great deal.
+
+So when the first ASER report
+came out, they didn't believe
+
+the result.
+
+That is not possible.
+
+They went ahead and did their
+own test, but they found the
+
+same thing again.
+
+So this suggests that there
+is something different.
+
+It's not only like disorganized
+places that are
+
+unable to deliver
+to their kids.
+
+Their is something maybe
+deeper than that.
+
+And Bihar did surprisingly
+well in not being at the
+
+absolute bottom of the
+barrel in this graph.
+
+So Bihar was happy.
+
+Another thing that's is maybe
+even more troubling is this
+
+survey has been done from 2005
+to 2010, every year.
+
+It's been released in January
+every year, on the Republic
+
+Day in India.
+
+And there is no progress.
+
+So India is progressing across
+all these dimensions, becoming
+
+richer, there are fewer
+poor people.
+
+We're seeing they're eating less
+and less, which is not
+
+progress, per se.
+
+But education, nothing,
+no progress.
+
+Also troubling is it's not
+an Indian exception.
+
+Surveys very similar to ASER
+have been done in Kenya and
+
+Uganda and Tanzania
+and in Pakistan.
+
+And they all find similar
+kind of things.
+
+A lot of children are in school,
+most of them can't
+
+read anything.
+
+Yep?
+
+AUDIENCE: Is there still
+progress across the board on
+
+average, like in the nation?
+
+Or the states are
+static as well?
+
+PROFESSOR: So you're
+exactly right.
+
+That's a very good question.
+
+It's no progress across the
+board in the nation, but the
+
+states are not static.
+
+Some states start doing well
+for a while, and means some
+
+states are moving down
+to compensate.
+
+So, for example, in the
+last report, 2010,
+
+Punjab had a big progress.
+
+So that's one of the things they
+are trying to look at is
+
+why is Punjab suddenly
+progressing?
+
+What are they doing
+that is different?
+
+And I'm going to be able to
+talk a bit about that.
+
+And in fact, in the Punjab
+example, what they seem to be
+
+doing that is different is
+really to try to insist on
+
+these core competencies
+in the schools.
+
+They have a period of time,
+every school day, two hours a
+
+day, which are devoted to
+teaching the kids at whatever
+
+level they are forgetting
+the curriculum.
+
+And that is what they think is
+the reason why Punjab is
+
+progressing.
+
+So what we are going
+to do today is--
+
+do we have evidence to suggest
+that, in fact, they're right?
+
+And that is the key problem and,
+therefore, the key of the
+
+success of Punjab.
+
+Meanwhile, some other state,
+like Uttar Pradesh, would be
+
+going down.
+
+Ben?
+
+AUDIENCE: I have a question.
+
+Is the student to teacher
+ratio more or less?
+
+I know these states are huge.
+
+But are they more or less
+the same across
+
+the different states?
+
+PROFESSOR: So it's a
+very good question.
+
+I think, they are, probably,
+generally
+
+more or less the same.
+
+And they are not horrible.
+
+Because, actually, being a
+teacher is not a bad job.
+
+So there are a number of
+teachers who are available.
+
+So you don't have the very,
+very, large class size that
+
+you have, for example, in a
+country like Kenya, where,
+
+after free primary education,
+the class size in grade one
+
+was easily 70 to 80 children
+per classroom.
+
+You have less of
+that in India.
+
+Yeah?
+
+AUDIENCE: So it seems like the
+enrollment is high, but do
+
+they also track that the
+attendance is high?
+
+PROFESSOR: So that's a
+very good question.
+
+And the answer is that, yes,
+they check attendance.
+
+And attendance is low.
+
+So attendance is low, both for
+teachers and for children.
+
+So in Bihar, for example, we
+have a survey of children's
+
+attendance.
+
+The rate of absence is between
+30 to 50% for kids.
+
+And we've done the same
+thing in several
+
+countries of the world.
+
+Generally, children's absence
+is very, very high.
+
+So kids are enrolled, but
+they don't show up.
+
+And it's not that they
+are ghost enrollees.
+
+This 30% attendance is not
+concentrated across 30% of
+
+kids who never come.
+
+It's every child who is absent
+one day, coming one day,
+
+absent on day, coming one day.
+
+And that is one problem.
+
+So we have a lot of absence
+of children.
+
+And we have a lot of absence
+of teachers as well.
+
+So a survey was done in four to
+five developing countries,
+
+by the World Bank,
+including India.
+
+They found a very large
+teacher absence rate.
+
+So in India, it was about
+25% absence rate.
+
+And that's about what ASER found
+as well, of teachers.
+
+So you show up to a school
+during school hours, and you
+
+have three of four
+teachers who are
+
+actually in the school.
+
+The second problem is that once
+they are in the school,
+
+it is not a given that they
+are actually teaching.
+
+So another one out of these four
+teachers is actually in
+
+school but not teaching.
+
+There was a funny report, a few
+years ago, describing what
+
+they were doing, ranging from
+drinking tea to drawing
+
+political posters.
+
+The reason being that a lot
+of these teaching jobs are
+
+patronage jobs, which are
+filled by the political
+
+parties, so they need to draw
+their posters sometimes.
+
+So that means that the teachers
+are present teaching
+
+half the time.
+
+The students are, themselves,
+present about half the time.
+
+That means the students get
+about a quarter of the time
+
+that they should get in
+front of a teacher.
+
+This is a where, [? Hookman's ?]
+point, that
+
+you need a bit of time of
+student-teacher interaction to
+
+get teaching.
+
+It actually becomes
+quite pertinent.
+
+Yep, sorry?
+
+AUDIENCE: I have a question
+about the standard curriculum.
+
+What kind of things
+does it teach?
+
+Is there any [INAUDIBLE]
+benefits from it?
+
+Are there any kids who are
+up to the curriculum?
+
+PROFESSOR: So that's a
+very good question.
+
+What is the curriculum?
+
+So the curriculum in India--
+
+and that actually is true in
+the countries I know--
+
+tends to be very ambitious.
+
+And there are various
+reasons why those
+
+curriculum are very ambitious.
+
+They are probably more ambitious
+than what is being
+
+taught in the US.
+
+Actually, significantly more
+ambitious than what is being
+
+taught in US primary schools.
+
+We once showed up to a school.
+
+We were with the Pratham team.
+
+The visit was announced.
+
+The teacher wanted
+to look good.
+
+And his idea of looking good was
+to draw things like that
+
+on the board, in this grade
+three class, so all the kids
+
+were like looking around.
+
+And it doesn't mean that this is
+what he actually does on a
+
+day in day out basis, but
+it means it is what
+
+they suggest to do.
+
+So it's not necessarily
+a bad curriculum.
+
+In fact, India has a lot of
+good, very good, very serious
+
+education experts who are
+thinking about educating the
+
+child to a real, true
+understanding of science.
+
+But for most of the children,
+it's completely above their
+
+head, very quickly.
+
+And then some of the children
+benefit from it.
+
+We can see an example of
+that very quickly.
+
+We'll see an example of
+that very quickly.
+
+Yes, [INAUDIBLE]?
+
+AUDIENCE: Is their proficiency
+in math as bad as in
+
+[INAUDIBLE]?
+
+PROFESSOR: It tends
+to be worse.
+
+So math is a bit worse
+than reading.
+
+For example, if you look at
+division, which is the
+
+equivalent of your standard two
+kid, you have like 20% of
+
+kids can do division.
+
+So that's where we are.
+
+So this quality of education,
+I was saying the other day,
+
+has not concerned the policy
+establishment, very much, for
+
+many years.
+
+The policy establishment has
+been more concerned about
+
+getting as many children as
+possible in schools, enrolled
+
+in schools.
+
+With the understanding that,
+oh, if we can manage to get
+
+them in schools, somehow
+learning will happen.
+
+And the Turkey experiment is,
+in a sense, an archetypal
+
+example of that, which is
+let's make education
+
+compulsory, let's have boarding
+schools, let's have
+
+buses that are going to
+bring the kids to
+
+the boarding school.
+
+And then black box,
+learning happens.
+
+You have an educated child.
+
+But it's been about 10 years
+since academics have been a
+
+bit puzzled at that.
+
+And looking at the quality of
+education saying, how do we
+
+make education actually work?
+
+What's important?
+
+And the first thing that jumps
+at you, when you go to a
+
+school in India, in Kenya, even
+in rural Morocco, which
+
+is a richer country,
+is that there is
+
+nothing in the school.
+
+The school is usually
+very bare.
+
+You have fewer desks
+than students.
+
+People are bunching like
+three to a desk.
+
+They will usually have a
+blackboard, very few
+
+textbooks, and, of course,
+nothing like computers and
+
+things like that.
+
+So the first generation of
+studies was about, well, they
+
+have none of that.
+
+How can they learn?
+
+Maybe what they need
+is more material.
+
+And in fact, when the idea of
+randomized evaluation started
+
+to be applied to development,
+Michael Kremer, who is a
+
+professor at Harvard, wanted to
+do a demonstration project,
+
+wanted to show that it is
+possible to do a randomized
+
+evaluation.
+
+And it's interesting.
+
+And he wanted, for demonstration
+purposes, an
+
+example where it would clear
+that it has an effect.
+
+And so he asked around,
+et cetera.
+
+And he found out that what would
+be obvious is textbooks.
+
+In Kenya, no one
+has textbooks.
+
+If only we give textbooks to the
+kids, obviously, they are
+
+going to learn better.
+
+So that was his first example
+that he chose, which was
+
+chosen specifically to
+demonstrate success.
+
+And running his experiment, he
+was learning how to do an
+
+experiment at the same time.
+
+So his first experiment was
+very small, 14 schools, 7
+
+treatment, 7 control,
+and found no effect.
+
+He thought about it, and he
+said, oh well, of course, it's
+
+because I have so few schools.
+
+And you remember, when you have
+schools, you need to take
+
+into account, when you calculate
+your standard error,
+
+that all these children
+are similar.
+
+So he said, oh well, my
+experiment is not big enough.
+
+So let's take a bigger
+sample of schools.
+
+He took 100 schools.
+
+He took half of them and
+again found no effect.
+
+So there he thought, well, maybe
+the test is too hard.
+
+I'm using the test,
+the normal test.
+
+Maybe that is too hard.
+
+Let me use a different test that
+is going to be able to
+
+discriminate progress even
+at a lower level.
+
+And he got his experiment
+started.
+
+And again, he found no effect.
+
+So there he started saying maybe
+there is no effect, even
+
+in a larger sample, even
+with a better test.
+
+So maybe there is no effect.
+
+So eventually, what he found is
+that, if you focus on the
+
+children, who were already doing
+well at the baseline,
+
+then they benefit from
+the textbooks.
+
+So that's a very long winded
+answer to your question, which
+
+is there are children who
+benefit from the curriculum
+
+and, therefore, benefit
+from the textbooks.
+
+But it's a small minority.
+
+And the explanation he gave is
+the textbooks are in English,
+
+which makes sense, because the
+curriculum in Kenyan schools
+
+is in English.
+
+But a lot of children don't even
+speak English, because
+
+English is their
+third language.
+
+They first speak their mother
+tongue, the local language.
+
+Then they learn Swahili in
+the first few grades.
+
+And then English is introduced
+in grade one as a language,
+
+and then as a language of
+instruction from grade three
+
+or grade four.
+
+But the problem is that because
+the kids aren't
+
+actually learning effectively,
+by the time they reach grade
+
+five or six, they actually don't
+know English, so the
+
+textbooks are of no use.
+
+So exposed, it could
+be understood what
+
+was going on here.
+
+And then they tried
+a bunch of stuff.
+
+Flip charts also
+have no effect.
+
+Cutting the class size in two,
+if you make no other
+
+differences, also
+has no effect.
+
+And a little bit worrisome,
+things like the deworming
+
+program, which increases
+attendance, but it didn't
+
+increase test scores.
+
+So it seemed that these
+extra school
+
+days also had no effect.
+
+So changing inputs
+just didn't work.
+
+So maybe it's a problem that is
+just incredibly difficult.
+
+So we were there a
+few years ago.
+
+So what this common with all
+this intervention is that they
+
+are just changing the inputs.
+
+They are doing more of the same,
+adding more textbooks,
+
+adding more teachers, adding
+more resources.
+
+But they are no change to the
+pedagogy and no change to the
+
+incentives.
+
+So no one is given incentives.
+
+The teachers are not
+given incentives.
+
+The students are not
+given incentives.
+
+The parents are not
+given incentives.
+
+And the pedagogy and the
+curriculum stays the same.
+
+So that's kind of where we were
+about five, six years
+
+ago, a little bit depressed.
+
+Picture us, this was our first
+set of randomized experiments
+
+and nothing works.
+
+So we were thinking, maybe, this
+is going to be the end of
+
+randomized experiments,
+because you can't be a
+
+doomsayer forever, otherwise
+people really hate you.
+
+So that's why we were
+a little bit sad.
+
+Rukmini came to visit us,
+shortly after that happened, a
+
+few years after the
+establishment of Pratham, came
+
+here to MIT.
+
+Because a former MIT student
+had gone to work
+
+for them as an intern.
+
+A former undergraduate
+student of ours had a
+
+relationship with them.
+
+So Pratham started in 1994.
+
+At that time, it was established
+by UNICEF to help
+
+some kids in Bombay.
+
+It would be your typical, small
+NGO doing some work in
+
+Bombay, particularly what they
+call bridge classes.
+
+Which is take a kid who is out
+of school, give them a course
+
+for a few months so that they
+can try and go back to their
+
+regular school.
+
+That's what they were doing.
+
+But they were ambitious.
+
+So there was the Rukmini that
+you heard and Madhav Chavan
+
+wanted to make a real
+difference.
+
+So since then, they're
+grown substantially.
+
+They've reached millions and
+millions of children.
+
+I think there are about 38
+million children, who are
+
+reached by the Pratham program,
+one way or the other,
+
+so about half the population of
+France, overall population
+
+of France, just in
+terms of scale.
+
+And so that's the largest
+non-governmental organization
+
+to do education in India,
+probably in the world.
+
+And their motto is "every child
+in school"-- that half
+
+of the world would
+agree with them--
+
+"and learning well"--
+
+is where, maybe, they have
+a little difference.
+
+So they came to us towards
+the beginning.
+
+And that's the reading
+that read for today.
+
+They wanted to evaluate the
+Balsakhi program, which was
+
+the flagship program
+at the time.
+
+Balsakhi means the friend
+of the child.
+
+So the Balsakhi is a young
+woman, from the
+
+community, so an adult.
+
+Like she said, you need
+some adult time.
+
+Barely an adult, some
+18-year-old, usually having
+
+only high school education,
+so grade 10 to 12.
+
+And Pratham would give them a
+very short training and then
+
+dump them into the school,
+with which they had an
+
+agreement with the teachers that
+the school would let them
+
+pull out the kids who were
+lagging behind in grade three
+
+of in grade four.
+
+So why is this a good
+demographic, the 18-year-old,
+
+grade 10 educated woman?
+
+Why is that a good goal
+to work with?
+
+Yep?
+
+AUDIENCE: She's more familiar
+with the community, so she can
+
+probably relate to
+[INAUDIBLE].
+
+PROFESSOR: So that is one reason
+is that she is more
+
+known to the community,
+because she's local.
+
+She's not much older.
+
+And she's not intimidating or
+scary for the parents, who,
+
+maybe, can work better
+with the kids.
+
+That's a very good reason.
+
+What's another reason?
+
+AUDIENCE: I would say for
+the teacher's as well.
+
+Maybe the teachers are not as
+intimidated that the balsakhi
+
+will go and teach these
+students some really
+
+innovative thing that would
+make [INAUDIBLE].
+
+PROFESSOR: Yes.
+
+So for the teachers, she might
+be not very intimidating,
+
+which will cut both ways.
+
+On the one hand, it's
+more easily
+
+acceptable for the teachers.
+
+On the other hand, there is a
+tendency that teacher would
+
+use the balsakhi to make
+the tea or other
+
+activities like that.
+
+And we are going to see some
+of that happening, not
+
+actually in Baroda.
+
+Yep?
+
+AUDIENCE: So she's locally
+trained, which makes sense in
+
+kind of [INAUDIBLE]
+perspective.
+
+PROFESSOR: Yes.
+
+She is locally trained,
+only for two weeks.
+
+This is very cheap.
+
+And there is another
+aspect of the cost.
+
+Yeah?
+
+AUDIENCE: Not about the cost,
+but she might be more
+
+motivated to help the
+[INAUDIBLE] children, because
+
+it's not like this is a second
+job she can perform.
+
+It's not a fallback option.
+
+It's something that she
+wants to do that is a
+
+period in her life.
+
+It seems a bit time sensitive.
+
+PROFESSOR: Yes.
+
+So she might be more motivated
+for this reason.
+
+Also for what you said earlier,
+that she's close to
+
+them, et cetera.
+
+But also this is something that
+she effectively chose to
+
+do at this point and not
+something that is just putting
+
+money in a bank account.
+
+AUDIENCE: She's not highly
+qualified, so the [INAUDIBLE].
+
+PROFESSOR: Right.
+
+She's not highly qualified,
+so she's cheap.
+
+What is another reason
+why she is cheap?
+
+Why don't these people go
+and do something else?
+
+AUDIENCE: Also there's a high
+turnover in these [INAUDIBLE]
+
+make a certain income to teach,
+so you're not really
+
+relying on this thing.
+
+It's [INAUDIBLE]
+
+quality of the teaching.
+
+It doesn't have to be like a
+small, really enthusiastic
+
+[INAUDIBLE].
+
+So it's easy to get
+[INAUDIBLE].
+
+PROFESSOR: Yeah.
+
+They have high turnover, which
+could be a plus or a minus.
+
+On the minus side, of course,
+you don't get the experience.
+
+On the plus side, you
+don't get tired.
+
+And you don't rely on people
+who have a huge vocation.
+
+You rely on people getting
+enthusiastic for one year.
+
+So very much along the model
+of Teach For America, where
+
+you get MIT, graduating from
+school, energetic about
+
+wanting to do this.
+
+A bit of what you're saying,
+which is it's what I want to
+
+do at this point in my life.
+
+And then by the time you
+don't want to do it
+
+any more, you stop.
+
+And there is one more thing
+about them, specifically,
+
+which makes them cheap.
+
+AUDIENCE: Everything
+about them.
+
+I mean I think there's like a
+good chance that they have
+
+families or that they're part of
+a family, and maybe that's
+
+why they're stuck in the area.
+
+And they don't necessarily
+have the ability to go
+
+somewhere else.
+
+PROFESSOR: Exactly.
+
+That's a very important point.
+
+Most of these women
+are unmarried.
+
+They are living at home.
+
+They are sort of waiting
+to be married.
+
+And there is actually not
+much they can do.
+
+Because the parents won't
+let them leave.
+
+And mostly, their parents won't
+let them work, because
+
+working is not becoming for a
+certain, sort of lower, middle
+
+class category woman, waiting
+to be married.
+
+You shouldn't be like working.
+
+You should be able to be--
+
+it's not a good signal for the
+family that they're not able
+
+to provide for you
+and all that.
+
+But this is hardly
+seen as working.
+
+This is more like volunteering
+and helping your community and
+
+things like that.
+
+So they can do that.
+
+So they are sort of available.
+
+So one part of the genius of
+Pratham is that they identify
+
+a group of people who
+are actually sort of
+
+available for free.
+
+Here, they pay them, but in
+future programs, that I'm
+
+going to talk to you a minute
+after, they're not even paid.
+
+They are just unpaid.
+
+They do that for a while.
+
+And that get some, presumably,
+other rewards of doing that,
+
+which are more in the form of
+intrinsic reward of seeing the
+
+kid progress, and, therefore,
+you also select people who are
+
+motivated in that dimension
+as one of you pointed out.
+
+So that's all of the pluses.
+
+The minuses you already
+mentioned.
+
+The turnover is one of them.
+
+You can't get them to
+get experienced.
+
+The second minus is
+that they're, of
+
+course, much less educated.
+
+Maybe there is some good reasons
+why a teacher needs a
+
+college degree.
+
+Maybe it's actually terrible
+to take the kid out of the
+
+classroom to put them in front
+of someone who knows nothing.
+
+So that's kind of the
+risk that would
+
+potentially be there.
+
+So that's the program.
+
+And when they came to see us,
+we were wondering how to
+
+evaluate this program, with
+them, in an experiment, in a
+
+way that is not going to cause
+a problem for them in the
+
+city, that's not going to hinder
+their work too much.
+
+And that's experimental design
+that we decided to
+
+adopt in a new place.
+
+So Vadodara and Gujarat, those
+were places where they had not
+
+worked at all.
+
+Had about 100 schools.
+
+A little more than 100 schools
+divided in two groups,
+
+randomly, with the
+computer, group A
+
+schools and group B schools.
+
+The group A schools
+got the balsakhi
+
+for grade three children.
+
+The group B schools
+got the balsakhi
+
+for grade four children.
+
+So what's an advantage of this
+design from the point of view
+
+of political acceptability?
+
+Why did we go like this, instead
+of doing the more
+
+standard thing, which would be
+to say, well, in group A
+
+treatment, and grade three and
+grade four get the balsakhi
+
+and group B, no one
+gets a balsakhi?
+
+AUDIENCE: Well, in a way, if you
+don't give one group any
+
+treatment at all, you're
+almost sabotaging your
+
+education [INAUDIBLE].
+
+PROFESSOR: Sabotaging
+is a strong word.
+
+But exactly the idea is that
+this allows you to be present
+
+in every school.
+
+So Pratham is not
+infinitely rich.
+
+They can easily argue-- and I
+think that was very true at
+
+that time-- that look,
+we can give you one
+
+balsakhi per school.
+
+We can't afford more.
+
+So you either put it in three
+or you put it in four.
+
+We can't give you both.
+
+But at least every school
+is being engaged with.
+
+So they are engaged with
+the system as a whole.
+
+And no school is
+disadvantaged.
+
+That makes it easier for the
+school system to say, yes,
+
+they are just working with us.
+
+They are part of us.
+
+It also makes data collection
+much easier, because you're
+
+involved with everyone.
+
+What is a potential danger
+of this design?
+
+The plus is what I just said.
+
+What's the potential minus?
+
+Since you have a balsakhi in
+every school, what's the
+
+potential minus?
+
+AUDIENCE: They might not just
+be teaching grade three.
+
+The might be overlapping grade
+three and four or something.
+
+PROFESSOR: Exactly.
+
+The balsakhi might take both
+groups, so that your control
+
+group becomes partly treated.
+
+Or even if it's not the
+balsakhi, the head teacher
+
+might say, oh great, we have
+a balsakhi for grade three.
+
+So we're going to take the
+teacher out of grade three and
+
+use it to divide grade
+four in two.
+
+And so grade four would
+be associated.
+
+Or they could say, well, since
+the grade three got the
+
+balsakhi, when some other
+organization comes with
+
+computers, well, we'll put
+them in grade four.
+
+So there is a danger of
+resources being reallocated
+
+across grades in a way that
+contaminates your treatment.
+
+So fortunately, that was not
+really an issue there, because
+
+in Vadodara, the way the school
+system is organized, a
+
+school is made of one teacher
+per grade, regardless.
+
+Sometimes in the same school
+building, you have more than
+
+one school.
+
+And that happens sometimes
+in the US as well.
+
+You have this charter school and
+the regular school sharing
+
+the same school building.
+
+In Vadodara what happened is,
+if it's a big school, it's
+
+actually a big school building,
+but under totally
+
+separate administration.
+
+So a school is made of five
+teachers and a head teacher.
+
+That's it.
+
+So there is less scope for
+reallocating, because you have
+
+your one teacher anyway.
+
+And they're also not very
+imaginative in terms of using
+
+the resources in the
+most optimal way.
+
+So that turned out not
+to be a problem.
+
+So the way we evaluated the
+program is then by comparing
+
+grade three, group
+A's treatment
+
+compared with control.
+
+And in grade four, that's
+the opposite.
+
+We also worked in Bombay.
+
+So that's the second year
+we have asked a group.
+
+So if you were a kid who was
+in grade three, in group A,
+
+you are treated in grade three
+and then, again, you are
+
+treated in grade four,
+because you would
+
+have moved one grade.
+
+If you were a kid who entered in
+grade four, you would never
+
+be treated.
+
+Or if you were a kid who entered
+grade three in group
+
+B, you also would never
+be treated.
+
+So we have kids treated one
+year, kids treated two years,
+
+and kids treated one year.
+
+And then in Bombay, we did
+something similar.
+
+This is Shobhini She used
+to work at Pratham.
+
+And now she's one of the
+executive director of J-PAL
+
+South Asia.
+
+You can say, hi, to her.
+
+And in Bombay, we did something
+similar, except we
+
+started in grade two, three,
+and then moved
+
+it to three, four.
+
+The reason why we switched is
+that they realized that they
+
+didn't have right pedagogy for
+engaging with the grade two
+
+children, that the grade two
+children were too small, and
+
+they didn't know how
+to deal with them.
+
+The initial plan was to do two,
+three and then reverse
+
+again, two, three.
+
+And then they turned out that
+they weren't happy with
+
+they're grade two, so they
+moved three, four.
+
+So that's kind of the idea.
+
+So this is the design.
+
+So in principle, now, we could
+say, well, they're good.
+
+We have the designs.
+
+Now, all we need to do is to
+compare treatment and control
+
+after one year and after
+two years, and
+
+we're going to be done.
+
+But unfortunately, when you run
+real experiments, you get
+
+real problems.
+
+I've yet to meet an experiment
+where there was no problems.
+
+And this was, at least,
+my first big one.
+
+So we had a lot of problems
+that I want to talk about.
+
+The first one is the way to
+evaluate the program was to
+
+administer a test
+in the school.
+
+And we had some issue
+with the test.
+
+The first one is that,
+as I was saying, a
+
+lot of kids are absent.
+
+And if we only tested the kids
+who were present in school, we
+
+have some attrition.
+
+Maybe in urban India,
+absenteeism is less bad, but
+
+maybe 20% of kids are absent on
+a given day, so they don't
+
+take the test.
+
+So why is that potentially a
+problem to have missing kids
+
+in the test?
+
+Yep?
+
+AUDIENCE: Maybe the kids that
+are absent are those that are
+
+more likely to not [INAUDIBLE]
+class, and so they either
+
+chose or their parents chose
+that, maybe, they could better
+
+use that time working
+from home.
+
+And so all the results
+are biased.
+
+Then you're only really
+testing the kids that
+
+understand more and you're
+ignoring the kids that
+
+understood the least.
+
+PROFESSOR: Exactly.
+
+So that could be the first
+problem, which is those kids,
+
+whom we are testing, they are
+not representative, because
+
+maybe they're the one who
+understand the most.
+
+And that could lead to an even
+bigger problem, because
+
+suppose the intervention is
+effective and most kids now
+
+understand better.
+
+Then what could happen with the
+attrition in the treatment
+
+group versus the
+control group?
+
+Now you all know very well,
+it's the kids who don't
+
+understand who don't come.
+
+And now the kids who understand
+better are in the
+
+treatment group.
+
+What might happen
+to attrition?
+
+AUDIENCE: The attrition would
+be less for the students who
+
+are in the treatment group.
+
+PROFESSOR: The attrition would
+be less for students who are
+
+in the treatment group.
+
+And the kids who are coming
+tends to be the weaker kids.
+
+So now we are comparing the
+strong kids in the control
+
+group to the strong kids plus
+some of the weak kids in the
+
+treatment group.
+
+So that will tend to make our
+estimate look smaller relative
+
+to what it should be.
+
+Because now we have a different
+population of
+
+students in the treatment
+and control groups.
+
+So we have a bias here.
+
+It goes in the direction of
+not finding an effect.
+
+So if we still find an
+effect, we're happy.
+
+But it's not the
+right estimate.
+
+So to solve this problem,
+what did we do?
+
+Did we rely, uniquely, on
+the test in the school?
+
+Yeah?
+
+AUDIENCE: You found the kids,
+even if they happened to be at
+
+home or elsewhere and
+administrated the test
+
+[INAUDIBLE].
+
+PROFESSOR: We went and looked
+for them, wherever they were,
+
+except if they'd left
+for the village.
+
+So the attrition ended up being
+low, less than 10%, and
+
+similar, now, in treatment
+and control school.
+
+Because it's not because people
+don't understand that
+
+they leave for the village.
+
+It's because they have something
+to do there.
+
+So that was the first thing.
+
+The second problem we had is
+that the testing instrument--
+
+actually, not in year
+1 but in year 0--
+
+we designed a test which
+was at grade level.
+
+We designed a test to
+test the curriculum.
+
+So it's like, if this is what
+should be tested, what's on
+
+the board, here, we tested
+at that level.
+
+So if they were supposed to
+learn Euclidean geometry,
+
+that's what was tested.
+
+And we had a big problem, which
+is that the teachers
+
+cheated like crazy.
+
+So the reason we saw that
+is that all of the
+
+tests were the same.
+
+So clearly, the teacher had
+written the answer on the
+
+board, and all the students
+were copying down.
+
+In one class, all the students
+had the same name.
+
+So the teacher clearly wrote the
+name, like a sample name,
+
+on the board.
+
+And all the students dutifully
+wrote down the name that they
+
+saw on the broad.
+
+So we said that's not working.
+
+There is a paper by Steve
+Levitt, who shows very subtle
+
+things, how you can
+detect cheating.
+
+That was easy.
+
+It didn't require a lot
+of imagination.
+
+It was pretty obvious that
+cheated like crazy to make
+
+their kids look better.
+
+So we thought about how we
+can solve this problem.
+
+We are going to administer a new
+test without the teacher,
+
+that some special Pratham staff
+is going to come to
+
+administer the test.
+
+And we did that.
+
+And then we realized that
+most of the students now
+
+had 0 on the test.
+
+So this test was way too hard,
+which is why the teacher had
+
+been cheating, because they
+were a bit embarrassed.
+
+So the solution here was to
+develop a much easier test
+
+that covered the competencies
+starting from, can you write
+
+your own name, to--
+
+I don't know--
+
+2 plus 2, finishing with a few
+questions such as as, Nancy
+
+goes to the market.
+
+And she buys three onions
+at 15 rupees.
+
+And how much change does she
+have, that kind of thing.
+
+So that's the problems
+that we had.
+
+Further problems we had, we
+had a problem in Bombay.
+
+Because the second year of the
+evaluation turned out to be
+
+2002 to 2003.
+
+Before that, September
+2001 happened.
+
+We were walking in a quite
+Muslim neighborhood of Bombay.
+
+A lot of kids were named like
+Osama and things like that.
+
+People were pretty upset about
+the US at the time.
+
+And so Pratham, maybe because
+of us, maybe just it would
+
+have been anywhere, was somehow
+seen, maybe, as an
+
+American presence.
+
+So some schools said that
+they don't want to
+
+work with the program.
+
+So about 30% of schools said
+that they did not want to work
+
+with the program.
+
+Or, in another set of schools,
+someone was identified, but
+
+they couldn't read, themselves,
+so they couldn't
+
+really be entrusted to teach
+reading to the kids.
+
+So they also didn't do it.
+
+So can we just drop all the
+schools that refuse to
+
+participate from the program?
+
+Can we just drop them
+from the analysis?
+
+AUDIENCE: Well, that's
+a selective bias.
+
+There is a some reasons for
+which they dropped, which make
+
+them inherently different
+from the other schools.
+
+PROFESSOR: Exactly.
+
+So we can't do that, because
+that's a selection bias.
+
+Maybe these are the weaker
+schools who are
+
+refusing the program.
+
+Maybe they are the stronger
+schools, because they are
+
+independently minded.
+
+Who knows?
+
+But what is clear is that's
+it's certainly not random.
+
+So we lose random control
+comparison.
+
+So what we do?
+
+Well, the first thing you can do
+is to say, well, I'm going
+
+to not measure the effect
+of the balsakhi program.
+
+I'm going to measure the effect
+of my intention to
+
+treat the schools with
+the balsakhi program.
+
+So we called that intention
+to treat.
+
+What an intention to treat is
+a Pratham official coming to
+
+the headmaster and saying,
+hey, we have a
+
+balsakhi for you.
+
+So this, we can do in an
+unbiased way, right?
+
+Because if we compare all the
+test scores in the school
+
+where someone has come and
+offered the program to the
+
+test scores in the school where
+no one has offered the
+
+program, there is no
+selection here.
+
+But it's not the effect
+of the program.
+
+It's the effect of my attempt
+to provide the program.
+
+So that's why we call it
+an intention to treat.
+
+It's not the treatment effect.
+
+It's the wishful thinking.
+
+It's like my attempt
+to treat you.
+
+Now, I wrote, here, on the
+board, if we wanted to know
+
+the effect of the program itself
+not the intention to
+
+treat, we can divide the
+intention to treat effect by
+
+the fraction of schools who
+accept the program.
+
+So, for example, if 70% of
+schools accept the program,
+
+and we find an effect of 10 on
+the test scores, a gain of 10
+
+points in the intention to
+treat, the intention to treat
+
+is 10 points.
+
+That's due to only 3/4
+of the schools.
+
+So we can blowup the estimate
+by dividing by 3/4, which is
+
+about multiplying by 1.25.
+
+So instead of 10, the
+effect is 12.5.
+
+So this is what's called
+a Wald estimate.
+
+When you divide your intention
+to treat by the fraction of
+
+the take-up of the program,
+which, here, we call that the
+
+first stage.
+
+So in the first stage, you offer
+a program, and then some
+
+fraction of people take it.
+
+In the second stage,
+that has an effect.
+
+And the combination of the first
+stage and the second
+
+stage produces the intention
+to treat.
+
+So now to go from the intention
+to treat the effect
+
+of the program, you
+do a scale-up by
+
+dividing by the take-up.
+
+So this is, in five sentences,
+you're instrumental viable
+
+estimate,
+
+We could spend about a
+whole semester on it.
+
+There are conditions
+under which this
+
+is valid to do this.
+
+There are conditions under
+which this is not valid.
+
+And this has interpretations
+which vary.
+
+So Josh Angrist, in the econ
+department, is the one who did
+
+most of the work on this.
+
+So the point it that-- but think
+of it in this simple
+
+way, for this kind of
+noncompliance problem--
+
+is let's just normalize
+the estimate by
+
+dividing by the take-up.
+
+It would also work if you have
+some school in the control
+
+group that managed to get
+the balsakhi anyway.
+
+Then you could divide by the
+difference between the take-up
+
+in the intention to treat group
+and the intention not to
+
+treat group.
+
+So if 10% of schools manage to
+get the program in the control
+
+group, you would divide your
+intention to treat by 27%
+
+minus 10%, that's 65%.
+
+And you would blow
+it up that way.
+
+What it amounts to doing is to
+say, this is my estimate of
+
+the effect of the program,
+assuming that the only reason
+
+why they're in the intention
+to treat effect is because
+
+those who might try to treat are
+more likely to be treated.
+
+So here are the results.
+
+The results are expressed in
+standard deviation of the
+
+unique test scores.
+
+What this means is that we take
+the mean of the control
+
+group and divide by the
+standard deviation.
+
+So the advantage of doing that--
+maybe you can see that
+
+more in recitation--
+
+is that every education
+program does that.
+
+So we can compare our results
+to what other people did.
+
+For year one, this is the
+standard deviation.
+
+This is the test score in
+treatment and the test score
+
+in control.
+
+That's the difference, 0.17.
+
+That's the standard error of
+this difference below.
+
+So you divide one
+by the other.
+
+You get a t-stat of about 1.7.
+
+So that's significant
+but at a 10% level.
+
+In year two, kids progressed.
+
+And the difference
+is much larger.
+
+So you get an effect of 0.4
+standard deviation in math and
+
+a 0.25 standard deviation in
+language and something similar
+
+for the standard four classes.
+
+So those are a large effect.
+
+To scale that up, one of the
+most famous education
+
+experiments is the Tennessee
+STAR class-size reduction
+
+experiment, where that
+reduced class-size in
+
+Tennessee from 20 to 8.
+
+It was very, very expensive
+program that had an effect of
+
+0.2 standard deviation.
+
+So 0.2 is considered to be a
+reasonably large effect.
+
+Here, in the second year of the
+program, we are way above
+
+that for math.
+
+Yep?
+
+AUDIENCE: How big is the
+standard deviation relative to
+
+the average score?
+
+PROFESSOR: So this is
+all normalized.
+
+So this is, in a sense,
+already standardized.
+
+This is already standardized
+to the average and to the
+
+standard deviation.
+
+AUDIENCE: But there
+is like a wide
+
+distribution in the classroom?
+
+PROFESSOR: You mean,
+is it wide?
+
+Yeah, so you can see, it's not
+very wide, in this case.
+
+Because the students are so
+weak that, I think, the
+
+distribution of test scores,
+in terms of points, is not
+
+that large compared to what
+you could find elsewhere.
+
+It's kind of a relatively
+tight distribution.
+
+So in terms of points,
+it's useful.
+
+There are other ways
+to look at this
+
+than standard deviation.
+
+For example, the fraction of
+kids who can do these kinds of
+
+things, so in percentage
+points.
+
+How many more kids
+can do division?
+
+How many more kids
+can do addition?
+
+Which are also useful
+to look at, which I
+
+don't have with me.
+
+That's a good point.
+
+So these estimates are large,
+but they're not very precise,
+
+because there's a lot of
+differences between kids.
+
+And one thing that really helps
+to control this noise is
+
+to control for how good
+where they before.
+
+Because test scores
+of children are
+
+extremely stable over time.
+
+The biggest predictor, sadly,
+of how a child does is how
+
+they did last year.
+
+And so, when we control for
+that, we get much more precise
+
+results, which are here.
+
+So these are a bunch
+of results.
+
+So this is the improvement in
+year 1, for both cities
+
+together, where we get an
+improvement of 0.2 in math,
+
+0.3 in language--
+
+sorry, opposite, 0.2 in math in
+year 1, 0.3 in math in year
+
+2, for verbal, 0.7, not
+significant in math, for
+
+verbal, 0.7 for year
+1, 0.15 for year 2.
+
+And then we can look at various
+aspects of it, where
+
+we get a slightly bigger effect
+for Vadodara and Bombay
+
+but, generally, quite similar
+results for math.
+
+And language has bigger effect
+in Vadodara than in Bombay.
+
+Bombay starts from
+a higher level.
+
+But across the broad, except
+with Bombay year two, you find
+
+pretty large effects,
+quite large effects.
+
+So this is very different
+from what we had
+
+with the test scores.
+
+Now, you might still wonder
+that these are for all the
+
+kids involved in the program.
+
+And you might still wonder
+whether the effect comes from
+
+helping the lower achieving
+kids, which is what you're
+
+trying to do, or it's coming
+from helping the higher
+
+achieving kids by removing
+these disturbing, lower
+
+achieving kids from their
+classroom for two hours a day.
+
+That would be fine.
+
+But the distributional effect
+would be very different.
+
+If the idea is that you just
+send the kids to recess, and
+
+they kind of hang-out, and
+learn strictly nothing,
+
+meanwhile, your 20, high
+achieving kids progress, that
+
+could give us those
+mean effects.
+
+But that is not necessarily
+something that we would be
+
+very excited about.
+
+So for that, what is important
+is then to look at what is the
+
+effect by sub-group?
+
+And what was the finding
+when we looked at
+
+sub-groups, who benefited?
+
+AUDIENCE: The lowest one third
+benefited the most.
+
+PROFESSOR: The lowest one
+benefited the most.
+
+And who was more likely
+to go to the balsakhi?
+
+Also the lowest one,
+fortunately.
+
+So when you look at the lowest
+one, you start finding a
+
+pretty large effect for the
+bottom third and a much weaker
+
+for the top third.
+
+For example, if you look at
+year 2, the effect for the
+
+bottom 1/3 is 0.5 standard
+deviation.
+
+That's starting to be
+a huge effect, 0.5
+
+standard deviation progress.
+
+0.3 for the middle
+one, and 0.03 for
+
+the top one, no effect.
+
+And this is your chance
+to go to the balsakhi.
+
+So your chance to go
+to the balsakhi
+
+declines with the group.
+
+So the point estimate of the
+effect declines at about the
+
+same rate as the point estimate
+for the balsakhi.
+
+So the next thing we did is a
+little bit the same exercise
+
+as adjusting the Bombay
+estimate, to go from this
+
+estimate of the effect of
+putting a balsakhi in the
+
+classroom, to are you going
+to the balsakhi?
+
+So basically, the effect, this
+0.5 standard deviation, is due
+
+to about 20% of kids
+who are actually
+
+going to the balsakhi.
+
+Because there doesn't seem to
+be an effect for the other
+
+children, which we see from
+looking at the pattern
+
+declining as the pattern
+of take-up declines.
+
+So now you can divide
+this 0.5 by 0.2.
+
+And you get the effect for
+people who go to the balsakhi
+
+of one standard deviation, which
+are very, very, very
+
+large effects, in the education
+literature.
+
+And if you divide 0.32
+by 0.16, you'll
+
+also find about 1.
+
+And this is, of course,
+unsignificant.
+
+But if you divided 0.4 by 0.06,
+taking the estimate
+
+seriously, again, you would find
+the same type of effect.
+
+So this is a program that was
+highly effective, for kids who
+
+were sent to the program, but
+had no effect on the kids who,
+
+in principle, should have also
+benefited from the reduction
+
+in class size.
+
+So what did we learn?
+
+We learned that it is possible
+to make a lot of progress,
+
+with a grade 10 educated woman
+trained for two weeks.
+
+And we also learned that
+teachers are not very good at
+
+exploiting freed-up resources.
+
+Yep?
+
+AUDIENCE: How much variability
+was there between the
+
+different thirds?
+
+If the top third isn't that much
+better off than then the
+
+bottom third, then that would
+say something different than,
+
+if the top third is very well
+educated whereas the bottom
+
+third is really not.
+
+PROFESSOR: So the bottom
+third, basically, knows
+
+nothing at all, for starters.
+
+Like they can't do anything
+at the beginning.
+
+They can't recognize letters,
+can't recognize numbers.
+
+Whereas the top third is not
+at grade level but can at
+
+least do something.
+
+So what I'm saying is not
+that we shouldn't care
+
+about the top third.
+
+We should care about them.
+
+But that program was really
+targeted toward the bottom.
+
+And so the big difference, in
+the context of this program,
+
+is that the top third didn't
+get the benefit from the
+
+program, because they weren't
+sent to the program.
+
+Except that there could have
+been indirect benefits from
+
+the fact that the teacher's
+now have a much
+
+smaller class size.
+
+Instead of 40 kids of very
+heterogeneous levels, they now
+
+have 20 of better level.
+
+So they could have adjusted
+their teaching to do better by
+
+these kids.
+
+And it seems that they didn't.
+
+So in terms of the whether
+this is an optimistic or
+
+pessimistic conclusion, it's
+kind of the glass is half-full
+
+or half-empty.
+
+The half-full part is
+you can do this.
+
+It's reasonably easy to make
+a lot of progress.
+
+Perhaps because kids start from
+such a low level, to go
+
+back to your question,
+initially.
+
+If the standard deviation is
+low, because everyone is at 0,
+
+then it's easy to make
+some progress.
+
+And you're going to see
+it very quickly.
+
+On the other hand, the teachers
+seem to not really be
+
+using the resources in a way
+that allows them to take
+
+advantage of this.
+
+So that's where we were
+at the end of this.
+
+And we had a bunch more
+questions that
+
+we wanted to ask.
+
+What do we still need to know?
+
+So suppose we would want to go
+from this program to, say,
+
+well, let's do a policy
+for all of India.
+
+What else do we need to know
+before we move further?
+
+Yeah?
+
+AUDIENCE: The thing, for me, is
+to understand what is the
+
+relation between attendance and
+how much those kids, those
+
+programs are actually
+effective?
+
+Because, I mean, you showed that
+enrollment, as a whole,
+
+doesn't have too much
+of an influence.
+
+But maybe attendance
+would help.
+
+PROFESSOR: Right.
+
+So we could say, well, maybe
+there are other things to look
+
+at, children's attendance,
+teacher's attendance.
+
+Maybe the big difference
+with the balsakhi is
+
+that they were there.
+
+Maybe that's just it.
+
+Can we change their learning
+just with incentives?
+
+AUDIENCE: Also, maybe look
+at the curriculum.
+
+Maybe the reason why the
+children are learning is
+
+because the material is more
+basic, whereas if you just
+
+stay in the classroom, the
+material is already too hard,
+
+and you're not able to do it.
+
+PROFESSOR: That's the
+other big contender.
+
+So you have both contenders.
+
+One is, OK, the balsakhi
+are actually there.
+
+The kids are going.
+
+That's why they are learning.
+
+The second is that's not-- the
+incentive to this is really
+
+the pedagogy, which is about
+the learning material.
+
+And if we could train the
+teachers to train at that
+
+level, we would have
+the same effects.
+
+AUDIENCE: The cost effectiveness
+of the program,
+
+[INAUDIBLE].
+
+PROFESSOR: Right, so we could
+say, what's the cost
+
+effectiveness in the city?
+
+We could look at the cost
+effectiveness elsewhere.
+
+AUDIENCE: Also, it could be
+interesting to see the effects
+
+of having more strict, I
+guess, passing policy.
+
+Because a lot of kids are
+advancing to the next grade
+
+without actually
+being prepared.
+
+And maybe making that a little
+bit more strict, so that they
+
+don't go to next level until
+they're actually prepared.
+
+That could improve.
+
+PROFESSOR: Yeah.
+
+It's a very good point.
+
+In fact, the policy is not
+strict at all at the moment.
+
+Rukmini says it the short
+video, everybody passes,
+
+regardless.
+
+So maybe having something where,
+actually, repeating is
+
+allowed or remedial education
+of some kind is
+
+provided would help.
+
+The other question one might
+ask is, is it only an urban
+
+phenomenon or would it also
+work in rural schools?
+
+Do you need to pay the people or
+could you have volunteers?
+
+Would it be sufficient to
+distribute materials, if it's
+
+a material question?
+
+Would you be able to motivate
+the teachers to do it, to
+
+focus on the students?
+
+Can you concentrate even more
+on the basics and make even
+
+more progress on the basics, by
+not trying to do remedial
+
+of everything, but just
+focusing on learning?
+
+So those were the questions
+that Pratham had.
+
+Those were the questions
+we had.
+
+Another question you could ask
+is, on the basics, you could
+
+ask the opposite question.
+
+You were saying that the
+students at the top, it's not
+
+that they are exactly ready
+to come to MIT.
+
+They are still way below
+grade level.
+
+Is there something that
+can be done for them?
+
+Or does this very simple
+pedagogy that Pratham has work
+
+only for to very low
+achieving kids?
+
+So we had all these questions.
+
+But it was many years ago.
+
+We had a lot of time.
+
+So we started looking at them.
+
+So the first thing we did was
+a new evaluation in Jaunpur,
+
+in Uttar Pradesh.
+
+In the first program, Pratham
+was running this program.
+
+And they called us
+to evaluate it.
+
+And we went and evaluated what
+it is they were doing.
+
+But with the Jaunpur program,
+we were working together.
+
+So this study is, actually,
+authored by Rukmini Banerji,
+
+along with the rest of us.
+
+We were now all working together
+to try to figure out,
+
+can we learn more
+what's going on?
+
+So Pratham renamed the balsakhi
+program as the Read
+
+India Program.
+
+And as they renamed it, they
+shifted to focus it on
+
+something even more basic and
+simple, on reading, and tried
+
+to spread out much more
+everywhere, not focusing on
+
+cities but also working in rural
+areas and working on a
+
+much larger scale.
+
+So we worked in rural
+Uttar Pradesh.
+
+We had three groups of villages,
+here, in Jaunpur.
+
+One group, where we just went
+to see all the parents, had
+
+village meetings, the
+women and Pratham.
+
+We went to see the parents
+and say, you know what?
+
+There are things you can do.
+
+You can advocate.
+
+We can lobby for more resources
+for your schools.
+
+You can get an extra teacher
+that the government will have
+
+to pay for.
+
+You can get scholarships,
+et cetera.
+
+That's the first treatment, to
+see whether parents would be
+
+able to engage with
+the system.
+
+The second thing we had is we
+realized that parents were
+
+overestimating how much
+their kids knew.
+
+So a first step, that Pratham
+has discovered, to get people
+
+excited about reading, is to
+train parents to administer
+
+the small Pratham test.
+
+So you go and say,
+Ben, read this.
+
+And Ben is like staring
+blankly.
+
+And then they realize, oh, my
+god, the kids can't read.
+
+And they have been giving their
+kids to the schools,
+
+faithfully, for years, and
+assuming that something would
+
+come out of it.
+
+And then they realize in
+this exercise that
+
+actually, not really.
+
+So the parents prepare a report
+card for the village.
+
+And then there was a
+lot of discussion.
+
+And the third was the Read
+India volunteer.
+
+At the end of this process,
+Pratham asked anybody, are
+
+their volunteers to
+learn Read India?
+
+In this case, they
+were not paid.
+
+People just came up, boys
+and girls, usually
+
+youngish boys and girls.
+
+They got trained by Pratham and
+stared running these camps
+
+for the students, Read
+India camps.
+
+And what did we find?
+
+That's kind of the result in
+one graph, kids who, at
+
+baseline, could not
+read anything.
+
+And this their result
+at end-line.
+
+These three lines look the same,
+control, information
+
+only, information plus test
+provided no significant
+
+difference.
+
+But there's a somewhat
+bigger jump for
+
+the Read India program.
+
+That jump, you might think,
+is really not that big.
+
+So first, I have to tell
+you, it's statistically
+
+significant.
+
+This is different than that.
+
+But second is, this jump is only
+due to 13% of kids who
+
+actually showed up.
+
+So only 13% of kids who couldn't
+read went to the
+
+reading camp.
+
+So we can do the same exercise,
+the same Josh
+
+Angrist exercise that we did
+for Bombay or we did for
+
+looking at the effect of the
+balsakhi, to look at the
+
+effect of Read India.
+
+So we divide this little
+bar by 13%.
+
+What is it going to do
+to my little bar.
+
+It's going to make it
+look much bigger.
+
+So this is what we have here.
+
+And that's what we find.
+
+So these are kids who couldn't
+read letters at baseline.
+
+And now I'm adding to the
+control group the little bar
+
+that have now become bigger.
+
+And we get to exactly 100%.
+
+So this suggests that 100% of
+the kids who actually attended
+
+the camp are able to read
+letters at end-line.
+
+So this is a program
+which is trying to
+
+get the kids to read.
+
+And it doesn't get them to read
+full paragraphs, but it
+
+put them one level up.
+
+And you can do the
+same exercise.
+
+Kids who were at letter levels
+are able to read paragraphs
+
+and kids who were at
+paragraph level are
+
+able to read stories.
+
+So this is a program that,
+as a program, is
+
+tremendously effective.
+
+But there were still some
+issues, which is that very few
+
+kids attended the camp.
+
+Why did only 13% of kids
+attend the camp?
+
+And that is something that
+was a puzzle for us.
+
+Next time, we'll spend much more
+time on why did only 13%
+
+of kids come to the camp.
+
+Therefore, the overall
+effect was low.
+
+Next time, we'll try
+to understand that.
+
+But today, I'll tell you what
+happened when we saw this
+
+result, which is we saw an
+effective pedagogy, where, if
+
+I managed to grab Ben by the
+collar and try to inculcate
+
+him how to read with Pratham
+technique, I can do it.
+
+He can learn letters.
+
+But on the other hand, if it's
+left to volunteers and left to
+
+the effort of the parents,
+we only managed to
+
+get 13% of the kids.
+
+So the next step was is it
+possible to integrate this
+
+within the school system?
+
+Because enrollment
+is already high.
+
+Students are already a captive
+audience in the school.
+
+If we could use the teachers
+to do this, then that would
+
+work better.
+
+So off we went.
+
+Pratham got a bunch of money,
+by the Gates and Hewlett
+
+Foundations, to expand
+the program
+
+in about 100 districts.
+
+That's how they reach 38
+million kids today.
+
+But they felt that they
+should try and
+
+work through the states.
+
+And so here the trade-off was,
+well, if it does work, if we
+
+can make it work with regular
+teachers, then we will have
+
+many more kids reached.
+
+So that's the advantage.
+
+The 13% will become 80%.
+
+On the other hand, the treatment
+effect might go from
+
+this very large treatment effect
+we have to a much lower
+
+treatment effect if the teachers
+are not willing or
+
+able to carry out the program.
+
+So that's the question.
+
+So the next experiment, we
+worked in two states, Bihar
+
+and Uttarakhand.
+
+In the meantime, UP
+got cut in two.
+
+And Uttarakhand is one of the
+big, mountainous states, a
+
+former part of UP, very
+beautiful place with
+
+mountains and stuff.
+
+So in Bihar, we contrasted
+four models in different
+
+state, a summer camp taught by
+government teachers, trained
+
+teachers to implement Pratham
+as part of their regular
+
+teaching, trained volunteers
+roughly like the Jaunpur
+
+model, and distribute
+only the material.
+
+Can you just distribute the
+material, the textbooks, and
+
+get an effect from that?
+
+That would be the best, because
+that's very cheap.
+
+In Uttarakhand, we tried this
+same teacher training as in
+
+Bihar and the volunteers.
+
+But the volunteers were put in
+the school, with the idea
+
+that, maybe, in this way,
+the kids would come.
+
+And what did we find?
+
+What we found is that, again,
+when you have the volunteer
+
+intervention, that again works
+extremely well, with effects
+
+similar to what we
+had in Jaunpur.
+
+So what we found in Jaunpur,
+we find the
+
+same thing in Bihar.
+
+It worked in the same way, with
+not very many kids going,
+
+but the kids who went
+really benefited.
+
+And what is interesting here
+is that it's not only basic
+
+reading level any more.
+
+It also covers more
+advanced skills.
+
+And the gains were felt
+at all levels.
+
+So the same approach of trying
+to teach what the kids don't
+
+know, it works at reading,
+but it also works at
+
+more advanced levels.
+
+So great.
+
+We had a big effect
+on learning.
+
+We were happy.
+
+However, the teacher
+intervention had very, very
+
+little effect.
+
+So training the teachers had
+very, very little effect.
+
+There is one effect on
+Hindi written tests.
+
+So if you squint, you find a
+little bit of an effect of the
+
+teachers but, basically,
+not much.
+
+And moreover, when you put the
+volunteers in the schools, the
+
+volunteers had no effect.
+
+In fact, what we found is when
+you put the volunteers in
+
+schools, the teacher
+is absent more.
+
+So they just stay home more.
+
+And the volunteers start
+teaching the kids.
+
+And then it has no impact.
+
+So what do we conclude?
+
+Is it that the teachers are just
+horrible, and they can
+
+absolutely, never teach
+anything to the kids?
+
+Well, we don't think that's
+the case, because of the
+
+summer camp.
+
+In the summer camp program,
+it's the teachers who were
+
+trained to teach.
+
+A teacher had to volunteer, and
+they were paid extra to
+
+teach summer camps.
+
+But they were still teachers.
+
+And they were trained.
+
+And they did it.
+
+And the summer camp effect
+was as large as
+
+the volunteer treatment.
+
+It means that teachers are able
+to teach kids to read if
+
+they want to.
+
+So the problem is that it's
+not that they can't.
+
+It's that usually they
+choose not to.
+
+And why do they choose not to?
+
+That's what we are going
+to see next time.
+
+Where are we?
+
+We know that we can improve
+the quality of education.
+
+Because you can take a high
+school graduate, train them
+
+for two weeks, and
+they can do it.
+
+And the puzzle is that, why
+is it not taken up more?
+
+Why is it not taken up more
+by the school system?
+
+When the teacher's are trained,
+it doesn't work.
+
+Why is not taken more by
+teachers themselves?
+
+Why is it not taken more by
+parents, who are not sending
+
+their kids to the reading camp
+when they have a chance?
+
+I mean some do but
+not that many.
+
+And finally, they are
+private schools.
+
+A lot of these kids are going
+to private schools.
+
+The private schools are somewhat
+more effective than
+
+the public schools but not
+tremendously more.
+
+So why aren't the private
+schools using those
+
+techniques?
+
+After all, nothing stops them.
+
+They can fire the teacher if
+they don't do what they do.
+
+They are more flexible.
+
+So why aren't the private
+school adopting that?
+
+So that's kind of where we
+are, which is there is an
+
+effective methodology, of very
+effective, you know.
+
+You can get everybody to read at
+least one more level, from
+
+where they were, in three
+months of a volunteer.
+
+We can increase their skills
+by one standard deviation.
+
+And yet this is not taken up.
+
+So this is not the technology.
+
+The technology exists.
+
+But it's not adopted, neither at
+the individual level nor at
+
+the system level.
+
+So we'll see where
+we are next time.
+
+And we'll conclude with you.
+
+AUDIENCE: How would
+you [INAUDIBLE]?
+
+PROFESSOR: Teachers are
+very well educated.
+
+Teachers have a BA in teaching
+plus a discipline.
+
+And it's a pretty competitive
+job to get.
+
+And it's very well paid.
+
+But it's very well paid at
+entry, and then you don't
+
+increase much.
+
+And you can never,
+ever be fired.
+
+So it's a very desirable job.
\ No newline at end of file
diff --git a/koHirQQ-Td0.txt b/koHirQQ-Td0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..300be580c2a1c0c43ba407aaa6ec283142a9ff93
--- /dev/null
+++ b/koHirQQ-Td0.txt
@@ -0,0 +1,1296 @@
+align:start position:0%
+ 
+today we're gonna look at Hookes law on
+
+ align:start position:0%
+today we're gonna look at Hookes law on
+ 
+
+ align:start position:0%
+today we're gonna look at Hookes law on
+cubic solids the Hookes law describes
+
+ align:start position:0%
+cubic solids the Hookes law describes
+ 
+
+ align:start position:0%
+cubic solids the Hookes law describes
+the behavior of Springs so we're going
+
+ align:start position:0%
+the behavior of Springs so we're going
+ 
+
+ align:start position:0%
+the behavior of Springs so we're going
+to do is gonna model the solid as a
+
+ align:start position:0%
+to do is gonna model the solid as a
+ 
+
+ align:start position:0%
+to do is gonna model the solid as a
+collection of Springs connecting a whole
+
+ align:start position:0%
+collection of Springs connecting a whole
+ 
+
+ align:start position:0%
+collection of Springs connecting a whole
+bunch of atoms in cubic lattice
+
+ align:start position:0%
+bunch of atoms in cubic lattice
+ 
+
+ align:start position:0%
+bunch of atoms in cubic lattice
+now disclaimer I'm probably gonna do
+
+ align:start position:0%
+now disclaimer I'm probably gonna do
+ 
+
+ align:start position:0%
+now disclaimer I'm probably gonna do
+this all wrong
+
+ align:start position:0%
+this all wrong
+ 
+
+ align:start position:0%
+this all wrong
+but what science if you don't make new
+
+ align:start position:0%
+but what science if you don't make new
+ 
+
+ align:start position:0%
+but what science if you don't make new
+mistakes right let's get started
+
+ align:start position:0%
+mistakes right let's get started
+ 
+
+ align:start position:0%
+mistakes right let's get started
+so what the potential that describes
+
+ align:start position:0%
+so what the potential that describes
+ 
+
+ align:start position:0%
+so what the potential that describes
+fairly well the behavior of the
+
+ align:start position:0%
+fairly well the behavior of the
+ 
+
+ align:start position:0%
+fairly well the behavior of the
+interaction between two atoms is the
+
+ align:start position:0%
+interaction between two atoms is the
+ 
+
+ align:start position:0%
+interaction between two atoms is the
+lennard-jones potential described to the
+
+ align:start position:0%
+lennard-jones potential described to the
+ 
+
+ align:start position:0%
+lennard-jones potential described to the
+founder halls interaction and it looks
+
+ align:start position:0%
+founder halls interaction and it looks
+ 
+
+ align:start position:0%
+founder halls interaction and it looks
+something like this it's a potential
+
+ align:start position:0%
+something like this it's a potential
+ 
+
+ align:start position:0%
+something like this it's a potential
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+term which goes R to the 1 over R to the
+
+ align:start position:0%
+term which goes R to the 1 over R to the
+ 
+
+ align:start position:0%
+term which goes R to the 1 over R to the
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+I'll only carriage put one over R over 6
+
+ align:start position:0%
+I'll only carriage put one over R over 6
+ 
+
+ align:start position:0%
+I'll only carriage put one over R over 6
+and as you can see as he atoms get very
+
+ align:start position:0%
+and as you can see as he atoms get very
+ 
+
+ align:start position:0%
+and as you can see as he atoms get very
+close they repel greatly and then they
+
+ align:start position:0%
+close they repel greatly and then they
+ 
+
+ align:start position:0%
+close they repel greatly and then they
+have a sweet spot here which is the
+
+ align:start position:0%
+have a sweet spot here which is the
+ 
+
+ align:start position:0%
+have a sweet spot here which is the
+distance they prefer to be at then to
+
+ align:start position:0%
+distance they prefer to be at then to
+ 
+
+ align:start position:0%
+distance they prefer to be at then to
+get further away they struck to repel
+
+ align:start position:0%
+get further away they struck to repel
+ 
+
+ align:start position:0%
+get further away they struck to repel
+more again so the atom likes to sit
+
+ align:start position:0%
+more again so the atom likes to sit
+ 
+
+ align:start position:0%
+more again so the atom likes to sit
+right there on that little potential
+
+ align:start position:0%
+right there on that little potential
+ 
+
+ align:start position:0%
+right there on that little potential
+will and slow written up in Mathematica
+
+ align:start position:0%
+will and slow written up in Mathematica
+ 
+
+ align:start position:0%
+will and slow written up in Mathematica
+you can see the equation here what each
+
+ align:start position:0%
+you can see the equation here what each
+ 
+
+ align:start position:0%
+you can see the equation here what each
+term means and I come here is I taking
+
+ align:start position:0%
+term means and I come here is I taking
+ 
+
+ align:start position:0%
+term means and I come here is I taking
+the derivative and so what that does is
+
+ align:start position:0%
+the derivative and so what that does is
+ 
+
+ align:start position:0%
+the derivative and so what that does is
+give me the force on the particle but
+
+ align:start position:0%
+give me the force on the particle but
+ 
+
+ align:start position:0%
+give me the force on the particle but
+it's in this potential so as you can see
+
+ align:start position:0%
+it's in this potential so as you can see
+ 
+
+ align:start position:0%
+it's in this potential so as you can see
+the forces high and positive on one set
+
+ align:start position:0%
+the forces high and positive on one set
+ 
+
+ align:start position:0%
+the forces high and positive on one set
+minute some closer to the other atom
+
+ align:start position:0%
+minute some closer to the other atom
+ 
+
+ align:start position:0%
+minute some closer to the other atom
+then the equilibrium distance and the
+
+ align:start position:0%
+then the equilibrium distance and the
+ 
+
+ align:start position:0%
+then the equilibrium distance and the
+force is negative way it's farther so it
+
+ align:start position:0%
+force is negative way it's farther so it
+ 
+
+ align:start position:0%
+force is negative way it's farther so it
+gets pulled towards the sweet spot that
+
+ align:start position:0%
+gets pulled towards the sweet spot that
+ 
+
+ align:start position:0%
+gets pulled towards the sweet spot that
+I mentioned earlier and here are the two
+
+ align:start position:0%
+I mentioned earlier and here are the two
+ 
+
+ align:start position:0%
+I mentioned earlier and here are the two
+pluses together so with Hookes law were
+
+ align:start position:0%
+pluses together so with Hookes law were
+ 
+
+ align:start position:0%
+pluses together so with Hookes law were
+modeling the atomic bonds as Springs and
+
+ align:start position:0%
+modeling the atomic bonds as Springs and
+ 
+
+ align:start position:0%
+modeling the atomic bonds as Springs and
+the way that's gonna work is we have
+
+ align:start position:0%
+the way that's gonna work is we have
+ 
+
+ align:start position:0%
+the way that's gonna work is we have
+books colleges that the force is
+
+ align:start position:0%
+books colleges that the force is
+ 
+
+ align:start position:0%
+books colleges that the force is
+proportional to the spring constant
+
+ align:start position:0%
+proportional to the spring constant
+ 
+
+ align:start position:0%
+proportional to the spring constant
+times the displacement with a further
+
+ align:start position:0%
+times the displacement with a further
+ 
+
+ align:start position:0%
+times the displacement with a further
+you pullet afraid of the force and it's
+
+ align:start position:0%
+you pullet afraid of the force and it's
+ 
+
+ align:start position:0%
+you pullet afraid of the force and it's
+linear relationship and the problem is
+
+ align:start position:0%
+linear relationship and the problem is
+ 
+
+ align:start position:0%
+linear relationship and the problem is
+though our lennard-jones potential is
+
+ align:start position:0%
+though our lennard-jones potential is
+ 
+
+ align:start position:0%
+though our lennard-jones potential is
+not known potential all right it's as
+
+ align:start position:0%
+not known potential all right it's as
+ 
+
+ align:start position:0%
+not known potential all right it's as
+weird wobbly shape but for Hookes law to
+
+ align:start position:0%
+weird wobbly shape but for Hookes law to
+ 
+
+ align:start position:0%
+weird wobbly shape but for Hookes law to
+work you have something else he has like
+
+ align:start position:0%
+work you have something else he has like
+ 
+
+ align:start position:0%
+work you have something else he has like
+a spring which has a parabolic potential
+
+ align:start position:0%
+a spring which has a parabolic potential
+ 
+
+ align:start position:0%
+a spring which has a parabolic potential
+well just how you get that linear
+
+ align:start position:0%
+well just how you get that linear
+ 
+
+ align:start position:0%
+well just how you get that linear
+horsewhip so when you take the
+
+ align:start position:0%
+horsewhip so when you take the
+ 
+
+ align:start position:0%
+horsewhip so when you take the
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+so what I've done is I'm thinking like
+
+ align:start position:0%
+so what I've done is I'm thinking like
+ 
+
+ align:start position:0%
+so what I've done is I'm thinking like
+use Mathematica it's wonderful map tools
+
+ align:start position:0%
+use Mathematica it's wonderful map tools
+ 
+
+ align:start position:0%
+use Mathematica it's wonderful map tools
+to take the Taylor expansion about that
+
+ align:start position:0%
+to take the Taylor expansion about that
+ 
+
+ align:start position:0%
+to take the Taylor expansion about that
+equilibrium play and you can see here
+
+ align:start position:0%
+equilibrium play and you can see here
+ 
+
+ align:start position:0%
+equilibrium play and you can see here
+this is the second order Taylor
+
+ align:start position:0%
+this is the second order Taylor
+ 
+
+ align:start position:0%
+this is the second order Taylor
+expansion so it's a parabola and if you
+
+ align:start position:0%
+expansion so it's a parabola and if you
+ 
+
+ align:start position:0%
+expansion so it's a parabola and if you
+look at this little manipulate here I
+
+ align:start position:0%
+look at this little manipulate here I
+ 
+
+ align:start position:0%
+look at this little manipulate here I
+have set it up so you can you know just
+
+ align:start position:0%
+have set it up so you can you know just
+ 
+
+ align:start position:0%
+have set it up so you can you know just
+the potential well depth you can choose
+
+ align:start position:0%
+the potential well depth you can choose
+ 
+
+ align:start position:0%
+the potential well depth you can choose
+the equilibrium distance you can look at
+
+ align:start position:0%
+the equilibrium distance you can look at
+ 
+
+ align:start position:0%
+the equilibrium distance you can look at
+the different order Taylor expansion so
+
+ align:start position:0%
+the different order Taylor expansion so
+ 
+
+ align:start position:0%
+the different order Taylor expansion so
+that's the first order it's aligned the
+
+ align:start position:0%
+that's the first order it's aligned the
+ 
+
+ align:start position:0%
+that's the first order it's aligned the
+second order is parabola so we're going
+
+ align:start position:0%
+second order is parabola so we're going
+ 
+
+ align:start position:0%
+second order is parabola so we're going
+to be using the other ones are just
+
+ align:start position:0%
+to be using the other ones are just
+ 
+
+ align:start position:0%
+to be using the other ones are just
+better and better approximations of the
+
+ align:start position:0%
+better and better approximations of the
+ 
+
+ align:start position:0%
+better and better approximations of the
+actual potential athletics supposedly
+
+ align:start position:0%
+actual potential athletics supposedly
+ 
+
+ align:start position:0%
+actual potential athletics supposedly
+can do negative powers but I'm not
+
+ align:start position:0%
+can do negative powers but I'm not
+ 
+
+ align:start position:0%
+can do negative powers but I'm not
+seeing that here so it'd be thicker the
+
+ align:start position:0%
+seeing that here so it'd be thicker the
+ 
+
+ align:start position:0%
+seeing that here so it'd be thicker the
+actual perfect model would be obviously
+
+ align:start position:0%
+actual perfect model would be obviously
+ 
+
+ align:start position:0%
+actual perfect model would be obviously
+1 over r12 is harder than a guitar
+
+ align:start position:0%
+1 over r12 is harder than a guitar
+ 
+
+ align:start position:0%
+1 over r12 is harder than a guitar
+so I differentiated that second order
+
+ align:start position:0%
+so I differentiated that second order
+ 
+
+ align:start position:0%
+so I differentiated that second order
+potential like that and you can see here
+
+ align:start position:0%
+potential like that and you can see here
+ 
+
+ align:start position:0%
+potential like that and you can see here
+the fort response for our generalized
+
+ align:start position:0%
+the fort response for our generalized
+ 
+
+ align:start position:0%
+the fort response for our generalized
+twirl approximated spring rod and so you
+
+ align:start position:0%
+twirl approximated spring rod and so you
+ 
+
+ align:start position:0%
+twirl approximated spring rod and so you
+can look at her here our force response
+
+ align:start position:0%
+can look at her here our force response
+ 
+
+ align:start position:0%
+can look at her here our force response
+here noticeably like be a blank before
+
+ align:start position:0%
+here noticeably like be a blank before
+ 
+
+ align:start position:0%
+here noticeably like be a blank before
+the force is positive on when the atoms
+
+ align:start position:0%
+the force is positive on when the atoms
+ 
+
+ align:start position:0%
+the force is positive on when the atoms
+are close together and negative in the
+
+ align:start position:0%
+are close together and negative in the
+ 
+
+ align:start position:0%
+are close together and negative in the
+further part so it gets pulled to that
+
+ align:start position:0%
+further part so it gets pulled to that
+ 
+
+ align:start position:0%
+further part so it gets pulled to that
+sweet spot and then finally Q with
+
+ align:start position:0%
+sweet spot and then finally Q with
+ 
+
+ align:start position:0%
+sweet spot and then finally Q with
+potential so you can see how exactly it
+
+ align:start position:0%
+potential so you can see how exactly it
+ 
+
+ align:start position:0%
+potential so you can see how exactly it
+interacts with that potential
+
+ align:start position:0%
+interacts with that potential
+ 
+
+ align:start position:0%
+interacts with that potential
+here's the box our potential with the
+
+ align:start position:0%
+here's the box our potential with the
+ 
+
+ align:start position:0%
+here's the box our potential with the
+actual energy on potential so you can
+
+ align:start position:0%
+actual energy on potential so you can
+ 
+
+ align:start position:0%
+actual energy on potential so you can
+see that it's not a very good
+
+ align:start position:0%
+see that it's not a very good
+ 
+
+ align:start position:0%
+see that it's not a very good
+approximation but very small
+
+ align:start position:0%
+approximation but very small
+ 
+
+ align:start position:0%
+approximation but very small
+displacements on the order of 0.1 times
+
+ align:start position:0%
+displacements on the order of 0.1 times
+ 
+
+ align:start position:0%
+displacements on the order of 0.1 times
+that minimum distance will probably be
+
+ align:start position:0%
+that minimum distance will probably be
+ 
+
+ align:start position:0%
+that minimum distance will probably be
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so I simplified it in here to get thee
+
+ align:start position:0%
+so I simplified it in here to get thee
+ 
+
+ align:start position:0%
+so I simplified it in here to get thee
+and then I second through it again just
+
+ align:start position:0%
+and then I second through it again just
+ 
+
+ align:start position:0%
+and then I second through it again just
+so I can get that slope and that'll be
+
+ align:start position:0%
+so I can get that slope and that'll be
+ 
+
+ align:start position:0%
+so I can get that slope and that'll be
+useful later so here we're modeling our
+
+ align:start position:0%
+useful later so here we're modeling our
+ 
+
+ align:start position:0%
+useful later so here we're modeling our
+cubic lattice saying we have something
+
+ align:start position:0%
+cubic lattice saying we have something
+ 
+
+ align:start position:0%
+cubic lattice saying we have something
+like alpha polonium which has this
+
+ align:start position:0%
+like alpha polonium which has this
+ 
+
+ align:start position:0%
+like alpha polonium which has this
+simple cubic structure the only metal
+
+ align:start position:0%
+simple cubic structure the only metal
+ 
+
+ align:start position:0%
+simple cubic structure the only metal
+that has the simple cubic structure with
+
+ align:start position:0%
+that has the simple cubic structure with
+ 
+
+ align:start position:0%
+that has the simple cubic structure with
+a single atom Latif so we have our Stern
+
+ align:start position:0%
+a single atom Latif so we have our Stern
+ 
+
+ align:start position:0%
+a single atom Latif so we have our Stern
+stress over here era strain hallucis
+
+ align:start position:0%
+stress over here era strain hallucis
+ 
+
+ align:start position:0%
+stress over here era strain hallucis
+fourth rank tensor that connects our
+
+ align:start position:0%
+fourth rank tensor that connects our
+ 
+
+ align:start position:0%
+fourth rank tensor that connects our
+second rank tensors of stress and strain
+
+ align:start position:0%
+second rank tensors of stress and strain
+ 
+
+ align:start position:0%
+second rank tensors of stress and strain
+but because of the 100
+
+ align:start position:0%
+but because of the 100
+ 
+
+ align:start position:0%
+but because of the 100
+of Mathematics and matrices we can
+
+ align:start position:0%
+of Mathematics and matrices we can
+ 
+
+ align:start position:0%
+of Mathematics and matrices we can
+actually break that down to 2/1 Richter
+
+ align:start position:0%
+actually break that down to 2/1 Richter
+ 
+
+ align:start position:0%
+actually break that down to 2/1 Richter
+first rate captures and a to quickly
+
+ align:start position:0%
+first rate captures and a to quickly
+ 
+
+ align:start position:0%
+first rate captures and a to quickly
+rank tensor which is pretty great I mean
+
+ align:start position:0%
+rank tensor which is pretty great I mean
+ 
+
+ align:start position:0%
+rank tensor which is pretty great I mean
+you don't want to do some really ugly
+
+ align:start position:0%
+you don't want to do some really ugly
+ 
+
+ align:start position:0%
+you don't want to do some really ugly
+mad
+
+ align:start position:0%
+mad
+ 
+
+ align:start position:0%
+mad
+and so I can find that infant uh small
+
+ align:start position:0%
+and so I can find that infant uh small
+ 
+
+ align:start position:0%
+and so I can find that infant uh small
+strain tensor if you're looking at a
+
+ align:start position:0%
+strain tensor if you're looking at a
+ 
+
+ align:start position:0%
+strain tensor if you're looking at a
+tiny tiny piece of the solid will look
+
+ align:start position:0%
+tiny tiny piece of the solid will look
+ 
+
+ align:start position:0%
+tiny tiny piece of the solid will look
+something like this it's this the
+
+ align:start position:0%
+something like this it's this the
+ 
+
+ align:start position:0%
+something like this it's this the
+epsilon IJ is equal to half of the
+
+ align:start position:0%
+epsilon IJ is equal to half of the
+ 
+
+ align:start position:0%
+epsilon IJ is equal to half of the
+displacements of in each direction of
+
+ align:start position:0%
+displacements of in each direction of
+ 
+
+ align:start position:0%
+displacements of in each direction of
+the decimal piece and so from that we
+
+ align:start position:0%
+the decimal piece and so from that we
+ 
+
+ align:start position:0%
+the decimal piece and so from that we
+can build it out to the second rate
+
+ align:start position:0%
+can build it out to the second rate
+ 
+
+ align:start position:0%
+can build it out to the second rate
+strain tensor which is this tensor here
+
+ align:start position:0%
+strain tensor which is this tensor here
+ 
+
+ align:start position:0%
+strain tensor which is this tensor here
+and it looks like this where u is the
+
+ align:start position:0%
+and it looks like this where u is the
+ 
+
+ align:start position:0%
+and it looks like this where u is the
+position so we have there's all these
+
+ align:start position:0%
+position so we have there's all these
+ 
+
+ align:start position:0%
+position so we have there's all these
+displacements but you can see along the
+
+ align:start position:0%
+displacements but you can see along the
+ 
+
+ align:start position:0%
+displacements but you can see along the
+principal axes are just four tional to
+
+ align:start position:0%
+principal axes are just four tional to
+ 
+
+ align:start position:0%
+principal axes are just four tional to
+the displacement of the directions along
+
+ align:start position:0%
+the displacement of the directions along
+ 
+
+ align:start position:0%
+the displacement of the directions along
+the other axis they're a little more
+
+ align:start position:0%
+the other axis they're a little more
+ 
+
+ align:start position:0%
+the other axis they're a little more
+complicated because you have things
+
+ align:start position:0%
+complicated because you have things
+ 
+
+ align:start position:0%
+complicated because you have things
+moving in two directions at once but the
+
+ align:start position:0%
+moving in two directions at once but the
+ 
+
+ align:start position:0%
+moving in two directions at once but the
+coolest part is that these edges are
+
+ align:start position:0%
+coolest part is that these edges are
+ 
+
+ align:start position:0%
+coolest part is that these edges are
+unique right because this thing is that
+
+ align:start position:0%
+unique right because this thing is that
+ 
+
+ align:start position:0%
+unique right because this thing is that
+that's the same as that and that is the
+
+ align:start position:0%
+that's the same as that and that is the
+ 
+
+ align:start position:0%
+that's the same as that and that is the
+same as that so what we can do is we can
+
+ align:start position:0%
+same as that so what we can do is we can
+ 
+
+ align:start position:0%
+same as that so what we can do is we can
+just break it out into these six unique
+
+ align:start position:0%
+just break it out into these six unique
+ 
+
+ align:start position:0%
+just break it out into these six unique
+things and then here's our second rank
+
+ align:start position:0%
+things and then here's our second rank
+ 
+
+ align:start position:0%
+things and then here's our second rank
+tensor like I said before of our
+
+ align:start position:0%
+tensor like I said before of our
+ 
+
+ align:start position:0%
+tensor like I said before of our
+elasticity but because music looks long
+
+ align:start position:0%
+elasticity but because music looks long
+ 
+
+ align:start position:0%
+elasticity but because music looks long
+these are springs and this is a simple
+
+ align:start position:0%
+these are springs and this is a simple
+ 
+
+ align:start position:0%
+these are springs and this is a simple
+cubic lattice so each atoms only
+
+ align:start position:0%
+cubic lattice so each atoms only
+ 
+
+ align:start position:0%
+cubic lattice so each atoms only
+attached to six of its neighbors and so
+
+ align:start position:0%
+attached to six of its neighbors and so
+ 
+
+ align:start position:0%
+attached to six of its neighbors and so
+it's not gonna have any weird stresses
+
+ align:start position:0%
+it's not gonna have any weird stresses
+ 
+
+ align:start position:0%
+it's not gonna have any weird stresses
+this is where I'm probably wrong but at
+
+ align:start position:0%
+this is where I'm probably wrong but at
+ 
+
+ align:start position:0%
+this is where I'm probably wrong but at
+this point we are gonna do this
+
+ align:start position:0%
+this point we are gonna do this
+ 
+
+ align:start position:0%
+this point we are gonna do this
+so here are diagonal elasticity values
+
+ align:start position:0%
+so here are diagonal elasticity values
+ 
+
+ align:start position:0%
+so here are diagonal elasticity values
+and if we do what I did before it's
+
+ align:start position:0%
+and if we do what I did before it's
+ 
+
+ align:start position:0%
+and if we do what I did before it's
+simplify that spin potential and grab
+
+ align:start position:0%
+simplify that spin potential and grab
+ 
+
+ align:start position:0%
+simplify that spin potential and grab
+the slope of that line we get our spring
+
+ align:start position:0%
+the slope of that line we get our spring
+ 
+
+ align:start position:0%
+the slope of that line we get our spring
+constant so if this were a spring that's
+
+ align:start position:0%
+constant so if this were a spring that's
+ 
+
+ align:start position:0%
+constant so if this were a spring that's
+what the spring constant would be and we
+
+ align:start position:0%
+what the spring constant would be and we
+ 
+
+ align:start position:0%
+what the spring constant would be and we
+just like right in here to our matrix
+
+ align:start position:0%
+just like right in here to our matrix
+ 
+
+ align:start position:0%
+just like right in here to our matrix
+and you get a look at cooks law so if
+
+ align:start position:0%
+and you get a look at cooks law so if
+ 
+
+ align:start position:0%
+and you get a look at cooks law so if
+everything is wonderful in many areas
+
+ align:start position:0%
+everything is wonderful in many areas
+ 
+
+ align:start position:0%
+everything is wonderful in many areas
+probably not but if it were we have this
+
+ align:start position:0%
+probably not but if it were we have this
+ 
+
+ align:start position:0%
+probably not but if it were we have this
+Hookes law and we could use that to
+
+ align:start position:0%
+Hookes law and we could use that to
+ 
+
+ align:start position:0%
+Hookes law and we could use that to
+determine from the strain stress or vice
+
+ align:start position:0%
+determine from the strain stress or vice
+ 
+
+ align:start position:0%
+determine from the strain stress or vice
+versa as you can see it looks something
+
+ align:start position:0%
+versa as you can see it looks something
+ 
+
+ align:start position:0%
+versa as you can see it looks something
+like this me so in the original position
+
+ align:start position:0%
+like this me so in the original position
+ 
+
+ align:start position:0%
+like this me so in the original position
+of the springs the black and then when
+
+ align:start position:0%
+of the springs the black and then when
+ 
+
+ align:start position:0%
+of the springs the black and then when
+you drag the atom over here you get this
+
+ align:start position:0%
+you drag the atom over here you get this
+ 
+
+ align:start position:0%
+you drag the atom over here you get this
+it is red to form spray
+
+ align:start position:0%
+it is red to form spray
+ 
+
+ align:start position:0%
+it is red to form spray
+listen you're squishy like stretch and
+
+ align:start position:0%
+listen you're squishy like stretch and
+ 
+
+ align:start position:0%
+listen you're squishy like stretch and
+yeah that's about it
\ No newline at end of file
diff --git a/l5J-t5NcHuQ.txt b/l5J-t5NcHuQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..153237c73ed41c7ebbc3ae1d397e31d7dfcc884e
--- /dev/null
+++ b/l5J-t5NcHuQ.txt
@@ -0,0 +1,729 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or to
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: My name
+is Mark Harvey,
+
+and I am teaching a
+course this semester
+
+on musical improvisation.
+
+We have our students
+here this evening,
+
+and [INAUDIBLE] the
+rest of you [INAUDIBLE].
+
+And in conjunction
+with the course,
+
+we're running this
+concert series,
+
+which is the last of
+four concerts we've had.
+
+And you see on the
+page that you picked up
+
+at the door, another very
+different kinds of programs
+
+that we've had.
+
+And we're thrilled to include
+in this particular [INAUDIBLE]
+
+we call Tre Corda with
+Tim Ray over here,
+
+Greg Hopkins, and
+Eugene Friesen.
+
+So please welcome them.
+
+[APPLAUSE]
+
+[MUSIC - TRE CORDA, "SHADOW
+ PLAY"]
+
+[APPLAUSE]
+
+TIM RAY: Thank you.
+
+Thanks very much.
+
+And thank you all
+for coming out.
+
+It's great to see a great
+audience here at MIT.
+
+We are Tre Corda and
+very glad to be here and.
+
+And as Mark mentioned,
+the gentlemen
+
+up here on stage-- on stage?
+
+Do we call this a stage?
+
+It's where we're playing,
+so I guess it's a stage.
+
+Anyway, I just
+want to remind you
+
+that is on trumpet and
+flugelhorn Greg Hopkins.
+
+[APPLAUSE]
+
+And on cello, Eugene Friesen.
+
+[APPLAUSE]
+
+So that first piece you heard
+was a composition of Eugene
+
+Friesen's called
+"Shadow Play," which
+
+of course is an
+amazing pizzicato
+
+technique on the cello.
+
+And we love to jump in on some
+of Eugene's pizzicato creations
+
+as we did on that song.
+
+We're celebrating a new CD.
+
+We have a new CD, the three
+of us, called Squeaky Toy.
+
+And we're going to
+play-- "Shadow Play,"
+
+the song we just played
+is on the new CD.
+
+And we're going to play some
+other ones on the new CD
+
+as well.
+
+And continuing on with
+another song from that disk.
+
+This is the first movement of
+the sonata for trumpet, cello,
+
+and piano composed
+by Greg Hopkins.
+
+And the title of this
+movement is "Sneakers."
+
+[MUSIC - TRE CORDA, "SNEAKERS"]
+
+[APPLAUSE]
+
+GREG HOPKINS: Thank
+you very much.
+
+Yeah, it's such a joy to have
+these wonderful musicians play
+
+the music you're
+hearing in your head.
+
+And it comes out like that.
+
+Thank you so much, guys.
+
+This next one I also wrote.
+
+And it's an homage
+to my late cat.
+
+His name was Cargassian.
+
+And he was very deft at walking
+in the dark up on the mantels.
+
+And you could hear the china
+just clinking together.
+
+Nothing ever fell or broke.
+
+But it just tingled
+a little bit.
+
+So you knew he was there.
+
+Anyway, so please
+enjoy "Cargassian."
+
+He had blue hair.
+
+Nothing to do with
+the [INAUDIBLE].
+
+[MUSIC - TRE CORDA,
+ "CARGASSIAN"]
+
+[APPLAUSE]
+
+TIM RAY: Eugene and
+I had the opportunity
+
+to work with some of the
+students in Mark Harvey's
+
+improvisation class today.
+
+And that's their assignment.
+
+They have to play
+that for us next week.
+
+[LAUGHTER]
+
+So [INAUDIBLE].
+
+GREG HOPKINS: Get stratching.
+
+TIM RAY: Get scratching.
+
+So we're going to continue on.
+
+This is a recent piece that
+I wrote, pretty recent.
+
+GREG HOPKINS: Tim, this is the
+first time we're playing it.
+
+TIM RAY: So I guess--
+
+[LAUGHTER]
+
+I guess that makes it recent.
+
+No, this was for the
+occasion of my wife
+
+and I, who's here tonight, for
+our 25th wedding anniversary,
+
+one of the things we
+did to mark that was we
+
+bought this clock,
+this big chiming clock.
+
+And there's a long story
+that goes behind it.
+
+But basically the ones
+that were really cool
+
+that sound beautiful and
+that look really nice,
+
+we couldn't afford those.
+
+[LAUGHTER]
+
+So we got this kind of sort
+of smallish and the case
+
+is a little misshapen.
+
+And it's only got one hand.
+
+And it makes this
+horrendous chiming sound.
+
+It's really bad.
+
+Like for the first month
+after we got the clock,
+
+every hour the
+dogs would run out
+
+of the room,
+because they thought
+
+something terrible
+was about to happen.
+
+But now the dogs are used to it.
+
+And we're used to it.
+
+We actually kind of fell in
+love with this clock now.
+
+Another thing I did for
+this was I wrote a song.
+
+And the title of
+this song is Joy.
+
+And if you listen
+at the end, you
+
+will here 25 chimes
+for the 25 years.
+
+[MUSIC - TRE CORDA, "JOY"]
+
+[APPLAUSE]
+
+[MUSIC - TRE CORDA]
+
+[APPLAUSE]
+
+TIM RAY: Thank you, thank you.
+
+That of course, from the opera
+Carmen, or our version of that.
+
+That's also kind of neat for us.
+
+Actually, Mark, I think
+summed it up perfectly
+
+before the show.
+
+He said, yeah, that manages to
+offend the French, the Spanish,
+
+and the Cubans all at once.
+
+I think he's right, too, not
+to mention classical music
+
+in general.
+
+So we're going to give
+Eugene a breather.
+
+And Greg and I are
+going to do a duet.
+
+And I don't know what
+we're going to play,
+
+because I never know
+what we're going to play.
+
+We'll find out
+when we get there.
+
+[INAUDIBLE]
+
+[MUSIC - TRE CORDA, "LITTLE
+ ROOTIE TOOTIE"]
+
+[APPLAUSE]
+
+OK.
+
+What song was that?
+
+First of all-- OK,
+title, anybody?
+
+Title?
+
+Yeah.
+
+Yeah, I was going
+to say, composer.
+
+Thelonious Monk, very good.
+
+Thank you, Alan.
+
+"Little Rootie Tootie,"
+is the name of that.
+
+Written for his
+son, apparently he
+
+called his son
+Little Rootie Tootie.
+
+EUGENE FRIESEN: And now for
+something completely different.
+
+TIM RAY: And now--
+Can you set this up?
+
+You can find the music.
+
+EUGENE FRIESEN: OK, sure thing.
+
+This shows a little of the
+different side of improvising.
+
+This is a piece that was
+originally a [INAUDIBLE].
+
+As we were discussing
+this afternoon, some of us
+
+benefit from launching
+into an improvisation
+
+by kind of limiting
+the boundaries
+
+of the language a little bit.
+
+In this case, this
+was pretty much
+
+a diotronic piece that
+was a free improve.
+
+It was recorded in a beautiful
+cathedral, St. John the Divine,
+
+in one November night in 1986.
+
+And thank goodness
+the tape was rolling.
+
+It turned out to
+be something that I
+
+wanted to play again and again.
+
+I call it "First Ride."
+
+And we went back and
+transcribed the original improvs
+
+so we could perform it again.
+
+Tim did an amazing
+job of reinventing
+
+the improvised piano part.
+
+I'm pretty much
+playing the cello part
+
+that was improvised that
+night some years ago.
+
+This is called "First Ride."
+
+[MUSIC - TRE CORDA, "FIRST
+ RIDE"]
+
+[APPLAUSE]
+
+TIM RAY: Thank have.
+
+Thanks very much.
+
+We've got a couple more left.
+
+Now I'm trying to decide.
+
+As you can see, we
+have way too much
+
+music for the time we have left.
+
+So we're going to pick and
+choose a little bit here.
+
+You guys want to do Bartok?
+
+Let's do Bartok.
+
+As I'm sure you've probably
+figured out by now,
+
+we're playing a lot
+with classical music.
+
+And we're obviously
+influenced by classical music.
+
+It's a lot of what we're doing.
+
+And now we're
+actually going to try
+
+to play some classical music.
+
+I know.
+
+I know, I thought
+the same thing.
+
+And these guys-- well, anyway.
+
+But of course, we're not
+going to play it straight.
+
+This is something else, and by
+the way, it's on the new CD.
+
+I was introduced to these piano
+pieces, Bartok, Bela Bartok,
+
+piano pieces back
+when I was at college.
+
+And I was immediately
+attracted to them
+
+because the title of
+them is "Improvisations."
+
+Then I thought, cool.
+
+I get to just make up stuff
+and call it classical music.
+
+But it turns out, it
+doesn't work that way.
+
+You have to play the
+notes that are out there.
+
+But they're called
+improvisations,
+
+but they're all written out.
+
+So I was a little disappointed.
+
+But nevertheless, I loved these.
+
+I play these pieces,
+and I love them.
+
+And I kind of rediscovered them
+by accident a few years ago.
+
+And I thought this would be
+great to, first of all, to try
+
+with the trio,
+and second of all,
+
+to actually put
+some improvisation
+
+into the "Improvisations."
+
+So with apologies
+to Bela Bartok.
+
+We're going to do three-- these
+are eight short piano pieces.
+
+And we're going to do three
+of them, number five, number
+
+three, and number eight.
+
+[MUSIC - TRE CORDA,
+ "IMPROVISATIONS"]
+
+[APPLAUSE]
+
+Thanks very much.
+
+Thank you.
+
+So we're going to
+do one more song
+
+and get our in the beautiful
+cool air once again.
+
+But before we do, a
+couple of reminders.
+
+If you're interested
+in a CD, we've
+
+got the new CD, the new
+Tre Corda CD, Squeaky Toy.
+
+And I'm told that my merchandise
+staff out there gives
+
+huge discounts to students.
+
+Huge discounts for students.
+
+And Greg Hopkins's new CD is
+also out on the table, right?
+
+Greg Hopkins has a new
+sextet, a quintet plus one,
+
+as he calls it, which to
+me sounds like a sextet,
+
+but apparently it's different.
+
+[LAUGHTER]
+
+GREG HOPKINS:
+You're the plus one.
+
+TIM RAY: I'm the plus one?
+
+OK.
+
+So look for that as well.
+
+We also have, for
+the new CD, you know,
+
+we're all old guys,
+relatively speaking.
+
+I'm very proud of myself.
+
+I actually have download cards
+out there, for a discount rate.
+
+I forget what the
+discount rate is.
+
+She'll tell you.
+
+You can buy a little
+download card.
+
+It's cheaper than a CD.
+
+That much I know.
+
+And go download
+it from a CD Baby.
+
+So that's a cool thing
+to do if you just
+
+want the digital,
+the ones and zeroes.
+
+That's a good way to do that.
+
+And mailing list, if you
+want to get on email list.
+
+You can also do
+that at the table.
+
+And I think that's it
+except for two more things.
+
+Of course I want to
+give a big thank you
+
+to MIT and to the folks
+here at Killian Hall
+
+for providing this
+beautiful space for us
+
+to play in, and particularly
+to my good friend
+
+Mark Harvey who invited us here.
+
+[APPLAUSE]
+
+As I said before, we're
+really glad to be finishing up
+
+the series of improvising
+groups here at MIT.
+
+And we're having a great time.
+
+And again, if you
+want to come find us,
+
+go sign up on our email list.
+
+And lastly, but not
+leastly, please help me
+
+thank once again on
+cello, Eugene Friesen.
+
+[APPLAUSE]
+
+And on trumpet, Greg Hopkins.
+
+[APPLAUSE]
+
+GREG HOPKINS: And our fearless
+leader, Tim Ray on piano.
+
+[APPLAUSE]
+
+TIM RAY: So I'm looking at
+three or four songs here.
+
+Should we-- do you have an idea?
+
+Oh, you're pointing at Greg.
+
+We could do "Theme Park" or
+we could "Church Rhythm."
+
+Let's do "Church Rhythm."
+
+OK, we're going to do another--
+we started with a Eugene
+
+Friesen composition.
+
+We're going to end with a
+Eugene Friesen composition.
+
+This is entitled,
+"Church Rhythm."
+
+[MUSIC - TRE CORDA, "CHURCH
+ RHYTHM"]
+
+[APPLAUSE]
\ No newline at end of file
diff --git a/lj66CYRmuNU.txt b/lj66CYRmuNU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..61b1d70eae59072549d1ed2563ccd99f778023b6
--- /dev/null
+++ b/lj66CYRmuNU.txt
@@ -0,0 +1,6763 @@
+align:start position:0%
+ 
+okay so we
+
+ align:start position:0%
+okay so we
+ 
+
+ align:start position:0%
+okay so we
+we're going to continue some factors
+
+ align:start position:0%
+we're going to continue some factors
+ 
+
+ align:start position:0%
+we're going to continue some factors
+we're going to continue the discussion
+
+ align:start position:0%
+we're going to continue the discussion
+ 
+
+ align:start position:0%
+we're going to continue the discussion
+of axonal growth today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talk a little more about what's
+
+ align:start position:0%
+talk a little more about what's
+ 
+
+ align:start position:0%
+talk a little more about what's
+guiding those axons when they're growing
+
+ align:start position:0%
+guiding those axons when they're growing
+ 
+
+ align:start position:0%
+guiding those axons when they're growing
+we talked about the two modes of growth
+
+ align:start position:0%
+we talked about the two modes of growth
+ 
+
+ align:start position:0%
+we talked about the two modes of growth
+last time
+
+ align:start position:0%
+last time
+ 
+
+ align:start position:0%
+last time
+so you know a little bit about how they
+
+ align:start position:0%
+so you know a little bit about how they
+ 
+
+ align:start position:0%
+so you know a little bit about how they
+develop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's many different aspects to the
+
+ align:start position:0%
+there's many different aspects to the
+ 
+
+ align:start position:0%
+there's many different aspects to the
+idea of exons competing with each other
+
+ align:start position:0%
+idea of exons competing with each other
+ 
+
+ align:start position:0%
+idea of exons competing with each other
+during development
+
+ align:start position:0%
+during development
+ 
+
+ align:start position:0%
+during development
+one thing they
+
+ align:start position:0%
+one thing they
+ 
+
+ align:start position:0%
+one thing they
+they compete for growth factor for
+
+ align:start position:0%
+they compete for growth factor for
+ 
+
+ align:start position:0%
+they compete for growth factor for
+example in some cases
+
+ align:start position:0%
+example in some cases
+ 
+
+ align:start position:0%
+example in some cases
+if they don't get enough they can
+
+ align:start position:0%
+if they don't get enough they can
+ 
+
+ align:start position:0%
+if they don't get enough they can
+don't get enough growth factor they can
+
+ align:start position:0%
+don't get enough growth factor they can
+ 
+
+ align:start position:0%
+don't get enough growth factor they can
+undergo apoptosis which is
+
+ align:start position:0%
+undergo apoptosis which is
+ 
+
+ align:start position:0%
+undergo apoptosis which is
+a kind of cell death
+
+ align:start position:0%
+a kind of cell death
+ 
+
+ align:start position:0%
+a kind of cell death
+sometimes it's called cell suicide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it lacks something to get some signal it
+
+ align:start position:0%
+it lacks something to get some signal it
+ 
+
+ align:start position:0%
+it lacks something to get some signal it
+will kill itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the first growth factor to be discovered
+
+ align:start position:0%
+the first growth factor to be discovered
+ 
+
+ align:start position:0%
+the first growth factor to be discovered
+was ngf the nerve growth factor
+
+ align:start position:0%
+was ngf the nerve growth factor
+ 
+
+ align:start position:0%
+was ngf the nerve growth factor
+and that was found later to be a member
+
+ align:start position:0%
+and that was found later to be a member
+ 
+
+ align:start position:0%
+and that was found later to be a member
+of a family of important growth factors
+
+ align:start position:0%
+of a family of important growth factors
+ 
+
+ align:start position:0%
+of a family of important growth factors
+the neurotrophins
+
+ align:start position:0%
+the neurotrophins
+ 
+
+ align:start position:0%
+the neurotrophins
+and i've just listed some of them there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these growth factors
+
+ align:start position:0%
+these growth factors
+ 
+
+ align:start position:0%
+these growth factors
+actually play a number of roles
+
+ align:start position:0%
+actually play a number of roles
+ 
+
+ align:start position:0%
+actually play a number of roles
+they're
+
+ align:start position:0%
+they're
+ 
+
+ align:start position:0%
+they're
+not just survival factors but they also
+
+ align:start position:0%
+not just survival factors but they also
+ 
+
+ align:start position:0%
+not just survival factors but they also
+they're trophic factors that promote
+
+ align:start position:0%
+they're trophic factors that promote
+ 
+
+ align:start position:0%
+they're trophic factors that promote
+growth
+
+ align:start position:0%
+growth
+ 
+
+ align:start position:0%
+growth
+they're also tropic
+
+ align:start position:0%
+they're also tropic
+ 
+
+ align:start position:0%
+they're also tropic
+they influence the direction of axon
+
+ align:start position:0%
+they influence the direction of axon
+ 
+
+ align:start position:0%
+they influence the direction of axon
+growth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for example i think i have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's talk about one experiment the
+
+ align:start position:0%
+let's talk about one experiment the
+ 
+
+ align:start position:0%
+let's talk about one experiment the
+first one really that
+
+ align:start position:0%
+first one really that
+ 
+
+ align:start position:0%
+first one really that
+directly showed in tissue culture
+
+ align:start position:0%
+directly showed in tissue culture
+ 
+
+ align:start position:0%
+directly showed in tissue culture
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+ngs have a tropic ngf has a tropic
+
+ align:start position:0%
+ngs have a tropic ngf has a tropic
+ 
+
+ align:start position:0%
+ngs have a tropic ngf has a tropic
+effect if this is a petri dish
+
+ align:start position:0%
+effect if this is a petri dish
+ 
+
+ align:start position:0%
+effect if this is a petri dish
+okay and you have
+
+ align:start position:0%
+okay and you have
+ 
+
+ align:start position:0%
+okay and you have
+get a smaller pin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and say you have here's a cell
+
+ align:start position:0%
+okay and say you have here's a cell
+ 
+
+ align:start position:0%
+okay and say you have here's a cell
+and it's growing an accent here's the
+
+ align:start position:0%
+and it's growing an accent here's the
+ 
+
+ align:start position:0%
+and it's growing an accent here's the
+growth cone okay
+
+ align:start position:0%
+growth cone okay
+ 
+
+ align:start position:0%
+growth cone okay
+it's growing there in the culture
+
+ align:start position:0%
+it's growing there in the culture
+ 
+
+ align:start position:0%
+it's growing there in the culture
+there'd probably be a lot of cells but
+
+ align:start position:0%
+there'd probably be a lot of cells but
+ 
+
+ align:start position:0%
+there'd probably be a lot of cells but
+we'll simplify it just have one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let's put up if you put
+
+ align:start position:0%
+so let's put up if you put
+ 
+
+ align:start position:0%
+so let's put up if you put
+this was done at harvard
+
+ align:start position:0%
+this was done at harvard
+ 
+
+ align:start position:0%
+this was done at harvard
+by jonathan harden he put a pipette in
+
+ align:start position:0%
+by jonathan harden he put a pipette in
+ 
+
+ align:start position:0%
+by jonathan harden he put a pipette in
+the tissue culture a pipet that
+
+ align:start position:0%
+the tissue culture a pipet that
+ 
+
+ align:start position:0%
+the tissue culture a pipet that
+contained a solution of ngf okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's do it a little more like he
+
+ align:start position:0%
+let's do it a little more like he
+ 
+
+ align:start position:0%
+let's do it a little more like he
+actually did it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's say he put the pipette and it's
+
+ align:start position:0%
+so let's say he put the pipette and it's
+ 
+
+ align:start position:0%
+so let's say he put the pipette and it's
+not drying there we
+
+ align:start position:0%
+not drying there we
+ 
+
+ align:start position:0%
+not drying there we
+like that he put it near the growth cone
+
+ align:start position:0%
+like that he put it near the growth cone
+ 
+
+ align:start position:0%
+like that he put it near the growth cone
+okay so what's it doing it contains a
+
+ align:start position:0%
+okay so what's it doing it contains a
+ 
+
+ align:start position:0%
+okay so what's it doing it contains a
+solution of ngf so it starts leaking the
+
+ align:start position:0%
+solution of ngf so it starts leaking the
+ 
+
+ align:start position:0%
+solution of ngf so it starts leaking the
+ngf
+
+ align:start position:0%
+ngf
+ 
+
+ align:start position:0%
+ngf
+it comes out of that
+
+ align:start position:0%
+it comes out of that
+ 
+
+ align:start position:0%
+it comes out of that
+and what
+
+ align:start position:0%
+and what
+ 
+
+ align:start position:0%
+and what
+happens there is that the growth come
+
+ align:start position:0%
+happens there is that the growth come
+ 
+
+ align:start position:0%
+happens there is that the growth come
+turns
+
+ align:start position:0%
+turns
+ 
+
+ align:start position:0%
+turns
+starts growing towards it okay so then
+
+ align:start position:0%
+starts growing towards it okay so then
+ 
+
+ align:start position:0%
+starts growing towards it okay so then
+he would move it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get rid of this one he moves it over
+
+ align:start position:0%
+get rid of this one he moves it over
+ 
+
+ align:start position:0%
+get rid of this one he moves it over
+here okay
+
+ align:start position:0%
+here okay
+ 
+
+ align:start position:0%
+here okay
+and what happened was
+
+ align:start position:0%
+and what happened was
+ 
+
+ align:start position:0%
+and what happened was
+this thing turns again
+
+ align:start position:0%
+this thing turns again
+ 
+
+ align:start position:0%
+this thing turns again
+and grows towards it so he can basically
+
+ align:start position:0%
+and grows towards it so he can basically
+ 
+
+ align:start position:0%
+and grows towards it so he can basically
+direct that growth cone around the petri
+
+ align:start position:0%
+direct that growth cone around the petri
+ 
+
+ align:start position:0%
+direct that growth cone around the petri
+dish by where the pipette is leaking
+
+ align:start position:0%
+dish by where the pipette is leaking
+ 
+
+ align:start position:0%
+dish by where the pipette is leaking
+the ngf
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the very simple experiment there were up
+
+ align:start position:0%
+the very simple experiment there were up
+ 
+
+ align:start position:0%
+the very simple experiment there were up
+until this point there were
+
+ align:start position:0%
+until this point there were
+ 
+
+ align:start position:0%
+until this point there were
+all the evidence for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chemo affinity of any sort was pretty
+
+ align:start position:0%
+chemo affinity of any sort was pretty
+ 
+
+ align:start position:0%
+chemo affinity of any sort was pretty
+indirect
+
+ align:start position:0%
+indirect
+ 
+
+ align:start position:0%
+indirect
+then they began with ngf to find out
+
+ align:start position:0%
+then they began with ngf to find out
+ 
+
+ align:start position:0%
+then they began with ngf to find out
+that these were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they directly influenced direction of
+
+ align:start position:0%
+they directly influenced direction of
+ 
+
+ align:start position:0%
+they directly influenced direction of
+growth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+romani cajole had postulated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chemical effects on axon growth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around 1900
+
+ align:start position:0%
+around 1900
+ 
+
+ align:start position:0%
+around 1900
+and then later roger sperry
+
+ align:start position:0%
+and then later roger sperry
+ 
+
+ align:start position:0%
+and then later roger sperry
+developed
+
+ align:start position:0%
+developed
+ 
+
+ align:start position:0%
+developed
+his theory of chemoaffinity that he
+
+ align:start position:0%
+his theory of chemoaffinity that he
+ 
+
+ align:start position:0%
+his theory of chemoaffinity that he
+thought could explain
+
+ align:start position:0%
+thought could explain
+ 
+
+ align:start position:0%
+thought could explain
+neuronal specificity and development in
+
+ align:start position:0%
+neuronal specificity and development in
+ 
+
+ align:start position:0%
+neuronal specificity and development in
+general that his accents grow to
+
+ align:start position:0%
+general that his accents grow to
+ 
+
+ align:start position:0%
+general that his accents grow to
+specific places in the nervous system
+
+ align:start position:0%
+specific places in the nervous system
+ 
+
+ align:start position:0%
+specific places in the nervous system
+because they're guided by chemical cues
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and he explained
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with that idea that exons will follow
+
+ align:start position:0%
+with that idea that exons will follow
+ 
+
+ align:start position:0%
+with that idea that exons will follow
+specific tracks and then when they reach
+
+ align:start position:0%
+specific tracks and then when they reach
+ 
+
+ align:start position:0%
+specific tracks and then when they reach
+their terminal areas they will form
+
+ align:start position:0%
+their terminal areas they will form
+ 
+
+ align:start position:0%
+their terminal areas they will form
+their specific connections which could
+
+ align:start position:0%
+their specific connections which could
+ 
+
+ align:start position:0%
+their specific connections which could
+be a map
+
+ align:start position:0%
+be a map
+ 
+
+ align:start position:0%
+be a map
+so we'll talk more about that today also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's talk about his experiments on
+
+ align:start position:0%
+let's talk about his experiments on
+ 
+
+ align:start position:0%
+let's talk about his experiments on
+axon growth which he did in using the
+
+ align:start position:0%
+axon growth which he did in using the
+ 
+
+ align:start position:0%
+axon growth which he did in using the
+phenomenon of regeneration in
+
+ align:start position:0%
+phenomenon of regeneration in
+ 
+
+ align:start position:0%
+phenomenon of regeneration in
+non-mammalian animals
+
+ align:start position:0%
+non-mammalian animals
+ 
+
+ align:start position:0%
+non-mammalian animals
+now his
+
+ align:start position:0%
+now his
+ 
+
+ align:start position:0%
+now his
+over the years he did this he used both
+
+ align:start position:0%
+over the years he did this he used both
+ 
+
+ align:start position:0%
+over the years he did this he used both
+frogs and goldfish
+
+ align:start position:0%
+frogs and goldfish
+ 
+
+ align:start position:0%
+frogs and goldfish
+most of the experiments are on frogs
+
+ align:start position:0%
+most of the experiments are on frogs
+ 
+
+ align:start position:0%
+most of the experiments are on frogs
+that we'll talk about okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are the we'll go through these
+
+ align:start position:0%
+these are the we'll go through these
+ 
+
+ align:start position:0%
+these are the we'll go through these
+these three things here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i think my computer just locked up
+
+ align:start position:0%
+so i think my computer just locked up
+ 
+
+ align:start position:0%
+so i think my computer just locked up
+now there we are
+
+ align:start position:0%
+now there we are
+ 
+
+ align:start position:0%
+now there we are
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's talk about that experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+many of you know this experiment already
+
+ align:start position:0%
+many of you know this experiment already
+ 
+
+ align:start position:0%
+many of you know this experiment already
+first of all if you crush the frog optic
+
+ align:start position:0%
+first of all if you crush the frog optic
+ 
+
+ align:start position:0%
+first of all if you crush the frog optic
+nerve
+
+ align:start position:0%
+nerve
+ 
+
+ align:start position:0%
+nerve
+it will regrow how do you know it will
+
+ align:start position:0%
+it will regrow how do you know it will
+ 
+
+ align:start position:0%
+it will regrow how do you know it will
+regrow well
+
+ align:start position:0%
+regrow well
+ 
+
+ align:start position:0%
+regrow well
+before it was known anatomically
+
+ align:start position:0%
+before it was known anatomically
+ 
+
+ align:start position:0%
+before it was known anatomically
+they just did it behaviorally and all of
+
+ align:start position:0%
+they just did it behaviorally and all of
+ 
+
+ align:start position:0%
+they just did it behaviorally and all of
+sperry's initial experiments were done
+
+ align:start position:0%
+sperry's initial experiments were done
+ 
+
+ align:start position:0%
+sperry's initial experiments were done
+with the behavioral assay
+
+ align:start position:0%
+with the behavioral assay
+ 
+
+ align:start position:0%
+with the behavioral assay
+so he would crush the
+
+ align:start position:0%
+so he would crush the
+ 
+
+ align:start position:0%
+so he would crush the
+optic nerve initially
+
+ align:start position:0%
+optic nerve initially
+ 
+
+ align:start position:0%
+optic nerve initially
+without any eye rotation just crush it
+
+ align:start position:0%
+without any eye rotation just crush it
+ 
+
+ align:start position:0%
+without any eye rotation just crush it
+and the animal was blind
+
+ align:start position:0%
+and the animal was blind
+ 
+
+ align:start position:0%
+and the animal was blind
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+but then if he keeps testing him
+
+ align:start position:0%
+but then if he keeps testing him
+ 
+
+ align:start position:0%
+but then if he keeps testing him
+eventually his vision comes back
+
+ align:start position:0%
+eventually his vision comes back
+ 
+
+ align:start position:0%
+eventually his vision comes back
+it not only comes back but it's
+
+ align:start position:0%
+it not only comes back but it's
+ 
+
+ align:start position:0%
+it not only comes back but it's
+it's pretty accurate
+
+ align:start position:0%
+it's pretty accurate
+ 
+
+ align:start position:0%
+it's pretty accurate
+that is he would
+
+ align:start position:0%
+that is he would
+ 
+
+ align:start position:0%
+that is he would
+orient
+
+ align:start position:0%
+orient
+ 
+
+ align:start position:0%
+orient
+to the worms presented
+
+ align:start position:0%
+to the worms presented
+ 
+
+ align:start position:0%
+to the worms presented
+or flies presented in various parts of
+
+ align:start position:0%
+or flies presented in various parts of
+ 
+
+ align:start position:0%
+or flies presented in various parts of
+the visual field
+
+ align:start position:0%
+the visual field
+ 
+
+ align:start position:0%
+the visual field
+accurately again
+
+ align:start position:0%
+accurately again
+ 
+
+ align:start position:0%
+accurately again
+indicating that
+
+ align:start position:0%
+indicating that
+ 
+
+ align:start position:0%
+indicating that
+the axons must have grown back to the
+
+ align:start position:0%
+the axons must have grown back to the
+ 
+
+ align:start position:0%
+the axons must have grown back to the
+correct position since perry wondered
+
+ align:start position:0%
+correct position since perry wondered
+ 
+
+ align:start position:0%
+correct position since perry wondered
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+why can they grow back to the right
+
+ align:start position:0%
+why can they grow back to the right
+ 
+
+ align:start position:0%
+why can they grow back to the right
+positions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so he tried an interesting experiment he
+
+ align:start position:0%
+so he tried an interesting experiment he
+ 
+
+ align:start position:0%
+so he tried an interesting experiment he
+crushed the nerve and he rotated the eye
+
+ align:start position:0%
+crushed the nerve and he rotated the eye
+ 
+
+ align:start position:0%
+crushed the nerve and he rotated the eye
+180 degrees
+
+ align:start position:0%
+180 degrees
+ 
+
+ align:start position:0%
+180 degrees
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if here's the frog in here's his eyes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and you draw a frog okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here's what he's doing he's
+
+ align:start position:0%
+and here's what he's doing he's
+ 
+
+ align:start position:0%
+and here's what he's doing he's
+initially you know he's presenting
+
+ align:start position:0%
+initially you know he's presenting
+ 
+
+ align:start position:0%
+initially you know he's presenting
+say puts a worm out here okay
+
+ align:start position:0%
+say puts a worm out here okay
+ 
+
+ align:start position:0%
+say puts a worm out here okay
+a normal frog
+
+ align:start position:0%
+a normal frog
+ 
+
+ align:start position:0%
+a normal frog
+the worm starts to move anyway
+
+ align:start position:0%
+the worm starts to move anyway
+ 
+
+ align:start position:0%
+the worm starts to move anyway
+the frog will make a sudden
+
+ align:start position:0%
+the frog will make a sudden
+ 
+
+ align:start position:0%
+the frog will make a sudden
+turn and flick out his tongue grab the
+
+ align:start position:0%
+turn and flick out his tongue grab the
+ 
+
+ align:start position:0%
+turn and flick out his tongue grab the
+frog he will do it accurately
+
+ align:start position:0%
+frog he will do it accurately
+ 
+
+ align:start position:0%
+frog he will do it accurately
+and of course if the nerve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if the nerve for that eye
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this eye
+
+ align:start position:0%
+this eye
+ 
+
+ align:start position:0%
+this eye
+has been crushed and they usually crush
+
+ align:start position:0%
+has been crushed and they usually crush
+ 
+
+ align:start position:0%
+has been crushed and they usually crush
+it just behind the eye
+
+ align:start position:0%
+it just behind the eye
+ 
+
+ align:start position:0%
+it just behind the eye
+okay if the nerve has been crushed
+
+ align:start position:0%
+okay if the nerve has been crushed
+ 
+
+ align:start position:0%
+okay if the nerve has been crushed
+he'll be blind in that eye and if he
+
+ align:start position:0%
+he'll be blind in that eye and if he
+ 
+
+ align:start position:0%
+he'll be blind in that eye and if he
+recovers he'll start to orient again but
+
+ align:start position:0%
+recovers he'll start to orient again but
+ 
+
+ align:start position:0%
+recovers he'll start to orient again but
+now he's rotated the eye 180 degrees so
+
+ align:start position:0%
+now he's rotated the eye 180 degrees so
+ 
+
+ align:start position:0%
+now he's rotated the eye 180 degrees so
+what happens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what happens is if the worm is here
+
+ align:start position:0%
+what happens is if the worm is here
+ 
+
+ align:start position:0%
+what happens is if the worm is here
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the frog turns that way
+
+ align:start position:0%
+the frog turns that way
+ 
+
+ align:start position:0%
+the frog turns that way
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+he turns in the wrong direction
+
+ align:start position:0%
+he turns in the wrong direction
+ 
+
+ align:start position:0%
+he turns in the wrong direction
+or if you place it
+
+ align:start position:0%
+or if you place it
+ 
+
+ align:start position:0%
+or if you place it
+you know on the floor in front of him
+
+ align:start position:0%
+you know on the floor in front of him
+ 
+
+ align:start position:0%
+you know on the floor in front of him
+he'll orient as if it's up there if you
+
+ align:start position:0%
+he'll orient as if it's up there if you
+ 
+
+ align:start position:0%
+he'll orient as if it's up there if you
+place it up here he'll orient down there
+
+ align:start position:0%
+place it up here he'll orient down there
+ 
+
+ align:start position:0%
+place it up here he'll orient down there
+it's 180 degrees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+disoriented
+
+ align:start position:0%
+disoriented
+ 
+
+ align:start position:0%
+disoriented
+so what does that mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it means that
+
+ align:start position:0%
+it means that
+ 
+
+ align:start position:0%
+it means that
+the behavior the reward
+
+ align:start position:0%
+the behavior the reward
+ 
+
+ align:start position:0%
+the behavior the reward
+the animals receiving isn't affecting
+
+ align:start position:0%
+the animals receiving isn't affecting
+ 
+
+ align:start position:0%
+the animals receiving isn't affecting
+he keeps orienting wrongly
+
+ align:start position:0%
+he keeps orienting wrongly
+ 
+
+ align:start position:0%
+he keeps orienting wrongly
+okay he simply
+
+ align:start position:0%
+okay he simply
+ 
+
+ align:start position:0%
+okay he simply
+has a miswired brain because you had
+
+ align:start position:0%
+has a miswired brain because you had
+ 
+
+ align:start position:0%
+has a miswired brain because you had
+rotated the eye and the connections
+
+ align:start position:0%
+rotated the eye and the connections
+ 
+
+ align:start position:0%
+rotated the eye and the connections
+reform according to
+
+ align:start position:0%
+reform according to
+ 
+
+ align:start position:0%
+reform according to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+retina
+
+ align:start position:0%
+retina
+ 
+
+ align:start position:0%
+retina
+okay not occurring the visual field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so as if that
+
+ align:start position:0%
+so as if that
+ 
+
+ align:start position:0%
+so as if that
+there's a program there set by
+
+ align:start position:0%
+there's a program there set by
+ 
+
+ align:start position:0%
+there's a program there set by
+properties of the retina that will
+
+ align:start position:0%
+properties of the retina that will
+ 
+
+ align:start position:0%
+properties of the retina that will
+determine where those exons grow in the
+
+ align:start position:0%
+determine where those exons grow in the
+ 
+
+ align:start position:0%
+determine where those exons grow in the
+tectum
+
+ align:start position:0%
+tectum
+ 
+
+ align:start position:0%
+tectum
+so he postulated there was a specific
+
+ align:start position:0%
+so he postulated there was a specific
+ 
+
+ align:start position:0%
+so he postulated there was a specific
+specific matching of chemical tags
+
+ align:start position:0%
+specific matching of chemical tags
+ 
+
+ align:start position:0%
+specific matching of chemical tags
+tags on those retinal gaming cells and
+
+ align:start position:0%
+tags on those retinal gaming cells and
+ 
+
+ align:start position:0%
+tags on those retinal gaming cells and
+their axons with
+
+ align:start position:0%
+their axons with
+ 
+
+ align:start position:0%
+their axons with
+matching chemical tags in the tectum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that was a sort of a strong form of the
+
+ align:start position:0%
+that was a sort of a strong form of the
+ 
+
+ align:start position:0%
+that was a sort of a strong form of the
+chemo affinity theory
+
+ align:start position:0%
+chemo affinity theory
+ 
+
+ align:start position:0%
+chemo affinity theory
+later it was argued that there that the
+
+ align:start position:0%
+later it was argued that there that the
+ 
+
+ align:start position:0%
+later it was argued that there that the
+required too many genes and so forth
+
+ align:start position:0%
+required too many genes and so forth
+ 
+
+ align:start position:0%
+required too many genes and so forth
+there were a lot of arguments about that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the theory has basically though been
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+worn out
+
+ align:start position:0%
+worn out
+ 
+
+ align:start position:0%
+worn out
+and not exactly in the form of sperry's
+
+ align:start position:0%
+and not exactly in the form of sperry's
+ 
+
+ align:start position:0%
+and not exactly in the form of sperry's
+initial work but uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+however
+
+ align:start position:0%
+however
+ 
+
+ align:start position:0%
+however
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+other experiments were done on
+
+ align:start position:0%
+other experiments were done on
+ 
+
+ align:start position:0%
+other experiments were done on
+regeneration and growth phenomena and
+
+ align:start position:0%
+regeneration and growth phenomena and
+ 
+
+ align:start position:0%
+regeneration and growth phenomena and
+they discovered
+
+ align:start position:0%
+they discovered
+ 
+
+ align:start position:0%
+they discovered
+some of them were done on
+
+ align:start position:0%
+some of them were done on
+ 
+
+ align:start position:0%
+some of them were done on
+hamsters here
+
+ align:start position:0%
+hamsters here
+ 
+
+ align:start position:0%
+hamsters here
+at mit in my lab and but many of them
+
+ align:start position:0%
+at mit in my lab and but many of them
+ 
+
+ align:start position:0%
+at mit in my lab and but many of them
+were done on frogs and on goldfish
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the work on
+
+ align:start position:0%
+the work on
+ 
+
+ align:start position:0%
+the work on
+frog or goldfish
+
+ align:start position:0%
+frog or goldfish
+ 
+
+ align:start position:0%
+frog or goldfish
+and the work on hamsters indicated that
+
+ align:start position:0%
+and the work on hamsters indicated that
+ 
+
+ align:start position:0%
+and the work on hamsters indicated that
+you could get
+
+ align:start position:0%
+you could get
+ 
+
+ align:start position:0%
+you could get
+distortions of these maps
+
+ align:start position:0%
+distortions of these maps
+ 
+
+ align:start position:0%
+distortions of these maps
+and that raised questions about exactly
+
+ align:start position:0%
+and that raised questions about exactly
+ 
+
+ align:start position:0%
+and that raised questions about exactly
+how the chemo affinity
+
+ align:start position:0%
+how the chemo affinity
+ 
+
+ align:start position:0%
+how the chemo affinity
+is working if it's working at all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do we mean by map compression or
+
+ align:start position:0%
+what do we mean by map compression or
+ 
+
+ align:start position:0%
+what do we mean by map compression or
+map expansion okay
+
+ align:start position:0%
+map expansion okay
+ 
+
+ align:start position:0%
+map expansion okay
+let's uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say here's the tectum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll deal with the right pectin
+
+ align:start position:0%
+we'll deal with the right pectin
+ 
+
+ align:start position:0%
+we'll deal with the right pectin
+and let's say you do this
+
+ align:start position:0%
+and let's say you do this
+ 
+
+ align:start position:0%
+and let's say you do this
+you eliminate the whole caudal half of
+
+ align:start position:0%
+you eliminate the whole caudal half of
+ 
+
+ align:start position:0%
+you eliminate the whole caudal half of
+the tectum or the lesion on the right
+
+ align:start position:0%
+the tectum or the lesion on the right
+ 
+
+ align:start position:0%
+the tectum or the lesion on the right
+side okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the question then is
+
+ align:start position:0%
+so the question then is
+ 
+
+ align:start position:0%
+so the question then is
+what happens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when the axons grow back and then only
+
+ align:start position:0%
+when the axons grow back and then only
+ 
+
+ align:start position:0%
+when the axons grow back and then only
+half the tectum's there
+
+ align:start position:0%
+half the tectum's there
+ 
+
+ align:start position:0%
+half the tectum's there
+well when that was done in the frog
+
+ align:start position:0%
+well when that was done in the frog
+ 
+
+ align:start position:0%
+well when that was done in the frog
+or in the goldfish
+
+ align:start position:0%
+or in the goldfish
+ 
+
+ align:start position:0%
+or in the goldfish
+initially they found
+
+ align:start position:0%
+initially they found
+ 
+
+ align:start position:0%
+initially they found
+that if
+
+ align:start position:0%
+that if
+ 
+
+ align:start position:0%
+that if
+if here's the retina okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is nasal retina and temporal
+
+ align:start position:0%
+and this is nasal retina and temporal
+ 
+
+ align:start position:0%
+and this is nasal retina and temporal
+retina
+
+ align:start position:0%
+retina
+ 
+
+ align:start position:0%
+retina
+superior and inferior retina
+
+ align:start position:0%
+superior and inferior retina
+ 
+
+ align:start position:0%
+superior and inferior retina
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+actually why don't we do it for visual
+
+ align:start position:0%
+actually why don't we do it for visual
+ 
+
+ align:start position:0%
+actually why don't we do it for visual
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+it's very confusing when you deal with
+
+ align:start position:0%
+it's very confusing when you deal with
+ 
+
+ align:start position:0%
+it's very confusing when you deal with
+both visual field and retina
+
+ align:start position:0%
+both visual field and retina
+ 
+
+ align:start position:0%
+both visual field and retina
+i sort of convert them quickly and
+
+ align:start position:0%
+i sort of convert them quickly and
+ 
+
+ align:start position:0%
+i sort of convert them quickly and
+automatically in my mind but
+
+ align:start position:0%
+automatically in my mind but
+ 
+
+ align:start position:0%
+automatically in my mind but
+it's not easy to when you begin to talk
+
+ align:start position:0%
+it's not easy to when you begin to talk
+ 
+
+ align:start position:0%
+it's not easy to when you begin to talk
+about it so let's deal with it the way
+
+ align:start position:0%
+about it so let's deal with it the way
+ 
+
+ align:start position:0%
+about it so let's deal with it the way
+the frog experiments were done they did
+
+ align:start position:0%
+the frog experiments were done they did
+ 
+
+ align:start position:0%
+the frog experiments were done they did
+the visual field they were mapping
+
+ align:start position:0%
+the visual field they were mapping
+ 
+
+ align:start position:0%
+the visual field they were mapping
+receptive fields electrophysiologically
+
+ align:start position:0%
+receptive fields electrophysiologically
+ 
+
+ align:start position:0%
+receptive fields electrophysiologically
+okay that was the way they did it
+
+ align:start position:0%
+okay that was the way they did it
+ 
+
+ align:start position:0%
+okay that was the way they did it
+okay so this is the visual field
+
+ align:start position:0%
+okay so this is the visual field
+ 
+
+ align:start position:0%
+okay so this is the visual field
+nasal field and temporal field
+
+ align:start position:0%
+nasal field and temporal field
+ 
+
+ align:start position:0%
+nasal field and temporal field
+superior inferior field and here's the
+
+ align:start position:0%
+superior inferior field and here's the
+ 
+
+ align:start position:0%
+superior inferior field and here's the
+tectum normally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this would be the nasal field
+
+ align:start position:0%
+this would be the nasal field
+ 
+
+ align:start position:0%
+this would be the nasal field
+temporal
+
+ align:start position:0%
+temporal
+ 
+
+ align:start position:0%
+temporal
+field this is superior with the psyche
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+superior field and the inferior field
+
+ align:start position:0%
+superior field and the inferior field
+ 
+
+ align:start position:0%
+superior field and the inferior field
+would be lateral okay now that's the way
+
+ align:start position:0%
+would be lateral okay now that's the way
+ 
+
+ align:start position:0%
+would be lateral okay now that's the way
+you would expect it to be mapped on both
+
+ align:start position:0%
+you would expect it to be mapped on both
+ 
+
+ align:start position:0%
+you would expect it to be mapped on both
+sides
+
+ align:start position:0%
+sides
+ 
+
+ align:start position:0%
+sides
+now here they're dealing with the field
+
+ align:start position:0%
+now here they're dealing with the field
+ 
+
+ align:start position:0%
+now here they're dealing with the field
+of the left eye
+
+ align:start position:0%
+of the left eye
+ 
+
+ align:start position:0%
+of the left eye
+okay and initially
+
+ align:start position:0%
+okay and initially
+ 
+
+ align:start position:0%
+okay and initially
+they found that if they had only half
+
+ align:start position:0%
+they found that if they had only half
+ 
+
+ align:start position:0%
+they found that if they had only half
+the tectum
+
+ align:start position:0%
+the tectum
+ 
+
+ align:start position:0%
+the tectum
+okay they got basically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recordings
+
+ align:start position:0%
+recordings
+ 
+
+ align:start position:0%
+recordings
+spots placed in this half of the field
+
+ align:start position:0%
+spots placed in this half of the field
+ 
+
+ align:start position:0%
+spots placed in this half of the field
+only would could be found in the tectum
+
+ align:start position:0%
+only would could be found in the tectum
+ 
+
+ align:start position:0%
+only would could be found in the tectum
+okay so they would record there and then
+
+ align:start position:0%
+okay so they would record there and then
+ 
+
+ align:start position:0%
+okay so they would record there and then
+they could record their responses here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry i don't know what i'm doing here
+
+ align:start position:0%
+sorry i don't know what i'm doing here
+ 
+
+ align:start position:0%
+sorry i don't know what i'm doing here
+hitting the right button i think
+
+ align:start position:0%
+hitting the right button i think
+ 
+
+ align:start position:0%
+hitting the right button i think
+so you see what they're doing they're
+
+ align:start position:0%
+so you see what they're doing they're
+ 
+
+ align:start position:0%
+so you see what they're doing they're
+recording and systematically across the
+
+ align:start position:0%
+recording and systematically across the
+ 
+
+ align:start position:0%
+recording and systematically across the
+tectum from different positions and then
+
+ align:start position:0%
+tectum from different positions and then
+ 
+
+ align:start position:0%
+tectum from different positions and then
+they map the receptive fields okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then
+
+ align:start position:0%
+but then
+ 
+
+ align:start position:0%
+but then
+over give it a little time
+
+ align:start position:0%
+over give it a little time
+ 
+
+ align:start position:0%
+over give it a little time
+and the thing reorganizes
+
+ align:start position:0%
+and the thing reorganizes
+ 
+
+ align:start position:0%
+and the thing reorganizes
+and they start getting
+
+ align:start position:0%
+and they start getting
+ 
+
+ align:start position:0%
+and they start getting
+receptive fields now throughout the
+
+ align:start position:0%
+receptive fields now throughout the
+ 
+
+ align:start position:0%
+receptive fields now throughout the
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+the temporal
+
+ align:start position:0%
+the temporal
+ 
+
+ align:start position:0%
+the temporal
+field
+
+ align:start position:0%
+field
+ 
+
+ align:start position:0%
+field
+they're finding now is represented here
+
+ align:start position:0%
+they're finding now is represented here
+ 
+
+ align:start position:0%
+they're finding now is represented here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so these spots here
+
+ align:start position:0%
+so these spots here
+ 
+
+ align:start position:0%
+so these spots here
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these three spots in the temporal field
+
+ align:start position:0%
+these three spots in the temporal field
+ 
+
+ align:start position:0%
+these three spots in the temporal field
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+like that okay normally they would be
+
+ align:start position:0%
+like that okay normally they would be
+ 
+
+ align:start position:0%
+like that okay normally they would be
+back here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now there so we say the map has been
+
+ align:start position:0%
+now there so we say the map has been
+ 
+
+ align:start position:0%
+now there so we say the map has been
+compressed the nasal field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry here
+
+ align:start position:0%
+sorry here
+ 
+
+ align:start position:0%
+sorry here
+they find represented up here
+
+ align:start position:0%
+they find represented up here
+ 
+
+ align:start position:0%
+they find represented up here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and similarly superior
+
+ align:start position:0%
+and similarly superior
+ 
+
+ align:start position:0%
+and similarly superior
+is over is near the midline and inferior
+
+ align:start position:0%
+is over is near the midline and inferior
+ 
+
+ align:start position:0%
+is over is near the midline and inferior
+is lateral so the whole map is
+
+ align:start position:0%
+is lateral so the whole map is
+ 
+
+ align:start position:0%
+is lateral so the whole map is
+compressed into the small tectum you
+
+ align:start position:0%
+compressed into the small tectum you
+ 
+
+ align:start position:0%
+compressed into the small tectum you
+understand the experiment
+
+ align:start position:0%
+understand the experiment
+ 
+
+ align:start position:0%
+understand the experiment
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's
+
+ align:start position:0%
+so that's
+ 
+
+ align:start position:0%
+so that's
+field compression okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now they tried another experiment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll draw here another field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'll just draw i'll just draw the
+
+ align:start position:0%
+and i'll just draw i'll just draw the
+ 
+
+ align:start position:0%
+and i'll just draw i'll just draw the
+retina here
+
+ align:start position:0%
+retina here
+ 
+
+ align:start position:0%
+retina here
+or the field corresponding to the retina
+
+ align:start position:0%
+or the field corresponding to the retina
+ 
+
+ align:start position:0%
+or the field corresponding to the retina
+and they basically
+
+ align:start position:0%
+and they basically
+ 
+
+ align:start position:0%
+and they basically
+ablated half the redness so for example
+
+ align:start position:0%
+ablated half the redness so for example
+ 
+
+ align:start position:0%
+ablated half the redness so for example
+they could do
+
+ align:start position:0%
+they could do
+ 
+
+ align:start position:0%
+they could do
+this they could eliminate half the
+
+ align:start position:0%
+this they could eliminate half the
+ 
+
+ align:start position:0%
+this they could eliminate half the
+retina
+
+ align:start position:0%
+retina
+ 
+
+ align:start position:0%
+retina
+they eliminated
+
+ align:start position:0%
+they eliminated
+ 
+
+ align:start position:0%
+they eliminated
+the whole nasal retina then the temporal
+
+ align:start position:0%
+the whole nasal retina then the temporal
+ 
+
+ align:start position:0%
+the whole nasal retina then the temporal
+field would be old
+
+ align:start position:0%
+field would be old
+ 
+
+ align:start position:0%
+field would be old
+sorry the
+
+ align:start position:0%
+sorry the
+ 
+
+ align:start position:0%
+sorry the
+temporal retina and the nasal field
+
+ align:start position:0%
+temporal retina and the nasal field
+ 
+
+ align:start position:0%
+temporal retina and the nasal field
+would disappear or nasal retin the
+
+ align:start position:0%
+would disappear or nasal retin the
+ 
+
+ align:start position:0%
+would disappear or nasal retin the
+temporal field would disappear
+
+ align:start position:0%
+temporal field would disappear
+ 
+
+ align:start position:0%
+temporal field would disappear
+okay so that was another way to do these
+
+ align:start position:0%
+okay so that was another way to do these
+ 
+
+ align:start position:0%
+okay so that was another way to do these
+experiments they would ablate a good
+
+ align:start position:0%
+experiments they would ablate a good
+ 
+
+ align:start position:0%
+experiments they would ablate a good
+part of the retina
+
+ align:start position:0%
+part of the retina
+ 
+
+ align:start position:0%
+part of the retina
+in the fish
+
+ align:start position:0%
+in the fish
+ 
+
+ align:start position:0%
+in the fish
+and then do the recording later
+
+ align:start position:0%
+and then do the recording later
+ 
+
+ align:start position:0%
+and then do the recording later
+what happens
+
+ align:start position:0%
+what happens
+ 
+
+ align:start position:0%
+what happens
+what happens when part of the
+
+ align:start position:0%
+what happens when part of the
+ 
+
+ align:start position:0%
+what happens when part of the
+retina is projecting into a whole tectum
+
+ align:start position:0%
+retina is projecting into a whole tectum
+ 
+
+ align:start position:0%
+retina is projecting into a whole tectum
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the result was again that if they
+
+ align:start position:0%
+and the result was again that if they
+ 
+
+ align:start position:0%
+and the result was again that if they
+gave it enough time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the field expanded so this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the half retina would expand its
+
+ align:start position:0%
+the half retina would expand its
+ 
+
+ align:start position:0%
+the half retina would expand its
+representation over the whole tectum
+
+ align:start position:0%
+representation over the whole tectum
+ 
+
+ align:start position:0%
+representation over the whole tectum
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those things were done in the hamster
+
+ align:start position:0%
+those things were done in the hamster
+ 
+
+ align:start position:0%
+those things were done in the hamster
+also yes question first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah good question is it always perfect
+
+ align:start position:0%
+yeah good question is it always perfect
+ 
+
+ align:start position:0%
+yeah good question is it always perfect
+in other words can you get mistakes
+
+ align:start position:0%
+in other words can you get mistakes
+ 
+
+ align:start position:0%
+in other words can you get mistakes
+they didn't pay too much it wasn't
+
+ align:start position:0%
+they didn't pay too much it wasn't
+ 
+
+ align:start position:0%
+they didn't pay too much it wasn't
+perfect
+
+ align:start position:0%
+perfect
+ 
+
+ align:start position:0%
+perfect
+but it was pretty good and within the
+
+ align:start position:0%
+but it was pretty good and within the
+ 
+
+ align:start position:0%
+but it was pretty good and within the
+limits of their recording
+
+ align:start position:0%
+limits of their recording
+ 
+
+ align:start position:0%
+limits of their recording
+so forth
+
+ align:start position:0%
+so forth
+ 
+
+ align:start position:0%
+so forth
+it wasn't clear just how degraded it was
+
+ align:start position:0%
+it wasn't clear just how degraded it was
+ 
+
+ align:start position:0%
+it wasn't clear just how degraded it was
+it didn't appear to be very degraded it
+
+ align:start position:0%
+it didn't appear to be very degraded it
+ 
+
+ align:start position:0%
+it didn't appear to be very degraded it
+did go through a transient period though
+
+ align:start position:0%
+did go through a transient period though
+ 
+
+ align:start position:0%
+did go through a transient period though
+where it was more disorganized that's
+
+ align:start position:0%
+where it was more disorganized that's
+ 
+
+ align:start position:0%
+where it was more disorganized that's
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+okay now we did those experiments also
+
+ align:start position:0%
+okay now we did those experiments also
+ 
+
+ align:start position:0%
+okay now we did those experiments also
+enhancers but hamsters don't regenerate
+
+ align:start position:0%
+enhancers but hamsters don't regenerate
+ 
+
+ align:start position:0%
+enhancers but hamsters don't regenerate
+so what do you do
+
+ align:start position:0%
+so what do you do
+ 
+
+ align:start position:0%
+so what do you do
+well if you make the lesions very early
+
+ align:start position:0%
+well if you make the lesions very early
+ 
+
+ align:start position:0%
+well if you make the lesions very early
+in life
+
+ align:start position:0%
+in life
+ 
+
+ align:start position:0%
+in life
+when the system is still developing the
+
+ align:start position:0%
+when the system is still developing the
+ 
+
+ align:start position:0%
+when the system is still developing the
+retinal
+
+ align:start position:0%
+retinal
+ 
+
+ align:start position:0%
+retinal
+retinotectal connection is still
+
+ align:start position:0%
+retinotectal connection is still
+ 
+
+ align:start position:0%
+retinotectal connection is still
+developing at birth
+
+ align:start position:0%
+developing at birth
+ 
+
+ align:start position:0%
+developing at birth
+at birth in the hamster the axons are
+
+ align:start position:0%
+at birth in the hamster the axons are
+ 
+
+ align:start position:0%
+at birth in the hamster the axons are
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+in this
+
+ align:start position:0%
+in this
+ 
+
+ align:start position:0%
+in this
+the end of their elongation period
+
+ align:start position:0%
+the end of their elongation period
+ 
+
+ align:start position:0%
+the end of their elongation period
+they're just starting to sprout these
+
+ align:start position:0%
+they're just starting to sprout these
+ 
+
+ align:start position:0%
+they're just starting to sprout these
+widespread arbors
+
+ align:start position:0%
+widespread arbors
+ 
+
+ align:start position:0%
+widespread arbors
+so we could take the caudal take them
+
+ align:start position:0%
+so we could take the caudal take them
+ 
+
+ align:start position:0%
+so we could take the caudal take them
+out in the hamster
+
+ align:start position:0%
+out in the hamster
+ 
+
+ align:start position:0%
+out in the hamster
+then we let them grow up
+
+ align:start position:0%
+then we let them grow up
+ 
+
+ align:start position:0%
+then we let them grow up
+and now rather than record we did
+
+ align:start position:0%
+and now rather than record we did
+ 
+
+ align:start position:0%
+and now rather than record we did
+anatomical experiments now how do you do
+
+ align:start position:0%
+anatomical experiments now how do you do
+ 
+
+ align:start position:0%
+anatomical experiments now how do you do
+how do you study
+
+ align:start position:0%
+how do you study
+ 
+
+ align:start position:0%
+how do you study
+topographic organization
+
+ align:start position:0%
+topographic organization
+ 
+
+ align:start position:0%
+topographic organization
+with neuroanatomical methods
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there were some advantages over
+
+ align:start position:0%
+there were some advantages over
+ 
+
+ align:start position:0%
+there were some advantages over
+physiology
+
+ align:start position:0%
+physiology
+ 
+
+ align:start position:0%
+physiology
+that was one of the disadvantages of the
+
+ align:start position:0%
+that was one of the disadvantages of the
+ 
+
+ align:start position:0%
+that was one of the disadvantages of the
+frog and
+
+ align:start position:0%
+frog and
+ 
+
+ align:start position:0%
+frog and
+goldfish experiments that they hadn't
+
+ align:start position:0%
+goldfish experiments that they hadn't
+ 
+
+ align:start position:0%
+goldfish experiments that they hadn't
+done the anatomy
+
+ align:start position:0%
+done the anatomy
+ 
+
+ align:start position:0%
+done the anatomy
+so what they're getting through their
+
+ align:start position:0%
+so what they're getting through their
+ 
+
+ align:start position:0%
+so what they're getting through their
+recordings doesn't tell you
+
+ align:start position:0%
+recordings doesn't tell you
+ 
+
+ align:start position:0%
+recordings doesn't tell you
+necessarily what the axons are doing of
+
+ align:start position:0%
+necessarily what the axons are doing of
+ 
+
+ align:start position:0%
+necessarily what the axons are doing of
+course you make the connection assume
+
+ align:start position:0%
+course you make the connection assume
+ 
+
+ align:start position:0%
+course you make the connection assume
+that you know what they're doing
+
+ align:start position:0%
+that you know what they're doing
+ 
+
+ align:start position:0%
+that you know what they're doing
+so we did in new hampshire and we
+
+ align:start position:0%
+so we did in new hampshire and we
+ 
+
+ align:start position:0%
+so we did in new hampshire and we
+discovered
+
+ align:start position:0%
+discovered
+ 
+
+ align:start position:0%
+discovered
+two things first of all
+
+ align:start position:0%
+two things first of all
+ 
+
+ align:start position:0%
+two things first of all
+if we
+
+ align:start position:0%
+if we
+ 
+
+ align:start position:0%
+if we
+took off the cobble tectum
+
+ align:start position:0%
+took off the cobble tectum
+ 
+
+ align:start position:0%
+took off the cobble tectum
+as they had done in the goldfish here
+
+ align:start position:0%
+as they had done in the goldfish here
+ 
+
+ align:start position:0%
+as they had done in the goldfish here
+as you see there at the left
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we eliminate the caudal half tectum and
+
+ align:start position:0%
+we eliminate the caudal half tectum and
+ 
+
+ align:start position:0%
+we eliminate the caudal half tectum and
+now we made for example a lesion
+
+ align:start position:0%
+now we made for example a lesion
+ 
+
+ align:start position:0%
+now we made for example a lesion
+a little lesion in the temple retina we
+
+ align:start position:0%
+a little lesion in the temple retina we
+ 
+
+ align:start position:0%
+a little lesion in the temple retina we
+were try using degeneration methods
+
+ align:start position:0%
+were try using degeneration methods
+ 
+
+ align:start position:0%
+were try using degeneration methods
+trace the degenerating accents from a
+
+ align:start position:0%
+trace the degenerating accents from a
+ 
+
+ align:start position:0%
+trace the degenerating accents from a
+little piece of the temple of the nasal
+
+ align:start position:0%
+little piece of the temple of the nasal
+ 
+
+ align:start position:0%
+little piece of the temple of the nasal
+retinas area
+
+ align:start position:0%
+retinas area
+ 
+
+ align:start position:0%
+retinas area
+temporal field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something that should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go here to a blue something that should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something that say should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+project back here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what happened
+
+ align:start position:0%
+what happened
+ 
+
+ align:start position:0%
+what happened
+well that part of the tectum is missing
+
+ align:start position:0%
+well that part of the tectum is missing
+ 
+
+ align:start position:0%
+well that part of the tectum is missing
+what do the accents do when they come
+
+ align:start position:0%
+what do the accents do when they come
+ 
+
+ align:start position:0%
+what do the accents do when they come
+and detect them what we found is they do
+
+ align:start position:0%
+and detect them what we found is they do
+ 
+
+ align:start position:0%
+and detect them what we found is they do
+generally go here
+
+ align:start position:0%
+generally go here
+ 
+
+ align:start position:0%
+generally go here
+indicating that there was a compression
+
+ align:start position:0%
+indicating that there was a compression
+ 
+
+ align:start position:0%
+indicating that there was a compression
+of the field
+
+ align:start position:0%
+of the field
+ 
+
+ align:start position:0%
+of the field
+but in addition we found inaccuracies we
+
+ align:start position:0%
+but in addition we found inaccuracies we
+ 
+
+ align:start position:0%
+but in addition we found inaccuracies we
+found little extra projections also but
+
+ align:start position:0%
+found little extra projections also but
+ 
+
+ align:start position:0%
+found little extra projections also but
+the main
+
+ align:start position:0%
+the main
+ 
+
+ align:start position:0%
+the main
+the main projection went to the right
+
+ align:start position:0%
+the main projection went to the right
+ 
+
+ align:start position:0%
+the main projection went to the right
+place if the map had been compressed and
+
+ align:start position:0%
+place if the map had been compressed and
+ 
+
+ align:start position:0%
+place if the map had been compressed and
+we did other other parts of the retina
+
+ align:start position:0%
+we did other other parts of the retina
+ 
+
+ align:start position:0%
+we did other other parts of the retina
+in such animals
+
+ align:start position:0%
+in such animals
+ 
+
+ align:start position:0%
+in such animals
+we also
+
+ align:start position:0%
+we also
+ 
+
+ align:start position:0%
+we also
+in some cases ablated the rostral tectum
+
+ align:start position:0%
+in some cases ablated the rostral tectum
+ 
+
+ align:start position:0%
+in some cases ablated the rostral tectum
+instead of the caudal tectum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for example if here's the tectum now
+
+ align:start position:0%
+so for example if here's the tectum now
+ 
+
+ align:start position:0%
+so for example if here's the tectum now
+and we ablated the whole rostral tectum
+
+ align:start position:0%
+and we ablated the whole rostral tectum
+ 
+
+ align:start position:0%
+and we ablated the whole rostral tectum
+now the axons
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the axons are coming in like this right
+
+ align:start position:0%
+the axons are coming in like this right
+ 
+
+ align:start position:0%
+the axons are coming in like this right
+here's the here's the optic tract
+
+ align:start position:0%
+here's the here's the optic tract
+ 
+
+ align:start position:0%
+here's the here's the optic tract
+so now they have to cross the area of
+
+ align:start position:0%
+so now they have to cross the area of
+ 
+
+ align:start position:0%
+so now they have to cross the area of
+damage
+
+ align:start position:0%
+damage
+ 
+
+ align:start position:0%
+damage
+and they did that
+
+ align:start position:0%
+and they did that
+ 
+
+ align:start position:0%
+and they did that
+if we were tracing a group of accents
+
+ align:start position:0%
+if we were tracing a group of accents
+ 
+
+ align:start position:0%
+if we were tracing a group of accents
+that were supposed to be going to the
+
+ align:start position:0%
+that were supposed to be going to the
+ 
+
+ align:start position:0%
+that were supposed to be going to the
+caudal end of the tectum
+
+ align:start position:0%
+caudal end of the tectum
+ 
+
+ align:start position:0%
+caudal end of the tectum
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+go to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say we were tracing axons that
+
+ align:start position:0%
+let's say we were tracing axons that
+ 
+
+ align:start position:0%
+let's say we were tracing axons that
+were supposed to be going here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we did find that they would go there
+
+ align:start position:0%
+we did find that they would go there
+ 
+
+ align:start position:0%
+we did find that they would go there
+but in addition we found mistakes
+
+ align:start position:0%
+but in addition we found mistakes
+ 
+
+ align:start position:0%
+but in addition we found mistakes
+occasionally found projections clear up
+
+ align:start position:0%
+occasionally found projections clear up
+ 
+
+ align:start position:0%
+occasionally found projections clear up
+in the front and they seem to be related
+
+ align:start position:0%
+in the front and they seem to be related
+ 
+
+ align:start position:0%
+in the front and they seem to be related
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+sort of a derailing of the axons when
+
+ align:start position:0%
+sort of a derailing of the axons when
+ 
+
+ align:start position:0%
+sort of a derailing of the axons when
+they were crossing the lesion area
+
+ align:start position:0%
+they were crossing the lesion area
+ 
+
+ align:start position:0%
+they were crossing the lesion area
+the organization of the axons the order
+
+ align:start position:0%
+the organization of the axons the order
+ 
+
+ align:start position:0%
+the organization of the axons the order
+of axons as they are entering their
+
+ align:start position:0%
+of axons as they are entering their
+ 
+
+ align:start position:0%
+of axons as they are entering their
+terminal areas seem to make a
+
+ align:start position:0%
+terminal areas seem to make a
+ 
+
+ align:start position:0%
+terminal areas seem to make a
+difference also
+
+ align:start position:0%
+difference also
+ 
+
+ align:start position:0%
+difference also
+that isn't something that was
+
+ align:start position:0%
+that isn't something that was
+ 
+
+ align:start position:0%
+that isn't something that was
+predicted by the chemo affinity theory
+
+ align:start position:0%
+predicted by the chemo affinity theory
+ 
+
+ align:start position:0%
+predicted by the chemo affinity theory
+but i can say in general
+
+ align:start position:0%
+but i can say in general
+ 
+
+ align:start position:0%
+but i can say in general
+that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inserted it in front
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that the map was
+
+ align:start position:0%
+that the map was
+ 
+
+ align:start position:0%
+that the map was
+accurate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are other experiments there that
+
+ align:start position:0%
+there are other experiments there that
+ 
+
+ align:start position:0%
+there are other experiments there that
+we could go through
+
+ align:start position:0%
+we could go through
+ 
+
+ align:start position:0%
+we could go through
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+it was later
+
+ align:start position:0%
+it was later
+ 
+
+ align:start position:0%
+it was later
+that they discovered that
+
+ align:start position:0%
+that they discovered that
+ 
+
+ align:start position:0%
+that they discovered that
+well before i go through this
+
+ align:start position:0%
+well before i go through this
+ 
+
+ align:start position:0%
+well before i go through this
+data on the chemical
+
+ align:start position:0%
+data on the chemical
+ 
+
+ align:start position:0%
+data on the chemical
+chemoaffinity
+
+ align:start position:0%
+chemoaffinity
+ 
+
+ align:start position:0%
+chemoaffinity
+what other ideas were there around that
+
+ align:start position:0%
+what other ideas were there around that
+ 
+
+ align:start position:0%
+what other ideas were there around that
+could explain the map formation
+
+ align:start position:0%
+could explain the map formation
+ 
+
+ align:start position:0%
+could explain the map formation
+it might it be possible even without
+
+ align:start position:0%
+it might it be possible even without
+ 
+
+ align:start position:0%
+it might it be possible even without
+chemical gradients to explain it
+
+ align:start position:0%
+chemical gradients to explain it
+ 
+
+ align:start position:0%
+chemical gradients to explain it
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+for one thing the axons had an order
+
+ align:start position:0%
+for one thing the axons had an order
+ 
+
+ align:start position:0%
+for one thing the axons had an order
+when they came in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go to this
+
+ align:start position:0%
+go to this
+ 
+
+ align:start position:0%
+go to this
+these axons here
+
+ align:start position:0%
+these axons here
+ 
+
+ align:start position:0%
+these axons here
+represented the superior field they came
+
+ align:start position:0%
+represented the superior field they came
+ 
+
+ align:start position:0%
+represented the superior field they came
+from inferior retina let's just indicate
+
+ align:start position:0%
+from inferior retina let's just indicate
+ 
+
+ align:start position:0%
+from inferior retina let's just indicate
+the field this these represented
+
+ align:start position:0%
+the field this these represented
+ 
+
+ align:start position:0%
+the field this these represented
+inferior field so the axons were already
+
+ align:start position:0%
+inferior field so the axons were already
+ 
+
+ align:start position:0%
+inferior field so the axons were already
+orderly in one axis of the field when
+
+ align:start position:0%
+orderly in one axis of the field when
+ 
+
+ align:start position:0%
+orderly in one axis of the field when
+they were entering
+
+ align:start position:0%
+they were entering
+ 
+
+ align:start position:0%
+they were entering
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's true for all the mammals
+
+ align:start position:0%
+and that's true for all the mammals
+ 
+
+ align:start position:0%
+and that's true for all the mammals
+anytime you see something in the upper
+
+ align:start position:0%
+anytime you see something in the upper
+ 
+
+ align:start position:0%
+anytime you see something in the upper
+visual field
+
+ align:start position:0%
+visual field
+ 
+
+ align:start position:0%
+visual field
+it's following this edge of the optic
+
+ align:start position:0%
+it's following this edge of the optic
+ 
+
+ align:start position:0%
+it's following this edge of the optic
+tract
+
+ align:start position:0%
+tract
+ 
+
+ align:start position:0%
+tract
+okay if you see something in the center
+
+ align:start position:0%
+okay if you see something in the center
+ 
+
+ align:start position:0%
+okay if you see something in the center
+of your field it comes in the center if
+
+ align:start position:0%
+of your field it comes in the center if
+ 
+
+ align:start position:0%
+of your field it comes in the center if
+you see something in the lower part of
+
+ align:start position:0%
+you see something in the lower part of
+ 
+
+ align:start position:0%
+you see something in the lower part of
+the original field
+
+ align:start position:0%
+the original field
+ 
+
+ align:start position:0%
+the original field
+it comes in laterally into the tectum
+
+ align:start position:0%
+it comes in laterally into the tectum
+ 
+
+ align:start position:0%
+it comes in laterally into the tectum
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well we did studies of that order and we
+
+ align:start position:0%
+well we did studies of that order and we
+ 
+
+ align:start position:0%
+well we did studies of that order and we
+found out that they become orderly by
+
+ align:start position:0%
+found out that they become orderly by
+ 
+
+ align:start position:0%
+found out that they become orderly by
+the time they reach the geniculate
+
+ align:start position:0%
+the time they reach the geniculate
+ 
+
+ align:start position:0%
+the time they reach the geniculate
+bodies
+
+ align:start position:0%
+bodies
+ 
+
+ align:start position:0%
+bodies
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what about the nasal temple axis
+
+ align:start position:0%
+what about the nasal temple axis
+ 
+
+ align:start position:0%
+what about the nasal temple axis
+well studies of some species indicated
+
+ align:start position:0%
+well studies of some species indicated
+ 
+
+ align:start position:0%
+well studies of some species indicated
+quite a bit of order
+
+ align:start position:0%
+quite a bit of order
+ 
+
+ align:start position:0%
+quite a bit of order
+but in the hamster it turns out that the
+
+ align:start position:0%
+but in the hamster it turns out that the
+ 
+
+ align:start position:0%
+but in the hamster it turns out that the
+nasal temporal axis
+
+ align:start position:0%
+nasal temporal axis
+ 
+
+ align:start position:0%
+nasal temporal axis
+axons from nasal and temporal were mixed
+
+ align:start position:0%
+axons from nasal and temporal were mixed
+ 
+
+ align:start position:0%
+axons from nasal and temporal were mixed
+in with each other
+
+ align:start position:0%
+in with each other
+ 
+
+ align:start position:0%
+in with each other
+so there had to be some factors sorting
+
+ align:start position:0%
+so there had to be some factors sorting
+ 
+
+ align:start position:0%
+so there had to be some factors sorting
+them out as they came into the tectum
+
+ align:start position:0%
+them out as they came into the tectum
+ 
+
+ align:start position:0%
+them out as they came into the tectum
+some people thought it might be time of
+
+ align:start position:0%
+some people thought it might be time of
+ 
+
+ align:start position:0%
+some people thought it might be time of
+arrival
+
+ align:start position:0%
+arrival
+ 
+
+ align:start position:0%
+arrival
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and there is some difference in temporal
+
+ align:start position:0%
+and there is some difference in temporal
+ 
+
+ align:start position:0%
+and there is some difference in temporal
+and nasal in time probably not accurate
+
+ align:start position:0%
+and nasal in time probably not accurate
+ 
+
+ align:start position:0%
+and nasal in time probably not accurate
+enough to explain some of these effects
+
+ align:start position:0%
+enough to explain some of these effects
+ 
+
+ align:start position:0%
+enough to explain some of these effects
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then later
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it was discovered that there are
+
+ align:start position:0%
+it was discovered that there are
+ 
+
+ align:start position:0%
+it was discovered that there are
+specific gradients of molecules
+
+ align:start position:0%
+specific gradients of molecules
+ 
+
+ align:start position:0%
+specific gradients of molecules
+in both the retina and the tectum
+
+ align:start position:0%
+in both the retina and the tectum
+ 
+
+ align:start position:0%
+in both the retina and the tectum
+the initial gradients that were
+
+ align:start position:0%
+the initial gradients that were
+ 
+
+ align:start position:0%
+the initial gradients that were
+described turned out not to be the
+
+ align:start position:0%
+described turned out not to be the
+ 
+
+ align:start position:0%
+described turned out not to be the
+important ones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then it was discovered that there
+
+ align:start position:0%
+but then it was discovered that there
+ 
+
+ align:start position:0%
+but then it was discovered that there
+this these two groups of molecules the
+
+ align:start position:0%
+this these two groups of molecules the
+ 
+
+ align:start position:0%
+this these two groups of molecules the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+efferens in the tectum
+
+ align:start position:0%
+efferens in the tectum
+ 
+
+ align:start position:0%
+efferens in the tectum
+and these tyrosine kinases and the
+
+ align:start position:0%
+and these tyrosine kinases and the
+ 
+
+ align:start position:0%
+and these tyrosine kinases and the
+retinal ganglion cells in their axons
+
+ align:start position:0%
+retinal ganglion cells in their axons
+ 
+
+ align:start position:0%
+retinal ganglion cells in their axons
+the eph family
+
+ align:start position:0%
+the eph family
+ 
+
+ align:start position:0%
+the eph family
+were distributed in gradient fashion
+
+ align:start position:0%
+were distributed in gradient fashion
+ 
+
+ align:start position:0%
+were distributed in gradient fashion
+there's not a single molecule like that
+
+ align:start position:0%
+there's not a single molecule like that
+ 
+
+ align:start position:0%
+there's not a single molecule like that
+there's several
+
+ align:start position:0%
+there's several
+ 
+
+ align:start position:0%
+there's several
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+distributed across the nasal temporal
+
+ align:start position:0%
+distributed across the nasal temporal
+ 
+
+ align:start position:0%
+distributed across the nasal temporal
+axis
+
+ align:start position:0%
+axis
+ 
+
+ align:start position:0%
+axis
+of the retina and there's a matching
+
+ align:start position:0%
+of the retina and there's a matching
+ 
+
+ align:start position:0%
+of the retina and there's a matching
+gradient in the raster caudal axis of
+
+ align:start position:0%
+gradient in the raster caudal axis of
+ 
+
+ align:start position:0%
+gradient in the raster caudal axis of
+the tectum
+
+ align:start position:0%
+the tectum
+ 
+
+ align:start position:0%
+the tectum
+and initially
+
+ align:start position:0%
+and initially
+ 
+
+ align:start position:0%
+and initially
+it was they just discovered the raster
+
+ align:start position:0%
+it was they just discovered the raster
+ 
+
+ align:start position:0%
+it was they just discovered the raster
+caudal axis nasal temporal field
+
+ align:start position:0%
+caudal axis nasal temporal field
+ 
+
+ align:start position:0%
+caudal axis nasal temporal field
+not the upper lower
+
+ align:start position:0%
+not the upper lower
+ 
+
+ align:start position:0%
+not the upper lower
+but they did then get evidence that they
+
+ align:start position:0%
+but they did then get evidence that they
+ 
+
+ align:start position:0%
+but they did then get evidence that they
+do play the kind of role postulated by
+
+ align:start position:0%
+do play the kind of role postulated by
+ 
+
+ align:start position:0%
+do play the kind of role postulated by
+sperry
+
+ align:start position:0%
+sperry
+ 
+
+ align:start position:0%
+sperry
+in that
+
+ align:start position:0%
+in that
+ 
+
+ align:start position:0%
+in that
+the first experiment showed that axons
+
+ align:start position:0%
+the first experiment showed that axons
+ 
+
+ align:start position:0%
+the first experiment showed that axons
+from the temporal retina don't like
+
+ align:start position:0%
+from the temporal retina don't like
+ 
+
+ align:start position:0%
+from the temporal retina don't like
+caudal tectum they're repelled from it
+
+ align:start position:0%
+caudal tectum they're repelled from it
+ 
+
+ align:start position:0%
+caudal tectum they're repelled from it
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that was done in tissue culture by
+
+ align:start position:0%
+and that was done in tissue culture by
+ 
+
+ align:start position:0%
+and that was done in tissue culture by
+taking membranes from the caudal
+
+ align:start position:0%
+taking membranes from the caudal
+ 
+
+ align:start position:0%
+taking membranes from the caudal
+technique from the rostral tectum and
+
+ align:start position:0%
+technique from the rostral tectum and
+ 
+
+ align:start position:0%
+technique from the rostral tectum and
+making little
+
+ align:start position:0%
+making little
+ 
+
+ align:start position:0%
+making little
+channels on the petri dish little lines
+
+ align:start position:0%
+channels on the petri dish little lines
+ 
+
+ align:start position:0%
+channels on the petri dish little lines
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+where you deposited the membranes and
+
+ align:start position:0%
+where you deposited the membranes and
+ 
+
+ align:start position:0%
+where you deposited the membranes and
+find out then where the accents from
+
+ align:start position:0%
+find out then where the accents from
+ 
+
+ align:start position:0%
+find out then where the accents from
+temporal retina or nasal retina will
+
+ align:start position:0%
+temporal retina or nasal retina will
+ 
+
+ align:start position:0%
+temporal retina or nasal retina will
+grow
+
+ align:start position:0%
+grow
+ 
+
+ align:start position:0%
+grow
+and accidents from the temporal retina
+
+ align:start position:0%
+and accidents from the temporal retina
+ 
+
+ align:start position:0%
+and accidents from the temporal retina
+simply don't like
+
+ align:start position:0%
+simply don't like
+ 
+
+ align:start position:0%
+simply don't like
+membranes of cells from the caudal
+
+ align:start position:0%
+membranes of cells from the caudal
+ 
+
+ align:start position:0%
+membranes of cells from the caudal
+tectum they're repelled by it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's specifically due to these
+
+ align:start position:0%
+and it's specifically due to these
+ 
+
+ align:start position:0%
+and it's specifically due to these
+molecules
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+molecules were found that could
+
+ align:start position:0%
+molecules were found that could
+ 
+
+ align:start position:0%
+molecules were found that could
+provide the
+
+ align:start position:0%
+provide the
+ 
+
+ align:start position:0%
+provide the
+the guidance for the upper lower field
+
+ align:start position:0%
+the guidance for the upper lower field
+ 
+
+ align:start position:0%
+the guidance for the upper lower field
+as well even though
+
+ align:start position:0%
+as well even though
+ 
+
+ align:start position:0%
+as well even though
+that axis is already represented in the
+
+ align:start position:0%
+that axis is already represented in the
+ 
+
+ align:start position:0%
+that axis is already represented in the
+tectum in the axons by the time the
+
+ align:start position:0%
+tectum in the axons by the time the
+ 
+
+ align:start position:0%
+tectum in the axons by the time the
+accents get there
+
+ align:start position:0%
+accents get there
+ 
+
+ align:start position:0%
+accents get there
+but in general
+
+ align:start position:0%
+but in general
+ 
+
+ align:start position:0%
+but in general
+the order of accents in the track
+
+ align:start position:0%
+the order of accents in the track
+ 
+
+ align:start position:0%
+the order of accents in the track
+isn't it's not sufficient to explain the
+
+ align:start position:0%
+isn't it's not sufficient to explain the
+ 
+
+ align:start position:0%
+isn't it's not sufficient to explain the
+precision of the map that seems to
+
+ align:start position:0%
+precision of the map that seems to
+ 
+
+ align:start position:0%
+precision of the map that seems to
+require the chemical guidance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when we talk about whether these
+
+ align:start position:0%
+so when we talk about whether these
+ 
+
+ align:start position:0%
+so when we talk about whether these
+molecules can explain all aspects of map
+
+ align:start position:0%
+molecules can explain all aspects of map
+ 
+
+ align:start position:0%
+molecules can explain all aspects of map
+formation the answer is no there are
+
+ align:start position:0%
+formation the answer is no there are
+ 
+
+ align:start position:0%
+formation the answer is no there are
+some aspects that they can't explain
+
+ align:start position:0%
+some aspects that they can't explain
+ 
+
+ align:start position:0%
+some aspects that they can't explain
+they can't explain mistakes that are
+
+ align:start position:0%
+they can't explain mistakes that are
+ 
+
+ align:start position:0%
+they can't explain mistakes that are
+made
+
+ align:start position:0%
+made
+ 
+
+ align:start position:0%
+made
+when you
+
+ align:start position:0%
+when you
+ 
+
+ align:start position:0%
+when you
+create lesions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they probably don't explain the initial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formation of the rough map
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but they do they are the major
+
+ align:start position:0%
+but they do they are the major
+ 
+
+ align:start position:0%
+but they do they are the major
+explanation for the topography
+
+ align:start position:0%
+explanation for the topography
+ 
+
+ align:start position:0%
+explanation for the topography
+there are some later effects of activity
+
+ align:start position:0%
+there are some later effects of activity
+ 
+
+ align:start position:0%
+there are some later effects of activity
+that also play a role
+
+ align:start position:0%
+that also play a role
+ 
+
+ align:start position:0%
+that also play a role
+that probably play are all independent
+
+ align:start position:0%
+that probably play are all independent
+ 
+
+ align:start position:0%
+that probably play are all independent
+of these
+
+ align:start position:0%
+of these
+ 
+
+ align:start position:0%
+of these
+these molecules
+
+ align:start position:0%
+these molecules
+ 
+
+ align:start position:0%
+these molecules
+but basically the uh
+
+ align:start position:0%
+but basically the uh
+ 
+
+ align:start position:0%
+but basically the uh
+this very ideas were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+borne out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not only these mistakes in the retina
+
+ align:start position:0%
+not only these mistakes in the retina
+ 
+
+ align:start position:0%
+not only these mistakes in the retina
+technical map were made
+
+ align:start position:0%
+technical map were made
+ 
+
+ align:start position:0%
+technical map were made
+but they seem to be relatively minor as
+
+ align:start position:0%
+but they seem to be relatively minor as
+ 
+
+ align:start position:0%
+but they seem to be relatively minor as
+far as function goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but we found with these early brain
+
+ align:start position:0%
+but we found with these early brain
+ 
+
+ align:start position:0%
+but we found with these early brain
+lesions we were making there were other
+
+ align:start position:0%
+lesions we were making there were other
+ 
+
+ align:start position:0%
+lesions we were making there were other
+kinds of violations of
+
+ align:start position:0%
+kinds of violations of
+ 
+
+ align:start position:0%
+kinds of violations of
+neural specificity rules
+
+ align:start position:0%
+neural specificity rules
+ 
+
+ align:start position:0%
+neural specificity rules
+so first of all we have to
+
+ align:start position:0%
+so first of all we have to
+ 
+
+ align:start position:0%
+so first of all we have to
+discriminate between regional and
+
+ align:start position:0%
+discriminate between regional and
+ 
+
+ align:start position:0%
+discriminate between regional and
+topographic specificity
+
+ align:start position:0%
+topographic specificity
+ 
+
+ align:start position:0%
+topographic specificity
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+topographic specificity is what we've
+
+ align:start position:0%
+topographic specificity is what we've
+ 
+
+ align:start position:0%
+topographic specificity is what we've
+been talking about one part of the
+
+ align:start position:0%
+been talking about one part of the
+ 
+
+ align:start position:0%
+been talking about one part of the
+retina goes to one part of the tectum
+
+ align:start position:0%
+retina goes to one part of the tectum
+ 
+
+ align:start position:0%
+retina goes to one part of the tectum
+another part of the right and it goes to
+
+ align:start position:0%
+another part of the right and it goes to
+ 
+
+ align:start position:0%
+another part of the right and it goes to
+another part of the tectum
+
+ align:start position:0%
+another part of the tectum
+ 
+
+ align:start position:0%
+another part of the tectum
+so what is regional specificity that
+
+ align:start position:0%
+so what is regional specificity that
+ 
+
+ align:start position:0%
+so what is regional specificity that
+simply means that accents from the
+
+ align:start position:0%
+simply means that accents from the
+ 
+
+ align:start position:0%
+simply means that accents from the
+retina go to the tectum but not to the
+
+ align:start position:0%
+retina go to the tectum but not to the
+ 
+
+ align:start position:0%
+retina go to the tectum but not to the
+inferior they go to the spherical is but
+
+ align:start position:0%
+inferior they go to the spherical is but
+ 
+
+ align:start position:0%
+inferior they go to the spherical is but
+not to the inferior colliculus they
+
+ align:start position:0%
+not to the inferior colliculus they
+ 
+
+ align:start position:0%
+not to the inferior colliculus they
+don't go
+
+ align:start position:0%
+don't go
+ 
+
+ align:start position:0%
+don't go
+they go to the superficial layers of the
+
+ align:start position:0%
+they go to the superficial layers of the
+ 
+
+ align:start position:0%
+they go to the superficial layers of the
+spirit calculus not to the deep layers
+
+ align:start position:0%
+spirit calculus not to the deep layers
+ 
+
+ align:start position:0%
+spirit calculus not to the deep layers
+of the spirit glitches okay they're
+
+ align:start position:0%
+of the spirit glitches okay they're
+ 
+
+ align:start position:0%
+of the spirit glitches okay they're
+regionally specific
+
+ align:start position:0%
+regionally specific
+ 
+
+ align:start position:0%
+regionally specific
+accents from the retina don't project
+
+ align:start position:0%
+accents from the retina don't project
+ 
+
+ align:start position:0%
+accents from the retina don't project
+into the somatosensory system or the
+
+ align:start position:0%
+into the somatosensory system or the
+ 
+
+ align:start position:0%
+into the somatosensory system or the
+auditory system okay they seem to know
+
+ align:start position:0%
+auditory system okay they seem to know
+ 
+
+ align:start position:0%
+auditory system okay they seem to know
+where to go that's regional specificity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+draw a little map of the midbrain here
+
+ align:start position:0%
+draw a little map of the midbrain here
+ 
+
+ align:start position:0%
+draw a little map of the midbrain here
+i can keep my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'm obviously hitting something here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is inferior colliculus seen from
+
+ align:start position:0%
+this is inferior colliculus seen from
+ 
+
+ align:start position:0%
+this is inferior colliculus seen from
+the side superior colliculus and here's
+
+ align:start position:0%
+the side superior colliculus and here's
+ 
+
+ align:start position:0%
+the side superior colliculus and here's
+the thalamus okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the lateral triniculate body
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where the retinal accents terminate
+
+ align:start position:0%
+where the retinal accents terminate
+ 
+
+ align:start position:0%
+where the retinal accents terminate
+okay so let's draw
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the course of an axon here coming into
+
+ align:start position:0%
+the course of an axon here coming into
+ 
+
+ align:start position:0%
+the course of an axon here coming into
+the spirit colliculus okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's terminating in these two structures
+
+ align:start position:0%
+it's terminating in these two structures
+ 
+
+ align:start position:0%
+it's terminating in these two structures
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and it's not
+
+ align:start position:0%
+and it's not
+ 
+
+ align:start position:0%
+and it's not
+terminating in the adjacent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thalamus here
+
+ align:start position:0%
+thalamus here
+ 
+
+ align:start position:0%
+thalamus here
+the medial geniculate body
+
+ align:start position:0%
+the medial geniculate body
+ 
+
+ align:start position:0%
+the medial geniculate body
+lp gets only a few
+
+ align:start position:0%
+lp gets only a few
+ 
+
+ align:start position:0%
+lp gets only a few
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+let's put in green here an axon coming
+
+ align:start position:0%
+let's put in green here an axon coming
+ 
+
+ align:start position:0%
+let's put in green here an axon coming
+from inferior curriculus that goes here
+
+ align:start position:0%
+from inferior curriculus that goes here
+ 
+
+ align:start position:0%
+from inferior curriculus that goes here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now what if we do this
+
+ align:start position:0%
+now what if we do this
+ 
+
+ align:start position:0%
+now what if we do this
+put in the red here let's take out
+
+ align:start position:0%
+put in the red here let's take out
+ 
+
+ align:start position:0%
+put in the red here let's take out
+superior colliculus
+
+ align:start position:0%
+superior colliculus
+ 
+
+ align:start position:0%
+superior colliculus
+but we'll also damage that track
+
+ align:start position:0%
+but we'll also damage that track
+ 
+
+ align:start position:0%
+but we'll also damage that track
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we did that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we found out that i'll use the heavy pen
+
+ align:start position:0%
+we found out that i'll use the heavy pen
+ 
+
+ align:start position:0%
+we found out that i'll use the heavy pen
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these axons not only went into the
+
+ align:start position:0%
+these axons not only went into the
+ 
+
+ align:start position:0%
+these axons not only went into the
+lateral draniculate body okay
+
+ align:start position:0%
+lateral draniculate body okay
+ 
+
+ align:start position:0%
+lateral draniculate body okay
+but they also invaded
+
+ align:start position:0%
+but they also invaded
+ 
+
+ align:start position:0%
+but they also invaded
+the medial junctual body so that's a
+
+ align:start position:0%
+the medial junctual body so that's a
+ 
+
+ align:start position:0%
+the medial junctual body so that's a
+sprouting axon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the key thing was we had to remove the
+
+ align:start position:0%
+the key thing was we had to remove the
+ 
+
+ align:start position:0%
+the key thing was we had to remove the
+normal input to the medial genicular
+
+ align:start position:0%
+normal input to the medial genicular
+ 
+
+ align:start position:0%
+normal input to the medial genicular
+body
+
+ align:start position:0%
+body
+ 
+
+ align:start position:0%
+body
+the optic tract goes right
+
+ align:start position:0%
+the optic tract goes right
+ 
+
+ align:start position:0%
+the optic tract goes right
+over the medial jacubed body at its
+
+ align:start position:0%
+over the medial jacubed body at its
+ 
+
+ align:start position:0%
+over the medial jacubed body at its
+caudal the cartilage of the tract okay
+
+ align:start position:0%
+caudal the cartilage of the tract okay
+ 
+
+ align:start position:0%
+caudal the cartilage of the tract okay
+they were always accents from the
+
+ align:start position:0%
+they were always accents from the
+ 
+
+ align:start position:0%
+they were always accents from the
+cartilage the optic tract
+
+ align:start position:0%
+cartilage the optic tract
+ 
+
+ align:start position:0%
+cartilage the optic tract
+so then we could have the retina
+
+ align:start position:0%
+so then we could have the retina
+ 
+
+ align:start position:0%
+so then we could have the retina
+projecting into the auditory system but
+
+ align:start position:0%
+projecting into the auditory system but
+ 
+
+ align:start position:0%
+projecting into the auditory system but
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+when we made these lesions and only when
+
+ align:start position:0%
+when we made these lesions and only when
+ 
+
+ align:start position:0%
+when we made these lesions and only when
+we made them early in life
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we took away the normal terminal area
+
+ align:start position:0%
+we took away the normal terminal area
+ 
+
+ align:start position:0%
+we took away the normal terminal area
+and when you do that axons tend to
+
+ align:start position:0%
+and when you do that axons tend to
+ 
+
+ align:start position:0%
+and when you do that axons tend to
+sprout other places
+
+ align:start position:0%
+sprout other places
+ 
+
+ align:start position:0%
+sprout other places
+but they tend to sprout in the places
+
+ align:start position:0%
+but they tend to sprout in the places
+ 
+
+ align:start position:0%
+but they tend to sprout in the places
+that have lost their normal termination
+
+ align:start position:0%
+that have lost their normal termination
+ 
+
+ align:start position:0%
+that have lost their normal termination
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it looks like chemical specificity
+
+ align:start position:0%
+so it looks like chemical specificity
+ 
+
+ align:start position:0%
+so it looks like chemical specificity
+then might represent the kind of
+
+ align:start position:0%
+then might represent the kind of
+ 
+
+ align:start position:0%
+then might represent the kind of
+relative preferences for the accents
+
+ align:start position:0%
+relative preferences for the accents
+ 
+
+ align:start position:0%
+relative preferences for the accents
+there may be some places they cannot
+
+ align:start position:0%
+there may be some places they cannot
+ 
+
+ align:start position:0%
+there may be some places they cannot
+terminate at all but there are some
+
+ align:start position:0%
+terminate at all but there are some
+ 
+
+ align:start position:0%
+terminate at all but there are some
+places they can terminate if you give
+
+ align:start position:0%
+places they can terminate if you give
+ 
+
+ align:start position:0%
+places they can terminate if you give
+them the space
+
+ align:start position:0%
+them the space
+ 
+
+ align:start position:0%
+them the space
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+certainly if you don't let them
+
+ align:start position:0%
+certainly if you don't let them
+ 
+
+ align:start position:0%
+certainly if you don't let them
+terminate in their normal places okay
+
+ align:start position:0%
+terminate in their normal places okay
+ 
+
+ align:start position:0%
+terminate in their normal places okay
+and that phenomenon of retina projecting
+
+ align:start position:0%
+and that phenomenon of retina projecting
+ 
+
+ align:start position:0%
+and that phenomenon of retina projecting
+into the auditory system has been
+
+ align:start position:0%
+into the auditory system has been
+ 
+
+ align:start position:0%
+into the auditory system has been
+studied a lot in the ferret
+
+ align:start position:0%
+studied a lot in the ferret
+ 
+
+ align:start position:0%
+studied a lot in the ferret
+by marie gonna cassour and his
+
+ align:start position:0%
+by marie gonna cassour and his
+ 
+
+ align:start position:0%
+by marie gonna cassour and his
+students in this building
+
+ align:start position:0%
+students in this building
+ 
+
+ align:start position:0%
+students in this building
+and we will probably mention those
+
+ align:start position:0%
+and we will probably mention those
+ 
+
+ align:start position:0%
+and we will probably mention those
+experiments later
+
+ align:start position:0%
+experiments later
+ 
+
+ align:start position:0%
+experiments later
+in the class
+
+ align:start position:0%
+in the class
+ 
+
+ align:start position:0%
+in the class
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+there have been a number of experiments
+
+ align:start position:0%
+there have been a number of experiments
+ 
+
+ align:start position:0%
+there have been a number of experiments
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+how specific regionally specific axons
+
+ align:start position:0%
+how specific regionally specific axons
+ 
+
+ align:start position:0%
+how specific regionally specific axons
+grow during their elongation period
+
+ align:start position:0%
+grow during their elongation period
+ 
+
+ align:start position:0%
+grow during their elongation period
+and i want to go through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just a few of those experiments first of
+
+ align:start position:0%
+just a few of those experiments first of
+ 
+
+ align:start position:0%
+just a few of those experiments first of
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+growth of axons in the grass upper leg
+
+ align:start position:0%
+growth of axons in the grass upper leg
+ 
+
+ align:start position:0%
+growth of axons in the grass upper leg
+which gave evidence for
+
+ align:start position:0%
+which gave evidence for
+ 
+
+ align:start position:0%
+which gave evidence for
+specific guidance by glio glial cells
+
+ align:start position:0%
+specific guidance by glio glial cells
+ 
+
+ align:start position:0%
+specific guidance by glio glial cells
+we call those glial cells guidepost
+
+ align:start position:0%
+we call those glial cells guidepost
+ 
+
+ align:start position:0%
+we call those glial cells guidepost
+cells
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we'll talk
+
+ align:start position:0%
+and then we'll talk
+ 
+
+ align:start position:0%
+and then we'll talk
+i may not finish today
+
+ align:start position:0%
+i may not finish today
+ 
+
+ align:start position:0%
+i may not finish today
+spinal cord
+
+ align:start position:0%
+spinal cord
+ 
+
+ align:start position:0%
+spinal cord
+studies that gave some new evidence for
+
+ align:start position:0%
+studies that gave some new evidence for
+ 
+
+ align:start position:0%
+studies that gave some new evidence for
+chemo specificity not in the topography
+
+ align:start position:0%
+chemo specificity not in the topography
+ 
+
+ align:start position:0%
+chemo specificity not in the topography
+formation not in termination patterns
+
+ align:start position:0%
+formation not in termination patterns
+ 
+
+ align:start position:0%
+formation not in termination patterns
+but in the course of the axons
+
+ align:start position:0%
+but in the course of the axons
+ 
+
+ align:start position:0%
+but in the course of the axons
+and then growth course of axon growth
+
+ align:start position:0%
+and then growth course of axon growth
+ 
+
+ align:start position:0%
+and then growth course of axon growth
+and then we have additional data on
+
+ align:start position:0%
+and then we have additional data on
+ 
+
+ align:start position:0%
+and then we have additional data on
+specific glial
+
+ align:start position:0%
+specific glial
+ 
+
+ align:start position:0%
+specific glial
+cell barriers to elongation
+
+ align:start position:0%
+cell barriers to elongation
+ 
+
+ align:start position:0%
+cell barriers to elongation
+first of all the grass upper leg okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a reconstruction of the
+
+ align:start position:0%
+this is a reconstruction of the
+ 
+
+ align:start position:0%
+this is a reconstruction of the
+leg in the embryonic grasshopper so it's
+
+ align:start position:0%
+leg in the embryonic grasshopper so it's
+ 
+
+ align:start position:0%
+leg in the embryonic grasshopper so it's
+sort of stubby
+
+ align:start position:0%
+sort of stubby
+ 
+
+ align:start position:0%
+sort of stubby
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here you see the the ganglion that
+
+ align:start position:0%
+here you see the the ganglion that
+ 
+
+ align:start position:0%
+here you see the the ganglion that
+they're calling cns or central nervous
+
+ align:start position:0%
+they're calling cns or central nervous
+ 
+
+ align:start position:0%
+they're calling cns or central nervous
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+and this shows
+
+ align:start position:0%
+and this shows
+ 
+
+ align:start position:0%
+and this shows
+the leg as if it were transparent and
+
+ align:start position:0%
+the leg as if it were transparent and
+ 
+
+ align:start position:0%
+the leg as if it were transparent and
+the cell bodies of these neurons are in
+
+ align:start position:0%
+the cell bodies of these neurons are in
+ 
+
+ align:start position:0%
+the cell bodies of these neurons are in
+the epithelium so they're a little
+
+ align:start position:0%
+the epithelium so they're a little
+ 
+
+ align:start position:0%
+the epithelium so they're a little
+different from the dorsal root ganglion
+
+ align:start position:0%
+different from the dorsal root ganglion
+ 
+
+ align:start position:0%
+different from the dorsal root ganglion
+cells in mammals
+
+ align:start position:0%
+cells in mammals
+ 
+
+ align:start position:0%
+cells in mammals
+but they send an axon then that grows
+
+ align:start position:0%
+but they send an axon then that grows
+ 
+
+ align:start position:0%
+but they send an axon then that grows
+according to a specific pattern
+
+ align:start position:0%
+according to a specific pattern
+ 
+
+ align:start position:0%
+according to a specific pattern
+towards the
+
+ align:start position:0%
+towards the
+ 
+
+ align:start position:0%
+towards the
+nervous system of this animal
+
+ align:start position:0%
+nervous system of this animal
+ 
+
+ align:start position:0%
+nervous system of this animal
+and they can reconstruct the pathway and
+
+ align:start position:0%
+and they can reconstruct the pathway and
+ 
+
+ align:start position:0%
+and they can reconstruct the pathway and
+they find it's quite consistent in its
+
+ align:start position:0%
+they find it's quite consistent in its
+ 
+
+ align:start position:0%
+they find it's quite consistent in its
+pattern
+
+ align:start position:0%
+pattern
+ 
+
+ align:start position:0%
+pattern
+you see the reconstruction here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they notice that at the points where
+
+ align:start position:0%
+and they notice that at the points where
+ 
+
+ align:start position:0%
+and they notice that at the points where
+it made these turns there were specific
+
+ align:start position:0%
+it made these turns there were specific
+ 
+
+ align:start position:0%
+it made these turns there were specific
+cells that the axons could be responding
+
+ align:start position:0%
+cells that the axons could be responding
+ 
+
+ align:start position:0%
+cells that the axons could be responding
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+and to test whether that were true
+
+ align:start position:0%
+and to test whether that were true
+ 
+
+ align:start position:0%
+and to test whether that were true
+whether those cells were acting as sort
+
+ align:start position:0%
+whether those cells were acting as sort
+ 
+
+ align:start position:0%
+whether those cells were acting as sort
+of guideposts
+
+ align:start position:0%
+of guideposts
+ 
+
+ align:start position:0%
+of guideposts
+they tried for example
+
+ align:start position:0%
+they tried for example
+ 
+
+ align:start position:0%
+they tried for example
+ablating
+
+ align:start position:0%
+ablating
+ 
+
+ align:start position:0%
+ablating
+like this one particular cell
+
+ align:start position:0%
+like this one particular cell
+ 
+
+ align:start position:0%
+like this one particular cell
+and when they ablated
+
+ align:start position:0%
+and when they ablated
+ 
+
+ align:start position:0%
+and when they ablated
+a particular cell along the path they
+
+ align:start position:0%
+a particular cell along the path they
+ 
+
+ align:start position:0%
+a particular cell along the path they
+could alter the pathway
+
+ align:start position:0%
+could alter the pathway
+ 
+
+ align:start position:0%
+could alter the pathway
+as you see in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in these
+
+ align:start position:0%
+in these
+ 
+
+ align:start position:0%
+in these
+experiments
+
+ align:start position:0%
+experiments
+ 
+
+ align:start position:0%
+experiments
+so they were calling those cells
+
+ align:start position:0%
+so they were calling those cells
+ 
+
+ align:start position:0%
+so they were calling those cells
+guideposts now how were they working
+
+ align:start position:0%
+guideposts now how were they working
+ 
+
+ align:start position:0%
+guideposts now how were they working
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+when the axon starts to grow here
+
+ align:start position:0%
+when the axon starts to grow here
+ 
+
+ align:start position:0%
+when the axon starts to grow here
+it sends out
+
+ align:start position:0%
+it sends out
+ 
+
+ align:start position:0%
+it sends out
+long filopodia
+
+ align:start position:0%
+long filopodia
+ 
+
+ align:start position:0%
+long filopodia
+the filipodia are so long that they
+
+ align:start position:0%
+the filipodia are so long that they
+ 
+
+ align:start position:0%
+the filipodia are so long that they
+could reach all the way
+
+ align:start position:0%
+could reach all the way
+ 
+
+ align:start position:0%
+could reach all the way
+to a guidepost cell
+
+ align:start position:0%
+to a guidepost cell
+ 
+
+ align:start position:0%
+to a guidepost cell
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that seemed to provide some point of
+
+ align:start position:0%
+that seemed to provide some point of
+ 
+
+ align:start position:0%
+that seemed to provide some point of
+adherence and the whole growth cone
+
+ align:start position:0%
+adherence and the whole growth cone
+ 
+
+ align:start position:0%
+adherence and the whole growth cone
+would move towards that cell but once
+
+ align:start position:0%
+would move towards that cell but once
+ 
+
+ align:start position:0%
+would move towards that cell but once
+getting there
+
+ align:start position:0%
+getting there
+ 
+
+ align:start position:0%
+getting there
+they didn't just stay there
+
+ align:start position:0%
+they didn't just stay there
+ 
+
+ align:start position:0%
+they didn't just stay there
+they sent out the long filipote again
+
+ align:start position:0%
+they sent out the long filipote again
+ 
+
+ align:start position:0%
+they sent out the long filipote again
+and reached the next one
+
+ align:start position:0%
+and reached the next one
+ 
+
+ align:start position:0%
+and reached the next one
+and then they would grow to that one and
+
+ align:start position:0%
+and then they would grow to that one and
+ 
+
+ align:start position:0%
+and then they would grow to that one and
+so forth from cell to cell until they
+
+ align:start position:0%
+so forth from cell to cell until they
+ 
+
+ align:start position:0%
+so forth from cell to cell until they
+reach the central nervous system so it's
+
+ align:start position:0%
+reach the central nervous system so it's
+ 
+
+ align:start position:0%
+reach the central nervous system so it's
+sort of like a connect the dots game
+
+ align:start position:0%
+sort of like a connect the dots game
+ 
+
+ align:start position:0%
+sort of like a connect the dots game
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+growing from one cell to the next
+
+ align:start position:0%
+growing from one cell to the next
+ 
+
+ align:start position:0%
+growing from one cell to the next
+and that was the theory of how these
+
+ align:start position:0%
+and that was the theory of how these
+ 
+
+ align:start position:0%
+and that was the theory of how these
+axons grow
+
+ align:start position:0%
+axons grow
+ 
+
+ align:start position:0%
+axons grow
+in the grasshopper leg
+
+ align:start position:0%
+in the grasshopper leg
+ 
+
+ align:start position:0%
+in the grasshopper leg
+where are we here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the later growing axons would follow
+
+ align:start position:0%
+and the later growing axons would follow
+ 
+
+ align:start position:0%
+and the later growing axons would follow
+those initial ones
+
+ align:start position:0%
+those initial ones
+ 
+
+ align:start position:0%
+those initial ones
+that we call the pioneering axons if
+
+ align:start position:0%
+that we call the pioneering axons if
+ 
+
+ align:start position:0%
+that we call the pioneering axons if
+they grow first okay
+
+ align:start position:0%
+they grow first okay
+ 
+
+ align:start position:0%
+they grow first okay
+they then asked well could they ablate
+
+ align:start position:0%
+they then asked well could they ablate
+ 
+
+ align:start position:0%
+they then asked well could they ablate
+the pioneer cell
+
+ align:start position:0%
+the pioneer cell
+ 
+
+ align:start position:0%
+the pioneer cell
+with the later ones do the same thing
+
+ align:start position:0%
+with the later ones do the same thing
+ 
+
+ align:start position:0%
+with the later ones do the same thing
+and the answer is yes
+
+ align:start position:0%
+and the answer is yes
+ 
+
+ align:start position:0%
+and the answer is yes
+but normally the later growing axons
+
+ align:start position:0%
+but normally the later growing axons
+ 
+
+ align:start position:0%
+but normally the later growing axons
+fasciculate along the first one okay
+
+ align:start position:0%
+fasciculate along the first one okay
+ 
+
+ align:start position:0%
+fasciculate along the first one okay
+they seem to follow it
+
+ align:start position:0%
+they seem to follow it
+ 
+
+ align:start position:0%
+they seem to follow it
+but any of them are capable of following
+
+ align:start position:0%
+but any of them are capable of following
+ 
+
+ align:start position:0%
+but any of them are capable of following
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+same course
+
+ align:start position:0%
+same course
+ 
+
+ align:start position:0%
+same course
+but when we looked at the optic tract in
+
+ align:start position:0%
+but when we looked at the optic tract in
+ 
+
+ align:start position:0%
+but when we looked at the optic tract in
+mammals
+
+ align:start position:0%
+mammals
+ 
+
+ align:start position:0%
+mammals
+we found that the later growing accents
+
+ align:start position:0%
+we found that the later growing accents
+ 
+
+ align:start position:0%
+we found that the later growing accents
+actually don't grow on the surfaces the
+
+ align:start position:0%
+actually don't grow on the surfaces the
+ 
+
+ align:start position:0%
+actually don't grow on the surfaces the
+earlier ones in fact they space
+
+ align:start position:0%
+earlier ones in fact they space
+ 
+
+ align:start position:0%
+earlier ones in fact they space
+themselves out in between the pioneers
+
+ align:start position:0%
+themselves out in between the pioneers
+ 
+
+ align:start position:0%
+themselves out in between the pioneers
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+they don't seem to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+following the same kind of rules that
+
+ align:start position:0%
+following the same kind of rules that
+ 
+
+ align:start position:0%
+following the same kind of rules that
+you get in the grasshopper lake
+
+ align:start position:0%
+you get in the grasshopper lake
+ 
+
+ align:start position:0%
+you get in the grasshopper lake
+so that's just a cautionary note there
+
+ align:start position:0%
+so that's just a cautionary note there
+ 
+
+ align:start position:0%
+so that's just a cautionary note there
+that what's discovered in one system may
+
+ align:start position:0%
+that what's discovered in one system may
+ 
+
+ align:start position:0%
+that what's discovered in one system may
+not be what you discover in every system
+
+ align:start position:0%
+not be what you discover in every system
+ 
+
+ align:start position:0%
+not be what you discover in every system
+uh i can see the time i think i'll start
+
+ align:start position:0%
+uh i can see the time i think i'll start
+ 
+
+ align:start position:0%
+uh i can see the time i think i'll start
+with this next time
\ No newline at end of file
diff --git a/mBGJOLE7ZUg.txt b/mBGJOLE7ZUg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1de11b2ae4bc1e1e16c80ed7793ba5af652041ef
--- /dev/null
+++ b/mBGJOLE7ZUg.txt
@@ -0,0 +1,1547 @@
+align:start position:0%
+ 
+welcome back to 820 special relativity
+
+ align:start position:0%
+welcome back to 820 special relativity
+ 
+
+ align:start position:0%
+welcome back to 820 special relativity
+in this section we talk about space time
+
+ align:start position:0%
+in this section we talk about space time
+ 
+
+ align:start position:0%
+in this section we talk about space time
+diagrams
+
+ align:start position:0%
+diagrams
+ 
+
+ align:start position:0%
+diagrams
+they turn out to be very useful tools to
+
+ align:start position:0%
+they turn out to be very useful tools to
+ 
+
+ align:start position:0%
+they turn out to be very useful tools to
+describe
+
+ align:start position:0%
+describe
+ 
+
+ align:start position:0%
+describe
+events or sequences of events in
+
+ align:start position:0%
+events or sequences of events in
+ 
+
+ align:start position:0%
+events or sequences of events in
+particular when observed by multiple
+
+ align:start position:0%
+particular when observed by multiple
+ 
+
+ align:start position:0%
+particular when observed by multiple
+observers
+
+ align:start position:0%
+observers
+ 
+
+ align:start position:0%
+observers
+so what is the space-time diagram
+
+ align:start position:0%
+so what is the space-time diagram
+ 
+
+ align:start position:0%
+so what is the space-time diagram
+here's an example
+
+ align:start position:0%
+here's an example
+ 
+
+ align:start position:0%
+here's an example
+you have an x-coordinate and a
+
+ align:start position:0%
+you have an x-coordinate and a
+ 
+
+ align:start position:0%
+you have an x-coordinate and a
+t-coordinate for space and time
+
+ align:start position:0%
+t-coordinate for space and time
+ 
+
+ align:start position:0%
+t-coordinate for space and time
+i plotted an event
+
+ align:start position:0%
+i plotted an event
+ 
+
+ align:start position:0%
+i plotted an event
+in blue here and the word line of events
+
+ align:start position:0%
+in blue here and the word line of events
+ 
+
+ align:start position:0%
+in blue here and the word line of events
+a word line is just the sequence of
+
+ align:start position:0%
+a word line is just the sequence of
+ 
+
+ align:start position:0%
+a word line is just the sequence of
+events as they occur
+
+ align:start position:0%
+events as they occur
+ 
+
+ align:start position:0%
+events as they occur
+um in this case um something seemed to
+
+ align:start position:0%
+um in this case um something seemed to
+ 
+
+ align:start position:0%
+um in this case um something seemed to
+be moving with constant velocity the
+
+ align:start position:0%
+be moving with constant velocity the
+ 
+
+ align:start position:0%
+be moving with constant velocity the
+world line is just the continuous line
+
+ align:start position:0%
+world line is just the continuous line
+ 
+
+ align:start position:0%
+world line is just the continuous line
+velocity of this event is delta x over
+
+ align:start position:0%
+velocity of this event is delta x over
+ 
+
+ align:start position:0%
+velocity of this event is delta x over
+delta t which is one over the slope
+
+ align:start position:0%
+delta t which is one over the slope
+ 
+
+ align:start position:0%
+delta t which is one over the slope
+let's have a look here so the time axis
+
+ align:start position:0%
+let's have a look here so the time axis
+ 
+
+ align:start position:0%
+let's have a look here so the time axis
+is defined as those events
+
+ align:start position:0%
+is defined as those events
+ 
+
+ align:start position:0%
+is defined as those events
+which all occur at the same space x
+
+ align:start position:0%
+which all occur at the same space x
+ 
+
+ align:start position:0%
+which all occur at the same space x
+equals zero
+
+ align:start position:0%
+equals zero
+ 
+
+ align:start position:0%
+equals zero
+while the x-axis is defined as those
+
+ align:start position:0%
+while the x-axis is defined as those
+ 
+
+ align:start position:0%
+while the x-axis is defined as those
+events which all occur simultaneously at
+
+ align:start position:0%
+events which all occur simultaneously at
+ 
+
+ align:start position:0%
+events which all occur simultaneously at
+the same time
+
+ align:start position:0%
+the same time
+ 
+
+ align:start position:0%
+the same time
+and then you can draw
+
+ align:start position:0%
+and then you can draw
+ 
+
+ align:start position:0%
+and then you can draw
+additional lines into
+
+ align:start position:0%
+additional lines into
+ 
+
+ align:start position:0%
+additional lines into
+the time space time diagram where for
+
+ align:start position:0%
+the time space time diagram where for
+ 
+
+ align:start position:0%
+the time space time diagram where for
+example all times are equal to one you
+
+ align:start position:0%
+example all times are equal to one you
+ 
+
+ align:start position:0%
+example all times are equal to one you
+might want to add a unit i omitted this
+
+ align:start position:0%
+might want to add a unit i omitted this
+ 
+
+ align:start position:0%
+might want to add a unit i omitted this
+here uh time might be given in seconds
+
+ align:start position:0%
+here uh time might be given in seconds
+ 
+
+ align:start position:0%
+here uh time might be given in seconds
+in days in hours and years
+
+ align:start position:0%
+in days in hours and years
+ 
+
+ align:start position:0%
+in days in hours and years
+however you like similar to space in
+
+ align:start position:0%
+however you like similar to space in
+ 
+
+ align:start position:0%
+however you like similar to space in
+meters or light years
+
+ align:start position:0%
+meters or light years
+ 
+
+ align:start position:0%
+meters or light years
+so lines here in green
+
+ align:start position:0%
+so lines here in green
+ 
+
+ align:start position:0%
+so lines here in green
+of the same time meaning time is
+
+ align:start position:0%
+of the same time meaning time is
+ 
+
+ align:start position:0%
+of the same time meaning time is
+constant they happen all events on that
+
+ align:start position:0%
+constant they happen all events on that
+ 
+
+ align:start position:0%
+constant they happen all events on that
+line happen simultaneously
+
+ align:start position:0%
+line happen simultaneously
+ 
+
+ align:start position:0%
+line happen simultaneously
+while in blue are those lines where
+
+ align:start position:0%
+while in blue are those lines where
+ 
+
+ align:start position:0%
+while in blue are those lines where
+events happen at the same location so x
+
+ align:start position:0%
+events happen at the same location so x
+ 
+
+ align:start position:0%
+events happen at the same location so x
+is equal constant some specific values
+
+ align:start position:0%
+is equal constant some specific values
+ 
+
+ align:start position:0%
+is equal constant some specific values
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+here in red i add one additional caveat
+
+ align:start position:0%
+here in red i add one additional caveat
+ 
+
+ align:start position:0%
+here in red i add one additional caveat
+which you are typically not aware or
+
+ align:start position:0%
+which you are typically not aware or
+ 
+
+ align:start position:0%
+which you are typically not aware or
+considering very much
+
+ align:start position:0%
+considering very much
+ 
+
+ align:start position:0%
+considering very much
+in diagrams is the role of tick marks
+
+ align:start position:0%
+in diagrams is the role of tick marks
+ 
+
+ align:start position:0%
+in diagrams is the role of tick marks
+here in this space-time diagram all tick
+
+ align:start position:0%
+here in this space-time diagram all tick
+ 
+
+ align:start position:0%
+here in this space-time diagram all tick
+marks are perpendicular to the axis
+
+ align:start position:0%
+marks are perpendicular to the axis
+ 
+
+ align:start position:0%
+marks are perpendicular to the axis
+it's also okay or correct here to say
+
+ align:start position:0%
+it's also okay or correct here to say
+ 
+
+ align:start position:0%
+it's also okay or correct here to say
+that they're in parallel to the second
+
+ align:start position:0%
+that they're in parallel to the second
+ 
+
+ align:start position:0%
+that they're in parallel to the second
+axis and we'll come back to this point
+
+ align:start position:0%
+axis and we'll come back to this point
+ 
+
+ align:start position:0%
+axis and we'll come back to this point
+later on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+an example
+
+ align:start position:0%
+an example
+ 
+
+ align:start position:0%
+an example
+um of a word line is simply you know
+
+ align:start position:0%
+um of a word line is simply you know
+ 
+
+ align:start position:0%
+um of a word line is simply you know
+drawing all events which correspond to
+
+ align:start position:0%
+drawing all events which correspond to
+ 
+
+ align:start position:0%
+drawing all events which correspond to
+me right professor is pacing in his
+
+ align:start position:0%
+me right professor is pacing in his
+ 
+
+ align:start position:0%
+me right professor is pacing in his
+office um
+
+ align:start position:0%
+office um
+ 
+
+ align:start position:0%
+office um
+you know maybe on a line just the x
+
+ align:start position:0%
+you know maybe on a line just the x
+ 
+
+ align:start position:0%
+you know maybe on a line just the x
+coordinate is plotted here time passes
+
+ align:start position:0%
+coordinate is plotted here time passes
+ 
+
+ align:start position:0%
+coordinate is plotted here time passes
+and i'm just placing the long changing
+
+ align:start position:0%
+and i'm just placing the long changing
+ 
+
+ align:start position:0%
+and i'm just placing the long changing
+direction each time each little segment
+
+ align:start position:0%
+direction each time each little segment
+ 
+
+ align:start position:0%
+direction each time each little segment
+with constant velocity that's the word
+
+ align:start position:0%
+with constant velocity that's the word
+ 
+
+ align:start position:0%
+with constant velocity that's the word
+line of me from some time t equal minus
+
+ align:start position:0%
+line of me from some time t equal minus
+ 
+
+ align:start position:0%
+line of me from some time t equal minus
+t to term time equal 40.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now a first concept question
+
+ align:start position:0%
+okay so now a first concept question
+ 
+
+ align:start position:0%
+okay so now a first concept question
+let's consider
+
+ align:start position:0%
+let's consider
+ 
+
+ align:start position:0%
+let's consider
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+the set of word lines one two three four
+
+ align:start position:0%
+the set of word lines one two three four
+ 
+
+ align:start position:0%
+the set of word lines one two three four
+and the question is which of the objects
+
+ align:start position:0%
+and the question is which of the objects
+ 
+
+ align:start position:0%
+and the question is which of the objects
+which correspond to the word line is
+
+ align:start position:0%
+which correspond to the word line is
+ 
+
+ align:start position:0%
+which correspond to the word line is
+moving the slowest
+
+ align:start position:0%
+moving the slowest
+ 
+
+ align:start position:0%
+moving the slowest
+so let's consider this for a second and
+
+ align:start position:0%
+so let's consider this for a second and
+ 
+
+ align:start position:0%
+so let's consider this for a second and
+then we look at this
+
+ align:start position:0%
+then we look at this
+ 
+
+ align:start position:0%
+then we look at this
+as the velocity is one over the slope
+
+ align:start position:0%
+as the velocity is one over the slope
+ 
+
+ align:start position:0%
+as the velocity is one over the slope
+the object that says steepest slope
+
+ align:start position:0%
+the object that says steepest slope
+ 
+
+ align:start position:0%
+the object that says steepest slope
+largest value of the slope is moving the
+
+ align:start position:0%
+largest value of the slope is moving the
+ 
+
+ align:start position:0%
+largest value of the slope is moving the
+slowest and in this case it's object
+
+ align:start position:0%
+slowest and in this case it's object
+ 
+
+ align:start position:0%
+slowest and in this case it's object
+number two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right now we want to actually make
+
+ align:start position:0%
+all right now we want to actually make
+ 
+
+ align:start position:0%
+all right now we want to actually make
+them useful
+
+ align:start position:0%
+them useful
+ 
+
+ align:start position:0%
+them useful
+yes they can be used in order to
+
+ align:start position:0%
+yes they can be used in order to
+ 
+
+ align:start position:0%
+yes they can be used in order to
+describe certain event lines but they're
+
+ align:start position:0%
+describe certain event lines but they're
+ 
+
+ align:start position:0%
+describe certain event lines but they're
+really use useful when you describe
+
+ align:start position:0%
+really use useful when you describe
+ 
+
+ align:start position:0%
+really use useful when you describe
+events happening for a different
+
+ align:start position:0%
+events happening for a different
+ 
+
+ align:start position:0%
+events happening for a different
+observer
+
+ align:start position:0%
+observer
+ 
+
+ align:start position:0%
+observer
+so in this activity i invite you to draw
+
+ align:start position:0%
+so in this activity i invite you to draw
+ 
+
+ align:start position:0%
+so in this activity i invite you to draw
+bob's base time diagram into analysis
+
+ align:start position:0%
+bob's base time diagram into analysis
+ 
+
+ align:start position:0%
+bob's base time diagram into analysis
+and then as a second step draw alice's
+
+ align:start position:0%
+and then as a second step draw alice's
+ 
+
+ align:start position:0%
+and then as a second step draw alice's
+space-time diagram into bobs
+
+ align:start position:0%
+space-time diagram into bobs
+ 
+
+ align:start position:0%
+space-time diagram into bobs
+the situation is very similar to
+
+ align:start position:0%
+the situation is very similar to
+ 
+
+ align:start position:0%
+the situation is very similar to
+previous ones discussed in this lecture
+
+ align:start position:0%
+previous ones discussed in this lecture
+ 
+
+ align:start position:0%
+previous ones discussed in this lecture
+alice is stationary and bob moving in
+
+ align:start position:0%
+alice is stationary and bob moving in
+ 
+
+ align:start position:0%
+alice is stationary and bob moving in
+this rocket with a velocity of half the
+
+ align:start position:0%
+this rocket with a velocity of half the
+ 
+
+ align:start position:0%
+this rocket with a velocity of half the
+speed of life light or a gamma factor of
+
+ align:start position:0%
+speed of life light or a gamma factor of
+ 
+
+ align:start position:0%
+speed of life light or a gamma factor of
+1.2
+
+ align:start position:0%
+1.2
+ 
+
+ align:start position:0%
+1.2
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+try go ahead just try to to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+show where is the time axis for bob
+
+ align:start position:0%
+show where is the time axis for bob
+ 
+
+ align:start position:0%
+show where is the time axis for bob
+and where is the spatial coordinate for
+
+ align:start position:0%
+and where is the spatial coordinate for
+ 
+
+ align:start position:0%
+and where is the spatial coordinate for
+bob
+
+ align:start position:0%
+bob
+ 
+
+ align:start position:0%
+bob
+okay so the way to approach this is the
+
+ align:start position:0%
+okay so the way to approach this is the
+ 
+
+ align:start position:0%
+okay so the way to approach this is the
+following we're going to use lawrence
+
+ align:start position:0%
+following we're going to use lawrence
+ 
+
+ align:start position:0%
+following we're going to use lawrence
+transformations
+
+ align:start position:0%
+transformations
+ 
+
+ align:start position:0%
+transformations
+in order to figure out what is the value
+
+ align:start position:0%
+in order to figure out what is the value
+ 
+
+ align:start position:0%
+in order to figure out what is the value
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+of bob's um
+
+ align:start position:0%
+of bob's um
+ 
+
+ align:start position:0%
+of bob's um
+time axis and space space access
+
+ align:start position:0%
+time axis and space space access
+ 
+
+ align:start position:0%
+time axis and space space access
+for different values of alice's
+
+ align:start position:0%
+for different values of alice's
+ 
+
+ align:start position:0%
+for different values of alice's
+space-time diagram so we start with
+
+ align:start position:0%
+space-time diagram so we start with
+ 
+
+ align:start position:0%
+space-time diagram so we start with
+drawing alice's space-time diagram and
+
+ align:start position:0%
+drawing alice's space-time diagram and
+ 
+
+ align:start position:0%
+drawing alice's space-time diagram and
+then if you want to find the x-axis as
+
+ align:start position:0%
+then if you want to find the x-axis as
+ 
+
+ align:start position:0%
+then if you want to find the x-axis as
+seen by bob we have to set the time
+
+ align:start position:0%
+seen by bob we have to set the time
+ 
+
+ align:start position:0%
+seen by bob we have to set the time
+for bob to equal zero
+
+ align:start position:0%
+for bob to equal zero
+ 
+
+ align:start position:0%
+for bob to equal zero
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+find the corresponding
+
+ align:start position:0%
+find the corresponding
+ 
+
+ align:start position:0%
+find the corresponding
+elements or tick marks on the axis so
+
+ align:start position:0%
+elements or tick marks on the axis so
+ 
+
+ align:start position:0%
+elements or tick marks on the axis so
+the first point we want to find is t b
+
+ align:start position:0%
+the first point we want to find is t b
+ 
+
+ align:start position:0%
+the first point we want to find is t b
+equals zero
+
+ align:start position:0%
+equals zero
+ 
+
+ align:start position:0%
+equals zero
+and t b at x e x b equal one
+
+ align:start position:0%
+and t b at x e x b equal one
+ 
+
+ align:start position:0%
+and t b at x e x b equal one
+so with the lawrence transformation we
+
+ align:start position:0%
+so with the lawrence transformation we
+ 
+
+ align:start position:0%
+so with the lawrence transformation we
+find that x a one
+
+ align:start position:0%
+find that x a one
+ 
+
+ align:start position:0%
+find that x a one
+so this point corresponds in alice's
+
+ align:start position:0%
+so this point corresponds in alice's
+ 
+
+ align:start position:0%
+so this point corresponds in alice's
+base time diagram to
+
+ align:start position:0%
+base time diagram to
+ 
+
+ align:start position:0%
+base time diagram to
+xa equal gamma equal 1.2 and t a equal
+
+ align:start position:0%
+xa equal gamma equal 1.2 and t a equal
+ 
+
+ align:start position:0%
+xa equal gamma equal 1.2 and t a equal
+gamma times v over c c square equal 0.6
+
+ align:start position:0%
+gamma times v over c c square equal 0.6
+ 
+
+ align:start position:0%
+gamma times v over c c square equal 0.6
+so we can make this
+
+ align:start position:0%
+so we can make this
+ 
+
+ align:start position:0%
+so we can make this
+find this first point and plot it in our
+
+ align:start position:0%
+find this first point and plot it in our
+ 
+
+ align:start position:0%
+find this first point and plot it in our
+diagram
+
+ align:start position:0%
+diagram
+ 
+
+ align:start position:0%
+diagram
+it's right here
+
+ align:start position:0%
+it's right here
+ 
+
+ align:start position:0%
+it's right here
+okay and then we move around and find
+
+ align:start position:0%
+okay and then we move around and find
+ 
+
+ align:start position:0%
+okay and then we move around and find
+the second point and the third point and
+
+ align:start position:0%
+the second point and the third point and
+ 
+
+ align:start position:0%
+the second point and the third point and
+we do the same for the time axis
+
+ align:start position:0%
+we do the same for the time axis
+ 
+
+ align:start position:0%
+we do the same for the time axis
+where xb is equal to zero and tb equal
+
+ align:start position:0%
+where xb is equal to zero and tb equal
+ 
+
+ align:start position:0%
+where xb is equal to zero and tb equal
+one then corresponds to
+
+ align:start position:0%
+one then corresponds to
+ 
+
+ align:start position:0%
+one then corresponds to
+0.6 in x a1 and 1.2 in xa2 so we find
+
+ align:start position:0%
+0.6 in x a1 and 1.2 in xa2 so we find
+ 
+
+ align:start position:0%
+0.6 in x a1 and 1.2 in xa2 so we find
+these points here
+
+ align:start position:0%
+these points here
+ 
+
+ align:start position:0%
+these points here
+i failed to say that the origin of those
+
+ align:start position:0%
+i failed to say that the origin of those
+ 
+
+ align:start position:0%
+i failed to say that the origin of those
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+space-time diagrams currencies
+
+ align:start position:0%
+space-time diagrams currencies
+ 
+
+ align:start position:0%
+space-time diagrams currencies
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is already it so we found found
+
+ align:start position:0%
+so this is already it so we found found
+ 
+
+ align:start position:0%
+so this is already it so we found found
+bob's time axis where xb is equal to
+
+ align:start position:0%
+bob's time axis where xb is equal to
+ 
+
+ align:start position:0%
+bob's time axis where xb is equal to
+zero and bob's
+
+ align:start position:0%
+zero and bob's
+ 
+
+ align:start position:0%
+zero and bob's
+x-axis where tb is equal 0. and i did
+
+ align:start position:0%
+x-axis where tb is equal 0. and i did
+ 
+
+ align:start position:0%
+x-axis where tb is equal 0. and i did
+draw those
+
+ align:start position:0%
+draw those
+ 
+
+ align:start position:0%
+draw those
+the stick marks
+
+ align:start position:0%
+the stick marks
+ 
+
+ align:start position:0%
+the stick marks
+parallel to the second axis so if i want
+
+ align:start position:0%
+parallel to the second axis so if i want
+ 
+
+ align:start position:0%
+parallel to the second axis so if i want
+to now find out
+
+ align:start position:0%
+to now find out
+ 
+
+ align:start position:0%
+to now find out
+the time axis for x b equal one i just
+
+ align:start position:0%
+the time axis for x b equal one i just
+ 
+
+ align:start position:0%
+the time axis for x b equal one i just
+have to follow along and draw a parallel
+
+ align:start position:0%
+have to follow along and draw a parallel
+ 
+
+ align:start position:0%
+have to follow along and draw a parallel
+um in the picture here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so the second question then is
+
+ align:start position:0%
+all right so the second question then is
+ 
+
+ align:start position:0%
+all right so the second question then is
+where is alice's where alice's axis in
+
+ align:start position:0%
+where is alice's where alice's axis in
+ 
+
+ align:start position:0%
+where is alice's where alice's axis in
+bob's space time direction so the
+
+ align:start position:0%
+bob's space time direction so the
+ 
+
+ align:start position:0%
+bob's space time direction so the
+procedure is very similar as before we
+
+ align:start position:0%
+procedure is very similar as before we
+ 
+
+ align:start position:0%
+procedure is very similar as before we
+draw alice's axis
+
+ align:start position:0%
+draw alice's axis
+ 
+
+ align:start position:0%
+draw alice's axis
+sorry we draw bob's axis and we find
+
+ align:start position:0%
+sorry we draw bob's axis and we find
+ 
+
+ align:start position:0%
+sorry we draw bob's axis and we find
+alex's axis x
+
+ align:start position:0%
+alex's axis x
+ 
+
+ align:start position:0%
+alex's axis x
+x-axis by setting t a equals zero and
+
+ align:start position:0%
+x-axis by setting t a equals zero and
+ 
+
+ align:start position:0%
+x-axis by setting t a equals zero and
+then we find the number of points
+
+ align:start position:0%
+then we find the number of points
+ 
+
+ align:start position:0%
+then we find the number of points
+and connect those and the time axis is
+
+ align:start position:0%
+and connect those and the time axis is
+ 
+
+ align:start position:0%
+and connect those and the time axis is
+found by setting
+
+ align:start position:0%
+found by setting
+ 
+
+ align:start position:0%
+found by setting
+x a equals zero and finding then uh
+
+ align:start position:0%
+x a equals zero and finding then uh
+ 
+
+ align:start position:0%
+x a equals zero and finding then uh
+points for various values of time
+
+ align:start position:0%
+points for various values of time
+ 
+
+ align:start position:0%
+points for various values of time
+and you see here this looks a little
+
+ align:start position:0%
+and you see here this looks a little
+ 
+
+ align:start position:0%
+and you see here this looks a little
+different than before i just zoom in
+
+ align:start position:0%
+different than before i just zoom in
+ 
+
+ align:start position:0%
+different than before i just zoom in
+here a little bit um what you find
+
+ align:start position:0%
+here a little bit um what you find
+ 
+
+ align:start position:0%
+here a little bit um what you find
+specifically because relative the
+
+ align:start position:0%
+specifically because relative the
+ 
+
+ align:start position:0%
+specifically because relative the
+direction of motion changes the positive
+
+ align:start position:0%
+direction of motion changes the positive
+ 
+
+ align:start position:0%
+direction of motion changes the positive
+values of x
+
+ align:start position:0%
+values of x
+ 
+
+ align:start position:0%
+values of x
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+positive values
+
+ align:start position:0%
+positive values
+ 
+
+ align:start position:0%
+positive values
+uh in negative
+
+ align:start position:0%
+uh in negative
+ 
+
+ align:start position:0%
+uh in negative
+the positive values of the x-axis
+
+ align:start position:0%
+the positive values of the x-axis
+ 
+
+ align:start position:0%
+the positive values of the x-axis
+are in the negative time direction where
+
+ align:start position:0%
+are in the negative time direction where
+ 
+
+ align:start position:0%
+are in the negative time direction where
+the negative values of x are in the
+
+ align:start position:0%
+the negative values of x are in the
+ 
+
+ align:start position:0%
+the negative values of x are in the
+positive times the time direction should
+
+ align:start position:0%
+positive times the time direction should
+ 
+
+ align:start position:0%
+positive times the time direction should
+be across bending here so this needs a
+
+ align:start position:0%
+be across bending here so this needs a
+ 
+
+ align:start position:0%
+be across bending here so this needs a
+little bit to get used to but you will
+
+ align:start position:0%
+little bit to get used to but you will
+ 
+
+ align:start position:0%
+little bit to get used to but you will
+later see by now draw
+
+ align:start position:0%
+later see by now draw
+ 
+
+ align:start position:0%
+later see by now draw
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+any of the two space-time diagrams
+
+ align:start position:0%
+any of the two space-time diagrams
+ 
+
+ align:start position:0%
+any of the two space-time diagrams
+specific sequence of events i can
+
+ align:start position:0%
+specific sequence of events i can
+ 
+
+ align:start position:0%
+specific sequence of events i can
+immediately read off
+
+ align:start position:0%
+immediately read off
+ 
+
+ align:start position:0%
+immediately read off
+how this event is perceived from bob's
+
+ align:start position:0%
+how this event is perceived from bob's
+ 
+
+ align:start position:0%
+how this event is perceived from bob's
+and from alice's perspective and this
+
+ align:start position:0%
+and from alice's perspective and this
+ 
+
+ align:start position:0%
+and from alice's perspective and this
+makes those space tag from very very
+
+ align:start position:0%
+makes those space tag from very very
+ 
+
+ align:start position:0%
+makes those space tag from very very
+useful tools
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/mHfn_7ym6to.txt b/mHfn_7ym6to.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0ccd2eb2d7fc2c446697a17bd135787cd216a314
--- /dev/null
+++ b/mHfn_7ym6to.txt
@@ -0,0 +1,2590 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+JOHN TSITSIKLIS: OK.
+
+We can start.
+
+Good morning.
+
+So we're going to start
+now a new unit.
+
+For the next couple of lectures,
+we will be talking
+
+about continuous random
+variables.
+
+So this is new material
+which is not going
+
+to be in the quiz.
+
+You are going to have a long
+break next week without any
+
+lecture, just a quiz and
+recitation and tutorial.
+
+So what's going to happen
+in this new unit?
+
+Basically, we want to do
+everything that we did for
+
+discrete random variables,
+reintroduce the same sort of
+
+concepts but see how they apply
+and how they need to be
+
+modified in order to talk about
+random variables that
+
+take continuous values.
+
+At some level, it's
+all the same.
+
+At some level, it's quite a bit
+harder because when things
+
+are continuous, calculus
+comes in.
+
+So the calculations that you
+have to do on the side
+
+sometimes need a little
+bit more thinking.
+
+In terms of new concepts,
+there's not going to be a
+
+whole lot today, some analogs
+of things we have done.
+
+We're going to introduce the
+concept of cumulative
+
+distribution functions, which
+allows us to deal with
+
+discrete and continuous
+random variables, all
+
+of them in one shot.
+
+And finally, introduce a famous
+kind of continuous
+
+random variable, the normal
+random variable.
+
+OK, so what's the story?
+
+Continuous random variables are
+random variables that take
+
+values over the continuum.
+
+So the numerical value of the
+random variable can be any
+
+real number.
+
+They don't take values just
+in a discrete set.
+
+So we have our sample space.
+
+The experiment happens.
+
+We get some omega, a sample
+point in the sample space.
+
+And once that point is
+determined, it determines the
+
+numerical value of the
+random variable.
+
+Remember, random variables are
+functions on the sample space.
+
+You pick a sample point.
+
+This determines the numerical
+value of the random variable.
+
+So that numerical value is going
+to be some real number
+
+on that line.
+
+Now we want to say something
+about the distribution of the
+
+random variable.
+
+We want to say which values are
+more likely than others to
+
+occur in a certain sense.
+
+For example, you may be
+interested in a particular
+
+event, the event that the random
+variable takes values
+
+in the interval from a to b.
+
+And we want to say something
+about the
+
+probability of that event.
+
+In principle, how
+is this done?
+
+You go back to the sample space,
+and you find all those
+
+outcomes for which the value of
+the random variable happens
+
+to be in that interval.
+
+The probability that the random
+variable falls here is
+
+the same as the probability of
+all outcomes that make the
+
+random variable to
+fall in there.
+
+So in principle, you can work on
+the original sample space,
+
+find the probability of this
+event, and you would be done.
+
+But similar to what happened in
+chapter 2, we want to kind
+
+of push the sample space in the
+background and just work
+
+directly on the real
+axis and talk about
+
+probabilities up here.
+
+So we want now a way to specify
+probabilities, how
+
+they are bunched together, or
+arranged, along the real line.
+
+So what did we do for discrete
+random variables?
+
+We introduced PMFs, probability
+mass functions.
+
+And the way that we described
+the random variable was by
+
+saying this point has so much
+mass on top of it, that point
+
+has so much mass on top
+of it, and so on.
+
+And so we assigned a total
+amount of 1 unit of
+
+probability.
+
+We assigned it to different
+masses, which we put at
+
+different points on
+the real axis.
+
+So that's what you do if
+somebody gives you a pound of
+
+discrete stuff, a pound of
+mass in little chunks.
+
+And you place those chunks
+at a few points.
+
+Now, in the continuous case,
+this total unit of probability
+
+mass does not sit just on
+discrete points but is spread
+
+all over the real axis.
+
+So now we're going to have a
+unit of mass that spreads on
+
+top of the real axis.
+
+How do we describe masses that
+are continuously spread?
+
+The way we describe them is
+by specifying densities.
+
+That is, how thick is the mass
+that's sitting here?
+
+How dense is the mass that's
+sitting there?
+
+So that's exactly what
+we're going to do.
+
+We're going to introduce the
+concept of a probability
+
+density function that tells us
+how probabilities accumulate
+
+at different parts
+of the real axis.
+
+So here's an example or a
+picture of a possible
+
+probability density function.
+
+What does that density function
+kind of convey
+
+intuitively?
+
+Well, that these x's
+are relatively
+
+less likely to occur.
+
+Those x's are somewhat more
+likely to occur because the
+
+density is higher.
+
+Now, for a more formal
+definition, we're going to say
+
+that a random variable X is said
+to be continuous if it
+
+can be described by a
+density function in
+
+the following sense.
+
+We have a density function.
+
+And we calculate probabilities
+of falling inside an interval
+
+by finding the area under
+the curve that sits
+
+on top of that interval.
+
+So that's sort of the defining
+relation for
+
+continuous random variables.
+
+It's an implicit definition.
+
+And it tells us a random
+variable is continuous if we
+
+can calculate probabilities
+this way.
+
+So the probability of falling
+in this interval is the area
+
+under this curve.
+
+Mathematically, it's the
+integral of the density over
+
+this particular interval.
+
+If the density happens to be
+constant over that interval,
+
+the area under the curve would
+be the length of the interval
+
+times the height of
+the density, which
+
+sort of makes sense.
+
+Now, because the density is not
+constant but it kind of
+
+moves around, what you need is
+to write down an integral.
+
+Now, this formula is very much
+analogous to what you would do
+
+for discrete random variables.
+
+For a discrete random variable,
+how do you calculate
+
+this probability?
+
+You look at all x's
+in this interval.
+
+And you add the probability mass
+function over that range.
+
+So just for comparison, this
+would be the formula for the
+
+discrete case--
+
+the sum over all x's in the
+interval from a to b over the
+
+probability mass function.
+
+And there is a syntactic analogy
+that's happening here
+
+and which will be a persistent
+theme when we deal with
+
+continuous random variables.
+
+Sums get replaced
+by integrals.
+
+In the discrete case, you add.
+
+In the continuous case,
+you integrate.
+
+Mass functions get replaced
+by density functions.
+
+So you can take pretty much any
+formula from the discrete
+
+case and translate it to a
+continuous analog of that
+
+formula, as we're
+going to see.
+
+OK.
+
+So let's take this
+now as our model.
+
+What is the probability that
+the random variable takes a
+
+specific value if we have a
+continuous random variable?
+
+Well, this would be the case.
+
+It's a case of a trivial
+interval, where the two end
+
+points coincide.
+
+So it would be the integral
+from a to itself.
+
+So you're integrating just
+over a single point.
+
+Now, when you integrate over
+a single point, the
+
+integral is just 0.
+
+The area under the curve, if
+you're only looking at a
+
+single point, it's 0.
+
+So big property of continuous
+random variables is that any
+
+individual point has
+0 probability.
+
+In particular, when you look at
+the value of the density,
+
+the density does not tell you
+the probability of that point.
+
+The point itself has
+0 probability.
+
+So the density tells you
+something a little different.
+
+We are going to see shortly
+what that is.
+
+Before we get there,
+can the density be
+
+an arbitrary function?
+
+Almost, but not quite.
+
+There are two things
+that we want.
+
+First, since densities
+are used to calculate
+
+probabilities, and since
+probabilities must be
+
+non-negative, the density should
+also be non-negative.
+
+Otherwise you would be getting
+negative probabilities, which
+
+is not a good thing.
+
+So that's a basic property
+that any density function
+
+should obey.
+
+The second property that we
+need is that the overall
+
+probability of the entire real
+line should be equal to 1.
+
+So if you ask me, what is the
+probability that x falls
+
+between minus infinity and plus
+infinity, well, we are
+
+sure that x is going to
+fall in that range.
+
+So the probability of that
+event should be 1.
+
+So the probability of being
+between minus infinity and
+
+plus infinity should be 1, which
+means that the integral
+
+from minus infinity to plus
+infinity should be 1.
+
+So that just tells us that
+there's 1 unit of total
+
+probability that's being
+spread over our space.
+
+Now, what's the best way to
+think intuitively about what
+
+the density function does?
+
+The interpretation that I find
+most natural and easy to
+
+convey the meaning of a
+density is to look at
+
+probabilities of small
+intervals.
+
+So let us take an x somewhere
+here and then x plus delta
+
+just next to it.
+
+So delta is a small number.
+
+And let's look at the
+probability of the event that
+
+we get a value in that range.
+
+For continuous random variables,
+the way we find the
+
+probability of falling in that
+range is by integrating the
+
+density over that range.
+
+So we're drawing this picture.
+
+And we want to take the
+area under this curve.
+
+Now, what happens if delta
+is a fairly small number?
+
+If delta is pretty small, our
+density is not going to change
+
+much over that range.
+
+So you can pretend that
+the density is
+
+approximately constant.
+
+And so to find the area under
+the curve, you just take the
+
+base times the height.
+
+And it doesn't matter where
+exactly you take the height in
+
+that interval, because the
+density doesn't change very
+
+much over that interval.
+
+And so the integral becomes just
+base times the height.
+
+So for small intervals, the
+probability of a small
+
+interval is approximately
+the density times delta.
+
+So densities essentially
+give us
+
+probabilities of small intervals.
+
+And if you want to think about
+it a little differently, you
+
+can take that delta from
+here and send it to
+
+the denominator there.
+
+And what this tells you
+is that the density is
+
+probability per unit length for
+intervals of small length.
+
+So the units of density are
+probability per unit length.
+
+Densities are not
+probabilities.
+
+They are rates at which
+probabilities accumulate,
+
+probabilities per unit length.
+
+And since densities are not
+probabilities, they don't have
+
+to be less than 1.
+
+Ordinary probabilities always
+must be less than 1.
+
+But density is a different
+kind of thing.
+
+It can get pretty big
+in some places.
+
+It can even sort of blow
+up in some places.
+
+As long as the total area under
+the curve is 1, other
+
+than that, the curve can do
+anything that it wants.
+
+Now, the density prescribes
+for us the
+
+probability of intervals.
+
+Sometimes we may want to find
+the probability of more
+
+general sets.
+
+How would we do that?
+
+Well, for nice sets, you will
+just integrate the density
+
+over that nice set.
+
+I'm not quite defining
+what "nice" means.
+
+That's a pretty technical
+topic in the theory of
+
+probability.
+
+But for our purposes, usually we
+will take b to be something
+
+like a union of intervals.
+
+So how do you find the
+probability of falling in the
+
+union of two intervals?
+
+Well, you find the probability
+of falling in that interval
+
+plus the probability of falling
+in that interval.
+
+So it's the integral over this
+interval plus the integral
+
+over that interval.
+
+And you think of this as just
+integrating over the union of
+
+the two intervals.
+
+So once you can calculate
+probabilities of intervals,
+
+then usually you are in
+business, and you can
+
+calculate anything else
+you might want.
+
+So the probability density
+function is a complete
+
+description of any statistical
+information we might be
+
+interested in for a continuous
+random variable.
+
+OK.
+
+So now we can start walking
+through the concepts and the
+
+definitions that we have for
+discrete random variables and
+
+translate them to the
+continuous case.
+
+The first big concept is the
+concept of the expectation.
+
+One can start with a
+mathematical definition.
+
+And here we put down
+a definition by
+
+just translating notation.
+
+Wherever we have a sum in
+the discrete case, we
+
+now write an integral.
+
+And wherever we had the
+probability mass function, we
+
+now throw in the probability
+density function.
+
+This formula--
+
+you may have seen it in
+freshman physics--
+
+basically, it again gives you
+the center of gravity of the
+
+picture that you have when
+you have the density.
+
+It's the center of gravity of
+the object sitting underneath
+
+the probability density
+function.
+
+So that the interpretation
+still applies.
+
+It's also true that our
+conceptual interpretation of
+
+what an expectation means is
+also valid in this case.
+
+That is, if you repeat an
+experiment a zillion times,
+
+each time drawing an independent
+sample of your
+
+random variable x, in the long
+run, the average that you are
+
+going to get should be
+the expectation.
+
+One can reason in a hand-waving
+way, sort of
+
+intuitively, the way we did it
+for the case of discrete
+
+random variables.
+
+But this is also a theorem
+of some sort.
+
+It's a limit theorem that we're
+going to visit later on
+
+in this class.
+
+Having defined the expectation
+and having claimed that the
+
+interpretation of the
+expectation is that same as
+
+before, then we can start taking
+just any formula you've
+
+seen before and just
+translate it.
+
+So for example, to find the
+expected value of a function
+
+of a continuous random variable,
+you do not have to
+
+find the PDF or PMF of g(X).
+
+You can just work directly with
+the original distribution
+
+of the random variable
+capital X.
+
+And this formula is the same
+as for the discrete case.
+
+Sums get replaced
+by integrals.
+
+And PMFs get replaced by PDFs.
+
+And in particular, the variance
+of a random variable
+
+is defined again the same way.
+
+The variance is the expected
+value, the average of the
+
+distance of X from the mean
+and then squared.
+
+So it's the expected value for
+a random variable that takes
+
+these numerical values.
+
+And same formula as before,
+integral and F instead of
+
+summation, and the P.
+
+And the formulas that we have
+derived or formulas that you
+
+have seen for the discrete case,
+they all go through the
+
+continuous case.
+
+So for example, the useful
+relation for variances, which
+
+is this one, remains true.
+
+All right.
+
+So time for an example.
+
+The most simple example of a
+continuous random variable
+
+that there is, is the so-called
+
+uniform random variable.
+
+So the uniform random variable
+is described by a density
+
+which is 0 except over
+an interval.
+
+And over that interval,
+it is constant.
+
+What is it meant to convey?
+
+It's trying to convey the idea
+that all x's in this range are
+
+equally likely.
+
+Well, that doesn't
+say very much.
+
+Any individual x has
+0 probability.
+
+So it's conveying a little
+more than that.
+
+What it is saying is that if I
+take an interval of a given
+
+length delta, and I take another
+interval of the same
+
+length, delta, under the uniform
+distribution, these
+
+two intervals are going to have
+the same probability.
+
+So being uniform means that
+intervals of same length have
+
+the same probability.
+
+So no interval is more likely
+than any other to occur.
+
+And in that sense, it conveys
+the idea of sort of complete
+
+randomness.
+
+Any little interval in our range
+is equally likely as any
+
+other little interval.
+
+All right.
+
+So what's the formula
+for this density?
+
+I only told you the range.
+
+What's the height?
+
+Well, the area under the density
+must be equal to 1.
+
+Total probability
+is equal to 1.
+
+And so the height, inescapably,
+is going to be 1
+
+over (b minus a).
+
+That's the height that makes
+the density integrate to 1.
+
+So that's the formula.
+
+And if you don't want to lose
+one point in your exam, you
+
+have to say that it's
+also 0, otherwise.
+
+OK.
+
+All right?
+
+That's sort of the
+complete answer.
+
+How about the expected value
+of this random variable?
+
+OK.
+
+You can find the expected value
+in two different ways.
+
+One is to start with
+the definition.
+
+And so you integrate
+over the range of
+
+interest times the density.
+
+And you figure out what that
+integral is going to be.
+
+Or you can be a little
+more clever.
+
+Since the center-of-gravity
+interpretation is still true,
+
+it must be the center of gravity
+of this picture.
+
+And the center of gravity is,
+of course, the midpoint.
+
+Whenever you have symmetry,
+the mean is always the
+
+midpoint of the diagram that
+gives you the PDF.
+
+OK.
+
+So that's the expected
+value of X.
+
+Finally, regarding the variance,
+well, there you will
+
+have to do a little
+bit of calculus.
+
+We can write down
+the definition.
+
+So it's an integral
+instead of a sum.
+
+A typical value of the random
+variable minus the expected
+
+value, squared, times
+the density.
+
+And we integrate.
+
+You do this integral, and you
+find it's (b minus a) squared
+
+over that number, which
+happens to be 12.
+
+Maybe more interesting is the
+standard deviation itself.
+
+And you see that the standard
+deviation is proportional to
+
+the width of that interval.
+
+This agrees with our intuition,
+that the standard
+
+deviation is meant to capture a
+sense of how spread out our
+
+distribution is.
+
+And the standard deviation has
+the same units as the random
+
+variable itself.
+
+So it's sort of good to-- you
+can interpret it in a
+
+reasonable way based
+on that picture.
+
+OK, yes.
+
+Now, let's go up one level and
+think about the following.
+
+So we have formulas for the
+discrete case, formulas for
+
+the continuous case.
+
+So you can write them
+side by side.
+
+One has sums, the other
+has integrals.
+
+Suppose you want to make an
+argument and say that
+
+something is true for every
+random variable.
+
+You would essentially need to
+do two separate proofs, for
+
+discrete and for continuous.
+
+Is there some way of dealing
+with random variables just one
+
+at a time, in one shot, using
+a sort of uniform notation?
+
+Is there a unifying concept?
+
+Luckily, there is one.
+
+It's the notion of the
+cumulative distribution
+
+function of a random variable.
+
+And it's a concept that applies
+equally well to
+
+discrete and continuous
+random variables.
+
+So it's an object that we can
+use to describe distributions
+
+in both cases, using just
+one piece of notation.
+
+So what's the definition?
+
+It's the probability that the
+random variable takes values
+
+less than a certain
+number little x.
+
+So you go to the diagram, and
+you see what's the probability
+
+that I'm falling to
+the left of this.
+
+And you specify those
+probabilities for all x's.
+
+In the continuous case, you
+calculate those probabilities
+
+using the integral formula.
+
+So you integrate from
+here up to x.
+
+In the discrete case, to find
+the probability to the left of
+
+some point, you go here, and
+you add probabilities again
+
+from the left.
+
+So the way that the cumulative
+distribution function is
+
+calculated is a little different
+in the continuous
+
+and discrete case.
+
+In one case you integrate.
+
+In the other, you sum.
+
+But leaving aside how it's being
+calculated, what the
+
+concept is, it's the same
+concept in both cases.
+
+So let's see what the shape of
+the cumulative distribution
+
+function would be in
+the two cases.
+
+So here what we want is to
+record for every little x the
+
+probability of falling
+to the left of x.
+
+So let's start here.
+
+Probability of falling to
+the left of here is 0--
+
+0, 0, 0.
+
+Once we get here and we start
+moving to the right, the
+
+probability of falling to the
+left of here is the area of
+
+this little rectangle.
+
+And the area of that little
+rectangle increases linearly
+
+as I keep moving.
+
+So accordingly, the CDF
+increases linearly until I get
+
+to that point.
+
+At that point, what's
+the value of my CDF?
+
+1.
+
+I have accumulated all the
+probability there is.
+
+I have integrated it.
+
+This total area has
+to be equal to 1.
+
+So it reaches 1, and then
+there's no more probability to
+
+be accumulated.
+
+It just stays at 1.
+
+So the value here
+is equal to 1.
+
+OK.
+
+How would you find the density
+if somebody gave you the CDF?
+
+The CDF is the integral
+of the density.
+
+Therefore, the density is the
+derivative of the CDF.
+
+So you look at this picture
+and take the derivative.
+
+Derivative is 0 here, 0 here.
+
+And it's a constant
+up there, which
+
+corresponds to that constant.
+
+So more generally, and an
+important thing to know, is
+
+that the derivative of the CDF
+is equal to the density--
+
+almost, with a little
+bit of an exception.
+
+What's the exception?
+
+At those places where the CDF
+does not have a derivative--
+
+here where it has a corner--
+
+the derivative is undefined.
+
+And in some sense, the
+density is also
+
+ambiguous at that point.
+
+Is my density at the endpoint,
+is it 0 or is it 1?
+
+It doesn't really matter.
+
+If you change the density at
+just a single point, it's not
+
+going to affect the
+value of any
+
+integral you ever calculate.
+
+So the value of the density at
+the endpoint, you can leave it
+
+as being ambiguous, or
+you can specify it.
+
+It doesn't matter.
+
+So at all places where the
+CDF has a derivative,
+
+this will be true.
+
+At those places where you have
+corners, which do show up
+
+sometimes, well, you
+don't really care.
+
+How about the discrete case?
+
+In the discrete case, the CDF
+has a more peculiar shape.
+
+So let's do the calculation.
+
+We want to find the
+probability of b
+
+to the left of here.
+
+That probability is 0, 0, 0.
+
+Once we cross that point, the
+probability of being to the
+
+left of here is 1/6.
+
+So as soon as we cross the
+point 1, we get the
+
+probability of 1/6, which means
+that the size of the
+
+jump that we have here is 1/6.
+
+Now, question.
+
+At this point 1, which is the
+correct value of the CDF?
+
+Is it 0, or is it 1/6?
+
+It's 1/6 because--
+
+you need to look carefully
+at the definitions, the
+
+probability of x being less
+than or equal to little x.
+
+If I take little x to be 1,
+it's the probability that
+
+capital X is less than
+or equal to 1.
+
+So it includes the event
+that x is equal to 1.
+
+So it includes this
+probability here.
+
+So at jump points, the correct
+value of the CDF is going to
+
+be this one.
+
+And now as I trace, x is
+going to the right.
+
+As soon as I cross this point,
+I have added another 3/6
+
+probability.
+
+So that 3/6 causes a
+jump to the CDF.
+
+And that determines
+the new value.
+
+And finally, once I cross
+the last point, I get
+
+another jump of 2/6.
+
+A general moral from these two
+examples and these pictures.
+
+CDFs are well defined
+in both cases.
+
+For the case of continuous
+random variables, the CDF will
+
+be a continuous function.
+
+It starts from 0.
+
+It eventually goes to 1
+and goes smoothly--
+
+well, continuously from smaller
+to higher values.
+
+It can only go up.
+
+It cannot go down since we're
+accumulating more and more
+
+probability as we are
+going to the right.
+
+In the discrete case, again
+it starts from 0,
+
+and it goes to 1.
+
+But it does it in a
+staircase manner.
+
+And you get a jump at each place
+where the PMF assigns a
+
+positive mass.
+
+So jumps in the CDF are
+associated with point masses
+
+in our distribution.
+
+In the continuous case, we don't
+have any point masses,
+
+so we do not have any
+jumps either.
+
+Now, besides saving
+us notation--
+
+we don't have to deal
+with discrete
+
+and continuous twice--
+
+CDFs give us actually a little
+more flexibility.
+
+Not all random variables are
+continuous or discrete.
+
+You can cook up random variables
+that are kind of
+
+neither or a mixture
+of the two.
+
+An example would be, let's
+say you play a game.
+
+And with a certain probability,
+you get a certain
+
+number of dollars
+in your hands.
+
+So you flip a coin.
+
+And with probability 1/2, you
+get a reward of 1/2 dollars.
+
+And with probability 1/2, you
+are led to a dark room where
+
+you spin a wheel of fortune.
+
+And that wheel of fortune gives
+you a random reward
+
+between 0 and 1.
+
+So any of these outcomes
+is possible.
+
+And the amount that you're
+going to get,
+
+let's say, is uniform.
+
+So you flip a coin.
+
+And depending on the outcome of
+the coin, either you get a
+
+certain value or you get a
+value that ranges over a
+
+continuous interval.
+
+So what kind of random
+variable is it?
+
+Is it continuous?
+
+Well, continuous random
+variables assign 0 probability
+
+to individual points.
+
+Is it the case here?
+
+No, because you have positive
+probability of
+
+obtaining 1/2 dollar.
+
+So our random variable
+is not continuous.
+
+Is it discrete?
+
+It's not discrete, because our
+random variable can take
+
+values also over a
+continuous range.
+
+So we call such a random
+variable a
+
+mixed random variable.
+
+If you were to draw its
+distribution very loosely,
+
+probably you would want to draw
+a picture like this one,
+
+which kind of conveys the
+idea of what's going on.
+
+So just think of this as a
+drawing of masses that are
+
+sitting over a table.
+
+We place an object that weighs
+half a pound, but it's an
+
+object that takes zero space.
+
+So half a pound is just sitting
+on top of that point.
+
+And we take another half-pound
+of probability and spread it
+
+uniformly over that interval.
+
+So this is like a piece that
+comes from mass functions.
+
+And that's a piece that looks
+more like a density function.
+
+And we just throw them together
+in the picture.
+
+I'm not trying to associate
+any formal
+
+meaning with this picture.
+
+It's just a schematic of how
+probabilities are distributed,
+
+help us visualize
+what's going on.
+
+Now, if you have taken classes
+on systems and all of that,
+
+you may have seen the concept
+of an impulse function.
+
+And you my start saying that,
+oh, I should treat this
+
+mathematically as a so-called
+impulse function.
+
+But we do not need this for our
+purposes in this class.
+
+Just think of this as a nice
+picture that conveys what's
+
+going on in this particular
+case.
+
+So now, what would the CDF
+look like in this case?
+
+The CDF is always well defined,
+no matter what kind
+
+of random variable you have.
+
+So the fact that it's not
+continuous, it's not discrete
+
+shouldn't be a problem as
+long as we can calculate
+
+probabilities of this kind.
+
+So the probability of falling
+to the left here is 0.
+
+Once I start crossing there, the
+probability of falling to
+
+the left of a point increases
+linearly with
+
+how far I have gone.
+
+So we get this linear
+increase.
+
+But as soon as I cross that
+point, I accumulate another
+
+1/2 unit of probability
+instantly.
+
+And once I accumulate that 1/2
+unit, it means that my CDF is
+
+going to have a jump of 1/2.
+
+And then afterwards, I still
+keep accumulating probability
+
+at a fixed rate, the rate
+being the density.
+
+And I keep accumulating, again,
+at a linear rate until
+
+I settle to 1.
+
+So this is a CDF that has
+certain pieces where it
+
+increases continuously.
+
+And that corresponds to the
+continuous part of our
+
+randomize variable.
+
+And it also has some places
+where it has discrete jumps.
+
+And those district jumps
+correspond to places in which
+
+we have placed a
+positive mass.
+
+And by the--
+
+OK, yeah.
+
+So this little 0 shouldn't
+be there.
+
+So let's cross it out.
+
+All right.
+
+So finally, we're going to take
+the remaining time and
+
+introduce our new friend.
+
+It's going to be the Gaussian
+or normal distribution.
+
+So it's the most important
+distribution there is in all
+
+of probability theory.
+
+It's plays a very
+central role.
+
+It shows up all over
+the place.
+
+We'll see later in the
+class in more detail
+
+why it shows up.
+
+But the quick preview
+is the following.
+
+If you have a phenomenon in
+which you measure a certain
+
+quantity, but that quantity is
+made up of lots and lots of
+
+random contributions--
+
+so your random variable is
+actually the sum of lots and
+
+lots of independent little
+random variables--
+
+then invariability, no matter
+what kind of distribution the
+
+little random variables have,
+their sum will turn out to
+
+have approximately a normal
+distribution.
+
+So this makes the normal
+distribution to arise very
+
+naturally in lots and
+lots of contexts.
+
+Whenever you have noise that's
+comprised of lots of different
+
+independent pieces of noise,
+then the end result will be a
+
+random variable that's normal.
+
+So we are going to come back
+to that topic later.
+
+But that's the preview comment,
+basically to argue
+
+that it's an important one.
+
+OK.
+
+And there's a special case.
+
+If you are dealing with a
+binomial distribution, which
+
+is the sum of lots of Bernoulli
+random variables,
+
+again you would expect that
+the binomial would start
+
+looking like a normal if you
+have many, many-- a large
+
+number of point fields.
+
+All right.
+
+So what's the math
+involved here?
+
+Let's parse the formula for
+the density of the normal.
+
+What we start with is the
+function X squared over 2.
+
+And if you are to plot X
+squared over 2, it's a
+
+parabola, and it has
+this shape --
+
+X squared over 2.
+
+Then what do we do?
+
+We take the negative exponential
+of this.
+
+So when X squared over
+2 is 0, then negative
+
+exponential is 1.
+
+When X squared over 2 increases,
+the negative
+
+exponential of that falls off,
+and it falls off pretty fast.
+
+So as this goes up, the
+formula for the
+
+density goes down.
+
+And because exponentials are
+pretty strong in how quickly
+
+they fall off, this means that
+the tails of this distribution
+
+actually do go down
+pretty fast.
+
+OK.
+
+So that explains the shape
+of the normal PDF.
+
+How about this factor 1
+over square root 2 pi?
+
+Where does this come from?
+
+Well, the integral has
+to be equal to 1.
+
+So you have to go and do your
+calculus exercise and find the
+
+integral of this the minus X
+squared over 2 function and
+
+then figure out, what constant
+do I need to put in front so
+
+that the integral
+is equal to 1?
+
+How do you evaluate
+that integral?
+
+Either you go to Mathematica
+or Wolfram's Alpha or
+
+whatever, and it tells
+you what it is.
+
+Or it's a very beautiful
+calculus exercise that you may
+
+have seen at some point.
+
+You throw in another exponential
+of this kind, you
+
+bring in polar coordinates, and
+somehow the answer comes
+
+beautifully out there.
+
+But in any case, this is the
+constant that you need to make
+
+it integrate to 1 and to be
+a legitimate density.
+
+We call this the standard
+normal.
+
+And for the standard normal,
+what is the expected value?
+
+Well, the symmetry, so
+it's equal to 0.
+
+What is the variance?
+
+Well, here there's
+no shortcut.
+
+You have to do another
+calculus exercise.
+
+And you find that the variance
+is equal to 1.
+
+OK.
+
+So this is a normal that's
+centered around 0.
+
+How about other types of normals
+that are centered at
+
+different places?
+
+So we can do the same
+kind of thing.
+
+Instead of centering it at 0,
+we can take some place where
+
+we want to center it, write down
+a quadratic such as (X
+
+minus mu) squared, and then
+take the negative
+
+exponential of that.
+
+And that gives us a normal
+density that's centered at mu.
+
+Now, I may wish to control
+the width of my density.
+
+To control the width of my
+density, equivalently I can
+
+control the width
+of my parabola.
+
+If my parabola is narrower, if
+my parabola looks like this,
+
+what's going to happen
+to the density?
+
+It's going to fall
+off much faster.
+
+OK.
+
+How do I make my parabola
+narrower or wider?
+
+I do it by putting in a
+constant down here.
+
+So by putting a sigma here, this
+stretches or widens my
+
+parabola by a factor of sigma.
+
+Let's see.
+
+Which way does it go?
+
+If sigma is very small,
+this is a big number.
+
+My parabola goes up quickly,
+which means my normal falls
+
+off very fast.
+
+So small sigma corresponds
+to a narrower density.
+
+And so it, therefore, should be
+intuitive that the standard
+
+deviation is proportional
+to sigma.
+
+Because that's the amount
+by which you
+
+are scaling the picture.
+
+And indeed, the standard
+deviation is sigma.
+
+And so the variance
+is sigma squared.
+
+So all that we have done here
+to create a general normal
+
+with a given mean and variance
+is to take this picture, shift
+
+it in space so that the mean
+sits at mu instead of 0, and
+
+then scale it by a
+factor of sigma.
+
+This gives us a normal
+with a given
+
+mean and a given variance.
+
+And the formula for
+it is this one.
+
+All right.
+
+Now, normal random variables
+have some wonderful
+
+properties.
+
+And one of them is that they
+behave nicely when you take
+
+linear functions of them.
+
+So let's fix some constants
+a and b, suppose that X is
+
+normal, and look at this
+linear function Y.
+
+What is the expected
+value of Y?
+
+Here we don't need
+anything special.
+
+We know that the expected value
+of a linear function is
+
+the linear function of
+the expectation.
+
+So the expected value is this.
+
+How about the variance?
+
+We know that the variance of a
+linear function doesn't care
+
+about the constant term.
+
+But the variance gets multiplied
+by a squared.
+
+So we get these variance, where
+sigma squared is the
+
+variance of the original
+normal.
+
+So have we used so far the
+property that X is normal?
+
+No, we haven't.
+
+This calculation here is true
+in general when you take a
+
+linear function of a
+random variable.
+
+But if X is normal, we get the
+other additional fact that Y
+
+is also going to be normal.
+
+So that's the nontrivial
+part of the fact that
+
+I'm claiming here.
+
+So linear functions of normal
+random variables are
+
+themselves normal.
+
+How do we convince ourselves
+about it?
+
+OK.
+
+It's something that we will do
+formerly in about two or three
+
+lectures from today.
+
+So we're going to prove it.
+
+But if you think about it
+intuitively, normal means this
+
+particular bell-shaped curve.
+
+And that bell-shaped curve could
+be sitting anywhere and
+
+could be scaled in any way.
+
+So you start with a
+bell-shaped curve.
+
+If you take X, which is bell
+shaped, and you multiply it by
+
+a constant, what does that do?
+
+Multiplying by a constant is
+just like scaling the axis or
+
+changing the units with which
+you're measuring it.
+
+So it will take a bell shape
+and spread it or narrow it.
+
+But it will still
+be a bell shape.
+
+And then when you add the
+constant, you just take that
+
+bell and move it elsewhere.
+
+So under linear transformations,
+bell shapes
+
+will remain bell shapes, just
+sitting at a different place
+
+and with a different width.
+
+And that sort of the intuition
+of why normals remain normals
+
+under this kind of
+transformation.
+
+So why is this useful?
+
+Well, OK.
+
+We have a formula
+for the density.
+
+But usually we want to calculate
+probabilities.
+
+How will you calculate
+probabilities?
+
+If I ask you, what's the
+probability that the normal is
+
+less than 3, how
+do you find it?
+
+You need to integrate the
+density from minus
+
+infinity up to 3.
+
+Unfortunately, the integral of
+the expression that shows up
+
+that you would have to
+calculate, an integral of this
+
+kind from, let's say, minus
+infinity to some number, is
+
+something that's not known
+in closed form.
+
+So if you're looking for a
+closed-form formula for this--
+
+X bar--
+
+if you're looking for a
+closed-form formula that gives
+
+you the value of this integral
+as a function of X bar, you're
+
+not going to find it.
+
+So what can we do?
+
+Well, since it's a useful
+integral, we can
+
+just tabulate it.
+
+Calculate it once and for all,
+for all values of X bar up to
+
+some precision, and have
+that table, and use it.
+
+That's what one does.
+
+OK, but now there is a catch.
+
+Are we going to write down a
+table for every conceivable
+
+type of normal distribution--
+
+that is, for every possible
+mean and every variance?
+
+I guess that would be
+a pretty long table.
+
+You don't want to do that.
+
+Fortunately, it's enough to
+have a table with the
+
+numerical values only for
+the standard normal.
+
+And once you have those, you can
+use them in a clever way
+
+to calculate probabilities for
+the more general case.
+
+So let's see how this is done.
+
+So our starting point is that
+someone has graciously
+
+calculated for us the values
+of the CDF, the cumulative
+
+distribution function, that is
+the probability of falling
+
+below a certain point for
+the standard normal
+
+and at various places.
+
+How do we read this table?
+
+The probability that X is
+less than, let's say,
+
+0.63 is this number.
+
+This number, 0.7357, is the
+probability that the standard
+
+normal is below 0.63.
+
+So the table refers to
+the standard normal.
+
+But someone, let's say, gives
+us some other numbers and
+
+tells us we're dealing with a
+normal with a certain mean and
+
+a certain variance.
+
+And we want to calculate the
+probability that the value of
+
+that random variable is less
+than or equal to 3.
+
+How are we going to do it?
+
+Well, there's a standard trick,
+which is so-called
+
+standardizing a random
+variable.
+
+Standardizing a random variable
+
+stands for the following.
+
+You look at the random
+variable, and you
+
+subtract the mean.
+
+This makes it a random
+variable with 0 mean.
+
+And then if I divide by the
+standard deviation, what
+
+happens to the variance of
+this random variable?
+
+Dividing by a number divides the
+variance by sigma squared.
+
+The original variance of
+X was sigma squared.
+
+So when I divide by sigma, I
+end up with unit variance.
+
+So after I do this
+transformation, I get a random
+
+variable that has 0 mean
+and unit variance.
+
+It is also normal.
+
+Why is its normal?
+
+Because this expression is a
+linear function of the X that
+
+I started with.
+
+It's a linear function of a
+normal random variable.
+
+Therefore, it is normal.
+
+And it is a standard normal.
+
+So by taking a general normal
+random variable and doing this
+
+standardization, you end up
+with a standard normal to
+
+which you can then
+apply the table.
+
+Sometimes one calls this
+the normalized score.
+
+If you're thinking about test
+results, how would you
+
+interpret this number?
+
+It tells you how many standard
+deviations are you
+
+away from the mean.
+
+This is how much you are
+away from the mean.
+
+And you count it in terms
+of how many standard
+
+deviations it is.
+
+So this number being equal to 3
+tells you that X happens to
+
+be 3 standard deviations
+above the mean.
+
+And I guess if you're looking
+at your quiz scores, very
+
+often that's the kind of number
+that you think about.
+
+So it's a useful quantity.
+
+But it's also useful for doing
+the calculation we're now
+
+going to do.
+
+So suppose that X has a mean of
+2 and a variance of 16, so
+
+a standard deviation of 4.
+
+And we're going to calculate the
+probability of this event.
+
+This event is described in terms
+of this X that has ugly
+
+means and variances.
+
+But we can take this event
+and rewrite it as
+
+an equivalent event.
+
+X less than 3 is this same as
+X minus 2 being less than 3
+
+minus 2, which is the same as
+this ratio being less than
+
+that ratio.
+
+So I'm subtracting from both
+sides of the inequality the
+
+mean and then dividing by
+the standard deviation.
+
+This event is the same
+as that event.
+
+Why do we like this
+better than that?
+
+We like it because this is the
+standardized, or normalized,
+
+version of X. We know that
+this is standard normal.
+
+And so we're asking the
+question, what's the
+
+probability that the standard
+normal is less than this
+
+number, which is 1/4?
+
+So that's the key property, that
+this is normal (0, 1).
+
+And so we can look up now with
+the table and ask for the
+
+probability that the standard
+normal random variable
+
+is less than 0.25.
+
+Where is that going to be?
+
+0.2, 0.25, it's here.
+
+So the answer is 0.987.
+
+So I guess this is just a drill
+that you could learn in
+
+high school.
+
+You didn't have to come here
+to learn about it.
+
+But it's a drill that's very
+useful when we will be
+
+calculating normal probabilities
+all the time.
+
+So make sure you know how to
+use the table and how to
+
+massage a general normal
+random variable into a
+
+standard normal random
+variable.
+
+OK.
+
+So just one more minute to look
+at the big picture and
+
+take stock of what we
+have done so far
+
+and where we're going.
+
+Chapter 2 was this part of the
+picture, where we dealt with
+
+discrete random variables.
+
+And this time, today, we
+started talking about
+
+continuous random variables.
+
+And we introduced the density
+function, which is the analog
+
+of the probability
+mass function.
+
+We have the concepts
+of expectation and
+
+variance and CDF.
+
+And this kind of notation
+applies to both discrete and
+
+continuous cases.
+
+They are calculated the same way
+in both cases except that
+
+in the continuous case,
+you use sums.
+
+In the discrete case,
+you use integrals.
+
+So on that side, you
+have integrals.
+
+In this case, you have sums.
+
+In this case, you always have
+Fs in your formulas.
+
+In this case, you always have
+Ps in your formulas.
+
+So what's there that's left
+for us to do is to look at
+
+these two concepts, joint
+probability mass functions and
+
+conditional mass functions, and
+figure out what would be
+
+the equivalent concepts on
+the continuous side.
+
+So we will need some notion of
+a joint density when we're
+
+dealing with multiple
+random variables.
+
+And we will also need the
+concept of conditional
+
+density, again for the case of
+continuous random variables.
+
+The intuition and the meaning
+of these objects is going to
+
+be exactly the same as here,
+only a little subtler because
+
+densities are not
+probabilities.
+
+They're rates at which
+probabilities accumulate.
+
+So that adds a little bit of
+potential confusion here,
+
+which, hopefully, we will fully
+resolve in the next
+
+couple of sections.
+
+All right.
+
+Thank you.
\ No newline at end of file
diff --git a/mKcWk_DmS7M.txt b/mKcWk_DmS7M.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8f16f3b4b3d63f20b2b93239a69b8b737ea75e64
--- /dev/null
+++ b/mKcWk_DmS7M.txt
@@ -0,0 +1,667 @@
+align:start position:0%
+ 
+the definition of the conditional PDF is
+
+ align:start position:0%
+the definition of the conditional PDF is
+ 
+
+ align:start position:0%
+the definition of the conditional PDF is
+very simple it is just this formula
+
+ align:start position:0%
+very simple it is just this formula
+ 
+
+ align:start position:0%
+very simple it is just this formula
+which is analogous to the one for the
+
+ align:start position:0%
+which is analogous to the one for the
+ 
+
+ align:start position:0%
+which is analogous to the one for the
+discrete case in all respects
+
+ align:start position:0%
+discrete case in all respects
+ 
+
+ align:start position:0%
+discrete case in all respects
+mathematical and intuitive it is very
+
+ align:start position:0%
+mathematical and intuitive it is very
+ 
+
+ align:start position:0%
+mathematical and intuitive it is very
+similar to the conditional pmf even so
+
+ align:start position:0%
+similar to the conditional pmf even so
+ 
+
+ align:start position:0%
+similar to the conditional pmf even so
+developing a solid grasp of this concept
+
+ align:start position:0%
+developing a solid grasp of this concept
+ 
+
+ align:start position:0%
+developing a solid grasp of this concept
+does take some further thinking so we
+
+ align:start position:0%
+does take some further thinking so we
+ 
+
+ align:start position:0%
+does take some further thinking so we
+will now make some observations that
+
+ align:start position:0%
+will now make some observations that
+ 
+
+ align:start position:0%
+will now make some observations that
+should be helpful in this respect a
+
+ align:start position:0%
+should be helpful in this respect a
+ 
+
+ align:start position:0%
+should be helpful in this respect a
+first and obvious observation is that
+
+ align:start position:0%
+first and obvious observation is that
+ 
+
+ align:start position:0%
+first and obvious observation is that
+the conditional PDF is non-negative it's
+
+ align:start position:0%
+the conditional PDF is non-negative it's
+ 
+
+ align:start position:0%
+the conditional PDF is non-negative it's
+defined when the denominator is positive
+
+ align:start position:0%
+defined when the denominator is positive
+ 
+
+ align:start position:0%
+defined when the denominator is positive
+the numerator is a non-negative quantity
+
+ align:start position:0%
+the numerator is a non-negative quantity
+ 
+
+ align:start position:0%
+the numerator is a non-negative quantity
+so it's always a non-negative quantity a
+
+ align:start position:0%
+so it's always a non-negative quantity a
+ 
+
+ align:start position:0%
+so it's always a non-negative quantity a
+more interesting observation is that for
+
+ align:start position:0%
+more interesting observation is that for
+ 
+
+ align:start position:0%
+more interesting observation is that for
+any given value of little Y the
+
+ align:start position:0%
+any given value of little Y the
+ 
+
+ align:start position:0%
+any given value of little Y the
+conditional PDF looks like a slice of
+
+ align:start position:0%
+conditional PDF looks like a slice of
+ 
+
+ align:start position:0%
+conditional PDF looks like a slice of
+the joint PDF indeed if you fix the
+
+ align:start position:0%
+the joint PDF indeed if you fix the
+ 
+
+ align:start position:0%
+the joint PDF indeed if you fix the
+value of little Y then the denominator
+
+ align:start position:0%
+value of little Y then the denominator
+ 
+
+ align:start position:0%
+value of little Y then the denominator
+in this definition is a constant and we
+
+ align:start position:0%
+in this definition is a constant and we
+ 
+
+ align:start position:0%
+in this definition is a constant and we
+have a function that varies with X
+
+ align:start position:0%
+have a function that varies with X
+ 
+
+ align:start position:0%
+have a function that varies with X
+that's the same way that the joint PDF
+
+ align:start position:0%
+that's the same way that the joint PDF
+ 
+
+ align:start position:0%
+that's the same way that the joint PDF
+varies with X pictorially let us
+
+ align:start position:0%
+varies with X pictorially let us
+ 
+
+ align:start position:0%
+varies with X pictorially let us
+consider this particular joint PDF and
+
+ align:start position:0%
+consider this particular joint PDF and
+ 
+
+ align:start position:0%
+consider this particular joint PDF and
+let this be the x-axis and let that be
+
+ align:start position:0%
+let this be the x-axis and let that be
+ 
+
+ align:start position:0%
+let this be the x-axis and let that be
+the y-axis if we fix a certain value of
+
+ align:start position:0%
+the y-axis if we fix a certain value of
+ 
+
+ align:start position:0%
+the y-axis if we fix a certain value of
+y if we condition on Y having taken this
+
+ align:start position:0%
+y if we condition on Y having taken this
+ 
+
+ align:start position:0%
+y if we condition on Y having taken this
+particular value so that our universe is
+
+ align:start position:0%
+particular value so that our universe is
+ 
+
+ align:start position:0%
+particular value so that our universe is
+now this particular line on that
+
+ align:start position:0%
+now this particular line on that
+ 
+
+ align:start position:0%
+now this particular line on that
+universe the value of the denominator in
+
+ align:start position:0%
+universe the value of the denominator in
+ 
+
+ align:start position:0%
+universe the value of the denominator in
+this definition is a constant and the
+
+ align:start position:0%
+this definition is a constant and the
+ 
+
+ align:start position:0%
+this definition is a constant and the
+conditional PDF is going to vary
+
+ align:start position:0%
+conditional PDF is going to vary
+ 
+
+ align:start position:0%
+conditional PDF is going to vary
+according to the height of the joint on
+
+ align:start position:0%
+according to the height of the joint on
+ 
+
+ align:start position:0%
+according to the height of the joint on
+that particular conditional universe so
+
+ align:start position:0%
+that particular conditional universe so
+ 
+
+ align:start position:0%
+that particular conditional universe so
+the height of the joint if we trace
+
+ align:start position:0%
+the height of the joint if we trace
+ 
+
+ align:start position:0%
+the height of the joint if we trace
+is one of those curves up here and goes
+
+ align:start position:0%
+is one of those curves up here and goes
+ 
+
+ align:start position:0%
+is one of those curves up here and goes
+down so it is really a slice taken out
+
+ align:start position:0%
+down so it is really a slice taken out
+ 
+
+ align:start position:0%
+down so it is really a slice taken out
+of the joint PDF if we condition on a
+
+ align:start position:0%
+of the joint PDF if we condition on a
+ 
+
+ align:start position:0%
+of the joint PDF if we condition on a
+different Y we get a different slice of
+
+ align:start position:0%
+different Y we get a different slice of
+ 
+
+ align:start position:0%
+different Y we get a different slice of
+the joint PDF and so on actually the
+
+ align:start position:0%
+the joint PDF and so on actually the
+ 
+
+ align:start position:0%
+the joint PDF and so on actually the
+conditional is not exactly the same as
+
+ align:start position:0%
+conditional is not exactly the same as
+ 
+
+ align:start position:0%
+conditional is not exactly the same as
+the slice we also have this term on the
+
+ align:start position:0%
+the slice we also have this term on the
+ 
+
+ align:start position:0%
+the slice we also have this term on the
+denominator that serves as a scaling
+
+ align:start position:0%
+denominator that serves as a scaling
+ 
+
+ align:start position:0%
+denominator that serves as a scaling
+factor it turns out that this scaling
+
+ align:start position:0%
+factor it turns out that this scaling
+ 
+
+ align:start position:0%
+factor it turns out that this scaling
+factor is exactly what we need for the
+
+ align:start position:0%
+factor is exactly what we need for the
+ 
+
+ align:start position:0%
+factor is exactly what we need for the
+conditional PDF given a specific value
+
+ align:start position:0%
+conditional PDF given a specific value
+ 
+
+ align:start position:0%
+conditional PDF given a specific value
+of little Y to integrate to one indeed
+
+ align:start position:0%
+of little Y to integrate to one indeed
+ 
+
+ align:start position:0%
+of little Y to integrate to one indeed
+if we fix little Y and take the integral
+
+ align:start position:0%
+if we fix little Y and take the integral
+ 
+
+ align:start position:0%
+if we fix little Y and take the integral
+over all X's using the definition and
+
+ align:start position:0%
+over all X's using the definition and
+ 
+
+ align:start position:0%
+over all X's using the definition and
+because this term is a constant and does
+
+ align:start position:0%
+because this term is a constant and does
+ 
+
+ align:start position:0%
+because this term is a constant and does
+not involve X we only need to integrate
+
+ align:start position:0%
+not involve X we only need to integrate
+ 
+
+ align:start position:0%
+not involve X we only need to integrate
+the numerator and we recognize that the
+
+ align:start position:0%
+the numerator and we recognize that the
+ 
+
+ align:start position:0%
+the numerator and we recognize that the
+numerator corresponds to our earlier
+
+ align:start position:0%
+numerator corresponds to our earlier
+ 
+
+ align:start position:0%
+numerator corresponds to our earlier
+formula for the marginal distribution
+
+ align:start position:0%
+formula for the marginal distribution
+ 
+
+ align:start position:0%
+formula for the marginal distribution
+the marginal PDF of Y from the joint
+
+ align:start position:0%
+the marginal PDF of Y from the joint
+ 
+
+ align:start position:0%
+the marginal PDF of Y from the joint
+this is how we recover the marginal PDF
+
+ align:start position:0%
+this is how we recover the marginal PDF
+ 
+
+ align:start position:0%
+this is how we recover the marginal PDF
+of Y so the numerator turns out to be
+
+ align:start position:0%
+of Y so the numerator turns out to be
+ 
+
+ align:start position:0%
+of Y so the numerator turns out to be
+the same as the denominator and so we
+
+ align:start position:0%
+the same as the denominator and so we
+ 
+
+ align:start position:0%
+the same as the denominator and so we
+get a ratio of 1 therefore the
+
+ align:start position:0%
+get a ratio of 1 therefore the
+ 
+
+ align:start position:0%
+get a ratio of 1 therefore the
+conditional PDF for a given value of the
+
+ align:start position:0%
+conditional PDF for a given value of the
+ 
+
+ align:start position:0%
+conditional PDF for a given value of the
+random variable Y behaves in all
+
+ align:start position:0%
+random variable Y behaves in all
+ 
+
+ align:start position:0%
+random variable Y behaves in all
+respects like an ordinary PDF it is
+
+ align:start position:0%
+respects like an ordinary PDF it is
+ 
+
+ align:start position:0%
+respects like an ordinary PDF it is
+non-negative and it integrates to 1 the
+
+ align:start position:0%
+non-negative and it integrates to 1 the
+ 
+
+ align:start position:0%
+non-negative and it integrates to 1 the
+last observation is that we can take
+
+ align:start position:0%
+last observation is that we can take
+ 
+
+ align:start position:0%
+last observation is that we can take
+this definition and move the denominator
+
+ align:start position:0%
+this definition and move the denominator
+ 
+
+ align:start position:0%
+this definition and move the denominator
+to the other side to obtain this formula
+
+ align:start position:0%
+to the other side to obtain this formula
+ 
+
+ align:start position:0%
+to the other side to obtain this formula
+which has the familiar form of the
+
+ align:start position:0%
+which has the familiar form of the
+ 
+
+ align:start position:0%
+which has the familiar form of the
+multiplication rule the probability of
+
+ align:start position:0%
+multiplication rule the probability of
+ 
+
+ align:start position:0%
+multiplication rule the probability of
+two events happening is the probability
+
+ align:start position:0%
+two events happening is the probability
+ 
+
+ align:start position:0%
+two events happening is the probability
+of the first times the probability of
+
+ align:start position:0%
+of the first times the probability of
+ 
+
+ align:start position:0%
+of the first times the probability of
+the second given the first except that
+
+ align:start position:0%
+the second given the first except that
+ 
+
+ align:start position:0%
+the second given the first except that
+here were not really dealing with
+
+ align:start position:0%
+here were not really dealing with
+ 
+
+ align:start position:0%
+here were not really dealing with
+probabilities we're dealing with
+
+ align:start position:0%
+probabilities we're dealing with
+ 
+
+ align:start position:0%
+probabilities we're dealing with
+densities by symmetry a similar formula
+
+ align:start position:0%
+densities by symmetry a similar formula
+ 
+
+ align:start position:0%
+densities by symmetry a similar formula
+must also be true when we interchange
+
+ align:start position:0%
+must also be true when we interchange
+ 
+
+ align:start position:0%
+must also be true when we interchange
+the role
+
+ align:start position:0%
+the role
+ 
+
+ align:start position:0%
+the role
+of x and y so algebraically everything
+
+ align:start position:0%
+of x and y so algebraically everything
+ 
+
+ align:start position:0%
+of x and y so algebraically everything
+is similar to what we have seen for the
+
+ align:start position:0%
+is similar to what we have seen for the
+ 
+
+ align:start position:0%
+is similar to what we have seen for the
+case of discrete random variables it's
+
+ align:start position:0%
+case of discrete random variables it's
+ 
+
+ align:start position:0%
+case of discrete random variables it's
+the same form of the multiplication rule
+
+ align:start position:0%
+the same form of the multiplication rule
+ 
+
+ align:start position:0%
+the same form of the multiplication rule
+although the interpretation is a bit
+
+ align:start position:0%
+although the interpretation is a bit
+ 
+
+ align:start position:0%
+although the interpretation is a bit
+different because densities are not
+
+ align:start position:0%
+different because densities are not
+ 
+
+ align:start position:0%
+different because densities are not
+probabilities
\ No newline at end of file
diff --git a/mUBmcbbJNf4.txt b/mUBmcbbJNf4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..89528aee81a19387f11f6eb94113cf5b036cd6f6
--- /dev/null
+++ b/mUBmcbbJNf4.txt
@@ -0,0 +1,4175 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help
+MIT OpenCourseWare
+
+continue to offer high quality,
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+NANCY LYNCH: OK so today, you're
+going to see something new.
+
+In fact all this
+week, you're going
+
+to see something that's quite
+different from what you've
+
+been studying in this course.
+
+These are algorithms.
+
+But they're for a completely
+different sort of model.
+
+Distributed algorithms,
+OK, so what are they?
+
+So now instead of
+having algorithms
+
+that run on a typical
+computer, you're
+
+going to have algorithms that
+run on a network of processors.
+
+Or it could be on
+one machine that
+
+has multiple processors,
+multi processors that memory.
+
+Much of computing is
+distributed algorithms now.
+
+They solve problems
+like communication
+
+on the internet, data
+management over a network,
+
+allocating resources
+in a network setting,
+
+synchronizing,
+reaching agreement
+
+among different agents
+at remote locations.
+
+So these are all distributed
+problems, not things
+
+that you just solve
+on one computer.
+
+The kinds of algorithms you
+design for these settings
+
+have to work under extremely
+difficult platforms
+
+because what you have is
+concurrent activity that's
+
+going on at many locations,
+many processors doing things
+
+at the same time.
+
+And you don't know exactly
+when everybody's going
+
+to perform their activities.
+
+You can have different
+sorts of timing uncertainty.
+
+The order of events isn't clear.
+
+There could be inputs that
+arrive at different locations.
+
+And then you also have to
+deal with failure and recovery
+
+of some of the processors or
+some of the channels involved
+
+in the computation.
+
+You don't think of
+any of this when
+
+you're just trying to run an
+algorithm on one computer.
+
+So distributed algorithms
+can be pretty complicated.
+
+It's not easy to design them.
+
+And after you design
+them, you still
+
+have to make sure
+they're correct.
+
+So there are issues involved
+in proving them correct
+
+and analyzing them.
+
+A little bit of
+history, the field
+
+pretty much started
+around the late '60s.
+
+Edsger Dijkstra was one of the
+earliest leaders in the field.
+
+He won of the first
+Turing Awards.
+
+Leslie Lamport won the
+Turing Award last year.
+
+Although he actually
+started as a very young guy,
+
+way back in the early
+days of the field.
+
+If you want to look at some
+sources, I have a book.
+
+There's another textbook
+by Attiya and Welch.
+
+There's a new series of
+monographs that basically
+
+try to summarize many of the
+important research topics
+
+in distributed computing theory.
+
+And the last two lines have a
+couple of the main conferences
+
+in the field.
+
+OK so I can't do that
+much in one week.
+
+What I'll do is just
+introduce the area,
+
+by showing you two common
+models for distributed networks.
+
+And just introduce a very
+few fundamental algorithms,
+
+and you'll see along the way
+some techniques for modeling
+
+and analyzing them.
+
+OK the two models here are
+synchronous distributed
+
+networks, and asynchronous
+distributed networks.
+
+The problems I'll look at
+in the synchronous setting
+
+are a simple problem of leader
+election, which is a symmetry
+
+breaking problem, basically.
+
+Maximal independence set
+problem, and then a couple
+
+of problems that should
+look familiar to you
+
+from the settings of this
+class, establishing structures
+
+like breadth-first spanning
+trees and shortest paths trees.
+
+In the asynchronous case
+I'll revisit these last two
+
+problems, setting up
+breadth-first and shortest path
+
+trees.
+
+OK so I mentioned
+something about modeling
+
+in proofs and analysis.
+
+Turns out, getting the
+formal models right
+
+and getting real
+proofs tends to be
+
+pretty important for
+distributed algorithms
+
+because with all the stuff
+going on, they're complicated.
+
+And it's easy to make mistakes.
+
+The kinds of models that we use
+are interacting state machines,
+
+inputs and outputs.
+
+They send each other messages.
+
+But the kinds of
+proofs you do typically
+
+use invariants, a
+technique that you're very
+
+familiar with from this class.
+
+You can still use them
+in a distributed setting.
+
+And you still prove them
+the same way, by induction.
+
+Something else that comes up a
+lot in the distributed setting
+
+is modeling and proofs
+using levels of abstraction.
+
+You might want to give
+an abstract description
+
+of an algorithm and
+prove that that works.
+
+And then you have a very
+detailed, complicated,
+
+lower level description that you
+can prove implements the higher
+
+level description.
+
+That's another
+popular technique.
+
+You use different kinds
+of complexity measures.
+
+For time complexity,
+you would measure rounds
+
+if it's the synchronous
+model, or some approximation
+
+to real time, if it's
+the asynchronous model.
+
+You also count communication,
+either the number
+
+of messages you send, or
+the total number of bits
+
+that you send in an algorithm.
+
+So throughout
+these two lectures,
+
+we'll be looking at
+distributed networks.
+
+So you start with a graph.
+
+Let's just look at
+undirected graphs this week.
+
+We use n in this
+field for what you're
+
+calling v, the total number
+of nodes in the network
+
+or vertices in the graph.
+
+We use the notation gamma of
+u to mean the neighbors of u
+
+in the graph.
+
+So every vertex of the graph has
+a set of immediate neighboring
+
+vertices.
+
+That's gamma of u.
+
+And the degree of u is the size
+of the neighborhood, the number
+
+of neighbors of the vertex.
+
+OK so we start with the graph.
+
+But now we're
+going to plunk down
+
+a process, some kind
+of active entity
+
+at each vertex of the graph.
+
+So this is some
+kind of automaton.
+
+If you've taken automata
+theory, it's not really
+
+finite state machines, it's more
+like infinite state automata
+
+that can interact
+with each other.
+
+So we usually talk about
+vertices in a graph, processes
+
+at the vertices of a graph.
+
+But sometimes we get
+sloppy and just say nodes.
+
+And we could mean either the
+vertex or the active thing
+
+running at the vertex.
+
+Can't keep them
+straight all the time.
+
+OK and then with the
+edges of the graph,
+
+we would put
+communication channels,
+
+one in each direction,
+so that the processes
+
+can communicate over the edges.
+
+This week I'm not going
+to talk about what
+
+happens when you introduce
+failures because we just
+
+don't have time.
+
+A lot of distributed computing
+theory deals with what
+
+happens when some of the
+components in your system fail.
+
+How do you cope with that?
+
+So we'll start right in
+with synchronous distributed
+
+algorithms.
+
+A source for that,
+if you're interested
+
+is the first technical
+chapter in my book.
+
+OK so you have processes
+at the nodes of a graph,
+
+like I just said.
+
+They communicate using messages.
+
+So think of each process as not
+knowing who his neighbors are,
+
+not knowing anything
+about the graph.
+
+So what do they have?
+
+They have ports.
+
+You could say they have output
+ports, on which they could send
+
+a message, and then some
+input ports on which messages
+
+can come in.
+
+So in general, the
+process doesn't know
+
+who the ports are connected to.
+
+It just has local
+names for the ports,
+
+like one, two, three,
+up to the degree.
+
+If you have any questions
+just stop me and ask,
+
+if something's not clear.
+
+Otherwise I'll go pretty fast.
+
+And I know that none
+of this is familiar.
+
+So in general, the
+processes don't have
+
+to be distinguishable at all.
+
+So they don't have to have
+special unique identifiers
+
+so you could tell
+the processes apart.
+
+They could be
+completely identical.
+
+Well if they have
+different numbers of ports,
+
+they're not exactly identical.
+
+They certainly
+know how many ports
+
+they have, and release the
+local names for the ports.
+
+Good so these are
+processes sitting
+
+at the nodes of the graph.
+
+What do they do?
+
+So they execute.
+
+And we talk about an
+execution of this network.
+
+It goes in synchronous
+rounds, and every round,
+
+every process
+looks at its state,
+
+and decides what
+messages it's going
+
+to send on all of the ports.
+
+So it could send different
+messages on different ports.
+
+So then what happens
+is all the messages
+
+that the processes decide to
+send get put onto the channels
+
+and they get delivered to
+the process at the other end.
+
+So the process of the
+other end is in some state.
+
+All these messages come in.
+
+It updates its state, based
+on the arriving messages.
+
+So it changes state in
+response to whatever comes in.
+
+And this is completely different
+from this semester so far.
+
+We're going to completely
+ignore the costs
+
+of the local computation.
+
+So each node can compute
+some complicated algorithm
+
+of the sort you've been
+studying in this class,
+
+and we usually don't
+consider that cost.
+
+We're more worried about
+the communication costs.
+
+And so we'll be focusing on the
+number of rounds that it takes,
+
+in the synchronous case, and
+the number of communication
+
+messages or bits.
+
+OK so far?
+
+So let's start on
+the first problem.
+
+Here's a graph.
+
+The nodes start out
+possibly identical,
+
+but you want to somehow
+distinguish one of them
+
+to be a leader.
+
+So you have this arbitrary,
+connected, undirected graph.
+
+And exactly one
+process is supposed
+
+to elect itself the leader.
+
+That means it outputs a
+special leader signal.
+
+so exactly one should do that.
+
+So why do you want a leader?
+
+Well in practice, leaders
+can coordinate things.
+
+They can take charge
+of communication,
+
+and inform other
+nodes when they're
+
+allowed to send messages.
+
+They can coordinate
+the processing of data.
+
+Basically it allows
+you to centralize
+
+some of the computation.
+
+It can schedule the
+other processes.
+
+It can allocate the resources.
+
+It could help to reach
+agreement among the processes,
+
+if they start out with
+different opinions about what
+
+is supposed to happen.
+
+All right so let's start
+out with a very simple case.
+
+You have a clique.
+
+Here's a four clique, where
+all the vertices are directly
+
+connected to all
+the other vertices,
+
+with two directional channels.
+
+And the processes are identical.
+
+So I should have
+asked you, instead
+
+of just giving the
+answer here, but are they
+
+able to elect a leader?
+
+So this theorem says that in
+general, that's impossible.
+
+Or it's not possible, in
+the most general case.
+
+If you have, no
+matter what n is,
+
+let's just say we have an
+n vertex clique for some n.
+
+It's not possible to have
+any algorithm that you
+
+can have all the processes
+run, if it's deterministic
+
+and the processes start
+out all indistinguishable.
+
+There's no way
+that they can elect
+
+a single node as a leader.
+
+So do you have an intuition
+for why that might be the case?
+
+Yeah.
+
+AUDIENCE: They're
+all connected, and
+
+the cross-problem
+communication in one round
+
+is equal, then to
+be equal likely
+
+to select each one of them.
+
+It would be--
+
+NANCY LYNCH: It's deterministic
+there's no likelihood here.
+
+And nobody is doing
+any selecting.
+
+You're talking as if there's
+somebody who's choosing
+
+a process to do something.
+
+There isn't anyone in charge.
+
+So this is a really
+different way of thinking.
+
+AUDIENCE: So every node is
+essentially the exact same.
+
+So if it says, OK, let's
+assume I'm going to be leader,
+
+everyone is going to assume
+they're going to be leader.
+
+NANCY LYNCH: That's exactly
+the right intuition.
+
+They can't
+distinguish themselves
+
+because they're always
+going to do the same thing.
+
+Let's look at a
+very simple case.
+
+Suppose we have just two nodes,
+two node clique, two nodes
+
+connected by channels.
+
+These are identical.
+
+They're deterministic.
+
+What can they do?
+
+Well you could try to design
+algorithms for one of them
+
+to elect itself as the leader.
+
+But you can show,
+by using induction,
+
+that the processes
+are actually going
+
+to remain in the same state
+as each other forever,
+
+however many rounds you execute.
+
+So let's slow down.
+
+We can work by contradiction.
+
+Suppose you have an algorithm
+that solves this problem.
+
+Both of the processes,
+they're identical.
+
+They start in the
+same start state.
+
+Let's say there's a
+unique start state.
+
+So we could prove by induction
+on the number of rounds
+
+that after any number
+of rounds, say r rounds,
+
+the processes are still
+in identical states.
+
+So the inductive step
+is, all right, they're
+
+in identical states after
+some number of rounds.
+
+Let's look at the next round.
+
+They're in the same state.
+
+So they generate
+the same messages.
+
+So they each other
+the same messages.
+
+They receive the same message.
+
+And then they make
+the same state change.
+
+So they stay in the same state.
+
+And you can tweak
+this, and say how this
+
+works for-- yeah, question?
+
+AUDIENCE: So in what ways is
+the proof a contradiction?
+
+NANCY LYNCH: I'm not finished.
+
+You're exactly right.
+
+We have to finish by using the
+requirements of the problem.
+
+Since the algorithm has to solve
+the leader election problem,
+
+the requirements say that
+eventually, one of them
+
+has to output leader.
+
+And what happens when he does?
+
+Anyone?
+
+Yeah.
+
+AUDIENCE: You have node also
+outputting the leader signal.
+
+NANCY LYNCH: Yeah the other one
+would also do the same thing.
+
+We're saying round by round,
+they stay in the same state.
+
+So as someone said before,
+when one guy outputs leader,
+
+at the same round the other
+guy will output leader as well.
+
+So that's a contradiction
+to the problem requirements.
+
+Notice we didn't
+assume anything at all
+
+about exactly how
+the algorithm works.
+
+We're just saying, however it
+works, it can't solve this,
+
+under the assumptions
+that the nodes
+
+are indistinguishable
+and deterministic.
+
+So as you can see,
+this will extend if you
+
+have larger cliques of size n.
+
+So now the process has
+not just one output port,
+
+it has n minus 1 output ports to
+connect to all the other nodes.
+
+Let's say they're numbered
+1 through n minus 1.
+
+And one of the possibilities,
+and one I'll use in this proof
+
+is that the ports happen to
+be numbered consistently.
+
+So that if you have output
+port number k at one node,
+
+it's connected to input port
+number k at the other end.
+
+So that's one way
+things can match up.
+
+All right if that's
+the case, we could
+
+do the same proof we just did.
+
+Show by induction that all
+the processes in the clique
+
+remain in the same
+state forever.
+
+So same proof.
+
+Suppose you have an
+algorithm that's solves it.
+
+They all began in
+the same state.
+
+You show by induction that
+they all remain the same state.
+
+Well so now we slow
+down a little bit.
+
+Each process sends a possibly
+different message on each port.
+
+But everybody sends the
+same message on port k
+
+because they're all
+indistinguishable.
+
+And then because the
+way the ports match up,
+
+everybody receives the
+same message on port k.
+
+And then they make the
+same state changes.
+
+AUDIENCE: Does this
+proof imply that there's
+
+a kernel for simplifying the
+graph when you find a clique?
+
+NANCY LYNCH: No because
+if you have a graph that
+
+consists of a clique
+and then let's say,
+
+some other stuff,
+maybe the leader
+
+could be somebody
+outside the clique.
+
+So you can't just
+say because there's
+
+a clique that you can't elect
+a leader because you could
+
+break the symmetry of the graph
+with other stuff in the graph.
+
+Yeah?
+
+AUDIENCE: What assumptions do
+we make to know that for each k,
+
+they receive the same message?
+
+NANCY LYNCH:
+Because everybody is
+
+going to send the same message
+on the same numbered port,
+
+because they're identical.
+
+And one way the ports
+can be hooked up,
+
+and we have to tolerate all
+ways they could be hooked up--
+
+say an adversary
+hooks them up-- is
+
+that port k,
+somebody's output port,
+
+is the other end's
+input port numbered k.
+
+So then they all
+receive the same message
+
+on their port number k.
+
+Yeah?
+
+AUDIENCE: Is it actually
+possible to always hook up
+
+the boards that way.
+
+I mean, it's like wrapped
+with three vertices.
+
+NANCY LYNCH: Well I'm
+just doing it for cliques.
+
+Yeah it is.
+
+Yeah you could do it.
+
+I mean you could have port
+one always going clockwise,
+
+and port two going
+counterclockwise,
+
+I mean, there's always a
+way to do that in a clique.
+
+I checked that.
+
+So what you've just seen is
+one of the very basic problems
+
+for distributed algorithms,
+which is breaking symmetry
+
+among identical processes.
+
+And you see that deterministic,
+indistinguishable processes
+
+just can't do it.
+
+So we have to have
+something more.
+
+So what do you
+think we could add
+
+to make this problem solvable?
+
+AUDIENCE: [INAUDIBLE] processes.
+
+NANCY LYNCH: I can't hear.
+
+AUDIENCE: Probability.
+
+Probability, OK, anything else?
+
+So we could have the processes
+actually distinguishable.
+
+The common way in this area is
+to say that each process has
+
+an identifier.
+
+Like, you buy a chip and it's
+got some identifier burned in.
+
+OK so you have some kind
+of unique identifiers.
+
+Or you can use randomness.
+
+OK for unique
+identifiers, you assume
+
+everybody has some
+number or some identifier
+
+that it knows what it is.
+
+It's built into its state, let's
+say, a special state variable.
+
+They're totally
+ordered, generally.
+
+They could be integers, or
+from some totally ordered set.
+
+When you say unique
+identifiers, is
+
+it means that different
+identifiers could
+
+appear any place in the graph.
+
+But each identifier can
+appear at most once.
+
+You can have a huge identifier
+space in a small graph.
+
+But you're Just selecting
+some identifiers
+
+to put in the
+processes in the graph.
+
+So that's one set up.
+
+And the other one, of
+course, is using randomness.
+
+So let's look at the
+unique identifiers first.
+
+Now the problem becomes easy.
+
+Let's look at the clique again.
+
+Suppose there's an
+algorithm-- well, let's
+
+construct an algorithm
+that consists
+
+of deterministic processes
+with unique identifiers.
+
+And we're going to guarantee
+to elect a leader in the graph.
+
+And moreover, it's
+just going to take
+
+one round of communication.
+
+And it's only going to
+use n squared messages.
+
+How could that work?
+
+Everybody in this click
+has a unique identifier.
+
+What would they do?
+
+Send it out, right?
+
+So you can just send
+it on all your ports.
+
+Everybody would send its
+unique identifier on all
+
+its output ports.
+
+And then they collect the unique
+identifiers from everyone else.
+
+So everybody sees the
+same set of identifiers.
+
+And so the process with the
+maximum unique identifier
+
+knows that it's the only
+one with that identifier.
+
+And it's the biggest one.
+
+So it can elect
+itself the leader.
+
+So all you is unique
+identifiers and the ability
+
+to exchange them reliably.
+
+And you can elect
+somebody easily.
+
+Randomness, well,
+various ways to do it.
+
+But one idea is the processes
+could just choose identifiers
+
+randomly.
+
+You take a sufficiently large
+set of possible identifiers,
+
+and so if they just choose
+uniformly at random,
+
+they're likely to choose
+all different identifiers.
+
+Once you have these
+randomly chosen identifiers
+
+you could use them like the
+really unique identifiers.
+
+The only thing is you might,
+there's a small chance
+
+that you'll have a duplicate.
+
+In which case, you want to be
+able to detect that and repeat
+
+this.
+
+So first of all, how big
+the a set do you need?
+
+Well here's an example.
+
+Suppose that you have
+the n processes choosing
+
+at random, independently
+from a space of size r.
+
+Identifiers are the
+numbers one through r.
+
+OK and r is going
+to depend on n.
+
+It's going to be like n
+squared, but it's also
+
+going to depend on epsilon,
+which is the error probability
+
+that you're interested in.
+
+Turns out that n squared over
+2 epsilon is good enough.
+
+OK so you have your IDs
+space at least that large.
+
+And then you can guarantee that
+with probability at least 1
+
+minus epsilon, all the
+numbers that everybody chooses
+
+are different.
+
+It's a very easy proof.
+
+The probability-- just look
+at two particular processes--
+
+what's the probability that
+they choose the same number?
+
+It's just 1 over r, right.
+
+Because they're both
+choosing at random.
+
+The first one chooses something.
+
+The probability
+that the second one
+
+chooses the same thing
+is just 1 over r.
+
+But now you can
+take a union bound,
+
+just add up the probabilities
+of any pair having a duplicate.
+
+And so you have n square
+around n squared over 2 pairs.
+
+And so multiplying 1 over
+r by n squared over 2
+
+still keeps your probability
+less than or equal to epsilon,
+
+your error probability.
+
+So you can choose
+identifiers using randomness.
+
+With large enough space,
+with very high probability,
+
+you can get them to
+be all different.
+
+And now here's how
+the algorithm works.
+
+So you get an algorithm that
+would finish in only one round,
+
+with probability
+1 minus epsilon.
+
+But it will be correct.
+
+And it will have
+repeated rounds,
+
+in case the first
+round doesn't work.
+
+But the expected
+time is just 1 over 1
+
+minus epsilon, not very big.
+
+What's the algorithm?
+
+Well processes just choose the
+random IDs from the big space,
+
+like we just said.
+
+They exchange their Ids.
+
+And now, everybody
+can see everyone's ID,
+
+but they also can tell
+if there's a duplicate.
+
+if the maximum is not unique.
+
+So if the maximum is unique,
+find the maximum wins.
+
+And everyone knows that.
+
+Otherwise you have a problem.
+
+And you have to repeat.
+
+And you just keep doing
+that until you succeed.
+
+So this can just
+continue, but it's
+
+likely to finish very fast,
+if you have a high likelihood
+
+of having no duplicates.
+
+Questions about the
+leader election?
+
+So the story was, it's
+impossible without something
+
+to help you distinguish
+some processes.
+
+You can do it with
+unique identifiers.
+
+You can do with randomness.
+
+Second problem is called
+maximal independent set.
+
+So you have a picture of
+a maximal independent set
+
+in a graph here.
+
+Let's try this.
+
+Yeah cursor.
+
+So the maximal independent
+set in the graph is here.
+
+But this is something I'll
+come back to a minute.
+
+This is actually a use of
+the maximal independent set
+
+to model what happens
+in a certain kind
+
+of biological system.
+
+What's a maximal
+independence set?
+
+So you start with a general,
+undirected graph network.
+
+And the problem is to choose
+a subset of the nodes so that
+
+they form what we call
+a maximal independent .
+
+Set let's break that down.
+
+What does this mean?
+
+Independent means you don't
+have any two neighbors that
+
+are both in the set.
+
+So you don't want to get
+two neighbors in the set.
+
+Maximal means that
+whatever set you choose,
+
+you can't add any more nodes
+without violating independence.
+
+So now this should
+look something
+
+like a couple of
+homework problems
+
+that you had from the
+beginning and recently.
+
+But I'm not saying that it's
+maximum independent set.
+
+I'm not saying you have to
+have the global, largest
+
+number of nodes.
+
+I'm just saying it has
+to be a local optimum,
+
+in the sense that you can't
+add any more nodes to your set
+
+without violating the
+independence property.
+
+Make sense?
+
+There's two examples,
+the same graph,
+
+two different maximal
+independent sets.
+
+The green nodes, here
+we have four green nodes
+
+that are independent, not
+neighbors of each other.
+
+And they're maximal,
+in that I couldn't
+
+add any of the red
+nodes into a set
+
+without violating the
+independence property.
+
+But then over here, we have a
+second maximal independent set
+
+for the same graph.
+
+Now we just have two nodes.
+
+And you can't add
+any of the red nodes
+
+without violating the
+independence property.
+
+In other words, every
+node is either in the MIS,
+
+or has a neighbor in the MIS.
+
+There's nothing else you can
+do to add notes to the MIS
+
+So the notion of maximal
+independence, that make sense?
+
+All right, so to make this
+a distributed problem,
+
+let's start out assuming we
+have no unique identifier.
+
+Actually, for this
+whole problem,
+
+we're not going to have
+unique identifiers.
+
+They're all going
+to be identical.
+
+The processes do need
+one piece of information,
+
+which is some approximation
+to n, the size of the network,
+
+the total number of vertices.
+
+So we would like to
+have these nodes somehow
+
+cooperate to compute an MIS
+of the entire network graph.
+
+What that means is every process
+should find out whether it
+
+is in the MIS or not.
+
+If it is, it should output n.
+
+And if it's not,
+it'll just output out.
+
+So you don't have to
+actually compute this,
+
+like you're used
+to solving problems
+
+like this, where somebody
+has to gather all
+
+the information in one place.
+
+Nobody gathers anything.
+
+Everybody just has to
+know whether or not
+
+they're in the MIS.
+
+So as you can
+imagine, this is going
+
+to be unsolvable
+in certain graphs
+
+by deterministic algorithms,
+by the same kind of symmetry
+
+breaking problems that you
+saw for leader election.
+
+So we're going to move right
+to randomized algorithms
+
+for this problem.
+
+Some applications
+of distributed MIS,
+
+well they come up in
+communication networks,
+
+where you want to choose--
+let's say you have a very
+
+dense network of processes.
+
+You want to choose just
+a few nodes, which would
+
+be like an overlay network.
+
+You would choose some
+nodes who could take charge
+
+of communication that you can
+communicate on this overlay
+
+network, and then in
+the end, each node
+
+can take care of communicating
+with its many neighbors.
+
+So that's a common
+sort of application.
+
+But it also comes
+up in other places.
+
+A great example is in
+developmental biology, where
+
+a couple of years ago, there
+was a paper in Science by Afek,
+
+Alon-- there's like
+eight authors on that.
+
+But Ziv Bar-Joseph was the
+lead author of this paper.
+
+So the idea is you have a
+bunch of cells in a fruit fly.
+
+And during development,
+some of those cells
+
+are supposed to
+distinguish themselves
+
+as being what's called
+sensory organ precursor cells.
+
+The properties that you
+want it that actually, you
+
+would like a maximal independent
+set of the cells to become
+
+distinguished in this way.
+
+So they wrote a paper about
+it, got published in Science.
+
+They basically designed a
+new distributed algorithm
+
+that closely mirrored what
+happened in the fruit fly
+
+during development.
+
+So what I'm going to show you
+is a very well-known algorithm,
+
+a classical algorithm for MIS.
+
+This is by Michael Luby.
+
+Very simple algorithm,
+it executes in phases.
+
+Each phase has two realms.
+
+So you start out with all
+the nodes being active.
+
+They're all involved.
+
+They don't know what they're
+going to end up with.
+
+And at each phase, some
+of the active nodes
+
+are going to decide
+they're in the MIS.
+
+Some others will decide
+they're out of the MIS.
+
+And some others won't know yet.
+
+So then you just continue
+to the next phase,
+
+with all the remaining nodes
+and the edges between them.
+
+So you're basically
+going to settle
+
+what happens with some
+subset of the nodes,
+
+and then reduce the
+graph and continue.
+
+So that's the algorithm.
+
+So what do you do in each phase?
+
+Here's what an active
+node does at a phase.
+
+Two rounds.
+
+The first round, it
+picks a random value
+
+in a large space, the same
+kind of idea as before.
+
+This time it's 1 up
+2 n to the fifth.
+
+It sends that random value
+to all its neighbors,
+
+receives the values from all
+its still active neighbors,
+
+and then it just looks to see
+if its value is greater than all
+
+the values it received.
+
+So then it's a local maximum.
+
+It has chosen a value
+that's strictly greater
+
+than the values chosen
+by all its neighbors.
+
+So then it decides to join
+the MIS and it outputs in.
+
+But now you want to make
+sure none of its neighbors--
+
+you know that none
+of its neighbors
+
+are going to join
+the MIS at round one.
+
+Because you know this
+guy's chosen value
+
+is larger, strictly larger,
+than all its neighbors.
+
+But now you want to tell them
+that they should not join.
+
+They should be out.
+
+So if you join the
+MIS you're going
+
+to announce that by sending
+messages to all your neighbors.
+
+And then anybody who
+receives an announcement can
+
+decide it's not going to be
+in the MIS and it outputs out.
+
+Because it knows it has a
+neighbor that's in the MIS.
+
+So if you decided in or out
+at this phase, you're done.
+
+You become inactive.
+
+And only the
+remaining active guys
+
+continue to the next phase.
+
+Make sense?
+
+any questions about how
+the algorithm works?
+
+And animation.
+
+All right so all the
+nodes start out identical.
+
+They all pick IDs.
+
+So here's some numbers
+that they pick.
+
+So which nodes are going
+to now join the MIS?
+
+16, and the one that chose 13.
+
+Good, so they're in the MIS.
+
+And then at the same phase,
+all of their neighbors,
+
+those for red nodes, are going
+to decide to be out of the MIS
+
+And now you're left with
+the remaining four nodes.
+
+We don't keep going
+with the same IDs.
+
+we start over.
+
+We want the rounds
+to be independent.
+
+So if they choose
+again, they get new IDs.
+
+And now the guy with the
+12 and the guy with the 18
+
+going to join the
+MIS at this phase.
+
+And their neighbors will
+decide not to be in the MIS.
+
+That leaves us with just one
+mode, the guy who had four.
+
+Next phase, he
+chooses another ID.
+
+But he has no neighbors
+so by default,
+
+he's bigger than
+all the neighbors.
+
+So he just joins the MIS.
+
+So that's how this works.
+
+Very simple algorithm,
+and it actually
+
+works to find an
+MIS very quickly.
+
+Why does this give
+you independence?
+
+How do we know that if
+this ever terminates,
+
+if everybody decides, how do
+we know that we don't ever
+
+have two neighbors that
+decided to be in the MIS?
+
+Yeah.
+
+AUDIENCE: Because once
+a node joins the MIS,
+
+it broadcasts to
+its neighbors that--
+
+NANCY LYNCH: Right.
+
+The only way you join
+the MIS is if you
+
+have the unique maximum
+value in your neighborhood.
+
+And when you do, all your
+neighbors become inactive.
+
+So you're certainly going
+to have independence.
+
+Maximality, if it
+terminates, the final set
+
+is not going to allow you
+to add any more nodes.
+
+Why?
+
+Because a node is only
+going to become inactive
+
+if it joins the MIS, or
+a neighbor joins the MIS.
+
+And we just continue
+this algorithm
+
+until all the nodes
+become inactive.
+
+So either the node is in the
+MIS or a neighbor is in the MIS.
+
+So you can't possibly
+add any more.
+
+Yes?
+
+So this has the
+basic correctness
+
+properties, but what
+you're probably wondering,
+
+is why is this efficient enough?
+
+Why is it efficient?
+
+Well we could say that with high
+probability, of probability 1,
+
+it will eventually terminate.
+
+More quantitative, we can
+state this theorem that says,
+
+with probability at
+least 1 minus 1 over n,
+
+all the nodes decide
+within four log n phases.
+
+Since n is the
+number of nodes, this
+
+doesn't tell us that you get
+probability 1 of eventually
+
+terminating.
+
+But we can repeat this
+and get the same sort
+
+of bound repeatedly
+for successive phases.
+
+But let's just focus on getting
+probability at least 1 minus 1
+
+over n that all nodes decide
+within about four log n phases.
+
+So let's see what
+this is saying.
+
+You have this big
+complicated graph.
+
+And in one round, for this to
+be like log n behavior, what
+
+has to happen at each phase?
+
+You have to reduce it by
+some constant fraction.
+
+The number of nodes,
+say, should go down.
+
+So it's sort of how
+the proof will go.
+
+So we start out
+with a Lemma saying,
+
+you're choosing
+these IDs at random.
+
+You want a high probability
+that they're all different.
+
+So we have a lemma like
+the one we had before.
+
+It says, the probability
+at least, we use 1 minus 1
+
+over n squared, in each phase.
+
+All these phases
+up to four log n,
+
+everybody's choosing a
+different random value.
+
+All the nodes choose different
+values at each phase.
+
+So this lets us
+ignore the possibility
+
+that you have repeats.
+
+So we'll come back
+to that at the end.
+
+All right, so we're going to
+pretend that in each phase,
+
+all the random
+numbers are different.
+
+So the key idea of this is
+to show that the graph has
+
+to shrink enough at each phase.
+
+So the way we're
+going to say that is
+
+not in terms of the
+nodes, but in terms
+
+of the number of edges.
+
+We're going to say at
+each phase, the expected
+
+number of edges that are
+live-- why is that shaking?
+
+OK.
+
+The expected number
+of edges that
+
+are live at the end of the
+phase is at most half the number
+
+that were live at the
+beginning of the phase.
+
+So an edge is live, if its
+endpoints are still live.
+
+So instead of talking about
+reducing the number of nodes
+
+by a constant
+fraction, I'm going
+
+to reduce the number
+of remaining edges
+
+by constant fraction
+of each phase.
+
+So this is what
+I'm going to prove.
+
+So now I've got only three
+slides, but the only three
+
+slides today that have
+calculations on them.
+
+So probably have
+to pay attention,
+
+if you want to follow
+the calculations online.
+
+So let's see why.
+
+But the goal is clear?
+
+We have to reduce
+the number of edges
+
+that remain by a factor of two.
+
+So this is actually a new
+proof of this algorithm's
+
+performance.
+
+The proof in the original
+papers is pretty complicated.
+
+This is a very
+intuitive, neat proof.
+
+So the first line
+of the proof says
+
+if you have a node that
+has a neighbor that
+
+chooses a value that's bigger
+than all of its own neighbors--
+
+so u has a neighbor w.
+
+W chooses a value that's
+bigger than all w's neighbors.
+
+But let's say more.
+
+Let's say it's also bigger than
+all of u's other neighbors,
+
+besides w.
+
+So w is really big, bigger
+than all w's neighbors,
+
+bigger than all of
+u's other neighbors.
+
+If that happens, then
+what happens to u?
+
+Well we know that w is going
+to decide to join the MIS.
+
+And u is going to
+definitely die,
+
+is not going to join the MIS.
+
+Right?
+
+OK?
+
+I don't want to lose
+people in the first line.
+
+Question?
+
+Here's a picture.
+
+Here's u.
+
+And it has a neighbor w.
+
+And let's say that w's chosen
+value is greater than all
+
+of w's neighbors, but
+also greater than all
+
+of u's other neighbors.
+
+Yes?
+
+If w has that, w is
+going to join the MIS,
+
+and u is going to
+definitely not join the MIS.
+
+It's going to decide
+out in this phase.
+
+OK so far?
+
+AUDIENCE: Why does you need
+w to have value greater
+
+than u's neighbors?
+
+Because if w is greater than
+all of its neighbors then it's--
+
+NANCY LYNCH: --be in the MIS
+and u will not be in the MIS.
+
+And that seems like
+it ought to be enough.
+
+But look at the next line.
+
+Well the line after this one.
+
+What's the probability that
+w chooses a value like that?
+
+So if it's going to be bigger
+than all u's neighbors, and all
+
+of w's neighbors,
+and keeping in mind
+
+that they are each
+other's neighbors,
+
+turns out that
+there is degree u,
+
+at most degree u plus degree
+w nodes involved here.
+
+W has to have the
+biggest of all of those,
+
+so it's going to
+have the probability
+
+1 over the number of nodes
+of being the biggest one.
+
+So it's just 1 over
+the degree of u
+
+plus the degree of
+w, the probability
+
+that w will choose
+a big enough value.
+
+But you ask, this
+is pessimistic.
+
+Why don't I just say that w
+is bigger than its own values?
+
+Because I want to
+do this next step.
+
+I want to say the probability
+that node u gets killed
+
+by one of its neighbors, any one
+of its neighbors in this phase.
+
+I can calculate that as the sum.
+
+The probability that node
+u is killed by a neighbor
+
+is at least the sum over
+all of its neighbors.
+
+You look at all the vertices
+in the neighbor set,
+
+and you add up this fraction.
+
+So why did I need to make that
+additional assumption before?
+
+That w is greater than
+all of u's neighbors,
+
+as well as all of
+its own neighbors.
+
+Yeah?
+
+AUDIENCE: So you can
+add a problem to--
+
+NANCY LYNCH: Yeah
+because otherwise these
+
+would be overlapping events.
+
+But this way I know they're
+definitely disjoint events.
+
+We can't have-- if we
+have w and w prime,
+
+you can't have both
+of those holding
+
+because the requirement for
+w is saying that its ID is
+
+bigger than w prime's ID.
+
+Because you have
+these disjoint events,
+
+you can just add
+the probabilities.
+
+And you know that
+the probability
+
+that u gets killed
+by some neighbor
+
+is at least this summation.
+
+OK so far?
+
+So now I'm going to calculate.
+
+But I wanted to
+focus on the edges.
+
+So let's see, this tells us a
+way that a node can get killed.
+
+But let's look at what happens
+for an edge getting killed.
+
+This is the probability
+that a node is killed.
+
+So the probability that
+an edge dies at this phase
+
+is at least the maximum
+of the probability
+
+that either of its
+two endpoints die.
+
+And let's just write
+it as the average.
+
+The probability
+that an edge dies
+
+is at least the average
+of the probability
+
+that it's two endpoints
+are killed, in this way.
+
+So for an edge, an edge is
+definitely going to die,
+
+if one of its endpoints dies.
+
+And then the edge dies if it
+dies in this particular way.
+
+So the probability an edge dies
+is at least the probability
+
+that one of the-- half the
+sum of the probabilities
+
+that the two end points die.
+
+It's the average probability.
+
+Makes sense?
+
+You might have to
+read this later.
+
+So now we can go from that to
+the expected number of edges
+
+that die.
+
+What is that?
+
+You just add up, over all,
+the edges, the probability
+
+that the edge dies.
+
+The expected number
+of edges that die
+
+is at least the sum over all
+of the edges of the probability
+
+that the two endpoints die.
+
+So you have the sum,
+over all of the edges.
+
+You add up for all the edges.
+
+The probability that
+one endpoint is killed,
+
+and the probability the
+other endpoint is killed.
+
+So what we have is this
+great big summation
+
+involving now the kill
+probabilities for vertices.
+
+So we have the kill
+probability for each vertex.
+
+How many times does that occur?
+
+If you have a vertex, u, it
+appears once for every edge
+
+that u is an endpoint of.
+
+So you have the kill probability
+for each node occurring exactly
+
+it's degree number of times.
+
+So that lets me rewrite
+this in terms of vertices.
+
+This sum is just 1/2 the
+sum over all the nodes
+
+of the probability that the node
+gets killed times its degree.
+
+So I'm calculating by
+replacing the description
+
+in terms of edges,
+by description
+
+in terms of vertices.
+
+More or less OK so far?
+
+So now what do I do?
+
+Well, I know the probability
+that u is killed.
+
+I have a bound for that
+up on the first line.
+
+So I'm just going
+to plug that in.
+
+So I get 1/2 the sum
+over all the nodes,
+
+the degree of the node times
+this summation that gives me
+
+the kill probability
+for that node.
+
+And now I play
+around with the sum.
+
+I can move the degree
+inside the second summation,
+
+and I get this.
+
+So now let's stare
+at this again.
+
+I have the sum over all
+nodes of the sum over all
+
+of its neighbors
+of some expression.
+
+But if I'm considering a
+node, every note and every one
+
+of its neighbors,
+that's like considering
+
+all the directed edges.
+
+I look at every u, and I
+look at every edge that
+
+connects u to something else.
+
+So I can write it as the sum
+over all the directed edges
+
+of this expression.
+
+So I get half of
+the sum over all the
+
+directed edges of
+this expression.
+
+But we were talking
+about undirected edges.
+
+And the undirected edges
+are being twice here, once
+
+for each direction.
+
+I can change this sum to a
+sum over undirected edges.
+
+But now I have the two
+endpoints to deal with.
+
+So I get the degree of u and
+the degree of v in the numerator
+
+because I'm looking at
+it from the point of view
+
+both of the endpoints
+of each edge.
+
+Well something
+drops out, so I have
+
+1/2 the sum over all the
+undirected edges of 1.
+
+So that's 1/2 of the
+number of undirected edges.
+
+So I don't expect you to
+get every step of this,
+
+but it's on three
+slides, so you can
+
+stare at this when you go home
+and make sure the steps work.
+
+But remember the
+point of this is
+
+to show that you reduce
+the number of edges
+
+by a factor of two, and it's
+done and sort of a clever way
+
+by counting the kill
+probabilities of vertices.
+
+So we get this, reducing
+the number of edges.
+
+And now we can just
+plug that back in
+
+to get our complexity bound
+for the entire algorithm.
+
+Remember the original theorem
+you're we were to prove
+
+is a probability bound for
+deciding within log n phases.
+
+Well you should have
+a pretty good idea
+
+of why that works
+because if at each phase,
+
+you're going to reduce
+the number of edges
+
+by around a factor
+of two, then it's
+
+going to take something
+like log n phases to finish.
+
+And I just put a proof sketch.
+
+The number of edges that are
+still alive after four log n
+
+phases, well you divide
+by 2 four log n times,
+
+so you get down to
+practically nothing.
+
+The probability any edges are
+alive at the end is very small.
+
+So you get a small probability
+the algorithm doesn't terminate
+
+within four log n phases.
+
+There's an extra little
+term I threw in here.
+
+You might have forgotten.
+
+There was a term that I needed
+for the small probability,
+
+that somebody chose
+duplicate IDs.
+
+So I'm bringing them
+back in at the end,
+
+in a little union bound.
+
+And we get our 1 over
+n probability this way.
+
+But the key idea is you
+reduce the number of edges
+
+by half at each stage.
+
+Enough for you to look at later,
+I guess to figure this out
+
+or you have any
+questions about this?
+
+So that's the last
+equations and calculation.
+
+I'm going to go onto a new
+idea, more conceptual stuff.
+
+Familiar problem,
+breadth-first spanning trees,
+
+setting up breadth-first
+paths to every node,
+
+but we're going to study
+it in our new setting.
+
+We have a connected graph.
+
+This time, let's suppose that
+it has a distinguished vertex,
+
+like it already has a leader.
+
+So it has a distinguished
+vertex in the graph
+
+that's going to become
+the root of the BFS tree.
+
+And the processes don't
+need any knowledge
+
+about the graph for this one.
+
+For the rest of the
+time today and Thursday,
+
+we'll assume the processes
+have unique identifiers,
+
+and I don't think we're
+using any probabilities.
+
+So this is just going to be
+using the unique identifiers
+
+to solve our problems.
+
+So everybody knows its
+own unique identifier.
+
+The root has a distinguished,
+generally known,
+
+unique identifier say i0.
+
+And the process that
+has i0 knows hey,
+
+I'm at the root of the graph.
+
+So the set up make sense?
+
+We might as well
+assume that everybody
+
+knows the unique identifiers
+of their neighbors
+
+because they could easily
+exchange information
+
+now, and match up who's
+connected on which port
+
+by a unique identifier.
+
+We'll just do deterministic.
+
+There'll be a little bit
+of non-determinism here.
+
+I'll say more about that.
+
+But I'm not going to worry
+about probabilities for this.
+
+Well that told you
+about the general setup.
+
+What are the processes
+supposed to do?
+
+Well they're supposed to compute
+a breadth-first spanning tree,
+
+rooted at vertex v0.
+
+The branches are
+going to be directed
+
+paths in this undirected
+graph, coming from v0.
+
+Spanning means they should
+reach all the vertices.
+
+And breadth-first means that
+if a vertex is at a distance
+
+d from v0, it will appear at
+depth d in this spanning tree.
+
+So everybody should get a
+shortest path from the root.
+
+Now how are we going to compute
+this in a distributed setting?
+
+Well now the output
+of a process is just
+
+going to be its
+parent in the tree.
+
+So we're not actually going
+to compute this tree anywhere
+
+as a whole.
+
+Everybody's just going to
+know its parent in the tree.
+
+Questions?
+
+Problem make sense?
+
+So this is just an example
+of a spanning tree,
+
+breadth-first spanning tree.
+
+This gives you shortest
+paths to all of the nodes, ,
+
+shortest in terms of
+the number of hops.
+
+So we can have a very,
+very simple algorithm.
+
+We're going to let the processes
+mark themselves as they
+
+get included in the tree.
+
+Starts out only the first
+process, i0, is marked.
+
+So do you want to give an idea,
+maybe, of how this might work?
+
+Sketch out-- yeah?
+
+AUDIENCE: The root will
+send out to its neighbors.
+
+And they will then
+mark themselves
+
+as the parent of
+whoever they heard from.
+
+Then they will--
+
+NANCY LYNCH: This
+is all synchronous.
+
+So that's great.
+
+They'll be doing this
+in synchronous rounds.
+
+So everybody will, at
+the certain distance,
+
+is going to get the message
+at the right number of rounds
+
+to mark their distance.
+
+OK so in round one,
+process i0 will
+
+send a special
+message, say search,
+
+to all of its neighbors.
+
+And anybody who receives
+a message in round one
+
+will mark itself,
+decide i0 is its parent,
+
+could output that i0 is
+my parent, parent i0.
+
+And then it can get
+ready for the next round,
+
+when it's supposed to
+send to continue this.
+
+So at later rounds, if you
+decided you're going to send,
+
+if you know you're supposed to
+send from the previous round,
+
+then you send a search message
+to all of your neighbors.
+
+Now the process is
+sitting there and it
+
+receives a search message.
+
+If he's already marked, then he
+should just ignore the message.
+
+Once you're included
+in the tree,
+
+you don't care if you
+get other messages,
+
+search messages on other paths.
+
+So you only do anything
+if you're not yet marked
+
+and you receive a message.
+
+And in that case, then
+you mark yourself.
+
+Then you mark
+yourself, and then you
+
+choose one of your neighbors
+as to be your parent.
+
+Now because this
+is synchronous, you
+
+have several nodes that could
+be sending at the same time.
+
+So one node could be
+receiving search messages
+
+from several different
+neighbors at once.
+
+Well, it wants to choose
+one of them as its parent,
+
+doesn't matter which
+one it chooses.
+
+So it can just choose
+nondeterminstically just
+
+arbitrarily.
+
+And then it decides that it
+will send the next round.
+
+Is the algorithm clear?
+
+So there's, I mentioned, a
+little bit of nondeterministic
+
+here, only in that a process
+can choose arbitrarily
+
+among several possible parents.
+
+And then we could
+put in a default,
+
+saying that it chooses the
+one with the smallest ID,
+
+if we really want to
+make it deterministic.
+
+But it's also OK to leave
+distributed algorithms
+
+nondeterministic.
+
+And here I should
+make a remark that
+
+shows how differently
+nondeterminism
+
+is regarded in the
+distributed setting,
+
+from the way it is for
+sequential algorithms.
+
+For distributed algorithms,
+there can be many options.
+
+And maybe they're all OK.
+
+But the algorithm is
+supposed to work correctly,
+
+no matter how you resolve
+the nondeterministic choices.
+
+So think about like
+np, and the other ways
+
+that you've seen
+nondeterminism so far.
+
+There you say you're lucky if
+there is a path to a choice.
+
+Here when you make a
+nondeterministic choice,
+
+or when the algorithm
+behaves nondeterministically,
+
+all the choices are
+supposed to work.
+
+It's like all the paths have to
+come up with correct answers.
+
+Do you have a question?
+
+AUDIENCE: Yes, whenever
+there's a sub- [INAUDIBLE],
+
+whenever there's
+a race condition,
+
+we locally assume that
+there wasn't a difference
+
+in local computation time.
+
+But if there is, even
+in the slightest,
+
+then they would get a parent
+[INAUDIBLE] before another one,
+
+it would still be a valid--
+
+NANCY LYNCH: So the
+synchronous model
+
+is more abstract than that.
+
+You don't model the
+local computation time.
+
+You're moving more toward
+an asynchronous model,
+
+where the steps can take
+differing amounts of time.
+
+Here we just assume you have
+an abstract model, where
+
+everybody does stuff
+at once, in each round.
+
+But you still have
+nondeterminism
+
+because they can all arrive
+at the same round somewhere.
+
+But it's OK.
+
+You can pick any one
+and it still works.
+
+So it should be not hard to
+see that this does give you
+
+a BFS tree because you're
+creating all the branches
+
+synchronously.
+
+And you're growing
+one hop at each round.
+
+It reaches all the
+nodes eventually
+
+because the graph is connected.
+
+And everybody sends messages
+once a node get marked.
+
+It sends messages
+to its neighbors.
+
+So eventually, the
+markings are going
+
+to reach all the neighbors,
+all the nodes in the graph.
+
+So here's how you get the
+example I showed before,
+
+simple breadth-first search.
+
+That's a search message
+sent by this guy.
+
+I put it to the
+right of the edge
+
+to indicate-- it's kind
+of hard to distinguish.
+
+But I put them on
+the right of the edge
+
+from the point of
+view of the sender.
+
+So he sends a search message.
+
+it gets there.
+
+This arrow just indicates
+that it reached the other end.
+
+And this guy has
+chosen the sender,
+
+which is the other direction
+on the arrow, as its parent.
+
+Now the recipient is going
+to send some search messages.
+
+So he sends four of them.
+
+They all get to the other end.
+
+And OK, so all these
+guys now get marked.
+
+They're included
+in the BFS tree.
+
+And now the next round,
+they all send some messages.
+
+I'm not putting in the messages
+where somebody would send back
+
+to a guy who sent to him.
+
+But I put in all the others.
+
+Some of them are
+going to be ignored.
+
+But you do get to a
+few new nodes this way.
+
+That's round three.
+
+Round four, everybody sends.
+
+And now you have all
+the nodes included.
+
+So this gives you
+the spanning tree
+
+that I showed at the
+beginning of this topic.
+
+This is not a very
+complicated algorithm.
+
+But I think you can see
+that things can get worse.
+
+And you want to argue about why
+the algorithms work correctly.
+
+So as I said before,
+a popular method
+
+of reasoning about
+the algorithms
+
+is to state invariance.
+
+So here, suppose
+I want to describe
+
+the state of the entire
+network, after some number, r,
+
+of rounds.
+
+what could you say about that?
+
+What's the case after r
+rounds of this algorithm?
+
+Yeah.
+
+AUDIENCE: All nodes at
+distance r from the root
+
+have been marked.
+
+NANCY LYNCH: All the nodes
+at distance r from the root
+
+have been marked.
+
+In fact, only those by
+round r, only the ones
+
+with distances up through
+r have been marked.
+
+So to state the invariance, if
+you want to state invariance,
+
+I have to say what's in
+the state of the processes.
+
+So all right, what can we say?
+
+So the process has a Boolean
+that says whether or not
+
+it's marked.
+
+It has a place to
+record a parent.
+
+And it has someplace
+where it puts information
+
+about whether it's
+supposed to send
+
+a message at the next round.
+
+And we also should
+know its UID, so I'll
+
+put that in another
+state variable.
+
+So here is something I
+can say in invariance.
+
+At the end of r rounds, as you
+said, at the end of r rounds
+
+exactly the processes
+at distance at most r
+
+from the source node, the
+root node, are marked.
+
+I can say a little more.
+
+I can say a process has its
+parents defined if and only
+
+if it's marked.
+
+So it doesn't just get market.
+
+It also computes a
+parent, and the parent
+
+gets computed at the point
+where it gets marked.
+
+Then I should say that
+the parent is correct.
+
+So for any process that's at
+distance d from the source,
+
+if the parent is
+defined, then it's
+
+in fact the UID of a process
+at distance d minus 1
+
+from the source.
+
+So that says it's
+actually getting
+
+a correct breadth-first tree.
+
+It's getting the parent
+on a shortest path.
+
+Yeah?
+
+AUDIENCE: Do these invariants
+[INAUDIBLE] for i0?
+
+NANCY LYNCH:
+Distance 0 is marked.
+
+i0 doesn't ever-- I
+see what you're saying.
+
+i0 doesn't have a parent.
+
+So I guess that we
+should say for i
+
+not equal to i0 in this case.
+
+So this would be a
+process other than i0.
+
+It would have its
+parent defined,
+
+if and only if it's marked.
+
+Well as I think
+you just noticed,
+
+the root node is marked but
+it doesn't have a parent.
+
+So it's an exception.
+
+But this should be,
+this doesn't involve i0.
+
+So the second one, I
+can fix that a bit.
+
+Other comments, questions?
+
+So if somebody wanted to
+do a formal correctness
+
+proof of an algorithm
+like this one,
+
+you would use these invariants.
+
+You prove it by induction.
+
+In fact there's
+quite a few people
+
+who use interactive theorem
+provers to do proofs
+
+like this because the algorithms
+can get pretty complicated,
+
+with a lot of variables.
+
+So you have to do
+some bookkeeping.
+
+You keep track of
+all these invariants,
+
+and then you want to prove that
+they're all true by induction.
+
+They all hold through
+an inductive step.
+
+So you can use an
+interactive theorem prover
+
+to help you do the bookkeeping.
+
+But even a manual proof
+in a research paper
+
+would use invariance
+in this style.
+
+OK complexity.
+
+So the number of rounds until
+everybody outputs their parent
+
+would be the maximum
+distance of any node from v0.
+
+So we can say that's at most
+the diameter of the graph.
+
+It could be less.
+
+It's just is the
+maximum distance
+
+from this particular node.
+
+Message complexity?
+
+Well how many messages are
+sent in this algorithm?
+
+So everybody is going
+to send messages
+
+only once on all of its edges.
+
+So that means all the
+edges get a message sent
+
+in each direction just once.
+
+So it's order of
+the number of edges.
+
+All right, so we can
+play around with this.
+
+So this algorithm just tells
+everybody who his parent is.
+
+But maybe when you're
+finished, you'd
+
+like to who your
+children are as well.
+
+For many uses of
+these trees, you'd
+
+like to have a parent be
+able to talk to its children
+
+in the tree.
+
+So how to do that?
+
+Well you can add a child
+pointer because anybody
+
+who gets a search message
+and selects its parents
+
+could send back a message
+to that parents saying, hey,
+
+I'm your child.
+
+And if you get a search message,
+and you decide that that's not
+
+your parent, you can
+help that guy out
+
+by sending a message saying
+you're not my parent.
+
+In the synchronous
+case, he would just
+
+know that, if he didn't
+get a parent message.
+
+But things are going to
+get more complicated.
+
+So we'll send parents
+or non parent responses
+
+to the search messages.
+
+Suppose we want to compute
+the distances from v0,
+
+not just to the parents are.
+
+Well that's easy.
+
+Everybody can just record
+its distances, as well as
+
+its parent and the mark.
+
+And then you just include
+your own distance value
+
+in your search message.
+
+And when somebody
+receives a search message,
+
+it sets its own distance to
+the received distance plus 1.
+
+So we can just keep track
+and add one to the distance.
+
+It's easy to augment
+this algorithm
+
+to get this extra information.
+
+All right, now how
+do the processes know
+
+when this is all finished?
+
+So everybody was able
+to output parent.
+
+I know who my parent is.
+
+But how does anybody
+know when the entire tree
+
+has been produced?
+
+Not so obvious.
+
+So in some settings, you
+might know an upper bound
+
+on the depth of the tree.
+
+And then you could just wait
+for that number of rounds.
+
+But what if you don't know that?
+
+You don't know anything
+about the graph.
+
+Nobody knows.
+
+So let's come up
+with an algorithm
+
+for process i0, the root,
+to know definitively
+
+that the tree has been
+completely constructed.
+
+Ideas?
+
+You're creating this
+by search messages.
+
+How is i0 going to
+know when its done?
+
+Yeah.
+
+AUDIENCE: Every time
+you mark a node,
+
+the node can send a
+message back to its parent,
+
+saying hi, I've been marked.
+
+Then you can probably get
+all the way back to the root.
+
+And then the root can count
+the number of-- actually,
+
+no if the root doesn't--
+
+NANCY LYNCH: Root doesn't
+know the number of nodes.
+
+So that's a good idea.
+
+AUDIENCE: If you
+don't have a child,
+
+you can tell your parent
+that you don't have a child.
+
+NANCY LYNCH: That's
+a good start.
+
+Was there another?
+
+Yeah.
+
+AUDIENCE: More
+generally, you just
+
+send a signal when you
+know your sub-tree is done.
+
+NANCY LYNCH: When you know
+you're sub-tree is done,
+
+so that means you're going
+to be communicating something
+
+up the tree.
+
+Right, so that's the idea
+that you're working toward.
+
+So a termination
+algorithm to inform i0
+
+when the tree is
+completely constructed.
+
+So let's say that the search
+messages get their responses.
+
+So everybody knows
+which nodes are their,
+
+which neighbors are its
+children, and which are not.
+
+So suppose a node
+has gotten responses
+
+to all of its search messages,
+knows who all its children are.
+
+Now the leaves in
+this tree are going
+
+to know that they're leaves.
+
+How do they know that?
+
+Propagating all these search
+messages, and I'm a leaf.
+
+How do I know I'm a leaf?
+
+AUDIENCE: You can't
+have children.
+
+NANCY LYNCH: Yeah, you send
+all these search messages,
+
+and everybody says, sorry
+you're not my parent.
+
+So you know you have no
+children because of the kind
+
+of responses you get.
+
+So now we're going
+to use what we
+
+call a convergecast strategy.
+
+Broadcast is sending things out.
+
+Convergecast is fanning
+in information back
+
+to the top of the tree.
+
+So the convergecast
+would say, all right,
+
+so the leaves would send
+a message to their parents
+
+saying they're done.
+
+Now if I'm some node in
+the middle of the tree,
+
+how do I know I'm done?
+
+Well it's what you said.
+
+You know that you
+can figure out when
+
+your entire sub-tree is done.
+
+Well first of all, you have
+to know your children are.
+
+It's kind of a
+two stage process.
+
+You have to know who
+your children are,
+
+by having received responses
+to all your search messages.
+
+And you wait to receive
+done messages from all
+
+of your actual children.
+
+So if I'm sitting in
+the middle of the tree,
+
+and I've got done messages
+from all my children,
+
+I know my whole
+sub-tree is done.
+
+Then I can send the done
+message to my parent.
+
+Got that?
+
+That's how convergecast works.
+
+And when it reaches
+the top, if i0
+
+knows who its children are,
+and it receives done messages
+
+from all its children, it
+knows the whole tree is done.
+
+So it can output that the
+tree construction is complete.
+
+And it could tell
+the others by sending
+
+a message down the tree,
+so they all know as well.
+
+Questions?
+
+AUDIENCE: Wouldn't i0
+be the last one to know?
+
+NANCY LYNCH: He'd
+be the last one.
+
+No, he'd be the first one to
+know that the whole tree is
+
+complete.
+
+Everybody else knows when
+their sub-tree is complete.
+
+So i0 still has to now send
+another message down the tree
+
+to tell everyone else the
+entire tree is complete.
+
+Is there another question?
+
+All right so this
+isn't showing that.
+
+This is just showing done
+messages, which are actually
+
+going in the opposite
+direction from these edges,
+
+going up the tree.
+
+But you can just see
+how they propagate up
+
+until the roots says done.
+
+No big deal.
+
+Complexity for termination.
+
+Well it just takes at most
+diameter rounds and n messages
+
+for this done information
+to come up to the top,
+
+once the tree
+actually is finished.
+
+Because now you're
+just sending messages
+
+on the paths in this
+tree, which are only,
+
+at most, diameter in length.
+
+And this is just the process
+i0 can tell everybody else.
+
+It doesn't take
+very long either.
+
+Applications, well suppose you
+construct a tree like this.
+
+And process i0 now wants
+to use it to communicate.
+
+It wants to send a
+whole batch of messages
+
+to all the other nodes.
+
+It can just send
+them now on the tree.
+
+It's an easy way to
+make sure messages reach
+
+everybody else in the network.
+
+Just send them on the edges
+of the breadth-first spanning
+
+tree.
+
+So now the messages,
+each individual message
+
+takes at most n
+message instances
+
+along the edges of the
+tree, because you only have
+
+to traverse the tree edges.
+
+No more dependence on the total
+number of edges in the network.
+
+And in fact, you can
+save time by pipelining
+
+a series of messages.
+
+So you can send them one
+round after the other.
+
+The other way, suppose you want
+to compute something globally.
+
+Suppose everybody starts
+with some initial value.
+
+And process i0 is going
+to try to determine
+
+the value of some function
+of everybody's initial value,
+
+like the minimum or maximum
+or the sum or anything.
+
+Well you can do this
+while convergecasting
+
+on an already built BFS tree.
+
+So everybody can just send
+their information up the tree,
+
+and i0 can collect it all.
+
+In general, you
+can accumulate, you
+
+can do data aggregation as you
+go up the paths of the tree.
+
+So the message size
+doesn't blow up.
+
+So if you want, for example,
+the sum of everybody's values,
+
+everybody just sends their
+values up in a convergecast.
+
+And each node computes
+the sum of all the values
+
+in its sub-tree.
+
+So this is pretty efficient.
+
+Make sense?
+
+I'm going to skip this.
+
+But you could do leader
+election in a general graph,
+
+If you don't have
+a leader, already,
+
+i0 by having everybody
+run a breadth-first search
+
+in parallel.
+
+But we'll skip that.
+
+Because I just wanted to
+have a couple of minutes
+
+to start the last topic, and
+we'll pick it up next time.
+
+So it's the obvious extension.
+
+Instead of just
+breadth-first search trees,
+
+let's put weights
+on the edges and try
+
+to compute shortest paths trees
+in terms of the total weight
+
+of the path.
+
+So we're going to add weights.
+
+It's an undirected graph.
+
+So it's just a weight
+for each undirected edge.
+
+I'll still have a starting
+node, vertex v0 with process i0.
+
+Still have unique identifiers.
+
+And I'll assume the processes
+know who their neighbors are.
+
+And they know the
+weights of the incident
+
+edges, their adjacent edges.
+
+But otherwise they
+don't need to know
+
+anything else about the graph.
+
+So again, this is
+a familiar problem.
+
+But we're looking at it
+in a very different way,
+
+by distributing it.
+
+so the processes are supposed to
+compute a shortest paths tree,
+
+in the sense that
+everybody should
+
+output its parent in the tree.
+
+And let's say they output
+the distance as well,
+
+the weighted distance
+from the root node.
+
+So this is called
+Bellman-Ford's algorithm.
+
+Again it's got the same name
+in the distributed setting.
+
+The Bellman-Ford
+shortest paths algorithm.
+
+So everybody is keeping
+track of their current best
+
+distance that they
+know, and their parent.
+
+And they know their
+unique identifier.
+
+And here's how the
+algorithm works.
+
+This will look
+familiar from when
+
+you had Bellman-Ford earlier.
+
+At every round,
+everybody is going
+
+to send its distance
+to its neighbors.
+
+Instead of just sending
+a search message,
+
+now it will send its actual
+distance information.
+
+And you receive the messages
+from your neighbors.
+
+And now you do a relaxation
+step, as you've seen before.
+
+You look at the current
+distance you have.
+
+And you see if you've
+gotten a new distance
+
+from a neighbor, such that if
+you add the new distance you
+
+receive to the weight of
+the edge between yourself
+
+and that neighbor, you
+get something better
+
+than what you had before.
+
+If you get that, then you're
+going to improve your distance.
+
+And if you improve
+your distance,
+
+then you're going
+to reset your parent
+
+to the sender of this new,
+better distance information.
+
+So does this
+algorithm make sense?
+
+It's like what you saw before.
+
+But there's no running
+through all the nodes.
+
+Each node is doing
+its own thing.
+
+It's waiting to get better
+distance information
+
+and re-computing.
+
+And then it's going to
+be sending out its better
+
+information at the next round.
+
+Question?
+
+So this is kind of a jump
+in the way of thinking.
+
+All right, so now I'm just
+going to end basically
+
+with an animation that'll
+show you the kinds of things
+
+that happen here.
+
+All right so you start
+out with the initial node.
+
+And what's recorded in the
+circle is the best distances.
+
+The rest of these, the best
+distance they know is infinity.
+
+So I didn't write that.
+
+So this guy knows 0 After one
+round, he sent two messages.
+
+The best distance each
+of these guys knows
+
+is just the weight of the
+edge between v0 and itself.
+
+So this guy's now estimating
+it's distance at 16
+
+and this guy at 1.
+
+16 is not very good because it's
+actually very roundabout routes
+
+that can get there.
+
+But it's going to take us some
+time to make that adjustment.
+
+After two rounds, everybody
+is sending their distance
+
+information.
+
+But now we get a
+correction here.
+
+This used to say 16.
+
+But now we have a
+two hop path that
+
+gives you a better distance.
+
+So you get the 1 plus the 14.
+
+So he's going to here,
+about the distance of 15
+
+as a result of what 1 sends.
+
+And some new guys get their
+distance is calculated
+
+And then after three rounds, it
+gets a little bit complicated.
+
+So maybe I'm just going to
+flip through it quickly and let
+
+you study later.
+
+But you see that you keep
+getting improvements,
+
+as you perform relaxation steps.
+
+As information gets to
+somebody by better paths that
+
+happen to have
+more hops, they're
+
+going to be reducing
+their estimates.
+
+I'm going to flip, and you
+see that this guy's estimate
+
+is going down.
+
+And in the end, after
+eight rounds of this,
+
+you end up with a
+very roundabout path
+
+that actually gives this
+guy a much better estimate.
+
+So you can see how that works.
+
+So the claim is that
+eventually, every process
+
+will have its distance being
+a correct minimum weight
+
+of the path, and its
+parent will be correct.
+
+I think maybe this is
+a good place to stop.
+
+We'll pick up with this
+algorithm and its analysis.
+
+Most of next time
+is going to be spent
+
+on asynchronous
+algorithms, which
+
+is a whole other
+level of complication.
+
+So I'll see you on Thursday.
\ No newline at end of file
diff --git a/nHcpzcATn1c.txt b/nHcpzcATn1c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0bd0a20aa10e74c9ffa80a8ce8aaecf08f0d29c3
--- /dev/null
+++ b/nHcpzcATn1c.txt
@@ -0,0 +1,9011 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
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+The following content is provided under
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+
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+ 
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+will help MIT Open Courseware continue
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+resources for free. To make a donation
+or view additional materials from
+
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+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Our our next module is called people,
+
+ align:start position:0%
+Our our next module is called people,
+ 
+
+ align:start position:0%
+Our our next module is called people,
+the heart of lean. And I'm going to
+
+ align:start position:0%
+the heart of lean. And I'm going to
+ 
+
+ align:start position:0%
+the heart of lean. And I'm going to
+start out with you uh by giving you the
+
+ align:start position:0%
+start out with you uh by giving you the
+ 
+
+ align:start position:0%
+start out with you uh by giving you the
+two primary messages that I want you to
+
+ align:start position:0%
+two primary messages that I want you to
+ 
+
+ align:start position:0%
+two primary messages that I want you to
+take away from this module. Those of you
+
+ align:start position:0%
+take away from this module. Those of you
+ 
+
+ align:start position:0%
+take away from this module. Those of you
+who've either taken classes with me or
+
+ align:start position:0%
+who've either taken classes with me or
+ 
+
+ align:start position:0%
+who've either taken classes with me or
+written papers with me or made
+
+ align:start position:0%
+written papers with me or made
+ 
+
+ align:start position:0%
+written papers with me or made
+presentations with me know I'm a big fan
+
+ align:start position:0%
+presentations with me know I'm a big fan
+ 
+
+ align:start position:0%
+presentations with me know I'm a big fan
+of this. Um putting all the messages up
+
+ align:start position:0%
+of this. Um putting all the messages up
+ 
+
+ align:start position:0%
+of this. Um putting all the messages up
+front because I want you to be able to
+
+ align:start position:0%
+front because I want you to be able to
+ 
+
+ align:start position:0%
+front because I want you to be able to
+hear how they are confirmed by some of
+
+ align:start position:0%
+hear how they are confirmed by some of
+ 
+
+ align:start position:0%
+hear how they are confirmed by some of
+the data I'm going to show you and some
+
+ align:start position:0%
+the data I'm going to show you and some
+ 
+
+ align:start position:0%
+the data I'm going to show you and some
+of the concepts we're talking about. So
+
+ align:start position:0%
+of the concepts we're talking about. So
+ 
+
+ align:start position:0%
+of the concepts we're talking about. So
+the first is that lean can only work if
+
+ align:start position:0%
+the first is that lean can only work if
+ 
+
+ align:start position:0%
+the first is that lean can only work if
+the people who are doing the work really
+
+ align:start position:0%
+the people who are doing the work really
+ 
+
+ align:start position:0%
+the people who are doing the work really
+wanted to succeed. and we saw that
+
+ align:start position:0%
+wanted to succeed. and we saw that
+ 
+
+ align:start position:0%
+wanted to succeed. and we saw that
+echoed at the New Balance Planter. We've
+
+ align:start position:0%
+echoed at the New Balance Planter. We've
+ 
+
+ align:start position:0%
+echoed at the New Balance Planter. We've
+heard that talked about in many modules
+
+ align:start position:0%
+heard that talked about in many modules
+ 
+
+ align:start position:0%
+heard that talked about in many modules
+during the course of this three-day
+
+ align:start position:0%
+during the course of this three-day
+ 
+
+ align:start position:0%
+during the course of this three-day
+class. The second one is that each one
+
+ align:start position:0%
+class. The second one is that each one
+ 
+
+ align:start position:0%
+class. The second one is that each one
+of you in this room are very shortly
+
+ align:start position:0%
+of you in this room are very shortly
+ 
+
+ align:start position:0%
+of you in this room are very shortly
+going to be in a power uh in a position
+
+ align:start position:0%
+going to be in a power uh in a position
+ 
+
+ align:start position:0%
+going to be in a power uh in a position
+to influence and to motivate people and
+
+ align:start position:0%
+to influence and to motivate people and
+ 
+
+ align:start position:0%
+to influence and to motivate people and
+have the power to actually make a
+
+ align:start position:0%
+have the power to actually make a
+ 
+
+ align:start position:0%
+have the power to actually make a
+difference. And we want you to pay
+
+ align:start position:0%
+difference. And we want you to pay
+ 
+
+ align:start position:0%
+difference. And we want you to pay
+attention to it for that reason because
+
+ align:start position:0%
+attention to it for that reason because
+ 
+
+ align:start position:0%
+attention to it for that reason because
+it's going to be very important.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So there are two distinctive features of
+
+ align:start position:0%
+So there are two distinctive features of
+ 
+
+ align:start position:0%
+So there are two distinctive features of
+a lot of these lean systems and a lot of
+
+ align:start position:0%
+a lot of these lean systems and a lot of
+ 
+
+ align:start position:0%
+a lot of these lean systems and a lot of
+time we spend focusing here on the
+
+ align:start position:0%
+time we spend focusing here on the
+ 
+
+ align:start position:0%
+time we spend focusing here on the
+production aspects of just in time but
+
+ align:start position:0%
+production aspects of just in time but
+ 
+
+ align:start position:0%
+production aspects of just in time but
+there's also a second system going on
+
+ align:start position:0%
+there's also a second system going on
+ 
+
+ align:start position:0%
+there's also a second system going on
+that these authors have called the
+
+ align:start position:0%
+that these authors have called the
+ 
+
+ align:start position:0%
+that these authors have called the
+respect for human system and they define
+
+ align:start position:0%
+respect for human system and they define
+ 
+
+ align:start position:0%
+respect for human system and they define
+it as a place where workers are allowed
+
+ align:start position:0%
+it as a place where workers are allowed
+ 
+
+ align:start position:0%
+it as a place where workers are allowed
+to display in full their capabilities
+
+ align:start position:0%
+to display in full their capabilities
+ 
+
+ align:start position:0%
+to display in full their capabilities
+through active participation in running
+
+ align:start position:0%
+through active participation in running
+ 
+
+ align:start position:0%
+through active participation in running
+and improving their own workshops. So we
+
+ align:start position:0%
+and improving their own workshops. So we
+ 
+
+ align:start position:0%
+and improving their own workshops. So we
+saw this at the New Balance factory tour
+
+ align:start position:0%
+saw this at the New Balance factory tour
+ 
+
+ align:start position:0%
+saw this at the New Balance factory tour
+and it was embodied by that eighth waste
+
+ align:start position:0%
+and it was embodied by that eighth waste
+ 
+
+ align:start position:0%
+and it was embodied by that eighth waste
+that they put up on the board. You know,
+
+ align:start position:0%
+that they put up on the board. You know,
+ 
+
+ align:start position:0%
+that they put up on the board. You know,
+we had shown you seven in class and they
+
+ align:start position:0%
+we had shown you seven in class and they
+ 
+
+ align:start position:0%
+we had shown you seven in class and they
+added eighth. The eighth waste was
+
+ align:start position:0%
+added eighth. The eighth waste was
+ 
+
+ align:start position:0%
+added eighth. The eighth waste was
+employee creativity. That's something
+
+ align:start position:0%
+employee creativity. That's something
+ 
+
+ align:start position:0%
+employee creativity. That's something
+that they did not want to waste. And it
+
+ align:start position:0%
+that they did not want to waste. And it
+ 
+
+ align:start position:0%
+that they did not want to waste. And it
+speaks very powerfully to how much they
+
+ align:start position:0%
+speaks very powerfully to how much they
+ 
+
+ align:start position:0%
+speaks very powerfully to how much they
+have taken to heart and implemented the
+
+ align:start position:0%
+have taken to heart and implemented the
+ 
+
+ align:start position:0%
+have taken to heart and implemented the
+respect for human system in their plant.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+As engineers, we spend a lot of time
+
+ align:start position:0%
+As engineers, we spend a lot of time
+ 
+
+ align:start position:0%
+As engineers, we spend a lot of time
+learning about, practicing, doing
+
+ align:start position:0%
+learning about, practicing, doing
+ 
+
+ align:start position:0%
+learning about, practicing, doing
+problem sets about what we think of as
+
+ align:start position:0%
+problem sets about what we think of as
+ 
+
+ align:start position:0%
+problem sets about what we think of as
+the hard stuff. All of the technical
+
+ align:start position:0%
+the hard stuff. All of the technical
+ 
+
+ align:start position:0%
+the hard stuff. All of the technical
+knowledge, the engineering science we're
+
+ align:start position:0%
+knowledge, the engineering science we're
+ 
+
+ align:start position:0%
+knowledge, the engineering science we're
+trying to
+
+ align:start position:0%
+trying to
+ 
+
+ align:start position:0%
+trying to
+learn. But as you have heard from a
+
+ align:start position:0%
+learn. But as you have heard from a
+ 
+
+ align:start position:0%
+learn. But as you have heard from a
+bunch of practitioners through the
+
+ align:start position:0%
+bunch of practitioners through the
+ 
+
+ align:start position:0%
+bunch of practitioners through the
+course of this class, the hard stuff is
+
+ align:start position:0%
+course of this class, the hard stuff is
+ 
+
+ align:start position:0%
+course of this class, the hard stuff is
+not the hard stuff. What's really hard
+
+ align:start position:0%
+not the hard stuff. What's really hard
+ 
+
+ align:start position:0%
+not the hard stuff. What's really hard
+is what they call the soft stuff. things
+
+ align:start position:0%
+is what they call the soft stuff. things
+ 
+
+ align:start position:0%
+is what they call the soft stuff. things
+that involve people, things that involve
+
+ align:start position:0%
+that involve people, things that involve
+ 
+
+ align:start position:0%
+that involve people, things that involve
+changing culture, changing work
+
+ align:start position:0%
+changing culture, changing work
+ 
+
+ align:start position:0%
+changing culture, changing work
+practices. So, at the end of this
+
+ align:start position:0%
+practices. So, at the end of this
+ 
+
+ align:start position:0%
+practices. So, at the end of this
+module, we want you to be able to
+
+ align:start position:0%
+module, we want you to be able to
+ 
+
+ align:start position:0%
+module, we want you to be able to
+explain why people really are the key to
+
+ align:start position:0%
+explain why people really are the key to
+ 
+
+ align:start position:0%
+explain why people really are the key to
+improving productivity in organizations,
+
+ align:start position:0%
+improving productivity in organizations,
+ 
+
+ align:start position:0%
+improving productivity in organizations,
+describe how you can be an effective
+
+ align:start position:0%
+describe how you can be an effective
+ 
+
+ align:start position:0%
+describe how you can be an effective
+member of a team, and be able to compare
+
+ align:start position:0%
+member of a team, and be able to compare
+ 
+
+ align:start position:0%
+member of a team, and be able to compare
+and contrast a little bit about
+
+ align:start position:0%
+and contrast a little bit about
+ 
+
+ align:start position:0%
+and contrast a little bit about
+leadership and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+management. We're going to start with a
+
+ align:start position:0%
+management. We're going to start with a
+ 
+
+ align:start position:0%
+management. We're going to start with a
+brief active learning exercise. And the
+
+ align:start position:0%
+brief active learning exercise. And the
+ 
+
+ align:start position:0%
+brief active learning exercise. And the
+question we'd like you to think about is
+
+ align:start position:0%
+question we'd like you to think about is
+ 
+
+ align:start position:0%
+question we'd like you to think about is
+what are the most important things that
+
+ align:start position:0%
+what are the most important things that
+ 
+
+ align:start position:0%
+what are the most important things that
+contribute to your job satisfaction. So
+
+ align:start position:0%
+contribute to your job satisfaction. So
+ 
+
+ align:start position:0%
+contribute to your job satisfaction. So
+is that being a student in a class or
+
+ align:start position:0%
+is that being a student in a class or
+ 
+
+ align:start position:0%
+is that being a student in a class or
+maybe you want to think about
+
+ align:start position:0%
+maybe you want to think about
+ 
+
+ align:start position:0%
+maybe you want to think about
+participating in an internship at a
+
+ align:start position:0%
+participating in an internship at a
+ 
+
+ align:start position:0%
+participating in an internship at a
+company? Think about the things that
+
+ align:start position:0%
+company? Think about the things that
+ 
+
+ align:start position:0%
+company? Think about the things that
+really mattered to you that made you
+
+ align:start position:0%
+really mattered to you that made you
+ 
+
+ align:start position:0%
+really mattered to you that made you
+feel like your job was satisfying. I'm
+
+ align:start position:0%
+feel like your job was satisfying. I'm
+ 
+
+ align:start position:0%
+feel like your job was satisfying. I'm
+going to ask for a brainstorm and I'm
+
+ align:start position:0%
+going to ask for a brainstorm and I'm
+ 
+
+ align:start position:0%
+going to ask for a brainstorm and I'm
+going to ask Hugh to come and be our
+
+ align:start position:0%
+going to ask Hugh to come and be our
+ 
+
+ align:start position:0%
+going to ask Hugh to come and be our
+notetaker. Thank you, Hugh. And I want
+
+ align:start position:0%
+notetaker. Thank you, Hugh. And I want
+ 
+
+ align:start position:0%
+notetaker. Thank you, Hugh. And I want
+to get a good amount of these up on the
+
+ align:start position:0%
+to get a good amount of these up on the
+ 
+
+ align:start position:0%
+to get a good amount of these up on the
+board. And then what I'd like to do is
+
+ align:start position:0%
+board. And then what I'd like to do is
+ 
+
+ align:start position:0%
+board. And then what I'd like to do is
+you'll take your sticky dots that I
+
+ align:start position:0%
+you'll take your sticky dots that I
+ 
+
+ align:start position:0%
+you'll take your sticky dots that I
+handed out
+
+ align:start position:0%
+handed out
+ 
+
+ align:start position:0%
+handed out
+earlier and I'd like you to select your
+
+ align:start position:0%
+earlier and I'd like you to select your
+ 
+
+ align:start position:0%
+earlier and I'd like you to select your
+three top reasons that are on the board
+
+ align:start position:0%
+three top reasons that are on the board
+ 
+
+ align:start position:0%
+three top reasons that are on the board
+for job satisfaction. Then we're going
+
+ align:start position:0%
+for job satisfaction. Then we're going
+ 
+
+ align:start position:0%
+for job satisfaction. Then we're going
+to be able to look to see where the
+
+ align:start position:0%
+to be able to look to see where the
+ 
+
+ align:start position:0%
+to be able to look to see where the
+preponderance is in the room. All right.
+
+ align:start position:0%
+preponderance is in the room. All right.
+ 
+
+ align:start position:0%
+preponderance is in the room. All right.
+So let's start the brainstorm with uh
+
+ align:start position:0%
+So let's start the brainstorm with uh
+ 
+
+ align:start position:0%
+So let's start the brainstorm with uh
+things that contribute to your job
+
+ align:start position:0%
+things that contribute to your job
+ 
+
+ align:start position:0%
+things that contribute to your job
+satisfaction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Anybody? Tim.
+
+ align:start position:0%
+Anybody? Tim.
+ 
+
+ align:start position:0%
+Anybody? Tim.
+Go ahead. Tim first. Recognition of
+
+ align:start position:0%
+Go ahead. Tim first. Recognition of
+ 
+
+ align:start position:0%
+Go ahead. Tim first. Recognition of
+achievement. Recognition of achievement
+
+ align:start position:0%
+achievement. Recognition of achievement
+ 
+
+ align:start position:0%
+achievement. Recognition of achievement
+men. So you would like to mentor.
+
+ align:start position:0%
+men. So you would like to mentor.
+ 
+
+ align:start position:0%
+men. So you would like to mentor.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Let's stop our brainstorming there
+
+ align:start position:0%
+Okay. Let's stop our brainstorming there
+ 
+
+ align:start position:0%
+Okay. Let's stop our brainstorming there
+unless somebody feels that their their
+
+ align:start position:0%
+unless somebody feels that their their
+ 
+
+ align:start position:0%
+unless somebody feels that their their
+one, two, or three choice is not already
+
+ align:start position:0%
+one, two, or three choice is not already
+ 
+
+ align:start position:0%
+one, two, or three choice is not already
+up here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So take your dots and before everybody
+
+ align:start position:0%
+So take your dots and before everybody
+ 
+
+ align:start position:0%
+So take your dots and before everybody
+makes a mass exodus up to the board, I'd
+
+ align:start position:0%
+makes a mass exodus up to the board, I'd
+ 
+
+ align:start position:0%
+makes a mass exodus up to the board, I'd
+like you to think about which are your
+
+ align:start position:0%
+like you to think about which are your
+ 
+
+ align:start position:0%
+like you to think about which are your
+top three, have those chosen first and
+
+ align:start position:0%
+top three, have those chosen first and
+ 
+
+ align:start position:0%
+top three, have those chosen first and
+then go up to the board and place a dot
+
+ align:start position:0%
+then go up to the board and place a dot
+ 
+
+ align:start position:0%
+then go up to the board and place a dot
+next to your one and then a dot next to
+
+ align:start position:0%
+next to your one and then a dot next to
+ 
+
+ align:start position:0%
+next to your one and then a dot next to
+number two and a dot next to number
+
+ align:start position:0%
+number two and a dot next to number
+ 
+
+ align:start position:0%
+number two and a dot next to number
+three. The only rules are you cannot
+
+ align:start position:0%
+three. The only rules are you cannot
+ 
+
+ align:start position:0%
+three. The only rules are you cannot
+vote for one thing multiple times. You
+
+ align:start position:0%
+vote for one thing multiple times. You
+ 
+
+ align:start position:0%
+vote for one thing multiple times. You
+actually have to distribute your dots
+
+ align:start position:0%
+actually have to distribute your dots
+ 
+
+ align:start position:0%
+actually have to distribute your dots
+among three choices so that we can can
+
+ align:start position:0%
+among three choices so that we can can
+ 
+
+ align:start position:0%
+among three choices so that we can can
+get a flavor for that. So and ideally
+
+ align:start position:0%
+get a flavor for that. So and ideally
+ 
+
+ align:start position:0%
+get a flavor for that. So and ideally
+you should choose in advance rather than
+
+ align:start position:0%
+you should choose in advance rather than
+ 
+
+ align:start position:0%
+you should choose in advance rather than
+watching the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, we're just going to give you 30
+
+ align:start position:0%
+So, we're just going to give you 30
+ 
+
+ align:start position:0%
+So, we're just going to give you 30
+seconds to get comfortable with your own
+
+ align:start position:0%
+seconds to get comfortable with your own
+ 
+
+ align:start position:0%
+seconds to get comfortable with your own
+thoughts about that and then we'll have
+
+ align:start position:0%
+thoughts about that and then we'll have
+ 
+
+ align:start position:0%
+thoughts about that and then we'll have
+people start marching up to the board.
+
+ align:start position:0%
+people start marching up to the board.
+ 
+
+ align:start position:0%
+people start marching up to the board.
+Very good. So, 30 seconds have passed.
+
+ align:start position:0%
+Very good. So, 30 seconds have passed.
+ 
+
+ align:start position:0%
+Very good. So, 30 seconds have passed.
+So, just start going up and placing your
+
+ align:start position:0%
+So, just start going up and placing your
+ 
+
+ align:start position:0%
+So, just start going up and placing your
+dots. Remember, one dot to one item.
+
+ align:start position:0%
+dots. Remember, one dot to one item.
+ 
+
+ align:start position:0%
+dots. Remember, one dot to one item.
+Yes, you can only use three dots even
+
+ align:start position:0%
+Yes, you can only use three dots even
+ 
+
+ align:start position:0%
+Yes, you can only use three dots even
+though your strips have four or more.
+
+ align:start position:0%
+though your strips have four or more.
+ 
+
+ align:start position:0%
+though your strips have four or more.
+It's a mismatch between the commodity of
+
+ align:start position:0%
+It's a mismatch between the commodity of
+ 
+
+ align:start position:0%
+It's a mismatch between the commodity of
+the dots and the nature of the exercise.
+
+ align:start position:0%
+the dots and the nature of the exercise.
+ 
+
+ align:start position:0%
+the dots and the nature of the exercise.
+So, you get one left over that you can
+
+ align:start position:0%
+So, you get one left over that you can
+ 
+
+ align:start position:0%
+So, you get one left over that you can
+you can put on your nose or your
+
+ align:start position:0%
+you can put on your nose or your
+ 
+
+ align:start position:0%
+you can put on your nose or your
+forehead or something like that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, let's take a look at how your
+
+ align:start position:0%
+Okay. So, let's take a look at how your
+ 
+
+ align:start position:0%
+Okay. So, let's take a look at how your
+preferences fell out as a class while
+
+ align:start position:0%
+preferences fell out as a class while
+ 
+
+ align:start position:0%
+preferences fell out as a class while
+I'm blinded by the projector. So your
+
+ align:start position:0%
+I'm blinded by the projector. So your
+ 
+
+ align:start position:0%
+I'm blinded by the projector. So your
+top choice, although it was a little bit
+
+ align:start position:0%
+top choice, although it was a little bit
+ 
+
+ align:start position:0%
+top choice, although it was a little bit
+of a tie, we had intellectual challenge
+
+ align:start position:0%
+of a tie, we had intellectual challenge
+ 
+
+ align:start position:0%
+of a tie, we had intellectual challenge
+as number one, personal contribution and
+
+ align:start position:0%
+as number one, personal contribution and
+ 
+
+ align:start position:0%
+as number one, personal contribution and
+making a difference as a close second,
+
+ align:start position:0%
+making a difference as a close second,
+ 
+
+ align:start position:0%
+making a difference as a close second,
+and even a close third is having good
+
+ align:start position:0%
+and even a close third is having good
+ 
+
+ align:start position:0%
+and even a close third is having good
+colleagues to work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with. Notice a couple of outliers.
+
+ align:start position:0%
+with. Notice a couple of outliers.
+ 
+
+ align:start position:0%
+with. Notice a couple of outliers.
+So where did uh so pay is coming up here
+
+ align:start position:0%
+So where did uh so pay is coming up here
+ 
+
+ align:start position:0%
+So where did uh so pay is coming up here
+as number eight. So uh as eight votes,
+
+ align:start position:0%
+as number eight. So uh as eight votes,
+ 
+
+ align:start position:0%
+as number eight. So uh as eight votes,
+number four. So, that's still important,
+
+ align:start position:0%
+number four. So, that's still important,
+ 
+
+ align:start position:0%
+number four. So, that's still important,
+but it didn't quite make our top three.
+
+ align:start position:0%
+but it didn't quite make our top three.
+ 
+
+ align:start position:0%
+but it didn't quite make our top three.
+Interesting to
+
+ align:start position:0%
+Interesting to
+ 
+
+ align:start position:0%
+Interesting to
+note. Uh, I'd like to compare your
+
+ align:start position:0%
+note. Uh, I'd like to compare your
+ 
+
+ align:start position:0%
+note. Uh, I'd like to compare your
+answers to some data we have from a
+
+ align:start position:0%
+answers to some data we have from a
+ 
+
+ align:start position:0%
+answers to some data we have from a
+survey that was actually done by Boeing.
+
+ align:start position:0%
+survey that was actually done by Boeing.
+ 
+
+ align:start position:0%
+survey that was actually done by Boeing.
+They do this every year and ask about
+
+ align:start position:0%
+They do this every year and ask about
+ 
+
+ align:start position:0%
+They do this every year and ask about
+the components of a person's job that
+
+ align:start position:0%
+the components of a person's job that
+ 
+
+ align:start position:0%
+the components of a person's job that
+are important to their job satisfaction.
+
+ align:start position:0%
+are important to their job satisfaction.
+ 
+
+ align:start position:0%
+are important to their job satisfaction.
+And we see a lot of similar
+
+ align:start position:0%
+And we see a lot of similar
+ 
+
+ align:start position:0%
+And we see a lot of similar
+results. What I'd like to start pointing
+
+ align:start position:0%
+results. What I'd like to start pointing
+ 
+
+ align:start position:0%
+results. What I'd like to start pointing
+out is that things in this side have a
+
+ align:start position:0%
+out is that things in this side have a
+ 
+
+ align:start position:0%
+out is that things in this side have a
+low correlation with job satisfaction.
+
+ align:start position:0%
+low correlation with job satisfaction.
+ 
+
+ align:start position:0%
+low correlation with job satisfaction.
+and things on this side of the chart
+
+ align:start position:0%
+and things on this side of the chart
+ 
+
+ align:start position:0%
+and things on this side of the chart
+have a higher uh a higher correlation
+
+ align:start position:0%
+have a higher uh a higher correlation
+ 
+
+ align:start position:0%
+have a higher uh a higher correlation
+with job satisfaction. So notice that
+
+ align:start position:0%
+with job satisfaction. So notice that
+ 
+
+ align:start position:0%
+with job satisfaction. So notice that
+pay is down here sort of lowest among
+
+ align:start position:0%
+pay is down here sort of lowest among
+ 
+
+ align:start position:0%
+pay is down here sort of lowest among
+the respondents of the survey who filled
+
+ align:start position:0%
+the respondents of the survey who filled
+ 
+
+ align:start position:0%
+the respondents of the survey who filled
+this out. And while it's not quite as
+
+ align:start position:0%
+this out. And while it's not quite as
+ 
+
+ align:start position:0%
+this out. And while it's not quite as
+low as our ranking of pay here, I think
+
+ align:start position:0%
+low as our ranking of pay here, I think
+ 
+
+ align:start position:0%
+low as our ranking of pay here, I think
+some of these other issues that we found
+
+ align:start position:0%
+some of these other issues that we found
+ 
+
+ align:start position:0%
+some of these other issues that we found
+are also ahead of pay uh in ours as well
+
+ align:start position:0%
+are also ahead of pay uh in ours as well
+ 
+
+ align:start position:0%
+are also ahead of pay uh in ours as well
+as in theirs. So some of the top ones,
+
+ align:start position:0%
+as in theirs. So some of the top ones,
+ 
+
+ align:start position:0%
+as in theirs. So some of the top ones,
+they're involved in
+
+ align:start position:0%
+they're involved in
+ 
+
+ align:start position:0%
+they're involved in
+decisions. You might think about that as
+
+ align:start position:0%
+decisions. You might think about that as
+ 
+
+ align:start position:0%
+decisions. You might think about that as
+making a difference. They're encouraged
+
+ align:start position:0%
+making a difference. They're encouraged
+ 
+
+ align:start position:0%
+making a difference. They're encouraged
+to come up with new and better ways,
+
+ align:start position:0%
+to come up with new and better ways,
+ 
+
+ align:start position:0%
+to come up with new and better ways,
+make good use of the skills. They get
+
+ align:start position:0%
+make good use of the skills. They get
+ 
+
+ align:start position:0%
+make good use of the skills. They get
+recognition for doing a job well done.
+
+ align:start position:0%
+recognition for doing a job well done.
+ 
+
+ align:start position:0%
+recognition for doing a job well done.
+The conditions allow me to be
+
+ align:start position:0%
+The conditions allow me to be
+ 
+
+ align:start position:0%
+The conditions allow me to be
+productive, and they have opportunities
+
+ align:start position:0%
+productive, and they have opportunities
+ 
+
+ align:start position:0%
+productive, and they have opportunities
+to improve their skills.
+
+ align:start position:0%
+to improve their skills.
+ 
+
+ align:start position:0%
+to improve their skills.
+These are all the things that came up as
+
+ align:start position:0%
+These are all the things that came up as
+ 
+
+ align:start position:0%
+These are all the things that came up as
+the key drivers to job satisfactions,
+
+ align:start position:0%
+the key drivers to job satisfactions,
+ 
+
+ align:start position:0%
+the key drivers to job satisfactions,
+which is contrary to what a lot of
+
+ align:start position:0%
+which is contrary to what a lot of
+ 
+
+ align:start position:0%
+which is contrary to what a lot of
+people think, which is, well, if I just
+
+ align:start position:0%
+people think, which is, well, if I just
+ 
+
+ align:start position:0%
+people think, which is, well, if I just
+get paid a lot, that that's a great job
+
+ align:start position:0%
+get paid a lot, that that's a great job
+ 
+
+ align:start position:0%
+get paid a lot, that that's a great job
+and I'm going to be really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happy. So, what really makes a worker
+
+ align:start position:0%
+happy. So, what really makes a worker
+ 
+
+ align:start position:0%
+happy. So, what really makes a worker
+happy then? We have two different
+
+ align:start position:0%
+happy then? We have two different
+ 
+
+ align:start position:0%
+happy then? We have two different
+schools of thought that have emerged
+
+ align:start position:0%
+schools of thought that have emerged
+ 
+
+ align:start position:0%
+schools of thought that have emerged
+over time. So, our first one was
+
+ align:start position:0%
+over time. So, our first one was
+ 
+
+ align:start position:0%
+over time. So, our first one was
+proposed back in the 1920s. Um, a
+
+ align:start position:0%
+proposed back in the 1920s. Um, a
+ 
+
+ align:start position:0%
+proposed back in the 1920s. Um, a
+product a happy worker is a productive
+
+ align:start position:0%
+product a happy worker is a productive
+ 
+
+ align:start position:0%
+product a happy worker is a productive
+worker. That was a school of
+
+ align:start position:0%
+worker. That was a school of
+ 
+
+ align:start position:0%
+worker. That was a school of
+thought. So if you believed that a happy
+
+ align:start position:0%
+thought. So if you believed that a happy
+ 
+
+ align:start position:0%
+thought. So if you believed that a happy
+worker led to a productive worker, what
+
+ align:start position:0%
+worker led to a productive worker, what
+ 
+
+ align:start position:0%
+worker led to a productive worker, what
+would your strategy be as a
+
+ align:start position:0%
+would your strategy be as a
+ 
+
+ align:start position:0%
+would your strategy be as a
+manager? Make people happy. Right? So
+
+ align:start position:0%
+manager? Make people happy. Right? So
+ 
+
+ align:start position:0%
+manager? Make people happy. Right? So
+arose the culture of a lot of human
+
+ align:start position:0%
+arose the culture of a lot of human
+ 
+
+ align:start position:0%
+arose the culture of a lot of human
+resource departments and the focus on
+
+ align:start position:0%
+resource departments and the focus on
+ 
+
+ align:start position:0%
+resource departments and the focus on
+trying to keep workers happy in the
+
+ align:start position:0%
+trying to keep workers happy in the
+ 
+
+ align:start position:0%
+trying to keep workers happy in the
+hopes that that would make them
+
+ align:start position:0%
+hopes that that would make them
+ 
+
+ align:start position:0%
+hopes that that would make them
+productive.
+
+ align:start position:0%
+productive.
+ 
+
+ align:start position:0%
+productive.
+Now in this day and age around 2000 we
+
+ align:start position:0%
+Now in this day and age around 2000 we
+ 
+
+ align:start position:0%
+Now in this day and age around 2000 we
+really have a somewhat similar but
+
+ align:start position:0%
+really have a somewhat similar but
+ 
+
+ align:start position:0%
+really have a somewhat similar but
+reflexive take on that that a productive
+
+ align:start position:0%
+reflexive take on that that a productive
+ 
+
+ align:start position:0%
+reflexive take on that that a productive
+worker is really a happy worker and this
+
+ align:start position:0%
+worker is really a happy worker and this
+ 
+
+ align:start position:0%
+worker is really a happy worker and this
+is where lean comes from. Work on
+
+ align:start position:0%
+is where lean comes from. Work on
+ 
+
+ align:start position:0%
+is where lean comes from. Work on
+productivity, work on making people able
+
+ align:start position:0%
+productivity, work on making people able
+ 
+
+ align:start position:0%
+productivity, work on making people able
+to contribute and make a difference and
+
+ align:start position:0%
+to contribute and make a difference and
+ 
+
+ align:start position:0%
+to contribute and make a difference and
+then the result is
+
+ align:start position:0%
+then the result is
+ 
+
+ align:start position:0%
+then the result is
+happiness. But either way that you look
+
+ align:start position:0%
+happiness. But either way that you look
+ 
+
+ align:start position:0%
+happiness. But either way that you look
+at it this is really a very virtuous
+
+ align:start position:0%
+at it this is really a very virtuous
+ 
+
+ align:start position:0%
+at it this is really a very virtuous
+circle. There's some link between
+
+ align:start position:0%
+circle. There's some link between
+ 
+
+ align:start position:0%
+circle. There's some link between
+happiness and productivity. And
+
+ align:start position:0%
+happiness and productivity. And
+ 
+
+ align:start position:0%
+happiness and productivity. And
+regardless of which way the causality
+
+ align:start position:0%
+regardless of which way the causality
+ 
+
+ align:start position:0%
+regardless of which way the causality
+goes, if we are working towards both of
+
+ align:start position:0%
+goes, if we are working towards both of
+ 
+
+ align:start position:0%
+goes, if we are working towards both of
+those, we're having a good
+
+ align:start position:0%
+those, we're having a good
+ 
+
+ align:start position:0%
+those, we're having a good
+team. So I want to take a couple charts
+
+ align:start position:0%
+team. So I want to take a couple charts
+ 
+
+ align:start position:0%
+team. So I want to take a couple charts
+to show you some uh research and
+
+ align:start position:0%
+to show you some uh research and
+ 
+
+ align:start position:0%
+to show you some uh research and
+quantitative examples that link employee
+
+ align:start position:0%
+quantitative examples that link employee
+ 
+
+ align:start position:0%
+quantitative examples that link employee
+productivity to uh employee
+
+ align:start position:0%
+productivity to uh employee
+ 
+
+ align:start position:0%
+productivity to uh employee
+happiness. And I'm going to use a case
+
+ align:start position:0%
+happiness. And I'm going to use a case
+ 
+
+ align:start position:0%
+happiness. And I'm going to use a case
+of Southwest Airlines. And there was a
+
+ align:start position:0%
+of Southwest Airlines. And there was a
+ 
+
+ align:start position:0%
+of Southwest Airlines. And there was a
+wonderful case study that was done on
+
+ align:start position:0%
+wonderful case study that was done on
+ 
+
+ align:start position:0%
+wonderful case study that was done on
+this by professor Jodie Hoffer Gatell
+
+ align:start position:0%
+this by professor Jodie Hoffer Gatell
+ 
+
+ align:start position:0%
+this by professor Jodie Hoffer Gatell
+who actually did her PhD work here at
+
+ align:start position:0%
+who actually did her PhD work here at
+ 
+
+ align:start position:0%
+who actually did her PhD work here at
+MIT and she's now at Brandeise
+
+ align:start position:0%
+MIT and she's now at Brandeise
+ 
+
+ align:start position:0%
+MIT and she's now at Brandeise
+University on the faculty there. Just to
+
+ align:start position:0%
+University on the faculty there. Just to
+ 
+
+ align:start position:0%
+University on the faculty there. Just to
+give you a basic overview of Southwest
+
+ align:start position:0%
+give you a basic overview of Southwest
+ 
+
+ align:start position:0%
+give you a basic overview of Southwest
+Airlines, they're known in the industry
+
+ align:start position:0%
+Airlines, they're known in the industry
+ 
+
+ align:start position:0%
+Airlines, they're known in the industry
+for having made a profit uh every year
+
+ align:start position:0%
+for having made a profit uh every year
+ 
+
+ align:start position:0%
+for having made a profit uh every year
+since it started operation even in some
+
+ align:start position:0%
+since it started operation even in some
+ 
+
+ align:start position:0%
+since it started operation even in some
+of the down times. You can see here the
+
+ align:start position:0%
+of the down times. You can see here the
+ 
+
+ align:start position:0%
+of the down times. You can see here the
+industry average profit is in the red.
+
+ align:start position:0%
+industry average profit is in the red.
+ 
+
+ align:start position:0%
+industry average profit is in the red.
+this axis which doesn't show up well on
+
+ align:start position:0%
+this axis which doesn't show up well on
+ 
+
+ align:start position:0%
+this axis which doesn't show up well on
+the screen here in gray is the uh the
+
+ align:start position:0%
+the screen here in gray is the uh the
+ 
+
+ align:start position:0%
+the screen here in gray is the uh the
+balance between unprofitable and
+
+ align:start position:0%
+balance between unprofitable and
+ 
+
+ align:start position:0%
+balance between unprofitable and
+profitable. Southwest is in the
+
+ align:start position:0%
+profitable. Southwest is in the
+ 
+
+ align:start position:0%
+profitable. Southwest is in the
+blue. Lots of people have looked towards
+
+ align:start position:0%
+blue. Lots of people have looked towards
+ 
+
+ align:start position:0%
+blue. Lots of people have looked towards
+Southwest as a great example. Certainly
+
+ align:start position:0%
+Southwest as a great example. Certainly
+ 
+
+ align:start position:0%
+Southwest as a great example. Certainly
+everyone in the airline industry looks
+
+ align:start position:0%
+everyone in the airline industry looks
+ 
+
+ align:start position:0%
+everyone in the airline industry looks
+at Southwest and what they're doing and
+
+ align:start position:0%
+at Southwest and what they're doing and
+ 
+
+ align:start position:0%
+at Southwest and what they're doing and
+how they can improve from some of their
+
+ align:start position:0%
+how they can improve from some of their
+ 
+
+ align:start position:0%
+how they can improve from some of their
+examples. So Southwest has had a great
+
+ align:start position:0%
+examples. So Southwest has had a great
+ 
+
+ align:start position:0%
+examples. So Southwest has had a great
+safety record. Only one fatality in 35
+
+ align:start position:0%
+safety record. Only one fatality in 35
+ 
+
+ align:start position:0%
+safety record. Only one fatality in 35
+years of operation.
+
+ align:start position:0%
+years of operation.
+ 
+
+ align:start position:0%
+years of operation.
+They fly only one make of aircraft.
+
+ align:start position:0%
+They fly only one make of aircraft.
+ 
+
+ align:start position:0%
+They fly only one make of aircraft.
+These are Boeing 737s. So, as you now
+
+ align:start position:0%
+These are Boeing 737s. So, as you now
+ 
+
+ align:start position:0%
+These are Boeing 737s. So, as you now
+know from a lot of your lean training,
+
+ align:start position:0%
+know from a lot of your lean training,
+ 
+
+ align:start position:0%
+know from a lot of your lean training,
+this is going to greatly simplify all
+
+ align:start position:0%
+this is going to greatly simplify all
+ 
+
+ align:start position:0%
+this is going to greatly simplify all
+their training procedures, their
+
+ align:start position:0%
+their training procedures, their
+ 
+
+ align:start position:0%
+their training procedures, their
+maintenance, their logistics on their
+
+ align:start position:0%
+maintenance, their logistics on their
+ 
+
+ align:start position:0%
+maintenance, their logistics on their
+fleet. Compare that with an airline that
+
+ align:start position:0%
+fleet. Compare that with an airline that
+ 
+
+ align:start position:0%
+fleet. Compare that with an airline that
+operates in mixed
+
+ align:start position:0%
+operates in mixed
+ 
+
+ align:start position:0%
+operates in mixed
+fleet. They have never had a layoff of
+
+ align:start position:0%
+fleet. They have never had a layoff of
+ 
+
+ align:start position:0%
+fleet. They have never had a layoff of
+employees to reduce their costs,
+
+ align:start position:0%
+employees to reduce their costs,
+ 
+
+ align:start position:0%
+employees to reduce their costs,
+including after the 911 downturn in this
+
+ align:start position:0%
+including after the 911 downturn in this
+ 
+
+ align:start position:0%
+including after the 911 downturn in this
+industry.
+
+ align:start position:0%
+industry.
+ 
+
+ align:start position:0%
+industry.
+They are the most highly unionized major
+
+ align:start position:0%
+They are the most highly unionized major
+ 
+
+ align:start position:0%
+They are the most highly unionized major
+US airline, which is counter to what
+
+ align:start position:0%
+US airline, which is counter to what
+ 
+
+ align:start position:0%
+US airline, which is counter to what
+people think intuitively. Um, I can
+
+ align:start position:0%
+people think intuitively. Um, I can
+ 
+
+ align:start position:0%
+people think intuitively. Um, I can
+actually give you some figures on
+
+ align:start position:0%
+actually give you some figures on
+ 
+
+ align:start position:0%
+actually give you some figures on
+unionization. Um, as of the writing of
+
+ align:start position:0%
+unionization. Um, as of the writing of
+ 
+
+ align:start position:0%
+unionization. Um, as of the writing of
+this, we had Southwest at 84% unionized,
+
+ align:start position:0%
+this, we had Southwest at 84% unionized,
+ 
+
+ align:start position:0%
+this, we had Southwest at 84% unionized,
+US Air at around 83, United around 81,
+
+ align:start position:0%
+US Air at around 83, United around 81,
+ 
+
+ align:start position:0%
+US Air at around 83, United around 81,
+and then people drop off from there. So,
+
+ align:start position:0%
+and then people drop off from there. So,
+ 
+
+ align:start position:0%
+and then people drop off from there. So,
+uh, it's not that it's a non-union
+
+ align:start position:0%
+uh, it's not that it's a non-union
+ 
+
+ align:start position:0%
+uh, it's not that it's a non-union
+airline. Southwest Airlines also has
+
+ align:start position:0%
+airline. Southwest Airlines also has
+ 
+
+ align:start position:0%
+airline. Southwest Airlines also has
+point-to-point service and not hub and
+
+ align:start position:0%
+point-to-point service and not hub and
+ 
+
+ align:start position:0%
+point-to-point service and not hub and
+spoke in terms of a root structure. And
+
+ align:start position:0%
+spoke in terms of a root structure. And
+ 
+
+ align:start position:0%
+spoke in terms of a root structure. And
+the thing to note about this is that
+
+ align:start position:0%
+the thing to note about this is that
+ 
+
+ align:start position:0%
+the thing to note about this is that
+actually point-to-point route structures
+
+ align:start position:0%
+actually point-to-point route structures
+ 
+
+ align:start position:0%
+actually point-to-point route structures
+tend to be less profitable business
+
+ align:start position:0%
+tend to be less profitable business
+ 
+
+ align:start position:0%
+tend to be less profitable business
+models than hub and spoke business
+
+ align:start position:0%
+models than hub and spoke business
+ 
+
+ align:start position:0%
+models than hub and spoke business
+models. So already Southwest is a little
+
+ align:start position:0%
+models. So already Southwest is a little
+ 
+
+ align:start position:0%
+models. So already Southwest is a little
+bit of at a disadvantage in terms of
+
+ align:start position:0%
+bit of at a disadvantage in terms of
+ 
+
+ align:start position:0%
+bit of at a disadvantage in terms of
+revenues because they're not generating
+
+ align:start position:0%
+revenues because they're not generating
+ 
+
+ align:start position:0%
+revenues because they're not generating
+as many revenues, but yet they maintain
+
+ align:start position:0%
+as many revenues, but yet they maintain
+ 
+
+ align:start position:0%
+as many revenues, but yet they maintain
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+profits. They consistently offer you
+
+ align:start position:0%
+profits. They consistently offer you
+ 
+
+ align:start position:0%
+profits. They consistently offer you
+some of the lowest fairs in this
+
+ align:start position:0%
+some of the lowest fairs in this
+ 
+
+ align:start position:0%
+some of the lowest fairs in this
+industry. They're a favorite of both
+
+ align:start position:0%
+industry. They're a favorite of both
+ 
+
+ align:start position:0%
+industry. They're a favorite of both
+investors and employees alike. Uh
+
+ align:start position:0%
+investors and employees alike. Uh
+ 
+
+ align:start position:0%
+investors and employees alike. Uh
+investors judge by the stock price of
+
+ align:start position:0%
+investors judge by the stock price of
+ 
+
+ align:start position:0%
+investors judge by the stock price of
+this airline and the
+
+ align:start position:0%
+this airline and the
+ 
+
+ align:start position:0%
+this airline and the
+capitalization. So what is it exactly
+
+ align:start position:0%
+capitalization. So what is it exactly
+ 
+
+ align:start position:0%
+capitalization. So what is it exactly
+that makes Southwest so successful?
+
+ align:start position:0%
+that makes Southwest so successful?
+ 
+
+ align:start position:0%
+that makes Southwest so successful?
+Now, Professor Hoffer Gatell argues in
+
+ align:start position:0%
+Now, Professor Hoffer Gatell argues in
+ 
+
+ align:start position:0%
+Now, Professor Hoffer Gatell argues in
+her book, The Southwest Airlines Way,
+
+ align:start position:0%
+her book, The Southwest Airlines Way,
+ 
+
+ align:start position:0%
+her book, The Southwest Airlines Way,
+that it's really a function of their
+
+ align:start position:0%
+that it's really a function of their
+ 
+
+ align:start position:0%
+that it's really a function of their
+organizational
+
+ align:start position:0%
+organizational
+ 
+
+ align:start position:0%
+organizational
+competency and their ability to build
+
+ align:start position:0%
+competency and their ability to build
+ 
+
+ align:start position:0%
+competency and their ability to build
+and sustain high performance
+
+ align:start position:0%
+and sustain high performance
+ 
+
+ align:start position:0%
+and sustain high performance
+relationships. And those are
+
+ align:start position:0%
+relationships. And those are
+ 
+
+ align:start position:0%
+relationships. And those are
+characterized by shared goals, shared
+
+ align:start position:0%
+characterized by shared goals, shared
+ 
+
+ align:start position:0%
+characterized by shared goals, shared
+knowledge, and mutual
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+respect. She introduces a concept called
+
+ align:start position:0%
+respect. She introduces a concept called
+ 
+
+ align:start position:0%
+respect. She introduces a concept called
+relational
+
+ align:start position:0%
+relational
+ 
+
+ align:start position:0%
+relational
+coordination. And she says there are
+
+ align:start position:0%
+coordination. And she says there are
+ 
+
+ align:start position:0%
+coordination. And she says there are
+three components of relational
+
+ align:start position:0%
+three components of relational
+ 
+
+ align:start position:0%
+three components of relational
+coordination. One is shared goals and
+
+ align:start position:0%
+coordination. One is shared goals and
+ 
+
+ align:start position:0%
+coordination. One is shared goals and
+these align employees to prioritize the
+
+ align:start position:0%
+these align employees to prioritize the
+ 
+
+ align:start position:0%
+these align employees to prioritize the
+success of the organization over their
+
+ align:start position:0%
+success of the organization over their
+ 
+
+ align:start position:0%
+success of the organization over their
+individual success over just doing their
+
+ align:start position:0%
+individual success over just doing their
+ 
+
+ align:start position:0%
+individual success over just doing their
+job. And the shared goals for Southwest
+
+ align:start position:0%
+job. And the shared goals for Southwest
+ 
+
+ align:start position:0%
+job. And the shared goals for Southwest
+are safety, satisfied customers, and
+
+ align:start position:0%
+are safety, satisfied customers, and
+ 
+
+ align:start position:0%
+are safety, satisfied customers, and
+on-time departure. It's very
+
+ align:start position:0%
+on-time departure. It's very
+ 
+
+ align:start position:0%
+on-time departure. It's very
+simple. Second aspect of relational
+
+ align:start position:0%
+simple. Second aspect of relational
+ 
+
+ align:start position:0%
+simple. Second aspect of relational
+coordination is shared knowledge. This
+
+ align:start position:0%
+coordination is shared knowledge. This
+ 
+
+ align:start position:0%
+coordination is shared knowledge. This
+enables visibility across all the
+
+ align:start position:0%
+enables visibility across all the
+ 
+
+ align:start position:0%
+enables visibility across all the
+different work processes. And at
+
+ align:start position:0%
+different work processes. And at
+ 
+
+ align:start position:0%
+different work processes. And at
+Southwest, the functional groups
+
+ align:start position:0%
+Southwest, the functional groups
+ 
+
+ align:start position:0%
+Southwest, the functional groups
+actually help each other. There's no
+
+ align:start position:0%
+actually help each other. There's no
+ 
+
+ align:start position:0%
+actually help each other. There's no
+issues with, well, this is my job and
+
+ align:start position:0%
+issues with, well, this is my job and
+ 
+
+ align:start position:0%
+issues with, well, this is my job and
+that's your job and I'm not going to do
+
+ align:start position:0%
+that's your job and I'm not going to do
+ 
+
+ align:start position:0%
+that's your job and I'm not going to do
+your job because it's not my job.
+
+ align:start position:0%
+your job because it's not my job.
+ 
+
+ align:start position:0%
+your job because it's not my job.
+Everybody helps out and handles
+
+ align:start position:0%
+Everybody helps out and handles
+ 
+
+ align:start position:0%
+Everybody helps out and handles
+everything. Third element in relational
+
+ align:start position:0%
+everything. Third element in relational
+ 
+
+ align:start position:0%
+everything. Third element in relational
+coordination is mutual respect. And this
+
+ align:start position:0%
+coordination is mutual respect. And this
+ 
+
+ align:start position:0%
+coordination is mutual respect. And this
+helps reduce barriers between people uh
+
+ align:start position:0%
+helps reduce barriers between people uh
+ 
+
+ align:start position:0%
+helps reduce barriers between people uh
+employees and groups of employees. And
+
+ align:start position:0%
+employees and groups of employees. And
+ 
+
+ align:start position:0%
+employees and groups of employees. And
+Southwest treats each employee group as
+
+ align:start position:0%
+Southwest treats each employee group as
+ 
+
+ align:start position:0%
+Southwest treats each employee group as
+just important as any other. And if you
+
+ align:start position:0%
+just important as any other. And if you
+ 
+
+ align:start position:0%
+just important as any other. And if you
+understand a little bit about airlines,
+
+ align:start position:0%
+understand a little bit about airlines,
+ 
+
+ align:start position:0%
+understand a little bit about airlines,
+you may have heard about the pilots
+
+ align:start position:0%
+you may have heard about the pilots
+ 
+
+ align:start position:0%
+you may have heard about the pilots
+union and the flight attendance union
+
+ align:start position:0%
+union and the flight attendance union
+ 
+
+ align:start position:0%
+union and the flight attendance union
+and the mechanics union and the
+
+ align:start position:0%
+and the mechanics union and the
+ 
+
+ align:start position:0%
+and the mechanics union and the
+shareholders and the managers. It's an
+
+ align:start position:0%
+shareholders and the managers. It's an
+ 
+
+ align:start position:0%
+shareholders and the managers. It's an
+organization. It's an industry that's
+
+ align:start position:0%
+organization. It's an industry that's
+ 
+
+ align:start position:0%
+organization. It's an industry that's
+often talked about in terms of groups of
+
+ align:start position:0%
+often talked about in terms of groups of
+ 
+
+ align:start position:0%
+often talked about in terms of groups of
+employees, always arguing for the best
+
+ align:start position:0%
+employees, always arguing for the best
+ 
+
+ align:start position:0%
+employees, always arguing for the best
+interests of their group. And Southwest
+
+ align:start position:0%
+interests of their group. And Southwest
+ 
+
+ align:start position:0%
+interests of their group. And Southwest
+treats its employees as they're all
+
+ align:start position:0%
+treats its employees as they're all
+ 
+
+ align:start position:0%
+treats its employees as they're all
+important.
+
+ align:start position:0%
+important.
+ 
+
+ align:start position:0%
+important.
+And we have to keep in mind that
+
+ align:start position:0%
+And we have to keep in mind that
+ 
+
+ align:start position:0%
+And we have to keep in mind that
+relational coordination, these three
+
+ align:start position:0%
+relational coordination, these three
+ 
+
+ align:start position:0%
+relational coordination, these three
+elements of shared gold, shared
+
+ align:start position:0%
+elements of shared gold, shared
+ 
+
+ align:start position:0%
+elements of shared gold, shared
+knowledge and mutual respect cannot be
+
+ align:start position:0%
+knowledge and mutual respect cannot be
+ 
+
+ align:start position:0%
+knowledge and mutual respect cannot be
+achieved without effective communication
+
+ align:start position:0%
+achieved without effective communication
+ 
+
+ align:start position:0%
+achieved without effective communication
+among all the people participating in
+
+ align:start position:0%
+among all the people participating in
+ 
+
+ align:start position:0%
+among all the people participating in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+enterprise. And Southwest encourages our
+
+ align:start position:0%
+enterprise. And Southwest encourages our
+ 
+
+ align:start position:0%
+enterprise. And Southwest encourages our
+employees to do this by communicating
+
+ align:start position:0%
+employees to do this by communicating
+ 
+
+ align:start position:0%
+employees to do this by communicating
+about the problem itself rather than
+
+ align:start position:0%
+about the problem itself rather than
+ 
+
+ align:start position:0%
+about the problem itself rather than
+thinking about assigning blame. Another
+
+ align:start position:0%
+thinking about assigning blame. Another
+ 
+
+ align:start position:0%
+thinking about assigning blame. Another
+way to think about this is is let's talk
+
+ align:start position:0%
+way to think about this is is let's talk
+ 
+
+ align:start position:0%
+way to think about this is is let's talk
+about the problems and not the people.
+
+ align:start position:0%
+about the problems and not the people.
+ 
+
+ align:start position:0%
+about the problems and not the people.
+separate out the people from whatever is
+
+ align:start position:0%
+separate out the people from whatever is
+ 
+
+ align:start position:0%
+separate out the people from whatever is
+happening that's giving us some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+troubles. And we want to remind you that
+
+ align:start position:0%
+troubles. And we want to remind you that
+ 
+
+ align:start position:0%
+troubles. And we want to remind you that
+this kind of open and honest
+
+ align:start position:0%
+this kind of open and honest
+ 
+
+ align:start position:0%
+this kind of open and honest
+communication and we heard a flavor of
+
+ align:start position:0%
+communication and we heard a flavor of
+ 
+
+ align:start position:0%
+communication and we heard a flavor of
+this this talked about at the New
+
+ align:start position:0%
+this this talked about at the New
+ 
+
+ align:start position:0%
+this this talked about at the New
+Balance Tour in terms of having meetings
+
+ align:start position:0%
+Balance Tour in terms of having meetings
+ 
+
+ align:start position:0%
+Balance Tour in terms of having meetings
+try to be productive working towards
+
+ align:start position:0%
+try to be productive working towards
+ 
+
+ align:start position:0%
+try to be productive working towards
+effective communications is really a
+
+ align:start position:0%
+effective communications is really a
+ 
+
+ align:start position:0%
+effective communications is really a
+hallmark of lean thinking organizations.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, we've talked about relational
+
+ align:start position:0%
+So, we've talked about relational
+ 
+
+ align:start position:0%
+So, we've talked about relational
+coordination sounds good, but does it
+
+ align:start position:0%
+coordination sounds good, but does it
+ 
+
+ align:start position:0%
+coordination sounds good, but does it
+actually do a lot for my enterprise in
+
+ align:start position:0%
+actually do a lot for my enterprise in
+ 
+
+ align:start position:0%
+actually do a lot for my enterprise in
+terms of productivity and can I can I
+
+ align:start position:0%
+terms of productivity and can I can I
+ 
+
+ align:start position:0%
+terms of productivity and can I can I
+see that or can I start to prove that?
+
+ align:start position:0%
+see that or can I start to prove that?
+ 
+
+ align:start position:0%
+see that or can I start to prove that?
+So, what uh Dr. Huffer Gatell did was
+
+ align:start position:0%
+So, what uh Dr. Huffer Gatell did was
+ 
+
+ align:start position:0%
+So, what uh Dr. Huffer Gatell did was
+she surveyed a number of different
+
+ align:start position:0%
+she surveyed a number of different
+ 
+
+ align:start position:0%
+she surveyed a number of different
+airlines and produced this graph to
+
+ align:start position:0%
+airlines and produced this graph to
+ 
+
+ align:start position:0%
+airlines and produced this graph to
+summarize some of the results. What you
+
+ align:start position:0%
+summarize some of the results. What you
+ 
+
+ align:start position:0%
+summarize some of the results. What you
+see on the x- axis is uh a measure of
+
+ align:start position:0%
+see on the x- axis is uh a measure of
+ 
+
+ align:start position:0%
+see on the x- axis is uh a measure of
+performance for an airline which is a
+
+ align:start position:0%
+performance for an airline which is a
+ 
+
+ align:start position:0%
+performance for an airline which is a
+combination of a lot of different
+
+ align:start position:0%
+combination of a lot of different
+ 
+
+ align:start position:0%
+combination of a lot of different
+factors rolled into one. And what you
+
+ align:start position:0%
+factors rolled into one. And what you
+ 
+
+ align:start position:0%
+factors rolled into one. And what you
+see on the y- axis which has gotten a
+
+ align:start position:0%
+see on the y- axis which has gotten a
+ 
+
+ align:start position:0%
+see on the y- axis which has gotten a
+little bit messed up in translation here
+
+ align:start position:0%
+little bit messed up in translation here
+ 
+
+ align:start position:0%
+little bit messed up in translation here
+is a measure of relational coordination
+
+ align:start position:0%
+is a measure of relational coordination
+ 
+
+ align:start position:0%
+is a measure of relational coordination
+that is achieved. And each of these dots
+
+ align:start position:0%
+that is achieved. And each of these dots
+ 
+
+ align:start position:0%
+that is achieved. And each of these dots
+represents a different airline and a
+
+ align:start position:0%
+represents a different airline and a
+ 
+
+ align:start position:0%
+represents a different airline and a
+different facility in different
+
+ align:start position:0%
+different facility in different
+ 
+
+ align:start position:0%
+different facility in different
+locations around the country. So there's
+
+ align:start position:0%
+locations around the country. So there's
+ 
+
+ align:start position:0%
+locations around the country. So there's
+Southwest and a bunch of other airlines
+
+ align:start position:0%
+Southwest and a bunch of other airlines
+ 
+
+ align:start position:0%
+Southwest and a bunch of other airlines
+scattered in here. And what you see is
+
+ align:start position:0%
+scattered in here. And what you see is
+ 
+
+ align:start position:0%
+scattered in here. And what you see is
+that Southwest, which has a pretty high
+
+ align:start position:0%
+that Southwest, which has a pretty high
+ 
+
+ align:start position:0%
+that Southwest, which has a pretty high
+relational coordination, is also doing
+
+ align:start position:0%
+relational coordination, is also doing
+ 
+
+ align:start position:0%
+relational coordination, is also doing
+very well on their performance
+
+ align:start position:0%
+very well on their performance
+ 
+
+ align:start position:0%
+very well on their performance
+index. So we might assume then that the
+
+ align:start position:0%
+index. So we might assume then that the
+ 
+
+ align:start position:0%
+index. So we might assume then that the
+uh relational coordination and improving
+
+ align:start position:0%
+uh relational coordination and improving
+ 
+
+ align:start position:0%
+uh relational coordination and improving
+that will result in increased
+
+ align:start position:0%
+that will result in increased
+ 
+
+ align:start position:0%
+that will result in increased
+performance. And that was for airlines.
+
+ align:start position:0%
+performance. And that was for airlines.
+ 
+
+ align:start position:0%
+performance. And that was for airlines.
+But what about other industries? So she
+
+ align:start position:0%
+But what about other industries? So she
+ 
+
+ align:start position:0%
+But what about other industries? So she
+did the same study for hospitals and saw
+
+ align:start position:0%
+did the same study for hospitals and saw
+ 
+
+ align:start position:0%
+did the same study for hospitals and saw
+very much the same result. So as you
+
+ align:start position:0%
+very much the same result. So as you
+ 
+
+ align:start position:0%
+very much the same result. So as you
+increase on your performance and
+
+ align:start position:0%
+increase on your performance and
+ 
+
+ align:start position:0%
+increase on your performance and
+relational coordination, you tend to
+
+ align:start position:0%
+relational coordination, you tend to
+ 
+
+ align:start position:0%
+relational coordination, you tend to
+increase in your productivity
+
+ align:start position:0%
+increase in your productivity
+ 
+
+ align:start position:0%
+increase in your productivity
+performance as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well. So does this actually move beyond
+
+ align:start position:0%
+well. So does this actually move beyond
+ 
+
+ align:start position:0%
+well. So does this actually move beyond
+airlines and
+
+ align:start position:0%
+airlines and
+ 
+
+ align:start position:0%
+airlines and
+hospitals? I don't have data for you on
+
+ align:start position:0%
+hospitals? I don't have data for you on
+ 
+
+ align:start position:0%
+hospitals? I don't have data for you on
+that, but I'll suggest that this kind of
+
+ align:start position:0%
+that, but I'll suggest that this kind of
+ 
+
+ align:start position:0%
+that, but I'll suggest that this kind of
+relational coordination is a big issue
+
+ align:start position:0%
+relational coordination is a big issue
+ 
+
+ align:start position:0%
+relational coordination is a big issue
+in all kinds of other work settings
+
+ align:start position:0%
+in all kinds of other work settings
+ 
+
+ align:start position:0%
+in all kinds of other work settings
+where there are certain characteristics.
+
+ align:start position:0%
+where there are certain characteristics.
+ 
+
+ align:start position:0%
+where there are certain characteristics.
+one of task interdependence where
+
+ align:start position:0%
+one of task interdependence where
+ 
+
+ align:start position:0%
+one of task interdependence where
+there's a lot of handoffs or
+
+ align:start position:0%
+there's a lot of handoffs or
+ 
+
+ align:start position:0%
+there's a lot of handoffs or
+codependence between items. They may
+
+ align:start position:0%
+codependence between items. They may
+ 
+
+ align:start position:0%
+codependence between items. They may
+involve feedback and iterations like a
+
+ align:start position:0%
+involve feedback and iterations like a
+ 
+
+ align:start position:0%
+involve feedback and iterations like a
+design cycle where there's a lot of
+
+ align:start position:0%
+design cycle where there's a lot of
+ 
+
+ align:start position:0%
+design cycle where there's a lot of
+uncertainty and there may be a lot of
+
+ align:start position:0%
+uncertainty and there may be a lot of
+ 
+
+ align:start position:0%
+uncertainty and there may be a lot of
+adjusting uh of plans that have to
+
+ align:start position:0%
+adjusting uh of plans that have to
+ 
+
+ align:start position:0%
+adjusting uh of plans that have to
+happen so a lot of communication is
+
+ align:start position:0%
+happen so a lot of communication is
+ 
+
+ align:start position:0%
+happen so a lot of communication is
+necessary or places where there's a lot
+
+ align:start position:0%
+necessary or places where there's a lot
+ 
+
+ align:start position:0%
+necessary or places where there's a lot
+of time constraints and so buffers for
+
+ align:start position:0%
+of time constraints and so buffers for
+ 
+
+ align:start position:0%
+of time constraints and so buffers for
+working out the relational issues just
+
+ align:start position:0%
+working out the relational issues just
+ 
+
+ align:start position:0%
+working out the relational issues just
+wouldn't exist.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So some of the example work settings
+
+ align:start position:0%
+So some of the example work settings
+ 
+
+ align:start position:0%
+So some of the example work settings
+where this might actually apply think
+
+ align:start position:0%
+where this might actually apply think
+ 
+
+ align:start position:0%
+where this might actually apply think
+product development, lots of team
+
+ align:start position:0%
+product development, lots of team
+ 
+
+ align:start position:0%
+product development, lots of team
+coordination, certainly lots of feedback
+
+ align:start position:0%
+coordination, certainly lots of feedback
+ 
+
+ align:start position:0%
+coordination, certainly lots of feedback
+and iteration and lots of uncertainty as
+
+ align:start position:0%
+and iteration and lots of uncertainty as
+ 
+
+ align:start position:0%
+and iteration and lots of uncertainty as
+you go forward with the design. We saw
+
+ align:start position:0%
+you go forward with the design. We saw
+ 
+
+ align:start position:0%
+you go forward with the design. We saw
+production in our Lego simulation. Uh
+
+ align:start position:0%
+production in our Lego simulation. Uh
+ 
+
+ align:start position:0%
+production in our Lego simulation. Uh
+operations will be the same and you can
+
+ align:start position:0%
+operations will be the same and you can
+ 
+
+ align:start position:0%
+operations will be the same and you can
+probably think of a lot of others. It's
+
+ align:start position:0%
+probably think of a lot of others. It's
+ 
+
+ align:start position:0%
+probably think of a lot of others. It's
+probably uh easier to think of settings
+
+ align:start position:0%
+probably uh easier to think of settings
+ 
+
+ align:start position:0%
+probably uh easier to think of settings
+where this would apply being engineers
+
+ align:start position:0%
+where this would apply being engineers
+ 
+
+ align:start position:0%
+where this would apply being engineers
+and how much we work in teams than in
+
+ align:start position:0%
+and how much we work in teams than in
+ 
+
+ align:start position:0%
+and how much we work in teams than in
+settings where this wouldn't apply.
+
+ align:start position:0%
+settings where this wouldn't apply.
+ 
+
+ align:start position:0%
+settings where this wouldn't apply.
+Yeah, Earl, you know, for this group,
+
+ align:start position:0%
+Yeah, Earl, you know, for this group,
+ 
+
+ align:start position:0%
+Yeah, Earl, you know, for this group,
+one of the things this department does
+
+ align:start position:0%
+one of the things this department does
+ 
+
+ align:start position:0%
+one of the things this department does
+is encourage a lot of uh teamwork and
+
+ align:start position:0%
+is encourage a lot of uh teamwork and
+ 
+
+ align:start position:0%
+is encourage a lot of uh teamwork and
+study groups and things like that. You
+
+ align:start position:0%
+study groups and things like that. You
+ 
+
+ align:start position:0%
+study groups and things like that. You
+know, that's
+
+ align:start position:0%
+know, that's
+ 
+
+ align:start position:0%
+know, that's
+another workplace activity where this
+
+ align:start position:0%
+another workplace activity where this
+ 
+
+ align:start position:0%
+another workplace activity where this
+type of thing will come in.
+
+ align:start position:0%
+type of thing will come in.
+ 
+
+ align:start position:0%
+type of thing will come in.
+Absolutely. It's a type of workplace
+
+ align:start position:0%
+Absolutely. It's a type of workplace
+ 
+
+ align:start position:0%
+Absolutely. It's a type of workplace
+activity where this comes into play and
+
+ align:start position:0%
+activity where this comes into play and
+ 
+
+ align:start position:0%
+activity where this comes into play and
+it's also partly the reason why we
+
+ align:start position:0%
+it's also partly the reason why we
+ 
+
+ align:start position:0%
+it's also partly the reason why we
+encourage a lot of this work in our
+
+ align:start position:0%
+encourage a lot of this work in our
+ 
+
+ align:start position:0%
+encourage a lot of this work in our
+aerrowastro undergraduate curriculum
+
+ align:start position:0%
+aerrowastro undergraduate curriculum
+ 
+
+ align:start position:0%
+aerrowastro undergraduate curriculum
+because it's going to be very important
+
+ align:start position:0%
+because it's going to be very important
+ 
+
+ align:start position:0%
+because it's going to be very important
+when you go to take jobs.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So in studying Southwest a little bit
+
+ align:start position:0%
+So in studying Southwest a little bit
+ 
+
+ align:start position:0%
+So in studying Southwest a little bit
+further uh Dr. Hofferell looked at these
+
+ align:start position:0%
+further uh Dr. Hofferell looked at these
+ 
+
+ align:start position:0%
+further uh Dr. Hofferell looked at these
+outcomes in terms of the performance in
+
+ align:start position:0%
+outcomes in terms of the performance in
+ 
+
+ align:start position:0%
+outcomes in terms of the performance in
+terms of quality and efficiency for
+
+ align:start position:0%
+terms of quality and efficiency for
+ 
+
+ align:start position:0%
+terms of quality and efficiency for
+airlines and she looked at some of the
+
+ align:start position:0%
+airlines and she looked at some of the
+ 
+
+ align:start position:0%
+airlines and she looked at some of the
+practices that Southwest Airlines had
+
+ align:start position:0%
+practices that Southwest Airlines had
+ 
+
+ align:start position:0%
+practices that Southwest Airlines had
+for achieving that and she grouped them
+
+ align:start position:0%
+for achieving that and she grouped them
+ 
+
+ align:start position:0%
+for achieving that and she grouped them
+into these 10 categories. And I'm not
+
+ align:start position:0%
+into these 10 categories. And I'm not
+ 
+
+ align:start position:0%
+into these 10 categories. And I'm not
+going to go into detail on any one of
+
+ align:start position:0%
+going to go into detail on any one of
+ 
+
+ align:start position:0%
+going to go into detail on any one of
+them, but should you be interested, you
+
+ align:start position:0%
+them, but should you be interested, you
+ 
+
+ align:start position:0%
+them, but should you be interested, you
+can pick up her book and get some more
+
+ align:start position:0%
+can pick up her book and get some more
+ 
+
+ align:start position:0%
+can pick up her book and get some more
+information on that. But it's important
+
+ align:start position:0%
+information on that. But it's important
+ 
+
+ align:start position:0%
+information on that. But it's important
+to understand that this is not a menu of
+
+ align:start position:0%
+to understand that this is not a menu of
+ 
+
+ align:start position:0%
+to understand that this is not a menu of
+things that you're going to choose from.
+
+ align:start position:0%
+things that you're going to choose from.
+ 
+
+ align:start position:0%
+things that you're going to choose from.
+These are 10 practices that almost exist
+
+ align:start position:0%
+These are 10 practices that almost exist
+ 
+
+ align:start position:0%
+These are 10 practices that almost exist
+to enable effective relational
+
+ align:start position:0%
+to enable effective relational
+ 
+
+ align:start position:0%
+to enable effective relational
+coordination to gain your your outcome.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if you have good relational
+
+ align:start position:0%
+So if you have good relational
+ 
+
+ align:start position:0%
+So if you have good relational
+coordination, what else does that get
+
+ align:start position:0%
+coordination, what else does that get
+ 
+
+ align:start position:0%
+coordination, what else does that get
+you? Leads you to higher reliability,
+
+ align:start position:0%
+you? Leads you to higher reliability,
+ 
+
+ align:start position:0%
+you? Leads you to higher reliability,
+better customer satisfaction, shorter
+
+ align:start position:0%
+better customer satisfaction, shorter
+ 
+
+ align:start position:0%
+better customer satisfaction, shorter
+turnaround time. All of these things
+
+ align:start position:0%
+turnaround time. All of these things
+ 
+
+ align:start position:0%
+turnaround time. All of these things
+very good for an
+
+ align:start position:0%
+very good for an
+ 
+
+ align:start position:0%
+very good for an
+airline. And when you have workforce
+
+ align:start position:0%
+airline. And when you have workforce
+ 
+
+ align:start position:0%
+airline. And when you have workforce
+productivity, you're going to get more
+
+ align:start position:0%
+productivity, you're going to get more
+ 
+
+ align:start position:0%
+productivity, you're going to get more
+revenue from more satisfied customers
+
+ align:start position:0%
+revenue from more satisfied customers
+ 
+
+ align:start position:0%
+revenue from more satisfied customers
+who keep coming back. If you have a
+
+ align:start position:0%
+who keep coming back. If you have a
+ 
+
+ align:start position:0%
+who keep coming back. If you have a
+smaller turnaround time, you're going to
+
+ align:start position:0%
+smaller turnaround time, you're going to
+ 
+
+ align:start position:0%
+smaller turnaround time, you're going to
+have airplanes more in the air and
+
+ align:start position:0%
+have airplanes more in the air and
+ 
+
+ align:start position:0%
+have airplanes more in the air and
+earning money for you. value added time
+
+ align:start position:0%
+earning money for you. value added time
+ 
+
+ align:start position:0%
+earning money for you. value added time
+as opposed to non-value added time. To
+
+ align:start position:0%
+as opposed to non-value added time. To
+ 
+
+ align:start position:0%
+as opposed to non-value added time. To
+put this in a lean context, you have
+
+ align:start position:0%
+put this in a lean context, you have
+ 
+
+ align:start position:0%
+put this in a lean context, you have
+less employee turnover. If you're happy,
+
+ align:start position:0%
+less employee turnover. If you're happy,
+ 
+
+ align:start position:0%
+less employee turnover. If you're happy,
+productive workforce, you have reduced
+
+ align:start position:0%
+productive workforce, you have reduced
+ 
+
+ align:start position:0%
+productive workforce, you have reduced
+cost from not having your employees idle
+
+ align:start position:0%
+cost from not having your employees idle
+ 
+
+ align:start position:0%
+cost from not having your employees idle
+because they're productive. And you in
+
+ align:start position:0%
+because they're productive. And you in
+ 
+
+ align:start position:0%
+because they're productive. And you in
+the end have happy, satisfied employees,
+
+ align:start position:0%
+the end have happy, satisfied employees,
+ 
+
+ align:start position:0%
+the end have happy, satisfied employees,
+which are productive employees, which
+
+ align:start position:0%
+which are productive employees, which
+ 
+
+ align:start position:0%
+which are productive employees, which
+are happy employees.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, we've established this link between
+
+ align:start position:0%
+So, we've established this link between
+ 
+
+ align:start position:0%
+So, we've established this link between
+uh worker motivation and attitudes and
+
+ align:start position:0%
+uh worker motivation and attitudes and
+ 
+
+ align:start position:0%
+uh worker motivation and attitudes and
+enterprise productivity. So, how does
+
+ align:start position:0%
+enterprise productivity. So, how does
+ 
+
+ align:start position:0%
+enterprise productivity. So, how does
+this all apply to you here today? And
+
+ align:start position:0%
+this all apply to you here today? And
+ 
+
+ align:start position:0%
+this all apply to you here today? And
+we're going to talk
+
+ align:start position:0%
+we're going to talk
+ 
+
+ align:start position:0%
+we're going to talk
+about how you can improve the
+
+ align:start position:0%
+about how you can improve the
+ 
+
+ align:start position:0%
+about how you can improve the
+effectiveness of people operating in a
+
+ align:start position:0%
+effectiveness of people operating in a
+ 
+
+ align:start position:0%
+effectiveness of people operating in a
+team environment and improving their
+
+ align:start position:0%
+team environment and improving their
+ 
+
+ align:start position:0%
+team environment and improving their
+process. And there's two elements that
+
+ align:start position:0%
+process. And there's two elements that
+ 
+
+ align:start position:0%
+process. And there's two elements that
+we're going to talk about. The first is
+
+ align:start position:0%
+we're going to talk about. The first is
+ 
+
+ align:start position:0%
+we're going to talk about. The first is
+what goes on in a leadership role to
+
+ align:start position:0%
+what goes on in a leadership role to
+ 
+
+ align:start position:0%
+what goes on in a leadership role to
+facilitate teams being effective. And
+
+ align:start position:0%
+facilitate teams being effective. And
+ 
+
+ align:start position:0%
+facilitate teams being effective. And
+we'll talk about leadership and
+
+ align:start position:0%
+we'll talk about leadership and
+ 
+
+ align:start position:0%
+we'll talk about leadership and
+management. And the second aspect we're
+
+ align:start position:0%
+management. And the second aspect we're
+ 
+
+ align:start position:0%
+management. And the second aspect we're
+going to talk about is teamwork, being
+
+ align:start position:0%
+going to talk about is teamwork, being
+ 
+
+ align:start position:0%
+going to talk about is teamwork, being
+able to work effectively and collaborate
+
+ align:start position:0%
+able to work effectively and collaborate
+ 
+
+ align:start position:0%
+able to work effectively and collaborate
+in groups of people. And you're going to
+
+ align:start position:0%
+in groups of people. And you're going to
+ 
+
+ align:start position:0%
+in groups of people. And you're going to
+find over the course of your career and
+
+ align:start position:0%
+find over the course of your career and
+ 
+
+ align:start position:0%
+find over the course of your career and
+sometimes from day to day or even hour
+
+ align:start position:0%
+sometimes from day to day or even hour
+ 
+
+ align:start position:0%
+sometimes from day to day or even hour
+to hour, you will be switching between
+
+ align:start position:0%
+to hour, you will be switching between
+ 
+
+ align:start position:0%
+to hour, you will be switching between
+all of these various roles. And in one
+
+ align:start position:0%
+all of these various roles. And in one
+ 
+
+ align:start position:0%
+all of these various roles. And in one
+circumstance, you may be leading a team.
+
+ align:start position:0%
+circumstance, you may be leading a team.
+ 
+
+ align:start position:0%
+circumstance, you may be leading a team.
+uh at the next meeting you may be uh
+
+ align:start position:0%
+uh at the next meeting you may be uh
+ 
+
+ align:start position:0%
+uh at the next meeting you may be uh
+working as part of the team and you may
+
+ align:start position:0%
+working as part of the team and you may
+ 
+
+ align:start position:0%
+working as part of the team and you may
+also find yourself responsible as a
+
+ align:start position:0%
+also find yourself responsible as a
+ 
+
+ align:start position:0%
+also find yourself responsible as a
+manager for a particular project. So
+
+ align:start position:0%
+manager for a particular project. So
+ 
+
+ align:start position:0%
+manager for a particular project. So
+these roles are going to be ones that
+
+ align:start position:0%
+these roles are going to be ones that
+ 
+
+ align:start position:0%
+these roles are going to be ones that
+keep coming up over the course of your
+
+ align:start position:0%
+keep coming up over the course of your
+ 
+
+ align:start position:0%
+keep coming up over the course of your
+career and for reasons we're going to
+
+ align:start position:0%
+career and for reasons we're going to
+ 
+
+ align:start position:0%
+career and for reasons we're going to
+discuss soon you're actually going to be
+
+ align:start position:0%
+discuss soon you're actually going to be
+ 
+
+ align:start position:0%
+discuss soon you're actually going to be
+taking on a lot of these
+
+ align:start position:0%
+taking on a lot of these
+ 
+
+ align:start position:0%
+taking on a lot of these
+responsibilities earlier than engineers
+
+ align:start position:0%
+responsibilities earlier than engineers
+ 
+
+ align:start position:0%
+responsibilities earlier than engineers
+who are maybe in this industry a couple
+
+ align:start position:0%
+who are maybe in this industry a couple
+ 
+
+ align:start position:0%
+who are maybe in this industry a couple
+of decades ago. So these kind of skills
+
+ align:start position:0%
+of decades ago. So these kind of skills
+ 
+
+ align:start position:0%
+of decades ago. So these kind of skills
+are very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important. As we said when we started
+
+ align:start position:0%
+important. As we said when we started
+ 
+
+ align:start position:0%
+important. As we said when we started
+out here, people are key to lean. If the
+
+ align:start position:0%
+out here, people are key to lean. If the
+ 
+
+ align:start position:0%
+out here, people are key to lean. If the
+people don't want to do it, lean's not
+
+ align:start position:0%
+people don't want to do it, lean's not
+ 
+
+ align:start position:0%
+people don't want to do it, lean's not
+going to be successful. People are
+
+ align:start position:0%
+going to be successful. People are
+ 
+
+ align:start position:0%
+going to be successful. People are
+really at the heart of this enterprise.
+
+ align:start position:0%
+really at the heart of this enterprise.
+ 
+
+ align:start position:0%
+really at the heart of this enterprise.
+It's it the enterprise is all about
+
+ align:start position:0%
+It's it the enterprise is all about
+ 
+
+ align:start position:0%
+It's it the enterprise is all about
+people. We have organizational
+
+ align:start position:0%
+people. We have organizational
+ 
+
+ align:start position:0%
+people. We have organizational
+structures. They exist to enable people.
+
+ align:start position:0%
+structures. They exist to enable people.
+ 
+
+ align:start position:0%
+structures. They exist to enable people.
+We have processes which tell us how
+
+ align:start position:0%
+We have processes which tell us how
+ 
+
+ align:start position:0%
+We have processes which tell us how
+people work and we have tasks which is
+
+ align:start position:0%
+people work and we have tasks which is
+ 
+
+ align:start position:0%
+people work and we have tasks which is
+what people do. So if you had an
+
+ align:start position:0%
+what people do. So if you had an
+ 
+
+ align:start position:0%
+what people do. So if you had an
+assembly plant without people, if you
+
+ align:start position:0%
+assembly plant without people, if you
+ 
+
+ align:start position:0%
+assembly plant without people, if you
+had a business that did not have people
+
+ align:start position:0%
+had a business that did not have people
+ 
+
+ align:start position:0%
+had a business that did not have people
+in it, would they actually be able to
+
+ align:start position:0%
+in it, would they actually be able to
+ 
+
+ align:start position:0%
+in it, would they actually be able to
+produce something to deliver value to
+
+ align:start position:0%
+produce something to deliver value to
+ 
+
+ align:start position:0%
+produce something to deliver value to
+make a profit? Absolutely not. And
+
+ align:start position:0%
+make a profit? Absolutely not. And
+ 
+
+ align:start position:0%
+make a profit? Absolutely not. And
+that's why human resources are talked
+
+ align:start position:0%
+that's why human resources are talked
+ 
+
+ align:start position:0%
+that's why human resources are talked
+about as the most important resource on
+
+ align:start position:0%
+about as the most important resource on
+ 
+
+ align:start position:0%
+about as the most important resource on
+any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+project. Let's talk for a minute to
+
+ align:start position:0%
+project. Let's talk for a minute to
+ 
+
+ align:start position:0%
+project. Let's talk for a minute to
+distinguish leadership from management.
+
+ align:start position:0%
+distinguish leadership from management.
+ 
+
+ align:start position:0%
+distinguish leadership from management.
+Both are very necessary and you're
+
+ align:start position:0%
+Both are very necessary and you're
+ 
+
+ align:start position:0%
+Both are very necessary and you're
+probably going to have to do both of
+
+ align:start position:0%
+probably going to have to do both of
+ 
+
+ align:start position:0%
+probably going to have to do both of
+these things over the course of your
+
+ align:start position:0%
+these things over the course of your
+ 
+
+ align:start position:0%
+these things over the course of your
+career. You can summarize leadership uh
+
+ align:start position:0%
+career. You can summarize leadership uh
+ 
+
+ align:start position:0%
+career. You can summarize leadership uh
+in a a catchphrase as doing the right
+
+ align:start position:0%
+in a a catchphrase as doing the right
+ 
+
+ align:start position:0%
+in a a catchphrase as doing the right
+thing and you can contrast that with
+
+ align:start position:0%
+thing and you can contrast that with
+ 
+
+ align:start position:0%
+thing and you can contrast that with
+management which is once you've selected
+
+ align:start position:0%
+management which is once you've selected
+ 
+
+ align:start position:0%
+management which is once you've selected
+the right thing to do. Management is
+
+ align:start position:0%
+the right thing to do. Management is
+ 
+
+ align:start position:0%
+the right thing to do. Management is
+understanding how to do that thing
+
+ align:start position:0%
+understanding how to do that thing
+ 
+
+ align:start position:0%
+understanding how to do that thing
+right. So a leader will focus on the
+
+ align:start position:0%
+right. So a leader will focus on the
+ 
+
+ align:start position:0%
+right. So a leader will focus on the
+organization and the people within the
+
+ align:start position:0%
+organization and the people within the
+ 
+
+ align:start position:0%
+organization and the people within the
+organization talking about vision and
+
+ align:start position:0%
+organization talking about vision and
+ 
+
+ align:start position:0%
+organization talking about vision and
+values and engaging them and empowering
+
+ align:start position:0%
+values and engaging them and empowering
+ 
+
+ align:start position:0%
+values and engaging them and empowering
+them and making change.
+
+ align:start position:0%
+them and making change.
+ 
+
+ align:start position:0%
+them and making change.
+A management focus will look at goal
+
+ align:start position:0%
+A management focus will look at goal
+ 
+
+ align:start position:0%
+A management focus will look at goal
+attainment. So we're talking decision-
+
+ align:start position:0%
+attainment. So we're talking decision-
+ 
+
+ align:start position:0%
+attainment. So we're talking decision-
+making, how we're going to structure an
+
+ align:start position:0%
+making, how we're going to structure an
+ 
+
+ align:start position:0%
+making, how we're going to structure an
+organization, what we need for human
+
+ align:start position:0%
+organization, what we need for human
+ 
+
+ align:start position:0%
+organization, what we need for human
+resources, how we manage conflicts, and
+
+ align:start position:0%
+resources, how we manage conflicts, and
+ 
+
+ align:start position:0%
+resources, how we manage conflicts, and
+how we get the other kind of resources,
+
+ align:start position:0%
+how we get the other kind of resources,
+ 
+
+ align:start position:0%
+how we get the other kind of resources,
+fiscal, technological, that we're going
+
+ align:start position:0%
+fiscal, technological, that we're going
+ 
+
+ align:start position:0%
+fiscal, technological, that we're going
+to need. You need both leadership and
+
+ align:start position:0%
+to need. You need both leadership and
+ 
+
+ align:start position:0%
+to need. You need both leadership and
+management in order to effectively
+
+ align:start position:0%
+management in order to effectively
+ 
+
+ align:start position:0%
+management in order to effectively
+motivate a team and get them productive
+
+ align:start position:0%
+motivate a team and get them productive
+ 
+
+ align:start position:0%
+motivate a team and get them productive
+and engaged in their task.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I want to step back in history a little
+
+ align:start position:0%
+I want to step back in history a little
+ 
+
+ align:start position:0%
+I want to step back in history a little
+bit and talk about how organizational
+
+ align:start position:0%
+bit and talk about how organizational
+ 
+
+ align:start position:0%
+bit and talk about how organizational
+charts and structures have evolved in
+
+ align:start position:0%
+charts and structures have evolved in
+ 
+
+ align:start position:0%
+charts and structures have evolved in
+the aerospace
+
+ align:start position:0%
+the aerospace
+ 
+
+ align:start position:0%
+the aerospace
+industry. Back from the 60s, we started
+
+ align:start position:0%
+industry. Back from the 60s, we started
+ 
+
+ align:start position:0%
+industry. Back from the 60s, we started
+with matrix organizations. And I'm sure
+
+ align:start position:0%
+with matrix organizations. And I'm sure
+ 
+
+ align:start position:0%
+with matrix organizations. And I'm sure
+that many of you have heard this
+
+ align:start position:0%
+that many of you have heard this
+ 
+
+ align:start position:0%
+that many of you have heard this
+terminology before. It's usually
+
+ align:start position:0%
+terminology before. It's usually
+ 
+
+ align:start position:0%
+terminology before. It's usually
+represented in this manner. We think
+
+ align:start position:0%
+represented in this manner. We think
+ 
+
+ align:start position:0%
+represented in this manner. We think
+about functions going down the vertical
+
+ align:start position:0%
+about functions going down the vertical
+ 
+
+ align:start position:0%
+about functions going down the vertical
+here and and programs that might utilize
+
+ align:start position:0%
+here and and programs that might utilize
+ 
+
+ align:start position:0%
+here and and programs that might utilize
+people from each of those functions
+
+ align:start position:0%
+people from each of those functions
+ 
+
+ align:start position:0%
+people from each of those functions
+going across the horizontal. And so a
+
+ align:start position:0%
+going across the horizontal. And so a
+ 
+
+ align:start position:0%
+going across the horizontal. And so a
+worker would kind of sit here at the
+
+ align:start position:0%
+worker would kind of sit here at the
+ 
+
+ align:start position:0%
+worker would kind of sit here at the
+intersection of a program and a
+
+ align:start position:0%
+intersection of a program and a
+ 
+
+ align:start position:0%
+intersection of a program and a
+function. And they would have two
+
+ align:start position:0%
+function. And they would have two
+ 
+
+ align:start position:0%
+function. And they would have two
+bosses. They would have their functional
+
+ align:start position:0%
+bosses. They would have their functional
+ 
+
+ align:start position:0%
+bosses. They would have their functional
+boss. So maybe they're in structures or
+
+ align:start position:0%
+boss. So maybe they're in structures or
+ 
+
+ align:start position:0%
+boss. So maybe they're in structures or
+propulsion or or thermal. And then they
+
+ align:start position:0%
+propulsion or or thermal. And then they
+ 
+
+ align:start position:0%
+propulsion or or thermal. And then they
+would have their program manager who was
+
+ align:start position:0%
+would have their program manager who was
+ 
+
+ align:start position:0%
+would have their program manager who was
+a second boss for
+
+ align:start position:0%
+a second boss for
+ 
+
+ align:start position:0%
+a second boss for
+them. And this matrix organization arose
+
+ align:start position:0%
+them. And this matrix organization arose
+ 
+
+ align:start position:0%
+them. And this matrix organization arose
+because technologies were changing so
+
+ align:start position:0%
+because technologies were changing so
+ 
+
+ align:start position:0%
+because technologies were changing so
+quickly that the programs wanted to be
+
+ align:start position:0%
+quickly that the programs wanted to be
+ 
+
+ align:start position:0%
+quickly that the programs wanted to be
+able to draw on the expertise from all
+
+ align:start position:0%
+able to draw on the expertise from all
+ 
+
+ align:start position:0%
+able to draw on the expertise from all
+the different engineering departments.
+
+ align:start position:0%
+the different engineering departments.
+ 
+
+ align:start position:0%
+the different engineering departments.
+and they thought that this would allow
+
+ align:start position:0%
+and they thought that this would allow
+ 
+
+ align:start position:0%
+and they thought that this would allow
+them to respond more agile to the kind
+
+ align:start position:0%
+them to respond more agile to the kind
+ 
+
+ align:start position:0%
+them to respond more agile to the kind
+of situation they found for their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+products. Now, as we change some of the
+
+ align:start position:0%
+products. Now, as we change some of the
+ 
+
+ align:start position:0%
+products. Now, as we change some of the
+situations we find ourselves in in
+
+ align:start position:0%
+situations we find ourselves in in
+ 
+
+ align:start position:0%
+situations we find ourselves in in
+aerospace where it's not necessarily
+
+ align:start position:0%
+aerospace where it's not necessarily
+ 
+
+ align:start position:0%
+aerospace where it's not necessarily
+about the the change of the technology,
+
+ align:start position:0%
+about the the change of the technology,
+ 
+
+ align:start position:0%
+about the the change of the technology,
+we may be refining our processes, we may
+
+ align:start position:0%
+we may be refining our processes, we may
+ 
+
+ align:start position:0%
+we may be refining our processes, we may
+be driving down costs, we may be
+
+ align:start position:0%
+be driving down costs, we may be
+ 
+
+ align:start position:0%
+be driving down costs, we may be
+responding to different needs. We are
+
+ align:start position:0%
+responding to different needs. We are
+ 
+
+ align:start position:0%
+responding to different needs. We are
+moving towards a different structure. We
+
+ align:start position:0%
+moving towards a different structure. We
+ 
+
+ align:start position:0%
+moving towards a different structure. We
+call it the integrated product and
+
+ align:start position:0%
+call it the integrated product and
+ 
+
+ align:start position:0%
+call it the integrated product and
+process teams. Now, one of the
+
+ align:start position:0%
+process teams. Now, one of the
+ 
+
+ align:start position:0%
+process teams. Now, one of the
+challenges of this matrix organization,
+
+ align:start position:0%
+challenges of this matrix organization,
+ 
+
+ align:start position:0%
+challenges of this matrix organization,
+you know, if you sat here, if you wanted
+
+ align:start position:0%
+you know, if you sat here, if you wanted
+ 
+
+ align:start position:0%
+you know, if you sat here, if you wanted
+to talk to somebody here, you don't have
+
+ align:start position:0%
+to talk to somebody here, you don't have
+ 
+
+ align:start position:0%
+to talk to somebody here, you don't have
+any direct link through those. So, you
+
+ align:start position:0%
+any direct link through those. So, you
+ 
+
+ align:start position:0%
+any direct link through those. So, you
+go to one of your bosses or to another
+
+ align:start position:0%
+go to one of your bosses or to another
+ 
+
+ align:start position:0%
+go to one of your bosses or to another
+boss or gosh forbid to both or a third
+
+ align:start position:0%
+boss or gosh forbid to both or a third
+ 
+
+ align:start position:0%
+boss or gosh forbid to both or a third
+before you get down to talk to the
+
+ align:start position:0%
+before you get down to talk to the
+ 
+
+ align:start position:0%
+before you get down to talk to the
+person you really need to. So, there's a
+
+ align:start position:0%
+person you really need to. So, there's a
+ 
+
+ align:start position:0%
+person you really need to. So, there's a
+lot of filtering of information and
+
+ align:start position:0%
+lot of filtering of information and
+ 
+
+ align:start position:0%
+lot of filtering of information and
+ineffective communications.
+
+ align:start position:0%
+ineffective communications.
+ 
+
+ align:start position:0%
+ineffective communications.
+One of the things that the IPT has
+
+ align:start position:0%
+One of the things that the IPT has
+ 
+
+ align:start position:0%
+One of the things that the IPT has
+successfully done is that it now lets
+
+ align:start position:0%
+successfully done is that it now lets
+ 
+
+ align:start position:0%
+successfully done is that it now lets
+communication happen at the level where
+
+ align:start position:0%
+communication happen at the level where
+ 
+
+ align:start position:0%
+communication happen at the level where
+work is being done. It drives down this
+
+ align:start position:0%
+work is being done. It drives down this
+ 
+
+ align:start position:0%
+work is being done. It drives down this
+communications to where it's most
+
+ align:start position:0%
+communications to where it's most
+ 
+
+ align:start position:0%
+communications to where it's most
+effective. Now you don't have filters on
+
+ align:start position:0%
+effective. Now you don't have filters on
+ 
+
+ align:start position:0%
+effective. Now you don't have filters on
+all of the talking that's going on and
+
+ align:start position:0%
+all of the talking that's going on and
+ 
+
+ align:start position:0%
+all of the talking that's going on and
+the coordination.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now notice as a result of this new uh
+
+ align:start position:0%
+Now notice as a result of this new uh
+ 
+
+ align:start position:0%
+Now notice as a result of this new uh
+structure, people who are in integrated
+
+ align:start position:0%
+structure, people who are in integrated
+ 
+
+ align:start position:0%
+structure, people who are in integrated
+product teams have to be responsible for
+
+ align:start position:0%
+product teams have to be responsible for
+ 
+
+ align:start position:0%
+product teams have to be responsible for
+a lot more managing and leading than
+
+ align:start position:0%
+a lot more managing and leading than
+ 
+
+ align:start position:0%
+a lot more managing and leading than
+they were doing in a matrix organization
+
+ align:start position:0%
+they were doing in a matrix organization
+ 
+
+ align:start position:0%
+they were doing in a matrix organization
+where you sat in the organization. You
+
+ align:start position:0%
+where you sat in the organization. You
+ 
+
+ align:start position:0%
+where you sat in the organization. You
+had not just one but two bosses or maybe
+
+ align:start position:0%
+had not just one but two bosses or maybe
+ 
+
+ align:start position:0%
+had not just one but two bosses or maybe
+more if you worked for several programs.
+
+ align:start position:0%
+more if you worked for several programs.
+ 
+
+ align:start position:0%
+more if you worked for several programs.
+Now here you are working in lower level
+
+ align:start position:0%
+Now here you are working in lower level
+ 
+
+ align:start position:0%
+Now here you are working in lower level
+teams that are really tackling different
+
+ align:start position:0%
+teams that are really tackling different
+ 
+
+ align:start position:0%
+teams that are really tackling different
+problems and you all are providing your
+
+ align:start position:0%
+problems and you all are providing your
+ 
+
+ align:start position:0%
+problems and you all are providing your
+own leadership and management and
+
+ align:start position:0%
+own leadership and management and
+ 
+
+ align:start position:0%
+own leadership and management and
+guidance for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that. So if you are now responsible for
+
+ align:start position:0%
+that. So if you are now responsible for
+ 
+
+ align:start position:0%
+that. So if you are now responsible for
+doing a lot more in terms of leading and
+
+ align:start position:0%
+doing a lot more in terms of leading and
+ 
+
+ align:start position:0%
+doing a lot more in terms of leading and
+managing it makes sense that companies
+
+ align:start position:0%
+managing it makes sense that companies
+ 
+
+ align:start position:0%
+managing it makes sense that companies
+are putting more resources towards
+
+ align:start position:0%
+are putting more resources towards
+ 
+
+ align:start position:0%
+are putting more resources towards
+developing your skills in that area.
+
+ align:start position:0%
+developing your skills in that area.
+ 
+
+ align:start position:0%
+developing your skills in that area.
+Companies are offering training. They're
+
+ align:start position:0%
+Companies are offering training. They're
+ 
+
+ align:start position:0%
+Companies are offering training. They're
+valuing experiences like this in school
+
+ align:start position:0%
+valuing experiences like this in school
+ 
+
+ align:start position:0%
+valuing experiences like this in school
+where we're able to develop some of
+
+ align:start position:0%
+where we're able to develop some of
+ 
+
+ align:start position:0%
+where we're able to develop some of
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+characteristics. And just to give you
+
+ align:start position:0%
+characteristics. And just to give you
+ 
+
+ align:start position:0%
+characteristics. And just to give you
+some examples from uh company literature
+
+ align:start position:0%
+some examples from uh company literature
+ 
+
+ align:start position:0%
+some examples from uh company literature
+that talk about this, this is from uh
+
+ align:start position:0%
+that talk about this, this is from uh
+ 
+
+ align:start position:0%
+that talk about this, this is from uh
+Boeing Air Force Systems employee
+
+ align:start position:0%
+Boeing Air Force Systems employee
+ 
+
+ align:start position:0%
+Boeing Air Force Systems employee
+involvement strategy. They produce whole
+
+ align:start position:0%
+involvement strategy. They produce whole
+ 
+
+ align:start position:0%
+involvement strategy. They produce whole
+documents to try to help you understand
+
+ align:start position:0%
+documents to try to help you understand
+ 
+
+ align:start position:0%
+documents to try to help you understand
+how to be an effective team player,
+
+ align:start position:0%
+how to be an effective team player,
+ 
+
+ align:start position:0%
+how to be an effective team player,
+leader, and manager. And I'm not going
+
+ align:start position:0%
+leader, and manager. And I'm not going
+ 
+
+ align:start position:0%
+leader, and manager. And I'm not going
+to spend time talking about these, but
+
+ align:start position:0%
+to spend time talking about these, but
+ 
+
+ align:start position:0%
+to spend time talking about these, but
+more to show you that this is very
+
+ align:start position:0%
+more to show you that this is very
+ 
+
+ align:start position:0%
+more to show you that this is very
+important that people spend a lot of
+
+ align:start position:0%
+important that people spend a lot of
+ 
+
+ align:start position:0%
+important that people spend a lot of
+time thinking about this and putting
+
+ align:start position:0%
+time thinking about this and putting
+ 
+
+ align:start position:0%
+time thinking about this and putting
+together strategies for helping their
+
+ align:start position:0%
+together strategies for helping their
+ 
+
+ align:start position:0%
+together strategies for helping their
+employees to do this
+
+ align:start position:0%
+employees to do this
+ 
+
+ align:start position:0%
+employees to do this
+effectively. They'll talk about team
+
+ align:start position:0%
+effectively. They'll talk about team
+ 
+
+ align:start position:0%
+effectively. They'll talk about team
+behaviors by stages of how teams
+
+ align:start position:0%
+behaviors by stages of how teams
+ 
+
+ align:start position:0%
+behaviors by stages of how teams
+develop. So teams will start in kind of
+
+ align:start position:0%
+develop. So teams will start in kind of
+ 
+
+ align:start position:0%
+develop. So teams will start in kind of
+a forming stage and it takes a while for
+
+ align:start position:0%
+a forming stage and it takes a while for
+ 
+
+ align:start position:0%
+a forming stage and it takes a while for
+them to ramp up to become truly high
+
+ align:start position:0%
+them to ramp up to become truly high
+ 
+
+ align:start position:0%
+them to ramp up to become truly high
+performing teams and they exhibit
+
+ align:start position:0%
+performing teams and they exhibit
+ 
+
+ align:start position:0%
+performing teams and they exhibit
+different behaviors and characteristics.
+
+ align:start position:0%
+different behaviors and characteristics.
+ 
+
+ align:start position:0%
+different behaviors and characteristics.
+And you can also talk about leadership
+
+ align:start position:0%
+And you can also talk about leadership
+ 
+
+ align:start position:0%
+And you can also talk about leadership
+in those very same stages and help you
+
+ align:start position:0%
+in those very same stages and help you
+ 
+
+ align:start position:0%
+in those very same stages and help you
+understand how to transition and grow
+
+ align:start position:0%
+understand how to transition and grow
+ 
+
+ align:start position:0%
+understand how to transition and grow
+your leadership
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+capabilities. So what I'd like to do now
+
+ align:start position:0%
+capabilities. So what I'd like to do now
+ 
+
+ align:start position:0%
+capabilities. So what I'd like to do now
+is engage in another active learning
+
+ align:start position:0%
+is engage in another active learning
+ 
+
+ align:start position:0%
+is engage in another active learning
+exercise. Um we call this personal
+
+ align:start position:0%
+exercise. Um we call this personal
+ 
+
+ align:start position:0%
+exercise. Um we call this personal
+values. It's going to run like this.
+
+ align:start position:0%
+values. It's going to run like this.
+ 
+
+ align:start position:0%
+values. It's going to run like this.
+We're going to give you five minutes to
+
+ align:start position:0%
+We're going to give you five minutes to
+ 
+
+ align:start position:0%
+We're going to give you five minutes to
+take that list of personal values and
+
+ align:start position:0%
+take that list of personal values and
+ 
+
+ align:start position:0%
+take that list of personal values and
+grade them. First you're going to grade
+
+ align:start position:0%
+grade them. First you're going to grade
+ 
+
+ align:start position:0%
+grade them. First you're going to grade
+them A, B, or C. most important,
+
+ align:start position:0%
+them A, B, or C. most important,
+ 
+
+ align:start position:0%
+them A, B, or C. most important,
+important, or least important. And then
+
+ align:start position:0%
+important, or least important. And then
+ 
+
+ align:start position:0%
+important, or least important. And then
+we want you to rank those values using
+
+ align:start position:0%
+we want you to rank those values using
+ 
+
+ align:start position:0%
+we want you to rank those values using
+your grade as a first sort. All right.
+
+ align:start position:0%
+your grade as a first sort. All right.
+ 
+
+ align:start position:0%
+your grade as a first sort. All right.
+So, you have five minutes. Go ahead and
+
+ align:start position:0%
+So, you have five minutes. Go ahead and
+ 
+
+ align:start position:0%
+So, you have five minutes. Go ahead and
+rank your own personal values,
+
+ align:start position:0%
+rank your own personal values,
+ 
+
+ align:start position:0%
+rank your own personal values,
+please. Uh, those people who actually
+
+ align:start position:0%
+please. Uh, those people who actually
+ 
+
+ align:start position:0%
+please. Uh, those people who actually
+finished the exercise, please raise your
+
+ align:start position:0%
+finished the exercise, please raise your
+ 
+
+ align:start position:0%
+finished the exercise, please raise your
+hand. I actually didn't finish it the
+
+ align:start position:0%
+hand. I actually didn't finish it the
+ 
+
+ align:start position:0%
+hand. I actually didn't finish it the
+first time I did it. Who finished it
+
+ align:start position:0%
+first time I did it. Who finished it
+ 
+
+ align:start position:0%
+first time I did it. Who finished it
+within five minutes? Raise your
+
+ align:start position:0%
+within five minutes? Raise your
+ 
+
+ align:start position:0%
+within five minutes? Raise your
+hands. Okay, so about half the class.
+
+ align:start position:0%
+hands. Okay, so about half the class.
+ 
+
+ align:start position:0%
+hands. Okay, so about half the class.
+All right, just keep that in mind. We're
+
+ align:start position:0%
+All right, just keep that in mind. We're
+ 
+
+ align:start position:0%
+All right, just keep that in mind. We're
+going to talk about it at the end of the
+
+ align:start position:0%
+going to talk about it at the end of the
+ 
+
+ align:start position:0%
+going to talk about it at the end of the
+exercise.
+
+ align:start position:0%
+exercise.
+ 
+
+ align:start position:0%
+exercise.
+Your next task is by tables. We've
+
+ align:start position:0%
+Your next task is by tables. We've
+ 
+
+ align:start position:0%
+Your next task is by tables. We've
+handed out a manila envelope
+
+ align:start position:0%
+handed out a manila envelope
+ 
+
+ align:start position:0%
+handed out a manila envelope
+there. Inside our cutouts of the values
+
+ align:start position:0%
+there. Inside our cutouts of the values
+ 
+
+ align:start position:0%
+there. Inside our cutouts of the values
+to help you to use in creating a team
+
+ align:start position:0%
+to help you to use in creating a team
+ 
+
+ align:start position:0%
+to help you to use in creating a team
+list of ranked values. So you did this
+
+ align:start position:0%
+list of ranked values. So you did this
+ 
+
+ align:start position:0%
+list of ranked values. So you did this
+on the personal level and now we want
+
+ align:start position:0%
+on the personal level and now we want
+ 
+
+ align:start position:0%
+on the personal level and now we want
+you to do it on the team level. So you
+
+ align:start position:0%
+you to do it on the team level. So you
+ 
+
+ align:start position:0%
+you to do it on the team level. So you
+may find these cutouts helpful because
+
+ align:start position:0%
+may find these cutouts helpful because
+ 
+
+ align:start position:0%
+may find these cutouts helpful because
+you can move them around. You don't have
+
+ align:start position:0%
+you can move them around. You don't have
+ 
+
+ align:start position:0%
+you can move them around. You don't have
+to worry about writing them down and
+
+ align:start position:0%
+to worry about writing them down and
+ 
+
+ align:start position:0%
+to worry about writing them down and
+scratching them out. So you have 10
+
+ align:start position:0%
+scratching them out. So you have 10
+ 
+
+ align:start position:0%
+scratching them out. So you have 10
+minutes to complete this task. Ready?
+
+ align:start position:0%
+minutes to complete this task. Ready?
+ 
+
+ align:start position:0%
+minutes to complete this task. Ready?
+Go. So at 240 we'll stop and we want a
+
+ align:start position:0%
+Go. So at 240 we'll stop and we want a
+ 
+
+ align:start position:0%
+Go. So at 240 we'll stop and we want a
+rank list from one to n.
+
+ align:start position:0%
+rank list from one to n.
+ 
+
+ align:start position:0%
+rank list from one to n.
+No ties.
+
+ align:start position:0%
+No ties.
+ 
+
+ align:start position:0%
+No ties.
+Okay. Time is up. Please stop working on
+
+ align:start position:0%
+Okay. Time is up. Please stop working on
+ 
+
+ align:start position:0%
+Okay. Time is up. Please stop working on
+your task.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Just where wherever you are,
+
+ align:start position:0%
+All right. Just where wherever you are,
+ 
+
+ align:start position:0%
+All right. Just where wherever you are,
+please please stop your work.
+
+ align:start position:0%
+please please stop your work.
+ 
+
+ align:start position:0%
+please please stop your work.
+And uh I need your groups to elect one
+
+ align:start position:0%
+And uh I need your groups to elect one
+ 
+
+ align:start position:0%
+And uh I need your groups to elect one
+representative to debrief us. All right.
+
+ align:start position:0%
+representative to debrief us. All right.
+ 
+
+ align:start position:0%
+representative to debrief us. All right.
+Okay. So, I'm looking for each group to
+
+ align:start position:0%
+Okay. So, I'm looking for each group to
+ 
+
+ align:start position:0%
+Okay. So, I'm looking for each group to
+give us a twominute debrief. In that
+
+ align:start position:0%
+give us a twominute debrief. In that
+ 
+
+ align:start position:0%
+give us a twominute debrief. In that
+debrief, I'd like to hear first your
+
+ align:start position:0%
+debrief, I'd like to hear first your
+ 
+
+ align:start position:0%
+debrief, I'd like to hear first your
+process for going about your task, and
+
+ align:start position:0%
+process for going about your task, and
+ 
+
+ align:start position:0%
+process for going about your task, and
+then I'd like to hear about the
+
+ align:start position:0%
+then I'd like to hear about the
+ 
+
+ align:start position:0%
+then I'd like to hear about the
+result. And which group would like to
+
+ align:start position:0%
+result. And which group would like to
+ 
+
+ align:start position:0%
+result. And which group would like to
+start us off? Volunteers.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Go ahead, Zoe. Okay. Um so
+
+ align:start position:0%
+All right. Go ahead, Zoe. Okay. Um so
+ 
+
+ align:start position:0%
+All right. Go ahead, Zoe. Okay. Um so
+our process because um we decided that
+
+ align:start position:0%
+our process because um we decided that
+ 
+
+ align:start position:0%
+our process because um we decided that
+since they were our own personal values
+
+ align:start position:0%
+since they were our own personal values
+ 
+
+ align:start position:0%
+since they were our own personal values
+in two minutes we probably couldn't
+
+ align:start position:0%
+in two minutes we probably couldn't
+ 
+
+ align:start position:0%
+in two minutes we probably couldn't
+actually agree on anything. So we
+
+ align:start position:0%
+actually agree on anything. So we
+ 
+
+ align:start position:0%
+actually agree on anything. So we
+averaged all our numbers to get our list
+
+ align:start position:0%
+averaged all our numbers to get our list
+ 
+
+ align:start position:0%
+averaged all our numbers to get our list
+um based on the lowest one being our the
+
+ align:start position:0%
+um based on the lowest one being our the
+ 
+
+ align:start position:0%
+um based on the lowest one being our the
+lowest average being our highest. And
+
+ align:start position:0%
+lowest average being our highest. And
+ 
+
+ align:start position:0%
+lowest average being our highest. And
+what we found is what that did is if
+
+ align:start position:0%
+what we found is what that did is if
+ 
+
+ align:start position:0%
+what we found is what that did is if
+there were some points of disagreement
+
+ align:start position:0%
+there were some points of disagreement
+ 
+
+ align:start position:0%
+there were some points of disagreement
+like we had a couple where there was
+
+ align:start position:0%
+like we had a couple where there was
+ 
+
+ align:start position:0%
+like we had a couple where there was
+someone had a one and someone had 18
+
+ align:start position:0%
+someone had a one and someone had 18
+ 
+
+ align:start position:0%
+someone had a one and someone had 18
+that automatically pushes out of the
+
+ align:start position:0%
+that automatically pushes out of the
+ 
+
+ align:start position:0%
+that automatically pushes out of the
+ones we're really considering for the
+
+ align:start position:0%
+ones we're really considering for the
+ 
+
+ align:start position:0%
+ones we're really considering for the
+top. Um, so our top three people seem to
+
+ align:start position:0%
+top. Um, so our top three people seem to
+ 
+
+ align:start position:0%
+top. Um, so our top three people seem to
+be pretty happy with overall and they
+
+ align:start position:0%
+be pretty happy with overall and they
+ 
+
+ align:start position:0%
+be pretty happy with overall and they
+were a sense of accomplishment, true
+
+ align:start position:0%
+were a sense of accomplishment, true
+ 
+
+ align:start position:0%
+were a sense of accomplishment, true
+friendship, and mature.
+
+ align:start position:0%
+friendship, and mature.
+ 
+
+ align:start position:0%
+friendship, and mature.
+Excellent. Okay, great. That's a good
+
+ align:start position:0%
+Excellent. Okay, great. That's a good
+ 
+
+ align:start position:0%
+Excellent. Okay, great. That's a good
+good template for the rest of the groups
+
+ align:start position:0%
+good template for the rest of the groups
+ 
+
+ align:start position:0%
+good template for the rest of the groups
+to follow. So, let's get the other
+
+ align:start position:0%
+to follow. So, let's get the other
+ 
+
+ align:start position:0%
+to follow. So, let's get the other
+debriefs. Who'd like to go
+
+ align:start position:0%
+debriefs. Who'd like to go
+ 
+
+ align:start position:0%
+debriefs. Who'd like to go
+next? Maybe you guys back. Who's your
+
+ align:start position:0%
+next? Maybe you guys back. Who's your
+ 
+
+ align:start position:0%
+next? Maybe you guys back. Who's your
+spokesperson? What was your process?
+
+ align:start position:0%
+spokesperson? What was your process?
+ 
+
+ align:start position:0%
+spokesperson? What was your process?
+We argue a lot.
+
+ align:start position:0%
+We argue a lot.
+ 
+
+ align:start position:0%
+We argue a lot.
+to us.
+
+ align:start position:0%
+to us.
+ 
+
+ align:start position:0%
+to us.
+Well, I think that people kind of had
+
+ align:start position:0%
+Well, I think that people kind of had
+ 
+
+ align:start position:0%
+Well, I think that people kind of had
+sort of we kind of had groups of things
+
+ align:start position:0%
+sort of we kind of had groups of things
+ 
+
+ align:start position:0%
+sort of we kind of had groups of things
+that belong to the top, middle, and
+
+ align:start position:0%
+that belong to the top, middle, and
+ 
+
+ align:start position:0%
+that belong to the top, middle, and
+bottom. And so within those, we just had
+
+ align:start position:0%
+bottom. And so within those, we just had
+ 
+
+ align:start position:0%
+bottom. And so within those, we just had
+some arguments about how to place
+
+ align:start position:0%
+some arguments about how to place
+ 
+
+ align:start position:0%
+some arguments about how to place
+things, but it actually came to some
+
+ align:start position:0%
+things, but it actually came to some
+ 
+
+ align:start position:0%
+things, but it actually came to some
+agreement. And so our top three were
+
+ align:start position:0%
+agreement. And so our top three were
+ 
+
+ align:start position:0%
+agreement. And so our top three were
+happiness, inner harmony, and a
+
+ align:start position:0%
+happiness, inner harmony, and a
+ 
+
+ align:start position:0%
+happiness, inner harmony, and a
+comfortable life.
+
+ align:start position:0%
+comfortable life.
+ 
+
+ align:start position:0%
+comfortable life.
+And how did you arrive at your first
+
+ align:start position:0%
+And how did you arrive at your first
+ 
+
+ align:start position:0%
+And how did you arrive at your first
+three groupings?
+
+ align:start position:0%
+three groupings?
+ 
+
+ align:start position:0%
+three groupings?
+Just throw in the top three. Um no no
+
+ align:start position:0%
+Just throw in the top three. Um no no
+ 
+
+ align:start position:0%
+Just throw in the top three. Um no no
+you had three initial groups and then
+
+ align:start position:0%
+you had three initial groups and then
+ 
+
+ align:start position:0%
+you had three initial groups and then
+you sorted within those groups. How did
+
+ align:start position:0%
+you sorted within those groups. How did
+ 
+
+ align:start position:0%
+you sorted within those groups. How did
+you get to that first cut? I guess
+
+ align:start position:0%
+you get to that first cut? I guess
+ 
+
+ align:start position:0%
+you get to that first cut? I guess
+mentally everybody had their sort of A B
+
+ align:start position:0%
+mentally everybody had their sort of A B
+ 
+
+ align:start position:0%
+mentally everybody had their sort of A B
+and C groups. So that's how we
+
+ align:start position:0%
+and C groups. So that's how we
+ 
+
+ align:start position:0%
+and C groups. So that's how we
+and was there a lot of consensus on
+
+ align:start position:0%
+and was there a lot of consensus on
+ 
+
+ align:start position:0%
+and was there a lot of consensus on
+which were A's, which were B's, which
+
+ align:start position:0%
+which were A's, which were B's, which
+ 
+
+ align:start position:0%
+which were A's, which were B's, which
+were C's? Yeah. Yeah.
+
+ align:start position:0%
+were C's? Yeah. Yeah.
+ 
+
+ align:start position:0%
+were C's? Yeah. Yeah.
+Okay. And how about this group next?
+
+ align:start position:0%
+Okay. And how about this group next?
+ 
+
+ align:start position:0%
+Okay. And how about this group next?
+Because I know you guys have been done
+
+ align:start position:0%
+Because I know you guys have been done
+ 
+
+ align:start position:0%
+Because I know you guys have been done
+for a while and have a lot of time to
+
+ align:start position:0%
+for a while and have a lot of time to
+ 
+
+ align:start position:0%
+for a while and have a lot of time to
+think about presenting it.
+
+ align:start position:0%
+think about presenting it.
+ 
+
+ align:start position:0%
+think about presenting it.
+I guess we actually had a similar
+
+ align:start position:0%
+I guess we actually had a similar
+ 
+
+ align:start position:0%
+I guess we actually had a similar
+method. We all decided that we wanted at
+
+ align:start position:0%
+method. We all decided that we wanted at
+ 
+
+ align:start position:0%
+method. We all decided that we wanted at
+the top of our list, our top three
+
+ align:start position:0%
+the top of our list, our top three
+ 
+
+ align:start position:0%
+the top of our list, our top three
+choices for all of us, we would have
+
+ align:start position:0%
+choices for all of us, we would have
+ 
+
+ align:start position:0%
+choices for all of us, we would have
+them towards the top of our list. And so
+
+ align:start position:0%
+them towards the top of our list. And so
+ 
+
+ align:start position:0%
+them towards the top of our list. And so
+from the middle and the last part, we
+
+ align:start position:0%
+from the middle and the last part, we
+ 
+
+ align:start position:0%
+from the middle and the last part, we
+knew that there was going to be a little
+
+ align:start position:0%
+knew that there was going to be a little
+ 
+
+ align:start position:0%
+knew that there was going to be a little
+bit of discussion. And so we were more
+
+ align:start position:0%
+bit of discussion. And so we were more
+ 
+
+ align:start position:0%
+bit of discussion. And so we were more
+flexible on what was going to go in each
+
+ align:start position:0%
+flexible on what was going to go in each
+ 
+
+ align:start position:0%
+flexible on what was going to go in each
+category. We all had more or less a
+
+ align:start position:0%
+category. We all had more or less a
+ 
+
+ align:start position:0%
+category. We all had more or less a
+similar mindset on what each of our
+
+ align:start position:0%
+similar mindset on what each of our
+ 
+
+ align:start position:0%
+similar mindset on what each of our
+values were. So our list came came out
+
+ align:start position:0%
+values were. So our list came came out
+ 
+
+ align:start position:0%
+values were. So our list came came out
+pretty neat. And what were your top
+
+ align:start position:0%
+pretty neat. And what were your top
+ 
+
+ align:start position:0%
+pretty neat. And what were your top
+three? Our top three were happiness,
+
+ align:start position:0%
+three? Our top three were happiness,
+ 
+
+ align:start position:0%
+three? Our top three were happiness,
+family security, true friendship. So
+
+ align:start position:0%
+family security, true friendship. So
+ 
+
+ align:start position:0%
+family security, true friendship. So
+were you satisfied with your process?
+
+ align:start position:0%
+were you satisfied with your process?
+ 
+
+ align:start position:0%
+were you satisfied with your process?
+So there's a lot of mathematical
+
+ align:start position:0%
+So there's a lot of mathematical
+ 
+
+ align:start position:0%
+So there's a lot of mathematical
+averaging for something that's very
+
+ align:start position:0%
+averaging for something that's very
+ 
+
+ align:start position:0%
+averaging for something that's very
+unmathematical like personal values.
+
+ align:start position:0%
+unmathematical like personal values.
+ 
+
+ align:start position:0%
+unmathematical like personal values.
+Go ahead, Tim. There are a number of
+
+ align:start position:0%
+Go ahead, Tim. There are a number of
+ 
+
+ align:start position:0%
+Go ahead, Tim. There are a number of
+them that you can all kind of agree on
+
+ align:start position:0%
+them that you can all kind of agree on
+ 
+
+ align:start position:0%
+them that you can all kind of agree on
+like, yeah, those are probably pretty
+
+ align:start position:0%
+like, yeah, those are probably pretty
+ 
+
+ align:start position:0%
+like, yeah, those are probably pretty
+important to all of us. But then there
+
+ align:start position:0%
+important to all of us. But then there
+ 
+
+ align:start position:0%
+important to all of us. But then there
+are certain ones where it's surprising
+
+ align:start position:0%
+are certain ones where it's surprising
+ 
+
+ align:start position:0%
+are certain ones where it's surprising
+where some people rank it one or two and
+
+ align:start position:0%
+where some people rank it one or two and
+ 
+
+ align:start position:0%
+where some people rank it one or two and
+others people rank it 17 or 18 and
+
+ align:start position:0%
+others people rank it 17 or 18 and
+ 
+
+ align:start position:0%
+others people rank it 17 or 18 and
+there's just absolutely no way to
+
+ align:start position:0%
+there's just absolutely no way to
+ 
+
+ align:start position:0%
+there's just absolutely no way to
+reconcile that. Like you could just you
+
+ align:start position:0%
+reconcile that. Like you could just you
+ 
+
+ align:start position:0%
+reconcile that. Like you could just you
+could just argue all day. Um so for
+
+ align:start position:0%
+could just argue all day. Um so for
+ 
+
+ align:start position:0%
+could just argue all day. Um so for
+cases like that, you know, okay, we'll
+
+ align:start position:0%
+cases like that, you know, okay, we'll
+ 
+
+ align:start position:0%
+cases like that, you know, okay, we'll
+just take the average.
+
+ align:start position:0%
+just take the average.
+ 
+
+ align:start position:0%
+just take the average.
+Um that's how we justified it to
+
+ align:start position:0%
+Um that's how we justified it to
+ 
+
+ align:start position:0%
+Um that's how we justified it to
+ourselves. Mark have comments on that. I
+
+ align:start position:0%
+ourselves. Mark have comments on that. I
+ 
+
+ align:start position:0%
+ourselves. Mark have comments on that. I
+don't even think people can def like
+
+ align:start position:0%
+don't even think people can def like
+ 
+
+ align:start position:0%
+don't even think people can def like
+come to agreement on what these things
+
+ align:start position:0%
+come to agreement on what these things
+ 
+
+ align:start position:0%
+come to agreement on what these things
+mean either. So you're like not even
+
+ align:start position:0%
+mean either. So you're like not even
+ 
+
+ align:start position:0%
+mean either. So you're like not even
+talking about the same things pretty
+
+ align:start position:0%
+talking about the same things pretty
+ 
+
+ align:start position:0%
+talking about the same things pretty
+hard. That's true. I I I think we've we
+
+ align:start position:0%
+hard. That's true. I I I think we've we
+ 
+
+ align:start position:0%
+hard. That's true. I I I think we've we
+definitely had disagreement I think on
+
+ align:start position:0%
+definitely had disagreement I think on
+ 
+
+ align:start position:0%
+definitely had disagreement I think on
+what inner harmony really means.
+
+ align:start position:0%
+what inner harmony really means.
+ 
+
+ align:start position:0%
+what inner harmony really means.
+So some words on the sheet didn't do it
+
+ align:start position:0%
+So some words on the sheet didn't do it
+ 
+
+ align:start position:0%
+So some words on the sheet didn't do it
+for you. Explain the concept of inner
+
+ align:start position:0%
+for you. Explain the concept of inner
+ 
+
+ align:start position:0%
+for you. Explain the concept of inner
+harmony. Well, I mean what it what it
+
+ align:start position:0%
+harmony. Well, I mean what it what it
+ 
+
+ align:start position:0%
+harmony. Well, I mean what it what it
+really means to you. But I think I think
+
+ align:start position:0%
+really means to you. But I think I think
+ 
+
+ align:start position:0%
+really means to you. But I think I think
+any process you choose is going to be
+
+ align:start position:0%
+any process you choose is going to be
+ 
+
+ align:start position:0%
+any process you choose is going to be
+arbitrary. So you might as well be
+
+ align:start position:0%
+arbitrary. So you might as well be
+ 
+
+ align:start position:0%
+arbitrary. So you might as well be
+systematic. I think that's kind of what
+
+ align:start position:0%
+systematic. I think that's kind of what
+ 
+
+ align:start position:0%
+systematic. I think that's kind of what
+we came to. Okay.
+
+ align:start position:0%
+we came to. Okay.
+ 
+
+ align:start position:0%
+we came to. Okay.
+Let's turn now from a discussion of the
+
+ align:start position:0%
+Let's turn now from a discussion of the
+ 
+
+ align:start position:0%
+Let's turn now from a discussion of the
+process you used to discussion of how
+
+ align:start position:0%
+process you used to discussion of how
+ 
+
+ align:start position:0%
+process you used to discussion of how
+the topic you were using. You you were
+
+ align:start position:0%
+the topic you were using. You you were
+ 
+
+ align:start position:0%
+the topic you were using. You you were
+dealing with this ranking of values and
+
+ align:start position:0%
+dealing with this ranking of values and
+ 
+
+ align:start position:0%
+dealing with this ranking of values and
+how emotions might have gotten into play
+
+ align:start position:0%
+how emotions might have gotten into play
+ 
+
+ align:start position:0%
+how emotions might have gotten into play
+because values are a pretty emotional
+
+ align:start position:0%
+because values are a pretty emotional
+ 
+
+ align:start position:0%
+because values are a pretty emotional
+thing. You personal values they are very
+
+ align:start position:0%
+thing. You personal values they are very
+ 
+
+ align:start position:0%
+thing. You personal values they are very
+uh closely held. Did those get in the
+
+ align:start position:0%
+uh closely held. Did those get in the
+ 
+
+ align:start position:0%
+uh closely held. Did those get in the
+way of getting your task done? Did you
+
+ align:start position:0%
+way of getting your task done? Did you
+ 
+
+ align:start position:0%
+way of getting your task done? Did you
+feel less satisfied with your task in
+
+ align:start position:0%
+feel less satisfied with your task in
+ 
+
+ align:start position:0%
+feel less satisfied with your task in
+your process because of the material you
+
+ align:start position:0%
+your process because of the material you
+ 
+
+ align:start position:0%
+your process because of the material you
+were dealing with and the task you were
+
+ align:start position:0%
+were dealing with and the task you were
+ 
+
+ align:start position:0%
+were dealing with and the task you were
+dealing with?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Not just to you. This is to to every
+
+ align:start position:0%
+Not just to you. This is to to every
+ 
+
+ align:start position:0%
+Not just to you. This is to to every
+group. You all did the same tasks and
+
+ align:start position:0%
+group. You all did the same tasks and
+ 
+
+ align:start position:0%
+group. You all did the same tasks and
+you all went about it ranking it either
+
+ align:start position:0%
+you all went about it ranking it either
+ 
+
+ align:start position:0%
+you all went about it ranking it either
+democratically or very mathematically.
+
+ align:start position:0%
+democratically or very mathematically.
+ 
+
+ align:start position:0%
+democratically or very mathematically.
+You somehow came to a consensus about a
+
+ align:start position:0%
+You somehow came to a consensus about a
+ 
+
+ align:start position:0%
+You somehow came to a consensus about a
+subject that a lot of people would
+
+ align:start position:0%
+subject that a lot of people would
+ 
+
+ align:start position:0%
+subject that a lot of people would
+consider is pretty sensitive. You know
+
+ align:start position:0%
+consider is pretty sensitive. You know
+ 
+
+ align:start position:0%
+consider is pretty sensitive. You know
+how you personally feel about it. So,
+
+ align:start position:0%
+how you personally feel about it. So,
+ 
+
+ align:start position:0%
+how you personally feel about it. So,
+were there any cases where your own
+
+ align:start position:0%
+were there any cases where your own
+ 
+
+ align:start position:0%
+were there any cases where your own
+personal feelings or emotions you felt
+
+ align:start position:0%
+personal feelings or emotions you felt
+ 
+
+ align:start position:0%
+personal feelings or emotions you felt
+like that was coming to a
+
+ align:start position:0%
+like that was coming to a
+ 
+
+ align:start position:0%
+like that was coming to a
+head? Go ahead and and be honest, Zoe.
+
+ align:start position:0%
+head? Go ahead and and be honest, Zoe.
+ 
+
+ align:start position:0%
+head? Go ahead and and be honest, Zoe.
+Um, I think it's interesting for this
+
+ align:start position:0%
+Um, I think it's interesting for this
+ 
+
+ align:start position:0%
+Um, I think it's interesting for this
+exercise how we have like some
+
+ align:start position:0%
+exercise how we have like some
+ 
+
+ align:start position:0%
+exercise how we have like some
+definitely communal values and some
+
+ align:start position:0%
+definitely communal values and some
+ 
+
+ align:start position:0%
+definitely communal values and some
+definitely personal values. And I'm not
+
+ align:start position:0%
+definitely personal values. And I'm not
+ 
+
+ align:start position:0%
+definitely personal values. And I'm not
+totally comfortable with first of all
+
+ align:start position:0%
+totally comfortable with first of all
+ 
+
+ align:start position:0%
+totally comfortable with first of all
+putting those together and second of all
+
+ align:start position:0%
+putting those together and second of all
+ 
+
+ align:start position:0%
+putting those together and second of all
+discussing them in the same ranking
+
+ align:start position:0%
+discussing them in the same ranking
+ 
+
+ align:start position:0%
+discussing them in the same ranking
+because I think I don't think it really
+
+ align:start position:0%
+because I think I don't think it really
+ 
+
+ align:start position:0%
+because I think I don't think it really
+matters whether you have compatibility
+
+ align:start position:0%
+matters whether you have compatibility
+ 
+
+ align:start position:0%
+matters whether you have compatibility
+in a group of people with your personal
+
+ align:start position:0%
+in a group of people with your personal
+ 
+
+ align:start position:0%
+in a group of people with your personal
+values as long as they actually are
+
+ align:start position:0%
+values as long as they actually are
+ 
+
+ align:start position:0%
+values as long as they actually are
+personal values and people believe that.
+
+ align:start position:0%
+personal values and people believe that.
+ 
+
+ align:start position:0%
+personal values and people believe that.
+But it would reduce the list and maybe
+
+ align:start position:0%
+But it would reduce the list and maybe
+ 
+
+ align:start position:0%
+But it would reduce the list and maybe
+be more interesting to try it actually
+
+ align:start position:0%
+be more interesting to try it actually
+ 
+
+ align:start position:0%
+be more interesting to try it actually
+because since we have a whole society
+
+ align:start position:0%
+because since we have a whole society
+ 
+
+ align:start position:0%
+because since we have a whole society
+structure, we kind of have to make
+
+ align:start position:0%
+structure, we kind of have to make
+ 
+
+ align:start position:0%
+structure, we kind of have to make
+decisions about values which are things
+
+ align:start position:0%
+decisions about values which are things
+ 
+
+ align:start position:0%
+decisions about values which are things
+that you can't normally discuss, but
+
+ align:start position:0%
+that you can't normally discuss, but
+ 
+
+ align:start position:0%
+that you can't normally discuss, but
+it's important to have no one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I'm not hearing a lot of stories
+
+ align:start position:0%
+So I'm not hearing a lot of stories
+ 
+
+ align:start position:0%
+So I'm not hearing a lot of stories
+about people getting emotional during
+
+ align:start position:0%
+about people getting emotional during
+ 
+
+ align:start position:0%
+about people getting emotional during
+this process and that's that's
+
+ align:start position:0%
+this process and that's that's
+ 
+
+ align:start position:0%
+this process and that's that's
+wonderful. Oh,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+laughing your
+
+ align:start position:0%
+laughing your
+ 
+
+ align:start position:0%
+laughing your
+laugh. I'm not sorry. So, does that
+
+ align:start position:0%
+laugh. I'm not sorry. So, does that
+ 
+
+ align:start position:0%
+laugh. I'm not sorry. So, does that
+laughter indicate that there was some
+
+ align:start position:0%
+laughter indicate that there was some
+ 
+
+ align:start position:0%
+laughter indicate that there was some
+emotional conflict going on during the
+
+ align:start position:0%
+emotional conflict going on during the
+ 
+
+ align:start position:0%
+emotional conflict going on during the
+test? People don't respect.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let me tell you that that this just
+
+ align:start position:0%
+Let me tell you that that this just
+ 
+
+ align:start position:0%
+Let me tell you that that this just
+might be uh an oddity in terms of how
+
+ align:start position:0%
+might be uh an oddity in terms of how
+ 
+
+ align:start position:0%
+might be uh an oddity in terms of how
+this exercise usually turns out because
+
+ align:start position:0%
+this exercise usually turns out because
+ 
+
+ align:start position:0%
+this exercise usually turns out because
+we normally get a lot of very oftentimes
+
+ align:start position:0%
+we normally get a lot of very oftentimes
+ 
+
+ align:start position:0%
+we normally get a lot of very oftentimes
+visceral discussion about these emotions
+
+ align:start position:0%
+visceral discussion about these emotions
+ 
+
+ align:start position:0%
+visceral discussion about these emotions
+and ranking them because it really does
+
+ align:start position:0%
+and ranking them because it really does
+ 
+
+ align:start position:0%
+and ranking them because it really does
+touch on the heartstrings of a lot of
+
+ align:start position:0%
+touch on the heartstrings of a lot of
+ 
+
+ align:start position:0%
+touch on the heartstrings of a lot of
+people. Uh when I first went through
+
+ align:start position:0%
+people. Uh when I first went through
+ 
+
+ align:start position:0%
+people. Uh when I first went through
+this exercise, I remember it like it was
+
+ align:start position:0%
+this exercise, I remember it like it was
+ 
+
+ align:start position:0%
+this exercise, I remember it like it was
+yesterday. We couldn't have had six more
+
+ align:start position:0%
+yesterday. We couldn't have had six more
+ 
+
+ align:start position:0%
+yesterday. We couldn't have had six more
+opposite people sitting at my table and
+
+ align:start position:0%
+opposite people sitting at my table and
+ 
+
+ align:start position:0%
+opposite people sitting at my table and
+there was no way that we were going to
+
+ align:start position:0%
+there was no way that we were going to
+ 
+
+ align:start position:0%
+there was no way that we were going to
+agree on our our values and being
+
+ align:start position:0%
+agree on our our values and being
+ 
+
+ align:start position:0%
+agree on our our values and being
+professionals with some age behind us,
+
+ align:start position:0%
+professionals with some age behind us,
+ 
+
+ align:start position:0%
+professionals with some age behind us,
+some more, some less. Uh we were all
+
+ align:start position:0%
+some more, some less. Uh we were all
+ 
+
+ align:start position:0%
+some more, some less. Uh we were all
+very strongly rooted in our individual
+
+ align:start position:0%
+very strongly rooted in our individual
+ 
+
+ align:start position:0%
+very strongly rooted in our individual
+values and and did not want to come to
+
+ align:start position:0%
+values and and did not want to come to
+ 
+
+ align:start position:0%
+values and and did not want to come to
+any kind of consensus on that and uh
+
+ align:start position:0%
+any kind of consensus on that and uh
+ 
+
+ align:start position:0%
+any kind of consensus on that and uh
+lots of emotions
+
+ align:start position:0%
+lots of emotions
+ 
+
+ align:start position:0%
+lots of emotions
+flying. So I bring that up because I
+
+ align:start position:0%
+flying. So I bring that up because I
+ 
+
+ align:start position:0%
+flying. So I bring that up because I
+want to talk about working in
+
+ align:start position:0%
+want to talk about working in
+ 
+
+ align:start position:0%
+want to talk about working in
+teams. Collaborating in teams can be
+
+ align:start position:0%
+teams. Collaborating in teams can be
+ 
+
+ align:start position:0%
+teams. Collaborating in teams can be
+very challenging. I think that if we
+
+ align:start position:0%
+very challenging. I think that if we
+ 
+
+ align:start position:0%
+very challenging. I think that if we
+read down this list here, you all can
+
+ align:start position:0%
+read down this list here, you all can
+ 
+
+ align:start position:0%
+read down this list here, you all can
+think to your own teamwork experiences,
+
+ align:start position:0%
+think to your own teamwork experiences,
+ 
+
+ align:start position:0%
+think to your own teamwork experiences,
+and I'm sure you'll see instances of
+
+ align:start position:0%
+and I'm sure you'll see instances of
+ 
+
+ align:start position:0%
+and I'm sure you'll see instances of
+each of these in your own experiences.
+
+ align:start position:0%
+each of these in your own experiences.
+ 
+
+ align:start position:0%
+each of these in your own experiences.
+So that you all have different goals and
+
+ align:start position:0%
+So that you all have different goals and
+ 
+
+ align:start position:0%
+So that you all have different goals and
+and values, personal values that you
+
+ align:start position:0%
+and values, personal values that you
+ 
+
+ align:start position:0%
+and values, personal values that you
+bring to accomplishing a task that can
+
+ align:start position:0%
+bring to accomplishing a task that can
+ 
+
+ align:start position:0%
+bring to accomplishing a task that can
+get in the way. You may not be skilled
+
+ align:start position:0%
+get in the way. You may not be skilled
+ 
+
+ align:start position:0%
+get in the way. You may not be skilled
+in what you're trying to do, but yet
+
+ align:start position:0%
+in what you're trying to do, but yet
+ 
+
+ align:start position:0%
+in what you're trying to do, but yet
+you're working on a
+
+ align:start position:0%
+you're working on a
+ 
+
+ align:start position:0%
+you're working on a
+team. People can get defensive about
+
+ align:start position:0%
+team. People can get defensive about
+ 
+
+ align:start position:0%
+team. People can get defensive about
+their work and egos get in the way and a
+
+ align:start position:0%
+their work and egos get in the way and a
+ 
+
+ align:start position:0%
+their work and egos get in the way and a
+lot of pride of ownership that can get
+
+ align:start position:0%
+lot of pride of ownership that can get
+ 
+
+ align:start position:0%
+lot of pride of ownership that can get
+in the way of working in teams.
+
+ align:start position:0%
+in the way of working in teams.
+ 
+
+ align:start position:0%
+in the way of working in teams.
+preconceived notions with which might
+
+ align:start position:0%
+preconceived notions with which might
+ 
+
+ align:start position:0%
+preconceived notions with which might
+not fit with your end objective or your
+
+ align:start position:0%
+not fit with your end objective or your
+ 
+
+ align:start position:0%
+not fit with your end objective or your
+process. Then we have different work
+
+ align:start position:0%
+process. Then we have different work
+ 
+
+ align:start position:0%
+process. Then we have different work
+styles too and you may find yourself uh
+
+ align:start position:0%
+styles too and you may find yourself uh
+ 
+
+ align:start position:0%
+styles too and you may find yourself uh
+sitting in in each of these different
+
+ align:start position:0%
+sitting in in each of these different
+ 
+
+ align:start position:0%
+sitting in in each of these different
+camps at different times for different
+
+ align:start position:0%
+camps at different times for different
+ 
+
+ align:start position:0%
+camps at different times for different
+projects that you're assigned to do.
+
+ align:start position:0%
+projects that you're assigned to do.
+ 
+
+ align:start position:0%
+projects that you're assigned to do.
+Sometimes you feel like I just really
+
+ align:start position:0%
+Sometimes you feel like I just really
+ 
+
+ align:start position:0%
+Sometimes you feel like I just really
+want to do this myself. Sometimes you
+
+ align:start position:0%
+want to do this myself. Sometimes you
+ 
+
+ align:start position:0%
+want to do this myself. Sometimes you
+think, oh, it's just too much work to
+
+ align:start position:0%
+think, oh, it's just too much work to
+ 
+
+ align:start position:0%
+think, oh, it's just too much work to
+collaborate with everybody else. I'll
+
+ align:start position:0%
+collaborate with everybody else. I'll
+ 
+
+ align:start position:0%
+collaborate with everybody else. I'll
+just do it on my own. And uh some some
+
+ align:start position:0%
+just do it on my own. And uh some some
+ 
+
+ align:start position:0%
+just do it on my own. And uh some some
+people just really would really like to
+
+ align:start position:0%
+people just really would really like to
+ 
+
+ align:start position:0%
+people just really would really like to
+take the lead and have themselves do all
+
+ align:start position:0%
+take the lead and have themselves do all
+ 
+
+ align:start position:0%
+take the lead and have themselves do all
+the work for other reasons. And you've
+
+ align:start position:0%
+the work for other reasons. And you've
+ 
+
+ align:start position:0%
+the work for other reasons. And you've
+probably seen instances of these in the
+
+ align:start position:0%
+probably seen instances of these in the
+ 
+
+ align:start position:0%
+probably seen instances of these in the
+people you worked with. So there's all
+
+ align:start position:0%
+people you worked with. So there's all
+ 
+
+ align:start position:0%
+people you worked with. So there's all
+kinds of different styles coming
+
+ align:start position:0%
+kinds of different styles coming
+ 
+
+ align:start position:0%
+kinds of different styles coming
+together and trying to work. And maybe
+
+ align:start position:0%
+together and trying to work. And maybe
+ 
+
+ align:start position:0%
+together and trying to work. And maybe
+you had a previous unsuccessful
+
+ align:start position:0%
+you had a previous unsuccessful
+ 
+
+ align:start position:0%
+you had a previous unsuccessful
+collaboration which then impacts your
+
+ align:start position:0%
+collaboration which then impacts your
+ 
+
+ align:start position:0%
+collaboration which then impacts your
+desire to work in teams. But some of the
+
+ align:start position:0%
+desire to work in teams. But some of the
+ 
+
+ align:start position:0%
+desire to work in teams. But some of the
+benefits are that you get more ideas and
+
+ align:start position:0%
+benefits are that you get more ideas and
+ 
+
+ align:start position:0%
+benefits are that you get more ideas and
+you get new ideas that you haven't had
+
+ align:start position:0%
+you get new ideas that you haven't had
+ 
+
+ align:start position:0%
+you get new ideas that you haven't had
+before. You get people with lots of
+
+ align:start position:0%
+before. You get people with lots of
+ 
+
+ align:start position:0%
+before. You get people with lots of
+backgrounds and expertise. You can share
+
+ align:start position:0%
+backgrounds and expertise. You can share
+ 
+
+ align:start position:0%
+backgrounds and expertise. You can share
+that workload and balance it in a lean
+
+ align:start position:0%
+that workload and balance it in a lean
+ 
+
+ align:start position:0%
+that workload and balance it in a lean
+environment. You'll have stronger
+
+ align:start position:0%
+environment. You'll have stronger
+ 
+
+ align:start position:0%
+environment. You'll have stronger
+problem solving skills by bringing
+
+ align:start position:0%
+problem solving skills by bringing
+ 
+
+ align:start position:0%
+problem solving skills by bringing
+together a diverse set of viewpoints.
+
+ align:start position:0%
+together a diverse set of viewpoints.
+ 
+
+ align:start position:0%
+together a diverse set of viewpoints.
+And this really improves design work
+
+ align:start position:0%
+And this really improves design work
+ 
+
+ align:start position:0%
+And this really improves design work
+which benefits from the variety and
+
+ align:start position:0%
+which benefits from the variety and
+ 
+
+ align:start position:0%
+which benefits from the variety and
+diversity of those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+opinions. Now in order to collaborate
+
+ align:start position:0%
+opinions. Now in order to collaborate
+ 
+
+ align:start position:0%
+opinions. Now in order to collaborate
+there's really three elements that go
+
+ align:start position:0%
+there's really three elements that go
+ 
+
+ align:start position:0%
+there's really three elements that go
+into that. One of them is a task which
+
+ align:start position:0%
+into that. One of them is a task which
+ 
+
+ align:start position:0%
+into that. One of them is a task which
+is what you're doing together. So for
+
+ align:start position:0%
+is what you're doing together. So for
+ 
+
+ align:start position:0%
+is what you're doing together. So for
+this exercise that was ranking all the
+
+ align:start position:0%
+this exercise that was ranking all the
+ 
+
+ align:start position:0%
+this exercise that was ranking all the
+personal values as a group. The second
+
+ align:start position:0%
+personal values as a group. The second
+ 
+
+ align:start position:0%
+personal values as a group. The second
+element is process which is how you're
+
+ align:start position:0%
+element is process which is how you're
+ 
+
+ align:start position:0%
+element is process which is how you're
+going to do that which each group
+
+ align:start position:0%
+going to do that which each group
+ 
+
+ align:start position:0%
+going to do that which each group
+actually settled on on a process very
+
+ align:start position:0%
+actually settled on on a process very
+ 
+
+ align:start position:0%
+actually settled on on a process very
+nicely and thought about that explicitly
+
+ align:start position:0%
+nicely and thought about that explicitly
+ 
+
+ align:start position:0%
+nicely and thought about that explicitly
+up front.
+
+ align:start position:0%
+up front.
+ 
+
+ align:start position:0%
+up front.
+Your process has got to talk about how
+
+ align:start position:0%
+Your process has got to talk about how
+ 
+
+ align:start position:0%
+Your process has got to talk about how
+you're going to schedule work,
+
+ align:start position:0%
+you're going to schedule work,
+ 
+
+ align:start position:0%
+you're going to schedule work,
+coordinate things, break it up, manage
+
+ align:start position:0%
+coordinate things, break it up, manage
+ 
+
+ align:start position:0%
+coordinate things, break it up, manage
+time and all that. But then there's this
+
+ align:start position:0%
+time and all that. But then there's this
+ 
+
+ align:start position:0%
+time and all that. But then there's this
+thing that we call a effect. These are
+
+ align:start position:0%
+thing that we call a effect. These are
+ 
+
+ align:start position:0%
+thing that we call a effect. These are
+the people's feelings about the work
+
+ align:start position:0%
+the people's feelings about the work
+ 
+
+ align:start position:0%
+the people's feelings about the work
+that they're doing. And this can be
+
+ align:start position:0%
+that they're doing. And this can be
+ 
+
+ align:start position:0%
+that they're doing. And this can be
+based on prior experiences or culture or
+
+ align:start position:0%
+based on prior experiences or culture or
+ 
+
+ align:start position:0%
+based on prior experiences or culture or
+biases, their personal values or their
+
+ align:start position:0%
+biases, their personal values or their
+ 
+
+ align:start position:0%
+biases, their personal values or their
+current experience and what's going
+
+ align:start position:0%
+current experience and what's going
+ 
+
+ align:start position:0%
+current experience and what's going
+on. So looking at this p this exercise
+
+ align:start position:0%
+on. So looking at this p this exercise
+ 
+
+ align:start position:0%
+on. So looking at this p this exercise
+we just finished on personal values.
+
+ align:start position:0%
+we just finished on personal values.
+ 
+
+ align:start position:0%
+we just finished on personal values.
+Sometimes when we do this with groups of
+
+ align:start position:0%
+Sometimes when we do this with groups of
+ 
+
+ align:start position:0%
+Sometimes when we do this with groups of
+people, we see this affect component
+
+ align:start position:0%
+people, we see this affect component
+ 
+
+ align:start position:0%
+people, we see this affect component
+getting in the way of being able to do a
+
+ align:start position:0%
+getting in the way of being able to do a
+ 
+
+ align:start position:0%
+getting in the way of being able to do a
+process correctly and accomplishing a
+
+ align:start position:0%
+process correctly and accomplishing a
+ 
+
+ align:start position:0%
+process correctly and accomplishing a
+task because people have such strong
+
+ align:start position:0%
+task because people have such strong
+ 
+
+ align:start position:0%
+task because people have such strong
+feelings about their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work. So affect and process are really
+
+ align:start position:0%
+work. So affect and process are really
+ 
+
+ align:start position:0%
+work. So affect and process are really
+there to support the goal that you're
+
+ align:start position:0%
+there to support the goal that you're
+ 
+
+ align:start position:0%
+there to support the goal that you're
+doing this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+task. How are some of the uh the
+
+ align:start position:0%
+task. How are some of the uh the
+ 
+
+ align:start position:0%
+task. How are some of the uh the
+challenges that you encounter in
+
+ align:start position:0%
+challenges that you encounter in
+ 
+
+ align:start position:0%
+challenges that you encounter in
+collaboration? How can we try to meet
+
+ align:start position:0%
+collaboration? How can we try to meet
+ 
+
+ align:start position:0%
+collaboration? How can we try to meet
+those? So, here are five ideas for you
+
+ align:start position:0%
+those? So, here are five ideas for you
+ 
+
+ align:start position:0%
+those? So, here are five ideas for you
+to think about and track practice in
+
+ align:start position:0%
+to think about and track practice in
+ 
+
+ align:start position:0%
+to think about and track practice in
+your own teamwork every day. Try to
+
+ align:start position:0%
+your own teamwork every day. Try to
+ 
+
+ align:start position:0%
+your own teamwork every day. Try to
+elaborate some of your key thinking in
+
+ align:start position:0%
+elaborate some of your key thinking in
+ 
+
+ align:start position:0%
+elaborate some of your key thinking in
+writing as well as verbally. Different
+
+ align:start position:0%
+writing as well as verbally. Different
+ 
+
+ align:start position:0%
+writing as well as verbally. Different
+modes of communication actually elicit
+
+ align:start position:0%
+modes of communication actually elicit
+ 
+
+ align:start position:0%
+modes of communication actually elicit
+different degrees of understanding from
+
+ align:start position:0%
+different degrees of understanding from
+ 
+
+ align:start position:0%
+different degrees of understanding from
+the people that you're working with.
+
+ align:start position:0%
+the people that you're working with.
+ 
+
+ align:start position:0%
+the people that you're working with.
+Having things written down in multiple
+
+ align:start position:0%
+Having things written down in multiple
+ 
+
+ align:start position:0%
+Having things written down in multiple
+ways in multiple mediums can be very
+
+ align:start position:0%
+ways in multiple mediums can be very
+ 
+
+ align:start position:0%
+ways in multiple mediums can be very
+effective.
+
+ align:start position:0%
+effective.
+ 
+
+ align:start position:0%
+effective.
+Make sure that you consider alternate
+
+ align:start position:0%
+Make sure that you consider alternate
+ 
+
+ align:start position:0%
+Make sure that you consider alternate
+ideas and solutions and try not to jump
+
+ align:start position:0%
+ideas and solutions and try not to jump
+ 
+
+ align:start position:0%
+ideas and solutions and try not to jump
+to consensus prematurely. Usually
+
+ align:start position:0%
+to consensus prematurely. Usually
+ 
+
+ align:start position:0%
+to consensus prematurely. Usually
+results in a better product to explore
+
+ align:start position:0%
+results in a better product to explore
+ 
+
+ align:start position:0%
+results in a better product to explore
+the whole design space that you might
+
+ align:start position:0%
+the whole design space that you might
+ 
+
+ align:start position:0%
+the whole design space that you might
+have than jumping into one solution. You
+
+ align:start position:0%
+have than jumping into one solution. You
+ 
+
+ align:start position:0%
+have than jumping into one solution. You
+want to pay careful attention to your
+
+ align:start position:0%
+want to pay careful attention to your
+ 
+
+ align:start position:0%
+want to pay careful attention to your
+process, especially if you think
+
+ align:start position:0%
+process, especially if you think
+ 
+
+ align:start position:0%
+process, especially if you think
+people's feelings, the affect part of
+
+ align:start position:0%
+people's feelings, the affect part of
+ 
+
+ align:start position:0%
+people's feelings, the affect part of
+what goes into collaboration might be
+
+ align:start position:0%
+what goes into collaboration might be
+ 
+
+ align:start position:0%
+what goes into collaboration might be
+getting in the
+
+ align:start position:0%
+getting in the
+ 
+
+ align:start position:0%
+getting in the
+way. You want to always constructively
+
+ align:start position:0%
+way. You want to always constructively
+ 
+
+ align:start position:0%
+way. You want to always constructively
+encounter problems and disagreements and
+
+ align:start position:0%
+encounter problems and disagreements and
+ 
+
+ align:start position:0%
+encounter problems and disagreements and
+do that directly and explicitly. We
+
+ align:start position:0%
+do that directly and explicitly. We
+ 
+
+ align:start position:0%
+do that directly and explicitly. We
+heard people talk about that at New
+
+ align:start position:0%
+heard people talk about that at New
+ 
+
+ align:start position:0%
+heard people talk about that at New
+Balance. We've talked about that in this
+
+ align:start position:0%
+Balance. We've talked about that in this
+ 
+
+ align:start position:0%
+Balance. We've talked about that in this
+course as being a key component of lean
+
+ align:start position:0%
+course as being a key component of lean
+ 
+
+ align:start position:0%
+course as being a key component of lean
+to be able to talk about problems and to
+
+ align:start position:0%
+to be able to talk about problems and to
+ 
+
+ align:start position:0%
+to be able to talk about problems and to
+do it in a productive manner. And
+
+ align:start position:0%
+do it in a productive manner. And
+ 
+
+ align:start position:0%
+do it in a productive manner. And
+lastly, give positive feedback directly
+
+ align:start position:0%
+lastly, give positive feedback directly
+ 
+
+ align:start position:0%
+lastly, give positive feedback directly
+and explicitly. So if a job is done
+
+ align:start position:0%
+and explicitly. So if a job is done
+ 
+
+ align:start position:0%
+and explicitly. So if a job is done
+well, make sure that you say that and
+
+ align:start position:0%
+well, make sure that you say that and
+ 
+
+ align:start position:0%
+well, make sure that you say that and
+take the chance to recognize it. That'll
+
+ align:start position:0%
+take the chance to recognize it. That'll
+ 
+
+ align:start position:0%
+take the chance to recognize it. That'll
+boost the team. So just to wrap
+
+ align:start position:0%
+boost the team. So just to wrap
+ 
+
+ align:start position:0%
+boost the team. So just to wrap
+up and convey those two messages to you,
+
+ align:start position:0%
+up and convey those two messages to you,
+ 
+
+ align:start position:0%
+up and convey those two messages to you,
+people really are at the heart of lean
+
+ align:start position:0%
+people really are at the heart of lean
+ 
+
+ align:start position:0%
+people really are at the heart of lean
+and the lean process just cannot work if
+
+ align:start position:0%
+and the lean process just cannot work if
+ 
+
+ align:start position:0%
+and the lean process just cannot work if
+the people who are doing the process do
+
+ align:start position:0%
+the people who are doing the process do
+ 
+
+ align:start position:0%
+the people who are doing the process do
+not believe in it. And two, each of you
+
+ align:start position:0%
+not believe in it. And two, each of you
+ 
+
+ align:start position:0%
+not believe in it. And two, each of you
+are going to be in a position at some
+
+ align:start position:0%
+are going to be in a position at some
+ 
+
+ align:start position:0%
+are going to be in a position at some
+time or other likely very soon to affect
+
+ align:start position:0%
+time or other likely very soon to affect
+ 
+
+ align:start position:0%
+time or other likely very soon to affect
+how a team operates and how processes
+
+ align:start position:0%
+how a team operates and how processes
+ 
+
+ align:start position:0%
+how a team operates and how processes
+and tasks get done. And this kind of
+
+ align:start position:0%
+and tasks get done. And this kind of
+ 
+
+ align:start position:0%
+and tasks get done. And this kind of
+knowledge that you're getting here in
+
+ align:start position:0%
+knowledge that you're getting here in
+ 
+
+ align:start position:0%
+knowledge that you're getting here in
+the people module will help you in
+
+ align:start position:0%
+the people module will help you in
+ 
+
+ align:start position:0%
+the people module will help you in
+meeting that challenge. So we have
+
+ align:start position:0%
+meeting that challenge. So we have
+ 
+
+ align:start position:0%
+meeting that challenge. So we have
+leadership, shared goals, shared
+
+ align:start position:0%
+leadership, shared goals, shared
+ 
+
+ align:start position:0%
+leadership, shared goals, shared
+knowledge, mutual respect,
+
+ align:start position:0%
+knowledge, mutual respect,
+ 
+
+ align:start position:0%
+knowledge, mutual respect,
+communication, and teamwork as some of
+
+ align:start position:0%
+communication, and teamwork as some of
+ 
+
+ align:start position:0%
+communication, and teamwork as some of
+our key people
+
+ align:start position:0%
+our key people
+ 
+
+ align:start position:0%
+our key people
+elements. So with that, I think we'll
+
+ align:start position:0%
+elements. So with that, I think we'll
+ 
+
+ align:start position:0%
+elements. So with that, I think we'll
+finish up with a module. Earl five
+
+ align:start position:0%
+finish up with a module. Earl five
+ 
+
+ align:start position:0%
+finish up with a module. Earl five
+minutes early,
+
+ align:start position:0%
+minutes early,
+ 
+
+ align:start position:0%
+minutes early,
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+but this does leave time for questions
+
+ align:start position:0%
+but this does leave time for questions
+ 
+
+ align:start position:0%
+but this does leave time for questions
+and discussion if anybody wants to to
+
+ align:start position:0%
+and discussion if anybody wants to to
+ 
+
+ align:start position:0%
+and discussion if anybody wants to to
+raise any issues. A few weeks ago, I was
+
+ align:start position:0%
+raise any issues. A few weeks ago, I was
+ 
+
+ align:start position:0%
+raise any issues. A few weeks ago, I was
+out at Boeing and Seattle and we went
+
+ align:start position:0%
+out at Boeing and Seattle and we went
+ 
+
+ align:start position:0%
+out at Boeing and Seattle and we went
+through an area in the shop and it
+
+ align:start position:0%
+through an area in the shop and it
+ 
+
+ align:start position:0%
+through an area in the shop and it
+actually was a group of people, hourly
+
+ align:start position:0%
+actually was a group of people, hourly
+ 
+
+ align:start position:0%
+actually was a group of people, hourly
+employees, who had no
+
+ align:start position:0%
+employees, who had no
+ 
+
+ align:start position:0%
+employees, who had no
+supervisor. They went ahead and they set
+
+ align:start position:0%
+supervisor. They went ahead and they set
+ 
+
+ align:start position:0%
+supervisor. They went ahead and they set
+up all their work and their schedules
+
+ align:start position:0%
+up all their work and their schedules
+ 
+
+ align:start position:0%
+up all their work and their schedules
+and they've been doing it for like three
+
+ align:start position:0%
+and they've been doing it for like three
+ 
+
+ align:start position:0%
+and they've been doing it for like three
+years now. I think that's great. They
+
+ align:start position:0%
+years now. I think that's great. They
+ 
+
+ align:start position:0%
+years now. I think that's great. They
+have the ownership. We took um we took
+
+ align:start position:0%
+have the ownership. We took um we took
+ 
+
+ align:start position:0%
+have the ownership. We took um we took
+the ASU uh MIT uh uh lean group through
+
+ align:start position:0%
+the ASU uh MIT uh uh lean group through
+ 
+
+ align:start position:0%
+the ASU uh MIT uh uh lean group through
+the Apache plant in Mesa and that's the
+
+ align:start position:0%
+the Apache plant in Mesa and that's the
+ 
+
+ align:start position:0%
+the Apache plant in Mesa and that's the
+we have what they call high performance
+
+ align:start position:0%
+we have what they call high performance
+ 
+
+ align:start position:0%
+we have what they call high performance
+work organizations under the C7 for four
+
+ align:start position:0%
+work organizations under the C7 for four
+ 
+
+ align:start position:0%
+work organizations under the C7 for four
+or five years. Those people do not
+
+ align:start position:0%
+or five years. Those people do not
+ 
+
+ align:start position:0%
+or five years. Those people do not
+operate with a supervisor. They set
+
+ align:start position:0%
+operate with a supervisor. They set
+ 
+
+ align:start position:0%
+operate with a supervisor. They set
+their own cost goals, schedule goals,
+
+ align:start position:0%
+their own cost goals, schedule goals,
+ 
+
+ align:start position:0%
+their own cost goals, schedule goals,
+and quality goals, right? And they
+
+ align:start position:0%
+and quality goals, right? And they
+ 
+
+ align:start position:0%
+and quality goals, right? And they
+literally get,
+
+ align:start position:0%
+literally get,
+ 
+
+ align:start position:0%
+literally get,
+this is hourly people, the equivalent of
+
+ align:start position:0%
+this is hourly people, the equivalent of
+ 
+
+ align:start position:0%
+this is hourly people, the equivalent of
+incentive compensation for beating those
+
+ align:start position:0%
+incentive compensation for beating those
+ 
+
+ align:start position:0%
+incentive compensation for beating those
+goals. And the folks and and those are
+
+ align:start position:0%
+goals. And the folks and and those are
+ 
+
+ align:start position:0%
+goals. And the folks and and those are
+high performance work organizations and
+
+ align:start position:0%
+high performance work organizations and
+ 
+
+ align:start position:0%
+high performance work organizations and
+they they meet the goals and beat them.
+
+ align:start position:0%
+they they meet the goals and beat them.
+ 
+
+ align:start position:0%
+they they meet the goals and beat them.
+And it's and it's an amazing operation.
+
+ align:start position:0%
+And it's and it's an amazing operation.
+ 
+
+ align:start position:0%
+And it's and it's an amazing operation.
+That's what these guys and it's all
+
+ align:start position:0%
+That's what these guys and it's all
+ 
+
+ align:start position:0%
+That's what these guys and it's all
+employee involvement
+
+ align:start position:0%
+employee involvement
+ 
+
+ align:start position:0%
+employee involvement
+and and they're they're developing like
+
+ align:start position:0%
+and and they're they're developing like
+ 
+
+ align:start position:0%
+and and they're they're developing like
+you said the goals and objects and
+
+ align:start position:0%
+you said the goals and objects and
+ 
+
+ align:start position:0%
+you said the goals and objects and
+they're doing it and there's no
+
+ align:start position:0%
+they're doing it and there's no
+ 
+
+ align:start position:0%
+they're doing it and there's no
+supervision. What a inverse. Usually
+
+ align:start position:0%
+supervision. What a inverse. Usually
+ 
+
+ align:start position:0%
+supervision. What a inverse. Usually
+laying off people at the bottom and
+
+ align:start position:0%
+laying off people at the bottom and
+ 
+
+ align:start position:0%
+laying off people at the bottom and
+keeping all the top. Nope. That does
+
+ align:start position:0%
+keeping all the top. Nope. That does
+ 
+
+ align:start position:0%
+keeping all the top. Nope. That does
+make a difference whether it's union or
+
+ align:start position:0%
+make a difference whether it's union or
+ 
+
+ align:start position:0%
+make a difference whether it's union or
+non-union. No.
+
+ align:start position:0%
+non-union. No.
+ 
+
+ align:start position:0%
+non-union. No.
+And um and it was interesting talking to
+
+ align:start position:0%
+And um and it was interesting talking to
+ 
+
+ align:start position:0%
+And um and it was interesting talking to
+those folks too because you can see the
+
+ align:start position:0%
+those folks too because you can see the
+ 
+
+ align:start position:0%
+those folks too because you can see the
+excitement. Crew excitement. They're
+
+ align:start position:0%
+excitement. Crew excitement. They're
+ 
+
+ align:start position:0%
+excitement. Crew excitement. They're
+proud. They're proud. Yeah. So Ida,
+
+ align:start position:0%
+proud. They're proud. Yeah. So Ida,
+ 
+
+ align:start position:0%
+proud. They're proud. Yeah. So Ida,
+while you're here, Yes. Can I ask you
+
+ align:start position:0%
+while you're here, Yes. Can I ask you
+ 
+
+ align:start position:0%
+while you're here, Yes. Can I ask you
+um someone has their you know feet on
+
+ align:start position:0%
+um someone has their you know feet on
+ 
+
+ align:start position:0%
+um someone has their you know feet on
+the front lines
+
+ align:start position:0%
+the front lines
+ 
+
+ align:start position:0%
+the front lines
+here. What what are some of
+
+ align:start position:0%
+here. What what are some of
+ 
+
+ align:start position:0%
+here. What what are some of
+the changes you see at Prattton Whitney
+
+ align:start position:0%
+the changes you see at Prattton Whitney
+ 
+
+ align:start position:0%
+the changes you see at Prattton Whitney
+you know as it goes through this green
+
+ align:start position:0%
+you know as it goes through this green
+ 
+
+ align:start position:0%
+you know as it goes through this green
+ACE change in in the people area when
+
+ align:start position:0%
+ACE change in in the people area when
+ 
+
+ align:start position:0%
+ACE change in in the people area when
+you started what you see now
+
+ align:start position:0%
+you started what you see now
+ 
+
+ align:start position:0%
+you started what you see now
+these these you know some of these
+
+ align:start position:0%
+these these you know some of these
+ 
+
+ align:start position:0%
+these these you know some of these
+students are going to be one of the one
+
+ align:start position:0%
+students are going to be one of the one
+ 
+
+ align:start position:0%
+students are going to be one of the one
+or more of these may be hired by your
+
+ align:start position:0%
+or more of these may be hired by your
+ 
+
+ align:start position:0%
+or more of these may be hired by your
+organization before long. What kind of
+
+ align:start position:0%
+organization before long. What kind of
+ 
+
+ align:start position:0%
+organization before long. What kind of
+environment are they going to be walking
+
+ align:start position:0%
+environment are they going to be walking
+ 
+
+ align:start position:0%
+environment are they going to be walking
+into? You'll you'll always have some of
+
+ align:start position:0%
+into? You'll you'll always have some of
+ 
+
+ align:start position:0%
+into? You'll you'll always have some of
+the naysayers, but over time I've seen
+
+ align:start position:0%
+the naysayers, but over time I've seen
+ 
+
+ align:start position:0%
+the naysayers, but over time I've seen
+more and more people getting engaged in
+
+ align:start position:0%
+more and more people getting engaged in
+ 
+
+ align:start position:0%
+more and more people getting engaged in
+this and really truly embracing it. And
+
+ align:start position:0%
+this and really truly embracing it. And
+ 
+
+ align:start position:0%
+this and really truly embracing it. And
+you can actually walk out in the shop
+
+ align:start position:0%
+you can actually walk out in the shop
+ 
+
+ align:start position:0%
+you can actually walk out in the shop
+areas and the hourly folks and the
+
+ align:start position:0%
+areas and the hourly folks and the
+ 
+
+ align:start position:0%
+areas and the hourly folks and the
+salary people and the management folks
+
+ align:start position:0%
+salary people and the management folks
+ 
+
+ align:start position:0%
+salary people and the management folks
+are talking it. So you actually see it
+
+ align:start position:0%
+are talking it. So you actually see it
+ 
+
+ align:start position:0%
+are talking it. So you actually see it
+where it's starting to to really take a,
+
+ align:start position:0%
+where it's starting to to really take a,
+ 
+
+ align:start position:0%
+where it's starting to to really take a,
+you know, people really getting engaged.
+
+ align:start position:0%
+you know, people really getting engaged.
+ 
+
+ align:start position:0%
+you know, people really getting engaged.
+And not only at Prattton Whitney,
+
+ align:start position:0%
+And not only at Prattton Whitney,
+ 
+
+ align:start position:0%
+And not only at Prattton Whitney,
+Prattton Whitney, United Technologies,
+
+ align:start position:0%
+Prattton Whitney, United Technologies,
+ 
+
+ align:start position:0%
+Prattton Whitney, United Technologies,
+the sun never sets throughout all the
+
+ align:start position:0%
+the sun never sets throughout all the
+ 
+
+ align:start position:0%
+the sun never sets throughout all the
+world. We're always some we're
+
+ align:start position:0%
+world. We're always some we're
+ 
+
+ align:start position:0%
+world. We're always some we're
+somewhere. We're, you know, England,
+
+ align:start position:0%
+somewhere. We're, you know, England,
+ 
+
+ align:start position:0%
+somewhere. We're, you know, England,
+China, anywhere. And so you get to see
+
+ align:start position:0%
+China, anywhere. And so you get to see
+ 
+
+ align:start position:0%
+China, anywhere. And so you get to see
+it going through all the corporation.
+
+ align:start position:0%
+it going through all the corporation.
+ 
+
+ align:start position:0%
+it going through all the corporation.
+So that embraces a lot of cultural
+
+ align:start position:0%
+So that embraces a lot of cultural
+ 
+
+ align:start position:0%
+So that embraces a lot of cultural
+differences too. Yes. Oh yes. But it's
+
+ align:start position:0%
+differences too. Yes. Oh yes. But it's
+ 
+
+ align:start position:0%
+differences too. Yes. Oh yes. But it's
+interesting though because we have some
+
+ align:start position:0%
+interesting though because we have some
+ 
+
+ align:start position:0%
+interesting though because we have some
+facilities in
+
+ align:start position:0%
+facilities in
+ 
+
+ align:start position:0%
+facilities in
+Singapore, man. They're they are just
+
+ align:start position:0%
+Singapore, man. They're they are just
+ 
+
+ align:start position:0%
+Singapore, man. They're they are just
+taking off. Absolutely taken off. It's I
+
+ align:start position:0%
+taking off. Absolutely taken off. It's I
+ 
+
+ align:start position:0%
+taking off. Absolutely taken off. It's I
+don't know if it's because they they
+
+ align:start position:0%
+don't know if it's because they they
+ 
+
+ align:start position:0%
+don't know if it's because they they
+are, you know, excited about working for
+
+ align:start position:0%
+are, you know, excited about working for
+ 
+
+ align:start position:0%
+are, you know, excited about working for
+a company or what what the difference
+
+ align:start position:0%
+a company or what what the difference
+ 
+
+ align:start position:0%
+a company or what what the difference
+is, but they seem to really embrace it
+
+ align:start position:0%
+is, but they seem to really embrace it
+ 
+
+ align:start position:0%
+is, but they seem to really embrace it
+and take off and and you see them all
+
+ align:start position:0%
+and take off and and you see them all
+ 
+
+ align:start position:0%
+and take off and and you see them all
+engaged and they're so excited about it
+
+ align:start position:0%
+engaged and they're so excited about it
+ 
+
+ align:start position:0%
+engaged and they're so excited about it
+because we've had a lot of our Singapore
+
+ align:start position:0%
+because we've had a lot of our Singapore
+ 
+
+ align:start position:0%
+because we've had a lot of our Singapore
+some other facilities actually get it,
+
+ align:start position:0%
+some other facilities actually get it,
+ 
+
+ align:start position:0%
+some other facilities actually get it,
+do it, and move on.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Since we have one more minute left, I'd
+
+ align:start position:0%
+Since we have one more minute left, I'd
+ 
+
+ align:start position:0%
+Since we have one more minute left, I'd
+actually like to ask you to take one of
+
+ align:start position:0%
+actually like to ask you to take one of
+ 
+
+ align:start position:0%
+actually like to ask you to take one of
+the index cards that I've got on center
+
+ align:start position:0%
+the index cards that I've got on center
+ 
+
+ align:start position:0%
+the index cards that I've got on center
+of your tables and I'd like each of you
+
+ align:start position:0%
+of your tables and I'd like each of you
+ 
+
+ align:start position:0%
+of your tables and I'd like each of you
+to write down there what the most
+
+ align:start position:0%
+to write down there what the most
+ 
+
+ align:start position:0%
+to write down there what the most
+important thing is that you learned from
+
+ align:start position:0%
+important thing is that you learned from
+ 
+
+ align:start position:0%
+important thing is that you learned from
+this module and then if you can just put
+
+ align:start position:0%
+this module and then if you can just put
+ 
+
+ align:start position:0%
+this module and then if you can just put
+that up here on the podium because I'd
+
+ align:start position:0%
+that up here on the podium because I'd
+ 
+
+ align:start position:0%
+that up here on the podium because I'd
+like to see what messages you all took
+
+ align:start position:0%
+like to see what messages you all took
+ 
+
+ align:start position:0%
+like to see what messages you all took
+away from
+
+ align:start position:0%
+away from
+ 
+
+ align:start position:0%
+away from
+it. And after you're done with that,
+
+ align:start position:0%
+it. And after you're done with that,
+ 
+
+ align:start position:0%
+it. And after you're done with that,
+we'll take a 15 minute break.
\ No newline at end of file
diff --git a/nTDuTIvSYaI.txt b/nTDuTIvSYaI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5a59c95e07678e9cd421b8aa457cb2962132b100
--- /dev/null
+++ b/nTDuTIvSYaI.txt
@@ -0,0 +1,875 @@
+align:start position:0%
+ 
+or seven Firebolt
+
+ align:start position:0%
+or seven Firebolt
+ 
+
+ align:start position:0%
+or seven Firebolt
+returning they have posted times
+
+ align:start position:0%
+returning they have posted times
+ 
+
+ align:start position:0%
+returning they have posted times
+yesterday posted scores of 8007 in their
+
+ align:start position:0%
+yesterday posted scores of 8007 in their
+ 
+
+ align:start position:0%
+yesterday posted scores of 8007 in their
+first trial 1047 1,47 in their second
+
+ align:start position:0%
+first trial 1047 1,47 in their second
+ 
+
+ align:start position:0%
+first trial 1047 1,47 in their second
+trial they're trying to
+
+ align:start position:0%
+trial they're trying to
+ 
+
+ align:start position:0%
+trial they're trying to
+beat uh Team
+
+ align:start position:0%
+beat uh Team
+ 
+
+ align:start position:0%
+beat uh Team
+nine who's currently in first place with
+
+ align:start position:0%
+nine who's currently in first place with
+ 
+
+ align:start position:0%
+nine who's currently in first place with
+a score of
+
+ align:start position:0%
+a score of
+ 
+
+ align:start position:0%
+a score of
+1,19
+
+ align:start position:0%
+1,19
+ 
+
+ align:start position:0%
+1,19
+points at the helm here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+controls at the controls is Chris
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pentacost right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they've just finished their second
+
+ align:start position:0%
+and they've just finished their second
+ 
+
+ align:start position:0%
+and they've just finished their second
+lap Brown crew is
+
+ align:start position:0%
+lap Brown crew is
+ 
+
+ align:start position:0%
+lap Brown crew is
+assisting in loading the eggs each team
+
+ align:start position:0%
+assisting in loading the eggs each team
+ 
+
+ align:start position:0%
+assisting in loading the eggs each team
+has 2
+
+ align:start position:0%
+has 2
+ 
+
+ align:start position:0%
+has 2
+minutes which to load their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+payload team seven Firebolt here has
+
+ align:start position:0%
+payload team seven Firebolt here has
+ 
+
+ align:start position:0%
+payload team seven Firebolt here has
+chosen to carry four
+
+ align:start position:0%
+chosen to carry four
+ 
+
+ align:start position:0%
+chosen to carry four
+eggs over 2 minutes and uh Team seven
+
+ align:start position:0%
+eggs over 2 minutes and uh Team seven
+ 
+
+ align:start position:0%
+eggs over 2 minutes and uh Team seven
+will be penalized
+
+ align:start position:0%
+will be penalized
+ 
+
+ align:start position:0%
+will be penalized
+ized one point per
+
+ align:start position:0%
+ized one point per
+ 
+
+ align:start position:0%
+ized one point per
+second but it's looking like they're
+
+ align:start position:0%
+second but it's looking like they're
+ 
+
+ align:start position:0%
+second but it's looking like they're
+going to be well underneath the 2minute
+
+ align:start position:0%
+going to be well underneath the 2minute
+ 
+
+ align:start position:0%
+going to be well underneath the 2minute
+limit
+
+ align:start position:0%
+limit
+ 
+
+ align:start position:0%
+limit
+for loading the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eggs team is checking out the plane to
+
+ align:start position:0%
+eggs team is checking out the plane to
+ 
+
+ align:start position:0%
+eggs team is checking out the plane to
+make sure everything is okay hands off
+
+ align:start position:0%
+make sure everything is okay hands off
+ 
+
+ align:start position:0%
+make sure everything is okay hands off
+as soon as the plane rolls we start
+
+ align:start position:0%
+as soon as the plane rolls we start
+ 
+
+ align:start position:0%
+as soon as the plane rolls we start
+counting the time for the endurance
+
+ align:start position:0%
+counting the time for the endurance
+ 
+
+ align:start position:0%
+counting the time for the endurance
+flight Chris at the control we expect a
+
+ align:start position:0%
+flight Chris at the control we expect a
+ 
+
+ align:start position:0%
+flight Chris at the control we expect a
+flying time
+
+ align:start position:0%
+flying time
+ 
+
+ align:start position:0%
+flying time
+of no less than 5
+
+ align:start position:0%
+of no less than 5
+ 
+
+ align:start position:0%
+of no less than 5
+minutes and they're looking today to
+
+ align:start position:0%
+minutes and they're looking today to
+ 
+
+ align:start position:0%
+minutes and they're looking today to
+break yesterday's time of 5 minutes and
+
+ align:start position:0%
+break yesterday's time of 5 minutes and
+ 
+
+ align:start position:0%
+break yesterday's time of 5 minutes and
+39 seconds at this point in time it's
+
+ align:start position:0%
+39 seconds at this point in time it's
+ 
+
+ align:start position:0%
+39 seconds at this point in time it's
+just a test of pilot skill and calm and
+
+ align:start position:0%
+just a test of pilot skill and calm and
+ 
+
+ align:start position:0%
+just a test of pilot skill and calm and
+determination
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and good luck
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good God you put me after
+
+ align:start position:0%
+good God you put me after
+ 
+
+ align:start position:0%
+good God you put me after
+Chris that's okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+got new team how many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this I
+
+ align:start position:0%
+this I
+ 
+
+ align:start position:0%
+this I
+think steady
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hands and it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+looks steady hands here it's part of the
+
+ align:start position:0%
+looks steady hands here it's part of the
+ 
+
+ align:start position:0%
+looks steady hands here it's part of the
+competition and it's making sure that
+
+ align:start position:0%
+competition and it's making sure that
+ 
+
+ align:start position:0%
+competition and it's making sure that
+you have a trained pilot
+
+ align:start position:0%
+you have a trained pilot
+ 
+
+ align:start position:0%
+you have a trained pilot
+and this team clearly did its uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+homework that's 2 minutes 2 minutes is
+
+ align:start position:0%
+homework that's 2 minutes 2 minutes is
+ 
+
+ align:start position:0%
+homework that's 2 minutes 2 minutes is
+the official time here the time to be
+
+ align:start position:0%
+the official time here the time to be
+ 
+
+ align:start position:0%
+the official time here the time to be
+with four eggs is 6 minutes and 3
+
+ align:start position:0%
+with four eggs is 6 minutes and 3
+ 
+
+ align:start position:0%
+with four eggs is 6 minutes and 3
+seconds which was established by team
+
+ align:start position:0%
+seconds which was established by team
+ 
+
+ align:start position:0%
+seconds which was established by team
+number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nine he halfway there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this part of the competition um it's not
+
+ align:start position:0%
+this part of the competition um it's not
+ 
+
+ align:start position:0%
+this part of the competition um it's not
+necessary to fly in a circular path you
+
+ align:start position:0%
+necessary to fly in a circular path you
+ 
+
+ align:start position:0%
+necessary to fly in a circular path you
+can fly anywhere you want but uh most of
+
+ align:start position:0%
+can fly anywhere you want but uh most of
+ 
+
+ align:start position:0%
+can fly anywhere you want but uh most of
+the pilots have chosen
+
+ align:start position:0%
+the pilots have chosen
+ 
+
+ align:start position:0%
+the pilots have chosen
+to fly in a circular path easier than
+
+ align:start position:0%
+to fly in a circular path easier than
+ 
+
+ align:start position:0%
+to fly in a circular path easier than
+figure8 in
+
+ align:start position:0%
+figure8 in
+ 
+
+ align:start position:0%
+figure8 in
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Space 3 minutes
+
+ align:start position:0%
+Space 3 minutes
+ 
+
+ align:start position:0%
+Space 3 minutes
+3 minutes is the official time the time
+
+ align:start position:0%
+3 minutes is the official time the time
+ 
+
+ align:start position:0%
+3 minutes is the official time the time
+to beat again is 6 minutes and 3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+WR that it sounded grally
+
+ align:start position:0%
+WR that it sounded grally
+ 
+
+ align:start position:0%
+WR that it sounded grally
+correct no I didn't to I had to a lot
+
+ align:start position:0%
+correct no I didn't to I had to a lot
+ 
+
+ align:start position:0%
+correct no I didn't to I had to a lot
+young any comments on this team for the
+
+ align:start position:0%
+young any comments on this team for the
+ 
+
+ align:start position:0%
+young any comments on this team for the
+uh very very smoothly um they have
+
+ align:start position:0%
+uh very very smoothly um they have
+ 
+
+ align:start position:0%
+uh very very smoothly um they have
+obviously been practicing a lot
+
+ align:start position:0%
+obviously been practicing a lot
+ 
+
+ align:start position:0%
+obviously been practicing a lot
+hopefully the practice is going to pay
+
+ align:start position:0%
+hopefully the practice is going to pay
+ 
+
+ align:start position:0%
+hopefully the practice is going to pay
+off uh the airplane's been cleaned up
+
+ align:start position:0%
+off uh the airplane's been cleaned up
+ 
+
+ align:start position:0%
+off uh the airplane's been cleaned up
+with tape I see appears to be flying a
+
+ align:start position:0%
+with tape I see appears to be flying a
+ 
+
+ align:start position:0%
+with tape I see appears to be flying a
+little bit uh tail down which doesn't
+
+ align:start position:0%
+little bit uh tail down which doesn't
+ 
+
+ align:start position:0%
+little bit uh tail down which doesn't
+please me but uh uh we'll see now I see
+
+ align:start position:0%
+please me but uh uh we'll see now I see
+ 
+
+ align:start position:0%
+please me but uh uh we'll see now I see
+at this level of quality of flying the
+
+ align:start position:0%
+at this level of quality of flying the
+ 
+
+ align:start position:0%
+at this level of quality of flying the
+the 1% 2% differ all really really make
+
+ align:start position:0%
+the 1% 2% differ all really really make
+ 
+
+ align:start position:0%
+the 1% 2% differ all really really make
+a difference all right how could they
+
+ align:start position:0%
+a difference all right how could they
+ 
+
+ align:start position:0%
+a difference all right how could they
+improve the tail down what's that
+
+ align:start position:0%
+improve the tail down what's that
+ 
+
+ align:start position:0%
+improve the tail down what's that
+indicative of perhaps uh Center Gravity
+
+ align:start position:0%
+indicative of perhaps uh Center Gravity
+ 
+
+ align:start position:0%
+indicative of perhaps uh Center Gravity
+shment the wings
+
+ align:start position:0%
+shment the wings
+ 
+
+ align:start position:0%
+shment the wings
+okay the plane is flying very
+
+ align:start position:0%
+okay the plane is flying very
+ 
+
+ align:start position:0%
+okay the plane is flying very
+efficiently uh appears to be a good
+
+ align:start position:0%
+efficiently uh appears to be a good
+ 
+
+ align:start position:0%
+efficiently uh appears to be a good
+match of the propeller to the load
+
+ align:start position:0%
+match of the propeller to the load
+ 
+
+ align:start position:0%
+match of the propeller to the load
+flying quiet is that a good flying very
+
+ align:start position:0%
+flying quiet is that a good flying very
+ 
+
+ align:start position:0%
+flying quiet is that a good flying very
+quietly appears the motor is uh is
+
+ align:start position:0%
+quietly appears the motor is uh is
+ 
+
+ align:start position:0%
+quietly appears the motor is uh is
+broken in which is uh very very a subtle
+
+ align:start position:0%
+broken in which is uh very very a subtle
+ 
+
+ align:start position:0%
+broken in which is uh very very a subtle
+Factor because we ordinarily don't ask
+
+ align:start position:0%
+Factor because we ordinarily don't ask
+ 
+
+ align:start position:0%
+Factor because we ordinarily don't ask
+the students to break in the motors but
+
+ align:start position:0%
+the students to break in the motors but
+ 
+
+ align:start position:0%
+the students to break in the motors but
+this motor is probably very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smooth looks like a very good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+flight that was Colonel young our main
+
+ align:start position:0%
+flight that was Colonel young our main
+ 
+
+ align:start position:0%
+flight that was Colonel young our main
+technical instructor in the
+
+ align:start position:0%
+technical instructor in the
+ 
+
+ align:start position:0%
+technical instructor in the
+course col young is a world class uh
+
+ align:start position:0%
+course col young is a world class uh
+ 
+
+ align:start position:0%
+course col young is a world class uh
+radio control modeler and that's 5
+
+ align:start position:0%
+radio control modeler and that's 5
+ 
+
+ align:start position:0%
+radio control modeler and that's 5
+minutes 5 minutes 5 minutes the time to
+
+ align:start position:0%
+minutes 5 minutes 5 minutes the time to
+ 
+
+ align:start position:0%
+minutes 5 minutes 5 minutes the time to
+beat is 1 minute and 3 more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds I know don't say anything bad
+
+ align:start position:0%
+seconds I know don't say anything bad
+ 
+
+ align:start position:0%
+seconds I know don't say anything bad
+thing any bad things about you all your
+
+ align:start position:0%
+thing any bad things about you all your
+ 
+
+ align:start position:0%
+thing any bad things about you all your
+mic just let me know when you shut it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+off that's 5:30 5 and 1/2 minutes 30 33
+
+ align:start position:0%
+off that's 5:30 5 and 1/2 minutes 30 33
+ 
+
+ align:start position:0%
+off that's 5:30 5 and 1/2 minutes 30 33
+more seconds we'll break the current
+
+ align:start position:0%
+more seconds we'll break the current
+ 
+
+ align:start position:0%
+more seconds we'll break the current
+winning
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time 557
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+their time was
+
+ align:start position:0%
+their time was
+ 
+
+ align:start position:0%
+their time was
+5:57 the time to beat was 6 minutes and
+
+ align:start position:0%
+5:57 the time to beat was 6 minutes and
+ 
+
+ align:start position:0%
+5:57 the time to beat was 6 minutes and
+3 seconds
\ No newline at end of file
diff --git a/nYe4OZVCnIs.txt b/nYe4OZVCnIs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3523a7ccfbc49761def762a7931bcc55aaaa9889
--- /dev/null
+++ b/nYe4OZVCnIs.txt
@@ -0,0 +1,475 @@
+align:start position:0%
+ 
+this will be a short tutorial on
+
+ align:start position:0%
+this will be a short tutorial on
+ 
+
+ align:start position:0%
+this will be a short tutorial on
+infinite series their definition and
+
+ align:start position:0%
+infinite series their definition and
+ 
+
+ align:start position:0%
+infinite series their definition and
+their basic properties what is an
+
+ align:start position:0%
+their basic properties what is an
+ 
+
+ align:start position:0%
+their basic properties what is an
+infinite series we are given a sequence
+
+ align:start position:0%
+infinite series we are given a sequence
+ 
+
+ align:start position:0%
+infinite series we are given a sequence
+of numbers AI indexed by I where I
+
+ align:start position:0%
+of numbers AI indexed by I where I
+ 
+
+ align:start position:0%
+of numbers AI indexed by I where I
+ranges from 1 to infinity
+
+ align:start position:0%
+ranges from 1 to infinity
+ 
+
+ align:start position:0%
+ranges from 1 to infinity
+so it's an infinite sequence and we want
+
+ align:start position:0%
+so it's an infinite sequence and we want
+ 
+
+ align:start position:0%
+so it's an infinite sequence and we want
+to add the terms of that sequence
+
+ align:start position:0%
+to add the terms of that sequence
+ 
+
+ align:start position:0%
+to add the terms of that sequence
+together we denote the resulting sum of
+
+ align:start position:0%
+together we denote the resulting sum of
+ 
+
+ align:start position:0%
+together we denote the resulting sum of
+that infinity of terms using this
+
+ align:start position:0%
+that infinity of terms using this
+ 
+
+ align:start position:0%
+that infinity of terms using this
+notation but what does that mean exactly
+
+ align:start position:0%
+notation but what does that mean exactly
+ 
+
+ align:start position:0%
+notation but what does that mean exactly
+what is the formal definition of an
+
+ align:start position:0%
+what is the formal definition of an
+ 
+
+ align:start position:0%
+what is the formal definition of an
+infinite series
+
+ align:start position:0%
+infinite series
+ 
+
+ align:start position:0%
+infinite series
+well the infinite series is defined as
+
+ align:start position:0%
+well the infinite series is defined as
+ 
+
+ align:start position:0%
+well the infinite series is defined as
+the limit as n goes to infinity of the
+
+ align:start position:0%
+the limit as n goes to infinity of the
+ 
+
+ align:start position:0%
+the limit as n goes to infinity of the
+finite series in which we add only the
+
+ align:start position:0%
+finite series in which we add only the
+ 
+
+ align:start position:0%
+finite series in which we add only the
+first n terms in the series however this
+
+ align:start position:0%
+first n terms in the series however this
+ 
+
+ align:start position:0%
+first n terms in the series however this
+definition makes sense only as long as
+
+ align:start position:0%
+definition makes sense only as long as
+ 
+
+ align:start position:0%
+definition makes sense only as long as
+the limit exists this brings up the
+
+ align:start position:0%
+the limit exists this brings up the
+ 
+
+ align:start position:0%
+the limit exists this brings up the
+question when does this limit exist the
+
+ align:start position:0%
+question when does this limit exist the
+ 
+
+ align:start position:0%
+question when does this limit exist the
+nicest case arises when all the terms
+
+ align:start position:0%
+nicest case arises when all the terms
+ 
+
+ align:start position:0%
+nicest case arises when all the terms
+are non-negative if all the terms are
+
+ align:start position:0%
+are non-negative if all the terms are
+ 
+
+ align:start position:0%
+are non-negative if all the terms are
+non-negative here's what's happening we
+
+ align:start position:0%
+non-negative here's what's happening we
+ 
+
+ align:start position:0%
+non-negative here's what's happening we
+consider the partial sum of the first n
+
+ align:start position:0%
+consider the partial sum of the first n
+ 
+
+ align:start position:0%
+consider the partial sum of the first n
+terms and then we increase n this means
+
+ align:start position:0%
+terms and then we increase n this means
+ 
+
+ align:start position:0%
+terms and then we increase n this means
+that we add more terms so the partial
+
+ align:start position:0%
+that we add more terms so the partial
+ 
+
+ align:start position:0%
+that we add more terms so the partial
+sum keeps becoming bigger and bigger the
+
+ align:start position:0%
+sum keeps becoming bigger and bigger the
+ 
+
+ align:start position:0%
+sum keeps becoming bigger and bigger the
+sequence of partial sums is a monotonic
+
+ align:start position:0%
+sequence of partial sums is a monotonic
+ 
+
+ align:start position:0%
+sequence of partial sums is a monotonic
+sequence now monotonic sequences always
+
+ align:start position:0%
+sequence now monotonic sequences always
+ 
+
+ align:start position:0%
+sequence now monotonic sequences always
+converge either to a finite number or to
+
+ align:start position:0%
+converge either to a finite number or to
+ 
+
+ align:start position:0%
+converge either to a finite number or to
+infinity in either case this limit will
+
+ align:start position:0%
+infinity in either case this limit will
+ 
+
+ align:start position:0%
+infinity in either case this limit will
+exist and therefore the series is well
+
+ align:start position:0%
+exist and therefore the series is well
+ 
+
+ align:start position:0%
+exist and therefore the series is well
+defined the situation is more
+
+ align:start position:0%
+defined the situation is more
+ 
+
+ align:start position:0%
+defined the situation is more
+complicated if the terms a I can have
+
+ align:start position:0%
+complicated if the terms a I can have
+ 
+
+ align:start position:0%
+complicated if the terms a I can have
+different signs in that case it's
+
+ align:start position:0%
+different signs in that case it's
+ 
+
+ align:start position:0%
+different signs in that case it's
+possible that the limit does not exist
+
+ align:start position:0%
+possible that the limit does not exist
+ 
+
+ align:start position:0%
+possible that the limit does not exist
+and so the series is not well defined
+
+ align:start position:0%
+and so the series is not well defined
+ 
+
+ align:start position:0%
+and so the series is not well defined
+the more interesting and complicated
+
+ align:start position:0%
+the more interesting and complicated
+ 
+
+ align:start position:0%
+the more interesting and complicated
+case is the following it's possible that
+
+ align:start position:0%
+case is the following it's possible that
+ 
+
+ align:start position:0%
+case is the following it's possible that
+this limit exists however if we
+
+ align:start position:0%
+this limit exists however if we
+ 
+
+ align:start position:0%
+this limit exists however if we
+rearrange the terms in the sequence we
+
+ align:start position:0%
+rearrange the terms in the sequence we
+ 
+
+ align:start position:0%
+rearrange the terms in the sequence we
+might get a different limit when can we
+
+ align:start position:0%
+might get a different limit when can we
+ 
+
+ align:start position:0%
+might get a different limit when can we
+avoid those complicated situations
+
+ align:start position:0%
+avoid those complicated situations
+ 
+
+ align:start position:0%
+avoid those complicated situations
+we can avoid them if it turns out that
+
+ align:start position:0%
+we can avoid them if it turns out that
+ 
+
+ align:start position:0%
+we can avoid them if it turns out that
+the sum of the absolute value of the
+
+ align:start position:0%
+the sum of the absolute value of the
+ 
+
+ align:start position:0%
+the sum of the absolute value of the
+numbers sums to a finite number now this
+
+ align:start position:0%
+numbers sums to a finite number now this
+ 
+
+ align:start position:0%
+numbers sums to a finite number now this
+series that we have here is an infinite
+
+ align:start position:0%
+series that we have here is an infinite
+ 
+
+ align:start position:0%
+series that we have here is an infinite
+series in which we add non-negative
+
+ align:start position:0%
+series in which we add non-negative
+ 
+
+ align:start position:0%
+series in which we add non-negative
+numbers and by the fact that we
+
+ align:start position:0%
+numbers and by the fact that we
+ 
+
+ align:start position:0%
+numbers and by the fact that we
+mentioned earlier this infinite series
+
+ align:start position:0%
+mentioned earlier this infinite series
+ 
+
+ align:start position:0%
+mentioned earlier this infinite series
+is always well defined that is going to
+
+ align:start position:0%
+is always well defined that is going to
+ 
+
+ align:start position:0%
+is always well defined that is going to
+be either finite or infinite if it turns
+
+ align:start position:0%
+be either finite or infinite if it turns
+ 
+
+ align:start position:0%
+be either finite or infinite if it turns
+out to be finite then the original
+
+ align:start position:0%
+out to be finite then the original
+ 
+
+ align:start position:0%
+out to be finite then the original
+series is guaranteed to be well defined
+
+ align:start position:0%
+series is guaranteed to be well defined
+ 
+
+ align:start position:0%
+series is guaranteed to be well defined
+to have a finite limit when we define it
+
+ align:start position:0%
+to have a finite limit when we define it
+ 
+
+ align:start position:0%
+to have a finite limit when we define it
+that way and furthermore that finite
+
+ align:start position:0%
+that way and furthermore that finite
+ 
+
+ align:start position:0%
+that way and furthermore that finite
+limit is the same even if we rearrange
+
+ align:start position:0%
+limit is the same even if we rearrange
+ 
+
+ align:start position:0%
+limit is the same even if we rearrange
+the different terms if we rearrange the
+
+ align:start position:0%
+the different terms if we rearrange the
+ 
+
+ align:start position:0%
+the different terms if we rearrange the
+sequence with which we sum the different
+
+ align:start position:0%
+sequence with which we sum the different
+ 
+
+ align:start position:0%
+sequence with which we sum the different
+terms
\ No newline at end of file
diff --git a/nr0RErrOPKk.txt b/nr0RErrOPKk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6c39c8a0e72b5bb25d5a580b6b8bb6249583d061
--- /dev/null
+++ b/nr0RErrOPKk.txt
@@ -0,0 +1,2275 @@
+align:start position:0%
+ 
+this is a short video following up on
+
+ align:start position:0%
+this is a short video following up on
+ 
+
+ align:start position:0%
+this is a short video following up on
+the unlocking of pitches where we will
+
+ align:start position:0%
+the unlocking of pitches where we will
+ 
+
+ align:start position:0%
+the unlocking of pitches where we will
+unlock duration and note objects in
+
+ align:start position:0%
+unlock duration and note objects in
+ 
+
+ align:start position:0%
+unlock duration and note objects in
+music 21 go ahead and start up your
+
+ align:start position:0%
+music 21 go ahead and start up your
+ 
+
+ align:start position:0%
+music 21 go ahead and start up your
+Jupiter notebook and let's get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+programming start with durations um so
+
+ align:start position:0%
+programming start with durations um so
+ 
+
+ align:start position:0%
+programming start with durations um so
+go ahead and from music 21 import
+
+ align:start position:0%
+go ahead and from music 21 import
+ 
+
+ align:start position:0%
+go ahead and from music 21 import
+duration and um that thing we've just
+
+ align:start position:0%
+duration and um that thing we've just
+ 
+
+ align:start position:0%
+duration and um that thing we've just
+imported duration is it um put a thumbs
+
+ align:start position:0%
+imported duration is it um put a thumbs
+ 
+
+ align:start position:0%
+imported duration is it um put a thumbs
+up if it's an object put a thumbs down
+
+ align:start position:0%
+up if it's an object put a thumbs down
+ 
+
+ align:start position:0%
+up if it's an object put a thumbs down
+if you think it's a
+
+ align:start position:0%
+if you think it's a
+ 
+
+ align:start position:0%
+if you think it's a
+module okay so in this case it is a
+
+ align:start position:0%
+module okay so in this case it is a
+ 
+
+ align:start position:0%
+module okay so in this case it is a
+module there if you didn't get it right
+
+ align:start position:0%
+module there if you didn't get it right
+ 
+
+ align:start position:0%
+module there if you didn't get it right
+no worries because there's no way you
+
+ align:start position:0%
+no worries because there's no way you
+ 
+
+ align:start position:0%
+no worries because there's no way you
+can actually tell just from that except
+
+ align:start position:0%
+can actually tell just from that except
+ 
+
+ align:start position:0%
+can actually tell just from that except
+for by convention python by convention
+
+ align:start position:0%
+for by convention python by convention
+ 
+
+ align:start position:0%
+for by convention python by convention
+we write our modules in lowercase we can
+
+ align:start position:0%
+we write our modules in lowercase we can
+ 
+
+ align:start position:0%
+we write our modules in lowercase we can
+see that it's a module by um taking it
+
+ align:start position:0%
+see that it's a module by um taking it
+ 
+
+ align:start position:0%
+see that it's a module by um taking it
+type Yay good i'' be terrible if I
+
+ align:start position:0%
+type Yay good i'' be terrible if I
+ 
+
+ align:start position:0%
+type Yay good i'' be terrible if I
+didn't within um the module there is uh
+
+ align:start position:0%
+didn't within um the module there is uh
+ 
+
+ align:start position:0%
+didn't within um the module there is uh
+usually an object with the same name as
+
+ align:start position:0%
+usually an object with the same name as
+ 
+
+ align:start position:0%
+usually an object with the same name as
+it I hit Tab and I get oh there is a
+
+ align:start position:0%
+it I hit Tab and I get oh there is a
+ 
+
+ align:start position:0%
+it I hit Tab and I get oh there is a
+duration object so we'll create one
+
+ align:start position:0%
+duration object so we'll create one
+ 
+
+ align:start position:0%
+duration object so we'll create one
+assign it to D and I'm going to create a
+
+ align:start position:0%
+assign it to D and I'm going to create a
+ 
+
+ align:start position:0%
+assign it to D and I'm going to create a
+duration of
+
+ align:start position:0%
+duration of
+ 
+
+ align:start position:0%
+duration of
+3.0 what I want you to do is open up the
+
+ align:start position:0%
+3.0 what I want you to do is open up the
+ 
+
+ align:start position:0%
+3.0 what I want you to do is open up the
+chat and don't um don't yet hit iner on
+
+ align:start position:0%
+chat and don't um don't yet hit iner on
+ 
+
+ align:start position:0%
+chat and don't um don't yet hit iner on
+it but if you could put what you think
+
+ align:start position:0%
+it but if you could put what you think
+ 
+
+ align:start position:0%
+it but if you could put what you think
+3.0 might
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+represent yep so we have a lot of um a
+
+ align:start position:0%
+represent yep so we have a lot of um a
+ 
+
+ align:start position:0%
+represent yep so we have a lot of um a
+lot of Beats going on um some I like
+
+ align:start position:0%
+lot of Beats going on um some I like
+ 
+
+ align:start position:0%
+lot of Beats going on um some I like
+qualification with some standard of how
+
+ align:start position:0%
+qualification with some standard of how
+ 
+
+ align:start position:0%
+qualification with some standard of how
+long a beat is um and we also have
+
+ align:start position:0%
+long a beat is um and we also have
+ 
+
+ align:start position:0%
+long a beat is um and we also have
+dotted half and things like that nobody
+
+ align:start position:0%
+dotted half and things like that nobody
+ 
+
+ align:start position:0%
+dotted half and things like that nobody
+seems to like our favorite uh thing
+
+ align:start position:0%
+seems to like our favorite uh thing
+ 
+
+ align:start position:0%
+seems to like our favorite uh thing
+milliseconds maybe if I had had
+
+ align:start position:0%
+milliseconds maybe if I had had
+ 
+
+ align:start position:0%
+milliseconds maybe if I had had
+purposely made my thing um
+
+ align:start position:0%
+purposely made my thing um
+ 
+
+ align:start position:0%
+purposely made my thing um
+3,000 than than people would have
+
+ align:start position:0%
+3,000 than than people would have
+ 
+
+ align:start position:0%
+3,000 than than people would have
+thought that um you know but it is a
+
+ align:start position:0%
+thought that um you know but it is a
+ 
+
+ align:start position:0%
+thought that um you know but it is a
+float it could be seconds or something
+
+ align:start position:0%
+float it could be seconds or something
+ 
+
+ align:start position:0%
+float it could be seconds or something
+uh in this case we'll figure it out um
+
+ align:start position:0%
+uh in this case we'll figure it out um
+ 
+
+ align:start position:0%
+uh in this case we'll figure it out um
+well okay that doesn't tell us much of
+
+ align:start position:0%
+well okay that doesn't tell us much of
+ 
+
+ align:start position:0%
+well okay that doesn't tell us much of
+anything and um what we can do is we can
+
+ align:start position:0%
+anything and um what we can do is we can
+ 
+
+ align:start position:0%
+anything and um what we can do is we can
+get the full name of this and see it is
+
+ align:start position:0%
+get the full name of this and see it is
+ 
+
+ align:start position:0%
+get the full name of this and see it is
+a dotted half so um it could be beat
+
+ align:start position:0%
+a dotted half so um it could be beat
+ 
+
+ align:start position:0%
+a dotted half so um it could be beat
+still I'll just go ahead and say in
+
+ align:start position:0%
+still I'll just go ahead and say in
+ 
+
+ align:start position:0%
+still I'll just go ahead and say in
+music 21 I made the decision to have um
+
+ align:start position:0%
+music 21 I made the decision to have um
+ 
+
+ align:start position:0%
+music 21 I made the decision to have um
+the number represent the number of
+
+ align:start position:0%
+the number represent the number of
+ 
+
+ align:start position:0%
+the number represent the number of
+quarter notes uh I may over time I have
+
+ align:start position:0%
+quarter notes uh I may over time I have
+ 
+
+ align:start position:0%
+quarter notes uh I may over time I have
+sometimes regretted that decision um but
+
+ align:start position:0%
+sometimes regretted that decision um but
+ 
+
+ align:start position:0%
+sometimes regretted that decision um but
+it had to be something and one of the
+
+ align:start position:0%
+it had to be something and one of the
+ 
+
+ align:start position:0%
+it had to be something and one of the
+reasons I decided not to go with half uh
+
+ align:start position:0%
+reasons I decided not to go with half uh
+ 
+
+ align:start position:0%
+reasons I decided not to go with half uh
+with Beats is that um the length the
+
+ align:start position:0%
+with Beats is that um the length the
+ 
+
+ align:start position:0%
+with Beats is that um the length the
+representation of a note in terms of
+
+ align:start position:0%
+representation of a note in terms of
+ 
+
+ align:start position:0%
+representation of a note in terms of
+Beats is dependent on something external
+
+ align:start position:0%
+Beats is dependent on something external
+ 
+
+ align:start position:0%
+Beats is dependent on something external
+and that is the ti signature right so 22
+
+ align:start position:0%
+and that is the ti signature right so 22
+ 
+
+ align:start position:0%
+and that is the ti signature right so 22
+has a different number of Beats from 68
+
+ align:start position:0%
+has a different number of Beats from 68
+ 
+
+ align:start position:0%
+has a different number of Beats from 68
+has a different number uh has a
+
+ align:start position:0%
+has a different number uh has a
+ 
+
+ align:start position:0%
+has a different number uh has a
+different type of beat from 68 which has
+
+ align:start position:0%
+different type of beat from 68 which has
+ 
+
+ align:start position:0%
+different type of beat from 68 which has
+a different type of beat from 44 so
+
+ align:start position:0%
+a different type of beat from 44 so
+ 
+
+ align:start position:0%
+a different type of beat from 44 so
+that's um that's one of the reasons uh
+
+ align:start position:0%
+that's um that's one of the reasons uh
+ 
+
+ align:start position:0%
+that's um that's one of the reasons uh
+going with this so every um every
+
+ align:start position:0%
+going with this so every um every
+ 
+
+ align:start position:0%
+going with this so every um every
+duration object has a full name it also
+
+ align:start position:0%
+duration object has a full name it also
+ 
+
+ align:start position:0%
+duration object has a full name it also
+has a
+
+ align:start position:0%
+has a
+ 
+
+ align:start position:0%
+has a
+type half and uh has a dots it's great
+
+ align:start position:0%
+type half and uh has a dots it's great
+ 
+
+ align:start position:0%
+type half and uh has a dots it's great
+um it also a something called quarter
+
+ align:start position:0%
+um it also a something called quarter
+ 
+
+ align:start position:0%
+um it also a something called quarter
+length which in this case um is yeah the
+
+ align:start position:0%
+length which in this case um is yeah the
+ 
+
+ align:start position:0%
+length which in this case um is yeah the
+number of quarters and that's not so bad
+
+ align:start position:0%
+number of quarters and that's not so bad
+ 
+
+ align:start position:0%
+number of quarters and that's not so bad
+but maybe uh I mean that's something you
+
+ align:start position:0%
+but maybe uh I mean that's something you
+ 
+
+ align:start position:0%
+but maybe uh I mean that's something you
+already knew how to do but maybe we do
+
+ align:start position:0%
+already knew how to do but maybe we do
+ 
+
+ align:start position:0%
+already knew how to do but maybe we do
+we can create a duration in a different
+
+ align:start position:0%
+we can create a duration in a different
+ 
+
+ align:start position:0%
+we can create a duration in a different
+way we'll say type equals whole and dots
+
+ align:start position:0%
+way we'll say type equals whole and dots
+ 
+
+ align:start position:0%
+way we'll say type equals whole and dots
+equals 4 and suddenly the quarter
+
+ align:start position:0%
+equals 4 and suddenly the quarter
+ 
+
+ align:start position:0%
+equals 4 and suddenly the quarter
+length of this is a little bit harder to
+
+ align:start position:0%
+length of this is a little bit harder to
+ 
+
+ align:start position:0%
+length of this is a little bit harder to
+compute anybody on off the top of their
+
+ align:start position:0%
+compute anybody on off the top of their
+ 
+
+ align:start position:0%
+compute anybody on off the top of their
+head right you're all too shy to say
+
+ align:start position:0%
+head right you're all too shy to say
+ 
+
+ align:start position:0%
+head right you're all too shy to say
+7.75 okay good well I don't I don't know
+
+ align:start position:0%
+7.75 okay good well I don't I don't know
+ 
+
+ align:start position:0%
+7.75 okay good well I don't I don't know
+that number okay so here are some of the
+
+ align:start position:0%
+that number okay so here are some of the
+ 
+
+ align:start position:0%
+that number okay so here are some of the
+things that that we can um that we can
+
+ align:start position:0%
+things that that we can um that we can
+ 
+
+ align:start position:0%
+things that that we can um that we can
+do can we um can we create a a triplet
+
+ align:start position:0%
+do can we um can we create a a triplet
+ 
+
+ align:start position:0%
+do can we um can we create a a triplet
+let's try
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that one onethird of a note so what kind
+
+ align:start position:0%
+that one onethird of a note so what kind
+ 
+
+ align:start position:0%
+that one onethird of a note so what kind
+of a triplet is that somebody shout it
+
+ align:start position:0%
+of a triplet is that somebody shout it
+ 
+
+ align:start position:0%
+of a triplet is that somebody shout it
+out an e triplet let's let's see type
+
+ align:start position:0%
+out an e triplet let's let's see type
+ 
+
+ align:start position:0%
+out an e triplet let's let's see type
+yay triplet so we can create trip blits
+
+ align:start position:0%
+yay triplet so we can create trip blits
+ 
+
+ align:start position:0%
+yay triplet so we can create trip blits
+um notice we'll go back to D here um
+
+ align:start position:0%
+um notice we'll go back to D here um
+ 
+
+ align:start position:0%
+um notice we'll go back to D here um
+notice that some durations are expressed
+
+ align:start position:0%
+notice that some durations are expressed
+ 
+
+ align:start position:0%
+notice that some durations are expressed
+in floats some are expressed in rational
+
+ align:start position:0%
+in floats some are expressed in rational
+ 
+
+ align:start position:0%
+in floats some are expressed in rational
+fractions and that tells you whether or
+
+ align:start position:0%
+fractions and that tells you whether or
+ 
+
+ align:start position:0%
+fractions and that tells you whether or
+not um you're going to safely be able to
+
+ align:start position:0%
+not um you're going to safely be able to
+ 
+
+ align:start position:0%
+not um you're going to safely be able to
+add them up and get an exact number uh
+
+ align:start position:0%
+add them up and get an exact number uh
+ 
+
+ align:start position:0%
+add them up and get an exact number uh
+anything that's a multiple of a power of
+
+ align:start position:0%
+anything that's a multiple of a power of
+ 
+
+ align:start position:0%
+anything that's a multiple of a power of
+two in binary will be exactly
+
+ align:start position:0%
+two in binary will be exactly
+ 
+
+ align:start position:0%
+two in binary will be exactly
+representable anything that isn't will
+
+ align:start position:0%
+representable anything that isn't will
+ 
+
+ align:start position:0%
+representable anything that isn't will
+be here so great so trip type is
+
+ align:start position:0%
+be here so great so trip type is
+ 
+
+ align:start position:0%
+be here so great so trip type is
+eth so it doesn't tell me anything about
+
+ align:start position:0%
+eth so it doesn't tell me anything about
+ 
+
+ align:start position:0%
+eth so it doesn't tell me anything about
+it its dots I hope are zero there's no
+
+ align:start position:0%
+it its dots I hope are zero there's no
+ 
+
+ align:start position:0%
+it its dots I hope are zero there's no
+dots there great um so there is
+
+ align:start position:0%
+dots there great um so there is
+ 
+
+ align:start position:0%
+dots there great um so there is
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+called tuplets which a tuplet is a type
+
+ align:start position:0%
+called tuplets which a tuplet is a type
+ 
+
+ align:start position:0%
+called tuplets which a tuplet is a type
+of U like a quadruplet a quintuplet
+
+ align:start position:0%
+of U like a quadruplet a quintuplet
+ 
+
+ align:start position:0%
+of U like a quadruplet a quintuplet
+triplet is the one we most know great
+
+ align:start position:0%
+triplet is the one we most know great
+ 
+
+ align:start position:0%
+triplet is the one we most know great
+what I want you to do is take a second
+
+ align:start position:0%
+what I want you to do is take a second
+ 
+
+ align:start position:0%
+what I want you to do is take a second
+and put in the chat what kind of object
+
+ align:start position:0%
+and put in the chat what kind of object
+ 
+
+ align:start position:0%
+and put in the chat what kind of object
+was just returned from um
+
+ align:start position:0%
+was just returned from um
+ 
+
+ align:start position:0%
+was just returned from um
+tuplets okay have um a couple different
+
+ align:start position:0%
+tuplets okay have um a couple different
+ 
+
+ align:start position:0%
+tuplets okay have um a couple different
+uh different answers but most people say
+
+ align:start position:0%
+uh different answers but most people say
+ 
+
+ align:start position:0%
+uh different answers but most people say
+it's a tuple right a tle of tuplets
+
+ align:start position:0%
+it's a tuple right a tle of tuplets
+ 
+
+ align:start position:0%
+it's a tuple right a tle of tuplets
+which you Tred not to say that she many
+
+ align:start position:0%
+which you Tred not to say that she many
+ 
+
+ align:start position:0%
+which you Tred not to say that she many
+times fast and you know it's a tupple um
+
+ align:start position:0%
+times fast and you know it's a tupple um
+ 
+
+ align:start position:0%
+times fast and you know it's a tupple um
+because it has this comma at the end so
+
+ align:start position:0%
+because it has this comma at the end so
+ 
+
+ align:start position:0%
+because it has this comma at the end so
+um it's an immutable a list of it and
+
+ align:start position:0%
+um it's an immutable a list of it and
+ 
+
+ align:start position:0%
+um it's an immutable a list of it and
+that means there you can have more than
+
+ align:start position:0%
+that means there you can have more than
+ 
+
+ align:start position:0%
+that means there you can have more than
+one tolet so you might have a triplet
+
+ align:start position:0%
+one tolet so you might have a triplet
+ 
+
+ align:start position:0%
+one tolet so you might have a triplet
+within a triplet and so on so those are
+
+ align:start position:0%
+within a triplet and so on so those are
+ 
+
+ align:start position:0%
+within a triplet and so on so those are
+some things we can do um
+
+ align:start position:0%
+some things we can do um
+ 
+
+ align:start position:0%
+some things we can do um
+the top so we can get at that darn tolet
+
+ align:start position:0%
+the top so we can get at that darn tolet
+ 
+
+ align:start position:0%
+the top so we can get at that darn tolet
+object I'm just trying to pull it out
+
+ align:start position:0%
+object I'm just trying to pull it out
+ 
+
+ align:start position:0%
+object I'm just trying to pull it out
+pull it out uh oh right it's not a
+
+ align:start position:0%
+pull it out uh oh right it's not a
+ 
+
+ align:start position:0%
+pull it out uh oh right it's not a
+graphical environment so um we'll get
+
+ align:start position:0%
+graphical environment so um we'll get
+ 
+
+ align:start position:0%
+graphical environment so um we'll get
+the first one we'll call it
+
+ align:start position:0%
+the first one we'll call it
+ 
+
+ align:start position:0%
+the first one we'll call it
+t and we'll see that the tuplet itself
+
+ align:start position:0%
+t and we'll see that the tuplet itself
+ 
+
+ align:start position:0%
+t and we'll see that the tuplet itself
+is also a complex object we can dir it
+
+ align:start position:0%
+is also a complex object we can dir it
+ 
+
+ align:start position:0%
+is also a complex object we can dir it
+and we can see it has certain things
+
+ align:start position:0%
+and we can see it has certain things
+ 
+
+ align:start position:0%
+and we can see it has certain things
+like tuplet multiplier which I happen to
+
+ align:start position:0%
+like tuplet multiplier which I happen to
+ 
+
+ align:start position:0%
+like tuplet multiplier which I happen to
+know is a meth
+
+ align:start position:0%
+know is a meth
+ 
+
+ align:start position:0%
+know is a meth
+and so we can see that when you throw
+
+ align:start position:0%
+and so we can see that when you throw
+ 
+
+ align:start position:0%
+and so we can see that when you throw
+this tuplet onto a note that note
+
+ align:start position:0%
+this tuplet onto a note that note
+ 
+
+ align:start position:0%
+this tuplet onto a note that note
+becomes 2/3 of its previous here are
+
+ align:start position:0%
+becomes 2/3 of its previous here are
+ 
+
+ align:start position:0%
+becomes 2/3 of its previous here are
+just some of the things you can do you
+
+ align:start position:0%
+just some of the things you can do you
+ 
+
+ align:start position:0%
+just some of the things you can do you
+will learn this in um in music in um the
+
+ align:start position:0%
+will learn this in um in music in um the
+ 
+
+ align:start position:0%
+will learn this in um in music in um the
+music 21 users guide two and three which
+
+ align:start position:0%
+music 21 users guide two and three which
+ 
+
+ align:start position:0%
+music 21 users guide two and three which
+we'll get through in a bit um some of
+
+ align:start position:0%
+we'll get through in a bit um some of
+ 
+
+ align:start position:0%
+we'll get through in a bit um some of
+the things you might see are
+
+ align:start position:0%
+the things you might see are
+ 
+
+ align:start position:0%
+the things you might see are
+um duration
+
+ align:start position:0%
+um duration
+ 
+
+ align:start position:0%
+um duration
+that obviously four is a whole people
+
+ align:start position:0%
+that obviously four is a whole people
+ 
+
+ align:start position:0%
+that obviously four is a whole people
+who like these things eight is a dotted
+
+ align:start position:0%
+who like these things eight is a dotted
+ 
+
+ align:start position:0%
+who like these things eight is a dotted
+a double whole note also called a brieve
+
+ align:start position:0%
+a double whole note also called a brieve
+ 
+
+ align:start position:0%
+a double whole note also called a brieve
+um which means short because there used
+
+ align:start position:0%
+um which means short because there used
+ 
+
+ align:start position:0%
+um which means short because there used
+to be longer notes and they're still
+
+ align:start position:0%
+to be longer notes and they're still
+ 
+
+ align:start position:0%
+to be longer notes and they're still
+somewhere and that's the longest
+
+ align:start position:0%
+somewhere and that's the longest
+ 
+
+ align:start position:0%
+somewhere and that's the longest
+possible note U which no longer exists
+
+ align:start position:0%
+possible note U which no longer exists
+ 
+
+ align:start position:0%
+possible note U which no longer exists
+except that somebody used a double the
+
+ align:start position:0%
+except that somebody used a double the
+ 
+
+ align:start position:0%
+except that somebody used a double the
+longest possible note but then at a
+
+ align:start position:0%
+longest possible note but then at a
+ 
+
+ align:start position:0%
+longest possible note but then at a
+certain point you can't do it similarly
+
+ align:start position:0%
+certain point you can't do it similarly
+ 
+
+ align:start position:0%
+certain point you can't do it similarly
+on the small side you can go
+
+ align:start position:0%
+on the small side you can go
+ 
+
+ align:start position:0%
+on the small side you can go
+um and let's get the type of
+
+ align:start position:0%
+um and let's get the type of
+ 
+
+ align:start position:0%
+um and let's get the type of
+that notice that the type of an eighth
+
+ align:start position:0%
+that notice that the type of an eighth
+ 
+
+ align:start position:0%
+that notice that the type of an eighth
+note is e i g h t the type of a 16th
+
+ align:start position:0%
+note is e i g h t the type of a 16th
+ 
+
+ align:start position:0%
+note is e i g h t the type of a 16th
+note um I misspelled 16th too many times
+
+ align:start position:0%
+note um I misspelled 16th too many times
+ 
+
+ align:start position:0%
+note um I misspelled 16th too many times
+so I decided U We Go From Here uh I
+
+ align:start position:0%
+so I decided U We Go From Here uh I
+ 
+
+ align:start position:0%
+so I decided U We Go From Here uh I
+don't think I know my fractions below
+
+ align:start position:0%
+don't think I know my fractions below
+ 
+
+ align:start position:0%
+don't think I know my fractions below
+that so we'll just keep going like that
+
+ align:start position:0%
+that so we'll just keep going like that
+ 
+
+ align:start position:0%
+that so we'll just keep going like that
+you can go down pretty far let's skip a
+
+ align:start position:0%
+you can go down pretty far let's skip a
+ 
+
+ align:start position:0%
+you can go down pretty far let's skip a
+bit oops or
+
+ align:start position:0%
+bit oops or
+ 
+
+ align:start position:0%
+bit oops or
+16 and you can go down to 14 20 1 24
+
+ align:start position:0%
+16 and you can go down to 14 20 1 24
+ 
+
+ align:start position:0%
+16 and you can go down to 14 20 1 24
+notes theoretically notes go on forever
+
+ align:start position:0%
+notes theoretically notes go on forever
+ 
+
+ align:start position:0%
+notes theoretically notes go on forever
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+um music 21 at a certain point says yeah
+
+ align:start position:0%
+um music 21 at a certain point says yeah
+ 
+
+ align:start position:0%
+um music 21 at a certain point says yeah
+this isn't representation music great I
+
+ align:start position:0%
+this isn't representation music great I
+ 
+
+ align:start position:0%
+this isn't representation music great I
+want to do um one more little exercise
+
+ align:start position:0%
+want to do um one more little exercise
+ 
+
+ align:start position:0%
+want to do um one more little exercise
+and this is a this is a trick question
+
+ align:start position:0%
+and this is a this is a trick question
+ 
+
+ align:start position:0%
+and this is a this is a trick question
+so just put um put your head what you
+
+ align:start position:0%
+so just put um put your head what you
+ 
+
+ align:start position:0%
+so just put um put your head what you
+think I'm going to sing something to you
+
+ align:start position:0%
+think I'm going to sing something to you
+ 
+
+ align:start position:0%
+think I'm going to sing something to you
+and you tell me how many notes I sang
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes I sang a eighth note tied to a 32nd
+
+ align:start position:0%
+yes I sang a eighth note tied to a 32nd
+ 
+
+ align:start position:0%
+yes I sang a eighth note tied to a 32nd
+note was slightly longer than half of a
+
+ align:start position:0%
+note was slightly longer than half of a
+ 
+
+ align:start position:0%
+note was slightly longer than half of a
+beat in my head so how do we deal with
+
+ align:start position:0%
+beat in my head so how do we deal with
+ 
+
+ align:start position:0%
+beat in my head so how do we deal with
+things like that well let's make it a
+
+ align:start position:0%
+things like that well let's make it a
+ 
+
+ align:start position:0%
+things like that well let's make it a
+whole note tied to a quarter note let's
+
+ align:start position:0%
+whole note tied to a quarter note let's
+ 
+
+ align:start position:0%
+whole note tied to a quarter note let's
+say the duration was fast so I'll call
+
+ align:start position:0%
+say the duration was fast so I'll call
+ 
+
+ align:start position:0%
+say the duration was fast so I'll call
+that an odd uh thing and by the way
+
+ align:start position:0%
+that an odd uh thing and by the way
+ 
+
+ align:start position:0%
+that an odd uh thing and by the way
+thank you one thank everybody for saying
+
+ align:start position:0%
+thank you one thank everybody for saying
+ 
+
+ align:start position:0%
+thank you one thank everybody for saying
+one and not saying seven because of you
+
+ align:start position:0%
+one and not saying seven because of you
+ 
+
+ align:start position:0%
+one and not saying seven because of you
+warbles too much but um let's take that
+
+ align:start position:0%
+warbles too much but um let's take that
+ 
+
+ align:start position:0%
+warbles too much but um let's take that
+uh eighth note tied to a 30 second note
+
+ align:start position:0%
+uh eighth note tied to a 30 second note
+ 
+
+ align:start position:0%
+uh eighth note tied to a 30 second note
+uh what is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+125 so we can see that you can create
+
+ align:start position:0%
+125 so we can see that you can create
+ 
+
+ align:start position:0%
+125 so we can see that you can create
+things and this says it's complex it is
+
+ align:start position:0%
+things and this says it's complex it is
+ 
+
+ align:start position:0%
+things and this says it's complex it is
+a duration that has multiple what I call
+
+ align:start position:0%
+a duration that has multiple what I call
+ 
+
+ align:start position:0%
+a duration that has multiple what I call
+components um which that there's an
+
+ align:start position:0%
+components um which that there's an
+ 
+
+ align:start position:0%
+components um which that there's an
+eighth and um an eighth and the 32nd
+
+ align:start position:0%
+eighth and um an eighth and the 32nd
+ 
+
+ align:start position:0%
+eighth and um an eighth and the 32nd
+that are put together and so what we
+
+ align:start position:0%
+that are put together and so what we
+ 
+
+ align:start position:0%
+that are put together and so what we
+mean by the length of a note will depend
+
+ align:start position:0%
+mean by the length of a note will depend
+ 
+
+ align:start position:0%
+mean by the length of a note will depend
+on where a note splits will depend on
+
+ align:start position:0%
+on where a note splits will depend on
+ 
+
+ align:start position:0%
+on where a note splits will depend on
+the context that we want to use it so if
+
+ align:start position:0%
+the context that we want to use it so if
+ 
+
+ align:start position:0%
+the context that we want to use it so if
+we're thinking about um hey he just
+
+ align:start position:0%
+we're thinking about um hey he just
+ 
+
+ align:start position:0%
+we're thinking about um hey he just
+saying that note in a sound context in a
+
+ align:start position:0%
+saying that note in a sound context in a
+ 
+
+ align:start position:0%
+saying that note in a sound context in a
+recording context obviously that's one
+
+ align:start position:0%
+recording context obviously that's one
+ 
+
+ align:start position:0%
+recording context obviously that's one
+note there's there's no other way around
+
+ align:start position:0%
+note there's there's no other way around
+ 
+
+ align:start position:0%
+note there's there's no other way around
+it but if we're thinking about it in a
+
+ align:start position:0%
+it but if we're thinking about it in a
+ 
+
+ align:start position:0%
+it but if we're thinking about it in a
+notation context and you're writing
+
+ align:start position:0%
+notation context and you're writing
+ 
+
+ align:start position:0%
+notation context and you're writing
+something that has to draw notes on a
+
+ align:start position:0%
+something that has to draw notes on a
+ 
+
+ align:start position:0%
+something that has to draw notes on a
+page you're going to want to put say
+
+ align:start position:0%
+page you're going to want to put say
+ 
+
+ align:start position:0%
+page you're going to want to put say
+that well that's actually two notes
+
+ align:start position:0%
+that well that's actually two notes
+ 
+
+ align:start position:0%
+that well that's actually two notes
+because there's no way to represent the
+
+ align:start position:0%
+because there's no way to represent the
+ 
+
+ align:start position:0%
+because there's no way to represent the
+duration that we heard with just one
+
+ align:start position:0%
+duration that we heard with just one
+ 
+
+ align:start position:0%
+duration that we heard with just one
+note so some of the things we're going
+
+ align:start position:0%
+note so some of the things we're going
+ 
+
+ align:start position:0%
+note so some of the things we're going
+to be working on this class is how do we
+
+ align:start position:0%
+to be working on this class is how do we
+ 
+
+ align:start position:0%
+to be working on this class is how do we
+move from different represent one
+
+ align:start position:0%
+move from different represent one
+ 
+
+ align:start position:0%
+move from different represent one
+representation to another so that um
+
+ align:start position:0%
+representation to another so that um
+ 
+
+ align:start position:0%
+representation to another so that um
+we're always using the
+
+ align:start position:0%
+we're always using the
+ 
+
+ align:start position:0%
+we're always using the
+representation that is most appropriate
+
+ align:start position:0%
+representation that is most appropriate
+ 
+
+ align:start position:0%
+representation that is most appropriate
+for the situation and so we'll spend a
+
+ align:start position:0%
+for the situation and so we'll spend a
+ 
+
+ align:start position:0%
+for the situation and so we'll spend a
+lot of time in this class um working on
+
+ align:start position:0%
+lot of time in this class um working on
+ 
+
+ align:start position:0%
+lot of time in this class um working on
+translations among
+
+ align:start position:0%
+translations among
+ 
+
+ align:start position:0%
+translations among
+representations okay remember you can
+
+ align:start position:0%
+representations okay remember you can
+ 
+
+ align:start position:0%
+representations okay remember you can
+always um take the directory of um of a
+
+ align:start position:0%
+always um take the directory of um of a
+ 
+
+ align:start position:0%
+always um take the directory of um of a
+music 21 or any python object to get
+
+ align:start position:0%
+music 21 or any python object to get
+ 
+
+ align:start position:0%
+music 21 or any python object to get
+some more things about it um but you can
+
+ align:start position:0%
+some more things about it um but you can
+ 
+
+ align:start position:0%
+some more things about it um but you can
+also uh in Jupiter you can put in
+
+ align:start position:0%
+also uh in Jupiter you can put in
+ 
+
+ align:start position:0%
+also uh in Jupiter you can put in
+question mark afterwards and get some
+
+ align:start position:0%
+question mark afterwards and get some
+ 
+
+ align:start position:0%
+question mark afterwards and get some
+docs or look at the Docks so now you
+
+ align:start position:0%
+docs or look at the Docks so now you
+ 
+
+ align:start position:0%
+docs or look at the Docks so now you
+have unlocked pitches and you have
+
+ align:start position:0%
+have unlocked pitches and you have
+ 
+
+ align:start position:0%
+have unlocked pitches and you have
+unlocked
+
+ align:start position:0%
+unlocked
+ 
+
+ align:start position:0%
+unlocked
+durations let's um move on to the last
+
+ align:start position:0%
+durations let's um move on to the last
+ 
+
+ align:start position:0%
+durations let's um move on to the last
+thing that we want that we're going to
+
+ align:start position:0%
+thing that we want that we're going to
+ 
+
+ align:start position:0%
+thing that we want that we're going to
+unlock today and that is those are
+
+ align:start position:0%
+unlock today and that is those are
+ 
+
+ align:start position:0%
+unlock today and that is those are
+notes
+
+ align:start position:0%
+notes
+ 
+
+ align:start position:0%
+notes
+so there are a million ways we could
+
+ align:start position:0%
+so there are a million ways we could
+ 
+
+ align:start position:0%
+so there are a million ways we could
+have called something a note um we could
+
+ align:start position:0%
+have called something a note um we could
+ 
+
+ align:start position:0%
+have called something a note um we could
+say um you know a note is the same thing
+
+ align:start position:0%
+say um you know a note is the same thing
+ 
+
+ align:start position:0%
+say um you know a note is the same thing
+as a pitch some people say that whatever
+
+ align:start position:0%
+as a pitch some people say that whatever
+ 
+
+ align:start position:0%
+as a pitch some people say that whatever
+but here's how I have chosen um and with
+
+ align:start position:0%
+but here's how I have chosen um and with
+ 
+
+ align:start position:0%
+but here's how I have chosen um and with
+my uh advisors and stuff how to
+
+ align:start position:0%
+my uh advisors and stuff how to
+ 
+
+ align:start position:0%
+my uh advisors and stuff how to
+represent a note a note takes in sort of
+
+ align:start position:0%
+represent a note a note takes in sort of
+ 
+
+ align:start position:0%
+represent a note a note takes in sort of
+a string just like a pitch just like we
+
+ align:start position:0%
+a string just like a pitch just like we
+ 
+
+ align:start position:0%
+a string just like a pitch just like we
+saw the pitch video um it's called a
+
+ align:start position:0%
+saw the pitch video um it's called a
+ 
+
+ align:start position:0%
+saw the pitch video um it's called a
+note it doesn't print the octave for
+
+ align:start position:0%
+note it doesn't print the octave for
+ 
+
+ align:start position:0%
+note it doesn't print the octave for
+some reason but and it has a name just
+
+ align:start position:0%
+some reason but and it has a name just
+ 
+
+ align:start position:0%
+some reason but and it has a name just
+like uh just like a pitch does but it
+
+ align:start position:0%
+like uh just like a pitch does but it
+ 
+
+ align:start position:0%
+like uh just like a pitch does but it
+also all those things are in a stored
+
+ align:start position:0%
+also all those things are in a stored
+ 
+
+ align:start position:0%
+also all those things are in a stored
+pitch object so a note has a pitch
+
+ align:start position:0%
+pitch object so a note has a pitch
+ 
+
+ align:start position:0%
+pitch object so a note has a pitch
+object and so you could change that and.
+
+ align:start position:0%
+object and so you could change that and.
+ 
+
+ align:start position:0%
+object and so you could change that and.
+pitch. octave equals 4
+
+ align:start position:0%
+pitch. octave equals 4
+ 
+
+ align:start position:0%
+pitch. octave equals 4
+see all that um but a note also has a
+
+ align:start position:0%
+see all that um but a note also has a
+ 
+
+ align:start position:0%
+see all that um but a note also has a
+duration and so in this case the default
+
+ align:start position:0%
+duration and so in this case the default
+ 
+
+ align:start position:0%
+duration and so in this case the default
+all notes start off with the duration of
+
+ align:start position:0%
+all notes start off with the duration of
+ 
+
+ align:start position:0%
+all notes start off with the duration of
+one quarter note I don't know why I'm
+
+ align:start position:0%
+one quarter note I don't know why I'm
+ 
+
+ align:start position:0%
+one quarter note I don't know why I'm
+privileging quarter notes but somehow I
+
+ align:start position:0%
+privileging quarter notes but somehow I
+ 
+
+ align:start position:0%
+privileging quarter notes but somehow I
+have um we can change the quarter length
+
+ align:start position:0%
+have um we can change the quarter length
+ 
+
+ align:start position:0%
+have um we can change the quarter length
+of that
+
+ align:start position:0%
+of that
+ 
+
+ align:start position:0%
+of that
+3.5 and
+
+ align:start position:0%
+3.5 and
+ 
+
+ align:start position:0%
+3.5 and
+then well has a full name so we can look
+
+ align:start position:0%
+then well has a full name so we can look
+ 
+
+ align:start position:0%
+then well has a full name so we can look
+at this be flat in octave 4 Double
+
+ align:start position:0%
+at this be flat in octave 4 Double
+ 
+
+ align:start position:0%
+at this be flat in octave 4 Double
+dotted half note okay so that's all
+
+ align:start position:0%
+dotted half note okay so that's all
+ 
+
+ align:start position:0%
+dotted half note okay so that's all
+there um hopefully this is working one
+
+ align:start position:0%
+there um hopefully this is working one
+ 
+
+ align:start position:0%
+there um hopefully this is working one
+cool thing that you can do that you
+
+ align:start position:0%
+cool thing that you can do that you
+ 
+
+ align:start position:0%
+cool thing that you can do that you
+can't do with a pitch or duration really
+
+ align:start position:0%
+can't do with a pitch or duration really
+ 
+
+ align:start position:0%
+can't do with a pitch or duration really
+is you can show a note it's weird that
+
+ align:start position:0%
+is you can show a note it's weird that
+ 
+
+ align:start position:0%
+is you can show a note it's weird that
+the first time it always takes longer
+
+ align:start position:0%
+the first time it always takes longer
+ 
+
+ align:start position:0%
+the first time it always takes longer
+and then later so here we go we have a
+
+ align:start position:0%
+and then later so here we go we have a
+ 
+
+ align:start position:0%
+and then later so here we go we have a
+particular note it figures out some kind
+
+ align:start position:0%
+particular note it figures out some kind
+ 
+
+ align:start position:0%
+particular note it figures out some kind
+of context for it has a couple other
+
+ align:start position:0%
+of context for it has a couple other
+ 
+
+ align:start position:0%
+of context for it has a couple other
+things we can do we can change the note
+
+ align:start position:0%
+things we can do we can change the note
+ 
+
+ align:start position:0%
+things we can do we can change the note
+head to be an X we can change the note
+
+ align:start position:0%
+head to be an X we can change the note
+ 
+
+ align:start position:0%
+head to be an X we can change the note
+to be no red I'm slightly color blind so
+
+ align:start position:0%
+to be no red I'm slightly color blind so
+ 
+
+ align:start position:0%
+to be no red I'm slightly color blind so
+I can't really see the difference but
+
+ align:start position:0%
+I can't really see the difference but
+ 
+
+ align:start position:0%
+I can't really see the difference but
+you can tell me that
+
+ align:start position:0%
+you can tell me that
+ 
+
+ align:start position:0%
+you can tell me that
+works yep and um we can also make it
+
+ align:start position:0%
+works yep and um we can also make it
+ 
+
+ align:start position:0%
+works yep and um we can also make it
+into a complex note so I think we
+
+ align:start position:0%
+into a complex note so I think we
+ 
+
+ align:start position:0%
+into a complex note so I think we
+learned
+
+ align:start position:0%
+learned
+ 
+
+ align:start position:0%
+learned
+6.25 couldn't be represented normally
+
+ align:start position:0%
+6.25 couldn't be represented normally
+ 
+
+ align:start position:0%
+6.25 couldn't be represented normally
+but we can see that um music 21 will
+
+ align:start position:0%
+but we can see that um music 21 will
+ 
+
+ align:start position:0%
+but we can see that um music 21 will
+figure out how many notes are necessary
+
+ align:start position:0%
+figure out how many notes are necessary
+ 
+
+ align:start position:0%
+figure out how many notes are necessary
+to represent it on the staff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's other miscellaneous
+
+ align:start position:0%
+there's other miscellaneous
+ 
+
+ align:start position:0%
+there's other miscellaneous
+things you can give it a
+
+ align:start position:0%
+things you can give it a
+ 
+
+ align:start position:0%
+things you can give it a
+lyric and so on so uh again everything
+
+ align:start position:0%
+lyric and so on so uh again everything
+ 
+
+ align:start position:0%
+lyric and so on so uh again everything
+there is in the during it and you'll see
+
+ align:start position:0%
+there is in the during it and you'll see
+ 
+
+ align:start position:0%
+there is in the during it and you'll see
+there's a lot of stuff and we're going
+
+ align:start position:0%
+there's a lot of stuff and we're going
+ 
+
+ align:start position:0%
+there's a lot of stuff and we're going
+to get through um a good chunk of
+
+ align:start position:0%
+to get through um a good chunk of
+ 
+
+ align:start position:0%
+to get through um a good chunk of
+looking these things
+
+ align:start position:0%
+looking these things
+ 
+
+ align:start position:0%
+looking these things
+later no you will not be ever quizzed on
+
+ align:start position:0%
+later no you will not be ever quizzed on
+ 
+
+ align:start position:0%
+later no you will not be ever quizzed on
+okay what does purge orphans mean on a
+
+ align:start position:0%
+okay what does purge orphans mean on a
+ 
+
+ align:start position:0%
+okay what does purge orphans mean on a
+note so it's not that kind of class but
+
+ align:start position:0%
+note so it's not that kind of class but
+ 
+
+ align:start position:0%
+note so it's not that kind of class but
+but we want you to um I want you to feel
+
+ align:start position:0%
+but we want you to um I want you to feel
+ 
+
+ align:start position:0%
+but we want you to um I want you to feel
+free play around with this play with
+
+ align:start position:0%
+free play around with this play with
+ 
+
+ align:start position:0%
+free play around with this play with
+anything except just like with pitch
+
+ align:start position:0%
+anything except just like with pitch
+ 
+
+ align:start position:0%
+anything except just like with pitch
+anything that begins with transpose is
+
+ align:start position:0%
+anything that begins with transpose is
+ 
+
+ align:start position:0%
+anything that begins with transpose is
+off limits um only because uh it'll make
+
+ align:start position:0%
+off limits um only because uh it'll make
+ 
+
+ align:start position:0%
+off limits um only because uh it'll make
+the problem set where we uh do a lot of
+
+ align:start position:0%
+the problem set where we uh do a lot of
+ 
+
+ align:start position:0%
+the problem set where we uh do a lot of
+things with intervals a lot less fun
+
+ align:start position:0%
+things with intervals a lot less fun
+ 
+
+ align:start position:0%
+things with intervals a lot less fun
+because you're not using anyhow uh this
+
+ align:start position:0%
+because you're not using anyhow uh this
+ 
+
+ align:start position:0%
+because you're not using anyhow uh this
+is the end of the locking for topic one
\ No newline at end of file
diff --git a/o8XojnApGc4.txt b/o8XojnApGc4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6045f7e8c2a789c369f5ce93fa73180604353960
--- /dev/null
+++ b/o8XojnApGc4.txt
@@ -0,0 +1,3427 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or to view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: I'm going to review
+what we did with the craft
+
+inequality just a little bit,
+because evidently a number of
+
+people were confused
+about this.
+
+I'm going to put a little more
+notation in with it.
+
+For some people,
+notation helps.
+
+For other people, it
+hinders things.
+
+But after you've thought about
+it a little bit, a little more
+
+notation can certainly
+be helpful.
+
+What we're trying to do in
+this craft inequality is,
+
+we're thinking of a set of
+symbols where, supposing that
+
+there's a codeword for each
+symbol, c of x is the codeword
+
+for symbol x, which is a string
+of binary digits.
+
+y1 up to y sub n.
+
+In the world of two-toed sloths,
+the representation of
+
+numbers that sloths use
+is binary, base 2.
+
+And therefore, they use the
+number associated with some
+
+sequence of bits like this would
+be the sum of y sub i,
+
+times 2 to the minus i.
+
+In other words, it's the same
+thing as a decimal, except
+
+it's in a world where
+people have two
+
+fingers instead of ten.
+
+There's an interval associated
+with this number, also.
+
+And the interval is what you
+would get if you took an
+
+arbitrary real number and
+rounded it down to l sub i.
+
+Well, in this case to
+m binary digits.
+
+So that interval, then,
+is the number itself.
+
+And the other side of
+the interval is that
+
+number itself --
+
+the two-toed sloth didn't like
+what I was going to say about
+
+it, and it changed my slide.
+
+So, is that extra factor the
+2 to the minus n, there.
+
+In other words, any number in
+that range, if you round it
+
+down to m significant binary
+digits is going to the this
+
+number here.
+
+Well the point of this, if the
+number, namely, this base 2
+
+expansion of a number y prime is
+in this interval, then y is
+
+going to be a prefix
+of y prime.
+
+Let me just give you some
+examples of that because
+
+saying it in words
+is confusing, the
+
+idea is very simple.
+
+Suppose you have a binary
+string, 011.
+
+That corresponds to
+the number 3/8.
+
+Namely, 1/4 plus 1/8.
+
+And the interval there is going
+to be the interval from
+
+3/8, including 3/8, up to 1/4.
+
+But not including 1/4.
+
+Namely, 1/4 will be represented
+as -- the sloth
+
+really is hitting hard
+this morning.
+
+Maybe I'm the sloth.
+
+OK.
+
+There we go.
+
+From 3/8 to 1/2.
+
+Namely, 1/2 is just 1.
+
+Nothing more than that.
+
+Or it could be 10 or
+100, and so forth.
+
+So then, as an example, 011 is
+going to be a prefix of all of
+
+these quantities here.
+
+That's a prefix of 0111 because
+0111 is 3/8 plus 1/16,
+
+which is in that interval
+we're talking about.
+
+0110 is a more interesting
+case.
+
+Because 0110 is itself,
+the number associated
+
+with it, is just 3/8.
+
+But what this is saying is, if
+you take the same number but
+
+expand it to four digits,
+according to what this says, r
+
+of y like is then in
+this interval.
+
+And therefore this prefix
+situation holds.
+
+So this is a prefix of this.
+
+Why do I make it
+so complicated?
+
+I make it so complicated because
+I want to talk about
+
+the length of that interval.
+
+And the length of these
+intervals is denoted in this
+
+diagram here.
+
+Anytime I have a number
+expressed to n binary digits,
+
+it covers an interval
+of 2 to the minus n.
+
+And because of this prefix
+property, as soon as one
+
+number covers an interval, no
+other number have its base in
+
+that interval.
+
+In other words, all of these
+intervals have to be disjoint,
+
+exactly as is indicated here.
+
+So when you add up the size of
+all these intervals, you have
+
+to get something less
+than or equal to 1.
+
+And that's the proof of
+the craft inequality.
+
+So, let's go on and talk about
+discrete source probabilities.
+
+Now the two-toed sloth has
+gotten his machine out there,
+
+he's really mad at
+me this morning.
+
+If we try to model English
+text, you know that some
+
+letters are far more probable
+than others.
+
+Namely, if you take an enormous
+amount of English
+
+text and you measure the
+relative frequency with which
+
+each letter occurs, you'll get
+more or less stable relative
+
+frequencies if you
+take enough text.
+
+And these letters are far more
+probable than these letters.
+
+So that gives you
+part of a model.
+
+You can also say that successive
+letters are going
+
+to be very dependent.
+
+Namely, t is very often followed
+by h, and h is often
+
+preceded by t.
+
+q u is even more of a case
+here, because as far as
+
+English language words are
+concerned, u always follows q.
+
+Some letter strings are words.
+
+Other letter strings
+are not words.
+
+There are constraints
+on grammar.
+
+And what is really the clincher,
+which says there's
+
+no way you're going to model
+English in any sensible nice
+
+way, is meaning.
+
+And even worse than that,
+depending on who writes the
+
+English, it might have meaning
+or it might not have meaning.
+
+And for those English texts that
+don't have any meaning,
+
+the entropy is going to depend
+very much on whether the
+
+meaningless text is written by
+a salesperson or it's written
+
+by James Joyce.
+
+And in one case you have --
+
+well, in one case you have an
+enormous amount of freedom in
+
+what this sequence
+of letters are.
+
+And in the other case you have
+letters which are very, very
+
+constrained.
+
+So what's the point of this?
+
+The point of this is, if you're
+interested in trying to
+
+find the source coding method
+for English, what you don't
+
+want to do is to start out
+trying to get the best
+
+statistical model of English
+that you can.
+
+Because it's a losing
+proposition.
+
+And by trying to do that, you'll
+spend all your time
+
+trying to get the model.
+
+And you won't get any insight
+into what you ought to do as
+
+far as source coding
+is concerned.
+
+This is pretty much true
+throughout all of technology.
+
+You don't solve problems by
+first getting too far into the
+
+details of what the problem is,
+before you start thinking
+
+about structures of possible
+solutions.
+
+In other words, we always deal
+with technological problems by
+
+dealing with toy
+problems first.
+
+Now, there's a difference
+between engineers who worry
+
+about toy problems.
+
+Because engineers, if they hate
+theory, usually, don't
+
+say what the toy problem is.
+
+But they have that toy problem
+very firmly in the back of
+
+their mind, because of
+all their experience.
+
+Theoreticians, on the other
+hand, make their models very,
+
+very explicit.
+
+They don't often like to say
+that they're toy models
+
+because DARPA doesn't tend to
+support things that are
+
+working on toy models.
+
+So they try to conceal this.
+
+And often they just
+hide the fact that
+
+they're using a model.
+
+So, all of this becomes
+very complicated.
+
+But, for you, if you're trying
+to do either engineering or
+
+mathematics or teaching, or
+just be a sensible person.
+
+When you're dealing with these
+problems, be explicit about
+
+what your models are.
+
+Try to understand the toy
+problems before you understand
+
+the more complicated problems.
+
+If you understand that out of
+this course, it'll be a
+
+worthwhile course for you.
+
+And, of course, you won't
+understand it until you get
+
+lots more experience.
+
+But believe me, that's
+the way it is.
+
+OK, so that's the whole
+point of this.
+
+You want to start with
+simple toy models.
+
+And I'm not just justifying the
+fact that we're going to
+
+study this incredibly
+simple model here,
+
+which is a toy model.
+
+But by studying this
+you will see that
+
+everything else follows.
+
+If you read Claude Shannon's
+work on information theory,
+
+this, in fact, is where
+he started.
+
+He started with a beautiful
+description of trying to model
+
+the English language.
+
+Finally wound up with
+talking about this.
+
+The conclusions he drew, from
+studying these discrete memory
+
+sources, lead to his general
+theorems about data
+
+compression on sources.
+
+They led to his general
+theorems about
+
+the capacity of channels.
+
+They led to the idea that you
+want to separate source coding
+
+from channel coding, and
+finally, they led to all of
+
+the modern ideas that we have
+about quantization.
+
+In other words, the simple
+ideas you get out of this
+
+generalize directly to
+everything that's known about
+
+information theory.
+
+So.
+
+Enough philosophy, let's get on
+with the business of what
+
+we're trying to do.
+
+A discrete memoryless sources
+has the following properties.
+
+The source output has to be an
+unending sequence, x1, x2, x3,
+
+blah, blah, blah, of random
+letters drawn from a finite
+
+alphabet, x.
+
+In other words, we are taking
+these real sources.
+
+And we're saying, let's make
+them not real now.
+
+Let's put a probability
+measure on them.
+
+And in this probability measure,
+one of the things
+
+that the probability measure
+will do will be to describe
+
+the probability on each one of
+these letters and the sequence
+
+in which it's coming
+out of the source.
+
+Each source output, x1, x2,
+blah, blah, blah, is selected
+
+from a common alphabet.
+
+Namely, if you're using English
+on one letter of the
+
+sequence, you're going to
+use English on every
+
+letter of the sequence.
+
+Going to use a common
+probability measure, with some
+
+probability mass function
+p sub x of x.
+
+This notation means this is the
+probability mass function
+
+for the chance variable X. A
+chance variable is like a
+
+random variable, except
+the objects are
+
+not necessarily numbers.
+
+The objects can be anything.
+
+So, a chance variable is a
+
+generalization of a random variable.
+
+So this probability mass
+function talks about the
+
+probability of each of the
+symbols in this alphabet x.
+
+Then the final thing is, each
+source output, x sub k, is
+
+statistically independent of all
+other source outputs, x1
+
+up x k minus 1, and x k
+plus 1 on to forever.
+
+This is a nice example, because
+if you're going to
+
+specify a source
+probabilistically, you have to
+
+somehow find a way of
+explaining what the
+
+probability of every possible
+event within this source is.
+
+This is an easy way
+of doing it.
+
+You say they're independent.
+
+And then you can find the
+probability of anything you
+
+want to find.
+
+So that's a generic
+way of putting
+
+probability measures on things.
+
+So then, we want to go into the
+idea of prefix-free codes
+
+for these discrete memory
+of the sources.
+
+We've already talked about
+prefix-free codes.
+
+We talked about the
+craft inequality.
+
+You might have thought it was
+a little bit strange talking
+
+about the strictly combinatorial
+property of
+
+codes without talking at all
+about the probabilities, which
+
+are the things that led us into
+talking about these codes
+
+in the first place.
+
+Namely, we want to use unequal
+length, variable length codes.
+
+Because of the fact that some
+letters are more likely than
+
+other letters.
+
+And eventually we'll be using
+them because of all these
+
+constraints between
+different words.
+
+So, for notation, let l of x be
+the length of the codeword
+
+for letter x in, the alphabet
+capital X. ok so that's the
+
+same as this y1 y2
+up to y sub n.
+
+At some strength of
+binary symbols.
+
+Capital L of x is a random
+variable, where capital L of x
+
+is equal to little l of x, where
+capital X equal to x.
+
+Now, what the heck
+does that mean?
+
+It's just notation.
+
+In other words, what we're
+starting out with is this
+
+ensemble of letters.
+
+We have a probability assignment
+on each letter in
+
+that alphabet.
+
+And then what we would like
+to talk about is a length
+
+function on those letters.
+
+So we have little l of x, which
+is defined for each x.
+
+We then want to talk about this
+as a random variable.
+
+Because when we choose some
+random letter, x, little x, of
+
+this ensemble, capital X, l of
+x becomes a random variable.
+
+We will always, in this course,
+use capital letters to
+
+talk about random variables.
+
+And we will always use little
+letters to talk about things
+
+which are not random
+variables.
+
+Excuse me, not not random
+variables but random variables
+
+or chance variables.
+
+I think we can probably
+leave it open now.
+
+It seems as if the sloth
+has gone away.
+
+So then we want to talk
+about the expected
+
+value of the length.
+
+You talk about the expected
+value of something, you're
+
+talking about the expected value
+of a random variable.
+
+We will also denote the expected
+value of this random
+
+variable L with a bar over it,
+which is the sum over the
+
+letters in the alphabet,
+of p of x times L of x.
+
+So all this is what you would do
+anyway if you never thought
+
+about this.
+
+Until, at some point, when
+you're taking a quiz or
+
+something and start to get
+confused and say, what is this
+
+stuff all about?
+
+I don't have any idea what
+this means after you've
+
+written five pages of stuff.
+
+So, it's worthwhile spending
+a little bit of time
+
+sorting that out.
+
+So, L bar is the number
+of encoder output
+
+bits per source symbol.
+
+In some strange sense.
+
+Namely, it's this
+expected value.
+
+Now, to finish this off, if we
+want to look at the number of
+
+binary digits to come out of
+the source when a long
+
+sequence of letters come
+out of the source --
+
+A long sequence of letters. x1,
+x2, x3, and so forth, come
+
+out of the source.
+
+They go into the encoder.
+
+The encoder is mapping each
+letter that comes out of the
+
+source into this codeword
+c of x.
+
+So we have a sequence of
+codewords which are all
+
+concatenated together.
+
+And, therefore, the total number
+of binary digits which
+
+has come out of the source
+corresponding to these n
+
+symbols that have come out of
+the source, is the sum of L of
+
+x1 plus L of x2 plus of x3 plus
+L of x4, and so forth.
+
+So we have a sum of independent
+random variables.
+
+Now, what do you know
+about sums of
+
+independent random variables?
+
+Well, the one thing you ought
+to know about, and which
+
+should be stamped on your brain
+because it's the central
+
+thing that makes any
+probabilistic theory make
+
+sense, it's the only way that
+we can ever understand our
+
+environment.
+
+You look at the past.
+
+You try to figure out
+from the past what's
+
+going on in the future.
+
+And the only way you can do
+that, the only tool you have,
+
+really, is this law
+of large, numbers.
+
+Which says, when you see a long
+sequence of things, from
+
+that long sequence of things,
+you sort of figure out
+
+what's going on.
+
+If you're dealing with a random
+variable, the thing you
+
+do is add up all of
+these numbers.
+
+You divide by the total number
+of them that you have.
+
+And that gives you the
+expected value.
+
+It gives you a typical value.
+
+What the law of large numbers
+really says is, if you look at
+
+the sum of binary digits out of
+this encoder, over a very
+
+long period of time, divide by
+the total number of symbols,
+
+that's a random variable
+again.
+
+And this random variable is,
+with high probability, going
+
+to be very, very close to this
+expected value, which is this
+
+quantity here.
+
+In other words, the ensemble
+average, which is this, is
+
+going to be very close
+to the time average.
+
+And the time average, now,
+is a random variable.
+
+And that's what the law
+of large numbers says.
+
+You see, the problem that we
+all have, dealing with real
+
+world problems, is that there's
+nobody to tell us this
+
+is what the ensemble is.
+
+Unless you believe somebody
+that doesn't know.
+
+And the only real evidence
+that you have
+
+is the actual sequence.
+
+And from the actual sequence,
+you then look at what happens
+
+for this particular sequence.
+
+You then build a model.
+
+And your model, by definition,
+has the expected value of L
+
+going to be equal to the
+expected value in the model
+
+that you've chosen.
+
+So.
+
+What's your objective?
+
+Your objective in trying to form
+a prefix-free code, then,
+
+is to find a set of integers,
+L of x, which satisfy the
+
+Kraft inequality.
+
+And they minimize L bar.
+
+In other words, what we're
+trying to do is, we're trying
+
+to choose a code which minimizes
+the expected length
+
+of the code.
+
+Which is really, over a long
+period of time, going to
+
+minimize the number of binary
+digits that come out of the
+
+source encoder.
+
+What we want to do is to choose
+these integers to
+
+minimize this.
+
+So what we're going to do now
+is, suppose our alphabet is
+
+just 1, 2, up to capital N.
+What am I doing here?
+
+I'm saying, we don't care about
+what these symbols are
+
+called, anyway.
+
+It's totally irrelevant what the
+names of the symbols are.
+
+So I will name them 1, 2, up to
+capital N. Probability mass
+
+function, then, I can denote as
+p sub 1 up to p sub capital
+
+N. In other words I've gotten
+rid of all these axes that
+
+were lousing up our equations
+all along.
+
+Now, I'll denote the unknown
+lengths by l1 up to l sub M.
+
+So the problem is, somebody
+gives you this set of numbers.
+
+p1 to p sub M, which is a PMF.
+
+In other words, these
+numbers add up to 1.
+
+And tells you, I want a
+prefix-free code which
+
+minimizes this expected
+length.
+
+Namely, the expected value
+corresponding to
+
+these lengths here.
+
+So, the expected length, to
+minimize it, what we want to
+
+do is to minimize over the
+choice of l1 up to l sub M.
+
+Subject to the craft inequality,
+we want to
+
+minimize this expected value.
+
+So we have a nice, clean,
+mathematical problem now.
+
+We want to minimize this sum,
+subject to this constraint.
+
+And the constraint includes
+the fact that all of these
+
+things have to be integers.
+
+Well, for those of you who have
+studied minimization,
+
+there's a funny thing in here.
+
+Because integer minimization
+problems tend to
+
+be very, very nasty.
+
+And, therefore, you look at
+this and you say, this is
+
+probably something I'm going
+to have trouble solving.
+
+Strangely enough, it isn't.
+
+But you would think it probably
+is something which
+
+will be hard to solve.
+
+So, since integers louse
+up minimization
+
+problems, what do we do?
+
+Well, we say, just for fun
+let's try to solve this
+
+problem without the integer
+constraint on it.
+
+Let's see what that leads
+to, and see if we can do
+
+anything with that.
+
+So we say, OK, let's try to
+minimize this function here
+
+over the integers l1 to l sub M,
+subject to this constraint.
+
+So we're minimizing this,
+subject to this constraint.
+
+Now, an easy way to
+do that -- yes.
+
+AUDIENCE: Are you
+
+saying that side length is
+not a fixed probability.
+
+PROFESSOR: No, I still have
+these fixed probabilities.
+
+I still have p1 up to p sub
+M, as known probabilities.
+
+But I'm going to say, let's
+suppose I can choose a length
+
+which is two point five bits
+instead of two bits.
+
+AUDIENCE: You're saying
+the shortest length
+
+[UNINTELLIGIBLE]
+
+PROFESSOR: Well, we're going to
+wind up there eventually.
+
+But for now, all I want to do
+is to look at this problem.
+
+If I start out by saying, assign
+shortest lengths to the
+
+biggest probabilities,
+I have two problems.
+
+One is, it's a little hard
+to prove to you that
+
+I want to do that.
+
+Although we'll do that
+later today.
+
+And the other is, it doesn't
+really give you the general
+
+properties that we want
+to know about this.
+
+So, for those two reasons, I
+want to just attack this as a
+
+straightforward mathematical
+problem.
+
+If you're a computer scientist,
+this looks strange.
+
+Because computer scientists
+like to attack problems by
+
+algorithms.
+
+Analog engineers like to attack
+problems by writing a
+
+complicated formula, and taking
+derivatives, and all
+
+sorts of things like that.
+
+We're going to be doing
+both of those
+
+things in this course.
+
+And you'll see that both
+of them lead to certain
+
+advantages.
+
+And here, we're taking, where
+the analog engineer's approach
+
+is saying, suppose this
+is a bunch of numbers.
+
+I want to minimize this
+function over a set of
+
+numbers, l1 up to
+l sub capital M.
+
+So, how do I do that?
+
+Well, this guy Lagrange, he
+was a great mathematician.
+
+He was also a great
+mathematician early enough
+
+that he could do some really
+trivial things and become
+
+famous for them.
+
+Just like Kraft that we were
+talking about before.
+
+But, unlike Kraft, Lagrange
+really did a lot of other very
+
+important things.
+
+And what Lagrange said was the
+following: Well, suppose I
+
+want to minimize this sum.
+
+And I want to have this
+constraint added in.
+
+Sort of what I want to do,
+then, is to minimize a
+
+weighted sum of this,
+which is what I'm
+
+interested in, and this.
+
+In other words, if I minimize
+this weighted sum here of
+
+these two things, I'm going to
+wind up with some sort of
+
+value for this.
+
+And some sort of
+value for this.
+
+By changing lambda, then, which
+stands for Lagrange, he
+
+was also clever in making
+himself famous that way, by
+
+changing lambda, I can change
+the balance between how
+
+important these two
+things are.
+
+And as I change the balance
+between how important they
+
+are, when I change it to just
+the right place, I'm going to
+
+have this constraint here
+satisfied with equality.
+
+So that's the whole idea of
+Lagrange minimization.
+
+So we take this function.
+
+How do you now minimize a
+
+function of multiple variables?
+
+Well, again it's a
+messy problem.
+
+But the first thing you
+can try to do is find
+
+a stationary point.
+
+So, let's always do the
+easy thing first.
+
+We take the partial derivative
+of this function here, with
+
+respect to l sub i.
+
+That's what we're trying
+to minimize.
+
+And what we get is p sub i minus
+lambda times the natural
+
+log of 2, times 2 the
+minus l sub i.
+
+I'm not very good at
+differentiation any more, so I
+
+only differentiate things
+which are easy.
+
+And that's easy.
+
+I want to find a stationary
+point, so I set
+
+this equal to 0.
+
+That makes the problem worse,
+because now I have a function
+
+of lambda and also all
+of these l sub i's.
+
+But now I choose l sub i, so
+that I satisfy the constraint.
+
+Namely, I choose lambda to
+satisfy this equation here.
+
+When I choose lambda to satisfy
+this equation here,
+
+what I get is p sub i is equal
+to 2 to the minus l i, and
+
+therefore, l sub i is equal
+to minus log p sub i.
+
+In other words, I have
+this equation here.
+
+What happens when I sum
+this equation over i?
+
+Let's look at it.
+
+We sum this over i.
+
+The sum of p i over i is 1 minus
+lambda times natural log
+
+of 2 times sum of 2 to
+the minus l sub i.
+
+And I want to make
+this equal to 1.
+
+So what I get is 1 is equal
+to this times lambda
+
+natural log of 2.
+
+So, I hope that choosing lambda
+equal to 1 over natural
+
+log of 2 is what I want to do.
+
+And when I do that, this
+becomes 1 here.
+
+And I just have 2 to the minus
+lambda i is equal to 1.
+
+OK, good.
+
+And then, going back to this
+equation, p sub i is equal to
+
+2 to the minus l sub i.
+
+OK, this is this arithmetic.
+
+I mean, if you don't follow what
+I'm doing, just look at
+
+it later and you'll find that
+there's nothing really there.
+
+So we wind up with these lengths
+being equal to the
+
+negative of the binary
+logarithms of these
+
+probabilities.
+
+It's only a stationary point.
+
+We don't know whether
+it's a minimum yet.
+
+And, unfortunately, we also
+have the problem of, they
+
+might not be integers.
+
+But, anyway, what we wind up
+with, then, if we ignore
+
+looking at these problems for
+the time being, is that the
+
+lengths are going to
+be equal to this.
+
+The expected value of the
+lengths is then going to be
+
+equal to the sum, over i, of
+minus p sub i times the
+
+logarithm of p sub i.
+
+When Shannon saw this, and when
+various other people saw
+
+it, they said, gee, this looks
+like the entropy of
+
+statistical mechanics.
+
+So let's call this
+quantity entropy.
+
+For no better reason
+than that.
+
+And it would probably have been
+far better if they called
+
+it something else.
+
+Because for years, there were
+physicists and philosophers
+
+trying to figure out what the
+deep relationship was between
+
+statistical mechanical
+entropy and
+
+information theoretic entropy.
+
+And there probably is such
+a relationship, but the
+
+relationship is far more
+complicated than understanding
+
+information theory.
+
+And it's far more
+complicated than
+
+understanding statistical mechanics.
+
+So I advise you to not worry
+about that one until after you
+
+understand what it means in an
+information theoretic sense.
+
+So h of x is what we call
+the entropy of the
+
+random variable x.
+
+And it really is the entropy
+associated with these
+
+logarithms of p sub i.
+
+So when you take functions of
+a random variable, a random
+
+variable carries along a
+lot of baggage with it.
+
+Including the probabilities
+of everything.
+
+And when you take the expected
+value of a random variable,
+
+the individual values of the
+sample points of that random
+
+variable are important.
+
+And the probabilities
+are important.
+
+Here we have something
+even stranger.
+
+Because it's only the
+probabilities that have
+
+anything to do with it.
+
+And this makes sense.
+
+We already said that these
+symbols have nothing to do
+
+with this problem we're
+dealing with.
+
+You can call the symbols
+whatever you
+
+want to call them.
+
+And, therefore, the only thing
+of any interest to us is these
+
+probabilities that we're
+dealing with.
+
+So H of x is a function only
+of these probabilities.
+
+It's the expected value
+of minus log p sub i.
+
+This is called entropy, and in
+fact we will find out very
+
+shortly that it really is the
+minimum number of bits per
+
+source symbol needed to
+represent the source.
+
+In other words, when we
+generalize the problem from
+
+just plain ordinary
+garden-variety oh prefix-free
+
+codes, we will find that this
+number is really what
+
+characterizes the whole
+problem for discrete
+
+memory-less sources.
+
+So let's go on and say
+more about that.
+
+Let's say something about
+bounds on the entropy.
+
+First, what's the relationship
+between the entropy and this
+
+minimum of the expected length
+that we started to talk about?
+
+And I claim that H of x is less
+than or equal to L min,
+
+which is less than the
+entropy plus 1.
+
+And why is that?
+
+We already have the machinery
+to see this.
+
+We almost have the machinery
+to see this.
+
+Namely, we have solved this
+minimization problem.
+
+We've only found a stationary
+point, but we've ignored the
+
+fact that we have an
+integer constraint.
+
+So, if you allow me to say for
+the time being that, in fact,
+
+when we solve the problem
+without worrying about
+
+integers, that it actually gives
+me a minimum, then in
+
+fact this follows very easily.
+
+Because what I'm going to do
+is to find those optimal
+
+lengths, which are
+non-integers.
+
+And then I can solve the prefix
+condition and get a
+
+code by simply increasing each
+of those numbers to the next
+
+integer up.
+
+In other words, I can take the
+ceiling function of each of
+
+those real numbers to
+get an integer.
+
+When I take the ceiling
+function, 2 to the minus l sub
+
+i is going to go down.
+
+So the craft inequality
+is still satisfied.
+
+So the entropy has to be less
+than or equal to this average.
+
+Has to be less than
+H of x plus 1.
+
+So the average is equal to H of
+x if and only if each these
+
+probabilities it an integer
+power of 2 to start with.
+
+In other words, the solution I
+came up with before is that
+
+the length I wanted should be
+equal to minus the logarithm
+
+to base 2, of p sub i.
+
+So if p sub i is already a power
+of 2 then I'm home free.
+
+Because I just pick that length
+to be minus log of p
+
+sub i, and it happens
+to be an integer.
+
+And I don't have
+to round it up.
+
+So if I let l1 to lM be these
+codeword lengths -- well,
+
+here's where I'm going
+to prove this to you.
+
+And the proof is the following:
+I want to prove
+
+that H of x is less than or
+equal to l min, which I'll
+
+just call here L bar.
+
+So H of x minus L bar is equal
+to, this is the entropy.
+
+This is the expected
+length here.
+
+I can rewrite this as the sum of
+p sub i times logarithm of
+
+2 to the minus l sub i
+divided by p sub i.
+
+That's just arithmetic.
+
+l sub i is equal to to logarithm
+of 2 to the l sub i,
+
+that's equal to minus
+the logarithm of 2
+
+the minus l sub i.
+
+So I get this.
+
+There's an inequality.
+
+Hate to call it an inequality,
+it's so trivial.
+
+Here's the point 1.
+
+If you plot a natural
+log of x.
+
+And if you compare it with the
+function x minus 1, you can
+
+see that natural log of
+x is less than or
+
+equal to x minus 1.
+
+Now, this an inequality which
+happens to be very useful in
+
+information theory.
+
+I would claim that any
+inequality that you can prove
+
+in information theory, by any
+means at all, I can prove
+
+using this inequality
+and nothing else.
+
+And I've believed that for
+50 years and nobody's
+
+proven me wrong yet.
+
+And also, this is something
+you can draw and remember.
+
+So it's simple.
+
+So the idea, then, is since this
+sum log of 2 to the minus
+
+l over p sub i is less than or
+equal to the natural log of 2
+
+times the natural logarithm
+of this.
+
+You just, here we go.
+
+For any u greater than 0,
+natural log of u is less than
+
+or equal to this.
+
+So the logarithm to the base 2
+of u is less than or equal to
+
+the logarithm to the base 2 of
+e, which is some number,
+
+times u minus 1.
+
+With equality at u equals 1.
+
+So this is less than
+or equal to this.
+
+And look how nice that is.
+
+The p sub i's cancel out and you
+get the sum over i, of 2
+
+the minus l i minus p sub i is
+less than or equal to 0.
+
+An equality occurs if, and only
+if, p sub i is equal to 2
+
+to the minus l i.
+
+OK?
+
+So that's all there is to it.
+
+And that establishes that --
+well, establishes part of this
+
+theorem here.
+
+And the other part we already
+established, And if you don't
+
+believe me, the notes do
+it more carefully.
+
+Well, this left us a serious
+problem unknown.
+
+Which is, how do you actually
+solve this integer
+
+minimization problem.
+
+How do you solve it if you have
+a big, long, complicated
+
+source with lots of
+probabilities in it?
+
+And everybody thought
+it was hopeless.
+
+Even Shannon thought
+it was hopeless.
+
+And Shannon sort of figured
+out ways to
+
+approach this problem.
+
+He said, well, you want
+to have about half the
+
+probability.
+
+Starting with 1, about
+half the probability
+
+starting with 0.
+
+So he would divide up the
+symbols in the alphabet, so he
+
+could come as close is possible
+to half of them being
+
+up here and half of them
+coming down here.
+
+And he would continue to do
+that, I mean, I don't usually
+
+like to write on the blackboard,
+but he would start
+
+out generating a
+code like this.
+
+And this would be approximately
+1/2.
+
+This is approximately 1/2.
+
+And then he would take
+these symbols.
+
+Split them, again,
+in probability.
+
+And everybody was starting the
+problem over here, and trying
+
+to generate a code working
+their way out.
+
+Well, Dave Huffman was a
+graduate student at the time.
+
+and he took Bob Fano's graduate
+course in information
+
+theory, I think a year or
+so later than Kraft did.
+
+And Bob Fano assigned as a
+homework problem, how do you
+
+solve this problem?
+
+Sneaky guy.
+
+And he was very amazed when Dave
+Hoffman came in next day
+
+and said, oh, it's easy,
+you do it this way.
+
+So the question is,
+how did he do it?
+
+Well, Huffman, instead of
+looking at the problem from
+
+here out, looked at the
+problem from here in.
+
+He was --
+
+I mean, this was before
+there was anything
+
+called computer science.
+
+But he thought like a computer
+scientist did.
+
+In other words, he thought
+algorithmically.
+
+And he also thought in terms
+of discrete problems.
+
+And therefore, he looked for
+properties that these optimum
+
+codes should have.
+
+And it was neat.
+
+So, he started out
+with a limit.
+
+He said, an optimal code has to
+have the property that a p
+
+i is greater than p sub j.
+
+Then the optimal length
+associated with p sub i,
+
+namely the optimal length of the
+i'th codeword, had to be
+
+less than or equal to the length
+of the j'th codeword.
+
+And you can see this
+by saying, well,
+
+suppose that's not true.
+
+Suppose that p i is
+greater than p j.
+
+And also, li is greater
+than lj.
+
+And then you say, OK,
+take this situation.
+
+We will interchange those two
+codewords in the code.
+
+And we'll look at what that
+does to the average.
+
+And if you work that through,
+you find out that since what
+
+you've done is, you've shortened
+the codeword
+
+associated with this and
+lengthened the codeword
+
+associated with this.
+
+You have changed the average
+length to make it smaller.
+
+Now, let me warn you
+about something.
+
+When you start looking at these
+properties, the most
+
+confusing thing is what happens
+when two probabilities
+
+are the same, or when two
+lengths are the same.
+
+And I would advise you to just
+ignore that problem, until you
+
+get an idea of what's
+going on.
+
+Namely, assume that all
+lengths are different.
+
+All probabilities
+are different.
+
+And then it's easy to
+see what's going on.
+
+And when you get all done, go
+back and straighten out the
+
+cases where things are equal.
+
+And I think the notes
+do this carefully.
+
+If you read books on information
+theory, about half
+
+of them do it carefully, and
+about half of them don't.
+
+So you should be suspicious.
+
+But anyway, that's one of those
+trivialities that you
+
+just have to sort out
+for yourself.
+
+OK.
+
+The next lemma is optimal
+prefix-free codes are full.
+
+We talked about what
+a full code is.
+
+When you draw this binary graph
+for it, you don't have
+
+any nodes in a binary graph --
+
+you don't have any leaves
+that are not
+
+associated with codewords.
+
+Because if you do, we showed
+you that shortened the
+
+codeword of the part of
+the tree on the other
+
+side of that leaf.
+
+In other words, if you have
+something here, if this is a
+
+codeword and this is not a
+codeword, then you just get
+
+rid of this, and bring
+that back here.
+
+But this is a whole tree
+stemming off here, you do the
+
+same thing.
+
+You take this whole tree and you
+bring it into there, and
+
+you throw this away.
+
+So, optimal prefix-free
+codes are full.
+
+So far there's nothing
+to this.
+
+The next part of it is the
+sibling of a codeword.
+
+And what's a sibling?
+
+Well, we used to call
+it a brother.
+
+But then couldn't do that
+because we have to call it a
+
+brother or sister.
+
+And that got to difficult.
+
+So people invented the word
+sibling, to talk about a
+
+brother or a sister.
+
+So the sibling of a codeword
+for is the string form by
+
+changing the last bit.
+
+In other words, in this
+family tree here, the
+
+sibling of this is this.
+
+The sibling of this is this.
+
+The sibling of this is this.
+
+So, a leaf can have a sibling
+which is an intermediate node,
+
+and vice versa.
+
+So then he said, the sibling
+of a codeword is a string
+
+formed by changing
+the last bit.
+
+I think he probably said the
+brother, but, anyway.
+
+For optimality, the sibling of
+each maximum length codeword
+
+is another codeword.
+
+Now, that's a really
+simple one.
+
+If I make this a codeword, and
+this is the maximal length
+
+codeword in this code I'm
+talking about, this can't be
+
+an intermediate node because
+then there would have to be
+
+longer codewords.
+
+And it can't be empty because
+these optimal
+
+codes are all full.
+
+And therefore, this has
+to have a sibling
+
+which is also a codeword.
+
+So the longest codewords
+have to have siblings.
+
+Well, that's easy enough.
+
+Incidentally, one of the
+problems that you have in
+
+proving this sort of thing is,
+what happens if you have
+
+zero-probability letters.
+
+Well, we just get rid of that
+problem and say, well, there
+
+aren't any zero-probability
+letters.
+
+Because if we want to come up
+with a sensible model for
+
+something, we're not going
+to create a codeword for
+
+something that can't happen.
+
+So, there are no
+zero-probability letters in
+
+this alphabet.
+
+I mean, if you want to put them
+in, it just complicates
+
+the whole thing.
+
+And you can do it.
+
+Then, finally, there's this
+lemma which says, there is an
+
+optimal prefix-free code in
+which, after you order the
+
+probabilities of all of the
+messages, namely you order p1
+
+to be greater than or equal
+to p2, greater than or
+
+equal to p sub m.
+
+In other words, we just rename
+the letters in the alphabet,
+
+so that letter m is less likely
+than letter m minus 1,
+
+and so forth.
+
+Back to 1.
+
+1 is the most probable,
+m is the least likely.
+
+Well, we've already concluded
+that we want to assign the
+
+longest messages to the least
+probable codewords.
+
+And this says, take the two
+least probable codewords and
+
+we can always make an optimal
+code in which those two
+
+codewords are siblings.
+
+And the reason for that is, one
+of them is not going to be
+
+longer than the other or else
+you can shorten the code by
+
+interchanging things.
+
+So there is an optimal
+prefix-free code in which the
+
+codeword for m minus 1.
+
+And the codeword for
+m are maximal
+
+length and they're siblings.
+
+So the Huffman algorithm first
+combines these two.
+
+And then looks at the reduced
+tree with m minus 1 nodes.
+
+Let me show you an
+example of that.
+
+So it starts out.
+
+Here, I've ordered the
+probabilities associated with
+
+a set of symbols.
+
+The symbols are 1, 2, 3, 4, 5.
+
+The two least likely messages
+are 0.1 and 0.15.
+
+Obviously, I could've
+interchanged these
+
+two if I want to.
+
+But why interchange them?
+
+So I say, OK, the last digit
+on this one, I'm going to
+
+assign to be a 0.
+
+The last digit on this, I'm
+going to assign to be a 1.
+
+And the important thing is,
+I'm going to make them
+
+siblings in this tree.
+
+And what I'm going to do now,
+terribly complicated thing,
+
+instead of building a tree from
+left to right, I'm going
+
+to build a tree from
+right to left.
+
+So when I get all done with
+the tree it's going to
+
+come in like this.
+
+And what I'm doing is starting
+out at the end, to start to
+
+build the end of the tree.
+
+And what happens after I go
+through this first step is, I
+
+say, OK there is an
+optimal code.
+
+In which these two
+quantities are
+
+siblings of maximal length.
+
+I now want to form an optimal
+code for these
+
+probabilities here.
+
+So, I go back and
+I iterate again.
+
+And I said, OK, if I have these
+probabilities here,
+
+what's the optimal code.
+
+Well, I could reorder
+the things.
+
+But now I know that the only
+thing I'm interested in is the
+
+two least likely symbols in
+this new alphabet here.
+
+Which is 0.2 and 0.15.
+
+So I combine those together.
+
+I tie them together as
+siblings in this last
+
+generation, however
+it works out.
+
+So then I have an alphabet
+of size three.
+
+And then down here,
+I have these
+
+two things tied together.
+
+These two things
+tied together.
+
+So I have a node of
+probability 0.25.
+
+I have a node of probability
+0.35, and I have a node of
+
+probability 0.4.
+
+I take the two least likely,
+and I tie them together.
+
+And then I have two nodes left,
+one with probability 0.6
+
+and one with probability 0.4.
+
+And I tie them together.
+
+And, presto, I have my whole
+code, except for flipping it
+
+over, to go from left to
+right if you like.
+
+Codes that go from
+left and right,
+
+instead of right to left.
+
+OK.
+
+I have swindled you.
+
+How have I swindled you?
+
+I mean, I've swindled you a
+little bit by talking about
+
+these things that might
+be equal or not equal.
+
+And that's not important.
+
+You can sort that
+out on your own.
+
+There's a very important
+swindle I pulled.
+
+And what's that?
+
+What's very incomplete
+in this argument?
+
+This part is fine.
+
+Nothing wrong here.
+
+We have a lemma which says, you
+can find an optimal code
+
+by tying these two
+things together.
+
+Yeah?
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+combine those two
+[UNINTELLIGIBLE] combination.
+
+PROFESSOR: You're saying,
+how do I know to
+
+combine these two?
+
+OK, which means what?
+
+Yeah.
+
+AUDIENCE: [UNINTELLIGIBLE]
+you've just added the
+
+probabilities --
+
+PROFESSOR: I've just added
+those two probabilities.
+
+So I have a new ensemble where
+I have four probabilities,
+
+0.25, 0.15, 0.2, and 0.4.
+
+And that's fine.
+
+I still have these things.
+
+No, there's no independence
+involved here at all.
+
+I mean, I started out
+with five letters.
+
+Which are disjoined.
+
+I now have four letters
+that are disjoined.
+
+What have I done?
+
+Yeah.
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: Yes.
+
+Yeah.
+
+I have assumed, now, that once I
+get these four symbols, if I
+
+have those four symbols, I can
+form an optimal code for those
+
+four symbols in which these two
+symbols get tied together.
+
+But how do I know that an
+optimal code for this reduced
+
+set of probabilities is also
+an optimal code for the
+
+original problem?
+
+I have tied these two
+things together.
+
+I know there's an optimal code
+in which these two things are
+
+tied together.
+
+I then have four symbols.
+
+I want to find a code for
+those four symbols.
+
+But I assume that the optimal
+code for these four symbols,
+
+when I break apart these two
+things, gives me an optimal
+
+code for five symbols.
+
+That's the sort of thing I
+want you people to start
+
+catching onto immediately.
+
+I want you to start asking
+those nasty questions.
+
+And those nasty questions are
+the things that say, OK, how
+
+do I know that this works?
+
+In other words, you're not
+here to learn these
+
+algorithms.
+
+I can tell you what the
+algorithm is in an instant.
+
+You can do the algorithm.
+
+A computer can do the algorithm
+about three thousand
+
+times faster than you can.
+
+And you can be replaced by a
+computer, if you only learn
+
+the algorithms.
+
+You can program the algorithm.
+
+You can probably find the
+computer that can program the
+
+algorithm too.
+
+And there's no need to program
+it more than once.
+
+So that after you've done that,
+you are useless again.
+
+So the only thing that's
+worthwhile for you is to be
+
+able to spot these problems
+and to understand
+
+what's going on.
+
+So.
+
+How do I know that this first
+optimization leads to the
+
+second optimization.
+
+After combining these two least
+likely codewords, or
+
+siblings, we've gotten a reduced
+set of probabilities.
+
+In this problem here, what we've
+done, the reduced set of
+
+probabilities are 0.4,
+0.2, 0.15, and 0.25.
+
+Why does finding the optimal
+code for this reduced set
+
+result in an optimal code
+for the original set?
+
+That's really the question
+that we're asking.
+
+Well, it's not hard.
+
+If you take any code for the
+reduced set, let's call the
+
+reduced set x prime, set
+of probabilities.
+
+Let the expected length
+of that be l prime.
+
+It's not necessarily an optimal
+code, but it's any old
+
+code that I generate.
+
+Any old code I generate for L
+prime, I can now take that
+
+code for l prime and I can
+expand it out to a code for L.
+
+Namely, I have this code here
+this, this, this, and that's
+
+the expanded --
+
+and now I can expand it into a
+code for the original set, by
+
+adding on this and this,
+as leaves on this.
+
+This leaf here then becomes
+an intermediate node.
+
+And I add two extra
+leaves to it.
+
+OK, well, it's not hard.
+
+The expected length for this
+code, for these five letters,
+
+I claim, is equal to the
+expected length for this
+
+reduced code, this, this,
+this, and this.
+
+Plus one extra digit for this.
+
+Plus one extra digit for this.
+
+So the expected length for L is
+the expected length for L
+
+prime plus 0.15 plus 0.1.
+
+Which says the following: if I
+want to minimize this, and I
+
+know that this has to be equal
+to this, and these two numbers
+
+are fixed, I can't
+change them.
+
+I can minimize this,
+by minimizing this.
+
+And that's the final step
+in the whole argument.
+
+And what's peculiar
+is that everybody
+
+learns the Huffman algorithm.
+
+And what Huffman did, which was
+really very smart, was to
+
+sort out this issue.
+
+And I can teach this to a
+hundred classes, and nobody
+
+will ever point out to me that
+there's a logical flaw in the
+
+whole argument.
+
+And you can look at most books
+on information theory and they
+
+never point out that
+there's that
+
+logical flaw there, either.
+
+So, anyway, that's the end
+of Huffman's algorithm.
+
+You can see when you look at
+this that this is really an
+
+extraordinarily easy
+thing to do.
+
+I mean, you can take
+an alphabet of
+
+several thousand symbols.
+
+All you have to do
+is order them.
+
+Tie the least two
+likely together.
+
+Assign a 1 and a 0 to them.
+
+Then, stick that into an
+ordered list again.
+
+Take the two least probable.
+
+Tie them together.
+
+Stick it into an ordered
+list again.
+
+And, if you have some minimal
+knowledge of data structures,
+
+you can do this with essentially
+on the order of
+
+one operation for each letter
+in this alphabet.
+
+So it really isn't a
+very difficult sum.
+
+So here's an integer problem
+which is really easy to solve.
+
+And the way to solve it is to
+look at the problem in the
+
+opposite way from what
+everybody else has
+
+looked at it in.
+
+Does this say you want to
+ignore everything that
+
+everybody else has done,
+and go your own way?
+
+Not quite.
+
+But it says that's one of the
+things you ought to try, if
+
+you find that everybody is doing
+something one way and
+
+you can find another way to
+look at, that's very rich.
+
+It might turn out to be nothing
+but it might turn out
+
+to be something very
+worthwhile.
+
+Let's now talk about this
+quantity, entropy.
+
+And for every chance variable,
+x, if that chance variable, x,
+
+is discrete and has a finite
+number of elements in it, so
+
+I'm talking about a chance
+variable x, what's a chance
+
+variable have tagging
+along after it?
+
+It has a set of n probabilities
+
+tagging along after it.
+
+That's what a chance
+variable is.
+
+A chance variable is not
+just the alphabet.
+
+A chance variable is the
+alphabet plus the
+
+probabilities.
+
+That's why you then talk about
+it having an entropy.
+
+And the entropy is the expected
+value of, minus the
+
+logarithm, of this
+PMF function.
+
+So, in fact, this is an unusual
+statistic in the sense
+
+that it has nothing to do with
+the symbol values, and
+
+everything to do with just
+the probabilities
+
+of the symbol values.
+
+And as we go on, you'll see that
+in fact this is a very
+
+important property of it.
+
+And dealing with the logarithms
+of these symbol
+
+values is, in fact, a much more
+worthwhile thing to do
+
+than dealing with the
+probabilities of the symbols.
+
+Now, let me pause again and see
+if anybody can have any
+
+idea of why logarithms of
+probabilities might be more
+
+significant than
+probabilities.
+
+And think of what we're going
+to be doing here.
+
+We're taking a sequence
+of letters.
+
+When I take a sequence of
+letters, what's the
+
+probability of the sequence
+of letters?
+
+If they're IID.
+
+Namely, we're looking --
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: It's the product
+of those probabilities.
+
+Now, if you agree with me that
+the probability theory is
+
+concerned 50% with the law of
+large numbers and 50% with
+
+everything else all put
+together, why is the logarithm
+
+of a probability important?
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: You change your
+product to a sum, yes.
+
+If you have a product of
+probabilities, you can talk
+
+about a sum of the logarithms
+of probabilities.
+
+That's why entropy is important
+
+in statistical mechanics.
+
+It also is, fundamentally,
+the reason why entropy is
+
+important in information
+theory.
+
+Is because what you're almost
+always interested in is a
+
+product of probabilities.
+
+And when you're interested in a
+product of probabilities and
+
+you want to use the law of large
+numbers, you turn that
+
+product of probabilities into
+a sum of the logarithms of
+
+probabilities.
+
+Fundamental idea.
+
+Shannon took eight years
+sorting all this out.
+
+And Shannon was by far the
+smartest person I've ever met.
+
+I mean, the problems that we
+worry about, he just, bip.
+
+Solves it with no
+effort at all.
+
+This one took them a
+while to sort out.
+
+It also took him a while to sort
+out the fact that once he
+
+sorted this out, he could sort
+out all of the other problems.
+
+As far as communications
+was concerned.
+
+So was quite important.
+
+I mean, I can tell you
+one of the peculiar
+
+things about Shannon.
+
+Just from the first time I ever
+talked to him about a
+
+technical problem.
+
+I'd just become a faculty
+member here.
+
+And his office was about five
+doors down from mine.
+
+And one day I screwed up my
+courage to go down and talk to
+
+the guy about a problem
+I was working on.
+
+And I thought it was a
+really neat problem.
+
+It had all sorts of pieces to
+it, all sorts of bells and
+
+whistles on it.
+
+And I started to explain
+it to him.
+
+And he said, well, can we look
+at a slightly simpler case
+
+where you throw out this part of
+it, you throw out one bell.
+
+Then he'd throw out a whistle.
+
+Then he'd throw out a bell.
+
+And I was going along with
+this and saying,
+
+yeah, I guess we could.
+
+We could.
+
+We can throw out all of these
+things without really losing
+
+the essence of the problem.
+
+And, finally, I started
+to get discouraged.
+
+Because this really neat
+research problem, this really
+
+important research problem,
+was turning a toy problem
+
+which was almost trivial.
+
+It had nothing to do, it
+seemed, with anything.
+
+And finally we got down
+to a certain point.
+
+And I said, yeah, but this is
+trivial, the solution is this.
+
+And he said, yeah.
+
+And then we started putting
+back all the pieces.
+
+And his genius was, he knew
+which things to throw out.
+
+So that each of the things we
+threw out, we could put them
+
+back in again.
+
+When we got done, the research
+problem was trivial.
+
+And his genius was in finding
+the right trivial
+
+example to look at.
+
+So, in fact, what you always
+want to look at, in the
+
+communications field -- and in
+most fields, I think -- is
+
+finding the really simple way
+of looking at something.
+
+Which means you have to throw
+out most of the nonsense.
+
+So, in this case, it's looking
+at entropy, which is the
+
+logarithm of a probability
+assignment.
+
+And you want to look at that
+because the logarithm of a
+
+probability assignment lets
+you add the logarithms of
+
+probabilities.
+
+Use the law of large numbers.
+
+And then you can talk about
+sequences of elements.
+
+Properties of entropy.
+
+For a discrete random
+chance variable.
+
+We have m elements
+in the alphabet.
+
+First thing is that the entropy
+is always greater than
+
+or equal to 0.
+
+Why is that?
+
+I'll let you figure it out.
+
+Why is the logarithm of a
+problem, minus the logarithm
+
+of a probability, greater
+than or equal to 0?
+
+Why is it non-negative?
+
+Yeah.
+
+AUDIENCE: [UNINTELLIGIBLE]
+
+PROFESSOR: Probabilities
+are always less than
+
+or equal to 1, yes.
+
+So this quantity here
+is always greater
+
+than or equal to 0.
+
+Because the logarithm
+of 1 is equal to 0.
+
+We have a quality here if
+x is deterministic.
+
+Which is just a special
+case there.
+
+Where you have an ensemble
+of one element and it has
+
+probability 1.
+
+Or, in fact, at this point you
+could add in things which have
+
+zero probability.
+
+Well, that's a little
+bit tricky.
+
+Because you add in something
+that's zero probability.
+
+And the logarithm of
+0 is infinity.
+
+So you're dealing with the
+expected value of a bunch of
+
+infinities, which each occur
+with zero probability.
+
+And you're forced to say, well,
+I think that 0 times log
+
+of 0 is equal to 0.
+
+And in fact, epsilon times log
+of episilon goes to 0 as
+
+epsilon goes to 0.
+
+But you save yourself a lot of
+worry by just leaving out
+
+things of zero probability.
+
+So H of x is greater
+than or equal to 0.
+
+We have equality if x
+is deterministic.
+
+H of x is less than or
+equal to log of m.
+
+The quality, if x
+is equiprobable.
+
+And how do I know that?
+
+I look at this again.
+
+I'm not going to prove it here
+but, essentially, this follows
+
+from saying that the natural
+logarithm of something is less
+
+than or equal to that
+something minus 1.
+
+And you take the difference of
+the entropy, and log of m.
+
+And, presto, it gives you the
+result that you want.
+
+So you've got the most entropy,
+if everything is
+
+equiprobable.
+
+For any code satisfying the
+Kraft inequality, the entropy
+
+is less than or equal
+to L bar.
+
+Well, that's what we
+already proved.
+
+Mainly in the middle of the
+lecture, we showed that for
+
+any code to satisfied the Kraft
+inequality, the entropy
+
+was always less than or equal to
+L bar, because the entropy
+
+is what you get if you minimize
+the expected length
+
+without the integer
+constraint.
+
+And L bar is what you get --
+well, L bar min is what you
+
+get when you minimize it with
+the integer constraint.
+
+I mean, you don't bother
+about minimizing it.
+
+You get something bigger
+than L min.
+
+So this is less than or equal to
+the length of any codeword.
+
+For the very best codeword, for
+the very best code, the
+
+expected value of the minimum
+is less than or equal to the
+
+entropy plus y.
+
+And you get that just by adding
+to each non-integer
+
+length the ceiling function.
+
+Which gives you, at most, one
+extra digit for each codeword.
+
+Now, here's the more
+interesting one.
+
+For independent chance
+variables, x and y, here's
+
+where the nice part about
+notation comes along.
+
+What's the entropy of x y?
+
+Well, what do I mean
+by x y first?
+
+I have a chance variable, x.
+
+And this chance variable x has
+an alphabet associated with
+
+it. x1 up to x sub m.
+
+I have a chance variable y.
+
+It has an alphabet associated
+with it.
+
+What's the sample space, what's
+the set of events
+
+corresponding to the chance
+variable x y?
+
+By x y, I mean a chance variable
+whose elements are
+
+the possible values
+of both x and y.
+
+So, I'm talking about the joint
+ensemble of x and y.
+
+I have a bunch of possible
+values for that.
+
+And those possible values, if
+I have m possibilities for
+
+each, I have m squared
+possible values
+
+for the two of them.
+
+So I'm talking about the
+expected value of minus the
+
+logarithm of the probability
+of x and y.
+
+In other words, I am trying
+to take the --
+
+let me write it out.
+
+I'm probably given conniptions
+to -- no?
+
+OK.
+
+I want to take p of x y of
+symbol x y, times minus the
+
+logarithm to the base 2
+of p sub x y of x y.
+
+That's what this means
+if I write it out.
+
+Well, this probability here is
+p sub x of little x, times p
+
+sub y of little y.
+
+Why is that?
+
+Because I'm assuming
+that they're
+
+independent of each other.
+
+And, therefore, the probability
+of two of them is
+
+the product of the
+probabilities, times minus log
+
+to the base 2.
+
+So if p sub x of x minus
+logarithm to the base 2 of p
+
+sub y of y.
+
+And I'm summing this over
+all x and all y.
+
+And the more sophisticated
+way to write this --
+
+things I say in lecture, you
+don't have to copy down
+
+because they're always
+in the notes.
+
+If they're not in the
+notes, it's probably
+
+wrong anyway, so.
+
+So this expected value is
+expected value of the
+
+logarithm of the probability
+of x y.
+
+Which is the expected value
+of the logarithm of p of
+
+x times p of y.
+
+And, since I have a logarithm
+of a product, that's the
+
+expected value of minus log p
+of x minus log p of y, which
+
+is the entropy of x plus
+the entropy of y.
+
+In other words, when I have a
+joint ensemble of even more
+
+independent quantities, The
+entropy the sequence is equal
+
+to the sum of the entropies of
+the individual elements in
+
+that sequence.
+
+Well, that's all I wanted
+to talk about today.
+
+If any of you have any questions
+to ask, you should
+
+ask them now.
+
+I went through Huffman coding
+pretty quickly, because it's
+
+something where you have
+to do some exercises on
+
+it to sort it out.
+
+And I didn't want to do
+any more than that.
\ No newline at end of file
diff --git a/o8Zdk_3wVSo.txt b/o8Zdk_3wVSo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c7cc2b457baf1a22c64e8ca2e09e41396cd524a5
--- /dev/null
+++ b/o8Zdk_3wVSo.txt
@@ -0,0 +1,324 @@
+Let us examine how to interpret
+the model we developed.
+
+One of the things
+we should look after
+
+is that there might be what
+is called multicollinearity.
+
+Multicollinearity occurs
+when the various independent
+
+variables are
+correlated, and this
+
+might confuse the coefficients--
+the betas-- in the model.
+
+So tests to address that involve
+checking the correlations
+
+of independent variables.
+
+If they are
+excessively high, this
+
+would mean that there
+might be multicollinearity,
+
+and you have to potentially
+revisit the model,
+
+as well as whether the signs
+of the coefficients make sense.
+
+Is the coefficient beta
+positive or negative?
+
+If it agrees with intuition,
+then multicollinearity
+
+has not been a problem,
+but if intuition suggests
+
+a different sign, this might
+be a sign of multicollinearity.
+
+The next important
+element is significance.
+
+So how do we
+interpret the results,
+
+and how do we understand whether
+we have a good model or not?
+
+For that purpose,
+let's take a look
+
+at what is called Area Under
+the Curve, or AUC for short.
+
+So the Area Under the Curve
+shows an absolute measure
+
+of quality of prediction-- in
+this particular case, 77.5%,
+
+which means that, given that
+the perfect score is 100%,
+
+so this is like a B,
+whereas, as we'll see later,
+
+a 50% score, which
+is pure guessing,
+
+is a 50% rate of success.
+
+So the area under the curve
+gives an absolute measure
+
+of quality, and it's less
+affected by various benchmarks.
+
+So it illustrates how
+accurate the model
+
+is on a more absolute sense.
+
+So what is a good AUC?
+
+The area on the right
+shows the maximum possible
+
+of a perfect prediction,
+whereas the area on this
+
+curve now-- it is 0.5,
+and it's pure guessing.
+
+Other outcome measures that
+are important for us to discuss
+
+is the so-called
+confusion matrix.
+
+So the matrix here is formulas
+for the various terms we use.
+
+The actual class is 0--
+means, in our example,
+
+good quality of care,
+and actual class = 1
+
+means poor quality of care,
+whereas the predicted class =
+
+0 means that will
+predict good quality,
+
+and the predicted class = 1 mean
+that we predict poor quality.
+
+So we define true
+negatives, short by TN.
+
+False positives, short by FP.
+
+False negatives, FN, and
+true positives by TP.
+
+So if N is the number
+of observations,
+
+the overall accuracy
+is basically
+
+the number of true negatives
+and true positives divided by N.
+
+It's basically the terms
+in the diagonal of this two
+
+by two matrix divided by
+the total observations.
+
+The overall error rate is
+the terms off-diagonal--
+
+the false positives, plus
+the false negatives, divided
+
+by the total number
+of observations.
+
+That's the overall
+measure of an error rate.
+
+An important component is
+the so-called sensitivity,
+
+and sensitivity is TP, the
+true positives, whenever
+
+we predict poor
+quality, and indeed it
+
+is poor quality, divided by TP,
+these true positives, plus FN,
+
+which is the total number
+of cases of poor quality.
+
+So this is the total
+number of times
+
+that we predict poor
+quality, and it is, indeed,
+
+poor quality, versus the
+total number of times
+
+the actual quality
+is, in fact, poor.
+
+False negative rate is FN,
+the number of false negatives,
+
+divided by the number
+of true positives,
+
+plus the number of
+false negatives.
+
+And specificity is
+TN, true negatives,
+
+the number of times we
+predict the quality is good,
+
+and, in fact, the
+quality is good,
+
+divided by this number,
+TN, plus false positives.
+
+So specificity is
+the number of times
+
+we predict the quality is
+good, and it is indeed good,
+
+versus the total times
+we have good quality,
+
+and the false
+positive error rate is
+
+1 minus the specificity.
+
+So in this particular example
+that we have discussed,
+
+quality of care, just
+like in linear regression,
+
+we want to make
+predictions on a test set
+
+to compute
+out-of-sample metrics.
+
+We develop the logistic
+regression model using data,
+
+but would like to make
+predictions out-of-sample.
+
+So in our test, we
+utilized 32 cases,
+
+and the R command that
+makes the statements
+
+about the quality of a
+prediction out-of-sample
+
+is illustrated
+here in the slide.
+
+So in that way, we
+make predictions
+
+about probabilities,
+of course, simply
+
+because logistic regression
+makes predictions
+
+about probabilities, and
+then we transform them
+
+to a binary outcome--
+the quality is good,
+
+or the quality is poor--
+using a threshold.
+
+In this particular example, we
+used a threshold value of 0.3,
+
+and in doing so, we obtain the
+following confusion matrix.
+
+So there were, as I
+mentioned, there are 32 cases,
+
+out of which 24 of them
+are actually good care,
+
+and eight of them are
+actually poor care.
+
+We observe that the overall
+accuracy of the model
+
+is 19 plus 6, is 25, over 32.
+
+The false positive rate is,
+in this case, 5 over 24,
+
+19 plus 5, whereas the true
+positive rate is 6 out of 8-- 6
+
+plus 2.
+
+Notice, if you compare this
+model with making always--
+
+let's say one
+alternative is to say
+
+we predict good
+care all the time.
+
+In that situation,
+we will be correct 19
+
+plus 5, 24 times, versus
+25 times, in our case.
+
+But notice that predicting
+always good care
+
+does not capture the dynamics
+of what is happening,
+
+versus the logistic
+regression model that
+
+is far more intelligent in
+capturing these effects.
\ No newline at end of file
diff --git a/ofgusnhQ07Q.txt b/ofgusnhQ07Q.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7c419ae71e89040115d6e8324e85f08aaf132783
--- /dev/null
+++ b/ofgusnhQ07Q.txt
@@ -0,0 +1,1187 @@
+align:start position:0%
+ 
+let's consider the motion of a car on a
+
+ align:start position:0%
+let's consider the motion of a car on a
+ 
+
+ align:start position:0%
+let's consider the motion of a car on a
+circular track and the track is
+
+ align:start position:0%
+circular track and the track is
+ 
+
+ align:start position:0%
+circular track and the track is
+frictionless and it's also banked so
+
+ align:start position:0%
+frictionless and it's also banked so
+ 
+
+ align:start position:0%
+frictionless and it's also banked so
+this is the overhead view of our
+
+ align:start position:0%
+this is the overhead view of our
+ 
+
+ align:start position:0%
+this is the overhead view of our
+circular track it has a radius R and
+
+ align:start position:0%
+circular track it has a radius R and
+ 
+
+ align:start position:0%
+circular track it has a radius R and
+here's our car moving at a constant
+
+ align:start position:0%
+here's our car moving at a constant
+ 
+
+ align:start position:0%
+here's our car moving at a constant
+velocity now from the side view when we
+
+ align:start position:0%
+velocity now from the side view when we
+ 
+
+ align:start position:0%
+velocity now from the side view when we
+want to look at that Bank turn let's
+
+ align:start position:0%
+want to look at that Bank turn let's
+ 
+
+ align:start position:0%
+want to look at that Bank turn let's
+draw a side view so here's our side view
+
+ align:start position:0%
+draw a side view so here's our side view
+ 
+
+ align:start position:0%
+draw a side view so here's our side view
+and the car is moving with the velocity
+
+ align:start position:0%
+and the car is moving with the velocity
+ 
+
+ align:start position:0%
+and the car is moving with the velocity
+into the plane of the figure now this
+
+ align:start position:0%
+into the plane of the figure now this
+ 
+
+ align:start position:0%
+into the plane of the figure now this
+surface here is frictionless and what
+
+ align:start position:0%
+surface here is frictionless and what
+ 
+
+ align:start position:0%
+surface here is frictionless and what
+we'd like to do is find out what speed
+
+ align:start position:0%
+we'd like to do is find out what speed
+ 
+
+ align:start position:0%
+we'd like to do is find out what speed
+the car can move such that it doesn't
+
+ align:start position:0%
+the car can move such that it doesn't
+ 
+
+ align:start position:0%
+the car can move such that it doesn't
+slide up or down the inclined plane so
+
+ align:start position:0%
+slide up or down the inclined plane so
+ 
+
+ align:start position:0%
+slide up or down the inclined plane so
+how should we analyze that well our
+
+ align:start position:0%
+how should we analyze that well our
+ 
+
+ align:start position:0%
+how should we analyze that well our
+approach will be to apply Newton's
+
+ align:start position:0%
+approach will be to apply Newton's
+ 
+
+ align:start position:0%
+approach will be to apply Newton's
+second law x' now what's very important
+
+ align:start position:0%
+second law x' now what's very important
+ 
+
+ align:start position:0%
+second law x' now what's very important
+to realize is this is circular motion
+
+ align:start position:0%
+to realize is this is circular motion
+ 
+
+ align:start position:0%
+to realize is this is circular motion
+and for circular motion we know that the
+
+ align:start position:0%
+and for circular motion we know that the
+ 
+
+ align:start position:0%
+and for circular motion we know that the
+car is accelerating towards the center
+
+ align:start position:0%
+car is accelerating towards the center
+ 
+
+ align:start position:0%
+car is accelerating towards the center
+of the circle now from the side view
+
+ align:start position:0%
+of the circle now from the side view
+ 
+
+ align:start position:0%
+of the circle now from the side view
+towards the center of the circle is in
+
+ align:start position:0%
+towards the center of the circle is in
+ 
+
+ align:start position:0%
+towards the center of the circle is in
+this direction so the car is
+
+ align:start position:0%
+this direction so the car is
+ 
+
+ align:start position:0%
+this direction so the car is
+accelerating radially inward and that
+
+ align:start position:0%
+accelerating radially inward and that
+ 
+
+ align:start position:0%
+accelerating radially inward and that
+will guide how we choose our coordinate
+
+ align:start position:0%
+will guide how we choose our coordinate
+ 
+
+ align:start position:0%
+will guide how we choose our coordinate
+system and so we can then write our free
+
+ align:start position:0%
+system and so we can then write our free
+ 
+
+ align:start position:0%
+system and so we can then write our free
+body force diagram so let's begin with
+
+ align:start position:0%
+body force diagram so let's begin with
+ 
+
+ align:start position:0%
+body force diagram so let's begin with
+the analysis so we don't need to see the
+
+ align:start position:0%
+the analysis so we don't need to see the
+ 
+
+ align:start position:0%
+the analysis so we don't need to see the
+overhead view anymore so I'll just
+
+ align:start position:0%
+overhead view anymore so I'll just
+ 
+
+ align:start position:0%
+overhead view anymore so I'll just
+remove that and then we can start
+
+ align:start position:0%
+remove that and then we can start
+ 
+
+ align:start position:0%
+remove that and then we can start
+drawing this is what we can refer to as
+
+ align:start position:0%
+drawing this is what we can refer to as
+ 
+
+ align:start position:0%
+drawing this is what we can refer to as
+our acceleration diagram and now let's
+
+ align:start position:0%
+our acceleration diagram and now let's
+ 
+
+ align:start position:0%
+our acceleration diagram and now let's
+draw the force diagram on the car as our
+
+ align:start position:0%
+draw the force diagram on the car as our
+ 
+
+ align:start position:0%
+draw the force diagram on the car as our
+choice of system so here's our angle fee
+
+ align:start position:0%
+choice of system so here's our angle fee
+ 
+
+ align:start position:0%
+choice of system so here's our angle fee
+because the acceleration was inward
+
+ align:start position:0%
+because the acceleration was inward
+ 
+
+ align:start position:0%
+because the acceleration was inward
+we're going to choose a radially outward
+
+ align:start position:0%
+we're going to choose a radially outward
+ 
+
+ align:start position:0%
+we're going to choose a radially outward
+coordinate and a vertical coordinate K
+
+ align:start position:0%
+coordinate and a vertical coordinate K
+ 
+
+ align:start position:0%
+coordinate and a vertical coordinate K
+add up notice that this is different
+
+ align:start position:0%
+add up notice that this is different
+ 
+
+ align:start position:0%
+add up notice that this is different
+than just a mass on a fixed inclined
+
+ align:start position:0%
+than just a mass on a fixed inclined
+ 
+
+ align:start position:0%
+than just a mass on a fixed inclined
+plane where we used unit vectors up and
+
+ align:start position:0%
+plane where we used unit vectors up and
+ 
+
+ align:start position:0%
+plane where we used unit vectors up and
+down the inclined plane the reason we
+
+ align:start position:0%
+down the inclined plane the reason we
+ 
+
+ align:start position:0%
+down the inclined plane the reason we
+choose our unit vectors like that to
+
+ align:start position:0%
+choose our unit vectors like that to
+ 
+
+ align:start position:0%
+choose our unit vectors like that to
+emphasize it again is we already know
+
+ align:start position:0%
+emphasize it again is we already know
+ 
+
+ align:start position:0%
+emphasize it again is we already know
+this is constrained motion it's circular
+
+ align:start position:0%
+this is constrained motion it's circular
+ 
+
+ align:start position:0%
+this is constrained motion it's circular
+motion
+
+ align:start position:0%
+motion
+ 
+
+ align:start position:0%
+motion
+now what are the free body what are the
+
+ align:start position:0%
+now what are the free body what are the
+ 
+
+ align:start position:0%
+now what are the free body what are the
+forces on the car well there's the
+
+ align:start position:0%
+forces on the car well there's the
+ 
+
+ align:start position:0%
+forces on the car well there's the
+normal force the plane on the car and
+
+ align:start position:0%
+normal force the plane on the car and
+ 
+
+ align:start position:0%
+normal force the plane on the car and
+the gravitational force
+
+ align:start position:0%
+the gravitational force
+ 
+
+ align:start position:0%
+the gravitational force
+now here whenever you're doing problems
+
+ align:start position:0%
+now here whenever you're doing problems
+ 
+
+ align:start position:0%
+now here whenever you're doing problems
+like this remember that the trig is
+
+ align:start position:0%
+like this remember that the trig is
+ 
+
+ align:start position:0%
+like this remember that the trig is
+crucial to get these angles right so
+
+ align:start position:0%
+crucial to get these angles right so
+ 
+
+ align:start position:0%
+crucial to get these angles right so
+that's the and that's C and that's our
+
+ align:start position:0%
+that's the and that's C and that's our
+ 
+
+ align:start position:0%
+that's the and that's C and that's our
+free body force diagram and now we can
+
+ align:start position:0%
+free body force diagram and now we can
+ 
+
+ align:start position:0%
+free body force diagram and now we can
+write down Newton's second law so we'll
+
+ align:start position:0%
+write down Newton's second law so we'll
+ 
+
+ align:start position:0%
+write down Newton's second law so we'll
+start out with our usual approach and we
+
+ align:start position:0%
+start out with our usual approach and we
+ 
+
+ align:start position:0%
+start out with our usual approach and we
+have two directions that we have to
+
+ align:start position:0%
+have two directions that we have to
+ 
+
+ align:start position:0%
+have two directions that we have to
+consider so in the radial direction
+
+ align:start position:0%
+consider so in the radial direction
+ 
+
+ align:start position:0%
+consider so in the radial direction
+there's an inward component of the
+
+ align:start position:0%
+there's an inward component of the
+ 
+
+ align:start position:0%
+there's an inward component of the
+normal force like that and that's
+
+ align:start position:0%
+normal force like that and that's
+ 
+
+ align:start position:0%
+normal force like that and that's
+opposite the angle so it's pointing
+
+ align:start position:0%
+opposite the angle so it's pointing
+ 
+
+ align:start position:0%
+opposite the angle so it's pointing
+opposite our direction so we have minus
+
+ align:start position:0%
+opposite our direction so we have minus
+ 
+
+ align:start position:0%
+opposite our direction so we have minus
+and sine fee the gravitational force is
+
+ align:start position:0%
+and sine fee the gravitational force is
+ 
+
+ align:start position:0%
+and sine fee the gravitational force is
+only in the negative K out direction and
+
+ align:start position:0%
+only in the negative K out direction and
+ 
+
+ align:start position:0%
+only in the negative K out direction and
+we know that the acceleration is inward
+
+ align:start position:0%
+we know that the acceleration is inward
+ 
+
+ align:start position:0%
+we know that the acceleration is inward
+and so there's a minus sign we have the
+
+ align:start position:0%
+and so there's a minus sign we have the
+ 
+
+ align:start position:0%
+and so there's a minus sign we have the
+mass and the constraint for circular
+
+ align:start position:0%
+mass and the constraint for circular
+ 
+
+ align:start position:0%
+mass and the constraint for circular
+motion is that that's B squared over R
+
+ align:start position:0%
+motion is that that's B squared over R
+ 
+
+ align:start position:0%
+motion is that that's B squared over R
+where R was the radius of that circle
+
+ align:start position:0%
+where R was the radius of that circle
+ 
+
+ align:start position:0%
+where R was the radius of that circle
+this can be thought of as a central
+
+ align:start position:0%
+this can be thought of as a central
+ 
+
+ align:start position:0%
+this can be thought of as a central
+central point now for the K hat
+
+ align:start position:0%
+central point now for the K hat
+ 
+
+ align:start position:0%
+central point now for the K hat
+direction we have a component of the
+
+ align:start position:0%
+direction we have a component of the
+ 
+
+ align:start position:0%
+direction we have a component of the
+normal force that's pointing up I'll
+
+ align:start position:0%
+normal force that's pointing up I'll
+ 
+
+ align:start position:0%
+normal force that's pointing up I'll
+just draw that that's adjacent to the
+
+ align:start position:0%
+just draw that that's adjacent to the
+ 
+
+ align:start position:0%
+just draw that that's adjacent to the
+angle so we have plus + cosine fee and
+
+ align:start position:0%
+angle so we have plus + cosine fee and
+ 
+
+ align:start position:0%
+angle so we have plus + cosine fee and
+we have the gravitational force downward
+
+ align:start position:0%
+we have the gravitational force downward
+ 
+
+ align:start position:0%
+we have the gravitational force downward
+minus mg and as far as the vertical
+
+ align:start position:0%
+minus mg and as far as the vertical
+ 
+
+ align:start position:0%
+minus mg and as far as the vertical
+direction goes because the car is going
+
+ align:start position:0%
+direction goes because the car is going
+ 
+
+ align:start position:0%
+direction goes because the car is going
+in a circle there is no acceleration up
+
+ align:start position:0%
+in a circle there is no acceleration up
+ 
+
+ align:start position:0%
+in a circle there is no acceleration up
+or down in the vertical direction again
+
+ align:start position:0%
+or down in the vertical direction again
+ 
+
+ align:start position:0%
+or down in the vertical direction again
+that's a constraint in this problem
+
+ align:start position:0%
+that's a constraint in this problem
+ 
+
+ align:start position:0%
+that's a constraint in this problem
+that's equal to zero
+
+ align:start position:0%
+that's equal to zero
+ 
+
+ align:start position:0%
+that's equal to zero
+so in this problem this is the side that
+
+ align:start position:0%
+so in this problem this is the side that
+ 
+
+ align:start position:0%
+so in this problem this is the side that
+we know and we're trying to figure out
+
+ align:start position:0%
+we know and we're trying to figure out
+ 
+
+ align:start position:0%
+we know and we're trying to figure out
+up to the speed V now how do we analyze
+
+ align:start position:0%
+up to the speed V now how do we analyze
+ 
+
+ align:start position:0%
+up to the speed V now how do we analyze
+this problem well you can see that if I
+
+ align:start position:0%
+this problem well you can see that if I
+ 
+
+ align:start position:0%
+this problem well you can see that if I
+write my two equations is and sine fee
+
+ align:start position:0%
+write my two equations is and sine fee
+ 
+
+ align:start position:0%
+write my two equations is and sine fee
+equals MV squared over R + and cosine
+
+ align:start position:0%
+equals MV squared over R + and cosine
+ 
+
+ align:start position:0%
+equals MV squared over R + and cosine
+fee equals mg we have two equations we
+
+ align:start position:0%
+fee equals mg we have two equations we
+ 
+
+ align:start position:0%
+fee equals mg we have two equations we
+have two unknowns vnn many times people
+
+ align:start position:0%
+have two unknowns vnn many times people
+ 
+
+ align:start position:0%
+have two unknowns vnn many times people
+just solve for n
+
+ align:start position:0%
+just solve for n
+ 
+
+ align:start position:0%
+just solve for n
+and try to find the equation and then
+
+ align:start position:0%
+and try to find the equation and then
+ 
+
+ align:start position:0%
+and try to find the equation and then
+substitute it in but you're also allowed
+
+ align:start position:0%
+substitute it in but you're also allowed
+ 
+
+ align:start position:0%
+substitute it in but you're also allowed
+to divide two equations and that's much
+
+ align:start position:0%
+to divide two equations and that's much
+ 
+
+ align:start position:0%
+to divide two equations and that's much
+easier the masses cancel and we get the
+
+ align:start position:0%
+easier the masses cancel and we get the
+ 
+
+ align:start position:0%
+easier the masses cancel and we get the
+relationship that tan P is V squared
+
+ align:start position:0%
+relationship that tan P is V squared
+ 
+
+ align:start position:0%
+relationship that tan P is V squared
+over R G and so we have our result that
+
+ align:start position:0%
+over R G and so we have our result that
+ 
+
+ align:start position:0%
+over R G and so we have our result that
+the speed that the car can travel on a
+
+ align:start position:0%
+the speed that the car can travel on a
+ 
+
+ align:start position:0%
+the speed that the car can travel on a
+frictionless inclined plane and maintain
+
+ align:start position:0%
+frictionless inclined plane and maintain
+ 
+
+ align:start position:0%
+frictionless inclined plane and maintain
+uniform circular motion is exactly the
+
+ align:start position:0%
+uniform circular motion is exactly the
+ 
+
+ align:start position:0%
+uniform circular motion is exactly the
+square root of RG 10 feet and that's how
+
+ align:start position:0%
+square root of RG 10 feet and that's how
+ 
+
+ align:start position:0%
+square root of RG 10 feet and that's how
+we analyze the motion of this car in a
+
+ align:start position:0%
+we analyze the motion of this car in a
+ 
+
+ align:start position:0%
+we analyze the motion of this car in a
+bank turn what we would now like to
+
+ align:start position:0%
+bank turn what we would now like to
+ 
+
+ align:start position:0%
+bank turn what we would now like to
+think about is what would happen if
+
+ align:start position:0%
+think about is what would happen if
+ 
+
+ align:start position:0%
+think about is what would happen if
+you're traveling faster or slower than
+
+ align:start position:0%
+you're traveling faster or slower than
+ 
+
+ align:start position:0%
+you're traveling faster or slower than
+this speed so suppose we have V prime
+
+ align:start position:0%
+this speed so suppose we have V prime
+ 
+
+ align:start position:0%
+this speed so suppose we have V prime
+bigger than the speed now what what that
+
+ align:start position:0%
+bigger than the speed now what what that
+ 
+
+ align:start position:0%
+bigger than the speed now what what that
+means is that the car is going faster
+
+ align:start position:0%
+means is that the car is going faster
+ 
+
+ align:start position:0%
+means is that the car is going faster
+and the new equilibrium if you asked
+
+ align:start position:0%
+and the new equilibrium if you asked
+ 
+
+ align:start position:0%
+and the new equilibrium if you asked
+what would the radius be such that
+
+ align:start position:0%
+what would the radius be such that
+ 
+
+ align:start position:0%
+what would the radius be such that
+traveling at V prime the car undergoes
+
+ align:start position:0%
+traveling at V prime the car undergoes
+ 
+
+ align:start position:0%
+traveling at V prime the car undergoes
+circular motion the prime would be equal
+
+ align:start position:0%
+circular motion the prime would be equal
+ 
+
+ align:start position:0%
+circular motion the prime would be equal
+to R prime G tan fee and so in order to
+
+ align:start position:0%
+to R prime G tan fee and so in order to
+ 
+
+ align:start position:0%
+to R prime G tan fee and so in order to
+go at this speed you have to go at a
+
+ align:start position:0%
+go at this speed you have to go at a
+ 
+
+ align:start position:0%
+go at this speed you have to go at a
+greater radius now what does that mean
+
+ align:start position:0%
+greater radius now what does that mean
+ 
+
+ align:start position:0%
+greater radius now what does that mean
+well that means that if the car is
+
+ align:start position:0%
+well that means that if the car is
+ 
+
+ align:start position:0%
+well that means that if the car is
+traveling at V so it's in this circular
+
+ align:start position:0%
+traveling at V so it's in this circular
+ 
+
+ align:start position:0%
+traveling at V so it's in this circular
+motion and now the driver increases the
+
+ align:start position:0%
+motion and now the driver increases the
+ 
+
+ align:start position:0%
+motion and now the driver increases the
+speed to V Prime the car will start to
+
+ align:start position:0%
+speed to V Prime the car will start to
+ 
+
+ align:start position:0%
+speed to V Prime the car will start to
+slide up the inclined plane remember
+
+ align:start position:0%
+slide up the inclined plane remember
+ 
+
+ align:start position:0%
+slide up the inclined plane remember
+it's frictionless until it reaches a as
+
+ align:start position:0%
+it's frictionless until it reaches a as
+ 
+
+ align:start position:0%
+it's frictionless until it reaches a as
+it starts slide up the inclined plane it
+
+ align:start position:0%
+it starts slide up the inclined plane it
+ 
+
+ align:start position:0%
+it starts slide up the inclined plane it
+will get to this new radius R prime but
+
+ align:start position:0%
+will get to this new radius R prime but
+ 
+
+ align:start position:0%
+will get to this new radius R prime but
+because a car will have a little nurse'
+
+ align:start position:0%
+because a car will have a little nurse'
+ 
+
+ align:start position:0%
+because a car will have a little nurse'
+it will overshoot that speed that radius
+
+ align:start position:0%
+it will overshoot that speed that radius
+ 
+
+ align:start position:0%
+it will overshoot that speed that radius
+and then it will start to come back down
+
+ align:start position:0%
+and then it will start to come back down
+ 
+
+ align:start position:0%
+and then it will start to come back down
+the inclined plane and it will oscillate
+
+ align:start position:0%
+the inclined plane and it will oscillate
+ 
+
+ align:start position:0%
+the inclined plane and it will oscillate
+about that point it won't be sinusoidal
+
+ align:start position:0%
+about that point it won't be sinusoidal
+ 
+
+ align:start position:0%
+about that point it won't be sinusoidal
+oscillations but there'll be a periodic
+
+ align:start position:0%
+oscillations but there'll be a periodic
+ 
+
+ align:start position:0%
+oscillations but there'll be a periodic
+oscillation about this new radius R
+
+ align:start position:0%
+oscillation about this new radius R
+ 
+
+ align:start position:0%
+oscillation about this new radius R
+the same thing too if we have the double
+
+ align:start position:0%
+the same thing too if we have the double
+ 
+
+ align:start position:0%
+the same thing too if we have the double
+Prime less than V then the double prime
+
+ align:start position:0%
+Prime less than V then the double prime
+ 
+
+ align:start position:0%
+Prime less than V then the double prime
+is equal to our double prime G tan fee
+
+ align:start position:0%
+is equal to our double prime G tan fee
+ 
+
+ align:start position:0%
+is equal to our double prime G tan fee
+now remember this double prime is not
+
+ align:start position:0%
+now remember this double prime is not
+ 
+
+ align:start position:0%
+now remember this double prime is not
+two derivatives I'm just using that as a
+
+ align:start position:0%
+two derivatives I'm just using that as a
+ 
+
+ align:start position:0%
+two derivatives I'm just using that as a
+notation to indicate different speeds so
+
+ align:start position:0%
+notation to indicate different speeds so
+ 
+
+ align:start position:0%
+notation to indicate different speeds so
+if the car is going along at speed V and
+
+ align:start position:0%
+if the car is going along at speed V and
+ 
+
+ align:start position:0%
+if the car is going along at speed V and
+slows down what will happen is the new
+
+ align:start position:0%
+slows down what will happen is the new
+ 
+
+ align:start position:0%
+slows down what will happen is the new
+equilibrium radius is smaller so the car
+
+ align:start position:0%
+equilibrium radius is smaller so the car
+ 
+
+ align:start position:0%
+equilibrium radius is smaller so the car
+slides down the inclined plane until it
+
+ align:start position:0%
+slides down the inclined plane until it
+ 
+
+ align:start position:0%
+slides down the inclined plane until it
+gets to our double prime it turns out
+
+ align:start position:0%
+gets to our double prime it turns out
+ 
+
+ align:start position:0%
+gets to our double prime it turns out
+that it will overshoot that a little bit
+
+ align:start position:0%
+that it will overshoot that a little bit
+ 
+
+ align:start position:0%
+that it will overshoot that a little bit
+and then start to move up and again it
+
+ align:start position:0%
+and then start to move up and again it
+ 
+
+ align:start position:0%
+and then start to move up and again it
+will oscillate around this new
+
+ align:start position:0%
+will oscillate around this new
+ 
+
+ align:start position:0%
+will oscillate around this new
+equilibrium length so on a frictionless
+
+ align:start position:0%
+equilibrium length so on a frictionless
+ 
+
+ align:start position:0%
+equilibrium length so on a frictionless
+inclined plane if you go faster this
+
+ align:start position:0%
+inclined plane if you go faster this
+ 
+
+ align:start position:0%
+inclined plane if you go faster this
+speed the car slides up if you go slower
+
+ align:start position:0%
+speed the car slides up if you go slower
+ 
+
+ align:start position:0%
+speed the car slides up if you go slower
+than the speed the car slides down
\ No newline at end of file
diff --git a/ojrj-UVh9N4.txt b/ojrj-UVh9N4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0029837024075e9930160e62565221b1fe5912fa
--- /dev/null
+++ b/ojrj-UVh9N4.txt
@@ -0,0 +1,956 @@
+Monomer of nucleic acids is
+called a nucleotide, which I
+
+will abbreviate NTIDE.
+
+And a nucleotide comprises
+three parts--
+
+a phosphate, a sugar,
+and a base.
+
+Phosphate, sugar, base --that we
+will abbreviate P-S-B. The
+
+polymer of nucleotides makes up
+ribonucleic acid, RNA; or
+
+deoxyribonucleic acid, DNA.
+
+You need to know the full
+names of those.
+
+I'm not going to
+write them out.
+
+And those are all
+polynucleotides.
+
+And the way that polynucleotides
+are put
+
+together is through the joining
+of the phosphate and
+
+sugar into a sugar phosphate
+backbone, from
+
+which the bases hang.
+
+And so they look kind
+of like this.
+
+There's phosphate,
+sugar, phosphate,
+
+sugar, phosphate, sugar.
+
+And from the sugar
+hangs the base.
+
+The phosphate and the sugar, as
+I've just said, forms the
+
+sugar phosphate backbone.
+
+And the bases, as we'll discuss
+in a moment, comprise
+
+the information that is encoded
+in nucleic acids.
+
+Let's talk more about this
+nucleotide and the structure
+
+of the nucleotide and the kinds
+of components there are
+
+in the nucleotide.
+
+The sugar of the nucleotide
+is a pentose.
+
+It's a five carbon sugar.
+
+It is called ribose,
+and it's cyclic.
+
+And it's called ribose in RNA,
+and as you will see,
+
+deoxyribose in DNA.
+
+There are four bases in DNA.
+
+They are called adenine,
+guanine,
+
+cytosine, and thymine.
+
+And they are abbreviated
+A, G, C, and T--
+
+by their first initial.
+
+But you need to know
+the whole name.
+
+In RNA, the bases are the same,
+
+except instead of thymine--
+
+there is no thymine.
+
+Instead, there is something
+called uracil, which is
+
+closely related, and
+abbreviated U.
+
+The bases have a particular
+structure.
+
+You do not need to be able to
+draw them, but you should be
+
+able to recognize the
+class of base.
+
+There is a class called
+purines, which
+
+comprise two rings.
+
+I'll show you some slides
+in a moment.
+
+And adenine and guanine fall
+into that category.
+
+And then, there's another class
+called pyrimidines,
+
+which are made of one ring.
+
+And cytosine, thymine, and
+uracil fall into that class.
+
+Let's draw the structure
+of a nucleotide
+
+out in chemical formula.
+
+We're not going to
+draw the bases.
+
+We're going to draw mostly the
+sugar and the phosphate,
+
+because it will be important
+when we think about
+
+polymerizing nucleotides.
+
+And then I'll show
+you some slides.
+
+So nucleotide structure--
+
+the best way to draw a
+nucleotide structure is to
+
+start with the sugar.
+
+So start with an oxygen.
+
+And then you can put
+in the carbons.
+
+And the carbons are numbered,
+because, in many
+
+macromolecules, there are so
+many carbons, it can be very
+
+useful to give them
+specific numbers.
+
+And that's true in the sugar.
+
+It's also true in the bases.
+
+But the sugar numberings
+of the carbons are very
+
+important for you.
+
+There's a one prime carbon, two
+prime, three prime, four
+
+prime, and five prime.
+
+The base is attached to
+the one prime carbon.
+
+And the phosphate is attached
+to the five prime carbon.
+
+The two prime and the three
+prime carbon are also notable.
+
+The three prime carbon always
+has a hydroxyl group.
+
+And it's this hydroxyl group and
+this hydroxyl group of the
+
+phosphate that react together
+when the sugar phosphate
+
+backbone forms covalent bonds.
+
+The two prime carbon can either
+have a hydrogen, as in
+
+DNA, or a hydroxyl as RNA.
+
+Hydroxyl groups are reactive,
+and having this extra hydroxyl
+
+group on RNA makes this
+sugar more reactive
+
+than the one in DNA.
+
+OK.
+
+That is your nucleotide
+structure.
+
+And you should know it.
+
+Let's see what we have
+for slides here.
+
+Nucleic acid monomer
+and polymer.
+
+We're going to draw in one
+moment the nucleic acid
+
+polymer on the board,
+but here it is.
+
+Here is the sugar, the base,
+and the phosphate group.
+
+All right.
+
+Let's think about how you
+actually get this sugar
+
+phosphate backbone formed.
+
+And let us draw formation
+of a dinucleotide.
+
+And I'm going to abbreviate on
+one of the nucleotides the
+
+phosphate as PO4, otherwise we
+won't fit this on the board.
+
+So let's put the sugars first.
+
+And let me actually just make
+sure that you guys understand
+
+that the sugar can be drawn as
+I've drawn it, with all the
+
+carbons there, or it can be
+drawn in this way, where the
+
+carbons are the apices, or
+at the ends of a line.
+
+If this is a new you-- if this
+is new organic chemistry
+
+formula to you or chemical
+formula to you, then please
+
+come and see one of us, and
+we'll make sure that you get
+
+up to speed, because you really
+do need to know that
+
+for this course.
+
+Okay so let us draw
+some sugars.
+
+Actually, I'm going to erase
+this one and put it even
+
+closer to the top of the board,
+because these are small
+
+boards no--
+
+new boards, nice but small.
+
+Okay.
+
+And we're going to put here
+a phosphate group.
+
+I'm going to extend this.
+
+And we'll put a phosphate
+group here.
+
+And we're going to put a base.
+
+And we're going to put a
+three prime hydroxyl.
+
+So here is the five
+prime carbon and
+
+the three prime hydroxyl.
+
+And this is going to
+be nucleotide one.
+
+And then we'll draw an identical
+one below it, which
+
+will be nucleotide two,
+where now I'll
+
+draw out the phosphate.
+
+Let's again start with the
+sugar and a hydroxyl.
+
+And then let's put
+in the phosphate.
+
+Okay.
+
+And this is going to
+be nucleotide two--
+
+so nucleotide one and
+nucleotide two.
+
+The phosphate, hydroxyl,
+and the sugar--
+
+and we can put in some
+negatives here.
+
+On the phosphate, that's fine.
+
+Depends on the pH as to what
+the ionization of the
+
+phosphate group is.
+
+This hydroxyl group and
+this phosphate group,
+
+are going to interact.
+
+And the outcome is going to be
+a dinucleotide, where the two
+
+nucleotides, as you will see,
+are joined by a particular
+
+linkage called a phosphodiester
+linkage or a
+
+phosphodiester bond.
+
+We'll leave a phosphate
+there attached to
+
+the five prime carbon.
+
+Here's the first base.
+
+And now, we've got--
+
+and I've got to fit it in.
+
+Okay.
+
+So here is our dinucleotide--
+
+slightly skewed, but OK.
+
+And there are three features
+that I want to point out to
+
+you on this dinucleotide.
+
+The first is the bond that
+joins them together,
+
+which is this guy.
+
+It is called a phosphodiester
+bond or
+
+phosphodiester linkage.
+
+And the second is that
+the two ends of this
+
+dinucleotide are different.
+
+On one end, there is a
+free phosphate group.
+
+And where there is a free
+phosphate group, that is
+
+called the five prime
+phosphate, or
+
+the five prime end.
+
+But the five prime end
+has got a phosphate.
+
+That's part of its property.
+
+On the other end, you'll
+see, there is a
+
+free hydroxyl group.
+
+And that is called the three
+prime hydroxyl, or
+
+the three prime end.
+
+And they're equivalent,
+pretty much.
+
+But you should know that at
+one side, there's a free
+
+hydroxyl group, the other side
+a free phosphate group.
+
+You will see later on that
+this is pivotal in
+
+synthesizing DNA, as in DNA
+replication and mitosis,
+
+meiosis, and so on.
+
+All right.
+
+Few more slides--
+
+here are the sugars that are
+found in nucleic acids.
+
+There's the deoxyribose
+and ribose.
+
+I just put these up
+for you for recap.
+
+Here are the bases.
+
+Here are the pyrimidines--
+
+cytosine, thymine,
+and uracil--
+
+and then the purines, with this
+
+interesting di-ring structure.
+
+This I drew for you, okay?
+
+And so it's on your
+PowerPoint.
+
+If you're a bit shaky as to
+what's on the board and how we
+
+got there, you can go and get
+this from the PowerPoints that
+
+I'll post after class.
+
+All right.
+
+Now, in contrast to lipids and
+carbohydrates, nucleic acids,
+
+and as you will see, proteins,
+have two extraordinary
+
+properties that allow them to
+encode information in really a
+
+way that is extremely rich.
+
+And those two properties I've
+already touched on.
+
+One is that the ends
+are different.
+
+They're different in a
+dinucleotide, and they're
+
+different in a polynucleotide
+that's a
+
+thousand nucleotides long.
+
+So they have different ends.
+
+And the bases have
+a linear order.
+
+And this linear order is part
+and parcel of the information
+
+that the nucleic acid encodes.
+
+So let's draw out,
+for instance---
+
+and we're going to start
+with five prime.
+
+Phosphate, sugar, phosphate,
+sugar, phosphate, sugar
+
+phosphate--
+
+and we're going to end with the
+sugar that has the three
+
+prime hydroxyl.
+
+Okay, so we've got a five prime
+and a three prime end.
+
+And from this, the bases
+are hanging.
+
+Now, when nucleotides are
+incorporated into a nucleic
+
+acid polymer, there is an order
+of synthesis, which is
+
+why the linear order of the
+molecule eventually can be
+
+used for information.
+
+The base nearest the free
+five prime phosphate
+
+is the first added.
+
+And the base--
+
+so it's part of the
+nucleotide--
+
+nearest the three prime hydroxyl
+is the last added.
+
+It's really important
+that you know this.
+
+Furthermore, when we write out
+nucleotides, nucleotide
+
+sequence, when we write out a
+nucleic acid sequence, we
+
+don't generally write the sugar
+phosphate backbone in.
+
+We just write the bases.
+
+So it's written five
+prime, base, base,
+
+base, base, three prime.
+
+But of course, the bases
+can be anything.
+
+So for example, we could have
+five prime, adenine, guanine,
+
+guanine, cytosine,
+three prime.
+
+And there's a convention that
+you have to follow.
+
+And it doesn't matter how long
+you're in this business.
+
+When you write out a nucleic
+acid polymer, you always write
+
+the five prime and the
+three prime end.
+
+I've been in this business for
+30 years now, and I still have
+
+to write the five prime and
+the three prime end.
+
+If you don't, you get lost, and
+you will get mixed up in
+
+your calculations, both in this
+course and in real life.
+
+Now, there are lots of
+combinations of bases, even
+
+though there are only
+four bases.
+
+For example, if there are four
+bases and you have a three
+
+nucleotide polymer--
+
+four bases, three possibilities,
+
+possibilities.
+
+Genes can be thousands and
+thousands of bases in length.
+
+And so the information, the
+combinatorics involved in the
+
+nucleic acid polymer
+is very large.
+
+So genes can be, let's say,
+100 to ten to the fifth
+
+nucleotides long.
+
+And so the number of
+possibilities is really
+
+extraordinary.
+
+And it's one of the reasons
+that all of life can be
+
+encoded in nucleic acids.
+
+And the last thing that
+I want to tell you
+
+about nucleic acids--
+
+which will become and will
+remain one of the most
+
+important things you learn
+in this class--
+
+is that DNA is usually
+double stranded.
+
+RNA is too, but it's really
+DNA that uses this in an
+
+extraordinarily important way.
+
+So DNA is usually
+double stranded.
+
+What does that mean?
+
+It gets to be double
+stranded via
+
+something called base pairing--
+
+you'll see what this
+means in a moment--
+
+which also means, or there's
+another term that's used,
+
+which is complementarity,
+as you will see.
+
+And this double strandedness
+does not
+
+involve covalent bonds.
+
+It involves that special type
+of bonds that we discussed
+
+last time, which are
+the hydrogen bonds.
+
+And there are rules
+about this.
+
+Adenine will form two hydrogen
+bonds with thymine or uracil.
+
+Guanine forms three hydrogen
+bonds with cytosine.
+
+And that is a rule that is one
+of the most important rules in
+
+nucleic acids.
+
+From your book, here is a
+picture of the two bases,
+
+adenine and thymine, that can
+be lain opposite one another
+
+such that these dotted lines
+are hydrogen bonds between
+
+oxygen and hydrogen or nitrogen
+and hydrogen--
+
+and the same kind of thing
+for guanine and cytosine.
+
+You don't need to know these
+structures, exactly, but you
+
+do need to know base pairing
+inside, outside, and
+
+never forget it.
+
+Okay.
+
+Why is this important?
+
+I'll tell you why this
+is important.
+
+It's important for DNA
+replication and for the
+
+passage of hereditary
+information from one
+
+generation to the next.
+
+So, in DNA replication, the
+idea is to pass genes on,
+
+unperturbed, in the same
+sequence from one generation
+
+to the next at every
+cell division.
+
+So let's just, for instance,
+start with a polymer here.
+
+Ah, and something else that I
+needed to tell you, which I
+
+will in a second, is that when
+nucleic acids form double
+
+stranded structure, one strand
+of nucleic acid--
+
+my one arm--
+
+will form a double stranded
+structure with another strand
+
+of nucleic acids, like so.
+
+Okay.
+
+That's what's referred
+to up there.
+
+The adenine's on one polymer.
+
+The thymine is on
+another polymer.
+
+When these polymers form, they
+form in what's called an
+
+anti-parallel direction.
+
+It's really hard to do.
+
+But if this is my five prime end
+and three prime end, the
+
+five prime end of one and the
+will be opposite the three
+
+prime end of another strand.
+
+I guess I can do it this way--
+
+topologically easier.
+
+Okay--
+
+so five prime opposite three
+prime, five prime opposite
+
+three prime.
+
+So let's draw the complement
+of this for
+
+the nucleotide polymer.
+
+There'll be thymine, cytosine,
+adenine, thymine.
+
+And look what I've done to the
+five primes and three prime.
+
+Means they are one five prime
+opposite a three prime, and
+
+the other three prime opposite
+a five prime.
+
+This arrangement called an
+anti-parallel arrangement of
+
+nucleic acids.
+
+And it is super important that
+you never forget this.
+
+During DNA replication, the
+strands of this double
+
+stranded polymer separate.
+
+And so you have five prime
+AGTA three prime--
+
+is one strand--
+
+plus three prime TCAT five
+prime-- two single strands.
+
+And here's the magic, and this
+is what Watson and Crick got
+
+the Nobel Prize for long ago
+for understanding that when
+
+DNA replicates, those strands
+get filled in.
+
+So this five prime AGTA three
+prime will now get synthesized
+
+opposite its complement--
+
+three prime of TCAT five
+prime plus this guy--
+
+three prime TCAT five prime will
+get its complement made.
+
+And look what you have got.
+
+You have started with one
+strand, one double stranded
+
+moiety, and you've landed up
+with two identical replicas of
+
+what you started with--
+
+so two identical replicates.
+
+That's redundant, but it really
+pushes the point home--
+
+two identical replicates of this
+parent molecule that we
+
+started with.
+
+We'll have a lot more to say
+about this when we spend a
+
+whole lecture on DNA
+replication, but you should
+
+understand that this is one of
+the profound natures of DNA as
+
+the hereditary information.
+
+And from your book-- double
+stranded DNA.
+
+We'll have more to say about
+this, but double stranded DNA,
+
+because of chemical
+considerations, goes into its
+
+most stable chemical state,
+which is this very beautiful
+
+double helix that has structure
+and is able to pack
+
+very tightly so that you
+can get lots of genetic
+
+information in one cell.
+
+Last thing about
+nucleic acids--
+
+RNA is often single stranded,
+but it can also form
+
+structures that are partially
+double stranded.
+
+And this is one such RNA
+that's formed this very
+
+complicated, partially double
+stranded molecule.
\ No newline at end of file
diff --git a/omqSBV--uQ4.txt b/omqSBV--uQ4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6d19909c0ece868208ed1a358a4c7f81fcaef42e
--- /dev/null
+++ b/omqSBV--uQ4.txt
@@ -0,0 +1,3027 @@
+align:start position:0%
+ 
+so our example is a well-known one it's
+
+ align:start position:0%
+so our example is a well-known one it's
+ 
+
+ align:start position:0%
+so our example is a well-known one it's
+a but it's a it's important to
+
+ align:start position:0%
+a but it's a it's important to
+ 
+
+ align:start position:0%
+a but it's a it's important to
+understand it and it's a good example
+
+ align:start position:0%
+understand it and it's a good example
+ 
+
+ align:start position:0%
+understand it and it's a good example
+it's a familiar one is the hydrogen
+
+ align:start position:0%
+it's a familiar one is the hydrogen
+ 
+
+ align:start position:0%
+it's a familiar one is the hydrogen
+molecule ionized and we spoke a little
+
+ align:start position:0%
+molecule ionized and we spoke a little
+ 
+
+ align:start position:0%
+molecule ionized and we spoke a little
+about it last time so let's do that now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so h2 plus hydrogen iron so what is this
+
+ align:start position:0%
+so h2 plus hydrogen iron so what is this
+ 
+
+ align:start position:0%
+so h2 plus hydrogen iron so what is this
+system well it is two protons sharing
+
+ align:start position:0%
+system well it is two protons sharing
+ 
+
+ align:start position:0%
+system well it is two protons sharing
+one electron that's basically it it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's the fact that if you have a
+
+ align:start position:0%
+it's the fact that if you have a
+ 
+
+ align:start position:0%
+it's the fact that if you have a
+hydrogen atom this is hydrogen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you could bring another proton and and
+
+ align:start position:0%
+you could bring another proton and and
+ 
+
+ align:start position:0%
+you could bring another proton and and
+form a bound state that's an important
+
+ align:start position:0%
+form a bound state that's an important
+ 
+
+ align:start position:0%
+form a bound state that's an important
+thing in order to think about it you see
+
+ align:start position:0%
+thing in order to think about it you see
+ 
+
+ align:start position:0%
+thing in order to think about it you see
+you can ask what is the bound state
+
+ align:start position:0%
+you can ask what is the bound state
+ 
+
+ align:start position:0%
+you can ask what is the bound state
+energy of your system it's the energy
+
+ align:start position:0%
+energy of your system it's the energy
+ 
+
+ align:start position:0%
+energy of your system it's the energy
+you need to dissociate your system but
+
+ align:start position:0%
+you need to dissociate your system but
+ 
+
+ align:start position:0%
+you need to dissociate your system but
+this system if you have two protons
+
+ align:start position:0%
+this system if you have two protons
+ 
+
+ align:start position:0%
+this system if you have two protons
+proton proton and one electron it can be
+
+ align:start position:0%
+proton proton and one electron it can be
+ 
+
+ align:start position:0%
+proton proton and one electron it can be
+dissociated in many ways it can be
+
+ align:start position:0%
+dissociated in many ways it can be
+ 
+
+ align:start position:0%
+dissociated in many ways it can be
+dissociated by just totally separating
+
+ align:start position:0%
+dissociated by just totally separating
+ 
+
+ align:start position:0%
+dissociated by just totally separating
+it and destroying it but it can be
+
+ align:start position:0%
+it and destroying it but it can be
+ 
+
+ align:start position:0%
+it and destroying it but it can be
+dissociated or liberated by just
+
+ align:start position:0%
+dissociated or liberated by just
+ 
+
+ align:start position:0%
+dissociated or liberated by just
+removing the protons
+
+ align:start position:0%
+removing the protons
+ 
+
+ align:start position:0%
+removing the protons
+so this is already a bouncy so if you
+
+ align:start position:0%
+so this is already a bouncy so if you
+ 
+
+ align:start position:0%
+so this is already a bouncy so if you
+think of energies you have the end bound
+
+ align:start position:0%
+think of energies you have the end bound
+ 
+
+ align:start position:0%
+think of energies you have the end bound
+state energy of hydrogen here hydrogen
+
+ align:start position:0%
+state energy of hydrogen here hydrogen
+ 
+
+ align:start position:0%
+state energy of hydrogen here hydrogen
+itself and the h2 iron h2 plus must be
+
+ align:start position:0%
+itself and the h2 iron h2 plus must be
+ 
+
+ align:start position:0%
+itself and the h2 iron h2 plus must be
+lower because you could imagine taking
+
+ align:start position:0%
+lower because you could imagine taking
+ 
+
+ align:start position:0%
+lower because you could imagine taking
+the proton out and somehow this system
+
+ align:start position:0%
+the proton out and somehow this system
+ 
+
+ align:start position:0%
+the proton out and somehow this system
+is a configuration which this proton is
+
+ align:start position:0%
+is a configuration which this proton is
+ 
+
+ align:start position:0%
+is a configuration which this proton is
+captured here so you should get lower
+
+ align:start position:0%
+captured here so you should get lower
+ 
+
+ align:start position:0%
+captured here so you should get lower
+energy than the hydrogen atom energy so
+
+ align:start position:0%
+energy than the hydrogen atom energy so
+ 
+
+ align:start position:0%
+energy than the hydrogen atom energy so
+that's the hydrogen iron and that should
+
+ align:start position:0%
+that's the hydrogen iron and that should
+ 
+
+ align:start position:0%
+that's the hydrogen iron and that should
+be still more energy than if you bring
+
+ align:start position:0%
+be still more energy than if you bring
+ 
+
+ align:start position:0%
+be still more energy than if you bring
+another electron which is the h2
+
+ align:start position:0%
+another electron which is the h2
+ 
+
+ align:start position:0%
+another electron which is the h2
+molecule you bring another electron this
+
+ align:start position:0%
+molecule you bring another electron this
+ 
+
+ align:start position:0%
+molecule you bring another electron this
+should bind this and a other electron
+
+ align:start position:0%
+should bind this and a other electron
+ 
+
+ align:start position:0%
+should bind this and a other electron
+and lower its energy even more so how
+
+ align:start position:0%
+and lower its energy even more so how
+ 
+
+ align:start position:0%
+and lower its energy even more so how
+does one solve for this hydrogen ion
+
+ align:start position:0%
+does one solve for this hydrogen ion
+ 
+
+ align:start position:0%
+does one solve for this hydrogen ion
+well as we discussed you first solve for
+
+ align:start position:0%
+well as we discussed you first solve for
+ 
+
+ align:start position:0%
+well as we discussed you first solve for
+the electronic wave function when the
+
+ align:start position:0%
+the electronic wave function when the
+ 
+
+ align:start position:0%
+the electronic wave function when the
+protons are separated a distance R so we
+
+ align:start position:0%
+protons are separated a distance R so we
+ 
+
+ align:start position:0%
+protons are separated a distance R so we
+said fix the lattice so here it is the
+
+ align:start position:0%
+said fix the lattice so here it is the
+ 
+
+ align:start position:0%
+said fix the lattice so here it is the
+lattice is fixed it's a separation
+
+ align:start position:0%
+lattice is fixed it's a separation
+ 
+
+ align:start position:0%
+lattice is fixed it's a separation
+capital R and now I'm supposed to find
+
+ align:start position:0%
+capital R and now I'm supposed to find
+ 
+
+ align:start position:0%
+capital R and now I'm supposed to find
+the electron wave function easy no
+
+ align:start position:0%
+the electron wave function easy no
+ 
+
+ align:start position:0%
+the electron wave function easy no
+that's already is hard we we spend
+
+ align:start position:0%
+that's already is hard we we spend
+ 
+
+ align:start position:0%
+that's already is hard we we spend
+several lectures you've been studying
+
+ align:start position:0%
+several lectures you've been studying
+ 
+
+ align:start position:0%
+several lectures you've been studying
+this three times already maybe in
+
+ align:start position:0%
+this three times already maybe in
+ 
+
+ align:start position:0%
+this three times already maybe in
+quantum mechanics the hydrogen atom one
+
+ align:start position:0%
+quantum mechanics the hydrogen atom one
+ 
+
+ align:start position:0%
+quantum mechanics the hydrogen atom one
+proton one electron two problems one
+
+ align:start position:0%
+proton one electron two problems one
+ 
+
+ align:start position:0%
+proton one electron two problems one
+electron is much harder I don't think
+
+ align:start position:0%
+electron is much harder I don't think
+ 
+
+ align:start position:0%
+electron is much harder I don't think
+there's a simple analytical way to solve
+
+ align:start position:0%
+there's a simple analytical way to solve
+ 
+
+ align:start position:0%
+there's a simple analytical way to solve
+it so already at this step we have
+
+ align:start position:0%
+it so already at this step we have
+ 
+
+ align:start position:0%
+it so already at this step we have
+trouble solving it what is the electron
+
+ align:start position:0%
+trouble solving it what is the electron
+ 
+
+ align:start position:0%
+trouble solving it what is the electron
+candle tone Yin in this case the
+
+ align:start position:0%
+candle tone Yin in this case the
+ 
+
+ align:start position:0%
+candle tone Yin in this case the
+electron is just one laplacian here
+
+ align:start position:0%
+electron is just one laplacian here
+ 
+
+ align:start position:0%
+electron is just one laplacian here
+minus h squared over two
+
+ align:start position:0%
+minus h squared over two
+ 
+
+ align:start position:0%
+minus h squared over two
+um for the electric variable and then
+
+ align:start position:0%
+um for the electric variable and then
+ 
+
+ align:start position:0%
+um for the electric variable and then
+the potential that is the interactions
+
+ align:start position:0%
+the potential that is the interactions
+ 
+
+ align:start position:0%
+the potential that is the interactions
+of the electron with the two nuclei so
+
+ align:start position:0%
+of the electron with the two nuclei so
+ 
+
+ align:start position:0%
+of the electron with the two nuclei so
+if we call this our this distance R 1
+
+ align:start position:0%
+if we call this our this distance R 1
+ 
+
+ align:start position:0%
+if we call this our this distance R 1
+and this distance R 2 that is the whole
+
+ align:start position:0%
+and this distance R 2 that is the whole
+ 
+
+ align:start position:0%
+and this distance R 2 that is the whole
+electron funnel tone Ian now don't think
+
+ align:start position:0%
+electron funnel tone Ian now don't think
+ 
+
+ align:start position:0%
+electron funnel tone Ian now don't think
+of R 1 and R 2 as you have two variables
+
+ align:start position:0%
+of R 1 and R 2 as you have two variables
+ 
+
+ align:start position:0%
+of R 1 and R 2 as you have two variables
+two positions no it's this there's just
+
+ align:start position:0%
+two positions no it's this there's just
+ 
+
+ align:start position:0%
+two positions no it's this there's just
+one position the dynamical variables for
+
+ align:start position:0%
+one position the dynamical variables for
+ 
+
+ align:start position:0%
+one position the dynamical variables for
+this electron is P and R for this
+
+ align:start position:0%
+this electron is P and R for this
+ 
+
+ align:start position:0%
+this electron is P and R for this
+electron R is the position of the leg
+
+ align:start position:0%
+electron R is the position of the leg
+ 
+
+ align:start position:0%
+electron R is the position of the leg
+that happens to be at R is equal to R 1
+
+ align:start position:0%
+that happens to be at R is equal to R 1
+ 
+
+ align:start position:0%
+that happens to be at R is equal to R 1
+and if you know so R 1 is really the
+
+ align:start position:0%
+and if you know so R 1 is really the
+ 
+
+ align:start position:0%
+and if you know so R 1 is really the
+length of our the position of the
+
+ align:start position:0%
+length of our the position of the
+ 
+
+ align:start position:0%
+length of our the position of the
+electrode and R 2 is the length of
+
+ align:start position:0%
+electrode and R 2 is the length of
+ 
+
+ align:start position:0%
+electrode and R 2 is the length of
+capital R if you wish all the way here -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our R R is the vector here as well so
+
+ align:start position:0%
+our R R is the vector here as well so
+ 
+
+ align:start position:0%
+our R R is the vector here as well so
+there's our 1 and our two but it's not
+
+ align:start position:0%
+there's our 1 and our two but it's not
+ 
+
+ align:start position:0%
+there's our 1 and our two but it's not
+two electrons or two variables it's just
+
+ align:start position:0%
+two electrons or two variables it's just
+ 
+
+ align:start position:0%
+two electrons or two variables it's just
+two distances that depend on this single
+
+ align:start position:0%
+two distances that depend on this single
+ 
+
+ align:start position:0%
+two distances that depend on this single
+position of the electron and this is the
+
+ align:start position:0%
+position of the electron and this is the
+ 
+
+ align:start position:0%
+position of the electron and this is the
+momentum operator of the electron okay
+
+ align:start position:0%
+momentum operator of the electron okay
+ 
+
+ align:start position:0%
+momentum operator of the electron okay
+so so you can't solve this that's life
+
+ align:start position:0%
+so so you can't solve this that's life
+ 
+
+ align:start position:0%
+so so you can't solve this that's life
+can't be solved but we can do something
+
+ align:start position:0%
+can't be solved but we can do something
+ 
+
+ align:start position:0%
+can't be solved but we can do something
+and we can do something variational we
+
+ align:start position:0%
+and we can do something variational we
+ 
+
+ align:start position:0%
+and we can do something variational we
+can try to find some kind of
+
+ align:start position:0%
+can try to find some kind of
+ 
+
+ align:start position:0%
+can try to find some kind of
+approximation for the state of the
+
+ align:start position:0%
+approximation for the state of the
+ 
+
+ align:start position:0%
+approximation for the state of the
+electron so we'll use that so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there is an answered that you could
+
+ align:start position:0%
+so there is an answered that you could
+ 
+
+ align:start position:0%
+so there is an answered that you could
+try at a variational wavefunction for
+
+ align:start position:0%
+try at a variational wavefunction for
+ 
+
+ align:start position:0%
+try at a variational wavefunction for
+even the electron you see in our
+
+ align:start position:0%
+even the electron you see in our
+ 
+
+ align:start position:0%
+even the electron you see in our
+argument that in this lecture we did the
+
+ align:start position:0%
+argument that in this lecture we did the
+ 
+
+ align:start position:0%
+argument that in this lecture we did the
+variation and approximation for the
+
+ align:start position:0%
+variation and approximation for the
+ 
+
+ align:start position:0%
+variation and approximation for the
+nuclear degrees of freedom or for
+
+ align:start position:0%
+nuclear degrees of freedom or for
+ 
+
+ align:start position:0%
+nuclear degrees of freedom or for
+nothing but even for the electron wave
+
+ align:start position:0%
+nothing but even for the electron wave
+ 
+
+ align:start position:0%
+nothing but even for the electron wave
+function I can't solve them so I have to
+
+ align:start position:0%
+function I can't solve them so I have to
+ 
+
+ align:start position:0%
+function I can't solve them so I have to
+do a variational method now this
+
+ align:start position:0%
+do a variational method now this
+ 
+
+ align:start position:0%
+do a variational method now this
+variational methods have become
+
+ align:start position:0%
+variational methods have become
+ 
+
+ align:start position:0%
+variational methods have become
+extremely sophisticated people do this
+
+ align:start position:0%
+extremely sophisticated people do this
+ 
+
+ align:start position:0%
+extremely sophisticated people do this
+with a series of eigenfunctions and find
+
+ align:start position:0%
+with a series of eigenfunctions and find
+ 
+
+ align:start position:0%
+with a series of eigenfunctions and find
+answers that converge with 15 digits
+
+ align:start position:0%
+answers that converge with 15 digits
+ 
+
+ align:start position:0%
+answers that converge with 15 digits
+accuracies it's just unbelievable what
+
+ align:start position:0%
+accuracies it's just unbelievable what
+ 
+
+ align:start position:0%
+accuracies it's just unbelievable what
+people can do that by now with this is a
+
+ align:start position:0%
+people can do that by now with this is a
+ 
+
+ align:start position:0%
+people can do that by now with this is a
+very nice and developed field but we'll
+
+ align:start position:0%
+very nice and developed field but we'll
+ 
+
+ align:start position:0%
+very nice and developed field but we'll
+do a baby version of it so this baby
+
+ align:start position:0%
+do a baby version of it so this baby
+ 
+
+ align:start position:0%
+do a baby version of it so this baby
+version is going to stay that my wave
+
+ align:start position:0%
+version is going to stay that my wave
+ 
+
+ align:start position:0%
+version is going to stay that my wave
+function for the electron as a function
+
+ align:start position:0%
+function for the electron as a function
+ 
+
+ align:start position:0%
+function for the electron as a function
+of position and as a function of the
+
+ align:start position:0%
+of position and as a function of the
+ 
+
+ align:start position:0%
+of position and as a function of the
+separation is going to be simple it's
+
+ align:start position:0%
+separation is going to be simple it's
+ 
+
+ align:start position:0%
+separation is going to be simple it's
+going to be a sum of ground state wave
+
+ align:start position:0%
+going to be a sum of ground state wave
+ 
+
+ align:start position:0%
+going to be a sum of ground state wave
+function it's gonna be a number a that's
+
+ align:start position:0%
+function it's gonna be a number a that's
+ 
+
+ align:start position:0%
+function it's gonna be a number a that's
+just a number times the ground state
+
+ align:start position:0%
+just a number times the ground state
+ 
+
+ align:start position:0%
+just a number times the ground state
+wave function based on the first proton
+
+ align:start position:0%
+wave function based on the first proton
+ 
+
+ align:start position:0%
+wave function based on the first proton
+plus the ground state wave function
+
+ align:start position:0%
+plus the ground state wave function
+ 
+
+ align:start position:0%
+plus the ground state wave function
+based on the second proton so this size
+
+ align:start position:0%
+based on the second proton so this size
+ 
+
+ align:start position:0%
+based on the second proton so this size
+R sy 0 of R is the ground state wave
+
+ align:start position:0%
+R sy 0 of R is the ground state wave
+ 
+
+ align:start position:0%
+R sy 0 of R is the ground state wave
+function of hydrogen by a0 cubed e to
+
+ align:start position:0%
+function of hydrogen by a0 cubed e to
+ 
+
+ align:start position:0%
+function of hydrogen by a0 cubed e to
+the minus R over a0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is called people have given it a
+
+ align:start position:0%
+this is called people have given it a
+ 
+
+ align:start position:0%
+this is called people have given it a
+name even though it's you would say is
+
+ align:start position:0%
+name even though it's you would say is
+ 
+
+ align:start position:0%
+name even though it's you would say is
+not that original to put some wave
+
+ align:start position:0%
+not that original to put some wave
+ 
+
+ align:start position:0%
+not that original to put some wave
+function like that this is a simple
+
+ align:start position:0%
+function like that this is a simple
+ 
+
+ align:start position:0%
+function like that this is a simple
+approximation and it's called the
+
+ align:start position:0%
+approximation and it's called the
+ 
+
+ align:start position:0%
+approximation and it's called the
+technique is called up LC a old
+
+ align:start position:0%
+technique is called up LC a old
+ 
+
+ align:start position:0%
+technique is called up LC a old
+technique and this calls for linear
+
+ align:start position:0%
+technique and this calls for linear
+ 
+
+ align:start position:0%
+technique and this calls for linear
+linear combination of atomic orbitals a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+big name for brother simple thing it has
+
+ align:start position:0%
+big name for brother simple thing it has
+ 
+
+ align:start position:0%
+big name for brother simple thing it has
+some nice things about this wave
+
+ align:start position:0%
+some nice things about this wave
+ 
+
+ align:start position:0%
+some nice things about this wave
+function this wave this system is
+
+ align:start position:0%
+function this wave this system is
+ 
+
+ align:start position:0%
+function this wave this system is
+invariant this molecule is invariant and
+
+ align:start position:0%
+invariant this molecule is invariant and
+ 
+
+ align:start position:0%
+invariant this molecule is invariant and
+they're taking a reflection around this
+
+ align:start position:0%
+they're taking a reflection around this
+ 
+
+ align:start position:0%
+they're taking a reflection around this
+thing changing the first proton and the
+
+ align:start position:0%
+thing changing the first proton and the
+ 
+
+ align:start position:0%
+thing changing the first proton and the
+second proton so that's the symmetry of
+
+ align:start position:0%
+second proton so that's the symmetry of
+ 
+
+ align:start position:0%
+second proton so that's the symmetry of
+your Hamiltonian and it's a symmetry of
+
+ align:start position:0%
+your Hamiltonian and it's a symmetry of
+ 
+
+ align:start position:0%
+your Hamiltonian and it's a symmetry of
+your habit that commutes with the
+
+ align:start position:0%
+your habit that commutes with the
+ 
+
+ align:start position:0%
+your habit that commutes with the
+Hamiltonian so you can demand that your
+
+ align:start position:0%
+Hamiltonian so you can demand that your
+ 
+
+ align:start position:0%
+Hamiltonian so you can demand that your
+wave functions have that symmetry and
+
+ align:start position:0%
+wave functions have that symmetry and
+ 
+
+ align:start position:0%
+wave functions have that symmetry and
+this is nice here because if you change
+
+ align:start position:0%
+this is nice here because if you change
+ 
+
+ align:start position:0%
+this is nice here because if you change
+R 1 and R 2 the wave function is
+
+ align:start position:0%
+R 1 and R 2 the wave function is
+ 
+
+ align:start position:0%
+R 1 and R 2 the wave function is
+invariant so that's a very nice thing
+
+ align:start position:0%
+invariant so that's a very nice thing
+ 
+
+ align:start position:0%
+invariant so that's a very nice thing
+about this wave function said it shows
+
+ align:start position:0%
+about this wave function said it shows
+ 
+
+ align:start position:0%
+about this wave function said it shows
+you see you can put in the variational
+
+ align:start position:0%
+you see you can put in the variational
+ 
+
+ align:start position:0%
+you see you can put in the variational
+method anything and it will still give
+
+ align:start position:0%
+method anything and it will still give
+ 
+
+ align:start position:0%
+method anything and it will still give
+you some answer but if you put something
+
+ align:start position:0%
+you some answer but if you put something
+ 
+
+ align:start position:0%
+you some answer but if you put something
+that mimics the real wave functions and
+
+ align:start position:0%
+that mimics the real wave functions and
+ 
+
+ align:start position:0%
+that mimics the real wave functions and
+the real wave function of the system is
+
+ align:start position:0%
+the real wave function of the system is
+ 
+
+ align:start position:0%
+the real wave function of the system is
+going to have a symmetry under the
+
+ align:start position:0%
+going to have a symmetry under the
+ 
+
+ align:start position:0%
+going to have a symmetry under the
+exchange of the two protons they're
+
+ align:start position:0%
+exchange of the two protons they're
+ 
+
+ align:start position:0%
+exchange of the two protons they're
+identical so this lot is that you've
+
+ align:start position:0%
+identical so this lot is that you've
+ 
+
+ align:start position:0%
+identical so this lot is that you've
+created has a symmetry so the electron
+
+ align:start position:0%
+created has a symmetry so the electron
+ 
+
+ align:start position:0%
+created has a symmetry so the electron
+configuration has to respect that
+
+ align:start position:0%
+configuration has to respect that
+ 
+
+ align:start position:0%
+configuration has to respect that
+symmetry
+
+ align:start position:0%
+symmetry
+ 
+
+ align:start position:0%
+symmetry
+so that's very nice now this is
+
+ align:start position:0%
+so that's very nice now this is
+ 
+
+ align:start position:0%
+so that's very nice now this is
+electronic wave function so I asked you
+
+ align:start position:0%
+electronic wave function so I asked you
+ 
+
+ align:start position:0%
+electronic wave function so I asked you
+is this wave function better where the
+
+ align:start position:0%
+is this wave function better where the
+ 
+
+ align:start position:0%
+is this wave function better where the
+protons are far away or when the protons
+
+ align:start position:0%
+protons are far away or when the protons
+ 
+
+ align:start position:0%
+protons are far away or when the protons
+are very close to each other give you a
+
+ align:start position:0%
+are very close to each other give you a
+ 
+
+ align:start position:0%
+are very close to each other give you a
+minute to think about it when is this
+
+ align:start position:0%
+minute to think about it when is this
+ 
+
+ align:start position:0%
+minute to think about it when is this
+approximation or this wave function
+
+ align:start position:0%
+approximation or this wave function
+ 
+
+ align:start position:0%
+approximation or this wave function
+better if the distance between the
+
+ align:start position:0%
+better if the distance between the
+ 
+
+ align:start position:0%
+better if the distance between the
+protons is very little or the distance
+
+ align:start position:0%
+protons is very little or the distance
+ 
+
+ align:start position:0%
+protons is very little or the distance
+between the protons is very large you're
+
+ align:start position:0%
+between the protons is very large you're
+ 
+
+ align:start position:0%
+between the protons is very large you're
+right in that when the two things
+
+ align:start position:0%
+right in that when the two things
+ 
+
+ align:start position:0%
+right in that when the two things
+collapse this looks like a true wave
+
+ align:start position:0%
+collapse this looks like a true wave
+ 
+
+ align:start position:0%
+collapse this looks like a true wave
+function because this is a solution when
+
+ align:start position:0%
+function because this is a solution when
+ 
+
+ align:start position:0%
+function because this is a solution when
+there's a single nucleus and a single
+
+ align:start position:0%
+there's a single nucleus and a single
+ 
+
+ align:start position:0%
+there's a single nucleus and a single
+electron but this is a solution for
+
+ align:start position:0%
+electron but this is a solution for
+ 
+
+ align:start position:0%
+electron but this is a solution for
+hydrogen and it gives you the ground
+
+ align:start position:0%
+hydrogen and it gives you the ground
+ 
+
+ align:start position:0%
+hydrogen and it gives you the ground
+state of hydrogen but when the two
+
+ align:start position:0%
+state of hydrogen but when the two
+ 
+
+ align:start position:0%
+state of hydrogen but when the two
+protons collab it has become helium
+
+ align:start position:0%
+protons collab it has become helium
+ 
+
+ align:start position:0%
+protons collab it has become helium
+nucleus it has two protons so it doesn't
+
+ align:start position:0%
+nucleus it has two protons so it doesn't
+ 
+
+ align:start position:0%
+nucleus it has two protons so it doesn't
+have the right decay rate it doesn't
+
+ align:start position:0%
+have the right decay rate it doesn't
+ 
+
+ align:start position:0%
+have the right decay rate it doesn't
+have the right Bohr radius on the other
+
+ align:start position:0%
+have the right Bohr radius on the other
+ 
+
+ align:start position:0%
+have the right Bohr radius on the other
+hand when they're far apart it does have
+
+ align:start position:0%
+hand when they're far apart it does have
+ 
+
+ align:start position:0%
+hand when they're far apart it does have
+the right thing so this is very good
+
+ align:start position:0%
+the right thing so this is very good
+ 
+
+ align:start position:0%
+the right thing so this is very good
+it's excellent when the things are far
+
+ align:start position:0%
+it's excellent when the things are far
+ 
+
+ align:start position:0%
+it's excellent when the things are far
+away but it's not great when they are
+
+ align:start position:0%
+away but it's not great when they are
+ 
+
+ align:start position:0%
+away but it's not great when they are
+close together so here you go you have
+
+ align:start position:0%
+close together so here you go you have
+ 
+
+ align:start position:0%
+close together so here you go you have
+to normalize this wave function even
+
+ align:start position:0%
+to normalize this wave function even
+ 
+
+ align:start position:0%
+to normalize this wave function even
+that takes some effort it turns out that
+
+ align:start position:0%
+that takes some effort it turns out that
+ 
+
+ align:start position:0%
+that takes some effort it turns out that
+the value of a nor for normalization the
+
+ align:start position:0%
+the value of a nor for normalization the
+ 
+
+ align:start position:0%
+the value of a nor for normalization the
+value of a is 1 over 2 1 plus a constant
+
+ align:start position:0%
+value of a is 1 over 2 1 plus a constant
+ 
+
+ align:start position:0%
+value of a is 1 over 2 1 plus a constant
+I and that constant I is e to the minus
+
+ align:start position:0%
+I and that constant I is e to the minus
+ 
+
+ align:start position:0%
+I and that constant I is e to the minus
+capital R over a naught times 1 plus R
+
+ align:start position:0%
+capital R over a naught times 1 plus R
+ 
+
+ align:start position:0%
+capital R over a naught times 1 plus R
+over a naught plus 1/3 of our over a
+
+ align:start position:0%
+over a naught plus 1/3 of our over a
+ 
+
+ align:start position:0%
+over a naught plus 1/3 of our over a
+naught squared Wow
+
+ align:start position:0%
+naught squared Wow
+ 
+
+ align:start position:0%
+naught squared Wow
+so very funny it's not so
+
+ align:start position:0%
+so very funny it's not so
+ 
+
+ align:start position:0%
+so very funny it's not so
+easy to even calculate the normalization
+
+ align:start position:0%
+easy to even calculate the normalization
+ 
+
+ align:start position:0%
+easy to even calculate the normalization
+of this thing and that's but that's a
+
+ align:start position:0%
+of this thing and that's but that's a
+ 
+
+ align:start position:0%
+of this thing and that's but that's a
+normalization and then recall that what
+
+ align:start position:0%
+normalization and then recall that what
+ 
+
+ align:start position:0%
+normalization and then recall that what
+we have to do is just put the electronic
+
+ align:start position:0%
+we have to do is just put the electronic
+ 
+
+ align:start position:0%
+we have to do is just put the electronic
+Hamiltonian
+
+ align:start position:0%
+Hamiltonian
+ 
+
+ align:start position:0%
+Hamiltonian
+inside this wave function this phi of r
+
+ align:start position:0%
+inside this wave function this phi of r
+ 
+
+ align:start position:0%
+inside this wave function this phi of r
+and this is going to give us an energy
+
+ align:start position:0%
+and this is going to give us an energy
+ 
+
+ align:start position:0%
+and this is going to give us an energy
+which is approximately the electronic
+
+ align:start position:0%
+which is approximately the electronic
+ 
+
+ align:start position:0%
+which is approximately the electronic
+energy as a function of R so you have to
+
+ align:start position:0%
+energy as a function of R so you have to
+ 
+
+ align:start position:0%
+energy as a function of R so you have to
+evaluate the Hamiltonian I'm sorry
+
+ align:start position:0%
+evaluate the Hamiltonian I'm sorry
+ 
+
+ align:start position:0%
+evaluate the Hamiltonian I'm sorry
+that's Hamiltonian there you have a
+
+ align:start position:0%
+that's Hamiltonian there you have a
+ 
+
+ align:start position:0%
+that's Hamiltonian there you have a
+square here
+
+ align:start position:0%
+square here
+ 
+
+ align:start position:0%
+square here
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+and now we evaluate this we have to do
+
+ align:start position:0%
+and now we evaluate this we have to do
+ 
+
+ align:start position:0%
+and now we evaluate this we have to do
+even more integrals and get what is the
+
+ align:start position:0%
+even more integrals and get what is the
+ 
+
+ align:start position:0%
+even more integrals and get what is the
+potential energy contributed by the
+
+ align:start position:0%
+potential energy contributed by the
+ 
+
+ align:start position:0%
+potential energy contributed by the
+electronic cloud so here is the function
+
+ align:start position:0%
+electronic cloud so here is the function
+ 
+
+ align:start position:0%
+electronic cloud so here is the function
+that you get so I'll plot here I'll call
+
+ align:start position:0%
+that you get so I'll plot here I'll call
+ 
+
+ align:start position:0%
+that you get so I'll plot here I'll call
+this calls for a variable X which is
+
+ align:start position:0%
+this calls for a variable X which is
+ 
+
+ align:start position:0%
+this calls for a variable X which is
+going to be the separation divided by a
+
+ align:start position:0%
+going to be the separation divided by a
+ 
+
+ align:start position:0%
+going to be the separation divided by a
+naught this is the separation between
+
+ align:start position:0%
+naught this is the separation between
+ 
+
+ align:start position:0%
+naught this is the separation between
+the protons divided by a naught so here
+
+ align:start position:0%
+the protons divided by a naught so here
+ 
+
+ align:start position:0%
+the protons divided by a naught so here
+is going to be the electronic energy as
+
+ align:start position:0%
+is going to be the electronic energy as
+ 
+
+ align:start position:0%
+is going to be the electronic energy as
+a function of X and here is X and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright so as X goes to 0 means the
+
+ align:start position:0%
+alright so as X goes to 0 means the
+ 
+
+ align:start position:0%
+alright so as X goes to 0 means the
+nuclei are going on top of each other
+
+ align:start position:0%
+nuclei are going on top of each other
+ 
+
+ align:start position:0%
+nuclei are going on top of each other
+that's the place where the wave function
+
+ align:start position:0%
+that's the place where the wave function
+ 
+
+ align:start position:0%
+that's the place where the wave function
+is not all that great and that's not so
+
+ align:start position:0%
+is not all that great and that's not so
+ 
+
+ align:start position:0%
+is not all that great and that's not so
+good it turns out that here you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus 3 redbirds remember the red Berg
+
+ align:start position:0%
+minus 3 redbirds remember the red Berg
+ 
+
+ align:start position:0%
+minus 3 redbirds remember the red Berg
+was eastward over to a naught and it's
+
+ align:start position:0%
+was eastward over to a naught and it's
+ 
+
+ align:start position:0%
+was eastward over to a naught and it's
+about 13 point 6 e V is just the ground
+
+ align:start position:0%
+about 13 point 6 e V is just the ground
+ 
+
+ align:start position:0%
+about 13 point 6 e V is just the ground
+state energy of a Hydra you do get that
+
+ align:start position:0%
+state energy of a Hydra you do get that
+ 
+
+ align:start position:0%
+state energy of a Hydra you do get that
+the energy due to the electronic
+
+ align:start position:0%
+the energy due to the electronic
+ 
+
+ align:start position:0%
+the energy due to the electronic
+configuration is negative and it goes to
+
+ align:start position:0%
+configuration is negative and it goes to
+ 
+
+ align:start position:0%
+configuration is negative and it goes to
+this value and then it starts to grow
+
+ align:start position:0%
+this value and then it starts to grow
+ 
+
+ align:start position:0%
+this value and then it starts to grow
+quadratically and goes up and I want to
+
+ align:start position:0%
+quadratically and goes up and I want to
+ 
+
+ align:start position:0%
+quadratically and goes up and I want to
+know in your opinion what's gonna be the
+
+ align:start position:0%
+know in your opinion what's gonna be the
+ 
+
+ align:start position:0%
+know in your opinion what's gonna be the
+next asymptote so what is it going to
+
+ align:start position:0%
+next asymptote so what is it going to
+ 
+
+ align:start position:0%
+next asymptote so what is it going to
+asymptote as
+
+ align:start position:0%
+asymptote as
+ 
+
+ align:start position:0%
+asymptote as
+goes to infinity let's make the analogy
+
+ align:start position:0%
+goes to infinity let's make the analogy
+ 
+
+ align:start position:0%
+goes to infinity let's make the analogy
+there right answer is it actually stops
+
+ align:start position:0%
+there right answer is it actually stops
+ 
+
+ align:start position:0%
+there right answer is it actually stops
+here and you remember this problem of
+
+ align:start position:0%
+here and you remember this problem of
+ 
+
+ align:start position:0%
+here and you remember this problem of
+the diffs of many times probably if you
+
+ align:start position:0%
+the diffs of many times probably if you
+ 
+
+ align:start position:0%
+the diffs of many times probably if you
+have a supposed to square well you have
+
+ align:start position:0%
+have a supposed to square well you have
+ 
+
+ align:start position:0%
+have a supposed to square well you have
+a wave function that is like that now if
+
+ align:start position:0%
+a wave function that is like that now if
+ 
+
+ align:start position:0%
+a wave function that is like that now if
+you have to square well and it has a
+
+ align:start position:0%
+you have to square well and it has a
+ 
+
+ align:start position:0%
+you have to square well and it has a
+ground state energy if you have to
+
+ align:start position:0%
+ground state energy if you have to
+ 
+
+ align:start position:0%
+ground state energy if you have to
+square wells like that and you ask what
+
+ align:start position:0%
+square wells like that and you ask what
+ 
+
+ align:start position:0%
+square wells like that and you ask what
+is the ground state energy the ground
+
+ align:start position:0%
+is the ground state energy the ground
+ 
+
+ align:start position:0%
+is the ground state energy the ground
+state energy is roughly equal to the
+
+ align:start position:0%
+state energy is roughly equal to the
+ 
+
+ align:start position:0%
+state energy is roughly equal to the
+ground state energy of a single square
+
+ align:start position:0%
+ground state energy of a single square
+ 
+
+ align:start position:0%
+ground state energy of a single square
+well because what happens is that the
+
+ align:start position:0%
+well because what happens is that the
+ 
+
+ align:start position:0%
+well because what happens is that the
+wave function goes like that well
+
+ align:start position:0%
+wave function goes like that well
+ 
+
+ align:start position:0%
+wave function goes like that well
+actually like that so yes the wave
+
+ align:start position:0%
+actually like that so yes the wave
+ 
+
+ align:start position:0%
+actually like that so yes the wave
+function spends equal time but it's the
+
+ align:start position:0%
+function spends equal time but it's the
+ 
+
+ align:start position:0%
+function spends equal time but it's the
+same energy as if there would be a
+
+ align:start position:0%
+same energy as if there would be a
+ 
+
+ align:start position:0%
+same energy as if there would be a
+single square well so here it is the
+
+ align:start position:0%
+single square well so here it is the
+ 
+
+ align:start position:0%
+single square well so here it is the
+protons are very far away in a symmetric
+
+ align:start position:0%
+protons are very far away in a symmetric
+ 
+
+ align:start position:0%
+protons are very far away in a symmetric
+state ground state the electron is half
+
+ align:start position:0%
+state ground state the electron is half
+ 
+
+ align:start position:0%
+state ground state the electron is half
+the times here half the times there but
+
+ align:start position:0%
+the times here half the times there but
+ 
+
+ align:start position:0%
+the times here half the times there but
+the energy is the same energy as if it
+
+ align:start position:0%
+the energy is the same energy as if it
+ 
+
+ align:start position:0%
+the energy is the same energy as if it
+would be in either one so this is an
+
+ align:start position:0%
+would be in either one so this is an
+ 
+
+ align:start position:0%
+would be in either one so this is an
+intuition that you may have from 804 805
+
+ align:start position:0%
+intuition that you may have from 804 805
+ 
+
+ align:start position:0%
+intuition that you may have from 804 805
+so so here it is that's what it does
+
+ align:start position:0%
+so so here it is that's what it does
+ 
+
+ align:start position:0%
+so so here it is that's what it does
+that's good in fact if you write the EE
+
+ align:start position:0%
+that's good in fact if you write the EE
+ 
+
+ align:start position:0%
+that's good in fact if you write the EE
+of X over redbirds it behaves here like
+
+ align:start position:0%
+of X over redbirds it behaves here like
+ 
+
+ align:start position:0%
+of X over redbirds it behaves here like
+minus 3 plus x squared plus dot dot so
+
+ align:start position:0%
+minus 3 plus x squared plus dot dot so
+ 
+
+ align:start position:0%
+minus 3 plus x squared plus dot dot so
+it starts growing and then asymptotes
+
+ align:start position:0%
+it starts growing and then asymptotes
+ 
+
+ align:start position:0%
+it starts growing and then asymptotes
+with a exponential there ok but what did
+
+ align:start position:0%
+with a exponential there ok but what did
+ 
+
+ align:start position:0%
+with a exponential there ok but what did
+we say was of the born-oppenheimer
+
+ align:start position:0%
+we say was of the born-oppenheimer
+ 
+
+ align:start position:0%
+we say was of the born-oppenheimer
+approximation was the idea that then you
+
+ align:start position:0%
+approximation was the idea that then you
+ 
+
+ align:start position:0%
+approximation was the idea that then you
+have dynamics of the nuclei
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+based on so born-oppenheimer tells you
+
+ align:start position:0%
+based on so born-oppenheimer tells you
+ 
+
+ align:start position:0%
+based on so born-oppenheimer tells you
+that the Hamiltonian for the nuclear
+
+ align:start position:0%
+that the Hamiltonian for the nuclear
+ 
+
+ align:start position:0%
+that the Hamiltonian for the nuclear
+degrees of freedom is given by H this H
+
+ align:start position:0%
+degrees of freedom is given by H this H
+ 
+
+ align:start position:0%
+degrees of freedom is given by H this H
+effective is capital P over 2m squared
+
+ align:start position:0%
+effective is capital P over 2m squared
+ 
+
+ align:start position:0%
+effective is capital P over 2m squared
+plus they are nuclear nuclear but then
+
+ align:start position:0%
+plus they are nuclear nuclear but then
+ 
+
+ align:start position:0%
+plus they are nuclear nuclear but then
+so Plus this electronic energy so this
+
+ align:start position:0%
+so Plus this electronic energy so this
+ 
+
+ align:start position:0%
+so Plus this electronic energy so this
+electronic energy we already calculated
+
+ align:start position:0%
+electronic energy we already calculated
+ 
+
+ align:start position:0%
+electronic energy we already calculated
+the nuclear nuclear potential in this
+
+ align:start position:0%
+the nuclear nuclear potential in this
+ 
+
+ align:start position:0%
+the nuclear nuclear potential in this
+case is the proton proton potential V
+
+ align:start position:0%
+case is the proton proton potential V
+ 
+
+ align:start position:0%
+case is the proton proton potential V
+and n is e squared over R it is
+
+ align:start position:0%
+and n is e squared over R it is
+ 
+
+ align:start position:0%
+and n is e squared over R it is
+repulsive you see this if you wanted to
+
+ align:start position:0%
+repulsive you see this if you wanted to
+ 
+
+ align:start position:0%
+repulsive you see this if you wanted to
+minimize the electronic energy you still
+
+ align:start position:0%
+minimize the electronic energy you still
+ 
+
+ align:start position:0%
+minimize the electronic energy you still
+don't get anything you you get a system
+
+ align:start position:0%
+don't get anything you you get a system
+ 
+
+ align:start position:0%
+don't get anything you you get a system
+that collapses to zero that's certainly
+
+ align:start position:0%
+that collapses to zero that's certainly
+ 
+
+ align:start position:0%
+that collapses to zero that's certainly
+not the molecule but this nm is this so
+
+ align:start position:0%
+not the molecule but this nm is this so
+ 
+
+ align:start position:0%
+not the molecule but this nm is this so
+we can write it as e squared over 2a is
+
+ align:start position:0%
+we can write it as e squared over 2a is
+ 
+
+ align:start position:0%
+we can write it as e squared over 2a is
+zero and then put a 2 over R over a zero
+
+ align:start position:0%
+zero and then put a 2 over R over a zero
+ 
+
+ align:start position:0%
+zero and then put a 2 over R over a zero
+to get all these numbers nicely so the V
+
+ align:start position:0%
+to get all these numbers nicely so the V
+ 
+
+ align:start position:0%
+to get all these numbers nicely so the V
+n n is a red Burk times 2 over X so in
+
+ align:start position:0%
+n n is a red Burk times 2 over X so in
+ 
+
+ align:start position:0%
+n n is a red Burk times 2 over X so in
+terms of X there V n n it's a 2 over X
+
+ align:start position:0%
+terms of X there V n n it's a 2 over X
+ 
+
+ align:start position:0%
+terms of X there V n n it's a 2 over X
+oops a 2 over X potential like that so
+
+ align:start position:0%
+oops a 2 over X potential like that so
+ 
+
+ align:start position:0%
+oops a 2 over X potential like that so
+now you have a possibility of getting a
+
+ align:start position:0%
+now you have a possibility of getting a
+ 
+
+ align:start position:0%
+now you have a possibility of getting a
+stable ground state so the potential for
+
+ align:start position:0%
+stable ground state so the potential for
+ 
+
+ align:start position:0%
+stable ground state so the potential for
+the nucleons so the total potential for
+
+ align:start position:0%
+the nucleons so the total potential for
+ 
+
+ align:start position:0%
+the nucleons so the total potential for
+the nucleons is the sum of these two
+
+ align:start position:0%
+the nucleons is the sum of these two
+ 
+
+ align:start position:0%
+the nucleons is the sum of these two
+potentials
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and how does it look well some of the
+
+ align:start position:0%
+and how does it look well some of the
+ 
+
+ align:start position:0%
+and how does it look well some of the
+two potential so e e of X plus V and n
+
+ align:start position:0%
+two potential so e e of X plus V and n
+ 
+
+ align:start position:0%
+two potential so e e of X plus V and n
+of X let's divide by red burg as a
+
+ align:start position:0%
+of X let's divide by red burg as a
+ 
+
+ align:start position:0%
+of X let's divide by red burg as a
+function of X goes off here is minus 1
+
+ align:start position:0%
+function of X goes off here is minus 1
+ 
+
+ align:start position:0%
+function of X goes off here is minus 1
+and it goes more or less like ok let me
+
+ align:start position:0%
+and it goes more or less like ok let me
+ 
+
+ align:start position:0%
+and it goes more or less like ok let me
+try to get this right 1 2 3 4 5 ok it
+
+ align:start position:0%
+try to get this right 1 2 3 4 5 ok it
+ 
+
+ align:start position:0%
+try to get this right 1 2 3 4 5 ok it
+goes up here down crosses the minus 1
+
+ align:start position:0%
+goes up here down crosses the minus 1
+ 
+
+ align:start position:0%
+goes up here down crosses the minus 1
+line and goes to a minimum here pretty
+
+ align:start position:0%
+line and goes to a minimum here pretty
+ 
+
+ align:start position:0%
+line and goes to a minimum here pretty
+much is something like that it's a
+
+ align:start position:0%
+much is something like that it's a
+ 
+
+ align:start position:0%
+much is something like that it's a
+rather little quadratic minimum is
+
+ align:start position:0%
+rather little quadratic minimum is
+ 
+
+ align:start position:0%
+rather little quadratic minimum is
+rather flat and these are the numbers
+
+ align:start position:0%
+rather flat and these are the numbers
+ 
+
+ align:start position:0%
+rather flat and these are the numbers
+you care for this is the minimum maybe
+
+ align:start position:0%
+you care for this is the minimum maybe
+ 
+
+ align:start position:0%
+you care for this is the minimum maybe
+doesn't look like that in my graph too
+
+ align:start position:0%
+doesn't look like that in my graph too
+ 
+
+ align:start position:0%
+doesn't look like that in my graph too
+well but it's a very flat minimum and
+
+ align:start position:0%
+well but it's a very flat minimum and
+ 
+
+ align:start position:0%
+well but it's a very flat minimum and
+are over a 0 at the minimum is in fact
+
+ align:start position:0%
+are over a 0 at the minimum is in fact
+ 
+
+ align:start position:0%
+are over a 0 at the minimum is in fact
+2.49 and E over red burg at the minimum
+
+ align:start position:0%
+2.49 and E over red burg at the minimum
+ 
+
+ align:start position:0%
+2.49 and E over red burg at the minimum
+is minus 1 point 2 9 7 so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those are our results now you have a
+
+ align:start position:0%
+those are our results now you have a
+ 
+
+ align:start position:0%
+those are our results now you have a
+potential you could calculate the
+
+ align:start position:0%
+potential you could calculate the
+ 
+
+ align:start position:0%
+potential you could calculate the
+quadratic term around the potential and
+
+ align:start position:0%
+quadratic term around the potential and
+ 
+
+ align:start position:0%
+quadratic term around the potential and
+then you get an approximate oscillation
+
+ align:start position:0%
+then you get an approximate oscillation
+ 
+
+ align:start position:0%
+then you get an approximate oscillation
+Hamiltonian that those would be the
+
+ align:start position:0%
+Hamiltonian that those would be the
+ 
+
+ align:start position:0%
+Hamiltonian that those would be the
+nuclear vibrations you could calculate
+
+ align:start position:0%
+nuclear vibrations you could calculate
+ 
+
+ align:start position:0%
+nuclear vibrations you could calculate
+the frequency of the nuclear vibrations
+
+ align:start position:0%
+the frequency of the nuclear vibrations
+ 
+
+ align:start position:0%
+the frequency of the nuclear vibrations
+and the energy of the nuclear vibrations
+
+ align:start position:0%
+and the energy of the nuclear vibrations
+ 
+
+ align:start position:0%
+and the energy of the nuclear vibrations
+it's a very simple but nice model you
+
+ align:start position:0%
+it's a very simple but nice model you
+ 
+
+ align:start position:0%
+it's a very simple but nice model you
+can calculate everything pretty much
+
+ align:start position:0%
+can calculate everything pretty much
+ 
+
+ align:start position:0%
+can calculate everything pretty much
+about this molecule and compare with
+
+ align:start position:0%
+about this molecule and compare with
+ 
+
+ align:start position:0%
+about this molecule and compare with
+experiments so how does it do the
+
+ align:start position:0%
+experiments so how does it do the
+ 
+
+ align:start position:0%
+experiments so how does it do the
+comparison with experiment it that's
+
+ align:start position:0%
+comparison with experiment it that's
+ 
+
+ align:start position:0%
+comparison with experiment it that's
+okay it doesn't do very well so let me
+
+ align:start position:0%
+okay it doesn't do very well so let me
+ 
+
+ align:start position:0%
+okay it doesn't do very well so let me
+tell you what what's happening so again
+
+ align:start position:0%
+tell you what what's happening so again
+ 
+
+ align:start position:0%
+tell you what what's happening so again
+we do get this system happily the
+
+ align:start position:0%
+we do get this system happily the
+ 
+
+ align:start position:0%
+we do get this system happily the
+minimum was below minus 1 the minus 1
+
+ align:start position:0%
+minimum was below minus 1 the minus 1
+ 
+
+ align:start position:0%
+minimum was below minus 1 the minus 1
+was the situation in which you have a
+
+ align:start position:0%
+was the situation in which you have a
+ 
+
+ align:start position:0%
+was the situation in which you have a
+hydrogen atom and a free proton so there
+
+ align:start position:0%
+hydrogen atom and a free proton so there
+ 
+
+ align:start position:0%
+hydrogen atom and a free proton so there
+is a bound state energy but the bound
+
+ align:start position:0%
+is a bound state energy but the bound
+ 
+
+ align:start position:0%
+is a bound state energy but the bound
+state energies not conceptually right to
+
+ align:start position:0%
+state energies not conceptually right to
+ 
+
+ align:start position:0%
+state energies not conceptually right to
+think of it as this big energy it's just
+
+ align:start position:0%
+think of it as this big energy it's just
+ 
+
+ align:start position:0%
+think of it as this big energy it's just
+this little part here in which this is
+
+ align:start position:0%
+this little part here in which this is
+ 
+
+ align:start position:0%
+this little part here in which this is
+the extra binding that you can have when
+
+ align:start position:0%
+the extra binding that you can have when
+ 
+
+ align:start position:0%
+the extra binding that you can have when
+you bring a proton near to the hydrogen
+
+ align:start position:0%
+you bring a proton near to the hydrogen
+ 
+
+ align:start position:0%
+you bring a proton near to the hydrogen
+atom so this extra part so the bound
+
+ align:start position:0%
+atom so this extra part so the bound
+ 
+
+ align:start position:0%
+atom so this extra part so the bound
+state energy I'll write a couple of
+
+ align:start position:0%
+state energy I'll write a couple of
+ 
+
+ align:start position:0%
+state energy I'll write a couple of
+words here and we'll stop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the bound state energy is e this e that
+
+ align:start position:0%
+the bound state energy is e this e that
+ 
+
+ align:start position:0%
+the bound state energy is e this e that
+we the term here at the minimum is minus
+
+ align:start position:0%
+we the term here at the minimum is minus
+ 
+
+ align:start position:0%
+we the term here at the minimum is minus
+one Redbird minus zero point one two
+
+ align:start position:0%
+one Redbird minus zero point one two
+ 
+
+ align:start position:0%
+one Redbird minus zero point one two
+nine seven read Burks which is minus one
+
+ align:start position:0%
+nine seven read Burks which is minus one
+ 
+
+ align:start position:0%
+nine seven read Burks which is minus one
+read burke - 1.76 Evy
+
+ align:start position:0%
+read burke - 1.76 Evy
+ 
+
+ align:start position:0%
+read burke - 1.76 Evy
+so this is what you would call the bound
+
+ align:start position:0%
+so this is what you would call the bound
+ 
+
+ align:start position:0%
+so this is what you would call the bound
+state energy of this system because it's
+
+ align:start position:0%
+state energy of this system because it's
+ 
+
+ align:start position:0%
+state energy of this system because it's
+the least energy you need to start to
+
+ align:start position:0%
+the least energy you need to start to
+ 
+
+ align:start position:0%
+the least energy you need to start to
+dissociate it not to dissociate it
+
+ align:start position:0%
+dissociate it not to dissociate it
+ 
+
+ align:start position:0%
+dissociate it not to dissociate it
+completely but to start the dissociated
+
+ align:start position:0%
+completely but to start the dissociated
+ 
+
+ align:start position:0%
+completely but to start the dissociated
+1.76 true value value is 2.8 evey so
+
+ align:start position:0%
+1.76 true value value is 2.8 evey so
+ 
+
+ align:start position:0%
+1.76 true value value is 2.8 evey so
+it's not great but sort of order of
+
+ align:start position:0%
+it's not great but sort of order of
+ 
+
+ align:start position:0%
+it's not great but sort of order of
+magnitude another thing that you can ask
+
+ align:start position:0%
+magnitude another thing that you can ask
+ 
+
+ align:start position:0%
+magnitude another thing that you can ask
+is what is the separation between the
+
+ align:start position:0%
+is what is the separation between the
+ 
+
+ align:start position:0%
+is what is the separation between the
+nuclei in this iron how far away are
+
+ align:start position:0%
+nuclei in this iron how far away are
+ 
+
+ align:start position:0%
+nuclei in this iron how far away are
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+and this gives a prediction that it's
+
+ align:start position:0%
+and this gives a prediction that it's
+ 
+
+ align:start position:0%
+and this gives a prediction that it's
+about two point forty nine a zero so
+
+ align:start position:0%
+about two point forty nine a zero so
+ 
+
+ align:start position:0%
+about two point forty nine a zero so
+separation is are equal to point forty
+
+ align:start position:0%
+separation is are equal to point forty
+ 
+
+ align:start position:0%
+separation is are equal to point forty
+nine a zero which is two point forty
+
+ align:start position:0%
+nine a zero which is two point forty
+ 
+
+ align:start position:0%
+nine a zero which is two point forty
+nine times zero point five to nine and
+
+ align:start position:0%
+nine times zero point five to nine and
+ 
+
+ align:start position:0%
+nine times zero point five to nine and
+strums it's about one point thirty two
+
+ align:start position:0%
+strums it's about one point thirty two
+ 
+
+ align:start position:0%
+strums it's about one point thirty two
+angstroms and through values two point
+
+ align:start position:0%
+angstroms and through values two point
+ 
+
+ align:start position:0%
+angstroms and through values two point
+experimental value about the of our our
+
+ align:start position:0%
+experimental value about the of our our
+ 
+
+ align:start position:0%
+experimental value about the of our our
+experiment it's not that far is 106 and
+
+ align:start position:0%
+experiment it's not that far is 106 and
+ 
+
+ align:start position:0%
+experiment it's not that far is 106 and
+so you know twenty percent there twenty
+
+ align:start position:0%
+so you know twenty percent there twenty
+ 
+
+ align:start position:0%
+so you know twenty percent there twenty
+five percent their words but it gives
+
+ align:start position:0%
+five percent their words but it gives
+ 
+
+ align:start position:0%
+five percent their words but it gives
+you a way to think about this system you
+
+ align:start position:0%
+you a way to think about this system you
+ 
+
+ align:start position:0%
+you a way to think about this system you
+get all the physics you understand the
+
+ align:start position:0%
+get all the physics you understand the
+ 
+
+ align:start position:0%
+get all the physics you understand the
+physics the born-oppenheimer physics is
+
+ align:start position:0%
+physics the born-oppenheimer physics is
+ 
+
+ align:start position:0%
+physics the born-oppenheimer physics is
+that they
+
+ align:start position:0%
+that they
+ 
+
+ align:start position:0%
+that they
+electron energy in the fix lattice is a
+
+ align:start position:0%
+electron energy in the fix lattice is a
+ 
+
+ align:start position:0%
+electron energy in the fix lattice is a
+potential term for the nuclei added to
+
+ align:start position:0%
+potential term for the nuclei added to
+ 
+
+ align:start position:0%
+potential term for the nuclei added to
+the nucleus nucleus repulsion gives you
+
+ align:start position:0%
+the nucleus nucleus repulsion gives you
+ 
+
+ align:start position:0%
+the nucleus nucleus repulsion gives you
+a total potential term for the nuclear
+
+ align:start position:0%
+a total potential term for the nuclear
+ 
+
+ align:start position:0%
+a total potential term for the nuclear
+degrees of freedom you can find the
+
+ align:start position:0%
+degrees of freedom you can find the
+ 
+
+ align:start position:0%
+degrees of freedom you can find the
+stable situation and if you want to do
+
+ align:start position:0%
+stable situation and if you want to do
+ 
+
+ align:start position:0%
+stable situation and if you want to do
+quantum mechanics and vibrations of the
+
+ align:start position:0%
+quantum mechanics and vibrations of the
+ 
+
+ align:start position:0%
+quantum mechanics and vibrations of the
+nuclear well do the harmonic oscillator
+
+ align:start position:0%
+nuclear well do the harmonic oscillator
+ 
+
+ align:start position:0%
+nuclear well do the harmonic oscillator
+associated with this thing nice thing is
+
+ align:start position:0%
+associated with this thing nice thing is
+ 
+
+ align:start position:0%
+associated with this thing nice thing is
+you can complicate these wave functions
+
+ align:start position:0%
+you can complicate these wave functions
+ 
+
+ align:start position:0%
+you can complicate these wave functions
+a little and get better and better
+
+ align:start position:0%
+a little and get better and better
+ 
+
+ align:start position:0%
+a little and get better and better
+answers and it's fun things that can be
+
+ align:start position:0%
+answers and it's fun things that can be
+ 
+
+ align:start position:0%
+answers and it's fun things that can be
+done numerically and you have a
+
+ align:start position:0%
+done numerically and you have a
+ 
+
+ align:start position:0%
+done numerically and you have a
+remarkably powerful tool to understand
+
+ align:start position:0%
+remarkably powerful tool to understand
+ 
+
+ align:start position:0%
+remarkably powerful tool to understand
+these things
+
+ align:start position:0%
+these things
+ 
+
+ align:start position:0%
+these things
+so with this we'll close our whole
+
+ align:start position:0%
+so with this we'll close our whole
+ 
+
+ align:start position:0%
+so with this we'll close our whole
+chapter and adiabatic physics and next
+
+ align:start position:0%
+chapter and adiabatic physics and next
+ 
+
+ align:start position:0%
+chapter and adiabatic physics and next
+time we will begin with scattering
\ No newline at end of file
diff --git a/papfq4sdC3w.txt b/papfq4sdC3w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b5e28cd90c31e2416ad73ecd40864324f01326a5
--- /dev/null
+++ b/papfq4sdC3w.txt
@@ -0,0 +1,2179 @@
+align:start position:0%
+ 
+okay so we have set up the problem we
+
+ align:start position:0%
+okay so we have set up the problem we
+ 
+
+ align:start position:0%
+okay so we have set up the problem we
+now have to understand what is the
+
+ align:start position:0%
+now have to understand what is the
+ 
+
+ align:start position:0%
+now have to understand what is the
+physics of this f of theta and Phi in a
+
+ align:start position:0%
+physics of this f of theta and Phi in a
+ 
+
+ align:start position:0%
+physics of this f of theta and Phi in a
+way solving the scattering problem means
+
+ align:start position:0%
+way solving the scattering problem means
+ 
+
+ align:start position:0%
+way solving the scattering problem means
+solving for the faders and Phi's now you
+
+ align:start position:0%
+solving for the faders and Phi's now you
+ 
+
+ align:start position:0%
+solving for the faders and Phi's now you
+would say okay that seems reasonable you
+
+ align:start position:0%
+would say okay that seems reasonable you
+ 
+
+ align:start position:0%
+would say okay that seems reasonable you
+know how the solution looks far away and
+
+ align:start position:0%
+know how the solution looks far away and
+ 
+
+ align:start position:0%
+know how the solution looks far away and
+that's where you're going to do the
+
+ align:start position:0%
+that's where you're going to do the
+ 
+
+ align:start position:0%
+that's where you're going to do the
+measurements that's where you have the
+
+ align:start position:0%
+measurements that's where you have the
+ 
+
+ align:start position:0%
+measurements that's where you have the
+detectors so we have to find what f of
+
+ align:start position:0%
+detectors so we have to find what f of
+ 
+
+ align:start position:0%
+detectors so we have to find what f of
+theta and Phi is but suppose you had it
+
+ align:start position:0%
+theta and Phi is but suppose you had it
+ 
+
+ align:start position:0%
+theta and Phi is but suppose you had it
+what have you learned if you have the F
+
+ align:start position:0%
+what have you learned if you have the F
+ 
+
+ align:start position:0%
+what have you learned if you have the F
+of theta and Phi so this is what we need
+
+ align:start position:0%
+of theta and Phi so this is what we need
+ 
+
+ align:start position:0%
+of theta and Phi so this is what we need
+to compute and we will build towards a
+
+ align:start position:0%
+to compute and we will build towards a
+ 
+
+ align:start position:0%
+to compute and we will build towards a
+computation of this using what is called
+
+ align:start position:0%
+computation of this using what is called
+ 
+
+ align:start position:0%
+computation of this using what is called
+partial waves waves and phase shifts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this will allow us to calculate the F of
+
+ align:start position:0%
+this will allow us to calculate the F of
+ 
+
+ align:start position:0%
+this will allow us to calculate the F of
+theta and Phi but doesn't tell you yet
+
+ align:start position:0%
+theta and Phi but doesn't tell you yet
+ 
+
+ align:start position:0%
+theta and Phi but doesn't tell you yet
+what f of theta and Phi is so the nice
+
+ align:start position:0%
+what f of theta and Phi is so the nice
+ 
+
+ align:start position:0%
+what f of theta and Phi is so the nice
+thing of this F of theta and Phi is that
+
+ align:start position:0%
+thing of this F of theta and Phi is that
+ 
+
+ align:start position:0%
+thing of this F of theta and Phi is that
+it gives you the cross section of the
+
+ align:start position:0%
+it gives you the cross section of the
+ 
+
+ align:start position:0%
+it gives you the cross section of the
+process so we need to understand what is
+
+ align:start position:0%
+process so we need to understand what is
+ 
+
+ align:start position:0%
+process so we need to understand what is
+the cross section so what is the cross
+
+ align:start position:0%
+the cross section so what is the cross
+ 
+
+ align:start position:0%
+the cross section so what is the cross
+section it's a way to quantify the fact
+
+ align:start position:0%
+section it's a way to quantify the fact
+ 
+
+ align:start position:0%
+section it's a way to quantify the fact
+of the scattering Center on the
+
+ align:start position:0%
+of the scattering Center on the
+ 
+
+ align:start position:0%
+of the scattering Center on the
+particles suppose you have your
+
+ align:start position:0%
+particles suppose you have your
+ 
+
+ align:start position:0%
+particles suppose you have your
+scattering Center you shoot particles in
+
+ align:start position:0%
+scattering Center you shoot particles in
+ 
+
+ align:start position:0%
+scattering Center you shoot particles in
+then you can say okay let me let's see
+
+ align:start position:0%
+then you can say okay let me let's see
+ 
+
+ align:start position:0%
+then you can say okay let me let's see
+with my detectors how many particles go
+
+ align:start position:0%
+with my detectors how many particles go
+ 
+
+ align:start position:0%
+with my detectors how many particles go
+off at an angle theta when you say three
+
+ align:start position:0%
+off at an angle theta when you say three
+ 
+
+ align:start position:0%
+off at an angle theta when you say three
+particles per second I'm finding us you
+
+ align:start position:0%
+particles per second I'm finding us you
+ 
+
+ align:start position:0%
+particles per second I'm finding us you
+should in particles I'm getting three
+
+ align:start position:0%
+should in particles I'm getting three
+ 
+
+ align:start position:0%
+should in particles I'm getting three
+particles per second in this detector at
+
+ align:start position:0%
+particles per second in this detector at
+ 
+
+ align:start position:0%
+particles per second in this detector at
+this angle my detector this angle
+
+ align:start position:0%
+this angle my detector this angle
+ 
+
+ align:start position:0%
+this angle my detector this angle
+coverts a solid angle of 100 and it's
+
+ align:start position:0%
+coverts a solid angle of 100 and it's
+ 
+
+ align:start position:0%
+coverts a solid angle of 100 and it's
+getting three particles per second then
+
+ align:start position:0%
+getting three particles per second then
+ 
+
+ align:start position:0%
+getting three particles per second then
+you can say okay what is the area of a
+
+ align:start position:0%
+you can say okay what is the area of a
+ 
+
+ align:start position:0%
+you can say okay what is the area of a
+target that out of the incoming beam
+
+ align:start position:0%
+target that out of the incoming beam
+ 
+
+ align:start position:0%
+target that out of the incoming beam
+captures three particles per second and
+
+ align:start position:0%
+captures three particles per second and
+ 
+
+ align:start position:0%
+captures three particles per second and
+maybe you know the lots of particles
+
+ align:start position:0%
+maybe you know the lots of particles
+ 
+
+ align:start position:0%
+maybe you know the lots of particles
+coming in but if you produce some area
+
+ align:start position:0%
+coming in but if you produce some area
+ 
+
+ align:start position:0%
+coming in but if you produce some area
+that area will capture three particles
+
+ align:start position:0%
+that area will capture three particles
+ 
+
+ align:start position:0%
+that area will capture three particles
+per second and that would be what we
+
+ align:start position:0%
+per second and that would be what we
+ 
+
+ align:start position:0%
+per second and that would be what we
+call the differential cross-section the
+
+ align:start position:0%
+call the differential cross-section the
+ 
+
+ align:start position:0%
+call the differential cross-section the
+value of the area that captures or just
+
+ align:start position:0%
+value of the area that captures or just
+ 
+
+ align:start position:0%
+value of the area that captures or just
+whose flux of particles is precisely
+
+ align:start position:0%
+whose flux of particles is precisely
+ 
+
+ align:start position:0%
+whose flux of particles is precisely
+what you're getting out there so if
+
+ align:start position:0%
+what you're getting out there so if
+ 
+
+ align:start position:0%
+what you're getting out there so if
+you're looking at some process in which
+
+ align:start position:0%
+you're looking at some process in which
+ 
+
+ align:start position:0%
+you're looking at some process in which
+there's this incoming particles and you
+
+ align:start position:0%
+there's this incoming particles and you
+ 
+
+ align:start position:0%
+there's this incoming particles and you
+look at some angle the Omega where
+
+ align:start position:0%
+look at some angle the Omega where
+ 
+
+ align:start position:0%
+look at some angle the Omega where
+there's a detector a detector that
+
+ align:start position:0%
+there's a detector a detector that
+ 
+
+ align:start position:0%
+there's a detector a detector that
+captures this angle you can associate to
+
+ align:start position:0%
+captures this angle you can associate to
+ 
+
+ align:start position:0%
+captures this angle you can associate to
+this object and D Sigma which is a
+
+ align:start position:0%
+this object and D Sigma which is a
+ 
+
+ align:start position:0%
+this object and D Sigma which is a
+differential cross-section with units of
+
+ align:start position:0%
+differential cross-section with units of
+ 
+
+ align:start position:0%
+differential cross-section with units of
+area and the physical interpretation of
+
+ align:start position:0%
+area and the physical interpretation of
+ 
+
+ align:start position:0%
+area and the physical interpretation of
+the D Sigma for this V Omega is that
+
+ align:start position:0%
+the D Sigma for this V Omega is that
+ 
+
+ align:start position:0%
+the D Sigma for this V Omega is that
+Sigma is the area that captures the
+
+ align:start position:0%
+Sigma is the area that captures the
+ 
+
+ align:start position:0%
+Sigma is the area that captures the
+amount of flux that you see going in
+
+ align:start position:0%
+amount of flux that you see going in
+ 
+
+ align:start position:0%
+amount of flux that you see going in
+this direction so it's a way this area's
+
+ align:start position:0%
+this direction so it's a way this area's
+ 
+
+ align:start position:0%
+this direction so it's a way this area's
+this differential cross-sections give
+
+ align:start position:0%
+this differential cross-sections give
+ 
+
+ align:start position:0%
+this differential cross-sections give
+you an idea or a concrete representation
+
+ align:start position:0%
+you an idea or a concrete representation
+ 
+
+ align:start position:0%
+you an idea or a concrete representation
+of how big the target is as seen by the
+
+ align:start position:0%
+of how big the target is as seen by the
+ 
+
+ align:start position:0%
+of how big the target is as seen by the
+particles that are coming in I'll write
+
+ align:start position:0%
+particles that are coming in I'll write
+ 
+
+ align:start position:0%
+particles that are coming in I'll write
+it in in a way that makes it clear so D
+
+ align:start position:0%
+it in in a way that makes it clear so D
+ 
+
+ align:start position:0%
+it in in a way that makes it clear so D
+Sigma which is called the differential
+
+ align:start position:0%
+Sigma which is called the differential
+ 
+
+ align:start position:0%
+Sigma which is called the differential
+cross-section torrential cross
+
+ align:start position:0%
+cross-section torrential cross
+ 
+
+ align:start position:0%
+cross-section torrential cross
+section is equal number of particles
+
+ align:start position:0%
+section is equal number of particles
+ 
+
+ align:start position:0%
+section is equal number of particles
+there's lots of words here but it's good
+
+ align:start position:0%
+there's lots of words here but it's good
+ 
+
+ align:start position:0%
+there's lots of words here but it's good
+to write them scattered per unit time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+into the solid angle D Omega divided by
+
+ align:start position:0%
+into the solid angle D Omega divided by
+ 
+
+ align:start position:0%
+into the solid angle D Omega divided by
+the flux of incident particles which is
+
+ align:start position:0%
+the flux of incident particles which is
+ 
+
+ align:start position:0%
+the flux of incident particles which is
+equal to the number of particles per
+
+ align:start position:0%
+equal to the number of particles per
+ 
+
+ align:start position:0%
+equal to the number of particles per
+unit area per unit time so it's it's
+
+ align:start position:0%
+unit area per unit time so it's it's
+ 
+
+ align:start position:0%
+unit area per unit time so it's it's
+this ratio number of particles scattered
+
+ align:start position:0%
+this ratio number of particles scattered
+ 
+
+ align:start position:0%
+this ratio number of particles scattered
+per unit time into solid angle D Omega
+
+ align:start position:0%
+per unit time into solid angle D Omega
+ 
+
+ align:start position:0%
+per unit time into solid angle D Omega
+particles have no units
+
+ align:start position:0%
+particles have no units
+ 
+
+ align:start position:0%
+particles have no units
+integers scatter per unit time is 1 over
+
+ align:start position:0%
+integers scatter per unit time is 1 over
+ 
+
+ align:start position:0%
+integers scatter per unit time is 1 over
+time into the solid angle D Omega has no
+
+ align:start position:0%
+time into the solid angle D Omega has no
+ 
+
+ align:start position:0%
+time into the solid angle D Omega has no
+units either the solid anglo flux of
+
+ align:start position:0%
+units either the solid anglo flux of
+ 
+
+ align:start position:0%
+units either the solid anglo flux of
+incident particles is particles that has
+
+ align:start position:0%
+incident particles is particles that has
+ 
+
+ align:start position:0%
+incident particles is particles that has
+no units over area over time so here you
+
+ align:start position:0%
+no units over area over time so here you
+ 
+
+ align:start position:0%
+no units over area over time so here you
+had over time here over time they cancel
+
+ align:start position:0%
+had over time here over time they cancel
+ 
+
+ align:start position:0%
+had over time here over time they cancel
+this is 1 over area that ratio therefore
+
+ align:start position:0%
+this is 1 over area that ratio therefore
+ 
+
+ align:start position:0%
+this is 1 over area that ratio therefore
+has units of area and this is what I was
+
+ align:start position:0%
+has units of area and this is what I was
+ 
+
+ align:start position:0%
+has units of area and this is what I was
+telling you the differential
+
+ align:start position:0%
+telling you the differential
+ 
+
+ align:start position:0%
+telling you the differential
+cross-section which is an area
+
+ align:start position:0%
+cross-section which is an area
+ 
+
+ align:start position:0%
+cross-section which is an area
+multiplied by the flux gives you the
+
+ align:start position:0%
+multiplied by the flux gives you the
+ 
+
+ align:start position:0%
+multiplied by the flux gives you the
+number of particles per unit time that
+
+ align:start position:0%
+number of particles per unit time that
+ 
+
+ align:start position:0%
+number of particles per unit time that
+are crossing a differential cross
+
+ align:start position:0%
+are crossing a differential cross
+ 
+
+ align:start position:0%
+are crossing a differential cross
+section area and those are set equal to
+
+ align:start position:0%
+section area and those are set equal to
+ 
+
+ align:start position:0%
+section area and those are set equal to
+the number of particles per unit time
+
+ align:start position:0%
+the number of particles per unit time
+ 
+
+ align:start position:0%
+the number of particles per unit time
+that end up within this solid angle so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for a given little solid angle you get
+
+ align:start position:0%
+for a given little solid angle you get
+ 
+
+ align:start position:0%
+for a given little solid angle you get
+the D Sigma which is small as well
+
+ align:start position:0%
+the D Sigma which is small as well
+ 
+
+ align:start position:0%
+the D Sigma which is small as well
+that's why it's called differential
+
+ align:start position:0%
+that's why it's called differential
+ 
+
+ align:start position:0%
+that's why it's called differential
+cross section so let's try to show
+
+ align:start position:0%
+cross section so let's try to show
+ 
+
+ align:start position:0%
+cross section so let's try to show
+that this the Sigma is really determined
+
+ align:start position:0%
+that this the Sigma is really determined
+ 
+
+ align:start position:0%
+that this the Sigma is really determined
+by f of theta and Phi this angle solid
+
+ align:start position:0%
+by f of theta and Phi this angle solid
+ 
+
+ align:start position:0%
+by f of theta and Phi this angle solid
+angle D Omega is happening at some theta
+
+ align:start position:0%
+angle D Omega is happening at some theta
+ 
+
+ align:start position:0%
+angle D Omega is happening at some theta
+and some Phi that's a position the
+
+ align:start position:0%
+and some Phi that's a position the
+ 
+
+ align:start position:0%
+and some Phi that's a position the
+center of the little solid angle a solid
+
+ align:start position:0%
+center of the little solid angle a solid
+ 
+
+ align:start position:0%
+center of the little solid angle a solid
+angle D Omega at Theta Phi so this is
+
+ align:start position:0%
+angle D Omega at Theta Phi so this is
+ 
+
+ align:start position:0%
+angle D Omega at Theta Phi so this is
+our dog down to just calculate the
+
+ align:start position:0%
+our dog down to just calculate the
+ 
+
+ align:start position:0%
+our dog down to just calculate the
+differential cross section okay so we
+
+ align:start position:0%
+differential cross section okay so we
+ 
+
+ align:start position:0%
+differential cross section okay so we
+have to compute these fluxes we can do
+
+ align:start position:0%
+have to compute these fluxes we can do
+ 
+
+ align:start position:0%
+have to compute these fluxes we can do
+it here now we're not working with wave
+
+ align:start position:0%
+it here now we're not working with wave
+ 
+
+ align:start position:0%
+it here now we're not working with wave
+packets we're working with energy
+
+ align:start position:0%
+packets we're working with energy
+ 
+
+ align:start position:0%
+packets we're working with energy
+eigenstates and we're gonna have a
+
+ align:start position:0%
+eigenstates and we're gonna have a
+ 
+
+ align:start position:0%
+eigenstates and we're gonna have a
+little bit of a funny intuition we're
+
+ align:start position:0%
+little bit of a funny intuition we're
+ 
+
+ align:start position:0%
+little bit of a funny intuition we're
+not we're gonna get it right but you you
+
+ align:start position:0%
+not we're gonna get it right but you you
+ 
+
+ align:start position:0%
+not we're gonna get it right but you you
+have to appreciate it's a little funny
+
+ align:start position:0%
+have to appreciate it's a little funny
+ 
+
+ align:start position:0%
+have to appreciate it's a little funny
+if I have a little volume and I say that
+
+ align:start position:0%
+if I have a little volume and I say that
+ 
+
+ align:start position:0%
+if I have a little volume and I say that
+I find the probability to find a
+
+ align:start position:0%
+I find the probability to find a
+ 
+
+ align:start position:0%
+I find the probability to find a
+particle there to be one half I would
+
+ align:start position:0%
+particle there to be one half I would
+ 
+
+ align:start position:0%
+particle there to be one half I would
+say that there's a half of a particle in
+
+ align:start position:0%
+say that there's a half of a particle in
+ 
+
+ align:start position:0%
+say that there's a half of a particle in
+that little volume if I have a volume
+
+ align:start position:0%
+that little volume if I have a volume
+ 
+
+ align:start position:0%
+that little volume if I have a volume
+that whose probability to find a
+
+ align:start position:0%
+that whose probability to find a
+ 
+
+ align:start position:0%
+that whose probability to find a
+particle is one I say okay I have one
+
+ align:start position:0%
+particle is one I say okay I have one
+ 
+
+ align:start position:0%
+particle is one I say okay I have one
+particle in here that's the rough
+
+ align:start position:0%
+particle in here that's the rough
+ 
+
+ align:start position:0%
+particle in here that's the rough
+intuition so for wave functions that are
+
+ align:start position:0%
+intuition so for wave functions that are
+ 
+
+ align:start position:0%
+intuition so for wave functions that are
+not normalizable it's almost like
+
+ align:start position:0%
+not normalizable it's almost like
+ 
+
+ align:start position:0%
+not normalizable it's almost like
+suppose I squared is equal to one in a
+
+ align:start position:0%
+suppose I squared is equal to one in a
+ 
+
+ align:start position:0%
+suppose I squared is equal to one in a
+momentum I can say you would be saying
+
+ align:start position:0%
+momentum I can say you would be saying
+ 
+
+ align:start position:0%
+momentum I can say you would be saying
+like you have a particle for every unit
+
+ align:start position:0%
+like you have a particle for every unit
+ 
+
+ align:start position:0%
+like you have a particle for every unit
+volume or side squared integrates to 1
+
+ align:start position:0%
+volume or side squared integrates to 1
+ 
+
+ align:start position:0%
+volume or side squared integrates to 1
+so that's roughly the intuition and it's
+
+ align:start position:0%
+so that's roughly the intuition and it's
+ 
+
+ align:start position:0%
+so that's roughly the intuition and it's
+a it's correct really to use if you if
+
+ align:start position:0%
+a it's correct really to use if you if
+ 
+
+ align:start position:0%
+a it's correct really to use if you if
+you think of the flux of incident
+
+ align:start position:0%
+you think of the flux of incident
+ 
+
+ align:start position:0%
+you think of the flux of incident
+particles so incident flux flux
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we think of it as the probability
+
+ align:start position:0%
+we think of it as the probability
+ 
+
+ align:start position:0%
+we think of it as the probability
+current which is number of particles per
+
+ align:start position:0%
+current which is number of particles per
+ 
+
+ align:start position:0%
+current which is number of particles per
+unit time per unit area so it's H bar
+
+ align:start position:0%
+unit time per unit area so it's H bar
+ 
+
+ align:start position:0%
+unit time per unit area so it's H bar
+over m imaginary part of the incident
+
+ align:start position:0%
+over m imaginary part of the incident
+ 
+
+ align:start position:0%
+over m imaginary part of the incident
+flux so I should use the incident wave
+
+ align:start position:0%
+flux so I should use the incident wave
+ 
+
+ align:start position:0%
+flux so I should use the incident wave
+function this Phi of our gradient Phi of
+
+ align:start position:0%
+function this Phi of our gradient Phi of
+ 
+
+ align:start position:0%
+function this Phi of our gradient Phi of
+R and Phi was e to the i kz that was the
+
+ align:start position:0%
+R and Phi was e to the i kz that was the
+ 
+
+ align:start position:0%
+R and Phi was e to the i kz that was the
+incident particle
+
+ align:start position:0%
+incident particle
+ 
+
+ align:start position:0%
+incident particle
+so this laplacian gives you not
+
+ align:start position:0%
+so this laplacian gives you not
+ 
+
+ align:start position:0%
+so this laplacian gives you not
+laplacian this gradient takes a grave
+
+ align:start position:0%
+laplacian this gradient takes a grave
+ 
+
+ align:start position:0%
+laplacian this gradient takes a grave
+and it produces an i k the rest gets
+
+ align:start position:0%
+and it produces an i k the rest gets
+ 
+
+ align:start position:0%
+and it produces an i k the rest gets
+cancelled and the imaginary part gives
+
+ align:start position:0%
+cancelled and the imaginary part gives
+ 
+
+ align:start position:0%
+cancelled and the imaginary part gives
+you K so this is h-bar K over m times
+
+ align:start position:0%
+you K so this is h-bar K over m times
+ 
+
+ align:start position:0%
+you K so this is h-bar K over m times
+the unit vector Z so that's the incident
+
+ align:start position:0%
+the unit vector Z so that's the incident
+ 
+
+ align:start position:0%
+the unit vector Z so that's the incident
+flux this can be thought as the number
+
+ align:start position:0%
+flux this can be thought as the number
+ 
+
+ align:start position:0%
+flux this can be thought as the number
+of particles per unit area and per unit
+
+ align:start position:0%
+of particles per unit area and per unit
+ 
+
+ align:start position:0%
+of particles per unit area and per unit
+time you can also think of it
+
+ align:start position:0%
+time you can also think of it
+ 
+
+ align:start position:0%
+time you can also think of it
+intuitively as Rho times V the incident
+
+ align:start position:0%
+intuitively as Rho times V the incident
+ 
+
+ align:start position:0%
+intuitively as Rho times V the incident
+flux is like the incident current the
+
+ align:start position:0%
+flux is like the incident current the
+ 
+
+ align:start position:0%
+flux is like the incident current the
+current densities Rho times V Rho is
+
+ align:start position:0%
+current densities Rho times V Rho is
+ 
+
+ align:start position:0%
+current densities Rho times V Rho is
+size squared Phi squared but that's
+
+ align:start position:0%
+size squared Phi squared but that's
+ 
+
+ align:start position:0%
+size squared Phi squared but that's
+equal to 1 and the velocity of the
+
+ align:start position:0%
+equal to 1 and the velocity of the
+ 
+
+ align:start position:0%
+equal to 1 and the velocity of the
+particles is the momentum over the mass
+
+ align:start position:0%
+particles is the momentum over the mass
+ 
+
+ align:start position:0%
+particles is the momentum over the mass
+but that's H K over m and if I put the
+
+ align:start position:0%
+but that's H K over m and if I put the
+ 
+
+ align:start position:0%
+but that's H K over m and if I put the
+direction and we'll have to put a Z so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's kind of the same thing Rho V the
+
+ align:start position:0%
+it's kind of the same thing Rho V the
+ 
+
+ align:start position:0%
+it's kind of the same thing Rho V the
+incident flux are always so this is the
+
+ align:start position:0%
+incident flux are always so this is the
+ 
+
+ align:start position:0%
+incident flux are always so this is the
+denominator of that big formula with
+
+ align:start position:0%
+denominator of that big formula with
+ 
+
+ align:start position:0%
+denominator of that big formula with
+have there the incident flux then we
+
+ align:start position:0%
+have there the incident flux then we
+ 
+
+ align:start position:0%
+have there the incident flux then we
+need the number of particles scattered
+
+ align:start position:0%
+need the number of particles scattered
+ 
+
+ align:start position:0%
+need the number of particles scattered
+per unit time we could do it with a flux
+
+ align:start position:0%
+per unit time we could do it with a flux
+ 
+
+ align:start position:0%
+per unit time we could do it with a flux
+calculation also in spherical
+
+ align:start position:0%
+calculation also in spherical
+ 
+
+ align:start position:0%
+calculation also in spherical
+coordinates but I can also do it
+
+ align:start position:0%
+coordinates but I can also do it
+ 
+
+ align:start position:0%
+coordinates but I can also do it
+intuitively so I'll do it intuitively
+
+ align:start position:0%
+intuitively so I'll do it intuitively
+ 
+
+ align:start position:0%
+intuitively so I'll do it intuitively
+you can try doing it using a probability
+
+ align:start position:0%
+you can try doing it using a probability
+ 
+
+ align:start position:0%
+you can try doing it using a probability
+current so intuitively what do we have
+
+ align:start position:0%
+current so intuitively what do we have
+ 
+
+ align:start position:0%
+current so intuitively what do we have
+we have a a dealmaker here and let's
+
+ align:start position:0%
+we have a a dealmaker here and let's
+ 
+
+ align:start position:0%
+we have a a dealmaker here and let's
+consider a little volume element here so
+
+ align:start position:0%
+consider a little volume element here so
+ 
+
+ align:start position:0%
+consider a little volume element here so
+a little volume element here you have
+
+ align:start position:0%
+a little volume element here you have
+ 
+
+ align:start position:0%
+a little volume element here you have
+our distance R a little V R so it's a
+
+ align:start position:0%
+our distance R a little V R so it's a
+ 
+
+ align:start position:0%
+our distance R a little V R so it's a
+small volume element here and let's
+
+ align:start position:0%
+small volume element here and let's
+ 
+
+ align:start position:0%
+small volume element here and let's
+calculate how many particles there are
+
+ align:start position:0%
+calculate how many particles there are
+ 
+
+ align:start position:0%
+calculate how many particles there are
+in this small little element so the n is
+
+ align:start position:0%
+in this small little element so the n is
+ 
+
+ align:start position:0%
+in this small little element so the n is
+number of particles in the little volume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume so I must square the wave
+
+ align:start position:0%
+volume so I must square the wave
+ 
+
+ align:start position:0%
+volume so I must square the wave
+function and multiply by the volume
+
+ align:start position:0%
+function and multiply by the volume
+ 
+
+ align:start position:0%
+function and multiply by the volume
+that's what you do so what is the square
+
+ align:start position:0%
+that's what you do so what is the square
+ 
+
+ align:start position:0%
+that's what you do so what is the square
+of the wave function now we are talking
+
+ align:start position:0%
+of the wave function now we are talking
+ 
+
+ align:start position:0%
+of the wave function now we are talking
+about the scattered wave function so I
+
+ align:start position:0%
+about the scattered wave function so I
+ 
+
+ align:start position:0%
+about the scattered wave function so I
+must take this part of the wave function
+
+ align:start position:0%
+must take this part of the wave function
+ 
+
+ align:start position:0%
+must take this part of the wave function
+and square it and multiply by the volume
+
+ align:start position:0%
+and square it and multiply by the volume
+ 
+
+ align:start position:0%
+and square it and multiply by the volume
+so we will have F of theta and Phi times
+
+ align:start position:0%
+so we will have F of theta and Phi times
+ 
+
+ align:start position:0%
+so we will have F of theta and Phi times
+e to the IKr
+
+ align:start position:0%
+e to the IKr
+ 
+
+ align:start position:0%
+e to the IKr
+over R all squared so that's the wave
+
+ align:start position:0%
+over R all squared so that's the wave
+ 
+
+ align:start position:0%
+over R all squared so that's the wave
+function squared that's size carrot
+
+ align:start position:0%
+function squared that's size carrot
+ 
+
+ align:start position:0%
+function squared that's size carrot
+squared times the air volume of this
+
+ align:start position:0%
+squared times the air volume of this
+ 
+
+ align:start position:0%
+squared times the air volume of this
+pillbox is R squared V Omega times the
+
+ align:start position:0%
+pillbox is R squared V Omega times the
+ 
+
+ align:start position:0%
+pillbox is R squared V Omega times the
+our our squared D Omega is the surface
+
+ align:start position:0%
+our our squared D Omega is the surface
+ 
+
+ align:start position:0%
+our our squared D Omega is the surface
+area of that little box the R is the
+
+ align:start position:0%
+area of that little box the R is the
+ 
+
+ align:start position:0%
+area of that little box the R is the
+little length there and therefore we
+
+ align:start position:0%
+little length there and therefore we
+ 
+
+ align:start position:0%
+little length there and therefore we
+have that volume over there
+
+ align:start position:0%
+have that volume over there
+ 
+
+ align:start position:0%
+have that volume over there
+so things simplify the N is equal
+
+ align:start position:0%
+so things simplify the N is equal
+ 
+
+ align:start position:0%
+so things simplify the N is equal
+therefore the R squared cancels and it's
+
+ align:start position:0%
+therefore the R squared cancels and it's
+ 
+
+ align:start position:0%
+therefore the R squared cancels and it's
+just F of theta Phi squared the Omega V
+
+ align:start position:0%
+just F of theta Phi squared the Omega V
+ 
+
+ align:start position:0%
+just F of theta Phi squared the Omega V
+R so with all these particles this is
+
+ align:start position:0%
+R so with all these particles this is
+ 
+
+ align:start position:0%
+R so with all these particles this is
+the number of particles inside the box
+
+ align:start position:0%
+the number of particles inside the box
+ 
+
+ align:start position:0%
+the number of particles inside the box
+but all these particles will go through
+
+ align:start position:0%
+but all these particles will go through
+ 
+
+ align:start position:0%
+but all these particles will go through
+in a little time DT which is equal to V
+
+ align:start position:0%
+in a little time DT which is equal to V
+ 
+
+ align:start position:0%
+in a little time DT which is equal to V
+R over the velocity this is the time to
+
+ align:start position:0%
+R over the velocity this is the time to
+ 
+
+ align:start position:0%
+R over the velocity this is the time to
+go through the box through the box DT is
+
+ align:start position:0%
+go through the box through the box DT is
+ 
+
+ align:start position:0%
+go through the box through the box DT is
+the R over the velocity and the velocity
+
+ align:start position:0%
+the R over the velocity and the velocity
+ 
+
+ align:start position:0%
+the R over the velocity and the velocity
+is H K over m so d R times the momentum
+
+ align:start position:0%
+is H K over m so d R times the momentum
+ 
+
+ align:start position:0%
+is H K over m so d R times the momentum
+over the mass which is H K over m okay
+
+ align:start position:0%
+over the mass which is H K over m okay
+ 
+
+ align:start position:0%
+over the mass which is H K over m okay
+so we have V n DT this is number of
+
+ align:start position:0%
+so we have V n DT this is number of
+ 
+
+ align:start position:0%
+so we have V n DT this is number of
+particles we divide them to form number
+
+ align:start position:0%
+particles we divide them to form number
+ 
+
+ align:start position:0%
+particles we divide them to form number
+of particles per unit time so the ratio
+
+ align:start position:0%
+of particles per unit time so the ratio
+ 
+
+ align:start position:0%
+of particles per unit time so the ratio
+DM DT is the numerator of this quantity
+
+ align:start position:0%
+DM DT is the numerator of this quantity
+ 
+
+ align:start position:0%
+DM DT is the numerator of this quantity
+here is numerator DM DT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean what do we get the dr cancels and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're dividing the NDT this factor goes
+
+ align:start position:0%
+we're dividing the NDT this factor goes
+ 
+
+ align:start position:0%
+we're dividing the NDT this factor goes
+into the numerator so we get h-bar K
+
+ align:start position:0%
+into the numerator so we get h-bar K
+ 
+
+ align:start position:0%
+into the numerator so we get h-bar K
+over m f of theta Phi squared D Omega so
+
+ align:start position:0%
+over m f of theta Phi squared D Omega so
+ 
+
+ align:start position:0%
+over m f of theta Phi squared D Omega so
+this is the numerator of that equation
+
+ align:start position:0%
+this is the numerator of that equation
+ 
+
+ align:start position:0%
+this is the numerator of that equation
+for the D Sigma so let's compute finish
+
+ align:start position:0%
+for the D Sigma so let's compute finish
+ 
+
+ align:start position:0%
+for the D Sigma so let's compute finish
+that we finally get off our
+
+ align:start position:0%
+that we finally get off our
+ 
+
+ align:start position:0%
+that we finally get off our
+identification and we get we get D Sigma
+
+ align:start position:0%
+identification and we get we get D Sigma
+ 
+
+ align:start position:0%
+identification and we get we get D Sigma
+is the numerator there which is this
+
+ align:start position:0%
+is the numerator there which is this
+ 
+
+ align:start position:0%
+is the numerator there which is this
+quantity H Bar K over m f of theta Phi
+
+ align:start position:0%
+quantity H Bar K over m f of theta Phi
+ 
+
+ align:start position:0%
+quantity H Bar K over m f of theta Phi
+squared times the Omega over H Bar K
+
+ align:start position:0%
+squared times the Omega over H Bar K
+ 
+
+ align:start position:0%
+squared times the Omega over H Bar K
+over m which is nice that all gonna
+
+ align:start position:0%
+over m which is nice that all gonna
+ 
+
+ align:start position:0%
+over m which is nice that all gonna
+cancel and then we get the nice formula
+
+ align:start position:0%
+cancel and then we get the nice formula
+ 
+
+ align:start position:0%
+cancel and then we get the nice formula
+that we were after this differential
+
+ align:start position:0%
+that we were after this differential
+ 
+
+ align:start position:0%
+that we were after this differential
+cross section it's just determined by
+
+ align:start position:0%
+cross section it's just determined by
+ 
+
+ align:start position:0%
+cross section it's just determined by
+the function f of theta phi that we need
+
+ align:start position:0%
+the function f of theta phi that we need
+ 
+
+ align:start position:0%
+the function f of theta phi that we need
+to calculate f of theta phi is our doll
+
+ align:start position:0%
+to calculate f of theta phi is our doll
+ 
+
+ align:start position:0%
+to calculate f of theta phi is our doll
+if we have it we have the differential
+
+ align:start position:0%
+if we have it we have the differential
+ 
+
+ align:start position:0%
+if we have it we have the differential
+cross section many people write this
+
+ align:start position:0%
+cross section many people write this
+ 
+
+ align:start position:0%
+cross section many people write this
+formula this way the Sigma D Omega is
+
+ align:start position:0%
+formula this way the Sigma D Omega is
+ 
+
+ align:start position:0%
+formula this way the Sigma D Omega is
+equal to f of theta phi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think that's okay I think in many ways
+
+ align:start position:0%
+I think that's okay I think in many ways
+ 
+
+ align:start position:0%
+I think that's okay I think in many ways
+this is a little clearer the small
+
+ align:start position:0%
+this is a little clearer the small
+ 
+
+ align:start position:0%
+this is a little clearer the small
+little area associated to a small little
+
+ align:start position:0%
+little area associated to a small little
+ 
+
+ align:start position:0%
+little area associated to a small little
+angle is given by that this is a ratio
+
+ align:start position:0%
+angle is given by that this is a ratio
+ 
+
+ align:start position:0%
+angle is given by that this is a ratio
+of differentials more than a derivative
+
+ align:start position:0%
+of differentials more than a derivative
+ 
+
+ align:start position:0%
+of differentials more than a derivative
+derivative with respect to solid angle
+
+ align:start position:0%
+derivative with respect to solid angle
+ 
+
+ align:start position:0%
+derivative with respect to solid angle
+doesn't mean too much I think so but
+
+ align:start position:0%
+doesn't mean too much I think so but
+ 
+
+ align:start position:0%
+doesn't mean too much I think so but
+this is another way people write it and
+
+ align:start position:0%
+this is another way people write it and
+ 
+
+ align:start position:0%
+this is another way people write it and
+finally people integrate this a total
+
+ align:start position:0%
+finally people integrate this a total
+ 
+
+ align:start position:0%
+finally people integrate this a total
+cross-section is the integral of the
+
+ align:start position:0%
+cross-section is the integral of the
+ 
+
+ align:start position:0%
+cross-section is the integral of the
+differential cross-section over looking
+
+ align:start position:0%
+differential cross-section over looking
+ 
+
+ align:start position:0%
+differential cross-section over looking
+at all solid angles so this means
+
+ align:start position:0%
+at all solid angles so this means
+ 
+
+ align:start position:0%
+at all solid angles so this means
+integrating F of theta Phi squared D
+
+ align:start position:0%
+integrating F of theta Phi squared D
+ 
+
+ align:start position:0%
+integrating F of theta Phi squared D
+Omega and that's the total cross-section
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we've set up the problem we what
+
+ align:start position:0%
+okay so we've set up the problem we what
+ 
+
+ align:start position:0%
+okay so we've set up the problem we what
+are the main things and wiffler we have
+
+ align:start position:0%
+are the main things and wiffler we have
+ 
+
+ align:start position:0%
+are the main things and wiffler we have
+the scattering Center we have our
+
+ align:start position:0%
+the scattering Center we have our
+ 
+
+ align:start position:0%
+the scattering Center we have our
+physical condition of a wave coming in
+
+ align:start position:0%
+physical condition of a wave coming in
+ 
+
+ align:start position:0%
+physical condition of a wave coming in
+our physical condition that the wave
+
+ align:start position:0%
+our physical condition that the wave
+ 
+
+ align:start position:0%
+our physical condition that the wave
+comes out those are represented here and
+
+ align:start position:0%
+comes out those are represented here and
+ 
+
+ align:start position:0%
+comes out those are represented here and
+this situation is saying that this is an
+
+ align:start position:0%
+this situation is saying that this is an
+ 
+
+ align:start position:0%
+this situation is saying that this is an
+approximate solution far away a wave
+
+ align:start position:0%
+approximate solution far away a wave
+ 
+
+ align:start position:0%
+approximate solution far away a wave
+coming out modulated by a theta and Phi
+
+ align:start position:0%
+coming out modulated by a theta and Phi
+ 
+
+ align:start position:0%
+coming out modulated by a theta and Phi
+dependence and your incoming wave this
+
+ align:start position:0%
+dependence and your incoming wave this
+ 
+
+ align:start position:0%
+dependence and your incoming wave this
+modulation is the thing that captures
+
+ align:start position:0%
+modulation is the thing that captures
+ 
+
+ align:start position:0%
+modulation is the thing that captures
+the effect of the potential and
+
+ align:start position:0%
+the effect of the potential and
+ 
+
+ align:start position:0%
+the effect of the potential and
+Associates to the strength of this
+
+ align:start position:0%
+Associates to the strength of this
+ 
+
+ align:start position:0%
+Associates to the strength of this
+potential its ability to scatter at the
+
+ align:start position:0%
+potential its ability to scatter at the
+ 
+
+ align:start position:0%
+potential its ability to scatter at the
+FIR a cross-section which is measurable
+
+ align:start position:0%
+FIR a cross-section which is measurable
+ 
+
+ align:start position:0%
+FIR a cross-section which is measurable
+which means the probability of
+
+ align:start position:0%
+which means the probability of
+ 
+
+ align:start position:0%
+which means the probability of
+interaction captured the probability of
+
+ align:start position:0%
+interaction captured the probability of
+ 
+
+ align:start position:0%
+interaction captured the probability of
+interaction this cross-sections are very
+
+ align:start position:0%
+interaction this cross-sections are very
+ 
+
+ align:start position:0%
+interaction this cross-sections are very
+important when you design an experiment
+
+ align:start position:0%
+important when you design an experiment
+ 
+
+ align:start position:0%
+important when you design an experiment
+with an accelerator you want to have a
+
+ align:start position:0%
+with an accelerator you want to have a
+ 
+
+ align:start position:0%
+with an accelerator you want to have a
+cross-section is sufficiently large
+
+ align:start position:0%
+cross-section is sufficiently large
+ 
+
+ align:start position:0%
+cross-section is sufficiently large
+because this cross-section is gonna tell
+
+ align:start position:0%
+because this cross-section is gonna tell
+ 
+
+ align:start position:0%
+because this cross-section is gonna tell
+you how many particles your detector is
+
+ align:start position:0%
+you how many particles your detector is
+ 
+
+ align:start position:0%
+you how many particles your detector is
+gonna get whether with the flux that you
+
+ align:start position:0%
+gonna get whether with the flux that you
+ 
+
+ align:start position:0%
+gonna get whether with the flux that you
+have with the beam intensity that you
+
+ align:start position:0%
+have with the beam intensity that you
+ 
+
+ align:start position:0%
+have with the beam intensity that you
+have you're going to get one Higgs a day
+
+ align:start position:0%
+have you're going to get one Higgs a day
+ 
+
+ align:start position:0%
+have you're going to get one Higgs a day
+or 500 pixels a day and it made a
+
+ align:start position:0%
+or 500 pixels a day and it made a
+ 
+
+ align:start position:0%
+or 500 pixels a day and it made a
+difference for the LHC it began with a
+
+ align:start position:0%
+difference for the LHC it began with a
+ 
+
+ align:start position:0%
+difference for the LHC it began with a
+few Higgs as a day and later it's
+
+ align:start position:0%
+few Higgs as a day and later it's
+ 
+
+ align:start position:0%
+few Higgs as a day and later it's
+getting a few hundred eggs a day so so
+
+ align:start position:0%
+getting a few hundred eggs a day so so
+ 
+
+ align:start position:0%
+getting a few hundred eggs a day so so
+those quantities are pretty important
\ No newline at end of file
diff --git a/pgEFvhkEp-c.txt b/pgEFvhkEp-c.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9ae9a83462722ac14f9be3a23132ffd6fe48f2f8
--- /dev/null
+++ b/pgEFvhkEp-c.txt
@@ -0,0 +1,1560 @@
+align:start position:0%
+ 
+so adiabatic result so last time we just
+
+ align:start position:0%
+so adiabatic result so last time we just
+ 
+
+ align:start position:0%
+so adiabatic result so last time we just
+followed and try to use an instantaneous
+
+ align:start position:0%
+followed and try to use an instantaneous
+ 
+
+ align:start position:0%
+followed and try to use an instantaneous
+eigenstate to construct the solution of
+
+ align:start position:0%
+eigenstate to construct the solution of
+ 
+
+ align:start position:0%
+eigenstate to construct the solution of
+the Schrodinger equation our result was
+
+ align:start position:0%
+the Schrodinger equation our result was
+ 
+
+ align:start position:0%
+the Schrodinger equation our result was
+that we couldn't quite construct the
+
+ align:start position:0%
+that we couldn't quite construct the
+ 
+
+ align:start position:0%
+that we couldn't quite construct the
+solution of the Schrodinger equation
+
+ align:start position:0%
+solution of the Schrodinger equation
+ 
+
+ align:start position:0%
+solution of the Schrodinger equation
+what we wrote didn't exactly solve the
+
+ align:start position:0%
+what we wrote didn't exactly solve the
+ 
+
+ align:start position:0%
+what we wrote didn't exactly solve the
+Schrodinger equation but we claimed that
+
+ align:start position:0%
+Schrodinger equation but we claimed that
+ 
+
+ align:start position:0%
+Schrodinger equation but we claimed that
+it was important and interesting and
+
+ align:start position:0%
+it was important and interesting and
+ 
+
+ align:start position:0%
+it was important and interesting and
+therefore let me remind you of what we
+
+ align:start position:0%
+therefore let me remind you of what we
+ 
+
+ align:start position:0%
+therefore let me remind you of what we
+said so we showed that the wave function
+
+ align:start position:0%
+said so we showed that the wave function
+ 
+
+ align:start position:0%
+said so we showed that the wave function
+psi of T could be written as a constant
+
+ align:start position:0%
+psi of T could be written as a constant
+ 
+
+ align:start position:0%
+psi of T could be written as a constant
+here e to the I theta of T e to the I
+
+ align:start position:0%
+here e to the I theta of T e to the I
+ 
+
+ align:start position:0%
+here e to the I theta of T e to the I
+gamma of T times this wave function and
+
+ align:start position:0%
+gamma of T times this wave function and
+ 
+
+ align:start position:0%
+gamma of T times this wave function and
+that wave function on here was what we
+
+ align:start position:0%
+that wave function on here was what we
+ 
+
+ align:start position:0%
+that wave function on here was what we
+call an instantaneous eigen state of the
+
+ align:start position:0%
+call an instantaneous eigen state of the
+ 
+
+ align:start position:0%
+call an instantaneous eigen state of the
+Hamiltonian so H of T acting on Phi of T
+
+ align:start position:0%
+Hamiltonian so H of T acting on Phi of T
+ 
+
+ align:start position:0%
+Hamiltonian so H of T acting on Phi of T
+was at any instant of time an eigen
+
+ align:start position:0%
+was at any instant of time an eigen
+ 
+
+ align:start position:0%
+was at any instant of time an eigen
+state nevertheless we said that this
+
+ align:start position:0%
+state nevertheless we said that this
+ 
+
+ align:start position:0%
+state nevertheless we said that this
+eigen states are not solutions of the
+
+ align:start position:0%
+eigen states are not solutions of the
+ 
+
+ align:start position:0%
+eigen states are not solutions of the
+Schrodinger equation in general they
+
+ align:start position:0%
+Schrodinger equation in general they
+ 
+
+ align:start position:0%
+Schrodinger equation in general they
+solve this funny timing inspired by the
+
+ align:start position:0%
+solve this funny timing inspired by the
+ 
+
+ align:start position:0%
+solve this funny timing inspired by the
+time independent Schrodinger equation
+
+ align:start position:0%
+time independent Schrodinger equation
+ 
+
+ align:start position:0%
+time independent Schrodinger equation
+this instantaneous eigenstate condition
+
+ align:start position:0%
+this instantaneous eigenstate condition
+ 
+
+ align:start position:0%
+this instantaneous eigenstate condition
+but when you try to solve the
+
+ align:start position:0%
+but when you try to solve the
+ 
+
+ align:start position:0%
+but when you try to solve the
+Schrodinger equation this PI of T would
+
+ align:start position:0%
+Schrodinger equation this PI of T would
+ 
+
+ align:start position:0%
+Schrodinger equation this PI of T would
+not solve it so we try to add things and
+
+ align:start position:0%
+not solve it so we try to add things and
+ 
+
+ align:start position:0%
+not solve it so we try to add things and
+we constructed what seemed to be close
+
+ align:start position:0%
+we constructed what seemed to be close
+ 
+
+ align:start position:0%
+we constructed what seemed to be close
+to a solution and there it is what was
+
+ align:start position:0%
+to a solution and there it is what was
+ 
+
+ align:start position:0%
+to a solution and there it is what was
+fade of T was a dynamical face it's
+
+ align:start position:0%
+fade of T was a dynamical face it's
+ 
+
+ align:start position:0%
+fade of T was a dynamical face it's
+called and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is defined by this integral if EFT was a
+
+ align:start position:0%
+is defined by this integral if EFT was a
+ 
+
+ align:start position:0%
+is defined by this integral if EFT was a
+constant it would be a minus e times T
+
+ align:start position:0%
+constant it would be a minus e times T
+ 
+
+ align:start position:0%
+constant it would be a minus e times T
+over H bar and this would be the
+
+ align:start position:0%
+over H bar and this would be the
+ 
+
+ align:start position:0%
+over H bar and this would be the
+familiar face that with which you
+
+ align:start position:0%
+familiar face that with which you
+ 
+
+ align:start position:0%
+familiar face that with which you
+evolved energy eigenstates the second
+
+ align:start position:0%
+evolved energy eigenstates the second
+ 
+
+ align:start position:0%
+evolved energy eigenstates the second
+term this gamma of T was a little more
+
+ align:start position:0%
+term this gamma of T was a little more
+ 
+
+ align:start position:0%
+term this gamma of T was a little more
+intricate we define intermediate thing
+
+ align:start position:0%
+intricate we define intermediate thing
+ 
+
+ align:start position:0%
+intricate we define intermediate thing
+called nu of T which was I times the
+
+ align:start position:0%
+called nu of T which was I times the
+ 
+
+ align:start position:0%
+called nu of T which was I times the
+inner product of the instantaneous
+
+ align:start position:0%
+inner product of the instantaneous
+ 
+
+ align:start position:0%
+inner product of the instantaneous
+eigenstate with the derivative with
+
+ align:start position:0%
+eigenstate with the derivative with
+ 
+
+ align:start position:0%
+eigenstate with the derivative with
+respect to time of the instantaneous
+
+ align:start position:0%
+respect to time of the instantaneous
+ 
+
+ align:start position:0%
+respect to time of the instantaneous
+eigenstate we argued that this factor
+
+ align:start position:0%
+eigenstate we argued that this factor
+ 
+
+ align:start position:0%
+eigenstate we argued that this factor
+over here was imaginary therefore we put
+
+ align:start position:0%
+over here was imaginary therefore we put
+ 
+
+ align:start position:0%
+over here was imaginary therefore we put
+an I so that nu is real and gamma of T
+
+ align:start position:0%
+an I so that nu is real and gamma of T
+ 
+
+ align:start position:0%
+an I so that nu is real and gamma of T
+so these were definitions is defined as
+
+ align:start position:0%
+so these were definitions is defined as
+ 
+
+ align:start position:0%
+so these were definitions is defined as
+0 2t DT prime nu of T Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ok so so the claim was that if you
+
+ align:start position:0%
+ok so so the claim was that if you
+ 
+
+ align:start position:0%
+ok so so the claim was that if you
+happen to have a wave function at a time
+
+ align:start position:0%
+happen to have a wave function at a time
+ 
+
+ align:start position:0%
+happen to have a wave function at a time
+equals 0 is in one of those
+
+ align:start position:0%
+equals 0 is in one of those
+ 
+
+ align:start position:0%
+equals 0 is in one of those
+instantaneous eigenstates it would
+
+ align:start position:0%
+instantaneous eigenstates it would
+ 
+
+ align:start position:0%
+instantaneous eigenstates it would
+remain in such instantaneous eigenstate
+
+ align:start position:0%
+remain in such instantaneous eigenstate
+ 
+
+ align:start position:0%
+remain in such instantaneous eigenstate
+up to phases that are calculable
+
+ align:start position:0%
+up to phases that are calculable
+ 
+
+ align:start position:0%
+up to phases that are calculable
+ok so let's make this a little more
+
+ align:start position:0%
+ok so let's make this a little more
+ 
+
+ align:start position:0%
+ok so let's make this a little more
+explicit in the sense of an adiabatic
+
+ align:start position:0%
+explicit in the sense of an adiabatic
+ 
+
+ align:start position:0%
+explicit in the sense of an adiabatic
+theorem so I'll also put here that this
+
+ align:start position:0%
+theorem so I'll also put here that this
+ 
+
+ align:start position:0%
+theorem so I'll also put here that this
+is not an exact solution so I would say
+
+ align:start position:0%
+is not an exact solution so I would say
+ 
+
+ align:start position:0%
+is not an exact solution so I would say
+the wave function at time T is roughly
+
+ align:start position:0%
+the wave function at time T is roughly
+ 
+
+ align:start position:0%
+the wave function at time T is roughly
+given by that quantity it's not exact
+
+ align:start position:0%
+given by that quantity it's not exact
+ 
+
+ align:start position:0%
+given by that quantity it's not exact
+because it's not an exact solution of
+
+ align:start position:0%
+because it's not an exact solution of
+ 
+
+ align:start position:0%
+because it's not an exact solution of
+the Schrodinger equation so if we want
+
+ align:start position:0%
+the Schrodinger equation so if we want
+ 
+
+ align:start position:0%
+the Schrodinger equation so if we want
+to state the adiabatic theorem a little
+
+ align:start position:0%
+to state the adiabatic theorem a little
+ 
+
+ align:start position:0%
+to state the adiabatic theorem a little
+more precisely we consider a set
+
+ align:start position:0%
+more precisely we consider a set
+ 
+
+ align:start position:0%
+more precisely we consider a set
+of instantaneous eigenstates
+
+ align:start position:0%
+of instantaneous eigenstates
+ 
+
+ align:start position:0%
+of instantaneous eigenstates
+instantaneous eigenstates and that is H
+
+ align:start position:0%
+instantaneous eigenstates and that is H
+ 
+
+ align:start position:0%
+instantaneous eigenstates and that is H
+of T sy n of T equal e n of T sy n of T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here n will go from 1 up to possibly
+
+ align:start position:0%
+and here n will go from 1 up to possibly
+ 
+
+ align:start position:0%
+and here n will go from 1 up to possibly
+infinity it just doesn't have to stop it
+
+ align:start position:0%
+infinity it just doesn't have to stop it
+ 
+
+ align:start position:0%
+infinity it just doesn't have to stop it
+can go on forever
+
+ align:start position:0%
+can go on forever
+ 
+
+ align:start position:0%
+can go on forever
+okay equipped with the instantaneous
+
+ align:start position:0%
+okay equipped with the instantaneous
+ 
+
+ align:start position:0%
+okay equipped with the instantaneous
+eigenstates you might decide that you
+
+ align:start position:0%
+eigenstates you might decide that you
+ 
+
+ align:start position:0%
+eigenstates you might decide that you
+initially want to be in a state subside
+
+ align:start position:0%
+initially want to be in a state subside
+ 
+
+ align:start position:0%
+initially want to be in a state subside
+at T equals 0 is given by sy k at 0
+
+ align:start position:0%
+at T equals 0 is given by sy k at 0
+ 
+
+ align:start position:0%
+at T equals 0 is given by sy k at 0
+that's your initial condition now you
+
+ align:start position:0%
+that's your initial condition now you
+ 
+
+ align:start position:0%
+that's your initial condition now you
+look at this and say okay when is the
+
+ align:start position:0%
+look at this and say okay when is the
+ 
+
+ align:start position:0%
+look at this and say okay when is the
+adiabatic result that you're going to
+
+ align:start position:0%
+adiabatic result that you're going to
+ 
+
+ align:start position:0%
+adiabatic result that you're going to
+stay roughly in that energy eigenstate
+
+ align:start position:0%
+stay roughly in that energy eigenstate
+ 
+
+ align:start position:0%
+stay roughly in that energy eigenstate
+going to be true this is going to
+
+ align:start position:0%
+going to be true this is going to
+ 
+
+ align:start position:0%
+going to be true this is going to
+require that as you have the energy EK
+
+ align:start position:0%
+require that as you have the energy EK
+ 
+
+ align:start position:0%
+require that as you have the energy EK
+as a function of time here is the energy
+
+ align:start position:0%
+as a function of time here is the energy
+ 
+
+ align:start position:0%
+as a function of time here is the energy
+EK as a function of time 0 you should
+
+ align:start position:0%
+EK as a function of time 0 you should
+ 
+
+ align:start position:0%
+EK as a function of time 0 you should
+have that this doesn't get mixed or
+
+ align:start position:0%
+have that this doesn't get mixed or
+ 
+
+ align:start position:0%
+have that this doesn't get mixed or
+doesn't coincide with some other energy
+
+ align:start position:0%
+doesn't coincide with some other energy
+ 
+
+ align:start position:0%
+doesn't coincide with some other energy
+like something like that a crossing or
+
+ align:start position:0%
+like something like that a crossing or
+ 
+
+ align:start position:0%
+like something like that a crossing or
+the de touch with another one you should
+
+ align:start position:0%
+the de touch with another one you should
+ 
+
+ align:start position:0%
+the de touch with another one you should
+keep them separate you know you know
+
+ align:start position:0%
+keep them separate you know you know
+ 
+
+ align:start position:0%
+keep them separate you know you know
+that the general perturbation theory
+
+ align:start position:0%
+that the general perturbation theory
+ 
+
+ align:start position:0%
+that the general perturbation theory
+makes life complicated and if you find
+
+ align:start position:0%
+makes life complicated and if you find
+ 
+
+ align:start position:0%
+makes life complicated and if you find
+another state that gets very close
+
+ align:start position:0%
+another state that gets very close
+ 
+
+ align:start position:0%
+another state that gets very close
+diabetic theorem or the adiabatic
+
+ align:start position:0%
+diabetic theorem or the adiabatic
+ 
+
+ align:start position:0%
+diabetic theorem or the adiabatic
+approximation might go wrong so we want
+
+ align:start position:0%
+approximation might go wrong so we want
+ 
+
+ align:start position:0%
+approximation might go wrong so we want
+other energy eigenstate here is ek minus
+
+ align:start position:0%
+other energy eigenstate here is ek minus
+ 
+
+ align:start position:0%
+other energy eigenstate here is ek minus
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and here is ek plus one so you have all
+
+ align:start position:0%
+and here is ek plus one so you have all
+ 
+
+ align:start position:0%
+and here is ek plus one so you have all
+this energy eigenvalues as a function of
+
+ align:start position:0%
+this energy eigenvalues as a function of
+ 
+
+ align:start position:0%
+this energy eigenvalues as a function of
+time and you want that for example EK
+
+ align:start position:0%
+time and you want that for example EK
+ 
+
+ align:start position:0%
+time and you want that for example EK
+you order all your energies and you want
+
+ align:start position:0%
+you order all your energies and you want
+ 
+
+ align:start position:0%
+you order all your energies and you want
+that EK of t is definitely less than e k
+
+ align:start position:0%
+that EK of t is definitely less than e k
+ 
+
+ align:start position:0%
+that EK of t is definitely less than e k
+plus 1 of T which is less than or equal
+
+ align:start position:0%
+plus 1 of T which is less than or equal
+ 
+
+ align:start position:0%
+plus 1 of T which is less than or equal
+to the other ones and this is definitely
+
+ align:start position:0%
+to the other ones and this is definitely
+ 
+
+ align:start position:0%
+to the other ones and this is definitely
+greater than e k minus 1 of T which is
+
+ align:start position:0%
+greater than e k minus 1 of T which is
+ 
+
+ align:start position:0%
+greater than e k minus 1 of T which is
+greater or equal than the other one so
+
+ align:start position:0%
+greater or equal than the other one so
+ 
+
+ align:start position:0%
+greater or equal than the other one so
+the energy instantaneous energy I can
+
+ align:start position:0%
+the energy instantaneous energy I can
+ 
+
+ align:start position:0%
+the energy instantaneous energy I can
+say that you are focusing should be well
+
+ align:start position:0%
+say that you are focusing should be well
+ 
+
+ align:start position:0%
+say that you are focusing should be well
+separated from the other ones otherwise
+
+ align:start position:0%
+separated from the other ones otherwise
+ 
+
+ align:start position:0%
+separated from the other ones otherwise
+you could run into difficulties so
+
+ align:start position:0%
+you could run into difficulties so
+ 
+
+ align:start position:0%
+you could run into difficulties so
+that's definitely necessary for this to
+
+ align:start position:0%
+that's definitely necessary for this to
+ 
+
+ align:start position:0%
+that's definitely necessary for this to
+hold then the adiabatic theorem says
+
+ align:start position:0%
+hold then the adiabatic theorem says
+ 
+
+ align:start position:0%
+hold then the adiabatic theorem says
+that psy of T will be approximately
+
+ align:start position:0%
+that psy of T will be approximately
+ 
+
+ align:start position:0%
+that psy of T will be approximately
+equal to e to the I theta K of T e to
+
+ align:start position:0%
+equal to e to the I theta K of T e to
+ 
+
+ align:start position:0%
+equal to e to the I theta K of T e to
+the I gamma K of T times psy k of T so
+
+ align:start position:0%
+the I gamma K of T times psy k of T so
+ 
+
+ align:start position:0%
+the I gamma K of T times psy k of T so
+I'm keeping the little difference of
+
+ align:start position:0%
+I'm keeping the little difference of
+ 
+
+ align:start position:0%
+I'm keeping the little difference of
+notation trying to be careful these wave
+
+ align:start position:0%
+notation trying to be careful these wave
+ 
+
+ align:start position:0%
+notation trying to be careful these wave
+functions at all times I put them with a
+
+ align:start position:0%
+functions at all times I put them with a
+ 
+
+ align:start position:0%
+functions at all times I put them with a
+line below the psy and this
+
+ align:start position:0%
+line below the psy and this
+ 
+
+ align:start position:0%
+line below the psy and this
+instantaneous energy eigenstates I don't
+
+ align:start position:0%
+instantaneous energy eigenstates I don't
+ 
+
+ align:start position:0%
+instantaneous energy eigenstates I don't
+put that so a little difference that
+
+ align:start position:0%
+put that so a little difference that
+ 
+
+ align:start position:0%
+put that so a little difference that
+should help you determine this now what
+
+ align:start position:0%
+should help you determine this now what
+ 
+
+ align:start position:0%
+should help you determine this now what
+are these theta k or gamma k are just
+
+ align:start position:0%
+are these theta k or gamma k are just
+ 
+
+ align:start position:0%
+are these theta k or gamma k are just
+the same quantities I might as well
+
+ align:start position:0%
+the same quantities I might as well
+ 
+
+ align:start position:0%
+the same quantities I might as well
+write them for completeness theta K of T
+
+ align:start position:0%
+write them for completeness theta K of T
+ 
+
+ align:start position:0%
+write them for completeness theta K of T
+is what you had before minus 1 over H
+
+ align:start position:0%
+is what you had before minus 1 over H
+ 
+
+ align:start position:0%
+is what you had before minus 1 over H
+bar 0 to T but this time EK of people do
+
+ align:start position:0%
+bar 0 to T but this time EK of people do
+ 
+
+ align:start position:0%
+bar 0 to T but this time EK of people do
+t prime then you have nu of T no K is
+
+ align:start position:0%
+t prime then you have nu of T no K is
+ 
+
+ align:start position:0%
+t prime then you have nu of T no K is
+equal to I sy K
+
+ align:start position:0%
+equal to I sy K
+ 
+
+ align:start position:0%
+equal to I sy K
+t sy k dot of T and finally the gamma K
+
+ align:start position:0%
+t sy k dot of T and finally the gamma K
+ 
+
+ align:start position:0%
+t sy k dot of T and finally the gamma K
+of T is the integral from 0 to t of nu
+
+ align:start position:0%
+of T is the integral from 0 to t of nu
+ 
+
+ align:start position:0%
+of T is the integral from 0 to t of nu
+of T prime V Prime
+
+ align:start position:0%
+of T prime V Prime
+ 
+
+ align:start position:0%
+of T prime V Prime
+okay everything with K corresponding to
+
+ align:start position:0%
+okay everything with K corresponding to
+ 
+
+ align:start position:0%
+okay everything with K corresponding to
+the K Tigan state so this is a more
+
+ align:start position:0%
+the K Tigan state so this is a more
+ 
+
+ align:start position:0%
+the K Tigan state so this is a more
+precise version already of the statement
+
+ align:start position:0%
+precise version already of the statement
+ 
+
+ align:start position:0%
+precise version already of the statement
+of the adiabatic approximation you want
+
+ align:start position:0%
+of the adiabatic approximation you want
+ 
+
+ align:start position:0%
+of the adiabatic approximation you want
+to make it even more precise will will
+
+ align:start position:0%
+to make it even more precise will will
+ 
+
+ align:start position:0%
+to make it even more precise will will
+say something about the error in this
+
+ align:start position:0%
+say something about the error in this
+ 
+
+ align:start position:0%
+say something about the error in this
+formula in a sense that hard work in the
+
+ align:start position:0%
+formula in a sense that hard work in the
+ 
+
+ align:start position:0%
+formula in a sense that hard work in the
+adiabatic approximation is telling you
+
+ align:start position:0%
+adiabatic approximation is telling you
+ 
+
+ align:start position:0%
+adiabatic approximation is telling you
+how much error there is so we will not
+
+ align:start position:0%
+how much error there is so we will not
+ 
+
+ align:start position:0%
+how much error there is so we will not
+go through the proof of the error
+
+ align:start position:0%
+go through the proof of the error
+ 
+
+ align:start position:0%
+go through the proof of the error
+we'll just motivate it and perhaps this
+
+ align:start position:0%
+we'll just motivate it and perhaps this
+ 
+
+ align:start position:0%
+we'll just motivate it and perhaps this
+will be discussed in recitation is an
+
+ align:start position:0%
+will be discussed in recitation is an
+ 
+
+ align:start position:0%
+will be discussed in recitation is an
+interesting subject and goes back to
+
+ align:start position:0%
+interesting subject and goes back to
+ 
+
+ align:start position:0%
+interesting subject and goes back to
+work of a born max born the one that
+
+ align:start position:0%
+work of a born max born the one that
+ 
+
+ align:start position:0%
+work of a born max born the one that
+gave the probabilistic interpretation of
+
+ align:start position:0%
+gave the probabilistic interpretation of
+ 
+
+ align:start position:0%
+gave the probabilistic interpretation of
+quantum mechanics and fog of folk space
+
+ align:start position:0%
+quantum mechanics and fog of folk space
+ 
+
+ align:start position:0%
+quantum mechanics and fog of folk space
+states of the harmonic oscillator they
+
+ align:start position:0%
+states of the harmonic oscillator they
+ 
+
+ align:start position:0%
+states of the harmonic oscillator they
+did the first work doing that then a
+
+ align:start position:0%
+did the first work doing that then a
+ 
+
+ align:start position:0%
+did the first work doing that then a
+Japanese fellow cattle in the middle 50
+
+ align:start position:0%
+Japanese fellow cattle in the middle 50
+ 
+
+ align:start position:0%
+Japanese fellow cattle in the middle 50
+so born and fog was 1928 I believe and
+
+ align:start position:0%
+so born and fog was 1928 I believe and
+ 
+
+ align:start position:0%
+so born and fog was 1928 I believe and
+in the 50s cattle improved the analysis
+
+ align:start position:0%
+in the 50s cattle improved the analysis
+ 
+
+ align:start position:0%
+in the 50s cattle improved the analysis
+of the adiabatic theorem and and this
+
+ align:start position:0%
+of the adiabatic theorem and and this
+ 
+
+ align:start position:0%
+of the adiabatic theorem and and this
+whole thing has many applications to the
+
+ align:start position:0%
+whole thing has many applications to the
+ 
+
+ align:start position:0%
+whole thing has many applications to the
+theory of molecules and spin States and
+
+ align:start position:0%
+theory of molecules and spin States and
+ 
+
+ align:start position:0%
+theory of molecules and spin States and
+systems we will see some of that we'll
+
+ align:start position:0%
+systems we will see some of that we'll
+ 
+
+ align:start position:0%
+systems we will see some of that we'll
+begin to see some of this today and and
+
+ align:start position:0%
+begin to see some of this today and and
+ 
+
+ align:start position:0%
+begin to see some of this today and and
+had a big revival with the discovery of
+
+ align:start position:0%
+had a big revival with the discovery of
+ 
+
+ align:start position:0%
+had a big revival with the discovery of
+Barry that there's quite a lot of
+
+ align:start position:0%
+Barry that there's quite a lot of
+ 
+
+ align:start position:0%
+Barry that there's quite a lot of
+physics in this face this face here this
+
+ align:start position:0%
+physics in this face this face here this
+ 
+
+ align:start position:0%
+physics in this face this face here this
+is the normal phase that you know
+
+ align:start position:0%
+is the normal phase that you know
+ 
+
+ align:start position:0%
+is the normal phase that you know
+for energy eigenstates slightly
+
+ align:start position:0%
+for energy eigenstates slightly
+ 
+
+ align:start position:0%
+for energy eigenstates slightly
+generalized but this face is very
+
+ align:start position:0%
+generalized but this face is very
+ 
+
+ align:start position:0%
+generalized but this face is very
+different and that's what Barry
+
+ align:start position:0%
+different and that's what Barry
+ 
+
+ align:start position:0%
+different and that's what Barry
+elaborated and explained and and show
+
+ align:start position:0%
+elaborated and explained and and show
+ 
+
+ align:start position:0%
+elaborated and explained and and show
+that it could be observable in some
+
+ align:start position:0%
+that it could be observable in some
+ 
+
+ align:start position:0%
+that it could be observable in some
+cases and it was a pretty nice discovery
+
+ align:start position:0%
+cases and it was a pretty nice discovery
+ 
+
+ align:start position:0%
+cases and it was a pretty nice discovery
+so so basically the idea badeck a
+
+ align:start position:0%
+so so basically the idea badeck a
+ 
+
+ align:start position:0%
+so so basically the idea badeck a
+statement here says that you don't jump
+
+ align:start position:0%
+statement here says that you don't jump
+ 
+
+ align:start position:0%
+statement here says that you don't jump
+to another instantaneous energy
+
+ align:start position:0%
+to another instantaneous energy
+ 
+
+ align:start position:0%
+to another instantaneous energy
+eigenstate you remain in that
+
+ align:start position:0%
+eigenstate you remain in that
+ 
+
+ align:start position:0%
+eigenstate you remain in that
+instantaneous energy eigenstate okay
+
+ align:start position:0%
+instantaneous energy eigenstate okay
+ 
+
+ align:start position:0%
+instantaneous energy eigenstate okay
+another thing that is important is that
+
+ align:start position:0%
+another thing that is important is that
+ 
+
+ align:start position:0%
+another thing that is important is that
+sometimes you say well these are faces
+
+ align:start position:0%
+sometimes you say well these are faces
+ 
+
+ align:start position:0%
+sometimes you say well these are faces
+when you have states the faces are
+
+ align:start position:0%
+when you have states the faces are
+ 
+
+ align:start position:0%
+when you have states the faces are
+unobservable overall faces of a state
+
+ align:start position:0%
+unobservable overall faces of a state
+ 
+
+ align:start position:0%
+unobservable overall faces of a state
+you calculate this state after a while
+
+ align:start position:0%
+you calculate this state after a while
+ 
+
+ align:start position:0%
+you calculate this state after a while
+it has a phase well that face of your
+
+ align:start position:0%
+it has a phase well that face of your
+ 
+
+ align:start position:0%
+it has a phase well that face of your
+physical state doesn't make any
+
+ align:start position:0%
+physical state doesn't make any
+ 
+
+ align:start position:0%
+physical state doesn't make any
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+well that's true the overall face of a
+
+ align:start position:0%
+well that's true the overall face of a
+ 
+
+ align:start position:0%
+well that's true the overall face of a
+state doesn't make any difference but if
+
+ align:start position:0%
+state doesn't make any difference but if
+ 
+
+ align:start position:0%
+state doesn't make any difference but if
+you have a system that is in a
+
+ align:start position:0%
+you have a system that is in a
+ 
+
+ align:start position:0%
+you have a system that is in a
+superposition of two quantum states one
+
+ align:start position:0%
+superposition of two quantum states one
+ 
+
+ align:start position:0%
+superposition of two quantum states one
+corresponding to one instantaneous
+
+ align:start position:0%
+corresponding to one instantaneous
+ 
+
+ align:start position:0%
+corresponding to one instantaneous
+energy and you say than one
+
+ align:start position:0%
+energy and you say than one
+ 
+
+ align:start position:0%
+energy and you say than one
+corresponding to another so there's psy
+
+ align:start position:0%
+corresponding to another so there's psy
+ 
+
+ align:start position:0%
+corresponding to another so there's psy
+equal to psi 1 and PSI 2 1 for each side
+
+ align:start position:0%
+equal to psi 1 and PSI 2 1 for each side
+ 
+
+ align:start position:0%
+equal to psi 1 and PSI 2 1 for each side
+1 by the linearity of quantum mechanics
+
+ align:start position:0%
+1 by the linearity of quantum mechanics
+ 
+
+ align:start position:0%
+1 by the linearity of quantum mechanics
+is gonna develop its own face try to is
+
+ align:start position:0%
+is gonna develop its own face try to is
+ 
+
+ align:start position:0%
+is gonna develop its own face try to is
+gonna develop its own face and now the
+
+ align:start position:0%
+gonna develop its own face and now the
+ 
+
+ align:start position:0%
+gonna develop its own face and now the
+relative face is observable when you
+
+ align:start position:0%
+relative face is observable when you
+ 
+
+ align:start position:0%
+relative face is observable when you
+have a superposition of states the
+
+ align:start position:0%
+have a superposition of states the
+ 
+
+ align:start position:0%
+have a superposition of states the
+relative face is observable and
+
+ align:start position:0%
+relative face is observable and
+ 
+
+ align:start position:0%
+relative face is observable and
+therefore if the two states evolve with
+
+ align:start position:0%
+therefore if the two states evolve with
+ 
+
+ align:start position:0%
+therefore if the two states evolve with
+different faces you can have observable
+
+ align:start position:0%
+different faces you can have observable
+ 
+
+ align:start position:0%
+different faces you can have observable
+consequences so so there is something
+
+ align:start position:0%
+consequences so so there is something
+ 
+
+ align:start position:0%
+consequences so so there is something
+that can happen here on something that
+
+ align:start position:0%
+that can happen here on something that
+ 
+
+ align:start position:0%
+that can happen here on something that
+can be measured
\ No newline at end of file
diff --git a/piFmQGn6VXE.txt b/piFmQGn6VXE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..01baeeb2e597fd90585ee7f92e08978297bd6682
--- /dev/null
+++ b/piFmQGn6VXE.txt
@@ -0,0 +1,11344 @@
+align:start position:0%
+ 
+so I'm going to tell you about the
+
+ align:start position:0%
+so I'm going to tell you about the
+ 
+
+ align:start position:0%
+so I'm going to tell you about the
+spectroscopic
+
+ align:start position:0%
+spectroscopic
+ 
+
+ align:start position:0%
+spectroscopic
+hamiltonian the diatomic
+
+ align:start position:0%
+hamiltonian the diatomic
+ 
+
+ align:start position:0%
+hamiltonian the diatomic
+molecules okay we call that the effect
+
+ align:start position:0%
+molecules okay we call that the effect
+ 
+
+ align:start position:0%
+molecules okay we call that the effect
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+hiltonium it's a matrix it's a fit model
+
+ align:start position:0%
+hiltonium it's a matrix it's a fit model
+ 
+
+ align:start position:0%
+hiltonium it's a matrix it's a fit model
+it represents everything that you can
+
+ align:start position:0%
+it represents everything that you can
+ 
+
+ align:start position:0%
+it represents everything that you can
+observe for a diatomic
+
+ align:start position:0%
+observe for a diatomic
+ 
+
+ align:start position:0%
+observe for a diatomic
+molecule it is not the exact
+
+ align:start position:0%
+molecule it is not the exact
+ 
+
+ align:start position:0%
+molecule it is not the exact
+hemon a Quantum chemist would not
+
+ align:start position:0%
+hemon a Quantum chemist would not
+ 
+
+ align:start position:0%
+hemon a Quantum chemist would not
+calculate that they could derive it if
+
+ align:start position:0%
+calculate that they could derive it if
+ 
+
+ align:start position:0%
+calculate that they could derive it if
+they chose to from what they can
+
+ align:start position:0%
+they chose to from what they can
+ 
+
+ align:start position:0%
+they chose to from what they can
+calculate but it's different in several
+
+ align:start position:0%
+calculate but it's different in several
+ 
+
+ align:start position:0%
+calculate but it's different in several
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+ways okay fundamental to the effective
+
+ align:start position:0%
+ways okay fundamental to the effective
+ 
+
+ align:start position:0%
+ways okay fundamental to the effective
+hamiltonian is a separation of variables
+
+ align:start position:0%
+hamiltonian is a separation of variables
+ 
+
+ align:start position:0%
+hamiltonian is a separation of variables
+to nuclear variables and electronic
+
+ align:start position:0%
+to nuclear variables and electronic
+ 
+
+ align:start position:0%
+to nuclear variables and electronic
+variables that's called the borop
+
+ align:start position:0%
+variables that's called the borop
+ 
+
+ align:start position:0%
+variables that's called the borop
+approximation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electronic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vibrational and rotational degrees of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tre these are
+
+ align:start position:0%
+tre these are
+ 
+
+ align:start position:0%
+tre these are
+nuclear this is
+
+ align:start position:0%
+nuclear this is
+ 
+
+ align:start position:0%
+nuclear this is
+electron uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now we're all
+
+ align:start position:0%
+and now we're all
+ 
+
+ align:start position:0%
+and now we're all
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+okay and so the born Oppenheimer
+
+ align:start position:0%
+okay and so the born Oppenheimer
+ 
+
+ align:start position:0%
+okay and so the born Oppenheimer
+approximation allows us to make this
+
+ align:start position:0%
+approximation allows us to make this
+ 
+
+ align:start position:0%
+approximation allows us to make this
+separation nothing really allows us to
+
+ align:start position:0%
+separation nothing really allows us to
+ 
+
+ align:start position:0%
+separation nothing really allows us to
+make this separation but we do
+
+ align:start position:0%
+make this separation but we do
+ 
+
+ align:start position:0%
+make this separation but we do
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+um what is it what is this separation
+
+ align:start position:0%
+um what is it what is this separation
+ 
+
+ align:start position:0%
+um what is it what is this separation
+good for
+
+ align:start position:0%
+good for
+ 
+
+ align:start position:0%
+good for
+well it enables us
+
+ align:start position:0%
+well it enables us
+ 
+
+ align:start position:0%
+well it enables us
+to approach the problem of a many
+
+ align:start position:0%
+to approach the problem of a many
+ 
+
+ align:start position:0%
+to approach the problem of a many
+electron atom a many electron molecule
+
+ align:start position:0%
+electron atom a many electron molecule
+ 
+
+ align:start position:0%
+electron atom a many electron molecule
+without having to deal with all of the
+
+ align:start position:0%
+without having to deal with all of the
+ 
+
+ align:start position:0%
+without having to deal with all of the
+degrees of freedom that would be
+
+ align:start position:0%
+degrees of freedom that would be
+ 
+
+ align:start position:0%
+degrees of freedom that would be
+associated with many electrons plus
+
+ align:start position:0%
+associated with many electrons plus
+ 
+
+ align:start position:0%
+associated with many electrons plus
+several
+
+ align:start position:0%
+several
+ 
+
+ align:start position:0%
+several
+nucleon it enables us to think about
+
+ align:start position:0%
+nucleon it enables us to think about
+ 
+
+ align:start position:0%
+nucleon it enables us to think about
+things called electronic States and
+
+ align:start position:0%
+things called electronic States and
+ 
+
+ align:start position:0%
+things called electronic States and
+rotation vibration levels of electronic
+
+ align:start position:0%
+rotation vibration levels of electronic
+ 
+
+ align:start position:0%
+rotation vibration levels of electronic
+States and that's an enormous
+
+ align:start position:0%
+States and that's an enormous
+ 
+
+ align:start position:0%
+States and that's an enormous
+simplification
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now a lot is slipped under the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rug uh
+
+ align:start position:0%
+rug uh
+ 
+
+ align:start position:0%
+rug uh
+these things that are slipped under the
+
+ align:start position:0%
+these things that are slipped under the
+ 
+
+ align:start position:0%
+these things that are slipped under the
+rug are going to be critical to
+
+ align:start position:0%
+rug are going to be critical to
+ 
+
+ align:start position:0%
+rug are going to be critical to
+understanding
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dynamics But first you need to have a
+
+ align:start position:0%
+Dynamics But first you need to have a
+ 
+
+ align:start position:0%
+Dynamics But first you need to have a
+picture of what would the molecules
+
+ align:start position:0%
+picture of what would the molecules
+ 
+
+ align:start position:0%
+picture of what would the molecules
+behave like if they were really simple
+
+ align:start position:0%
+behave like if they were really simple
+ 
+
+ align:start position:0%
+behave like if they were really simple
+if nature had been more kind but then
+
+ align:start position:0%
+if nature had been more kind but then
+ 
+
+ align:start position:0%
+if nature had been more kind but then
+there'd be no Dynamics there'd be no
+
+ align:start position:0%
+there'd be no Dynamics there'd be no
+ 
+
+ align:start position:0%
+there'd be no Dynamics there'd be no
+life you know it would that be such a
+
+ align:start position:0%
+life you know it would that be such a
+ 
+
+ align:start position:0%
+life you know it would that be such a
+good thing um
+
+ align:start position:0%
+good thing um
+ 
+
+ align:start position:0%
+good thing um
+welome um and uh uh so we're going to
+
+ align:start position:0%
+welome um and uh uh so we're going to
+ 
+
+ align:start position:0%
+welome um and uh uh so we're going to
+create a
+
+ align:start position:0%
+create a
+ 
+
+ align:start position:0%
+create a
+world um which we
+
+ align:start position:0%
+world um which we
+ 
+
+ align:start position:0%
+world um which we
+understand which is free of all these
+
+ align:start position:0%
+understand which is free of all these
+ 
+
+ align:start position:0%
+understand which is free of all these
+difficult terms and then we're going to
+
+ align:start position:0%
+difficult terms and then we're going to
+ 
+
+ align:start position:0%
+difficult terms and then we're going to
+bring these difficult terms in use this
+
+ align:start position:0%
+bring these difficult terms in use this
+ 
+
+ align:start position:0%
+bring these difficult terms in use this
+simple picture that we started with in
+
+ align:start position:0%
+simple picture that we started with in
+ 
+
+ align:start position:0%
+simple picture that we started with in
+order to be able to calculate all of the
+
+ align:start position:0%
+order to be able to calculate all of the
+ 
+
+ align:start position:0%
+order to be able to calculate all of the
+complexities that we
+
+ align:start position:0%
+complexities that we
+ 
+
+ align:start position:0%
+complexities that we
+would we had suppressed when we defined
+
+ align:start position:0%
+would we had suppressed when we defined
+ 
+
+ align:start position:0%
+would we had suppressed when we defined
+the simple
+
+ align:start position:0%
+the simple
+ 
+
+ align:start position:0%
+the simple
+World okay why datomic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+molecules well they're not
+
+ align:start position:0%
+molecules well they're not
+ 
+
+ align:start position:0%
+molecules well they're not
+atoms and chemists are generally
+
+ align:start position:0%
+atoms and chemists are generally
+ 
+
+ align:start position:0%
+atoms and chemists are generally
+interested in molecules this is the
+
+ align:start position:0%
+interested in molecules this is the
+ 
+
+ align:start position:0%
+interested in molecules this is the
+simplest thing that has all of the
+
+ align:start position:0%
+simplest thing that has all of the
+ 
+
+ align:start position:0%
+simplest thing that has all of the
+complexity of
+
+ align:start position:0%
+complexity of
+ 
+
+ align:start position:0%
+complexity of
+chemistry diatomic molecules are also
+
+ align:start position:0%
+chemistry diatomic molecules are also
+ 
+
+ align:start position:0%
+chemistry diatomic molecules are also
+special
+
+ align:start position:0%
+special
+ 
+
+ align:start position:0%
+special
+because of several things you can go
+
+ align:start position:0%
+because of several things you can go
+ 
+
+ align:start position:0%
+because of several things you can go
+from ins
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spectum to the effective
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hiltonium and there is an
+
+ align:start position:0%
+hiltonium and there is an
+ 
+
+ align:start position:0%
+hiltonium and there is an
+exact inversion
+
+ align:start position:0%
+exact inversion
+ 
+
+ align:start position:0%
+exact inversion
+this is not true for any other kind of
+
+ align:start position:0%
+this is not true for any other kind of
+ 
+
+ align:start position:0%
+this is not true for any other kind of
+molecule so one can approach the problem
+
+ align:start position:0%
+molecule so one can approach the problem
+ 
+
+ align:start position:0%
+molecule so one can approach the problem
+of diatomic molecules without having to
+
+ align:start position:0%
+of diatomic molecules without having to
+ 
+
+ align:start position:0%
+of diatomic molecules without having to
+make any assumptions of
+
+ align:start position:0%
+make any assumptions of
+ 
+
+ align:start position:0%
+make any assumptions of
+models one
+
+ align:start position:0%
+models one
+ 
+
+ align:start position:0%
+models one
+can then take that approach and a lot of
+
+ align:start position:0%
+can then take that approach and a lot of
+ 
+
+ align:start position:0%
+can then take that approach and a lot of
+the approximations that work and use
+
+ align:start position:0%
+the approximations that work and use
+ 
+
+ align:start position:0%
+the approximations that work and use
+them for more complicated
+
+ align:start position:0%
+them for more complicated
+ 
+
+ align:start position:0%
+them for more complicated
+systems with confidence is that you know
+
+ align:start position:0%
+systems with confidence is that you know
+ 
+
+ align:start position:0%
+systems with confidence is that you know
+the limits of these assumptions and
+
+ align:start position:0%
+the limits of these assumptions and
+ 
+
+ align:start position:0%
+the limits of these assumptions and
+approaches in
+
+ align:start position:0%
+approaches in
+ 
+
+ align:start position:0%
+approaches in
+Botts you can also
+
+ align:start position:0%
+Botts you can also
+ 
+
+ align:start position:0%
+Botts you can also
+have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sample of all relevant States now you're
+
+ align:start position:0%
+sample of all relevant States now you're
+ 
+
+ align:start position:0%
+sample of all relevant States now you're
+not going to look at all states of the
+
+ align:start position:0%
+not going to look at all states of the
+ 
+
+ align:start position:0%
+not going to look at all states of the
+molecule but with a datomic molecule you
+
+ align:start position:0%
+molecule but with a datomic molecule you
+ 
+
+ align:start position:0%
+molecule but with a datomic molecule you
+can essentially measure everything that
+
+ align:start position:0%
+can essentially measure everything that
+ 
+
+ align:start position:0%
+can essentially measure everything that
+is relevant to whatever question you
+
+ align:start position:0%
+is relevant to whatever question you
+ 
+
+ align:start position:0%
+is relevant to whatever question you
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+ask because the vibrational density of
+
+ align:start position:0%
+ask because the vibrational density of
+ 
+
+ align:start position:0%
+ask because the vibrational density of
+states and the electronic density of
+
+ align:start position:0%
+states and the electronic density of
+ 
+
+ align:start position:0%
+states and the electronic density of
+States increases very very slowly and so
+
+ align:start position:0%
+States increases very very slowly and so
+ 
+
+ align:start position:0%
+States increases very very slowly and so
+one can resolve all of the stuff that
+
+ align:start position:0%
+one can resolve all of the stuff that
+ 
+
+ align:start position:0%
+one can resolve all of the stuff that
+you need to create your model and to
+
+ align:start position:0%
+you need to create your model and to
+ 
+
+ align:start position:0%
+you need to create your model and to
+answer your
+
+ align:start position:0%
+answer your
+ 
+
+ align:start position:0%
+answer your
+questions and this is not generally true
+
+ align:start position:0%
+questions and this is not generally true
+ 
+
+ align:start position:0%
+questions and this is not generally true
+for polyatomic molecules in fact it's
+
+ align:start position:0%
+for polyatomic molecules in fact it's
+ 
+
+ align:start position:0%
+for polyatomic molecules in fact it's
+almost never
+
+ align:start position:0%
+almost never
+ 
+
+ align:start position:0%
+almost never
+true so we need somehow to develop ways
+
+ align:start position:0%
+true so we need somehow to develop ways
+ 
+
+ align:start position:0%
+true so we need somehow to develop ways
+of extrapolating into polyatomic
+
+ align:start position:0%
+of extrapolating into polyatomic
+ 
+
+ align:start position:0%
+of extrapolating into polyatomic
+molecules to deal with this rapid
+
+ align:start position:0%
+molecules to deal with this rapid
+ 
+
+ align:start position:0%
+molecules to deal with this rapid
+increase of density of states and
+
+ align:start position:0%
+increase of density of states and
+ 
+
+ align:start position:0%
+increase of density of states and
+complexity and we use datomic pictures
+
+ align:start position:0%
+complexity and we use datomic pictures
+ 
+
+ align:start position:0%
+complexity and we use datomic pictures
+as a way of doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay I said there is an effective
+
+ align:start position:0%
+it okay I said there is an effective
+ 
+
+ align:start position:0%
+it okay I said there is an effective
+hamiltonian which is our model for
+
+ align:start position:0%
+hamiltonian which is our model for
+ 
+
+ align:start position:0%
+hamiltonian which is our model for
+representing everything in diatomic
+
+ align:start position:0%
+representing everything in diatomic
+ 
+
+ align:start position:0%
+representing everything in diatomic
+molecule and how is it different from
+
+ align:start position:0%
+molecule and how is it different from
+ 
+
+ align:start position:0%
+molecule and how is it different from
+the exact
+
+ align:start position:0%
+the exact
+ 
+
+ align:start position:0%
+the exact
+hamiltoni
+
+ align:start position:0%
+hamiltoni
+ 
+
+ align:start position:0%
+hamiltoni
+well you might start with the exact
+
+ align:start position:0%
+well you might start with the exact
+ 
+
+ align:start position:0%
+well you might start with the exact
+hamiltonian
+
+ align:start position:0%
+hamiltonian
+ 
+
+ align:start position:0%
+hamiltonian
+and uh you would partition the exact
+
+ align:start position:0%
+and uh you would partition the exact
+ 
+
+ align:start position:0%
+and uh you would partition the exact
+hamiltonian
+
+ align:start position:0%
+hamiltonian
+ 
+
+ align:start position:0%
+hamiltonian
+into zero order picture plus everything
+
+ align:start position:0%
+into zero order picture plus everything
+ 
+
+ align:start position:0%
+into zero order picture plus everything
+else okay this zero order picture is
+
+ align:start position:0%
+else okay this zero order picture is
+ 
+
+ align:start position:0%
+else okay this zero order picture is
+based on
+
+ align:start position:0%
+based on
+ 
+
+ align:start position:0%
+based on
+models that you
+
+ align:start position:0%
+models that you
+ 
+
+ align:start position:0%
+models that you
+understand and can calculate
+
+ align:start position:0%
+understand and can calculate
+ 
+
+ align:start position:0%
+understand and can calculate
+with this is the simple World it might
+
+ align:start position:0%
+with this is the simple World it might
+ 
+
+ align:start position:0%
+with this is the simple World it might
+be uh
+
+ align:start position:0%
+be uh
+ 
+
+ align:start position:0%
+be uh
+um rigid rotor harmonic oscillator
+
+ align:start position:0%
+um rigid rotor harmonic oscillator
+ 
+
+ align:start position:0%
+um rigid rotor harmonic oscillator
+hydrogen atom particle in a
+
+ align:start position:0%
+hydrogen atom particle in a
+ 
+
+ align:start position:0%
+hydrogen atom particle in a
+box the particle in a box is a good
+
+ align:start position:0%
+box the particle in a box is a good
+ 
+
+ align:start position:0%
+box the particle in a box is a good
+representation for veence electronic
+
+ align:start position:0%
+representation for veence electronic
+ 
+
+ align:start position:0%
+representation for veence electronic
+States the hydrogen atom is a good
+
+ align:start position:0%
+States the hydrogen atom is a good
+ 
+
+ align:start position:0%
+States the hydrogen atom is a good
+representation for ridberg electronic
+
+ align:start position:0%
+representation for ridberg electronic
+ 
+
+ align:start position:0%
+representation for ridberg electronic
+States the vibration that harmonic
+
+ align:start position:0%
+States the vibration that harmonic
+ 
+
+ align:start position:0%
+States the vibration that harmonic
+oscillator is a good representation for
+
+ align:start position:0%
+oscillator is a good representation for
+ 
+
+ align:start position:0%
+oscillator is a good representation for
+vibration a rotor for rotation and so we
+
+ align:start position:0%
+vibration a rotor for rotation and so we
+ 
+
+ align:start position:0%
+vibration a rotor for rotation and so we
+might put in things for which we have
+
+ align:start position:0%
+might put in things for which we have
+ 
+
+ align:start position:0%
+might put in things for which we have
+Exact Solutions and we know how they
+
+ align:start position:0%
+Exact Solutions and we know how they
+ 
+
+ align:start position:0%
+Exact Solutions and we know how they
+work and we have igen functions of
+
+ align:start position:0%
+work and we have igen functions of
+ 
+
+ align:start position:0%
+work and we have igen functions of
+this which we can use to evaluate Matrix
+
+ align:start position:0%
+this which we can use to evaluate Matrix
+ 
+
+ align:start position:0%
+this which we can use to evaluate Matrix
+elements of whatever is
+
+ align:start position:0%
+elements of whatever is
+ 
+
+ align:start position:0%
+elements of whatever is
+inconvenient now there's a lot of stuff
+
+ align:start position:0%
+inconvenient now there's a lot of stuff
+ 
+
+ align:start position:0%
+inconvenient now there's a lot of stuff
+that I'm hiding here but that's the
+
+ align:start position:0%
+that I'm hiding here but that's the
+ 
+
+ align:start position:0%
+that I'm hiding here but that's the
+formal
+
+ align:start position:0%
+formal
+ 
+
+ align:start position:0%
+formal
+approach and
+
+ align:start position:0%
+approach and
+ 
+
+ align:start position:0%
+approach and
+this is an extremely good time to ask
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions so this enables us to define a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+complete
+
+ align:start position:0%
+complete
+ 
+
+ align:start position:0%
+complete
+basis
+
+ align:start position:0%
+basis
+ 
+
+ align:start position:0%
+basis
+set in other words we have a complete
+
+ align:start position:0%
+set in other words we have a complete
+ 
+
+ align:start position:0%
+set in other words we have a complete
+set of wave functions or bras and
+
+ align:start position:0%
+set of wave functions or bras and
+ 
+
+ align:start position:0%
+set of wave functions or bras and
+cats that uh enables us to evaluate the
+
+ align:start position:0%
+cats that uh enables us to evaluate the
+ 
+
+ align:start position:0%
+cats that uh enables us to evaluate the
+effects of the terms that we've decided
+
+ align:start position:0%
+effects of the terms that we've decided
+ 
+
+ align:start position:0%
+effects of the terms that we've decided
+to exclude from
+
+ align:start position:0%
+to exclude from
+ 
+
+ align:start position:0%
+to exclude from
+azero we can choose which terms we put
+
+ align:start position:0%
+azero we can choose which terms we put
+ 
+
+ align:start position:0%
+azero we can choose which terms we put
+in h zero depending on which
+
+ align:start position:0%
+in h zero depending on which
+ 
+
+ align:start position:0%
+in h zero depending on which
+interactions we think are important and
+
+ align:start position:0%
+interactions we think are important and
+ 
+
+ align:start position:0%
+interactions we think are important and
+ought to be dealt with in the zero order
+
+ align:start position:0%
+ought to be dealt with in the zero order
+ 
+
+ align:start position:0%
+ought to be dealt with in the zero order
+model and which ones are only small
+
+ align:start position:0%
+model and which ones are only small
+ 
+
+ align:start position:0%
+model and which ones are only small
+preservations that we won't have to that
+
+ align:start position:0%
+preservations that we won't have to that
+ 
+
+ align:start position:0%
+preservations that we won't have to that
+that we we will have to deal with but
+
+ align:start position:0%
+that we we will have to deal with but
+ 
+
+ align:start position:0%
+that we we will have to deal with but
+will not be necessary for being able to
+
+ align:start position:0%
+will not be necessary for being able to
+ 
+
+ align:start position:0%
+will not be necessary for being able to
+recognize in either the abidal
+
+ align:start position:0%
+recognize in either the abidal
+ 
+
+ align:start position:0%
+recognize in either the abidal
+calculations or your
+
+ align:start position:0%
+calculations or your
+ 
+
+ align:start position:0%
+calculations or your
+spectrum
+
+ align:start position:0%
+spectrum
+ 
+
+ align:start position:0%
+spectrum
+complexities and we'll see how that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+works okay so we Divine the divide the
+
+ align:start position:0%
+works okay so we Divine the divide the
+ 
+
+ align:start position:0%
+works okay so we Divine the divide the
+hamiltonian into a zero order part and
+
+ align:start position:0%
+hamiltonian into a zero order part and
+ 
+
+ align:start position:0%
+hamiltonian into a zero order part and
+everything
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else then we have essentially an
+
+ align:start position:0%
+else then we have essentially an
+ 
+
+ align:start position:0%
+else then we have essentially an
+infinite
+
+ align:start position:0%
+infinite
+ 
+
+ align:start position:0%
+infinite
+Matrix which is no
+
+ align:start position:0%
+Matrix which is no
+ 
+
+ align:start position:0%
+Matrix which is no
+use and we have to approximately block
+
+ align:start position:0%
+use and we have to approximately block
+ 
+
+ align:start position:0%
+use and we have to approximately block
+diagonal eyes it and that's called the
+
+ align:start position:0%
+diagonal eyes it and that's called the
+ 
+
+ align:start position:0%
+diagonal eyes it and that's called the
+van Le or contact
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transformation and this is basically
+
+ align:start position:0%
+transformation and this is basically
+ 
+
+ align:start position:0%
+transformation and this is basically
+second order perturbation
+
+ align:start position:0%
+second order perturbation
+ 
+
+ align:start position:0%
+second order perturbation
+Theory it's a procedure which is
+
+ align:start position:0%
+Theory it's a procedure which is
+ 
+
+ align:start position:0%
+Theory it's a procedure which is
+describable
+
+ align:start position:0%
+describable
+ 
+
+ align:start position:0%
+describable
+exactly and it enables us to take this
+
+ align:start position:0%
+exactly and it enables us to take this
+ 
+
+ align:start position:0%
+exactly and it enables us to take this
+infinite Matrix which is the exact
+
+ align:start position:0%
+infinite Matrix which is the exact
+ 
+
+ align:start position:0%
+infinite Matrix which is the exact
+hamiltonian and cut it down to small
+
+ align:start position:0%
+hamiltonian and cut it down to small
+ 
+
+ align:start position:0%
+hamiltonian and cut it down to small
+pieces blocks that we can
+
+ align:start position:0%
+pieces blocks that we can
+ 
+
+ align:start position:0%
+pieces blocks that we can
+diagonalize and we think of that as our
+
+ align:start position:0%
+diagonalize and we think of that as our
+ 
+
+ align:start position:0%
+diagonalize and we think of that as our
+fit model as the effective hamiltonan
+
+ align:start position:0%
+fit model as the effective hamiltonan
+ 
+
+ align:start position:0%
+fit model as the effective hamiltonan
+this is an essential part about which I
+
+ align:start position:0%
+this is an essential part about which I
+ 
+
+ align:start position:0%
+this is an essential part about which I
+will talk very
+
+ align:start position:0%
+will talk very
+ 
+
+ align:start position:0%
+will talk very
+little but it is the difference between
+
+ align:start position:0%
+little but it is the difference between
+ 
+
+ align:start position:0%
+little but it is the difference between
+what a Quantum chemist would calculate
+
+ align:start position:0%
+what a Quantum chemist would calculate
+ 
+
+ align:start position:0%
+what a Quantum chemist would calculate
+and what a spectroscopist would
+
+ align:start position:0%
+and what a spectroscopist would
+ 
+
+ align:start position:0%
+and what a spectroscopist would
+manipulate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and that gives us the effect of H
+
+ align:start position:0%
+so and that gives us the effect of H
+ 
+
+ align:start position:0%
+so and that gives us the effect of H
+which is a matrix that has a bunch
+
+ align:start position:0%
+which is a matrix that has a bunch
+ 
+
+ align:start position:0%
+which is a matrix that has a bunch
+of blocks along the diagonal and some
+
+ align:start position:0%
+of blocks along the diagonal and some
+ 
+
+ align:start position:0%
+of blocks along the diagonal and some
+small stuff off the diagonal that we're
+
+ align:start position:0%
+small stuff off the diagonal that we're
+ 
+
+ align:start position:0%
+small stuff off the diagonal that we're
+allowed to
+
+ align:start position:0%
+allowed to
+ 
+
+ align:start position:0%
+allowed to
+neglect except Whenever there
+
+ align:start position:0%
+neglect except Whenever there
+ 
+
+ align:start position:0%
+neglect except Whenever there
+occurs
+
+ align:start position:0%
+occurs
+ 
+
+ align:start position:0%
+occurs
+accidental degeneracies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's possible that we have a bunch of uh
+
+ align:start position:0%
+it's possible that we have a bunch of uh
+ 
+
+ align:start position:0%
+it's possible that we have a bunch of uh
+States associated with this
+
+ align:start position:0%
+States associated with this
+ 
+
+ align:start position:0%
+States associated with this
+block and they have their own energies
+
+ align:start position:0%
+block and they have their own energies
+ 
+
+ align:start position:0%
+block and they have their own energies
+and bunch of States associate with this
+
+ align:start position:0%
+and bunch of States associate with this
+ 
+
+ align:start position:0%
+and bunch of States associate with this
+block and there's a tiny term here uh
+
+ align:start position:0%
+block and there's a tiny term here uh
+ 
+
+ align:start position:0%
+block and there's a tiny term here uh
+that couples States in these two blocks
+
+ align:start position:0%
+that couples States in these two blocks
+ 
+
+ align:start position:0%
+that couples States in these two blocks
+and normally the energies are very
+
+ align:start position:0%
+and normally the energies are very
+ 
+
+ align:start position:0%
+and normally the energies are very
+different the difference in zero order
+
+ align:start position:0%
+different the difference in zero order
+ 
+
+ align:start position:0%
+different the difference in zero order
+energies or block energies are large
+
+ align:start position:0%
+energies or block energies are large
+ 
+
+ align:start position:0%
+energies or block energies are large
+compared to the coupling terms and so we
+
+ align:start position:0%
+compared to the coupling terms and so we
+ 
+
+ align:start position:0%
+compared to the coupling terms and so we
+can ignore
+
+ align:start position:0%
+can ignore
+ 
+
+ align:start position:0%
+can ignore
+them we do but when by accident the
+
+ align:start position:0%
+them we do but when by accident the
+ 
+
+ align:start position:0%
+them we do but when by accident the
+levels get close together we can't and
+
+ align:start position:0%
+levels get close together we can't and
+ 
+
+ align:start position:0%
+levels get close together we can't and
+we have to do something special and
+
+ align:start position:0%
+we have to do something special and
+ 
+
+ align:start position:0%
+we have to do something special and
+that's called Dynamics it's called a
+
+ align:start position:0%
+that's called Dynamics it's called a
+ 
+
+ align:start position:0%
+that's called Dynamics it's called a
+perturbation it's called the interesting
+
+ align:start position:0%
+perturbation it's called the interesting
+ 
+
+ align:start position:0%
+perturbation it's called the interesting
+stuff it's the stuff that most textbooks
+
+ align:start position:0%
+stuff it's the stuff that most textbooks
+ 
+
+ align:start position:0%
+stuff it's the stuff that most textbooks
+slip under the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rock so we have a procedure for
+
+ align:start position:0%
+rock so we have a procedure for
+ 
+
+ align:start position:0%
+rock so we have a procedure for
+simplifying the exact hamiltonian and uh
+
+ align:start position:0%
+simplifying the exact hamiltonian and uh
+ 
+
+ align:start position:0%
+simplifying the exact hamiltonian and uh
+there's complicated Dynamics because
+
+ align:start position:0%
+there's complicated Dynamics because
+ 
+
+ align:start position:0%
+there's complicated Dynamics because
+these blocks also have offal
+
+ align:start position:0%
+these blocks also have offal
+ 
+
+ align:start position:0%
+these blocks also have offal
+elements but those are sort of part of
+
+ align:start position:0%
+elements but those are sort of part of
+ 
+
+ align:start position:0%
+elements but those are sort of part of
+our zero order model and then there are
+
+ align:start position:0%
+our zero order model and then there are
+ 
+
+ align:start position:0%
+our zero order model and then there are
+these exceptional things which lead to
+
+ align:start position:0%
+these exceptional things which lead to
+ 
+
+ align:start position:0%
+these exceptional things which lead to
+unexpected and useful energy flow
+
+ align:start position:0%
+unexpected and useful energy flow
+ 
+
+ align:start position:0%
+unexpected and useful energy flow
+between different parts of a system that
+
+ align:start position:0%
+between different parts of a system that
+ 
+
+ align:start position:0%
+between different parts of a system that
+are normally not in communication
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes I had two questions so is the van
+
+ align:start position:0%
+yes I had two questions so is the van
+ 
+
+ align:start position:0%
+yes I had two questions so is the van
+like transformation the purpose is is to
+
+ align:start position:0%
+like transformation the purpose is is to
+ 
+
+ align:start position:0%
+like transformation the purpose is is to
+minimize those off diagonal elements
+
+ align:start position:0%
+minimize those off diagonal elements
+ 
+
+ align:start position:0%
+minimize those off diagonal elements
+between the blocks ex the
+
+ align:start position:0%
+between the blocks ex the
+ 
+
+ align:start position:0%
+between the blocks ex the
+go is it designed such that it's an
+
+ align:start position:0%
+go is it designed such that it's an
+ 
+
+ align:start position:0%
+go is it designed such that it's an
+optimization machine to minimize that or
+
+ align:start position:0%
+optimization machine to minimize that or
+ 
+
+ align:start position:0%
+optimization machine to minimize that or
+is it a set routine which which does
+
+ align:start position:0%
+is it a set routine which which does
+ 
+
+ align:start position:0%
+is it a set routine which which does
+that which is known to do that it's a
+
+ align:start position:0%
+that which is known to do that it's a
+ 
+
+ align:start position:0%
+that which is known to do that it's a
+set routine it's so you the the
+
+ align:start position:0%
+set routine it's so you the the
+ 
+
+ align:start position:0%
+set routine it's so you the the
+procedure is to um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is to correct to add terms on the
+
+ align:start position:0%
+is to correct to add terms on the
+ 
+
+ align:start position:0%
+is to correct to add terms on the
+diagonal and off the diagonal in each of
+
+ align:start position:0%
+diagonal and off the diagonal in each of
+ 
+
+ align:start position:0%
+diagonal and off the diagonal in each of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+blocks that compensate for these outof
+
+ align:start position:0%
+blocks that compensate for these outof
+ 
+
+ align:start position:0%
+blocks that compensate for these outof
+block
+
+ align:start position:0%
+block
+ 
+
+ align:start position:0%
+block
+terms and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so let's call this the n and this the
+
+ align:start position:0%
+um so let's call this the n and this the
+ 
+
+ align:start position:0%
+um so let's call this the n and this the
+M Block
+
+ align:start position:0%
+M Block
+ 
+
+ align:start position:0%
+M Block
+okay so we have a matrix element between
+
+ align:start position:0%
+okay so we have a matrix element between
+ 
+
+ align:start position:0%
+okay so we have a matrix element between
+one member of the N block and one member
+
+ align:start position:0%
+one member of the N block and one member
+ 
+
+ align:start position:0%
+one member of the N block and one member
+of I and one member of the N
+
+ align:start position:0%
+of I and one member of the N
+ 
+
+ align:start position:0%
+of I and one member of the N
+BL okay so that's an offal Matrix
+
+ align:start position:0%
+BL okay so that's an offal Matrix
+ 
+
+ align:start position:0%
+BL okay so that's an offal Matrix
+element it's an auto
+
+ align:start position:0%
+element it's an auto
+ 
+
+ align:start position:0%
+element it's an auto
+block
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix okay
+
+ align:start position:0%
+Matrix okay
+ 
+
+ align:start position:0%
+Matrix okay
+and so second order perturbation Theory
+
+ align:start position:0%
+and so second order perturbation Theory
+ 
+
+ align:start position:0%
+and so second order perturbation Theory
+would would say well we could cons we
+
+ align:start position:0%
+would would say well we could cons we
+ 
+
+ align:start position:0%
+would would say well we could cons we
+can uh correct the
+
+ align:start position:0%
+can uh correct the
+ 
+
+ align:start position:0%
+can uh correct the
+energies of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we have an offal Matrix element
+
+ align:start position:0%
+okay so we have an offal Matrix element
+ 
+
+ align:start position:0%
+okay so we have an offal Matrix element
+between the I the I element of the N
+
+ align:start position:0%
+between the I the I element of the N
+ 
+
+ align:start position:0%
+between the I the I element of the N
+block and the M the J element of the in
+
+ align:start position:0%
+block and the M the J element of the in
+ 
+
+ align:start position:0%
+block and the M the J element of the in
+block and so then we come back via the
+
+ align:start position:0%
+block and so then we come back via the
+ 
+
+ align:start position:0%
+block and so then we come back via the
+same from the same place place but to a
+
+ align:start position:0%
+same from the same place place but to a
+ 
+
+ align:start position:0%
+same from the same place place but to a
+different member of the uh the N block
+
+ align:start position:0%
+different member of the uh the N block
+ 
+
+ align:start position:0%
+different member of the uh the N block
+so this is going to be a direction to
+
+ align:start position:0%
+so this is going to be a direction to
+ 
+
+ align:start position:0%
+so this is going to be a direction to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+uh n i n k element of the N
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+block so that's an off diagonal or
+
+ align:start position:0%
+block so that's an off diagonal or
+ 
+
+ align:start position:0%
+block so that's an off diagonal or
+diagonal element of that one block and
+
+ align:start position:0%
+diagonal element of that one block and
+ 
+
+ align:start position:0%
+diagonal element of that one block and
+uh so then we have uh e
+
+ align:start position:0%
+uh so then we have uh e
+ 
+
+ align:start position:0%
+uh so then we have uh e
+n i e n k 2- e
+
+ align:start position:0%
+n i e n k 2- e
+ 
+
+ align:start position:0%
+n i e n k 2- e
+m so this is second order perturbation
+
+ align:start position:0%
+m so this is second order perturbation
+ 
+
+ align:start position:0%
+m so this is second order perturbation
+the it's a matrix element square and
+
+ align:start position:0%
+the it's a matrix element square and
+ 
+
+ align:start position:0%
+the it's a matrix element square and
+this is an energy denominator and we're
+
+ align:start position:0%
+this is an energy denominator and we're
+ 
+
+ align:start position:0%
+this is an energy denominator and we're
+taking an average of these two guys that
+
+ align:start position:0%
+taking an average of these two guys that
+ 
+
+ align:start position:0%
+taking an average of these two guys that
+are near each
+
+ align:start position:0%
+are near each
+ 
+
+ align:start position:0%
+are near each
+other and now this
+
+ align:start position:0%
+other and now this
+ 
+
+ align:start position:0%
+other and now this
+remote and that's the correction that
+
+ align:start position:0%
+remote and that's the correction that
+ 
+
+ align:start position:0%
+remote and that's the correction that
+you automatically calculate
+
+ align:start position:0%
+you automatically calculate
+ 
+
+ align:start position:0%
+you automatically calculate
+to the elements in these various BLS and
+
+ align:start position:0%
+to the elements in these various BLS and
+ 
+
+ align:start position:0%
+to the elements in these various BLS and
+you don't have to diagonalize a matrix
+
+ align:start position:0%
+you don't have to diagonalize a matrix
+ 
+
+ align:start position:0%
+you don't have to diagonalize a matrix
+or anything it's just you look at what
+
+ align:start position:0%
+or anything it's just you look at what
+ 
+
+ align:start position:0%
+or anything it's just you look at what
+the hamiltonian tells you and you
+
+ align:start position:0%
+the hamiltonian tells you and you
+ 
+
+ align:start position:0%
+the hamiltonian tells you and you
+automatically make these Corrections and
+
+ align:start position:0%
+automatically make these Corrections and
+ 
+
+ align:start position:0%
+automatically make these Corrections and
+that leads to all sorts of
+
+ align:start position:0%
+that leads to all sorts of
+ 
+
+ align:start position:0%
+that leads to all sorts of
+horrible ugly uh second order constants
+
+ align:start position:0%
+horrible ugly uh second order constants
+ 
+
+ align:start position:0%
+horrible ugly uh second order constants
+and confusion about what is in the
+
+ align:start position:0%
+and confusion about what is in the
+ 
+
+ align:start position:0%
+and confusion about what is in the
+effect of
+
+ align:start position:0%
+effect of
+ 
+
+ align:start position:0%
+effect of
+hiltonium because we call the things in
+
+ align:start position:0%
+hiltonium because we call the things in
+ 
+
+ align:start position:0%
+hiltonium because we call the things in
+the the effect of heloni by the same
+
+ align:start position:0%
+the the effect of heloni by the same
+ 
+
+ align:start position:0%
+the the effect of heloni by the same
+names that the quantum chemists call
+
+ align:start position:0%
+names that the quantum chemists call
+ 
+
+ align:start position:0%
+names that the quantum chemists call
+those elements in the exact
+
+ align:start position:0%
+those elements in the exact
+ 
+
+ align:start position:0%
+those elements in the exact
+Hamilton and so there is
+
+ align:start position:0%
+Hamilton and so there is
+ 
+
+ align:start position:0%
+Hamilton and so there is
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+contamination dick Zer called it
+
+ align:start position:0%
+contamination dick Zer called it
+ 
+
+ align:start position:0%
+contamination dick Zer called it
+confusion or mixing of the mechanical
+
+ align:start position:0%
+confusion or mixing of the mechanical
+ 
+
+ align:start position:0%
+confusion or mixing of the mechanical
+and electronic significance of
+
+ align:start position:0%
+and electronic significance of
+ 
+
+ align:start position:0%
+and electronic significance of
+parameters and he wrote a very beautiful
+
+ align:start position:0%
+parameters and he wrote a very beautiful
+ 
+
+ align:start position:0%
+parameters and he wrote a very beautiful
+paper in the early' 70s where he talked
+
+ align:start position:0%
+paper in the early' 70s where he talked
+ 
+
+ align:start position:0%
+paper in the early' 70s where he talked
+about how you separate these mechanic
+
+ align:start position:0%
+about how you separate these mechanic
+ 
+
+ align:start position:0%
+about how you separate these mechanic
+and electronic uh meanings of
+
+ align:start position:0%
+and electronic uh meanings of
+ 
+
+ align:start position:0%
+and electronic uh meanings of
+parameters U but mostly spectroscopist
+
+ align:start position:0%
+parameters U but mostly spectroscopist
+ 
+
+ align:start position:0%
+parameters U but mostly spectroscopist
+don't care about that because you need
+
+ align:start position:0%
+don't care about that because you need
+ 
+
+ align:start position:0%
+don't care about that because you need
+to fit your spectrum and what you get
+
+ align:start position:0%
+to fit your spectrum and what you get
+ 
+
+ align:start position:0%
+to fit your spectrum and what you get
+when you fit the spectrum is Not Just
+
+ align:start position:0%
+when you fit the spectrum is Not Just
+ 
+
+ align:start position:0%
+when you fit the spectrum is Not Just
+Energy a formula that fits the energy
+
+ align:start position:0%
+Energy a formula that fits the energy
+ 
+
+ align:start position:0%
+Energy a formula that fits the energy
+levels but you get quasi igen vectors
+
+ align:start position:0%
+levels but you get quasi igen vectors
+ 
+
+ align:start position:0%
+levels but you get quasi igen vectors
+which enable you to calculate whatever
+
+ align:start position:0%
+which enable you to calculate whatever
+ 
+
+ align:start position:0%
+which enable you to calculate whatever
+you want and you do make some small
+
+ align:start position:0%
+you want and you do make some small
+ 
+
+ align:start position:0%
+you want and you do make some small
+errors but you be and you have to worry
+
+ align:start position:0%
+errors but you be and you have to worry
+ 
+
+ align:start position:0%
+errors but you be and you have to worry
+about what was that transformation you
+
+ align:start position:0%
+about what was that transformation you
+ 
+
+ align:start position:0%
+about what was that transformation you
+did but it's completely
+
+ align:start position:0%
+did but it's completely
+ 
+
+ align:start position:0%
+did but it's completely
+mechanical and uh you can undo it in a
+
+ align:start position:0%
+mechanical and uh you can undo it in a
+ 
+
+ align:start position:0%
+mechanical and uh you can undo it in a
+sense to make a connection between the
+
+ align:start position:0%
+sense to make a connection between the
+ 
+
+ align:start position:0%
+sense to make a connection between the
+exact hilon and the spectroscopic one
+
+ align:start position:0%
+exact hilon and the spectroscopic one
+ 
+
+ align:start position:0%
+exact hilon and the spectroscopic one
+you said you had two questions oh the
+
+ align:start position:0%
+you said you had two questions oh the
+ 
+
+ align:start position:0%
+you said you had two questions oh the
+other one was just practically how big
+
+ align:start position:0%
+other one was just practically how big
+ 
+
+ align:start position:0%
+other one was just practically how big
+are those block diagonals like if you
+
+ align:start position:0%
+are those block diagonals like if you
+ 
+
+ align:start position:0%
+are those block diagonals like if you
+had a like an actual problem you were
+
+ align:start position:0%
+had a like an actual problem you were
+ 
+
+ align:start position:0%
+had a like an actual problem you were
+working on it' be really big but again
+
+ align:start position:0%
+working on it' be really big but again
+ 
+
+ align:start position:0%
+working on it' be really big but again
+that's those blocks are more or less
+
+ align:start position:0%
+that's those blocks are more or less
+ 
+
+ align:start position:0%
+that's those blocks are more or less
+self-defining from your zero order model
+
+ align:start position:0%
+self-defining from your zero order model
+ 
+
+ align:start position:0%
+self-defining from your zero order model
+so you try to make it so those block
+
+ align:start position:0%
+so you try to make it so those block
+ 
+
+ align:start position:0%
+so you try to make it so those block
+diagonals are as big as the computer can
+
+ align:start position:0%
+diagonals are as big as the computer can
+ 
+
+ align:start position:0%
+diagonals are as big as the computer can
+handle uh unless it's not necessary
+
+ align:start position:0%
+handle uh unless it's not necessary
+ 
+
+ align:start position:0%
+handle uh unless it's not necessary
+right okay yes okay I know those
+
+ align:start position:0%
+right okay yes okay I know those
+ 
+
+ align:start position:0%
+right okay yes okay I know those
+typically just like each block represent
+
+ align:start position:0%
+typically just like each block represent
+ 
+
+ align:start position:0%
+typically just like each block represent
+practically like a a vibration and So
+
+ align:start position:0%
+practically like a a vibration and So
+ 
+
+ align:start position:0%
+practically like a a vibration and So
+within the block you're diagonalizing
+
+ align:start position:0%
+within the block you're diagonalizing
+ 
+
+ align:start position:0%
+within the block you're diagonalizing
+get the rotational I mean what is it
+
+ align:start position:0%
+get the rotational I mean what is it
+ 
+
+ align:start position:0%
+get the rotational I mean what is it
+practically what what do the blocks
+
+ align:start position:0%
+practically what what do the blocks
+ 
+
+ align:start position:0%
+practically what what do the blocks
+represent well uh have you heard us say
+
+ align:start position:0%
+represent well uh have you heard us say
+ 
+
+ align:start position:0%
+represent well uh have you heard us say
+something like a trip p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh a triplet Pi state is a collection of
+
+ align:start position:0%
+uh a triplet Pi state is a collection of
+ 
+
+ align:start position:0%
+uh a triplet Pi state is a collection of
+six independent electronic states that
+
+ align:start position:0%
+six independent electronic states that
+ 
+
+ align:start position:0%
+six independent electronic states that
+are somehow represented as one
+
+ align:start position:0%
+are somehow represented as one
+ 
+
+ align:start position:0%
+are somehow represented as one
+state okay so it's it's a things six
+
+ align:start position:0%
+state okay so it's it's a things six
+ 
+
+ align:start position:0%
+state okay so it's it's a things six
+things that belong
+
+ align:start position:0%
+things that belong
+ 
+
+ align:start position:0%
+things that belong
+together and there's offal elements
+
+ align:start position:0%
+together and there's offal elements
+ 
+
+ align:start position:0%
+together and there's offal elements
+there's stuff in there or suppose you
+
+ align:start position:0%
+there's stuff in there or suppose you
+ 
+
+ align:start position:0%
+there's stuff in there or suppose you
+have a a triplet Pi State and a triplet
+
+ align:start position:0%
+have a a triplet Pi State and a triplet
+ 
+
+ align:start position:0%
+have a a triplet Pi State and a triplet
+Sigma state that are near each other and
+
+ align:start position:0%
+Sigma state that are near each other and
+ 
+
+ align:start position:0%
+Sigma state that are near each other and
+that are so close block is an electronic
+
+ align:start position:0%
+that are so close block is an electronic
+ 
+
+ align:start position:0%
+that are so close block is an electronic
+State each block might be one electronic
+
+ align:start position:0%
+State each block might be one electronic
+ 
+
+ align:start position:0%
+State each block might be one electronic
+state or two or sometimes uh when
+
+ align:start position:0%
+state or two or sometimes uh when
+ 
+
+ align:start position:0%
+state or two or sometimes uh when
+there's true complex some serious
+
+ align:start position:0%
+there's true complex some serious
+ 
+
+ align:start position:0%
+there's true complex some serious
+uh Interstate coupling uh you you have
+
+ align:start position:0%
+uh Interstate coupling uh you you have
+ 
+
+ align:start position:0%
+uh Interstate coupling uh you you have
+all of the vibrational levels of two
+
+ align:start position:0%
+all of the vibrational levels of two
+ 
+
+ align:start position:0%
+all of the vibrational levels of two
+states in one big
+
+ align:start position:0%
+states in one big
+ 
+
+ align:start position:0%
+states in one big
+block so it's whatever you need whenever
+
+ align:start position:0%
+block so it's whatever you need whenever
+ 
+
+ align:start position:0%
+block so it's whatever you need whenever
+the interaction Matrix element is large
+
+ align:start position:0%
+the interaction Matrix element is large
+ 
+
+ align:start position:0%
+the interaction Matrix element is large
+compared to the energy differences you
+
+ align:start position:0%
+compared to the energy differences you
+ 
+
+ align:start position:0%
+compared to the energy differences you
+have to stick it into something that you
+
+ align:start position:0%
+have to stick it into something that you
+ 
+
+ align:start position:0%
+have to stick it into something that you
+diagonalize rather than something you
+
+ align:start position:0%
+diagonalize rather than something you
+ 
+
+ align:start position:0%
+diagonalize rather than something you
+use a formula from second order
+
+ align:start position:0%
+use a formula from second order
+ 
+
+ align:start position:0%
+use a formula from second order
+perturbation
+
+ align:start position:0%
+perturbation
+ 
+
+ align:start position:0%
+perturbation
+Theory okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um are you
+
+ align:start position:0%
+um are you
+ 
+
+ align:start position:0%
+um are you
+okay uh defend
+
+ align:start position:0%
+okay uh defend
+ 
+
+ align:start position:0%
+okay uh defend
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+yourself okay I mean uh I am not
+
+ align:start position:0%
+yourself okay I mean uh I am not
+ 
+
+ align:start position:0%
+yourself okay I mean uh I am not
+determined to finish 15 pages of notes
+
+ align:start position:0%
+determined to finish 15 pages of notes
+ 
+
+ align:start position:0%
+determined to finish 15 pages of notes
+it makes my life easier if uh I only get
+
+ align:start position:0%
+it makes my life easier if uh I only get
+ 
+
+ align:start position:0%
+it makes my life easier if uh I only get
+through three or four the lecture
+
+ align:start position:0%
+through three or four the lecture
+ 
+
+ align:start position:0%
+through three or four the lecture
+are we all set I mean try to formulate a
+
+ align:start position:0%
+are we all set I mean try to formulate a
+ 
+
+ align:start position:0%
+are we all set I mean try to formulate a
+question uh I know for the people who've
+
+ align:start position:0%
+question uh I know for the people who've
+ 
+
+ align:start position:0%
+question uh I know for the people who've
+only had 561 this is a reach but I'm
+
+ align:start position:0%
+only had 561 this is a reach but I'm
+ 
+
+ align:start position:0%
+only had 561 this is a reach but I'm
+trying to talk about the ideas rather
+
+ align:start position:0%
+trying to talk about the ideas rather
+ 
+
+ align:start position:0%
+trying to talk about the ideas rather
+than the equations that's why I didn't
+
+ align:start position:0%
+than the equations that's why I didn't
+ 
+
+ align:start position:0%
+than the equations that's why I didn't
+want to write this I had to think about
+
+ align:start position:0%
+want to write this I had to think about
+ 
+
+ align:start position:0%
+want to write this I had to think about
+this for a second
+
+ align:start position:0%
+this for a second
+ 
+
+ align:start position:0%
+this for a second
+yes um so from that block diagonal do
+
+ align:start position:0%
+yes um so from that block diagonal do
+ 
+
+ align:start position:0%
+yes um so from that block diagonal do
+you get the basic um the basic elements
+
+ align:start position:0%
+you get the basic um the basic elements
+ 
+
+ align:start position:0%
+you get the basic um the basic elements
+the basic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vibration the this thing will reproduce
+
+ align:start position:0%
+vibration the this thing will reproduce
+ 
+
+ align:start position:0%
+vibration the this thing will reproduce
+what you would observe in the
+
+ align:start position:0%
+what you would observe in the
+ 
+
+ align:start position:0%
+what you would observe in the
+experiment okay so the this effective
+
+ align:start position:0%
+experiment okay so the this effective
+ 
+
+ align:start position:0%
+experiment okay so the this effective
+hamiltonian
+
+ align:start position:0%
+hamiltonian
+ 
+
+ align:start position:0%
+hamiltonian
+and uh make sure that I answer your
+
+ align:start position:0%
+and uh make sure that I answer your
+ 
+
+ align:start position:0%
+and uh make sure that I answer your
+question rather than what I think you're
+
+ align:start position:0%
+question rather than what I think you're
+ 
+
+ align:start position:0%
+question rather than what I think you're
+asking
+
+ align:start position:0%
+asking
+ 
+
+ align:start position:0%
+asking
+this is a
+
+ align:start position:0%
+this is a
+ 
+
+ align:start position:0%
+this is a
+model which is expressed in terms of
+
+ align:start position:0%
+model which is expressed in terms of
+ 
+
+ align:start position:0%
+model which is expressed in terms of
+molecular constants like omeg e spin
+
+ align:start position:0%
+molecular constants like omeg e spin
+ 
+
+ align:start position:0%
+molecular constants like omeg e spin
+orbit constant rotational
+
+ align:start position:0%
+orbit constant rotational
+ 
+
+ align:start position:0%
+orbit constant rotational
+constant uh you know some perturbation
+
+ align:start position:0%
+constant uh you know some perturbation
+ 
+
+ align:start position:0%
+constant uh you know some perturbation
+term it's a bunch of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers that when you adjust them so
+
+ align:start position:0%
+numbers that when you adjust them so
+ 
+
+ align:start position:0%
+numbers that when you adjust them so
+that the igen values of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix match the energy levels you say
+
+ align:start position:0%
+Matrix match the energy levels you say
+ 
+
+ align:start position:0%
+Matrix match the energy levels you say
+I've got the optimum values of these
+
+ align:start position:0%
+I've got the optimum values of these
+ 
+
+ align:start position:0%
+I've got the optimum values of these
+parameters so this is a model expressed
+
+ align:start position:0%
+parameters so this is a model expressed
+ 
+
+ align:start position:0%
+parameters so this is a model expressed
+in terms of a bunch of adjustable
+
+ align:start position:0%
+in terms of a bunch of adjustable
+ 
+
+ align:start position:0%
+in terms of a bunch of adjustable
+constants that we think have physical
+
+ align:start position:0%
+constants that we think have physical
+ 
+
+ align:start position:0%
+constants that we think have physical
+significance and we have a v squar
+
+ align:start position:0%
+significance and we have a v squar
+ 
+
+ align:start position:0%
+significance and we have a v squar
+fitting
+
+ align:start position:0%
+fitting
+ 
+
+ align:start position:0%
+fitting
+procedure which adjusts these parameters
+
+ align:start position:0%
+procedure which adjusts these parameters
+ 
+
+ align:start position:0%
+procedure which adjusts these parameters
+to match the
+
+ align:start position:0%
+to match the
+ 
+
+ align:start position:0%
+to match the
+experiment or if we have an ainitial
+
+ align:start position:0%
+experiment or if we have an ainitial
+ 
+
+ align:start position:0%
+experiment or if we have an ainitial
+calculation if we calculate the wave
+
+ align:start position:0%
+calculation if we calculate the wave
+ 
+
+ align:start position:0%
+calculation if we calculate the wave
+functions and we want to calculate the
+
+ align:start position:0%
+functions and we want to calculate the
+ 
+
+ align:start position:0%
+functions and we want to calculate the
+molecular properties we convert the
+
+ align:start position:0%
+molecular properties we convert the
+ 
+
+ align:start position:0%
+molecular properties we convert the
+quantities in the ab initial calculation
+
+ align:start position:0%
+quantities in the ab initial calculation
+ 
+
+ align:start position:0%
+quantities in the ab initial calculation
+to these molecular constants we put them
+
+ align:start position:0%
+to these molecular constants we put them
+ 
+
+ align:start position:0%
+to these molecular constants we put them
+into a matrix and we calculate the
+
+ align:start position:0%
+into a matrix and we calculate the
+ 
+
+ align:start position:0%
+into a matrix and we calculate the
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+level did that
+
+ align:start position:0%
+level did that
+ 
+
+ align:start position:0%
+level did that
+help
+
+ align:start position:0%
+help
+ 
+
+ align:start position:0%
+help
+everybody
+
+ align:start position:0%
+everybody
+ 
+
+ align:start position:0%
+everybody
+okay right so now we're ready to
+
+ align:start position:0%
+okay right so now we're ready to
+ 
+
+ align:start position:0%
+okay right so now we're ready to
+actually start to talk about the
+
+ align:start position:0%
+actually start to talk about the
+ 
+
+ align:start position:0%
+actually start to talk about the
+critical thing that enables us to do all
+
+ align:start position:0%
+critical thing that enables us to do all
+ 
+
+ align:start position:0%
+critical thing that enables us to do all
+of this and that's the borop armor
+
+ align:start position:0%
+of this and that's the borop armor
+ 
+
+ align:start position:0%
+of this and that's the borop armor
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+and there's a lot of confusion about the
+
+ align:start position:0%
+and there's a lot of confusion about the
+ 
+
+ align:start position:0%
+and there's a lot of confusion about the
+borim approximation because a lot of
+
+ align:start position:0%
+borim approximation because a lot of
+ 
+
+ align:start position:0%
+borim approximation because a lot of
+people worry
+
+ align:start position:0%
+people worry
+ 
+
+ align:start position:0%
+people worry
+about is this approximation valid or
+
+ align:start position:0%
+about is this approximation valid or
+ 
+
+ align:start position:0%
+about is this approximation valid or
+not we don't
+
+ align:start position:0%
+not we don't
+ 
+
+ align:start position:0%
+not we don't
+care it's a self fixing
+
+ align:start position:0%
+care it's a self fixing
+ 
+
+ align:start position:0%
+care it's a self fixing
+approximation the it's a method for
+
+ align:start position:0%
+approximation the it's a method for
+ 
+
+ align:start position:0%
+approximation the it's a method for
+defining a basic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+set a set of
+
+ align:start position:0%
+set a set of
+ 
+
+ align:start position:0%
+set a set of
+functions which is complete and which
+
+ align:start position:0%
+functions which is complete and which
+ 
+
+ align:start position:0%
+functions which is complete and which
+enables us to calculate all of the Bor
+
+ align:start position:0%
+enables us to calculate all of the Bor
+ 
+
+ align:start position:0%
+enables us to calculate all of the Bor
+aimer breakdown phenomena all of the
+
+ align:start position:0%
+aimer breakdown phenomena all of the
+ 
+
+ align:start position:0%
+aimer breakdown phenomena all of the
+stuff that is outside of the borap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximation and in
+
+ align:start position:0%
+approximation and in
+ 
+
+ align:start position:0%
+approximation and in
+fact as you'll see in the next few
+
+ align:start position:0%
+fact as you'll see in the next few
+ 
+
+ align:start position:0%
+fact as you'll see in the next few
+minutes spectroscopist don't even use
+
+ align:start position:0%
+minutes spectroscopist don't even use
+ 
+
+ align:start position:0%
+minutes spectroscopist don't even use
+the born aimer functions they use
+
+ align:start position:0%
+the born aimer functions they use
+ 
+
+ align:start position:0%
+the born aimer functions they use
+something else called the diabetic
+
+ align:start position:0%
+something else called the diabetic
+ 
+
+ align:start position:0%
+something else called the diabetic
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+okay the borop approximation is the
+
+ align:start position:0%
+okay the borop approximation is the
+ 
+
+ align:start position:0%
+okay the borop approximation is the
+basis for separating electronic motions
+
+ align:start position:0%
+basis for separating electronic motions
+ 
+
+ align:start position:0%
+basis for separating electronic motions
+from nuclear motions and the basic
+
+ align:start position:0%
+from nuclear motions and the basic
+ 
+
+ align:start position:0%
+from nuclear motions and the basic
+justification for that which is I
+
+ align:start position:0%
+justification for that which is I
+ 
+
+ align:start position:0%
+justification for that which is I
+believe irrelevant is that electrons
+
+ align:start position:0%
+believe irrelevant is that electrons
+ 
+
+ align:start position:0%
+believe irrelevant is that electrons
+move fast relative to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nucleon so because of this we have the
+
+ align:start position:0%
+nucleon so because of this we have the
+ 
+
+ align:start position:0%
+nucleon so because of this we have the
+idea of electronic States and potential
+
+ align:start position:0%
+idea of electronic States and potential
+ 
+
+ align:start position:0%
+idea of electronic States and potential
+energy curves or potential energy
+
+ align:start position:0%
+energy curves or potential energy
+ 
+
+ align:start position:0%
+energy curves or potential energy
+surfaces what is the born Oppenheimer
+
+ align:start position:0%
+surfaces what is the born Oppenheimer
+ 
+
+ align:start position:0%
+surfaces what is the born Oppenheimer
+approximation
+
+ align:start position:0%
+approximation
+ 
+
+ align:start position:0%
+approximation
+it say clamp the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nuclei so there's no nuclear motion no
+
+ align:start position:0%
+nuclei so there's no nuclear motion no
+ 
+
+ align:start position:0%
+nuclei so there's no nuclear motion no
+nuclear kinetic energy no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation and
+
+ align:start position:0%
+rotation and
+ 
+
+ align:start position:0%
+rotation and
+Sol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electronic okay so that's a perfectly
+
+ align:start position:0%
+electronic okay so that's a perfectly
+ 
+
+ align:start position:0%
+electronic okay so that's a perfectly
+sensible procedure because what it does
+
+ align:start position:0%
+sensible procedure because what it does
+ 
+
+ align:start position:0%
+sensible procedure because what it does
+it says we solve the electronic problem
+
+ align:start position:0%
+it says we solve the electronic problem
+ 
+
+ align:start position:0%
+it says we solve the electronic problem
+and there is no nuclear coupling there's
+
+ align:start position:0%
+and there is no nuclear coupling there's
+ 
+
+ align:start position:0%
+and there is no nuclear coupling there's
+nothing no
+
+ align:start position:0%
+nothing no
+ 
+
+ align:start position:0%
+nothing no
+rotation that causes trouble no
+
+ align:start position:0%
+rotation that causes trouble no
+ 
+
+ align:start position:0%
+rotation that causes trouble no
+vibration that causes
+
+ align:start position:0%
+vibration that causes
+ 
+
+ align:start position:0%
+vibration that causes
+trouble and we get a bunch of so what we
+
+ align:start position:0%
+trouble and we get a bunch of so what we
+ 
+
+ align:start position:0%
+trouble and we get a bunch of so what we
+do is we
+
+ align:start position:0%
+do is we
+ 
+
+ align:start position:0%
+do is we
+calculate for a diatomic molecule I can
+
+ align:start position:0%
+calculate for a diatomic molecule I can
+ 
+
+ align:start position:0%
+calculate for a diatomic molecule I can
+draw this for a polyatomic molecule it's
+
+ align:start position:0%
+draw this for a polyatomic molecule it's
+ 
+
+ align:start position:0%
+draw this for a polyatomic molecule it's
+a little harder but we get a bunch of
+
+ align:start position:0%
+a little harder but we get a bunch of
+ 
+
+ align:start position:0%
+a little harder but we get a bunch of
+energy levels
+
+ align:start position:0%
+energy levels
+ 
+
+ align:start position:0%
+energy levels
+at each inter nuclear distance so we we
+
+ align:start position:0%
+at each inter nuclear distance so we we
+ 
+
+ align:start position:0%
+at each inter nuclear distance so we we
+might have a series of energy levels
+
+ align:start position:0%
+might have a series of energy levels
+ 
+
+ align:start position:0%
+might have a series of energy levels
+that it look sort of like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this or we might have a series of energy
+
+ align:start position:0%
+this or we might have a series of energy
+ 
+
+ align:start position:0%
+this or we might have a series of energy
+levels look like
+
+ align:start position:0%
+levels look like
+ 
+
+ align:start position:0%
+levels look like
+that and so we say okay here is a Val
+
+ align:start position:0%
+that and so we say okay here is a Val
+ 
+
+ align:start position:0%
+that and so we say okay here is a Val
+electronic State here's a repulsive
+
+ align:start position:0%
+electronic State here's a repulsive
+ 
+
+ align:start position:0%
+electronic State here's a repulsive
+electronic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+State and now we're at the beginning
+
+ align:start position:0%
+State and now we're at the beginning
+ 
+
+ align:start position:0%
+State and now we're at the beginning
+for the bound electronic
+
+ align:start position:0%
+for the bound electronic
+ 
+
+ align:start position:0%
+for the bound electronic
+State we can solve for the vibrational
+
+ align:start position:0%
+State we can solve for the vibrational
+ 
+
+ align:start position:0%
+State we can solve for the vibrational
+levels of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem simply by saying okay here's a
+
+ align:start position:0%
+problem simply by saying okay here's a
+ 
+
+ align:start position:0%
+problem simply by saying okay here's a
+potential energy curve let us use
+
+ align:start position:0%
+potential energy curve let us use
+ 
+
+ align:start position:0%
+potential energy curve let us use
+numerov Ki or some numerical integration
+
+ align:start position:0%
+numerov Ki or some numerical integration
+ 
+
+ align:start position:0%
+numerov Ki or some numerical integration
+procedure to calculate the vibrational
+
+ align:start position:0%
+procedure to calculate the vibrational
+ 
+
+ align:start position:0%
+procedure to calculate the vibrational
+WG functions the vibrational I states of
+
+ align:start position:0%
+WG functions the vibrational I states of
+ 
+
+ align:start position:0%
+WG functions the vibrational I states of
+this isolated
+
+ align:start position:0%
+this isolated
+ 
+
+ align:start position:0%
+this isolated
+potential we can find the Continuum wave
+
+ align:start position:0%
+potential we can find the Continuum wave
+ 
+
+ align:start position:0%
+potential we can find the Continuum wave
+functions Again by using the same
+
+ align:start position:0%
+functions Again by using the same
+ 
+
+ align:start position:0%
+functions Again by using the same
+idea so you solve a differential
+
+ align:start position:0%
+idea so you solve a differential
+ 
+
+ align:start position:0%
+idea so you solve a differential
+equation and you get the nuclear wave
+
+ align:start position:0%
+equation and you get the nuclear wave
+ 
+
+ align:start position:0%
+equation and you get the nuclear wave
+functions associated with these
+
+ align:start position:0%
+functions associated with these
+ 
+
+ align:start position:0%
+functions associated with these
+electronic wave
+
+ align:start position:0%
+electronic wave
+ 
+
+ align:start position:0%
+electronic wave
+functions so now we've allowed the
+
+ align:start position:0%
+functions so now we've allowed the
+ 
+
+ align:start position:0%
+functions so now we've allowed the
+nuclei to vibrate we've included the
+
+ align:start position:0%
+nuclei to vibrate we've included the
+ 
+
+ align:start position:0%
+nuclei to vibrate we've included the
+nuclear kinetic energy but
+
+ align:start position:0%
+nuclear kinetic energy but
+ 
+
+ align:start position:0%
+nuclear kinetic energy but
+only when it operates on the
+
+ align:start position:0%
+only when it operates on the
+ 
+
+ align:start position:0%
+only when it operates on the
+nuclei and not on the
+
+ align:start position:0%
+nuclei and not on the
+ 
+
+ align:start position:0%
+nuclei and not on the
+electrons the electonic wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+functions are explicit functions
+
+ align:start position:0%
+functions are explicit functions
+ 
+
+ align:start position:0%
+functions are explicit functions
+of the electron nuclear
+
+ align:start position:0%
+of the electron nuclear
+ 
+
+ align:start position:0%
+of the electron nuclear
+coordinate but implicit functions of the
+
+ align:start position:0%
+coordinate but implicit functions of the
+ 
+
+ align:start position:0%
+coordinate but implicit functions of the
+inter nuclear
+
+ align:start position:0%
+inter nuclear
+ 
+
+ align:start position:0%
+inter nuclear
+coordinate so the nuclear kinetic energy
+
+ align:start position:0%
+coordinate so the nuclear kinetic energy
+ 
+
+ align:start position:0%
+coordinate so the nuclear kinetic energy
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+basically that that
+
+ align:start position:0%
+basically that that
+ 
+
+ align:start position:0%
+basically that that
+operator that has that acts on this it
+
+ align:start position:0%
+operator that has that acts on this it
+ 
+
+ align:start position:0%
+operator that has that acts on this it
+gives and so so we can uh calculate the
+
+ align:start position:0%
+gives and so so we can uh calculate the
+ 
+
+ align:start position:0%
+gives and so so we can uh calculate the
+first derivative of
+
+ align:start position:0%
+first derivative of
+ 
+
+ align:start position:0%
+first derivative of
+s and that's going to give some
+
+ align:start position:0%
+s and that's going to give some
+ 
+
+ align:start position:0%
+s and that's going to give some
+constant time some other wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+function though this might be a small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant but
+
+ align:start position:0%
+constant but
+ 
+
+ align:start position:0%
+constant but
+uh this
+
+ align:start position:0%
+uh this
+ 
+
+ align:start position:0%
+uh this
+operator when operating on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the product of the electronic and
+
+ align:start position:0%
+the product of the electronic and
+ 
+
+ align:start position:0%
+the product of the electronic and
+vibrational wave
+
+ align:start position:0%
+vibrational wave
+ 
+
+ align:start position:0%
+vibrational wave
+function can you have the second der of
+
+ align:start position:0%
+function can you have the second der of
+ 
+
+ align:start position:0%
+function can you have the second der of
+this times the vibrational wave function
+
+ align:start position:0%
+this times the vibrational wave function
+ 
+
+ align:start position:0%
+this times the vibrational wave function
+you have first Der of this times the
+
+ align:start position:0%
+you have first Der of this times the
+ 
+
+ align:start position:0%
+you have first Der of this times the
+first derivative of the vibrational wave
+
+ align:start position:0%
+first derivative of the vibrational wave
+ 
+
+ align:start position:0%
+first derivative of the vibrational wave
+function you can have no derivative of
+
+ align:start position:0%
+function you can have no derivative of
+ 
+
+ align:start position:0%
+function you can have no derivative of
+this and the second der so there's a
+
+ align:start position:0%
+this and the second der so there's a
+ 
+
+ align:start position:0%
+this and the second der so there's a
+whole bunch of stuff that we're not yet
+
+ align:start position:0%
+whole bunch of stuff that we're not yet
+ 
+
+ align:start position:0%
+whole bunch of stuff that we're not yet
+bringing in and that's slipped under to
+
+ align:start position:0%
+bringing in and that's slipped under to
+ 
+
+ align:start position:0%
+bringing in and that's slipped under to
+the right that's the Bor that's one of
+
+ align:start position:0%
+the right that's the Bor that's one of
+ 
+
+ align:start position:0%
+the right that's the Bor that's one of
+the Boro breakdown terms but we can
+
+ align:start position:0%
+the Boro breakdown terms but we can
+ 
+
+ align:start position:0%
+the Boro breakdown terms but we can
+calculate them
+
+ align:start position:0%
+calculate them
+ 
+
+ align:start position:0%
+calculate them
+there's nothing mysterious about it we
+
+ align:start position:0%
+there's nothing mysterious about it we
+ 
+
+ align:start position:0%
+there's nothing mysterious about it we
+have when we solve theordinary
+
+ align:start position:0%
+have when we solve theordinary
+ 
+
+ align:start position:0%
+have when we solve theordinary
+electronic ordinary equation we get
+
+ align:start position:0%
+electronic ordinary equation we get
+ 
+
+ align:start position:0%
+electronic ordinary equation we get
+these curves we can find the W
+
+ align:start position:0%
+these curves we can find the W
+ 
+
+ align:start position:0%
+these curves we can find the W
+vibrational wave functions of these
+
+ align:start position:0%
+vibrational wave functions of these
+ 
+
+ align:start position:0%
+vibrational wave functions of these
+curves we can find the rotational wave
+
+ align:start position:0%
+curves we can find the rotational wave
+ 
+
+ align:start position:0%
+curves we can find the rotational wave
+functions of these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curves so we can let the nuclei start to
+
+ align:start position:0%
+curves so we can let the nuclei start to
+ 
+
+ align:start position:0%
+curves so we can let the nuclei start to
+move and we know what to do but we know
+
+ align:start position:0%
+move and we know what to do but we know
+ 
+
+ align:start position:0%
+move and we know what to do but we know
+when we do that we're cheating there's
+
+ align:start position:0%
+when we do that we're cheating there's
+ 
+
+ align:start position:0%
+when we do that we're cheating there's
+something we have to go back and work
+
+ align:start position:0%
+something we have to go back and work
+ 
+
+ align:start position:0%
+something we have to go back and work
+worry about but we normally don't worry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we expect potential curves to look
+
+ align:start position:0%
+okay we expect potential curves to look
+ 
+
+ align:start position:0%
+okay we expect potential curves to look
+like one or the other of
+
+ align:start position:0%
+like one or the other of
+ 
+
+ align:start position:0%
+like one or the other of
+these but sometimes we get a potential
+
+ align:start position:0%
+these but sometimes we get a potential
+ 
+
+ align:start position:0%
+these but sometimes we get a potential
+curve that looks like this another one
+
+ align:start position:0%
+curve that looks like this another one
+ 
+
+ align:start position:0%
+curve that looks like this another one
+that looks sort of like
+
+ align:start position:0%
+that looks sort of like
+ 
+
+ align:start position:0%
+that looks sort of like
+that or sometimes we get potential
+
+ align:start position:0%
+that or sometimes we get potential
+ 
+
+ align:start position:0%
+that or sometimes we get potential
+curves that have two Minima and then
+
+ align:start position:0%
+curves that have two Minima and then
+ 
+
+ align:start position:0%
+curves that have two Minima and then
+another one sort of like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and this is the truth This Is What
+
+ align:start position:0%
+that and this is the truth This Is What
+ 
+
+ align:start position:0%
+that and this is the truth This Is What
+You Get by clamping the nuclei and
+
+ align:start position:0%
+You Get by clamping the nuclei and
+ 
+
+ align:start position:0%
+You Get by clamping the nuclei and
+solving the electronic shter equation
+
+ align:start position:0%
+solving the electronic shter equation
+ 
+
+ align:start position:0%
+solving the electronic shter equation
+and these things are called avoided
+
+ align:start position:0%
+and these things are called avoided
+ 
+
+ align:start position:0%
+and these things are called avoided
+Crossings because states of the same
+
+ align:start position:0%
+Crossings because states of the same
+ 
+
+ align:start position:0%
+Crossings because states of the same
+symmetry cannot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cross and non Crossing room
+
+ align:start position:0%
+cross and non Crossing room
+ 
+
+ align:start position:0%
+cross and non Crossing room
+this is bad
+
+ align:start position:0%
+this is bad
+ 
+
+ align:start position:0%
+this is bad
+because these curves have shapes that
+
+ align:start position:0%
+because these curves have shapes that
+ 
+
+ align:start position:0%
+because these curves have shapes that
+are offensive to us to our to our sense
+
+ align:start position:0%
+are offensive to us to our to our sense
+ 
+
+ align:start position:0%
+are offensive to us to our to our sense
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+Simplicity and it's also a
+
+ align:start position:0%
+Simplicity and it's also a
+ 
+
+ align:start position:0%
+Simplicity and it's also a
+warning that the vibr the electronic way
+
+ align:start position:0%
+warning that the vibr the electronic way
+ 
+
+ align:start position:0%
+warning that the vibr the electronic way
+function is going to undergo a very
+
+ align:start position:0%
+function is going to undergo a very
+ 
+
+ align:start position:0%
+function is going to undergo a very
+dramatic change of electronic character
+
+ align:start position:0%
+dramatic change of electronic character
+ 
+
+ align:start position:0%
+dramatic change of electronic character
+as you go through this and a slower
+
+ align:start position:0%
+as you go through this and a slower
+ 
+
+ align:start position:0%
+as you go through this and a slower
+change of electronic character as you go
+
+ align:start position:0%
+change of electronic character as you go
+ 
+
+ align:start position:0%
+change of electronic character as you go
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+that well cuz why would the the curve do
+
+ align:start position:0%
+that well cuz why would the the curve do
+ 
+
+ align:start position:0%
+that well cuz why would the the curve do
+that that's you know it can't do
+
+ align:start position:0%
+that that's you know it can't do
+ 
+
+ align:start position:0%
+that that's you know it can't do
+that unless the electronic character
+
+ align:start position:0%
+that unless the electronic character
+ 
+
+ align:start position:0%
+that unless the electronic character
+changes
+
+ align:start position:0%
+changes
+ 
+
+ align:start position:0%
+changes
+so we we say
+
+ align:start position:0%
+so we we say
+ 
+
+ align:start position:0%
+so we we say
+Well there must be another kind of
+
+ align:start position:0%
+Well there must be another kind of
+ 
+
+ align:start position:0%
+Well there must be another kind of
+approximation that does not allow the
+
+ align:start position:0%
+approximation that does not allow the
+ 
+
+ align:start position:0%
+approximation that does not allow the
+electronic wind function to
+
+ align:start position:0%
+electronic wind function to
+ 
+
+ align:start position:0%
+electronic wind function to
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+rapidly with inter through distance
+
+ align:start position:0%
+rapidly with inter through distance
+ 
+
+ align:start position:0%
+rapidly with inter through distance
+so these kinds of curves are the borop
+
+ align:start position:0%
+so these kinds of curves are the borop
+ 
+
+ align:start position:0%
+so these kinds of curves are the borop
+or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+adiabatic curves and what we want are
+
+ align:start position:0%
+adiabatic curves and what we want are
+ 
+
+ align:start position:0%
+adiabatic curves and what we want are
+called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diabetic now adiabetic has the sense of
+
+ align:start position:0%
+diabetic now adiabetic has the sense of
+ 
+
+ align:start position:0%
+diabetic now adiabetic has the sense of
+moving slowly and diabetic is the set of
+
+ align:start position:0%
+moving slowly and diabetic is the set of
+ 
+
+ align:start position:0%
+moving slowly and diabetic is the set of
+moving fast and this gets to the last
+
+ align:start position:0%
+moving fast and this gets to the last
+ 
+
+ align:start position:0%
+moving fast and this gets to the last
+lecture we talk about land down xener
+
+ align:start position:0%
+lecture we talk about land down xener
+ 
+
+ align:start position:0%
+lecture we talk about land down xener
+but the diabetic curves are the curves
+
+ align:start position:0%
+but the diabetic curves are the curves
+ 
+
+ align:start position:0%
+but the diabetic curves are the curves
+that would be obtained by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+allowing
+
+ align:start position:0%
+allowing
+ 
+
+ align:start position:0%
+allowing
+these things to
+
+ align:start position:0%
+these things to
+ 
+
+ align:start position:0%
+these things to
+extrapolate and they're the the curves
+
+ align:start position:0%
+extrapolate and they're the the curves
+ 
+
+ align:start position:0%
+extrapolate and they're the the curves
+that don't change electronic character
+
+ align:start position:0%
+that don't change electronic character
+ 
+
+ align:start position:0%
+that don't change electronic character
+remember if the electronic character
+
+ align:start position:0%
+remember if the electronic character
+ 
+
+ align:start position:0%
+remember if the electronic character
+changes with r rapidly Matrix elements
+
+ align:start position:0%
+changes with r rapidly Matrix elements
+ 
+
+ align:start position:0%
+changes with r rapidly Matrix elements
+of D byd electronic Matrix elements of D
+
+ align:start position:0%
+of D byd electronic Matrix elements of D
+ 
+
+ align:start position:0%
+of D byd electronic Matrix elements of D
+bydr are going to be huge and if they're
+
+ align:start position:0%
+bydr are going to be huge and if they're
+ 
+
+ align:start position:0%
+bydr are going to be huge and if they're
+big then we're going to have they're
+
+ align:start position:0%
+big then we're going to have they're
+ 
+
+ align:start position:0%
+big then we're going to have they're
+going to be large compared to the
+
+ align:start position:0%
+going to be large compared to the
+ 
+
+ align:start position:0%
+going to be large compared to the
+separations between the zero order
+
+ align:start position:0%
+separations between the zero order
+ 
+
+ align:start position:0%
+separations between the zero order
+States and we're going to have to
+
+ align:start position:0%
+States and we're going to have to
+ 
+
+ align:start position:0%
+States and we're going to have to
+diagonalize a big
+
+ align:start position:0%
+diagonalize a big
+ 
+
+ align:start position:0%
+diagonalize a big
+Matrix which means trouble it means you
+
+ align:start position:0%
+Matrix which means trouble it means you
+ 
+
+ align:start position:0%
+Matrix which means trouble it means you
+either have to know the answer before
+
+ align:start position:0%
+either have to know the answer before
+ 
+
+ align:start position:0%
+either have to know the answer before
+you start or you have to do a lot of
+
+ align:start position:0%
+you start or you have to do a lot of
+ 
+
+ align:start position:0%
+you start or you have to do a lot of
+work in order to get from what you can
+
+ align:start position:0%
+work in order to get from what you can
+ 
+
+ align:start position:0%
+work in order to get from what you can
+observe and what you can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculate now you what you need to do is
+
+ align:start position:0%
+calculate now you what you need to do is
+ 
+
+ align:start position:0%
+calculate now you what you need to do is
+clear uh the diabetic
+
+ align:start position:0%
+clear uh the diabetic
+ 
+
+ align:start position:0%
+clear uh the diabetic
+representation when you have this almost
+
+ align:start position:0%
+representation when you have this almost
+ 
+
+ align:start position:0%
+representation when you have this almost
+Singularity or cusp in the way fun in
+
+ align:start position:0%
+Singularity or cusp in the way fun in
+ 
+
+ align:start position:0%
+Singularity or cusp in the way fun in
+the uh potential curve uh when that
+
+ align:start position:0%
+the uh potential curve uh when that
+ 
+
+ align:start position:0%
+the uh potential curve uh when that
+occurs you know this is the wrong
+
+ align:start position:0%
+occurs you know this is the wrong
+ 
+
+ align:start position:0%
+occurs you know this is the wrong
+representation when this occurs it might
+
+ align:start position:0%
+representation when this occurs it might
+ 
+
+ align:start position:0%
+representation when this occurs it might
+be the right
+
+ align:start position:0%
+be the right
+ 
+
+ align:start position:0%
+be the right
+representation right wrong is based on
+
+ align:start position:0%
+representation right wrong is based on
+ 
+
+ align:start position:0%
+representation right wrong is based on
+convenience not based on something that
+
+ align:start position:0%
+convenience not based on something that
+ 
+
+ align:start position:0%
+convenience not based on something that
+gives you a good or bad fit to the
+
+ align:start position:0%
+gives you a good or bad fit to the
+ 
+
+ align:start position:0%
+gives you a good or bad fit to the
+energy levels either representation all
+
+ align:start position:0%
+energy levels either representation all
+ 
+
+ align:start position:0%
+energy levels either representation all
+representations which are
+
+ align:start position:0%
+representations which are
+ 
+
+ align:start position:0%
+representations which are
+complete give you the same quality of
+
+ align:start position:0%
+complete give you the same quality of
+ 
+
+ align:start position:0%
+complete give you the same quality of
+representation of fitting The
+
+ align:start position:0%
+representation of fitting The
+ 
+
+ align:start position:0%
+representation of fitting The
+observed uh energy levels and
+
+ align:start position:0%
+observed uh energy levels and
+ 
+
+ align:start position:0%
+observed uh energy levels and
+calculating all of the dynamical
+
+ align:start position:0%
+calculating all of the dynamical
+ 
+
+ align:start position:0%
+calculating all of the dynamical
+quantities it's just what they're called
+
+ align:start position:0%
+quantities it's just what they're called
+ 
+
+ align:start position:0%
+quantities it's just what they're called
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+different and if you chose
+
+ align:start position:0%
+different and if you chose
+ 
+
+ align:start position:0%
+different and if you chose
+a an physically appropriate model your
+
+ align:start position:0%
+a an physically appropriate model your
+ 
+
+ align:start position:0%
+a an physically appropriate model your
+labors will be less and
+
+ align:start position:0%
+labors will be less and
+ 
+
+ align:start position:0%
+labors will be less and
+the uh the resemblance between the zero
+
+ align:start position:0%
+the uh the resemblance between the zero
+ 
+
+ align:start position:0%
+the uh the resemblance between the zero
+order
+
+ align:start position:0%
+order
+ 
+
+ align:start position:0%
+order
+model and what you could could observe
+
+ align:start position:0%
+model and what you could could observe
+ 
+
+ align:start position:0%
+model and what you could could observe
+or calculate will be much
+
+ align:start position:0%
+or calculate will be much
+ 
+
+ align:start position:0%
+or calculate will be much
+greater than if you chose an
+
+ align:start position:0%
+greater than if you chose an
+ 
+
+ align:start position:0%
+greater than if you chose an
+inappropriate model and this is good for
+
+ align:start position:0%
+inappropriate model and this is good for
+ 
+
+ align:start position:0%
+inappropriate model and this is good for
+experimentalists because your model
+
+ align:start position:0%
+experimentalists because your model
+ 
+
+ align:start position:0%
+experimentalists because your model
+before you include a lot of off diagonal
+
+ align:start position:0%
+before you include a lot of off diagonal
+ 
+
+ align:start position:0%
+before you include a lot of off diagonal
+elements needs to resemble what you can
+
+ align:start position:0%
+elements needs to resemble what you can
+ 
+
+ align:start position:0%
+elements needs to resemble what you can
+observe otherwise you're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lost
+
+ align:start position:0%
+lost
+ 
+
+ align:start position:0%
+lost
+okay the distance of closest
+
+ align:start position:0%
+okay the distance of closest
+ 
+
+ align:start position:0%
+okay the distance of closest
+approach between these potential curves
+
+ align:start position:0%
+approach between these potential curves
+ 
+
+ align:start position:0%
+approach between these potential curves
+is twice the coupling Matrix
+
+ align:start position:0%
+is twice the coupling Matrix
+ 
+
+ align:start position:0%
+is twice the coupling Matrix
+element twice the electronic coupling
+
+ align:start position:0%
+element twice the electronic coupling
+ 
+
+ align:start position:0%
+element twice the electronic coupling
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+element we know from perturbation theory
+
+ align:start position:0%
+element we know from perturbation theory
+ 
+
+ align:start position:0%
+element we know from perturbation theory
+that as you try to make two levels get
+
+ align:start position:0%
+that as you try to make two levels get
+ 
+
+ align:start position:0%
+that as you try to make two levels get
+degenerate they can never get closer
+
+ align:start position:0%
+degenerate they can never get closer
+ 
+
+ align:start position:0%
+degenerate they can never get closer
+together than twice the Matrix element
+
+ align:start position:0%
+together than twice the Matrix element
+ 
+
+ align:start position:0%
+together than twice the Matrix element
+coupling the zero order
+
+ align:start position:0%
+coupling the zero order
+ 
+
+ align:start position:0%
+coupling the zero order
+levels those of you who don't know that
+
+ align:start position:0%
+levels those of you who don't know that
+ 
+
+ align:start position:0%
+levels those of you who don't know that
+will know
+
+ align:start position:0%
+will know
+ 
+
+ align:start position:0%
+will know
+it but so these are the energies is a
+
+ align:start position:0%
+it but so these are the energies is a
+ 
+
+ align:start position:0%
+it but so these are the energies is a
+function of r and so these curves tell
+
+ align:start position:0%
+function of r and so these curves tell
+ 
+
+ align:start position:0%
+function of r and so these curves tell
+you can't get any closer than this so
+
+ align:start position:0%
+you can't get any closer than this so
+ 
+
+ align:start position:0%
+you can't get any closer than this so
+that means that there is
+
+ align:start position:0%
+that means that there is
+ 
+
+ align:start position:0%
+that means that there is
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+electronic coupling term which is half
+
+ align:start position:0%
+electronic coupling term which is half
+ 
+
+ align:start position:0%
+electronic coupling term which is half
+that distance of closest
+
+ align:start position:0%
+that distance of closest
+ 
+
+ align:start position:0%
+that distance of closest
+approach now in the adiabatic picture we
+
+ align:start position:0%
+approach now in the adiabatic picture we
+ 
+
+ align:start position:0%
+approach now in the adiabatic picture we
+diagonalize the electronic hamiltonian
+
+ align:start position:0%
+diagonalize the electronic hamiltonian
+ 
+
+ align:start position:0%
+diagonalize the electronic hamiltonian
+and we ignore the nuclear kinetic
+
+ align:start position:0%
+and we ignore the nuclear kinetic
+ 
+
+ align:start position:0%
+and we ignore the nuclear kinetic
+energy the other approach is we're going
+
+ align:start position:0%
+energy the other approach is we're going
+ 
+
+ align:start position:0%
+energy the other approach is we're going
+to to diagonalize the nuclear kinetic
+
+ align:start position:0%
+to to diagonalize the nuclear kinetic
+ 
+
+ align:start position:0%
+to to diagonalize the nuclear kinetic
+energy simply by making the electronic
+
+ align:start position:0%
+energy simply by making the electronic
+ 
+
+ align:start position:0%
+energy simply by making the electronic
+wave functions not tend strongly on
+
+ align:start position:0%
+wave functions not tend strongly on
+ 
+
+ align:start position:0%
+wave functions not tend strongly on
+R and we're not going to diagonalize the
+
+ align:start position:0%
+R and we're not going to diagonalize the
+ 
+
+ align:start position:0%
+R and we're not going to diagonalize the
+electronic
+
+ align:start position:0%
+electronic
+ 
+
+ align:start position:0%
+electronic
+hemon this is a simple idea but it's
+
+ align:start position:0%
+hemon this is a simple idea but it's
+ 
+
+ align:start position:0%
+hemon this is a simple idea but it's
+computationally IL
+
+ align:start position:0%
+computationally IL
+ 
+
+ align:start position:0%
+computationally IL
+defined
+
+ align:start position:0%
+defined
+ 
+
+ align:start position:0%
+defined
+because we
+
+ align:start position:0%
+because we
+ 
+
+ align:start position:0%
+because we
+know how to collect the nuclei we know
+
+ align:start position:0%
+know how to collect the nuclei we know
+ 
+
+ align:start position:0%
+know how to collect the nuclei we know
+how to say the nuclear kinetic energy
+
+ align:start position:0%
+how to say the nuclear kinetic energy
+ 
+
+ align:start position:0%
+how to say the nuclear kinetic energy
+terms and the
+
+ align:start position:0%
+terms and the
+ 
+
+ align:start position:0%
+terms and the
+rotation are going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ignored the inter electronic repulsion
+
+ align:start position:0%
+ignored the inter electronic repulsion
+ 
+
+ align:start position:0%
+ignored the inter electronic repulsion
+that's 1 / r i j or e^2 r i j Su I not
+
+ align:start position:0%
+that's 1 / r i j or e^2 r i j Su I not
+ 
+
+ align:start position:0%
+that's 1 / r i j or e^2 r i j Su I not
+equal it's a lot of
+
+ align:start position:0%
+equal it's a lot of
+ 
+
+ align:start position:0%
+equal it's a lot of
+terms and you don't know which one to
+
+ align:start position:0%
+terms and you don't know which one to
+ 
+
+ align:start position:0%
+terms and you don't know which one to
+make to to ignore there's no way
+
+ align:start position:0%
+make to to ignore there's no way
+ 
+
+ align:start position:0%
+make to to ignore there's no way
+computationally from scratch
+
+ align:start position:0%
+computationally from scratch
+ 
+
+ align:start position:0%
+computationally from scratch
+to suppress a term in electronic
+
+ align:start position:0%
+to suppress a term in electronic
+ 
+
+ align:start position:0%
+to suppress a term in electronic
+hemil so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hamilton
+
+ align:start position:0%
+Hamilton
+ 
+
+ align:start position:0%
+Hamilton
+electronic plus
+
+ align:start position:0%
+electronic plus
+ 
+
+ align:start position:0%
+electronic plus
+rotation plus spin
+
+ align:start position:0%
+rotation plus spin
+ 
+
+ align:start position:0%
+rotation plus spin
+orbit these are the important terms in
+
+ align:start position:0%
+orbit these are the important terms in
+ 
+
+ align:start position:0%
+orbit these are the important terms in
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+hamiltonian and these are the two terms
+
+ align:start position:0%
+hamiltonian and these are the two terms
+ 
+
+ align:start position:0%
+hamiltonian and these are the two terms
+that that we would want
+
+ align:start position:0%
+that that we would want
+ 
+
+ align:start position:0%
+that that we would want
+to play fast and loose with if we wanted
+
+ align:start position:0%
+to play fast and loose with if we wanted
+ 
+
+ align:start position:0%
+to play fast and loose with if we wanted
+to define a diabetic basis set rotation
+
+ align:start position:0%
+to define a diabetic basis set rotation
+ 
+
+ align:start position:0%
+to define a diabetic basis set rotation
+well that's just
+
+ align:start position:0%
+well that's just
+ 
+
+ align:start position:0%
+well that's just
+ignored uh I'm sorry uh so we can turn
+
+ align:start position:0%
+ignored uh I'm sorry uh so we can turn
+ 
+
+ align:start position:0%
+ignored uh I'm sorry uh so we can turn
+off the spin
+
+ align:start position:0%
+off the spin
+ 
+
+ align:start position:0%
+off the spin
+orbit but we can't turn off specific
+
+ align:start position:0%
+orbit but we can't turn off specific
+ 
+
+ align:start position:0%
+orbit but we can't turn off specific
+terms inter electronic repulsion
+
+ align:start position:0%
+terms inter electronic repulsion
+ 
+
+ align:start position:0%
+terms inter electronic repulsion
+hamiltoni so we have two
+
+ align:start position:0%
+hamiltoni so we have two
+ 
+
+ align:start position:0%
+hamiltoni so we have two
+different adiabatic pictures
+
+ align:start position:0%
+different adiabatic pictures
+ 
+
+ align:start position:0%
+different adiabatic pictures
+adiabatic
+
+ align:start position:0%
+adiabatic
+ 
+
+ align:start position:0%
+adiabatic
+relativistic that's the full smear
+
+ align:start position:0%
+relativistic that's the full smear
+ 
+
+ align:start position:0%
+relativistic that's the full smear
+that's that's the borof and haror every
+
+ align:start position:0%
+that's that's the borof and haror every
+ 
+
+ align:start position:0%
+that's that's the borof and haror every
+uh everything is clamped every we're
+
+ align:start position:0%
+uh everything is clamped every we're
+ 
+
+ align:start position:0%
+uh everything is clamped every we're
+solving the electronic plus spin orbits
+
+ align:start position:0%
+solving the electronic plus spin orbits
+ 
+
+ align:start position:0%
+solving the electronic plus spin orbits
+and then we have Rel adiabatic non
+
+ align:start position:0%
+and then we have Rel adiabatic non
+ 
+
+ align:start position:0%
+and then we have Rel adiabatic non
+relativistic where we turn this thing
+
+ align:start position:0%
+relativistic where we turn this thing
+ 
+
+ align:start position:0%
+relativistic where we turn this thing
+off and so we can when spit orbit is
+
+ align:start position:0%
+off and so we can when spit orbit is
+ 
+
+ align:start position:0%
+off and so we can when spit orbit is
+important we can diabeti by turning off
+
+ align:start position:0%
+important we can diabeti by turning off
+ 
+
+ align:start position:0%
+important we can diabeti by turning off
+this ter but there's no way
+
+ align:start position:0%
+this ter but there's no way
+ 
+
+ align:start position:0%
+this ter but there's no way
+computationally we can
+
+ align:start position:0%
+computationally we can
+ 
+
+ align:start position:0%
+computationally we can
+diabeti by turning off something in here
+
+ align:start position:0%
+diabeti by turning off something in here
+ 
+
+ align:start position:0%
+diabeti by turning off something in here
+instead we have to use a uh a simple
+
+ align:start position:0%
+instead we have to use a uh a simple
+ 
+
+ align:start position:0%
+instead we have to use a uh a simple
+model
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let me try to describe what we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do so we start with the adiabatic
+
+ align:start position:0%
+do so we start with the adiabatic
+ 
+
+ align:start position:0%
+do so we start with the adiabatic
+potential curves
+
+ align:start position:0%
+potential curves
+ 
+
+ align:start position:0%
+potential curves
+so they might look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay and so immediately from these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curves we know to H electronic
+
+ align:start position:0%
+curves we know to H electronic
+ 
+
+ align:start position:0%
+curves we know to H electronic
+one2 the coupling Matrix
+
+ align:start position:0%
+one2 the coupling Matrix
+ 
+
+ align:start position:0%
+one2 the coupling Matrix
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+on then we have to make two
+
+ align:start position:0%
+on then we have to make two
+ 
+
+ align:start position:0%
+on then we have to make two
+approximations one is that there are
+
+ align:start position:0%
+approximations one is that there are
+ 
+
+ align:start position:0%
+approximations one is that there are
+only two curves that are interactive the
+
+ align:start position:0%
+only two curves that are interactive the
+ 
+
+ align:start position:0%
+only two curves that are interactive the
+effects of other curves can be
+
+ align:start position:0%
+effects of other curves can be
+ 
+
+ align:start position:0%
+effects of other curves can be
+ignored this is usually a good
+
+ align:start position:0%
+ignored this is usually a good
+ 
+
+ align:start position:0%
+ignored this is usually a good
+approximation but it's not always a good
+
+ align:start position:0%
+approximation but it's not always a good
+ 
+
+ align:start position:0%
+approximation but it's not always a good
+approximation so two states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+only the other approximation is that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diabetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curves are are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linear in the crossing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+region in other words we have a
+
+ align:start position:0%
+region in other words we have a
+ 
+
+ align:start position:0%
+region in other words we have a
+diabetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve and another diic curve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so what we want to determine is
+
+ align:start position:0%
+okay and so what we want to determine is
+ 
+
+ align:start position:0%
+okay and so what we want to determine is
+the energy of the crossing the inter
+
+ align:start position:0%
+the energy of the crossing the inter
+ 
+
+ align:start position:0%
+the energy of the crossing the inter
+nuclear distance of the crossing and the
+
+ align:start position:0%
+nuclear distance of the crossing and the
+ 
+
+ align:start position:0%
+nuclear distance of the crossing and the
+coupling Matrix
+
+ align:start position:0%
+coupling Matrix
+ 
+
+ align:start position:0%
+coupling Matrix
+element
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cross okay and
+
+ align:start position:0%
+cross okay and
+ 
+
+ align:start position:0%
+cross okay and
+and there's a couple of pages what I
+
+ align:start position:0%
+and there's a couple of pages what I
+ 
+
+ align:start position:0%
+and there's a couple of pages what I
+call non-lecture cuz I don't want to go
+
+ align:start position:0%
+call non-lecture cuz I don't want to go
+ 
+
+ align:start position:0%
+call non-lecture cuz I don't want to go
+through the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formulas at the Crossing these two are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal and so you get an equation for the
+
+ align:start position:0%
+equal and so you get an equation for the
+ 
+
+ align:start position:0%
+equal and so you get an equation for the
+value of the crosssection radi from
+
+ align:start position:0%
+value of the crosssection radi from
+ 
+
+ align:start position:0%
+value of the crosssection radi from
+these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+con you also have the 80 value
+
+ align:start position:0%
+con you also have the 80 value
+ 
+
+ align:start position:0%
+con you also have the 80 value
+curves which are what you're given of an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+issue you don't have to make any
+
+ align:start position:0%
+issue you don't have to make any
+ 
+
+ align:start position:0%
+issue you don't have to make any
+assumptions about the form of these but
+
+ align:start position:0%
+assumptions about the form of these but
+ 
+
+ align:start position:0%
+assumptions about the form of these but
+at the Crossing radius the difference
+
+ align:start position:0%
+at the Crossing radius the difference
+ 
+
+ align:start position:0%
+at the Crossing radius the difference
+between these two is a minimum so the
+
+ align:start position:0%
+between these two is a minimum so the
+ 
+
+ align:start position:0%
+between these two is a minimum so the
+derivative of the difference is
+
+ align:start position:0%
+derivative of the difference is
+ 
+
+ align:start position:0%
+derivative of the difference is
+zero and that gives
+
+ align:start position:0%
+zero and that gives
+ 
+
+ align:start position:0%
+zero and that gives
+you uh uh the
+
+ align:start position:0%
+you uh uh the
+ 
+
+ align:start position:0%
+you uh uh the
+the the value the R value at which that
+
+ align:start position:0%
+the the value the R value at which that
+ 
+
+ align:start position:0%
+the the value the R value at which that
+difference is
+
+ align:start position:0%
+difference is
+ 
+
+ align:start position:0%
+difference is
+smallest that's the crossing
+
+ align:start position:0%
+smallest that's the crossing
+ 
+
+ align:start position:0%
+smallest that's the crossing
+radius the energy difference at this r
+
+ align:start position:0%
+radius the energy difference at this r
+ 
+
+ align:start position:0%
+radius the energy difference at this r
+value is uh
+
+ align:start position:0%
+value is uh
+ 
+
+ align:start position:0%
+value is uh
+um is twice the Matrix
+
+ align:start position:0%
+um is twice the Matrix
+ 
+
+ align:start position:0%
+um is twice the Matrix
+element the average energy of the
+
+ align:start position:0%
+element the average energy of the
+ 
+
+ align:start position:0%
+element the average energy of the
+crossing value is the energy of the
+
+ align:start position:0%
+crossing value is the energy of the
+ 
+
+ align:start position:0%
+crossing value is the energy of the
+Crossing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so basically you have everything you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+so given these
+
+ align:start position:0%
+so given these
+ 
+
+ align:start position:0%
+so given these
+things you can calculate these critical
+
+ align:start position:0%
+things you can calculate these critical
+ 
+
+ align:start position:0%
+things you can calculate these critical
+quantities and now we have a 2x2 matrix
+
+ align:start position:0%
+quantities and now we have a 2x2 matrix
+ 
+
+ align:start position:0%
+quantities and now we have a 2x2 matrix
+which describes everything that happens
+
+ align:start position:0%
+which describes everything that happens
+ 
+
+ align:start position:0%
+which describes everything that happens
+involving these two states yes what
+
+ align:start position:0%
+involving these two states yes what
+ 
+
+ align:start position:0%
+involving these two states yes what
+exactly is the crossing
+
+ align:start position:0%
+exactly is the crossing
+ 
+
+ align:start position:0%
+exactly is the crossing
+radius it's it's the internuclear I'm
+
+ align:start position:0%
+radius it's it's the internuclear I'm
+ 
+
+ align:start position:0%
+radius it's it's the internuclear I'm
+sorry I should have said the crossing
+
+ align:start position:0%
+sorry I should have said the crossing
+ 
+
+ align:start position:0%
+sorry I should have said the crossing
+internuclear distance okay okay so at
+
+ align:start position:0%
+internuclear distance okay okay so at
+ 
+
+ align:start position:0%
+internuclear distance okay okay so at
+some internuclear distance the diabetic
+
+ align:start position:0%
+some internuclear distance the diabetic
+ 
+
+ align:start position:0%
+some internuclear distance the diabetic
+curves cross and the adiabatic curves
+
+ align:start position:0%
+curves cross and the adiabatic curves
+ 
+
+ align:start position:0%
+curves cross and the adiabatic curves
+have reached their minimum vertical
+
+ align:start position:0%
+have reached their minimum vertical
+ 
+
+ align:start position:0%
+have reached their minimum vertical
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+separation and that's what we want to
+
+ align:start position:0%
+separation and that's what we want to
+ 
+
+ align:start position:0%
+separation and that's what we want to
+determine so we want to know RC EC
+
+ align:start position:0%
+determine so we want to know RC EC
+ 
+
+ align:start position:0%
+determine so we want to know RC EC
+and and this and they are all obtainable
+
+ align:start position:0%
+and and this and they are all obtainable
+ 
+
+ align:start position:0%
+and and this and they are all obtainable
+by exploring the ab initial curves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so then you
+
+ align:start position:0%
+so then you
+ 
+
+ align:start position:0%
+so then you
+splice uh you say okay the diabetic
+
+ align:start position:0%
+splice uh you say okay the diabetic
+ 
+
+ align:start position:0%
+splice uh you say okay the diabetic
+curves just go through that
+
+ align:start position:0%
+curves just go through that
+ 
+
+ align:start position:0%
+curves just go through that
+Crossing they're linear at the Crossing
+
+ align:start position:0%
+Crossing they're linear at the Crossing
+ 
+
+ align:start position:0%
+Crossing they're linear at the Crossing
+and then they sort of join the uh the ad
+
+ align:start position:0%
+and then they sort of join the uh the ad
+ 
+
+ align:start position:0%
+and then they sort of join the uh the ad
+vatic curves or we can say all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so we have a 2X two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+describes the two level
+
+ align:start position:0%
+describes the two level
+ 
+
+ align:start position:0%
+describes the two level
+interaction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay whenever you have a 2X two
+
+ align:start position:0%
+so okay whenever you have a 2X two
+ 
+
+ align:start position:0%
+so okay whenever you have a 2X two
+problem it's always useful to separate
+
+ align:start position:0%
+problem it's always useful to separate
+ 
+
+ align:start position:0%
+problem it's always useful to separate
+out so suppose you have a 2x2 problem E1
+
+ align:start position:0%
+out so suppose you have a 2x2 problem E1
+ 
+
+ align:start position:0%
+out so suppose you have a 2x2 problem E1
+b b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+E2 it's always useful to separate out
+
+ align:start position:0%
+E2 it's always useful to separate out
+ 
+
+ align:start position:0%
+E2 it's always useful to separate out
+the average energy so we have E1 + E2
+
+ align:start position:0%
+the average energy so we have E1 + E2
+ 
+
+ align:start position:0%
+the average energy so we have E1 + E2
+over 2 E1 +
+
+ align:start position:0%
+over 2 E1 +
+ 
+
+ align:start position:0%
+over 2 E1 +
+E2 over 2 0
+
+ align:start position:0%
+E2 over 2 0
+ 
+
+ align:start position:0%
+E2 over 2 0
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+plus E1 - E2
+
+ align:start position:0%
+plus E1 - E2
+ 
+
+ align:start position:0%
+plus E1 - E2
+for 2 v
+
+ align:start position:0%
+for 2 v
+ 
+
+ align:start position:0%
+for 2 v
+v minus
+
+ align:start position:0%
+v minus
+ 
+
+ align:start position:0%
+v minus
+e1- E2
+
+ align:start position:0%
+e1- E2
+ 
+
+ align:start position:0%
+e1- E2
+two okay so whenever you're facing a 2X
+
+ align:start position:0%
+two okay so whenever you're facing a 2X
+ 
+
+ align:start position:0%
+two okay so whenever you're facing a 2X
+two problem it's useful to write it this
+
+ align:start position:0%
+two problem it's useful to write it this
+ 
+
+ align:start position:0%
+two problem it's useful to write it this
+way because this you know the
+
+ align:start position:0%
+way because this you know the
+ 
+
+ align:start position:0%
+way because this you know the
+solutions they're just V ^2 plus or
+
+ align:start position:0%
+solutions they're just V ^2 plus or
+ 
+
+ align:start position:0%
+solutions they're just V ^2 plus or
+minus uh plus uh e1- e
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 so we have whenever we have a 2x2
+
+ align:start position:0%
+2 so we have whenever we have a 2x2
+ 
+
+ align:start position:0%
+2 so we have whenever we have a 2x2
+problem we take out the average energy
+
+ align:start position:0%
+problem we take out the average energy
+ 
+
+ align:start position:0%
+problem we take out the average energy
+and we get the symmetric 2x2 matrix we
+
+ align:start position:0%
+and we get the symmetric 2x2 matrix we
+ 
+
+ align:start position:0%
+and we get the symmetric 2x2 matrix we
+know the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solutions so what I wrote on page six of
+
+ align:start position:0%
+solutions so what I wrote on page six of
+ 
+
+ align:start position:0%
+solutions so what I wrote on page six of
+the notes is the symmetrized the average
+
+ align:start position:0%
+the notes is the symmetrized the average
+ 
+
+ align:start position:0%
+the notes is the symmetrized the average
+energy in the diabetic representation
+
+ align:start position:0%
+energy in the diabetic representation
+ 
+
+ align:start position:0%
+energy in the diabetic representation
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the what
+
+ align:start position:0%
+the what
+ 
+
+ align:start position:0%
+the what
+remains and so we
+
+ align:start position:0%
+remains and so we
+ 
+
+ align:start position:0%
+remains and so we
+have uh B1 minus B2
+
+ align:start position:0%
+have uh B1 minus B2
+ 
+
+ align:start position:0%
+have uh B1 minus B2
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+iine the diab curves this
+
+ align:start position:0%
+iine the diab curves this
+ 
+
+ align:start position:0%
+iine the diab curves this
+way two r - I
+
+ align:start position:0%
+way two r - I
+ 
+
+ align:start position:0%
+way two r - I
+C-
+
+ align:start position:0%
+C-
+ 
+
+ align:start position:0%
+C-
+D12 2- r
+
+ align:start position:0%
+D12 2- r
+ 
+
+ align:start position:0%
+D12 2- r
+c d v this is the
+
+ align:start position:0%
+c d v this is the
+ 
+
+ align:start position:0%
+c d v this is the
+Matrix that we need to
+
+ align:start position:0%
+Matrix that we need to
+ 
+
+ align:start position:0%
+Matrix that we need to
+solve it's a 2x2 matrix it's
+
+ align:start position:0%
+solve it's a 2x2 matrix it's
+ 
+
+ align:start position:0%
+solve it's a 2x2 matrix it's
+diagonalized by unitary transformation
+
+ align:start position:0%
+diagonalized by unitary transformation
+ 
+
+ align:start position:0%
+diagonalized by unitary transformation
+the unitary transformation has the form
+
+ align:start position:0%
+the unitary transformation has the form
+ 
+
+ align:start position:0%
+the unitary transformation has the form
+cosine thet
+
+ align:start position:0%
+cosine thet
+ 
+
+ align:start position:0%
+cosine thet
+sinus
+
+ align:start position:0%
+sinus
+ 
+
+ align:start position:0%
+sinus
+sin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cosine but this transformation is a
+
+ align:start position:0%
+cosine but this transformation is a
+ 
+
+ align:start position:0%
+cosine but this transformation is a
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+of R inter Nu
+
+ align:start position:0%
+of R inter Nu
+ 
+
+ align:start position:0%
+of R inter Nu
+distance and so we have the
+
+ align:start position:0%
+distance and so we have the
+ 
+
+ align:start position:0%
+distance and so we have the
+transformation that diagonalize this
+
+ align:start position:0%
+transformation that diagonalize this
+ 
+
+ align:start position:0%
+transformation that diagonalize this
+Matrix which is an explicit function of
+
+ align:start position:0%
+Matrix which is an explicit function of
+ 
+
+ align:start position:0%
+Matrix which is an explicit function of
+r now this Theta is complicated
+
+ align:start position:0%
+r now this Theta is complicated
+ 
+
+ align:start position:0%
+r now this Theta is complicated
+combination of all of the control
+
+ align:start position:0%
+combination of all of the control
+ 
+
+ align:start position:0%
+combination of all of the control
+parameters so there's some algebra but
+
+ align:start position:0%
+parameters so there's some algebra but
+ 
+
+ align:start position:0%
+parameters so there's some algebra but
+basically you know what this is and so
+
+ align:start position:0%
+basically you know what this is and so
+ 
+
+ align:start position:0%
+basically you know what this is and so
+one can write the I functions
+
+ align:start position:0%
+one can write the I functions
+ 
+
+ align:start position:0%
+one can write the I functions
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+2x2 matrix what are they those are the
+
+ align:start position:0%
+2x2 matrix what are they those are the
+ 
+
+ align:start position:0%
+2x2 matrix what are they those are the
+anabatic
+
+ align:start position:0%
+anabatic
+ 
+
+ align:start position:0%
+anabatic
+states we can write the igen functions
+
+ align:start position:0%
+states we can write the igen functions
+ 
+
+ align:start position:0%
+states we can write the igen functions
+as an explicit linear combination of the
+
+ align:start position:0%
+as an explicit linear combination of the
+ 
+
+ align:start position:0%
+as an explicit linear combination of the
+diabetic
+
+ align:start position:0%
+diabetic
+ 
+
+ align:start position:0%
+diabetic
+States we can calculate Matrix elements
+
+ align:start position:0%
+States we can calculate Matrix elements
+ 
+
+ align:start position:0%
+States we can calculate Matrix elements
+of D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bydr because now we have an explicit
+
+ align:start position:0%
+bydr because now we have an explicit
+ 
+
+ align:start position:0%
+bydr because now we have an explicit
+function of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r and so all of the necessary Matrix
+
+ align:start position:0%
+r and so all of the necessary Matrix
+ 
+
+ align:start position:0%
+r and so all of the necessary Matrix
+elements are
+
+ align:start position:0%
+elements are
+ 
+
+ align:start position:0%
+elements are
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+soluble and so the
+
+ align:start position:0%
+soluble and so the
+ 
+
+ align:start position:0%
+soluble and so the
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+transformation which is a model between
+
+ align:start position:0%
+transformation which is a model between
+ 
+
+ align:start position:0%
+transformation which is a model between
+Tic and diabetic enables us
+
+ align:start position:0%
+Tic and diabetic enables us
+ 
+
+ align:start position:0%
+Tic and diabetic enables us
+conveniently
+
+ align:start position:0%
+conveniently
+ 
+
+ align:start position:0%
+conveniently
+to calculate all of the off diagonal
+
+ align:start position:0%
+to calculate all of the off diagonal
+ 
+
+ align:start position:0%
+to calculate all of the off diagonal
+matrix elements in terms of parameters
+
+ align:start position:0%
+matrix elements in terms of parameters
+ 
+
+ align:start position:0%
+matrix elements in terms of parameters
+that describe either the diabetic or
+
+ align:start position:0%
+that describe either the diabetic or
+ 
+
+ align:start position:0%
+that describe either the diabetic or
+adiabetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential things that we can get from
+
+ align:start position:0%
+potential things that we can get from
+ 
+
+ align:start position:0%
+potential things that we can get from
+either experiment or from a initial
+
+ align:start position:0%
+either experiment or from a initial
+ 
+
+ align:start position:0%
+either experiment or from a initial
+calculation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it is also very
+
+ align:start position:0%
+so it is also very
+ 
+
+ align:start position:0%
+so it is also very
+common when you have a two-state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interaction so here
+
+ align:start position:0%
+interaction so here
+ 
+
+ align:start position:0%
+interaction so here
+is uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh here's diabetic state number one and
+
+ align:start position:0%
+uh here's diabetic state number one and
+ 
+
+ align:start position:0%
+uh here's diabetic state number one and
+here's diabetic state number two and
+
+ align:start position:0%
+here's diabetic state number two and
+ 
+
+ align:start position:0%
+here's diabetic state number two and
+here is the ground state and if we
+
+ align:start position:0%
+here is the ground state and if we
+ 
+
+ align:start position:0%
+here is the ground state and if we
+excite this system with a short
+
+ align:start position:0%
+excite this system with a short
+ 
+
+ align:start position:0%
+excite this system with a short
+pulse it is very common that the only
+
+ align:start position:0%
+pulse it is very common that the only
+ 
+
+ align:start position:0%
+pulse it is very common that the only
+state only one of these two states can
+
+ align:start position:0%
+state only one of these two states can
+ 
+
+ align:start position:0%
+state only one of these two states can
+be excited by an allow transition from
+
+ align:start position:0%
+be excited by an allow transition from
+ 
+
+ align:start position:0%
+be excited by an allow transition from
+the ground state and so what one makes
+
+ align:start position:0%
+the ground state and so what one makes
+ 
+
+ align:start position:0%
+the ground state and so what one makes
+is some kind of superposition
+
+ align:start position:0%
+is some kind of superposition
+ 
+
+ align:start position:0%
+is some kind of superposition
+uh of
+
+ align:start position:0%
+uh of
+ 
+
+ align:start position:0%
+uh of
+the so we have the diabetic States and
+
+ align:start position:0%
+the so we have the diabetic States and
+ 
+
+ align:start position:0%
+the so we have the diabetic States and
+we have
+
+ align:start position:0%
+we have
+ 
+
+ align:start position:0%
+we have
+the so this is the this is the higher
+
+ align:start position:0%
+the so this is the this is the higher
+ 
+
+ align:start position:0%
+the so this is the this is the higher
+energy I State and the lower energy I
+
+ align:start position:0%
+energy I State and the lower energy I
+ 
+
+ align:start position:0%
+energy I State and the lower energy I
+state so I do this
+
+ align:start position:0%
+state so I do this
+ 
+
+ align:start position:0%
+state so I do this
+stupidly so we have a short pulse short
+
+ align:start position:0%
+stupidly so we have a short pulse short
+ 
+
+ align:start position:0%
+stupidly so we have a short pulse short
+enough to cover both of
+
+ align:start position:0%
+enough to cover both of
+ 
+
+ align:start position:0%
+enough to cover both of
+these so we make a superposition of
+
+ align:start position:0%
+these so we make a superposition of
+ 
+
+ align:start position:0%
+these so we make a superposition of
+these two igen
+
+ align:start position:0%
+these two igen
+ 
+
+ align:start position:0%
+these two igen
+states which is
+
+ align:start position:0%
+states which is
+ 
+
+ align:start position:0%
+states which is
+at T equals z purely the basis state
+
+ align:start position:0%
+at T equals z purely the basis state
+ 
+
+ align:start position:0%
+at T equals z purely the basis state
+that has the allowed
+
+ align:start position:0%
+that has the allowed
+ 
+
+ align:start position:0%
+that has the allowed
+transition and now we've got Quantum
+
+ align:start position:0%
+transition and now we've got Quantum
+ 
+
+ align:start position:0%
+transition and now we've got Quantum
+beats we have the system going back and
+
+ align:start position:0%
+beats we have the system going back and
+ 
+
+ align:start position:0%
+beats we have the system going back and
+forth between uh these two igen
+
+ align:start position:0%
+forth between uh these two igen
+ 
+
+ align:start position:0%
+forth between uh these two igen
+states uh uh I'm sorry we have this the
+
+ align:start position:0%
+states uh uh I'm sorry we have this the
+ 
+
+ align:start position:0%
+states uh uh I'm sorry we have this the
+system going back and forth between the
+
+ align:start position:0%
+system going back and forth between the
+ 
+
+ align:start position:0%
+system going back and forth between the
+two zero order States so at the time of
+
+ align:start position:0%
+two zero order States so at the time of
+ 
+
+ align:start position:0%
+two zero order States so at the time of
+the exitation it looks like allowed zero
+
+ align:start position:0%
+the exitation it looks like allowed zero
+ 
+
+ align:start position:0%
+the exitation it looks like allowed zero
+order State and then it moves towards
+
+ align:start position:0%
+order State and then it moves towards
+ 
+
+ align:start position:0%
+order State and then it moves towards
+the other disallows your order state so
+
+ align:start position:0%
+the other disallows your order state so
+ 
+
+ align:start position:0%
+the other disallows your order state so
+there's a kind of Dynamics the system is
+
+ align:start position:0%
+there's a kind of Dynamics the system is
+ 
+
+ align:start position:0%
+there's a kind of Dynamics the system is
+changing its diabetic character with
+
+ align:start position:0%
+changing its diabetic character with
+ 
+
+ align:start position:0%
+changing its diabetic character with
+time now we can also record the Spectrum
+
+ align:start position:0%
+time now we can also record the Spectrum
+ 
+
+ align:start position:0%
+time now we can also record the Spectrum
+in the frequency domain and measure
+
+ align:start position:0%
+in the frequency domain and measure
+ 
+
+ align:start position:0%
+in the frequency domain and measure
+these I States and measure
+
+ align:start position:0%
+these I States and measure
+ 
+
+ align:start position:0%
+these I States and measure
+characteristics of their wave functions
+
+ align:start position:0%
+characteristics of their wave functions
+ 
+
+ align:start position:0%
+characteristics of their wave functions
+and conclude the same thing about the
+
+ align:start position:0%
+and conclude the same thing about the
+ 
+
+ align:start position:0%
+and conclude the same thing about the
+potential dynamics that you can excite
+
+ align:start position:0%
+potential dynamics that you can excite
+ 
+
+ align:start position:0%
+potential dynamics that you can excite
+so all
+
+ align:start position:0%
+so all
+ 
+
+ align:start position:0%
+so all
+right that wasn't what I had planned to
+
+ align:start position:0%
+right that wasn't what I had planned to
+ 
+
+ align:start position:0%
+right that wasn't what I had planned to
+say on this uh yes so just to sum this
+
+ align:start position:0%
+say on this uh yes so just to sum this
+ 
+
+ align:start position:0%
+say on this uh yes so just to sum this
+up the only reason that you're you're
+
+ align:start position:0%
+up the only reason that you're you're
+ 
+
+ align:start position:0%
+up the only reason that you're you're
+working between to this ad
+
+ align:start position:0%
+working between to this ad
+ 
+
+ align:start position:0%
+working between to this ad
+diabatic these there's just two
+
+ align:start position:0%
+diabatic these there's just two
+ 
+
+ align:start position:0%
+diabatic these there's just two
+limits that try to model reality you get
+
+ align:start position:0%
+limits that try to model reality you get
+ 
+
+ align:start position:0%
+limits that try to model reality you get
+the the the real coupling between these
+
+ align:start position:0%
+the the the real coupling between these
+ 
+
+ align:start position:0%
+the the the real coupling between these
+two states you're just mixing the two
+
+ align:start position:0%
+two states you're just mixing the two
+ 
+
+ align:start position:0%
+two states you're just mixing the two
+different limits that's right some
+
+ align:start position:0%
+different limits that's right some
+ 
+
+ align:start position:0%
+different limits that's right some
+clever way that gives you and that's all
+
+ align:start position:0%
+clever way that gives you and that's all
+ 
+
+ align:start position:0%
+clever way that gives you and that's all
+you're getting out of reality is neither
+
+ align:start position:0%
+you're getting out of reality is neither
+ 
+
+ align:start position:0%
+you're getting out of reality is neither
+limit right and it's often true
+
+ align:start position:0%
+limit right and it's often true
+ 
+
+ align:start position:0%
+limit right and it's often true
+that the energy levels that you observe
+
+ align:start position:0%
+that the energy levels that you observe
+ 
+
+ align:start position:0%
+that the energy levels that you observe
+in the Spectrum or that you calculate I
+
+ align:start position:0%
+in the Spectrum or that you calculate I
+ 
+
+ align:start position:0%
+in the Spectrum or that you calculate I
+an issue by doing everything with the
+
+ align:start position:0%
+an issue by doing everything with the
+ 
+
+ align:start position:0%
+an issue by doing everything with the
+exact Honan are closer to one limit or
+
+ align:start position:0%
+exact Honan are closer to one limit or
+ 
+
+ align:start position:0%
+exact Honan are closer to one limit or
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other um and there's a table at on the
+
+ align:start position:0%
+other um and there's a table at on the
+ 
+
+ align:start position:0%
+other um and there's a table at on the
+last page on the next to the last page
+
+ align:start position:0%
+last page on the next to the last page
+ 
+
+ align:start position:0%
+last page on the next to the last page
+of what I handed
+
+ align:start position:0%
+of what I handed
+ 
+
+ align:start position:0%
+of what I handed
+you where there's a two electronic State
+
+ align:start position:0%
+you where there's a two electronic State
+ 
+
+ align:start position:0%
+you where there's a two electronic State
+interaction in Silicon monoxide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what you see is that the vibrational
+
+ align:start position:0%
+and what you see is that the vibrational
+ 
+
+ align:start position:0%
+and what you see is that the vibrational
+energy levels calculated from the
+
+ align:start position:0%
+energy levels calculated from the
+ 
+
+ align:start position:0%
+energy levels calculated from the
+adiabetic potential
+
+ align:start position:0%
+adiabetic potential
+ 
+
+ align:start position:0%
+adiabetic potential
+curve or from the diabetic potential
+
+ align:start position:0%
+curve or from the diabetic potential
+ 
+
+ align:start position:0%
+curve or from the diabetic potential
+curve without considering the
+
+ align:start position:0%
+curve without considering the
+ 
+
+ align:start position:0%
+curve without considering the
+interactions between the two potential
+
+ align:start position:0%
+interactions between the two potential
+ 
+
+ align:start position:0%
+interactions between the two potential
+Curves in uh that uh the diabet the
+
+ align:start position:0%
+Curves in uh that uh the diabet the
+ 
+
+ align:start position:0%
+Curves in uh that uh the diabet the
+adiabetic potential curve in this case
+
+ align:start position:0%
+adiabetic potential curve in this case
+ 
+
+ align:start position:0%
+adiabetic potential curve in this case
+gives a better ref representation of The
+
+ align:start position:0%
+gives a better ref representation of The
+ 
+
+ align:start position:0%
+gives a better ref representation of The
+observed vibrational
+
+ align:start position:0%
+observed vibrational
+ 
+
+ align:start position:0%
+observed vibrational
+levels but not
+
+ align:start position:0%
+levels but not
+ 
+
+ align:start position:0%
+levels but not
+perfect this is the result of an exact
+
+ align:start position:0%
+perfect this is the result of an exact
+ 
+
+ align:start position:0%
+perfect this is the result of an exact
+fit so when one includes either the
+
+ align:start position:0%
+fit so when one includes either the
+ 
+
+ align:start position:0%
+fit so when one includes either the
+nuclear kinetic energy coupling between
+
+ align:start position:0%
+nuclear kinetic energy coupling between
+ 
+
+ align:start position:0%
+nuclear kinetic energy coupling between
+the levels of the adiabetic curve or the
+
+ align:start position:0%
+the levels of the adiabetic curve or the
+ 
+
+ align:start position:0%
+the levels of the adiabetic curve or the
+electronic coupling between levels of
+
+ align:start position:0%
+electronic coupling between levels of
+ 
+
+ align:start position:0%
+electronic coupling between levels of
+the diabetic curves you get it exactly
+
+ align:start position:0%
+the diabetic curves you get it exactly
+ 
+
+ align:start position:0%
+the diabetic curves you get it exactly
+to the energy level and you get the igen
+
+ align:start position:0%
+to the energy level and you get the igen
+ 
+
+ align:start position:0%
+to the energy level and you get the igen
+vectors and you can have the igen
+
+ align:start position:0%
+vectors and you can have the igen
+ 
+
+ align:start position:0%
+vectors and you can have the igen
+vectors in either representation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it it's not this table is not saying
+
+ align:start position:0%
+it it's not this table is not saying
+ 
+
+ align:start position:0%
+it it's not this table is not saying
+that neither representation is very good
+
+ align:start position:0%
+that neither representation is very good
+ 
+
+ align:start position:0%
+that neither representation is very good
+both are perfect but one is closer to
+
+ align:start position:0%
+both are perfect but one is closer to
+ 
+
+ align:start position:0%
+both are perfect but one is closer to
+reality than the
+
+ align:start position:0%
+reality than the
+ 
+
+ align:start position:0%
+reality than the
+other and usually you want to use the
+
+ align:start position:0%
+other and usually you want to use the
+ 
+
+ align:start position:0%
+other and usually you want to use the
+representation that's closer to reality
+
+ align:start position:0%
+representation that's closer to reality
+ 
+
+ align:start position:0%
+representation that's closer to reality
+in this case uh there's only a small
+
+ align:start position:0%
+in this case uh there's only a small
+ 
+
+ align:start position:0%
+in this case uh there's only a small
+advantage to one picture over the other
+
+ align:start position:0%
+advantage to one picture over the other
+ 
+
+ align:start position:0%
+advantage to one picture over the other
+usually there is a huge advantage and
+
+ align:start position:0%
+usually there is a huge advantage and
+ 
+
+ align:start position:0%
+usually there is a huge advantage and
+one can know in advance whether you want
+
+ align:start position:0%
+one can know in advance whether you want
+ 
+
+ align:start position:0%
+one can know in advance whether you want
+the adiabetic or diabetic by comparing
+
+ align:start position:0%
+the adiabetic or diabetic by comparing
+ 
+
+ align:start position:0%
+the adiabetic or diabetic by comparing
+certain
+
+ align:start position:0%
+certain
+ 
+
+ align:start position:0%
+certain
+quantities which is not what I want to
+
+ align:start position:0%
+quantities which is not what I want to
+ 
+
+ align:start position:0%
+quantities which is not what I want to
+talk about
+
+ align:start position:0%
+talk about
+ 
+
+ align:start position:0%
+talk about
+now okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now I want
+
+ align:start position:0%
+so now I want
+ 
+
+ align:start position:0%
+so now I want
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to go
+
+ align:start position:0%
+to go
+ 
+
+ align:start position:0%
+to go
+to electronic vibration rotation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we get a potential
+
+ align:start position:0%
+so we get a potential
+ 
+
+ align:start position:0%
+so we get a potential
+curve somehow it could be adiabetic or
+
+ align:start position:0%
+curve somehow it could be adiabetic or
+ 
+
+ align:start position:0%
+curve somehow it could be adiabetic or
+diabetic it's for the I electronic State
+
+ align:start position:0%
+diabetic it's for the I electronic State
+ 
+
+ align:start position:0%
+diabetic it's for the I electronic State
+I we just count up from the bottom uh we
+
+ align:start position:0%
+I we just count up from the bottom uh we
+ 
+
+ align:start position:0%
+I we just count up from the bottom uh we
+and uh we can find the all of the
+
+ align:start position:0%
+and uh we can find the all of the
+ 
+
+ align:start position:0%
+and uh we can find the all of the
+vibrational levels of this potential
+
+ align:start position:0%
+vibrational levels of this potential
+ 
+
+ align:start position:0%
+vibrational levels of this potential
+curve by solving by doing a numerical
+
+ align:start position:0%
+curve by solving by doing a numerical
+ 
+
+ align:start position:0%
+curve by solving by doing a numerical
+integration by solving the nuclear
+
+ align:start position:0%
+integration by solving the nuclear
+ 
+
+ align:start position:0%
+integration by solving the nuclear
+kinetic energy is a nuclear shorer
+
+ align:start position:0%
+kinetic energy is a nuclear shorer
+ 
+
+ align:start position:0%
+kinetic energy is a nuclear shorer
+equation and so we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the vibrational wave functions all of
+
+ align:start position:0%
+uh the vibrational wave functions all of
+ 
+
+ align:start position:0%
+uh the vibrational wave functions all of
+them for all vibrational levels and the
+
+ align:start position:0%
+them for all vibrational levels and the
+ 
+
+ align:start position:0%
+them for all vibrational levels and the
+Continuum associated with this potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gr
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we get the Wun functions we get the
+
+ align:start position:0%
+so we get the Wun functions we get the
+ 
+
+ align:start position:0%
+so we get the Wun functions we get the
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+levels we can fit the energy levels
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um what it's called The Don
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expansion
+
+ align:start position:0%
+expansion
+ 
+
+ align:start position:0%
+expansion
+m y
+
+ align:start position:0%
+m y
+ 
+
+ align:start position:0%
+m y
+these are Dam constants y 1 0 is Omega 0
+
+ align:start position:0%
+these are Dam constants y 1 0 is Omega 0
+ 
+
+ align:start position:0%
+these are Dam constants y 1 0 is Omega 0
+Omega e and Y 01 is t e vibrational
+
+ align:start position:0%
+Omega e and Y 01 is t e vibrational
+ 
+
+ align:start position:0%
+Omega e and Y 01 is t e vibrational
+frequency rotational constant there's
+
+ align:start position:0%
+frequency rotational constant there's
+ 
+
+ align:start position:0%
+frequency rotational constant there's
+lots
+
+ align:start position:0%
+lots
+ 
+
+ align:start position:0%
+lots
+more so these are this is a no Insight
+
+ align:start position:0%
+more so these are this is a no Insight
+ 
+
+ align:start position:0%
+more so these are this is a no Insight
+no knowledge empirical representation of
+
+ align:start position:0%
+no knowledge empirical representation of
+ 
+
+ align:start position:0%
+no knowledge empirical representation of
+the I
+
+ align:start position:0%
+the I
+ 
+
+ align:start position:0%
+the I
+energies calculated from the potential
+
+ align:start position:0%
+energies calculated from the potential
+ 
+
+ align:start position:0%
+energies calculated from the potential
+Cur
+
+ align:start position:0%
+Cur
+ 
+
+ align:start position:0%
+Cur
+and these are the things that
+
+ align:start position:0%
+and these are the things that
+ 
+
+ align:start position:0%
+and these are the things that
+spectroscopist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+publish so one can do a Le squares
+
+ align:start position:0%
+publish so one can do a Le squares
+ 
+
+ align:start position:0%
+publish so one can do a Le squares
+fit to the igen values or one can do all
+
+ align:start position:0%
+fit to the igen values or one can do all
+ 
+
+ align:start position:0%
+fit to the igen values or one can do all
+least squares fit but one can write V of
+
+ align:start position:0%
+least squares fit but one can write V of
+ 
+
+ align:start position:0%
+least squares fit but one can write V of
+r v
+
+ align:start position:0%
+r v
+ 
+
+ align:start position:0%
+r v
+of V of i as uh um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+I to
+
+ align:start position:0%
+I to
+ 
+
+ align:start position:0%
+I to
+whatever a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i to the I
+
+ align:start position:0%
+i to the I
+ 
+
+ align:start position:0%
+i to the I
+power is r- re over re re is the inter
+
+ align:start position:0%
+power is r- re over re re is the inter
+ 
+
+ align:start position:0%
+power is r- re over re re is the inter
+equili distance and this is a convenient
+
+ align:start position:0%
+equili distance and this is a convenient
+ 
+
+ align:start position:0%
+equili distance and this is a convenient
+parameter and that's the dunam expansion
+
+ align:start position:0%
+parameter and that's the dunam expansion
+ 
+
+ align:start position:0%
+parameter and that's the dunam expansion
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+potential and these are a bunch of
+
+ align:start position:0%
+potential and these are a bunch of
+ 
+
+ align:start position:0%
+potential and these are a bunch of
+empirical parameters determined by
+
+ align:start position:0%
+empirical parameters determined by
+ 
+
+ align:start position:0%
+empirical parameters determined by
+fitting this to the potential and there
+
+ align:start position:0%
+fitting this to the potential and there
+ 
+
+ align:start position:0%
+fitting this to the potential and there
+is a Dunham inversion that enables you
+
+ align:start position:0%
+is a Dunham inversion that enables you
+ 
+
+ align:start position:0%
+is a Dunham inversion that enables you
+to calculate these
+
+ align:start position:0%
+to calculate these
+ 
+
+ align:start position:0%
+to calculate these
+things uh to calculate these things from
+
+ align:start position:0%
+things uh to calculate these things from
+ 
+
+ align:start position:0%
+things uh to calculate these things from
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+things there's lots of ways of going
+
+ align:start position:0%
+things there's lots of ways of going
+ 
+
+ align:start position:0%
+things there's lots of ways of going
+between the potential and the constants
+
+ align:start position:0%
+between the potential and the constants
+ 
+
+ align:start position:0%
+between the potential and the constants
+or the constants and the potential and
+
+ align:start position:0%
+or the constants and the potential and
+ 
+
+ align:start position:0%
+or the constants and the potential and
+they mostly involve puration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theory okay okay now I slip something
+
+ align:start position:0%
+Theory okay okay now I slip something
+ 
+
+ align:start position:0%
+Theory okay okay now I slip something
+under the
+
+ align:start position:0%
+under the
+ 
+
+ align:start position:0%
+under the
+rug or at least I since I'm not looking
+
+ align:start position:0%
+rug or at least I since I'm not looking
+ 
+
+ align:start position:0%
+rug or at least I since I'm not looking
+at my notes I'm doing it out of
+
+ align:start position:0%
+at my notes I'm doing it out of
+ 
+
+ align:start position:0%
+at my notes I'm doing it out of
+order we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have a effective potential which is
+
+ align:start position:0%
+have a effective potential which is
+ 
+
+ align:start position:0%
+have a effective potential which is
+gotten from the clamp nuclei potential
+
+ align:start position:0%
+gotten from the clamp nuclei potential
+ 
+
+ align:start position:0%
+gotten from the clamp nuclei potential
+in other words J equals
+
+ align:start position:0%
+in other words J equals
+ 
+
+ align:start position:0%
+in other words J equals
+z plus the explicitly
+
+ align:start position:0%
+z plus the explicitly
+ 
+
+ align:start position:0%
+z plus the explicitly
+known uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+centrifugal correction to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potential okay this is the inter
+
+ align:start position:0%
+potential okay this is the inter
+ 
+
+ align:start position:0%
+potential okay this is the inter
+distance this is the reduced Mass this
+
+ align:start position:0%
+distance this is the reduced Mass this
+ 
+
+ align:start position:0%
+distance this is the reduced Mass this
+is the rotational angular
+
+ align:start position:0%
+is the rotational angular
+ 
+
+ align:start position:0%
+is the rotational angular
+momentum so this is the bare potential
+
+ align:start position:0%
+momentum so this is the bare potential
+ 
+
+ align:start position:0%
+momentum so this is the bare potential
+no rotation now we
+
+ align:start position:0%
+no rotation now we
+ 
+
+ align:start position:0%
+no rotation now we
+fix clamp nuclei approximation by
+
+ align:start position:0%
+fix clamp nuclei approximation by
+ 
+
+ align:start position:0%
+fix clamp nuclei approximation by
+allowing the nuclei to
+
+ align:start position:0%
+allowing the nuclei to
+ 
+
+ align:start position:0%
+allowing the nuclei to
+rotate that's one of the terms that we
+
+ align:start position:0%
+rotate that's one of the terms that we
+ 
+
+ align:start position:0%
+rotate that's one of the terms that we
+neglected and that enables us to
+
+ align:start position:0%
+neglected and that enables us to
+ 
+
+ align:start position:0%
+neglected and that enables us to
+calculate to derive the J dependent
+
+ align:start position:0%
+calculate to derive the J dependent
+ 
+
+ align:start position:0%
+calculate to derive the J dependent
+effective potential and the I values of
+
+ align:start position:0%
+effective potential and the I values of
+ 
+
+ align:start position:0%
+effective potential and the I values of
+that going to give
+
+ align:start position:0%
+that going to give
+ 
+
+ align:start position:0%
+that going to give
+us e of B and
+
+ align:start position:0%
+us e of B and
+ 
+
+ align:start position:0%
+us e of B and
+J okay
+
+ align:start position:0%
+J okay
+ 
+
+ align:start position:0%
+J okay
+so the abonal potential curve enables us
+
+ align:start position:0%
+so the abonal potential curve enables us
+ 
+
+ align:start position:0%
+so the abonal potential curve enables us
+to calculate all of these things all of
+
+ align:start position:0%
+to calculate all of these things all of
+ 
+
+ align:start position:0%
+to calculate all of these things all of
+these things allow us to compute the
+
+ align:start position:0%
+these things allow us to compute the
+ 
+
+ align:start position:0%
+these things allow us to compute the
+molecular constants by fitting or by
+
+ align:start position:0%
+molecular constants by fitting or by
+ 
+
+ align:start position:0%
+molecular constants by fitting or by
+fitting the curve and doing the Dom
+
+ align:start position:0%
+fitting the curve and doing the Dom
+ 
+
+ align:start position:0%
+fitting the curve and doing the Dom
+version or using perturbation Theory
+
+ align:start position:0%
+version or using perturbation Theory
+ 
+
+ align:start position:0%
+version or using perturbation Theory
+there are lots of connections but so
+
+ align:start position:0%
+there are lots of connections but so
+ 
+
+ align:start position:0%
+there are lots of connections but so
+everything is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we've included the rotation this is
+
+ align:start position:0%
+okay we've included the rotation this is
+ 
+
+ align:start position:0%
+okay we've included the rotation this is
+the bar
+
+ align:start position:0%
+the bar
+ 
+
+ align:start position:0%
+the bar
+nuclei we call
+
+ align:start position:0%
+nuclei we call
+ 
+
+ align:start position:0%
+nuclei we call
+this the rotational constant
+
+ align:start position:0%
+this the rotational constant
+ 
+
+ align:start position:0%
+this the rotational constant
+operator it becomes a constant when we
+
+ align:start position:0%
+operator it becomes a constant when we
+ 
+
+ align:start position:0%
+operator it becomes a constant when we
+take the vibration Matrix element of
+
+ align:start position:0%
+take the vibration Matrix element of
+ 
+
+ align:start position:0%
+take the vibration Matrix element of
+it vibrational expectation value of it
+
+ align:start position:0%
+it vibrational expectation value of it
+ 
+
+ align:start position:0%
+it vibrational expectation value of it
+so if we do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this v
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+i that becomes b of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+e okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right now we're on page
+
+ align:start position:0%
+right now we're on page
+ 
+
+ align:start position:0%
+right now we're on page
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+nine so the born Oppenheimer
+
+ align:start position:0%
+nine so the born Oppenheimer
+ 
+
+ align:start position:0%
+nine so the born Oppenheimer
+approximation enable us to
+
+ align:start position:0%
+approximation enable us to
+ 
+
+ align:start position:0%
+approximation enable us to
+calculate electronic energy levels for
+
+ align:start position:0%
+calculate electronic energy levels for
+ 
+
+ align:start position:0%
+calculate electronic energy levels for
+the I state but they're normally called
+
+ align:start position:0%
+the I state but they're normally called
+ 
+
+ align:start position:0%
+the I state but they're normally called
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+ofv and it enabled us to get
+
+ align:start position:0%
+ofv and it enabled us to get
+ 
+
+ align:start position:0%
+ofv and it enabled us to get
+a uh I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh then by allowing the molecule to
+
+ align:start position:0%
+uh then by allowing the molecule to
+ 
+
+ align:start position:0%
+uh then by allowing the molecule to
+rotate
+
+ align:start position:0%
+rotate
+ 
+
+ align:start position:0%
+rotate
+we have
+
+ align:start position:0%
+we have
+ 
+
+ align:start position:0%
+we have
+this and we still
+
+ align:start position:0%
+this and we still
+ 
+
+ align:start position:0%
+this and we still
+haven't
+
+ align:start position:0%
+haven't
+ 
+
+ align:start position:0%
+haven't
+included all of the couplings between
+
+ align:start position:0%
+included all of the couplings between
+ 
+
+ align:start position:0%
+included all of the couplings between
+electronic States either the nuclear
+
+ align:start position:0%
+electronic States either the nuclear
+ 
+
+ align:start position:0%
+electronic States either the nuclear
+kinetic energy
+
+ align:start position:0%
+kinetic energy
+ 
+
+ align:start position:0%
+kinetic energy
+couplings or if we've gone to a diabetic
+
+ align:start position:0%
+couplings or if we've gone to a diabetic
+ 
+
+ align:start position:0%
+couplings or if we've gone to a diabetic
+representation the electronic C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this provides the separation that we
+
+ align:start position:0%
+but this provides the separation that we
+ 
+
+ align:start position:0%
+but this provides the separation that we
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+between electronic and nuclear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motions and then we can say all right
+
+ align:start position:0%
+motions and then we can say all right
+ 
+
+ align:start position:0%
+motions and then we can say all right
+are we going to have a model that
+
+ align:start position:0%
+are we going to have a model that
+ 
+
+ align:start position:0%
+are we going to have a model that
+describes the different parts of the
+
+ align:start position:0%
+describes the different parts of the
+ 
+
+ align:start position:0%
+describes the different parts of the
+problem the electronic part of the
+
+ align:start position:0%
+problem the electronic part of the
+ 
+
+ align:start position:0%
+problem the electronic part of the
+problem are we going to try to explain
+
+ align:start position:0%
+problem are we going to try to explain
+ 
+
+ align:start position:0%
+problem are we going to try to explain
+it as something related to something
+
+ align:start position:0%
+it as something related to something
+ 
+
+ align:start position:0%
+it as something related to something
+that we understand well like the
+
+ align:start position:0%
+that we understand well like the
+ 
+
+ align:start position:0%
+that we understand well like the
+hydrogen atom or like the particle in a
+
+ align:start position:0%
+hydrogen atom or like the particle in a
+ 
+
+ align:start position:0%
+hydrogen atom or like the particle in a
+box and veence
+
+ align:start position:0%
+box and veence
+ 
+
+ align:start position:0%
+box and veence
+states
+
+ align:start position:0%
+states
+ 
+
+ align:start position:0%
+states
+are reasonably well described
+
+ align:start position:0%
+are reasonably well described
+ 
+
+ align:start position:0%
+are reasonably well described
+by orbitals which correspond to
+
+ align:start position:0%
+by orbitals which correspond to
+ 
+
+ align:start position:0%
+by orbitals which correspond to
+different I states of the particle in a
+
+ align:start position:0%
+different I states of the particle in a
+ 
+
+ align:start position:0%
+different I states of the particle in a
+box the energy levels get farther and
+
+ align:start position:0%
+box the energy levels get farther and
+ 
+
+ align:start position:0%
+box the energy levels get farther and
+farther apart as you go up and as you go
+
+ align:start position:0%
+farther apart as you go up and as you go
+ 
+
+ align:start position:0%
+farther apart as you go up and as you go
+up in energy they have more and more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nodes and or they could be the hydrogen
+
+ align:start position:0%
+nodes and or they could be the hydrogen
+ 
+
+ align:start position:0%
+nodes and or they could be the hydrogen
+atom for rberg
+
+ align:start position:0%
+atom for rberg
+ 
+
+ align:start position:0%
+atom for rberg
+States and so you can sort of have a
+
+ align:start position:0%
+States and so you can sort of have a
+ 
+
+ align:start position:0%
+States and so you can sort of have a
+model for this and then you can have a
+
+ align:start position:0%
+model for this and then you can have a
+ 
+
+ align:start position:0%
+model for this and then you can have a
+model for this you can say it really
+
+ align:start position:0%
+model for this you can say it really
+ 
+
+ align:start position:0%
+model for this you can say it really
+wanted to be a harmonic oscillator but
+
+ align:start position:0%
+wanted to be a harmonic oscillator but
+ 
+
+ align:start position:0%
+wanted to be a harmonic oscillator but
+there's some some terms that involve
+
+ align:start position:0%
+there's some some terms that involve
+ 
+
+ align:start position:0%
+there's some some terms that involve
+cubic and Cordic powers of our or we can
+
+ align:start position:0%
+cubic and Cordic powers of our or we can
+ 
+
+ align:start position:0%
+cubic and Cordic powers of our or we can
+make it a Morse oscillator and we can
+
+ align:start position:0%
+make it a Morse oscillator and we can
+ 
+
+ align:start position:0%
+make it a Morse oscillator and we can
+represent a lot of the molecular
+
+ align:start position:0%
+represent a lot of the molecular
+ 
+
+ align:start position:0%
+represent a lot of the molecular
+constants by using the harmonic
+
+ align:start position:0%
+constants by using the harmonic
+ 
+
+ align:start position:0%
+constants by using the harmonic
+oscillator plus anharmonic Corrections
+
+ align:start position:0%
+oscillator plus anharmonic Corrections
+ 
+
+ align:start position:0%
+oscillator plus anharmonic Corrections
+or the Morse oscillator and we get
+
+ align:start position:0%
+or the Morse oscillator and we get
+ 
+
+ align:start position:0%
+or the Morse oscillator and we get
+relationships between molecular
+
+ align:start position:0%
+relationships between molecular
+ 
+
+ align:start position:0%
+relationships between molecular
+constants that help us in leveraging our
+
+ align:start position:0%
+constants that help us in leveraging our
+ 
+
+ align:start position:0%
+constants that help us in leveraging our
+finite number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observations so we're ready to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+begin so in order to real be begin we
+
+ align:start position:0%
+begin so in order to real be begin we
+ 
+
+ align:start position:0%
+begin so in order to real be begin we
+need to say well what did we really
+
+ align:start position:0%
+need to say well what did we really
+ 
+
+ align:start position:0%
+need to say well what did we really
+leave out and I'm going to summarize
+
+ align:start position:0%
+leave out and I'm going to summarize
+ 
+
+ align:start position:0%
+leave out and I'm going to summarize
+this for the electronic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem if we take a diabetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture and most spectroscopists are
+
+ align:start position:0%
+picture and most spectroscopists are
+ 
+
+ align:start position:0%
+picture and most spectroscopists are
+most comfortable in the diabetic
+
+ align:start position:0%
+most comfortable in the diabetic
+ 
+
+ align:start position:0%
+most comfortable in the diabetic
+representation because it is the one
+
+ align:start position:0%
+representation because it is the one
+ 
+
+ align:start position:0%
+representation because it is the one
+where the electronic wave function
+
+ align:start position:0%
+where the electronic wave function
+ 
+
+ align:start position:0%
+where the electronic wave function
+doesn't do gymnastic is a function of
+
+ align:start position:0%
+doesn't do gymnastic is a function of
+ 
+
+ align:start position:0%
+doesn't do gymnastic is a function of
+molecular geometry so we're more
+
+ align:start position:0%
+molecular geometry so we're more
+ 
+
+ align:start position:0%
+molecular geometry so we're more
+comfortable thinking about the
+
+ align:start position:0%
+comfortable thinking about the
+ 
+
+ align:start position:0%
+comfortable thinking about the
+electronic uh problem in a diabetic
+
+ align:start position:0%
+electronic uh problem in a diabetic
+ 
+
+ align:start position:0%
+electronic uh problem in a diabetic
+picture and that's no big deal so uh and
+
+ align:start position:0%
+picture and that's no big deal so uh and
+ 
+
+ align:start position:0%
+picture and that's no big deal so uh and
+in that case this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+missing or ad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+OFA by R is missing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vib
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vibrational
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem we could use a harmonic
+
+ align:start position:0%
+problem we could use a harmonic
+ 
+
+ align:start position:0%
+problem we could use a harmonic
+oscillator and
+
+ align:start position:0%
+oscillator and
+ 
+
+ align:start position:0%
+oscillator and
+includ powers of R cub and
+
+ align:start position:0%
+includ powers of R cub and
+ 
+
+ align:start position:0%
+includ powers of R cub and
+R4 Etc or we can use a Morse picture
+
+ align:start position:0%
+R4 Etc or we can use a Morse picture
+ 
+
+ align:start position:0%
+R4 Etc or we can use a Morse picture
+and uh uh so treating cubic and Cordic
+
+ align:start position:0%
+and uh uh so treating cubic and Cordic
+ 
+
+ align:start position:0%
+and uh uh so treating cubic and Cordic
+terms or the power series expansion of
+
+ align:start position:0%
+terms or the power series expansion of
+ 
+
+ align:start position:0%
+terms or the power series expansion of
+the Morse potential in cubic and Cordic
+
+ align:start position:0%
+the Morse potential in cubic and Cordic
+ 
+
+ align:start position:0%
+the Morse potential in cubic and Cordic
+terms we can treat them as
+
+ align:start position:0%
+terms we can treat them as
+ 
+
+ align:start position:0%
+terms we can treat them as
+perations so there's lots of things you
+
+ align:start position:0%
+perations so there's lots of things you
+ 
+
+ align:start position:0%
+perations so there's lots of things you
+can do for the vibration and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation now I lied to you before I said
+
+ align:start position:0%
+rotation now I lied to you before I said
+ 
+
+ align:start position:0%
+rotation now I lied to you before I said
+the rotational angular momentum that
+
+ align:start position:0%
+the rotational angular momentum that
+ 
+
+ align:start position:0%
+the rotational angular momentum that
+goes with the c drial potential is j
+
+ align:start position:0%
+goes with the c drial potential is j
+ 
+
+ align:start position:0%
+goes with the c drial potential is j
+s it's
+
+ align:start position:0%
+s it's
+ 
+
+ align:start position:0%
+s it's
+not it's the nuclear
+
+ align:start position:0%
+not it's the nuclear
+ 
+
+ align:start position:0%
+not it's the nuclear
+rotation it's j - l -
+
+ align:start position:0%
+rotation it's j - l -
+ 
+
+ align:start position:0%
+rotation it's j - l -
+s squ which is equal to r² where this is
+
+ align:start position:0%
+s squ which is equal to r² where this is
+ 
+
+ align:start position:0%
+s squ which is equal to r² where this is
+now not the internuclear distance but
+
+ align:start position:0%
+now not the internuclear distance but
+ 
+
+ align:start position:0%
+now not the internuclear distance but
+the quantum the operator associated with
+
+ align:start position:0%
+the quantum the operator associated with
+ 
+
+ align:start position:0%
+the quantum the operator associated with
+the nuclear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation and
+
+ align:start position:0%
+rotation and
+ 
+
+ align:start position:0%
+rotation and
+so we got some something some work to do
+
+ align:start position:0%
+so we got some something some work to do
+ 
+
+ align:start position:0%
+so we got some something some work to do
+here to correct
+
+ align:start position:0%
+here to correct
+ 
+
+ align:start position:0%
+here to correct
+for uh the fact that you could have
+
+ align:start position:0%
+for uh the fact that you could have
+ 
+
+ align:start position:0%
+for uh the fact that you could have
+nonzero electron orbital and electron
+
+ align:start position:0%
+nonzero electron orbital and electron
+ 
+
+ align:start position:0%
+nonzero electron orbital and electron
+spin angular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we wanted to use b j j
+
+ align:start position:0%
+so we wanted to use b j j
+ 
+
+ align:start position:0%
+so we wanted to use b j j
++1 because this says the rotational
+
+ align:start position:0%
++1 because this says the rotational
+ 
+
+ align:start position:0%
++1 because this says the rotational
+levels are given by a constant times an
+
+ align:start position:0%
+levels are given by a constant times an
+ 
+
+ align:start position:0%
+levels are given by a constant times an
+integer
+
+ align:start position:0%
+integer
+ 
+
+ align:start position:0%
+integer
+an integer plus one but we know J could
+
+ align:start position:0%
+an integer plus one but we know J could
+ 
+
+ align:start position:0%
+an integer plus one but we know J could
+also be a half
+
+ align:start position:0%
+also be a half
+ 
+
+ align:start position:0%
+also be a half
+integer but
+
+ align:start position:0%
+integer but
+ 
+
+ align:start position:0%
+integer but
+we we have a pattern of rotational
+
+ align:start position:0%
+we we have a pattern of rotational
+ 
+
+ align:start position:0%
+we we have a pattern of rotational
+energy levels they're given us basically
+
+ align:start position:0%
+energy levels they're given us basically
+ 
+
+ align:start position:0%
+energy levels they're given us basically
+by one constant and some
+
+ align:start position:0%
+by one constant and some
+ 
+
+ align:start position:0%
+by one constant and some
+magic expression in the quantum numbers
+
+ align:start position:0%
+magic expression in the quantum numbers
+ 
+
+ align:start position:0%
+magic expression in the quantum numbers
+well it's going to be more complicated
+
+ align:start position:0%
+well it's going to be more complicated
+ 
+
+ align:start position:0%
+well it's going to be more complicated
+here and we're going to discover L's
+
+ align:start position:0%
+here and we're going to discover L's
+ 
+
+ align:start position:0%
+here and we're going to discover L's
+cases so the hamiltonian is written as a
+
+ align:start position:0%
+cases so the hamiltonian is written as a
+ 
+
+ align:start position:0%
+cases so the hamiltonian is written as a
+sum of
+
+ align:start position:0%
+sum of
+ 
+
+ align:start position:0%
+sum of
+the electronic
+
+ align:start position:0%
+the electronic
+ 
+
+ align:start position:0%
+the electronic
+hamiltonian the vibrational hamiltonian
+
+ align:start position:0%
+hamiltonian the vibrational hamiltonian
+ 
+
+ align:start position:0%
+hamiltonian the vibrational hamiltonian
+which I which is really sort of part of
+
+ align:start position:0%
+which I which is really sort of part of
+ 
+
+ align:start position:0%
+which I which is really sort of part of
+this plus spit
+
+ align:start position:0%
+this plus spit
+ 
+
+ align:start position:0%
+this plus spit
+orbit plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now I need to
+
+ align:start position:0%
+now I need to
+ 
+
+ align:start position:0%
+now I need to
+uh tell you about the various terms in
+
+ align:start position:0%
+uh tell you about the various terms in
+ 
+
+ align:start position:0%
+uh tell you about the various terms in
+each of these operators and classify by
+
+ align:start position:0%
+each of these operators and classify by
+ 
+
+ align:start position:0%
+each of these operators and classify by
+them according to their
+
+ align:start position:0%
+them according to their
+ 
+
+ align:start position:0%
+them according to their
+type and uh uh so we can know something
+
+ align:start position:0%
+type and uh uh so we can know something
+ 
+
+ align:start position:0%
+type and uh uh so we can know something
+about the selection rules for nonzero
+
+ align:start position:0%
+about the selection rules for nonzero
+ 
+
+ align:start position:0%
+about the selection rules for nonzero
+Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+elements so we want to have a simple way
+
+ align:start position:0%
+elements so we want to have a simple way
+ 
+
+ align:start position:0%
+elements so we want to have a simple way
+of doing
+
+ align:start position:0%
+of doing
+ 
+
+ align:start position:0%
+of doing
+this and this is the way I do it for
+
+ align:start position:0%
+this and this is the way I do it for
+ 
+
+ align:start position:0%
+this and this is the way I do it for
+the perturbation term associated with
+
+ align:start position:0%
+the perturbation term associated with
+ 
+
+ align:start position:0%
+the perturbation term associated with
+the electronic show
+
+ align:start position:0%
+the electronic show
+ 
+
+ align:start position:0%
+the electronic show
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes okay this guy is a problem well what
+
+ align:start position:0%
+yes okay this guy is a problem well what
+ 
+
+ align:start position:0%
+yes okay this guy is a problem well what
+is it r i j is the square root of R1 s i
+
+ align:start position:0%
+is it r i j is the square root of R1 s i
+ 
+
+ align:start position:0%
+is it r i j is the square root of R1 s i
+r i 2 + r j 2 - 2 r i r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+j this is a
+
+ align:start position:0%
+j this is a
+ 
+
+ align:start position:0%
+j this is a
+scalar operator with respect to electron
+
+ align:start position:0%
+scalar operator with respect to electron
+ 
+
+ align:start position:0%
+scalar operator with respect to electron
+I this is a scalar operator with respect
+
+ align:start position:0%
+I this is a scalar operator with respect
+ 
+
+ align:start position:0%
+I this is a scalar operator with respect
+to electron
+
+ align:start position:0%
+to electron
+ 
+
+ align:start position:0%
+to electron
+J this is a vector operator with respect
+
+ align:start position:0%
+J this is a vector operator with respect
+ 
+
+ align:start position:0%
+J this is a vector operator with respect
+to either electron I or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J because it's a dotproduct of two
+
+ align:start position:0%
+J because it's a dotproduct of two
+ 
+
+ align:start position:0%
+J because it's a dotproduct of two
+different Vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operators so this guy destroys all of
+
+ align:start position:0%
+operators so this guy destroys all of
+ 
+
+ align:start position:0%
+operators so this guy destroys all of
+the one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electron uh quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers it has Matrix elements Delta
+
+ align:start position:0%
+numbers it has Matrix elements Delta
+ 
+
+ align:start position:0%
+numbers it has Matrix elements Delta
+L plus orus one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or0 um L LJ plus or minus one or zero
+
+ align:start position:0%
+or0 um L LJ plus or minus one or zero
+ 
+
+ align:start position:0%
+or0 um L LJ plus or minus one or zero
+but this is a vector with respect to any
+
+ align:start position:0%
+but this is a vector with respect to any
+ 
+
+ align:start position:0%
+but this is a vector with respect to any
+many electron angular
+
+ align:start position:0%
+many electron angular
+ 
+
+ align:start position:0%
+many electron angular
+momentum so the total j or the total
+
+ align:start position:0%
+momentum so the total j or the total
+ 
+
+ align:start position:0%
+momentum so the total j or the total
+L this is a vector this is a vector
+
+ align:start position:0%
+L this is a vector this is a vector
+ 
+
+ align:start position:0%
+L this is a vector this is a vector
+dotproduct of two vectors is a scalar so
+
+ align:start position:0%
+dotproduct of two vectors is a scalar so
+ 
+
+ align:start position:0%
+dotproduct of two vectors is a scalar so
+this is a scalar operator with respect
+
+ align:start position:0%
+this is a scalar operator with respect
+ 
+
+ align:start position:0%
+this is a scalar operator with respect
+to all of the many electron angular
+
+ align:start position:0%
+to all of the many electron angular
+ 
+
+ align:start position:0%
+to all of the many electron angular
+momentum so that means Delta j = z Delta
+
+ align:start position:0%
+momentum so that means Delta j = z Delta
+ 
+
+ align:start position:0%
+momentum so that means Delta j = z Delta
+L = 0 Delta s =
+
+ align:start position:0%
+L = 0 Delta s =
+ 
+
+ align:start position:0%
+L = 0 Delta s =
+z Delta
+
+ align:start position:0%
+z Delta
+ 
+
+ align:start position:0%
+z Delta
+j z = 0 Delta l z = z Delta s z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z and they're
+
+ align:start position:0%
+z and they're
+ 
+
+ align:start position:0%
+z and they're
+independent of Omega which is the IG
+
+ align:start position:0%
+independent of Omega which is the IG
+ 
+
+ align:start position:0%
+independent of Omega which is the IG
+value of
+
+ align:start position:0%
+value of
+ 
+
+ align:start position:0%
+value of
+JZ Lambda which is the IG value of
+
+ align:start position:0%
+JZ Lambda which is the IG value of
+ 
+
+ align:start position:0%
+JZ Lambda which is the IG value of
+LZ and
+
+ align:start position:0%
+LZ and
+ 
+
+ align:start position:0%
+LZ and
+sigma that's the property of a scalar
+
+ align:start position:0%
+sigma that's the property of a scalar
+ 
+
+ align:start position:0%
+sigma that's the property of a scalar
+operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's diagonal and it's independent
+
+ align:start position:0%
+it's diagonal and it's independent
+ 
+
+ align:start position:0%
+it's diagonal and it's independent
+projection
+
+ align:start position:0%
+projection
+ 
+
+ align:start position:0%
+projection
+quads so this says well this thing is
+
+ align:start position:0%
+quads so this says well this thing is
+ 
+
+ align:start position:0%
+quads so this says well this thing is
+only going to operate between electronic
+
+ align:start position:0%
+only going to operate between electronic
+ 
+
+ align:start position:0%
+only going to operate between electronic
+states of the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symetry hence the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+noncrossing okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now for the rotational P I'm going to
+
+ align:start position:0%
+now for the rotational P I'm going to
+ 
+
+ align:start position:0%
+now for the rotational P I'm going to
+have to stop pretty soon but I got
+
+ align:start position:0%
+have to stop pretty soon but I got
+ 
+
+ align:start position:0%
+have to stop pretty soon but I got
+pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+far the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotational is B of
+
+ align:start position:0%
+rotational is B of
+ 
+
+ align:start position:0%
+rotational is B of
+R time J L
+
+ align:start position:0%
+R time J L
+ 
+
+ align:start position:0%
+R time J L
+s² and so this becomes B of R
+
+ align:start position:0%
+s² and so this becomes B of R
+ 
+
+ align:start position:0%
+s² and so this becomes B of R
+times bunch of stuff j s
+
+ align:start position:0%
+times bunch of stuff j s
+ 
+
+ align:start position:0%
+times bunch of stuff j s
+- j z
+
+ align:start position:0%
+- j z
+ 
+
+ align:start position:0%
+- j z
+2+ L 2 - L Z 2 plus s² - s
+
+ align:start position:0%
+2+ L 2 - L Z 2 plus s² - s
+ 
+
+ align:start position:0%
+2+ L 2 - L Z 2 plus s² - s
+c² those are all of the diagonal
+
+ align:start position:0%
+c² those are all of the diagonal
+ 
+
+ align:start position:0%
+c² those are all of the diagonal
+elements in L's case
+
+ align:start position:0%
+elements in L's case
+ 
+
+ align:start position:0%
+elements in L's case
+a but we don't know what L's case a is
+
+ align:start position:0%
+a but we don't know what L's case a is
+ 
+
+ align:start position:0%
+a but we don't know what L's case a is
+good but you know you see these things
+
+ align:start position:0%
+good but you know you see these things
+ 
+
+ align:start position:0%
+good but you know you see these things
+and you say i' be pretty happy and then
+
+ align:start position:0%
+and you say i' be pretty happy and then
+ 
+
+ align:start position:0%
+and you say i' be pretty happy and then
+we have
+
+ align:start position:0%
+we have
+ 
+
+ align:start position:0%
+we have
+minus J + lus plus J - l+ these are
+
+ align:start position:0%
+minus J + lus plus J - l+ these are
+ 
+
+ align:start position:0%
+minus J + lus plus J - l+ these are
+raising and lowering operators
+
+ align:start position:0%
+raising and lowering operators
+ 
+
+ align:start position:0%
+raising and lowering operators
+minus J + s- + S Jus
+
+ align:start position:0%
+minus J + s- + S Jus
+ 
+
+ align:start position:0%
+minus J + s- + S Jus
+s+ plus L +
+
+ align:start position:0%
+s+ plus L +
+ 
+
+ align:start position:0%
+s+ plus L +
+S
+
+ align:start position:0%
+S
+ 
+
+ align:start position:0%
+S
+L that's
+
+ align:start position:0%
+L that's
+ 
+
+ align:start position:0%
+L that's
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+so these have Matrix elements off
+
+ align:start position:0%
+so these have Matrix elements off
+ 
+
+ align:start position:0%
+so these have Matrix elements off
+diagonal in Omega and Lambda
+
+ align:start position:0%
+diagonal in Omega and Lambda
+ 
+
+ align:start position:0%
+diagonal in Omega and Lambda
+off diagonal Omega and
+
+ align:start position:0%
+off diagonal Omega and
+ 
+
+ align:start position:0%
+off diagonal Omega and
+sigma off diagonal in Lambda and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sigma this is called L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uncoupling this is called spin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uncoupling and this is small but it's
+
+ align:start position:0%
+uncoupling and this is small but it's
+ 
+
+ align:start position:0%
+uncoupling and this is small but it's
+called rotation electronic or spin
+
+ align:start position:0%
+called rotation electronic or spin
+ 
+
+ align:start position:0%
+called rotation electronic or spin
+electronic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is what we have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consider so a basis
+
+ align:start position:0%
+consider so a basis
+ 
+
+ align:start position:0%
+consider so a basis
+set of this form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enables us to deal with all of the terms
+
+ align:start position:0%
+enables us to deal with all of the terms
+ 
+
+ align:start position:0%
+enables us to deal with all of the terms
+here now I put l in
+
+ align:start position:0%
+here now I put l in
+ 
+
+ align:start position:0%
+here now I put l in
+parentheses the reason I put l in
+
+ align:start position:0%
+parentheses the reason I put l in
+ 
+
+ align:start position:0%
+parentheses the reason I put l in
+parenthesis is that an atom a molecule
+
+ align:start position:0%
+parenthesis is that an atom a molecule
+ 
+
+ align:start position:0%
+parenthesis is that an atom a molecule
+is not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+round and or in order for the orbital
+
+ align:start position:0%
+round and or in order for the orbital
+ 
+
+ align:start position:0%
+round and or in order for the orbital
+angular momentum to be
+
+ align:start position:0%
+angular momentum to be
+ 
+
+ align:start position:0%
+angular momentum to be
+defined it needs to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+round you can think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the effect of the two nuclei on the
+
+ align:start position:0%
+uh the effect of the two nuclei on the
+ 
+
+ align:start position:0%
+uh the effect of the two nuclei on the
+wave functions around each atom there's
+
+ align:start position:0%
+wave functions around each atom there's
+ 
+
+ align:start position:0%
+wave functions around each atom there's
+a star effect it causes L to
+
+ align:start position:0%
+a star effect it causes L to
+ 
+
+ align:start position:0%
+a star effect it causes L to
+mix but it preserves the projections of
+
+ align:start position:0%
+mix but it preserves the projections of
+ 
+
+ align:start position:0%
+mix but it preserves the projections of
+L along this axis so L is totally wiped
+
+ align:start position:0%
+L along this axis so L is totally wiped
+ 
+
+ align:start position:0%
+L along this axis so L is totally wiped
+out but its projections are
+
+ align:start position:0%
+out but its projections are
+ 
+
+ align:start position:0%
+out but its projections are
+preserved so isn't that what L accounts
+
+ align:start position:0%
+preserved so isn't that what L accounts
+ 
+
+ align:start position:0%
+preserved so isn't that what L accounts
+for I'm sorry isn't L the the rejection
+
+ align:start position:0%
+for I'm sorry isn't L the the rejection
+ 
+
+ align:start position:0%
+for I'm sorry isn't L the the rejection
+Lambda is the projection of L but
+
+ align:start position:0%
+Lambda is the projection of L but
+ 
+
+ align:start position:0%
+Lambda is the projection of L but
+because of the cylindrical
+
+ align:start position:0%
+because of the cylindrical
+ 
+
+ align:start position:0%
+because of the cylindrical
+symmetry Lambda gets preserved right but
+
+ align:start position:0%
+symmetry Lambda gets preserved right but
+ 
+
+ align:start position:0%
+symmetry Lambda gets preserved right but
+L is
+
+ align:start position:0%
+L is
+ 
+
+ align:start position:0%
+L is
+destroyed okay when we lose this quantum
+
+ align:start position:0%
+destroyed okay when we lose this quantum
+ 
+
+ align:start position:0%
+destroyed okay when we lose this quantum
+number we lose the ability to evaluate
+
+ align:start position:0%
+number we lose the ability to evaluate
+ 
+
+ align:start position:0%
+number we lose the ability to evaluate
+these Matrix elements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explicitly and these Matrix element this
+
+ align:start position:0%
+explicitly and these Matrix element this
+ 
+
+ align:start position:0%
+explicitly and these Matrix element this
+Matrix element
+
+ align:start position:0%
+Matrix element
+ 
+
+ align:start position:0%
+Matrix element
+explicitly and we lose the ability to
+
+ align:start position:0%
+explicitly and we lose the ability to
+ 
+
+ align:start position:0%
+explicitly and we lose the ability to
+use KP Gordon coefficients
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to perform
+
+ align:start position:0%
+to perform
+ 
+
+ align:start position:0%
+to perform
+transformations of anger momentum from
+
+ align:start position:0%
+transformations of anger momentum from
+ 
+
+ align:start position:0%
+transformations of anger momentum from
+one coupling case to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another so it's kind of a
+
+ align:start position:0%
+another so it's kind of a
+ 
+
+ align:start position:0%
+another so it's kind of a
+tragedy but there are ways around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it the reason it's not such a bad thing
+
+ align:start position:0%
+it the reason it's not such a bad thing
+ 
+
+ align:start position:0%
+it the reason it's not such a bad thing
+is that states with different values of
+
+ align:start position:0%
+is that states with different values of
+ 
+
+ align:start position:0%
+is that states with different values of
+Lambda are usually relatively far apart
+
+ align:start position:0%
+Lambda are usually relatively far apart
+ 
+
+ align:start position:0%
+Lambda are usually relatively far apart
+states with different values of Sigma
+
+ align:start position:0%
+states with different values of Sigma
+ 
+
+ align:start position:0%
+states with different values of Sigma
+are usually close together and so we
+
+ align:start position:0%
+are usually close together and so we
+ 
+
+ align:start position:0%
+are usually close together and so we
+talk about things called multip
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+states which we denote by 2 s +1
+
+ align:start position:0%
+states which we denote by 2 s +1
+ 
+
+ align:start position:0%
+states which we denote by 2 s +1
+Lambda and these multiplet states have
+
+ align:start position:0%
+Lambda and these multiplet states have
+ 
+
+ align:start position:0%
+Lambda and these multiplet states have
+several values of Omega where Omega can
+
+ align:start position:0%
+several values of Omega where Omega can
+ 
+
+ align:start position:0%
+several values of Omega where Omega can
+go from uh Lambda Plus
+
+ align:start position:0%
+go from uh Lambda Plus
+ 
+
+ align:start position:0%
+go from uh Lambda Plus
+s down
+
+ align:start position:0%
+s down
+ 
+
+ align:start position:0%
+s down
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+Lambda minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s there's a little bit of complexity
+
+ align:start position:0%
+s there's a little bit of complexity
+ 
+
+ align:start position:0%
+s there's a little bit of complexity
+here Lambda minus in steps of
+
+ align:start position:0%
+here Lambda minus in steps of
+ 
+
+ align:start position:0%
+here Lambda minus in steps of
+one and so uh depending on whether uh
+
+ align:start position:0%
+one and so uh depending on whether uh
+ 
+
+ align:start position:0%
+one and so uh depending on whether uh
+Lambda is larger or small smaller than S
+
+ align:start position:0%
+Lambda is larger or small smaller than S
+ 
+
+ align:start position:0%
+Lambda is larger or small smaller than S
+we get a certain number of components to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s+1 and uh these states are
+
+ align:start position:0%
+s+1 and uh these states are
+ 
+
+ align:start position:0%
+s+1 and uh these states are
+essentially replications of each
+
+ align:start position:0%
+essentially replications of each
+ 
+
+ align:start position:0%
+essentially replications of each
+other we don't say for each of the
+
+ align:start position:0%
+other we don't say for each of the
+ 
+
+ align:start position:0%
+other we don't say for each of the
+omegas of a state like this we have a
+
+ align:start position:0%
+omegas of a state like this we have a
+ 
+
+ align:start position:0%
+omegas of a state like this we have a
+separate potential curve so we get a
+
+ align:start position:0%
+separate potential curve so we get a
+ 
+
+ align:start position:0%
+separate potential curve so we get a
+bunch of states that belong together in
+
+ align:start position:0%
+bunch of states that belong together in
+ 
+
+ align:start position:0%
+bunch of states that belong together in
+spectroscopy they're natural groupings
+
+ align:start position:0%
+spectroscopy they're natural groupings
+ 
+
+ align:start position:0%
+spectroscopy they're natural groupings
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+states the most common of which is
+
+ align:start position:0%
+states the most common of which is
+ 
+
+ align:start position:0%
+states the most common of which is
+called a multiplet state like triplet Pi
+
+ align:start position:0%
+called a multiplet state like triplet Pi
+ 
+
+ align:start position:0%
+called a multiplet state like triplet Pi
+or triplet Sigma or douet Sigma
+
+ align:start position:0%
+or triplet Sigma or douet Sigma
+ 
+
+ align:start position:0%
+or triplet Sigma or douet Sigma
+whatever the only time the
+
+ align:start position:0%
+whatever the only time the
+ 
+
+ align:start position:0%
+whatever the only time the
+textbook is going to give you what you
+
+ align:start position:0%
+textbook is going to give you what you
+ 
+
+ align:start position:0%
+textbook is going to give you what you
+would like for a rotational levels is
+
+ align:start position:0%
+would like for a rotational levels is
+ 
+
+ align:start position:0%
+would like for a rotational levels is
+for a state which has no spin or orbital
+
+ align:start position:0%
+for a state which has no spin or orbital
+ 
+
+ align:start position:0%
+for a state which has no spin or orbital
+Ang
+
+ align:start position:0%
+Ang
+ 
+
+ align:start position:0%
+Ang
+momentum okay then J is equal to R and
+
+ align:start position:0%
+momentum okay then J is equal to R and
+ 
+
+ align:start position:0%
+momentum okay then J is equal to R and
+everything was correct but whenever you
+
+ align:start position:0%
+everything was correct but whenever you
+ 
+
+ align:start position:0%
+everything was correct but whenever you
+have or nonzero Lambda or nonzero s or
+
+ align:start position:0%
+have or nonzero Lambda or nonzero s or
+ 
+
+ align:start position:0%
+have or nonzero Lambda or nonzero s or
+both you get these multiple States and
+
+ align:start position:0%
+both you get these multiple States and
+ 
+
+ align:start position:0%
+both you get these multiple States and
+this is a grouping of states that belong
+
+ align:start position:0%
+this is a grouping of states that belong
+ 
+
+ align:start position:0%
+this is a grouping of states that belong
+together it's a natural block
+
+ align:start position:0%
+together it's a natural block
+ 
+
+ align:start position:0%
+together it's a natural block
+diagonalization of the hamiltonian and
+
+ align:start position:0%
+diagonalization of the hamiltonian and
+ 
+
+ align:start position:0%
+diagonalization of the hamiltonian and
+the opal elements within that block
+
+ align:start position:0%
+the opal elements within that block
+ 
+
+ align:start position:0%
+the opal elements within that block
+given by
+
+ align:start position:0%
+given by
+ 
+
+ align:start position:0%
+given by
+this this is between different
+
+ align:start position:0%
+this this is between different
+ 
+
+ align:start position:0%
+this this is between different
+electronic States so that's why we
+
+ align:start position:0%
+electronic States so that's why we
+ 
+
+ align:start position:0%
+electronic States so that's why we
+aren't really so harmed by the in
+
+ align:start position:0%
+aren't really so harmed by the in
+ 
+
+ align:start position:0%
+aren't really so harmed by the in
+ability to know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B so this brings me to the last thing
+
+ align:start position:0%
+B so this brings me to the last thing
+ 
+
+ align:start position:0%
+B so this brings me to the last thing
+that I'm going to talk briefly
+
+ align:start position:0%
+that I'm going to talk briefly
+ 
+
+ align:start position:0%
+that I'm going to talk briefly
+about and that's on the bottom of page
+
+ align:start position:0%
+about and that's on the bottom of page
+ 
+
+ align:start position:0%
+about and that's on the bottom of page
+13 there is a very beautiful paper by
+
+ align:start position:0%
+13 there is a very beautiful paper by
+ 
+
+ align:start position:0%
+13 there is a very beautiful paper by
+Nikon and
+
+ align:start position:0%
+Nikon and
+ 
+
+ align:start position:0%
+Nikon and
+Zer which says okay we've got several
+
+ align:start position:0%
+Zer which says okay we've got several
+ 
+
+ align:start position:0%
+Zer which says okay we've got several
+terms in the Hamilton
+
+ align:start position:0%
+terms in the Hamilton
+ 
+
+ align:start position:0%
+terms in the Hamilton
+we have the electronic
+
+ align:start position:0%
+we have the electronic
+ 
+
+ align:start position:0%
+we have the electronic
+term we have spin orbit we have the
+
+ align:start position:0%
+term we have spin orbit we have the
+ 
+
+ align:start position:0%
+term we have spin orbit we have the
+rotational
+
+ align:start position:0%
+rotational
+ 
+
+ align:start position:0%
+rotational
+term and we're going
+
+ align:start position:0%
+term and we're going
+ 
+
+ align:start position:0%
+term and we're going
+to choose a zero order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hamiltonian which is a good
+
+ align:start position:0%
+hamiltonian which is a good
+ 
+
+ align:start position:0%
+hamiltonian which is a good
+representation of the rotational and
+
+ align:start position:0%
+representation of the rotational and
+ 
+
+ align:start position:0%
+representation of the rotational and
+fine
+
+ align:start position:0%
+fine
+ 
+
+ align:start position:0%
+fine
+structure uh that is different for each
+
+ align:start position:0%
+structure uh that is different for each
+ 
+
+ align:start position:0%
+structure uh that is different for each
+of the relative orderings of magnitudes
+
+ align:start position:0%
+of the relative orderings of magnitudes
+ 
+
+ align:start position:0%
+of the relative orderings of magnitudes
+of these terms
+
+ align:start position:0%
+of these terms
+ 
+
+ align:start position:0%
+of these terms
+so the usual
+
+ align:start position:0%
+so the usual
+ 
+
+ align:start position:0%
+so the usual
+ordering is the electronic is
+
+ align:start position:0%
+ordering is the electronic is
+ 
+
+ align:start position:0%
+ordering is the electronic is
+large compared to the spin orbit
+
+ align:start position:0%
+large compared to the spin orbit
+ 
+
+ align:start position:0%
+large compared to the spin orbit
+compared to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rotation so we have multipet
+
+ align:start position:0%
+rotation so we have multipet
+ 
+
+ align:start position:0%
+rotation so we have multipet
+States the rotation is small the spin
+
+ align:start position:0%
+States the rotation is small the spin
+ 
+
+ align:start position:0%
+States the rotation is small the spin
+orbit is Big we have multiple States and
+
+ align:start position:0%
+orbit is Big we have multiple States and
+ 
+
+ align:start position:0%
+orbit is Big we have multiple States and
+case a is what happens in this limit
+
+ align:start position:0%
+case a is what happens in this limit
+ 
+
+ align:start position:0%
+case a is what happens in this limit
+if we make spin or bit small compared to
+
+ align:start position:0%
+if we make spin or bit small compared to
+ 
+
+ align:start position:0%
+if we make spin or bit small compared to
+rotation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then then we get case
+
+ align:start position:0%
+then then we get case
+ 
+
+ align:start position:0%
+then then we get case
+b the rotational pattern forming quantum
+
+ align:start position:0%
+b the rotational pattern forming quantum
+ 
+
+ align:start position:0%
+b the rotational pattern forming quantum
+number is J here the energy levels are
+
+ align:start position:0%
+number is J here the energy levels are
+ 
+
+ align:start position:0%
+number is J here the energy levels are
+given by DJJ
+
+ align:start position:0%
+given by DJJ
+ 
+
+ align:start position:0%
+given by DJJ
++1 the rotational pattern forming
+
+ align:start position:0%
++1 the rotational pattern forming
+ 
+
+ align:start position:0%
++1 the rotational pattern forming
+quantum number is n which is defined as
+
+ align:start position:0%
+quantum number is n which is defined as
+ 
+
+ align:start position:0%
+quantum number is n which is defined as
+j- s the total momentum exclusive of
+
+ align:start position:0%
+j- s the total momentum exclusive of
+ 
+
+ align:start position:0%
+j- s the total momentum exclusive of
+Spin and the rotational pattern form
+
+ align:start position:0%
+Spin and the rotational pattern form
+ 
+
+ align:start position:0%
+Spin and the rotational pattern form
+number is n and the rotational levels
+
+ align:start position:0%
+number is n and the rotational levels
+ 
+
+ align:start position:0%
+number is n and the rotational levels
+are given by this this is often half
+
+ align:start position:0%
+are given by this this is often half
+ 
+
+ align:start position:0%
+are given by this this is often half
+integer this is always integer uh
+
+ align:start position:0%
+integer this is always integer uh
+ 
+
+ align:start position:0%
+integer this is always integer uh
+they're different the pattern of energy
+
+ align:start position:0%
+they're different the pattern of energy
+ 
+
+ align:start position:0%
+they're different the pattern of energy
+levels is different it's nice to know
+
+ align:start position:0%
+levels is different it's nice to know
+ 
+
+ align:start position:0%
+levels is different it's nice to know
+what which it's going to be so if you
+
+ align:start position:0%
+what which it's going to be so if you
+ 
+
+ align:start position:0%
+what which it's going to be so if you
+have three
+
+ align:start position:0%
+have three
+ 
+
+ align:start position:0%
+have three
+objects you can order them in six
+
+ align:start position:0%
+objects you can order them in six
+ 
+
+ align:start position:0%
+objects you can order them in six
+different ways
+
+ align:start position:0%
+different ways
+ 
+
+ align:start position:0%
+different ways
+and they correspond to H's cases A B C D
+
+ align:start position:0%
+and they correspond to H's cases A B C D
+ 
+
+ align:start position:0%
+and they correspond to H's cases A B C D
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+nothing d e and nothing
\ No newline at end of file
diff --git a/qA83eznsKp8.txt b/qA83eznsKp8.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0f3c29c848474f24fba49f7abd30d6477fcd0710
--- /dev/null
+++ b/qA83eznsKp8.txt
@@ -0,0 +1,3331 @@
+align:start position:0%
+ 
+Hi, welcome back to recitation. In
+
+ align:start position:0%
+Hi, welcome back to recitation. In
+ 
+
+ align:start position:0%
+Hi, welcome back to recitation. In
+lecture, you've been learning about
+
+ align:start position:0%
+lecture, you've been learning about
+ 
+
+ align:start position:0%
+lecture, you've been learning about
+triple integration and I have a problem
+
+ align:start position:0%
+triple integration and I have a problem
+ 
+
+ align:start position:0%
+triple integration and I have a problem
+here for you on computing a volume of a
+
+ align:start position:0%
+here for you on computing a volume of a
+ 
+
+ align:start position:0%
+here for you on computing a volume of a
+region using a triple integral. So,
+
+ align:start position:0%
+region using a triple integral. So,
+ 
+
+ align:start position:0%
+region using a triple integral. So,
+let's look at this. So, I have a volume
+
+ align:start position:0%
+let's look at this. So, I have a volume
+ 
+
+ align:start position:0%
+let's look at this. So, I have a volume
+and I'm describing it to you. It's the
+
+ align:start position:0%
+and I'm describing it to you. It's the
+ 
+
+ align:start position:0%
+and I'm describing it to you. It's the
+volume uh inside the paraboid z = x^2 +
+
+ align:start position:0%
+volume uh inside the paraboid z = x^2 +
+ 
+
+ align:start position:0%
+volume uh inside the paraboid z = x^2 +
+y^2 and bounded by the plane z = 2 y. So
+
+ align:start position:0%
+y^2 and bounded by the plane z = 2 y. So
+ 
+
+ align:start position:0%
+y^2 and bounded by the plane z = 2 y. So
+I've drawn a little picture here for
+
+ align:start position:0%
+I've drawn a little picture here for
+ 
+
+ align:start position:0%
+I've drawn a little picture here for
+you. So this is the this is the paraboid
+
+ align:start position:0%
+you. So this is the this is the paraboid
+ 
+
+ align:start position:0%
+you. So this is the this is the paraboid
+here. And we're just sort of taking a
+
+ align:start position:0%
+here. And we're just sort of taking a
+ 
+
+ align:start position:0%
+here. And we're just sort of taking a
+plain cut of it. And so this is going to
+
+ align:start position:0%
+plain cut of it. And so this is going to
+ 
+
+ align:start position:0%
+plain cut of it. And so this is going to
+slice off some chunk of that paraboid.
+
+ align:start position:0%
+slice off some chunk of that paraboid.
+ 
+
+ align:start position:0%
+slice off some chunk of that paraboid.
+And what I want to know is what's the
+
+ align:start position:0%
+And what I want to know is what's the
+ 
+
+ align:start position:0%
+And what I want to know is what's the
+what's the volume of that of that piece
+
+ align:start position:0%
+what's the volume of that of that piece
+ 
+
+ align:start position:0%
+what's the volume of that of that piece
+that gets cut off by that plane there.
+
+ align:start position:0%
+that gets cut off by that plane there.
+ 
+
+ align:start position:0%
+that gets cut off by that plane there.
+So below the plane and above the
+
+ align:start position:0%
+So below the plane and above the
+ 
+
+ align:start position:0%
+So below the plane and above the
+paraboid. So why don't you pause the
+
+ align:start position:0%
+paraboid. So why don't you pause the
+ 
+
+ align:start position:0%
+paraboid. So why don't you pause the
+video, take some time, work out this
+
+ align:start position:0%
+video, take some time, work out this
+ 
+
+ align:start position:0%
+video, take some time, work out this
+problem, come back and we can work on it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together. I hope you had some luck with
+
+ align:start position:0%
+together. I hope you had some luck with
+ 
+
+ align:start position:0%
+together. I hope you had some luck with
+this problem. I think it's a bit of a
+
+ align:start position:0%
+this problem. I think it's a bit of a
+ 
+
+ align:start position:0%
+this problem. I think it's a bit of a
+tricky one. So let's start to work
+
+ align:start position:0%
+tricky one. So let's start to work
+ 
+
+ align:start position:0%
+tricky one. So let's start to work
+through it together. Um, so sometimes
+
+ align:start position:0%
+through it together. Um, so sometimes
+ 
+
+ align:start position:0%
+through it together. Um, so sometimes
+you have a problem with a triple
+
+ align:start position:0%
+you have a problem with a triple
+ 
+
+ align:start position:0%
+you have a problem with a triple
+integral and you know you need to set up
+
+ align:start position:0%
+integral and you know you need to set up
+ 
+
+ align:start position:0%
+integral and you know you need to set up
+your bounds of integration and sometimes
+
+ align:start position:0%
+your bounds of integration and sometimes
+ 
+
+ align:start position:0%
+your bounds of integration and sometimes
+you can look at it and it's just clear
+
+ align:start position:0%
+you can look at it and it's just clear
+ 
+
+ align:start position:0%
+you can look at it and it's just clear
+what they are. You know if you're
+
+ align:start position:0%
+what they are. You know if you're
+ 
+
+ align:start position:0%
+what they are. You know if you're
+integrating over a cube life is really
+
+ align:start position:0%
+integrating over a cube life is really
+ 
+
+ align:start position:0%
+integrating over a cube life is really
+easy. Um, but in this case this this
+
+ align:start position:0%
+easy. Um, but in this case this this
+ 
+
+ align:start position:0%
+easy. Um, but in this case this this
+region that we want to integrate over is
+
+ align:start position:0%
+region that we want to integrate over is
+ 
+
+ align:start position:0%
+region that we want to integrate over is
+kind of more complicated to understand,
+
+ align:start position:0%
+kind of more complicated to understand,
+ 
+
+ align:start position:0%
+kind of more complicated to understand,
+right? So it's easy to see well
+
+ align:start position:0%
+right? So it's easy to see well
+ 
+
+ align:start position:0%
+right? So it's easy to see well
+relatively easy to see what the bounds
+
+ align:start position:0%
+relatively easy to see what the bounds
+ 
+
+ align:start position:0%
+relatively easy to see what the bounds
+on Z are. So let's let me draw a couple
+
+ align:start position:0%
+on Z are. So let's let me draw a couple
+ 
+
+ align:start position:0%
+on Z are. So let's let me draw a couple
+of one one two-dimensional picture. So
+
+ align:start position:0%
+of one one two-dimensional picture. So
+ 
+
+ align:start position:0%
+of one one two-dimensional picture. So
+let's I'm going to draw the the the YZ
+
+ align:start position:0%
+let's I'm going to draw the the the YZ
+ 
+
+ align:start position:0%
+let's I'm going to draw the the the YZ
+plane cross-section
+
+ align:start position:0%
+plane cross-section
+ 
+
+ align:start position:0%
+plane cross-section
+here. So in the YZ plane cross-section
+
+ align:start position:0%
+here. So in the YZ plane cross-section
+ 
+
+ align:start position:0%
+here. So in the YZ plane cross-section
+this paraboid
+
+ align:start position:0%
+this paraboid
+ 
+
+ align:start position:0%
+this paraboid
+just becomes a parabola. So that becomes
+
+ align:start position:0%
+just becomes a parabola. So that becomes
+ 
+
+ align:start position:0%
+just becomes a parabola. So that becomes
+the parabola Z = Y^2 which is you know a
+
+ align:start position:0%
+the parabola Z = Y^2 which is you know a
+ 
+
+ align:start position:0%
+the parabola Z = Y^2 which is you know a
+plain section of the paraboid Z = X^2 +
+
+ align:start position:0%
+plain section of the paraboid Z = X^2 +
+ 
+
+ align:start position:0%
+plain section of the paraboid Z = X^2 +
+Y^2. And this plane z = 2y becomes the
+
+ align:start position:0%
+Y^2. And this plane z = 2y becomes the
+ 
+
+ align:start position:0%
+Y^2. And this plane z = 2y becomes the
+line z =
+
+ align:start position:0%
+line z =
+ 
+
+ align:start position:0%
+line z =
+2y. So and this little sliver is a plain
+
+ align:start position:0%
+2y. So and this little sliver is a plain
+ 
+
+ align:start position:0%
+2y. So and this little sliver is a plain
+section of the region in question. So we
+
+ align:start position:0%
+section of the region in question. So we
+ 
+
+ align:start position:0%
+section of the region in question. So we
+see that z is going from the paraboid to
+
+ align:start position:0%
+see that z is going from the paraboid to
+ 
+
+ align:start position:0%
+see that z is going from the paraboid to
+the plane. Um and over here we see that
+
+ align:start position:0%
+the plane. Um and over here we see that
+ 
+
+ align:start position:0%
+the plane. Um and over here we see that
+z is going from the paraboid to the
+
+ align:start position:0%
+z is going from the paraboid to the
+ 
+
+ align:start position:0%
+z is going from the paraboid to the
+plane. But what we need really need to
+
+ align:start position:0%
+plane. But what we need really need to
+ 
+
+ align:start position:0%
+plane. But what we need really need to
+understand then is what the relationship
+
+ align:start position:0%
+understand then is what the relationship
+ 
+
+ align:start position:0%
+understand then is what the relationship
+between x and y is. So what is the
+
+ align:start position:0%
+between x and y is. So what is the
+ 
+
+ align:start position:0%
+between x and y is. So what is the
+shadow of this region? how how are X and
+
+ align:start position:0%
+shadow of this region? how how are X and
+ 
+
+ align:start position:0%
+shadow of this region? how how are X and
+Y related to each other, how can we
+
+ align:start position:0%
+Y related to each other, how can we
+ 
+
+ align:start position:0%
+Y related to each other, how can we
+bound X in terms of Y or Y in terms of X
+
+ align:start position:0%
+bound X in terms of Y or Y in terms of X
+ 
+
+ align:start position:0%
+bound X in terms of Y or Y in terms of X
+or you know should we use cylindrical
+
+ align:start position:0%
+or you know should we use cylindrical
+ 
+
+ align:start position:0%
+or you know should we use cylindrical
+coordinates or what? Um and so in order
+
+ align:start position:0%
+coordinates or what? Um and so in order
+ 
+
+ align:start position:0%
+coordinates or what? Um and so in order
+to do that what we need to do is we need
+
+ align:start position:0%
+to do that what we need to do is we need
+ 
+
+ align:start position:0%
+to do that what we need to do is we need
+to figure out when you when you project
+
+ align:start position:0%
+to figure out when you when you project
+ 
+
+ align:start position:0%
+to figure out when you when you project
+this region down when you when you
+
+ align:start position:0%
+this region down when you when you
+ 
+
+ align:start position:0%
+this region down when you when you
+flatten it along Z so you're you're
+
+ align:start position:0%
+flatten it along Z so you're you're
+ 
+
+ align:start position:0%
+flatten it along Z so you're you're
+disregarding Z now and then you're just
+
+ align:start position:0%
+disregarding Z now and then you're just
+ 
+
+ align:start position:0%
+disregarding Z now and then you're just
+looking at its shadow its footprint in
+
+ align:start position:0%
+looking at its shadow its footprint in
+ 
+
+ align:start position:0%
+looking at its shadow its footprint in
+the in the XY plane. You want to figure
+
+ align:start position:0%
+the in the XY plane. You want to figure
+ 
+
+ align:start position:0%
+the in the XY plane. You want to figure
+out what what is that region? What does
+
+ align:start position:0%
+out what what is that region? What does
+ 
+
+ align:start position:0%
+out what what is that region? What does
+it look like? So you know somehow we'll
+
+ align:start position:0%
+it look like? So you know somehow we'll
+ 
+
+ align:start position:0%
+it look like? So you know somehow we'll
+project down there'll be some region
+
+ align:start position:0%
+project down there'll be some region
+ 
+
+ align:start position:0%
+project down there'll be some region
+R down here. So I'll call this region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R and that region will be the projection
+
+ align:start position:0%
+R and that region will be the projection
+ 
+
+ align:start position:0%
+R and that region will be the projection
+of this of this solid region down and it
+
+ align:start position:0%
+of this of this solid region down and it
+ 
+
+ align:start position:0%
+of this of this solid region down and it
+has some boundary curve C say the
+
+ align:start position:0%
+has some boundary curve C say the
+ 
+
+ align:start position:0%
+has some boundary curve C say the
+boundary curve of the region R. um just
+
+ align:start position:0%
+boundary curve of the region R. um just
+ 
+
+ align:start position:0%
+boundary curve of the region R. um just
+you know in case we need to refer to
+
+ align:start position:0%
+you know in case we need to refer to
+ 
+
+ align:start position:0%
+you know in case we need to refer to
+them later it's good to give them
+
+ align:start position:0%
+them later it's good to give them
+ 
+
+ align:start position:0%
+them later it's good to give them
+letters so that we can so that they have
+
+ align:start position:0%
+letters so that we can so that they have
+ 
+
+ align:start position:0%
+letters so that we can so that they have
+names. So what we need to figure out now
+
+ align:start position:0%
+names. So what we need to figure out now
+ 
+
+ align:start position:0%
+names. So what we need to figure out now
+is what is this region R. Now this is
+
+ align:start position:0%
+is what is this region R. Now this is
+ 
+
+ align:start position:0%
+is what is this region R. Now this is
+tough to do by just sort of intuitive
+
+ align:start position:0%
+tough to do by just sort of intuitive
+ 
+
+ align:start position:0%
+tough to do by just sort of intuitive
+reasoning or just by looking at this
+
+ align:start position:0%
+reasoning or just by looking at this
+ 
+
+ align:start position:0%
+reasoning or just by looking at this
+picture that I've drawn. So in this case
+
+ align:start position:0%
+picture that I've drawn. So in this case
+ 
+
+ align:start position:0%
+picture that I've drawn. So in this case
+we're kind of forced to use some
+
+ align:start position:0%
+we're kind of forced to use some
+ 
+
+ align:start position:0%
+we're kind of forced to use some
+algebra. All right. So what do we know
+
+ align:start position:0%
+algebra. All right. So what do we know
+ 
+
+ align:start position:0%
+algebra. All right. So what do we know
+about about this region R and this curve
+
+ align:start position:0%
+about about this region R and this curve
+ 
+
+ align:start position:0%
+about about this region R and this curve
+C? Well C is what we get. It's the
+
+ align:start position:0%
+C? Well C is what we get. It's the
+ 
+
+ align:start position:0%
+C? Well C is what we get. It's the
+projection downwards of the
+
+ align:start position:0%
+projection downwards of the
+ 
+
+ align:start position:0%
+projection downwards of the
+curve of intersection of this plane with
+
+ align:start position:0%
+curve of intersection of this plane with
+ 
+
+ align:start position:0%
+curve of intersection of this plane with
+this paraboid. Right? So it's the
+
+ align:start position:0%
+this paraboid. Right? So it's the
+ 
+
+ align:start position:0%
+this paraboid. Right? So it's the
+projection down of this curve of
+
+ align:start position:0%
+projection down of this curve of
+ 
+
+ align:start position:0%
+projection down of this curve of
+intersection. So what does that mean
+
+ align:start position:0%
+intersection. So what does that mean
+ 
+
+ align:start position:0%
+intersection. So what does that mean
+about its equation? Well, it means it's
+
+ align:start position:0%
+about its equation? Well, it means it's
+ 
+
+ align:start position:0%
+about its equation? Well, it means it's
+what we get if we set uh these two, you
+
+ align:start position:0%
+what we get if we set uh these two, you
+ 
+
+ align:start position:0%
+what we get if we set uh these two, you
+know, if we if we solve for Z in one of
+
+ align:start position:0%
+know, if we if we solve for Z in one of
+ 
+
+ align:start position:0%
+know, if we if we solve for Z in one of
+the two equations of the surfaces and
+
+ align:start position:0%
+the two equations of the surfaces and
+ 
+
+ align:start position:0%
+the two equations of the surfaces and
+plug it into the other, and that'll give
+
+ align:start position:0%
+plug it into the other, and that'll give
+ 
+
+ align:start position:0%
+plug it into the other, and that'll give
+us an equation with just X and Y, and
+
+ align:start position:0%
+us an equation with just X and Y, and
+ 
+
+ align:start position:0%
+us an equation with just X and Y, and
+that will be the equation of this curve
+
+ align:start position:0%
+that will be the equation of this curve
+ 
+
+ align:start position:0%
+that will be the equation of this curve
+C.
+
+ align:start position:0%
+C.
+ 
+
+ align:start position:0%
+C.
+Okay. So in our case that means that we
+
+ align:start position:0%
+Okay. So in our case that means that we
+ 
+
+ align:start position:0%
+Okay. So in our case that means that we
+have to so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C is given by this equation x^2 + y^2 =
+
+ align:start position:0%
+C is given by this equation x^2 + y^2 =
+ 
+
+ align:start position:0%
+C is given by this equation x^2 + y^2 =
+2 y. All right. So whenever x^2 + y^2 =
+
+ align:start position:0%
+2 y. All right. So whenever x^2 + y^2 =
+ 
+
+ align:start position:0%
+2 y. All right. So whenever x^2 + y^2 =
+2 y that's a point xy such that the
+
+ align:start position:0%
+2 y that's a point xy such that the
+ 
+
+ align:start position:0%
+2 y that's a point xy such that the
+directly above that point is a place
+
+ align:start position:0%
+directly above that point is a place
+ 
+
+ align:start position:0%
+directly above that point is a place
+where the plane intersects the the
+
+ align:start position:0%
+where the plane intersects the the
+ 
+
+ align:start position:0%
+where the plane intersects the the
+paraboid. Well okay. So what is this
+
+ align:start position:0%
+paraboid. Well okay. So what is this
+ 
+
+ align:start position:0%
+paraboid. Well okay. So what is this
+curve? Well, a little bit of algebra can
+
+ align:start position:0%
+curve? Well, a little bit of algebra can
+ 
+
+ align:start position:0%
+curve? Well, a little bit of algebra can
+help us sort that out. If you bring the
+
+ align:start position:0%
+help us sort that out. If you bring the
+ 
+
+ align:start position:0%
+help us sort that out. If you bring the
+2 y over here and complete the square,
+
+ align:start position:0%
+2 y over here and complete the square,
+ 
+
+ align:start position:0%
+2 y over here and complete the square,
+you you can see that we can rewrite this
+
+ align:start position:0%
+you you can see that we can rewrite this
+ 
+
+ align:start position:0%
+you you can see that we can rewrite this
+as x^2 + y -1^ 2 = 1. I've just I've
+
+ align:start position:0%
+as x^2 + y -1^ 2 = 1. I've just I've
+ 
+
+ align:start position:0%
+as x^2 + y -1^ 2 = 1. I've just I've
+brought the 2 y over. I've added one to
+
+ align:start position:0%
+brought the 2 y over. I've added one to
+ 
+
+ align:start position:0%
+brought the 2 y over. I've added one to
+both sides and I've
+
+ align:start position:0%
+both sides and I've
+ 
+
+ align:start position:0%
+both sides and I've
+I've factored this the y part. And so
+
+ align:start position:0%
+I've factored this the y part. And so
+ 
+
+ align:start position:0%
+I've factored this the y part. And so
+this equation this is an easy equation
+
+ align:start position:0%
+this equation this is an easy equation
+ 
+
+ align:start position:0%
+this equation this is an easy equation
+to recognize. This is the equation of a
+
+ align:start position:0%
+to recognize. This is the equation of a
+ 
+
+ align:start position:0%
+to recognize. This is the equation of a
+circle uh with center 01 and radius one.
+
+ align:start position:0%
+circle uh with center 01 and radius one.
+ 
+
+ align:start position:0%
+circle uh with center 01 and radius one.
+So let's let's draw that then. So here's
+
+ align:start position:0%
+So let's let's draw that then. So here's
+ 
+
+ align:start position:0%
+So let's let's draw that then. So here's
+a picture of what the shadow looks like
+
+ align:start position:0%
+a picture of what the shadow looks like
+ 
+
+ align:start position:0%
+a picture of what the shadow looks like
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+the xy plane. So it's at the center is
+
+ align:start position:0%
+the xy plane. So it's at the center is
+ 
+
+ align:start position:0%
+the xy plane. So it's at the center is
+at height one and then it's
+
+ align:start position:0%
+at height one and then it's
+ 
+
+ align:start position:0%
+at height one and then it's
+this circle. Uh that's almost a circle.
+
+ align:start position:0%
+this circle. Uh that's almost a circle.
+ 
+
+ align:start position:0%
+this circle. Uh that's almost a circle.
+Looks enough like a circle for my
+
+ align:start position:0%
+Looks enough like a circle for my
+ 
+
+ align:start position:0%
+Looks enough like a circle for my
+purposes. So this is the region R. It's
+
+ align:start position:0%
+purposes. So this is the region R. It's
+ 
+
+ align:start position:0%
+purposes. So this is the region R. It's
+a circular region of radius one with
+
+ align:start position:0%
+a circular region of radius one with
+ 
+
+ align:start position:0%
+a circular region of radius one with
+center 01.
+
+ align:start position:0%
+center 01.
+ 
+
+ align:start position:0%
+center 01.
+Okay, great. So, I'm gonna just shade
+
+ align:start position:0%
+Okay, great. So, I'm gonna just shade
+ 
+
+ align:start position:0%
+Okay, great. So, I'm gonna just shade
+that in again because I like doing that.
+
+ align:start position:0%
+that in again because I like doing that.
+ 
+
+ align:start position:0%
+that in again because I like doing that.
+Okay, so that's that's the region R.
+
+ align:start position:0%
+Okay, so that's that's the region R.
+ 
+
+ align:start position:0%
+Okay, so that's that's the region R.
+That is So, what is this region R? It's
+
+ align:start position:0%
+That is So, what is this region R? It's
+ 
+
+ align:start position:0%
+That is So, what is this region R? It's
+the shadow of our solid region. Let's
+
+ align:start position:0%
+the shadow of our solid region. Let's
+ 
+
+ align:start position:0%
+the shadow of our solid region. Let's
+look back over here. It's the shadow of
+
+ align:start position:0%
+look back over here. It's the shadow of
+ 
+
+ align:start position:0%
+look back over here. It's the shadow of
+our solid region in the xy plane. So,
+
+ align:start position:0%
+our solid region in the xy plane. So,
+ 
+
+ align:start position:0%
+our solid region in the xy plane. So,
+when you project down, that's the region
+
+ align:start position:0%
+when you project down, that's the region
+ 
+
+ align:start position:0%
+when you project down, that's the region
+that you get. So, why do we need that?
+
+ align:start position:0%
+that you get. So, why do we need that?
+ 
+
+ align:start position:0%
+that you get. So, why do we need that?
+Because that tells us, so we know when
+
+ align:start position:0%
+Because that tells us, so we know when
+ 
+
+ align:start position:0%
+Because that tells us, so we know when
+we set up this triple integral, Z is
+
+ align:start position:0%
+we set up this triple integral, Z is
+ 
+
+ align:start position:0%
+we set up this triple integral, Z is
+going to be going from the paraboid up
+
+ align:start position:0%
+going to be going from the paraboid up
+ 
+
+ align:start position:0%
+going to be going from the paraboid up
+to the plane. But then we're going to
+
+ align:start position:0%
+to the plane. But then we're going to
+ 
+
+ align:start position:0%
+to the plane. But then we're going to
+need on the that's that's going to be
+
+ align:start position:0%
+need on the that's that's going to be
+ 
+
+ align:start position:0%
+need on the that's that's going to be
+the innermost integral. But then the
+
+ align:start position:0%
+the innermost integral. But then the
+ 
+
+ align:start position:0%
+the innermost integral. But then the
+middle integral is going to be you know
+
+ align:start position:0%
+middle integral is going to be you know
+ 
+
+ align:start position:0%
+middle integral is going to be you know
+y in terms of x or x in terms of y or if
+
+ align:start position:0%
+y in terms of x or x in terms of y or if
+ 
+
+ align:start position:0%
+y in terms of x or x in terms of y or if
+we do polar coordinates it's going to be
+
+ align:start position:0%
+we do polar coordinates it's going to be
+ 
+
+ align:start position:0%
+we do polar coordinates it's going to be
+you know cylindrical coordinates it's
+
+ align:start position:0%
+you know cylindrical coordinates it's
+ 
+
+ align:start position:0%
+you know cylindrical coordinates it's
+going to be r in terms of theta. So we
+
+ align:start position:0%
+going to be r in terms of theta. So we
+ 
+
+ align:start position:0%
+going to be r in terms of theta. So we
+need to figure out sort of what what the
+
+ align:start position:0%
+need to figure out sort of what what the
+ 
+
+ align:start position:0%
+need to figure out sort of what what the
+boundary is what that region looks like
+
+ align:start position:0%
+boundary is what that region looks like
+ 
+
+ align:start position:0%
+boundary is what that region looks like
+over which we'll be integrating um for
+
+ align:start position:0%
+over which we'll be integrating um for
+ 
+
+ align:start position:0%
+over which we'll be integrating um for
+those for the outer two integrals. So
+
+ align:start position:0%
+those for the outer two integrals. So
+ 
+
+ align:start position:0%
+those for the outer two integrals. So
+okay so well okay so now I've been
+
+ align:start position:0%
+okay so well okay so now I've been
+ 
+
+ align:start position:0%
+okay so well okay so now I've been
+saying oh we could use cylindrical we
+
+ align:start position:0%
+saying oh we could use cylindrical we
+ 
+
+ align:start position:0%
+saying oh we could use cylindrical we
+could use rectangular. What do we want
+
+ align:start position:0%
+could use rectangular. What do we want
+ 
+
+ align:start position:0%
+could use rectangular. What do we want
+to use? Well, so this is a circle. It's
+
+ align:start position:0%
+to use? Well, so this is a circle. It's
+ 
+
+ align:start position:0%
+to use? Well, so this is a circle. It's
+a circle. It's not centered at the at
+
+ align:start position:0%
+a circle. It's not centered at the at
+ 
+
+ align:start position:0%
+a circle. It's not centered at the at
+the origin, but it is tangent to one of
+
+ align:start position:0%
+the origin, but it is tangent to one of
+ 
+
+ align:start position:0%
+the origin, but it is tangent to one of
+the axes at the origin. Um, so this is a
+
+ align:start position:0%
+the axes at the origin. Um, so this is a
+ 
+
+ align:start position:0%
+the axes at the origin. Um, so this is a
+nice a reasonably nice situation to to
+
+ align:start position:0%
+nice a reasonably nice situation to to
+ 
+
+ align:start position:0%
+nice a reasonably nice situation to to
+to do polar coordinates in. Now, you
+
+ align:start position:0%
+to do polar coordinates in. Now, you
+ 
+
+ align:start position:0%
+to do polar coordinates in. Now, you
+have to remember you have to remember
+
+ align:start position:0%
+have to remember you have to remember
+ 
+
+ align:start position:0%
+have to remember you have to remember
+back from when you learn or cylindrical
+
+ align:start position:0%
+back from when you learn or cylindrical
+ 
+
+ align:start position:0%
+back from when you learn or cylindrical
+coordinates. You have to remember um
+
+ align:start position:0%
+coordinates. You have to remember um
+ 
+
+ align:start position:0%
+coordinates. You have to remember um
+from when you learned cylindrical and
+
+ align:start position:0%
+from when you learned cylindrical and
+ 
+
+ align:start position:0%
+from when you learned cylindrical and
+polar coordinates what what the equation
+
+ align:start position:0%
+polar coordinates what what the equation
+ 
+
+ align:start position:0%
+polar coordinates what what the equation
+of such a circle is. And so I'm gonna
+
+ align:start position:0%
+of such a circle is. And so I'm gonna
+ 
+
+ align:start position:0%
+of such a circle is. And so I'm gonna
+write it down here and and I'm going to
+
+ align:start position:0%
+write it down here and and I'm going to
+ 
+
+ align:start position:0%
+write it down here and and I'm going to
+invite you to go uh look up why this is
+
+ align:start position:0%
+invite you to go uh look up why this is
+ 
+
+ align:start position:0%
+invite you to go uh look up why this is
+true if you don't remember um that this
+
+ align:start position:0%
+true if you don't remember um that this
+ 
+
+ align:start position:0%
+true if you don't remember um that this
+that this curve has equation in polar.
+
+ align:start position:0%
+that this curve has equation in polar.
+ 
+
+ align:start position:0%
+that this curve has equation in polar.
+So this is the these are the x and y
+
+ align:start position:0%
+So this is the these are the x and y
+ 
+
+ align:start position:0%
+So this is the these are the x and y
+axes here. So this equation sorry this
+
+ align:start position:0%
+axes here. So this equation sorry this
+ 
+
+ align:start position:0%
+axes here. So this equation sorry this
+curve has in polar coordinates the
+
+ align:start position:0%
+curve has in polar coordinates the
+ 
+
+ align:start position:0%
+curve has in polar coordinates the
+equation r = 2 sin
+
+ align:start position:0%
+equation r = 2 sin
+ 
+
+ align:start position:0%
+equation r = 2 sin
+theta. All right. So that gives me this
+
+ align:start position:0%
+theta. All right. So that gives me this
+ 
+
+ align:start position:0%
+theta. All right. So that gives me this
+curve here, the outer boundary. And now
+
+ align:start position:0%
+curve here, the outer boundary. And now
+ 
+
+ align:start position:0%
+curve here, the outer boundary. And now
+what I want is I don't just want the
+
+ align:start position:0%
+what I want is I don't just want the
+ 
+
+ align:start position:0%
+what I want is I don't just want the
+curve. I want to integrate over the
+
+ align:start position:0%
+curve. I want to integrate over the
+ 
+
+ align:start position:0%
+curve. I want to integrate over the
+whole region. Um, and I want to
+
+ align:start position:0%
+whole region. Um, and I want to
+ 
+
+ align:start position:0%
+whole region. Um, and I want to
+integrate over it once. Remember polar
+
+ align:start position:0%
+integrate over it once. Remember polar
+ 
+
+ align:start position:0%
+integrate over it once. Remember polar
+coordinates are a little tricky because
+
+ align:start position:0%
+coordinates are a little tricky because
+ 
+
+ align:start position:0%
+coordinates are a little tricky because
+you have to worry about are you
+
+ align:start position:0%
+you have to worry about are you
+ 
+
+ align:start position:0%
+you have to worry about are you
+overlapping and so on. Um, so so how
+
+ align:start position:0%
+overlapping and so on. Um, so so how
+ 
+
+ align:start position:0%
+overlapping and so on. Um, so so how
+does this work? At at at theta equals 0,
+
+ align:start position:0%
+does this work? At at at theta equals 0,
+ 
+
+ align:start position:0%
+does this work? At at at theta equals 0,
+we're at the origin and then as theta
+
+ align:start position:0%
+we're at the origin and then as theta
+ 
+
+ align:start position:0%
+we're at the origin and then as theta
+grows, um, we we get further and further
+
+ align:start position:0%
+grows, um, we we get further and further
+ 
+
+ align:start position:0%
+grows, um, we we get further and further
+away. So we are sort of this is
+
+ align:start position:0%
+away. So we are sort of this is
+ 
+
+ align:start position:0%
+away. So we are sort of this is
+our radius growing out and then at pi /
+
+ align:start position:0%
+our radius growing out and then at pi /
+ 
+
+ align:start position:0%
+our radius growing out and then at pi /
+2 we're at the top point of the circle
+
+ align:start position:0%
+2 we're at the top point of the circle
+ 
+
+ align:start position:0%
+2 we're at the top point of the circle
+and then as it comes back into pi it
+
+ align:start position:0%
+and then as it comes back into pi it
+ 
+
+ align:start position:0%
+and then as it comes back into pi it
+comes back in. So we want theta from
+
+ align:start position:0%
+comes back in. So we want theta from
+ 
+
+ align:start position:0%
+comes back in. So we want theta from
+going from 0 less than or equal to theta
+
+ align:start position:0%
+going from 0 less than or equal to theta
+ 
+
+ align:start position:0%
+going from 0 less than or equal to theta
+less than or equal to pi here. So at pi
+
+ align:start position:0%
+less than or equal to pi here. So at pi
+ 
+
+ align:start position:0%
+less than or equal to pi here. So at pi
+over 2 it's at the top and at pi it
+
+ align:start position:0%
+over 2 it's at the top and at pi it
+ 
+
+ align:start position:0%
+over 2 it's at the top and at pi it
+comes back for the first time. And what
+
+ align:start position:0%
+comes back for the first time. And what
+ 
+
+ align:start position:0%
+comes back for the first time. And what
+about r? Well it looks like r has to go
+
+ align:start position:0%
+about r? Well it looks like r has to go
+ 
+
+ align:start position:0%
+about r? Well it looks like r has to go
+all the way out to 2 sin theta. And in
+
+ align:start position:0%
+all the way out to 2 sin theta. And in
+ 
+
+ align:start position:0%
+all the way out to 2 sin theta. And in
+fact we always want it to start at the
+
+ align:start position:0%
+fact we always want it to start at the
+ 
+
+ align:start position:0%
+fact we always want it to start at the
+origin. So we always want r to go from
+
+ align:start position:0%
+origin. So we always want r to go from
+ 
+
+ align:start position:0%
+origin. So we always want r to go from
+zero to this outer boundary 2 sin theta.
+
+ align:start position:0%
+zero to this outer boundary 2 sin theta.
+ 
+
+ align:start position:0%
+zero to this outer boundary 2 sin theta.
+So this describes this this region big r
+
+ align:start position:0%
+So this describes this this region big r
+ 
+
+ align:start position:0%
+So this describes this this region big r
+that we're trying to integrate over this
+
+ align:start position:0%
+that we're trying to integrate over this
+ 
+
+ align:start position:0%
+that we're trying to integrate over this
+circular region in polar coordinates. So
+
+ align:start position:0%
+circular region in polar coordinates. So
+ 
+
+ align:start position:0%
+circular region in polar coordinates. So
+okay. So so it's a fairly easy
+
+ align:start position:0%
+okay. So so it's a fairly easy
+ 
+
+ align:start position:0%
+okay. So so it's a fairly easy
+description of polar coordinates. You
+
+ align:start position:0%
+description of polar coordinates. You
+ 
+
+ align:start position:0%
+description of polar coordinates. You
+could also describe it in rectangular
+
+ align:start position:0%
+could also describe it in rectangular
+ 
+
+ align:start position:0%
+could also describe it in rectangular
+coordinates and you could try to solve
+
+ align:start position:0%
+coordinates and you could try to solve
+ 
+
+ align:start position:0%
+coordinates and you could try to solve
+the problem that way. Um, I'm not going
+
+ align:start position:0%
+the problem that way. Um, I'm not going
+ 
+
+ align:start position:0%
+the problem that way. Um, I'm not going
+to do it for you, but but you could give
+
+ align:start position:0%
+to do it for you, but but you could give
+ 
+
+ align:start position:0%
+to do it for you, but but you could give
+it a shot and and see if you can come
+
+ align:start position:0%
+it a shot and and see if you can come
+ 
+
+ align:start position:0%
+it a shot and and see if you can come
+out with the same answer in the end that
+
+ align:start position:0%
+out with the same answer in the end that
+ 
+
+ align:start position:0%
+out with the same answer in the end that
+we do.
+
+ align:start position:0%
+we do.
+ 
+
+ align:start position:0%
+we do.
+Um, so okay. So now what have we done?
+
+ align:start position:0%
+Um, so okay. So now what have we done?
+ 
+
+ align:start position:0%
+Um, so okay. So now what have we done?
+Well, we we know I haven't written our
+
+ align:start position:0%
+Well, we we know I haven't written our
+ 
+
+ align:start position:0%
+Well, we we know I haven't written our
+bounds on let me write our bounds on Z
+
+ align:start position:0%
+bounds on let me write our bounds on Z
+ 
+
+ align:start position:0%
+bounds on let me write our bounds on Z
+right here. So we know that Z is going
+
+ align:start position:0%
+right here. So we know that Z is going
+ 
+
+ align:start position:0%
+right here. So we know that Z is going
+from the paraboid. So that's from if we
+
+ align:start position:0%
+from the paraboid. So that's from if we
+ 
+
+ align:start position:0%
+from the paraboid. So that's from if we
+look at the paraboid Z = X^2 + Y^2. But
+
+ align:start position:0%
+look at the paraboid Z = X^2 + Y^2. But
+ 
+
+ align:start position:0%
+look at the paraboid Z = X^2 + Y^2. But
+we're working in cylindrical coordinates
+
+ align:start position:0%
+we're working in cylindrical coordinates
+ 
+
+ align:start position:0%
+we're working in cylindrical coordinates
+now. So we need to write this in terms
+
+ align:start position:0%
+now. So we need to write this in terms
+ 
+
+ align:start position:0%
+now. So we need to write this in terms
+of r and theta. So that's z is going
+
+ align:start position:0%
+of r and theta. So that's z is going
+ 
+
+ align:start position:0%
+of r and theta. So that's z is going
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+r^2 and it's going up to the plane z = 2
+
+ align:start position:0%
+r^2 and it's going up to the plane z = 2
+ 
+
+ align:start position:0%
+r^2 and it's going up to the plane z = 2
+y. Now y in in cylindrical coordinates
+
+ align:start position:0%
+y. Now y in in cylindrical coordinates
+ 
+
+ align:start position:0%
+y. Now y in in cylindrical coordinates
+is r sin theta. So z is going from r 2
+
+ align:start position:0%
+is r sin theta. So z is going from r 2
+ 
+
+ align:start position:0%
+is r sin theta. So z is going from r 2
+to 2 r sin theta. So let's go write that
+
+ align:start position:0%
+to 2 r sin theta. So let's go write that
+ 
+
+ align:start position:0%
+to 2 r sin theta. So let's go write that
+down over here. So z is going from
+
+ align:start position:0%
+down over here. So z is going from
+ 
+
+ align:start position:0%
+down over here. So z is going from
+whoops not just ignore that from r 2 is
+
+ align:start position:0%
+whoops not just ignore that from r 2 is
+ 
+
+ align:start position:0%
+whoops not just ignore that from r 2 is
+less than or equal to z and it's going
+
+ align:start position:0%
+less than or equal to z and it's going
+ 
+
+ align:start position:0%
+less than or equal to z and it's going
+all the way up to 2
+
+ align:start position:0%
+all the way up to 2
+ 
+
+ align:start position:0%
+all the way up to 2
+r sin theta. So these three
+
+ align:start position:0%
+r sin theta. So these three
+ 
+
+ align:start position:0%
+r sin theta. So these three
+equations describe our region. Yeah. 0
+
+ align:start position:0%
+equations describe our region. Yeah. 0
+ 
+
+ align:start position:0%
+equations describe our region. Yeah. 0
+less than theta less than pi that just
+
+ align:start position:0%
+less than theta less than pi that just
+ 
+
+ align:start position:0%
+less than theta less than pi that just
+says theta. Okay. Then when when theta
+
+ align:start position:0%
+says theta. Okay. Then when when theta
+ 
+
+ align:start position:0%
+says theta. Okay. Then when when theta
+is going from 0 to pi, r going from 0 to
+
+ align:start position:0%
+is going from 0 to pi, r going from 0 to
+ 
+
+ align:start position:0%
+is going from 0 to pi, r going from 0 to
+2 sin theta that says well in the xy
+
+ align:start position:0%
+2 sin theta that says well in the xy
+ 
+
+ align:start position:0%
+2 sin theta that says well in the xy
+plane we're tracing out this shadow,
+
+ align:start position:0%
+plane we're tracing out this shadow,
+ 
+
+ align:start position:0%
+plane we're tracing out this shadow,
+this circular shadow. And then as z goes
+
+ align:start position:0%
+this circular shadow. And then as z goes
+ 
+
+ align:start position:0%
+this circular shadow. And then as z goes
+from r^ 2 to 2 r sin theta that says
+
+ align:start position:0%
+from r^ 2 to 2 r sin theta that says
+ 
+
+ align:start position:0%
+from r^ 2 to 2 r sin theta that says
+okay so above this shadow we're we're
+
+ align:start position:0%
+okay so above this shadow we're we're
+ 
+
+ align:start position:0%
+okay so above this shadow we're we're
+above the paraboid and below the plane.
+
+ align:start position:0%
+above the paraboid and below the plane.
+ 
+
+ align:start position:0%
+above the paraboid and below the plane.
+So that's exactly the region that we
+
+ align:start position:0%
+So that's exactly the region that we
+ 
+
+ align:start position:0%
+So that's exactly the region that we
+want. Uh so okay so now how do we get
+
+ align:start position:0%
+want. Uh so okay so now how do we get
+ 
+
+ align:start position:0%
+want. Uh so okay so now how do we get
+its volume after we figured this out?
+
+ align:start position:0%
+its volume after we figured this out?
+ 
+
+ align:start position:0%
+its volume after we figured this out?
+Well we we just write down a triple
+
+ align:start position:0%
+Well we we just write down a triple
+ 
+
+ align:start position:0%
+Well we we just write down a triple
+integral right and we write down a
+
+ align:start position:0%
+integral right and we write down a
+ 
+
+ align:start position:0%
+integral right and we write down a
+triple integral. So
+
+ align:start position:0%
+triple integral. So
+ 
+
+ align:start position:0%
+triple integral. So
+V the volume of a region D is equal to
+
+ align:start position:0%
+V the volume of a region D is equal to
+ 
+
+ align:start position:0%
+V the volume of a region D is equal to
+the triple integral over that solid of
+
+ align:start position:0%
+the triple integral over that solid of
+ 
+
+ align:start position:0%
+the triple integral over that solid of
+DV. Okay. And in our case in in
+
+ align:start position:0%
+DV. Okay. And in our case in in
+ 
+
+ align:start position:0%
+DV. Okay. And in our case in in
+cylindrical coordinates DV is going to
+
+ align:start position:0%
+cylindrical coordinates DV is going to
+ 
+
+ align:start position:0%
+cylindrical coordinates DV is going to
+be DZ
+
+ align:start position:0%
+be DZ
+ 
+
+ align:start position:0%
+be DZ
+* R DR D theta or R DZ D R D theta.
+
+ align:start position:0%
+* R DR D theta or R DZ D R D theta.
+ 
+
+ align:start position:0%
+* R DR D theta or R DZ D R D theta.
+Okay. Okay, so this is equal to so if
+
+ align:start position:0%
+Okay. Okay, so this is equal to so if
+ 
+
+ align:start position:0%
+Okay. Okay, so this is equal to so if
+we're
+
+ align:start position:0%
+we're
+ 
+
+ align:start position:0%
+we're
+integrating okay, so it becomes r
+
+ align:start position:0%
+integrating okay, so it becomes r
+ 
+
+ align:start position:0%
+integrating okay, so it becomes r
+dz d r d
+
+ align:start position:0%
+dz d r d
+ 
+
+ align:start position:0%
+dz d r d
+theta. And now we need to put in our
+
+ align:start position:0%
+theta. And now we need to put in our
+ 
+
+ align:start position:0%
+theta. And now we need to put in our
+bounds. So we said if we look over on
+
+ align:start position:0%
+bounds. So we said if we look over on
+ 
+
+ align:start position:0%
+bounds. So we said if we look over on
+this side of me, here they are. And
+
+ align:start position:0%
+this side of me, here they are. And
+ 
+
+ align:start position:0%
+this side of me, here they are. And
+these are our bounds that we're going to
+
+ align:start position:0%
+these are our bounds that we're going to
+ 
+
+ align:start position:0%
+these are our bounds that we're going to
+be using. So theta is going from 0 to
+
+ align:start position:0%
+be using. So theta is going from 0 to
+ 
+
+ align:start position:0%
+be using. So theta is going from 0 to
+pi and r is going from 0 to
+
+ align:start position:0%
+pi and r is going from 0 to
+ 
+
+ align:start position:0%
+pi and r is going from 0 to
+2 sin theta and z is going from r 2 to 2
+
+ align:start position:0%
+2 sin theta and z is going from r 2 to 2
+ 
+
+ align:start position:0%
+2 sin theta and z is going from r 2 to 2
+r sin
+
+ align:start position:0%
+r sin
+ 
+
+ align:start position:0%
+r sin
+theta. So this triple integral gives us
+
+ align:start position:0%
+theta. So this triple integral gives us
+ 
+
+ align:start position:0%
+theta. So this triple integral gives us
+precisely the volume of our region. Um,
+
+ align:start position:0%
+precisely the volume of our region. Um,
+ 
+
+ align:start position:0%
+precisely the volume of our region. Um,
+and in order to figure out what that
+
+ align:start position:0%
+and in order to figure out what that
+ 
+
+ align:start position:0%
+and in order to figure out what that
+volume is, we just have to evaluate this
+
+ align:start position:0%
+volume is, we just have to evaluate this
+ 
+
+ align:start position:0%
+volume is, we just have to evaluate this
+integral. So, let's start doing that. I
+
+ align:start position:0%
+integral. So, let's start doing that. I
+ 
+
+ align:start position:0%
+integral. So, let's start doing that. I
+don't think I'm going to go quite all
+
+ align:start position:0%
+don't think I'm going to go quite all
+ 
+
+ align:start position:0%
+don't think I'm going to go quite all
+the way. Um, but I'll but I'll do most
+
+ align:start position:0%
+the way. Um, but I'll but I'll do most
+ 
+
+ align:start position:0%
+the way. Um, but I'll but I'll do most
+of the work. Um, so, okay, so let's do
+
+ align:start position:0%
+of the work. Um, so, okay, so let's do
+ 
+
+ align:start position:0%
+of the work. Um, so, okay, so let's do
+the innermost integral first. Whenever
+
+ align:start position:0%
+the innermost integral first. Whenever
+ 
+
+ align:start position:0%
+the innermost integral first. Whenever
+you have a triple integral like this, a
+
+ align:start position:0%
+you have a triple integral like this, a
+ 
+
+ align:start position:0%
+you have a triple integral like this, a
+nice iterated integral, you always start
+
+ align:start position:0%
+nice iterated integral, you always start
+ 
+
+ align:start position:0%
+nice iterated integral, you always start
+at the inside and work your way out.
+
+ align:start position:0%
+at the inside and work your way out.
+ 
+
+ align:start position:0%
+at the inside and work your way out.
+Well, here, so our integrant is r, and
+
+ align:start position:0%
+Well, here, so our integrant is r, and
+ 
+
+ align:start position:0%
+Well, here, so our integrant is r, and
+we're integrating with respect to z, and
+
+ align:start position:0%
+we're integrating with respect to z, and
+ 
+
+ align:start position:0%
+we're integrating with respect to z, and
+r doesn't have any z's in it. So, okay.
+
+ align:start position:0%
+r doesn't have any z's in it. So, okay.
+ 
+
+ align:start position:0%
+r doesn't have any z's in it. So, okay.
+So, this inner integral is going to be
+
+ align:start position:0%
+So, this inner integral is going to be
+ 
+
+ align:start position:0%
+So, this inner integral is going to be
+easy. So I'm going to rewrite this is
+
+ align:start position:0%
+easy. So I'm going to rewrite this is
+ 
+
+ align:start position:0%
+easy. So I'm going to rewrite this is
+equal to well we keep our outer two
+
+ align:start position:0%
+equal to well we keep our outer two
+ 
+
+ align:start position:0%
+equal to well we keep our outer two
+bounds. So it's still from 0 to pi and
+
+ align:start position:0%
+bounds. So it's still from 0 to pi and
+ 
+
+ align:start position:0%
+bounds. So it's still from 0 to pi and
+it's still from 0 to
+
+ align:start position:0%
+it's still from 0 to
+ 
+
+ align:start position:0%
+it's still from 0 to
+2 sin theta of so now we get okay 2 r^ 2
+
+ align:start position:0%
+2 sin theta of so now we get okay 2 r^ 2
+ 
+
+ align:start position:0%
+2 sin theta of so now we get okay 2 r^ 2
+sin theta - r cubed dr r d theta. So
+
+ align:start position:0%
+sin theta - r cubed dr r d theta. So
+ 
+
+ align:start position:0%
+sin theta - r cubed dr r d theta. So
+what I've done here is I've just I've
+
+ align:start position:0%
+what I've done here is I've just I've
+ 
+
+ align:start position:0%
+what I've done here is I've just I've
+just integrated. I get the
+
+ align:start position:0%
+just integrated. I get the
+ 
+
+ align:start position:0%
+just integrated. I get the
+anti-derivative of R DZ is RZ. And so
+
+ align:start position:0%
+anti-derivative of R DZ is RZ. And so
+ 
+
+ align:start position:0%
+anti-derivative of R DZ is RZ. And so
+then I take the difference between those
+
+ align:start position:0%
+then I take the difference between those
+ 
+
+ align:start position:0%
+then I take the difference between those
+two bounds. So I get R * 2 R sin theta -
+
+ align:start position:0%
+two bounds. So I get R * 2 R sin theta -
+ 
+
+ align:start position:0%
+two bounds. So I get R * 2 R sin theta -
+R * R 2. So that's R * 2 R sin theta is
+
+ align:start position:0%
+R * R 2. So that's R * 2 R sin theta is
+ 
+
+ align:start position:0%
+R * R 2. So that's R * 2 R sin theta is
+2 R^ 2 sin theta - R * R is - R cub.
+
+ align:start position:0%
+2 R^ 2 sin theta - R * R is - R cub.
+ 
+
+ align:start position:0%
+2 R^ 2 sin theta - R * R is - R cub.
+Okay, so I've just done the first
+
+ align:start position:0%
+Okay, so I've just done the first
+ 
+
+ align:start position:0%
+Okay, so I've just done the first
+integral. So now um integrating with
+
+ align:start position:0%
+integral. So now um integrating with
+ 
+
+ align:start position:0%
+integral. So now um integrating with
+respect to R. Okay, this second one
+
+ align:start position:0%
+respect to R. Okay, this second one
+ 
+
+ align:start position:0%
+respect to R. Okay, this second one
+isn't so bad either. we've as far as r
+
+ align:start position:0%
+isn't so bad either. we've as far as r
+ 
+
+ align:start position:0%
+isn't so bad either. we've as far as r
+is concerned this is just a polomial
+
+ align:start position:0%
+is concerned this is just a polomial
+ 
+
+ align:start position:0%
+is concerned this is just a polomial
+theta is constant with respect to r um
+
+ align:start position:0%
+theta is constant with respect to r um
+ 
+
+ align:start position:0%
+theta is constant with respect to r um
+when we're doing an integral like this
+
+ align:start position:0%
+when we're doing an integral like this
+ 
+
+ align:start position:0%
+when we're doing an integral like this
+so okay so the second integral is not
+
+ align:start position:0%
+so okay so the second integral is not
+ 
+
+ align:start position:0%
+so okay so the second integral is not
+too bad either so this is the integral
+
+ align:start position:0%
+too bad either so this is the integral
+ 
+
+ align:start position:0%
+too bad either so this is the integral
+so our outer integral from 0 to pi
+
+ align:start position:0%
+so our outer integral from 0 to pi
+ 
+
+ align:start position:0%
+so our outer integral from 0 to pi
+sticks around let's put not do this one
+
+ align:start position:0%
+sticks around let's put not do this one
+ 
+
+ align:start position:0%
+sticks around let's put not do this one
+in one fell swoop I think um so it's
+
+ align:start position:0%
+in one fell swoop I think um so it's
+ 
+
+ align:start position:0%
+in one fell swoop I think um so it's
+going to become 2 r cub over
+
+ align:start position:0%
+going to become 2 r cub over
+ 
+
+ align:start position:0%
+going to become 2 r cub over
+3 sin theta minus r 4 over 4 and we're
+
+ align:start position:0%
+3 sin theta minus r 4 over 4 and we're
+ 
+
+ align:start position:0%
+3 sin theta minus r 4 over 4 and we're
+taking that between r = 0 and r = 2 sin
+
+ align:start position:0%
+taking that between r = 0 and r = 2 sin
+ 
+
+ align:start position:0%
+taking that between r = 0 and r = 2 sin
+theta and then that whole thing is going
+
+ align:start position:0%
+theta and then that whole thing is going
+ 
+
+ align:start position:0%
+theta and then that whole thing is going
+to be integrated d
+
+ align:start position:0%
+to be integrated d
+ 
+
+ align:start position:0%
+to be integrated d
+theta. Uh so what do we get when we plug
+
+ align:start position:0%
+theta. Uh so what do we get when we plug
+ 
+
+ align:start position:0%
+theta. Uh so what do we get when we plug
+this in? Well at r equals 0 this is just
+
+ align:start position:0%
+this in? Well at r equals 0 this is just
+ 
+
+ align:start position:0%
+this in? Well at r equals 0 this is just
+zero. So that's easy and so we need the
+
+ align:start position:0%
+zero. So that's easy and so we need the
+ 
+
+ align:start position:0%
+zero. So that's easy and so we need the
+top one r= 2 sin theta. So this is going
+
+ align:start position:0%
+top one r= 2 sin theta. So this is going
+ 
+
+ align:start position:0%
+top one r= 2 sin theta. So this is going
+to give me something like 16/3 sin to
+
+ align:start position:0%
+to give me something like 16/3 sin to
+ 
+
+ align:start position:0%
+to give me something like 16/3 sin to
+the 4th theta minus 4 sin^ 4 theta. So I
+
+ align:start position:0%
+the 4th theta minus 4 sin^ 4 theta. So I
+ 
+
+ align:start position:0%
+the 4th theta minus 4 sin^ 4 theta. So I
+think that works out to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4/3 sin to the 4th theta d theta between
+
+ align:start position:0%
+4/3 sin to the 4th theta d theta between
+ 
+
+ align:start position:0%
+4/3 sin to the 4th theta d theta between
+zero and pi. Um so now you have to
+
+ align:start position:0%
+zero and pi. Um so now you have to
+ 
+
+ align:start position:0%
+zero and pi. Um so now you have to
+remember how to do integrals like this.
+
+ align:start position:0%
+remember how to do integrals like this.
+ 
+
+ align:start position:0%
+remember how to do integrals like this.
+Um, so this is, uh, you know, something
+
+ align:start position:0%
+Um, so this is, uh, you know, something
+ 
+
+ align:start position:0%
+Um, so this is, uh, you know, something
+you probably learned back in the, uh,
+
+ align:start position:0%
+you probably learned back in the, uh,
+ 
+
+ align:start position:0%
+you probably learned back in the, uh,
+the trig integrals section of your
+
+ align:start position:0%
+the trig integrals section of your
+ 
+
+ align:start position:0%
+the trig integrals section of your
+calculus 1 or 1801 class. So, um, so
+
+ align:start position:0%
+calculus 1 or 1801 class. So, um, so
+ 
+
+ align:start position:0%
+calculus 1 or 1801 class. So, um, so
+when it's an even power here, I think
+
+ align:start position:0%
+when it's an even power here, I think
+ 
+
+ align:start position:0%
+when it's an even power here, I think
+the thing that we do is we we use our
+
+ align:start position:0%
+the thing that we do is we we use our
+ 
+
+ align:start position:0%
+the thing that we do is we we use our
+our half angle formulas. So, um, now I'm
+
+ align:start position:0%
+our half angle formulas. So, um, now I'm
+ 
+
+ align:start position:0%
+our half angle formulas. So, um, now I'm
+just going to I'm going to tell you what
+
+ align:start position:0%
+just going to I'm going to tell you what
+ 
+
+ align:start position:0%
+just going to I'm going to tell you what
+your final steps are. So, first you're
+
+ align:start position:0%
+your final steps are. So, first you're
+ 
+
+ align:start position:0%
+your final steps are. So, first you're
+going to use your half angle formula.
+
+ align:start position:0%
+going to use your half angle formula.
+ 
+
+ align:start position:0%
+going to use your half angle formula.
+So, what is that half angle formula? So
+
+ align:start position:0%
+So, what is that half angle formula? So
+ 
+
+ align:start position:0%
+So, what is that half angle formula? So
+it's sin^ 2 theta is equal to 1 -
+
+ align:start position:0%
+it's sin^ 2 theta is equal to 1 -
+ 
+
+ align:start position:0%
+it's sin^ 2 theta is equal to 1 -
+cossine 2 theta /
+
+ align:start position:0%
+cossine 2 theta /
+ 
+
+ align:start position:0%
+cossine 2 theta /
+2. So you're going to have to plug this
+
+ align:start position:0%
+2. So you're going to have to plug this
+ 
+
+ align:start position:0%
+2. So you're going to have to plug this
+in here, right? Sin to the 4th is sin^
+
+ align:start position:0%
+in here, right? Sin to the 4th is sin^
+ 
+
+ align:start position:0%
+in here, right? Sin to the 4th is sin^
+2. And then you're going to have a
+
+ align:start position:0%
+2. And then you're going to have a
+ 
+
+ align:start position:0%
+2. And then you're going to have a
+cosine^ 2 theta. So you're going to have
+
+ align:start position:0%
+cosine^ 2 theta. So you're going to have
+ 
+
+ align:start position:0%
+cosine^ 2 theta. So you're going to have
+to use the the the double angle formula
+
+ align:start position:0%
+to use the the the double angle formula
+ 
+
+ align:start position:0%
+to use the the the double angle formula
+again. This time you're going to have to
+
+ align:start position:0%
+again. This time you're going to have to
+ 
+
+ align:start position:0%
+again. This time you're going to have to
+use the double angle formula for cosine,
+
+ align:start position:0%
+use the double angle formula for cosine,
+ 
+
+ align:start position:0%
+use the double angle formula for cosine,
+which is very similar, although not
+
+ align:start position:0%
+which is very similar, although not
+ 
+
+ align:start position:0%
+which is very similar, although not
+exactly the same. So you're going to
+
+ align:start position:0%
+exactly the same. So you're going to
+ 
+
+ align:start position:0%
+exactly the same. So you're going to
+have to use those two uh double angle
+
+ align:start position:0%
+have to use those two uh double angle
+ 
+
+ align:start position:0%
+have to use those two uh double angle
+formulas. After that, you'll have
+
+ align:start position:0%
+formulas. After that, you'll have
+ 
+
+ align:start position:0%
+formulas. After that, you'll have
+something that's straightforward to
+
+ align:start position:0%
+something that's straightforward to
+ 
+
+ align:start position:0%
+something that's straightforward to
+integrate. Um so you'll you'll have
+
+ align:start position:0%
+integrate. Um so you'll you'll have
+ 
+
+ align:start position:0%
+integrate. Um so you'll you'll have
+something that's straightforward to
+
+ align:start position:0%
+something that's straightforward to
+ 
+
+ align:start position:0%
+something that's straightforward to
+integrate. You'll integrate it. And if
+
+ align:start position:0%
+integrate. You'll integrate it. And if
+ 
+
+ align:start position:0%
+integrate. You'll integrate it. And if
+I'm not
+
+ align:start position:0%
+I'm not
+ 
+
+ align:start position:0%
+I'm not
+mistaken, what you get at the
+
+ align:start position:0%
+mistaken, what you get at the
+ 
+
+ align:start position:0%
+mistaken, what you get at the
+end is that you just get a a fairly nice
+
+ align:start position:0%
+end is that you just get a a fairly nice
+ 
+
+ align:start position:0%
+end is that you just get a a fairly nice
+and simple pi over two as your answer.
+
+ align:start position:0%
+and simple pi over two as your answer.
+ 
+
+ align:start position:0%
+and simple pi over two as your answer.
+So you can check your your work there
+
+ align:start position:0%
+So you can check your your work there
+ 
+
+ align:start position:0%
+So you can check your your work there
+and make sure that that you got out pi
+
+ align:start position:0%
+and make sure that that you got out pi
+ 
+
+ align:start position:0%
+and make sure that that you got out pi
+over two at the end. And hopefully if
+
+ align:start position:0%
+over two at the end. And hopefully if
+ 
+
+ align:start position:0%
+over two at the end. And hopefully if
+you if you tried to do this dur using
+
+ align:start position:0%
+you if you tried to do this dur using
+ 
+
+ align:start position:0%
+you if you tried to do this dur using
+rectangular coordinates, you also came
+
+ align:start position:0%
+rectangular coordinates, you also came
+ 
+
+ align:start position:0%
+rectangular coordinates, you also came
+out with something like this as well. In
+
+ align:start position:0%
+out with something like this as well. In
+ 
+
+ align:start position:0%
+out with something like this as well. In
+that case, you you would have to do a
+
+ align:start position:0%
+that case, you you would have to do a
+ 
+
+ align:start position:0%
+that case, you you would have to do a
+trig substitution at some point to to
+
+ align:start position:0%
+trig substitution at some point to to
+ 
+
+ align:start position:0%
+trig substitution at some point to to
+evaluate your integrals or or you might
+
+ align:start position:0%
+evaluate your integrals or or you might
+ 
+
+ align:start position:0%
+evaluate your integrals or or you might
+have an arc sign involved. Something
+
+ align:start position:0%
+have an arc sign involved. Something
+ 
+
+ align:start position:0%
+have an arc sign involved. Something
+something like that will happen. Um but
+
+ align:start position:0%
+something like that will happen. Um but
+ 
+
+ align:start position:0%
+something like that will happen. Um but
+it should also give you pi over two of
+
+ align:start position:0%
+it should also give you pi over two of
+ 
+
+ align:start position:0%
+it should also give you pi over two of
+course because it's the same region just
+
+ align:start position:0%
+course because it's the same region just
+ 
+
+ align:start position:0%
+course because it's the same region just
+just described in a different way. So
+
+ align:start position:0%
+just described in a different way. So
+ 
+
+ align:start position:0%
+just described in a different way. So
+let me quickly recap what we did.
+
+ align:start position:0%
+let me quickly recap what we did.
+ 
+
+ align:start position:0%
+let me quickly recap what we did.
+Way back over here, we had this
+
+ align:start position:0%
+Way back over here, we had this
+ 
+
+ align:start position:0%
+Way back over here, we had this
+description of this region. So it was
+
+ align:start position:0%
+description of this region. So it was
+ 
+
+ align:start position:0%
+description of this region. So it was
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+region above a paraboid and below a
+
+ align:start position:0%
+region above a paraboid and below a
+ 
+
+ align:start position:0%
+region above a paraboid and below a
+plane. And so when we're setting this
+
+ align:start position:0%
+plane. And so when we're setting this
+ 
+
+ align:start position:0%
+plane. And so when we're setting this
+up, we have to figure out we have to
+
+ align:start position:0%
+up, we have to figure out we have to
+ 
+
+ align:start position:0%
+up, we have to figure out we have to
+figure out in order to do a triple
+
+ align:start position:0%
+figure out in order to do a triple
+ 
+
+ align:start position:0%
+figure out in order to do a triple
+integral over this region in order to
+
+ align:start position:0%
+integral over this region in order to
+ 
+
+ align:start position:0%
+integral over this region in order to
+find its volume. We have to know well we
+
+ align:start position:0%
+find its volume. We have to know well we
+ 
+
+ align:start position:0%
+find its volume. We have to know well we
+have to know we have to pick an order of
+
+ align:start position:0%
+have to know we have to pick an order of
+ 
+
+ align:start position:0%
+have to know we have to pick an order of
+integration and then we have to know
+
+ align:start position:0%
+integration and then we have to know
+ 
+
+ align:start position:0%
+integration and then we have to know
+what the what the bounds are for the
+
+ align:start position:0%
+what the what the bounds are for the
+ 
+
+ align:start position:0%
+what the what the bounds are for the
+inside terms of the outer two variables
+
+ align:start position:0%
+inside terms of the outer two variables
+ 
+
+ align:start position:0%
+inside terms of the outer two variables
+for the middle one in terms of the
+
+ align:start position:0%
+for the middle one in terms of the
+ 
+
+ align:start position:0%
+for the middle one in terms of the
+outermost one and so on. So in this case
+
+ align:start position:0%
+outermost one and so on. So in this case
+ 
+
+ align:start position:0%
+outermost one and so on. So in this case
+that means first it was it was a natural
+
+ align:start position:0%
+that means first it was it was a natural
+ 
+
+ align:start position:0%
+that means first it was it was a natural
+choice to make Z the last variable sorry
+
+ align:start position:0%
+choice to make Z the last variable sorry
+ 
+
+ align:start position:0%
+choice to make Z the last variable sorry
+the first variable the innermost
+
+ align:start position:0%
+the first variable the innermost
+ 
+
+ align:start position:0%
+the first variable the innermost
+variable and so then after that we
+
+ align:start position:0%
+variable and so then after that we
+ 
+
+ align:start position:0%
+variable and so then after that we
+needed to project to find the
+
+ align:start position:0%
+needed to project to find the
+ 
+
+ align:start position:0%
+needed to project to find the
+relationship between in the XY plane
+
+ align:start position:0%
+relationship between in the XY plane
+ 
+
+ align:start position:0%
+relationship between in the XY plane
+between the other variables. Now in this
+
+ align:start position:0%
+between the other variables. Now in this
+ 
+
+ align:start position:0%
+between the other variables. Now in this
+case we decided after we we figured out
+
+ align:start position:0%
+case we decided after we we figured out
+ 
+
+ align:start position:0%
+case we decided after we we figured out
+so we did that by solving this this
+
+ align:start position:0%
+so we did that by solving this this
+ 
+
+ align:start position:0%
+so we did that by solving this this
+little algebra problem here. We solved
+
+ align:start position:0%
+little algebra problem here. We solved
+ 
+
+ align:start position:0%
+little algebra problem here. We solved
+for Z in the two surfaces that we were
+
+ align:start position:0%
+for Z in the two surfaces that we were
+ 
+
+ align:start position:0%
+for Z in the two surfaces that we were
+um that we were given and we set them
+
+ align:start position:0%
+um that we were given and we set them
+ 
+
+ align:start position:0%
+um that we were given and we set them
+equal to each other. And so this gives
+
+ align:start position:0%
+equal to each other. And so this gives
+ 
+
+ align:start position:0%
+equal to each other. And so this gives
+us a description for the boundary curve
+
+ align:start position:0%
+us a description for the boundary curve
+ 
+
+ align:start position:0%
+us a description for the boundary curve
+for our region. And because it's a nice
+
+ align:start position:0%
+for our region. And because it's a nice
+ 
+
+ align:start position:0%
+for our region. And because it's a nice
+circle um this this suggested that one
+
+ align:start position:0%
+circle um this this suggested that one
+ 
+
+ align:start position:0%
+circle um this this suggested that one
+possibility was cylindrical coordinates.
+
+ align:start position:0%
+possibility was cylindrical coordinates.
+ 
+
+ align:start position:0%
+possibility was cylindrical coordinates.
+So we went ahead and we found in
+
+ align:start position:0%
+So we went ahead and we found in
+ 
+
+ align:start position:0%
+So we went ahead and we found in
+cylindrical coordinates the the
+
+ align:start position:0%
+cylindrical coordinates the the
+ 
+
+ align:start position:0%
+cylindrical coordinates the the
+description of this shadow and that then
+
+ align:start position:0%
+description of this shadow and that then
+ 
+
+ align:start position:0%
+description of this shadow and that then
+we used the the knowledge we previously
+
+ align:start position:0%
+we used the the knowledge we previously
+ 
+
+ align:start position:0%
+we used the the knowledge we previously
+had to describe the whole region in
+
+ align:start position:0%
+had to describe the whole region in
+ 
+
+ align:start position:0%
+had to describe the whole region in
+cylindrical coordinates. So, we had this
+
+ align:start position:0%
+cylindrical coordinates. So, we had this
+ 
+
+ align:start position:0%
+cylindrical coordinates. So, we had this
+description of our entire region. And
+
+ align:start position:0%
+description of our entire region. And
+ 
+
+ align:start position:0%
+description of our entire region. And
+then to compute its volume, we just set
+
+ align:start position:0%
+then to compute its volume, we just set
+ 
+
+ align:start position:0%
+then to compute its volume, we just set
+up a triple integral. Volume is equal to
+
+ align:start position:0%
+up a triple integral. Volume is equal to
+ 
+
+ align:start position:0%
+up a triple integral. Volume is equal to
+the triple integral DV. Um, in our case,
+
+ align:start position:0%
+the triple integral DV. Um, in our case,
+ 
+
+ align:start position:0%
+the triple integral DV. Um, in our case,
+DV since we're in cylindrical
+
+ align:start position:0%
+DV since we're in cylindrical
+ 
+
+ align:start position:0%
+DV since we're in cylindrical
+coordinates, that's R DZ D R D theta. We
+
+ align:start position:0%
+coordinates, that's R DZ D R D theta. We
+ 
+
+ align:start position:0%
+coordinates, that's R DZ D R D theta. We
+put in our bounds and then we evaluated
+
+ align:start position:0%
+put in our bounds and then we evaluated
+ 
+
+ align:start position:0%
+put in our bounds and then we evaluated
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+integral. I'll stop there.
\ No newline at end of file
diff --git a/qQqtsa1e-Jg.txt b/qQqtsa1e-Jg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..abc0d06edf08255a2c626a9c7c9d2ab35b6e233c
--- /dev/null
+++ b/qQqtsa1e-Jg.txt
@@ -0,0 +1,331 @@
+RAVEL: CMS.801 is a required
+course for master's students in
+
+the Comparative Media Studies
+Program.
+
+They ideally take it in the
+first semester of their second
+
+year.
+And the goal of the class is to
+
+provide them with some
+historical depth and perspective
+
+on media change.
+In other words,
+
+most of these students come to
+the program with some background
+
+in a media industry or with an
+undergraduate degree in which
+
+they have majored in a series of
+studies that is relevant to CMS.
+
+But many of them don't have
+that kind of historical
+
+perspective.
+And the goal of the class is to
+
+look at earlier points of media
+change.
+
+In the version of the class
+that I teach,
+
+we began with the transition
+from scrolls to codex books,
+
+in other words,
+the book as we know it today,
+
+which takes place around 400
+AD.
+
+And we move forward through the
+advent of the printing press in
+
+Europe.
+In the 19th century,
+
+we talk about the beginnings of
+photography, radio,
+
+various sound technologies.
+And, in the version of the
+
+course that I taught,
+we end with early film.
+
+And the point is for students
+who are hyper-aware of media
+
+change today,
+as a result of the digital
+
+revolution, to have a
+comparative perspective so they
+
+can get a better sense of what
+really is new,
+
+revolutionary,
+radical and what has been seen
+
+and done before.
+It is kind of the historian's
+
+conceit.
+I am a historian by training,
+
+and it is kind of the
+historian's conceit to say there
+
+are no new things under the sun.
+Students in this class are
+
+evaluated based on their class
+participation.
+
+It is a three hour a week
+seminar, and it met in the
+
+evenings in the fall of 2004.
+And class participation is
+
+absolutely vital.
+This is not a lecture class.
+
+In some instances,
+particularly in earlier
+
+historical periods where
+students might not have much
+
+background, I will provide maybe
+a ten or fifteen minute
+
+mini-lecture to give them the
+historical context for the
+
+readings that we have done.
+But, by and large,
+
+it is a discussion.
+So part of the evaluation
+
+method is simply their
+contribution to the class
+
+discussion.
+Each student also has the
+
+opportunity, either by
+themselves or sometimes in
+
+tandem with another classmate to
+lead a discussion.
+
+That is probably not the right
+term.
+
+To make a presentation based on
+that week's readings which will
+
+both summarize and also pose
+provocative questions to get the
+
+discussion rolling.
+The presentations were often
+
+quite interesting,
+involved PowerPoint
+
+presentations or the use of
+websites.
+
+They were multi-media
+experiences themselves.
+
+And then finally,
+in addition to class
+
+participation and the one
+presentation,
+
+the students wrote a 20 page
+paper at the end of the
+
+semester.
+I offered them the opportunity
+
+to submit a final project in
+some format other than the
+
+traditional hardcopy paper.
+Interestingly enough none of
+
+the students took me up on that
+this term.
+
+My goal, in teaching the class,
+was always to respect the
+
+integrity and the totality of
+the past to try to place media
+
+change in as much context as
+possible.
+
+And, in so doing,
+to think about similarities and
+
+differences, not just between
+the media change itself,
+
+but also between the cultural,
+social, political,
+
+economic context in which these
+media changes were taking place.
+
+Course material of CMS.801 fits
+into the CMS,
+
+the Comparative Media Studies
+program in the following way.
+
+First of all,
+remember that this is a
+
+graduate level course.
+By the time the students come
+
+to this class they have already
+taken, done a year of coursework
+
+at MIT, and they have had
+required courses in media theory
+
+and practice.
+And I believe also in some
+
+technological aspects of various
+media industries.
+
+So my goal is really to
+complement the more contemporary
+
+aspects of the class by
+providing historical dimension.
+
+That is not to say the class is
+atheoretical.
+
+We began as browsers of the
+website, we will see,
+
+by reading the book by Walter
+Ong, "Orality and Literacy:
+
+The Technologizing of the
+Word."
+
+In that same week we read
+Marshall McLuhan's
+
+"Understanding Media [Change?]."
+Two very different perspectives
+
+on media but using them in an
+effort to provide a kind of
+
+theoretical framework or,
+in some cases,
+
+just punching bags for us to
+bounce off and be in dialogue
+
+with for the rest of the term.
+Well, the sort of day-to-day
+
+life of CMS.801,
+I really actually prefer to
+
+think of it in sort of weekly
+units.
+
+We have an email discussion
+list.
+
+And, in some weeks during the
+fall 2004 semester,
+
+that discussion list was quite
+active with people exchanging
+
+ideas about readings or passing
+on URLs of articles and things
+
+they would come across online
+that they thought were relevant
+
+to our class discussion.
+So the discussion continues at
+
+perhaps a less intense level
+outside of the three hours that
+
+we meet every week as well.
+Within the three hour class,
+
+the pattern typically is I will
+begin with a few administrative
+
+announcements,
+and then I turn things over to
+
+the student or students who are
+presenting that material that
+
+week.
+And it was very interesting the
+
+pattern that student
+presentations took during the
+
+course of the term.
+As the semester went on the
+
+presentations got lengthier and
+lengthier.
+
+And, in response,
+the rest of the students and
+
+myself also began to intervene
+in the presentations to ask
+
+questions to say,
+well, how does this relate to
+
+what we read two weeks ago?
+And, by the end of the term,
+
+the presentations basically
+were the whole three hour
+
+session.
+And it was very hard for the
+
+presenters to get a word in
+edgewise after they had begun
+
+their initial presentation.
+So it was that kind of a class
+
+dynamic.
\ No newline at end of file
diff --git a/qk6l3z5ab0o.txt b/qk6l3z5ab0o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..869112d53faa2fcebe9471c4d90a413ceba61d9c
--- /dev/null
+++ b/qk6l3z5ab0o.txt
@@ -0,0 +1,2243 @@
+align:start position:0%
+ 
+good so let's do then our transitions so
+
+ align:start position:0%
+good so let's do then our transitions so
+ 
+
+ align:start position:0%
+good so let's do then our transitions so
+we do the constant perturbation constant
+
+ align:start position:0%
+we do the constant perturbation constant
+ 
+
+ align:start position:0%
+we do the constant perturbation constant
+perturbation so as we said Delta H is
+
+ align:start position:0%
+perturbation so as we said Delta H is
+ 
+
+ align:start position:0%
+perturbation so as we said Delta H is
+equal to V and it's time independent it
+
+ align:start position:0%
+equal to V and it's time independent it
+ 
+
+ align:start position:0%
+equal to V and it's time independent it
+just begins at time zero and we'll
+
+ align:start position:0%
+just begins at time zero and we'll
+ 
+
+ align:start position:0%
+just begins at time zero and we'll
+examine what's going on by time T zero
+
+ align:start position:0%
+examine what's going on by time T zero
+ 
+
+ align:start position:0%
+examine what's going on by time T zero
+so what are we gonna do we're gonna
+
+ align:start position:0%
+so what are we gonna do we're gonna
+ 
+
+ align:start position:0%
+so what are we gonna do we're gonna
+examine a transition to go from some
+
+ align:start position:0%
+examine a transition to go from some
+ 
+
+ align:start position:0%
+examine a transition to go from some
+initial state I initial state to a final
+
+ align:start position:0%
+initial state I initial state to a final
+ 
+
+ align:start position:0%
+initial state I initial state to a final
+state F so we don't have to say much
+
+ align:start position:0%
+state F so we don't have to say much
+ 
+
+ align:start position:0%
+state F so we don't have to say much
+about what the Hamiltonian is or
+
+ align:start position:0%
+about what the Hamiltonian is or
+ 
+
+ align:start position:0%
+about what the Hamiltonian is or
+anything for us V is gonna have a
+
+ align:start position:0%
+anything for us V is gonna have a
+ 
+
+ align:start position:0%
+anything for us V is gonna have a
+constant it's going to have some matrix
+
+ align:start position:0%
+constant it's going to have some matrix
+ 
+
+ align:start position:0%
+constant it's going to have some matrix
+elements that once we do an example you
+
+ align:start position:0%
+elements that once we do an example you
+ 
+
+ align:start position:0%
+elements that once we do an example you
+can calculate but for the time being we
+
+ align:start position:0%
+can calculate but for the time being we
+ 
+
+ align:start position:0%
+can calculate but for the time being we
+need not know too much so I'm gonna use
+
+ align:start position:0%
+need not know too much so I'm gonna use
+ 
+
+ align:start position:0%
+need not know too much so I'm gonna use
+that key formula that was derived
+
+ align:start position:0%
+that key formula that was derived
+ 
+
+ align:start position:0%
+that key formula that was derived
+already about perturbation theory and
+
+ align:start position:0%
+already about perturbation theory and
+ 
+
+ align:start position:0%
+already about perturbation theory and
+how you get the transition amplitude so
+
+ align:start position:0%
+how you get the transition amplitude so
+ 
+
+ align:start position:0%
+how you get the transition amplitude so
+we know that the coefficient C
+
+ align:start position:0%
+we know that the coefficient C
+ 
+
+ align:start position:0%
+we know that the coefficient C
+associated to the M state to first order
+
+ align:start position:0%
+associated to the M state to first order
+ 
+
+ align:start position:0%
+associated to the M state to first order
+in perturbation theory at a time T
+
+ align:start position:0%
+in perturbation theory at a time T
+ 
+
+ align:start position:0%
+in perturbation theory at a time T
+naught can be computed as a sum over all
+
+ align:start position:0%
+naught can be computed as a sum over all
+ 
+
+ align:start position:0%
+naught can be computed as a sum over all
+n integral from 0 to t naught e to the I
+
+ align:start position:0%
+n integral from 0 to t naught e to the I
+ 
+
+ align:start position:0%
+n integral from 0 to t naught e to the I
+Omega M M T prime Delta H M and T prime
+
+ align:start position:0%
+Omega M M T prime Delta H M and T prime
+ 
+
+ align:start position:0%
+Omega M M T prime Delta H M and T prime
+over I h-bar C and 0 DT Prime so let me
+
+ align:start position:0%
+over I h-bar C and 0 DT Prime so let me
+ 
+
+ align:start position:0%
+over I h-bar C and 0 DT Prime so let me
+just say a few words you may have seen
+
+ align:start position:0%
+just say a few words you may have seen
+ 
+
+ align:start position:0%
+just say a few words you may have seen
+this yesterday and
+
+ align:start position:0%
+this yesterday and
+ 
+
+ align:start position:0%
+this yesterday and
+cetacean here it is
+
+ align:start position:0%
+cetacean here it is
+ 
+
+ align:start position:0%
+cetacean here it is
+the state has described in this usual
+
+ align:start position:0%
+the state has described in this usual
+ 
+
+ align:start position:0%
+the state has described in this usual
+language of sight tilde of T was
+
+ align:start position:0%
+language of sight tilde of T was
+ 
+
+ align:start position:0%
+language of sight tilde of T was
+described as a sum of C ends of piece
+
+ align:start position:0%
+described as a sum of C ends of piece
+ 
+
+ align:start position:0%
+described as a sum of C ends of piece
+amps and we calculate those in
+
+ align:start position:0%
+amps and we calculate those in
+ 
+
+ align:start position:0%
+amps and we calculate those in
+perturbation theory so C ends we know
+
+ align:start position:0%
+perturbation theory so C ends we know
+ 
+
+ align:start position:0%
+perturbation theory so C ends we know
+them at time equals zero we imagine we
+
+ align:start position:0%
+them at time equals zero we imagine we
+ 
+
+ align:start position:0%
+them at time equals zero we imagine we
+know the initial state and we want to
+
+ align:start position:0%
+know the initial state and we want to
+ 
+
+ align:start position:0%
+know the initial state and we want to
+calculate them later well to first order
+
+ align:start position:0%
+calculate them later well to first order
+ 
+
+ align:start position:0%
+calculate them later well to first order
+in perturbation Theory the C ends are
+
+ align:start position:0%
+in perturbation Theory the C ends are
+ 
+
+ align:start position:0%
+in perturbation Theory the C ends are
+called C ends once and they're given by
+
+ align:start position:0%
+called C ends once and they're given by
+ 
+
+ align:start position:0%
+called C ends once and they're given by
+this formula first order in perturbation
+
+ align:start position:0%
+this formula first order in perturbation
+ 
+
+ align:start position:0%
+this formula first order in perturbation
+theory because we have a single delta
+
+ align:start position:0%
+theory because we have a single delta
+ 
+
+ align:start position:0%
+theory because we have a single delta
+eij this omega mm is the energy of em
+
+ align:start position:0%
+eij this omega mm is the energy of em
+ 
+
+ align:start position:0%
+eij this omega mm is the energy of em
+minus the energy of n over h-bar and
+
+ align:start position:0%
+minus the energy of n over h-bar and
+ 
+
+ align:start position:0%
+minus the energy of n over h-bar and
+that's it that's those are all our
+
+ align:start position:0%
+that's it that's those are all our
+ 
+
+ align:start position:0%
+that's it that's those are all our
+symbols so what do we have to do now we
+
+ align:start position:0%
+symbols so what do we have to do now we
+ 
+
+ align:start position:0%
+symbols so what do we have to do now we
+have a transition from some initial
+
+ align:start position:0%
+have a transition from some initial
+ 
+
+ align:start position:0%
+have a transition from some initial
+state to a final state so what does that
+
+ align:start position:0%
+state to a final state so what does that
+ 
+
+ align:start position:0%
+state to a final state so what does that
+mean it means that C m0 they it only
+
+ align:start position:0%
+mean it means that C m0 they it only
+ 
+
+ align:start position:0%
+mean it means that C m0 they it only
+exists when n represents the initial
+
+ align:start position:0%
+exists when n represents the initial
+ 
+
+ align:start position:0%
+exists when n represents the initial
+state so I'll just write Delta and I at
+
+ align:start position:0%
+state so I'll just write Delta and I at
+ 
+
+ align:start position:0%
+state so I'll just write Delta and I at
+time equals 0 system is in the state I
+
+ align:start position:0%
+time equals 0 system is in the state I
+ 
+
+ align:start position:0%
+time equals 0 system is in the state I
+and that currently not were asking for
+
+ align:start position:0%
+and that currently not were asking for
+ 
+
+ align:start position:0%
+and that currently not were asking for
+the probability to go into a final state
+
+ align:start position:0%
+the probability to go into a final state
+ 
+
+ align:start position:0%
+the probability to go into a final state
+so instead of using N and M we're just
+
+ align:start position:0%
+so instead of using N and M we're just
+ 
+
+ align:start position:0%
+so instead of using N and M we're just
+using F and I and therefore we'll have m
+
+ align:start position:0%
+using F and I and therefore we'll have m
+ 
+
+ align:start position:0%
+using F and I and therefore we'll have m
+equal F with this to fact the formula
+
+ align:start position:0%
+equal F with this to fact the formula
+ 
+
+ align:start position:0%
+equal F with this to fact the formula
+becomes C F the amplitude to first order
+
+ align:start position:0%
+becomes C F the amplitude to first order
+ 
+
+ align:start position:0%
+becomes C F the amplitude to first order
+in perturbation theory to have to be in
+
+ align:start position:0%
+in perturbation theory to have to be in
+ 
+
+ align:start position:0%
+in perturbation theory to have to be in
+the state F at time T naught if the sum
+
+ align:start position:0%
+the state F at time T naught if the sum
+ 
+
+ align:start position:0%
+the state F at time T naught if the sum
+is gone some
+
+ align:start position:0%
+is gone some
+ 
+
+ align:start position:0%
+is gone some
+/ n just applies for n equals I so I
+
+ align:start position:0%
+/ n just applies for n equals I so I
+ 
+
+ align:start position:0%
+/ n just applies for n equals I so I
+will go here we'll have 1 over I h-bar 0
+
+ align:start position:0%
+will go here we'll have 1 over I h-bar 0
+ 
+
+ align:start position:0%
+will go here we'll have 1 over I h-bar 0
+to T naught e to the I Omega final state
+
+ align:start position:0%
+to T naught e to the I Omega final state
+ 
+
+ align:start position:0%
+to T naught e to the I Omega final state
+to initial state that's M an n P prime V
+
+ align:start position:0%
+to initial state that's M an n P prime V
+ 
+
+ align:start position:0%
+to initial state that's M an n P prime V
+F I because the Delta H is V and we're
+
+ align:start position:0%
+F I because the Delta H is V and we're
+ 
+
+ align:start position:0%
+F I because the Delta H is V and we're
+going from initial to final so fi here
+
+ align:start position:0%
+going from initial to final so fi here
+ 
+
+ align:start position:0%
+going from initial to final so fi here
+and then DT Prime it's all gone it's all
+
+ align:start position:0%
+and then DT Prime it's all gone it's all
+ 
+
+ align:start position:0%
+and then DT Prime it's all gone it's all
+become very simple though you would say
+
+ align:start position:0%
+become very simple though you would say
+ 
+
+ align:start position:0%
+become very simple though you would say
+to simple we have this is time
+
+ align:start position:0%
+to simple we have this is time
+ 
+
+ align:start position:0%
+to simple we have this is time
+independent so it goes out of the
+
+ align:start position:0%
+independent so it goes out of the
+ 
+
+ align:start position:0%
+independent so it goes out of the
+interval so we just have the interval of
+
+ align:start position:0%
+interval so we just have the interval of
+ 
+
+ align:start position:0%
+interval so we just have the interval of
+an exponential here that's very very
+
+ align:start position:0%
+an exponential here that's very very
+ 
+
+ align:start position:0%
+an exponential here that's very very
+easy
+
+ align:start position:0%
+easy
+ 
+
+ align:start position:0%
+easy
+what is VF I in case V I so this goes
+
+ align:start position:0%
+what is VF I in case V I so this goes
+ 
+
+ align:start position:0%
+what is VF I in case V I so this goes
+out and we just have to integrate this
+
+ align:start position:0%
+out and we just have to integrate this
+ 
+
+ align:start position:0%
+out and we just have to integrate this
+function I'll write it in a way that is
+
+ align:start position:0%
+function I'll write it in a way that is
+ 
+
+ align:start position:0%
+function I'll write it in a way that is
+simpler maybe you skip a line I don't
+
+ align:start position:0%
+simpler maybe you skip a line I don't
+ 
+
+ align:start position:0%
+simpler maybe you skip a line I don't
+want to just count the factors of eyes
+
+ align:start position:0%
+want to just count the factors of eyes
+ 
+
+ align:start position:0%
+want to just count the factors of eyes
+and doing the integral when you
+
+ align:start position:0%
+and doing the integral when you
+ 
+
+ align:start position:0%
+and doing the integral when you
+integrate this you get another
+
+ align:start position:0%
+integrate this you get another
+ 
+
+ align:start position:0%
+integrate this you get another
+exponential you're going to get the
+
+ align:start position:0%
+exponential you're going to get the
+ 
+
+ align:start position:0%
+exponential you're going to get the
+exponential at T naught minus
+
+ align:start position:0%
+exponential at T naught minus
+ 
+
+ align:start position:0%
+exponential at T naught minus
+exponential at zero alright so we don't
+
+ align:start position:0%
+exponential at zero alright so we don't
+ 
+
+ align:start position:0%
+exponential at zero alright so we don't
+want to do our integral so I'll just
+
+ align:start position:0%
+want to do our integral so I'll just
+ 
+
+ align:start position:0%
+want to do our integral so I'll just
+write the answer we're saying we get the
+
+ align:start position:0%
+write the answer we're saying we get the
+ 
+
+ align:start position:0%
+write the answer we're saying we get the
+exponential here at T naught minus the
+
+ align:start position:0%
+exponential here at T naught minus the
+ 
+
+ align:start position:0%
+exponential here at T naught minus the
+value at zero then you take half of the
+
+ align:start position:0%
+value at zero then you take half of the
+ 
+
+ align:start position:0%
+value at zero then you take half of the
+exponential out to form a sign this is
+
+ align:start position:0%
+exponential out to form a sign this is
+ 
+
+ align:start position:0%
+exponential out to form a sign this is
+our simple matter so I will not do the
+
+ align:start position:0%
+our simple matter so I will not do the
+ 
+
+ align:start position:0%
+our simple matter so I will not do the
+integral here you get VF I over EF minus
+
+ align:start position:0%
+integral here you get VF I over EF minus
+ 
+
+ align:start position:0%
+integral here you get VF I over EF minus
+e I eat to the I Omega F I T naught over
+
+ align:start position:0%
+e I eat to the I Omega F I T naught over
+ 
+
+ align:start position:0%
+e I eat to the I Omega F I T naught over
+2 minus 2 I signed
+
+ align:start position:0%
+2 minus 2 I signed
+ 
+
+ align:start position:0%
+2 minus 2 I signed
+of Omega F I T naught over to you can't
+
+ align:start position:0%
+of Omega F I T naught over to you can't
+ 
+
+ align:start position:0%
+of Omega F I T naught over to you can't
+believe that I think you can believe the
+
+ align:start position:0%
+believe that I think you can believe the
+ 
+
+ align:start position:0%
+believe that I think you can believe the
+sign and I have everything here the H
+
+ align:start position:0%
+sign and I have everything here the H
+ 
+
+ align:start position:0%
+sign and I have everything here the H
+bar helped turn the Omega if I into e f
+
+ align:start position:0%
+bar helped turn the Omega if I into e f
+ 
+
+ align:start position:0%
+bar helped turn the Omega if I into e f
+minus e I so we can now compute the
+
+ align:start position:0%
+minus e I so we can now compute the
+ 
+
+ align:start position:0%
+minus e I so we can now compute the
+transition amplitude to go from or
+
+ align:start position:0%
+transition amplitude to go from or
+ 
+
+ align:start position:0%
+transition amplitude to go from or
+transition probability to go from the
+
+ align:start position:0%
+transition probability to go from the
+ 
+
+ align:start position:0%
+transition probability to go from the
+initial to the final state so we'll
+
+ align:start position:0%
+initial to the final state so we'll
+ 
+
+ align:start position:0%
+initial to the final state so we'll
+write it like this
+
+ align:start position:0%
+write it like this
+ 
+
+ align:start position:0%
+write it like this
+all right to F it's a little funny I
+
+ align:start position:0%
+all right to F it's a little funny I
+ 
+
+ align:start position:0%
+all right to F it's a little funny I
+don't know you can write it whichever
+
+ align:start position:0%
+don't know you can write it whichever
+ 
+
+ align:start position:0%
+don't know you can write it whichever
+way you want some people like it like
+
+ align:start position:0%
+way you want some people like it like
+ 
+
+ align:start position:0%
+way you want some people like it like
+that I'm gonna do it in the sense that
+
+ align:start position:0%
+that I'm gonna do it in the sense that
+ 
+
+ align:start position:0%
+that I'm gonna do it in the sense that
+the initial state always appears as a
+
+ align:start position:0%
+the initial state always appears as a
+ 
+
+ align:start position:0%
+the initial state always appears as a
+kept the final state as a bra so you
+
+ align:start position:0%
+kept the final state as a bra so you
+ 
+
+ align:start position:0%
+kept the final state as a bra so you
+draw the arrow like that more or less to
+
+ align:start position:0%
+draw the arrow like that more or less to
+ 
+
+ align:start position:0%
+draw the arrow like that more or less to
+keep the sense of order in your brain
+
+ align:start position:0%
+keep the sense of order in your brain
+ 
+
+ align:start position:0%
+keep the sense of order in your brain
+but if it doesn't help you write it
+
+ align:start position:0%
+but if it doesn't help you write it
+ 
+
+ align:start position:0%
+but if it doesn't help you write it
+whichever way you want PF I at peeing a
+
+ align:start position:0%
+whichever way you want PF I at peeing a
+ 
+
+ align:start position:0%
+whichever way you want PF I at peeing a
+lot one is the norm squared of this
+
+ align:start position:0%
+lot one is the norm squared of this
+ 
+
+ align:start position:0%
+lot one is the norm squared of this
+coefficient CF one of the probability to
+
+ align:start position:0%
+coefficient CF one of the probability to
+ 
+
+ align:start position:0%
+coefficient CF one of the probability to
+be found in the final state it has to do
+
+ align:start position:0%
+be found in the final state it has to do
+ 
+
+ align:start position:0%
+be found in the final state it has to do
+with the norm square of this thing so
+
+ align:start position:0%
+with the norm square of this thing so
+ 
+
+ align:start position:0%
+with the norm square of this thing so
+it's this that's part of what was
+
+ align:start position:0%
+it's this that's part of what was
+ 
+
+ align:start position:0%
+it's this that's part of what was
+reviewed yesterday squared so what do we
+
+ align:start position:0%
+reviewed yesterday squared so what do we
+ 
+
+ align:start position:0%
+reviewed yesterday squared so what do we
+get that simplifies quite a bit we get
+
+ align:start position:0%
+get that simplifies quite a bit we get
+ 
+
+ align:start position:0%
+get that simplifies quite a bit we get
+VF I squared times for signs squared
+
+ align:start position:0%
+VF I squared times for signs squared
+ 
+
+ align:start position:0%
+VF I squared times for signs squared
+Omega F I T naught over 2 over EF minus
+
+ align:start position:0%
+Omega F I T naught over 2 over EF minus
+ 
+
+ align:start position:0%
+Omega F I T naught over 2 over EF minus
+e squared and this is unit free
+
+ align:start position:0%
+e squared and this is unit free
+ 
+
+ align:start position:0%
+e squared and this is unit free
+this has units of energy V is a
+
+ align:start position:0%
+this has units of energy V is a
+ 
+
+ align:start position:0%
+this has units of energy V is a
+variation of the Hamilton has units of
+
+ align:start position:0%
+variation of the Hamilton has units of
+ 
+
+ align:start position:0%
+variation of the Hamilton has units of
+energy when you put states states are
+
+ align:start position:0%
+energy when you put states states are
+ 
+
+ align:start position:0%
+energy when you put states states are
+normalized so it doesn't change the
+
+ align:start position:0%
+normalized so it doesn't change the
+ 
+
+ align:start position:0%
+normalized so it doesn't change the
+units and this has units of energy
+
+ align:start position:0%
+units and this has units of energy
+ 
+
+ align:start position:0%
+units and this has units of energy
+squared this has no units and this is
+
+ align:start position:0%
+squared this has no units and this is
+ 
+
+ align:start position:0%
+squared this has no units and this is
+the answer a little strange there's a
+
+ align:start position:0%
+the answer a little strange there's a
+ 
+
+ align:start position:0%
+the answer a little strange there's a
+periodic variation on the transition
+
+ align:start position:0%
+periodic variation on the transition
+ 
+
+ align:start position:0%
+periodic variation on the transition
+probability and what does it mean to
+
+ align:start position:0%
+probability and what does it mean to
+ 
+
+ align:start position:0%
+probability and what does it mean to
+have a weak perturbation we can ask
+
+ align:start position:0%
+have a weak perturbation we can ask
+ 
+
+ align:start position:0%
+have a weak perturbation we can ask
+already and the answer in general is
+
+ align:start position:0%
+already and the answer in general is
+ 
+
+ align:start position:0%
+already and the answer in general is
+quite simple it's a pragmatic answer a
+
+ align:start position:0%
+quite simple it's a pragmatic answer a
+ 
+
+ align:start position:0%
+quite simple it's a pragmatic answer a
+perturbation is weak if this answer is
+
+ align:start position:0%
+perturbation is weak if this answer is
+ 
+
+ align:start position:0%
+perturbation is weak if this answer is
+very little very small suppose this
+
+ align:start position:0%
+very little very small suppose this
+ 
+
+ align:start position:0%
+very little very small suppose this
+probability comes out to be three you
+
+ align:start position:0%
+probability comes out to be three you
+ 
+
+ align:start position:0%
+probability comes out to be three you
+know it's already too big but if this is
+
+ align:start position:0%
+know it's already too big but if this is
+ 
+
+ align:start position:0%
+know it's already too big but if this is
+ten to the minus six times this function
+
+ align:start position:0%
+ten to the minus six times this function
+ 
+
+ align:start position:0%
+ten to the minus six times this function
+that's reasonable you're shining atoms
+
+ align:start position:0%
+that's reasonable you're shining atoms
+ 
+
+ align:start position:0%
+that's reasonable you're shining atoms
+and one in a million goes and gets
+
+ align:start position:0%
+and one in a million goes and gets
+ 
+
+ align:start position:0%
+and one in a million goes and gets
+ionized that that's a reasonable thing
+
+ align:start position:0%
+ionized that that's a reasonable thing
+ 
+
+ align:start position:0%
+ionized that that's a reasonable thing
+so the perturbation theory is valid for
+
+ align:start position:0%
+so the perturbation theory is valid for
+ 
+
+ align:start position:0%
+so the perturbation theory is valid for
+whatever time you use this formula as
+
+ align:start position:0%
+whatever time you use this formula as
+ 
+
+ align:start position:0%
+whatever time you use this formula as
+long as this number is small and this
+
+ align:start position:0%
+long as this number is small and this
+ 
+
+ align:start position:0%
+long as this number is small and this
+could be arranged by having vfi
+
+ align:start position:0%
+could be arranged by having vfi
+ 
+
+ align:start position:0%
+could be arranged by having vfi
+sufficiently small I want to understand
+
+ align:start position:0%
+sufficiently small I want to understand
+ 
+
+ align:start position:0%
+sufficiently small I want to understand
+this function better because this is a
+
+ align:start position:0%
+this function better because this is a
+ 
+
+ align:start position:0%
+this function better because this is a
+transition from initial state to final
+
+ align:start position:0%
+transition from initial state to final
+ 
+
+ align:start position:0%
+transition from initial state to final
+state then it looks like that so let's
+
+ align:start position:0%
+state then it looks like that so let's
+ 
+
+ align:start position:0%
+state then it looks like that so let's
+understand it better
+
+ align:start position:0%
+understand it better
+ 
+
+ align:start position:0%
+understand it better
+suppose one EF is different from E I and
+
+ align:start position:0%
+suppose one EF is different from E I and
+ 
+
+ align:start position:0%
+suppose one EF is different from E I and
+how does it look well it looked like
+
+ align:start position:0%
+how does it look well it looked like
+ 
+
+ align:start position:0%
+how does it look well it looked like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+I brought some other chalk not that it
+
+ align:start position:0%
+I brought some other chalk not that it
+ 
+
+ align:start position:0%
+I brought some other chalk not that it
+helps too much but there it looks like
+
+ align:start position:0%
+helps too much but there it looks like
+ 
+
+ align:start position:0%
+helps too much but there it looks like
+this as a function of time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the height here is height 4vf I squared
+
+ align:start position:0%
+the height here is height 4vf I squared
+ 
+
+ align:start position:0%
+the height here is height 4vf I squared
+over EF minus e I squared and it's
+
+ align:start position:0%
+over EF minus e I squared and it's
+ 
+
+ align:start position:0%
+over EF minus e I squared and it's
+oscillatory it goes to zero again at
+
+ align:start position:0%
+oscillatory it goes to zero again at
+ 
+
+ align:start position:0%
+oscillatory it goes to zero again at
+time 2 PI over Omega F I okay so this is
+
+ align:start position:0%
+time 2 PI over Omega F I okay so this is
+ 
+
+ align:start position:0%
+time 2 PI over Omega F I okay so this is
+the oscillation actually for small time
+
+ align:start position:0%
+the oscillation actually for small time
+ 
+
+ align:start position:0%
+the oscillation actually for small time
+this grows quadratically and then it
+
+ align:start position:0%
+this grows quadratically and then it
+ 
+
+ align:start position:0%
+this grows quadratically and then it
+starts blowing up so here while the
+
+ align:start position:0%
+starts blowing up so here while the
+ 
+
+ align:start position:0%
+starts blowing up so here while the
+initial behavior would be quadratic for
+
+ align:start position:0%
+initial behavior would be quadratic for
+ 
+
+ align:start position:0%
+initial behavior would be quadratic for
+small time this actually is quadratic as
+
+ align:start position:0%
+small time this actually is quadratic as
+ 
+
+ align:start position:0%
+small time this actually is quadratic as
+we will see in a second but you can more
+
+ align:start position:0%
+we will see in a second but you can more
+ 
+
+ align:start position:0%
+we will see in a second but you can more
+or less see by the expansion of the sign
+
+ align:start position:0%
+or less see by the expansion of the sign
+ 
+
+ align:start position:0%
+or less see by the expansion of the sign
+then the initial quadratic growth gets
+
+ align:start position:0%
+then the initial quadratic growth gets
+ 
+
+ align:start position:0%
+then the initial quadratic growth gets
+tamed and becomes an oscillation here
+
+ align:start position:0%
+tamed and becomes an oscillation here
+ 
+
+ align:start position:0%
+tamed and becomes an oscillation here
+this is valid for all times if this
+
+ align:start position:0%
+this is valid for all times if this
+ 
+
+ align:start position:0%
+this is valid for all times if this
+number is relatively small so that we
+
+ align:start position:0%
+number is relatively small so that we
+ 
+
+ align:start position:0%
+number is relatively small so that we
+believe perturbation theory and that's
+
+ align:start position:0%
+believe perturbation theory and that's
+ 
+
+ align:start position:0%
+believe perturbation theory and that's
+that for that case it's also interesting
+
+ align:start position:0%
+that for that case it's also interesting
+ 
+
+ align:start position:0%
+that for that case it's also interesting
+that this gets suppressed as the energy
+
+ align:start position:0%
+that this gets suppressed as the energy
+ 
+
+ align:start position:0%
+that this gets suppressed as the energy
+of the final state is different more and
+
+ align:start position:0%
+of the final state is different more and
+ 
+
+ align:start position:0%
+of the final state is different more and
+more different from the energy of the
+
+ align:start position:0%
+more different from the energy of the
+ 
+
+ align:start position:0%
+more different from the energy of the
+initial state so it always oscillates
+
+ align:start position:0%
+initial state so it always oscillates
+ 
+
+ align:start position:0%
+initial state so it always oscillates
+but if they stayed your transition is
+
+ align:start position:0%
+but if they stayed your transition is
+ 
+
+ align:start position:0%
+but if they stayed your transition is
+very far away it's going to be extremely
+
+ align:start position:0%
+very far away it's going to be extremely
+ 
+
+ align:start position:0%
+very far away it's going to be extremely
+suppressed by the quadratic factor so
+
+ align:start position:0%
+suppressed by the quadratic factor so
+ 
+
+ align:start position:0%
+suppressed by the quadratic factor so
+this is an important suppression this is
+
+ align:start position:0%
+this is an important suppression this is
+ 
+
+ align:start position:0%
+this is an important suppression this is
+saying that transitions that change the
+
+ align:start position:0%
+saying that transitions that change the
+ 
+
+ align:start position:0%
+saying that transitions that change the
+energy are not that favored a constant
+
+ align:start position:0%
+energy are not that favored a constant
+ 
+
+ align:start position:0%
+energy are not that favored a constant
+perturbation doesn't supply really
+
+ align:start position:0%
+perturbation doesn't supply really
+ 
+
+ align:start position:0%
+perturbation doesn't supply really
+energy to produce transitions that
+
+ align:start position:0%
+energy to produce transitions that
+ 
+
+ align:start position:0%
+energy to produce transitions that
+change the energy much and they are
+
+ align:start position:0%
+change the energy much and they are
+ 
+
+ align:start position:0%
+change the energy much and they are
+suppressed so they produce them but they
+
+ align:start position:0%
+suppressed so they produce them but they
+ 
+
+ align:start position:0%
+suppressed so they produce them but they
+are suppressed the other case that is of
+
+ align:start position:0%
+are suppressed the other case that is of
+ 
+
+ align:start position:0%
+are suppressed the other case that is of
+interest is the case when EF is equal
+
+ align:start position:0%
+interest is the case when EF is equal
+ 
+
+ align:start position:0%
+interest is the case when EF is equal
+tewi I I'm not saying that the state F
+
+ align:start position:0%
+tewi I I'm not saying that the state F
+ 
+
+ align:start position:0%
+tewi I I'm not saying that the state F
+is the same as the state I nor all it's
+
+ align:start position:0%
+is the same as the state I nor all it's
+ 
+
+ align:start position:0%
+is the same as the state I nor all it's
+a different state
+
+ align:start position:0%
+a different state
+ 
+
+ align:start position:0%
+a different state
+but happens to have the same energy and
+
+ align:start position:0%
+but happens to have the same energy and
+ 
+
+ align:start position:0%
+but happens to have the same energy and
+in that case we must take the limit as
+
+ align:start position:0%
+in that case we must take the limit as
+ 
+
+ align:start position:0%
+in that case we must take the limit as
+EF goes to e I remember Omega F I is EF
+
+ align:start position:0%
+EF goes to e I remember Omega F I is EF
+ 
+
+ align:start position:0%
+EF goes to e I remember Omega F I is EF
+minus VI sub over H bar so the limit as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+EF goes to e i of this P I F is how much
+
+ align:start position:0%
+EF goes to e i of this P I F is how much
+ 
+
+ align:start position:0%
+EF goes to e i of this P I F is how much
+I'll kind of do it in my head here we
+
+ align:start position:0%
+I'll kind of do it in my head here we
+ 
+
+ align:start position:0%
+I'll kind of do it in my head here we
+have an H bar here that is gonna be left
+
+ align:start position:0%
+have an H bar here that is gonna be left
+ 
+
+ align:start position:0%
+have an H bar here that is gonna be left
+over 1 over H bar so H bar squared this
+
+ align:start position:0%
+over 1 over H bar so H bar squared this
+ 
+
+ align:start position:0%
+over 1 over H bar so H bar squared this
+is gonna cancel the 4 is gonna cancel
+
+ align:start position:0%
+is gonna cancel the 4 is gonna cancel
+ 
+
+ align:start position:0%
+is gonna cancel the 4 is gonna cancel
+with this and we're gonna get V F I
+
+ align:start position:0%
+with this and we're gonna get V F I
+ 
+
+ align:start position:0%
+with this and we're gonna get V F I
+squared over H squared t naught squared
+
+ align:start position:0%
+squared over H squared t naught squared
+ 
+
+ align:start position:0%
+squared over H squared t naught squared
+okay so here it is the quadratic
+
+ align:start position:0%
+okay so here it is the quadratic
+ 
+
+ align:start position:0%
+okay so here it is the quadratic
+behavior when the energy of the final
+
+ align:start position:0%
+behavior when the energy of the final
+ 
+
+ align:start position:0%
+behavior when the energy of the final
+state is the same as the energy of your
+
+ align:start position:0%
+state is the same as the energy of your
+ 
+
+ align:start position:0%
+state is the same as the energy of your
+original state now the transition
+
+ align:start position:0%
+original state now the transition
+ 
+
+ align:start position:0%
+original state now the transition
+probability starts to grow quadratical
+
+ align:start position:0%
+probability starts to grow quadratical
+ 
+
+ align:start position:0%
+probability starts to grow quadratical
+that cannot be valid for too long time
+
+ align:start position:0%
+that cannot be valid for too long time
+ 
+
+ align:start position:0%
+that cannot be valid for too long time
+because eventually P that number grows
+
+ align:start position:0%
+because eventually P that number grows
+ 
+
+ align:start position:0%
+because eventually P that number grows
+without bound and that number could
+
+ align:start position:0%
+without bound and that number could
+ 
+
+ align:start position:0%
+without bound and that number could
+become as big as 1 and that transition
+
+ align:start position:0%
+become as big as 1 and that transition
+ 
+
+ align:start position:0%
+become as big as 1 and that transition
+is not reasonable so so this is valid
+
+ align:start position:0%
+is not reasonable so so this is valid
+ 
+
+ align:start position:0%
+is not reasonable so so this is valid
+for live up to some max to 0 and it's up
+
+ align:start position:0%
+for live up to some max to 0 and it's up
+ 
+
+ align:start position:0%
+for live up to some max to 0 and it's up
+to you depends on what vfi is how long
+
+ align:start position:0%
+to you depends on what vfi is how long
+ 
+
+ align:start position:0%
+to you depends on what vfi is how long
+you can trust this so this is a growth
+
+ align:start position:0%
+you can trust this so this is a growth
+ 
+
+ align:start position:0%
+you can trust this so this is a growth
+this is the same growth we observe here
+
+ align:start position:0%
+this is the same growth we observe here
+ 
+
+ align:start position:0%
+this is the same growth we observe here
+the limit as EF goes to e I go to
+
+ align:start position:0%
+the limit as EF goes to e I go to
+ 
+
+ align:start position:0%
+the limit as EF goes to e I go to
+zero is actually the same as the limit
+
+ align:start position:0%
+zero is actually the same as the limit
+ 
+
+ align:start position:0%
+zero is actually the same as the limit
+as T goes to zero so it's the same
+
+ align:start position:0%
+as T goes to zero so it's the same
+ 
+
+ align:start position:0%
+as T goes to zero so it's the same
+quadratic behavior so finally what's
+
+ align:start position:0%
+quadratic behavior so finally what's
+ 
+
+ align:start position:0%
+quadratic behavior so finally what's
+going to happen what are we aiming here
+
+ align:start position:0%
+going to happen what are we aiming here
+ 
+
+ align:start position:0%
+going to happen what are we aiming here
+where we're aiming to the case where we
+
+ align:start position:0%
+where we're aiming to the case where we
+ 
+
+ align:start position:0%
+where we're aiming to the case where we
+have in the energy line we have the
+
+ align:start position:0%
+have in the energy line we have the
+ 
+
+ align:start position:0%
+have in the energy line we have the
+initial energy e I and then we're gonna
+
+ align:start position:0%
+initial energy e I and then we're gonna
+ 
+
+ align:start position:0%
+initial energy e I and then we're gonna
+have a continuum of final states that
+
+ align:start position:0%
+have a continuum of final states that
+ 
+
+ align:start position:0%
+have a continuum of final states that
+overlap with E I all over there
+
+ align:start position:0%
+overlap with E I all over there
+ 
+
+ align:start position:0%
+overlap with E I all over there
+that's EF all over them of course with
+
+ align:start position:0%
+that's EF all over them of course with
+ 
+
+ align:start position:0%
+that's EF all over them of course with
+our box if you come with your microscope
+
+ align:start position:0%
+our box if you come with your microscope
+ 
+
+ align:start position:0%
+our box if you come with your microscope
+you see lines here but they're all there
+
+ align:start position:0%
+you see lines here but they're all there
+ 
+
+ align:start position:0%
+you see lines here but they're all there
+there's a continuum overlapping with
+
+ align:start position:0%
+there's a continuum overlapping with
+ 
+
+ align:start position:0%
+there's a continuum overlapping with
+this and now we're going to attempt to
+
+ align:start position:0%
+this and now we're going to attempt to
+ 
+
+ align:start position:0%
+this and now we're going to attempt to
+sum over the continuum and what should
+
+ align:start position:0%
+sum over the continuum and what should
+ 
+
+ align:start position:0%
+sum over the continuum and what should
+we observe we should observe that when
+
+ align:start position:0%
+we observe we should observe that when
+ 
+
+ align:start position:0%
+we observe we should observe that when
+we Arabic n't in UUM physically what do
+
+ align:start position:0%
+we Arabic n't in UUM physically what do
+ 
+
+ align:start position:0%
+we Arabic n't in UUM physically what do
+we need we need to find what is called a
+
+ align:start position:0%
+we need we need to find what is called a
+ 
+
+ align:start position:0%
+we need we need to find what is called a
+transition rate in which you have a
+
+ align:start position:0%
+transition rate in which you have a
+ 
+
+ align:start position:0%
+transition rate in which you have a
+transiently probability of transition
+
+ align:start position:0%
+transiently probability of transition
+ 
+
+ align:start position:0%
+transiently probability of transition
+per unit time is a constant you see you
+
+ align:start position:0%
+per unit time is a constant you see you
+ 
+
+ align:start position:0%
+per unit time is a constant you see you
+have a phenom of your shining light on
+
+ align:start position:0%
+have a phenom of your shining light on
+ 
+
+ align:start position:0%
+have a phenom of your shining light on
+an atom okay you shine light and you
+
+ align:start position:0%
+an atom okay you shine light and you
+ 
+
+ align:start position:0%
+an atom okay you shine light and you
+wait eventually the atom are ionized is
+
+ align:start position:0%
+wait eventually the atom are ionized is
+ 
+
+ align:start position:0%
+wait eventually the atom are ionized is
+photoelectric effect but if you have a
+
+ align:start position:0%
+photoelectric effect but if you have a
+ 
+
+ align:start position:0%
+photoelectric effect but if you have a
+billion atoms then you can shine light
+
+ align:start position:0%
+billion atoms then you can shine light
+ 
+
+ align:start position:0%
+billion atoms then you can shine light
+and you're gonna have a transition rate
+
+ align:start position:0%
+and you're gonna have a transition rate
+ 
+
+ align:start position:0%
+and you're gonna have a transition rate
+basically how many atoms are going to
+
+ align:start position:0%
+basically how many atoms are going to
+ 
+
+ align:start position:0%
+basically how many atoms are going to
+happen to ionize so we need in order to
+
+ align:start position:0%
+happen to ionize so we need in order to
+ 
+
+ align:start position:0%
+happen to ionize so we need in order to
+have a transition rate the probability
+
+ align:start position:0%
+have a transition rate the probability
+ 
+
+ align:start position:0%
+have a transition rate the probability
+that you transition has to be
+
+ align:start position:0%
+that you transition has to be
+ 
+
+ align:start position:0%
+that you transition has to be
+proportional to the time that the
+
+ align:start position:0%
+proportional to the time that the
+ 
+
+ align:start position:0%
+proportional to the time that the
+perturbation has been acting so the
+
+ align:start position:0%
+perturbation has been acting so the
+ 
+
+ align:start position:0%
+perturbation has been acting so the
+probability of transition
+
+ align:start position:0%
+probability of transition
+ 
+
+ align:start position:0%
+probability of transition
+must grow linear in T therefore you have
+
+ align:start position:0%
+must grow linear in T therefore you have
+ 
+
+ align:start position:0%
+must grow linear in T therefore you have
+a transition rate which is the
+
+ align:start position:0%
+a transition rate which is the
+ 
+
+ align:start position:0%
+a transition rate which is the
+probability of transition per unit time
+
+ align:start position:0%
+probability of transition per unit time
+ 
+
+ align:start position:0%
+probability of transition per unit time
+so you can grouse linear in time so per
+
+ align:start position:0%
+so you can grouse linear in time so per
+ 
+
+ align:start position:0%
+so you can grouse linear in time so per
+unit time you have a transition rate so
+
+ align:start position:0%
+unit time you have a transition rate so
+ 
+
+ align:start position:0%
+unit time you have a transition rate so
+somehow look what's happening here
+
+ align:start position:0%
+somehow look what's happening here
+ 
+
+ align:start position:0%
+somehow look what's happening here
+when EF is different than E I the proble
+
+ align:start position:0%
+when EF is different than E I the proble
+ 
+
+ align:start position:0%
+when EF is different than E I the proble
+the transition probability is not linear
+
+ align:start position:0%
+the transition probability is not linear
+ 
+
+ align:start position:0%
+the transition probability is not linear
+in time it does this when e approaches
+
+ align:start position:0%
+in time it does this when e approaches
+ 
+
+ align:start position:0%
+in time it does this when e approaches
+EF approaches e I the probability of
+
+ align:start position:0%
+EF approaches e I the probability of
+ 
+
+ align:start position:0%
+EF approaches e I the probability of
+transition goes quadratic in time and
+
+ align:start position:0%
+transition goes quadratic in time and
+ 
+
+ align:start position:0%
+transition goes quadratic in time and
+what we want is a probability of
+
+ align:start position:0%
+what we want is a probability of
+ 
+
+ align:start position:0%
+what we want is a probability of
+transition that grows linear in time
+
+ align:start position:0%
+transition that grows linear in time
+ 
+
+ align:start position:0%
+transition that grows linear in time
+that would define a transition rate so
+
+ align:start position:0%
+that would define a transition rate so
+ 
+
+ align:start position:0%
+that would define a transition rate so
+so how is that going to happen well
+
+ align:start position:0%
+so how is that going to happen well
+ 
+
+ align:start position:0%
+so how is that going to happen well
+we'll see it happen within in front of
+
+ align:start position:0%
+we'll see it happen within in front of
+ 
+
+ align:start position:0%
+we'll see it happen within in front of
+our eyes the magic of integration is
+
+ align:start position:0%
+our eyes the magic of integration is
+ 
+
+ align:start position:0%
+our eyes the magic of integration is
+gonna do it and moreover we're gonna see
+
+ align:start position:0%
+gonna do it and moreover we're gonna see
+ 
+
+ align:start position:0%
+gonna do it and moreover we're gonna see
+that consistent with this intuition most
+
+ align:start position:0%
+that consistent with this intuition most
+ 
+
+ align:start position:0%
+that consistent with this intuition most
+of the transitions that are relevant are
+
+ align:start position:0%
+of the transitions that are relevant are
+ 
+
+ align:start position:0%
+of the transitions that are relevant are
+happening within Heisenberg's
+
+ align:start position:0%
+happening within Heisenberg's
+ 
+
+ align:start position:0%
+happening within Heisenberg's
+uncertainty principle of a little energy
+
+ align:start position:0%
+uncertainty principle of a little energy
+ 
+
+ align:start position:0%
+uncertainty principle of a little energy
+interval here around the eye so this
+
+ align:start position:0%
+interval here around the eye so this
+ 
+
+ align:start position:0%
+interval here around the eye so this
+will be considered to be at the end of
+
+ align:start position:0%
+will be considered to be at the end of
+ 
+
+ align:start position:0%
+will be considered to be at the end of
+the day energy conserving transitions
+
+ align:start position:0%
+the day energy conserving transitions
+ 
+
+ align:start position:0%
+the day energy conserving transitions
+the Hamiltonian the Delta V helps the
+
+ align:start position:0%
+the Hamiltonian the Delta V helps the
+ 
+
+ align:start position:0%
+the Hamiltonian the Delta V helps the
+transition happen but doesn't supply
+
+ align:start position:0%
+transition happen but doesn't supply
+ 
+
+ align:start position:0%
+transition happen but doesn't supply
+energy at the end of the day so this is
+
+ align:start position:0%
+energy at the end of the day so this is
+ 
+
+ align:start position:0%
+energy at the end of the day so this is
+what we're getting to
\ No newline at end of file
diff --git a/rLlZpnT02ZU.txt b/rLlZpnT02ZU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b4315bd36ad206cee736886c937c45ec2309cf28
--- /dev/null
+++ b/rLlZpnT02ZU.txt
@@ -0,0 +1,13507 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+data points and then I do it again do it
+
+ align:start position:0%
+data points and then I do it again do it
+ 
+
+ align:start position:0%
+data points and then I do it again do it
+again and again then in average the
+
+ align:start position:0%
+again and again then in average the
+ 
+
+ align:start position:0%
+again and again then in average the
+number I should get should be close to
+
+ align:start position:0%
+number I should get should be close to
+ 
+
+ align:start position:0%
+number I should get should be close to
+the true parameter that I'm looking for
+
+ align:start position:0%
+the true parameter that I'm looking for
+ 
+
+ align:start position:0%
+the true parameter that I'm looking for
+the fluctuations that are due to the
+
+ align:start position:0%
+the fluctuations that are due to the
+ 
+
+ align:start position:0%
+the fluctuations that are due to the
+fact that I get different samples every
+
+ align:start position:0%
+fact that I get different samples every
+ 
+
+ align:start position:0%
+fact that I get different samples every
+time should somewhat vanish and so what
+
+ align:start position:0%
+time should somewhat vanish and so what
+ 
+
+ align:start position:0%
+time should somewhat vanish and so what
+I want is to have a small bias hopefully
+
+ align:start position:0%
+I want is to have a small bias hopefully
+ 
+
+ align:start position:0%
+I want is to have a small bias hopefully
+a zero bias if this thing is zero then
+
+ align:start position:0%
+a zero bias if this thing is zero then
+ 
+
+ align:start position:0%
+a zero bias if this thing is zero then
+we say that the estimator is unbiased
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is definitely a property
+
+ align:start position:0%
+okay so this is definitely a property
+ 
+
+ align:start position:0%
+okay so this is definitely a property
+that we're gonna look be looking for and
+
+ align:start position:0%
+that we're gonna look be looking for and
+ 
+
+ align:start position:0%
+that we're gonna look be looking for and
+estimator trying to find them to be
+
+ align:start position:0%
+estimator trying to find them to be
+ 
+
+ align:start position:0%
+estimator trying to find them to be
+unbiased but we'll see that it's
+
+ align:start position:0%
+unbiased but we'll see that it's
+ 
+
+ align:start position:0%
+unbiased but we'll see that it's
+actually maybe not enough all right so
+
+ align:start position:0%
+actually maybe not enough all right so
+ 
+
+ align:start position:0%
+actually maybe not enough all right so
+one biasness should not be something you
+
+ align:start position:0%
+one biasness should not be something you
+ 
+
+ align:start position:0%
+one biasness should not be something you
+don't you lose your sleep over something
+
+ align:start position:0%
+don't you lose your sleep over something
+ 
+
+ align:start position:0%
+don't you lose your sleep over something
+that's slightly better is the risk
+
+ align:start position:0%
+that's slightly better is the risk
+ 
+
+ align:start position:0%
+that's slightly better is the risk
+so really the quadratics risk which is
+
+ align:start position:0%
+so really the quadratics risk which is
+ 
+
+ align:start position:0%
+so really the quadratics risk which is
+expectation of so if I have an estimator
+
+ align:start position:0%
+expectation of so if I have an estimator
+ 
+
+ align:start position:0%
+expectation of so if I have an estimator
+theta hat I'm gonna look at the
+
+ align:start position:0%
+theta hat I'm gonna look at the
+ 
+
+ align:start position:0%
+theta hat I'm gonna look at the
+expectation of theta hat n minus theta
+
+ align:start position:0%
+expectation of theta hat n minus theta
+ 
+
+ align:start position:0%
+expectation of theta hat n minus theta
+squared and what we showed last time is
+
+ align:start position:0%
+squared and what we showed last time is
+ 
+
+ align:start position:0%
+squared and what we showed last time is
+that we can actually by inserting in
+
+ align:start position:0%
+that we can actually by inserting in
+ 
+
+ align:start position:0%
+that we can actually by inserting in
+there adding and removing the
+
+ align:start position:0%
+there adding and removing the
+ 
+
+ align:start position:0%
+there adding and removing the
+expectation of theta hat we actually get
+
+ align:start position:0%
+expectation of theta hat we actually get
+ 
+
+ align:start position:0%
+expectation of theta hat we actually get
+something where this thing can be
+
+ align:start position:0%
+something where this thing can be
+ 
+
+ align:start position:0%
+something where this thing can be
+decomposed as the square of the bias
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus the variance which is just the
+
+ align:start position:0%
+plus the variance which is just the
+ 
+
+ align:start position:0%
+plus the variance which is just the
+expectation of theta hat minus its
+
+ align:start position:0%
+expectation of theta hat minus its
+ 
+
+ align:start position:0%
+expectation of theta hat minus its
+expectation
+
+ align:start position:0%
+expectation
+ 
+
+ align:start position:0%
+expectation
+squared okay that came from the fact
+
+ align:start position:0%
+squared okay that came from the fact
+ 
+
+ align:start position:0%
+squared okay that came from the fact
+that when I added and removed the
+
+ align:start position:0%
+that when I added and removed the
+ 
+
+ align:start position:0%
+that when I added and removed the
+expectation of theta hat in there the
+
+ align:start position:0%
+expectation of theta hat in there the
+ 
+
+ align:start position:0%
+expectation of theta hat in there the
+cross terms canceled all right so that
+
+ align:start position:0%
+cross terms canceled all right so that
+ 
+
+ align:start position:0%
+cross terms canceled all right so that
+was the bias squared and this is the
+
+ align:start position:0%
+was the bias squared and this is the
+ 
+
+ align:start position:0%
+was the bias squared and this is the
+variance okay and so for example if the
+
+ align:start position:0%
+variance okay and so for example if the
+ 
+
+ align:start position:0%
+variance okay and so for example if the
+static risk goes to zero then that means
+
+ align:start position:0%
+static risk goes to zero then that means
+ 
+
+ align:start position:0%
+static risk goes to zero then that means
+that theta hat converges to theta in the
+
+ align:start position:0%
+that theta hat converges to theta in the
+ 
+
+ align:start position:0%
+that theta hat converges to theta in the
+l2 sense and and here we know that if we
+
+ align:start position:0%
+l2 sense and and here we know that if we
+ 
+
+ align:start position:0%
+l2 sense and and here we know that if we
+want this to go to zero this is the sum
+
+ align:start position:0%
+want this to go to zero this is the sum
+ 
+
+ align:start position:0%
+want this to go to zero this is the sum
+of two positive terms we need to have
+
+ align:start position:0%
+of two positive terms we need to have
+ 
+
+ align:start position:0%
+of two positive terms we need to have
+both the bias that goes to zero and the
+
+ align:start position:0%
+both the bias that goes to zero and the
+ 
+
+ align:start position:0%
+both the bias that goes to zero and the
+variance that goes to zero so we need to
+
+ align:start position:0%
+variance that goes to zero so we need to
+ 
+
+ align:start position:0%
+variance that goes to zero so we need to
+control both of those things and so
+
+ align:start position:0%
+control both of those things and so
+ 
+
+ align:start position:0%
+control both of those things and so
+there is usually an inherent trade-off
+
+ align:start position:0%
+there is usually an inherent trade-off
+ 
+
+ align:start position:0%
+there is usually an inherent trade-off
+between getting a small bias and getting
+
+ align:start position:0%
+between getting a small bias and getting
+ 
+
+ align:start position:0%
+between getting a small bias and getting
+a small variance if you reduce one too
+
+ align:start position:0%
+a small variance if you reduce one too
+ 
+
+ align:start position:0%
+a small variance if you reduce one too
+much then the variance of the other one
+
+ align:start position:0%
+much then the variance of the other one
+ 
+
+ align:start position:0%
+much then the variance of the other one
+is gonna increase then the other one is
+
+ align:start position:0%
+is gonna increase then the other one is
+ 
+
+ align:start position:0%
+is gonna increase then the other one is
+gonna increase or the opposite that
+
+ align:start position:0%
+gonna increase or the opposite that
+ 
+
+ align:start position:0%
+gonna increase or the opposite that
+happens a lot but not so much actually
+
+ align:start position:0%
+happens a lot but not so much actually
+ 
+
+ align:start position:0%
+happens a lot but not so much actually
+in this class so let's just look at a
+
+ align:start position:0%
+in this class so let's just look at a
+ 
+
+ align:start position:0%
+in this class so let's just look at a
+couple of examples right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so examples so if I do for example X 1 X
+
+ align:start position:0%
+so examples so if I do for example X 1 X
+ 
+
+ align:start position:0%
+so examples so if I do for example X 1 X
+n that are IID Bernoulli and I'm gonna
+
+ align:start position:0%
+n that are IID Bernoulli and I'm gonna
+ 
+
+ align:start position:0%
+n that are IID Bernoulli and I'm gonna
+write it theta so that we keep the same
+
+ align:start position:0%
+write it theta so that we keep the same
+ 
+
+ align:start position:0%
+write it theta so that we keep the same
+notation then theta hat what is the
+
+ align:start position:0%
+notation then theta hat what is the
+ 
+
+ align:start position:0%
+notation then theta hat what is the
+theta hat that we proposed many times
+
+ align:start position:0%
+theta hat that we proposed many times
+ 
+
+ align:start position:0%
+theta hat that we proposed many times
+it's just X bar right xn bar the average
+
+ align:start position:0%
+it's just X bar right xn bar the average
+ 
+
+ align:start position:0%
+it's just X bar right xn bar the average
+of the x i's so what is the bias of this
+
+ align:start position:0%
+of the x i's so what is the bias of this
+ 
+
+ align:start position:0%
+of the x i's so what is the bias of this
+guy well to know the bias I just have to
+
+ align:start position:0%
+guy well to know the bias I just have to
+ 
+
+ align:start position:0%
+guy well to know the bias I just have to
+remove data from the expectation what is
+
+ align:start position:0%
+remove data from the expectation what is
+ 
+
+ align:start position:0%
+remove data from the expectation what is
+the expectation of xn of xn bar well by
+
+ align:start position:0%
+the expectation of xn of xn bar well by
+ 
+
+ align:start position:0%
+the expectation of xn of xn bar well by
+linearity of the expectation is just the
+
+ align:start position:0%
+linearity of the expectation is just the
+ 
+
+ align:start position:0%
+linearity of the expectation is just the
+average of the expectations but since
+
+ align:start position:0%
+average of the expectations but since
+ 
+
+ align:start position:0%
+average of the expectations but since
+all my x i's are burning with the same
+
+ align:start position:0%
+all my x i's are burning with the same
+ 
+
+ align:start position:0%
+all my x i's are burning with the same
+theta then each of this guy is actually
+
+ align:start position:0%
+theta then each of this guy is actually
+ 
+
+ align:start position:0%
+theta then each of this guy is actually
+equal to theta so this thing is actually
+
+ align:start position:0%
+equal to theta so this thing is actually
+ 
+
+ align:start position:0%
+equal to theta so this thing is actually
+theta which means that this isn't biased
+
+ align:start position:0%
+theta which means that this isn't biased
+ 
+
+ align:start position:0%
+theta which means that this isn't biased
+right ok now what is the variance of
+
+ align:start position:0%
+right ok now what is the variance of
+ 
+
+ align:start position:0%
+right ok now what is the variance of
+this guy okay so if you forgot the
+
+ align:start position:0%
+this guy okay so if you forgot the
+ 
+
+ align:start position:0%
+this guy okay so if you forgot the
+properties of the variance for sum of
+
+ align:start position:0%
+properties of the variance for sum of
+ 
+
+ align:start position:0%
+properties of the variance for sum of
+independent random variables now it's
+
+ align:start position:0%
+independent random variables now it's
+ 
+
+ align:start position:0%
+independent random variables now it's
+time to wake up so we have the variance
+
+ align:start position:0%
+time to wake up so we have the variance
+ 
+
+ align:start position:0%
+time to wake up so we have the variance
+of something that looks like 1 over n
+
+ align:start position:0%
+of something that looks like 1 over n
+ 
+
+ align:start position:0%
+of something that looks like 1 over n
+sum from I equal 1 to N of X I right so
+
+ align:start position:0%
+sum from I equal 1 to N of X I right so
+ 
+
+ align:start position:0%
+sum from I equal 1 to N of X I right so
+it's of the form variance of a constant
+
+ align:start position:0%
+it's of the form variance of a constant
+ 
+
+ align:start position:0%
+it's of the form variance of a constant
+times a random variable so the first
+
+ align:start position:0%
+times a random variable so the first
+ 
+
+ align:start position:0%
+times a random variable so the first
+thing I'm gonna do is pull out the
+
+ align:start position:0%
+thing I'm gonna do is pull out the
+ 
+
+ align:start position:0%
+thing I'm gonna do is pull out the
+constant but we know that the variance
+
+ align:start position:0%
+constant but we know that the variance
+ 
+
+ align:start position:0%
+constant but we know that the variance
+lives on the squares scale so when I
+
+ align:start position:0%
+lives on the squares scale so when I
+ 
+
+ align:start position:0%
+lives on the squares scale so when I
+pull out a constant outside of the
+
+ align:start position:0%
+pull out a constant outside of the
+ 
+
+ align:start position:0%
+pull out a constant outside of the
+variance it comes out with a square
+
+ align:start position:0%
+variance it comes out with a square
+ 
+
+ align:start position:0%
+variance it comes out with a square
+right the variance of a times X is a
+
+ align:start position:0%
+right the variance of a times X is a
+ 
+
+ align:start position:0%
+right the variance of a times X is a
+squared times the variance of X so this
+
+ align:start position:0%
+squared times the variance of X so this
+ 
+
+ align:start position:0%
+squared times the variance of X so this
+is equal to 1 over N squared times the
+
+ align:start position:0%
+is equal to 1 over N squared times the
+ 
+
+ align:start position:0%
+is equal to 1 over N squared times the
+variance of the sum so now we want to
+
+ align:start position:0%
+variance of the sum so now we want to
+ 
+
+ align:start position:0%
+variance of the sum so now we want to
+always do what we want to do right so we
+
+ align:start position:0%
+always do what we want to do right so we
+ 
+
+ align:start position:0%
+always do what we want to do right so we
+have the variance of the sum we would
+
+ align:start position:0%
+have the variance of the sum we would
+ 
+
+ align:start position:0%
+have the variance of the sum we would
+like somehow to see that this is the sum
+
+ align:start position:0%
+like somehow to see that this is the sum
+ 
+
+ align:start position:0%
+like somehow to see that this is the sum
+of the variances and in general we are
+
+ align:start position:0%
+of the variances and in general we are
+ 
+
+ align:start position:0%
+of the variances and in general we are
+now allowed to say that but we are
+
+ align:start position:0%
+now allowed to say that but we are
+ 
+
+ align:start position:0%
+now allowed to say that but we are
+because my X eyes are actually
+
+ align:start position:0%
+because my X eyes are actually
+ 
+
+ align:start position:0%
+because my X eyes are actually
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+right so this is actually equal to one
+
+ align:start position:0%
+right so this is actually equal to one
+ 
+
+ align:start position:0%
+right so this is actually equal to one
+over N squared sum from I equal 1 to N
+
+ align:start position:0%
+over N squared sum from I equal 1 to N
+ 
+
+ align:start position:0%
+over N squared sum from I equal 1 to N
+of the variance of each of the X I and
+
+ align:start position:0%
+of the variance of each of the X I and
+ 
+
+ align:start position:0%
+of the variance of each of the X I and
+that's by independence okay so this is
+
+ align:start position:0%
+that's by independence okay so this is
+ 
+
+ align:start position:0%
+that's by independence okay so this is
+basic probability and now what is the
+
+ align:start position:0%
+basic probability and now what is the
+ 
+
+ align:start position:0%
+basic probability and now what is the
+variance of exercise where again they're
+
+ align:start position:0%
+variance of exercise where again they're
+ 
+
+ align:start position:0%
+variance of exercise where again they're
+all the same distribution so the
+
+ align:start position:0%
+all the same distribution so the
+ 
+
+ align:start position:0%
+all the same distribution so the
+variance of X is the same as the
+
+ align:start position:0%
+variance of X is the same as the
+ 
+
+ align:start position:0%
+variance of X is the same as the
+variance of X 1 and so each of those
+
+ align:start position:0%
+variance of X 1 and so each of those
+ 
+
+ align:start position:0%
+variance of X 1 and so each of those
+guys is variance what what is the
+
+ align:start position:0%
+guys is variance what what is the
+ 
+
+ align:start position:0%
+guys is variance what what is the
+variance of a Bernoulli we've said it
+
+ align:start position:0%
+variance of a Bernoulli we've said it
+ 
+
+ align:start position:0%
+variance of a Bernoulli we've said it
+once it's theta a times 1 minus state ok
+
+ align:start position:0%
+once it's theta a times 1 minus state ok
+ 
+
+ align:start position:0%
+once it's theta a times 1 minus state ok
+and so now I'm gonna have the sum of n
+
+ align:start position:0%
+and so now I'm gonna have the sum of n
+ 
+
+ align:start position:0%
+and so now I'm gonna have the sum of n
+times the constant so I get n times the
+
+ align:start position:0%
+times the constant so I get n times the
+ 
+
+ align:start position:0%
+times the constant so I get n times the
+constant divided by n square so one of
+
+ align:start position:0%
+constant divided by n square so one of
+ 
+
+ align:start position:0%
+constant divided by n square so one of
+the n is gonna cancel and so the whole
+
+ align:start position:0%
+the n is gonna cancel and so the whole
+ 
+
+ align:start position:0%
+the n is gonna cancel and so the whole
+thing here is actually equal to theta 1
+
+ align:start position:0%
+thing here is actually equal to theta 1
+ 
+
+ align:start position:0%
+thing here is actually equal to theta 1
+minus theta divided by n so if I'm
+
+ align:start position:0%
+minus theta divided by n so if I'm
+ 
+
+ align:start position:0%
+minus theta divided by n so if I'm
+interested in the ecstatic risk and
+
+ align:start position:0%
+interested in the ecstatic risk and
+ 
+
+ align:start position:0%
+interested in the ecstatic risk and
+again I should just say risk because
+
+ align:start position:0%
+again I should just say risk because
+ 
+
+ align:start position:0%
+again I should just say risk because
+this is the only risk we're gonna be
+
+ align:start position:0%
+this is the only risk we're gonna be
+ 
+
+ align:start position:0%
+this is the only risk we're gonna be
+actually looking at yeah this
+
+ align:start position:0%
+actually looking at yeah this
+ 
+
+ align:start position:0%
+actually looking at yeah this
+parenthesis should really stop here I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really wanted to put the dratted compare
+
+ align:start position:0%
+really wanted to put the dratted compare
+ 
+
+ align:start position:0%
+really wanted to put the dratted compare
+anthesis so the risk of this guy is what
+
+ align:start position:0%
+anthesis so the risk of this guy is what
+ 
+
+ align:start position:0%
+anthesis so the risk of this guy is what
+well is the expectation of X bar and
+
+ align:start position:0%
+well is the expectation of X bar and
+ 
+
+ align:start position:0%
+well is the expectation of X bar and
+minus theta squared and we know it's the
+
+ align:start position:0%
+minus theta squared and we know it's the
+ 
+
+ align:start position:0%
+minus theta squared and we know it's the
+square of the variance so it's the
+
+ align:start position:0%
+square of the variance so it's the
+ 
+
+ align:start position:0%
+square of the variance so it's the
+square of the bias which we know is zero
+
+ align:start position:0%
+square of the bias which we know is zero
+ 
+
+ align:start position:0%
+square of the bias which we know is zero
+so it's zero squared plus the variance
+
+ align:start position:0%
+so it's zero squared plus the variance
+ 
+
+ align:start position:0%
+so it's zero squared plus the variance
+which is theta 1 plus theta 1 minus
+
+ align:start position:0%
+which is theta 1 plus theta 1 minus
+ 
+
+ align:start position:0%
+which is theta 1 plus theta 1 minus
+theta divided by n ok so it's just fader
+
+ align:start position:0%
+theta divided by n ok so it's just fader
+ 
+
+ align:start position:0%
+theta divided by n ok so it's just fader
+1 minus theta divided by n so this is
+
+ align:start position:0%
+1 minus theta divided by n so this is
+ 
+
+ align:start position:0%
+1 minus theta divided by n so this is
+just summarizing the performance of an
+
+ align:start position:0%
+just summarizing the performance of an
+ 
+
+ align:start position:0%
+just summarizing the performance of an
+estimator which is a random variable I
+
+ align:start position:0%
+estimator which is a random variable I
+ 
+
+ align:start position:0%
+estimator which is a random variable I
+mean it's complicated if I really wanted
+
+ align:start position:0%
+mean it's complicated if I really wanted
+ 
+
+ align:start position:0%
+mean it's complicated if I really wanted
+to describe it I would just tell you the
+
+ align:start position:0%
+to describe it I would just tell you the
+ 
+
+ align:start position:0%
+to describe it I would just tell you the
+entire distribution of this random
+
+ align:start position:0%
+entire distribution of this random
+ 
+
+ align:start position:0%
+entire distribution of this random
+variable but now what I'm doing is I'm
+
+ align:start position:0%
+variable but now what I'm doing is I'm
+ 
+
+ align:start position:0%
+variable but now what I'm doing is I'm
+saying well let's just take this random
+
+ align:start position:0%
+saying well let's just take this random
+ 
+
+ align:start position:0%
+saying well let's just take this random
+variable remove theta from it and see
+
+ align:start position:0%
+variable remove theta from it and see
+ 
+
+ align:start position:0%
+variable remove theta from it and see
+how small the fluctuations around theta
+
+ align:start position:0%
+how small the fluctuations around theta
+ 
+
+ align:start position:0%
+how small the fluctuations around theta
+n squared the squared fluctuations
+
+ align:start position:0%
+n squared the squared fluctuations
+ 
+
+ align:start position:0%
+n squared the squared fluctuations
+around theta are
+
+ align:start position:0%
+around theta are
+ 
+
+ align:start position:0%
+around theta are
+expectation all right so that's what the
+
+ align:start position:0%
+expectation all right so that's what the
+ 
+
+ align:start position:0%
+expectation all right so that's what the
+quadratic risk is doing and in a way
+
+ align:start position:0%
+quadratic risk is doing and in a way
+ 
+
+ align:start position:0%
+quadratic risk is doing and in a way
+this decomposition is the sum of the by
+
+ align:start position:0%
+this decomposition is the sum of the by
+ 
+
+ align:start position:0%
+this decomposition is the sum of the by
+square and the variance is really
+
+ align:start position:0%
+square and the variance is really
+ 
+
+ align:start position:0%
+square and the variance is really
+telling you that it it it is really
+
+ align:start position:0%
+telling you that it it it is really
+ 
+
+ align:start position:0%
+telling you that it it it is really
+accounting for the bias which is well
+
+ align:start position:0%
+accounting for the bias which is well
+ 
+
+ align:start position:0%
+accounting for the bias which is well
+even if I had an infinite amount of
+
+ align:start position:0%
+even if I had an infinite amount of
+ 
+
+ align:start position:0%
+even if I had an infinite amount of
+observation it's this thing doing the
+
+ align:start position:0%
+observation it's this thing doing the
+ 
+
+ align:start position:0%
+observation it's this thing doing the
+right thing and the other thing is
+
+ align:start position:0%
+right thing and the other thing is
+ 
+
+ align:start position:0%
+right thing and the other thing is
+actually the variance so for finite
+
+ align:start position:0%
+actually the variance so for finite
+ 
+
+ align:start position:0%
+actually the variance so for finite
+number of observations what are the
+
+ align:start position:0%
+number of observations what are the
+ 
+
+ align:start position:0%
+number of observations what are the
+fluctuations all right then you can see
+
+ align:start position:0%
+fluctuations all right then you can see
+ 
+
+ align:start position:0%
+fluctuations all right then you can see
+that those things bias and variance are
+
+ align:start position:0%
+that those things bias and variance are
+ 
+
+ align:start position:0%
+that those things bias and variance are
+actually very different so so I don't
+
+ align:start position:0%
+actually very different so so I don't
+ 
+
+ align:start position:0%
+actually very different so so I don't
+have any colors here so you're gonna
+
+ align:start position:0%
+have any colors here so you're gonna
+ 
+
+ align:start position:0%
+have any colors here so you're gonna
+have to really follow the speed of the
+
+ align:start position:0%
+have to really follow the speed of the
+ 
+
+ align:start position:0%
+have to really follow the speed of the
+the order in which I draw those curves
+
+ align:start position:0%
+the order in which I draw those curves
+ 
+
+ align:start position:0%
+the order in which I draw those curves
+all right so let's find I'm gonna give
+
+ align:start position:0%
+all right so let's find I'm gonna give
+ 
+
+ align:start position:0%
+all right so let's find I'm gonna give
+you three candidates estimators so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+estimators for theta okay so the first
+
+ align:start position:0%
+estimators for theta okay so the first
+ 
+
+ align:start position:0%
+estimators for theta okay so the first
+one is definitely xn bar that will be a
+
+ align:start position:0%
+one is definitely xn bar that will be a
+ 
+
+ align:start position:0%
+one is definitely xn bar that will be a
+good candidate estimator the second one
+
+ align:start position:0%
+good candidate estimator the second one
+ 
+
+ align:start position:0%
+good candidate estimator the second one
+is gonna be 0.5 because you know after
+
+ align:start position:0%
+is gonna be 0.5 because you know after
+ 
+
+ align:start position:0%
+is gonna be 0.5 because you know after
+all why should I bother if it's actually
+
+ align:start position:0%
+all why should I bother if it's actually
+ 
+
+ align:start position:0%
+all why should I bother if it's actually
+gonna be right so you know if it for
+
+ align:start position:0%
+gonna be right so you know if it for
+ 
+
+ align:start position:0%
+gonna be right so you know if it for
+example if I ask you to predict the
+
+ align:start position:0%
+example if I ask you to predict the
+ 
+
+ align:start position:0%
+example if I ask you to predict the
+score of some candidate in some election
+
+ align:start position:0%
+score of some candidate in some election
+ 
+
+ align:start position:0%
+score of some candidate in some election
+then since you know it's gonna be very
+
+ align:start position:0%
+then since you know it's gonna be very
+ 
+
+ align:start position:0%
+then since you know it's gonna be very
+close to 0.5 you might as well just
+
+ align:start position:0%
+close to 0.5 you might as well just
+ 
+
+ align:start position:0%
+close to 0.5 you might as well just
+throw out 0.5 in you're not gonna be
+
+ align:start position:0%
+throw out 0.5 in you're not gonna be
+ 
+
+ align:start position:0%
+throw out 0.5 in you're not gonna be
+very far from reality and it's actually
+
+ align:start position:0%
+very far from reality and it's actually
+ 
+
+ align:start position:0%
+very far from reality and it's actually
+gonna cost you zero time in $0 to come
+
+ align:start position:0%
+gonna cost you zero time in $0 to come
+ 
+
+ align:start position:0%
+gonna cost you zero time in $0 to come
+up with this so sometimes you know maybe
+
+ align:start position:0%
+up with this so sometimes you know maybe
+ 
+
+ align:start position:0%
+up with this so sometimes you know maybe
+just a good old guess is actually doing
+
+ align:start position:0%
+just a good old guess is actually doing
+ 
+
+ align:start position:0%
+just a good old guess is actually doing
+the job for you of course for candid
+
+ align:start position:0%
+the job for you of course for candid
+ 
+
+ align:start position:0%
+the job for you of course for candid
+presidential elections or something like
+
+ align:start position:0%
+presidential elections or something like
+ 
+
+ align:start position:0%
+presidential elections or something like
+this is not very helpful if your
+
+ align:start position:0%
+this is not very helpful if your
+ 
+
+ align:start position:0%
+this is not very helpful if your
+prediction is telling you this but you
+
+ align:start position:0%
+prediction is telling you this but you
+ 
+
+ align:start position:0%
+prediction is telling you this but you
+know I said was something different that
+
+ align:start position:0%
+know I said was something different that
+ 
+
+ align:start position:0%
+know I said was something different that
+would be a good way to generate some
+
+ align:start position:0%
+would be a good way to generate some
+ 
+
+ align:start position:0%
+would be a good way to generate some
+close to one for a coin for example
+
+ align:start position:0%
+close to one for a coin for example
+ 
+
+ align:start position:0%
+close to one for a coin for example
+right if I give you a coin you never
+
+ align:start position:0%
+right if I give you a coin you never
+ 
+
+ align:start position:0%
+right if I give you a coin you never
+know maybe it's slightly biased but the
+
+ align:start position:0%
+know maybe it's slightly biased but the
+ 
+
+ align:start position:0%
+know maybe it's slightly biased but the
+good guess just looking at it expecting
+
+ align:start position:0%
+good guess just looking at it expecting
+ 
+
+ align:start position:0%
+good guess just looking at it expecting
+it maybe there's something crazy
+
+ align:start position:0%
+it maybe there's something crazy
+ 
+
+ align:start position:0%
+it maybe there's something crazy
+happening with the structure of it
+
+ align:start position:0%
+happening with the structure of it
+ 
+
+ align:start position:0%
+happening with the structure of it
+you're gonna guess that it's point five
+
+ align:start position:0%
+you're gonna guess that it's point five
+ 
+
+ align:start position:0%
+you're gonna guess that it's point five
+without trying to collect information
+
+ align:start position:0%
+without trying to collect information
+ 
+
+ align:start position:0%
+without trying to collect information
+and let's find another one which is well
+
+ align:start position:0%
+and let's find another one which is well
+ 
+
+ align:start position:0%
+and let's find another one which is well
+you know I have a lot of observations
+
+ align:start position:0%
+you know I have a lot of observations
+ 
+
+ align:start position:0%
+you know I have a lot of observations
+but you know I'm recording this couples
+
+ align:start position:0%
+but you know I'm recording this couples
+ 
+
+ align:start position:0%
+but you know I'm recording this couples
+kissing but you know I am on a budget I
+
+ align:start position:0%
+kissing but you know I am on a budget I
+ 
+
+ align:start position:0%
+kissing but you know I am on a budget I
+don't have time to travel all around the
+
+ align:start position:0%
+don't have time to travel all around the
+ 
+
+ align:start position:0%
+don't have time to travel all around the
+world and collect some people so really
+
+ align:start position:0%
+world and collect some people so really
+ 
+
+ align:start position:0%
+world and collect some people so really
+I'm just gonna look at the first couple
+
+ align:start position:0%
+I'm just gonna look at the first couple
+ 
+
+ align:start position:0%
+I'm just gonna look at the first couple
+and go home so my father estimators
+
+ align:start position:0%
+and go home so my father estimators
+ 
+
+ align:start position:0%
+and go home so my father estimators
+dx1 all right I just take the first
+
+ align:start position:0%
+dx1 all right I just take the first
+ 
+
+ align:start position:0%
+dx1 all right I just take the first
+observation zero one and that's it okay
+
+ align:start position:0%
+observation zero one and that's it okay
+ 
+
+ align:start position:0%
+observation zero one and that's it okay
+so now I'm gonna I want to actually
+
+ align:start position:0%
+so now I'm gonna I want to actually
+ 
+
+ align:start position:0%
+so now I'm gonna I want to actually
+understand what the behavior of those
+
+ align:start position:0%
+understand what the behavior of those
+ 
+
+ align:start position:0%
+understand what the behavior of those
+guys is alright so we know and so we
+
+ align:start position:0%
+guys is alright so we know and so we
+ 
+
+ align:start position:0%
+guys is alright so we know and so we
+know that for this guy the bias is 0 and
+
+ align:start position:0%
+know that for this guy the bias is 0 and
+ 
+
+ align:start position:0%
+know that for this guy the bias is 0 and
+the variance is equal to theta 1 minus
+
+ align:start position:0%
+the variance is equal to theta 1 minus
+ 
+
+ align:start position:0%
+the variance is equal to theta 1 minus
+theta divided by n okay what is the bias
+
+ align:start position:0%
+theta divided by n okay what is the bias
+ 
+
+ align:start position:0%
+theta divided by n okay what is the bias
+of this guy 0.5 0.5 minus theta right so
+
+ align:start position:0%
+of this guy 0.5 0.5 minus theta right so
+ 
+
+ align:start position:0%
+of this guy 0.5 0.5 minus theta right so
+the bias 0.5 minus theta what is the
+
+ align:start position:0%
+the bias 0.5 minus theta what is the
+ 
+
+ align:start position:0%
+the bias 0.5 minus theta what is the
+variance of this guy what is the
+
+ align:start position:0%
+variance of this guy what is the
+ 
+
+ align:start position:0%
+variance of this guy what is the
+variance of 0.5 zero right just the
+
+ align:start position:0%
+variance of 0.5 zero right just the
+ 
+
+ align:start position:0%
+variance of 0.5 zero right just the
+deterministic number so there's no
+
+ align:start position:0%
+deterministic number so there's no
+ 
+
+ align:start position:0%
+deterministic number so there's no
+fluctuations for this guy
+
+ align:start position:0%
+fluctuations for this guy
+ 
+
+ align:start position:0%
+fluctuations for this guy
+what is the bias well x1 is actually
+
+ align:start position:0%
+what is the bias well x1 is actually
+ 
+
+ align:start position:0%
+what is the bias well x1 is actually
+just for simplicity I can think of it as
+
+ align:start position:0%
+just for simplicity I can think of it as
+ 
+
+ align:start position:0%
+just for simplicity I can think of it as
+being x1 bar the average of itself so
+
+ align:start position:0%
+being x1 bar the average of itself so
+ 
+
+ align:start position:0%
+being x1 bar the average of itself so
+that wherever I saw an end for this guy
+
+ align:start position:0%
+that wherever I saw an end for this guy
+ 
+
+ align:start position:0%
+that wherever I saw an end for this guy
+I can replace it by 1 and that will give
+
+ align:start position:0%
+I can replace it by 1 and that will give
+ 
+
+ align:start position:0%
+I can replace it by 1 and that will give
+me my formula so the bias is still going
+
+ align:start position:0%
+me my formula so the bias is still going
+ 
+
+ align:start position:0%
+me my formula so the bias is still going
+to be 0 and the variance is going to be
+
+ align:start position:0%
+to be 0 and the variance is going to be
+ 
+
+ align:start position:0%
+to be 0 and the variance is going to be
+equal to theta 1 minus theta ok so now I
+
+ align:start position:0%
+equal to theta 1 minus theta ok so now I
+ 
+
+ align:start position:0%
+equal to theta 1 minus theta ok so now I
+have those three estimators well if I
+
+ align:start position:0%
+have those three estimators well if I
+ 
+
+ align:start position:0%
+have those three estimators well if I
+compare x1 and X and bar then clearly I
+
+ align:start position:0%
+compare x1 and X and bar then clearly I
+ 
+
+ align:start position:0%
+compare x1 and X and bar then clearly I
+have 0 bias in both cases that's good
+
+ align:start position:0%
+have 0 bias in both cases that's good
+ 
+
+ align:start position:0%
+have 0 bias in both cases that's good
+and I have the variance that's actually
+
+ align:start position:0%
+and I have the variance that's actually
+ 
+
+ align:start position:0%
+and I have the variance that's actually
+n times smaller and when I use my n
+
+ align:start position:0%
+n times smaller and when I use my n
+ 
+
+ align:start position:0%
+n times smaller and when I use my n
+observations than when I don't so those
+
+ align:start position:0%
+observations than when I don't so those
+ 
+
+ align:start position:0%
+observations than when I don't so those
+two guys on this two front you can
+
+ align:start position:0%
+two guys on this two front you can
+ 
+
+ align:start position:0%
+two guys on this two front you can
+actually look at the two numbers and say
+
+ align:start position:0%
+actually look at the two numbers and say
+ 
+
+ align:start position:0%
+actually look at the two numbers and say
+well the first number is the same the
+
+ align:start position:0%
+well the first number is the same the
+ 
+
+ align:start position:0%
+well the first number is the same the
+second number is better for the other
+
+ align:start position:0%
+second number is better for the other
+ 
+
+ align:start position:0%
+second number is better for the other
+guy so I will definitely go for this guy
+
+ align:start position:0%
+guy so I will definitely go for this guy
+ 
+
+ align:start position:0%
+guy so I will definitely go for this guy
+compared to this guy all right so this
+
+ align:start position:0%
+compared to this guy all right so this
+ 
+
+ align:start position:0%
+compared to this guy all right so this
+guy is going but not this guy well if I
+
+ align:start position:0%
+guy is going but not this guy well if I
+ 
+
+ align:start position:0%
+guy is going but not this guy well if I
+look at the bias the variance is 0 it's
+
+ align:start position:0%
+look at the bias the variance is 0 it's
+ 
+
+ align:start position:0%
+look at the bias the variance is 0 it's
+always beating the variance of this guy
+
+ align:start position:0%
+always beating the variance of this guy
+ 
+
+ align:start position:0%
+always beating the variance of this guy
+and if I look at the bias it's actually
+
+ align:start position:0%
+and if I look at the bias it's actually
+ 
+
+ align:start position:0%
+and if I look at the bias it's actually
+really not that bad right at 0.5 minus
+
+ align:start position:0%
+really not that bad right at 0.5 minus
+ 
+
+ align:start position:0%
+really not that bad right at 0.5 minus
+theta in particular if theta is 0.5 then
+
+ align:start position:0%
+theta in particular if theta is 0.5 then
+ 
+
+ align:start position:0%
+theta in particular if theta is 0.5 then
+this guy is strictly better and so you
+
+ align:start position:0%
+this guy is strictly better and so you
+ 
+
+ align:start position:0%
+this guy is strictly better and so you
+can actually now look at what the the
+
+ align:start position:0%
+can actually now look at what the the
+ 
+
+ align:start position:0%
+can actually now look at what the the
+dratted risk looks like
+
+ align:start position:0%
+dratted risk looks like
+ 
+
+ align:start position:0%
+dratted risk looks like
+all right so here what I'm going to do
+
+ align:start position:0%
+all right so here what I'm going to do
+ 
+
+ align:start position:0%
+all right so here what I'm going to do
+is I'm going to take my truth theta so
+
+ align:start position:0%
+is I'm going to take my truth theta so
+ 
+
+ align:start position:0%
+is I'm going to take my truth theta so
+it's going to range between 0 and 1 and
+
+ align:start position:0%
+it's going to range between 0 and 1 and
+ 
+
+ align:start position:0%
+it's going to range between 0 and 1 and
+we know that those two things are
+
+ align:start position:0%
+we know that those two things are
+ 
+
+ align:start position:0%
+we know that those two things are
+functions of theta so I can only
+
+ align:start position:0%
+functions of theta so I can only
+ 
+
+ align:start position:0%
+functions of theta so I can only
+understand them if I plot them as
+
+ align:start position:0%
+understand them if I plot them as
+ 
+
+ align:start position:0%
+understand them if I plot them as
+functions of theta all right and so now
+
+ align:start position:0%
+functions of theta all right and so now
+ 
+
+ align:start position:0%
+functions of theta all right and so now
+I'm going to actually plot the y axis is
+
+ align:start position:0%
+I'm going to actually plot the y axis is
+ 
+
+ align:start position:0%
+I'm going to actually plot the y axis is
+going to be the risk okay
+
+ align:start position:0%
+going to be the risk okay
+ 
+
+ align:start position:0%
+going to be the risk okay
+so what is the risk of the estimator 0.5
+
+ align:start position:0%
+so what is the risk of the estimator 0.5
+ 
+
+ align:start position:0%
+so what is the risk of the estimator 0.5
+this one is easy well it's 0 plus the
+
+ align:start position:0%
+this one is easy well it's 0 plus the
+ 
+
+ align:start position:0%
+this one is easy well it's 0 plus the
+square of 0.5 minus theta okay
+
+ align:start position:0%
+square of 0.5 minus theta okay
+ 
+
+ align:start position:0%
+square of 0.5 minus theta okay
+so we know that that's theta it's
+
+ align:start position:0%
+so we know that that's theta it's
+ 
+
+ align:start position:0%
+so we know that that's theta it's
+actually going to be 0 and then it's
+
+ align:start position:0%
+actually going to be 0 and then it's
+ 
+
+ align:start position:0%
+actually going to be 0 and then it's
+going to be a square so at 0 is going to
+
+ align:start position:0%
+going to be a square so at 0 is going to
+ 
+
+ align:start position:0%
+going to be a square so at 0 is going to
+be 0.25 and at 1 it's gonna be 0.25 as
+
+ align:start position:0%
+be 0.25 and at 1 it's gonna be 0.25 as
+ 
+
+ align:start position:0%
+be 0.25 and at 1 it's gonna be 0.25 as
+well so it looks like this actually sir
+
+ align:start position:0%
+well so it looks like this actually sir
+ 
+
+ align:start position:0%
+well so it looks like this actually sir
+let me put the point 5 where it should
+
+ align:start position:0%
+let me put the point 5 where it should
+ 
+
+ align:start position:0%
+let me put the point 5 where it should
+be okay so this here is the risk of 0.5
+
+ align:start position:0%
+be okay so this here is the risk of 0.5
+ 
+
+ align:start position:0%
+be okay so this here is the risk of 0.5
+I'll write it like this okay so when
+
+ align:start position:0%
+I'll write it like this okay so when
+ 
+
+ align:start position:0%
+I'll write it like this okay so when
+theta is very close to 0.5 I'm very
+
+ align:start position:0%
+theta is very close to 0.5 I'm very
+ 
+
+ align:start position:0%
+theta is very close to 0.5 I'm very
+happy when theta I gets large farther
+
+ align:start position:0%
+happy when theta I gets large farther
+ 
+
+ align:start position:0%
+happy when theta I gets large farther
+it's a little less a little bit annoying
+
+ align:start position:0%
+it's a little less a little bit annoying
+ 
+
+ align:start position:0%
+it's a little less a little bit annoying
+and then here I want to plot the risk of
+
+ align:start position:0%
+and then here I want to plot the risk of
+ 
+
+ align:start position:0%
+and then here I want to plot the risk of
+this guy so another thing with the risk
+
+ align:start position:0%
+this guy so another thing with the risk
+ 
+
+ align:start position:0%
+this guy so another thing with the risk
+of this guy is that it will depend on n
+
+ align:start position:0%
+of this guy is that it will depend on n
+ 
+
+ align:start position:0%
+of this guy is that it will depend on n
+so I will just pick some n that I'm
+
+ align:start position:0%
+so I will just pick some n that I'm
+ 
+
+ align:start position:0%
+so I will just pick some n that I'm
+happy with just so that I can actually
+
+ align:start position:0%
+happy with just so that I can actually
+ 
+
+ align:start position:0%
+happy with just so that I can actually
+draw a line of a curve otherwise I'm
+
+ align:start position:0%
+draw a line of a curve otherwise I'm
+ 
+
+ align:start position:0%
+draw a line of a curve otherwise I'm
+gonna have to plot one curve for value
+
+ align:start position:0%
+gonna have to plot one curve for value
+ 
+
+ align:start position:0%
+gonna have to plot one curve for value
+of n so let's just say for example that
+
+ align:start position:0%
+of n so let's just say for example that
+ 
+
+ align:start position:0%
+of n so let's just say for example that
+n is equal to 10 and so now I need to
+
+ align:start position:0%
+n is equal to 10 and so now I need to
+ 
+
+ align:start position:0%
+n is equal to 10 and so now I need to
+plot the function theta 1 minus theta
+
+ align:start position:0%
+plot the function theta 1 minus theta
+ 
+
+ align:start position:0%
+plot the function theta 1 minus theta
+divided by 10 alright we know that theta
+
+ align:start position:0%
+divided by 10 alright we know that theta
+ 
+
+ align:start position:0%
+divided by 10 alright we know that theta
+1 minus theta is a curve that goes like
+
+ align:start position:0%
+1 minus theta is a curve that goes like
+ 
+
+ align:start position:0%
+1 minus theta is a curve that goes like
+this it takes value at one half it takes
+
+ align:start position:0%
+this it takes value at one half it takes
+ 
+
+ align:start position:0%
+this it takes value at one half it takes
+value 1/4 that's the maximum and it's
+
+ align:start position:0%
+value 1/4 that's the maximum and it's
+ 
+
+ align:start position:0%
+value 1/4 that's the maximum and it's
+zero at the end okay so really if n is
+
+ align:start position:0%
+zero at the end okay so really if n is
+ 
+
+ align:start position:0%
+zero at the end okay so really if n is
+equal to 1 this is what the variance
+
+ align:start position:0%
+equal to 1 this is what the variance
+ 
+
+ align:start position:0%
+equal to 1 this is what the variance
+looks like right device doesn't count in
+
+ align:start position:0%
+looks like right device doesn't count in
+ 
+
+ align:start position:0%
+looks like right device doesn't count in
+the risk yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sure can you move all right are you guys
+
+ align:start position:0%
+sure can you move all right are you guys
+ 
+
+ align:start position:0%
+sure can you move all right are you guys
+good all right so now I have this
+
+ align:start position:0%
+good all right so now I have this
+ 
+
+ align:start position:0%
+good all right so now I have this
+picture and I know I'm going to up to 25
+
+ align:start position:0%
+picture and I know I'm going to up to 25
+ 
+
+ align:start position:0%
+picture and I know I'm going to up to 25
+and there's a place where those curves
+
+ align:start position:0%
+and there's a place where those curves
+ 
+
+ align:start position:0%
+and there's a place where those curves
+cross so if you're sure let's say you're
+
+ align:start position:0%
+cross so if you're sure let's say you're
+ 
+
+ align:start position:0%
+cross so if you're sure let's say you're
+talking about that presents an election
+
+ align:start position:0%
+talking about that presents an election
+ 
+
+ align:start position:0%
+talking about that presents an election
+you know that those things are gonna be
+
+ align:start position:0%
+you know that those things are gonna be
+ 
+
+ align:start position:0%
+you know that those things are gonna be
+really close maybe you're actually
+
+ align:start position:0%
+really close maybe you're actually
+ 
+
+ align:start position:0%
+really close maybe you're actually
+better by predicting 0.5 if you know
+
+ align:start position:0%
+better by predicting 0.5 if you know
+ 
+
+ align:start position:0%
+better by predicting 0.5 if you know
+it's not gonna go too far but that's
+
+ align:start position:0%
+it's not gonna go too far but that's
+ 
+
+ align:start position:0%
+it's not gonna go too far but that's
+through one observation right so that's
+
+ align:start position:0%
+through one observation right so that's
+ 
+
+ align:start position:0%
+through one observation right so that's
+the risk of x1 but if I look at the risk
+
+ align:start position:0%
+the risk of x1 but if I look at the risk
+ 
+
+ align:start position:0%
+the risk of x1 but if I look at the risk
+of xn all I'm doing is just crushing
+
+ align:start position:0%
+of xn all I'm doing is just crushing
+ 
+
+ align:start position:0%
+of xn all I'm doing is just crushing
+this curve down to zero so as n
+
+ align:start position:0%
+this curve down to zero so as n
+ 
+
+ align:start position:0%
+this curve down to zero so as n
+increases is gonna look more and more
+
+ align:start position:0%
+increases is gonna look more and more
+ 
+
+ align:start position:0%
+increases is gonna look more and more
+like this it's the same curve divided by
+
+ align:start position:0%
+like this it's the same curve divided by
+ 
+
+ align:start position:0%
+like this it's the same curve divided by
+n okay
+
+ align:start position:0%
+n okay
+ 
+
+ align:start position:0%
+n okay
+and so now I can just start to
+
+ align:start position:0%
+and so now I can just start to
+ 
+
+ align:start position:0%
+and so now I can just start to
+understand that for different values of
+
+ align:start position:0%
+understand that for different values of
+ 
+
+ align:start position:0%
+understand that for different values of
+Thetas now I'm gonna have to be very
+
+ align:start position:0%
+Thetas now I'm gonna have to be very
+ 
+
+ align:start position:0%
+Thetas now I'm gonna have to be very
+close to theta is equal to one half if I
+
+ align:start position:0%
+close to theta is equal to one half if I
+ 
+
+ align:start position:0%
+close to theta is equal to one half if I
+want to start saying that xn bar is
+
+ align:start position:0%
+want to start saying that xn bar is
+ 
+
+ align:start position:0%
+want to start saying that xn bar is
+worse than the naive estimator is your
+
+ align:start position:0%
+worse than the naive estimator is your
+ 
+
+ align:start position:0%
+worse than the naive estimator is your
+0.5 okay yeah so either you can well
+
+ align:start position:0%
+0.5 okay yeah so either you can well
+ 
+
+ align:start position:0%
+0.5 okay yeah so either you can well
+when you have an unbiased estimator it's
+
+ align:start position:0%
+when you have an unbiased estimator it's
+ 
+
+ align:start position:0%
+when you have an unbiased estimator it's
+simple it's just telling you is the
+
+ align:start position:0%
+simple it's just telling you is the
+ 
+
+ align:start position:0%
+simple it's just telling you is the
+variance right because the theta that
+
+ align:start position:0%
+variance right because the theta that
+ 
+
+ align:start position:0%
+variance right because the theta that
+you have over there is really right so
+
+ align:start position:0%
+you have over there is really right so
+ 
+
+ align:start position:0%
+you have over there is really right so
+in the definition of the risk the theta
+
+ align:start position:0%
+in the definition of the risk the theta
+ 
+
+ align:start position:0%
+in the definition of the risk the theta
+that you have here if you're in biased
+
+ align:start position:0%
+that you have here if you're in biased
+ 
+
+ align:start position:0%
+that you have here if you're in biased
+is really the expectation of theta hat
+
+ align:start position:0%
+is really the expectation of theta hat
+ 
+
+ align:start position:0%
+is really the expectation of theta hat
+right so that's really just the variance
+
+ align:start position:0%
+right so that's really just the variance
+ 
+
+ align:start position:0%
+right so that's really just the variance
+so the risk is really telling you how
+
+ align:start position:0%
+so the risk is really telling you how
+ 
+
+ align:start position:0%
+so the risk is really telling you how
+much fluctuations I have around my
+
+ align:start position:0%
+much fluctuations I have around my
+ 
+
+ align:start position:0%
+much fluctuations I have around my
+expectation if I'm biased but actually
+
+ align:start position:0%
+expectation if I'm biased but actually
+ 
+
+ align:start position:0%
+expectation if I'm biased but actually
+here is telling you how much
+
+ align:start position:0%
+here is telling you how much
+ 
+
+ align:start position:0%
+here is telling you how much
+fluctuations I have an average around
+
+ align:start position:0%
+fluctuations I have an average around
+ 
+
+ align:start position:0%
+fluctuations I have an average around
+theta so if you understand the notion of
+
+ align:start position:0%
+theta so if you understand the notion of
+ 
+
+ align:start position:0%
+theta so if you understand the notion of
+variance as being what now it's just
+
+ align:start position:0%
+variance as being what now it's just
+ 
+
+ align:start position:0%
+variance as being what now it's just
+like variance so when you I mean if you
+
+ align:start position:0%
+like variance so when you I mean if you
+ 
+
+ align:start position:0%
+like variance so when you I mean if you
+claim you understand what variances it's
+
+ align:start position:0%
+claim you understand what variances it's
+ 
+
+ align:start position:0%
+claim you understand what variances it's
+telling you what is the expected
+
+ align:start position:0%
+telling you what is the expected
+ 
+
+ align:start position:0%
+telling you what is the expected
+expected squared fluctuation around the
+
+ align:start position:0%
+expected squared fluctuation around the
+ 
+
+ align:start position:0%
+expected squared fluctuation around the
+expectation of my random variable right
+
+ align:start position:0%
+expectation of my random variable right
+ 
+
+ align:start position:0%
+expectation of my random variable right
+they're telling you in average how far
+
+ align:start position:0%
+they're telling you in average how far
+ 
+
+ align:start position:0%
+they're telling you in average how far
+I'm gonna be and you take this square
+
+ align:start position:0%
+I'm gonna be and you take this square
+ 
+
+ align:start position:0%
+I'm gonna be and you take this square
+because you want to cancel the signs
+
+ align:start position:0%
+because you want to cancel the signs
+ 
+
+ align:start position:0%
+because you want to cancel the signs
+otherwise you're gonna get 0 and here
+
+ align:start position:0%
+otherwise you're gonna get 0 and here
+ 
+
+ align:start position:0%
+otherwise you're gonna get 0 and here
+it's saying well I really don't care
+
+ align:start position:0%
+it's saying well I really don't care
+ 
+
+ align:start position:0%
+it's saying well I really don't care
+what the expectation of theta hat is
+
+ align:start position:0%
+what the expectation of theta hat is
+ 
+
+ align:start position:0%
+what the expectation of theta hat is
+what I want to get to is theta so I'm
+
+ align:start position:0%
+what I want to get to is theta so I'm
+ 
+
+ align:start position:0%
+what I want to get to is theta so I'm
+looking at
+
+ align:start position:0%
+looking at
+ 
+
+ align:start position:0%
+looking at
+the expectation of the squared
+
+ align:start position:0%
+the expectation of the squared
+ 
+
+ align:start position:0%
+the expectation of the squared
+fluctuations around theta itself if I'm
+
+ align:start position:0%
+fluctuations around theta itself if I'm
+ 
+
+ align:start position:0%
+fluctuations around theta itself if I'm
+Minh biased they coincide coincide with
+
+ align:start position:0%
+Minh biased they coincide coincide with
+ 
+
+ align:start position:0%
+Minh biased they coincide coincide with
+the variance but if I'm biased then I
+
+ align:start position:0%
+the variance but if I'm biased then I
+ 
+
+ align:start position:0%
+the variance but if I'm biased then I
+have to account for the fact that I'm
+
+ align:start position:0%
+have to account for the fact that I'm
+ 
+
+ align:start position:0%
+have to account for the fact that I'm
+really not computing the okay all right
+
+ align:start position:0%
+really not computing the okay all right
+ 
+
+ align:start position:0%
+really not computing the okay all right
+are there any questions so here what I
+
+ align:start position:0%
+are there any questions so here what I
+ 
+
+ align:start position:0%
+are there any questions so here what I
+really want to illustrate is that the
+
+ align:start position:0%
+really want to illustrate is that the
+ 
+
+ align:start position:0%
+really want to illustrate is that the
+risk itself is a function of theta and
+
+ align:start position:0%
+risk itself is a function of theta and
+ 
+
+ align:start position:0%
+risk itself is a function of theta and
+most of the times and so for different
+
+ align:start position:0%
+most of the times and so for different
+ 
+
+ align:start position:0%
+most of the times and so for different
+data some estimators are gonna be better
+
+ align:start position:0%
+data some estimators are gonna be better
+ 
+
+ align:start position:0%
+data some estimators are gonna be better
+than others but there's also the entire
+
+ align:start position:0%
+than others but there's also the entire
+ 
+
+ align:start position:0%
+than others but there's also the entire
+range of estimators those that are
+
+ align:start position:0%
+range of estimators those that are
+ 
+
+ align:start position:0%
+range of estimators those that are
+really biased but the bias completely
+
+ align:start position:0%
+really biased but the bias completely
+ 
+
+ align:start position:0%
+really biased but the bias completely
+vanish and so here you see you have no
+
+ align:start position:0%
+vanish and so here you see you have no
+ 
+
+ align:start position:0%
+vanish and so here you see you have no
+bias but the variance can be large or
+
+ align:start position:0%
+bias but the variance can be large or
+ 
+
+ align:start position:0%
+bias but the variance can be large or
+you have zero bias so you have a bias
+
+ align:start position:0%
+you have zero bias so you have a bias
+ 
+
+ align:start position:0%
+you have zero bias so you have a bias
+but the variance is zero you can
+
+ align:start position:0%
+but the variance is zero you can
+ 
+
+ align:start position:0%
+but the variance is zero you can
+actually have this trade-off and you can
+
+ align:start position:0%
+actually have this trade-off and you can
+ 
+
+ align:start position:0%
+actually have this trade-off and you can
+find things that are in the entire range
+
+ align:start position:0%
+find things that are in the entire range
+ 
+
+ align:start position:0%
+find things that are in the entire range
+okay in general okay
+
+ align:start position:0%
+okay in general okay
+ 
+
+ align:start position:0%
+okay in general okay
+so those things are actually those
+
+ align:start position:0%
+so those things are actually those
+ 
+
+ align:start position:0%
+so those things are actually those
+trade-offs between bias and variance are
+
+ align:start position:0%
+trade-offs between bias and variance are
+ 
+
+ align:start position:0%
+trade-offs between bias and variance are
+usually much better Illustrated if we're
+
+ align:start position:0%
+usually much better Illustrated if we're
+ 
+
+ align:start position:0%
+usually much better Illustrated if we're
+talking about multivariate parameters if
+
+ align:start position:0%
+talking about multivariate parameters if
+ 
+
+ align:start position:0%
+talking about multivariate parameters if
+I actually look at a parameter which is
+
+ align:start position:0%
+I actually look at a parameter which is
+ 
+
+ align:start position:0%
+I actually look at a parameter which is
+the mean of some multivariate Gaussian
+
+ align:start position:0%
+the mean of some multivariate Gaussian
+ 
+
+ align:start position:0%
+the mean of some multivariate Gaussian
+so an entire vector then the bias is
+
+ align:start position:0%
+so an entire vector then the bias is
+ 
+
+ align:start position:0%
+so an entire vector then the bias is
+gonna I can make the bias bigger by
+
+ align:start position:0%
+gonna I can make the bias bigger by
+ 
+
+ align:start position:0%
+gonna I can make the bias bigger by
+making by for example forcing all the
+
+ align:start position:0%
+making by for example forcing all the
+ 
+
+ align:start position:0%
+making by for example forcing all the
+coordinates of my estimator to be the
+
+ align:start position:0%
+coordinates of my estimator to be the
+ 
+
+ align:start position:0%
+coordinates of my estimator to be the
+same so here I'm gonna get some bias but
+
+ align:start position:0%
+same so here I'm gonna get some bias but
+ 
+
+ align:start position:0%
+same so here I'm gonna get some bias but
+the variance is actually getting much
+
+ align:start position:0%
+the variance is actually getting much
+ 
+
+ align:start position:0%
+the variance is actually getting much
+better because I get to average all the
+
+ align:start position:0%
+better because I get to average all the
+ 
+
+ align:start position:0%
+better because I get to average all the
+coordinates for this guy
+
+ align:start position:0%
+coordinates for this guy
+ 
+
+ align:start position:0%
+coordinates for this guy
+and so really the bias-variance tradeoff
+
+ align:start position:0%
+and so really the bias-variance tradeoff
+ 
+
+ align:start position:0%
+and so really the bias-variance tradeoff
+is when you have a multiple parameters
+
+ align:start position:0%
+is when you have a multiple parameters
+ 
+
+ align:start position:0%
+is when you have a multiple parameters
+to estimate it's a vector of parameters
+
+ align:start position:0%
+to estimate it's a vector of parameters
+ 
+
+ align:start position:0%
+to estimate it's a vector of parameters
+a multivariate parameter is the bias
+
+ align:start position:0%
+a multivariate parameter is the bias
+ 
+
+ align:start position:0%
+a multivariate parameter is the bias
+increases when you're trying to pull
+
+ align:start position:0%
+increases when you're trying to pull
+ 
+
+ align:start position:0%
+increases when you're trying to pull
+more information across the different
+
+ align:start position:0%
+more information across the different
+ 
+
+ align:start position:0%
+more information across the different
+components at the to actually have a
+
+ align:start position:0%
+components at the to actually have a
+ 
+
+ align:start position:0%
+components at the to actually have a
+lower variance okay so the more you
+
+ align:start position:0%
+lower variance okay so the more you
+ 
+
+ align:start position:0%
+lower variance okay so the more you
+average the lower the variance right
+
+ align:start position:0%
+average the lower the variance right
+ 
+
+ align:start position:0%
+average the lower the variance right
+that's exactly what we've Illustrated as
+
+ align:start position:0%
+that's exactly what we've Illustrated as
+ 
+
+ align:start position:0%
+that's exactly what we've Illustrated as
+n increases the variance decreases like
+
+ align:start position:0%
+n increases the variance decreases like
+ 
+
+ align:start position:0%
+n increases the variance decreases like
+1 over N or theta of 1 minus 3 over N
+
+ align:start position:0%
+1 over N or theta of 1 minus 3 over N
+ 
+
+ align:start position:0%
+1 over N or theta of 1 minus 3 over N
+and so this is how it happens in general
+
+ align:start position:0%
+and so this is how it happens in general
+ 
+
+ align:start position:0%
+and so this is how it happens in general
+in this class it's mostly one
+
+ align:start position:0%
+in this class it's mostly one
+ 
+
+ align:start position:0%
+in this class it's mostly one
+dimensional parameter estimation so it's
+
+ align:start position:0%
+dimensional parameter estimation so it's
+ 
+
+ align:start position:0%
+dimensional parameter estimation so it's
+gonna be a little harder to illustrate
+
+ align:start position:0%
+gonna be a little harder to illustrate
+ 
+
+ align:start position:0%
+gonna be a little harder to illustrate
+that but if you do for example non
+
+ align:start position:0%
+that but if you do for example non
+ 
+
+ align:start position:0%
+that but if you do for example non
+parametric estimation that's all you do
+
+ align:start position:0%
+parametric estimation that's all you do
+ 
+
+ align:start position:0%
+parametric estimation that's all you do
+there's like just wise variants trade
+
+ align:start position:0%
+there's like just wise variants trade
+ 
+
+ align:start position:0%
+there's like just wise variants trade
+offs all the time okay and in between
+
+ align:start position:0%
+offs all the time okay and in between
+ 
+
+ align:start position:0%
+offs all the time okay and in between
+when you have high dimensional
+
+ align:start position:0%
+when you have high dimensional
+ 
+
+ align:start position:0%
+when you have high dimensional
+parametric estimation that happens a lot
+
+ align:start position:0%
+parametric estimation that happens a lot
+ 
+
+ align:start position:0%
+parametric estimation that happens a lot
+as well okay so I'm just gonna go
+
+ align:start position:0%
+as well okay so I'm just gonna go
+ 
+
+ align:start position:0%
+as well okay so I'm just gonna go
+quickly through those two remaining
+
+ align:start position:0%
+quickly through those two remaining
+ 
+
+ align:start position:0%
+quickly through those two remaining
+slides because we've actually seen them
+
+ align:start position:0%
+slides because we've actually seen them
+ 
+
+ align:start position:0%
+slides because we've actually seen them
+but I
+
+ align:start position:0%
+but I
+ 
+
+ align:start position:0%
+but I
+just wanted you to have somewhere a
+
+ align:start position:0%
+just wanted you to have somewhere a
+ 
+
+ align:start position:0%
+just wanted you to have somewhere a
+formal definition of what a confidence
+
+ align:start position:0%
+formal definition of what a confidence
+ 
+
+ align:start position:0%
+formal definition of what a confidence
+interval is and so we fixed a
+
+ align:start position:0%
+interval is and so we fixed a
+ 
+
+ align:start position:0%
+interval is and so we fixed a
+statistical model for n observations X 1
+
+ align:start position:0%
+statistical model for n observations X 1
+ 
+
+ align:start position:0%
+statistical model for n observations X 1
+to X n the parameter theta here is one
+
+ align:start position:0%
+to X n the parameter theta here is one
+ 
+
+ align:start position:0%
+to X n the parameter theta here is one
+dimensional theta is a subset of the
+
+ align:start position:0%
+dimensional theta is a subset of the
+ 
+
+ align:start position:0%
+dimensional theta is a subset of the
+real line and that's why I call I talk
+
+ align:start position:0%
+real line and that's why I call I talk
+ 
+
+ align:start position:0%
+real line and that's why I call I talk
+about intervals right that interval is a
+
+ align:start position:0%
+about intervals right that interval is a
+ 
+
+ align:start position:0%
+about intervals right that interval is a
+subset of the line if I had a subset of
+
+ align:start position:0%
+subset of the line if I had a subset of
+ 
+
+ align:start position:0%
+subset of the line if I had a subset of
+R 2 for example that would no longer be
+
+ align:start position:0%
+R 2 for example that would no longer be
+ 
+
+ align:start position:0%
+R 2 for example that would no longer be
+called an interval but a region okay
+
+ align:start position:0%
+called an interval but a region okay
+ 
+
+ align:start position:0%
+called an interval but a region okay
+just because that's just we could see a
+
+ align:start position:0%
+just because that's just we could see a
+ 
+
+ align:start position:0%
+just because that's just we could see a
+set but confidence sets but people like
+
+ align:start position:0%
+set but confidence sets but people like
+ 
+
+ align:start position:0%
+set but confidence sets but people like
+to say conference region okay so an
+
+ align:start position:0%
+to say conference region okay so an
+ 
+
+ align:start position:0%
+to say conference region okay so an
+interval is just a one-dimensional
+
+ align:start position:0%
+interval is just a one-dimensional
+ 
+
+ align:start position:0%
+interval is just a one-dimensional
+conference region and it has to be an
+
+ align:start position:0%
+conference region and it has to be an
+ 
+
+ align:start position:0%
+conference region and it has to be an
+interval as well okay so a confidence
+
+ align:start position:0%
+interval as well okay so a confidence
+ 
+
+ align:start position:0%
+interval as well okay so a confidence
+interval of level 1 minus alpha all
+
+ align:start position:0%
+interval of level 1 minus alpha all
+ 
+
+ align:start position:0%
+interval of level 1 minus alpha all
+right so we refer to the quality of a
+
+ align:start position:0%
+right so we refer to the quality of a
+ 
+
+ align:start position:0%
+right so we refer to the quality of a
+confidence interval is actually called
+
+ align:start position:0%
+confidence interval is actually called
+ 
+
+ align:start position:0%
+confidence interval is actually called
+its level it takes value 1 minus alpha
+
+ align:start position:0%
+its level it takes value 1 minus alpha
+ 
+
+ align:start position:0%
+its level it takes value 1 minus alpha
+for some positive alpha and so the
+
+ align:start position:0%
+for some positive alpha and so the
+ 
+
+ align:start position:0%
+for some positive alpha and so the
+confidence level the level of the
+
+ align:start position:0%
+confidence level the level of the
+ 
+
+ align:start position:0%
+confidence level the level of the
+confidence interval is between 0 & 1 the
+
+ align:start position:0%
+confidence interval is between 0 & 1 the
+ 
+
+ align:start position:0%
+confidence interval is between 0 & 1 the
+closer to 1 it is the better the
+
+ align:start position:0%
+closer to 1 it is the better the
+ 
+
+ align:start position:0%
+closer to 1 it is the better the
+confidence interval the closer to 0 the
+
+ align:start position:0%
+confidence interval the closer to 0 the
+ 
+
+ align:start position:0%
+confidence interval the closer to 0 the
+worse it is okay and so for any random
+
+ align:start position:0%
+worse it is okay and so for any random
+ 
+
+ align:start position:0%
+worse it is okay and so for any random
+interval so a confidence interval is a
+
+ align:start position:0%
+interval so a confidence interval is a
+ 
+
+ align:start position:0%
+interval so a confidence interval is a
+random interval the bounds of this
+
+ align:start position:0%
+random interval the bounds of this
+ 
+
+ align:start position:0%
+random interval the bounds of this
+interval depends on random data all
+
+ align:start position:0%
+interval depends on random data all
+ 
+
+ align:start position:0%
+interval depends on random data all
+right just like we had x-bar plus minus
+
+ align:start position:0%
+right just like we had x-bar plus minus
+ 
+
+ align:start position:0%
+right just like we had x-bar plus minus
+1 1 over square root of n for example or
+
+ align:start position:0%
+1 1 over square root of n for example or
+ 
+
+ align:start position:0%
+1 1 over square root of n for example or
+two over square root of n this x-bar was
+
+ align:start position:0%
+two over square root of n this x-bar was
+ 
+
+ align:start position:0%
+two over square root of n this x-bar was
+the random thing that would make
+
+ align:start position:0%
+the random thing that would make
+ 
+
+ align:start position:0%
+the random thing that would make
+fluctuate those guys all right and so
+
+ align:start position:0%
+fluctuate those guys all right and so
+ 
+
+ align:start position:0%
+fluctuate those guys all right and so
+now I have an interval and now I have
+
+ align:start position:0%
+now I have an interval and now I have
+ 
+
+ align:start position:0%
+now I have an interval and now I have
+its boundaries but now the boundaries
+
+ align:start position:0%
+its boundaries but now the boundaries
+ 
+
+ align:start position:0%
+its boundaries but now the boundaries
+are not allowed to depend on my unknown
+
+ align:start position:0%
+are not allowed to depend on my unknown
+ 
+
+ align:start position:0%
+are not allowed to depend on my unknown
+parameter otherwise it's not a
+
+ align:start position:0%
+parameter otherwise it's not a
+ 
+
+ align:start position:0%
+parameter otherwise it's not a
+confidence interval just like an
+
+ align:start position:0%
+confidence interval just like an
+ 
+
+ align:start position:0%
+confidence interval just like an
+estimator that depends on the unknown
+
+ align:start position:0%
+estimator that depends on the unknown
+ 
+
+ align:start position:0%
+estimator that depends on the unknown
+parameter is not an estimator
+
+ align:start position:0%
+parameter is not an estimator
+ 
+
+ align:start position:0%
+parameter is not an estimator
+all right the conference interval has to
+
+ align:start position:0%
+all right the conference interval has to
+ 
+
+ align:start position:0%
+all right the conference interval has to
+be something that I can compute once I
+
+ align:start position:0%
+be something that I can compute once I
+ 
+
+ align:start position:0%
+be something that I can compute once I
+collect data and so what I want is that
+
+ align:start position:0%
+collect data and so what I want is that
+ 
+
+ align:start position:0%
+collect data and so what I want is that
+so there's this weird notation the fact
+
+ align:start position:0%
+so there's this weird notation the fact
+ 
+
+ align:start position:0%
+so there's this weird notation the fact
+that I write theta that I can't in so
+
+ align:start position:0%
+that I write theta that I can't in so
+ 
+
+ align:start position:0%
+that I write theta that I can't in so
+that's the probability that I contains
+
+ align:start position:0%
+that's the probability that I contains
+ 
+
+ align:start position:0%
+that's the probability that I contains
+theta you're used to seeing theta
+
+ align:start position:0%
+theta you're used to seeing theta
+ 
+
+ align:start position:0%
+theta you're used to seeing theta
+belongs to I but here I really want to
+
+ align:start position:0%
+belongs to I but here I really want to
+ 
+
+ align:start position:0%
+belongs to I but here I really want to
+emphasize that the randomness is in I
+
+ align:start position:0%
+emphasize that the randomness is in I
+ 
+
+ align:start position:0%
+emphasize that the randomness is in I
+and so the way you actually say it when
+
+ align:start position:0%
+and so the way you actually say it when
+ 
+
+ align:start position:0%
+and so the way you actually say it when
+you read this formula is the probability
+
+ align:start position:0%
+you read this formula is the probability
+ 
+
+ align:start position:0%
+you read this formula is the probability
+that I contains theta is at least 1
+
+ align:start position:0%
+that I contains theta is at least 1
+ 
+
+ align:start position:0%
+that I contains theta is at least 1
+minus alpha all right so it better be
+
+ align:start position:0%
+minus alpha all right so it better be
+ 
+
+ align:start position:0%
+minus alpha all right so it better be
+close to 1 right you want one - ow
+
+ align:start position:0%
+close to 1 right you want one - ow
+ 
+
+ align:start position:0%
+close to 1 right you want one - ow
+to be very close to one because it's
+
+ align:start position:0%
+to be very close to one because it's
+ 
+
+ align:start position:0%
+to be very close to one because it's
+really telling you that whatever random
+
+ align:start position:0%
+really telling you that whatever random
+ 
+
+ align:start position:0%
+really telling you that whatever random
+variable I'm giving you my error bars
+
+ align:start position:0%
+variable I'm giving you my error bars
+ 
+
+ align:start position:0%
+variable I'm giving you my error bars
+are actually covering the right theta
+
+ align:start position:0%
+are actually covering the right theta
+ 
+
+ align:start position:0%
+are actually covering the right theta
+okay and I want this to be true but I
+
+ align:start position:0%
+okay and I want this to be true but I
+ 
+
+ align:start position:0%
+okay and I want this to be true but I
+want this since I don't know what my
+
+ align:start position:0%
+want this since I don't know what my
+ 
+
+ align:start position:0%
+want this since I don't know what my
+confidence my parameter theta is I want
+
+ align:start position:0%
+confidence my parameter theta is I want
+ 
+
+ align:start position:0%
+confidence my parameter theta is I want
+this to hold true for all possible
+
+ align:start position:0%
+this to hold true for all possible
+ 
+
+ align:start position:0%
+this to hold true for all possible
+values of the parameters that nature may
+
+ align:start position:0%
+values of the parameters that nature may
+ 
+
+ align:start position:0%
+values of the parameters that nature may
+have company have come up with from okay
+
+ align:start position:0%
+have company have come up with from okay
+ 
+
+ align:start position:0%
+have company have come up with from okay
+so I want this so there's theta that
+
+ align:start position:0%
+so I want this so there's theta that
+ 
+
+ align:start position:0%
+so I want this so there's theta that
+changes here so the distribution of the
+
+ align:start position:0%
+changes here so the distribution of the
+ 
+
+ align:start position:0%
+changes here so the distribution of the
+interval is actually changing with theta
+
+ align:start position:0%
+interval is actually changing with theta
+ 
+
+ align:start position:0%
+interval is actually changing with theta
+hopefully and theta is changing with
+
+ align:start position:0%
+hopefully and theta is changing with
+ 
+
+ align:start position:0%
+hopefully and theta is changing with
+this guy so regardless of the value of
+
+ align:start position:0%
+this guy so regardless of the value of
+ 
+
+ align:start position:0%
+this guy so regardless of the value of
+theta that I'm getting I want that the
+
+ align:start position:0%
+theta that I'm getting I want that the
+ 
+
+ align:start position:0%
+theta that I'm getting I want that the
+probability that it contains the theta
+
+ align:start position:0%
+probability that it contains the theta
+ 
+
+ align:start position:0%
+probability that it contains the theta
+is actually larger than one minus alpha
+
+ align:start position:0%
+is actually larger than one minus alpha
+ 
+
+ align:start position:0%
+is actually larger than one minus alpha
+okay so I'll come back to in a second I
+
+ align:start position:0%
+okay so I'll come back to in a second I
+ 
+
+ align:start position:0%
+okay so I'll come back to in a second I
+just want to say that here we have we
+
+ align:start position:0%
+just want to say that here we have we
+ 
+
+ align:start position:0%
+just want to say that here we have we
+can talk about asymptotic level and
+
+ align:start position:0%
+can talk about asymptotic level and
+ 
+
+ align:start position:0%
+can talk about asymptotic level and
+that's typically when you use central
+
+ align:start position:0%
+that's typically when you use central
+ 
+
+ align:start position:0%
+that's typically when you use central
+limit theorem to control to compute this
+
+ align:start position:0%
+limit theorem to control to compute this
+ 
+
+ align:start position:0%
+limit theorem to control to compute this
+guy then you're not guaranteed that the
+
+ align:start position:0%
+guy then you're not guaranteed that the
+ 
+
+ align:start position:0%
+guy then you're not guaranteed that the
+value is at least one minus alpha for
+
+ align:start position:0%
+value is at least one minus alpha for
+ 
+
+ align:start position:0%
+value is at least one minus alpha for
+every n but it's actually in the limit
+
+ align:start position:0%
+every n but it's actually in the limit
+ 
+
+ align:start position:0%
+every n but it's actually in the limit
+larger than one minus alpha
+
+ align:start position:0%
+larger than one minus alpha
+ 
+
+ align:start position:0%
+larger than one minus alpha
+okay so if I may be for each fix then
+
+ align:start position:0%
+okay so if I may be for each fix then
+ 
+
+ align:start position:0%
+okay so if I may be for each fix then
+it's going to be not true but for as n
+
+ align:start position:0%
+it's going to be not true but for as n
+ 
+
+ align:start position:0%
+it's going to be not true but for as n
+goes to infinity it's actually going to
+
+ align:start position:0%
+goes to infinity it's actually going to
+ 
+
+ align:start position:0%
+goes to infinity it's actually going to
+become true if you want this to hold for
+
+ align:start position:0%
+become true if you want this to hold for
+ 
+
+ align:start position:0%
+become true if you want this to hold for
+every N you actually need to use things
+
+ align:start position:0%
+every N you actually need to use things
+ 
+
+ align:start position:0%
+every N you actually need to use things
+such as have things in equality that we
+
+ align:start position:0%
+such as have things in equality that we
+ 
+
+ align:start position:0%
+such as have things in equality that we
+described at some point okay so as a
+
+ align:start position:0%
+described at some point okay so as a
+ 
+
+ align:start position:0%
+described at some point okay so as a
+rule of thumb once you if you use the
+
+ align:start position:0%
+rule of thumb once you if you use the
+ 
+
+ align:start position:0%
+rule of thumb once you if you use the
+central limit theorem you're dealing
+
+ align:start position:0%
+central limit theorem you're dealing
+ 
+
+ align:start position:0%
+central limit theorem you're dealing
+with a confidence interval with
+
+ align:start position:0%
+with a confidence interval with
+ 
+
+ align:start position:0%
+with a confidence interval with
+asymptotic level one minus alpha and the
+
+ align:start position:0%
+asymptotic level one minus alpha and the
+ 
+
+ align:start position:0%
+asymptotic level one minus alpha and the
+reason is because you actually want to
+
+ align:start position:0%
+reason is because you actually want to
+ 
+
+ align:start position:0%
+reason is because you actually want to
+get some the quintiles of the normal the
+
+ align:start position:0%
+get some the quintiles of the normal the
+ 
+
+ align:start position:0%
+get some the quintiles of the normal the
+Gaussian distribution that comes from
+
+ align:start position:0%
+Gaussian distribution that comes from
+ 
+
+ align:start position:0%
+Gaussian distribution that comes from
+the central limit theorem and if you
+
+ align:start position:0%
+the central limit theorem and if you
+ 
+
+ align:start position:0%
+the central limit theorem and if you
+want to use huffing for example you
+
+ align:start position:0%
+want to use huffing for example you
+ 
+
+ align:start position:0%
+want to use huffing for example you
+might actually get away with a
+
+ align:start position:0%
+might actually get away with a
+ 
+
+ align:start position:0%
+might actually get away with a
+confidence interval that's actually true
+
+ align:start position:0%
+confidence interval that's actually true
+ 
+
+ align:start position:0%
+confidence interval that's actually true
+even not asymptotically just the regular
+
+ align:start position:0%
+even not asymptotically just the regular
+ 
+
+ align:start position:0%
+even not asymptotically just the regular
+comfortable okay so this is the formal
+
+ align:start position:0%
+comfortable okay so this is the formal
+ 
+
+ align:start position:0%
+comfortable okay so this is the formal
+definition it's a bit of a mouthful but
+
+ align:start position:0%
+definition it's a bit of a mouthful but
+ 
+
+ align:start position:0%
+definition it's a bit of a mouthful but
+we actually the best way to understand
+
+ align:start position:0%
+we actually the best way to understand
+ 
+
+ align:start position:0%
+we actually the best way to understand
+them is to build them all right now at
+
+ align:start position:0%
+them is to build them all right now at
+ 
+
+ align:start position:0%
+them is to build them all right now at
+some point I said and I think it was
+
+ align:start position:0%
+some point I said and I think it was
+ 
+
+ align:start position:0%
+some point I said and I think it was
+part of the homework right so here I
+
+ align:start position:0%
+part of the homework right so here I
+ 
+
+ align:start position:0%
+part of the homework right so here I
+really say the probability the true
+
+ align:start position:0%
+really say the probability the true
+ 
+
+ align:start position:0%
+really say the probability the true
+parameter belongs to the confidence
+
+ align:start position:0%
+parameter belongs to the confidence
+ 
+
+ align:start position:0%
+parameter belongs to the confidence
+interval is actually 1 minus alpha and
+
+ align:start position:0%
+interval is actually 1 minus alpha and
+ 
+
+ align:start position:0%
+interval is actually 1 minus alpha and
+so that's because here this confidence
+
+ align:start position:0%
+so that's because here this confidence
+ 
+
+ align:start position:0%
+so that's because here this confidence
+interval is still a random variable now
+
+ align:start position:0%
+interval is still a random variable now
+ 
+
+ align:start position:0%
+interval is still a random variable now
+if I start plugging in numbers instead
+
+ align:start position:0%
+if I start plugging in numbers instead
+ 
+
+ align:start position:0%
+if I start plugging in numbers instead
+of the random variables x1 to xn I start
+
+ align:start position:0%
+of the random variables x1 to xn I start
+ 
+
+ align:start position:0%
+of the random variables x1 to xn I start
+putting 1
+
+ align:start position:0%
+putting 1
+ 
+
+ align:start position:0%
+putting 1
+zero one zero zero zero one like I did
+
+ align:start position:0%
+zero one zero zero zero one like I did
+ 
+
+ align:start position:0%
+zero one zero zero zero one like I did
+for the kiss example then in this case
+
+ align:start position:0%
+for the kiss example then in this case
+ 
+
+ align:start position:0%
+for the kiss example then in this case
+the random interval is actually going to
+
+ align:start position:0%
+the random interval is actually going to
+ 
+
+ align:start position:0%
+the random interval is actually going to
+be 0.42 0.65 and this guy the
+
+ align:start position:0%
+be 0.42 0.65 and this guy the
+ 
+
+ align:start position:0%
+be 0.42 0.65 and this guy the
+probability data belongs to it is not
+
+ align:start position:0%
+probability data belongs to it is not
+ 
+
+ align:start position:0%
+probability data belongs to it is not
+one minus alpha
+
+ align:start position:0%
+one minus alpha
+ 
+
+ align:start position:0%
+one minus alpha
+it's just either zero if it's not in
+
+ align:start position:0%
+it's just either zero if it's not in
+ 
+
+ align:start position:0%
+it's just either zero if it's not in
+there or 20 fits in there okay so so
+
+ align:start position:0%
+there or 20 fits in there okay so so
+ 
+
+ align:start position:0%
+there or 20 fits in there okay so so
+there's here's the example that we had
+
+ align:start position:0%
+there's here's the example that we had
+ 
+
+ align:start position:0%
+there's here's the example that we had
+right so just let's look at back into
+
+ align:start position:0%
+right so just let's look at back into
+ 
+
+ align:start position:0%
+right so just let's look at back into
+our you know favorite example which is
+
+ align:start position:0%
+our you know favorite example which is
+ 
+
+ align:start position:0%
+our you know favorite example which is
+the average of Bernoulli random
+
+ align:start position:0%
+the average of Bernoulli random
+ 
+
+ align:start position:0%
+the average of Bernoulli random
+variables so we studied that maybe
+
+ align:start position:0%
+variables so we studied that maybe
+ 
+
+ align:start position:0%
+variables so we studied that maybe
+that's the third time already so the
+
+ align:start position:0%
+that's the third time already so the
+ 
+
+ align:start position:0%
+that's the third time already so the
+sample average xn bar is a strongly
+
+ align:start position:0%
+sample average xn bar is a strongly
+ 
+
+ align:start position:0%
+sample average xn bar is a strongly
+consistent estimator of P right that was
+
+ align:start position:0%
+consistent estimator of P right that was
+ 
+
+ align:start position:0%
+consistent estimator of P right that was
+one of the properties that we wanted
+
+ align:start position:0%
+one of the properties that we wanted
+ 
+
+ align:start position:0%
+one of the properties that we wanted
+this strongly consistent means that as n
+
+ align:start position:0%
+this strongly consistent means that as n
+ 
+
+ align:start position:0%
+this strongly consistent means that as n
+goes to infinity converges almost surely
+
+ align:start position:0%
+goes to infinity converges almost surely
+ 
+
+ align:start position:0%
+goes to infinity converges almost surely
+to the true parameter that's the strong
+
+ align:start position:0%
+to the true parameter that's the strong
+ 
+
+ align:start position:0%
+to the true parameter that's the strong
+law of large number it is consistent
+
+ align:start position:0%
+law of large number it is consistent
+ 
+
+ align:start position:0%
+law of large number it is consistent
+also because it's strong consistent so
+
+ align:start position:0%
+also because it's strong consistent so
+ 
+
+ align:start position:0%
+also because it's strong consistent so
+it also comes all the converges in
+
+ align:start position:0%
+it also comes all the converges in
+ 
+
+ align:start position:0%
+it also comes all the converges in
+probability which makes it consistent
+
+ align:start position:0%
+probability which makes it consistent
+ 
+
+ align:start position:0%
+probability which makes it consistent
+it's in biased we've seen that we've
+
+ align:start position:0%
+it's in biased we've seen that we've
+ 
+
+ align:start position:0%
+it's in biased we've seen that we've
+actually computed it's a quadratic risk
+
+ align:start position:0%
+actually computed it's a quadratic risk
+ 
+
+ align:start position:0%
+actually computed it's a quadratic risk
+and now what I have is that if I look at
+
+ align:start position:0%
+and now what I have is that if I look at
+ 
+
+ align:start position:0%
+and now what I have is that if I look at
+thanks to the central limit theorem we
+
+ align:start position:0%
+thanks to the central limit theorem we
+ 
+
+ align:start position:0%
+thanks to the central limit theorem we
+actually did this we built a confidence
+
+ align:start position:0%
+actually did this we built a confidence
+ 
+
+ align:start position:0%
+actually did this we built a confidence
+interval at level one minus alpha
+
+ align:start position:0%
+interval at level one minus alpha
+ 
+
+ align:start position:0%
+interval at level one minus alpha
+right asymptotic level sorry asymptotic
+
+ align:start position:0%
+right asymptotic level sorry asymptotic
+ 
+
+ align:start position:0%
+right asymptotic level sorry asymptotic
+level one minus alpha
+
+ align:start position:0%
+level one minus alpha
+ 
+
+ align:start position:0%
+level one minus alpha
+alright and so here this is how we did
+
+ align:start position:0%
+alright and so here this is how we did
+ 
+
+ align:start position:0%
+alright and so here this is how we did
+it let me just go through it again so we
+
+ align:start position:0%
+it let me just go through it again so we
+ 
+
+ align:start position:0%
+it let me just go through it again so we
+know from the central limit theorem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the central limit theorem tells us
+
+ align:start position:0%
+so the central limit theorem tells us
+ 
+
+ align:start position:0%
+so the central limit theorem tells us
+that xn bar minus P divided by square
+
+ align:start position:0%
+that xn bar minus P divided by square
+ 
+
+ align:start position:0%
+that xn bar minus P divided by square
+root of P 1 minus P square root of n
+
+ align:start position:0%
+root of P 1 minus P square root of n
+ 
+
+ align:start position:0%
+root of P 1 minus P square root of n
+converges and distribution as n goes to
+
+ align:start position:0%
+converges and distribution as n goes to
+ 
+
+ align:start position:0%
+converges and distribution as n goes to
+infinity to some standard normal
+
+ align:start position:0%
+infinity to some standard normal
+ 
+
+ align:start position:0%
+infinity to some standard normal
+distribution right so what it means is
+
+ align:start position:0%
+distribution right so what it means is
+ 
+
+ align:start position:0%
+distribution right so what it means is
+that if I look at the probability under
+
+ align:start position:0%
+that if I look at the probability under
+ 
+
+ align:start position:0%
+that if I look at the probability under
+the true P that's greater than xn bar
+
+ align:start position:0%
+the true P that's greater than xn bar
+ 
+
+ align:start position:0%
+the true P that's greater than xn bar
+minus P divided by square root of P 1
+
+ align:start position:0%
+minus P divided by square root of P 1
+ 
+
+ align:start position:0%
+minus P divided by square root of P 1
+minus P is less than Q alpha over 2
+
+ align:start position:0%
+minus P is less than Q alpha over 2
+ 
+
+ align:start position:0%
+minus P is less than Q alpha over 2
+where this is the definition of the
+
+ align:start position:0%
+where this is the definition of the
+ 
+
+ align:start position:0%
+where this is the definition of the
+quintile then this guy and I'm actually
+
+ align:start position:0%
+quintile then this guy and I'm actually
+ 
+
+ align:start position:0%
+quintile then this guy and I'm actually
+going to use the write the same notation
+
+ align:start position:0%
+going to use the write the same notation
+ 
+
+ align:start position:0%
+going to use the write the same notation
+limit as n goes to infinity right this
+
+ align:start position:0%
+limit as n goes to infinity right this
+ 
+
+ align:start position:0%
+limit as n goes to infinity right this
+is the same thing right so this is
+
+ align:start position:0%
+is the same thing right so this is
+ 
+
+ align:start position:0%
+is the same thing right so this is
+actually going to be equal to 1 minus
+
+ align:start position:0%
+actually going to be equal to 1 minus
+ 
+
+ align:start position:0%
+actually going to be equal to 1 minus
+alpha right that's exactly what I did
+
+ align:start position:0%
+alpha right that's exactly what I did
+ 
+
+ align:start position:0%
+alpha right that's exactly what I did
+last time this is by definition of the
+
+ align:start position:0%
+last time this is by definition of the
+ 
+
+ align:start position:0%
+last time this is by definition of the
+quantile of a standard Gaussian and of
+
+ align:start position:0%
+quantile of a standard Gaussian and of
+ 
+
+ align:start position:0%
+quantile of a standard Gaussian and of
+limiting distribution okay so the
+
+ align:start position:0%
+limiting distribution okay so the
+ 
+
+ align:start position:0%
+limiting distribution okay so the
+probabilities computed on this guy as in
+
+ align:start position:0%
+probabilities computed on this guy as in
+ 
+
+ align:start position:0%
+probabilities computed on this guy as in
+the limit converges to the probability
+
+ align:start position:0%
+the limit converges to the probability
+ 
+
+ align:start position:0%
+the limit converges to the probability
+computer on this guy and we know that
+
+ align:start position:0%
+computer on this guy and we know that
+ 
+
+ align:start position:0%
+computer on this guy and we know that
+this is just the probability the
+
+ align:start position:0%
+this is just the probability the
+ 
+
+ align:start position:0%
+this is just the probability the
+absolute value of some n0 1 is less than
+
+ align:start position:0%
+absolute value of some n0 1 is less than
+ 
+
+ align:start position:0%
+absolute value of some n0 1 is less than
+Q alpha over 2 okay and so in particular
+
+ align:start position:0%
+Q alpha over 2 okay and so in particular
+ 
+
+ align:start position:0%
+Q alpha over 2 okay and so in particular
+if it's equal then I can put them larger
+
+ align:start position:0%
+if it's equal then I can put them larger
+ 
+
+ align:start position:0%
+if it's equal then I can put them larger
+than or equal to which guarantees my
+
+ align:start position:0%
+than or equal to which guarantees my
+ 
+
+ align:start position:0%
+than or equal to which guarantees my
+asymptotic confidence level and I just
+
+ align:start position:0%
+asymptotic confidence level and I just
+ 
+
+ align:start position:0%
+asymptotic confidence level and I just
+solved for P all right so this is
+
+ align:start position:0%
+solved for P all right so this is
+ 
+
+ align:start position:0%
+solved for P all right so this is
+equivalent to the limit as n goes to
+
+ align:start position:0%
+equivalent to the limit as n goes to
+ 
+
+ align:start position:0%
+equivalent to the limit as n goes to
+infinity of the probability that theta
+
+ align:start position:0%
+infinity of the probability that theta
+ 
+
+ align:start position:0%
+infinity of the probability that theta
+is between xn bar minus Q alpha over 2
+
+ align:start position:0%
+is between xn bar minus Q alpha over 2
+ 
+
+ align:start position:0%
+is between xn bar minus Q alpha over 2
+divided by x square root of P 1 minus P
+
+ align:start position:0%
+divided by x square root of P 1 minus P
+ 
+
+ align:start position:0%
+divided by x square root of P 1 minus P
+divided by Sturdevant xn bar plus Q
+
+ align:start position:0%
+divided by Sturdevant xn bar plus Q
+ 
+
+ align:start position:0%
+divided by Sturdevant xn bar plus Q
+alpha over 2 square root of P 1 minus P
+
+ align:start position:0%
+alpha over 2 square root of P 1 minus P
+ 
+
+ align:start position:0%
+alpha over 2 square root of P 1 minus P
+divided by square root of n is larger
+
+ align:start position:0%
+divided by square root of n is larger
+ 
+
+ align:start position:0%
+divided by square root of n is larger
+than or equal to 1 minus alpha and so
+
+ align:start position:0%
+than or equal to 1 minus alpha and so
+ 
+
+ align:start position:0%
+than or equal to 1 minus alpha and so
+there you go I have my confidence
+
+ align:start position:0%
+there you go I have my confidence
+ 
+
+ align:start position:0%
+there you go I have my confidence
+interval
+
+ align:start position:0%
+interval
+ 
+
+ align:start position:0%
+interval
+except that not right we just said that
+
+ align:start position:0%
+except that not right we just said that
+ 
+
+ align:start position:0%
+except that not right we just said that
+the balance of a confidence interval may
+
+ align:start position:0%
+the balance of a confidence interval may
+ 
+
+ align:start position:0%
+the balance of a confidence interval may
+not depend on the unknown parameter and
+
+ align:start position:0%
+not depend on the unknown parameter and
+ 
+
+ align:start position:0%
+not depend on the unknown parameter and
+here they do and so we actually came up
+
+ align:start position:0%
+here they do and so we actually came up
+ 
+
+ align:start position:0%
+here they do and so we actually came up
+with two ways of getting rid of this
+
+ align:start position:0%
+with two ways of getting rid of this
+ 
+
+ align:start position:0%
+with two ways of getting rid of this
+since we only need this thing so this
+
+ align:start position:0%
+since we only need this thing so this
+ 
+
+ align:start position:0%
+since we only need this thing so this
+thing as we said is really equal
+
+ align:start position:0%
+thing as we said is really equal
+ 
+
+ align:start position:0%
+thing as we said is really equal
+every time I'm gonna make this guy
+
+ align:start position:0%
+every time I'm gonna make this guy
+ 
+
+ align:start position:0%
+every time I'm gonna make this guy
+smaller and this guy larger I'm only
+
+ align:start position:0%
+smaller and this guy larger I'm only
+ 
+
+ align:start position:0%
+smaller and this guy larger I'm only
+going to increase the probability and so
+
+ align:start position:0%
+going to increase the probability and so
+ 
+
+ align:start position:0%
+going to increase the probability and so
+what we do is we actually just take the
+
+ align:start position:0%
+what we do is we actually just take the
+ 
+
+ align:start position:0%
+what we do is we actually just take the
+largest possible value for P one minus P
+
+ align:start position:0%
+largest possible value for P one minus P
+ 
+
+ align:start position:0%
+largest possible value for P one minus P
+which makes the interval as large as
+
+ align:start position:0%
+which makes the interval as large as
+ 
+
+ align:start position:0%
+which makes the interval as large as
+possible okay and so now I have this I
+
+ align:start position:0%
+possible okay and so now I have this I
+ 
+
+ align:start position:0%
+possible okay and so now I have this I
+just do one of the two tricks I replace
+
+ align:start position:0%
+just do one of the two tricks I replace
+ 
+
+ align:start position:0%
+just do one of the two tricks I replace
+P 1 minus P by their upper bound which
+
+ align:start position:0%
+P 1 minus P by their upper bound which
+ 
+
+ align:start position:0%
+P 1 minus P by their upper bound which
+is 1/4 okay as we said P 1 minus P the
+
+ align:start position:0%
+is 1/4 okay as we said P 1 minus P the
+ 
+
+ align:start position:0%
+is 1/4 okay as we said P 1 minus P the
+function looks like this so I just take
+
+ align:start position:0%
+function looks like this so I just take
+ 
+
+ align:start position:0%
+function looks like this so I just take
+the value here at 1/2 or I can use
+
+ align:start position:0%
+the value here at 1/2 or I can use
+ 
+
+ align:start position:0%
+the value here at 1/2 or I can use
+Slutsky and say that if I replace P by
+
+ align:start position:0%
+Slutsky and say that if I replace P by
+ 
+
+ align:start position:0%
+Slutsky and say that if I replace P by
+xn bar but it's the same as just
+
+ align:start position:0%
+xn bar but it's the same as just
+ 
+
+ align:start position:0%
+xn bar but it's the same as just
+replacing P by xn bar here and by
+
+ align:start position:0%
+replacing P by xn bar here and by
+ 
+
+ align:start position:0%
+replacing P by xn bar here and by
+Slutsky we know that this is actually
+
+ align:start position:0%
+Slutsky we know that this is actually
+ 
+
+ align:start position:0%
+Slutsky we know that this is actually
+converging also to some standard
+
+ align:start position:0%
+converging also to some standard
+ 
+
+ align:start position:0%
+converging also to some standard
+Gaussian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oK we've seen that when we saw Slutsky
+
+ align:start position:0%
+oK we've seen that when we saw Slutsky
+ 
+
+ align:start position:0%
+oK we've seen that when we saw Slutsky
+as an example all right and so those two
+
+ align:start position:0%
+as an example all right and so those two
+ 
+
+ align:start position:0%
+as an example all right and so those two
+things actually just because I'm taking
+
+ align:start position:0%
+things actually just because I'm taking
+ 
+
+ align:start position:0%
+things actually just because I'm taking
+the limit and I'm only caring about the
+
+ align:start position:0%
+the limit and I'm only caring about the
+ 
+
+ align:start position:0%
+the limit and I'm only caring about the
+asymptotic confidence level I can
+
+ align:start position:0%
+asymptotic confidence level I can
+ 
+
+ align:start position:0%
+asymptotic confidence level I can
+actually just plug in consistent
+
+ align:start position:0%
+actually just plug in consistent
+ 
+
+ align:start position:0%
+actually just plug in consistent
+quantities in there such as xn bar where
+
+ align:start position:0%
+quantities in there such as xn bar where
+ 
+
+ align:start position:0%
+quantities in there such as xn bar where
+I don't have a P and that gives me
+
+ align:start position:0%
+I don't have a P and that gives me
+ 
+
+ align:start position:0%
+I don't have a P and that gives me
+another contrast number all right so
+
+ align:start position:0%
+another contrast number all right so
+ 
+
+ align:start position:0%
+another contrast number all right so
+this by now hopefully after doing it
+
+ align:start position:0%
+this by now hopefully after doing it
+ 
+
+ align:start position:0%
+this by now hopefully after doing it
+three times you should really really be
+
+ align:start position:0%
+three times you should really really be
+ 
+
+ align:start position:0%
+three times you should really really be
+comfortable with just creating this
+
+ align:start position:0%
+comfortable with just creating this
+ 
+
+ align:start position:0%
+comfortable with just creating this
+conference interval right we did it
+
+ align:start position:0%
+conference interval right we did it
+ 
+
+ align:start position:0%
+conference interval right we did it
+three times in class I think you
+
+ align:start position:0%
+three times in class I think you
+ 
+
+ align:start position:0%
+three times in class I think you
+probably did it another couple times in
+
+ align:start position:0%
+probably did it another couple times in
+ 
+
+ align:start position:0%
+probably did it another couple times in
+your homework so just make sure you're
+
+ align:start position:0%
+your homework so just make sure you're
+ 
+
+ align:start position:0%
+your homework so just make sure you're
+comfortable with this all right that's
+
+ align:start position:0%
+comfortable with this all right that's
+ 
+
+ align:start position:0%
+comfortable with this all right that's
+one of the basic things you would want
+
+ align:start position:0%
+one of the basic things you would want
+ 
+
+ align:start position:0%
+one of the basic things you would want
+to know are there any questions so we're
+
+ align:start position:0%
+to know are there any questions so we're
+ 
+
+ align:start position:0%
+to know are there any questions so we're
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's not Slutsky right so so so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Slutsky tells you that if you stucks is
+
+ align:start position:0%
+Slutsky tells you that if you stucks is
+ 
+
+ align:start position:0%
+Slutsky tells you that if you stucks is
+about combining two types of convergence
+
+ align:start position:0%
+about combining two types of convergence
+ 
+
+ align:start position:0%
+about combining two types of convergence
+right so Slutsky tells you that if you
+
+ align:start position:0%
+right so Slutsky tells you that if you
+ 
+
+ align:start position:0%
+right so Slutsky tells you that if you
+actually have one xn that converges to X
+
+ align:start position:0%
+actually have one xn that converges to X
+ 
+
+ align:start position:0%
+actually have one xn that converges to X
+and distribution and yn that converges
+
+ align:start position:0%
+and distribution and yn that converges
+ 
+
+ align:start position:0%
+and distribution and yn that converges
+to Y in probability then you can
+
+ align:start position:0%
+to Y in probability then you can
+ 
+
+ align:start position:0%
+to Y in probability then you can
+actually multiply xn and yn and get that
+
+ align:start position:0%
+actually multiply xn and yn and get that
+ 
+
+ align:start position:0%
+actually multiply xn and yn and get that
+the limiting distribution is the product
+
+ align:start position:0%
+the limiting distribution is the product
+ 
+
+ align:start position:0%
+the limiting distribution is the product
+of X and X and y where X is now a
+
+ align:start position:0%
+of X and X and y where X is now a
+ 
+
+ align:start position:0%
+of X and X and y where X is now a
+constant okay and here we have the
+
+ align:start position:0%
+constant okay and here we have the
+ 
+
+ align:start position:0%
+constant okay and here we have the
+constant which is 1 okay so but I did
+
+ align:start position:0%
+constant which is 1 okay so but I did
+ 
+
+ align:start position:0%
+constant which is 1 okay so but I did
+that already right
+
+ align:start position:0%
+that already right
+ 
+
+ align:start position:0%
+that already right
+using Slutsky to replace it for the FIR
+
+ align:start position:0%
+using Slutsky to replace it for the FIR
+ 
+
+ align:start position:0%
+using Slutsky to replace it for the FIR
+to replace PN P by xn bar we've done
+
+ align:start position:0%
+to replace PN P by xn bar we've done
+ 
+
+ align:start position:0%
+to replace PN P by xn bar we've done
+that last time maybe a couple times ago
+
+ align:start position:0%
+that last time maybe a couple times ago
+ 
+
+ align:start position:0%
+that last time maybe a couple times ago
+actually yeah that's correct
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so of course the answer the short answer
+
+ align:start position:0%
+so of course the answer the short answer
+ 
+
+ align:start position:0%
+so of course the answer the short answer
+is no for so here's how I would you
+
+ align:start position:0%
+is no for so here's how I would you
+ 
+
+ align:start position:0%
+is no for so here's how I would you
+would go about thinking about which
+
+ align:start position:0%
+would go about thinking about which
+ 
+
+ align:start position:0%
+would go about thinking about which
+might let it better right so there's
+
+ align:start position:0%
+might let it better right so there's
+ 
+
+ align:start position:0%
+might let it better right so there's
+always the more conservative method the
+
+ align:start position:0%
+always the more conservative method the
+ 
+
+ align:start position:0%
+always the more conservative method the
+first one the only thing you're losing
+
+ align:start position:0%
+first one the only thing you're losing
+ 
+
+ align:start position:0%
+first one the only thing you're losing
+is the rate of convergence of the
+
+ align:start position:0%
+is the rate of convergence of the
+ 
+
+ align:start position:0%
+is the rate of convergence of the
+central limit theorem all right so it's
+
+ align:start position:0%
+central limit theorem all right so it's
+ 
+
+ align:start position:0%
+central limit theorem all right so it's
+essentially if n is large enough so that
+
+ align:start position:0%
+essentially if n is large enough so that
+ 
+
+ align:start position:0%
+essentially if n is large enough so that
+the central limit theorem approximation
+
+ align:start position:0%
+the central limit theorem approximation
+ 
+
+ align:start position:0%
+the central limit theorem approximation
+is very good then that's all you're
+
+ align:start position:0%
+is very good then that's all you're
+ 
+
+ align:start position:0%
+is very good then that's all you're
+gonna be you're gonna be losing right of
+
+ align:start position:0%
+gonna be you're gonna be losing right of
+ 
+
+ align:start position:0%
+gonna be you're gonna be losing right of
+course the price to pace that you're
+
+ align:start position:0%
+course the price to pace that you're
+ 
+
+ align:start position:0%
+course the price to pace that you're
+comfortable is wider than it would be if
+
+ align:start position:0%
+comfortable is wider than it would be if
+ 
+
+ align:start position:0%
+comfortable is wider than it would be if
+you were to use let's key for this
+
+ align:start position:0%
+you were to use let's key for this
+ 
+
+ align:start position:0%
+you were to use let's key for this
+particular problem right typically wider
+
+ align:start position:0%
+particular problem right typically wider
+ 
+
+ align:start position:0%
+particular problem right typically wider
+actually it is always wider all right
+
+ align:start position:0%
+actually it is always wider all right
+ 
+
+ align:start position:0%
+actually it is always wider all right
+and so because xn bar my 1 minus xn bar
+
+ align:start position:0%
+and so because xn bar my 1 minus xn bar
+ 
+
+ align:start position:0%
+and so because xn bar my 1 minus xn bar
+is always less than 1/4 as well and so
+
+ align:start position:0%
+is always less than 1/4 as well and so
+ 
+
+ align:start position:0%
+is always less than 1/4 as well and so
+so that's that's that's the first the
+
+ align:start position:0%
+so that's that's that's the first the
+ 
+
+ align:start position:0%
+so that's that's that's the first the
+first thing you know so Slutsky
+
+ align:start position:0%
+first thing you know so Slutsky
+ 
+
+ align:start position:0%
+first thing you know so Slutsky
+basically adds you're relying on the
+
+ align:start position:0%
+basically adds you're relying on the
+ 
+
+ align:start position:0%
+basically adds you're relying on the
+central limit you're relying on these
+
+ align:start position:0%
+central limit you're relying on these
+ 
+
+ align:start position:0%
+central limit you're relying on these
+synthetics again now of course you don't
+
+ align:start position:0%
+synthetics again now of course you don't
+ 
+
+ align:start position:0%
+synthetics again now of course you don't
+want to be conservative because you
+
+ align:start position:0%
+want to be conservative because you
+ 
+
+ align:start position:0%
+want to be conservative because you
+actually want to squeeze as much from
+
+ align:start position:0%
+actually want to squeeze as much from
+ 
+
+ align:start position:0%
+actually want to squeeze as much from
+your data as you can right so it depends
+
+ align:start position:0%
+your data as you can right so it depends
+ 
+
+ align:start position:0%
+your data as you can right so it depends
+on how comfortable and how critical it
+
+ align:start position:0%
+on how comfortable and how critical it
+ 
+
+ align:start position:0%
+on how comfortable and how critical it
+is for you to put a valid error bars
+
+ align:start position:0%
+is for you to put a valid error bars
+ 
+
+ align:start position:0%
+is for you to put a valid error bars
+right if they're valid in this entire
+
+ align:start position:0%
+right if they're valid in this entire
+ 
+
+ align:start position:0%
+right if they're valid in this entire
+extend maybe you're actually gonna go
+
+ align:start position:0%
+extend maybe you're actually gonna go
+ 
+
+ align:start position:0%
+extend maybe you're actually gonna go
+with Slutsky so it actually gives you
+
+ align:start position:0%
+with Slutsky so it actually gives you
+ 
+
+ align:start position:0%
+with Slutsky so it actually gives you
+slightly narrower confidence intervals
+
+ align:start position:0%
+slightly narrower confidence intervals
+ 
+
+ align:start position:0%
+slightly narrower confidence intervals
+and and so you feel like you're a little
+
+ align:start position:0%
+and and so you feel like you're a little
+ 
+
+ align:start position:0%
+and and so you feel like you're a little
+more company you you have a more precise
+
+ align:start position:0%
+more company you you have a more precise
+ 
+
+ align:start position:0%
+more company you you have a more precise
+answer now if you really need to be
+
+ align:start position:0%
+answer now if you really need to be
+ 
+
+ align:start position:0%
+answer now if you really need to be
+super conservative then you're actually
+
+ align:start position:0%
+super conservative then you're actually
+ 
+
+ align:start position:0%
+super conservative then you're actually
+gonna go with a with the P 1 minus P
+
+ align:start position:0%
+gonna go with a with the P 1 minus P
+ 
+
+ align:start position:0%
+gonna go with a with the P 1 minus P
+actually if you need to be even more
+
+ align:start position:0%
+actually if you need to be even more
+ 
+
+ align:start position:0%
+actually if you need to be even more
+conservative you were gonna go with hub
+
+ align:start position:0%
+conservative you were gonna go with hub
+ 
+
+ align:start position:0%
+conservative you were gonna go with hub
+ding so you don't even have to rely on
+
+ align:start position:0%
+ding so you don't even have to rely on
+ 
+
+ align:start position:0%
+ding so you don't even have to rely on
+the asymptotic level at all but then
+
+ align:start position:0%
+the asymptotic level at all but then
+ 
+
+ align:start position:0%
+the asymptotic level at all but then
+your comforts interval becomes twice as
+
+ align:start position:0%
+your comforts interval becomes twice as
+ 
+
+ align:start position:0%
+your comforts interval becomes twice as
+wide and twice as wide and it becomes
+
+ align:start position:0%
+wide and twice as wide and it becomes
+ 
+
+ align:start position:0%
+wide and twice as wide and it becomes
+wider and wider as you go right so
+
+ align:start position:0%
+wider and wider as you go right so
+ 
+
+ align:start position:0%
+wider and wider as you go right so
+depends on the I mean there's a lot of
+
+ align:start position:0%
+depends on the I mean there's a lot of
+ 
+
+ align:start position:0%
+depends on the I mean there's a lot of
+that in statistics which is you know
+
+ align:start position:0%
+that in statistics which is you know
+ 
+
+ align:start position:0%
+that in statistics which is you know
+gauging how critical it is for you to
+
+ align:start position:0%
+gauging how critical it is for you to
+ 
+
+ align:start position:0%
+gauging how critical it is for you to
+output valid error bounds or if they're
+
+ align:start position:0%
+output valid error bounds or if they're
+ 
+
+ align:start position:0%
+output valid error bounds or if they're
+really just here to be indicative of you
+
+ align:start position:0%
+really just here to be indicative of you
+ 
+
+ align:start position:0%
+really just here to be indicative of you
+know the precision of the estimator that
+
+ align:start position:0%
+know the precision of the estimator that
+ 
+
+ align:start position:0%
+know the precision of the estimator that
+you you gave from a more qualitative
+
+ align:start position:0%
+you you gave from a more qualitative
+ 
+
+ align:start position:0%
+you you gave from a more qualitative
+perspective yeah so here there's
+
+ align:start position:0%
+perspective yeah so here there's
+ 
+
+ align:start position:0%
+perspective yeah so here there's
+basically a bunch of errors there's one
+
+ align:start position:0%
+basically a bunch of errors there's one
+ 
+
+ align:start position:0%
+basically a bunch of errors there's one
+that's so there's a theorem called bear
+
+ align:start position:0%
+that's so there's a theorem called bear
+ 
+
+ align:start position:0%
+that's so there's a theorem called bear
+yes and that qualifies how far this
+
+ align:start position:0%
+yes and that qualifies how far this
+ 
+
+ align:start position:0%
+yes and that qualifies how far this
+probability is from 1 minus alpha
+
+ align:start position:0%
+probability is from 1 minus alpha
+ 
+
+ align:start position:0%
+probability is from 1 minus alpha
+but the constants are terrible so
+
+ align:start position:0%
+but the constants are terrible so
+ 
+
+ align:start position:0%
+but the constants are terrible so
+they're it's not very helpful but it
+
+ align:start position:0%
+they're it's not very helpful but it
+ 
+
+ align:start position:0%
+they're it's not very helpful but it
+tells you as n grows how smaller this
+
+ align:start position:0%
+tells you as n grows how smaller this
+ 
+
+ align:start position:0%
+tells you as n grows how smaller this
+thing is growth becomes smaller and then
+
+ align:start position:0%
+thing is growth becomes smaller and then
+ 
+
+ align:start position:0%
+thing is growth becomes smaller and then
+for Slutsky
+
+ align:start position:0%
+for Slutsky
+ 
+
+ align:start position:0%
+for Slutsky
+again you're multiplying something that
+
+ align:start position:0%
+again you're multiplying something that
+ 
+
+ align:start position:0%
+again you're multiplying something that
+converges by something that fluctuates
+
+ align:start position:0%
+converges by something that fluctuates
+ 
+
+ align:start position:0%
+converges by something that fluctuates
+around one so you need to understand how
+
+ align:start position:0%
+around one so you need to understand how
+ 
+
+ align:start position:0%
+around one so you need to understand how
+this thing fluctuates now there's
+
+ align:start position:0%
+this thing fluctuates now there's
+ 
+
+ align:start position:0%
+this thing fluctuates now there's
+something that shows up is basically
+
+ align:start position:0%
+something that shows up is basically
+ 
+
+ align:start position:0%
+something that shows up is basically
+what is the slope of the function 1 over
+
+ align:start position:0%
+what is the slope of the function 1 over
+ 
+
+ align:start position:0%
+what is the slope of the function 1 over
+square root of x 1 minus x around the
+
+ align:start position:0%
+square root of x 1 minus x around the
+ 
+
+ align:start position:0%
+square root of x 1 minus x around the
+value you're interested in and so if
+
+ align:start position:0%
+value you're interested in and so if
+ 
+
+ align:start position:0%
+value you're interested in and so if
+this function is super sharp then small
+
+ align:start position:0%
+this function is super sharp then small
+ 
+
+ align:start position:0%
+this function is super sharp then small
+fluctuations of xn bar around its
+
+ align:start position:0%
+fluctuations of xn bar around its
+ 
+
+ align:start position:0%
+fluctuations of xn bar around its
+expectation they're going to lead to
+
+ align:start position:0%
+expectation they're going to lead to
+ 
+
+ align:start position:0%
+expectation they're going to lead to
+really high fluctuations in the function
+
+ align:start position:0%
+really high fluctuations in the function
+ 
+
+ align:start position:0%
+really high fluctuations in the function
+itself right so if you're looking at if
+
+ align:start position:0%
+itself right so if you're looking at if
+ 
+
+ align:start position:0%
+itself right so if you're looking at if
+you have F of xn bar and F around say
+
+ align:start position:0%
+you have F of xn bar and F around say
+ 
+
+ align:start position:0%
+you have F of xn bar and F around say
+the true P if F is really sharp like
+
+ align:start position:0%
+the true P if F is really sharp like
+ 
+
+ align:start position:0%
+the true P if F is really sharp like
+that then if you move a little bit here
+
+ align:start position:0%
+that then if you move a little bit here
+ 
+
+ align:start position:0%
+that then if you move a little bit here
+then you're gonna move really that's
+
+ align:start position:0%
+then you're gonna move really that's
+ 
+
+ align:start position:0%
+then you're gonna move really that's
+what the function here the function
+
+ align:start position:0%
+what the function here the function
+ 
+
+ align:start position:0%
+what the function here the function
+you're interested in is 1 over square
+
+ align:start position:0%
+you're interested in is 1 over square
+ 
+
+ align:start position:0%
+you're interested in is 1 over square
+root of X 1 minus X right so what does
+
+ align:start position:0%
+root of X 1 minus X right so what does
+ 
+
+ align:start position:0%
+root of X 1 minus X right so what does
+this function look like around the point
+
+ align:start position:0%
+this function look like around the point
+ 
+
+ align:start position:0%
+this function look like around the point
+where you think P's the true parameter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's derivative really is what's matters
+
+ align:start position:0%
+it's derivative really is what's matters
+ 
+
+ align:start position:0%
+it's derivative really is what's matters
+okay any other question ok so it's
+
+ align:start position:0%
+okay any other question ok so it's
+ 
+
+ align:start position:0%
+okay any other question ok so it's
+important because now we're gonna switch
+
+ align:start position:0%
+important because now we're gonna switch
+ 
+
+ align:start position:0%
+important because now we're gonna switch
+to the real you know let's do some
+
+ align:start position:0%
+to the real you know let's do some
+ 
+
+ align:start position:0%
+to the real you know let's do some
+hardcore computation type of thing
+
+ align:start position:0%
+hardcore computation type of thing
+ 
+
+ align:start position:0%
+hardcore computation type of thing
+alright so in this chapter we're going
+
+ align:start position:0%
+alright so in this chapter we're going
+ 
+
+ align:start position:0%
+alright so in this chapter we're going
+to talk about maximum likelihood
+
+ align:start position:0%
+to talk about maximum likelihood
+ 
+
+ align:start position:0%
+to talk about maximum likelihood
+estimation who has already seen maximum
+
+ align:start position:0%
+estimation who has already seen maximum
+ 
+
+ align:start position:0%
+estimation who has already seen maximum
+likelihood estimation okay and who knows
+
+ align:start position:0%
+likelihood estimation okay and who knows
+ 
+
+ align:start position:0%
+likelihood estimation okay and who knows
+what a convex function is okay so we'll
+
+ align:start position:0%
+what a convex function is okay so we'll
+ 
+
+ align:start position:0%
+what a convex function is okay so we'll
+do a little bit of reminders on those
+
+ align:start position:0%
+do a little bit of reminders on those
+ 
+
+ align:start position:0%
+do a little bit of reminders on those
+things so those things are when we do
+
+ align:start position:0%
+things so those things are when we do
+ 
+
+ align:start position:0%
+things so those things are when we do
+maximum likelihood estimation and
+
+ align:start position:0%
+maximum likelihood estimation and
+ 
+
+ align:start position:0%
+maximum likelihood estimation and
+likelihood is a function so we need to
+
+ align:start position:0%
+likelihood is a function so we need to
+ 
+
+ align:start position:0%
+likelihood is a function so we need to
+maximize a function that's basically
+
+ align:start position:0%
+maximize a function that's basically
+ 
+
+ align:start position:0%
+maximize a function that's basically
+what we need to do and if I give you a
+
+ align:start position:0%
+what we need to do and if I give you a
+ 
+
+ align:start position:0%
+what we need to do and if I give you a
+function you need to know how to
+
+ align:start position:0%
+function you need to know how to
+ 
+
+ align:start position:0%
+function you need to know how to
+maximize this function sometimes you
+
+ align:start position:0%
+maximize this function sometimes you
+ 
+
+ align:start position:0%
+maximize this function sometimes you
+have closed form solutions you can take
+
+ align:start position:0%
+have closed form solutions you can take
+ 
+
+ align:start position:0%
+have closed form solutions you can take
+the derivative and put a set it equal to
+
+ align:start position:0%
+the derivative and put a set it equal to
+ 
+
+ align:start position:0%
+the derivative and put a set it equal to
+zero and solve it but sometimes you
+
+ align:start position:0%
+zero and solve it but sometimes you
+ 
+
+ align:start position:0%
+zero and solve it but sometimes you
+actually need to resort to algorithms to
+
+ align:start position:0%
+actually need to resort to algorithms to
+ 
+
+ align:start position:0%
+actually need to resort to algorithms to
+do that then there's an entire industry
+
+ align:start position:0%
+do that then there's an entire industry
+ 
+
+ align:start position:0%
+do that then there's an entire industry
+doing that
+
+ align:start position:0%
+doing that
+ 
+
+ align:start position:0%
+doing that
+and and we'll briefly touched upon it
+
+ align:start position:0%
+and and we'll briefly touched upon it
+ 
+
+ align:start position:0%
+and and we'll briefly touched upon it
+but this is definitely not the focus of
+
+ align:start position:0%
+but this is definitely not the focus of
+ 
+
+ align:start position:0%
+but this is definitely not the focus of
+this class okay so before diving
+
+ align:start position:0%
+this class okay so before diving
+ 
+
+ align:start position:0%
+this class okay so before diving
+directly into the definition of the
+
+ align:start position:0%
+directly into the definition of the
+ 
+
+ align:start position:0%
+directly into the definition of the
+likelihood and what is the definition of
+
+ align:start position:0%
+likelihood and what is the definition of
+ 
+
+ align:start position:0%
+likelihood and what is the definition of
+the maximum likelihood estimator what
+
+ align:start position:0%
+the maximum likelihood estimator what
+ 
+
+ align:start position:0%
+the maximum likelihood estimator what
+I'm going to try to do is to give you an
+
+ align:start position:0%
+I'm going to try to do is to give you an
+ 
+
+ align:start position:0%
+I'm going to try to do is to give you an
+insight for what we're actually doing
+
+ align:start position:0%
+insight for what we're actually doing
+ 
+
+ align:start position:0%
+insight for what we're actually doing
+when we do maximum likely estimation
+
+ align:start position:0%
+when we do maximum likely estimation
+ 
+
+ align:start position:0%
+when we do maximum likely estimation
+okay so remember we have a model on the
+
+ align:start position:0%
+okay so remember we have a model on the
+ 
+
+ align:start position:0%
+okay so remember we have a model on the
+sample space Yi and some candidate
+
+ align:start position:0%
+sample space Yi and some candidate
+ 
+
+ align:start position:0%
+sample space Yi and some candidate
+distributions P theta and really your
+
+ align:start position:0%
+distributions P theta and really your
+ 
+
+ align:start position:0%
+distributions P theta and really your
+goal is to estimate a true theta star
+
+ align:start position:0%
+goal is to estimate a true theta star
+ 
+
+ align:start position:0%
+goal is to estimate a true theta star
+the one that generated some data x1 to
+
+ align:start position:0%
+the one that generated some data x1 to
+ 
+
+ align:start position:0%
+the one that generated some data x1 to
+xn in an iid fashion but this theta star
+
+ align:start position:0%
+xn in an iid fashion but this theta star
+ 
+
+ align:start position:0%
+xn in an iid fashion but this theta star
+is really a proxy for us to know that we
+
+ align:start position:0%
+is really a proxy for us to know that we
+ 
+
+ align:start position:0%
+is really a proxy for us to know that we
+actually understand the distribution
+
+ align:start position:0%
+actually understand the distribution
+ 
+
+ align:start position:0%
+actually understand the distribution
+itself the goal of knowing P state of
+
+ align:start position:0%
+itself the goal of knowing P state of
+ 
+
+ align:start position:0%
+itself the goal of knowing P state of
+knowing theta star is so that you can
+
+ align:start position:0%
+knowing theta star is so that you can
+ 
+
+ align:start position:0%
+knowing theta star is so that you can
+actually know what p theta star is right
+
+ align:start position:0%
+actually know what p theta star is right
+ 
+
+ align:start position:0%
+actually know what p theta star is right
+otherwise it has well sometimes we said
+
+ align:start position:0%
+otherwise it has well sometimes we said
+ 
+
+ align:start position:0%
+otherwise it has well sometimes we said
+it has some meaning itself but really
+
+ align:start position:0%
+it has some meaning itself but really
+ 
+
+ align:start position:0%
+it has some meaning itself but really
+you want to know what the distribution
+
+ align:start position:0%
+you want to know what the distribution
+ 
+
+ align:start position:0%
+you want to know what the distribution
+is and so your goal is to actually come
+
+ align:start position:0%
+is and so your goal is to actually come
+ 
+
+ align:start position:0%
+is and so your goal is to actually come
+up with the distribution hopefully that
+
+ align:start position:0%
+up with the distribution hopefully that
+ 
+
+ align:start position:0%
+up with the distribution hopefully that
+comes from the family P theta that's
+
+ align:start position:0%
+comes from the family P theta that's
+ 
+
+ align:start position:0%
+comes from the family P theta that's
+close to p theta star okay so in a way
+
+ align:start position:0%
+close to p theta star okay so in a way
+ 
+
+ align:start position:0%
+close to p theta star okay so in a way
+what does it mean to have two
+
+ align:start position:0%
+what does it mean to have two
+ 
+
+ align:start position:0%
+what does it mean to have two
+distributions that are close it means
+
+ align:start position:0%
+distributions that are close it means
+ 
+
+ align:start position:0%
+distributions that are close it means
+that when you compute probabilities on
+
+ align:start position:0%
+that when you compute probabilities on
+ 
+
+ align:start position:0%
+that when you compute probabilities on
+one distributions you should have the
+
+ align:start position:0%
+one distributions you should have the
+ 
+
+ align:start position:0%
+one distributions you should have the
+same probability on the other
+
+ align:start position:0%
+same probability on the other
+ 
+
+ align:start position:0%
+same probability on the other
+distribution pretty much all right so
+
+ align:start position:0%
+distribution pretty much all right so
+ 
+
+ align:start position:0%
+distribution pretty much all right so
+what we can do we say well now I have
+
+ align:start position:0%
+what we can do we say well now I have
+ 
+
+ align:start position:0%
+what we can do we say well now I have
+two candidate distributions so theta hat
+
+ align:start position:0%
+two candidate distributions so theta hat
+ 
+
+ align:start position:0%
+two candidate distributions so theta hat
+leads to a candidate distribution p
+
+ align:start position:0%
+leads to a candidate distribution p
+ 
+
+ align:start position:0%
+leads to a candidate distribution p
+theta hat and this is the truth theta
+
+ align:start position:0%
+theta hat and this is the truth theta
+ 
+
+ align:start position:0%
+theta hat and this is the truth theta
+star that leads to the true distribution
+
+ align:start position:0%
+star that leads to the true distribution
+ 
+
+ align:start position:0%
+star that leads to the true distribution
+p theta star according to which my data
+
+ align:start position:0%
+p theta star according to which my data
+ 
+
+ align:start position:0%
+p theta star according to which my data
+was drawn okay
+
+ align:start position:0%
+was drawn okay
+ 
+
+ align:start position:0%
+was drawn okay
+that's my candidate as a statistician
+
+ align:start position:0%
+that's my candidate as a statistician
+ 
+
+ align:start position:0%
+that's my candidate as a statistician
+I'm supposed to come up with a good
+
+ align:start position:0%
+I'm supposed to come up with a good
+ 
+
+ align:start position:0%
+I'm supposed to come up with a good
+candidate and this is the truth okay and
+
+ align:start position:0%
+candidate and this is the truth okay and
+ 
+
+ align:start position:0%
+candidate and this is the truth okay and
+what I want is that if you actually give
+
+ align:start position:0%
+what I want is that if you actually give
+ 
+
+ align:start position:0%
+what I want is that if you actually give
+me the distribution then I want one I'm
+
+ align:start position:0%
+me the distribution then I want one I'm
+ 
+
+ align:start position:0%
+me the distribution then I want one I'm
+computing probabilities for this guy I
+
+ align:start position:0%
+computing probabilities for this guy I
+ 
+
+ align:start position:0%
+computing probabilities for this guy I
+know what the probabilities for the
+
+ align:start position:0%
+know what the probabilities for the
+ 
+
+ align:start position:0%
+know what the probabilities for the
+other guys are okay and so really what I
+
+ align:start position:0%
+other guys are okay and so really what I
+ 
+
+ align:start position:0%
+other guys are okay and so really what I
+want is that if
+
+ align:start position:0%
+want is that if
+ 
+
+ align:start position:0%
+want is that if
+computes a probability under stata hats
+
+ align:start position:0%
+computes a probability under stata hats
+ 
+
+ align:start position:0%
+computes a probability under stata hats
+of some interval a B it should be pretty
+
+ align:start position:0%
+of some interval a B it should be pretty
+ 
+
+ align:start position:0%
+of some interval a B it should be pretty
+close to the probability under status
+
+ align:start position:0%
+close to the probability under status
+ 
+
+ align:start position:0%
+close to the probability under status
+star of a b and more generally if i want
+
+ align:start position:0%
+star of a b and more generally if i want
+ 
+
+ align:start position:0%
+star of a b and more generally if i want
+to take the union of two intervals i
+
+ align:start position:0%
+to take the union of two intervals i
+ 
+
+ align:start position:0%
+to take the union of two intervals i
+want this to be true if i take just half
+
+ align:start position:0%
+want this to be true if i take just half
+ 
+
+ align:start position:0%
+want this to be true if i take just half
+lines i want this to be true from 0 to
+
+ align:start position:0%
+lines i want this to be true from 0 to
+ 
+
+ align:start position:0%
+lines i want this to be true from 0 to
+infinity for example things like this i
+
+ align:start position:0%
+infinity for example things like this i
+ 
+
+ align:start position:0%
+infinity for example things like this i
+want this to be true for all of them at
+
+ align:start position:0%
+want this to be true for all of them at
+ 
+
+ align:start position:0%
+want this to be true for all of them at
+once and so what i do is that i write a
+
+ align:start position:0%
+once and so what i do is that i write a
+ 
+
+ align:start position:0%
+once and so what i do is that i write a
+for a probability event and I want that
+
+ align:start position:0%
+for a probability event and I want that
+ 
+
+ align:start position:0%
+for a probability event and I want that
+p hat of a is close to p star of a for
+
+ align:start position:0%
+p hat of a is close to p star of a for
+ 
+
+ align:start position:0%
+p hat of a is close to p star of a for
+any event a in the sample space right
+
+ align:start position:0%
+any event a in the sample space right
+ 
+
+ align:start position:0%
+any event a in the sample space right
+does that sound like a reasonable goal
+
+ align:start position:0%
+does that sound like a reasonable goal
+ 
+
+ align:start position:0%
+does that sound like a reasonable goal
+for a statistician okay so in particular
+
+ align:start position:0%
+for a statistician okay so in particular
+ 
+
+ align:start position:0%
+for a statistician okay so in particular
+if I want those two because I want the
+
+ align:start position:0%
+if I want those two because I want the
+ 
+
+ align:start position:0%
+if I want those two because I want the
+absolute value of their difference to be
+
+ align:start position:0%
+absolute value of their difference to be
+ 
+
+ align:start position:0%
+absolute value of their difference to be
+close to zero all right and this turns
+
+ align:start position:0%
+close to zero all right and this turns
+ 
+
+ align:start position:0%
+close to zero all right and this turns
+out to be if I want this to hold for all
+
+ align:start position:0%
+out to be if I want this to hold for all
+ 
+
+ align:start position:0%
+out to be if I want this to hold for all
+possible A's right I have all possible
+
+ align:start position:0%
+possible A's right I have all possible
+ 
+
+ align:start position:0%
+possible A's right I have all possible
+events so I'm gonna actually maximize
+
+ align:start position:0%
+events so I'm gonna actually maximize
+ 
+
+ align:start position:0%
+events so I'm gonna actually maximize
+over this events and I'm gonna look at
+
+ align:start position:0%
+over this events and I'm gonna look at
+ 
+
+ align:start position:0%
+over this events and I'm gonna look at
+the worst possible event on which theta
+
+ align:start position:0%
+the worst possible event on which theta
+ 
+
+ align:start position:0%
+the worst possible event on which theta
+hat can depart from theta star and so
+
+ align:start position:0%
+hat can depart from theta star and so
+ 
+
+ align:start position:0%
+hat can depart from theta star and so
+rather than defining it specifically for
+
+ align:start position:0%
+rather than defining it specifically for
+ 
+
+ align:start position:0%
+rather than defining it specifically for
+theta hat and theta star I'm just gonna
+
+ align:start position:0%
+theta hat and theta star I'm just gonna
+ 
+
+ align:start position:0%
+theta hat and theta star I'm just gonna
+say well if you give me two probability
+
+ align:start position:0%
+say well if you give me two probability
+ 
+
+ align:start position:0%
+say well if you give me two probability
+measures P theta and P theta prime I
+
+ align:start position:0%
+measures P theta and P theta prime I
+ 
+
+ align:start position:0%
+measures P theta and P theta prime I
+want to know how close they are well if
+
+ align:start position:0%
+want to know how close they are well if
+ 
+
+ align:start position:0%
+want to know how close they are well if
+I want to measure how close they are by
+
+ align:start position:0%
+I want to measure how close they are by
+ 
+
+ align:start position:0%
+I want to measure how close they are by
+how they can defer when I measure the
+
+ align:start position:0%
+how they can defer when I measure the
+ 
+
+ align:start position:0%
+how they can defer when I measure the
+probability of some event I'm just
+
+ align:start position:0%
+probability of some event I'm just
+ 
+
+ align:start position:0%
+probability of some event I'm just
+looking at the absolute value of the
+
+ align:start position:0%
+looking at the absolute value of the
+ 
+
+ align:start position:0%
+looking at the absolute value of the
+difference of the probabilities and I'm
+
+ align:start position:0%
+difference of the probabilities and I'm
+ 
+
+ align:start position:0%
+difference of the probabilities and I'm
+just maximizing over the worst possible
+
+ align:start position:0%
+just maximizing over the worst possible
+ 
+
+ align:start position:0%
+just maximizing over the worst possible
+event that might actually make them
+
+ align:start position:0%
+event that might actually make them
+ 
+
+ align:start position:0%
+event that might actually make them
+defer agreed that's a pretty strong
+
+ align:start position:0%
+defer agreed that's a pretty strong
+ 
+
+ align:start position:0%
+defer agreed that's a pretty strong
+notion so if the total variation between
+
+ align:start position:0%
+notion so if the total variation between
+ 
+
+ align:start position:0%
+notion so if the total variation between
+theta and theta prime is small then it
+
+ align:start position:0%
+theta and theta prime is small then it
+ 
+
+ align:start position:0%
+theta and theta prime is small then it
+means that for all possible aids that
+
+ align:start position:0%
+means that for all possible aids that
+ 
+
+ align:start position:0%
+means that for all possible aids that
+you give me then P theta of a is gonna
+
+ align:start position:0%
+you give me then P theta of a is gonna
+ 
+
+ align:start position:0%
+you give me then P theta of a is gonna
+be close to P theta prime of a alright
+
+ align:start position:0%
+be close to P theta prime of a alright
+ 
+
+ align:start position:0%
+be close to P theta prime of a alright
+so because if let's say I just found the
+
+ align:start position:0%
+so because if let's say I just found the
+ 
+
+ align:start position:0%
+so because if let's say I just found the
+balance of bound on the total variation
+
+ align:start position:0%
+balance of bound on the total variation
+ 
+
+ align:start position:0%
+balance of bound on the total variation
+distance which is 0.01
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so that means that this is
+
+ align:start position:0%
+all right so that means that this is
+ 
+
+ align:start position:0%
+all right so that means that this is
+going to be larger than the max over a
+
+ align:start position:0%
+going to be larger than the max over a
+ 
+
+ align:start position:0%
+going to be larger than the max over a
+of P theta minus P theta prime of a okay
+
+ align:start position:0%
+of P theta minus P theta prime of a okay
+ 
+
+ align:start position:0%
+of P theta minus P theta prime of a okay
+so which means that for any a actually
+
+ align:start position:0%
+so which means that for any a actually
+ 
+
+ align:start position:0%
+so which means that for any a actually
+let me write P theta hat and P theta
+
+ align:start position:0%
+let me write P theta hat and P theta
+ 
+
+ align:start position:0%
+let me write P theta hat and P theta
+star like we said did a hat and theta
+
+ align:start position:0%
+star like we said did a hat and theta
+ 
+
+ align:start position:0%
+star like we said did a hat and theta
+star and so if I have a balancing on the
+
+ align:start position:0%
+star and so if I have a balancing on the
+ 
+
+ align:start position:0%
+star and so if I have a balancing on the
+total variation which is 0.01 that means
+
+ align:start position:0%
+total variation which is 0.01 that means
+ 
+
+ align:start position:0%
+total variation which is 0.01 that means
+that P theta hat every time I compute a
+
+ align:start position:0%
+that P theta hat every time I compute a
+ 
+
+ align:start position:0%
+that P theta hat every time I compute a
+probability on P theta hat it's
+
+ align:start position:0%
+probability on P theta hat it's
+ 
+
+ align:start position:0%
+probability on P theta hat it's
+basically in the interval P theta star
+
+ align:start position:0%
+basically in the interval P theta star
+ 
+
+ align:start position:0%
+basically in the interval P theta star
+of a there's one that I really wanted to
+
+ align:start position:0%
+of a there's one that I really wanted to
+ 
+
+ align:start position:0%
+of a there's one that I really wanted to
+compute plus or minus 0.01 okay this has
+
+ align:start position:0%
+compute plus or minus 0.01 okay this has
+ 
+
+ align:start position:0%
+compute plus or minus 0.01 okay this has
+nothing to do with conference interval
+
+ align:start position:0%
+nothing to do with conference interval
+ 
+
+ align:start position:0%
+nothing to do with conference interval
+is just telling me how far I am from the
+
+ align:start position:0%
+is just telling me how far I am from the
+ 
+
+ align:start position:0%
+is just telling me how far I am from the
+value I'm actually trying to compute
+
+ align:start position:0%
+value I'm actually trying to compute
+ 
+
+ align:start position:0%
+value I'm actually trying to compute
+okay and that's true for all a and
+
+ align:start position:0%
+okay and that's true for all a and
+ 
+
+ align:start position:0%
+okay and that's true for all a and
+that's key that squared this Max comes
+
+ align:start position:0%
+that's key that squared this Max comes
+ 
+
+ align:start position:0%
+that's key that squared this Max comes
+into play it just says I want this to
+
+ align:start position:0%
+into play it just says I want this to
+ 
+
+ align:start position:0%
+into play it just says I want this to
+this bound to hold for all possible a's
+
+ align:start position:0%
+this bound to hold for all possible a's
+ 
+
+ align:start position:0%
+this bound to hold for all possible a's
+at once okay so this is actually very
+
+ align:start position:0%
+at once okay so this is actually very
+ 
+
+ align:start position:0%
+at once okay so this is actually very
+well known distance between probability
+
+ align:start position:0%
+well known distance between probability
+ 
+
+ align:start position:0%
+well known distance between probability
+measures it's the total variation
+
+ align:start position:0%
+measures it's the total variation
+ 
+
+ align:start position:0%
+measures it's the total variation
+distance it's extremely central into
+
+ align:start position:0%
+distance it's extremely central into
+ 
+
+ align:start position:0%
+distance it's extremely central into
+probabilistic analysis and it
+
+ align:start position:0%
+probabilistic analysis and it
+ 
+
+ align:start position:0%
+probabilistic analysis and it
+essentially tells you that every time if
+
+ align:start position:0%
+essentially tells you that every time if
+ 
+
+ align:start position:0%
+essentially tells you that every time if
+two probabilities tribution czar close
+
+ align:start position:0%
+two probabilities tribution czar close
+ 
+
+ align:start position:0%
+two probabilities tribution czar close
+that it means that every time a computer
+
+ align:start position:0%
+that it means that every time a computer
+ 
+
+ align:start position:0%
+that it means that every time a computer
+probability under p theta but I really
+
+ align:start position:0%
+probability under p theta but I really
+ 
+
+ align:start position:0%
+probability under p theta but I really
+fit I really actually have data from p
+
+ align:start position:0%
+fit I really actually have data from p
+ 
+
+ align:start position:0%
+fit I really actually have data from p
+theta prime then the error is no larger
+
+ align:start position:0%
+theta prime then the error is no larger
+ 
+
+ align:start position:0%
+theta prime then the error is no larger
+than the Toleration okay so this is
+
+ align:start position:0%
+than the Toleration okay so this is
+ 
+
+ align:start position:0%
+than the Toleration okay so this is
+maybe not the most convenient way of
+
+ align:start position:0%
+maybe not the most convenient way of
+ 
+
+ align:start position:0%
+maybe not the most convenient way of
+defining a distance right I mean how are
+
+ align:start position:0%
+defining a distance right I mean how are
+ 
+
+ align:start position:0%
+defining a distance right I mean how are
+you gonna you know in reality how are
+
+ align:start position:0%
+you gonna you know in reality how are
+ 
+
+ align:start position:0%
+you gonna you know in reality how are
+you gonna compute this maximum over all
+
+ align:start position:0%
+you gonna compute this maximum over all
+ 
+
+ align:start position:0%
+you gonna compute this maximum over all
+possible events I mean it's just crazy
+
+ align:start position:0%
+possible events I mean it's just crazy
+ 
+
+ align:start position:0%
+possible events I mean it's just crazy
+right there's an infinite number of them
+
+ align:start position:0%
+right there's an infinite number of them
+ 
+
+ align:start position:0%
+right there's an infinite number of them
+it's it's much larger than the number of
+
+ align:start position:0%
+it's it's much larger than the number of
+ 
+
+ align:start position:0%
+it's it's much larger than the number of
+intervals for example so it's a bit
+
+ align:start position:0%
+intervals for example so it's a bit
+ 
+
+ align:start position:0%
+intervals for example so it's a bit
+annoying and so there's actually a way
+
+ align:start position:0%
+annoying and so there's actually a way
+ 
+
+ align:start position:0%
+annoying and so there's actually a way
+to compress it by just looking at the
+
+ align:start position:0%
+to compress it by just looking at the
+ 
+
+ align:start position:0%
+to compress it by just looking at the
+basically function distance or vector
+
+ align:start position:0%
+basically function distance or vector
+ 
+
+ align:start position:0%
+basically function distance or vector
+distance between pair
+
+ align:start position:0%
+distance between pair
+ 
+
+ align:start position:0%
+distance between pair
+math functions or probability density
+
+ align:start position:0%
+math functions or probability density
+ 
+
+ align:start position:0%
+math functions or probability density
+function okay so I'm gonna start with
+
+ align:start position:0%
+function okay so I'm gonna start with
+ 
+
+ align:start position:0%
+function okay so I'm gonna start with
+the discrete version of the total
+
+ align:start position:0%
+the discrete version of the total
+ 
+
+ align:start position:0%
+the discrete version of the total
+variation so throughout this chapter I
+
+ align:start position:0%
+variation so throughout this chapter I
+ 
+
+ align:start position:0%
+variation so throughout this chapter I
+will make the difference between
+
+ align:start position:0%
+will make the difference between
+ 
+
+ align:start position:0%
+will make the difference between
+discrete random variables and continuous
+
+ align:start position:0%
+discrete random variables and continuous
+ 
+
+ align:start position:0%
+discrete random variables and continuous
+random variables it really doesn't
+
+ align:start position:0%
+random variables it really doesn't
+ 
+
+ align:start position:0%
+random variables it really doesn't
+matter all that means is that when I
+
+ align:start position:0%
+matter all that means is that when I
+ 
+
+ align:start position:0%
+matter all that means is that when I
+talk about discrete I will talk about
+
+ align:start position:0%
+talk about discrete I will talk about
+ 
+
+ align:start position:0%
+talk about discrete I will talk about
+probability mass functions and when I
+
+ align:start position:0%
+probability mass functions and when I
+ 
+
+ align:start position:0%
+probability mass functions and when I
+talk about continuous I will talk about
+
+ align:start position:0%
+talk about continuous I will talk about
+ 
+
+ align:start position:0%
+talk about continuous I will talk about
+probability density functions when I
+
+ align:start position:0%
+probability density functions when I
+ 
+
+ align:start position:0%
+probability density functions when I
+talk about probability functions
+
+ align:start position:0%
+talk about probability functions
+ 
+
+ align:start position:0%
+talk about probability functions
+probability mass functions I talk about
+
+ align:start position:0%
+probability mass functions I talk about
+ 
+
+ align:start position:0%
+probability mass functions I talk about
+sums when I talk about probability
+
+ align:start position:0%
+sums when I talk about probability
+ 
+
+ align:start position:0%
+sums when I talk about probability
+density functions I talk about integrals
+
+ align:start position:0%
+density functions I talk about integrals
+ 
+
+ align:start position:0%
+density functions I talk about integrals
+but they're all the same thing really
+
+ align:start position:0%
+but they're all the same thing really
+ 
+
+ align:start position:0%
+but they're all the same thing really
+okay so let's start with the probability
+
+ align:start position:0%
+okay so let's start with the probability
+ 
+
+ align:start position:0%
+okay so let's start with the probability
+mass function right everybody remembers
+
+ align:start position:0%
+mass function right everybody remembers
+ 
+
+ align:start position:0%
+mass function right everybody remembers
+what the probability mass function of a
+
+ align:start position:0%
+what the probability mass function of a
+ 
+
+ align:start position:0%
+what the probability mass function of a
+discrete random variable is this is the
+
+ align:start position:0%
+discrete random variable is this is the
+ 
+
+ align:start position:0%
+discrete random variable is this is the
+function that tells me for each possible
+
+ align:start position:0%
+function that tells me for each possible
+ 
+
+ align:start position:0%
+function that tells me for each possible
+value that it can take the probability
+
+ align:start position:0%
+value that it can take the probability
+ 
+
+ align:start position:0%
+value that it can take the probability
+they takes this value alright so the
+
+ align:start position:0%
+they takes this value alright so the
+ 
+
+ align:start position:0%
+they takes this value alright so the
+probability mass function PMF it's just
+
+ align:start position:0%
+probability mass function PMF it's just
+ 
+
+ align:start position:0%
+probability mass function PMF it's just
+a function for all X in the sample space
+
+ align:start position:0%
+a function for all X in the sample space
+ 
+
+ align:start position:0%
+a function for all X in the sample space
+tells me the probability that my random
+
+ align:start position:0%
+tells me the probability that my random
+ 
+
+ align:start position:0%
+tells me the probability that my random
+variable is equal to this little value
+
+ align:start position:0%
+variable is equal to this little value
+ 
+
+ align:start position:0%
+variable is equal to this little value
+okay and I will denote it by P sub theta
+
+ align:start position:0%
+okay and I will denote it by P sub theta
+ 
+
+ align:start position:0%
+okay and I will denote it by P sub theta
+of X so what I want is of course that
+
+ align:start position:0%
+of X so what I want is of course that
+ 
+
+ align:start position:0%
+of X so what I want is of course that
+the sum of the probabilities is 1 and I
+
+ align:start position:0%
+the sum of the probabilities is 1 and I
+ 
+
+ align:start position:0%
+the sum of the probabilities is 1 and I
+want them to be non-negative actually
+
+ align:start position:0%
+want them to be non-negative actually
+ 
+
+ align:start position:0%
+want them to be non-negative actually
+typically we will assume that they're
+
+ align:start position:0%
+typically we will assume that they're
+ 
+
+ align:start position:0%
+typically we will assume that they're
+positive otherwise we can just remove
+
+ align:start position:0%
+positive otherwise we can just remove
+ 
+
+ align:start position:0%
+positive otherwise we can just remove
+this X from the sample space okay and so
+
+ align:start position:0%
+this X from the sample space okay and so
+ 
+
+ align:start position:0%
+this X from the sample space okay and so
+then I have the the tool variation
+
+ align:start position:0%
+then I have the the tool variation
+ 
+
+ align:start position:0%
+then I have the the tool variation
+distance I mean it's supposed to be the
+
+ align:start position:0%
+distance I mean it's supposed to be the
+ 
+
+ align:start position:0%
+distance I mean it's supposed to be the
+maximum over all sets of of subsets of e
+
+ align:start position:0%
+maximum over all sets of of subsets of e
+ 
+
+ align:start position:0%
+maximum over all sets of of subsets of e
+such that the probability of theta minus
+
+ align:start position:0%
+such that the probability of theta minus
+ 
+
+ align:start position:0%
+such that the probability of theta minus
+/ of a minus probability center prime of
+
+ align:start position:0%
+/ of a minus probability center prime of
+ 
+
+ align:start position:0%
+/ of a minus probability center prime of
+a it's complicated but really there's
+
+ align:start position:0%
+a it's complicated but really there's
+ 
+
+ align:start position:0%
+a it's complicated but really there's
+this beautiful formula that tells me
+
+ align:start position:0%
+this beautiful formula that tells me
+ 
+
+ align:start position:0%
+this beautiful formula that tells me
+that if I look at the total variation
+
+ align:start position:0%
+that if I look at the total variation
+ 
+
+ align:start position:0%
+that if I look at the total variation
+between P theta and peas that are prime
+
+ align:start position:0%
+between P theta and peas that are prime
+ 
+
+ align:start position:0%
+between P theta and peas that are prime
+it's actually equal to just one half of
+
+ align:start position:0%
+it's actually equal to just one half of
+ 
+
+ align:start position:0%
+it's actually equal to just one half of
+the sum for all X in E of the absolute
+
+ align:start position:0%
+the sum for all X in E of the absolute
+ 
+
+ align:start position:0%
+the sum for all X in E of the absolute
+difference between
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P theta X and P theta prime of X okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's something you can compute if I
+
+ align:start position:0%
+that's something you can compute if I
+ 
+
+ align:start position:0%
+that's something you can compute if I
+give you two probability mass functions
+
+ align:start position:0%
+give you two probability mass functions
+ 
+
+ align:start position:0%
+give you two probability mass functions
+you can compute this immediately but if
+
+ align:start position:0%
+you can compute this immediately but if
+ 
+
+ align:start position:0%
+you can compute this immediately but if
+I give you just the density's and the
+
+ align:start position:0%
+I give you just the density's and the
+ 
+
+ align:start position:0%
+I give you just the density's and the
+original distribution the original
+
+ align:start position:0%
+original distribution the original
+ 
+
+ align:start position:0%
+original distribution the original
+definition where you have to max over
+
+ align:start position:0%
+definition where you have to max over
+ 
+
+ align:start position:0%
+definition where you have to max over
+all possible events it's not very gonna
+
+ align:start position:0%
+all possible events it's not very gonna
+ 
+
+ align:start position:0%
+all possible events it's not very gonna
+be able to do that very quickly alright
+
+ align:start position:0%
+be able to do that very quickly alright
+ 
+
+ align:start position:0%
+be able to do that very quickly alright
+so this is really the the one you can
+
+ align:start position:0%
+so this is really the the one you can
+ 
+
+ align:start position:0%
+so this is really the the one you can
+work with but the other one is really
+
+ align:start position:0%
+work with but the other one is really
+ 
+
+ align:start position:0%
+work with but the other one is really
+telling you what it's doing for you it's
+
+ align:start position:0%
+telling you what it's doing for you it's
+ 
+
+ align:start position:0%
+telling you what it's doing for you it's
+controlling the difference of
+
+ align:start position:0%
+controlling the difference of
+ 
+
+ align:start position:0%
+controlling the difference of
+probabilities you can compute on any
+
+ align:start position:0%
+probabilities you can compute on any
+ 
+
+ align:start position:0%
+probabilities you can compute on any
+event but here is just telling you well
+
+ align:start position:0%
+event but here is just telling you well
+ 
+
+ align:start position:0%
+event but here is just telling you well
+if you do it for each simple event its
+
+ align:start position:0%
+if you do it for each simple event its
+ 
+
+ align:start position:0%
+if you do it for each simple event its
+act little X it's actually simple now if
+
+ align:start position:0%
+act little X it's actually simple now if
+ 
+
+ align:start position:0%
+act little X it's actually simple now if
+we have continuous random variables
+
+ align:start position:0%
+we have continuous random variables
+ 
+
+ align:start position:0%
+we have continuous random variables
+right so by the way I didn't mention but
+
+ align:start position:0%
+right so by the way I didn't mention but
+ 
+
+ align:start position:0%
+right so by the way I didn't mention but
+discreet means bernly binomial but not
+
+ align:start position:0%
+discreet means bernly binomial but not
+ 
+
+ align:start position:0%
+discreet means bernly binomial but not
+only does that have finite support like
+
+ align:start position:0%
+only does that have finite support like
+ 
+
+ align:start position:0%
+only does that have finite support like
+by newly
+
+ align:start position:0%
+by newly
+ 
+
+ align:start position:0%
+by newly
+bernly as support of size to binomial
+
+ align:start position:0%
+bernly as support of size to binomial
+ 
+
+ align:start position:0%
+bernly as support of size to binomial
+and PS support of size N and there's n
+
+ align:start position:0%
+and PS support of size N and there's n
+ 
+
+ align:start position:0%
+and PS support of size N and there's n
+possible values it can take but also
+
+ align:start position:0%
+possible values it can take but also
+ 
+
+ align:start position:0%
+possible values it can take but also
+Poisson right Westone distribution can
+
+ align:start position:0%
+Poisson right Westone distribution can
+ 
+
+ align:start position:0%
+Poisson right Westone distribution can
+take an infinite number of values right
+
+ align:start position:0%
+take an infinite number of values right
+ 
+
+ align:start position:0%
+take an infinite number of values right
+all the positive integers non-negative
+
+ align:start position:0%
+all the positive integers non-negative
+ 
+
+ align:start position:0%
+all the positive integers non-negative
+integers okay and so now we have also
+
+ align:start position:0%
+integers okay and so now we have also
+ 
+
+ align:start position:0%
+integers okay and so now we have also
+the continuous one such as Gaussian
+
+ align:start position:0%
+the continuous one such as Gaussian
+ 
+
+ align:start position:0%
+the continuous one such as Gaussian
+exponential and what characterizes those
+
+ align:start position:0%
+exponential and what characterizes those
+ 
+
+ align:start position:0%
+exponential and what characterizes those
+guys is that they have a probability
+
+ align:start position:0%
+guys is that they have a probability
+ 
+
+ align:start position:0%
+guys is that they have a probability
+density okay so the density remember the
+
+ align:start position:0%
+density okay so the density remember the
+ 
+
+ align:start position:0%
+density okay so the density remember the
+way I use my density is when I want to
+
+ align:start position:0%
+way I use my density is when I want to
+ 
+
+ align:start position:0%
+way I use my density is when I want to
+compute the probability of belonging to
+
+ align:start position:0%
+compute the probability of belonging to
+ 
+
+ align:start position:0%
+compute the probability of belonging to
+some event a the probability X falling
+
+ align:start position:0%
+some event a the probability X falling
+ 
+
+ align:start position:0%
+some event a the probability X falling
+to some subset of the rail line a is
+
+ align:start position:0%
+to some subset of the rail line a is
+ 
+
+ align:start position:0%
+to some subset of the rail line a is
+simply the integral of the density on
+
+ align:start position:0%
+simply the integral of the density on
+ 
+
+ align:start position:0%
+simply the integral of the density on
+this set all right that's the famous
+
+ align:start position:0%
+this set all right that's the famous
+ 
+
+ align:start position:0%
+this set all right that's the famous
+area under the curve thing all right so
+
+ align:start position:0%
+area under the curve thing all right so
+ 
+
+ align:start position:0%
+area under the curve thing all right so
+since for each possible value the
+
+ align:start position:0%
+since for each possible value the
+ 
+
+ align:start position:0%
+since for each possible value the
+probability at X so I hope you remember
+
+ align:start position:0%
+probability at X so I hope you remember
+ 
+
+ align:start position:0%
+probability at X so I hope you remember
+that stuff that's just probably
+
+ align:start position:0%
+that stuff that's just probably
+ 
+
+ align:start position:0%
+that stuff that's just probably
+something that you must remember from
+
+ align:start position:0%
+something that you must remember from
+ 
+
+ align:start position:0%
+something that you must remember from
+probability but essentially we know that
+
+ align:start position:0%
+probability but essentially we know that
+ 
+
+ align:start position:0%
+probability but essentially we know that
+the probability at X is equal to little
+
+ align:start position:0%
+the probability at X is equal to little
+ 
+
+ align:start position:0%
+the probability at X is equal to little
+X is zero for a continuous random
+
+ align:start position:0%
+X is zero for a continuous random
+ 
+
+ align:start position:0%
+X is zero for a continuous random
+variable for all possible X's right
+
+ align:start position:0%
+variable for all possible X's right
+ 
+
+ align:start position:0%
+variable for all possible X's right
+there's just none of them that actually
+
+ align:start position:0%
+there's just none of them that actually
+ 
+
+ align:start position:0%
+there's just none of them that actually
+gets weight so what we have to do is to
+
+ align:start position:0%
+gets weight so what we have to do is to
+ 
+
+ align:start position:0%
+gets weight so what we have to do is to
+describe the fact that it's in some
+
+ align:start position:0%
+describe the fact that it's in some
+ 
+
+ align:start position:0%
+describe the fact that it's in some
+little region
+
+ align:start position:0%
+little region
+ 
+
+ align:start position:0%
+little region
+so the probability that it's on in some
+
+ align:start position:0%
+so the probability that it's on in some
+ 
+
+ align:start position:0%
+so the probability that it's on in some
+interval say a B this is the integral
+
+ align:start position:0%
+interval say a B this is the integral
+ 
+
+ align:start position:0%
+interval say a B this is the integral
+between a and B of F theta of X DX okay
+
+ align:start position:0%
+between a and B of F theta of X DX okay
+ 
+
+ align:start position:0%
+between a and B of F theta of X DX okay
+so I have this density such as the
+
+ align:start position:0%
+so I have this density such as the
+ 
+
+ align:start position:0%
+so I have this density such as the
+Gaussian one and the probability that
+
+ align:start position:0%
+Gaussian one and the probability that
+ 
+
+ align:start position:0%
+Gaussian one and the probability that
+I'd belong to the interval a B is just
+
+ align:start position:0%
+I'd belong to the interval a B is just
+ 
+
+ align:start position:0%
+I'd belong to the interval a B is just
+the area under the curve between a and B
+
+ align:start position:0%
+the area under the curve between a and B
+ 
+
+ align:start position:0%
+the area under the curve between a and B
+okay if you don't remember that please
+
+ align:start position:0%
+okay if you don't remember that please
+ 
+
+ align:start position:0%
+okay if you don't remember that please
+take it
+
+ align:start position:0%
+take it
+ 
+
+ align:start position:0%
+take it
+remedy okay so this function f just like
+
+ align:start position:0%
+remedy okay so this function f just like
+ 
+
+ align:start position:0%
+remedy okay so this function f just like
+P is non-negative and rather than
+
+ align:start position:0%
+P is non-negative and rather than
+ 
+
+ align:start position:0%
+P is non-negative and rather than
+something to one it integrates to 1 when
+
+ align:start position:0%
+something to one it integrates to 1 when
+ 
+
+ align:start position:0%
+something to one it integrates to 1 when
+I integrate over the entire sample space
+
+ align:start position:0%
+I integrate over the entire sample space
+ 
+
+ align:start position:0%
+I integrate over the entire sample space
+E and now the total variation well it
+
+ align:start position:0%
+E and now the total variation well it
+ 
+
+ align:start position:0%
+E and now the total variation well it
+takes basically the same form right I
+
+ align:start position:0%
+takes basically the same form right I
+ 
+
+ align:start position:0%
+takes basically the same form right I
+said that you essentially replace sums
+
+ align:start position:0%
+said that you essentially replace sums
+ 
+
+ align:start position:0%
+said that you essentially replace sums
+by integrals when you're dealing with
+
+ align:start position:0%
+by integrals when you're dealing with
+ 
+
+ align:start position:0%
+by integrals when you're dealing with
+densities and here it's just saying
+
+ align:start position:0%
+densities and here it's just saying
+ 
+
+ align:start position:0%
+densities and here it's just saying
+rather than having half of the sum of
+
+ align:start position:0%
+rather than having half of the sum of
+ 
+
+ align:start position:0%
+rather than having half of the sum of
+the absolute values you have half of the
+
+ align:start position:0%
+the absolute values you have half of the
+ 
+
+ align:start position:0%
+the absolute values you have half of the
+integral of the absolute again if I give
+
+ align:start position:0%
+integral of the absolute again if I give
+ 
+
+ align:start position:0%
+integral of the absolute again if I give
+you two densities and if you're not too
+
+ align:start position:0%
+you two densities and if you're not too
+ 
+
+ align:start position:0%
+you two densities and if you're not too
+bad at calculus which you will often be
+
+ align:start position:0%
+bad at calculus which you will often be
+ 
+
+ align:start position:0%
+bad at calculus which you will often be
+because there's lots of them you can
+
+ align:start position:0%
+because there's lots of them you can
+ 
+
+ align:start position:0%
+because there's lots of them you can
+actually not compute
+
+ align:start position:0%
+actually not compute
+ 
+
+ align:start position:0%
+actually not compute
+but if I give you for example two
+
+ align:start position:0%
+but if I give you for example two
+ 
+
+ align:start position:0%
+but if I give you for example two
+Gaussian densities exponential minus x
+
+ align:start position:0%
+Gaussian densities exponential minus x
+ 
+
+ align:start position:0%
+Gaussian densities exponential minus x
+squared blah blah blah and I say just
+
+ align:start position:0%
+squared blah blah blah and I say just
+ 
+
+ align:start position:0%
+squared blah blah blah and I say just
+compute the total variation distance you
+
+ align:start position:0%
+compute the total variation distance you
+ 
+
+ align:start position:0%
+compute the total variation distance you
+could actually write it as an integral
+
+ align:start position:0%
+could actually write it as an integral
+ 
+
+ align:start position:0%
+could actually write it as an integral
+now whether you can actually reduce this
+
+ align:start position:0%
+now whether you can actually reduce this
+ 
+
+ align:start position:0%
+now whether you can actually reduce this
+integral to some particular number is
+
+ align:start position:0%
+integral to some particular number is
+ 
+
+ align:start position:0%
+integral to some particular number is
+another story but you could technically
+
+ align:start position:0%
+another story but you could technically
+ 
+
+ align:start position:0%
+another story but you could technically
+do it right and so now so you have
+
+ align:start position:0%
+do it right and so now so you have
+ 
+
+ align:start position:0%
+do it right and so now so you have
+actually a handle on this thing you
+
+ align:start position:0%
+actually a handle on this thing you
+ 
+
+ align:start position:0%
+actually a handle on this thing you
+could technically ask Mathematica where
+
+ align:start position:0%
+could technically ask Mathematica where
+ 
+
+ align:start position:0%
+could technically ask Mathematica where
+as asking Mathematica to take the max
+
+ align:start position:0%
+as asking Mathematica to take the max
+ 
+
+ align:start position:0%
+as asking Mathematica to take the max
+over all possible events is gonna be
+
+ align:start position:0%
+over all possible events is gonna be
+ 
+
+ align:start position:0%
+over all possible events is gonna be
+difficult alright so the total variation
+
+ align:start position:0%
+difficult alright so the total variation
+ 
+
+ align:start position:0%
+difficult alright so the total variation
+has some properties just so let's look
+
+ align:start position:0%
+has some properties just so let's look
+ 
+
+ align:start position:0%
+has some properties just so let's look
+let's keep on the board the definition
+
+ align:start position:0%
+let's keep on the board the definition
+ 
+
+ align:start position:0%
+let's keep on the board the definition
+that involves say the densities okay so
+
+ align:start position:0%
+that involves say the densities okay so
+ 
+
+ align:start position:0%
+that involves say the densities okay so
+think Gaussian in your mind and you have
+
+ align:start position:0%
+think Gaussian in your mind and you have
+ 
+
+ align:start position:0%
+think Gaussian in your mind and you have
+two Gaussian one with min theta and one
+
+ align:start position:0%
+two Gaussian one with min theta and one
+ 
+
+ align:start position:0%
+two Gaussian one with min theta and one
+with mean beta Prime and I'm looking at
+
+ align:start position:0%
+with mean beta Prime and I'm looking at
+ 
+
+ align:start position:0%
+with mean beta Prime and I'm looking at
+a total variation between those two guys
+
+ align:start position:0%
+a total variation between those two guys
+ 
+
+ align:start position:0%
+a total variation between those two guys
+okay so if I look at P theta minus sorry
+
+ align:start position:0%
+okay so if I look at P theta minus sorry
+ 
+
+ align:start position:0%
+okay so if I look at P theta minus sorry
+TV between P theta and P theta Prime
+
+ align:start position:0%
+TV between P theta and P theta Prime
+ 
+
+ align:start position:0%
+TV between P theta and P theta Prime
+this is equal to one-half of the
+
+ align:start position:0%
+this is equal to one-half of the
+ 
+
+ align:start position:0%
+this is equal to one-half of the
+integral between F theta f theta Prime
+
+ align:start position:0%
+integral between F theta f theta Prime
+ 
+
+ align:start position:0%
+integral between F theta f theta Prime
+and when I don't write it so I don't
+
+ align:start position:0%
+and when I don't write it so I don't
+ 
+
+ align:start position:0%
+and when I don't write it so I don't
+write X DX but it's there and then I
+
+ align:start position:0%
+write X DX but it's there and then I
+ 
+
+ align:start position:0%
+write X DX but it's there and then I
+integrate over over E okay so what is
+
+ align:start position:0%
+integrate over over E okay so what is
+ 
+
+ align:start position:0%
+integrate over over E okay so what is
+this thing doing for me it's just saying
+
+ align:start position:0%
+this thing doing for me it's just saying
+ 
+
+ align:start position:0%
+this thing doing for me it's just saying
+well if I have so think of two gaussians
+
+ align:start position:0%
+well if I have so think of two gaussians
+ 
+
+ align:start position:0%
+well if I have so think of two gaussians
+for example I have one left here and one
+
+ align:start position:0%
+for example I have one left here and one
+ 
+
+ align:start position:0%
+for example I have one left here and one
+that's here okay so this is let's say F
+
+ align:start position:0%
+that's here okay so this is let's say F
+ 
+
+ align:start position:0%
+that's here okay so this is let's say F
+theta F theta Prime this guy is doing
+
+ align:start position:0%
+theta F theta Prime this guy is doing
+ 
+
+ align:start position:0%
+theta F theta Prime this guy is doing
+what it's computing the absolute value
+
+ align:start position:0%
+what it's computing the absolute value
+ 
+
+ align:start position:0%
+what it's computing the absolute value
+of the difference between F theta and F
+
+ align:start position:0%
+of the difference between F theta and F
+ 
+
+ align:start position:0%
+of the difference between F theta and F
+theta Prime so you can check for
+
+ align:start position:0%
+theta Prime so you can check for
+ 
+
+ align:start position:0%
+theta Prime so you can check for
+yourself that graphically this I can
+
+ align:start position:0%
+yourself that graphically this I can
+ 
+
+ align:start position:0%
+yourself that graphically this I can
+represent as an area not under the curve
+
+ align:start position:0%
+represent as an area not under the curve
+ 
+
+ align:start position:0%
+represent as an area not under the curve
+but between the curves alright so this
+
+ align:start position:0%
+but between the curves alright so this
+ 
+
+ align:start position:0%
+but between the curves alright so this
+is this guy now this guy is really the
+
+ align:start position:0%
+is this guy now this guy is really the
+ 
+
+ align:start position:0%
+is this guy now this guy is really the
+integral of the absolute value so this
+
+ align:start position:0%
+integral of the absolute value so this
+ 
+
+ align:start position:0%
+integral of the absolute value so this
+thing here this area this is two times
+
+ align:start position:0%
+thing here this area this is two times
+ 
+
+ align:start position:0%
+thing here this area this is two times
+the total variation okay thus killing
+
+ align:start position:0%
+the total variation okay thus killing
+ 
+
+ align:start position:0%
+the total variation okay thus killing
+one half really doesn't matter it's just
+
+ align:start position:0%
+one half really doesn't matter it's just
+ 
+
+ align:start position:0%
+one half really doesn't matter it's just
+if I want to have an actual
+
+ align:start position:0%
+if I want to have an actual
+ 
+
+ align:start position:0%
+if I want to have an actual
+correspondence between the maximum and
+
+ align:start position:0%
+correspondence between the maximum and
+ 
+
+ align:start position:0%
+correspondence between the maximum and
+the and the other guy I have to do this
+
+ align:start position:0%
+the and the other guy I have to do this
+ 
+
+ align:start position:0%
+the and the other guy I have to do this
+okay so this is what it looks like so we
+
+ align:start position:0%
+okay so this is what it looks like so we
+ 
+
+ align:start position:0%
+okay so this is what it looks like so we
+have this definition and and so we have
+
+ align:start position:0%
+have this definition and and so we have
+ 
+
+ align:start position:0%
+have this definition and and so we have
+a couple of properties that come into
+
+ align:start position:0%
+a couple of properties that come into
+ 
+
+ align:start position:0%
+a couple of properties that come into
+this the first one is that it's
+
+ align:start position:0%
+this the first one is that it's
+ 
+
+ align:start position:0%
+this the first one is that it's
+symmetric TV of P theta and P theta
+
+ align:start position:0%
+symmetric TV of P theta and P theta
+ 
+
+ align:start position:0%
+symmetric TV of P theta and P theta
+prime is the same as the TV between P
+
+ align:start position:0%
+prime is the same as the TV between P
+ 
+
+ align:start position:0%
+prime is the same as the TV between P
+theta Prime and P theta well that's
+
+ align:start position:0%
+theta Prime and P theta well that's
+ 
+
+ align:start position:0%
+theta Prime and P theta well that's
+pretty obvious from this definition
+
+ align:start position:0%
+pretty obvious from this definition
+ 
+
+ align:start position:0%
+pretty obvious from this definition
+right I just flipped those two I get the
+
+ align:start position:0%
+right I just flipped those two I get the
+ 
+
+ align:start position:0%
+right I just flipped those two I get the
+same number it's actually also true if I
+
+ align:start position:0%
+same number it's actually also true if I
+ 
+
+ align:start position:0%
+same number it's actually also true if I
+take the maximum all right those things
+
+ align:start position:0%
+take the maximum all right those things
+ 
+
+ align:start position:0%
+take the maximum all right those things
+are completely symmetric in theta and
+
+ align:start position:0%
+are completely symmetric in theta and
+ 
+
+ align:start position:0%
+are completely symmetric in theta and
+theta prime can just flip them it's not
+
+ align:start position:0%
+theta prime can just flip them it's not
+ 
+
+ align:start position:0%
+theta prime can just flip them it's not
+negative is that clear to everyone that
+
+ align:start position:0%
+negative is that clear to everyone that
+ 
+
+ align:start position:0%
+negative is that clear to everyone that
+this thing is non-negative right I
+
+ align:start position:0%
+this thing is non-negative right I
+ 
+
+ align:start position:0%
+this thing is non-negative right I
+integrate an absolute value so this
+
+ align:start position:0%
+integrate an absolute value so this
+ 
+
+ align:start position:0%
+integrate an absolute value so this
+thing is going to give me some
+
+ align:start position:0%
+thing is going to give me some
+ 
+
+ align:start position:0%
+thing is going to give me some
+non-negative number and so if I
+
+ align:start position:0%
+non-negative number and so if I
+ 
+
+ align:start position:0%
+non-negative number and so if I
+integrate this non negative number it's
+
+ align:start position:0%
+integrate this non negative number it's
+ 
+
+ align:start position:0%
+integrate this non negative number it's
+going to be a non-negative number the
+
+ align:start position:0%
+going to be a non-negative number the
+ 
+
+ align:start position:0%
+going to be a non-negative number the
+fact also that it's an area tells me
+
+ align:start position:0%
+fact also that it's an area tells me
+ 
+
+ align:start position:0%
+fact also that it's an area tells me
+that it's going to be non-negative the
+
+ align:start position:0%
+that it's going to be non-negative the
+ 
+
+ align:start position:0%
+that it's going to be non-negative the
+nice thing is that if TV is equal to
+
+ align:start position:0%
+nice thing is that if TV is equal to
+ 
+
+ align:start position:0%
+nice thing is that if TV is equal to
+zero then the two distributions
+
+ align:start position:0%
+zero then the two distributions
+ 
+
+ align:start position:0%
+zero then the two distributions
+two probabilities are the same that
+
+ align:start position:0%
+two probabilities are the same that
+ 
+
+ align:start position:0%
+two probabilities are the same that
+means that for every a p theta of a is
+
+ align:start position:0%
+means that for every a p theta of a is
+ 
+
+ align:start position:0%
+means that for every a p theta of a is
+equal to p theta prime of a now there's
+
+ align:start position:0%
+equal to p theta prime of a now there's
+ 
+
+ align:start position:0%
+equal to p theta prime of a now there's
+two ways to see that the first one is to
+
+ align:start position:0%
+two ways to see that the first one is to
+ 
+
+ align:start position:0%
+two ways to see that the first one is to
+say that if this integral is equal to
+
+ align:start position:0%
+say that if this integral is equal to
+ 
+
+ align:start position:0%
+say that if this integral is equal to
+zero then that means that for all almost
+
+ align:start position:0%
+zero then that means that for all almost
+ 
+
+ align:start position:0%
+zero then that means that for all almost
+all X F theta is equal to F theta Prime
+
+ align:start position:0%
+all X F theta is equal to F theta Prime
+ 
+
+ align:start position:0%
+all X F theta is equal to F theta Prime
+the only way I can integrate a
+
+ align:start position:0%
+the only way I can integrate a
+ 
+
+ align:start position:0%
+the only way I can integrate a
+non-negative function and get zero is
+
+ align:start position:0%
+non-negative function and get zero is
+ 
+
+ align:start position:0%
+non-negative function and get zero is
+that it fits zero pretty much everywhere
+
+ align:start position:0%
+that it fits zero pretty much everywhere
+ 
+
+ align:start position:0%
+that it fits zero pretty much everywhere
+okay and so what it means is that the
+
+ align:start position:0%
+okay and so what it means is that the
+ 
+
+ align:start position:0%
+okay and so what it means is that the
+two densities have to be the same pretty
+
+ align:start position:0%
+two densities have to be the same pretty
+ 
+
+ align:start position:0%
+two densities have to be the same pretty
+much everywhere which means that the
+
+ align:start position:0%
+much everywhere which means that the
+ 
+
+ align:start position:0%
+much everywhere which means that the
+distributions are the same but this is
+
+ align:start position:0%
+distributions are the same but this is
+ 
+
+ align:start position:0%
+distributions are the same but this is
+not really the way you want to do this
+
+ align:start position:0%
+not really the way you want to do this
+ 
+
+ align:start position:0%
+not really the way you want to do this
+because you have to understand what you
+
+ align:start position:0%
+because you have to understand what you
+ 
+
+ align:start position:0%
+because you have to understand what you
+know pretty much everywhere means which
+
+ align:start position:0%
+know pretty much everywhere means which
+ 
+
+ align:start position:0%
+know pretty much everywhere means which
+I should really say almost every word
+
+ align:start position:0%
+I should really say almost every word
+ 
+
+ align:start position:0%
+I should really say almost every word
+that's the formal way of saying it
+
+ align:start position:0%
+that's the formal way of saying it
+ 
+
+ align:start position:0%
+that's the formal way of saying it
+but let's go to this this to definition
+
+ align:start position:0%
+but let's go to this this to definition
+ 
+
+ align:start position:0%
+but let's go to this this to definition
+which is gone okay yeah that's the one
+
+ align:start position:0%
+which is gone okay yeah that's the one
+ 
+
+ align:start position:0%
+which is gone okay yeah that's the one
+here the max of those two guys if this
+
+ align:start position:0%
+here the max of those two guys if this
+ 
+
+ align:start position:0%
+here the max of those two guys if this
+maximum is equal to zero I have a
+
+ align:start position:0%
+maximum is equal to zero I have a
+ 
+
+ align:start position:0%
+maximum is equal to zero I have a
+maximum of non-negative numbers they're
+
+ align:start position:0%
+maximum of non-negative numbers they're
+ 
+
+ align:start position:0%
+maximum of non-negative numbers they're
+absolute values right their maximum is
+
+ align:start position:0%
+absolute values right their maximum is
+ 
+
+ align:start position:0%
+absolute values right their maximum is
+equal to zero well they better be all
+
+ align:start position:0%
+equal to zero well they better be all
+ 
+
+ align:start position:0%
+equal to zero well they better be all
+equal to zero because if one is not
+
+ align:start position:0%
+equal to zero because if one is not
+ 
+
+ align:start position:0%
+equal to zero because if one is not
+equal to zero then the maximum is not
+
+ align:start position:0%
+equal to zero then the maximum is not
+ 
+
+ align:start position:0%
+equal to zero then the maximum is not
+equal to okay so those two guys for
+
+ align:start position:0%
+equal to okay so those two guys for
+ 
+
+ align:start position:0%
+equal to okay so those two guys for
+those two things to be for the maximum
+
+ align:start position:0%
+those two things to be for the maximum
+ 
+
+ align:start position:0%
+those two things to be for the maximum
+to be equal to zero then each of the
+
+ align:start position:0%
+to be equal to zero then each of the
+ 
+
+ align:start position:0%
+to be equal to zero then each of the
+individual absolute values have to be
+
+ align:start position:0%
+individual absolute values have to be
+ 
+
+ align:start position:0%
+individual absolute values have to be
+equal to zero which means that the
+
+ align:start position:0%
+equal to zero which means that the
+ 
+
+ align:start position:0%
+equal to zero which means that the
+probability here is equal to this
+
+ align:start position:0%
+probability here is equal to this
+ 
+
+ align:start position:0%
+probability here is equal to this
+probability here for every event a okay
+
+ align:start position:0%
+probability here for every event a okay
+ 
+
+ align:start position:0%
+probability here for every event a okay
+so those two things this is nice right
+
+ align:start position:0%
+so those two things this is nice right
+ 
+
+ align:start position:0%
+so those two things this is nice right
+that's called definiteness the total
+
+ align:start position:0%
+that's called definiteness the total
+ 
+
+ align:start position:0%
+that's called definiteness the total
+variation equal to 0 implies that P
+
+ align:start position:0%
+variation equal to 0 implies that P
+ 
+
+ align:start position:0%
+variation equal to 0 implies that P
+theta is equal to P theta Prime so
+
+ align:start position:0%
+theta is equal to P theta Prime so
+ 
+
+ align:start position:0%
+theta is equal to P theta Prime so
+that's really some notion of distance
+
+ align:start position:0%
+that's really some notion of distance
+ 
+
+ align:start position:0%
+that's really some notion of distance
+right that's what we want if this
+
+ align:start position:0%
+right that's what we want if this
+ 
+
+ align:start position:0%
+right that's what we want if this
+thing's being small implied that piece
+
+ align:start position:0%
+thing's being small implied that piece
+ 
+
+ align:start position:0%
+thing's being small implied that piece
+theta could be all over the place
+
+ align:start position:0%
+theta could be all over the place
+ 
+
+ align:start position:0%
+theta could be all over the place
+compared to P theta prime that would not
+
+ align:start position:0%
+compared to P theta prime that would not
+ 
+
+ align:start position:0%
+compared to P theta prime that would not
+help very much now there's also the
+
+ align:start position:0%
+help very much now there's also the
+ 
+
+ align:start position:0%
+help very much now there's also the
+triangle inequality that follows
+
+ align:start position:0%
+triangle inequality that follows
+ 
+
+ align:start position:0%
+triangle inequality that follows
+immediately from the triangle inequality
+
+ align:start position:0%
+immediately from the triangle inequality
+ 
+
+ align:start position:0%
+immediately from the triangle inequality
+inside the inside this guy right if I
+
+ align:start position:0%
+inside the inside this guy right if I
+ 
+
+ align:start position:0%
+inside the inside this guy right if I
+squeeze in some F theta prime prime in
+
+ align:start position:0%
+squeeze in some F theta prime prime in
+ 
+
+ align:start position:0%
+squeeze in some F theta prime prime in
+there I'm gonna use the triangle
+
+ align:start position:0%
+there I'm gonna use the triangle
+ 
+
+ align:start position:0%
+there I'm gonna use the triangle
+inequality and get the triangle
+
+ align:start position:0%
+inequality and get the triangle
+ 
+
+ align:start position:0%
+inequality and get the triangle
+inequality for the whole thing okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll do it for you now okay so let's
+
+ align:start position:0%
+I'll do it for you now okay so let's
+ 
+
+ align:start position:0%
+I'll do it for you now okay so let's
+just prove that those two things are
+
+ align:start position:0%
+just prove that those two things are
+ 
+
+ align:start position:0%
+just prove that those two things are
+actually giving me the same definition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so what I'm gonna do is I'm
+
+ align:start position:0%
+all right so what I'm gonna do is I'm
+ 
+
+ align:start position:0%
+all right so what I'm gonna do is I'm
+actually going to start with the second
+
+ align:start position:0%
+actually going to start with the second
+ 
+
+ align:start position:0%
+actually going to start with the second
+one and I'm gonna write I'm gonna start
+
+ align:start position:0%
+one and I'm gonna write I'm gonna start
+ 
+
+ align:start position:0%
+one and I'm gonna write I'm gonna start
+with the density version but as an
+
+ align:start position:0%
+with the density version but as an
+ 
+
+ align:start position:0%
+with the density version but as an
+exercise you can do it for the PMF
+
+ align:start position:0%
+exercise you can do it for the PMF
+ 
+
+ align:start position:0%
+exercise you can do it for the PMF
+version if you prefer so I'm gonna start
+
+ align:start position:0%
+version if you prefer so I'm gonna start
+ 
+
+ align:start position:0%
+version if you prefer so I'm gonna start
+with the fact that F okay so I'm gonna
+
+ align:start position:0%
+with the fact that F okay so I'm gonna
+ 
+
+ align:start position:0%
+with the fact that F okay so I'm gonna
+write f of G so I don't have to write
+
+ align:start position:0%
+write f of G so I don't have to write
+ 
+
+ align:start position:0%
+write f of G so I don't have to write
+the F and G right so think of this as
+
+ align:start position:0%
+the F and G right so think of this as
+ 
+
+ align:start position:0%
+the F and G right so think of this as
+being absurd thither and think of this
+
+ align:start position:0%
+being absurd thither and think of this
+ 
+
+ align:start position:0%
+being absurd thither and think of this
+guy as being F sub theta prime I just
+
+ align:start position:0%
+guy as being F sub theta prime I just
+ 
+
+ align:start position:0%
+guy as being F sub theta prime I just
+don't want to have to write in this is
+
+ align:start position:0%
+don't want to have to write in this is
+ 
+
+ align:start position:0%
+don't want to have to write in this is
+all the time okay so I'm gonna start
+
+ align:start position:0%
+all the time okay so I'm gonna start
+ 
+
+ align:start position:0%
+all the time okay so I'm gonna start
+with this thing the integral of f of X
+
+ align:start position:0%
+with this thing the integral of f of X
+ 
+
+ align:start position:0%
+with this thing the integral of f of X
+minus G of X DX okay the first thing I'm
+
+ align:start position:0%
+minus G of X DX okay the first thing I'm
+ 
+
+ align:start position:0%
+minus G of X DX okay the first thing I'm
+gonna do is this is an absolute value so
+
+ align:start position:0%
+gonna do is this is an absolute value so
+ 
+
+ align:start position:0%
+gonna do is this is an absolute value so
+either the number in the absolute value
+
+ align:start position:0%
+either the number in the absolute value
+ 
+
+ align:start position:0%
+either the number in the absolute value
+is positive and I actually kept it like
+
+ align:start position:0%
+is positive and I actually kept it like
+ 
+
+ align:start position:0%
+is positive and I actually kept it like
+that or it's negative and I flip that
+
+ align:start position:0%
+that or it's negative and I flip that
+ 
+
+ align:start position:0%
+that or it's negative and I flip that
+sign okay so let's just split between
+
+ align:start position:0%
+sign okay so let's just split between
+ 
+
+ align:start position:0%
+sign okay so let's just split between
+those two cases all right so this thing
+
+ align:start position:0%
+those two cases all right so this thing
+ 
+
+ align:start position:0%
+those two cases all right so this thing
+is equal to 1/2 the integral of so let
+
+ align:start position:0%
+is equal to 1/2 the integral of so let
+ 
+
+ align:start position:0%
+is equal to 1/2 the integral of so let
+me actually write the set a star as
+
+ align:start position:0%
+me actually write the set a star as
+ 
+
+ align:start position:0%
+me actually write the set a star as
+being the set of X's such that f of X is
+
+ align:start position:0%
+being the set of X's such that f of X is
+ 
+
+ align:start position:0%
+being the set of X's such that f of X is
+larger than G of X okay so that's the
+
+ align:start position:0%
+larger than G of X okay so that's the
+ 
+
+ align:start position:0%
+larger than G of X okay so that's the
+set on which the difference is going to
+
+ align:start position:0%
+set on which the difference is going to
+ 
+
+ align:start position:0%
+set on which the difference is going to
+be positive or the difference is going
+
+ align:start position:0%
+be positive or the difference is going
+ 
+
+ align:start position:0%
+be positive or the difference is going
+to be negative right so this again is
+
+ align:start position:0%
+to be negative right so this again is
+ 
+
+ align:start position:0%
+to be negative right so this again is
+equivalent to f of X minus G of X is
+
+ align:start position:0%
+equivalent to f of X minus G of X is
+ 
+
+ align:start position:0%
+equivalent to f of X minus G of X is
+positive all right
+
+ align:start position:0%
+positive all right
+ 
+
+ align:start position:0%
+positive all right
+okay everybody agrees so this is the set
+
+ align:start position:0%
+okay everybody agrees so this is the set
+ 
+
+ align:start position:0%
+okay everybody agrees so this is the set
+I'm interested in so now I'm going to
+
+ align:start position:0%
+I'm interested in so now I'm going to
+ 
+
+ align:start position:0%
+I'm interested in so now I'm going to
+split my integral integral into two
+
+ align:start position:0%
+split my integral integral into two
+ 
+
+ align:start position:0%
+split my integral integral into two
+parts in a a star so of so on a star f
+
+ align:start position:0%
+parts in a a star so of so on a star f
+ 
+
+ align:start position:0%
+parts in a a star so of so on a star f
+is larger than G so the absolute value
+
+ align:start position:0%
+is larger than G so the absolute value
+ 
+
+ align:start position:0%
+is larger than G so the absolute value
+is just the difference itself so here I
+
+ align:start position:0%
+is just the difference itself so here I
+ 
+
+ align:start position:0%
+is just the difference itself so here I
+put parentheses rather than absolute
+
+ align:start position:0%
+put parentheses rather than absolute
+ 
+
+ align:start position:0%
+put parentheses rather than absolute
+value and then I have plus
+
+ align:start position:0%
+value and then I have plus
+ 
+
+ align:start position:0%
+value and then I have plus
+one half of the integral of the condor
+
+ align:start position:0%
+one half of the integral of the condor
+ 
+
+ align:start position:0%
+one half of the integral of the condor
+complement what are you guys used to to
+
+ align:start position:0%
+complement what are you guys used to to
+ 
+
+ align:start position:0%
+complement what are you guys used to to
+write the compliment to the sea or the
+
+ align:start position:0%
+write the compliment to the sea or the
+ 
+
+ align:start position:0%
+write the compliment to the sea or the
+bar to the sea okay and so here on the
+
+ align:start position:0%
+bar to the sea okay and so here on the
+ 
+
+ align:start position:0%
+bar to the sea okay and so here on the
+compliment then f is less than G so this
+
+ align:start position:0%
+compliment then f is less than G so this
+ 
+
+ align:start position:0%
+compliment then f is less than G so this
+is actually really G of X minus f of X
+
+ align:start position:0%
+is actually really G of X minus f of X
+ 
+
+ align:start position:0%
+is actually really G of X minus f of X
+DX okay everybody's with me here so I
+
+ align:start position:0%
+DX okay everybody's with me here so I
+ 
+
+ align:start position:0%
+DX okay everybody's with me here so I
+just said I mean those are just
+
+ align:start position:0%
+just said I mean those are just
+ 
+
+ align:start position:0%
+just said I mean those are just
+rewriting what the definition of the
+
+ align:start position:0%
+rewriting what the definition of the
+ 
+
+ align:start position:0%
+rewriting what the definition of the
+absolute value is okay so now there's
+
+ align:start position:0%
+absolute value is okay so now there's
+ 
+
+ align:start position:0%
+absolute value is okay so now there's
+there's nice things that I know about F
+
+ align:start position:0%
+there's nice things that I know about F
+ 
+
+ align:start position:0%
+there's nice things that I know about F
+and G and the two nice things is that
+
+ align:start position:0%
+and G and the two nice things is that
+ 
+
+ align:start position:0%
+and G and the two nice things is that
+the integral of F is equal to 1 and the
+
+ align:start position:0%
+the integral of F is equal to 1 and the
+ 
+
+ align:start position:0%
+the integral of F is equal to 1 and the
+integral of G is equal to 1 right this
+
+ align:start position:0%
+integral of G is equal to 1 right this
+ 
+
+ align:start position:0%
+integral of G is equal to 1 right this
+implies that the integral of F minus G
+
+ align:start position:0%
+implies that the integral of F minus G
+ 
+
+ align:start position:0%
+implies that the integral of F minus G
+is equal to what 0 ok and so now that
+
+ align:start position:0%
+is equal to what 0 ok and so now that
+ 
+
+ align:start position:0%
+is equal to what 0 ok and so now that
+means that if I want you just go from
+
+ align:start position:0%
+means that if I want you just go from
+ 
+
+ align:start position:0%
+means that if I want you just go from
+the integral here on a compliment to the
+
+ align:start position:0%
+the integral here on a compliment to the
+ 
+
+ align:start position:0%
+the integral here on a compliment to the
+integral on a or on a star compliment to
+
+ align:start position:0%
+integral on a or on a star compliment to
+ 
+
+ align:start position:0%
+integral on a or on a star compliment to
+the integral on a star I just have to
+
+ align:start position:0%
+the integral on a star I just have to
+ 
+
+ align:start position:0%
+the integral on a star I just have to
+flip the sign right so that implies that
+
+ align:start position:0%
+flip the sign right so that implies that
+ 
+
+ align:start position:0%
+flip the sign right so that implies that
+an integral on a star compliment of G of
+
+ align:start position:0%
+an integral on a star compliment of G of
+ 
+
+ align:start position:0%
+an integral on a star compliment of G of
+X minus f of X DX this is simply equal
+
+ align:start position:0%
+X minus f of X DX this is simply equal
+ 
+
+ align:start position:0%
+X minus f of X DX this is simply equal
+to the integral on a star of f of X
+
+ align:start position:0%
+to the integral on a star of f of X
+ 
+
+ align:start position:0%
+to the integral on a star of f of X
+minus G of X DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right so now this guy becomes
+
+ align:start position:0%
+okay all right so now this guy becomes
+ 
+
+ align:start position:0%
+okay all right so now this guy becomes
+this guy over there all right so I have
+
+ align:start position:0%
+this guy over there all right so I have
+ 
+
+ align:start position:0%
+this guy over there all right so I have
+one half of this plus one half of the
+
+ align:start position:0%
+one half of this plus one half of the
+ 
+
+ align:start position:0%
+one half of this plus one half of the
+same guy so it means that one half of
+
+ align:start position:0%
+same guy so it means that one half of
+ 
+
+ align:start position:0%
+same guy so it means that one half of
+the integral between F we took of F
+
+ align:start position:0%
+the integral between F we took of F
+ 
+
+ align:start position:0%
+the integral between F we took of F
+minus G absolute value so that was my
+
+ align:start position:0%
+minus G absolute value so that was my
+ 
+
+ align:start position:0%
+minus G absolute value so that was my
+original definition this thing is
+
+ align:start position:0%
+original definition this thing is
+ 
+
+ align:start position:0%
+original definition this thing is
+actually equal to the integral on a star
+
+ align:start position:0%
+actually equal to the integral on a star
+ 
+
+ align:start position:0%
+actually equal to the integral on a star
+of f of X minus G of X DX okay
+
+ align:start position:0%
+of f of X minus G of X DX okay
+ 
+
+ align:start position:0%
+of f of X minus G of X DX okay
+and this is simply equal to P of a star
+
+ align:start position:0%
+and this is simply equal to P of a star
+ 
+
+ align:start position:0%
+and this is simply equal to P of a star
+so say p f of a star minus P G of a star
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which one is larger than the other one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it is just look at this board what the
+
+ align:start position:0%
+it is just look at this board what the
+ 
+
+ align:start position:0%
+it is just look at this board what the
+first one has to be larger because this
+
+ align:start position:0%
+first one has to be larger because this
+ 
+
+ align:start position:0%
+first one has to be larger because this
+thing is actually equal to a
+
+ align:start position:0%
+thing is actually equal to a
+ 
+
+ align:start position:0%
+thing is actually equal to a
+non-negative number okay so now I have
+
+ align:start position:0%
+non-negative number okay so now I have
+ 
+
+ align:start position:0%
+non-negative number okay so now I have
+this absolute value of two things
+
+ align:start position:0%
+this absolute value of two things
+ 
+
+ align:start position:0%
+this absolute value of two things
+and so I'm closer to the actual
+
+ align:start position:0%
+and so I'm closer to the actual
+ 
+
+ align:start position:0%
+and so I'm closer to the actual
+definition but I still need to show you
+
+ align:start position:0%
+definition but I still need to show you
+ 
+
+ align:start position:0%
+definition but I still need to show you
+that this thing is the maximum value
+
+ align:start position:0%
+that this thing is the maximum value
+ 
+
+ align:start position:0%
+that this thing is the maximum value
+right so this is definitely at most the
+
+ align:start position:0%
+right so this is definitely at most the
+ 
+
+ align:start position:0%
+right so this is definitely at most the
+maximum over a of P f of a minus P G of
+
+ align:start position:0%
+maximum over a of P f of a minus P G of
+ 
+
+ align:start position:0%
+maximum over a of P f of a minus P G of
+a that's certainly true right we agree
+
+ align:start position:0%
+a that's certainly true right we agree
+ 
+
+ align:start position:0%
+a that's certainly true right we agree
+with this because this is just for one
+
+ align:start position:0%
+with this because this is just for one
+ 
+
+ align:start position:0%
+with this because this is just for one
+specific a and I'm bounding it by the
+
+ align:start position:0%
+specific a and I'm bounding it by the
+ 
+
+ align:start position:0%
+specific a and I'm bounding it by the
+maximum over all possible ways so that's
+
+ align:start position:0%
+maximum over all possible ways so that's
+ 
+
+ align:start position:0%
+maximum over all possible ways so that's
+clearly true so now I have to go the
+
+ align:start position:0%
+clearly true so now I have to go the
+ 
+
+ align:start position:0%
+clearly true so now I have to go the
+other way around I have to show you that
+
+ align:start position:0%
+other way around I have to show you that
+ 
+
+ align:start position:0%
+other way around I have to show you that
+the max is actually this guy a star so
+
+ align:start position:0%
+the max is actually this guy a star so
+ 
+
+ align:start position:0%
+the max is actually this guy a star so
+why would that be true well let's just
+
+ align:start position:0%
+why would that be true well let's just
+ 
+
+ align:start position:0%
+why would that be true well let's just
+inspect this thing over there all right
+
+ align:start position:0%
+inspect this thing over there all right
+ 
+
+ align:start position:0%
+inspect this thing over there all right
+so we want to show that if I take any
+
+ align:start position:0%
+so we want to show that if I take any
+ 
+
+ align:start position:0%
+so we want to show that if I take any
+other a in this integral then this guy a
+
+ align:start position:0%
+other a in this integral then this guy a
+ 
+
+ align:start position:0%
+other a in this integral then this guy a
+star it's actually going to decrease its
+
+ align:start position:0%
+star it's actually going to decrease its
+ 
+
+ align:start position:0%
+star it's actually going to decrease its
+value so we have this function I'm gonna
+
+ align:start position:0%
+value so we have this function I'm gonna
+ 
+
+ align:start position:0%
+value so we have this function I'm gonna
+call this function Delta okay and what
+
+ align:start position:0%
+call this function Delta okay and what
+ 
+
+ align:start position:0%
+call this function Delta okay and what
+we have is so let's say this function
+
+ align:start position:0%
+we have is so let's say this function
+ 
+
+ align:start position:0%
+we have is so let's say this function
+looks like this now it's the difference
+
+ align:start position:0%
+looks like this now it's the difference
+ 
+
+ align:start position:0%
+looks like this now it's the difference
+between two densities it doesn't have to
+
+ align:start position:0%
+between two densities it doesn't have to
+ 
+
+ align:start position:0%
+between two densities it doesn't have to
+integrate it doesn't have to be
+
+ align:start position:0%
+integrate it doesn't have to be
+ 
+
+ align:start position:0%
+integrate it doesn't have to be
+non-negative but it certainly has to
+
+ align:start position:0%
+non-negative but it certainly has to
+ 
+
+ align:start position:0%
+non-negative but it certainly has to
+integrate to zero okay and so now I take
+
+ align:start position:0%
+integrate to zero okay and so now I take
+ 
+
+ align:start position:0%
+integrate to zero okay and so now I take
+this thing and the a star what is the
+
+ align:start position:0%
+this thing and the a star what is the
+ 
+
+ align:start position:0%
+this thing and the a star what is the
+set a star here the set a star is the
+
+ align:start position:0%
+set a star here the set a star is the
+ 
+
+ align:start position:0%
+set a star here the set a star is the
+set over which the function Delta is
+
+ align:start position:0%
+set over which the function Delta is
+ 
+
+ align:start position:0%
+set over which the function Delta is
+non-negative right right so that's just
+
+ align:start position:0%
+non-negative right right so that's just
+ 
+
+ align:start position:0%
+non-negative right right so that's just
+the definition a star was the set over
+
+ align:start position:0%
+the definition a star was the set over
+ 
+
+ align:start position:0%
+the definition a star was the set over
+which F minus G was positive and F minus
+
+ align:start position:0%
+which F minus G was positive and F minus
+ 
+
+ align:start position:0%
+which F minus G was positive and F minus
+G which is called Delta so what it means
+
+ align:start position:0%
+G which is called Delta so what it means
+ 
+
+ align:start position:0%
+G which is called Delta so what it means
+is that what I'm really integrating is
+
+ align:start position:0%
+is that what I'm really integrating is
+ 
+
+ align:start position:0%
+is that what I'm really integrating is
+Delta on this set
+
+ align:start position:0%
+Delta on this set
+ 
+
+ align:start position:0%
+Delta on this set
+so it's this area under the curve just
+
+ align:start position:0%
+so it's this area under the curve just
+ 
+
+ align:start position:0%
+so it's this area under the curve just
+on the positive things agreed
+
+ align:start position:0%
+on the positive things agreed
+ 
+
+ align:start position:0%
+on the positive things agreed
+so now let's just make some tiny
+
+ align:start position:0%
+so now let's just make some tiny
+ 
+
+ align:start position:0%
+so now let's just make some tiny
+variations around this guy if I take a
+
+ align:start position:0%
+variations around this guy if I take a
+ 
+
+ align:start position:0%
+variations around this guy if I take a
+to be larger than a star right so let me
+
+ align:start position:0%
+to be larger than a star right so let me
+ 
+
+ align:start position:0%
+to be larger than a star right so let me
+add for example this part here that
+
+ align:start position:0%
+add for example this part here that
+ 
+
+ align:start position:0%
+add for example this part here that
+means that when I compute my integral
+
+ align:start position:0%
+means that when I compute my integral
+ 
+
+ align:start position:0%
+means that when I compute my integral
+I'm removing this area under the curve
+
+ align:start position:0%
+I'm removing this area under the curve
+ 
+
+ align:start position:0%
+I'm removing this area under the curve
+right it's negative the integral here is
+
+ align:start position:0%
+right it's negative the integral here is
+ 
+
+ align:start position:0%
+right it's negative the integral here is
+negative so if I start adding something
+
+ align:start position:0%
+negative so if I start adding something
+ 
+
+ align:start position:0%
+negative so if I start adding something
+to a the value goes lower if I start
+
+ align:start position:0%
+to a the value goes lower if I start
+ 
+
+ align:start position:0%
+to a the value goes lower if I start
+removing something from a like say this
+
+ align:start position:0%
+removing something from a like say this
+ 
+
+ align:start position:0%
+removing something from a like say this
+guy I'm actually removing this value
+
+ align:start position:0%
+guy I'm actually removing this value
+ 
+
+ align:start position:0%
+guy I'm actually removing this value
+from the integral so there's no way I'm
+
+ align:start position:0%
+from the integral so there's no way I'm
+ 
+
+ align:start position:0%
+from the integral so there's no way I'm
+actually stuck this a star is the one
+
+ align:start position:0%
+actually stuck this a star is the one
+ 
+
+ align:start position:0%
+actually stuck this a star is the one
+that actually maximizes the integral of
+
+ align:start position:0%
+that actually maximizes the integral of
+ 
+
+ align:start position:0%
+that actually maximizes the integral of
+this function all right so there was we
+
+ align:start position:0%
+this function all right so there was we
+ 
+
+ align:start position:0%
+this function all right so there was we
+use the fact that for any function say
+
+ align:start position:0%
+use the fact that for any function say
+ 
+
+ align:start position:0%
+use the fact that for any function say
+Delta the integral over a of Delta is
+
+ align:start position:0%
+Delta the integral over a of Delta is
+ 
+
+ align:start position:0%
+Delta the integral over a of Delta is
+less than the integral over the set of
+
+ align:start position:0%
+less than the integral over the set of
+ 
+
+ align:start position:0%
+less than the integral over the set of
+X's such that Delta of X is non-negative
+
+ align:start position:0%
+X's such that Delta of X is non-negative
+ 
+
+ align:start position:0%
+X's such that Delta of X is non-negative
+of Delta of X DX okay and that's an
+
+ align:start position:0%
+of Delta of X DX okay and that's an
+ 
+
+ align:start position:0%
+of Delta of X DX okay and that's an
+obvious fact just by picture say okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's true for all things
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's actually equal we know that the
+
+ align:start position:0%
+it's actually equal we know that the
+ 
+
+ align:start position:0%
+it's actually equal we know that the
+integral of F minus G is integral Delta
+
+ align:start position:0%
+integral of F minus G is integral Delta
+ 
+
+ align:start position:0%
+integral of F minus G is integral Delta
+is zero so there's actually exactly the
+
+ align:start position:0%
+is zero so there's actually exactly the
+ 
+
+ align:start position:0%
+is zero so there's actually exactly the
+same area above and below but you yeah
+
+ align:start position:0%
+same area above and below but you yeah
+ 
+
+ align:start position:0%
+same area above and below but you yeah
+you're right you could go to the extreme
+
+ align:start position:0%
+you're right you could go to the extreme
+ 
+
+ align:start position:0%
+you're right you could go to the extreme
+cases you're right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no it's actually it's actually still be
+
+ align:start position:0%
+no it's actually it's actually still be
+ 
+
+ align:start position:0%
+no it's actually it's actually still be
+true even if there was if this was a
+
+ align:start position:0%
+true even if there was if this was a
+ 
+
+ align:start position:0%
+true even if there was if this was a
+constant that would still be true here I
+
+ align:start position:0%
+constant that would still be true here I
+ 
+
+ align:start position:0%
+constant that would still be true here I
+never used the fact that the integral is
+
+ align:start position:0%
+never used the fact that the integral is
+ 
+
+ align:start position:0%
+never used the fact that the integral is
+equal to zero okay I could shift this
+
+ align:start position:0%
+equal to zero okay I could shift this
+ 
+
+ align:start position:0%
+equal to zero okay I could shift this
+function by one so that the integral of
+
+ align:start position:0%
+function by one so that the integral of
+ 
+
+ align:start position:0%
+function by one so that the integral of
+Delta is equal to one and it still it
+
+ align:start position:0%
+Delta is equal to one and it still it
+ 
+
+ align:start position:0%
+Delta is equal to one and it still it
+would still be true that it's maximized
+
+ align:start position:0%
+would still be true that it's maximized
+ 
+
+ align:start position:0%
+would still be true that it's maximized
+when I take a to be the set where it's
+
+ align:start position:0%
+when I take a to be the set where it's
+ 
+
+ align:start position:0%
+when I take a to be the set where it's
+positive just need to make sure that
+
+ align:start position:0%
+positive just need to make sure that
+ 
+
+ align:start position:0%
+positive just need to make sure that
+there's some place where it is but
+
+ align:start position:0%
+there's some place where it is but
+ 
+
+ align:start position:0%
+there's some place where it is but
+that's about it
+
+ align:start position:0%
+that's about it
+ 
+
+ align:start position:0%
+that's about it
+okay of course we use this but before
+
+ align:start position:0%
+okay of course we use this but before
+ 
+
+ align:start position:0%
+okay of course we use this but before
+when we made this thing but just the
+
+ align:start position:0%
+when we made this thing but just the
+ 
+
+ align:start position:0%
+when we made this thing but just the
+last argument this last fact does not
+
+ align:start position:0%
+last argument this last fact does not
+ 
+
+ align:start position:0%
+last argument this last fact does not
+require that okay all right so now we
+
+ align:start position:0%
+require that okay all right so now we
+ 
+
+ align:start position:0%
+require that okay all right so now we
+have this notion of okay so we have this
+
+ align:start position:0%
+have this notion of okay so we have this
+ 
+
+ align:start position:0%
+have this notion of okay so we have this
+notion of distance between probability
+
+ align:start position:0%
+notion of distance between probability
+ 
+
+ align:start position:0%
+notion of distance between probability
+measures right I mean this things are
+
+ align:start position:0%
+measures right I mean this things are
+ 
+
+ align:start position:0%
+measures right I mean this things are
+exactly what's if I were to be in a
+
+ align:start position:0%
+exactly what's if I were to be in a
+ 
+
+ align:start position:0%
+exactly what's if I were to be in a
+formal math class and I said here are
+
+ align:start position:0%
+formal math class and I said here are
+ 
+
+ align:start position:0%
+formal math class and I said here are
+the axioms that a distance should
+
+ align:start position:0%
+the axioms that a distance should
+ 
+
+ align:start position:0%
+the axioms that a distance should
+satisfy those are exactly these things
+
+ align:start position:0%
+satisfy those are exactly these things
+ 
+
+ align:start position:0%
+satisfy those are exactly these things
+if it's not satisfying this thing it's
+
+ align:start position:0%
+if it's not satisfying this thing it's
+ 
+
+ align:start position:0%
+if it's not satisfying this thing it's
+called pseudo distance or quasi distance
+
+ align:start position:0%
+called pseudo distance or quasi distance
+ 
+
+ align:start position:0%
+called pseudo distance or quasi distance
+or just metric or nothing at all
+
+ align:start position:0%
+or just metric or nothing at all
+ 
+
+ align:start position:0%
+or just metric or nothing at all
+honestly okay so it's a distance it's
+
+ align:start position:0%
+honestly okay so it's a distance it's
+ 
+
+ align:start position:0%
+honestly okay so it's a distance it's
+symmetric non-negative equal to zero
+
+ align:start position:0%
+symmetric non-negative equal to zero
+ 
+
+ align:start position:0%
+symmetric non-negative equal to zero
+when if and only if the two arguments
+
+ align:start position:0%
+when if and only if the two arguments
+ 
+
+ align:start position:0%
+when if and only if the two arguments
+are equal and it satisfies the triangle
+
+ align:start position:0%
+are equal and it satisfies the triangle
+ 
+
+ align:start position:0%
+are equal and it satisfies the triangle
+inequality all right and so that means
+
+ align:start position:0%
+inequality all right and so that means
+ 
+
+ align:start position:0%
+inequality all right and so that means
+that so we have this actual total
+
+ align:start position:0%
+that so we have this actual total
+ 
+
+ align:start position:0%
+that so we have this actual total
+variation distance between travel
+
+ align:start position:0%
+variation distance between travel
+ 
+
+ align:start position:0%
+variation distance between travel
+distributions and here is now a
+
+ align:start position:0%
+distributions and here is now a
+ 
+
+ align:start position:0%
+distributions and here is now a
+statistical strategy to implement our
+
+ align:start position:0%
+statistical strategy to implement our
+ 
+
+ align:start position:0%
+statistical strategy to implement our
+goal remember our goal was to spit out a
+
+ align:start position:0%
+goal remember our goal was to spit out a
+ 
+
+ align:start position:0%
+goal remember our goal was to spit out a
+theta hat which was closed so such that
+
+ align:start position:0%
+theta hat which was closed so such that
+ 
+
+ align:start position:0%
+theta hat which was closed so such that
+P theta hat
+
+ align:start position:0%
+P theta hat
+ 
+
+ align:start position:0%
+P theta hat
+was close to P theta star so hopefully
+
+ align:start position:0%
+was close to P theta star so hopefully
+ 
+
+ align:start position:0%
+was close to P theta star so hopefully
+we're trying to minimize the total
+
+ align:start position:0%
+we're trying to minimize the total
+ 
+
+ align:start position:0%
+we're trying to minimize the total
+variation distance between piece theta
+
+ align:start position:0%
+variation distance between piece theta
+ 
+
+ align:start position:0%
+variation distance between piece theta
+hat and P theta star now we cannot do
+
+ align:start position:0%
+hat and P theta star now we cannot do
+ 
+
+ align:start position:0%
+hat and P theta star now we cannot do
+that because just by this fact this this
+
+ align:start position:0%
+that because just by this fact this this
+ 
+
+ align:start position:0%
+that because just by this fact this this
+slide if we wanted to do that directly
+
+ align:start position:0%
+slide if we wanted to do that directly
+ 
+
+ align:start position:0%
+slide if we wanted to do that directly
+we would just take well let's take theta
+
+ align:start position:0%
+we would just take well let's take theta
+ 
+
+ align:start position:0%
+we would just take well let's take theta
+hat equals theta star and that will give
+
+ align:start position:0%
+hat equals theta star and that will give
+ 
+
+ align:start position:0%
+hat equals theta star and that will give
+me the value 0 and that's the minimum
+
+ align:start position:0%
+me the value 0 and that's the minimum
+ 
+
+ align:start position:0%
+me the value 0 and that's the minimum
+possible value it can take the problem
+
+ align:start position:0%
+possible value it can take the problem
+ 
+
+ align:start position:0%
+possible value it can take the problem
+is that we don't know what the toe
+
+ align:start position:0%
+is that we don't know what the toe
+ 
+
+ align:start position:0%
+is that we don't know what the toe
+variation is to something that we don't
+
+ align:start position:0%
+variation is to something that we don't
+ 
+
+ align:start position:0%
+variation is to something that we don't
+know we know how to compute all
+
+ align:start position:0%
+know we know how to compute all
+ 
+
+ align:start position:0%
+know we know how to compute all
+variations if I give you the two
+
+ align:start position:0%
+variations if I give you the two
+ 
+
+ align:start position:0%
+variations if I give you the two
+arguments but here one of the arguments
+
+ align:start position:0%
+arguments but here one of the arguments
+ 
+
+ align:start position:0%
+arguments but here one of the arguments
+is not known P theta star is not known
+
+ align:start position:0%
+is not known P theta star is not known
+ 
+
+ align:start position:0%
+is not known P theta star is not known
+to us so we need to estimate it and so
+
+ align:start position:0%
+to us so we need to estimate it and so
+ 
+
+ align:start position:0%
+to us so we need to estimate it and so
+here's a strategy just build an
+
+ align:start position:0%
+here's a strategy just build an
+ 
+
+ align:start position:0%
+here's a strategy just build an
+estimator of the total variation
+
+ align:start position:0%
+estimator of the total variation
+ 
+
+ align:start position:0%
+estimator of the total variation
+distance between P theta and pset estar
+
+ align:start position:0%
+distance between P theta and pset estar
+ 
+
+ align:start position:0%
+distance between P theta and pset estar
+for all candidate theta all possible
+
+ align:start position:0%
+for all candidate theta all possible
+ 
+
+ align:start position:0%
+for all candidate theta all possible
+theta and capital theta all right
+
+ align:start position:0%
+theta and capital theta all right
+ 
+
+ align:start position:0%
+theta and capital theta all right
+now if this is a good estimate then when
+
+ align:start position:0%
+now if this is a good estimate then when
+ 
+
+ align:start position:0%
+now if this is a good estimate then when
+I minimize it I should get something
+
+ align:start position:0%
+I minimize it I should get something
+ 
+
+ align:start position:0%
+I minimize it I should get something
+that's close to P theta star alright so
+
+ align:start position:0%
+that's close to P theta star alright so
+ 
+
+ align:start position:0%
+that's close to P theta star alright so
+here's the strategy this is my function
+
+ align:start position:0%
+here's the strategy this is my function
+ 
+
+ align:start position:0%
+here's the strategy this is my function
+that map's theta to the total variation
+
+ align:start position:0%
+that map's theta to the total variation
+ 
+
+ align:start position:0%
+that map's theta to the total variation
+between P theta and P theta star
+
+ align:start position:0%
+between P theta and P theta star
+ 
+
+ align:start position:0%
+between P theta and P theta star
+I know it's minimized at theta star
+
+ align:start position:0%
+I know it's minimized at theta star
+ 
+
+ align:start position:0%
+I know it's minimized at theta star
+right that's definitely P TV of piece
+
+ align:start position:0%
+right that's definitely P TV of piece
+ 
+
+ align:start position:0%
+right that's definitely P TV of piece
+and and the value here the y-axis should
+
+ align:start position:0%
+and and the value here the y-axis should
+ 
+
+ align:start position:0%
+and and the value here the y-axis should
+say zero and so I don't know this guy so
+
+ align:start position:0%
+say zero and so I don't know this guy so
+ 
+
+ align:start position:0%
+say zero and so I don't know this guy so
+I'm gonna estimate it by some estimator
+
+ align:start position:0%
+I'm gonna estimate it by some estimator
+ 
+
+ align:start position:0%
+I'm gonna estimate it by some estimator
+that comes from my data hopefully the
+
+ align:start position:0%
+that comes from my data hopefully the
+ 
+
+ align:start position:0%
+that comes from my data hopefully the
+more data I have the better this
+
+ align:start position:0%
+more data I have the better this
+ 
+
+ align:start position:0%
+more data I have the better this
+estimator is and I'm gonna try to
+
+ align:start position:0%
+estimator is and I'm gonna try to
+ 
+
+ align:start position:0%
+estimator is and I'm gonna try to
+minimize this estimator now and if the
+
+ align:start position:0%
+minimize this estimator now and if the
+ 
+
+ align:start position:0%
+minimize this estimator now and if the
+two things are closed and the minima
+
+ align:start position:0%
+two things are closed and the minima
+ 
+
+ align:start position:0%
+two things are closed and the minima
+should be closed alright that's a pretty
+
+ align:start position:0%
+should be closed alright that's a pretty
+ 
+
+ align:start position:0%
+should be closed alright that's a pretty
+good estimation strategy the problem is
+
+ align:start position:0%
+good estimation strategy the problem is
+ 
+
+ align:start position:0%
+good estimation strategy the problem is
+that it's very unclear how you would
+
+ align:start position:0%
+that it's very unclear how you would
+ 
+
+ align:start position:0%
+that it's very unclear how you would
+build this estimator of TV of the tool
+
+ align:start position:0%
+build this estimator of TV of the tool
+ 
+
+ align:start position:0%
+build this estimator of TV of the tool
+variation right so building estimators
+
+ align:start position:0%
+variation right so building estimators
+ 
+
+ align:start position:0%
+variation right so building estimators
+as I said typically consists in
+
+ align:start position:0%
+as I said typically consists in
+ 
+
+ align:start position:0%
+as I said typically consists in
+replacing expectations by averages but
+
+ align:start position:0%
+replacing expectations by averages but
+ 
+
+ align:start position:0%
+replacing expectations by averages but
+there's no simple way of expressing the
+
+ align:start position:0%
+there's no simple way of expressing the
+ 
+
+ align:start position:0%
+there's no simple way of expressing the
+total variation distance as the
+
+ align:start position:0%
+total variation distance as the
+ 
+
+ align:start position:0%
+total variation distance as the
+expectations with respect to theta star
+
+ align:start position:0%
+expectations with respect to theta star
+ 
+
+ align:start position:0%
+expectations with respect to theta star
+of anything so what we're gonna do is
+
+ align:start position:0%
+of anything so what we're gonna do is
+ 
+
+ align:start position:0%
+of anything so what we're gonna do is
+we're going to move from total variation
+
+ align:start position:0%
+we're going to move from total variation
+ 
+
+ align:start position:0%
+we're going to move from total variation
+distance to another notion of distance
+
+ align:start position:0%
+distance to another notion of distance
+ 
+
+ align:start position:0%
+distance to another notion of distance
+that sort of has the same properties and
+
+ align:start position:0%
+that sort of has the same properties and
+ 
+
+ align:start position:0%
+that sort of has the same properties and
+the same feeling and the same
+
+ align:start position:0%
+the same feeling and the same
+ 
+
+ align:start position:0%
+the same feeling and the same
+motivations as the total variation
+
+ align:start position:0%
+motivations as the total variation
+ 
+
+ align:start position:0%
+motivations as the total variation
+distance but for this guy we will be
+
+ align:start position:0%
+distance but for this guy we will be
+ 
+
+ align:start position:0%
+distance but for this guy we will be
+able to build an estimate for it because
+
+ align:start position:0%
+able to build an estimate for it because
+ 
+
+ align:start position:0%
+able to build an estimate for it because
+it's actually going to be of the form
+
+ align:start position:0%
+it's actually going to be of the form
+ 
+
+ align:start position:0%
+it's actually going to be of the form
+expectation of something and we're gonna
+
+ align:start position:0%
+expectation of something and we're gonna
+ 
+
+ align:start position:0%
+expectation of something and we're gonna
+be able to replace the expectation by
+
+ align:start position:0%
+be able to replace the expectation by
+ 
+
+ align:start position:0%
+be able to replace the expectation by
+average and then minimize this average
+
+ align:start position:0%
+average and then minimize this average
+ 
+
+ align:start position:0%
+average and then minimize this average
+all right so this surrogates for tall
+
+ align:start position:0%
+all right so this surrogates for tall
+ 
+
+ align:start position:0%
+all right so this surrogates for tall
+variation distance is actually called
+
+ align:start position:0%
+variation distance is actually called
+ 
+
+ align:start position:0%
+variation distance is actually called
+the kullbackleibler divergence and why
+
+ align:start position:0%
+the kullbackleibler divergence and why
+ 
+
+ align:start position:0%
+the kullbackleibler divergence and why
+we call it divergence is because it's
+
+ align:start position:0%
+we call it divergence is because it's
+ 
+
+ align:start position:0%
+we call it divergence is because it's
+actually not a distance it's not gonna
+
+ align:start position:0%
+actually not a distance it's not gonna
+ 
+
+ align:start position:0%
+actually not a distance it's not gonna
+be symmetric to start with okay so this
+
+ align:start position:0%
+be symmetric to start with okay so this
+ 
+
+ align:start position:0%
+be symmetric to start with okay so this
+kullback-leibler or even KL divergence I
+
+ align:start position:0%
+kullback-leibler or even KL divergence I
+ 
+
+ align:start position:0%
+kullback-leibler or even KL divergence I
+will just refer to it as KL is actually
+
+ align:start position:0%
+will just refer to it as KL is actually
+ 
+
+ align:start position:0%
+will just refer to it as KL is actually
+just more convenient but it has some
+
+ align:start position:0%
+just more convenient but it has some
+ 
+
+ align:start position:0%
+just more convenient but it has some
+roots coming from information theory
+
+ align:start position:0%
+roots coming from information theory
+ 
+
+ align:start position:0%
+roots coming from information theory
+which I will not delve into but if any
+
+ align:start position:0%
+which I will not delve into but if any
+ 
+
+ align:start position:0%
+which I will not delve into but if any
+of you is actually a course six students
+
+ align:start position:0%
+of you is actually a course six students
+ 
+
+ align:start position:0%
+of you is actually a course six students
+I'm sure you've seen that in some course
+
+ align:start position:0%
+I'm sure you've seen that in some course
+ 
+
+ align:start position:0%
+I'm sure you've seen that in some course
+on I know that has any content on
+
+ align:start position:0%
+on I know that has any content on
+ 
+
+ align:start position:0%
+on I know that has any content on
+information theory all right so the KL
+
+ align:start position:0%
+information theory all right so the KL
+ 
+
+ align:start position:0%
+information theory all right so the KL
+divergence between two probability
+
+ align:start position:0%
+divergence between two probability
+ 
+
+ align:start position:0%
+divergence between two probability
+measures P theta and P theta prime and
+
+ align:start position:0%
+measures P theta and P theta prime and
+ 
+
+ align:start position:0%
+measures P theta and P theta prime and
+here as I said it's not gonna be the
+
+ align:start position:0%
+here as I said it's not gonna be the
+ 
+
+ align:start position:0%
+here as I said it's not gonna be the
+symmetric so it's very important for you
+
+ align:start position:0%
+symmetric so it's very important for you
+ 
+
+ align:start position:0%
+symmetric so it's very important for you
+to specify which order you stays between
+
+ align:start position:0%
+to specify which order you stays between
+ 
+
+ align:start position:0%
+to specify which order you stays between
+P theta and P theta Prime and it's
+
+ align:start position:0%
+P theta and P theta Prime and it's
+ 
+
+ align:start position:0%
+P theta and P theta Prime and it's
+different from saying between P theta
+
+ align:start position:0%
+different from saying between P theta
+ 
+
+ align:start position:0%
+different from saying between P theta
+Prime and T and P theta and so we
+
+ align:start position:0%
+Prime and T and P theta and so we
+ 
+
+ align:start position:0%
+Prime and T and P theta and so we
+denoted by KL and it's so remember
+
+ align:start position:0%
+denoted by KL and it's so remember
+ 
+
+ align:start position:0%
+denoted by KL and it's so remember
+before we had either the summer or the
+
+ align:start position:0%
+before we had either the summer or the
+ 
+
+ align:start position:0%
+before we had either the summer or the
+integral of one-half of the distance
+
+ align:start position:0%
+integral of one-half of the distance
+ 
+
+ align:start position:0%
+integral of one-half of the distance
+absolute value of the distance between
+
+ align:start position:0%
+absolute value of the distance between
+ 
+
+ align:start position:0%
+absolute value of the distance between
+the PMF and one-half of the absolute
+
+ align:start position:0%
+the PMF and one-half of the absolute
+ 
+
+ align:start position:0%
+the PMF and one-half of the absolute
+values of the distances between the
+
+ align:start position:0%
+values of the distances between the
+ 
+
+ align:start position:0%
+values of the distances between the
+distributed the probability density
+
+ align:start position:0%
+distributed the probability density
+ 
+
+ align:start position:0%
+distributed the probability density
+functions and now we replace this
+
+ align:start position:0%
+functions and now we replace this
+ 
+
+ align:start position:0%
+functions and now we replace this
+absolute value of the distance divided
+
+ align:start position:0%
+absolute value of the distance divided
+ 
+
+ align:start position:0%
+absolute value of the distance divided
+by two by this weird function write this
+
+ align:start position:0%
+by two by this weird function write this
+ 
+
+ align:start position:0%
+by two by this weird function write this
+function is P theta log P theta divided
+
+ align:start position:0%
+function is P theta log P theta divided
+ 
+
+ align:start position:0%
+function is P theta log P theta divided
+by P theta prime that's the function
+
+ align:start position:0%
+by P theta prime that's the function
+ 
+
+ align:start position:0%
+by P theta prime that's the function
+alright
+
+ align:start position:0%
+alright
+ 
+
+ align:start position:0%
+alright
+that's a weird function okay so this was
+
+ align:start position:0%
+that's a weird function okay so this was
+ 
+
+ align:start position:0%
+that's a weird function okay so this was
+what we had so that's the TV and the key
+
+ align:start position:0%
+what we had so that's the TV and the key
+ 
+
+ align:start position:0%
+what we had so that's the TV and the key
+all if I use the same notation F and G
+
+ align:start position:0%
+all if I use the same notation F and G
+ 
+
+ align:start position:0%
+all if I use the same notation F and G
+is integral of f of X log of f of X over
+
+ align:start position:0%
+is integral of f of X log of f of X over
+ 
+
+ align:start position:0%
+is integral of f of X log of f of X over
+G of X DX okay it's a bit different
+
+ align:start position:0%
+G of X DX okay it's a bit different
+ 
+
+ align:start position:0%
+G of X DX okay it's a bit different
+and if I go I go from discreet to
+
+ align:start position:0%
+and if I go I go from discreet to
+ 
+
+ align:start position:0%
+and if I go I go from discreet to
+continuous using an interval everybody
+
+ align:start position:0%
+continuous using an interval everybody
+ 
+
+ align:start position:0%
+continuous using an interval everybody
+can read this everybody's fine with this
+
+ align:start position:0%
+can read this everybody's fine with this
+ 
+
+ align:start position:0%
+can read this everybody's fine with this
+is there any you know uncertainty about
+
+ align:start position:0%
+is there any you know uncertainty about
+ 
+
+ align:start position:0%
+is there any you know uncertainty about
+the actual definition here so here I go
+
+ align:start position:0%
+the actual definition here so here I go
+ 
+
+ align:start position:0%
+the actual definition here so here I go
+straight to the definition which is just
+
+ align:start position:0%
+straight to the definition which is just
+ 
+
+ align:start position:0%
+straight to the definition which is just
+plug in the functions into some integral
+
+ align:start position:0%
+plug in the functions into some integral
+ 
+
+ align:start position:0%
+plug in the functions into some integral
+and compute okay so I don't bother with
+
+ align:start position:0%
+and compute okay so I don't bother with
+ 
+
+ align:start position:0%
+and compute okay so I don't bother with
+Maxima or anything there I mean there is
+
+ align:start position:0%
+Maxima or anything there I mean there is
+ 
+
+ align:start position:0%
+Maxima or anything there I mean there is
+something like that but it's certainly
+
+ align:start position:0%
+something like that but it's certainly
+ 
+
+ align:start position:0%
+something like that but it's certainly
+not as natural as a tool variation yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes just because you it's hard to build
+
+ align:start position:0%
+yes just because you it's hard to build
+ 
+
+ align:start position:0%
+yes just because you it's hard to build
+anything from tool variation because I
+
+ align:start position:0%
+anything from tool variation because I
+ 
+
+ align:start position:0%
+anything from tool variation because I
+don't know it right so it's very
+
+ align:start position:0%
+don't know it right so it's very
+ 
+
+ align:start position:0%
+don't know it right so it's very
+difficult but if you can actually and
+
+ align:start position:0%
+difficult but if you can actually and
+ 
+
+ align:start position:0%
+difficult but if you can actually and
+even computing it between two gaussians
+
+ align:start position:0%
+even computing it between two gaussians
+ 
+
+ align:start position:0%
+even computing it between two gaussians
+just try it for yourself and you know
+
+ align:start position:0%
+just try it for yourself and you know
+ 
+
+ align:start position:0%
+just try it for yourself and you know
+please stop doing it after at most six
+
+ align:start position:0%
+please stop doing it after at most six
+ 
+
+ align:start position:0%
+please stop doing it after at most six
+minutes because you won't be able to do
+
+ align:start position:0%
+minutes because you won't be able to do
+ 
+
+ align:start position:0%
+minutes because you won't be able to do
+it and so it's just very hard to
+
+ align:start position:0%
+it and so it's just very hard to
+ 
+
+ align:start position:0%
+it and so it's just very hard to
+manipulate like this integral of
+
+ align:start position:0%
+manipulate like this integral of
+ 
+
+ align:start position:0%
+manipulate like this integral of
+absolute values of differences between
+
+ align:start position:0%
+absolute values of differences between
+ 
+
+ align:start position:0%
+absolute values of differences between
+probability density function at least
+
+ align:start position:0%
+probability density function at least
+ 
+
+ align:start position:0%
+probability density function at least
+for the probability and C functions
+
+ align:start position:0%
+for the probability and C functions
+ 
+
+ align:start position:0%
+for the probability and C functions
+we're used to manipulate is actually
+
+ align:start position:0%
+we're used to manipulate is actually
+ 
+
+ align:start position:0%
+we're used to manipulate is actually
+your nightmare and so people prefer KL
+
+ align:start position:0%
+your nightmare and so people prefer KL
+ 
+
+ align:start position:0%
+your nightmare and so people prefer KL
+because for the Gaussian this is going
+
+ align:start position:0%
+because for the Gaussian this is going
+ 
+
+ align:start position:0%
+because for the Gaussian this is going
+to be theta minus theta prime squared
+
+ align:start position:0%
+to be theta minus theta prime squared
+ 
+
+ align:start position:0%
+to be theta minus theta prime squared
+and then we're gonna be happy okay and
+
+ align:start position:0%
+and then we're gonna be happy okay and
+ 
+
+ align:start position:0%
+and then we're gonna be happy okay and
+so those things are much easier to
+
+ align:start position:0%
+so those things are much easier to
+ 
+
+ align:start position:0%
+so those things are much easier to
+manipulate but it's really the total
+
+ align:start position:0%
+manipulate but it's really the total
+ 
+
+ align:start position:0%
+manipulate but it's really the total
+variation is telling you how far in the
+
+ align:start position:0%
+variation is telling you how far in the
+ 
+
+ align:start position:0%
+variation is telling you how far in the
+worst case the two probabilities can be
+
+ align:start position:0%
+worst case the two probabilities can be
+ 
+
+ align:start position:0%
+worst case the two probabilities can be
+this is really the intrinsic notion of
+
+ align:start position:0%
+this is really the intrinsic notion of
+ 
+
+ align:start position:0%
+this is really the intrinsic notion of
+closeness between probabilities so
+
+ align:start position:0%
+closeness between probabilities so
+ 
+
+ align:start position:0%
+closeness between probabilities so
+that's really the one if we could that's
+
+ align:start position:0%
+that's really the one if we could that's
+ 
+
+ align:start position:0%
+that's really the one if we could that's
+the one we would go after sometimes
+
+ align:start position:0%
+the one we would go after sometimes
+ 
+
+ align:start position:0%
+the one we would go after sometimes
+people will compute them numerically so
+
+ align:start position:0%
+people will compute them numerically so
+ 
+
+ align:start position:0%
+people will compute them numerically so
+that they can say oh here is the tool
+
+ align:start position:0%
+that they can say oh here is the tool
+ 
+
+ align:start position:0%
+that they can say oh here is the tool
+variation distance I have between those
+
+ align:start position:0%
+variation distance I have between those
+ 
+
+ align:start position:0%
+variation distance I have between those
+two things and then and then you
+
+ align:start position:0%
+two things and then and then you
+ 
+
+ align:start position:0%
+two things and then and then you
+actually know that that means they're
+
+ align:start position:0%
+actually know that that means they're
+ 
+
+ align:start position:0%
+actually know that that means they're
+close because the absolute value if I
+
+ align:start position:0%
+close because the absolute value if I
+ 
+
+ align:start position:0%
+close because the absolute value if I
+tell you to variation is 0.01 like we
+
+ align:start position:0%
+tell you to variation is 0.01 like we
+ 
+
+ align:start position:0%
+tell you to variation is 0.01 like we
+did here it has a very specific meaning
+
+ align:start position:0%
+did here it has a very specific meaning
+ 
+
+ align:start position:0%
+did here it has a very specific meaning
+if I tell you the KL divergence is 0.01
+
+ align:start position:0%
+if I tell you the KL divergence is 0.01
+ 
+
+ align:start position:0%
+if I tell you the KL divergence is 0.01
+it's not clear what it means all right
+
+ align:start position:0%
+it's not clear what it means all right
+ 
+
+ align:start position:0%
+it's not clear what it means all right
+okay so what are the properties the KL
+
+ align:start position:0%
+okay so what are the properties the KL
+ 
+
+ align:start position:0%
+okay so what are the properties the KL
+divergence between P theta and P theta
+
+ align:start position:0%
+divergence between P theta and P theta
+ 
+
+ align:start position:0%
+divergence between P theta and P theta
+prime is different from the KL
+
+ align:start position:0%
+prime is different from the KL
+ 
+
+ align:start position:0%
+prime is different from the KL
+divergence between P theta Prime and P
+
+ align:start position:0%
+divergence between P theta Prime and P
+ 
+
+ align:start position:0%
+divergence between P theta Prime and P
+theta in general of course in general
+
+ align:start position:0%
+theta in general of course in general
+ 
+
+ align:start position:0%
+theta in general of course in general
+because the theta is equal to theta
+
+ align:start position:0%
+because the theta is equal to theta
+ 
+
+ align:start position:0%
+because the theta is equal to theta
+prime then this certainly is true okay
+
+ align:start position:0%
+prime then this certainly is true okay
+ 
+
+ align:start position:0%
+prime then this certainly is true okay
+so there's cases when it's not true okay
+
+ align:start position:0%
+so there's cases when it's not true okay
+ 
+
+ align:start position:0%
+so there's cases when it's not true okay
+the KL divergence is non-negative
+
+ align:start position:0%
+the KL divergence is non-negative
+ 
+
+ align:start position:0%
+the KL divergence is non-negative
+who knows the Jensen's inequality here
+
+ align:start position:0%
+who knows the Jensen's inequality here
+ 
+
+ align:start position:0%
+who knows the Jensen's inequality here
+that should be a subset of the people
+
+ align:start position:0%
+that should be a subset of the people
+ 
+
+ align:start position:0%
+that should be a subset of the people
+who risk their hand when they asked when
+
+ align:start position:0%
+who risk their hand when they asked when
+ 
+
+ align:start position:0%
+who risk their hand when they asked when
+I asked what a convex function is all
+
+ align:start position:0%
+I asked what a convex function is all
+ 
+
+ align:start position:0%
+I asked what a convex function is all
+right so you know what Jensen's
+
+ align:start position:0%
+right so you know what Jensen's
+ 
+
+ align:start position:0%
+right so you know what Jensen's
+inequality is this is Jensen's the proof
+
+ align:start position:0%
+inequality is this is Jensen's the proof
+ 
+
+ align:start position:0%
+inequality is this is Jensen's the proof
+is just one step Jensen's inequality
+
+ align:start position:0%
+is just one step Jensen's inequality
+ 
+
+ align:start position:0%
+is just one step Jensen's inequality
+which will not go into details but
+
+ align:start position:0%
+which will not go into details but
+ 
+
+ align:start position:0%
+which will not go into details but
+that's basically an inequality involving
+
+ align:start position:0%
+that's basically an inequality involving
+ 
+
+ align:start position:0%
+that's basically an inequality involving
+expectation of a convex function of a
+
+ align:start position:0%
+expectation of a convex function of a
+ 
+
+ align:start position:0%
+expectation of a convex function of a
+random variable compares to the convex
+
+ align:start position:0%
+random variable compares to the convex
+ 
+
+ align:start position:0%
+random variable compares to the convex
+function of the expectation of a random
+
+ align:start position:0%
+function of the expectation of a random
+ 
+
+ align:start position:0%
+function of the expectation of a random
+variable all right you can if you know
+
+ align:start position:0%
+variable all right you can if you know
+ 
+
+ align:start position:0%
+variable all right you can if you know
+Jensen have fun and prove it what's
+
+ align:start position:0%
+Jensen have fun and prove it what's
+ 
+
+ align:start position:0%
+Jensen have fun and prove it what's
+really nice is that if the KL is equal
+
+ align:start position:0%
+really nice is that if the KL is equal
+ 
+
+ align:start position:0%
+really nice is that if the KL is equal
+to zero then the two distributions are
+
+ align:start position:0%
+to zero then the two distributions are
+ 
+
+ align:start position:0%
+to zero then the two distributions are
+the same and that's something we're
+
+ align:start position:0%
+the same and that's something we're
+ 
+
+ align:start position:0%
+the same and that's something we're
+looking for everything else we're happy
+
+ align:start position:0%
+looking for everything else we're happy
+ 
+
+ align:start position:0%
+looking for everything else we're happy
+to throw out and actually if you pay
+
+ align:start position:0%
+to throw out and actually if you pay
+ 
+
+ align:start position:0%
+to throw out and actually if you pay
+attention we're actually really throwing
+
+ align:start position:0%
+attention we're actually really throwing
+ 
+
+ align:start position:0%
+attention we're actually really throwing
+up everything else so they're not
+
+ align:start position:0%
+up everything else so they're not
+ 
+
+ align:start position:0%
+up everything else so they're not
+symmetric it does not try and satisfy
+
+ align:start position:0%
+symmetric it does not try and satisfy
+ 
+
+ align:start position:0%
+symmetric it does not try and satisfy
+the triangle inequality in general but
+
+ align:start position:0%
+the triangle inequality in general but
+ 
+
+ align:start position:0%
+the triangle inequality in general but
+it's non-negative and it's 0 if and only
+
+ align:start position:0%
+it's non-negative and it's 0 if and only
+ 
+
+ align:start position:0%
+it's non-negative and it's 0 if and only
+if the two distributions are the same
+
+ align:start position:0%
+if the two distributions are the same
+ 
+
+ align:start position:0%
+if the two distributions are the same
+and that's all we care about and that's
+
+ align:start position:0%
+and that's all we care about and that's
+ 
+
+ align:start position:0%
+and that's all we care about and that's
+what we call the divergence rather than
+
+ align:start position:0%
+what we call the divergence rather than
+ 
+
+ align:start position:0%
+what we call the divergence rather than
+a distance because and divergences will
+
+ align:start position:0%
+a distance because and divergences will
+ 
+
+ align:start position:0%
+a distance because and divergences will
+be enough for our purposes ok actually
+
+ align:start position:0%
+be enough for our purposes ok actually
+ 
+
+ align:start position:0%
+be enough for our purposes ok actually
+this asymmetry the fact that it's not
+
+ align:start position:0%
+this asymmetry the fact that it's not
+ 
+
+ align:start position:0%
+this asymmetry the fact that it's not
+flipping right the first time I saw it I
+
+ align:start position:0%
+flipping right the first time I saw it I
+ 
+
+ align:start position:0%
+flipping right the first time I saw it I
+was just too annoyed I was like can we
+
+ align:start position:0%
+was just too annoyed I was like can we
+ 
+
+ align:start position:0%
+was just too annoyed I was like can we
+just like I don't take the average of
+
+ align:start position:0%
+just like I don't take the average of
+ 
+
+ align:start position:0%
+just like I don't take the average of
+the KL between P theta and piece theta
+
+ align:start position:0%
+the KL between P theta and piece theta
+ 
+
+ align:start position:0%
+the KL between P theta and piece theta
+prime and PCI prime and P theta right
+
+ align:start position:0%
+prime and PCI prime and P theta right
+ 
+
+ align:start position:0%
+prime and PCI prime and P theta right
+you would think maybe you could do this
+
+ align:start position:0%
+you would think maybe you could do this
+ 
+
+ align:start position:0%
+you would think maybe you could do this
+right you just symmetrize it by just
+
+ align:start position:0%
+right you just symmetrize it by just
+ 
+
+ align:start position:0%
+right you just symmetrize it by just
+taking the average of the 2 possible
+
+ align:start position:0%
+taking the average of the 2 possible
+ 
+
+ align:start position:0%
+taking the average of the 2 possible
+values that can take the problem is that
+
+ align:start position:0%
+values that can take the problem is that
+ 
+
+ align:start position:0%
+values that can take the problem is that
+this will still not satisfy the triangle
+
+ align:start position:0%
+this will still not satisfy the triangle
+ 
+
+ align:start position:0%
+this will still not satisfy the triangle
+inequality and there's no way basically
+
+ align:start position:0%
+inequality and there's no way basically
+ 
+
+ align:start position:0%
+inequality and there's no way basically
+to turn it into something that is a
+
+ align:start position:0%
+to turn it into something that is a
+ 
+
+ align:start position:0%
+to turn it into something that is a
+distance but the divergence is doing a
+
+ align:start position:0%
+distance but the divergence is doing a
+ 
+
+ align:start position:0%
+distance but the divergence is doing a
+pretty good thing for us and this is
+
+ align:start position:0%
+pretty good thing for us and this is
+ 
+
+ align:start position:0%
+pretty good thing for us and this is
+well what will allow us to estimate it
+
+ align:start position:0%
+well what will allow us to estimate it
+ 
+
+ align:start position:0%
+well what will allow us to estimate it
+and basically overcome what we could not
+
+ align:start position:0%
+and basically overcome what we could not
+ 
+
+ align:start position:0%
+and basically overcome what we could not
+do with the with the total variation all
+
+ align:start position:0%
+do with the with the total variation all
+ 
+
+ align:start position:0%
+do with the with the total variation all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+so the first thing that you want to
+
+ align:start position:0%
+so the first thing that you want to
+ 
+
+ align:start position:0%
+so the first thing that you want to
+notice is that two variation distance
+
+ align:start position:0%
+notice is that two variation distance
+ 
+
+ align:start position:0%
+notice is that two variation distance
+the KL divergence re is actually an
+
+ align:start position:0%
+the KL divergence re is actually an
+ 
+
+ align:start position:0%
+the KL divergence re is actually an
+expectation of something right look at
+
+ align:start position:0%
+expectation of something right look at
+ 
+
+ align:start position:0%
+expectation of something right look at
+what it is here it's the integral of
+
+ align:start position:0%
+what it is here it's the integral of
+ 
+
+ align:start position:0%
+what it is here it's the integral of
+some function against a density that's
+
+ align:start position:0%
+some function against a density that's
+ 
+
+ align:start position:0%
+some function against a density that's
+exactly the definition of an int of an
+
+ align:start position:0%
+exactly the definition of an int of an
+ 
+
+ align:start position:0%
+exactly the definition of an int of an
+expectation right so this is the
+
+ align:start position:0%
+expectation right so this is the
+ 
+
+ align:start position:0%
+expectation right so this is the
+expectation of this particular function
+
+ align:start position:0%
+expectation of this particular function
+ 
+
+ align:start position:0%
+expectation of this particular function
+with respect to this
+
+ align:start position:0%
+with respect to this
+ 
+
+ align:start position:0%
+with respect to this
+density F so in particular if I call
+
+ align:start position:0%
+density F so in particular if I call
+ 
+
+ align:start position:0%
+density F so in particular if I call
+this density F if I say I want the true
+
+ align:start position:0%
+this density F if I say I want the true
+ 
+
+ align:start position:0%
+this density F if I say I want the true
+distribution to be the first argument
+
+ align:start position:0%
+distribution to be the first argument
+ 
+
+ align:start position:0%
+distribution to be the first argument
+this is an expectation with respect to
+
+ align:start position:0%
+this is an expectation with respect to
+ 
+
+ align:start position:0%
+this is an expectation with respect to
+the true distribution from which my data
+
+ align:start position:0%
+the true distribution from which my data
+ 
+
+ align:start position:0%
+the true distribution from which my data
+is actually drawn of the log of this
+
+ align:start position:0%
+is actually drawn of the log of this
+ 
+
+ align:start position:0%
+is actually drawn of the log of this
+ratio so haha I'm a statistician now I
+
+ align:start position:0%
+ratio so haha I'm a statistician now I
+ 
+
+ align:start position:0%
+ratio so haha I'm a statistician now I
+have an expectation I can replace it by
+
+ align:start position:0%
+have an expectation I can replace it by
+ 
+
+ align:start position:0%
+have an expectation I can replace it by
+an average because I have data from this
+
+ align:start position:0%
+an average because I have data from this
+ 
+
+ align:start position:0%
+an average because I have data from this
+distribution and I could actually
+
+ align:start position:0%
+distribution and I could actually
+ 
+
+ align:start position:0%
+distribution and I could actually
+replace the expectation by an average
+
+ align:start position:0%
+replace the expectation by an average
+ 
+
+ align:start position:0%
+replace the expectation by an average
+and try to minimize here the problem is
+
+ align:start position:0%
+and try to minimize here the problem is
+ 
+
+ align:start position:0%
+and try to minimize here the problem is
+that actually the star here should be in
+
+ align:start position:0%
+that actually the star here should be in
+ 
+
+ align:start position:0%
+that actually the star here should be in
+front of the theta n of the p right
+
+ align:start position:0%
+front of the theta n of the p right
+ 
+
+ align:start position:0%
+front of the theta n of the p right
+that's piece theta star not P star theta
+
+ align:start position:0%
+that's piece theta star not P star theta
+ 
+
+ align:start position:0%
+that's piece theta star not P star theta
+but here I still cannot compute it
+
+ align:start position:0%
+but here I still cannot compute it
+ 
+
+ align:start position:0%
+but here I still cannot compute it
+because I have this piece this piece did
+
+ align:start position:0%
+because I have this piece this piece did
+ 
+
+ align:start position:0%
+because I have this piece this piece did
+I started I chose up I don't know what
+
+ align:start position:0%
+I started I chose up I don't know what
+ 
+
+ align:start position:0%
+I started I chose up I don't know what
+it is and that's now where the log plays
+
+ align:start position:0%
+it is and that's now where the log plays
+ 
+
+ align:start position:0%
+it is and that's now where the log plays
+a role if you actually pay attention I
+
+ align:start position:0%
+a role if you actually pay attention I
+ 
+
+ align:start position:0%
+a role if you actually pay attention I
+said you can use Jensen to prove all
+
+ align:start position:0%
+said you can use Jensen to prove all
+ 
+
+ align:start position:0%
+said you can use Jensen to prove all
+this stuff you could actually replace
+
+ align:start position:0%
+this stuff you could actually replace
+ 
+
+ align:start position:0%
+this stuff you could actually replace
+the log by any concave function and that
+
+ align:start position:0%
+the log by any concave function and that
+ 
+
+ align:start position:0%
+the log by any concave function and that
+would be a F divergence that's called an
+
+ align:start position:0%
+would be a F divergence that's called an
+ 
+
+ align:start position:0%
+would be a F divergence that's called an
+F divergence but the log itself is a
+
+ align:start position:0%
+F divergence but the log itself is a
+ 
+
+ align:start position:0%
+F divergence but the log itself is a
+various very specific property which
+
+ align:start position:0%
+various very specific property which
+ 
+
+ align:start position:0%
+various very specific property which
+allows us to say that the log of the
+
+ align:start position:0%
+allows us to say that the log of the
+ 
+
+ align:start position:0%
+allows us to say that the log of the
+ratio is the ratio of the logs now this
+
+ align:start position:0%
+ratio is the ratio of the logs now this
+ 
+
+ align:start position:0%
+ratio is the ratio of the logs now this
+thing here does not depend on theta if I
+
+ align:start position:0%
+thing here does not depend on theta if I
+ 
+
+ align:start position:0%
+thing here does not depend on theta if I
+think of this KL divergence as a
+
+ align:start position:0%
+think of this KL divergence as a
+ 
+
+ align:start position:0%
+think of this KL divergence as a
+function of theta then the first part is
+
+ align:start position:0%
+function of theta then the first part is
+ 
+
+ align:start position:0%
+function of theta then the first part is
+actually a constant if I change theta
+
+ align:start position:0%
+actually a constant if I change theta
+ 
+
+ align:start position:0%
+actually a constant if I change theta
+this thing is never going to change
+
+ align:start position:0%
+this thing is never going to change
+ 
+
+ align:start position:0%
+this thing is never going to change
+it depends only on theta star so if I
+
+ align:start position:0%
+it depends only on theta star so if I
+ 
+
+ align:start position:0%
+it depends only on theta star so if I
+look at this function KL
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I look at the function data maps
+
+ align:start position:0%
+so if I look at the function data maps
+ 
+
+ align:start position:0%
+so if I look at the function data maps
+to KL P theta star P theta it's of the
+
+ align:start position:0%
+to KL P theta star P theta it's of the
+ 
+
+ align:start position:0%
+to KL P theta star P theta it's of the
+form expectation with respect to theta
+
+ align:start position:0%
+form expectation with respect to theta
+ 
+
+ align:start position:0%
+form expectation with respect to theta
+star log of P theta star of X and then I
+
+ align:start position:0%
+star log of P theta star of X and then I
+ 
+
+ align:start position:0%
+star log of P theta star of X and then I
+have minus expectation with respect
+
+ align:start position:0%
+have minus expectation with respect
+ 
+
+ align:start position:0%
+have minus expectation with respect
+Taylor star of log of P theta of X now
+
+ align:start position:0%
+Taylor star of log of P theta of X now
+ 
+
+ align:start position:0%
+Taylor star of log of P theta of X now
+as I said this thing here this second
+
+ align:start position:0%
+as I said this thing here this second
+ 
+
+ align:start position:0%
+as I said this thing here this second
+expectation is a function of theta when
+
+ align:start position:0%
+expectation is a function of theta when
+ 
+
+ align:start position:0%
+expectation is a function of theta when
+theta changes this thing is gonna change
+
+ align:start position:0%
+theta changes this thing is gonna change
+ 
+
+ align:start position:0%
+theta changes this thing is gonna change
+and that's a good thing we want
+
+ align:start position:0%
+and that's a good thing we want
+ 
+
+ align:start position:0%
+and that's a good thing we want
+something that reflects our clothes
+
+ align:start position:0%
+something that reflects our clothes
+ 
+
+ align:start position:0%
+something that reflects our clothes
+theta and theta star R but this thing is
+
+ align:start position:0%
+theta and theta star R but this thing is
+ 
+
+ align:start position:0%
+theta and theta star R but this thing is
+not going to change this is a fixed
+
+ align:start position:0%
+not going to change this is a fixed
+ 
+
+ align:start position:0%
+not going to change this is a fixed
+value it's go actually it's the negative
+
+ align:start position:0%
+value it's go actually it's the negative
+ 
+
+ align:start position:0%
+value it's go actually it's the negative
+entropy of P theta star and if you've
+
+ align:start position:0%
+entropy of P theta star and if you've
+ 
+
+ align:start position:0%
+entropy of P theta star and if you've
+heard of KL you've probably heard of
+
+ align:start position:0%
+heard of KL you've probably heard of
+ 
+
+ align:start position:0%
+heard of KL you've probably heard of
+entropy and that's what the it's
+
+ align:start position:0%
+entropy and that's what the it's
+ 
+
+ align:start position:0%
+entropy and that's what the it's
+basically minus the entropy and that's
+
+ align:start position:0%
+basically minus the entropy and that's
+ 
+
+ align:start position:0%
+basically minus the entropy and that's
+the quantity that just depends on theta
+
+ align:start position:0%
+the quantity that just depends on theta
+ 
+
+ align:start position:0%
+the quantity that just depends on theta
+star but it's just a number right that
+
+ align:start position:0%
+star but it's just a number right that
+ 
+
+ align:start position:0%
+star but it's just a number right that
+could compute this number if I told you
+
+ align:start position:0%
+could compute this number if I told you
+ 
+
+ align:start position:0%
+could compute this number if I told you
+this is a n theta star one so now I'm
+
+ align:start position:0%
+this is a n theta star one so now I'm
+ 
+
+ align:start position:0%
+this is a n theta star one so now I'm
+gonna try to minimize the estimate of
+
+ align:start position:0%
+gonna try to minimize the estimate of
+ 
+
+ align:start position:0%
+gonna try to minimize the estimate of
+this function and minimizing a function
+
+ align:start position:0%
+this function and minimizing a function
+ 
+
+ align:start position:0%
+this function and minimizing a function
+or a function plus a constant is the
+
+ align:start position:0%
+or a function plus a constant is the
+ 
+
+ align:start position:0%
+or a function plus a constant is the
+same thing right I'm just shifting the
+
+ align:start position:0%
+same thing right I'm just shifting the
+ 
+
+ align:start position:0%
+same thing right I'm just shifting the
+function here here but it's the same
+
+ align:start position:0%
+function here here but it's the same
+ 
+
+ align:start position:0%
+function here here but it's the same
+minimizer okay so the function that
+
+ align:start position:0%
+minimizer okay so the function that
+ 
+
+ align:start position:0%
+minimizer okay so the function that
+map's kiyul to theta 2 T L of P theta
+
+ align:start position:0%
+map's kiyul to theta 2 T L of P theta
+ 
+
+ align:start position:0%
+map's kiyul to theta 2 T L of P theta
+star to P theta is of the form constant
+
+ align:start position:0%
+star to P theta is of the form constant
+ 
+
+ align:start position:0%
+star to P theta is of the form constant
+minus this expectation of a log of P
+
+ align:start position:0%
+minus this expectation of a log of P
+ 
+
+ align:start position:0%
+minus this expectation of a log of P
+theta everybody agrees are there any
+
+ align:start position:0%
+theta everybody agrees are there any
+ 
+
+ align:start position:0%
+theta everybody agrees are there any
+questions about this
+
+ align:start position:0%
+questions about this
+ 
+
+ align:start position:0%
+questions about this
+are there any remarks including I have
+
+ align:start position:0%
+are there any remarks including I have
+ 
+
+ align:start position:0%
+are there any remarks including I have
+no idea what's happening right now here
+
+ align:start position:0%
+no idea what's happening right now here
+ 
+
+ align:start position:0%
+no idea what's happening right now here
+you go yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're not a this is not a method just
+
+ align:start position:0%
+so we're not a this is not a method just
+ 
+
+ align:start position:0%
+so we're not a this is not a method just
+yet right I'm just describing to you
+
+ align:start position:0%
+yet right I'm just describing to you
+ 
+
+ align:start position:0%
+yet right I'm just describing to you
+what the KL divergence between to
+
+ align:start position:0%
+what the KL divergence between to
+ 
+
+ align:start position:0%
+what the KL divergence between to
+distribution and if you really wanted to
+
+ align:start position:0%
+distribution and if you really wanted to
+ 
+
+ align:start position:0%
+distribution and if you really wanted to
+compute it you would need to know what
+
+ align:start position:0%
+compute it you would need to know what
+ 
+
+ align:start position:0%
+compute it you would need to know what
+piece theta stories and what P theta is
+
+ align:start position:0%
+piece theta stories and what P theta is
+ 
+
+ align:start position:0%
+piece theta stories and what P theta is
+and so here I'm just saying at some
+
+ align:start position:0%
+and so here I'm just saying at some
+ 
+
+ align:start position:0%
+and so here I'm just saying at some
+point we still so here you see it so now
+
+ align:start position:0%
+point we still so here you see it so now
+ 
+
+ align:start position:0%
+point we still so here you see it so now
+let's move on to one step
+
+ align:start position:0%
+let's move on to one step
+ 
+
+ align:start position:0%
+let's move on to one step
+I don't know expectation of theta star
+
+ align:start position:0%
+I don't know expectation of theta star
+ 
+
+ align:start position:0%
+I don't know expectation of theta star
+but I have data that comes from
+
+ align:start position:0%
+but I have data that comes from
+ 
+
+ align:start position:0%
+but I have data that comes from
+distribution P theta star so the
+
+ align:start position:0%
+distribution P theta star so the
+ 
+
+ align:start position:0%
+distribution P theta star so the
+expectation by the law of large numbers
+
+ align:start position:0%
+expectation by the law of large numbers
+ 
+
+ align:start position:0%
+expectation by the law of large numbers
+should be close to the average and so
+
+ align:start position:0%
+should be close to the average and so
+ 
+
+ align:start position:0%
+should be close to the average and so
+what I'm doing is I'm replacing any
+
+ align:start position:0%
+what I'm doing is I'm replacing any
+ 
+
+ align:start position:0%
+what I'm doing is I'm replacing any
+expand access as a very standard
+
+ align:start position:0%
+expand access as a very standard
+ 
+
+ align:start position:0%
+expand access as a very standard
+estimation method you write something as
+
+ align:start position:0%
+estimation method you write something as
+ 
+
+ align:start position:0%
+estimation method you write something as
+an expectation with respect to the data
+
+ align:start position:0%
+an expectation with respect to the data
+ 
+
+ align:start position:0%
+an expectation with respect to the data
+generating process of some function and
+
+ align:start position:0%
+generating process of some function and
+ 
+
+ align:start position:0%
+generating process of some function and
+then you replace this by the average of
+
+ align:start position:0%
+then you replace this by the average of
+ 
+
+ align:start position:0%
+then you replace this by the average of
+this function and the lower part number
+
+ align:start position:0%
+this function and the lower part number
+ 
+
+ align:start position:0%
+this function and the lower part number
+tells me that those two quantities
+
+ align:start position:0%
+tells me that those two quantities
+ 
+
+ align:start position:0%
+tells me that those two quantities
+should actually be close now it doesn't
+
+ align:start position:0%
+should actually be close now it doesn't
+ 
+
+ align:start position:0%
+should actually be close now it doesn't
+mean that's gonna be the end of the day
+
+ align:start position:0%
+mean that's gonna be the end of the day
+ 
+
+ align:start position:0%
+mean that's gonna be the end of the day
+right when we did the xn bar that was
+
+ align:start position:0%
+right when we did the xn bar that was
+ 
+
+ align:start position:0%
+right when we did the xn bar that was
+the end of the day we had an expectation
+
+ align:start position:0%
+the end of the day we had an expectation
+ 
+
+ align:start position:0%
+the end of the day we had an expectation
+we replaced it by an average and then we
+
+ align:start position:0%
+we replaced it by an average and then we
+ 
+
+ align:start position:0%
+we replaced it by an average and then we
+were gone but here we still have to do
+
+ align:start position:0%
+were gone but here we still have to do
+ 
+
+ align:start position:0%
+were gone but here we still have to do
+something because this is not telling me
+
+ align:start position:0%
+something because this is not telling me
+ 
+
+ align:start position:0%
+something because this is not telling me
+what theta is now I still have to
+
+ align:start position:0%
+what theta is now I still have to
+ 
+
+ align:start position:0%
+what theta is now I still have to
+minimize this average okay so this is
+
+ align:start position:0%
+minimize this average okay so this is
+ 
+
+ align:start position:0%
+minimize this average okay so this is
+now my candidate estimator for TL TL hat
+
+ align:start position:0%
+now my candidate estimator for TL TL hat
+ 
+
+ align:start position:0%
+now my candidate estimator for TL TL hat
+and that's the one where I said well
+
+ align:start position:0%
+and that's the one where I said well
+ 
+
+ align:start position:0%
+and that's the one where I said well
+it's gonna be of the form a constant and
+
+ align:start position:0%
+it's gonna be of the form a constant and
+ 
+
+ align:start position:0%
+it's gonna be of the form a constant and
+this constant I don't know you're right
+
+ align:start position:0%
+this constant I don't know you're right
+ 
+
+ align:start position:0%
+this constant I don't know you're right
+I have no idea what this constant is it
+
+ align:start position:0%
+I have no idea what this constant is it
+ 
+
+ align:start position:0%
+I have no idea what this constant is it
+depends on piece data star but then I
+
+ align:start position:0%
+depends on piece data star but then I
+ 
+
+ align:start position:0%
+depends on piece data star but then I
+have minus something that I can
+
+ align:start position:0%
+have minus something that I can
+ 
+
+ align:start position:0%
+have minus something that I can
+completely compute if you give me data
+
+ align:start position:0%
+completely compute if you give me data
+ 
+
+ align:start position:0%
+completely compute if you give me data
+and theta I can compute this entire
+
+ align:start position:0%
+and theta I can compute this entire
+ 
+
+ align:start position:0%
+and theta I can compute this entire
+thing and now what I claim is that the
+
+ align:start position:0%
+thing and now what I claim is that the
+ 
+
+ align:start position:0%
+thing and now what I claim is that the
+minimizer of F or F was for f of X or f
+
+ align:start position:0%
+minimizer of F or F was for f of X or f
+ 
+
+ align:start position:0%
+minimizer of F or F was for f of X or f
+of X plus 4 are the same thing right or
+
+ align:start position:0%
+of X plus 4 are the same thing right or
+ 
+
+ align:start position:0%
+of X plus 4 are the same thing right or
+say 4 plus f of X I'm just shifting the
+
+ align:start position:0%
+say 4 plus f of X I'm just shifting the
+ 
+
+ align:start position:0%
+say 4 plus f of X I'm just shifting the
+the plot of my function up and down but
+
+ align:start position:0%
+the plot of my function up and down but
+ 
+
+ align:start position:0%
+the plot of my function up and down but
+the minimizer stays exactly where it is
+
+ align:start position:0%
+the minimizer stays exactly where it is
+ 
+
+ align:start position:0%
+the minimizer stays exactly where it is
+right if I think I have a function so
+
+ align:start position:0%
+right if I think I have a function so
+ 
+
+ align:start position:0%
+right if I think I have a function so
+now I have a function of theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is kale hat of P theta star T theta
+
+ align:start position:0%
+this is kale hat of P theta star T theta
+ 
+
+ align:start position:0%
+this is kale hat of P theta star T theta
+and it's of the form it's a function
+
+ align:start position:0%
+and it's of the form it's a function
+ 
+
+ align:start position:0%
+and it's of the form it's a function
+like this I don't know where this
+
+ align:start position:0%
+like this I don't know where this
+ 
+
+ align:start position:0%
+like this I don't know where this
+function is it might very well be this
+
+ align:start position:0%
+function is it might very well be this
+ 
+
+ align:start position:0%
+function is it might very well be this
+function or this function every time
+
+ align:start position:0%
+function or this function every time
+ 
+
+ align:start position:0%
+function or this function every time
+it's a translation on the y-axis of all
+
+ align:start position:0%
+it's a translation on the y-axis of all
+ 
+
+ align:start position:0%
+it's a translation on the y-axis of all
+these guys and the value that I
+
+ align:start position:0%
+these guys and the value that I
+ 
+
+ align:start position:0%
+these guys and the value that I
+translated by depends on theta star I
+
+ align:start position:0%
+translated by depends on theta star I
+ 
+
+ align:start position:0%
+translated by depends on theta star I
+don't know what it is but what I claim
+
+ align:start position:0%
+don't know what it is but what I claim
+ 
+
+ align:start position:0%
+don't know what it is but what I claim
+is that the minimizer is always this guy
+
+ align:start position:0%
+is that the minimizer is always this guy
+ 
+
+ align:start position:0%
+is that the minimizer is always this guy
+regardless of what the value is okay so
+
+ align:start position:0%
+regardless of what the value is okay so
+ 
+
+ align:start position:0%
+regardless of what the value is okay so
+when I say constant it's a constant with
+
+ align:start position:0%
+when I say constant it's a constant with
+ 
+
+ align:start position:0%
+when I say constant it's a constant with
+respect to theta it's an unknown
+
+ align:start position:0%
+respect to theta it's an unknown
+ 
+
+ align:start position:0%
+respect to theta it's an unknown
+constant but it's with respect to theta
+
+ align:start position:0%
+constant but it's with respect to theta
+ 
+
+ align:start position:0%
+constant but it's with respect to theta
+so without loss of generality I can
+
+ align:start position:0%
+so without loss of generality I can
+ 
+
+ align:start position:0%
+so without loss of generality I can
+assume that this constant is zero
+
+ align:start position:0%
+assume that this constant is zero
+ 
+
+ align:start position:0%
+assume that this constant is zero
+for my purse Pacific my purposes or 25
+
+ align:start position:0%
+for my purse Pacific my purposes or 25
+ 
+
+ align:start position:0%
+for my purse Pacific my purposes or 25
+if you prefer alright so we'll just keep
+
+ align:start position:0%
+if you prefer alright so we'll just keep
+ 
+
+ align:start position:0%
+if you prefer alright so we'll just keep
+going on this property next time and
+
+ align:start position:0%
+going on this property next time and
+ 
+
+ align:start position:0%
+going on this property next time and
+we'll see how from here we can move on
+
+ align:start position:0%
+we'll see how from here we can move on
+ 
+
+ align:start position:0%
+we'll see how from here we can move on
+to the likelihood is actually gonna come
+
+ align:start position:0%
+to the likelihood is actually gonna come
+ 
+
+ align:start position:0%
+to the likelihood is actually gonna come
+out of this formula Thanks
\ No newline at end of file
diff --git a/rqkvDrYmKcc.txt b/rqkvDrYmKcc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b61a00bfd15839fb7a6372f957e80a4a18c98997
--- /dev/null
+++ b/rqkvDrYmKcc.txt
@@ -0,0 +1,2243 @@
+align:start position:0%
+ 
+Welcome back to recitation. In this
+
+ align:start position:0%
+Welcome back to recitation. In this
+ 
+
+ align:start position:0%
+Welcome back to recitation. In this
+video, I want us to work on the
+
+ align:start position:0%
+video, I want us to work on the
+ 
+
+ align:start position:0%
+video, I want us to work on the
+following problem. A very shallow
+
+ align:start position:0%
+following problem. A very shallow
+ 
+
+ align:start position:0%
+following problem. A very shallow
+circular reflecting pool has uniform
+
+ align:start position:0%
+circular reflecting pool has uniform
+ 
+
+ align:start position:0%
+circular reflecting pool has uniform
+depth D and radius R. And this is in
+
+ align:start position:0%
+depth D and radius R. And this is in
+ 
+
+ align:start position:0%
+depth D and radius R. And this is in
+meters. And a disinfecting chemical is
+
+ align:start position:0%
+meters. And a disinfecting chemical is
+ 
+
+ align:start position:0%
+meters. And a disinfecting chemical is
+released at its center. After a few
+
+ align:start position:0%
+released at its center. After a few
+ 
+
+ align:start position:0%
+released at its center. After a few
+hours of symmetrical diffusion outward,
+
+ align:start position:0%
+hours of symmetrical diffusion outward,
+ 
+
+ align:start position:0%
+hours of symmetrical diffusion outward,
+the concentration at a point little r
+
+ align:start position:0%
+the concentration at a point little r
+ 
+
+ align:start position:0%
+the concentration at a point little r
+meters from the center is k over 1 plus
+
+ align:start position:0%
+meters from the center is k over 1 plus
+ 
+
+ align:start position:0%
+meters from the center is k over 1 plus
+r^ 2 g per cubic meter. The k here is a
+
+ align:start position:0%
+r^ 2 g per cubic meter. The k here is a
+ 
+
+ align:start position:0%
+r^ 2 g per cubic meter. The k here is a
+constant. So we drop some chemical into
+
+ align:start position:0%
+constant. So we drop some chemical into
+ 
+
+ align:start position:0%
+constant. So we drop some chemical into
+the middle of the pool and then it
+
+ align:start position:0%
+the middle of the pool and then it
+ 
+
+ align:start position:0%
+the middle of the pool and then it
+diffuses outward. That's the idea there.
+
+ align:start position:0%
+diffuses outward. That's the idea there.
+ 
+
+ align:start position:0%
+diffuses outward. That's the idea there.
+Now the question is the following. What
+
+ align:start position:0%
+Now the question is the following. What
+ 
+
+ align:start position:0%
+Now the question is the following. What
+amount of chemical was released into the
+
+ align:start position:0%
+amount of chemical was released into the
+ 
+
+ align:start position:0%
+amount of chemical was released into the
+pool? And obviously the amount will be
+
+ align:start position:0%
+pool? And obviously the amount will be
+ 
+
+ align:start position:0%
+pool? And obviously the amount will be
+in grams. Now, to give you a hint,
+
+ align:start position:0%
+in grams. Now, to give you a hint,
+ 
+
+ align:start position:0%
+in grams. Now, to give you a hint,
+probably you want to draw a a picture of
+
+ align:start position:0%
+probably you want to draw a a picture of
+ 
+
+ align:start position:0%
+probably you want to draw a a picture of
+this and then maybe get some estimates
+
+ align:start position:0%
+this and then maybe get some estimates
+ 
+
+ align:start position:0%
+this and then maybe get some estimates
+or some
+
+ align:start position:0%
+or some
+ 
+
+ align:start position:0%
+or some
+approximations using shells or you might
+
+ align:start position:0%
+approximations using shells or you might
+ 
+
+ align:start position:0%
+approximations using shells or you might
+just say, you know, some strips, some
+
+ align:start position:0%
+just say, you know, some strips, some
+ 
+
+ align:start position:0%
+just say, you know, some strips, some
+shells probably is the better word for
+
+ align:start position:0%
+shells probably is the better word for
+ 
+
+ align:start position:0%
+shells probably is the better word for
+it. And then you should think about the
+
+ align:start position:0%
+it. And then you should think about the
+ 
+
+ align:start position:0%
+it. And then you should think about the
+fact that as you get better and better
+
+ align:start position:0%
+fact that as you get better and better
+ 
+
+ align:start position:0%
+fact that as you get better and better
+estimates, your approximation should
+
+ align:start position:0%
+estimates, your approximation should
+ 
+
+ align:start position:0%
+estimates, your approximation should
+tend toward an integral. So, with that
+
+ align:start position:0%
+tend toward an integral. So, with that
+ 
+
+ align:start position:0%
+tend toward an integral. So, with that
+hint, I'll give you a little time to
+
+ align:start position:0%
+hint, I'll give you a little time to
+ 
+
+ align:start position:0%
+hint, I'll give you a little time to
+work on this, and when we come back,
+
+ align:start position:0%
+work on this, and when we come back,
+ 
+
+ align:start position:0%
+work on this, and when we come back,
+I'll show you how I do it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, welcome back. Hopefully you were
+
+ align:start position:0%
+Okay, welcome back. Hopefully you were
+ 
+
+ align:start position:0%
+Okay, welcome back. Hopefully you were
+able to make some headway. And so let me
+
+ align:start position:0%
+able to make some headway. And so let me
+ 
+
+ align:start position:0%
+able to make some headway. And so let me
+start off by doing what I asked you to
+
+ align:start position:0%
+start off by doing what I asked you to
+ 
+
+ align:start position:0%
+start off by doing what I asked you to
+do, which is draw a picture. Now, this
+
+ align:start position:0%
+do, which is draw a picture. Now, this
+ 
+
+ align:start position:0%
+do, which is draw a picture. Now, this
+is the first picture is fairly
+
+ align:start position:0%
+is the first picture is fairly
+ 
+
+ align:start position:0%
+is the first picture is fairly
+simple. The first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+picture is my pool, right? But that's
+
+ align:start position:0%
+picture is my pool, right? But that's
+ 
+
+ align:start position:0%
+picture is my pool, right? But that's
+not quite enough to tell me uh some
+
+ align:start position:0%
+not quite enough to tell me uh some
+ 
+
+ align:start position:0%
+not quite enough to tell me uh some
+estimates. But what do we have? So the
+
+ align:start position:0%
+estimates. But what do we have? So the
+ 
+
+ align:start position:0%
+estimates. But what do we have? So the
+the pool has radius capital R and depth
+
+ align:start position:0%
+the pool has radius capital R and depth
+ 
+
+ align:start position:0%
+the pool has radius capital R and depth
+D. And when I said we want to do some
+
+ align:start position:0%
+D. And when I said we want to do some
+ 
+
+ align:start position:0%
+D. And when I said we want to do some
+approximation, what I really meant
+
+ align:start position:0%
+approximation, what I really meant
+ 
+
+ align:start position:0%
+approximation, what I really meant
+is is we want to let me actually get
+
+ align:start position:0%
+is is we want to let me actually get
+ 
+
+ align:start position:0%
+is is we want to let me actually get
+another color here. If we want to say
+
+ align:start position:0%
+another color here. If we want to say
+ 
+
+ align:start position:0%
+another color here. If we want to say
+take some fixed radius out and assume
+
+ align:start position:0%
+take some fixed radius out and assume
+ 
+
+ align:start position:0%
+take some fixed radius out and assume
+that let me actually draw this behind
+
+ align:start position:0%
+that let me actually draw this behind
+ 
+
+ align:start position:0%
+that let me actually draw this behind
+some fixed radius out and assume that
+
+ align:start position:0%
+some fixed radius out and assume that
+ 
+
+ align:start position:0%
+some fixed radius out and assume that
+that the diffusion is constant for some
+
+ align:start position:0%
+that the diffusion is constant for some
+ 
+
+ align:start position:0%
+that the diffusion is constant for some
+small bit some small strip like this
+
+ align:start position:0%
+small bit some small strip like this
+ 
+
+ align:start position:0%
+small bit some small strip like this
+which actually you notice is going to be
+
+ align:start position:0%
+which actually you notice is going to be
+ 
+
+ align:start position:0%
+which actually you notice is going to be
+rotated around because all of this is
+
+ align:start position:0%
+rotated around because all of this is
+ 
+
+ align:start position:0%
+rotated around because all of this is
+relative to distance from the center.
+
+ align:start position:0%
+relative to distance from the center.
+ 
+
+ align:start position:0%
+relative to distance from the center.
+So, I'm hoping that you can see kind of
+
+ align:start position:0%
+So, I'm hoping that you can see kind of
+ 
+
+ align:start position:0%
+So, I'm hoping that you can see kind of
+what this drawing is doing. Essentially,
+
+ align:start position:0%
+what this drawing is doing. Essentially,
+ 
+
+ align:start position:0%
+what this drawing is doing. Essentially,
+what we have here is if we open that up,
+
+ align:start position:0%
+what we have here is if we open that up,
+ 
+
+ align:start position:0%
+what we have here is if we open that up,
+this blue cylindrical shell is
+
+ align:start position:0%
+this blue cylindrical shell is
+ 
+
+ align:start position:0%
+this blue cylindrical shell is
+approximately a
+
+ align:start position:0%
+approximately a
+ 
+
+ align:start position:0%
+approximately a
+piece that doesn't quite look flat, but
+
+ align:start position:0%
+piece that doesn't quite look flat, but
+ 
+
+ align:start position:0%
+piece that doesn't quite look flat, but
+a piece that looks
+
+ align:start position:0%
+a piece that looks
+ 
+
+ align:start position:0%
+a piece that looks
+like Oh, well, we'll just stick with
+
+ align:start position:0%
+like Oh, well, we'll just stick with
+ 
+
+ align:start position:0%
+like Oh, well, we'll just stick with
+that. A little prism here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's approximately, if I were to
+
+ align:start position:0%
+So that's approximately, if I were to
+ 
+
+ align:start position:0%
+So that's approximately, if I were to
+cut this blue cylindrical shell here
+
+ align:start position:0%
+cut this blue cylindrical shell here
+ 
+
+ align:start position:0%
+cut this blue cylindrical shell here
+open and lay it down flat, it would be
+
+ align:start position:0%
+open and lay it down flat, it would be
+ 
+
+ align:start position:0%
+open and lay it down flat, it would be
+approximately a piece kind of like this,
+
+ align:start position:0%
+approximately a piece kind of like this,
+ 
+
+ align:start position:0%
+approximately a piece kind of like this,
+right? And so what we're going to do is
+
+ align:start position:0%
+right? And so what we're going to do is
+ 
+
+ align:start position:0%
+right? And so what we're going to do is
+is estimate first how what amount of
+
+ align:start position:0%
+is estimate first how what amount of
+ 
+
+ align:start position:0%
+is estimate first how what amount of
+chemical is released based on pieces
+
+ align:start position:0%
+chemical is released based on pieces
+ 
+
+ align:start position:0%
+chemical is released based on pieces
+that look like this. And then we're
+
+ align:start position:0%
+that look like this. And then we're
+ 
+
+ align:start position:0%
+that look like this. And then we're
+going to let those pieces get very very
+
+ align:start position:0%
+going to let those pieces get very very
+ 
+
+ align:start position:0%
+going to let those pieces get very very
+narrow and and get more and more of
+
+ align:start position:0%
+narrow and and get more and more of
+ 
+
+ align:start position:0%
+narrow and and get more and more of
+them. And this should remind you of
+
+ align:start position:0%
+them. And this should remind you of
+ 
+
+ align:start position:0%
+them. And this should remind you of
+reman sums and how remon sums as you let
+
+ align:start position:0%
+reman sums and how remon sums as you let
+ 
+
+ align:start position:0%
+reman sums and how remon sums as you let
+the the uh number of things you're
+
+ align:start position:0%
+the the uh number of things you're
+ 
+
+ align:start position:0%
+the the uh number of things you're
+summing over tend to zero sorry 10 to
+
+ align:start position:0%
+summing over tend to zero sorry 10 to
+ 
+
+ align:start position:0%
+summing over tend to zero sorry 10 to
+infinity and
+
+ align:start position:0%
+infinity and
+ 
+
+ align:start position:0%
+infinity and
+so so that the the little pieces are
+
+ align:start position:0%
+so so that the the little pieces are
+ 
+
+ align:start position:0%
+so so that the the little pieces are
+getting narrower and narrower you're
+
+ align:start position:0%
+getting narrower and narrower you're
+ 
+
+ align:start position:0%
+getting narrower and narrower you're
+actually going to end up with an
+
+ align:start position:0%
+actually going to end up with an
+ 
+
+ align:start position:0%
+actually going to end up with an
+integral. So this is where we're headed.
+
+ align:start position:0%
+integral. So this is where we're headed.
+ 
+
+ align:start position:0%
+integral. So this is where we're headed.
+So let's let's just make sure we
+
+ align:start position:0%
+So let's let's just make sure we
+ 
+
+ align:start position:0%
+So let's let's just make sure we
+understand kind of all the pieces that
+
+ align:start position:0%
+understand kind of all the pieces that
+ 
+
+ align:start position:0%
+understand kind of all the pieces that
+are happening. What we're going to do is
+
+ align:start position:0%
+are happening. What we're going to do is
+ 
+
+ align:start position:0%
+are happening. What we're going to do is
+we're going to take a bunch of these
+
+ align:start position:0%
+we're going to take a bunch of these
+ 
+
+ align:start position:0%
+we're going to take a bunch of these
+cylinders and let's just determine that
+
+ align:start position:0%
+cylinders and let's just determine that
+ 
+
+ align:start position:0%
+cylinders and let's just determine that
+we'll take n of them. I shouldn't say
+
+ align:start position:0%
+we'll take n of them. I shouldn't say
+ 
+
+ align:start position:0%
+we'll take n of them. I shouldn't say
+cylinders, sorry, I should say shells.
+
+ align:start position:0%
+cylinders, sorry, I should say shells.
+ 
+
+ align:start position:0%
+cylinders, sorry, I should say shells.
+We're going to take n of these shell
+
+ align:start position:0%
+We're going to take n of these shell
+ 
+
+ align:start position:0%
+We're going to take n of these shell
+type things. So, I'm going to say the
+
+ align:start position:0%
+type things. So, I'm going to say the
+ 
+
+ align:start position:0%
+type things. So, I'm going to say the
+radi I'm going to start with r0 equals
+
+ align:start position:0%
+radi I'm going to start with r0 equals
+ 
+
+ align:start position:0%
+radi I'm going to start with r0 equals
+0. And I'm going to take n different
+
+ align:start position:0%
+0. And I'm going to take n different
+ 
+
+ align:start position:0%
+0. And I'm going to take n different
+radi. So,
+
+ align:start position:0%
+radi. So,
+ 
+
+ align:start position:0%
+radi. So,
+r0 r1 up to sorry this is zero to rn is
+
+ align:start position:0%
+r0 r1 up to sorry this is zero to rn is
+ 
+
+ align:start position:0%
+r0 r1 up to sorry this is zero to rn is
+equal to capital r. So I guess I'm
+
+ align:start position:0%
+equal to capital r. So I guess I'm
+ 
+
+ align:start position:0%
+equal to capital r. So I guess I'm
+taking n plus one, but zero is not
+
+ align:start position:0%
+taking n plus one, but zero is not
+ 
+
+ align:start position:0%
+taking n plus one, but zero is not
+really a radius. But I have n different
+
+ align:start position:0%
+really a radius. But I have n different
+ 
+
+ align:start position:0%
+really a radius. But I have n different
+partitions. For each partition of this
+
+ align:start position:0%
+partitions. For each partition of this
+ 
+
+ align:start position:0%
+partitions. For each partition of this
+big cylinder, I get a piece like this,
+
+ align:start position:0%
+big cylinder, I get a piece like this,
+ 
+
+ align:start position:0%
+big cylinder, I get a piece like this,
+right? I get a piece that when I open it
+
+ align:start position:0%
+right? I get a piece that when I open it
+ 
+
+ align:start position:0%
+right? I get a piece that when I open it
+up looks approximately like this. Now
+
+ align:start position:0%
+up looks approximately like this. Now
+ 
+
+ align:start position:0%
+up looks approximately like this. Now
+what I want is a total amount. I want
+
+ align:start position:0%
+what I want is a total amount. I want
+ 
+
+ align:start position:0%
+what I want is a total amount. I want
+grams, right? And what I'm given, if we
+
+ align:start position:0%
+grams, right? And what I'm given, if we
+ 
+
+ align:start position:0%
+grams, right? And what I'm given, if we
+come back over here, what I'm given is
+
+ align:start position:0%
+come back over here, what I'm given is
+ 
+
+ align:start position:0%
+come back over here, what I'm given is
+the concentration at a certain
+
+ align:start position:0%
+the concentration at a certain
+ 
+
+ align:start position:0%
+the concentration at a certain
+radius, it's K over 1 plus R 2 g per
+
+ align:start position:0%
+radius, it's K over 1 plus R 2 g per
+ 
+
+ align:start position:0%
+radius, it's K over 1 plus R 2 g per
+cubic meter. Now, if nothing else, you
+
+ align:start position:0%
+cubic meter. Now, if nothing else, you
+ 
+
+ align:start position:0%
+cubic meter. Now, if nothing else, you
+should have looked at this problem and
+
+ align:start position:0%
+should have looked at this problem and
+ 
+
+ align:start position:0%
+should have looked at this problem and
+seen, well, if I want grams, and I have
+
+ align:start position:0%
+seen, well, if I want grams, and I have
+ 
+
+ align:start position:0%
+seen, well, if I want grams, and I have
+something in grams per cubic meter,
+
+ align:start position:0%
+something in grams per cubic meter,
+ 
+
+ align:start position:0%
+something in grams per cubic meter,
+somewhere I'm going to need something
+
+ align:start position:0%
+somewhere I'm going to need something
+ 
+
+ align:start position:0%
+somewhere I'm going to need something
+with cubic meters to cancel this unit,
+
+ align:start position:0%
+with cubic meters to cancel this unit,
+ 
+
+ align:start position:0%
+with cubic meters to cancel this unit,
+so I end up with grams. So if nothing
+
+ align:start position:0%
+so I end up with grams. So if nothing
+ 
+
+ align:start position:0%
+so I end up with grams. So if nothing
+else then maybe you can you can think oh
+
+ align:start position:0%
+else then maybe you can you can think oh
+ 
+
+ align:start position:0%
+else then maybe you can you can think oh
+I need to understand volume of something
+
+ align:start position:0%
+I need to understand volume of something
+ 
+
+ align:start position:0%
+I need to understand volume of something
+in order to solve this
+
+ align:start position:0%
+in order to solve this
+ 
+
+ align:start position:0%
+in order to solve this
+problem. Right now if we have n
+
+ align:start position:0%
+problem. Right now if we have n
+ 
+
+ align:start position:0%
+problem. Right now if we have n
+different partitions so n shells that
+
+ align:start position:0%
+different partitions so n shells that
+ 
+
+ align:start position:0%
+different partitions so n shells that
+all started off as this sort of blue
+
+ align:start position:0%
+all started off as this sort of blue
+ 
+
+ align:start position:0%
+all started off as this sort of blue
+type thing and I open up and look like
+
+ align:start position:0%
+type thing and I open up and look like
+ 
+
+ align:start position:0%
+type thing and I open up and look like
+this then I want to figure out what is
+
+ align:start position:0%
+this then I want to figure out what is
+ 
+
+ align:start position:0%
+this then I want to figure out what is
+the volume of these shells. Once I know
+
+ align:start position:0%
+the volume of these shells. Once I know
+ 
+
+ align:start position:0%
+the volume of these shells. Once I know
+the volume of that shell, I can figure
+
+ align:start position:0%
+the volume of that shell, I can figure
+ 
+
+ align:start position:0%
+the volume of that shell, I can figure
+out the
+
+ align:start position:0%
+out the
+ 
+
+ align:start position:0%
+out the
+amount roughly of chemical in that piece
+
+ align:start position:0%
+amount roughly of chemical in that piece
+ 
+
+ align:start position:0%
+amount roughly of chemical in that piece
+by multiplying by the
+
+ align:start position:0%
+by multiplying by the
+ 
+
+ align:start position:0%
+by multiplying by the
+concentration. So, let's figure out what
+
+ align:start position:0%
+concentration. So, let's figure out what
+ 
+
+ align:start position:0%
+concentration. So, let's figure out what
+this volume is in terms of these little
+
+ align:start position:0%
+this volume is in terms of these little
+ 
+
+ align:start position:0%
+this volume is in terms of these little
+radi I'm looking at. Well, when I open
+
+ align:start position:0%
+radi I'm looking at. Well, when I open
+ 
+
+ align:start position:0%
+radi I'm looking at. Well, when I open
+it up, what do I get? We're assuming
+
+ align:start position:0%
+it up, what do I get? We're assuming
+ 
+
+ align:start position:0%
+it up, what do I get? We're assuming
+this here is this little segment here.
+
+ align:start position:0%
+this here is this little segment here.
+ 
+
+ align:start position:0%
+this here is this little segment here.
+And so, that's our delta r. That's our
+
+ align:start position:0%
+And so, that's our delta r. That's our
+ 
+
+ align:start position:0%
+And so, that's our delta r. That's our
+change in radius. That's how much I'm
+
+ align:start position:0%
+change in radius. That's how much I'm
+ 
+
+ align:start position:0%
+change in radius. That's how much I'm
+changing. So this would be some r sub
+
+ align:start position:0%
+changing. So this would be some r sub
+ 
+
+ align:start position:0%
+changing. So this would be some r sub
+subscript i and this would be some r
+
+ align:start position:0%
+subscript i and this would be some r
+ 
+
+ align:start position:0%
+subscript i and this would be some r
+subscript i + one. And let's assume that
+
+ align:start position:0%
+subscript i + one. And let's assume that
+ 
+
+ align:start position:0%
+subscript i + one. And let's assume that
+we're taking everything from the smaller
+
+ align:start position:0%
+we're taking everything from the smaller
+ 
+
+ align:start position:0%
+we're taking everything from the smaller
+radius. We're going to do everything
+
+ align:start position:0%
+radius. We're going to do everything
+ 
+
+ align:start position:0%
+radius. We're going to do everything
+from the smaller radius. So then when I
+
+ align:start position:0%
+from the smaller radius. So then when I
+ 
+
+ align:start position:0%
+from the smaller radius. So then when I
+open this up, this circle is going to be
+
+ align:start position:0%
+open this up, this circle is going to be
+ 
+
+ align:start position:0%
+open this up, this circle is going to be
+my length. So my length is 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pi r subi. And then the height is easy.
+
+ align:start position:0%
+pi r subi. And then the height is easy.
+ 
+
+ align:start position:0%
+pi r subi. And then the height is easy.
+The height is constant. The height is
+
+ align:start position:0%
+The height is constant. The height is
+ 
+
+ align:start position:0%
+The height is constant. The height is
+just capital
+
+ align:start position:0%
+just capital
+ 
+
+ align:start position:0%
+just capital
+D. Right? So the volume of each
+
+ align:start position:0%
+D. Right? So the volume of each
+ 
+
+ align:start position:0%
+D. Right? So the volume of each
+shell come over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here. The volume of a shell is something
+
+ align:start position:0%
+here. The volume of a shell is something
+ 
+
+ align:start position:0%
+here. The volume of a shell is something
+like 2 pi R subi
+
+ align:start position:0%
+like 2 pi R subi
+ 
+
+ align:start position:0%
+like 2 pi R subi
+*
+
+ align:start position:0%
+*
+ 
+
+ align:start position:0%
+*
+D time
+
+ align:start position:0%
+D time
+ 
+
+ align:start position:0%
+D time
+deltar. And so then the amount of
+
+ align:start position:0%
+deltar. And so then the amount of
+ 
+
+ align:start position:0%
+deltar. And so then the amount of
+chemical in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shell is going to be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+volume times the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concentration. Right? The volume times
+
+ align:start position:0%
+concentration. Right? The volume times
+ 
+
+ align:start position:0%
+concentration. Right? The volume times
+the concentration. So the volume is
+
+ align:start position:0%
+the concentration. So the volume is
+ 
+
+ align:start position:0%
+the concentration. So the volume is
+again this. I'm going to put the d in
+
+ align:start position:0%
+again this. I'm going to put the d in
+ 
+
+ align:start position:0%
+again this. I'm going to put the d in
+front of the r subi. 2 pi d r sub i
+
+ align:start position:0%
+front of the r subi. 2 pi d r sub i
+ 
+
+ align:start position:0%
+front of the r subi. 2 pi d r sub i
+delta r times the concentration which if
+
+ align:start position:0%
+delta r times the concentration which if
+ 
+
+ align:start position:0%
+delta r times the concentration which if
+we come back over here the concentration
+
+ align:start position:0%
+we come back over here the concentration
+ 
+
+ align:start position:0%
+we come back over here the concentration
+is k / 1 + r 2 g per cubic meter the r
+
+ align:start position:0%
+is k / 1 + r 2 g per cubic meter the r
+ 
+
+ align:start position:0%
+is k / 1 + r 2 g per cubic meter the r
+in this case is the r subi I'm assuming
+
+ align:start position:0%
+in this case is the r subi I'm assuming
+ 
+
+ align:start position:0%
+in this case is the r subi I'm assuming
+because I'm approximating this that
+
+ align:start position:0%
+because I'm approximating this that
+ 
+
+ align:start position:0%
+because I'm approximating this that
+everywhere in the shell uh has the same
+
+ align:start position:0%
+everywhere in the shell uh has the same
+ 
+
+ align:start position:0%
+everywhere in the shell uh has the same
+concentration has the concentration of
+
+ align:start position:0%
+concentration has the concentration of
+ 
+
+ align:start position:0%
+concentration has the concentration of
+the interior radius so if we come back
+
+ align:start position:0%
+the interior radius so if we come back
+ 
+
+ align:start position:0%
+the interior radius so if we come back
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+here we're going to write k over 1 plus
+
+ align:start position:0%
+here we're going to write k over 1 plus
+ 
+
+ align:start position:0%
+here we're going to write k over 1 plus
+r subi^ 2. And now what do I get do to
+
+ align:start position:0%
+r subi^ 2. And now what do I get do to
+ 
+
+ align:start position:0%
+r subi^ 2. And now what do I get do to
+to estimate the amount in the entire
+
+ align:start position:0%
+to estimate the amount in the entire
+ 
+
+ align:start position:0%
+to estimate the amount in the entire
+pool? Well, I add all of these up. So
+
+ align:start position:0%
+pool? Well, I add all of these up. So
+ 
+
+ align:start position:0%
+pool? Well, I add all of these up. So
+let
+
+ align:start position:0%
+let
+ 
+
+ align:start position:0%
+let
+me let me come over here and write down
+
+ align:start position:0%
+me let me come over here and write down
+ 
+
+ align:start position:0%
+me let me come over here and write down
+what the sum will look like. So I'm
+
+ align:start position:0%
+what the sum will look like. So I'm
+ 
+
+ align:start position:0%
+what the sum will look like. So I'm
+going to be summing from i equals I said
+
+ align:start position:0%
+going to be summing from i equals I said
+ 
+
+ align:start position:0%
+going to be summing from i equals I said
+I was taking the interior radius I think
+
+ align:start position:0%
+I was taking the interior radius I think
+ 
+
+ align:start position:0%
+I was taking the interior radius I think
+i= 0 to n minus
+
+ align:start position:0%
+i= 0 to n minus
+ 
+
+ align:start position:0%
+i= 0 to n minus
+one of this
+
+ align:start position:0%
+one of this
+ 
+
+ align:start position:0%
+one of this
+quantity 2 pi d. Let me put the K in
+
+ align:start position:0%
+quantity 2 pi d. Let me put the K in
+ 
+
+ align:start position:0%
+quantity 2 pi d. Let me put the K in
+there as well.
+
+ align:start position:0%
+there as well.
+ 
+
+ align:start position:0%
+there as well.
+K. And then R subi over 1 + R subi
+
+ align:start position:0%
+K. And then R subi over 1 + R subi
+ 
+
+ align:start position:0%
+K. And then R subi over 1 + R subi
+squared delta R. So this is our
+
+ align:start position:0%
+squared delta R. So this is our
+ 
+
+ align:start position:0%
+squared delta R. So this is our
+approximation of the amount of chemical
+
+ align:start position:0%
+approximation of the amount of chemical
+ 
+
+ align:start position:0%
+approximation of the amount of chemical
+all the amount of chemical in the pool.
+
+ align:start position:0%
+all the amount of chemical in the pool.
+ 
+
+ align:start position:0%
+all the amount of chemical in the pool.
+And again, we always want to check and
+
+ align:start position:0%
+And again, we always want to check and
+ 
+
+ align:start position:0%
+And again, we always want to check and
+make sure I didn't write in any units,
+
+ align:start position:0%
+make sure I didn't write in any units,
+ 
+
+ align:start position:0%
+make sure I didn't write in any units,
+but did the units make sense? Well, we
+
+ align:start position:0%
+but did the units make sense? Well, we
+ 
+
+ align:start position:0%
+but did the units make sense? Well, we
+know the units make sense because when I
+
+ align:start position:0%
+know the units make sense because when I
+ 
+
+ align:start position:0%
+know the units make sense because when I
+did the amount in a shell, I did volume
+
+ align:start position:0%
+did the amount in a shell, I did volume
+ 
+
+ align:start position:0%
+did the amount in a shell, I did volume
+times concentration. And volume times
+
+ align:start position:0%
+times concentration. And volume times
+ 
+
+ align:start position:0%
+times concentration. And volume times
+concentration is going to be in grams.
+
+ align:start position:0%
+concentration is going to be in grams.
+ 
+
+ align:start position:0%
+concentration is going to be in grams.
+This is in cubic meters. This is in
+
+ align:start position:0%
+This is in cubic meters. This is in
+ 
+
+ align:start position:0%
+This is in cubic meters. This is in
+grams per cubic meter. So, I know I'm I
+
+ align:start position:0%
+grams per cubic meter. So, I know I'm I
+ 
+
+ align:start position:0%
+grams per cubic meter. So, I know I'm I
+have the right units. So, that's a a
+
+ align:start position:0%
+have the right units. So, that's a a
+ 
+
+ align:start position:0%
+have the right units. So, that's a a
+good way to check. Doesn't guarantee
+
+ align:start position:0%
+good way to check. Doesn't guarantee
+ 
+
+ align:start position:0%
+good way to check. Doesn't guarantee
+you've done it correctly, but at least
+
+ align:start position:0%
+you've done it correctly, but at least
+ 
+
+ align:start position:0%
+you've done it correctly, but at least
+you can check and make sure you didn't
+
+ align:start position:0%
+you can check and make sure you didn't
+ 
+
+ align:start position:0%
+you can check and make sure you didn't
+do it. You know, you know that uh how
+
+ align:start position:0%
+do it. You know, you know that uh how
+ 
+
+ align:start position:0%
+do it. You know, you know that uh how
+would I say this? I would say that if if
+
+ align:start position:0%
+would I say this? I would say that if if
+ 
+
+ align:start position:0%
+would I say this? I would say that if if
+the units were not in grams, you'd know
+
+ align:start position:0%
+the units were not in grams, you'd know
+ 
+
+ align:start position:0%
+the units were not in grams, you'd know
+you did something wrong. So, at least
+
+ align:start position:0%
+you did something wrong. So, at least
+ 
+
+ align:start position:0%
+you did something wrong. So, at least
+now we know, okay, it passes the first
+
+ align:start position:0%
+now we know, okay, it passes the first
+ 
+
+ align:start position:0%
+now we know, okay, it passes the first
+smell test. Now, what do I do to find
+
+ align:start position:0%
+smell test. Now, what do I do to find
+ 
+
+ align:start position:0%
+smell test. Now, what do I do to find
+the exact value? Well, what I want to do
+
+ align:start position:0%
+the exact value? Well, what I want to do
+ 
+
+ align:start position:0%
+the exact value? Well, what I want to do
+is I want to come back over to the
+
+ align:start position:0%
+is I want to come back over to the
+ 
+
+ align:start position:0%
+is I want to come back over to the
+picture I have here, and I want to let
+
+ align:start position:0%
+picture I have here, and I want to let
+ 
+
+ align:start position:0%
+picture I have here, and I want to let
+these shells get smaller and smaller.
+
+ align:start position:0%
+these shells get smaller and smaller.
+ 
+
+ align:start position:0%
+these shells get smaller and smaller.
+And how do I let those shells get
+
+ align:start position:0%
+And how do I let those shells get
+ 
+
+ align:start position:0%
+And how do I let those shells get
+smaller and smaller, narrower and
+
+ align:start position:0%
+smaller and smaller, narrower and
+ 
+
+ align:start position:0%
+smaller and smaller, narrower and
+narrower, I should say. I let them get
+
+ align:start position:0%
+narrower, I should say. I let them get
+ 
+
+ align:start position:0%
+narrower, I should say. I let them get
+narrower by increasing the number of uh
+
+ align:start position:0%
+narrower by increasing the number of uh
+ 
+
+ align:start position:0%
+narrower by increasing the number of uh
+radi on which I do this kind of
+
+ align:start position:0%
+radi on which I do this kind of
+ 
+
+ align:start position:0%
+radi on which I do this kind of
+operation. So I'm coming over here and
+
+ align:start position:0%
+operation. So I'm coming over here and
+ 
+
+ align:start position:0%
+operation. So I'm coming over here and
+now I'm letting the n get bigger and
+
+ align:start position:0%
+now I'm letting the n get bigger and
+ 
+
+ align:start position:0%
+now I'm letting the n get bigger and
+bigger. And as n gets bigger and bigger,
+
+ align:start position:0%
+bigger. And as n gets bigger and bigger,
+ 
+
+ align:start position:0%
+bigger. And as n gets bigger and bigger,
+these values are still determined the
+
+ align:start position:0%
+these values are still determined the
+ 
+
+ align:start position:0%
+these values are still determined the
+same way. But over here, this n is
+
+ align:start position:0%
+same way. But over here, this n is
+ 
+
+ align:start position:0%
+same way. But over here, this n is
+getting larger and larger. So I can take
+
+ align:start position:0%
+getting larger and larger. So I can take
+ 
+
+ align:start position:0%
+getting larger and larger. So I can take
+the limit as n goes to infinity of this
+
+ align:start position:0%
+the limit as n goes to infinity of this
+ 
+
+ align:start position:0%
+the limit as n goes to infinity of this
+quantity to get the exact amount. What
+
+ align:start position:0%
+quantity to get the exact amount. What
+ 
+
+ align:start position:0%
+quantity to get the exact amount. What
+is the limit as n goes to infinity of
+
+ align:start position:0%
+is the limit as n goes to infinity of
+ 
+
+ align:start position:0%
+is the limit as n goes to infinity of
+that exact of of this? This is actually
+
+ align:start position:0%
+that exact of of this? This is actually
+ 
+
+ align:start position:0%
+that exact of of this? This is actually
+an integral. It's the integral from 0 to
+
+ align:start position:0%
+an integral. It's the integral from 0 to
+ 
+
+ align:start position:0%
+an integral. It's the integral from 0 to
+capital R because my radius is ranging
+
+ align:start position:0%
+capital R because my radius is ranging
+ 
+
+ align:start position:0%
+capital R because my radius is ranging
+from zero to that big R of this exact
+
+ align:start position:0%
+from zero to that big R of this exact
+ 
+
+ align:start position:0%
+from zero to that big R of this exact
+function of R, right? So I'm going to
+
+ align:start position:0%
+function of R, right? So I'm going to
+ 
+
+ align:start position:0%
+function of R, right? So I'm going to
+put the 2 pi d K out here and then I get
+
+ align:start position:0%
+put the 2 pi d K out here and then I get
+ 
+
+ align:start position:0%
+put the 2 pi d K out here and then I get
+little r over 1 plus r 2 and the delta r
+
+ align:start position:0%
+little r over 1 plus r 2 and the delta r
+ 
+
+ align:start position:0%
+little r over 1 plus r 2 and the delta r
+becomes our dr. So this is in fact going
+
+ align:start position:0%
+becomes our dr. So this is in fact going
+ 
+
+ align:start position:0%
+becomes our dr. So this is in fact going
+to be the amount in grams of the
+
+ align:start position:0%
+to be the amount in grams of the
+ 
+
+ align:start position:0%
+to be the amount in grams of the
+chemical that was released into the
+
+ align:start position:0%
+chemical that was released into the
+ 
+
+ align:start position:0%
+chemical that was released into the
+pool. So we've set up our integral. I
+
+ align:start position:0%
+pool. So we've set up our integral. I
+ 
+
+ align:start position:0%
+pool. So we've set up our integral. I
+think I'll stop here. If you want to go
+
+ align:start position:0%
+think I'll stop here. If you want to go
+ 
+
+ align:start position:0%
+think I'll stop here. If you want to go
+further and determine it, you can. And
+
+ align:start position:0%
+further and determine it, you can. And
+ 
+
+ align:start position:0%
+further and determine it, you can. And
+um you may want to think about what
+
+ align:start position:0%
+um you may want to think about what
+ 
+
+ align:start position:0%
+um you may want to think about what
+strategy obviously what strategy you
+
+ align:start position:0%
+strategy obviously what strategy you
+ 
+
+ align:start position:0%
+strategy obviously what strategy you
+want to use in order to solve this
+
+ align:start position:0%
+want to use in order to solve this
+ 
+
+ align:start position:0%
+want to use in order to solve this
+problem. I'll give you a hint. Maybe the
+
+ align:start position:0%
+problem. I'll give you a hint. Maybe the
+ 
+
+ align:start position:0%
+problem. I'll give you a hint. Maybe the
+best way to solve this problem is the
+
+ align:start position:0%
+best way to solve this problem is the
+ 
+
+ align:start position:0%
+best way to solve this problem is the
+fact that when you take the derivative
+
+ align:start position:0%
+fact that when you take the derivative
+ 
+
+ align:start position:0%
+fact that when you take the derivative
+of 1 plus r 2, you actually get 2 r. And
+
+ align:start position:0%
+of 1 plus r 2, you actually get 2 r. And
+ 
+
+ align:start position:0%
+of 1 plus r 2, you actually get 2 r. And
+so that derivative is almost up here. So
+
+ align:start position:0%
+so that derivative is almost up here. So
+ 
+
+ align:start position:0%
+so that derivative is almost up here. So
+maybe this is a good uh a good hint to
+
+ align:start position:0%
+maybe this is a good uh a good hint to
+ 
+
+ align:start position:0%
+maybe this is a good uh a good hint to
+give you how you would continue this
+
+ align:start position:0%
+give you how you would continue this
+ 
+
+ align:start position:0%
+give you how you would continue this
+problem. But I'll stop there. So let me
+
+ align:start position:0%
+problem. But I'll stop there. So let me
+ 
+
+ align:start position:0%
+problem. But I'll stop there. So let me
+just let me just go back one more time
+
+ align:start position:0%
+just let me just go back one more time
+ 
+
+ align:start position:0%
+just let me just go back one more time
+and remind you what we were doing. What
+
+ align:start position:0%
+and remind you what we were doing. What
+ 
+
+ align:start position:0%
+and remind you what we were doing. What
+we were doing if we come back over here
+
+ align:start position:0%
+we were doing if we come back over here
+ 
+
+ align:start position:0%
+we were doing if we come back over here
+is we were given a situation where we
+
+ align:start position:0%
+is we were given a situation where we
+ 
+
+ align:start position:0%
+is we were given a situation where we
+knew a certain
+
+ align:start position:0%
+knew a certain
+ 
+
+ align:start position:0%
+knew a certain
+function of the radius the distance from
+
+ align:start position:0%
+function of the radius the distance from
+ 
+
+ align:start position:0%
+function of the radius the distance from
+the center. And we wanted to determine
+
+ align:start position:0%
+the center. And we wanted to determine
+ 
+
+ align:start position:0%
+the center. And we wanted to determine
+the total amount of of uh chemical that
+
+ align:start position:0%
+the total amount of of uh chemical that
+ 
+
+ align:start position:0%
+the total amount of of uh chemical that
+was released into the pool. And so we
+
+ align:start position:0%
+was released into the pool. And so we
+ 
+
+ align:start position:0%
+was released into the pool. And so we
+estimated we figured out a way to
+
+ align:start position:0%
+estimated we figured out a way to
+ 
+
+ align:start position:0%
+estimated we figured out a way to
+estimate it in terms of splitting up the
+
+ align:start position:0%
+estimate it in terms of splitting up the
+ 
+
+ align:start position:0%
+estimate it in terms of splitting up the
+radi. We had a we had the radius from
+
+ align:start position:0%
+radi. We had a we had the radius from
+ 
+
+ align:start position:0%
+radi. We had a we had the radius from
+zero to to big r and we just divided up
+
+ align:start position:0%
+zero to to big r and we just divided up
+ 
+
+ align:start position:0%
+zero to to big r and we just divided up
+the radi and assumed certain things were
+
+ align:start position:0%
+the radi and assumed certain things were
+ 
+
+ align:start position:0%
+the radi and assumed certain things were
+constant in in these regions and we
+
+ align:start position:0%
+constant in in these regions and we
+ 
+
+ align:start position:0%
+constant in in these regions and we
+determined the right function to find if
+
+ align:start position:0%
+determined the right function to find if
+ 
+
+ align:start position:0%
+determined the right function to find if
+we move over here over here we
+
+ align:start position:0%
+we move over here over here we
+ 
+
+ align:start position:0%
+we move over here over here we
+determined the right function to find
+
+ align:start position:0%
+determined the right function to find
+ 
+
+ align:start position:0%
+determined the right function to find
+the amount of chemical in a certain
+
+ align:start position:0%
+the amount of chemical in a certain
+ 
+
+ align:start position:0%
+the amount of chemical in a certain
+shell assuming that the concentration
+
+ align:start position:0%
+shell assuming that the concentration
+ 
+
+ align:start position:0%
+shell assuming that the concentration
+was constant throughout that shell. And
+
+ align:start position:0%
+was constant throughout that shell. And
+ 
+
+ align:start position:0%
+was constant throughout that shell. And
+then what we do is we know that if we
+
+ align:start position:0%
+then what we do is we know that if we
+ 
+
+ align:start position:0%
+then what we do is we know that if we
+let those shells get arbitrarily narrow,
+
+ align:start position:0%
+let those shells get arbitrarily narrow,
+ 
+
+ align:start position:0%
+let those shells get arbitrarily narrow,
+that means that we're letting the number
+
+ align:start position:0%
+that means that we're letting the number
+ 
+
+ align:start position:0%
+that means that we're letting the number
+of radi over which we're doing this go
+
+ align:start position:0%
+of radi over which we're doing this go
+ 
+
+ align:start position:0%
+of radi over which we're doing this go
+to infinity. And we know that this
+
+ align:start position:0%
+to infinity. And we know that this
+ 
+
+ align:start position:0%
+to infinity. And we know that this
+summation that we have here as n goes to
+
+ align:start position:0%
+summation that we have here as n goes to
+ 
+
+ align:start position:0%
+summation that we have here as n goes to
+infinity becomes an
+
+ align:start position:0%
+infinity becomes an
+ 
+
+ align:start position:0%
+infinity becomes an
+integral. So that's really we exploited
+
+ align:start position:0%
+integral. So that's really we exploited
+ 
+
+ align:start position:0%
+integral. So that's really we exploited
+what we know about this this sum and and
+
+ align:start position:0%
+what we know about this this sum and and
+ 
+
+ align:start position:0%
+what we know about this this sum and and
+uh letting this partition letting the
+
+ align:start position:0%
+uh letting this partition letting the
+ 
+
+ align:start position:0%
+uh letting this partition letting the
+delta r get arbitrarily small that that
+
+ align:start position:0%
+delta r get arbitrarily small that that
+ 
+
+ align:start position:0%
+delta r get arbitrarily small that that
+in the limit goes to an integral and
+
+ align:start position:0%
+in the limit goes to an integral and
+ 
+
+ align:start position:0%
+in the limit goes to an integral and
+then that's something we can
+
+ align:start position:0%
+then that's something we can
+ 
+
+ align:start position:0%
+then that's something we can
+definitively calculate. So I think I
+
+ align:start position:0%
+definitively calculate. So I think I
+ 
+
+ align:start position:0%
+definitively calculate. So I think I
+will stop there.
\ No newline at end of file
diff --git a/sQx1Y_CArYA.txt b/sQx1Y_CArYA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c506573b4f53ee7f980d3ab971ef6a1d7656de1d
--- /dev/null
+++ b/sQx1Y_CArYA.txt
@@ -0,0 +1,2041 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: All right, so we're
+going to try to finish up
+
+oxidation reduction today.
+
+The next unit we're heading
+into is transition metals.
+
+So, in the last class we were
+talking about delta e knots of
+
+cells, so the standard potential
+of a particular
+
+electric chemical cell.
+
+And as we ended class last
+time, you had a clicker
+
+question, which you told me what
+the reaction was at the
+
+anode and the reaction at the
+cathode for this particular
+
+electric chemical cell.
+
+So, now we're going to consider,
+we're going to
+
+calculate what this delta e
+nought is for this cell.
+
+So we have an equation that we
+can use to calculate delta e
+
+nought of a cell, and that is
+that the delta e or the
+
+potential of the cell, is
+equal to the standard
+
+reduction potential for the
+reaction that's occurring at
+
+the cathode, minus the standard
+reduction potential
+
+for the reaction that's
+occurring at the anode.
+
+So you told me which reaction
+was occurring at the anode and
+
+which at the cathode
+last time.
+
+So we can just go ahead and use
+that information in here.
+
+So the reaction that's occurring
+at the cathode is
+
+the copper reaction, and the
+reaction and the anode is the
+
+zinc reaction, and note here,
+I have these written as
+
+reduction potentials, because
+we're going to be plugging in
+
+the standard reduction potential
+into this equation.
+
+So, where do we get our standard
+reduction potentials?
+
+Well, your textbook has tables
+of many standard reduction
+
+potentials.
+
+And, of course, on an exam
+you would be given that
+
+information.
+
+And the standard reduction
+potentials were measured
+
+against the standard
+hydrogen electrode.
+
+So, now we talked last time
+about what some of these
+
+abbreviations mean.
+
+So we can look up the values
+and they're all going to be
+
+listed as reduction reactions,
+because they are standard
+
+reduction potentials.
+
+So all the reactions, if
+you're looking for ones
+
+written as oxidation, you'll be
+out of luck, they'll all be
+
+written as reductions.
+
+So here, written as a reduction,
+zinc plus 2, two
+
+electrons to zinc solid,
+copper plus 2 plus two
+
+electrons to copper solid, and
+you can look up those standard
+
+reduction potentials.
+
+And then you can plug them
+in to your equation.
+
+Again, the equation is the
+standard reduction potential
+
+for the couple at the cathode
+minus the standard reduction
+
+potential for the reaction
+at the anode.
+
+So the reaction at the cathode
+is the copper reaction, and so
+
+we have -- we put in here 0 .
+
+3 4 0 2, and then minus, and the
+zinc reduction potential's
+
+negative, so it's minus
+a minus 0 .
+
+7 6 2 8, and then if we add
+that together we get a
+
+positive value of 1 .
+
+1 0 3.
+
+And so in doing these, this is a
+pretty easy thing to do, but
+
+I'm sort of emphasizing it
+because a lot of people
+
+out-clever themselves
+in doing this.
+
+They say, well, one thing's
+being oxidized in this
+
+reaction, one thing's being
+reduced, so I'm looking up a
+
+standard reduction potential,
+I'm going to change the sign,
+
+and then plug it in and
+change the sign again.
+
+And so they change the sign so
+many times and they come up
+
+with the wrong answer.
+
+So just a hint in doing these
+problems, if you always think
+
+that the equation is asking you
+for the standard reduction
+
+potential, look that value
+up and put it in.
+
+Don't do anything fancy with
+signs, just use this equation
+
+as written, plugging in the
+standard reduction potentials,
+
+and you'll be all set and you
+won't have any problems
+
+getting it wrong.
+
+So try not to out-clever
+yourself and flip signs around
+
+many times in doing
+these problems.
+
+All right, so we have a value,
+a positive value then for our
+
+potential for the cell.
+
+So we can ask the question, in
+this type of cell, would the
+
+flow of electrons
+be spontaneous?
+
+What tells us if something
+is spontaneous?
+
+Delta g tells us if something
+is going to be spontaneous.
+
+And we mentioned last time
+a connection between
+
+delta g and delta e.
+
+So, delta g tells us if
+something will be spontaneous,
+
+and we talked last time of this
+equation that delta g
+
+nought for the cell is equal to
+minus n, n here being moles
+
+of electrons times Faraday's
+constant, times the delta e
+
+nought for the cell.
+
+So here again, we're relating
+back to thermodynamics, back
+
+to delta g, and we're thinking
+about whether things are going
+
+to be spontaneous or not.
+
+So, if we have a positive value
+for delta e nought of
+
+the cell, what's going to be
+true then for delta g?
+
+It'll be negative, and so
+will it be spontaneous?
+
+Yes.
+
+So, if delta e nought is
+positive, delta g will be
+
+negative, and if delta g is
+negative, the reaction will,
+
+in fact, be spontaneous.
+
+So the answer, then, is yes.
+
+So now let me introduce some
+more terms to you.
+
+Galvanic cell is an electric
+chemical cell in which a
+
+spontaneous chemical reaction
+is used to generate an
+
+electric current.
+
+So on a problem, which you may
+have on your problem-set and
+
+have already looked at this,
+it'll say something about for
+
+a galvanic cell.
+
+Well, that wasn't just kind of
+random information they're
+
+throwing out, they're telling
+you that the reaction's going
+
+to be spontaneous
+in that cell.
+
+So that will often tell you
+what reaction had to be
+
+happening at the anode, and
+what reaction had to be
+
+happening at the cathode.
+
+Because you need to have it be
+spontaneous, you need a value
+
+for delta e nought, then
+it's positive.
+
+So, the information that it's
+a galvanic cell tells you a
+
+lot about the problem.
+
+In contrast, we have
+electrolitic cell, and in this
+
+case, we can put in energy to
+provide, to be able to drive a
+
+non-spontaneous reaction.
+
+So you can generate a current
+to then force and
+
+non-spontaneous reaction
+to go.
+
+So these are 2 different
+kinds of cells.
+
+So again, whether something's
+spontaneous or not comes back
+
+to our friend delta g.
+
+So if a cell is operating
+spontaneously, that means
+
+you're going to have a delta
+e nought of the cell that's
+
+positive, which means that
+the delta g of the
+
+cell will be negative.
+
+And we can calculate these delta
+e noughts of the cell
+
+from the standard reduction
+potentials, which some nice
+
+person measured for
+us against the
+
+standard hydrogen electrode.
+
+And so we can look up those
+values and then we can
+
+calculate delta e nought of a
+cell, we'll know something
+
+about whether it will be a
+spontaneous reaction or not.
+
+So now let's think about the
+size and the sign of standard
+
+reduction potentials and what
+they tell us about a
+
+particular reaction.
+
+So the meaning of the standard
+reduction potential that you
+
+can look up in your book.
+
+So first let's think about what
+happens or what would be
+
+true if we had a large positive
+delta e nought.
+
+And that's going to mean that
+the element is easy to reduce.
+
+So let's look at an example.
+
+At the top of your table,
+you're going to see this
+
+particular reduction with this
+
+particular reduction potential.
+
+So we have f two gas plus 2
+electrons going to 2 f minus.
+
+And the standard reduction
+potential for this is measured
+
+at plus 2 .
+
+8 7 volts.
+
+So, as written, that's the
+value of the standard
+
+reduction potential.
+
+That's a large positive number,
+so that's going to
+
+mean that it's easy to
+add electrons to f 2.
+
+The delta g nought would
+be favorable for that.
+
+So then, you can tell me, does
+that make f 2 a good oxidizing
+
+agent or not and why?
+
+OK, let's do 10 seconds.
+
+Good.
+
+Yes, it is easy to reduce.
+
+So it's easy to add electrons,
+which makes it a good
+
+oxidizing agent.
+
+So let's go back
+to the slides.
+
+So, a good oxidizing agent is
+something that oxidizes other
+
+elements and gets
+reduced itself.
+
+So it goes around oxidizing
+things,
+
+it's an agent of oxidation.
+
+So something that easy to reduce
+is going to be a good
+
+oxidizing agent.
+
+And something that's easy to
+reduce is going to have a
+
+large positive standard
+reduction potential.
+
+So, one way to sort of remember
+this is for a
+
+particular couple.
+
+If something has a large
+positive delta e nought, the
+
+oxidized species, the oxidized
+species here is the f 2, it's,
+
+of these two things, it's
+the one that's oxidized.
+
+So the oxidized species
+is very oxidizing.
+
+So that's one way
+to remember it.
+
+Large positive delta
+e nought, oxidized
+
+species is very oxidizing.
+
+So, here is a list that is
+similar to what you would see
+
+in the back of your book, and
+we just talked about this
+
+couple between fluoride gas and
+a fluoride minus up here
+
+with this large positive
+standard reduction potential,
+
+and as it says up
+here, oxidized
+
+form is strongly oxidizing.
+
+Now, here we have positive
+numbers, and now we start to
+
+go to small negative numbers,
+and by the time we get down
+
+here, we have a large negative
+number for the standard
+
+reduction potential, and this
+is between lithium plus and
+
+lithium solid.
+
+So, let's consider what would be
+true down on the other end
+
+of the table.
+
+So a large negative delta e
+nought means that the element
+
+is hard to reduce.
+
+So let's look at this reaction
+with lithium.
+
+So we have lithium plus
+with lithium plus 1.
+
+When you add one electron to
+it, you get lithium solid.
+
+And the standard reduction
+potential for doing that
+
+reaction is minus 3 .
+
+0 4 5 volts.
+
+So, that's hard to add electrons
+to lithium plus 1 --
+
+lithium plus 1 is very happy
+being lithium plus 1, it
+
+doesn't want that electron back,
+and so that would be a
+
+non-spontaneous, unfavorable
+reaction.
+
+So, is lithium plus 1 a
+good oxidizing agent?
+
+No, it's not a good oxidizing
+agent, but something around
+
+here is going to be
+a good agent.
+
+Lithium solid is a good
+reducing agent.
+
+So, lithium solid likes to
+reduce other things, lithium
+
+solid likes to be oxidized,
+lithium prefers to be
+
+lithium plus 1.
+
+So it's very happy to be lithium
+plus 1, so the solid
+
+form is a good reducing agent.
+
+So, if we think about what's
+true at the bottom of the
+
+table, then if we have a couple
+of plus 1 to the solid,
+
+then if you have a large
+negative standard reduction
+
+potential, the reduced species
+is very reducing.
+
+So the reduced species here is
+the lithium solid, it is a
+
+good reducing agent.
+
+So, large negative reduced
+species is reducing.
+
+And if we go back to work table
+then, up here we have
+
+the big positive numbers.
+
+The oxidized form of this
+first couple is very
+
+oxidizing, at the bottom you
+have the large negative
+
+numbers, and the reduced
+form of that
+
+couple is very reducing.
+
+And you're going to be asked
+questions, given different
+
+elements in problem-sets or on
+exams and saying which of
+
+these is the better oxidizing
+agent, which of these is the
+
+better reducing agent, and be
+able to compare, and you need
+
+to think about where it is,
+which are the bigger positive
+
+numbers, bigger negative
+numbers, and you can make
+
+those comparisons, and if you
+remember on the top, big
+
+positive, oxidized form very
+oxidizing, big negative,
+
+reduced form very reducing,
+you'll be all set to answer
+
+those questions.
+
+And some of this should be
+sort of intuitive of the
+
+things that we've talked about
+already in this course.
+
+So we think about the periodic
+table for a minute, and here
+
+are some of the potentials,
+lithium is easy to oxidize,
+
+it's a good reducing agent.
+
+If it's lithium plus 1, then
+it has a noble gas
+
+configuration, it's
+very happy there.
+
+Whereas fluoride can get its
+noble gas configuration if
+
+it's f minus, so it's easy to
+reduce and that makes it a
+
+good oxidizing agent.
+
+So you can think about this
+in terms of it's sort of
+
+intuitive if you think about
+what you know about those
+
+elements going into this unit.
+
+So now, let's think about
+calculating a standard
+
+reduction potential for
+this particular
+
+electric chemical cell.
+
+So we're given equations and
+we want to calculate a
+
+standard potential for this.
+
+So, in doing this then, we're
+going to use our standard
+
+reduction potentials on this
+table, it's a little hard to
+
+see, so I'll go back
+over there.
+
+So now we have to figure out
+if we see this equation,
+
+what's the reaction that's
+going on at the cathode?
+
+First tell me what's happening
+at the cathode -- is it an
+
+oxidation or reduction happening
+at the cathode?
+
+The reduction is happening
+at the cathode.
+
+Now look at that equation up
+there and tell me what is
+
+being reduced -- which
+element is being
+
+reduced in that equation?
+
+The iron is being reduced.
+
+So we're going to write the 1/2
+reaction, that's balance,
+
+so there were two iron 3's.
+
+And on the other side there's
+two iron plus 2's, and how
+
+many electrons am I talking
+about here? two electrons.
+
+So we have the reduction
+reaction.
+
+Then at the anode, the anode has
+an oxidation going on, and
+
+we only have one choice left
+of what's being oxidized.
+
+So, we have -- and
+again balanced.
+
+We have 2 i minus, and this is
+an aqueous solution going to i
+
+2 solid plus two electrons.
+
+So we have now our two 1/2
+reactions written out, and we
+
+can look at the potentials for
+the standard reduction
+
+potentials, which we'll
+need to calculate
+
+the e for the cell.
+
+So now we want to calculate
+e nought for the cell, and
+
+that's going to be
+equal to the e
+
+for the cathode reaction.
+
+And that particular couple at
+the cathode, we're looking
+
+then at iron 3 plus going to
+iron 2 plus -- that's the
+
+reduction potential that we're
+going to be looking up.
+
+And then we also need another
+standard reduction potential,
+
+the one for the couple at the
+anode, and the couple at the
+
+anode that we're looking
+up is i 2 to i minus.
+
+So, if you can see that up
+there, it's also in your
+
+handout, then we can plug
+in those values.
+
+So, for iron, we have plus 0 .
+
+7 7 0 volts minus plus 0 .
+
+5 3 5 volts.
+
+And that's going to equal 0 .
+
+2 3 5 volts, which is
+a positive number.
+
+So what would be true about this
+reaction in terms of it
+
+being spontaneous or
+non-spontaneous?
+
+Right, so it would be
+spontaneous, because you have
+
+a positive value for delta e, so
+we'd have a negative value
+
+for delta g.
+
+All right, so now, let's think
+about what the good oxidizing
+
+and reducing agents are here,
+and let's have a clicker
+
+question for that.
+
+So, which is the better
+oxidizing agent, iron plus 3
+
+or i 2, and which is the better
+reducing agent, i minus
+
+or iron plus 2?
+
+So think about that one.
+
+All right, let's take
+10 seconds.
+
+Very good.
+
+So the trick here is to, again,
+think about these two
+
+different potentials.
+
+Now, unlike the example we had
+before, we had a big positive
+
+and a big negative
+value, these are
+
+both positive values.
+
+But one of them is bigger than
+the other, and so the better
+
+oxidizing one is going to be
+the one of these two, these
+
+are both the oxidized form.
+
+So the one with the bigger
+positive number, the oxidized
+
+species will be better at
+oxidizing, and so that would
+
+be the iron plus 3, that's the
+bigger positive number.
+
+Whereas here, when we're
+considering which is the
+
+better reducing agent, we're
+looking at the two reduced
+
+species here, and here the
+thing with the smaller a
+
+positive number, the reduced
+form will be a better reducing
+
+agent, more reducing.
+
+So again, you can look at where
+those are in the table
+
+and the size difference
+between them to
+
+get the right answer.
+
+So, very good.
+
+OK, so now, I want to consider
+a biological example for a
+
+minute, and I'm going to ask a
+question that we we'll then
+
+answer at the end of class.
+
+So in cells, things have
+reduction potentials.
+
+Vitamin B12 has a reduction
+potential.
+
+In fact, it has one of the
+largest negative reduction
+
+potentials of any biologically
+occurring molecule.
+
+And so it has to be reduced
+to be active in the body.
+
+So how can something with a very
+large negative reduction
+
+potential be reduced?
+
+That's the question.
+
+Why should you care?
+
+Well, because vitamin
+B12 needs to be
+
+reduced to be active.
+
+And the proper functioning of
+enzymes, there's only actually
+
+two that you have in humans that
+require B12 -- one that
+
+requires B12 and folic acid is
+thought to be important in
+
+preventing heart disease, birth
+defects, and B12 hs
+
+recently been linked
+to mental health.
+
+In particular, a lack of B12 has
+been linked to dementia.
+
+So, these are all pretty
+significant things.
+
+So, one thing that I think is
+kind of interesting here when
+
+they talk about heart disease,
+how many people have heard of
+
+cholesterol?
+
+How many people have heard
+of homocysteine?
+
+Would you be surprised to know
+that homocysteine is a better
+
+indicator of whether you'll
+have heart trouble than
+
+cholesterol?
+
+Yes.
+
+You would think that you would
+have heard of the one that was
+
+a better link.
+
+Well, homocysteine is actually
+a better link to indicate
+
+whether you might have heart
+problems, but the thing is
+
+that there's not a whole lot
+of money to be made there,
+
+whereas there's a lot of money
+to be made in drugs that lower
+
+cholesterol.
+
+So you may realize, if you think
+about where you get your
+
+medical information, it's often
+from commercials where
+
+someone's trying to sell
+you something.
+
+And so if there isn't much money
+to be made, say, the
+
+treatment for a condition might
+be taking vitamins,
+
+which there's not a whole lot of
+money to be made there, you
+
+don't hear as much about it.
+
+So, it's important to consider
+the source of information
+
+about your health, and as
+scientists, you can all
+
+evaluate information about
+your health now.
+
+All right, so vitamin B12 is
+very important, you really
+
+need vitamin B12 to be
+a healthy person.
+
+And most people at MIT are maybe
+at this stage are not
+
+that worried of heart disease.
+
+Many of you are probably not
+worried yet about having
+
+children with birth defects,
+but maybe some of you are
+
+worried about mental recognition
+of particular
+
+facts for exams coming up, and
+so you may be concerned about
+
+B12 to keep sharp mentally.
+
+So, where do you get vitamin
+B12 and folic acid in your
+
+diet and how is it reduced?
+
+So let's first consider where
+you get it in your diet.
+
+So, does anyone know where you
+get vitamin B12 in your diet?
+
+I heard vegetables.
+
+Anyone agree with vegetables?
+
+I didn't say if anyone liked
+vegetables, does anyone agree
+
+that vitamin B12 come
+from vegetables.
+
+It doesn't.
+
+Where does vitamin
+B12 come from?
+
+So, red meat is a good source of
+vitamin B12, all meat is a
+
+good source the vitamin B12.
+
+Plants do not use vitamin
+B12 at all.
+
+So, people who are vegan are
+in trouble in terms of how
+
+much vitamin B12 they get, but
+luckily there are vitamin
+
+tablets that can help
+take care of this.
+
+So meat is really the best
+source of vitamin B12.
+
+So, I'm always looking for good
+references to vitamin
+
+B12, and I saw one recently.
+
+Has anyone seen the HBO
+series, True Blood.
+
+One person.
+
+OK, if you watch that, you will
+notice that if you date a
+
+vampire, you have to make sure
+you get extra vitamin B12, and
+
+that Sookie, of True Blood is
+taking vitamin B12 tablets
+
+just to be on the safe side.
+
+So, vitamin B12.
+
+What about folic acid?
+
+Anyone know where you
+get folic acid?
+
+In the fall, what happens,
+people say let's go outside
+
+and look at the trees or look
+at the pretty foliage.
+
+Any suggestion of where
+folic acid comes from?
+
+Oh, wait a minute.
+
+I was at a meeting once where
+there was a whole lecture
+
+about how Norwegian beer was the
+best source of folic acid,
+
+and it was, perhaps, not
+coincidentally reported by
+
+Norwegian scientists.
+
+They would not vouch for any
+other kinds, but some -- but
+
+it does come from barleys,
+vegetables,
+
+this kind of thing.
+
+So, here is a secret
+for healthy diet.
+
+Have some of you seen the orange
+juice commercial that
+
+says "Drink orange juice, it's
+good for your heart." That's
+
+because of this, so that
+actually is potentially true.
+
+So you get a lot of folic acid
+in orange juice, and folic
+
+acid is, in fact, good
+for your heart.
+
+So, who would have guessed,
+some of the claims are
+
+actually true.
+
+All right, but we still have a
+problem, we still need to know
+
+how its reduced in the body.
+
+And so we're going to come back
+to that at the end of the
+
+lecture and answer that
+if we get that far.
+
+All right, so we need to do a
+couple more things first so
+
+everyone can finish their
+problem-sets, and the things
+
+we're going to do is we're
+going to look adding and
+
+subtracting 1/2 cell reactions,
+and then get to one
+
+of my favorite things, which
+is the Nernst equation.
+
+All right.
+
+So, some of you may have
+encountered this problem on
+
+the problem-set already.
+
+Suppose you need you know a
+standard reduction potential
+
+and it's not given to you in
+the back of the book, but
+
+other things are given to you
+in the back of the book.
+
+Can you calculate the
+thing you need
+
+from related equations?
+
+So suppose you really want to
+know the reduction couple for
+
+copper 2 going to copper 1.
+
+But that's not given.
+
+You find copper 2 with two
+electrons going to copper 0,
+
+and you find copper 0 going
+to copper plus 1 with one
+
+electron, and you'll realize
+that if you combine these
+
+equations, you'll get
+the desired one.
+
+So if you add these together,
+you have copper 2 with one
+
+electron, one electron
+cancels out here.
+
+The copper solids cancel
+out and you're left
+
+with copper plus 1.
+
+So you add these together,
+and you know the
+
+potentials for these.
+
+How do you get the standard
+potential for the thing that
+
+you've come up with, for
+the sum of those?
+
+So, as someone actually asked
+me before class, you have to
+
+go back to free energy, and you
+do, but I'm going to drive
+
+an equation so that you don't
+have to go all the way back,
+
+but this is, in fact, how you
+do the problem, you think
+
+about the different
+free energies.
+
+So, the new reaction, the new
+delta g for that new reaction
+
+will be equal to the delta g
+knot for the reduction minus
+
+the oxidation reaction here.
+
+But we can substitute for
+delta g this minus n,
+
+Faraday's constant times our
+reduction potential, and put
+
+it in to this equation here.
+
+And so we have it for the new
+reaction, and then the 2
+
+reactions that we're
+adding together.
+
+So we have Faraday's constant in
+common, so that's going to
+
+cancel out.
+
+And we can also move n 3 to
+the other side, because we
+
+want to solve for this new e
+value, this new standard
+
+reduction potential.
+
+And so that's going to be equal
+to the number of moles
+
+that are involved in the
+reaction that's the reduction
+
+times its reduction potential
+minus the number of moles
+
+involved in the oxidation
+reaction with its reduction
+
+potential, and then the number
+of moles for the reaction that
+
+-- this new reaction
+in question.
+
+So we can use, then, this
+equation to look for a 1/2
+
+cell reaction that is the sum
+of two other reactions.
+
+So let's go and use that
+equation, then.
+
+So here we have the known values
+-- we know the couple
+
+for copper 2 to copper 0, we
+know the couple for copper 1
+
+to copper solid, and this
+is what we want to know.
+
+So we can use this equation.
+
+Which of these reactions is the
+reduction, what value am I
+
+going to put in here?
+
+Which of these goes into
+the reduction?
+
+Which of these is a reduction
+reaction?
+
+Yeah.
+
+And how many moles of electrons
+are involved?
+
+So, we put in 2 times 0 .
+
+3 4 0 volts, and then over here
+in the oxidation, there's
+
+one electron involved, and we
+put in our other potential.
+
+So 1 times 0 .
+
+5 2 2.
+
+And what are the number of moles
+of electrons for our
+
+desired, final reaction?
+
+1.
+
+And so, then we can do the
+math and come up with an
+
+answer of 0 .
+
+1 5 8 volts.
+
+And so now we've just come
+up with a new reduction
+
+potential, we've calculated a
+new reduction potential for
+
+this 1/2 cell reaction
+right here.
+
+So, this equation will be given
+to you on an exam and
+
+all you need to do is
+know how to use it.
+
+So we've calculated now the
+standard reduction potential
+
+for copper 2 to copper plus 1.
+
+So, just a little note about
+when you're going to use this
+
+and when you're going to use
+the other equation that I
+
+showed you.
+
+So, if we're talking about a
+whole electric chemical cell,
+
+the number of moles that are
+released at the anode are
+
+going to equal the number of
+moles taken up at the cathode
+
+and be the number of
+moles involved
+
+in the overall equation.
+
+So this equation is not
+necessary, and for a full
+
+electric chemical cell, we're
+going to use the equation that
+
+I gave you before for this delta
+e nought for the cell,
+
+so we just use this.
+
+But if it's not a whole electric
+chemical cell you're
+
+talking about, if you're talking
+about calculating a
+
+1/2 cell potential, then you
+need to use this equation.
+
+Both of these equations will
+be given to you on
+
+sheets for the exam.
+
+This one's for an electric
+chemical cell, this one's for
+
+calculating a 1/2
+cell potential.
+
+So again, if it's 1/2 cell
+potential, you want to use
+
+this equation.
+
+OK, so now the Nernst
+equation.
+
+So, some of you may have
+encountered in your life where
+
+you go to turn something on
+and you discover that the
+
+battery is dead.
+
+So, an exhausted battery is
+a sign that your chemical
+
+reaction has reached
+equilibrium.
+
+At equilibrium, you're going
+to have a zero difference
+
+potential across your
+electrodes, and the battery
+
+will be not useful to
+you at that point.
+
+So, if you -- instead of getting
+annoyed next time you
+
+have a dead battery, you can
+think about all, ah, it's
+
+finally reached equilibrium.
+
+So, we need to think about,
+then, to think about how these
+
+cell reactions are happening,
+how the potential is going to
+
+change with the composition of
+the ingredients in those
+
+electrochemical cells.
+
+So, we know something about
+equilibrium and components of
+
+reactions again.
+
+So this is a nice lecture to
+give coming up with a week
+
+before the exam, because now
+we're going back and reviewing
+
+the first material on the exam
+from chemical equilibrium.
+
+So, we know that delta g is
+going to change as the
+
+components change until
+equilibrium is reached.
+
+And when equilibrium is reached
+our delta g is going
+
+to be equal to zero.
+
+Before equilibrium is reached,
+delta g will depend on the
+
+delta g nought for the equation,
+r t and the natural
+
+log of q, where q is what?
+
+What's q?
+
+The reaction quotient.
+
+So we saw this before and we're
+back to using it again.
+
+So what do we know about the
+relationship between delta g
+
+nought and delta e?
+
+We know that delta g nought is
+equal to minus n, moles of
+
+electrons times Faraday's
+constant times delta e nought.
+
+So, we can combine some
+things around.
+
+So we can take our equation
+that we saw in chemical
+
+equilibrium and substitute in
+values that are related to
+
+standard reduction potentials.
+
+So we can put in, for this delta
+g, minus n Faraday's
+
+constant times the delta e.
+
+And for delta g nought, we put
+in the same thing but now we
+
+have delta e nought.
+
+And we have r t, gas constant
+times temperature times the
+
+natural log of q, our
+reaction quotient.
+
+Now we can divide both sides
+by n and Faraday's constant
+
+and we come up with the
+Nernst equation.
+
+So the Nernst equation tells us
+the potential for a cell at
+
+any given time, at any given
+component of ingredients in
+
+the cell, any amounts of, say,
+your zinc plus 2, compared to
+
+the standard potential for that
+cell, which you're going
+
+to calculate from your standard
+reduction potentials
+
+in the table, and then you have
+this term, gas constant
+
+times temperature, number of
+moles of electrons involved,
+
+Faraday's constant, and you need
+to know q, the particular
+
+composition of the cell
+at that given time.
+
+So, just a hint in doing Nernst
+equation problems, if
+
+you're given a problem and it's
+giving you concentrations
+
+of things at a particular time,
+that should be a clue
+
+that the Nernst equation is
+going to be what you're going
+
+to want to use here.
+
+So, let let's look
+at an example.
+
+Say we have a -- we want to
+calculate the cell potential
+
+at a given time at 25 degrees,
+and we know our zinc plus 2
+
+ions or 0 .
+
+1 0 molar and copper
+2 ions are 0 .
+
+0 0 1 0 molar, and this is the
+equation for that cell.
+
+So we can look up, again, our
+values in the table, and the
+
+first thing we're going to do,
+if we're going to use to
+
+Nernst equation, is to calculate
+the standard
+
+potential for that particular
+cell, and here are the values
+
+from the table, and why don't
+you go ahead and calculate
+
+that for me.
+
+All right, so let's just take
+10 more seconds on that.
+
+OK, so let's see if we can get
+into the 90's pretty soon,
+
+because we should be
+able to do that for
+
+this particular one.
+
+All right, let's go back to
+the presentation here.
+
+So it was actually, this
+was pretty easy.
+
+I didn't actually mean for these
+two things to show up,
+
+to help you out of what the
+reaction at the cathode and
+
+the anode was, so that
+was an easier
+
+question than I had intended.
+
+So, first you need to think
+about if you're given an
+
+equation here, what's happening
+at the cathode,
+
+what's happening at the anode.
+
+As it's written, you can look
+and see so copper plus 2 is
+
+going to copper solid, zinc
+solid's going to zinc plus 2,
+
+so you can think about which is
+the cathode reaction, which
+
+is the anode, which has a
+reduction, which has an
+
+oxidation going on, and then
+once you know which couples
+
+you're talking about, then you
+can plug in your values.
+
+So, at the cathode, we're going
+from copper plus 2 to
+
+copper solid.
+
+We put in our standard reduction
+potential, using the
+
+equation we have a minus, and
+then the standard reduction
+
+potential at the anode, so we
+have the oxidation from zinc
+
+solid to zinc plus 2, and we
+put in this value and we
+
+calculate the number here.
+
+So then, we have that, we
+also need to know q.
+
+So why don't you tell
+me what q is now?
+
+OK, let's just do 10 more
+seconds on this.
+
+OK.
+
+So here, if we go back, q is
+going to be equal to products
+
+over reactants, except things
+that are solids are not are
+
+not changing during
+the equilibrium so
+
+we leave those out.
+
+So it's going to be
+concentration of zinc plus 2
+
+over the concentration of
+copper, which gives you a
+
+value of 1 .
+
+0 times 10 to the 2.
+
+So, just a review of q, if you
+need help calculating q's,
+
+we're going to have to extra
+problems for the exam coming
+
+up to be posted on Friday.
+
+So, this'll be used
+in several units.
+
+So then you need to know n, and
+then we have everything to
+
+go back to the Nernst
+equation.
+
+So how many moles of electrons
+are involved in this?
+
+2.
+
+Sometimes it's not so obvious,
+so this can trick people, so
+
+make sure that you pay
+attention to this.
+
+This one is a pretty
+obvious one.
+
+All right, now we have
+everything that we can put in.
+
+You calculated the standard
+potential for the cell, you
+
+calculated q, and you told
+me how many moles of
+
+electrons there are.
+
+So we can go and put this in.
+
+So we calculated positive 1 .
+
+0 3 volts minus the gas
+constant times the
+
+temperature, it was at room
+temperature, natural log of q.
+
+We had two moles of electrons
+and Faraday's constant here.
+
+And now if we do the math,
+this whole term
+
+comes out to 0 .
+
+0 5 9 2 volts, and we get our
+answer, which is a positive
+
+number there.
+
+So, just a note about
+units and constants.
+
+Where did volts come
+from here?
+
+Well, the moles canceled out,
+and the kelvin canceled out,
+
+and we are left with joules per
+Coulomb, and conveniently
+
+for us, joules per Coulomb
+is a volt.
+
+So, all our units add up here.
+
+And just a note about a
+significant figures in doing
+
+these problems, the Nernst
+equation, boy, significant
+
+figure fun.
+
+If you want to make sure
+you know significant
+
+figures, here you go.
+
+Significant figure rules for
+logs, we have significant
+
+figure rules for multiplication
+and division,
+
+and then significant figure
+rules for subtraction.
+
+So, one equation gives you
+every type of significant
+
+figure rule.
+
+So, that can be a lot
+of fun as well.
+
+All right, but I'm going to try
+to make it easier for you
+
+on an exam and avoid
+some math mistakes.
+
+All the problems I'm going
+to give you are at room
+
+temperature.
+
+And so, the gas constant is a
+constant, temperature for
+
+these problems is going to be
+a constant, always room
+
+temperature, Faraday's constant
+is a constant.
+
+So, all of these, I'm going to
+give you the value that they
+
+all add up to, and if you use
+log instead of natural log,
+
+there's this value as well.
+
+So, these will be given to you
+on an exam, so you'll see
+
+these equations on the exam as
+well and you can use them.
+
+So, this is for natural log,
+this is for log, so we are not
+
+going to test your ability to
+multiply room temperature
+
+times the gas constant divided
+by Faraday's constant.
+
+So that's going to make it a
+little easier in doing these
+
+problems.
+
+All right, so what about
+at equilibrium.
+
+What does q equal
+at equilibrium?
+
+So, q equals k at equilibrium.
+
+What does delta g equal
+at equilibrium?
+
+Zero.
+
+And so that means that we knew
+before, from this equation,
+
+when this is equal to zero, then
+delta g knot equals minus
+
+r t, natural log of k, so q
+equals k at equilibrium.
+
+And so we had this equation
+that we used before.
+
+We now have this equation, so
+here it related delta g knot
+
+to the equilibrium constant,
+here we relate delta g nought
+
+to delta e nought And
+so, I think you
+
+can see what's coming.
+
+We are going to relate these two
+together and come up with
+
+an expression where are you
+can calculate equilibrium
+
+constants from standard
+reduction potentials.
+
+So, you may be asked
+to do this as well.
+
+So everything in these
+units are, in fact,
+
+related to each other.
+
+And the only thing we have left
+today, the answer to this
+
+question about how B12 is
+reduced in the body.
+
+So, you're just going to have
+to wait to find out, don't
+
+worry you won't get heart
+disease between now and
+
+Friday, and I'll let
+you know how it all
+
+works out on Friday.
\ No newline at end of file
diff --git a/srxexLishgY.txt b/srxexLishgY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..536bb2524b461fa6403d64492b039e072617df8e
--- /dev/null
+++ b/srxexLishgY.txt
@@ -0,0 +1,7296 @@
+align:start position:0%
+ 
+Okay, this lecture is like the beginning
+
+ align:start position:0%
+Okay, this lecture is like the beginning
+ 
+
+ align:start position:0%
+Okay, this lecture is like the beginning
+of the second half of this course
+
+ align:start position:0%
+of the second half of this course
+ 
+
+ align:start position:0%
+of the second half of this course
+because up to now we paid a lot of
+
+ align:start position:0%
+because up to now we paid a lot of
+ 
+
+ align:start position:0%
+because up to now we paid a lot of
+attention to rectangular
+
+ align:start position:0%
+attention to rectangular
+ 
+
+ align:start position:0%
+attention to rectangular
+matrices.
+
+ align:start position:0%
+matrices.
+ 
+
+ align:start position:0%
+matrices.
+Now concentrating on square matrices. So
+
+ align:start position:0%
+Now concentrating on square matrices. So
+ 
+
+ align:start position:0%
+Now concentrating on square matrices. So
+we've got two big topics. the
+
+ align:start position:0%
+we've got two big topics. the
+ 
+
+ align:start position:0%
+we've got two big topics. the
+determinant of a square matrix. So this
+
+ align:start position:0%
+determinant of a square matrix. So this
+ 
+
+ align:start position:0%
+determinant of a square matrix. So this
+is the first lecture in that new chapter
+
+ align:start position:0%
+is the first lecture in that new chapter
+ 
+
+ align:start position:0%
+is the first lecture in that new chapter
+on determinants and the reason the big
+
+ align:start position:0%
+on determinants and the reason the big
+ 
+
+ align:start position:0%
+on determinants and the reason the big
+reason we need the determinants is for
+
+ align:start position:0%
+reason we need the determinants is for
+ 
+
+ align:start position:0%
+reason we need the determinants is for
+the igen values. So this is really
+
+ align:start position:0%
+the igen values. So this is really
+ 
+
+ align:start position:0%
+the igen values. So this is really
+determinants and igen values the next
+
+ align:start position:0%
+determinants and igen values the next
+ 
+
+ align:start position:0%
+determinants and igen values the next
+big big chunk of
+
+ align:start position:0%
+big big chunk of
+ 
+
+ align:start position:0%
+big big chunk of
+1806. Okay. So the determinant is a
+
+ align:start position:0%
+1806. Okay. So the determinant is a
+ 
+
+ align:start position:0%
+1806. Okay. So the determinant is a
+number associated with every square
+
+ align:start position:0%
+number associated with every square
+ 
+
+ align:start position:0%
+number associated with every square
+matrix. So every square matrix has this
+
+ align:start position:0%
+matrix. So every square matrix has this
+ 
+
+ align:start position:0%
+matrix. So every square matrix has this
+number associated with it called its
+
+ align:start position:0%
+number associated with it called its
+ 
+
+ align:start position:0%
+number associated with it called its
+determinant. Uh I'll I'll often write it
+
+ align:start position:0%
+determinant. Uh I'll I'll often write it
+ 
+
+ align:start position:0%
+determinant. Uh I'll I'll often write it
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+deta or often also I'll write it as
+
+ align:start position:0%
+deta or often also I'll write it as
+ 
+
+ align:start position:0%
+deta or often also I'll write it as
+uh a with vertical bars. So that's going
+
+ align:start position:0%
+uh a with vertical bars. So that's going
+ 
+
+ align:start position:0%
+uh a with vertical bars. So that's going
+to mean the determinant of the matrix.
+
+ align:start position:0%
+to mean the determinant of the matrix.
+ 
+
+ align:start position:0%
+to mean the determinant of the matrix.
+That's going to mean this one like magic
+
+ align:start position:0%
+That's going to mean this one like magic
+ 
+
+ align:start position:0%
+That's going to mean this one like magic
+number. Well, one number can't tell
+
+ align:start position:0%
+number. Well, one number can't tell
+ 
+
+ align:start position:0%
+number. Well, one number can't tell
+you what the whole matrix
+
+ align:start position:0%
+you what the whole matrix
+ 
+
+ align:start position:0%
+you what the whole matrix
+was, but this one number just packs in
+
+ align:start position:0%
+was, but this one number just packs in
+ 
+
+ align:start position:0%
+was, but this one number just packs in
+as much information as possible into a
+
+ align:start position:0%
+as much information as possible into a
+ 
+
+ align:start position:0%
+as much information as possible into a
+single number. And of course the one
+
+ align:start position:0%
+single number. And of course the one
+ 
+
+ align:start position:0%
+single number. And of course the one
+fact that you've seen before and we have
+
+ align:start position:0%
+fact that you've seen before and we have
+ 
+
+ align:start position:0%
+fact that you've seen before and we have
+to see it again
+
+ align:start position:0%
+to see it again
+ 
+
+ align:start position:0%
+to see it again
+is the matrix is invertible when the
+
+ align:start position:0%
+is the matrix is invertible when the
+ 
+
+ align:start position:0%
+is the matrix is invertible when the
+determinant is not zero. The matrix is
+
+ align:start position:0%
+determinant is not zero. The matrix is
+ 
+
+ align:start position:0%
+determinant is not zero. The matrix is
+singular when the determinant is zero.
+
+ align:start position:0%
+singular when the determinant is zero.
+ 
+
+ align:start position:0%
+singular when the determinant is zero.
+So that's the determinant will be a test
+
+ align:start position:0%
+So that's the determinant will be a test
+ 
+
+ align:start position:0%
+So that's the determinant will be a test
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+invertability. But the determin's got a
+
+ align:start position:0%
+invertability. But the determin's got a
+ 
+
+ align:start position:0%
+invertability. But the determin's got a
+lot more to it than that. So let me
+
+ align:start position:0%
+lot more to it than that. So let me
+ 
+
+ align:start position:0%
+lot more to it than that. So let me
+start. Okay. Now the question is how to
+
+ align:start position:0%
+start. Okay. Now the question is how to
+ 
+
+ align:start position:0%
+start. Okay. Now the question is how to
+start. Do I give you a big formula for
+
+ align:start position:0%
+start. Do I give you a big formula for
+ 
+
+ align:start position:0%
+start. Do I give you a big formula for
+the determinant all in one gulp? I don't
+
+ align:start position:0%
+the determinant all in one gulp? I don't
+ 
+
+ align:start position:0%
+the determinant all in one gulp? I don't
+think so. That big formula has got too
+
+ align:start position:0%
+think so. That big formula has got too
+ 
+
+ align:start position:0%
+think so. That big formula has got too
+much packed in it. I would
+
+ align:start position:0%
+much packed in it. I would
+ 
+
+ align:start position:0%
+much packed in it. I would
+rather start with
+
+ align:start position:0%
+rather start with
+ 
+
+ align:start position:0%
+rather start with
+three properties of the determinant.
+
+ align:start position:0%
+three properties of the determinant.
+ 
+
+ align:start position:0%
+three properties of the determinant.
+Three three properties that it has. And
+
+ align:start position:0%
+Three three properties that it has. And
+ 
+
+ align:start position:0%
+Three three properties that it has. And
+and let me tell you property one. The
+
+ align:start position:0%
+and let me tell you property one. The
+ 
+
+ align:start position:0%
+and let me tell you property one. The
+determinant of the identity is one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I I wish the other two properties
+
+ align:start position:0%
+Okay, I I wish the other two properties
+ 
+
+ align:start position:0%
+Okay, I I wish the other two properties
+were as easy to tell you as that. But
+
+ align:start position:0%
+were as easy to tell you as that. But
+ 
+
+ align:start position:0%
+were as easy to tell you as that. But
+actually the second property is pretty
+
+ align:start position:0%
+actually the second property is pretty
+ 
+
+ align:start position:0%
+actually the second property is pretty
+straightforward too. And then once we
+
+ align:start position:0%
+straightforward too. And then once we
+ 
+
+ align:start position:0%
+straightforward too. And then once we
+get the
+
+ align:start position:0%
+get the
+ 
+
+ align:start position:0%
+get the
+third, we will actually have the
+
+ align:start position:0%
+third, we will actually have the
+ 
+
+ align:start position:0%
+third, we will actually have the
+determinant. Those three properties
+
+ align:start position:0%
+determinant. Those three properties
+ 
+
+ align:start position:0%
+determinant. Those three properties
+define the determinant and we can then
+
+ align:start position:0%
+define the determinant and we can then
+ 
+
+ align:start position:0%
+define the determinant and we can then
+we can figure out well what is the
+
+ align:start position:0%
+we can figure out well what is the
+ 
+
+ align:start position:0%
+we can figure out well what is the
+determinant? What's a formula for it?
+
+ align:start position:0%
+determinant? What's a formula for it?
+ 
+
+ align:start position:0%
+determinant? What's a formula for it?
+Okay, can I tell you the second
+
+ align:start position:0%
+Okay, can I tell you the second
+ 
+
+ align:start position:0%
+Okay, can I tell you the second
+property? This that just like scales the
+
+ align:start position:0%
+property? This that just like scales the
+ 
+
+ align:start position:0%
+property? This that just like scales the
+determinant so that the identity matrix
+
+ align:start position:0%
+determinant so that the identity matrix
+ 
+
+ align:start position:0%
+determinant so that the identity matrix
+has determinant one. Now the second
+
+ align:start position:0%
+has determinant one. Now the second
+ 
+
+ align:start position:0%
+has determinant one. Now the second
+property is what happens if you exchange
+
+ align:start position:0%
+property is what happens if you exchange
+ 
+
+ align:start position:0%
+property is what happens if you exchange
+two rows of a matrix? What happens to
+
+ align:start position:0%
+two rows of a matrix? What happens to
+ 
+
+ align:start position:0%
+two rows of a matrix? What happens to
+the determinant? So, so property two is
+
+ align:start position:0%
+the determinant? So, so property two is
+ 
+
+ align:start position:0%
+the determinant? So, so property two is
+exchange
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rows. Reverse the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sign of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determinant. A lot of plus and minus
+
+ align:start position:0%
+determinant. A lot of plus and minus
+ 
+
+ align:start position:0%
+determinant. A lot of plus and minus
+signs. I even wrote here plus and minus
+
+ align:start position:0%
+signs. I even wrote here plus and minus
+ 
+
+ align:start position:0%
+signs. I even wrote here plus and minus
+signs because this is like that's what
+
+ align:start position:0%
+signs because this is like that's what
+ 
+
+ align:start position:0%
+signs because this is like that's what
+you have to pay attention to in the
+
+ align:start position:0%
+you have to pay attention to in the
+ 
+
+ align:start position:0%
+you have to pay attention to in the
+formulas and properties of determinants.
+
+ align:start position:0%
+formulas and properties of determinants.
+ 
+
+ align:start position:0%
+formulas and properties of determinants.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+that you see what I mean by a property
+
+ align:start position:0%
+that you see what I mean by a property
+ 
+
+ align:start position:0%
+that you see what I mean by a property
+here. I I I'm I haven't yet told you
+
+ align:start position:0%
+here. I I I'm I haven't yet told you
+ 
+
+ align:start position:0%
+here. I I I'm I haven't yet told you
+what the determinant is but whatever it
+
+ align:start position:0%
+what the determinant is but whatever it
+ 
+
+ align:start position:0%
+what the determinant is but whatever it
+is if I exchange two rows to get a
+
+ align:start position:0%
+is if I exchange two rows to get a
+ 
+
+ align:start position:0%
+is if I exchange two rows to get a
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+matrix that reverses the sign of the
+
+ align:start position:0%
+matrix that reverses the sign of the
+ 
+
+ align:start position:0%
+matrix that reverses the sign of the
+determinant. And so now
+
+ align:start position:0%
+determinant. And so now
+ 
+
+ align:start position:0%
+determinant. And so now
+actually what matrices do we now know
+
+ align:start position:0%
+actually what matrices do we now know
+ 
+
+ align:start position:0%
+actually what matrices do we now know
+the determinant of from from one and
+
+ align:start position:0%
+the determinant of from from one and
+ 
+
+ align:start position:0%
+the determinant of from from one and
+two I now know the determinant well I
+
+ align:start position:0%
+two I now know the determinant well I
+ 
+
+ align:start position:0%
+two I now know the determinant well I
+certainly know the determinant of the
+
+ align:start position:0%
+certainly know the determinant of the
+ 
+
+ align:start position:0%
+certainly know the determinant of the
+identity matrix and now I know the
+
+ align:start position:0%
+identity matrix and now I know the
+ 
+
+ align:start position:0%
+identity matrix and now I know the
+determinant of every other matrix that
+
+ align:start position:0%
+determinant of every other matrix that
+ 
+
+ align:start position:0%
+determinant of every other matrix that
+comes from row
+
+ align:start position:0%
+comes from row
+ 
+
+ align:start position:0%
+comes from row
+exchanges from the identity still. So
+
+ align:start position:0%
+exchanges from the identity still. So
+ 
+
+ align:start position:0%
+exchanges from the identity still. So
+what matrices have I got at this
+
+ align:start position:0%
+what matrices have I got at this
+ 
+
+ align:start position:0%
+what matrices have I got at this
+point? the permutations. Right? At this
+
+ align:start position:0%
+point? the permutations. Right? At this
+ 
+
+ align:start position:0%
+point? the permutations. Right? At this
+point, I know every permutation matrix.
+
+ align:start position:0%
+point, I know every permutation matrix.
+ 
+
+ align:start position:0%
+point, I know every permutation matrix.
+So now I'm saying the determinant of a
+
+ align:start position:0%
+So now I'm saying the determinant of a
+ 
+
+ align:start position:0%
+So now I'm saying the determinant of a
+permutation matrix is one or minus
+
+ align:start position:0%
+permutation matrix is one or minus
+ 
+
+ align:start position:0%
+permutation matrix is one or minus
+one. One or minus one depending whether
+
+ align:start position:0%
+one. One or minus one depending whether
+ 
+
+ align:start position:0%
+one. One or minus one depending whether
+the number of exchanges was
+
+ align:start position:0%
+the number of exchanges was
+ 
+
+ align:start position:0%
+the number of exchanges was
+even or the number of exchanges was odd.
+
+ align:start position:0%
+even or the number of exchanges was odd.
+ 
+
+ align:start position:0%
+even or the number of exchanges was odd.
+So this is the determinant of a
+
+ align:start position:0%
+So this is the determinant of a
+ 
+
+ align:start position:0%
+So this is the determinant of a
+permutation. Now P is back to standing
+
+ align:start position:0%
+permutation. Now P is back to standing
+ 
+
+ align:start position:0%
+permutation. Now P is back to standing
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+permutation. Okay. So if if I I could
+
+ align:start position:0%
+permutation. Okay. So if if I I could
+ 
+
+ align:start position:0%
+permutation. Okay. So if if I I could
+carry on this board, I could like do the
+
+ align:start position:0%
+carry on this board, I could like do the
+ 
+
+ align:start position:0%
+carry on this board, I could like do the
+2x twos. So property one tells me that
+
+ align:start position:0%
+2x twos. So property one tells me that
+ 
+
+ align:start position:0%
+2x twos. So property one tells me that
+this 2x two matrix Oh, I better write
+
+ align:start position:0%
+this 2x two matrix Oh, I better write
+ 
+
+ align:start position:0%
+this 2x two matrix Oh, I better write
+absolute I mean I better write vertical
+
+ align:start position:0%
+absolute I mean I better write vertical
+ 
+
+ align:start position:0%
+absolute I mean I better write vertical
+bars not brackets for that
+
+ align:start position:0%
+bars not brackets for that
+ 
+
+ align:start position:0%
+bars not brackets for that
+determinant. Property one said in the 2x
+
+ align:start position:0%
+determinant. Property one said in the 2x
+ 
+
+ align:start position:0%
+determinant. Property one said in the 2x
+two case that this matrix has
+
+ align:start position:0%
+two case that this matrix has
+ 
+
+ align:start position:0%
+two case that this matrix has
+determinant
+
+ align:start position:0%
+determinant
+ 
+
+ align:start position:0%
+determinant
+one. Property two tells me that this
+
+ align:start position:0%
+one. Property two tells me that this
+ 
+
+ align:start position:0%
+one. Property two tells me that this
+matrix has
+
+ align:start position:0%
+matrix has
+ 
+
+ align:start position:0%
+matrix has
+determinant what negative
+
+ align:start position:0%
+determinant what negative
+ 
+
+ align:start position:0%
+determinant what negative
+1. This is like 2x two. And now I
+
+ align:start position:0%
+1. This is like 2x two. And now I
+ 
+
+ align:start position:0%
+1. This is like 2x two. And now I
+finally want to get well ultimately I
+
+ align:start position:0%
+finally want to get well ultimately I
+ 
+
+ align:start position:0%
+finally want to get well ultimately I
+want to get to a the formula that we all
+
+ align:start position:0%
+want to get to a the formula that we all
+ 
+
+ align:start position:0%
+want to get to a the formula that we all
+know.
+
+ align:start position:0%
+know.
+ 
+
+ align:start position:0%
+know.
+Let me put that way over here. That the
+
+ align:start position:0%
+Let me put that way over here. That the
+ 
+
+ align:start position:0%
+Let me put that way over here. That the
+determinant of a general 2x two
+
+ align:start position:0%
+determinant of a general 2x two
+ 
+
+ align:start position:0%
+determinant of a general 2x two
+is a d minus b c.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I I I'm going to leave that up
+
+ align:start position:0%
+Okay, I I I'm going to leave that up
+ 
+
+ align:start position:0%
+Okay, I I I'm going to leave that up
+like as one as as the 2 by two case that
+
+ align:start position:0%
+like as one as as the 2 by two case that
+ 
+
+ align:start position:0%
+like as one as as the 2 by two case that
+we already know so that every
+
+ align:start position:0%
+we already know so that every
+ 
+
+ align:start position:0%
+we already know so that every
+property I can like check that it's
+
+ align:start position:0%
+property I can like check that it's
+ 
+
+ align:start position:0%
+property I can like check that it's
+correct for 2 by
+
+ align:start position:0%
+correct for 2 by
+ 
+
+ align:start position:0%
+correct for 2 by
+twos. But the whole point of these
+
+ align:start position:0%
+twos. But the whole point of these
+ 
+
+ align:start position:0%
+twos. But the whole point of these
+properties is that they're going to give
+
+ align:start position:0%
+properties is that they're going to give
+ 
+
+ align:start position:0%
+properties is that they're going to give
+me a formula for n byn. That's the whole
+
+ align:start position:0%
+me a formula for n byn. That's the whole
+ 
+
+ align:start position:0%
+me a formula for n byn. That's the whole
+point. they're going to give me this
+
+ align:start position:0%
+point. they're going to give me this
+ 
+
+ align:start position:0%
+point. they're going to give me this
+number that that's a test for
+
+ align:start position:0%
+number that that's a test for
+ 
+
+ align:start position:0%
+number that that's a test for
+invertability and other great properties
+
+ align:start position:0%
+invertability and other great properties
+ 
+
+ align:start position:0%
+invertability and other great properties
+for any size matrix. Okay, now you see
+
+ align:start position:0%
+for any size matrix. Okay, now you see
+ 
+
+ align:start position:0%
+for any size matrix. Okay, now you see
+I'm
+
+ align:start position:0%
+I'm
+ 
+
+ align:start position:0%
+I'm
+like slowing down because property three
+
+ align:start position:0%
+like slowing down because property three
+ 
+
+ align:start position:0%
+like slowing down because property three
+is the key property. Property three is
+
+ align:start position:0%
+is the key property. Property three is
+ 
+
+ align:start position:0%
+is the key property. Property three is
+the key property. And can I somehow
+
+ align:start position:0%
+the key property. And can I somehow
+ 
+
+ align:start position:0%
+the key property. And can I somehow
+describe it? Maybe I'll separate it into
+
+ align:start position:0%
+describe it? Maybe I'll separate it into
+ 
+
+ align:start position:0%
+describe it? Maybe I'll separate it into
+3 A and 3B.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Property 3A says that if I have that if
+
+ align:start position:0%
+Property 3A says that if I have that if
+ 
+
+ align:start position:0%
+Property 3A says that if I have that if
+I multiply one of the rows, say the
+
+ align:start position:0%
+I multiply one of the rows, say the
+ 
+
+ align:start position:0%
+I multiply one of the rows, say the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+row
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by a number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T. I'm going to erase that. That that
+
+ align:start position:0%
+T. I'm going to erase that. That that
+ 
+
+ align:start position:0%
+T. I'm going to erase that. That that
+that's like what I'm headed for, but I'm
+
+ align:start position:0%
+that's like what I'm headed for, but I'm
+ 
+
+ align:start position:0%
+that's like what I'm headed for, but I'm
+not there yet. Uh that's the one we
+
+ align:start position:0%
+not there yet. Uh that's the one we
+ 
+
+ align:start position:0%
+not there yet. Uh that's the one we
+know. and you'll see that it's checked
+
+ align:start position:0%
+know. and you'll see that it's checked
+ 
+
+ align:start position:0%
+know. and you'll see that it's checked
+out by by each uh
+
+ align:start position:0%
+out by by each uh
+ 
+
+ align:start position:0%
+out by by each uh
+property. Okay. Now, what's so this is
+
+ align:start position:0%
+property. Okay. Now, what's so this is
+ 
+
+ align:start position:0%
+property. Okay. Now, what's so this is
+for any
+
+ align:start position:0%
+for any
+ 
+
+ align:start position:0%
+for any
+matrix? For any matrix, if I multiply
+
+ align:start position:0%
+matrix? For any matrix, if I multiply
+ 
+
+ align:start position:0%
+matrix? For any matrix, if I multiply
+one row by T and leave the other row or
+
+ align:start position:0%
+one row by T and leave the other row or
+ 
+
+ align:start position:0%
+one row by T and leave the other row or
+or other N minus one rows alone, what
+
+ align:start position:0%
+or other N minus one rows alone, what
+ 
+
+ align:start position:0%
+or other N minus one rows alone, what
+happens to the
+
+ align:start position:0%
+happens to the
+ 
+
+ align:start position:0%
+happens to the
+determinant? The factor T comes
+
+ align:start position:0%
+determinant? The factor T comes
+ 
+
+ align:start position:0%
+determinant? The factor T comes
+out. It's T times this determinant.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's not hard. I shouldn't have made a
+
+ align:start position:0%
+That's not hard. I shouldn't have made a
+ 
+
+ align:start position:0%
+That's not hard. I shouldn't have made a
+big deal out of property 3A. And 3B is
+
+ align:start position:0%
+big deal out of property 3A. And 3B is
+ 
+
+ align:start position:0%
+big deal out of property 3A. And 3B is
+that if is is if I keep I'm always
+
+ align:start position:0%
+that if is is if I keep I'm always
+ 
+
+ align:start position:0%
+that if is is if I keep I'm always
+keeping this second row the same or the
+
+ align:start position:0%
+keeping this second row the same or the
+ 
+
+ align:start position:0%
+keeping this second row the same or the
+last n minus one rows are all staying
+
+ align:start position:0%
+last n minus one rows are all staying
+ 
+
+ align:start position:0%
+last n minus one rows are all staying
+the same. I'm just working I'm just
+
+ align:start position:0%
+the same. I'm just working I'm just
+ 
+
+ align:start position:0%
+the same. I'm just working I'm just
+looking inside the first row. And if I
+
+ align:start position:0%
+looking inside the first row. And if I
+ 
+
+ align:start position:0%
+looking inside the first row. And if I
+have an a plus a prime there and a b + b
+
+ align:start position:0%
+have an a plus a prime there and a b + b
+ 
+
+ align:start position:0%
+have an a plus a prime there and a b + b
+prime
+
+ align:start position:0%
+prime
+ 
+
+ align:start position:0%
+prime
+there. Sorry, I didn't ah why don't I'll
+
+ align:start position:0%
+there. Sorry, I didn't ah why don't I'll
+ 
+
+ align:start position:0%
+there. Sorry, I didn't ah why don't I'll
+use an eraser to do it right. B + B
+
+ align:start position:0%
+use an eraser to do it right. B + B
+ 
+
+ align:start position:0%
+use an eraser to do it right. B + B
+prime there. Do you see what I'm doing?
+
+ align:start position:0%
+prime there. Do you see what I'm doing?
+ 
+
+ align:start position:0%
+prime there. Do you see what I'm doing?
+This property and this property are
+
+ align:start position:0%
+This property and this property are
+ 
+
+ align:start position:0%
+This property and this property are
+about linear
+
+ align:start position:0%
+about linear
+ 
+
+ align:start position:0%
+about linear
+combinations of the first row only
+
+ align:start position:0%
+combinations of the first row only
+ 
+
+ align:start position:0%
+combinations of the first row only
+leaving the other rows unchanged. They
+
+ align:start position:0%
+leaving the other rows unchanged. They
+ 
+
+ align:start position:0%
+leaving the other rows unchanged. They
+they'll they'll copy along.
+
+ align:start position:0%
+they'll they'll copy along.
+ 
+
+ align:start position:0%
+they'll they'll copy along.
+Then then I get the sum this breaks up
+
+ align:start position:0%
+Then then I get the sum this breaks up
+ 
+
+ align:start position:0%
+Then then I get the sum this breaks up
+into the sum of this
+
+ align:start position:0%
+into the sum of this
+ 
+
+ align:start position:0%
+into the sum of this
+determinant and this one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If I'm putting up formulas, maybe I can
+
+ align:start position:0%
+If I'm putting up formulas, maybe I can
+ 
+
+ align:start position:0%
+If I'm putting up formulas, maybe I can
+try to say it in words. The determinant
+
+ align:start position:0%
+try to say it in words. The determinant
+ 
+
+ align:start position:0%
+try to say it in words. The determinant
+is a linear
+
+ align:start position:0%
+is a linear
+ 
+
+ align:start position:0%
+is a linear
+function. It it behaves like a a linear
+
+ align:start position:0%
+function. It it behaves like a a linear
+ 
+
+ align:start position:0%
+function. It it behaves like a a linear
+function of the first
+
+ align:start position:0%
+function of the first
+ 
+
+ align:start position:0%
+function of the first
+row if all the other rows stay the same.
+
+ align:start position:0%
+row if all the other rows stay the same.
+ 
+
+ align:start position:0%
+row if all the other rows stay the same.
+I am not saying that the I am let me
+
+ align:start position:0%
+I am not saying that the I am let me
+ 
+
+ align:start position:0%
+I am not saying that the I am let me
+emphasize I am not saying that the
+
+ align:start position:0%
+emphasize I am not saying that the
+ 
+
+ align:start position:0%
+emphasize I am not saying that the
+determinant of a plus b
+
+ align:start position:0%
+determinant of a plus b
+ 
+
+ align:start position:0%
+determinant of a plus b
+is determinant of
+
+ align:start position:0%
+is determinant of
+ 
+
+ align:start position:0%
+is determinant of
+A plus determinant of B. I am not saying
+
+ align:start position:0%
+A plus determinant of B. I am not saying
+ 
+
+ align:start position:0%
+A plus determinant of B. I am not saying
+that. I better Can I How do I get it
+
+ align:start position:0%
+that. I better Can I How do I get it
+ 
+
+ align:start position:0%
+that. I better Can I How do I get it
+onto tape that I'm not saying that? You
+
+ align:start position:0%
+onto tape that I'm not saying that? You
+ 
+
+ align:start position:0%
+onto tape that I'm not saying that? You
+see, this would allow
+
+ align:start position:0%
+see, this would allow
+ 
+
+ align:start position:0%
+see, this would allow
+uh all the rows, you know, A to have a
+
+ align:start position:0%
+uh all the rows, you know, A to have a
+ 
+
+ align:start position:0%
+uh all the rows, you know, A to have a
+bunch of rows, B to have a bunch of
+
+ align:start position:0%
+bunch of rows, B to have a bunch of
+ 
+
+ align:start position:0%
+bunch of rows, B to have a bunch of
+rows. That's not the linearity I'm
+
+ align:start position:0%
+rows. That's not the linearity I'm
+ 
+
+ align:start position:0%
+rows. That's not the linearity I'm
+after. I'm only after linearity in each
+
+ align:start position:0%
+after. I'm only after linearity in each
+ 
+
+ align:start position:0%
+after. I'm only after linearity in each
+row.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Linear for each
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+row. Well, you may say I only talked
+
+ align:start position:0%
+row. Well, you may say I only talked
+ 
+
+ align:start position:0%
+row. Well, you may say I only talked
+about the first row, but I claim it's
+
+ align:start position:0%
+about the first row, but I claim it's
+ 
+
+ align:start position:0%
+about the first row, but I claim it's
+also linear in the second row. If I had
+
+ align:start position:0%
+also linear in the second row. If I had
+ 
+
+ align:start position:0%
+also linear in the second row. If I had
+this, but not I can't I can't have a
+
+ align:start position:0%
+this, but not I can't I can't have a
+ 
+
+ align:start position:0%
+this, but not I can't I can't have a
+combination in both first and second
+
+ align:start position:0%
+combination in both first and second
+ 
+
+ align:start position:0%
+combination in both first and second
+row. If I had a combination in the
+
+ align:start position:0%
+row. If I had a combination in the
+ 
+
+ align:start position:0%
+row. If I had a combination in the
+second row, then I could use rule two to
+
+ align:start position:0%
+second row, then I could use rule two to
+ 
+
+ align:start position:0%
+second row, then I could use rule two to
+put it up in the first row, use my use
+
+ align:start position:0%
+put it up in the first row, use my use
+ 
+
+ align:start position:0%
+put it up in the first row, use my use
+my property and then use rule two again
+
+ align:start position:0%
+my property and then use rule two again
+ 
+
+ align:start position:0%
+my property and then use rule two again
+to put it back.
+
+ align:start position:0%
+to put it back.
+ 
+
+ align:start position:0%
+to put it back.
+So each row is okay, not only the first
+
+ align:start position:0%
+So each row is okay, not only the first
+ 
+
+ align:start position:0%
+So each row is okay, not only the first
+row but each row
+
+ align:start position:0%
+row but each row
+ 
+
+ align:start position:0%
+row but each row
+separately. Okay, those are the three
+
+ align:start position:0%
+separately. Okay, those are the three
+ 
+
+ align:start position:0%
+separately. Okay, those are the three
+properties. And from those properties,
+
+ align:start position:0%
+properties. And from those properties,
+ 
+
+ align:start position:0%
+properties. And from those properties,
+so that's properties one, two, three.
+
+ align:start position:0%
+so that's properties one, two, three.
+ 
+
+ align:start position:0%
+so that's properties one, two, three.
+from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those I want to get all I want to learn
+
+ align:start position:0%
+those I want to get all I want to learn
+ 
+
+ align:start position:0%
+those I want to get all I want to learn
+a lot more about the
+
+ align:start position:0%
+a lot more about the
+ 
+
+ align:start position:0%
+a lot more about the
+determinant let me take an example what
+
+ align:start position:0%
+determinant let me take an example what
+ 
+
+ align:start position:0%
+determinant let me take an example what
+what would I like to learn I would like
+
+ align:start position:0%
+what would I like to learn I would like
+ 
+
+ align:start position:0%
+what would I like to learn I would like
+to learn that so here's a property four
+
+ align:start position:0%
+to learn that so here's a property four
+ 
+
+ align:start position:0%
+to learn that so here's a property four
+let me use the same numbering as here
+
+ align:start position:0%
+let me use the same numbering as here
+ 
+
+ align:start position:0%
+let me use the same numbering as here
+property
+
+ align:start position:0%
+property
+ 
+
+ align:start position:0%
+property
+four is if two rows are equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the determinant
+
+ align:start position:0%
+the determinant
+ 
+
+ align:start position:0%
+the determinant
+is zero. Okay. So, property
+
+ align:start position:0%
+is zero. Okay. So, property
+ 
+
+ align:start position:0%
+is zero. Okay. So, property
+four, two equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rows lead to
+
+ align:start position:0%
+rows lead to
+ 
+
+ align:start position:0%
+rows lead to
+determinant equals
+
+ align:start position:0%
+determinant equals
+ 
+
+ align:start position:0%
+determinant equals
+zero. Right?
+
+ align:start position:0%
+zero. Right?
+ 
+
+ align:start position:0%
+zero. Right?
+Now of course I can in the 2x two case I
+
+ align:start position:0%
+Now of course I can in the 2x two case I
+ 
+
+ align:start position:0%
+Now of course I can in the 2x two case I
+can check sure the determinant of
+
+ align:start position:0%
+can check sure the determinant of
+ 
+
+ align:start position:0%
+can check sure the determinant of
+ab comes out zero
+
+ align:start position:0%
+ab comes out zero
+ 
+
+ align:start position:0%
+ab comes out zero
+but I want to see why it's true for n
+
+ align:start position:0%
+but I want to see why it's true for n
+ 
+
+ align:start position:0%
+but I want to see why it's true for n
+byn suppose row one equals row 3 for a 7
+
+ align:start position:0%
+byn suppose row one equals row 3 for a 7
+ 
+
+ align:start position:0%
+byn suppose row one equals row 3 for a 7
+by7
+
+ align:start position:0%
+by7
+ 
+
+ align:start position:0%
+by7
+matrix so two rows are the same in a big
+
+ align:start position:0%
+matrix so two rows are the same in a big
+ 
+
+ align:start position:0%
+matrix so two rows are the same in a big
+matrix and all I have to work with is
+
+ align:start position:0%
+matrix and all I have to work with is
+ 
+
+ align:start position:0%
+matrix and all I have to work with is
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+properties the exchange property which
+
+ align:start position:0%
+properties the exchange property which
+ 
+
+ align:start position:0%
+properties the exchange property which
+flips the sign and the linearity
+
+ align:start position:0%
+flips the sign and the linearity
+ 
+
+ align:start position:0%
+flips the sign and the linearity
+property which is works in each row
+
+ align:start position:0%
+property which is works in each row
+ 
+
+ align:start position:0%
+property which is works in each row
+separately.
+
+ align:start position:0%
+separately.
+ 
+
+ align:start position:0%
+separately.
+Okay, can you see the reason? How do I
+
+ align:start position:0%
+Okay, can you see the reason? How do I
+ 
+
+ align:start position:0%
+Okay, can you see the reason? How do I
+how do I get this one out of properties
+
+ align:start position:0%
+how do I get this one out of properties
+ 
+
+ align:start position:0%
+how do I get this one out of properties
+one two three because that's all I have
+
+ align:start position:0%
+one two three because that's all I have
+ 
+
+ align:start position:0%
+one two three because that's all I have
+to work with. Everything has to come
+
+ align:start position:0%
+to work with. Everything has to come
+ 
+
+ align:start position:0%
+to work with. Everything has to come
+from properties one two three. Okay. So
+
+ align:start position:0%
+from properties one two three. Okay. So
+ 
+
+ align:start position:0%
+from properties one two three. Okay. So
+suppose I have a matrix and two rows are
+
+ align:start position:0%
+suppose I have a matrix and two rows are
+ 
+
+ align:start position:0%
+suppose I have a matrix and two rows are
+equal. How do I see that its determinant
+
+ align:start position:0%
+equal. How do I see that its determinant
+ 
+
+ align:start position:0%
+equal. How do I see that its determinant
+has to be
+
+ align:start position:0%
+has to be
+ 
+
+ align:start position:0%
+has to be
+zero from these
+
+ align:start position:0%
+zero from these
+ 
+
+ align:start position:0%
+zero from these
+properties? I do an
+
+ align:start position:0%
+properties? I do an
+ 
+
+ align:start position:0%
+properties? I do an
+exchange. Property two is just set up
+
+ align:start position:0%
+exchange. Property two is just set up
+ 
+
+ align:start position:0%
+exchange. Property two is just set up
+for this. Use property two. Use exchange
+
+ align:start position:0%
+for this. Use property two. Use exchange
+ 
+
+ align:start position:0%
+for this. Use property two. Use exchange
+exchange
+
+ align:start position:0%
+exchange
+ 
+
+ align:start position:0%
+exchange
+rows. exchange those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rows and I get the same
+
+ align:start position:0%
+rows and I get the same
+ 
+
+ align:start position:0%
+rows and I get the same
+matrix of course because those rows were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equal so the determinant didn't change
+
+ align:start position:0%
+equal so the determinant didn't change
+ 
+
+ align:start position:0%
+equal so the determinant didn't change
+but on the other hand property two says
+
+ align:start position:0%
+but on the other hand property two says
+ 
+
+ align:start position:0%
+but on the other hand property two says
+that the sign did change so the so I I
+
+ align:start position:0%
+that the sign did change so the so I I
+ 
+
+ align:start position:0%
+that the sign did change so the so I I
+have a determinant whose sign doesn't
+
+ align:start position:0%
+have a determinant whose sign doesn't
+ 
+
+ align:start position:0%
+have a determinant whose sign doesn't
+change and does change and the only
+
+ align:start position:0%
+change and does change and the only
+ 
+
+ align:start position:0%
+change and does change and the only
+possibility ility then is that the
+
+ align:start position:0%
+possibility ility then is that the
+ 
+
+ align:start position:0%
+possibility ility then is that the
+determinant is zero. You see the
+
+ align:start position:0%
+determinant is zero. You see the
+ 
+
+ align:start position:0%
+determinant is zero. You see the
+reasoning there? Straightforward
+
+ align:start position:0%
+reasoning there? Straightforward
+ 
+
+ align:start position:0%
+reasoning there? Straightforward
+property two just told us, hey, if we've
+
+ align:start position:0%
+property two just told us, hey, if we've
+ 
+
+ align:start position:0%
+property two just told us, hey, if we've
+got two equal
+
+ align:start position:0%
+got two equal
+ 
+
+ align:start position:0%
+got two equal
+rows, we we've got
+
+ align:start position:0%
+rows, we we've got
+ 
+
+ align:start position:0%
+rows, we we've got
+um a zero determinant. And of course in
+
+ align:start position:0%
+um a zero determinant. And of course in
+ 
+
+ align:start position:0%
+um a zero determinant. And of course in
+our minds that matches the fact that if
+
+ align:start position:0%
+our minds that matches the fact that if
+ 
+
+ align:start position:0%
+our minds that matches the fact that if
+I have two equal rows, the matrix isn't
+
+ align:start position:0%
+I have two equal rows, the matrix isn't
+ 
+
+ align:start position:0%
+I have two equal rows, the matrix isn't
+invertible. If I have two equal rows, I
+
+ align:start position:0%
+invertible. If I have two equal rows, I
+ 
+
+ align:start position:0%
+invertible. If I have two equal rows, I
+know that the rank is less than n. Okay,
+
+ align:start position:0%
+know that the rank is less than n. Okay,
+ 
+
+ align:start position:0%
+know that the rank is less than n. Okay,
+ready for property
+
+ align:start position:0%
+ready for property
+ 
+
+ align:start position:0%
+ready for property
+five? Now, property five you'll
+
+ align:start position:0%
+five? Now, property five you'll
+ 
+
+ align:start position:0%
+five? Now, property five you'll
+recognize
+
+ align:start position:0%
+recognize
+ 
+
+ align:start position:0%
+recognize
+as a
+
+ align:start position:0%
+as a
+ 
+
+ align:start position:0%
+as a
+key. It says
+
+ align:start position:0%
+key. It says
+ 
+
+ align:start position:0%
+key. It says
+that the elimination step that I'm
+
+ align:start position:0%
+that the elimination step that I'm
+ 
+
+ align:start position:0%
+that the elimination step that I'm
+always doing.
+
+ align:start position:0%
+always doing.
+ 
+
+ align:start position:0%
+always doing.
+Subtract a
+
+ align:start position:0%
+Subtract a
+ 
+
+ align:start position:0%
+Subtract a
+multiple subtract some multiple L times
+
+ align:start position:0%
+multiple subtract some multiple L times
+ 
+
+ align:start position:0%
+multiple subtract some multiple L times
+row one from
+
+ align:start position:0%
+row one from
+ 
+
+ align:start position:0%
+row one from
+another row
+
+ align:start position:0%
+another row
+ 
+
+ align:start position:0%
+another row
+row k let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say you remember why I did that that in
+
+ align:start position:0%
+say you remember why I did that that in
+ 
+
+ align:start position:0%
+say you remember why I did that that in
+elimination I'm I'm always choosing this
+
+ align:start position:0%
+elimination I'm I'm always choosing this
+ 
+
+ align:start position:0%
+elimination I'm I'm always choosing this
+multiplier so as to produce
+
+ align:start position:0%
+multiplier so as to produce
+ 
+
+ align:start position:0%
+multiplier so as to produce
+zero in that in that
+
+ align:start position:0%
+zero in that in that
+ 
+
+ align:start position:0%
+zero in that in that
+position or or row i from row k maybe I
+
+ align:start position:0%
+position or or row i from row k maybe I
+ 
+
+ align:start position:0%
+position or or row i from row k maybe I
+should just make very clear that there's
+
+ align:start position:0%
+should just make very clear that there's
+ 
+
+ align:start position:0%
+should just make very clear that there's
+nothing special about row one
+
+ align:start position:0%
+nothing special about row one
+ 
+
+ align:start position:0%
+nothing special about row one
+here. Okay. So that you can see why I
+
+ align:start position:0%
+here. Okay. So that you can see why I
+ 
+
+ align:start position:0%
+here. Okay. So that you can see why I
+want that one because that will allow me
+
+ align:start position:0%
+want that one because that will allow me
+ 
+
+ align:start position:0%
+want that one because that will allow me
+to start with this full matrix whose
+
+ align:start position:0%
+to start with this full matrix whose
+ 
+
+ align:start position:0%
+to start with this full matrix whose
+determinant I don't know and I can do
+
+ align:start position:0%
+determinant I don't know and I can do
+ 
+
+ align:start position:0%
+determinant I don't know and I can do
+elimination and clean it out. I can get
+
+ align:start position:0%
+elimination and clean it out. I can get
+ 
+
+ align:start position:0%
+elimination and clean it out. I can get
+zeros below the diagonal by these
+
+ align:start position:0%
+zeros below the diagonal by these
+ 
+
+ align:start position:0%
+zeros below the diagonal by these
+elimination steps. And the point is that
+
+ align:start position:0%
+elimination steps. And the point is that
+ 
+
+ align:start position:0%
+elimination steps. And the point is that
+the that the
+
+ align:start position:0%
+the that the
+ 
+
+ align:start position:0%
+the that the
+determinant the
+
+ align:start position:0%
+determinant the
+ 
+
+ align:start position:0%
+determinant the
+determinant doesn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change. So all those steps of
+
+ align:start position:0%
+change. So all those steps of
+ 
+
+ align:start position:0%
+change. So all those steps of
+elimination are are okay not changing
+
+ align:start position:0%
+elimination are are okay not changing
+ 
+
+ align:start position:0%
+elimination are are okay not changing
+the determinant in our in our language
+
+ align:start position:0%
+the determinant in our in our language
+ 
+
+ align:start position:0%
+the determinant in our in our language
+in in the early chapter. The determinant
+
+ align:start position:0%
+in in the early chapter. The determinant
+ 
+
+ align:start position:0%
+in in the early chapter. The determinant
+of a is going to be the same as the
+
+ align:start position:0%
+of a is going to be the same as the
+ 
+
+ align:start position:0%
+of a is going to be the same as the
+determinant of u, the upper triangular
+
+ align:start position:0%
+determinant of u, the upper triangular
+ 
+
+ align:start position:0%
+determinant of u, the upper triangular
+one that just has the pivots on the
+
+ align:start position:0%
+one that just has the pivots on the
+ 
+
+ align:start position:0%
+one that just has the pivots on the
+diagonal. That's why we'll want this
+
+ align:start position:0%
+diagonal. That's why we'll want this
+ 
+
+ align:start position:0%
+diagonal. That's why we'll want this
+property. Okay, do you see where that
+
+ align:start position:0%
+property. Okay, do you see where that
+ 
+
+ align:start position:0%
+property. Okay, do you see where that
+property is coming
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+from? Let let me do the 2x two case. Let
+
+ align:start position:0%
+from? Let let me do the 2x two case. Let
+ 
+
+ align:start position:0%
+from? Let let me do the 2x two case. Let
+me do the 2 x two case here. So, uh I'll
+
+ align:start position:0%
+me do the 2 x two case here. So, uh I'll
+ 
+
+ align:start position:0%
+me do the 2 x two case here. So, uh I'll
+I'll keep property five going along. So,
+
+ align:start position:0%
+I'll keep property five going along. So,
+ 
+
+ align:start position:0%
+I'll keep property five going along. So,
+what am I doing? I'm going to keep I'm
+
+ align:start position:0%
+what am I doing? I'm going to keep I'm
+ 
+
+ align:start position:0%
+what am I doing? I'm going to keep I'm
+going to have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+AB CD, but I'm going to subtract L times
+
+ align:start position:0%
+AB CD, but I'm going to subtract L times
+ 
+
+ align:start position:0%
+AB CD, but I'm going to subtract L times
+the first row from the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+row. And that's the
+
+ align:start position:0%
+row. And that's the
+ 
+
+ align:start position:0%
+row. And that's the
+determinant. And of course, I can
+
+ align:start position:0%
+determinant. And of course, I can
+ 
+
+ align:start position:0%
+determinant. And of course, I can
+multiply that out and figure out sure
+
+ align:start position:0%
+multiply that out and figure out sure
+ 
+
+ align:start position:0%
+multiply that out and figure out sure
+enough a D minus BC is there. And this
+
+ align:start position:0%
+enough a D minus BC is there. And this
+ 
+
+ align:start position:0%
+enough a D minus BC is there. And this
+minus ALB plus A alb cancels out. But I
+
+ align:start position:0%
+minus ALB plus A alb cancels out. But I
+ 
+
+ align:start position:0%
+minus ALB plus A alb cancels out. But I
+just cheated, right? I've got to use the
+
+ align:start position:0%
+just cheated, right? I've got to use the
+ 
+
+ align:start position:0%
+just cheated, right? I've got to use the
+property. So what property? Well, of
+
+ align:start position:0%
+property. So what property? Well, of
+ 
+
+ align:start position:0%
+property. So what property? Well, of
+course, this is a com. I'm keeping the
+
+ align:start position:0%
+course, this is a com. I'm keeping the
+ 
+
+ align:start position:0%
+course, this is a com. I'm keeping the
+first row the same. And the second row
+
+ align:start position:0%
+first row the same. And the second row
+ 
+
+ align:start position:0%
+first row the same. And the second row
+has a C and a D. And then there's the
+
+ align:start position:0%
+has a C and a D. And then there's the
+ 
+
+ align:start position:0%
+has a C and a D. And then there's the
+determinant of the A and the B and the
+
+ align:start position:0%
+determinant of the A and the B and the
+ 
+
+ align:start position:0%
+determinant of the A and the B and the
+minus L A and the minus LB.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So what property was
+
+ align:start position:0%
+So what property was
+ 
+
+ align:start position:0%
+So what property was
+that?
+
+ align:start position:0%
+that?
+ 
+
+ align:start position:0%
+that?
+3B. I kept one row the same and I had a
+
+ align:start position:0%
+3B. I kept one row the same and I had a
+ 
+
+ align:start position:0%
+3B. I kept one row the same and I had a
+combination in the second in the other
+
+ align:start position:0%
+combination in the second in the other
+ 
+
+ align:start position:0%
+combination in the second in the other
+row and I just separated it
+
+ align:start position:0%
+row and I just separated it
+ 
+
+ align:start position:0%
+row and I just separated it
+out. Okay. So that's property three.
+
+ align:start position:0%
+out. Okay. So that's property three.
+ 
+
+ align:start position:0%
+out. Okay. So that's property three.
+This is by number three. 3B if you like.
+
+ align:start position:0%
+This is by number three. 3B if you like.
+ 
+
+ align:start position:0%
+This is by number three. 3B if you like.
+Okay. Now use 3A. How how do you use
+
+ align:start position:0%
+Okay. Now use 3A. How how do you use
+ 
+
+ align:start position:0%
+Okay. Now use 3A. How how do you use
+3A, which says I can factor out an L? I
+
+ align:start position:0%
+3A, which says I can factor out an L? I
+ 
+
+ align:start position:0%
+3A, which says I can factor out an L? I
+can factor out a minus L here. I can
+
+ align:start position:0%
+can factor out a minus L here. I can
+ 
+
+ align:start position:0%
+can factor out a minus L here. I can
+factor a minus L out from this row. No
+
+ align:start position:0%
+factor a minus L out from this row. No
+ 
+
+ align:start position:0%
+factor a minus L out from this row. No
+problem. That was
+
+ align:start position:0%
+problem. That was
+ 
+
+ align:start position:0%
+problem. That was
+3A. So now I've used property three. And
+
+ align:start position:0%
+3A. So now I've used property three. And
+ 
+
+ align:start position:0%
+3A. So now I've used property three. And
+now I'm ready for the
+
+ align:start position:0%
+now I'm ready for the
+ 
+
+ align:start position:0%
+now I'm ready for the
+kill. Property four says that this
+
+ align:start position:0%
+kill. Property four says that this
+ 
+
+ align:start position:0%
+kill. Property four says that this
+determinant
+
+ align:start position:0%
+determinant
+ 
+
+ align:start position:0%
+determinant
+is zero, has two equal rows.
+
+ align:start position:0%
+is zero, has two equal rows.
+ 
+
+ align:start position:0%
+is zero, has two equal rows.
+Do you see how that would always work? I
+
+ align:start position:0%
+Do you see how that would always work? I
+ 
+
+ align:start position:0%
+Do you see how that would always work? I
+subtract off a multiple of one row from
+
+ align:start position:0%
+subtract off a multiple of one row from
+ 
+
+ align:start position:0%
+subtract off a multiple of one row from
+another one. It gives me a combination
+
+ align:start position:0%
+another one. It gives me a combination
+ 
+
+ align:start position:0%
+another one. It gives me a combination
+in row K of the old
+
+ align:start position:0%
+in row K of the old
+ 
+
+ align:start position:0%
+in row K of the old
+row and L times this copy of a higher
+
+ align:start position:0%
+row and L times this copy of a higher
+ 
+
+ align:start position:0%
+row and L times this copy of a higher
+row. And then if I since I have two
+
+ align:start position:0%
+row. And then if I since I have two
+ 
+
+ align:start position:0%
+row. And then if I since I have two
+equal rows, that's zero. So the
+
+ align:start position:0%
+equal rows, that's zero. So the
+ 
+
+ align:start position:0%
+equal rows, that's zero. So the
+determinant after elimination is the
+
+ align:start position:0%
+determinant after elimination is the
+ 
+
+ align:start position:0%
+determinant after elimination is the
+same as before. Good. Okay. Now let's
+
+ align:start position:0%
+same as before. Good. Okay. Now let's
+ 
+
+ align:start position:0%
+same as before. Good. Okay. Now let's
+see if I rescue my glasses I can see
+
+ align:start position:0%
+see if I rescue my glasses I can see
+ 
+
+ align:start position:0%
+see if I rescue my glasses I can see
+what's property six. Oh six is easy pl
+
+ align:start position:0%
+what's property six. Oh six is easy pl
+ 
+
+ align:start position:0%
+what's property six. Oh six is easy pl
+of space
+
+ align:start position:0%
+of space
+ 
+
+ align:start position:0%
+of space
+row of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zeros leads to determinant of a equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero a complete row of zeros. So I'm I'm
+
+ align:start position:0%
+zero a complete row of zeros. So I'm I'm
+ 
+
+ align:start position:0%
+zero a complete row of zeros. So I'm I'm
+again this is like
+
+ align:start position:0%
+again this is like
+ 
+
+ align:start position:0%
+again this is like
+uh something that I'll use in the
+
+ align:start position:0%
+uh something that I'll use in the
+ 
+
+ align:start position:0%
+uh something that I'll use in the
+singular case. Actually you can you can
+
+ align:start position:0%
+singular case. Actually you can you can
+ 
+
+ align:start position:0%
+singular case. Actually you can you can
+look ahead to why I need these
+
+ align:start position:0%
+look ahead to why I need these
+ 
+
+ align:start position:0%
+look ahead to why I need these
+properties. So I'm going to use property
+
+ align:start position:0%
+properties. So I'm going to use property
+ 
+
+ align:start position:0%
+properties. So I'm going to use property
+five the elimination use this stuff to
+
+ align:start position:0%
+five the elimination use this stuff to
+ 
+
+ align:start position:0%
+five the elimination use this stuff to
+say that this determinant is the same as
+
+ align:start position:0%
+say that this determinant is the same as
+ 
+
+ align:start position:0%
+say that this determinant is the same as
+that determinant and I'll produce a zero
+
+ align:start position:0%
+that determinant and I'll produce a zero
+ 
+
+ align:start position:0%
+that determinant and I'll produce a zero
+there. But what if I also produce a zero
+
+ align:start position:0%
+there. But what if I also produce a zero
+ 
+
+ align:start position:0%
+there. But what if I also produce a zero
+there? What if elimination gives a row
+
+ align:start position:0%
+there? What if elimination gives a row
+ 
+
+ align:start position:0%
+there? What if elimination gives a row
+of zeros? Then I that that used to be my
+
+ align:start position:0%
+of zeros? Then I that that used to be my
+ 
+
+ align:start position:0%
+of zeros? Then I that that used to be my
+test for
+
+ align:start position:0%
+test for
+ 
+
+ align:start position:0%
+test for
+singular not invertible rank two rank
+
+ align:start position:0%
+singular not invertible rank two rank
+ 
+
+ align:start position:0%
+singular not invertible rank two rank
+less than n and now I'm seeing it's also
+
+ align:start position:0%
+less than n and now I'm seeing it's also
+ 
+
+ align:start position:0%
+less than n and now I'm seeing it's also
+gives determinant zero. Uh how do I get
+
+ align:start position:0%
+gives determinant zero. Uh how do I get
+ 
+
+ align:start position:0%
+gives determinant zero. Uh how do I get
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+one from the previous properties because
+
+ align:start position:0%
+one from the previous properties because
+ 
+
+ align:start position:0%
+one from the previous properties because
+I this is not a new law this has got to
+
+ align:start position:0%
+I this is not a new law this has got to
+ 
+
+ align:start position:0%
+I this is not a new law this has got to
+come from the old
+
+ align:start position:0%
+come from the old
+ 
+
+ align:start position:0%
+come from the old
+one. So what what shall I do? 3. Yeah,
+
+ align:start position:0%
+one. So what what shall I do? 3. Yeah,
+ 
+
+ align:start position:0%
+one. So what what shall I do? 3. Yeah,
+use that's brilliant. Use 3A with T
+
+ align:start position:0%
+use that's brilliant. Use 3A with T
+ 
+
+ align:start position:0%
+use that's brilliant. Use 3A with T
+equals Z. Right. So I have this I have
+
+ align:start position:0%
+equals Z. Right. So I have this I have
+ 
+
+ align:start position:0%
+equals Z. Right. So I have this I have
+this Z 0 CD and I'm trying to show that
+
+ align:start position:0%
+this Z 0 CD and I'm trying to show that
+ 
+
+ align:start position:0%
+this Z 0 CD and I'm trying to show that
+that determinant is
+
+ align:start position:0%
+that determinant is
+ 
+
+ align:start position:0%
+that determinant is
+zero. Okay. So but zero is the same as
+
+ align:start position:0%
+zero. Okay. So but zero is the same as
+ 
+
+ align:start position:0%
+zero. Okay. So but zero is the same as
+five. Can I take T equal 5 just to like
+
+ align:start position:0%
+five. Can I take T equal 5 just to like
+ 
+
+ align:start position:0%
+five. Can I take T equal 5 just to like
+pin it down? I'll multiply this row by
+
+ align:start position:0%
+pin it down? I'll multiply this row by
+ 
+
+ align:start position:0%
+pin it down? I'll multiply this row by
+five. Five. Well then five of this
+
+ align:start position:0%
+five. Five. Well then five of this
+ 
+
+ align:start position:0%
+five. Five. Well then five of this
+should if I if there's a factor
+
+ align:start position:0%
+should if I if there's a factor
+ 
+
+ align:start position:0%
+should if I if there's a factor
+five in
+
+ align:start position:0%
+five in
+ 
+
+ align:start position:0%
+five in
+that you see
+
+ align:start position:0%
+that you see
+ 
+
+ align:start position:0%
+that you see
+what so this is property 3 a with with
+
+ align:start position:0%
+what so this is property 3 a with with
+ 
+
+ align:start position:0%
+what so this is property 3 a with with
+taking as five if I multiply a row by
+
+ align:start position:0%
+taking as five if I multiply a row by
+ 
+
+ align:start position:0%
+taking as five if I multiply a row by
+five outcomes a five so why am I why the
+
+ align:start position:0%
+five outcomes a five so why am I why the
+ 
+
+ align:start position:0%
+five outcomes a five so why am I why the
+heck am I doing
+
+ align:start position:0%
+heck am I doing
+ 
+
+ align:start position:0%
+heck am I doing
+this oh
+
+ align:start position:0%
+this oh
+ 
+
+ align:start position:0%
+this oh
+because that's still 0 0
+
+ align:start position:0%
+because that's still 0 0
+ 
+
+ align:start position:0%
+because that's still 0 0
+So that's this determinant equals 5 *
+
+ align:start position:0%
+So that's this determinant equals 5 *
+ 
+
+ align:start position:0%
+So that's this determinant equals 5 *
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+determinant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the determinant has to be zero. I I
+
+ align:start position:0%
+and the determinant has to be zero. I I
+ 
+
+ align:start position:0%
+and the determinant has to be zero. I I
+think I I didn't do that the very best
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way. You were Yeah, you had the idea
+
+ align:start position:0%
+way. You were Yeah, you had the idea
+ 
+
+ align:start position:0%
+way. You were Yeah, you had the idea
+better. Multiply. Yeah. Yeah. Take T
+
+ align:start position:0%
+better. Multiply. Yeah. Yeah. Take T
+ 
+
+ align:start position:0%
+better. Multiply. Yeah. Yeah. Take T
+equals Z. Was that your idea? Yeah.
+
+ align:start position:0%
+equals Z. Was that your idea? Yeah.
+ 
+
+ align:start position:0%
+equals Z. Was that your idea? Yeah.
+Better. Take T equals Z. in rule 3B. If
+
+ align:start position:0%
+Better. Take T equals Z. in rule 3B. If
+ 
+
+ align:start position:0%
+Better. Take T equals Z. in rule 3B. If
+T is zero in rule 3B, can I bring the
+
+ align:start position:0%
+T is zero in rule 3B, can I bring the
+ 
+
+ align:start position:0%
+T is zero in rule 3B, can I bring the
+camera back to rule 3B?
+
+ align:start position:0%
+camera back to rule 3B?
+ 
+
+ align:start position:0%
+camera back to rule 3B?
+Sorry. If if T is
+
+ align:start position:0%
+Sorry. If if T is
+ 
+
+ align:start position:0%
+Sorry. If if T is
+zero, then I have a Z 0 there and the
+
+ align:start position:0%
+zero, then I have a Z 0 there and the
+ 
+
+ align:start position:0%
+zero, then I have a Z 0 there and the
+determinant is zero. Okay? One way or
+
+ align:start position:0%
+determinant is zero. Okay? One way or
+ 
+
+ align:start position:0%
+determinant is zero. Okay? One way or
+another, a row of zeros mean zero
+
+ align:start position:0%
+another, a row of zeros mean zero
+ 
+
+ align:start position:0%
+another, a row of zeros mean zero
+determinant.
+
+ align:start position:0%
+determinant.
+ 
+
+ align:start position:0%
+determinant.
+Okay? Now I have to get serious.
+
+ align:start position:0%
+Okay? Now I have to get serious.
+ 
+
+ align:start position:0%
+Okay? Now I have to get serious.
+the the next properties are the ones
+
+ align:start position:0%
+the the next properties are the ones
+ 
+
+ align:start position:0%
+the the next properties are the ones
+that we we're building up to.
+
+ align:start position:0%
+that we we're building up to.
+ 
+
+ align:start position:0%
+that we we're building up to.
+Okay, so I can do
+
+ align:start position:0%
+Okay, so I can do
+ 
+
+ align:start position:0%
+Okay, so I can do
+elimination. I can reduce to a
+
+ align:start position:0%
+elimination. I can reduce to a
+ 
+
+ align:start position:0%
+elimination. I can reduce to a
+triangular
+
+ align:start position:0%
+triangular
+ 
+
+ align:start position:0%
+triangular
+matrix. And now what's the determinant
+
+ align:start position:0%
+matrix. And now what's the determinant
+ 
+
+ align:start position:0%
+matrix. And now what's the determinant
+of that triangular matrix? Suppose
+
+ align:start position:0%
+of that triangular matrix? Suppose
+ 
+
+ align:start position:0%
+of that triangular matrix? Suppose
+suppose I all right rule
+
+ align:start position:0%
+suppose I all right rule
+ 
+
+ align:start position:0%
+suppose I all right rule
+seven. So suppose my matrix is now
+
+ align:start position:0%
+seven. So suppose my matrix is now
+ 
+
+ align:start position:0%
+seven. So suppose my matrix is now
+triangular. So it's
+
+ align:start position:0%
+triangular. So it's
+ 
+
+ align:start position:0%
+triangular. So it's
+got so I even give these the names of
+
+ align:start position:0%
+got so I even give these the names of
+ 
+
+ align:start position:0%
+got so I even give these the names of
+the pivots D1 D2 to DN and stuff is up
+
+ align:start position:0%
+the pivots D1 D2 to DN and stuff is up
+ 
+
+ align:start position:0%
+the pivots D1 D2 to DN and stuff is up
+here. I don't know what that
+
+ align:start position:0%
+here. I don't know what that
+ 
+
+ align:start position:0%
+here. I don't know what that
+is. But what I do know is this is all
+
+ align:start position:0%
+is. But what I do know is this is all
+ 
+
+ align:start position:0%
+is. But what I do know is this is all
+zero. That's all
+
+ align:start position:0%
+zero. That's all
+ 
+
+ align:start position:0%
+zero. That's all
+zero. And I would like to know the
+
+ align:start position:0%
+zero. And I would like to know the
+ 
+
+ align:start position:0%
+zero. And I would like to know the
+determinant because elimination will get
+
+ align:start position:0%
+determinant because elimination will get
+ 
+
+ align:start position:0%
+determinant because elimination will get
+me to this. So once I'm here, what's the
+
+ align:start position:0%
+me to this. So once I'm here, what's the
+ 
+
+ align:start position:0%
+me to this. So once I'm here, what's the
+determinant? Let me use an eraser to get
+
+ align:start position:0%
+determinant? Let me use an eraser to get
+ 
+
+ align:start position:0%
+determinant? Let me use an eraser to get
+those get that vertical bar again. So
+
+ align:start position:0%
+those get that vertical bar again. So
+ 
+
+ align:start position:0%
+those get that vertical bar again. So
+that I'm taking the determinant of u so
+
+ align:start position:0%
+that I'm taking the determinant of u so
+ 
+
+ align:start position:0%
+that I'm taking the determinant of u so
+that so what is the
+
+ align:start position:0%
+that so what is the
+ 
+
+ align:start position:0%
+that so what is the
+determinant of an upper triangular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrix? Do you know the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+answer? It's just the product of the
+
+ align:start position:0%
+answer? It's just the product of the
+ 
+
+ align:start position:0%
+answer? It's just the product of the
+D's.
+
+ align:start position:0%
+D's.
+ 
+
+ align:start position:0%
+D's.
+the these things that I don't even put
+
+ align:start position:0%
+the these things that I don't even put
+ 
+
+ align:start position:0%
+the these things that I don't even put
+in letters for because they don't
+
+ align:start position:0%
+in letters for because they don't
+ 
+
+ align:start position:0%
+in letters for because they don't
+matter. The determinant is d1 * d2
+
+ align:start position:0%
+matter. The determinant is d1 * d2
+ 
+
+ align:start position:0%
+matter. The determinant is d1 * d2
+*
+
+ align:start position:0%
+*
+ 
+
+ align:start position:0%
+*
+dn. If I have a triangular
+
+ align:start position:0%
+dn. If I have a triangular
+ 
+
+ align:start position:0%
+dn. If I have a triangular
+matrix, then the diagonal is all I have
+
+ align:start position:0%
+matrix, then the diagonal is all I have
+ 
+
+ align:start position:0%
+matrix, then the diagonal is all I have
+to look at.
+
+ align:start position:0%
+to look at.
+ 
+
+ align:start position:0%
+to look at.
+And that's that's telling us then we now
+
+ align:start position:0%
+And that's that's telling us then we now
+ 
+
+ align:start position:0%
+And that's that's telling us then we now
+have the way that mat
+
+ align:start position:0%
+have the way that mat
+ 
+
+ align:start position:0%
+have the way that mat
+lab any reasonable software would
+
+ align:start position:0%
+lab any reasonable software would
+ 
+
+ align:start position:0%
+lab any reasonable software would
+compute a determinant. If I have a a
+
+ align:start position:0%
+compute a determinant. If I have a a
+ 
+
+ align:start position:0%
+compute a determinant. If I have a a
+matrix of size
+
+ align:start position:0%
+matrix of size
+ 
+
+ align:start position:0%
+matrix of size
+100 the way I would actually compute its
+
+ align:start position:0%
+100 the way I would actually compute its
+ 
+
+ align:start position:0%
+100 the way I would actually compute its
+determinant would be
+
+ align:start position:0%
+determinant would be
+ 
+
+ align:start position:0%
+determinant would be
+elimination make it triangular multiply
+
+ align:start position:0%
+elimination make it triangular multiply
+ 
+
+ align:start position:0%
+elimination make it triangular multiply
+the pivots together the product of the
+
+ align:start position:0%
+the pivots together the product of the
+ 
+
+ align:start position:0%
+the pivots together the product of the
+pivots. product of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pivots. Now, there's
+
+ align:start position:0%
+pivots. Now, there's
+ 
+
+ align:start position:0%
+pivots. Now, there's
+always in
+
+ align:start position:0%
+always in
+ 
+
+ align:start position:0%
+always in
+determinance a plus or a minus sign to
+
+ align:start position:0%
+determinance a plus or a minus sign to
+ 
+
+ align:start position:0%
+determinance a plus or a minus sign to
+remember. Where does that come in to
+
+ align:start position:0%
+remember. Where does that come in to
+ 
+
+ align:start position:0%
+remember. Where does that come in to
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+rule? Could it be could the determinant
+
+ align:start position:0%
+rule? Could it be could the determinant
+ 
+
+ align:start position:0%
+rule? Could it be could the determinant
+be minus the product of the
+
+ align:start position:0%
+be minus the product of the
+ 
+
+ align:start position:0%
+be minus the product of the
+pivots? The determinant is d1 d2 to dn.
+
+ align:start position:0%
+pivots? The determinant is d1 d2 to dn.
+ 
+
+ align:start position:0%
+pivots? The determinant is d1 d2 to dn.
+No doubt about that. But to get to this
+
+ align:start position:0%
+No doubt about that. But to get to this
+ 
+
+ align:start position:0%
+No doubt about that. But to get to this
+triangular form, we may have had to do a
+
+ align:start position:0%
+triangular form, we may have had to do a
+ 
+
+ align:start position:0%
+triangular form, we may have had to do a
+row exchange. So,
+
+ align:start position:0%
+row exchange. So,
+ 
+
+ align:start position:0%
+row exchange. So,
+so this it's the product of the pivots.
+
+ align:start position:0%
+so this it's the product of the pivots.
+ 
+
+ align:start position:0%
+so this it's the product of the pivots.
+If there were no row exchanges, if if
+
+ align:start position:0%
+If there were no row exchanges, if if
+ 
+
+ align:start position:0%
+If there were no row exchanges, if if
+SLU code, the simple LU code, just
+
+ align:start position:0%
+SLU code, the simple LU code, just
+ 
+
+ align:start position:0%
+SLU code, the simple LU code, just
+square LU went right through. If we had
+
+ align:start position:0%
+square LU went right through. If we had
+ 
+
+ align:start position:0%
+square LU went right through. If we had
+to do some row exchanges, then we've got
+
+ align:start position:0%
+to do some row exchanges, then we've got
+ 
+
+ align:start position:0%
+to do some row exchanges, then we've got
+to watch plus or minus. Okay, but the
+
+ align:start position:0%
+to watch plus or minus. Okay, but the
+ 
+
+ align:start position:0%
+to watch plus or minus. Okay, but the
+this law is simply that. Okay, how do I
+
+ align:start position:0%
+this law is simply that. Okay, how do I
+ 
+
+ align:start position:0%
+this law is simply that. Okay, how do I
+prove
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that? Let's see. Let me suppose that
+
+ align:start position:0%
+that? Let's see. Let me suppose that
+ 
+
+ align:start position:0%
+that? Let's see. Let me suppose that
+these are not
+
+ align:start position:0%
+these are not
+ 
+
+ align:start position:0%
+these are not
+zero. The pivots are not
+
+ align:start position:0%
+zero. The pivots are not
+ 
+
+ align:start position:0%
+zero. The pivots are not
+zero. And tell me how do I show that
+
+ align:start position:0%
+zero. And tell me how do I show that
+ 
+
+ align:start position:0%
+zero. And tell me how do I show that
+none of this upper stuff makes any
+
+ align:start position:0%
+none of this upper stuff makes any
+ 
+
+ align:start position:0%
+none of this upper stuff makes any
+difference? How do I get zeros
+
+ align:start position:0%
+difference? How do I get zeros
+ 
+
+ align:start position:0%
+difference? How do I get zeros
+there? By elimination. Right? I just
+
+ align:start position:0%
+there? By elimination. Right? I just
+ 
+
+ align:start position:0%
+there? By elimination. Right? I just
+multiply this row by the right number,
+
+ align:start position:0%
+multiply this row by the right number,
+ 
+
+ align:start position:0%
+multiply this row by the right number,
+subtract from that row, kills
+
+ align:start position:0%
+subtract from that row, kills
+ 
+
+ align:start position:0%
+subtract from that row, kills
+that. I multiply this row by the right
+
+ align:start position:0%
+that. I multiply this row by the right
+ 
+
+ align:start position:0%
+that. I multiply this row by the right
+number, kills that. By the right number,
+
+ align:start position:0%
+number, kills that. By the right number,
+ 
+
+ align:start position:0%
+number, kills that. By the right number,
+kills that. I can kill every one of
+
+ align:start position:0%
+kills that. I can kill every one of
+ 
+
+ align:start position:0%
+kills that. I can kill every one of
+these off diagonal terms, no problem.
+
+ align:start position:0%
+these off diagonal terms, no problem.
+ 
+
+ align:start position:0%
+these off diagonal terms, no problem.
+And I'm just left with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+diagonal. Well, strictly speaking, I
+
+ align:start position:0%
+diagonal. Well, strictly speaking, I
+ 
+
+ align:start position:0%
+diagonal. Well, strictly speaking, I
+still have to figure out why is for a
+
+ align:start position:0%
+still have to figure out why is for a
+ 
+
+ align:start position:0%
+still have to figure out why is for a
+diagonal matrix. Now why is that the
+
+ align:start position:0%
+diagonal matrix. Now why is that the
+ 
+
+ align:start position:0%
+diagonal matrix. Now why is that the
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determinant? I mean we sure hope it is
+
+ align:start position:0%
+determinant? I mean we sure hope it is
+ 
+
+ align:start position:0%
+determinant? I mean we sure hope it is
+but why I have to go back to properties
+
+ align:start position:0%
+but why I have to go back to properties
+ 
+
+ align:start position:0%
+but why I have to go back to properties
+1 2
+
+ align:start position:0%
+1 2
+ 
+
+ align:start position:0%
+1 2
+3. Why is now that the matrix is
+
+ align:start position:0%
+3. Why is now that the matrix is
+ 
+
+ align:start position:0%
+3. Why is now that the matrix is
+suddenly
+
+ align:start position:0%
+suddenly
+ 
+
+ align:start position:0%
+suddenly
+diagonal? How do I know that the
+
+ align:start position:0%
+diagonal? How do I know that the
+ 
+
+ align:start position:0%
+diagonal? How do I know that the
+determinant is just a product of those
+
+ align:start position:0%
+determinant is just a product of those
+ 
+
+ align:start position:0%
+determinant is just a product of those
+diagonal entries? Well, what am I going
+
+ align:start position:0%
+diagonal entries? Well, what am I going
+ 
+
+ align:start position:0%
+diagonal entries? Well, what am I going
+to use? I'm going to use property 3A. Is
+
+ align:start position:0%
+to use? I'm going to use property 3A. Is
+ 
+
+ align:start position:0%
+to use? I'm going to use property 3A. Is
+that right? I'll I'll I'll factor this
+
+ align:start position:0%
+that right? I'll I'll I'll factor this
+ 
+
+ align:start position:0%
+that right? I'll I'll I'll factor this
+I'll factor this I'll factor that D1 out
+
+ align:start position:0%
+I'll factor this I'll factor that D1 out
+ 
+
+ align:start position:0%
+I'll factor this I'll factor that D1 out
+and have one and have the first row will
+
+ align:start position:0%
+and have one and have the first row will
+ 
+
+ align:start position:0%
+and have one and have the first row will
+be that and then I'll factor out the D2.
+
+ align:start position:0%
+be that and then I'll factor out the D2.
+ 
+
+ align:start position:0%
+be that and then I'll factor out the D2.
+Should I can I put the D2 here and the
+
+ align:start position:0%
+Should I can I put the D2 here and the
+ 
+
+ align:start position:0%
+Should I can I put the D2 here and the
+second row will look like that and so
+
+ align:start position:0%
+second row will look like that and so
+ 
+
+ align:start position:0%
+second row will look like that and so
+on. So I factored out all the D's and
+
+ align:start position:0%
+on. So I factored out all the D's and
+ 
+
+ align:start position:0%
+on. So I factored out all the D's and
+what am I left with? The identity. And
+
+ align:start position:0%
+what am I left with? The identity. And
+ 
+
+ align:start position:0%
+what am I left with? The identity. And
+what rule do I finally get to use?
+
+ align:start position:0%
+what rule do I finally get to use?
+ 
+
+ align:start position:0%
+what rule do I finally get to use?
+rule one finally this is the point where
+
+ align:start position:0%
+rule one finally this is the point where
+ 
+
+ align:start position:0%
+rule one finally this is the point where
+rule one finally chips in and says that
+
+ align:start position:0%
+rule one finally chips in and says that
+ 
+
+ align:start position:0%
+rule one finally chips in and says that
+that determinant is one so it's the
+
+ align:start position:0%
+that determinant is one so it's the
+ 
+
+ align:start position:0%
+that determinant is one so it's the
+product of the D's. So this was rules
+
+ align:start position:0%
+product of the D's. So this was rules
+ 
+
+ align:start position:0%
+product of the D's. So this was rules
+rules five to do
+
+ align:start position:0%
+rules five to do
+ 
+
+ align:start position:0%
+rules five to do
+elimination 3 a to factor out the d's
+
+ align:start position:0%
+elimination 3 a to factor out the d's
+ 
+
+ align:start position:0%
+elimination 3 a to factor out the d's
+and and our best friend rule one and
+
+ align:start position:0%
+and and our best friend rule one and
+ 
+
+ align:start position:0%
+and and our best friend rule one and
+possibly rule two the exchanges may have
+
+ align:start position:0%
+possibly rule two the exchanges may have
+ 
+
+ align:start position:0%
+possibly rule two the exchanges may have
+been needed also.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, now I guess I have to consider
+
+ align:start position:0%
+Okay, now I guess I have to consider
+ 
+
+ align:start position:0%
+Okay, now I guess I have to consider
+also the case if some D is
+
+ align:start position:0%
+also the case if some D is
+ 
+
+ align:start position:0%
+also the case if some D is
+zero because I was assuming I could use
+
+ align:start position:0%
+zero because I was assuming I could use
+ 
+
+ align:start position:0%
+zero because I was assuming I could use
+the D's to clean out and make it
+
+ align:start position:0%
+the D's to clean out and make it
+ 
+
+ align:start position:0%
+the D's to clean out and make it
+diagonal. But what if what if one of
+
+ align:start position:0%
+diagonal. But what if what if one of
+ 
+
+ align:start position:0%
+diagonal. But what if what if one of
+those diagonal entries is zero? Well,
+
+ align:start position:0%
+those diagonal entries is zero? Well,
+ 
+
+ align:start position:0%
+those diagonal entries is zero? Well,
+then with elimination, we know that we
+
+ align:start position:0%
+then with elimination, we know that we
+ 
+
+ align:start position:0%
+then with elimination, we know that we
+can get a row of zeros.
+
+ align:start position:0%
+can get a row of zeros.
+ 
+
+ align:start position:0%
+can get a row of zeros.
+And for a row of zeros, I'm using rule
+
+ align:start position:0%
+And for a row of zeros, I'm using rule
+ 
+
+ align:start position:0%
+And for a row of zeros, I'm using rule
+six. The determinant is zero. And that's
+
+ align:start position:0%
+six. The determinant is zero. And that's
+ 
+
+ align:start position:0%
+six. The determinant is zero. And that's
+right. So, so I can check the singular
+
+ align:start position:0%
+right. So, so I can check the singular
+ 
+
+ align:start position:0%
+right. So, so I can check the singular
+case. In fact, I can now get to the key
+
+ align:start position:0%
+case. In fact, I can now get to the key
+ 
+
+ align:start position:0%
+case. In fact, I can now get to the key
+point that determinant of
+
+ align:start position:0%
+point that determinant of
+ 
+
+ align:start position:0%
+point that determinant of
+a is zero exactly when exactly
+
+ align:start position:0%
+a is zero exactly when exactly
+ 
+
+ align:start position:0%
+a is zero exactly when exactly
+when a is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+single and otherwise it's not zero. So
+
+ align:start position:0%
+single and otherwise it's not zero. So
+ 
+
+ align:start position:0%
+single and otherwise it's not zero. So
+that the determinant is a fair test for
+
+ align:start position:0%
+that the determinant is a fair test for
+ 
+
+ align:start position:0%
+that the determinant is a fair test for
+invertability or
+
+ align:start position:0%
+invertability or
+ 
+
+ align:start position:0%
+invertability or
+non-invertability. Okay. So I must be
+
+ align:start position:0%
+non-invertability. Okay. So I must be
+ 
+
+ align:start position:0%
+non-invertability. Okay. So I must be
+close to that because I can take any
+
+ align:start position:0%
+close to that because I can take any
+ 
+
+ align:start position:0%
+close to that because I can take any
+matrix and get there. Do I did I have
+
+ align:start position:0%
+matrix and get there. Do I did I have
+ 
+
+ align:start position:0%
+matrix and get there. Do I did I have
+anything to
+
+ align:start position:0%
+anything to
+ 
+
+ align:start position:0%
+anything to
+say? The the proof that starts by saying
+
+ align:start position:0%
+say? The the proof that starts by saying
+ 
+
+ align:start position:0%
+say? The the proof that starts by saying
+by elimination go from A to U. Oh yeah.
+
+ align:start position:0%
+by elimination go from A to U. Oh yeah.
+ 
+
+ align:start position:0%
+by elimination go from A to U. Oh yeah.
+actually looks to me like I don't
+
+ align:start position:0%
+actually looks to me like I don't
+ 
+
+ align:start position:0%
+actually looks to me like I don't
+haven't said anything brand new
+
+ align:start position:0%
+haven't said anything brand new
+ 
+
+ align:start position:0%
+haven't said anything brand new
+here that that really I've got
+
+ align:start position:0%
+here that that really I've got
+ 
+
+ align:start position:0%
+here that that really I've got
+this because let's just remember the
+
+ align:start position:0%
+this because let's just remember the
+ 
+
+ align:start position:0%
+this because let's just remember the
+reasoning by elimination I can go
+
+ align:start position:0%
+reasoning by elimination I can go
+ 
+
+ align:start position:0%
+reasoning by elimination I can go
+from the original A to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U. Well, okay. Now suppose the matrix is
+
+ align:start position:0%
+U. Well, okay. Now suppose the matrix is
+ 
+
+ align:start position:0%
+U. Well, okay. Now suppose the matrix is
+is is singular. Okay. If the matrix is
+
+ align:start position:0%
+is is singular. Okay. If the matrix is
+ 
+
+ align:start position:0%
+is is singular. Okay. If the matrix is
+singular, what what happens? Then by
+
+ align:start position:0%
+singular, what what happens? Then by
+ 
+
+ align:start position:0%
+singular, what what happens? Then by
+elimination, I get a row of
+
+ align:start position:0%
+elimination, I get a row of
+ 
+
+ align:start position:0%
+elimination, I get a row of
+zeros and therefore the determinant is
+
+ align:start position:0%
+zeros and therefore the determinant is
+ 
+
+ align:start position:0%
+zeros and therefore the determinant is
+zero. And if the matrix is not singular,
+
+ align:start position:0%
+zero. And if the matrix is not singular,
+ 
+
+ align:start position:0%
+zero. And if the matrix is not singular,
+I don't get zero. So maybe do you want
+
+ align:start position:0%
+I don't get zero. So maybe do you want
+ 
+
+ align:start position:0%
+I don't get zero. So maybe do you want
+me to put this like in two parts? The
+
+ align:start position:0%
+me to put this like in two parts? The
+ 
+
+ align:start position:0%
+me to put this like in two parts? The
+determinant of a is not zero
+
+ align:start position:0%
+determinant of a is not zero
+ 
+
+ align:start position:0%
+determinant of a is not zero
+when a is inverted.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because I I've
+
+ align:start position:0%
+because I I've
+ 
+
+ align:start position:0%
+because I I've
+already in chapter two we figured out
+
+ align:start position:0%
+already in chapter two we figured out
+ 
+
+ align:start position:0%
+already in chapter two we figured out
+when is the matrix invertible. It's
+
+ align:start position:0%
+when is the matrix invertible. It's
+ 
+
+ align:start position:0%
+when is the matrix invertible. It's
+invertible when elimination produces a
+
+ align:start position:0%
+invertible when elimination produces a
+ 
+
+ align:start position:0%
+invertible when elimination produces a
+full set of pivots and now and we now we
+
+ align:start position:0%
+full set of pivots and now and we now we
+ 
+
+ align:start position:0%
+full set of pivots and now and we now we
+know the determinant is the product of
+
+ align:start position:0%
+know the determinant is the product of
+ 
+
+ align:start position:0%
+know the determinant is the product of
+those nonzero numbers. So those are the
+
+ align:start position:0%
+those nonzero numbers. So those are the
+ 
+
+ align:start position:0%
+those nonzero numbers. So those are the
+two cases the if it's singular I go to a
+
+ align:start position:0%
+two cases the if it's singular I go to a
+ 
+
+ align:start position:0%
+two cases the if it's singular I go to a
+row of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zeros. If it's invertible I go to u and
+
+ align:start position:0%
+zeros. If it's invertible I go to u and
+ 
+
+ align:start position:0%
+zeros. If it's invertible I go to u and
+then to the diagonal d and then which
+
+ align:start position:0%
+then to the diagonal d and then which
+ 
+
+ align:start position:0%
+then to the diagonal d and then which
+and then to d1 d2 up to
+
+ align:start position:0%
+and then to d1 d2 up to
+ 
+
+ align:start position:0%
+and then to d1 d2 up to
+dn as the formula. So we we have a
+
+ align:start position:0%
+dn as the formula. So we we have a
+ 
+
+ align:start position:0%
+dn as the formula. So we we have a
+formula
+
+ align:start position:0%
+formula
+ 
+
+ align:start position:0%
+formula
+now. We have a formula for the
+
+ align:start position:0%
+now. We have a formula for the
+ 
+
+ align:start position:0%
+now. We have a formula for the
+determinant and it's actually a very
+
+ align:start position:0%
+determinant and it's actually a very
+ 
+
+ align:start position:0%
+determinant and it's actually a very
+much more practical formula than the AD
+
+ align:start position:0%
+much more practical formula than the AD
+ 
+
+ align:start position:0%
+much more practical formula than the AD
+minus BC
+
+ align:start position:0%
+minus BC
+ 
+
+ align:start position:0%
+minus BC
+formula. Is it correct? I maybe should
+
+ align:start position:0%
+formula. Is it correct? I maybe should
+ 
+
+ align:start position:0%
+formula. Is it correct? I maybe should
+just let's just check that 2x two. What
+
+ align:start position:0%
+just let's just check that 2x two. What
+ 
+
+ align:start position:0%
+just let's just check that 2x two. What
+are the pivots of a 2x two
+
+ align:start position:0%
+are the pivots of a 2x two
+ 
+
+ align:start position:0%
+are the pivots of a 2x two
+matrix? What what does elimination do
+
+ align:start position:0%
+matrix? What what does elimination do
+ 
+
+ align:start position:0%
+matrix? What what does elimination do
+with that 2x2 matrix?
+
+ align:start position:0%
+with that 2x2 matrix?
+ 
+
+ align:start position:0%
+with that 2x2 matrix?
+it. There's the first pivot. Fine.
+
+ align:start position:0%
+it. There's the first pivot. Fine.
+ 
+
+ align:start position:0%
+it. There's the first pivot. Fine.
+What's the second
+
+ align:start position:0%
+What's the second
+ 
+
+ align:start position:0%
+What's the second
+pivot? We subtract. So, so, so I'm
+
+ align:start position:0%
+pivot? We subtract. So, so, so I'm
+ 
+
+ align:start position:0%
+pivot? We subtract. So, so, so I'm
+putting it in its upper triangular form.
+
+ align:start position:0%
+putting it in its upper triangular form.
+ 
+
+ align:start position:0%
+putting it in its upper triangular form.
+What do I, my multiplier
+
+ align:start position:0%
+What do I, my multiplier
+ 
+
+ align:start position:0%
+What do I, my multiplier
+is C over A, right? I multiply that row
+
+ align:start position:0%
+is C over A, right? I multiply that row
+ 
+
+ align:start position:0%
+is C over A, right? I multiply that row
+by C / A and I subtract to get that
+
+ align:start position:0%
+by C / A and I subtract to get that
+ 
+
+ align:start position:0%
+by C / A and I subtract to get that
+zero. And here I have D minus C / A time
+
+ align:start position:0%
+zero. And here I have D minus C / A time
+ 
+
+ align:start position:0%
+zero. And here I have D minus C / A time
+B.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's the elimination on a 2x two.
+
+ align:start position:0%
+That's the elimination on a 2x two.
+ 
+
+ align:start position:0%
+That's the elimination on a 2x two.
+So I've finally discovered that the
+
+ align:start position:0%
+So I've finally discovered that the
+ 
+
+ align:start position:0%
+So I've finally discovered that the
+determinant of this matrix I' I've just
+
+ align:start position:0%
+determinant of this matrix I' I've just
+ 
+
+ align:start position:0%
+determinant of this matrix I' I've just
+I've got it from the properties not by
+
+ align:start position:0%
+I've got it from the properties not by
+ 
+
+ align:start position:0%
+I've got it from the properties not by
+knowing the answer from last
+
+ align:start position:0%
+knowing the answer from last
+ 
+
+ align:start position:0%
+knowing the answer from last
+year that the determinant of this 2x two
+
+ align:start position:0%
+year that the determinant of this 2x two
+ 
+
+ align:start position:0%
+year that the determinant of this 2x two
+is the product of a times that and of
+
+ align:start position:0%
+is the product of a times that and of
+ 
+
+ align:start position:0%
+is the product of a times that and of
+course when I multiply a by that the
+
+ align:start position:0%
+course when I multiply a by that the
+ 
+
+ align:start position:0%
+course when I multiply a by that the
+product of that and that is a d minus
+
+ align:start position:0%
+product of that and that is a d minus
+ 
+
+ align:start position:0%
+product of that and that is a d minus
+the a's cancel bc
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's great provided A isn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero. If A was zero, that step wasn't
+
+ align:start position:0%
+zero. If A was zero, that step wasn't
+ 
+
+ align:start position:0%
+zero. If A was zero, that step wasn't
+allowed. Zero wasn't a pivot. So that's
+
+ align:start position:0%
+allowed. Zero wasn't a pivot. So that's
+ 
+
+ align:start position:0%
+allowed. Zero wasn't a pivot. So that's
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+I've I've covered all the bases. I have
+
+ align:start position:0%
+I've I've covered all the bases. I have
+ 
+
+ align:start position:0%
+I've I've covered all the bases. I have
+to if if A is zero, then I have to do
+
+ align:start position:0%
+to if if A is zero, then I have to do
+ 
+
+ align:start position:0%
+to if if A is zero, then I have to do
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+exchange. And if the exchange doesn't
+
+ align:start position:0%
+exchange. And if the exchange doesn't
+ 
+
+ align:start position:0%
+exchange. And if the exchange doesn't
+work, it's because A is singular.
+
+ align:start position:0%
+work, it's because A is singular.
+ 
+
+ align:start position:0%
+work, it's because A is singular.
+Okay, those are
+
+ align:start position:0%
+Okay, those are
+ 
+
+ align:start position:0%
+Okay, those are
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+the those are the direct properties of
+
+ align:start position:0%
+the those are the direct properties of
+ 
+
+ align:start position:0%
+the those are the direct properties of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+determinant. And now finally, I've got
+
+ align:start position:0%
+determinant. And now finally, I've got
+ 
+
+ align:start position:0%
+determinant. And now finally, I've got
+two more nine and 10.
+
+ align:start position:0%
+two more nine and 10.
+ 
+
+ align:start position:0%
+two more nine and 10.
+And
+
+ align:start position:0%
+And
+ 
+
+ align:start position:0%
+And
+that's I I think you can like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh the ones we've got
+
+ align:start position:0%
+uh the ones we've got
+ 
+
+ align:start position:0%
+uh the ones we've got
+here are so are are totally connected
+
+ align:start position:0%
+here are so are are totally connected
+ 
+
+ align:start position:0%
+here are so are are totally connected
+with our elimination
+
+ align:start position:0%
+with our elimination
+ 
+
+ align:start position:0%
+with our elimination
+process and and what whether pivots are
+
+ align:start position:0%
+process and and what whether pivots are
+ 
+
+ align:start position:0%
+process and and what whether pivots are
+available and whether or whether we get
+
+ align:start position:0%
+available and whether or whether we get
+ 
+
+ align:start position:0%
+available and whether or whether we get
+a row of zeros. I think all that you can
+
+ align:start position:0%
+a row of zeros. I think all that you can
+ 
+
+ align:start position:0%
+a row of zeros. I think all that you can
+swallow in one shot. Let me tell you
+
+ align:start position:0%
+swallow in one shot. Let me tell you
+ 
+
+ align:start position:0%
+swallow in one shot. Let me tell you
+properties nine and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+10. They're quick to write
+
+ align:start position:0%
+10. They're quick to write
+ 
+
+ align:start position:0%
+10. They're quick to write
+down. They're very, very
+
+ align:start position:0%
+down. They're very, very
+ 
+
+ align:start position:0%
+down. They're very, very
+useful. So, I'll just write them down
+
+ align:start position:0%
+useful. So, I'll just write them down
+ 
+
+ align:start position:0%
+useful. So, I'll just write them down
+and use them. Property nine says that
+
+ align:start position:0%
+and use them. Property nine says that
+ 
+
+ align:start position:0%
+and use them. Property nine says that
+the determinant of a product if I
+
+ align:start position:0%
+the determinant of a product if I
+ 
+
+ align:start position:0%
+the determinant of a product if I
+multiply two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrices. So if I multiply two matrices
+
+ align:start position:0%
+matrices. So if I multiply two matrices
+ 
+
+ align:start position:0%
+matrices. So if I multiply two matrices
+A and
+
+ align:start position:0%
+A and
+ 
+
+ align:start position:0%
+A and
+B that the determinant of the product
+
+ align:start position:0%
+B that the determinant of the product
+ 
+
+ align:start position:0%
+B that the determinant of the product
+is determinant of
+
+ align:start position:0%
+is determinant of
+ 
+
+ align:start position:0%
+is determinant of
+A times determinant of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B. And for me that one is
+
+ align:start position:0%
+B. And for me that one is
+ 
+
+ align:start position:0%
+B. And for me that one is
+like that's a very valuable property and
+
+ align:start position:0%
+like that's a very valuable property and
+ 
+
+ align:start position:0%
+like that's a very valuable property and
+it's sort of like partly coming out of
+
+ align:start position:0%
+it's sort of like partly coming out of
+ 
+
+ align:start position:0%
+it's sort of like partly coming out of
+the blue because we haven't been
+
+ align:start position:0%
+the blue because we haven't been
+ 
+
+ align:start position:0%
+the blue because we haven't been
+multiplying matrices. And here suddenly
+
+ align:start position:0%
+multiplying matrices. And here suddenly
+ 
+
+ align:start position:0%
+multiplying matrices. And here suddenly
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determinant has this multiplying
+
+ align:start position:0%
+determinant has this multiplying
+ 
+
+ align:start position:0%
+determinant has this multiplying
+property. Remember it didn't have the
+
+ align:start position:0%
+property. Remember it didn't have the
+ 
+
+ align:start position:0%
+property. Remember it didn't have the
+linear property. It didn't have the
+
+ align:start position:0%
+linear property. It didn't have the
+ 
+
+ align:start position:0%
+linear property. It didn't have the
+adding property. The determinant of a
+
+ align:start position:0%
+adding property. The determinant of a
+ 
+
+ align:start position:0%
+adding property. The determinant of a
+plus b is not the sum of the determinant
+
+ align:start position:0%
+plus b is not the sum of the determinant
+ 
+
+ align:start position:0%
+plus b is not the sum of the determinant
+but the determinant of a times b is the
+
+ align:start position:0%
+but the determinant of a times b is the
+ 
+
+ align:start position:0%
+but the determinant of a times b is the
+product of it is the product of it.
+
+ align:start position:0%
+product of it is the product of it.
+ 
+
+ align:start position:0%
+product of it is the product of it.
+Okay. So for
+
+ align:start position:0%
+Okay. So for
+ 
+
+ align:start position:0%
+Okay. So for
+example, what's the determinant of a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse using that property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nine? Let me let me put that under here
+
+ align:start position:0%
+nine? Let me let me put that under here
+ 
+
+ align:start position:0%
+nine? Let me let me put that under here
+because the camera is happier if it can
+
+ align:start position:0%
+because the camera is happier if it can
+ 
+
+ align:start position:0%
+because the camera is happier if it can
+focus on both at once. So let me put it
+
+ align:start position:0%
+focus on both at once. So let me put it
+ 
+
+ align:start position:0%
+focus on both at once. So let me put it
+underneath. The determinant of a inverse
+
+ align:start position:0%
+underneath. The determinant of a inverse
+ 
+
+ align:start position:0%
+underneath. The determinant of a inverse
+because I I won't and the property 10
+
+ align:start position:0%
+because I I won't and the property 10
+ 
+
+ align:start position:0%
+because I I won't and the property 10
+will come
+
+ align:start position:0%
+will come
+ 
+
+ align:start position:0%
+will come
+uh in that
+
+ align:start position:0%
+uh in that
+ 
+
+ align:start position:0%
+uh in that
+space. What what does this tell me about
+
+ align:start position:0%
+space. What what does this tell me about
+ 
+
+ align:start position:0%
+space. What what does this tell me about
+a inverse its determinant? Okay. Well,
+
+ align:start position:0%
+a inverse its determinant? Okay. Well,
+ 
+
+ align:start position:0%
+a inverse its determinant? Okay. Well,
+what do I know about a
+
+ align:start position:0%
+what do I know about a
+ 
+
+ align:start position:0%
+what do I know about a
+inverse? I know that a inverse time a is
+
+ align:start position:0%
+inverse? I know that a inverse time a is
+ 
+
+ align:start position:0%
+inverse? I know that a inverse time a is
+odd. So, what am I going to do?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm going to take determinants of both
+
+ align:start position:0%
+I'm going to take determinants of both
+ 
+
+ align:start position:0%
+I'm going to take determinants of both
+sides. The determinant of I is one and
+
+ align:start position:0%
+sides. The determinant of I is one and
+ 
+
+ align:start position:0%
+sides. The determinant of I is one and
+what's the determinant of A inverse
+
+ align:start position:0%
+what's the determinant of A inverse
+ 
+
+ align:start position:0%
+what's the determinant of A inverse
+A? That's a product of two matrices A
+
+ align:start position:0%
+A? That's a product of two matrices A
+ 
+
+ align:start position:0%
+A? That's a product of two matrices A
+and B. So it's the product of the
+
+ align:start position:0%
+and B. So it's the product of the
+ 
+
+ align:start position:0%
+and B. So it's the product of the
+determinant. So what am I learning? I'm
+
+ align:start position:0%
+determinant. So what am I learning? I'm
+ 
+
+ align:start position:0%
+determinant. So what am I learning? I'm
+learning that the determinant of A
+
+ align:start position:0%
+learning that the determinant of A
+ 
+
+ align:start position:0%
+learning that the determinant of A
+inverse times the determinant of
+
+ align:start position:0%
+inverse times the determinant of
+ 
+
+ align:start position:0%
+inverse times the determinant of
+A is the determinant of I. That's this
+
+ align:start position:0%
+A is the determinant of I. That's this
+ 
+
+ align:start position:0%
+A is the determinant of I. That's this
+one. Again, I happily use property one.
+
+ align:start position:0%
+one. Again, I happily use property one.
+ 
+
+ align:start position:0%
+one. Again, I happily use property one.
+Okay. So, that tells me that the
+
+ align:start position:0%
+Okay. So, that tells me that the
+ 
+
+ align:start position:0%
+Okay. So, that tells me that the
+determinant of a inverse is one over
+
+ align:start position:0%
+determinant of a inverse is one over
+ 
+
+ align:start position:0%
+determinant of a inverse is one over
+here's my here's my conclusion is one
+
+ align:start position:0%
+here's my here's my conclusion is one
+ 
+
+ align:start position:0%
+here's my here's my conclusion is one
+over the determinant of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a. I guess that that I I always try to
+
+ align:start position:0%
+a. I guess that that I I always try to
+ 
+
+ align:start position:0%
+a. I guess that that I I always try to
+think well do we know some cases of
+
+ align:start position:0%
+think well do we know some cases of
+ 
+
+ align:start position:0%
+think well do we know some cases of
+that? Of course we know it's right
+
+ align:start position:0%
+that? Of course we know it's right
+ 
+
+ align:start position:0%
+that? Of course we know it's right
+already if a is diagonal. If a is a
+
+ align:start position:0%
+already if a is diagonal. If a is a
+ 
+
+ align:start position:0%
+already if a is diagonal. If a is a
+diagonal
+
+ align:start position:0%
+diagonal
+ 
+
+ align:start position:0%
+diagonal
+matrix then it's determined as just a
+
+ align:start position:0%
+matrix then it's determined as just a
+ 
+
+ align:start position:0%
+matrix then it's determined as just a
+product of those numbers. So if if a is
+
+ align:start position:0%
+product of those numbers. So if if a is
+ 
+
+ align:start position:0%
+product of those numbers. So if if a is
+for example 2
+
+ align:start position:0%
+for example 2
+ 
+
+ align:start position:0%
+for example 2
+3 then we know that a inverse is 12
+
+ align:start position:0%
+3 then we know that a inverse is 12
+ 
+
+ align:start position:0%
+3 then we know that a inverse is 12
+1/3 and sure enough that has
+
+ align:start position:0%
+1/3 and sure enough that has
+ 
+
+ align:start position:0%
+1/3 and sure enough that has
+determinant six and that has determinant
+
+ align:start position:0%
+determinant six and that has determinant
+ 
+
+ align:start position:0%
+determinant six and that has determinant
+16 and our rule
+
+ align:start position:0%
+16 and our rule
+ 
+
+ align:start position:0%
+16 and our rule
+checks. So somehow this proof this
+
+ align:start position:0%
+checks. So somehow this proof this
+ 
+
+ align:start position:0%
+checks. So somehow this proof this
+property has to somehow the proof of of
+
+ align:start position:0%
+property has to somehow the proof of of
+ 
+
+ align:start position:0%
+property has to somehow the proof of of
+that property if we can boil it down to
+
+ align:start position:0%
+that property if we can boil it down to
+ 
+
+ align:start position:0%
+that property if we can boil it down to
+diagonal matrices then we can read it
+
+ align:start position:0%
+diagonal matrices then we can read it
+ 
+
+ align:start position:0%
+diagonal matrices then we can read it
+off whether it's A and A inverse or two
+
+ align:start position:0%
+off whether it's A and A inverse or two
+ 
+
+ align:start position:0%
+off whether it's A and A inverse or two
+different diagonal matrices A and B for
+
+ align:start position:0%
+different diagonal matrices A and B for
+ 
+
+ align:start position:0%
+different diagonal matrices A and B for
+diagonal. So what am I saying? I'm
+
+ align:start position:0%
+diagonal. So what am I saying? I'm
+ 
+
+ align:start position:0%
+diagonal. So what am I saying? I'm
+saying for diagonal matrices,
+
+ align:start position:0%
+saying for diagonal matrices,
+ 
+
+ align:start position:0%
+saying for diagonal matrices,
+check. But we'd have to do elimination
+
+ align:start position:0%
+check. But we'd have to do elimination
+ 
+
+ align:start position:0%
+check. But we'd have to do elimination
+steps. We'd have to patiently do the the
+
+ align:start position:0%
+steps. We'd have to patiently do the the
+ 
+
+ align:start position:0%
+steps. We'd have to patiently do the the
+uh argument if we want to use these
+
+ align:start position:0%
+uh argument if we want to use these
+ 
+
+ align:start position:0%
+uh argument if we want to use these
+previous properties to get it for other
+
+ align:start position:0%
+previous properties to get it for other
+ 
+
+ align:start position:0%
+previous properties to get it for other
+matrices. It it also tells me what just
+
+ align:start position:0%
+matrices. It it also tells me what just
+ 
+
+ align:start position:0%
+matrices. It it also tells me what just
+let's see what else it's telling me.
+
+ align:start position:0%
+let's see what else it's telling me.
+ 
+
+ align:start position:0%
+let's see what else it's telling me.
+What's the determinant of of a squ? If I
+
+ align:start position:0%
+What's the determinant of of a squ? If I
+ 
+
+ align:start position:0%
+What's the determinant of of a squ? If I
+take a matrix and square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it, then the determinant just got
+
+ align:start position:0%
+it, then the determinant just got
+ 
+
+ align:start position:0%
+it, then the determinant just got
+squared, right? The determinant of a
+
+ align:start position:0%
+squared, right? The determinant of a
+ 
+
+ align:start position:0%
+squared, right? The determinant of a
+squared is the determinant of a time the
+
+ align:start position:0%
+squared is the determinant of a time the
+ 
+
+ align:start position:0%
+squared is the determinant of a time the
+determinant of a. So if I square the
+
+ align:start position:0%
+determinant of a. So if I square the
+ 
+
+ align:start position:0%
+determinant of a. So if I square the
+matrix, I square the determinant. If I
+
+ align:start position:0%
+matrix, I square the determinant. If I
+ 
+
+ align:start position:0%
+matrix, I square the determinant. If I
+double the
+
+ align:start position:0%
+double the
+ 
+
+ align:start position:0%
+double the
+matrix, what do I do to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determinant? Think about that. If I
+
+ align:start position:0%
+determinant? Think about that. If I
+ 
+
+ align:start position:0%
+determinant? Think about that. If I
+double the matrix, So the determinant of
+
+ align:start position:0%
+double the matrix, So the determinant of
+ 
+
+ align:start position:0%
+double the matrix, So the determinant of
+a so I'm writing down like facts that
+
+ align:start position:0%
+a so I'm writing down like facts that
+ 
+
+ align:start position:0%
+a so I'm writing down like facts that
+follow the determinant of a
+
+ align:start position:0%
+follow the determinant of a
+ 
+
+ align:start position:0%
+follow the determinant of a
+squared is the determinant of a all
+
+ align:start position:0%
+squared is the determinant of a all
+ 
+
+ align:start position:0%
+squared is the determinant of a all
+squared the determinant of 2
+
+ align:start position:0%
+squared the determinant of 2
+ 
+
+ align:start position:0%
+squared the determinant of 2
+a is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what that's a +
+
+ align:start position:0%
+what that's a +
+ 
+
+ align:start position:0%
+what that's a +
+a but wait there I I don't want the
+
+ align:start position:0%
+a but wait there I I don't want the
+ 
+
+ align:start position:0%
+a but wait there I I don't want the
+answer to determinant of A here that's
+
+ align:start position:0%
+answer to determinant of A here that's
+ 
+
+ align:start position:0%
+answer to determinant of A here that's
+wrong. It's not two determinant of A.
+
+ align:start position:0%
+wrong. It's not two determinant of A.
+ 
+
+ align:start position:0%
+wrong. It's not two determinant of A.
+What is it? What's what's the number
+
+ align:start position:0%
+What is it? What's what's the number
+ 
+
+ align:start position:0%
+What is it? What's what's the number
+that I have to multiply determinant of A
+
+ align:start position:0%
+that I have to multiply determinant of A
+ 
+
+ align:start position:0%
+that I have to multiply determinant of A
+by? If I if I double the whole matrix.
+
+ align:start position:0%
+by? If I if I double the whole matrix.
+ 
+
+ align:start position:0%
+by? If I if I double the whole matrix.
+If I double every entry in the matrix,
+
+ align:start position:0%
+If I double every entry in the matrix,
+ 
+
+ align:start position:0%
+If I double every entry in the matrix,
+what happens to the
+
+ align:start position:0%
+what happens to the
+ 
+
+ align:start position:0%
+what happens to the
+determinant? It suppose it's an N byN
+
+ align:start position:0%
+determinant? It suppose it's an N byN
+ 
+
+ align:start position:0%
+determinant? It suppose it's an N byN
+matrix. 2 to the N, right? Two to the
+
+ align:start position:0%
+matrix. 2 to the N, right? Two to the
+ 
+
+ align:start position:0%
+matrix. 2 to the N, right? Two to the
+nth. Now, why is it 2 to the nth and not
+
+ align:start position:0%
+nth. Now, why is it 2 to the nth and not
+ 
+
+ align:start position:0%
+nth. Now, why is it 2 to the nth and not
+just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two? So, why is it 2 to the
+
+ align:start position:0%
+two? So, why is it 2 to the
+ 
+
+ align:start position:0%
+two? So, why is it 2 to the
+nth? Because I'm factoring out two from
+
+ align:start position:0%
+nth? Because I'm factoring out two from
+ 
+
+ align:start position:0%
+nth? Because I'm factoring out two from
+every row. There's a factor, this has a
+
+ align:start position:0%
+every row. There's a factor, this has a
+ 
+
+ align:start position:0%
+every row. There's a factor, this has a
+factor two in every row. So, I can
+
+ align:start position:0%
+factor two in every row. So, I can
+ 
+
+ align:start position:0%
+factor two in every row. So, I can
+factor two out of the first row. I
+
+ align:start position:0%
+factor two out of the first row. I
+ 
+
+ align:start position:0%
+factor two out of the first row. I
+factor a different two out of the second
+
+ align:start position:0%
+factor a different two out of the second
+ 
+
+ align:start position:0%
+factor a different two out of the second
+row, a different two out of the nth row.
+
+ align:start position:0%
+row, a different two out of the nth row.
+ 
+
+ align:start position:0%
+row, a different two out of the nth row.
+So, I've got all those twos coming out.
+
+ align:start position:0%
+So, I've got all those twos coming out.
+ 
+
+ align:start position:0%
+So, I've got all those twos coming out.
+So, it's it's It's like volume really.
+
+ align:start position:0%
+So, it's it's It's like volume really.
+ 
+
+ align:start position:0%
+So, it's it's It's like volume really.
+And that's the that's one of the great
+
+ align:start position:0%
+And that's the that's one of the great
+ 
+
+ align:start position:0%
+And that's the that's one of the great
+applications of determinant. If I if if
+
+ align:start position:0%
+applications of determinant. If I if if
+ 
+
+ align:start position:0%
+applications of determinant. If I if if
+if I have a
+
+ align:start position:0%
+if I have a
+ 
+
+ align:start position:0%
+if I have a
+box and I double all the
+
+ align:start position:0%
+box and I double all the
+ 
+
+ align:start position:0%
+box and I double all the
+sides, I multiply the volume by 2 to the
+
+ align:start position:0%
+sides, I multiply the volume by 2 to the
+ 
+
+ align:start position:0%
+sides, I multiply the volume by 2 to the
+n. If it's a box in three dimensions,
+
+ align:start position:0%
+n. If it's a box in three dimensions,
+ 
+
+ align:start position:0%
+n. If it's a box in three dimensions,
+I've multiplied the volume by
+
+ align:start position:0%
+I've multiplied the volume by
+ 
+
+ align:start position:0%
+I've multiplied the volume by
+8. And that's so that's this is rule 3A
+
+ align:start position:0%
+8. And that's so that's this is rule 3A
+ 
+
+ align:start position:0%
+8. And that's so that's this is rule 3A
+here. This is rule
+
+ align:start position:0%
+here. This is rule
+ 
+
+ align:start position:0%
+here. This is rule
+nine. And notice the way this rule sort
+
+ align:start position:0%
+nine. And notice the way this rule sort
+ 
+
+ align:start position:0%
+nine. And notice the way this rule sort
+of checks out with a singular non-s
+
+ align:start position:0%
+of checks out with a singular non-s
+ 
+
+ align:start position:0%
+of checks out with a singular non-s
+singular
+
+ align:start position:0%
+singular
+ 
+
+ align:start position:0%
+singular
+stuff.
+
+ align:start position:0%
+stuff.
+ 
+
+ align:start position:0%
+stuff.
+That that if a is
+
+ align:start position:0%
+That that if a is
+ 
+
+ align:start position:0%
+That that if a is
+invertible, what does that mean about
+
+ align:start position:0%
+invertible, what does that mean about
+ 
+
+ align:start position:0%
+invertible, what does that mean about
+its determinant? It's not zero. And
+
+ align:start position:0%
+its determinant? It's not zero. And
+ 
+
+ align:start position:0%
+its determinant? It's not zero. And
+therefore, this makes sense.
+
+ align:start position:0%
+therefore, this makes sense.
+ 
+
+ align:start position:0%
+therefore, this makes sense.
+the case when determinant of a is zero.
+
+ align:start position:0%
+the case when determinant of a is zero.
+ 
+
+ align:start position:0%
+the case when determinant of a is zero.
+That's the case where my
+
+ align:start position:0%
+That's the case where my
+ 
+
+ align:start position:0%
+That's the case where my
+formula doesn't work anymore. If
+
+ align:start position:0%
+formula doesn't work anymore. If
+ 
+
+ align:start position:0%
+formula doesn't work anymore. If
+determinant of a is zero, this is this
+
+ align:start position:0%
+determinant of a is zero, this is this
+ 
+
+ align:start position:0%
+determinant of a is zero, this is this
+is ridiculous. And that's ridiculous. A
+
+ align:start position:0%
+is ridiculous. And that's ridiculous. A
+ 
+
+ align:start position:0%
+is ridiculous. And that's ridiculous. A
+inverse doesn't
+
+ align:start position:0%
+inverse doesn't
+ 
+
+ align:start position:0%
+inverse doesn't
+exist. And one over zero doesn't make
+
+ align:start position:0%
+exist. And one over zero doesn't make
+ 
+
+ align:start position:0%
+exist. And one over zero doesn't make
+sense. Okay,
+
+ align:start position:0%
+sense. Okay,
+ 
+
+ align:start position:0%
+sense. Okay,
+so don't miss this property. It's sort
+
+ align:start position:0%
+so don't miss this property. It's sort
+ 
+
+ align:start position:0%
+so don't miss this property. It's sort
+of like amazing that it can. And the
+
+ align:start position:0%
+of like amazing that it can. And the
+ 
+
+ align:start position:0%
+of like amazing that it can. And the
+10th
+
+ align:start position:0%
+10th
+ 
+
+ align:start position:0%
+10th
+property
+
+ align:start position:0%
+property
+ 
+
+ align:start position:0%
+property
+is equally simple to state that the
+
+ align:start position:0%
+is equally simple to state that the
+ 
+
+ align:start position:0%
+is equally simple to state that the
+determinant of a transpose equals the
+
+ align:start position:0%
+determinant of a transpose equals the
+ 
+
+ align:start position:0%
+determinant of a transpose equals the
+determinant of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a. And of course, let's just check it on
+
+ align:start position:0%
+a. And of course, let's just check it on
+ 
+
+ align:start position:0%
+a. And of course, let's just check it on
+the AB CD
+
+ align:start position:0%
+the AB CD
+ 
+
+ align:start position:0%
+the AB CD
+guy. We could check that. Sure enough,
+
+ align:start position:0%
+guy. We could check that. Sure enough,
+ 
+
+ align:start position:0%
+guy. We could check that. Sure enough,
+that's AB CD. It works.
+
+ align:start position:0%
+that's AB CD. It works.
+ 
+
+ align:start position:0%
+that's AB CD. It works.
+It's a d minus bc. It's a d minus bc.
+
+ align:start position:0%
+It's a d minus bc. It's a d minus bc.
+ 
+
+ align:start position:0%
+It's a d minus bc. It's a d minus bc.
+Sure enough. So that that transposing
+
+ align:start position:0%
+Sure enough. So that that transposing
+ 
+
+ align:start position:0%
+Sure enough. So that that transposing
+did not change the
+
+ align:start position:0%
+did not change the
+ 
+
+ align:start position:0%
+did not change the
+determinant. But what it does change is
+
+ align:start position:0%
+determinant. But what it does change is
+ 
+
+ align:start position:0%
+determinant. But what it does change is
+uh well what it what it does is it lists
+
+ align:start position:0%
+uh well what it what it does is it lists
+ 
+
+ align:start position:0%
+uh well what it what it does is it lists
+so all I've been working with
+
+ align:start position:0%
+so all I've been working with
+ 
+
+ align:start position:0%
+so all I've been working with
+rows. If a if a row is all zeros the
+
+ align:start position:0%
+rows. If a if a row is all zeros the
+ 
+
+ align:start position:0%
+rows. If a if a row is all zeros the
+determinant is zero. But now with rule
+
+ align:start position:0%
+determinant is zero. But now with rule
+ 
+
+ align:start position:0%
+determinant is zero. But now with rule
+10, I know what to do. If a column is
+
+ align:start position:0%
+10, I know what to do. If a column is
+ 
+
+ align:start position:0%
+10, I know what to do. If a column is
+all zero, if a column is all zero,
+
+ align:start position:0%
+all zero, if a column is all zero,
+ 
+
+ align:start position:0%
+all zero, if a column is all zero,
+what's the
+
+ align:start position:0%
+what's the
+ 
+
+ align:start position:0%
+what's the
+determinant? Zero again. So like all
+
+ align:start position:0%
+determinant? Zero again. So like all
+ 
+
+ align:start position:0%
+determinant? Zero again. So like all
+those properties about rows, exchanging
+
+ align:start position:0%
+those properties about rows, exchanging
+ 
+
+ align:start position:0%
+those properties about rows, exchanging
+two rows reverses the sign. Now
+
+ align:start position:0%
+two rows reverses the sign. Now
+ 
+
+ align:start position:0%
+two rows reverses the sign. Now
+exchanging two columns reverses the sign
+
+ align:start position:0%
+exchanging two columns reverses the sign
+ 
+
+ align:start position:0%
+exchanging two columns reverses the sign
+because I can always if I want to see
+
+ align:start position:0%
+because I can always if I want to see
+ 
+
+ align:start position:0%
+because I can always if I want to see
+why I can transpose those columns become
+
+ align:start position:0%
+why I can transpose those columns become
+ 
+
+ align:start position:0%
+why I can transpose those columns become
+rows. I do the exchange I transpose back
+
+ align:start position:0%
+rows. I do the exchange I transpose back
+ 
+
+ align:start position:0%
+rows. I do the exchange I transpose back
+and I've done a column operation.
+
+ align:start position:0%
+and I've done a column operation.
+ 
+
+ align:start position:0%
+and I've done a column operation.
+So in in in conclusion, there was
+
+ align:start position:0%
+So in in in conclusion, there was
+ 
+
+ align:start position:0%
+So in in in conclusion, there was
+nothing special about row one because I
+
+ align:start position:0%
+nothing special about row one because I
+ 
+
+ align:start position:0%
+nothing special about row one because I
+could exchange rows. And now there's
+
+ align:start position:0%
+could exchange rows. And now there's
+ 
+
+ align:start position:0%
+could exchange rows. And now there's
+nothing special about rows that that
+
+ align:start position:0%
+nothing special about rows that that
+ 
+
+ align:start position:0%
+nothing special about rows that that
+isn't equally true for columns because
+
+ align:start position:0%
+isn't equally true for columns because
+ 
+
+ align:start position:0%
+isn't equally true for columns because
+this is the same. Okay. And again, maybe
+
+ align:start position:0%
+this is the same. Okay. And again, maybe
+ 
+
+ align:start position:0%
+this is the same. Okay. And again, maybe
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+won't Oh, let's see. Do we maybe it's
+
+ align:start position:0%
+won't Oh, let's see. Do we maybe it's
+ 
+
+ align:start position:0%
+won't Oh, let's see. Do we maybe it's
+worth seeing a quick proof of this
+
+ align:start position:0%
+worth seeing a quick proof of this
+ 
+
+ align:start position:0%
+worth seeing a quick proof of this
+number 10? A quick a quick uh proof of
+
+ align:start position:0%
+number 10? A quick a quick uh proof of
+ 
+
+ align:start position:0%
+number 10? A quick a quick uh proof of
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+10. Let me take the this is number
+
+ align:start position:0%
+10. Let me take the this is number
+ 
+
+ align:start position:0%
+10. Let me take the this is number
+10. A
+
+ align:start position:0%
+10. A
+ 
+
+ align:start position:0%
+10. A
+transpose equals
+
+ align:start position:0%
+transpose equals
+ 
+
+ align:start position:0%
+transpose equals
+a determinant of a transpose equals
+
+ align:start position:0%
+a determinant of a transpose equals
+ 
+
+ align:start position:0%
+a determinant of a transpose equals
+determinant of a. That's what I should
+
+ align:start position:0%
+determinant of a. That's what I should
+ 
+
+ align:start position:0%
+determinant of a. That's what I should
+have said. Okay. So let let's just uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let a typical matrix A if I use
+
+ align:start position:0%
+let a typical matrix A if I use
+ 
+
+ align:start position:0%
+let a typical matrix A if I use
+elimination is factors into
+
+ align:start position:0%
+elimination is factors into
+ 
+
+ align:start position:0%
+elimination is factors into
+LU and the transpose
+
+ align:start position:0%
+LU and the transpose
+ 
+
+ align:start position:0%
+LU and the transpose
+is U transpose
+
+ align:start position:0%
+is U transpose
+ 
+
+ align:start position:0%
+is U transpose
+LRPOSE. This
+
+ align:start position:0%
+LRPOSE. This
+ 
+
+ align:start position:0%
+LRPOSE. This
+is let me this is to prove
+
+ align:start position:0%
+is let me this is to prove
+ 
+
+ align:start position:0%
+is let me this is to prove
+So this is this is prove this is prove
+
+ align:start position:0%
+So this is this is prove this is prove
+ 
+
+ align:start position:0%
+So this is this is prove this is prove
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+using well I don't know which ones I'll
+
+ align:start position:0%
+using well I don't know which ones I'll
+ 
+
+ align:start position:0%
+using well I don't know which ones I'll
+use so I'll put them all in one to nine.
+
+ align:start position:0%
+use so I'll put them all in one to nine.
+ 
+
+ align:start position:0%
+use so I'll put them all in one to nine.
+Okay I'm going to prove number 10 by
+
+ align:start position:0%
+Okay I'm going to prove number 10 by
+ 
+
+ align:start position:0%
+Okay I'm going to prove number 10 by
+using one to nine. I won't cover every
+
+ align:start position:0%
+using one to nine. I won't cover every
+ 
+
+ align:start position:0%
+using one to nine. I won't cover every
+case but I'll cover almost every case.
+
+ align:start position:0%
+case but I'll cover almost every case.
+ 
+
+ align:start position:0%
+case but I'll cover almost every case.
+So in almost every case a can factor
+
+ align:start position:0%
+So in almost every case a can factor
+ 
+
+ align:start position:0%
+So in almost every case a can factor
+into lu and arpose can factor into that.
+
+ align:start position:0%
+into lu and arpose can factor into that.
+ 
+
+ align:start position:0%
+into lu and arpose can factor into that.
+Now what do I do next? So I want to
+
+ align:start position:0%
+Now what do I do next? So I want to
+ 
+
+ align:start position:0%
+Now what do I do next? So I want to
+prove that these are the
+
+ align:start position:0%
+prove that these are the
+ 
+
+ align:start position:0%
+prove that these are the
+same. I see a product
+
+ align:start position:0%
+same. I see a product
+ 
+
+ align:start position:0%
+same. I see a product
+here. So I use rule
+
+ align:start position:0%
+here. So I use rule
+ 
+
+ align:start position:0%
+here. So I use rule
+nine. So now what I want to prove is so
+
+ align:start position:0%
+nine. So now what I want to prove is so
+ 
+
+ align:start position:0%
+nine. So now what I want to prove is so
+I now I know that this is L u this is U
+
+ align:start position:0%
+I now I know that this is L u this is U
+ 
+
+ align:start position:0%
+I now I know that this is L u this is U
+transpose and
+
+ align:start position:0%
+transpose and
+ 
+
+ align:start position:0%
+transpose and
+LRPOS. Now just for practice what are
+
+ align:start position:0%
+LRPOS. Now just for practice what are
+ 
+
+ align:start position:0%
+LRPOS. Now just for practice what are
+all those determinants?
+
+ align:start position:0%
+all those determinants?
+ 
+
+ align:start position:0%
+all those determinants?
+So this is this is this is prove this
+
+ align:start position:0%
+So this is this is this is prove this
+ 
+
+ align:start position:0%
+So this is this is this is prove this
+prove this prove this and now I'm ready
+
+ align:start position:0%
+prove this prove this and now I'm ready
+ 
+
+ align:start position:0%
+prove this prove this and now I'm ready
+to do
+
+ align:start position:0%
+to do
+ 
+
+ align:start position:0%
+to do
+it. What's the determinant of
+
+ align:start position:0%
+it. What's the determinant of
+ 
+
+ align:start position:0%
+it. What's the determinant of
+L? You remember what L is? It's this
+
+ align:start position:0%
+L? You remember what L is? It's this
+ 
+
+ align:start position:0%
+L? You remember what L is? It's this
+lower triangular matrix with ones on the
+
+ align:start position:0%
+lower triangular matrix with ones on the
+ 
+
+ align:start position:0%
+lower triangular matrix with ones on the
+diagonal. So what is the determinant of
+
+ align:start position:0%
+diagonal. So what is the determinant of
+ 
+
+ align:start position:0%
+diagonal. So what is the determinant of
+that guy? It's
+
+ align:start position:0%
+that guy? It's
+ 
+
+ align:start position:0%
+that guy? It's
+one. Anytime I have this triangular
+
+ align:start position:0%
+one. Anytime I have this triangular
+ 
+
+ align:start position:0%
+one. Anytime I have this triangular
+matrix, I can get rid of all the
+
+ align:start position:0%
+matrix, I can get rid of all the
+ 
+
+ align:start position:0%
+matrix, I can get rid of all the
+nonzeros down to the diagonal case. The
+
+ align:start position:0%
+nonzeros down to the diagonal case. The
+ 
+
+ align:start position:0%
+nonzeros down to the diagonal case. The
+determinant of L is one. How about the
+
+ align:start position:0%
+determinant of L is one. How about the
+ 
+
+ align:start position:0%
+determinant of L is one. How about the
+determinant of L
+
+ align:start position:0%
+determinant of L
+ 
+
+ align:start position:0%
+determinant of L
+transpose? That's triangular also,
+
+ align:start position:0%
+transpose? That's triangular also,
+ 
+
+ align:start position:0%
+transpose? That's triangular also,
+right? Still got those ones on the
+
+ align:start position:0%
+right? Still got those ones on the
+ 
+
+ align:start position:0%
+right? Still got those ones on the
+diagonal. It's just the
+
+ align:start position:0%
+diagonal. It's just the
+ 
+
+ align:start position:0%
+diagonal. It's just the
+nonzeros flip to the other side of the
+
+ align:start position:0%
+nonzeros flip to the other side of the
+ 
+
+ align:start position:0%
+nonzeros flip to the other side of the
+diagonal, but they didn't matter anyway.
+
+ align:start position:0%
+diagonal, but they didn't matter anyway.
+ 
+
+ align:start position:0%
+diagonal, but they didn't matter anyway.
+That's my proof really that once I've
+
+ align:start position:0%
+That's my proof really that once I've
+ 
+
+ align:start position:0%
+That's my proof really that once I've
+got triangular matrices L and L
+
+ align:start position:0%
+got triangular matrices L and L
+ 
+
+ align:start position:0%
+got triangular matrices L and L
+transpose or U and U transpose when
+
+ align:start position:0%
+transpose or U and U transpose when
+ 
+
+ align:start position:0%
+transpose or U and U transpose when
+they're triangular I'm down to the
+
+ align:start position:0%
+they're triangular I'm down to the
+ 
+
+ align:start position:0%
+they're triangular I'm down to the
+product of the diagonal and if I
+
+ align:start position:0%
+product of the diagonal and if I
+ 
+
+ align:start position:0%
+product of the diagonal and if I
+transpose who
+
+ align:start position:0%
+transpose who
+ 
+
+ align:start position:0%
+transpose who
+cares okay
+
+ align:start position:0%
+cares okay
+ 
+
+ align:start position:0%
+cares okay
+so that's not I didn't put in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+every comma and and cross every E in
+
+ align:start position:0%
+every comma and and cross every E in
+ 
+
+ align:start position:0%
+every comma and and cross every E in
+that proof. But that's really the proof.
+
+ align:start position:0%
+that proof. But that's really the proof.
+ 
+
+ align:start position:0%
+that proof. But that's really the proof.
+That's the like concrete proof that
+
+ align:start position:0%
+That's the like concrete proof that
+ 
+
+ align:start position:0%
+That's the like concrete proof that
+that get get down to triangular matrices
+
+ align:start position:0%
+that get get down to triangular matrices
+ 
+
+ align:start position:0%
+that get get down to triangular matrices
+and then get down to diagonal matrices.
+
+ align:start position:0%
+and then get down to diagonal matrices.
+ 
+
+ align:start position:0%
+and then get down to diagonal matrices.
+Okay, one more comment which I I have to
+
+ align:start position:0%
+Okay, one more comment which I I have to
+ 
+
+ align:start position:0%
+Okay, one more comment which I I have to
+make because all math professors
+
+ align:start position:0%
+make because all math professors
+ 
+
+ align:start position:0%
+make because all math professors
+watching this
+
+ align:start position:0%
+watching this
+ 
+
+ align:start position:0%
+watching this
+will be waiting for it. Okay, so they
+
+ align:start position:0%
+will be waiting for it. Okay, so they
+ 
+
+ align:start position:0%
+will be waiting for it. Okay, so they
+had to wait until the last minute.
+
+ align:start position:0%
+had to wait until the last minute.
+ 
+
+ align:start position:0%
+had to wait until the last minute.
+What I way way back in property two I
+
+ align:start position:0%
+What I way way back in property two I
+ 
+
+ align:start position:0%
+What I way way back in property two I
+said that if you do a row exchange the
+
+ align:start position:0%
+said that if you do a row exchange the
+ 
+
+ align:start position:0%
+said that if you do a row exchange the
+determinant changes sign. So if I do
+
+ align:start position:0%
+determinant changes sign. So if I do
+ 
+
+ align:start position:0%
+determinant changes sign. So if I do
+seven row exchanges the determinant
+
+ align:start position:0%
+seven row exchanges the determinant
+ 
+
+ align:start position:0%
+seven row exchanges the determinant
+changes sign. But it would it be
+
+ align:start position:0%
+changes sign. But it would it be
+ 
+
+ align:start position:0%
+changes sign. But it would it be
+possible to to produce the same matrix
+
+ align:start position:0%
+possible to to produce the same matrix
+ 
+
+ align:start position:0%
+possible to to produce the same matrix
+with seven row exchanges and with 10 row
+
+ align:start position:0%
+with seven row exchanges and with 10 row
+ 
+
+ align:start position:0%
+with seven row exchanges and with 10 row
+exchanges. If that were
+
+ align:start position:0%
+exchanges. If that were
+ 
+
+ align:start position:0%
+exchanges. If that were
+possible, that would be a bad thing,
+
+ align:start position:0%
+possible, that would be a bad thing,
+ 
+
+ align:start position:0%
+possible, that would be a bad thing,
+right? If I could, why would it be bad?
+
+ align:start position:0%
+right? If I could, why would it be bad?
+ 
+
+ align:start position:0%
+right? If I could, why would it be bad?
+My whole lecture would die, right?
+
+ align:start position:0%
+My whole lecture would die, right?
+ 
+
+ align:start position:0%
+My whole lecture would die, right?
+Because rule two said that if you do
+
+ align:start position:0%
+Because rule two said that if you do
+ 
+
+ align:start position:0%
+Because rule two said that if you do
+seven row
+
+ align:start position:0%
+seven row
+ 
+
+ align:start position:0%
+seven row
+exchanges, then the sign of the
+
+ align:start position:0%
+exchanges, then the sign of the
+ 
+
+ align:start position:0%
+exchanges, then the sign of the
+determinant reverses. But if you do 10
+
+ align:start position:0%
+determinant reverses. But if you do 10
+ 
+
+ align:start position:0%
+determinant reverses. But if you do 10
+row exchanges, the sign of the
+
+ align:start position:0%
+row exchanges, the sign of the
+ 
+
+ align:start position:0%
+row exchanges, the sign of the
+determinant stays the same because minus
+
+ align:start position:0%
+determinant stays the same because minus
+ 
+
+ align:start position:0%
+determinant stays the same because minus
+one 10 times is + one. Okay?
+
+ align:start position:0%
+one 10 times is + one. Okay?
+ 
+
+ align:start position:0%
+one 10 times is + one. Okay?
+So there's a hidden fact here that
+
+ align:start position:0%
+So there's a hidden fact here that
+ 
+
+ align:start position:0%
+So there's a hidden fact here that
+every like every permutation the
+
+ align:start position:0%
+every like every permutation the
+ 
+
+ align:start position:0%
+every like every permutation the
+permutations are either odd or
+
+ align:start position:0%
+permutations are either odd or
+ 
+
+ align:start position:0%
+permutations are either odd or
+even I could get the permutation with
+
+ align:start position:0%
+even I could get the permutation with
+ 
+
+ align:start position:0%
+even I could get the permutation with
+seven row exchanges then I could
+
+ align:start position:0%
+seven row exchanges then I could
+ 
+
+ align:start position:0%
+seven row exchanges then I could
+probably get it with 21 or 23 or
+
+ align:start position:0%
+probably get it with 21 or 23 or
+ 
+
+ align:start position:0%
+probably get it with 21 or 23 or
+101 if it's an odd one or an even number
+
+ align:start position:0%
+101 if it's an odd one or an even number
+ 
+
+ align:start position:0%
+101 if it's an odd one or an even number
+of permutations. So, but that's the key
+
+ align:start position:0%
+of permutations. So, but that's the key
+ 
+
+ align:start position:0%
+of permutations. So, but that's the key
+fact that this takes another little
+
+ align:start position:0%
+fact that this takes another little
+ 
+
+ align:start position:0%
+fact that this takes another little
+algebraic trick to see. And that means
+
+ align:start position:0%
+algebraic trick to see. And that means
+ 
+
+ align:start position:0%
+algebraic trick to see. And that means
+that the determinant is well defined by
+
+ align:start position:0%
+that the determinant is well defined by
+ 
+
+ align:start position:0%
+that the determinant is well defined by
+properties 1 2 3 and it's got properties
+
+ align:start position:0%
+properties 1 2 3 and it's got properties
+ 
+
+ align:start position:0%
+properties 1 2 3 and it's got properties
+4 to 10. Okay, that's today and I'll try
+
+ align:start position:0%
+4 to 10. Okay, that's today and I'll try
+ 
+
+ align:start position:0%
+4 to 10. Okay, that's today and I'll try
+to get the homework for next Wednesday
+
+ align:start position:0%
+to get the homework for next Wednesday
+ 
+
+ align:start position:0%
+to get the homework for next Wednesday
+onto the web.
+
+ align:start position:0%
+onto the web.
+ 
+
+ align:start position:0%
+onto the web.
+Thank you for coming.
\ No newline at end of file
diff --git a/swdDzsfFflo.txt b/swdDzsfFflo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a45af872e4f8e63eefac1c694a670bed8729f5b5
--- /dev/null
+++ b/swdDzsfFflo.txt
@@ -0,0 +1,352 @@
+Virtual memory allows programs to behave as
+if they have a larger memory than they actually
+
+do.
+
+The way this works is by using virtual addresses,
+which refer to addresses on disk, in our programs.
+
+The virtual addresses are translated into
+physical addresses using the page map which
+
+is a lookup table that has one entry per virtual
+page.
+
+The page map knows whether the virtual page
+is in physical memory and if so it immediately
+
+returns the physical page number.
+
+If the page is not in physical memory, then
+this causes a fault which means that the virtual
+
+page must be brought in from disk to physical
+memory before it can be accessed.
+
+To do this the least recently used (LRU) page
+in the physical memory is removed to make
+
+room for the address that is currently being
+requested.
+
+The page map is also updated with the new
+mapping of virtual to physical pages.
+
+Since bringing data to and from disk is an
+expensive operation, data is moved in chunks.
+
+This makes sense because of the concept of
+locality which we studied as part of our Caches
+
+unit.
+
+The idea is that instructions, or data, that
+are close to the current address are likely
+
+to be accessed as well, so it makes sense
+to fetch more than one word of data at a time.
+
+This is especially true if the cost of fetching
+the first word is significantly higher than
+
+the cost of fetching adjacent memory locations
+as is the case with accesses to disk.
+
+So data is moved back and forth from disk
+in pages.
+
+The size of a page is the same in both virtual
+and physical memory.
+
+Lets look at an example of how virtual memory
+is used.
+
+While it is usually the case that the virtual
+address space is larger than the physical
+
+address space, this is not a requirement and
+in this problem the virtual address space
+
+happens to be smaller than the physical address
+space.
+
+Specifically, virtual addresses are 16 bits
+long so they can address 2^16 bytes.
+
+Physical addresses are 20 bits long so that
+means that our physical memory is of size
+
+2^20 bytes.
+
+Our page size is 2^8 bytes or 256 bytes per
+page.
+
+This means that the 16 bit virtual address
+consists of 8 bits of page offset and another
+
+8 bits for the virtual page number (or VPN).
+
+The 20 bit physical address consists of the
+same 8 bit page offset and another 12 bits
+
+for the physical page number (or PPN).
+
+The first question we want to consider is
+what is the size of the page map in this example?
+
+Recall that a page map has 1 entry per virtual
+page in order to map each virtual page to
+
+a physical page.
+
+This means that the number of entries in the
+page map is 2^8 where 8 is the number of bits
+
+in the VPN.
+
+The size of each page map entry is 14 bits,
+12 for the PPN, 1 for the dirty bit and 1
+
+for the resident bit.
+
+Suppose that you are told that the page size
+is doubled in size so that there are now 2^9
+
+bytes per page, but the size of your physical
+and virtual addresses remain the same.
+
+We would like to determine what effect this
+change would have on some of the page map
+
+attributes.
+
+The first question is how does the size of
+each page map entry in bits change?
+
+Since the size of a physical address continues
+to be 20 bits long, then the change in page
+
+offset size from 8 to 9 bits implies that
+the size of the PPN decreased by 1 bit from
+
+12 to 11.
+
+This implies that the size of each page map
+entry also decreases by 1 bit.
+
+How are the number of entries in the page
+map affected by the change in page size?
+
+Since the number of entries in a page map
+is equal to the number of virtual pages, that
+
+means that if the size of each page doubled,
+then we have half as many virtual pages.
+
+This is shown in the size of the VPN which
+has decreased from 8 to 7 bits.
+
+This also means that the number of entries
+in the page map have halved in size from 2^8
+
+entries down to 2^7 entries.
+
+How about the number of accesses of the page
+map that are required to translate a single
+
+virtual address?
+
+This parameter does not change as a result
+of the pages doubling in size.
+
+Suppose we return to our original page size
+of 256 bytes per page.
+
+We now execute these two lines of code, a
+load followed by a store operation.
+
+The comment after each instruction shows us
+the value of the PC when each of the instructions
+
+is executed, so it is telling us that the
+load instruction is at address 0x1FC and the
+
+store instruction is at address 0x200.
+
+To execute these two lines of code, we must
+first fetch each instruction and then perform
+
+the data access required by that instruction.
+
+Since our pages are 2^8 bytes long, that means
+that the bottom 8 bits of our address correspond
+
+to the page offset.
+
+Notice that our instruction addresses are
+specified in hex so 8 bits correspond to the
+
+bottom 2 hex characters.
+
+This means that when accessing the LD instruction,
+the VPN = 1 (which is what remains of our
+
+virtual address after removing the bottom
+8 bits.)
+
+The data accessed by the LD instruction comes
+from VPN 3.
+
+Next we fetch the store instruction from VPN
+2, and finally we store an updated value to
+
+VPN 6.
+
+Given the page map shown here, we would like
+to determine the unique physical addresses
+
+that are accessed by this code segment.
+
+Recall that the four virtual addresses that
+will be accessed are:
+
+0x1FC which is in VPN 1
+0x34C which is in VPN 3
+
+0x200 which is in VPN 2
+and 0x604 which is in VPN 6.
+
+Assume that all the code and data required
+to handle page faults is located at physical
+
+page 0, your goal is to determine the 5 different
+physical pages that will get accessed and
+
+the order in which they will get accessed
+by this code segment.
+
+We begin by looking up VPN 1 in our page map.
+
+We see that its resident bit is set to 1.
+
+This means that the virtual page is in physical
+memory and its PPN is 0x007.
+
+Thus the first physical page that we access
+is page 0x7, and the first physical address
+
+is determined by concatenating the PPN to
+the page offset.
+
+This results in a physical address of 0x7FC.
+
+Next, we want to load the data at virtual
+address 0x34C which is in VPN 3.
+
+Looking up VPN 3 in our page map, we find
+out that its not resident in physical memory.
+
+This means that we need to make room for it
+by removing the least recently used page from
+
+physical memory.
+
+The least recently used page is VPN 2 which
+maps to PPN 0x602.
+
+Since the dirty bit of our LRU page is 0,
+that means that we have not done any writes
+
+to this page while it was in physical memory
+so the version in physical memory and on disk
+
+are identical.
+
+So to free up physical page 0x602, all we
+need to do is change the resident bit of VPN
+
+2 to 0 and now we can bring VPN 3 into physical
+page 0x602.
+
+Recall that the code for handling the page
+fault is in physical page 0 so the second
+
+physical page that we access is page 0.
+
+The updated page map, after handling the page
+fault, looks like this, where the resident
+
+bit for VPN 2 has been set to 0, and PPN 0x602
+is now used for VPN 3.
+
+Since this is a LD operation, we are not modifying
+the page so the dirty bit is set to 0.
+
+The physical address for virtual address 0x34C
+is now 0x6024C which is now in VPN 0x602.
+
+Next we need to fetch the store instruction
+from virtual address 0x200 which is in VPN
+
+2.
+
+Since we just removed VPN 2 from physical
+memory we get another page fault.
+
+This time we will remove the next LRU page
+from physical memory in order to make room
+
+for VPN 2 once again.
+
+In this case, the dirty bit is set to 1 which
+means that we have written to PPN 0x097 after
+
+it was fetched from disk.
+
+This means that the page fault handler will
+need to first write physical page 0x097 back
+
+to virtual page 5 before we can use physical
+page 0x097 for VPN 2.
+
+After handling the page fault, our updated
+page map looks like this.
+
+VPN 5 is no longer resident, and instead VPN
+2 is resident in physical page 0x097.
+
+In addition, we set the dirty bit to 0 because
+we have not made any changes to this virtual
+
+page.
+
+We now know that virtual address 0x200 maps
+to physical address 0x09700 after the handling
+
+of the page fault.
+
+Finally, we need to perform the store to virtual
+address 0x604 which is in VPN 6.
+
+Since VPN 6 is resident in physical memory,
+we can access it at physical page 0x790 as
+
+shown in the page map.
+
+This means that virtual address 0x604 maps
+to physical address 0x79004.
+
+Note that because the dirty bit of VPN 6 was
+already a 1, we don't need to make any further
+
+modifications to the page map as a result
+of executing the store operation.
+
+If the dirty bit had been a 0, then we would
+have set it to 1.
+
+So the five physical pages that were accessed
+by this program are: page 0x7, page 0 for
+
+the page faults, page 0x602, page 0x097, and
+page 0x790.
\ No newline at end of file
diff --git a/t0eXy4RKEys.txt b/t0eXy4RKEys.txt
new file mode 100644
index 0000000000000000000000000000000000000000..700846195f4bec742af27f300d828db82cebe604
--- /dev/null
+++ b/t0eXy4RKEys.txt
@@ -0,0 +1,13784 @@
+align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+last time we discussed the tca cycle
+
+ align:start position:0%
+last time we discussed the tca cycle
+ 
+
+ align:start position:0%
+last time we discussed the tca cycle
+and that allows us to then you know
+
+ align:start position:0%
+and that allows us to then you know
+ 
+
+ align:start position:0%
+and that allows us to then you know
+say how we can take glucose and
+
+ align:start position:0%
+say how we can take glucose and
+ 
+
+ align:start position:0%
+say how we can take glucose and
+completely oxidized
+
+ align:start position:0%
+completely oxidized
+ 
+
+ align:start position:0%
+completely oxidized
+those six glucose carbons into co2 and
+
+ align:start position:0%
+those six glucose carbons into co2 and
+ 
+
+ align:start position:0%
+those six glucose carbons into co2 and
+you know of course glycolysis converts
+
+ align:start position:0%
+you know of course glycolysis converts
+ 
+
+ align:start position:0%
+you know of course glycolysis converts
+glucose into two pyruvate
+
+ align:start position:0%
+glucose into two pyruvate
+ 
+
+ align:start position:0%
+glucose into two pyruvate
+pyruvate has three carbons and then
+
+ align:start position:0%
+pyruvate has three carbons and then
+ 
+
+ align:start position:0%
+pyruvate has three carbons and then
+pyruvate dehydrogenase can
+
+ align:start position:0%
+pyruvate dehydrogenase can
+ 
+
+ align:start position:0%
+pyruvate dehydrogenase can
+release the first of those carbons of
+
+ align:start position:0%
+release the first of those carbons of
+ 
+
+ align:start position:0%
+release the first of those carbons of
+co2
+
+ align:start position:0%
+co2
+ 
+
+ align:start position:0%
+co2
+generates an acetyl coa that acetyl coa
+
+ align:start position:0%
+generates an acetyl coa that acetyl coa
+ 
+
+ align:start position:0%
+generates an acetyl coa that acetyl coa
+then enters the tca cycle
+
+ align:start position:0%
+then enters the tca cycle
+ 
+
+ align:start position:0%
+then enters the tca cycle
+and two other co2s are released one at
+
+ align:start position:0%
+and two other co2s are released one at
+ 
+
+ align:start position:0%
+and two other co2s are released one at
+the isocitrate dehydrogenase step
+
+ align:start position:0%
+the isocitrate dehydrogenase step
+ 
+
+ align:start position:0%
+the isocitrate dehydrogenase step
+one at the alpha-ketoglutarate
+
+ align:start position:0%
+one at the alpha-ketoglutarate
+ 
+
+ align:start position:0%
+one at the alpha-ketoglutarate
+dehydrogenase step
+
+ align:start position:0%
+dehydrogenase step
+ 
+
+ align:start position:0%
+dehydrogenase step
+now we discussed that the tca cycle is
+
+ align:start position:0%
+now we discussed that the tca cycle is
+ 
+
+ align:start position:0%
+now we discussed that the tca cycle is
+useful because it
+
+ align:start position:0%
+useful because it
+ 
+
+ align:start position:0%
+useful because it
+allows you to oxidize anything that can
+
+ align:start position:0%
+allows you to oxidize anything that can
+ 
+
+ align:start position:0%
+allows you to oxidize anything that can
+be turned into
+
+ align:start position:0%
+be turned into
+ 
+
+ align:start position:0%
+be turned into
+acetyl coa into co2 and that includes
+
+ align:start position:0%
+acetyl coa into co2 and that includes
+ 
+
+ align:start position:0%
+acetyl coa into co2 and that includes
+fatty acids which
+
+ align:start position:0%
+fatty acids which
+ 
+
+ align:start position:0%
+fatty acids which
+we will spend a lot of time talking
+
+ align:start position:0%
+we will spend a lot of time talking
+ 
+
+ align:start position:0%
+we will spend a lot of time talking
+about today
+
+ align:start position:0%
+about today
+ 
+
+ align:start position:0%
+about today
+now the tca cycle as i mentioned just by
+
+ align:start position:0%
+now the tca cycle as i mentioned just by
+ 
+
+ align:start position:0%
+now the tca cycle as i mentioned just by
+review
+
+ align:start position:0%
+review
+ 
+
+ align:start position:0%
+review
+is also very useful as a way to make
+
+ align:start position:0%
+is also very useful as a way to make
+ 
+
+ align:start position:0%
+is also very useful as a way to make
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+lots of useful intermediates but we
+
+ align:start position:0%
+lots of useful intermediates but we
+ 
+
+ align:start position:0%
+lots of useful intermediates but we
+discussed last time if we're going to do
+
+ align:start position:0%
+discussed last time if we're going to do
+ 
+
+ align:start position:0%
+discussed last time if we're going to do
+that that is
+
+ align:start position:0%
+that that is
+ 
+
+ align:start position:0%
+that that is
+because it functions as a cycle if we
+
+ align:start position:0%
+because it functions as a cycle if we
+ 
+
+ align:start position:0%
+because it functions as a cycle if we
+remove some stuff from the cycle
+
+ align:start position:0%
+remove some stuff from the cycle
+ 
+
+ align:start position:0%
+remove some stuff from the cycle
+something has to be added back in
+
+ align:start position:0%
+something has to be added back in
+ 
+
+ align:start position:0%
+something has to be added back in
+so-called anaplerosis
+
+ align:start position:0%
+so-called anaplerosis
+ 
+
+ align:start position:0%
+so-called anaplerosis
+in order to have it continue to function
+
+ align:start position:0%
+in order to have it continue to function
+ 
+
+ align:start position:0%
+in order to have it continue to function
+as a cycle
+
+ align:start position:0%
+as a cycle
+ 
+
+ align:start position:0%
+as a cycle
+now you'll note we weren't explicit
+
+ align:start position:0%
+now you'll note we weren't explicit
+ 
+
+ align:start position:0%
+now you'll note we weren't explicit
+about this but this is oxidation
+
+ align:start position:0%
+about this but this is oxidation
+ 
+
+ align:start position:0%
+about this but this is oxidation
+remember carbon oxidation is generally
+
+ align:start position:0%
+remember carbon oxidation is generally
+ 
+
+ align:start position:0%
+remember carbon oxidation is generally
+favorable so delta g of this will be
+
+ align:start position:0%
+favorable so delta g of this will be
+ 
+
+ align:start position:0%
+favorable so delta g of this will be
+less than zero
+
+ align:start position:0%
+less than zero
+ 
+
+ align:start position:0%
+less than zero
+however unlike glycolysis where we
+
+ align:start position:0%
+however unlike glycolysis where we
+ 
+
+ align:start position:0%
+however unlike glycolysis where we
+discussed that most of the
+
+ align:start position:0%
+discussed that most of the
+ 
+
+ align:start position:0%
+discussed that most of the
+you know harnessing of energy that is
+
+ align:start position:0%
+you know harnessing of energy that is
+ 
+
+ align:start position:0%
+you know harnessing of energy that is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+favorable oxidation of glucose to
+
+ align:start position:0%
+favorable oxidation of glucose to
+ 
+
+ align:start position:0%
+favorable oxidation of glucose to
+pyruvate
+
+ align:start position:0%
+pyruvate
+ 
+
+ align:start position:0%
+pyruvate
+was captured to directly keep an atp adp
+
+ align:start position:0%
+was captured to directly keep an atp adp
+ 
+
+ align:start position:0%
+was captured to directly keep an atp adp
+ratio high in the cell
+
+ align:start position:0%
+ratio high in the cell
+ 
+
+ align:start position:0%
+ratio high in the cell
+you can see that most of the energy
+
+ align:start position:0%
+you can see that most of the energy
+ 
+
+ align:start position:0%
+you can see that most of the energy
+output of the tca cycle
+
+ align:start position:0%
+output of the tca cycle
+ 
+
+ align:start position:0%
+output of the tca cycle
+isn't actually direct synthesis of atp
+
+ align:start position:0%
+isn't actually direct synthesis of atp
+ 
+
+ align:start position:0%
+isn't actually direct synthesis of atp
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+gtp instead what we have is we have most
+
+ align:start position:0%
+gtp instead what we have is we have most
+ 
+
+ align:start position:0%
+gtp instead what we have is we have most
+of that energy is being captured
+
+ align:start position:0%
+of that energy is being captured
+ 
+
+ align:start position:0%
+of that energy is being captured
+in charging up a ratio of nadh to nad
+
+ align:start position:0%
+in charging up a ratio of nadh to nad
+ 
+
+ align:start position:0%
+in charging up a ratio of nadh to nad
+or fadh2 to fad and we'll see over the
+
+ align:start position:0%
+or fadh2 to fad and we'll see over the
+ 
+
+ align:start position:0%
+or fadh2 to fad and we'll see over the
+next several lectures how we can
+
+ align:start position:0%
+next several lectures how we can
+ 
+
+ align:start position:0%
+next several lectures how we can
+harness electron transfer from those
+
+ align:start position:0%
+harness electron transfer from those
+ 
+
+ align:start position:0%
+harness electron transfer from those
+molecules to oxygen
+
+ align:start position:0%
+molecules to oxygen
+ 
+
+ align:start position:0%
+molecules to oxygen
+to make atp as well as do some other
+
+ align:start position:0%
+to make atp as well as do some other
+ 
+
+ align:start position:0%
+to make atp as well as do some other
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+but before we get to that i want to
+
+ align:start position:0%
+but before we get to that i want to
+ 
+
+ align:start position:0%
+but before we get to that i want to
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+focus a bit on fat which of course is
+
+ align:start position:0%
+focus a bit on fat which of course is
+ 
+
+ align:start position:0%
+focus a bit on fat which of course is
+the most reduced
+
+ align:start position:0%
+the most reduced
+ 
+
+ align:start position:0%
+the most reduced
+carbon biomolecule in the cell and so
+
+ align:start position:0%
+carbon biomolecule in the cell and so
+ 
+
+ align:start position:0%
+carbon biomolecule in the cell and so
+that's chains of of
+
+ align:start position:0%
+that's chains of of
+ 
+
+ align:start position:0%
+that's chains of of
+fully reduced carbon
+
+ align:start position:0%
+fully reduced carbon
+ 
+
+ align:start position:0%
+fully reduced carbon
+and of course this is the most
+
+ align:start position:0%
+and of course this is the most
+ 
+
+ align:start position:0%
+and of course this is the most
+chemically dense way to
+
+ align:start position:0%
+chemically dense way to
+ 
+
+ align:start position:0%
+chemically dense way to
+store energy as as as carbon intuitively
+
+ align:start position:0%
+store energy as as as carbon intuitively
+ 
+
+ align:start position:0%
+store energy as as as carbon intuitively
+you know this because what's
+
+ align:start position:0%
+you know this because what's
+ 
+
+ align:start position:0%
+you know this because what's
+oil and gas it's chains of reduced
+
+ align:start position:0%
+oil and gas it's chains of reduced
+ 
+
+ align:start position:0%
+oil and gas it's chains of reduced
+hydrocarbons
+
+ align:start position:0%
+hydrocarbons
+ 
+
+ align:start position:0%
+hydrocarbons
+of course those are better fuels than
+
+ align:start position:0%
+of course those are better fuels than
+ 
+
+ align:start position:0%
+of course those are better fuels than
+wood which are you know as we saw before
+
+ align:start position:0%
+wood which are you know as we saw before
+ 
+
+ align:start position:0%
+wood which are you know as we saw before
+is based on carbohydrate
+
+ align:start position:0%
+is based on carbohydrate
+ 
+
+ align:start position:0%
+is based on carbohydrate
+uh out you know alcohol carbons
+
+ align:start position:0%
+uh out you know alcohol carbons
+ 
+
+ align:start position:0%
+uh out you know alcohol carbons
+you also know intuitively that fat has
+
+ align:start position:0%
+you also know intuitively that fat has
+ 
+
+ align:start position:0%
+you also know intuitively that fat has
+more calories than sugar
+
+ align:start position:0%
+more calories than sugar
+ 
+
+ align:start position:0%
+more calories than sugar
+exactly same ideas and so
+
+ align:start position:0%
+exactly same ideas and so
+ 
+
+ align:start position:0%
+exactly same ideas and so
+i want to start by discussing what
+
+ align:start position:0%
+i want to start by discussing what
+ 
+
+ align:start position:0%
+i want to start by discussing what
+biological fat is
+
+ align:start position:0%
+biological fat is
+ 
+
+ align:start position:0%
+biological fat is
+and then that will lead into a
+
+ align:start position:0%
+and then that will lead into a
+ 
+
+ align:start position:0%
+and then that will lead into a
+discussion about how we can oxidize the
+
+ align:start position:0%
+discussion about how we can oxidize the
+ 
+
+ align:start position:0%
+discussion about how we can oxidize the
+fat
+
+ align:start position:0%
+fat
+ 
+
+ align:start position:0%
+fat
+also as a way to get energy
+
+ align:start position:0%
+also as a way to get energy
+ 
+
+ align:start position:0%
+also as a way to get energy
+now most biological fat is packaged into
+
+ align:start position:0%
+now most biological fat is packaged into
+ 
+
+ align:start position:0%
+now most biological fat is packaged into
+molecules called
+
+ align:start position:0%
+molecules called
+ 
+
+ align:start position:0%
+molecules called
+lipids and so i want to make clear that
+
+ align:start position:0%
+lipids and so i want to make clear that
+ 
+
+ align:start position:0%
+lipids and so i want to make clear that
+lipids are not the same thing as fat
+
+ align:start position:0%
+lipids are not the same thing as fat
+ 
+
+ align:start position:0%
+lipids are not the same thing as fat
+more correctly a lipid contains
+
+ align:start position:0%
+more correctly a lipid contains
+ 
+
+ align:start position:0%
+more correctly a lipid contains
+fat or more precisely something called a
+
+ align:start position:0%
+fat or more precisely something called a
+ 
+
+ align:start position:0%
+fat or more precisely something called a
+fatty acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so what is a fatty acid well it's
+
+ align:start position:0%
+and so what is a fatty acid well it's
+ 
+
+ align:start position:0%
+and so what is a fatty acid well it's
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+fully saturated hydrocarbon with a
+
+ align:start position:0%
+fully saturated hydrocarbon with a
+ 
+
+ align:start position:0%
+fully saturated hydrocarbon with a
+carboxylic acid
+
+ align:start position:0%
+carboxylic acid
+ 
+
+ align:start position:0%
+carboxylic acid
+on the end and so we have a
+
+ align:start position:0%
+on the end and so we have a
+ 
+
+ align:start position:0%
+on the end and so we have a
+carboxylic acid followed by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some chain of fully saturated
+
+ align:start position:0%
+some chain of fully saturated
+ 
+
+ align:start position:0%
+some chain of fully saturated
+hydrocarbons and so it
+
+ align:start position:0%
+hydrocarbons and so it
+ 
+
+ align:start position:0%
+hydrocarbons and so it
+differs from oil and gasoline in that it
+
+ align:start position:0%
+differs from oil and gasoline in that it
+ 
+
+ align:start position:0%
+differs from oil and gasoline in that it
+has this
+
+ align:start position:0%
+has this
+ 
+
+ align:start position:0%
+has this
+uh carboxylic acid handle if you will
+
+ align:start position:0%
+uh carboxylic acid handle if you will
+ 
+
+ align:start position:0%
+uh carboxylic acid handle if you will
+on the end that basically allows biology
+
+ align:start position:0%
+on the end that basically allows biology
+ 
+
+ align:start position:0%
+on the end that basically allows biology
+to build and break down
+
+ align:start position:0%
+to build and break down
+ 
+
+ align:start position:0%
+to build and break down
+these um these these uh fatty acids
+
+ align:start position:0%
+these um these these uh fatty acids
+ 
+
+ align:start position:0%
+these um these these uh fatty acids
+now most biological fatty acids have
+
+ align:start position:0%
+now most biological fatty acids have
+ 
+
+ align:start position:0%
+now most biological fatty acids have
+even
+
+ align:start position:0%
+even
+ 
+
+ align:start position:0%
+even
+numbers of carbons
+
+ align:start position:0%
+numbers of carbons
+ 
+
+ align:start position:0%
+numbers of carbons
+and it turns out that that's a
+
+ align:start position:0%
+and it turns out that that's a
+ 
+
+ align:start position:0%
+and it turns out that that's a
+consequence of the fact that it's built
+
+ align:start position:0%
+consequence of the fact that it's built
+ 
+
+ align:start position:0%
+consequence of the fact that it's built
+and broken down
+
+ align:start position:0%
+and broken down
+ 
+
+ align:start position:0%
+and broken down
+into these two carbon acetyl coa units
+
+ align:start position:0%
+into these two carbon acetyl coa units
+ 
+
+ align:start position:0%
+into these two carbon acetyl coa units
+and the most common lengths that is how
+
+ align:start position:0%
+and the most common lengths that is how
+ 
+
+ align:start position:0%
+and the most common lengths that is how
+long
+
+ align:start position:0%
+long
+ 
+
+ align:start position:0%
+long
+these chains are so in biology they can
+
+ align:start position:0%
+these chains are so in biology they can
+ 
+
+ align:start position:0%
+these chains are so in biology they can
+vary anywhere from 4 to 36 carbons long
+
+ align:start position:0%
+vary anywhere from 4 to 36 carbons long
+ 
+
+ align:start position:0%
+vary anywhere from 4 to 36 carbons long
+but the most common ones are 12 to 24
+
+ align:start position:0%
+but the most common ones are 12 to 24
+ 
+
+ align:start position:0%
+but the most common ones are 12 to 24
+carbons
+
+ align:start position:0%
+carbons
+ 
+
+ align:start position:0%
+carbons
+with 16 carbons and 18 carbons being
+
+ align:start position:0%
+with 16 carbons and 18 carbons being
+ 
+
+ align:start position:0%
+with 16 carbons and 18 carbons being
+by far the most abundant in cells
+
+ align:start position:0%
+by far the most abundant in cells
+ 
+
+ align:start position:0%
+by far the most abundant in cells
+now it's worth mentioning what some of
+
+ align:start position:0%
+now it's worth mentioning what some of
+ 
+
+ align:start position:0%
+now it's worth mentioning what some of
+the names of
+
+ align:start position:0%
+the names of
+ 
+
+ align:start position:0%
+the names of
+these more common ones are because
+
+ align:start position:0%
+these more common ones are because
+ 
+
+ align:start position:0%
+these more common ones are because
+you'll see them
+
+ align:start position:0%
+you'll see them
+ 
+
+ align:start position:0%
+you'll see them
+and so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fully saturated
+
+ align:start position:0%
+fully saturated
+ 
+
+ align:start position:0%
+fully saturated
+16 carbon fatty acids so 16 carbons
+
+ align:start position:0%
+16 carbon fatty acids so 16 carbons
+ 
+
+ align:start position:0%
+16 carbon fatty acids so 16 carbons
+total
+
+ align:start position:0%
+total
+ 
+
+ align:start position:0%
+total
+14 15 16 including the carboxylic acid
+
+ align:start position:0%
+14 15 16 including the carboxylic acid
+ 
+
+ align:start position:0%
+14 15 16 including the carboxylic acid
+this is referred to as palmitate
+
+ align:start position:0%
+this is referred to as palmitate
+ 
+
+ align:start position:0%
+this is referred to as palmitate
+or it's drawn in the acid form palmitic
+
+ align:start position:0%
+or it's drawn in the acid form palmitic
+ 
+
+ align:start position:0%
+or it's drawn in the acid form palmitic
+acid and the
+
+ align:start position:0%
+acid and the
+ 
+
+ align:start position:0%
+acid and the
+systematic name for this is hexadecinoic
+
+ align:start position:0%
+systematic name for this is hexadecinoic
+ 
+
+ align:start position:0%
+systematic name for this is hexadecinoic
+acid the other common one the 18
+
+ align:start position:0%
+acid the other common one the 18
+ 
+
+ align:start position:0%
+acid the other common one the 18
+carbon version
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so same molecule but two carbons longer
+
+ align:start position:0%
+so same molecule but two carbons longer
+ 
+
+ align:start position:0%
+so same molecule but two carbons longer
+that's referred to as steerate
+
+ align:start position:0%
+that's referred to as steerate
+ 
+
+ align:start position:0%
+that's referred to as steerate
+or stearic acid if drawn in the acid
+
+ align:start position:0%
+or stearic acid if drawn in the acid
+ 
+
+ align:start position:0%
+or stearic acid if drawn in the acid
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+or the systematic name would be octa
+
+ align:start position:0%
+or the systematic name would be octa
+ 
+
+ align:start position:0%
+or the systematic name would be octa
+deca noic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acid now oftentimes
+
+ align:start position:0%
+acid now oftentimes
+ 
+
+ align:start position:0%
+acid now oftentimes
+things like palmitate can also be drawn
+
+ align:start position:0%
+things like palmitate can also be drawn
+ 
+
+ align:start position:0%
+things like palmitate can also be drawn
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's 16 carbons another way to
+
+ align:start position:0%
+so there's 16 carbons another way to
+ 
+
+ align:start position:0%
+so there's 16 carbons another way to
+draw palmitate
+
+ align:start position:0%
+draw palmitate
+ 
+
+ align:start position:0%
+draw palmitate
+and you'll note that palmitate as well
+
+ align:start position:0%
+and you'll note that palmitate as well
+ 
+
+ align:start position:0%
+and you'll note that palmitate as well
+as stearate here
+
+ align:start position:0%
+as stearate here
+ 
+
+ align:start position:0%
+as stearate here
+are fully saturated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what do i mean by saturated i mean
+
+ align:start position:0%
+what do i mean by saturated i mean
+ 
+
+ align:start position:0%
+what do i mean by saturated i mean
+fully saturated by electrons there's no
+
+ align:start position:0%
+fully saturated by electrons there's no
+ 
+
+ align:start position:0%
+fully saturated by electrons there's no
+way to reduce
+
+ align:start position:0%
+way to reduce
+ 
+
+ align:start position:0%
+way to reduce
+this molecule further unless of course
+
+ align:start position:0%
+this molecule further unless of course
+ 
+
+ align:start position:0%
+this molecule further unless of course
+we reduce the
+
+ align:start position:0%
+we reduce the
+ 
+
+ align:start position:0%
+we reduce the
+the carboxylic acid on the end
+
+ align:start position:0%
+the carboxylic acid on the end
+ 
+
+ align:start position:0%
+the carboxylic acid on the end
+and so palmitate would be the most
+
+ align:start position:0%
+and so palmitate would be the most
+ 
+
+ align:start position:0%
+and so palmitate would be the most
+saturated 16 carbon fatty acid
+
+ align:start position:0%
+saturated 16 carbon fatty acid
+ 
+
+ align:start position:0%
+saturated 16 carbon fatty acid
+stearate is the most saturated 18 carbon
+
+ align:start position:0%
+stearate is the most saturated 18 carbon
+ 
+
+ align:start position:0%
+stearate is the most saturated 18 carbon
+fatty acid now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i add a double bond to
+
+ align:start position:0%
+if i add a double bond to
+ 
+
+ align:start position:0%
+if i add a double bond to
+one of these molecules that's an
+
+ align:start position:0%
+one of these molecules that's an
+ 
+
+ align:start position:0%
+one of these molecules that's an
+oxidation
+
+ align:start position:0%
+oxidation
+ 
+
+ align:start position:0%
+oxidation
+so just like when we added a double bond
+
+ align:start position:0%
+so just like when we added a double bond
+ 
+
+ align:start position:0%
+so just like when we added a double bond
+to succinate to make fumarate in the tca
+
+ align:start position:0%
+to succinate to make fumarate in the tca
+ 
+
+ align:start position:0%
+to succinate to make fumarate in the tca
+cycle
+
+ align:start position:0%
+cycle
+ 
+
+ align:start position:0%
+cycle
+i showed that last time that's an
+
+ align:start position:0%
+i showed that last time that's an
+ 
+
+ align:start position:0%
+i showed that last time that's an
+oxidation reaction
+
+ align:start position:0%
+oxidation reaction
+ 
+
+ align:start position:0%
+oxidation reaction
+and so an unsaturated fatty acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a fatty acid that is no longer fully
+
+ align:start position:0%
+is a fatty acid that is no longer fully
+ 
+
+ align:start position:0%
+is a fatty acid that is no longer fully
+saturated with electrons that mean it is
+
+ align:start position:0%
+saturated with electrons that mean it is
+ 
+
+ align:start position:0%
+saturated with electrons that mean it is
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+fully reduced and so remember you store
+
+ align:start position:0%
+fully reduced and so remember you store
+ 
+
+ align:start position:0%
+fully reduced and so remember you store
+energy as reduced carbon
+
+ align:start position:0%
+energy as reduced carbon
+ 
+
+ align:start position:0%
+energy as reduced carbon
+and so an unsaturated fatty acid stores
+
+ align:start position:0%
+and so an unsaturated fatty acid stores
+ 
+
+ align:start position:0%
+and so an unsaturated fatty acid stores
+less
+
+ align:start position:0%
+less
+ 
+
+ align:start position:0%
+less
+energy than a saturated fatty acid
+
+ align:start position:0%
+energy than a saturated fatty acid
+ 
+
+ align:start position:0%
+energy than a saturated fatty acid
+because it's more oxidized than the
+
+ align:start position:0%
+because it's more oxidized than the
+ 
+
+ align:start position:0%
+because it's more oxidized than the
+saturated
+
+ align:start position:0%
+saturated
+ 
+
+ align:start position:0%
+saturated
+fatty acid and so this is a couple
+
+ align:start position:0%
+fatty acid and so this is a couple
+ 
+
+ align:start position:0%
+fatty acid and so this is a couple
+examples here so here's the
+
+ align:start position:0%
+examples here so here's the
+ 
+
+ align:start position:0%
+examples here so here's the
+example of a 16 carbon
+
+ align:start position:0%
+example of a 16 carbon
+ 
+
+ align:start position:0%
+example of a 16 carbon
+unsaturated fatty acid
+
+ align:start position:0%
+unsaturated fatty acid
+ 
+
+ align:start position:0%
+unsaturated fatty acid
+so i introduce a double bond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i'll draw it in the fatty and the acid
+
+ align:start position:0%
+i'll draw it in the fatty and the acid
+ 
+
+ align:start position:0%
+i'll draw it in the fatty and the acid
+form here and so here you got
+
+ align:start position:0%
+form here and so here you got
+ 
+
+ align:start position:0%
+form here and so here you got
+5 6 7 8 plus seven is fifteen
+
+ align:start position:0%
+5 6 7 8 plus seven is fifteen
+ 
+
+ align:start position:0%
+5 6 7 8 plus seven is fifteen
+sixteen carbons total one double bond
+
+ align:start position:0%
+sixteen carbons total one double bond
+ 
+
+ align:start position:0%
+sixteen carbons total one double bond
+this is palmito
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+leic acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more systematically named hexa
+
+ align:start position:0%
+more systematically named hexa
+ 
+
+ align:start position:0%
+more systematically named hexa
+design
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acid and the 18-carbon version
+
+ align:start position:0%
+acid and the 18-carbon version
+ 
+
+ align:start position:0%
+acid and the 18-carbon version
+would be as follows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so i added two extra carbons on
+
+ align:start position:0%
+okay so i added two extra carbons on
+ 
+
+ align:start position:0%
+okay so i added two extra carbons on
+this end of the molecule this is oleic
+
+ align:start position:0%
+this end of the molecule this is oleic
+ 
+
+ align:start position:0%
+this end of the molecule this is oleic
+acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or octa
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dassinolic
+
+ align:start position:0%
+dassinolic
+ 
+
+ align:start position:0%
+dassinolic
+acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now note i put a double bond in here
+
+ align:start position:0%
+now note i put a double bond in here
+ 
+
+ align:start position:0%
+now note i put a double bond in here
+you'll remember from
+
+ align:start position:0%
+you'll remember from
+ 
+
+ align:start position:0%
+you'll remember from
+organic chemistry that double bonds can
+
+ align:start position:0%
+organic chemistry that double bonds can
+ 
+
+ align:start position:0%
+organic chemistry that double bonds can
+exist
+
+ align:start position:0%
+exist
+ 
+
+ align:start position:0%
+exist
+in a trans or a cis
+
+ align:start position:0%
+in a trans or a cis
+ 
+
+ align:start position:0%
+in a trans or a cis
+form and so if it's trans
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it would be like this if it's cis
+
+ align:start position:0%
+it would be like this if it's cis
+ 
+
+ align:start position:0%
+it would be like this if it's cis
+the double bond would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that in the carbon chain
+
+ align:start position:0%
+like that in the carbon chain
+ 
+
+ align:start position:0%
+like that in the carbon chain
+and so just to show you here on the
+
+ align:start position:0%
+and so just to show you here on the
+ 
+
+ align:start position:0%
+and so just to show you here on the
+models that this
+
+ align:start position:0%
+models that this
+ 
+
+ align:start position:0%
+models that this
+can matter so here's a double bonded
+
+ align:start position:0%
+can matter so here's a double bonded
+ 
+
+ align:start position:0%
+can matter so here's a double bonded
+carbon
+
+ align:start position:0%
+carbon
+ 
+
+ align:start position:0%
+carbon
+and so these two red guys are cis to
+
+ align:start position:0%
+and so these two red guys are cis to
+ 
+
+ align:start position:0%
+and so these two red guys are cis to
+each other
+
+ align:start position:0%
+each other
+ 
+
+ align:start position:0%
+each other
+and this purple is trans to that now if
+
+ align:start position:0%
+and this purple is trans to that now if
+ 
+
+ align:start position:0%
+and this purple is trans to that now if
+i put this
+
+ align:start position:0%
+i put this
+ 
+
+ align:start position:0%
+i put this
+onto a fatty acid chain you can see that
+
+ align:start position:0%
+onto a fatty acid chain you can see that
+ 
+
+ align:start position:0%
+onto a fatty acid chain you can see that
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+a big difference there so if i add
+
+ align:start position:0%
+a big difference there so if i add
+ 
+
+ align:start position:0%
+a big difference there so if i add
+the double bond in here and it's
+
+ align:start position:0%
+the double bond in here and it's
+ 
+
+ align:start position:0%
+the double bond in here and it's
+continue the chain
+
+ align:start position:0%
+continue the chain
+ 
+
+ align:start position:0%
+continue the chain
+here on a transbond it's a relatively
+
+ align:start position:0%
+here on a transbond it's a relatively
+ 
+
+ align:start position:0%
+here on a transbond it's a relatively
+straight molecule
+
+ align:start position:0%
+straight molecule
+ 
+
+ align:start position:0%
+straight molecule
+whereas if i go here in a cis bond i now
+
+ align:start position:0%
+whereas if i go here in a cis bond i now
+ 
+
+ align:start position:0%
+whereas if i go here in a cis bond i now
+introduce a kink
+
+ align:start position:0%
+introduce a kink
+ 
+
+ align:start position:0%
+introduce a kink
+into the alkyl chain so
+
+ align:start position:0%
+into the alkyl chain so
+ 
+
+ align:start position:0%
+into the alkyl chain so
+biological fatty acids are always
+
+ align:start position:0%
+biological fatty acids are always
+ 
+
+ align:start position:0%
+biological fatty acids are always
+cis and this is structurally important
+
+ align:start position:0%
+cis and this is structurally important
+ 
+
+ align:start position:0%
+cis and this is structurally important
+because it actually creates
+
+ align:start position:0%
+because it actually creates
+ 
+
+ align:start position:0%
+because it actually creates
+this kink in fatty acids that are
+
+ align:start position:0%
+this kink in fatty acids that are
+ 
+
+ align:start position:0%
+this kink in fatty acids that are
+not fully saturated now
+
+ align:start position:0%
+not fully saturated now
+ 
+
+ align:start position:0%
+not fully saturated now
+obviously as you might guess the number
+
+ align:start position:0%
+obviously as you might guess the number
+ 
+
+ align:start position:0%
+obviously as you might guess the number
+of double bonds and the locations of the
+
+ align:start position:0%
+of double bonds and the locations of the
+ 
+
+ align:start position:0%
+of double bonds and the locations of the
+double bonds
+
+ align:start position:0%
+double bonds
+ 
+
+ align:start position:0%
+double bonds
+will change the structure and therefore
+
+ align:start position:0%
+will change the structure and therefore
+ 
+
+ align:start position:0%
+will change the structure and therefore
+the properties of the fatty acids
+
+ align:start position:0%
+the properties of the fatty acids
+ 
+
+ align:start position:0%
+the properties of the fatty acids
+and so we need a nomenclature that
+
+ align:start position:0%
+and so we need a nomenclature that
+ 
+
+ align:start position:0%
+and so we need a nomenclature that
+allows us to
+
+ align:start position:0%
+allows us to
+ 
+
+ align:start position:0%
+allows us to
+describe what's going on here and so
+
+ align:start position:0%
+describe what's going on here and so
+ 
+
+ align:start position:0%
+describe what's going on here and so
+the simplest nomenclature is as follows
+
+ align:start position:0%
+the simplest nomenclature is as follows
+ 
+
+ align:start position:0%
+the simplest nomenclature is as follows
+where we basically
+
+ align:start position:0%
+where we basically
+ 
+
+ align:start position:0%
+where we basically
+have the number of carbons and the fatty
+
+ align:start position:0%
+have the number of carbons and the fatty
+ 
+
+ align:start position:0%
+have the number of carbons and the fatty
+acids say
+
+ align:start position:0%
+acids say
+ 
+
+ align:start position:0%
+acids say
+18 followed by the number
+
+ align:start position:0%
+18 followed by the number
+ 
+
+ align:start position:0%
+18 followed by the number
+of double bonds okay so an 18
+
+ align:start position:0%
+of double bonds okay so an 18
+ 
+
+ align:start position:0%
+of double bonds okay so an 18
+1 fatty acid that's oleic
+
+ align:start position:0%
+1 fatty acid that's oleic
+ 
+
+ align:start position:0%
+1 fatty acid that's oleic
+acid so 18 carbons long one double bond
+
+ align:start position:0%
+acid so 18 carbons long one double bond
+ 
+
+ align:start position:0%
+acid so 18 carbons long one double bond
+18 0 would be steric
+
+ align:start position:0%
+18 0 would be steric
+ 
+
+ align:start position:0%
+18 0 would be steric
+acid 18 carbons long zero double bonds
+
+ align:start position:0%
+acid 18 carbons long zero double bonds
+ 
+
+ align:start position:0%
+acid 18 carbons long zero double bonds
+16 0 palmitate palmitic acid
+
+ align:start position:0%
+16 0 palmitate palmitic acid
+ 
+
+ align:start position:0%
+16 0 palmitate palmitic acid
+16 carbons long zero double bonds
+
+ align:start position:0%
+16 carbons long zero double bonds
+ 
+
+ align:start position:0%
+16 carbons long zero double bonds
+so if we have one double bond
+
+ align:start position:0%
+so if we have one double bond
+ 
+
+ align:start position:0%
+so if we have one double bond
+oftentimes this is referred to as a mufa
+
+ align:start position:0%
+oftentimes this is referred to as a mufa
+ 
+
+ align:start position:0%
+oftentimes this is referred to as a mufa
+or mono
+
+ align:start position:0%
+or mono
+ 
+
+ align:start position:0%
+or mono
+unsaturated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fatty acid and of course if i have many
+
+ align:start position:0%
+fatty acid and of course if i have many
+ 
+
+ align:start position:0%
+fatty acid and of course if i have many
+double bonds more than one that's a pufa
+
+ align:start position:0%
+double bonds more than one that's a pufa
+ 
+
+ align:start position:0%
+double bonds more than one that's a pufa
+or a poly unsaturated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fatty acid probably heard those terms
+
+ align:start position:0%
+fatty acid probably heard those terms
+ 
+
+ align:start position:0%
+fatty acid probably heard those terms
+so what's an example of a
+
+ align:start position:0%
+so what's an example of a
+ 
+
+ align:start position:0%
+so what's an example of a
+polyunsaturated fat
+
+ align:start position:0%
+polyunsaturated fat
+ 
+
+ align:start position:0%
+polyunsaturated fat
+fatty acid well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a common one is an 18 2
+
+ align:start position:0%
+a common one is an 18 2
+ 
+
+ align:start position:0%
+a common one is an 18 2
+polyunsaturated fatty acids 18 carbons 2
+
+ align:start position:0%
+polyunsaturated fatty acids 18 carbons 2
+ 
+
+ align:start position:0%
+polyunsaturated fatty acids 18 carbons 2
+double bonds
+
+ align:start position:0%
+double bonds
+ 
+
+ align:start position:0%
+double bonds
+the common biological one is called
+
+ align:start position:0%
+the common biological one is called
+ 
+
+ align:start position:0%
+the common biological one is called
+linoleic
+
+ align:start position:0%
+linoleic
+ 
+
+ align:start position:0%
+linoleic
+acid and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ch3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ok and so
+
+ align:start position:0%
+ok and so
+ 
+
+ align:start position:0%
+ok and so
+one two double bonds four five six seven
+
+ align:start position:0%
+one two double bonds four five six seven
+ 
+
+ align:start position:0%
+one two double bonds four five six seven
+eight nine ten seventeen eighteen
+
+ align:start position:0%
+eight nine ten seventeen eighteen
+ 
+
+ align:start position:0%
+eight nine ten seventeen eighteen
+carbons total
+
+ align:start position:0%
+carbons total
+ 
+
+ align:start position:0%
+carbons total
+eighteen two fatty acid linoleic
+
+ align:start position:0%
+eighteen two fatty acid linoleic
+ 
+
+ align:start position:0%
+eighteen two fatty acid linoleic
+acid formal name is octa
+
+ align:start position:0%
+acid formal name is octa
+ 
+
+ align:start position:0%
+acid formal name is octa
+deca diene
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acid okay that make it more unsaturated
+
+ align:start position:0%
+acid okay that make it more unsaturated
+ 
+
+ align:start position:0%
+acid okay that make it more unsaturated
+so in 18 3
+
+ align:start position:0%
+so in 18 3
+ 
+
+ align:start position:0%
+so in 18 3
+okay that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+linolenic acid
+
+ align:start position:0%
+linolenic acid
+ 
+
+ align:start position:0%
+linolenic acid
+or octa deca
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+triene noec
+
+ align:start position:0%
+triene noec
+ 
+
+ align:start position:0%
+triene noec
+acid and i
+
+ align:start position:0%
+acid and i
+ 
+
+ align:start position:0%
+acid and i
+painfully draw out the
+
+ align:start position:0%
+painfully draw out the
+ 
+
+ align:start position:0%
+painfully draw out the
+entire thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we got one two three double bonds
+
+ align:start position:0%
+so we got one two three double bonds
+ 
+
+ align:start position:0%
+so we got one two three double bonds
+one two three four five six seven eight
+
+ align:start position:0%
+one two three four five six seven eight
+ 
+
+ align:start position:0%
+one two three four five six seven eight
+nine
+
+ align:start position:0%
+nine
+ 
+
+ align:start position:0%
+nine
+ten seventeen eighteen carbons total
+
+ align:start position:0%
+ten seventeen eighteen carbons total
+ 
+
+ align:start position:0%
+ten seventeen eighteen carbons total
+eighteen three um polyunsaturated fatty
+
+ align:start position:0%
+eighteen three um polyunsaturated fatty
+ 
+
+ align:start position:0%
+eighteen three um polyunsaturated fatty
+acid with
+
+ align:start position:0%
+acid with
+ 
+
+ align:start position:0%
+acid with
+three double bonds in it in all of these
+
+ align:start position:0%
+three double bonds in it in all of these
+ 
+
+ align:start position:0%
+three double bonds in it in all of these
+cases all of those double bonds
+
+ align:start position:0%
+cases all of those double bonds
+ 
+
+ align:start position:0%
+cases all of those double bonds
+are cis double bonds and you'll also
+
+ align:start position:0%
+are cis double bonds and you'll also
+ 
+
+ align:start position:0%
+are cis double bonds and you'll also
+notice
+
+ align:start position:0%
+notice
+ 
+
+ align:start position:0%
+notice
+that the spacing
+
+ align:start position:0%
+that the spacing
+ 
+
+ align:start position:0%
+that the spacing
+of them is not
+
+ align:start position:0%
+of them is not
+ 
+
+ align:start position:0%
+of them is not
+entirely random either at least as i
+
+ align:start position:0%
+entirely random either at least as i
+ 
+
+ align:start position:0%
+entirely random either at least as i
+drew it
+
+ align:start position:0%
+drew it
+ 
+
+ align:start position:0%
+drew it
+the first of all is that these are not
+
+ align:start position:0%
+the first of all is that these are not
+ 
+
+ align:start position:0%
+the first of all is that these are not
+conjugated double bonds so you see that
+
+ align:start position:0%
+conjugated double bonds so you see that
+ 
+
+ align:start position:0%
+conjugated double bonds so you see that
+there's
+
+ align:start position:0%
+there's
+ 
+
+ align:start position:0%
+there's
+a carbon in all cases between the double
+
+ align:start position:0%
+a carbon in all cases between the double
+ 
+
+ align:start position:0%
+a carbon in all cases between the double
+bond
+
+ align:start position:0%
+bond
+ 
+
+ align:start position:0%
+bond
+and also you'll notice that most of the
+
+ align:start position:0%
+and also you'll notice that most of the
+ 
+
+ align:start position:0%
+and also you'll notice that most of the
+double bonds are actually started
+
+ align:start position:0%
+double bonds are actually started
+ 
+
+ align:start position:0%
+double bonds are actually started
+and if you count from this end from the
+
+ align:start position:0%
+and if you count from this end from the
+ 
+
+ align:start position:0%
+and if you count from this end from the
+carb from from the acid end
+
+ align:start position:0%
+carb from from the acid end
+ 
+
+ align:start position:0%
+carb from from the acid end
+this would be carbon 9 and 10 so 1 plus
+
+ align:start position:0%
+this would be carbon 9 and 10 so 1 plus
+ 
+
+ align:start position:0%
+this would be carbon 9 and 10 so 1 plus
+7 is 8
+
+ align:start position:0%
+7 is 8
+ 
+
+ align:start position:0%
+7 is 8
+9 10. each of them the first double bond
+
+ align:start position:0%
+9 10. each of them the first double bond
+ 
+
+ align:start position:0%
+9 10. each of them the first double bond
+i put in is
+
+ align:start position:0%
+i put in is
+ 
+
+ align:start position:0%
+i put in is
+between carbons 9 and 10 going in this
+
+ align:start position:0%
+between carbons 9 and 10 going in this
+ 
+
+ align:start position:0%
+between carbons 9 and 10 going in this
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+and that's a consequence of the
+
+ align:start position:0%
+and that's a consequence of the
+ 
+
+ align:start position:0%
+and that's a consequence of the
+conserved enzymes that introduce these
+
+ align:start position:0%
+conserved enzymes that introduce these
+ 
+
+ align:start position:0%
+conserved enzymes that introduce these
+double bonds into the molecule
+
+ align:start position:0%
+double bonds into the molecule
+ 
+
+ align:start position:0%
+double bonds into the molecule
+now obviously this spacing
+
+ align:start position:0%
+now obviously this spacing
+ 
+
+ align:start position:0%
+now obviously this spacing
+matters um and so we need a way in the
+
+ align:start position:0%
+matters um and so we need a way in the
+ 
+
+ align:start position:0%
+matters um and so we need a way in the
+nomenclature in order to
+
+ align:start position:0%
+nomenclature in order to
+ 
+
+ align:start position:0%
+nomenclature in order to
+denote that that is where exactly the
+
+ align:start position:0%
+denote that that is where exactly the
+ 
+
+ align:start position:0%
+denote that that is where exactly the
+double bonds are
+
+ align:start position:0%
+double bonds are
+ 
+
+ align:start position:0%
+double bonds are
+located and there's sort of two ways we
+
+ align:start position:0%
+located and there's sort of two ways we
+ 
+
+ align:start position:0%
+located and there's sort of two ways we
+can count we can count from one end or
+
+ align:start position:0%
+can count we can count from one end or
+ 
+
+ align:start position:0%
+can count we can count from one end or
+we can count from the other end
+
+ align:start position:0%
+we can count from the other end
+ 
+
+ align:start position:0%
+we can count from the other end
+now the most systematic way
+
+ align:start position:0%
+now the most systematic way
+ 
+
+ align:start position:0%
+now the most systematic way
+uh correct way now is to count from the
+
+ align:start position:0%
+uh correct way now is to count from the
+ 
+
+ align:start position:0%
+uh correct way now is to count from the
+carboxylic acid end so very similar to
+
+ align:start position:0%
+carboxylic acid end so very similar to
+ 
+
+ align:start position:0%
+carboxylic acid end so very similar to
+sugars we counted carbon one of sugars
+
+ align:start position:0%
+sugars we counted carbon one of sugars
+ 
+
+ align:start position:0%
+sugars we counted carbon one of sugars
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+the one that was closest to the end of
+
+ align:start position:0%
+the one that was closest to the end of
+ 
+
+ align:start position:0%
+the one that was closest to the end of
+the molecule where the
+
+ align:start position:0%
+the molecule where the
+ 
+
+ align:start position:0%
+the molecule where the
+carbonyl was located so same thing in
+
+ align:start position:0%
+carbonyl was located so same thing in
+ 
+
+ align:start position:0%
+carbonyl was located so same thing in
+fatty acids so this would be carbon one
+
+ align:start position:0%
+fatty acids so this would be carbon one
+ 
+
+ align:start position:0%
+fatty acids so this would be carbon one
+count in that direction and so the
+
+ align:start position:0%
+count in that direction and so the
+ 
+
+ align:start position:0%
+count in that direction and so the
+nomenclature would be then to put in a
+
+ align:start position:0%
+nomenclature would be then to put in a
+ 
+
+ align:start position:0%
+nomenclature would be then to put in a
+delta
+
+ align:start position:0%
+delta
+ 
+
+ align:start position:0%
+delta
+nine would be a double bond between the
+
+ align:start position:0%
+nine would be a double bond between the
+ 
+
+ align:start position:0%
+nine would be a double bond between the
+ninth
+
+ align:start position:0%
+ninth
+ 
+
+ align:start position:0%
+ninth
+and tenth carbon counting from the
+
+ align:start position:0%
+and tenth carbon counting from the
+ 
+
+ align:start position:0%
+and tenth carbon counting from the
+carboxylic acid
+
+ align:start position:0%
+carboxylic acid
+ 
+
+ align:start position:0%
+carboxylic acid
+and so the 18
+
+ align:start position:0%
+and so the 18
+ 
+
+ align:start position:0%
+and so the 18
+2 fatty acid i drew here linoleic acid
+
+ align:start position:0%
+2 fatty acid i drew here linoleic acid
+ 
+
+ align:start position:0%
+2 fatty acid i drew here linoleic acid
+would more precisely be 18
+
+ align:start position:0%
+would more precisely be 18
+ 
+
+ align:start position:0%
+would more precisely be 18
+2 delta 9 delta 12 that's because it's
+
+ align:start position:0%
+2 delta 9 delta 12 that's because it's
+ 
+
+ align:start position:0%
+2 delta 9 delta 12 that's because it's
+carbon 9
+
+ align:start position:0%
+carbon 9
+ 
+
+ align:start position:0%
+carbon 9
+10 11 12. so carbon 9 and 10
+
+ align:start position:0%
+10 11 12. so carbon 9 and 10
+ 
+
+ align:start position:0%
+10 11 12. so carbon 9 and 10
+and 12 and 13. linolenic acid
+
+ align:start position:0%
+and 12 and 13. linolenic acid
+ 
+
+ align:start position:0%
+and 12 and 13. linolenic acid
+18 3 delta 9 12
+
+ align:start position:0%
+18 3 delta 9 12
+ 
+
+ align:start position:0%
+18 3 delta 9 12
+15 so 9 10 11 12
+
+ align:start position:0%
+15 so 9 10 11 12
+ 
+
+ align:start position:0%
+15 so 9 10 11 12
+13 14 15 to say
+
+ align:start position:0%
+13 14 15 to say
+ 
+
+ align:start position:0%
+13 14 15 to say
+where the double bonds are in the
+
+ align:start position:0%
+where the double bonds are in the
+ 
+
+ align:start position:0%
+where the double bonds are in the
+polyunsaturated fatty acids as you can
+
+ align:start position:0%
+polyunsaturated fatty acids as you can
+ 
+
+ align:start position:0%
+polyunsaturated fatty acids as you can
+see most polyunsaturated fatty acids as
+
+ align:start position:0%
+see most polyunsaturated fatty acids as
+ 
+
+ align:start position:0%
+see most polyunsaturated fatty acids as
+a consequence that they're not
+
+ align:start position:0%
+a consequence that they're not
+ 
+
+ align:start position:0%
+a consequence that they're not
+conjugated
+
+ align:start position:0%
+conjugated
+ 
+
+ align:start position:0%
+conjugated
+are placed every you'll see that the
+
+ align:start position:0%
+are placed every you'll see that the
+ 
+
+ align:start position:0%
+are placed every you'll see that the
+double bonds are placed every three
+
+ align:start position:0%
+double bonds are placed every three
+ 
+
+ align:start position:0%
+double bonds are placed every three
+carbons
+
+ align:start position:0%
+carbons
+ 
+
+ align:start position:0%
+carbons
+now this three carbon spacing
+
+ align:start position:0%
+now this three carbon spacing
+ 
+
+ align:start position:0%
+now this three carbon spacing
+is maintained even in the
+
+ align:start position:0%
+is maintained even in the
+ 
+
+ align:start position:0%
+is maintained even in the
+often in biology even in the exceptions
+
+ align:start position:0%
+often in biology even in the exceptions
+ 
+
+ align:start position:0%
+often in biology even in the exceptions
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+the first one is not between carbon 9
+
+ align:start position:0%
+the first one is not between carbon 9
+ 
+
+ align:start position:0%
+the first one is not between carbon 9
+and 10 and so
+
+ align:start position:0%
+and 10 and so
+ 
+
+ align:start position:0%
+and 10 and so
+a classic example of that is the
+
+ align:start position:0%
+a classic example of that is the
+ 
+
+ align:start position:0%
+a classic example of that is the
+polyunsaturated fatty acid arachidonic
+
+ align:start position:0%
+polyunsaturated fatty acid arachidonic
+ 
+
+ align:start position:0%
+polyunsaturated fatty acid arachidonic
+acid
+
+ align:start position:0%
+acid
+ 
+
+ align:start position:0%
+acid
+which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a 20 carbon fatty acid with four double
+
+ align:start position:0%
+a 20 carbon fatty acid with four double
+ 
+
+ align:start position:0%
+a 20 carbon fatty acid with four double
+bonds at carbons 5
+
+ align:start position:0%
+bonds at carbons 5
+ 
+
+ align:start position:0%
+bonds at carbons 5
+8 11 and 14. so arachidonic acid
+
+ align:start position:0%
+8 11 and 14. so arachidonic acid
+ 
+
+ align:start position:0%
+8 11 and 14. so arachidonic acid
+you may have heard in the past is a key
+
+ align:start position:0%
+you may have heard in the past is a key
+ 
+
+ align:start position:0%
+you may have heard in the past is a key
+signaling fatty acid
+
+ align:start position:0%
+signaling fatty acid
+ 
+
+ align:start position:0%
+signaling fatty acid
+it's mobilized and used to generate some
+
+ align:start position:0%
+it's mobilized and used to generate some
+ 
+
+ align:start position:0%
+it's mobilized and used to generate some
+inflammatory mediators it's the enzyme
+
+ align:start position:0%
+inflammatory mediators it's the enzyme
+ 
+
+ align:start position:0%
+inflammatory mediators it's the enzyme
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+acts on this to generate the
+
+ align:start position:0%
+acts on this to generate the
+ 
+
+ align:start position:0%
+acts on this to generate the
+inflammatory mediators is the target
+
+ align:start position:0%
+inflammatory mediators is the target
+ 
+
+ align:start position:0%
+inflammatory mediators is the target
+of very common drugs like the like
+
+ align:start position:0%
+of very common drugs like the like
+ 
+
+ align:start position:0%
+of very common drugs like the like
+aspirin
+
+ align:start position:0%
+aspirin
+ 
+
+ align:start position:0%
+aspirin
+or other non-steroidal anti-inflammatory
+
+ align:start position:0%
+or other non-steroidal anti-inflammatory
+ 
+
+ align:start position:0%
+or other non-steroidal anti-inflammatory
+drugs
+
+ align:start position:0%
+drugs
+ 
+
+ align:start position:0%
+drugs
+ibuprofen etc and this molecule drawing
+
+ align:start position:0%
+ibuprofen etc and this molecule drawing
+ 
+
+ align:start position:0%
+ibuprofen etc and this molecule drawing
+it like this
+
+ align:start position:0%
+it like this
+ 
+
+ align:start position:0%
+it like this
+should fully describe to you what it
+
+ align:start position:0%
+should fully describe to you what it
+ 
+
+ align:start position:0%
+should fully describe to you what it
+would look like all right
+
+ align:start position:0%
+would look like all right
+ 
+
+ align:start position:0%
+would look like all right
+now there's also an older nomenclature
+
+ align:start position:0%
+now there's also an older nomenclature
+ 
+
+ align:start position:0%
+now there's also an older nomenclature
+that numbers fatty acids to name them
+
+ align:start position:0%
+that numbers fatty acids to name them
+ 
+
+ align:start position:0%
+that numbers fatty acids to name them
+and where the double bonds are located
+
+ align:start position:0%
+and where the double bonds are located
+ 
+
+ align:start position:0%
+and where the double bonds are located
+not from the carbonyl side but from the
+
+ align:start position:0%
+not from the carbonyl side but from the
+ 
+
+ align:start position:0%
+not from the carbonyl side but from the
+other end of the molecule and i
+
+ align:start position:0%
+other end of the molecule and i
+ 
+
+ align:start position:0%
+other end of the molecule and i
+mentioned this nomenclature because it's
+
+ align:start position:0%
+mentioned this nomenclature because it's
+ 
+
+ align:start position:0%
+mentioned this nomenclature because it's
+still
+
+ align:start position:0%
+still
+ 
+
+ align:start position:0%
+still
+used quite often in popular culture
+
+ align:start position:0%
+used quite often in popular culture
+ 
+
+ align:start position:0%
+used quite often in popular culture
+and so to do this it's basically refers
+
+ align:start position:0%
+and so to do this it's basically refers
+ 
+
+ align:start position:0%
+and so to do this it's basically refers
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+this i guess as the alpha carbon so
+
+ align:start position:0%
+this i guess as the alpha carbon so
+ 
+
+ align:start position:0%
+this i guess as the alpha carbon so
+counting in greek
+
+ align:start position:0%
+counting in greek
+ 
+
+ align:start position:0%
+counting in greek
+going this direction the final carbon
+
+ align:start position:0%
+going this direction the final carbon
+ 
+
+ align:start position:0%
+going this direction the final carbon
+in the fatty acid omega the last letter
+
+ align:start position:0%
+in the fatty acid omega the last letter
+ 
+
+ align:start position:0%
+in the fatty acid omega the last letter
+of the greek
+
+ align:start position:0%
+of the greek
+ 
+
+ align:start position:0%
+of the greek
+alphabet and so if you count from the
+
+ align:start position:0%
+alphabet and so if you count from the
+ 
+
+ align:start position:0%
+alphabet and so if you count from the
+other end we could also give this
+
+ align:start position:0%
+other end we could also give this
+ 
+
+ align:start position:0%
+other end we could also give this
+a a different nomenclature
+
+ align:start position:0%
+a a different nomenclature
+ 
+
+ align:start position:0%
+a a different nomenclature
+and so in this case our 18 3
+
+ align:start position:0%
+and so in this case our 18 3
+ 
+
+ align:start position:0%
+and so in this case our 18 3
+lino lay our 18 3 linolenic acid 183
+
+ align:start position:0%
+lino lay our 18 3 linolenic acid 183
+ 
+
+ align:start position:0%
+lino lay our 18 3 linolenic acid 183
+delta 9 12
+
+ align:start position:0%
+delta 9 12
+ 
+
+ align:start position:0%
+delta 9 12
+15 we could also say is 18
+
+ align:start position:0%
+15 we could also say is 18
+ 
+
+ align:start position:0%
+15 we could also say is 18
+3 omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three six nine so now we're counting
+
+ align:start position:0%
+three six nine so now we're counting
+ 
+
+ align:start position:0%
+three six nine so now we're counting
+from this
+
+ align:start position:0%
+from this
+ 
+
+ align:start position:0%
+from this
+end one two three first double the bond
+
+ align:start position:0%
+end one two three first double the bond
+ 
+
+ align:start position:0%
+end one two three first double the bond
+four five six next double bond seven 8 9
+
+ align:start position:0%
+four five six next double bond seven 8 9
+ 
+
+ align:start position:0%
+four five six next double bond seven 8 9
+next double bond and so
+
+ align:start position:0%
+next double bond and so
+ 
+
+ align:start position:0%
+next double bond and so
+thus 18 1 by this nomenclature
+
+ align:start position:0%
+thus 18 1 by this nomenclature
+ 
+
+ align:start position:0%
+thus 18 1 by this nomenclature
+18 1 delta 9 would be the same as
+
+ align:start position:0%
+18 1 delta 9 would be the same as
+ 
+
+ align:start position:0%
+18 1 delta 9 would be the same as
+18 1 omega 9
+
+ align:start position:0%
+18 1 omega 9
+ 
+
+ align:start position:0%
+18 1 omega 9
+because it's obviously meeting in the
+
+ align:start position:0%
+because it's obviously meeting in the
+ 
+
+ align:start position:0%
+because it's obviously meeting in the
+middle but if we did 18
+
+ align:start position:0%
+middle but if we did 18
+ 
+
+ align:start position:0%
+middle but if we did 18
+1 delta 12
+
+ align:start position:0%
+1 delta 12
+ 
+
+ align:start position:0%
+1 delta 12
+that would be 18 1 omega 6 18
+
+ align:start position:0%
+that would be 18 1 omega 6 18
+ 
+
+ align:start position:0%
+that would be 18 1 omega 6 18
+1 delta 15 would be 18 1
+
+ align:start position:0%
+1 delta 15 would be 18 1
+ 
+
+ align:start position:0%
+1 delta 15 would be 18 1
+omega 3. and so i mentioned this because
+
+ align:start position:0%
+omega 3. and so i mentioned this because
+ 
+
+ align:start position:0%
+omega 3. and so i mentioned this because
+you'll hear about so-called omega-3
+
+ align:start position:0%
+you'll hear about so-called omega-3
+ 
+
+ align:start position:0%
+you'll hear about so-called omega-3
+fatty acids
+
+ align:start position:0%
+fatty acids
+ 
+
+ align:start position:0%
+fatty acids
+the major omega-3 fatty acid that
+
+ align:start position:0%
+the major omega-3 fatty acid that
+ 
+
+ align:start position:0%
+the major omega-3 fatty acid that
+they're talking about
+
+ align:start position:0%
+they're talking about
+ 
+
+ align:start position:0%
+they're talking about
+is linolenic acid and it's an omega-3
+
+ align:start position:0%
+is linolenic acid and it's an omega-3
+ 
+
+ align:start position:0%
+is linolenic acid and it's an omega-3
+fatty acid using the nomenclature
+
+ align:start position:0%
+fatty acid using the nomenclature
+ 
+
+ align:start position:0%
+fatty acid using the nomenclature
+counting from the other side
+
+ align:start position:0%
+counting from the other side
+ 
+
+ align:start position:0%
+counting from the other side
+or you could also say it's 18 3 delta 9
+
+ align:start position:0%
+or you could also say it's 18 3 delta 9
+ 
+
+ align:start position:0%
+or you could also say it's 18 3 delta 9
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+15. now i want to mention one of the
+
+ align:start position:0%
+15. now i want to mention one of the
+ 
+
+ align:start position:0%
+15. now i want to mention one of the
+reasons you hear about omega-3 fatty
+
+ align:start position:0%
+reasons you hear about omega-3 fatty
+ 
+
+ align:start position:0%
+reasons you hear about omega-3 fatty
+acids is that
+
+ align:start position:0%
+acids is that
+ 
+
+ align:start position:0%
+acids is that
+in general these are there are fatty
+
+ align:start position:0%
+in general these are there are fatty
+ 
+
+ align:start position:0%
+in general these are there are fatty
+acids such as those that humans cannot
+
+ align:start position:0%
+acids such as those that humans cannot
+ 
+
+ align:start position:0%
+acids such as those that humans cannot
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+and so we have to get those from the
+
+ align:start position:0%
+and so we have to get those from the
+ 
+
+ align:start position:0%
+and so we have to get those from the
+diets and so this is the concept called
+
+ align:start position:0%
+diets and so this is the concept called
+ 
+
+ align:start position:0%
+diets and so this is the concept called
+essential
+
+ align:start position:0%
+essential
+ 
+
+ align:start position:0%
+essential
+fatty acids and so somewhat like
+
+ align:start position:0%
+fatty acids and so somewhat like
+ 
+
+ align:start position:0%
+fatty acids and so somewhat like
+vitamins there's
+
+ align:start position:0%
+vitamins there's
+ 
+
+ align:start position:0%
+vitamins there's
+things out there that our physiology
+
+ align:start position:0%
+things out there that our physiology
+ 
+
+ align:start position:0%
+things out there that our physiology
+uses that we have to get
+
+ align:start position:0%
+uses that we have to get
+ 
+
+ align:start position:0%
+uses that we have to get
+from other organisms making and
+
+ align:start position:0%
+from other organisms making and
+ 
+
+ align:start position:0%
+from other organisms making and
+therefore we have to
+
+ align:start position:0%
+therefore we have to
+ 
+
+ align:start position:0%
+therefore we have to
+eat them and so if you hear this term
+
+ align:start position:0%
+eat them and so if you hear this term
+ 
+
+ align:start position:0%
+eat them and so if you hear this term
+essential fatty acid
+
+ align:start position:0%
+essential fatty acid
+ 
+
+ align:start position:0%
+essential fatty acid
+it's basically referring to specific
+
+ align:start position:0%
+it's basically referring to specific
+ 
+
+ align:start position:0%
+it's basically referring to specific
+fatty acids where we lack the enzymes
+
+ align:start position:0%
+fatty acids where we lack the enzymes
+ 
+
+ align:start position:0%
+fatty acids where we lack the enzymes
+to place all the double bonds um
+
+ align:start position:0%
+to place all the double bonds um
+ 
+
+ align:start position:0%
+to place all the double bonds um
+to be in the place where it's useful for
+
+ align:start position:0%
+to be in the place where it's useful for
+ 
+
+ align:start position:0%
+to be in the place where it's useful for
+for some
+
+ align:start position:0%
+for some
+ 
+
+ align:start position:0%
+for some
+aspect of our our biology
+
+ align:start position:0%
+aspect of our our biology
+ 
+
+ align:start position:0%
+aspect of our our biology
+all right now lots of nomenclature here
+
+ align:start position:0%
+all right now lots of nomenclature here
+ 
+
+ align:start position:0%
+all right now lots of nomenclature here
+nature the reason i discuss this is
+
+ align:start position:0%
+nature the reason i discuss this is
+ 
+
+ align:start position:0%
+nature the reason i discuss this is
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+this diversity of chain length and
+
+ align:start position:0%
+this diversity of chain length and
+ 
+
+ align:start position:0%
+this diversity of chain length and
+double bonds
+
+ align:start position:0%
+double bonds
+ 
+
+ align:start position:0%
+double bonds
+creates different properties and nature
+
+ align:start position:0%
+creates different properties and nature
+ 
+
+ align:start position:0%
+creates different properties and nature
+uses these diverse
+
+ align:start position:0%
+uses these diverse
+ 
+
+ align:start position:0%
+uses these diverse
+chemical properties of the fatty acids
+
+ align:start position:0%
+chemical properties of the fatty acids
+ 
+
+ align:start position:0%
+chemical properties of the fatty acids
+that is different change lengths and
+
+ align:start position:0%
+that is different change lengths and
+ 
+
+ align:start position:0%
+that is different change lengths and
+different degrees of saturation or
+
+ align:start position:0%
+different degrees of saturation or
+ 
+
+ align:start position:0%
+different degrees of saturation or
+unsaturation
+
+ align:start position:0%
+unsaturation
+ 
+
+ align:start position:0%
+unsaturation
+positions of the of of the double bonds
+
+ align:start position:0%
+positions of the of of the double bonds
+ 
+
+ align:start position:0%
+positions of the of of the double bonds
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+take advantage of those properties to do
+
+ align:start position:0%
+take advantage of those properties to do
+ 
+
+ align:start position:0%
+take advantage of those properties to do
+different things
+
+ align:start position:0%
+different things
+ 
+
+ align:start position:0%
+different things
+in biology and so a lot of this has to
+
+ align:start position:0%
+in biology and so a lot of this has to
+ 
+
+ align:start position:0%
+in biology and so a lot of this has to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+a lot of why fatty acids are useful is
+
+ align:start position:0%
+a lot of why fatty acids are useful is
+ 
+
+ align:start position:0%
+a lot of why fatty acids are useful is
+that they are not
+
+ align:start position:0%
+that they are not
+ 
+
+ align:start position:0%
+that they are not
+soluble in water or poorly soluble in
+
+ align:start position:0%
+soluble in water or poorly soluble in
+ 
+
+ align:start position:0%
+soluble in water or poorly soluble in
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+you know this just from the common
+
+ align:start position:0%
+you know this just from the common
+ 
+
+ align:start position:0%
+you know this just from the common
+experience of making salad dressing
+
+ align:start position:0%
+experience of making salad dressing
+ 
+
+ align:start position:0%
+experience of making salad dressing
+and so you mix the oil and the vinegar
+
+ align:start position:0%
+and so you mix the oil and the vinegar
+ 
+
+ align:start position:0%
+and so you mix the oil and the vinegar
+in the salad dressing and so the
+
+ align:start position:0%
+in the salad dressing and so the
+ 
+
+ align:start position:0%
+in the salad dressing and so the
+oil is largely made out of fatty acids
+
+ align:start position:0%
+oil is largely made out of fatty acids
+ 
+
+ align:start position:0%
+oil is largely made out of fatty acids
+made out of lipids
+
+ align:start position:0%
+made out of lipids
+ 
+
+ align:start position:0%
+made out of lipids
+and those fatty acids are not soluble
+
+ align:start position:0%
+and those fatty acids are not soluble
+ 
+
+ align:start position:0%
+and those fatty acids are not soluble
+soluble in the vinegar part the water
+
+ align:start position:0%
+soluble in the vinegar part the water
+ 
+
+ align:start position:0%
+soluble in the vinegar part the water
+part of the molecule
+
+ align:start position:0%
+part of the molecule
+ 
+
+ align:start position:0%
+part of the molecule
+okay now the fatty acid themselves
+
+ align:start position:0%
+okay now the fatty acid themselves
+ 
+
+ align:start position:0%
+okay now the fatty acid themselves
+the chain length and the number of
+
+ align:start position:0%
+the chain length and the number of
+ 
+
+ align:start position:0%
+the chain length and the number of
+double bonds
+
+ align:start position:0%
+double bonds
+ 
+
+ align:start position:0%
+double bonds
+will affect other properties such as the
+
+ align:start position:0%
+will affect other properties such as the
+ 
+
+ align:start position:0%
+will affect other properties such as the
+melting temperature
+
+ align:start position:0%
+melting temperature
+ 
+
+ align:start position:0%
+melting temperature
+so in general the melting
+
+ align:start position:0%
+so in general the melting
+ 
+
+ align:start position:0%
+so in general the melting
+temperature of a fatty acid
+
+ align:start position:0%
+temperature of a fatty acid
+ 
+
+ align:start position:0%
+temperature of a fatty acid
+will decrease with shorter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chain length
+
+ align:start position:0%
+chain length
+ 
+
+ align:start position:0%
+chain length
+and decrease with
+
+ align:start position:0%
+and decrease with
+ 
+
+ align:start position:0%
+and decrease with
+more unsaturation so
+
+ align:start position:0%
+more unsaturation so
+ 
+
+ align:start position:0%
+more unsaturation so
+more double bonds so the more double
+
+ align:start position:0%
+more double bonds so the more double
+ 
+
+ align:start position:0%
+more double bonds so the more double
+bonds i put in and the shorter it is
+
+ align:start position:0%
+bonds i put in and the shorter it is
+ 
+
+ align:start position:0%
+bonds i put in and the shorter it is
+the lower the melting temperature
+
+ align:start position:0%
+the lower the melting temperature
+ 
+
+ align:start position:0%
+the lower the melting temperature
+and so you guys know this from just
+
+ align:start position:0%
+and so you guys know this from just
+ 
+
+ align:start position:0%
+and so you guys know this from just
+cooking experience
+
+ align:start position:0%
+cooking experience
+ 
+
+ align:start position:0%
+cooking experience
+um to be the case and so
+
+ align:start position:0%
+um to be the case and so
+ 
+
+ align:start position:0%
+um to be the case and so
+animal fatty acids
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tend to be more saturated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and because they're more saturated they
+
+ align:start position:0%
+and because they're more saturated they
+ 
+
+ align:start position:0%
+and because they're more saturated they
+have a
+
+ align:start position:0%
+have a
+ 
+
+ align:start position:0%
+have a
+higher melting temperature and so their
+
+ align:start position:0%
+higher melting temperature and so their
+ 
+
+ align:start position:0%
+higher melting temperature and so their
+solids at room temperature
+
+ align:start position:0%
+solids at room temperature
+ 
+
+ align:start position:0%
+solids at room temperature
+so think about it animal fat butter lard
+
+ align:start position:0%
+so think about it animal fat butter lard
+ 
+
+ align:start position:0%
+so think about it animal fat butter lard
+these things are solids at room
+
+ align:start position:0%
+these things are solids at room
+ 
+
+ align:start position:0%
+these things are solids at room
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+so plant fatty acids
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they tend to be more
+
+ align:start position:0%
+they tend to be more
+ 
+
+ align:start position:0%
+they tend to be more
+unsaturated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fatty acids and they're liquids at room
+
+ align:start position:0%
+fatty acids and they're liquids at room
+ 
+
+ align:start position:0%
+fatty acids and they're liquids at room
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+and you know this because cooking oil
+
+ align:start position:0%
+and you know this because cooking oil
+ 
+
+ align:start position:0%
+and you know this because cooking oil
+made from plants
+
+ align:start position:0%
+made from plants
+ 
+
+ align:start position:0%
+made from plants
+is typically a liquid at room
+
+ align:start position:0%
+is typically a liquid at room
+ 
+
+ align:start position:0%
+is typically a liquid at room
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+now you might be aware that olive oil is
+
+ align:start position:0%
+now you might be aware that olive oil is
+ 
+
+ align:start position:0%
+now you might be aware that olive oil is
+a mono unsaturated it has a lot of
+
+ align:start position:0%
+a mono unsaturated it has a lot of
+ 
+
+ align:start position:0%
+a mono unsaturated it has a lot of
+monounsaturated fatty acids a lot of
+
+ align:start position:0%
+monounsaturated fatty acids a lot of
+ 
+
+ align:start position:0%
+monounsaturated fatty acids a lot of
+mufas
+
+ align:start position:0%
+mufas
+ 
+
+ align:start position:0%
+mufas
+olive oil unlike other plant oils which
+
+ align:start position:0%
+olive oil unlike other plant oils which
+ 
+
+ align:start position:0%
+olive oil unlike other plant oils which
+are more polyunsaturated fatty acids if
+
+ align:start position:0%
+are more polyunsaturated fatty acids if
+ 
+
+ align:start position:0%
+are more polyunsaturated fatty acids if
+you put those in the refrigerator
+
+ align:start position:0%
+you put those in the refrigerator
+ 
+
+ align:start position:0%
+you put those in the refrigerator
+the olive oil will tend to form a solid
+
+ align:start position:0%
+the olive oil will tend to form a solid
+ 
+
+ align:start position:0%
+the olive oil will tend to form a solid
+whereas your canola oil will not and
+
+ align:start position:0%
+whereas your canola oil will not and
+ 
+
+ align:start position:0%
+whereas your canola oil will not and
+that's a consequence of the fact that
+
+ align:start position:0%
+that's a consequence of the fact that
+ 
+
+ align:start position:0%
+that's a consequence of the fact that
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+more unsaturated fatty acids there are
+
+ align:start position:0%
+more unsaturated fatty acids there are
+ 
+
+ align:start position:0%
+more unsaturated fatty acids there are
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+um lower the melting temperature and so
+
+ align:start position:0%
+um lower the melting temperature and so
+ 
+
+ align:start position:0%
+um lower the melting temperature and so
+the more likely it is to be a liquid or
+
+ align:start position:0%
+the more likely it is to be a liquid or
+ 
+
+ align:start position:0%
+the more likely it is to be a liquid or
+a salad
+
+ align:start position:0%
+a salad
+ 
+
+ align:start position:0%
+a salad
+in the fridge or at room temperature
+
+ align:start position:0%
+in the fridge or at room temperature
+ 
+
+ align:start position:0%
+in the fridge or at room temperature
+across these
+
+ align:start position:0%
+across these
+ 
+
+ align:start position:0%
+across these
+different fatty acids to show here on
+
+ align:start position:0%
+different fatty acids to show here on
+ 
+
+ align:start position:0%
+different fatty acids to show here on
+the slide here's just
+
+ align:start position:0%
+the slide here's just
+ 
+
+ align:start position:0%
+the slide here's just
+something i stole from the textbook it
+
+ align:start position:0%
+something i stole from the textbook it
+ 
+
+ align:start position:0%
+something i stole from the textbook it
+basically gives the
+
+ align:start position:0%
+basically gives the
+ 
+
+ align:start position:0%
+basically gives the
+composition of some things you might be
+
+ align:start position:0%
+composition of some things you might be
+ 
+
+ align:start position:0%
+composition of some things you might be
+aware of so olive oil butter
+
+ align:start position:0%
+aware of so olive oil butter
+ 
+
+ align:start position:0%
+aware of so olive oil butter
+and beef fat so you can see as we go
+
+ align:start position:0%
+and beef fat so you can see as we go
+ 
+
+ align:start position:0%
+and beef fat so you can see as we go
+down the spectrum here
+
+ align:start position:0%
+down the spectrum here
+ 
+
+ align:start position:0%
+down the spectrum here
+you have um longer chain lengths
+
+ align:start position:0%
+you have um longer chain lengths
+ 
+
+ align:start position:0%
+you have um longer chain lengths
+and a reduction in the number of double
+
+ align:start position:0%
+and a reduction in the number of double
+ 
+
+ align:start position:0%
+and a reduction in the number of double
+bonds
+
+ align:start position:0%
+bonds
+ 
+
+ align:start position:0%
+bonds
+and of course b fat if you've ever
+
+ align:start position:0%
+and of course b fat if you've ever
+ 
+
+ align:start position:0%
+and of course b fat if you've ever
+handled it is
+
+ align:start position:0%
+handled it is
+ 
+
+ align:start position:0%
+handled it is
+a much firmer solid at room temperature
+
+ align:start position:0%
+a much firmer solid at room temperature
+ 
+
+ align:start position:0%
+a much firmer solid at room temperature
+than butter is which is of course
+
+ align:start position:0%
+than butter is which is of course
+ 
+
+ align:start position:0%
+than butter is which is of course
+solid at room temperature whereas olive
+
+ align:start position:0%
+solid at room temperature whereas olive
+ 
+
+ align:start position:0%
+solid at room temperature whereas olive
+oil
+
+ align:start position:0%
+oil
+ 
+
+ align:start position:0%
+oil
+is not and that follows this with the
+
+ align:start position:0%
+is not and that follows this with the
+ 
+
+ align:start position:0%
+is not and that follows this with the
+number the chain length and the double
+
+ align:start position:0%
+number the chain length and the double
+ 
+
+ align:start position:0%
+number the chain length and the double
+bonds really affecting the melting
+
+ align:start position:0%
+bonds really affecting the melting
+ 
+
+ align:start position:0%
+bonds really affecting the melting
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+of these different fats just a couple of
+
+ align:start position:0%
+of these different fats just a couple of
+ 
+
+ align:start position:0%
+of these different fats just a couple of
+sides so you can better
+
+ align:start position:0%
+sides so you can better
+ 
+
+ align:start position:0%
+sides so you can better
+understand your food and so you may have
+
+ align:start position:0%
+understand your food and so you may have
+ 
+
+ align:start position:0%
+understand your food and so you may have
+heard about or seen on the side of your
+
+ align:start position:0%
+heard about or seen on the side of your
+ 
+
+ align:start position:0%
+heard about or seen on the side of your
+food packaging
+
+ align:start position:0%
+food packaging
+ 
+
+ align:start position:0%
+food packaging
+hydrogenated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oils so what's a hydrogenated
+
+ align:start position:0%
+oils so what's a hydrogenated
+ 
+
+ align:start position:0%
+oils so what's a hydrogenated
+oil well that's basically taking a plant
+
+ align:start position:0%
+oil well that's basically taking a plant
+ 
+
+ align:start position:0%
+oil well that's basically taking a plant
+oil
+
+ align:start position:0%
+oil
+ 
+
+ align:start position:0%
+oil
+which has unsaturated unsaturated fatty
+
+ align:start position:0%
+which has unsaturated unsaturated fatty
+ 
+
+ align:start position:0%
+which has unsaturated unsaturated fatty
+acids
+
+ align:start position:0%
+acids
+ 
+
+ align:start position:0%
+acids
+and hydrogen hydrogenating it that is
+
+ align:start position:0%
+and hydrogen hydrogenating it that is
+ 
+
+ align:start position:0%
+and hydrogen hydrogenating it that is
+adding hydrogen
+
+ align:start position:0%
+adding hydrogen
+ 
+
+ align:start position:0%
+adding hydrogen
+well what is that it's not really the
+
+ align:start position:0%
+well what is that it's not really the
+ 
+
+ align:start position:0%
+well what is that it's not really the
+hydrogen that's being added it's adding
+
+ align:start position:0%
+hydrogen that's being added it's adding
+ 
+
+ align:start position:0%
+hydrogen that's being added it's adding
+electrons so it's taking it from being
+
+ align:start position:0%
+electrons so it's taking it from being
+ 
+
+ align:start position:0%
+electrons so it's taking it from being
+a unsaturated fatty acid to chemically
+
+ align:start position:0%
+a unsaturated fatty acid to chemically
+ 
+
+ align:start position:0%
+a unsaturated fatty acid to chemically
+making it a saturated fatty acid
+
+ align:start position:0%
+making it a saturated fatty acid
+ 
+
+ align:start position:0%
+making it a saturated fatty acid
+and it's a way to take plant oils and
+
+ align:start position:0%
+and it's a way to take plant oils and
+ 
+
+ align:start position:0%
+and it's a way to take plant oils and
+make it such that it's solid at room
+
+ align:start position:0%
+make it such that it's solid at room
+ 
+
+ align:start position:0%
+make it such that it's solid at room
+temperature
+
+ align:start position:0%
+temperature
+ 
+
+ align:start position:0%
+temperature
+an example of a hydrogenated oil would
+
+ align:start position:0%
+an example of a hydrogenated oil would
+ 
+
+ align:start position:0%
+an example of a hydrogenated oil would
+be margarine
+
+ align:start position:0%
+be margarine
+ 
+
+ align:start position:0%
+be margarine
+okay plant oil that would be liquid
+
+ align:start position:0%
+okay plant oil that would be liquid
+ 
+
+ align:start position:0%
+okay plant oil that would be liquid
+reduce it chemically such that it's
+
+ align:start position:0%
+reduce it chemically such that it's
+ 
+
+ align:start position:0%
+reduce it chemically such that it's
+fully saturated
+
+ align:start position:0%
+fully saturated
+ 
+
+ align:start position:0%
+fully saturated
+and now it's a solid at room temperature
+
+ align:start position:0%
+and now it's a solid at room temperature
+ 
+
+ align:start position:0%
+and now it's a solid at room temperature
+sure you've also heard of so-called
+
+ align:start position:0%
+sure you've also heard of so-called
+ 
+
+ align:start position:0%
+sure you've also heard of so-called
+trans fats so what's a trans fat other
+
+ align:start position:0%
+trans fats so what's a trans fat other
+ 
+
+ align:start position:0%
+trans fats so what's a trans fat other
+than something
+
+ align:start position:0%
+than something
+ 
+
+ align:start position:0%
+than something
+cooked up in the devil's kitchen so
+
+ align:start position:0%
+cooked up in the devil's kitchen so
+ 
+
+ align:start position:0%
+cooked up in the devil's kitchen so
+trans fats are basically taking
+
+ align:start position:0%
+trans fats are basically taking
+ 
+
+ align:start position:0%
+trans fats are basically taking
+animal fat and introducing chemically
+
+ align:start position:0%
+animal fat and introducing chemically
+ 
+
+ align:start position:0%
+animal fat and introducing chemically
+double bonds
+
+ align:start position:0%
+double bonds
+ 
+
+ align:start position:0%
+double bonds
+into them such that you have this solid
+
+ align:start position:0%
+into them such that you have this solid
+ 
+
+ align:start position:0%
+into them such that you have this solid
+that is now a liquid
+
+ align:start position:0%
+that is now a liquid
+ 
+
+ align:start position:0%
+that is now a liquid
+at room temperature now this is done
+
+ align:start position:0%
+at room temperature now this is done
+ 
+
+ align:start position:0%
+at room temperature now this is done
+chemically to introduce those double
+
+ align:start position:0%
+chemically to introduce those double
+ 
+
+ align:start position:0%
+chemically to introduce those double
+bonds and so if you're introducing a
+
+ align:start position:0%
+bonds and so if you're introducing a
+ 
+
+ align:start position:0%
+bonds and so if you're introducing a
+double bond chemically
+
+ align:start position:0%
+double bond chemically
+ 
+
+ align:start position:0%
+double bond chemically
+by oxidizing the fatty acid you'll get
+
+ align:start position:0%
+by oxidizing the fatty acid you'll get
+ 
+
+ align:start position:0%
+by oxidizing the fatty acid you'll get
+some cis and some trans
+
+ align:start position:0%
+some cis and some trans
+ 
+
+ align:start position:0%
+some cis and some trans
+cis is what biology does because it
+
+ align:start position:0%
+cis is what biology does because it
+ 
+
+ align:start position:0%
+cis is what biology does because it
+introduces them with an enzyme
+
+ align:start position:0%
+introduces them with an enzyme
+ 
+
+ align:start position:0%
+introduces them with an enzyme
+trans versus cis is not controlled when
+
+ align:start position:0%
+trans versus cis is not controlled when
+ 
+
+ align:start position:0%
+trans versus cis is not controlled when
+it's done chemically
+
+ align:start position:0%
+it's done chemically
+ 
+
+ align:start position:0%
+it's done chemically
+and so this leads to these unnatural
+
+ align:start position:0%
+and so this leads to these unnatural
+ 
+
+ align:start position:0%
+and so this leads to these unnatural
+trans fatty acids which
+
+ align:start position:0%
+trans fatty acids which
+ 
+
+ align:start position:0%
+trans fatty acids which
+lead to health issues and are now banned
+
+ align:start position:0%
+lead to health issues and are now banned
+ 
+
+ align:start position:0%
+lead to health issues and are now banned
+in many cities including here in
+
+ align:start position:0%
+in many cities including here in
+ 
+
+ align:start position:0%
+in many cities including here in
+cambridge massachusetts
+
+ align:start position:0%
+cambridge massachusetts
+ 
+
+ align:start position:0%
+cambridge massachusetts
+right last aside is is all of us have
+
+ align:start position:0%
+right last aside is is all of us have
+ 
+
+ align:start position:0%
+right last aside is is all of us have
+probably experienced
+
+ align:start position:0%
+probably experienced
+ 
+
+ align:start position:0%
+probably experienced
+are oils or fats going rancid
+
+ align:start position:0%
+are oils or fats going rancid
+ 
+
+ align:start position:0%
+are oils or fats going rancid
+so what is that so that's oxygen
+
+ align:start position:0%
+so what is that so that's oxygen
+ 
+
+ align:start position:0%
+so what is that so that's oxygen
+oxidizing
+
+ align:start position:0%
+oxidizing
+ 
+
+ align:start position:0%
+oxidizing
+the the fatty acid and so if you want to
+
+ align:start position:0%
+the the fatty acid and so if you want to
+ 
+
+ align:start position:0%
+the the fatty acid and so if you want to
+protect your oil from going rancid the
+
+ align:start position:0%
+protect your oil from going rancid the
+ 
+
+ align:start position:0%
+protect your oil from going rancid the
+thing to do is just keep it
+
+ align:start position:0%
+thing to do is just keep it
+ 
+
+ align:start position:0%
+thing to do is just keep it
+sealed right keep oxygen away from it
+
+ align:start position:0%
+sealed right keep oxygen away from it
+ 
+
+ align:start position:0%
+sealed right keep oxygen away from it
+and your oil will last
+
+ align:start position:0%
+and your oil will last
+ 
+
+ align:start position:0%
+and your oil will last
+a lot longer okay so
+
+ align:start position:0%
+a lot longer okay so
+ 
+
+ align:start position:0%
+a lot longer okay so
+that's fatty acids in biology
+
+ align:start position:0%
+that's fatty acids in biology
+ 
+
+ align:start position:0%
+that's fatty acids in biology
+most fatty acids aren't sitting around
+
+ align:start position:0%
+most fatty acids aren't sitting around
+ 
+
+ align:start position:0%
+most fatty acids aren't sitting around
+by themselves
+
+ align:start position:0%
+by themselves
+ 
+
+ align:start position:0%
+by themselves
+they're esterified to an alcohol and
+
+ align:start position:0%
+they're esterified to an alcohol and
+ 
+
+ align:start position:0%
+they're esterified to an alcohol and
+as we mentioned in an earlier lecture a
+
+ align:start position:0%
+as we mentioned in an earlier lecture a
+ 
+
+ align:start position:0%
+as we mentioned in an earlier lecture a
+lipid
+
+ align:start position:0%
+lipid
+ 
+
+ align:start position:0%
+lipid
+equals a fatty acid
+
+ align:start position:0%
+equals a fatty acid
+ 
+
+ align:start position:0%
+equals a fatty acid
+that's esterified
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to an alcohol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we spent some time in the
+
+ align:start position:0%
+all right so we spent some time in the
+ 
+
+ align:start position:0%
+all right so we spent some time in the
+prior lecture
+
+ align:start position:0%
+prior lecture
+ 
+
+ align:start position:0%
+prior lecture
+talking about doing this to make
+
+ align:start position:0%
+talking about doing this to make
+ 
+
+ align:start position:0%
+talking about doing this to make
+phospholipids all right and that's an
+
+ align:start position:0%
+phospholipids all right and that's an
+ 
+
+ align:start position:0%
+phospholipids all right and that's an
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+of a lipid fatty acids esterified to
+
+ align:start position:0%
+of a lipid fatty acids esterified to
+ 
+
+ align:start position:0%
+of a lipid fatty acids esterified to
+make this
+
+ align:start position:0%
+make this
+ 
+
+ align:start position:0%
+make this
+um this phospholipid which gave us both
+
+ align:start position:0%
+um this phospholipid which gave us both
+ 
+
+ align:start position:0%
+um this phospholipid which gave us both
+a polar and a nonpolar end
+
+ align:start position:0%
+a polar and a nonpolar end
+ 
+
+ align:start position:0%
+a polar and a nonpolar end
+and allowed us to create membranes and
+
+ align:start position:0%
+and allowed us to create membranes and
+ 
+
+ align:start position:0%
+and allowed us to create membranes and
+so lipids have lots of
+
+ align:start position:0%
+so lipids have lots of
+ 
+
+ align:start position:0%
+so lipids have lots of
+important functions in cells and so
+
+ align:start position:0%
+important functions in cells and so
+ 
+
+ align:start position:0%
+important functions in cells and so
+there's the
+
+ align:start position:0%
+there's the
+ 
+
+ align:start position:0%
+there's the
+barrier function which was basically
+
+ align:start position:0%
+barrier function which was basically
+ 
+
+ align:start position:0%
+barrier function which was basically
+membranes things like phospholipids we
+
+ align:start position:0%
+membranes things like phospholipids we
+ 
+
+ align:start position:0%
+membranes things like phospholipids we
+talked about last time
+
+ align:start position:0%
+talked about last time
+ 
+
+ align:start position:0%
+talked about last time
+there's also signaling functions
+
+ align:start position:0%
+there's also signaling functions
+ 
+
+ align:start position:0%
+there's also signaling functions
+of lipids so i mentioned arachidonic
+
+ align:start position:0%
+of lipids so i mentioned arachidonic
+ 
+
+ align:start position:0%
+of lipids so i mentioned arachidonic
+acid
+
+ align:start position:0%
+acid
+ 
+
+ align:start position:0%
+acid
+earlier you'll certainly encounter
+
+ align:start position:0%
+earlier you'll certainly encounter
+ 
+
+ align:start position:0%
+earlier you'll certainly encounter
+signaling
+
+ align:start position:0%
+signaling
+ 
+
+ align:start position:0%
+signaling
+functions of lipids and other courses
+
+ align:start position:0%
+functions of lipids and other courses
+ 
+
+ align:start position:0%
+functions of lipids and other courses
+and then the last one which is really
+
+ align:start position:0%
+and then the last one which is really
+ 
+
+ align:start position:0%
+and then the last one which is really
+the reason why we talk about it now is
+
+ align:start position:0%
+the reason why we talk about it now is
+ 
+
+ align:start position:0%
+the reason why we talk about it now is
+lipids are great for energy storage
+
+ align:start position:0%
+lipids are great for energy storage
+ 
+
+ align:start position:0%
+lipids are great for energy storage
+because it's the most um reduced
+
+ align:start position:0%
+because it's the most um reduced
+ 
+
+ align:start position:0%
+because it's the most um reduced
+carbon so the most dense way to store
+
+ align:start position:0%
+carbon so the most dense way to store
+ 
+
+ align:start position:0%
+carbon so the most dense way to store
+energy as reduced carbon
+
+ align:start position:0%
+energy as reduced carbon
+ 
+
+ align:start position:0%
+energy as reduced carbon
+so the simplest lipid
+
+ align:start position:0%
+so the simplest lipid
+ 
+
+ align:start position:0%
+so the simplest lipid
+and the one used for energy storage is
+
+ align:start position:0%
+and the one used for energy storage is
+ 
+
+ align:start position:0%
+and the one used for energy storage is
+referred to
+
+ align:start position:0%
+referred to
+ 
+
+ align:start position:0%
+referred to
+as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+triacyl glyceride often abbreviated
+
+ align:start position:0%
+triacyl glyceride often abbreviated
+ 
+
+ align:start position:0%
+triacyl glyceride often abbreviated
+as a tag triacylglyceride
+
+ align:start position:0%
+as a tag triacylglyceride
+ 
+
+ align:start position:0%
+as a tag triacylglyceride
+and we can see now how we can make a
+
+ align:start position:0%
+and we can see now how we can make a
+ 
+
+ align:start position:0%
+and we can see now how we can make a
+triacylglyceride
+
+ align:start position:0%
+triacylglyceride
+ 
+
+ align:start position:0%
+triacylglyceride
+as well as how it relates to other
+
+ align:start position:0%
+as well as how it relates to other
+ 
+
+ align:start position:0%
+as well as how it relates to other
+pathways in
+
+ align:start position:0%
+pathways in
+ 
+
+ align:start position:0%
+pathways in
+metabolism that we've encountered and so
+
+ align:start position:0%
+metabolism that we've encountered and so
+ 
+
+ align:start position:0%
+metabolism that we've encountered and so
+here's our
+
+ align:start position:0%
+here's our
+ 
+
+ align:start position:0%
+here's our
+old friend from glycolysis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hopefully you recognize this molecule as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the phosphorylated triose
+
+ align:start position:0%
+the phosphorylated triose
+ 
+
+ align:start position:0%
+the phosphorylated triose
+dihydroxyacetone
+
+ align:start position:0%
+dihydroxyacetone
+ 
+
+ align:start position:0%
+dihydroxyacetone
+phosphate also an intermediate in
+
+ align:start position:0%
+phosphate also an intermediate in
+ 
+
+ align:start position:0%
+phosphate also an intermediate in
+glycolysis
+
+ align:start position:0%
+glycolysis
+ 
+
+ align:start position:0%
+glycolysis
+and so if we
+
+ align:start position:0%
+and so if we
+ 
+
+ align:start position:0%
+and so if we
+reduce this ketone to
+
+ align:start position:0%
+reduce this ketone to
+ 
+
+ align:start position:0%
+reduce this ketone to
+the alcohol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so two electrons from nad plus
+
+ align:start position:0%
+so two electrons from nad plus
+ 
+
+ align:start position:0%
+so two electrons from nad plus
+nadh um reduce that
+
+ align:start position:0%
+nadh um reduce that
+ 
+
+ align:start position:0%
+nadh um reduce that
+ketone that'll oxidize the nadh to nad
+
+ align:start position:0%
+ketone that'll oxidize the nadh to nad
+ 
+
+ align:start position:0%
+ketone that'll oxidize the nadh to nad
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+if we also remove the phosphate now what
+
+ align:start position:0%
+if we also remove the phosphate now what
+ 
+
+ align:start position:0%
+if we also remove the phosphate now what
+do we have
+
+ align:start position:0%
+do we have
+ 
+
+ align:start position:0%
+do we have
+now we have the alcohol
+
+ align:start position:0%
+now we have the alcohol
+ 
+
+ align:start position:0%
+now we have the alcohol
+and this molecule is
+
+ align:start position:0%
+and this molecule is
+ 
+
+ align:start position:0%
+and this molecule is
+glycerol all right and so now this
+
+ align:start position:0%
+glycerol all right and so now this
+ 
+
+ align:start position:0%
+glycerol all right and so now this
+glycerol as we talked about before
+
+ align:start position:0%
+glycerol as we talked about before
+ 
+
+ align:start position:0%
+glycerol as we talked about before
+we can take three fatty acids esterify
+
+ align:start position:0%
+we can take three fatty acids esterify
+ 
+
+ align:start position:0%
+we can take three fatty acids esterify
+them to
+
+ align:start position:0%
+them to
+ 
+
+ align:start position:0%
+them to
+each of those alcohols
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and now we have a
+
+ align:start position:0%
+okay and now we have a
+ 
+
+ align:start position:0%
+okay and now we have a
+glycerol molecule with three fatty acid
+
+ align:start position:0%
+glycerol molecule with three fatty acid
+ 
+
+ align:start position:0%
+glycerol molecule with three fatty acid
+uh three fatty acids esterified to the
+
+ align:start position:0%
+uh three fatty acids esterified to the
+ 
+
+ align:start position:0%
+uh three fatty acids esterified to the
+alcohols
+
+ align:start position:0%
+alcohols
+ 
+
+ align:start position:0%
+alcohols
+on the glycerol this is a
+
+ align:start position:0%
+on the glycerol this is a
+ 
+
+ align:start position:0%
+on the glycerol this is a
+dry acyl glyceride now of course
+
+ align:start position:0%
+dry acyl glyceride now of course
+ 
+
+ align:start position:0%
+dry acyl glyceride now of course
+triacclycerides are not soluble in water
+
+ align:start position:0%
+triacclycerides are not soluble in water
+ 
+
+ align:start position:0%
+triacclycerides are not soluble in water
+and so when we make these in cells
+
+ align:start position:0%
+and so when we make these in cells
+ 
+
+ align:start position:0%
+and so when we make these in cells
+for energy storage they're
+
+ align:start position:0%
+for energy storage they're
+ 
+
+ align:start position:0%
+for energy storage they're
+stored as so-called lipid droplets and
+
+ align:start position:0%
+stored as so-called lipid droplets and
+ 
+
+ align:start position:0%
+stored as so-called lipid droplets and
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if you look here at the slide here's an
+
+ align:start position:0%
+if you look here at the slide here's an
+ 
+
+ align:start position:0%
+if you look here at the slide here's an
+example this up here
+
+ align:start position:0%
+example this up here
+ 
+
+ align:start position:0%
+example this up here
+is an adipocyte from an animal this down
+
+ align:start position:0%
+is an adipocyte from an animal this down
+ 
+
+ align:start position:0%
+is an adipocyte from an animal this down
+here i think is a plant
+
+ align:start position:0%
+here i think is a plant
+ 
+
+ align:start position:0%
+here i think is a plant
+cell and so in both cases
+
+ align:start position:0%
+cell and so in both cases
+ 
+
+ align:start position:0%
+cell and so in both cases
+you have these large
+
+ align:start position:0%
+you have these large
+ 
+
+ align:start position:0%
+you have these large
+droplets that would be basically
+
+ align:start position:0%
+droplets that would be basically
+ 
+
+ align:start position:0%
+droplets that would be basically
+droplets of
+
+ align:start position:0%
+droplets of
+ 
+
+ align:start position:0%
+droplets of
+triacylglycerides that basically form as
+
+ align:start position:0%
+triacylglycerides that basically form as
+ 
+
+ align:start position:0%
+triacylglycerides that basically form as
+a way for
+
+ align:start position:0%
+a way for
+ 
+
+ align:start position:0%
+a way for
+long-term energy storage and so while we
+
+ align:start position:0%
+long-term energy storage and so while we
+ 
+
+ align:start position:0%
+long-term energy storage and so while we
+think of at least as people our
+
+ align:start position:0%
+think of at least as people our
+ 
+
+ align:start position:0%
+think of at least as people our
+adipocytes are fat cells as storing our
+
+ align:start position:0%
+adipocytes are fat cells as storing our
+ 
+
+ align:start position:0%
+adipocytes are fat cells as storing our
+fat they do
+
+ align:start position:0%
+fat they do
+ 
+
+ align:start position:0%
+fat they do
+but they're really specialized cell
+
+ align:start position:0%
+but they're really specialized cell
+ 
+
+ align:start position:0%
+but they're really specialized cell
+types that have these
+
+ align:start position:0%
+types that have these
+ 
+
+ align:start position:0%
+types that have these
+giant lipid droplets whereas many cells
+
+ align:start position:0%
+giant lipid droplets whereas many cells
+ 
+
+ align:start position:0%
+giant lipid droplets whereas many cells
+actually have much smaller lipid
+
+ align:start position:0%
+actually have much smaller lipid
+ 
+
+ align:start position:0%
+actually have much smaller lipid
+droplets as a way to
+
+ align:start position:0%
+droplets as a way to
+ 
+
+ align:start position:0%
+droplets as a way to
+store um store tricylglycerides as a way
+
+ align:start position:0%
+store um store tricylglycerides as a way
+ 
+
+ align:start position:0%
+store um store tricylglycerides as a way
+to store
+
+ align:start position:0%
+to store
+ 
+
+ align:start position:0%
+to store
+energy as reduced carbon
+
+ align:start position:0%
+energy as reduced carbon
+ 
+
+ align:start position:0%
+energy as reduced carbon
+all right i also want to say that if you
+
+ align:start position:0%
+all right i also want to say that if you
+ 
+
+ align:start position:0%
+all right i also want to say that if you
+look at this
+
+ align:start position:0%
+look at this
+ 
+
+ align:start position:0%
+look at this
+unlike the phospholipids that we
+
+ align:start position:0%
+unlike the phospholipids that we
+ 
+
+ align:start position:0%
+unlike the phospholipids that we
+described earlier
+
+ align:start position:0%
+described earlier
+ 
+
+ align:start position:0%
+described earlier
+as ways to build membranes these don't
+
+ align:start position:0%
+as ways to build membranes these don't
+ 
+
+ align:start position:0%
+as ways to build membranes these don't
+have a charge on them and so they're
+
+ align:start position:0%
+have a charge on them and so they're
+ 
+
+ align:start position:0%
+have a charge on them and so they're
+sometimes referred to
+
+ align:start position:0%
+sometimes referred to
+ 
+
+ align:start position:0%
+sometimes referred to
+as so-called neutral
+
+ align:start position:0%
+as so-called neutral
+ 
+
+ align:start position:0%
+as so-called neutral
+lipids and it's really this neutral
+
+ align:start position:0%
+lipids and it's really this neutral
+ 
+
+ align:start position:0%
+lipids and it's really this neutral
+lipids that allow them to
+
+ align:start position:0%
+lipids that allow them to
+ 
+
+ align:start position:0%
+lipids that allow them to
+clump together in these oil particles if
+
+ align:start position:0%
+clump together in these oil particles if
+ 
+
+ align:start position:0%
+clump together in these oil particles if
+you will these lipid droplets in cells
+
+ align:start position:0%
+you will these lipid droplets in cells
+ 
+
+ align:start position:0%
+you will these lipid droplets in cells
+that are good for energy storage
+
+ align:start position:0%
+that are good for energy storage
+ 
+
+ align:start position:0%
+that are good for energy storage
+now why specifically are neutral lipids
+
+ align:start position:0%
+now why specifically are neutral lipids
+ 
+
+ align:start position:0%
+now why specifically are neutral lipids
+good for energy storage well
+
+ align:start position:0%
+good for energy storage well
+ 
+
+ align:start position:0%
+good for energy storage well
+really chemically dense way to store
+
+ align:start position:0%
+really chemically dense way to store
+ 
+
+ align:start position:0%
+really chemically dense way to store
+energy the most reduced carbon
+
+ align:start position:0%
+energy the most reduced carbon
+ 
+
+ align:start position:0%
+energy the most reduced carbon
+and by forming these droplets
+
+ align:start position:0%
+and by forming these droplets
+ 
+
+ align:start position:0%
+and by forming these droplets
+okay not unlike the oil in your salad
+
+ align:start position:0%
+okay not unlike the oil in your salad
+ 
+
+ align:start position:0%
+okay not unlike the oil in your salad
+dressing and other
+
+ align:start position:0%
+dressing and other
+ 
+
+ align:start position:0%
+dressing and other
+neutral lipid forming droplets within
+
+ align:start position:0%
+neutral lipid forming droplets within
+ 
+
+ align:start position:0%
+neutral lipid forming droplets within
+the vinegar
+
+ align:start position:0%
+the vinegar
+ 
+
+ align:start position:0%
+the vinegar
+this is a way that you store reduced
+
+ align:start position:0%
+this is a way that you store reduced
+ 
+
+ align:start position:0%
+this is a way that you store reduced
+carbon without having to carry around
+
+ align:start position:0%
+carbon without having to carry around
+ 
+
+ align:start position:0%
+carbon without having to carry around
+water and so if we store energy as
+
+ align:start position:0%
+water and so if we store energy as
+ 
+
+ align:start position:0%
+water and so if we store energy as
+carbohydrates
+
+ align:start position:0%
+carbohydrates
+ 
+
+ align:start position:0%
+carbohydrates
+starch or glycogen these molecules
+
+ align:start position:0%
+starch or glycogen these molecules
+ 
+
+ align:start position:0%
+starch or glycogen these molecules
+have to exist in water so you're
+
+ align:start position:0%
+have to exist in water so you're
+ 
+
+ align:start position:0%
+have to exist in water so you're
+carrying around the starch and glycogen
+
+ align:start position:0%
+carrying around the starch and glycogen
+ 
+
+ align:start position:0%
+carrying around the starch and glycogen
+but as an animal we're also carrying
+
+ align:start position:0%
+but as an animal we're also carrying
+ 
+
+ align:start position:0%
+but as an animal we're also carrying
+around the water
+
+ align:start position:0%
+around the water
+ 
+
+ align:start position:0%
+around the water
+if we're carrying around reduced carbon
+
+ align:start position:0%
+if we're carrying around reduced carbon
+ 
+
+ align:start position:0%
+if we're carrying around reduced carbon
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+lipids we can now exclude the water from
+
+ align:start position:0%
+lipids we can now exclude the water from
+ 
+
+ align:start position:0%
+lipids we can now exclude the water from
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+and so it's much more dense and we can
+
+ align:start position:0%
+and so it's much more dense and we can
+ 
+
+ align:start position:0%
+and so it's much more dense and we can
+in a more efficient way
+
+ align:start position:0%
+in a more efficient way
+ 
+
+ align:start position:0%
+in a more efficient way
+carry around this um this material
+
+ align:start position:0%
+carry around this um this material
+ 
+
+ align:start position:0%
+carry around this um this material
+without having to carry the water and so
+
+ align:start position:0%
+without having to carry the water and so
+ 
+
+ align:start position:0%
+without having to carry the water and so
+gram for gram
+
+ align:start position:0%
+gram for gram
+ 
+
+ align:start position:0%
+gram for gram
+fat is a much more efficient way to
+
+ align:start position:0%
+fat is a much more efficient way to
+ 
+
+ align:start position:0%
+fat is a much more efficient way to
+pack on calories that we can burn later
+
+ align:start position:0%
+pack on calories that we can burn later
+ 
+
+ align:start position:0%
+pack on calories that we can burn later
+than storing it as carbohydrate
+
+ align:start position:0%
+than storing it as carbohydrate
+ 
+
+ align:start position:0%
+than storing it as carbohydrate
+fat's also nice because it forms a nice
+
+ align:start position:0%
+fat's also nice because it forms a nice
+ 
+
+ align:start position:0%
+fat's also nice because it forms a nice
+insulator
+
+ align:start position:0%
+insulator
+ 
+
+ align:start position:0%
+insulator
+and so it makes sense as animals we need
+
+ align:start position:0%
+and so it makes sense as animals we need
+ 
+
+ align:start position:0%
+and so it makes sense as animals we need
+to survive the winter
+
+ align:start position:0%
+to survive the winter
+ 
+
+ align:start position:0%
+to survive the winter
+pack on all kinds of calories as fat
+
+ align:start position:0%
+pack on all kinds of calories as fat
+ 
+
+ align:start position:0%
+pack on all kinds of calories as fat
+don't have to carry around as water
+
+ align:start position:0%
+don't have to carry around as water
+ 
+
+ align:start position:0%
+don't have to carry around as water
+just have the energy there is reduce
+
+ align:start position:0%
+just have the energy there is reduce
+ 
+
+ align:start position:0%
+just have the energy there is reduce
+carbon and then we can slowly release it
+
+ align:start position:0%
+carbon and then we can slowly release it
+ 
+
+ align:start position:0%
+carbon and then we can slowly release it
+over the course of the winter where
+
+ align:start position:0%
+over the course of the winter where
+ 
+
+ align:start position:0%
+over the course of the winter where
+we as well as use it to keep us warm and
+
+ align:start position:0%
+we as well as use it to keep us warm and
+ 
+
+ align:start position:0%
+we as well as use it to keep us warm and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+um build up those stores again during
+
+ align:start position:0%
+um build up those stores again during
+ 
+
+ align:start position:0%
+um build up those stores again during
+the summer months when there's when
+
+ align:start position:0%
+the summer months when there's when
+ 
+
+ align:start position:0%
+the summer months when there's when
+there's more food
+
+ align:start position:0%
+there's more food
+ 
+
+ align:start position:0%
+there's more food
+available fat of course has months worth
+
+ align:start position:0%
+available fat of course has months worth
+ 
+
+ align:start position:0%
+available fat of course has months worth
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+energy packed into it whereas
+
+ align:start position:0%
+energy packed into it whereas
+ 
+
+ align:start position:0%
+energy packed into it whereas
+carbohydrates that we carry around our
+
+ align:start position:0%
+carbohydrates that we carry around our
+ 
+
+ align:start position:0%
+carbohydrates that we carry around our
+glycogen
+
+ align:start position:0%
+glycogen
+ 
+
+ align:start position:0%
+glycogen
+has less than a day's worth of energy so
+
+ align:start position:0%
+has less than a day's worth of energy so
+ 
+
+ align:start position:0%
+has less than a day's worth of energy so
+we could live off of our fat for
+
+ align:start position:0%
+we could live off of our fat for
+ 
+
+ align:start position:0%
+we could live off of our fat for
+the winter we can't live off of our
+
+ align:start position:0%
+the winter we can't live off of our
+ 
+
+ align:start position:0%
+the winter we can't live off of our
+glycogen for
+
+ align:start position:0%
+glycogen for
+ 
+
+ align:start position:0%
+glycogen for
+the winter now the big trade-off here is
+
+ align:start position:0%
+the winter now the big trade-off here is
+ 
+
+ align:start position:0%
+the winter now the big trade-off here is
+that it's much slower to mobilize fat
+
+ align:start position:0%
+that it's much slower to mobilize fat
+ 
+
+ align:start position:0%
+that it's much slower to mobilize fat
+we have to get into these lipid droplets
+
+ align:start position:0%
+we have to get into these lipid droplets
+ 
+
+ align:start position:0%
+we have to get into these lipid droplets
+and break off
+
+ align:start position:0%
+and break off
+ 
+
+ align:start position:0%
+and break off
+little pieces of it get them into
+
+ align:start position:0%
+little pieces of it get them into
+ 
+
+ align:start position:0%
+little pieces of it get them into
+aqueously water-soluble
+
+ align:start position:0%
+aqueously water-soluble
+ 
+
+ align:start position:0%
+aqueously water-soluble
+pieces to break it down um glycogen of
+
+ align:start position:0%
+pieces to break it down um glycogen of
+ 
+
+ align:start position:0%
+pieces to break it down um glycogen of
+course is already
+
+ align:start position:0%
+course is already
+ 
+
+ align:start position:0%
+course is already
+in water can break it down much faster
+
+ align:start position:0%
+in water can break it down much faster
+ 
+
+ align:start position:0%
+in water can break it down much faster
+and so it's much slower to mobilize the
+
+ align:start position:0%
+and so it's much slower to mobilize the
+ 
+
+ align:start position:0%
+and so it's much slower to mobilize the
+fat
+
+ align:start position:0%
+fat
+ 
+
+ align:start position:0%
+fat
+but it can be much uh more efficient in
+
+ align:start position:0%
+but it can be much uh more efficient in
+ 
+
+ align:start position:0%
+but it can be much uh more efficient in
+terms of what's stored
+
+ align:start position:0%
+terms of what's stored
+ 
+
+ align:start position:0%
+terms of what's stored
+whereas uh glycogen can be mobilized a
+
+ align:start position:0%
+whereas uh glycogen can be mobilized a
+ 
+
+ align:start position:0%
+whereas uh glycogen can be mobilized a
+lot faster
+
+ align:start position:0%
+lot faster
+ 
+
+ align:start position:0%
+lot faster
+and that's really part of our physiology
+
+ align:start position:0%
+and that's really part of our physiology
+ 
+
+ align:start position:0%
+and that's really part of our physiology
+you will burn your glycogen first
+
+ align:start position:0%
+you will burn your glycogen first
+ 
+
+ align:start position:0%
+you will burn your glycogen first
+when you exercise before you start
+
+ align:start position:0%
+when you exercise before you start
+ 
+
+ align:start position:0%
+when you exercise before you start
+burning a lot of fat and i think many
+
+ align:start position:0%
+burning a lot of fat and i think many
+ 
+
+ align:start position:0%
+burning a lot of fat and i think many
+have heard about that from just reading
+
+ align:start position:0%
+have heard about that from just reading
+ 
+
+ align:start position:0%
+have heard about that from just reading
+and thinking about
+
+ align:start position:0%
+and thinking about
+ 
+
+ align:start position:0%
+and thinking about
+what you know about exercise physiology
+
+ align:start position:0%
+what you know about exercise physiology
+ 
+
+ align:start position:0%
+what you know about exercise physiology
+okay now again i want to make the point
+
+ align:start position:0%
+okay now again i want to make the point
+ 
+
+ align:start position:0%
+okay now again i want to make the point
+that we all know that fat has more
+
+ align:start position:0%
+that we all know that fat has more
+ 
+
+ align:start position:0%
+that we all know that fat has more
+calories
+
+ align:start position:0%
+calories
+ 
+
+ align:start position:0%
+calories
+than sugar and the reason for that is to
+
+ align:start position:0%
+than sugar and the reason for that is to
+ 
+
+ align:start position:0%
+than sugar and the reason for that is to
+be clear
+
+ align:start position:0%
+be clear
+ 
+
+ align:start position:0%
+be clear
+is because it's more reduced and so the
+
+ align:start position:0%
+is because it's more reduced and so the
+ 
+
+ align:start position:0%
+is because it's more reduced and so the
+energy that's released from burning fat
+
+ align:start position:0%
+energy that's released from burning fat
+ 
+
+ align:start position:0%
+energy that's released from burning fat
+just like the energy that's released
+
+ align:start position:0%
+just like the energy that's released
+ 
+
+ align:start position:0%
+just like the energy that's released
+from burning sugar
+
+ align:start position:0%
+from burning sugar
+ 
+
+ align:start position:0%
+from burning sugar
+comes because the transfer of electrons
+
+ align:start position:0%
+comes because the transfer of electrons
+ 
+
+ align:start position:0%
+comes because the transfer of electrons
+from the reduced hydrocarbon to oxygen
+
+ align:start position:0%
+from the reduced hydrocarbon to oxygen
+ 
+
+ align:start position:0%
+from the reduced hydrocarbon to oxygen
+is favorable and that is how energy is
+
+ align:start position:0%
+is favorable and that is how energy is
+ 
+
+ align:start position:0%
+is favorable and that is how energy is
+released
+
+ align:start position:0%
+released
+ 
+
+ align:start position:0%
+released
+and so fat is more reduced than sugar
+
+ align:start position:0%
+and so fat is more reduced than sugar
+ 
+
+ align:start position:0%
+and so fat is more reduced than sugar
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+more electrons to transfer
+
+ align:start position:0%
+more electrons to transfer
+ 
+
+ align:start position:0%
+more electrons to transfer
+and so more energy released than burning
+
+ align:start position:0%
+and so more energy released than burning
+ 
+
+ align:start position:0%
+and so more energy released than burning
+sugar
+
+ align:start position:0%
+sugar
+ 
+
+ align:start position:0%
+sugar
+all right so now let's go through in a
+
+ align:start position:0%
+all right so now let's go through in a
+ 
+
+ align:start position:0%
+all right so now let's go through in a
+pathway sense
+
+ align:start position:0%
+pathway sense
+ 
+
+ align:start position:0%
+pathway sense
+how does nature rather than taking
+
+ align:start position:0%
+how does nature rather than taking
+ 
+
+ align:start position:0%
+how does nature rather than taking
+gasoline and just igniting it and
+
+ align:start position:0%
+gasoline and just igniting it and
+ 
+
+ align:start position:0%
+gasoline and just igniting it and
+releasing a lot of energy
+
+ align:start position:0%
+releasing a lot of energy
+ 
+
+ align:start position:0%
+releasing a lot of energy
+how does nature stepwise break down
+
+ align:start position:0%
+how does nature stepwise break down
+ 
+
+ align:start position:0%
+how does nature stepwise break down
+fatty acids in a way that that energy
+
+ align:start position:0%
+fatty acids in a way that that energy
+ 
+
+ align:start position:0%
+fatty acids in a way that that energy
+release can be controlled
+
+ align:start position:0%
+release can be controlled
+ 
+
+ align:start position:0%
+release can be controlled
+in the same way we described it for
+
+ align:start position:0%
+in the same way we described it for
+ 
+
+ align:start position:0%
+in the same way we described it for
+carbohydrates
+
+ align:start position:0%
+carbohydrates
+ 
+
+ align:start position:0%
+carbohydrates
+glycolysis in the tca cycle controlled
+
+ align:start position:0%
+glycolysis in the tca cycle controlled
+ 
+
+ align:start position:0%
+glycolysis in the tca cycle controlled
+stepwise energy release that can be
+
+ align:start position:0%
+stepwise energy release that can be
+ 
+
+ align:start position:0%
+stepwise energy release that can be
+captured to do things like
+
+ align:start position:0%
+captured to do things like
+ 
+
+ align:start position:0%
+captured to do things like
+make it atp okay um
+
+ align:start position:0%
+make it atp okay um
+ 
+
+ align:start position:0%
+make it atp okay um
+how is the same thing work for oxidation
+
+ align:start position:0%
+how is the same thing work for oxidation
+ 
+
+ align:start position:0%
+how is the same thing work for oxidation
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+fatty acids well if as organisms
+
+ align:start position:0%
+fatty acids well if as organisms
+ 
+
+ align:start position:0%
+fatty acids well if as organisms
+we store fatty acids in these
+
+ align:start position:0%
+we store fatty acids in these
+ 
+
+ align:start position:0%
+we store fatty acids in these
+triacylglycerides or other
+
+ align:start position:0%
+triacylglycerides or other
+ 
+
+ align:start position:0%
+triacylglycerides or other
+neutral lipids the first step is we have
+
+ align:start position:0%
+neutral lipids the first step is we have
+ 
+
+ align:start position:0%
+neutral lipids the first step is we have
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+get them out of the neutral lipids
+
+ align:start position:0%
+get them out of the neutral lipids
+ 
+
+ align:start position:0%
+get them out of the neutral lipids
+and so if we start with a
+
+ align:start position:0%
+and so if we start with a
+ 
+
+ align:start position:0%
+and so if we start with a
+triacylglyceride
+
+ align:start position:0%
+triacylglyceride
+ 
+
+ align:start position:0%
+triacylglyceride
+the first step is to use a lipase
+
+ align:start position:0%
+the first step is to use a lipase
+ 
+
+ align:start position:0%
+the first step is to use a lipase
+molecule so a lipase just breaks that
+
+ align:start position:0%
+molecule so a lipase just breaks that
+ 
+
+ align:start position:0%
+molecule so a lipase just breaks that
+ester bond and so you basically now have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+glycerol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus the three fatty acids
+
+ align:start position:0%
+plus the three fatty acids
+ 
+
+ align:start position:0%
+plus the three fatty acids
+we're going to spend most our time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+most of our time today discussing how
+
+ align:start position:0%
+most of our time today discussing how
+ 
+
+ align:start position:0%
+most of our time today discussing how
+you break down the fatty acids
+
+ align:start position:0%
+you break down the fatty acids
+ 
+
+ align:start position:0%
+you break down the fatty acids
+however i want to mention should be
+
+ align:start position:0%
+however i want to mention should be
+ 
+
+ align:start position:0%
+however i want to mention should be
+clear how you're also going to
+
+ align:start position:0%
+clear how you're also going to
+ 
+
+ align:start position:0%
+clear how you're also going to
+metabolize the glycerol
+
+ align:start position:0%
+metabolize the glycerol
+ 
+
+ align:start position:0%
+metabolize the glycerol
+so glycerol we can oxidize
+
+ align:start position:0%
+so glycerol we can oxidize
+ 
+
+ align:start position:0%
+so glycerol we can oxidize
+the glycerol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now if we oxidize that
+
+ align:start position:0%
+okay so now if we oxidize that
+ 
+
+ align:start position:0%
+okay so now if we oxidize that
+alcohol what are we going to get we're
+
+ align:start position:0%
+alcohol what are we going to get we're
+ 
+
+ align:start position:0%
+alcohol what are we going to get we're
+going to get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dihydroxyacetone and then if we
+
+ align:start position:0%
+dihydroxyacetone and then if we
+ 
+
+ align:start position:0%
+dihydroxyacetone and then if we
+phosphorylate one of the ends of
+
+ align:start position:0%
+phosphorylate one of the ends of
+ 
+
+ align:start position:0%
+phosphorylate one of the ends of
+that with atp now we get
+
+ align:start position:0%
+that with atp now we get
+ 
+
+ align:start position:0%
+that with atp now we get
+dihydroxyacetone phosphate and that of
+
+ align:start position:0%
+dihydroxyacetone phosphate and that of
+ 
+
+ align:start position:0%
+dihydroxyacetone phosphate and that of
+course can go into
+
+ align:start position:0%
+course can go into
+ 
+
+ align:start position:0%
+course can go into
+glycol
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+glycolysis generate pyruvate generate
+
+ align:start position:0%
+glycolysis generate pyruvate generate
+ 
+
+ align:start position:0%
+glycolysis generate pyruvate generate
+seo coa
+
+ align:start position:0%
+seo coa
+ 
+
+ align:start position:0%
+seo coa
+oxidize that oxidal coa in the tca cycle
+
+ align:start position:0%
+oxidize that oxidal coa in the tca cycle
+ 
+
+ align:start position:0%
+oxidize that oxidal coa in the tca cycle
+get energy from the glycerol part of of
+
+ align:start position:0%
+get energy from the glycerol part of of
+ 
+
+ align:start position:0%
+get energy from the glycerol part of of
+the lipid
+
+ align:start position:0%
+the lipid
+ 
+
+ align:start position:0%
+the lipid
+all right so what about oxidizing
+
+ align:start position:0%
+all right so what about oxidizing
+ 
+
+ align:start position:0%
+all right so what about oxidizing
+the fatty acids well the first thing
+
+ align:start position:0%
+the fatty acids well the first thing
+ 
+
+ align:start position:0%
+the fatty acids well the first thing
+we have to talk about to oxidize the
+
+ align:start position:0%
+we have to talk about to oxidize the
+ 
+
+ align:start position:0%
+we have to talk about to oxidize the
+fatty acids is
+
+ align:start position:0%
+fatty acids is
+ 
+
+ align:start position:0%
+fatty acids is
+where is this going to occur in the cell
+
+ align:start position:0%
+where is this going to occur in the cell
+ 
+
+ align:start position:0%
+where is this going to occur in the cell
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+lipid droplets are floating out there in
+
+ align:start position:0%
+lipid droplets are floating out there in
+ 
+
+ align:start position:0%
+lipid droplets are floating out there in
+the cell
+
+ align:start position:0%
+the cell
+ 
+
+ align:start position:0%
+the cell
+and so you mobilize these pieces
+
+ align:start position:0%
+and so you mobilize these pieces
+ 
+
+ align:start position:0%
+and so you mobilize these pieces
+with the lipase well the glycerol now is
+
+ align:start position:0%
+with the lipase well the glycerol now is
+ 
+
+ align:start position:0%
+with the lipase well the glycerol now is
+sitting there in the cytosol
+
+ align:start position:0%
+sitting there in the cytosol
+ 
+
+ align:start position:0%
+sitting there in the cytosol
+that can form dihydroxyacetone phosphate
+
+ align:start position:0%
+that can form dihydroxyacetone phosphate
+ 
+
+ align:start position:0%
+that can form dihydroxyacetone phosphate
+and be burned in glycolysis which is in
+
+ align:start position:0%
+and be burned in glycolysis which is in
+ 
+
+ align:start position:0%
+and be burned in glycolysis which is in
+the cytosol
+
+ align:start position:0%
+the cytosol
+ 
+
+ align:start position:0%
+the cytosol
+but once we generate that pyruvate
+
+ align:start position:0%
+but once we generate that pyruvate
+ 
+
+ align:start position:0%
+but once we generate that pyruvate
+remember that pyruvate had to get into
+
+ align:start position:0%
+remember that pyruvate had to get into
+ 
+
+ align:start position:0%
+remember that pyruvate had to get into
+the mitochondria
+
+ align:start position:0%
+the mitochondria
+ 
+
+ align:start position:0%
+the mitochondria
+where we turned it into acetyl-coa so
+
+ align:start position:0%
+where we turned it into acetyl-coa so
+ 
+
+ align:start position:0%
+where we turned it into acetyl-coa so
+the acetyl-coa was present in the
+
+ align:start position:0%
+the acetyl-coa was present in the
+ 
+
+ align:start position:0%
+the acetyl-coa was present in the
+mitochondrial matrix
+
+ align:start position:0%
+mitochondrial matrix
+ 
+
+ align:start position:0%
+mitochondrial matrix
+so that is here in the matrix of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mitochondria
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where the tca cycle happens so remember
+
+ align:start position:0%
+where the tca cycle happens so remember
+ 
+
+ align:start position:0%
+where the tca cycle happens so remember
+glycolysis in the cytosol
+
+ align:start position:0%
+glycolysis in the cytosol
+ 
+
+ align:start position:0%
+glycolysis in the cytosol
+tca cycle in the matrix and so that
+
+ align:start position:0%
+tca cycle in the matrix and so that
+ 
+
+ align:start position:0%
+tca cycle in the matrix and so that
+pyruvate needed to get into the matrix
+
+ align:start position:0%
+pyruvate needed to get into the matrix
+ 
+
+ align:start position:0%
+pyruvate needed to get into the matrix
+so we could turn it into acetyl-coa and
+
+ align:start position:0%
+so we could turn it into acetyl-coa and
+ 
+
+ align:start position:0%
+so we could turn it into acetyl-coa and
+then that acetyl-coa was in the right
+
+ align:start position:0%
+then that acetyl-coa was in the right
+ 
+
+ align:start position:0%
+then that acetyl-coa was in the right
+place
+
+ align:start position:0%
+place
+ 
+
+ align:start position:0%
+place
+to generate um to be entered into the
+
+ align:start position:0%
+to generate um to be entered into the
+ 
+
+ align:start position:0%
+to generate um to be entered into the
+tca cycle
+
+ align:start position:0%
+tca cycle
+ 
+
+ align:start position:0%
+tca cycle
+and turned into co2
+
+ align:start position:0%
+and turned into co2
+ 
+
+ align:start position:0%
+and turned into co2
+well fatty acid oxidation has the same
+
+ align:start position:0%
+well fatty acid oxidation has the same
+ 
+
+ align:start position:0%
+well fatty acid oxidation has the same
+thing and so if those fatty acids are
+
+ align:start position:0%
+thing and so if those fatty acids are
+ 
+
+ align:start position:0%
+thing and so if those fatty acids are
+generated out here in the cytosol when
+
+ align:start position:0%
+generated out here in the cytosol when
+ 
+
+ align:start position:0%
+generated out here in the cytosol when
+their
+
+ align:start position:0%
+their
+ 
+
+ align:start position:0%
+their
+lipases remove them from the lipid
+
+ align:start position:0%
+lipases remove them from the lipid
+ 
+
+ align:start position:0%
+lipases remove them from the lipid
+droplet it turns out
+
+ align:start position:0%
+droplet it turns out
+ 
+
+ align:start position:0%
+droplet it turns out
+we're going to burn the acetyl coa we
+
+ align:start position:0%
+we're going to burn the acetyl coa we
+ 
+
+ align:start position:0%
+we're going to burn the acetyl coa we
+get from the bake breakdown of the fatty
+
+ align:start position:0%
+get from the bake breakdown of the fatty
+ 
+
+ align:start position:0%
+get from the bake breakdown of the fatty
+acids
+
+ align:start position:0%
+acids
+ 
+
+ align:start position:0%
+acids
+that acetyl coa needs to be in the
+
+ align:start position:0%
+that acetyl coa needs to be in the
+ 
+
+ align:start position:0%
+that acetyl coa needs to be in the
+matrix so it has access to the tca cycle
+
+ align:start position:0%
+matrix so it has access to the tca cycle
+ 
+
+ align:start position:0%
+matrix so it has access to the tca cycle
+and so we're going to get we need to get
+
+ align:start position:0%
+and so we're going to get we need to get
+ 
+
+ align:start position:0%
+and so we're going to get we need to get
+the fatty acid from the cytosol
+
+ align:start position:0%
+the fatty acid from the cytosol
+ 
+
+ align:start position:0%
+the fatty acid from the cytosol
+inside the mitochondria now part of this
+
+ align:start position:0%
+inside the mitochondria now part of this
+ 
+
+ align:start position:0%
+inside the mitochondria now part of this
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+our coe group that i drew last time is
+
+ align:start position:0%
+our coe group that i drew last time is
+ 
+
+ align:start position:0%
+our coe group that i drew last time is
+this giant molecule
+
+ align:start position:0%
+this giant molecule
+ 
+
+ align:start position:0%
+this giant molecule
+and so acetyl coa is not this little
+
+ align:start position:0%
+and so acetyl coa is not this little
+ 
+
+ align:start position:0%
+and so acetyl coa is not this little
+two-carbon unit it's this big giant
+
+ align:start position:0%
+two-carbon unit it's this big giant
+ 
+
+ align:start position:0%
+two-carbon unit it's this big giant
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+and so by generating the acetyl-coa in
+
+ align:start position:0%
+and so by generating the acetyl-coa in
+ 
+
+ align:start position:0%
+and so by generating the acetyl-coa in
+the mitochondria we obviate the need to
+
+ align:start position:0%
+the mitochondria we obviate the need to
+ 
+
+ align:start position:0%
+the mitochondria we obviate the need to
+get this giant coa group across
+
+ align:start position:0%
+get this giant coa group across
+ 
+
+ align:start position:0%
+get this giant coa group across
+the mitochondrial membranes but of
+
+ align:start position:0%
+the mitochondrial membranes but of
+ 
+
+ align:start position:0%
+the mitochondrial membranes but of
+course we do need to get the fatty acid
+
+ align:start position:0%
+course we do need to get the fatty acid
+ 
+
+ align:start position:0%
+course we do need to get the fatty acid
+into the right location as well
+
+ align:start position:0%
+into the right location as well
+ 
+
+ align:start position:0%
+into the right location as well
+and so the way that that fatty acid is
+
+ align:start position:0%
+and so the way that that fatty acid is
+ 
+
+ align:start position:0%
+and so the way that that fatty acid is
+transported there
+
+ align:start position:0%
+transported there
+ 
+
+ align:start position:0%
+transported there
+is actually via a system called the
+
+ align:start position:0%
+is actually via a system called the
+ 
+
+ align:start position:0%
+is actually via a system called the
+carnitine
+
+ align:start position:0%
+carnitine
+ 
+
+ align:start position:0%
+carnitine
+shuttle but there's sort of a little bit
+
+ align:start position:0%
+shuttle but there's sort of a little bit
+ 
+
+ align:start position:0%
+shuttle but there's sort of a little bit
+of a roundabout way to do it and that is
+
+ align:start position:0%
+of a roundabout way to do it and that is
+ 
+
+ align:start position:0%
+of a roundabout way to do it and that is
+we are going to need to do two things
+
+ align:start position:0%
+we are going to need to do two things
+ 
+
+ align:start position:0%
+we are going to need to do two things
+get the fatty acid
+
+ align:start position:0%
+get the fatty acid
+ 
+
+ align:start position:0%
+get the fatty acid
+inside the mitochondria as well as
+
+ align:start position:0%
+inside the mitochondria as well as
+ 
+
+ align:start position:0%
+inside the mitochondria as well as
+activate it
+
+ align:start position:0%
+activate it
+ 
+
+ align:start position:0%
+activate it
+with this coenzyme
+
+ align:start position:0%
+with this coenzyme
+ 
+
+ align:start position:0%
+with this coenzyme
+a group and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it turns out that the fatty acid is
+
+ align:start position:0%
+it turns out that the fatty acid is
+ 
+
+ align:start position:0%
+it turns out that the fatty acid is
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+activated in the cytosol by adding
+
+ align:start position:0%
+activated in the cytosol by adding
+ 
+
+ align:start position:0%
+activated in the cytosol by adding
+the coenzyme a group to the acid on the
+
+ align:start position:0%
+the coenzyme a group to the acid on the
+ 
+
+ align:start position:0%
+the coenzyme a group to the acid on the
+end
+
+ align:start position:0%
+end
+ 
+
+ align:start position:0%
+end
+very much like acetyl coa and so
+
+ align:start position:0%
+very much like acetyl coa and so
+ 
+
+ align:start position:0%
+very much like acetyl coa and so
+here is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some generic chain length
+
+ align:start position:0%
+some generic chain length
+ 
+
+ align:start position:0%
+some generic chain length
+fatty acid and it turns out that there's
+
+ align:start position:0%
+fatty acid and it turns out that there's
+ 
+
+ align:start position:0%
+fatty acid and it turns out that there's
+an enzyme
+
+ align:start position:0%
+an enzyme
+ 
+
+ align:start position:0%
+an enzyme
+called acyl co-asynthetase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that is going to take
+
+ align:start position:0%
+that is going to take
+ 
+
+ align:start position:0%
+that is going to take
+atp
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and adenylate
+
+ align:start position:0%
+and adenylate
+ 
+
+ align:start position:0%
+and adenylate
+this acid group on
+
+ align:start position:0%
+this acid group on
+ 
+
+ align:start position:0%
+this acid group on
+the fatty acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so this is basically
+
+ align:start position:0%
+okay and so this is basically
+ 
+
+ align:start position:0%
+okay and so this is basically
+an amp that's been used to adenylate
+
+ align:start position:0%
+an amp that's been used to adenylate
+ 
+
+ align:start position:0%
+an amp that's been used to adenylate
+the fatty acid itself
+
+ align:start position:0%
+the fatty acid itself
+ 
+
+ align:start position:0%
+the fatty acid itself
+now you'll notice by doing this we
+
+ align:start position:0%
+now you'll notice by doing this we
+ 
+
+ align:start position:0%
+now you'll notice by doing this we
+generate a pyrophosphate
+
+ align:start position:0%
+generate a pyrophosphate
+ 
+
+ align:start position:0%
+generate a pyrophosphate
+and that pyrophosphate can be turned
+
+ align:start position:0%
+and that pyrophosphate can be turned
+ 
+
+ align:start position:0%
+and that pyrophosphate can be turned
+into two inorganic phosphates
+
+ align:start position:0%
+into two inorganic phosphates
+ 
+
+ align:start position:0%
+into two inorganic phosphates
+same trick we've seen before that
+
+ align:start position:0%
+same trick we've seen before that
+ 
+
+ align:start position:0%
+same trick we've seen before that
+basically can pull
+
+ align:start position:0%
+basically can pull
+ 
+
+ align:start position:0%
+basically can pull
+a reaction that otherwise would be
+
+ align:start position:0%
+a reaction that otherwise would be
+ 
+
+ align:start position:0%
+a reaction that otherwise would be
+unfavorable forward in this case
+
+ align:start position:0%
+unfavorable forward in this case
+ 
+
+ align:start position:0%
+unfavorable forward in this case
+it's adding the co-a group
+
+ align:start position:0%
+it's adding the co-a group
+ 
+
+ align:start position:0%
+it's adding the co-a group
+to this fatty acid and
+
+ align:start position:0%
+to this fatty acid and
+ 
+
+ align:start position:0%
+to this fatty acid and
+what happens next is is that uh
+
+ align:start position:0%
+what happens next is is that uh
+ 
+
+ align:start position:0%
+what happens next is is that uh
+co-a comes in and replaces the amp
+
+ align:start position:0%
+co-a comes in and replaces the amp
+ 
+
+ align:start position:0%
+co-a comes in and replaces the amp
+such that you generate this
+
+ align:start position:0%
+such that you generate this
+ 
+
+ align:start position:0%
+such that you generate this
+fatty acyl
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coa molecule which is basically acetyl
+
+ align:start position:0%
+coa molecule which is basically acetyl
+ 
+
+ align:start position:0%
+coa molecule which is basically acetyl
+coa
+
+ align:start position:0%
+coa
+ 
+
+ align:start position:0%
+coa
+but with some arbitrary longer
+
+ align:start position:0%
+but with some arbitrary longer
+ 
+
+ align:start position:0%
+but with some arbitrary longer
+number of of reduced hydrocarbons
+
+ align:start position:0%
+number of of reduced hydrocarbons
+ 
+
+ align:start position:0%
+number of of reduced hydrocarbons
+in the chain so not a two carbon unit
+
+ align:start position:0%
+in the chain so not a two carbon unit
+ 
+
+ align:start position:0%
+in the chain so not a two carbon unit
+but a fatty acid a many carbon unit
+
+ align:start position:0%
+but a fatty acid a many carbon unit
+ 
+
+ align:start position:0%
+but a fatty acid a many carbon unit
+fatty acid with whatever
+
+ align:start position:0%
+fatty acid with whatever
+ 
+
+ align:start position:0%
+fatty acid with whatever
+other properties happen to be on that
+
+ align:start position:0%
+other properties happen to be on that
+ 
+
+ align:start position:0%
+other properties happen to be on that
+fatty acid
+
+ align:start position:0%
+fatty acid
+ 
+
+ align:start position:0%
+fatty acid
+where now you have this fatty acyl coa
+
+ align:start position:0%
+where now you have this fatty acyl coa
+ 
+
+ align:start position:0%
+where now you have this fatty acyl coa
+instead of
+
+ align:start position:0%
+instead of
+ 
+
+ align:start position:0%
+instead of
+the fatty acid so it turns out this
+
+ align:start position:0%
+the fatty acid so it turns out this
+ 
+
+ align:start position:0%
+the fatty acid so it turns out this
+fatty acyl coa then
+
+ align:start position:0%
+fatty acyl coa then
+ 
+
+ align:start position:0%
+fatty acyl coa then
+is subjected to a shuttle called the
+
+ align:start position:0%
+is subjected to a shuttle called the
+ 
+
+ align:start position:0%
+is subjected to a shuttle called the
+carnitine shuttle
+
+ align:start position:0%
+carnitine shuttle
+ 
+
+ align:start position:0%
+carnitine shuttle
+to actually get it into the mitochondria
+
+ align:start position:0%
+to actually get it into the mitochondria
+ 
+
+ align:start position:0%
+to actually get it into the mitochondria
+and so what is carnitine
+
+ align:start position:0%
+and so what is carnitine
+ 
+
+ align:start position:0%
+and so what is carnitine
+so carnitine is a
+
+ align:start position:0%
+so carnitine is a
+ 
+
+ align:start position:0%
+so carnitine is a
+small molecule looks like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this here is carnitine
+
+ align:start position:0%
+okay so this here is carnitine
+ 
+
+ align:start position:0%
+okay so this here is carnitine
+and it turns out that this hydroxyl
+
+ align:start position:0%
+and it turns out that this hydroxyl
+ 
+
+ align:start position:0%
+and it turns out that this hydroxyl
+group
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically is swapped for the koa
+
+ align:start position:0%
+basically is swapped for the koa
+ 
+
+ align:start position:0%
+basically is swapped for the koa
+on the fatty acyl coa and so if this
+
+ align:start position:0%
+on the fatty acyl coa and so if this
+ 
+
+ align:start position:0%
+on the fatty acyl coa and so if this
+here is some
+
+ align:start position:0%
+here is some
+ 
+
+ align:start position:0%
+here is some
+generic fatty acyl coated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you end up with this molecule which is
+
+ align:start position:0%
+you end up with this molecule which is
+ 
+
+ align:start position:0%
+you end up with this molecule which is
+called
+
+ align:start position:0%
+called
+ 
+
+ align:start position:0%
+called
+a fatty acyl
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+carnitine so all i've done is take the
+
+ align:start position:0%
+carnitine so all i've done is take the
+ 
+
+ align:start position:0%
+carnitine so all i've done is take the
+coa off
+
+ align:start position:0%
+coa off
+ 
+
+ align:start position:0%
+coa off
+and move the fatty acid to make this
+
+ align:start position:0%
+and move the fatty acid to make this
+ 
+
+ align:start position:0%
+and move the fatty acid to make this
+ester here with the alcohol on the
+
+ align:start position:0%
+ester here with the alcohol on the
+ 
+
+ align:start position:0%
+ester here with the alcohol on the
+carnitine and this
+
+ align:start position:0%
+carnitine and this
+ 
+
+ align:start position:0%
+carnitine and this
+fatty acyl carnitine can now be
+
+ align:start position:0%
+fatty acyl carnitine can now be
+ 
+
+ align:start position:0%
+fatty acyl carnitine can now be
+transported across
+
+ align:start position:0%
+transported across
+ 
+
+ align:start position:0%
+transported across
+the mitochondrial membrane so from the
+
+ align:start position:0%
+the mitochondrial membrane so from the
+ 
+
+ align:start position:0%
+the mitochondrial membrane so from the
+cytosol to the mitochondria
+
+ align:start position:0%
+cytosol to the mitochondria
+ 
+
+ align:start position:0%
+cytosol to the mitochondria
+here we have our fatty acyl
+
+ align:start position:0%
+here we have our fatty acyl
+ 
+
+ align:start position:0%
+here we have our fatty acyl
+carnitine and then that fatty acyl
+
+ align:start position:0%
+carnitine and then that fatty acyl
+ 
+
+ align:start position:0%
+carnitine and then that fatty acyl
+carnitine exchange
+
+ align:start position:0%
+carnitine exchange
+ 
+
+ align:start position:0%
+carnitine exchange
+a coa
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the carnitine and regenerate the
+
+ align:start position:0%
+for the carnitine and regenerate the
+ 
+
+ align:start position:0%
+for the carnitine and regenerate the
+fatty acyl
+
+ align:start position:0%
+fatty acyl
+ 
+
+ align:start position:0%
+fatty acyl
+coa in the mitochondrial matrix
+
+ align:start position:0%
+coa in the mitochondrial matrix
+ 
+
+ align:start position:0%
+coa in the mitochondrial matrix
+this whole process is referred to as the
+
+ align:start position:0%
+this whole process is referred to as the
+ 
+
+ align:start position:0%
+this whole process is referred to as the
+carnitine shuttle and is effectively a
+
+ align:start position:0%
+carnitine shuttle and is effectively a
+ 
+
+ align:start position:0%
+carnitine shuttle and is effectively a
+complex way
+
+ align:start position:0%
+complex way
+ 
+
+ align:start position:0%
+complex way
+to move fatty acids from the cytosol
+
+ align:start position:0%
+to move fatty acids from the cytosol
+ 
+
+ align:start position:0%
+to move fatty acids from the cytosol
+fatty acyl coas from the cytosol into
+
+ align:start position:0%
+fatty acyl coas from the cytosol into
+ 
+
+ align:start position:0%
+fatty acyl coas from the cytosol into
+the mitochondria where they can be
+
+ align:start position:0%
+the mitochondria where they can be
+ 
+
+ align:start position:0%
+the mitochondria where they can be
+oxidized
+
+ align:start position:0%
+oxidized
+ 
+
+ align:start position:0%
+oxidized
+here's another picture of it that is
+
+ align:start position:0%
+here's another picture of it that is
+ 
+
+ align:start position:0%
+here's another picture of it that is
+maybe drawn in a
+
+ align:start position:0%
+maybe drawn in a
+ 
+
+ align:start position:0%
+maybe drawn in a
+different way because it's a little bit
+
+ align:start position:0%
+different way because it's a little bit
+ 
+
+ align:start position:0%
+different way because it's a little bit
+confusing as something to describe but
+
+ align:start position:0%
+confusing as something to describe but
+ 
+
+ align:start position:0%
+confusing as something to describe but
+basically you generate
+
+ align:start position:0%
+basically you generate
+ 
+
+ align:start position:0%
+basically you generate
+this fatty acyl coa
+
+ align:start position:0%
+this fatty acyl coa
+ 
+
+ align:start position:0%
+this fatty acyl coa
+in the um in the cytosol
+
+ align:start position:0%
+in the um in the cytosol
+ 
+
+ align:start position:0%
+in the um in the cytosol
+and then the fatty acyl coa is
+
+ align:start position:0%
+and then the fatty acyl coa is
+ 
+
+ align:start position:0%
+and then the fatty acyl coa is
+exchanged for fatty acyl carnitine fatty
+
+ align:start position:0%
+exchanged for fatty acyl carnitine fatty
+ 
+
+ align:start position:0%
+exchanged for fatty acyl carnitine fatty
+acyl carnitine goes into the matrix and
+
+ align:start position:0%
+acyl carnitine goes into the matrix and
+ 
+
+ align:start position:0%
+acyl carnitine goes into the matrix and
+these used to regenerate the
+
+ align:start position:0%
+these used to regenerate the
+ 
+
+ align:start position:0%
+these used to regenerate the
+fatty acyl coa the enzymes that do this
+
+ align:start position:0%
+fatty acyl coa the enzymes that do this
+ 
+
+ align:start position:0%
+fatty acyl coa the enzymes that do this
+is something called cpt or carnitine
+
+ align:start position:0%
+is something called cpt or carnitine
+ 
+
+ align:start position:0%
+is something called cpt or carnitine
+palmitoel
+
+ align:start position:0%
+palmitoel
+ 
+
+ align:start position:0%
+palmitoel
+transferase um
+
+ align:start position:0%
+transferase um
+ 
+
+ align:start position:0%
+transferase um
+and write that down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+carnitine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is obviously refers to palmitate
+
+ align:start position:0%
+which is obviously refers to palmitate
+ 
+
+ align:start position:0%
+which is obviously refers to palmitate
+as a common
+
+ align:start position:0%
+as a common
+ 
+
+ align:start position:0%
+as a common
+fatty acid although cpt will catalyze
+
+ align:start position:0%
+fatty acid although cpt will catalyze
+ 
+
+ align:start position:0%
+fatty acid although cpt will catalyze
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+fatty acyl carnitine fatty acyl coa
+
+ align:start position:0%
+fatty acyl carnitine fatty acyl coa
+ 
+
+ align:start position:0%
+fatty acyl carnitine fatty acyl coa
+interconversions
+
+ align:start position:0%
+interconversions
+ 
+
+ align:start position:0%
+interconversions
+and so by doing that inner conversion in
+
+ align:start position:0%
+and so by doing that inner conversion in
+ 
+
+ align:start position:0%
+and so by doing that inner conversion in
+the cytosolic side and the mitochondrial
+
+ align:start position:0%
+the cytosolic side and the mitochondrial
+ 
+
+ align:start position:0%
+the cytosolic side and the mitochondrial
+side
+
+ align:start position:0%
+side
+ 
+
+ align:start position:0%
+side
+you can use carnitine as a handle to
+
+ align:start position:0%
+you can use carnitine as a handle to
+ 
+
+ align:start position:0%
+you can use carnitine as a handle to
+transfer
+
+ align:start position:0%
+transfer
+ 
+
+ align:start position:0%
+transfer
+fatty acyl coast from one compartment to
+
+ align:start position:0%
+fatty acyl coast from one compartment to
+ 
+
+ align:start position:0%
+fatty acyl coast from one compartment to
+another all right
+
+ align:start position:0%
+another all right
+ 
+
+ align:start position:0%
+another all right
+now once that fatty acyl coa is in the
+
+ align:start position:0%
+now once that fatty acyl coa is in the
+ 
+
+ align:start position:0%
+now once that fatty acyl coa is in the
+mitochondria
+
+ align:start position:0%
+mitochondria
+ 
+
+ align:start position:0%
+mitochondria
+it can now be used as a way
+
+ align:start position:0%
+it can now be used as a way
+ 
+
+ align:start position:0%
+it can now be used as a way
+to now be oxidized to acetyl-coa
+
+ align:start position:0%
+to now be oxidized to acetyl-coa
+ 
+
+ align:start position:0%
+to now be oxidized to acetyl-coa
+okay so now let's discuss the series of
+
+ align:start position:0%
+okay so now let's discuss the series of
+ 
+
+ align:start position:0%
+okay so now let's discuss the series of
+steps
+
+ align:start position:0%
+steps
+ 
+
+ align:start position:0%
+steps
+that is referred to as fatty acid
+
+ align:start position:0%
+that is referred to as fatty acid
+ 
+
+ align:start position:0%
+that is referred to as fatty acid
+oxidation
+
+ align:start position:0%
+oxidation
+ 
+
+ align:start position:0%
+oxidation
+and abbreviated fao and so of course we
+
+ align:start position:0%
+and abbreviated fao and so of course we
+ 
+
+ align:start position:0%
+and abbreviated fao and so of course we
+start here with our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generic fatty acyl
+
+ align:start position:0%
+generic fatty acyl
+ 
+
+ align:start position:0%
+generic fatty acyl
+coa in the matrix of the mitochondria
+
+ align:start position:0%
+coa in the matrix of the mitochondria
+ 
+
+ align:start position:0%
+coa in the matrix of the mitochondria
+of some arbitrary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+chain length okay and so
+
+ align:start position:0%
+chain length okay and so
+ 
+
+ align:start position:0%
+chain length okay and so
+the first thing that we're going to do
+
+ align:start position:0%
+the first thing that we're going to do
+ 
+
+ align:start position:0%
+the first thing that we're going to do
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+oxidize this carbon-carbon bond that is
+
+ align:start position:0%
+oxidize this carbon-carbon bond that is
+ 
+
+ align:start position:0%
+oxidize this carbon-carbon bond that is
+introduce a double bond here
+
+ align:start position:0%
+introduce a double bond here
+ 
+
+ align:start position:0%
+introduce a double bond here
+that's an oxidation reaction it's
+
+ align:start position:0%
+that's an oxidation reaction it's
+ 
+
+ align:start position:0%
+that's an oxidation reaction it's
+exactly the same reaction
+
+ align:start position:0%
+exactly the same reaction
+ 
+
+ align:start position:0%
+exactly the same reaction
+that we saw convert succinate to
+
+ align:start position:0%
+that we saw convert succinate to
+ 
+
+ align:start position:0%
+that we saw convert succinate to
+fumarate
+
+ align:start position:0%
+fumarate
+ 
+
+ align:start position:0%
+fumarate
+in the tca cycle that reaction
+
+ align:start position:0%
+in the tca cycle that reaction
+ 
+
+ align:start position:0%
+in the tca cycle that reaction
+used fad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as an electron acceptor so we oxidize
+
+ align:start position:0%
+as an electron acceptor so we oxidize
+ 
+
+ align:start position:0%
+as an electron acceptor so we oxidize
+that carbon-carbon bond
+
+ align:start position:0%
+that carbon-carbon bond
+ 
+
+ align:start position:0%
+that carbon-carbon bond
+fad gets reduced to fadh2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is carried out by an enzyme called
+
+ align:start position:0%
+this is carried out by an enzyme called
+ 
+
+ align:start position:0%
+this is carried out by an enzyme called
+acyl
+
+ align:start position:0%
+acyl
+ 
+
+ align:start position:0%
+acyl
+coa dehydrogenase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and generates that intermediate
+
+ align:start position:0%
+and generates that intermediate
+ 
+
+ align:start position:0%
+and generates that intermediate
+again now just like we did in the tca
+
+ align:start position:0%
+again now just like we did in the tca
+ 
+
+ align:start position:0%
+again now just like we did in the tca
+cycle when we converted
+
+ align:start position:0%
+cycle when we converted
+ 
+
+ align:start position:0%
+cycle when we converted
+fumarate into malate we added water
+
+ align:start position:0%
+fumarate into malate we added water
+ 
+
+ align:start position:0%
+fumarate into malate we added water
+across
+
+ align:start position:0%
+across
+ 
+
+ align:start position:0%
+across
+this double bond to exactly
+
+ align:start position:0%
+this double bond to exactly
+ 
+
+ align:start position:0%
+this double bond to exactly
+the same thing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that generates this intermediate
+
+ align:start position:0%
+okay that generates this intermediate
+ 
+
+ align:start position:0%
+okay that generates this intermediate
+now we can oxidize this
+
+ align:start position:0%
+now we can oxidize this
+ 
+
+ align:start position:0%
+now we can oxidize this
+carbon here this alcohol oxidize it to
+
+ align:start position:0%
+carbon here this alcohol oxidize it to
+ 
+
+ align:start position:0%
+carbon here this alcohol oxidize it to
+the ketone of course you know how
+
+ align:start position:0%
+the ketone of course you know how
+ 
+
+ align:start position:0%
+the ketone of course you know how
+to do this we've now seen it a million
+
+ align:start position:0%
+to do this we've now seen it a million
+ 
+
+ align:start position:0%
+to do this we've now seen it a million
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+okay so that generates this
+
+ align:start position:0%
+okay so that generates this
+ 
+
+ align:start position:0%
+okay so that generates this
+hydride ion which can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transferred to nad plus
+
+ align:start position:0%
+transferred to nad plus
+ 
+
+ align:start position:0%
+transferred to nad plus
+reducing it to nadh
+
+ align:start position:0%
+reducing it to nadh
+ 
+
+ align:start position:0%
+reducing it to nadh
+okay and now we can
+
+ align:start position:0%
+okay and now we can
+ 
+
+ align:start position:0%
+okay and now we can
+what happens next is co-a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+basically breaks that carbon-carbon bond
+
+ align:start position:0%
+basically breaks that carbon-carbon bond
+ 
+
+ align:start position:0%
+basically breaks that carbon-carbon bond
+and what are we left with we're left
+
+ align:start position:0%
+and what are we left with we're left
+ 
+
+ align:start position:0%
+and what are we left with we're left
+with over here release of
+
+ align:start position:0%
+with over here release of
+ 
+
+ align:start position:0%
+with over here release of
+a acetyl
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coa group which can then go down and be
+
+ align:start position:0%
+coa group which can then go down and be
+ 
+
+ align:start position:0%
+coa group which can then go down and be
+further oxidized
+
+ align:start position:0%
+further oxidized
+ 
+
+ align:start position:0%
+further oxidized
+in the tca cycle as well as
+
+ align:start position:0%
+in the tca cycle as well as
+ 
+
+ align:start position:0%
+in the tca cycle as well as
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fatty acyl coa
+
+ align:start position:0%
+fatty acyl coa
+ 
+
+ align:start position:0%
+fatty acyl coa
+that is two carbon shorter than
+
+ align:start position:0%
+that is two carbon shorter than
+ 
+
+ align:start position:0%
+that is two carbon shorter than
+the one we started with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that can then go back up
+
+ align:start position:0%
+that can then go back up
+ 
+
+ align:start position:0%
+that can then go back up
+repeat the cycle again until
+
+ align:start position:0%
+repeat the cycle again until
+ 
+
+ align:start position:0%
+repeat the cycle again until
+if you start with an even number of
+
+ align:start position:0%
+if you start with an even number of
+ 
+
+ align:start position:0%
+if you start with an even number of
+carbons the last one leaves you with
+
+ align:start position:0%
+carbons the last one leaves you with
+ 
+
+ align:start position:0%
+carbons the last one leaves you with
+two acetyl coa molecules
+
+ align:start position:0%
+two acetyl coa molecules
+ 
+
+ align:start position:0%
+two acetyl coa molecules
+and so per two carbon units that we run
+
+ align:start position:0%
+and so per two carbon units that we run
+ 
+
+ align:start position:0%
+and so per two carbon units that we run
+through this cycle of fatty acid
+
+ align:start position:0%
+through this cycle of fatty acid
+ 
+
+ align:start position:0%
+through this cycle of fatty acid
+oxidation what we get is we get
+
+ align:start position:0%
+oxidation what we get is we get
+ 
+
+ align:start position:0%
+oxidation what we get is we get
+an acetyl coa it comes out
+
+ align:start position:0%
+an acetyl coa it comes out
+ 
+
+ align:start position:0%
+an acetyl coa it comes out
+we get an fadh2
+
+ align:start position:0%
+we get an fadh2
+ 
+
+ align:start position:0%
+we get an fadh2
+and we get on nadh
+
+ align:start position:0%
+and we get on nadh
+ 
+
+ align:start position:0%
+and we get on nadh
+now of course if we start with an
+
+ align:start position:0%
+now of course if we start with an
+ 
+
+ align:start position:0%
+now of course if we start with an
+unsaturated fatty acid
+
+ align:start position:0%
+unsaturated fatty acid
+ 
+
+ align:start position:0%
+unsaturated fatty acid
+we don't have to introduce the double
+
+ align:start position:0%
+we don't have to introduce the double
+ 
+
+ align:start position:0%
+we don't have to introduce the double
+bond into it we don't get the fadh2
+
+ align:start position:0%
+bond into it we don't get the fadh2
+ 
+
+ align:start position:0%
+bond into it we don't get the fadh2
+we get less energy produced
+
+ align:start position:0%
+we get less energy produced
+ 
+
+ align:start position:0%
+we get less energy produced
+um from that molecule
+
+ align:start position:0%
+um from that molecule
+ 
+
+ align:start position:0%
+um from that molecule
+and so if this acetyl coa goes on and
+
+ align:start position:0%
+and so if this acetyl coa goes on and
+ 
+
+ align:start position:0%
+and so if this acetyl coa goes on and
+enters the tca cycle
+
+ align:start position:0%
+enters the tca cycle
+ 
+
+ align:start position:0%
+enters the tca cycle
+well then we get and we fully oxidize it
+
+ align:start position:0%
+well then we get and we fully oxidize it
+ 
+
+ align:start position:0%
+well then we get and we fully oxidize it
+to co2
+
+ align:start position:0%
+to co2
+ 
+
+ align:start position:0%
+to co2
+we get three more nadh we get another
+
+ align:start position:0%
+we get three more nadh we get another
+ 
+
+ align:start position:0%
+we get three more nadh we get another
+fadh2
+
+ align:start position:0%
+fadh2
+ 
+
+ align:start position:0%
+fadh2
+and we get a gtp it's written up there
+
+ align:start position:0%
+and we get a gtp it's written up there
+ 
+
+ align:start position:0%
+and we get a gtp it's written up there
+as a reminder
+
+ align:start position:0%
+as a reminder
+ 
+
+ align:start position:0%
+as a reminder
+and so with a fully saturated
+
+ align:start position:0%
+and so with a fully saturated
+ 
+
+ align:start position:0%
+and so with a fully saturated
+per two carbons out we basically get
+
+ align:start position:0%
+per two carbons out we basically get
+ 
+
+ align:start position:0%
+per two carbons out we basically get
+four nadhs two fadh2s and a gdp
+
+ align:start position:0%
+four nadhs two fadh2s and a gdp
+ 
+
+ align:start position:0%
+four nadhs two fadh2s and a gdp
+and that's a fair amount of energy
+
+ align:start position:0%
+and that's a fair amount of energy
+ 
+
+ align:start position:0%
+and that's a fair amount of energy
+if you will released from the oxidation
+
+ align:start position:0%
+if you will released from the oxidation
+ 
+
+ align:start position:0%
+if you will released from the oxidation
+of this fatty acid all the way to
+
+ align:start position:0%
+of this fatty acid all the way to
+ 
+
+ align:start position:0%
+of this fatty acid all the way to
+co2 we'll come back to that accounting
+
+ align:start position:0%
+co2 we'll come back to that accounting
+ 
+
+ align:start position:0%
+co2 we'll come back to that accounting
+in a second but first i want to say what
+
+ align:start position:0%
+in a second but first i want to say what
+ 
+
+ align:start position:0%
+in a second but first i want to say what
+happens if you happen to start
+
+ align:start position:0%
+happens if you happen to start
+ 
+
+ align:start position:0%
+happens if you happen to start
+with an odd number of carbons so i
+
+ align:start position:0%
+with an odd number of carbons so i
+ 
+
+ align:start position:0%
+with an odd number of carbons so i
+mentioned that most biological fatty
+
+ align:start position:0%
+mentioned that most biological fatty
+ 
+
+ align:start position:0%
+mentioned that most biological fatty
+acids have even numbers of carbons
+
+ align:start position:0%
+acids have even numbers of carbons
+ 
+
+ align:start position:0%
+acids have even numbers of carbons
+but there are odd chain numbers of
+
+ align:start position:0%
+but there are odd chain numbers of
+ 
+
+ align:start position:0%
+but there are odd chain numbers of
+odd chain carbon lengths of fatty acids
+
+ align:start position:0%
+odd chain carbon lengths of fatty acids
+ 
+
+ align:start position:0%
+odd chain carbon lengths of fatty acids
+some bacteria make these sometimes it
+
+ align:start position:0%
+some bacteria make these sometimes it
+ 
+
+ align:start position:0%
+some bacteria make these sometimes it
+just happens obviously if you do that
+
+ align:start position:0%
+just happens obviously if you do that
+ 
+
+ align:start position:0%
+just happens obviously if you do that
+you'll end up at the end with this
+
+ align:start position:0%
+you'll end up at the end with this
+ 
+
+ align:start position:0%
+you'll end up at the end with this
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+which is a three carbon acyl coa called
+
+ align:start position:0%
+which is a three carbon acyl coa called
+ 
+
+ align:start position:0%
+which is a three carbon acyl coa called
+propionil
+
+ align:start position:0%
+propionil
+ 
+
+ align:start position:0%
+propionil
+coa
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so cells need a way to deal with
+
+ align:start position:0%
+and so cells need a way to deal with
+ 
+
+ align:start position:0%
+and so cells need a way to deal with
+this three carbon propineal coa
+
+ align:start position:0%
+this three carbon propineal coa
+ 
+
+ align:start position:0%
+this three carbon propineal coa
+well the way they deal with it is they
+
+ align:start position:0%
+well the way they deal with it is they
+ 
+
+ align:start position:0%
+well the way they deal with it is they
+carboxylate it
+
+ align:start position:0%
+carboxylate it
+ 
+
+ align:start position:0%
+carboxylate it
+so we're going to add a co2 to a
+
+ align:start position:0%
+so we're going to add a co2 to a
+ 
+
+ align:start position:0%
+so we're going to add a co2 to a
+molecule how do we do that well we need
+
+ align:start position:0%
+molecule how do we do that well we need
+ 
+
+ align:start position:0%
+molecule how do we do that well we need
+a cofactor
+
+ align:start position:0%
+a cofactor
+ 
+
+ align:start position:0%
+a cofactor
+remember we did this with the
+
+ align:start position:0%
+remember we did this with the
+ 
+
+ align:start position:0%
+remember we did this with the
+pyruvate carboxylase reaction this was
+
+ align:start position:0%
+pyruvate carboxylase reaction this was
+ 
+
+ align:start position:0%
+pyruvate carboxylase reaction this was
+the reaction of biotin
+
+ align:start position:0%
+the reaction of biotin
+ 
+
+ align:start position:0%
+the reaction of biotin
+so we started with bicarbonate we
+
+ align:start position:0%
+so we started with bicarbonate we
+ 
+
+ align:start position:0%
+so we started with bicarbonate we
+phosphorylated
+
+ align:start position:0%
+phosphorylated
+ 
+
+ align:start position:0%
+phosphorylated
+the bicarbonate
+
+ align:start position:0%
+the bicarbonate
+ 
+
+ align:start position:0%
+the bicarbonate
+and then that phosphorylated bicarbonate
+
+ align:start position:0%
+and then that phosphorylated bicarbonate
+ 
+
+ align:start position:0%
+and then that phosphorylated bicarbonate
+there was biotin in the active site of
+
+ align:start position:0%
+there was biotin in the active site of
+ 
+
+ align:start position:0%
+there was biotin in the active site of
+the enzyme
+
+ align:start position:0%
+the enzyme
+ 
+
+ align:start position:0%
+the enzyme
+that released the phosphate they had
+
+ align:start position:0%
+that released the phosphate they had
+ 
+
+ align:start position:0%
+that released the phosphate they had
+enzyme biotin
+
+ align:start position:0%
+enzyme biotin
+ 
+
+ align:start position:0%
+enzyme biotin
+with a co2 on it and so
+
+ align:start position:0%
+with a co2 on it and so
+ 
+
+ align:start position:0%
+with a co2 on it and so
+if we take this propyneal coa here which
+
+ align:start position:0%
+if we take this propyneal coa here which
+ 
+
+ align:start position:0%
+if we take this propyneal coa here which
+is drawn in the
+
+ align:start position:0%
+is drawn in the
+ 
+
+ align:start position:0%
+is drawn in the
+enol form i mean sorry in the keto form
+
+ align:start position:0%
+enol form i mean sorry in the keto form
+ 
+
+ align:start position:0%
+enol form i mean sorry in the keto form
+and we redraw it in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+enol form of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+propanil coa
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we carry out similar reaction that we
+
+ align:start position:0%
+we carry out similar reaction that we
+ 
+
+ align:start position:0%
+we carry out similar reaction that we
+saw before
+
+ align:start position:0%
+saw before
+ 
+
+ align:start position:0%
+saw before
+and now we end up with this molecule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so effectively adding the co2 to this
+
+ align:start position:0%
+so effectively adding the co2 to this
+ 
+
+ align:start position:0%
+so effectively adding the co2 to this
+carbon
+
+ align:start position:0%
+carbon
+ 
+
+ align:start position:0%
+carbon
+to the second carbon in and that's this
+
+ align:start position:0%
+to the second carbon in and that's this
+ 
+
+ align:start position:0%
+to the second carbon in and that's this
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+which is called methyl
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+malianil coe
+
+ align:start position:0%
+malianil coe
+ 
+
+ align:start position:0%
+malianil coe
+i'm going to redraw methylmalonyl coa
+
+ align:start position:0%
+i'm going to redraw methylmalonyl coa
+ 
+
+ align:start position:0%
+i'm going to redraw methylmalonyl coa
+just to show you how cells deal
+
+ align:start position:0%
+just to show you how cells deal
+ 
+
+ align:start position:0%
+just to show you how cells deal
+with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is methylmalonyl coa i just
+
+ align:start position:0%
+okay so this is methylmalonyl coa i just
+ 
+
+ align:start position:0%
+okay so this is methylmalonyl coa i just
+redrew it in a way that there's some
+
+ align:start position:0%
+redrew it in a way that there's some
+ 
+
+ align:start position:0%
+redrew it in a way that there's some
+colors on the different
+
+ align:start position:0%
+colors on the different
+ 
+
+ align:start position:0%
+colors on the different
+molecules what i'm going to do is i'm
+
+ align:start position:0%
+molecules what i'm going to do is i'm
+ 
+
+ align:start position:0%
+molecules what i'm going to do is i'm
+basically going to take this group
+
+ align:start position:0%
+basically going to take this group
+ 
+
+ align:start position:0%
+basically going to take this group
+and this group and swap their
+
+ align:start position:0%
+and this group and swap their
+ 
+
+ align:start position:0%
+and this group and swap their
+positions um and if i do that
+
+ align:start position:0%
+positions um and if i do that
+ 
+
+ align:start position:0%
+positions um and if i do that
+i will end up with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this molecule which hopefully you
+
+ align:start position:0%
+this molecule which hopefully you
+ 
+
+ align:start position:0%
+this molecule which hopefully you
+recognize as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+succinal coa from the tca cycle
+
+ align:start position:0%
+succinal coa from the tca cycle
+ 
+
+ align:start position:0%
+succinal coa from the tca cycle
+now the mechanism for how that swap
+
+ align:start position:0%
+now the mechanism for how that swap
+ 
+
+ align:start position:0%
+now the mechanism for how that swap
+happens i don't have
+
+ align:start position:0%
+happens i don't have
+ 
+
+ align:start position:0%
+happens i don't have
+time to go into but this complex
+
+ align:start position:0%
+time to go into but this complex
+ 
+
+ align:start position:0%
+time to go into but this complex
+intramolecular rearrangement requires
+
+ align:start position:0%
+intramolecular rearrangement requires
+ 
+
+ align:start position:0%
+intramolecular rearrangement requires
+a cofactor that cofactor comes from
+
+ align:start position:0%
+a cofactor that cofactor comes from
+ 
+
+ align:start position:0%
+a cofactor that cofactor comes from
+vitamin b12
+
+ align:start position:0%
+vitamin b12
+ 
+
+ align:start position:0%
+vitamin b12
+and so here's a picture of vitamin b12
+
+ align:start position:0%
+and so here's a picture of vitamin b12
+ 
+
+ align:start position:0%
+and so here's a picture of vitamin b12
+you can see by looking at it why i don't
+
+ align:start position:0%
+you can see by looking at it why i don't
+ 
+
+ align:start position:0%
+you can see by looking at it why i don't
+want to draw that out for you
+
+ align:start position:0%
+want to draw that out for you
+ 
+
+ align:start position:0%
+want to draw that out for you
+it's a cobalt containing cofactor
+
+ align:start position:0%
+it's a cobalt containing cofactor
+ 
+
+ align:start position:0%
+it's a cobalt containing cofactor
+sometimes referred to as cobalamin
+
+ align:start position:0%
+sometimes referred to as cobalamin
+ 
+
+ align:start position:0%
+sometimes referred to as cobalamin
+if you're interested you can look up the
+
+ align:start position:0%
+if you're interested you can look up the
+ 
+
+ align:start position:0%
+if you're interested you can look up the
+chemistry for how
+
+ align:start position:0%
+chemistry for how
+ 
+
+ align:start position:0%
+chemistry for how
+vitamin b12 helps catalyze this
+
+ align:start position:0%
+vitamin b12 helps catalyze this
+ 
+
+ align:start position:0%
+vitamin b12 helps catalyze this
+intramolecular rearrangement to go from
+
+ align:start position:0%
+intramolecular rearrangement to go from
+ 
+
+ align:start position:0%
+intramolecular rearrangement to go from
+methylmalonyl coa to succinyl coa
+
+ align:start position:0%
+methylmalonyl coa to succinyl coa
+ 
+
+ align:start position:0%
+methylmalonyl coa to succinyl coa
+but the important take home is is that
+
+ align:start position:0%
+but the important take home is is that
+ 
+
+ align:start position:0%
+but the important take home is is that
+if you have an odd chain fatty acid
+
+ align:start position:0%
+if you have an odd chain fatty acid
+ 
+
+ align:start position:0%
+if you have an odd chain fatty acid
+use a biotin containing enzyme to
+
+ align:start position:0%
+use a biotin containing enzyme to
+ 
+
+ align:start position:0%
+use a biotin containing enzyme to
+carboxylate propyneal coa
+
+ align:start position:0%
+carboxylate propyneal coa
+ 
+
+ align:start position:0%
+carboxylate propyneal coa
+to methylmalonyl coa and then b12 to
+
+ align:start position:0%
+to methylmalonyl coa and then b12 to
+ 
+
+ align:start position:0%
+to methylmalonyl coa and then b12 to
+rearrange that methylmalonyl coa to
+
+ align:start position:0%
+rearrange that methylmalonyl coa to
+ 
+
+ align:start position:0%
+rearrange that methylmalonyl coa to
+suctional coa
+
+ align:start position:0%
+suctional coa
+ 
+
+ align:start position:0%
+suctional coa
+and now this can enter the tca cycle and
+
+ align:start position:0%
+and now this can enter the tca cycle and
+ 
+
+ align:start position:0%
+and now this can enter the tca cycle and
+be oxidized
+
+ align:start position:0%
+be oxidized
+ 
+
+ align:start position:0%
+be oxidized
+as well all right so
+
+ align:start position:0%
+as well all right so
+ 
+
+ align:start position:0%
+as well all right so
+now you have the details of how you can
+
+ align:start position:0%
+now you have the details of how you can
+ 
+
+ align:start position:0%
+now you have the details of how you can
+start
+
+ align:start position:0%
+start
+ 
+
+ align:start position:0%
+start
+with a fatty acid and
+
+ align:start position:0%
+with a fatty acid and
+ 
+
+ align:start position:0%
+with a fatty acid and
+oxidize it to co2
+
+ align:start position:0%
+oxidize it to co2
+ 
+
+ align:start position:0%
+oxidize it to co2
+now i think it's useful if we compare
+
+ align:start position:0%
+now i think it's useful if we compare
+ 
+
+ align:start position:0%
+now i think it's useful if we compare
+the output of what we can get from
+
+ align:start position:0%
+the output of what we can get from
+ 
+
+ align:start position:0%
+the output of what we can get from
+glucose oxidation to co2 carbohydrate
+
+ align:start position:0%
+glucose oxidation to co2 carbohydrate
+ 
+
+ align:start position:0%
+glucose oxidation to co2 carbohydrate
+oxidation to co2
+
+ align:start position:0%
+oxidation to co2
+ 
+
+ align:start position:0%
+oxidation to co2
+to what we can get if we start with a
+
+ align:start position:0%
+to what we can get if we start with a
+ 
+
+ align:start position:0%
+to what we can get if we start with a
+fatty acid
+
+ align:start position:0%
+fatty acid
+ 
+
+ align:start position:0%
+fatty acid
+and oxidize it to co2 and sort of
+
+ align:start position:0%
+and oxidize it to co2 and sort of
+ 
+
+ align:start position:0%
+and oxidize it to co2 and sort of
+illustrate
+
+ align:start position:0%
+illustrate
+ 
+
+ align:start position:0%
+illustrate
+that there are more calories in fat than
+
+ align:start position:0%
+that there are more calories in fat than
+ 
+
+ align:start position:0%
+that there are more calories in fat than
+there are
+
+ align:start position:0%
+there are
+ 
+
+ align:start position:0%
+there are
+in sugar and so for this comparison
+
+ align:start position:0%
+in sugar and so for this comparison
+ 
+
+ align:start position:0%
+in sugar and so for this comparison
+we'll start we'll compare glucose
+
+ align:start position:0%
+we'll start we'll compare glucose
+ 
+
+ align:start position:0%
+we'll start we'll compare glucose
+which of course has six carbons
+
+ align:start position:0%
+which of course has six carbons
+ 
+
+ align:start position:0%
+which of course has six carbons
+in it to a
+
+ align:start position:0%
+in it to a
+ 
+
+ align:start position:0%
+in it to a
+six zero fatty acid also six
+
+ align:start position:0%
+six zero fatty acid also six
+ 
+
+ align:start position:0%
+six zero fatty acid also six
+carbons and what do we get if we take
+
+ align:start position:0%
+carbons and what do we get if we take
+ 
+
+ align:start position:0%
+carbons and what do we get if we take
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+less reduced versus more reduced
+
+ align:start position:0%
+less reduced versus more reduced
+ 
+
+ align:start position:0%
+less reduced versus more reduced
+molecule
+
+ align:start position:0%
+molecule
+ 
+
+ align:start position:0%
+molecule
+and fully oxidize it to co2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right well if we start with glucose
+
+ align:start position:0%
+all right well if we start with glucose
+ 
+
+ align:start position:0%
+all right well if we start with glucose
+so if we take that glucose and we run
+
+ align:start position:0%
+so if we take that glucose and we run
+ 
+
+ align:start position:0%
+so if we take that glucose and we run
+glycolysis
+
+ align:start position:0%
+glycolysis
+ 
+
+ align:start position:0%
+glycolysis
+and so take that glucose and turn it
+
+ align:start position:0%
+and so take that glucose and turn it
+ 
+
+ align:start position:0%
+and so take that glucose and turn it
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+two pyruvate molecules of course we get
+
+ align:start position:0%
+two pyruvate molecules of course we get
+ 
+
+ align:start position:0%
+two pyruvate molecules of course we get
+from that
+
+ align:start position:0%
+from that
+ 
+
+ align:start position:0%
+from that
+two atps and two
+
+ align:start position:0%
+two atps and two
+ 
+
+ align:start position:0%
+two atps and two
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+nadhs and then if we take those
+
+ align:start position:0%
+nadhs and then if we take those
+ 
+
+ align:start position:0%
+nadhs and then if we take those
+two pyruvate molecules and turn them
+
+ align:start position:0%
+two pyruvate molecules and turn them
+ 
+
+ align:start position:0%
+two pyruvate molecules and turn them
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+two acetyl coas
+
+ align:start position:0%
+two acetyl coas
+ 
+
+ align:start position:0%
+two acetyl coas
+plus two co2s that's the pyruvate
+
+ align:start position:0%
+plus two co2s that's the pyruvate
+ 
+
+ align:start position:0%
+plus two co2s that's the pyruvate
+dehydrogenase reaction
+
+ align:start position:0%
+dehydrogenase reaction
+ 
+
+ align:start position:0%
+dehydrogenase reaction
+we get two more nadhs
+
+ align:start position:0%
+we get two more nadhs
+ 
+
+ align:start position:0%
+we get two more nadhs
+and then if we take those two acetyl
+
+ align:start position:0%
+and then if we take those two acetyl
+ 
+
+ align:start position:0%
+and then if we take those two acetyl
+coas
+
+ align:start position:0%
+coas
+ 
+
+ align:start position:0%
+coas
+and turn them into four co2s
+
+ align:start position:0%
+and turn them into four co2s
+ 
+
+ align:start position:0%
+and turn them into four co2s
+that's the tca cycle what do we get out
+
+ align:start position:0%
+that's the tca cycle what do we get out
+ 
+
+ align:start position:0%
+that's the tca cycle what do we get out
+we get two
+
+ align:start position:0%
+we get two
+ 
+
+ align:start position:0%
+we get two
+gtp molecules
+
+ align:start position:0%
+gtp molecules
+ 
+
+ align:start position:0%
+gtp molecules
+we get um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two fadh2
+
+ align:start position:0%
+two fadh2
+ 
+
+ align:start position:0%
+two fadh2
+molecules from the succinate
+
+ align:start position:0%
+molecules from the succinate
+ 
+
+ align:start position:0%
+molecules from the succinate
+dehydrogenase step
+
+ align:start position:0%
+dehydrogenase step
+ 
+
+ align:start position:0%
+dehydrogenase step
+and we get two times three equals six
+
+ align:start position:0%
+and we get two times three equals six
+ 
+
+ align:start position:0%
+and we get two times three equals six
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+nadhs and so our
+
+ align:start position:0%
+nadhs and so our
+ 
+
+ align:start position:0%
+nadhs and so our
+total yield is four
+
+ align:start position:0%
+total yield is four
+ 
+
+ align:start position:0%
+total yield is four
+atp equivalents remember the gtps can be
+
+ align:start position:0%
+atp equivalents remember the gtps can be
+ 
+
+ align:start position:0%
+atp equivalents remember the gtps can be
+interconverted with atp
+
+ align:start position:0%
+interconverted with atp
+ 
+
+ align:start position:0%
+interconverted with atp
+two fadh2s
+
+ align:start position:0%
+two fadh2s
+ 
+
+ align:start position:0%
+two fadh2s
+and six
+
+ align:start position:0%
+and six
+ 
+
+ align:start position:0%
+and six
+seven eight nine ten
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nadhs all right what if we start with
+
+ align:start position:0%
+nadhs all right what if we start with
+ 
+
+ align:start position:0%
+nadhs all right what if we start with
+our
+
+ align:start position:0%
+our
+ 
+
+ align:start position:0%
+our
+six zero fatty acid
+
+ align:start position:0%
+six zero fatty acid
+ 
+
+ align:start position:0%
+six zero fatty acid
+well to metabolize
+
+ align:start position:0%
+well to metabolize
+ 
+
+ align:start position:0%
+well to metabolize
+it first we have to take that fatty acid
+
+ align:start position:0%
+it first we have to take that fatty acid
+ 
+
+ align:start position:0%
+it first we have to take that fatty acid
+and we have to make
+
+ align:start position:0%
+and we have to make
+ 
+
+ align:start position:0%
+and we have to make
+our fatty acyl coa that's going to cost
+
+ align:start position:0%
+our fatty acyl coa that's going to cost
+ 
+
+ align:start position:0%
+our fatty acyl coa that's going to cost
+us
+
+ align:start position:0%
+us
+ 
+
+ align:start position:0%
+us
+two atp y2 atp
+
+ align:start position:0%
+two atp y2 atp
+ 
+
+ align:start position:0%
+two atp y2 atp
+because remember when we charge that
+
+ align:start position:0%
+because remember when we charge that
+ 
+
+ align:start position:0%
+because remember when we charge that
+fatty acyl coa
+
+ align:start position:0%
+fatty acyl coa
+ 
+
+ align:start position:0%
+fatty acyl coa
+which is now erased i think yes it is
+
+ align:start position:0%
+which is now erased i think yes it is
+ 
+
+ align:start position:0%
+which is now erased i think yes it is
+um we converted an atp to an amp
+
+ align:start position:0%
+um we converted an atp to an amp
+ 
+
+ align:start position:0%
+um we converted an atp to an amp
+and so that's two atp equivalents to
+
+ align:start position:0%
+and so that's two atp equivalents to
+ 
+
+ align:start position:0%
+and so that's two atp equivalents to
+charge that
+
+ align:start position:0%
+charge that
+ 
+
+ align:start position:0%
+charge that
+fatty acid to a fatty acyl coa
+
+ align:start position:0%
+fatty acid to a fatty acyl coa
+ 
+
+ align:start position:0%
+fatty acid to a fatty acyl coa
+next we take that fatty acyl coa
+
+ align:start position:0%
+next we take that fatty acyl coa
+ 
+
+ align:start position:0%
+next we take that fatty acyl coa
+and we turn it into three
+
+ align:start position:0%
+and we turn it into three
+ 
+
+ align:start position:0%
+and we turn it into three
+acetyl coa molecules via
+
+ align:start position:0%
+acetyl coa molecules via
+ 
+
+ align:start position:0%
+acetyl coa molecules via
+fatty acid oxidation cycle that's
+
+ align:start position:0%
+fatty acid oxidation cycle that's
+ 
+
+ align:start position:0%
+fatty acid oxidation cycle that's
+two trips around to generate
+
+ align:start position:0%
+two trips around to generate
+ 
+
+ align:start position:0%
+two trips around to generate
+the three acetyl coas so that'll give us
+
+ align:start position:0%
+the three acetyl coas so that'll give us
+ 
+
+ align:start position:0%
+the three acetyl coas so that'll give us
+two fadh2s and two
+
+ align:start position:0%
+two fadh2s and two
+ 
+
+ align:start position:0%
+two fadh2s and two
+nadhs all right
+
+ align:start position:0%
+nadhs all right
+ 
+
+ align:start position:0%
+nadhs all right
+and then once we have those three acetyl
+
+ align:start position:0%
+and then once we have those three acetyl
+ 
+
+ align:start position:0%
+and then once we have those three acetyl
+coas
+
+ align:start position:0%
+coas
+ 
+
+ align:start position:0%
+coas
+we can turn them into six co2s in the
+
+ align:start position:0%
+we can turn them into six co2s in the
+ 
+
+ align:start position:0%
+we can turn them into six co2s in the
+tca cycle
+
+ align:start position:0%
+tca cycle
+ 
+
+ align:start position:0%
+tca cycle
+so that's three gtps three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fadh2s and three times three is nine
+
+ align:start position:0%
+fadh2s and three times three is nine
+ 
+
+ align:start position:0%
+fadh2s and three times three is nine
+nadhs for a total
+
+ align:start position:0%
+nadhs for a total
+ 
+
+ align:start position:0%
+nadhs for a total
+yield of three minus two is
+
+ align:start position:0%
+yield of three minus two is
+ 
+
+ align:start position:0%
+yield of three minus two is
+one atp equivalent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eleven sorry
+
+ align:start position:0%
+eleven sorry
+ 
+
+ align:start position:0%
+eleven sorry
+five fadh2
+
+ align:start position:0%
+five fadh2
+ 
+
+ align:start position:0%
+five fadh2
+and 11 nadhs
+
+ align:start position:0%
+and 11 nadhs
+ 
+
+ align:start position:0%
+and 11 nadhs
+all right now
+
+ align:start position:0%
+all right now
+ 
+
+ align:start position:0%
+all right now
+i went through this exercise because
+
+ align:start position:0%
+i went through this exercise because
+ 
+
+ align:start position:0%
+i went through this exercise because
+it's not immediately apparent that the
+
+ align:start position:0%
+it's not immediately apparent that the
+ 
+
+ align:start position:0%
+it's not immediately apparent that the
+yield of fatty acid oxidation
+
+ align:start position:0%
+yield of fatty acid oxidation
+ 
+
+ align:start position:0%
+yield of fatty acid oxidation
+gives you more energy from full
+
+ align:start position:0%
+gives you more energy from full
+ 
+
+ align:start position:0%
+gives you more energy from full
+oxidation
+
+ align:start position:0%
+oxidation
+ 
+
+ align:start position:0%
+oxidation
+than oxidizing the equivalent
+
+ align:start position:0%
+than oxidizing the equivalent
+ 
+
+ align:start position:0%
+than oxidizing the equivalent
+carbohydrate
+
+ align:start position:0%
+carbohydrate
+ 
+
+ align:start position:0%
+carbohydrate
+at least in terms of atp you get four
+
+ align:start position:0%
+at least in terms of atp you get four
+ 
+
+ align:start position:0%
+at least in terms of atp you get four
+atps directly from
+
+ align:start position:0%
+atps directly from
+ 
+
+ align:start position:0%
+atps directly from
+full oxidation of glucose whereas you
+
+ align:start position:0%
+full oxidation of glucose whereas you
+ 
+
+ align:start position:0%
+full oxidation of glucose whereas you
+only get one
+
+ align:start position:0%
+only get one
+ 
+
+ align:start position:0%
+only get one
+atp equivalent directly from the
+
+ align:start position:0%
+atp equivalent directly from the
+ 
+
+ align:start position:0%
+atp equivalent directly from the
+complete oxidation
+
+ align:start position:0%
+complete oxidation
+ 
+
+ align:start position:0%
+complete oxidation
+of this six carbon fatty acid
+
+ align:start position:0%
+of this six carbon fatty acid
+ 
+
+ align:start position:0%
+of this six carbon fatty acid
+coa now i say this because
+
+ align:start position:0%
+coa now i say this because
+ 
+
+ align:start position:0%
+coa now i say this because
+most of the energy if you will that's
+
+ align:start position:0%
+most of the energy if you will that's
+ 
+
+ align:start position:0%
+most of the energy if you will that's
+released
+
+ align:start position:0%
+released
+ 
+
+ align:start position:0%
+released
+from oxidation of fat and sugar isn't
+
+ align:start position:0%
+from oxidation of fat and sugar isn't
+ 
+
+ align:start position:0%
+from oxidation of fat and sugar isn't
+actually directly producing
+
+ align:start position:0%
+actually directly producing
+ 
+
+ align:start position:0%
+actually directly producing
+atp it's actually being used to charge
+
+ align:start position:0%
+atp it's actually being used to charge
+ 
+
+ align:start position:0%
+atp it's actually being used to charge
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+this nadh
+
+ align:start position:0%
+this nadh
+ 
+
+ align:start position:0%
+this nadh
+nad plus or fadh2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fad ratios in the cell
+
+ align:start position:0%
+fad ratios in the cell
+ 
+
+ align:start position:0%
+fad ratios in the cell
+which we will see is
+
+ align:start position:0%
+which we will see is
+ 
+
+ align:start position:0%
+which we will see is
+also a lot of energy because those
+
+ align:start position:0%
+also a lot of energy because those
+ 
+
+ align:start position:0%
+also a lot of energy because those
+electrons can be transferred
+
+ align:start position:0%
+electrons can be transferred
+ 
+
+ align:start position:0%
+electrons can be transferred
+to oxygen and be used to do other work
+
+ align:start position:0%
+to oxygen and be used to do other work
+ 
+
+ align:start position:0%
+to oxygen and be used to do other work
+down the road now
+
+ align:start position:0%
+down the road now
+ 
+
+ align:start position:0%
+down the road now
+your book will tell you that each of
+
+ align:start position:0%
+your book will tell you that each of
+ 
+
+ align:start position:0%
+your book will tell you that each of
+these nadhs or fadh2s
+
+ align:start position:0%
+these nadhs or fadh2s
+ 
+
+ align:start position:0%
+these nadhs or fadh2s
+are worth on the order of one to three
+
+ align:start position:0%
+are worth on the order of one to three
+ 
+
+ align:start position:0%
+are worth on the order of one to three
+atp
+
+ align:start position:0%
+atp
+ 
+
+ align:start position:0%
+atp
+and i guess this kind of fits
+
+ align:start position:0%
+and i guess this kind of fits
+ 
+
+ align:start position:0%
+and i guess this kind of fits
+intuitively what you might guess based
+
+ align:start position:0%
+intuitively what you might guess based
+ 
+
+ align:start position:0%
+intuitively what you might guess based
+on the thermodynamics of the gap dh
+
+ align:start position:0%
+on the thermodynamics of the gap dh
+ 
+
+ align:start position:0%
+on the thermodynamics of the gap dh
+reaction so if you go back to that
+
+ align:start position:0%
+reaction so if you go back to that
+ 
+
+ align:start position:0%
+reaction so if you go back to that
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+our oxidative phosphorylation we
+
+ align:start position:0%
+our oxidative phosphorylation we
+ 
+
+ align:start position:0%
+our oxidative phosphorylation we
+described at gap dh
+
+ align:start position:0%
+described at gap dh
+ 
+
+ align:start position:0%
+described at gap dh
+roughly generated an atp
+
+ align:start position:0%
+roughly generated an atp
+ 
+
+ align:start position:0%
+roughly generated an atp
+okay and so even if
+
+ align:start position:0%
+okay and so even if
+ 
+
+ align:start position:0%
+okay and so even if
+we say one atp equals an fadh2 or an
+
+ align:start position:0%
+we say one atp equals an fadh2 or an
+ 
+
+ align:start position:0%
+we say one atp equals an fadh2 or an
+nadh which
+
+ align:start position:0%
+nadh which
+ 
+
+ align:start position:0%
+nadh which
+of course there's not a direct
+
+ align:start position:0%
+of course there's not a direct
+ 
+
+ align:start position:0%
+of course there's not a direct
+relationship to that
+
+ align:start position:0%
+relationship to that
+ 
+
+ align:start position:0%
+relationship to that
+you can still even with that say that
+
+ align:start position:0%
+you can still even with that say that
+ 
+
+ align:start position:0%
+you can still even with that say that
+our fatty acid oxidation if we add up
+
+ align:start position:0%
+our fatty acid oxidation if we add up
+ 
+
+ align:start position:0%
+our fatty acid oxidation if we add up
+all these numbers
+
+ align:start position:0%
+all these numbers
+ 
+
+ align:start position:0%
+all these numbers
+we would get you know 17
+
+ align:start position:0%
+we would get you know 17
+ 
+
+ align:start position:0%
+we would get you know 17
+whereas if we add up all these numbers
+
+ align:start position:0%
+whereas if we add up all these numbers
+ 
+
+ align:start position:0%
+whereas if we add up all these numbers
+we get 16.
+
+ align:start position:0%
+we get 16.
+ 
+
+ align:start position:0%
+we get 16.
+so i guess that says that there's more
+
+ align:start position:0%
+so i guess that says that there's more
+ 
+
+ align:start position:0%
+so i guess that says that there's more
+coming from fatty acid oxidation than
+
+ align:start position:0%
+coming from fatty acid oxidation than
+ 
+
+ align:start position:0%
+coming from fatty acid oxidation than
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+uh complete glucose oxidation but you
+
+ align:start position:0%
+uh complete glucose oxidation but you
+ 
+
+ align:start position:0%
+uh complete glucose oxidation but you
+probably also learned in high school or
+
+ align:start position:0%
+probably also learned in high school or
+ 
+
+ align:start position:0%
+probably also learned in high school or
+somewhere else that
+
+ align:start position:0%
+somewhere else that
+ 
+
+ align:start position:0%
+somewhere else that
+nadh gives you more atp than fadh2
+
+ align:start position:0%
+nadh gives you more atp than fadh2
+ 
+
+ align:start position:0%
+nadh gives you more atp than fadh2
+that's true our goal is to understand
+
+ align:start position:0%
+that's true our goal is to understand
+ 
+
+ align:start position:0%
+that's true our goal is to understand
+why that's the case
+
+ align:start position:0%
+why that's the case
+ 
+
+ align:start position:0%
+why that's the case
+and so you'll actually those numbers
+
+ align:start position:0%
+and so you'll actually those numbers
+ 
+
+ align:start position:0%
+and so you'll actually those numbers
+will only get better
+
+ align:start position:0%
+will only get better
+ 
+
+ align:start position:0%
+will only get better
+for fatty acid oxidation in terms of atp
+
+ align:start position:0%
+for fatty acid oxidation in terms of atp
+ 
+
+ align:start position:0%
+for fatty acid oxidation in terms of atp
+equivalence
+
+ align:start position:0%
+equivalence
+ 
+
+ align:start position:0%
+equivalence
+when we can describe how to do those
+
+ align:start position:0%
+when we can describe how to do those
+ 
+
+ align:start position:0%
+when we can describe how to do those
+conversions however to really appreciate
+
+ align:start position:0%
+conversions however to really appreciate
+ 
+
+ align:start position:0%
+conversions however to really appreciate
+how these electron carriers equal
+
+ align:start position:0%
+how these electron carriers equal
+ 
+
+ align:start position:0%
+how these electron carriers equal
+energy and equal biological energy we
+
+ align:start position:0%
+energy and equal biological energy we
+ 
+
+ align:start position:0%
+energy and equal biological energy we
+really need to go back
+
+ align:start position:0%
+really need to go back
+ 
+
+ align:start position:0%
+really need to go back
+and revisit some concepts
+
+ align:start position:0%
+and revisit some concepts
+ 
+
+ align:start position:0%
+and revisit some concepts
+in bioenergetics and thermodynamics
+
+ align:start position:0%
+in bioenergetics and thermodynamics
+ 
+
+ align:start position:0%
+in bioenergetics and thermodynamics
+to really understand what biological
+
+ align:start position:0%
+to really understand what biological
+ 
+
+ align:start position:0%
+to really understand what biological
+energy is
+
+ align:start position:0%
+energy is
+ 
+
+ align:start position:0%
+energy is
+and that'll also help us understand
+
+ align:start position:0%
+and that'll also help us understand
+ 
+
+ align:start position:0%
+and that'll also help us understand
+mitochondrial oxidative phosphorylation
+
+ align:start position:0%
+mitochondrial oxidative phosphorylation
+ 
+
+ align:start position:0%
+mitochondrial oxidative phosphorylation
+which is really the process that allows
+
+ align:start position:0%
+which is really the process that allows
+ 
+
+ align:start position:0%
+which is really the process that allows
+us to
+
+ align:start position:0%
+us to
+ 
+
+ align:start position:0%
+us to
+interconvert these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+electron carriers and their ability to
+
+ align:start position:0%
+electron carriers and their ability to
+ 
+
+ align:start position:0%
+electron carriers and their ability to
+transfer electrons to oxygen
+
+ align:start position:0%
+transfer electrons to oxygen
+ 
+
+ align:start position:0%
+transfer electrons to oxygen
+as a way to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generate favorably synthesized atp
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so hopefully you will remember
+
+ align:start position:0%
+okay so hopefully you will remember
+ 
+
+ align:start position:0%
+okay so hopefully you will remember
+from our previous lectures that for any
+
+ align:start position:0%
+from our previous lectures that for any
+ 
+
+ align:start position:0%
+from our previous lectures that for any
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+any pathway any process to occur
+
+ align:start position:0%
+any pathway any process to occur
+ 
+
+ align:start position:0%
+any pathway any process to occur
+it has to be thermodynamically favorable
+
+ align:start position:0%
+it has to be thermodynamically favorable
+ 
+
+ align:start position:0%
+it has to be thermodynamically favorable
+that is delta g has to be less than zero
+
+ align:start position:0%
+that is delta g has to be less than zero
+ 
+
+ align:start position:0%
+that is delta g has to be less than zero
+and remember atp to adp was useful
+
+ align:start position:0%
+and remember atp to adp was useful
+ 
+
+ align:start position:0%
+and remember atp to adp was useful
+because that reaction is very favorable
+
+ align:start position:0%
+because that reaction is very favorable
+ 
+
+ align:start position:0%
+because that reaction is very favorable
+and so we could couple
+
+ align:start position:0%
+and so we could couple
+ 
+
+ align:start position:0%
+and so we could couple
+atp to adp conversion to otherwise
+
+ align:start position:0%
+atp to adp conversion to otherwise
+ 
+
+ align:start position:0%
+atp to adp conversion to otherwise
+unfavorable reactions
+
+ align:start position:0%
+unfavorable reactions
+ 
+
+ align:start position:0%
+unfavorable reactions
+and that is what allowed us to have atp
+
+ align:start position:0%
+and that is what allowed us to have atp
+ 
+
+ align:start position:0%
+and that is what allowed us to have atp
+be useful
+
+ align:start position:0%
+be useful
+ 
+
+ align:start position:0%
+be useful
+and it was useful because delta g equals
+
+ align:start position:0%
+and it was useful because delta g equals
+ 
+
+ align:start position:0%
+and it was useful because delta g equals
+delta g
+
+ align:start position:0%
+delta g
+ 
+
+ align:start position:0%
+delta g
+naught prime plus rt times the log
+
+ align:start position:0%
+naught prime plus rt times the log
+ 
+
+ align:start position:0%
+naught prime plus rt times the log
+of the products of the reaction
+
+ align:start position:0%
+of the products of the reaction
+ 
+
+ align:start position:0%
+of the products of the reaction
+over the reactants of the reaction
+
+ align:start position:0%
+over the reactants of the reaction
+ 
+
+ align:start position:0%
+over the reactants of the reaction
+and so if adp is a product
+
+ align:start position:0%
+and so if adp is a product
+ 
+
+ align:start position:0%
+and so if adp is a product
+an atp is a reactant it was actually
+
+ align:start position:0%
+an atp is a reactant it was actually
+ 
+
+ align:start position:0%
+an atp is a reactant it was actually
+that atp adp ratio
+
+ align:start position:0%
+that atp adp ratio
+ 
+
+ align:start position:0%
+that atp adp ratio
+that was providing the energy if you
+
+ align:start position:0%
+that was providing the energy if you
+ 
+
+ align:start position:0%
+that was providing the energy if you
+will to
+
+ align:start position:0%
+will to
+ 
+
+ align:start position:0%
+will to
+drive the reaction
+
+ align:start position:0%
+drive the reaction
+ 
+
+ align:start position:0%
+drive the reaction
+all right this was also
+
+ align:start position:0%
+all right this was also
+ 
+
+ align:start position:0%
+all right this was also
+if you recall why we described that
+
+ align:start position:0%
+if you recall why we described that
+ 
+
+ align:start position:0%
+if you recall why we described that
+oxidation of reduced carbon
+
+ align:start position:0%
+oxidation of reduced carbon
+ 
+
+ align:start position:0%
+oxidation of reduced carbon
+because it was favorable was able to be
+
+ align:start position:0%
+because it was favorable was able to be
+ 
+
+ align:start position:0%
+because it was favorable was able to be
+coupled to reactions that keep this atp
+
+ align:start position:0%
+coupled to reactions that keep this atp
+ 
+
+ align:start position:0%
+coupled to reactions that keep this atp
+adp ratio high
+
+ align:start position:0%
+adp ratio high
+ 
+
+ align:start position:0%
+adp ratio high
+so that that high ratio could then
+
+ align:start position:0%
+so that that high ratio could then
+ 
+
+ align:start position:0%
+so that that high ratio could then
+support
+
+ align:start position:0%
+support
+ 
+
+ align:start position:0%
+support
+otherwise unfavorable reactions
+
+ align:start position:0%
+otherwise unfavorable reactions
+ 
+
+ align:start position:0%
+otherwise unfavorable reactions
+but now you hopefully appreciate that in
+
+ align:start position:0%
+but now you hopefully appreciate that in
+ 
+
+ align:start position:0%
+but now you hopefully appreciate that in
+reality
+
+ align:start position:0%
+reality
+ 
+
+ align:start position:0%
+reality
+most of the energy
+
+ align:start position:0%
+most of the energy
+ 
+
+ align:start position:0%
+most of the energy
+from carbon oxidation is not directly
+
+ align:start position:0%
+from carbon oxidation is not directly
+ 
+
+ align:start position:0%
+from carbon oxidation is not directly
+captured as atp
+
+ align:start position:0%
+captured as atp
+ 
+
+ align:start position:0%
+captured as atp
+it's being used to charge up these other
+
+ align:start position:0%
+it's being used to charge up these other
+ 
+
+ align:start position:0%
+it's being used to charge up these other
+ratios
+
+ align:start position:0%
+ratios
+ 
+
+ align:start position:0%
+ratios
+nad nadh fad
+
+ align:start position:0%
+nad nadh fad
+ 
+
+ align:start position:0%
+nad nadh fad
+and the energetics of doing that follow
+
+ align:start position:0%
+and the energetics of doing that follow
+ 
+
+ align:start position:0%
+and the energetics of doing that follow
+exactly the same rules as atp or really
+
+ align:start position:0%
+exactly the same rules as atp or really
+ 
+
+ align:start position:0%
+exactly the same rules as atp or really
+any other reaction
+
+ align:start position:0%
+any other reaction
+ 
+
+ align:start position:0%
+any other reaction
+okay and effectively it's the transfer
+
+ align:start position:0%
+okay and effectively it's the transfer
+ 
+
+ align:start position:0%
+okay and effectively it's the transfer
+of electrons
+
+ align:start position:0%
+of electrons
+ 
+
+ align:start position:0%
+of electrons
+that is favorable or not that really
+
+ align:start position:0%
+that is favorable or not that really
+ 
+
+ align:start position:0%
+that is favorable or not that really
+is going on here
+
+ align:start position:0%
+is going on here
+ 
+
+ align:start position:0%
+is going on here
+just like we discussed for
+
+ align:start position:0%
+just like we discussed for
+ 
+
+ align:start position:0%
+just like we discussed for
+atp to adp and so we can couple other
+
+ align:start position:0%
+atp to adp and so we can couple other
+ 
+
+ align:start position:0%
+atp to adp and so we can couple other
+reactions to those ratios as a way to
+
+ align:start position:0%
+reactions to those ratios as a way to
+ 
+
+ align:start position:0%
+reactions to those ratios as a way to
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+other reactions possible
+
+ align:start position:0%
+other reactions possible
+ 
+
+ align:start position:0%
+other reactions possible
+now ultimately it turns out that these
+
+ align:start position:0%
+now ultimately it turns out that these
+ 
+
+ align:start position:0%
+now ultimately it turns out that these
+things these redox ratios are more
+
+ align:start position:0%
+things these redox ratios are more
+ 
+
+ align:start position:0%
+things these redox ratios are more
+useful than atp
+
+ align:start position:0%
+useful than atp
+ 
+
+ align:start position:0%
+useful than atp
+because these electron transfers
+
+ align:start position:0%
+because these electron transfers
+ 
+
+ align:start position:0%
+because these electron transfers
+favorable electron transfers
+
+ align:start position:0%
+favorable electron transfers
+ 
+
+ align:start position:0%
+favorable electron transfers
+remember biological energy is all about
+
+ align:start position:0%
+remember biological energy is all about
+ 
+
+ align:start position:0%
+remember biological energy is all about
+oxidation and reduction
+
+ align:start position:0%
+oxidation and reduction
+ 
+
+ align:start position:0%
+oxidation and reduction
+can be used to drive atp we'll see that
+
+ align:start position:0%
+can be used to drive atp we'll see that
+ 
+
+ align:start position:0%
+can be used to drive atp we'll see that
+when we described how oxfos
+
+ align:start position:0%
+when we described how oxfos
+ 
+
+ align:start position:0%
+when we described how oxfos
+in the mitochondria really works but it
+
+ align:start position:0%
+in the mitochondria really works but it
+ 
+
+ align:start position:0%
+in the mitochondria really works but it
+can be used for other things as well
+
+ align:start position:0%
+can be used for other things as well
+ 
+
+ align:start position:0%
+can be used for other things as well
+we'll see we can use it to make heat we
+
+ align:start position:0%
+we'll see we can use it to make heat we
+ 
+
+ align:start position:0%
+we'll see we can use it to make heat we
+can do it other work like move ions etc
+
+ align:start position:0%
+can do it other work like move ions etc
+ 
+
+ align:start position:0%
+can do it other work like move ions etc
+and so we can even make glucose right
+
+ align:start position:0%
+and so we can even make glucose right
+ 
+
+ align:start position:0%
+and so we can even make glucose right
+gluconeogenesis we needed a source of
+
+ align:start position:0%
+gluconeogenesis we needed a source of
+ 
+
+ align:start position:0%
+gluconeogenesis we needed a source of
+nadh
+
+ align:start position:0%
+nadh
+ 
+
+ align:start position:0%
+nadh
+and so ultimately all biological energy
+
+ align:start position:0%
+and so ultimately all biological energy
+ 
+
+ align:start position:0%
+and so ultimately all biological energy
+of course has to come from the sun and
+
+ align:start position:0%
+of course has to come from the sun and
+ 
+
+ align:start position:0%
+of course has to come from the sun and
+photosynthesis
+
+ align:start position:0%
+photosynthesis
+ 
+
+ align:start position:0%
+photosynthesis
+also is about capturing solar energy as
+
+ align:start position:0%
+also is about capturing solar energy as
+ 
+
+ align:start position:0%
+also is about capturing solar energy as
+these oxidation and reduction pairs
+
+ align:start position:0%
+these oxidation and reduction pairs
+ 
+
+ align:start position:0%
+these oxidation and reduction pairs
+and so if we
+
+ align:start position:0%
+and so if we
+ 
+
+ align:start position:0%
+and so if we
+appreciate this what we realize is that
+
+ align:start position:0%
+appreciate this what we realize is that
+ 
+
+ align:start position:0%
+appreciate this what we realize is that
+it's really these transfers of electrons
+
+ align:start position:0%
+it's really these transfers of electrons
+ 
+
+ align:start position:0%
+it's really these transfers of electrons
+remember there's no free electrons in
+
+ align:start position:0%
+remember there's no free electrons in
+ 
+
+ align:start position:0%
+remember there's no free electrons in
+biology
+
+ align:start position:0%
+biology
+ 
+
+ align:start position:0%
+biology
+and so it's really coupling oxidation
+
+ align:start position:0%
+and so it's really coupling oxidation
+ 
+
+ align:start position:0%
+and so it's really coupling oxidation
+and reduction reactions that are
+
+ align:start position:0%
+and reduction reactions that are
+ 
+
+ align:start position:0%
+and reduction reactions that are
+favorable
+
+ align:start position:0%
+favorable
+ 
+
+ align:start position:0%
+favorable
+that ends up being how bioenergetics
+
+ align:start position:0%
+that ends up being how bioenergetics
+ 
+
+ align:start position:0%
+that ends up being how bioenergetics
+largely works now i like to be explicit
+
+ align:start position:0%
+largely works now i like to be explicit
+ 
+
+ align:start position:0%
+largely works now i like to be explicit
+about this because sometimes people get
+
+ align:start position:0%
+about this because sometimes people get
+ 
+
+ align:start position:0%
+about this because sometimes people get
+confused by oxidation and reduction
+
+ align:start position:0%
+confused by oxidation and reduction
+ 
+
+ align:start position:0%
+confused by oxidation and reduction
+reactions and focus on
+
+ align:start position:0%
+reactions and focus on
+ 
+
+ align:start position:0%
+reactions and focus on
+charge and i just want to point out
+
+ align:start position:0%
+charge and i just want to point out
+ 
+
+ align:start position:0%
+charge and i just want to point out
+oxidation and reduction reactions are
+
+ align:start position:0%
+oxidation and reduction reactions are
+ 
+
+ align:start position:0%
+oxidation and reduction reactions are
+really
+
+ align:start position:0%
+really
+ 
+
+ align:start position:0%
+really
+moving electrons and this is
+
+ align:start position:0%
+moving electrons and this is
+ 
+
+ align:start position:0%
+moving electrons and this is
+irrelevant of
+
+ align:start position:0%
+irrelevant of
+ 
+
+ align:start position:0%
+irrelevant of
+charge okay so i add an electron to an
+
+ align:start position:0%
+charge okay so i add an electron to an
+ 
+
+ align:start position:0%
+charge okay so i add an electron to an
+uncharged molecule i get a negatively
+
+ align:start position:0%
+uncharged molecule i get a negatively
+ 
+
+ align:start position:0%
+uncharged molecule i get a negatively
+charged molecule add it to a positively
+
+ align:start position:0%
+charged molecule add it to a positively
+ 
+
+ align:start position:0%
+charged molecule add it to a positively
+charged molecule get a neutral molecule
+
+ align:start position:0%
+charged molecule get a neutral molecule
+ 
+
+ align:start position:0%
+charged molecule get a neutral molecule
+add it to a more positively charged
+
+ align:start position:0%
+add it to a more positively charged
+ 
+
+ align:start position:0%
+add it to a more positively charged
+molecule now i have a positively charged
+
+ align:start position:0%
+molecule now i have a positively charged
+ 
+
+ align:start position:0%
+molecule now i have a positively charged
+molecule it's adding these electrons
+
+ align:start position:0%
+molecule it's adding these electrons
+ 
+
+ align:start position:0%
+molecule it's adding these electrons
+each of these are reduction reactions
+
+ align:start position:0%
+each of these are reduction reactions
+ 
+
+ align:start position:0%
+each of these are reduction reactions
+in that direction they would be
+
+ align:start position:0%
+in that direction they would be
+ 
+
+ align:start position:0%
+in that direction they would be
+oxidation reactions
+
+ align:start position:0%
+oxidation reactions
+ 
+
+ align:start position:0%
+oxidation reactions
+and so nad plus plus
+
+ align:start position:0%
+and so nad plus plus
+ 
+
+ align:start position:0%
+and so nad plus plus
+two electrons going to nadh
+
+ align:start position:0%
+two electrons going to nadh
+ 
+
+ align:start position:0%
+two electrons going to nadh
+fad plus two electrons
+
+ align:start position:0%
+fad plus two electrons
+ 
+
+ align:start position:0%
+fad plus two electrons
+going to fad h2
+
+ align:start position:0%
+going to fad h2
+ 
+
+ align:start position:0%
+going to fad h2
+all reductions in this direction all
+
+ align:start position:0%
+all reductions in this direction all
+ 
+
+ align:start position:0%
+all reductions in this direction all
+oxidations
+
+ align:start position:0%
+oxidations
+ 
+
+ align:start position:0%
+oxidations
+in that direction now because there's
+
+ align:start position:0%
+in that direction now because there's
+ 
+
+ align:start position:0%
+in that direction now because there's
+not free electrons these react
+
+ align:start position:0%
+not free electrons these react
+ 
+
+ align:start position:0%
+not free electrons these react
+these reactions have to happen in pairs
+
+ align:start position:0%
+these reactions have to happen in pairs
+ 
+
+ align:start position:0%
+these reactions have to happen in pairs
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+if we consider a pair here's lactate
+
+ align:start position:0%
+if we consider a pair here's lactate
+ 
+
+ align:start position:0%
+if we consider a pair here's lactate
+inner conversion with pyruvate
+
+ align:start position:0%
+inner conversion with pyruvate
+ 
+
+ align:start position:0%
+inner conversion with pyruvate
+so alcohol and lactate to the
+
+ align:start position:0%
+so alcohol and lactate to the
+ 
+
+ align:start position:0%
+so alcohol and lactate to the
+ketone and pyruvate this direction is an
+
+ align:start position:0%
+ketone and pyruvate this direction is an
+ 
+
+ align:start position:0%
+ketone and pyruvate this direction is an
+oxidation
+
+ align:start position:0%
+oxidation
+ 
+
+ align:start position:0%
+oxidation
+that means the electrons have to go
+
+ align:start position:0%
+that means the electrons have to go
+ 
+
+ align:start position:0%
+that means the electrons have to go
+somewhere
+
+ align:start position:0%
+somewhere
+ 
+
+ align:start position:0%
+somewhere
+nad plus to nadh
+
+ align:start position:0%
+nad plus to nadh
+ 
+
+ align:start position:0%
+nad plus to nadh
+this is a reduction we go from pyruvate
+
+ align:start position:0%
+this is a reduction we go from pyruvate
+ 
+
+ align:start position:0%
+this is a reduction we go from pyruvate
+to lactate
+
+ align:start position:0%
+to lactate
+ 
+
+ align:start position:0%
+to lactate
+that's a reduction we can re-oxidize
+
+ align:start position:0%
+that's a reduction we can re-oxidize
+ 
+
+ align:start position:0%
+that's a reduction we can re-oxidize
+nadh
+
+ align:start position:0%
+nadh
+ 
+
+ align:start position:0%
+nadh
+back to nad plus of course you'll
+
+ align:start position:0%
+back to nad plus of course you'll
+ 
+
+ align:start position:0%
+back to nad plus of course you'll
+remember from
+
+ align:start position:0%
+remember from
+ 
+
+ align:start position:0%
+remember from
+glycolysis fermentation this inner
+
+ align:start position:0%
+glycolysis fermentation this inner
+ 
+
+ align:start position:0%
+glycolysis fermentation this inner
+conversion is
+
+ align:start position:0%
+conversion is
+ 
+
+ align:start position:0%
+conversion is
+catalyzed by ldh and effectively
+
+ align:start position:0%
+catalyzed by ldh and effectively
+ 
+
+ align:start position:0%
+catalyzed by ldh and effectively
+if you're going to use lactate for
+
+ align:start position:0%
+if you're going to use lactate for
+ 
+
+ align:start position:0%
+if you're going to use lactate for
+energy so we oxidize the lactate
+
+ align:start position:0%
+energy so we oxidize the lactate
+ 
+
+ align:start position:0%
+energy so we oxidize the lactate
+generate nadh we're going to use it for
+
+ align:start position:0%
+generate nadh we're going to use it for
+ 
+
+ align:start position:0%
+generate nadh we're going to use it for
+fermentation
+
+ align:start position:0%
+fermentation
+ 
+
+ align:start position:0%
+fermentation
+we produce lactate re-oxidize the nadh
+
+ align:start position:0%
+we produce lactate re-oxidize the nadh
+ 
+
+ align:start position:0%
+we produce lactate re-oxidize the nadh
+nadh back to nad plus
+
+ align:start position:0%
+nadh back to nad plus
+ 
+
+ align:start position:0%
+nadh back to nad plus
+how does ldh know which direction to go
+
+ align:start position:0%
+how does ldh know which direction to go
+ 
+
+ align:start position:0%
+how does ldh know which direction to go
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+how does any reaction any pathway know
+
+ align:start position:0%
+how does any reaction any pathway know
+ 
+
+ align:start position:0%
+how does any reaction any pathway know
+which direction to go in
+
+ align:start position:0%
+which direction to go in
+ 
+
+ align:start position:0%
+which direction to go in
+it's delta g delta g equals delta g
+
+ align:start position:0%
+it's delta g delta g equals delta g
+ 
+
+ align:start position:0%
+it's delta g delta g equals delta g
+naught prime plus rt
+
+ align:start position:0%
+naught prime plus rt
+ 
+
+ align:start position:0%
+naught prime plus rt
+times the log of in this case the
+
+ align:start position:0%
+times the log of in this case the
+ 
+
+ align:start position:0%
+times the log of in this case the
+pyruvate lactate ratio
+
+ align:start position:0%
+pyruvate lactate ratio
+ 
+
+ align:start position:0%
+pyruvate lactate ratio
+times the nadh nad plus ratio
+
+ align:start position:0%
+times the nadh nad plus ratio
+ 
+
+ align:start position:0%
+times the nadh nad plus ratio
+and so how oxidized or reduced
+
+ align:start position:0%
+and so how oxidized or reduced
+ 
+
+ align:start position:0%
+and so how oxidized or reduced
+nad plus nadh is will determine
+
+ align:start position:0%
+nad plus nadh is will determine
+ 
+
+ align:start position:0%
+nad plus nadh is will determine
+how oxidized and reduced the pyruvate
+
+ align:start position:0%
+how oxidized and reduced the pyruvate
+ 
+
+ align:start position:0%
+how oxidized and reduced the pyruvate
+lactate
+
+ align:start position:0%
+lactate
+ 
+
+ align:start position:0%
+lactate
+ratio is in other words
+
+ align:start position:0%
+ratio is in other words
+ 
+
+ align:start position:0%
+ratio is in other words
+this must be true for absolutely any
+
+ align:start position:0%
+this must be true for absolutely any
+ 
+
+ align:start position:0%
+this must be true for absolutely any
+redox pair
+
+ align:start position:0%
+redox pair
+ 
+
+ align:start position:0%
+redox pair
+and in general remember carbon oxidation
+
+ align:start position:0%
+and in general remember carbon oxidation
+ 
+
+ align:start position:0%
+and in general remember carbon oxidation
+is favorable
+
+ align:start position:0%
+is favorable
+ 
+
+ align:start position:0%
+is favorable
+and that's because oxidizing carbon
+
+ align:start position:0%
+and that's because oxidizing carbon
+ 
+
+ align:start position:0%
+and that's because oxidizing carbon
+to give those electrons to something
+
+ align:start position:0%
+to give those electrons to something
+ 
+
+ align:start position:0%
+to give those electrons to something
+downstream ultimately oxygen
+
+ align:start position:0%
+downstream ultimately oxygen
+ 
+
+ align:start position:0%
+downstream ultimately oxygen
+is favorable that's really what's
+
+ align:start position:0%
+is favorable that's really what's
+ 
+
+ align:start position:0%
+is favorable that's really what's
+driving
+
+ align:start position:0%
+driving
+ 
+
+ align:start position:0%
+driving
+each of these pathways
+
+ align:start position:0%
+each of these pathways
+ 
+
+ align:start position:0%
+each of these pathways
+now how favorable any of this is of
+
+ align:start position:0%
+now how favorable any of this is of
+ 
+
+ align:start position:0%
+now how favorable any of this is of
+course can be quantified
+
+ align:start position:0%
+course can be quantified
+ 
+
+ align:start position:0%
+course can be quantified
+and if we want to know this for this
+
+ align:start position:0%
+and if we want to know this for this
+ 
+
+ align:start position:0%
+and if we want to know this for this
+redox pair or any redox pair
+
+ align:start position:0%
+redox pair or any redox pair
+ 
+
+ align:start position:0%
+redox pair or any redox pair
+of course this is related to some
+
+ align:start position:0%
+of course this is related to some
+ 
+
+ align:start position:0%
+of course this is related to some
+equilibrium constant and we've already
+
+ align:start position:0%
+equilibrium constant and we've already
+ 
+
+ align:start position:0%
+equilibrium constant and we've already
+discussed that we can
+
+ align:start position:0%
+discussed that we can
+ 
+
+ align:start position:0%
+discussed that we can
+have this term delta g not prime that is
+
+ align:start position:0%
+have this term delta g not prime that is
+ 
+
+ align:start position:0%
+have this term delta g not prime that is
+relevant to the equilibrium constant but
+
+ align:start position:0%
+relevant to the equilibrium constant but
+ 
+
+ align:start position:0%
+relevant to the equilibrium constant but
+it's still because delta g determines
+
+ align:start position:0%
+it's still because delta g determines
+ 
+
+ align:start position:0%
+it's still because delta g determines
+what happens it's still that equilibrium
+
+ align:start position:0%
+what happens it's still that equilibrium
+ 
+
+ align:start position:0%
+what happens it's still that equilibrium
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+plus the ratios of the reactants and
+
+ align:start position:0%
+plus the ratios of the reactants and
+ 
+
+ align:start position:0%
+plus the ratios of the reactants and
+products that will really determine if
+
+ align:start position:0%
+products that will really determine if
+ 
+
+ align:start position:0%
+products that will really determine if
+the reaction happens
+
+ align:start position:0%
+the reaction happens
+ 
+
+ align:start position:0%
+the reaction happens
+however it turns out it's useful to
+
+ align:start position:0%
+however it turns out it's useful to
+ 
+
+ align:start position:0%
+however it turns out it's useful to
+think about
+
+ align:start position:0%
+think about
+ 
+
+ align:start position:0%
+think about
+when electrons can go to donated or
+
+ align:start position:0%
+when electrons can go to donated or
+ 
+
+ align:start position:0%
+when electrons can go to donated or
+accepted in lots of different
+
+ align:start position:0%
+accepted in lots of different
+ 
+
+ align:start position:0%
+accepted in lots of different
+reactions it's useful to come up with a
+
+ align:start position:0%
+reactions it's useful to come up with a
+ 
+
+ align:start position:0%
+reactions it's useful to come up with a
+term that helps us know
+
+ align:start position:0%
+term that helps us know
+ 
+
+ align:start position:0%
+term that helps us know
+what is the propensity of an individual
+
+ align:start position:0%
+what is the propensity of an individual
+ 
+
+ align:start position:0%
+what is the propensity of an individual
+pair
+
+ align:start position:0%
+pair
+ 
+
+ align:start position:0%
+pair
+to accept or donate an electron in
+
+ align:start position:0%
+to accept or donate an electron in
+ 
+
+ align:start position:0%
+to accept or donate an electron in
+either direction and we have a term
+
+ align:start position:0%
+either direction and we have a term
+ 
+
+ align:start position:0%
+either direction and we have a term
+for this it's denoted e naught prime
+
+ align:start position:0%
+for this it's denoted e naught prime
+ 
+
+ align:start position:0%
+for this it's denoted e naught prime
+which is the standard
+
+ align:start position:0%
+which is the standard
+ 
+
+ align:start position:0%
+which is the standard
+reduction potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that basically describes for a pair of
+
+ align:start position:0%
+that basically describes for a pair of
+ 
+
+ align:start position:0%
+that basically describes for a pair of
+molecules
+
+ align:start position:0%
+molecules
+ 
+
+ align:start position:0%
+molecules
+nad plus nadh pyruvate and lactate
+
+ align:start position:0%
+nad plus nadh pyruvate and lactate
+ 
+
+ align:start position:0%
+nad plus nadh pyruvate and lactate
+in an oxidation or reduction reaction
+
+ align:start position:0%
+in an oxidation or reduction reaction
+ 
+
+ align:start position:0%
+in an oxidation or reduction reaction
+how likely
+
+ align:start position:0%
+how likely
+ 
+
+ align:start position:0%
+how likely
+is it to give up its electrons in one
+
+ align:start position:0%
+is it to give up its electrons in one
+ 
+
+ align:start position:0%
+is it to give up its electrons in one
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+or the other and so the units of this is
+
+ align:start position:0%
+or the other and so the units of this is
+ 
+
+ align:start position:0%
+or the other and so the units of this is
+volts and the standard reduction
+
+ align:start position:0%
+volts and the standard reduction
+ 
+
+ align:start position:0%
+volts and the standard reduction
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+can be calculated as follows and of
+
+ align:start position:0%
+can be calculated as follows and of
+ 
+
+ align:start position:0%
+can be calculated as follows and of
+course it's related to the
+
+ align:start position:0%
+course it's related to the
+ 
+
+ align:start position:0%
+course it's related to the
+equilibrium constant of a
+
+ align:start position:0%
+equilibrium constant of a
+ 
+
+ align:start position:0%
+equilibrium constant of a
+reaction and so the equilibrium constant
+
+ align:start position:0%
+reaction and so the equilibrium constant
+ 
+
+ align:start position:0%
+reaction and so the equilibrium constant
+of a reaction delta g not prime related
+
+ align:start position:0%
+of a reaction delta g not prime related
+ 
+
+ align:start position:0%
+of a reaction delta g not prime related
+to the equilibrium constant
+
+ align:start position:0%
+to the equilibrium constant
+ 
+
+ align:start position:0%
+to the equilibrium constant
+is this formula n is the number of
+
+ align:start position:0%
+is this formula n is the number of
+ 
+
+ align:start position:0%
+is this formula n is the number of
+electrons transferred
+
+ align:start position:0%
+electrons transferred
+ 
+
+ align:start position:0%
+electrons transferred
+f is the faraday constant and delta
+
+ align:start position:0%
+f is the faraday constant and delta
+ 
+
+ align:start position:0%
+f is the faraday constant and delta
+e naught prime is the change
+
+ align:start position:0%
+e naught prime is the change
+ 
+
+ align:start position:0%
+e naught prime is the change
+in standard reduction potential from
+
+ align:start position:0%
+in standard reduction potential from
+ 
+
+ align:start position:0%
+in standard reduction potential from
+election
+
+ align:start position:0%
+election
+ 
+
+ align:start position:0%
+election
+or from electron donation from one pair
+
+ align:start position:0%
+or from electron donation from one pair
+ 
+
+ align:start position:0%
+or from electron donation from one pair
+to the next pair
+
+ align:start position:0%
+to the next pair
+ 
+
+ align:start position:0%
+to the next pair
+all right so if we use our lactate
+
+ align:start position:0%
+all right so if we use our lactate
+ 
+
+ align:start position:0%
+all right so if we use our lactate
+pyruvate example
+
+ align:start position:0%
+pyruvate example
+ 
+
+ align:start position:0%
+pyruvate example
+okay we have
+
+ align:start position:0%
+okay we have
+ 
+
+ align:start position:0%
+okay we have
+lactate going to
+
+ align:start position:0%
+lactate going to
+ 
+
+ align:start position:0%
+lactate going to
+pyruvate plus two electrons
+
+ align:start position:0%
+pyruvate plus two electrons
+ 
+
+ align:start position:0%
+pyruvate plus two electrons
+so that's the electron donor it's being
+
+ align:start position:0%
+so that's the electron donor it's being
+ 
+
+ align:start position:0%
+so that's the electron donor it's being
+oxidized and then you have nad
+
+ align:start position:0%
+oxidized and then you have nad
+ 
+
+ align:start position:0%
+oxidized and then you have nad
+plus plus
+
+ align:start position:0%
+plus plus
+ 
+
+ align:start position:0%
+plus plus
+the electrons going to nadh
+
+ align:start position:0%
+the electrons going to nadh
+ 
+
+ align:start position:0%
+the electrons going to nadh
+it's being reduced two electrons of
+
+ align:start position:0%
+it's being reduced two electrons of
+ 
+
+ align:start position:0%
+it's being reduced two electrons of
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+it's being reduced and so this
+
+ align:start position:0%
+it's being reduced and so this
+ 
+
+ align:start position:0%
+it's being reduced and so this
+has a standard reduction potential
+
+ align:start position:0%
+has a standard reduction potential
+ 
+
+ align:start position:0%
+has a standard reduction potential
+this half reaction has a standard
+
+ align:start position:0%
+this half reaction has a standard
+ 
+
+ align:start position:0%
+this half reaction has a standard
+reduction potential and so the
+
+ align:start position:0%
+reduction potential and so the
+ 
+
+ align:start position:0%
+reduction potential and so the
+difference
+
+ align:start position:0%
+difference
+ 
+
+ align:start position:0%
+difference
+between these standard reduction
+
+ align:start position:0%
+between these standard reduction
+ 
+
+ align:start position:0%
+between these standard reduction
+potentials
+
+ align:start position:0%
+potentials
+ 
+
+ align:start position:0%
+potentials
+that is who receives the electrons
+
+ align:start position:0%
+that is who receives the electrons
+ 
+
+ align:start position:0%
+that is who receives the electrons
+delta e naught prime 2 minus
+
+ align:start position:0%
+delta e naught prime 2 minus
+ 
+
+ align:start position:0%
+delta e naught prime 2 minus
+delta e naught prime 1 gives us
+
+ align:start position:0%
+delta e naught prime 1 gives us
+ 
+
+ align:start position:0%
+delta e naught prime 1 gives us
+this change in standard reduction
+
+ align:start position:0%
+this change in standard reduction
+ 
+
+ align:start position:0%
+this change in standard reduction
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+which i can plug into this formula
+
+ align:start position:0%
+which i can plug into this formula
+ 
+
+ align:start position:0%
+which i can plug into this formula
+which is related to the equilibrium
+
+ align:start position:0%
+which is related to the equilibrium
+ 
+
+ align:start position:0%
+which is related to the equilibrium
+constant and tells me
+
+ align:start position:0%
+constant and tells me
+ 
+
+ align:start position:0%
+constant and tells me
+which direction of electron transfer
+
+ align:start position:0%
+which direction of electron transfer
+ 
+
+ align:start position:0%
+which direction of electron transfer
+is going to be favored at least at
+
+ align:start position:0%
+is going to be favored at least at
+ 
+
+ align:start position:0%
+is going to be favored at least at
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+and so if this number
+
+ align:start position:0%
+and so if this number
+ 
+
+ align:start position:0%
+and so if this number
+is related to equilibrium there's a
+
+ align:start position:0%
+is related to equilibrium there's a
+ 
+
+ align:start position:0%
+is related to equilibrium there's a
+negative here
+
+ align:start position:0%
+negative here
+ 
+
+ align:start position:0%
+negative here
+and so if this term is
+
+ align:start position:0%
+and so if this term is
+ 
+
+ align:start position:0%
+and so if this term is
+positive delta g not prime will be
+
+ align:start position:0%
+positive delta g not prime will be
+ 
+
+ align:start position:0%
+positive delta g not prime will be
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+and that means that electron transfer
+
+ align:start position:0%
+and that means that electron transfer
+ 
+
+ align:start position:0%
+and that means that electron transfer
+will be favored at equilibrium
+
+ align:start position:0%
+will be favored at equilibrium
+ 
+
+ align:start position:0%
+will be favored at equilibrium
+if this number is negative that means
+
+ align:start position:0%
+if this number is negative that means
+ 
+
+ align:start position:0%
+if this number is negative that means
+the reverse
+
+ align:start position:0%
+the reverse
+ 
+
+ align:start position:0%
+the reverse
+electron transfer will be favored at
+
+ align:start position:0%
+electron transfer will be favored at
+ 
+
+ align:start position:0%
+electron transfer will be favored at
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+and so it stands to reason then
+
+ align:start position:0%
+and so it stands to reason then
+ 
+
+ align:start position:0%
+and so it stands to reason then
+that electron transfer
+
+ align:start position:0%
+that electron transfer
+ 
+
+ align:start position:0%
+that electron transfer
+from smaller
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+standard reduction potential to larger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+standard reduction potentials will be
+
+ align:start position:0%
+standard reduction potentials will be
+ 
+
+ align:start position:0%
+standard reduction potentials will be
+favored hopefully that makes sense
+
+ align:start position:0%
+favored hopefully that makes sense
+ 
+
+ align:start position:0%
+favored hopefully that makes sense
+so smaller to larger now that could be
+
+ align:start position:0%
+so smaller to larger now that could be
+ 
+
+ align:start position:0%
+so smaller to larger now that could be
+less uh more negative to less negative
+
+ align:start position:0%
+less uh more negative to less negative
+ 
+
+ align:start position:0%
+less uh more negative to less negative
+negative to positive positive to more
+
+ align:start position:0%
+negative to positive positive to more
+ 
+
+ align:start position:0%
+negative to positive positive to more
+positive
+
+ align:start position:0%
+positive
+ 
+
+ align:start position:0%
+positive
+as long as that delta
+
+ align:start position:0%
+as long as that delta
+ 
+
+ align:start position:0%
+as long as that delta
+is positive electron transfer
+
+ align:start position:0%
+is positive electron transfer
+ 
+
+ align:start position:0%
+is positive electron transfer
+will be favored now of course the
+
+ align:start position:0%
+will be favored now of course the
+ 
+
+ align:start position:0%
+will be favored now of course the
+ratios still matter okay
+
+ align:start position:0%
+ratios still matter okay
+ 
+
+ align:start position:0%
+ratios still matter okay
+but this standard reduction potential is
+
+ align:start position:0%
+but this standard reduction potential is
+ 
+
+ align:start position:0%
+but this standard reduction potential is
+useful
+
+ align:start position:0%
+useful
+ 
+
+ align:start position:0%
+useful
+because it can help us know which
+
+ align:start position:0%
+because it can help us know which
+ 
+
+ align:start position:0%
+because it can help us know which
+direction transfer
+
+ align:start position:0%
+direction transfer
+ 
+
+ align:start position:0%
+direction transfer
+wants to occur between any redox pairs
+
+ align:start position:0%
+wants to occur between any redox pairs
+ 
+
+ align:start position:0%
+wants to occur between any redox pairs
+at equilibrium and so
+
+ align:start position:0%
+at equilibrium and so
+ 
+
+ align:start position:0%
+at equilibrium and so
+recognizing this you must know that
+
+ align:start position:0%
+recognizing this you must know that
+ 
+
+ align:start position:0%
+recognizing this you must know that
+carbon oxidation electron transfer
+
+ align:start position:0%
+carbon oxidation electron transfer
+ 
+
+ align:start position:0%
+carbon oxidation electron transfer
+in general is going to be favored to
+
+ align:start position:0%
+in general is going to be favored to
+ 
+
+ align:start position:0%
+in general is going to be favored to
+nadh uh to to nad to make nadh
+
+ align:start position:0%
+nadh uh to to nad to make nadh
+ 
+
+ align:start position:0%
+nadh uh to to nad to make nadh
+and in general that nad elect nadh
+
+ align:start position:0%
+and in general that nad elect nadh
+ 
+
+ align:start position:0%
+and in general that nad elect nadh
+electron transfer is going to be favored
+
+ align:start position:0%
+electron transfer is going to be favored
+ 
+
+ align:start position:0%
+electron transfer is going to be favored
+to oxygen
+
+ align:start position:0%
+to oxygen
+ 
+
+ align:start position:0%
+to oxygen
+and it's coupling those favorable
+
+ align:start position:0%
+and it's coupling those favorable
+ 
+
+ align:start position:0%
+and it's coupling those favorable
+electron transfers
+
+ align:start position:0%
+electron transfers
+ 
+
+ align:start position:0%
+electron transfers
+that ultimately is allowing the system
+
+ align:start position:0%
+that ultimately is allowing the system
+ 
+
+ align:start position:0%
+that ultimately is allowing the system
+to use oxidation and reduction reactions
+
+ align:start position:0%
+to use oxidation and reduction reactions
+ 
+
+ align:start position:0%
+to use oxidation and reduction reactions
+to drive these various pathways
+
+ align:start position:0%
+to drive these various pathways
+ 
+
+ align:start position:0%
+to drive these various pathways
+and that that energy release from these
+
+ align:start position:0%
+and that that energy release from these
+ 
+
+ align:start position:0%
+and that that energy release from these
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+transfer reactions can be used to make
+
+ align:start position:0%
+transfer reactions can be used to make
+ 
+
+ align:start position:0%
+transfer reactions can be used to make
+atp
+
+ align:start position:0%
+atp
+ 
+
+ align:start position:0%
+atp
+and do other work as we will talk about
+
+ align:start position:0%
+and do other work as we will talk about
+ 
+
+ align:start position:0%
+and do other work as we will talk about
+in great detail in the next lecture
\ No newline at end of file
diff --git a/t73rjeOj0eY.txt b/t73rjeOj0eY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0a3ad5dbfb1d5078cefce3ea8fdf1fa293a71613
--- /dev/null
+++ b/t73rjeOj0eY.txt
@@ -0,0 +1,3826 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Sometimes
+psychologists like to talk
+
+about two aspects of our mind,
+the hot and the cool.
+
+So the cool parts we've been
+talking about recently,
+
+thinking parts, like language,
+thought, things related to
+
+intelligence, problem solving,
+the rational aspects of the
+
+human mind.
+
+And today we're going to focus
+on maybe the hottest of the
+
+hot, the emotions that we feel
+and that color our lives in
+
+terms of intensity and arousal
+and what matters to us.
+
+And so we'll talk a little bit
+about, just very briefly about
+
+a thumbnail history of the
+study of emotion, the
+
+scientific study of emotion,
+ideas about how to define it,
+
+a few models of emotion, how
+emotion might work, some big
+
+questions about things like is
+emotion universal, does it
+
+correlate to bodily feelings?
+
+Why do we have emotion?
+
+And then things about the
+brain basis of emotions.
+
+So we have a huge number of
+words, by one count about 550
+
+words, that describe the
+feelings we have,
+
+the emotions we have.
+
+And there's a lot of overlap
+conceptually among them, but
+
+we have so many words because
+we think that, we feel that
+
+from our daily lives, the
+feelings and emotions that we
+
+have are such a big part of our
+human existence, how we
+
+relate to other people, how we
+feel when we're by ourselves.
+
+Emotions are just a big,
+big part of how we
+
+go about our lives.
+
+And they're readily apparent
+to us everywhere we look on
+
+the faces of others.
+
+Positive emotions, negative
+emotions, fearful emotions,
+
+you see them around
+you all the time.
+
+In psychology, a lot of ideas
+about formulating the field go
+
+back to William James, who
+worked at Harvard, who
+
+articulated in many ways, in
+language that's still relevant
+
+to this day, the basic ideas,
+the basic things about being a
+
+human that one wants to
+understand out of a
+
+psychology.
+
+And he wrote about emotion this
+way, "If you can conceive
+
+of yourself suddenly stripped of
+all the emotion with which
+
+our world now inspires you, no
+one portion of the universe
+
+would have more important
+characteristics beyond
+
+another; and the whole character
+of its things and
+
+series of events would be
+without significance,
+
+character, expression, or
+perspective." That what we
+
+fear, what we desire, what
+we enjoy, what we find
+
+disgusting--
+
+we'll talk a little bit about
+disgust today-- that all those
+
+things tell us what's important
+and whether it's to
+
+be avoided or approached,
+enjoyed or loathed.
+
+And so people have thought
+about emotions.
+
+You could pick a million
+different cultural directions.
+
+Here's a picture from
+Greek philosophy.
+
+But you could pick
+practically every
+
+culture around the world.
+
+You can't be a human and
+not think about the
+
+feelings you have.
+
+But kind of strikingly in terms
+of research, for a very,
+
+very long time compared to
+language or thinking or many
+
+topics, people didn't study
+emotion because it seemed hard
+
+to study scientifically.
+
+And it's still harder to study
+scientifically in many ways, I
+
+think, than cognition.
+
+But there's been tremendous
+progress in bringing
+
+scientific approaches to
+understanding something about
+
+emotions in you and I. And
+like many things, it was
+
+reinvigorated around the
+Renaissance and the mystery of
+
+Mona Lisa's smile.
+
+And now there's entire journals
+and conferences and
+
+organizations of scientific
+psychology
+
+devoted to study emotion.
+
+It's a big part of our lives.
+
+You would think in the study of
+the human mind and brain it
+
+would be a big endeavor.
+
+And it is now.
+
+But that wouldn't have been
+true even 20 years ago.
+
+How might we define emotion
+just to sort of have some
+
+boundaries?
+
+So we could say that emotions
+are biologically-based
+
+responses to situations
+that are seen
+
+as personally relevant.
+
+They are shaped by learning and
+usually involves changes
+
+in peripheral physiology.
+
+Your hands are trembling
+or things like that.
+
+Your heart is pounding.
+
+Expressive behavior, the
+intonation with which you
+
+speak, the facial expression
+that you
+
+have or see in others.
+
+And subjective experience.
+
+The emotions you have go with
+what you feel is going on
+
+inside you.
+
+Research has tried to
+distinguish between moods and
+
+emotions, and talk about moods
+as diffuse, long-lasting
+
+emotional states.
+
+When you're in a funk or a
+positive mood over days,
+
+weeks, months, that's
+not what we're going
+
+to talk about today.
+
+That's interesting and
+important also.
+
+We're going to talk about
+emotions, which are very
+
+punctate, immediate responses
+to situations, to a specific
+
+thing or a specific stress or
+a specific element of your
+
+environment, an immediate,
+strong response.
+
+And within that, one more
+distinction has turned out to
+
+be useful for thinking about
+emotions between two
+
+dimensions, arousal, or
+you could call it
+
+intensity, and valence.
+
+Arousal means things that are
+exciting, intense, if they're
+
+high arousal, or calm
+or lethargic
+
+if they're low arousal.
+
+Valence refers to whether it's
+a positive thing that makes
+
+you elated or contented,
+negative sad or gloomy.
+
+And you can already
+see, for example,
+
+take positive valence.
+
+Elated is high arousal.
+
+Contented, ah, that's
+low arousal.
+
+They're both positive, but
+they're kind of different.
+
+So is calm versus lethargic.
+
+Being calm can be
+sometimes good.
+
+Feeling really slow, really
+lethargic, also is low
+
+arousal, but it's usually not
+a desirable low arousal.
+
+And so people think that they
+can take basically these two
+
+dimensions, valence and arousal,
+and use it as a
+
+useful way to say something
+like calm is here.
+
+It's a little bit positive
+and it's low
+
+on the arousal dimension.
+
+Excited is up here.
+
+It's a positive valence.
+
+Different things, gloomy is
+negative and it's fairly
+
+intense feeling, as opposed
+to merely lethargic.
+
+These two dimensions can cover
+a big sense of the life of
+
+emotions that inhabit us.
+
+And a huge question, and one
+that's brutally hard to
+
+satisfy in some deep scientific
+way, of course, is
+
+it restricted to humans?
+
+So if you hang around pets
+and animals in various
+
+circumstances, you can't help
+but feel they have emotions.
+
+It's just very hard for us
+to ask them to fill out
+
+questionnaires telling
+us their emotions.
+
+Here's a chimp that has lost
+its mother recently.
+
+Here's a dog going out
+for a good old night.
+
+Here's an armadillo
+going, whee!
+
+It looks pretty aroused.
+
+We don't know how much of this
+in some cases is us reading
+
+human feelings into their
+expressions, how much of that
+
+is them feeling the
+same as we do.
+
+There's a lot of sense,
+obviously, that many species
+
+have feelings as
+well as humans.
+
+We'll focus just on
+humans today.
+
+And the other thing that's
+important is
+
+they're shaped by learning.
+
+What that means is many
+different things, but for
+
+example, they can vary from
+one culture to another in
+
+certain ways.
+
+And here's one example of a
+movie that's bringing tears to
+
+everybody's eyes, except
+this person who
+
+finds it utterly hilarious.
+
+If you work in emotion
+research, I can
+
+tell you you get that.
+
+I worked a little bit on that.
+
+You show some really horrible
+pictures to everybody.
+
+They go, oh, horrible,
+horrible, horrible.
+
+And somebody else
+starts laughing.
+
+It's like horror movies.
+
+Have you've been around horror
+movies where some people are
+
+really scared out of their seats
+and very worried about
+
+the characters and other
+people think
+
+it's all pretty funny?
+
+So that's your prospective.
+
+It's not an automatic response
+to many situations.
+
+So how have people thought about
+the emotion you feel
+
+when a bear jumps out of your
+closet unexpectedly?
+
+Here's the logical one.
+
+Common sense.
+
+Bear is scary.
+
+You feel fearful.
+
+That's your subjective
+experience.
+
+And your body starts to
+do things like your
+
+heart starts to pump.
+
+Your sweat glands start
+to sweat, because
+
+you go, this is dangerous.
+
+This is scary.
+
+Here comes my body.
+
+That would be the
+intuitive one.
+
+My heart is pounding because
+I feel afraid.
+
+Interestingly, you can reverse
+the order and find some things
+
+that are better explained
+that way.
+
+It's sometimes nice, sometimes
+people will say, oh my gosh.
+
+Everything in psychology
+is so obvious.
+
+For some reason, they always
+say, my grandmother
+
+would have known it.
+
+I don't know why they
+pick that example.
+
+Show us something that science
+only can tell you.
+
+So here's a very clever reversal
+from William James
+
+and also Lange.
+
+They reversed it.
+
+They said that first comes the
+bodily response to the
+
+situation and second comes your
+mind interpreting your
+
+body's primary response.
+
+The exact opposite order of
+why we feel as we do.
+
+"We feel sorry because we cry,
+angry because we strike,
+
+afraid because we tremble, and
+not that we strike, cry, or
+
+tremble because we are sorry,
+angry, or fearful." He sees
+
+the exact opposite.
+
+Here it says first comes an
+emotion that's shaking your
+
+body in some way, and then comes
+to your mind saying,
+
+aha, I'm afraid--
+
+pretty fast--
+
+or I'm happy or whatever.
+
+Here's some examples, because
+you could think, OK, yes, you
+
+can cleverly reverse them.
+
+But is there any science to
+suggest that in some cases
+
+that relationship
+does reverse?
+
+So here's what people did.
+
+And I'll show you a
+picture for this.
+
+They said, how can peripheral
+bodily events, things on sort
+
+of the edge of our bodies,
+influence the
+
+emotions we feel inside?
+
+So they would have people do
+things like hold a pencil
+
+tightly between their
+teeth and--
+
+look at that pencil.
+
+They're not told to smile.
+
+They're just told to keep
+that pencil there.
+
+And what does that look like?
+
+A smile, right?
+
+OK.
+
+You've tricked the person's
+face into smiling.
+
+And they don't even know
+that, necessarily.
+
+They're thinking, this is a
+weird psychology experiment
+
+about how long can you hold a
+pencil in your mouth, although
+
+they're going to know something
+more in a moment.
+
+Or between the lips,
+hold that pencil.
+
+Now, does this person
+look happy?
+
+No.
+
+A little bit not happy, right?
+
+OK.
+
+And then you have them watch a
+funny movie that most people
+
+find funny.
+
+And they rate how much
+they like it.
+
+And the person who had this one
+rates it as more enjoyable
+
+than the person holding a pencil
+this way, as if already
+
+having the muscles in your face
+moved into a position
+
+that typically signals happiness
+or laughter makes
+
+you feel happy inside and the
+funny movie is even funnier.
+
+Being in a somewhat neutral to
+negative position makes that
+
+same funny movie seem
+less funny.
+
+You're interpreting where your
+muscles are that normally go
+
+with one emotion or another,
+and that's driving your
+
+internal final emotion about how
+you feel about the movie.
+
+Was there a question?
+
+AUDIENCE: Could it require more
+
+concentration, or patience?
+
+PROFESSOR: Does one require
+more concentration?
+
+That's an excellent question,
+because we always like to say,
+
+oh, it's this thing.
+
+What if this is a harder
+thing like that?
+
+And so when one have to
+hope-- and I have to
+
+admit I don't know--
+
+that they've controlled for
+things like that in some way.
+
+If you read the research paper,
+
+you'd want to be concerned.
+
+That's an excellent question.
+
+If this is just harder work than
+maybe you're paying less
+
+attention to the movie and just
+hanging onto that pencil.
+
+I don't know.
+
+And I have to hope they did
+a good job on this.
+
+That's an excellent question.
+
+And here's other ones, again,
+where they're trying to get
+
+the face to go smiley
+or go frowny.
+
+And then they just ask them,
+how do you feel?
+
+And this person will rate
+themselves as feeling happier
+
+than this person as they answer
+on a piece of paper in
+
+front of them.
+
+Again, they're trying to say, if
+I can move your peripheral
+
+facial expressions into--
+
+your muscles into expressions,
+the feelings will follow from
+
+the expressions.
+
+You can also do something else,
+which is you can tell
+
+people-- so Paul Ekman, his name
+will come up a lot today.
+
+He's done a fantastic amount of
+the key research on this,
+
+making emotions into a research
+topic in many ways.
+
+What he developed is a way that
+he said, I'm going to
+
+describe objectively which
+muscles are in which position
+
+for each of six fundamental
+emotional expressions.
+
+We'll come back to those.
+
+So he would tell a person, raise
+your eyebrows and pull
+
+them together.
+
+Raise your upper eyelids.
+
+Now stretch your lips
+horizontally back
+
+towards your ears.
+
+So what he's giving this person,
+step by step, is
+
+directions that move the muscles
+into an expression of
+
+fear, by the time you
+end up there.
+
+The participant usually doesn't
+know that, because
+
+it's so weird.
+
+You're moving your mouth.
+
+You're moving--
+
+it's just so weird.
+
+But then they can do these
+kinds of experiments.
+
+And these people will report a
+fearful movie as being more
+
+fearful than somebody who just
+gets to sit there or whose
+
+muscles are moved into
+a happy position.
+
+So all of a sudden you've got
+all these peripheral things
+
+being interpreted by our mind
+as a signal for what emotion
+
+you have, or enhancing
+it anyway.
+
+And then because any strong
+theory usually turns out to be
+
+not nearly complicated enough,
+you get the wishy-washy middle
+
+that probably covers more of
+the truth, which is both
+
+things are going on.
+
+Both you're having a subjective
+cognitive
+
+interpretation of your
+environment and a bodily
+
+response, maybe more
+in parallel than
+
+one driving the other.
+
+So again, how can peripheral
+bodily
+
+events influence emotions?
+
+One idea that's floated around,
+and probably true, is
+
+that the perception or
+thought, your mental
+
+interpretation of your emotion
+tells you the type of emotion.
+
+so if a bear jumps out, you
+can say, OK, I know
+
+something's pretty intense.
+
+And I can tell you right
+away it's bad.
+
+But if something wonderful
+jumps out of your closet
+
+unexpectedly, then you
+go, oh my gosh.
+
+I can't believe Lindsay Lohan
+is visiting me and I didn't
+
+even know it.
+
+Then if that is considered
+a good visit, that would
+
+influence again, the
+interpretation, but the
+
+intensity might come from
+the bodily parts.
+
+How intense it is might
+be signaled from that.
+
+So here's a couple of ways
+that people explore this.
+
+Here's a study from years ago
+from Schacter, where he
+
+injected people with
+adrenaline--
+
+adrenaline is the neurohormone
+that goes with high arousal,
+
+it raises your heart rate--
+
+or a placebo.
+
+So he's directly taking the
+chemical that we normally
+
+produce under higher
+arousal conditions.
+
+And the first question you might
+ask is, and you might be
+
+curious about, if somebody gave
+you a shot of adrenaline,
+
+what would happen?
+
+Would you like jump out
+of your seat and run
+
+laps around the room?
+
+What would you do?
+
+And surprisingly, all by
+itself, not very much.
+
+People said they feel a bit
+jittery, like if you've had
+
+maybe a little too much
+coffee or Red Bull--
+
+is that the current?--
+
+that little jittery feeling.
+
+But they're not like jumping
+up and do jumping jacks and
+
+one-armed push-ups and
+stuff like that.
+
+Now, having had the placebo or
+the adrenaline injected into
+
+you, and you don't know
+that, they show you an
+
+emotion-eliciting--
+
+they'll show you a movie,
+like a horror movie.
+
+And the people who had the
+adrenaline will report more
+
+fear when they see the horror
+movie, more anger when they
+
+get insulted.
+
+That's a fun experiment
+when you insult them.
+
+I'm sure the IRB, you have
+to be pretty careful.
+
+More laughter for a comedy.
+
+Adrenaline seemed to amplify the
+intensity of the emotion.
+
+But the emotion was driven
+by the situation.
+
+Does that make sense?
+
+OK?
+
+But here's something quite
+interesting about humans,
+
+which is that if you told
+them, we've given you
+
+adrenaline and it usually
+amplifies stuff, then it
+
+disappeared.
+
+Once the person knew that, they
+could discount that in
+
+their mind.
+
+So it's not like adrenaline is
+your master, and that I must
+
+have twice as big a response.
+
+Once you knew that was in the
+picture, then the ratings went
+
+back to placebo.
+
+It's not that biology
+is destiny.
+
+But under normal circumstances,
+it seems like
+
+the adrenaline accentuates
+the intensity.
+
+So that would go with the
+possibility that peripheral
+
+stuff drives the intensity,
+peripherally injected
+
+adrenaline, and our mind's
+
+interpretation drives the content.
+
+Here's a sort of fun, slightly
+sexist experiment that in the
+
+end, I think, explains the
+following phenomenon.
+
+When you see famous movie stars
+go into a movie set, on
+
+set, or whatever they call it,
+you incredibly often hear
+
+about romances occurring between
+the leads, right?
+
+And there's debates about what
+this is just the press agent
+
+selling their movie
+or whatever.
+
+But you hear that all
+the time, right?
+
+OK.
+
+So I'm going to tell you
+why that happens
+
+when it really happens.
+
+I can't really tell you that.
+
+But I can tell you an
+experiment that
+
+might touch on that.
+
+So here's the experiment.
+
+This was done by Dutton
+and Aron in
+
+North Vancouver, Canada.
+
+And they did the experiment in
+an area where there were two
+
+bridges not right next to each
+other, pretty near each other.
+
+One was a flimsy suspension
+bridge, five feet wide,
+
+swaying and wobbling 320
+feet over jagged
+
+boulders and river rapids.
+
+So you have to imagine
+Indiana Jones, OK?
+
+And you come to this
+bridge and you're
+
+going, I don't know.
+
+OK.
+
+The other one, upstream, same
+river, same Canadian district.
+
+There's a steady, low,
+broad bridge.
+
+No problem at all.
+
+You could drive your car
+over that, no problem.
+
+Two bridges over the
+same waters, one
+
+seeming scary, one not.
+
+Then what they did is in the
+middle of each bridge they
+
+placed an attractive, in this
+case female, confederate.
+
+Maybe somebody's done the
+reverse gender experiment.
+
+I don't know.
+
+Anyway, as men walk across the
+bridge, they ask them to fill
+
+out a questionnaire, some
+boring questionnaire.
+
+And they casually mentioned that
+if that person, as they
+
+finish the questionnaire, has
+more questions, he can call
+
+the woman providing the
+questionnaire at home.
+
+And she provides him
+her home number.
+
+And the measure that they have
+is how many phone calls go
+
+from the male subjects to the
+female experimenter at home.
+
+And they're betting that it's
+not really scientific
+
+curiosity that's driving a
+lot of the phone calling.
+
+But here's what they
+actually find.
+
+More males will call that female
+at home if they were on
+
+the dangerous bridge than
+on the safe bridge.
+
+That's the actual finding.
+
+And the interpretation is this,
+the dangerous bridge,
+
+because of the true feeling of
+danger, produces high arousal,
+
+increased adrenalin.
+
+And that's misinterpreted, if
+you want to call it that, by
+
+the male because he thinks now
+he's super-attracted to that
+
+woman because of the
+swaying bridge.
+
+Another reason to take somebody
+you want to win over,
+
+whatever the gender situation
+is, a really scary roller
+
+coaster ride is highly
+recommended together with that
+
+warm beverage, as long as it
+doesn't spill on them.
+
+I'm making you too powerful
+to control people.
+
+Again, the arousal of the bridge
+has been misinterpreted
+
+by that person as an intense
+attraction to that woman.
+
+And you could imagine making
+movies are probably high
+
+arousal exciting situations,
+and that would promote
+
+romantic relations and high
+intense situations that might
+
+not otherwise occur.
+
+Yes?
+
+AUDIENCE: [INAUDIBLE]?
+
+They had to randomly assign
+them to one bridge or the
+
+other, you would hope.
+
+I can tell you there's been a
+bunch of other experiments
+
+sort of like this.
+
+This is the most what you could
+call ecological, silly,
+
+or sexist, you could figure.
+
+But they all go with this idea
+that if you're in a high
+
+arousal situation, you sort of
+move over that arousal into
+
+whatever it is you're
+encoding.
+
+Does that make sense?
+
+And in this case, because you're
+creating an interaction
+
+between a man and woman, it's
+promoting this probability of
+
+a sense of romance
+in the male.
+
+Is that OK?
+
+But it could be any situation.
+
+The arousal will make it-- if
+it's something, it can make
+
+you feel worse about it.
+
+AUDIENCE: [INAUDIBLE]?
+
+PROFESSOR: Ah.
+
+Totally excellent question.
+
+You're asking awesome
+questions.
+
+I have to assume-- and I should
+
+know this, but I don't--
+
+that they weren't.
+
+Yes, because if you had males
+self-selecting, you had some
+
+males running to the danger
+bridge, drawn to danger, and
+
+others saying, oh, please give
+me a safe road, is that the
+
+real difference.
+
+So you have to presume
+they did something to
+
+control that, yes.
+
+Excellent question.
+
+The current view is something
+like that there's two factors,
+
+that there's both.
+
+A bodily response that happens
+pretty fast, pretty
+
+automatically, pretty
+unconsciously.
+
+There's a lot of
+interpretation.
+
+And the combination of that
+bodily response and an
+
+interpretation leads you finally
+to the subjective
+
+experience you have, and
+probably works differently for
+
+different emotions.
+
+And things are complicated.
+
+But we're pretty far from this
+first guess in terms of the
+
+fact that peripheral things can
+have very powerful effects
+
+on how you interpret situations,
+the intensity of
+
+your interpretations.
+
+And the intensity itself can
+change the behaviors that
+
+follows the situation.
+
+Three questions in the field
+are, are emotions universal?
+
+Are they in you from
+when you're born?
+
+Are they the same for people
+around the world?
+
+Do they have unique
+physiological signatures?
+
+Could we define--
+
+if we knew your heart rate, if
+we knew your pulse and so on,
+
+could we know what emotional
+state you're in.
+
+And then speculations as to why
+we have emotions at all.
+
+What's the use of
+having emotions?
+
+Brilliant as he is in so many
+ways, in many ways this
+
+dialogue began in modern times
+with Charles Darwin, who
+
+noticed that animals had very
+striking facial expressions,
+
+as we saw before.
+
+And that made him think about
+the evolution of facial
+
+expressions.
+
+This is one of his drawings
+of a cat.
+
+Here are infants having early
+displays of emotions, joy,
+
+disgust, surprise, sadness,
+anger, fear.
+
+So people have been very
+impressed that very early on
+
+infants are having the full
+array of expressions.
+
+Of course, they might
+see them.
+
+From moments from their birth
+they have people around them.
+
+But it's very early, that's
+almost for sure.
+
+A really interesting line of
+research-- and I'll show you
+
+an example-- has been looking
+at emotional expressions,
+
+emotional facial expressions, in
+people who are born deaf or
+
+born blind, so they never
+hear intonation.
+
+They never see a facial
+expression.
+
+They can't learn it from
+their environments.
+
+So they're sort of a natural
+window into is this inborn in
+
+us, or do we learn it from
+people around us?
+
+Here's an experiment where they
+took spontaneous facial
+
+expressions of emotion in
+athletes from both the
+
+Olympics and the Paralympics.
+
+And they looked especially at
+congenitally blind people,
+
+born blind, never saw a face,
+and sighted athletes.
+
+And they looked at the
+expressions after winning or
+
+losing an Olympic-level match.
+
+Before I show you this, you
+may know the story.
+
+What happens after
+an Olympic event?
+
+Somebody wins and where
+do they go?
+
+You know this podium thing?
+
+The gold medal winners up here,
+and the silvers here and
+
+the bronzes here.
+
+And they've also done
+studies--this
+
+is just a side note--
+
+saying, who looks the happiest
+in those pictures?
+
+AUDIENCE: Bronze.
+
+PROFESSOR: The bronze
+medal winner.
+
+Who looks the saddest
+in those pictures?
+
+AUDIENCE: Silver.
+
+PROFESSOR: The silver, right?
+
+Because the bronze medal
+winner's going, thank goodness
+
+I came in third place.
+
+I'm on the podium.
+
+I have an Olympic medal.
+
+If I'm in fourth place, fourth
+through infinity gets the same
+
+Olympic medal, right?
+
+The silver medalist, what's
+he or she thinking?
+
+On average.
+
+Man, if I had just one more
+fraction of a millisecond, I
+
+could be the gold medalist.
+
+It's kind of an interesting
+thing of when we consider
+
+things satisfactory or not.
+
+But now let's turn back
+to this question.
+
+Here's two people who just lost
+Olympic medal matches.
+
+And your question is which is a
+sighted person and which is
+
+a blind person?
+
+And to the extent it's hard to
+be certain, that would be a
+
+big suggestion that these
+expressions are inborn in us,
+
+because a person who's never
+seen a sad expression still
+
+has a sad expression.
+
+And the answer is, that's the
+blind athlete and that's the
+
+sighted athlete.
+
+So it's pretty convincing, I
+think, that we're born with
+
+this set of expressions as a
+core entity of being human.
+
+Even though we're born with
+that, we live in different
+
+cultures, very different
+cultures around the world, and
+
+even within countries and
+across countries.
+
+So how universal are these
+sorts of things?
+
+And there's lots of evidence
+of a degree of influence of
+
+cultures around this
+core universality.
+
+So does a smile mean friendship
+to everyone?
+
+And again, Ekman and Izard made
+a big study in which they
+
+argued that as far as they can
+tell in looking around at
+
+facial expressions, there's
+six basic emotional
+
+expressions that signal
+feelings, happiness, sadness,
+
+fear, anger, surprise,
+or disgust.
+
+These are all people who are
+trained to try to make the
+
+perfect expression
+of those things.
+
+They look kind of weird
+by themselves, right?
+
+They look kind of weird.
+
+You don't see a neutral
+one here.
+
+Maybe we'll see a neutral
+one later.
+
+Neutral is kind of weird,
+because you
+
+go, well, it's neutral.
+
+But I can tell you, a totally
+neutral face looking at you
+
+can be kind of creepy.
+
+Because if you interact with
+somebody and they have no
+
+expression at all, it's
+a little disturbing.
+
+But these are ones are pretty
+universally recognized, but
+
+not completely.
+
+Let's take Westerners,
+people from the
+
+United States or Europe.
+
+We're not perfect in that.
+
+Even with these posed pictures,
+this is how often
+
+people came up with the
+correct labels.
+
+Pretty often, not perfect.
+
+There's a lot of mystery
+at the edges of this.
+
+But here's how people came up
+from non-Western cultures for
+
+the same Western faces.
+
+Well above chance, but not the
+same as Westerners looking at
+
+Western expressions.
+
+And it would reverse if
+Westerners had to look at
+
+non-Western expressions.
+
+So there's definitely a degree
+of cultural influences on the
+
+recognition of these expressions
+as well.
+
+It's partly innate and
+universal, and there's a
+
+cultural overlay as well.
+
+This is a joke.
+
+"Shoot!
+
+You've got not only the wrong
+planet, but you've got the
+
+wrong solar system.
+
+I mean, a wrong planet
+I can understand.
+
+But a wrong solar system--" And
+you can tell with just a
+
+little information that this
+is a sheepish smile of
+
+embarrassment.
+
+And this is a little bit of
+the body expression of a
+
+little bit of irksomeness.
+
+Irked.
+
+But here's an isolated
+pre-literate
+
+tribe in New Guinea.
+
+And that smile looks like the
+smile of any kid you ever saw.
+
+That's sadness, the sadness
+of any kid you every saw.
+
+That's a little bit
+of a disgust.
+
+And some people have built up
+a model, something like
+
+there's things in the
+environment that happen that
+
+drive some sort of facial
+affect program.
+
+Your muscles in your face move
+to express 6 or so different
+
+kinds of feelings.
+
+Cultural rules about what should
+you show, what should
+
+you not show in different
+cultures.
+
+Some face's expressions are more
+appreciated than others.
+
+And finally, all of that
+moves into the facial
+
+expression you make.
+
+So now the second question we
+have, we think to a first
+
+approximation emotions, at least
+as far as we can tell,
+
+are pretty universal but there's
+cultural and learned
+
+pieces as well.
+
+Do emotions have unique
+physiological signatures?
+
+Can we tell from your
+
+physiology what you're feeling?
+
+And there was a lot of hope that
+this would work, because
+
+intuitively emotions differ
+from one another.
+
+Our body feels different
+as we go from
+
+one emotion to another.
+
+And we use language words like
+"she got hot and bothered."
+
+"You make my blood boil." "He's
+just letting off steam."
+
+Different physiologies go
+with different feelings.
+
+And so people hoped they could
+make decision trees like this.
+
+Let's measure your heart
+rate, high or low.
+
+Well, if it's high, then we
+get your skin temperature.
+
+And then we can tell if you're
+angry or fear or sad.
+
+That you could make a decision
+tree by looking at peripheral
+
+measures of physiology.
+
+But it never worked.
+
+It's never been strongly
+discriminating.
+
+People have not been able
+to have a physiological
+
+fingerprint for the emotion
+that you feel that's
+
+reasonably accurate.
+
+Yes?
+
+AUDIENCE: So why are they
+[INAUDIBLE] as something that
+
+could go in that tree,
+for instance?
+
+Could they measure chemical
+concentrations in places?
+
+PROFESSOR: It's possible, yes.
+
+Here's a very good question.
+
+Here they're measuring
+peripheral physiology or
+
+autonomic systems, skin
+temperature, heart rate.
+
+Could there be other things
+like chemicals, right?
+
+So I'd say yes, but we just
+don't know them well enough.
+
+Or could you have brain measures
+that ultimately would
+
+be sophisticated enough?
+
+I can tell you that brain
+measures are not that
+
+good at that now.
+
+But could they be someday?
+
+Yes.
+
+So yes, it's the specific
+measures that we have.
+
+A really deep question will be
+at some level when you're
+
+fearful and I'm fearful, how
+identical will those be,
+
+depending on our cultural
+background, depending on
+
+situations we've experienced?
+
+We can both agree we're scared
+of something, but it could be
+
+pretty different.
+
+So it's a really
+deep question.
+
+In the end, how close are these
+things from one person
+
+to another?
+
+Now, at least at speculative
+is why we have emotions.
+
+And sometimes people think
+it's intrapersonal
+
+functions within us.
+
+We're organizing ourselves--
+what's our basic feeling?
+
+Are we basically happy or sad
+about something or fearful of
+
+something?--
+
+so that we use that feeling as
+a source of information to
+
+sort of pull ourselves
+to say, this is
+
+basically where I'm at.
+
+It's a source of information
+for me.
+
+And it can tell me what behavior
+makes sense to do in
+
+this context.
+
+And then from one person to
+another, interpersonally.
+
+What does that person feel?
+
+What am I signalling
+to that person?
+
+So here's an experiment.
+
+And I'll show you just a brief
+YouTube video on this, because
+
+I think it's really cute.
+
+But it's almost a life and death
+experiment, although no
+
+infant was harmed in the making
+of this experiment.
+
+So what they do is, this
+is a visual cliff.
+
+An infant is put on this,
+a very tiny baby.
+
+Here it's hard Plexiglas.
+
+There is no danger
+to the baby.
+
+But there is a drop here
+and a drop here.
+
+Now, as the baby approaches
+this, they're not used to the
+
+idea of Plexiglas.
+
+Even you and I would be pretty
+worried about that if it was
+
+on a larger scale.
+
+We'd want to be pretty sure
+about the strength of the
+
+Plexiglas But to the infant's
+eyes, they're approaching what
+
+they call a visual cliff.
+
+On the other side--
+
+I'll show the film
+in a moment--
+
+is a mother.
+
+And the mother can either be
+showing a positive expression
+
+or a negative expression.
+
+And look what happens to the
+infants in this perilous
+
+situation where they see a drop
+that's a big, and how
+
+much they trust their mother's
+expression to know what to do.
+
+So if the mother is looking
+happy, like it's OK.
+
+This is going to be great.
+
+We're having a lot of fun.
+
+3/4 of the time the infant
+goes for it.
+
+If the mother looks
+scary, never.
+
+They're making kind of a
+dangerous decision entirely on
+
+the facial expression of the
+mother and their trust that
+
+the mother knows the right thing
+to do and is giving them
+
+the right advice.
+
+Sometimes everything in
+psychology can just seem like,
+
+oh, it's just another thing.
+
+But facial expressions are an
+unbelievable powerful way that
+
+we communicate with
+one another.
+
+Here's an extremely clever
+experiment from Adam Anderson,
+
+who happened to be a
+postdoctoral fellow in my lab,
+
+but he did this completely
+independently.
+
+Here's the question.
+
+So we have some different
+expressions.
+
+And you could say, well, are
+they completely random as to
+
+what the actual expression is?
+
+We haven't even asked this.
+
+Why does a smile go one way and
+a frown go the other way?
+
+Does it mean anything or are
+they just arbitrary signals of
+
+different emotions that have
+evolved over time?
+
+And he's almost the first
+person I know to
+
+even ask this question.
+
+And he looked at two emotions
+that we'll come back to in
+
+just a little bit, fear,
+and disgust.
+
+And he thought, well, look, it's
+kind of interesting what
+
+fear and disgust do.
+
+For example, fear, your eyes
+get bigger, disgust--
+
+think about something
+really stinky--
+
+you close your eyes.
+
+You sort of scrunch
+up your nose.
+
+Look at this.
+
+And he looked at and measured
+how airflow patterns and
+
+different things happen when you
+go into those expressions,
+
+non-arbitrary properties
+of an expression.
+
+And then he did psychological
+expressions.
+
+He got people to get into
+these expressions.
+
+And he found that if they were
+in a fearful expression, that
+
+they would feel like they had a
+wider field of view, and if
+
+it's disgust, a smaller.
+
+Now think about this
+for a moment.
+
+When it's fearful, do you want
+to feel like you know what's
+
+going on around you?
+
+Or do you want to sit back
+and think about stuff?
+
+Or do you want to
+say like, uh-oh.
+
+Where do I run?
+
+What's going on?
+
+When you go into some disgusting
+situation, do you
+
+want to really look
+around a lot?
+
+Or are you kind of happy to
+find some way out of it?
+
+Same thing with your nose.
+
+Here's the air velocity that's
+passing through your nose when
+
+you're fearful and when
+you're disgusted.
+
+Now you don't even
+think about that.
+
+Who's thinking, I'm controlling
+my air velocity?
+
+But why do you think you might
+want to really sample your
+
+environment when you feel
+danger, visually and in an
+
+olfactory way?
+
+Why do you think you might
+want to sample?
+
+Well, you want to know
+what's going on.
+
+You want the information
+as fast as possible.
+
+Do I run?
+
+Do I duck?
+
+What do I do?
+
+Do I fight, flee?
+
+What do I do?
+
+I have moments to decide,
+because I'm in danger.
+
+If you're in a disgust
+situation, are you interested,
+
+typically, in exploring the
+olfactory environment in as
+
+much detail as you can?
+
+Usually not.
+
+So it's kind of interesting.
+
+The very first time --
+
+I know, it's very clever --
+
+asked where do these expressions
+come from?
+
+Well, maybe they tend, to a
+certain extent, to exaggerate
+
+or diminish forms of sensory
+input that are relevant for
+
+the emotion.
+
+So for the last little bit I'm
+going to talk about for a
+
+little while what we know
+about the brain
+
+basis of some emotions.
+
+We already talked about the idea
+that the amygdala plays a
+
+special role in fear.
+
+And I'll show you a couple
+different ways in
+
+which that's true.
+
+This is just sitting in front of
+the hippocampus, one on the
+
+left, one on the right,
+the core elements
+
+of your limbic system.
+
+Here it is viewed from the
+side, the amygdala.
+
+Here's the actual amygdala
+from a post-mortem brain.
+
+And there's another whole level
+of analysis that animal
+
+researchers do that we can't
+touch today, which is the
+
+amygdala itself is made out of
+bundles of neurons called
+
+nuclei, very distinct ones that
+have different roles,
+
+different inputs, different
+outputs.
+
+And in animal research, where
+you can selectively influence
+
+one or the other, you can see
+they have quite different
+
+specific roles.
+
+In humans we don't have that
+precision of control, so we
+
+sort of have some clump average
+
+statements about the amygdala.
+
+But really we're mixing together
+a few functions.
+
+So you already saw this picture,
+that animals, mice or
+
+rats, that have an amygdala
+removed lose the fear they
+
+ought to have of a cat.
+
+In primate studies, they found
+that if they have amygdala
+
+lesions, the loss of threat
+appreciation impairs social
+
+fitness, that animals that don't
+know what they ought to
+
+be afraid of get into
+big trouble.
+
+They lose their position in
+dominance hierarchies.
+
+You may know primate groups
+tend to have dominance
+
+hierarchies, a sort of
+alpha male and so on.
+
+They slide down that.
+
+If they lesion the dominant
+male, the alpha male, the male
+
+who wins all the fights and
+controls the group, that
+
+animal will fall down the
+hierarchy and become
+
+subordinate.
+
+And in the wild, they've shown
+that if they do lesions and
+
+return the animal to the social
+situation, they get
+
+rejected by the other animals,
+because the other animals feel
+
+there's something weird
+about the animals.
+
+And they're often isolated and
+they get to early death,
+
+because the other animals
+are not helping them
+
+or supporting them.
+
+So very important for learning
+what's dangerous.
+
+Here's an experiment with rhesus
+monkeys lesioned at two
+
+weeks as infants, returned to
+their mothers, and tested at
+
+eight weeks.
+
+And here's an example of
+something, this is if you show
+
+an animal a novel object.
+
+And this is how often
+they respond to it.
+
+Young animals will often not
+explore it, because they go,
+
+well, I don't know.
+
+That could be dangerous.
+
+They're waiting for their
+mother's expression.
+
+Here's the other animals with
+the amygdala lesions.
+
+They'll explore it.
+
+In a sense, they're fearless.
+
+But that's probably not an ideal
+thing to do when you're
+
+an infant exploring the world.
+
+Or they'll put food only or
+food next to a play snake.
+
+Snakes are dangerous
+for monkeys.
+
+They usually don't want to
+figure out at this age is it a
+
+play snake or a real snake?
+
+They just say, I don't really
+need to eat that.
+
+So everybody likes the food.
+
+Put the snake next to it, and
+the control animals go, no, I
+
+don't think so, basically.
+
+The amygdala ones, what's
+for dinner?
+
+And the answer is, if it's a
+real snake, you're for dinner.
+
+So they lose the fear of things
+they ought to have fear
+
+of, they lose fear of unknown
+things, fear of things they
+
+ought to be afraid of.
+
+So the amygdala plays this
+really important role.
+
+Fear sometimes is maybe the
+best understood emotion in
+
+terms of brain processes, and
+maybe the most studied, partly
+
+because we've had some success
+in understanding what's going
+
+on and partly because fear is
+maybe the emotion that most
+
+people think is closer
+to survival.
+
+You fear what kills you.
+
+You fear what pains you.
+
+That's a very powerful emotion
+for survival and safety.
+
+And you can do fear
+conditioning.
+
+We talked about conditioning
+before in all species, from
+
+humans to primates, other
+mammals, fruit flies.
+
+All of them have, to a first
+approximation, similar fear
+
+conditioning.
+
+It's as if you're alive, you
+have to fear things that are
+
+scary and dangerous.
+
+So people have done fear
+conditioning experiments.
+
+And now you know
+this very well.
+
+You might hear a tone that's
+not scary at first.
+
+If you put it with something
+that you don't like, like a
+
+foot shock, you get fearful
+to the tone.
+
+And what people have discovered
+kind of remarkably
+
+is that you can make lesions in
+many parts of the brain and
+
+you don't affect that learned
+fearfulness to the tone.
+
+But if you make a damage in the
+part of the amygdala, you
+
+abolish that learning.
+
+These animals fail to learn the
+signal of something that
+
+is coming up to be painful
+and dangerous.
+
+And you can even make large
+lesions in the cortex.
+
+That doesn't affect anything.
+
+And these animals with the
+amygdala lesions, they have an
+
+intact unconditioned response.
+
+When they get the shock, they
+jump like the other animals.
+
+They don't like it.
+
+It's not that they
+can't feel pain.
+
+They can't learn that the tone
+predicts the painful stimulus.
+
+They can't learn the warning
+signal of danger.
+
+There's very few patients with
+amygdala injuries only.
+
+But there's a few.
+
+So here's a patient, SM, who's
+been studied by Damasio and
+
+his colleagues.
+
+This is where the amygdala
+ought to be.
+
+It's a developmental disorder
+where this is calcified very
+
+early in development.
+
+It's not an adult lesion.
+
+But it seems to be fairly
+amygdala-specific.
+
+And people have done
+a couple of
+
+experiments with these patients.
+
+And it's sort of guided our
+understanding of what the
+
+amygdala does in you and I.
+Here's one example where they
+
+did conditioning.
+
+Again, in this case they
+didn't use shocks.
+
+They used a super-loud
+boat horn that's
+
+pretty noxious to people.
+
+People don't like it.
+
+And they preceded that with
+something gentle that warned
+
+you it was coming.
+
+Here's the initial response.
+
+And here's the important
+thing.
+
+With humans, of course
+you can--
+
+well, let me just say they
+managed a skin response, a
+
+galvanic skin response
+to the bad tones.
+
+So here's the conditioned
+stimulus, the response to the
+
+boat horns in the conditioning,
+what predicts
+
+the boat horns.
+
+Here's the response
+to the baseline.
+
+And here's the performance of
+patients with amnesia who have
+
+the amygdala--
+
+controls, I'm sorry, who both
+can tell you they're
+
+responding selectively to the
+scariest tones and also
+
+remember perfectly well.
+
+At the end of the testing
+session, you go, what went on?
+
+And they say, oh yes.
+
+Well, when I got one signal I
+got a horrible boat horn.
+
+And when I heard the other
+signal, I got nothing.
+
+It's easy.
+
+You do that for half an hour.
+
+You get one visual signal that
+means boat horn coming up, one
+
+visual signal, nothing
+coming up.
+
+If you have patients who have
+amygdala lesions, that
+
+galvanic skin response doesn't
+happen, even though they tell
+
+you perfectly well afterwards
+what happened.
+
+So they know just like everybody
+else that they got a
+
+certain signal that went with
+a noxious boat horn.
+
+But their body is not learning
+that association.
+
+If a patient has hippocampal
+damage, their body learns that
+
+association, but they don't
+remember it afterwards
+
+consciously.
+
+So you can separate out two
+kinds of learning, a
+
+hippocampal-dependent learning
+of the facts of the session,
+
+and an amygdala-dependent
+learning, which is a bodily
+
+response to learning that
+something is dangerous and
+
+unpleasant.
+
+Now, we often learn things like
+the visual cliff without
+
+having to have a boat horn
+and practice, right?
+
+If somebody tells you that
+something is dangerous, or you
+
+figure out that something is
+dangerous, you don't have to
+
+go through a terrible experience
+to pretty much
+
+decide you're not
+going to do it.
+
+So here's an experiment that was
+aimed at showing you that.
+
+What people were shown-- there's
+a funny human subjects
+
+wrinkle to this I'll
+just tell you.
+
+This occurred at Yale,
+where they had a
+
+blue square came on.
+
+That means safe.
+
+You can just relax.
+
+Nothing bad's going to happen.
+
+But when the yellow square
+comes on, get ready.
+
+You might get a somewhat
+unpleasant shock.
+
+But they never give
+them a shock.
+
+So you're not learning
+that way.
+
+You just factually learn that
+something is safe and
+
+something is dangerous.
+
+And here is the amygdala
+response to the scary one, to
+
+a neutral situation, and
+to the one where you
+
+know, ah, I'm safe.
+
+So you never got the shock.
+
+You never got the shock.
+
+You were just told
+about the shock.
+
+You didn't have to get
+it, but you're human.
+
+You can figure this out.
+
+And your amygdala is going, you
+know, I can just figure
+
+out that's dangerous.
+
+That's baseline.
+
+And that's the absence of
+danger, positive safety.
+
+The Yale IRB, hilariously I
+think, said, oh, but you're
+
+deceiving the people, because
+you tell them they might get a
+
+shock and they never
+got a shock.
+
+So you have to give them one
+shock at the end of the
+
+experiment.
+
+So dutifully, the experimenters
+gave them one
+
+shock after the experiment was
+over so they were honest.
+
+Because during the experiment,
+as they measured the brain
+
+activation in the amygdala
+responding to the threat of
+
+pain without any pain
+being associated--
+
+we're smart.
+
+We can learn something is
+dangerous just by thinking it
+
+through, and it engages the same
+part of the brain that
+
+learns by actual painful
+experience.
+
+Now how about memory?
+
+So here's the way this
+study was done.
+
+People viewed a slide
+story with an
+
+emotional middle section.
+
+So an example would be this,
+parents are home having
+
+breakfast with a kid.
+
+Parents go to work.
+
+Kid walks to school, kind of
+tragically, but these are all
+
+slides, again, nobody
+was injured,
+
+child is hit by a car.
+
+Something high arousing
+happens in the
+
+middle of the story.
+
+Everybody runs to
+the hospital.
+
+The kid is OK.
+
+When people ask a week later or
+something like that, a week
+
+later, tell me about the stories
+I told you last week.
+
+There's a number of stories.
+
+People have best memory for
+the part where something
+
+highly arousing happened, like
+the child was hit by a car.
+
+That makes sense, right?
+
+Kid having breakfast, huh.
+
+Kid OK, huh.
+
+Car accident with a kid,
+you're aroused and you
+
+remember that better.
+
+Emotion is amplifying memory.
+
+The patients with the amygdala
+lesions don't have that memory
+
+bump based on emotion.
+
+The emotion is not enhancing
+their memory.
+
+And you can imagine that there's
+a pretty good reason
+
+for emotions to enhance
+memory, right?
+
+If something is fearful,
+delightful, horribly
+
+disgusting, those are all good
+reasons to remember.
+
+Let's do that again,
+if it's great.
+
+Let's avoid that, if
+it's terrible.
+
+It's a good idea for emotions
+to drive memory formation.
+
+And in your brain and mine, it
+appears the amygdala has this
+
+role of transforming emotions
+into memories.
+
+Now we also talked about
+six facial expressions.
+
+And I showed you this before.
+
+The same patients have trouble
+in recognizing fearful facial
+
+expressions.
+
+So the amygdala in so many
+different ways, learning,
+
+memory, perception of faces,
+seems to play this
+
+huge role in fear.
+
+And kind of interesting way,
+because you might have the
+
+intuition--
+
+and a lot of this came
+from Freud--
+
+that a lot of emotions are
+happening kind of under our
+
+conscious awareness.
+
+We almost discover them after,
+like why am I angry with this
+
+person, or why am I so happy?
+
+We have to think it
+through, almost.
+
+If you show subliminal fearful
+faces versus happy faces,
+
+subliminally presented so people
+can't tell you what the
+
+facial expression was, still
+they turn on the amygdala.
+
+So unconscious perception
+of a fearful
+
+face engages the amygdala.
+
+You don't have to go through
+consciousness.
+
+Cortical blindness.
+
+We talked about that earlier
+in the course, where you're
+
+blind in one visual field.
+
+And yet individual patients, a
+couple of them with cortical
+
+blindness, if they were shown
+a fearful stimulus in the
+
+cortically blind field, still
+turn on, in the cortically
+
+blind field, the amygdala for a
+fearful face versus a happy
+
+face, which indicates that a
+non-conscious, subcortical
+
+pathway that doesn't intersect
+with conscious thought or
+
+cortex, is sending information
+from your eyes to your
+
+amygdala, a different pathway.
+
+And people have speculated that
+maybe again because fear
+
+is survival and danger, we might
+have a super-highway of
+
+information that sends
+dangerous information
+
+immediately to our amygdala.
+
+It doesn't wait for you to think
+a lot, so to speak, in
+
+your cortex.
+
+Boom.
+
+Danger, danger, danger, even
+before you process the rest of
+
+the situation.
+
+So we talked about fear and the
+threat in the amygdala.
+
+I'll just say a word
+about disgust.
+
+People think there's many
+reasons things we can be
+
+disgusted at or about, but
+that maybe in terms of
+
+evolution, it might have been
+a pretty good signal for
+
+contaminated food, food that
+makes you sick, things to
+
+avoid that make you sick.
+
+And it turns out another part of
+the brain called the insula
+
+is pretty important for that.
+
+So here's the amygdala
+left and right.
+
+Here's the insula that
+you have, left and
+
+right, outlined in purple.
+
+And again, just like with the
+amygdala, patients with
+
+lesions of the insula don't
+recognize facial expressions.
+
+And imaging wise, if you see a
+disgusted face, that turns on
+
+that part of the
+brain as well.
+
+So those are the best understood
+brain pieces of
+
+emotion by far.
+
+So now those are patient things,
+so let me turn for a
+
+moment, lastly to a few imaging
+studies of typical
+
+people and some topics
+on emotion.
+
+So here's some terrible
+pictures from 9/11.
+
+"The horror of the moment"--
+and we always
+
+imagine we'll remember--
+
+and we've already talked a
+little bit about this in
+
+flashbulb memories--
+
+emotionally things correctly
+for a long time.
+
+"'The horrors of that moment,'
+the King went on, 'I shall
+
+never forget.'" This
+is Lewis Carroll,
+
+Through the Looking Glass.
+
+"'You will though,' the Queen
+said, 'if you don't make a
+
+memorandum of it.'"
+
+And now you know that Lewis
+Carroll was talking about the
+
+amygdala, right?
+
+You didn't know that before,
+but you know that now.
+
+Because if the amygdala isn't
+there, the emotional intensity
+
+doesn't make the memory more
+permanent or more powerful.
+
+So Larry Cahill at UC Irvine did
+the first brain study on
+
+this topic.
+
+And what he did is he showed
+students while they were
+
+getting PET scanning, Positron
+Emission Tomography, short
+
+films that were either
+powerfully
+
+emotional or neutral.
+
+And then he brought them
+back three weeks later.
+
+And here's what he found.
+
+The more activation there
+was in the amygdala--
+
+each square here is a
+different person--
+
+the more they remembered
+the emotional stuff.
+
+But it didn't matter
+for neutral things.
+
+So the amygdala seems
+unimportant for neutral
+
+information, but the more it
+was engaged, the more they
+
+remembered emotional
+information.
+
+So this is sort of evidence in
+the typical human mind of a
+
+relationship between
+the amygdala
+
+and emotional memories.
+
+So here's an experiment actually
+that we did at
+
+Stanford, where we showed
+people stimuli that were
+
+either neutral, somewhat
+negative-- and I'm going to
+
+show you something that's
+very negative.
+
+If you don't want to look, close
+your eyes for a moment.
+
+Close your eyes.
+
+Here we go.
+
+Very negative.
+
+OK.
+
+Sorry.
+
+It turns out if we don't show
+you something that negative,
+
+it's hard to get your
+brain pumped up.
+
+It doesn't have to be
+that sad, but it has
+
+to be pretty intense.
+
+So we show you things
+like this.
+
+And we record your brain
+response for each of those.
+
+And here's what we do.
+
+We ask you to tell us
+how bad is this?
+
+So the baby picture was
+bad for most people.
+
+We wait three weeks, pretty long
+time, and then we test
+
+your memory for the scenes
+from before.
+
+We test your memory three weeks
+later, pretty long time.
+
+And here's what we see.
+
+Two things.
+
+In the left amygdala in this
+study, here's what you rated
+
+as terrible, pretty bad,
+somewhat bad, and neutral.
+
+So the amygdala is responding
+to your subjective sense of
+
+terribleness.
+
+Now, we were really looking
+at arousal and negativity.
+
+We didn't look at
+positive ones.
+
+I can tell you in
+other studies--
+
+and here's a trick
+in research.
+
+I'm going to tell you now--
+
+I only have a couple more
+slides, but I'm going to tell
+
+you a little bit about insider
+things on imaging, just so you
+
+understand imaging as as human
+and fallible a form of
+
+research as anything, which
+you might suspect anyway.
+
+So we show these things.
+
+And we got these responses.
+
+So that's going with your
+subjective sense of
+
+how bad films are.
+
+And then we tested people's
+memory, what we also found was
+
+that memory was best
+when we got the
+
+biggest amygdala response.
+
+So that's just like
+you heard before.
+
+So that all seemed find and
+lined up with a prior result.
+
+But here was the slight surprise
+in the thing that
+
+followed and that still gets
+cited fairly often.
+
+It's the research that I've
+been affiliated with that
+
+still gets cited most often in
+newspapers and magazines.
+
+Anyway, so this was a study
+that you saw before.
+
+And the thing I didn't emphasize
+to you was that this
+
+was in the right amygdala,
+in the right hemisphere.
+
+It doesn't really matter.
+
+It just happened to be there.
+
+Our study at Stanford was
+in the left hemisphere.
+
+This is where we were getting
+the emotion memory responses.
+
+And so we were very
+deep scientists.
+
+And we said, what could
+be going on?
+
+Why is Larry Cahill at
+UC Irvine getting
+
+it in the left amygdala?
+
+The more active it is, the
+more you would remember
+
+emotional information.
+
+And why is he getting it in the
+right amygdala and we're
+
+getting it in the left?
+
+So we took a piece of paper
+and we wrote down the
+
+different things that
+people had found.
+
+Oh.
+
+The story I was going
+to tell you is about
+
+Stephan Hamann's study.
+
+So Stephan Hamann at Emory did
+a study where he said, OK.
+
+All this amygdala response to
+negative things, does it also
+
+respond to positive things?
+
+That's a good question.
+
+And the answer is yes.
+
+But it turns out in many
+experiments it doesn't look
+
+that way, because you saw, for
+those of you who looked at
+
+that horrible-looking baby
+picture, what would be an
+
+equal positive powerful
+picture?
+
+Let's try this one.
+
+Everybody agrees it's cute when
+there's little children
+
+around a birthday cake.
+
+Smile, she smiles.
+
+Powerful, unless it's
+your kid, maybe.
+
+Powerful image.
+
+Powerful as the face
+of the infant?
+
+No.
+
+So it's a really interesting
+thing.
+
+It's very hard to get positive
+stimuli that are as potent as
+
+negative stimuli.
+
+You can get a million negative
+stimuli from the internet and
+
+it's very hard to get
+very positive ones.
+
+Having said that, we said, let's
+just think about the
+
+negative ones for the moment.
+
+So our studies were
+fMRI, PET, PET.
+
+Ours were all with women.
+
+And these were all with men.
+
+And you could go, well,
+why did that happen?
+
+It's good that it's half women
+and half men, because these
+
+were Positron Emission
+Tomography.
+
+That involves injecting
+radioactive stuff into people
+
+to do that kind of imaging.
+
+And many IRBs say, well, let's
+not have women do it, because
+
+they could be unknowingly
+pregnant.
+
+They could be.
+
+And we shouldn't be giving
+radioactive stuff just for an
+
+experiment.
+
+You could have debates about
+that, but that's the thought.
+
+Why not let the men get their
+radioactive stuff?
+
+We don't really need them.
+
+Then so when we did this study,
+we said, well, these
+
+were all with men.
+
+It seems in fairness we should
+do it with women too.
+
+We just thought that seemed
+fair, kind of.
+
+We didn't have any big
+thought about that.
+
+And again, we were getting left
+amygdala and they were
+
+getting right amygdala.
+
+Pictures or films, different.
+
+And this caught our eye,
+that we had done
+
+studies with women.
+
+We were getting left amygdala.
+
+They did it with men,
+with right amygdala.
+
+So deep scientists that we were,
+Larry Cahill said, I'll
+
+test men and women.
+
+And we said, we'll test
+men and women.
+
+And here's what we found.
+
+And these are averages, but
+one critical thing that we
+
+discovered-- we didn't know
+this-- is that to the extent--
+
+and these are averages, of
+course these are averages--
+
+that you compare men and women,
+on average women have
+
+better memory for emotional life
+events, faster production
+
+of autobiographical memories
+to cues, more accurate in
+
+dating memories.
+
+So these dating studies are
+pretty useful, because you
+
+never know how accurate a person
+is when they have a
+
+memory for something.
+
+What they do in the dating
+studies is they have people
+
+who are dating keep
+diaries, for
+
+example, in the fall semester.
+
+And presumably those are
+reasonably accurate.
+
+They're filling them
+in every day.
+
+And then things happen over the
+holidays and some people
+
+remain dating and some don't.
+
+So you go back to them in March,
+and you go, in your
+
+fall, when the two of you were
+going out, tell us about what
+
+you did in November.
+
+And they can say who's
+more accurate.
+
+And they have almost a virtual
+record, because they have the
+
+responses that the men and
+women put down that day.
+
+And on average-- these
+are averages-- the
+
+women were more accurate.
+
+And wives scored higher than
+husbands on vividness of
+
+memories for first date, last
+vacation, recent argument.
+
+So these are all averages.
+
+There's lots of overlap, but
+an average is that way.
+
+And so Larry Cahill went
+and did this thing.
+
+And sure enough, again, as he
+found before, for men, the
+
+more they turned on the right
+amygdala, the more certain
+
+they were to remember
+negative films.
+
+And for women, the more they
+turned on the left amygdala,
+
+the more certain they
+would remember
+
+negative films on average.
+
+Now, the thing to know is, on
+average again, when you have
+
+people rate the kinds
+of pictures we
+
+use, how do you think--
+
+here it is.
+
+This is one example where your
+stereotype guesses probably
+
+play out for the averages.
+
+Who rates this as more scary,
+or who says it's more scary,
+
+men or women?
+
+OK.
+
+So positive or negative,
+I should say
+
+for positive or negative.
+
+Here's the women, not finding
+this a particularly--
+
+on average, and there's
+a range of responses--
+
+positive picture.
+
+Here's men going, pretty cool.
+
+What DVD did that come from?
+
+So people are always asking,
+what does this really mean?
+
+Are men just knowing they have
+to do this or whatever?
+
+Who knows?
+
+There's no answer to this about
+whether it's social
+
+things or biology.
+
+Certainly social things are
+a big part of the story.
+
+When we have people rate the
+pictures in the scanner,
+
+here's the women rating here's
+the worst pictures.
+
+And look at the men.
+
+They're less willing to rate
+these pictures as bad.
+
+Again, psychologists who see
+these data say, well, maybe
+
+the men think they're never
+supposed to rate them as bad,
+
+because we're tough guys
+and nothing's so bad.
+
+I mean, I don't know.
+
+Who knows?
+
+But this is the ratings.
+
+Now, if we look at the
+activation of the men and
+
+women on the left as they rate
+them, the worse they rate it,
+
+the more intense they find it,
+the more they turned on their
+
+left amygdala.
+
+So at the moment they're rating
+them, men and women
+
+look very similar.
+
+But when we relate it to their
+memory, two things happen.
+
+First, the women did have
+superior memory to the men.
+
+These were Stanford
+undergraduates, probably not
+
+that dissimilar on average to
+the people in this room.
+
+And quite strikingly, as you
+saw it, activation in the
+
+right hemisphere predicted
+memory in men, and the left
+
+hemisphere for women.
+
+So I know there's been a
+lot of right and left.
+
+But here we think
+was the message.
+
+And it's kind of stood
+the test of time a
+
+little bit, on average.
+
+What you see here is the part of
+the left amygdala turned on
+
+for women as they're
+rating it.
+
+The more intense,
+the more active.
+
+In relation to whether they form
+a long term memory, the
+
+more active, the more likely
+they'll remember it.
+
+And kind of the physical
+overlap of the two.
+
+In men, more active in that
+amygdala on the left during
+
+the rating, but doesn't
+seem to be
+
+involved in memory formation.
+
+In the hippocampus, again,
+overlap, overlap, overlap.
+
+No apparent overlap
+in the men.
+
+So what happens literally in the
+brain, I mean, literally
+
+as far as we can measure it, in
+women on average there was
+
+more overlap between the parts
+of the brain engaged as you
+
+evaluate something and the parts
+of the brain that make
+
+the memory of that.
+
+And in men, on average it was
+as if, here's my emotional
+
+rating on the right, and here's
+what I'm going to
+
+remember on the left.
+
+Kind of a separation of
+those processes in
+
+the most simple sense.
+
+Now here's a huge question.
+
+Does this brain imaging study
+tell us anything about whether
+
+this is in the genes of boys and
+girls as they're born or a
+
+consequence of socialization
+or both?
+
+It's incredibly intuitive for
+people to think that if you
+
+see it in the brain it's
+hardwired and genetic or
+
+hormonal or something.
+
+Brain imaging data never
+tells you that.
+
+It never tells you that.
+
+It just tells you by this age,
+this is what's going on.
+
+And you don't have to know much
+psychology to know that
+
+we're all hugely influenced to
+varying degrees, but we're all
+
+hugely influenced by social
+influences on what it is to be
+
+a male or a female in our
+families, in our cultures, in
+
+our societies.
+
+Whether something's in your
+genes or in your culture, it
+
+shows up in your brain.
+
+And we can't tell those
+two things apart.
+
+Is this anything to do
+with how we're born?
+
+Is this anything to do with how
+Hollywood pitches movies
+
+that are about video game
+battles versus chick flicks,
+
+how they're pitching that and
+trying to tell us we're
+
+supposed to like something?
+
+Who knows?
+
+We can't tell if it's social
+or genetic at all.
\ No newline at end of file
diff --git a/twdF0EIbFds.txt b/twdF0EIbFds.txt
new file mode 100644
index 0000000000000000000000000000000000000000..75d4babe0fee93218781042c237b1a43c2e77b7a
--- /dev/null
+++ b/twdF0EIbFds.txt
@@ -0,0 +1,2051 @@
+align:start position:0%
+ 
+scattering in one dimension in one day
+
+ align:start position:0%
+scattering in one dimension in one day
+ 
+
+ align:start position:0%
+scattering in one dimension in one day
+and up we will consider a world that is
+
+ align:start position:0%
+and up we will consider a world that is
+ 
+
+ align:start position:0%
+and up we will consider a world that is
+just one dimensional X and in fact
+
+ align:start position:0%
+just one dimensional X and in fact
+ 
+
+ align:start position:0%
+just one dimensional X and in fact
+there's an infinite barrier at x equals
+
+ align:start position:0%
+there's an infinite barrier at x equals
+ 
+
+ align:start position:0%
+there's an infinite barrier at x equals
+zero x equals zero infinite barrier
+
+ align:start position:0%
+zero x equals zero infinite barrier
+ 
+
+ align:start position:0%
+zero x equals zero infinite barrier
+nothing goes beyond there on the other
+
+ align:start position:0%
+nothing goes beyond there on the other
+ 
+
+ align:start position:0%
+nothing goes beyond there on the other
+hand in here up to some distance R there
+
+ align:start position:0%
+hand in here up to some distance R there
+ 
+
+ align:start position:0%
+hand in here up to some distance R there
+could be a potential V of X so we will
+
+ align:start position:0%
+could be a potential V of X so we will
+ 
+
+ align:start position:0%
+could be a potential V of X so we will
+have a potential V of X will have the
+
+ align:start position:0%
+have a potential V of X will have the
+ 
+
+ align:start position:0%
+have a potential V of X will have the
+following properties will be identically
+
+ align:start position:0%
+following properties will be identically
+ 
+
+ align:start position:0%
+following properties will be identically
+0 for X greater than R which is called
+
+ align:start position:0%
+0 for X greater than R which is called
+ 
+
+ align:start position:0%
+0 for X greater than R which is called
+the range of the potential it will be
+
+ align:start position:0%
+the range of the potential it will be
+ 
+
+ align:start position:0%
+the range of the potential it will be
+some function V of X for X in between R
+
+ align:start position:0%
+some function V of X for X in between R
+ 
+
+ align:start position:0%
+some function V of X for X in between R
+and 0 and it will be infinity for X less
+
+ align:start position:0%
+and 0 and it will be infinity for X less
+ 
+
+ align:start position:0%
+and 0 and it will be infinity for X less
+or equal than 0 this is your potential
+
+ align:start position:0%
+or equal than 0 this is your potential
+ 
+
+ align:start position:0%
+or equal than 0 this is your potential
+it's a potential of range our range of
+
+ align:start position:0%
+it's a potential of range our range of
+ 
+
+ align:start position:0%
+it's a potential of range our range of
+the potential and the experiment that we
+
+ align:start position:0%
+the potential and the experiment that we
+ 
+
+ align:start position:0%
+the potential and the experiment that we
+think about this somebody at X equal
+
+ align:start position:0%
+think about this somebody at X equal
+ 
+
+ align:start position:0%
+think about this somebody at X equal
+plus infinity throwing waves into this
+
+ align:start position:0%
+plus infinity throwing waves into this
+ 
+
+ align:start position:0%
+plus infinity throwing waves into this
+potential and this observer can only get
+
+ align:start position:0%
+potential and this observer can only get
+ 
+
+ align:start position:0%
+potential and this observer can only get
+better reflected wave and from that
+
+ align:start position:0%
+better reflected wave and from that
+ 
+
+ align:start position:0%
+better reflected wave and from that
+reflected wave the observer wants to
+
+ align:start position:0%
+reflected wave the observer wants to
+ 
+
+ align:start position:0%
+reflected wave the observer wants to
+diffuse the type of the potential that
+
+ align:start position:0%
+diffuse the type of the potential that
+ 
+
+ align:start position:0%
+diffuse the type of the potential that
+you have there and that's absolutely the
+
+ align:start position:0%
+you have there and that's absolutely the
+ 
+
+ align:start position:0%
+you have there and that's absolutely the
+way physics goes in particle physics in
+
+ align:start position:0%
+way physics goes in particle physics in
+ 
+
+ align:start position:0%
+way physics goes in particle physics in
+LHC you throw protons or electrons
+
+ align:start position:0%
+LHC you throw protons or electrons
+ 
+
+ align:start position:0%
+LHC you throw protons or electrons
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+and you just catch what flies out of the
+
+ align:start position:0%
+and you just catch what flies out of the
+ 
+
+ align:start position:0%
+and you just catch what flies out of the
+collision with all the detectors and
+
+ align:start position:0%
+collision with all the detectors and
+ 
+
+ align:start position:0%
+collision with all the detectors and
+read that they done deduce what happened
+
+ align:start position:0%
+read that they done deduce what happened
+ 
+
+ align:start position:0%
+read that they done deduce what happened
+at the collision what potential was
+
+ align:start position:0%
+at the collision what potential was
+ 
+
+ align:start position:0%
+at the collision what potential was
+there what forces were there was there a
+
+ align:start position:0%
+there what forces were there was there a
+ 
+
+ align:start position:0%
+there what forces were there was there a
+new particle it's all found by looking
+
+ align:start position:0%
+new particle it's all found by looking
+ 
+
+ align:start position:0%
+new particle it's all found by looking
+at what comes out and flies away so
+
+ align:start position:0%
+at what comes out and flies away so
+ 
+
+ align:start position:0%
+at what comes out and flies away so
+there's an enormous amount of
+
+ align:start position:0%
+there's an enormous amount of
+ 
+
+ align:start position:0%
+there's an enormous amount of
+information on the potential from the
+
+ align:start position:0%
+information on the potential from the
+ 
+
+ align:start position:0%
+information on the potential from the
+data that comes out of you throwing in
+
+ align:start position:0%
+data that comes out of you throwing in
+ 
+
+ align:start position:0%
+data that comes out of you throwing in
+some particles in and waiting to see
+
+ align:start position:0%
+some particles in and waiting to see
+ 
+
+ align:start position:0%
+some particles in and waiting to see
+what comes back to you so we will always
+
+ align:start position:0%
+what comes back to you so we will always
+ 
+
+ align:start position:0%
+what comes back to you so we will always
+have this infinite wall and this
+
+ align:start position:0%
+have this infinite wall and this
+ 
+
+ align:start position:0%
+have this infinite wall and this
+infinite wall at x equals zero means
+
+ align:start position:0%
+infinite wall at x equals zero means
+ 
+
+ align:start position:0%
+infinite wall at x equals zero means
+that X less than zero is never relevant
+
+ align:start position:0%
+that X less than zero is never relevant
+ 
+
+ align:start position:0%
+that X less than zero is never relevant
+and this is analogous those two are the
+
+ align:start position:0%
+and this is analogous those two are the
+ 
+
+ align:start position:0%
+and this is analogous those two are the
+variable are in radial coordinates for
+
+ align:start position:0%
+variable are in radial coordinates for
+ 
+
+ align:start position:0%
+variable are in radial coordinates for
+which the radial distance is never
+
+ align:start position:0%
+which the radial distance is never
+ 
+
+ align:start position:0%
+which the radial distance is never
+negative so in fact what we'll do here
+
+ align:start position:0%
+negative so in fact what we'll do here
+ 
+
+ align:start position:0%
+negative so in fact what we'll do here
+has immediate applications when we will
+
+ align:start position:0%
+has immediate applications when we will
+ 
+
+ align:start position:0%
+has immediate applications when we will
+consider not in this course scattering
+
+ align:start position:0%
+consider not in this course scattering
+ 
+
+ align:start position:0%
+consider not in this course scattering
+in three dimensions so to begin this
+
+ align:start position:0%
+in three dimensions so to begin this
+ 
+
+ align:start position:0%
+in three dimensions so to begin this
+will solve the simplest case when you
+
+ align:start position:0%
+will solve the simplest case when you
+ 
+
+ align:start position:0%
+will solve the simplest case when you
+have no potential whatsoever now no
+
+ align:start position:0%
+have no potential whatsoever now no
+ 
+
+ align:start position:0%
+have no potential whatsoever now no
+potential means still the barrier at x
+
+ align:start position:0%
+potential means still the barrier at x
+ 
+
+ align:start position:0%
+potential means still the barrier at x
+equals zero the infinite barrier but in
+
+ align:start position:0%
+equals zero the infinite barrier but in
+ 
+
+ align:start position:0%
+equals zero the infinite barrier but in
+between 0 and R nothing is happening so
+
+ align:start position:0%
+between 0 and R nothing is happening so
+ 
+
+ align:start position:0%
+between 0 and R nothing is happening so
+you have just the case of no potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tential is the case where you have the
+
+ align:start position:0%
+tential is the case where you have the
+ 
+
+ align:start position:0%
+tential is the case where you have the
+barrier here and X is over there and up
+
+ align:start position:0%
+barrier here and X is over there and up
+ 
+
+ align:start position:0%
+barrier here and X is over there and up
+to R nothing is happening it's just the
+
+ align:start position:0%
+to R nothing is happening it's just the
+ 
+
+ align:start position:0%
+to R nothing is happening it's just the
+wall that's all there is just one wall
+
+ align:start position:0%
+wall that's all there is just one wall
+ 
+
+ align:start position:0%
+wall that's all there is just one wall
+so this is V
+
+ align:start position:0%
+so this is V
+ 
+
+ align:start position:0%
+so this is V
+you know potential is V is equal to V of
+
+ align:start position:0%
+you know potential is V is equal to V of
+ 
+
+ align:start position:0%
+you know potential is V is equal to V of
+X is equal to 0 for X greater than 0 and
+
+ align:start position:0%
+X is equal to 0 for X greater than 0 and
+ 
+
+ align:start position:0%
+X is equal to 0 for X greater than 0 and
+it's infinity for X less or equal and 0
+
+ align:start position:0%
+it's infinity for X less or equal and 0
+ 
+
+ align:start position:0%
+it's infinity for X less or equal and 0
+so in this case let's assume we have an
+
+ align:start position:0%
+so in this case let's assume we have an
+ 
+
+ align:start position:0%
+so in this case let's assume we have an
+incident wave an incident wave must be
+
+ align:start position:0%
+incident wave an incident wave must be
+ 
+
+ align:start position:0%
+incident wave an incident wave must be
+propagating in this way so the incident
+
+ align:start position:0%
+propagating in this way so the incident
+ 
+
+ align:start position:0%
+propagating in this way so the incident
+wave is an e to the minus I K X and if
+
+ align:start position:0%
+wave is an e to the minus I K X and if
+ 
+
+ align:start position:0%
+wave is an e to the minus I K X and if
+you have an outgoing wave would be some
+
+ align:start position:0%
+you have an outgoing wave would be some
+ 
+
+ align:start position:0%
+you have an outgoing wave would be some
+sort of e to the ikx these are the only
+
+ align:start position:0%
+sort of e to the ikx these are the only
+ 
+
+ align:start position:0%
+sort of e to the ikx these are the only
+things that can be there they correspond
+
+ align:start position:0%
+things that can be there they correspond
+ 
+
+ align:start position:0%
+things that can be there they correspond
+to energy eigenstate this is the bromley
+
+ align:start position:0%
+to energy eigenstate this is the bromley
+ 
+
+ align:start position:0%
+to energy eigenstate this is the bromley
+wave function of a particle with
+
+ align:start position:0%
+wave function of a particle with
+ 
+
+ align:start position:0%
+wave function of a particle with
+momentum okay in one direction or in the
+
+ align:start position:0%
+momentum okay in one direction or in the
+ 
+
+ align:start position:0%
+momentum okay in one direction or in the
+other direction but let's combine them
+
+ align:start position:0%
+other direction but let's combine them
+ 
+
+ align:start position:0%
+other direction but let's combine them
+in a way to produce a simple solution so
+
+ align:start position:0%
+in a way to produce a simple solution so
+ 
+
+ align:start position:0%
+in a way to produce a simple solution so
+this a solution Phi of X will be the
+
+ align:start position:0%
+this a solution Phi of X will be the
+ 
+
+ align:start position:0%
+this a solution Phi of X will be the
+solution will be a combination with
+
+ align:start position:0%
+solution will be a combination with
+ 
+
+ align:start position:0%
+solution will be a combination with
+similar e to the ikx and e to the minus
+
+ align:start position:0%
+similar e to the ikx and e to the minus
+ 
+
+ align:start position:0%
+similar e to the ikx and e to the minus
+ikx and I should make the wave function
+
+ align:start position:0%
+ikx and I should make the wave function
+ 
+
+ align:start position:0%
+ikx and I should make the wave function
+vanish at x equals 0 at x equals 0 both
+
+ align:start position:0%
+vanish at x equals 0 at x equals 0 both
+ 
+
+ align:start position:0%
+vanish at x equals 0 at x equals 0 both
+Exponential's are equal to 1 so if I
+
+ align:start position:0%
+Exponential's are equal to 1 so if I
+ 
+
+ align:start position:0%
+Exponential's are equal to 1 so if I
+want them to cancel I should put the
+
+ align:start position:0%
+want them to cancel I should put the
+ 
+
+ align:start position:0%
+want them to cancel I should put the
+minus so in order to simplify this best
+
+ align:start position:0%
+minus so in order to simplify this best
+ 
+
+ align:start position:0%
+minus so in order to simplify this best
+possible way we can put a 1 over 2 eyes
+
+ align:start position:0%
+possible way we can put a 1 over 2 eyes
+ 
+
+ align:start position:0%
+possible way we can put a 1 over 2 eyes
+over there so that we have a sine
+
+ align:start position:0%
+over there so that we have a sine
+ 
+
+ align:start position:0%
+over there so that we have a sine
+function and the sine function is
+
+ align:start position:0%
+function and the sine function is
+ 
+
+ align:start position:0%
+function and the sine function is
+particularly nice so we'll have e to the
+
+ align:start position:0%
+particularly nice so we'll have e to the
+ 
+
+ align:start position:0%
+particularly nice so we'll have e to the
+output like this e to the minus ikx
+
+ align:start position:0%
+output like this e to the minus ikx
+ 
+
+ align:start position:0%
+output like this e to the minus ikx
+plus e to the ikx over 2i and this is
+
+ align:start position:0%
+plus e to the ikx over 2i and this is
+ 
+
+ align:start position:0%
+plus e to the ikx over 2i and this is
+just the sine function sine of KX which
+
+ align:start position:0%
+just the sine function sine of KX which
+ 
+
+ align:start position:0%
+just the sine function sine of KX which
+you would admit it's a V solution over
+
+ align:start position:0%
+you would admit it's a V solution over
+ 
+
+ align:start position:0%
+you would admit it's a V solution over
+here a sine of KX on the other hand I
+
+ align:start position:0%
+here a sine of KX on the other hand I
+ 
+
+ align:start position:0%
+here a sine of KX on the other hand I
+can think of this solution as having an
+
+ align:start position:0%
+can think of this solution as having an
+ 
+
+ align:start position:0%
+can think of this solution as having an
+incoming wave wave which is minus e to
+
+ align:start position:0%
+incoming wave wave which is minus e to
+ 
+
+ align:start position:0%
+incoming wave wave which is minus e to
+the minus ikx over 2i and then outgoing
+
+ align:start position:0%
+the minus ikx over 2i and then outgoing
+ 
+
+ align:start position:0%
+the minus ikx over 2i and then outgoing
+wave wave of e to the ikx over 2i so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the representation of the
+
+ align:start position:0%
+this is the representation of the
+ 
+
+ align:start position:0%
+this is the representation of the
+solution when nothing is happening and
+
+ align:start position:0%
+solution when nothing is happening and
+ 
+
+ align:start position:0%
+solution when nothing is happening and
+the good thing about this solution is
+
+ align:start position:0%
+the good thing about this solution is
+ 
+
+ align:start position:0%
+the good thing about this solution is
+that it tells us what we should write
+
+ align:start position:0%
+that it tells us what we should write
+ 
+
+ align:start position:0%
+that it tells us what we should write
+gives us an idea of what we should write
+
+ align:start position:0%
+gives us an idea of what we should write
+ 
+
+ align:start position:0%
+gives us an idea of what we should write
+when something really is happening so
+
+ align:start position:0%
+when something really is happening so
+ 
+
+ align:start position:0%
+when something really is happening so
+now let's consider how we would write
+
+ align:start position:0%
+now let's consider how we would write
+ 
+
+ align:start position:0%
+now let's consider how we would write
+the general experiment in which you send
+
+ align:start position:0%
+the general experiment in which you send
+ 
+
+ align:start position:0%
+the general experiment in which you send
+in a wave but this time there is really
+
+ align:start position:0%
+in a wave but this time there is really
+ 
+
+ align:start position:0%
+in a wave but this time there is really
+a potential so let's consider now if no
+
+ align:start position:0%
+a potential so let's consider now if no
+ 
+
+ align:start position:0%
+a potential so let's consider now if no
+potential was there and now yes
+
+ align:start position:0%
+potential was there and now yes
+ 
+
+ align:start position:0%
+potential was there and now yes
+potential so no potential here so what
+
+ align:start position:0%
+potential so no potential here so what
+ 
+
+ align:start position:0%
+potential so no potential here so what
+does it mean yes potential well it means
+
+ align:start position:0%
+does it mean yes potential well it means
+ 
+
+ align:start position:0%
+does it mean yes potential well it means
+that you have this and you have some
+
+ align:start position:0%
+that you have this and you have some
+ 
+
+ align:start position:0%
+that you have this and you have some
+potential there up to some distance R
+
+ align:start position:0%
+potential there up to some distance R
+ 
+
+ align:start position:0%
+potential there up to some distance R
+and then it flattens out and something
+
+ align:start position:0%
+and then it flattens out and something
+ 
+
+ align:start position:0%
+and then it flattens out and something
+happens so in order to compare we'll
+
+ align:start position:0%
+happens so in order to compare we'll
+ 
+
+ align:start position:0%
+happens so in order to compare we'll
+take an incoming wave the same
+
+ align:start position:0%
+take an incoming wave the same
+ 
+
+ align:start position:0%
+take an incoming wave the same
+as the one where there was no potential
+
+ align:start position:0%
+as the one where there was no potential
+ 
+
+ align:start position:0%
+as the one where there was no potential
+so let's take an incoming wave wave
+
+ align:start position:0%
+so let's take an incoming wave wave
+ 
+
+ align:start position:0%
+so let's take an incoming wave wave
+which is of the form e to the minus I KX
+
+ align:start position:0%
+which is of the form e to the minus I KX
+ 
+
+ align:start position:0%
+which is of the form e to the minus I KX
+x minus over to I but I must say here I
+
+ align:start position:0%
+x minus over to I but I must say here I
+ 
+
+ align:start position:0%
+x minus over to I but I must say here I
+must write something more I must say
+
+ align:start position:0%
+must write something more I must say
+ 
+
+ align:start position:0%
+must write something more I must say
+that X is greater than R otherwise this
+
+ align:start position:0%
+that X is greater than R otherwise this
+ 
+
+ align:start position:0%
+that X is greater than R otherwise this
+is not the solution you see in the
+
+ align:start position:0%
+is not the solution you see in the
+ 
+
+ align:start position:0%
+is not the solution you see in the
+region where the potential really exists
+
+ align:start position:0%
+region where the potential really exists
+ 
+
+ align:start position:0%
+region where the potential really exists
+where the goes up and down you don't
+
+ align:start position:0%
+where the goes up and down you don't
+ 
+
+ align:start position:0%
+where the goes up and down you don't
+know the solution it would think solving
+
+ align:start position:0%
+know the solution it would think solving
+ 
+
+ align:start position:0%
+know the solution it would think solving
+the Schrodinger equation you know the
+
+ align:start position:0%
+the Schrodinger equation you know the
+ 
+
+ align:start position:0%
+the Schrodinger equation you know the
+solution where the potential is 0 so yes
+
+ align:start position:0%
+solution where the potential is 0 so yes
+ 
+
+ align:start position:0%
+solution where the potential is 0 so yes
+this incoming wave is a solution of the
+
+ align:start position:0%
+this incoming wave is a solution of the
+ 
+
+ align:start position:0%
+this incoming wave is a solution of the
+Schrodinger equation in this potential
+
+ align:start position:0%
+Schrodinger equation in this potential
+ 
+
+ align:start position:0%
+Schrodinger equation in this potential
+when X is greater than R and how about
+
+ align:start position:0%
+when X is greater than R and how about
+ 
+
+ align:start position:0%
+when X is greater than R and how about
+the outgoing wave wave well we would
+
+ align:start position:0%
+the outgoing wave wave well we would
+ 
+
+ align:start position:0%
+the outgoing wave wave well we would
+like to write it like that so we say 1
+
+ align:start position:0%
+like to write it like that so we say 1
+ 
+
+ align:start position:0%
+like to write it like that so we say 1
+over 2i e to the ikx it's also an
+
+ align:start position:0%
+over 2i e to the ikx it's also an
+ 
+
+ align:start position:0%
+over 2i e to the ikx it's also an
+outgoing wave so and we have no hope of
+
+ align:start position:0%
+outgoing wave so and we have no hope of
+ 
+
+ align:start position:0%
+outgoing wave so and we have no hope of
+solving it here finding what's happening
+
+ align:start position:0%
+solving it here finding what's happening
+ 
+
+ align:start position:0%
+solving it here finding what's happening
+here unless we solve complicated
+
+ align:start position:0%
+here unless we solve complicated
+ 
+
+ align:start position:0%
+here unless we solve complicated
+equation but then let's look outside
+
+ align:start position:0%
+equation but then let's look outside
+ 
+
+ align:start position:0%
+equation but then let's look outside
+we're still looking outside but that
+
+ align:start position:0%
+we're still looking outside but that
+ 
+
+ align:start position:0%
+we're still looking outside but that
+cannot be the outgoing wave this is the
+
+ align:start position:0%
+cannot be the outgoing wave this is the
+ 
+
+ align:start position:0%
+cannot be the outgoing wave this is the
+same as the other one and there's a
+
+ align:start position:0%
+same as the other one and there's a
+ 
+
+ align:start position:0%
+same as the other one and there's a
+potential so something must be different
+
+ align:start position:0%
+potential so something must be different
+ 
+
+ align:start position:0%
+potential so something must be different
+on the other hand if you think about it
+
+ align:start position:0%
+on the other hand if you think about it
+ 
+
+ align:start position:0%
+on the other hand if you think about it
+very little can be different because you
+
+ align:start position:0%
+very little can be different because you
+ 
+
+ align:start position:0%
+very little can be different because you
+must have a solution with zero potential
+
+ align:start position:0%
+must have a solution with zero potential
+ 
+
+ align:start position:0%
+must have a solution with zero potential
+and you know this this plane waves going
+
+ align:start position:0%
+and you know this this plane waves going
+ 
+
+ align:start position:0%
+and you know this this plane waves going
+out are the only things that exist and
+
+ align:start position:0%
+out are the only things that exist and
+ 
+
+ align:start position:0%
+out are the only things that exist and
+now you decide oh if that's the case
+
+ align:start position:0%
+now you decide oh if that's the case
+ 
+
+ align:start position:0%
+now you decide oh if that's the case
+I cannot put another function of X there
+
+ align:start position:0%
+I cannot put another function of X there
+ 
+
+ align:start position:0%
+I cannot put another function of X there
+because that's not a solution the best I
+
+ align:start position:0%
+because that's not a solution the best I
+ 
+
+ align:start position:0%
+because that's not a solution the best I
+can do is multiply by a number because
+
+ align:start position:0%
+can do is multiply by a number because
+ 
+
+ align:start position:0%
+can do is multiply by a number because
+maybe there's very little outgoing wave
+
+ align:start position:0%
+maybe there's very little outgoing wave
+ 
+
+ align:start position:0%
+maybe there's very little outgoing wave
+or there's not but then I think of
+
+ align:start position:0%
+or there's not but then I think of
+ 
+
+ align:start position:0%
+or there's not but then I think of
+another thing remember if you had a to
+
+ align:start position:0%
+another thing remember if you had a to
+ 
+
+ align:start position:0%
+another thing remember if you had a to
+the a e to the minus ikx plus b e to the
+
+ align:start position:0%
+the a e to the minus ikx plus b e to the
+ 
+
+ align:start position:0%
+the a e to the minus ikx plus b e to the
+ikx well the probability current was
+
+ align:start position:0%
+ikx well the probability current was
+ 
+
+ align:start position:0%
+ikx well the probability current was
+proportional to a squared minus b
+
+ align:start position:0%
+proportional to a squared minus b
+ 
+
+ align:start position:0%
+proportional to a squared minus b
+squared and this time however you have
+
+ align:start position:0%
+squared and this time however you have
+ 
+
+ align:start position:0%
+squared and this time however you have
+your sending in a wave and you're
+
+ align:start position:0%
+your sending in a wave and you're
+ 
+
+ align:start position:0%
+your sending in a wave and you're
+getting back a wave and this is a
+
+ align:start position:0%
+getting back a wave and this is a
+ 
+
+ align:start position:0%
+getting back a wave and this is a
+stationary state we're trying to get
+
+ align:start position:0%
+stationary state we're trying to get
+ 
+
+ align:start position:0%
+stationary state we're trying to get
+energy eigenstate solutions of some
+
+ align:start position:0%
+energy eigenstate solutions of some
+ 
+
+ align:start position:0%
+energy eigenstate solutions of some
+energy just like this energy and the
+
+ align:start position:0%
+energy just like this energy and the
+ 
+
+ align:start position:0%
+energy just like this energy and the
+only way it can happen is if they carry
+
+ align:start position:0%
+only way it can happen is if they carry
+ 
+
+ align:start position:0%
+only way it can happen is if they carry
+the same amount of probability
+
+ align:start position:0%
+the same amount of probability
+ 
+
+ align:start position:0%
+the same amount of probability
+probability cannot be accumulating here
+
+ align:start position:0%
+probability cannot be accumulating here
+ 
+
+ align:start position:0%
+probability cannot be accumulating here
+nor it can be being depleted there as
+
+ align:start position:0%
+nor it can be being depleted there as
+ 
+
+ align:start position:0%
+nor it can be being depleted there as
+well so the currents associated to the
+
+ align:start position:0%
+well so the currents associated to the
+ 
+
+ align:start position:0%
+well so the currents associated to the
+two waves must be the same and the
+
+ align:start position:0%
+two waves must be the same and the
+ 
+
+ align:start position:0%
+two waves must be the same and the
+currents are proportional to those
+
+ align:start position:0%
+currents are proportional to those
+ 
+
+ align:start position:0%
+currents are proportional to those
+numbers that multiply this thing square
+
+ align:start position:0%
+numbers that multiply this thing square
+ 
+
+ align:start position:0%
+numbers that multiply this thing square
+so in fact a squared must be equal to B
+
+ align:start position:0%
+so in fact a squared must be equal to B
+ 
+
+ align:start position:0%
+so in fact a squared must be equal to B
+squared and therefore we cannot have
+
+ align:start position:0%
+squared and therefore we cannot have
+ 
+
+ align:start position:0%
+squared and therefore we cannot have
+like a one-third here it would just ruin
+
+ align:start position:0%
+like a one-third here it would just ruin
+ 
+
+ align:start position:0%
+like a one-third here it would just ruin
+everything so the only thing I can have
+
+ align:start position:0%
+everything so the only thing I can have
+ 
+
+ align:start position:0%
+everything so the only thing I can have
+is a face
+
+ align:start position:0%
+is a face
+ 
+
+ align:start position:0%
+is a face
+the only thing cannot depend on X
+
+ align:start position:0%
+the only thing cannot depend on X
+ 
+
+ align:start position:0%
+the only thing cannot depend on X
+because otherwise I don't solve the
+
+ align:start position:0%
+because otherwise I don't solve the
+ 
+
+ align:start position:0%
+because otherwise I don't solve the
+equation cannot be a number that is less
+
+ align:start position:0%
+equation cannot be a number that is less
+ 
+
+ align:start position:0%
+equation cannot be a number that is less
+than one or bigger than one the only
+
+ align:start position:0%
+than one or bigger than one the only
+ 
+
+ align:start position:0%
+than one or bigger than one the only
+thing we can put here is a face so we'll
+
+ align:start position:0%
+thing we can put here is a face so we'll
+ 
+
+ align:start position:0%
+thing we can put here is a face so we'll
+put an e to the 2i Delta and this Delta
+
+ align:start position:0%
+put an e to the 2i Delta and this Delta
+ 
+
+ align:start position:0%
+put an e to the 2i Delta and this Delta
+will depend on K or will depend on the
+
+ align:start position:0%
+will depend on K or will depend on the
+ 
+
+ align:start position:0%
+will depend on K or will depend on the
+energy and it will depend on what your
+
+ align:start position:0%
+energy and it will depend on what your
+ 
+
+ align:start position:0%
+energy and it will depend on what your
+potential is but owning for
+
+ align:start position:0%
+potential is but owning for
+ 
+
+ align:start position:0%
+potential is but owning for
+raishin of this thing is in this Delta
+
+ align:start position:0%
+raishin of this thing is in this Delta
+ 
+
+ align:start position:0%
+raishin of this thing is in this Delta
+that depends on K and you say well
+
+ align:start position:0%
+that depends on K and you say well
+ 
+
+ align:start position:0%
+that depends on K and you say well
+that's very little you just have one
+
+ align:start position:0%
+that's very little you just have one
+ 
+
+ align:start position:0%
+that's very little you just have one
+phase one number that you could
+
+ align:start position:0%
+phase one number that you could
+ 
+
+ align:start position:0%
+phase one number that you could
+calculate and see but remember if you
+
+ align:start position:0%
+calculate and see but remember if you
+ 
+
+ align:start position:0%
+calculate and see but remember if you
+have a delta of K you could measure it
+
+ align:start position:0%
+have a delta of K you could measure it
+ 
+
+ align:start position:0%
+have a delta of K you could measure it
+for all values of K by sending particles
+
+ align:start position:0%
+for all values of K by sending particles
+ 
+
+ align:start position:0%
+for all values of K by sending particles
+of different energies and get now whole
+
+ align:start position:0%
+of different energies and get now whole
+ 
+
+ align:start position:0%
+of different energies and get now whole
+function and with a whole function Delta
+
+ align:start position:0%
+function and with a whole function Delta
+ 
+
+ align:start position:0%
+function and with a whole function Delta
+of K you have some probability of
+
+ align:start position:0%
+of K you have some probability of
+ 
+
+ align:start position:0%
+of K you have some probability of
+getting important information about the
+
+ align:start position:0%
+getting important information about the
+ 
+
+ align:start position:0%
+getting important information about the
+potential so we'll have a phase there
+
+ align:start position:0%
+potential so we'll have a phase there
+ 
+
+ align:start position:0%
+potential so we'll have a phase there
+eetu the I Delta of K and let's
+
+ align:start position:0%
+eetu the I Delta of K and let's
+ 
+
+ align:start position:0%
+eetu the I Delta of K and let's
+summarize here it's a deal to current
+
+ align:start position:0%
+summarize here it's a deal to current
+ 
+
+ align:start position:0%
+summarize here it's a deal to current
+conservation the current and this wave
+
+ align:start position:0%
+conservation the current and this wave
+ 
+
+ align:start position:0%
+conservation the current and this wave
+and the current outgoing waves should be
+
+ align:start position:0%
+and the current outgoing waves should be
+ 
+
+ align:start position:0%
+and the current outgoing waves should be
+the same and it also note that no extra
+
+ align:start position:0%
+the same and it also note that no extra
+ 
+
+ align:start position:0%
+the same and it also note that no extra
+X dependence is allowed so this will
+
+ align:start position:0%
+X dependence is allowed so this will
+ 
+
+ align:start position:0%
+X dependence is allowed so this will
+produce that J incident will be equal to
+
+ align:start position:0%
+produce that J incident will be equal to
+ 
+
+ align:start position:0%
+produce that J incident will be equal to
+J reflected now you could say okay very
+
+ align:start position:0%
+J reflected now you could say okay very
+ 
+
+ align:start position:0%
+J reflected now you could say okay very
+good so there's Delta there's a phase
+
+ align:start position:0%
+good so there's Delta there's a phase
+ 
+
+ align:start position:0%
+good so there's Delta there's a phase
+should I define it from zero to 2pi from
+
+ align:start position:0%
+should I define it from zero to 2pi from
+ 
+
+ align:start position:0%
+should I define it from zero to 2pi from
+minus PI to PI it's kind of natural to
+
+ align:start position:0%
+minus PI to PI it's kind of natural to
+ 
+
+ align:start position:0%
+minus PI to PI it's kind of natural to
+define it from minus PI to PI and you
+
+ align:start position:0%
+define it from minus PI to PI and you
+ 
+
+ align:start position:0%
+define it from minus PI to PI and you
+could look at what it is but as we will
+
+ align:start position:0%
+could look at what it is but as we will
+ 
+
+ align:start position:0%
+could look at what it is but as we will
+see from another theorem of Levinson's
+
+ align:start position:0%
+see from another theorem of Levinson's
+ 
+
+ align:start position:0%
+see from another theorem of Levinson's
+theorem it will be convenient to just
+
+ align:start position:0%
+theorem it will be convenient to just
+ 
+
+ align:start position:0%
+theorem it will be convenient to just
+simply say okay you fix the phase Delta
+
+ align:start position:0%
+simply say okay you fix the phase Delta
+ 
+
+ align:start position:0%
+simply say okay you fix the phase Delta
+K equals zero at zero energy scattering
+
+ align:start position:0%
+K equals zero at zero energy scattering
+ 
+
+ align:start position:0%
+K equals zero at zero energy scattering
+you read what is your Delta and as you
+
+ align:start position:0%
+you read what is your Delta and as you
+ 
+
+ align:start position:0%
+you read what is your Delta and as you
+increase the energy the phase will
+
+ align:start position:0%
+increase the energy the phase will
+ 
+
+ align:start position:0%
+increase the energy the phase will
+change so if you have a phase for
+
+ align:start position:0%
+change so if you have a phase for
+ 
+
+ align:start position:0%
+change so if you have a phase for
+example on a circle and the face starts
+
+ align:start position:0%
+example on a circle and the face starts
+ 
+
+ align:start position:0%
+example on a circle and the face starts
+to grow and to grow and to grow
+
+ align:start position:0%
+to grow and to grow and to grow
+ 
+
+ align:start position:0%
+to grow and to grow and to grow
+want to grow and to go here uh well
+
+ align:start position:0%
+want to grow and to go here uh well
+ 
+
+ align:start position:0%
+want to grow and to go here uh well
+should you call this pie and this - pine
+
+ align:start position:0%
+should you call this pie and this - pine
+ 
+
+ align:start position:0%
+should you call this pie and this - pine
+no you Pro just if it keeps growing with
+
+ align:start position:0%
+no you Pro just if it keeps growing with
+ 
+
+ align:start position:0%
+no you Pro just if it keeps growing with
+energy and it might happen that the face
+
+ align:start position:0%
+energy and it might happen that the face
+ 
+
+ align:start position:0%
+energy and it might happen that the face
+keeps growing with energy well pi 2 pi 3
+
+ align:start position:0%
+keeps growing with energy well pi 2 pi 3
+ 
+
+ align:start position:0%
+keeps growing with energy well pi 2 pi 3
+PI 4 PI just just keep the phase
+
+ align:start position:0%
+PI 4 PI just just keep the phase
+ 
+
+ align:start position:0%
+PI 4 PI just just keep the phase
+continuous so keeping the phase
+
+ align:start position:0%
+continuous so keeping the phase
+ 
+
+ align:start position:0%
+continuous so keeping the phase
+continuous is probably the best way to
+
+ align:start position:0%
+continuous is probably the best way to
+ 
+
+ align:start position:0%
+continuous is probably the best way to
+think about the face you start at some
+
+ align:start position:0%
+think about the face you start at some
+ 
+
+ align:start position:0%
+think about the face you start at some
+value of the face and then track it
+
+ align:start position:0%
+value of the face and then track it
+ 
+
+ align:start position:0%
+value of the face and then track it
+continuously there's always a problem
+
+ align:start position:0%
+continuously there's always a problem
+ 
+
+ align:start position:0%
+continuously there's always a problem
+with faces and angles they can be PI or
+
+ align:start position:0%
+with faces and angles they can be PI or
+ 
+
+ align:start position:0%
+with faces and angles they can be PI or
+- pi is the same angle but try for
+
+ align:start position:0%
+- pi is the same angle but try for
+ 
+
+ align:start position:0%
+- pi is the same angle but try for
+continuity in defining the face when
+
+ align:start position:0%
+continuity in defining the face when
+ 
+
+ align:start position:0%
+continuity in defining the face when
+when we'll face that problem so let's
+
+ align:start position:0%
+when we'll face that problem so let's
+ 
+
+ align:start position:0%
+when we'll face that problem so let's
+write the solution oh we have this so
+
+ align:start position:0%
+write the solution oh we have this so
+ 
+
+ align:start position:0%
+write the solution oh we have this so
+the total solution we call the solution
+
+ align:start position:0%
+the total solution we call the solution
+ 
+
+ align:start position:0%
+the total solution we call the solution
+with no potential Phi this one will cups
+
+ align:start position:0%
+with no potential Phi this one will cups
+ 
+
+ align:start position:0%
+with no potential Phi this one will cups
+I of X will be 1 over 2i the first term
+
+ align:start position:0%
+I of X will be 1 over 2i the first term
+ 
+
+ align:start position:0%
+I of X will be 1 over 2i the first term
+e to the ikx plus 2i Delta minus e to
+
+ align:start position:0%
+e to the ikx plus 2i Delta minus e to
+ 
+
+ align:start position:0%
+e to the ikx plus 2i Delta minus e to
+the minus ikx it's convenient to pull
+
+ align:start position:0%
+the minus ikx it's convenient to pull
+ 
+
+ align:start position:0%
+the minus ikx it's convenient to pull
+out of I Delta to make the two terms
+
+ align:start position:0%
+out of I Delta to make the two terms
+ 
+
+ align:start position:0%
+out of I Delta to make the two terms
+have opposite arguments so e to the I K
+
+ align:start position:0%
+have opposite arguments so e to the I K
+ 
+
+ align:start position:0%
+have opposite arguments so e to the I K
+X plus I Delta and or e to the ikx plus
+
+ align:start position:0%
+X plus I Delta and or e to the ikx plus
+ 
+
+ align:start position:0%
+X plus I Delta and or e to the ikx plus
+delta parentheses minus e to the minus i
+
+ align:start position:0%
+delta parentheses minus e to the minus i
+ 
+
+ align:start position:0%
+delta parentheses minus e to the minus i
+KX plus delta so this is e to the i
+
+ align:start position:0%
+KX plus delta so this is e to the i
+ 
+
+ align:start position:0%
+KX plus delta so this is e to the i
+delta x sine of KX plus delta so that's
+
+ align:start position:0%
+delta x sine of KX plus delta so that's
+ 
+
+ align:start position:0%
+delta x sine of KX plus delta so that's
+the full scattered wave not the full
+
+ align:start position:0%
+the full scattered wave not the full
+ 
+
+ align:start position:0%
+the full scattered wave not the full
+reflected now that words again this is
+
+ align:start position:0%
+reflected now that words again this is
+ 
+
+ align:start position:0%
+reflected now that words again this is
+the full wave that you have for X
+
+ align:start position:0%
+the full wave that you have for X
+ 
+
+ align:start position:0%
+the full wave that you have for X
+greater than R so let's write it hips I
+
+ align:start position:0%
+greater than R so let's write it hips I
+ 
+
+ align:start position:0%
+greater than R so let's write it hips I
+of X it's not the reflected wave
+
+ align:start position:0%
+of X it's not the reflected wave
+ 
+
+ align:start position:0%
+of X it's not the reflected wave
+northern come is everything we include
+
+ align:start position:0%
+northern come is everything we include
+ 
+
+ align:start position:0%
+northern come is everything we include
+its for X greater than R
+
+ align:start position:0%
+its for X greater than R
+ 
+
+ align:start position:0%
+its for X greater than R
+but we include the incoming and outgoing
+
+ align:start position:0%
+but we include the incoming and outgoing
+ 
+
+ align:start position:0%
+but we include the incoming and outgoing
+things because both are defined for X
+
+ align:start position:0%
+things because both are defined for X
+ 
+
+ align:start position:0%
+things because both are defined for X
+greater than R so the total wave is this
+
+ align:start position:0%
+greater than R so the total wave is this
+ 
+
+ align:start position:0%
+greater than R so the total wave is this
+one and you notice that if the phase
+
+ align:start position:0%
+one and you notice that if the phase
+ 
+
+ align:start position:0%
+one and you notice that if the phase
+shift is zero you are nicely back to the
+
+ align:start position:0%
+shift is zero you are nicely back to the
+ 
+
+ align:start position:0%
+shift is zero you are nicely back to the
+wave function Phi that we found before
\ No newline at end of file
diff --git a/u6ud7JD0fV4.txt b/u6ud7JD0fV4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ba3fc606d65d7afddd9184562360e0835eb22276
--- /dev/null
+++ b/u6ud7JD0fV4.txt
@@ -0,0 +1,1115 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The non-uniqueness of voltage in an MQS
+
+ align:start position:0%
+The non-uniqueness of voltage in an MQS
+ 
+
+ align:start position:0%
+The non-uniqueness of voltage in an MQS
+system can seem
+
+ align:start position:0%
+system can seem
+ 
+
+ align:start position:0%
+system can seem
+paradoxical. Yet, it is essential to the
+
+ align:start position:0%
+paradoxical. Yet, it is essential to the
+ 
+
+ align:start position:0%
+paradoxical. Yet, it is essential to the
+behavior of a common transformer.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+When the electric field intensity is
+
+ align:start position:0%
+When the electric field intensity is
+ 
+
+ align:start position:0%
+When the electric field intensity is
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+irrotational, we can count on its having
+
+ align:start position:0%
+irrotational, we can count on its having
+ 
+
+ align:start position:0%
+irrotational, we can count on its having
+no circulation around a closed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+path. This means that its integral
+
+ align:start position:0%
+path. This means that its integral
+ 
+
+ align:start position:0%
+path. This means that its integral
+between two points is the same
+
+ align:start position:0%
+between two points is the same
+ 
+
+ align:start position:0%
+between two points is the same
+regardless of path.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If the magnetic flux density in
+
+ align:start position:0%
+If the magnetic flux density in
+ 
+
+ align:start position:0%
+If the magnetic flux density in
+Faraday's law is important, the line
+
+ align:start position:0%
+Faraday's law is important, the line
+ 
+
+ align:start position:0%
+Faraday's law is important, the line
+integral of the electric field intensity
+
+ align:start position:0%
+integral of the electric field intensity
+ 
+
+ align:start position:0%
+integral of the electric field intensity
+is path
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dependent. This experiment emphasizes
+
+ align:start position:0%
+dependent. This experiment emphasizes
+ 
+
+ align:start position:0%
+dependent. This experiment emphasizes
+this by showing how the voltages
+
+ align:start position:0%
+this by showing how the voltages
+ 
+
+ align:start position:0%
+this by showing how the voltages
+measured by these
+
+ align:start position:0%
+measured by these
+ 
+
+ align:start position:0%
+measured by these
+leads and the
+
+ align:start position:0%
+leads and the
+ 
+
+ align:start position:0%
+leads and the
+oscilloscope are path
+
+ align:start position:0%
+oscilloscope are path
+ 
+
+ align:start position:0%
+oscilloscope are path
+dependent. Here's the ground lead of the
+
+ align:start position:0%
+dependent. Here's the ground lead of the
+ 
+
+ align:start position:0%
+dependent. Here's the ground lead of the
+oscilloscope.
+
+ align:start position:0%
+oscilloscope.
+ 
+
+ align:start position:0%
+oscilloscope.
+Here's the top trace
+
+ align:start position:0%
+Here's the top trace
+ 
+
+ align:start position:0%
+Here's the top trace
+lead and connected to the same point is
+
+ align:start position:0%
+lead and connected to the same point is
+ 
+
+ align:start position:0%
+lead and connected to the same point is
+this bottom trace
+
+ align:start position:0%
+this bottom trace
+ 
+
+ align:start position:0%
+this bottom trace
+lead. A magnetic flux is created in a
+
+ align:start position:0%
+lead. A magnetic flux is created in a
+ 
+
+ align:start position:0%
+lead. A magnetic flux is created in a
+tooidal magnetizable core by driving
+
+ align:start position:0%
+tooidal magnetizable core by driving
+ 
+
+ align:start position:0%
+tooidal magnetizable core by driving
+this winding with a syosoidal current.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Because it is a highly permeable ferite,
+
+ align:start position:0%
+Because it is a highly permeable ferite,
+ 
+
+ align:start position:0%
+Because it is a highly permeable ferite,
+the core guides a magnetic flux density
+
+ align:start position:0%
+the core guides a magnetic flux density
+ 
+
+ align:start position:0%
+the core guides a magnetic flux density
+B that is much greater than that in the
+
+ align:start position:0%
+B that is much greater than that in the
+ 
+
+ align:start position:0%
+B that is much greater than that in the
+surrounding
+
+ align:start position:0%
+surrounding
+ 
+
+ align:start position:0%
+surrounding
+air. Looped in series around the core
+
+ align:start position:0%
+air. Looped in series around the core
+ 
+
+ align:start position:0%
+air. Looped in series around the core
+are two resistors of unequal
+
+ align:start position:0%
+are two resistors of unequal
+ 
+
+ align:start position:0%
+are two resistors of unequal
+values. The terminals of these resistors
+
+ align:start position:0%
+values. The terminals of these resistors
+ 
+
+ align:start position:0%
+values. The terminals of these resistors
+are connected together to form a pair of
+
+ align:start position:0%
+are connected together to form a pair of
+ 
+
+ align:start position:0%
+are connected together to form a pair of
+nodes.
+
+ align:start position:0%
+nodes.
+ 
+
+ align:start position:0%
+nodes.
+One of these nodes is
+
+ align:start position:0%
+One of these nodes is
+ 
+
+ align:start position:0%
+One of these nodes is
+grounded. The other is connected to high
+
+ align:start position:0%
+grounded. The other is connected to high
+ 
+
+ align:start position:0%
+grounded. The other is connected to high
+impedance oscilloscope inputs through
+
+ align:start position:0%
+impedance oscilloscope inputs through
+ 
+
+ align:start position:0%
+impedance oscilloscope inputs through
+the two leads that follow different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+paths. Here's the ground
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lead. And we'll use a dual trace
+
+ align:start position:0%
+lead. And we'll use a dual trace
+ 
+
+ align:start position:0%
+lead. And we'll use a dual trace
+oscilloscope to display the voltages.
+
+ align:start position:0%
+oscilloscope to display the voltages.
+ 
+
+ align:start position:0%
+oscilloscope to display the voltages.
+Here's the lead connected to the top
+
+ align:start position:0%
+Here's the lead connected to the top
+ 
+
+ align:start position:0%
+Here's the lead connected to the top
+trace and then this lead is connected to
+
+ align:start position:0%
+trace and then this lead is connected to
+ 
+
+ align:start position:0%
+trace and then this lead is connected to
+the bottom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trace. The voltage is observed with the
+
+ align:start position:0%
+trace. The voltage is observed with the
+ 
+
+ align:start position:0%
+trace. The voltage is observed with the
+leads connected to the same node not
+
+ align:start position:0%
+leads connected to the same node not
+ 
+
+ align:start position:0%
+leads connected to the same node not
+only differ in magnitude but are 180°
+
+ align:start position:0%
+only differ in magnitude but are 180°
+ 
+
+ align:start position:0%
+only differ in magnitude but are 180°
+out of
+
+ align:start position:0%
+out of
+ 
+
+ align:start position:0%
+out of
+phase. The ratio of the voltage
+
+ align:start position:0%
+phase. The ratio of the voltage
+ 
+
+ align:start position:0%
+phase. The ratio of the voltage
+magnitudes is three.
+
+ align:start position:0%
+magnitudes is three.
+ 
+
+ align:start position:0%
+magnitudes is three.
+This is the ratio of the
+
+ align:start position:0%
+This is the ratio of the
+ 
+
+ align:start position:0%
+This is the ratio of the
+resistances. The probes are connected to
+
+ align:start position:0%
+resistances. The probes are connected to
+ 
+
+ align:start position:0%
+resistances. The probes are connected to
+the same node and yet the voltages
+
+ align:start position:0%
+the same node and yet the voltages
+ 
+
+ align:start position:0%
+the same node and yet the voltages
+differ by a factor of three and are 180°
+
+ align:start position:0%
+differ by a factor of three and are 180°
+ 
+
+ align:start position:0%
+differ by a factor of three and are 180°
+out of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phase. We check to see that we don't
+
+ align:start position:0%
+phase. We check to see that we don't
+ 
+
+ align:start position:0%
+phase. We check to see that we don't
+have the traces on different scales by
+
+ align:start position:0%
+have the traces on different scales by
+ 
+
+ align:start position:0%
+have the traces on different scales by
+reversing the trace connections.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Reversal of the leads results in a
+
+ align:start position:0%
+Reversal of the leads results in a
+ 
+
+ align:start position:0%
+Reversal of the leads results in a
+reversal of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+traces. Faraday's integral law accounts
+
+ align:start position:0%
+traces. Faraday's integral law accounts
+ 
+
+ align:start position:0%
+traces. Faraday's integral law accounts
+for this seeming failure of Kirkov's
+
+ align:start position:0%
+for this seeming failure of Kirkov's
+ 
+
+ align:start position:0%
+for this seeming failure of Kirkov's
+voltage law for how it is that different
+
+ align:start position:0%
+voltage law for how it is that different
+ 
+
+ align:start position:0%
+voltage law for how it is that different
+voltages are measured by probes
+
+ align:start position:0%
+voltages are measured by probes
+ 
+
+ align:start position:0%
+voltages are measured by probes
+connected between the same
+
+ align:start position:0%
+connected between the same
+ 
+
+ align:start position:0%
+connected between the same
+nodes. This is a cross-section of the
+
+ align:start position:0%
+nodes. This is a cross-section of the
+ 
+
+ align:start position:0%
+nodes. This is a cross-section of the
+core. The pair of resistors are
+
+ align:start position:0%
+core. The pair of resistors are
+ 
+
+ align:start position:0%
+core. The pair of resistors are
+connected in series.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The node that is connected to the ground
+
+ align:start position:0%
+The node that is connected to the ground
+ 
+
+ align:start position:0%
+The node that is connected to the ground
+terminal of each probe is
+
+ align:start position:0%
+terminal of each probe is
+ 
+
+ align:start position:0%
+terminal of each probe is
+here. One scope terminal is connected to
+
+ align:start position:0%
+here. One scope terminal is connected to
+ 
+
+ align:start position:0%
+here. One scope terminal is connected to
+the other node like
+
+ align:start position:0%
+the other node like
+ 
+
+ align:start position:0%
+the other node like
+this. While the other is connected like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this. The scope resistances are very
+
+ align:start position:0%
+this. The scope resistances are very
+ 
+
+ align:start position:0%
+this. The scope resistances are very
+large compared to either
+
+ align:start position:0%
+large compared to either
+ 
+
+ align:start position:0%
+large compared to either
+R1 or to R2.
+
+ align:start position:0%
+R1 or to R2.
+ 
+
+ align:start position:0%
+R1 or to R2.
+So the current carried by the
+
+ align:start position:0%
+So the current carried by the
+ 
+
+ align:start position:0%
+So the current carried by the
+oscilloscope leads is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negligible. This means that if there is
+
+ align:start position:0%
+negligible. This means that if there is
+ 
+
+ align:start position:0%
+negligible. This means that if there is
+a current I through one of the series
+
+ align:start position:0%
+a current I through one of the series
+ 
+
+ align:start position:0%
+a current I through one of the series
+resistors, it must be the same as that
+
+ align:start position:0%
+resistors, it must be the same as that
+ 
+
+ align:start position:0%
+resistors, it must be the same as that
+through the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other because it encloses the time
+
+ align:start position:0%
+other because it encloses the time
+ 
+
+ align:start position:0%
+other because it encloses the time
+varying magnetic flux carried by the
+
+ align:start position:0%
+varying magnetic flux carried by the
+ 
+
+ align:start position:0%
+varying magnetic flux carried by the
+core. There is a current circulating
+
+ align:start position:0%
+core. There is a current circulating
+ 
+
+ align:start position:0%
+core. There is a current circulating
+through the resistors.
+
+ align:start position:0%
+through the resistors.
+ 
+
+ align:start position:0%
+through the resistors.
+The induction of this current is
+
+ align:start position:0%
+The induction of this current is
+ 
+
+ align:start position:0%
+The induction of this current is
+predicted by Ohm's law and Faraday's
+
+ align:start position:0%
+predicted by Ohm's law and Faraday's
+ 
+
+ align:start position:0%
+predicted by Ohm's law and Faraday's
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+law. Here the T
+
+ align:start position:0%
+law. Here the T
+ 
+
+ align:start position:0%
+law. Here the T
+contour is the path of circulation
+
+ align:start position:0%
+contour is the path of circulation
+ 
+
+ align:start position:0%
+contour is the path of circulation
+through the
+
+ align:start position:0%
+through the
+ 
+
+ align:start position:0%
+through the
+resistors and the surface cuts through
+
+ align:start position:0%
+resistors and the surface cuts through
+ 
+
+ align:start position:0%
+resistors and the surface cuts through
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+core. The voltage measured by trace one
+
+ align:start position:0%
+core. The voltage measured by trace one
+ 
+
+ align:start position:0%
+core. The voltage measured by trace one
+is determined by applying Faraday's
+
+ align:start position:0%
+is determined by applying Faraday's
+ 
+
+ align:start position:0%
+is determined by applying Faraday's
+integral law to this contour.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it links a negligible magnetic
+
+ align:start position:0%
+because it links a negligible magnetic
+ 
+
+ align:start position:0%
+because it links a negligible magnetic
+flux. What is measured is just what is
+
+ align:start position:0%
+flux. What is measured is just what is
+ 
+
+ align:start position:0%
+flux. What is measured is just what is
+expected. The negative of the current
+
+ align:start position:0%
+expected. The negative of the current
+ 
+
+ align:start position:0%
+expected. The negative of the current
+times the resistance R
+
+ align:start position:0%
+times the resistance R
+ 
+
+ align:start position:0%
+times the resistance R
+sub1. The voltage measured by trace 2
+
+ align:start position:0%
+sub1. The voltage measured by trace 2
+ 
+
+ align:start position:0%
+sub1. The voltage measured by trace 2
+follows from this contour and is the
+
+ align:start position:0%
+follows from this contour and is the
+ 
+
+ align:start position:0%
+follows from this contour and is the
+same current but multiplied by plus R
+
+ align:start position:0%
+same current but multiplied by plus R
+ 
+
+ align:start position:0%
+same current but multiplied by plus R
+sub 2.
+
+ align:start position:0%
+sub 2.
+ 
+
+ align:start position:0%
+sub 2.
+The current out of the positive terminal
+
+ align:start position:0%
+The current out of the positive terminal
+ 
+
+ align:start position:0%
+The current out of the positive terminal
+of R sub1 is that into the positive
+
+ align:start position:0%
+of R sub1 is that into the positive
+ 
+
+ align:start position:0%
+of R sub1 is that into the positive
+terminal of R
+
+ align:start position:0%
+terminal of R
+ 
+
+ align:start position:0%
+terminal of R
+sub2. When voltage one is positive,
+
+ align:start position:0%
+sub2. When voltage one is positive,
+ 
+
+ align:start position:0%
+sub2. When voltage one is positive,
+voltage two must be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative. The ratio of the voltages is
+
+ align:start position:0%
+negative. The ratio of the voltages is
+ 
+
+ align:start position:0%
+negative. The ratio of the voltages is
+the negative ratio of the
+
+ align:start position:0%
+the negative ratio of the
+ 
+
+ align:start position:0%
+the negative ratio of the
+resistances. In our case, the ratio of
+
+ align:start position:0%
+resistances. In our case, the ratio of
+ 
+
+ align:start position:0%
+resistances. In our case, the ratio of
+the resistances is 30 ohms to 10 ohms.
+
+ align:start position:0%
+the resistances is 30 ohms to 10 ohms.
+ 
+
+ align:start position:0%
+the resistances is 30 ohms to 10 ohms.
+three. Just as we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measured, if the probe leads follow the
+
+ align:start position:0%
+measured, if the probe leads follow the
+ 
+
+ align:start position:0%
+measured, if the probe leads follow the
+same paths, the signals should be the
+
+ align:start position:0%
+same paths, the signals should be the
+ 
+
+ align:start position:0%
+same paths, the signals should be the
+same.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If we remove one of the leads and then
+
+ align:start position:0%
+If we remove one of the leads and then
+ 
+
+ align:start position:0%
+If we remove one of the leads and then
+connect the other one to its own
+
+ align:start position:0%
+connect the other one to its own
+ 
+
+ align:start position:0%
+connect the other one to its own
+ground after having looped the lead
+
+ align:start position:0%
+ground after having looped the lead
+ 
+
+ align:start position:0%
+ground after having looped the lead
+through the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+core, what we see is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this. Just as the series resistors form
+
+ align:start position:0%
+this. Just as the series resistors form
+ 
+
+ align:start position:0%
+this. Just as the series resistors form
+the secondary of a transformer, so now
+
+ align:start position:0%
+the secondary of a transformer, so now
+ 
+
+ align:start position:0%
+the secondary of a transformer, so now
+the lead itself is a one-turn secondary.
+
+ align:start position:0%
+the lead itself is a one-turn secondary.
+ 
+
+ align:start position:0%
+the lead itself is a one-turn secondary.
+The measured voltage is simply the time
+
+ align:start position:0%
+The measured voltage is simply the time
+ 
+
+ align:start position:0%
+The measured voltage is simply the time
+rate of change of the flux through the
+
+ align:start position:0%
+rate of change of the flux through the
+ 
+
+ align:start position:0%
+rate of change of the flux through the
+core.
\ No newline at end of file
diff --git a/uM5AoUgCA00.txt b/uM5AoUgCA00.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bd923ff694d78377683bf59cc388b816ffbc8093
--- /dev/null
+++ b/uM5AoUgCA00.txt
@@ -0,0 +1,15307 @@
+align:start position:0%
+ 
+we'll start off by talking a little bit
+
+ align:start position:0%
+we'll start off by talking a little bit
+ 
+
+ align:start position:0%
+we'll start off by talking a little bit
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+review of things we've done last time
+
+ align:start position:0%
+review of things we've done last time
+ 
+
+ align:start position:0%
+review of things we've done last time
+perspective projection
+
+ align:start position:0%
+perspective projection
+ 
+
+ align:start position:0%
+perspective projection
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a little bit about
+
+ align:start position:0%
+a little bit about
+ 
+
+ align:start position:0%
+a little bit about
+things that are relevant to the homework
+
+ align:start position:0%
+things that are relevant to the homework
+ 
+
+ align:start position:0%
+things that are relevant to the homework
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+particularly the last two questions
+
+ align:start position:0%
+particularly the last two questions
+ 
+
+ align:start position:0%
+particularly the last two questions
+and we'll
+
+ align:start position:0%
+and we'll
+ 
+
+ align:start position:0%
+and we'll
+go from perspective projection to
+
+ align:start position:0%
+go from perspective projection to
+ 
+
+ align:start position:0%
+go from perspective projection to
+motion so in perspective projection we
+
+ align:start position:0%
+motion so in perspective projection we
+ 
+
+ align:start position:0%
+motion so in perspective projection we
+have a relationship between points in
+
+ align:start position:0%
+have a relationship between points in
+ 
+
+ align:start position:0%
+have a relationship between points in
+the environment and points in the image
+
+ align:start position:0%
+the environment and points in the image
+ 
+
+ align:start position:0%
+the environment and points in the image
+and we found that we had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this simple relationship
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between the 3d world and the 2d world
+
+ align:start position:0%
+between the 3d world and the 2d world
+ 
+
+ align:start position:0%
+between the 3d world and the 2d world
+as long as we pick a suitable coordinate
+
+ align:start position:0%
+as long as we pick a suitable coordinate
+ 
+
+ align:start position:0%
+as long as we pick a suitable coordinate
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+with the origin at the center of
+
+ align:start position:0%
+with the origin at the center of
+ 
+
+ align:start position:0%
+with the origin at the center of
+projection and the z-axis along the
+
+ align:start position:0%
+projection and the z-axis along the
+ 
+
+ align:start position:0%
+projection and the z-axis along the
+optical axis
+
+ align:start position:0%
+optical axis
+ 
+
+ align:start position:0%
+optical axis
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+but then we're going to
+
+ align:start position:0%
+but then we're going to
+ 
+
+ align:start position:0%
+but then we're going to
+go from that to motion by uh
+
+ align:start position:0%
+go from that to motion by uh
+ 
+
+ align:start position:0%
+go from that to motion by uh
+differentiating that equation
+
+ align:start position:0%
+differentiating that equation
+ 
+
+ align:start position:0%
+differentiating that equation
+and then we'll
+
+ align:start position:0%
+and then we'll
+ 
+
+ align:start position:0%
+and then we'll
+talk about
+
+ align:start position:0%
+talk about
+ 
+
+ align:start position:0%
+talk about
+motion of brightness patterns in the
+
+ align:start position:0%
+motion of brightness patterns in the
+ 
+
+ align:start position:0%
+motion of brightness patterns in the
+image
+
+ align:start position:0%
+image
+ 
+
+ align:start position:0%
+image
+itself
+
+ align:start position:0%
+itself
+ 
+
+ align:start position:0%
+itself
+okay so we had that and then we had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+vector version
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh let's see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+is only slightly more compact
+
+ align:start position:0%
+is only slightly more compact
+ 
+
+ align:start position:0%
+is only slightly more compact
+so it's not uh in this case a great help
+
+ align:start position:0%
+so it's not uh in this case a great help
+ 
+
+ align:start position:0%
+so it's not uh in this case a great help
+but we'll use both of them we'll switch
+
+ align:start position:0%
+but we'll use both of them we'll switch
+ 
+
+ align:start position:0%
+but we'll use both of them we'll switch
+back and forth and use whatever is
+
+ align:start position:0%
+back and forth and use whatever is
+ 
+
+ align:start position:0%
+back and forth and use whatever is
+suitable for the problem that we're
+
+ align:start position:0%
+suitable for the problem that we're
+ 
+
+ align:start position:0%
+suitable for the problem that we're
+dealing with
+
+ align:start position:0%
+dealing with
+ 
+
+ align:start position:0%
+dealing with
+so let's um
+
+ align:start position:0%
+so let's um
+ 
+
+ align:start position:0%
+so let's um
+let's start with motion
+
+ align:start position:0%
+let's start with motion
+ 
+
+ align:start position:0%
+let's start with motion
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+that's a static
+
+ align:start position:0%
+that's a static
+ 
+
+ align:start position:0%
+that's a static
+setup and we can easily relate points in
+
+ align:start position:0%
+setup and we can easily relate points in
+ 
+
+ align:start position:0%
+setup and we can easily relate points in
+the environment to points in the image
+
+ align:start position:0%
+the environment to points in the image
+ 
+
+ align:start position:0%
+the environment to points in the image
+now what what if there's motion what if
+
+ align:start position:0%
+now what what if there's motion what if
+ 
+
+ align:start position:0%
+now what what if there's motion what if
+that point in the environment moves
+
+ align:start position:0%
+that point in the environment moves
+ 
+
+ align:start position:0%
+that point in the environment moves
+obviously there will be some motion in
+
+ align:start position:0%
+obviously there will be some motion in
+ 
+
+ align:start position:0%
+obviously there will be some motion in
+the image and if we can find out what
+
+ align:start position:0%
+the image and if we can find out what
+ 
+
+ align:start position:0%
+the image and if we can find out what
+that relationship is then maybe in some
+
+ align:start position:0%
+that relationship is then maybe in some
+ 
+
+ align:start position:0%
+that relationship is then maybe in some
+circumstances we can invert that so that
+
+ align:start position:0%
+circumstances we can invert that so that
+ 
+
+ align:start position:0%
+circumstances we can invert that so that
+we can measure the motion of brightness
+
+ align:start position:0%
+we can measure the motion of brightness
+ 
+
+ align:start position:0%
+we can measure the motion of brightness
+patterns in the image as you do in the
+
+ align:start position:0%
+patterns in the image as you do in the
+ 
+
+ align:start position:0%
+patterns in the image as you do in the
+homework problem and somehow use that to
+
+ align:start position:0%
+homework problem and somehow use that to
+ 
+
+ align:start position:0%
+homework problem and somehow use that to
+figure out what's happening out in the
+
+ align:start position:0%
+figure out what's happening out in the
+ 
+
+ align:start position:0%
+figure out what's happening out in the
+world so we just differentiate
+
+ align:start position:0%
+world so we just differentiate
+ 
+
+ align:start position:0%
+world so we just differentiate
+we take our
+
+ align:start position:0%
+we take our
+ 
+
+ align:start position:0%
+we take our
+perspective
+
+ align:start position:0%
+perspective
+ 
+
+ align:start position:0%
+perspective
+equation and we differentiate so we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now on the right hand side
+
+ align:start position:0%
+now on the right hand side
+ 
+
+ align:start position:0%
+now on the right hand side
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+we have a ratio
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so there are two parts to the
+
+ align:start position:0%
+and so there are two parts to the
+ 
+
+ align:start position:0%
+and so there are two parts to the
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um we just apply the rule for
+
+ align:start position:0%
+um we just apply the rule for
+ 
+
+ align:start position:0%
+um we just apply the rule for
+differentiation of a ratio
+
+ align:start position:0%
+differentiation of a ratio
+ 
+
+ align:start position:0%
+differentiation of a ratio
+and what i'm going to do a lot is
+
+ align:start position:0%
+and what i'm going to do a lot is
+ 
+
+ align:start position:0%
+and what i'm going to do a lot is
+reduce the
+
+ align:start position:0%
+reduce the
+ 
+
+ align:start position:0%
+reduce the
+intimidation level of the equation
+
+ align:start position:0%
+intimidation level of the equation
+ 
+
+ align:start position:0%
+intimidation level of the equation
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+substituting more easily digested
+
+ align:start position:0%
+substituting more easily digested
+ 
+
+ align:start position:0%
+substituting more easily digested
+symbols so in this case we've got all
+
+ align:start position:0%
+symbols so in this case we've got all
+ 
+
+ align:start position:0%
+symbols so in this case we've got all
+these derivatives well what are they
+
+ align:start position:0%
+these derivatives well what are they
+ 
+
+ align:start position:0%
+these derivatives well what are they
+they're really velocities so there's
+
+ align:start position:0%
+they're really velocities so there's
+ 
+
+ align:start position:0%
+they're really velocities so there's
+going to be a velocity in the image in
+
+ align:start position:0%
+going to be a velocity in the image in
+ 
+
+ align:start position:0%
+going to be a velocity in the image in
+the x direction which i'll call u
+
+ align:start position:0%
+the x direction which i'll call u
+ 
+
+ align:start position:0%
+the x direction which i'll call u
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+there's a velocity in the real world
+
+ align:start position:0%
+there's a velocity in the real world
+ 
+
+ align:start position:0%
+there's a velocity in the real world
+in the x direction which i'll call big u
+
+ align:start position:0%
+in the x direction which i'll call big u
+ 
+
+ align:start position:0%
+in the x direction which i'll call big u
+and then we have
+
+ align:start position:0%
+and then we have
+ 
+
+ align:start position:0%
+and then we have
+a velocity in the real world in the z
+
+ align:start position:0%
+a velocity in the real world in the z
+ 
+
+ align:start position:0%
+a velocity in the real world in the z
+direction which i'll hold w
+
+ align:start position:0%
+direction which i'll hold w
+ 
+
+ align:start position:0%
+direction which i'll hold w
+so that looks a little bit less scary
+
+ align:start position:0%
+so that looks a little bit less scary
+ 
+
+ align:start position:0%
+so that looks a little bit less scary
+and of course i can do the same in the y
+
+ align:start position:0%
+and of course i can do the same in the y
+ 
+
+ align:start position:0%
+and of course i can do the same in the y
+direction so apply the same idea over
+
+ align:start position:0%
+direction so apply the same idea over
+ 
+
+ align:start position:0%
+direction so apply the same idea over
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the forward direction that is
+
+ align:start position:0%
+so that's the forward direction that is
+ 
+
+ align:start position:0%
+so that's the forward direction that is
+if you tell me what the motion vector is
+
+ align:start position:0%
+if you tell me what the motion vector is
+ 
+
+ align:start position:0%
+if you tell me what the motion vector is
+in 3d
+
+ align:start position:0%
+in 3d
+ 
+
+ align:start position:0%
+in 3d
+here's the formula to tell me what the
+
+ align:start position:0%
+here's the formula to tell me what the
+ 
+
+ align:start position:0%
+here's the formula to tell me what the
+motion vector is in 2d
+
+ align:start position:0%
+motion vector is in 2d
+ 
+
+ align:start position:0%
+motion vector is in 2d
+and of course we might want to invert
+
+ align:start position:0%
+and of course we might want to invert
+ 
+
+ align:start position:0%
+and of course we might want to invert
+that but for the moment let's go with
+
+ align:start position:0%
+that but for the moment let's go with
+ 
+
+ align:start position:0%
+that but for the moment let's go with
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+now we can rewrite this in various forms
+
+ align:start position:0%
+now we can rewrite this in various forms
+ 
+
+ align:start position:0%
+now we can rewrite this in various forms
+and since we'll use this a lot let's do
+
+ align:start position:0%
+and since we'll use this a lot let's do
+ 
+
+ align:start position:0%
+and since we'll use this a lot let's do
+that so one thing we can do is
+
+ align:start position:0%
+that so one thing we can do is
+ 
+
+ align:start position:0%
+that so one thing we can do is
+we can split up
+
+ align:start position:0%
+we can split up
+ 
+
+ align:start position:0%
+we can split up
+these terms into
+
+ align:start position:0%
+these terms into
+ 
+
+ align:start position:0%
+these terms into
+1 over z
+
+ align:start position:0%
+1 over z
+ 
+
+ align:start position:0%
+1 over z
+x over z
+
+ align:start position:0%
+x over z
+ 
+
+ align:start position:0%
+x over z
+and why is that useful well because we
+
+ align:start position:0%
+and why is that useful well because we
+ 
+
+ align:start position:0%
+and why is that useful well because we
+know that x over c is little x over f so
+
+ align:start position:0%
+know that x over c is little x over f so
+ 
+
+ align:start position:0%
+know that x over c is little x over f so
+we can rewrite this
+
+ align:start position:0%
+we can rewrite this
+ 
+
+ align:start position:0%
+we can rewrite this
+using image coordinates
+
+ align:start position:0%
+using image coordinates
+ 
+
+ align:start position:0%
+using image coordinates
+and we end up with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+one thing this allows us to do is to ask
+
+ align:start position:0%
+one thing this allows us to do is to ask
+ 
+
+ align:start position:0%
+one thing this allows us to do is to ask
+the question uh where in the image is
+
+ align:start position:0%
+the question uh where in the image is
+ 
+
+ align:start position:0%
+the question uh where in the image is
+there no motion
+
+ align:start position:0%
+there no motion
+ 
+
+ align:start position:0%
+there no motion
+so if
+
+ align:start position:0%
+so if
+ 
+
+ align:start position:0%
+so if
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+we're looking at the
+
+ align:start position:0%
+we're looking at the
+ 
+
+ align:start position:0%
+we're looking at the
+movement of brightness patterns in the
+
+ align:start position:0%
+movement of brightness patterns in the
+ 
+
+ align:start position:0%
+movement of brightness patterns in the
+image there may be some places where
+
+ align:start position:0%
+image there may be some places where
+ 
+
+ align:start position:0%
+image there may be some places where
+there isn't any and those are of
+
+ align:start position:0%
+there isn't any and those are of
+ 
+
+ align:start position:0%
+there isn't any and those are of
+particular interest
+
+ align:start position:0%
+particular interest
+ 
+
+ align:start position:0%
+particular interest
+first of all because we can find them
+
+ align:start position:0%
+first of all because we can find them
+ 
+
+ align:start position:0%
+first of all because we can find them
+using image processing techniques and
+
+ align:start position:0%
+using image processing techniques and
+ 
+
+ align:start position:0%
+using image processing techniques and
+then because they tell us something
+
+ align:start position:0%
+then because they tell us something
+ 
+
+ align:start position:0%
+then because they tell us something
+about the environment or the motion so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+see if we set this
+
+ align:start position:0%
+see if we set this
+ 
+
+ align:start position:0%
+see if we set this
+equal to zero
+
+ align:start position:0%
+equal to zero
+ 
+
+ align:start position:0%
+equal to zero
+uh we find that's true at a point x
+
+ align:start position:0%
+uh we find that's true at a point x
+ 
+
+ align:start position:0%
+uh we find that's true at a point x
+naught such that x naught over f is a
+
+ align:start position:0%
+naught such that x naught over f is a
+ 
+
+ align:start position:0%
+naught such that x naught over f is a
+big u of a big w and similarly for this
+
+ align:start position:0%
+big u of a big w and similarly for this
+ 
+
+ align:start position:0%
+big u of a big w and similarly for this
+one equal to zero and so the point x
+
+ align:start position:0%
+one equal to zero and so the point x
+ 
+
+ align:start position:0%
+one equal to zero and so the point x
+naught y naught is that uh sort after
+
+ align:start position:0%
+naught y naught is that uh sort after
+ 
+
+ align:start position:0%
+naught y naught is that uh sort after
+point where there is no image motion and
+
+ align:start position:0%
+point where there is no image motion and
+ 
+
+ align:start position:0%
+point where there is no image motion and
+we call it the focus of expansion and in
+
+ align:start position:0%
+we call it the focus of expansion and in
+ 
+
+ align:start position:0%
+we call it the focus of expansion and in
+the case of a simple situation like i'm
+
+ align:start position:0%
+the case of a simple situation like i'm
+ 
+
+ align:start position:0%
+the case of a simple situation like i'm
+approaching the wall
+
+ align:start position:0%
+approaching the wall
+ 
+
+ align:start position:0%
+approaching the wall
+the focus of expansion is the point
+
+ align:start position:0%
+the focus of expansion is the point
+ 
+
+ align:start position:0%
+the focus of expansion is the point
+towards which i'm heading
+
+ align:start position:0%
+towards which i'm heading
+ 
+
+ align:start position:0%
+towards which i'm heading
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+we can just express it directly in terms
+
+ align:start position:0%
+we can just express it directly in terms
+ 
+
+ align:start position:0%
+we can just express it directly in terms
+of the 3d motion vector and you'll
+
+ align:start position:0%
+of the 3d motion vector and you'll
+ 
+
+ align:start position:0%
+of the 3d motion vector and you'll
+notice that this is actually just a
+
+ align:start position:0%
+notice that this is actually just a
+ 
+
+ align:start position:0%
+notice that this is actually just a
+projection
+
+ align:start position:0%
+projection
+ 
+
+ align:start position:0%
+projection
+of the 3d motion vector
+
+ align:start position:0%
+of the 3d motion vector
+ 
+
+ align:start position:0%
+of the 3d motion vector
+into the image plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i take that same diagram over there
+
+ align:start position:0%
+so i take that same diagram over there
+ 
+
+ align:start position:0%
+so i take that same diagram over there
+and now instead of mapping
+
+ align:start position:0%
+and now instead of mapping
+ 
+
+ align:start position:0%
+and now instead of mapping
+the vector to the point p i'm mapping
+
+ align:start position:0%
+the vector to the point p i'm mapping
+ 
+
+ align:start position:0%
+the vector to the point p i'm mapping
+the velocity
+
+ align:start position:0%
+the velocity
+ 
+
+ align:start position:0%
+the velocity
+and if i do that
+
+ align:start position:0%
+and if i do that
+ 
+
+ align:start position:0%
+and if i do that
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+that defines this point x naught y
+
+ align:start position:0%
+that defines this point x naught y
+ 
+
+ align:start position:0%
+that defines this point x naught y
+naught in the image where there is no
+
+ align:start position:0%
+naught in the image where there is no
+ 
+
+ align:start position:0%
+naught in the image where there is no
+motion and that's called the focus of
+
+ align:start position:0%
+motion and that's called the focus of
+ 
+
+ align:start position:0%
+motion and that's called the focus of
+expansion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh that's a useful thing
+
+ align:start position:0%
+okay uh that's a useful thing
+ 
+
+ align:start position:0%
+okay uh that's a useful thing
+because if you can find the focus of
+
+ align:start position:0%
+because if you can find the focus of
+ 
+
+ align:start position:0%
+because if you can find the focus of
+expansion
+
+ align:start position:0%
+expansion
+ 
+
+ align:start position:0%
+expansion
+you all you need to do is connect that
+
+ align:start position:0%
+you all you need to do is connect that
+ 
+
+ align:start position:0%
+you all you need to do is connect that
+point x naught y naught to this to the
+
+ align:start position:0%
+point x naught y naught to this to the
+ 
+
+ align:start position:0%
+point x naught y naught to this to the
+origin and you have a vector that tells
+
+ align:start position:0%
+origin and you have a vector that tells
+ 
+
+ align:start position:0%
+origin and you have a vector that tells
+you the direction of motion so
+
+ align:start position:0%
+you the direction of motion so
+ 
+
+ align:start position:0%
+you the direction of motion so
+a nice example
+
+ align:start position:0%
+a nice example
+ 
+
+ align:start position:0%
+a nice example
+of inverting that process
+
+ align:start position:0%
+of inverting that process
+ 
+
+ align:start position:0%
+of inverting that process
+okay now once we have the focus of
+
+ align:start position:0%
+okay now once we have the focus of
+ 
+
+ align:start position:0%
+okay now once we have the focus of
+expansion we can rewrite those equations
+
+ align:start position:0%
+expansion we can rewrite those equations
+ 
+
+ align:start position:0%
+expansion we can rewrite those equations
+yet one more time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so there are a couple of things
+
+ align:start position:0%
+and so there are a couple of things
+ 
+
+ align:start position:0%
+and so there are a couple of things
+there that are of interest
+
+ align:start position:0%
+there that are of interest
+ 
+
+ align:start position:0%
+there that are of interest
+one of them is that
+
+ align:start position:0%
+one of them is that
+ 
+
+ align:start position:0%
+one of them is that
+the f's cancel
+
+ align:start position:0%
+the f's cancel
+ 
+
+ align:start position:0%
+the f's cancel
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we can do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we actually can get an idea of
+
+ align:start position:0%
+and then we actually can get an idea of
+ 
+
+ align:start position:0%
+and then we actually can get an idea of
+what the image is going to look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's suppose this is the image plane
+
+ align:start position:0%
+let's suppose this is the image plane
+ 
+
+ align:start position:0%
+let's suppose this is the image plane
+now we're looking at it straight on and
+
+ align:start position:0%
+now we're looking at it straight on and
+ 
+
+ align:start position:0%
+now we're looking at it straight on and
+suppose that
+
+ align:start position:0%
+suppose that
+ 
+
+ align:start position:0%
+suppose that
+this is our focus of expansion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you know we're moving with respect
+
+ align:start position:0%
+and you know we're moving with respect
+ 
+
+ align:start position:0%
+and you know we're moving with respect
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the environment is moving with respect
+
+ align:start position:0%
+the environment is moving with respect
+ 
+
+ align:start position:0%
+the environment is moving with respect
+to us so we're moving with respect to
+
+ align:start position:0%
+to us so we're moving with respect to
+ 
+
+ align:start position:0%
+to us so we're moving with respect to
+environment you know einstein said that
+
+ align:start position:0%
+environment you know einstein said that
+ 
+
+ align:start position:0%
+environment you know einstein said that
+it's all relative it doesn't matter the
+
+ align:start position:0%
+it's all relative it doesn't matter the
+ 
+
+ align:start position:0%
+it's all relative it doesn't matter the
+only thing we can determine is the
+
+ align:start position:0%
+only thing we can determine is the
+ 
+
+ align:start position:0%
+only thing we can determine is the
+difference between the two motions
+
+ align:start position:0%
+difference between the two motions
+ 
+
+ align:start position:0%
+difference between the two motions
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+there will be no image motion here and
+
+ align:start position:0%
+there will be no image motion here and
+ 
+
+ align:start position:0%
+there will be no image motion here and
+what about other places well this uh
+
+ align:start position:0%
+what about other places well this uh
+ 
+
+ align:start position:0%
+what about other places well this uh
+tells you
+
+ align:start position:0%
+tells you
+ 
+
+ align:start position:0%
+tells you
+exactly what the pattern will be like
+
+ align:start position:0%
+exactly what the pattern will be like
+ 
+
+ align:start position:0%
+exactly what the pattern will be like
+right so if we
+
+ align:start position:0%
+right so if we
+ 
+
+ align:start position:0%
+right so if we
+go to the right such that x naught minus
+
+ align:start position:0%
+go to the right such that x naught minus
+ 
+
+ align:start position:0%
+go to the right such that x naught minus
+x is
+
+ align:start position:0%
+x is
+ 
+
+ align:start position:0%
+x is
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+uh positive while we keep this one zero
+
+ align:start position:0%
+uh positive while we keep this one zero
+ 
+
+ align:start position:0%
+uh positive while we keep this one zero
+what happens is well u will become
+
+ align:start position:0%
+what happens is well u will become
+ 
+
+ align:start position:0%
+what happens is well u will become
+larger the further we go away the larger
+
+ align:start position:0%
+larger the further we go away the larger
+ 
+
+ align:start position:0%
+larger the further we go away the larger
+so we'll have a little vector here
+
+ align:start position:0%
+so we'll have a little vector here
+ 
+
+ align:start position:0%
+so we'll have a little vector here
+that tells us the image motion at that
+
+ align:start position:0%
+that tells us the image motion at that
+ 
+
+ align:start position:0%
+that tells us the image motion at that
+point and another vector over here which
+
+ align:start position:0%
+point and another vector over here which
+ 
+
+ align:start position:0%
+point and another vector over here which
+is perhaps larger
+
+ align:start position:0%
+is perhaps larger
+ 
+
+ align:start position:0%
+is perhaps larger
+and then we can go to where this is
+
+ align:start position:0%
+and then we can go to where this is
+ 
+
+ align:start position:0%
+and then we can go to where this is
+negative so the other side
+
+ align:start position:0%
+negative so the other side
+ 
+
+ align:start position:0%
+negative so the other side
+draw a vector here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so i'm starting to draw a little vector
+
+ align:start position:0%
+so i'm starting to draw a little vector
+ 
+
+ align:start position:0%
+so i'm starting to draw a little vector
+diagram
+
+ align:start position:0%
+diagram
+ 
+
+ align:start position:0%
+diagram
+um of the
+
+ align:start position:0%
+um of the
+ 
+
+ align:start position:0%
+um of the
+motion field if you like how things are
+
+ align:start position:0%
+motion field if you like how things are
+ 
+
+ align:start position:0%
+motion field if you like how things are
+expanding from that point
+
+ align:start position:0%
+expanding from that point
+ 
+
+ align:start position:0%
+expanding from that point
+and i can do the same in the y direction
+
+ align:start position:0%
+and i can do the same in the y direction
+ 
+
+ align:start position:0%
+and i can do the same in the y direction
+so i suppose i keep x naught equals x
+
+ align:start position:0%
+so i suppose i keep x naught equals x
+ 
+
+ align:start position:0%
+so i suppose i keep x naught equals x
+but i change y naught
+
+ align:start position:0%
+but i change y naught
+ 
+
+ align:start position:0%
+but i change y naught
+so i'm going along this line
+
+ align:start position:0%
+so i'm going along this line
+ 
+
+ align:start position:0%
+so i'm going along this line
+i'm going to get vectors that point this
+
+ align:start position:0%
+i'm going to get vectors that point this
+ 
+
+ align:start position:0%
+i'm going to get vectors that point this
+way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+let me be adventurous and go off at
+
+ align:start position:0%
+let me be adventurous and go off at
+ 
+
+ align:start position:0%
+let me be adventurous and go off at
+right angles where
+
+ align:start position:0%
+right angles where
+ 
+
+ align:start position:0%
+right angles where
+x naught minus x is the same as y naught
+
+ align:start position:0%
+x naught minus x is the same as y naught
+ 
+
+ align:start position:0%
+x naught minus x is the same as y naught
+minus y well that means that u and v are
+
+ align:start position:0%
+minus y well that means that u and v are
+ 
+
+ align:start position:0%
+minus y well that means that u and v are
+going to be the same
+
+ align:start position:0%
+going to be the same
+ 
+
+ align:start position:0%
+going to be the same
+that means i'm going to get a vector at
+
+ align:start position:0%
+that means i'm going to get a vector at
+ 
+
+ align:start position:0%
+that means i'm going to get a vector at
+45 degrees right so
+
+ align:start position:0%
+45 degrees right so
+ 
+
+ align:start position:0%
+45 degrees right so
+and opposite direction like that
+
+ align:start position:0%
+and opposite direction like that
+ 
+
+ align:start position:0%
+and opposite direction like that
+and i think you can see
+
+ align:start position:0%
+and i think you can see
+ 
+
+ align:start position:0%
+and i think you can see
+that we're going to fill in this this
+
+ align:start position:0%
+that we're going to fill in this this
+ 
+
+ align:start position:0%
+that we're going to fill in this this
+whole diagram
+
+ align:start position:0%
+whole diagram
+ 
+
+ align:start position:0%
+whole diagram
+this little vector diagram with arrows
+
+ align:start position:0%
+this little vector diagram with arrows
+ 
+
+ align:start position:0%
+this little vector diagram with arrows
+that are pointing outwards from the
+
+ align:start position:0%
+that are pointing outwards from the
+ 
+
+ align:start position:0%
+that are pointing outwards from the
+focus of expansion that that's what this
+
+ align:start position:0%
+focus of expansion that that's what this
+ 
+
+ align:start position:0%
+focus of expansion that that's what this
+equation says that all these vectors are
+
+ align:start position:0%
+equation says that all these vectors are
+ 
+
+ align:start position:0%
+equation says that all these vectors are
+radiating outward and that's why it's
+
+ align:start position:0%
+radiating outward and that's why it's
+ 
+
+ align:start position:0%
+radiating outward and that's why it's
+called the focus of expansion so i'm
+
+ align:start position:0%
+called the focus of expansion so i'm
+ 
+
+ align:start position:0%
+called the focus of expansion so i'm
+moving towards that wall
+
+ align:start position:0%
+moving towards that wall
+ 
+
+ align:start position:0%
+moving towards that wall
+and this is the place i'm actually going
+
+ align:start position:0%
+and this is the place i'm actually going
+ 
+
+ align:start position:0%
+and this is the place i'm actually going
+to hit
+
+ align:start position:0%
+to hit
+ 
+
+ align:start position:0%
+to hit
+you know maybe going at an angle
+
+ align:start position:0%
+you know maybe going at an angle
+ 
+
+ align:start position:0%
+you know maybe going at an angle
+but my whole
+
+ align:start position:0%
+but my whole
+ 
+
+ align:start position:0%
+but my whole
+image is looming it's uh
+
+ align:start position:0%
+image is looming it's uh
+ 
+
+ align:start position:0%
+image is looming it's uh
+zooming outwards which
+
+ align:start position:0%
+zooming outwards which
+ 
+
+ align:start position:0%
+zooming outwards which
+is a useful clue
+
+ align:start position:0%
+is a useful clue
+ 
+
+ align:start position:0%
+is a useful clue
+uh useful cue for
+
+ align:start position:0%
+uh useful cue for
+ 
+
+ align:start position:0%
+uh useful cue for
+measuring distance and velocity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as you saw in the homework problem
+
+ align:start position:0%
+as you saw in the homework problem
+ 
+
+ align:start position:0%
+as you saw in the homework problem
+there's this scale factor ambiguity that
+
+ align:start position:0%
+there's this scale factor ambiguity that
+ 
+
+ align:start position:0%
+there's this scale factor ambiguity that
+because of perspective projection
+
+ align:start position:0%
+because of perspective projection
+ 
+
+ align:start position:0%
+because of perspective projection
+we can't actually tell absolute
+
+ align:start position:0%
+we can't actually tell absolute
+ 
+
+ align:start position:0%
+we can't actually tell absolute
+distances
+
+ align:start position:0%
+distances
+ 
+
+ align:start position:0%
+distances
+and we have a similar phenomena here
+
+ align:start position:0%
+and we have a similar phenomena here
+ 
+
+ align:start position:0%
+and we have a similar phenomena here
+but what we
+
+ align:start position:0%
+but what we
+ 
+
+ align:start position:0%
+but what we
+can tell is is this ratio
+
+ align:start position:0%
+can tell is is this ratio
+ 
+
+ align:start position:0%
+can tell is is this ratio
+and so this whole field depends uh
+
+ align:start position:0%
+and so this whole field depends uh
+ 
+
+ align:start position:0%
+and so this whole field depends uh
+critically on that ratio so so what is
+
+ align:start position:0%
+critically on that ratio so so what is
+ 
+
+ align:start position:0%
+critically on that ratio so so what is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+w over z
+
+ align:start position:0%
+w over z
+ 
+
+ align:start position:0%
+w over z
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and if i make that larger then you know
+
+ align:start position:0%
+and if i make that larger then you know
+ 
+
+ align:start position:0%
+and if i make that larger then you know
+the vectors will be larger that means
+
+ align:start position:0%
+the vectors will be larger that means
+ 
+
+ align:start position:0%
+the vectors will be larger that means
+i'm sort of getting closer to the
+
+ align:start position:0%
+i'm sort of getting closer to the
+ 
+
+ align:start position:0%
+i'm sort of getting closer to the
+surface i'm about to hit it
+
+ align:start position:0%
+surface i'm about to hit it
+ 
+
+ align:start position:0%
+surface i'm about to hit it
+conversely if i make it smaller
+
+ align:start position:0%
+conversely if i make it smaller
+ 
+
+ align:start position:0%
+conversely if i make it smaller
+that will be smaller if i make it
+
+ align:start position:0%
+that will be smaller if i make it
+ 
+
+ align:start position:0%
+that will be smaller if i make it
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+what happens well all of these vectors
+
+ align:start position:0%
+what happens well all of these vectors
+ 
+
+ align:start position:0%
+what happens well all of these vectors
+are reversed so it's a focus of
+
+ align:start position:0%
+are reversed so it's a focus of
+ 
+
+ align:start position:0%
+are reversed so it's a focus of
+compression
+
+ align:start position:0%
+compression
+ 
+
+ align:start position:0%
+compression
+there's no there's no such term but we
+
+ align:start position:0%
+there's no there's no such term but we
+ 
+
+ align:start position:0%
+there's no there's no such term but we
+could call it that um it's just the
+
+ align:start position:0%
+could call it that um it's just the
+ 
+
+ align:start position:0%
+could call it that um it's just the
+inverse of the focus of expansion and
+
+ align:start position:0%
+inverse of the focus of expansion and
+ 
+
+ align:start position:0%
+inverse of the focus of expansion and
+that's what happens if i'm moving away
+
+ align:start position:0%
+that's what happens if i'm moving away
+ 
+
+ align:start position:0%
+that's what happens if i'm moving away
+from the surface so i'm taking off from
+
+ align:start position:0%
+from the surface so i'm taking off from
+ 
+
+ align:start position:0%
+from the surface so i'm taking off from
+the lunar surface and the image is sort
+
+ align:start position:0%
+the lunar surface and the image is sort
+ 
+
+ align:start position:0%
+the lunar surface and the image is sort
+of compressing on
+
+ align:start position:0%
+of compressing on
+ 
+
+ align:start position:0%
+of compressing on
+as i leave so
+
+ align:start position:0%
+as i leave so
+ 
+
+ align:start position:0%
+as i leave so
+okay well um
+
+ align:start position:0%
+okay well um
+ 
+
+ align:start position:0%
+okay well um
+so what is this well let's turn it on
+
+ align:start position:0%
+so what is this well let's turn it on
+ 
+
+ align:start position:0%
+so what is this well let's turn it on
+its head
+
+ align:start position:0%
+its head
+ 
+
+ align:start position:0%
+its head
+uh what is z over w
+
+ align:start position:0%
+uh what is z over w
+ 
+
+ align:start position:0%
+uh what is z over w
+and w of course is the rate of change of
+
+ align:start position:0%
+and w of course is the rate of change of
+ 
+
+ align:start position:0%
+and w of course is the rate of change of
+z
+
+ align:start position:0%
+z
+ 
+
+ align:start position:0%
+z
+so we got z over dz dt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what are the units of that so z is in
+
+ align:start position:0%
+what are the units of that so z is in
+ 
+
+ align:start position:0%
+what are the units of that so z is in
+say meters and dz dt is in meters per
+
+ align:start position:0%
+say meters and dz dt is in meters per
+ 
+
+ align:start position:0%
+say meters and dz dt is in meters per
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+so the units of that ratio are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+seconds and so uh can you think of what
+
+ align:start position:0%
+seconds and so uh can you think of what
+ 
+
+ align:start position:0%
+seconds and so uh can you think of what
+that quantity is
+
+ align:start position:0%
+that quantity is
+ 
+
+ align:start position:0%
+that quantity is
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+time to impact
+
+ align:start position:0%
+time to impact
+ 
+
+ align:start position:0%
+time to impact
+great so
+
+ align:start position:0%
+great so
+ 
+
+ align:start position:0%
+great so
+that's going to tell me
+
+ align:start position:0%
+that's going to tell me
+ 
+
+ align:start position:0%
+that's going to tell me
+how long it's going to take before i
+
+ align:start position:0%
+how long it's going to take before i
+ 
+
+ align:start position:0%
+how long it's going to take before i
+crash into this surface
+
+ align:start position:0%
+crash into this surface
+ 
+
+ align:start position:0%
+crash into this surface
+and so that's uh a quantity that we're
+
+ align:start position:0%
+and so that's uh a quantity that we're
+ 
+
+ align:start position:0%
+and so that's uh a quantity that we're
+going to spend some time thinking about
+
+ align:start position:0%
+going to spend some time thinking about
+ 
+
+ align:start position:0%
+going to spend some time thinking about
+uh both because it's important if you're
+
+ align:start position:0%
+uh both because it's important if you're
+ 
+
+ align:start position:0%
+uh both because it's important if you're
+say landing a
+
+ align:start position:0%
+say landing a
+ 
+
+ align:start position:0%
+say landing a
+nasa
+
+ align:start position:0%
+nasa
+ 
+
+ align:start position:0%
+nasa
+craft on europa
+
+ align:start position:0%
+craft on europa
+ 
+
+ align:start position:0%
+craft on europa
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+or if you're a fly landing on the
+
+ align:start position:0%
+or if you're a fly landing on the
+ 
+
+ align:start position:0%
+or if you're a fly landing on the
+ceiling
+
+ align:start position:0%
+ceiling
+ 
+
+ align:start position:0%
+ceiling
+uh and also it turns out to be
+
+ align:start position:0%
+uh and also it turns out to be
+ 
+
+ align:start position:0%
+uh and also it turns out to be
+relatively easy to compute compared to
+
+ align:start position:0%
+relatively easy to compute compared to
+ 
+
+ align:start position:0%
+relatively easy to compute compared to
+some of the other things that we'll be
+
+ align:start position:0%
+some of the other things that we'll be
+ 
+
+ align:start position:0%
+some of the other things that we'll be
+looking at
+
+ align:start position:0%
+looking at
+ 
+
+ align:start position:0%
+looking at
+by the way the
+
+ align:start position:0%
+by the way the
+ 
+
+ align:start position:0%
+by the way the
+landing on europa is a jpl
+
+ align:start position:0%
+landing on europa is a jpl
+ 
+
+ align:start position:0%
+landing on europa is a jpl
+rfp
+
+ align:start position:0%
+rfp
+ 
+
+ align:start position:0%
+rfp
+they wanted to have
+
+ align:start position:0%
+they wanted to have
+ 
+
+ align:start position:0%
+they wanted to have
+industry give them ideas of you know how
+
+ align:start position:0%
+industry give them ideas of you know how
+ 
+
+ align:start position:0%
+industry give them ideas of you know how
+they're going to do that and how much
+
+ align:start position:0%
+they're going to do that and how much
+ 
+
+ align:start position:0%
+they're going to do that and how much
+it's going to cost and
+
+ align:start position:0%
+it's going to cost and
+ 
+
+ align:start position:0%
+it's going to cost and
+well we told them that this is the right
+
+ align:start position:0%
+well we told them that this is the right
+ 
+
+ align:start position:0%
+well we told them that this is the right
+way to do it and we never heard from
+
+ align:start position:0%
+way to do it and we never heard from
+ 
+
+ align:start position:0%
+way to do it and we never heard from
+them again so i don't know so
+
+ align:start position:0%
+them again so i don't know so
+ 
+
+ align:start position:0%
+them again so i don't know so
+so if uh that craft crashes on europa
+
+ align:start position:0%
+so if uh that craft crashes on europa
+ 
+
+ align:start position:0%
+so if uh that craft crashes on europa
+don't blame me i told them what to do so
+
+ align:start position:0%
+don't blame me i told them what to do so
+ 
+
+ align:start position:0%
+don't blame me i told them what to do so
+okay so um
+
+ align:start position:0%
+okay so um
+ 
+
+ align:start position:0%
+okay so um
+this is beginning to
+
+ align:start position:0%
+this is beginning to
+ 
+
+ align:start position:0%
+this is beginning to
+look kind of promising because we can
+
+ align:start position:0%
+look kind of promising because we can
+ 
+
+ align:start position:0%
+look kind of promising because we can
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+see our way to inverting this imaging
+
+ align:start position:0%
+see our way to inverting this imaging
+ 
+
+ align:start position:0%
+see our way to inverting this imaging
+process and getting some useful
+
+ align:start position:0%
+process and getting some useful
+ 
+
+ align:start position:0%
+process and getting some useful
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+just from the way the brightness pattern
+
+ align:start position:0%
+just from the way the brightness pattern
+ 
+
+ align:start position:0%
+just from the way the brightness pattern
+in the image changes
+
+ align:start position:0%
+in the image changes
+ 
+
+ align:start position:0%
+in the image changes
+but i need to
+
+ align:start position:0%
+but i need to
+ 
+
+ align:start position:0%
+but i need to
+torture you a little bit more
+
+ align:start position:0%
+torture you a little bit more
+ 
+
+ align:start position:0%
+torture you a little bit more
+and do this in vector form and
+
+ align:start position:0%
+and do this in vector form and
+ 
+
+ align:start position:0%
+and do this in vector form and
+we'll see later why this is useful right
+
+ align:start position:0%
+we'll see later why this is useful right
+ 
+
+ align:start position:0%
+we'll see later why this is useful right
+now it's not saving us a whole lot in
+
+ align:start position:0%
+now it's not saving us a whole lot in
+ 
+
+ align:start position:0%
+now it's not saving us a whole lot in
+terms of writing going from the scale
+
+ align:start position:0%
+terms of writing going from the scale
+ 
+
+ align:start position:0%
+terms of writing going from the scale
+the component form to the vector form
+
+ align:start position:0%
+the component form to the vector form
+ 
+
+ align:start position:0%
+the component form to the vector form
+but uh
+
+ align:start position:0%
+but uh
+ 
+
+ align:start position:0%
+but uh
+we'll see that it does eventually okay
+
+ align:start position:0%
+we'll see that it does eventually okay
+ 
+
+ align:start position:0%
+we'll see that it does eventually okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+instead of differentiating the component
+
+ align:start position:0%
+instead of differentiating the component
+ 
+
+ align:start position:0%
+instead of differentiating the component
+versions we're going to now
+
+ align:start position:0%
+versions we're going to now
+ 
+
+ align:start position:0%
+versions we're going to now
+differentiate the vector form and of
+
+ align:start position:0%
+differentiate the vector form and of
+ 
+
+ align:start position:0%
+differentiate the vector form and of
+course it's very similar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what's the time derivative of a
+
+ align:start position:0%
+so what's the time derivative of a
+ 
+
+ align:start position:0%
+so what's the time derivative of a
+vector well
+
+ align:start position:0%
+vector well
+ 
+
+ align:start position:0%
+vector well
+you know it's just the vector where
+
+ align:start position:0%
+you know it's just the vector where
+ 
+
+ align:start position:0%
+you know it's just the vector where
+you've differentiated each of the
+
+ align:start position:0%
+you've differentiated each of the
+ 
+
+ align:start position:0%
+you've differentiated each of the
+components with respect to time so it's
+
+ align:start position:0%
+components with respect to time so it's
+ 
+
+ align:start position:0%
+components with respect to time so it's
+nothing very fancy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have that term again that
+
+ align:start position:0%
+so we have that term again that
+ 
+
+ align:start position:0%
+so we have that term again that
+corresponds to this first part here but
+
+ align:start position:0%
+corresponds to this first part here but
+ 
+
+ align:start position:0%
+corresponds to this first part here but
+because it's a ratio and because r can
+
+ align:start position:0%
+because it's a ratio and because r can
+ 
+
+ align:start position:0%
+because it's a ratio and because r can
+be changing big r can be changing we
+
+ align:start position:0%
+be changing big r can be changing we
+ 
+
+ align:start position:0%
+be changing big r can be changing we
+need to take account of the fact that
+
+ align:start position:0%
+need to take account of the fact that
+ 
+
+ align:start position:0%
+need to take account of the fact that
+it's a ratio and we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+to make it look slightly less
+
+ align:start position:0%
+to make it look slightly less
+ 
+
+ align:start position:0%
+to make it look slightly less
+intimidating we'll switch from
+
+ align:start position:0%
+intimidating we'll switch from
+ 
+
+ align:start position:0%
+intimidating we'll switch from
+leibniz to newtonian notation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again the underline always means that
+
+ align:start position:0%
+again the underline always means that
+ 
+
+ align:start position:0%
+again the underline always means that
+it's a
+
+ align:start position:0%
+it's a
+ 
+
+ align:start position:0%
+it's a
+vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'm splitting this up a bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the dot here denotes
+
+ align:start position:0%
+okay so the dot here denotes
+ 
+
+ align:start position:0%
+okay so the dot here denotes
+differentiation with respect to time
+
+ align:start position:0%
+differentiation with respect to time
+ 
+
+ align:start position:0%
+differentiation with respect to time
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+uh we have two terms one of which is
+
+ align:start position:0%
+uh we have two terms one of which is
+ 
+
+ align:start position:0%
+uh we have two terms one of which is
+sort of obvious scaling
+
+ align:start position:0%
+sort of obvious scaling
+ 
+
+ align:start position:0%
+sort of obvious scaling
+that there's a certain uh motion in 3d
+
+ align:start position:0%
+that there's a certain uh motion in 3d
+ 
+
+ align:start position:0%
+that there's a certain uh motion in 3d
+and it's going to be magnified or
+
+ align:start position:0%
+and it's going to be magnified or
+ 
+
+ align:start position:0%
+and it's going to be magnified or
+de-magnified by the ratio of
+
+ align:start position:0%
+de-magnified by the ratio of
+ 
+
+ align:start position:0%
+de-magnified by the ratio of
+of these two distances so
+
+ align:start position:0%
+of these two distances so
+ 
+
+ align:start position:0%
+of these two distances so
+there's a big motion out here it's a
+
+ align:start position:0%
+there's a big motion out here it's a
+ 
+
+ align:start position:0%
+there's a big motion out here it's a
+smaller motion in there by the ratio of
+
+ align:start position:0%
+smaller motion in there by the ratio of
+ 
+
+ align:start position:0%
+smaller motion in there by the ratio of
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+but then there's this other term that
+
+ align:start position:0%
+but then there's this other term that
+ 
+
+ align:start position:0%
+but then there's this other term that
+corresponds to motion in depth that we
+
+ align:start position:0%
+corresponds to motion in depth that we
+ 
+
+ align:start position:0%
+corresponds to motion in depth that we
+have to take into account
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i rewrote it this way
+
+ align:start position:0%
+and i rewrote it this way
+ 
+
+ align:start position:0%
+and i rewrote it this way
+because again we can make use of the
+
+ align:start position:0%
+because again we can make use of the
+ 
+
+ align:start position:0%
+because again we can make use of the
+fact that we have this perspective
+
+ align:start position:0%
+fact that we have this perspective
+ 
+
+ align:start position:0%
+fact that we have this perspective
+projection equation and so we can
+
+ align:start position:0%
+projection equation and so we can
+ 
+
+ align:start position:0%
+projection equation and so we can
+introduce the the image coordinates
+
+ align:start position:0%
+introduce the the image coordinates
+ 
+
+ align:start position:0%
+introduce the the image coordinates
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so focus of expansion again would be
+
+ align:start position:0%
+so focus of expansion again would be
+ 
+
+ align:start position:0%
+so focus of expansion again would be
+where r dot is zero
+
+ align:start position:0%
+where r dot is zero
+ 
+
+ align:start position:0%
+where r dot is zero
+and so that corresponds to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one oh let me put the one over f on the
+
+ align:start position:0%
+one oh let me put the one over f on the
+ 
+
+ align:start position:0%
+one oh let me put the one over f on the
+other side that's easier
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we basically get the same equations i
+
+ align:start position:0%
+we basically get the same equations i
+ 
+
+ align:start position:0%
+we basically get the same equations i
+mean if we just write out the
+
+ align:start position:0%
+mean if we just write out the
+ 
+
+ align:start position:0%
+mean if we just write out the
+components of that equation we get
+
+ align:start position:0%
+components of that equation we get
+ 
+
+ align:start position:0%
+components of that equation we get
+what we had before
+
+ align:start position:0%
+what we had before
+ 
+
+ align:start position:0%
+what we had before
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+just wanted to do one more little trick
+
+ align:start position:0%
+just wanted to do one more little trick
+ 
+
+ align:start position:0%
+just wanted to do one more little trick
+which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the appendix of the book we have some
+
+ align:start position:0%
+in the appendix of the book we have some
+ 
+
+ align:start position:0%
+in the appendix of the book we have some
+useful
+
+ align:start position:0%
+useful
+ 
+
+ align:start position:0%
+useful
+results about
+
+ align:start position:0%
+results about
+ 
+
+ align:start position:0%
+results about
+all sorts of simple math that's needed
+
+ align:start position:0%
+all sorts of simple math that's needed
+ 
+
+ align:start position:0%
+all sorts of simple math that's needed
+one of which has to do with uh vector
+
+ align:start position:0%
+one of which has to do with uh vector
+ 
+
+ align:start position:0%
+one of which has to do with uh vector
+equations and with
+
+ align:start position:0%
+equations and with
+ 
+
+ align:start position:0%
+equations and with
+manipulating
+
+ align:start position:0%
+manipulating
+ 
+
+ align:start position:0%
+manipulating
+you know cross products of cross
+
+ align:start position:0%
+you know cross products of cross
+ 
+
+ align:start position:0%
+you know cross products of cross
+products that kind of thing
+
+ align:start position:0%
+products that kind of thing
+ 
+
+ align:start position:0%
+products that kind of thing
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+i typically don't remember how to do so
+
+ align:start position:0%
+i typically don't remember how to do so
+ 
+
+ align:start position:0%
+i typically don't remember how to do so
+i'll go to the appendix of the book and
+
+ align:start position:0%
+i'll go to the appendix of the book and
+ 
+
+ align:start position:0%
+i'll go to the appendix of the book and
+the appendix is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+under materials on the seller website
+
+ align:start position:0%
+under materials on the seller website
+ 
+
+ align:start position:0%
+under materials on the seller website
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+let me first transform this one more
+
+ align:start position:0%
+let me first transform this one more
+ 
+
+ align:start position:0%
+let me first transform this one more
+time so we've got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's just rewriting this
+
+ align:start position:0%
+okay that's just rewriting this
+ 
+
+ align:start position:0%
+okay that's just rewriting this
+and now we use
+
+ align:start position:0%
+and now we use
+ 
+
+ align:start position:0%
+and now we use
+a result
+
+ align:start position:0%
+a result
+ 
+
+ align:start position:0%
+a result
+and the reason we do this is because
+
+ align:start position:0%
+and the reason we do this is because
+ 
+
+ align:start position:0%
+and the reason we do this is because
+it allows us to make some general
+
+ align:start position:0%
+it allows us to make some general
+ 
+
+ align:start position:0%
+it allows us to make some general
+statements about the flow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so cross product of cross products
+
+ align:start position:0%
+okay so cross product of cross products
+ 
+
+ align:start position:0%
+okay so cross product of cross products
+can be expressed as a difference of dot
+
+ align:start position:0%
+can be expressed as a difference of dot
+ 
+
+ align:start position:0%
+can be expressed as a difference of dot
+products
+
+ align:start position:0%
+products
+ 
+
+ align:start position:0%
+products
+now you can match up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these two lines
+
+ align:start position:0%
+these two lines
+ 
+
+ align:start position:0%
+these two lines
+and you can see where we're going with
+
+ align:start position:0%
+and you can see where we're going with
+ 
+
+ align:start position:0%
+and you can see where we're going with
+this which is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so finally there we have the
+
+ align:start position:0%
+okay so finally there we have the
+ 
+
+ align:start position:0%
+okay so finally there we have the
+image motion expressed in terms of world
+
+ align:start position:0%
+image motion expressed in terms of world
+ 
+
+ align:start position:0%
+image motion expressed in terms of world
+motion
+
+ align:start position:0%
+motion
+ 
+
+ align:start position:0%
+motion
+using this
+
+ align:start position:0%
+using this
+ 
+
+ align:start position:0%
+using this
+somewhat odd looking expression so why
+
+ align:start position:0%
+somewhat odd looking expression so why
+ 
+
+ align:start position:0%
+somewhat odd looking expression so why
+is this of interest well the first thing
+
+ align:start position:0%
+is this of interest well the first thing
+ 
+
+ align:start position:0%
+is this of interest well the first thing
+you can say is that
+
+ align:start position:0%
+you can say is that
+ 
+
+ align:start position:0%
+you can say is that
+the result is perpendicular to z right
+
+ align:start position:0%
+the result is perpendicular to z right
+ 
+
+ align:start position:0%
+the result is perpendicular to z right
+because if you take the cross product of
+
+ align:start position:0%
+because if you take the cross product of
+ 
+
+ align:start position:0%
+because if you take the cross product of
+two vectors the result is perpendicular
+
+ align:start position:0%
+two vectors the result is perpendicular
+ 
+
+ align:start position:0%
+two vectors the result is perpendicular
+to both of the vectors
+
+ align:start position:0%
+to both of the vectors
+ 
+
+ align:start position:0%
+to both of the vectors
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+r dot equals zero
+
+ align:start position:0%
+r dot equals zero
+ 
+
+ align:start position:0%
+r dot equals zero
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+r dot z equals zero excuse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+me so is is that surprising that the
+
+ align:start position:0%
+me so is is that surprising that the
+ 
+
+ align:start position:0%
+me so is is that surprising that the
+image motion is perpendicular to the
+
+ align:start position:0%
+image motion is perpendicular to the
+ 
+
+ align:start position:0%
+image motion is perpendicular to the
+z-axis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+image motions
+
+ align:start position:0%
+image motions
+ 
+
+ align:start position:0%
+image motions
+in that plane
+
+ align:start position:0%
+in that plane
+ 
+
+ align:start position:0%
+in that plane
+right z-axis is there no no of course
+
+ align:start position:0%
+right z-axis is there no no of course
+ 
+
+ align:start position:0%
+right z-axis is there no no of course
+it's obvious i mean it couldn't be any
+
+ align:start position:0%
+it's obvious i mean it couldn't be any
+ 
+
+ align:start position:0%
+it's obvious i mean it couldn't be any
+other way if we got it this is a good
+
+ align:start position:0%
+other way if we got it this is a good
+ 
+
+ align:start position:0%
+other way if we got it this is a good
+way to check the result if we got
+
+ align:start position:0%
+way to check the result if we got
+ 
+
+ align:start position:0%
+way to check the result if we got
+anything else there'd be a problem
+
+ align:start position:0%
+anything else there'd be a problem
+ 
+
+ align:start position:0%
+anything else there'd be a problem
+because so
+
+ align:start position:0%
+because so
+ 
+
+ align:start position:0%
+because so
+um in the image we only have 2d we have
+
+ align:start position:0%
+um in the image we only have 2d we have
+ 
+
+ align:start position:0%
+um in the image we only have 2d we have
+x y
+
+ align:start position:0%
+x y
+ 
+
+ align:start position:0%
+x y
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we have as velocities u and v we don't
+
+ align:start position:0%
+we have as velocities u and v we don't
+ 
+
+ align:start position:0%
+we have as velocities u and v we don't
+have a velocity in the z direction that
+
+ align:start position:0%
+have a velocity in the z direction that
+ 
+
+ align:start position:0%
+have a velocity in the z direction that
+would be popping out of the image so
+
+ align:start position:0%
+would be popping out of the image so
+ 
+
+ align:start position:0%
+would be popping out of the image so
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+interesting and then something else we
+
+ align:start position:0%
+interesting and then something else we
+ 
+
+ align:start position:0%
+interesting and then something else we
+can look at is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+what if
+
+ align:start position:0%
+what if
+ 
+
+ align:start position:0%
+what if
+the image motion is radially outward or
+
+ align:start position:0%
+the image motion is radially outward or
+ 
+
+ align:start position:0%
+the image motion is radially outward or
+inward that is it's uh
+
+ align:start position:0%
+inward that is it's uh
+ 
+
+ align:start position:0%
+inward that is it's uh
+the motion is along the radius vector to
+
+ align:start position:0%
+the motion is along the radius vector to
+ 
+
+ align:start position:0%
+the motion is along the radius vector to
+the point in the scene
+
+ align:start position:0%
+the point in the scene
+ 
+
+ align:start position:0%
+the point in the scene
+what do you expect will happen to the
+
+ align:start position:0%
+what do you expect will happen to the
+ 
+
+ align:start position:0%
+what do you expect will happen to the
+image motion in that case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you have the baseball coming straight
+
+ align:start position:0%
+so you have the baseball coming straight
+ 
+
+ align:start position:0%
+so you have the baseball coming straight
+for you its image is doing what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's expanding but it's not moving right
+
+ align:start position:0%
+it's expanding but it's not moving right
+ 
+
+ align:start position:0%
+it's expanding but it's not moving right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this is the case where we would expect
+
+ align:start position:0%
+this is the case where we would expect
+ 
+
+ align:start position:0%
+this is the case where we would expect
+image motion
+
+ align:start position:0%
+image motion
+ 
+
+ align:start position:0%
+image motion
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+and now we check this formula
+
+ align:start position:0%
+and now we check this formula
+ 
+
+ align:start position:0%
+and now we check this formula
+okay if r dot and r are parallel when we
+
+ align:start position:0%
+okay if r dot and r are parallel when we
+ 
+
+ align:start position:0%
+okay if r dot and r are parallel when we
+take their cross product now the cross
+
+ align:start position:0%
+take their cross product now the cross
+ 
+
+ align:start position:0%
+take their cross product now the cross
+products length is proportional to the
+
+ align:start position:0%
+products length is proportional to the
+ 
+
+ align:start position:0%
+products length is proportional to the
+sign of the angle between the two
+
+ align:start position:0%
+sign of the angle between the two
+ 
+
+ align:start position:0%
+sign of the angle between the two
+vectors well if they're the same vector
+
+ align:start position:0%
+vectors well if they're the same vector
+ 
+
+ align:start position:0%
+vectors well if they're the same vector
+then that angle is zero and so the sign
+
+ align:start position:0%
+then that angle is zero and so the sign
+ 
+
+ align:start position:0%
+then that angle is zero and so the sign
+is zero and so
+
+ align:start position:0%
+is zero and so
+ 
+
+ align:start position:0%
+is zero and so
+so this formula while it you know it uh
+
+ align:start position:0%
+so this formula while it you know it uh
+ 
+
+ align:start position:0%
+so this formula while it you know it uh
+took a little bit of work to get there
+
+ align:start position:0%
+took a little bit of work to get there
+ 
+
+ align:start position:0%
+took a little bit of work to get there
+it's helpful for answering certain
+
+ align:start position:0%
+it's helpful for answering certain
+ 
+
+ align:start position:0%
+it's helpful for answering certain
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+and we can right away check things like
+
+ align:start position:0%
+and we can right away check things like
+ 
+
+ align:start position:0%
+and we can right away check things like
+this okay if
+
+ align:start position:0%
+this okay if
+ 
+
+ align:start position:0%
+this okay if
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+if the thing is coming straight at you
+
+ align:start position:0%
+if the thing is coming straight at you
+ 
+
+ align:start position:0%
+if the thing is coming straight at you
+or you're moving directly towards it
+
+ align:start position:0%
+or you're moving directly towards it
+ 
+
+ align:start position:0%
+or you're moving directly towards it
+there'll be no image motion well that's
+
+ align:start position:0%
+there'll be no image motion well that's
+ 
+
+ align:start position:0%
+there'll be no image motion well that's
+our focus of expansion right so if i'm
+
+ align:start position:0%
+our focus of expansion right so if i'm
+ 
+
+ align:start position:0%
+our focus of expansion right so if i'm
+moving towards the wall
+
+ align:start position:0%
+moving towards the wall
+ 
+
+ align:start position:0%
+moving towards the wall
+that is the point where
+
+ align:start position:0%
+that is the point where
+ 
+
+ align:start position:0%
+that is the point where
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+motion vector lines up with the
+
+ align:start position:0%
+motion vector lines up with the
+ 
+
+ align:start position:0%
+motion vector lines up with the
+direction to that point and so i get no
+
+ align:start position:0%
+direction to that point and so i get no
+ 
+
+ align:start position:0%
+direction to that point and so i get no
+image motion
+
+ align:start position:0%
+image motion
+ 
+
+ align:start position:0%
+image motion
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+while we're here
+
+ align:start position:0%
+while we're here
+ 
+
+ align:start position:0%
+while we're here
+we can look at some flow fields
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+so we already saw
+
+ align:start position:0%
+so we already saw
+ 
+
+ align:start position:0%
+so we already saw
+a flow field up there
+
+ align:start position:0%
+a flow field up there
+ 
+
+ align:start position:0%
+a flow field up there
+for a general motion towards some point
+
+ align:start position:0%
+for a general motion towards some point
+ 
+
+ align:start position:0%
+for a general motion towards some point
+and we could look at
+
+ align:start position:0%
+and we could look at
+ 
+
+ align:start position:0%
+and we could look at
+just a couple of other cases so let's
+
+ align:start position:0%
+just a couple of other cases so let's
+ 
+
+ align:start position:0%
+just a couple of other cases so let's
+suppose that um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know u v and w could be anything but
+
+ align:start position:0%
+you know u v and w could be anything but
+ 
+
+ align:start position:0%
+you know u v and w could be anything but
+let's make it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+we're assuming now that two of those
+
+ align:start position:0%
+we're assuming now that two of those
+ 
+
+ align:start position:0%
+we're assuming now that two of those
+components are zero so there's only
+
+ align:start position:0%
+components are zero so there's only
+ 
+
+ align:start position:0%
+components are zero so there's only
+motion in the world in in the x
+
+ align:start position:0%
+motion in the world in in the x
+ 
+
+ align:start position:0%
+motion in the world in in the x
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+and then what do we expect uh in the
+
+ align:start position:0%
+and then what do we expect uh in the
+ 
+
+ align:start position:0%
+and then what do we expect uh in the
+image
+
+ align:start position:0%
+image
+ 
+
+ align:start position:0%
+image
+well from our formulas uh
+
+ align:start position:0%
+well from our formulas uh
+ 
+
+ align:start position:0%
+well from our formulas uh
+we see that uh the the only component of
+
+ align:start position:0%
+we see that uh the the only component of
+ 
+
+ align:start position:0%
+we see that uh the the only component of
+the image motion
+
+ align:start position:0%
+the image motion
+ 
+
+ align:start position:0%
+the image motion
+is a little little u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if the world
+
+ align:start position:0%
+if the world
+ 
+
+ align:start position:0%
+if the world
+is moving in x or i'm moving in x
+
+ align:start position:0%
+is moving in x or i'm moving in x
+ 
+
+ align:start position:0%
+is moving in x or i'm moving in x
+relative to the world
+
+ align:start position:0%
+relative to the world
+ 
+
+ align:start position:0%
+relative to the world
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the vector field
+
+ align:start position:0%
+the vector field
+ 
+
+ align:start position:0%
+the vector field
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+how brightness patterns move in the
+
+ align:start position:0%
+how brightness patterns move in the
+ 
+
+ align:start position:0%
+how brightness patterns move in the
+image looks like this
+
+ align:start position:0%
+image looks like this
+ 
+
+ align:start position:0%
+image looks like this
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+one thing that to note though is that
+
+ align:start position:0%
+one thing that to note though is that
+ 
+
+ align:start position:0%
+one thing that to note though is that
+the length of those vectors
+
+ align:start position:0%
+the length of those vectors
+ 
+
+ align:start position:0%
+the length of those vectors
+is not the same that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the length depends on z or if you like
+
+ align:start position:0%
+the length depends on z or if you like
+ 
+
+ align:start position:0%
+the length depends on z or if you like
+the inverse of z
+
+ align:start position:0%
+the inverse of z
+ 
+
+ align:start position:0%
+the inverse of z
+and so on so if you look at all of these
+
+ align:start position:0%
+and so on so if you look at all of these
+ 
+
+ align:start position:0%
+and so on so if you look at all of these
+formulas you know we've got r dot z
+
+ align:start position:0%
+formulas you know we've got r dot z
+ 
+
+ align:start position:0%
+formulas you know we've got r dot z
+which is big z and look at those
+
+ align:start position:0%
+which is big z and look at those
+ 
+
+ align:start position:0%
+which is big z and look at those
+formulas up there you've got one over z
+
+ align:start position:0%
+formulas up there you've got one over z
+ 
+
+ align:start position:0%
+formulas up there you've got one over z
+so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes this is a very simple vector field
+
+ align:start position:0%
+yes this is a very simple vector field
+ 
+
+ align:start position:0%
+yes this is a very simple vector field
+but the vectors aren't all the same
+
+ align:start position:0%
+but the vectors aren't all the same
+ 
+
+ align:start position:0%
+but the vectors aren't all the same
+so that kind of
+
+ align:start position:0%
+so that kind of
+ 
+
+ align:start position:0%
+so that kind of
+is unpleasant at the same time
+
+ align:start position:0%
+is unpleasant at the same time
+ 
+
+ align:start position:0%
+is unpleasant at the same time
+um when something's unpleasant you can
+
+ align:start position:0%
+um when something's unpleasant you can
+ 
+
+ align:start position:0%
+um when something's unpleasant you can
+offer you can sometimes take advantage
+
+ align:start position:0%
+offer you can sometimes take advantage
+ 
+
+ align:start position:0%
+offer you can sometimes take advantage
+of that so in this case
+
+ align:start position:0%
+of that so in this case
+ 
+
+ align:start position:0%
+of that so in this case
+if we had a vector field like this one
+
+ align:start position:0%
+if we had a vector field like this one
+ 
+
+ align:start position:0%
+if we had a vector field like this one
+thing we could try and do is
+
+ align:start position:0%
+thing we could try and do is
+ 
+
+ align:start position:0%
+thing we could try and do is
+recover depth
+
+ align:start position:0%
+recover depth
+ 
+
+ align:start position:0%
+recover depth
+right because these things are all
+
+ align:start position:0%
+right because these things are all
+ 
+
+ align:start position:0%
+right because these things are all
+inversely proportional to depth
+
+ align:start position:0%
+inversely proportional to depth
+ 
+
+ align:start position:0%
+inversely proportional to depth
+and so again an
+
+ align:start position:0%
+and so again an
+ 
+
+ align:start position:0%
+and so again an
+illustration of how once we understand
+
+ align:start position:0%
+illustration of how once we understand
+ 
+
+ align:start position:0%
+illustration of how once we understand
+the forward process uh we can trim that
+
+ align:start position:0%
+the forward process uh we can trim that
+ 
+
+ align:start position:0%
+the forward process uh we can trim that
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+to try and
+
+ align:start position:0%
+to try and
+ 
+
+ align:start position:0%
+to try and
+solve the inverse problem
+
+ align:start position:0%
+solve the inverse problem
+ 
+
+ align:start position:0%
+solve the inverse problem
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay u is zero and
+
+ align:start position:0%
+okay u is zero and
+ 
+
+ align:start position:0%
+okay u is zero and
+let's try this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well you know that's just turning
+
+ align:start position:0%
+well you know that's just turning
+ 
+
+ align:start position:0%
+well you know that's just turning
+everything 90 degrees so that's not very
+
+ align:start position:0%
+everything 90 degrees so that's not very
+ 
+
+ align:start position:0%
+everything 90 degrees so that's not very
+interesting
+
+ align:start position:0%
+interesting
+ 
+
+ align:start position:0%
+interesting
+the same idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now i guess to exploit this idea of
+
+ align:start position:0%
+now i guess to exploit this idea of
+ 
+
+ align:start position:0%
+now i guess to exploit this idea of
+recovering uh depth from these fields it
+
+ align:start position:0%
+recovering uh depth from these fields it
+ 
+
+ align:start position:0%
+recovering uh depth from these fields it
+we would need to um
+
+ align:start position:0%
+we would need to um
+ 
+
+ align:start position:0%
+we would need to um
+know z we need to know the velocity so
+
+ align:start position:0%
+know z we need to know the velocity so
+ 
+
+ align:start position:0%
+know z we need to know the velocity so
+there's sort of
+
+ align:start position:0%
+there's sort of
+ 
+
+ align:start position:0%
+there's sort of
+uh two things affecting what these
+
+ align:start position:0%
+uh two things affecting what these
+ 
+
+ align:start position:0%
+uh two things affecting what these
+pictures look like
+
+ align:start position:0%
+pictures look like
+ 
+
+ align:start position:0%
+pictures look like
+one is the object the shape the distance
+
+ align:start position:0%
+one is the object the shape the distance
+ 
+
+ align:start position:0%
+one is the object the shape the distance
+and the other one is the motion and if
+
+ align:start position:0%
+and the other one is the motion and if
+ 
+
+ align:start position:0%
+and the other one is the motion and if
+we know either one of the two then we
+
+ align:start position:0%
+we know either one of the two then we
+ 
+
+ align:start position:0%
+we know either one of the two then we
+can calculate the other one of course in
+
+ align:start position:0%
+can calculate the other one of course in
+ 
+
+ align:start position:0%
+can calculate the other one of course in
+practice often we don't know either one
+
+ align:start position:0%
+practice often we don't know either one
+ 
+
+ align:start position:0%
+practice often we don't know either one
+and we'd like to recover both
+
+ align:start position:0%
+and we'd like to recover both
+ 
+
+ align:start position:0%
+and we'd like to recover both
+and then often we end up with the ill
+
+ align:start position:0%
+and then often we end up with the ill
+ 
+
+ align:start position:0%
+and then often we end up with the ill
+pose problem
+
+ align:start position:0%
+pose problem
+ 
+
+ align:start position:0%
+pose problem
+how about u is zero v is zero
+
+ align:start position:0%
+how about u is zero v is zero
+ 
+
+ align:start position:0%
+how about u is zero v is zero
+w is not equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we already drew that diagram up
+
+ align:start position:0%
+well we already drew that diagram up
+ 
+
+ align:start position:0%
+well we already drew that diagram up
+there kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right if we look at the equations we're
+
+ align:start position:0%
+right if we look at the equations we're
+ 
+
+ align:start position:0%
+right if we look at the equations we're
+just going to get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f o e is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the simplest uh case of of
+
+ align:start position:0%
+so that's the simplest uh case of of
+ 
+
+ align:start position:0%
+so that's the simplest uh case of of
+that picture where the focus of
+
+ align:start position:0%
+that picture where the focus of
+ 
+
+ align:start position:0%
+that picture where the focus of
+expansion is right in the center of the
+
+ align:start position:0%
+expansion is right in the center of the
+ 
+
+ align:start position:0%
+expansion is right in the center of the
+image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+this is starting to hint at some of the
+
+ align:start position:0%
+this is starting to hint at some of the
+ 
+
+ align:start position:0%
+this is starting to hint at some of the
+things we're going to pursue
+
+ align:start position:0%
+things we're going to pursue
+ 
+
+ align:start position:0%
+things we're going to pursue
+we you know develop the equations for
+
+ align:start position:0%
+we you know develop the equations for
+ 
+
+ align:start position:0%
+we you know develop the equations for
+some transformation like this between
+
+ align:start position:0%
+some transformation like this between
+ 
+
+ align:start position:0%
+some transformation like this between
+something in the world and something in
+
+ align:start position:0%
+something in the world and something in
+ 
+
+ align:start position:0%
+something in the world and something in
+the image and then we try to invert it
+
+ align:start position:0%
+the image and then we try to invert it
+ 
+
+ align:start position:0%
+the image and then we try to invert it
+and the forward one is always
+
+ align:start position:0%
+and the forward one is always
+ 
+
+ align:start position:0%
+and the forward one is always
+simple you know there's the equation up
+
+ align:start position:0%
+simple you know there's the equation up
+ 
+
+ align:start position:0%
+simple you know there's the equation up
+there just plug in whatever
+
+ align:start position:0%
+there just plug in whatever
+ 
+
+ align:start position:0%
+there just plug in whatever
+the inverse isn't because often there
+
+ align:start position:0%
+the inverse isn't because often there
+ 
+
+ align:start position:0%
+the inverse isn't because often there
+may be more than one solution or there
+
+ align:start position:0%
+may be more than one solution or there
+ 
+
+ align:start position:0%
+may be more than one solution or there
+may be no solution or there may be an
+
+ align:start position:0%
+may be no solution or there may be an
+ 
+
+ align:start position:0%
+may be no solution or there may be an
+infinite number of solutions or
+
+ align:start position:0%
+infinite number of solutions or
+ 
+
+ align:start position:0%
+infinite number of solutions or
+it's imposed in the sense that if you
+
+ align:start position:0%
+it's imposed in the sense that if you
+ 
+
+ align:start position:0%
+it's imposed in the sense that if you
+make some small measurement error
+
+ align:start position:0%
+make some small measurement error
+ 
+
+ align:start position:0%
+make some small measurement error
+the answer is going to be perturbed by a
+
+ align:start position:0%
+the answer is going to be perturbed by a
+ 
+
+ align:start position:0%
+the answer is going to be perturbed by a
+large amount so we'll have to be careful
+
+ align:start position:0%
+large amount so we'll have to be careful
+ 
+
+ align:start position:0%
+large amount so we'll have to be careful
+about that
+
+ align:start position:0%
+about that
+ 
+
+ align:start position:0%
+about that
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+talking of
+
+ align:start position:0%
+talking of
+ 
+
+ align:start position:0%
+talking of
+motion of image brightness patterns
+
+ align:start position:0%
+motion of image brightness patterns
+ 
+
+ align:start position:0%
+motion of image brightness patterns
+let's talk about that
+
+ align:start position:0%
+let's talk about that
+ 
+
+ align:start position:0%
+let's talk about that
+that was
+
+ align:start position:0%
+that was
+ 
+
+ align:start position:0%
+that was
+you know that's in the homework problem
+
+ align:start position:0%
+you know that's in the homework problem
+ 
+
+ align:start position:0%
+you know that's in the homework problem
+so let's
+
+ align:start position:0%
+so let's
+ 
+
+ align:start position:0%
+so let's
+talk a little bit about that
+
+ align:start position:0%
+talk a little bit about that
+ 
+
+ align:start position:0%
+talk a little bit about that
+so we'll ignore for the moment where
+
+ align:start position:0%
+so we'll ignore for the moment where
+ 
+
+ align:start position:0%
+so we'll ignore for the moment where
+these images come from
+
+ align:start position:0%
+these images come from
+ 
+
+ align:start position:0%
+these images come from
+uh what what is an image well an image
+
+ align:start position:0%
+uh what what is an image well an image
+ 
+
+ align:start position:0%
+uh what what is an image well an image
+is a 2d
+
+ align:start position:0%
+is a 2d
+ 
+
+ align:start position:0%
+is a 2d
+pattern of brightness values so it's you
+
+ align:start position:0%
+pattern of brightness values so it's you
+ 
+
+ align:start position:0%
+pattern of brightness values so it's you
+know e as a function of x and y if you
+
+ align:start position:0%
+know e as a function of x and y if you
+ 
+
+ align:start position:0%
+know e as a function of x and y if you
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we already said something about that in
+
+ align:start position:0%
+we already said something about that in
+ 
+
+ align:start position:0%
+we already said something about that in
+terms of brightness being power per unit
+
+ align:start position:0%
+terms of brightness being power per unit
+ 
+
+ align:start position:0%
+terms of brightness being power per unit
+area we will make that more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+clear later on
+
+ align:start position:0%
+clear later on
+ 
+
+ align:start position:0%
+clear later on
+right so his question was you know what
+
+ align:start position:0%
+right so his question was you know what
+ 
+
+ align:start position:0%
+right so his question was you know what
+about color and yes we will be talking
+
+ align:start position:0%
+about color and yes we will be talking
+ 
+
+ align:start position:0%
+about color and yes we will be talking
+about color at some point
+
+ align:start position:0%
+about color at some point
+ 
+
+ align:start position:0%
+about color at some point
+which is kind of in the way is this
+
+ align:start position:0%
+which is kind of in the way is this
+ 
+
+ align:start position:0%
+which is kind of in the way is this
+repeated three times
+
+ align:start position:0%
+repeated three times
+ 
+
+ align:start position:0%
+repeated three times
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a couple of reasons not to bring it in
+
+ align:start position:0%
+a couple of reasons not to bring it in
+ 
+
+ align:start position:0%
+a couple of reasons not to bring it in
+at this point one is
+
+ align:start position:0%
+at this point one is
+ 
+
+ align:start position:0%
+at this point one is
+we'll we'll do it
+
+ align:start position:0%
+we'll we'll do it
+ 
+
+ align:start position:0%
+we'll we'll do it
+more simply just using gray levels
+
+ align:start position:0%
+more simply just using gray levels
+ 
+
+ align:start position:0%
+more simply just using gray levels
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+color is
+
+ align:start position:0%
+color is
+ 
+
+ align:start position:0%
+color is
+peculiarly human-centric in that the
+
+ align:start position:0%
+peculiarly human-centric in that the
+ 
+
+ align:start position:0%
+peculiarly human-centric in that the
+only reason that we use three numbers to
+
+ align:start position:0%
+only reason that we use three numbers to
+ 
+
+ align:start position:0%
+only reason that we use three numbers to
+represent color is because our
+
+ align:start position:0%
+represent color is because our
+ 
+
+ align:start position:0%
+represent color is because our
+particular color sensing system has
+
+ align:start position:0%
+particular color sensing system has
+ 
+
+ align:start position:0%
+particular color sensing system has
+three sensors
+
+ align:start position:0%
+three sensors
+ 
+
+ align:start position:0%
+three sensors
+but we'll talk about all of that uh
+
+ align:start position:0%
+but we'll talk about all of that uh
+ 
+
+ align:start position:0%
+but we'll talk about all of that uh
+later on for for now
+
+ align:start position:0%
+later on for for now
+ 
+
+ align:start position:0%
+later on for for now
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+assume that we have uh taken rgb and
+
+ align:start position:0%
+assume that we have uh taken rgb and
+ 
+
+ align:start position:0%
+assume that we have uh taken rgb and
+turned it into
+
+ align:start position:0%
+turned it into
+ 
+
+ align:start position:0%
+turned it into
+brightness
+
+ align:start position:0%
+brightness
+ 
+
+ align:start position:0%
+brightness
+which is uh you know depending on who
+
+ align:start position:0%
+which is uh you know depending on who
+ 
+
+ align:start position:0%
+which is uh you know depending on who
+you read
+
+ align:start position:0%
+you read
+ 
+
+ align:start position:0%
+you read
+some combination of the three components
+
+ align:start position:0%
+some combination of the three components
+ 
+
+ align:start position:0%
+some combination of the three components
+mostly g
+
+ align:start position:0%
+mostly g
+ 
+
+ align:start position:0%
+mostly g
+because human
+
+ align:start position:0%
+because human
+ 
+
+ align:start position:0%
+because human
+vision is most sensitive to
+
+ align:start position:0%
+vision is most sensitive to
+ 
+
+ align:start position:0%
+vision is most sensitive to
+g and judges
+
+ align:start position:0%
+g and judges
+ 
+
+ align:start position:0%
+g and judges
+absolute brightness
+
+ align:start position:0%
+absolute brightness
+ 
+
+ align:start position:0%
+absolute brightness
+based on some combination of r g and b
+
+ align:start position:0%
+based on some combination of r g and b
+ 
+
+ align:start position:0%
+based on some combination of r g and b
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now a couple of things i'm going to do
+
+ align:start position:0%
+now a couple of things i'm going to do
+ 
+
+ align:start position:0%
+now a couple of things i'm going to do
+repeatedly so i want to kind of
+
+ align:start position:0%
+repeatedly so i want to kind of
+ 
+
+ align:start position:0%
+repeatedly so i want to kind of
+preemptively talk about them one of them
+
+ align:start position:0%
+preemptively talk about them one of them
+ 
+
+ align:start position:0%
+preemptively talk about them one of them
+is i'm going to be switching back and
+
+ align:start position:0%
+is i'm going to be switching back and
+ 
+
+ align:start position:0%
+is i'm going to be switching back and
+forth between continuous and discrete so
+
+ align:start position:0%
+forth between continuous and discrete so
+ 
+
+ align:start position:0%
+forth between continuous and discrete so
+these days with everything being digital
+
+ align:start position:0%
+these days with everything being digital
+ 
+
+ align:start position:0%
+these days with everything being digital
+of course the images we get are
+
+ align:start position:0%
+of course the images we get are
+ 
+
+ align:start position:0%
+of course the images we get are
+discrete they're quantized they're
+
+ align:start position:0%
+discrete they're quantized they're
+ 
+
+ align:start position:0%
+discrete they're quantized they're
+quantized in space
+
+ align:start position:0%
+quantized in space
+ 
+
+ align:start position:0%
+quantized in space
+and typically on a rectangular grid
+
+ align:start position:0%
+and typically on a rectangular grid
+ 
+
+ align:start position:0%
+and typically on a rectangular grid
+which is kind of not the best grid to
+
+ align:start position:0%
+which is kind of not the best grid to
+ 
+
+ align:start position:0%
+which is kind of not the best grid to
+use but that's what we use
+
+ align:start position:0%
+use but that's what we use
+ 
+
+ align:start position:0%
+use but that's what we use
+and then in brightness so we also don't
+
+ align:start position:0%
+and then in brightness so we also don't
+ 
+
+ align:start position:0%
+and then in brightness so we also don't
+get continuous values for brightness
+
+ align:start position:0%
+get continuous values for brightness
+ 
+
+ align:start position:0%
+get continuous values for brightness
+we get them quantized often to as few as
+
+ align:start position:0%
+we get them quantized often to as few as
+ 
+
+ align:start position:0%
+we get them quantized often to as few as
+eight bits
+
+ align:start position:0%
+eight bits
+ 
+
+ align:start position:0%
+eight bits
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+it turns out that
+
+ align:start position:0%
+it turns out that
+ 
+
+ align:start position:0%
+it turns out that
+a lot of what we do is easier to
+
+ align:start position:0%
+a lot of what we do is easier to
+ 
+
+ align:start position:0%
+a lot of what we do is easier to
+understand in the continuous domain so
+
+ align:start position:0%
+understand in the continuous domain so
+ 
+
+ align:start position:0%
+understand in the continuous domain so
+i've talked here about you know e of x y
+
+ align:start position:0%
+i've talked here about you know e of x y
+ 
+
+ align:start position:0%
+i've talked here about you know e of x y
+that's my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brightness pattern for any x and y it'll
+
+ align:start position:0%
+brightness pattern for any x and y it'll
+ 
+
+ align:start position:0%
+brightness pattern for any x and y it'll
+tell me what the brightness is the power
+
+ align:start position:0%
+tell me what the brightness is the power
+ 
+
+ align:start position:0%
+tell me what the brightness is the power
+per unit area but in practice you know
+
+ align:start position:0%
+per unit area but in practice you know
+ 
+
+ align:start position:0%
+per unit area but in practice you know
+it's going to be more like i have an
+
+ align:start position:0%
+it's going to be more like i have an
+ 
+
+ align:start position:0%
+it's going to be more like i have an
+array of numbers with two indices
+
+ align:start position:0%
+array of numbers with two indices
+ 
+
+ align:start position:0%
+array of numbers with two indices
+and i'm dealing with
+
+ align:start position:0%
+and i'm dealing with
+ 
+
+ align:start position:0%
+and i'm dealing with
+e sub whatever
+
+ align:start position:0%
+e sub whatever
+ 
+
+ align:start position:0%
+e sub whatever
+correspondingly
+
+ align:start position:0%
+correspondingly
+ 
+
+ align:start position:0%
+correspondingly
+in the continuous domain we'll often be
+
+ align:start position:0%
+in the continuous domain we'll often be
+ 
+
+ align:start position:0%
+in the continuous domain we'll often be
+taking integrals you know for example
+
+ align:start position:0%
+taking integrals you know for example
+ 
+
+ align:start position:0%
+taking integrals you know for example
+within some measurement that's local at
+
+ align:start position:0%
+within some measurement that's local at
+ 
+
+ align:start position:0%
+within some measurement that's local at
+a pixel but we want to extend it over
+
+ align:start position:0%
+a pixel but we want to extend it over
+ 
+
+ align:start position:0%
+a pixel but we want to extend it over
+the whole image and we take either you
+
+ align:start position:0%
+the whole image and we take either you
+ 
+
+ align:start position:0%
+the whole image and we take either you
+know a single integral or double
+
+ align:start position:0%
+know a single integral or double
+ 
+
+ align:start position:0%
+know a single integral or double
+integral well of course in the discrete
+
+ align:start position:0%
+integral well of course in the discrete
+ 
+
+ align:start position:0%
+integral well of course in the discrete
+world we'll be taking you know sums
+
+ align:start position:0%
+world we'll be taking you know sums
+ 
+
+ align:start position:0%
+world we'll be taking you know sums
+but you know those are very
+
+ align:start position:0%
+but you know those are very
+ 
+
+ align:start position:0%
+but you know those are very
+straightforward transformations
+
+ align:start position:0%
+straightforward transformations
+ 
+
+ align:start position:0%
+straightforward transformations
+but they're very useful because on the
+
+ align:start position:0%
+but they're very useful because on the
+ 
+
+ align:start position:0%
+but they're very useful because on the
+one hand we want to implement this as
+
+ align:start position:0%
+one hand we want to implement this as
+ 
+
+ align:start position:0%
+one hand we want to implement this as
+actual code and on the other hand we'd
+
+ align:start position:0%
+actual code and on the other hand we'd
+ 
+
+ align:start position:0%
+actual code and on the other hand we'd
+like to make it
+
+ align:start position:0%
+like to make it
+ 
+
+ align:start position:0%
+like to make it
+easier to develop the math and it's
+
+ align:start position:0%
+easier to develop the math and it's
+ 
+
+ align:start position:0%
+easier to develop the math and it's
+almost
+
+ align:start position:0%
+almost
+ 
+
+ align:start position:0%
+almost
+inevitable that
+
+ align:start position:0%
+inevitable that
+ 
+
+ align:start position:0%
+inevitable that
+it's easier in the continuous world
+
+ align:start position:0%
+it's easier in the continuous world
+ 
+
+ align:start position:0%
+it's easier in the continuous world
+then we get the derivative so
+
+ align:start position:0%
+then we get the derivative so
+ 
+
+ align:start position:0%
+then we get the derivative so
+of course
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the continuous world i can look at
+
+ align:start position:0%
+in the continuous world i can look at
+ 
+
+ align:start position:0%
+in the continuous world i can look at
+the x and y derivative of brightness and
+
+ align:start position:0%
+the x and y derivative of brightness and
+ 
+
+ align:start position:0%
+the x and y derivative of brightness and
+the combination of these two is called
+
+ align:start position:0%
+the combination of these two is called
+ 
+
+ align:start position:0%
+the combination of these two is called
+the brightness gradient which is going
+
+ align:start position:0%
+the brightness gradient which is going
+ 
+
+ align:start position:0%
+the brightness gradient which is going
+to be very important in
+
+ align:start position:0%
+to be very important in
+ 
+
+ align:start position:0%
+to be very important in
+many of the things we do and in
+
+ align:start position:0%
+many of the things we do and in
+ 
+
+ align:start position:0%
+many of the things we do and in
+practice i'm going to approximate those
+
+ align:start position:0%
+practice i'm going to approximate those
+ 
+
+ align:start position:0%
+practice i'm going to approximate those
+by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know making some sort of
+
+ align:start position:0%
+you know making some sort of
+ 
+
+ align:start position:0%
+you know making some sort of
+difference first difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll see that you know that's one
+
+ align:start position:0%
+and we'll see that you know that's one
+ 
+
+ align:start position:0%
+and we'll see that you know that's one
+way of doing it
+
+ align:start position:0%
+way of doing it
+ 
+
+ align:start position:0%
+way of doing it
+it's not a particularly good way of
+
+ align:start position:0%
+it's not a particularly good way of
+ 
+
+ align:start position:0%
+it's not a particularly good way of
+approximating the first derivative but
+
+ align:start position:0%
+approximating the first derivative but
+ 
+
+ align:start position:0%
+approximating the first derivative but
+uh we will talk about others and
+
+ align:start position:0%
+uh we will talk about others and
+ 
+
+ align:start position:0%
+uh we will talk about others and
+i don't know just in terms of uh writing
+
+ align:start position:0%
+i don't know just in terms of uh writing
+ 
+
+ align:start position:0%
+i don't know just in terms of uh writing
+this is easier to write than that so
+
+ align:start position:0%
+this is easier to write than that so
+ 
+
+ align:start position:0%
+this is easier to write than that so
+i know that's not a big argument but
+
+ align:start position:0%
+i know that's not a big argument but
+ 
+
+ align:start position:0%
+i know that's not a big argument but
+we'll find that
+
+ align:start position:0%
+we'll find that
+ 
+
+ align:start position:0%
+we'll find that
+some of these things have a closed form
+
+ align:start position:0%
+some of these things have a closed form
+ 
+
+ align:start position:0%
+some of these things have a closed form
+solution in the continuous domain that
+
+ align:start position:0%
+solution in the continuous domain that
+ 
+
+ align:start position:0%
+solution in the continuous domain that
+you can easily obtain and it's harder to
+
+ align:start position:0%
+you can easily obtain and it's harder to
+ 
+
+ align:start position:0%
+you can easily obtain and it's harder to
+do the same in the discrete domain so
+
+ align:start position:0%
+do the same in the discrete domain so
+ 
+
+ align:start position:0%
+do the same in the discrete domain so
+i'll be switching back and forth okay
+
+ align:start position:0%
+i'll be switching back and forth okay
+ 
+
+ align:start position:0%
+i'll be switching back and forth okay
+with that in mind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's look at our 1d
+
+ align:start position:0%
+let's look at our 1d
+ 
+
+ align:start position:0%
+let's look at our 1d
+image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+of course images are
+
+ align:start position:0%
+of course images are
+ 
+
+ align:start position:0%
+of course images are
+typically 2d they are 1d sensors and
+
+ align:start position:0%
+typically 2d they are 1d sensors and
+ 
+
+ align:start position:0%
+typically 2d they are 1d sensors and
+they have some benefits one of them is
+
+ align:start position:0%
+they have some benefits one of them is
+ 
+
+ align:start position:0%
+they have some benefits one of them is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+you can build a 1d sensor with
+
+ align:start position:0%
+you can build a 1d sensor with
+ 
+
+ align:start position:0%
+you can build a 1d sensor with
+a much larger number of pixels in one
+
+ align:start position:0%
+a much larger number of pixels in one
+ 
+
+ align:start position:0%
+a much larger number of pixels in one
+direction than you can a 2d sensor so a
+
+ align:start position:0%
+direction than you can a 2d sensor so a
+ 
+
+ align:start position:0%
+direction than you can a 2d sensor so a
+2d sensor although these days you know
+
+ align:start position:0%
+2d sensor although these days you know
+ 
+
+ align:start position:0%
+2d sensor although these days you know
+2d sensor could be i don't know
+
+ align:start position:0%
+2d sensor could be i don't know
+ 
+
+ align:start position:0%
+2d sensor could be i don't know
+2k by 4k some huge number uh but linear
+
+ align:start position:0%
+2k by 4k some huge number uh but linear
+ 
+
+ align:start position:0%
+2k by 4k some huge number uh but linear
+sensors have been around with many
+
+ align:start position:0%
+sensors have been around with many
+ 
+
+ align:start position:0%
+sensors have been around with many
+thousands of pixels
+
+ align:start position:0%
+thousands of pixels
+ 
+
+ align:start position:0%
+thousands of pixels
+and the disadvantage of a linear sensor
+
+ align:start position:0%
+and the disadvantage of a linear sensor
+ 
+
+ align:start position:0%
+and the disadvantage of a linear sensor
+is to to get a real image you need to
+
+ align:start position:0%
+is to to get a real image you need to
+ 
+
+ align:start position:0%
+is to to get a real image you need to
+scan it
+
+ align:start position:0%
+scan it
+ 
+
+ align:start position:0%
+scan it
+and this is done quite a lot in industry
+
+ align:start position:0%
+and this is done quite a lot in industry
+ 
+
+ align:start position:0%
+and this is done quite a lot in industry
+where things are moving along on a
+
+ align:start position:0%
+where things are moving along on a
+ 
+
+ align:start position:0%
+where things are moving along on a
+conveyor belt and you can use a
+
+ align:start position:0%
+conveyor belt and you can use a
+ 
+
+ align:start position:0%
+conveyor belt and you can use a
+relatively cheap very high resolution
+
+ align:start position:0%
+relatively cheap very high resolution
+ 
+
+ align:start position:0%
+relatively cheap very high resolution
+linear array sensor and the conveyor
+
+ align:start position:0%
+linear array sensor and the conveyor
+ 
+
+ align:start position:0%
+linear array sensor and the conveyor
+belt motion provides the other dimension
+
+ align:start position:0%
+belt motion provides the other dimension
+ 
+
+ align:start position:0%
+belt motion provides the other dimension
+of the image it's also used in satellite
+
+ align:start position:0%
+of the image it's also used in satellite
+ 
+
+ align:start position:0%
+of the image it's also used in satellite
+imaging where
+
+ align:start position:0%
+imaging where
+ 
+
+ align:start position:0%
+imaging where
+very high quality 1d
+
+ align:start position:0%
+very high quality 1d
+ 
+
+ align:start position:0%
+very high quality 1d
+sensors
+
+ align:start position:0%
+sensors
+ 
+
+ align:start position:0%
+sensors
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+used and then the motion of the
+
+ align:start position:0%
+used and then the motion of the
+ 
+
+ align:start position:0%
+used and then the motion of the
+satellite provides the scanning to
+
+ align:start position:0%
+satellite provides the scanning to
+ 
+
+ align:start position:0%
+satellite provides the scanning to
+produce an image
+
+ align:start position:0%
+produce an image
+ 
+
+ align:start position:0%
+produce an image
+anyway suppose we have a 1d image and
+
+ align:start position:0%
+anyway suppose we have a 1d image and
+ 
+
+ align:start position:0%
+anyway suppose we have a 1d image and
+suppose things move
+
+ align:start position:0%
+suppose things move
+ 
+
+ align:start position:0%
+suppose things move
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is at time
+
+ align:start position:0%
+so this is at time
+ 
+
+ align:start position:0%
+so this is at time
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+and this is at time t plus delta t
+
+ align:start position:0%
+and this is at time t plus delta t
+ 
+
+ align:start position:0%
+and this is at time t plus delta t
+and you know think think of your optical
+
+ align:start position:0%
+and you know think think of your optical
+ 
+
+ align:start position:0%
+and you know think think of your optical
+mouse you're holding it down on the
+
+ align:start position:0%
+mouse you're holding it down on the
+ 
+
+ align:start position:0%
+mouse you're holding it down on the
+table it has a short focal length lens
+
+ align:start position:0%
+table it has a short focal length lens
+ 
+
+ align:start position:0%
+table it has a short focal length lens
+that's imaging the surface of the table
+
+ align:start position:0%
+that's imaging the surface of the table
+ 
+
+ align:start position:0%
+that's imaging the surface of the table
+and if there's some texture to it as
+
+ align:start position:0%
+and if there's some texture to it as
+ 
+
+ align:start position:0%
+and if there's some texture to it as
+there is on on the wood over here
+
+ align:start position:0%
+there is on on the wood over here
+ 
+
+ align:start position:0%
+there is on on the wood over here
+then that texture is mapped onto the
+
+ align:start position:0%
+then that texture is mapped onto the
+ 
+
+ align:start position:0%
+then that texture is mapped onto the
+image and if you move the mouse then the
+
+ align:start position:0%
+image and if you move the mouse then the
+ 
+
+ align:start position:0%
+image and if you move the mouse then the
+image of that surface will move and your
+
+ align:start position:0%
+image of that surface will move and your
+ 
+
+ align:start position:0%
+image of that surface will move and your
+job is to accurately estimate
+
+ align:start position:0%
+job is to accurately estimate
+ 
+
+ align:start position:0%
+job is to accurately estimate
+how fast it's moving
+
+ align:start position:0%
+how fast it's moving
+ 
+
+ align:start position:0%
+how fast it's moving
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+here's the picture before we you know
+
+ align:start position:0%
+here's the picture before we you know
+ 
+
+ align:start position:0%
+here's the picture before we you know
+two time steps and
+
+ align:start position:0%
+two time steps and
+ 
+
+ align:start position:0%
+two time steps and
+and so we're trying to figure out you
+
+ align:start position:0%
+and so we're trying to figure out you
+ 
+
+ align:start position:0%
+and so we're trying to figure out you
+know how do i
+
+ align:start position:0%
+know how do i
+ 
+
+ align:start position:0%
+know how do i
+determine what happens so let's suppose
+
+ align:start position:0%
+determine what happens so let's suppose
+ 
+
+ align:start position:0%
+determine what happens so let's suppose
+we have a
+
+ align:start position:0%
+we have a
+ 
+
+ align:start position:0%
+we have a
+velocity of uh u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+um we've moved
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by that amount so let me indicate that
+
+ align:start position:0%
+by that amount so let me indicate that
+ 
+
+ align:start position:0%
+by that amount so let me indicate that
+over here so that's
+
+ align:start position:0%
+over here so that's
+ 
+
+ align:start position:0%
+over here so that's
+delta x
+
+ align:start position:0%
+delta x
+ 
+
+ align:start position:0%
+delta x
+now we're making some assumptions here
+
+ align:start position:0%
+now we're making some assumptions here
+ 
+
+ align:start position:0%
+now we're making some assumptions here
+that we'll get back to in a second
+
+ align:start position:0%
+that we'll get back to in a second
+ 
+
+ align:start position:0%
+that we'll get back to in a second
+one of them is that the brightness
+
+ align:start position:0%
+one of them is that the brightness
+ 
+
+ align:start position:0%
+one of them is that the brightness
+doesn't change
+
+ align:start position:0%
+doesn't change
+ 
+
+ align:start position:0%
+doesn't change
+and so you know if your optical mouse is
+
+ align:start position:0%
+and so you know if your optical mouse is
+ 
+
+ align:start position:0%
+and so you know if your optical mouse is
+looking at the surface of the table
+
+ align:start position:0%
+looking at the surface of the table
+ 
+
+ align:start position:0%
+looking at the surface of the table
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+presumably between one frame and the
+
+ align:start position:0%
+presumably between one frame and the
+ 
+
+ align:start position:0%
+presumably between one frame and the
+next the illumination isn't changing
+
+ align:start position:0%
+next the illumination isn't changing
+ 
+
+ align:start position:0%
+next the illumination isn't changing
+it's using an led with a constant
+
+ align:start position:0%
+it's using an led with a constant
+ 
+
+ align:start position:0%
+it's using an led with a constant
+current and it's taking 2 000 frames a
+
+ align:start position:0%
+current and it's taking 2 000 frames a
+ 
+
+ align:start position:0%
+current and it's taking 2 000 frames a
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+so it's unlikely to change the geometry
+
+ align:start position:0%
+so it's unlikely to change the geometry
+ 
+
+ align:start position:0%
+so it's unlikely to change the geometry
+is changing a little bit because you've
+
+ align:start position:0%
+is changing a little bit because you've
+ 
+
+ align:start position:0%
+is changing a little bit because you've
+moved and now you're looking at the
+
+ align:start position:0%
+moved and now you're looking at the
+ 
+
+ align:start position:0%
+moved and now you're looking at the
+surface from a slightly different angle
+
+ align:start position:0%
+surface from a slightly different angle
+ 
+
+ align:start position:0%
+surface from a slightly different angle
+but for most surfaces the change in
+
+ align:start position:0%
+but for most surfaces the change in
+ 
+
+ align:start position:0%
+but for most surfaces the change in
+brightness due to that is very small
+
+ align:start position:0%
+brightness due to that is very small
+ 
+
+ align:start position:0%
+brightness due to that is very small
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+right here the way i've drawn these
+
+ align:start position:0%
+right here the way i've drawn these
+ 
+
+ align:start position:0%
+right here the way i've drawn these
+curves i've assumed constant brightness
+
+ align:start position:0%
+curves i've assumed constant brightness
+ 
+
+ align:start position:0%
+curves i've assumed constant brightness
+so let's get it right out front
+
+ align:start position:0%
+so let's get it right out front
+ 
+
+ align:start position:0%
+so let's get it right out front
+constant brightness assumption
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll see that there are
+
+ align:start position:0%
+and we'll see that there are
+ 
+
+ align:start position:0%
+and we'll see that there are
+circumstances where that doesn't apply
+
+ align:start position:0%
+circumstances where that doesn't apply
+ 
+
+ align:start position:0%
+circumstances where that doesn't apply
+but there are lots of cases where that
+
+ align:start position:0%
+but there are lots of cases where that
+ 
+
+ align:start position:0%
+but there are lots of cases where that
+is the case for example as i'm walking
+
+ align:start position:0%
+is the case for example as i'm walking
+ 
+
+ align:start position:0%
+is the case for example as i'm walking
+around the room you know your shirt
+
+ align:start position:0%
+around the room you know your shirt
+ 
+
+ align:start position:0%
+around the room you know your shirt
+still looks maroonish red and it doesn't
+
+ align:start position:0%
+still looks maroonish red and it doesn't
+ 
+
+ align:start position:0%
+still looks maroonish red and it doesn't
+really change
+
+ align:start position:0%
+really change
+ 
+
+ align:start position:0%
+really change
+and so we are
+
+ align:start position:0%
+and so we are
+ 
+
+ align:start position:0%
+and so we are
+used to most of the world being somewhat
+
+ align:start position:0%
+used to most of the world being somewhat
+ 
+
+ align:start position:0%
+used to most of the world being somewhat
+constant in
+
+ align:start position:0%
+constant in
+ 
+
+ align:start position:0%
+constant in
+color
+
+ align:start position:0%
+color
+ 
+
+ align:start position:0%
+color
+constant in brightness as well
+
+ align:start position:0%
+constant in brightness as well
+ 
+
+ align:start position:0%
+constant in brightness as well
+even though we know that there's
+
+ align:start position:0%
+even though we know that there's
+ 
+
+ align:start position:0%
+even though we know that there's
+circumstances where that's not the case
+
+ align:start position:0%
+circumstances where that's not the case
+ 
+
+ align:start position:0%
+circumstances where that's not the case
+for example if i look at the reflection
+
+ align:start position:0%
+for example if i look at the reflection
+ 
+
+ align:start position:0%
+for example if i look at the reflection
+of the lights up there in my cell phone
+
+ align:start position:0%
+of the lights up there in my cell phone
+ 
+
+ align:start position:0%
+of the lights up there in my cell phone
+they of course move relative to the cell
+
+ align:start position:0%
+they of course move relative to the cell
+ 
+
+ align:start position:0%
+they of course move relative to the cell
+phone as i move around so and we'll
+
+ align:start position:0%
+phone as i move around so and we'll
+ 
+
+ align:start position:0%
+phone as i move around so and we'll
+we'll talk uh some more about that
+
+ align:start position:0%
+we'll talk uh some more about that
+ 
+
+ align:start position:0%
+we'll talk uh some more about that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+sort of enlarge a little piece of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we we're blowing up
+
+ align:start position:0%
+okay so we we're blowing up
+ 
+
+ align:start position:0%
+okay so we we're blowing up
+this area and why am i doing that well
+
+ align:start position:0%
+this area and why am i doing that well
+ 
+
+ align:start position:0%
+this area and why am i doing that well
+i'd like to use a linear approximation
+
+ align:start position:0%
+i'd like to use a linear approximation
+ 
+
+ align:start position:0%
+i'd like to use a linear approximation
+so i'm assuming that this curve so
+
+ align:start position:0%
+so i'm assuming that this curve so
+ 
+
+ align:start position:0%
+so i'm assuming that this curve so
+second assumption i'm assuming for the
+
+ align:start position:0%
+second assumption i'm assuming for the
+ 
+
+ align:start position:0%
+second assumption i'm assuming for the
+moment this curve is relatively smooth
+
+ align:start position:0%
+moment this curve is relatively smooth
+ 
+
+ align:start position:0%
+moment this curve is relatively smooth
+such that if i look at a small enough
+
+ align:start position:0%
+such that if i look at a small enough
+ 
+
+ align:start position:0%
+such that if i look at a small enough
+part of it i can approximate it as a
+
+ align:start position:0%
+part of it i can approximate it as a
+ 
+
+ align:start position:0%
+part of it i can approximate it as a
+line
+
+ align:start position:0%
+line
+ 
+
+ align:start position:0%
+line
+okay and then there's a change in
+
+ align:start position:0%
+okay and then there's a change in
+ 
+
+ align:start position:0%
+okay and then there's a change in
+brightness
+
+ align:start position:0%
+brightness
+ 
+
+ align:start position:0%
+brightness
+and there's
+
+ align:start position:0%
+and there's
+ 
+
+ align:start position:0%
+and there's
+some slope here and the slope
+
+ align:start position:0%
+some slope here and the slope
+ 
+
+ align:start position:0%
+some slope here and the slope
+relates the
+
+ align:start position:0%
+relates the
+ 
+
+ align:start position:0%
+relates the
+motion
+
+ align:start position:0%
+motion
+ 
+
+ align:start position:0%
+motion
+to the change in brightness you can see
+
+ align:start position:0%
+to the change in brightness you can see
+ 
+
+ align:start position:0%
+to the change in brightness you can see
+where this is going i'd like to use the
+
+ align:start position:0%
+where this is going i'd like to use the
+ 
+
+ align:start position:0%
+where this is going i'd like to use the
+change in brightness to determine the
+
+ align:start position:0%
+change in brightness to determine the
+ 
+
+ align:start position:0%
+change in brightness to determine the
+motion
+
+ align:start position:0%
+motion
+ 
+
+ align:start position:0%
+motion
+because you know
+
+ align:start position:0%
+because you know
+ 
+
+ align:start position:0%
+because you know
+how else are we going to measure the
+
+ align:start position:0%
+how else are we going to measure the
+ 
+
+ align:start position:0%
+how else are we going to measure the
+motion in the image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the pixels stay in the same place
+
+ align:start position:0%
+the pixels stay in the same place
+ 
+
+ align:start position:0%
+the pixels stay in the same place
+all we've got is the brightness at the
+
+ align:start position:0%
+all we've got is the brightness at the
+ 
+
+ align:start position:0%
+all we've got is the brightness at the
+pixel is changing and somehow we have to
+
+ align:start position:0%
+pixel is changing and somehow we have to
+ 
+
+ align:start position:0%
+pixel is changing and somehow we have to
+invert that
+
+ align:start position:0%
+invert that
+ 
+
+ align:start position:0%
+invert that
+uh relationship
+
+ align:start position:0%
+uh relationship
+ 
+
+ align:start position:0%
+uh relationship
+okay so uh
+
+ align:start position:0%
+okay so uh
+ 
+
+ align:start position:0%
+okay so uh
+so in terms of e of x and t
+
+ align:start position:0%
+so in terms of e of x and t
+ 
+
+ align:start position:0%
+so in terms of e of x and t
+uh what is this slope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so this is in the x direction
+
+ align:start position:0%
+right so this is in the x direction
+ 
+
+ align:start position:0%
+right so this is in the x direction
+and that's the rate of change of e with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x and so it's
+
+ align:start position:0%
+x and so it's
+ 
+
+ align:start position:0%
+x and so it's
+d e d x okay
+
+ align:start position:0%
+d e d x okay
+ 
+
+ align:start position:0%
+d e d x okay
+slope
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i'm going to write it that way we'll
+
+ align:start position:0%
+and i'm going to write it that way we'll
+ 
+
+ align:start position:0%
+and i'm going to write it that way we'll
+as a partial derivative
+
+ align:start position:0%
+as a partial derivative
+ 
+
+ align:start position:0%
+as a partial derivative
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know i might as well use the correct
+
+ align:start position:0%
+you know i might as well use the correct
+ 
+
+ align:start position:0%
+you know i might as well use the correct
+notation right away we're going to need
+
+ align:start position:0%
+notation right away we're going to need
+ 
+
+ align:start position:0%
+notation right away we're going to need
+partial derivatives because we have both
+
+ align:start position:0%
+partial derivatives because we have both
+ 
+
+ align:start position:0%
+partial derivatives because we have both
+x and y and t
+
+ align:start position:0%
+x and y and t
+ 
+
+ align:start position:0%
+x and y and t
+and so we need to be clear about
+
+ align:start position:0%
+and so we need to be clear about
+ 
+
+ align:start position:0%
+and so we need to be clear about
+which type of differentiation we're
+
+ align:start position:0%
+which type of differentiation we're
+ 
+
+ align:start position:0%
+which type of differentiation we're
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+then that's the slope so that means that
+
+ align:start position:0%
+then that's the slope so that means that
+ 
+
+ align:start position:0%
+then that's the slope so that means that
+delta e must be the slope
+
+ align:start position:0%
+delta e must be the slope
+ 
+
+ align:start position:0%
+delta e must be the slope
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+delta x
+
+ align:start position:0%
+delta x
+ 
+
+ align:start position:0%
+delta x
+and so that's going to be and i'm going
+
+ align:start position:0%
+and so that's going to be and i'm going
+ 
+
+ align:start position:0%
+and so that's going to be and i'm going
+to write this as e sub x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so again in order to
+
+ align:start position:0%
+um so again in order to
+ 
+
+ align:start position:0%
+um so again in order to
+simplify notation i will often
+
+ align:start position:0%
+simplify notation i will often
+ 
+
+ align:start position:0%
+simplify notation i will often
+use subscripts to denote partial
+
+ align:start position:0%
+use subscripts to denote partial
+ 
+
+ align:start position:0%
+use subscripts to denote partial
+derivatives
+
+ align:start position:0%
+derivatives
+ 
+
+ align:start position:0%
+derivatives
+and you know e sub x and e sub y we use
+
+ align:start position:0%
+and you know e sub x and e sub y we use
+ 
+
+ align:start position:0%
+and you know e sub x and e sub y we use
+so much that it would be a pain to have
+
+ align:start position:0%
+so much that it would be a pain to have
+ 
+
+ align:start position:0%
+so much that it would be a pain to have
+to write them out in full every time
+
+ align:start position:0%
+to write them out in full every time
+ 
+
+ align:start position:0%
+to write them out in full every time
+as we indicated those are the components
+
+ align:start position:0%
+as we indicated those are the components
+ 
+
+ align:start position:0%
+as we indicated those are the components
+of the brightness gradient which is used
+
+ align:start position:0%
+of the brightness gradient which is used
+ 
+
+ align:start position:0%
+of the brightness gradient which is used
+for all sorts of things including edge
+
+ align:start position:0%
+for all sorts of things including edge
+ 
+
+ align:start position:0%
+for all sorts of things including edge
+detection
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now
+
+ align:start position:0%
+okay so now
+ 
+
+ align:start position:0%
+okay so now
+let me divide through by
+
+ align:start position:0%
+let me divide through by
+ 
+
+ align:start position:0%
+let me divide through by
+delta t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this i guess in the limit as i take
+
+ align:start position:0%
+this i guess in the limit as i take
+ 
+
+ align:start position:0%
+this i guess in the limit as i take
+smaller and smaller time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+steps is going to be
+
+ align:start position:0%
+steps is going to be
+ 
+
+ align:start position:0%
+steps is going to be
+that partial derivatives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if you like i can rewrite it one
+
+ align:start position:0%
+and if you like i can rewrite it one
+ 
+
+ align:start position:0%
+and if you like i can rewrite it one
+more time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+you can see here why
+
+ align:start position:0%
+you can see here why
+ 
+
+ align:start position:0%
+you can see here why
+you know using the switch to the
+
+ align:start position:0%
+you know using the switch to the
+ 
+
+ align:start position:0%
+you know using the switch to the
+continuous domain is helpful because
+
+ align:start position:0%
+continuous domain is helpful because
+ 
+
+ align:start position:0%
+continuous domain is helpful because
+uh i can take the limit here as delta t
+
+ align:start position:0%
+uh i can take the limit here as delta t
+ 
+
+ align:start position:0%
+uh i can take the limit here as delta t
+becomes uh
+
+ align:start position:0%
+becomes uh
+ 
+
+ align:start position:0%
+becomes uh
+approaches zero and get the partial
+
+ align:start position:0%
+approaches zero and get the partial
+ 
+
+ align:start position:0%
+approaches zero and get the partial
+derivative uh of course in practice i'm
+
+ align:start position:0%
+derivative uh of course in practice i'm
+ 
+
+ align:start position:0%
+derivative uh of course in practice i'm
+getting frames at a fixed rate and they
+
+ align:start position:0%
+getting frames at a fixed rate and they
+ 
+
+ align:start position:0%
+getting frames at a fixed rate and they
+have a certain interval i can't make
+
+ align:start position:0%
+have a certain interval i can't make
+ 
+
+ align:start position:0%
+have a certain interval i can't make
+that interval infinitely small
+
+ align:start position:0%
+that interval infinitely small
+ 
+
+ align:start position:0%
+that interval infinitely small
+so i end up with a much messier
+
+ align:start position:0%
+so i end up with a much messier
+ 
+
+ align:start position:0%
+so i end up with a much messier
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+but the two are obviously related
+
+ align:start position:0%
+but the two are obviously related
+ 
+
+ align:start position:0%
+but the two are obviously related
+okay so that's the result for 1d image
+
+ align:start position:0%
+okay so that's the result for 1d image
+ 
+
+ align:start position:0%
+okay so that's the result for 1d image
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that allows us to recover the motion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so one thing i probably glossed over is
+
+ align:start position:0%
+so one thing i probably glossed over is
+ 
+
+ align:start position:0%
+so one thing i probably glossed over is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+as we go from
+
+ align:start position:0%
+as we go from
+ 
+
+ align:start position:0%
+as we go from
+t to t plus delta t uh the brightness
+
+ align:start position:0%
+t to t plus delta t uh the brightness
+ 
+
+ align:start position:0%
+t to t plus delta t uh the brightness
+decreases so this delta e over here is
+
+ align:start position:0%
+decreases so this delta e over here is
+ 
+
+ align:start position:0%
+decreases so this delta e over here is
+actually in for positive slope the delta
+
+ align:start position:0%
+actually in for positive slope the delta
+ 
+
+ align:start position:0%
+actually in for positive slope the delta
+e will be negative so that
+
+ align:start position:0%
+e will be negative so that
+ 
+
+ align:start position:0%
+e will be negative so that
+may have gotten lost in here somewhere
+
+ align:start position:0%
+may have gotten lost in here somewhere
+ 
+
+ align:start position:0%
+may have gotten lost in here somewhere
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remarkably
+
+ align:start position:0%
+remarkably
+ 
+
+ align:start position:0%
+remarkably
+from a single pixel
+
+ align:start position:0%
+from a single pixel
+ 
+
+ align:start position:0%
+from a single pixel
+i can get the velocity in this 1d case
+
+ align:start position:0%
+i can get the velocity in this 1d case
+ 
+
+ align:start position:0%
+i can get the velocity in this 1d case
+now importantly that's not true in the
+
+ align:start position:0%
+now importantly that's not true in the
+ 
+
+ align:start position:0%
+now importantly that's not true in the
+2d case and after all that's the case we
+
+ align:start position:0%
+2d case and after all that's the case we
+ 
+
+ align:start position:0%
+2d case and after all that's the case we
+want to solve so we're going to
+
+ align:start position:0%
+want to solve so we're going to
+ 
+
+ align:start position:0%
+want to solve so we're going to
+have to work a little bit harder
+
+ align:start position:0%
+have to work a little bit harder
+ 
+
+ align:start position:0%
+have to work a little bit harder
+and now the couple of things you'll see
+
+ align:start position:0%
+and now the couple of things you'll see
+ 
+
+ align:start position:0%
+and now the couple of things you'll see
+first of all
+
+ align:start position:0%
+first of all
+ 
+
+ align:start position:0%
+first of all
+the faster things are moving
+
+ align:start position:0%
+the faster things are moving
+ 
+
+ align:start position:0%
+the faster things are moving
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+larger
+
+ align:start position:0%
+larger
+ 
+
+ align:start position:0%
+larger
+et will be well that's not a surprise if
+
+ align:start position:0%
+et will be well that's not a surprise if
+ 
+
+ align:start position:0%
+et will be well that's not a surprise if
+if the brightness is changing uh slowly
+
+ align:start position:0%
+if the brightness is changing uh slowly
+ 
+
+ align:start position:0%
+if the brightness is changing uh slowly
+then you speed things up then the
+
+ align:start position:0%
+then you speed things up then the
+ 
+
+ align:start position:0%
+then you speed things up then the
+brightness will change more rapidly it's
+
+ align:start position:0%
+brightness will change more rapidly it's
+ 
+
+ align:start position:0%
+brightness will change more rapidly it's
+like you know taking your youtube video
+
+ align:start position:0%
+like you know taking your youtube video
+ 
+
+ align:start position:0%
+like you know taking your youtube video
+and changing the playback rate the um
+
+ align:start position:0%
+and changing the playback rate the um
+ 
+
+ align:start position:0%
+and changing the playback rate the um
+when you change the playback rate you
+
+ align:start position:0%
+when you change the playback rate you
+ 
+
+ align:start position:0%
+when you change the playback rate you
+change all the velocities by the same
+
+ align:start position:0%
+change all the velocities by the same
+ 
+
+ align:start position:0%
+change all the velocities by the same
+factor
+
+ align:start position:0%
+factor
+ 
+
+ align:start position:0%
+factor
+and there and then you
+
+ align:start position:0%
+and there and then you
+ 
+
+ align:start position:0%
+and there and then you
+have more rapid changes of brightness
+
+ align:start position:0%
+have more rapid changes of brightness
+ 
+
+ align:start position:0%
+have more rapid changes of brightness
+you know intuitively obvious another
+
+ align:start position:0%
+you know intuitively obvious another
+ 
+
+ align:start position:0%
+you know intuitively obvious another
+thing you'll notice is that
+
+ align:start position:0%
+thing you'll notice is that
+ 
+
+ align:start position:0%
+thing you'll notice is that
+there's a problem
+
+ align:start position:0%
+there's a problem
+ 
+
+ align:start position:0%
+there's a problem
+if e x is zero
+
+ align:start position:0%
+if e x is zero
+ 
+
+ align:start position:0%
+if e x is zero
+right we can't do this
+
+ align:start position:0%
+right we can't do this
+ 
+
+ align:start position:0%
+right we can't do this
+if e x is zero so if we're for example
+
+ align:start position:0%
+if e x is zero so if we're for example
+ 
+
+ align:start position:0%
+if e x is zero so if we're for example
+at uh
+
+ align:start position:0%
+at uh
+ 
+
+ align:start position:0%
+at uh
+suppose we are up here
+
+ align:start position:0%
+suppose we are up here
+ 
+
+ align:start position:0%
+suppose we are up here
+well then if the thing moves the
+
+ align:start position:0%
+well then if the thing moves the
+ 
+
+ align:start position:0%
+well then if the thing moves the
+brightness change doesn't change or
+
+ align:start position:0%
+brightness change doesn't change or
+ 
+
+ align:start position:0%
+brightness change doesn't change or
+changes only a tiny bit and so from that
+
+ align:start position:0%
+changes only a tiny bit and so from that
+ 
+
+ align:start position:0%
+changes only a tiny bit and so from that
+you can't really tell how far it moved
+
+ align:start position:0%
+you can't really tell how far it moved
+ 
+
+ align:start position:0%
+you can't really tell how far it moved
+you pretty much have the same result if
+
+ align:start position:0%
+you pretty much have the same result if
+ 
+
+ align:start position:0%
+you pretty much have the same result if
+it moved that much or whatever so
+
+ align:start position:0%
+it moved that much or whatever so
+ 
+
+ align:start position:0%
+it moved that much or whatever so
+and you know just in terms of
+
+ align:start position:0%
+and you know just in terms of
+ 
+
+ align:start position:0%
+and you know just in terms of
+uh implementation you're dividing by
+
+ align:start position:0%
+uh implementation you're dividing by
+ 
+
+ align:start position:0%
+uh implementation you're dividing by
+zero so that's
+
+ align:start position:0%
+zero so that's
+ 
+
+ align:start position:0%
+zero so that's
+uh not going to be good and it's not
+
+ align:start position:0%
+uh not going to be good and it's not
+ 
+
+ align:start position:0%
+uh not going to be good and it's not
+just zero it's when it's very small
+
+ align:start position:0%
+just zero it's when it's very small
+ 
+
+ align:start position:0%
+just zero it's when it's very small
+why is that well because when it's very
+
+ align:start position:0%
+why is that well because when it's very
+ 
+
+ align:start position:0%
+why is that well because when it's very
+small it probably means that you don't
+
+ align:start position:0%
+small it probably means that you don't
+ 
+
+ align:start position:0%
+small it probably means that you don't
+know it
+
+ align:start position:0%
+know it
+ 
+
+ align:start position:0%
+know it
+accurately as a result of the fact that
+
+ align:start position:0%
+accurately as a result of the fact that
+ 
+
+ align:start position:0%
+accurately as a result of the fact that
+you obtain it by subtracting two pixel
+
+ align:start position:0%
+you obtain it by subtracting two pixel
+ 
+
+ align:start position:0%
+you obtain it by subtracting two pixel
+values so so let's just again
+
+ align:start position:0%
+values so so let's just again
+ 
+
+ align:start position:0%
+values so so let's just again
+you know go over this we're
+
+ align:start position:0%
+you know go over this we're
+ 
+
+ align:start position:0%
+you know go over this we're
+approximating this by saying it's one
+
+ align:start position:0%
+approximating this by saying it's one
+ 
+
+ align:start position:0%
+approximating this by saying it's one
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+delta x e of x plus delta x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right well you know that's fancy
+
+ align:start position:0%
+right well you know that's fancy
+ 
+
+ align:start position:0%
+right well you know that's fancy
+notation but basically
+
+ align:start position:0%
+notation but basically
+ 
+
+ align:start position:0%
+notation but basically
+the two pixels we take this value and we
+
+ align:start position:0%
+the two pixels we take this value and we
+ 
+
+ align:start position:0%
+the two pixels we take this value and we
+subtract that value so we read out the
+
+ align:start position:0%
+subtract that value so we read out the
+ 
+
+ align:start position:0%
+subtract that value so we read out the
+gray level there read out the gray value
+
+ align:start position:0%
+gray level there read out the gray value
+ 
+
+ align:start position:0%
+gray level there read out the gray value
+there subtract them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's how we estimate our
+
+ align:start position:0%
+that's how we estimate our
+ 
+
+ align:start position:0%
+that's how we estimate our
+brightness derivatives and similarly so
+
+ align:start position:0%
+brightness derivatives and similarly so
+ 
+
+ align:start position:0%
+brightness derivatives and similarly so
+what do we do with et well et is derived
+
+ align:start position:0%
+what do we do with et well et is derived
+ 
+
+ align:start position:0%
+what do we do with et well et is derived
+the same way except that
+
+ align:start position:0%
+the same way except that
+ 
+
+ align:start position:0%
+the same way except that
+we have two frames
+
+ align:start position:0%
+we have two frames
+ 
+
+ align:start position:0%
+we have two frames
+and we pick the same pixel
+
+ align:start position:0%
+and we pick the same pixel
+ 
+
+ align:start position:0%
+and we pick the same pixel
+out of the two frames
+
+ align:start position:0%
+out of the two frames
+ 
+
+ align:start position:0%
+out of the two frames
+and we subtract their gray values
+
+ align:start position:0%
+and we subtract their gray values
+ 
+
+ align:start position:0%
+and we subtract their gray values
+right so it's just in a different
+
+ align:start position:0%
+right so it's just in a different
+ 
+
+ align:start position:0%
+right so it's just in a different
+direction that we're approximating the
+
+ align:start position:0%
+direction that we're approximating the
+ 
+
+ align:start position:0%
+direction that we're approximating the
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+why is that important well if they're um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is a small brightness gradient e x is
+
+ align:start position:0%
+is a small brightness gradient e x is
+ 
+
+ align:start position:0%
+is a small brightness gradient e x is
+small then those two values will be very
+
+ align:start position:0%
+small then those two values will be very
+ 
+
+ align:start position:0%
+small then those two values will be very
+similar
+
+ align:start position:0%
+similar
+ 
+
+ align:start position:0%
+similar
+and since they are not known precisely
+
+ align:start position:0%
+and since they are not known precisely
+ 
+
+ align:start position:0%
+and since they are not known precisely
+they have error measurement error in
+
+ align:start position:0%
+they have error measurement error in
+ 
+
+ align:start position:0%
+they have error measurement error in
+them we're now subtracting two
+
+ align:start position:0%
+them we're now subtracting two
+ 
+
+ align:start position:0%
+them we're now subtracting two
+quantities that are similar in size so
+
+ align:start position:0%
+quantities that are similar in size so
+ 
+
+ align:start position:0%
+quantities that are similar in size so
+we get a smaller quantity and it has
+
+ align:start position:0%
+we get a smaller quantity and it has
+ 
+
+ align:start position:0%
+we get a smaller quantity and it has
+it's mostly noise at some point
+
+ align:start position:0%
+it's mostly noise at some point
+ 
+
+ align:start position:0%
+it's mostly noise at some point
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+that tells us that this is something to
+
+ align:start position:0%
+that tells us that this is something to
+ 
+
+ align:start position:0%
+that tells us that this is something to
+avoid
+
+ align:start position:0%
+avoid
+ 
+
+ align:start position:0%
+avoid
+we we don't want to be and that makes
+
+ align:start position:0%
+we we don't want to be and that makes
+ 
+
+ align:start position:0%
+we we don't want to be and that makes
+sense i mean if the image is uniform and
+
+ align:start position:0%
+sense i mean if the image is uniform and
+ 
+
+ align:start position:0%
+sense i mean if the image is uniform and
+brightness e x is zero um you know you
+
+ align:start position:0%
+brightness e x is zero um you know you
+ 
+
+ align:start position:0%
+brightness e x is zero um you know you
+can move it and you can't tell that it
+
+ align:start position:0%
+can move it and you can't tell that it
+ 
+
+ align:start position:0%
+can move it and you can't tell that it
+moved i mean you'd have to have some
+
+ align:start position:0%
+moved i mean you'd have to have some
+ 
+
+ align:start position:0%
+moved i mean you'd have to have some
+reference point like some texture on it
+
+ align:start position:0%
+reference point like some texture on it
+ 
+
+ align:start position:0%
+reference point like some texture on it
+to tell that it moved and you know if
+
+ align:start position:0%
+to tell that it moved and you know if
+ 
+
+ align:start position:0%
+to tell that it moved and you know if
+you had texture on it e x wouldn't be
+
+ align:start position:0%
+you had texture on it e x wouldn't be
+ 
+
+ align:start position:0%
+you had texture on it e x wouldn't be
+zero so
+
+ align:start position:0%
+zero so
+ 
+
+ align:start position:0%
+zero so
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+i i know i'm sort of belaboring this
+
+ align:start position:0%
+i i know i'm sort of belaboring this
+ 
+
+ align:start position:0%
+i i know i'm sort of belaboring this
+over and over again but it's very
+
+ align:start position:0%
+over and over again but it's very
+ 
+
+ align:start position:0%
+over and over again but it's very
+important because it means that this
+
+ align:start position:0%
+important because it means that this
+ 
+
+ align:start position:0%
+important because it means that this
+type of measurement is a very noisy and
+
+ align:start position:0%
+type of measurement is a very noisy and
+ 
+
+ align:start position:0%
+type of measurement is a very noisy and
+b
+
+ align:start position:0%
+b
+ 
+
+ align:start position:0%
+b
+not trustworthy unless certain image
+
+ align:start position:0%
+not trustworthy unless certain image
+ 
+
+ align:start position:0%
+not trustworthy unless certain image
+conditions are satisfied
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and then the next thing you can do
+
+ align:start position:0%
+okay and then the next thing you can do
+ 
+
+ align:start position:0%
+okay and then the next thing you can do
+and say well well we can estimate
+
+ align:start position:0%
+and say well well we can estimate
+ 
+
+ align:start position:0%
+and say well well we can estimate
+velocity from a single pixel but we got
+
+ align:start position:0%
+velocity from a single pixel but we got
+ 
+
+ align:start position:0%
+velocity from a single pixel but we got
+lots of pixels and that you know that's
+
+ align:start position:0%
+lots of pixels and that you know that's
+ 
+
+ align:start position:0%
+lots of pixels and that you know that's
+part of what we're going to be using
+
+ align:start position:0%
+part of what we're going to be using
+ 
+
+ align:start position:0%
+part of what we're going to be using
+heavily that okay the single pixel
+
+ align:start position:0%
+heavily that okay the single pixel
+ 
+
+ align:start position:0%
+heavily that okay the single pixel
+result is not great
+
+ align:start position:0%
+result is not great
+ 
+
+ align:start position:0%
+result is not great
+but we got a million or 10 million and
+
+ align:start position:0%
+but we got a million or 10 million and
+ 
+
+ align:start position:0%
+but we got a million or 10 million and
+so we can do
+
+ align:start position:0%
+so we can do
+ 
+
+ align:start position:0%
+so we can do
+things like least squares
+
+ align:start position:0%
+things like least squares
+ 
+
+ align:start position:0%
+things like least squares
+to improve the result
+
+ align:start position:0%
+to improve the result
+ 
+
+ align:start position:0%
+to improve the result
+dramatically so it may be that the
+
+ align:start position:0%
+dramatically so it may be that the
+ 
+
+ align:start position:0%
+dramatically so it may be that the
+result from a single pixel is really
+
+ align:start position:0%
+result from a single pixel is really
+ 
+
+ align:start position:0%
+result from a single pixel is really
+flaky but that's okay because we divide
+
+ align:start position:0%
+flaky but that's okay because we divide
+ 
+
+ align:start position:0%
+flaky but that's okay because we divide
+the error by a thousand
+
+ align:start position:0%
+the error by a thousand
+ 
+
+ align:start position:0%
+the error by a thousand
+uh if we uh think about the statistics
+
+ align:start position:0%
+uh if we uh think about the statistics
+ 
+
+ align:start position:0%
+uh if we uh think about the statistics
+of having a million of these uh pixels
+
+ align:start position:0%
+of having a million of these uh pixels
+ 
+
+ align:start position:0%
+of having a million of these uh pixels
+so um i keep on saying they're noisy and
+
+ align:start position:0%
+so um i keep on saying they're noisy and
+ 
+
+ align:start position:0%
+so um i keep on saying they're noisy and
+at the same time i'm saying we can do
+
+ align:start position:0%
+at the same time i'm saying we can do
+ 
+
+ align:start position:0%
+at the same time i'm saying we can do
+this and the reason we can do it is
+
+ align:start position:0%
+this and the reason we can do it is
+ 
+
+ align:start position:0%
+this and the reason we can do it is
+because we got lots of them so
+
+ align:start position:0%
+because we got lots of them so
+ 
+
+ align:start position:0%
+because we got lots of them so
+okay so we talked about how to
+
+ align:start position:0%
+okay so we talked about how to
+ 
+
+ align:start position:0%
+okay so we talked about how to
+approximate
+
+ align:start position:0%
+approximate
+ 
+
+ align:start position:0%
+approximate
+how to switch back and forth between the
+
+ align:start position:0%
+how to switch back and forth between the
+ 
+
+ align:start position:0%
+how to switch back and forth between the
+continuous world and the approximate
+
+ align:start position:0%
+continuous world and the approximate
+ 
+
+ align:start position:0%
+continuous world and the approximate
+the discrete world and
+
+ align:start position:0%
+the discrete world and
+ 
+
+ align:start position:0%
+the discrete world and
+now i don't want to give away the
+
+ align:start position:0%
+now i don't want to give away the
+ 
+
+ align:start position:0%
+now i don't want to give away the
+solution to the homework problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the next step i guess would be to
+
+ align:start position:0%
+but the next step i guess would be to
+ 
+
+ align:start position:0%
+but the next step i guess would be to
+get a bunch of these and combine them so
+
+ align:start position:0%
+get a bunch of these and combine them so
+ 
+
+ align:start position:0%
+get a bunch of these and combine them so
+we might do something like this
+
+ align:start position:0%
+we might do something like this
+ 
+
+ align:start position:0%
+we might do something like this
+you know if we have n pixels
+
+ align:start position:0%
+you know if we have n pixels
+ 
+
+ align:start position:0%
+you know if we have n pixels
+then we might try something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so now instead of just using a two
+
+ align:start position:0%
+right so now instead of just using a two
+ 
+
+ align:start position:0%
+right so now instead of just using a two
+pixels we use those two pixels to do the
+
+ align:start position:0%
+pixels we use those two pixels to do the
+ 
+
+ align:start position:0%
+pixels we use those two pixels to do the
+calculation then we use these two pixels
+
+ align:start position:0%
+calculation then we use these two pixels
+ 
+
+ align:start position:0%
+calculation then we use these two pixels
+to do the calculation then we use those
+
+ align:start position:0%
+to do the calculation then we use those
+ 
+
+ align:start position:0%
+to do the calculation then we use those
+two pixels to the calculation and so on
+
+ align:start position:0%
+two pixels to the calculation and so on
+ 
+
+ align:start position:0%
+two pixels to the calculation and so on
+and so we add them up so we have a lot
+
+ align:start position:0%
+and so we add them up so we have a lot
+ 
+
+ align:start position:0%
+and so we add them up so we have a lot
+of noisy measurements and we take the
+
+ align:start position:0%
+of noisy measurements and we take the
+ 
+
+ align:start position:0%
+of noisy measurements and we take the
+average and magically
+
+ align:start position:0%
+average and magically
+ 
+
+ align:start position:0%
+average and magically
+things improve and so just without going
+
+ align:start position:0%
+things improve and so just without going
+ 
+
+ align:start position:0%
+things improve and so just without going
+into you know hairy statistics or
+
+ align:start position:0%
+into you know hairy statistics or
+ 
+
+ align:start position:0%
+into you know hairy statistics or
+assumptions about probability
+
+ align:start position:0%
+assumptions about probability
+ 
+
+ align:start position:0%
+assumptions about probability
+distributions roughly speaking
+
+ align:start position:0%
+distributions roughly speaking
+ 
+
+ align:start position:0%
+distributions roughly speaking
+when you average n values you you reduce
+
+ align:start position:0%
+when you average n values you you reduce
+ 
+
+ align:start position:0%
+when you average n values you you reduce
+the standard deviation by this square
+
+ align:start position:0%
+the standard deviation by this square
+ 
+
+ align:start position:0%
+the standard deviation by this square
+root of n so
+
+ align:start position:0%
+root of n so
+ 
+
+ align:start position:0%
+root of n so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and you know when you have these
+
+ align:start position:0%
+and you know when you have these
+ 
+
+ align:start position:0%
+and you know when you have these
+political surveys and they say they have
+
+ align:start position:0%
+political surveys and they say they have
+ 
+
+ align:start position:0%
+political surveys and they say they have
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+five percent margin of error what they
+
+ align:start position:0%
+five percent margin of error what they
+ 
+
+ align:start position:0%
+five percent margin of error what they
+mean is that they
+
+ align:start position:0%
+mean is that they
+ 
+
+ align:start position:0%
+mean is that they
+they talk to 400 people
+
+ align:start position:0%
+they talk to 400 people
+ 
+
+ align:start position:0%
+they talk to 400 people
+right because one of uh square root of
+
+ align:start position:0%
+right because one of uh square root of
+ 
+
+ align:start position:0%
+right because one of uh square root of
+400 is 20 1 over 20 is 0.05 so
+
+ align:start position:0%
+400 is 20 1 over 20 is 0.05 so
+ 
+
+ align:start position:0%
+400 is 20 1 over 20 is 0.05 so
+same principle
+
+ align:start position:0%
+same principle
+ 
+
+ align:start position:0%
+same principle
+so um it doesn't improve linearly with n
+
+ align:start position:0%
+so um it doesn't improve linearly with n
+ 
+
+ align:start position:0%
+so um it doesn't improve linearly with n
+unfortunately that would be even better
+
+ align:start position:0%
+unfortunately that would be even better
+ 
+
+ align:start position:0%
+unfortunately that would be even better
+but it doesn't improve with the square
+
+ align:start position:0%
+but it doesn't improve with the square
+ 
+
+ align:start position:0%
+but it doesn't improve with the square
+root of n so if we have a million pixel
+
+ align:start position:0%
+root of n so if we have a million pixel
+ 
+
+ align:start position:0%
+root of n so if we have a million pixel
+image it improves by a factor of a
+
+ align:start position:0%
+image it improves by a factor of a
+ 
+
+ align:start position:0%
+image it improves by a factor of a
+thousand which is you know pretty
+
+ align:start position:0%
+thousand which is you know pretty
+ 
+
+ align:start position:0%
+thousand which is you know pretty
+significant
+
+ align:start position:0%
+significant
+ 
+
+ align:start position:0%
+significant
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now if we just did this in this simple
+
+ align:start position:0%
+now if we just did this in this simple
+ 
+
+ align:start position:0%
+now if we just did this in this simple
+way we'd still run into trouble
+
+ align:start position:0%
+way we'd still run into trouble
+ 
+
+ align:start position:0%
+way we'd still run into trouble
+first of all you know if e x is really
+
+ align:start position:0%
+first of all you know if e x is really
+ 
+
+ align:start position:0%
+first of all you know if e x is really
+zero you'd be dividing by zero so you
+
+ align:start position:0%
+zero you'd be dividing by zero so you
+ 
+
+ align:start position:0%
+zero you'd be dividing by zero so you
+can't do that i guess you could leave
+
+ align:start position:0%
+can't do that i guess you could leave
+ 
+
+ align:start position:0%
+can't do that i guess you could leave
+those pixels out
+
+ align:start position:0%
+those pixels out
+ 
+
+ align:start position:0%
+those pixels out
+and then if e x is small you still have
+
+ align:start position:0%
+and then if e x is small you still have
+ 
+
+ align:start position:0%
+and then if e x is small you still have
+an answer which is relatively bad so
+
+ align:start position:0%
+an answer which is relatively bad so
+ 
+
+ align:start position:0%
+an answer which is relatively bad so
+there are places where the slope is
+
+ align:start position:0%
+there are places where the slope is
+ 
+
+ align:start position:0%
+there are places where the slope is
+large where you get good information and
+
+ align:start position:0%
+large where you get good information and
+ 
+
+ align:start position:0%
+large where you get good information and
+now you're polluting it by adding in as
+
+ align:start position:0%
+now you're polluting it by adding in as
+ 
+
+ align:start position:0%
+now you're polluting it by adding in as
+an equal you know information from
+
+ align:start position:0%
+an equal you know information from
+ 
+
+ align:start position:0%
+an equal you know information from
+places where the slope is low and
+
+ align:start position:0%
+places where the slope is low and
+ 
+
+ align:start position:0%
+places where the slope is low and
+and that's why in the homework problem
+
+ align:start position:0%
+and that's why in the homework problem
+ 
+
+ align:start position:0%
+and that's why in the homework problem
+we talk about weighting so don't just
+
+ align:start position:0%
+we talk about weighting so don't just
+ 
+
+ align:start position:0%
+we talk about weighting so don't just
+take an average and treat each of them
+
+ align:start position:0%
+take an average and treat each of them
+ 
+
+ align:start position:0%
+take an average and treat each of them
+equally but
+
+ align:start position:0%
+equally but
+ 
+
+ align:start position:0%
+equally but
+you know multiply by some weight factor
+
+ align:start position:0%
+you know multiply by some weight factor
+ 
+
+ align:start position:0%
+you know multiply by some weight factor
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+then of course you what happens to the
+
+ align:start position:0%
+then of course you what happens to the
+ 
+
+ align:start position:0%
+then of course you what happens to the
+one over n well you have to compensate
+
+ align:start position:0%
+one over n well you have to compensate
+ 
+
+ align:start position:0%
+one over n well you have to compensate
+for the fact that you've now switched to
+
+ align:start position:0%
+for the fact that you've now switched to
+ 
+
+ align:start position:0%
+for the fact that you've now switched to
+uh using uh weights
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay um
+
+ align:start position:0%
+okay um
+ 
+
+ align:start position:0%
+okay um
+as we mentioned
+
+ align:start position:0%
+as we mentioned
+ 
+
+ align:start position:0%
+as we mentioned
+uh images are really 2d so let's extend
+
+ align:start position:0%
+uh images are really 2d so let's extend
+ 
+
+ align:start position:0%
+uh images are really 2d so let's extend
+this analysis to 2d and see what happens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now some of this may you know seem
+
+ align:start position:0%
+now some of this may you know seem
+ 
+
+ align:start position:0%
+now some of this may you know seem
+tedious and repetitive to some of you
+
+ align:start position:0%
+tedious and repetitive to some of you
+ 
+
+ align:start position:0%
+tedious and repetitive to some of you
+but we're all on different wavelengths
+
+ align:start position:0%
+but we're all on different wavelengths
+ 
+
+ align:start position:0%
+but we're all on different wavelengths
+so i'm going to get the next result
+
+ align:start position:0%
+so i'm going to get the next result
+ 
+
+ align:start position:0%
+so i'm going to get the next result
+in several different ways
+
+ align:start position:0%
+in several different ways
+ 
+
+ align:start position:0%
+in several different ways
+and you know different approaches may
+
+ align:start position:0%
+and you know different approaches may
+ 
+
+ align:start position:0%
+and you know different approaches may
+appeal to
+
+ align:start position:0%
+appeal to
+ 
+
+ align:start position:0%
+appeal to
+different people so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me do it this way so let's start by
+
+ align:start position:0%
+let me do it this way so let's start by
+ 
+
+ align:start position:0%
+let me do it this way so let's start by
+talking about the image volume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so think about
+
+ align:start position:0%
+so think about
+ 
+
+ align:start position:0%
+so think about
+you know video
+
+ align:start position:0%
+you know video
+ 
+
+ align:start position:0%
+you know video
+and we're stitching together the frames
+
+ align:start position:0%
+and we're stitching together the frames
+ 
+
+ align:start position:0%
+and we're stitching together the frames
+so each of these cross sections
+
+ align:start position:0%
+so each of these cross sections
+ 
+
+ align:start position:0%
+so each of these cross sections
+is a frame
+
+ align:start position:0%
+is a frame
+ 
+
+ align:start position:0%
+is a frame
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we end up with
+
+ align:start position:0%
+we end up with
+ 
+
+ align:start position:0%
+we end up with
+this three-dimensional thing
+
+ align:start position:0%
+this three-dimensional thing
+ 
+
+ align:start position:0%
+this three-dimensional thing
+which is brightness as a function of
+
+ align:start position:0%
+which is brightness as a function of
+ 
+
+ align:start position:0%
+which is brightness as a function of
+x y and t
+
+ align:start position:0%
+x y and t
+ 
+
+ align:start position:0%
+x y and t
+and typically in practice we slice it
+
+ align:start position:0%
+and typically in practice we slice it
+ 
+
+ align:start position:0%
+and typically in practice we slice it
+across this way but we could slice this
+
+ align:start position:0%
+across this way but we could slice this
+ 
+
+ align:start position:0%
+across this way but we could slice this
+volume any way you like and in some
+
+ align:start position:0%
+volume any way you like and in some
+ 
+
+ align:start position:0%
+volume any way you like and in some
+cases
+
+ align:start position:0%
+cases
+ 
+
+ align:start position:0%
+cases
+there are advantages to slicing it in in
+
+ align:start position:0%
+there are advantages to slicing it in in
+ 
+
+ align:start position:0%
+there are advantages to slicing it in in
+different ways
+
+ align:start position:0%
+different ways
+ 
+
+ align:start position:0%
+different ways
+okay so that's part one and sometimes
+
+ align:start position:0%
+okay so that's part one and sometimes
+ 
+
+ align:start position:0%
+okay so that's part one and sometimes
+it's useful to
+
+ align:start position:0%
+it's useful to
+ 
+
+ align:start position:0%
+it's useful to
+visualize things this way
+
+ align:start position:0%
+visualize things this way
+ 
+
+ align:start position:0%
+visualize things this way
+then we're going to be using partial
+
+ align:start position:0%
+then we're going to be using partial
+ 
+
+ align:start position:0%
+then we're going to be using partial
+derivatives so what are they
+
+ align:start position:0%
+derivatives so what are they
+ 
+
+ align:start position:0%
+derivatives so what are they
+well it's just the derivatives in the
+
+ align:start position:0%
+well it's just the derivatives in the
+ 
+
+ align:start position:0%
+well it's just the derivatives in the
+axis directions here so we'll be dealing
+
+ align:start position:0%
+axis directions here so we'll be dealing
+ 
+
+ align:start position:0%
+axis directions here so we'll be dealing
+with you know d e d x
+
+ align:start position:0%
+with you know d e d x
+ 
+
+ align:start position:0%
+with you know d e d x
+the e d y and the e d t
+
+ align:start position:0%
+the e d y and the e d t
+ 
+
+ align:start position:0%
+the e d y and the e d t
+and just as we've been discussing
+
+ align:start position:0%
+and just as we've been discussing
+ 
+
+ align:start position:0%
+and just as we've been discussing
+we approximate them by taking
+
+ align:start position:0%
+we approximate them by taking
+ 
+
+ align:start position:0%
+we approximate them by taking
+differences first differences of
+
+ align:start position:0%
+differences first differences of
+ 
+
+ align:start position:0%
+differences first differences of
+neighboring pixels
+
+ align:start position:0%
+neighboring pixels
+ 
+
+ align:start position:0%
+neighboring pixels
+in either the x the y or the t direction
+
+ align:start position:0%
+in either the x the y or the t direction
+ 
+
+ align:start position:0%
+in either the x the y or the t direction
+from frame to frame so you know that
+
+ align:start position:0%
+from frame to frame so you know that
+ 
+
+ align:start position:0%
+from frame to frame so you know that
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+all that is
+
+ align:start position:0%
+all that is
+ 
+
+ align:start position:0%
+all that is
+okay so what's you know some people find
+
+ align:start position:0%
+okay so what's you know some people find
+ 
+
+ align:start position:0%
+okay so what's you know some people find
+partial derivatives a little bit more
+
+ align:start position:0%
+partial derivatives a little bit more
+ 
+
+ align:start position:0%
+partial derivatives a little bit more
+scary than
+
+ align:start position:0%
+scary than
+ 
+
+ align:start position:0%
+scary than
+uh ordinary derivatives but that's all
+
+ align:start position:0%
+uh ordinary derivatives but that's all
+ 
+
+ align:start position:0%
+uh ordinary derivatives but that's all
+it is we're just taking
+
+ align:start position:0%
+it is we're just taking
+ 
+
+ align:start position:0%
+it is we're just taking
+the derivatives in those three
+
+ align:start position:0%
+the derivatives in those three
+ 
+
+ align:start position:0%
+the derivatives in those three
+directions
+
+ align:start position:0%
+directions
+ 
+
+ align:start position:0%
+directions
+whereas we could be doing something more
+
+ align:start position:0%
+whereas we could be doing something more
+ 
+
+ align:start position:0%
+whereas we could be doing something more
+complicated
+
+ align:start position:0%
+complicated
+ 
+
+ align:start position:0%
+complicated
+so let's think about that so suppose
+
+ align:start position:0%
+so let's think about that so suppose
+ 
+
+ align:start position:0%
+so let's think about that so suppose
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+um you know this video is for me moving
+
+ align:start position:0%
+um you know this video is for me moving
+ 
+
+ align:start position:0%
+um you know this video is for me moving
+through an environment
+
+ align:start position:0%
+through an environment
+ 
+
+ align:start position:0%
+through an environment
+and there's some object in the
+
+ align:start position:0%
+and there's some object in the
+ 
+
+ align:start position:0%
+and there's some object in the
+environment
+
+ align:start position:0%
+environment
+ 
+
+ align:start position:0%
+environment
+that um i'm tracking and at time t 0 you
+
+ align:start position:0%
+that um i'm tracking and at time t 0 you
+ 
+
+ align:start position:0%
+that um i'm tracking and at time t 0 you
+know it's there in the image and then in
+
+ align:start position:0%
+know it's there in the image and then in
+ 
+
+ align:start position:0%
+know it's there in the image and then in
+the next frame it's over here and so on
+
+ align:start position:0%
+the next frame it's over here and so on
+ 
+
+ align:start position:0%
+the next frame it's over here and so on
+so it follows some sort of path
+
+ align:start position:0%
+so it follows some sort of path
+ 
+
+ align:start position:0%
+so it follows some sort of path
+in this three dimensional volume
+
+ align:start position:0%
+in this three dimensional volume
+ 
+
+ align:start position:0%
+in this three dimensional volume
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know i could do this for other
+
+ align:start position:0%
+you know i could do this for other
+ 
+
+ align:start position:0%
+you know i could do this for other
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+and develop this whole
+
+ align:start position:0%
+and develop this whole
+ 
+
+ align:start position:0%
+and develop this whole
+set of curves but let me let's just
+
+ align:start position:0%
+set of curves but let me let's just
+ 
+
+ align:start position:0%
+set of curves but let me let's just
+focus on one now one of the things i
+
+ align:start position:0%
+focus on one now one of the things i
+ 
+
+ align:start position:0%
+focus on one now one of the things i
+might want to do is
+
+ align:start position:0%
+might want to do is
+ 
+
+ align:start position:0%
+might want to do is
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+see how this changes so when i'm looking
+
+ align:start position:0%
+see how this changes so when i'm looking
+ 
+
+ align:start position:0%
+see how this changes so when i'm looking
+at uh different frames of an image
+
+ align:start position:0%
+at uh different frames of an image
+ 
+
+ align:start position:0%
+at uh different frames of an image
+often what i want to do is not take the
+
+ align:start position:0%
+often what i want to do is not take the
+ 
+
+ align:start position:0%
+often what i want to do is not take the
+derivative at a pixel and see how it
+
+ align:start position:0%
+derivative at a pixel and see how it
+ 
+
+ align:start position:0%
+derivative at a pixel and see how it
+changes to the next time frame but i
+
+ align:start position:0%
+changes to the next time frame but i
+ 
+
+ align:start position:0%
+changes to the next time frame but i
+want to follow an object and see how how
+
+ align:start position:0%
+want to follow an object and see how how
+ 
+
+ align:start position:0%
+want to follow an object and see how how
+it changes and in many cases
+
+ align:start position:0%
+it changes and in many cases
+ 
+
+ align:start position:0%
+it changes and in many cases
+i'm going to make the constant
+
+ align:start position:0%
+i'm going to make the constant
+ 
+
+ align:start position:0%
+i'm going to make the constant
+brightness assumption that it's not
+
+ align:start position:0%
+brightness assumption that it's not
+ 
+
+ align:start position:0%
+brightness assumption that it's not
+changing in brightness
+
+ align:start position:0%
+changing in brightness
+ 
+
+ align:start position:0%
+changing in brightness
+and so i would like to express some
+
+ align:start position:0%
+and so i would like to express some
+ 
+
+ align:start position:0%
+and so i would like to express some
+constraint on the derivative along this
+
+ align:start position:0%
+constraint on the derivative along this
+ 
+
+ align:start position:0%
+constraint on the derivative along this
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+and so i could have a curve
+
+ align:start position:0%
+and so i could have a curve
+ 
+
+ align:start position:0%
+and so i could have a curve
+how do i define that well one way is to
+
+ align:start position:0%
+how do i define that well one way is to
+ 
+
+ align:start position:0%
+how do i define that well one way is to
+give x and y as a function of t
+
+ align:start position:0%
+give x and y as a function of t
+ 
+
+ align:start position:0%
+give x and y as a function of t
+so this green curve
+
+ align:start position:0%
+so this green curve
+ 
+
+ align:start position:0%
+so this green curve
+for each time t i can give an x and a y
+
+ align:start position:0%
+for each time t i can give an x and a y
+ 
+
+ align:start position:0%
+for each time t i can give an x and a y
+that's how i define that curve
+
+ align:start position:0%
+that's how i define that curve
+ 
+
+ align:start position:0%
+that's how i define that curve
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then what i'd like to do is look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the total derivative
+
+ align:start position:0%
+the total derivative
+ 
+
+ align:start position:0%
+the total derivative
+uh along that curve
+
+ align:start position:0%
+uh along that curve
+ 
+
+ align:start position:0%
+uh along that curve
+right keeping in mind that along that
+
+ align:start position:0%
+right keeping in mind that along that
+ 
+
+ align:start position:0%
+right keeping in mind that along that
+curve not only is t changing but x and y
+
+ align:start position:0%
+curve not only is t changing but x and y
+ 
+
+ align:start position:0%
+curve not only is t changing but x and y
+are changing in some defined way so so
+
+ align:start position:0%
+are changing in some defined way so so
+ 
+
+ align:start position:0%
+are changing in some defined way so so
+this is the total derivative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in what we're going to be doing we'll
+
+ align:start position:0%
+in what we're going to be doing we'll
+ 
+
+ align:start position:0%
+in what we're going to be doing we'll
+set that to zero because we're assuming
+
+ align:start position:0%
+set that to zero because we're assuming
+ 
+
+ align:start position:0%
+set that to zero because we're assuming
+that this point maintains its brightness
+
+ align:start position:0%
+that this point maintains its brightness
+ 
+
+ align:start position:0%
+that this point maintains its brightness
+and then i can use uh the chain rule to
+
+ align:start position:0%
+and then i can use uh the chain rule to
+ 
+
+ align:start position:0%
+and then i can use uh the chain rule to
+split this up so i'm going to get
+
+ align:start position:0%
+split this up so i'm going to get
+ 
+
+ align:start position:0%
+split this up so i'm going to get
+dx dt times the edx
+
+ align:start position:0%
+dx dt times the edx
+ 
+
+ align:start position:0%
+dx dt times the edx
+plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so i can take this total derivative and
+
+ align:start position:0%
+so i can take this total derivative and
+ 
+
+ align:start position:0%
+so i can take this total derivative and
+express it in terms of partial
+
+ align:start position:0%
+express it in terms of partial
+ 
+
+ align:start position:0%
+express it in terms of partial
+derivatives
+
+ align:start position:0%
+derivatives
+ 
+
+ align:start position:0%
+derivatives
+and again that looks kind of
+
+ align:start position:0%
+and again that looks kind of
+ 
+
+ align:start position:0%
+and again that looks kind of
+intimidating but i can easily rewrite
+
+ align:start position:0%
+intimidating but i can easily rewrite
+ 
+
+ align:start position:0%
+intimidating but i can easily rewrite
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's equivalent to what we had for
+
+ align:start position:0%
+so that's equivalent to what we had for
+ 
+
+ align:start position:0%
+so that's equivalent to what we had for
+1d motion
+
+ align:start position:0%
+1d motion
+ 
+
+ align:start position:0%
+1d motion
+right so this is showing um a
+
+ align:start position:0%
+right so this is showing um a
+ 
+
+ align:start position:0%
+right so this is showing um a
+relationship between the brightness
+
+ align:start position:0%
+relationship between the brightness
+ 
+
+ align:start position:0%
+relationship between the brightness
+gradient and and the image motion
+
+ align:start position:0%
+gradient and and the image motion
+ 
+
+ align:start position:0%
+gradient and and the image motion
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if i know the image motion and i know
+
+ align:start position:0%
+if i know the image motion and i know
+ 
+
+ align:start position:0%
+if i know the image motion and i know
+the image i can predict how it's going
+
+ align:start position:0%
+the image i can predict how it's going
+ 
+
+ align:start position:0%
+the image i can predict how it's going
+to change
+
+ align:start position:0%
+to change
+ 
+
+ align:start position:0%
+to change
+and you know very simple i just use this
+
+ align:start position:0%
+and you know very simple i just use this
+ 
+
+ align:start position:0%
+and you know very simple i just use this
+formula and what we're more interested
+
+ align:start position:0%
+formula and what we're more interested
+ 
+
+ align:start position:0%
+formula and what we're more interested
+in doing is we've got images image
+
+ align:start position:0%
+in doing is we've got images image
+ 
+
+ align:start position:0%
+in doing is we've got images image
+sequences and we want to find u and b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's where we're going now
+
+ align:start position:0%
+okay so that's where we're going now
+ 
+
+ align:start position:0%
+okay so that's where we're going now
+over here we could just solve for u
+
+ align:start position:0%
+over here we could just solve for u
+ 
+
+ align:start position:0%
+over here we could just solve for u
+because we had a single equation in a
+
+ align:start position:0%
+because we had a single equation in a
+ 
+
+ align:start position:0%
+because we had a single equation in a
+single unknown
+
+ align:start position:0%
+single unknown
+ 
+
+ align:start position:0%
+single unknown
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and and that's another thing we're going
+
+ align:start position:0%
+and and that's another thing we're going
+ 
+
+ align:start position:0%
+and and that's another thing we're going
+to do a lot is equation counting
+
+ align:start position:0%
+to do a lot is equation counting
+ 
+
+ align:start position:0%
+to do a lot is equation counting
+you know how many degrees of freedom how
+
+ align:start position:0%
+you know how many degrees of freedom how
+ 
+
+ align:start position:0%
+you know how many degrees of freedom how
+many numbers are there that we don't
+
+ align:start position:0%
+many numbers are there that we don't
+ 
+
+ align:start position:0%
+many numbers are there that we don't
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+and how many constraints do we have
+
+ align:start position:0%
+and how many constraints do we have
+ 
+
+ align:start position:0%
+and how many constraints do we have
+over here
+
+ align:start position:0%
+over here
+ 
+
+ align:start position:0%
+over here
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+we have one constraint one
+
+ align:start position:0%
+we have one constraint one
+ 
+
+ align:start position:0%
+we have one constraint one
+that equation we have one unknown u
+
+ align:start position:0%
+that equation we have one unknown u
+ 
+
+ align:start position:0%
+that equation we have one unknown u
+perfect match so
+
+ align:start position:0%
+perfect match so
+ 
+
+ align:start position:0%
+perfect match so
+uh we know that uh we are likely to get
+
+ align:start position:0%
+uh we know that uh we are likely to get
+ 
+
+ align:start position:0%
+uh we know that uh we are likely to get
+a finite number of solutions
+
+ align:start position:0%
+a finite number of solutions
+ 
+
+ align:start position:0%
+a finite number of solutions
+and because it's linear we get one
+
+ align:start position:0%
+and because it's linear we get one
+ 
+
+ align:start position:0%
+and because it's linear we get one
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+but when you look at this you'll see
+
+ align:start position:0%
+but when you look at this you'll see
+ 
+
+ align:start position:0%
+but when you look at this you'll see
+there's one equation one constraint
+
+ align:start position:0%
+there's one equation one constraint
+ 
+
+ align:start position:0%
+there's one equation one constraint
+but we've got two unknowns right we've
+
+ align:start position:0%
+but we've got two unknowns right we've
+ 
+
+ align:start position:0%
+but we've got two unknowns right we've
+got uh
+
+ align:start position:0%
+got uh
+ 
+
+ align:start position:0%
+got uh
+u and v
+
+ align:start position:0%
+u and v
+ 
+
+ align:start position:0%
+u and v
+so if we're trying to recover the
+
+ align:start position:0%
+so if we're trying to recover the
+ 
+
+ align:start position:0%
+so if we're trying to recover the
+optical flow which is that vector field
+
+ align:start position:0%
+optical flow which is that vector field
+ 
+
+ align:start position:0%
+optical flow which is that vector field
+that we're just discussing
+
+ align:start position:0%
+that we're just discussing
+ 
+
+ align:start position:0%
+that we're just discussing
+um it's like we don't have enough uh
+
+ align:start position:0%
+um it's like we don't have enough uh
+ 
+
+ align:start position:0%
+um it's like we don't have enough uh
+information here to do that
+
+ align:start position:0%
+information here to do that
+ 
+
+ align:start position:0%
+information here to do that
+which is dramatically different from the
+
+ align:start position:0%
+which is dramatically different from the
+ 
+
+ align:start position:0%
+which is dramatically different from the
+1d case where you know we have a match
+
+ align:start position:0%
+1d case where you know we have a match
+ 
+
+ align:start position:0%
+1d case where you know we have a match
+between the number of equations and the
+
+ align:start position:0%
+between the number of equations and the
+ 
+
+ align:start position:0%
+between the number of equations and the
+number of unknowns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so uh what what do we know so are
+
+ align:start position:0%
+okay so uh what what do we know so are
+ 
+
+ align:start position:0%
+okay so uh what what do we know so are
+we lost at c is is it hopeless and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's look at just what that
+
+ align:start position:0%
+let's look at just what that
+ 
+
+ align:start position:0%
+let's look at just what that
+constraint provides us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so again the overall objective here is
+
+ align:start position:0%
+so again the overall objective here is
+ 
+
+ align:start position:0%
+so again the overall objective here is
+we have a time varying image or in the
+
+ align:start position:0%
+we have a time varying image or in the
+ 
+
+ align:start position:0%
+we have a time varying image or in the
+discrete case
+
+ align:start position:0%
+discrete case
+ 
+
+ align:start position:0%
+discrete case
+a sequence of image frames
+
+ align:start position:0%
+a sequence of image frames
+ 
+
+ align:start position:0%
+a sequence of image frames
+and we're trying to recover the motion
+
+ align:start position:0%
+and we're trying to recover the motion
+ 
+
+ align:start position:0%
+and we're trying to recover the motion
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we find that
+
+ align:start position:0%
+we find that
+ 
+
+ align:start position:0%
+we find that
+assuming that things don't change in
+
+ align:start position:0%
+assuming that things don't change in
+ 
+
+ align:start position:0%
+assuming that things don't change in
+brightness the images don't change as
+
+ align:start position:0%
+brightness the images don't change as
+ 
+
+ align:start position:0%
+brightness the images don't change as
+they move
+
+ align:start position:0%
+they move
+ 
+
+ align:start position:0%
+they move
+we end up with that constraint equation
+
+ align:start position:0%
+we end up with that constraint equation
+ 
+
+ align:start position:0%
+we end up with that constraint equation
+and what is it towards well one way to
+
+ align:start position:0%
+and what is it towards well one way to
+ 
+
+ align:start position:0%
+and what is it towards well one way to
+think about it is
+
+ align:start position:0%
+think about it is
+ 
+
+ align:start position:0%
+think about it is
+to plot it in velocity space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know we're used to plotting
+
+ align:start position:0%
+so you know we're used to plotting
+ 
+
+ align:start position:0%
+so you know we're used to plotting
+images with x and y as coordinate
+
+ align:start position:0%
+images with x and y as coordinate
+ 
+
+ align:start position:0%
+images with x and y as coordinate
+axes but actually um for some purposes
+
+ align:start position:0%
+axes but actually um for some purposes
+ 
+
+ align:start position:0%
+axes but actually um for some purposes
+uh it's useful to have a different kind
+
+ align:start position:0%
+uh it's useful to have a different kind
+ 
+
+ align:start position:0%
+uh it's useful to have a different kind
+of representation and this is one and
+
+ align:start position:0%
+of representation and this is one and
+ 
+
+ align:start position:0%
+of representation and this is one and
+what it means is that
+
+ align:start position:0%
+what it means is that
+ 
+
+ align:start position:0%
+what it means is that
+any point in here is a particular
+
+ align:start position:0%
+any point in here is a particular
+ 
+
+ align:start position:0%
+any point in here is a particular
+velocity
+
+ align:start position:0%
+velocity
+ 
+
+ align:start position:0%
+velocity
+that velocity
+
+ align:start position:0%
+that velocity
+ 
+
+ align:start position:0%
+that velocity
+and you know for example this is zero
+
+ align:start position:0%
+and you know for example this is zero
+ 
+
+ align:start position:0%
+and you know for example this is zero
+velocity it's not going anywhere
+
+ align:start position:0%
+velocity it's not going anywhere
+ 
+
+ align:start position:0%
+velocity it's not going anywhere
+velocity space
+
+ align:start position:0%
+velocity space
+ 
+
+ align:start position:0%
+velocity space
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+was used at one time in physics much
+
+ align:start position:0%
+was used at one time in physics much
+ 
+
+ align:start position:0%
+was used at one time in physics much
+more than it is now and it's actually uh
+
+ align:start position:0%
+more than it is now and it's actually uh
+ 
+
+ align:start position:0%
+more than it is now and it's actually uh
+kind of neat
+
+ align:start position:0%
+kind of neat
+ 
+
+ align:start position:0%
+kind of neat
+for example you know if you look at
+
+ align:start position:0%
+for example you know if you look at
+ 
+
+ align:start position:0%
+for example you know if you look at
+planetary orbits they're ellipses with
+
+ align:start position:0%
+planetary orbits they're ellipses with
+ 
+
+ align:start position:0%
+planetary orbits they're ellipses with
+the sun at one focus
+
+ align:start position:0%
+the sun at one focus
+ 
+
+ align:start position:0%
+the sun at one focus
+and ellipses are sort of complicated
+
+ align:start position:0%
+and ellipses are sort of complicated
+ 
+
+ align:start position:0%
+and ellipses are sort of complicated
+if you plot it in velocity space they're
+
+ align:start position:0%
+if you plot it in velocity space they're
+ 
+
+ align:start position:0%
+if you plot it in velocity space they're
+circles which was exploited
+
+ align:start position:0%
+circles which was exploited
+ 
+
+ align:start position:0%
+circles which was exploited
+in the early days before people could
+
+ align:start position:0%
+in the early days before people could
+ 
+
+ align:start position:0%
+in the early days before people could
+just you know feed equations into a
+
+ align:start position:0%
+just you know feed equations into a
+ 
+
+ align:start position:0%
+just you know feed equations into a
+computer and have them solve
+
+ align:start position:0%
+computer and have them solve
+ 
+
+ align:start position:0%
+computer and have them solve
+where they have to reason about things
+
+ align:start position:0%
+where they have to reason about things
+ 
+
+ align:start position:0%
+where they have to reason about things
+geometrically anyway velocity space is
+
+ align:start position:0%
+geometrically anyway velocity space is
+ 
+
+ align:start position:0%
+geometrically anyway velocity space is
+sort of neat and here we have a
+
+ align:start position:0%
+sort of neat and here we have a
+ 
+
+ align:start position:0%
+sort of neat and here we have a
+constraint in velocity space so this is
+
+ align:start position:0%
+constraint in velocity space so this is
+ 
+
+ align:start position:0%
+constraint in velocity space so this is
+saying that
+
+ align:start position:0%
+saying that
+ 
+
+ align:start position:0%
+saying that
+okay before we open our eyes and looked
+
+ align:start position:0%
+okay before we open our eyes and looked
+ 
+
+ align:start position:0%
+okay before we open our eyes and looked
+at the image we didn't know anything the
+
+ align:start position:0%
+at the image we didn't know anything the
+ 
+
+ align:start position:0%
+at the image we didn't know anything the
+velocity could be anywhere in this plane
+
+ align:start position:0%
+velocity could be anywhere in this plane
+ 
+
+ align:start position:0%
+velocity could be anywhere in this plane
+but now we have one constraint on it so
+
+ align:start position:0%
+but now we have one constraint on it so
+ 
+
+ align:start position:0%
+but now we have one constraint on it so
+what does that tell us that must
+
+ align:start position:0%
+what does that tell us that must
+ 
+
+ align:start position:0%
+what does that tell us that must
+somehow
+
+ align:start position:0%
+somehow
+ 
+
+ align:start position:0%
+somehow
+limit
+
+ align:start position:0%
+limit
+ 
+
+ align:start position:0%
+limit
+the solution space
+
+ align:start position:0%
+the solution space
+ 
+
+ align:start position:0%
+the solution space
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+yes it's a linear equation in u and v
+
+ align:start position:0%
+yes it's a linear equation in u and v
+ 
+
+ align:start position:0%
+yes it's a linear equation in u and v
+and so linear equation in 2d world
+
+ align:start position:0%
+and so linear equation in 2d world
+ 
+
+ align:start position:0%
+and so linear equation in 2d world
+corresponds to what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+line yes y equals mx plus c for example
+
+ align:start position:0%
+line yes y equals mx plus c for example
+ 
+
+ align:start position:0%
+line yes y equals mx plus c for example
+so it's going to be a line
+
+ align:start position:0%
+so it's going to be a line
+ 
+
+ align:start position:0%
+so it's going to be a line
+and that's great because it means that
+
+ align:start position:0%
+and that's great because it means that
+ 
+
+ align:start position:0%
+and that's great because it means that
+okay we haven't solved the problem but
+
+ align:start position:0%
+okay we haven't solved the problem but
+ 
+
+ align:start position:0%
+okay we haven't solved the problem but
+we've come a long way so before
+
+ align:start position:0%
+we've come a long way so before
+ 
+
+ align:start position:0%
+we've come a long way so before
+it could be anywhere now it's going to
+
+ align:start position:0%
+it could be anywhere now it's going to
+ 
+
+ align:start position:0%
+it could be anywhere now it's going to
+be on the line and what we really like
+
+ align:start position:0%
+be on the line and what we really like
+ 
+
+ align:start position:0%
+be on the line and what we really like
+is to pin it down to a point so we've
+
+ align:start position:0%
+is to pin it down to a point so we've
+ 
+
+ align:start position:0%
+is to pin it down to a point so we've
+come part way and so what line is it
+
+ align:start position:0%
+come part way and so what line is it
+ 
+
+ align:start position:0%
+come part way and so what line is it
+well we can rewrite that equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that and
+
+ align:start position:0%
+like that and
+ 
+
+ align:start position:0%
+like that and
+rewrite it a bit more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by normalizing this vector so i'm
+
+ align:start position:0%
+by normalizing this vector so i'm
+ 
+
+ align:start position:0%
+by normalizing this vector so i'm
+turning this vector into a unit vector
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first of all again a
+
+ align:start position:0%
+so first of all again a
+ 
+
+ align:start position:0%
+so first of all again a
+reminder that this is the brightness
+
+ align:start position:0%
+reminder that this is the brightness
+ 
+
+ align:start position:0%
+reminder that this is the brightness
+gradient and the brightness gradient is
+
+ align:start position:0%
+gradient and the brightness gradient is
+ 
+
+ align:start position:0%
+gradient and the brightness gradient is
+very important for all sorts of things
+
+ align:start position:0%
+very important for all sorts of things
+ 
+
+ align:start position:0%
+very important for all sorts of things
+if it's zero nothing much is happening
+
+ align:start position:0%
+if it's zero nothing much is happening
+ 
+
+ align:start position:0%
+if it's zero nothing much is happening
+because the brightness is constant
+
+ align:start position:0%
+because the brightness is constant
+ 
+
+ align:start position:0%
+because the brightness is constant
+and more likely
+
+ align:start position:0%
+and more likely
+ 
+
+ align:start position:0%
+and more likely
+it has a high value at a transition
+
+ align:start position:0%
+it has a high value at a transition
+ 
+
+ align:start position:0%
+it has a high value at a transition
+between now if i'm looking at the
+
+ align:start position:0%
+between now if i'm looking at the
+ 
+
+ align:start position:0%
+between now if i'm looking at the
+transition between the wall and the
+
+ align:start position:0%
+transition between the wall and the
+ 
+
+ align:start position:0%
+transition between the wall and the
+blackboard there's a big change in
+
+ align:start position:0%
+blackboard there's a big change in
+ 
+
+ align:start position:0%
+blackboard there's a big change in
+brightness and therefore the derivatives
+
+ align:start position:0%
+brightness and therefore the derivatives
+ 
+
+ align:start position:0%
+brightness and therefore the derivatives
+will be large and therefore the
+
+ align:start position:0%
+will be large and therefore the
+ 
+
+ align:start position:0%
+will be large and therefore the
+brightness gradient will be large
+
+ align:start position:0%
+brightness gradient will be large
+ 
+
+ align:start position:0%
+brightness gradient will be large
+and not only that but the brightness
+
+ align:start position:0%
+and not only that but the brightness
+ 
+
+ align:start position:0%
+and not only that but the brightness
+gradient as a vector will be pointing
+
+ align:start position:0%
+gradient as a vector will be pointing
+ 
+
+ align:start position:0%
+gradient as a vector will be pointing
+perpendicular to the transition
+
+ align:start position:0%
+perpendicular to the transition
+ 
+
+ align:start position:0%
+perpendicular to the transition
+right because e x is very large here e y
+
+ align:start position:0%
+right because e x is very large here e y
+ 
+
+ align:start position:0%
+right because e x is very large here e y
+is zero so
+
+ align:start position:0%
+is zero so
+ 
+
+ align:start position:0%
+is zero so
+so so this brightness gradient is very
+
+ align:start position:0%
+so so this brightness gradient is very
+ 
+
+ align:start position:0%
+so so this brightness gradient is very
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+and this is
+
+ align:start position:0%
+and this is
+ 
+
+ align:start position:0%
+and this is
+a unit vector as you can easily tell by
+
+ align:start position:0%
+a unit vector as you can easily tell by
+ 
+
+ align:start position:0%
+a unit vector as you can easily tell by
+taking the sum of squares of the two
+
+ align:start position:0%
+taking the sum of squares of the two
+ 
+
+ align:start position:0%
+taking the sum of squares of the two
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+and why am i doing this well because i'm
+
+ align:start position:0%
+and why am i doing this well because i'm
+ 
+
+ align:start position:0%
+and why am i doing this well because i'm
+interested in the component of u and v
+
+ align:start position:0%
+interested in the component of u and v
+ 
+
+ align:start position:0%
+interested in the component of u and v
+in this direction the direction
+
+ align:start position:0%
+in this direction the direction
+ 
+
+ align:start position:0%
+in this direction the direction
+specified by the unit vector and it's
+
+ align:start position:0%
+specified by the unit vector and it's
+ 
+
+ align:start position:0%
+specified by the unit vector and it's
+this constant
+
+ align:start position:0%
+this constant
+ 
+
+ align:start position:0%
+this constant
+and so what this is saying is that
+
+ align:start position:0%
+and so what this is saying is that
+ 
+
+ align:start position:0%
+and so what this is saying is that
+you know u and v are perpendicular to
+
+ align:start position:0%
+you know u and v are perpendicular to
+ 
+
+ align:start position:0%
+you know u and v are perpendicular to
+some line
+
+ align:start position:0%
+some line
+ 
+
+ align:start position:0%
+some line
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is what it looks like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can check that i mean basically
+
+ align:start position:0%
+you can check that i mean basically
+ 
+
+ align:start position:0%
+you can check that i mean basically
+you need to find this point
+
+ align:start position:0%
+you need to find this point
+ 
+
+ align:start position:0%
+you need to find this point
+and then calculate the distance from the
+
+ align:start position:0%
+and then calculate the distance from the
+ 
+
+ align:start position:0%
+and then calculate the distance from the
+origin and it's going to going to be
+
+ align:start position:0%
+origin and it's going to going to be
+ 
+
+ align:start position:0%
+origin and it's going to going to be
+that so
+
+ align:start position:0%
+that so
+ 
+
+ align:start position:0%
+that so
+not too interested right now in the
+
+ align:start position:0%
+not too interested right now in the
+ 
+
+ align:start position:0%
+not too interested right now in the
+details of that other than
+
+ align:start position:0%
+details of that other than
+ 
+
+ align:start position:0%
+details of that other than
+that we've shown that it's a line and
+
+ align:start position:0%
+that we've shown that it's a line and
+ 
+
+ align:start position:0%
+that we've shown that it's a line and
+that the line depends uh on the
+
+ align:start position:0%
+that the line depends uh on the
+ 
+
+ align:start position:0%
+that the line depends uh on the
+brightness gradient
+
+ align:start position:0%
+brightness gradient
+ 
+
+ align:start position:0%
+brightness gradient
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+it tells us a lot of things already one
+
+ align:start position:0%
+it tells us a lot of things already one
+ 
+
+ align:start position:0%
+it tells us a lot of things already one
+of them is that
+
+ align:start position:0%
+of them is that
+ 
+
+ align:start position:0%
+of them is that
+when you make this localized measurement
+
+ align:start position:0%
+when you make this localized measurement
+ 
+
+ align:start position:0%
+when you make this localized measurement
+and you are under constraint you don't
+
+ align:start position:0%
+and you are under constraint you don't
+ 
+
+ align:start position:0%
+and you are under constraint you don't
+have enough
+
+ align:start position:0%
+have enough
+ 
+
+ align:start position:0%
+have enough
+equations
+
+ align:start position:0%
+equations
+ 
+
+ align:start position:0%
+equations
+you do know something
+
+ align:start position:0%
+you do know something
+ 
+
+ align:start position:0%
+you do know something
+you know for example in this diagram i
+
+ align:start position:0%
+you know for example in this diagram i
+ 
+
+ align:start position:0%
+you know for example in this diagram i
+don't know what u and b is
+
+ align:start position:0%
+don't know what u and b is
+ 
+
+ align:start position:0%
+don't know what u and b is
+but suppose that i
+
+ align:start position:0%
+but suppose that i
+ 
+
+ align:start position:0%
+but suppose that i
+give you a different coordinate system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+locally you're going to see linear
+
+ align:start position:0%
+locally you're going to see linear
+ 
+
+ align:start position:0%
+locally you're going to see linear
+patterns you won't see that if if i keep
+
+ align:start position:0%
+patterns you won't see that if if i keep
+ 
+
+ align:start position:0%
+patterns you won't see that if if i keep
+on magnifying this
+
+ align:start position:0%
+on magnifying this
+ 
+
+ align:start position:0%
+on magnifying this
+you know it's going to be more and more
+
+ align:start position:0%
+you know it's going to be more and more
+ 
+
+ align:start position:0%
+you know it's going to be more and more
+like a
+
+ align:start position:0%
+like a
+ 
+
+ align:start position:0%
+like a
+linear relationship
+
+ align:start position:0%
+linear relationship
+ 
+
+ align:start position:0%
+linear relationship
+and so the argument is that if you look
+
+ align:start position:0%
+and so the argument is that if you look
+ 
+
+ align:start position:0%
+and so the argument is that if you look
+through an aperture you cannot determine
+
+ align:start position:0%
+through an aperture you cannot determine
+ 
+
+ align:start position:0%
+through an aperture you cannot determine
+the motion you can you can determine the
+
+ align:start position:0%
+the motion you can you can determine the
+ 
+
+ align:start position:0%
+the motion you can you can determine the
+motion in the direction of the
+
+ align:start position:0%
+motion in the direction of the
+ 
+
+ align:start position:0%
+motion in the direction of the
+brightness gradient so that's
+
+ align:start position:0%
+brightness gradient so that's
+ 
+
+ align:start position:0%
+brightness gradient so that's
+that's what we
+
+ align:start position:0%
+that's what we
+ 
+
+ align:start position:0%
+that's what we
+what we did over here
+
+ align:start position:0%
+what we did over here
+ 
+
+ align:start position:0%
+what we did over here
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+in the 1d case that we were done here
+
+ align:start position:0%
+in the 1d case that we were done here
+ 
+
+ align:start position:0%
+in the 1d case that we were done here
+in the 2d case we're not done because we
+
+ align:start position:0%
+in the 2d case we're not done because we
+ 
+
+ align:start position:0%
+in the 2d case we're not done because we
+have a mismatch
+
+ align:start position:0%
+have a mismatch
+ 
+
+ align:start position:0%
+have a mismatch
+of constraints and unknowns
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so um we need more constraints so we
+
+ align:start position:0%
+and so um we need more constraints so we
+ 
+
+ align:start position:0%
+and so um we need more constraints so we
+need to know something else
+
+ align:start position:0%
+need to know something else
+ 
+
+ align:start position:0%
+need to know something else
+and sometimes you know there's prior
+
+ align:start position:0%
+and sometimes you know there's prior
+ 
+
+ align:start position:0%
+and sometimes you know there's prior
+knowledge of the environment that helps
+
+ align:start position:0%
+knowledge of the environment that helps
+ 
+
+ align:start position:0%
+knowledge of the environment that helps
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+sometimes you can look again at another
+
+ align:start position:0%
+sometimes you can look again at another
+ 
+
+ align:start position:0%
+sometimes you can look again at another
+time and get extra information
+
+ align:start position:0%
+time and get extra information
+ 
+
+ align:start position:0%
+time and get extra information
+um now let's suppose that we have the
+
+ align:start position:0%
+um now let's suppose that we have the
+ 
+
+ align:start position:0%
+um now let's suppose that we have the
+optical mouse problem
+
+ align:start position:0%
+optical mouse problem
+ 
+
+ align:start position:0%
+optical mouse problem
+where the whole image is moving as one
+
+ align:start position:0%
+where the whole image is moving as one
+ 
+
+ align:start position:0%
+where the whole image is moving as one
+you know you're over a flat surface at a
+
+ align:start position:0%
+you know you're over a flat surface at a
+ 
+
+ align:start position:0%
+you know you're over a flat surface at a
+constant distance from the lens
+
+ align:start position:0%
+constant distance from the lens
+ 
+
+ align:start position:0%
+constant distance from the lens
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+to a very high degree of approximation
+
+ align:start position:0%
+to a very high degree of approximation
+ 
+
+ align:start position:0%
+to a very high degree of approximation
+the image is just moving as one so we
+
+ align:start position:0%
+the image is just moving as one so we
+ 
+
+ align:start position:0%
+the image is just moving as one so we
+don't just have one pixel we we can do
+
+ align:start position:0%
+don't just have one pixel we we can do
+ 
+
+ align:start position:0%
+don't just have one pixel we we can do
+the same thing at two pixels
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's a pixel one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's at pixel 2.
+
+ align:start position:0%
+and that's at pixel 2.
+ 
+
+ align:start position:0%
+and that's at pixel 2.
+and our job is to recover u and v
+
+ align:start position:0%
+and our job is to recover u and v
+ 
+
+ align:start position:0%
+and our job is to recover u and v
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+it's a two linear equations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh we can write them that way
+
+ align:start position:0%
+uh we can write them that way
+ 
+
+ align:start position:0%
+uh we can write them that way
+and then solve now because we've got uh
+
+ align:start position:0%
+and then solve now because we've got uh
+ 
+
+ align:start position:0%
+and then solve now because we've got uh
+two constraints now
+
+ align:start position:0%
+two constraints now
+ 
+
+ align:start position:0%
+two constraints now
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+we have enough constraint to solve for
+
+ align:start position:0%
+we have enough constraint to solve for
+ 
+
+ align:start position:0%
+we have enough constraint to solve for
+uh the two unknowns and you know it's
+
+ align:start position:0%
+uh the two unknowns and you know it's
+ 
+
+ align:start position:0%
+uh the two unknowns and you know it's
+just a linear equation so it's very
+
+ align:start position:0%
+just a linear equation so it's very
+ 
+
+ align:start position:0%
+just a linear equation so it's very
+simple
+
+ align:start position:0%
+simple
+ 
+
+ align:start position:0%
+simple
+and if
+
+ align:start position:0%
+and if
+ 
+
+ align:start position:0%
+and if
+we can actually write it write the
+
+ align:start position:0%
+we can actually write it write the
+ 
+
+ align:start position:0%
+we can actually write it write the
+answer out explicitly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so it's very mechanical i mean we just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+invert this two by two matrix
+
+ align:start position:0%
+invert this two by two matrix
+ 
+
+ align:start position:0%
+invert this two by two matrix
+and you know multiply the result by
+
+ align:start position:0%
+and you know multiply the result by
+ 
+
+ align:start position:0%
+and you know multiply the result by
+that vector and we're done
+
+ align:start position:0%
+that vector and we're done
+ 
+
+ align:start position:0%
+that vector and we're done
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+what is this
+
+ align:start position:0%
+what is this
+ 
+
+ align:start position:0%
+what is this
+well this is the determinant of that
+
+ align:start position:0%
+well this is the determinant of that
+ 
+
+ align:start position:0%
+well this is the determinant of that
+matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you know for two by two and three by
+
+ align:start position:0%
+so you know for two by two and three by
+ 
+
+ align:start position:0%
+so you know for two by two and three by
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+we can explicitly write it down
+
+ align:start position:0%
+we can explicitly write it down
+ 
+
+ align:start position:0%
+we can explicitly write it down
+otherwise we'll just use gaussian
+
+ align:start position:0%
+otherwise we'll just use gaussian
+ 
+
+ align:start position:0%
+otherwise we'll just use gaussian
+elimination to solve the set of linear
+
+ align:start position:0%
+elimination to solve the set of linear
+ 
+
+ align:start position:0%
+elimination to solve the set of linear
+equations
+
+ align:start position:0%
+equations
+ 
+
+ align:start position:0%
+equations
+okay so um
+
+ align:start position:0%
+okay so um
+ 
+
+ align:start position:0%
+okay so um
+in a way we're done we we need two
+
+ align:start position:0%
+in a way we're done we we need two
+ 
+
+ align:start position:0%
+in a way we're done we we need two
+pixels we can solve this and now you
+
+ align:start position:0%
+pixels we can solve this and now you
+ 
+
+ align:start position:0%
+pixels we can solve this and now you
+know it's noisy so we can improve the
+
+ align:start position:0%
+know it's noisy so we can improve the
+ 
+
+ align:start position:0%
+know it's noisy so we can improve the
+result by taking more than two pixels
+
+ align:start position:0%
+result by taking more than two pixels
+ 
+
+ align:start position:0%
+result by taking more than two pixels
+but before we do that
+
+ align:start position:0%
+but before we do that
+ 
+
+ align:start position:0%
+but before we do that
+it's always important to
+
+ align:start position:0%
+it's always important to
+ 
+
+ align:start position:0%
+it's always important to
+check the edge conditions
+
+ align:start position:0%
+check the edge conditions
+ 
+
+ align:start position:0%
+check the edge conditions
+like you know this can fail
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it fails when the determinant is
+
+ align:start position:0%
+and it fails when the determinant is
+ 
+
+ align:start position:0%
+and it fails when the determinant is
+zero right so we um when does that
+
+ align:start position:0%
+zero right so we um when does that
+ 
+
+ align:start position:0%
+zero right so we um when does that
+happen
+
+ align:start position:0%
+happen
+ 
+
+ align:start position:0%
+happen
+well uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can that happen well uh sure let's
+
+ align:start position:0%
+can that happen well uh sure let's
+ 
+
+ align:start position:0%
+can that happen well uh sure let's
+rewrite it one more time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we have this nice linear method
+
+ align:start position:0%
+okay so we have this nice linear method
+ 
+
+ align:start position:0%
+okay so we have this nice linear method
+that if we make these measurements at
+
+ align:start position:0%
+that if we make these measurements at
+ 
+
+ align:start position:0%
+that if we make these measurements at
+two pixels we can solve for the motion
+
+ align:start position:0%
+two pixels we can solve for the motion
+ 
+
+ align:start position:0%
+two pixels we can solve for the motion
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+uh it won't work
+
+ align:start position:0%
+uh it won't work
+ 
+
+ align:start position:0%
+uh it won't work
+if this is the case so what is that
+
+ align:start position:0%
+if this is the case so what is that
+ 
+
+ align:start position:0%
+if this is the case so what is that
+well this tells you something about the
+
+ align:start position:0%
+well this tells you something about the
+ 
+
+ align:start position:0%
+well this tells you something about the
+brightness gradient right this is the
+
+ align:start position:0%
+brightness gradient right this is the
+ 
+
+ align:start position:0%
+brightness gradient right this is the
+direction of the brightness gradient
+
+ align:start position:0%
+direction of the brightness gradient
+ 
+
+ align:start position:0%
+direction of the brightness gradient
+well the tangent of it right so
+
+ align:start position:0%
+well the tangent of it right so
+ 
+
+ align:start position:0%
+well the tangent of it right so
+what this is saying is that
+
+ align:start position:0%
+what this is saying is that
+ 
+
+ align:start position:0%
+what this is saying is that
+you have a problem
+
+ align:start position:0%
+you have a problem
+ 
+
+ align:start position:0%
+you have a problem
+if they're
+
+ align:start position:0%
+if they're
+ 
+
+ align:start position:0%
+if they're
+related
+
+ align:start position:0%
+related
+ 
+
+ align:start position:0%
+related
+so this is where the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+don't have to be the same i mean
+
+ align:start position:0%
+don't have to be the same i mean
+ 
+
+ align:start position:0%
+don't have to be the same i mean
+obviously if
+
+ align:start position:0%
+obviously if
+ 
+
+ align:start position:0%
+obviously if
+the brightness gradients are the same
+
+ align:start position:0%
+the brightness gradients are the same
+ 
+
+ align:start position:0%
+the brightness gradients are the same
+and you subtract
+
+ align:start position:0%
+and you subtract
+ 
+
+ align:start position:0%
+and you subtract
+those two quantities you get zero and
+
+ align:start position:0%
+those two quantities you get zero and
+ 
+
+ align:start position:0%
+those two quantities you get zero and
+things blow up
+
+ align:start position:0%
+things blow up
+ 
+
+ align:start position:0%
+things blow up
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+they don't have to be the same they just
+
+ align:start position:0%
+they don't have to be the same they just
+ 
+
+ align:start position:0%
+they don't have to be the same they just
+need to be proportional to each other
+
+ align:start position:0%
+need to be proportional to each other
+ 
+
+ align:start position:0%
+need to be proportional to each other
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+we're just saying that the ratio of e y
+
+ align:start position:0%
+we're just saying that the ratio of e y
+ 
+
+ align:start position:0%
+we're just saying that the ratio of e y
+to e x is the same
+
+ align:start position:0%
+to e x is the same
+ 
+
+ align:start position:0%
+to e x is the same
+and that makes sense again because
+
+ align:start position:0%
+and that makes sense again because
+ 
+
+ align:start position:0%
+and that makes sense again because
+that means that
+
+ align:start position:0%
+that means that
+ 
+
+ align:start position:0%
+that means that
+the brightness gradient is the same in
+
+ align:start position:0%
+the brightness gradient is the same in
+ 
+
+ align:start position:0%
+the brightness gradient is the same in
+the two places that means that the
+
+ align:start position:0%
+the two places that means that the
+ 
+
+ align:start position:0%
+the two places that means that the
+constraint we get out of the equation is
+
+ align:start position:0%
+constraint we get out of the equation is
+ 
+
+ align:start position:0%
+constraint we get out of the equation is
+in the same direction it's not providing
+
+ align:start position:0%
+in the same direction it's not providing
+ 
+
+ align:start position:0%
+in the same direction it's not providing
+new information
+
+ align:start position:0%
+new information
+ 
+
+ align:start position:0%
+new information
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+go back to this diagram
+
+ align:start position:0%
+go back to this diagram
+ 
+
+ align:start position:0%
+go back to this diagram
+we now have two parallel lines
+
+ align:start position:0%
+we now have two parallel lines
+ 
+
+ align:start position:0%
+we now have two parallel lines
+well if there's no measurement noise
+
+ align:start position:0%
+well if there's no measurement noise
+ 
+
+ align:start position:0%
+well if there's no measurement noise
+they'll be on top of each other
+
+ align:start position:0%
+they'll be on top of each other
+ 
+
+ align:start position:0%
+they'll be on top of each other
+and then you intersect them and what you
+
+ align:start position:0%
+and then you intersect them and what you
+ 
+
+ align:start position:0%
+and then you intersect them and what you
+get well the same line so that's not
+
+ align:start position:0%
+get well the same line so that's not
+ 
+
+ align:start position:0%
+get well the same line so that's not
+very interesting uh or if you have noise
+
+ align:start position:0%
+very interesting uh or if you have noise
+ 
+
+ align:start position:0%
+very interesting uh or if you have noise
+it'll be even worse because they won't
+
+ align:start position:0%
+it'll be even worse because they won't
+ 
+
+ align:start position:0%
+it'll be even worse because they won't
+even intersect so
+
+ align:start position:0%
+even intersect so
+ 
+
+ align:start position:0%
+even intersect so
+so um this tells you a number of things
+
+ align:start position:0%
+so um this tells you a number of things
+ 
+
+ align:start position:0%
+so um this tells you a number of things
+one of them is okay
+
+ align:start position:0%
+one of them is okay
+ 
+
+ align:start position:0%
+one of them is okay
+this isn't going to work if the
+
+ align:start position:0%
+this isn't going to work if the
+ 
+
+ align:start position:0%
+this isn't going to work if the
+brightness gradient is the same
+
+ align:start position:0%
+brightness gradient is the same
+ 
+
+ align:start position:0%
+brightness gradient is the same
+everywhere and that makes perfect sense
+
+ align:start position:0%
+everywhere and that makes perfect sense
+ 
+
+ align:start position:0%
+everywhere and that makes perfect sense
+that's the aperture problem
+
+ align:start position:0%
+that's the aperture problem
+ 
+
+ align:start position:0%
+that's the aperture problem
+uh it also tells you that
+
+ align:start position:0%
+uh it also tells you that
+ 
+
+ align:start position:0%
+uh it also tells you that
+maybe you need to
+
+ align:start position:0%
+maybe you need to
+ 
+
+ align:start position:0%
+maybe you need to
+somehow weight contributions from
+
+ align:start position:0%
+somehow weight contributions from
+ 
+
+ align:start position:0%
+somehow weight contributions from
+different image regions
+
+ align:start position:0%
+different image regions
+ 
+
+ align:start position:0%
+different image regions
+based on this maybe you don't want to
+
+ align:start position:0%
+based on this maybe you don't want to
+ 
+
+ align:start position:0%
+based on this maybe you don't want to
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+have contributions from a lot of image
+
+ align:start position:0%
+have contributions from a lot of image
+ 
+
+ align:start position:0%
+have contributions from a lot of image
+regions with the same brightness
+
+ align:start position:0%
+regions with the same brightness
+ 
+
+ align:start position:0%
+regions with the same brightness
+gradient because they're not really
+
+ align:start position:0%
+gradient because they're not really
+ 
+
+ align:start position:0%
+gradient because they're not really
+providing good constraint they're all
+
+ align:start position:0%
+providing good constraint they're all
+ 
+
+ align:start position:0%
+providing good constraint they're all
+sort of doing the same thing
+
+ align:start position:0%
+sort of doing the same thing
+ 
+
+ align:start position:0%
+sort of doing the same thing
+so that tells you that rather than take
+
+ align:start position:0%
+so that tells you that rather than take
+ 
+
+ align:start position:0%
+so that tells you that rather than take
+this result for two pixels and then
+
+ align:start position:0%
+this result for two pixels and then
+ 
+
+ align:start position:0%
+this result for two pixels and then
+apply it to other pairs of pixels and
+
+ align:start position:0%
+apply it to other pairs of pixels and
+ 
+
+ align:start position:0%
+apply it to other pairs of pixels and
+just take the average you'll want to
+
+ align:start position:0%
+just take the average you'll want to
+ 
+
+ align:start position:0%
+just take the average you'll want to
+weight it in some way so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and you know that's kind of kuji i
+
+ align:start position:0%
+um and you know that's kind of kuji i
+ 
+
+ align:start position:0%
+um and you know that's kind of kuji i
+mean that's
+
+ align:start position:0%
+mean that's
+ 
+
+ align:start position:0%
+mean that's
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+trying to fix a problem
+
+ align:start position:0%
+trying to fix a problem
+ 
+
+ align:start position:0%
+trying to fix a problem
+in a simple way
+
+ align:start position:0%
+in a simple way
+ 
+
+ align:start position:0%
+in a simple way
+but we can do
+
+ align:start position:0%
+but we can do
+ 
+
+ align:start position:0%
+but we can do
+we can do this much better
+
+ align:start position:0%
+we can do this much better
+ 
+
+ align:start position:0%
+we can do this much better
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have this equation
+
+ align:start position:0%
+we have this equation
+ 
+
+ align:start position:0%
+we have this equation
+that's supposedly true everywhere in the
+
+ align:start position:0%
+that's supposedly true everywhere in the
+ 
+
+ align:start position:0%
+that's supposedly true everywhere in the
+image
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right this is our magic equation which
+
+ align:start position:0%
+right this is our magic equation which
+ 
+
+ align:start position:0%
+right this is our magic equation which
+relates image motion to brightness
+
+ align:start position:0%
+relates image motion to brightness
+ 
+
+ align:start position:0%
+relates image motion to brightness
+gradients
+
+ align:start position:0%
+gradients
+ 
+
+ align:start position:0%
+gradients
+and um that's supposed to be zero now if
+
+ align:start position:0%
+and um that's supposed to be zero now if
+ 
+
+ align:start position:0%
+and um that's supposed to be zero now if
+there's a this measurement noise it
+
+ align:start position:0%
+there's a this measurement noise it
+ 
+
+ align:start position:0%
+there's a this measurement noise it
+won't be zero it hopefully will be small
+
+ align:start position:0%
+won't be zero it hopefully will be small
+ 
+
+ align:start position:0%
+won't be zero it hopefully will be small
+if you plug in the wrong values of u and
+
+ align:start position:0%
+if you plug in the wrong values of u and
+ 
+
+ align:start position:0%
+if you plug in the wrong values of u and
+b it won't be zero
+
+ align:start position:0%
+b it won't be zero
+ 
+
+ align:start position:0%
+b it won't be zero
+so maybe one way of solving this problem
+
+ align:start position:0%
+so maybe one way of solving this problem
+ 
+
+ align:start position:0%
+so maybe one way of solving this problem
+is to
+
+ align:start position:0%
+is to
+ 
+
+ align:start position:0%
+is to
+search
+
+ align:start position:0%
+search
+ 
+
+ align:start position:0%
+search
+for u and v
+
+ align:start position:0%
+for u and v
+ 
+
+ align:start position:0%
+for u and v
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+makes that zero or if you can't make it
+
+ align:start position:0%
+makes that zero or if you can't make it
+ 
+
+ align:start position:0%
+makes that zero or if you can't make it
+zero make it as small as possible
+
+ align:start position:0%
+zero make it as small as possible
+ 
+
+ align:start position:0%
+zero make it as small as possible
+and so that motivates this approach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what's going on here
+
+ align:start position:0%
+okay so what's going on here
+ 
+
+ align:start position:0%
+okay so what's going on here
+well the integrand is just this
+
+ align:start position:0%
+well the integrand is just this
+ 
+
+ align:start position:0%
+well the integrand is just this
+expression and if everything was perfect
+
+ align:start position:0%
+expression and if everything was perfect
+ 
+
+ align:start position:0%
+expression and if everything was perfect
+and you had the correct values of u and
+
+ align:start position:0%
+and you had the correct values of u and
+ 
+
+ align:start position:0%
+and you had the correct values of u and
+b the integrand would be zero and you
+
+ align:start position:0%
+b the integrand would be zero and you
+ 
+
+ align:start position:0%
+b the integrand would be zero and you
+integrate it over the whole image you
+
+ align:start position:0%
+integrate it over the whole image you
+ 
+
+ align:start position:0%
+integrate it over the whole image you
+get zero
+
+ align:start position:0%
+get zero
+ 
+
+ align:start position:0%
+get zero
+and that's the smallest you can get
+
+ align:start position:0%
+and that's the smallest you can get
+ 
+
+ align:start position:0%
+and that's the smallest you can get
+because it's quadratic it can't get less
+
+ align:start position:0%
+because it's quadratic it can't get less
+ 
+
+ align:start position:0%
+because it's quadratic it can't get less
+than zero so that's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you plug in the wrong values of u and
+
+ align:start position:0%
+if you plug in the wrong values of u and
+ 
+
+ align:start position:0%
+if you plug in the wrong values of u and
+v
+
+ align:start position:0%
+v
+ 
+
+ align:start position:0%
+v
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+it will not be zero and so
+
+ align:start position:0%
+it will not be zero and so
+ 
+
+ align:start position:0%
+it will not be zero and so
+you can base a strategy for finding u
+
+ align:start position:0%
+you can base a strategy for finding u
+ 
+
+ align:start position:0%
+you can base a strategy for finding u
+and v on on that
+
+ align:start position:0%
+and v on on that
+ 
+
+ align:start position:0%
+and v on on that
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now uh there are cases where this is
+
+ align:start position:0%
+now uh there are cases where this is
+ 
+
+ align:start position:0%
+now uh there are cases where this is
+going to fail
+
+ align:start position:0%
+going to fail
+ 
+
+ align:start position:0%
+going to fail
+you know one is if uh i don't know you
+
+ align:start position:0%
+you know one is if uh i don't know you
+ 
+
+ align:start position:0%
+you know one is if uh i don't know you
+uh without a light in a
+
+ align:start position:0%
+uh without a light in a
+ 
+
+ align:start position:0%
+uh without a light in a
+coal mine uh if e is zero you know all
+
+ align:start position:0%
+coal mine uh if e is zero you know all
+ 
+
+ align:start position:0%
+coal mine uh if e is zero you know all
+hope is lost obviously
+
+ align:start position:0%
+hope is lost obviously
+ 
+
+ align:start position:0%
+hope is lost obviously
+if e x and e y are zero uh all hope is
+
+ align:start position:0%
+if e x and e y are zero uh all hope is
+ 
+
+ align:start position:0%
+if e x and e y are zero uh all hope is
+lost because
+
+ align:start position:0%
+lost because
+ 
+
+ align:start position:0%
+lost because
+that means you're looking at a wall
+
+ align:start position:0%
+that means you're looking at a wall
+ 
+
+ align:start position:0%
+that means you're looking at a wall
+that's you know constant brightness and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you won't be able to see it moving
+
+ align:start position:0%
+you won't be able to see it moving
+ 
+
+ align:start position:0%
+you won't be able to see it moving
+because there's nothing on it to catch
+
+ align:start position:0%
+because there's nothing on it to catch
+ 
+
+ align:start position:0%
+because there's nothing on it to catch
+your attention and to track
+
+ align:start position:0%
+your attention and to track
+ 
+
+ align:start position:0%
+your attention and to track
+if there was some texture on it then e x
+
+ align:start position:0%
+if there was some texture on it then e x
+ 
+
+ align:start position:0%
+if there was some texture on it then e x
+and e y would not be zero in some places
+
+ align:start position:0%
+and e y would not be zero in some places
+ 
+
+ align:start position:0%
+and e y would not be zero in some places
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+okay and so
+
+ align:start position:0%
+okay and so
+ 
+
+ align:start position:0%
+okay and so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+this is sort of approach we're going to
+
+ align:start position:0%
+this is sort of approach we're going to
+ 
+
+ align:start position:0%
+this is sort of approach we're going to
+use a lot so we have this constraint
+
+ align:start position:0%
+use a lot so we have this constraint
+ 
+
+ align:start position:0%
+use a lot so we have this constraint
+which would apply
+
+ align:start position:0%
+which would apply
+ 
+
+ align:start position:0%
+which would apply
+in ideal case
+
+ align:start position:0%
+in ideal case
+ 
+
+ align:start position:0%
+in ideal case
+where we know the answer u and v
+
+ align:start position:0%
+where we know the answer u and v
+ 
+
+ align:start position:0%
+where we know the answer u and v
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we're going to
+
+ align:start position:0%
+we're going to
+ 
+
+ align:start position:0%
+we're going to
+take contributions of that and now we
+
+ align:start position:0%
+take contributions of that and now we
+ 
+
+ align:start position:0%
+take contributions of that and now we
+can't just add them because some of them
+
+ align:start position:0%
+can't just add them because some of them
+ 
+
+ align:start position:0%
+can't just add them because some of them
+might be positive and some might be
+
+ align:start position:0%
+might be positive and some might be
+ 
+
+ align:start position:0%
+might be positive and some might be
+negative so it doesn't make sense to
+
+ align:start position:0%
+negative so it doesn't make sense to
+ 
+
+ align:start position:0%
+negative so it doesn't make sense to
+minimize the the integral of them
+
+ align:start position:0%
+minimize the the integral of them
+ 
+
+ align:start position:0%
+minimize the the integral of them
+we turn them into something that's
+
+ align:start position:0%
+we turn them into something that's
+ 
+
+ align:start position:0%
+we turn them into something that's
+always positive by squaring it and so
+
+ align:start position:0%
+always positive by squaring it and so
+ 
+
+ align:start position:0%
+always positive by squaring it and so
+we're going to find these answers by
+
+ align:start position:0%
+we're going to find these answers by
+ 
+
+ align:start position:0%
+we're going to find these answers by
+minimizing that now in this case
+
+ align:start position:0%
+minimizing that now in this case
+ 
+
+ align:start position:0%
+minimizing that now in this case
+you know this is pretty straightforward
+
+ align:start position:0%
+you know this is pretty straightforward
+ 
+
+ align:start position:0%
+you know this is pretty straightforward
+we now take that
+
+ align:start position:0%
+we now take that
+ 
+
+ align:start position:0%
+we now take that
+and this is a calculus problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so so this is a function of u and
+
+ align:start position:0%
+right so so this is a function of u and
+ 
+
+ align:start position:0%
+right so so this is a function of u and
+v
+
+ align:start position:0%
+v
+ 
+
+ align:start position:0%
+v
+and uh we're going to
+
+ align:start position:0%
+and uh we're going to
+ 
+
+ align:start position:0%
+and uh we're going to
+set the derivatives with respect to u
+
+ align:start position:0%
+set the derivatives with respect to u
+ 
+
+ align:start position:0%
+set the derivatives with respect to u
+and v equal to zero and in this case
+
+ align:start position:0%
+and v equal to zero and in this case
+ 
+
+ align:start position:0%
+and v equal to zero and in this case
+we're lucky enough that the equations
+
+ align:start position:0%
+we're lucky enough that the equations
+ 
+
+ align:start position:0%
+we're lucky enough that the equations
+are linear and we can solve it and
+
+ align:start position:0%
+are linear and we can solve it and
+ 
+
+ align:start position:0%
+are linear and we can solve it and
+actually the answer is very similar to
+
+ align:start position:0%
+actually the answer is very similar to
+ 
+
+ align:start position:0%
+actually the answer is very similar to
+our uh
+
+ align:start position:0%
+our uh
+ 
+
+ align:start position:0%
+our uh
+very similar to this
+
+ align:start position:0%
+very similar to this
+ 
+
+ align:start position:0%
+very similar to this
+we have we're going to end up with two
+
+ align:start position:0%
+we have we're going to end up with two
+ 
+
+ align:start position:0%
+we have we're going to end up with two
+equations and two unknowns right uh one
+
+ align:start position:0%
+equations and two unknowns right uh one
+ 
+
+ align:start position:0%
+equations and two unknowns right uh one
+equation from uh the derivative with
+
+ align:start position:0%
+equation from uh the derivative with
+ 
+
+ align:start position:0%
+equation from uh the derivative with
+respect to u is zero and one with the
+
+ align:start position:0%
+respect to u is zero and one with the
+ 
+
+ align:start position:0%
+respect to u is zero and one with the
+derivative of v is zero so
+
+ align:start position:0%
+derivative of v is zero so
+ 
+
+ align:start position:0%
+derivative of v is zero so
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um so and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the so two equations two unknowns uh
+
+ align:start position:0%
+the so two equations two unknowns uh
+ 
+
+ align:start position:0%
+the so two equations two unknowns uh
+cool but that can fail right because
+
+ align:start position:0%
+cool but that can fail right because
+ 
+
+ align:start position:0%
+cool but that can fail right because
+they might not actually be different
+
+ align:start position:0%
+they might not actually be different
+ 
+
+ align:start position:0%
+they might not actually be different
+equations they might be linearly
+
+ align:start position:0%
+equations they might be linearly
+ 
+
+ align:start position:0%
+equations they might be linearly
+dependent so we'd want to worry about
+
+ align:start position:0%
+dependent so we'd want to worry about
+ 
+
+ align:start position:0%
+dependent so we'd want to worry about
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and in this case the failure mode is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that turns out to be the determinant of
+
+ align:start position:0%
+that turns out to be the determinant of
+ 
+
+ align:start position:0%
+that turns out to be the determinant of
+that two by two matrix so that
+
+ align:start position:0%
+that two by two matrix so that
+ 
+
+ align:start position:0%
+that two by two matrix so that
+corresponds to to this thing over here
+
+ align:start position:0%
+corresponds to to this thing over here
+ 
+
+ align:start position:0%
+corresponds to to this thing over here
+and in in this case uh that's uh when
+
+ align:start position:0%
+and in in this case uh that's uh when
+ 
+
+ align:start position:0%
+and in in this case uh that's uh when
+things fail so so when can that happen
+
+ align:start position:0%
+things fail so so when can that happen
+ 
+
+ align:start position:0%
+things fail so so when can that happen
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+well uh certainly if e is zero
+
+ align:start position:0%
+well uh certainly if e is zero
+ 
+
+ align:start position:0%
+well uh certainly if e is zero
+or e is a constant
+
+ align:start position:0%
+or e is a constant
+ 
+
+ align:start position:0%
+or e is a constant
+right because then e x and e y are zero
+
+ align:start position:0%
+right because then e x and e y are zero
+ 
+
+ align:start position:0%
+right because then e x and e y are zero
+um or
+
+ align:start position:0%
+um or
+ 
+
+ align:start position:0%
+um or
+maybe if just e x is zero everywhere
+
+ align:start position:0%
+maybe if just e x is zero everywhere
+ 
+
+ align:start position:0%
+maybe if just e x is zero everywhere
+right because then this is this integral
+
+ align:start position:0%
+right because then this is this integral
+ 
+
+ align:start position:0%
+right because then this is this integral
+is zero and that integral is zero
+
+ align:start position:0%
+is zero and that integral is zero
+ 
+
+ align:start position:0%
+is zero and that integral is zero
+so let's see so if e x is zero and e y
+
+ align:start position:0%
+so let's see so if e x is zero and e y
+ 
+
+ align:start position:0%
+so let's see so if e x is zero and e y
+is not zero
+
+ align:start position:0%
+is not zero
+ 
+
+ align:start position:0%
+is not zero
+uh what is that well that means that i
+
+ align:start position:0%
+uh what is that well that means that i
+ 
+
+ align:start position:0%
+uh what is that well that means that i
+have one of those pictures that only
+
+ align:start position:0%
+have one of those pictures that only
+ 
+
+ align:start position:0%
+have one of those pictures that only
+varies in one direction
+
+ align:start position:0%
+varies in one direction
+ 
+
+ align:start position:0%
+varies in one direction
+right e x is zero meaning it's constant
+
+ align:start position:0%
+right e x is zero meaning it's constant
+ 
+
+ align:start position:0%
+right e x is zero meaning it's constant
+in the horizontal direction
+
+ align:start position:0%
+in the horizontal direction
+ 
+
+ align:start position:0%
+in the horizontal direction
+e y is non-zero it's varying in
+
+ align:start position:0%
+e y is non-zero it's varying in
+ 
+
+ align:start position:0%
+e y is non-zero it's varying in
+brightness in the vertical direction and
+
+ align:start position:0%
+brightness in the vertical direction and
+ 
+
+ align:start position:0%
+brightness in the vertical direction and
+if i were to draw isofoads they'd look
+
+ align:start position:0%
+if i were to draw isofoads they'd look
+ 
+
+ align:start position:0%
+if i were to draw isofoads they'd look
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+right so here
+
+ align:start position:0%
+right so here
+ 
+
+ align:start position:0%
+right so here
+e x is zero e y is not zero
+
+ align:start position:0%
+e x is zero e y is not zero
+ 
+
+ align:start position:0%
+e x is zero e y is not zero
+and we know that the problem is a
+
+ align:start position:0%
+and we know that the problem is a
+ 
+
+ align:start position:0%
+and we know that the problem is a
+problem if i move in this direction
+
+ align:start position:0%
+problem if i move in this direction
+ 
+
+ align:start position:0%
+problem if i move in this direction
+the image doesn't change so
+
+ align:start position:0%
+the image doesn't change so
+ 
+
+ align:start position:0%
+the image doesn't change so
+console
+
+ align:start position:0%
+console
+ 
+
+ align:start position:0%
+console
+okay so e x equals 0 is a problem
+
+ align:start position:0%
+okay so e x equals 0 is a problem
+ 
+
+ align:start position:0%
+okay so e x equals 0 is a problem
+similarly e y equals 0 is a problem
+
+ align:start position:0%
+similarly e y equals 0 is a problem
+ 
+
+ align:start position:0%
+similarly e y equals 0 is a problem
+just turned 90 degrees
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so those are kind of obvious i mean we
+
+ align:start position:0%
+so those are kind of obvious i mean we
+ 
+
+ align:start position:0%
+so those are kind of obvious i mean we
+know those aren't going to work
+
+ align:start position:0%
+know those aren't going to work
+ 
+
+ align:start position:0%
+know those aren't going to work
+is there anything else well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how about e x equals e y
+
+ align:start position:0%
+how about e x equals e y
+ 
+
+ align:start position:0%
+how about e x equals e y
+well if that's the case then these two
+
+ align:start position:0%
+well if that's the case then these two
+ 
+
+ align:start position:0%
+well if that's the case then these two
+integrals are the same
+
+ align:start position:0%
+integrals are the same
+ 
+
+ align:start position:0%
+integrals are the same
+and actually that integral is the same
+
+ align:start position:0%
+and actually that integral is the same
+ 
+
+ align:start position:0%
+and actually that integral is the same
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+so this you know
+
+ align:start position:0%
+so this you know
+ 
+
+ align:start position:0%
+so this you know
+we're going to get
+
+ align:start position:0%
+we're going to get
+ 
+
+ align:start position:0%
+we're going to get
+integral e x squared all squared minus
+
+ align:start position:0%
+integral e x squared all squared minus
+ 
+
+ align:start position:0%
+integral e x squared all squared minus
+this thing all squared zero so
+
+ align:start position:0%
+this thing all squared zero so
+ 
+
+ align:start position:0%
+this thing all squared zero so
+so that's bad so what is that well
+
+ align:start position:0%
+so that's bad so what is that well
+ 
+
+ align:start position:0%
+so that's bad so what is that well
+that's where our isophotes uh are
+
+ align:start position:0%
+that's where our isophotes uh are
+ 
+
+ align:start position:0%
+that's where our isophotes uh are
+running at 45 degrees
+
+ align:start position:0%
+running at 45 degrees
+ 
+
+ align:start position:0%
+running at 45 degrees
+right because the brightness gradient
+
+ align:start position:0%
+right because the brightness gradient
+ 
+
+ align:start position:0%
+right because the brightness gradient
+has the same x component as y component
+
+ align:start position:0%
+has the same x component as y component
+ 
+
+ align:start position:0%
+has the same x component as y component
+the brightness gradient is perpendicular
+
+ align:start position:0%
+the brightness gradient is perpendicular
+ 
+
+ align:start position:0%
+the brightness gradient is perpendicular
+to the isophote
+
+ align:start position:0%
+to the isophote
+ 
+
+ align:start position:0%
+to the isophote
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+e x e y means it's a 45 degree angle for
+
+ align:start position:0%
+e x e y means it's a 45 degree angle for
+ 
+
+ align:start position:0%
+e x e y means it's a 45 degree angle for
+the gradient so the isophoto 45 degrees
+
+ align:start position:0%
+the gradient so the isophoto 45 degrees
+ 
+
+ align:start position:0%
+the gradient so the isophoto 45 degrees
+down so so that's the picture for that
+
+ align:start position:0%
+down so so that's the picture for that
+ 
+
+ align:start position:0%
+down so so that's the picture for that
+and you know of course
+
+ align:start position:0%
+and you know of course
+ 
+
+ align:start position:0%
+and you know of course
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+is really the same thing as that just
+
+ align:start position:0%
+is really the same thing as that just
+ 
+
+ align:start position:0%
+is really the same thing as that just
+rotate it and one of the things we're
+
+ align:start position:0%
+rotate it and one of the things we're
+ 
+
+ align:start position:0%
+rotate it and one of the things we're
+going to do is
+
+ align:start position:0%
+going to do is
+ 
+
+ align:start position:0%
+going to do is
+say that well
+
+ align:start position:0%
+say that well
+ 
+
+ align:start position:0%
+say that well
+something shouldn't depend on our choice
+
+ align:start position:0%
+something shouldn't depend on our choice
+ 
+
+ align:start position:0%
+something shouldn't depend on our choice
+of x and y in the image coordinate
+
+ align:start position:0%
+of x and y in the image coordinate
+ 
+
+ align:start position:0%
+of x and y in the image coordinate
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+i mean the answer would be different but
+
+ align:start position:0%
+i mean the answer would be different but
+ 
+
+ align:start position:0%
+i mean the answer would be different but
+in the new coordinate system it should
+
+ align:start position:0%
+in the new coordinate system it should
+ 
+
+ align:start position:0%
+in the new coordinate system it should
+mean the same thing so in this case
+
+ align:start position:0%
+mean the same thing so in this case
+ 
+
+ align:start position:0%
+mean the same thing so in this case
+i shouldn't get some result that's
+
+ align:start position:0%
+i shouldn't get some result that's
+ 
+
+ align:start position:0%
+i shouldn't get some result that's
+particular to the x or y axis it should
+
+ align:start position:0%
+particular to the x or y axis it should
+ 
+
+ align:start position:0%
+particular to the x or y axis it should
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+give me the same result if i rotate so
+
+ align:start position:0%
+give me the same result if i rotate so
+ 
+
+ align:start position:0%
+give me the same result if i rotate so
+that's a 45 degree rotation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i can get any rotation
+
+ align:start position:0%
+i can get any rotation
+ 
+
+ align:start position:0%
+i can get any rotation
+by doing something like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right because then e y over e x is some
+
+ align:start position:0%
+right because then e y over e x is some
+ 
+
+ align:start position:0%
+right because then e y over e x is some
+constant and that's the tangent of the
+
+ align:start position:0%
+constant and that's the tangent of the
+ 
+
+ align:start position:0%
+constant and that's the tangent of the
+angle of rotation or something like that
+
+ align:start position:0%
+angle of rotation or something like that
+ 
+
+ align:start position:0%
+angle of rotation or something like that
+plug that in here and of course you'll
+
+ align:start position:0%
+plug that in here and of course you'll
+ 
+
+ align:start position:0%
+plug that in here and of course you'll
+see that
+
+ align:start position:0%
+see that
+ 
+
+ align:start position:0%
+see that
+you get you know k squared times the
+
+ align:start position:0%
+you get you know k squared times the
+ 
+
+ align:start position:0%
+you get you know k squared times the
+integral over here and the k squared
+
+ align:start position:0%
+integral over here and the k squared
+ 
+
+ align:start position:0%
+integral over here and the k squared
+appears over there they cancel each
+
+ align:start position:0%
+appears over there they cancel each
+ 
+
+ align:start position:0%
+appears over there they cancel each
+other out so these are so this is
+
+ align:start position:0%
+other out so these are so this is
+ 
+
+ align:start position:0%
+other out so these are so this is
+actually the most general case all of
+
+ align:start position:0%
+actually the most general case all of
+ 
+
+ align:start position:0%
+actually the most general case all of
+these others are just special cases of
+
+ align:start position:0%
+these others are just special cases of
+ 
+
+ align:start position:0%
+these others are just special cases of
+that one
+
+ align:start position:0%
+that one
+ 
+
+ align:start position:0%
+that one
+so that
+
+ align:start position:0%
+so that
+ 
+
+ align:start position:0%
+so that
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+summarizes all of the cases we found
+
+ align:start position:0%
+summarizes all of the cases we found
+ 
+
+ align:start position:0%
+summarizes all of the cases we found
+they're all
+
+ align:start position:0%
+they're all
+ 
+
+ align:start position:0%
+they're all
+you know with isophotes at some angle
+
+ align:start position:0%
+you know with isophotes at some angle
+ 
+
+ align:start position:0%
+you know with isophotes at some angle
+parallel lines
+
+ align:start position:0%
+parallel lines
+ 
+
+ align:start position:0%
+parallel lines
+um and then you know important question
+
+ align:start position:0%
+um and then you know important question
+ 
+
+ align:start position:0%
+um and then you know important question
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+is that it
+
+ align:start position:0%
+is that it
+ 
+
+ align:start position:0%
+is that it
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+it turns out yes uh that's it
+
+ align:start position:0%
+it turns out yes uh that's it
+ 
+
+ align:start position:0%
+it turns out yes uh that's it
+and it's not easy to prove you
+
+ align:start position:0%
+and it's not easy to prove you
+ 
+
+ align:start position:0%
+and it's not easy to prove you
+you need to
+
+ align:start position:0%
+you need to
+ 
+
+ align:start position:0%
+you need to
+at least use the triangle inequality or
+
+ align:start position:0%
+at least use the triangle inequality or
+ 
+
+ align:start position:0%
+at least use the triangle inequality or
+something profound like that so
+
+ align:start position:0%
+something profound like that so
+ 
+
+ align:start position:0%
+something profound like that so
+it's actually not that hard but i i
+
+ align:start position:0%
+it's actually not that hard but i i
+ 
+
+ align:start position:0%
+it's actually not that hard but i i
+think it's
+
+ align:start position:0%
+think it's
+ 
+
+ align:start position:0%
+think it's
+not uh really useful to
+
+ align:start position:0%
+not uh really useful to
+ 
+
+ align:start position:0%
+not uh really useful to
+go there anyway so um
+
+ align:start position:0%
+go there anyway so um
+ 
+
+ align:start position:0%
+go there anyway so um
+when can we do it well as soon as
+
+ align:start position:0%
+when can we do it well as soon as
+ 
+
+ align:start position:0%
+when can we do it well as soon as
+there's curvature in the isofoads right
+
+ align:start position:0%
+there's curvature in the isofoads right
+ 
+
+ align:start position:0%
+there's curvature in the isofoads right
+because if the isofoat looks like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if i move it
+
+ align:start position:0%
+if i move it
+ 
+
+ align:start position:0%
+if i move it
+sort of tangent to the isophote
+
+ align:start position:0%
+sort of tangent to the isophote
+ 
+
+ align:start position:0%
+sort of tangent to the isophote
+there are still changes
+
+ align:start position:0%
+there are still changes
+ 
+
+ align:start position:0%
+there are still changes
+so the only problem is where the
+
+ align:start position:0%
+so the only problem is where the
+ 
+
+ align:start position:0%
+so the only problem is where the
+isophotes are all straight lines
+
+ align:start position:0%
+isophotes are all straight lines
+ 
+
+ align:start position:0%
+isophotes are all straight lines
+parallel straight lines
+
+ align:start position:0%
+parallel straight lines
+ 
+
+ align:start position:0%
+parallel straight lines
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in another way of thinking about it if
+
+ align:start position:0%
+in another way of thinking about it if
+ 
+
+ align:start position:0%
+in another way of thinking about it if
+you have areas in the image where
+
+ align:start position:0%
+you have areas in the image where
+ 
+
+ align:start position:0%
+you have areas in the image where
+there's a quote corner
+
+ align:start position:0%
+there's a quote corner
+ 
+
+ align:start position:0%
+there's a quote corner
+you know something where the isophote
+
+ align:start position:0%
+you know something where the isophote
+ 
+
+ align:start position:0%
+you know something where the isophote
+makes a sharp turn
+
+ align:start position:0%
+makes a sharp turn
+ 
+
+ align:start position:0%
+makes a sharp turn
+so here the brightness gradients
+
+ align:start position:0%
+so here the brightness gradients
+ 
+
+ align:start position:0%
+so here the brightness gradients
+if there's some small area where the
+
+ align:start position:0%
+if there's some small area where the
+ 
+
+ align:start position:0%
+if there's some small area where the
+directions of the brightness gradients
+
+ align:start position:0%
+directions of the brightness gradients
+ 
+
+ align:start position:0%
+directions of the brightness gradients
+change a lot that's good right because
+
+ align:start position:0%
+change a lot that's good right because
+ 
+
+ align:start position:0%
+change a lot that's good right because
+what we're worried about is that the
+
+ align:start position:0%
+what we're worried about is that the
+ 
+
+ align:start position:0%
+what we're worried about is that the
+brightness gradients are all parallel to
+
+ align:start position:0%
+brightness gradients are all parallel to
+ 
+
+ align:start position:0%
+brightness gradients are all parallel to
+each other that's the bad situation
+
+ align:start position:0%
+each other that's the bad situation
+ 
+
+ align:start position:0%
+each other that's the bad situation
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+for many purposes like image alignment
+
+ align:start position:0%
+for many purposes like image alignment
+ 
+
+ align:start position:0%
+for many purposes like image alignment
+and recognition
+
+ align:start position:0%
+and recognition
+ 
+
+ align:start position:0%
+and recognition
+we look for places that are quote
+
+ align:start position:0%
+we look for places that are quote
+ 
+
+ align:start position:0%
+we look for places that are quote
+interesting and one interesting way is
+
+ align:start position:0%
+interesting and one interesting way is
+ 
+
+ align:start position:0%
+interesting and one interesting way is
+to look at the isophobic curvature or
+
+ align:start position:0%
+to look at the isophobic curvature or
+ 
+
+ align:start position:0%
+to look at the isophobic curvature or
+equivalently the rapid turning of the
+
+ align:start position:0%
+equivalently the rapid turning of the
+ 
+
+ align:start position:0%
+equivalently the rapid turning of the
+brightness gradients
+
+ align:start position:0%
+brightness gradients
+ 
+
+ align:start position:0%
+brightness gradients
+because in other areas of the image
+
+ align:start position:0%
+because in other areas of the image
+ 
+
+ align:start position:0%
+because in other areas of the image
+there's less constraint you know if i if
+
+ align:start position:0%
+there's less constraint you know if i if
+ 
+
+ align:start position:0%
+there's less constraint you know if i if
+i have a part of the image that looks
+
+ align:start position:0%
+i have a part of the image that looks
+ 
+
+ align:start position:0%
+i have a part of the image that looks
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+on its own it doesn't provide enough
+
+ align:start position:0%
+on its own it doesn't provide enough
+ 
+
+ align:start position:0%
+on its own it doesn't provide enough
+constraint
+
+ align:start position:0%
+constraint
+ 
+
+ align:start position:0%
+constraint
+now if next to it is another area of the
+
+ align:start position:0%
+now if next to it is another area of the
+ 
+
+ align:start position:0%
+now if next to it is another area of the
+image
+
+ align:start position:0%
+image
+ 
+
+ align:start position:0%
+image
+where things you know look like this
+
+ align:start position:0%
+where things you know look like this
+ 
+
+ align:start position:0%
+where things you know look like this
+if i have both of these then that's fine
+
+ align:start position:0%
+if i have both of these then that's fine
+ 
+
+ align:start position:0%
+if i have both of these then that's fine
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+if everything has the same gradient
+
+ align:start position:0%
+if everything has the same gradient
+ 
+
+ align:start position:0%
+if everything has the same gradient
+direction that's not not satisfactory
+
+ align:start position:0%
+direction that's not not satisfactory
+ 
+
+ align:start position:0%
+direction that's not not satisfactory
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+homework problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theoretically due and uh on thursday
+
+ align:start position:0%
+theoretically due and uh on thursday
+ 
+
+ align:start position:0%
+theoretically due and uh on thursday
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+i know we haven't done a whole lot on
+
+ align:start position:0%
+i know we haven't done a whole lot on
+ 
+
+ align:start position:0%
+i know we haven't done a whole lot on
+this so if you have problems with it
+
+ align:start position:0%
+this so if you have problems with it
+ 
+
+ align:start position:0%
+this so if you have problems with it
+send me email
+
+ align:start position:0%
+send me email
+ 
+
+ align:start position:0%
+send me email
+and i'm i may say something that doesn't
+
+ align:start position:0%
+and i'm i may say something that doesn't
+ 
+
+ align:start position:0%
+and i'm i may say something that doesn't
+give away the answer but helps you
+
+ align:start position:0%
+give away the answer but helps you
+ 
+
+ align:start position:0%
+give away the answer but helps you
+and we'll go from there
+
+ align:start position:0%
+and we'll go from there
+ 
+
+ align:start position:0%
+and we'll go from there
+what we're going to do next is
+
+ align:start position:0%
+what we're going to do next is
+ 
+
+ align:start position:0%
+what we're going to do next is
+talk a little bit about this concept of
+
+ align:start position:0%
+talk a little bit about this concept of
+ 
+
+ align:start position:0%
+talk a little bit about this concept of
+noise gain
+
+ align:start position:0%
+noise gain
+ 
+
+ align:start position:0%
+noise gain
+so the idea is that
+
+ align:start position:0%
+so the idea is that
+ 
+
+ align:start position:0%
+so the idea is that
+all this time we in the back we've been
+
+ align:start position:0%
+all this time we in the back we've been
+ 
+
+ align:start position:0%
+all this time we in the back we've been
+thinking about oh we only have pixels
+
+ align:start position:0%
+thinking about oh we only have pixels
+ 
+
+ align:start position:0%
+thinking about oh we only have pixels
+with eight bits and they're noisy and
+
+ align:start position:0%
+with eight bits and they're noisy and
+ 
+
+ align:start position:0%
+with eight bits and they're noisy and
+our calculations are going to be flaky
+
+ align:start position:0%
+our calculations are going to be flaky
+ 
+
+ align:start position:0%
+our calculations are going to be flaky
+unless this determinant is large and so
+
+ align:start position:0%
+unless this determinant is large and so
+ 
+
+ align:start position:0%
+unless this determinant is large and so
+on so there's a lot of attention to not
+
+ align:start position:0%
+on so there's a lot of attention to not
+ 
+
+ align:start position:0%
+on so there's a lot of attention to not
+just you know a formula for computing
+
+ align:start position:0%
+just you know a formula for computing
+ 
+
+ align:start position:0%
+just you know a formula for computing
+the answer but making sure that the
+
+ align:start position:0%
+the answer but making sure that the
+ 
+
+ align:start position:0%
+the answer but making sure that the
+answer is actually meaningful as opposed
+
+ align:start position:0%
+answer is actually meaningful as opposed
+ 
+
+ align:start position:0%
+answer is actually meaningful as opposed
+to you know you've taken two noisy
+
+ align:start position:0%
+to you know you've taken two noisy
+ 
+
+ align:start position:0%
+to you know you've taken two noisy
+numbers and divided them by each other
+
+ align:start position:0%
+numbers and divided them by each other
+ 
+
+ align:start position:0%
+numbers and divided them by each other
+and the result is not
+
+ align:start position:0%
+and the result is not
+ 
+
+ align:start position:0%
+and the result is not
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+predictable so in noise gain
+
+ align:start position:0%
+predictable so in noise gain
+ 
+
+ align:start position:0%
+predictable so in noise gain
+that's a very precise way of talking
+
+ align:start position:0%
+that's a very precise way of talking
+ 
+
+ align:start position:0%
+that's a very precise way of talking
+about it which is saying if i make this
+
+ align:start position:0%
+about it which is saying if i make this
+ 
+
+ align:start position:0%
+about it which is saying if i make this
+much of a change in the image
+
+ align:start position:0%
+much of a change in the image
+ 
+
+ align:start position:0%
+much of a change in the image
+what is the change in the result so in
+
+ align:start position:0%
+what is the change in the result so in
+ 
+
+ align:start position:0%
+what is the change in the result so in
+this case
+
+ align:start position:0%
+this case
+ 
+
+ align:start position:0%
+this case
+i'm trying to get the velocity of motion
+
+ align:start position:0%
+i'm trying to get the velocity of motion
+ 
+
+ align:start position:0%
+i'm trying to get the velocity of motion
+how much is the velocity of motion going
+
+ align:start position:0%
+how much is the velocity of motion going
+ 
+
+ align:start position:0%
+how much is the velocity of motion going
+to change if i change the brightness
+
+ align:start position:0%
+to change if i change the brightness
+ 
+
+ align:start position:0%
+to change if i change the brightness
+gradient somewhere i have the wrong
+
+ align:start position:0%
+gradient somewhere i have the wrong
+ 
+
+ align:start position:0%
+gradient somewhere i have the wrong
+measurement it's slightly off and of
+
+ align:start position:0%
+measurement it's slightly off and of
+ 
+
+ align:start position:0%
+measurement it's slightly off and of
+course we want that to be not sensitive
+
+ align:start position:0%
+course we want that to be not sensitive
+ 
+
+ align:start position:0%
+course we want that to be not sensitive
+we don't want it to be very sensitive to
+
+ align:start position:0%
+we don't want it to be very sensitive to
+ 
+
+ align:start position:0%
+we don't want it to be very sensitive to
+noise and so we'll
+
+ align:start position:0%
+noise and so we'll
+ 
+
+ align:start position:0%
+noise and so we'll
+make that clear
+
+ align:start position:0%
+make that clear
+ 
+
+ align:start position:0%
+make that clear
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+in terms of a one-dimensional
+
+ align:start position:0%
+in terms of a one-dimensional
+ 
+
+ align:start position:0%
+in terms of a one-dimensional
+transformation where we know the forward
+
+ align:start position:0%
+transformation where we know the forward
+ 
+
+ align:start position:0%
+transformation where we know the forward
+function and we're trying to invert it
+
+ align:start position:0%
+function and we're trying to invert it
+ 
+
+ align:start position:0%
+function and we're trying to invert it
+and we want to know when that inversion
+
+ align:start position:0%
+and we want to know when that inversion
+ 
+
+ align:start position:0%
+and we want to know when that inversion
+is sensible and when it's not
+
+ align:start position:0%
+is sensible and when it's not
+ 
+
+ align:start position:0%
+is sensible and when it's not
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+oh questions
\ No newline at end of file
diff --git a/uVGQayrQ9JA.txt b/uVGQayrQ9JA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e51ecf0e3722c8deff80791201f255ce7b279b14
--- /dev/null
+++ b/uVGQayrQ9JA.txt
@@ -0,0 +1,875 @@
+align:start position:0%
+ 
+but this does get me to the why this
+
+ align:start position:0%
+but this does get me to the why this
+ 
+
+ align:start position:0%
+but this does get me to the why this
+matters which has to do with how you
+
+ align:start position:0%
+matters which has to do with how you
+ 
+
+ align:start position:0%
+matters which has to do with how you
+cook pasta
+
+ align:start position:0%
+cook pasta
+ 
+
+ align:start position:0%
+cook pasta
+and of course
+
+ align:start position:0%
+and of course
+ 
+
+ align:start position:0%
+and of course
+of course since we're talking about o2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when when i have finished cooking pasta
+
+ align:start position:0%
+when when i have finished cooking pasta
+ 
+
+ align:start position:0%
+when when i have finished cooking pasta
+what do i do
+
+ align:start position:0%
+what do i do
+ 
+
+ align:start position:0%
+what do i do
+i pour it there it is through it's like
+
+ align:start position:0%
+i pour it there it is through it's like
+ 
+
+ align:start position:0%
+i pour it there it is through it's like
+it's sophisticated
+
+ align:start position:0%
+it's sophisticated
+ 
+
+ align:start position:0%
+it's sophisticated
+i pour it through a colander that's a
+
+ align:start position:0%
+i pour it through a colander that's a
+ 
+
+ align:start position:0%
+i pour it through a colander that's a
+membrane
+
+ align:start position:0%
+membrane
+ 
+
+ align:start position:0%
+membrane
+that's a membrane you did use a membrane
+
+ align:start position:0%
+that's a membrane you did use a membrane
+ 
+
+ align:start position:0%
+that's a membrane you did use a membrane
+you did a filter now but i
+
+ align:start position:0%
+you did a filter now but i
+ 
+
+ align:start position:0%
+you did a filter now but i
+could also have done that separation
+
+ align:start position:0%
+could also have done that separation
+ 
+
+ align:start position:0%
+could also have done that separation
+that same separation
+
+ align:start position:0%
+that same separation
+ 
+
+ align:start position:0%
+that same separation
+i could have left it on the stove i
+
+ align:start position:0%
+i could have left it on the stove i
+ 
+
+ align:start position:0%
+i could have left it on the stove i
+could have
+
+ align:start position:0%
+could have
+ 
+
+ align:start position:0%
+could have
+and it would have boiled out all the
+
+ align:start position:0%
+and it would have boiled out all the
+ 
+
+ align:start position:0%
+and it would have boiled out all the
+water and left me still
+
+ align:start position:0%
+water and left me still
+ 
+
+ align:start position:0%
+water and left me still
+with the pasta separated from the water
+
+ align:start position:0%
+with the pasta separated from the water
+ 
+
+ align:start position:0%
+with the pasta separated from the water
+i've accomplished the same exact thing
+
+ align:start position:0%
+i've accomplished the same exact thing
+ 
+
+ align:start position:0%
+i've accomplished the same exact thing
+i have separated the pasta from the
+
+ align:start position:0%
+i have separated the pasta from the
+ 
+
+ align:start position:0%
+i have separated the pasta from the
+water task done
+
+ align:start position:0%
+water task done
+ 
+
+ align:start position:0%
+water task done
+pasta may not taste as good
+
+ align:start position:0%
+pasta may not taste as good
+ 
+
+ align:start position:0%
+pasta may not taste as good
+but you've done this but see the thing
+
+ align:start position:0%
+but you've done this but see the thing
+ 
+
+ align:start position:0%
+but you've done this but see the thing
+is that if you separate things
+
+ align:start position:0%
+is that if you separate things
+ 
+
+ align:start position:0%
+is that if you separate things
+this way versus that way you can just
+
+ align:start position:0%
+this way versus that way you can just
+ 
+
+ align:start position:0%
+this way versus that way you can just
+feel how much less energy it's going to
+
+ align:start position:0%
+feel how much less energy it's going to
+ 
+
+ align:start position:0%
+feel how much less energy it's going to
+take in fact you can save over 80
+
+ align:start position:0%
+take in fact you can save over 80
+ 
+
+ align:start position:0%
+take in fact you can save over 80
+percent of the energy
+
+ align:start position:0%
+percent of the energy
+ 
+
+ align:start position:0%
+percent of the energy
+if you do a membrane-based separation as
+
+ align:start position:0%
+if you do a membrane-based separation as
+ 
+
+ align:start position:0%
+if you do a membrane-based separation as
+opposed to a thermal one
+
+ align:start position:0%
+opposed to a thermal one
+ 
+
+ align:start position:0%
+opposed to a thermal one
+goes in tight so those are two ways to
+
+ align:start position:0%
+goes in tight so those are two ways to
+ 
+
+ align:start position:0%
+goes in tight so those are two ways to
+separate positive but see there's two
+
+ align:start position:0%
+separate positive but see there's two
+ 
+
+ align:start position:0%
+separate positive but see there's two
+ways to separate lots of things
+
+ align:start position:0%
+ways to separate lots of things
+ 
+
+ align:start position:0%
+ways to separate lots of things
+like how about one to ten nanometer
+
+ align:start position:0%
+like how about one to ten nanometer
+ 
+
+ align:start position:0%
+like how about one to ten nanometer
+particles how about chemistry
+
+ align:start position:0%
+particles how about chemistry
+ 
+
+ align:start position:0%
+particles how about chemistry
+how about molecules how do you separate
+
+ align:start position:0%
+how about molecules how do you separate
+ 
+
+ align:start position:0%
+how about molecules how do you separate
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+well you got the same two ways and if
+
+ align:start position:0%
+well you got the same two ways and if
+ 
+
+ align:start position:0%
+well you got the same two ways and if
+you count up all the things we separate
+
+ align:start position:0%
+you count up all the things we separate
+ 
+
+ align:start position:0%
+you count up all the things we separate
+this way it's a lot it goes on and on
+
+ align:start position:0%
+this way it's a lot it goes on and on
+ 
+
+ align:start position:0%
+this way it's a lot it goes on and on
+and it will go all the way down the
+
+ align:start position:0%
+and it will go all the way down the
+ 
+
+ align:start position:0%
+and it will go all the way down the
+infinite corridor
+
+ align:start position:0%
+infinite corridor
+ 
+
+ align:start position:0%
+infinite corridor
+this is how we do chemistry in fact if
+
+ align:start position:0%
+this is how we do chemistry in fact if
+ 
+
+ align:start position:0%
+this is how we do chemistry in fact if
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+has anyone seen this on the side of the
+
+ align:start position:0%
+has anyone seen this on the side of the
+ 
+
+ align:start position:0%
+has anyone seen this on the side of the
+road
+
+ align:start position:0%
+road
+ 
+
+ align:start position:0%
+road
+that's a distillation column it's a big
+
+ align:start position:0%
+that's a distillation column it's a big
+ 
+
+ align:start position:0%
+that's a distillation column it's a big
+pasta cooker
+
+ align:start position:0%
+pasta cooker
+ 
+
+ align:start position:0%
+pasta cooker
+that's all you're doing is boiling one
+
+ align:start position:0%
+that's all you're doing is boiling one
+ 
+
+ align:start position:0%
+that's all you're doing is boiling one
+molecule off of another
+
+ align:start position:0%
+molecule off of another
+ 
+
+ align:start position:0%
+molecule off of another
+over a long time with a whole lot of
+
+ align:start position:0%
+over a long time with a whole lot of
+ 
+
+ align:start position:0%
+over a long time with a whole lot of
+fossil fuel
+
+ align:start position:0%
+fossil fuel
+ 
+
+ align:start position:0%
+fossil fuel
+right in fact if you look at the u.s
+
+ align:start position:0%
+right in fact if you look at the u.s
+ 
+
+ align:start position:0%
+right in fact if you look at the u.s
+energy consumption 30 roughly
+
+ align:start position:0%
+energy consumption 30 roughly
+ 
+
+ align:start position:0%
+energy consumption 30 roughly
+a third it goes into industry 40 percent
+
+ align:start position:0%
+a third it goes into industry 40 percent
+ 
+
+ align:start position:0%
+a third it goes into industry 40 percent
+of that is for this one thing
+
+ align:start position:0%
+of that is for this one thing
+ 
+
+ align:start position:0%
+of that is for this one thing
+it's boiling pasta but the pus is one
+
+ align:start position:0%
+it's boiling pasta but the pus is one
+ 
+
+ align:start position:0%
+it's boiling pasta but the pus is one
+nanometer to 10 nanometer particles
+
+ align:start position:0%
+nanometer to 10 nanometer particles
+ 
+
+ align:start position:0%
+nanometer to 10 nanometer particles
+40 goes into boiling one chemical
+
+ align:start position:0%
+40 goes into boiling one chemical
+ 
+
+ align:start position:0%
+40 goes into boiling one chemical
+species off of another separation
+
+ align:start position:0%
+species off of another separation
+ 
+
+ align:start position:0%
+species off of another separation
+separation that's 12
+
+ align:start position:0%
+separation that's 12
+ 
+
+ align:start position:0%
+separation that's 12
+of all the energy that's the same as
+
+ align:start position:0%
+of all the energy that's the same as
+ 
+
+ align:start position:0%
+of all the energy that's the same as
+every single drop of gasoline in every
+
+ align:start position:0%
+every single drop of gasoline in every
+ 
+
+ align:start position:0%
+every single drop of gasoline in every
+single car
+
+ align:start position:0%
+single car
+ 
+
+ align:start position:0%
+single car
+truck and bus that's just to give you a
+
+ align:start position:0%
+truck and bus that's just to give you a
+ 
+
+ align:start position:0%
+truck and bus that's just to give you a
+sense of how much energy that is
+
+ align:start position:0%
+sense of how much energy that is
+ 
+
+ align:start position:0%
+sense of how much energy that is
+i say well why aren't we using a
+
+ align:start position:0%
+i say well why aren't we using a
+ 
+
+ align:start position:0%
+i say well why aren't we using a
+colander why don't we just pour it
+
+ align:start position:0%
+colander why don't we just pour it
+ 
+
+ align:start position:0%
+colander why don't we just pour it
+through a colander like we do
+
+ align:start position:0%
+through a colander like we do
+ 
+
+ align:start position:0%
+through a colander like we do
+our boiling pasta well we do that for
+
+ align:start position:0%
+our boiling pasta well we do that for
+ 
+
+ align:start position:0%
+our boiling pasta well we do that for
+one field desalination
+
+ align:start position:0%
+one field desalination
+ 
+
+ align:start position:0%
+one field desalination
+i got it why this matters on that
+
+ align:start position:0%
+i got it why this matters on that
+ 
+
+ align:start position:0%
+i got it why this matters on that
+another time but we don't do it for all
+
+ align:start position:0%
+another time but we don't do it for all
+ 
+
+ align:start position:0%
+another time but we don't do it for all
+those other things and there's a really
+
+ align:start position:0%
+those other things and there's a really
+ 
+
+ align:start position:0%
+those other things and there's a really
+simple reason
+
+ align:start position:0%
+simple reason
+ 
+
+ align:start position:0%
+simple reason
+we don't have the right pasta colander
+
+ align:start position:0%
+we don't have the right pasta colander
+ 
+
+ align:start position:0%
+we don't have the right pasta colander
+we don't there's no option
+
+ align:start position:0%
+we don't there's no option
+ 
+
+ align:start position:0%
+we don't there's no option
+for that size scale that can withstand
+
+ align:start position:0%
+for that size scale that can withstand
+ 
+
+ align:start position:0%
+for that size scale that can withstand
+the conditions
+
+ align:start position:0%
+the conditions
+ 
+
+ align:start position:0%
+the conditions
+that are in all of those chemical
+
+ align:start position:0%
+that are in all of those chemical
+ 
+
+ align:start position:0%
+that are in all of those chemical
+separations but if we did
+
+ align:start position:0%
+separations but if we did
+ 
+
+ align:start position:0%
+separations but if we did
+this we could we take so much o2 out of
+
+ align:start position:0%
+this we could we take so much o2 out of
+ 
+
+ align:start position:0%
+this we could we take so much o2 out of
+the air
+
+ align:start position:0%
+the air
+ 
+
+ align:start position:0%
+the air
+we need o2 but we don't want the n2 so
+
+ align:start position:0%
+we need o2 but we don't want the n2 so
+ 
+
+ align:start position:0%
+we need o2 but we don't want the n2 so
+we have to separate
+
+ align:start position:0%
+we have to separate
+ 
+
+ align:start position:0%
+we have to separate
+how do we do it we go cryogenic we go to
+
+ align:start position:0%
+how do we do it we go cryogenic we go to
+ 
+
+ align:start position:0%
+how do we do it we go cryogenic we go to
+very very cold temperatures which is the
+
+ align:start position:0%
+very very cold temperatures which is the
+ 
+
+ align:start position:0%
+very very cold temperatures which is the
+same as boiling
+
+ align:start position:0%
+same as boiling
+ 
+
+ align:start position:0%
+same as boiling
+right you're lower but you're still
+
+ align:start position:0%
+right you're lower but you're still
+ 
+
+ align:start position:0%
+right you're lower but you're still
+spending all this fossil fuel to lower
+
+ align:start position:0%
+spending all this fossil fuel to lower
+ 
+
+ align:start position:0%
+spending all this fossil fuel to lower
+the temperature
+
+ align:start position:0%
+the temperature
+ 
+
+ align:start position:0%
+the temperature
+that's how much o2 we generate each year
+
+ align:start position:0%
+that's how much o2 we generate each year
+ 
+
+ align:start position:0%
+that's how much o2 we generate each year
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and this is how much energy it takes
+
+ align:start position:0%
+and this is how much energy it takes
+ 
+
+ align:start position:0%
+and this is how much energy it takes
+it's like half a percent of all u.s
+
+ align:start position:0%
+it's like half a percent of all u.s
+ 
+
+ align:start position:0%
+it's like half a percent of all u.s
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+just to get but what if
+
+ align:start position:0%
+just to get but what if
+ 
+
+ align:start position:0%
+just to get but what if
+you could use something like o2's
+
+ align:start position:0%
+you could use something like o2's
+ 
+
+ align:start position:0%
+you could use something like o2's
+paramagnetism
+
+ align:start position:0%
+paramagnetism
+ 
+
+ align:start position:0%
+paramagnetism
+what if you could use something about
+
+ align:start position:0%
+what if you could use something about
+ 
+
+ align:start position:0%
+what if you could use something about
+the chemistry of o2 to do this
+
+ align:start position:0%
+the chemistry of o2 to do this
+ 
+
+ align:start position:0%
+the chemistry of o2 to do this
+separation
+
+ align:start position:0%
+separation
+ 
+
+ align:start position:0%
+separation
+more efficiently lower energy or maybe
+
+ align:start position:0%
+more efficiently lower energy or maybe
+ 
+
+ align:start position:0%
+more efficiently lower energy or maybe
+make a new colander
+
+ align:start position:0%
+make a new colander
+ 
+
+ align:start position:0%
+make a new colander
+that does that and if any of you have
+
+ align:start position:0%
+that does that and if any of you have
+ 
+
+ align:start position:0%
+that does that and if any of you have
+ideas
+
+ align:start position:0%
+ideas
+ 
+
+ align:start position:0%
+ideas
+come talk to me this is a problem i care
+
+ align:start position:0%
+come talk to me this is a problem i care
+ 
+
+ align:start position:0%
+come talk to me this is a problem i care
+a lot about
\ No newline at end of file
diff --git a/uiUZ_KkZr8U.txt b/uiUZ_KkZr8U.txt
new file mode 100644
index 0000000000000000000000000000000000000000..18b7c9dadcfab452817ad784fb91f8a8a1320214
--- /dev/null
+++ b/uiUZ_KkZr8U.txt
@@ -0,0 +1,9480 @@
+align:start position:0%
+ 
+Now, what do we call these things? Pan
+
+ align:start position:0%
+Now, what do we call these things? Pan
+ 
+
+ align:start position:0%
+Now, what do we call these things? Pan
+out. What do we call these things? Pan
+
+ align:start position:0%
+out. What do we call these things? Pan
+ 
+
+ align:start position:0%
+out. What do we call these things? Pan
+out.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And to make up,
+
+ align:start position:0%
+And to make up,
+ 
+
+ align:start position:0%
+And to make up,
+to pan out.
+
+ align:start position:0%
+to pan out.
+ 
+
+ align:start position:0%
+to pan out.
+To make up.
+
+ align:start position:0%
+To make up.
+ 
+
+ align:start position:0%
+To make up.
+We call these things phrasal verbs.
+
+ align:start position:0%
+We call these things phrasal verbs.
+ 
+
+ align:start position:0%
+We call these things phrasal verbs.
+Phrasal verbs. Phrasal verbs. Okay. A
+
+ align:start position:0%
+Phrasal verbs. Phrasal verbs. Okay. A
+ 
+
+ align:start position:0%
+Phrasal verbs. Phrasal verbs. Okay. A
+verb usually has phrasal verbs usually
+
+ align:start position:0%
+verb usually has phrasal verbs usually
+ 
+
+ align:start position:0%
+verb usually has phrasal verbs usually
+have one verb and one particle or it
+
+ align:start position:0%
+have one verb and one particle or it
+ 
+
+ align:start position:0%
+have one verb and one particle or it
+could have two more uh one particle and
+
+ align:start position:0%
+could have two more uh one particle and
+ 
+
+ align:start position:0%
+could have two more uh one particle and
+one preposition at the end. So what's
+
+ align:start position:0%
+one preposition at the end. So what's
+ 
+
+ align:start position:0%
+one preposition at the end. So what's
+the difference between a particle and a
+
+ align:start position:0%
+the difference between a particle and a
+ 
+
+ align:start position:0%
+the difference between a particle and a
+preposition?
+
+ align:start position:0%
+preposition?
+ 
+
+ align:start position:0%
+preposition?
+Does anybody What's a preposition?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Give me some examples of prepositions.
+
+ align:start position:0%
+Give me some examples of prepositions.
+ 
+
+ align:start position:0%
+Give me some examples of prepositions.
+Huh? Prepositions
+
+ align:start position:0%
+Huh? Prepositions
+ 
+
+ align:start position:0%
+Huh? Prepositions
+in of of of f of from at from. Okay,
+
+ align:start position:0%
+in of of of f of from at from. Okay,
+ 
+
+ align:start position:0%
+in of of of f of from at from. Okay,
+those are prepositions, right? Out of
+
+ align:start position:0%
+those are prepositions, right? Out of
+ 
+
+ align:start position:0%
+those are prepositions, right? Out of
+up. These it kind of look like
+
+ align:start position:0%
+up. These it kind of look like
+ 
+
+ align:start position:0%
+up. These it kind of look like
+prepositions, but they actually have
+
+ align:start position:0%
+prepositions, but they actually have
+ 
+
+ align:start position:0%
+prepositions, but they actually have
+some meaning. These are called adverbial
+
+ align:start position:0%
+some meaning. These are called adverbial
+ 
+
+ align:start position:0%
+some meaning. These are called adverbial
+particles. Adverbs, they have some
+
+ align:start position:0%
+particles. Adverbs, they have some
+ 
+
+ align:start position:0%
+particles. Adverbs, they have some
+meaning. Okay.
+
+ align:start position:0%
+meaning. Okay.
+ 
+
+ align:start position:0%
+meaning. Okay.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+now if you turn to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this handout
+
+ align:start position:0%
+this handout
+ 
+
+ align:start position:0%
+this handout
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+page 65 in your course packet. Page 65.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is where we left off
+
+ align:start position:0%
+This is where we left off
+ 
+
+ align:start position:0%
+This is where we left off
+last time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, this sentence these compare these
+
+ align:start position:0%
+Okay, this sentence these compare these
+ 
+
+ align:start position:0%
+Okay, this sentence these compare these
+two sentences.
+
+ align:start position:0%
+two sentences.
+ 
+
+ align:start position:0%
+two sentences.
+Compare these two sentences.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What do we stress here in this sentence?
+
+ align:start position:0%
+What do we stress here in this sentence?
+ 
+
+ align:start position:0%
+What do we stress here in this sentence?
+Looking. Looking. Okay. looking. She was
+
+ align:start position:0%
+Looking. Looking. Okay. looking. She was
+ 
+
+ align:start position:0%
+Looking. Looking. Okay. looking. She was
+looking at me. Repeat after me. She was
+
+ align:start position:0%
+looking at me. Repeat after me. She was
+ 
+
+ align:start position:0%
+looking at me. Repeat after me. She was
+looking at me. She was looking at me.
+
+ align:start position:0%
+looking at me. She was looking at me.
+ 
+
+ align:start position:0%
+looking at me. She was looking at me.
+She was looking at me. She was looking
+
+ align:start position:0%
+She was looking at me. She was looking
+ 
+
+ align:start position:0%
+She was looking at me. She was looking
+at me. Okay. What about this one?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+She looked away. She looked away from
+
+ align:start position:0%
+She looked away. She looked away from
+ 
+
+ align:start position:0%
+She looked away. She looked away from
+me. She looked away from me. So, there's
+
+ align:start position:0%
+me. She looked away from me. So, there's
+ 
+
+ align:start position:0%
+me. She looked away from me. So, there's
+more stress on away. She looked away
+
+ align:start position:0%
+more stress on away. She looked away
+ 
+
+ align:start position:0%
+more stress on away. She looked away
+from me. She looked away from me. She
+
+ align:start position:0%
+from me. She looked away from me. She
+ 
+
+ align:start position:0%
+from me. She looked away from me. She
+looked away from me. She looked away
+
+ align:start position:0%
+looked away from me. She looked away
+ 
+
+ align:start position:0%
+looked away from me. She looked away
+from me. Lu. Okay. Lincoln, she looked
+
+ align:start position:0%
+from me. Lu. Okay. Lincoln, she looked
+ 
+
+ align:start position:0%
+from me. Lu. Okay. Lincoln, she looked
+away from me. She looked away from me.
+
+ align:start position:0%
+away from me. She looked away from me.
+ 
+
+ align:start position:0%
+away from me. She looked away from me.
+She looked away from me. She looked away
+
+ align:start position:0%
+She looked away from me. She looked away
+ 
+
+ align:start position:0%
+She looked away from me. She looked away
+from me. Okay. So, if a phrasal verb has
+
+ align:start position:0%
+from me. Okay. So, if a phrasal verb has
+ 
+
+ align:start position:0%
+from me. Okay. So, if a phrasal verb has
+a preposition, preposition does not get
+
+ align:start position:0%
+a preposition, preposition does not get
+ 
+
+ align:start position:0%
+a preposition, preposition does not get
+any stress. Okay. No stress. So, it gets
+
+ align:start position:0%
+any stress. Okay. No stress. So, it gets
+ 
+
+ align:start position:0%
+any stress. Okay. No stress. So, it gets
+reduced. She was looking at me. She was
+
+ align:start position:0%
+reduced. She was looking at me. She was
+ 
+
+ align:start position:0%
+reduced. She was looking at me. She was
+looking at it. Instead of at, instead of
+
+ align:start position:0%
+looking at it. Instead of at, instead of
+ 
+
+ align:start position:0%
+looking at it. Instead of at, instead of
+at, you say something like it. She was
+
+ align:start position:0%
+at, you say something like it. She was
+ 
+
+ align:start position:0%
+at, you say something like it. She was
+looking at me. She was looking at me.
+
+ align:start position:0%
+looking at me. She was looking at me.
+ 
+
+ align:start position:0%
+looking at me. She was looking at me.
+She was looking at me. She was looking
+
+ align:start position:0%
+She was looking at me. She was looking
+ 
+
+ align:start position:0%
+She was looking at me. She was looking
+at me. But here, she looked away from
+
+ align:start position:0%
+at me. But here, she looked away from
+ 
+
+ align:start position:0%
+at me. But here, she looked away from
+me. She looked away from me. She looked
+
+ align:start position:0%
+me. She looked away from me. She looked
+ 
+
+ align:start position:0%
+me. She looked away from me. She looked
+away from me. She looked away from me.
+
+ align:start position:0%
+away from me. She looked away from me.
+ 
+
+ align:start position:0%
+away from me. She looked away from me.
+Okay, so there's more stress on the last
+
+ align:start position:0%
+Okay, so there's more stress on the last
+ 
+
+ align:start position:0%
+Okay, so there's more stress on the last
+word. Pan out. Pan out. Make up. Make
+
+ align:start position:0%
+word. Pan out. Pan out. Make up. Make
+ 
+
+ align:start position:0%
+word. Pan out. Pan out. Make up. Make
+up. Pan out. Pan out. Makeup. Make up.
+
+ align:start position:0%
+up. Pan out. Pan out. Makeup. Make up.
+ 
+
+ align:start position:0%
+up. Pan out. Pan out. Makeup. Make up.
+Okay. So, let's compare these two sets
+
+ align:start position:0%
+Okay. So, let's compare these two sets
+ 
+
+ align:start position:0%
+Okay. So, let's compare these two sets
+of examples.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Which words would you stress in this
+
+ align:start position:0%
+Which words would you stress in this
+ 
+
+ align:start position:0%
+Which words would you stress in this
+sentence?
+
+ align:start position:0%
+sentence?
+ 
+
+ align:start position:0%
+sentence?
+called and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me get my pen.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+there's more stress on. She
+
+ align:start position:0%
+there's more stress on. She
+ 
+
+ align:start position:0%
+there's more stress on. She
+called on the phone. She called on the
+
+ align:start position:0%
+called on the phone. She called on the
+ 
+
+ align:start position:0%
+called on the phone. She called on the
+phone. She called on the phone. She
+
+ align:start position:0%
+phone. She called on the phone. She
+ 
+
+ align:start position:0%
+phone. She called on the phone. She
+called on the phone. She called on the
+
+ align:start position:0%
+called on the phone. She called on the
+ 
+
+ align:start position:0%
+called on the phone. She called on the
+phone. What about this?
+
+ align:start position:0%
+phone. What about this?
+ 
+
+ align:start position:0%
+phone. What about this?
+She called off the lady.
+
+ align:start position:0%
+She called off the lady.
+ 
+
+ align:start position:0%
+She called off the lady.
+She called off. Okay. There's stress
+
+ align:start position:0%
+She called off. Okay. There's stress
+ 
+
+ align:start position:0%
+She called off. Okay. There's stress
+here. Stress here and stress here. But
+
+ align:start position:0%
+here. Stress here and stress here. But
+ 
+
+ align:start position:0%
+here. Stress here and stress here. But
+there is no stress here. Okay. So, she
+
+ align:start position:0%
+there is no stress here. Okay. So, she
+ 
+
+ align:start position:0%
+there is no stress here. Okay. So, she
+called on the phone. She called the
+
+ align:start position:0%
+called on the phone. She called the
+ 
+
+ align:start position:0%
+called on the phone. She called the
+phone. She called off She called off the
+
+ align:start position:0%
+phone. She called off She called off the
+ 
+
+ align:start position:0%
+phone. She called off She called off the
+meeting. She called off the meeting. She
+
+ align:start position:0%
+meeting. She called off the meeting. She
+ 
+
+ align:start position:0%
+meeting. She called off the meeting. She
+called off the meeting. She called off
+
+ align:start position:0%
+called off the meeting. She called off
+ 
+
+ align:start position:0%
+called off the meeting. She called off
+the meeting. Okay. She called off the
+
+ align:start position:0%
+the meeting. Okay. She called off the
+ 
+
+ align:start position:0%
+the meeting. Okay. She called off the
+meeting. She called off the meeting.
+
+ align:start position:0%
+meeting. She called off the meeting.
+ 
+
+ align:start position:0%
+meeting. She called off the meeting.
+What about this one?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Think about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one gets more stressed. Okay. Think
+
+ align:start position:0%
+this one gets more stressed. Okay. Think
+ 
+
+ align:start position:0%
+this one gets more stressed. Okay. Think
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You have many things to think about.
+
+ align:start position:0%
+You have many things to think about.
+ 
+
+ align:start position:0%
+You have many things to think about.
+You have many things to think about.
+
+ align:start position:0%
+You have many things to think about.
+ 
+
+ align:start position:0%
+You have many things to think about.
+But this one
+
+ align:start position:0%
+But this one
+ 
+
+ align:start position:0%
+But this one
+would love to bring about bring about
+
+ align:start position:0%
+would love to bring about bring about
+ 
+
+ align:start position:0%
+would love to bring about bring about
+bring about bring about bring about
+
+ align:start position:0%
+bring about bring about bring about
+ 
+
+ align:start position:0%
+bring about bring about bring about
+Okay, that's a change we'd like to bring
+
+ align:start position:0%
+Okay, that's a change we'd like to bring
+ 
+
+ align:start position:0%
+Okay, that's a change we'd like to bring
+about.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's a change we'd like to bring
+
+ align:start position:0%
+That's a change we'd like to bring
+ 
+
+ align:start position:0%
+That's a change we'd like to bring
+about. That's a change we'd like to
+
+ align:start position:0%
+about. That's a change we'd like to
+ 
+
+ align:start position:0%
+about. That's a change we'd like to
+bring about.
+
+ align:start position:0%
+bring about.
+ 
+
+ align:start position:0%
+bring about.
+Okay. Now, here I'm telling you this is
+
+ align:start position:0%
+Okay. Now, here I'm telling you this is
+ 
+
+ align:start position:0%
+Okay. Now, here I'm telling you this is
+a preposition here, but this is a
+
+ align:start position:0%
+a preposition here, but this is a
+ 
+
+ align:start position:0%
+a preposition here, but this is a
+particle.
+
+ align:start position:0%
+particle.
+ 
+
+ align:start position:0%
+particle.
+Okay. So we put stress here, right?
+
+ align:start position:0%
+Okay. So we put stress here, right?
+ 
+
+ align:start position:0%
+Okay. So we put stress here, right?
+There's stress here. No stress here.
+
+ align:start position:0%
+There's stress here. No stress here.
+ 
+
+ align:start position:0%
+There's stress here. No stress here.
+Stress here. But there's
+
+ align:start position:0%
+Stress here. But there's
+ 
+
+ align:start position:0%
+Stress here. But there's
+one more stress here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if you say so say this
+
+ align:start position:0%
+So if you say so say this
+ 
+
+ align:start position:0%
+So if you say so say this
+and there's there's stress there's
+
+ align:start position:0%
+and there's there's stress there's
+ 
+
+ align:start position:0%
+and there's there's stress there's
+stress here definitely because these are
+
+ align:start position:0%
+stress here definitely because these are
+ 
+
+ align:start position:0%
+stress here definitely because these are
+content words.
+
+ align:start position:0%
+content words.
+ 
+
+ align:start position:0%
+content words.
+She she turned on a red light. She
+
+ align:start position:0%
+She she turned on a red light. She
+ 
+
+ align:start position:0%
+She she turned on a red light. She
+turned on a red light. She turned on a
+
+ align:start position:0%
+turned on a red light. She turned on a
+ 
+
+ align:start position:0%
+turned on a red light. She turned on a
+red light. She turned on red light. But
+
+ align:start position:0%
+red light. She turned on red light. But
+ 
+
+ align:start position:0%
+red light. She turned on red light. But
+this one, she turned on. She turned on a
+
+ align:start position:0%
+this one, she turned on. She turned on a
+ 
+
+ align:start position:0%
+this one, she turned on. She turned on a
+red light. She turned on.
+
+ align:start position:0%
+red light. She turned on.
+ 
+
+ align:start position:0%
+red light. She turned on.
+What's the difference?
+
+ align:start position:0%
+What's the difference?
+ 
+
+ align:start position:0%
+What's the difference?
+Meaning is the Okay. What's What's the
+
+ align:start position:0%
+Meaning is the Okay. What's What's the
+ 
+
+ align:start position:0%
+Meaning is the Okay. What's What's the
+meaning?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Example, if she drive car, she take a
+
+ align:start position:0%
+Example, if she drive car, she take a
+ 
+
+ align:start position:0%
+Example, if she drive car, she take a
+left on the Which one? The first one.
+
+ align:start position:0%
+left on the Which one? The first one.
+ 
+
+ align:start position:0%
+left on the Which one? The first one.
+The second one. First one. Okay. You're
+
+ align:start position:0%
+The second one. First one. Okay. You're
+ 
+
+ align:start position:0%
+The second one. First one. Okay. You're
+driving and she turned on a red light.
+
+ align:start position:0%
+driving and she turned on a red light.
+ 
+
+ align:start position:0%
+driving and she turned on a red light.
+She turned on a red light. Okay. And you
+
+ align:start position:0%
+She turned on a red light. Okay. And you
+ 
+
+ align:start position:0%
+She turned on a red light. Okay. And you
+can get a ticket. Uh, you can make a
+
+ align:start position:0%
+can get a ticket. Uh, you can make a
+ 
+
+ align:start position:0%
+can get a ticket. Uh, you can make a
+right turn on a red light, but sometimes
+
+ align:start position:0%
+right turn on a red light, but sometimes
+ 
+
+ align:start position:0%
+right turn on a red light, but sometimes
+uh in LA you can make a left. You can
+
+ align:start position:0%
+uh in LA you can make a left. You can
+ 
+
+ align:start position:0%
+uh in LA you can make a left. You can
+make a right turn on the red light
+
+ align:start position:0%
+make a right turn on the red light
+ 
+
+ align:start position:0%
+make a right turn on the red light
+anytime. But not in Boston. Not in
+
+ align:start position:0%
+anytime. But not in Boston. Not in
+ 
+
+ align:start position:0%
+anytime. But not in Boston. Not in
+Boston. Really? No turn. Yeah. No turn
+
+ align:start position:0%
+Boston. Really? No turn. Yeah. No turn
+ 
+
+ align:start position:0%
+Boston. Really? No turn. Yeah. No turn
+on. No turn on red. Yeah. There is some
+
+ align:start position:0%
+on. No turn on red. Yeah. There is some
+ 
+
+ align:start position:0%
+on. No turn on red. Yeah. There is some
+sign on land. But if there's no sign,
+
+ align:start position:0%
+sign on land. But if there's no sign,
+ 
+
+ align:start position:0%
+sign on land. But if there's no sign,
+can you can you turn on red? Okay. Okay.
+
+ align:start position:0%
+can you can you turn on red? Okay. Okay.
+ 
+
+ align:start position:0%
+can you can you turn on red? Okay. Okay.
+You can turn. Okay. In Korea, can you
+
+ align:start position:0%
+You can turn. Okay. In Korea, can you
+ 
+
+ align:start position:0%
+You can turn. Okay. In Korea, can you
+turn on the red light? Right. Right.
+
+ align:start position:0%
+turn on the red light? Right. Right.
+ 
+
+ align:start position:0%
+turn on the red light? Right. Right.
+Turn. Oh, you could do that. Oh, okay.
+
+ align:start position:0%
+Turn. Oh, you could do that. Oh, okay.
+ 
+
+ align:start position:0%
+Turn. Oh, you could do that. Oh, okay.
+This one. What does that mean?
+
+ align:start position:0%
+This one. What does that mean?
+ 
+
+ align:start position:0%
+This one. What does that mean?
+Turned on. She turned on a red light.
+
+ align:start position:0%
+Turned on. She turned on a red light.
+ 
+
+ align:start position:0%
+Turned on. She turned on a red light.
+She turned on. Okay. She turned on.
+
+ align:start position:0%
+She turned on. Okay. She turned on.
+ 
+
+ align:start position:0%
+She turned on. Okay. She turned on.
+Okay. So, so you say turn it on, right?
+
+ align:start position:0%
+Okay. So, so you say turn it on, right?
+ 
+
+ align:start position:0%
+Okay. So, so you say turn it on, right?
+Turn it on. Turn it on. Turn it on.
+
+ align:start position:0%
+Turn it on. Turn it on. Turn it on.
+ 
+
+ align:start position:0%
+Turn it on. Turn it on. Turn it on.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sometimes uh sometimes it's easy to tell
+
+ align:start position:0%
+Sometimes uh sometimes it's easy to tell
+ 
+
+ align:start position:0%
+Sometimes uh sometimes it's easy to tell
+whether
+
+ align:start position:0%
+whether
+ 
+
+ align:start position:0%
+whether
+uh whether something is a particle,
+
+ align:start position:0%
+uh whether something is a particle,
+ 
+
+ align:start position:0%
+uh whether something is a particle,
+adverbial particle or a preposition, but
+
+ align:start position:0%
+adverbial particle or a preposition, but
+ 
+
+ align:start position:0%
+adverbial particle or a preposition, but
+sometimes it's kind of hard to tell.
+
+ align:start position:0%
+sometimes it's kind of hard to tell.
+ 
+
+ align:start position:0%
+sometimes it's kind of hard to tell.
+Most of the time, not all the time, most
+
+ align:start position:0%
+Most of the time, not all the time, most
+ 
+
+ align:start position:0%
+Most of the time, not all the time, most
+of the time, if you could put uh if you
+
+ align:start position:0%
+of the time, if you could put uh if you
+ 
+
+ align:start position:0%
+of the time, if you could put uh if you
+could move the word, then it's a
+
+ align:start position:0%
+could move the word, then it's a
+ 
+
+ align:start position:0%
+could move the word, then it's a
+particle. Turn it on. Turn it on or turn
+
+ align:start position:0%
+particle. Turn it on. Turn it on or turn
+ 
+
+ align:start position:0%
+particle. Turn it on. Turn it on or turn
+on the red light. Okay, but let's talk
+
+ align:start position:0%
+on the red light. Okay, but let's talk
+ 
+
+ align:start position:0%
+on the red light. Okay, but let's talk
+about your problem. You can't say lack.
+
+ align:start position:0%
+about your problem. You can't say lack.
+ 
+
+ align:start position:0%
+about your problem. You can't say lack.
+Let's talk your problem about, right? So
+
+ align:start position:0%
+Let's talk your problem about, right? So
+ 
+
+ align:start position:0%
+Let's talk your problem about, right? So
+that's a preposition usually.
+
+ align:start position:0%
+that's a preposition usually.
+ 
+
+ align:start position:0%
+that's a preposition usually.
+Any questions about this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sentence again?
+
+ align:start position:0%
+sentence again?
+ 
+
+ align:start position:0%
+sentence again?
+She turned on. She turned in a red
+
+ align:start position:0%
+She turned on. She turned in a red
+ 
+
+ align:start position:0%
+She turned on. She turned in a red
+light. She turn there's more stress in
+
+ align:start position:0%
+light. She turn there's more stress in
+ 
+
+ align:start position:0%
+light. She turn there's more stress in
+here. She turned in a red light. But
+
+ align:start position:0%
+here. She turned in a red light. But
+ 
+
+ align:start position:0%
+here. She turned in a red light. But
+here this one gets she turned on. So the
+
+ align:start position:0%
+here this one gets she turned on. So the
+ 
+
+ align:start position:0%
+here this one gets she turned on. So the
+most important thing is here it becomes
+
+ align:start position:0%
+most important thing is here it becomes
+ 
+
+ align:start position:0%
+most important thing is here it becomes
+turned on. You don't say turn on turned
+
+ align:start position:0%
+turned on. You don't say turn on turned
+ 
+
+ align:start position:0%
+turned on. You don't say turn on turned
+on. He turned on turn. She turned on a
+
+ align:start position:0%
+on. He turned on turn. She turned on a
+ 
+
+ align:start position:0%
+on. He turned on turn. She turned on a
+red light. So the val
+
+ align:start position:0%
+red light. So the val
+ 
+
+ align:start position:0%
+red light. So the val
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+Where's my chalk?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Here.
+
+ align:start position:0%
+Here.
+ 
+
+ align:start position:0%
+Here.
+The first one would be turn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+turn done turn done turn done. The vowel
+
+ align:start position:0%
+turn done turn done turn done. The vowel
+ 
+
+ align:start position:0%
+turn done turn done turn done. The vowel
+is awah turned up because it gets
+
+ align:start position:0%
+is awah turned up because it gets
+ 
+
+ align:start position:0%
+is awah turned up because it gets
+reduced. All right. But the second one
+
+ align:start position:0%
+reduced. All right. But the second one
+ 
+
+ align:start position:0%
+reduced. All right. But the second one
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+turned on. Okay. Turned on. Turned on.
+
+ align:start position:0%
+turned on. Okay. Turned on. Turned on.
+ 
+
+ align:start position:0%
+turned on. Okay. Turned on. Turned on.
+The vowels are different. Turned on.
+
+ align:start position:0%
+The vowels are different. Turned on.
+ 
+
+ align:start position:0%
+The vowels are different. Turned on.
+Turned on. Turned on a red light. She
+
+ align:start position:0%
+Turned on. Turned on a red light. She
+ 
+
+ align:start position:0%
+Turned on. Turned on a red light. She
+turned on a red light. Turned on. On.
+
+ align:start position:0%
+turned on a red light. Turned on. On.
+ 
+
+ align:start position:0%
+turned on a red light. Turned on. On.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Today we're going to uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+try to do three things. We already
+
+ align:start position:0%
+try to do three things. We already
+ 
+
+ align:start position:0%
+try to do three things. We already
+talked about phrasal verbs and we're
+
+ align:start position:0%
+talked about phrasal verbs and we're
+ 
+
+ align:start position:0%
+talked about phrasal verbs and we're
+going to talk about we're going to
+
+ align:start position:0%
+going to talk about we're going to
+ 
+
+ align:start position:0%
+going to talk about we're going to
+discuss chapter unit 8 of our listening
+
+ align:start position:0%
+discuss chapter unit 8 of our listening
+ 
+
+ align:start position:0%
+discuss chapter unit 8 of our listening
+book.
+
+ align:start position:0%
+book.
+ 
+
+ align:start position:0%
+book.
+And then we're going to talk about
+
+ align:start position:0%
+And then we're going to talk about
+ 
+
+ align:start position:0%
+And then we're going to talk about
+sentence stress and rhythm.
+
+ align:start position:0%
+sentence stress and rhythm.
+ 
+
+ align:start position:0%
+sentence stress and rhythm.
+For homework for Thursday, I want you to
+
+ align:start position:0%
+For homework for Thursday, I want you to
+ 
+
+ align:start position:0%
+For homework for Thursday, I want you to
+read chapter nine of our textbook,
+
+ align:start position:0%
+read chapter nine of our textbook,
+ 
+
+ align:start position:0%
+read chapter nine of our textbook,
+Accurate English, okay? And do unit
+
+ align:start position:0%
+Accurate English, okay? And do unit
+ 
+
+ align:start position:0%
+Accurate English, okay? And do unit
+seven of our listening book. for that
+
+ align:start position:0%
+seven of our listening book. for that
+ 
+
+ align:start position:0%
+seven of our listening book. for that
+listening book.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh, turn to page 95. This is for
+
+ align:start position:0%
+Uh, turn to page 95. This is for
+ 
+
+ align:start position:0%
+Uh, turn to page 95. This is for
+homework. Turn to page 95.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is your book.
+
+ align:start position:0%
+This is your book.
+ 
+
+ align:start position:0%
+This is your book.
+Look at this book. Something's
+
+ align:start position:0%
+Look at this book. Something's
+ 
+
+ align:start position:0%
+Look at this book. Something's
+something's wrong here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Keep them separated.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Uh, page 95.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Page 95. Okay. You have the sentence
+
+ align:start position:0%
+Page 95. Okay. You have the sentence
+ 
+
+ align:start position:0%
+Page 95. Okay. You have the sentence
+under notice, right? Imagine if Wall
+
+ align:start position:0%
+under notice, right? Imagine if Wall
+ 
+
+ align:start position:0%
+under notice, right? Imagine if Wall
+Street. Did you find those two sentences
+
+ align:start position:0%
+Street. Did you find those two sentences
+ 
+
+ align:start position:0%
+Street. Did you find those two sentences
+starting with imagine on page 95? Yes.
+
+ align:start position:0%
+starting with imagine on page 95? Yes.
+ 
+
+ align:start position:0%
+starting with imagine on page 95? Yes.
+Yes. Everyone. Yes. Page 95. Yeah. I
+
+ align:start position:0%
+Yes. Everyone. Yes. Page 95. Yeah. I
+ 
+
+ align:start position:0%
+Yes. Everyone. Yes. Page 95. Yeah. I
+want you to take I want you to listen to
+
+ align:start position:0%
+want you to take I want you to listen to
+ 
+
+ align:start position:0%
+want you to take I want you to listen to
+that as many times as you need to. Oku.
+
+ align:start position:0%
+that as many times as you need to. Oku.
+ 
+
+ align:start position:0%
+that as many times as you need to. Oku.
+Okay. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And then I want you to
+
+ align:start position:0%
+Okay. And then I want you to
+ 
+
+ align:start position:0%
+Okay. And then I want you to
+come up with a phonetic transcription.
+
+ align:start position:0%
+come up with a phonetic transcription.
+ 
+
+ align:start position:0%
+come up with a phonetic transcription.
+Analyze the sentences, the words in
+
+ align:start position:0%
+Analyze the sentences, the words in
+ 
+
+ align:start position:0%
+Analyze the sentences, the words in
+bold. Words in bold. Okay? Especially
+
+ align:start position:0%
+bold. Words in bold. Okay? Especially
+ 
+
+ align:start position:0%
+bold. Words in bold. Okay? Especially
+going to write this here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, this is in the first sentence. The
+
+ align:start position:0%
+Okay, this is in the first sentence. The
+ 
+
+ align:start position:0%
+Okay, this is in the first sentence. The
+second in the second sentence we have.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, we have this in your in the first
+
+ align:start position:0%
+Okay, we have this in your in the first
+ 
+
+ align:start position:0%
+Okay, we have this in your in the first
+sentence, right? Listen very carefully
+
+ align:start position:0%
+sentence, right? Listen very carefully
+ 
+
+ align:start position:0%
+sentence, right? Listen very carefully
+how the speaker actually says had known.
+
+ align:start position:0%
+how the speaker actually says had known.
+ 
+
+ align:start position:0%
+how the speaker actually says had known.
+Okay, she's not going to say had known.
+
+ align:start position:0%
+Okay, she's not going to say had known.
+ 
+
+ align:start position:0%
+Okay, she's not going to say had known.
+she's gonna uh pronounce it a little
+
+ align:start position:0%
+she's gonna uh pronounce it a little
+ 
+
+ align:start position:0%
+she's gonna uh pronounce it a little
+differently because it occurs in
+
+ align:start position:0%
+differently because it occurs in
+ 
+
+ align:start position:0%
+differently because it occurs in
+irregular speech. Okay? Certain things
+
+ align:start position:0%
+irregular speech. Okay? Certain things
+ 
+
+ align:start position:0%
+irregular speech. Okay? Certain things
+get reduced.
+
+ align:start position:0%
+get reduced.
+ 
+
+ align:start position:0%
+get reduced.
+This one again, she's not going to say
+
+ align:start position:0%
+This one again, she's not going to say
+ 
+
+ align:start position:0%
+This one again, she's not going to say
+they'd have sent him. She's not going to
+
+ align:start position:0%
+they'd have sent him. She's not going to
+ 
+
+ align:start position:0%
+they'd have sent him. She's not going to
+say they have sent him. She's going to
+
+ align:start position:0%
+say they have sent him. She's going to
+ 
+
+ align:start position:0%
+say they have sent him. She's going to
+say it in a different way. She's going
+
+ align:start position:0%
+say it in a different way. She's going
+ 
+
+ align:start position:0%
+say it in a different way. She's going
+to reduce certain sounds. Okay? So, I
+
+ align:start position:0%
+to reduce certain sounds. Okay? So, I
+ 
+
+ align:start position:0%
+to reduce certain sounds. Okay? So, I
+want you to write a phonetic trans
+
+ align:start position:0%
+want you to write a phonetic trans
+ 
+
+ align:start position:0%
+want you to write a phonetic trans
+transcription of this string.
+
+ align:start position:0%
+transcription of this string.
+ 
+
+ align:start position:0%
+transcription of this string.
+You know, like
+
+ align:start position:0%
+You know, like
+ 
+
+ align:start position:0%
+You know, like
+you know they
+
+ align:start position:0%
+you know they
+ 
+
+ align:start position:0%
+you know they
+Okay. Do the linking too. Do the linking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll do that on Thursday.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Let's turn to
+
+ align:start position:0%
+Let's turn to
+ 
+
+ align:start position:0%
+Let's turn to
+any questions about the homework.
+
+ align:start position:0%
+any questions about the homework.
+ 
+
+ align:start position:0%
+any questions about the homework.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Chapter 8
+
+ align:start position:0%
+Chapter 8
+ 
+
+ align:start position:0%
+Chapter 8
+in your book.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Chapter uh let's turn to page 104 and
+
+ align:start position:0%
+Chapter uh let's turn to page 104 and
+ 
+
+ align:start position:0%
+Chapter uh let's turn to page 104 and
+105. 104 and 105.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+104 and 105. Vocabulary.
+
+ align:start position:0%
+104 and 105. Vocabulary.
+ 
+
+ align:start position:0%
+104 and 105. Vocabulary.
+Vocabulary.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. How do you say the first one?
+
+ align:start position:0%
+Okay. How do you say the first one?
+ 
+
+ align:start position:0%
+Okay. How do you say the first one?
+First word.
+
+ align:start position:0%
+First word.
+ 
+
+ align:start position:0%
+First word.
+Page 104.
+
+ align:start position:0%
+Page 104.
+ 
+
+ align:start position:0%
+Page 104.
+Huh?
+
+ align:start position:0%
+Huh?
+ 
+
+ align:start position:0%
+Huh?
+Copay. Copay. Copay. Okay. There is
+
+ align:start position:0%
+Copay. Copay. Copay. Okay. There is
+ 
+
+ align:start position:0%
+Copay. Copay. Copay. Okay. There is
+more. This is like this works like a
+
+ align:start position:0%
+more. This is like this works like a
+ 
+
+ align:start position:0%
+more. This is like this works like a
+compound. Co-ay. Two stresses. Co-ay.
+
+ align:start position:0%
+compound. Co-ay. Two stresses. Co-ay.
+ 
+
+ align:start position:0%
+compound. Co-ay. Two stresses. Co-ay.
+More stresses on the co. Co-ay. Co-ay.
+
+ align:start position:0%
+More stresses on the co. Co-ay. Co-ay.
+ 
+
+ align:start position:0%
+More stresses on the co. Co-ay. Co-ay.
+What does that mean? Anyone?
+
+ align:start position:0%
+What does that mean? Anyone?
+ 
+
+ align:start position:0%
+What does that mean? Anyone?
+Huh? Pay together. No, we have the
+
+ align:start position:0%
+Huh? Pay together. No, we have the
+ 
+
+ align:start position:0%
+Huh? Pay together. No, we have the
+definition on page 105. 105. 105. Okay.
+
+ align:start position:0%
+definition on page 105. 105. 105. Okay.
+ 
+
+ align:start position:0%
+definition on page 105. 105. 105. Okay.
+Do you know 105?
+
+ align:start position:0%
+Do you know 105?
+ 
+
+ align:start position:0%
+Do you know 105?
+Paid by Chino. Chino. Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This was homework people. Home supposed
+
+ align:start position:0%
+This was homework people. Home supposed
+ 
+
+ align:start position:0%
+This was homework people. Home supposed
+to be done at home. Okay. Who's done
+
+ align:start position:0%
+to be done at home. Okay. Who's done
+ 
+
+ align:start position:0%
+to be done at home. Okay. Who's done
+homework? Who's done this homework?
+
+ align:start position:0%
+homework? Who's done this homework?
+ 
+
+ align:start position:0%
+homework? Who's done this homework?
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Number one. Number one. Copay. I paid by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Louder.
+
+ align:start position:0%
+Louder.
+ 
+
+ align:start position:0%
+Louder.
+being paid by insured
+
+ align:start position:0%
+being paid by insured
+ 
+
+ align:start position:0%
+being paid by insured
+patients for doctor's visit. Okay.
+
+ align:start position:0%
+patients for doctor's visit. Okay.
+ 
+
+ align:start position:0%
+patients for doctor's visit. Okay.
+Insured. What's the next one?
+
+ align:start position:0%
+Insured. What's the next one?
+ 
+
+ align:start position:0%
+Insured. What's the next one?
+Patience.
+
+ align:start position:0%
+Patience.
+ 
+
+ align:start position:0%
+Patience.
+Patience. Patience. Okay. Patience.
+
+ align:start position:0%
+Patience. Patience. Okay. Patience.
+ 
+
+ align:start position:0%
+Patience. Patience. Okay. Patience.
+Patience. Okay. Number two. Number two.
+
+ align:start position:0%
+Patience. Okay. Number two. Number two.
+ 
+
+ align:start position:0%
+Patience. Okay. Number two. Number two.
+You want number two?
+
+ align:start position:0%
+You want number two?
+ 
+
+ align:start position:0%
+You want number two?
+Huh? Louder. Louder. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Insurance company. Number eight.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A oh a number number. Okay. Letter A.
+
+ align:start position:0%
+A oh a number number. Okay. Letter A.
+ 
+
+ align:start position:0%
+A oh a number number. Okay. Letter A.
+Letter A. Okay. One more time. One more
+
+ align:start position:0%
+Letter A. Okay. One more time. One more
+ 
+
+ align:start position:0%
+Letter A. Okay. One more time. One more
+time.
+
+ align:start position:0%
+time.
+ 
+
+ align:start position:0%
+time.
+1 medical provided by one insurance
+
+ align:start position:0%
+1 medical provided by one insurance
+ 
+
+ align:start position:0%
+1 medical provided by one insurance
+company.
+
+ align:start position:0%
+company.
+ 
+
+ align:start position:0%
+company.
+Main source of medical care. Provides.
+
+ align:start position:0%
+Main source of medical care. Provides.
+ 
+
+ align:start position:0%
+Main source of medical care. Provides.
+Provided. Provided. Very good. Provided
+
+ align:start position:0%
+Provided. Provided. Very good. Provided
+ 
+
+ align:start position:0%
+Provided. Provided. Very good. Provided
+everyone. Provided. Provided. Provided.
+
+ align:start position:0%
+everyone. Provided. Provided. Provided.
+ 
+
+ align:start position:0%
+everyone. Provided. Provided. Provided.
+Provided. That's very important. Having
+
+ align:start position:0%
+Provided. That's very important. Having
+ 
+
+ align:start position:0%
+Provided. That's very important. Having
+the flap. Provided. Provided. Provided.
+
+ align:start position:0%
+the flap. Provided. Provided. Provided.
+ 
+
+ align:start position:0%
+the flap. Provided. Provided. Provided.
+That's the past participle. Okay.
+
+ align:start position:0%
+That's the past participle. Okay.
+ 
+
+ align:start position:0%
+That's the past participle. Okay.
+Provided. provided.
+
+ align:start position:0%
+Provided. provided.
+ 
+
+ align:start position:0%
+Provided. provided.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Next.
+
+ align:start position:0%
+Next.
+ 
+
+ align:start position:0%
+Next.
+Next. Who
+
+ align:start position:0%
+Next. Who
+ 
+
+ align:start position:0%
+Next. Who
+who wants to do number three?
+
+ align:start position:0%
+who wants to do number three?
+ 
+
+ align:start position:0%
+who wants to do number three?
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+No. Read the read read the vocabulary
+
+ align:start position:0%
+No. Read the read read the vocabulary
+ 
+
+ align:start position:0%
+No. Read the read read the vocabulary
+word too.
+
+ align:start position:0%
+word too.
+ 
+
+ align:start position:0%
+word too.
+Huh?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. We just did this together. Now we
+
+ align:start position:0%
+Okay. We just did this together. Now we
+ 
+
+ align:start position:0%
+Okay. We just did this together. Now we
+have three words here. Among the three
+
+ align:start position:0%
+have three words here. Among the three
+ 
+
+ align:start position:0%
+have three words here. Among the three
+words, which one is going to get most
+
+ align:start position:0%
+words, which one is going to get most
+ 
+
+ align:start position:0%
+words, which one is going to get most
+stress, the strongest?
+
+ align:start position:0%
+stress, the strongest?
+ 
+
+ align:start position:0%
+stress, the strongest?
+The middle one. Up. Up. Fed up. Okay.
+
+ align:start position:0%
+The middle one. Up. Up. Fed up. Okay.
+ 
+
+ align:start position:0%
+The middle one. Up. Up. Fed up. Okay.
+Fed up with They're fed up with this
+
+ align:start position:0%
+Fed up with They're fed up with this
+ 
+
+ align:start position:0%
+Fed up with They're fed up with this
+system.
+
+ align:start position:0%
+system.
+ 
+
+ align:start position:0%
+system.
+Okay. They're fed up with the system.
+
+ align:start position:0%
+Okay. They're fed up with the system.
+ 
+
+ align:start position:0%
+Okay. They're fed up with the system.
+I'm fed up with this.
+
+ align:start position:0%
+I'm fed up with this.
+ 
+
+ align:start position:0%
+I'm fed up with this.
+I'm fed up with this. I'm fed up. Fed
+
+ align:start position:0%
+I'm fed up with this. I'm fed up. Fed
+ 
+
+ align:start position:0%
+I'm fed up with this. I'm fed up. Fed
+up. Okay. That becomes a flap. Fed up.
+
+ align:start position:0%
+up. Okay. That becomes a flap. Fed up.
+ 
+
+ align:start position:0%
+up. Okay. That becomes a flap. Fed up.
+D becomes a flap, right? Because it
+
+ align:start position:0%
+D becomes a flap, right? Because it
+ 
+
+ align:start position:0%
+D becomes a flap, right? Because it
+comes uh between two vowels. Fed up. Fed
+
+ align:start position:0%
+comes uh between two vowels. Fed up. Fed
+ 
+
+ align:start position:0%
+comes uh between two vowels. Fed up. Fed
+up.
+
+ align:start position:0%
+up.
+ 
+
+ align:start position:0%
+up.
+Fed up. Fed up. Fed up. Fed up. Okay.
+
+ align:start position:0%
+Fed up. Fed up. Fed up. Fed up. Okay.
+ 
+
+ align:start position:0%
+Fed up. Fed up. Fed up. Fed up. Okay.
+Fed up with the system. Fed up with the
+
+ align:start position:0%
+Fed up with the system. Fed up with the
+ 
+
+ align:start position:0%
+Fed up with the system. Fed up with the
+system. And the answer is
+
+ align:start position:0%
+system. And the answer is
+ 
+
+ align:start position:0%
+system. And the answer is
+huh? Tired of.
+
+ align:start position:0%
+huh? Tired of.
+ 
+
+ align:start position:0%
+huh? Tired of.
+Okay. Do the linking.
+
+ align:start position:0%
+Okay. Do the linking.
+ 
+
+ align:start position:0%
+Okay. Do the linking.
+Tired of tired. Now that that becomes a
+
+ align:start position:0%
+Tired of tired. Now that that becomes a
+ 
+
+ align:start position:0%
+Tired of tired. Now that that becomes a
+flap too. Tired of tired of tired of
+
+ align:start position:0%
+flap too. Tired of tired of tired of
+ 
+
+ align:start position:0%
+flap too. Tired of tired of tired of
+tired of tired of tired of tired of
+
+ align:start position:0%
+tired of tired of tired of tired of
+ 
+
+ align:start position:0%
+tired of tired of tired of tired of
+tired of Okay. Next. Number four.
+
+ align:start position:0%
+tired of Okay. Next. Number four.
+ 
+
+ align:start position:0%
+tired of Okay. Next. Number four.
+Number four. Ready.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Acute. Acute care.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Retha medical care for people with
+
+ align:start position:0%
+Okay. Retha medical care for people with
+ 
+
+ align:start position:0%
+Okay. Retha medical care for people with
+severe injuries or illness that may have
+
+ align:start position:0%
+severe injuries or illness that may have
+ 
+
+ align:start position:0%
+severe injuries or illness that may have
+been. Okay. Medical care for people with
+
+ align:start position:0%
+been. Okay. Medical care for people with
+ 
+
+ align:start position:0%
+been. Okay. Medical care for people with
+severe the stress is very severe severe
+
+ align:start position:0%
+severe the stress is very severe severe
+ 
+
+ align:start position:0%
+severe the stress is very severe severe
+injuries or what?
+
+ align:start position:0%
+injuries or what?
+ 
+
+ align:start position:0%
+injuries or what?
+Next one. Ill. Read the word. getting
+
+ align:start position:0%
+Next one. Ill. Read the word. getting
+ 
+
+ align:start position:0%
+Next one. Ill. Read the word. getting
+illnesses. Huh? Illnesses. Illnesses.
+
+ align:start position:0%
+illnesses. Huh? Illnesses. Illnesses.
+ 
+
+ align:start position:0%
+illnesses. Huh? Illnesses. Illnesses.
+Okay, it's a plural. Illnesses.
+
+ align:start position:0%
+Okay, it's a plural. Illnesses.
+ 
+
+ align:start position:0%
+Okay, it's a plural. Illnesses.
+Illnesses. Illnesses. Illnesses.
+
+ align:start position:0%
+Illnesses. Illnesses. Illnesses.
+ 
+
+ align:start position:0%
+Illnesses. Illnesses. Illnesses.
+Okay. Number five. Number five.
+
+ align:start position:0%
+Okay. Number five. Number five.
+ 
+
+ align:start position:0%
+Okay. Number five. Number five.
+Five.
+
+ align:start position:0%
+Five.
+ 
+
+ align:start position:0%
+Five.
+Ming.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Itemized. Huh? Itized.
+
+ align:start position:0%
+Itemized. Huh? Itized.
+ 
+
+ align:start position:0%
+Itemized. Huh? Itized.
+Itemized. Itized. T becomes a flap.
+
+ align:start position:0%
+Itemized. Itized. T becomes a flap.
+ 
+
+ align:start position:0%
+Itemized. Itized. T becomes a flap.
+Itemized. Itemized. Itemized. And the
+
+ align:start position:0%
+Itemized. Itemized. Itemized. And the
+ 
+
+ align:start position:0%
+Itemized. Itemized. Itemized. And the
+answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+With all the past.
+
+ align:start position:0%
+With all the past.
+ 
+
+ align:start position:0%
+With all the past.
+One more time. With all the parts
+
+ align:start position:0%
+One more time. With all the parts
+ 
+
+ align:start position:0%
+One more time. With all the parts
+listed.
+
+ align:start position:0%
+listed.
+ 
+
+ align:start position:0%
+listed.
+With with all. With all. Okay. Your
+
+ align:start position:0%
+With with all. With all. Okay. Your
+ 
+
+ align:start position:0%
+With with all. With all. Okay. Your
+tongue. With with all the parts listed.
+
+ align:start position:0%
+tongue. With with all the parts listed.
+ 
+
+ align:start position:0%
+tongue. With with all the parts listed.
+With all the parts. With all the parts
+
+ align:start position:0%
+With all the parts. With all the parts
+ 
+
+ align:start position:0%
+With all the parts. With all the parts
+listed. With all with all. Okay. You say
+
+ align:start position:0%
+listed. With all with all. Okay. You say
+ 
+
+ align:start position:0%
+listed. With all with all. Okay. You say
+with first with all th. Okay. With all
+
+ align:start position:0%
+with first with all th. Okay. With all
+ 
+
+ align:start position:0%
+with first with all th. Okay. With all
+with all the parts listed. With all the
+
+ align:start position:0%
+with all the parts listed. With all the
+ 
+
+ align:start position:0%
+with all the parts listed. With all the
+parts listed.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Six. Back therein.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+One more time. Very good. The answer.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Loud. Loud. Ly.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Someone
+
+ align:start position:0%
+Someone
+ 
+
+ align:start position:0%
+Someone
+comparing motor vehicles and machinery.
+
+ align:start position:0%
+comparing motor vehicles and machinery.
+ 
+
+ align:start position:0%
+comparing motor vehicles and machinery.
+Very good. Motor. Motor. That becomes a
+
+ align:start position:0%
+Very good. Motor. Motor. That becomes a
+ 
+
+ align:start position:0%
+Very good. Motor. Motor. That becomes a
+motor. Motor. Motor vehicles. Motor
+
+ align:start position:0%
+motor. Motor. Motor vehicles. Motor
+ 
+
+ align:start position:0%
+motor. Motor. Motor vehicles. Motor
+vehicles. The machinery. Machinery.
+
+ align:start position:0%
+vehicles. The machinery. Machinery.
+ 
+
+ align:start position:0%
+vehicles. The machinery. Machinery.
+Motor vehicles. Number seven. Seven is
+
+ align:start position:0%
+Motor vehicles. Number seven. Seven is
+ 
+
+ align:start position:0%
+Motor vehicles. Number seven. Seven is
+hard. Who is number seven?
+
+ align:start position:0%
+hard. Who is number seven?
+ 
+
+ align:start position:0%
+hard. Who is number seven?
+Number seven. Jan. Okay. Uh osteopath.
+
+ align:start position:0%
+Number seven. Jan. Okay. Uh osteopath.
+ 
+
+ align:start position:0%
+Number seven. Jan. Okay. Uh osteopath.
+Very good. Is uh letter see a doctor.
+
+ align:start position:0%
+Very good. Is uh letter see a doctor.
+ 
+
+ align:start position:0%
+Very good. Is uh letter see a doctor.
+Doctor who treats muscles and bones. A
+
+ align:start position:0%
+Doctor who treats muscles and bones. A
+ 
+
+ align:start position:0%
+Doctor who treats muscles and bones. A
+doctor. Doctor. Doctor becomes a
+
+ align:start position:0%
+doctor. Doctor. Doctor becomes a
+ 
+
+ align:start position:0%
+doctor. Doctor. Doctor becomes a
+unaspirated teeth. Doctor Doctor. A
+
+ align:start position:0%
+unaspirated teeth. Doctor Doctor. A
+ 
+
+ align:start position:0%
+unaspirated teeth. Doctor Doctor. A
+doctor with a doctor who treats muscles
+
+ align:start position:0%
+doctor with a doctor who treats muscles
+ 
+
+ align:start position:0%
+doctor with a doctor who treats muscles
+and bones. Okay. Osteopath. Osteopath.
+
+ align:start position:0%
+and bones. Okay. Osteopath. Osteopath.
+ 
+
+ align:start position:0%
+and bones. Okay. Osteopath. Osteopath.
+There is what? There is a primary stress
+
+ align:start position:0%
+There is what? There is a primary stress
+ 
+
+ align:start position:0%
+There is what? There is a primary stress
+on a and secondary stress and path.
+
+ align:start position:0%
+on a and secondary stress and path.
+ 
+
+ align:start position:0%
+on a and secondary stress and path.
+Osteopath.
+
+ align:start position:0%
+Osteopath.
+ 
+
+ align:start position:0%
+Osteopath.
+Osteopath. Osteopath. Okay. Eight.
+
+ align:start position:0%
+Osteopath. Osteopath. Okay. Eight.
+ 
+
+ align:start position:0%
+Osteopath. Osteopath. Okay. Eight.
+Eight.
+
+ align:start position:0%
+Eight.
+ 
+
+ align:start position:0%
+Eight.
+No. Eight. Eight. Eight.
+
+ align:start position:0%
+No. Eight. Eight. Eight.
+ 
+
+ align:start position:0%
+No. Eight. Eight. Eight.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Bruce.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Letter J. Letter what? J. J. No. J. J.
+
+ align:start position:0%
+Letter J. Letter what? J. J. No. J. J.
+ 
+
+ align:start position:0%
+Letter J. Letter what? J. J. No. J. J.
+J.
+
+ align:start position:0%
+J.
+ 
+
+ align:start position:0%
+J.
+J. J. Lip routing. J J. Okay. J. The
+
+ align:start position:0%
+J. J. Lip routing. J J. Okay. J. The
+ 
+
+ align:start position:0%
+J. J. Lip routing. J J. Okay. J. The
+answer
+
+ align:start position:0%
+answer
+ 
+
+ align:start position:0%
+answer
+purple or brown marks mark on your on
+
+ align:start position:0%
+purple or brown marks mark on your on
+ 
+
+ align:start position:0%
+purple or brown marks mark on your on
+your skin from a hole or heat. Okay.
+
+ align:start position:0%
+your skin from a hole or heat. Okay.
+ 
+
+ align:start position:0%
+your skin from a hole or heat. Okay.
+Purple or brown mark on mark on your
+
+ align:start position:0%
+Purple or brown mark on mark on your
+ 
+
+ align:start position:0%
+Purple or brown mark on mark on your
+mark
+
+ align:start position:0%
+mark
+ 
+
+ align:start position:0%
+mark
+on your skin. Mark mark on your skin.
+
+ align:start position:0%
+on your skin. Mark mark on your skin.
+ 
+
+ align:start position:0%
+on your skin. Mark mark on your skin.
+Okay. Lincoln. Do the Lincoln. Mark on
+
+ align:start position:0%
+Okay. Lincoln. Do the Lincoln. Mark on
+ 
+
+ align:start position:0%
+Okay. Lincoln. Do the Lincoln. Mark on
+your skin. Mark on your skin. Mark
+
+ align:start position:0%
+your skin. Mark on your skin. Mark
+ 
+
+ align:start position:0%
+your skin. Mark on your skin. Mark
+on your skin. Mark on your skin. Mark on
+
+ align:start position:0%
+on your skin. Mark on your skin. Mark on
+ 
+
+ align:start position:0%
+on your skin. Mark on your skin. Mark on
+your skin. Mark on your skin. Okay.
+
+ align:start position:0%
+your skin. Mark on your skin. Okay.
+ 
+
+ align:start position:0%
+your skin. Mark on your skin. Okay.
+Nine.
+
+ align:start position:0%
+Nine.
+ 
+
+ align:start position:0%
+Nine.
+Nine.
+
+ align:start position:0%
+Nine.
+ 
+
+ align:start position:0%
+Nine.
+Nine.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh,
+
+ align:start position:0%
+Oh,
+ 
+
+ align:start position:0%
+Oh,
+suitor. Okay, that's actually that's a
+
+ align:start position:0%
+suitor. Okay, that's actually that's a
+ 
+
+ align:start position:0%
+suitor. Okay, that's actually that's a
+good good guess. Good guess. Very. Now
+
+ align:start position:0%
+good good guess. Good guess. Very. Now
+ 
+
+ align:start position:0%
+good good guess. Good guess. Very. Now
+I'm really happy that you said suitor
+
+ align:start position:0%
+I'm really happy that you said suitor
+ 
+
+ align:start position:0%
+I'm really happy that you said suitor
+because he's actually applying the rule
+
+ align:start position:0%
+because he's actually applying the rule
+ 
+
+ align:start position:0%
+because he's actually applying the rule
+that we learned in class. T becomes two
+
+ align:start position:0%
+that we learned in class. T becomes two
+ 
+
+ align:start position:0%
+that we learned in class. T becomes two
+T between two vowels to become suitor.
+
+ align:start position:0%
+T between two vowels to become suitor.
+ 
+
+ align:start position:0%
+T between two vowels to become suitor.
+But you should have looked it up in the
+
+ align:start position:0%
+But you should have looked it up in the
+ 
+
+ align:start position:0%
+But you should have looked it up in the
+dictionary. Okay, I look it up. Okay,
+
+ align:start position:0%
+dictionary. Okay, I look it up. Okay,
+ 
+
+ align:start position:0%
+dictionary. Okay, I look it up. Okay,
+suture tray. Very good. Suture suture
+
+ align:start position:0%
+suture tray. Very good. Suture suture
+ 
+
+ align:start position:0%
+suture tray. Very good. Suture suture
+trade. The answer is letter. Letter E.
+
+ align:start position:0%
+trade. The answer is letter. Letter E.
+ 
+
+ align:start position:0%
+trade. The answer is letter. Letter E.
+Trade with material for sewing a wound.
+
+ align:start position:0%
+Trade with material for sewing a wound.
+ 
+
+ align:start position:0%
+Trade with material for sewing a wound.
+Very good. Sewing a wound.
+
+ align:start position:0%
+Very good. Sewing a wound.
+ 
+
+ align:start position:0%
+Very good. Sewing a wound.
+10. 10.
+
+ align:start position:0%
+10. 10.
+ 
+
+ align:start position:0%
+10. 10.
+sterilized.
+
+ align:start position:0%
+sterilized.
+ 
+
+ align:start position:0%
+sterilized.
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+K completely clean from any bacteria.
+
+ align:start position:0%
+K completely clean from any bacteria.
+ 
+
+ align:start position:0%
+K completely clean from any bacteria.
+One more time. Completely clean from any
+
+ align:start position:0%
+One more time. Completely clean from any
+ 
+
+ align:start position:0%
+One more time. Completely clean from any
+bacteria. Bacteria. Bacteria. Bacteria.
+
+ align:start position:0%
+bacteria. Bacteria. Bacteria. Bacteria.
+ 
+
+ align:start position:0%
+bacteria. Bacteria. Bacteria. Bacteria.
+Bacteria. Okay. Uh 11. Teddy.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+There
+
+ align:start position:0%
+There
+ 
+
+ align:start position:0%
+There
+action of giving through a leader.
+
+ align:start position:0%
+action of giving through a leader.
+ 
+
+ align:start position:0%
+action of giving through a leader.
+Okay, one more time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The act the act of giving a
+
+ align:start position:0%
+The act the act of giving a
+ 
+
+ align:start position:0%
+The act the act of giving a
+su
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through through through a needle through
+
+ align:start position:0%
+through through through a needle through
+ 
+
+ align:start position:0%
+through through through a needle through
+a needle through a needle needle needle.
+
+ align:start position:0%
+a needle through a needle needle needle.
+ 
+
+ align:start position:0%
+a needle through a needle needle needle.
+The D becomes a flap too. Needle.
+
+ align:start position:0%
+The D becomes a flap too. Needle.
+ 
+
+ align:start position:0%
+The D becomes a flap too. Needle.
+Needle. Needle. Needle. Through a
+
+ align:start position:0%
+Needle. Needle. Needle. Through a
+ 
+
+ align:start position:0%
+Needle. Needle. Needle. Through a
+needle. Needle. Needle. Through a
+
+ align:start position:0%
+needle. Needle. Needle. Through a
+ 
+
+ align:start position:0%
+needle. Needle. Needle. Through a
+needle. Needle. Needle. Okay.
+
+ align:start position:0%
+needle. Needle. Needle. Okay.
+ 
+
+ align:start position:0%
+needle. Needle. Needle. Okay.
+12.
+
+ align:start position:0%
+12.
+ 
+
+ align:start position:0%
+12.
+Huh?
+
+ align:start position:0%
+Huh?
+ 
+
+ align:start position:0%
+Huh?
+One more time. Anest.
+
+ align:start position:0%
+One more time. Anest.
+ 
+
+ align:start position:0%
+One more time. Anest.
+Uh, anest. Anest. Don't forget the s.
+
+ align:start position:0%
+Uh, anest. Anest. Don't forget the s.
+ 
+
+ align:start position:0%
+Uh, anest. Anest. Don't forget the s.
+Anestize.
+
+ align:start position:0%
+Anestize.
+ 
+
+ align:start position:0%
+Anestize.
+Anesize.
+
+ align:start position:0%
+Anesize.
+ 
+
+ align:start position:0%
+Anesize.
+Anestize. Anesize. Okay. Here. I I I I
+
+ align:start position:0%
+Anestize. Anesize. Okay. Here. I I I I
+ 
+
+ align:start position:0%
+Anestize. Anesize. Okay. Here. I I I I
+told you this before, right? When when
+
+ align:start position:0%
+told you this before, right? When when
+ 
+
+ align:start position:0%
+told you this before, right? When when
+you have s and th together, it's very
+
+ align:start position:0%
+you have s and th together, it's very
+ 
+
+ align:start position:0%
+you have s and th together, it's very
+difficult to go from anesthetize. Anest
+
+ align:start position:0%
+difficult to go from anesthetize. Anest
+ 
+
+ align:start position:0%
+difficult to go from anesthetize. Anest
+I can do it. Anesthetize. Anest anest.
+
+ align:start position:0%
+I can do it. Anesthetize. Anest anest.
+ 
+
+ align:start position:0%
+I can do it. Anesthetize. Anest anest.
+Usually I I I say it like a d. Anest
+
+ align:start position:0%
+Usually I I I say it like a d. Anest
+ 
+
+ align:start position:0%
+Usually I I I say it like a d. Anest
+when n th the when they come together I
+
+ align:start position:0%
+when n th the when they come together I
+ 
+
+ align:start position:0%
+when n th the when they come together I
+say it like anestize. I don't try to put
+
+ align:start position:0%
+say it like anestize. I don't try to put
+ 
+
+ align:start position:0%
+say it like anestize. I don't try to put
+my tongue between my teeth because it's
+
+ align:start position:0%
+my tongue between my teeth because it's
+ 
+
+ align:start position:0%
+my tongue between my teeth because it's
+too it's too hard. I say anesthetize.
+
+ align:start position:0%
+too it's too hard. I say anesthetize.
+ 
+
+ align:start position:0%
+too it's too hard. I say anesthetize.
+Anesthetize. Okay. The answer
+
+ align:start position:0%
+Anesthetize. Okay. The answer
+ 
+
+ align:start position:0%
+Anesthetize. Okay. The answer
+give a drop to stop a person from
+
+ align:start position:0%
+give a drop to stop a person from
+ 
+
+ align:start position:0%
+give a drop to stop a person from
+feeling pain. Okay, that was a very
+
+ align:start position:0%
+feeling pain. Okay, that was a very
+ 
+
+ align:start position:0%
+feeling pain. Okay, that was a very
+confident answer cuz there's only one
+
+ align:start position:0%
+confident answer cuz there's only one
+ 
+
+ align:start position:0%
+confident answer cuz there's only one
+left.
+
+ align:start position:0%
+left.
+ 
+
+ align:start position:0%
+left.
+Okay, any questions about the
+
+ align:start position:0%
+Okay, any questions about the
+ 
+
+ align:start position:0%
+Okay, any questions about the
+vocabulary?
+
+ align:start position:0%
+vocabulary?
+ 
+
+ align:start position:0%
+vocabulary?
+Any questions? No. Okay, I'll play uh
+
+ align:start position:0%
+Any questions? No. Okay, I'll play uh
+ 
+
+ align:start position:0%
+Any questions? No. Okay, I'll play uh
+the whole interview once.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Subract eight.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+At the end, what do you say? We're going
+
+ align:start position:0%
+At the end, what do you say? We're going
+ 
+
+ align:start position:0%
+At the end, what do you say? We're going
+to let you get back to. We're going to
+
+ align:start position:0%
+to let you get back to. We're going to
+ 
+
+ align:start position:0%
+to let you get back to. We're going to
+let you get back. Get back to. That's
+
+ align:start position:0%
+let you get back. Get back to. That's
+ 
+
+ align:start position:0%
+let you get back. Get back to. That's
+again, back is an adverbial
+
+ align:start position:0%
+again, back is an adverbial
+ 
+
+ align:start position:0%
+again, back is an adverbial
+particle. So, that gets more stressed.
+
+ align:start position:0%
+particle. So, that gets more stressed.
+ 
+
+ align:start position:0%
+particle. So, that gets more stressed.
+We're going to let you get back to
+
+ align:start position:0%
+We're going to let you get back to
+ 
+
+ align:start position:0%
+We're going to let you get back to
+practicing more productive medicine.
+
+ align:start position:0%
+practicing more productive medicine.
+ 
+
+ align:start position:0%
+practicing more productive medicine.
+Okay. When you get off the phone, you
+
+ align:start position:0%
+Okay. When you get off the phone, you
+ 
+
+ align:start position:0%
+Okay. When you get off the phone, you
+talk to your friends, you say, "Okay,
+
+ align:start position:0%
+talk to your friends, you say, "Okay,
+ 
+
+ align:start position:0%
+talk to your friends, you say, "Okay,
+I'm going to let you get back to your
+
+ align:start position:0%
+I'm going to let you get back to your
+ 
+
+ align:start position:0%
+I'm going to let you get back to your
+studies." Okay? you talk to your uh I
+
+ align:start position:0%
+studies." Okay? you talk to your uh I
+ 
+
+ align:start position:0%
+studies." Okay? you talk to your uh I
+don't know your office mate and then you
+
+ align:start position:0%
+don't know your office mate and then you
+ 
+
+ align:start position:0%
+don't know your office mate and then you
+okay I'll let you get back to your work
+
+ align:start position:0%
+okay I'll let you get back to your work
+ 
+
+ align:start position:0%
+okay I'll let you get back to your work
+I'll let you get back I'll let you I
+
+ align:start position:0%
+I'll let you get back I'll let you I
+ 
+
+ align:start position:0%
+I'll let you get back I'll let you I
+mean it's an interesting phrase right
+
+ align:start position:0%
+mean it's an interesting phrase right
+ 
+
+ align:start position:0%
+mean it's an interesting phrase right
+I'll let you get let it's like giving
+
+ align:start position:0%
+I'll let you get let it's like giving
+ 
+
+ align:start position:0%
+I'll let you get let it's like giving
+permission right but we just say it I'll
+
+ align:start position:0%
+permission right but we just say it I'll
+ 
+
+ align:start position:0%
+permission right but we just say it I'll
+let you get back I'll let you get back
+
+ align:start position:0%
+let you get back I'll let you get back
+ 
+
+ align:start position:0%
+let you get back I'll let you get back
+to your work okay I'll let you get back
+
+ align:start position:0%
+to your work okay I'll let you get back
+ 
+
+ align:start position:0%
+to your work okay I'll let you get back
+I'll let you get back okay this word how
+
+ align:start position:0%
+I'll let you get back okay this word how
+ 
+
+ align:start position:0%
+I'll let you get back okay this word how
+do you say this what's the verb this is
+
+ align:start position:0%
+do you say this what's the verb this is
+ 
+
+ align:start position:0%
+do you say this what's the verb this is
+an adjective right what's the verb form
+
+ align:start position:0%
+an adjective right what's the verb form
+ 
+
+ align:start position:0%
+an adjective right what's the verb form
+Compare. Compare, right? Compare. Verb
+
+ align:start position:0%
+Compare. Compare, right? Compare. Verb
+ 
+
+ align:start position:0%
+Compare. Compare, right? Compare. Verb
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+Where's the stress? Compare. Right.
+
+ align:start position:0%
+Where's the stress? Compare. Right.
+ 
+
+ align:start position:0%
+Where's the stress? Compare. Right.
+Okay. This is an adjective.
+
+ align:start position:0%
+Okay. This is an adjective.
+ 
+
+ align:start position:0%
+Okay. This is an adjective.
+Now, how do you say this? Comparable.
+
+ align:start position:0%
+Now, how do you say this? Comparable.
+ 
+
+ align:start position:0%
+Now, how do you say this? Comparable.
+Comparable. Comparable.
+
+ align:start position:0%
+Comparable. Comparable.
+ 
+
+ align:start position:0%
+Comparable. Comparable.
+Comparable.
+
+ align:start position:0%
+Comparable.
+ 
+
+ align:start position:0%
+Comparable.
+No.
+
+ align:start position:0%
+No.
+ 
+
+ align:start position:0%
+No.
+No, it's not comparable. She said in the
+
+ align:start position:0%
+No, it's not comparable. She said in the
+ 
+
+ align:start position:0%
+No, it's not comparable. She said in the
+interview,
+
+ align:start position:0%
+interview,
+ 
+
+ align:start position:0%
+interview,
+okay, stress is here. uncomfortable. So
+
+ align:start position:0%
+okay, stress is here. uncomfortable. So
+ 
+
+ align:start position:0%
+okay, stress is here. uncomfortable. So
+you say
+
+ align:start position:0%
+you say
+ 
+
+ align:start position:0%
+you say
+stress is here
+
+ align:start position:0%
+stress is here
+ 
+
+ align:start position:0%
+stress is here
+comparable
+
+ align:start position:0%
+comparable
+ 
+
+ align:start position:0%
+comparable
+comparable. Okay. Comparable.
+
+ align:start position:0%
+comparable. Okay. Comparable.
+ 
+
+ align:start position:0%
+comparable. Okay. Comparable.
+Okay. Comparable.
+
+ align:start position:0%
+Okay. Comparable.
+ 
+
+ align:start position:0%
+Okay. Comparable.
+Here stress is here. Compare.
+
+ align:start position:0%
+Here stress is here. Compare.
+ 
+
+ align:start position:0%
+Here stress is here. Compare.
+Well, it's here. I mean compare.
+
+ align:start position:0%
+Well, it's here. I mean compare.
+ 
+
+ align:start position:0%
+Well, it's here. I mean compare.
+Compare. Does anyone say compare? I mean
+
+ align:start position:0%
+Compare. Does anyone say compare? I mean
+ 
+
+ align:start position:0%
+Compare. Does anyone say compare? I mean
+because I I have a California accent.
+
+ align:start position:0%
+because I I have a California accent.
+ 
+
+ align:start position:0%
+because I I have a California accent.
+After R. Before R, everything is E.
+
+ align:start position:0%
+After R. Before R, everything is E.
+ 
+
+ align:start position:0%
+After R. Before R, everything is E.
+It's compare. But here since stress is
+
+ align:start position:0%
+It's compare. But here since stress is
+ 
+
+ align:start position:0%
+It's compare. But here since stress is
+on the first syllable, it becomes Oh,
+
+ align:start position:0%
+on the first syllable, it becomes Oh,
+ 
+
+ align:start position:0%
+on the first syllable, it becomes Oh,
+okay. Comparable. Comparable.
+
+ align:start position:0%
+okay. Comparable. Comparable.
+ 
+
+ align:start position:0%
+okay. Comparable. Comparable.
+Comparable. Comparable. Comparable.
+
+ align:start position:0%
+Comparable. Comparable. Comparable.
+ 
+
+ align:start position:0%
+Comparable. Comparable. Comparable.
+About the same. They're comparable.
+
+ align:start position:0%
+About the same. They're comparable.
+ 
+
+ align:start position:0%
+About the same. They're comparable.
+About the same. They can be compared.
+
+ align:start position:0%
+About the same. They can be compared.
+ 
+
+ align:start position:0%
+About the same. They can be compared.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+There's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in my dialect in in California English.
+
+ align:start position:0%
+in my dialect in in California English.
+ 
+
+ align:start position:0%
+in my dialect in in California English.
+Okay. So
+
+ align:start position:0%
+Okay. So
+ 
+
+ align:start position:0%
+Okay. So
+we we talked about this, right? Mary
+
+ align:start position:0%
+we we talked about this, right? Mary
+ 
+
+ align:start position:0%
+we we talked about this, right? Mary
+Mary
+
+ align:start position:0%
+Mary
+ 
+
+ align:start position:0%
+Mary
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+what what else is there? Oh, M A R R Y.
+
+ align:start position:0%
+what what else is there? Oh, M A R R Y.
+ 
+
+ align:start position:0%
+what what else is there? Oh, M A R R Y.
+Right here in in my English, California
+
+ align:start position:0%
+Right here in in my English, California
+ 
+
+ align:start position:0%
+Right here in in my English, California
+English, everything is E. Mary, Mary,
+
+ align:start position:0%
+English, everything is E. Mary, Mary,
+ 
+
+ align:start position:0%
+English, everything is E. Mary, Mary,
+Mary. Okay. But my friend from New
+
+ align:start position:0%
+Mary. Okay. But my friend from New
+ 
+
+ align:start position:0%
+Mary. Okay. But my friend from New
+Jersey, he says
+
+ align:start position:0%
+Jersey, he says
+ 
+
+ align:start position:0%
+Jersey, he says
+my name is Barry. Barry. Barry. Barry.
+
+ align:start position:0%
+my name is Barry. Barry. Barry. Barry.
+ 
+
+ align:start position:0%
+my name is Barry. Barry. Barry. Barry.
+That sounds that sounds horrible to me.
+
+ align:start position:0%
+That sounds that sounds horrible to me.
+ 
+
+ align:start position:0%
+That sounds that sounds horrible to me.
+Okay. As they would say here, I say
+
+ align:start position:0%
+Okay. As they would say here, I say
+ 
+
+ align:start position:0%
+Okay. As they would say here, I say
+horrible. What people say horrible here.
+
+ align:start position:0%
+horrible. What people say horrible here.
+ 
+
+ align:start position:0%
+horrible. What people say horrible here.
+Here. Now, we heard this phrase in the
+
+ align:start position:0%
+Here. Now, we heard this phrase in the
+ 
+
+ align:start position:0%
+Here. Now, we heard this phrase in the
+interview.
+
+ align:start position:0%
+interview.
+ 
+
+ align:start position:0%
+interview.
+What does that mean? Start a business.
+
+ align:start position:0%
+What does that mean? Start a business.
+ 
+
+ align:start position:0%
+What does that mean? Start a business.
+Huh? Start a business. Start start a
+
+ align:start position:0%
+Huh? Start a business. Start start a
+ 
+
+ align:start position:0%
+Huh? Start a business. Start start a
+business as a lawyer or a doctor. Okay.
+
+ align:start position:0%
+business as a lawyer or a doctor. Okay.
+ 
+
+ align:start position:0%
+business as a lawyer or a doctor. Okay.
+Start a business as a lawyer or doctor.
+
+ align:start position:0%
+Start a business as a lawyer or doctor.
+ 
+
+ align:start position:0%
+Start a business as a lawyer or doctor.
+Any Yes. Usually
+
+ align:start position:0%
+Any Yes. Usually
+ 
+
+ align:start position:0%
+Any Yes. Usually
+originally Yes. It was either a lawyer
+
+ align:start position:0%
+originally Yes. It was either a lawyer
+ 
+
+ align:start position:0%
+originally Yes. It was either a lawyer
+at first lawyer and then doctor, but now
+
+ align:start position:0%
+at first lawyer and then doctor, but now
+ 
+
+ align:start position:0%
+at first lawyer and then doctor, but now
+it's it means just any business. Any
+
+ align:start position:0%
+it's it means just any business. Any
+ 
+
+ align:start position:0%
+it's it means just any business. Any
+business.
+
+ align:start position:0%
+business.
+ 
+
+ align:start position:0%
+business.
+What's a shingle?
+
+ align:start position:0%
+What's a shingle?
+ 
+
+ align:start position:0%
+What's a shingle?
+Shingle. It's it's a sign board. It's a
+
+ align:start position:0%
+Shingle. It's it's a sign board. It's a
+ 
+
+ align:start position:0%
+Shingle. It's it's a sign board. It's a
+piece of wood. Okay. It's actually
+
+ align:start position:0%
+piece of wood. Okay. It's actually
+ 
+
+ align:start position:0%
+piece of wood. Okay. It's actually
+literally roof. Roof on the rooftop. Uh
+
+ align:start position:0%
+literally roof. Roof on the rooftop. Uh
+ 
+
+ align:start position:0%
+literally roof. Roof on the rooftop. Uh
+it's but here it means you the piece of
+
+ align:start position:0%
+it's but here it means you the piece of
+ 
+
+ align:start position:0%
+it's but here it means you the piece of
+wood that you use as a small signboard.
+
+ align:start position:0%
+wood that you use as a small signboard.
+ 
+
+ align:start position:0%
+wood that you use as a small signboard.
+It's my office. Okay. Hung out. So
+
+ align:start position:0%
+It's my office. Okay. Hung out. So
+ 
+
+ align:start position:0%
+It's my office. Okay. Hung out. So
+hung out hung out becomes here becomes a
+
+ align:start position:0%
+hung out hung out becomes here becomes a
+ 
+
+ align:start position:0%
+hung out hung out becomes here becomes a
+flap. Hang out a sink shingle.
+
+ align:start position:0%
+flap. Hang out a sink shingle.
+ 
+
+ align:start position:0%
+flap. Hang out a sink shingle.
+H
+
+ align:start position:0%
+H
+ 
+
+ align:start position:0%
+H
+out a shingle.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now let's turn to page 110.
+
+ align:start position:0%
+Now let's turn to page 110.
+ 
+
+ align:start position:0%
+Now let's turn to page 110.
+Page 110
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+looking at language usage present unreal
+
+ align:start position:0%
+looking at language usage present unreal
+ 
+
+ align:start position:0%
+looking at language usage present unreal
+versus future real conditions.
+
+ align:start position:0%
+versus future real conditions.
+ 
+
+ align:start position:0%
+versus future real conditions.
+Okay, here in this book they say present
+
+ align:start position:0%
+Okay, here in this book they say present
+ 
+
+ align:start position:0%
+Okay, here in this book they say present
+unreal.
+
+ align:start position:0%
+unreal.
+ 
+
+ align:start position:0%
+unreal.
+So it's but it's more like future
+
+ align:start position:0%
+So it's but it's more like future
+ 
+
+ align:start position:0%
+So it's but it's more like future
+hypothetical. We we we kind of did this
+
+ align:start position:0%
+hypothetical. We we we kind of did this
+ 
+
+ align:start position:0%
+hypothetical. We we we kind of did this
+when we talked about uh unit 10,
+
+ align:start position:0%
+when we talked about uh unit 10,
+ 
+
+ align:start position:0%
+when we talked about uh unit 10,
+remember?
+
+ align:start position:0%
+remember?
+ 
+
+ align:start position:0%
+remember?
+Do you have
+
+ align:start position:0%
+Do you have
+ 
+
+ align:start position:0%
+Do you have
+Do you have a car?
+
+ align:start position:0%
+Do you have a car?
+ 
+
+ align:start position:0%
+Do you have a car?
+If no. Say no. No. If I had a car, I
+
+ align:start position:0%
+If no. Say no. No. If I had a car, I
+ 
+
+ align:start position:0%
+If no. Say no. No. If I had a car, I
+would be here. Yeah.
+
+ align:start position:0%
+would be here. Yeah.
+ 
+
+ align:start position:0%
+would be here. Yeah.
+Okay. One more time. Do you have a car?
+
+ align:start position:0%
+Okay. One more time. Do you have a car?
+ 
+
+ align:start position:0%
+Okay. One more time. Do you have a car?
+No. If I had a car. Had a If I had a
+
+ align:start position:0%
+No. If I had a car. Had a If I had a
+ 
+
+ align:start position:0%
+No. If I had a car. Had a If I had a
+swap. If I had a car, if I had a car, if
+
+ align:start position:0%
+swap. If I had a car, if I had a car, if
+ 
+
+ align:start position:0%
+swap. If I had a car, if I had a car, if
+I had a car, if I had a car, I wouldn't
+
+ align:start position:0%
+I had a car, if I had a car, I wouldn't
+ 
+
+ align:start position:0%
+I had a car, if I had a car, I wouldn't
+be here. You I wouldn't wouldn't
+
+ align:start position:0%
+be here. You I wouldn't wouldn't
+ 
+
+ align:start position:0%
+be here. You I wouldn't wouldn't
+wouldn't. That becomes a flap. Wouldn't
+
+ align:start position:0%
+wouldn't. That becomes a flap. Wouldn't
+ 
+
+ align:start position:0%
+wouldn't. That becomes a flap. Wouldn't
+be here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Why not? Why not?
+
+ align:start position:0%
+Why not? Why not?
+ 
+
+ align:start position:0%
+Why not? Why not?
+Sigh. Ty, Ty, do you have a girlfriend?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+No. I don't want you to answer the
+
+ align:start position:0%
+No. I don't want you to answer the
+ 
+
+ align:start position:0%
+No. I don't want you to answer the
+question factually, okay? Every answer
+
+ align:start position:0%
+question factually, okay? Every answer
+ 
+
+ align:start position:0%
+question factually, okay? Every answer
+starts with no if I did. Okay. No. If I
+
+ align:start position:0%
+starts with no if I did. Okay. No. If I
+ 
+
+ align:start position:0%
+starts with no if I did. Okay. No. If I
+did, I wouldn't be here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I mean, what does having a car having a
+
+ align:start position:0%
+I mean, what does having a car having a
+ 
+
+ align:start position:0%
+I mean, what does having a car having a
+girlfriend coming have have to do with
+
+ align:start position:0%
+girlfriend coming have have to do with
+ 
+
+ align:start position:0%
+girlfriend coming have have to do with
+come to class? Coming to class makes no
+
+ align:start position:0%
+come to class? Coming to class makes no
+ 
+
+ align:start position:0%
+come to class? Coming to class makes no
+sense. Okay. So,
+
+ align:start position:0%
+sense. Okay. So,
+ 
+
+ align:start position:0%
+sense. Okay. So,
+now that's that that's uh that's present
+
+ align:start position:0%
+now that's that that's uh that's present
+ 
+
+ align:start position:0%
+now that's that that's uh that's present
+unreal. Okay. Because you don't have a
+
+ align:start position:0%
+unreal. Okay. Because you don't have a
+ 
+
+ align:start position:0%
+unreal. Okay. Because you don't have a
+car. You're going to have a girlfriend
+
+ align:start position:0%
+car. You're going to have a girlfriend
+ 
+
+ align:start position:0%
+car. You're going to have a girlfriend
+right now. Okay. And present on me is
+
+ align:start position:0%
+right now. Okay. And present on me is
+ 
+
+ align:start position:0%
+right now. Okay. And present on me is
+something like
+
+ align:start position:0%
+something like
+ 
+
+ align:start position:0%
+something like
+something like if I were Spider-Man, if
+
+ align:start position:0%
+something like if I were Spider-Man, if
+ 
+
+ align:start position:0%
+something like if I were Spider-Man, if
+I were Spider-Man, I'm not Spider-Man,
+
+ align:start position:0%
+I were Spider-Man, I'm not Spider-Man,
+ 
+
+ align:start position:0%
+I were Spider-Man, I'm not Spider-Man,
+right? If I were Spider-Man, I wouldn't
+
+ align:start position:0%
+right? If I were Spider-Man, I wouldn't
+ 
+
+ align:start position:0%
+right? If I were Spider-Man, I wouldn't
+be living in Boston. Where would I have
+
+ align:start position:0%
+be living in Boston. Where would I have
+ 
+
+ align:start position:0%
+be living in Boston. Where would I have
+to live? York. New York. Okay. If I were
+
+ align:start position:0%
+to live? York. New York. Okay. If I were
+ 
+
+ align:start position:0%
+to live? York. New York. Okay. If I were
+Spider-Man, uh, I would be I would be
+
+ align:start position:0%
+Spider-Man, uh, I would be I would be
+ 
+
+ align:start position:0%
+Spider-Man, uh, I would be I would be
+living in New York. All right. That's
+
+ align:start position:0%
+living in New York. All right. That's
+ 
+
+ align:start position:0%
+living in New York. All right. That's
+that's um present unreal. But here what
+
+ align:start position:0%
+that's um present unreal. But here what
+ 
+
+ align:start position:0%
+that's um present unreal. But here what
+we have actually is future hypothetical.
+
+ align:start position:0%
+we have actually is future hypothetical.
+ 
+
+ align:start position:0%
+we have actually is future hypothetical.
+It's a little different. I mean because
+
+ align:start position:0%
+It's a little different. I mean because
+ 
+
+ align:start position:0%
+It's a little different. I mean because
+it's something that could happen. So if
+
+ align:start position:0%
+it's something that could happen. So if
+ 
+
+ align:start position:0%
+it's something that could happen. So if
+you look at I'll play this segment
+
+ align:start position:0%
+you look at I'll play this segment
+ 
+
+ align:start position:0%
+you look at I'll play this segment
+page 110.
+
+ align:start position:0%
+page 110.
+ 
+
+ align:start position:0%
+page 110.
+Okay. So point of this section is let's
+
+ align:start position:0%
+Okay. So point of this section is let's
+ 
+
+ align:start position:0%
+Okay. So point of this section is let's
+say I went in went in with went in
+
+ align:start position:0%
+say I went in went in with went in
+ 
+
+ align:start position:0%
+say I went in went in with went in
+again. Went in went in there more stress
+
+ align:start position:0%
+again. Went in went in there more stress
+ 
+
+ align:start position:0%
+again. Went in went in there more stress
+than went in. Went in with went in went
+
+ align:start position:0%
+than went in. Went in with went in went
+ 
+
+ align:start position:0%
+than went in. Went in with went in went
+in with. Okay. went in with let's say I
+
+ align:start position:0%
+in with. Okay. went in with let's say I
+ 
+
+ align:start position:0%
+in with. Okay. went in with let's say I
+went in with, you know, a bruise or a
+
+ align:start position:0%
+went in with, you know, a bruise or a
+ 
+
+ align:start position:0%
+went in with, you know, a bruise or a
+cut and you had to bandage me up. Had
+
+ align:start position:0%
+cut and you had to bandage me up. Had
+ 
+
+ align:start position:0%
+cut and you had to bandage me up. Had
+to. I mean, that's strange, right? Why
+
+ align:start position:0%
+to. I mean, that's strange, right? Why
+ 
+
+ align:start position:0%
+to. I mean, that's strange, right? Why
+do you use a past tense verb here?
+
+ align:start position:0%
+do you use a past tense verb here?
+ 
+
+ align:start position:0%
+do you use a past tense verb here?
+That's because
+
+ align:start position:0%
+That's because
+ 
+
+ align:start position:0%
+That's because
+let's say we're talking about unreal.
+
+ align:start position:0%
+let's say we're talking about unreal.
+ 
+
+ align:start position:0%
+let's say we're talking about unreal.
+Not this is not real hypothetical
+
+ align:start position:0%
+Not this is not real hypothetical
+ 
+
+ align:start position:0%
+Not this is not real hypothetical
+situation. This is something that could
+
+ align:start position:0%
+situation. This is something that could
+ 
+
+ align:start position:0%
+situation. This is something that could
+happen, right?
+
+ align:start position:0%
+happen, right?
+ 
+
+ align:start position:0%
+happen, right?
+Unreal present is something like you
+
+ align:start position:0%
+Unreal present is something like you
+ 
+
+ align:start position:0%
+Unreal present is something like you
+don't have a car, but if I did have a
+
+ align:start position:0%
+don't have a car, but if I did have a
+ 
+
+ align:start position:0%
+don't have a car, but if I did have a
+car, that's unreal. Okay, I'm not
+
+ align:start position:0%
+car, that's unreal. Okay, I'm not
+ 
+
+ align:start position:0%
+car, that's unreal. Okay, I'm not
+Spider-Man. If I were Spider-Man, that's
+
+ align:start position:0%
+Spider-Man. If I were Spider-Man, that's
+ 
+
+ align:start position:0%
+Spider-Man. If I were Spider-Man, that's
+unreal. But this is we're talking about
+
+ align:start position:0%
+unreal. But this is we're talking about
+ 
+
+ align:start position:0%
+unreal. But this is we're talking about
+a hypothetical situation. So, this is
+
+ align:start position:0%
+a hypothetical situation. So, this is
+ 
+
+ align:start position:0%
+a hypothetical situation. So, this is
+actually uh more correctly, we should
+
+ align:start position:0%
+actually uh more correctly, we should
+ 
+
+ align:start position:0%
+actually uh more correctly, we should
+call this future hypothetical. Okay? So,
+
+ align:start position:0%
+call this future hypothetical. Okay? So,
+ 
+
+ align:start position:0%
+call this future hypothetical. Okay? So,
+if you're talking about and we're
+
+ align:start position:0%
+if you're talking about and we're
+ 
+
+ align:start position:0%
+if you're talking about and we're
+talking about something future, let's
+
+ align:start position:0%
+talking about something future, let's
+ 
+
+ align:start position:0%
+talking about something future, let's
+say, okay, if I if I went in, if I went
+
+ align:start position:0%
+say, okay, if I if I went in, if I went
+ 
+
+ align:start position:0%
+say, okay, if I if I went in, if I went
+in like tomorrow, tomorrow if I went in,
+
+ align:start position:0%
+in like tomorrow, tomorrow if I went in,
+ 
+
+ align:start position:0%
+in like tomorrow, tomorrow if I went in,
+you could do that tomorrow if I went in.
+
+ align:start position:0%
+you could do that tomorrow if I went in.
+ 
+
+ align:start position:0%
+you could do that tomorrow if I went in.
+Okay, if you do that, you're actually
+
+ align:start position:0%
+Okay, if you do that, you're actually
+ 
+
+ align:start position:0%
+Okay, if you do that, you're actually
+telling the listener, this is
+
+ align:start position:0%
+telling the listener, this is
+ 
+
+ align:start position:0%
+telling the listener, this is
+hypothetical situation. This is
+
+ align:start position:0%
+hypothetical situation. This is
+ 
+
+ align:start position:0%
+hypothetical situation. This is
+hypothetical situation, and you're
+
+ align:start position:0%
+hypothetical situation, and you're
+ 
+
+ align:start position:0%
+hypothetical situation, and you're
+actually showing more uncertainty.
+
+ align:start position:0%
+actually showing more uncertainty.
+ 
+
+ align:start position:0%
+actually showing more uncertainty.
+Okay? So you could actually use a past
+
+ align:start position:0%
+Okay? So you could actually use a past
+ 
+
+ align:start position:0%
+Okay? So you could actually use a past
+tense verb to talk about a future event
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but after a while they start using
+
+ align:start position:0%
+but after a while they start using
+ 
+
+ align:start position:0%
+but after a while they start using
+actually a present tense verb, right?
+
+ align:start position:0%
+actually a present tense verb, right?
+ 
+
+ align:start position:0%
+actually a present tense verb, right?
+So after a couple of turns they are
+
+ align:start position:0%
+So after a couple of turns they are
+ 
+
+ align:start position:0%
+So after a couple of turns they are
+actually using future real conditions
+
+ align:start position:0%
+actually using future real conditions
+ 
+
+ align:start position:0%
+actually using future real conditions
+and this this sometimes happens in real
+
+ align:start position:0%
+and this this sometimes happens in real
+ 
+
+ align:start position:0%
+and this this sometimes happens in real
+conversations. Okay, Dr. Greg, I still
+
+ align:start position:0%
+conversations. Okay, Dr. Greg, I still
+ 
+
+ align:start position:0%
+conversations. Okay, Dr. Greg, I still
+I' I apostrophe D. That's I would still
+
+ align:start position:0%
+I' I apostrophe D. That's I would still
+ 
+
+ align:start position:0%
+I' I apostrophe D. That's I would still
+charge for my labor. I would have to.
+
+ align:start position:0%
+charge for my labor. I would have to.
+ 
+
+ align:start position:0%
+charge for my labor. I would have to.
+Okay, I would have to. That's I I' I'd
+
+ align:start position:0%
+Okay, I would have to. That's I I' I'd
+ 
+
+ align:start position:0%
+Okay, I would have to. That's I I' I'd
+have to. That's future hypothetical. But
+
+ align:start position:0%
+have to. That's future hypothetical. But
+ 
+
+ align:start position:0%
+have to. That's future hypothetical. But
+then later on she says he said she says
+
+ align:start position:0%
+then later on she says he said she says
+ 
+
+ align:start position:0%
+then later on she says he said she says
+because my instruments will have to be
+
+ align:start position:0%
+because my instruments will have to be
+ 
+
+ align:start position:0%
+because my instruments will have to be
+sterilized. Will have to be. Now that's
+
+ align:start position:0%
+sterilized. Will have to be. Now that's
+ 
+
+ align:start position:0%
+sterilized. Will have to be. Now that's
+real conditions.
+
+ align:start position:0%
+real conditions.
+ 
+
+ align:start position:0%
+real conditions.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Okay. Uh,
+
+ align:start position:0%
+Okay. Uh,
+ 
+
+ align:start position:0%
+Okay. Uh,
+let's analyze the first sentence.
+
+ align:start position:0%
+let's analyze the first sentence.
+ 
+
+ align:start position:0%
+let's analyze the first sentence.
+Let's analyze the first sentence
+
+ align:start position:0%
+Let's analyze the first sentence
+ 
+
+ align:start position:0%
+Let's analyze the first sentence
+said by seagull.
+
+ align:start position:0%
+said by seagull.
+ 
+
+ align:start position:0%
+said by seagull.
+I want you to do the linking. Okay? Link
+
+ align:start position:0%
+I want you to do the linking. Okay? Link
+ 
+
+ align:start position:0%
+I want you to do the linking. Okay? Link
+between any words, any sounds that are
+
+ align:start position:0%
+between any words, any sounds that are
+ 
+
+ align:start position:0%
+between any words, any sounds that are
+linked like this. Okay? And get rid of
+
+ align:start position:0%
+linked like this. Okay? And get rid of
+ 
+
+ align:start position:0%
+linked like this. Okay? And get rid of
+any sounds.
+
+ align:start position:0%
+any sounds.
+ 
+
+ align:start position:0%
+any sounds.
+Get rid of any sounds that are there
+
+ align:start position:0%
+Get rid of any sounds that are there
+ 
+
+ align:start position:0%
+Get rid of any sounds that are there
+that we don't say.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What's that?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I'll
+
+ align:start position:0%
+Okay, I'll
+ 
+
+ align:start position:0%
+Okay, I'll
+start search off here. We say
+
+ align:start position:0%
+start search off here. We say
+ 
+
+ align:start position:0%
+start search off here. We say
+we have the first linking or blending.
+
+ align:start position:0%
+we have the first linking or blending.
+ 
+
+ align:start position:0%
+we have the first linking or blending.
+Let's say instead of let's say we say
+
+ align:start position:0%
+Let's say instead of let's say we say
+ 
+
+ align:start position:0%
+Let's say instead of let's say we say
+let's say let's say right let's say okay
+
+ align:start position:0%
+let's say let's say right let's say okay
+ 
+
+ align:start position:0%
+let's say let's say right let's say okay
+okay who wants to do the rest from here
+
+ align:start position:0%
+okay who wants to do the rest from here
+ 
+
+ align:start position:0%
+okay who wants to do the rest from here
+to here and who wants one two three one
+
+ align:start position:0%
+to here and who wants one two three one
+ 
+
+ align:start position:0%
+to here and who wants one two three one
+two three
+
+ align:start position:0%
+two three
+ 
+
+ align:start position:0%
+two three
+number one any brave soldier
+
+ align:start position:0%
+number one any brave soldier
+ 
+
+ align:start position:0%
+number one any brave soldier
+number one one remember I want you to be
+
+ align:start position:0%
+number one one remember I want you to be
+ 
+
+ align:start position:0%
+number one one remember I want you to be
+wrong so I can teach you thing. Hurry
+
+ align:start position:0%
+wrong so I can teach you thing. Hurry
+ 
+
+ align:start position:0%
+wrong so I can teach you thing. Hurry
+up. Hurry up. We don't have all day.
+
+ align:start position:0%
+up. Hurry up. We don't have all day.
+ 
+
+ align:start position:0%
+up. Hurry up. We don't have all day.
+Okay. Number one.
+
+ align:start position:0%
+Okay. Number one.
+ 
+
+ align:start position:0%
+Okay. Number one.
+Two. Number two. Two. Two.
+
+ align:start position:0%
+Two. Number two. Two. Two.
+ 
+
+ align:start position:0%
+Two. Number two. Two. Two.
+Two. Two. Very good. No. Two.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Three.
+
+ align:start position:0%
+Three.
+ 
+
+ align:start position:0%
+Three.
+Three.
+
+ align:start position:0%
+Three.
+ 
+
+ align:start position:0%
+Three.
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+get rid of cross out the sound that you
+
+ align:start position:0%
+get rid of cross out the sound that you
+ 
+
+ align:start position:0%
+get rid of cross out the sound that you
+we don't say. If you add a sound
+
+ align:start position:0%
+we don't say. If you add a sound
+ 
+
+ align:start position:0%
+we don't say. If you add a sound
+um add a sound add a sound.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. What do you think?
+
+ align:start position:0%
+Okay. What do you think?
+ 
+
+ align:start position:0%
+Okay. What do you think?
+Great.
+
+ align:start position:0%
+Great.
+ 
+
+ align:start position:0%
+Great.
+Great.
+
+ align:start position:0%
+Great.
+ 
+
+ align:start position:0%
+Great.
+All right. Great.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Any other disagreements? Does anybody
+
+ align:start position:0%
+Any other disagreements? Does anybody
+ 
+
+ align:start position:0%
+Any other disagreements? Does anybody
+want to add anything else?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+No.
+
+ align:start position:0%
+No.
+ 
+
+ align:start position:0%
+No.
+Okay. Let's talk about the first one.
+
+ align:start position:0%
+Okay. Let's talk about the first one.
+ 
+
+ align:start position:0%
+Okay. Let's talk about the first one.
+Let's say this is good. All right. Let's
+
+ align:start position:0%
+Let's say this is good. All right. Let's
+ 
+
+ align:start position:0%
+Let's say this is good. All right. Let's
+say I there's more stress here. When
+
+ align:start position:0%
+say I there's more stress here. When
+ 
+
+ align:start position:0%
+say I there's more stress here. When
+what why do you get rid of the T here?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Really? We get rid of the T.
+
+ align:start position:0%
+Really? We get rid of the T.
+ 
+
+ align:start position:0%
+Really? We get rid of the T.
+What?
+
+ align:start position:0%
+What?
+ 
+
+ align:start position:0%
+What?
+Huh? 20. 20. Very good. 20.
+
+ align:start position:0%
+Huh? 20. 20. Very good. 20.
+ 
+
+ align:start position:0%
+Huh? 20. 20. Very good. 20.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+When you have and T together, sometimes,
+
+ align:start position:0%
+When you have and T together, sometimes,
+ 
+
+ align:start position:0%
+When you have and T together, sometimes,
+most of the time, we get rid of the T,
+
+ align:start position:0%
+most of the time, we get rid of the T,
+ 
+
+ align:start position:0%
+most of the time, we get rid of the T,
+right? Center.
+
+ align:start position:0%
+right? Center.
+ 
+
+ align:start position:0%
+right? Center.
+Center. Right. That's very good. Went.
+
+ align:start position:0%
+Center. Right. That's very good. Went.
+ 
+
+ align:start position:0%
+Center. Right. That's very good. Went.
+So, went in. I went in with
+
+ align:start position:0%
+So, went in. I went in with
+ 
+
+ align:start position:0%
+So, went in. I went in with
+went in with you know. Okay. Very good.
+
+ align:start position:0%
+went in with you know. Okay. Very good.
+ 
+
+ align:start position:0%
+went in with you know. Okay. Very good.
+Uh so you say when in
+
+ align:start position:0%
+Uh so you say when in
+ 
+
+ align:start position:0%
+Uh so you say when in
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+a bruise or a bruise or very good
+
+ align:start position:0%
+a bruise or a bruise or very good
+ 
+
+ align:start position:0%
+a bruise or a bruise or very good
+bruise. Okay. Ends with a consonant
+
+ align:start position:0%
+bruise. Okay. Ends with a consonant
+ 
+
+ align:start position:0%
+bruise. Okay. Ends with a consonant
+starts with a vowel with Lincoln. V
+
+ align:start position:0%
+starts with a vowel with Lincoln. V
+ 
+
+ align:start position:0%
+starts with a vowel with Lincoln. V
+again constant. Lincoln
+
+ align:start position:0%
+again constant. Lincoln
+ 
+
+ align:start position:0%
+again constant. Lincoln
+bruisor. Bru.
+
+ align:start position:0%
+bruisor. Bru.
+ 
+
+ align:start position:0%
+bruisor. Bru.
+And if you listen to it, actually he he
+
+ align:start position:0%
+And if you listen to it, actually he he
+ 
+
+ align:start position:0%
+And if you listen to it, actually he he
+says it too really slowly. So he
+
+ align:start position:0%
+says it too really slowly. So he
+ 
+
+ align:start position:0%
+says it too really slowly. So he
+actually links this together too. Cuten
+
+ align:start position:0%
+actually links this together too. Cuten
+ 
+
+ align:start position:0%
+actually links this together too. Cuten
+cut. Cuten. Okay. And and you and and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh and you like a palization and you
+
+ align:start position:0%
+oh and you like a palization and you
+ 
+
+ align:start position:0%
+oh and you like a palization and you
+Yeah, that's good. and and
+
+ align:start position:0%
+Yeah, that's good. and and
+ 
+
+ align:start position:0%
+Yeah, that's good. and and
+but I think he says just and you I think
+
+ align:start position:0%
+but I think he says just and you I think
+ 
+
+ align:start position:0%
+but I think he says just and you I think
+he just get rid of there are two
+
+ align:start position:0%
+he just get rid of there are two
+ 
+
+ align:start position:0%
+he just get rid of there are two
+possibilities and you and
+
+ align:start position:0%
+possibilities and you and
+ 
+
+ align:start position:0%
+possibilities and you and
+you or get rid of the D like N get rid
+
+ align:start position:0%
+you or get rid of the D like N get rid
+ 
+
+ align:start position:0%
+you or get rid of the D like N get rid
+of the T and you and you very good this
+
+ align:start position:0%
+of the T and you and you very good this
+ 
+
+ align:start position:0%
+of the T and you and you very good this
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+had to had to uh
+
+ align:start position:0%
+had to had to uh
+ 
+
+ align:start position:0%
+had to had to uh
+you can consider this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+had to had I think rather than actually
+
+ align:start position:0%
+had to had I think rather than actually
+ 
+
+ align:start position:0%
+had to had I think rather than actually
+considering it as disappearing D we
+
+ align:start position:0%
+considering it as disappearing D we
+ 
+
+ align:start position:0%
+considering it as disappearing D we
+unreleased D had to had to unreed
+
+ align:start position:0%
+unreleased D had to had to unreed
+ 
+
+ align:start position:0%
+unreleased D had to had to unreed
+unreleased but there's still there's
+
+ align:start position:0%
+unreleased but there's still there's
+ 
+
+ align:start position:0%
+unreleased but there's still there's
+definitely link in here had to bandage
+
+ align:start position:0%
+definitely link in here had to bandage
+ 
+
+ align:start position:0%
+definitely link in here had to bandage
+me
+
+ align:start position:0%
+me
+ 
+
+ align:start position:0%
+me
+very good look bandage me up me up and
+
+ align:start position:0%
+very good look bandage me up me up and
+ 
+
+ align:start position:0%
+very good look bandage me up me up and
+where is the stress
+
+ align:start position:0%
+where is the stress
+ 
+
+ align:start position:0%
+where is the stress
+y okay bandage me up bandage me up okay
+
+ align:start position:0%
+y okay bandage me up bandage me up okay
+ 
+
+ align:start position:0%
+y okay bandage me up bandage me up okay
+So listen, I'll play this again the
+
+ align:start position:0%
+So listen, I'll play this again the
+ 
+
+ align:start position:0%
+So listen, I'll play this again the
+first part. Listen very carefully. So
+
+ align:start position:0%
+first part. Listen very carefully. So
+ 
+
+ align:start position:0%
+first part. Listen very carefully. So
+he'll say something like let's say let's
+
+ align:start position:0%
+he'll say something like let's say let's
+ 
+
+ align:start position:0%
+he'll say something like let's say let's
+say I went in with went in with you know
+
+ align:start position:0%
+say I went in with went in with you know
+ 
+
+ align:start position:0%
+say I went in with went in with you know
+a bruise or a cut and you a bruise or a
+
+ align:start position:0%
+a bruise or a cut and you a bruise or a
+ 
+
+ align:start position:0%
+a bruise or a cut and you a bruise or a
+cut and you had to bandage me up.
+
+ align:start position:0%
+cut and you had to bandage me up.
+ 
+
+ align:start position:0%
+cut and you had to bandage me up.
+Had to had to bandage me up. Yeah. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Too fast.
+
+ align:start position:0%
+Too fast.
+ 
+
+ align:start position:0%
+Too fast.
+Went in with. Went in. She didn't. He
+
+ align:start position:0%
+Went in with. Went in. She didn't. He
+ 
+
+ align:start position:0%
+Went in with. Went in. She didn't. He
+did not say I went in with. Right. Went
+
+ align:start position:0%
+did not say I went in with. Right. Went
+ 
+
+ align:start position:0%
+did not say I went in with. Right. Went
+in with. That was clear. Went in with.
+
+ align:start position:0%
+in with. That was clear. Went in with.
+ 
+
+ align:start position:0%
+in with. That was clear. Went in with.
+Let's say let's say was clear, right?
+
+ align:start position:0%
+Let's say let's say was clear, right?
+ 
+
+ align:start position:0%
+Let's say let's say was clear, right?
+Let's say he did not say let's say let's
+
+ align:start position:0%
+Let's say he did not say let's say let's
+ 
+
+ align:start position:0%
+Let's say he did not say let's say let's
+let's say let's say I went in with. Went
+
+ align:start position:0%
+let's say let's say I went in with. Went
+ 
+
+ align:start position:0%
+let's say let's say I went in with. Went
+in with. Went in with. Okay. Bru a
+
+ align:start position:0%
+in with. Went in with. Okay. Bru a
+ 
+
+ align:start position:0%
+in with. Went in with. Okay. Bru a
+bruise or a cut. So, he has a very nice
+
+ align:start position:0%
+bruise or a cut. So, he has a very nice
+ 
+
+ align:start position:0%
+bruise or a cut. So, he has a very nice
+rhythm. A bruise or a cut. A bruise or a
+
+ align:start position:0%
+rhythm. A bruise or a cut. A bruise or a
+ 
+
+ align:start position:0%
+rhythm. A bruise or a cut. A bruise or a
+cut. And that's what we're going to talk
+
+ align:start position:0%
+cut. And that's what we're going to talk
+ 
+
+ align:start position:0%
+cut. And that's what we're going to talk
+about. Rhythm. Rhythm. After this
+
+ align:start position:0%
+about. Rhythm. Rhythm. After this
+ 
+
+ align:start position:0%
+about. Rhythm. Rhythm. After this
+rhythm. Okay. A bruise. A bruise or a
+
+ align:start position:0%
+rhythm. Okay. A bruise. A bruise or a
+ 
+
+ align:start position:0%
+rhythm. Okay. A bruise. A bruise or a
+cut. Bruise or a He goes up on certain
+
+ align:start position:0%
+cut. Bruise or a He goes up on certain
+ 
+
+ align:start position:0%
+cut. Bruise or a He goes up on certain
+words, right? The words that you go up
+
+ align:start position:0%
+words, right? The words that you go up
+ 
+
+ align:start position:0%
+words, right? The words that you go up
+on are actually content words, nouns. A
+
+ align:start position:0%
+on are actually content words, nouns. A
+ 
+
+ align:start position:0%
+on are actually content words, nouns. A
+bruise or he goes
+
+ align:start position:0%
+bruise or he goes
+ 
+
+ align:start position:0%
+bruise or he goes
+a a bruise or a cut. a bruise or a cut.
+
+ align:start position:0%
+a a bruise or a cut. a bruise or a cut.
+ 
+
+ align:start position:0%
+a a bruise or a cut. a bruise or a cut.
+Then you a bruise a bruise or a cut and
+
+ align:start position:0%
+Then you a bruise a bruise or a cut and
+ 
+
+ align:start position:0%
+Then you a bruise a bruise or a cut and
+and you had to bandage me up. Bandage me
+
+ align:start position:0%
+and you had to bandage me up. Bandage me
+ 
+
+ align:start position:0%
+and you had to bandage me up. Bandage me
+up. Bandage me. Bandage me up. Okay, one
+
+ align:start position:0%
+up. Bandage me. Bandage me up. Okay, one
+ 
+
+ align:start position:0%
+up. Bandage me. Bandage me up. Okay, one
+more.
+
+ align:start position:0%
+more.
+ 
+
+ align:start position:0%
+more.
+Okay, now let's turn to page 112.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+pronunciation. Uh, noun compounds.
+
+ align:start position:0%
+pronunciation. Uh, noun compounds.
+ 
+
+ align:start position:0%
+pronunciation. Uh, noun compounds.
+Remember the noun compounds? Compound
+
+ align:start position:0%
+Remember the noun compounds? Compound
+ 
+
+ align:start position:0%
+Remember the noun compounds? Compound
+nouns. Yes. What happens? Which word
+
+ align:start position:0%
+nouns. Yes. What happens? Which word
+ 
+
+ align:start position:0%
+nouns. Yes. What happens? Which word
+gets more stress? The first first one.
+
+ align:start position:0%
+gets more stress? The first first one.
+ 
+
+ align:start position:0%
+gets more stress? The first first one.
+First one. Okay. So, uh, like exercise
+
+ align:start position:0%
+First one. Okay. So, uh, like exercise
+ 
+
+ align:start position:0%
+First one. Okay. So, uh, like exercise
+on bottom of page 112. Don't you like
+
+ align:start position:0%
+on bottom of page 112. Don't you like
+ 
+
+ align:start position:0%
+on bottom of page 112. Don't you like
+that music? No. It's really giving me a
+
+ align:start position:0%
+that music? No. It's really giving me a
+ 
+
+ align:start position:0%
+that music? No. It's really giving me a
+headache. Headache. Headache. Headache.
+
+ align:start position:0%
+headache. Headache. Headache. Headache.
+ 
+
+ align:start position:0%
+headache. Headache. Headache. Headache.
+Headache. Headache. Headache. Headache.
+
+ align:start position:0%
+Headache. Headache. Headache. Headache.
+ 
+
+ align:start position:0%
+Headache. Headache. Headache. Headache.
+That becomes a flap. Headache. Headache.
+
+ align:start position:0%
+That becomes a flap. Headache. Headache.
+ 
+
+ align:start position:0%
+That becomes a flap. Headache. Headache.
+Headache. Headache. Headache. Headache.
+
+ align:start position:0%
+Headache. Headache. Headache. Headache.
+ 
+
+ align:start position:0%
+Headache. Headache. Headache. Headache.
+Headache. Headache. Okay. So, we'll do
+
+ align:start position:0%
+Headache. Headache. Okay. So, we'll do
+ 
+
+ align:start position:0%
+Headache. Headache. Okay. So, we'll do
+this with a partner. Okay.
+
+ align:start position:0%
+this with a partner. Okay.
+ 
+
+ align:start position:0%
+this with a partner. Okay.
+We'll do AB AB.
+
+ align:start position:0%
+We'll do AB AB.
+ 
+
+ align:start position:0%
+We'll do AB AB.
+Okay. AB A
+
+ align:start position:0%
+Okay. AB A
+ 
+
+ align:start position:0%
+Okay. AB A
+A B A B A
+
+ align:start position:0%
+A B A B A
+ 
+
+ align:start position:0%
+A B A B A
+B A B A B
+
+ align:start position:0%
+B A B A B
+ 
+
+ align:start position:0%
+B A B A B
+A B.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Three. Three of you together.
+
+ align:start position:0%
+Okay. Three. Three of you together.
+ 
+
+ align:start position:0%
+Okay. Three. Three of you together.
+Okay. So, go through the 10 sentences.
+
+ align:start position:0%
+Okay. So, go through the 10 sentences.
+ 
+
+ align:start position:0%
+Okay. So, go through the 10 sentences.
+Page 112 113.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Make sure that you put more stress on
+
+ align:start position:0%
+Make sure that you put more stress on
+ 
+
+ align:start position:0%
+Make sure that you put more stress on
+the first one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ice skating broke my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gach.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+When I went ice skating, I broke my
+
+ align:start position:0%
+When I went ice skating, I broke my
+ 
+
+ align:start position:0%
+When I went ice skating, I broke my
+my kneecap. Kneecap.
+
+ align:start position:0%
+my kneecap. Kneecap.
+ 
+
+ align:start position:0%
+my kneecap. Kneecap.
+You eat too much food. No wonder
+
+ align:start position:0%
+You eat too much food. No wonder
+ 
+
+ align:start position:0%
+You eat too much food. No wonder
+you always feel uncomfortable.
+
+ align:start position:0%
+you always feel uncomfortable.
+ 
+
+ align:start position:0%
+you always feel uncomfortable.
+I know. I really have to do something
+
+ align:start position:0%
+I know. I really have to do something
+ 
+
+ align:start position:0%
+I know. I really have to do something
+about this pepper.
+
+ align:start position:0%
+about this pepper.
+ 
+
+ align:start position:0%
+about this pepper.
+Spicy food.
+
+ align:start position:0%
+Spicy food.
+ 
+
+ align:start position:0%
+Spicy food.
+Suit long food.
+
+ align:start position:0%
+Suit long food.
+ 
+
+ align:start position:0%
+Suit long food.
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Question.
+
+ align:start position:0%
+Question.
+ 
+
+ align:start position:0%
+Question.
+I wish I turn it off. Turn it off. Turn
+
+ align:start position:0%
+I wish I turn it off. Turn it off. Turn
+ 
+
+ align:start position:0%
+I wish I turn it off. Turn it off. Turn
+it off. Turn it off.
+
+ align:start position:0%
+it off. Turn it off.
+ 
+
+ align:start position:0%
+it off. Turn it off.
+Switch is off. Yes. Turn it off. Turn it
+
+ align:start position:0%
+Switch is off. Yes. Turn it off. Turn it
+ 
+
+ align:start position:0%
+Switch is off. Yes. Turn it off. Turn it
+off. Turn it. No.
+
+ align:start position:0%
+off. Turn it. No.
+ 
+
+ align:start position:0%
+off. Turn it. No.
+Turn it off. Turn it off. Link. Turn it
+
+ align:start position:0%
+Turn it off. Turn it off. Link. Turn it
+ 
+
+ align:start position:0%
+Turn it off. Turn it off. Link. Turn it
+off. Turn it off. Turn it off. Turn it
+
+ align:start position:0%
+off. Turn it off. Turn it off. Turn it
+ 
+
+ align:start position:0%
+off. Turn it off. Turn it off. Turn it
+off.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+myself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It goes like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sore.
+
+ align:start position:0%
+sore.
+ 
+
+ align:start position:0%
+sore.
+Armpit. Armpit.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh, no. No. Sore is an adjective.
+
+ align:start position:0%
+Oh, no. No. Sore is an adjective.
+ 
+
+ align:start position:0%
+Oh, no. No. Sore is an adjective.
+Armpit.
+
+ align:start position:0%
+Armpit.
+ 
+
+ align:start position:0%
+Armpit.
+A sore armpit. A sore armpit. Armpit is
+
+ align:start position:0%
+A sore armpit. A sore armpit. Armpit is
+ 
+
+ align:start position:0%
+A sore armpit. A sore armpit. Armpit is
+a compound noun.
+
+ align:start position:0%
+a compound noun.
+ 
+
+ align:start position:0%
+a compound noun.
+Is an adjective. Armpit.
+
+ align:start position:0%
+Is an adjective. Armpit.
+ 
+
+ align:start position:0%
+Is an adjective. Armpit.
+Armpit.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+Take care. Back. Back. Back. Back.
+
+ align:start position:0%
+Take care. Back. Back. Back. Back.
+ 
+
+ align:start position:0%
+Take care. Back. Back. Back. Back.
+Where? From
+
+ align:start position:0%
+Where? From
+ 
+
+ align:start position:0%
+Where? From
+exercise. Back. Back. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+How did your checkup checkup go at the
+
+ align:start position:0%
+How did your checkup checkup go at the
+ 
+
+ align:start position:0%
+How did your checkup checkup go at the
+doctor's? One more time. How did your
+
+ align:start position:0%
+doctor's? One more time. How did your
+ 
+
+ align:start position:0%
+doctor's? One more time. How did your
+checkup go at the doctors?
+
+ align:start position:0%
+checkup go at the doctors?
+ 
+
+ align:start position:0%
+checkup go at the doctors?
+Checkup. Checkup.
+
+ align:start position:0%
+Checkup. Checkup.
+ 
+
+ align:start position:0%
+Checkup. Checkup.
+Well, everything
+
+ align:start position:0%
+Well, everything
+ 
+
+ align:start position:0%
+Well, everything
+except that he found the irregular
+
+ align:start position:0%
+except that he found the irregular
+ 
+
+ align:start position:0%
+except that he found the irregular
+heartbeat.
+
+ align:start position:0%
+heartbeat.
+ 
+
+ align:start position:0%
+heartbeat.
+He wants me He wants me to really check
+
+ align:start position:0%
+He wants me He wants me to really check
+ 
+
+ align:start position:0%
+He wants me He wants me to really check
+the check again in a month. Check again.
+
+ align:start position:0%
+the check again in a month. Check again.
+ 
+
+ align:start position:0%
+the check again in a month. Check again.
+Check again. No, it's not gain like set.
+
+ align:start position:0%
+Check again. No, it's not gain like set.
+ 
+
+ align:start position:0%
+Check again. No, it's not gain like set.
+S I said check again. Check again. Check
+
+ align:start position:0%
+S I said check again. Check again. Check
+ 
+
+ align:start position:0%
+S I said check again. Check again. Check
+again. Yes. Not a or but e like said
+
+ align:start position:0%
+again. Yes. Not a or but e like said
+ 
+
+ align:start position:0%
+again. Yes. Not a or but e like said
+again.
+
+ align:start position:0%
+again.
+ 
+
+ align:start position:0%
+again.
+Okay,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's do this together.
+
+ align:start position:0%
+let's do this together.
+ 
+
+ align:start position:0%
+let's do this together.
+The second sentence.
+
+ align:start position:0%
+The second sentence.
+ 
+
+ align:start position:0%
+The second sentence.
+I wish they
+
+ align:start position:0%
+I wish they
+ 
+
+ align:start position:0%
+I wish they
+Okay, how are you going to How do you
+
+ align:start position:0%
+Okay, how are you going to How do you
+ 
+
+ align:start position:0%
+Okay, how are you going to How do you
+say this?
+
+ align:start position:0%
+say this?
+ 
+
+ align:start position:0%
+say this?
+What's the first sound?
+
+ align:start position:0%
+What's the first sound?
+ 
+
+ align:start position:0%
+What's the first sound?
+Tur. It's not turn. Okay. Turn. Turn.
+
+ align:start position:0%
+Tur. It's not turn. Okay. Turn. Turn.
+ 
+
+ align:start position:0%
+Tur. It's not turn. Okay. Turn. Turn.
+Say turn. You're finished. Okay. Turn.
+
+ align:start position:0%
+Say turn. You're finished. Okay. Turn.
+ 
+
+ align:start position:0%
+Say turn. You're finished. Okay. Turn.
+Turn.
+
+ align:start position:0%
+Turn.
+ 
+
+ align:start position:0%
+Turn.
+Turn.
+
+ align:start position:0%
+Turn.
+ 
+
+ align:start position:0%
+Turn.
+Turn it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. It becomes a flat.
+
+ align:start position:0%
+Okay. It becomes a flat.
+ 
+
+ align:start position:0%
+Okay. It becomes a flat.
+Okay. Where's the stress? Stress.
+
+ align:start position:0%
+Okay. Where's the stress? Stress.
+ 
+
+ align:start position:0%
+Okay. Where's the stress? Stress.
+Off. Okay. Turn it off. Turn it off.
+
+ align:start position:0%
+Off. Okay. Turn it off. Turn it off.
+ 
+
+ align:start position:0%
+Off. Okay. Turn it off. Turn it off.
+Turn it off.
+
+ align:start position:0%
+Turn it off.
+ 
+
+ align:start position:0%
+Turn it off.
+Turn
+
+ align:start position:0%
+Turn
+ 
+
+ align:start position:0%
+Turn
+it off. Turn it off. Turn it off. Turn
+
+ align:start position:0%
+it off. Turn it off. Turn it off. Turn
+ 
+
+ align:start position:0%
+it off. Turn it off. Turn it off. Turn
+it off. Turn it off. Turn it off. Turn
+
+ align:start position:0%
+it off. Turn it off. Turn it off. Turn
+ 
+
+ align:start position:0%
+it off. Turn it off. Turn it off. Turn
+it off. Turn it off. Turn it off. Turn
+
+ align:start position:0%
+it off. Turn it off. Turn it off. Turn
+ 
+
+ align:start position:0%
+it off. Turn it off. Turn it off. Turn
+it off. Turn it off. Turn it off. I wish
+
+ align:start position:0%
+it off. Turn it off. Turn it off. I wish
+ 
+
+ align:start position:0%
+it off. Turn it off. Turn it off. I wish
+they turn it off. I wish they turn it
+
+ align:start position:0%
+they turn it off. I wish they turn it
+ 
+
+ align:start position:0%
+they turn it off. I wish they turn it
+off. They What's they here?
+
+ align:start position:0%
+off. They What's they here?
+ 
+
+ align:start position:0%
+off. They What's they here?
+Would Okay.
+
+ align:start position:0%
+Would Okay.
+ 
+
+ align:start position:0%
+Would Okay.
+If you say wish, you have to say would.
+
+ align:start position:0%
+If you say wish, you have to say would.
+ 
+
+ align:start position:0%
+If you say wish, you have to say would.
+You can't say will.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Questions.
+
+ align:start position:0%
+Questions.
+ 
+
+ align:start position:0%
+Questions.
+Questions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A sore. I had a question about uh 78.
+
+ align:start position:0%
+A sore. I had a question about uh 78.
+ 
+
+ align:start position:0%
+A sore. I had a question about uh 78.
+I have a sore. Sore is an adjective.
+
+ align:start position:0%
+I have a sore. Sore is an adjective.
+ 
+
+ align:start position:0%
+I have a sore. Sore is an adjective.
+Armpit is the compound noun. Armpit.
+
+ align:start position:0%
+Armpit is the compound noun. Armpit.
+ 
+
+ align:start position:0%
+Armpit is the compound noun. Armpit.
+Armpit. Armpit. Armpit. Okay. Any other
+
+ align:start position:0%
+Armpit. Armpit. Armpit. Okay. Any other
+ 
+
+ align:start position:0%
+Armpit. Armpit. Armpit. Okay. Any other
+questions?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Huh? Armpit. Sore. Armpit.
+
+ align:start position:0%
+Huh? Armpit. Sore. Armpit.
+ 
+
+ align:start position:0%
+Huh? Armpit. Sore. Armpit.
+Arm. That actually I had no idea. I
+
+ align:start position:0%
+Arm. That actually I had no idea. I
+ 
+
+ align:start position:0%
+Arm. That actually I had no idea. I
+heard. So you you go swimming and how do
+
+ align:start position:0%
+heard. So you you go swimming and how do
+ 
+
+ align:start position:0%
+heard. So you you go swimming and how do
+you get a sore armpit? Sore shoulder. I
+
+ align:start position:0%
+you get a sore armpit? Sore shoulder. I
+ 
+
+ align:start position:0%
+you get a sore armpit? Sore shoulder. I
+I couldn't understand this. Armpit is
+
+ align:start position:0%
+I couldn't understand this. Armpit is
+ 
+
+ align:start position:0%
+I couldn't understand this. Armpit is
+this is armpit. How do you get how do
+
+ align:start position:0%
+this is armpit. How do you get how do
+ 
+
+ align:start position:0%
+this is armpit. How do you get how do
+you get a sore armpit?
+
+ align:start position:0%
+you get a sore armpit?
+ 
+
+ align:start position:0%
+you get a sore armpit?
+I don't know. I was reading this
+
+ align:start position:0%
+I don't know. I was reading this
+ 
+
+ align:start position:0%
+I don't know. I was reading this
+friction. Cuz because a friction
+
+ align:start position:0%
+friction. Cuz because a friction
+ 
+
+ align:start position:0%
+friction. Cuz because a friction
+you get a sore armpit.
+
+ align:start position:0%
+you get a sore armpit.
+ 
+
+ align:start position:0%
+you get a sore armpit.
+I don't know. I'm not much of a swimmer.
+
+ align:start position:0%
+I don't know. I'm not much of a swimmer.
+ 
+
+ align:start position:0%
+I don't know. I'm not much of a swimmer.
+So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I don't know. How do you get a sore
+
+ align:start position:0%
+uh I don't know. How do you get a sore
+ 
+
+ align:start position:0%
+uh I don't know. How do you get a sore
+armpit?
+
+ align:start position:0%
+armpit?
+ 
+
+ align:start position:0%
+armpit?
+I do not know that.
+
+ align:start position:0%
+I do not know that.
+ 
+
+ align:start position:0%
+I do not know that.
+Okay. Now, any other questions?
+
+ align:start position:0%
+Okay. Now, any other questions?
+ 
+
+ align:start position:0%
+Okay. Now, any other questions?
+If not, let's move on to
+
+ align:start position:0%
+If not, let's move on to
+ 
+
+ align:start position:0%
+If not, let's move on to
+uh uh course packet page 70.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, we're just going to have to Okay,
+
+ align:start position:0%
+So, we're just going to have to Okay,
+ 
+
+ align:start position:0%
+So, we're just going to have to Okay,
+just look at uh your course packet page
+
+ align:start position:0%
+just look at uh your course packet page
+ 
+
+ align:start position:0%
+just look at uh your course packet page
+70.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, read the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first word. Volunteer. Volunteer. And
+
+ align:start position:0%
+first word. Volunteer. Volunteer. And
+ 
+
+ align:start position:0%
+first word. Volunteer. Volunteer. And
+the uh on the right hand you have she
+
+ align:start position:0%
+the uh on the right hand you have she
+ 
+
+ align:start position:0%
+the uh on the right hand you have she
+can hear. She can hear. She can hear.
+
+ align:start position:0%
+can hear. She can hear. She can hear.
+ 
+
+ align:start position:0%
+can hear. She can hear. She can hear.
+And next
+
+ align:start position:0%
+And next
+ 
+
+ align:start position:0%
+And next
+presented. Presented.
+
+ align:start position:0%
+presented. Presented.
+ 
+
+ align:start position:0%
+presented. Presented.
+Next.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Next. Economics.
+
+ align:start position:0%
+Next. Economics.
+ 
+
+ align:start position:0%
+Next. Economics.
+Economics. Economics. Where's the
+
+ align:start position:0%
+Economics. Economics. Where's the
+ 
+
+ align:start position:0%
+Economics. Economics. Where's the
+stress? Economics. Economics. Economics.
+
+ align:start position:0%
+stress? Economics. Economics. Economics.
+ 
+
+ align:start position:0%
+stress? Economics. Economics. Economics.
+There's uh economics. Economics. There's
+
+ align:start position:0%
+There's uh economics. Economics. There's
+ 
+
+ align:start position:0%
+There's uh economics. Economics. There's
+no economics. Economics. Next. In the
+
+ align:start position:0%
+no economics. Economics. Next. In the
+ 
+
+ align:start position:0%
+no economics. Economics. Next. In the
+comics. In the comics. In the comics. In
+
+ align:start position:0%
+comics. In the comics. In the comics. In
+ 
+
+ align:start position:0%
+comics. In the comics. In the comics. In
+the comics. Economics. Next.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Approximate.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Approximate. Approximate. This is an
+
+ align:start position:0%
+Approximate. Approximate. This is an
+ 
+
+ align:start position:0%
+Approximate. Approximate. This is an
+adjective, right?
+
+ align:start position:0%
+adjective, right?
+ 
+
+ align:start position:0%
+adjective, right?
+Approximate.
+
+ align:start position:0%
+Approximate.
+ 
+
+ align:start position:0%
+Approximate.
+Approximate. Approximate. Adverb.
+
+ align:start position:0%
+Approximate. Approximate. Adverb.
+ 
+
+ align:start position:0%
+Approximate. Approximate. Adverb.
+Approximately approximately.
+
+ align:start position:0%
+Approximately approximately.
+ 
+
+ align:start position:0%
+Approximately approximately.
+Approximately. Approximately. And next.
+
+ align:start position:0%
+Approximately. Approximately. And next.
+ 
+
+ align:start position:0%
+Approximately. Approximately. And next.
+Box of it.
+
+ align:start position:0%
+Box of it.
+ 
+
+ align:start position:0%
+Box of it.
+Next. Electrification.
+
+ align:start position:0%
+Next. Electrification.
+ 
+
+ align:start position:0%
+Next. Electrification.
+Okay, slow down. Electrification.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Electrification.
+
+ align:start position:0%
+Electrification.
+ 
+
+ align:start position:0%
+Electrification.
+Electrification.
+
+ align:start position:0%
+Electrification.
+ 
+
+ align:start position:0%
+Electrification.
+Electrification.
+
+ align:start position:0%
+Electrification.
+ 
+
+ align:start position:0%
+Electrification.
+Electrification.
+
+ align:start position:0%
+Electrification.
+ 
+
+ align:start position:0%
+Electrification.
+Electrification.
+
+ align:start position:0%
+Electrification.
+ 
+
+ align:start position:0%
+Electrification.
+Electrification. In the sentence, she
+
+ align:start position:0%
+Electrification. In the sentence, she
+ 
+
+ align:start position:0%
+Electrification. In the sentence, she
+went to the station.
+
+ align:start position:0%
+went to the station.
+ 
+
+ align:start position:0%
+went to the station.
+She went to the station. She went to the
+
+ align:start position:0%
+She went to the station. She went to the
+ 
+
+ align:start position:0%
+She went to the station. She went to the
+station. She went to the station. She
+
+ align:start position:0%
+station. She went to the station. She
+ 
+
+ align:start position:0%
+station. She went to the station. She
+went to the station. So,
+
+ align:start position:0%
+went to the station. So,
+ 
+
+ align:start position:0%
+went to the station. So,
+we have we talked about word stress,
+
+ align:start position:0%
+we have we talked about word stress,
+ 
+
+ align:start position:0%
+we have we talked about word stress,
+right? In any words, there is one
+
+ align:start position:0%
+right? In any words, there is one
+ 
+
+ align:start position:0%
+right? In any words, there is one
+syllable that is always stressed. Okay?
+
+ align:start position:0%
+syllable that is always stressed. Okay?
+ 
+
+ align:start position:0%
+syllable that is always stressed. Okay?
+More than any other uh syllables in
+
+ align:start position:0%
+More than any other uh syllables in
+ 
+
+ align:start position:0%
+More than any other uh syllables in
+English words.
+
+ align:start position:0%
+English words.
+ 
+
+ align:start position:0%
+English words.
+And in sentences
+
+ align:start position:0%
+And in sentences
+ 
+
+ align:start position:0%
+And in sentences
+or phrases, we have certain words that
+
+ align:start position:0%
+or phrases, we have certain words that
+ 
+
+ align:start position:0%
+or phrases, we have certain words that
+are more stressed than others.
+
+ align:start position:0%
+are more stressed than others.
+ 
+
+ align:start position:0%
+are more stressed than others.
+That's how we get a rhythm. That's what
+
+ align:start position:0%
+That's how we get a rhythm. That's what
+ 
+
+ align:start position:0%
+That's how we get a rhythm. That's what
+we mean by sentence stress. If you have
+
+ align:start position:0%
+we mean by sentence stress. If you have
+ 
+
+ align:start position:0%
+we mean by sentence stress. If you have
+a sentence stress, then you you get a
+
+ align:start position:0%
+a sentence stress, then you you get a
+ 
+
+ align:start position:0%
+a sentence stress, then you you get a
+good rhythm in English. Okay? You you
+
+ align:start position:0%
+good rhythm in English. Okay? You you
+ 
+
+ align:start position:0%
+good rhythm in English. Okay? You you
+don't just stress any other words, any
+
+ align:start position:0%
+don't just stress any other words, any
+ 
+
+ align:start position:0%
+don't just stress any other words, any
+words that you want to feel like
+
+ align:start position:0%
+words that you want to feel like
+ 
+
+ align:start position:0%
+words that you want to feel like
+stressing, but there are rules about
+
+ align:start position:0%
+stressing, but there are rules about
+ 
+
+ align:start position:0%
+stressing, but there are rules about
+that.
+
+ align:start position:0%
+that.
+ 
+
+ align:start position:0%
+that.
+Why does that happen? That happens
+
+ align:start position:0%
+Why does that happen? That happens
+ 
+
+ align:start position:0%
+Why does that happen? That happens
+because English is very strange. I think
+
+ align:start position:0%
+because English is very strange. I think
+ 
+
+ align:start position:0%
+because English is very strange. I think
+I told you this before a couple of
+
+ align:start position:0%
+I told you this before a couple of
+ 
+
+ align:start position:0%
+I told you this before a couple of
+times. English is like the probably the
+
+ align:start position:0%
+times. English is like the probably the
+ 
+
+ align:start position:0%
+times. English is like the probably the
+only language that are commonly spoken
+
+ align:start position:0%
+only language that are commonly spoken
+ 
+
+ align:start position:0%
+only language that are commonly spoken
+in the world which is a uh stress timed
+
+ align:start position:0%
+in the world which is a uh stress timed
+ 
+
+ align:start position:0%
+in the world which is a uh stress timed
+language. Stress English is a stress
+
+ align:start position:0%
+language. Stress English is a stress
+ 
+
+ align:start position:0%
+language. Stress English is a stress
+timed language. But any other words that
+
+ align:start position:0%
+timed language. But any other words that
+ 
+
+ align:start position:0%
+timed language. But any other words that
+you can think of? Korean, Japanese,
+
+ align:start position:0%
+you can think of? Korean, Japanese,
+ 
+
+ align:start position:0%
+you can think of? Korean, Japanese,
+Chinese,
+
+ align:start position:0%
+Chinese,
+ 
+
+ align:start position:0%
+Chinese,
+uh I don't know, Indonesian,
+
+ align:start position:0%
+uh I don't know, Indonesian,
+ 
+
+ align:start position:0%
+uh I don't know, Indonesian,
+Thai,
+
+ align:start position:0%
+Thai,
+ 
+
+ align:start position:0%
+Thai,
+Tai,
+
+ align:start position:0%
+Tai,
+ 
+
+ align:start position:0%
+Tai,
+Spanish,
+
+ align:start position:0%
+Spanish,
+ 
+
+ align:start position:0%
+Spanish,
+French,
+
+ align:start position:0%
+French,
+ 
+
+ align:start position:0%
+French,
+uh Italian,
+
+ align:start position:0%
+uh Italian,
+ 
+
+ align:start position:0%
+uh Italian,
+uh maybe except uh German. German maybe
+
+ align:start position:0%
+uh maybe except uh German. German maybe
+ 
+
+ align:start position:0%
+uh maybe except uh German. German maybe
+like stress point.
+
+ align:start position:0%
+like stress point.
+ 
+
+ align:start position:0%
+like stress point.
+Those are syllable times language
+
+ align:start position:0%
+Those are syllable times language
+ 
+
+ align:start position:0%
+Those are syllable times language
+languages meaning if you have more
+
+ align:start position:0%
+languages meaning if you have more
+ 
+
+ align:start position:0%
+languages meaning if you have more
+syllables it'll take longer time to say
+
+ align:start position:0%
+syllables it'll take longer time to say
+ 
+
+ align:start position:0%
+syllables it'll take longer time to say
+those sentences but in English it
+
+ align:start position:0%
+those sentences but in English it
+ 
+
+ align:start position:0%
+those sentences but in English it
+doesn't matter how many syllables you
+
+ align:start position:0%
+doesn't matter how many syllables you
+ 
+
+ align:start position:0%
+doesn't matter how many syllables you
+have what's really important is the
+
+ align:start position:0%
+have what's really important is the
+ 
+
+ align:start position:0%
+have what's really important is the
+number of stresses
+
+ align:start position:0%
+number of stresses
+ 
+
+ align:start position:0%
+number of stresses
+if in a sentence if you have more
+
+ align:start position:0%
+if in a sentence if you have more
+ 
+
+ align:start position:0%
+if in a sentence if you have more
+stressed syllables or more stressed
+
+ align:start position:0%
+stressed syllables or more stressed
+ 
+
+ align:start position:0%
+stressed syllables or more stressed
+words then it'll take longer time to say
+
+ align:start position:0%
+words then it'll take longer time to say
+ 
+
+ align:start position:0%
+words then it'll take longer time to say
+those sentences okay so for instance is
+
+ align:start position:0%
+those sentences okay so for instance is
+ 
+
+ align:start position:0%
+those sentences okay so for instance is
+cats chase mice. Okay, I'll do this.
+
+ align:start position:0%
+cats chase mice. Okay, I'll do this.
+ 
+
+ align:start position:0%
+cats chase mice. Okay, I'll do this.
+Cats chase mice. There are three words.
+
+ align:start position:0%
+Cats chase mice. There are three words.
+ 
+
+ align:start position:0%
+Cats chase mice. There are three words.
+Cats chase mice. Makes sense, right?
+
+ align:start position:0%
+Cats chase mice. Makes sense, right?
+ 
+
+ align:start position:0%
+Cats chase mice. Makes sense, right?
+Cats chase mice. Cats chased mice. Cats
+
+ align:start position:0%
+Cats chase mice. Cats chased mice. Cats
+ 
+
+ align:start position:0%
+Cats chase mice. Cats chased mice. Cats
+chased mice. The next The cats chased
+
+ align:start position:0%
+chased mice. The next The cats chased
+ 
+
+ align:start position:0%
+chased mice. The next The cats chased
+mice. The cats have chased mice. The
+
+ align:start position:0%
+mice. The cats have chased mice. The
+ 
+
+ align:start position:0%
+mice. The cats have chased mice. The
+cats have The cats have chased mice. The
+
+ align:start position:0%
+cats have The cats have chased mice. The
+ 
+
+ align:start position:0%
+cats have The cats have chased mice. The
+cats have chased mice. The cats have
+
+ align:start position:0%
+cats have chased mice. The cats have
+ 
+
+ align:start position:0%
+cats have chased mice. The cats have
+chased the mice. The cats have chased
+
+ align:start position:0%
+chased the mice. The cats have chased
+ 
+
+ align:start position:0%
+chased the mice. The cats have chased
+the mice. The cats been chasing the
+
+ align:start position:0%
+the mice. The cats been chasing the
+ 
+
+ align:start position:0%
+the mice. The cats been chasing the
+mice. The cats have been chasing the
+
+ align:start position:0%
+mice. The cats have been chasing the
+ 
+
+ align:start position:0%
+mice. The cats have been chasing the
+mice. The cats might have been chasing
+
+ align:start position:0%
+mice. The cats might have been chasing
+ 
+
+ align:start position:0%
+mice. The cats might have been chasing
+the mice.
+
+ align:start position:0%
+the mice.
+ 
+
+ align:start position:0%
+the mice.
+Okay, the last one is a little bit more
+
+ align:start position:0%
+Okay, the last one is a little bit more
+ 
+
+ align:start position:0%
+Okay, the last one is a little bit more
+difficult. But here we have 1 2 3 4 5
+
+ align:start position:0%
+difficult. But here we have 1 2 3 4 5
+ 
+
+ align:start position:0%
+difficult. But here we have 1 2 3 4 5
+six. We have we have six one two three
+
+ align:start position:0%
+six. We have we have six one two three
+ 
+
+ align:start position:0%
+six. We have we have six one two three
+five. We have six sentences, right? You
+
+ align:start position:0%
+five. We have six sentences, right? You
+ 
+
+ align:start position:0%
+five. We have six sentences, right? You
+have six sentences. And all those six
+
+ align:start position:0%
+have six sentences. And all those six
+ 
+
+ align:start position:0%
+have six sentences. And all those six
+sentences have three stressed words.
+
+ align:start position:0%
+sentences have three stressed words.
+ 
+
+ align:start position:0%
+sentences have three stressed words.
+They have only three stresses.
+
+ align:start position:0%
+They have only three stresses.
+ 
+
+ align:start position:0%
+They have only three stresses.
+So it takes roughly the same amount of
+
+ align:start position:0%
+So it takes roughly the same amount of
+ 
+
+ align:start position:0%
+So it takes roughly the same amount of
+time to say the first one and the last
+
+ align:start position:0%
+time to say the first one and the last
+ 
+
+ align:start position:0%
+time to say the first one and the last
+one.
+
+ align:start position:0%
+one.
+ 
+
+ align:start position:0%
+one.
+Even though the last one has many more
+
+ align:start position:0%
+Even though the last one has many more
+ 
+
+ align:start position:0%
+Even though the last one has many more
+syllables, right?
+
+ align:start position:0%
+syllables, right?
+ 
+
+ align:start position:0%
+syllables, right?
+So, we could we could do this. I wish I
+
+ align:start position:0%
+So, we could we could do this. I wish I
+ 
+
+ align:start position:0%
+So, we could we could do this. I wish I
+had my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh, that's weird. What happened?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I'll I'll do this. You can just
+
+ align:start position:0%
+Okay, I'll I'll do this. You can just
+ 
+
+ align:start position:0%
+Okay, I'll I'll do this. You can just
+You can You can just watch.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+One, two, three. There through stress.
+
+ align:start position:0%
+One, two, three. There through stress.
+ 
+
+ align:start position:0%
+One, two, three. There through stress.
+One, two, three. One, two, three. Cats
+
+ align:start position:0%
+One, two, three. One, two, three. Cats
+ 
+
+ align:start position:0%
+One, two, three. One, two, three. Cats
+chase. Just Just listen.
+
+ align:start position:0%
+chase. Just Just listen.
+ 
+
+ align:start position:0%
+chase. Just Just listen.
+Cats chase mice. The cats chase mice.
+
+ align:start position:0%
+Cats chase mice. The cats chase mice.
+ 
+
+ align:start position:0%
+Cats chase mice. The cats chase mice.
+The cats have chased mice. The cats have
+
+ align:start position:0%
+The cats have chased mice. The cats have
+ 
+
+ align:start position:0%
+The cats have chased mice. The cats have
+chased the mice. The cats been chasing
+
+ align:start position:0%
+chased the mice. The cats been chasing
+ 
+
+ align:start position:0%
+chased the mice. The cats been chasing
+the mice. The cats might have been
+
+ align:start position:0%
+the mice. The cats might have been
+ 
+
+ align:start position:0%
+the mice. The cats might have been
+chasing the mice. Oh, the last one was
+
+ align:start position:0%
+chasing the mice. Oh, the last one was
+ 
+
+ align:start position:0%
+chasing the mice. Oh, the last one was
+the cats. Whatever. There were too many
+
+ align:start position:0%
+the cats. Whatever. There were too many
+ 
+
+ align:start position:0%
+the cats. Whatever. There were too many
+too many syllables there. But we could
+
+ align:start position:0%
+too many syllables there. But we could
+ 
+
+ align:start position:0%
+too many syllables there. But we could
+do this in English because English
+
+ align:start position:0%
+do this in English because English
+ 
+
+ align:start position:0%
+do this in English because English
+follows stress patterns. That's like
+
+ align:start position:0%
+follows stress patterns. That's like
+ 
+
+ align:start position:0%
+follows stress patterns. That's like
+music, playing music. Okay. So that's
+
+ align:start position:0%
+music, playing music. Okay. So that's
+ 
+
+ align:start position:0%
+music, playing music. Okay. So that's
+how you get a rhythm in English.
+
+ align:start position:0%
+how you get a rhythm in English.
+ 
+
+ align:start position:0%
+how you get a rhythm in English.
+In order to do that, you have to reduce
+
+ align:start position:0%
+In order to do that, you have to reduce
+ 
+
+ align:start position:0%
+In order to do that, you have to reduce
+certain sounds. That's why we get
+
+ align:start position:0%
+certain sounds. That's why we get
+ 
+
+ align:start position:0%
+certain sounds. That's why we get
+reduced sounds in a word and in
+
+ align:start position:0%
+reduced sounds in a word and in
+ 
+
+ align:start position:0%
+reduced sounds in a word and in
+sentences.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay? We'll do this together later.
+
+ align:start position:0%
+Okay? We'll do this together later.
+ 
+
+ align:start position:0%
+Okay? We'll do this together later.
+Uh if you turn over the page,
+
+ align:start position:0%
+Uh if you turn over the page,
+ 
+
+ align:start position:0%
+Uh if you turn over the page,
+turn over the page.
+
+ align:start position:0%
+turn over the page.
+ 
+
+ align:start position:0%
+turn over the page.
+So the uh page 71 next page.
+
+ align:start position:0%
+So the uh page 71 next page.
+ 
+
+ align:start position:0%
+So the uh page 71 next page.
+So the question is
+
+ align:start position:0%
+So the question is
+ 
+
+ align:start position:0%
+So the question is
+which words do you stress and which
+
+ align:start position:0%
+which words do you stress and which
+ 
+
+ align:start position:0%
+which words do you stress and which
+words do you not stress?
+
+ align:start position:0%
+words do you not stress?
+ 
+
+ align:start position:0%
+words do you not stress?
+You stress the
+
+ align:start position:0%
+You stress the
+ 
+
+ align:start position:0%
+You stress the
+content words. You and you do not stress
+
+ align:start position:0%
+content words. You and you do not stress
+ 
+
+ align:start position:0%
+content words. You and you do not stress
+the function words. What are the content
+
+ align:start position:0%
+the function words. What are the content
+ 
+
+ align:start position:0%
+the function words. What are the content
+words? What are the function words? You
+
+ align:start position:0%
+words? What are the function words? You
+ 
+
+ align:start position:0%
+words? What are the function words? You
+can turn to page 86 in your book. Page
+
+ align:start position:0%
+can turn to page 86 in your book. Page
+ 
+
+ align:start position:0%
+can turn to page 86 in your book. Page
+86.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+page 86 in your book. Okay.
+
+ align:start position:0%
+page 86 in your book. Okay.
+ 
+
+ align:start position:0%
+page 86 in your book. Okay.
+On page 86, we have rules for stress in
+
+ align:start position:0%
+On page 86, we have rules for stress in
+ 
+
+ align:start position:0%
+On page 86, we have rules for stress in
+one syllable words, right? Rules for
+
+ align:start position:0%
+one syllable words, right? Rules for
+ 
+
+ align:start position:0%
+one syllable words, right? Rules for
+stress in one one syllable words. But
+
+ align:start position:0%
+stress in one one syllable words. But
+ 
+
+ align:start position:0%
+stress in one one syllable words. But
+it's actually page one uh no in your
+
+ align:start position:0%
+it's actually page one uh no in your
+ 
+
+ align:start position:0%
+it's actually page one uh no in your
+book in your book textbook page 86.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is not just for one syllable words,
+
+ align:start position:0%
+This is not just for one syllable words,
+ 
+
+ align:start position:0%
+This is not just for one syllable words,
+but this is uh rules for stress in in a
+
+ align:start position:0%
+but this is uh rules for stress in in a
+ 
+
+ align:start position:0%
+but this is uh rules for stress in in a
+sentence. On page 86,
+
+ align:start position:0%
+sentence. On page 86,
+ 
+
+ align:start position:0%
+sentence. On page 86,
+the following one syllable words are
+
+ align:start position:0%
+the following one syllable words are
+ 
+
+ align:start position:0%
+the following one syllable words are
+usually unstressed. Okay, the following
+
+ align:start position:0%
+usually unstressed. Okay, the following
+ 
+
+ align:start position:0%
+usually unstressed. Okay, the following
+words are usually unstressed in a
+
+ align:start position:0%
+words are usually unstressed in a
+ 
+
+ align:start position:0%
+words are usually unstressed in a
+sentence. Articles, pronouns,
+
+ align:start position:0%
+sentence. Articles, pronouns,
+ 
+
+ align:start position:0%
+sentence. Articles, pronouns,
+prepositions, conjunctions, auxiliary
+
+ align:start position:0%
+prepositions, conjunctions, auxiliary
+ 
+
+ align:start position:0%
+prepositions, conjunctions, auxiliary
+verbs. Okay, auxiliary verbs and a
+
+ align:start position:0%
+verbs. Okay, auxiliary verbs and a
+ 
+
+ align:start position:0%
+verbs. Okay, auxiliary verbs and a
+linking verb. These are
+
+ align:start position:0%
+linking verb. These are
+ 
+
+ align:start position:0%
+linking verb. These are
+function or content words. function.
+
+ align:start position:0%
+function or content words. function.
+ 
+
+ align:start position:0%
+function or content words. function.
+Function. They just serve a function,
+
+ align:start position:0%
+Function. They just serve a function,
+ 
+
+ align:start position:0%
+Function. They just serve a function,
+grammatical function. They don't have
+
+ align:start position:0%
+grammatical function. They don't have
+ 
+
+ align:start position:0%
+grammatical function. They don't have
+any real meanings. Okay. The following
+
+ align:start position:0%
+any real meanings. Okay. The following
+ 
+
+ align:start position:0%
+any real meanings. Okay. The following
+words are usually stressed in a
+
+ align:start position:0%
+words are usually stressed in a
+ 
+
+ align:start position:0%
+words are usually stressed in a
+sentence,
+
+ align:start position:0%
+sentence,
+ 
+
+ align:start position:0%
+sentence,
+nouns,
+
+ align:start position:0%
+nouns,
+ 
+
+ align:start position:0%
+nouns,
+adjectives,
+
+ align:start position:0%
+adjectives,
+ 
+
+ align:start position:0%
+adjectives,
+verbs, adverbs,
+
+ align:start position:0%
+verbs, adverbs,
+ 
+
+ align:start position:0%
+verbs, adverbs,
+numbers, question words, demonstratives.
+
+ align:start position:0%
+numbers, question words, demonstratives.
+ 
+
+ align:start position:0%
+numbers, question words, demonstratives.
+Okay, these are function words or
+
+ align:start position:0%
+Okay, these are function words or
+ 
+
+ align:start position:0%
+Okay, these are function words or
+content words. Content words. Content
+
+ align:start position:0%
+content words. Content words. Content
+ 
+
+ align:start position:0%
+content words. Content words. Content
+words. Okay, they have some sort of
+
+ align:start position:0%
+words. Okay, they have some sort of
+ 
+
+ align:start position:0%
+words. Okay, they have some sort of
+content. They carry meaning.
+
+ align:start position:0%
+content. They carry meaning.
+ 
+
+ align:start position:0%
+content. They carry meaning.
+Okay. So what do you do? You stress
+
+ align:start position:0%
+Okay. So what do you do? You stress
+ 
+
+ align:start position:0%
+Okay. So what do you do? You stress
+content word or function word? You
+
+ align:start position:0%
+content word or function word? You
+ 
+
+ align:start position:0%
+content word or function word? You
+stress the content words in a sentence.
+
+ align:start position:0%
+stress the content words in a sentence.
+ 
+
+ align:start position:0%
+stress the content words in a sentence.
+Okay. What happens to the function
+
+ align:start position:0%
+Okay. What happens to the function
+ 
+
+ align:start position:0%
+Okay. What happens to the function
+words?
+
+ align:start position:0%
+words?
+ 
+
+ align:start position:0%
+words?
+The vowels get reduced. Sometimes we get
+
+ align:start position:0%
+The vowels get reduced. Sometimes we get
+ 
+
+ align:start position:0%
+The vowels get reduced. Sometimes we get
+rid of certain consonants too. Okay.
+
+ align:start position:0%
+rid of certain consonants too. Okay.
+ 
+
+ align:start position:0%
+rid of certain consonants too. Okay.
+That's how we get a rhythm in English.
+
+ align:start position:0%
+That's how we get a rhythm in English.
+ 
+
+ align:start position:0%
+That's how we get a rhythm in English.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+if you go back to your course packet
+
+ align:start position:0%
+if you go back to your course packet
+ 
+
+ align:start position:0%
+if you go back to your course packet
+page 71
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+content words versus function words
+
+ align:start position:0%
+content words versus function words
+ 
+
+ align:start position:0%
+content words versus function words
+rhythm in English is created by
+
+ align:start position:0%
+rhythm in English is created by
+ 
+
+ align:start position:0%
+rhythm in English is created by
+stressing
+
+ align:start position:0%
+stressing
+ 
+
+ align:start position:0%
+stressing
+stressing content content words and by
+
+ align:start position:0%
+stressing content content words and by
+ 
+
+ align:start position:0%
+stressing content content words and by
+reducing the vowels and function words.
+
+ align:start position:0%
+reducing the vowels and function words.
+ 
+
+ align:start position:0%
+reducing the vowels and function words.
+Okay
+
+ align:start position:0%
+Okay
+ 
+
+ align:start position:0%
+Okay
+you can do this da da da da d ta is a
+
+ align:start position:0%
+you can do this da da da da d ta is a
+ 
+
+ align:start position:0%
+you can do this da da da da d ta is a
+stress. Okay, repeat after me. D
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Bill is in front of the room. Bill is in
+
+ align:start position:0%
+Bill is in front of the room. Bill is in
+ 
+
+ align:start position:0%
+Bill is in front of the room. Bill is in
+front of the room. One more time. Bill
+
+ align:start position:0%
+front of the room. One more time. Bill
+ 
+
+ align:start position:0%
+front of the room. One more time. Bill
+is in front of the room. Bill is in
+
+ align:start position:0%
+is in front of the room. Bill is in
+ 
+
+ align:start position:0%
+is in front of the room. Bill is in
+front of the room. Annie is away for the
+
+ align:start position:0%
+front of the room. Annie is away for the
+ 
+
+ align:start position:0%
+front of the room. Annie is away for the
+day. Ann is away for the day. Annie is
+
+ align:start position:0%
+day. Ann is away for the day. Annie is
+ 
+
+ align:start position:0%
+day. Ann is away for the day. Annie is
+away for the day. Ann is away for the
+
+ align:start position:0%
+away for the day. Ann is away for the
+ 
+
+ align:start position:0%
+away for the day. Ann is away for the
+day. Nice. is a town by the sea. Nice is
+
+ align:start position:0%
+day. Nice. is a town by the sea. Nice is
+ 
+
+ align:start position:0%
+day. Nice. is a town by the sea. Nice is
+a town by the sea. Okay.
+
+ align:start position:0%
+a town by the sea. Okay.
+ 
+
+ align:start position:0%
+a town by the sea. Okay.
+Huh?
+
+ align:start position:0%
+Huh?
+ 
+
+ align:start position:0%
+Huh?
+Uh, this is an inverted sentence. A town
+
+ align:start position:0%
+Uh, this is an inverted sentence. A town
+ 
+
+ align:start position:0%
+Uh, this is an inverted sentence. A town
+by the sea is nice.
+
+ align:start position:0%
+by the sea is nice.
+ 
+
+ align:start position:0%
+by the sea is nice.
+It's nice. We have the adjective at the
+
+ align:start position:0%
+It's nice. We have the adjective at the
+ 
+
+ align:start position:0%
+It's nice. We have the adjective at the
+beginning. Nice is a town by the sea.
+
+ align:start position:0%
+beginning. Nice is a town by the sea.
+ 
+
+ align:start position:0%
+beginning. Nice is a town by the sea.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So, here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Bill. And you want to say it like
+
+ align:start position:0%
+Okay. Bill. And you want to say it like
+ 
+
+ align:start position:0%
+Okay. Bill. And you want to say it like
+not Bill is in but Bill.
+
+ align:start position:0%
+not Bill is in but Bill.
+ 
+
+ align:start position:0%
+not Bill is in but Bill.
+Okay. Do the licking. Billen.
+
+ align:start position:0%
+Okay. Do the licking. Billen.
+ 
+
+ align:start position:0%
+Okay. Do the licking. Billen.
+Billisen.
+
+ align:start position:0%
+Billisen.
+ 
+
+ align:start position:0%
+Billisen.
+And what do you do with the next one?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Frana.
+
+ align:start position:0%
+Frana.
+ 
+
+ align:start position:0%
+Frana.
+Get rid of the T. Okay.
+
+ align:start position:0%
+Get rid of the T. Okay.
+ 
+
+ align:start position:0%
+Get rid of the T. Okay.
+And get rid of the Okay. Franada.
+
+ align:start position:0%
+And get rid of the Okay. Franada.
+ 
+
+ align:start position:0%
+And get rid of the Okay. Franada.
+Franada.
+
+ align:start position:0%
+Franada.
+ 
+
+ align:start position:0%
+Franada.
+Franada.
+
+ align:start position:0%
+Franada.
+ 
+
+ align:start position:0%
+Franada.
+Franada. Okay. Bill is in front of the
+
+ align:start position:0%
+Franada. Okay. Bill is in front of the
+ 
+
+ align:start position:0%
+Franada. Okay. Bill is in front of the
+room. Bill is in front of the room. Bill
+
+ align:start position:0%
+room. Bill is in front of the room. Bill
+ 
+
+ align:start position:0%
+room. Bill is in front of the room. Bill
+is in front of the room. Bill is in
+
+ align:start position:0%
+is in front of the room. Bill is in
+ 
+
+ align:start position:0%
+is in front of the room. Bill is in
+front of the room. Okay. The rhythm is
+
+ align:start position:0%
+front of the room. Okay. The rhythm is
+ 
+
+ align:start position:0%
+front of the room. Okay. The rhythm is
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh uh Okay. Bill is in front of the
+
+ align:start position:0%
+uh uh Okay. Bill is in front of the
+ 
+
+ align:start position:0%
+uh uh Okay. Bill is in front of the
+room. Bill is in front of the room.
+
+ align:start position:0%
+room. Bill is in front of the room.
+ 
+
+ align:start position:0%
+room. Bill is in front of the room.
+Annie is away for the day. Annie is away
+
+ align:start position:0%
+Annie is away for the day. Annie is away
+ 
+
+ align:start position:0%
+Annie is away for the day. Annie is away
+for the day. Okay. N
+
+ align:start position:0%
+for the day. Okay. N
+ 
+
+ align:start position:0%
+for the day. Okay. N
+says nice
+
+ align:start position:0%
+says nice
+ 
+
+ align:start position:0%
+says nice
+is a town by the sea.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, let's do the next five
+
+ align:start position:0%
+Okay. So, let's do the next five
+ 
+
+ align:start position:0%
+Okay. So, let's do the next five
+sentences.
+
+ align:start position:0%
+sentences.
+ 
+
+ align:start position:0%
+sentences.
+Next to the next uh the next five
+
+ align:start position:0%
+Next to the next uh the next five
+ 
+
+ align:start position:0%
+Next to the next uh the next five
+sentences. Oh, actually
+
+ align:start position:0%
+sentences. Oh, actually
+ 
+
+ align:start position:0%
+sentences. Oh, actually
+okay. I want you to do this at home.
+
+ align:start position:0%
+okay. I want you to do this at home.
+ 
+
+ align:start position:0%
+okay. I want you to do this at home.
+Okay. For instance,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay. Now, the first thing, find the
+
+ align:start position:0%
+okay. Now, the first thing, find the
+ 
+
+ align:start position:0%
+okay. Now, the first thing, find the
+right mattress. The first thing that you
+
+ align:start position:0%
+right mattress. The first thing that you
+ 
+
+ align:start position:0%
+right mattress. The first thing that you
+need to do is in a sentence, how many
+
+ align:start position:0%
+need to do is in a sentence, how many
+ 
+
+ align:start position:0%
+need to do is in a sentence, how many
+syllables
+
+ align:start position:0%
+syllables
+ 
+
+ align:start position:0%
+syllables
+are there? That's the first thing that
+
+ align:start position:0%
+are there? That's the first thing that
+ 
+
+ align:start position:0%
+are there? That's the first thing that
+you have to figure out. How many
+
+ align:start position:0%
+you have to figure out. How many
+ 
+
+ align:start position:0%
+you have to figure out. How many
+syllables does try to sleep? You
+
+ align:start position:0%
+syllables does try to sleep? You
+ 
+
+ align:start position:0%
+syllables does try to sleep? You
+promised the phone. How many syllables
+
+ align:start position:0%
+promised the phone. How many syllables
+ 
+
+ align:start position:0%
+promised the phone. How many syllables
+are there? I'd like to sleep. I'd like
+
+ align:start position:0%
+are there? I'd like to sleep. I'd like
+ 
+
+ align:start position:0%
+are there? I'd like to sleep. I'd like
+to sleep. How many syllables? Now, after
+
+ align:start position:0%
+to sleep. How many syllables? Now, after
+ 
+
+ align:start position:0%
+to sleep. How many syllables? Now, after
+that, first figure out how many
+
+ align:start position:0%
+that, first figure out how many
+ 
+
+ align:start position:0%
+that, first figure out how many
+syllables uh each sentence has. After
+
+ align:start position:0%
+syllables uh each sentence has. After
+ 
+
+ align:start position:0%
+syllables uh each sentence has. After
+that, you want to figure out, okay,
+
+ align:start position:0%
+that, you want to figure out, okay,
+ 
+
+ align:start position:0%
+that, you want to figure out, okay,
+which one is a content word, which one
+
+ align:start position:0%
+which one is a content word, which one
+ 
+
+ align:start position:0%
+which one is a content word, which one
+is a function word. Okay? and ta and you
+
+ align:start position:0%
+is a function word. Okay? and ta and you
+ 
+
+ align:start position:0%
+is a function word. Okay? and ta and you
+know content for instance like promised
+
+ align:start position:0%
+know content for instance like promised
+ 
+
+ align:start position:0%
+know content for instance like promised
+has many syllables
+
+ align:start position:0%
+has many syllables
+ 
+
+ align:start position:0%
+has many syllables
+which one is which one is stressed okay
+
+ align:start position:0%
+which one is which one is stressed okay
+ 
+
+ align:start position:0%
+which one is which one is stressed okay
+you need to figure that out
+
+ align:start position:0%
+you need to figure that out
+ 
+
+ align:start position:0%
+you need to figure that out
+so do that
+
+ align:start position:0%
+so do that
+ 
+
+ align:start position:0%
+so do that
+and then the next thing that I want you
+
+ align:start position:0%
+and then the next thing that I want you
+ 
+
+ align:start position:0%
+and then the next thing that I want you
+to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next thing that I want you to do uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's turn to page Page 89 in your book.
+
+ align:start position:0%
+let's turn to page Page 89 in your book.
+ 
+
+ align:start position:0%
+let's turn to page Page 89 in your book.
+Page 89 in your book.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Page 9. Page 89 in your book.
+
+ align:start position:0%
+Page 9. Page 89 in your book.
+ 
+
+ align:start position:0%
+Page 9. Page 89 in your book.
+88.89.
+
+ align:start position:0%
+88.89.
+ 
+
+ align:start position:0%
+88.89.
+You have 8889. You have
+
+ align:start position:0%
+You have 8889. You have
+ 
+
+ align:start position:0%
+You have 8889. You have
+uh examples of reduced function words.
+
+ align:start position:0%
+uh examples of reduced function words.
+ 
+
+ align:start position:0%
+uh examples of reduced function words.
+On page 8889.
+
+ align:start position:0%
+On page 8889.
+ 
+
+ align:start position:0%
+On page 8889.
+Okay. 8889.
+
+ align:start position:0%
+Okay. 8889.
+ 
+
+ align:start position:0%
+Okay. 8889.
+Pay special attention to number five.
+
+ align:start position:0%
+Pay special attention to number five.
+ 
+
+ align:start position:0%
+Pay special attention to number five.
+Auxiliary verbs. Okay. Number five.
+
+ align:start position:0%
+Auxiliary verbs. Okay. Number five.
+ 
+
+ align:start position:0%
+Auxiliary verbs. Okay. Number five.
+Number five. And I want you to practice.
+
+ align:start position:0%
+Number five. And I want you to practice.
+ 
+
+ align:start position:0%
+Number five. And I want you to practice.
+Cats chase mice. The cats chase mice.
+
+ align:start position:0%
+Cats chase mice. The cats chase mice.
+ 
+
+ align:start position:0%
+Cats chase mice. The cats chase mice.
+Okay. I want you. One, two, three. One,
+
+ align:start position:0%
+Okay. I want you. One, two, three. One,
+ 
+
+ align:start position:0%
+Okay. I want you. One, two, three. One,
+two. You can stomp along. One, two,
+
+ align:start position:0%
+two. You can stomp along. One, two,
+ 
+
+ align:start position:0%
+two. You can stomp along. One, two,
+three. Cat. Say it really slow. Cats
+
+ align:start position:0%
+three. Cat. Say it really slow. Cats
+ 
+
+ align:start position:0%
+three. Cat. Say it really slow. Cats
+chase mice. The cats chase mice. The
+
+ align:start position:0%
+chase mice. The cats chase mice. The
+ 
+
+ align:start position:0%
+chase mice. The cats chase mice. The
+cats. The cha. The cats. But you need to
+
+ align:start position:0%
+cats. The cha. The cats. But you need to
+ 
+
+ align:start position:0%
+cats. The cha. The cats. But you need to
+apply the rules. I don't want you to say
+
+ align:start position:0%
+apply the rules. I don't want you to say
+ 
+
+ align:start position:0%
+apply the rules. I don't want you to say
+the cats have chased the cats have. If
+
+ align:start position:0%
+the cats have chased the cats have. If
+ 
+
+ align:start position:0%
+the cats have chased the cats have. If
+you want to say, if you're going to try
+
+ align:start position:0%
+you want to say, if you're going to try
+ 
+
+ align:start position:0%
+you want to say, if you're going to try
+to say cats have, that's gonna be too
+
+ align:start position:0%
+to say cats have, that's gonna be too
+ 
+
+ align:start position:0%
+to say cats have, that's gonna be too
+difficult. You need to say the cat
+
+ align:start position:0%
+difficult. You need to say the cat
+ 
+
+ align:start position:0%
+difficult. You need to say the cat
+is going to disappear, right? Cat. So
+
+ align:start position:0%
+is going to disappear, right? Cat. So
+ 
+
+ align:start position:0%
+is going to disappear, right? Cat. So
+you're going to say cat.
+
+ align:start position:0%
+you're going to say cat.
+ 
+
+ align:start position:0%
+you're going to say cat.
+You can you can have cat or cat. Cats
+
+ align:start position:0%
+You can you can have cat or cat. Cats
+ 
+
+ align:start position:0%
+You can you can have cat or cat. Cats
+chased mice. Okay. Next one.
+
+ align:start position:0%
+chased mice. Okay. Next one.
+ 
+
+ align:start position:0%
+chased mice. Okay. Next one.
+The last one. The cats might have might.
+
+ align:start position:0%
+The last one. The cats might have might.
+ 
+
+ align:start position:0%
+The last one. The cats might have might.
+You don't want to say You don't want to
+
+ align:start position:0%
+You don't want to say You don't want to
+ 
+
+ align:start position:0%
+You don't want to say You don't want to
+say might have been. That's gonna take
+
+ align:start position:0%
+say might have been. That's gonna take
+ 
+
+ align:start position:0%
+say might have been. That's gonna take
+too long. Might have been. Might have
+
+ align:start position:0%
+too long. Might have been. Might have
+ 
+
+ align:start position:0%
+too long. Might have been. Might have
+been. Might have been. Okay. The first
+
+ align:start position:0%
+been. Might have been. Okay. The first
+ 
+
+ align:start position:0%
+been. Might have been. Okay. The first
+one. Might have been. But I want you to
+
+ align:start position:0%
+one. Might have been. But I want you to
+ 
+
+ align:start position:0%
+one. Might have been. But I want you to
+write it down. I want you to write it
+
+ align:start position:0%
+write it down. I want you to write it
+ 
+
+ align:start position:0%
+write it down. I want you to write it
+down in your in your in your course
+
+ align:start position:0%
+down in your in your in your course
+ 
+
+ align:start position:0%
+down in your in your in your course
+packet. I want you to analyze it first.
+
+ align:start position:0%
+packet. I want you to analyze it first.
+ 
+
+ align:start position:0%
+packet. I want you to analyze it first.
+Okay?
+
+ align:start position:0%
+Okay?
+ 
+
+ align:start position:0%
+Okay?
+If you have this, I want you to analy.
+
+ align:start position:0%
+If you have this, I want you to analy.
+ 
+
+ align:start position:0%
+If you have this, I want you to analy.
+Okay?
+
+ align:start position:0%
+Okay?
+ 
+
+ align:start position:0%
+Okay?
+Right. Write the phonetic symbols. My
+
+ align:start position:0%
+Right. Write the phonetic symbols. My
+ 
+
+ align:start position:0%
+Right. Write the phonetic symbols. My
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+this disappears. So, uh, okay. And we
+
+ align:start position:0%
+this disappears. So, uh, okay. And we
+ 
+
+ align:start position:0%
+this disappears. So, uh, okay. And we
+get rid of that. Okay. So, like this.
+
+ align:start position:0%
+get rid of that. Okay. So, like this.
+ 
+
+ align:start position:0%
+get rid of that. Okay. So, like this.
+Might have been. Might have been. Might
+
+ align:start position:0%
+Might have been. Might have been. Might
+ 
+
+ align:start position:0%
+Might have been. Might have been. Might
+have been. The cats might might have
+
+ align:start position:0%
+have been. The cats might might have
+ 
+
+ align:start position:0%
+have been. The cats might might have
+been. Might have been. Might have been.
+
+ align:start position:0%
+been. Might have been. Might have been.
+ 
+
+ align:start position:0%
+been. Might have been. Might have been.
+At first, say it really slowly. Might
+
+ align:start position:0%
+At first, say it really slowly. Might
+ 
+
+ align:start position:0%
+At first, say it really slowly. Might
+have been. Might have been. Might have
+
+ align:start position:0%
+have been. Might have been. Might have
+ 
+
+ align:start position:0%
+have been. Might have been. Might have
+been. The cats might have been chasing
+
+ align:start position:0%
+been. The cats might have been chasing
+ 
+
+ align:start position:0%
+been. The cats might have been chasing
+the mice. Or the one before that, you
+
+ align:start position:0%
+the mice. Or the one before that, you
+ 
+
+ align:start position:0%
+the mice. Or the one before that, you
+could say,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the cats.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If you do this, you write it like, okay,
+
+ align:start position:0%
+If you do this, you write it like, okay,
+ 
+
+ align:start position:0%
+If you do this, you write it like, okay,
+cat.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, you can either you can keep this
+
+ align:start position:0%
+Okay, you can either you can keep this
+ 
+
+ align:start position:0%
+Okay, you can either you can keep this
+or get rid of this the catin. Okay. Then
+
+ align:start position:0%
+or get rid of this the catin. Okay. Then
+ 
+
+ align:start position:0%
+or get rid of this the catin. Okay. Then
+you you practice
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cat. Cat. Cat.
\ No newline at end of file
diff --git a/unTWUTwum1s.txt b/unTWUTwum1s.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b8b519a72d96503cffcc9203dcb2d7cb5c752d9e
--- /dev/null
+++ b/unTWUTwum1s.txt
@@ -0,0 +1,14320 @@
+align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+welcome so this is
+
+ align:start position:0%
+welcome so this is
+ 
+
+ align:start position:0%
+welcome so this is
+243 I hope you're in the right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+place
+
+ align:start position:0%
+place
+ 
+
+ align:start position:0%
+place
+um okay my name is Johan Pao
+
+ align:start position:0%
+um okay my name is Johan Pao
+ 
+
+ align:start position:0%
+um okay my name is Johan Pao
+Beretta and
+
+ align:start position:0%
+Beretta and
+ 
+
+ align:start position:0%
+Beretta and
+um I am very very happy to teach this
+
+ align:start position:0%
+um I am very very happy to teach this
+ 
+
+ align:start position:0%
+um I am very very happy to teach this
+course it's as you know it's the first
+
+ align:start position:0%
+course it's as you know it's the first
+ 
+
+ align:start position:0%
+course it's as you know it's the first
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+um this
+
+ align:start position:0%
+um this
+ 
+
+ align:start position:0%
+um this
+spring although this course been taught
+
+ align:start position:0%
+spring although this course been taught
+ 
+
+ align:start position:0%
+spring although this course been taught
+very similar in poly Technic of Milano
+
+ align:start position:0%
+very similar in poly Technic of Milano
+ 
+
+ align:start position:0%
+very similar in poly Technic of Milano
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+about maybe 12
+
+ align:start position:0%
+about maybe 12
+ 
+
+ align:start position:0%
+about maybe 12
+years um for the first year um PhD
+
+ align:start position:0%
+years um for the first year um PhD
+ 
+
+ align:start position:0%
+years um for the first year um PhD
+students in energy in the energy program
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'm using view graphs that I've
+
+ align:start position:0%
+so I'm using view graphs that I've
+ 
+
+ align:start position:0%
+so I'm using view graphs that I've
+developed over the
+
+ align:start position:0%
+developed over the
+ 
+
+ align:start position:0%
+developed over the
+years in fact this is a very particular
+
+ align:start position:0%
+years in fact this is a very particular
+ 
+
+ align:start position:0%
+years in fact this is a very particular
+year for thermodynamics as you know it's
+
+ align:start position:0%
+year for thermodynamics as you know it's
+ 
+
+ align:start position:0%
+year for thermodynamics as you know it's
+the 200 uh uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+birthday and
+
+ align:start position:0%
+birthday and
+ 
+
+ align:start position:0%
+birthday and
+I I like to
+
+ align:start position:0%
+I I like to
+ 
+
+ align:start position:0%
+I I like to
+say that
+
+ align:start position:0%
+say that
+ 
+
+ align:start position:0%
+say that
+um right
+
+ align:start position:0%
+um right
+ 
+
+ align:start position:0%
+um right
+now I I am uh I reached onethird of the
+
+ align:start position:0%
+now I I am uh I reached onethird of the
+ 
+
+ align:start position:0%
+now I I am uh I reached onethird of the
+age of
+
+ align:start position:0%
+age of
+ 
+
+ align:start position:0%
+age of
+thermodynamics when I started studying
+
+ align:start position:0%
+thermodynamics when I started studying
+ 
+
+ align:start position:0%
+thermodynamics when I started studying
+it uh
+
+ align:start position:0%
+it uh
+ 
+
+ align:start position:0%
+it uh
+1978 it was
+
+ align:start position:0%
+1978 it was
+ 
+
+ align:start position:0%
+1978 it was
+17th
+
+ align:start position:0%
+17th
+ 
+
+ align:start position:0%
+17th
+so uh it's my entire uh academic career
+
+ align:start position:0%
+so uh it's my entire uh academic career
+ 
+
+ align:start position:0%
+so uh it's my entire uh academic career
+has been around
+
+ align:start position:0%
+has been around
+ 
+
+ align:start position:0%
+has been around
+this of course carau is only one of many
+
+ align:start position:0%
+this of course carau is only one of many
+ 
+
+ align:start position:0%
+this of course carau is only one of many
+who have contributed
+
+ align:start position:0%
+who have contributed
+ 
+
+ align:start position:0%
+who have contributed
+over the two centu term Dynamics like
+
+ align:start position:0%
+over the two centu term Dynamics like
+ 
+
+ align:start position:0%
+over the two centu term Dynamics like
+carau Jew ranking elol Claus Kelvin m v
+
+ align:start position:0%
+carau Jew ranking elol Claus Kelvin m v
+ 
+
+ align:start position:0%
+carau Jew ranking elol Claus Kelvin m v
+deral
+
+ align:start position:0%
+deral
+ 
+
+ align:start position:0%
+deral
+Gibbs bolman van plank dhan n
+
+ align:start position:0%
+Gibbs bolman van plank dhan n
+ 
+
+ align:start position:0%
+Gibbs bolman van plank dhan n
+sommerfield Kate odor Einstein Kenan and
+
+ align:start position:0%
+sommerfield Kate odor Einstein Kenan and
+ 
+
+ align:start position:0%
+sommerfield Kate odor Einstein Kenan and
+I say a few words more about him FY
+
+ align:start position:0%
+I say a few words more about him FY
+ 
+
+ align:start position:0%
+I say a few words more about him FY
+gugenheim onager Zigler the gr pin
+
+ align:start position:0%
+gugenheim onager Zigler the gr pin
+ 
+
+ align:start position:0%
+gugenheim onager Zigler the gr pin
+mazour atopos
+
+ align:start position:0%
+mazour atopos
+ 
+
+ align:start position:0%
+mazour atopos
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+PRS and I apologize for those
+
+ align:start position:0%
+PRS and I apologize for those
+ 
+
+ align:start position:0%
+PRS and I apologize for those
+who I I I haven't uh written uh down
+
+ align:start position:0%
+who I I I haven't uh written uh down
+ 
+
+ align:start position:0%
+who I I I haven't uh written uh down
+there actually may notice that the only
+
+ align:start position:0%
+there actually may notice that the only
+ 
+
+ align:start position:0%
+there actually may notice that the only
+person currently alive is U John
+
+ align:start position:0%
+person currently alive is U John
+ 
+
+ align:start position:0%
+person currently alive is U John
+prit but he deserves I believe a place
+
+ align:start position:0%
+prit but he deserves I believe a place
+ 
+
+ align:start position:0%
+prit but he deserves I believe a place
+there anyway for he deserved it for a
+
+ align:start position:0%
+there anyway for he deserved it for a
+ 
+
+ align:start position:0%
+there anyway for he deserved it for a
+long time uh
+
+ align:start position:0%
+long time uh
+ 
+
+ align:start position:0%
+long time uh
+now the reason I'm
+
+ align:start position:0%
+now the reason I'm
+ 
+
+ align:start position:0%
+now the reason I'm
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+particularly happy about teaching this
+
+ align:start position:0%
+particularly happy about teaching this
+ 
+
+ align:start position:0%
+particularly happy about teaching this
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+here it uh goes back to Kenan and
+
+ align:start position:0%
+here it uh goes back to Kenan and
+ 
+
+ align:start position:0%
+here it uh goes back to Kenan and
+atopos
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I like to reference them I mean Kenan
+
+ align:start position:0%
+um I like to reference them I mean Kenan
+ 
+
+ align:start position:0%
+um I like to reference them I mean Kenan
+atopos but also the late professor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gios
+
+ align:start position:0%
+gios
+ 
+
+ align:start position:0%
+gios
+uh sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as the Kenan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+School of of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thermodynamics
+
+ align:start position:0%
+thermodynamics
+ 
+
+ align:start position:0%
+thermodynamics
+because Kenan who by the way was uh uh
+
+ align:start position:0%
+because Kenan who by the way was uh uh
+ 
+
+ align:start position:0%
+because Kenan who by the way was uh uh
+using the office downstairs in 3-
+
+ align:start position:0%
+using the office downstairs in 3-
+ 
+
+ align:start position:0%
+using the office downstairs in 3-
+339 as we also did me atopos for a few
+
+ align:start position:0%
+339 as we also did me atopos for a few
+ 
+
+ align:start position:0%
+339 as we also did me atopos for a few
+years and me for just uh five years when
+
+ align:start position:0%
+years and me for just uh five years when
+ 
+
+ align:start position:0%
+years and me for just uh five years when
+I was young uh we used the same room so
+
+ align:start position:0%
+I was young uh we used the same room so
+ 
+
+ align:start position:0%
+I was young uh we used the same room so
+that was a privilege for
+
+ align:start position:0%
+that was a privilege for
+ 
+
+ align:start position:0%
+that was a privilege for
+me uh as you see these are the
+
+ align:start position:0%
+me uh as you see these are the
+ 
+
+ align:start position:0%
+me uh as you see these are the
+books uh that have characterized this uh
+
+ align:start position:0%
+books uh that have characterized this uh
+ 
+
+ align:start position:0%
+books uh that have characterized this uh
+School of uh teaching from Dynamics you
+
+ align:start position:0%
+School of uh teaching from Dynamics you
+ 
+
+ align:start position:0%
+School of uh teaching from Dynamics you
+will see it's kind of different from the
+
+ align:start position:0%
+will see it's kind of different from the
+ 
+
+ align:start position:0%
+will see it's kind of different from the
+traditional
+
+ align:start position:0%
+traditional
+ 
+
+ align:start position:0%
+traditional
+Exposition uh I like to say more General
+
+ align:start position:0%
+Exposition uh I like to say more General
+ 
+
+ align:start position:0%
+Exposition uh I like to say more General
+and more uh free of uh uh vicious
+
+ align:start position:0%
+and more uh free of uh uh vicious
+ 
+
+ align:start position:0%
+and more uh free of uh uh vicious
+logical Loops that are typical of
+
+ align:start position:0%
+logical Loops that are typical of
+ 
+
+ align:start position:0%
+logical Loops that are typical of
+theistic presentations of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thermodynamics Professor
+
+ align:start position:0%
+thermodynamics Professor
+ 
+
+ align:start position:0%
+thermodynamics Professor
+gpos has been
+
+ align:start position:0%
+gpos has been
+ 
+
+ align:start position:0%
+gpos has been
+teaching this course or maybe the course
+
+ align:start position:0%
+teaching this course or maybe the course
+ 
+
+ align:start position:0%
+teaching this course or maybe the course
+that now has become
+
+ align:start position:0%
+that now has become
+ 
+
+ align:start position:0%
+that now has become
+242 uh it used to be called
+
+ align:start position:0%
+242 uh it used to be called
+ 
+
+ align:start position:0%
+242 uh it used to be called
+2451 he thought that for about 20 or
+
+ align:start position:0%
+2451 he thought that for about 20 or
+ 
+
+ align:start position:0%
+2451 he thought that for about 20 or
+maybe 25 years
+
+ align:start position:0%
+maybe 25 years
+ 
+
+ align:start position:0%
+maybe 25 years
+and I helped him uh during those years
+
+ align:start position:0%
+and I helped him uh during those years
+ 
+
+ align:start position:0%
+and I helped him uh during those years
+and then we came up with this book this
+
+ align:start position:0%
+and then we came up with this book this
+ 
+
+ align:start position:0%
+and then we came up with this book this
+book uh uh is uh in the background of uh
+
+ align:start position:0%
+book uh uh is uh in the background of uh
+ 
+
+ align:start position:0%
+book uh uh is uh in the background of uh
+what we will we will do
+
+ align:start position:0%
+what we will we will do
+ 
+
+ align:start position:0%
+what we will we will do
+here uh only in the background not that
+
+ align:start position:0%
+here uh only in the background not that
+ 
+
+ align:start position:0%
+here uh only in the background not that
+we are going to cover the book but it
+
+ align:start position:0%
+we are going to cover the book but it
+ 
+
+ align:start position:0%
+we are going to cover the book but it
+helps me a lot the the fact that uh when
+
+ align:start position:0%
+helps me a lot the the fact that uh when
+ 
+
+ align:start position:0%
+helps me a lot the the fact that uh when
+in class I would say you can prove or it
+
+ align:start position:0%
+in class I would say you can prove or it
+ 
+
+ align:start position:0%
+in class I would say you can prove or it
+can be proved you can find the proofs
+
+ align:start position:0%
+can be proved you can find the proofs
+ 
+
+ align:start position:0%
+can be proved you can find the proofs
+all in all details in that book which is
+
+ align:start position:0%
+all in all details in that book which is
+ 
+
+ align:start position:0%
+all in all details in that book which is
+uh I mean
+
+ align:start position:0%
+uh I mean
+ 
+
+ align:start position:0%
+uh I mean
+very good for my from my point of view
+
+ align:start position:0%
+very good for my from my point of view
+ 
+
+ align:start position:0%
+very good for my from my point of view
+because I don't need to spend time
+
+ align:start position:0%
+because I don't need to spend time
+ 
+
+ align:start position:0%
+because I don't need to spend time
+repeating the proofs except only very
+
+ align:start position:0%
+repeating the proofs except only very
+ 
+
+ align:start position:0%
+repeating the proofs except only very
+few fundamental ones and easy
+
+ align:start position:0%
+few fundamental ones and easy
+ 
+
+ align:start position:0%
+few fundamental ones and easy
+ones uh but you can find them there and
+
+ align:start position:0%
+ones uh but you can find them there and
+ 
+
+ align:start position:0%
+ones uh but you can find them there and
+if you are uh very fond of the subject
+
+ align:start position:0%
+if you are uh very fond of the subject
+ 
+
+ align:start position:0%
+if you are uh very fond of the subject
+you want to go deep you you may study it
+
+ align:start position:0%
+you want to go deep you you may study it
+ 
+
+ align:start position:0%
+you want to go deep you you may study it
+there and you may come and discuss uh
+
+ align:start position:0%
+there and you may come and discuss uh
+ 
+
+ align:start position:0%
+there and you may come and discuss uh
+them uh uh my office anytime you want
+
+ align:start position:0%
+them uh uh my office anytime you want
+ 
+
+ align:start position:0%
+them uh uh my office anytime you want
+actually my office hours are anytime uh
+
+ align:start position:0%
+actually my office hours are anytime uh
+ 
+
+ align:start position:0%
+actually my office hours are anytime uh
+uh either by a pointer or just drop by
+
+ align:start position:0%
+uh either by a pointer or just drop by
+ 
+
+ align:start position:0%
+uh either by a pointer or just drop by
+most of the times all the time I'll will
+
+ align:start position:0%
+most of the times all the time I'll will
+ 
+
+ align:start position:0%
+most of the times all the time I'll will
+be in the office working so um you can
+
+ align:start position:0%
+be in the office working so um you can
+ 
+
+ align:start position:0%
+be in the office working so um you can
+come or call
+
+ align:start position:0%
+come or call
+ 
+
+ align:start position:0%
+come or call
+anytime if you want we can set up also
+
+ align:start position:0%
+anytime if you want we can set up also
+ 
+
+ align:start position:0%
+anytime if you want we can set up also
+more official uh uh office
+
+ align:start position:0%
+more official uh uh office
+ 
+
+ align:start position:0%
+more official uh uh office
+hours um now the objective of this
+
+ align:start position:0%
+hours um now the objective of this
+ 
+
+ align:start position:0%
+hours um now the objective of this
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+uh is not
+
+ align:start position:0%
+uh is not
+ 
+
+ align:start position:0%
+uh is not
+applications because I presume that the
+
+ align:start position:0%
+applications because I presume that the
+ 
+
+ align:start position:0%
+applications because I presume that the
+applications have been seen already in
+
+ align:start position:0%
+applications have been seen already in
+ 
+
+ align:start position:0%
+applications have been seen already in
+previous courses that you've been
+
+ align:start position:0%
+previous courses that you've been
+ 
+
+ align:start position:0%
+previous courses that you've been
+exposed to or maybe in your uh doctoral
+
+ align:start position:0%
+exposed to or maybe in your uh doctoral
+ 
+
+ align:start position:0%
+exposed to or maybe in your uh doctoral
+or Master's thesis
+
+ align:start position:0%
+or Master's thesis
+ 
+
+ align:start position:0%
+or Master's thesis
+work what I want to put the emphasis on
+
+ align:start position:0%
+work what I want to put the emphasis on
+ 
+
+ align:start position:0%
+work what I want to put the emphasis on
+is a broad perspective on uh the
+
+ align:start position:0%
+is a broad perspective on uh the
+ 
+
+ align:start position:0%
+is a broad perspective on uh the
+assumptions that are uh needed to make
+
+ align:start position:0%
+assumptions that are uh needed to make
+ 
+
+ align:start position:0%
+assumptions that are uh needed to make
+or that are behind certain
+
+ align:start position:0%
+or that are behind certain
+ 
+
+ align:start position:0%
+or that are behind certain
+models standard
+
+ align:start position:0%
+models standard
+ 
+
+ align:start position:0%
+models standard
+models little nonstandard models uh
+
+ align:start position:0%
+models little nonstandard models uh
+ 
+
+ align:start position:0%
+models little nonstandard models uh
+models that uh you use
+
+ align:start position:0%
+models that uh you use
+ 
+
+ align:start position:0%
+models that uh you use
+in uh physics and in
+
+ align:start position:0%
+in uh physics and in
+ 
+
+ align:start position:0%
+in uh physics and in
+engineering because thermodynamics as
+
+ align:start position:0%
+engineering because thermodynamics as
+ 
+
+ align:start position:0%
+engineering because thermodynamics as
+you know uh uh covers
+
+ align:start position:0%
+you know uh uh covers
+ 
+
+ align:start position:0%
+you know uh uh covers
+applications in an enormous amount of
+
+ align:start position:0%
+applications in an enormous amount of
+ 
+
+ align:start position:0%
+applications in an enormous amount of
+fields so no no body can really say I
+
+ align:start position:0%
+fields so no no body can really say I
+ 
+
+ align:start position:0%
+fields so no no body can really say I
+know all applications of
+
+ align:start position:0%
+know all applications of
+ 
+
+ align:start position:0%
+know all applications of
+thermodynamics they they're essentially
+
+ align:start position:0%
+thermodynamics they they're essentially
+ 
+
+ align:start position:0%
+thermodynamics they they're essentially
+infinite the good thing since we are in
+
+ align:start position:0%
+infinite the good thing since we are in
+ 
+
+ align:start position:0%
+infinite the good thing since we are in
+an engineering department is that as you
+
+ align:start position:0%
+an engineering department is that as you
+ 
+
+ align:start position:0%
+an engineering department is that as you
+know carau was an engineer
+
+ align:start position:0%
+know carau was an engineer
+ 
+
+ align:start position:0%
+know carau was an engineer
+thermodynamics started from
+
+ align:start position:0%
+thermodynamics started from
+ 
+
+ align:start position:0%
+thermodynamics started from
+engineering and then it was picked up by
+
+ align:start position:0%
+engineering and then it was picked up by
+ 
+
+ align:start position:0%
+engineering and then it was picked up by
+physicists and so it goes back and forth
+
+ align:start position:0%
+physicists and so it goes back and forth
+ 
+
+ align:start position:0%
+physicists and so it goes back and forth
+so we share uh the subject we we
+
+ align:start position:0%
+so we share uh the subject we we
+ 
+
+ align:start position:0%
+so we share uh the subject we we
+Engineers share the subject the subject
+
+ align:start position:0%
+Engineers share the subject the subject
+ 
+
+ align:start position:0%
+Engineers share the subject the subject
+with the physicist and the physicist
+
+ align:start position:0%
+with the physicist and the physicist
+ 
+
+ align:start position:0%
+with the physicist and the physicist
+share it with Engineers not only
+
+ align:start position:0%
+share it with Engineers not only
+ 
+
+ align:start position:0%
+share it with Engineers not only
+engineer I mean all kinds of engineering
+
+ align:start position:0%
+engineer I mean all kinds of engineering
+ 
+
+ align:start position:0%
+engineer I mean all kinds of engineering
+so including chemistry chemical
+
+ align:start position:0%
+so including chemistry chemical
+ 
+
+ align:start position:0%
+so including chemistry chemical
+engineering is very strong in very
+
+ align:start position:0%
+engineering is very strong in very
+ 
+
+ align:start position:0%
+engineering is very strong in very
+strong uh
+
+ align:start position:0%
+strong uh
+ 
+
+ align:start position:0%
+strong uh
+history and DEP about
+
+ align:start position:0%
+history and DEP about
+ 
+
+ align:start position:0%
+history and DEP about
+thermodynamics now the emphasis of of
+
+ align:start position:0%
+thermodynamics now the emphasis of of
+ 
+
+ align:start position:0%
+thermodynamics now the emphasis of of
+the course is on non
+
+ align:start position:0%
+the course is on non
+ 
+
+ align:start position:0%
+the course is on non
+equilibrium uh until when I did my PhD
+
+ align:start position:0%
+equilibrium uh until when I did my PhD
+ 
+
+ align:start position:0%
+equilibrium uh until when I did my PhD
+studies here uh
+
+ align:start position:0%
+studies here uh
+ 
+
+ align:start position:0%
+studies here uh
+thermodynamics in those times was
+
+ align:start position:0%
+thermodynamics in those times was
+ 
+
+ align:start position:0%
+thermodynamics in those times was
+considered a dead
+
+ align:start position:0%
+considered a dead
+ 
+
+ align:start position:0%
+considered a dead
+subject because everybody was thinking
+
+ align:start position:0%
+subject because everybody was thinking
+ 
+
+ align:start position:0%
+subject because everybody was thinking
+with thermodynamics is just
+
+ align:start position:0%
+with thermodynamics is just
+ 
+
+ align:start position:0%
+with thermodynamics is just
+equilibrium um and in fact that was a
+
+ align:start position:0%
+equilibrium um and in fact that was a
+ 
+
+ align:start position:0%
+equilibrium um and in fact that was a
+um for a still uh few years later maybe
+
+ align:start position:0%
+um for a still uh few years later maybe
+ 
+
+ align:start position:0%
+um for a still uh few years later maybe
+in the the late
+
+ align:start position:0%
+in the the late
+ 
+
+ align:start position:0%
+in the the late
+90s that uh there's been
+
+ align:start position:0%
+90s that uh there's been
+ 
+
+ align:start position:0%
+90s that uh there's been
+a Revival of thermodynamics because of
+
+ align:start position:0%
+a Revival of thermodynamics because of
+ 
+
+ align:start position:0%
+a Revival of thermodynamics because of
+non equilibrium because of ir reversible
+
+ align:start position:0%
+non equilibrium because of ir reversible
+ 
+
+ align:start position:0%
+non equilibrium because of ir reversible
+processes now and also because of
+
+ align:start position:0%
+processes now and also because of
+ 
+
+ align:start position:0%
+processes now and also because of
+quantum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thermodynamics now it is a an enormous
+
+ align:start position:0%
+thermodynamics now it is a an enormous
+ 
+
+ align:start position:0%
+thermodynamics now it is a an enormous
+field Quantum thermodynamics in those
+
+ align:start position:0%
+field Quantum thermodynamics in those
+ 
+
+ align:start position:0%
+field Quantum thermodynamics in those
+times it was considered
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+useless and asopos andos
+
+ align:start position:0%
+useless and asopos andos
+ 
+
+ align:start position:0%
+useless and asopos andos
+in my opinion are the true pioneers of
+
+ align:start position:0%
+in my opinion are the true pioneers of
+ 
+
+ align:start position:0%
+in my opinion are the true pioneers of
+of that subject even though there since
+
+ align:start position:0%
+of that subject even though there since
+ 
+
+ align:start position:0%
+of that subject even though there since
+their point of view was not
+
+ align:start position:0%
+their point of view was not
+ 
+
+ align:start position:0%
+their point of view was not
+standard uh they're not so recognized
+
+ align:start position:0%
+standard uh they're not so recognized
+ 
+
+ align:start position:0%
+standard uh they're not so recognized
+not everywhere as
+
+ align:start position:0%
+not everywhere as
+ 
+
+ align:start position:0%
+not everywhere as
+Pioneers but if you read the recent U uh
+
+ align:start position:0%
+Pioneers but if you read the recent U uh
+ 
+
+ align:start position:0%
+Pioneers but if you read the recent U uh
+paper in science or scientific America
+
+ align:start position:0%
+paper in science or scientific America
+ 
+
+ align:start position:0%
+paper in science or scientific America
+uh about Quantum Dynamics I think it's
+
+ align:start position:0%
+uh about Quantum Dynamics I think it's
+ 
+
+ align:start position:0%
+uh about Quantum Dynamics I think it's
+called Quantum Ste te Punk um who was
+
+ align:start position:0%
+called Quantum Ste te Punk um who was
+ 
+
+ align:start position:0%
+called Quantum Ste te Punk um who was
+written by uh by the way the winner of a
+
+ align:start position:0%
+written by uh by the way the winner of a
+ 
+
+ align:start position:0%
+written by uh by the way the winner of a
+of the of a prein price in
+
+ align:start position:0%
+of the of a prein price in
+ 
+
+ align:start position:0%
+of the of a prein price in
+thermodynamics
+
+ align:start position:0%
+thermodynamics
+ 
+
+ align:start position:0%
+thermodynamics
+uh which I happen to be involved with uh
+
+ align:start position:0%
+uh which I happen to be involved with uh
+ 
+
+ align:start position:0%
+uh which I happen to be involved with uh
+uh well she wrote this book steampunk
+
+ align:start position:0%
+uh well she wrote this book steampunk
+ 
+
+ align:start position:0%
+uh well she wrote this book steampunk
+Quantum thermodynamics and also this
+
+ align:start position:0%
+Quantum thermodynamics and also this
+ 
+
+ align:start position:0%
+Quantum thermodynamics and also this
+science article where she does recognize
+
+ align:start position:0%
+science article where she does recognize
+ 
+
+ align:start position:0%
+science article where she does recognize
+the roles of atopos and
+
+ align:start position:0%
+the roles of atopos and
+ 
+
+ align:start position:0%
+the roles of atopos and
+gios uh so the course is three parts one
+
+ align:start position:0%
+gios uh so the course is three parts one
+ 
+
+ align:start position:0%
+gios uh so the course is three parts one
+the first part is the review of the
+
+ align:start position:0%
+the first part is the review of the
+ 
+
+ align:start position:0%
+the first part is the review of the
+basic concepts and definitions but with
+
+ align:start position:0%
+basic concepts and definitions but with
+ 
+
+ align:start position:0%
+basic concepts and definitions but with
+this emphasis on non
+
+ align:start position:0%
+this emphasis on non
+ 
+
+ align:start position:0%
+this emphasis on non
+equilibrium uh especially on the
+
+ align:start position:0%
+equilibrium uh especially on the
+ 
+
+ align:start position:0%
+equilibrium uh especially on the
+definition of entropy for non
+
+ align:start position:0%
+definition of entropy for non
+ 
+
+ align:start position:0%
+definition of entropy for non
+equilibrium States and in particular uh
+
+ align:start position:0%
+equilibrium States and in particular uh
+ 
+
+ align:start position:0%
+equilibrium States and in particular uh
+we will see an interesting U aspect of
+
+ align:start position:0%
+we will see an interesting U aspect of
+ 
+
+ align:start position:0%
+we will see an interesting U aspect of
+what uh heat interaction is and the
+
+ align:start position:0%
+what uh heat interaction is and the
+ 
+
+ align:start position:0%
+what uh heat interaction is and the
+generalization of the concept of heat
+
+ align:start position:0%
+generalization of the concept of heat
+ 
+
+ align:start position:0%
+generalization of the concept of heat
+interaction that is useful for
+
+ align:start position:0%
+interaction that is useful for
+ 
+
+ align:start position:0%
+interaction that is useful for
+describing the uh non states of continum
+
+ align:start position:0%
+describing the uh non states of continum
+ 
+
+ align:start position:0%
+describing the uh non states of continum
+like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fluids the second
+
+ align:start position:0%
+fluids the second
+ 
+
+ align:start position:0%
+fluids the second
+part which is focused on U chemical
+
+ align:start position:0%
+part which is focused on U chemical
+ 
+
+ align:start position:0%
+part which is focused on U chemical
+potentials or electrochemical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+potentials uh so multicomponent systems
+
+ align:start position:0%
+potentials uh so multicomponent systems
+ 
+
+ align:start position:0%
+potentials uh so multicomponent systems
+and the role that chemical potentials U
+
+ align:start position:0%
+and the role that chemical potentials U
+ 
+
+ align:start position:0%
+and the role that chemical potentials U
+have in describing
+
+ align:start position:0%
+have in describing
+ 
+
+ align:start position:0%
+have in describing
+them so I'm not reading all these typ
+
+ align:start position:0%
+them so I'm not reading all these typ
+ 
+
+ align:start position:0%
+them so I'm not reading all these typ
+and the the last part the last third of
+
+ align:start position:0%
+and the the last part the last third of
+ 
+
+ align:start position:0%
+and the the last part the last third of
+the course
+
+ align:start position:0%
+the course
+ 
+
+ align:start position:0%
+the course
+is more explicitly on the standard
+
+ align:start position:0%
+is more explicitly on the standard
+ 
+
+ align:start position:0%
+is more explicitly on the standard
+theories of non-equilibrium like uh
+
+ align:start position:0%
+theories of non-equilibrium like uh
+ 
+
+ align:start position:0%
+theories of non-equilibrium like uh
+particular the role of reciprocal
+
+ align:start position:0%
+particular the role of reciprocal
+ 
+
+ align:start position:0%
+particular the role of reciprocal
+relations and uh the again
+
+ align:start position:0%
+relations and uh the again
+ 
+
+ align:start position:0%
+relations and uh the again
+the the assumptions that are needed to
+
+ align:start position:0%
+the the assumptions that are needed to
+ 
+
+ align:start position:0%
+the the assumptions that are needed to
+describe these states which are non
+
+ align:start position:0%
+describe these states which are non
+ 
+
+ align:start position:0%
+describe these states which are non
+equilibrium and how they evolve in time
+
+ align:start position:0%
+equilibrium and how they evolve in time
+ 
+
+ align:start position:0%
+equilibrium and how they evolve in time
+and um how
+
+ align:start position:0%
+and um how
+ 
+
+ align:start position:0%
+and um how
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+relate uh the entropy production by
+
+ align:start position:0%
+relate uh the entropy production by
+ 
+
+ align:start position:0%
+relate uh the entropy production by
+irreversibility to the various fluxes
+
+ align:start position:0%
+irreversibility to the various fluxes
+ 
+
+ align:start position:0%
+irreversibility to the various fluxes
+and forces in
+
+ align:start position:0%
+and forces in
+ 
+
+ align:start position:0%
+and forces in
+play
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah this is about the grading uh
+
+ align:start position:0%
+so yeah this is about the grading uh
+ 
+
+ align:start position:0%
+so yeah this is about the grading uh
+policy there will be um
+
+ align:start position:0%
+policy there will be um
+ 
+
+ align:start position:0%
+policy there will be um
+a everything is going to be oral the
+
+ align:start position:0%
+a everything is going to be oral the
+ 
+
+ align:start position:0%
+a everything is going to be oral the
+emphasis the reason why this is very
+
+ align:start position:0%
+emphasis the reason why this is very
+ 
+
+ align:start position:0%
+emphasis the reason why this is very
+unusual ual it May Scare some of
+
+ align:start position:0%
+unusual ual it May Scare some of
+ 
+
+ align:start position:0%
+unusual ual it May Scare some of
+you if if it does scare you and you
+
+ align:start position:0%
+you if if it does scare you and you
+ 
+
+ align:start position:0%
+you if if it does scare you and you
+still have to take the
+
+ align:start position:0%
+still have to take the
+ 
+
+ align:start position:0%
+still have to take the
+qualifiers uh consider it as a practice
+
+ align:start position:0%
+qualifiers uh consider it as a practice
+ 
+
+ align:start position:0%
+qualifiers uh consider it as a practice
+for for that purpose
+
+ align:start position:0%
+for for that purpose
+ 
+
+ align:start position:0%
+for for that purpose
+um if you are instead
+
+ align:start position:0%
+um if you are instead
+ 
+
+ align:start position:0%
+um if you are instead
+uh pass that and you are aiming to a
+
+ align:start position:0%
+uh pass that and you are aiming to a
+ 
+
+ align:start position:0%
+uh pass that and you are aiming to a
+career in academics where you might have
+
+ align:start position:0%
+career in academics where you might have
+ 
+
+ align:start position:0%
+career in academics where you might have
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+chance that your duty among your duties
+
+ align:start position:0%
+chance that your duty among your duties
+ 
+
+ align:start position:0%
+chance that your duty among your duties
+you have to teach the subject which is
+
+ align:start position:0%
+you have to teach the subject which is
+ 
+
+ align:start position:0%
+you have to teach the subject which is
+typical if you go to mechanical
+
+ align:start position:0%
+typical if you go to mechanical
+ 
+
+ align:start position:0%
+typical if you go to mechanical
+engineering department typically nobody
+
+ align:start position:0%
+engineering department typically nobody
+ 
+
+ align:start position:0%
+engineering department typically nobody
+wants to teach thermodynamics so they if
+
+ align:start position:0%
+wants to teach thermodynamics so they if
+ 
+
+ align:start position:0%
+wants to teach thermodynamics so they if
+you're the new one you do it until
+
+ align:start position:0%
+you're the new one you do it until
+ 
+
+ align:start position:0%
+you're the new one you do it until
+somebody else
+
+ align:start position:0%
+somebody else
+ 
+
+ align:start position:0%
+somebody else
+comes uh
+
+ align:start position:0%
+comes uh
+ 
+
+ align:start position:0%
+comes uh
+Well I this is the reason why I provide
+
+ align:start position:0%
+Well I this is the reason why I provide
+ 
+
+ align:start position:0%
+Well I this is the reason why I provide
+the viewrs I provide the
+
+ align:start position:0%
+the viewrs I provide the
+ 
+
+ align:start position:0%
+the viewrs I provide the
+videos uh so I want to make it easy for
+
+ align:start position:0%
+videos uh so I want to make it easy for
+ 
+
+ align:start position:0%
+videos uh so I want to make it easy for
+you if you want to teach it this way
+
+ align:start position:0%
+you if you want to teach it this way
+ 
+
+ align:start position:0%
+you if you want to teach it this way
+because it's already done okay um
+
+ align:start position:0%
+because it's already done okay um
+ 
+
+ align:start position:0%
+because it's already done okay um
+and I'm very happy uh to share uh all
+
+ align:start position:0%
+and I'm very happy uh to share uh all
+ 
+
+ align:start position:0%
+and I'm very happy uh to share uh all
+this because as as I said uh this is my
+
+ align:start position:0%
+this because as as I said uh this is my
+ 
+
+ align:start position:0%
+this because as as I said uh this is my
+uh life
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+subject so there will be um one homework
+
+ align:start position:0%
+subject so there will be um one homework
+ 
+
+ align:start position:0%
+subject so there will be um one homework
+and uh four midterms essentially there
+
+ align:start position:0%
+and uh four midterms essentially there
+ 
+
+ align:start position:0%
+and uh four midterms essentially there
+so five items that you have to do they
+
+ align:start position:0%
+so five items that you have to do they
+ 
+
+ align:start position:0%
+so five items that you have to do they
+are all take
+
+ align:start position:0%
+are all take
+ 
+
+ align:start position:0%
+are all take
+home uh as soon as as and they are all
+
+ align:start position:0%
+home uh as soon as as and they are all
+ 
+
+ align:start position:0%
+home uh as soon as as and they are all
+of the kind that you are give you one or
+
+ align:start position:0%
+of the kind that you are give you one or
+ 
+
+ align:start position:0%
+of the kind that you are give you one or
+two VI graphs of the ones that I use in
+
+ align:start position:0%
+two VI graphs of the ones that I use in
+ 
+
+ align:start position:0%
+two VI graphs of the ones that I use in
+class and you have to repeat in your own
+
+ align:start position:0%
+class and you have to repeat in your own
+ 
+
+ align:start position:0%
+class and you have to repeat in your own
+way in front of a camera no more than
+
+ align:start position:0%
+way in front of a camera no more than
+ 
+
+ align:start position:0%
+way in front of a camera no more than
+five minutes uh the words that go in
+
+ align:start position:0%
+five minutes uh the words that go in
+ 
+
+ align:start position:0%
+five minutes uh the words that go in
+between the equations that or the the
+
+ align:start position:0%
+between the equations that or the the
+ 
+
+ align:start position:0%
+between the equations that or the the
+things that are written on the uh on The
+
+ align:start position:0%
+things that are written on the uh on The
+ 
+
+ align:start position:0%
+things that are written on the uh on The
+View graphs so that's essentially a
+
+ align:start position:0%
+View graphs so that's essentially a
+ 
+
+ align:start position:0%
+View graphs so that's essentially a
+short lecture uh that you give on that
+
+ align:start position:0%
+short lecture uh that you give on that
+ 
+
+ align:start position:0%
+short lecture uh that you give on that
+subject following using the you can use
+
+ align:start position:0%
+subject following using the you can use
+ 
+
+ align:start position:0%
+subject following using the you can use
+uh you can use the videos you can use
+
+ align:start position:0%
+uh you can use the videos you can use
+ 
+
+ align:start position:0%
+uh you can use the videos you can use
+whatever you want to to to do them so I
+
+ align:start position:0%
+whatever you want to to to do them so I
+ 
+
+ align:start position:0%
+whatever you want to to to do them so I
+would consider those
+
+ align:start position:0%
+would consider those
+ 
+
+ align:start position:0%
+would consider those
+easy uh so you shouldn't be concerned
+
+ align:start position:0%
+easy uh so you shouldn't be concerned
+ 
+
+ align:start position:0%
+easy uh so you shouldn't be concerned
+about grades that you get out of this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+course and yes there is also a final
+
+ align:start position:0%
+course and yes there is also a final
+ 
+
+ align:start position:0%
+course and yes there is also a final
+exam which is also oral that's oral in
+
+ align:start position:0%
+exam which is also oral that's oral in
+ 
+
+ align:start position:0%
+exam which is also oral that's oral in
+presence it lasts 30 minutes
+
+ align:start position:0%
+presence it lasts 30 minutes
+ 
+
+ align:start position:0%
+presence it lasts 30 minutes
+uh and also for that uh um it's the same
+
+ align:start position:0%
+uh and also for that uh um it's the same
+ 
+
+ align:start position:0%
+uh and also for that uh um it's the same
+idea I I tell you take the view graph on
+
+ align:start position:0%
+idea I I tell you take the view graph on
+ 
+
+ align:start position:0%
+idea I I tell you take the view graph on
+say chemical
+
+ align:start position:0%
+say chemical
+ 
+
+ align:start position:0%
+say chemical
+equilibrium and talk about it so you
+
+ align:start position:0%
+equilibrium and talk about it so you
+ 
+
+ align:start position:0%
+equilibrium and talk about it so you
+don't have to memorize anything you you
+
+ align:start position:0%
+don't have to memorize anything you you
+ 
+
+ align:start position:0%
+don't have to memorize anything you you
+have the view graphs you can also take
+
+ align:start position:0%
+have the view graphs you can also take
+ 
+
+ align:start position:0%
+have the view graphs you can also take
+your own U hand notes or your whatever
+
+ align:start position:0%
+your own U hand notes or your whatever
+ 
+
+ align:start position:0%
+your own U hand notes or your whatever
+you want uh as long as you don't come
+
+ align:start position:0%
+you want uh as long as you don't come
+ 
+
+ align:start position:0%
+you want uh as long as you don't come
+without anything and you waste all the
+
+ align:start position:0%
+without anything and you waste all the
+ 
+
+ align:start position:0%
+without anything and you waste all the
+30 minutes trying to write a couple of
+
+ align:start position:0%
+30 minutes trying to write a couple of
+ 
+
+ align:start position:0%
+30 minutes trying to write a couple of
+the formulas you remember because that's
+
+ align:start position:0%
+the formulas you remember because that's
+ 
+
+ align:start position:0%
+the formulas you remember because that's
+I consider a waste of time it doesn't
+
+ align:start position:0%
+I consider a waste of time it doesn't
+ 
+
+ align:start position:0%
+I consider a waste of time it doesn't
+allow me to uh check that you have tried
+
+ align:start position:0%
+allow me to uh check that you have tried
+ 
+
+ align:start position:0%
+allow me to uh check that you have tried
+to go uh over uh all of the things that
+
+ align:start position:0%
+to go uh over uh all of the things that
+ 
+
+ align:start position:0%
+to go uh over uh all of the things that
+we have covered the actually the
+
+ align:start position:0%
+we have covered the actually the
+ 
+
+ align:start position:0%
+we have covered the actually the
+um the final is going to cover only the
+
+ align:start position:0%
+um the final is going to cover only the
+ 
+
+ align:start position:0%
+um the final is going to cover only the
+second and third
+
+ align:start position:0%
+second and third
+ 
+
+ align:start position:0%
+second and third
+part uh of of of the of the
+
+ align:start position:0%
+part uh of of of the of the
+ 
+
+ align:start position:0%
+part uh of of of the of the
+course uh okay so
+
+ align:start position:0%
+course uh okay so
+ 
+
+ align:start position:0%
+course uh okay so
+let's get
+
+ align:start position:0%
+let's get
+ 
+
+ align:start position:0%
+let's get
+started
+
+ align:start position:0%
+started
+ 
+
+ align:start position:0%
+started
+thermodynamics so what's
+
+ align:start position:0%
+thermodynamics so what's
+ 
+
+ align:start position:0%
+thermodynamics so what's
+thermodynamics do any of you have an
+
+ align:start position:0%
+thermodynamics do any of you have an
+ 
+
+ align:start position:0%
+thermodynamics do any of you have an
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+of what what's the definition of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thermodynamics don't be scared I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean no you're shy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay that that's
+
+ align:start position:0%
+yeah okay that that's
+ 
+
+ align:start position:0%
+yeah okay that that's
+two I
+
+ align:start position:0%
+two I
+ 
+
+ align:start position:0%
+two I
+would anything anything more like
+
+ align:start position:0%
+would anything anything more like
+ 
+
+ align:start position:0%
+would anything anything more like
+General how you use you you use
+
+ align:start position:0%
+General how you use you you use
+ 
+
+ align:start position:0%
+General how you use you you use
+thermodynamics in your uh in your
+
+ align:start position:0%
+thermodynamics in your uh in your
+ 
+
+ align:start position:0%
+thermodynamics in your uh in your
+research what do you use it for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe you do molecular Dynamic
+
+ align:start position:0%
+maybe you do molecular Dynamic
+ 
+
+ align:start position:0%
+maybe you do molecular Dynamic
+simulations that's a way to compute
+
+ align:start position:0%
+simulations that's a way to compute
+ 
+
+ align:start position:0%
+simulations that's a way to compute
+properties of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stuff in
+
+ align:start position:0%
+stuff in
+ 
+
+ align:start position:0%
+stuff in
+fact
+
+ align:start position:0%
+fact
+ 
+
+ align:start position:0%
+fact
+yeah heat and work are
+
+ align:start position:0%
+yeah heat and work are
+ 
+
+ align:start position:0%
+yeah heat and work are
+certainly peculiar
+
+ align:start position:0%
+certainly peculiar
+ 
+
+ align:start position:0%
+certainly peculiar
+um kinds of interactions that occur that
+
+ align:start position:0%
+um kinds of interactions that occur that
+ 
+
+ align:start position:0%
+um kinds of interactions that occur that
+are described in thermodynamics
+
+ align:start position:0%
+are described in thermodynamics
+ 
+
+ align:start position:0%
+are described in thermodynamics
+but in general thermodynamics is
+
+ align:start position:0%
+but in general thermodynamics is
+ 
+
+ align:start position:0%
+but in general thermodynamics is
+a is a subject where you say let me use
+
+ align:start position:0%
+a is a subject where you say let me use
+ 
+
+ align:start position:0%
+a is a subject where you say let me use
+words that I haven't defined yet but uh
+
+ align:start position:0%
+words that I haven't defined yet but uh
+ 
+
+ align:start position:0%
+words that I haven't defined yet but uh
+it's a subject that um
+
+ align:start position:0%
+it's a subject that um
+ 
+
+ align:start position:0%
+it's a subject that um
+um allows you to compute properties of
+
+ align:start position:0%
+um allows you to compute properties of
+ 
+
+ align:start position:0%
+um allows you to compute properties of
+physical
+
+ align:start position:0%
+physical
+ 
+
+ align:start position:0%
+physical
+systems and see how they change with
+
+ align:start position:0%
+systems and see how they change with
+ 
+
+ align:start position:0%
+systems and see how they change with
+time and how they are maybe transferred
+
+ align:start position:0%
+time and how they are maybe transferred
+ 
+
+ align:start position:0%
+time and how they are maybe transferred
+from one system to the other like by
+
+ align:start position:0%
+from one system to the other like by
+ 
+
+ align:start position:0%
+from one system to the other like by
+means of heat and War
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so
+
+ align:start position:0%
+all right so
+ 
+
+ align:start position:0%
+all right so
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+property state of the
+
+ align:start position:0%
+property state of the
+ 
+
+ align:start position:0%
+property state of the
+system also the word
+
+ align:start position:0%
+system also the word
+ 
+
+ align:start position:0%
+system also the word
+process okay so this is why I want to
+
+ align:start position:0%
+process okay so this is why I want to
+ 
+
+ align:start position:0%
+process okay so this is why I want to
+spend some time in uh
+
+ align:start position:0%
+spend some time in uh
+ 
+
+ align:start position:0%
+spend some time in uh
+defining these things these words
+
+ align:start position:0%
+defining these things these words
+ 
+
+ align:start position:0%
+defining these things these words
+because these
+
+ align:start position:0%
+because these
+ 
+
+ align:start position:0%
+because these
+words are loaded of meaning
+
+ align:start position:0%
+words are loaded of meaning
+ 
+
+ align:start position:0%
+words are loaded of meaning
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+therefore uh represent
+
+ align:start position:0%
+therefore uh represent
+ 
+
+ align:start position:0%
+therefore uh represent
+restrictions uh within the theory of
+
+ align:start position:0%
+restrictions uh within the theory of
+ 
+
+ align:start position:0%
+restrictions uh within the theory of
+thermodynamics actually thermodynamics
+
+ align:start position:0%
+thermodynamics actually thermodynamics
+ 
+
+ align:start position:0%
+thermodynamics actually thermodynamics
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+really modeling you want to model
+
+ align:start position:0%
+really modeling you want to model
+ 
+
+ align:start position:0%
+really modeling you want to model
+physical
+
+ align:start position:0%
+physical
+ 
+
+ align:start position:0%
+physical
+reality exactly like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+physics or or mechanics uh does some
+
+ align:start position:0%
+physics or or mechanics uh does some
+ 
+
+ align:start position:0%
+physics or or mechanics uh does some
+modeling of certain aspects it's also uh
+
+ align:start position:0%
+modeling of certain aspects it's also uh
+ 
+
+ align:start position:0%
+modeling of certain aspects it's also uh
+similar
+
+ align:start position:0%
+similar
+ 
+
+ align:start position:0%
+similar
+um so the key word is
+
+ align:start position:0%
+um so the key word is
+ 
+
+ align:start position:0%
+um so the key word is
+modeling you want to describe
+
+ align:start position:0%
+modeling you want to describe
+ 
+
+ align:start position:0%
+modeling you want to describe
+a a glass of water a bottle of water the
+
+ align:start position:0%
+a a glass of water a bottle of water the
+ 
+
+ align:start position:0%
+a a glass of water a bottle of water the
+water in a bottle
+
+ align:start position:0%
+water in a bottle
+ 
+
+ align:start position:0%
+water in a bottle
+and uh you make a model you typically
+
+ align:start position:0%
+and uh you make a model you typically
+ 
+
+ align:start position:0%
+and uh you make a model you typically
+simplifying the situation to make it
+
+ align:start position:0%
+simplifying the situation to make it
+ 
+
+ align:start position:0%
+simplifying the situation to make it
+contain enough of what you need to
+
+ align:start position:0%
+contain enough of what you need to
+ 
+
+ align:start position:0%
+contain enough of what you need to
+describe that water but nothing
+
+ align:start position:0%
+describe that water but nothing
+ 
+
+ align:start position:0%
+describe that water but nothing
+more so sometimes this system this will
+
+ align:start position:0%
+more so sometimes this system this will
+ 
+
+ align:start position:0%
+more so sometimes this system this will
+be a system the water inside this
+
+ align:start position:0%
+be a system the water inside this
+ 
+
+ align:start position:0%
+be a system the water inside this
+container and uh uh this system is
+
+ align:start position:0%
+container and uh uh this system is
+ 
+
+ align:start position:0%
+container and uh uh this system is
+interacting with the air that surrounds
+
+ align:start position:0%
+interacting with the air that surrounds
+ 
+
+ align:start position:0%
+interacting with the air that surrounds
+it so you need to consider both the
+
+ align:start position:0%
+it so you need to consider both the
+ 
+
+ align:start position:0%
+it so you need to consider both the
+water and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+surroundings but most of the times you
+
+ align:start position:0%
+surroundings but most of the times you
+ 
+
+ align:start position:0%
+surroundings but most of the times you
+don't need to consider what happens in
+
+ align:start position:0%
+don't need to consider what happens in
+ 
+
+ align:start position:0%
+don't need to consider what happens in
+say the corridor of your lab or what
+
+ align:start position:0%
+say the corridor of your lab or what
+ 
+
+ align:start position:0%
+say the corridor of your lab or what
+happens where is the moon right now so
+
+ align:start position:0%
+happens where is the moon right now so
+ 
+
+ align:start position:0%
+happens where is the moon right now so
+you can simplify by
+
+ align:start position:0%
+you can simplify by
+ 
+
+ align:start position:0%
+you can simplify by
+removing unnecessary aspects of your
+
+ align:start position:0%
+removing unnecessary aspects of your
+ 
+
+ align:start position:0%
+removing unnecessary aspects of your
+physical reality and
+
+ align:start position:0%
+physical reality and
+ 
+
+ align:start position:0%
+physical reality and
+concentrating on what you really want to
+
+ align:start position:0%
+concentrating on what you really want to
+ 
+
+ align:start position:0%
+concentrating on what you really want to
+represent uh and also you want
+
+ align:start position:0%
+represent uh and also you want
+ 
+
+ align:start position:0%
+represent uh and also you want
+to simplify
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh as you know I can describe water
+
+ align:start position:0%
+so uh as you know I can describe water
+ 
+
+ align:start position:0%
+so uh as you know I can describe water
+as if uh it's composed of molecules and
+
+ align:start position:0%
+as if uh it's composed of molecules and
+ 
+
+ align:start position:0%
+as if uh it's composed of molecules and
+molecules can be considered for certain
+
+ align:start position:0%
+molecules can be considered for certain
+ 
+
+ align:start position:0%
+molecules can be considered for certain
+aspects um like
+
+ align:start position:0%
+aspects um like
+ 
+
+ align:start position:0%
+aspects um like
+U
+
+ align:start position:0%
+U
+ 
+
+ align:start position:0%
+U
+indivisible like atoms in the democratus
+
+ align:start position:0%
+indivisible like atoms in the democratus
+ 
+
+ align:start position:0%
+indivisible like atoms in the democratus
+sense no you cannot split them but if
+
+ align:start position:0%
+sense no you cannot split them but if
+ 
+
+ align:start position:0%
+sense no you cannot split them but if
+you're interested in uh
+
+ align:start position:0%
+you're interested in uh
+ 
+
+ align:start position:0%
+you're interested in uh
+chemistry well then the molecule can be
+
+ align:start position:0%
+chemistry well then the molecule can be
+ 
+
+ align:start position:0%
+chemistry well then the molecule can be
+split and then the building blocks are
+
+ align:start position:0%
+split and then the building blocks are
+ 
+
+ align:start position:0%
+split and then the building blocks are
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+atoms or if you're interested in uh
+
+ align:start position:0%
+atoms or if you're interested in uh
+ 
+
+ align:start position:0%
+atoms or if you're interested in uh
+nuclear uh
+
+ align:start position:0%
+nuclear uh
+ 
+
+ align:start position:0%
+nuclear uh
+phenomena they building blocks and not
+
+ align:start position:0%
+phenomena they building blocks and not
+ 
+
+ align:start position:0%
+phenomena they building blocks and not
+even the atoms there are the protons the
+
+ align:start position:0%
+even the atoms there are the protons the
+ 
+
+ align:start position:0%
+even the atoms there are the protons the
+neutrons the
+
+ align:start position:0%
+neutrons the
+ 
+
+ align:start position:0%
+neutrons the
+electrons if can even go to lower level
+
+ align:start position:0%
+electrons if can even go to lower level
+ 
+
+ align:start position:0%
+electrons if can even go to lower level
+description it can go to quarks and the
+
+ align:start position:0%
+description it can go to quarks and the
+ 
+
+ align:start position:0%
+description it can go to quarks and the
+quarks can be split into Maybe spring uh
+
+ align:start position:0%
+quarks can be split into Maybe spring uh
+ 
+
+ align:start position:0%
+quarks can be split into Maybe spring uh
+string theories and things like that all
+
+ align:start position:0%
+string theories and things like that all
+ 
+
+ align:start position:0%
+string theories and things like that all
+right so who knows uh if there is a a
+
+ align:start position:0%
+right so who knows uh if there is a a
+ 
+
+ align:start position:0%
+right so who knows uh if there is a a
+bottom level of description for things
+
+ align:start position:0%
+bottom level of description for things
+ 
+
+ align:start position:0%
+bottom level of description for things
+but not for every model you need to go
+
+ align:start position:0%
+but not for every model you need to go
+ 
+
+ align:start position:0%
+but not for every model you need to go
+that deep you just use whatever is
+
+ align:start position:0%
+that deep you just use whatever is
+ 
+
+ align:start position:0%
+that deep you just use whatever is
+necessary for enough for the phenomena
+
+ align:start position:0%
+necessary for enough for the phenomena
+ 
+
+ align:start position:0%
+necessary for enough for the phenomena
+you want to describe so that's the let's
+
+ align:start position:0%
+you want to describe so that's the let's
+ 
+
+ align:start position:0%
+you want to describe so that's the let's
+call it art of modeling
+
+ align:start position:0%
+call it art of modeling
+ 
+
+ align:start position:0%
+call it art of modeling
+to get rid of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unnecessary so usually a system uh we we
+
+ align:start position:0%
+unnecessary so usually a system uh we we
+ 
+
+ align:start position:0%
+unnecessary so usually a system uh we we
+agree and we understand that is made up
+
+ align:start position:0%
+agree and we understand that is made up
+ 
+
+ align:start position:0%
+agree and we understand that is made up
+physical systems made made up of
+
+ align:start position:0%
+physical systems made made up of
+ 
+
+ align:start position:0%
+physical systems made made up of
+constituents that could be the molecules
+
+ align:start position:0%
+constituents that could be the molecules
+ 
+
+ align:start position:0%
+constituents that could be the molecules
+the atoms the nuclei the the protons the
+
+ align:start position:0%
+the atoms the nuclei the the protons the
+ 
+
+ align:start position:0%
+the atoms the nuclei the the protons the
+nucleons uh and so on depending on the
+
+ align:start position:0%
+nucleons uh and so on depending on the
+ 
+
+ align:start position:0%
+nucleons uh and so on depending on the
+level of description you choose
+
+ align:start position:0%
+level of description you choose
+ 
+
+ align:start position:0%
+level of description you choose
+then you so you set up this bunch of
+
+ align:start position:0%
+then you so you set up this bunch of
+ 
+
+ align:start position:0%
+then you so you set up this bunch of
+molecules which are the ingredients of
+
+ align:start position:0%
+molecules which are the ingredients of
+ 
+
+ align:start position:0%
+molecules which are the ingredients of
+your object of study that's not yet a
+
+ align:start position:0%
+your object of study that's not yet a
+ 
+
+ align:start position:0%
+your object of study that's not yet a
+system you have to explain or describe
+
+ align:start position:0%
+system you have to explain or describe
+ 
+
+ align:start position:0%
+system you have to explain or describe
+how they interact with each other for
+
+ align:start position:0%
+how they interact with each other for
+ 
+
+ align:start position:0%
+how they interact with each other for
+example in a molecular Dynamic
+
+ align:start position:0%
+example in a molecular Dynamic
+ 
+
+ align:start position:0%
+example in a molecular Dynamic
+simulation you want to describe uh what
+
+ align:start position:0%
+simulation you want to describe uh what
+ 
+
+ align:start position:0%
+simulation you want to describe uh what
+kind of potential uh like ler Johns our
+
+ align:start position:0%
+kind of potential uh like ler Johns our
+ 
+
+ align:start position:0%
+kind of potential uh like ler Johns our
+spheres uh soft spheres and things like
+
+ align:start position:0%
+spheres uh soft spheres and things like
+ 
+
+ align:start position:0%
+spheres uh soft spheres and things like
+that okay so these are
+
+ align:start position:0%
+that okay so these are
+ 
+
+ align:start position:0%
+that okay so these are
+uh um internal forces between the
+
+ align:start position:0%
+uh um internal forces between the
+ 
+
+ align:start position:0%
+uh um internal forces between the
+constituents of your
+
+ align:start position:0%
+constituents of your
+ 
+
+ align:start position:0%
+constituents of your
+system and then you also have to um
+
+ align:start position:0%
+system and then you also have to um
+ 
+
+ align:start position:0%
+system and then you also have to um
+because most of the times your system is
+
+ align:start position:0%
+because most of the times your system is
+ 
+
+ align:start position:0%
+because most of the times your system is
+confined for example the air in this
+
+ align:start position:0%
+confined for example the air in this
+ 
+
+ align:start position:0%
+confined for example the air in this
+room is confined by the walls or the
+
+ align:start position:0%
+room is confined by the walls or the
+ 
+
+ align:start position:0%
+room is confined by the walls or the
+water here is confined by the bottle and
+
+ align:start position:0%
+water here is confined by the bottle and
+ 
+
+ align:start position:0%
+water here is confined by the bottle and
+uh so you want to uh describe uh also
+
+ align:start position:0%
+uh so you want to uh describe uh also
+ 
+
+ align:start position:0%
+uh so you want to uh describe uh also
+the what I would call the external
+
+ align:start position:0%
+the what I would call the external
+ 
+
+ align:start position:0%
+the what I would call the external
+forces as something
+
+ align:start position:0%
+forces as something
+ 
+
+ align:start position:0%
+forces as something
+that puts in the model the effect of the
+
+ align:start position:0%
+that puts in the model the effect of the
+ 
+
+ align:start position:0%
+that puts in the model the effect of the
+walls but these effect external forces
+
+ align:start position:0%
+walls but these effect external forces
+ 
+
+ align:start position:0%
+walls but these effect external forces
+must be particularly
+
+ align:start position:0%
+must be particularly
+ 
+
+ align:start position:0%
+must be particularly
+simple and there it's written that
+
+ align:start position:0%
+simple and there it's written that
+ 
+
+ align:start position:0%
+simple and there it's written that
+you should U the those forces should not
+
+ align:start position:0%
+you should U the those forces should not
+ 
+
+ align:start position:0%
+you should U the those forces should not
+depend on the coordinates of
+
+ align:start position:0%
+depend on the coordinates of
+ 
+
+ align:start position:0%
+depend on the coordinates of
+constituents that are not
+
+ align:start position:0%
+constituents that are not
+ 
+
+ align:start position:0%
+constituents that are not
+the constituents of your
+
+ align:start position:0%
+the constituents of your
+ 
+
+ align:start position:0%
+the constituents of your
+system so what does that mean for
+
+ align:start position:0%
+system so what does that mean for
+ 
+
+ align:start position:0%
+system so what does that mean for
+example the walls yes the walls are made
+
+ align:start position:0%
+example the walls yes the walls are made
+ 
+
+ align:start position:0%
+example the walls yes the walls are made
+of molecules so when I
+
+ align:start position:0%
+of molecules so when I
+ 
+
+ align:start position:0%
+of molecules so when I
+have a molecule of oxygen that goes and
+
+ align:start position:0%
+have a molecule of oxygen that goes and
+ 
+
+ align:start position:0%
+have a molecule of oxygen that goes and
+hits the wall and it bounces back uh
+
+ align:start position:0%
+hits the wall and it bounces back uh
+ 
+
+ align:start position:0%
+hits the wall and it bounces back uh
+what affects that
+
+ align:start position:0%
+what affects that
+ 
+
+ align:start position:0%
+what affects that
+bouncing is certainly the molecules of
+
+ align:start position:0%
+bouncing is certainly the molecules of
+ 
+
+ align:start position:0%
+bouncing is certainly the molecules of
+the W okay but you don't
+
+ align:start position:0%
+the W okay but you don't
+ 
+
+ align:start position:0%
+the W okay but you don't
+need
+
+ align:start position:0%
+need
+ 
+
+ align:start position:0%
+need
+to uh describe to include the the
+
+ align:start position:0%
+to uh describe to include the the
+ 
+
+ align:start position:0%
+to uh describe to include the the
+molecules of the W in your model unless
+
+ align:start position:0%
+molecules of the W in your model unless
+ 
+
+ align:start position:0%
+molecules of the W in your model unless
+you're interested in the effects also of
+
+ align:start position:0%
+you're interested in the effects also of
+ 
+
+ align:start position:0%
+you're interested in the effects also of
+what happens inside the wall you could
+
+ align:start position:0%
+what happens inside the wall you could
+ 
+
+ align:start position:0%
+what happens inside the wall you could
+just describe that as a like
+
+ align:start position:0%
+just describe that as a like
+ 
+
+ align:start position:0%
+just describe that as a like
+a mirror bouncing or in elastic bouncing
+
+ align:start position:0%
+a mirror bouncing or in elastic bouncing
+ 
+
+ align:start position:0%
+a mirror bouncing or in elastic bouncing
+or in elastic bouncing can Define rules
+
+ align:start position:0%
+or in elastic bouncing can Define rules
+ 
+
+ align:start position:0%
+or in elastic bouncing can Define rules
+of how the walls behave when particles
+
+ align:start position:0%
+of how the walls behave when particles
+ 
+
+ align:start position:0%
+of how the walls behave when particles
+go uh and uh go and uh hit
+
+ align:start position:0%
+go uh and uh go and uh hit
+ 
+
+ align:start position:0%
+go uh and uh go and uh hit
+them uh so these
+
+ align:start position:0%
+them uh so these
+ 
+
+ align:start position:0%
+them uh so these
+rules may depend on some control
+
+ align:start position:0%
+rules may depend on some control
+ 
+
+ align:start position:0%
+rules may depend on some control
+parameters for example where the wall is
+
+ align:start position:0%
+parameters for example where the wall is
+ 
+
+ align:start position:0%
+parameters for example where the wall is
+you could have a classical piston on you
+
+ align:start position:0%
+you could have a classical piston on you
+ 
+
+ align:start position:0%
+you could have a classical piston on you
+can move a wall okay so and so you
+
+ align:start position:0%
+can move a wall okay so and so you
+ 
+
+ align:start position:0%
+can move a wall okay so and so you
+control the position of the wall you
+
+ align:start position:0%
+control the position of the wall you
+ 
+
+ align:start position:0%
+control the position of the wall you
+could also
+
+ align:start position:0%
+could also
+ 
+
+ align:start position:0%
+could also
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+um other with other parameters what the
+
+ align:start position:0%
+um other with other parameters what the
+ 
+
+ align:start position:0%
+um other with other parameters what the
+worldall does to your particles okay as
+
+ align:start position:0%
+worldall does to your particles okay as
+ 
+
+ align:start position:0%
+worldall does to your particles okay as
+long as it that effect is not um
+
+ align:start position:0%
+long as it that effect is not um
+ 
+
+ align:start position:0%
+long as it that effect is not um
+dependent on within your model of uh
+
+ align:start position:0%
+dependent on within your model of uh
+ 
+
+ align:start position:0%
+dependent on within your model of uh
+the coordinates of those uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+particles so if the external forces are
+
+ align:start position:0%
+particles so if the external forces are
+ 
+
+ align:start position:0%
+particles so if the external forces are
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+kind then we can call it a
+
+ align:start position:0%
+kind then we can call it a
+ 
+
+ align:start position:0%
+kind then we can call it a
+system and here is a counter example for
+
+ align:start position:0%
+system and here is a counter example for
+ 
+
+ align:start position:0%
+system and here is a counter example for
+example suppose I have a hydrogen
+
+ align:start position:0%
+example suppose I have a hydrogen
+ 
+
+ align:start position:0%
+example suppose I have a hydrogen
+atom with a proton and an electron and
+
+ align:start position:0%
+atom with a proton and an electron and
+ 
+
+ align:start position:0%
+atom with a proton and an electron and
+we all know that
+
+ align:start position:0%
+we all know that
+ 
+
+ align:start position:0%
+we all know that
+electrostatics Mak such that the the
+
+ align:start position:0%
+electrostatics Mak such that the the
+ 
+
+ align:start position:0%
+electrostatics Mak such that the the
+force uh um sorry for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Interruption so the force between proton
+
+ align:start position:0%
+Interruption so the force between proton
+ 
+
+ align:start position:0%
+Interruption so the force between proton
+and electron depends on the relative
+
+ align:start position:0%
+and electron depends on the relative
+ 
+
+ align:start position:0%
+and electron depends on the relative
+distance of of of between the
+
+ align:start position:0%
+distance of of of between the
+ 
+
+ align:start position:0%
+distance of of of between the
+two and
+
+ align:start position:0%
+two and
+ 
+
+ align:start position:0%
+two and
+so if I have an electron which is bound
+
+ align:start position:0%
+so if I have an electron which is bound
+ 
+
+ align:start position:0%
+so if I have an electron which is bound
+in an atom and I want to consider it as
+
+ align:start position:0%
+in an atom and I want to consider it as
+ 
+
+ align:start position:0%
+in an atom and I want to consider it as
+my system I
+
+ align:start position:0%
+my system I
+ 
+
+ align:start position:0%
+my system I
+cannot that cannot be a system
+
+ align:start position:0%
+cannot that cannot be a system
+ 
+
+ align:start position:0%
+cannot that cannot be a system
+because the for the external Force
+
+ align:start position:0%
+because the for the external Force
+ 
+
+ align:start position:0%
+because the for the external Force
+depends on the
+
+ align:start position:0%
+depends on the
+ 
+
+ align:start position:0%
+depends on the
+coordinates of the
+
+ align:start position:0%
+coordinates of the
+ 
+
+ align:start position:0%
+coordinates of the
+proton so if you want to consider that
+
+ align:start position:0%
+proton so if you want to consider that
+ 
+
+ align:start position:0%
+proton so if you want to consider that
+situation you have to INE include the
+
+ align:start position:0%
+situation you have to INE include the
+ 
+
+ align:start position:0%
+situation you have to INE include the
+proton in your
+
+ align:start position:0%
+proton in your
+ 
+
+ align:start position:0%
+proton in your
+system or you have
+
+ align:start position:0%
+system or you have
+ 
+
+ align:start position:0%
+system or you have
+to or you can only do it if the electron
+
+ align:start position:0%
+to or you can only do it if the electron
+ 
+
+ align:start position:0%
+to or you can only do it if the electron
+is in a situation where the effect of
+
+ align:start position:0%
+is in a situation where the effect of
+ 
+
+ align:start position:0%
+is in a situation where the effect of
+the proton is independent of the
+
+ align:start position:0%
+the proton is independent of the
+ 
+
+ align:start position:0%
+the proton is independent of the
+relative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+position those are very
+
+ align:start position:0%
+position those are very
+ 
+
+ align:start position:0%
+position those are very
+few except if the electron is very far
+
+ align:start position:0%
+few except if the electron is very far
+ 
+
+ align:start position:0%
+few except if the electron is very far
+away from the proton so like is a free
+
+ align:start position:0%
+away from the proton so like is a free
+ 
+
+ align:start position:0%
+away from the proton so like is a free
+particle Okay so the word system is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+loaded and as I said uh most of the
+
+ align:start position:0%
+loaded and as I said uh most of the
+ 
+
+ align:start position:0%
+loaded and as I said uh most of the
+times you need your system which is
+
+ align:start position:0%
+times you need your system which is
+ 
+
+ align:start position:0%
+times you need your system which is
+confined by say the walls according to
+
+ align:start position:0%
+confined by say the walls according to
+ 
+
+ align:start position:0%
+confined by say the walls according to
+those rules and also you need another
+
+ align:start position:0%
+those rules and also you need another
+ 
+
+ align:start position:0%
+those rules and also you need another
+system to be outside which is capable of
+
+ align:start position:0%
+system to be outside which is capable of
+ 
+
+ align:start position:0%
+system to be outside which is capable of
+interacting with it for example uh
+
+ align:start position:0%
+interacting with it for example uh
+ 
+
+ align:start position:0%
+interacting with it for example uh
+usually we call that the environment of
+
+ align:start position:0%
+usually we call that the environment of
+ 
+
+ align:start position:0%
+usually we call that the environment of
+the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which in principle is the rest of the
+
+ align:start position:0%
+which in principle is the rest of the
+ 
+
+ align:start position:0%
+which in principle is the rest of the
+universe but in practice is that little
+
+ align:start position:0%
+universe but in practice is that little
+ 
+
+ align:start position:0%
+universe but in practice is that little
+part of the rest of the universe that is
+
+ align:start position:0%
+part of the rest of the universe that is
+ 
+
+ align:start position:0%
+part of the rest of the universe that is
+relevant to your uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+application okay so once we have defined
+
+ align:start position:0%
+application okay so once we have defined
+ 
+
+ align:start position:0%
+application okay so once we have defined
+the word system we said well we want to
+
+ align:start position:0%
+the word system we said well we want to
+ 
+
+ align:start position:0%
+the word system we said well we want to
+study the properties so how do we study
+
+ align:start position:0%
+study the properties so how do we study
+ 
+
+ align:start position:0%
+study the properties so how do we study
+properties well we go to the lab and we
+
+ align:start position:0%
+properties well we go to the lab and we
+ 
+
+ align:start position:0%
+properties well we go to the lab and we
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+measurements those are are called in
+
+ align:start position:0%
+measurements those are are called in
+ 
+
+ align:start position:0%
+measurements those are are called in
+general physical observables the things
+
+ align:start position:0%
+general physical observables the things
+ 
+
+ align:start position:0%
+general physical observables the things
+that you can measure are physical
+
+ align:start position:0%
+that you can measure are physical
+ 
+
+ align:start position:0%
+that you can measure are physical
+observables and they correspond to
+
+ align:start position:0%
+observables and they correspond to
+ 
+
+ align:start position:0%
+observables and they correspond to
+measurement procedures so uh recipes
+
+ align:start position:0%
+measurement procedures so uh recipes
+ 
+
+ align:start position:0%
+measurement procedures so uh recipes
+that you apply in a
+
+ align:start position:0%
+that you apply in a
+ 
+
+ align:start position:0%
+that you apply in a
+lab uh that you should be able to apply
+
+ align:start position:0%
+lab uh that you should be able to apply
+ 
+
+ align:start position:0%
+lab uh that you should be able to apply
+in any lab so the given recipes should
+
+ align:start position:0%
+in any lab so the given recipes should
+ 
+
+ align:start position:0%
+in any lab so the given recipes should
+not be lab dependent otherwise it
+
+ align:start position:0%
+not be lab dependent otherwise it
+ 
+
+ align:start position:0%
+not be lab dependent otherwise it
+gives something that is not um feature
+
+ align:start position:0%
+gives something that is not um feature
+ 
+
+ align:start position:0%
+gives something that is not um feature
+of your system it's a feature of your
+
+ align:start position:0%
+of your system it's a feature of your
+ 
+
+ align:start position:0%
+of your system it's a feature of your
+system in your lab so the lab is part of
+
+ align:start position:0%
+system in your lab so the lab is part of
+ 
+
+ align:start position:0%
+system in your lab so the lab is part of
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+system okay but it's that's not enough
+
+ align:start position:0%
+system okay but it's that's not enough
+ 
+
+ align:start position:0%
+system okay but it's that's not enough
+not all physical
+
+ align:start position:0%
+not all physical
+ 
+
+ align:start position:0%
+not all physical
+observables can be called
+
+ align:start position:0%
+observables can be called
+ 
+
+ align:start position:0%
+observables can be called
+properties in order for them to be
+
+ align:start position:0%
+properties in order for them to be
+ 
+
+ align:start position:0%
+properties in order for them to be
+called properties you need the result or
+
+ align:start position:0%
+called properties you need the result or
+ 
+
+ align:start position:0%
+called properties you need the result or
+the outcome of the measurement to be
+
+ align:start position:0%
+the outcome of the measurement to be
+ 
+
+ align:start position:0%
+the outcome of the measurement to be
+dependent again within your model on a
+
+ align:start position:0%
+dependent again within your model on a
+ 
+
+ align:start position:0%
+dependent again within your model on a
+single instant of time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so take this example a point Mass
+
+ align:start position:0%
+so take this example a point Mass
+ 
+
+ align:start position:0%
+so take this example a point Mass
+particle that moves along the
+
+ align:start position:0%
+particle that moves along the
+ 
+
+ align:start position:0%
+particle that moves along the
+trajectory so yes if you take two
+
+ align:start position:0%
+trajectory so yes if you take two
+ 
+
+ align:start position:0%
+trajectory so yes if you take two
+instance of time T1 and T2 and measure
+
+ align:start position:0%
+instance of time T1 and T2 and measure
+ 
+
+ align:start position:0%
+instance of time T1 and T2 and measure
+with a stick the
+
+ align:start position:0%
+with a stick the
+ 
+
+ align:start position:0%
+with a stick the
+distance uh between those two
+
+ align:start position:0%
+distance uh between those two
+ 
+
+ align:start position:0%
+distance uh between those two
+points that's certainly a physical
+
+ align:start position:0%
+points that's certainly a physical
+ 
+
+ align:start position:0%
+points that's certainly a physical
+observable you measure it there is a
+
+ align:start position:0%
+observable you measure it there is a
+ 
+
+ align:start position:0%
+observable you measure it there is a
+measuring procedure take the stick and
+
+ align:start position:0%
+measuring procedure take the stick and
+ 
+
+ align:start position:0%
+measuring procedure take the stick and
+measure it but it depends on two times
+
+ align:start position:0%
+measure it but it depends on two times
+ 
+
+ align:start position:0%
+measure it but it depends on two times
+it's not a
+
+ align:start position:0%
+it's not a
+ 
+
+ align:start position:0%
+it's not a
+property even if you divide it by the
+
+ align:start position:0%
+property even if you divide it by the
+ 
+
+ align:start position:0%
+property even if you divide it by the
+time interval between those two instants
+
+ align:start position:0%
+time interval between those two instants
+ 
+
+ align:start position:0%
+time interval between those two instants
+uh you get a ratio which looks like a
+
+ align:start position:0%
+uh you get a ratio which looks like a
+ 
+
+ align:start position:0%
+uh you get a ratio which looks like a
+you would call it the average uh travel
+
+ align:start position:0%
+you would call it the average uh travel
+ 
+
+ align:start position:0%
+you would call it the average uh travel
+travel distance but that's again not a
+
+ align:start position:0%
+travel distance but that's again not a
+ 
+
+ align:start position:0%
+travel distance but that's again not a
+property because it depends on both T1
+
+ align:start position:0%
+property because it depends on both T1
+ 
+
+ align:start position:0%
+property because it depends on both T1
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T2 instead we all know that if you take
+
+ align:start position:0%
+T2 instead we all know that if you take
+ 
+
+ align:start position:0%
+T2 instead we all know that if you take
+the limit of T2 go going to T1 and
+
+ align:start position:0%
+the limit of T2 go going to T1 and
+ 
+
+ align:start position:0%
+the limit of T2 go going to T1 and
+measured only for a short uh uh distance
+
+ align:start position:0%
+measured only for a short uh uh distance
+ 
+
+ align:start position:0%
+measured only for a short uh uh distance
+that same ratio that one tends to a
+
+ align:start position:0%
+that same ratio that one tends to a
+ 
+
+ align:start position:0%
+that same ratio that one tends to a
+property that we call the velocity so
+
+ align:start position:0%
+property that we call the velocity so
+ 
+
+ align:start position:0%
+property that we call the velocity so
+that is a property and it it is assigned
+
+ align:start position:0%
+that is a property and it it is assigned
+ 
+
+ align:start position:0%
+that is a property and it it is assigned
+to the time T1 to the single uh time
+
+ align:start position:0%
+to the time T1 to the single uh time
+ 
+
+ align:start position:0%
+to the time T1 to the single uh time
+interval so this is what we mean by
+
+ align:start position:0%
+interval so this is what we mean by
+ 
+
+ align:start position:0%
+interval so this is what we mean by
+properties and properties there are many
+
+ align:start position:0%
+properties and properties there are many
+ 
+
+ align:start position:0%
+properties and properties there are many
+properties that you can uh uh
+
+ align:start position:0%
+properties that you can uh uh
+ 
+
+ align:start position:0%
+properties that you can uh uh
+describe and that they are defined by
+
+ align:start position:0%
+describe and that they are defined by
+ 
+
+ align:start position:0%
+describe and that they are defined by
+the various measurement process
+
+ align:start position:0%
+the various measurement process
+ 
+
+ align:start position:0%
+the various measurement process
+procedures that you can devise in order
+
+ align:start position:0%
+procedures that you can devise in order
+ 
+
+ align:start position:0%
+procedures that you can devise in order
+to stud to study your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system uh for
+
+ align:start position:0%
+system uh for
+ 
+
+ align:start position:0%
+system uh for
+example if this is my system I could
+
+ align:start position:0%
+example if this is my system I could
+ 
+
+ align:start position:0%
+example if this is my system I could
+count how many molecules are in there so
+
+ align:start position:0%
+count how many molecules are in there so
+ 
+
+ align:start position:0%
+count how many molecules are in there so
+counting is a good maybe difficult but
+
+ align:start position:0%
+counting is a good maybe difficult but
+ 
+
+ align:start position:0%
+counting is a good maybe difficult but
+it's a well defined uh measurement
+
+ align:start position:0%
+it's a well defined uh measurement
+ 
+
+ align:start position:0%
+it's a well defined uh measurement
+procedure so I can count how many
+
+ align:start position:0%
+procedure so I can count how many
+ 
+
+ align:start position:0%
+procedure so I can count how many
+molecules and if there is not only water
+
+ align:start position:0%
+molecules and if there is not only water
+ 
+
+ align:start position:0%
+molecules and if there is not only water
+but maybe there is also carbon dioxide I
+
+ align:start position:0%
+but maybe there is also carbon dioxide I
+ 
+
+ align:start position:0%
+but maybe there is also carbon dioxide I
+should count how many water molecules
+
+ align:start position:0%
+should count how many water molecules
+ 
+
+ align:start position:0%
+should count how many water molecules
+and how many carbon dioxide maybe some
+
+ align:start position:0%
+and how many carbon dioxide maybe some
+ 
+
+ align:start position:0%
+and how many carbon dioxide maybe some
+oxygen some nitrogen uh all right then I
+
+ align:start position:0%
+oxygen some nitrogen uh all right then I
+ 
+
+ align:start position:0%
+oxygen some nitrogen uh all right then I
+can also measure
+
+ align:start position:0%
+can also measure
+ 
+
+ align:start position:0%
+can also measure
+if my system is um variable volume not
+
+ align:start position:0%
+if my system is um variable volume not
+ 
+
+ align:start position:0%
+if my system is um variable volume not
+this bottle but if if this is a variable
+
+ align:start position:0%
+this bottle but if if this is a variable
+ 
+
+ align:start position:0%
+this bottle but if if this is a variable
+volume uh
+
+ align:start position:0%
+volume uh
+ 
+
+ align:start position:0%
+volume uh
+container um then I can also measure the
+
+ align:start position:0%
+container um then I can also measure the
+ 
+
+ align:start position:0%
+container um then I can also measure the
+volume at a given instant of time right
+
+ align:start position:0%
+volume at a given instant of time right
+ 
+
+ align:start position:0%
+volume at a given instant of time right
+so that's another it's not really
+
+ align:start position:0%
+so that's another it's not really
+ 
+
+ align:start position:0%
+so that's another it's not really
+property because it's the value of one
+
+ align:start position:0%
+property because it's the value of one
+ 
+
+ align:start position:0%
+property because it's the value of one
+of those that we would call the
+
+ align:start position:0%
+of those that we would call the
+ 
+
+ align:start position:0%
+of those that we would call the
+parameters of the external that
+
+ align:start position:0%
+parameters of the external that
+ 
+
+ align:start position:0%
+parameters of the external that
+characterize the external
+
+ align:start position:0%
+characterize the external
+ 
+
+ align:start position:0%
+characterize the external
+forces and these parameters yes for a
+
+ align:start position:0%
+forces and these parameters yes for a
+ 
+
+ align:start position:0%
+forces and these parameters yes for a
+lot of um situations in which you want
+
+ align:start position:0%
+lot of um situations in which you want
+ 
+
+ align:start position:0%
+lot of um situations in which you want
+to study properties of
+
+ align:start position:0%
+to study properties of
+ 
+
+ align:start position:0%
+to study properties of
+substances volume is the main and only
+
+ align:start position:0%
+substances volume is the main and only
+ 
+
+ align:start position:0%
+substances volume is the main and only
+parameter but
+
+ align:start position:0%
+parameter but
+ 
+
+ align:start position:0%
+parameter but
+uh as you go especially for small
+
+ align:start position:0%
+uh as you go especially for small
+ 
+
+ align:start position:0%
+uh as you go especially for small
+systems that's not true anymore so the
+
+ align:start position:0%
+systems that's not true anymore so the
+ 
+
+ align:start position:0%
+systems that's not true anymore so the
+shape of your container
+
+ align:start position:0%
+shape of your container
+ 
+
+ align:start position:0%
+shape of your container
+matters we will see we more about this
+
+ align:start position:0%
+matters we will see we more about this
+ 
+
+ align:start position:0%
+matters we will see we more about this
+uh so for example if you want to
+
+ align:start position:0%
+uh so for example if you want to
+ 
+
+ align:start position:0%
+uh so for example if you want to
+describe the geometry of this um room uh
+
+ align:start position:0%
+describe the geometry of this um room uh
+ 
+
+ align:start position:0%
+describe the geometry of this um room uh
+you need many parameters this is it is
+
+ align:start position:0%
+you need many parameters this is it is
+ 
+
+ align:start position:0%
+you need many parameters this is it is
+just a box it would be L1 L2 L3 but if
+
+ align:start position:0%
+just a box it would be L1 L2 L3 but if
+ 
+
+ align:start position:0%
+just a box it would be L1 L2 L3 but if
+you consider all the detail
+
+ align:start position:0%
+you consider all the detail
+ 
+
+ align:start position:0%
+you consider all the detail
+uh like there is a there is a there is a
+
+ align:start position:0%
+uh like there is a there is a there is a
+ 
+
+ align:start position:0%
+uh like there is a there is a there is a
+corner there you got tables how many
+
+ align:start position:0%
+corner there you got tables how many
+ 
+
+ align:start position:0%
+corner there you got tables how many
+parameters you need you need a lot of
+
+ align:start position:0%
+parameters you need you need a lot of
+ 
+
+ align:start position:0%
+parameters you need you need a lot of
+parameters and they all count for some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+properties but maybe not so these are
+
+ align:start position:0%
+properties but maybe not so these are
+ 
+
+ align:start position:0%
+properties but maybe not so these are
+still just the
+
+ align:start position:0%
+still just the
+ 
+
+ align:start position:0%
+still just the
+parameters at that instant of time and
+
+ align:start position:0%
+parameters at that instant of time and
+ 
+
+ align:start position:0%
+parameters at that instant of time and
+then you can start measuring uh
+
+ align:start position:0%
+then you can start measuring uh
+ 
+
+ align:start position:0%
+then you can start measuring uh
+properties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+properties depend on um the model you
+
+ align:start position:0%
+properties depend on um the model you
+ 
+
+ align:start position:0%
+properties depend on um the model you
+are considering for example
+
+ align:start position:0%
+are considering for example
+ 
+
+ align:start position:0%
+are considering for example
+suppose um suppose I consider a the
+
+ align:start position:0%
+suppose um suppose I consider a the
+ 
+
+ align:start position:0%
+suppose um suppose I consider a the
+simplest
+
+ align:start position:0%
+simplest
+ 
+
+ align:start position:0%
+simplest
+uh mechanic classical mechanical uh uh
+
+ align:start position:0%
+uh mechanic classical mechanical uh uh
+ 
+
+ align:start position:0%
+uh mechanic classical mechanical uh uh
+system a particle a single particle in a
+
+ align:start position:0%
+system a particle a single particle in a
+ 
+
+ align:start position:0%
+system a particle a single particle in a
+box and let's make this box one
+
+ align:start position:0%
+box and let's make this box one
+ 
+
+ align:start position:0%
+box and let's make this box one
+dimension so it's even simpler just it
+
+ align:start position:0%
+dimension so it's even simpler just it
+ 
+
+ align:start position:0%
+dimension so it's even simpler just it
+can move back and forth between as X
+
+ align:start position:0%
+can move back and forth between as X
+ 
+
+ align:start position:0%
+can move back and forth between as X
+goes from Zer to
+
+ align:start position:0%
+goes from Zer to
+ 
+
+ align:start position:0%
+goes from Zer to
+L
+
+ align:start position:0%
+L
+ 
+
+ align:start position:0%
+L
+okay okay so this is a your particle a
+
+ align:start position:0%
+okay okay so this is a your particle a
+ 
+
+ align:start position:0%
+okay okay so this is a your particle a
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+mass m you have to specify M so it's a
+
+ align:start position:0%
+mass m you have to specify M so it's a
+ 
+
+ align:start position:0%
+mass m you have to specify M so it's a
+parameter of your uh of your system the
+
+ align:start position:0%
+parameter of your uh of your system the
+ 
+
+ align:start position:0%
+parameter of your uh of your system the
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+particles uh at times T well it's equal
+
+ align:start position:0%
+particles uh at times T well it's equal
+ 
+
+ align:start position:0%
+particles uh at times T well it's equal
+to one it's just one particle at any
+
+ align:start position:0%
+to one it's just one particle at any
+ 
+
+ align:start position:0%
+to one it's just one particle at any
+time so it's a constant also
+
+ align:start position:0%
+time so it's a constant also
+ 
+
+ align:start position:0%
+time so it's a constant also
+m is just m at any
+
+ align:start position:0%
+m is just m at any
+ 
+
+ align:start position:0%
+m is just m at any
+time what else can I measure well I can
+
+ align:start position:0%
+time what else can I measure well I can
+ 
+
+ align:start position:0%
+time what else can I measure well I can
+measure where the particle is so that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X that may
+
+ align:start position:0%
+X that may
+ 
+
+ align:start position:0%
+X that may
+change so that's a variable
+
+ align:start position:0%
+change so that's a variable
+ 
+
+ align:start position:0%
+change so that's a variable
+property I can also uh measure x dot
+
+ align:start position:0%
+property I can also uh measure x dot
+ 
+
+ align:start position:0%
+property I can also uh measure x dot
+the rate of change like we did there for
+
+ align:start position:0%
+the rate of change like we did there for
+ 
+
+ align:start position:0%
+the rate of change like we did there for
+velocity okay so it turns out as you
+
+ align:start position:0%
+velocity okay so it turns out as you
+ 
+
+ align:start position:0%
+velocity okay so it turns out as you
+know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that these two essentially or their
+
+ align:start position:0%
+that these two essentially or their
+ 
+
+ align:start position:0%
+that these two essentially or their
+equivalent position and
+
+ align:start position:0%
+equivalent position and
+ 
+
+ align:start position:0%
+equivalent position and
+momentum uh are the independent
+
+ align:start position:0%
+momentum uh are the independent
+ 
+
+ align:start position:0%
+momentum uh are the independent
+properties if you measure
+
+ align:start position:0%
+properties if you measure
+ 
+
+ align:start position:0%
+properties if you measure
+those with those measurement results you
+
+ align:start position:0%
+those with those measurement results you
+ 
+
+ align:start position:0%
+those with those measurement results you
+can compute all other properties of that
+
+ align:start position:0%
+can compute all other properties of that
+ 
+
+ align:start position:0%
+can compute all other properties of that
+system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so the list of properties this P1 P2
+
+ align:start position:0%
+uh so the list of properties this P1 P2
+ 
+
+ align:start position:0%
+uh so the list of properties this P1 P2
+dot dot um is typically
+
+ align:start position:0%
+dot dot um is typically
+ 
+
+ align:start position:0%
+dot dot um is typically
+infinite why well because uh even for
+
+ align:start position:0%
+infinite why well because uh even for
+ 
+
+ align:start position:0%
+infinite why well because uh even for
+this simple system if I know X may I
+
+ align:start position:0%
+this simple system if I know X may I
+ 
+
+ align:start position:0%
+this simple system if I know X may I
+maybe I want to compute X squar or X
+
+ align:start position:0%
+maybe I want to compute X squar or X
+ 
+
+ align:start position:0%
+maybe I want to compute X squar or X
+cubed or x to the n and n can be
+
+ align:start position:0%
+cubed or x to the n and n can be
+ 
+
+ align:start position:0%
+cubed or x to the n and n can be
+anything so uh I have an infinite number
+
+ align:start position:0%
+anything so uh I have an infinite number
+ 
+
+ align:start position:0%
+anything so uh I have an infinite number
+of properties
+
+ align:start position:0%
+of properties
+ 
+
+ align:start position:0%
+of properties
+but I could shorten the list by just
+
+ align:start position:0%
+but I could shorten the list by just
+ 
+
+ align:start position:0%
+but I could shorten the list by just
+using the independent ones or a set of
+
+ align:start position:0%
+using the independent ones or a set of
+ 
+
+ align:start position:0%
+using the independent ones or a set of
+independent ones okay so let's say that
+
+ align:start position:0%
+independent ones okay so let's say that
+ 
+
+ align:start position:0%
+independent ones okay so let's say that
+these in this list are the independent
+
+ align:start position:0%
+these in this list are the independent
+ 
+
+ align:start position:0%
+these in this list are the independent
+ones those that are strictly needed in
+
+ align:start position:0%
+ones those that are strictly needed in
+ 
+
+ align:start position:0%
+ones those that are strictly needed in
+order to compute all the other
+
+ align:start position:0%
+order to compute all the other
+ 
+
+ align:start position:0%
+order to compute all the other
+properties all right so if you know at
+
+ align:start position:0%
+properties all right so if you know at
+ 
+
+ align:start position:0%
+properties all right so if you know at
+one instant of time T all these numbers
+
+ align:start position:0%
+one instant of time T all these numbers
+ 
+
+ align:start position:0%
+one instant of time T all these numbers
+because each one of them is a number so
+
+ align:start position:0%
+because each one of them is a number so
+ 
+
+ align:start position:0%
+because each one of them is a number so
+if you have that list of numbers there
+
+ align:start position:0%
+if you have that list of numbers there
+ 
+
+ align:start position:0%
+if you have that list of numbers there
+is nothing else you can say or you can
+
+ align:start position:0%
+is nothing else you can say or you can
+ 
+
+ align:start position:0%
+is nothing else you can say or you can
+measure about your system at that
+
+ align:start position:0%
+measure about your system at that
+ 
+
+ align:start position:0%
+measure about your system at that
+instant of time there's no other
+
+ align:start position:0%
+instant of time there's no other
+ 
+
+ align:start position:0%
+instant of time there's no other
+property so that thing fixes all the
+
+ align:start position:0%
+property so that thing fixes all the
+ 
+
+ align:start position:0%
+property so that thing fixes all the
+properties that is what we call State so
+
+ align:start position:0%
+properties that is what we call State so
+ 
+
+ align:start position:0%
+properties that is what we call State so
+the state of a system is a list of
+
+ align:start position:0%
+the state of a system is a list of
+ 
+
+ align:start position:0%
+the state of a system is a list of
+numbers from which you can compute uh
+
+ align:start position:0%
+numbers from which you can compute uh
+ 
+
+ align:start position:0%
+numbers from which you can compute uh
+all its properties at one instant of
+
+ align:start position:0%
+all its properties at one instant of
+ 
+
+ align:start position:0%
+all its properties at one instant of
+time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+system let's make
+
+ align:start position:0%
+system let's make
+ 
+
+ align:start position:0%
+system let's make
+it here in another theory for example
+
+ align:start position:0%
+it here in another theory for example
+ 
+
+ align:start position:0%
+it here in another theory for example
+not for example another important theory
+
+ align:start position:0%
+not for example another important theory
+ 
+
+ align:start position:0%
+not for example another important theory
+is quantum
+
+ align:start position:0%
+is quantum
+ 
+
+ align:start position:0%
+is quantum
+mechanics and then you know that quantum
+
+ align:start position:0%
+mechanics and then you know that quantum
+ 
+
+ align:start position:0%
+mechanics and then you know that quantum
+mechanics the story is a bit uh more
+
+ align:start position:0%
+mechanics the story is a bit uh more
+ 
+
+ align:start position:0%
+mechanics the story is a bit uh more
+complicated
+
+ align:start position:0%
+complicated
+ 
+
+ align:start position:0%
+complicated
+because uh for example example if you
+
+ align:start position:0%
+because uh for example example if you
+ 
+
+ align:start position:0%
+because uh for example example if you
+want to measure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+position um cannot really talk about or
+
+ align:start position:0%
+position um cannot really talk about or
+ 
+
+ align:start position:0%
+position um cannot really talk about or
+you're not completely allowed to think
+
+ align:start position:0%
+you're not completely allowed to think
+ 
+
+ align:start position:0%
+you're not completely allowed to think
+of the particle adding position until
+
+ align:start position:0%
+of the particle adding position until
+ 
+
+ align:start position:0%
+of the particle adding position until
+you measure if you ask the particle
+
+ align:start position:0%
+you measure if you ask the particle
+ 
+
+ align:start position:0%
+you measure if you ask the particle
+where are you so you make a measurement
+
+ align:start position:0%
+where are you so you make a measurement
+ 
+
+ align:start position:0%
+where are you so you make a measurement
+uh a measurement act for position the
+
+ align:start position:0%
+uh a measurement act for position the
+ 
+
+ align:start position:0%
+uh a measurement act for position the
+particle is compelled to give you an
+
+ align:start position:0%
+particle is compelled to give you an
+ 
+
+ align:start position:0%
+particle is compelled to give you an
+answer so it will answer yes and here
+
+ align:start position:0%
+answer so it will answer yes and here
+ 
+
+ align:start position:0%
+answer so it will answer yes and here
+but you cannot
+
+ align:start position:0%
+but you cannot
+ 
+
+ align:start position:0%
+but you cannot
+um infer from that single act of
+
+ align:start position:0%
+um infer from that single act of
+ 
+
+ align:start position:0%
+um infer from that single act of
+measurement that the next time you have
+
+ align:start position:0%
+measurement that the next time you have
+ 
+
+ align:start position:0%
+measurement that the next time you have
+the same system in the same state if you
+
+ align:start position:0%
+the same system in the same state if you
+ 
+
+ align:start position:0%
+the same system in the same state if you
+perform a measurement act the particle
+
+ align:start position:0%
+perform a measurement act the particle
+ 
+
+ align:start position:0%
+perform a measurement act the particle
+give you the same answer all you can
+
+ align:start position:0%
+give you the same answer all you can
+ 
+
+ align:start position:0%
+give you the same answer all you can
+predict is the probability all you can
+
+ align:start position:0%
+predict is the probability all you can
+ 
+
+ align:start position:0%
+predict is the probability all you can
+represent is the probability to get an
+
+ align:start position:0%
+represent is the probability to get an
+ 
+
+ align:start position:0%
+represent is the probability to get an
+answer so the so uh if the probability
+
+ align:start position:0%
+answer so the so uh if the probability
+ 
+
+ align:start position:0%
+answer so the so uh if the probability
+to have the particle between X and X
+
+ align:start position:0%
+to have the particle between X and X
+ 
+
+ align:start position:0%
+to have the particle between X and X
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+DX and the probability is the this the
+
+ align:start position:0%
+DX and the probability is the this the
+ 
+
+ align:start position:0%
+DX and the probability is the this the
+area here of this curve and this curve
+
+ align:start position:0%
+area here of this curve and this curve
+ 
+
+ align:start position:0%
+area here of this curve and this curve
+uh is obtain like
+
+ align:start position:0%
+uh is obtain like
+ 
+
+ align:start position:0%
+uh is obtain like
+the the it's the wave function modulus
+
+ align:start position:0%
+the the it's the wave function modulus
+ 
+
+ align:start position:0%
+the the it's the wave function modulus
+squared something like
+
+ align:start position:0%
+squared something like
+ 
+
+ align:start position:0%
+squared something like
+that times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX okay so that's the probability
+
+ align:start position:0%
+DX okay so that's the probability
+ 
+
+ align:start position:0%
+DX okay so that's the probability
+density uh
+
+ align:start position:0%
+density uh
+ 
+
+ align:start position:0%
+density uh
+and okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for this
+
+ align:start position:0%
+so for this
+ 
+
+ align:start position:0%
+so for this
+particularly
+
+ align:start position:0%
+particularly
+ 
+
+ align:start position:0%
+particularly
+simple uh quantum mechanical
+
+ align:start position:0%
+simple uh quantum mechanical
+ 
+
+ align:start position:0%
+simple uh quantum mechanical
+System since you need a function in
+
+ align:start position:0%
+System since you need a function in
+ 
+
+ align:start position:0%
+System since you need a function in
+order to describe the
+
+ align:start position:0%
+order to describe the
+ 
+
+ align:start position:0%
+order to describe the
+probabilities um a function is an
+
+ align:start position:0%
+probabilities um a function is an
+ 
+
+ align:start position:0%
+probabilities um a function is an
+infinite set of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numbers because it has a value here
+
+ align:start position:0%
+numbers because it has a value here
+ 
+
+ align:start position:0%
+numbers because it has a value here
+there's another value here and another
+
+ align:start position:0%
+there's another value here and another
+ 
+
+ align:start position:0%
+there's another value here and another
+there so this is an infinite set of
+
+ align:start position:0%
+there so this is an infinite set of
+ 
+
+ align:start position:0%
+there so this is an infinite set of
+numbers so this is a system which has an
+
+ align:start position:0%
+numbers so this is a system which has an
+ 
+
+ align:start position:0%
+numbers so this is a system which has an
+infinite number of independent
+
+ align:start position:0%
+infinite number of independent
+ 
+
+ align:start position:0%
+infinite number of independent
+properties which are though U thanks to
+
+ align:start position:0%
+properties which are though U thanks to
+ 
+
+ align:start position:0%
+properties which are though U thanks to
+mathematics expressible in terms of a
+
+ align:start position:0%
+mathematics expressible in terms of a
+ 
+
+ align:start position:0%
+mathematics expressible in terms of a
+single
+
+ align:start position:0%
+single
+ 
+
+ align:start position:0%
+single
+function in more complicated situations
+
+ align:start position:0%
+function in more complicated situations
+ 
+
+ align:start position:0%
+function in more complicated situations
+uh the function is not the wave function
+
+ align:start position:0%
+uh the function is not the wave function
+ 
+
+ align:start position:0%
+uh the function is not the wave function
+and is called the the density
+
+ align:start position:0%
+and is called the the density
+ 
+
+ align:start position:0%
+and is called the the density
+operator but uh still it's a
+
+ align:start position:0%
+operator but uh still it's a
+ 
+
+ align:start position:0%
+operator but uh still it's a
+mathematical object that contains all
+
+ align:start position:0%
+mathematical object that contains all
+ 
+
+ align:start position:0%
+mathematical object that contains all
+the probabilities of measurement Act of
+
+ align:start position:0%
+the probabilities of measurement Act of
+ 
+
+ align:start position:0%
+the probabilities of measurement Act of
+any uh physical observable that
+
+ align:start position:0%
+any uh physical observable that
+ 
+
+ align:start position:0%
+any uh physical observable that
+qualifies as a property so having raow
+
+ align:start position:0%
+qualifies as a property so having raow
+ 
+
+ align:start position:0%
+qualifies as a property so having raow
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+t u gives you allows you to compute the
+
+ align:start position:0%
+t u gives you allows you to compute the
+ 
+
+ align:start position:0%
+t u gives you allows you to compute the
+values of all uh uh properties for a for
+
+ align:start position:0%
+values of all uh uh properties for a for
+ 
+
+ align:start position:0%
+values of all uh uh properties for a for
+a Quantum system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's the word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+State usually one says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+in Easy exp exposition of thermodynamics
+
+ align:start position:0%
+in Easy exp exposition of thermodynamics
+ 
+
+ align:start position:0%
+in Easy exp exposition of thermodynamics
+one says well the state of the system is
+
+ align:start position:0%
+one says well the state of the system is
+ 
+
+ align:start position:0%
+one says well the state of the system is
+it condition at a given instant of time
+
+ align:start position:0%
+it condition at a given instant of time
+ 
+
+ align:start position:0%
+it condition at a given instant of time
+okay that's what we mean by Condition
+
+ align:start position:0%
+okay that's what we mean by Condition
+ 
+
+ align:start position:0%
+okay that's what we mean by Condition
+it's a list of numbers all the values of
+
+ align:start position:0%
+it's a list of numbers all the values of
+ 
+
+ align:start position:0%
+it's a list of numbers all the values of
+all the properties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the next stage is that if I want if I
+
+ align:start position:0%
+the next stage is that if I want if I
+ 
+
+ align:start position:0%
+the next stage is that if I want if I
+know the state of a system and actually
+
+ align:start position:0%
+know the state of a system and actually
+ 
+
+ align:start position:0%
+know the state of a system and actually
+here I'm going to use the letter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A to represent um uh okay we use it for
+
+ align:start position:0%
+A to represent um uh okay we use it for
+ 
+
+ align:start position:0%
+A to represent um uh okay we use it for
+several
+
+ align:start position:0%
+several
+ 
+
+ align:start position:0%
+several
+purposes the Box typically represents
+
+ align:start position:0%
+purposes the Box typically represents
+ 
+
+ align:start position:0%
+purposes the Box typically represents
+the idea of system and a is the name of
+
+ align:start position:0%
+the idea of system and a is the name of
+ 
+
+ align:start position:0%
+the idea of system and a is the name of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+system a sub one
+
+ align:start position:0%
+system a sub one
+ 
+
+ align:start position:0%
+system a sub one
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+really a at time T1 so a sub one is
+
+ align:start position:0%
+really a at time T1 so a sub one is
+ 
+
+ align:start position:0%
+really a at time T1 so a sub one is
+defined as uh the list of all the
+
+ align:start position:0%
+defined as uh the list of all the
+ 
+
+ align:start position:0%
+defined as uh the list of all the
+properties at the given instant of time
+
+ align:start position:0%
+properties at the given instant of time
+ 
+
+ align:start position:0%
+properties at the given instant of time
+T1 that's just for short
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+end so if I know now the state I want to
+
+ align:start position:0%
+end so if I know now the state I want to
+ 
+
+ align:start position:0%
+end so if I know now the state I want to
+see how the state evolves in
+
+ align:start position:0%
+see how the state evolves in
+ 
+
+ align:start position:0%
+see how the state evolves in
+time and the state
+
+ align:start position:0%
+time and the state
+ 
+
+ align:start position:0%
+time and the state
+namely the
+
+ align:start position:0%
+namely the
+ 
+
+ align:start position:0%
+namely the
+properties can change in
+
+ align:start position:0%
+properties can change in
+ 
+
+ align:start position:0%
+properties can change in
+time uh by many reasons due to many uh
+
+ align:start position:0%
+time uh by many reasons due to many uh
+ 
+
+ align:start position:0%
+time uh by many reasons due to many uh
+uh phenomena some of them are related to
+
+ align:start position:0%
+uh phenomena some of them are related to
+ 
+
+ align:start position:0%
+uh phenomena some of them are related to
+the effect of internal
+
+ align:start position:0%
+the effect of internal
+ 
+
+ align:start position:0%
+the effect of internal
+forces like particles in a box that
+
+ align:start position:0%
+forces like particles in a box that
+ 
+
+ align:start position:0%
+forces like particles in a box that
+would Collide and the effect of a
+
+ align:start position:0%
+would Collide and the effect of a
+ 
+
+ align:start position:0%
+would Collide and the effect of a
+collision uh makes their positions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change uh
+
+ align:start position:0%
+change uh
+ 
+
+ align:start position:0%
+change uh
+they are due they may be due also to the
+
+ align:start position:0%
+they are due they may be due also to the
+ 
+
+ align:start position:0%
+they are due they may be due also to the
+external forces collision with the
+
+ align:start position:0%
+external forces collision with the
+ 
+
+ align:start position:0%
+external forces collision with the
+wall or change of the position of a
+
+ align:start position:0%
+wall or change of the position of a
+ 
+
+ align:start position:0%
+wall or change of the position of a
+wall
+
+ align:start position:0%
+wall
+ 
+
+ align:start position:0%
+wall
+okay so somehow you could uh say that if
+
+ align:start position:0%
+okay so somehow you could uh say that if
+ 
+
+ align:start position:0%
+okay so somehow you could uh say that if
+you're
+
+ align:start position:0%
+you're
+ 
+
+ align:start position:0%
+you're
+not playing around with the parameters
+
+ align:start position:0%
+not playing around with the parameters
+ 
+
+ align:start position:0%
+not playing around with the parameters
+of the system changing the walls uh or
+
+ align:start position:0%
+of the system changing the walls uh or
+ 
+
+ align:start position:0%
+of the system changing the walls uh or
+moving the walls uh and what happens is
+
+ align:start position:0%
+moving the walls uh and what happens is
+ 
+
+ align:start position:0%
+moving the walls uh and what happens is
+just due to the internal forces uh you
+
+ align:start position:0%
+just due to the internal forces uh you
+ 
+
+ align:start position:0%
+just due to the internal forces uh you
+call that internal Dynamics you call it
+
+ align:start position:0%
+call that internal Dynamics you call it
+ 
+
+ align:start position:0%
+call that internal Dynamics you call it
+a spontaneous
+
+ align:start position:0%
+a spontaneous
+ 
+
+ align:start position:0%
+a spontaneous
+process within the system it happens all
+
+ align:start position:0%
+process within the system it happens all
+ 
+
+ align:start position:0%
+process within the system it happens all
+within the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system if
+
+ align:start position:0%
+system if
+ 
+
+ align:start position:0%
+system if
+instead the the change of your state so
+
+ align:start position:0%
+instead the the change of your state so
+ 
+
+ align:start position:0%
+instead the the change of your state so
+the change of the properties is due to
+
+ align:start position:0%
+the change of the properties is due to
+ 
+
+ align:start position:0%
+the change of the properties is due to
+uh either what uh to what you do to the
+
+ align:start position:0%
+uh either what uh to what you do to the
+ 
+
+ align:start position:0%
+uh either what uh to what you do to the
+to the walls to the moving of the
+
+ align:start position:0%
+to the walls to the moving of the
+ 
+
+ align:start position:0%
+to the walls to the moving of the
+parameters
+
+ align:start position:0%
+parameters
+ 
+
+ align:start position:0%
+parameters
+or to what happens uh on the outside of
+
+ align:start position:0%
+or to what happens uh on the outside of
+ 
+
+ align:start position:0%
+or to what happens uh on the outside of
+your system so
+
+ align:start position:0%
+your system so
+ 
+
+ align:start position:0%
+your system so
+if I have some hot hot air that goes
+
+ align:start position:0%
+if I have some hot hot air that goes
+ 
+
+ align:start position:0%
+if I have some hot hot air that goes
+around this this bottle and therefore
+
+ align:start position:0%
+around this this bottle and therefore
+ 
+
+ align:start position:0%
+around this this bottle and therefore
+there's a heat exchange through the wall
+
+ align:start position:0%
+there's a heat exchange through the wall
+ 
+
+ align:start position:0%
+there's a heat exchange through the wall
+that is going to heat up the bottle or
+
+ align:start position:0%
+that is going to heat up the bottle or
+ 
+
+ align:start position:0%
+that is going to heat up the bottle or
+maybe cool it down you put the bottom in
+
+ align:start position:0%
+maybe cool it down you put the bottom in
+ 
+
+ align:start position:0%
+maybe cool it down you put the bottom in
+the refrigerator it cools
+
+ align:start position:0%
+the refrigerator it cools
+ 
+
+ align:start position:0%
+the refrigerator it cools
+down all right that
+
+ align:start position:0%
+down all right that
+ 
+
+ align:start position:0%
+down all right that
+uh is an
+
+ align:start position:0%
+uh is an
+ 
+
+ align:start position:0%
+uh is an
+interaction and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh interactions are very several kinds
+
+ align:start position:0%
+uh interactions are very several kinds
+ 
+
+ align:start position:0%
+uh interactions are very several kinds
+and we we will spend time in describing
+
+ align:start position:0%
+and we we will spend time in describing
+ 
+
+ align:start position:0%
+and we we will spend time in describing
+and U giving models for these kind of
+
+ align:start position:0%
+and U giving models for these kind of
+ 
+
+ align:start position:0%
+and U giving models for these kind of
+interactions first of all work and then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+heat you will notice that uh we will
+
+ align:start position:0%
+heat you will notice that uh we will
+ 
+
+ align:start position:0%
+heat you will notice that uh we will
+Define heat we will not we do not start
+
+ align:start position:0%
+Define heat we will not we do not start
+ 
+
+ align:start position:0%
+Define heat we will not we do not start
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+heat and this is very important uh if
+
+ align:start position:0%
+heat and this is very important uh if
+ 
+
+ align:start position:0%
+heat and this is very important uh if
+you're fan of um logical
+
+ align:start position:0%
+you're fan of um logical
+ 
+
+ align:start position:0%
+you're fan of um logical
+consistency because uh heat uh is
+
+ align:start position:0%
+consistency because uh heat uh is
+ 
+
+ align:start position:0%
+consistency because uh heat uh is
+typically
+
+ align:start position:0%
+typically
+ 
+
+ align:start position:0%
+typically
+defined uh by euristic arguments and by
+
+ align:start position:0%
+defined uh by euristic arguments and by
+ 
+
+ align:start position:0%
+defined uh by euristic arguments and by
+a lot of hand waving even by the best
+
+ align:start position:0%
+a lot of hand waving even by the best
+ 
+
+ align:start position:0%
+a lot of hand waving even by the best
+physicist so if you go uh there is a
+
+ align:start position:0%
+physicist so if you go uh there is a
+ 
+
+ align:start position:0%
+physicist so if you go uh there is a
+series of lecture I'll mention another
+
+ align:start position:0%
+series of lecture I'll mention another
+ 
+
+ align:start position:0%
+series of lecture I'll mention another
+in a moment that you may know by Fineman
+
+ align:start position:0%
+in a moment that you may know by Fineman
+ 
+
+ align:start position:0%
+in a moment that you may know by Fineman
+that you find on YouTube he was a
+
+ align:start position:0%
+that you find on YouTube he was a
+ 
+
+ align:start position:0%
+that you find on YouTube he was a
+wonderful
+
+ align:start position:0%
+wonderful
+ 
+
+ align:start position:0%
+wonderful
+professor in the
+
+ align:start position:0%
+professor in the
+ 
+
+ align:start position:0%
+professor in the
+60s and U he has this very funny
+
+ align:start position:0%
+60s and U he has this very funny
+ 
+
+ align:start position:0%
+60s and U he has this very funny
+lectures was a great teacher and you
+
+ align:start position:0%
+lectures was a great teacher and you
+ 
+
+ align:start position:0%
+lectures was a great teacher and you
+should see how uh he how much hand
+
+ align:start position:0%
+should see how uh he how much hand
+ 
+
+ align:start position:0%
+should see how uh he how much hand
+waving he does in order to describe what
+
+ align:start position:0%
+waving he does in order to describe what
+ 
+
+ align:start position:0%
+waving he does in order to describe what
+heat is because it has to do with molec
+
+ align:start position:0%
+heat is because it has to do with molec
+ 
+
+ align:start position:0%
+heat is because it has to do with molec
+agitation and all that all right yes you
+
+ align:start position:0%
+agitation and all that all right yes you
+ 
+
+ align:start position:0%
+agitation and all that all right yes you
+can do it that
+
+ align:start position:0%
+can do it that
+ 
+
+ align:start position:0%
+can do it that
+way and you see here we do it in
+
+ align:start position:0%
+way and you see here we do it in
+ 
+
+ align:start position:0%
+way and you see here we do it in
+entirely different way which is
+
+ align:start position:0%
+entirely different way which is
+ 
+
+ align:start position:0%
+entirely different way which is
+equivalent but uh you will see where it
+
+ align:start position:0%
+equivalent but uh you will see where it
+ 
+
+ align:start position:0%
+equivalent but uh you will see where it
+where it deres from it is a heat is
+
+ align:start position:0%
+where it deres from it is a heat is
+ 
+
+ align:start position:0%
+where it deres from it is a heat is
+going to be a consequence of the laws of
+
+ align:start position:0%
+going to be a consequence of the laws of
+ 
+
+ align:start position:0%
+going to be a consequence of the laws of
+thermodynamics
+
+ align:start position:0%
+thermodynamics
+ 
+
+ align:start position:0%
+thermodynamics
+uh which which is the way it should
+
+ align:start position:0%
+uh which which is the way it should
+ 
+
+ align:start position:0%
+uh which which is the way it should
+because after all heat as you correctly
+
+ align:start position:0%
+because after all heat as you correctly
+ 
+
+ align:start position:0%
+because after all heat as you correctly
+mentioned is
+
+ align:start position:0%
+mentioned is
+ 
+
+ align:start position:0%
+mentioned is
+a it's a PEC peculiar concept of of
+
+ align:start position:0%
+a it's a PEC peculiar concept of of
+ 
+
+ align:start position:0%
+a it's a PEC peculiar concept of of
+thermodynamics so uh how could
+
+ align:start position:0%
+thermodynamics so uh how could
+ 
+
+ align:start position:0%
+thermodynamics so uh how could
+you pretend or or or or or attempt to
+
+ align:start position:0%
+you pretend or or or or or attempt to
+ 
+
+ align:start position:0%
+you pretend or or or or or attempt to
+describe it by just using mechanical
+
+ align:start position:0%
+describe it by just using mechanical
+ 
+
+ align:start position:0%
+describe it by just using mechanical
+Concepts all right more of that uh as we
+
+ align:start position:0%
+Concepts all right more of that uh as we
+ 
+
+ align:start position:0%
+Concepts all right more of that uh as we
+go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+along um if a system under goes uh
+
+ align:start position:0%
+along um if a system under goes uh
+ 
+
+ align:start position:0%
+along um if a system under goes uh
+spontaneous processes and is unable to
+
+ align:start position:0%
+spontaneous processes and is unable to
+ 
+
+ align:start position:0%
+spontaneous processes and is unable to
+affect the state of the environment we
+
+ align:start position:0%
+affect the state of the environment we
+ 
+
+ align:start position:0%
+affect the state of the environment we
+call it an isolated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system all right so we have the state
+
+ align:start position:0%
+system all right so we have the state
+ 
+
+ align:start position:0%
+system all right so we have the state
+and we want to describe how the state
+
+ align:start position:0%
+and we want to describe how the state
+ 
+
+ align:start position:0%
+and we want to describe how the state
+evolves in
+
+ align:start position:0%
+evolves in
+ 
+
+ align:start position:0%
+evolves in
+time now this picture is a
+
+ align:start position:0%
+time now this picture is a
+ 
+
+ align:start position:0%
+time now this picture is a
+trajectory but this trajectory is you
+
+ align:start position:0%
+trajectory but this trajectory is you
+ 
+
+ align:start position:0%
+trajectory but this trajectory is you
+have to understand it as a a trajectory
+
+ align:start position:0%
+have to understand it as a a trajectory
+ 
+
+ align:start position:0%
+have to understand it as a a trajectory
+in state space so
+
+ align:start position:0%
+in state space so
+ 
+
+ align:start position:0%
+in state space so
+uh for every independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+property you should think of having
+
+ align:start position:0%
+property you should think of having
+ 
+
+ align:start position:0%
+property you should think of having
+suppose you have uh just three
+
+ align:start position:0%
+suppose you have uh just three
+ 
+
+ align:start position:0%
+suppose you have uh just three
+independent properties like XY
+
+ align:start position:0%
+independent properties like XY
+ 
+
+ align:start position:0%
+independent properties like XY
+z uh then the state is a point here but
+
+ align:start position:0%
+z uh then the state is a point here but
+ 
+
+ align:start position:0%
+z uh then the state is a point here but
+if I have more independent properties I
+
+ align:start position:0%
+if I have more independent properties I
+ 
+
+ align:start position:0%
+if I have more independent properties I
+need more axis one for each independent
+
+ align:start position:0%
+need more axis one for each independent
+ 
+
+ align:start position:0%
+need more axis one for each independent
+property so I need a multi-dimensional
+
+ align:start position:0%
+property so I need a multi-dimensional
+ 
+
+ align:start position:0%
+property so I need a multi-dimensional
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+not easy to draw on the Blackboard but
+
+ align:start position:0%
+not easy to draw on the Blackboard but
+ 
+
+ align:start position:0%
+not easy to draw on the Blackboard but
+easy to well easy to imagine it's an
+
+ align:start position:0%
+easy to well easy to imagine it's an
+ 
+
+ align:start position:0%
+easy to well easy to imagine it's an
+abstract idea so that's what we mean by
+
+ align:start position:0%
+abstract idea so that's what we mean by
+ 
+
+ align:start position:0%
+abstract idea so that's what we mean by
+uh State space and the state that
+
+ align:start position:0%
+uh State space and the state that
+ 
+
+ align:start position:0%
+uh State space and the state that
+evolves in time we call it the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trajectory
+
+ align:start position:0%
+trajectory
+ 
+
+ align:start position:0%
+trajectory
+typically the description of the the
+
+ align:start position:0%
+typically the description of the the
+ 
+
+ align:start position:0%
+typically the description of the the
+trajectory in your in our models is the
+
+ align:start position:0%
+trajectory in your in our models is the
+ 
+
+ align:start position:0%
+trajectory in your in our models is the
+Sol
+
+ align:start position:0%
+Sol
+ 
+
+ align:start position:0%
+Sol
+solution of a differential equation that
+
+ align:start position:0%
+solution of a differential equation that
+ 
+
+ align:start position:0%
+solution of a differential equation that
+we call the equation of motion of the
+
+ align:start position:0%
+we call the equation of motion of the
+ 
+
+ align:start position:0%
+we call the equation of motion of the
+system which says the rate of change of
+
+ align:start position:0%
+system which says the rate of change of
+ 
+
+ align:start position:0%
+system which says the rate of change of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+State uh is some function of the state
+
+ align:start position:0%
+State uh is some function of the state
+ 
+
+ align:start position:0%
+State uh is some function of the state
+itself and of the various forces
+
+ align:start position:0%
+itself and of the various forces
+ 
+
+ align:start position:0%
+itself and of the various forces
+external forces or parameters of things
+
+ align:start position:0%
+external forces or parameters of things
+ 
+
+ align:start position:0%
+external forces or parameters of things
+that you can control from outside of the
+
+ align:start position:0%
+that you can control from outside of the
+ 
+
+ align:start position:0%
+that you can control from outside of the
+external forces like squeezing the
+
+ align:start position:0%
+external forces like squeezing the
+ 
+
+ align:start position:0%
+external forces like squeezing the
+bottle or things like
+
+ align:start position:0%
+bottle or things like
+ 
+
+ align:start position:0%
+bottle or things like
+that okay so that's the equation of
+
+ align:start position:0%
+that okay so that's the equation of
+ 
+
+ align:start position:0%
+that okay so that's the equation of
+motion if your
+
+ align:start position:0%
+motion if your
+ 
+
+ align:start position:0%
+motion if your
+model has the equation of motion like in
+
+ align:start position:0%
+model has the equation of motion like in
+ 
+
+ align:start position:0%
+model has the equation of motion like in
+uh molecular Dynamic simulations I
+
+ align:start position:0%
+uh molecular Dynamic simulations I
+ 
+
+ align:start position:0%
+uh molecular Dynamic simulations I
+believe you do have the equations of
+
+ align:start position:0%
+believe you do have the equations of
+ 
+
+ align:start position:0%
+believe you do have the equations of
+motion and those are exactly what you
+
+ align:start position:0%
+motion and those are exactly what you
+ 
+
+ align:start position:0%
+motion and those are exactly what you
+solve in order to see the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+evolve then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by analyzing that equation of motion or
+
+ align:start position:0%
+by analyzing that equation of motion or
+ 
+
+ align:start position:0%
+by analyzing that equation of motion or
+maybe the results maybe the results will
+
+ align:start position:0%
+maybe the results maybe the results will
+ 
+
+ align:start position:0%
+maybe the results maybe the results will
+suggest ideas about analyzing the
+
+ align:start position:0%
+suggest ideas about analyzing the
+ 
+
+ align:start position:0%
+suggest ideas about analyzing the
+equation and finding some um
+
+ align:start position:0%
+equation and finding some um
+ 
+
+ align:start position:0%
+equation and finding some um
+General uh features of that time uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Evolution these features if you can
+
+ align:start position:0%
+Evolution these features if you can
+ 
+
+ align:start position:0%
+Evolution these features if you can
+prove them that they are theorems of
+
+ align:start position:0%
+prove them that they are theorems of
+ 
+
+ align:start position:0%
+prove them that they are theorems of
+equational
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion some
+
+ align:start position:0%
+motion some
+ 
+
+ align:start position:0%
+motion some
+of these
+
+ align:start position:0%
+of these
+ 
+
+ align:start position:0%
+of these
+theorems are
+
+ align:start position:0%
+theorems are
+ 
+
+ align:start position:0%
+theorems are
+features of all models good models
+
+ align:start position:0%
+features of all models good models
+ 
+
+ align:start position:0%
+features of all models good models
+successful models of physical
+
+ align:start position:0%
+successful models of physical
+ 
+
+ align:start position:0%
+successful models of physical
+reality in other words what I'm saying
+
+ align:start position:0%
+reality in other words what I'm saying
+ 
+
+ align:start position:0%
+reality in other words what I'm saying
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+that if you're describing a piece of of
+
+ align:start position:0%
+that if you're describing a piece of of
+ 
+
+ align:start position:0%
+that if you're describing a piece of of
+physical
+
+ align:start position:0%
+physical
+ 
+
+ align:start position:0%
+physical
+reality with a with your
+
+ align:start position:0%
+reality with a with your
+ 
+
+ align:start position:0%
+reality with a with your
+model that
+
+ align:start position:0%
+model that
+ 
+
+ align:start position:0%
+model that
+model uh so it have equation of
+
+ align:start position:0%
+model uh so it have equation of
+ 
+
+ align:start position:0%
+model uh so it have equation of
+motion it we and that equation of motion
+
+ align:start position:0%
+motion it we and that equation of motion
+ 
+
+ align:start position:0%
+motion it we and that equation of motion
+will have a couple always have a couple
+
+ align:start position:0%
+will have a couple always have a couple
+ 
+
+ align:start position:0%
+will have a couple always have a couple
+of uh theorems no matter what the what
+
+ align:start position:0%
+of uh theorems no matter what the what
+ 
+
+ align:start position:0%
+of uh theorems no matter what the what
+the system is small or large complicated
+
+ align:start position:0%
+the system is small or large complicated
+ 
+
+ align:start position:0%
+the system is small or large complicated
+or simple
+
+ align:start position:0%
+or simple
+ 
+
+ align:start position:0%
+or simple
+um those two theorems are General
+
+ align:start position:0%
+um those two theorems are General
+ 
+
+ align:start position:0%
+um those two theorems are General
+features of all modeling assumptions for
+
+ align:start position:0%
+features of all modeling assumptions for
+ 
+
+ align:start position:0%
+features of all modeling assumptions for
+modeling um or or modeling of of
+
+ align:start position:0%
+modeling um or or modeling of of
+ 
+
+ align:start position:0%
+modeling um or or modeling of of
+physical reality uh then
+
+ align:start position:0%
+physical reality uh then
+ 
+
+ align:start position:0%
+physical reality uh then
+is what we call I mean they become so
+
+ align:start position:0%
+is what we call I mean they become so
+ 
+
+ align:start position:0%
+is what we call I mean they become so
+important these results because they're
+
+ align:start position:0%
+important these results because they're
+ 
+
+ align:start position:0%
+important these results because they're
+General that we call them
+
+ align:start position:0%
+General that we call them
+ 
+
+ align:start position:0%
+General that we call them
+laws like law of conservation of
+
+ align:start position:0%
+laws like law of conservation of
+ 
+
+ align:start position:0%
+laws like law of conservation of
+momentum
+
+ align:start position:0%
+momentum
+ 
+
+ align:start position:0%
+momentum
+uh and here in particular we will be
+
+ align:start position:0%
+uh and here in particular we will be
+ 
+
+ align:start position:0%
+uh and here in particular we will be
+concerned about those that have to do
+
+ align:start position:0%
+concerned about those that have to do
+ 
+
+ align:start position:0%
+concerned about those that have to do
+with energy and entropy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the message here is that
+
+ align:start position:0%
+but the message here is that
+ 
+
+ align:start position:0%
+but the message here is that
+uh these
+
+ align:start position:0%
+uh these
+ 
+
+ align:start position:0%
+uh these
+results if you add the equation of
+
+ align:start position:0%
+results if you add the equation of
+ 
+
+ align:start position:0%
+results if you add the equation of
+motion are theorems of the equation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion however there is an alternative
+
+ align:start position:0%
+motion however there is an alternative
+ 
+
+ align:start position:0%
+motion however there is an alternative
+suppose you don't have the equation of
+
+ align:start position:0%
+suppose you don't have the equation of
+ 
+
+ align:start position:0%
+suppose you don't have the equation of
+motion or you don't want to solve the
+
+ align:start position:0%
+motion or you don't want to solve the
+ 
+
+ align:start position:0%
+motion or you don't want to solve the
+entire equation or motion for your
+
+ align:start position:0%
+entire equation or motion for your
+ 
+
+ align:start position:0%
+entire equation or motion for your
+system because perhaps it's too
+
+ align:start position:0%
+system because perhaps it's too
+ 
+
+ align:start position:0%
+system because perhaps it's too
+complicated I mean can you imagine
+
+ align:start position:0%
+complicated I mean can you imagine
+ 
+
+ align:start position:0%
+complicated I mean can you imagine
+solving the equation of motion for 10 to
+
+ align:start position:0%
+solving the equation of motion for 10 to
+ 
+
+ align:start position:0%
+solving the equation of motion for 10 to
+the how many I mean 10 to the 23
+
+ align:start position:0%
+the how many I mean 10 to the 23
+ 
+
+ align:start position:0%
+the how many I mean 10 to the 23
+particles uh U if you do your molecular
+
+ align:start position:0%
+particles uh U if you do your molecular
+ 
+
+ align:start position:0%
+particles uh U if you do your molecular
+Dynamics
+
+ align:start position:0%
+Dynamics
+ 
+
+ align:start position:0%
+Dynamics
+simulations the number of particles may
+
+ align:start position:0%
+simulations the number of particles may
+ 
+
+ align:start position:0%
+simulations the number of particles may
+be I don't know million but not 10 to
+
+ align:start position:0%
+be I don't know million but not 10 to
+ 
+
+ align:start position:0%
+be I don't know million but not 10 to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+go so not only it is Impractical to
+
+ align:start position:0%
+go so not only it is Impractical to
+ 
+
+ align:start position:0%
+go so not only it is Impractical to
+actually do
+
+ align:start position:0%
+actually do
+ 
+
+ align:start position:0%
+actually do
+it but
+
+ align:start position:0%
+it but
+ 
+
+ align:start position:0%
+it but
+uh is actually
+
+ align:start position:0%
+uh is actually
+ 
+
+ align:start position:0%
+uh is actually
+useless
+
+ align:start position:0%
+useless
+ 
+
+ align:start position:0%
+useless
+because you can uh extract uh a lot of
+
+ align:start position:0%
+because you can uh extract uh a lot of
+ 
+
+ align:start position:0%
+because you can uh extract uh a lot of
+information by by first of all studying
+
+ align:start position:0%
+information by by first of all studying
+ 
+
+ align:start position:0%
+information by by first of all studying
+smaller systems as long as they're not
+
+ align:start position:0%
+smaller systems as long as they're not
+ 
+
+ align:start position:0%
+smaller systems as long as they're not
+too small we will
+
+ align:start position:0%
+too small we will
+ 
+
+ align:start position:0%
+too small we will
+see uh but
+
+ align:start position:0%
+see uh but
+ 
+
+ align:start position:0%
+see uh but
+also you may not need all the details of
+
+ align:start position:0%
+also you may not need all the details of
+ 
+
+ align:start position:0%
+also you may not need all the details of
+the time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Evolution however even if you
+
+ align:start position:0%
+Evolution however even if you
+ 
+
+ align:start position:0%
+Evolution however even if you
+give up the description in terms of a
+
+ align:start position:0%
+give up the description in terms of a
+ 
+
+ align:start position:0%
+give up the description in terms of a
+full dynamical description in terms of
+
+ align:start position:0%
+full dynamical description in terms of
+ 
+
+ align:start position:0%
+full dynamical description in terms of
+the full equation of
+
+ align:start position:0%
+the full equation of
+ 
+
+ align:start position:0%
+the full equation of
+motion you shouldn't forget about these
+
+ align:start position:0%
+motion you shouldn't forget about these
+ 
+
+ align:start position:0%
+motion you shouldn't forget about these
+two theorems that any equation of motion
+
+ align:start position:0%
+two theorems that any equation of motion
+ 
+
+ align:start position:0%
+two theorems that any equation of motion
+must
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satisfy at that level of the scription
+
+ align:start position:0%
+satisfy at that level of the scription
+ 
+
+ align:start position:0%
+satisfy at that level of the scription
+you call them fundamental principle you
+
+ align:start position:0%
+you call them fundamental principle you
+ 
+
+ align:start position:0%
+you call them fundamental principle you
+call them laws you call them
+
+ align:start position:0%
+call them laws you call them
+ 
+
+ align:start position:0%
+call them laws you call them
+postulates they become the starting
+
+ align:start position:0%
+postulates they become the starting
+ 
+
+ align:start position:0%
+postulates they become the starting
+point something that you
+
+ align:start position:0%
+point something that you
+ 
+
+ align:start position:0%
+point something that you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+uh must be satisfied by your
+
+ align:start position:0%
+uh must be satisfied by your
+ 
+
+ align:start position:0%
+uh must be satisfied by your
+model and so instead of describing the
+
+ align:start position:0%
+model and so instead of describing the
+ 
+
+ align:start position:0%
+model and so instead of describing the
+entire time Evolution we
+
+ align:start position:0%
+entire time Evolution we
+ 
+
+ align:start position:0%
+entire time Evolution we
+use when we can or when it is
+
+ align:start position:0%
+use when we can or when it is
+ 
+
+ align:start position:0%
+use when we can or when it is
+enough we use the idea of process the
+
+ align:start position:0%
+enough we use the idea of process the
+ 
+
+ align:start position:0%
+enough we use the idea of process the
+idea of process is not only an initial
+
+ align:start position:0%
+idea of process is not only an initial
+ 
+
+ align:start position:0%
+idea of process is not only an initial
+and a final state of your system on
+
+ align:start position:0%
+and a final state of your system on
+ 
+
+ align:start position:0%
+and a final state of your system on
+which you want to check that those laws
+
+ align:start position:0%
+which you want to check that those laws
+ 
+
+ align:start position:0%
+which you want to check that those laws
+are are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satisfied yes you do need an initial and
+
+ align:start position:0%
+satisfied yes you do need an initial and
+ 
+
+ align:start position:0%
+satisfied yes you do need an initial and
+final state but you also need to
+
+ align:start position:0%
+final state but you also need to
+ 
+
+ align:start position:0%
+final state but you also need to
+describe the
+
+ align:start position:0%
+describe the
+ 
+
+ align:start position:0%
+describe the
+effects that the time evolution of your
+
+ align:start position:0%
+effects that the time evolution of your
+ 
+
+ align:start position:0%
+effects that the time evolution of your
+system induced in the uh rest in the in
+
+ align:start position:0%
+system induced in the uh rest in the in
+ 
+
+ align:start position:0%
+system induced in the uh rest in the in
+the environment of the system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so how do I
+
+ align:start position:0%
+so how do I
+ 
+
+ align:start position:0%
+so how do I
+describe the effects on the environment
+
+ align:start position:0%
+describe the effects on the environment
+ 
+
+ align:start position:0%
+describe the effects on the environment
+of the system well let's call B the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+environment the effects on
+
+ align:start position:0%
+environment the effects on
+ 
+
+ align:start position:0%
+environment the effects on
+b i describ by the change of its
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state what else can I do more than just
+
+ align:start position:0%
+state what else can I do more than just
+ 
+
+ align:start position:0%
+state what else can I do more than just
+saying how all the properties of the
+
+ align:start position:0%
+saying how all the properties of the
+ 
+
+ align:start position:0%
+saying how all the properties of the
+change during this
+
+ align:start position:0%
+change during this
+ 
+
+ align:start position:0%
+change during this
+process so I lose track of the details
+
+ align:start position:0%
+process so I lose track of the details
+ 
+
+ align:start position:0%
+process so I lose track of the details
+of how it goes from A1 to A2 and how the
+
+ align:start position:0%
+of how it goes from A1 to A2 and how the
+ 
+
+ align:start position:0%
+of how it goes from A1 to A2 and how the
+environment goes from B1 to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B2 uh and that's the
+
+ align:start position:0%
+B2 uh and that's the
+ 
+
+ align:start position:0%
+B2 uh and that's the
+simplification but I need to describe
+
+ align:start position:0%
+simplification but I need to describe
+ 
+
+ align:start position:0%
+simplification but I need to describe
+the initial and final states of my
+
+ align:start position:0%
+the initial and final states of my
+ 
+
+ align:start position:0%
+the initial and final states of my
+system and of the environment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so that's is what that's the idea
+
+ align:start position:0%
+that so that's is what that's the idea
+ 
+
+ align:start position:0%
+that so that's is what that's the idea
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+process the meaning of the word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process and now we get uh ready to um
+
+ align:start position:0%
+process and now we get uh ready to um
+ 
+
+ align:start position:0%
+process and now we get uh ready to um
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+um to introduce the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+law in order to introduce the first flaw
+
+ align:start position:0%
+law in order to introduce the first flaw
+ 
+
+ align:start position:0%
+law in order to introduce the first flaw
+we need uh to
+
+ align:start position:0%
+we need uh to
+ 
+
+ align:start position:0%
+we need uh to
+Define so a particular kind of process
+
+ align:start position:0%
+Define so a particular kind of process
+ 
+
+ align:start position:0%
+Define so a particular kind of process
+that allows us to
+
+ align:start position:0%
+that allows us to
+ 
+
+ align:start position:0%
+that allows us to
+connect this more general theory that we
+
+ align:start position:0%
+connect this more general theory that we
+ 
+
+ align:start position:0%
+connect this more general theory that we
+are constructing to what we know from
+
+ align:start position:0%
+are constructing to what we know from
+ 
+
+ align:start position:0%
+are constructing to what we know from
+mechanics so we consider the simplest uh
+
+ align:start position:0%
+mechanics so we consider the simplest uh
+ 
+
+ align:start position:0%
+mechanics so we consider the simplest uh
+mechanical object something like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that here it's represented by a a mass
+
+ align:start position:0%
+that here it's represented by a a mass
+ 
+
+ align:start position:0%
+that here it's represented by a a mass
+in a gravity field like
+
+ align:start position:0%
+in a gravity field like
+ 
+
+ align:start position:0%
+in a gravity field like
+weight that's why we we're going to call
+
+ align:start position:0%
+weight that's why we we're going to call
+ 
+
+ align:start position:0%
+weight that's why we we're going to call
+this particular kind of process a weight
+
+ align:start position:0%
+this particular kind of process a weight
+ 
+
+ align:start position:0%
+this particular kind of process a weight
+process so a weight process is one in
+
+ align:start position:0%
+process so a weight process is one in
+ 
+
+ align:start position:0%
+process so a weight process is one in
+which the external effect you remember
+
+ align:start position:0%
+which the external effect you remember
+ 
+
+ align:start position:0%
+which the external effect you remember
+here this the external effect is the
+
+ align:start position:0%
+here this the external effect is the
+ 
+
+ align:start position:0%
+here this the external effect is the
+change of state of your system in this
+
+ align:start position:0%
+change of state of your system in this
+ 
+
+ align:start position:0%
+change of state of your system in this
+case for the weight process B is just
+
+ align:start position:0%
+case for the weight process B is just
+ 
+
+ align:start position:0%
+case for the weight process B is just
+the weight or the only effect that
+
+ align:start position:0%
+the weight or the only effect that
+ 
+
+ align:start position:0%
+the weight or the only effect that
+occurs outside of your system is the
+
+ align:start position:0%
+occurs outside of your system is the
+ 
+
+ align:start position:0%
+occurs outside of your system is the
+change in height or El
+
+ align:start position:0%
+change in height or El
+ 
+
+ align:start position:0%
+change in height or El
+of your
+
+ align:start position:0%
+of your
+ 
+
+ align:start position:0%
+of your
+weight of a
+
+ align:start position:0%
+weight of a
+ 
+
+ align:start position:0%
+weight of a
+weight so if if you have a process like
+
+ align:start position:0%
+weight so if if you have a process like
+ 
+
+ align:start position:0%
+weight so if if you have a process like
+this your system changes from one state
+
+ align:start position:0%
+this your system changes from one state
+ 
+
+ align:start position:0%
+this your system changes from one state
+to another and the only external effect
+
+ align:start position:0%
+to another and the only external effect
+ 
+
+ align:start position:0%
+to another and the only external effect
+is the change in elevation of a weight
+
+ align:start position:0%
+is the change in elevation of a weight
+ 
+
+ align:start position:0%
+is the change in elevation of a weight
+you call it we call it weight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process if there is no change if the not
+
+ align:start position:0%
+process if there is no change if the not
+ 
+
+ align:start position:0%
+process if there is no change if the not
+even the the weight so if Z1 is equal to
+
+ align:start position:0%
+even the the weight so if Z1 is equal to
+ 
+
+ align:start position:0%
+even the the weight so if Z1 is equal to
+Z2 is equal to
+
+ align:start position:0%
+Z2 is equal to
+ 
+
+ align:start position:0%
+Z2 is equal to
+Z1 then there are no external
+
+ align:start position:0%
+Z1 then there are no external
+ 
+
+ align:start position:0%
+Z1 then there are no external
+effects this could be a spontaneous
+
+ align:start position:0%
+effects this could be a spontaneous
+ 
+
+ align:start position:0%
+effects this could be a spontaneous
+process but the idea of spontaneous
+
+ align:start position:0%
+process but the idea of spontaneous
+ 
+
+ align:start position:0%
+process but the idea of spontaneous
+process is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+really uh more demanding it requires
+
+ align:start position:0%
+really uh more demanding it requires
+ 
+
+ align:start position:0%
+really uh more demanding it requires
+that at all instance of time from T1 to
+
+ align:start position:0%
+that at all instance of time from T1 to
+ 
+
+ align:start position:0%
+that at all instance of time from T1 to
+T2 the weight
+
+ align:start position:0%
+T2 the weight
+ 
+
+ align:start position:0%
+T2 the weight
+outside doesn't move
+
+ align:start position:0%
+outside doesn't move
+ 
+
+ align:start position:0%
+outside doesn't move
+instead you could have a
+
+ align:start position:0%
+instead you could have a
+ 
+
+ align:start position:0%
+instead you could have a
+zero uh change in elevation weight
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process in which it's only the initial
+
+ align:start position:0%
+process in which it's only the initial
+ 
+
+ align:start position:0%
+process in which it's only the initial
+and final elevation of of the weight
+
+ align:start position:0%
+and final elevation of of the weight
+ 
+
+ align:start position:0%
+and final elevation of of the weight
+that are the same but during the process
+
+ align:start position:0%
+that are the same but during the process
+ 
+
+ align:start position:0%
+that are the same but during the process
+it may have went have gone up or down as
+
+ align:start position:0%
+it may have went have gone up or down as
+ 
+
+ align:start position:0%
+it may have went have gone up or down as
+long as at the end it goes back to the
+
+ align:start position:0%
+long as at the end it goes back to the
+ 
+
+ align:start position:0%
+long as at the end it goes back to the
+initial uh height then it would be zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so why is a way process uh
+
+ align:start position:0%
+okay so why is a way process uh
+ 
+
+ align:start position:0%
+okay so why is a way process uh
+important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because it
+
+ align:start position:0%
+because it
+ 
+
+ align:start position:0%
+because it
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+enters um the statement of the first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+law I know that
+
+ align:start position:0%
+law I know that
+ 
+
+ align:start position:0%
+law I know that
+usually uh especially in engineering
+
+ align:start position:0%
+usually uh especially in engineering
+ 
+
+ align:start position:0%
+usually uh especially in engineering
+applications but on not only uh you say
+
+ align:start position:0%
+applications but on not only uh you say
+ 
+
+ align:start position:0%
+applications but on not only uh you say
+all right I'm going to write the first
+
+ align:start position:0%
+all right I'm going to write the first
+ 
+
+ align:start position:0%
+all right I'm going to write the first
+law and by first law that what what you
+
+ align:start position:0%
+law and by first law that what what you
+ 
+
+ align:start position:0%
+law and by first law that what what you
+mean is really uh what we will call the
+
+ align:start position:0%
+mean is really uh what we will call the
+ 
+
+ align:start position:0%
+mean is really uh what we will call the
+energy balance
+
+ align:start position:0%
+energy balance
+ 
+
+ align:start position:0%
+energy balance
+equation okay but the first law in fact
+
+ align:start position:0%
+equation okay but the first law in fact
+ 
+
+ align:start position:0%
+equation okay but the first law in fact
+the way we're introducing
+
+ align:start position:0%
+the way we're introducing
+ 
+
+ align:start position:0%
+the way we're introducing
+here uh contains much more than just the
+
+ align:start position:0%
+here uh contains much more than just the
+ 
+
+ align:start position:0%
+here uh contains much more than just the
+idea of energy conservation which and
+
+ align:start position:0%
+idea of energy conservation which and
+ 
+
+ align:start position:0%
+idea of energy conservation which and
+and energy exchangeability that is
+
+ align:start position:0%
+and energy exchangeability that is
+ 
+
+ align:start position:0%
+and energy exchangeability that is
+behind the the energy balance equation
+
+ align:start position:0%
+behind the the energy balance equation
+ 
+
+ align:start position:0%
+behind the the energy balance equation
+as we will see in a second but uh uh it
+
+ align:start position:0%
+as we will see in a second but uh uh it
+ 
+
+ align:start position:0%
+as we will see in a second but uh uh it
+also is what guarantees the existence of
+
+ align:start position:0%
+also is what guarantees the existence of
+ 
+
+ align:start position:0%
+also is what guarantees the existence of
+property energy for every
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system and it does
+
+ align:start position:0%
+system and it does
+ 
+
+ align:start position:0%
+system and it does
+so because we have loaded the word
+
+ align:start position:0%
+so because we have loaded the word
+ 
+
+ align:start position:0%
+so because we have loaded the word
+system if you go back to the to that
+
+ align:start position:0%
+system if you go back to the to that
+ 
+
+ align:start position:0%
+system if you go back to the to that
+picture of the proton and the electron
+
+ align:start position:0%
+picture of the proton and the electron
+ 
+
+ align:start position:0%
+picture of the proton and the electron
+okay and I said all right I cannot take
+
+ align:start position:0%
+okay and I said all right I cannot take
+ 
+
+ align:start position:0%
+okay and I said all right I cannot take
+the electron and call it a system it
+
+ align:start position:0%
+the electron and call it a system it
+ 
+
+ align:start position:0%
+the electron and call it a system it
+doesn't qualify as a system and in
+
+ align:start position:0%
+doesn't qualify as a system and in
+ 
+
+ align:start position:0%
+doesn't qualify as a system and in
+fact for this thing which is not a
+
+ align:start position:0%
+fact for this thing which is not a
+ 
+
+ align:start position:0%
+fact for this thing which is not a
+system I cannot apply the first law and
+
+ align:start position:0%
+system I cannot apply the first law and
+ 
+
+ align:start position:0%
+system I cannot apply the first law and
+as you will see the consequence of the
+
+ align:start position:0%
+as you will see the consequence of the
+ 
+
+ align:start position:0%
+as you will see the consequence of the
+first law will be the existence of
+
+ align:start position:0%
+first law will be the existence of
+ 
+
+ align:start position:0%
+first law will be the existence of
+property energy this thing doesn't have
+
+ align:start position:0%
+property energy this thing doesn't have
+ 
+
+ align:start position:0%
+property energy this thing doesn't have
+energy you cannot Define the energy of
+
+ align:start position:0%
+energy you cannot Define the energy of
+ 
+
+ align:start position:0%
+energy you cannot Define the energy of
+the electron when Bound in a
+
+ align:start position:0%
+the electron when Bound in a
+ 
+
+ align:start position:0%
+the electron when Bound in a
+proton why not
+
+ align:start position:0%
+proton why not
+ 
+
+ align:start position:0%
+proton why not
+well yes if you have an electron without
+
+ align:start position:0%
+well yes if you have an electron without
+ 
+
+ align:start position:0%
+well yes if you have an electron without
+the proton far away it has its own rest
+
+ align:start position:0%
+the proton far away it has its own rest
+ 
+
+ align:start position:0%
+the proton far away it has its own rest
+mass and maybe you can Define its energy
+
+ align:start position:0%
+mass and maybe you can Define its energy
+ 
+
+ align:start position:0%
+mass and maybe you can Define its energy
+as uh us using uh this famous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formula but when it is bound to a proton
+
+ align:start position:0%
+formula but when it is bound to a proton
+ 
+
+ align:start position:0%
+formula but when it is bound to a proton
+and so there is
+
+ align:start position:0%
+and so there is
+ 
+
+ align:start position:0%
+and so there is
+a electrostatic
+
+ align:start position:0%
+a electrostatic
+ 
+
+ align:start position:0%
+a electrostatic
+interaction uh there is some energy that
+
+ align:start position:0%
+interaction uh there is some energy that
+ 
+
+ align:start position:0%
+interaction uh there is some energy that
+is related to this interaction it's
+
+ align:start position:0%
+is related to this interaction it's
+ 
+
+ align:start position:0%
+is related to this interaction it's
+called the interaction
+
+ align:start position:0%
+called the interaction
+ 
+
+ align:start position:0%
+called the interaction
+energy it's a property of the
+
+ align:start position:0%
+energy it's a property of the
+ 
+
+ align:start position:0%
+energy it's a property of the
+pair and there is no
+
+ align:start position:0%
+pair and there is no
+ 
+
+ align:start position:0%
+pair and there is no
+way no uh logical way in which you can
+
+ align:start position:0%
+way no uh logical way in which you can
+ 
+
+ align:start position:0%
+way no uh logical way in which you can
+assign part of this energy to the
+
+ align:start position:0%
+assign part of this energy to the
+ 
+
+ align:start position:0%
+assign part of this energy to the
+electron and part to the
+
+ align:start position:0%
+electron and part to the
+ 
+
+ align:start position:0%
+electron and part to the
+proton so that system doesn't have
+
+ align:start position:0%
+proton so that system doesn't have
+ 
+
+ align:start position:0%
+proton so that system doesn't have
+energy and so I'm happy that we have
+
+ align:start position:0%
+energy and so I'm happy that we have
+ 
+
+ align:start position:0%
+energy and so I'm happy that we have
+excluded it yes I'll be there in a
+
+ align:start position:0%
+excluded it yes I'll be there in a
+ 
+
+ align:start position:0%
+excluded it yes I'll be there in a
+moment uh I'm happy that we have
+
+ align:start position:0%
+moment uh I'm happy that we have
+ 
+
+ align:start position:0%
+moment uh I'm happy that we have
+excluded it by our definition of system
+
+ align:start position:0%
+excluded it by our definition of system
+ 
+
+ align:start position:0%
+excluded it by our definition of system
+so that we we will be able to say that
+
+ align:start position:0%
+so that we we will be able to say that
+ 
+
+ align:start position:0%
+so that we we will be able to say that
+every system as energy as a property
+
+ align:start position:0%
+every system as energy as a property
+ 
+
+ align:start position:0%
+every system as energy as a property
+every system satisfies the first flow
+
+ align:start position:0%
+every system satisfies the first flow
+ 
+
+ align:start position:0%
+every system satisfies the first flow
+the way we State we state
+
+ align:start position:0%
+the way we State we state
+ 
+
+ align:start position:0%
+the way we State we state
+it but it has to be a system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes the
+
+ align:start position:0%
+yes the
+ 
+
+ align:start position:0%
+yes the
+limit uh no for by for the electron by
+
+ align:start position:0%
+limit uh no for by for the electron by
+ 
+
+ align:start position:0%
+limit uh no for by for the electron by
+itself
+
+ align:start position:0%
+itself
+ 
+
+ align:start position:0%
+itself
+no but if I
+
+ align:start position:0%
+no but if I
+ 
+
+ align:start position:0%
+no but if I
+consider uh the atom and the atom is far
+
+ align:start position:0%
+consider uh the atom and the atom is far
+ 
+
+ align:start position:0%
+consider uh the atom and the atom is far
+from everything else
+
+ align:start position:0%
+from everything else
+ 
+
+ align:start position:0%
+from everything else
+then the
+
+ align:start position:0%
+then the
+ 
+
+ align:start position:0%
+then the
+two uh I mean this Force becomes an
+
+ align:start position:0%
+two uh I mean this Force becomes an
+ 
+
+ align:start position:0%
+two uh I mean this Force becomes an
+internal
+
+ align:start position:0%
+internal
+ 
+
+ align:start position:0%
+internal
+force and that energy the interaction
+
+ align:start position:0%
+force and that energy the interaction
+ 
+
+ align:start position:0%
+force and that energy the interaction
+energy becomes part of the energy of my
+
+ align:start position:0%
+energy becomes part of the energy of my
+ 
+
+ align:start position:0%
+energy becomes part of the energy of my
+system so for example in ter ter
+
+ align:start position:0%
+system so for example in ter ter
+ 
+
+ align:start position:0%
+system so for example in ter ter
+of hamiltonians if you familiar with
+
+ align:start position:0%
+of hamiltonians if you familiar with
+ 
+
+ align:start position:0%
+of hamiltonians if you familiar with
+that you would write the hamiltonian of
+
+ align:start position:0%
+that you would write the hamiltonian of
+ 
+
+ align:start position:0%
+that you would write the hamiltonian of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+uh which is the thing that represents
+
+ align:start position:0%
+uh which is the thing that represents
+ 
+
+ align:start position:0%
+uh which is the thing that represents
+the energy when the electron will be by
+
+ align:start position:0%
+the energy when the electron will be by
+ 
+
+ align:start position:0%
+the energy when the electron will be by
+itself the the amoni of the proton and
+
+ align:start position:0%
+itself the the amoni of the proton and
+ 
+
+ align:start position:0%
+itself the the amoni of the proton and
+then the interaction energy between
+
+ align:start position:0%
+then the interaction energy between
+ 
+
+ align:start position:0%
+then the interaction energy between
+electron and
+
+ align:start position:0%
+electron and
+ 
+
+ align:start position:0%
+electron and
+proton so that's well defined for this
+
+ align:start position:0%
+proton so that's well defined for this
+ 
+
+ align:start position:0%
+proton so that's well defined for this
+entire system for the combin
+
+ align:start position:0%
+entire system for the combin
+ 
+
+ align:start position:0%
+entire system for the combin
+for this actually for the only system
+
+ align:start position:0%
+for this actually for the only system
+ 
+
+ align:start position:0%
+for this actually for the only system
+you can Define for this
+
+ align:start position:0%
+you can Define for this
+ 
+
+ align:start position:0%
+you can Define for this
+situation but uh you cannot say ah okay
+
+ align:start position:0%
+situation but uh you cannot say ah okay
+ 
+
+ align:start position:0%
+situation but uh you cannot say ah okay
+but this is the energy of the electron
+
+ align:start position:0%
+but this is the energy of the electron
+ 
+
+ align:start position:0%
+but this is the energy of the electron
+no this would be the energy of the
+
+ align:start position:0%
+no this would be the energy of the
+ 
+
+ align:start position:0%
+no this would be the energy of the
+electron if the proton were weren't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no no no it's just this is just an
+
+ align:start position:0%
+no no no it's just this is just an
+ 
+
+ align:start position:0%
+no no no it's just this is just an
+example and this is the re the reason
+
+ align:start position:0%
+example and this is the re the reason
+ 
+
+ align:start position:0%
+example and this is the re the reason
+why I need okay suppose you have this is
+
+ align:start position:0%
+why I need okay suppose you have this is
+ 
+
+ align:start position:0%
+why I need okay suppose you have this is
+the moon and this is the
+
+ align:start position:0%
+the moon and this is the
+ 
+
+ align:start position:0%
+the moon and this is the
+earth okay same
+
+ align:start position:0%
+earth okay same
+ 
+
+ align:start position:0%
+earth okay same
+thing there is a gravitational force
+
+ align:start position:0%
+thing there is a gravitational force
+ 
+
+ align:start position:0%
+thing there is a gravitational force
+okay uh
+
+ align:start position:0%
+okay uh
+ 
+
+ align:start position:0%
+okay uh
+if you cannot consider just the
+
+ align:start position:0%
+if you cannot consider just the
+ 
+
+ align:start position:0%
+if you cannot consider just the
+moon as a
+
+ align:start position:0%
+moon as a
+ 
+
+ align:start position:0%
+moon as a
+system if for what you you want to
+
+ align:start position:0%
+system if for what you you want to
+ 
+
+ align:start position:0%
+system if for what you you want to
+describe it is important what it's uh
+
+ align:start position:0%
+describe it is important what it's uh
+ 
+
+ align:start position:0%
+describe it is important what it's uh
+interaction with the Earth
+
+ align:start position:0%
+interaction with the Earth
+ 
+
+ align:start position:0%
+interaction with the Earth
+is for the moon for the Moon is simpler
+
+ align:start position:0%
+is for the moon for the Moon is simpler
+ 
+
+ align:start position:0%
+is for the moon for the Moon is simpler
+in the sense that uh if you consider
+
+ align:start position:0%
+in the sense that uh if you consider
+ 
+
+ align:start position:0%
+in the sense that uh if you consider
+short instance of time in which the
+
+ align:start position:0%
+short instance of time in which the
+ 
+
+ align:start position:0%
+short instance of time in which the
+Earth is relatively fixed
+
+ align:start position:0%
+Earth is relatively fixed
+ 
+
+ align:start position:0%
+Earth is relatively fixed
+so there is no change in the relative
+
+ align:start position:0%
+so there is no change in the relative
+ 
+
+ align:start position:0%
+so there is no change in the relative
+distance then maybe for that instant of
+
+ align:start position:0%
+distance then maybe for that instant of
+ 
+
+ align:start position:0%
+distance then maybe for that instant of
+time the move the mo the moon will move
+
+ align:start position:0%
+time the move the mo the moon will move
+ 
+
+ align:start position:0%
+time the move the mo the moon will move
+a little bit the relative distance will
+
+ align:start position:0%
+a little bit the relative distance will
+ 
+
+ align:start position:0%
+a little bit the relative distance will
+not change so within that time frame
+
+ align:start position:0%
+not change so within that time frame
+ 
+
+ align:start position:0%
+not change so within that time frame
+maybe you can neglect uh the
+
+ align:start position:0%
+maybe you can neglect uh the
+ 
+
+ align:start position:0%
+maybe you can neglect uh the
+gravitational effect from from the
+
+ align:start position:0%
+gravitational effect from from the
+ 
+
+ align:start position:0%
+gravitational effect from from the
+Earth but it's exactly the same um uh
+
+ align:start position:0%
+Earth but it's exactly the same um uh
+ 
+
+ align:start position:0%
+Earth but it's exactly the same um uh
+idea or um
+
+ align:start position:0%
+idea or um
+ 
+
+ align:start position:0%
+idea or um
+or say suppose this is the air molecules
+
+ align:start position:0%
+or say suppose this is the air molecules
+ 
+
+ align:start position:0%
+or say suppose this is the air molecules
+like o2 molecules that are in this room
+
+ align:start position:0%
+like o2 molecules that are in this room
+ 
+
+ align:start position:0%
+like o2 molecules that are in this room
+and this is
+
+ align:start position:0%
+and this is
+ 
+
+ align:start position:0%
+and this is
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+cement molecules in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wall if
+
+ align:start position:0%
+wall if
+ 
+
+ align:start position:0%
+wall if
+I can model the cement molecules in such
+
+ align:start position:0%
+I can model the cement molecules in such
+ 
+
+ align:start position:0%
+I can model the cement molecules in such
+a way that they are uh they imply a
+
+ align:start position:0%
+a way that they are uh they imply a
+ 
+
+ align:start position:0%
+a way that they are uh they imply a
+fixed um effect on the molecules
+
+ align:start position:0%
+fixed um effect on the molecules
+ 
+
+ align:start position:0%
+fixed um effect on the molecules
+outside so that this becomes an external
+
+ align:start position:0%
+outside so that this becomes an external
+ 
+
+ align:start position:0%
+outside so that this becomes an external
+force that does not depend on the
+
+ align:start position:0%
+force that does not depend on the
+ 
+
+ align:start position:0%
+force that does not depend on the
+position or or the movement of the of
+
+ align:start position:0%
+position or or the movement of the of
+ 
+
+ align:start position:0%
+position or or the movement of the of
+the the cement molecules in the wall
+
+ align:start position:0%
+the the cement molecules in the wall
+ 
+
+ align:start position:0%
+the the cement molecules in the wall
+then this is an external force and
+
+ align:start position:0%
+then this is an external force and
+ 
+
+ align:start position:0%
+then this is an external force and
+essentially what I do is substitute
+
+ align:start position:0%
+essentially what I do is substitute
+ 
+
+ align:start position:0%
+essentially what I do is substitute
+this with a an effective
+
+ align:start position:0%
+this with a an effective
+ 
+
+ align:start position:0%
+this with a an effective
+potential uh uh of the out side onto my
+
+ align:start position:0%
+potential uh uh of the out side onto my
+ 
+
+ align:start position:0%
+potential uh uh of the out side onto my
+internal molecules and that effective
+
+ align:start position:0%
+internal molecules and that effective
+ 
+
+ align:start position:0%
+internal molecules and that effective
+potential is a way to describe external
+
+ align:start position:0%
+potential is a way to describe external
+ 
+
+ align:start position:0%
+potential is a way to describe external
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+forces
+
+ align:start position:0%
+forces
+ 
+
+ align:start position:0%
+forces
+okay so and this is what you need to do
+
+ align:start position:0%
+okay so and this is what you need to do
+ 
+
+ align:start position:0%
+okay so and this is what you need to do
+uh in order to come up with something
+
+ align:start position:0%
+uh in order to come up with something
+ 
+
+ align:start position:0%
+uh in order to come up with something
+that you can call a system and to which
+
+ align:start position:0%
+that you can call a system and to which
+ 
+
+ align:start position:0%
+that you can call a system and to which
+you can assign an energy that's what any
+
+ align:start position:0%
+you can assign an energy that's what any
+ 
+
+ align:start position:0%
+you can assign an energy that's what any
+model in physics is is uh is um is
+
+ align:start position:0%
+model in physics is is uh is um is
+ 
+
+ align:start position:0%
+model in physics is is uh is um is
+about all right
+
+ align:start position:0%
+about all right
+ 
+
+ align:start position:0%
+about all right
+I'll be happy to discuss it later more
+
+ align:start position:0%
+I'll be happy to discuss it later more
+ 
+
+ align:start position:0%
+I'll be happy to discuss it later more
+if you
+
+ align:start position:0%
+if you
+ 
+
+ align:start position:0%
+if you
+want later on any
+
+ align:start position:0%
+want later on any
+ 
+
+ align:start position:0%
+want later on any
+day okay so all right so what's the
+
+ align:start position:0%
+day okay so all right so what's the
+ 
+
+ align:start position:0%
+day okay so all right so what's the
+first law first law
+
+ align:start position:0%
+first law first law
+ 
+
+ align:start position:0%
+first law first law
+says this important uh it's actually
+
+ align:start position:0%
+says this important uh it's actually
+ 
+
+ align:start position:0%
+says this important uh it's actually
+made up of two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statements the first one is that you
+
+ align:start position:0%
+statements the first one is that you
+ 
+
+ align:start position:0%
+statements the first one is that you
+take any
+
+ align:start position:0%
+take any
+ 
+
+ align:start position:0%
+take any
+system and take any two states of your
+
+ align:start position:0%
+system and take any two states of your
+ 
+
+ align:start position:0%
+system and take any two states of your
+system they can always be interconnected
+
+ align:start position:0%
+system they can always be interconnected
+ 
+
+ align:start position:0%
+system they can always be interconnected
+via a wave
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process so it's it's a matter of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+existence in your
+
+ align:start position:0%
+existence in your
+ 
+
+ align:start position:0%
+existence in your
+model you must allow this in order for
+
+ align:start position:0%
+model you must allow this in order for
+ 
+
+ align:start position:0%
+model you must allow this in order for
+it to be a good
+
+ align:start position:0%
+it to be a good
+ 
+
+ align:start position:0%
+it to be a good
+model you have to find a way to
+
+ align:start position:0%
+model you have to find a way to
+ 
+
+ align:start position:0%
+model you have to find a way to
+interconnect now there is something
+
+ align:start position:0%
+interconnect now there is something
+ 
+
+ align:start position:0%
+interconnect now there is something
+wrong in this slide I'll have to correct
+
+ align:start position:0%
+wrong in this slide I'll have to correct
+ 
+
+ align:start position:0%
+wrong in this slide I'll have to correct
+it the
+
+ align:start position:0%
+it the
+ 
+
+ align:start position:0%
+it the
+arrow because the law doesn't
+
+ align:start position:0%
+arrow because the law doesn't
+ 
+
+ align:start position:0%
+arrow because the law doesn't
+say that you can always do it in this
+
+ align:start position:0%
+say that you can always do it in this
+ 
+
+ align:start position:0%
+say that you can always do it in this
+direction it says you can interconnect
+
+ align:start position:0%
+direction it says you can interconnect
+ 
+
+ align:start position:0%
+direction it says you can interconnect
+them so if if you cannot go from A1 to
+
+ align:start position:0%
+them so if if you cannot go from A1 to
+ 
+
+ align:start position:0%
+them so if if you cannot go from A1 to
+A2 then you can do it from A2 to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+A1
+
+ align:start position:0%
+A1
+ 
+
+ align:start position:0%
+A1
+okay the second Ascension is
+
+ align:start position:0%
+okay the second Ascension is
+ 
+
+ align:start position:0%
+okay the second Ascension is
+about how
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much potential energy because we from
+
+ align:start position:0%
+much potential energy because we from
+ 
+
+ align:start position:0%
+much potential energy because we from
+mechanics we know that the the weight
+
+ align:start position:0%
+mechanics we know that the the weight
+ 
+
+ align:start position:0%
+mechanics we know that the the weight
+that goes up and down in gravity field
+
+ align:start position:0%
+that goes up and down in gravity field
+ 
+
+ align:start position:0%
+that goes up and down in gravity field
+has a change in potential energy okay
+
+ align:start position:0%
+has a change in potential energy okay
+ 
+
+ align:start position:0%
+has a change in potential energy okay
+so the potential energy uh change of
+
+ align:start position:0%
+so the potential energy uh change of
+ 
+
+ align:start position:0%
+so the potential energy uh change of
+your weight here depends
+
+ align:start position:0%
+your weight here depends
+ 
+
+ align:start position:0%
+your weight here depends
+only on the pair of states
+
+ align:start position:0%
+only on the pair of states
+ 
+
+ align:start position:0%
+only on the pair of states
+not on the particular way or a
+
+ align:start position:0%
+not on the particular way or a
+ 
+
+ align:start position:0%
+not on the particular way or a
+particular weight
+
+ align:start position:0%
+particular weight
+ 
+
+ align:start position:0%
+particular weight
+process with which you can go from one
+
+ align:start position:0%
+process with which you can go from one
+ 
+
+ align:start position:0%
+process with which you can go from one
+to the other or in other words all way
+
+ align:start position:0%
+to the other or in other words all way
+ 
+
+ align:start position:0%
+to the other or in other words all way
+processes that interconnect those two
+
+ align:start position:0%
+processes that interconnect those two
+ 
+
+ align:start position:0%
+processes that interconnect those two
+states have the same external
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+effect or equivalent at the external
+
+ align:start position:0%
+effect or equivalent at the external
+ 
+
+ align:start position:0%
+effect or equivalent at the external
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+because sure I'm using the weight in a
+
+ align:start position:0%
+because sure I'm using the weight in a
+ 
+
+ align:start position:0%
+because sure I'm using the weight in a
+gravity field build as a prototype of
+
+ align:start position:0%
+gravity field build as a prototype of
+ 
+
+ align:start position:0%
+gravity field build as a prototype of
+mechanical effect but you could also use
+
+ align:start position:0%
+mechanical effect but you could also use
+ 
+
+ align:start position:0%
+mechanical effect but you could also use
+um a charge in an electric
+
+ align:start position:0%
+um a charge in an electric
+ 
+
+ align:start position:0%
+um a charge in an electric
+field or you could use a a point mass
+
+ align:start position:0%
+field or you could use a a point mass
+ 
+
+ align:start position:0%
+field or you could use a a point mass
+that changes from one velocity to a
+
+ align:start position:0%
+that changes from one velocity to a
+ 
+
+ align:start position:0%
+that changes from one velocity to a
+higher velocity so the kinetic energy
+
+ align:start position:0%
+higher velocity so the kinetic energy
+ 
+
+ align:start position:0%
+higher velocity so the kinetic energy
+changes anything that is purely
+
+ align:start position:0%
+changes anything that is purely
+ 
+
+ align:start position:0%
+changes anything that is purely
+mechanical is the right hand side of
+
+ align:start position:0%
+mechanical is the right hand side of
+ 
+
+ align:start position:0%
+mechanical is the right hand side of
+that it's this external effect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah those two assertions in the first
+
+ align:start position:0%
+yeah those two assertions in the first
+ 
+
+ align:start position:0%
+yeah those two assertions in the first
+law allow you to define a measurement
+
+ align:start position:0%
+law allow you to define a measurement
+ 
+
+ align:start position:0%
+law allow you to define a measurement
+procedure for property energy because as
+
+ align:start position:0%
+procedure for property energy because as
+ 
+
+ align:start position:0%
+procedure for property energy because as
+we said before a property is
+
+ align:start position:0%
+we said before a property is
+ 
+
+ align:start position:0%
+we said before a property is
+defined by a measurement procedure and
+
+ align:start position:0%
+defined by a measurement procedure and
+ 
+
+ align:start position:0%
+defined by a measurement procedure and
+what's the measurement procedure for
+
+ align:start position:0%
+what's the measurement procedure for
+ 
+
+ align:start position:0%
+what's the measurement procedure for
+energy well you come to my love
+
+ align:start position:0%
+energy well you come to my love
+ 
+
+ align:start position:0%
+energy well you come to my love
+with your system in a given uh State and
+
+ align:start position:0%
+with your system in a given uh State and
+ 
+
+ align:start position:0%
+with your system in a given uh State and
+you ask me to measure uh its energy and
+
+ align:start position:0%
+you ask me to measure uh its energy and
+ 
+
+ align:start position:0%
+you ask me to measure uh its energy and
+I take your
+
+ align:start position:0%
+I take your
+ 
+
+ align:start position:0%
+I take your
+system and I ask you to
+
+ align:start position:0%
+system and I ask you to
+ 
+
+ align:start position:0%
+system and I ask you to
+pay uh and then I'll tell you before you
+
+ align:start position:0%
+pay uh and then I'll tell you before you
+ 
+
+ align:start position:0%
+pay uh and then I'll tell you before you
+leave that
+
+ align:start position:0%
+leave that
+ 
+
+ align:start position:0%
+leave that
+look really yeah on the door is written
+
+ align:start position:0%
+look really yeah on the door is written
+ 
+
+ align:start position:0%
+look really yeah on the door is written
+that I measure energy I actually measure
+
+ align:start position:0%
+that I measure energy I actually measure
+ 
+
+ align:start position:0%
+that I measure energy I actually measure
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+differences okay
+
+ align:start position:0%
+differences okay
+ 
+
+ align:start position:0%
+differences okay
+so you have to pick another state of
+
+ align:start position:0%
+so you have to pick another state of
+ 
+
+ align:start position:0%
+so you have to pick another state of
+your system that I will consider as a
+
+ align:start position:0%
+your system that I will consider as a
+ 
+
+ align:start position:0%
+your system that I will consider as a
+reference and then I will measure the
+
+ align:start position:0%
+reference and then I will measure the
+ 
+
+ align:start position:0%
+reference and then I will measure the
+difference in energy between those two
+
+ align:start position:0%
+difference in energy between those two
+ 
+
+ align:start position:0%
+difference in energy between those two
+states and how do I do
+
+ align:start position:0%
+states and how do I do
+ 
+
+ align:start position:0%
+states and how do I do
+it well once you're gone because I don't
+
+ align:start position:0%
+it well once you're gone because I don't
+ 
+
+ align:start position:0%
+it well once you're gone because I don't
+want to uh show you my secrets I go on
+
+ align:start position:0%
+want to uh show you my secrets I go on
+ 
+
+ align:start position:0%
+want to uh show you my secrets I go on
+my shelves and find way processes and I
+
+ align:start position:0%
+my shelves and find way processes and I
+ 
+
+ align:start position:0%
+my shelves and find way processes and I
+find one that fits that allows me to
+
+ align:start position:0%
+find one that fits that allows me to
+ 
+
+ align:start position:0%
+find one that fits that allows me to
+change the state of your system from the
+
+ align:start position:0%
+change the state of your system from the
+ 
+
+ align:start position:0%
+change the state of your system from the
+reference one that you have chosen to
+
+ align:start position:0%
+reference one that you have chosen to
+ 
+
+ align:start position:0%
+reference one that you have chosen to
+the actual State you're interested
+
+ align:start position:0%
+the actual State you're interested
+ 
+
+ align:start position:0%
+the actual State you're interested
+in and I measure how
+
+ align:start position:0%
+in and I measure how
+ 
+
+ align:start position:0%
+in and I measure how
+much um gravitational potential energy
+
+ align:start position:0%
+much um gravitational potential energy
+ 
+
+ align:start position:0%
+much um gravitational potential energy
+change uh the weight has undergone when
+
+ align:start position:0%
+change uh the weight has undergone when
+ 
+
+ align:start position:0%
+change uh the weight has undergone when
+I did that so that's a that's a
+
+ align:start position:0%
+I did that so that's a that's a
+ 
+
+ align:start position:0%
+I did that so that's a that's a
+measurement procedure and I'll give you
+
+ align:start position:0%
+measurement procedure and I'll give you
+ 
+
+ align:start position:0%
+measurement procedure and I'll give you
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+course the units are already those of
+
+ align:start position:0%
+course the units are already those of
+ 
+
+ align:start position:0%
+course the units are already those of
+potential energy so they the of energy
+
+ align:start position:0%
+potential energy so they the of energy
+ 
+
+ align:start position:0%
+potential energy so they the of energy
+Jewel in
+
+ align:start position:0%
+Jewel in
+ 
+
+ align:start position:0%
+Jewel in
+si and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and what's nice of these two
+
+ align:start position:0%
+um and what's nice of these two
+ 
+
+ align:start position:0%
+um and what's nice of these two
+assertions is that they Val for any
+
+ align:start position:0%
+assertions is that they Val for any
+ 
+
+ align:start position:0%
+assertions is that they Val for any
+system any well defined system
+
+ align:start position:0%
+system any well defined system
+ 
+
+ align:start position:0%
+system any well defined system
+here and so and so you in principle can
+
+ align:start position:0%
+here and so and so you in principle can
+ 
+
+ align:start position:0%
+here and so and so you in principle can
+find this uh weight process for any pair
+
+ align:start position:0%
+find this uh weight process for any pair
+ 
+
+ align:start position:0%
+find this uh weight process for any pair
+of states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using that
+
+ align:start position:0%
+using that
+ 
+
+ align:start position:0%
+using that
+definition you can prove now if you're
+
+ align:start position:0%
+definition you can prove now if you're
+ 
+
+ align:start position:0%
+definition you can prove now if you're
+interested in the proof go to the
+
+ align:start position:0%
+interested in the proof go to the
+ 
+
+ align:start position:0%
+interested in the proof go to the
+book because I want to go quickly over
+
+ align:start position:0%
+book because I want to go quickly over
+ 
+
+ align:start position:0%
+book because I want to go quickly over
+these things because presumably uh these
+
+ align:start position:0%
+these things because presumably uh these
+ 
+
+ align:start position:0%
+these things because presumably uh these
+are uh easy Concepts but uh the proofs
+
+ align:start position:0%
+are uh easy Concepts but uh the proofs
+ 
+
+ align:start position:0%
+are uh easy Concepts but uh the proofs
+are not that uh obvious but you can
+
+ align:start position:0%
+are not that uh obvious but you can
+ 
+
+ align:start position:0%
+are not that uh obvious but you can
+prove from those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+statements this fact that um
+
+ align:start position:0%
+statements this fact that um
+ 
+
+ align:start position:0%
+statements this fact that um
+energy differences are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+additive so if I consider a system which
+
+ align:start position:0%
+additive so if I consider a system which
+ 
+
+ align:start position:0%
+additive so if I consider a system which
+is composite of two
+
+ align:start position:0%
+is composite of two
+ 
+
+ align:start position:0%
+is composite of two
+subsystems namely the definition of
+
+ align:start position:0%
+subsystems namely the definition of
+ 
+
+ align:start position:0%
+subsystems namely the definition of
+system applies for each of them so I
+
+ align:start position:0%
+system applies for each of them so I
+ 
+
+ align:start position:0%
+system applies for each of them so I
+consider a composite system C which for
+
+ align:start position:0%
+consider a composite system C which for
+ 
+
+ align:start position:0%
+consider a composite system C which for
+example could be the entire mini
+
+ align:start position:0%
+example could be the entire mini
+ 
+
+ align:start position:0%
+example could be the entire mini
+Universe namely my system plus the
+
+ align:start position:0%
+Universe namely my system plus the
+ 
+
+ align:start position:0%
+Universe namely my system plus the
+environment or could be just two systems
+
+ align:start position:0%
+environment or could be just two systems
+ 
+
+ align:start position:0%
+environment or could be just two systems
+so system C doesn't have to be isolated
+
+ align:start position:0%
+so system C doesn't have to be isolated
+ 
+
+ align:start position:0%
+so system C doesn't have to be isolated
+ated
+
+ align:start position:0%
+ated
+ 
+
+ align:start position:0%
+ated
+and in in either case you can
+
+ align:start position:0%
+and in in either case you can
+ 
+
+ align:start position:0%
+and in in either case you can
+prove by applying that same measurement
+
+ align:start position:0%
+prove by applying that same measurement
+ 
+
+ align:start position:0%
+prove by applying that same measurement
+procedure that defines energy that we
+
+ align:start position:0%
+procedure that defines energy that we
+ 
+
+ align:start position:0%
+procedure that defines energy that we
+have just seen if you apply to
+
+ align:start position:0%
+have just seen if you apply to
+ 
+
+ align:start position:0%
+have just seen if you apply to
+system a in state A1 you get a
+
+ align:start position:0%
+system a in state A1 you get a
+ 
+
+ align:start position:0%
+system a in state A1 you get a
+number I call it e energy of system a in
+
+ align:start position:0%
+number I call it e energy of system a in
+ 
+
+ align:start position:0%
+number I call it e energy of system a in
+state T1 or sayate state one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B in this I apply the measurement
+
+ align:start position:0%
+B in this I apply the measurement
+ 
+
+ align:start position:0%
+B in this I apply the measurement
+procedure I get the value for for for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B and then I
+
+ align:start position:0%
+B and then I
+ 
+
+ align:start position:0%
+B and then I
+also apply the measurement procedure to
+
+ align:start position:0%
+also apply the measurement procedure to
+ 
+
+ align:start position:0%
+also apply the measurement procedure to
+to the composite system when uh the
+
+ align:start position:0%
+to the composite system when uh the
+ 
+
+ align:start position:0%
+to the composite system when uh the
+state of the composite system that I
+
+ align:start position:0%
+state of the composite system that I
+ 
+
+ align:start position:0%
+state of the composite system that I
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+C11 is actually
+
+ align:start position:0%
+C11 is actually
+ 
+
+ align:start position:0%
+C11 is actually
+C11 is actually A1 B1 so it means that
+
+ align:start position:0%
+C11 is actually A1 B1 so it means that
+ 
+
+ align:start position:0%
+C11 is actually A1 B1 so it means that
+the it's it's the state in which
+
+ align:start position:0%
+the it's it's the state in which
+ 
+
+ align:start position:0%
+the it's it's the state in which
+subsystem a is in state one and
+
+ align:start position:0%
+subsystem a is in state one and
+ 
+
+ align:start position:0%
+subsystem a is in state one and
+subsystem B is in state
+
+ align:start position:0%
+subsystem B is in state
+ 
+
+ align:start position:0%
+subsystem B is in state
+B1 all
+
+ align:start position:0%
+B1 all
+ 
+
+ align:start position:0%
+B1 all
+right the theorem
+
+ align:start position:0%
+right the theorem
+ 
+
+ align:start position:0%
+right the theorem
+says that the difference between
+
+ align:start position:0%
+says that the difference between
+ 
+
+ align:start position:0%
+says that the difference between
+energy the difference in energy for
+
+ align:start position:0%
+energy the difference in energy for
+ 
+
+ align:start position:0%
+energy the difference in energy for
+system C from with respect to the
+
+ align:start position:0%
+system C from with respect to the
+ 
+
+ align:start position:0%
+system C from with respect to the
+reference is equal to the sum of the
+
+ align:start position:0%
+reference is equal to the sum of the
+ 
+
+ align:start position:0%
+reference is equal to the sum of the
+differences uh of of energy for a and b
+
+ align:start position:0%
+differences uh of of energy for a and b
+ 
+
+ align:start position:0%
+differences uh of of energy for a and b
+with respect to their respective
+
+ align:start position:0%
+with respect to their respective
+ 
+
+ align:start position:0%
+with respect to their respective
+references
+
+ align:start position:0%
+references
+ 
+
+ align:start position:0%
+references
+provided provided that I have chosen as
+
+ align:start position:0%
+provided provided that I have chosen as
+ 
+
+ align:start position:0%
+provided provided that I have chosen as
+reference a compatible reference for
+
+ align:start position:0%
+reference a compatible reference for
+ 
+
+ align:start position:0%
+reference a compatible reference for
+system C so uh I cannot choose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+arbitrarily the value for the reference
+
+ align:start position:0%
+arbitrarily the value for the reference
+ 
+
+ align:start position:0%
+arbitrarily the value for the reference
+uh energy for a and for B and also for
+
+ align:start position:0%
+uh energy for a and for B and also for
+ 
+
+ align:start position:0%
+uh energy for a and for B and also for
+C
+
+ align:start position:0%
+C
+ 
+
+ align:start position:0%
+C
+otherwise uh I cannot I do not get
+
+ align:start position:0%
+otherwise uh I cannot I do not get
+ 
+
+ align:start position:0%
+otherwise uh I cannot I do not get
+additivity of the values I only get
+
+ align:start position:0%
+additivity of the values I only get
+ 
+
+ align:start position:0%
+additivity of the values I only get
+additivity of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differences all
+
+ align:start position:0%
+differences all
+ 
+
+ align:start position:0%
+differences all
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+another almost trivial consequence of
+
+ align:start position:0%
+another almost trivial consequence of
+ 
+
+ align:start position:0%
+another almost trivial consequence of
+the definition of
+
+ align:start position:0%
+the definition of
+ 
+
+ align:start position:0%
+the definition of
+energy is that when the external effect
+
+ align:start position:0%
+energy is that when the external effect
+ 
+
+ align:start position:0%
+energy is that when the external effect
+when they when you have a a weight
+
+ align:start position:0%
+when they when you have a a weight
+ 
+
+ align:start position:0%
+when they when you have a a weight
+process so the only external effect is
+
+ align:start position:0%
+process so the only external effect is
+ 
+
+ align:start position:0%
+process so the only external effect is
+the changing height in a of a
+
+ align:start position:0%
+the changing height in a of a
+ 
+
+ align:start position:0%
+the changing height in a of a
+weight and the weight doesn't change in
+
+ align:start position:0%
+weight and the weight doesn't change in
+ 
+
+ align:start position:0%
+weight and the weight doesn't change in
+height so there is no external
+
+ align:start position:0%
+height so there is no external
+ 
+
+ align:start position:0%
+height so there is no external
+effect then E2 is equal to E1 so that's
+
+ align:start position:0%
+effect then E2 is equal to E1 so that's
+ 
+
+ align:start position:0%
+effect then E2 is equal to E1 so that's
+the principle of energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conservation so energy is conserved in a
+
+ align:start position:0%
+conservation so energy is conserved in a
+ 
+
+ align:start position:0%
+conservation so energy is conserved in a
+no net
+
+ align:start position:0%
+no net
+ 
+
+ align:start position:0%
+no net
+effect uh uh weight
+
+ align:start position:0%
+effect uh uh weight
+ 
+
+ align:start position:0%
+effect uh uh weight
+process the
+
+ align:start position:0%
+process the
+ 
+
+ align:start position:0%
+process the
+other idea which is important is the
+
+ align:start position:0%
+other idea which is important is the
+ 
+
+ align:start position:0%
+other idea which is important is the
+fact that energy
+
+ align:start position:0%
+fact that energy
+ 
+
+ align:start position:0%
+fact that energy
+can
+
+ align:start position:0%
+can
+ 
+
+ align:start position:0%
+can
+be uh exchanged so in other words you
+
+ align:start position:0%
+be uh exchanged so in other words you
+ 
+
+ align:start position:0%
+be uh exchanged so in other words you
+can
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U you may have energy of your system so
+
+ align:start position:0%
+U you may have energy of your system so
+ 
+
+ align:start position:0%
+U you may have energy of your system so
+the energy of your
+
+ align:start position:0%
+the energy of your
+ 
+
+ align:start position:0%
+the energy of your
+system uh may
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change but if it changes or suppose it
+
+ align:start position:0%
+change but if it changes or suppose it
+ 
+
+ align:start position:0%
+change but if it changes or suppose it
+goes down for one system it must must go
+
+ align:start position:0%
+goes down for one system it must must go
+ 
+
+ align:start position:0%
+goes down for one system it must must go
+up for some other system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh so this is a consequence of uh the
+
+ align:start position:0%
+uh so this is a consequence of uh the
+ 
+
+ align:start position:0%
+uh so this is a consequence of uh the
+two aspects that we have just seen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+conservation if system C is
+
+ align:start position:0%
+conservation if system C is
+ 
+
+ align:start position:0%
+conservation if system C is
+isolated we've seen here no change
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outside so the energy is concerned
+
+ align:start position:0%
+outside so the energy is concerned
+ 
+
+ align:start position:0%
+outside so the energy is concerned
+but the energy is also additive so if
+
+ align:start position:0%
+but the energy is also additive so if
+ 
+
+ align:start position:0%
+but the energy is also additive so if
+you combine these two it says that uh
+
+ align:start position:0%
+you combine these two it says that uh
+ 
+
+ align:start position:0%
+you combine these two it says that uh
+whatever change of energy occurs for air
+
+ align:start position:0%
+whatever change of energy occurs for air
+ 
+
+ align:start position:0%
+whatever change of energy occurs for air
+a system a is equal an opposite in sign
+
+ align:start position:0%
+a system a is equal an opposite in sign
+ 
+
+ align:start position:0%
+a system a is equal an opposite in sign
+to the change in B so if it goes down
+
+ align:start position:0%
+to the change in B so if it goes down
+ 
+
+ align:start position:0%
+to the change in B so if it goes down
+for a goes up for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B most of the
+
+ align:start position:0%
+B most of the
+ 
+
+ align:start position:0%
+B most of the
+times our interest is in system a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so if our focus is on system a the
+
+ align:start position:0%
+and so if our focus is on system a the
+ 
+
+ align:start position:0%
+and so if our focus is on system a the
+effect on system
+
+ align:start position:0%
+effect on system
+ 
+
+ align:start position:0%
+effect on system
+B we sometimes call it uh energy
+
+ align:start position:0%
+B we sometimes call it uh energy
+ 
+
+ align:start position:0%
+B we sometimes call it uh energy
+transferred or actually in most of the
+
+ align:start position:0%
+transferred or actually in most of the
+ 
+
+ align:start position:0%
+transferred or actually in most of the
+times we call it energy exchanged
+
+ align:start position:0%
+times we call it energy exchanged
+ 
+
+ align:start position:0%
+times we call it energy exchanged
+between A and
+
+ align:start position:0%
+between A and
+ 
+
+ align:start position:0%
+between A and
+B because the idea is that if if this
+
+ align:start position:0%
+B because the idea is that if if this
+ 
+
+ align:start position:0%
+B because the idea is that if if this
+appears from a and appears from from B
+
+ align:start position:0%
+appears from a and appears from from B
+ 
+
+ align:start position:0%
+appears from a and appears from from B
+it has been
+
+ align:start position:0%
+it has been
+ 
+
+ align:start position:0%
+it has been
+exchanged now you
+
+ align:start position:0%
+exchanged now you
+ 
+
+ align:start position:0%
+exchanged now you
+could you could argue well maybe is this
+
+ align:start position:0%
+could you could argue well maybe is this
+ 
+
+ align:start position:0%
+could you could argue well maybe is this
+really uh a
+
+ align:start position:0%
+really uh a
+ 
+
+ align:start position:0%
+really uh a
+transfer and the argument uh um is
+
+ align:start position:0%
+transfer and the argument uh um is
+ 
+
+ align:start position:0%
+transfer and the argument uh um is
+fascinating you should uh I I I refer
+
+ align:start position:0%
+fascinating you should uh I I I refer
+ 
+
+ align:start position:0%
+fascinating you should uh I I I refer
+you to this um wonderful lecture by fan
+
+ align:start position:0%
+you to this um wonderful lecture by fan
+ 
+
+ align:start position:0%
+you to this um wonderful lecture by fan
+uh I added this just so you don't have
+
+ align:start position:0%
+uh I added this just so you don't have
+ 
+
+ align:start position:0%
+uh I added this just so you don't have
+it in your slide but I'll post it in
+
+ align:start position:0%
+it in your slide but I'll post it in
+ 
+
+ align:start position:0%
+it in your slide but I'll post it in
+today's post with the final slides for
+
+ align:start position:0%
+today's post with the final slides for
+ 
+
+ align:start position:0%
+today's post with the final slides for
+today and there is a link to the
+
+ align:start position:0%
+today and there is a link to the
+ 
+
+ align:start position:0%
+today and there is a link to the
+YouTube um lecture in which uh in a very
+
+ align:start position:0%
+YouTube um lecture in which uh in a very
+ 
+
+ align:start position:0%
+YouTube um lecture in which uh in a very
+funny way he uh describes these U
+
+ align:start position:0%
+funny way he uh describes these U
+ 
+
+ align:start position:0%
+funny way he uh describes these U
+principles of uh great conservation
+
+ align:start position:0%
+principles of uh great conservation
+ 
+
+ align:start position:0%
+principles of uh great conservation
+principles it explains why they're
+
+ align:start position:0%
+principles it explains why they're
+ 
+
+ align:start position:0%
+principles it explains why they're
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+uh but here the reference is because he
+
+ align:start position:0%
+uh but here the reference is because he
+ 
+
+ align:start position:0%
+uh but here the reference is because he
+explains also that using relativity
+
+ align:start position:0%
+explains also that using relativity
+ 
+
+ align:start position:0%
+explains also that using relativity
+Concepts uh but in a simple
+
+ align:start position:0%
+Concepts uh but in a simple
+ 
+
+ align:start position:0%
+Concepts uh but in a simple
+way
+
+ align:start position:0%
+way
+ 
+
+ align:start position:0%
+way
+um it explains that um things cannot
+
+ align:start position:0%
+um it explains that um things cannot
+ 
+
+ align:start position:0%
+um it explains that um things cannot
+just U if a property is
+
+ align:start position:0%
+just U if a property is
+ 
+
+ align:start position:0%
+just U if a property is
+conserved uh it also must be um actually
+
+ align:start position:0%
+conserved uh it also must be um actually
+ 
+
+ align:start position:0%
+conserved uh it also must be um actually
+transferable um how does you say um
+
+ align:start position:0%
+transferable um how does you say um
+ 
+
+ align:start position:0%
+transferable um how does you say um
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+transferable um across the interface
+
+ align:start position:0%
+transferable um across the interface
+ 
+
+ align:start position:0%
+transferable um across the interface
+between one system and the other cannot
+
+ align:start position:0%
+between one system and the other cannot
+ 
+
+ align:start position:0%
+between one system and the other cannot
+it doesn't simply disappear here and
+
+ align:start position:0%
+it doesn't simply disappear here and
+ 
+
+ align:start position:0%
+it doesn't simply disappear here and
+reappear but it's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moves across the boundary so that's what
+
+ align:start position:0%
+moves across the boundary so that's what
+ 
+
+ align:start position:0%
+moves across the boundary so that's what
+we call uh local local
+
+ align:start position:0%
+we call uh local local
+ 
+
+ align:start position:0%
+we call uh local local
+conservation uh all right so for our for
+
+ align:start position:0%
+conservation uh all right so for our for
+ 
+
+ align:start position:0%
+conservation uh all right so for our for
+our purposes in order to obtain the
+
+ align:start position:0%
+our purposes in order to obtain the
+ 
+
+ align:start position:0%
+our purposes in order to obtain the
+equation that we usually call the energy
+
+ align:start position:0%
+equation that we usually call the energy
+ 
+
+ align:start position:0%
+equation that we usually call the energy
+balance equation we
+
+ align:start position:0%
+balance equation we
+ 
+
+ align:start position:0%
+balance equation we
+rewrite this right hand side with
+
+ align:start position:0%
+rewrite this right hand side with
+ 
+
+ align:start position:0%
+rewrite this right hand side with
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+symbol which is this symbol here it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+uh the superscript means
+
+ align:start position:0%
+uh the superscript means
+ 
+
+ align:start position:0%
+uh the superscript means
+transferred from B to a the arrow
+
+ align:start position:0%
+transferred from B to a the arrow
+ 
+
+ align:start position:0%
+transferred from B to a the arrow
+matters
+
+ align:start position:0%
+matters
+ 
+
+ align:start position:0%
+matters
+during the time or during the process
+
+ align:start position:0%
+during the time or during the process
+ 
+
+ align:start position:0%
+during the time or during the process
+one two so during the time interval T1
+
+ align:start position:0%
+one two so during the time interval T1
+ 
+
+ align:start position:0%
+one two so during the time interval T1
+T2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so that uh with this way of of
+
+ align:start position:0%
+okay so so that uh with this way of of
+ 
+
+ align:start position:0%
+okay so so that uh with this way of of
+of defining uh you can rewrite this
+
+ align:start position:0%
+of defining uh you can rewrite this
+ 
+
+ align:start position:0%
+of defining uh you can rewrite this
+equation as uh the energy balance like
+
+ align:start position:0%
+equation as uh the energy balance like
+ 
+
+ align:start position:0%
+equation as uh the energy balance like
+here E2 minus E1 is equal to E
+
+ align:start position:0%
+here E2 minus E1 is equal to E
+ 
+
+ align:start position:0%
+here E2 minus E1 is equal to E
+A received from here I already started
+
+ align:start position:0%
+A received from here I already started
+ 
+
+ align:start position:0%
+A received from here I already started
+simplifying the notation so I dropped
+
+ align:start position:0%
+simplifying the notation so I dropped
+ 
+
+ align:start position:0%
+simplifying the notation so I dropped
+the B but I should have written
+
+ align:start position:0%
+the B but I should have written
+ 
+
+ align:start position:0%
+the B but I should have written
+B Because
+
+ align:start position:0%
+B Because
+ 
+
+ align:start position:0%
+B Because
+B is the environment of
+
+ align:start position:0%
+B is the environment of
+ 
+
+ align:start position:0%
+B is the environment of
+a and the
+
+ align:start position:0%
+a and the
+ 
+
+ align:start position:0%
+a and the
+arrow on the symbol is the equivalent of
+
+ align:start position:0%
+arrow on the symbol is the equivalent of
+ 
+
+ align:start position:0%
+arrow on the symbol is the equivalent of
+what of what you usually um you're used
+
+ align:start position:0%
+what of what you usually um you're used
+ 
+
+ align:start position:0%
+what of what you usually um you're used
+to as the like the sign convention for
+
+ align:start position:0%
+to as the like the sign convention for
+ 
+
+ align:start position:0%
+to as the like the sign convention for
+energy
+
+ align:start position:0%
+energy
+ 
+
+ align:start position:0%
+energy
+exchanges now some people like to
+
+ align:start position:0%
+exchanges now some people like to
+ 
+
+ align:start position:0%
+exchanges now some people like to
+say consider uh heat positive If U going
+
+ align:start position:0%
+say consider uh heat positive If U going
+ 
+
+ align:start position:0%
+say consider uh heat positive If U going
+out and work positive if going in or
+
+ align:start position:0%
+out and work positive if going in or
+ 
+
+ align:start position:0%
+out and work positive if going in or
+vice
+
+ align:start position:0%
+vice
+ 
+
+ align:start position:0%
+vice
+versa this notation allows you to Define
+
+ align:start position:0%
+versa this notation allows you to Define
+ 
+
+ align:start position:0%
+versa this notation allows you to Define
+whatever uh whatever using the
+
+ align:start position:0%
+whatever uh whatever using the
+ 
+
+ align:start position:0%
+whatever uh whatever using the
+arrow and the
+
+ align:start position:0%
+arrow and the
+ 
+
+ align:start position:0%
+arrow and the
+fact that this symbol here which we
+
+ align:start position:0%
+fact that this symbol here which we
+ 
+
+ align:start position:0%
+fact that this symbol here which we
+would call
+
+ align:start position:0%
+would call
+ 
+
+ align:start position:0%
+would call
+Energy exchange can have both positive
+
+ align:start position:0%
+Energy exchange can have both positive
+ 
+
+ align:start position:0%
+Energy exchange can have both positive
+and negative
+
+ align:start position:0%
+and negative
+ 
+
+ align:start position:0%
+and negative
+signs negative values if if it is
+
+ align:start position:0%
+signs negative values if if it is
+ 
+
+ align:start position:0%
+signs negative values if if it is
+positive it means that the uh the flow
+
+ align:start position:0%
+positive it means that the uh the flow
+ 
+
+ align:start position:0%
+positive it means that the uh the flow
+of energy is in the direction of the
+
+ align:start position:0%
+of energy is in the direction of the
+ 
+
+ align:start position:0%
+of energy is in the direction of the
+arrow so in that case it's positive if
+
+ align:start position:0%
+arrow so in that case it's positive if
+ 
+
+ align:start position:0%
+arrow so in that case it's positive if
+in but you could also Define it as
+
+ align:start position:0%
+in but you could also Define it as
+ 
+
+ align:start position:0%
+in but you could also Define it as
+positive out in that way the energy
+
+ align:start position:0%
+positive out in that way the energy
+ 
+
+ align:start position:0%
+positive out in that way the energy
+balance is written this
+
+ align:start position:0%
+balance is written this
+ 
+
+ align:start position:0%
+balance is written this
+way okay so you choose the sign
+
+ align:start position:0%
+way okay so you choose the sign
+ 
+
+ align:start position:0%
+way okay so you choose the sign
+convention
+
+ align:start position:0%
+convention
+ 
+
+ align:start position:0%
+convention
+which allows you
+
+ align:start position:0%
+which allows you
+ 
+
+ align:start position:0%
+which allows you
+to avoid having a to have a figure or
+
+ align:start position:0%
+to avoid having a to have a figure or
+ 
+
+ align:start position:0%
+to avoid having a to have a figure or
+figure like here
+
+ align:start position:0%
+figure like here
+ 
+
+ align:start position:0%
+figure like here
+to give meaning to properties that are
+
+ align:start position:0%
+to give meaning to properties that are
+ 
+
+ align:start position:0%
+to give meaning to properties that are
+not just numbers because they have
+
+ align:start position:0%
+not just numbers because they have
+ 
+
+ align:start position:0%
+not just numbers because they have
+because interactions the energy change
+
+ align:start position:0%
+because interactions the energy change
+ 
+
+ align:start position:0%
+because interactions the energy change
+exchanged via an interaction between two
+
+ align:start position:0%
+exchanged via an interaction between two
+ 
+
+ align:start position:0%
+exchanged via an interaction between two
+systems uh has not only a value but also
+
+ align:start position:0%
+systems uh has not only a value but also
+ 
+
+ align:start position:0%
+systems uh has not only a value but also
+a Direction so it's like a vector it's a
+
+ align:start position:0%
+a Direction so it's like a vector it's a
+ 
+
+ align:start position:0%
+a Direction so it's like a vector it's a
+little simpler than a vector because
+
+ align:start position:0%
+little simpler than a vector because
+ 
+
+ align:start position:0%
+little simpler than a vector because
+it's just in or
+
+ align:start position:0%
+it's just in or
+ 
+
+ align:start position:0%
+it's just in or
+out but it's it has two items the amount
+
+ align:start position:0%
+out but it's it has two items the amount
+ 
+
+ align:start position:0%
+out but it's it has two items the amount
+and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Direction all right and then sometimes
+
+ align:start position:0%
+Direction all right and then sometimes
+ 
+
+ align:start position:0%
+Direction all right and then sometimes
+we also write the energy balance
+
+ align:start position:0%
+we also write the energy balance
+ 
+
+ align:start position:0%
+we also write the energy balance
+equation in a rate form so we divide by
+
+ align:start position:0%
+equation in a rate form so we divide by
+ 
+
+ align:start position:0%
+equation in a rate form so we divide by
+the the time interval that
+
+ align:start position:0%
+the the time interval that
+ 
+
+ align:start position:0%
+the the time interval that
+occurs uh between 21
+
+ align:start position:0%
+occurs uh between 21
+ 
+
+ align:start position:0%
+occurs uh between 21
+and if that time interval is uh
+
+ align:start position:0%
+and if that time interval is uh
+ 
+
+ align:start position:0%
+and if that time interval is uh
+infinitesimal meaning that we can follow
+
+ align:start position:0%
+infinitesimal meaning that we can follow
+ 
+
+ align:start position:0%
+infinitesimal meaning that we can follow
+the process as a function of time we can
+
+ align:start position:0%
+the process as a function of time we can
+ 
+
+ align:start position:0%
+the process as a function of time we can
+follow we actually this is a a more
+
+ align:start position:0%
+follow we actually this is a a more
+ 
+
+ align:start position:0%
+follow we actually this is a a more
+refined description that allows you not
+
+ align:start position:0%
+refined description that allows you not
+ 
+
+ align:start position:0%
+refined description that allows you not
+only in finite times intervals but also
+
+ align:start position:0%
+only in finite times intervals but also
+ 
+
+ align:start position:0%
+only in finite times intervals but also
+infinitesimal time intervals uh then you
+
+ align:start position:0%
+infinitesimal time intervals uh then you
+ 
+
+ align:start position:0%
+infinitesimal time intervals uh then you
+can write it in the form of a
+
+ align:start position:0%
+can write it in the form of a
+ 
+
+ align:start position:0%
+can write it in the form of a
+differential equation so the rate of
+
+ align:start position:0%
+differential equation so the rate of
+ 
+
+ align:start position:0%
+differential equation so the rate of
+change of the energy is equal to the
+
+ align:start position:0%
+change of the energy is equal to the
+ 
+
+ align:start position:0%
+change of the energy is equal to the
+energy the rate at which energy is
+
+ align:start position:0%
+energy the rate at which energy is
+ 
+
+ align:start position:0%
+energy the rate at which energy is
+transferred into your
+
+ align:start position:0%
+transferred into your
+ 
+
+ align:start position:0%
+transferred into your
+system okay so this is the energy
+
+ align:start position:0%
+system okay so this is the energy
+ 
+
+ align:start position:0%
+system okay so this is the energy
+balance
+
+ align:start position:0%
+balance
+ 
+
+ align:start position:0%
+balance
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+uh yeah I don't know if you survive but
+
+ align:start position:0%
+uh yeah I don't know if you survive but
+ 
+
+ align:start position:0%
+uh yeah I don't know if you survive but
+uh I'll try to uh finish maybe a couple
+
+ align:start position:0%
+uh I'll try to uh finish maybe a couple
+ 
+
+ align:start position:0%
+uh I'll try to uh finish maybe a couple
+of minutes before but uh I prefer not to
+
+ align:start position:0%
+of minutes before but uh I prefer not to
+ 
+
+ align:start position:0%
+of minutes before but uh I prefer not to
+make a take a break because it uh uh it
+
+ align:start position:0%
+make a take a break because it uh uh it
+ 
+
+ align:start position:0%
+make a take a break because it uh uh it
+makes it
+
+ align:start position:0%
+makes it
+ 
+
+ align:start position:0%
+makes it
+um it allows you to go away that's the
+
+ align:start position:0%
+um it allows you to go away that's the
+ 
+
+ align:start position:0%
+um it allows you to go away that's the
+problem I don't want you to go
+
+ align:start position:0%
+problem I don't want you to go
+ 
+
+ align:start position:0%
+problem I don't want you to go
+away okay now
+
+ align:start position:0%
+away okay now
+ 
+
+ align:start position:0%
+away okay now
+um so I want to give the ingredients and
+
+ align:start position:0%
+um so I want to give the ingredients and
+ 
+
+ align:start position:0%
+um so I want to give the ingredients and
+maybe also the statement of the second
+
+ align:start position:0%
+maybe also the statement of the second
+ 
+
+ align:start position:0%
+maybe also the statement of the second
+law so that you so that you can see that
+
+ align:start position:0%
+law so that you so that you can see that
+ 
+
+ align:start position:0%
+law so that you so that you can see that
+uh in a couple of hours of uh of lecture
+
+ align:start position:0%
+uh in a couple of hours of uh of lecture
+ 
+
+ align:start position:0%
+uh in a couple of hours of uh of lecture
+you can uh do
+
+ align:start position:0%
+you can uh do
+ 
+
+ align:start position:0%
+you can uh do
+you can get almost to the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+law the second law at least in the
+
+ align:start position:0%
+law the second law at least in the
+ 
+
+ align:start position:0%
+law the second law at least in the
+statement that we are going to
+
+ align:start position:0%
+statement that we are going to
+ 
+
+ align:start position:0%
+statement that we are going to
+adopt has to do with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+States and certain types of states in
+
+ align:start position:0%
+States and certain types of states in
+ 
+
+ align:start position:0%
+States and certain types of states in
+particular the stable equilibrium States
+
+ align:start position:0%
+particular the stable equilibrium States
+ 
+
+ align:start position:0%
+particular the stable equilibrium States
+will play a fundamental role in uh key
+
+ align:start position:0%
+will play a fundamental role in uh key
+ 
+
+ align:start position:0%
+will play a fundamental role in uh key
+role Central role in the second law so
+
+ align:start position:0%
+role Central role in the second law so
+ 
+
+ align:start position:0%
+role Central role in the second law so
+we need to Define what we mean by that
+
+ align:start position:0%
+we need to Define what we mean by that
+ 
+
+ align:start position:0%
+we need to Define what we mean by that
+so we can uh classify
+
+ align:start position:0%
+so we can uh classify
+ 
+
+ align:start position:0%
+so we can uh classify
+States uh according to uh two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+criteria so that makes four four
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possibilities uh the roles here are
+
+ align:start position:0%
+possibilities uh the roles here are
+ 
+
+ align:start position:0%
+possibilities uh the roles here are
+characterized by whether the state
+
+ align:start position:0%
+characterized by whether the state
+ 
+
+ align:start position:0%
+characterized by whether the state
+changes in time or does not change this
+
+ align:start position:0%
+changes in time or does not change this
+ 
+
+ align:start position:0%
+changes in time or does not change this
+time and the columns
+
+ align:start position:0%
+time and the columns
+ 
+
+ align:start position:0%
+time and the columns
+by what is the cause for those
+
+ align:start position:0%
+by what is the cause for those
+ 
+
+ align:start position:0%
+by what is the cause for those
+changes why does it change does it
+
+ align:start position:0%
+changes why does it change does it
+ 
+
+ align:start position:0%
+changes why does it change does it
+change because of something that uh
+
+ align:start position:0%
+change because of something that uh
+ 
+
+ align:start position:0%
+change because of something that uh
+occurs outside so it's an interaction
+
+ align:start position:0%
+occurs outside so it's an interaction
+ 
+
+ align:start position:0%
+occurs outside so it's an interaction
+with an external system with the
+
+ align:start position:0%
+with an external system with the
+ 
+
+ align:start position:0%
+with an external system with the
+environment of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system or does it
+
+ align:start position:0%
+system or does it
+ 
+
+ align:start position:0%
+system or does it
+occur uh even if those interactions are
+
+ align:start position:0%
+occur uh even if those interactions are
+ 
+
+ align:start position:0%
+occur uh even if those interactions are
+turned
+
+ align:start position:0%
+turned
+ 
+
+ align:start position:0%
+turned
+off so for example uh in a spont is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+proc and these are the various
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+possibilities so we call Un steady state
+
+ align:start position:0%
+possibilities so we call Un steady state
+ 
+
+ align:start position:0%
+possibilities so we call Un steady state
+if it changes with time and that is
+
+ align:start position:0%
+if it changes with time and that is
+ 
+
+ align:start position:0%
+if it changes with time and that is
+because of external interactions the
+
+ align:start position:0%
+because of external interactions the
+ 
+
+ align:start position:0%
+because of external interactions the
+the the the typical
+
+ align:start position:0%
+the the the typical
+ 
+
+ align:start position:0%
+the the the typical
+example just to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+consider um bath
+
+ align:start position:0%
+consider um bath
+ 
+
+ align:start position:0%
+consider um bath
+tub in which you have water coming in
+
+ align:start position:0%
+tub in which you have water coming in
+ 
+
+ align:start position:0%
+tub in which you have water coming in
+from the foret and you have a drain open
+
+ align:start position:0%
+from the foret and you have a drain open
+ 
+
+ align:start position:0%
+from the foret and you have a drain open
+okay so if the flow rate and suppose
+
+ align:start position:0%
+okay so if the flow rate and suppose
+ 
+
+ align:start position:0%
+okay so if the flow rate and suppose
+that this is a simple simple system in
+
+ align:start position:0%
+that this is a simple simple system in
+ 
+
+ align:start position:0%
+that this is a simple simple system in
+which uh the
+
+ align:start position:0%
+which uh the
+ 
+
+ align:start position:0%
+which uh the
+only uh proper
+
+ align:start position:0%
+only uh proper
+ 
+
+ align:start position:0%
+only uh proper
+relevant property is the
+
+ align:start position:0%
+relevant property is the
+ 
+
+ align:start position:0%
+relevant property is the
+shape and position of this interface
+
+ align:start position:0%
+shape and position of this interface
+ 
+
+ align:start position:0%
+shape and position of this interface
+between Water and
+
+ align:start position:0%
+between Water and
+ 
+
+ align:start position:0%
+between Water and
+Air okay
+
+ align:start position:0%
+Air okay
+ 
+
+ align:start position:0%
+Air okay
+so an unsteady state would be one in
+
+ align:start position:0%
+so an unsteady state would be one in
+ 
+
+ align:start position:0%
+so an unsteady state would be one in
+which the level changes because there is
+
+ align:start position:0%
+which the level changes because there is
+ 
+
+ align:start position:0%
+which the level changes because there is
+no balance between the inflow and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outflow If instead you have uh that the
+
+ align:start position:0%
+outflow If instead you have uh that the
+ 
+
+ align:start position:0%
+outflow If instead you have uh that the
+state doesn't change in other words you
+
+ align:start position:0%
+state doesn't change in other words you
+ 
+
+ align:start position:0%
+state doesn't change in other words you
+have a flat
+
+ align:start position:0%
+have a flat
+ 
+
+ align:start position:0%
+have a flat
+surface that stays put at the same at
+
+ align:start position:0%
+surface that stays put at the same at
+ 
+
+ align:start position:0%
+surface that stays put at the same at
+the given height all the
+
+ align:start position:0%
+the given height all the
+ 
+
+ align:start position:0%
+the given height all the
+time it means that but this is due to
+
+ align:start position:0%
+time it means that but this is due to
+ 
+
+ align:start position:0%
+time it means that but this is due to
+the fact that there is balance between
+
+ align:start position:0%
+the fact that there is balance between
+ 
+
+ align:start position:0%
+the fact that there is balance between
+inflow and outflow that's a steady
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state if I turn the flow off and uh
+
+ align:start position:0%
+state if I turn the flow off and uh
+ 
+
+ align:start position:0%
+state if I turn the flow off and uh
+close the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+drain and the surface is flat and
+
+ align:start position:0%
+drain and the surface is flat and
+ 
+
+ align:start position:0%
+drain and the surface is flat and
+doesn't move that is an equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+State If It Moves because maybe I shake
+
+ align:start position:0%
+State If It Moves because maybe I shake
+ 
+
+ align:start position:0%
+State If It Moves because maybe I shake
+it and there are waves that is a
+
+ align:start position:0%
+it and there are waves that is a
+ 
+
+ align:start position:0%
+it and there are waves that is a
+non-equilibrium
+
+ align:start position:0%
+non-equilibrium
+ 
+
+ align:start position:0%
+non-equilibrium
+state it in the non equilibrium state
+
+ align:start position:0%
+state it in the non equilibrium state
+ 
+
+ align:start position:0%
+state it in the non equilibrium state
+dat the moving aspect is related to the
+
+ align:start position:0%
+dat the moving aspect is related to the
+ 
+
+ align:start position:0%
+dat the moving aspect is related to the
+internal Dynamics not to the um
+
+ align:start position:0%
+internal Dynamics not to the um
+ 
+
+ align:start position:0%
+internal Dynamics not to the um
+interactions with the what what's
+
+ align:start position:0%
+interactions with the what what's
+ 
+
+ align:start position:0%
+interactions with the what what's
+outside not with external interactions
+
+ align:start position:0%
+outside not with external interactions
+ 
+
+ align:start position:0%
+outside not with external interactions
+okay so that's the idea of this
+
+ align:start position:0%
+okay so that's the idea of this
+ 
+
+ align:start position:0%
+okay so that's the idea of this
+nomenclature that we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use now let's focus on
+
+ align:start position:0%
+use now let's focus on
+ 
+
+ align:start position:0%
+use now let's focus on
+equilibrium right there is equilibrium
+
+ align:start position:0%
+equilibrium right there is equilibrium
+ 
+
+ align:start position:0%
+equilibrium right there is equilibrium
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+equilibrium the concept of equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is known from
+
+ align:start position:0%
+is known from
+ 
+
+ align:start position:0%
+is known from
+um uh mechanics so I'm sure you've seen
+
+ align:start position:0%
+um uh mechanics so I'm sure you've seen
+ 
+
+ align:start position:0%
+um uh mechanics so I'm sure you've seen
+it some somehow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+somewhere this the stability of
+
+ align:start position:0%
+somewhere this the stability of
+ 
+
+ align:start position:0%
+somewhere this the stability of
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+also is important it is important in uh
+
+ align:start position:0%
+also is important it is important in uh
+ 
+
+ align:start position:0%
+also is important it is important in uh
+mechanics it is important in uh in the
+
+ align:start position:0%
+mechanics it is important in uh in the
+ 
+
+ align:start position:0%
+mechanics it is important in uh in the
+entire uh physics
+
+ align:start position:0%
+entire uh physics
+ 
+
+ align:start position:0%
+entire uh physics
+now if we go back to that idea of uh
+
+ align:start position:0%
+now if we go back to that idea of uh
+ 
+
+ align:start position:0%
+now if we go back to that idea of uh
+describing the change of
+
+ align:start position:0%
+describing the change of
+ 
+
+ align:start position:0%
+describing the change of
+state in state space so that's
+
+ align:start position:0%
+state in state space so that's
+ 
+
+ align:start position:0%
+state in state space so that's
+A1 a of
+
+ align:start position:0%
+A1 a of
+ 
+
+ align:start position:0%
+A1 a of
+T1 and this is a of T2 with the
+
+ align:start position:0%
+T1 and this is a of T2 with the
+ 
+
+ align:start position:0%
+T1 and this is a of T2 with the
+understanding that now the black this
+
+ align:start position:0%
+understanding that now the black this
+ 
+
+ align:start position:0%
+understanding that now the black this
+point represents a point in a
+
+ align:start position:0%
+point represents a point in a
+ 
+
+ align:start position:0%
+point represents a point in a
+multi-dimensional space in which each
+
+ align:start position:0%
+multi-dimensional space in which each
+ 
+
+ align:start position:0%
+multi-dimensional space in which each
+axis is an independent property
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is the solution of a
+
+ align:start position:0%
+okay so this is the solution of a
+ 
+
+ align:start position:0%
+okay so this is the solution of a
+differential equation which is the
+
+ align:start position:0%
+differential equation which is the
+ 
+
+ align:start position:0%
+differential equation which is the
+equation of motion of your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system all right so if the state is
+
+ align:start position:0%
+system all right so if the state is
+ 
+
+ align:start position:0%
+system all right so if the state is
+changing because as time goes on it
+
+ align:start position:0%
+changing because as time goes on it
+ 
+
+ align:start position:0%
+changing because as time goes on it
+moves from here to there this is not an
+
+ align:start position:0%
+moves from here to there this is not an
+ 
+
+ align:start position:0%
+moves from here to there this is not an
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+State okay
+
+ align:start position:0%
+State okay
+ 
+
+ align:start position:0%
+State okay
+an equilibrium state would be one in
+
+ align:start position:0%
+an equilibrium state would be one in
+ 
+
+ align:start position:0%
+an equilibrium state would be one in
+which the state does not change so
+
+ align:start position:0%
+which the state does not change so
+ 
+
+ align:start position:0%
+which the state does not change so
+what's the trajectory the trajectory is
+
+ align:start position:0%
+what's the trajectory the trajectory is
+ 
+
+ align:start position:0%
+what's the trajectory the trajectory is
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+point you start there and you remain
+
+ align:start position:0%
+point you start there and you remain
+ 
+
+ align:start position:0%
+point you start there and you remain
+there so that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium the question is of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stability is whether trajectories that
+
+ align:start position:0%
+stability is whether trajectories that
+ 
+
+ align:start position:0%
+stability is whether trajectories that
+are nearby where do they go
+
+ align:start position:0%
+are nearby where do they go
+ 
+
+ align:start position:0%
+are nearby where do they go
+okay you know let me you play it with
+
+ align:start position:0%
+okay you know let me you play it with
+ 
+
+ align:start position:0%
+okay you know let me you play it with
+the with the game of mathematicians who
+
+ align:start position:0%
+the with the game of mathematicians who
+ 
+
+ align:start position:0%
+the with the game of mathematicians who
+likes epsilons and Deltas okay uh so the
+
+ align:start position:0%
+likes epsilons and Deltas okay uh so the
+ 
+
+ align:start position:0%
+likes epsilons and Deltas okay uh so the
+mathematician in this case the
+
+ align:start position:0%
+mathematician in this case the
+ 
+
+ align:start position:0%
+mathematician in this case the
+mathematician's name is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+liapunov maybe there is
+
+ align:start position:0%
+liapunov maybe there is
+ 
+
+ align:start position:0%
+liapunov maybe there is
+a not sure about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+U right sorry for the spelling maybe
+
+ align:start position:0%
+U right sorry for the spelling maybe
+ 
+
+ align:start position:0%
+U right sorry for the spelling maybe
+it's wrong
+
+ align:start position:0%
+it's wrong
+ 
+
+ align:start position:0%
+it's wrong
+I'm not sure about the O
+
+ align:start position:0%
+I'm not sure about the O
+ 
+
+ align:start position:0%
+I'm not sure about the O
+there yeah I don't think there is there
+
+ align:start position:0%
+there yeah I don't think there is there
+ 
+
+ align:start position:0%
+there yeah I don't think there is there
+is okay all right so yuno
+
+ align:start position:0%
+is okay all right so yuno
+ 
+
+ align:start position:0%
+is okay all right so yuno
+says give me if the state this state
+
+ align:start position:0%
+says give me if the state this state
+ 
+
+ align:start position:0%
+says give me if the state this state
+equilibrium state is stable give me any
+
+ align:start position:0%
+equilibrium state is stable give me any
+ 
+
+ align:start position:0%
+equilibrium state is stable give me any
+small number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Epsilon then I can
+
+ align:start position:0%
+Epsilon then I can
+ 
+
+ align:start position:0%
+Epsilon then I can
+find a smaller number Delta which is a
+
+ align:start position:0%
+find a smaller number Delta which is a
+ 
+
+ align:start position:0%
+find a smaller number Delta which is a
+function of Epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+such
+
+ align:start position:0%
+such
+ 
+
+ align:start position:0%
+such
+that if I consider uh all the states
+
+ align:start position:0%
+that if I consider uh all the states
+ 
+
+ align:start position:0%
+that if I consider uh all the states
+that are within distance
+
+ align:start position:0%
+that are within distance
+ 
+
+ align:start position:0%
+that are within distance
+Delta uh from the equilibrium State So
+
+ align:start position:0%
+Delta uh from the equilibrium State So
+ 
+
+ align:start position:0%
+Delta uh from the equilibrium State So
+within this small uh hypers sphere ball
+
+ align:start position:0%
+within this small uh hypers sphere ball
+ 
+
+ align:start position:0%
+within this small uh hypers sphere ball
+of radius
+
+ align:start position:0%
+of radius
+ 
+
+ align:start position:0%
+of radius
+Delta any
+
+ align:start position:0%
+Delta any
+ 
+
+ align:start position:0%
+Delta any
+trajectory that
+
+ align:start position:0%
+trajectory that
+ 
+
+ align:start position:0%
+trajectory that
+goes that has a point in there
+
+ align:start position:0%
+goes that has a point in there
+ 
+
+ align:start position:0%
+goes that has a point in there
+will not evolve farther
+
+ align:start position:0%
+will not evolve farther
+ 
+
+ align:start position:0%
+will not evolve farther
+away than the bigger
+
+ align:start position:0%
+away than the bigger
+ 
+
+ align:start position:0%
+away than the bigger
+sphere so it will stay closed so to
+
+ align:start position:0%
+sphere so it will stay closed so to
+ 
+
+ align:start position:0%
+sphere so it will stay closed so to
+speak that's the
+
+ align:start position:0%
+speak that's the
+ 
+
+ align:start position:0%
+speak that's the
+idea so this would
+
+ align:start position:0%
+idea so this would
+ 
+
+ align:start position:0%
+idea so this would
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stable but actually this this definition
+
+ align:start position:0%
+stable but actually this this definition
+ 
+
+ align:start position:0%
+stable but actually this this definition
+of stability is
+
+ align:start position:0%
+of stability is
+ 
+
+ align:start position:0%
+of stability is
+locally locally
+
+ align:start position:0%
+locally locally
+ 
+
+ align:start position:0%
+locally locally
+stable okay so then that would be a
+
+ align:start position:0%
+stable okay so then that would be a
+ 
+
+ align:start position:0%
+stable okay so then that would be a
+feature of this
+
+ align:start position:0%
+feature of this
+ 
+
+ align:start position:0%
+feature of this
+state and also of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+state
+
+ align:start position:0%
+state
+ 
+
+ align:start position:0%
+state
+however and I'm not going to because I
+
+ align:start position:0%
+however and I'm not going to because I
+ 
+
+ align:start position:0%
+however and I'm not going to because I
+don't remember it and doesn't matter uh
+
+ align:start position:0%
+don't remember it and doesn't matter uh
+ 
+
+ align:start position:0%
+don't remember it and doesn't matter uh
+to give you the Epsilon version of the
+
+ align:start position:0%
+to give you the Epsilon version of the
+ 
+
+ align:start position:0%
+to give you the Epsilon version of the
+uh meta stability but it can be done I
+
+ align:start position:0%
+uh meta stability but it can be done I
+ 
+
+ align:start position:0%
+uh meta stability but it can be done I
+can give you the reference for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that there is a difference between this
+
+ align:start position:0%
+that there is a difference between this
+ 
+
+ align:start position:0%
+that there is a difference between this
+locally stable uh state and equilibrium
+
+ align:start position:0%
+locally stable uh state and equilibrium
+ 
+
+ align:start position:0%
+locally stable uh state and equilibrium
+State and these other locally stable
+
+ align:start position:0%
+State and these other locally stable
+ 
+
+ align:start position:0%
+State and these other locally stable
+equilibrium State this one which we call
+
+ align:start position:0%
+equilibrium State this one which we call
+ 
+
+ align:start position:0%
+equilibrium State this one which we call
+Meta
+
+ align:start position:0%
+Meta
+ 
+
+ align:start position:0%
+Meta
+stable is such
+
+ align:start position:0%
+stable is such
+ 
+
+ align:start position:0%
+stable is such
+that look what I can do I
+
+ align:start position:0%
+that look what I can do I
+ 
+
+ align:start position:0%
+that look what I can do I
+can in a weight
+
+ align:start position:0%
+can in a weight
+ 
+
+ align:start position:0%
+can in a weight
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+take this mass or whatever it is take it
+
+ align:start position:0%
+take this mass or whatever it is take it
+ 
+
+ align:start position:0%
+take this mass or whatever it is take it
+up he up to the Casp and then take it
+
+ align:start position:0%
+up he up to the Casp and then take it
+ 
+
+ align:start position:0%
+up he up to the Casp and then take it
+down to this same level so that we are
+
+ align:start position:0%
+down to this same level so that we are
+ 
+
+ align:start position:0%
+down to this same level so that we are
+at the same level
+
+ align:start position:0%
+at the same level
+ 
+
+ align:start position:0%
+at the same level
+here so in order to do that I had to
+
+ align:start position:0%
+here so in order to do that I had to
+ 
+
+ align:start position:0%
+here so in order to do that I had to
+spend some uh energy from the weight
+
+ align:start position:0%
+spend some uh energy from the weight
+ 
+
+ align:start position:0%
+spend some uh energy from the weight
+outside to pull the mass
+
+ align:start position:0%
+outside to pull the mass
+ 
+
+ align:start position:0%
+outside to pull the mass
+up but then that
+
+ align:start position:0%
+up but then that
+ 
+
+ align:start position:0%
+up but then that
+energy uh is given back to the
+
+ align:start position:0%
+energy uh is given back to the
+ 
+
+ align:start position:0%
+energy uh is given back to the
+weight at least if I get exactly to the
+
+ align:start position:0%
+weight at least if I get exactly to the
+ 
+
+ align:start position:0%
+weight at least if I get exactly to the
+same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+height at that stage I have been able to
+
+ align:start position:0%
+height at that stage I have been able to
+ 
+
+ align:start position:0%
+height at that stage I have been able to
+do what I have been able to change the
+
+ align:start position:0%
+do what I have been able to change the
+ 
+
+ align:start position:0%
+do what I have been able to change the
+state into a different an entirely
+
+ align:start position:0%
+state into a different an entirely
+ 
+
+ align:start position:0%
+state into a different an entirely
+different state this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one which if I let it go it will start
+
+ align:start position:0%
+one which if I let it go it will start
+ 
+
+ align:start position:0%
+one which if I let it go it will start
+bouncing back and
+
+ align:start position:0%
+bouncing back and
+ 
+
+ align:start position:0%
+bouncing back and
+forth okay so definitely this situation
+
+ align:start position:0%
+forth okay so definitely this situation
+ 
+
+ align:start position:0%
+forth okay so definitely this situation
+in which the thing bounces back and
+
+ align:start position:0%
+in which the thing bounces back and
+ 
+
+ align:start position:0%
+in which the thing bounces back and
+forth is different from this one all
+
+ align:start position:0%
+forth is different from this one all
+ 
+
+ align:start position:0%
+forth is different from this one all
+right so
+
+ align:start position:0%
+right so
+ 
+
+ align:start position:0%
+right so
+stable equilibrium
+
+ align:start position:0%
+stable equilibrium
+ 
+
+ align:start position:0%
+stable equilibrium
+state I'm sorry this meta stable
+
+ align:start position:0%
+state I'm sorry this meta stable
+ 
+
+ align:start position:0%
+state I'm sorry this meta stable
+equilibrium State I have been able to
+
+ align:start position:0%
+equilibrium State I have been able to
+ 
+
+ align:start position:0%
+equilibrium State I have been able to
+change it to a different state without
+
+ align:start position:0%
+change it to a different state without
+ 
+
+ align:start position:0%
+change it to a different state without
+leaving any external
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+effects whereas this is not possible for
+
+ align:start position:0%
+effects whereas this is not possible for
+ 
+
+ align:start position:0%
+effects whereas this is not possible for
+these lower U lowest uh energy
+
+ align:start position:0%
+these lower U lowest uh energy
+ 
+
+ align:start position:0%
+these lower U lowest uh energy
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+State because if I want to go if you
+
+ align:start position:0%
+State because if I want to go if you
+ 
+
+ align:start position:0%
+State because if I want to go if you
+want to change it
+
+ align:start position:0%
+want to change it
+ 
+
+ align:start position:0%
+want to change it
+wherever I want to go I need to spend
+
+ align:start position:0%
+wherever I want to go I need to spend
+ 
+
+ align:start position:0%
+wherever I want to go I need to spend
+some energy and it will not return it
+
+ align:start position:0%
+some energy and it will not return it
+ 
+
+ align:start position:0%
+some energy and it will not return it
+back to
+
+ align:start position:0%
+back to
+ 
+
+ align:start position:0%
+back to
+me all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so with this in mind the idea and
+
+ align:start position:0%
+right so with this in mind the idea and
+ 
+
+ align:start position:0%
+right so with this in mind the idea and
+the actual definition of stable
+
+ align:start position:0%
+the actual definition of stable
+ 
+
+ align:start position:0%
+the actual definition of stable
+equilibrium state which is important
+
+ align:start position:0%
+equilibrium state which is important
+ 
+
+ align:start position:0%
+equilibrium state which is important
+very important for the statement for our
+
+ align:start position:0%
+very important for the statement for our
+ 
+
+ align:start position:0%
+very important for the statement for our
+statement of the second law
+
+ align:start position:0%
+statement of the second law
+ 
+
+ align:start position:0%
+statement of the second law
+is stay equilibrium state is an
+
+ align:start position:0%
+is stay equilibrium state is an
+ 
+
+ align:start position:0%
+is stay equilibrium state is an
+equilibrium state that cannot be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+changed uh without
+
+ align:start position:0%
+changed uh without
+ 
+
+ align:start position:0%
+changed uh without
+leaving uh
+
+ align:start position:0%
+leaving uh
+ 
+
+ align:start position:0%
+leaving uh
+net external
+
+ align:start position:0%
+net external
+ 
+
+ align:start position:0%
+net external
+effects
+
+ align:start position:0%
+effects
+ 
+
+ align:start position:0%
+effects
+without uh net external effects I cannot
+
+ align:start position:0%
+without uh net external effects I cannot
+ 
+
+ align:start position:0%
+without uh net external effects I cannot
+change a stable equilibrium
+
+ align:start position:0%
+change a stable equilibrium
+ 
+
+ align:start position:0%
+change a stable equilibrium
+State and why is that
+
+ align:start position:0%
+State and why is that
+ 
+
+ align:start position:0%
+State and why is that
+important oh sorry uh right I have the
+
+ align:start position:0%
+important oh sorry uh right I have the
+ 
+
+ align:start position:0%
+important oh sorry uh right I have the
+time no okay why is that important we'll
+
+ align:start position:0%
+time no okay why is that important we'll
+ 
+
+ align:start position:0%
+time no okay why is that important we'll
+return then to the previous
+
+ align:start position:0%
+return then to the previous
+ 
+
+ align:start position:0%
+return then to the previous
+slide because the second law is about
+
+ align:start position:0%
+slide because the second law is about
+ 
+
+ align:start position:0%
+slide because the second law is about
+this question IT addresses and gives an
+
+ align:start position:0%
+this question IT addresses and gives an
+ 
+
+ align:start position:0%
+this question IT addresses and gives an
+answer to this question how many stable
+
+ align:start position:0%
+answer to this question how many stable
+ 
+
+ align:start position:0%
+answer to this question how many stable
+equum states does a system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have we all know the answer that
+
+ align:start position:0%
+have we all know the answer that
+ 
+
+ align:start position:0%
+have we all know the answer that
+mechanics gives no mechanics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+says one only one is the minimum
+
+ align:start position:0%
+says one only one is the minimum
+ 
+
+ align:start position:0%
+says one only one is the minimum
+energy provided of course you have
+
+ align:start position:0%
+energy provided of course you have
+ 
+
+ align:start position:0%
+energy provided of course you have
+fixed uh the number of particles and the
+
+ align:start position:0%
+fixed uh the number of particles and the
+ 
+
+ align:start position:0%
+fixed uh the number of particles and the
+values of the parameters of your
+
+ align:start position:0%
+values of the parameters of your
+ 
+
+ align:start position:0%
+values of the parameters of your
+external
+
+ align:start position:0%
+external
+ 
+
+ align:start position:0%
+external
+forces okay
+
+ align:start position:0%
+forces okay
+ 
+
+ align:start position:0%
+forces okay
+so that's the answer in
+
+ align:start position:0%
+so that's the answer in
+ 
+
+ align:start position:0%
+so that's the answer in
+mechanics there is only one equilibrium
+
+ align:start position:0%
+mechanics there is only one equilibrium
+ 
+
+ align:start position:0%
+mechanics there is only one equilibrium
+state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+however the statement that we will uh
+
+ align:start position:0%
+however the statement that we will uh
+ 
+
+ align:start position:0%
+however the statement that we will uh
+adopt which is due to atopos and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Kenan uh is
+
+ align:start position:0%
+Kenan uh is
+ 
+
+ align:start position:0%
+Kenan uh is
+that no in
+
+ align:start position:0%
+that no in
+ 
+
+ align:start position:0%
+that no in
+thermodynamics that's not
+
+ align:start position:0%
+thermodynamics that's not
+ 
+
+ align:start position:0%
+thermodynamics that's not
+true uh there is a one stable
+
+ align:start position:0%
+true uh there is a one stable
+ 
+
+ align:start position:0%
+true uh there is a one stable
+equilibrium State once you have
+
+ align:start position:0%
+equilibrium State once you have
+ 
+
+ align:start position:0%
+equilibrium State once you have
+fixed the numbers the number of
+
+ align:start position:0%
+fixed the numbers the number of
+ 
+
+ align:start position:0%
+fixed the numbers the number of
+particles and the values of the
+
+ align:start position:0%
+particles and the values of the
+ 
+
+ align:start position:0%
+particles and the values of the
+parameters you have one equilibrium
+
+ align:start position:0%
+parameters you have one equilibrium
+ 
+
+ align:start position:0%
+parameters you have one equilibrium
+State stable equilibrium state for every
+
+ align:start position:0%
+State stable equilibrium state for every
+ 
+
+ align:start position:0%
+State stable equilibrium state for every
+value of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy which of
+
+ align:start position:0%
+energy which of
+ 
+
+ align:start position:0%
+energy which of
+course appears to be a
+
+ align:start position:0%
+course appears to be a
+ 
+
+ align:start position:0%
+course appears to be a
+contradiction
+
+ align:start position:0%
+contradiction
+ 
+
+ align:start position:0%
+contradiction
+with uh mechanics and as you know people
+
+ align:start position:0%
+with uh mechanics and as you know people
+ 
+
+ align:start position:0%
+with uh mechanics and as you know people
+have G uh on for
+
+ align:start position:0%
+have G uh on for
+ 
+
+ align:start position:0%
+have G uh on for
+a cental talking about this uh
+
+ align:start position:0%
+a cental talking about this uh
+ 
+
+ align:start position:0%
+a cental talking about this uh
+discrepancy between mechanics and
+
+ align:start position:0%
+discrepancy between mechanics and
+ 
+
+ align:start position:0%
+discrepancy between mechanics and
+thermodynamics and how do we resolve it
+
+ align:start position:0%
+thermodynamics and how do we resolve it
+ 
+
+ align:start position:0%
+thermodynamics and how do we resolve it
+and so on we'll see that there is no
+
+ align:start position:0%
+and so on we'll see that there is no
+ 
+
+ align:start position:0%
+and so on we'll see that there is no
+discrepancy and there is no um serious
+
+ align:start position:0%
+discrepancy and there is no um serious
+ 
+
+ align:start position:0%
+discrepancy and there is no um serious
+uh problem the moment we realize that
+
+ align:start position:0%
+uh problem the moment we realize that
+ 
+
+ align:start position:0%
+uh problem the moment we realize that
+the States considered in mechanics is
+
+ align:start position:0%
+the States considered in mechanics is
+ 
+
+ align:start position:0%
+the States considered in mechanics is
+just a subset of the States considered
+
+ align:start position:0%
+just a subset of the States considered
+ 
+
+ align:start position:0%
+just a subset of the States considered
+in thermodynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and it actually we will see that this
+
+ align:start position:0%
+uh and it actually we will see that this
+ 
+
+ align:start position:0%
+uh and it actually we will see that this
+is the subset of states for which the
+
+ align:start position:0%
+is the subset of states for which the
+ 
+
+ align:start position:0%
+is the subset of states for which the
+entropy is equal to zero but we haven't
+
+ align:start position:0%
+entropy is equal to zero but we haven't
+ 
+
+ align:start position:0%
+entropy is equal to zero but we haven't
+defined entropy yet entropy definition
+
+ align:start position:0%
+defined entropy yet entropy definition
+ 
+
+ align:start position:0%
+defined entropy yet entropy definition
+will come next time uh and uh uh so for
+
+ align:start position:0%
+will come next time uh and uh uh so for
+ 
+
+ align:start position:0%
+will come next time uh and uh uh so for
+the moment I think I would finish since
+
+ align:start position:0%
+the moment I think I would finish since
+ 
+
+ align:start position:0%
+the moment I think I would finish since
+I promised five minutes earlier uh and
+
+ align:start position:0%
+I promised five minutes earlier uh and
+ 
+
+ align:start position:0%
+I promised five minutes earlier uh and
+uh we'll uh take it uh from here
+
+ align:start position:0%
+uh we'll uh take it uh from here
+ 
+
+ align:start position:0%
+uh we'll uh take it uh from here
+okay
\ No newline at end of file
diff --git a/v3k6BbBLULI.txt b/v3k6BbBLULI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..652f9e402f27753bbb8d466f060ab7e03fff1e9f
--- /dev/null
+++ b/v3k6BbBLULI.txt
@@ -0,0 +1,8891 @@
+align:start position:0%
+ 
+okay so um today we're want to start
+
+ align:start position:0%
+okay so um today we're want to start
+ 
+
+ align:start position:0%
+okay so um today we're want to start
+talking about the long run I've been
+
+ align:start position:0%
+talking about the long run I've been
+ 
+
+ align:start position:0%
+talking about the long run I've been
+talking about the business cycles and
+
+ align:start position:0%
+talking about the business cycles and
+ 
+
+ align:start position:0%
+talking about the business cycles and
+today we're going to start talking about
+
+ align:start position:0%
+today we're going to start talking about
+ 
+
+ align:start position:0%
+today we're going to start talking about
+things that happen over decades H but
+
+ align:start position:0%
+things that happen over decades H but
+ 
+
+ align:start position:0%
+things that happen over decades H but
+before I do that before we finish with
+
+ align:start position:0%
+before I do that before we finish with
+ 
+
+ align:start position:0%
+before I do that before we finish with
+the the short run medium run I just
+
+ align:start position:0%
+the the short run medium run I just
+ 
+
+ align:start position:0%
+the the short run medium run I just
+don't want you to I want I don't want to
+
+ align:start position:0%
+don't want you to I want I don't want to
+ 
+
+ align:start position:0%
+don't want you to I want I don't want to
+give you the impression that that you
+
+ align:start position:0%
+give you the impression that that you
+ 
+
+ align:start position:0%
+give you the impression that that you
+know once you understand the ISL MPC
+
+ align:start position:0%
+know once you understand the ISL MPC
+ 
+
+ align:start position:0%
+know once you understand the ISL MPC
+sort of you you can start managing
+
+ align:start position:0%
+sort of you you can start managing
+ 
+
+ align:start position:0%
+sort of you you can start managing
+monetary
+
+ align:start position:0%
+monetary
+ 
+
+ align:start position:0%
+monetary
+policy immediately I
+
+ align:start position:0%
+policy immediately I
+ 
+
+ align:start position:0%
+policy immediately I
+I there's a lot of noise of all sort of
+
+ align:start position:0%
+I there's a lot of noise of all sort of
+ 
+
+ align:start position:0%
+I there's a lot of noise of all sort of
+kind of complexity in the real world of
+
+ align:start position:0%
+kind of complexity in the real world of
+ 
+
+ align:start position:0%
+kind of complexity in the real world of
+course that can make um policies
+
+ align:start position:0%
+course that can make um policies
+ 
+
+ align:start position:0%
+course that can make um policies
+uh uh very hard to manage in practice
+
+ align:start position:0%
+uh uh very hard to manage in practice
+ 
+
+ align:start position:0%
+uh uh very hard to manage in practice
+macroeconomic policies and one
+
+ align:start position:0%
+macroeconomic policies and one
+ 
+
+ align:start position:0%
+macroeconomic policies and one
+fundamental principle I would say is
+
+ align:start position:0%
+fundamental principle I would say is
+ 
+
+ align:start position:0%
+fundamental principle I would say is
+that policy makers understand that speed
+
+ align:start position:0%
+that policy makers understand that speed
+ 
+
+ align:start position:0%
+that policy makers understand that speed
+can kill okay and uh that's very obvious
+
+ align:start position:0%
+can kill okay and uh that's very obvious
+ 
+
+ align:start position:0%
+can kill okay and uh that's very obvious
+during financial crisis there we all
+
+ align:start position:0%
+during financial crisis there we all
+ 
+
+ align:start position:0%
+during financial crisis there we all
+understand that ER the response needs to
+
+ align:start position:0%
+understand that ER the response needs to
+ 
+
+ align:start position:0%
+understand that ER the response needs to
+be large it has to be a response with
+
+ align:start position:0%
+be large it has to be a response with
+ 
+
+ align:start position:0%
+be large it has to be a response with
+overwhelming Force essentially because
+
+ align:start position:0%
+overwhelming Force essentially because
+ 
+
+ align:start position:0%
+overwhelming Force essentially because
+things are happening so fast that very
+
+ align:start position:0%
+things are happening so fast that very
+ 
+
+ align:start position:0%
+things are happening so fast that very
+few corporations even healthy
+
+ align:start position:0%
+few corporations even healthy
+ 
+
+ align:start position:0%
+few corporations even healthy
+corporations that that can adjust
+
+ align:start position:0%
+corporations that that can adjust
+ 
+
+ align:start position:0%
+corporations that that can adjust
+quickly enough uh to the PACE at which
+
+ align:start position:0%
+quickly enough uh to the PACE at which
+ 
+
+ align:start position:0%
+quickly enough uh to the PACE at which
+things are changing prices become
+
+ align:start position:0%
+things are changing prices become
+ 
+
+ align:start position:0%
+things are changing prices become
+noninformative uh fire cells take place
+
+ align:start position:0%
+noninformative uh fire cells take place
+ 
+
+ align:start position:0%
+noninformative uh fire cells take place
+and and and obviously it's very
+
+ align:start position:0%
+and and and obviously it's very
+ 
+
+ align:start position:0%
+and and and obviously it's very
+difficult to make economic decisions in
+
+ align:start position:0%
+difficult to make economic decisions in
+ 
+
+ align:start position:0%
+difficult to make economic decisions in
+that context and so that's the reason
+
+ align:start position:0%
+that context and so that's the reason
+ 
+
+ align:start position:0%
+that context and so that's the reason
+they are the speed in the on the on the
+
+ align:start position:0%
+they are the speed in the on the on the
+ 
+
+ align:start position:0%
+they are the speed in the on the on the
+policy Direction goes very clearly in
+
+ align:start position:0%
+policy Direction goes very clearly in
+ 
+
+ align:start position:0%
+policy Direction goes very clearly in
+One Direction do it quickly and very
+
+ align:start position:0%
+One Direction do it quickly and very
+ 
+
+ align:start position:0%
+One Direction do it quickly and very
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+now on the other hand ER when you're
+
+ align:start position:0%
+now on the other hand ER when you're
+ 
+
+ align:start position:0%
+now on the other hand ER when you're
+going through a period in which you're
+
+ align:start position:0%
+going through a period in which you're
+ 
+
+ align:start position:0%
+going through a period in which you're
+are hiking interest rates for example
+
+ align:start position:0%
+are hiking interest rates for example
+ 
+
+ align:start position:0%
+are hiking interest rates for example
+ER like we're going through now um the
+
+ align:start position:0%
+ER like we're going through now um the
+ 
+
+ align:start position:0%
+ER like we're going through now um the
+the Tendencies towards gradualism to do
+
+ align:start position:0%
+the Tendencies towards gradualism to do
+ 
+
+ align:start position:0%
+the Tendencies towards gradualism to do
+it very slowly because something can
+
+ align:start position:0%
+it very slowly because something can
+ 
+
+ align:start position:0%
+it very slowly because something can
+break along the path and it's often the
+
+ align:start position:0%
+break along the path and it's often the
+ 
+
+ align:start position:0%
+break along the path and it's often the
+case that with for sufficiently large
+
+ align:start position:0%
+case that with for sufficiently large
+ 
+
+ align:start position:0%
+case that with for sufficiently large
+adjustments something breaks okay and so
+
+ align:start position:0%
+adjustments something breaks okay and so
+ 
+
+ align:start position:0%
+adjustments something breaks okay and so
+here you have an example of sort of
+
+ align:start position:0%
+here you have an example of sort of
+ 
+
+ align:start position:0%
+here you have an example of sort of
+major episodes of hiking in the US and
+
+ align:start position:0%
+major episodes of hiking in the US and
+ 
+
+ align:start position:0%
+major episodes of hiking in the US and
+things that have happened about those
+
+ align:start position:0%
+things that have happened about those
+ 
+
+ align:start position:0%
+things that have happened about those
+those H major episodes
+
+ align:start position:0%
+those H major episodes
+ 
+
+ align:start position:0%
+those H major episodes
+this one actually I I have a personal
+
+ align:start position:0%
+this one actually I I have a personal
+ 
+
+ align:start position:0%
+this one actually I I have a personal
+attachment to that one because you know
+
+ align:start position:0%
+attachment to that one because you know
+ 
+
+ align:start position:0%
+attachment to that one because you know
+I was studying in Chile around then
+
+ align:start position:0%
+I was studying in Chile around then
+ 
+
+ align:start position:0%
+I was studying in Chile around then
+everything was going wonderfully massive
+
+ align:start position:0%
+everything was going wonderfully massive
+ 
+
+ align:start position:0%
+everything was going wonderfully massive
+Capital flows to Chile emerging markets
+
+ align:start position:0%
+Capital flows to Chile emerging markets
+ 
+
+ align:start position:0%
+Capital flows to Chile emerging markets
+were very popular we all felt very
+
+ align:start position:0%
+were very popular we all felt very
+ 
+
+ align:start position:0%
+were very popular we all felt very
+wealthy rich and so on and right after I
+
+ align:start position:0%
+wealthy rich and so on and right after I
+ 
+
+ align:start position:0%
+wealthy rich and so on and right after I
+finished College ER I was not planning
+
+ align:start position:0%
+finished College ER I was not planning
+ 
+
+ align:start position:0%
+finished College ER I was not planning
+to come to the usy things were going
+
+ align:start position:0%
+to come to the usy things were going
+ 
+
+ align:start position:0%
+to come to the usy things were going
+very well in Chile H but the US decided
+
+ align:start position:0%
+very well in Chile H but the US decided
+ 
+
+ align:start position:0%
+very well in Chile H but the US decided
+to hike interest rate very aggressively
+
+ align:start position:0%
+to hike interest rate very aggressively
+ 
+
+ align:start position:0%
+to hike interest rate very aggressively
+all of the sudden Capital flows to
+
+ align:start position:0%
+all of the sudden Capital flows to
+ 
+
+ align:start position:0%
+all of the sudden Capital flows to
+emergy markets disappear we went into an
+
+ align:start position:0%
+emergy markets disappear we went into an
+ 
+
+ align:start position:0%
+emergy markets disappear we went into an
+enormous financial crisis I lost I had
+
+ align:start position:0%
+enormous financial crisis I lost I had
+ 
+
+ align:start position:0%
+enormous financial crisis I lost I had
+no opportunity cost and I had to come to
+
+ align:start position:0%
+no opportunity cost and I had to come to
+ 
+
+ align:start position:0%
+no opportunity cost and I had to come to
+study to the US that that's my so I know
+
+ align:start position:0%
+study to the US that that's my so I know
+ 
+
+ align:start position:0%
+study to the US that that's my so I know
+that hikes aggressive hikes can matter
+
+ align:start position:0%
+that hikes aggressive hikes can matter
+ 
+
+ align:start position:0%
+that hikes aggressive hikes can matter
+can make differences to people but and
+
+ align:start position:0%
+can make differences to people but and
+ 
+
+ align:start position:0%
+can make differences to people but and
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+was there's a decade that followed that
+
+ align:start position:0%
+was there's a decade that followed that
+ 
+
+ align:start position:0%
+was there's a decade that followed that
+episode that is called the L decade of
+
+ align:start position:0%
+episode that is called the L decade of
+ 
+
+ align:start position:0%
+episode that is called the L decade of
+Latin America essentially so things did
+
+ align:start position:0%
+Latin America essentially so things did
+ 
+
+ align:start position:0%
+Latin America essentially so things did
+break and and one of the main reasons
+
+ align:start position:0%
+break and and one of the main reasons
+ 
+
+ align:start position:0%
+break and and one of the main reasons
+they did break is because at the time
+
+ align:start position:0%
+they did break is because at the time
+ 
+
+ align:start position:0%
+they did break is because at the time
+most of the capital close that's not
+
+ align:start position:0%
+most of the capital close that's not
+ 
+
+ align:start position:0%
+most of the capital close that's not
+what happens today we really being
+
+ align:start position:0%
+what happens today we really being
+ 
+
+ align:start position:0%
+what happens today we really being
+managed by global Banks and the banks
+
+ align:start position:0%
+managed by global Banks and the banks
+ 
+
+ align:start position:0%
+managed by global Banks and the banks
+can get very distressed when interest
+
+ align:start position:0%
+can get very distressed when interest
+ 
+
+ align:start position:0%
+can get very distressed when interest
+rate rise H very very quickly and so
+
+ align:start position:0%
+rate rise H very very quickly and so
+ 
+
+ align:start position:0%
+rate rise H very very quickly and so
+that that was essentially a problem with
+
+ align:start position:0%
+that that was essentially a problem with
+ 
+
+ align:start position:0%
+that that was essentially a problem with
+us the US Banks major Global Banks but
+
+ align:start position:0%
+us the US Banks major Global Banks but
+ 
+
+ align:start position:0%
+us the US Banks major Global Banks but
+the US Banks in particular that trigger
+
+ align:start position:0%
+the US Banks in particular that trigger
+ 
+
+ align:start position:0%
+the US Banks in particular that trigger
+an Emerging Market
+
+ align:start position:0%
+an Emerging Market
+ 
+
+ align:start position:0%
+an Emerging Market
+crisis this one also had huge
+
+ align:start position:0%
+crisis this one also had huge
+ 
+
+ align:start position:0%
+crisis this one also had huge
+consequences actually and it's
+
+ align:start position:0%
+consequences actually and it's
+ 
+
+ align:start position:0%
+consequences actually and it's
+interesting because this episode is is
+
+ align:start position:0%
+interesting because this episode is is
+ 
+
+ align:start position:0%
+interesting because this episode is is
+similar to to to to what we're going on
+
+ align:start position:0%
+similar to to to to what we're going on
+ 
+
+ align:start position:0%
+similar to to to to what we're going on
+what is going on right now or what may
+
+ align:start position:0%
+what is going on right now or what may
+ 
+
+ align:start position:0%
+what is going on right now or what may
+happen in soon so this is episode of
+
+ align:start position:0%
+happen in soon so this is episode of
+ 
+
+ align:start position:0%
+happen in soon so this is episode of
+hikes that ended what is called The
+
+ align:start position:0%
+hikes that ended what is called The
+ 
+
+ align:start position:0%
+hikes that ended what is called The
+Savings and Loan crisis and those so the
+
+ align:start position:0%
+Savings and Loan crisis and those so the
+ 
+
+ align:start position:0%
+Savings and Loan crisis and those so the
+best parallel to today are the small
+
+ align:start position:0%
+best parallel to today are the small
+ 
+
+ align:start position:0%
+best parallel to today are the small
+Regional Banks if you will and they they
+
+ align:start position:0%
+Regional Banks if you will and they they
+ 
+
+ align:start position:0%
+Regional Banks if you will and they they
+weren't able to withstand this sort of
+
+ align:start position:0%
+weren't able to withstand this sort of
+ 
+
+ align:start position:0%
+weren't able to withstand this sort of
+sharp rise in interest rate which is
+
+ align:start position:0%
+sharp rise in interest rate which is
+ 
+
+ align:start position:0%
+sharp rise in interest rate which is
+very much what is going on right now in
+
+ align:start position:0%
+very much what is going on right now in
+ 
+
+ align:start position:0%
+very much what is going on right now in
+the US this one actually end up with
+
+ align:start position:0%
+the US this one actually end up with
+ 
+
+ align:start position:0%
+the US this one actually end up with
+also another problem which is the the
+
+ align:start position:0%
+also another problem which is the the
+ 
+
+ align:start position:0%
+also another problem which is the the
+the bubble burst in Japan episode of
+
+ align:start position:0%
+the bubble burst in Japan episode of
+ 
+
+ align:start position:0%
+the bubble burst in Japan episode of
+hiking in the US and there we had a
+
+ align:start position:0%
+hiking in the US and there we had a
+ 
+
+ align:start position:0%
+hiking in the US and there we had a
+major crisis in in Japan the price of
+
+ align:start position:0%
+major crisis in in Japan the price of
+ 
+
+ align:start position:0%
+major crisis in in Japan the price of
+real estate
+
+ align:start position:0%
+real estate
+ 
+
+ align:start position:0%
+real estate
+collapsed ER and and essentially they
+
+ align:start position:0%
+collapsed ER and and essentially they
+ 
+
+ align:start position:0%
+collapsed ER and and essentially they
+since then they have never been able to
+
+ align:start position:0%
+since then they have never been able to
+ 
+
+ align:start position:0%
+since then they have never been able to
+grow as they used to before that that
+
+ align:start position:0%
+grow as they used to before that that
+ 
+
+ align:start position:0%
+grow as they used to before that that
+episode that's called sometimes the
+
+ align:start position:0%
+episode that's called sometimes the
+ 
+
+ align:start position:0%
+episode that's called sometimes the
+tequila crisis it's a Mexican
+
+ align:start position:0%
+tequila crisis it's a Mexican
+ 
+
+ align:start position:0%
+tequila crisis it's a Mexican
+Bond crisis and it was again the result
+
+ align:start position:0%
+Bond crisis and it was again the result
+ 
+
+ align:start position:0%
+Bond crisis and it was again the result
+of a hiking episode in the US conditions
+
+ align:start position:0%
+of a hiking episode in the US conditions
+ 
+
+ align:start position:0%
+of a hiking episode in the US conditions
+tighten to Emerging Market ER their bone
+
+ align:start position:0%
+tighten to Emerging Market ER their bone
+ 
+
+ align:start position:0%
+tighten to Emerging Market ER their bone
+Market essentially
+
+ align:start position:0%
+Market essentially
+ 
+
+ align:start position:0%
+Market essentially
+exploded um well this is the global
+
+ align:start position:0%
+exploded um well this is the global
+ 
+
+ align:start position:0%
+exploded um well this is the global
+financial crisis the Great Recession it
+
+ align:start position:0%
+financial crisis the Great Recession it
+ 
+
+ align:start position:0%
+financial crisis the Great Recession it
+was again preceded by episode of sort of
+
+ align:start position:0%
+was again preceded by episode of sort of
+ 
+
+ align:start position:0%
+was again preceded by episode of sort of
+aggressive hikes which eventually er um
+
+ align:start position:0%
+aggressive hikes which eventually er um
+ 
+
+ align:start position:0%
+aggressive hikes which eventually er um
+led to a turn around as house prices
+
+ align:start position:0%
+led to a turn around as house prices
+ 
+
+ align:start position:0%
+led to a turn around as house prices
+were Rising steadily throughout the
+
+ align:start position:0%
+were Rising steadily throughout the
+ 
+
+ align:start position:0%
+were Rising steadily throughout the
+episode and a lot of financial assets
+
+ align:start position:0%
+episode and a lot of financial assets
+ 
+
+ align:start position:0%
+episode and a lot of financial assets
+were created around that housing wealth
+
+ align:start position:0%
+were created around that housing wealth
+ 
+
+ align:start position:0%
+were created around that housing wealth
+that was been created that hike and
+
+ align:start position:0%
+that was been created that hike and
+ 
+
+ align:start position:0%
+that was been created that hike and
+interest rate eventually put a stop an
+
+ align:start position:0%
+interest rate eventually put a stop an
+ 
+
+ align:start position:0%
+interest rate eventually put a stop an
+end to that that appreciation of house
+
+ align:start position:0%
+end to that that appreciation of house
+ 
+
+ align:start position:0%
+end to that that appreciation of house
+prices in fact they turn around and it
+
+ align:start position:0%
+prices in fact they turn around and it
+ 
+
+ align:start position:0%
+prices in fact they turn around and it
+led to a very significant financial
+
+ align:start position:0%
+led to a very significant financial
+ 
+
+ align:start position:0%
+led to a very significant financial
+crisis and this is where we're at right
+
+ align:start position:0%
+crisis and this is where we're at right
+ 
+
+ align:start position:0%
+crisis and this is where we're at right
+now okay and so we already seen sort of
+
+ align:start position:0%
+now okay and so we already seen sort of
+ 
+
+ align:start position:0%
+now okay and so we already seen sort of
+some Tremors and so on so the point is
+
+ align:start position:0%
+some Tremors and so on so the point is
+ 
+
+ align:start position:0%
+some Tremors and so on so the point is
+when when sometimes you say well why is
+
+ align:start position:0%
+when when sometimes you say well why is
+ 
+
+ align:start position:0%
+when when sometimes you say well why is
+isn't the FED more aggressive if we have
+
+ align:start position:0%
+isn't the FED more aggressive if we have
+ 
+
+ align:start position:0%
+isn't the FED more aggressive if we have
+high inflation and go very quickly at it
+
+ align:start position:0%
+high inflation and go very quickly at it
+ 
+
+ align:start position:0%
+high inflation and go very quickly at it
+well it's because things can go wrong
+
+ align:start position:0%
+well it's because things can go wrong
+ 
+
+ align:start position:0%
+well it's because things can go wrong
+okay and it it typically happens that
+
+ align:start position:0%
+okay and it it typically happens that
+ 
+
+ align:start position:0%
+okay and it it typically happens that
+things do go wrong you don't know
+
+ align:start position:0%
+things do go wrong you don't know
+ 
+
+ align:start position:0%
+things do go wrong you don't know
+exactly what will blow up but something
+
+ align:start position:0%
+exactly what will blow up but something
+ 
+
+ align:start position:0%
+exactly what will blow up but something
+may blow up and typically is associated
+
+ align:start position:0%
+may blow up and typically is associated
+ 
+
+ align:start position:0%
+may blow up and typically is associated
+to some Financial Market that is very
+
+ align:start position:0%
+to some Financial Market that is very
+ 
+
+ align:start position:0%
+to some Financial Market that is very
+hot and the market and the banks are
+
+ align:start position:0%
+hot and the market and the banks are
+ 
+
+ align:start position:0%
+hot and the market and the banks are
+always involved in that because the
+
+ align:start position:0%
+always involved in that because the
+ 
+
+ align:start position:0%
+always involved in that because the
+banks are very
+
+ align:start position:0%
+banks are very
+ 
+
+ align:start position:0%
+banks are very
+lever you know they have little Capital
+
+ align:start position:0%
+lever you know they have little Capital
+ 
+
+ align:start position:0%
+lever you know they have little Capital
+relative to the assets they have and
+
+ align:start position:0%
+relative to the assets they have and
+ 
+
+ align:start position:0%
+relative to the assets they have and
+that means small variation in the price
+
+ align:start position:0%
+that means small variation in the price
+ 
+
+ align:start position:0%
+that means small variation in the price
+of assets can lead to very large H
+
+ align:start position:0%
+of assets can lead to very large H
+ 
+
+ align:start position:0%
+of assets can lead to very large H
+changes in the value of their
+
+ align:start position:0%
+changes in the value of their
+ 
+
+ align:start position:0%
+changes in the value of their
+capital anyway so just a warning so if
+
+ align:start position:0%
+capital anyway so just a warning so if
+ 
+
+ align:start position:0%
+capital anyway so just a warning so if
+you get a job at the FED please be
+
+ align:start position:0%
+you get a job at the FED please be
+ 
+
+ align:start position:0%
+you get a job at the FED please be
+careful okay now let me switch gears and
+
+ align:start position:0%
+careful okay now let me switch gears and
+ 
+
+ align:start position:0%
+careful okay now let me switch gears and
+and we're going to talk about um um
+
+ align:start position:0%
+and we're going to talk about um um
+ 
+
+ align:start position:0%
+and we're going to talk about um um
+something a little different from what
+
+ align:start position:0%
+something a little different from what
+ 
+
+ align:start position:0%
+something a little different from what
+we have been discussing up to now so
+
+ align:start position:0%
+we have been discussing up to now so
+ 
+
+ align:start position:0%
+we have been discussing up to now so
+this is some this is growth projections
+
+ align:start position:0%
+this is some this is growth projections
+ 
+
+ align:start position:0%
+this is some this is growth projections
+for different regions in the world ER
+
+ align:start position:0%
+for different regions in the world ER
+ 
+
+ align:start position:0%
+for different regions in the world ER
+this is something that is in publishing
+
+ align:start position:0%
+this is something that is in publishing
+ 
+
+ align:start position:0%
+this is something that is in publishing
+by the IMF it's called the world
+
+ align:start position:0%
+by the IMF it's called the world
+ 
+
+ align:start position:0%
+by the IMF it's called the world
+economic Outlook I think I mentioned it
+
+ align:start position:0%
+economic Outlook I think I mentioned it
+ 
+
+ align:start position:0%
+economic Outlook I think I mentioned it
+before and here you have some forecast
+
+ align:start position:0%
+before and here you have some forecast
+ 
+
+ align:start position:0%
+before and here you have some forecast
+you know well this is actually what
+
+ align:start position:0%
+you know well this is actually what
+ 
+
+ align:start position:0%
+you know well this is actually what
+happened so growth in the global economy
+
+ align:start position:0%
+happened so growth in the global economy
+ 
+
+ align:start position:0%
+happened so growth in the global economy
+was about 3.4% 2022 advanced economies
+
+ align:start position:0%
+was about 3.4% 2022 advanced economies
+ 
+
+ align:start position:0%
+was about 3.4% 2022 advanced economies
+grew at 2.7% emerging markets and
+
+ align:start position:0%
+grew at 2.7% emerging markets and
+ 
+
+ align:start position:0%
+grew at 2.7% emerging markets and
+developing economies at
+
+ align:start position:0%
+developing economies at
+ 
+
+ align:start position:0%
+developing economies at
+3.9% and then you see forast and the
+
+ align:start position:0%
+3.9% and then you see forast and the
+ 
+
+ align:start position:0%
+3.9% and then you see forast and the
+further out you go er um the okay the
+
+ align:start position:0%
+further out you go er um the okay the
+ 
+
+ align:start position:0%
+further out you go er um the okay the
+further out you go sort of it's less
+
+ align:start position:0%
+further out you go sort of it's less
+ 
+
+ align:start position:0%
+further out you go sort of it's less
+related to the current cycle is more
+
+ align:start position:0%
+related to the current cycle is more
+ 
+
+ align:start position:0%
+related to the current cycle is more
+related to what is structural the
+
+ align:start position:0%
+related to what is structural the
+ 
+
+ align:start position:0%
+related to what is structural the
+structural
+
+ align:start position:0%
+structural
+ 
+
+ align:start position:0%
+structural
+growth of the different parts of the
+
+ align:start position:0%
+growth of the different parts of the
+ 
+
+ align:start position:0%
+growth of the different parts of the
+world and you see that for
+
+ align:start position:0%
+world and you see that for
+ 
+
+ align:start position:0%
+world and you see that for
+2024 the global economy is projected
+
+ align:start position:0%
+2024 the global economy is projected
+ 
+
+ align:start position:0%
+2024 the global economy is projected
+expected to grow at around 3.1% this
+
+ align:start position:0%
+expected to grow at around 3.1% this
+ 
+
+ align:start position:0%
+expected to grow at around 3.1% this
+forecast were made before the mess
+
+ align:start position:0%
+forecast were made before the mess
+ 
+
+ align:start position:0%
+forecast were made before the mess
+Financial mess that we're going on right
+
+ align:start position:0%
+Financial mess that we're going on right
+ 
+
+ align:start position:0%
+Financial mess that we're going on right
+now so probably the next World economic
+
+ align:start position:0%
+now so probably the next World economic
+ 
+
+ align:start position:0%
+now so probably the next World economic
+Outlook will have at least for 2023 will
+
+ align:start position:0%
+Outlook will have at least for 2023 will
+ 
+
+ align:start position:0%
+Outlook will have at least for 2023 will
+will downgrade the growth probably not
+
+ align:start position:0%
+will downgrade the growth probably not
+ 
+
+ align:start position:0%
+will downgrade the growth probably not
+for 2024 but yes for 2023 anyways
+
+ align:start position:0%
+for 2024 but yes for 2023 anyways
+ 
+
+ align:start position:0%
+for 2024 but yes for 2023 anyways
+advanced economies expected to grow
+
+ align:start position:0%
+advanced economies expected to grow
+ 
+
+ align:start position:0%
+advanced economies expected to grow
+1.4% emerging markets at
+
+ align:start position:0%
+1.4% emerging markets at
+ 
+
+ align:start position:0%
+1.4% emerging markets at
+4.2% so
+
+ align:start position:0%
+4.2% so
+ 
+
+ align:start position:0%
+4.2% so
+these forecasts are based on on a
+
+ align:start position:0%
+these forecasts are based on on a
+ 
+
+ align:start position:0%
+these forecasts are based on on a
+combination of cyclical factors
+
+ align:start position:0%
+combination of cyclical factors
+ 
+
+ align:start position:0%
+combination of cyclical factors
+fluctuations of the short run medium run
+
+ align:start position:0%
+fluctuations of the short run medium run
+ 
+
+ align:start position:0%
+fluctuations of the short run medium run
+the kind of things we have been
+
+ align:start position:0%
+the kind of things we have been
+ 
+
+ align:start position:0%
+the kind of things we have been
+discussing up to now some economies will
+
+ align:start position:0%
+discussing up to now some economies will
+ 
+
+ align:start position:0%
+discussing up to now some economies will
+have to go through recession some
+
+ align:start position:0%
+have to go through recession some
+ 
+
+ align:start position:0%
+have to go through recession some
+economies are going through Booms that
+
+ align:start position:0%
+economies are going through Booms that
+ 
+
+ align:start position:0%
+economies are going through Booms that
+probably dominates 20 the forus on 2023
+
+ align:start position:0%
+probably dominates 20 the forus on 2023
+ 
+
+ align:start position:0%
+probably dominates 20 the forus on 2023
+but as I said before the further out you
+
+ align:start position:0%
+but as I said before the further out you
+ 
+
+ align:start position:0%
+but as I said before the further out you
+go the more the less relevant is the
+
+ align:start position:0%
+go the more the less relevant is the
+ 
+
+ align:start position:0%
+go the more the less relevant is the
+current business cycle and the more
+
+ align:start position:0%
+current business cycle and the more
+ 
+
+ align:start position:0%
+current business cycle and the more
+relevant is the structural trend of the
+
+ align:start position:0%
+relevant is the structural trend of the
+ 
+
+ align:start position:0%
+relevant is the structural trend of the
+different regions of the world okay so I
+
+ align:start position:0%
+different regions of the world okay so I
+ 
+
+ align:start position:0%
+different regions of the world okay so I
+would that in this when they formulated
+
+ align:start position:0%
+would that in this when they formulated
+ 
+
+ align:start position:0%
+would that in this when they formulated
+this forecast this is very much based on
+
+ align:start position:0%
+this forecast this is very much based on
+ 
+
+ align:start position:0%
+this forecast this is very much based on
+more longer run growth model the kind of
+
+ align:start position:0%
+more longer run growth model the kind of
+ 
+
+ align:start position:0%
+more longer run growth model the kind of
+models we're going to discuss now okay
+
+ align:start position:0%
+models we're going to discuss now okay
+ 
+
+ align:start position:0%
+models we're going to discuss now okay
+while this is probably totally dominated
+
+ align:start position:0%
+while this is probably totally dominated
+ 
+
+ align:start position:0%
+while this is probably totally dominated
+by the kind of things we discuss up to
+
+ align:start position:0%
+by the kind of things we discuss up to
+ 
+
+ align:start position:0%
+by the kind of things we discuss up to
+now okay
+
+ align:start position:0%
+now okay
+ 
+
+ align:start position:0%
+now okay
+um there are several things that that
+
+ align:start position:0%
+um there are several things that that
+ 
+
+ align:start position:0%
+um there are several things that that
+that are interesting here aside from
+
+ align:start position:0%
+that are interesting here aside from
+ 
+
+ align:start position:0%
+that are interesting here aside from
+sort of the the the
+
+ align:start position:0%
+sort of the the the
+ 
+
+ align:start position:0%
+sort of the the the
+fluctuations year to year one thing you
+
+ align:start position:0%
+fluctuations year to year one thing you
+ 
+
+ align:start position:0%
+fluctuations year to year one thing you
+can see for example is that regardless
+
+ align:start position:0%
+can see for example is that regardless
+ 
+
+ align:start position:0%
+can see for example is that regardless
+of year
+
+ align:start position:0%
+of year
+ 
+
+ align:start position:0%
+of year
+on average Emerging Markets tend to grow
+
+ align:start position:0%
+on average Emerging Markets tend to grow
+ 
+
+ align:start position:0%
+on average Emerging Markets tend to grow
+faster than develop economies advanced
+
+ align:start position:0%
+faster than develop economies advanced
+ 
+
+ align:start position:0%
+faster than develop economies advanced
+economies okay so one of the things we
+
+ align:start position:0%
+economies okay so one of the things we
+ 
+
+ align:start position:0%
+economies okay so one of the things we
+want to understand is why is that the
+
+ align:start position:0%
+want to understand is why is that the
+ 
+
+ align:start position:0%
+want to understand is why is that the
+case okay but that's is very clear here
+
+ align:start position:0%
+case okay but that's is very clear here
+ 
+
+ align:start position:0%
+case okay but that's is very clear here
+that's the first model we're going to
+
+ align:start position:0%
+that's the first model we're going to
+ 
+
+ align:start position:0%
+that's the first model we're going to
+look at which probably will happen on
+
+ align:start position:0%
+look at which probably will happen on
+ 
+
+ align:start position:0%
+look at which probably will happen on
+Wednesday we'll try to explain
+
+ align:start position:0%
+Wednesday we'll try to explain
+ 
+
+ align:start position:0%
+Wednesday we'll try to explain
+essentially that why is it that these
+
+ align:start position:0%
+essentially that why is it that these
+ 
+
+ align:start position:0%
+essentially that why is it that these
+guys tend to grow faster than the
+
+ align:start position:0%
+guys tend to grow faster than the
+ 
+
+ align:start position:0%
+guys tend to grow faster than the
+advanced economies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so growth is important I mean the
+
+ align:start position:0%
+okay so growth is important I mean the
+ 
+
+ align:start position:0%
+okay so growth is important I mean the
+standing economic growth is hugely
+
+ align:start position:0%
+standing economic growth is hugely
+ 
+
+ align:start position:0%
+standing economic growth is hugely
+important for the weal for understanding
+
+ align:start position:0%
+important for the weal for understanding
+ 
+
+ align:start position:0%
+important for the weal for understanding
+sort of the health of an economy here
+
+ align:start position:0%
+sort of the health of an economy here
+ 
+
+ align:start position:0%
+sort of the health of an economy here
+you see this comes from the textbook er
+
+ align:start position:0%
+you see this comes from the textbook er
+ 
+
+ align:start position:0%
+you see this comes from the textbook er
+er the the US GDP in 20 20
+
+ align:start position:0%
+er the the US GDP in 20 20
+ 
+
+ align:start position:0%
+er the the US GDP in 20 20
+uh2 from
+
+ align:start position:0%
+uh2 from
+ 
+
+ align:start position:0%
+uh2 from
+1890 to to 2017 I think is this one the
+
+ align:start position:0%
+1890 to to 2017 I think is this one the
+ 
+
+ align:start position:0%
+1890 to to 2017 I think is this one the
+the end year the important thing to
+
+ align:start position:0%
+the end year the important thing to
+ 
+
+ align:start position:0%
+the end year the important thing to
+notice here is how large is the change
+
+ align:start position:0%
+notice here is how large is the change
+ 
+
+ align:start position:0%
+notice here is how large is the change
+in GDP in during the period I mean GDP
+
+ align:start position:0%
+in GDP in during the period I mean GDP
+ 
+
+ align:start position:0%
+in GDP in during the period I mean GDP
+here measuring the same prices so 20
+
+ align:start position:0%
+here measuring the same prices so 20
+ 
+
+ align:start position:0%
+here measuring the same prices so 20
+2012 prices is 50 times that in 1890
+
+ align:start position:0%
+2012 prices is 50 times that in 1890
+ 
+
+ align:start position:0%
+2012 prices is 50 times that in 1890
+that's a big thing I mean when we talk
+
+ align:start position:0%
+that's a big thing I mean when we talk
+ 
+
+ align:start position:0%
+that's a big thing I mean when we talk
+about business cycle fluctuations we're
+
+ align:start position:0%
+about business cycle fluctuations we're
+ 
+
+ align:start position:0%
+about business cycle fluctuations we're
+talking about in an economy like the US
+
+ align:start position:0%
+talking about in an economy like the US
+ 
+
+ align:start position:0%
+talking about in an economy like the US
+two two and a half% up 3% up and down
+
+ align:start position:0%
+two two and a half% up 3% up and down
+ 
+
+ align:start position:0%
+two two and a half% up 3% up and down
+this is 50 times so over longer period
+
+ align:start position:0%
+this is 50 times so over longer period
+ 
+
+ align:start position:0%
+this is 50 times so over longer period
+of time you can almost ignore the
+
+ align:start position:0%
+of time you can almost ignore the
+ 
+
+ align:start position:0%
+of time you can almost ignore the
+business cycle and it's all about that
+
+ align:start position:0%
+business cycle and it's all about that
+ 
+
+ align:start position:0%
+business cycle and it's all about that
+long run H trend
+
+ align:start position:0%
+long run H trend
+ 
+
+ align:start position:0%
+long run H trend
+here what is this episode so so you here
+
+ align:start position:0%
+here what is this episode so so you here
+ 
+
+ align:start position:0%
+here what is this episode so so you here
+if you if you look at this picture know
+
+ align:start position:0%
+if you if you look at this picture know
+ 
+
+ align:start position:0%
+if you if you look at this picture know
+especially the F out you are on the on
+
+ align:start position:0%
+especially the F out you are on the on
+ 
+
+ align:start position:0%
+especially the F out you are on the on
+the on the room what dominates here is
+
+ align:start position:0%
+the on the room what dominates here is
+ 
+
+ align:start position:0%
+the on the room what dominates here is
+clearly the
+
+ align:start position:0%
+clearly the
+ 
+
+ align:start position:0%
+clearly the
+trend the only action you see really
+
+ align:start position:0%
+trend the only action you see really
+ 
+
+ align:start position:0%
+trend the only action you see really
+significant action different from the
+
+ align:start position:0%
+significant action different from the
+ 
+
+ align:start position:0%
+significant action different from the
+trend is around here what happened
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there it's the Great Depression so even
+
+ align:start position:0%
+there it's the Great Depression so even
+ 
+
+ align:start position:0%
+there it's the Great Depression so even
+the Great Depression you know doesn't
+
+ align:start position:0%
+the Great Depression you know doesn't
+ 
+
+ align:start position:0%
+the Great Depression you know doesn't
+look that big relative to what the trend
+
+ align:start position:0%
+look that big relative to what the trend
+ 
+
+ align:start position:0%
+look that big relative to what the trend
+can do so
+
+ align:start position:0%
+can do so
+ 
+
+ align:start position:0%
+can do so
+of course it's very difficult to affect
+
+ align:start position:0%
+of course it's very difficult to affect
+ 
+
+ align:start position:0%
+of course it's very difficult to affect
+the trend of a country but the trend
+
+ align:start position:0%
+the trend of a country but the trend
+ 
+
+ align:start position:0%
+the trend of a country but the trend
+makes a huge difference for the welfare
+
+ align:start position:0%
+makes a huge difference for the welfare
+ 
+
+ align:start position:0%
+makes a huge difference for the welfare
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+the economic well-being of a
+
+ align:start position:0%
+the economic well-being of a
+ 
+
+ align:start position:0%
+the economic well-being of a
+country
+
+ align:start position:0%
+country
+ 
+
+ align:start position:0%
+country
+good now a lot of that is because also
+
+ align:start position:0%
+good now a lot of that is because also
+ 
+
+ align:start position:0%
+good now a lot of that is because also
+the US population grew up grew up grew
+
+ align:start position:0%
+the US population grew up grew up grew
+ 
+
+ align:start position:0%
+the US population grew up grew up grew
+up and grew a lot during this episode
+
+ align:start position:0%
+up and grew a lot during this episode
+ 
+
+ align:start position:0%
+up and grew a lot during this episode
+so often when you look at sort of long
+
+ align:start position:0%
+so often when you look at sort of long
+ 
+
+ align:start position:0%
+so often when you look at sort of long
+run Trends rather than looking at the
+
+ align:start position:0%
+run Trends rather than looking at the
+ 
+
+ align:start position:0%
+run Trends rather than looking at the
+level of GDP you tend to look at the
+
+ align:start position:0%
+level of GDP you tend to look at the
+ 
+
+ align:start position:0%
+level of GDP you tend to look at the
+level of GDP per person per capita or
+
+ align:start position:0%
+level of GDP per person per capita or
+ 
+
+ align:start position:0%
+level of GDP per person per capita or
+something like that and that picture is
+
+ align:start position:0%
+something like that and that picture is
+ 
+
+ align:start position:0%
+something like that and that picture is
+exactly the same pictures as the
+
+ align:start position:0%
+exactly the same pictures as the
+ 
+
+ align:start position:0%
+exactly the same pictures as the
+previous one but divided by population
+
+ align:start position:0%
+previous one but divided by population
+ 
+
+ align:start position:0%
+previous one but divided by population
+at each point in time okay and and and
+
+ align:start position:0%
+at each point in time okay and and and
+ 
+
+ align:start position:0%
+at each point in time okay and and and
+and that's an important over long
+
+ align:start position:0%
+and that's an important over long
+ 
+
+ align:start position:0%
+and that's an important over long
+periods of you at the business cycle
+
+ align:start position:0%
+periods of you at the business cycle
+ 
+
+ align:start position:0%
+periods of you at the business cycle
+frequency you can almost ignore changes
+
+ align:start position:0%
+frequency you can almost ignore changes
+ 
+
+ align:start position:0%
+frequency you can almost ignore changes
+in popul no Chang ination you can ignore
+
+ align:start position:0%
+in popul no Chang ination you can ignore
+ 
+
+ align:start position:0%
+in popul no Chang ination you can ignore
+completely unless you are in a war you
+
+ align:start position:0%
+completely unless you are in a war you
+ 
+
+ align:start position:0%
+completely unless you are in a war you
+can you worry about other things labor
+
+ align:start position:0%
+can you worry about other things labor
+ 
+
+ align:start position:0%
+can you worry about other things labor
+force participation and stuff like that
+
+ align:start position:0%
+force participation and stuff like that
+ 
+
+ align:start position:0%
+force participation and stuff like that
+but population is irrelevant that the
+
+ align:start position:0%
+but population is irrelevant that the
+ 
+
+ align:start position:0%
+but population is irrelevant that the
+business cycle growth is irrelevant at
+
+ align:start position:0%
+business cycle growth is irrelevant at
+ 
+
+ align:start position:0%
+business cycle growth is irrelevant at
+the business cycle frequency but not
+
+ align:start position:0%
+the business cycle frequency but not
+ 
+
+ align:start position:0%
+the business cycle frequency but not
+over long periods of time in this period
+
+ align:start position:0%
+over long periods of time in this period
+ 
+
+ align:start position:0%
+over long periods of time in this period
+here population in the US increased from
+
+ align:start position:0%
+here population in the US increased from
+ 
+
+ align:start position:0%
+here population in the US increased from
+63 million to 320 million so that's a
+
+ align:start position:0%
+63 million to 320 million so that's a
+ 
+
+ align:start position:0%
+63 million to 320 million so that's a
+lot more workers in principle that you
+
+ align:start position:0%
+lot more workers in principle that you
+ 
+
+ align:start position:0%
+lot more workers in principle that you
+have you know for that economy so a lot
+
+ align:start position:0%
+have you know for that economy so a lot
+ 
+
+ align:start position:0%
+have you know for that economy so a lot
+of that trend is explained by population
+
+ align:start position:0%
+of that trend is explained by population
+ 
+
+ align:start position:0%
+of that trend is explained by population
+growth and that's one of the reason
+
+ align:start position:0%
+growth and that's one of the reason
+ 
+
+ align:start position:0%
+growth and that's one of the reason
+sorry a lot of the trend in this picture
+
+ align:start position:0%
+sorry a lot of the trend in this picture
+ 
+
+ align:start position:0%
+sorry a lot of the trend in this picture
+here is explained by population growth
+
+ align:start position:0%
+here is explained by population growth
+ 
+
+ align:start position:0%
+here is explained by population growth
+that's one of the reasons we're in a
+
+ align:start position:0%
+that's one of the reasons we're in a
+ 
+
+ align:start position:0%
+that's one of the reasons we're in a
+tricky time in the global economy
+
+ align:start position:0%
+tricky time in the global economy
+ 
+
+ align:start position:0%
+tricky time in the global economy
+because there are many important regions
+
+ align:start position:0%
+because there are many important regions
+ 
+
+ align:start position:0%
+because there are many important regions
+of the world where population is no
+
+ align:start position:0%
+of the world where population is no
+ 
+
+ align:start position:0%
+of the world where population is no
+longer growing so we got used to a
+
+ align:start position:0%
+longer growing so we got used to a
+ 
+
+ align:start position:0%
+longer growing so we got used to a
+period in which population growth was
+
+ align:start position:0%
+period in which population growth was
+ 
+
+ align:start position:0%
+period in which population growth was
+very steady and high and now you know
+
+ align:start position:0%
+very steady and high and now you know
+ 
+
+ align:start position:0%
+very steady and high and now you know
+many parts of the world important parts
+
+ align:start position:0%
+many parts of the world important parts
+ 
+
+ align:start position:0%
+many parts of the world important parts
+of of the world have negative population
+
+ align:start position:0%
+of of the world have negative population
+ 
+
+ align:start position:0%
+of of the world have negative population
+growth Japan Korea China most of
+
+ align:start position:0%
+growth Japan Korea China most of
+ 
+
+ align:start position:0%
+growth Japan Korea China most of
+Continental Europe H even places in
+
+ align:start position:0%
+Continental Europe H even places in
+ 
+
+ align:start position:0%
+Continental Europe H even places in
+Latin America and so on so so this is a
+
+ align:start position:0%
+Latin America and so on so so this is a
+ 
+
+ align:start position:0%
+Latin America and so on so so this is a
+big change for the world
+
+ align:start position:0%
+big change for the world
+ 
+
+ align:start position:0%
+big change for the world
+but anyways during that period there was
+
+ align:start position:0%
+but anyways during that period there was
+ 
+
+ align:start position:0%
+but anyways during that period there was
+a lot of population growth and in the US
+
+ align:start position:0%
+a lot of population growth and in the US
+ 
+
+ align:start position:0%
+a lot of population growth and in the US
+in particular when again as I said
+
+ align:start position:0%
+in particular when again as I said
+ 
+
+ align:start position:0%
+in particular when again as I said
+before from 63 to 320 million so if you
+
+ align:start position:0%
+before from 63 to 320 million so if you
+ 
+
+ align:start position:0%
+before from 63 to 320 million so if you
+really want to measure sort of welfare
+
+ align:start position:0%
+really want to measure sort of welfare
+ 
+
+ align:start position:0%
+really want to measure sort of welfare
+of the economy how well how the
+
+ align:start position:0%
+of the economy how well how the
+ 
+
+ align:start position:0%
+of the economy how well how the
+well-being of
+
+ align:start position:0%
+well-being of
+ 
+
+ align:start position:0%
+well-being of
+individuals in in in in the US the
+
+ align:start position:0%
+individuals in in in in the US the
+ 
+
+ align:start position:0%
+individuals in in in in the US the
+previous picture is misleading because
+
+ align:start position:0%
+previous picture is misleading because
+ 
+
+ align:start position:0%
+previous picture is misleading because
+you have to yeah it's the final Pi is 50
+
+ align:start position:0%
+you have to yeah it's the final Pi is 50
+ 
+
+ align:start position:0%
+you have to yeah it's the final Pi is 50
+times larger than the first one than the
+
+ align:start position:0%
+times larger than the first one than the
+ 
+
+ align:start position:0%
+times larger than the first one than the
+beginning Pi but you have 320 million
+
+ align:start position:0%
+beginning Pi but you have 320 million
+ 
+
+ align:start position:0%
+beginning Pi but you have 320 million
+people to split it among as opposed to
+
+ align:start position:0%
+people to split it among as opposed to
+ 
+
+ align:start position:0%
+people to split it among as opposed to
+63 million so this picture captures that
+
+ align:start position:0%
+63 million so this picture captures that
+ 
+
+ align:start position:0%
+63 million so this picture captures that
+statistic that is often described when
+
+ align:start position:0%
+statistic that is often described when
+ 
+
+ align:start position:0%
+statistic that is often described when
+you talk about long run
+
+ align:start position:0%
+you talk about long run
+ 
+
+ align:start position:0%
+you talk about long run
+growth ER is GDP per person and you
+
+ align:start position:0%
+growth ER is GDP per person and you
+ 
+
+ align:start position:0%
+growth ER is GDP per person and you
+still see that what dominates this
+
+ align:start position:0%
+still see that what dominates this
+ 
+
+ align:start position:0%
+still see that what dominates this
+picture is a trend ER but the difference
+
+ align:start position:0%
+picture is a trend ER but the difference
+ 
+
+ align:start position:0%
+picture is a trend ER but the difference
+between this out out GDP per person in
+
+ align:start position:0%
+between this out out GDP per person in
+ 
+
+ align:start position:0%
+between this out out GDP per person in
+the US at the end of the sample versus
+
+ align:start position:0%
+the US at the end of the sample versus
+ 
+
+ align:start position:0%
+the US at the end of the sample versus
+the beginning of the sample is 10 to1
+
+ align:start position:0%
+the beginning of the sample is 10 to1
+ 
+
+ align:start position:0%
+the beginning of the sample is 10 to1
+not 50 to1 so it makes a difference
+
+ align:start position:0%
+not 50 to1 so it makes a difference
+ 
+
+ align:start position:0%
+not 50 to1 so it makes a difference
+population it's still big it's still
+
+ align:start position:0%
+population it's still big it's still
+ 
+
+ align:start position:0%
+population it's still big it's still
+what dominates this picture is that of
+
+ align:start position:0%
+what dominates this picture is that of
+ 
+
+ align:start position:0%
+what dominates this picture is that of
+course the Great Recession looks bigger
+
+ align:start position:0%
+course the Great Recession looks bigger
+ 
+
+ align:start position:0%
+course the Great Recession looks bigger
+now because you know you comparing it
+
+ align:start position:0%
+now because you know you comparing it
+ 
+
+ align:start position:0%
+now because you know you comparing it
+with with a number that grows by a
+
+ align:start position:0%
+with with a number that grows by a
+ 
+
+ align:start position:0%
+with with a number that grows by a
+factor of 10 not by a factor of 50
+
+ align:start position:0%
+factor of 10 not by a factor of 50
+ 
+
+ align:start position:0%
+factor of 10 not by a factor of 50
+that's so it looks bigger naturally know
+
+ align:start position:0%
+that's so it looks bigger naturally know
+ 
+
+ align:start position:0%
+that's so it looks bigger naturally know
+the same 30% decline output is a lot
+
+ align:start position:0%
+the same 30% decline output is a lot
+ 
+
+ align:start position:0%
+the same 30% decline output is a lot
+bigger when you're comparing it with
+
+ align:start position:0%
+bigger when you're comparing it with
+ 
+
+ align:start position:0%
+bigger when you're comparing it with
+the a factor of 10 than when you're
+
+ align:start position:0%
+the a factor of 10 than when you're
+ 
+
+ align:start position:0%
+the a factor of 10 than when you're
+comparing it with a factor of 50 but
+
+ align:start position:0%
+comparing it with a factor of 50 but
+ 
+
+ align:start position:0%
+comparing it with a factor of 50 but
+still it looks bigger but the picture is
+
+ align:start position:0%
+still it looks bigger but the picture is
+ 
+
+ align:start position:0%
+still it looks bigger but the picture is
+dominated by the
+
+ align:start position:0%
+dominated by the
+ 
+
+ align:start position:0%
+dominated by the
+so all this to say that we're going to
+
+ align:start position:0%
+so all this to say that we're going to
+ 
+
+ align:start position:0%
+so all this to say that we're going to
+study now is very important it's not
+
+ align:start position:0%
+study now is very important it's not
+ 
+
+ align:start position:0%
+study now is very important it's not
+what dominates the day-to-day news
+
+ align:start position:0%
+what dominates the day-to-day news
+ 
+
+ align:start position:0%
+what dominates the day-to-day news
+because it happens slowly and over time
+
+ align:start position:0%
+because it happens slowly and over time
+ 
+
+ align:start position:0%
+because it happens slowly and over time
+but it is very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important so how do we measure these
+
+ align:start position:0%
+important so how do we measure these
+ 
+
+ align:start position:0%
+important so how do we measure these
+things well when you're looking within a
+
+ align:start position:0%
+things well when you're looking within a
+ 
+
+ align:start position:0%
+things well when you're looking within a
+country you do reasonably well not
+
+ align:start position:0%
+country you do reasonably well not
+ 
+
+ align:start position:0%
+country you do reasonably well not
+perfect but reasonably well and perhaps
+
+ align:start position:0%
+perfect but reasonably well and perhaps
+ 
+
+ align:start position:0%
+perfect but reasonably well and perhaps
+not over periods as long as I want I
+
+ align:start position:0%
+not over periods as long as I want I
+ 
+
+ align:start position:0%
+not over periods as long as I want I
+show you by looking at GDP per capita
+
+ align:start position:0%
+show you by looking at GDP per capita
+ 
+
+ align:start position:0%
+show you by looking at GDP per capita
+that's that's fine is you measure it
+
+ align:start position:0%
+that's that's fine is you measure it
+ 
+
+ align:start position:0%
+that's that's fine is you measure it
+real GDP per capita that's about fine
+
+ align:start position:0%
+real GDP per capita that's about fine
+ 
+
+ align:start position:0%
+real GDP per capita that's about fine
+but when you compare across different
+
+ align:start position:0%
+but when you compare across different
+ 
+
+ align:start position:0%
+but when you compare across different
+regions of the world and so on those
+
+ align:start position:0%
+regions of the world and so on those
+ 
+
+ align:start position:0%
+regions of the world and so on those
+comparisons is very misleading so to say
+
+ align:start position:0%
+comparisons is very misleading so to say
+ 
+
+ align:start position:0%
+comparisons is very misleading so to say
+that the US has um I don't know
+
+ align:start position:0%
+that the US has um I don't know
+ 
+
+ align:start position:0%
+that the US has um I don't know
+ER what is the US GDP per capita today
+
+ align:start position:0%
+ER what is the US GDP per capita today
+ 
+
+ align:start position:0%
+ER what is the US GDP per capita today
+in the US somebody should check it but
+
+ align:start position:0%
+in the US somebody should check it but
+ 
+
+ align:start position:0%
+in the US somebody should check it but
+but about maybe $70,000 something like
+
+ align:start position:0%
+but about maybe $70,000 something like
+ 
+
+ align:start position:0%
+but about maybe $70,000 something like
+that I don't know ER and then then then
+
+ align:start position:0%
+that I don't know ER and then then then
+ 
+
+ align:start position:0%
+that I don't know ER and then then then
+you see a another country that has say
+
+ align:start position:0%
+you see a another country that has say
+ 
+
+ align:start position:0%
+you see a another country that has say
+Italy $50,000 per
+
+ align:start position:0%
+Italy $50,000 per
+ 
+
+ align:start position:0%
+Italy $50,000 per
+capita that comparison is not that
+
+ align:start position:0%
+capita that comparison is not that
+ 
+
+ align:start position:0%
+capita that comparison is not that
+meaningful it's indicative of something
+
+ align:start position:0%
+meaningful it's indicative of something
+ 
+
+ align:start position:0%
+meaningful it's indicative of something
+but it's not completely meaningful and
+
+ align:start position:0%
+but it's not completely meaningful and
+ 
+
+ align:start position:0%
+but it's not completely meaningful and
+I'm going to show you an example which
+
+ align:start position:0%
+I'm going to show you an example which
+ 
+
+ align:start position:0%
+I'm going to show you an example which
+is much more extreme than that but the
+
+ align:start position:0%
+is much more extreme than that but the
+ 
+
+ align:start position:0%
+is much more extreme than that but the
+reason is not very meaningful is
+
+ align:start position:0%
+reason is not very meaningful is
+ 
+
+ align:start position:0%
+reason is not very meaningful is
+essentially because the prices are not
+
+ align:start position:0%
+essentially because the prices are not
+ 
+
+ align:start position:0%
+essentially because the prices are not
+the same across different parts of the
+
+ align:start position:0%
+the same across different parts of the
+ 
+
+ align:start position:0%
+the same across different parts of the
+world so we have a method to to to to do
+
+ align:start position:0%
+world so we have a method to to to to do
+ 
+
+ align:start position:0%
+world so we have a method to to to to do
+that to to be able to compare across
+
+ align:start position:0%
+that to to be able to compare across
+ 
+
+ align:start position:0%
+that to to be able to compare across
+countries and again even for a one a
+
+ align:start position:0%
+countries and again even for a one a
+ 
+
+ align:start position:0%
+countries and again even for a one a
+given country over long long period of
+
+ align:start position:0%
+given country over long long period of
+ 
+
+ align:start position:0%
+given country over long long period of
+time we make a correction to the GDP
+
+ align:start position:0%
+time we make a correction to the GDP
+ 
+
+ align:start position:0%
+time we make a correction to the GDP
+numbers we have and we make we call them
+
+ align:start position:0%
+numbers we have and we make we call them
+ 
+
+ align:start position:0%
+numbers we have and we make we call them
+we correct them by what is called the
+
+ align:start position:0%
+we correct them by what is called the
+ 
+
+ align:start position:0%
+we correct them by what is called the
+PPP purchasing power parity and I'll
+
+ align:start position:0%
+PPP purchasing power parity and I'll
+ 
+
+ align:start position:0%
+PPP purchasing power parity and I'll
+explain what that is okay so whenever
+
+ align:start position:0%
+explain what that is okay so whenever
+ 
+
+ align:start position:0%
+explain what that is okay so whenever
+almost whenever you see comparisons of a
+
+ align:start position:0%
+almost whenever you see comparisons of a
+ 
+
+ align:start position:0%
+almost whenever you see comparisons of a
+GDP per capita across countries when
+
+ align:start position:0%
+GDP per capita across countries when
+ 
+
+ align:start position:0%
+GDP per capita across countries when
+somebody's doing a growth analysis is
+
+ align:start position:0%
+somebody's doing a growth analysis is
+ 
+
+ align:start position:0%
+somebody's doing a growth analysis is
+going to be PPP adjusted okay now let me
+
+ align:start position:0%
+going to be PPP adjusted okay now let me
+ 
+
+ align:start position:0%
+going to be PPP adjusted okay now let me
+explain the logic of
+
+ align:start position:0%
+explain the logic of
+ 
+
+ align:start position:0%
+explain the logic of
+PB
+
+ align:start position:0%
+PB
+ 
+
+ align:start position:0%
+PB
+um and and and again I said within the
+
+ align:start position:0%
+um and and and again I said within the
+ 
+
+ align:start position:0%
+um and and and again I said within the
+same country over periods perhaps not
+
+ align:start position:0%
+same country over periods perhaps not
+ 
+
+ align:start position:0%
+same country over periods perhaps not
+300 years but over periods of 40 years
+
+ align:start position:0%
+300 years but over periods of 40 years
+ 
+
+ align:start position:0%
+300 years but over periods of 40 years
+it's reasonable H to use just real GDP
+
+ align:start position:0%
+it's reasonable H to use just real GDP
+ 
+
+ align:start position:0%
+it's reasonable H to use just real GDP
+but when you start comparing sort of you
+
+ align:start position:0%
+but when you start comparing sort of you
+ 
+
+ align:start position:0%
+but when you start comparing sort of you
+know bana versus the US it gets a lot
+
+ align:start position:0%
+know bana versus the US it gets a lot
+ 
+
+ align:start position:0%
+know bana versus the US it gets a lot
+tricky trickier because there's a lot of
+
+ align:start position:0%
+tricky trickier because there's a lot of
+ 
+
+ align:start position:0%
+tricky trickier because there's a lot of
+goods that are a lot cheaper in poorer
+
+ align:start position:0%
+goods that are a lot cheaper in poorer
+ 
+
+ align:start position:0%
+goods that are a lot cheaper in poorer
+countries in particular food okay and
+
+ align:start position:0%
+countries in particular food okay and
+ 
+
+ align:start position:0%
+countries in particular food okay and
+and so so you have to be careful with
+
+ align:start position:0%
+and so so you have to be careful with
+ 
+
+ align:start position:0%
+and so so you have to be careful with
+those comparisons so I'm going to give
+
+ align:start position:0%
+those comparisons so I'm going to give
+ 
+
+ align:start position:0%
+those comparisons so I'm going to give
+you this example which is somewhat
+
+ align:start position:0%
+you this example which is somewhat
+ 
+
+ align:start position:0%
+you this example which is somewhat
+hypothetical but the numbers are not
+
+ align:start position:0%
+hypothetical but the numbers are not
+ 
+
+ align:start position:0%
+hypothetical but the numbers are not
+crazy so suppose you have a a two
+
+ align:start position:0%
+crazy so suppose you have a a two
+ 
+
+ align:start position:0%
+crazy so suppose you have a a two
+economies the US and Russia
+
+ align:start position:0%
+economies the US and Russia
+ 
+
+ align:start position:0%
+economies the US and Russia
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um anyways
+
+ align:start position:0%
+um anyways
+ 
+
+ align:start position:0%
+um anyways
+ER and suppose that that in both
+
+ align:start position:0%
+ER and suppose that that in both
+ 
+
+ align:start position:0%
+ER and suppose that that in both
+economies ER households consume houses
+
+ align:start position:0%
+economies ER households consume houses
+ 
+
+ align:start position:0%
+economies ER households consume houses
+and firms consume cars and
+
+ align:start position:0%
+and firms consume cars and
+ 
+
+ align:start position:0%
+and firms consume cars and
+food okay and suppose that the average
+
+ align:start position:0%
+food okay and suppose that the average
+ 
+
+ align:start position:0%
+food okay and suppose that the average
+consumer in the US buys one car a year
+
+ align:start position:0%
+consumer in the US buys one car a year
+ 
+
+ align:start position:0%
+consumer in the US buys one car a year
+for $10,000 and a bundle of food for
+
+ align:start position:0%
+for $10,000 and a bundle of food for
+ 
+
+ align:start position:0%
+for $10,000 and a bundle of food for
+$10,000 as well okay so the total
+
+ align:start position:0%
+$10,000 as well okay so the total
+ 
+
+ align:start position:0%
+$10,000 as well okay so the total
+expenditure in consumption for this
+
+ align:start position:0%
+expenditure in consumption for this
+ 
+
+ align:start position:0%
+expenditure in consumption for this
+household on average is about $20,000 a
+
+ align:start position:0%
+household on average is about $20,000 a
+ 
+
+ align:start position:0%
+household on average is about $20,000 a
+year that's what a US household consumes
+
+ align:start position:0%
+year that's what a US household consumes
+ 
+
+ align:start position:0%
+year that's what a US household consumes
+these numbers are fantasy numbers but
+
+ align:start position:0%
+these numbers are fantasy numbers but
+ 
+
+ align:start position:0%
+these numbers are fantasy numbers but
+the big picture is not that fantasy
+
+ align:start position:0%
+the big picture is not that fantasy
+ 
+
+ align:start position:0%
+the big picture is not that fantasy
+ER
+
+ align:start position:0%
+ER
+ 
+
+ align:start position:0%
+ER
+Russia the average consumer buys
+
+ align:start position:0%
+Russia the average consumer buys
+ 
+
+ align:start position:0%
+Russia the average consumer buys
+0.07 cars a year for 40,000 rubles and
+
+ align:start position:0%
+0.07 cars a year for 40,000 rubles and
+ 
+
+ align:start position:0%
+0.07 cars a year for 40,000 rubles and
+the same bundle of food that in the US
+
+ align:start position:0%
+the same bundle of food that in the US
+ 
+
+ align:start position:0%
+the same bundle of food that in the US
+okay same assume that same bundle of
+
+ align:start position:0%
+okay same assume that same bundle of
+ 
+
+ align:start position:0%
+okay same assume that same bundle of
+food goes for 880,000
+
+ align:start position:0%
+food goes for 880,000
+ 
+
+ align:start position:0%
+food goes for 880,000
+rubles so the total expenditure of this
+
+ align:start position:0%
+rubles so the total expenditure of this
+ 
+
+ align:start position:0%
+rubles so the total expenditure of this
+H average household in Russia is
+
+ align:start position:0%
+H average household in Russia is
+ 
+
+ align:start position:0%
+H average household in Russia is
+120,000 rubles suppose that exchange is
+
+ align:start position:0%
+120,000 rubles suppose that exchange is
+ 
+
+ align:start position:0%
+120,000 rubles suppose that exchange is
+60 rubles per dollar this thing has
+
+ align:start position:0%
+60 rubles per dollar this thing has
+ 
+
+ align:start position:0%
+60 rubles per dollar this thing has
+moved a lot recent times but suppose
+
+ align:start position:0%
+moved a lot recent times but suppose
+ 
+
+ align:start position:0%
+moved a lot recent times but suppose
+that's the the number of rubles per
+
+ align:start position:0%
+that's the the number of rubles per
+ 
+
+ align:start position:0%
+that's the the number of rubles per
+dollar so you divide $120,000 and you
+
+ align:start position:0%
+dollar so you divide $120,000 and you
+ 
+
+ align:start position:0%
+dollar so you divide $120,000 and you
+want to convert them into Dollars you
+
+ align:start position:0%
+want to convert them into Dollars you
+ 
+
+ align:start position:0%
+want to convert them into Dollars you
+divide the 120,000 rubles by 60,000
+
+ align:start position:0%
+divide the 120,000 rubles by 60,000
+ 
+
+ align:start position:0%
+divide the 120,000 rubles by 60,000
+rubles per dollar and then you get how
+
+ align:start position:0%
+rubles per dollar and then you get how
+ 
+
+ align:start position:0%
+rubles per dollar and then you get how
+much the Russians spend a Russian
+
+ align:start position:0%
+much the Russians spend a Russian
+ 
+
+ align:start position:0%
+much the Russians spend a Russian
+household on average spends on on on
+
+ align:start position:0%
+household on average spends on on on
+ 
+
+ align:start position:0%
+household on average spends on on on
+consumption in a year and and it's
+
+ align:start position:0%
+consumption in a year and and it's
+ 
+
+ align:start position:0%
+consumption in a year and and it's
+$2,000 a year okay so here you have
+
+ align:start position:0%
+$2,000 a year okay so here you have
+ 
+
+ align:start position:0%
+$2,000 a year okay so here you have
+120,000 divided by 60 is 2,000 that's
+
+ align:start position:0%
+120,000 divided by 60 is 2,000 that's
+ 
+
+ align:start position:0%
+120,000 divided by 60 is 2,000 that's
+the number of dollar
+
+ align:start position:0%
+the number of dollar
+ 
+
+ align:start position:0%
+the number of dollar
+that an average household in Russia
+
+ align:start position:0%
+that an average household in Russia
+ 
+
+ align:start position:0%
+that an average household in Russia
+consumes so the question
+
+ align:start position:0%
+consumes so the question
+ 
+
+ align:start position:0%
+consumes so the question
+is you have a US household spends
+
+ align:start position:0%
+is you have a US household spends
+ 
+
+ align:start position:0%
+is you have a US household spends
+$20,000 a year a Russian household
+
+ align:start position:0%
+$20,000 a year a Russian household
+ 
+
+ align:start position:0%
+$20,000 a year a Russian household
+spends $22,000 a year and the question
+
+ align:start position:0%
+spends $22,000 a year and the question
+ 
+
+ align:start position:0%
+spends $22,000 a year and the question
+is then is Russia 10 times poorer than
+
+ align:start position:0%
+is then is Russia 10 times poorer than
+ 
+
+ align:start position:0%
+is then is Russia 10 times poorer than
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+US
+
+ align:start position:0%
+US
+ 
+
+ align:start position:0%
+US
+okay that if you were to compare real
+
+ align:start position:0%
+okay that if you were to compare real
+ 
+
+ align:start position:0%
+okay that if you were to compare real
+GDP that would be answer so yeah they
+
+ align:start position:0%
+GDP that would be answer so yeah they
+ 
+
+ align:start position:0%
+GDP that would be answer so yeah they
+and it's true if you look at a again in
+
+ align:start position:0%
+and it's true if you look at a again in
+ 
+
+ align:start position:0%
+and it's true if you look at a again in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+example if you look at the at the real
+
+ align:start position:0%
+example if you look at the at the real
+ 
+
+ align:start position:0%
+example if you look at the at the real
+GDP numbers of on the same year
+
+ align:start position:0%
+GDP numbers of on the same year
+ 
+
+ align:start position:0%
+GDP numbers of on the same year
+converted all into dollars that answer
+
+ align:start position:0%
+converted all into dollars that answer
+ 
+
+ align:start position:0%
+converted all into dollars that answer
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+correct but it doesn't represent the
+
+ align:start position:0%
+correct but it doesn't represent the
+ 
+
+ align:start position:0%
+correct but it doesn't represent the
+point is that it doesn't represent
+
+ align:start position:0%
+point is that it doesn't represent
+ 
+
+ align:start position:0%
+point is that it doesn't represent
+really The Well beinging of the average
+
+ align:start position:0%
+really The Well beinging of the average
+ 
+
+ align:start position:0%
+really The Well beinging of the average
+household in Russia for this reason at
+
+ align:start position:0%
+household in Russia for this reason at
+ 
+
+ align:start position:0%
+household in Russia for this reason at
+least why not well
+
+ align:start position:0%
+least why not well
+ 
+
+ align:start position:0%
+least why not well
+let's what you ultimately matter is how
+
+ align:start position:0%
+let's what you ultimately matter is how
+ 
+
+ align:start position:0%
+let's what you ultimately matter is how
+much real Goods the house
+
+ align:start position:0%
+much real Goods the house
+ 
+
+ align:start position:0%
+much real Goods the house
+consumes that's what really matters I
+
+ align:start position:0%
+consumes that's what really matters I
+ 
+
+ align:start position:0%
+consumes that's what really matters I
+mean if you live in a country where the
+
+ align:start position:0%
+mean if you live in a country where the
+ 
+
+ align:start position:0%
+mean if you live in a country where the
+price of everything is zero your
+
+ align:start position:0%
+price of everything is zero your
+ 
+
+ align:start position:0%
+price of everything is zero your
+consumption expenditure consumption will
+
+ align:start position:0%
+consumption expenditure consumption will
+ 
+
+ align:start position:0%
+consumption expenditure consumption will
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+zero but that doesn't mean that you are
+
+ align:start position:0%
+zero but that doesn't mean that you are
+ 
+
+ align:start position:0%
+zero but that doesn't mean that you are
+as unhappy as somebody that consumes
+
+ align:start position:0%
+as unhappy as somebody that consumes
+ 
+
+ align:start position:0%
+as unhappy as somebody that consumes
+zero you're consuming whatever it is it
+
+ align:start position:0%
+zero you're consuming whatever it is it
+ 
+
+ align:start position:0%
+zero you're consuming whatever it is it
+happens the prices tend to be very low
+
+ align:start position:0%
+happens the prices tend to be very low
+ 
+
+ align:start position:0%
+happens the prices tend to be very low
+and that's essentially the story here as
+
+ align:start position:0%
+and that's essentially the story here as
+ 
+
+ align:start position:0%
+and that's essentially the story here as
+I said before it tends to be the case
+
+ align:start position:0%
+I said before it tends to be the case
+ 
+
+ align:start position:0%
+I said before it tends to be the case
+that in poorer countries a lot of things
+
+ align:start position:0%
+that in poorer countries a lot of things
+ 
+
+ align:start position:0%
+that in poorer countries a lot of things
+are cheaper there is certain very high
+
+ align:start position:0%
+are cheaper there is certain very high
+ 
+
+ align:start position:0%
+are cheaper there is certain very high
+tech things that that are not even
+
+ align:start position:0%
+tech things that that are not even
+ 
+
+ align:start position:0%
+tech things that that are not even
+consumed in poorer countries so you have
+
+ align:start position:0%
+consumed in poorer countries so you have
+ 
+
+ align:start position:0%
+consumed in poorer countries so you have
+to adjust for that as well but a lot of
+
+ align:start position:0%
+to adjust for that as well but a lot of
+ 
+
+ align:start position:0%
+to adjust for that as well but a lot of
+the regular things the bulk of the
+
+ align:start position:0%
+the regular things the bulk of the
+ 
+
+ align:start position:0%
+the regular things the bulk of the
+purchases tend to be a lot cheaper in
+
+ align:start position:0%
+purchases tend to be a lot cheaper in
+ 
+
+ align:start position:0%
+purchases tend to be a lot cheaper in
+poorer countries and that's exactly what
+
+ align:start position:0%
+poorer countries and that's exactly what
+ 
+
+ align:start position:0%
+poorer countries and that's exactly what
+is behind the reason why in this example
+
+ align:start position:0%
+is behind the reason why in this example
+ 
+
+ align:start position:0%
+is behind the reason why in this example
+the answer is
+
+ align:start position:0%
+the answer is
+ 
+
+ align:start position:0%
+the answer is
+no it's not true that the Russians are
+
+ align:start position:0%
+no it's not true that the Russians are
+ 
+
+ align:start position:0%
+no it's not true that the Russians are
+10 time that Russian household in this
+
+ align:start position:0%
+10 time that Russian household in this
+ 
+
+ align:start position:0%
+10 time that Russian household in this
+example is 10 times poorer than the US
+
+ align:start position:0%
+example is 10 times poorer than the US
+ 
+
+ align:start position:0%
+example is 10 times poorer than the US
+let's check it so that's our
+
+ align:start position:0%
+let's check it so that's our
+ 
+
+ align:start position:0%
+let's check it so that's our
+example and I said no so fast
+
+ align:start position:0%
+example and I said no so fast
+ 
+
+ align:start position:0%
+example and I said no so fast
+let's use so assume that the goods are
+
+ align:start position:0%
+let's use so assume that the goods are
+ 
+
+ align:start position:0%
+let's use so assume that the goods are
+the same so the cars that the Russians
+
+ align:start position:0%
+the same so the cars that the Russians
+ 
+
+ align:start position:0%
+the same so the cars that the Russians
+buy is the same as the as the cars that
+
+ align:start position:0%
+buy is the same as the as the cars that
+ 
+
+ align:start position:0%
+buy is the same as the as the cars that
+the US households buy that was
+
+ align:start position:0%
+the US households buy that was
+ 
+
+ align:start position:0%
+the US households buy that was
+truer a few months ago than now but but
+
+ align:start position:0%
+truer a few months ago than now but but
+ 
+
+ align:start position:0%
+truer a few months ago than now but but
+assume that's the case it's just that
+
+ align:start position:0%
+assume that's the case it's just that
+ 
+
+ align:start position:0%
+assume that's the case it's just that
+the Russians by you know change their
+
+ align:start position:0%
+the Russians by you know change their
+ 
+
+ align:start position:0%
+the Russians by you know change their
+cars less frequently in this example the
+
+ align:start position:0%
+cars less frequently in this example the
+ 
+
+ align:start position:0%
+cars less frequently in this example the
+US household is changing the car once a
+
+ align:start position:0%
+US household is changing the car once a
+ 
+
+ align:start position:0%
+US household is changing the car once a
+year while while while the Russians are
+
+ align:start position:0%
+year while while while the Russians are
+ 
+
+ align:start position:0%
+year while while while the Russians are
+changing the car you know less than once
+
+ align:start position:0%
+changing the car you know less than once
+ 
+
+ align:start position:0%
+changing the car you know less than once
+every 10 year one every 15 years or
+
+ align:start position:0%
+every 10 year one every 15 years or
+ 
+
+ align:start position:0%
+every 10 year one every 15 years or
+so let's assume also that the the bundle
+
+ align:start position:0%
+so let's assume also that the the bundle
+ 
+
+ align:start position:0%
+so let's assume also that the the bundle
+of the of food is exactly the same in
+
+ align:start position:0%
+of the of food is exactly the same in
+ 
+
+ align:start position:0%
+of the of food is exactly the same in
+both Place places so since the car is
+
+ align:start position:0%
+both Place places so since the car is
+ 
+
+ align:start position:0%
+both Place places so since the car is
+the same and the and the and the and the
+
+ align:start position:0%
+the same and the and the and the and the
+ 
+
+ align:start position:0%
+the same and the and the and the and the
+bundle of food is the same I can use us
+
+ align:start position:0%
+bundle of food is the same I can use us
+ 
+
+ align:start position:0%
+bundle of food is the same I can use us
+prices to
+
+ align:start position:0%
+prices to
+ 
+
+ align:start position:0%
+prices to
+measure Uh Russian consumption and
+
+ align:start position:0%
+measure Uh Russian consumption and
+ 
+
+ align:start position:0%
+measure Uh Russian consumption and
+that's is comparable to what us
+
+ align:start position:0%
+that's is comparable to what us
+ 
+
+ align:start position:0%
+that's is comparable to what us
+consumption is because I'm taking I'm
+
+ align:start position:0%
+consumption is because I'm taking I'm
+ 
+
+ align:start position:0%
+consumption is because I'm taking I'm
+trying to convert the goods they're
+
+ align:start position:0%
+trying to convert the goods they're
+ 
+
+ align:start position:0%
+trying to convert the goods they're
+consuming into something is comparable
+
+ align:start position:0%
+consuming into something is comparable
+ 
+
+ align:start position:0%
+consuming into something is comparable
+to what the US consumes since the goods
+
+ align:start position:0%
+to what the US consumes since the goods
+ 
+
+ align:start position:0%
+to what the US consumes since the goods
+themselves are the same if I value them
+
+ align:start position:0%
+themselves are the same if I value them
+ 
+
+ align:start position:0%
+themselves are the same if I value them
+at the same price either of the two
+
+ align:start position:0%
+at the same price either of the two
+ 
+
+ align:start position:0%
+at the same price either of the two
+prices but at the same prices then I'm
+
+ align:start position:0%
+prices but at the same prices then I'm
+ 
+
+ align:start position:0%
+prices but at the same prices then I'm
+going to be able to make the comparison
+
+ align:start position:0%
+going to be able to make the comparison
+ 
+
+ align:start position:0%
+going to be able to make the comparison
+I really want that's what purchase power
+
+ align:start position:0%
+I really want that's what purchase power
+ 
+
+ align:start position:0%
+I really want that's what purchase power
+PVP adjustment means okay so look at our
+
+ align:start position:0%
+PVP adjustment means okay so look at our
+ 
+
+ align:start position:0%
+PVP adjustment means okay so look at our
+particular example here the Russian
+
+ align:start position:0%
+particular example here the Russian
+ 
+
+ align:start position:0%
+particular example here the Russian
+would household would be consuming 0.07
+
+ align:start position:0%
+would household would be consuming 0.07
+ 
+
+ align:start position:0%
+would household would be consuming 0.07
+cars times 10,000 dollar which is the
+
+ align:start position:0%
+cars times 10,000 dollar which is the
+ 
+
+ align:start position:0%
+cars times 10,000 dollar which is the
+price of a car plus one unit of of the
+
+ align:start position:0%
+price of a car plus one unit of of the
+ 
+
+ align:start position:0%
+price of a car plus one unit of of the
+bundle of of of of food and the price us
+
+ align:start position:0%
+bundle of of of of food and the price us
+ 
+
+ align:start position:0%
+bundle of of of of food and the price us
+price is 10,000 for that so the total
+
+ align:start position:0%
+price is 10,000 for that so the total
+ 
+
+ align:start position:0%
+price is 10,000 for that so the total
+consumption of the household PPP
+
+ align:start position:0%
+consumption of the household PPP
+ 
+
+ align:start position:0%
+consumption of the household PPP
+adjusted the Russian household is
+
+ align:start position:0%
+adjusted the Russian household is
+ 
+
+ align:start position:0%
+adjusted the Russian household is
+10,700 okay that's not one10 it's
+
+ align:start position:0%
+10,700 okay that's not one10 it's
+ 
+
+ align:start position:0%
+10,700 okay that's not one10 it's
+53% of us consumption so true Russian
+
+ align:start position:0%
+53% of us consumption so true Russian
+ 
+
+ align:start position:0%
+53% of us consumption so true Russian
+household is poorer than than than than
+
+ align:start position:0%
+household is poorer than than than than
+ 
+
+ align:start position:0%
+household is poorer than than than than
+an average US household but it's not 10
+
+ align:start position:0%
+an average US household but it's not 10
+ 
+
+ align:start position:0%
+an average US household but it's not 10
+poor no it has it's
+
+ align:start position:0%
+poor no it has it's
+ 
+
+ align:start position:0%
+poor no it has it's
+a is
+
+ align:start position:0%
+a is
+ 
+
+ align:start position:0%
+a is
+53% uh as rich as the US household okay
+
+ align:start position:0%
+53% uh as rich as the US household okay
+ 
+
+ align:start position:0%
+53% uh as rich as the US household okay
+and so this is big and all the numbers
+
+ align:start position:0%
+and so this is big and all the numbers
+ 
+
+ align:start position:0%
+and so this is big and all the numbers
+I'm going to show you next especially
+
+ align:start position:0%
+I'm going to show you next especially
+ 
+
+ align:start position:0%
+I'm going to show you next especially
+when we compare across sort of countries
+
+ align:start position:0%
+when we compare across sort of countries
+ 
+
+ align:start position:0%
+when we compare across sort of countries
+that are very different in terms of
+
+ align:start position:0%
+that are very different in terms of
+ 
+
+ align:start position:0%
+that are very different in terms of
+level of development and so on have
+
+ align:start position:0%
+level of development and so on have
+ 
+
+ align:start position:0%
+level of development and so on have
+these kind of Corrections built in okay
+
+ align:start position:0%
+these kind of Corrections built in okay
+ 
+
+ align:start position:0%
+these kind of Corrections built in okay
+if you need the data for these kind of
+
+ align:start position:0%
+if you need the data for these kind of
+ 
+
+ align:start position:0%
+if you need the data for these kind of
+things for whatever reason you find them
+
+ align:start position:0%
+things for whatever reason you find them
+ 
+
+ align:start position:0%
+things for whatever reason you find them
+in what is called the pen tables the pen
+
+ align:start position:0%
+in what is called the pen tables the pen
+ 
+
+ align:start position:0%
+in what is called the pen tables the pen
+tables essentially collects all the
+
+ align:start position:0%
+tables essentially collects all the
+ 
+
+ align:start position:0%
+tables essentially collects all the
+national accounts of all places and
+
+ align:start position:0%
+national accounts of all places and
+ 
+
+ align:start position:0%
+national accounts of all places and
+makes these
+
+ align:start position:0%
+makes these
+ 
+
+ align:start position:0%
+makes these
+Corrections the problem is they don't
+
+ align:start position:0%
+Corrections the problem is they don't
+ 
+
+ align:start position:0%
+Corrections the problem is they don't
+have update them very frequently but but
+
+ align:start position:0%
+have update them very frequently but but
+ 
+
+ align:start position:0%
+have update them very frequently but but
+if you look in Fred for example which
+
+ align:start position:0%
+if you look in Fred for example which
+ 
+
+ align:start position:0%
+if you look in Fred for example which
+you use in one of the p sets there will
+
+ align:start position:0%
+you use in one of the p sets there will
+ 
+
+ align:start position:0%
+you use in one of the p sets there will
+be numbers for a few countries that have
+
+ align:start position:0%
+be numbers for a few countries that have
+ 
+
+ align:start position:0%
+be numbers for a few countries that have
+this um PPP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+adjustment okay so that that's that's
+
+ align:start position:0%
+adjustment okay so that that's that's
+ 
+
+ align:start position:0%
+adjustment okay so that that's that's
+going to remain in the background now
+
+ align:start position:0%
+going to remain in the background now
+ 
+
+ align:start position:0%
+going to remain in the background now
+but I just wanted to tell you how how
+
+ align:start position:0%
+but I just wanted to tell you how how
+ 
+
+ align:start position:0%
+but I just wanted to tell you how how
+you construct numbers when you want to
+
+ align:start position:0%
+you construct numbers when you want to
+ 
+
+ align:start position:0%
+you construct numbers when you want to
+talk about long run and comparison
+
+ align:start position:0%
+talk about long run and comparison
+ 
+
+ align:start position:0%
+talk about long run and comparison
+across
+
+ align:start position:0%
+across
+ 
+
+ align:start position:0%
+across
+countries first set of numbers here look
+
+ align:start position:0%
+countries first set of numbers here look
+ 
+
+ align:start position:0%
+countries first set of numbers here look
+at these are obviously all today at
+
+ align:start position:0%
+at these are obviously all today at
+ 
+
+ align:start position:0%
+at these are obviously all today at
+least develop economies look at the
+
+ align:start position:0%
+least develop economies look at the
+ 
+
+ align:start position:0%
+least develop economies look at the
+growth between 1950 2017 obviously the
+
+ align:start position:0%
+growth between 1950 2017 obviously the
+ 
+
+ align:start position:0%
+growth between 1950 2017 obviously the
+war created a big mess there but before
+
+ align:start position:0%
+war created a big mess there but before
+ 
+
+ align:start position:0%
+war created a big mess there but before
+that so let's start from
+
+ align:start position:0%
+that so let's start from
+ 
+
+ align:start position:0%
+that so let's start from
+1950 and what you see here is you know
+
+ align:start position:0%
+1950 and what you see here is you know
+ 
+
+ align:start position:0%
+1950 and what you see here is you know
+France on average during this period
+
+ align:start position:0%
+France on average during this period
+ 
+
+ align:start position:0%
+France on average during this period
+France grew 2017 I think is the last yes
+
+ align:start position:0%
+France grew 2017 I think is the last yes
+ 
+
+ align:start position:0%
+France grew 2017 I think is the last yes
+it's the last
+
+ align:start position:0%
+it's the last
+ 
+
+ align:start position:0%
+it's the last
+year I think they were recently updated
+
+ align:start position:0%
+year I think they were recently updated
+ 
+
+ align:start position:0%
+year I think they were recently updated
+but at least when the book was published
+
+ align:start position:0%
+but at least when the book was published
+ 
+
+ align:start position:0%
+but at least when the book was published
+that was the last year they had pen
+
+ align:start position:0%
+that was the last year they had pen
+ 
+
+ align:start position:0%
+that was the last year they had pen
+tables for but
+
+ align:start position:0%
+tables for but
+ 
+
+ align:start position:0%
+tables for but
+um er France grew on average 2.6% per
+
+ align:start position:0%
+um er France grew on average 2.6% per
+ 
+
+ align:start position:0%
+um er France grew on average 2.6% per
+year on average they also had a business
+
+ align:start position:0%
+year on average they also had a business
+ 
+
+ align:start position:0%
+year on average they also had a business
+cycle and so on but on average 2.6% per
+
+ align:start position:0%
+cycle and so on but on average 2.6% per
+ 
+
+ align:start position:0%
+cycle and so on but on average 2.6% per
+year Japan during this period grew by
+
+ align:start position:0%
+year Japan during this period grew by
+ 
+
+ align:start position:0%
+year Japan during this period grew by
+four four
+
+ align:start position:0%
+four four
+ 
+
+ align:start position:0%
+four four
+4.1% the UK 2.1% the US 2% so the
+
+ align:start position:0%
+4.1% the UK 2.1% the US 2% so the
+ 
+
+ align:start position:0%
+4.1% the UK 2.1% the US 2% so the
+developed World essentially grew around
+
+ align:start position:0%
+developed World essentially grew around
+ 
+
+ align:start position:0%
+developed World essentially grew around
+2.7% on average during this
+
+ align:start position:0%
+2.7% on average during this
+ 
+
+ align:start position:0%
+2.7% on average during this
+period look at the effect that that this
+
+ align:start position:0%
+period look at the effect that that this
+ 
+
+ align:start position:0%
+period look at the effect that that this
+has on on the level of GDP per per per
+
+ align:start position:0%
+has on on the level of GDP per per per
+ 
+
+ align:start position:0%
+has on on the level of GDP per per per
+per person and all this PPP
+
+ align:start position:0%
+per person and all this PPP
+ 
+
+ align:start position:0%
+per person and all this PPP
+adjusted ER for the case of
+
+ align:start position:0%
+adjusted ER for the case of
+ 
+
+ align:start position:0%
+adjusted ER for the case of
+France 5.6 times so they started with
+
+ align:start position:0%
+France 5.6 times so they started with
+ 
+
+ align:start position:0%
+France 5.6 times so they started with
+$7,000 and they were close to $40,000 in
+
+ align:start position:0%
+$7,000 and they were close to $40,000 in
+ 
+
+ align:start position:0%
+$7,000 and they were close to $40,000 in
+2017 so the r is RA
+
+ align:start position:0%
+2017 so the r is RA
+ 
+
+ align:start position:0%
+2017 so the r is RA
+5.6 look at the US the US is 2% and that
+
+ align:start position:0%
+5.6 look at the US the US is 2% and that
+ 
+
+ align:start position:0%
+5.6 look at the US the US is 2% and that
+ratio is is still richer than France per
+
+ align:start position:0%
+ratio is is still richer than France per
+ 
+
+ align:start position:0%
+ratio is is still richer than France per
+per person in
+
+ align:start position:0%
+per person in
+ 
+
+ align:start position:0%
+per person in
+2017 but but the ratio of that to that
+
+ align:start position:0%
+2017 but but the ratio of that to that
+ 
+
+ align:start position:0%
+2017 but but the ratio of that to that
+is smaller than that so over a long
+
+ align:start position:0%
+is smaller than that so over a long
+ 
+
+ align:start position:0%
+is smaller than that so over a long
+period of time that's what a trend in
+
+ align:start position:0%
+period of time that's what a trend in
+ 
+
+ align:start position:0%
+period of time that's what a trend in
+the picture capture a small difference
+
+ align:start position:0%
+the picture capture a small difference
+ 
+
+ align:start position:0%
+the picture capture a small difference
+in the rate of growth if they are
+
+ align:start position:0%
+in the rate of growth if they are
+ 
+
+ align:start position:0%
+in the rate of growth if they are
+sustained for a long period of time can
+
+ align:start position:0%
+sustained for a long period of time can
+ 
+
+ align:start position:0%
+sustained for a long period of time can
+make quite a bit of difference for the
+
+ align:start position:0%
+make quite a bit of difference for the
+ 
+
+ align:start position:0%
+make quite a bit of difference for the
+change in in GDP okay and so what do you
+
+ align:start position:0%
+change in in GDP okay and so what do you
+ 
+
+ align:start position:0%
+change in in GDP okay and so what do you
+what is the first what is the p is I
+
+ align:start position:0%
+what is the first what is the p is I
+ 
+
+ align:start position:0%
+what is the first what is the p is I
+mean let's find the pattern here here
+
+ align:start position:0%
+mean let's find the pattern here here
+ 
+
+ align:start position:0%
+mean let's find the pattern here here
+there's a very clear pattern in that
+
+ align:start position:0%
+there's a very clear pattern in that
+ 
+
+ align:start position:0%
+there's a very clear pattern in that
+picture in that table what is it do you
+
+ align:start position:0%
+picture in that table what is it do you
+ 
+
+ align:start position:0%
+picture in that table what is it do you
+can you spot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it I hadn't
+
+ align:start position:0%
+it I hadn't
+ 
+
+ align:start position:0%
+it I hadn't
+actually realized it when I was looking
+
+ align:start position:0%
+actually realized it when I was looking
+ 
+
+ align:start position:0%
+actually realized it when I was looking
+at my notes and then I realized is very
+
+ align:start position:0%
+at my notes and then I realized is very
+ 
+
+ align:start position:0%
+at my notes and then I realized is very
+clear in this table that's the reason I
+
+ align:start position:0%
+clear in this table that's the reason I
+ 
+
+ align:start position:0%
+clear in this table that's the reason I
+added this line I updated the slide this
+
+ align:start position:0%
+added this line I updated the slide this
+ 
+
+ align:start position:0%
+added this line I updated the slide this
+morning do you see a pattern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes the higher growth rate have a higher
+
+ align:start position:0%
+yes the higher growth rate have a higher
+ 
+
+ align:start position:0%
+yes the higher growth rate have a higher
+multiple yeah well that's yes that but
+
+ align:start position:0%
+multiple yeah well that's yes that but
+ 
+
+ align:start position:0%
+multiple yeah well that's yes that but
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+math okay which is so it's a true
+
+ align:start position:0%
+math okay which is so it's a true
+ 
+
+ align:start position:0%
+math okay which is so it's a true
+statement but that's just
+
+ align:start position:0%
+statement but that's just
+ 
+
+ align:start position:0%
+statement but that's just
+math there's an economic thing that that
+
+ align:start position:0%
+math there's an economic thing that that
+ 
+
+ align:start position:0%
+math there's an economic thing that that
+that I want
+
+ align:start position:0%
+that I want
+ 
+
+ align:start position:0%
+that I want
+to so so you're right but but I want
+
+ align:start position:0%
+to so so you're right but but I want
+ 
+
+ align:start position:0%
+to so so you're right but but I want
+they should have clarified there's an
+
+ align:start position:0%
+they should have clarified there's an
+ 
+
+ align:start position:0%
+they should have clarified there's an
+economic pattern there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let let me simplify just look at these
+
+ align:start position:0%
+let let me simplify just look at these
+ 
+
+ align:start position:0%
+let let me simplify just look at these
+two columns because a higher number here
+
+ align:start position:0%
+two columns because a higher number here
+ 
+
+ align:start position:0%
+two columns because a higher number here
+simply sorry a higher number here simply
+
+ align:start position:0%
+simply sorry a higher number here simply
+ 
+
+ align:start position:0%
+simply sorry a higher number here simply
+means that you had a higher rate of
+
+ align:start position:0%
+means that you had a higher rate of
+ 
+
+ align:start position:0%
+means that you had a higher rate of
+growth that's your math fact so ignore
+
+ align:start position:0%
+growth that's your math fact so ignore
+ 
+
+ align:start position:0%
+growth that's your math fact so ignore
+this column what I suggest is that you
+
+ align:start position:0%
+this column what I suggest is that you
+ 
+
+ align:start position:0%
+this column what I suggest is that you
+just look at these two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+columns do you see a
+
+ align:start position:0%
+columns do you see a
+ 
+
+ align:start position:0%
+columns do you see a
+pattern just look at these two columns
+
+ align:start position:0%
+pattern just look at these two columns
+ 
+
+ align:start position:0%
+pattern just look at these two columns
+this one in a sense just repeats
+
+ align:start position:0%
+this one in a sense just repeats
+ 
+
+ align:start position:0%
+this one in a sense just repeats
+information that is here for the reason
+
+ align:start position:0%
+information that is here for the reason
+ 
+
+ align:start position:0%
+information that is here for the reason
+you describe but just look at these two
+
+ align:start position:0%
+you describe but just look at these two
+ 
+
+ align:start position:0%
+you describe but just look at these two
+columns is there a pattern
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there exactly very important Richard
+
+ align:start position:0%
+there exactly very important Richard
+ 
+
+ align:start position:0%
+there exactly very important Richard
+countri sent to grow slower the richest
+
+ align:start position:0%
+countri sent to grow slower the richest
+ 
+
+ align:start position:0%
+countri sent to grow slower the richest
+country here is the US had the lowest
+
+ align:start position:0%
+country here is the US had the lowest
+ 
+
+ align:start position:0%
+country here is the US had the lowest
+rate of growth on
+
+ align:start position:0%
+rate of growth on
+ 
+
+ align:start position:0%
+rate of growth on
+average the poorest was Japan there and
+
+ align:start position:0%
+average the poorest was Japan there and
+ 
+
+ align:start position:0%
+average the poorest was Japan there and
+they had the highest rate of growth okay
+
+ align:start position:0%
+they had the highest rate of growth okay
+ 
+
+ align:start position:0%
+they had the highest rate of growth okay
+so that's a very important correlation
+
+ align:start position:0%
+so that's a very important correlation
+ 
+
+ align:start position:0%
+so that's a very important correlation
+and again the first model we're going to
+
+ align:start position:0%
+and again the first model we're going to
+ 
+
+ align:start position:0%
+and again the first model we're going to
+see of economic growth is going to
+
+ align:start position:0%
+see of economic growth is going to
+ 
+
+ align:start position:0%
+see of economic growth is going to
+explain that correlation why is that we
+
+ align:start position:0%
+explain that correlation why is that we
+ 
+
+ align:start position:0%
+explain that correlation why is that we
+see
+
+ align:start position:0%
+see
+ 
+
+ align:start position:0%
+see
+that those were for five economy you
+
+ align:start position:0%
+that those were for five economy you
+ 
+
+ align:start position:0%
+that those were for five economy you
+could say it's an accident but look at
+
+ align:start position:0%
+could say it's an accident but look at
+ 
+
+ align:start position:0%
+could say it's an accident but look at
+this this this is just a this is rich
+
+ align:start position:0%
+this this this is just a this is rich
+ 
+
+ align:start position:0%
+this this this is just a this is rich
+countries in general since 1950s and you
+
+ align:start position:0%
+countries in general since 1950s and you
+ 
+
+ align:start position:0%
+countries in general since 1950s and you
+look at here in this axis you have the
+
+ align:start position:0%
+look at here in this axis you have the
+ 
+
+ align:start position:0%
+look at here in this axis you have the
+annual rate of growth the average rate
+
+ align:start position:0%
+annual rate of growth the average rate
+ 
+
+ align:start position:0%
+annual rate of growth the average rate
+of growth and here the GDP per person in
+
+ align:start position:0%
+of growth and here the GDP per person in
+ 
+
+ align:start position:0%
+of growth and here the GDP per person in
+1950 so at the beginning of the sample
+
+ align:start position:0%
+1950 so at the beginning of the sample
+ 
+
+ align:start position:0%
+1950 so at the beginning of the sample
+1950 these countries had have this level
+
+ align:start position:0%
+1950 these countries had have this level
+ 
+
+ align:start position:0%
+1950 these countries had have this level
+of GDP per capita and then here is the
+
+ align:start position:0%
+of GDP per capita and then here is the
+ 
+
+ align:start position:0%
+of GDP per capita and then here is the
+rate of growth on average from 1950 to
+
+ align:start position:0%
+rate of growth on average from 1950 to
+ 
+
+ align:start position:0%
+rate of growth on average from 1950 to
+1987 and it's very clear there that
+
+ align:start position:0%
+1987 and it's very clear there that
+ 
+
+ align:start position:0%
+1987 and it's very clear there that
+there's a downward sloping pattern no so
+
+ align:start position:0%
+there's a downward sloping pattern no so
+ 
+
+ align:start position:0%
+there's a downward sloping pattern no so
+that's the same fact now for many more
+
+ align:start position:0%
+that's the same fact now for many more
+ 
+
+ align:start position:0%
+that's the same fact now for many more
+countries there's a downward sloping
+
+ align:start position:0%
+countries there's a downward sloping
+ 
+
+ align:start position:0%
+countries there's a downward sloping
+relationship really the richest
+
+ align:start position:0%
+relationship really the richest
+ 
+
+ align:start position:0%
+relationship really the richest
+countries tend to grow much slower than
+
+ align:start position:0%
+countries tend to grow much slower than
+ 
+
+ align:start position:0%
+countries tend to grow much slower than
+the countries were poorer at the
+
+ align:start position:0%
+the countries were poorer at the
+ 
+
+ align:start position:0%
+the countries were poorer at the
+beginning of the
+
+ align:start position:0%
+beginning of the
+ 
+
+ align:start position:0%
+beginning of the
+sample
+
+ align:start position:0%
+sample
+ 
+
+ align:start position:0%
+sample
+okay there are some interesting
+
+ align:start position:0%
+okay there are some interesting
+ 
+
+ align:start position:0%
+okay there are some interesting
+liers like Mexico and and is an
+
+ align:start position:0%
+liers like Mexico and and is an
+ 
+
+ align:start position:0%
+liers like Mexico and and is an
+interesting in itself I'm not going to
+
+ align:start position:0%
+interesting in itself I'm not going to
+ 
+
+ align:start position:0%
+interesting in itself I'm not going to
+say a lot about why that's the case
+
+ align:start position:0%
+say a lot about why that's the case
+ 
+
+ align:start position:0%
+say a lot about why that's the case
+but but but let me for now stick to the
+
+ align:start position:0%
+but but but let me for now stick to the
+ 
+
+ align:start position:0%
+but but but let me for now stick to the
+to the pattern the dominant pattern
+
+ align:start position:0%
+to the pattern the dominant pattern
+ 
+
+ align:start position:0%
+to the pattern the dominant pattern
+which is is a downward sloping
+
+ align:start position:0%
+which is is a downward sloping
+ 
+
+ align:start position:0%
+which is is a downward sloping
+relationship that's another way of
+
+ align:start position:0%
+relationship that's another way of
+ 
+
+ align:start position:0%
+relationship that's another way of
+seeing it and this is for just a bigger
+
+ align:start position:0%
+seeing it and this is for just a bigger
+ 
+
+ align:start position:0%
+seeing it and this is for just a bigger
+variety of countries I have Botana China
+
+ align:start position:0%
+variety of countries I have Botana China
+ 
+
+ align:start position:0%
+variety of countries I have Botana China
+Thailand and so on and and you see here
+
+ align:start position:0%
+Thailand and so on and and you see here
+ 
+
+ align:start position:0%
+Thailand and so on and and you see here
+GDP at the beginning of the 1950 and GDP
+
+ align:start position:0%
+GDP at the beginning of the 1950 and GDP
+ 
+
+ align:start position:0%
+GDP at the beginning of the 1950 and GDP
+rate
+
+ align:start position:0%
+rate
+ 
+
+ align:start position:0%
+rate
+2018 and the pattern here which is
+
+ align:start position:0%
+2018 and the pattern here which is
+ 
+
+ align:start position:0%
+2018 and the pattern here which is
+essentially a repetition of the pattern
+
+ align:start position:0%
+essentially a repetition of the pattern
+ 
+
+ align:start position:0%
+essentially a repetition of the pattern
+that I showed you before is that there
+
+ align:start position:0%
+that I showed you before is that there
+ 
+
+ align:start position:0%
+that I showed you before is that there
+is much more compression here than
+
+ align:start position:0%
+is much more compression here than
+ 
+
+ align:start position:0%
+is much more compression here than
+here how can you have more compression
+
+ align:start position:0%
+here how can you have more compression
+ 
+
+ align:start position:0%
+here how can you have more compression
+here than here well because there is
+
+ align:start position:0%
+here than here well because there is
+ 
+
+ align:start position:0%
+here than here well because there is
+some sort of convergence no there's a
+
+ align:start position:0%
+some sort of convergence no there's a
+ 
+
+ align:start position:0%
+some sort of convergence no there's a
+sense of convergence is that those that
+
+ align:start position:0%
+sense of convergence is that those that
+ 
+
+ align:start position:0%
+sense of convergence is that those that
+were poorer tend to grow a little faster
+
+ align:start position:0%
+were poorer tend to grow a little faster
+ 
+
+ align:start position:0%
+were poorer tend to grow a little faster
+than those that were richer and
+
+ align:start position:0%
+than those that were richer and
+ 
+
+ align:start position:0%
+than those that were richer and
+therefore they tend to converge to each
+
+ align:start position:0%
+therefore they tend to converge to each
+ 
+
+ align:start position:0%
+therefore they tend to converge to each
+other so that's the the point I'm
+
+ align:start position:0%
+other so that's the the point I'm
+ 
+
+ align:start position:0%
+other so that's the the point I'm
+highlighting here a lot of this persion
+
+ align:start position:0%
+highlighting here a lot of this persion
+ 
+
+ align:start position:0%
+highlighting here a lot of this persion
+1950 much less isers in 2018 that means
+
+ align:start position:0%
+1950 much less isers in 2018 that means
+ 
+
+ align:start position:0%
+1950 much less isers in 2018 that means
+that on average the poorer countries are
+
+ align:start position:0%
+that on average the poorer countries are
+ 
+
+ align:start position:0%
+that on average the poorer countries are
+growing faster than the Richer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+countries and again all this is per
+
+ align:start position:0%
+countries and again all this is per
+ 
+
+ align:start position:0%
+countries and again all this is per
+capita PPP adjust and all that okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+picture again sort of makes the the
+
+ align:start position:0%
+picture again sort of makes the the
+ 
+
+ align:start position:0%
+picture again sort of makes the the
+point but now it takes a much many more
+
+ align:start position:0%
+point but now it takes a much many more
+ 
+
+ align:start position:0%
+point but now it takes a much many more
+countries and you can what the point of
+
+ align:start position:0%
+countries and you can what the point of
+ 
+
+ align:start position:0%
+countries and you can what the point of
+this picture is in the book is is is to
+
+ align:start position:0%
+this picture is in the book is is is to
+ 
+
+ align:start position:0%
+this picture is in the book is is is to
+highlight that it's a little messy the
+
+ align:start position:0%
+highlight that it's a little messy the
+ 
+
+ align:start position:0%
+highlight that it's a little messy the
+picture but to highlight that if you
+
+ align:start position:0%
+picture but to highlight that if you
+ 
+
+ align:start position:0%
+picture but to highlight that if you
+look in different regions oecd a major
+
+ align:start position:0%
+look in different regions oecd a major
+ 
+
+ align:start position:0%
+look in different regions oecd a major
+the major economies H tend to the
+
+ align:start position:0%
+the major economies H tend to the
+ 
+
+ align:start position:0%
+the major economies H tend to the
+pattern I show you holds if you look at
+
+ align:start position:0%
+pattern I show you holds if you look at
+ 
+
+ align:start position:0%
+pattern I show you holds if you look at
+only isolate only the blue the blue
+
+ align:start position:0%
+only isolate only the blue the blue
+ 
+
+ align:start position:0%
+only isolate only the blue the blue
+squares you tend to see that negative
+
+ align:start position:0%
+squares you tend to see that negative
+ 
+
+ align:start position:0%
+squares you tend to see that negative
+relationship if you look at within
+
+ align:start position:0%
+relationship if you look at within
+ 
+
+ align:start position:0%
+relationship if you look at within
+Asia it's also it's a little bit noisier
+
+ align:start position:0%
+Asia it's also it's a little bit noisier
+ 
+
+ align:start position:0%
+Asia it's also it's a little bit noisier
+but you also tend to see a negative
+
+ align:start position:0%
+but you also tend to see a negative
+ 
+
+ align:start position:0%
+but you also tend to see a negative
+relationship
+
+ align:start position:0%
+relationship
+ 
+
+ align:start position:0%
+relationship
+okay if you look at
+
+ align:start position:0%
+okay if you look at
+ 
+
+ align:start position:0%
+okay if you look at
+Africa that relationship is lost
+
+ align:start position:0%
+Africa that relationship is lost
+ 
+
+ align:start position:0%
+Africa that relationship is lost
+completely
+
+ align:start position:0%
+completely
+ 
+
+ align:start position:0%
+completely
+okay so so when you look at the world as
+
+ align:start position:0%
+okay so so when you look at the world as
+ 
+
+ align:start position:0%
+okay so so when you look at the world as
+a whole
+
+ align:start position:0%
+a whole
+ 
+
+ align:start position:0%
+a whole
+the picture is not as neat as the one I
+
+ align:start position:0%
+the picture is not as neat as the one I
+ 
+
+ align:start position:0%
+the picture is not as neat as the one I
+show you because there are certain
+
+ align:start position:0%
+show you because there are certain
+ 
+
+ align:start position:0%
+show you because there are certain
+pockets of the world that are not
+
+ align:start position:0%
+pockets of the world that are not
+ 
+
+ align:start position:0%
+pockets of the world that are not
+behaving according to the kind of mods I
+
+ align:start position:0%
+behaving according to the kind of mods I
+ 
+
+ align:start position:0%
+behaving according to the kind of mods I
+want I discuss in the next few lectures
+
+ align:start position:0%
+want I discuss in the next few lectures
+ 
+
+ align:start position:0%
+want I discuss in the next few lectures
+and the reason they're not behaving is
+
+ align:start position:0%
+and the reason they're not behaving is
+ 
+
+ align:start position:0%
+and the reason they're not behaving is
+entirely it's almost outside economics
+
+ align:start position:0%
+entirely it's almost outside economics
+ 
+
+ align:start position:0%
+entirely it's almost outside economics
+it has it's political conflicts Wars and
+
+ align:start position:0%
+it has it's political conflicts Wars and
+ 
+
+ align:start position:0%
+it has it's political conflicts Wars and
+things of that nature which continuously
+
+ align:start position:0%
+things of that nature which continuously
+ 
+
+ align:start position:0%
+things of that nature which continuously
+disrupt sort of the economic forces that
+
+ align:start position:0%
+disrupt sort of the economic forces that
+ 
+
+ align:start position:0%
+disrupt sort of the economic forces that
+I'm going to highlight in the next few
+
+ align:start position:0%
+I'm going to highlight in the next few
+ 
+
+ align:start position:0%
+I'm going to highlight in the next few
+lectures
+
+ align:start position:0%
+lectures
+ 
+
+ align:start position:0%
+lectures
+okay so that's a different different
+
+ align:start position:0%
+okay so that's a different different
+ 
+
+ align:start position:0%
+okay so that's a different different
+different issue where going to be about
+
+ align:start position:0%
+different issue where going to be about
+ 
+
+ align:start position:0%
+different issue where going to be about
+the all the moles I'll show you next are
+
+ align:start position:0%
+the all the moles I'll show you next are
+ 
+
+ align:start position:0%
+the all the moles I'll show you next are
+about the blue and the and the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+green squares and and and triangles
+
+ align:start position:0%
+green squares and and and triangles
+ 
+
+ align:start position:0%
+green squares and and and triangles
+there not about the red
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ones what about so I look I show you
+
+ align:start position:0%
+ones what about so I look I show you
+ 
+
+ align:start position:0%
+ones what about so I look I show you
+what happens across countries over over
+
+ align:start position:0%
+what happens across countries over over
+ 
+
+ align:start position:0%
+what happens across countries over over
+certain period of time which is long but
+
+ align:start position:0%
+certain period of time which is long but
+ 
+
+ align:start position:0%
+certain period of time which is long but
+not that long here you see what happens
+
+ align:start position:0%
+not that long here you see what happens
+ 
+
+ align:start position:0%
+not that long here you see what happens
+in longer here history there are two
+
+ align:start position:0%
+in longer here history there are two
+ 
+
+ align:start position:0%
+in longer here history there are two
+patterns that I like to highlight here
+
+ align:start position:0%
+patterns that I like to highlight here
+ 
+
+ align:start position:0%
+patterns that I like to highlight here
+is that H first for a while sort of you
+
+ align:start position:0%
+is that H first for a while sort of you
+ 
+
+ align:start position:0%
+is that H first for a while sort of you
+you didn't see much but but you tend to
+
+ align:start position:0%
+you didn't see much but but you tend to
+ 
+
+ align:start position:0%
+you didn't see much but but you tend to
+see a sort of a big acceleration in the
+
+ align:start position:0%
+see a sort of a big acceleration in the
+ 
+
+ align:start position:0%
+see a sort of a big acceleration in the
+Western World especially around the the
+
+ align:start position:0%
+Western World especially around the the
+ 
+
+ align:start position:0%
+Western World especially around the the
+1950s or so okay so so clearly the
+
+ align:start position:0%
+1950s or so okay so so clearly the
+ 
+
+ align:start position:0%
+1950s or so okay so so clearly the
+Western world was growing faster than
+
+ align:start position:0%
+Western world was growing faster than
+ 
+
+ align:start position:0%
+Western world was growing faster than
+the rest of the world H the Western
+
+ align:start position:0%
+the rest of the world H the Western
+ 
+
+ align:start position:0%
+the rest of the world H the Western
+Hemisphere this is a um um world Bank
+
+ align:start position:0%
+Hemisphere this is a um um world Bank
+ 
+
+ align:start position:0%
+Hemisphere this is a um um world Bank
+IFI type type
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+grouping and and you see that there's a
+
+ align:start position:0%
+grouping and and you see that there's a
+ 
+
+ align:start position:0%
+grouping and and you see that there's a
+very fast acceleration in growth in this
+
+ align:start position:0%
+very fast acceleration in growth in this
+ 
+
+ align:start position:0%
+very fast acceleration in growth in this
+episode here Western Europe H was also
+
+ align:start position:0%
+episode here Western Europe H was also
+ 
+
+ align:start position:0%
+episode here Western Europe H was also
+flattish and then picked up very
+
+ align:start position:0%
+flattish and then picked up very
+ 
+
+ align:start position:0%
+flattish and then picked up very
+strongly there and you see the different
+
+ align:start position:0%
+strongly there and you see the different
+ 
+
+ align:start position:0%
+strongly there and you see the different
+regions of the world and again you see
+
+ align:start position:0%
+regions of the world and again you see
+ 
+
+ align:start position:0%
+regions of the world and again you see
+the sub Sahara Africa region that sort
+
+ align:start position:0%
+the sub Sahara Africa region that sort
+ 
+
+ align:start position:0%
+the sub Sahara Africa region that sort
+of has hasn't really picked up okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+much longer history well that's the way
+
+ align:start position:0%
+much longer history well that's the way
+ 
+
+ align:start position:0%
+much longer history well that's the way
+it looks for the world as a whole
+
+ align:start position:0%
+it looks for the world as a whole
+ 
+
+ align:start position:0%
+it looks for the world as a whole
+okay you know exponential pictures tend
+
+ align:start position:0%
+okay you know exponential pictures tend
+ 
+
+ align:start position:0%
+okay you know exponential pictures tend
+to look like that but but this is more
+
+ align:start position:0%
+to look like that but but this is more
+ 
+
+ align:start position:0%
+to look like that but but this is more
+dramatic than exponential and again what
+
+ align:start position:0%
+dramatic than exponential and again what
+ 
+
+ align:start position:0%
+dramatic than exponential and again what
+happens is
+
+ align:start position:0%
+happens is
+ 
+
+ align:start position:0%
+happens is
+that what happen here is is going to be
+
+ align:start position:0%
+that what happen here is is going to be
+ 
+
+ align:start position:0%
+that what happen here is is going to be
+very different from from the kind of
+
+ align:start position:0%
+very different from from the kind of
+ 
+
+ align:start position:0%
+very different from from the kind of
+mods I'll describe
+
+ align:start position:0%
+mods I'll describe
+ 
+
+ align:start position:0%
+mods I'll describe
+next this period here is mostly
+
+ align:start position:0%
+next this period here is mostly
+ 
+
+ align:start position:0%
+next this period here is mostly
+dominated by what's called sort of the
+
+ align:start position:0%
+dominated by what's called sort of the
+ 
+
+ align:start position:0%
+dominated by what's called sort of the
+malthusian era which is essentially
+
+ align:start position:0%
+malthusian era which is essentially
+ 
+
+ align:start position:0%
+malthusian era which is essentially
+people live population grew and so on
+
+ align:start position:0%
+people live population grew and so on
+ 
+
+ align:start position:0%
+people live population grew and so on
+depending on how good was the the
+
+ align:start position:0%
+depending on how good was the the
+ 
+
+ align:start position:0%
+depending on how good was the the
+harvest that year and so on no so so you
+
+ align:start position:0%
+harvest that year and so on no so so you
+ 
+
+ align:start position:0%
+harvest that year and so on no so so you
+had this mod in which you know his
+
+ align:start position:0%
+had this mod in which you know his
+ 
+
+ align:start position:0%
+had this mod in which you know his
+population grew faster that was a main
+
+ align:start position:0%
+population grew faster that was a main
+ 
+
+ align:start position:0%
+population grew faster that was a main
+driver of of of growth well but you know
+
+ align:start position:0%
+driver of of of growth well but you know
+ 
+
+ align:start position:0%
+driver of of of growth well but you know
+there wasn't enough food to sustain a a
+
+ align:start position:0%
+there wasn't enough food to sustain a a
+ 
+
+ align:start position:0%
+there wasn't enough food to sustain a a
+higher population and then you stay
+
+ align:start position:0%
+higher population and then you stay
+ 
+
+ align:start position:0%
+higher population and then you stay
+soort of there was a fight between food
+
+ align:start position:0%
+soort of there was a fight between food
+ 
+
+ align:start position:0%
+soort of there was a fight between food
+and and and people and and and no much
+
+ align:start position:0%
+and and and people and and and no much
+ 
+
+ align:start position:0%
+and and and people and and and no much
+space for most people were in
+
+ align:start position:0%
+space for most people were in
+ 
+
+ align:start position:0%
+space for most people were in
+agriculture and and the and and and
+
+ align:start position:0%
+agriculture and and the and and and
+ 
+
+ align:start position:0%
+agriculture and and the and and and
+there wasn't sort of
+
+ align:start position:0%
+there wasn't sort of
+ 
+
+ align:start position:0%
+there wasn't sort of
+much to build on nowadays there are
+
+ align:start position:0%
+much to build on nowadays there are
+ 
+
+ align:start position:0%
+much to build on nowadays there are
+pocket in the world and we had the
+
+ align:start position:0%
+pocket in the world and we had the
+ 
+
+ align:start position:0%
+pocket in the world and we had the
+severe situations during covid but food
+
+ align:start position:0%
+severe situations during covid but food
+ 
+
+ align:start position:0%
+severe situations during covid but food
+is not really a constraint for growth
+
+ align:start position:0%
+is not really a constraint for growth
+ 
+
+ align:start position:0%
+is not really a constraint for growth
+for the world as a whole
+
+ align:start position:0%
+for the world as a whole
+ 
+
+ align:start position:0%
+for the world as a whole
+okay and but you see
+
+ align:start position:0%
+okay and but you see
+ 
+
+ align:start position:0%
+okay and but you see
+so in other words had you taken this
+
+ align:start position:0%
+so in other words had you taken this
+ 
+
+ align:start position:0%
+so in other words had you taken this
+course in 20 in year 1000 or in the
+
+ align:start position:0%
+course in 20 in year 1000 or in the
+ 
+
+ align:start position:0%
+course in 20 in year 1000 or in the
+Renaissance nobody would have talked
+
+ align:start position:0%
+Renaissance nobody would have talked
+ 
+
+ align:start position:0%
+Renaissance nobody would have talked
+about growth it's not something that
+
+ align:start position:0%
+about growth it's not something that
+ 
+
+ align:start position:0%
+about growth it's not something that
+happened really it's it's a very modern
+
+ align:start position:0%
+happened really it's it's a very modern
+ 
+
+ align:start position:0%
+happened really it's it's a very modern
+thing to think about these pictures with
+
+ align:start position:0%
+thing to think about these pictures with
+ 
+
+ align:start position:0%
+thing to think about these pictures with
+these long Trends and so on
+
+ align:start position:0%
+these long Trends and so on
+ 
+
+ align:start position:0%
+these long Trends and so on
+okay I mean there you would have talked
+
+ align:start position:0%
+okay I mean there you would have talked
+ 
+
+ align:start position:0%
+okay I mean there you would have talked
+about a lot more interesting things than
+
+ align:start position:0%
+about a lot more interesting things than
+ 
+
+ align:start position:0%
+about a lot more interesting things than
+this but but not not about growth that's
+
+ align:start position:0%
+this but but not not about growth that's
+ 
+
+ align:start position:0%
+this but but not not about growth that's
+for sure and growth the last point I I
+
+ align:start position:0%
+for sure and growth the last point I I
+ 
+
+ align:start position:0%
+for sure and growth the last point I I
+think I want to make about this is it
+
+ align:start position:0%
+think I want to make about this is it
+ 
+
+ align:start position:0%
+think I want to make about this is it
+makes a big
+
+ align:start position:0%
+makes a big
+ 
+
+ align:start position:0%
+makes a big
+difference I don't know if you can read
+
+ align:start position:0%
+difference I don't know if you can read
+ 
+
+ align:start position:0%
+difference I don't know if you can read
+that I I can't but er um what I have
+
+ align:start position:0%
+that I I can't but er um what I have
+ 
+
+ align:start position:0%
+that I I can't but er um what I have
+here is GDP per capita in
+
+ align:start position:0%
+here is GDP per capita in
+ 
+
+ align:start position:0%
+here is GDP per capita in
+1950 versus GDP per capita in 2016
+
+ align:start position:0%
+1950 versus GDP per capita in 2016
+ 
+
+ align:start position:0%
+1950 versus GDP per capita in 2016
+and you have this isoquants here you
+
+ align:start position:0%
+and you have this isoquants here you
+ 
+
+ align:start position:0%
+and you have this isoquants here you
+move you as you move up so this line
+
+ align:start position:0%
+move you as you move up so this line
+ 
+
+ align:start position:0%
+move you as you move up so this line
+here is what happens to countries that
+
+ align:start position:0%
+here is what happens to countries that
+ 
+
+ align:start position:0%
+here is what happens to countries that
+is a 45 degree line so if you are on the
+
+ align:start position:0%
+is a 45 degree line so if you are on the
+ 
+
+ align:start position:0%
+is a 45 degree line so if you are on the
+45 degree line means that you haven't
+
+ align:start position:0%
+45 degree line means that you haven't
+ 
+
+ align:start position:0%
+45 degree line means that you haven't
+grown at all during this period no
+
+ align:start position:0%
+grown at all during this period no
+ 
+
+ align:start position:0%
+grown at all during this period no
+because that means that your GDP per
+
+ align:start position:0%
+because that means that your GDP per
+ 
+
+ align:start position:0%
+because that means that your GDP per
+capita 1950 is the same as you g GDP per
+
+ align:start position:0%
+capita 1950 is the same as you g GDP per
+ 
+
+ align:start position:0%
+capita 1950 is the same as you g GDP per
+capita in 2016 that means on average you
+
+ align:start position:0%
+capita in 2016 that means on average you
+ 
+
+ align:start position:0%
+capita in 2016 that means on average you
+grow okay but as I keep moving these
+
+ align:start position:0%
+grow okay but as I keep moving these
+ 
+
+ align:start position:0%
+grow okay but as I keep moving these
+lines up means you grew faster and fter
+
+ align:start position:0%
+lines up means you grew faster and fter
+ 
+
+ align:start position:0%
+lines up means you grew faster and fter
+faster and
+
+ align:start position:0%
+faster and
+ 
+
+ align:start position:0%
+faster and
+faster okay so and if you if you move
+
+ align:start position:0%
+faster okay so and if you if you move
+ 
+
+ align:start position:0%
+faster okay so and if you if you move
+along this line here that means you have
+
+ align:start position:0%
+along this line here that means you have
+ 
+
+ align:start position:0%
+along this line here that means you have
+negative growth on average during that
+
+ align:start position:0%
+negative growth on average during that
+ 
+
+ align:start position:0%
+negative growth on average during that
+period okay so each of these lines
+
+ align:start position:0%
+period okay so each of these lines
+ 
+
+ align:start position:0%
+period okay so each of these lines
+represents multiples so I think this is
+
+ align:start position:0%
+represents multiples so I think this is
+ 
+
+ align:start position:0%
+represents multiples so I think this is
+for example this top line here is 30
+
+ align:start position:0%
+for example this top line here is 30
+ 
+
+ align:start position:0%
+for example this top line here is 30
+times richer these are guys that grew
+
+ align:start position:0%
+times richer these are guys that grew
+ 
+
+ align:start position:0%
+times richer these are guys that grew
+very very fast yeah you I cannot read
+
+ align:start position:0%
+very very fast yeah you I cannot read
+ 
+
+ align:start position:0%
+very very fast yeah you I cannot read
+either but I I sort of know who is in
+
+ align:start position:0%
+either but I I sort of know who is in
+ 
+
+ align:start position:0%
+either but I I sort of know who is in
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+Place
+
+ align:start position:0%
+Place
+ 
+
+ align:start position:0%
+Place
+h this is an example here this is
+
+ align:start position:0%
+h this is an example here this is
+ 
+
+ align:start position:0%
+h this is an example here this is
+Taiwan okay this is Taiwan and H this is
+
+ align:start position:0%
+Taiwan okay this is Taiwan and H this is
+ 
+
+ align:start position:0%
+Taiwan okay this is Taiwan and H this is
+Singapore they have a name how do we
+
+ align:start position:0%
+Singapore they have a name how do we
+ 
+
+ align:start position:0%
+Singapore they have a name how do we
+call those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+countries no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well the Asian tigers they grew very
+
+ align:start position:0%
+well the Asian tigers they grew very
+ 
+
+ align:start position:0%
+well the Asian tigers they grew very
+very strong for for a long time since
+
+ align:start position:0%
+very strong for for a long time since
+ 
+
+ align:start position:0%
+very strong for for a long time since
+the 60s or so but there you see you can
+
+ align:start position:0%
+the 60s or so but there you see you can
+ 
+
+ align:start position:0%
+the 60s or so but there you see you can
+compare if you could see you would see
+
+ align:start position:0%
+compare if you could see you would see
+ 
+
+ align:start position:0%
+compare if you could see you would see
+that you know that that Taiwan and the
+
+ align:start position:0%
+that you know that that Taiwan and the
+ 
+
+ align:start position:0%
+that you know that that Taiwan and the
+Democratic Republic of Congo had the
+
+ align:start position:0%
+Democratic Republic of Congo had the
+ 
+
+ align:start position:0%
+Democratic Republic of Congo had the
+same GDP in
+
+ align:start position:0%
+same GDP in
+ 
+
+ align:start position:0%
+same GDP in
+1950 okay now the Republic Democratic
+
+ align:start position:0%
+1950 okay now the Republic Democratic
+ 
+
+ align:start position:0%
+1950 okay now the Republic Democratic
+Republic of of of of Congo has less GDP
+
+ align:start position:0%
+Republic of of of of Congo has less GDP
+ 
+
+ align:start position:0%
+Republic of of of of Congo has less GDP
+than it had ER in 1950 it had 1700 here
+
+ align:start position:0%
+than it had ER in 1950 it had 1700 here
+ 
+
+ align:start position:0%
+than it had ER in 1950 it had 1700 here
+and 800 today while Taiwan Taiwan has 30
+
+ align:start position:0%
+and 800 today while Taiwan Taiwan has 30
+ 
+
+ align:start position:0%
+and 800 today while Taiwan Taiwan has 30
+times what it used to
+
+ align:start position:0%
+times what it used to
+ 
+
+ align:start position:0%
+times what it used to
+have and so today is one of the richest
+
+ align:start position:0%
+have and so today is one of the richest
+ 
+
+ align:start position:0%
+have and so today is one of the richest
+economies in the world close to 7
+
+ align:start position:0%
+economies in the world close to 7
+ 
+
+ align:start position:0%
+economies in the world close to 7
+$50,000 per capita while the Republic of
+
+ align:start position:0%
+$50,000 per capita while the Republic of
+ 
+
+ align:start position:0%
+$50,000 per capita while the Republic of
+Congo ER has
+
+ align:start position:0%
+Congo ER has
+ 
+
+ align:start position:0%
+Congo ER has
+700 $800 per capita so growth makes a
+
+ align:start position:0%
+700 $800 per capita so growth makes a
+ 
+
+ align:start position:0%
+700 $800 per capita so growth makes a
+big big difference okay and these are
+
+ align:start position:0%
+big big difference okay and these are
+ 
+
+ align:start position:0%
+big big difference okay and these are
+not that many years I mean you know this
+
+ align:start position:0%
+not that many years I mean you know this
+ 
+
+ align:start position:0%
+not that many years I mean you know this
+is just 70 years H and I can assure you
+
+ align:start position:0%
+is just 70 years H and I can assure you
+ 
+
+ align:start position:0%
+is just 70 years H and I can assure you
+that these people they have other
+
+ align:start position:0%
+that these people they have other
+ 
+
+ align:start position:0%
+that these people they have other
+concerns but
+
+ align:start position:0%
+concerns but
+ 
+
+ align:start position:0%
+concerns but
+their standard of living is a lot higher
+
+ align:start position:0%
+their standard of living is a lot higher
+ 
+
+ align:start position:0%
+their standard of living is a lot higher
+than these people and at some point they
+
+ align:start position:0%
+than these people and at some point they
+ 
+
+ align:start position:0%
+than these people and at some point they
+were the same the big difference is some
+
+ align:start position:0%
+were the same the big difference is some
+ 
+
+ align:start position:0%
+were the same the big difference is some
+countries that grew and some
+
+ align:start position:0%
+countries that grew and some
+ 
+
+ align:start position:0%
+countries that grew and some
+countries got a stuck um where is
+
+ align:start position:0%
+countries got a stuck um where is
+ 
+
+ align:start position:0%
+countries got a stuck um where is
+Argentina here I don't know somewhere
+
+ align:start position:0%
+Argentina here I don't know somewhere
+ 
+
+ align:start position:0%
+Argentina here I don't know somewhere
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+probably it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Argentina I don't know I cannot
+
+ align:start position:0%
+Argentina I don't know I cannot
+ 
+
+ align:start position:0%
+Argentina I don't know I cannot
+see have the chance here I can say okay
+
+ align:start position:0%
+see have the chance here I can say okay
+ 
+
+ align:start position:0%
+see have the chance here I can say okay
+good so growth that's make a difference
+
+ align:start position:0%
+good so growth that's make a difference
+ 
+
+ align:start position:0%
+good so growth that's make a difference
+and he has made a huge the world we see
+
+ align:start position:0%
+and he has made a huge the world we see
+ 
+
+ align:start position:0%
+and he has made a huge the world we see
+today and the countries we think as rich
+
+ align:start position:0%
+today and the countries we think as rich
+ 
+
+ align:start position:0%
+today and the countries we think as rich
+or poor were not the same countries that
+
+ align:start position:0%
+or poor were not the same countries that
+ 
+
+ align:start position:0%
+or poor were not the same countries that
+you thought in in those terms in
+
+ align:start position:0%
+you thought in in those terms in
+ 
+
+ align:start position:0%
+you thought in in those terms in
+1950 Asia is one of the most prominent
+
+ align:start position:0%
+1950 Asia is one of the most prominent
+ 
+
+ align:start position:0%
+1950 Asia is one of the most prominent
+differences they have massive growth
+
+ align:start position:0%
+differences they have massive growth
+ 
+
+ align:start position:0%
+differences they have massive growth
+through the
+
+ align:start position:0%
+through the
+ 
+
+ align:start position:0%
+through the
+60s
+
+ align:start position:0%
+60s
+ 
+
+ align:start position:0%
+60s
+um starting with Japan but then the rest
+
+ align:start position:0%
+um starting with Japan but then the rest
+ 
+
+ align:start position:0%
+um starting with Japan but then the rest
+and again were the famous the Tigers
+
+ align:start position:0%
+and again were the famous the Tigers
+ 
+
+ align:start position:0%
+and again were the famous the Tigers
+Hong Kong Taiwan
+
+ align:start position:0%
+Hong Kong Taiwan
+ 
+
+ align:start position:0%
+Hong Kong Taiwan
+Singapore uh
+
+ align:start position:0%
+Singapore uh
+ 
+
+ align:start position:0%
+Singapore uh
+and Korea South
+
+ align:start position:0%
+and Korea South
+ 
+
+ align:start position:0%
+and Korea South
+Korea good so let's start building some
+
+ align:start position:0%
+Korea good so let's start building some
+ 
+
+ align:start position:0%
+Korea good so let's start building some
+moles of what we have just
+
+ align:start position:0%
+moles of what we have just
+ 
+
+ align:start position:0%
+moles of what we have just
+seen remember when we look at the short
+
+ align:start position:0%
+seen remember when we look at the short
+ 
+
+ align:start position:0%
+seen remember when we look at the short
+run we really didn't care about the
+
+ align:start position:0%
+run we really didn't care about the
+ 
+
+ align:start position:0%
+run we really didn't care about the
+supply side of the economy remember it
+
+ align:start position:0%
+supply side of the economy remember it
+ 
+
+ align:start position:0%
+supply side of the economy remember it
+was all about demand they said well you
+
+ align:start position:0%
+was all about demand they said well you
+ 
+
+ align:start position:0%
+was all about demand they said well you
+know demand look what consumers invest
+
+ align:start position:0%
+know demand look what consumers invest
+ 
+
+ align:start position:0%
+know demand look what consumers invest
+firms and governments do with demand
+
+ align:start position:0%
+firms and governments do with demand
+ 
+
+ align:start position:0%
+firms and governments do with demand
+that determines output and output
+
+ align:start position:0%
+that determines output and output
+ 
+
+ align:start position:0%
+that determines output and output
+happens well it happens we didn't really
+
+ align:start position:0%
+happens well it happens we didn't really
+ 
+
+ align:start position:0%
+happens well it happens we didn't really
+care too much about it then when we talk
+
+ align:start position:0%
+care too much about it then when we talk
+ 
+
+ align:start position:0%
+care too much about it then when we talk
+about the medium term we say okay we're
+
+ align:start position:0%
+about the medium term we say okay we're
+ 
+
+ align:start position:0%
+about the medium term we say okay we're
+going to no no we have to care because
+
+ align:start position:0%
+going to no no we have to care because
+ 
+
+ align:start position:0%
+going to no no we have to care because
+you know to produce you need workers and
+
+ align:start position:0%
+you know to produce you need workers and
+ 
+
+ align:start position:0%
+you know to produce you need workers and
+and you know workers are not going to
+
+ align:start position:0%
+and you know workers are not going to
+ 
+
+ align:start position:0%
+and you know workers are not going to
+work for any wage and so we had to begin
+
+ align:start position:0%
+work for any wage and so we had to begin
+ 
+
+ align:start position:0%
+work for any wage and so we had to begin
+to talk about ER the the supply side of
+
+ align:start position:0%
+to talk about ER the the supply side of
+ 
+
+ align:start position:0%
+to talk about ER the the supply side of
+the economy but we made it very simple
+
+ align:start position:0%
+the economy but we made it very simple
+ 
+
+ align:start position:0%
+the economy but we made it very simple
+we just look at the problem of wage
+
+ align:start position:0%
+we just look at the problem of wage
+ 
+
+ align:start position:0%
+we just look at the problem of wage
+bargaining and price setting but the
+
+ align:start position:0%
+bargaining and price setting but the
+ 
+
+ align:start position:0%
+bargaining and price setting but the
+production function itself wasn't that
+
+ align:start position:0%
+production function itself wasn't that
+ 
+
+ align:start position:0%
+production function itself wasn't that
+interesting it was outputting equal to
+
+ align:start position:0%
+interesting it was outputting equal to
+ 
+
+ align:start position:0%
+interesting it was outputting equal to
+labor and I told you it's very
+
+ align:start position:0%
+labor and I told you it's very
+ 
+
+ align:start position:0%
+labor and I told you it's very
+unrealistic but it was convenient for
+
+ align:start position:0%
+unrealistic but it was convenient for
+ 
+
+ align:start position:0%
+unrealistic but it was convenient for
+that part of the course because Capital
+
+ align:start position:0%
+that part of the course because Capital
+ 
+
+ align:start position:0%
+that part of the course because Capital
+doesn't grow that fast so typical
+
+ align:start position:0%
+doesn't grow that fast so typical
+ 
+
+ align:start position:0%
+doesn't grow that fast so typical
+production function we have both capital
+
+ align:start position:0%
+production function we have both capital
+ 
+
+ align:start position:0%
+production function we have both capital
+and labor but at the business cycle
+
+ align:start position:0%
+and labor but at the business cycle
+ 
+
+ align:start position:0%
+and labor but at the business cycle
+frequency investment the change in
+
+ align:start position:0%
+frequency investment the change in
+ 
+
+ align:start position:0%
+frequency investment the change in
+capital can be large but the stock of
+
+ align:start position:0%
+capital can be large but the stock of
+ 
+
+ align:start position:0%
+capital can be large but the stock of
+capital doesn't move that much and so
+
+ align:start position:0%
+capital doesn't move that much and so
+ 
+
+ align:start position:0%
+capital doesn't move that much and so
+you can ignore it for business cycle
+
+ align:start position:0%
+you can ignore it for business cycle
+ 
+
+ align:start position:0%
+you can ignore it for business cycle
+type fluctuations but if we want to look
+
+ align:start position:0%
+type fluctuations but if we want to look
+ 
+
+ align:start position:0%
+type fluctuations but if we want to look
+at the long run Capital plays a huge
+
+ align:start position:0%
+at the long run Capital plays a huge
+ 
+
+ align:start position:0%
+at the long run Capital plays a huge
+role capital accumulation and so we have
+
+ align:start position:0%
+role capital accumulation and so we have
+ 
+
+ align:start position:0%
+role capital accumulation and so we have
+to be explicit about the role of capital
+
+ align:start position:0%
+to be explicit about the role of capital
+ 
+
+ align:start position:0%
+to be explicit about the role of capital
+in the the production
+
+ align:start position:0%
+in the the production
+ 
+
+ align:start position:0%
+in the the production
+function so this is going to be our now
+
+ align:start position:0%
+function so this is going to be our now
+ 
+
+ align:start position:0%
+function so this is going to be our now
+and now we're going to forget about
+
+ align:start position:0%
+and now we're going to forget about
+ 
+
+ align:start position:0%
+and now we're going to forget about
+aggregate demand we're going to say look
+
+ align:start position:0%
+aggregate demand we're going to say look
+ 
+
+ align:start position:0%
+aggregate demand we're going to say look
+we're going to focus about AGG supply
+
+ align:start position:0%
+we're going to focus about AGG supply
+ 
+
+ align:start position:0%
+we're going to focus about AGG supply
+and demand will do whatever it needs to
+
+ align:start position:0%
+and demand will do whatever it needs to
+ 
+
+ align:start position:0%
+and demand will do whatever it needs to
+do so so so we get what what the supply
+
+ align:start position:0%
+do so so so we get what what the supply
+ 
+
+ align:start position:0%
+do so so so we get what what the supply
+site says so output now will be will be
+
+ align:start position:0%
+site says so output now will be will be
+ 
+
+ align:start position:0%
+site says so output now will be will be
+a an increasing function of both capital
+
+ align:start position:0%
+a an increasing function of both capital
+ 
+
+ align:start position:0%
+a an increasing function of both capital
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+labor now this function will have a
+
+ align:start position:0%
+labor now this function will have a
+ 
+
+ align:start position:0%
+labor now this function will have a
+bunch of er properties which are many of
+
+ align:start position:0%
+bunch of er properties which are many of
+ 
+
+ align:start position:0%
+bunch of er properties which are many of
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+are no at a broad level they are
+
+ align:start position:0%
+are no at a broad level they are
+ 
+
+ align:start position:0%
+are no at a broad level they are
+empirically validated but they're also
+
+ align:start position:0%
+empirically validated but they're also
+ 
+
+ align:start position:0%
+empirically validated but they're also
+very convenient from the modeling point
+
+ align:start position:0%
+very convenient from the modeling point
+ 
+
+ align:start position:0%
+very convenient from the modeling point
+of view the first and most
+
+ align:start position:0%
+of view the first and most
+ 
+
+ align:start position:0%
+of view the first and most
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+property um is constant returns to
+
+ align:start position:0%
+property um is constant returns to
+ 
+
+ align:start position:0%
+property um is constant returns to
+scale okay we're going to use a lot of
+
+ align:start position:0%
+scale okay we're going to use a lot of
+ 
+
+ align:start position:0%
+scale okay we're going to use a lot of
+property so so please get that concept
+
+ align:start position:0%
+property so so please get that concept
+ 
+
+ align:start position:0%
+property so so please get that concept
+constant return to scale means simply
+
+ align:start position:0%
+constant return to scale means simply
+ 
+
+ align:start position:0%
+constant return to scale means simply
+that if you scale the factors of
+
+ align:start position:0%
+that if you scale the factors of
+ 
+
+ align:start position:0%
+that if you scale the factors of
+production you also scale the output
+
+ align:start position:0%
+production you also scale the output
+ 
+
+ align:start position:0%
+production you also scale the output
+okay so say if x is 1.1 that means if
+
+ align:start position:0%
+okay so say if x is 1.1 that means if
+ 
+
+ align:start position:0%
+okay so say if x is 1.1 that means if
+you increase capital and labor by 10%
+
+ align:start position:0%
+you increase capital and labor by 10%
+ 
+
+ align:start position:0%
+you increase capital and labor by 10%
+you get 10% more output okay so that's
+
+ align:start position:0%
+you get 10% more output okay so that's
+ 
+
+ align:start position:0%
+you get 10% more output okay so that's
+Conant return to scale if I scale all
+
+ align:start position:0%
+Conant return to scale if I scale all
+ 
+
+ align:start position:0%
+Conant return to scale if I scale all
+the factors of production by the same
+
+ align:start position:0%
+the factors of production by the same
+ 
+
+ align:start position:0%
+the factors of production by the same
+amount the same proportion then output
+
+ align:start position:0%
+amount the same proportion then output
+ 
+
+ align:start position:0%
+amount the same proportion then output
+Grows by the same proportion it's
+
+ align:start position:0%
+Grows by the same proportion it's
+ 
+
+ align:start position:0%
+Grows by the same proportion it's
+scalable that's what it mean constant
+
+ align:start position:0%
+scalable that's what it mean constant
+ 
+
+ align:start position:0%
+scalable that's what it mean constant
+return to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scale very important property what comes
+
+ align:start position:0%
+scale very important property what comes
+ 
+
+ align:start position:0%
+scale very important property what comes
+next decreasing returns to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Capital that
+
+ align:start position:0%
+Capital that
+ 
+
+ align:start position:0%
+Capital that
+is H as you increase capital for a fixed
+
+ align:start position:0%
+is H as you increase capital for a fixed
+ 
+
+ align:start position:0%
+is H as you increase capital for a fixed
+amount of Labor so conent scale is a
+
+ align:start position:0%
+amount of Labor so conent scale is a
+ 
+
+ align:start position:0%
+amount of Labor so conent scale is a
+property of scaling everything
+
+ align:start position:0%
+property of scaling everything
+ 
+
+ align:start position:0%
+property of scaling everything
+up the property I'm describing here is
+
+ align:start position:0%
+up the property I'm describing here is
+ 
+
+ align:start position:0%
+up the property I'm describing here is
+what happens if we increase only K what
+
+ align:start position:0%
+what happens if we increase only K what
+ 
+
+ align:start position:0%
+what happens if we increase only K what
+happens to Output if we increase only K
+
+ align:start position:0%
+happens to Output if we increase only K
+ 
+
+ align:start position:0%
+happens to Output if we increase only K
+but fixing
+
+ align:start position:0%
+but fixing
+ 
+
+ align:start position:0%
+but fixing
+n in other words set this to one and
+
+ align:start position:0%
+n in other words set this to one and
+ 
+
+ align:start position:0%
+n in other words set this to one and
+start moving this
+
+ align:start position:0%
+start moving this
+ 
+
+ align:start position:0%
+start moving this
+up you're not going to get X here you're
+
+ align:start position:0%
+up you're not going to get X here you're
+ 
+
+ align:start position:0%
+up you're not going to get X here you're
+going to get something different from
+
+ align:start position:0%
+going to get something different from
+ 
+
+ align:start position:0%
+going to get something different from
+X and but this tells you is that yes
+
+ align:start position:0%
+X and but this tells you is that yes
+ 
+
+ align:start position:0%
+X and but this tells you is that yes
+you're going to get more output but less
+
+ align:start position:0%
+you're going to get more output but less
+ 
+
+ align:start position:0%
+you're going to get more output but less
+and less the more Capital you
+
+ align:start position:0%
+and less the more Capital you
+ 
+
+ align:start position:0%
+and less the more Capital you
+have Okay so this says for example
+
+ align:start position:0%
+have Okay so this says for example
+ 
+
+ align:start position:0%
+have Okay so this says for example
+suppose you start with 100 workers and
+
+ align:start position:0%
+suppose you start with 100 workers and
+ 
+
+ align:start position:0%
+suppose you start with 100 workers and
+100 units of capital and it happens that
+
+ align:start position:0%
+100 units of capital and it happens that
+ 
+
+ align:start position:0%
+100 units of capital and it happens that
+this produces 100 units of
+
+ align:start position:0%
+this produces 100 units of
+ 
+
+ align:start position:0%
+this produces 100 units of
+goods if you add now 10 units of capital
+
+ align:start position:0%
+goods if you add now 10 units of capital
+ 
+
+ align:start position:0%
+goods if you add now 10 units of capital
+say you're going to
+
+ align:start position:0%
+say you're going to
+ 
+
+ align:start position:0%
+say you're going to
+get seven units of output not 10 seven
+
+ align:start position:0%
+get seven units of output not 10 seven
+ 
+
+ align:start position:0%
+get seven units of output not 10 seven
+because you didn't increase labor had I
+
+ align:start position:0%
+because you didn't increase labor had I
+ 
+
+ align:start position:0%
+because you didn't increase labor had I
+increased labor also by by 10 I would
+
+ align:start position:0%
+increased labor also by by 10 I would
+ 
+
+ align:start position:0%
+increased labor also by by 10 I would
+have gotten 10 of output but I
+
+ align:start position:0%
+have gotten 10 of output but I
+ 
+
+ align:start position:0%
+have gotten 10 of output but I
+increasing only h capital by 10 then and
+
+ align:start position:0%
+increasing only h capital by 10 then and
+ 
+
+ align:start position:0%
+increasing only h capital by 10 then and
+keeping output fixed then labor fixed
+
+ align:start position:0%
+keeping output fixed then labor fixed
+ 
+
+ align:start position:0%
+keeping output fixed then labor fixed
+then output will increase by less than
+
+ align:start position:0%
+then output will increase by less than
+ 
+
+ align:start position:0%
+then output will increase by less than
+10 but what this decrease in returns to
+
+ align:start position:0%
+10 but what this decrease in returns to
+ 
+
+ align:start position:0%
+10 but what this decrease in returns to
+Capital says is that now if you increase
+
+ align:start position:0%
+Capital says is that now if you increase
+ 
+
+ align:start position:0%
+Capital says is that now if you increase
+again from 110 to 120 units of capital
+
+ align:start position:0%
+again from 110 to 120 units of capital
+ 
+
+ align:start position:0%
+again from 110 to 120 units of capital
+you're going to get get less than seven
+
+ align:start position:0%
+you're going to get get less than seven
+ 
+
+ align:start position:0%
+you're going to get get less than seven
+units of output more you're going to get
+
+ align:start position:0%
+units of output more you're going to get
+ 
+
+ align:start position:0%
+units of output more you're going to get
+five and if you increase a again from
+
+ align:start position:0%
+five and if you increase a again from
+ 
+
+ align:start position:0%
+five and if you increase a again from
+120 to 130 you're going to get less than
+
+ align:start position:0%
+120 to 130 you're going to get less than
+ 
+
+ align:start position:0%
+120 to 130 you're going to get less than
+five you're going to get three and so on
+
+ align:start position:0%
+five you're going to get three and so on
+ 
+
+ align:start position:0%
+five you're going to get three and so on
+so forth that's decreasing returns to
+
+ align:start position:0%
+so forth that's decreasing returns to
+ 
+
+ align:start position:0%
+so forth that's decreasing returns to
+scale and and decreasing returns to
+
+ align:start position:0%
+scale and and decreasing returns to
+ 
+
+ align:start position:0%
+scale and and decreasing returns to
+Capital and the reason for that is is
+
+ align:start position:0%
+Capital and the reason for that is is
+ 
+
+ align:start position:0%
+Capital and the reason for that is is
+economically is that more and more
+
+ align:start position:0%
+economically is that more and more
+ 
+
+ align:start position:0%
+economically is that more and more
+capital is working with a fixed number
+
+ align:start position:0%
+capital is working with a fixed number
+ 
+
+ align:start position:0%
+capital is working with a fixed number
+of workers so labor becomes very scarce
+
+ align:start position:0%
+of workers so labor becomes very scarce
+ 
+
+ align:start position:0%
+of workers so labor becomes very scarce
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+capital okay and that's the reason so so
+
+ align:start position:0%
+capital okay and that's the reason so so
+ 
+
+ align:start position:0%
+capital okay and that's the reason so so
+you have very little
+
+ align:start position:0%
+you have very little
+ 
+
+ align:start position:0%
+you have very little
+the other these are factors of
+
+ align:start position:0%
+the other these are factors of
+ 
+
+ align:start position:0%
+the other these are factors of
+production which are complementary they
+
+ align:start position:0%
+production which are complementary they
+ 
+
+ align:start position:0%
+production which are complementary they
+need each other labor and capital if you
+
+ align:start position:0%
+need each other labor and capital if you
+ 
+
+ align:start position:0%
+need each other labor and capital if you
+fix one and it start increasing only one
+
+ align:start position:0%
+fix one and it start increasing only one
+ 
+
+ align:start position:0%
+fix one and it start increasing only one
+then it's harder and harder for each
+
+ align:start position:0%
+then it's harder and harder for each
+ 
+
+ align:start position:0%
+then it's harder and harder for each
+extra new unit of this one to work with
+
+ align:start position:0%
+extra new unit of this one to work with
+ 
+
+ align:start position:0%
+extra new unit of this one to work with
+sort of fewer and fewer of the other
+
+ align:start position:0%
+sort of fewer and fewer of the other
+ 
+
+ align:start position:0%
+sort of fewer and fewer of the other
+factor of production so the same
+
+ align:start position:0%
+factor of production so the same
+ 
+
+ align:start position:0%
+factor of production so the same
+principle applies to labor if you fix
+
+ align:start position:0%
+principle applies to labor if you fix
+ 
+
+ align:start position:0%
+principle applies to labor if you fix
+capital and you only increase labor then
+
+ align:start position:0%
+capital and you only increase labor then
+ 
+
+ align:start position:0%
+capital and you only increase labor then
+initially you get a big jumping output
+
+ align:start position:0%
+initially you get a big jumping output
+ 
+
+ align:start position:0%
+initially you get a big jumping output
+but it's going to be smaller and smaller
+
+ align:start position:0%
+but it's going to be smaller and smaller
+ 
+
+ align:start position:0%
+but it's going to be smaller and smaller
+and smaller the more you keep adding a
+
+ align:start position:0%
+and smaller the more you keep adding a
+ 
+
+ align:start position:0%
+and smaller the more you keep adding a
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+labor okay so in pi so let me One X that
+
+ align:start position:0%
+labor okay so in pi so let me One X that
+ 
+
+ align:start position:0%
+labor okay so in pi so let me One X that
+we're going to use
+
+ align:start position:0%
+we're going to use
+ 
+
+ align:start position:0%
+we're going to use
+throughout is we want to make x one of
+
+ align:start position:0%
+throughout is we want to make x one of
+ 
+
+ align:start position:0%
+throughout is we want to make x one of
+our favorite X will be 1 /
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n you see what I'm trying to do when we
+
+ align:start position:0%
+n you see what I'm trying to do when we
+ 
+
+ align:start position:0%
+n you see what I'm trying to do when we
+set x equal to 1 / n so that x equal to
+
+ align:start position:0%
+set x equal to 1 / n so that x equal to
+ 
+
+ align:start position:0%
+set x equal to 1 / n so that x equal to
+1 / n what I get here is output per
+
+ align:start position:0%
+1 / n what I get here is output per
+ 
+
+ align:start position:0%
+1 / n what I get here is output per
+person
+
+ align:start position:0%
+person
+ 
+
+ align:start position:0%
+person
+no that's what I
+
+ align:start position:0%
+no that's what I
+ 
+
+ align:start position:0%
+no that's what I
+get y Over
+
+ align:start position:0%
+get y Over
+ 
+
+ align:start position:0%
+get y Over
+N so if I set xal to 1/ n i can using
+
+ align:start position:0%
+N so if I set xal to 1/ n i can using
+ 
+
+ align:start position:0%
+N so if I set xal to 1/ n i can using
+con to scale I know that this is equal
+
+ align:start position:0%
+con to scale I know that this is equal
+ 
+
+ align:start position:0%
+con to scale I know that this is equal
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+y/n k/ n n/ n so that is one so this guy
+
+ align:start position:0%
+y/n k/ n n/ n so that is one so this guy
+ 
+
+ align:start position:0%
+y/n k/ n n/ n so that is one so this guy
+doesn't move and I have now
+
+ align:start position:0%
+doesn't move and I have now
+ 
+
+ align:start position:0%
+doesn't move and I have now
+that a output per person is increasing
+
+ align:start position:0%
+that a output per person is increasing
+ 
+
+ align:start position:0%
+that a output per person is increasing
+in capital per worker worker and
+
+ align:start position:0%
+in capital per worker worker and
+ 
+
+ align:start position:0%
+in capital per worker worker and
+population this part of the course are
+
+ align:start position:0%
+population this part of the course are
+ 
+
+ align:start position:0%
+population this part of the course are
+the same for get an EMP employment and
+
+ align:start position:0%
+the same for get an EMP employment and
+ 
+
+ align:start position:0%
+the same for get an EMP employment and
+is population is employment if labor
+
+ align:start position:0%
+is population is employment if labor
+ 
+
+ align:start position:0%
+is population is employment if labor
+force is everything I'm not this is not
+
+ align:start position:0%
+force is everything I'm not this is not
+ 
+
+ align:start position:0%
+force is everything I'm not this is not
+a place to worry about unemployment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay so remember that all the plots
+
+ align:start position:0%
+okay okay so remember that all the plots
+ 
+
+ align:start position:0%
+okay okay so remember that all the plots
+I show you the different Figures were
+
+ align:start position:0%
+I show you the different Figures were
+ 
+
+ align:start position:0%
+I show you the different Figures were
+about this variable how it changed over
+
+ align:start position:0%
+about this variable how it changed over
+ 
+
+ align:start position:0%
+about this variable how it changed over
+time how was different across different
+
+ align:start position:0%
+time how was different across different
+ 
+
+ align:start position:0%
+time how was different across different
+countries how grew at a different rate
+
+ align:start position:0%
+countries how grew at a different rate
+ 
+
+ align:start position:0%
+countries how grew at a different rate
+in in different countries but from this
+
+ align:start position:0%
+in in different countries but from this
+ 
+
+ align:start position:0%
+in in different countries but from this
+very simple model you see that in order
+
+ align:start position:0%
+very simple model you see that in order
+ 
+
+ align:start position:0%
+very simple model you see that in order
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+explain the change in this or growth in
+
+ align:start position:0%
+explain the change in this or growth in
+ 
+
+ align:start position:0%
+explain the change in this or growth in
+why over and why one country grows more
+
+ align:start position:0%
+why over and why one country grows more
+ 
+
+ align:start position:0%
+why over and why one country grows more
+than the other you have with the simple
+
+ align:start position:0%
+than the other you have with the simple
+ 
+
+ align:start position:0%
+than the other you have with the simple
+model only two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+options so if I tell you country a grew
+
+ align:start position:0%
+options so if I tell you country a grew
+ 
+
+ align:start position:0%
+options so if I tell you country a grew
+more over this period than grew more per
+
+ align:start position:0%
+more over this period than grew more per
+ 
+
+ align:start position:0%
+more over this period than grew more per
+per person than this other
+
+ align:start position:0%
+per person than this other
+ 
+
+ align:start position:0%
+per person than this other
+country er um over this period of time
+
+ align:start position:0%
+country er um over this period of time
+ 
+
+ align:start position:0%
+country er um over this period of time
+there are only two options here the
+
+ align:start position:0%
+there are only two options here the
+ 
+
+ align:start position:0%
+there are only two options here the
+first one is that in that country there
+
+ align:start position:0%
+first one is that in that country there
+ 
+
+ align:start position:0%
+first one is that in that country there
+was more capital accumulation per worker
+
+ align:start position:0%
+was more capital accumulation per worker
+ 
+
+ align:start position:0%
+was more capital accumulation per worker
+so K Over N went up no if K Over N goes
+
+ align:start position:0%
+so K Over N went up no if K Over N goes
+ 
+
+ align:start position:0%
+so K Over N went up no if K Over N goes
+up more in one country than the other
+
+ align:start position:0%
+up more in one country than the other
+ 
+
+ align:start position:0%
+up more in one country than the other
+one y Over N will go up more in that
+
+ align:start position:0%
+one y Over N will go up more in that
+ 
+
+ align:start position:0%
+one y Over N will go up more in that
+country than the other one and the other
+
+ align:start position:0%
+country than the other one and the other
+ 
+
+ align:start position:0%
+country than the other one and the other
+option is that the this H function
+
+ align:start position:0%
+option is that the this H function
+ 
+
+ align:start position:0%
+option is that the this H function
+itself shifted
+
+ align:start position:0%
+itself shifted
+ 
+
+ align:start position:0%
+itself shifted
+up so for any given amount of K Over N
+
+ align:start position:0%
+up so for any given amount of K Over N
+ 
+
+ align:start position:0%
+up so for any given amount of K Over N
+now you could produ more y over n and
+
+ align:start position:0%
+now you could produ more y over n and
+ 
+
+ align:start position:0%
+now you could produ more y over n and
+that's what we call technological
+
+ align:start position:0%
+that's what we call technological
+ 
+
+ align:start position:0%
+that's what we call technological
+progress that's a second thing so so if
+
+ align:start position:0%
+progress that's a second thing so so if
+ 
+
+ align:start position:0%
+progress that's a second thing so so if
+if if the difference in in in in growth
+
+ align:start position:0%
+if if the difference in in in in growth
+ 
+
+ align:start position:0%
+if if the difference in in in in growth
+of output per
+
+ align:start position:0%
+of output per
+ 
+
+ align:start position:0%
+of output per
+person is due to an increasing K Over
+
+ align:start position:0%
+person is due to an increasing K Over
+ 
+
+ align:start position:0%
+person is due to an increasing K Over
+end well we call that a capill
+
+ align:start position:0%
+end well we call that a capill
+ 
+
+ align:start position:0%
+end well we call that a capill
+accumulation mechanism if it is because
+
+ align:start position:0%
+accumulation mechanism if it is because
+ 
+
+ align:start position:0%
+accumulation mechanism if it is because
+the function f shifts up that's
+
+ align:start position:0%
+the function f shifts up that's
+ 
+
+ align:start position:0%
+the function f shifts up that's
+technological progress and what we're
+
+ align:start position:0%
+technological progress and what we're
+ 
+
+ align:start position:0%
+technological progress and what we're
+going to do is in the next lecture we're
+
+ align:start position:0%
+going to do is in the next lecture we're
+ 
+
+ align:start position:0%
+going to do is in the next lecture we're
+going to talk about this channel the
+
+ align:start position:0%
+going to talk about this channel the
+ 
+
+ align:start position:0%
+going to talk about this channel the
+capital accumulation Channel and in the
+
+ align:start position:0%
+capital accumulation Channel and in the
+ 
+
+ align:start position:0%
+capital accumulation Channel and in the
+lecture after the spring break we're
+
+ align:start position:0%
+lecture after the spring break we're
+ 
+
+ align:start position:0%
+lecture after the spring break we're
+going to talk about shift in the
+
+ align:start position:0%
+going to talk about shift in the
+ 
+
+ align:start position:0%
+going to talk about shift in the
+function f so in in in in
+
+ align:start position:0%
+function f so in in in in
+ 
+
+ align:start position:0%
+function f so in in in in
+figures
+
+ align:start position:0%
+figures
+ 
+
+ align:start position:0%
+figures
+so fixing the technology that this is
+
+ align:start position:0%
+so fixing the technology that this is
+ 
+
+ align:start position:0%
+so fixing the technology that this is
+the function f is fixed and you just
+
+ align:start position:0%
+the function f is fixed and you just
+ 
+
+ align:start position:0%
+the function f is fixed and you just
+move K Over N this is the picture you
+
+ align:start position:0%
+move K Over N this is the picture you
+ 
+
+ align:start position:0%
+move K Over N this is the picture you
+have now that's a produ this I'm
+
+ align:start position:0%
+have now that's a produ this I'm
+ 
+
+ align:start position:0%
+have now that's a produ this I'm
+plotting this function here as a
+
+ align:start position:0%
+plotting this function here as a
+ 
+
+ align:start position:0%
+plotting this function here as a
+function of k/ n for a fixed function f
+
+ align:start position:0%
+function of k/ n for a fixed function f
+ 
+
+ align:start position:0%
+function of k/ n for a fixed function f
+and that's what you get so output per I
+
+ align:start position:0%
+and that's what you get so output per I
+ 
+
+ align:start position:0%
+and that's what you get so output per I
+have here Capital per worker and output
+
+ align:start position:0%
+have here Capital per worker and output
+ 
+
+ align:start position:0%
+have here Capital per worker and output
+per per
+
+ align:start position:0%
+per per
+ 
+
+ align:start position:0%
+per per
+worker and you see that obviously it's
+
+ align:start position:0%
+worker and you see that obviously it's
+ 
+
+ align:start position:0%
+worker and you see that obviously it's
+in an increasing function the more
+
+ align:start position:0%
+in an increasing function the more
+ 
+
+ align:start position:0%
+in an increasing function the more
+Capital per worker you have the more
+
+ align:start position:0%
+Capital per worker you have the more
+ 
+
+ align:start position:0%
+Capital per worker you have the more
+output per worker you'll
+
+ align:start position:0%
+output per worker you'll
+ 
+
+ align:start position:0%
+output per worker you'll
+produce but it's also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concave why is it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+concave that's decrease in returns to
+
+ align:start position:0%
+concave that's decrease in returns to
+ 
+
+ align:start position:0%
+concave that's decrease in returns to
+Capital is look for any when you have
+
+ align:start position:0%
+Capital is look for any when you have
+ 
+
+ align:start position:0%
+Capital is look for any when you have
+very little Capital per work
+
+ align:start position:0%
+very little Capital per work
+ 
+
+ align:start position:0%
+very little Capital per work
+a change in capital per worker gives
+
+ align:start position:0%
+a change in capital per worker gives
+ 
+
+ align:start position:0%
+a change in capital per worker gives
+gives you a big jumping output per
+
+ align:start position:0%
+gives you a big jumping output per
+ 
+
+ align:start position:0%
+gives you a big jumping output per
+worker because you know there was sort
+
+ align:start position:0%
+worker because you know there was sort
+ 
+
+ align:start position:0%
+worker because you know there was sort
+of very little Capital that was the
+
+ align:start position:0%
+of very little Capital that was the
+ 
+
+ align:start position:0%
+of very little Capital that was the
+problem of that
+
+ align:start position:0%
+problem of that
+ 
+
+ align:start position:0%
+problem of that
+economy when the economy has more and
+
+ align:start position:0%
+economy when the economy has more and
+ 
+
+ align:start position:0%
+economy when the economy has more and
+more Capital the same change in capital
+
+ align:start position:0%
+more Capital the same change in capital
+ 
+
+ align:start position:0%
+more Capital the same change in capital
+leads to a much smaller change in output
+
+ align:start position:0%
+leads to a much smaller change in output
+ 
+
+ align:start position:0%
+leads to a much smaller change in output
+here at this level when when Capital per
+
+ align:start position:0%
+here at this level when when Capital per
+ 
+
+ align:start position:0%
+here at this level when when Capital per
+worker was very low the economy was very
+
+ align:start position:0%
+worker was very low the economy was very
+ 
+
+ align:start position:0%
+worker was very low the economy was very
+poor then this change LED to this change
+
+ align:start position:0%
+poor then this change LED to this change
+ 
+
+ align:start position:0%
+poor then this change LED to this change
+in output per capita at this level of
+
+ align:start position:0%
+in output per capita at this level of
+ 
+
+ align:start position:0%
+in output per capita at this level of
+wealth if you get as capital economies
+
+ align:start position:0%
+wealth if you get as capital economies
+ 
+
+ align:start position:0%
+wealth if you get as capital economies
+with higher Capital are richer Capital
+
+ align:start position:0%
+with higher Capital are richer Capital
+ 
+
+ align:start position:0%
+with higher Capital are richer Capital
+per worker the same change this change
+
+ align:start position:0%
+per worker the same change this change
+ 
+
+ align:start position:0%
+per worker the same change this change
+is of the same size as that leads to a
+
+ align:start position:0%
+is of the same size as that leads to a
+ 
+
+ align:start position:0%
+is of the same size as that leads to a
+much smaller change in
+
+ align:start position:0%
+much smaller change in
+ 
+
+ align:start position:0%
+much smaller change in
+output okay and that's a result of
+
+ align:start position:0%
+output okay and that's a result of
+ 
+
+ align:start position:0%
+output okay and that's a result of
+decreasing returns to
+
+ align:start position:0%
+decreasing returns to
+ 
+
+ align:start position:0%
+decreasing returns to
+Capital and that's the other option
+
+ align:start position:0%
+Capital and that's the other option
+ 
+
+ align:start position:0%
+Capital and that's the other option
+again that's what we're going to talk
+
+ align:start position:0%
+again that's what we're going to talk
+ 
+
+ align:start position:0%
+again that's what we're going to talk
+about in the next lecture this this one
+
+ align:start position:0%
+about in the next lecture this this one
+ 
+
+ align:start position:0%
+about in the next lecture this this one
+and two lectures from now we're going to
+
+ align:start position:0%
+and two lectures from now we're going to
+ 
+
+ align:start position:0%
+and two lectures from now we're going to
+talk about growth that comes from shift
+
+ align:start position:0%
+talk about growth that comes from shift
+ 
+
+ align:start position:0%
+talk about growth that comes from shift
+in the production function this
+
+ align:start position:0%
+in the production function this
+ 
+
+ align:start position:0%
+in the production function this
+technological progress
+
+ align:start position:0%
+technological progress
+ 
+
+ align:start position:0%
+technological progress
+okay very good see you on Wednesday
\ No newline at end of file
diff --git a/v5fOm80VAnc.txt b/v5fOm80VAnc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..670f239ff7fec5312dddace6fc7857a7ad9edf0d
--- /dev/null
+++ b/v5fOm80VAnc.txt
@@ -0,0 +1,883 @@
+align:start position:0%
+ 
+before we dive into the heart of the
+
+ align:start position:0%
+before we dive into the heart of the
+ 
+
+ align:start position:0%
+before we dive into the heart of the
+subject I want to make a few comments on
+
+ align:start position:0%
+subject I want to make a few comments on
+ 
+
+ align:start position:0%
+subject I want to make a few comments on
+the different problem types that show up
+
+ align:start position:0%
+the different problem types that show up
+ 
+
+ align:start position:0%
+the different problem types that show up
+in the field of inference you can think
+
+ align:start position:0%
+in the field of inference you can think
+ 
+
+ align:start position:0%
+in the field of inference you can think
+of a general distinction between model
+
+ align:start position:0%
+of a general distinction between model
+ 
+
+ align:start position:0%
+of a general distinction between model
+building versus making inferences about
+
+ align:start position:0%
+building versus making inferences about
+ 
+
+ align:start position:0%
+building versus making inferences about
+unobserved variables we said a little
+
+ align:start position:0%
+unobserved variables we said a little
+ 
+
+ align:start position:0%
+unobserved variables we said a little
+earlier that one of the main uses of the
+
+ align:start position:0%
+earlier that one of the main uses of the
+ 
+
+ align:start position:0%
+earlier that one of the main uses of the
+field of inference is to construct
+
+ align:start position:0%
+field of inference is to construct
+ 
+
+ align:start position:0%
+field of inference is to construct
+models of certain situations but in many
+
+ align:start position:0%
+models of certain situations but in many
+ 
+
+ align:start position:0%
+models of certain situations but in many
+cases we already have a model on the
+
+ align:start position:0%
+cases we already have a model on the
+ 
+
+ align:start position:0%
+cases we already have a model on the
+other hand there may be variables that
+
+ align:start position:0%
+other hand there may be variables that
+ 
+
+ align:start position:0%
+other hand there may be variables that
+are unknown that are unobserved
+
+ align:start position:0%
+are unknown that are unobserved
+ 
+
+ align:start position:0%
+are unknown that are unobserved
+variables that are part of the model but
+
+ align:start position:0%
+variables that are part of the model but
+ 
+
+ align:start position:0%
+variables that are part of the model but
+whose values are not known in such cases
+
+ align:start position:0%
+whose values are not known in such cases
+ 
+
+ align:start position:0%
+whose values are not known in such cases
+we still want to use data to make some
+
+ align:start position:0%
+we still want to use data to make some
+ 
+
+ align:start position:0%
+we still want to use data to make some
+predictions or decisions about those
+
+ align:start position:0%
+predictions or decisions about those
+ 
+
+ align:start position:0%
+predictions or decisions about those
+unobserved variables so model building
+
+ align:start position:0%
+unobserved variables so model building
+ 
+
+ align:start position:0%
+unobserved variables so model building
+might or might not be part of the
+
+ align:start position:0%
+might or might not be part of the
+ 
+
+ align:start position:0%
+might or might not be part of the
+problem that we're dealing with to
+
+ align:start position:0%
+problem that we're dealing with to
+ 
+
+ align:start position:0%
+problem that we're dealing with to
+illustrate the difference between these
+
+ align:start position:0%
+illustrate the difference between these
+ 
+
+ align:start position:0%
+illustrate the difference between these
+two versions of the problem let us think
+
+ align:start position:0%
+two versions of the problem let us think
+ 
+
+ align:start position:0%
+two versions of the problem let us think
+of a concrete setting you have a
+
+ align:start position:0%
+of a concrete setting you have a
+ 
+
+ align:start position:0%
+of a concrete setting you have a
+transmitter who is sending a signal call
+
+ align:start position:0%
+transmitter who is sending a signal call
+ 
+
+ align:start position:0%
+transmitter who is sending a signal call
+it s and that signal goes through some
+
+ align:start position:0%
+it s and that signal goes through some
+ 
+
+ align:start position:0%
+it s and that signal goes through some
+medium it could be just the atmosphere
+
+ align:start position:0%
+medium it could be just the atmosphere
+ 
+
+ align:start position:0%
+medium it could be just the atmosphere
+and what that medium does is that it
+
+ align:start position:0%
+and what that medium does is that it
+ 
+
+ align:start position:0%
+and what that medium does is that it
+attenuates the signal by a certain
+
+ align:start position:0%
+attenuates the signal by a certain
+ 
+
+ align:start position:0%
+attenuates the signal by a certain
+factor a and then as the signal travels
+
+ align:start position:0%
+factor a and then as the signal travels
+ 
+
+ align:start position:0%
+factor a and then as the signal travels
+it also gets hit by some noise call it W
+
+ align:start position:0%
+it also gets hit by some noise call it W
+ 
+
+ align:start position:0%
+it also gets hit by some noise call it W
+and what the receiver sees is an
+
+ align:start position:0%
+and what the receiver sees is an
+ 
+
+ align:start position:0%
+and what the receiver sees is an
+observation X so this situation is
+
+ align:start position:0%
+observation X so this situation is
+ 
+
+ align:start position:0%
+observation X so this situation is
+described by this simple equation here
+
+ align:start position:0%
+described by this simple equation here
+ 
+
+ align:start position:0%
+described by this simple equation here
+this situation often brings up the
+
+ align:start position:0%
+this situation often brings up the
+ 
+
+ align:start position:0%
+this situation often brings up the
+following inference problem we want to
+
+ align:start position:0%
+following inference problem we want to
+ 
+
+ align:start position:0%
+following inference problem we want to
+find out what the medium is how do we do
+
+ align:start position:0%
+find out what the medium is how do we do
+ 
+
+ align:start position:0%
+find out what the medium is how do we do
+this we send a pilot signal s that is a
+
+ align:start position:0%
+this we send a pilot signal s that is a
+ 
+
+ align:start position:0%
+this we send a pilot signal s that is a
+signal that we know what it is we
+
+ align:start position:0%
+signal that we know what it is we
+ 
+
+ align:start position:0%
+signal that we know what it is we
+observe X and then using this equation
+
+ align:start position:0%
+observe X and then using this equation
+ 
+
+ align:start position:0%
+observe X and then using this equation
+and knowing that W is random noise
+
+ align:start position:0%
+and knowing that W is random noise
+ 
+
+ align:start position:0%
+and knowing that W is random noise
+coming from some distribution we try to
+
+ align:start position:0%
+coming from some distribution we try to
+ 
+
+ align:start position:0%
+coming from some distribution we try to
+make an inference about the variable
+
+ align:start position:0%
+make an inference about the variable
+ 
+
+ align:start position:0%
+make an inference about the variable
+so this is an instance of model building
+
+ align:start position:0%
+so this is an instance of model building
+ 
+
+ align:start position:0%
+so this is an instance of model building
+we are trying to make a model of the
+
+ align:start position:0%
+we are trying to make a model of the
+ 
+
+ align:start position:0%
+we are trying to make a model of the
+medium that's involved but we can also
+
+ align:start position:0%
+medium that's involved but we can also
+ 
+
+ align:start position:0%
+medium that's involved but we can also
+think of a different problem suppose
+
+ align:start position:0%
+think of a different problem suppose
+ 
+
+ align:start position:0%
+think of a different problem suppose
+that we know what the medium is perhaps
+
+ align:start position:0%
+that we know what the medium is perhaps
+ 
+
+ align:start position:0%
+that we know what the medium is perhaps
+we already went through this particular
+
+ align:start position:0%
+we already went through this particular
+ 
+
+ align:start position:0%
+we already went through this particular
+phase here but we're sitting at the
+
+ align:start position:0%
+phase here but we're sitting at the
+ 
+
+ align:start position:0%
+phase here but we're sitting at the
+receiver and we do not know what has
+
+ align:start position:0%
+receiver and we do not know what has
+ 
+
+ align:start position:0%
+receiver and we do not know what has
+been sent and we want to find out what s
+
+ align:start position:0%
+been sent and we want to find out what s
+ 
+
+ align:start position:0%
+been sent and we want to find out what s
+is so we are looking again at this
+
+ align:start position:0%
+is so we are looking again at this
+ 
+
+ align:start position:0%
+is so we are looking again at this
+equation this time we know a and we're
+
+ align:start position:0%
+equation this time we know a and we're
+ 
+
+ align:start position:0%
+equation this time we know a and we're
+trying to make inferences about s you
+
+ align:start position:0%
+trying to make inferences about s you
+ 
+
+ align:start position:0%
+trying to make inferences about s you
+notice that these two versions of the
+
+ align:start position:0%
+notice that these two versions of the
+ 
+
+ align:start position:0%
+notice that these two versions of the
+problem are essentially of the same
+
+ align:start position:0%
+problem are essentially of the same
+ 
+
+ align:start position:0%
+problem are essentially of the same
+mathematical structure we have a linear
+
+ align:start position:0%
+mathematical structure we have a linear
+ 
+
+ align:start position:0%
+mathematical structure we have a linear
+equation in one case we know s we want
+
+ align:start position:0%
+equation in one case we know s we want
+ 
+
+ align:start position:0%
+equation in one case we know s we want
+to find out a in the other case we know
+
+ align:start position:0%
+to find out a in the other case we know
+ 
+
+ align:start position:0%
+to find out a in the other case we know
+a we want to find out what s is so even
+
+ align:start position:0%
+a we want to find out what s is so even
+ 
+
+ align:start position:0%
+a we want to find out what s is so even
+though the interpretation of these two
+
+ align:start position:0%
+though the interpretation of these two
+ 
+
+ align:start position:0%
+though the interpretation of these two
+problems are quite different the
+
+ align:start position:0%
+problems are quite different the
+ 
+
+ align:start position:0%
+problems are quite different the
+mathematical structure is exactly the
+
+ align:start position:0%
+mathematical structure is exactly the
+ 
+
+ align:start position:0%
+mathematical structure is exactly the
+same this is fortunate it means that one
+
+ align:start position:0%
+same this is fortunate it means that one
+ 
+
+ align:start position:0%
+same this is fortunate it means that one
+and the same methodology will be
+
+ align:start position:0%
+and the same methodology will be
+ 
+
+ align:start position:0%
+and the same methodology will be
+applicable to both types of problems
+
+ align:start position:0%
+applicable to both types of problems
+ 
+
+ align:start position:0%
+applicable to both types of problems
+there is another distinction between
+
+ align:start position:0%
+there is another distinction between
+ 
+
+ align:start position:0%
+there is another distinction between
+problem types which turns out to be a
+
+ align:start position:0%
+problem types which turns out to be a
+ 
+
+ align:start position:0%
+problem types which turns out to be a
+little more substantial there are
+
+ align:start position:0%
+little more substantial there are
+ 
+
+ align:start position:0%
+little more substantial there are
+problems that we call hypothesis testing
+
+ align:start position:0%
+problems that we call hypothesis testing
+ 
+
+ align:start position:0%
+problems that we call hypothesis testing
+problems in those problems the unknown
+
+ align:start position:0%
+problems in those problems the unknown
+ 
+
+ align:start position:0%
+problems in those problems the unknown
+takes one out of a few possible values
+
+ align:start position:0%
+takes one out of a few possible values
+ 
+
+ align:start position:0%
+takes one out of a few possible values
+that is we may have a few different
+
+ align:start position:0%
+that is we may have a few different
+ 
+
+ align:start position:0%
+that is we may have a few different
+alternative models of the world and
+
+ align:start position:0%
+alternative models of the world and
+ 
+
+ align:start position:0%
+alternative models of the world and
+we're trying to figure out which one of
+
+ align:start position:0%
+we're trying to figure out which one of
+ 
+
+ align:start position:0%
+we're trying to figure out which one of
+those models is the correct one we are
+
+ align:start position:0%
+those models is the correct one we are
+ 
+
+ align:start position:0%
+those models is the correct one we are
+going to decide in favor of one of the
+
+ align:start position:0%
+going to decide in favor of one of the
+ 
+
+ align:start position:0%
+going to decide in favor of one of the
+candidate models and what we want to
+
+ align:start position:0%
+candidate models and what we want to
+ 
+
+ align:start position:0%
+candidate models and what we want to
+achieve is that we make a correct
+
+ align:start position:0%
+achieve is that we make a correct
+ 
+
+ align:start position:0%
+achieve is that we make a correct
+decision or if not we want to have a
+
+ align:start position:0%
+decision or if not we want to have a
+ 
+
+ align:start position:0%
+decision or if not we want to have a
+small probability of making an incorrect
+
+ align:start position:0%
+small probability of making an incorrect
+ 
+
+ align:start position:0%
+small probability of making an incorrect
+decision an example of this kind is the
+
+ align:start position:0%
+decision an example of this kind is the
+ 
+
+ align:start position:0%
+decision an example of this kind is the
+radar detection problem that we had
+
+ align:start position:0%
+radar detection problem that we had
+ 
+
+ align:start position:0%
+radar detection problem that we had
+discussed in the very beginning of this
+
+ align:start position:0%
+discussed in the very beginning of this
+ 
+
+ align:start position:0%
+discussed in the very beginning of this
+course in which we were getting a signal
+
+ align:start position:0%
+course in which we were getting a signal
+ 
+
+ align:start position:0%
+course in which we were getting a signal
+we were getting a radar reading and the
+
+ align:start position:0%
+we were getting a radar reading and the
+ 
+
+ align:start position:0%
+we were getting a radar reading and the
+question was to make an inference
+
+ align:start position:0%
+question was to make an inference
+ 
+
+ align:start position:0%
+question was to make an inference
+whether the radar is seeing an airplane
+
+ align:start position:0%
+whether the radar is seeing an airplane
+ 
+
+ align:start position:0%
+whether the radar is seeing an airplane
+or whether an
+
+ align:start position:0%
+or whether an
+ 
+
+ align:start position:0%
+or whether an
+plane is not present so in hypothesis
+
+ align:start position:0%
+plane is not present so in hypothesis
+ 
+
+ align:start position:0%
+plane is not present so in hypothesis
+testing problems were essentially making
+
+ align:start position:0%
+testing problems were essentially making
+ 
+
+ align:start position:0%
+testing problems were essentially making
+a choice out of a small number of
+
+ align:start position:0%
+a choice out of a small number of
+ 
+
+ align:start position:0%
+a choice out of a small number of
+discrete possible choices instead in
+
+ align:start position:0%
+discrete possible choices instead in
+ 
+
+ align:start position:0%
+discrete possible choices instead in
+estimation problems the unknown
+
+ align:start position:0%
+estimation problems the unknown
+ 
+
+ align:start position:0%
+estimation problems the unknown
+quantities are more of a numerical type
+
+ align:start position:0%
+quantities are more of a numerical type
+ 
+
+ align:start position:0%
+quantities are more of a numerical type
+they could even take continuous values
+
+ align:start position:0%
+they could even take continuous values
+ 
+
+ align:start position:0%
+they could even take continuous values
+and what we want to do is to come up
+
+ align:start position:0%
+and what we want to do is to come up
+ 
+
+ align:start position:0%
+and what we want to do is to come up
+with an estimate of an unknown quantity
+
+ align:start position:0%
+with an estimate of an unknown quantity
+ 
+
+ align:start position:0%
+with an estimate of an unknown quantity
+that is close to the true but unknown
+
+ align:start position:0%
+that is close to the true but unknown
+ 
+
+ align:start position:0%
+that is close to the true but unknown
+value of the quantity that we're trying
+
+ align:start position:0%
+value of the quantity that we're trying
+ 
+
+ align:start position:0%
+value of the quantity that we're trying
+to estimate so here our performance
+
+ align:start position:0%
+to estimate so here our performance
+ 
+
+ align:start position:0%
+to estimate so here our performance
+objective is in terms of some kind of
+
+ align:start position:0%
+objective is in terms of some kind of
+ 
+
+ align:start position:0%
+objective is in terms of some kind of
+distance function we want to be close to
+
+ align:start position:0%
+distance function we want to be close to
+ 
+
+ align:start position:0%
+distance function we want to be close to
+the truth and typically we have a
+
+ align:start position:0%
+the truth and typically we have a
+ 
+
+ align:start position:0%
+the truth and typically we have a
+continuum of possible choices that is
+
+ align:start position:0%
+continuum of possible choices that is
+ 
+
+ align:start position:0%
+continuum of possible choices that is
+our estimates can be general real
+
+ align:start position:0%
+our estimates can be general real
+ 
+
+ align:start position:0%
+our estimates can be general real
+numbers generally speaking these two
+
+ align:start position:0%
+numbers generally speaking these two
+ 
+
+ align:start position:0%
+numbers generally speaking these two
+types of problems hypothesis testing and
+
+ align:start position:0%
+types of problems hypothesis testing and
+ 
+
+ align:start position:0%
+types of problems hypothesis testing and
+estimation have some significant
+
+ align:start position:0%
+estimation have some significant
+ 
+
+ align:start position:0%
+estimation have some significant
+differences in the way that they are
+
+ align:start position:0%
+differences in the way that they are
+ 
+
+ align:start position:0%
+differences in the way that they are
+treated as we will be seeing next
\ No newline at end of file
diff --git a/vK7T72HPQ10.txt b/vK7T72HPQ10.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b85208713af256abd655b5fad8b7088507dd4289
--- /dev/null
+++ b/vK7T72HPQ10.txt
@@ -0,0 +1,2371 @@
+align:start position:0%
+ 
+so I'm gonna do today this identical
+
+ align:start position:0%
+so I'm gonna do today this identical
+ 
+
+ align:start position:0%
+so I'm gonna do today this identical
+particles will continue with identical
+
+ align:start position:0%
+particles will continue with identical
+ 
+
+ align:start position:0%
+particles will continue with identical
+particles will get almost to the
+
+ align:start position:0%
+particles will get almost to the
+ 
+
+ align:start position:0%
+particles will get almost to the
+resolution of the issue of exchange
+
+ align:start position:0%
+resolution of the issue of exchange
+ 
+
+ align:start position:0%
+resolution of the issue of exchange
+degeneracy in order to do the generate
+
+ align:start position:0%
+degeneracy in order to do the generate
+ 
+
+ align:start position:0%
+degeneracy in order to do the generate
+this identical particles properly you
+
+ align:start position:0%
+this identical particles properly you
+ 
+
+ align:start position:0%
+this identical particles properly you
+have to do a bit of group Theory your
+
+ align:start position:0%
+have to do a bit of group Theory your
+ 
+
+ align:start position:0%
+have to do a bit of group Theory your
+understanding with permutation operators
+
+ align:start position:0%
+understanding with permutation operators
+ 
+
+ align:start position:0%
+understanding with permutation operators
+are well so it allows you to think about
+
+ align:start position:0%
+are well so it allows you to think about
+ 
+
+ align:start position:0%
+are well so it allows you to think about
+this matters more clearly so that's what
+
+ align:start position:0%
+this matters more clearly so that's what
+ 
+
+ align:start position:0%
+this matters more clearly so that's what
+we have to do today so let me review so
+
+ align:start position:0%
+we have to do today so let me review so
+ 
+
+ align:start position:0%
+we have to do today so let me review so
+we were doing identical particles and we
+
+ align:start position:0%
+we were doing identical particles and we
+ 
+
+ align:start position:0%
+we were doing identical particles and we
+spoke of exchange degeneracy we had say
+
+ align:start position:0%
+spoke of exchange degeneracy we had say
+ 
+
+ align:start position:0%
+spoke of exchange degeneracy we had say
+for the state of two spins identical
+
+ align:start position:0%
+for the state of two spins identical
+ 
+
+ align:start position:0%
+for the state of two spins identical
+spins we said could be represented by
+
+ align:start position:0%
+spins we said could be represented by
+ 
+
+ align:start position:0%
+spins we said could be represented by
+this state or by the state in which you
+
+ align:start position:0%
+this state or by the state in which you
+ 
+
+ align:start position:0%
+this state or by the state in which you
+exchange the plusses and minuses so for
+
+ align:start position:0%
+exchange the plusses and minuses so for
+ 
+
+ align:start position:0%
+exchange the plusses and minuses so for
+identical so the prom of exchange the
+
+ align:start position:0%
+identical so the prom of exchange the
+ 
+
+ align:start position:0%
+identical so the prom of exchange the
+generous is that for identical particles
+
+ align:start position:0%
+generous is that for identical particles
+ 
+
+ align:start position:0%
+generous is that for identical particles
+you would almost say that these two
+
+ align:start position:0%
+you would almost say that these two
+ 
+
+ align:start position:0%
+you would almost say that these two
+states are equivalent you know one
+
+ align:start position:0%
+states are equivalent you know one
+ 
+
+ align:start position:0%
+states are equivalent you know one
+particle is in plus one particle is in -
+
+ align:start position:0%
+particle is in plus one particle is in -
+ 
+
+ align:start position:0%
+particle is in plus one particle is in -
+they are identical so you cannot tell
+
+ align:start position:0%
+they are identical so you cannot tell
+ 
+
+ align:start position:0%
+they are identical so you cannot tell
+whether it's a first or a second so you
+
+ align:start position:0%
+whether it's a first or a second so you
+ 
+
+ align:start position:0%
+whether it's a first or a second so you
+would say these two states are
+
+ align:start position:0%
+would say these two states are
+ 
+
+ align:start position:0%
+would say these two states are
+equivalent but we saw that that leads to
+
+ align:start position:0%
+equivalent but we saw that that leads to
+ 
+
+ align:start position:0%
+equivalent but we saw that that leads to
+a contradiction if this two states are
+
+ align:start position:0%
+a contradiction if this two states are
+ 
+
+ align:start position:0%
+a contradiction if this two states are
+equivalent any linear superposition of
+
+ align:start position:0%
+equivalent any linear superposition of
+ 
+
+ align:start position:0%
+equivalent any linear superposition of
+them should be equivalent and then when
+
+ align:start position:0%
+them should be equivalent and then when
+ 
+
+ align:start position:0%
+them should be equivalent and then when
+we ask the question of the probability
+
+ align:start position:0%
+we ask the question of the probability
+ 
+
+ align:start position:0%
+we ask the question of the probability
+of finding these states in a particular
+
+ align:start position:0%
+of finding these states in a particular
+ 
+
+ align:start position:0%
+of finding these states in a particular
+state that was along the x direction
+
+ align:start position:0%
+state that was along the x direction
+ 
+
+ align:start position:0%
+state that was along the x direction
+both spins along the x direction we
+
+ align:start position:0%
+both spins along the x direction we
+ 
+
+ align:start position:0%
+both spins along the x direction we
+found that it depended on what linear
+
+ align:start position:0%
+found that it depended on what linear
+ 
+
+ align:start position:0%
+found that it depended on what linear
+combination you took here so it's just
+
+ align:start position:0%
+combination you took here so it's just
+ 
+
+ align:start position:0%
+combination you took here so it's just
+not consistent with the principles of
+
+ align:start position:0%
+not consistent with the principles of
+ 
+
+ align:start position:0%
+not consistent with the principles of
+quantum mechanics to say that these two
+
+ align:start position:0%
+quantum mechanics to say that these two
+ 
+
+ align:start position:0%
+quantum mechanics to say that these two
+states are equivalent so they're not and
+
+ align:start position:0%
+states are equivalent so they're not and
+ 
+
+ align:start position:0%
+states are equivalent so they're not and
+we better
+
+ align:start position:0%
+we better
+ 
+
+ align:start position:0%
+we better
+and how we can solve this problem now I
+
+ align:start position:0%
+and how we can solve this problem now I
+ 
+
+ align:start position:0%
+and how we can solve this problem now I
+think the solution in a sense you've
+
+ align:start position:0%
+think the solution in a sense you've
+ 
+
+ align:start position:0%
+think the solution in a sense you've
+heard before and you know how you're
+
+ align:start position:0%
+heard before and you know how you're
+ 
+
+ align:start position:0%
+heard before and you know how you're
+supposed to work with identical
+
+ align:start position:0%
+supposed to work with identical
+ 
+
+ align:start position:0%
+supposed to work with identical
+particles but I think going through this
+
+ align:start position:0%
+particles but I think going through this
+ 
+
+ align:start position:0%
+particles but I think going through this
+in detail and seeing what is this
+
+ align:start position:0%
+in detail and seeing what is this
+ 
+
+ align:start position:0%
+in detail and seeing what is this
+structure of operators and Hilbert
+
+ align:start position:0%
+structure of operators and Hilbert
+ 
+
+ align:start position:0%
+structure of operators and Hilbert
+spaces that leads to that solution why
+
+ align:start position:0%
+spaces that leads to that solution why
+ 
+
+ align:start position:0%
+spaces that leads to that solution why
+that solution is the unique solution to
+
+ align:start position:0%
+that solution is the unique solution to
+ 
+
+ align:start position:0%
+that solution is the unique solution to
+this problem it's interesting so we
+
+ align:start position:0%
+this problem it's interesting so we
+ 
+
+ align:start position:0%
+this problem it's interesting so we
+begin with permutation operators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operators so we consider a two particle
+
+ align:start position:0%
+operators so we consider a two particle
+ 
+
+ align:start position:0%
+operators so we consider a two particle
+system we'll begin with two particles
+
+ align:start position:0%
+system we'll begin with two particles
+ 
+
+ align:start position:0%
+system we'll begin with two particles
+and then we'll eventually generalize to
+
+ align:start position:0%
+and then we'll eventually generalize to
+ 
+
+ align:start position:0%
+and then we'll eventually generalize to
+n particles will do everything for two
+
+ align:start position:0%
+n particles will do everything for two
+ 
+
+ align:start position:0%
+n particles will do everything for two
+particles first so the particles they
+
+ align:start position:0%
+particles first so the particles they
+ 
+
+ align:start position:0%
+particles first so the particles they
+will live on a vector space V each one
+
+ align:start position:0%
+will live on a vector space V each one
+ 
+
+ align:start position:0%
+will live on a vector space V each one
+so that the set of two particles lives
+
+ align:start position:0%
+so that the set of two particles lives
+ 
+
+ align:start position:0%
+so that the set of two particles lives
+on V tensor V so each particle has a set
+
+ align:start position:0%
+on V tensor V so each particle has a set
+ 
+
+ align:start position:0%
+on V tensor V so each particle has a set
+of possible states that are the vectors
+
+ align:start position:0%
+of possible states that are the vectors
+ 
+
+ align:start position:0%
+of possible states that are the vectors
+in V and the two particles have a set of
+
+ align:start position:0%
+in V and the two particles have a set of
+ 
+
+ align:start position:0%
+in V and the two particles have a set of
+possible states that are the vectors in
+
+ align:start position:0%
+possible states that are the vectors in
+ 
+
+ align:start position:0%
+possible states that are the vectors in
+V tensor V now for the moment whether
+
+ align:start position:0%
+V tensor V now for the moment whether
+ 
+
+ align:start position:0%
+V tensor V now for the moment whether
+they're identical or not identical will
+
+ align:start position:0%
+they're identical or not identical will
+ 
+
+ align:start position:0%
+they're identical or not identical will
+play no role will play no role
+
+ align:start position:0%
+play no role will play no role
+ 
+
+ align:start position:0%
+play no role will play no role
+throughout this lecture where we
+
+ align:start position:0%
+throughout this lecture where we
+ 
+
+ align:start position:0%
+throughout this lecture where we
+understand those operators in Hilbert
+
+ align:start position:0%
+understand those operators in Hilbert
+ 
+
+ align:start position:0%
+understand those operators in Hilbert
+spaces so it will not matter so the
+
+ align:start position:0%
+spaces so it will not matter so the
+ 
+
+ align:start position:0%
+spaces so it will not matter so the
+particles may be distinguishable may not
+
+ align:start position:0%
+particles may be distinguishable may not
+ 
+
+ align:start position:0%
+particles may be distinguishable may not
+be distinguishable and we will write
+
+ align:start position:0%
+be distinguishable and we will write
+ 
+
+ align:start position:0%
+be distinguishable and we will write
+States here in V tensor V bases States
+
+ align:start position:0%
+States here in V tensor V bases States
+ 
+
+ align:start position:0%
+States here in V tensor V bases States
+for example as UI 1 tensor u2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you I'm sorry you J - so with little I
+
+ align:start position:0%
+you I'm sorry you J - so with little I
+ 
+
+ align:start position:0%
+you I'm sorry you J - so with little I
+and little J the noting different
+
+ align:start position:0%
+and little J the noting different
+ 
+
+ align:start position:0%
+and little J the noting different
+integers those are different basis
+
+ align:start position:0%
+integers those are different basis
+ 
+
+ align:start position:0%
+integers those are different basis
+vectors and this is a set of basis
+
+ align:start position:0%
+vectors and this is a set of basis
+ 
+
+ align:start position:0%
+vectors and this is a set of basis
+vectors in V tensor V so basis vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for all I and J now sometimes we get a
+
+ align:start position:0%
+for all I and J now sometimes we get a
+ 
+
+ align:start position:0%
+for all I and J now sometimes we get a
+little lazy and we stop writing the one
+
+ align:start position:0%
+little lazy and we stop writing the one
+ 
+
+ align:start position:0%
+little lazy and we stop writing the one
+and two and we write it as UI tenser UJ
+
+ align:start position:0%
+and two and we write it as UI tenser UJ
+ 
+
+ align:start position:0%
+and two and we write it as UI tenser UJ
+or even we can get more lazy and just
+
+ align:start position:0%
+or even we can get more lazy and just
+ 
+
+ align:start position:0%
+or even we can get more lazy and just
+write UI UJ so if we do that you should
+
+ align:start position:0%
+write UI UJ so if we do that you should
+ 
+
+ align:start position:0%
+write UI UJ so if we do that you should
+know you really mean this whole thing so
+
+ align:start position:0%
+know you really mean this whole thing so
+ 
+
+ align:start position:0%
+know you really mean this whole thing so
+what is a permutation operator is a
+
+ align:start position:0%
+what is a permutation operator is a
+ 
+
+ align:start position:0%
+what is a permutation operator is a
+linear operator that does some funny
+
+ align:start position:0%
+linear operator that does some funny
+ 
+
+ align:start position:0%
+linear operator that does some funny
+thing on the state so let's look into it
+
+ align:start position:0%
+thing on the state so let's look into it
+ 
+
+ align:start position:0%
+thing on the state so let's look into it
+so a permutation operator P - 1 that's a
+
+ align:start position:0%
+so a permutation operator P - 1 that's a
+ 
+
+ align:start position:0%
+so a permutation operator P - 1 that's a
+name I will give it P - 1 is a linear
+
+ align:start position:0%
+name I will give it P - 1 is a linear
+ 
+
+ align:start position:0%
+name I will give it P - 1 is a linear
+operator acting on the space me answer
+
+ align:start position:0%
+operator acting on the space me answer
+ 
+
+ align:start position:0%
+operator acting on the space me answer
+me linear operator and this is called
+
+ align:start position:0%
+me linear operator and this is called
+ 
+
+ align:start position:0%
+me linear operator and this is called
+the permutation operator so to know what
+
+ align:start position:0%
+the permutation operator so to know what
+ 
+
+ align:start position:0%
+the permutation operator so to know what
+this permutation operator is you need to
+
+ align:start position:0%
+this permutation operator is you need to
+ 
+
+ align:start position:0%
+this permutation operator is you need to
+know how it acts on a basis state so
+
+ align:start position:0%
+know how it acts on a basis state so
+ 
+
+ align:start position:0%
+know how it acts on a basis state so
+let's put one of these basis States u i1
+
+ align:start position:0%
+let's put one of these basis States u i1
+ 
+
+ align:start position:0%
+let's put one of these basis States u i1
+tenser UJ - and this permutation
+
+ align:start position:0%
+tenser UJ - and this permutation
+ 
+
+ align:start position:0%
+tenser UJ - and this permutation
+operator you just need to know how it
+
+ align:start position:0%
+operator you just need to know how it
+ 
+
+ align:start position:0%
+operator you just need to know how it
+acts on a bay in the basis a that's the
+
+ align:start position:0%
+acts on a bay in the basis a that's the
+ 
+
+ align:start position:0%
+acts on a bay in the basis a that's the
+safest way always to know that you have
+
+ align:start position:0%
+safest way always to know that you have
+ 
+
+ align:start position:0%
+safest way always to know that you have
+a linear operator if you know how it
+
+ align:start position:0%
+a linear operator if you know how it
+ 
+
+ align:start position:0%
+a linear operator if you know how it
+acts on a basis then
+
+ align:start position:0%
+acts on a basis then
+ 
+
+ align:start position:0%
+acts on a basis then
+some of basis States you know because
+
+ align:start position:0%
+some of basis States you know because
+ 
+
+ align:start position:0%
+some of basis States you know because
+it's linear on the other hand if
+
+ align:start position:0%
+it's linear on the other hand if
+ 
+
+ align:start position:0%
+it's linear on the other hand if
+somebody tells you this operator does
+
+ align:start position:0%
+somebody tells you this operator does
+ 
+
+ align:start position:0%
+somebody tells you this operator does
+this to all vectors something maybe it's
+
+ align:start position:0%
+this to all vectors something maybe it's
+ 
+
+ align:start position:0%
+this to all vectors something maybe it's
+not a linear operator it may be a more
+
+ align:start position:0%
+not a linear operator it may be a more
+ 
+
+ align:start position:0%
+not a linear operator it may be a more
+complicated thing so here what it will
+
+ align:start position:0%
+complicated thing so here what it will
+ 
+
+ align:start position:0%
+complicated thing so here what it will
+do is we'll put the state that was in
+
+ align:start position:0%
+do is we'll put the state that was in
+ 
+
+ align:start position:0%
+do is we'll put the state that was in
+two in position one and put the state
+
+ align:start position:0%
+two in position one and put the state
+ 
+
+ align:start position:0%
+two in position one and put the state
+that was in one in position two so it
+
+ align:start position:0%
+that was in one in position two so it
+ 
+
+ align:start position:0%
+that was in one in position two so it
+will take you j1 tensor you I - so the
+
+ align:start position:0%
+will take you j1 tensor you I - so the
+ 
+
+ align:start position:0%
+will take you j1 tensor you I - so the
+state in to this first thing that says
+
+ align:start position:0%
+state in to this first thing that says
+ 
+
+ align:start position:0%
+state in to this first thing that says
+that the state into should be put in
+
+ align:start position:0%
+that the state into should be put in
+ 
+
+ align:start position:0%
+that the state into should be put in
+position one so the J label it was u J
+
+ align:start position:0%
+position one so the J label it was u J
+ 
+
+ align:start position:0%
+position one so the J label it was u J
+now is in position 1 and the state that
+
+ align:start position:0%
+now is in position 1 and the state that
+ 
+
+ align:start position:0%
+now is in position 1 and the state that
+was in one should go to position 2 it's
+
+ align:start position:0%
+was in one should go to position 2 it's
+ 
+
+ align:start position:0%
+was in one should go to position 2 it's
+kind of the one thing we never do is
+
+ align:start position:0%
+kind of the one thing we never do is
+ 
+
+ align:start position:0%
+kind of the one thing we never do is
+flip this things the first particle goes
+
+ align:start position:0%
+flip this things the first particle goes
+ 
+
+ align:start position:0%
+flip this things the first particle goes
+before the second particle that's our
+
+ align:start position:0%
+before the second particle that's our
+ 
+
+ align:start position:0%
+before the second particle that's our
+order of things but the state has moved
+
+ align:start position:0%
+order of things but the state has moved
+ 
+
+ align:start position:0%
+order of things but the state has moved
+okay so this is how the prescription of
+
+ align:start position:0%
+okay so this is how the prescription of
+ 
+
+ align:start position:0%
+okay so this is how the prescription of
+what this does and then you realize
+
+ align:start position:0%
+what this does and then you realize
+ 
+
+ align:start position:0%
+what this does and then you realize
+already one property that p21
+
+ align:start position:0%
+already one property that p21
+ 
+
+ align:start position:0%
+already one property that p21
+p21 if you let it up twice in a state it
+
+ align:start position:0%
+p21 if you let it up twice in a state it
+ 
+
+ align:start position:0%
+p21 if you let it up twice in a state it
+will flip the IJ labels the first time
+
+ align:start position:0%
+will flip the IJ labels the first time
+ 
+
+ align:start position:0%
+will flip the IJ labels the first time
+and it will flip them again the second
+
+ align:start position:0%
+and it will flip them again the second
+ 
+
+ align:start position:0%
+and it will flip them again the second
+time so this is the unit operator so
+
+ align:start position:0%
+time so this is the unit operator so
+ 
+
+ align:start position:0%
+time so this is the unit operator so
+it's its inverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's a nice thing now
+
+ align:start position:0%
+so that's a nice thing now
+ 
+
+ align:start position:0%
+so that's a nice thing now
+perhaps a little less obvious but kind
+
+ align:start position:0%
+perhaps a little less obvious but kind
+ 
+
+ align:start position:0%
+perhaps a little less obvious but kind
+of still simple is that p21 is hermitian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do you check that an operator is
+
+ align:start position:0%
+how do you check that an operator is
+ 
+
+ align:start position:0%
+how do you check that an operator is
+hermitian an operator m is hermitian if
+
+ align:start position:0%
+hermitian an operator m is hermitian if
+ 
+
+ align:start position:0%
+hermitian an operator m is hermitian if
+you have for example m alpha beta is
+
+ align:start position:0%
+you have for example m alpha beta is
+ 
+
+ align:start position:0%
+you have for example m alpha beta is
+equal to alpha and beta the m operator
+
+ align:start position:0%
+equal to alpha and beta the m operator
+ 
+
+ align:start position:0%
+equal to alpha and beta the m operator
+moves from this position to the other
+
+ align:start position:0%
+moves from this position to the other
+ 
+
+ align:start position:0%
+moves from this position to the other
+with an M dagger but if M is hermitian
+
+ align:start position:0%
+with an M dagger but if M is hermitian
+ 
+
+ align:start position:0%
+with an M dagger but if M is hermitian
+it will work like that so let's try this
+
+ align:start position:0%
+it will work like that so let's try this
+ 
+
+ align:start position:0%
+it will work like that so let's try this
+with the operator p21
+
+ align:start position:0%
+with the operator p21
+ 
+
+ align:start position:0%
+with the operator p21
+so we'll try a p21 on the state alpha
+
+ align:start position:0%
+so we'll try a p21 on the state alpha
+ 
+
+ align:start position:0%
+so we'll try a p21 on the state alpha
+and then inner product with a state beta
+
+ align:start position:0%
+and then inner product with a state beta
+ 
+
+ align:start position:0%
+and then inner product with a state beta
+so we need a number of letters so let's
+
+ align:start position:0%
+so we need a number of letters so let's
+ 
+
+ align:start position:0%
+so we need a number of letters so let's
+do it here p21 on a state alpha which
+
+ align:start position:0%
+do it here p21 on a state alpha which
+ 
+
+ align:start position:0%
+do it here p21 on a state alpha which
+will be u i1 UJ - inner product with
+
+ align:start position:0%
+will be u i1 UJ - inner product with
+ 
+
+ align:start position:0%
+will be u i1 UJ - inner product with
+state beta u k1 u l2 ok here it is
+
+ align:start position:0%
+state beta u k1 u l2 ok here it is
+ 
+
+ align:start position:0%
+state beta u k1 u l2 ok here it is
+p21 acting on some state alpha inner
+
+ align:start position:0%
+p21 acting on some state alpha inner
+ 
+
+ align:start position:0%
+p21 acting on some state alpha inner
+prior with a state beta we'll evaluate
+
+ align:start position:0%
+prior with a state beta we'll evaluate
+ 
+
+ align:start position:0%
+prior with a state beta we'll evaluate
+it well we can evaluate it quickly I
+
+ align:start position:0%
+it well we can evaluate it quickly I
+ 
+
+ align:start position:0%
+it well we can evaluate it quickly I
+think this flips the J and I so the J is
+
+ align:start position:0%
+think this flips the J and I so the J is
+ 
+
+ align:start position:0%
+think this flips the J and I so the J is
+now on the first particle and the case
+
+ align:start position:0%
+now on the first particle and the case
+ 
+
+ align:start position:0%
+now on the first particle and the case
+on the first particle so the inner
+
+ align:start position:0%
+on the first particle so the inner
+ 
+
+ align:start position:0%
+on the first particle so the inner
+product assuming this is an orthonormal
+
+ align:start position:0%
+product assuming this is an orthonormal
+ 
+
+ align:start position:0%
+product assuming this is an orthonormal
+basis is just Delta JK
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and here this operator moves the aisle
+
+ align:start position:0%
+and here this operator moves the aisle
+ 
+
+ align:start position:0%
+and here this operator moves the aisle
+able to position - and here you have an
+
+ align:start position:0%
+able to position - and here you have an
+ 
+
+ align:start position:0%
+able to position - and here you have an
+L in position - therefore it's a Delta
+
+ align:start position:0%
+L in position - therefore it's a Delta
+ 
+
+ align:start position:0%
+L in position - therefore it's a Delta
+il on the other hand we can calculate
+
+ align:start position:0%
+il on the other hand we can calculate
+ 
+
+ align:start position:0%
+il on the other hand we can calculate
+this UI 1 UJ 2 and now put the P 2 1
+
+ align:start position:0%
+this UI 1 UJ 2 and now put the P 2 1
+ 
+
+ align:start position:0%
+this UI 1 UJ 2 and now put the P 2 1
+operator here between the UK 1 and the
+
+ align:start position:0%
+operator here between the UK 1 and the
+ 
+
+ align:start position:0%
+operator here between the UK 1 and the
+UL 2 this time you flip the KML so the L
+
+ align:start position:0%
+UL 2 this time you flip the KML so the L
+ 
+
+ align:start position:0%
+UL 2 this time you flip the KML so the L
+ends up in the first Hilbert space will
+
+ align:start position:0%
+ends up in the first Hilbert space will
+ 
+
+ align:start position:0%
+ends up in the first Hilbert space will
+there's an I so you get Delta L I and
+
+ align:start position:0%
+there's an I so you get Delta L I and
+ 
+
+ align:start position:0%
+there's an I so you get Delta L I and
+the KA ends up in the second Philbert
+
+ align:start position:0%
+the KA ends up in the second Philbert
+ 
+
+ align:start position:0%
+the KA ends up in the second Philbert
+space where you have a J here so you
+
+ align:start position:0%
+space where you have a J here so you
+ 
+
+ align:start position:0%
+space where you have a J here so you
+have a J with a K and this two are the
+
+ align:start position:0%
+have a J with a K and this two are the
+ 
+
+ align:start position:0%
+have a J with a K and this two are the
+same and intuition of course--i I've
+
+ align:start position:0%
+same and intuition of course--i I've
+ 
+
+ align:start position:0%
+same and intuition of course--i I've
+written all these equations but the
+
+ align:start position:0%
+written all these equations but the
+ 
+
+ align:start position:0%
+written all these equations but the
+intuition is if you have an inner
+
+ align:start position:0%
+intuition is if you have an inner
+ 
+
+ align:start position:0%
+intuition is if you have an inner
+product that this Chronicle Delta same
+
+ align:start position:0%
+product that this Chronicle Delta same
+ 
+
+ align:start position:0%
+product that this Chronicle Delta same
+you exchange to here the result is the
+
+ align:start position:0%
+you exchange to here the result is the
+ 
+
+ align:start position:0%
+you exchange to here the result is the
+same as if you exchange to here it will
+
+ align:start position:0%
+same as if you exchange to here it will
+ 
+
+ align:start position:0%
+same as if you exchange to here it will
+do the same thing so it's a hermitian
+
+ align:start position:0%
+do the same thing so it's a hermitian
+ 
+
+ align:start position:0%
+do the same thing so it's a hermitian
+operator so operator p21 is hermitian
+
+ align:start position:0%
+operator so operator p21 is hermitian
+ 
+
+ align:start position:0%
+operator so operator p21 is hermitian
+that means that the relation P - 1 P 2 1
+
+ align:start position:0%
+that means that the relation P - 1 P 2 1
+ 
+
+ align:start position:0%
+that means that the relation P - 1 P 2 1
+equal 1 since this is hermitian speed 2
+
+ align:start position:0%
+equal 1 since this is hermitian speed 2
+ 
+
+ align:start position:0%
+equal 1 since this is hermitian speed 2
+1 dagger
+
+ align:start position:0%
+1 dagger
+ 
+
+ align:start position:0%
+1 dagger
+P 2 1 equal 1 so we learn that also the
+
+ align:start position:0%
+P 2 1 equal 1 so we learn that also the
+ 
+
+ align:start position:0%
+P 2 1 equal 1 so we learn that also the
+operator is unitary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+p21 unitary that's nice because that
+
+ align:start position:0%
+p21 unitary that's nice because that
+ 
+
+ align:start position:0%
+p21 unitary that's nice because that
+means that could be a symmetry in in
+
+ align:start position:0%
+means that could be a symmetry in in
+ 
+
+ align:start position:0%
+means that could be a symmetry in in
+quantum mechanics
+
+ align:start position:0%
+quantum mechanics
+ 
+
+ align:start position:0%
+quantum mechanics
+operators in quantum mechanics that
+
+ align:start position:0%
+operators in quantum mechanics that
+ 
+
+ align:start position:0%
+operators in quantum mechanics that
+preserve the norm of states can be
+
+ align:start position:0%
+preserve the norm of states can be
+ 
+
+ align:start position:0%
+preserve the norm of states can be
+symmetries and p21 is unitary so okay so
+
+ align:start position:0%
+symmetries and p21 is unitary so okay so
+ 
+
+ align:start position:0%
+symmetries and p21 is unitary so okay so
+we have our operator p21 let's do things
+
+ align:start position:0%
+we have our operator p21 let's do things
+ 
+
+ align:start position:0%
+we have our operator p21 let's do things
+with it so we can define two things with
+
+ align:start position:0%
+with it so we can define two things with
+ 
+
+ align:start position:0%
+with it so we can define two things with
+p21 define this operator s which will be
+
+ align:start position:0%
+p21 define this operator s which will be
+ 
+
+ align:start position:0%
+p21 define this operator s which will be
+1/2 1 plus P 2 1 and the operator a
+
+ align:start position:0%
+1/2 1 plus P 2 1 and the operator a
+ 
+
+ align:start position:0%
+1/2 1 plus P 2 1 and the operator a
+which is 1/2 1 minus P 2 1 and here
+
+ align:start position:0%
+which is 1/2 1 minus P 2 1 and here
+ 
+
+ align:start position:0%
+which is 1/2 1 minus P 2 1 and here
+comes the claim these two operators are
+
+ align:start position:0%
+comes the claim these two operators are
+ 
+
+ align:start position:0%
+comes the claim these two operators are
+orthogonal projectors
+
+ align:start position:0%
+orthogonal projectors
+ 
+
+ align:start position:0%
+orthogonal projectors
+there are thumbnail projectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+projectors so let's review what that
+
+ align:start position:0%
+projectors so let's review what that
+ 
+
+ align:start position:0%
+projectors so let's review what that
+means
+
+ align:start position:0%
+means
+ 
+
+ align:start position:0%
+means
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so basically let me say what it means uh
+
+ align:start position:0%
+so basically let me say what it means uh
+ 
+
+ align:start position:0%
+so basically let me say what it means uh
+an operator is an orthogonal projector
+
+ align:start position:0%
+an operator is an orthogonal projector
+ 
+
+ align:start position:0%
+an operator is an orthogonal projector
+the test is that the operator squared is
+
+ align:start position:0%
+the test is that the operator squared is
+ 
+
+ align:start position:0%
+the test is that the operator squared is
+equal to itself that's the name of a
+
+ align:start position:0%
+equal to itself that's the name of a
+ 
+
+ align:start position:0%
+equal to itself that's the name of a
+projector and the other thing is that it
+
+ align:start position:0%
+projector and the other thing is that it
+ 
+
+ align:start position:0%
+projector and the other thing is that it
+must be hermitian these two things must
+
+ align:start position:0%
+must be hermitian these two things must
+ 
+
+ align:start position:0%
+must be hermitian these two things must
+happen for something to be an orthogonal
+
+ align:start position:0%
+happen for something to be an orthogonal
+ 
+
+ align:start position:0%
+happen for something to be an orthogonal
+projector basically what does it mean to
+
+ align:start position:0%
+projector basically what does it mean to
+ 
+
+ align:start position:0%
+projector basically what does it mean to
+be an orthogonal projectors an operator
+
+ align:start position:0%
+be an orthogonal projectors an operator
+ 
+
+ align:start position:0%
+be an orthogonal projectors an operator
+that projects to some space so an
+
+ align:start position:0%
+that projects to some space so an
+ 
+
+ align:start position:0%
+that projects to some space so an
+operator has a set of states that are in
+
+ align:start position:0%
+operator has a set of states that are in
+ 
+
+ align:start position:0%
+operator has a set of states that are in
+its image in the range of the operator
+
+ align:start position:0%
+its image in the range of the operator
+ 
+
+ align:start position:0%
+its image in the range of the operator
+that's what it projects into it has a
+
+ align:start position:0%
+that's what it projects into it has a
+ 
+
+ align:start position:0%
+that's what it projects into it has a
+null space the things that are killed by
+
+ align:start position:0%
+null space the things that are killed by
+ 
+
+ align:start position:0%
+null space the things that are killed by
+the projector a projector has precisely
+
+ align:start position:0%
+the projector a projector has precisely
+ 
+
+ align:start position:0%
+the projector a projector has precisely
+that kind of thing so so the thing that
+
+ align:start position:0%
+that kind of thing so so the thing that
+ 
+
+ align:start position:0%
+that kind of thing so so the thing that
+makes it an orthogonal projector is that
+
+ align:start position:0%
+makes it an orthogonal projector is that
+ 
+
+ align:start position:0%
+makes it an orthogonal projector is that
+the range of the projector the vectors
+
+ align:start position:0%
+the range of the projector the vectors
+ 
+
+ align:start position:0%
+the range of the projector the vectors
+that you get are orthogonal to the
+
+ align:start position:0%
+that you get are orthogonal to the
+ 
+
+ align:start position:0%
+that you get are orthogonal to the
+vectors that are killed by the projector
+
+ align:start position:0%
+vectors that are killed by the projector
+ 
+
+ align:start position:0%
+vectors that are killed by the projector
+so everything if things the holes vector
+
+ align:start position:0%
+so everything if things the holes vector
+ 
+
+ align:start position:0%
+so everything if things the holes vector
+space splits into two parts what do you
+
+ align:start position:0%
+space splits into two parts what do you
+ 
+
+ align:start position:0%
+space splits into two parts what do you
+get from the projector and the rest and
+
+ align:start position:0%
+get from the projector and the rest and
+ 
+
+ align:start position:0%
+get from the projector and the rest and
+the rest is things that are killed by
+
+ align:start position:0%
+the rest is things that are killed by
+ 
+
+ align:start position:0%
+the rest is things that are killed by
+the projector and they're orthogonal to
+
+ align:start position:0%
+the projector and they're orthogonal to
+ 
+
+ align:start position:0%
+the projector and they're orthogonal to
+it so let me say here a projector piece
+
+ align:start position:0%
+it so let me say here a projector piece
+ 
+
+ align:start position:0%
+it so let me say here a projector piece
+up you to you subset of V is orthogonal
+
+ align:start position:0%
+up you to you subset of V is orthogonal
+ 
+
+ align:start position:0%
+up you to you subset of V is orthogonal
+so this is 805 type stuff if the vector
+
+ align:start position:0%
+so this is 805 type stuff if the vector
+ 
+
+ align:start position:0%
+so this is 805 type stuff if the vector
+space can be written as the null space
+
+ align:start position:0%
+space can be written as the null space
+ 
+
+ align:start position:0%
+space can be written as the null space
+of PU plus the range of PU
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with now of PU perpendicular or
+
+ align:start position:0%
+with now of PU perpendicular or
+ 
+
+ align:start position:0%
+with now of PU perpendicular or
+orthogonal to range so this is the
+
+ align:start position:0%
+orthogonal to range so this is the
+ 
+
+ align:start position:0%
+orthogonal to range so this is the
+definition of an orthogonal projector
+
+ align:start position:0%
+definition of an orthogonal projector
+ 
+
+ align:start position:0%
+definition of an orthogonal projector
+and here is of course a simple claim of
+
+ align:start position:0%
+and here is of course a simple claim of
+ 
+
+ align:start position:0%
+and here is of course a simple claim of
+a hermitian operator P such that P
+
+ align:start position:0%
+a hermitian operator P such that P
+ 
+
+ align:start position:0%
+a hermitian operator P such that P
+squared is equal to P is an orthogonal
+
+ align:start position:0%
+squared is equal to P is an orthogonal
+ 
+
+ align:start position:0%
+squared is equal to P is an orthogonal
+projector projector okay so that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+second claim so let's let's see again
+
+ align:start position:0%
+second claim so let's let's see again
+ 
+
+ align:start position:0%
+second claim so let's let's see again
+what we want to show is that these are
+
+ align:start position:0%
+what we want to show is that these are
+ 
+
+ align:start position:0%
+what we want to show is that these are
+projectors and they're orthogonal
+
+ align:start position:0%
+projectors and they're orthogonal
+ 
+
+ align:start position:0%
+projectors and they're orthogonal
+projectors and this is what it means but
+
+ align:start position:0%
+projectors and this is what it means but
+ 
+
+ align:start position:0%
+projectors and this is what it means but
+practically speaking all we have to do
+
+ align:start position:0%
+practically speaking all we have to do
+ 
+
+ align:start position:0%
+practically speaking all we have to do
+is check that this operator satisfies
+
+ align:start position:0%
+is check that this operator satisfies
+ 
+
+ align:start position:0%
+is check that this operator satisfies
+this and are hermitian so all you need
+
+ align:start position:0%
+this and are hermitian so all you need
+ 
+
+ align:start position:0%
+this and are hermitian so all you need
+to do let me explain why this is the
+
+ align:start position:0%
+to do let me explain why this is the
+ 
+
+ align:start position:0%
+to do let me explain why this is the
+case so whenever you have let's do a
+
+ align:start position:0%
+case so whenever you have let's do a
+ 
+
+ align:start position:0%
+case so whenever you have let's do a
+little proof so if you have a vector a
+
+ align:start position:0%
+little proof so if you have a vector a
+ 
+
+ align:start position:0%
+little proof so if you have a vector a
+vector can be written as the projector
+
+ align:start position:0%
+vector can be written as the projector
+ 
+
+ align:start position:0%
+vector can be written as the projector
+times the vector plus one minus the
+
+ align:start position:0%
+times the vector plus one minus the
+ 
+
+ align:start position:0%
+times the vector plus one minus the
+projector acting on the vector this the
+
+ align:start position:0%
+projector acting on the vector this the
+ 
+
+ align:start position:0%
+projector acting on the vector this the
+projector on the vector is in the range
+
+ align:start position:0%
+projector on the vector is in the range
+ 
+
+ align:start position:0%
+projector on the vector is in the range
+of P because the range of P are the
+
+ align:start position:0%
+of P because the range of P are the
+ 
+
+ align:start position:0%
+of P because the range of P are the
+vectors obtained by acting with P
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moreover this is in the null of P why
+
+ align:start position:0%
+moreover this is in the null of P why
+ 
+
+ align:start position:0%
+moreover this is in the null of P why
+because P kills these vectors how do you
+
+ align:start position:0%
+because P kills these vectors how do you
+ 
+
+ align:start position:0%
+because P kills these vectors how do you
+check that P acting on that vector P
+
+ align:start position:0%
+check that P acting on that vector P
+ 
+
+ align:start position:0%
+check that P acting on that vector P
+with this is P but P squared is equal to
+
+ align:start position:0%
+with this is P but P squared is equal to
+ 
+
+ align:start position:0%
+with this is P but P squared is equal to
+P so you get 0 so here it is the vector
+
+ align:start position:0%
+P so you get 0 so here it is the vector
+ 
+
+ align:start position:0%
+P so you get 0 so here it is the vector
+space decomposes into the range of
+
+ align:start position:0%
+space decomposes into the range of
+ 
+
+ align:start position:0%
+space decomposes into the range of
+people as the now of P so that's the
+
+ align:start position:0%
+people as the now of P so that's the
+ 
+
+ align:start position:0%
+people as the now of P so that's the
+first claim for orthogonal projector the
+
+ align:start position:0%
+first claim for orthogonal projector the
+ 
+
+ align:start position:0%
+first claim for orthogonal projector the
+second claim is that these are
+
+ align:start position:0%
+second claim is that these are
+ 
+
+ align:start position:0%
+second claim is that these are
+orthogonal so if I take P V something in
+
+ align:start position:0%
+orthogonal so if I take P V something in
+ 
+
+ align:start position:0%
+orthogonal so if I take P V something in
+the range of P and 1 minus P B tilde
+
+ align:start position:0%
+the range of P and 1 minus P B tilde
+ 
+
+ align:start position:0%
+the range of P and 1 minus P B tilde
+something in the null space of P this
+
+ align:start position:0%
+something in the null space of P this
+ 
+
+ align:start position:0%
+something in the null space of P this
+should be your Thorin oh and this is
+
+ align:start position:0%
+should be your Thorin oh and this is
+ 
+
+ align:start position:0%
+should be your Thorin oh and this is
+clear because I can move now this
+
+ align:start position:0%
+clear because I can move now this
+ 
+
+ align:start position:0%
+clear because I can move now this
+operator to the other side and it would
+
+ align:start position:0%
+operator to the other side and it would
+ 
+
+ align:start position:0%
+operator to the other side and it would
+be V P dagger 1 minus P V tilde and
+
+ align:start position:0%
+be V P dagger 1 minus P V tilde and
+ 
+
+ align:start position:0%
+be V P dagger 1 minus P V tilde and
+since P is hermitian that's where you
+
+ align:start position:0%
+since P is hermitian that's where you
+ 
+
+ align:start position:0%
+since P is hermitian that's where you
+use that piece permission this is V P 1
+
+ align:start position:0%
+use that piece permission this is V P 1
+ 
+
+ align:start position:0%
+use that piece permission this is V P 1
+minus P V tilde and that's equal to 0
+
+ align:start position:0%
+minus P V tilde and that's equal to 0
+ 
+
+ align:start position:0%
+minus P V tilde and that's equal to 0
+because P times 1 minus P already is 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so okay these are our conditions
+
+ align:start position:0%
+so okay these are our conditions
+ 
+
+ align:start position:0%
+so okay these are our conditions
+orthogonal projectors are very nice
+
+ align:start position:0%
+orthogonal projectors are very nice
+ 
+
+ align:start position:0%
+orthogonal projectors are very nice
+these are the really good things you
+
+ align:start position:0%
+these are the really good things you
+ 
+
+ align:start position:0%
+these are the really good things you
+have a projector that decomposes into
+
+ align:start position:0%
+have a projector that decomposes into
+ 
+
+ align:start position:0%
+have a projector that decomposes into
+two parts just by having P squared equal
+
+ align:start position:0%
+two parts just by having P squared equal
+ 
+
+ align:start position:0%
+two parts just by having P squared equal
+P but to have our thousand now you need
+
+ align:start position:0%
+P but to have our thousand now you need
+ 
+
+ align:start position:0%
+P but to have our thousand now you need
+that it be
+
+ align:start position:0%
+that it be
+ 
+
+ align:start position:0%
+that it be
+our mission so what is our situation
+
+ align:start position:0%
+our mission so what is our situation
+ 
+
+ align:start position:0%
+our mission so what is our situation
+with those operators they are hermitian
+
+ align:start position:0%
+with those operators they are hermitian
+ 
+
+ align:start position:0%
+with those operators they are hermitian
+so so SNA a are hermitian because one is
+
+ align:start position:0%
+so so SNA a are hermitian because one is
+ 
+
+ align:start position:0%
+so so SNA a are hermitian because one is
+hermitian and p2 one is hermitian so the
+
+ align:start position:0%
+hermitian and p2 one is hermitian so the
+ 
+
+ align:start position:0%
+hermitian and p2 one is hermitian so the
+operators are hermitian and they are
+
+ align:start position:0%
+operators are hermitian and they are
+ 
+
+ align:start position:0%
+operators are hermitian and they are
+projectors because well you check them
+
+ align:start position:0%
+projectors because well you check them
+ 
+
+ align:start position:0%
+projectors because well you check them
+you multiply them by themselves so we
+
+ align:start position:0%
+you multiply them by themselves so we
+ 
+
+ align:start position:0%
+you multiply them by themselves so we
+can do the two of them simultaneously
+
+ align:start position:0%
+can do the two of them simultaneously
+ 
+
+ align:start position:0%
+can do the two of them simultaneously
+this is with a plus sign that's s with a
+
+ align:start position:0%
+this is with a plus sign that's s with a
+ 
+
+ align:start position:0%
+this is with a plus sign that's s with a
+minus sign
+
+ align:start position:0%
+minus sign
+ 
+
+ align:start position:0%
+minus sign
+it's a so we need to show that s squared
+
+ align:start position:0%
+it's a so we need to show that s squared
+ 
+
+ align:start position:0%
+it's a so we need to show that s squared
+is equal to s and a squared is equal to
+
+ align:start position:0%
+is equal to s and a squared is equal to
+ 
+
+ align:start position:0%
+is equal to s and a squared is equal to
+a so here we have both cases so the
+
+ align:start position:0%
+a so here we have both cases so the
+ 
+
+ align:start position:0%
+a so here we have both cases so the
+proud is one-fourth then plus minus 2p2
+
+ align:start position:0%
+proud is one-fourth then plus minus 2p2
+ 
+
+ align:start position:0%
+proud is one-fourth then plus minus 2p2
+one and then the product of these
+
+ align:start position:0%
+one and then the product of these
+ 
+
+ align:start position:0%
+one and then the product of these
+operators with themselves plus minus and
+
+ align:start position:0%
+operators with themselves plus minus and
+ 
+
+ align:start position:0%
+operators with themselves plus minus and
+plus minus always gives you a plus and
+
+ align:start position:0%
+plus minus always gives you a plus and
+ 
+
+ align:start position:0%
+plus minus always gives you a plus and
+p21 times beta1 we showed that that's
+
+ align:start position:0%
+p21 times beta1 we showed that that's
+ 
+
+ align:start position:0%
+p21 times beta1 we showed that that's
+equal to one so happily this one and one
+
+ align:start position:0%
+equal to one so happily this one and one
+ 
+
+ align:start position:0%
+equal to one so happily this one and one
+give it to this another two divides here
+
+ align:start position:0%
+give it to this another two divides here
+ 
+
+ align:start position:0%
+give it to this another two divides here
+this is 1/2 1 plus minus P 2 1 so that's
+
+ align:start position:0%
+this is 1/2 1 plus minus P 2 1 so that's
+ 
+
+ align:start position:0%
+this is 1/2 1 plus minus P 2 1 so that's
+what we wanted to show with the top sign
+
+ align:start position:0%
+what we wanted to show with the top sign
+ 
+
+ align:start position:0%
+what we wanted to show with the top sign
+s times s is equal to s with the bottom
+
+ align:start position:0%
+s times s is equal to s with the bottom
+ 
+
+ align:start position:0%
+s times s is equal to s with the bottom
+sign ma a times a is equal to a
\ No newline at end of file
diff --git a/vQYQR8iNU-o.txt b/vQYQR8iNU-o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f9a734adaa68b2e092ee5cc82f675ca141a793b0
--- /dev/null
+++ b/vQYQR8iNU-o.txt
@@ -0,0 +1,3304 @@
+align:start position:0%
+ 
+so now let's synthesize
+
+ align:start position:0%
+so now let's synthesize
+ 
+
+ align:start position:0%
+so now let's synthesize
+all of our models of aerosol generation
+
+ align:start position:0%
+all of our models of aerosol generation
+ 
+
+ align:start position:0%
+all of our models of aerosol generation
+and dynamics
+
+ align:start position:0%
+and dynamics
+ 
+
+ align:start position:0%
+and dynamics
+in a well-mixed indoor space and
+
+ align:start position:0%
+in a well-mixed indoor space and
+ 
+
+ align:start position:0%
+in a well-mixed indoor space and
+epidemiological models of spreading and
+
+ align:start position:0%
+epidemiological models of spreading and
+ 
+
+ align:start position:0%
+epidemiological models of spreading and
+transfer of disease in that space
+
+ align:start position:0%
+transfer of disease in that space
+ 
+
+ align:start position:0%
+transfer of disease in that space
+and formulate a safety guideline for
+
+ align:start position:0%
+and formulate a safety guideline for
+ 
+
+ align:start position:0%
+and formulate a safety guideline for
+covet 19 assuming indoor airborne
+
+ align:start position:0%
+covet 19 assuming indoor airborne
+ 
+
+ align:start position:0%
+covet 19 assuming indoor airborne
+transmission
+
+ align:start position:0%
+transmission
+ 
+
+ align:start position:0%
+transmission
+in a well mixed room and so there's a
+
+ align:start position:0%
+in a well mixed room and so there's a
+ 
+
+ align:start position:0%
+in a well mixed room and so there's a
+number of ways we could go about this
+
+ align:start position:0%
+number of ways we could go about this
+ 
+
+ align:start position:0%
+number of ways we could go about this
+and the approach that i would like to
+
+ align:start position:0%
+and the approach that i would like to
+ 
+
+ align:start position:0%
+and the approach that i would like to
+propose is that we require that the
+
+ align:start position:0%
+propose is that we require that the
+ 
+
+ align:start position:0%
+propose is that we require that the
+indoor reproductive number is less than
+
+ align:start position:0%
+indoor reproductive number is less than
+ 
+
+ align:start position:0%
+indoor reproductive number is less than
+some tolerance
+
+ align:start position:0%
+some tolerance
+ 
+
+ align:start position:0%
+some tolerance
+so this epsilon here is the tolerance
+
+ align:start position:0%
+so this epsilon here is the tolerance
+ 
+
+ align:start position:0%
+so this epsilon here is the tolerance
+so typically something might be a lot
+
+ align:start position:0%
+so typically something might be a lot
+ 
+
+ align:start position:0%
+so typically something might be a lot
+less than one or maybe like
+
+ align:start position:0%
+less than one or maybe like
+ 
+
+ align:start position:0%
+less than one or maybe like
+maybe you could allow it to be closer to
+
+ align:start position:0%
+maybe you could allow it to be closer to
+ 
+
+ align:start position:0%
+maybe you could allow it to be closer to
+one and so that is essentially
+
+ align:start position:0%
+one and so that is essentially
+ 
+
+ align:start position:0%
+one and so that is essentially
+the probability of a transmission from
+
+ align:start position:0%
+the probability of a transmission from
+ 
+
+ align:start position:0%
+the probability of a transmission from
+one infector that enters the room
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at t equals zero
+
+ align:start position:0%
+at t equals zero
+ 
+
+ align:start position:0%
+at t equals zero
+and stays for a time
+
+ align:start position:0%
+and stays for a time
+ 
+
+ align:start position:0%
+and stays for a time
+tau okay in the presence of a total
+
+ align:start position:0%
+tau okay in the presence of a total
+ 
+
+ align:start position:0%
+tau okay in the presence of a total
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+n people in the room which is the
+
+ align:start position:0%
+n people in the room which is the
+ 
+
+ align:start position:0%
+n people in the room which is the
+occupancy of the room
+
+ align:start position:0%
+occupancy of the room
+ 
+
+ align:start position:0%
+occupancy of the room
+so obviously this doesn't handle every
+
+ align:start position:0%
+so obviously this doesn't handle every
+ 
+
+ align:start position:0%
+so obviously this doesn't handle every
+possible situation
+
+ align:start position:0%
+possible situation
+ 
+
+ align:start position:0%
+possible situation
+it is possible if there's a very
+
+ align:start position:0%
+it is possible if there's a very
+ 
+
+ align:start position:0%
+it is possible if there's a very
+prevalent infection rate
+
+ align:start position:0%
+prevalent infection rate
+ 
+
+ align:start position:0%
+prevalent infection rate
+in the community that the room may find
+
+ align:start position:0%
+in the community that the room may find
+ 
+
+ align:start position:0%
+in the community that the room may find
+several infectors entering at once
+
+ align:start position:0%
+several infectors entering at once
+ 
+
+ align:start position:0%
+several infectors entering at once
+in which case we could certainly you
+
+ align:start position:0%
+in which case we could certainly you
+ 
+
+ align:start position:0%
+in which case we could certainly you
+know increase this number and then the
+
+ align:start position:0%
+know increase this number and then the
+ 
+
+ align:start position:0%
+know increase this number and then the
+one here
+
+ align:start position:0%
+one here
+ 
+
+ align:start position:0%
+one here
+would really would be replaced by i0 as
+
+ align:start position:0%
+would really would be replaced by i0 as
+ 
+
+ align:start position:0%
+would really would be replaced by i0 as
+we've seen before
+
+ align:start position:0%
+we've seen before
+ 
+
+ align:start position:0%
+we've seen before
+on the other hand if you're interested
+
+ align:start position:0%
+on the other hand if you're interested
+ 
+
+ align:start position:0%
+on the other hand if you're interested
+in controlling the spread of the disease
+
+ align:start position:0%
+in controlling the spread of the disease
+ 
+
+ align:start position:0%
+in controlling the spread of the disease
+and you're not worried about a specific
+
+ align:start position:0%
+and you're not worried about a specific
+ 
+
+ align:start position:0%
+and you're not worried about a specific
+person but you just want to say i would
+
+ align:start position:0%
+person but you just want to say i would
+ 
+
+ align:start position:0%
+person but you just want to say i would
+like to make this room
+
+ align:start position:0%
+like to make this room
+ 
+
+ align:start position:0%
+like to make this room
+not contribute to spreading the disease
+
+ align:start position:0%
+not contribute to spreading the disease
+ 
+
+ align:start position:0%
+not contribute to spreading the disease
+and imagine if
+
+ align:start position:0%
+and imagine if
+ 
+
+ align:start position:0%
+and imagine if
+everybody did that then no rooms would
+
+ align:start position:0%
+everybody did that then no rooms would
+ 
+
+ align:start position:0%
+everybody did that then no rooms would
+contribute to brain disease
+
+ align:start position:0%
+contribute to brain disease
+ 
+
+ align:start position:0%
+contribute to brain disease
+so then this criteria would say that if
+
+ align:start position:0%
+so then this criteria would say that if
+ 
+
+ align:start position:0%
+so then this criteria would say that if
+two infectors came
+
+ align:start position:0%
+two infectors came
+ 
+
+ align:start position:0%
+two infectors came
+they might infect two people or three
+
+ align:start position:0%
+they might infect two people or three
+ 
+
+ align:start position:0%
+they might infect two people or three
+infectors you're worried about three
+
+ align:start position:0%
+infectors you're worried about three
+ 
+
+ align:start position:0%
+infectors you're worried about three
+people right what we want to make sure
+
+ align:start position:0%
+people right what we want to make sure
+ 
+
+ align:start position:0%
+people right what we want to make sure
+is that the number of factors
+
+ align:start position:0%
+is that the number of factors
+ 
+
+ align:start position:0%
+is that the number of factors
+is not growing so in other words if
+
+ align:start position:0%
+is not growing so in other words if
+ 
+
+ align:start position:0%
+is not growing so in other words if
+there's one infector they don't infect
+
+ align:start position:0%
+there's one infector they don't infect
+ 
+
+ align:start position:0%
+there's one infector they don't infect
+another one okay so the fact that there
+
+ align:start position:0%
+another one okay so the fact that there
+ 
+
+ align:start position:0%
+another one okay so the fact that there
+are more infectors gives a chance of at
+
+ align:start position:0%
+are more infectors gives a chance of at
+ 
+
+ align:start position:0%
+are more infectors gives a chance of at
+least some infection
+
+ align:start position:0%
+least some infection
+ 
+
+ align:start position:0%
+least some infection
+but this seems like a more general and
+
+ align:start position:0%
+but this seems like a more general and
+ 
+
+ align:start position:0%
+but this seems like a more general and
+simpler
+
+ align:start position:0%
+simpler
+ 
+
+ align:start position:0%
+simpler
+criterion it's also a little bit like
+
+ align:start position:0%
+criterion it's also a little bit like
+ 
+
+ align:start position:0%
+criterion it's also a little bit like
+when the fire department looks at a room
+
+ align:start position:0%
+when the fire department looks at a room
+ 
+
+ align:start position:0%
+when the fire department looks at a room
+and decides on an occupancy limit for an
+
+ align:start position:0%
+and decides on an occupancy limit for an
+ 
+
+ align:start position:0%
+and decides on an occupancy limit for an
+indoor space
+
+ align:start position:0%
+indoor space
+ 
+
+ align:start position:0%
+indoor space
+there's no fire going on they're not
+
+ align:start position:0%
+there's no fire going on they're not
+ 
+
+ align:start position:0%
+there's no fire going on they're not
+estimating what's the probability of a
+
+ align:start position:0%
+estimating what's the probability of a
+ 
+
+ align:start position:0%
+estimating what's the probability of a
+fire
+
+ align:start position:0%
+fire
+ 
+
+ align:start position:0%
+fire
+it's a conditional probability they're
+
+ align:start position:0%
+it's a conditional probability they're
+ 
+
+ align:start position:0%
+it's a conditional probability they're
+saying if there's a fire
+
+ align:start position:0%
+saying if there's a fire
+ 
+
+ align:start position:0%
+saying if there's a fire
+we want to make sure these people can
+
+ align:start position:0%
+we want to make sure these people can
+ 
+
+ align:start position:0%
+we want to make sure these people can
+get out and so they think about where
+
+ align:start position:0%
+get out and so they think about where
+ 
+
+ align:start position:0%
+get out and so they think about where
+the fire might start start where the
+
+ align:start position:0%
+the fire might start start where the
+ 
+
+ align:start position:0%
+the fire might start start where the
+smoke is where the exits
+
+ align:start position:0%
+smoke is where the exits
+ 
+
+ align:start position:0%
+smoke is where the exits
+and how many people can realistically
+
+ align:start position:0%
+and how many people can realistically
+ 
+
+ align:start position:0%
+and how many people can realistically
+get out of that room
+
+ align:start position:0%
+get out of that room
+ 
+
+ align:start position:0%
+get out of that room
+before the fire and the smoke reach a
+
+ align:start position:0%
+before the fire and the smoke reach a
+ 
+
+ align:start position:0%
+before the fire and the smoke reach a
+dangerous level
+
+ align:start position:0%
+dangerous level
+ 
+
+ align:start position:0%
+dangerous level
+so this indoor safety guideline has a
+
+ align:start position:0%
+so this indoor safety guideline has a
+ 
+
+ align:start position:0%
+so this indoor safety guideline has a
+similar flavor where we're essentially
+
+ align:start position:0%
+similar flavor where we're essentially
+ 
+
+ align:start position:0%
+similar flavor where we're essentially
+defining
+
+ align:start position:0%
+defining
+ 
+
+ align:start position:0%
+defining
+here the number of people and also the
+
+ align:start position:0%
+here the number of people and also the
+ 
+
+ align:start position:0%
+here the number of people and also the
+amount of occupancy time
+
+ align:start position:0%
+amount of occupancy time
+ 
+
+ align:start position:0%
+amount of occupancy time
+that would be allowable so that it'd be
+
+ align:start position:0%
+that would be allowable so that it'd be
+ 
+
+ align:start position:0%
+that would be allowable so that it'd be
+unlikely for one infector to create
+
+ align:start position:0%
+unlikely for one infector to create
+ 
+
+ align:start position:0%
+unlikely for one infector to create
+a new infection and hence spread the
+
+ align:start position:0%
+a new infection and hence spread the
+ 
+
+ align:start position:0%
+a new infection and hence spread the
+disease
+
+ align:start position:0%
+disease
+ 
+
+ align:start position:0%
+disease
+so that is the basic thinking so this is
+
+ align:start position:0%
+so that is the basic thinking so this is
+ 
+
+ align:start position:0%
+so that is the basic thinking so this is
+the um
+
+ align:start position:0%
+the um
+ 
+
+ align:start position:0%
+the um
+so it's basically the conditional
+
+ align:start position:0%
+so it's basically the conditional
+ 
+
+ align:start position:0%
+so it's basically the conditional
+probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of spreading
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+given this
+
+ align:start position:0%
+given this
+ 
+
+ align:start position:0%
+given this
+that an infector enters at time 0 and
+
+ align:start position:0%
+that an infector enters at time 0 and
+ 
+
+ align:start position:0%
+that an infector enters at time 0 and
+stays for time t
+
+ align:start position:0%
+stays for time t
+ 
+
+ align:start position:0%
+stays for time t
+so so that's basically how we formulate
+
+ align:start position:0%
+so so that's basically how we formulate
+ 
+
+ align:start position:0%
+so so that's basically how we formulate
+the guideline and now let's think about
+
+ align:start position:0%
+the guideline and now let's think about
+ 
+
+ align:start position:0%
+the guideline and now let's think about
+already at this level without getting
+
+ align:start position:0%
+already at this level without getting
+ 
+
+ align:start position:0%
+already at this level without getting
+into the details of what
+
+ align:start position:0%
+into the details of what
+ 
+
+ align:start position:0%
+into the details of what
+goes into beta which we've already
+
+ align:start position:0%
+goes into beta which we've already
+ 
+
+ align:start position:0%
+goes into beta which we've already
+talked about there's a very important
+
+ align:start position:0%
+talked about there's a very important
+ 
+
+ align:start position:0%
+talked about there's a very important
+concept here
+
+ align:start position:0%
+concept here
+ 
+
+ align:start position:0%
+concept here
+which is that if i define
+
+ align:start position:0%
+which is that if i define
+ 
+
+ align:start position:0%
+which is that if i define
+beta with brackets here to be the
+
+ align:start position:0%
+beta with brackets here to be the
+ 
+
+ align:start position:0%
+beta with brackets here to be the
+average
+
+ align:start position:0%
+average
+ 
+
+ align:start position:0%
+average
+transmission rate so the transmission
+
+ align:start position:0%
+transmission rate so the transmission
+ 
+
+ align:start position:0%
+transmission rate so the transmission
+rate may be changing in time
+
+ align:start position:0%
+rate may be changing in time
+ 
+
+ align:start position:0%
+rate may be changing in time
+for example as droplets are building up
+
+ align:start position:0%
+for example as droplets are building up
+ 
+
+ align:start position:0%
+for example as droplets are building up
+in the room as we've discussed
+
+ align:start position:0%
+in the room as we've discussed
+ 
+
+ align:start position:0%
+in the room as we've discussed
+but let's just think of kind of an
+
+ align:start position:0%
+but let's just think of kind of an
+ 
+
+ align:start position:0%
+but let's just think of kind of an
+average transmission rate
+
+ align:start position:0%
+average transmission rate
+ 
+
+ align:start position:0%
+average transmission rate
+then this integral in time is just beta
+
+ align:start position:0%
+then this integral in time is just beta
+ 
+
+ align:start position:0%
+then this integral in time is just beta
+brackets
+
+ align:start position:0%
+brackets
+ 
+
+ align:start position:0%
+brackets
+beta average times tau and so if i put
+
+ align:start position:0%
+beta average times tau and so if i put
+ 
+
+ align:start position:0%
+beta average times tau and so if i put
+the beta bracket on the other side i
+
+ align:start position:0%
+the beta bracket on the other side i
+ 
+
+ align:start position:0%
+the beta bracket on the other side i
+arrive at a very fundamental result
+
+ align:start position:0%
+arrive at a very fundamental result
+ 
+
+ align:start position:0%
+arrive at a very fundamental result
+which is that the number of susceptibles
+
+ align:start position:0%
+which is that the number of susceptibles
+ 
+
+ align:start position:0%
+which is that the number of susceptibles
+in the room which is roughly the
+
+ align:start position:0%
+in the room which is roughly the
+ 
+
+ align:start position:0%
+in the room which is roughly the
+occupancy
+
+ align:start position:0%
+occupancy
+ 
+
+ align:start position:0%
+occupancy
+although if you're very low occupancy
+
+ align:start position:0%
+although if you're very low occupancy
+ 
+
+ align:start position:0%
+although if you're very low occupancy
+it's everybody but the infected person
+
+ align:start position:0%
+it's everybody but the infected person
+ 
+
+ align:start position:0%
+it's everybody but the infected person
+so it's n minus one
+
+ align:start position:0%
+so it's n minus one
+ 
+
+ align:start position:0%
+so it's n minus one
+times the typical time spent in the room
+
+ align:start position:0%
+times the typical time spent in the room
+ 
+
+ align:start position:0%
+times the typical time spent in the room
+by the infected person
+
+ align:start position:0%
+by the infected person
+ 
+
+ align:start position:0%
+by the infected person
+is less than the tolerance divided by
+
+ align:start position:0%
+is less than the tolerance divided by
+ 
+
+ align:start position:0%
+is less than the tolerance divided by
+the average transmission rate
+
+ align:start position:0%
+the average transmission rate
+ 
+
+ align:start position:0%
+the average transmission rate
+this is a very simple and very general
+
+ align:start position:0%
+this is a very simple and very general
+ 
+
+ align:start position:0%
+this is a very simple and very general
+relationship which does not depend on
+
+ align:start position:0%
+relationship which does not depend on
+ 
+
+ align:start position:0%
+relationship which does not depend on
+the details
+
+ align:start position:0%
+the details
+ 
+
+ align:start position:0%
+the details
+of beta okay but what it's telling you
+
+ align:start position:0%
+of beta okay but what it's telling you
+ 
+
+ align:start position:0%
+of beta okay but what it's telling you
+is something which already you may
+
+ align:start position:0%
+is something which already you may
+ 
+
+ align:start position:0%
+is something which already you may
+recognize is
+
+ align:start position:0%
+recognize is
+ 
+
+ align:start position:0%
+recognize is
+very different than any of the existing
+
+ align:start position:0%
+very different than any of the existing
+ 
+
+ align:start position:0%
+very different than any of the existing
+official safety guidelines
+
+ align:start position:0%
+official safety guidelines
+ 
+
+ align:start position:0%
+official safety guidelines
+official safety guidelines always limit
+
+ align:start position:0%
+official safety guidelines always limit
+ 
+
+ align:start position:0%
+official safety guidelines always limit
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+quantity for example they might limit
+
+ align:start position:0%
+quantity for example they might limit
+ 
+
+ align:start position:0%
+quantity for example they might limit
+the number of people in a room they
+
+ align:start position:0%
+the number of people in a room they
+ 
+
+ align:start position:0%
+the number of people in a room they
+also can get a limit such as that from
+
+ align:start position:0%
+also can get a limit such as that from
+ 
+
+ align:start position:0%
+also can get a limit such as that from
+social distancing so you could take the
+
+ align:start position:0%
+social distancing so you could take the
+ 
+
+ align:start position:0%
+social distancing so you could take the
+area of the room
+
+ align:start position:0%
+area of the room
+ 
+
+ align:start position:0%
+area of the room
+divide by a little six foot radius
+
+ align:start position:0%
+divide by a little six foot radius
+ 
+
+ align:start position:0%
+divide by a little six foot radius
+around each person
+
+ align:start position:0%
+around each person
+ 
+
+ align:start position:0%
+around each person
+or six foot three foot radius or a six
+
+ align:start position:0%
+or six foot three foot radius or a six
+ 
+
+ align:start position:0%
+or six foot three foot radius or a six
+foot separation
+
+ align:start position:0%
+foot separation
+ 
+
+ align:start position:0%
+foot separation
+and get an occupancy so you fix n
+
+ align:start position:0%
+and get an occupancy so you fix n
+ 
+
+ align:start position:0%
+and get an occupancy so you fix n
+the problem with that is that time has
+
+ align:start position:0%
+the problem with that is that time has
+ 
+
+ align:start position:0%
+the problem with that is that time has
+to play a role
+
+ align:start position:0%
+to play a role
+ 
+
+ align:start position:0%
+to play a role
+if a certain number of people are in a
+
+ align:start position:0%
+if a certain number of people are in a
+ 
+
+ align:start position:0%
+if a certain number of people are in a
+room for a very short time
+
+ align:start position:0%
+room for a very short time
+ 
+
+ align:start position:0%
+room for a very short time
+it's really unlikely to have any
+
+ align:start position:0%
+it's really unlikely to have any
+ 
+
+ align:start position:0%
+it's really unlikely to have any
+transmission but if the same number
+
+ align:start position:0%
+transmission but if the same number
+ 
+
+ align:start position:0%
+transmission but if the same number
+stays for a very long time eventually
+
+ align:start position:0%
+stays for a very long time eventually
+ 
+
+ align:start position:0%
+stays for a very long time eventually
+some transmission must take place so
+
+ align:start position:0%
+some transmission must take place so
+ 
+
+ align:start position:0%
+some transmission must take place so
+time has to be important
+
+ align:start position:0%
+time has to be important
+ 
+
+ align:start position:0%
+time has to be important
+you will also find limits on time the
+
+ align:start position:0%
+you will also find limits on time the
+ 
+
+ align:start position:0%
+you will also find limits on time the
+cdc defines a contact where transmission
+
+ align:start position:0%
+cdc defines a contact where transmission
+ 
+
+ align:start position:0%
+cdc defines a contact where transmission
+is possible as being within six feet of
+
+ align:start position:0%
+is possible as being within six feet of
+ 
+
+ align:start position:0%
+is possible as being within six feet of
+an infectious person
+
+ align:start position:0%
+an infectious person
+ 
+
+ align:start position:0%
+an infectious person
+for more than 15 minutes so there's a
+
+ align:start position:0%
+for more than 15 minutes so there's a
+ 
+
+ align:start position:0%
+for more than 15 minutes so there's a
+time constraint there so it says that
+
+ align:start position:0%
+time constraint there so it says that
+ 
+
+ align:start position:0%
+time constraint there so it says that
+after 15 minutes you should expect to be
+
+ align:start position:0%
+after 15 minutes you should expect to be
+ 
+
+ align:start position:0%
+after 15 minutes you should expect to be
+potentially infected but the problem is
+
+ align:start position:0%
+potentially infected but the problem is
+ 
+
+ align:start position:0%
+potentially infected but the problem is
+that that's not accounting for
+
+ align:start position:0%
+that that's not accounting for
+ 
+
+ align:start position:0%
+that that's not accounting for
+transmission rate factors such as
+
+ align:start position:0%
+transmission rate factors such as
+ 
+
+ align:start position:0%
+transmission rate factors such as
+ventilation and all the things that
+
+ align:start position:0%
+ventilation and all the things that
+ 
+
+ align:start position:0%
+ventilation and all the things that
+we've discussed
+
+ align:start position:0%
+we've discussed
+ 
+
+ align:start position:0%
+we've discussed
+and also the occupancy so how many
+
+ align:start position:0%
+and also the occupancy so how many
+ 
+
+ align:start position:0%
+and also the occupancy so how many
+people could you transmit it to if
+
+ align:start position:0%
+people could you transmit it to if
+ 
+
+ align:start position:0%
+people could you transmit it to if
+you're by yourself in a room or there's
+
+ align:start position:0%
+you're by yourself in a room or there's
+ 
+
+ align:start position:0%
+you're by yourself in a room or there's
+only two or three people in a very large
+
+ align:start position:0%
+only two or three people in a very large
+ 
+
+ align:start position:0%
+only two or three people in a very large
+space are you really going to transmit
+
+ align:start position:0%
+space are you really going to transmit
+ 
+
+ align:start position:0%
+space are you really going to transmit
+in 15 minutes
+
+ align:start position:0%
+in 15 minutes
+ 
+
+ align:start position:0%
+in 15 minutes
+not necessarily and anyway so that is
+
+ align:start position:0%
+not necessarily and anyway so that is
+ 
+
+ align:start position:0%
+not necessarily and anyway so that is
+the problem with those kinds of
+
+ align:start position:0%
+the problem with those kinds of
+ 
+
+ align:start position:0%
+the problem with those kinds of
+criteria and it can be easily seen by
+
+ align:start position:0%
+criteria and it can be easily seen by
+ 
+
+ align:start position:0%
+criteria and it can be easily seen by
+plotting this relationship here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so by the way this quantity here
+
+ align:start position:0%
+so by the way this quantity here
+ 
+
+ align:start position:0%
+so by the way this quantity here
+which is the product of n and t or n
+
+ align:start position:0%
+which is the product of n and t or n
+ 
+
+ align:start position:0%
+which is the product of n and t or n
+minus 1 and t
+
+ align:start position:0%
+minus 1 and t
+ 
+
+ align:start position:0%
+minus 1 and t
+is what i like to call the cumulative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cumulative
+
+ align:start position:0%
+cumulative
+ 
+
+ align:start position:0%
+cumulative
+exposure time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the time that you're exposed to the
+
+ align:start position:0%
+so the time that you're exposed to the
+ 
+
+ align:start position:0%
+so the time that you're exposed to the
+affected individual tau
+
+ align:start position:0%
+affected individual tau
+ 
+
+ align:start position:0%
+affected individual tau
+is multiplied by how many other people
+
+ align:start position:0%
+is multiplied by how many other people
+ 
+
+ align:start position:0%
+is multiplied by how many other people
+are in the room
+
+ align:start position:0%
+are in the room
+ 
+
+ align:start position:0%
+are in the room
+because that's how many people could get
+
+ align:start position:0%
+because that's how many people could get
+ 
+
+ align:start position:0%
+because that's how many people could get
+infected so
+
+ align:start position:0%
+infected so
+ 
+
+ align:start position:0%
+infected so
+the more people that there are the more
+
+ align:start position:0%
+the more people that there are the more
+ 
+
+ align:start position:0%
+the more people that there are the more
+chance that one of them could be
+
+ align:start position:0%
+chance that one of them could be
+ 
+
+ align:start position:0%
+chance that one of them could be
+infected in a well-mixed room
+
+ align:start position:0%
+infected in a well-mixed room
+ 
+
+ align:start position:0%
+infected in a well-mixed room
+and so you really don't have a bound
+
+ align:start position:0%
+and so you really don't have a bound
+ 
+
+ align:start position:0%
+and so you really don't have a bound
+just on time it's really this product
+
+ align:start position:0%
+just on time it's really this product
+ 
+
+ align:start position:0%
+just on time it's really this product
+that's important
+
+ align:start position:0%
+that's important
+ 
+
+ align:start position:0%
+that's important
+and so let's plot what this looks like
+
+ align:start position:0%
+and so let's plot what this looks like
+ 
+
+ align:start position:0%
+and so let's plot what this looks like
+now so if we have here the time
+
+ align:start position:0%
+now so if we have here the time
+ 
+
+ align:start position:0%
+now so if we have here the time
+and here the occupancy
+
+ align:start position:0%
+and here the occupancy
+ 
+
+ align:start position:0%
+and here the occupancy
+then this guideline is a bound
+
+ align:start position:0%
+then this guideline is a bound
+ 
+
+ align:start position:0%
+then this guideline is a bound
+that looks like this it saturates
+
+ align:start position:0%
+that looks like this it saturates
+ 
+
+ align:start position:0%
+that looks like this it saturates
+at one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so basically if you're below this
+
+ align:start position:0%
+so basically if you're below this
+ 
+
+ align:start position:0%
+so basically if you're below this
+guideline here
+
+ align:start position:0%
+guideline here
+ 
+
+ align:start position:0%
+guideline here
+you're considered safe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and up here is potentially unsafe
+
+ align:start position:0%
+and up here is potentially unsafe
+ 
+
+ align:start position:0%
+and up here is potentially unsafe
+meaning that given
+
+ align:start position:0%
+meaning that given
+ 
+
+ align:start position:0%
+meaning that given
+the tolerance that you've chosen you
+
+ align:start position:0%
+the tolerance that you've chosen you
+ 
+
+ align:start position:0%
+the tolerance that you've chosen you
+would expect that there could be a
+
+ align:start position:0%
+would expect that there could be a
+ 
+
+ align:start position:0%
+would expect that there could be a
+transmission with greater than that
+
+ align:start position:0%
+transmission with greater than that
+ 
+
+ align:start position:0%
+transmission with greater than that
+probability okay it saturates a one
+
+ align:start position:0%
+probability okay it saturates a one
+ 
+
+ align:start position:0%
+probability okay it saturates a one
+because it'll never go below one because
+
+ align:start position:0%
+because it'll never go below one because
+ 
+
+ align:start position:0%
+because it'll never go below one because
+with one person you're not going to
+
+ align:start position:0%
+with one person you're not going to
+ 
+
+ align:start position:0%
+with one person you're not going to
+transmit to anybody
+
+ align:start position:0%
+transmit to anybody
+ 
+
+ align:start position:0%
+transmit to anybody
+so it's okay so an occupancy of one is
+
+ align:start position:0%
+so it's okay so an occupancy of one is
+ 
+
+ align:start position:0%
+so it's okay so an occupancy of one is
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+except in a building where perhaps other
+
+ align:start position:0%
+except in a building where perhaps other
+ 
+
+ align:start position:0%
+except in a building where perhaps other
+people have come and gone from that room
+
+ align:start position:0%
+people have come and gone from that room
+ 
+
+ align:start position:0%
+people have come and gone from that room
+or ventilation is bringing particles
+
+ align:start position:0%
+or ventilation is bringing particles
+ 
+
+ align:start position:0%
+or ventilation is bringing particles
+from other rooms and we'll come back to
+
+ align:start position:0%
+from other rooms and we'll come back to
+ 
+
+ align:start position:0%
+from other rooms and we'll come back to
+that but just at the simple level of
+
+ align:start position:0%
+that but just at the simple level of
+ 
+
+ align:start position:0%
+that but just at the simple level of
+analyzing one room obviously one is fine
+
+ align:start position:0%
+analyzing one room obviously one is fine
+ 
+
+ align:start position:0%
+analyzing one room obviously one is fine
+and here you see a very fundamental
+
+ align:start position:0%
+and here you see a very fundamental
+ 
+
+ align:start position:0%
+and here you see a very fundamental
+problem that i was just
+
+ align:start position:0%
+problem that i was just
+ 
+
+ align:start position:0%
+problem that i was just
+alluding to which is that if i put the
+
+ align:start position:0%
+alluding to which is that if i put the
+ 
+
+ align:start position:0%
+alluding to which is that if i put the
+standard guidelines on for example
+
+ align:start position:0%
+standard guidelines on for example
+ 
+
+ align:start position:0%
+standard guidelines on for example
+a limit on number of people
+
+ align:start position:0%
+a limit on number of people
+ 
+
+ align:start position:0%
+a limit on number of people
+so this could be a fixed occupancy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in fact in massachusetts for example
+
+ align:start position:0%
+and in fact in massachusetts for example
+ 
+
+ align:start position:0%
+and in fact in massachusetts for example
+right now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a guideline which says n is less
+
+ align:start position:0%
+there's a guideline which says n is less
+ 
+
+ align:start position:0%
+there's a guideline which says n is less
+than 25.
+
+ align:start position:0%
+than 25.
+ 
+
+ align:start position:0%
+than 25.
+no more than 25 persons can congregate
+
+ align:start position:0%
+no more than 25 persons can congregate
+ 
+
+ align:start position:0%
+no more than 25 persons can congregate
+in a room
+
+ align:start position:0%
+in a room
+ 
+
+ align:start position:0%
+in a room
+in fact i'm teaching a class right now
+
+ align:start position:0%
+in fact i'm teaching a class right now
+ 
+
+ align:start position:0%
+in fact i'm teaching a class right now
+which we have 51 people
+
+ align:start position:0%
+which we have 51 people
+ 
+
+ align:start position:0%
+which we have 51 people
+and i was able to split into two rooms
+
+ align:start position:0%
+and i was able to split into two rooms
+ 
+
+ align:start position:0%
+and i was able to split into two rooms
+and then this role came along and then
+
+ align:start position:0%
+and then this role came along and then
+ 
+
+ align:start position:0%
+and then this role came along and then
+we had to start doing
+
+ align:start position:0%
+we had to start doing
+ 
+
+ align:start position:0%
+we had to start doing
+three remotely broadcasting between
+
+ align:start position:0%
+three remotely broadcasting between
+ 
+
+ align:start position:0%
+three remotely broadcasting between
+those rooms
+
+ align:start position:0%
+those rooms
+ 
+
+ align:start position:0%
+those rooms
+because we have a 25 person role the
+
+ align:start position:0%
+because we have a 25 person role the
+ 
+
+ align:start position:0%
+because we have a 25 person role the
+problem with that rule is it doesn't
+
+ align:start position:0%
+problem with that rule is it doesn't
+ 
+
+ align:start position:0%
+problem with that rule is it doesn't
+take into account time what if my class
+
+ align:start position:0%
+take into account time what if my class
+ 
+
+ align:start position:0%
+take into account time what if my class
+is only five minutes long or let's say
+
+ align:start position:0%
+is only five minutes long or let's say
+ 
+
+ align:start position:0%
+is only five minutes long or let's say
+it's one hour long okay
+
+ align:start position:0%
+it's one hour long okay
+ 
+
+ align:start position:0%
+it's one hour long okay
+in that time if i don't have an
+
+ align:start position:0%
+in that time if i don't have an
+ 
+
+ align:start position:0%
+in that time if i don't have an
+expectation transmission
+
+ align:start position:0%
+expectation transmission
+ 
+
+ align:start position:0%
+expectation transmission
+i should be okay on the other hand if
+
+ align:start position:0%
+i should be okay on the other hand if
+ 
+
+ align:start position:0%
+i should be okay on the other hand if
+those 20 people sit in the classroom
+
+ align:start position:0%
+those 20 people sit in the classroom
+ 
+
+ align:start position:0%
+those 20 people sit in the classroom
+for several weeks it's pretty likely
+
+ align:start position:0%
+for several weeks it's pretty likely
+ 
+
+ align:start position:0%
+for several weeks it's pretty likely
+that if an affected person is among them
+
+ align:start position:0%
+that if an affected person is among them
+ 
+
+ align:start position:0%
+that if an affected person is among them
+there will be a transmission so
+
+ align:start position:0%
+there will be a transmission so
+ 
+
+ align:start position:0%
+there will be a transmission so
+time has to come in and that you see
+
+ align:start position:0%
+time has to come in and that you see
+ 
+
+ align:start position:0%
+time has to come in and that you see
+very clearly here from the crossing of
+
+ align:start position:0%
+very clearly here from the crossing of
+ 
+
+ align:start position:0%
+very clearly here from the crossing of
+the fixed occupancy
+
+ align:start position:0%
+the fixed occupancy
+ 
+
+ align:start position:0%
+the fixed occupancy
+with the safety guideline
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for a short amount of time the fixed
+
+ align:start position:0%
+so for a short amount of time the fixed
+ 
+
+ align:start position:0%
+so for a short amount of time the fixed
+occupancy which is telling you
+
+ align:start position:0%
+occupancy which is telling you
+ 
+
+ align:start position:0%
+occupancy which is telling you
+you should be under this so basically
+
+ align:start position:0%
+you should be under this so basically
+ 
+
+ align:start position:0%
+you should be under this so basically
+you should only have a lower occupancy
+
+ align:start position:0%
+you should only have a lower occupancy
+ 
+
+ align:start position:0%
+you should only have a lower occupancy
+so this is a
+
+ align:start position:0%
+so this is a
+ 
+
+ align:start position:0%
+so this is a
+fixed occupancy bound for example the
+
+ align:start position:0%
+fixed occupancy bound for example the
+ 
+
+ align:start position:0%
+fixed occupancy bound for example the
+one in massachusetts
+
+ align:start position:0%
+one in massachusetts
+ 
+
+ align:start position:0%
+one in massachusetts
+at first this is too conservative
+
+ align:start position:0%
+at first this is too conservative
+ 
+
+ align:start position:0%
+at first this is too conservative
+so you are telling people they cannot be
+
+ align:start position:0%
+so you are telling people they cannot be
+ 
+
+ align:start position:0%
+so you are telling people they cannot be
+in this space but until this amount of
+
+ align:start position:0%
+in this space but until this amount of
+ 
+
+ align:start position:0%
+in this space but until this amount of
+time has passed it's very unlikely that
+
+ align:start position:0%
+time has passed it's very unlikely that
+ 
+
+ align:start position:0%
+time has passed it's very unlikely that
+anybody would transmit
+
+ align:start position:0%
+anybody would transmit
+ 
+
+ align:start position:0%
+anybody would transmit
+imagine this time is one minute okay
+
+ align:start position:0%
+imagine this time is one minute okay
+ 
+
+ align:start position:0%
+imagine this time is one minute okay
+it's pretty unlikely that you're going
+
+ align:start position:0%
+it's pretty unlikely that you're going
+ 
+
+ align:start position:0%
+it's pretty unlikely that you're going
+to have a transmission
+
+ align:start position:0%
+to have a transmission
+ 
+
+ align:start position:0%
+to have a transmission
+on the other hand if you keep waiting
+
+ align:start position:0%
+on the other hand if you keep waiting
+ 
+
+ align:start position:0%
+on the other hand if you keep waiting
+you always cross the yellow line
+
+ align:start position:0%
+you always cross the yellow line
+ 
+
+ align:start position:0%
+you always cross the yellow line
+and over here it's it's too
+
+ align:start position:0%
+and over here it's it's too
+ 
+
+ align:start position:0%
+and over here it's it's too
+uh risky and too dangerous
+
+ align:start position:0%
+uh risky and too dangerous
+ 
+
+ align:start position:0%
+uh risky and too dangerous
+basically because you're allowing people
+
+ align:start position:0%
+basically because you're allowing people
+ 
+
+ align:start position:0%
+basically because you're allowing people
+to think that they're safe because only
+
+ align:start position:0%
+to think that they're safe because only
+ 
+
+ align:start position:0%
+to think that they're safe because only
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+but if let's say this crossover happens
+
+ align:start position:0%
+but if let's say this crossover happens
+ 
+
+ align:start position:0%
+but if let's say this crossover happens
+after one hour
+
+ align:start position:0%
+after one hour
+ 
+
+ align:start position:0%
+after one hour
+and the people are in the room for five
+
+ align:start position:0%
+and the people are in the room for five
+ 
+
+ align:start position:0%
+and the people are in the room for five
+hours there's a very high risk of
+
+ align:start position:0%
+hours there's a very high risk of
+ 
+
+ align:start position:0%
+hours there's a very high risk of
+transmission
+
+ align:start position:0%
+transmission
+ 
+
+ align:start position:0%
+transmission
+so just putting out a number like 25
+
+ align:start position:0%
+so just putting out a number like 25
+ 
+
+ align:start position:0%
+so just putting out a number like 25
+doesn't really protect you because these
+
+ align:start position:0%
+doesn't really protect you because these
+ 
+
+ align:start position:0%
+doesn't really protect you because these
+lines
+
+ align:start position:0%
+lines
+ 
+
+ align:start position:0%
+lines
+always cross you will always cross the
+
+ align:start position:0%
+always cross you will always cross the
+ 
+
+ align:start position:0%
+always cross you will always cross the
+safety guideline at a certain
+
+ align:start position:0%
+safety guideline at a certain
+ 
+
+ align:start position:0%
+safety guideline at a certain
+time that's the safe time okay
+
+ align:start position:0%
+time that's the safe time okay
+ 
+
+ align:start position:0%
+time that's the safe time okay
+similarly so basically so let me just
+
+ align:start position:0%
+similarly so basically so let me just
+ 
+
+ align:start position:0%
+similarly so basically so let me just
+kind of stress that here so this is
+
+ align:start position:0%
+kind of stress that here so this is
+ 
+
+ align:start position:0%
+kind of stress that here so this is
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+what we're really concerned is this
+
+ align:start position:0%
+what we're really concerned is this
+ 
+
+ align:start position:0%
+what we're really concerned is this
+we're very concerned about
+
+ align:start position:0%
+we're very concerned about
+ 
+
+ align:start position:0%
+we're very concerned about
+situations where a guideline is giving
+
+ align:start position:0%
+situations where a guideline is giving
+ 
+
+ align:start position:0%
+situations where a guideline is giving
+people the sense of
+
+ align:start position:0%
+people the sense of
+ 
+
+ align:start position:0%
+people the sense of
+protection and in fact they're at high
+
+ align:start position:0%
+protection and in fact they're at high
+ 
+
+ align:start position:0%
+protection and in fact they're at high
+risk
+
+ align:start position:0%
+risk
+ 
+
+ align:start position:0%
+risk
+we're also concerned about this case
+
+ align:start position:0%
+we're also concerned about this case
+ 
+
+ align:start position:0%
+we're also concerned about this case
+here because for example
+
+ align:start position:0%
+here because for example
+ 
+
+ align:start position:0%
+here because for example
+as in the case of my class we might be
+
+ align:start position:0%
+as in the case of my class we might be
+ 
+
+ align:start position:0%
+as in the case of my class we might be
+causing some damage to people's
+
+ align:start position:0%
+causing some damage to people's
+ 
+
+ align:start position:0%
+causing some damage to people's
+education or to their businesses or to
+
+ align:start position:0%
+education or to their businesses or to
+ 
+
+ align:start position:0%
+education or to their businesses or to
+the economy
+
+ align:start position:0%
+the economy
+ 
+
+ align:start position:0%
+the economy
+by shutting down a certain space or
+
+ align:start position:0%
+by shutting down a certain space or
+ 
+
+ align:start position:0%
+by shutting down a certain space or
+imposing a limit
+
+ align:start position:0%
+imposing a limit
+ 
+
+ align:start position:0%
+imposing a limit
+that doesn't have really strong
+
+ align:start position:0%
+that doesn't have really strong
+ 
+
+ align:start position:0%
+that doesn't have really strong
+scientific basis because we don't expect
+
+ align:start position:0%
+scientific basis because we don't expect
+ 
+
+ align:start position:0%
+scientific basis because we don't expect
+transmission to happen under those
+
+ align:start position:0%
+transmission to happen under those
+ 
+
+ align:start position:0%
+transmission to happen under those
+circumstances
+
+ align:start position:0%
+circumstances
+ 
+
+ align:start position:0%
+circumstances
+so we're concerned about both but i'm
+
+ align:start position:0%
+so we're concerned about both but i'm
+ 
+
+ align:start position:0%
+so we're concerned about both but i'm
+particularly concerned about the overly
+
+ align:start position:0%
+particularly concerned about the overly
+ 
+
+ align:start position:0%
+particularly concerned about the overly
+risky case because that is contributing
+
+ align:start position:0%
+risky case because that is contributing
+ 
+
+ align:start position:0%
+risky case because that is contributing
+to transmission of the disease
+
+ align:start position:0%
+to transmission of the disease
+ 
+
+ align:start position:0%
+to transmission of the disease
+and potentially loss of life
+
+ align:start position:0%
+and potentially loss of life
+ 
+
+ align:start position:0%
+and potentially loss of life
+now if we look in the other direction we
+
+ align:start position:0%
+now if we look in the other direction we
+ 
+
+ align:start position:0%
+now if we look in the other direction we
+have the same kind of issue
+
+ align:start position:0%
+have the same kind of issue
+ 
+
+ align:start position:0%
+have the same kind of issue
+so we have if we have a time limit for
+
+ align:start position:0%
+so we have if we have a time limit for
+ 
+
+ align:start position:0%
+so we have if we have a time limit for
+example let's say here
+
+ align:start position:0%
+example let's say here
+ 
+
+ align:start position:0%
+example let's say here
+you know this could be um like this
+
+ align:start position:0%
+you know this could be um like this
+ 
+
+ align:start position:0%
+you know this could be um like this
+so this would be a fixed
+
+ align:start position:0%
+so this would be a fixed
+ 
+
+ align:start position:0%
+so this would be a fixed
+time for example 15 minutes
+
+ align:start position:0%
+time for example 15 minutes
+ 
+
+ align:start position:0%
+time for example 15 minutes
+from the cdc is the time they recommend
+
+ align:start position:0%
+from the cdc is the time they recommend
+ 
+
+ align:start position:0%
+from the cdc is the time they recommend
+for contact so that's a pretty short
+
+ align:start position:0%
+for contact so that's a pretty short
+ 
+
+ align:start position:0%
+for contact so that's a pretty short
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+okay and what any what a guide like that
+
+ align:start position:0%
+okay and what any what a guide like that
+ 
+
+ align:start position:0%
+okay and what any what a guide like that
+says is that if you're
+
+ align:start position:0%
+says is that if you're
+ 
+
+ align:start position:0%
+says is that if you're
+in the presence of an effective person
+
+ align:start position:0%
+in the presence of an effective person
+ 
+
+ align:start position:0%
+in the presence of an effective person
+sufficiently close
+
+ align:start position:0%
+sufficiently close
+ 
+
+ align:start position:0%
+sufficiently close
+for 15 minutes then you know
+
+ align:start position:0%
+for 15 minutes then you know
+ 
+
+ align:start position:0%
+for 15 minutes then you know
+here you're safe but over here you're
+
+ align:start position:0%
+here you're safe but over here you're
+ 
+
+ align:start position:0%
+here you're safe but over here you're
+unsafe but again you have the same
+
+ align:start position:0%
+unsafe but again you have the same
+ 
+
+ align:start position:0%
+unsafe but again you have the same
+phenomena now 15 minutes is a pretty
+
+ align:start position:0%
+phenomena now 15 minutes is a pretty
+ 
+
+ align:start position:0%
+phenomena now 15 minutes is a pretty
+short time so that's
+
+ align:start position:0%
+short time so that's
+ 
+
+ align:start position:0%
+short time so that's
+typically going to be safe but again in
+
+ align:start position:0%
+typically going to be safe but again in
+ 
+
+ align:start position:0%
+typically going to be safe but again in
+this region it's too conservative
+
+ align:start position:0%
+this region it's too conservative
+ 
+
+ align:start position:0%
+this region it's too conservative
+so that so the blue here is still too
+
+ align:start position:0%
+so that so the blue here is still too
+ 
+
+ align:start position:0%
+so that so the blue here is still too
+conservative
+
+ align:start position:0%
+conservative
+ 
+
+ align:start position:0%
+conservative
+but now when you get up here even the
+
+ align:start position:0%
+but now when you get up here even the
+ 
+
+ align:start position:0%
+but now when you get up here even the
+15-minute rule
+
+ align:start position:0%
+15-minute rule
+ 
+
+ align:start position:0%
+15-minute rule
+eventually becomes unsafe because if
+
+ align:start position:0%
+eventually becomes unsafe because if
+ 
+
+ align:start position:0%
+eventually becomes unsafe because if
+there's a very large amount of people in
+
+ align:start position:0%
+there's a very large amount of people in
+ 
+
+ align:start position:0%
+there's a very large amount of people in
+a room and they also can interact with
+
+ align:start position:0%
+a room and they also can interact with
+ 
+
+ align:start position:0%
+a room and they also can interact with
+each other through a well-make space
+
+ align:start position:0%
+each other through a well-make space
+ 
+
+ align:start position:0%
+each other through a well-make space
+so i'm not talking about a really really
+
+ align:start position:0%
+so i'm not talking about a really really
+ 
+
+ align:start position:0%
+so i'm not talking about a really really
+big room i'm talking about a small
+
+ align:start position:0%
+big room i'm talking about a small
+ 
+
+ align:start position:0%
+big room i'm talking about a small
+enough room
+
+ align:start position:0%
+enough room
+ 
+
+ align:start position:0%
+enough room
+that you could expect air to be
+
+ align:start position:0%
+that you could expect air to be
+ 
+
+ align:start position:0%
+that you could expect air to be
+transmitted between the people in that
+
+ align:start position:0%
+transmitted between the people in that
+ 
+
+ align:start position:0%
+transmitted between the people in that
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+then if i keep increasing occupancy
+
+ align:start position:0%
+then if i keep increasing occupancy
+ 
+
+ align:start position:0%
+then if i keep increasing occupancy
+again i cross that line there's always a
+
+ align:start position:0%
+again i cross that line there's always a
+ 
+
+ align:start position:0%
+again i cross that line there's always a
+crossing
+
+ align:start position:0%
+crossing
+ 
+
+ align:start position:0%
+crossing
+so you cannot have a guideline only
+
+ align:start position:0%
+so you cannot have a guideline only
+ 
+
+ align:start position:0%
+so you cannot have a guideline only
+based on time
+
+ align:start position:0%
+based on time
+ 
+
+ align:start position:0%
+based on time
+or only based on occupancy if you think
+
+ align:start position:0%
+or only based on occupancy if you think
+ 
+
+ align:start position:0%
+or only based on occupancy if you think
+of this limit for example
+
+ align:start position:0%
+of this limit for example
+ 
+
+ align:start position:0%
+of this limit for example
+how about we take uh you know
+
+ align:start position:0%
+how about we take uh you know
+ 
+
+ align:start position:0%
+how about we take uh you know
+for the 15-minute rule what if i put 15
+
+ align:start position:0%
+for the 15-minute rule what if i put 15
+ 
+
+ align:start position:0%
+for the 15-minute rule what if i put 15
+people or maybe 20 people into a small
+
+ align:start position:0%
+people or maybe 20 people into a small
+ 
+
+ align:start position:0%
+people or maybe 20 people into a small
+tent just this let's say a little bit
+
+ align:start position:0%
+tent just this let's say a little bit
+ 
+
+ align:start position:0%
+tent just this let's say a little bit
+bigger than the size of this board
+
+ align:start position:0%
+bigger than the size of this board
+ 
+
+ align:start position:0%
+bigger than the size of this board
+and everybody's standing close together
+
+ align:start position:0%
+and everybody's standing close together
+ 
+
+ align:start position:0%
+and everybody's standing close together
+we might pass the infection in much less
+
+ align:start position:0%
+we might pass the infection in much less
+ 
+
+ align:start position:0%
+we might pass the infection in much less
+time than 15 minutes because we have a
+
+ align:start position:0%
+time than 15 minutes because we have a
+ 
+
+ align:start position:0%
+time than 15 minutes because we have a
+chance to infect each other and if i
+
+ align:start position:0%
+chance to infect each other and if i
+ 
+
+ align:start position:0%
+chance to infect each other and if i
+keep going up i'm going to cross that
+
+ align:start position:0%
+keep going up i'm going to cross that
+ 
+
+ align:start position:0%
+keep going up i'm going to cross that
+line and the tent also has a very small
+
+ align:start position:0%
+line and the tent also has a very small
+ 
+
+ align:start position:0%
+line and the tent also has a very small
+volume
+
+ align:start position:0%
+volume
+ 
+
+ align:start position:0%
+volume
+poor ventilation and this yellow curve
+
+ align:start position:0%
+poor ventilation and this yellow curve
+ 
+
+ align:start position:0%
+poor ventilation and this yellow curve
+is very low
+
+ align:start position:0%
+is very low
+ 
+
+ align:start position:0%
+is very low
+okay so this concept of the cumulative
+
+ align:start position:0%
+okay so this concept of the cumulative
+ 
+
+ align:start position:0%
+okay so this concept of the cumulative
+exposure time is really important to
+
+ align:start position:0%
+exposure time is really important to
+ 
+
+ align:start position:0%
+exposure time is really important to
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+because it's very general it really
+
+ align:start position:0%
+because it's very general it really
+ 
+
+ align:start position:0%
+because it's very general it really
+isn't so tied to the details of the
+
+ align:start position:0%
+isn't so tied to the details of the
+ 
+
+ align:start position:0%
+isn't so tied to the details of the
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+and it just shows you that any bound on
+
+ align:start position:0%
+and it just shows you that any bound on
+ 
+
+ align:start position:0%
+and it just shows you that any bound on
+one parameter such as occupancy
+
+ align:start position:0%
+one parameter such as occupancy
+ 
+
+ align:start position:0%
+one parameter such as occupancy
+time and i should mention also social
+
+ align:start position:0%
+time and i should mention also social
+ 
+
+ align:start position:0%
+time and i should mention also social
+distance
+
+ align:start position:0%
+distance
+ 
+
+ align:start position:0%
+distance
+because that's the big one which is
+
+ align:start position:0%
+because that's the big one which is
+ 
+
+ align:start position:0%
+because that's the big one which is
+happening right now
+
+ align:start position:0%
+happening right now
+ 
+
+ align:start position:0%
+happening right now
+social distance guidelines so this would
+
+ align:start position:0%
+social distance guidelines so this would
+ 
+
+ align:start position:0%
+social distance guidelines so this would
+be that the
+
+ align:start position:0%
+be that the
+ 
+
+ align:start position:0%
+be that the
+distance d is greater than six feet
+
+ align:start position:0%
+distance d is greater than six feet
+ 
+
+ align:start position:0%
+distance d is greater than six feet
+and that's a cdc guideline in the united
+
+ align:start position:0%
+and that's a cdc guideline in the united
+ 
+
+ align:start position:0%
+and that's a cdc guideline in the united
+states it can be greater than one meter
+
+ align:start position:0%
+states it can be greater than one meter
+ 
+
+ align:start position:0%
+states it can be greater than one meter
+which is which is around which is three
+
+ align:start position:0%
+which is which is around which is three
+ 
+
+ align:start position:0%
+which is which is around which is three
+feet uh and that's from the world health
+
+ align:start position:0%
+feet uh and that's from the world health
+ 
+
+ align:start position:0%
+feet uh and that's from the world health
+organization
+
+ align:start position:0%
+organization
+ 
+
+ align:start position:0%
+organization
+so about half the distance that leads to
+
+ align:start position:0%
+so about half the distance that leads to
+ 
+
+ align:start position:0%
+so about half the distance that leads to
+a guideline where there's still a
+
+ align:start position:0%
+a guideline where there's still a
+ 
+
+ align:start position:0%
+a guideline where there's still a
+maximum
+
+ align:start position:0%
+maximum
+ 
+
+ align:start position:0%
+maximum
+occupancy which is
+
+ align:start position:0%
+occupancy which is
+ 
+
+ align:start position:0%
+occupancy which is
+the area of the room uh divided by
+
+ align:start position:0%
+the area of the room uh divided by
+ 
+
+ align:start position:0%
+the area of the room uh divided by
+you know d squared or by some other
+
+ align:start position:0%
+you know d squared or by some other
+ 
+
+ align:start position:0%
+you know d squared or by some other
+factor depending how you think people
+
+ align:start position:0%
+factor depending how you think people
+ 
+
+ align:start position:0%
+factor depending how you think people
+are going to be arranged but basically
+
+ align:start position:0%
+are going to be arranged but basically
+ 
+
+ align:start position:0%
+are going to be arranged but basically
+you go into the room
+
+ align:start position:0%
+you go into the room
+ 
+
+ align:start position:0%
+you go into the room
+you map out that spacing and you arrive
+
+ align:start position:0%
+you map out that spacing and you arrive
+ 
+
+ align:start position:0%
+you map out that spacing and you arrive
+at a fixed occupancy this is being done
+
+ align:start position:0%
+at a fixed occupancy this is being done
+ 
+
+ align:start position:0%
+at a fixed occupancy this is being done
+everywhere
+
+ align:start position:0%
+everywhere
+ 
+
+ align:start position:0%
+everywhere
+including here at mit right now and
+
+ align:start position:0%
+including here at mit right now and
+ 
+
+ align:start position:0%
+including here at mit right now and
+that still leads to fixed occupancy so
+
+ align:start position:0%
+that still leads to fixed occupancy so
+ 
+
+ align:start position:0%
+that still leads to fixed occupancy so
+regardless of how it was derived you
+
+ align:start position:0%
+regardless of how it was derived you
+ 
+
+ align:start position:0%
+regardless of how it was derived you
+still have a fixed occupancy which is
+
+ align:start position:0%
+still have a fixed occupancy which is
+ 
+
+ align:start position:0%
+still have a fixed occupancy which is
+too conservative first
+
+ align:start position:0%
+too conservative first
+ 
+
+ align:start position:0%
+too conservative first
+and eventually is too risky and you must
+
+ align:start position:0%
+and eventually is too risky and you must
+ 
+
+ align:start position:0%
+and eventually is too risky and you must
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+where is that crossover point because
+
+ align:start position:0%
+where is that crossover point because
+ 
+
+ align:start position:0%
+where is that crossover point because
+occupancy and time
+
+ align:start position:0%
+occupancy and time
+ 
+
+ align:start position:0%
+occupancy and time
+are linked
+
+ align:start position:0%
+are linked
+ 
+
+ align:start position:0%
+are linked
+you
\ No newline at end of file
diff --git a/vhIwuNJzVG4.txt b/vhIwuNJzVG4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a0e81911c3c2cb14619523ff05f87ced8886ca27
--- /dev/null
+++ b/vhIwuNJzVG4.txt
@@ -0,0 +1,978 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation, or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK.
+
+Welcome.
+
+This is great.
+
+It almost looks like the
+beginning of the Fall, at
+
+least outside.
+
+So, what we are going to do,
+is it's going to be a very
+
+exciting month.
+
+And mainly the reason for doing
+this course, is I think
+
+we are about a software
+crisis.
+
+So there's an interesting quote
+I want to start with.
+
+This is somebody very famous in
+computer science, who spoke
+
+during his student
+award lecture.
+
+His point was, when the
+computers were small, there's
+
+no problem.
+
+When computers got bigger,
+this is basically when
+
+software started having
+problems.
+
+So, the first software crisis,
+in fact, happened around the
+
+'60s and '70s.
+
+The problem for the first
+software crisis was people are
+
+writing Assembly language
+program.
+
+When the computers are small,
+and memory was small, it was
+
+completely doable.
+
+No problem.
+
+But as computers became larger
+and larger, it became very
+
+hard to write Assembly language
+programs. And what
+
+they needed was some kind of
+abstraction portability.
+
+So you should be able to go
+every two years, to not have
+
+to rewrite the programs
+in there.
+
+So you need portability and
+you need some level of
+
+abstraction.
+
+So, what that means is instead
+of writing all Assembly
+
+hacking and dealing with every
+hardware feature, you can
+
+erase about that.
+
+And the way that we solved it,
+in that generation is, we,
+
+came up with these high level
+languages like Fortran and C.
+
+And what those did was, they
+kind of provided a common
+
+machine language across
+these machines.
+
+And so what these did was, they
+looked at all machines
+
+those days, the uniprocessors,
+and kind of abstracted out:
+
+First of all, all the common
+properties made available for
+
+the programmer.
+
+So it didn't really lead the
+programmer too far away from
+
+the machine.
+
+But it abstracted out
+all the differences.
+
+So by doing that, we avoided,
+we managed to get these
+
+languagese like C and Fortran.
+
+Weren't very fast.
+Pretty efficient.
+
+And working through this.
+
+So that's how we avoided the
+first software crisis.
+
+And I think that a lot of really
+good work happened, and
+
+a few people got Turing
+Awards for doing
+
+these kind of things.
+
+And then, we faced a second
+software crisis in
+
+the '80s and '90s.
+
+The problem there was, C was
+great if two guys sit in a
+
+corner and write a program.
+
+When Microsoft started
+programming Word, Word suite,
+
+with a few hundred programmers,
+the problem was
+
+the bugs never went away.
+
+The project was supposed
+to finish in a year.
+
+It lasted three years.
+
+And bugs kept coming
+and coming.
+
+And they had no idea when the
+project was going to finish.
+
+Because the way you write in a
+small piece of code really
+
+didn't scale.
+
+And, this was a huge crisis for
+people, who said we will
+
+never be able write large
+programs. Because these
+
+programs will never work.
+
+They're going to be brittle.
+
+And the problem there is we
+want to be able to build
+
+software that's composable,
+malleable, and maintainable.
+
+So software should be: Multiple
+people should
+
+be able to do it.
+
+Compose it.
+
+And the requirements say it
+should be easy to change and
+
+easy to maintain.
+
+The interesting thing is, we
+never cared about high
+
+performance at that time.
+
+Moore's law.
+
+They started to take
+care of that.
+
+The way we solved
+that crisis --
+
+Again, a lot of people got very
+famous for doing that, is
+
+came up with things like
+
+object-oriented programming languages.
+
+C#, C++, and now C# and Java,
+basically made it possible
+
+for, now, hundreds if not
+thousands of people to develop
+
+programs. If you look at
+something like new Microsoft
+
+products coming out, thousands
+of people are involved.
+
+And still they manage to
+get it out on time.
+
+And, also we did a bunch
+of better tools.
+
+Things like component
+libraries,
+
+and tools like Purify.
+
+And we developed a lot of
+software engineering
+
+methodology to develop
+software.
+
+We made it more of a process
+than an ad hoc art-form.
+
+This is great.
+
+So here we are today.
+
+We are very happy.
+
+A lot of programmers, yes.
+
+Unfortunately, programmers are
+pretty oblivious to what's
+
+happening in hardware.
+
+We don't care.
+
+Programs don't have to know
+about what things are running.
+
+You have these nice
+virtual machines.
+
+And, of course, Moore's law,
+this great new thing is going
+
+to come and take
+care of all us.
+
+If you want speed, just
+wait six months, the
+
+machines will be faster.
+
+And that's the thing we
+have been going on.
+
+The nice thing is, these
+programs, programs written
+
+even in the '70s, still run.
+
+Probably two, three, orders of
+magnitude faster, because
+
+processors today have gotten
+really fast. And this
+
+abstraction gave us huge
+amounts of power.
+
+Just say, don't care
+what's underneath.
+
+We are going to sit up there,
+and just basically program.
+
+We were very happy with that.
+
+The problem is, we are running
+into an issue here.
+
+So, we are at the beginning of
+this third software crisis.
+
+What I call the software
+crisis due to
+
+the multicore menace.
+
+So, multicore, for hardware
+people, it's a good
+
+opportunity.
+
+But for software people, its
+kind of a menace in there.
+
+Problem is, sequential programs
+are left behind by
+
+Moore's law.
+
+And, as you see, as probably a
+lot of you know, that you're
+
+not going to get performance
+on sequential programs,
+
+increased performance, without
+dealing with this
+
+And -- the key thing here is,
+so why don't we just stop?
+
+OK.
+
+Good.
+
+We have the programs. Machines
+today run very fast. Isn't
+
+that good enough?
+
+The problem is, we
+want it all.
+
+We need to support
+new features.
+
+We need to support things like
+large datasets in the same
+
+programs. And we kind of keep
+expecting a certain
+
+performance gain every year.
+
+To sustain portability and
+malleability, we assume that
+
+every few years, the machines'
+performance will double.
+
+Because we believe in that.
+
+For example, Microsoft Word at
+the beginning, ten years ago,
+
+it still works.
+
+But it didn't have Spellcheck
+running in the background.
+
+We didn't deal with
+very large images.
+
+We didn't deal with XML
+formats in there.
+
+And, then of course, next
+generation, we probably want
+
+to have integrated video, audio,
+voice recognition, all
+
+those things in there.
+
+And, we need that power.
+
+We rely on that power.
+
+And this is going to be a big
+problem, because sequential
+
+programs are stuck.
+
+They're not going to provide
+that power anymore.
+
+And it's critical.
+
+This kind of power is critical
+to keep up the
+
+current rate of evolution.
+
+And, if we get stuck there,
+we are going to have
+
+a big crisis happening.
+
+So, how is this happening?
+
+I talked about Moore's law.
+
+So this the obligatory
+slide of Moore's law.
+
+So if you look at it, going from
+even before the 1970's,
+
+we had this amazing, amazing
+growth in the number of
+
+transistors available.
+
+So Moore's law doesn't say
+anything about performance.
+
+It says about the number
+of transistors
+
+available on a die.
+
+Every 18 months, it doubles.
+
+So, this basically -- some
+people even say -- this is the
+
+basis of these last two decades
+of economic expansion.
+
+Because we got all this amazing
+power, because of this
+
+kind of growth in here.
+
+The problem is, if you
+look at performance,
+
+it's flattening out.
+
+So, this is spec numbers.
+
+Kind of the way you measure
+performance is to have this
+
+set of programs that
+we can keep
+
+running on these machines.
+
+And we keep running on
+these same machines.
+
+So even though we are getting
+twice the amount of
+
+transistors, this is kind
+of flattening out.
+
+And then, for the last few
+years, it's almost constant.
+
+We're not getting anything
+from there.
+
+And so, we're still running from
+the fumes of that amazing
+
+growth rates we had
+in this time.
+
+And now we're kind of flattening
+out in here.
+
+And why is this?
+
+The main reason for this is, I
+will talk about four things.
+
+One
+
+is power consumption.
+
+Wire delay, and DRAM access
+time, and diminishing returns.
+
+So I'll go a little bit into
+these details, to kind of give
+
+you an overview of why
+this happened.
+
+The first thing is power.
+
+So as we go about, we keep
+taking more and more power.
+
+Right now, if you look at the
+one Moore trend, that,
+
+normally, these one point-some
+volts that these processors
+
+run, this draws more
+current than any of
+
+your houses back home.
+
+I mean, that's amazing.
+
+The houses probably draw
+like 150 amps.
+
+And in one volt, we are drawing
+about 150 watts.
+
+So there's that much current
+going to those things.
+
+And, heat is a big issue.
+
+So this still shows, OK, power,
+we are flattening out.
+
+But another interesting thing
+is power efficiency.
+
+So, we are trying to use
+these transistors.
+
+We are trying to do more and
+more out of these transistors.
+
+And if you look at how many
+watts, you are spending to get
+
+one of those spec rates, that's
+basically how much to
+
+do the same amount of work, we
+are spending a lot more power.
+
+Because we are building these
+things that have very marginal
+
+return today.
+
+That is the problem in
+building the current
+
+super-scaled type things.
+
+Because it doesn't go.
+
+This power efficiency.
+
+This is why Google is building
+their shops next to the Grand
+
+Coulee dam, because they are
+sucking in so much power.
+
+Because power efficiency is
+a big issue for them.
+
+And, today, microprocessors,
+most the cost of it is more
+
+than purchasing.
+
+It's basically feeding it with
+power and cooling it.
+
+So another problem
+is wire delay.
+
+If you try to build this
+monolithic, large process.
+
+So what happened is, in the
+good old days, within the
+
+clock cycle, in the processor
+[UNINTELLIGIBLE] this side.
+
+You can basically send a wire
+from one end to another
+
+processor, still within
+one clock cycle.
+
+So if you are building this
+monolithic thing, it's almost
+
+like sitting in a room.
+
+When I talk, the other end
+of the room will hear it
+
+instantaneously.
+
+Because I'm talking slowly,
+or you're clocking slowly.
+
+And today, we are around this
+area, So what that means is,
+
+in a clock cycle, you can't
+get a wire for more than a
+
+small part of the chip.
+
+So it's almost like trying to
+communicate in this building.
+
+I want to tell something to
+everybody, I can't broadcast.
+
+Somebody has to go next-door
+to tell somebody to get the
+
+information through
+the entire thing.
+
+Takes time.
+
+And as we go more and more, this
+is going to be harder and
+
+harder and harder.
+
+And what that means is, trying
+to build large, monolithic,
+
+processors like we did to keep
+the Moore's law kind of
+
+performance going,
+is not working.
+
+And we have this problem.
+
+Interesting third issue
+is DRAM access time.
+
+So what's happening is
+
+microprocessors going like this.
+
+Performance gets faster
+and faster.
+
+DRAM gets doubled only
+about every 10 years.
+
+And because of that, there's
+this interesting mismatch.
+
+If you are trying to get to
+DRAM, if you put things in
+
+DRAM, it's almost -- about 10
+years ago the kind of latency
+
+we had to the disk, is now
+we are having to DRAM.
+
+So the way we look at this
+activity, the costs of it are
+
+going to get big.
+
+And it's also a power issue
+because if you're on chip,
+
+it's probably two orders of
+magnitude cheaper to get to a
+
+word on chip then go all the way
+outside, get to the DRAM
+
+and get things out.
+
+And so, between power and this,
+is also creating a huge
+
+amount of issue, an
+impossibility for us to keep
+
+this kind of Moore's law type
+performance to keep going.
+
+The final thing is diminishing
+returns.
+
+So if you look at the `80s,
+that is the era of
+
+superscalars.
+
+We had amazing performance
+improvements.
+
+For example, when you started
+the decade, every CPI speed,
+
+clocks per instructions.
+
+How many clocks you had to run
+to get one instruction going?
+
+At the beginning of the decade,
+you had to have about
+
+10 clock cycles to execute
+one instruction on
+
+[UNINTELLIGIBLE].
+
+At the end of the decade, we
+went about one clock cycle
+
+[UNINTELLIGIBLE]
+
+we get a new instruction
+graduated from that.
+
+And that gave an amazing
+performance boost.
+
+And in the '90s, we had an era
+of diminishing returns.
+
+We kind of went from this
+two-way, superscaled, almost
+
+like six-way out of order, out
+of issue, branch prediction,
+
+everything's predicated.
+
+And this huge pipeline.
+
+Amazingly complex machines.
+
+But we went from one clock per
+instruction to about half a
+
+clock per instruction.
+
+So we just doubled that
+kind of performance.
+
+And performance was below
+expectations, and projects got
+
+delayed and cancelled.
+
+One thing that failed --
+
+I'm not going to talk
+about that much.
+
+Is, even at this time, you could
+get that clock frequency
+
+higher and higher.
+
+And because of power and other
+physical limitations, we are
+
+also hitting a wall in
+clock frequency.
+
+We are not getting -- because at
+that time, if you realize,
+
+everybody [UNINTELLIGIBLE]
+saying how fast
+
+their machine ran.
+
+And they have stopped that,
+because they can't get
+
+machines to double their
+frequencies any more.
+
+So, between those two, your
+performance kind of stuck.
+
+So that is why now we are
+starting the new era of
+
+multicores.
+
+We need explicit parallelism.
+
+We can't build these large
+monolithic things that keep
+
+giving you performance
+every few years.
+
+That stopped.
+
+And we can build a sequential
+machine where what you get in
+
+10 years' time will almost be
+same as what you get today.
+
+But, we get more and
+more silicon.
+
+It's doubling.
+
+Moore's law still keeps going.
+
+So what you do with that silicon
+is replicate, and
+
+build more.
+
+And that's where we are going.
+
+So, if you look at what's
+happening, the unicores are a
+
+dying breed.
+
+The last big one was Intel had
+this project that tried to
+
+build very fast, amazing,
+superscalar machines.
+
+All those projects had
+to get cancelled.
+
+Because they could not
+get the performance.
+
+Power was way too high,
+they couldn't get
+
+the power in there.
+
+And those things
+got cancelled.
+
+And as you see, there's
+more and more
+
+multicores coming in there.
+
+In fact, if you look at
+it, multicores are
+
+here in a big way.
+
+If you look all these machines,
+the Pentium line of
+
+uniprocessors.
+
+From recent time, there had been
+four cores, eight cores
+
+and even machines that have
+more than 256 cores.
+
+Small cores, but we are
+basically going into -- that's
+
+a new trend.
+
+And if you look at the trend
+line, it's an interesting
+
+trend line going in there.
+
+So, what I'm going to do
+now is switch gears.
+
+Because, we had Mike [? Brown ?]
+from IBM.
+
+We are very fortunate to have
+him here to give us a feel
+
+about the cell processor.
+
+Because we are going to spend
+this month really getting to
+
+understand cell processing.
+
+And really taking advantage
+of that.
+
+And he had done huge amounts
+of work with cells.
+
+He's at IBM TJ Watson.
+
+And so he's going to, in the
+next hour, hour and half, he's
+
+going to give us the
+lowdown on cell.
+
+And then I will conclude with
+a little bit more remarks
+
+about how we are going to
+do the class structure.
+
+OK.
+
+Mike.
+
+Hopefully -- he has to catch a
+flight, so we will kind of go
+
+fast. Hopefully you guys
+[INAUDIBLE] go without too
+
+much of a break.
+
+So if things get too tired, let
+us know so we'll see if we
+
+can put a break in the middle.
\ No newline at end of file
diff --git a/w6_KvH6fFe0.txt b/w6_KvH6fFe0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..da9926505a4a24297ec5df398fc5b76749bb3c52
--- /dev/null
+++ b/w6_KvH6fFe0.txt
@@ -0,0 +1,14859 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so kind of I try to do this at least
+
+ align:start position:0%
+so kind of I try to do this at least
+ 
+
+ align:start position:0%
+so kind of I try to do this at least
+every other class we have we remember
+
+ align:start position:0%
+every other class we have we remember
+ 
+
+ align:start position:0%
+every other class we have we remember
+the context but class one as you
+
+ align:start position:0%
+the context but class one as you
+ 
+
+ align:start position:0%
+the context but class one as you
+remember was all about the economic
+
+ align:start position:0%
+remember was all about the economic
+ 
+
+ align:start position:0%
+remember was all about the economic
+growth theory and the economic growth
+
+ align:start position:0%
+growth theory and the economic growth
+ 
+
+ align:start position:0%
+growth theory and the economic growth
+context for innovation policy and we did
+
+ align:start position:0%
+context for innovation policy and we did
+ 
+
+ align:start position:0%
+context for innovation policy and we did
+you know growth economics and how it
+
+ align:start position:0%
+you know growth economics and how it
+ 
+
+ align:start position:0%
+you know growth economics and how it
+broke away from classical economics
+
+ align:start position:0%
+broke away from classical economics
+ 
+
+ align:start position:0%
+broke away from classical economics
+around developing a new theory of growth
+
+ align:start position:0%
+around developing a new theory of growth
+ 
+
+ align:start position:0%
+around developing a new theory of growth
+so solo argued that this technological
+
+ align:start position:0%
+so solo argued that this technological
+ 
+
+ align:start position:0%
+so solo argued that this technological
+unrelated intervention
+
+ align:start position:0%
+unrelated intervention
+ 
+
+ align:start position:0%
+unrelated intervention
+innovation and that that's a we
+
+ align:start position:0%
+innovation and that that's a we
+ 
+
+ align:start position:0%
+innovation and that that's a we
+concluded that was a key direct
+
+ align:start position:0%
+concluded that was a key direct
+ 
+
+ align:start position:0%
+concluded that was a key direct
+innovation factor so we could loosely
+
+ align:start position:0%
+innovation factor so we could loosely
+ 
+
+ align:start position:0%
+innovation factor so we could loosely
+although in accurately translate that
+
+ align:start position:0%
+although in accurately translate that
+ 
+
+ align:start position:0%
+although in accurately translate that
+concept as saying you've got to do R&D
+
+ align:start position:0%
+concept as saying you've got to do R&D
+ 
+
+ align:start position:0%
+concept as saying you've got to do R&D
+and then we read Romer and Romer argued
+
+ align:start position:0%
+and then we read Romer and Romer argued
+ 
+
+ align:start position:0%
+and then we read Romer and Romer argued
+that behind that R&D system is human
+
+ align:start position:0%
+that behind that R&D system is human
+ 
+
+ align:start position:0%
+that behind that R&D system is human
+capital engaged in research that's
+
+ align:start position:0%
+capital engaged in research that's
+ 
+
+ align:start position:0%
+capital engaged in research that's
+another foundational direct innovation
+
+ align:start position:0%
+another foundational direct innovation
+ 
+
+ align:start position:0%
+another foundational direct innovation
+factor you can't get you can't build an
+
+ align:start position:0%
+factor you can't get you can't build an
+ 
+
+ align:start position:0%
+factor you can't get you can't build an
+innovation system without these two
+
+ align:start position:0%
+innovation system without these two
+ 
+
+ align:start position:0%
+innovation system without these two
+elements arguably so it's the Rd and the
+
+ align:start position:0%
+elements arguably so it's the Rd and the
+ 
+
+ align:start position:0%
+elements arguably so it's the Rd and the
+talent behind it those give us to direct
+
+ align:start position:0%
+talent behind it those give us to direct
+ 
+
+ align:start position:0%
+talent behind it those give us to direct
+factors then in class two we talked
+
+ align:start position:0%
+factors then in class two we talked
+ 
+
+ align:start position:0%
+factors then in class two we talked
+about the indirect elements in this
+
+ align:start position:0%
+about the indirect elements in this
+ 
+
+ align:start position:0%
+about the indirect elements in this
+larger ecosystem and government controls
+
+ align:start position:0%
+larger ecosystem and government controls
+ 
+
+ align:start position:0%
+larger ecosystem and government controls
+some private sector controls more but
+
+ align:start position:0%
+some private sector controls more but
+ 
+
+ align:start position:0%
+some private sector controls more but
+that gives us an idea of looking at
+
+ align:start position:0%
+that gives us an idea of looking at
+ 
+
+ align:start position:0%
+that gives us an idea of looking at
+innovation as a system which Richard
+
+ align:start position:0%
+innovation as a system which Richard
+ 
+
+ align:start position:0%
+innovation as a system which Richard
+Nelson contributed to and then within
+
+ align:start position:0%
+Nelson contributed to and then within
+ 
+
+ align:start position:0%
+Nelson contributed to and then within
+that system you look at the strength of
+
+ align:start position:0%
+that system you look at the strength of
+ 
+
+ align:start position:0%
+that system you look at the strength of
+the innovation actors and you can begin
+
+ align:start position:0%
+the innovation actors and you can begin
+ 
+
+ align:start position:0%
+the innovation actors and you can begin
+to think of your innovation organization
+
+ align:start position:0%
+to think of your innovation organization
+ 
+
+ align:start position:0%
+to think of your innovation organization
+as a third direct innovation factor and
+
+ align:start position:0%
+as a third direct innovation factor and
+ 
+
+ align:start position:0%
+as a third direct innovation factor and
+that leads us into the whole problem of
+
+ align:start position:0%
+that leads us into the whole problem of
+ 
+
+ align:start position:0%
+that leads us into the whole problem of
+how do you cross the valley of death if
+
+ align:start position:0%
+how do you cross the valley of death if
+ 
+
+ align:start position:0%
+how do you cross the valley of death if
+you've got a disconnected model classes
+
+ align:start position:0%
+you've got a disconnected model classes
+ 
+
+ align:start position:0%
+you've got a disconnected model classes
+three and four were case studies on
+
+ align:start position:0%
+three and four were case studies on
+ 
+
+ align:start position:0%
+three and four were case studies on
+manufacturing so we took a deep dive
+
+ align:start position:0%
+manufacturing so we took a deep dive
+ 
+
+ align:start position:0%
+manufacturing so we took a deep dive
+into a very current set of practical
+
+ align:start position:0%
+into a very current set of practical
+ 
+
+ align:start position:0%
+into a very current set of practical
+ongoing problems to try and think about
+
+ align:start position:0%
+ongoing problems to try and think about
+ 
+
+ align:start position:0%
+ongoing problems to try and think about
+some of those innovation organization
+
+ align:start position:0%
+some of those innovation organization
+ 
+
+ align:start position:0%
+some of those innovation organization
+lessons in a manufacturing context class
+
+ align:start position:0%
+lessons in a manufacturing context class
+ 
+
+ align:start position:0%
+lessons in a manufacturing context class
+five was explicitly about innovation
+
+ align:start position:0%
+five was explicitly about innovation
+ 
+
+ align:start position:0%
+five was explicitly about innovation
+organization and we looked at David
+
+ align:start position:0%
+organization and we looked at David
+ 
+
+ align:start position:0%
+organization and we looked at David
+Hart's kind of analysis of the ideology
+
+ align:start position:0%
+Hart's kind of analysis of the ideology
+ 
+
+ align:start position:0%
+Hart's kind of analysis of the ideology
+behind
+
+ align:start position:0%
+behind
+ 
+
+ align:start position:0%
+behind
+looking at innovation in the political
+
+ align:start position:0%
+looking at innovation in the political
+ 
+
+ align:start position:0%
+looking at innovation in the political
+system and the conservative the
+
+ align:start position:0%
+system and the conservative the
+ 
+
+ align:start position:0%
+system and the conservative the
+association list which is the public
+
+ align:start position:0%
+association list which is the public
+ 
+
+ align:start position:0%
+association list which is the public
+private the national security models all
+
+ align:start position:0%
+private the national security models all
+ 
+
+ align:start position:0%
+private the national security models all
+those all those issues are still very
+
+ align:start position:0%
+those all those issues are still very
+ 
+
+ align:start position:0%
+those all those issues are still very
+much very much with us and in that
+
+ align:start position:0%
+much very much with us and in that
+ 
+
+ align:start position:0%
+much very much with us and in that
+question we also talked about Donald
+
+ align:start position:0%
+question we also talked about Donald
+ 
+
+ align:start position:0%
+question we also talked about Donald
+Stokes work where he critiqued the split
+
+ align:start position:0%
+Stokes work where he critiqued the split
+ 
+
+ align:start position:0%
+Stokes work where he critiqued the split
+in the u.s. innovation organizational
+
+ align:start position:0%
+in the u.s. innovation organizational
+ 
+
+ align:start position:0%
+in the u.s. innovation organizational
+system between front-end innovation the
+
+ align:start position:0%
+system between front-end innovation the
+ 
+
+ align:start position:0%
+system between front-end innovation the
+our side and the later stages so that
+
+ align:start position:0%
+our side and the later stages so that
+ 
+
+ align:start position:0%
+our side and the later stages so that
+there's a when we organized to do
+
+ align:start position:0%
+there's a when we organized to do
+ 
+
+ align:start position:0%
+there's a when we organized to do
+essentially a research model at the end
+
+ align:start position:0%
+essentially a research model at the end
+ 
+
+ align:start position:0%
+essentially a research model at the end
+of war to under that pipeline model that
+
+ align:start position:0%
+of war to under that pipeline model that
+ 
+
+ align:start position:0%
+of war to under that pipeline model that
+boniva Bush gave us we missed issues
+
+ align:start position:0%
+boniva Bush gave us we missed issues
+ 
+
+ align:start position:0%
+boniva Bush gave us we missed issues
+that subsidy and rose in the economy and
+
+ align:start position:0%
+that subsidy and rose in the economy and
+ 
+
+ align:start position:0%
+that subsidy and rose in the economy and
+became really deep sources of problems
+
+ align:start position:0%
+became really deep sources of problems
+ 
+
+ align:start position:0%
+became really deep sources of problems
+about the connections to the follow-on
+
+ align:start position:0%
+about the connections to the follow-on
+ 
+
+ align:start position:0%
+about the connections to the follow-on
+implementation back into the innovation
+
+ align:start position:0%
+implementation back into the innovation
+ 
+
+ align:start position:0%
+implementation back into the innovation
+system stages class six was about
+
+ align:start position:0%
+system stages class six was about
+ 
+
+ align:start position:0%
+system stages class six was about
+crossing this this valley of death how
+
+ align:start position:0%
+crossing this this valley of death how
+ 
+
+ align:start position:0%
+crossing this this valley of death how
+do you build a bridging models that get
+
+ align:start position:0%
+do you build a bridging models that get
+ 
+
+ align:start position:0%
+do you build a bridging models that get
+you across from a pipeline innovation
+
+ align:start position:0%
+you across from a pipeline innovation
+ 
+
+ align:start position:0%
+you across from a pipeline innovation
+model across to the later stages that's
+
+ align:start position:0%
+model across to the later stages that's
+ 
+
+ align:start position:0%
+model across to the later stages that's
+not easy in our system and then we also
+
+ align:start position:0%
+not easy in our system and then we also
+ 
+
+ align:start position:0%
+not easy in our system and then we also
+talked about the fact that we run two
+
+ align:start position:0%
+talked about the fact that we run two
+ 
+
+ align:start position:0%
+talked about the fact that we run two
+parallel systems in the u.s. so Vernon
+
+ align:start position:0%
+parallel systems in the u.s. so Vernon
+ 
+
+ align:start position:0%
+parallel systems in the u.s. so Vernon
+Rutan's book is war necessary for
+
+ align:start position:0%
+Rutan's book is war necessary for
+ 
+
+ align:start position:0%
+Rutan's book is war necessary for
+economic growth introduced us into the
+
+ align:start position:0%
+economic growth introduced us into the
+ 
+
+ align:start position:0%
+economic growth introduced us into the
+whole defense innovation system which is
+
+ align:start position:0%
+whole defense innovation system which is
+ 
+
+ align:start position:0%
+whole defense innovation system which is
+not disconnected right that's a pretty
+
+ align:start position:0%
+not disconnected right that's a pretty
+ 
+
+ align:start position:0%
+not disconnected right that's a pretty
+connected model and the Defense
+
+ align:start position:0%
+connected model and the Defense
+ 
+
+ align:start position:0%
+connected model and the Defense
+Department will typically perform the
+
+ align:start position:0%
+Department will typically perform the
+ 
+
+ align:start position:0%
+Department will typically perform the
+research the development it will do
+
+ align:start position:0%
+research the development it will do
+ 
+
+ align:start position:0%
+research the development it will do
+demonstration in will do the testbed it
+
+ align:start position:0%
+demonstration in will do the testbed it
+ 
+
+ align:start position:0%
+demonstration in will do the testbed it
+will move to the advanced prototypes and
+
+ align:start position:0%
+will move to the advanced prototypes and
+ 
+
+ align:start position:0%
+will move to the advanced prototypes and
+will often provide an initial market for
+
+ align:start position:0%
+will often provide an initial market for
+ 
+
+ align:start position:0%
+will often provide an initial market for
+emerging technologies that's a very
+
+ align:start position:0%
+emerging technologies that's a very
+ 
+
+ align:start position:0%
+emerging technologies that's a very
+different organizational system as we
+
+ align:start position:0%
+different organizational system as we
+ 
+
+ align:start position:0%
+different organizational system as we
+discussed from what's the civilian
+
+ align:start position:0%
+discussed from what's the civilian
+ 
+
+ align:start position:0%
+discussed from what's the civilian
+agencies are up to class seven was
+
+ align:start position:0%
+agencies are up to class seven was
+ 
+
+ align:start position:0%
+agencies are up to class seven was
+innovation at the face-to-face level
+
+ align:start position:0%
+innovation at the face-to-face level
+ 
+
+ align:start position:0%
+innovation at the face-to-face level
+that's our whole great groups theory so
+
+ align:start position:0%
+that's our whole great groups theory so
+ 
+
+ align:start position:0%
+that's our whole great groups theory so
+if innovation has to do with
+
+ align:start position:0%
+if innovation has to do with
+ 
+
+ align:start position:0%
+if innovation has to do with
+institutions which it certainly does how
+
+ align:start position:0%
+institutions which it certainly does how
+ 
+
+ align:start position:0%
+institutions which it certainly does how
+are those institutions organized and how
+
+ align:start position:0%
+are those institutions organized and how
+ 
+
+ align:start position:0%
+are those institutions organized and how
+do they connect and how how are the
+
+ align:start position:0%
+do they connect and how how are the
+ 
+
+ align:start position:0%
+do they connect and how how are the
+handoffs between the actors but in the
+
+ align:start position:0%
+handoffs between the actors but in the
+ 
+
+ align:start position:0%
+handoffs between the actors but in the
+end people own innovation not
+
+ align:start position:0%
+end people own innovation not
+ 
+
+ align:start position:0%
+end people own innovation not
+institutions
+
+ align:start position:0%
+institutions
+ 
+
+ align:start position:0%
+institutions
+it's very face to face
+
+ align:start position:0%
+it's very face to face
+ 
+
+ align:start position:0%
+it's very face to face
+and then the great groups classes you
+
+ align:start position:0%
+and then the great groups classes you
+ 
+
+ align:start position:0%
+and then the great groups classes you
+remember well we talked about some of
+
+ align:start position:0%
+remember well we talked about some of
+ 
+
+ align:start position:0%
+remember well we talked about some of
+the rule sets that tend to guide the way
+
+ align:start position:0%
+the rule sets that tend to guide the way
+ 
+
+ align:start position:0%
+the rule sets that tend to guide the way
+in which great group innovate based
+
+ align:start position:0%
+in which great group innovate based
+ 
+
+ align:start position:0%
+in which great group innovate based
+innovation operates and again that
+
+ align:start position:0%
+innovation operates and again that
+ 
+
+ align:start position:0%
+innovation operates and again that
+drives us back to this third innovation
+
+ align:start position:0%
+drives us back to this third innovation
+ 
+
+ align:start position:0%
+drives us back to this third innovation
+factor what does innovation look like
+
+ align:start position:0%
+factor what does innovation look like
+ 
+
+ align:start position:0%
+factor what does innovation look like
+from an organizational point of view
+
+ align:start position:0%
+from an organizational point of view
+ 
+
+ align:start position:0%
+from an organizational point of view
+from a systems point of view from an
+
+ align:start position:0%
+from a systems point of view from an
+ 
+
+ align:start position:0%
+from a systems point of view from an
+actor's point of view performance but
+
+ align:start position:0%
+actor's point of view performance but
+ 
+
+ align:start position:0%
+actor's point of view performance but
+also how does innovation look at the
+
+ align:start position:0%
+also how does innovation look at the
+ 
+
+ align:start position:0%
+also how does innovation look at the
+face-to-face level and then in class a
+
+ align:start position:0%
+face-to-face level and then in class a
+ 
+
+ align:start position:0%
+face-to-face level and then in class a
+we talked about DARPA which is an
+
+ align:start position:0%
+we talked about DARPA which is an
+ 
+
+ align:start position:0%
+we talked about DARPA which is an
+institution that actually attempts to do
+
+ align:start position:0%
+institution that actually attempts to do
+ 
+
+ align:start position:0%
+institution that actually attempts to do
+both on a good day
+
+ align:start position:0%
+both on a good day
+ 
+
+ align:start position:0%
+both on a good day
+that'll do it will support that
+
+ align:start position:0%
+that'll do it will support that
+ 
+
+ align:start position:0%
+that'll do it will support that
+connectedness of innovation institutions
+
+ align:start position:0%
+connectedness of innovation institutions
+ 
+
+ align:start position:0%
+connectedness of innovation institutions
+being connected using that defense model
+
+ align:start position:0%
+being connected using that defense model
+ 
+
+ align:start position:0%
+being connected using that defense model
+but it will also attempt to build great
+
+ align:start position:0%
+but it will also attempt to build great
+ 
+
+ align:start position:0%
+but it will also attempt to build great
+groups and we talked about JCR Licklider
+
+ align:start position:0%
+groups and we talked about JCR Licklider
+ 
+
+ align:start position:0%
+groups and we talked about JCR Licklider
+and the evolution of the IT revolution a
+
+ align:start position:0%
+and the evolution of the IT revolution a
+ 
+
+ align:start position:0%
+and the evolution of the IT revolution a
+lot of the origins of which came out of
+
+ align:start position:0%
+lot of the origins of which came out of
+ 
+
+ align:start position:0%
+lot of the origins of which came out of
+DARPA supported research as an example
+
+ align:start position:0%
+DARPA supported research as an example
+ 
+
+ align:start position:0%
+DARPA supported research as an example
+of that so now we're gonna do some more
+
+ align:start position:0%
+of that so now we're gonna do some more
+ 
+
+ align:start position:0%
+of that so now we're gonna do some more
+case studies in the in today's class
+
+ align:start position:0%
+case studies in the in today's class
+ 
+
+ align:start position:0%
+case studies in the in today's class
+really looking at the life science
+
+ align:start position:0%
+really looking at the life science
+ 
+
+ align:start position:0%
+really looking at the life science
+innovation system and how does that
+
+ align:start position:0%
+innovation system and how does that
+ 
+
+ align:start position:0%
+innovation system and how does that
+function and we're going to take a lot
+
+ align:start position:0%
+function and we're going to take a lot
+ 
+
+ align:start position:0%
+function and we're going to take a lot
+of the lessons that we've been learning
+
+ align:start position:0%
+of the lessons that we've been learning
+ 
+
+ align:start position:0%
+of the lessons that we've been learning
+and try and fit them into analyzing this
+
+ align:start position:0%
+and try and fit them into analyzing this
+ 
+
+ align:start position:0%
+and try and fit them into analyzing this
+really important piece in to do this
+
+ align:start position:0%
+really important piece in to do this
+ 
+
+ align:start position:0%
+really important piece in to do this
+territory all right let me give you a
+
+ align:start position:0%
+territory all right let me give you a
+ 
+
+ align:start position:0%
+territory all right let me give you a
+quick NIH historical backdrop right
+
+ align:start position:0%
+quick NIH historical backdrop right
+ 
+
+ align:start position:0%
+quick NIH historical backdrop right
+remember the pre-world War two and the
+
+ align:start position:0%
+remember the pre-world War two and the
+ 
+
+ align:start position:0%
+remember the pre-world War two and the
+war two context NIH s stood up as a
+
+ align:start position:0%
+war two context NIH s stood up as a
+ 
+
+ align:start position:0%
+war two context NIH s stood up as a
+venire Bush basic research organization
+
+ align:start position:0%
+venire Bush basic research organization
+ 
+
+ align:start position:0%
+venire Bush basic research organization
+so Franklin Roosevelt and Vannevar Bush
+
+ align:start position:0%
+so Franklin Roosevelt and Vannevar Bush
+ 
+
+ align:start position:0%
+so Franklin Roosevelt and Vannevar Bush
+see what happens in war two right they
+
+ align:start position:0%
+see what happens in war two right they
+ 
+
+ align:start position:0%
+see what happens in war two right they
+see the development of antibiotics led
+
+ align:start position:0%
+see the development of antibiotics led
+ 
+
+ align:start position:0%
+see the development of antibiotics led
+by penicillin right and the effects are
+
+ align:start position:0%
+by penicillin right and the effects are
+ 
+
+ align:start position:0%
+by penicillin right and the effects are
+breathtaking absolutely breathtaking
+
+ align:start position:0%
+breathtaking absolutely breathtaking
+ 
+
+ align:start position:0%
+breathtaking absolutely breathtaking
+so suddenly we fight a war and you
+
+ align:start position:0%
+so suddenly we fight a war and you
+ 
+
+ align:start position:0%
+so suddenly we fight a war and you
+probably won't die of disease right
+
+ align:start position:0%
+probably won't die of disease right
+ 
+
+ align:start position:0%
+probably won't die of disease right
+you'll actually die of battlefield
+
+ align:start position:0%
+you'll actually die of battlefield
+ 
+
+ align:start position:0%
+you'll actually die of battlefield
+injuries which has never happened before
+
+ align:start position:0%
+injuries which has never happened before
+ 
+
+ align:start position:0%
+injuries which has never happened before
+and that immediately has an effect
+
+ align:start position:0%
+and that immediately has an effect
+ 
+
+ align:start position:0%
+and that immediately has an effect
+removes pneumonia from the number one
+
+ align:start position:0%
+removes pneumonia from the number one
+ 
+
+ align:start position:0%
+removes pneumonia from the number one
+cause of death in the United States you
+
+ align:start position:0%
+cause of death in the United States you
+ 
+
+ align:start position:0%
+cause of death in the United States you
+know consider the further down the
+
+ align:start position:0%
+know consider the further down the
+ 
+
+ align:start position:0%
+know consider the further down the
+it's very dramatic Bush and Rosa will
+
+ align:start position:0%
+it's very dramatic Bush and Rosa will
+ 
+
+ align:start position:0%
+it's very dramatic Bush and Rosa will
+see this and understand how powerful
+
+ align:start position:0%
+see this and understand how powerful
+ 
+
+ align:start position:0%
+see this and understand how powerful
+that model is and so one of the theories
+
+ align:start position:0%
+that model is and so one of the theories
+ 
+
+ align:start position:0%
+that model is and so one of the theories
+in the endless frontier that veneer Bush
+
+ align:start position:0%
+in the endless frontier that veneer Bush
+ 
+
+ align:start position:0%
+in the endless frontier that veneer Bush
+puts out as you remember is that there's
+
+ align:start position:0%
+puts out as you remember is that there's
+ 
+
+ align:start position:0%
+puts out as you remember is that there's
+gonna be a war against disease and
+
+ align:start position:0%
+gonna be a war against disease and
+ 
+
+ align:start position:0%
+gonna be a war against disease and
+they've just seen what this model is
+
+ align:start position:0%
+they've just seen what this model is
+ 
+
+ align:start position:0%
+they've just seen what this model is
+right so they want to do it now Truman
+
+ align:start position:0%
+right so they want to do it now Truman
+ 
+
+ align:start position:0%
+right so they want to do it now Truman
+as you remember vetoes the one agency
+
+ align:start position:0%
+as you remember vetoes the one agency
+ 
+
+ align:start position:0%
+as you remember vetoes the one agency
+one-tenth National Science Foundation
+
+ align:start position:0%
+one-tenth National Science Foundation
+ 
+
+ align:start position:0%
+one-tenth National Science Foundation
+role right so he vetoes that and like is
+
+ align:start position:0%
+role right so he vetoes that and like is
+ 
+
+ align:start position:0%
+role right so he vetoes that and like is
+it 47 or 49 and that leaves a void so
+
+ align:start position:0%
+it 47 or 49 and that leaves a void so
+ 
+
+ align:start position:0%
+it 47 or 49 and that leaves a void so
+voids tend to get filled so this little
+
+ align:start position:0%
+voids tend to get filled so this little
+ 
+
+ align:start position:0%
+voids tend to get filled so this little
+research outfit that's part of the
+
+ align:start position:0%
+research outfit that's part of the
+ 
+
+ align:start position:0%
+research outfit that's part of the
+Public Health Service the National
+
+ align:start position:0%
+Public Health Service the National
+ 
+
+ align:start position:0%
+Public Health Service the National
+Institute of Health becomes the National
+
+ align:start position:0%
+Institute of Health becomes the National
+ 
+
+ align:start position:0%
+Institute of Health becomes the National
+Institutes and really starts scaling up
+
+ align:start position:0%
+Institutes and really starts scaling up
+ 
+
+ align:start position:0%
+Institutes and really starts scaling up
+right so follows a Vannevar Bush basic
+
+ align:start position:0%
+right so follows a Vannevar Bush basic
+ 
+
+ align:start position:0%
+right so follows a Vannevar Bush basic
+research model but it you know evolves
+
+ align:start position:0%
+research model but it you know evolves
+ 
+
+ align:start position:0%
+research model but it you know evolves
+in this kind of gap of organizational
+
+ align:start position:0%
+in this kind of gap of organizational
+ 
+
+ align:start position:0%
+in this kind of gap of organizational
+leadership in a way and fills that void
+
+ align:start position:0%
+leadership in a way and fills that void
+ 
+
+ align:start position:0%
+leadership in a way and fills that void
+and then over time disease groups tend
+
+ align:start position:0%
+and then over time disease groups tend
+ 
+
+ align:start position:0%
+and then over time disease groups tend
+to be very active politically right if
+
+ align:start position:0%
+to be very active politically right if
+ 
+
+ align:start position:0%
+to be very active politically right if
+you have a disease or if a loved one has
+
+ align:start position:0%
+you have a disease or if a loved one has
+ 
+
+ align:start position:0%
+you have a disease or if a loved one has
+a disease you tend to be very active in
+
+ align:start position:0%
+a disease you tend to be very active in
+ 
+
+ align:start position:0%
+a disease you tend to be very active in
+the disease group and these disease
+
+ align:start position:0%
+the disease group and these disease
+ 
+
+ align:start position:0%
+the disease group and these disease
+groups push their disease in Congress
+
+ align:start position:0%
+groups push their disease in Congress
+ 
+
+ align:start position:0%
+groups push their disease in Congress
+and Congress keeps adding institutes and
+
+ align:start position:0%
+and Congress keeps adding institutes and
+ 
+
+ align:start position:0%
+and Congress keeps adding institutes and
+centers on to the model when it reaches
+
+ align:start position:0%
+centers on to the model when it reaches
+ 
+
+ align:start position:0%
+centers on to the model when it reaches
+a complete unmanageable number of 27
+
+ align:start position:0%
+a complete unmanageable number of 27
+ 
+
+ align:start position:0%
+a complete unmanageable number of 27
+finally Congress actually tries to
+
+ align:start position:0%
+finally Congress actually tries to
+ 
+
+ align:start position:0%
+finally Congress actually tries to
+restrain itself but it's it creates an
+
+ align:start position:0%
+restrain itself but it's it creates an
+ 
+
+ align:start position:0%
+restrain itself but it's it creates an
+organizational model that's problematic
+
+ align:start position:0%
+organizational model that's problematic
+ 
+
+ align:start position:0%
+organizational model that's problematic
+now another feature here is there's a
+
+ align:start position:0%
+now another feature here is there's a
+ 
+
+ align:start position:0%
+now another feature here is there's a
+line from Tony felt she was one of the
+
+ align:start position:0%
+line from Tony felt she was one of the
+ 
+
+ align:start position:0%
+line from Tony felt she was one of the
+director of Nyad quite famous one of the
+
+ align:start position:0%
+director of Nyad quite famous one of the
+ 
+
+ align:start position:0%
+director of Nyad quite famous one of the
+Nyad was one of the leaders in and
+
+ align:start position:0%
+Nyad was one of the leaders in and
+ 
+
+ align:start position:0%
+Nyad was one of the leaders in and
+getting on all kinds of infectious
+
+ align:start position:0%
+getting on all kinds of infectious
+ 
+
+ align:start position:0%
+getting on all kinds of infectious
+diseases including aids but Tony foul
+
+ align:start position:0%
+diseases including aids but Tony foul
+ 
+
+ align:start position:0%
+diseases including aids but Tony foul
+she writes in 2003 the path to product
+
+ align:start position:0%
+she writes in 2003 the path to product
+ 
+
+ align:start position:0%
+she writes in 2003 the path to product
+development has not been a part of my
+
+ align:start position:0%
+development has not been a part of my
+ 
+
+ align:start position:0%
+development has not been a part of my
+adds research strategy
+
+ align:start position:0%
+adds research strategy
+ 
+
+ align:start position:0%
+adds research strategy
+right other words that's not on the
+
+ align:start position:0%
+right other words that's not on the
+ 
+
+ align:start position:0%
+right other words that's not on the
+table they're worried about their basic
+
+ align:start position:0%
+table they're worried about their basic
+ 
+
+ align:start position:0%
+table they're worried about their basic
+research results so what did NIH and
+
+ align:start position:0%
+research results so what did NIH and
+ 
+
+ align:start position:0%
+research results so what did NIH and
+arguably the biotech model that's is
+
+ align:start position:0%
+arguably the biotech model that's is
+ 
+
+ align:start position:0%
+arguably the biotech model that's is
+spawned from it what did they get right
+
+ align:start position:0%
+spawned from it what did they get right
+ 
+
+ align:start position:0%
+spawned from it what did they get right
+and they get a lot of things right it's
+
+ align:start position:0%
+and they get a lot of things right it's
+ 
+
+ align:start position:0%
+and they get a lot of things right it's
+an amazing system it's a remarkable
+
+ align:start position:0%
+an amazing system it's a remarkable
+ 
+
+ align:start position:0%
+an amazing system it's a remarkable
+story of success so even though we're
+
+ align:start position:0%
+story of success so even though we're
+ 
+
+ align:start position:0%
+story of success so even though we're
+going to be critical today it is an
+
+ align:start position:0%
+going to be critical today it is an
+ 
+
+ align:start position:0%
+going to be critical today it is an
+amazing success story
+
+ align:start position:0%
+amazing success story
+ 
+
+ align:start position:0%
+amazing success story
+and IH trained everybody right created
+
+ align:start position:0%
+and IH trained everybody right created
+ 
+
+ align:start position:0%
+and IH trained everybody right created
+this huge education system that put a
+
+ align:start position:0%
+this huge education system that put a
+ 
+
+ align:start position:0%
+this huge education system that put a
+lot of talent on the task in Roemer's
+
+ align:start position:0%
+lot of talent on the task in Roemer's
+ 
+
+ align:start position:0%
+lot of talent on the task in Roemer's
+terms this knowledge base helped spawn a
+
+ align:start position:0%
+terms this knowledge base helped spawn a
+ 
+
+ align:start position:0%
+terms this knowledge base helped spawn a
+remarkable entrepreneurial biotech
+
+ align:start position:0%
+remarkable entrepreneurial biotech
+ 
+
+ align:start position:0%
+remarkable entrepreneurial biotech
+startup model and we talked about
+
+ align:start position:0%
+startup model and we talked about
+ 
+
+ align:start position:0%
+startup model and we talked about
+Genentech during our great groups class
+
+ align:start position:0%
+Genentech during our great groups class
+ 
+
+ align:start position:0%
+Genentech during our great groups class
+that's the first that's a very good
+
+ align:start position:0%
+that's the first that's a very good
+ 
+
+ align:start position:0%
+that's the first that's a very good
+example of what then flourished and you
+
+ align:start position:0%
+example of what then flourished and you
+ 
+
+ align:start position:0%
+example of what then flourished and you
+know Boyer and Swanson where the
+
+ align:start position:0%
+know Boyer and Swanson where the
+ 
+
+ align:start position:0%
+know Boyer and Swanson where the
+founders Boyer comes out of that NIH
+
+ align:start position:0%
+founders Boyer comes out of that NIH
+ 
+
+ align:start position:0%
+founders Boyer comes out of that NIH
+funded system
+
+ align:start position:0%
+funded system
+ 
+
+ align:start position:0%
+funded system
+biotechs have been able to get venture
+
+ align:start position:0%
+biotechs have been able to get venture
+ 
+
+ align:start position:0%
+biotechs have been able to get venture
+capital support even though they have a
+
+ align:start position:0%
+capital support even though they have a
+ 
+
+ align:start position:0%
+capital support even though they have a
+10 to 15 years stand-up model right
+
+ align:start position:0%
+10 to 15 years stand-up model right
+ 
+
+ align:start position:0%
+10 to 15 years stand-up model right
+which is a remarkable accomplishment no
+
+ align:start position:0%
+which is a remarkable accomplishment no
+ 
+
+ align:start position:0%
+which is a remarkable accomplishment no
+other sector is able to get mentor
+
+ align:start position:0%
+other sector is able to get mentor
+ 
+
+ align:start position:0%
+other sector is able to get mentor
+capital money unless they're no more
+
+ align:start position:0%
+capital money unless they're no more
+ 
+
+ align:start position:0%
+capital money unless they're no more
+than a couple of years out of production
+
+ align:start position:0%
+than a couple of years out of production
+ 
+
+ align:start position:0%
+than a couple of years out of production
+biotechs have been able to break that
+
+ align:start position:0%
+biotechs have been able to break that
+ 
+
+ align:start position:0%
+biotechs have been able to break that
+and get long-term support for R&D and
+
+ align:start position:0%
+and get long-term support for R&D and
+ 
+
+ align:start position:0%
+and get long-term support for R&D and
+the key to this is they've been the
+
+ align:start position:0%
+the key to this is they've been the
+ 
+
+ align:start position:0%
+the key to this is they've been the
+value of IP so there is a working
+
+ align:start position:0%
+value of IP so there is a working
+ 
+
+ align:start position:0%
+value of IP so there is a working
+monopoly model in the biotech sector so
+
+ align:start position:0%
+monopoly model in the biotech sector so
+ 
+
+ align:start position:0%
+monopoly model in the biotech sector so
+if you're you know first a patent a new
+
+ align:start position:0%
+if you're you know first a patent a new
+ 
+
+ align:start position:0%
+if you're you know first a patent a new
+drug you are given a monopoly rent for a
+
+ align:start position:0%
+drug you are given a monopoly rent for a
+ 
+
+ align:start position:0%
+drug you are given a monopoly rent for a
+20 year time period right - the time it
+
+ align:start position:0%
+20 year time period right - the time it
+ 
+
+ align:start position:0%
+20 year time period right - the time it
+gets you to get through clinical trials
+
+ align:start position:0%
+gets you to get through clinical trials
+ 
+
+ align:start position:0%
+gets you to get through clinical trials
+with NIH which can be seven years so
+
+ align:start position:0%
+with NIH which can be seven years so
+ 
+
+ align:start position:0%
+with NIH which can be seven years so
+it's a 13 year run where you're assured
+
+ align:start position:0%
+it's a 13 year run where you're assured
+ 
+
+ align:start position:0%
+it's a 13 year run where you're assured
+of monopoly rents and unlike the hard
+
+ align:start position:0%
+of monopoly rents and unlike the hard
+ 
+
+ align:start position:0%
+of monopoly rents and unlike the hard
+technology sector it's harder to stand
+
+ align:start position:0%
+technology sector it's harder to stand
+ 
+
+ align:start position:0%
+technology sector it's harder to stand
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+in effect copycat fixes right copy cut
+
+ align:start position:0%
+in effect copycat fixes right copy cut
+ 
+
+ align:start position:0%
+in effect copycat fixes right copy cut
+drugs so you really do get a significant
+
+ align:start position:0%
+drugs so you really do get a significant
+ 
+
+ align:start position:0%
+drugs so you really do get a significant
+run typically if you get if you're first
+
+ align:start position:0%
+run typically if you get if you're first
+ 
+
+ align:start position:0%
+run typically if you get if you're first
+to patent and you get a head first
+
+ align:start position:0%
+to patent and you get a head first
+ 
+
+ align:start position:0%
+to patent and you get a head first
+through the clinical trial process so
+
+ align:start position:0%
+through the clinical trial process so
+ 
+
+ align:start position:0%
+through the clinical trial process so
+that's created a that's been the enabler
+
+ align:start position:0%
+that's created a that's been the enabler
+ 
+
+ align:start position:0%
+that's created a that's been the enabler
+that allows this financing system to
+
+ align:start position:0%
+that allows this financing system to
+ 
+
+ align:start position:0%
+that allows this financing system to
+work the other key feature is FDA's
+
+ align:start position:0%
+work the other key feature is FDA's
+ 
+
+ align:start position:0%
+work the other key feature is FDA's
+approval so FDA gives you in stage 1
+
+ align:start position:0%
+approval so FDA gives you in stage 1
+ 
+
+ align:start position:0%
+approval so FDA gives you in stage 1
+stage 2 stage 3 clinical trials
+
+ align:start position:0%
+stage 2 stage 3 clinical trials
+ 
+
+ align:start position:0%
+stage 2 stage 3 clinical trials
+everybody if you're developing a cancer
+
+ align:start position:0%
+everybody if you're developing a cancer
+ 
+
+ align:start position:0%
+everybody if you're developing a cancer
+drug you know exactly what your chances
+
+ align:start position:0%
+drug you know exactly what your chances
+ 
+
+ align:start position:0%
+drug you know exactly what your chances
+are on getting through those from stage
+
+ align:start position:0%
+are on getting through those from stage
+ 
+
+ align:start position:0%
+are on getting through those from stage
+1 to stage 2 and stage 2 to stage 3
+
+ align:start position:0%
+1 to stage 2 and stage 2 to stage 3
+ 
+
+ align:start position:0%
+1 to stage 2 and stage 2 to stage 3
+right you know and from stage 3 to final
+
+ align:start position:0%
+right you know and from stage 3 to final
+ 
+
+ align:start position:0%
+right you know and from stage 3 to final
+drug approval you know just what your
+
+ align:start position:0%
+drug approval you know just what your
+ 
+
+ align:start position:0%
+drug approval you know just what your
+chances are so that enables venture
+
+ align:start position:0%
+chances are so that enables venture
+ 
+
+ align:start position:0%
+chances are so that enables venture
+capitalists to tee off their stages of
+
+ align:start position:0%
+capitalists to tee off their stages of
+ 
+
+ align:start position:0%
+capitalists to tee off their stages of
+financing to your success in the
+
+ align:start position:0%
+financing to your success in the
+ 
+
+ align:start position:0%
+financing to your success in the
+clinical trials process there is no
+
+ align:start position:0%
+clinical trials process there is no
+ 
+
+ align:start position:0%
+clinical trials process there is no
+benchmarking system like this in any
+
+ align:start position:0%
+benchmarking system like this in any
+ 
+
+ align:start position:0%
+benchmarking system like this in any
+other sector in the economy it works
+
+ align:start position:0%
+other sector in the economy it works
+ 
+
+ align:start position:0%
+other sector in the economy it works
+amazingly well and then another big
+
+ align:start position:0%
+amazingly well and then another big
+ 
+
+ align:start position:0%
+amazingly well and then another big
+difference between life science and
+
+ align:start position:0%
+difference between life science and
+ 
+
+ align:start position:0%
+difference between life science and
+everything else is that if FDA approves
+
+ align:start position:0%
+everything else is that if FDA approves
+ 
+
+ align:start position:0%
+everything else is that if FDA approves
+your drug you are guaranteed a market in
+
+ align:start position:0%
+your drug you are guaranteed a market in
+ 
+
+ align:start position:0%
+your drug you are guaranteed a market in
+fact our wonderful legal system is such
+
+ align:start position:0%
+fact our wonderful legal system is such
+ 
+
+ align:start position:0%
+fact our wonderful legal system is such
+that if a doctor fails to prescribe the
+
+ align:start position:0%
+that if a doctor fails to prescribe the
+ 
+
+ align:start position:0%
+that if a doctor fails to prescribe the
+medicine which is fitted to your problem
+
+ align:start position:0%
+medicine which is fitted to your problem
+ 
+
+ align:start position:0%
+medicine which is fitted to your problem
+the next day the doctor gets sued right
+
+ align:start position:0%
+the next day the doctor gets sued right
+ 
+
+ align:start position:0%
+the next day the doctor gets sued right
+so there's this huge forcing mechanism
+
+ align:start position:0%
+so there's this huge forcing mechanism
+ 
+
+ align:start position:0%
+so there's this huge forcing mechanism
+in the system there's nothing like a
+
+ align:start position:0%
+in the system there's nothing like a
+ 
+
+ align:start position:0%
+in the system there's nothing like a
+certification that guarantees you a
+
+ align:start position:0%
+certification that guarantees you a
+ 
+
+ align:start position:0%
+certification that guarantees you a
+market on the next day there's nothing
+
+ align:start position:0%
+market on the next day there's nothing
+ 
+
+ align:start position:0%
+market on the next day there's nothing
+like this anywhere else in our system
+
+ align:start position:0%
+like this anywhere else in our system
+ 
+
+ align:start position:0%
+like this anywhere else in our system
+it's a remarkable thing and we can start
+
+ align:start position:0%
+it's a remarkable thing and we can start
+ 
+
+ align:start position:0%
+it's a remarkable thing and we can start
+to think about how you get analogous
+
+ align:start position:0%
+to think about how you get analogous
+ 
+
+ align:start position:0%
+to think about how you get analogous
+certification processes and benchmarking
+
+ align:start position:0%
+certification processes and benchmarking
+ 
+
+ align:start position:0%
+certification processes and benchmarking
+processes in place in more physical
+
+ align:start position:0%
+processes in place in more physical
+ 
+
+ align:start position:0%
+processes in place in more physical
+science based technologies would be very
+
+ align:start position:0%
+science based technologies would be very
+ 
+
+ align:start position:0%
+science based technologies would be very
+interesting you haven't done it but
+
+ align:start position:0%
+interesting you haven't done it but
+ 
+
+ align:start position:0%
+interesting you haven't done it but
+there's a lot to be learned from this
+
+ align:start position:0%
+there's a lot to be learned from this
+ 
+
+ align:start position:0%
+there's a lot to be learned from this
+sector because of the system it's set up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+upstairs Downstairs has historically
+
+ align:start position:0%
+upstairs Downstairs has historically
+ 
+
+ align:start position:0%
+upstairs Downstairs has historically
+been a problem particularly in European
+
+ align:start position:0%
+been a problem particularly in European
+ 
+
+ align:start position:0%
+been a problem particularly in European
+science but also in US science whereas
+
+ align:start position:0%
+science but also in US science whereas
+ 
+
+ align:start position:0%
+science but also in US science whereas
+the academic researchers have disdained
+
+ align:start position:0%
+the academic researchers have disdained
+ 
+
+ align:start position:0%
+the academic researchers have disdained
+for the company researchers that has
+
+ align:start position:0%
+for the company researchers that has
+ 
+
+ align:start position:0%
+for the company researchers that has
+really broken up and broken apart in the
+
+ align:start position:0%
+really broken up and broken apart in the
+ 
+
+ align:start position:0%
+really broken up and broken apart in the
+life science side so outstanding
+
+ align:start position:0%
+life science side so outstanding
+ 
+
+ align:start position:0%
+life science side so outstanding
+academics think Boyer
+
+ align:start position:0%
+academics think Boyer
+ 
+
+ align:start position:0%
+academics think Boyer
+who have who spent time in a biotech
+
+ align:start position:0%
+who have who spent time in a biotech
+ 
+
+ align:start position:0%
+who have who spent time in a biotech
+that's not created as a sound career
+
+ align:start position:0%
+that's not created as a sound career
+ 
+
+ align:start position:0%
+that's not created as a sound career
+path Boyer had to break the ground he
+
+ align:start position:0%
+path Boyer had to break the ground he
+ 
+
+ align:start position:0%
+path Boyer had to break the ground he
+got a lot of flack for it at the time
+
+ align:start position:0%
+got a lot of flack for it at the time
+ 
+
+ align:start position:0%
+got a lot of flack for it at the time
+but over time it's become accepted that
+
+ align:start position:0%
+but over time it's become accepted that
+ 
+
+ align:start position:0%
+but over time it's become accepted that
+you can have an academic career moved to
+
+ align:start position:0%
+you can have an academic career moved to
+ 
+
+ align:start position:0%
+you can have an academic career moved to
+a biotech move back to an academic
+
+ align:start position:0%
+a biotech move back to an academic
+ 
+
+ align:start position:0%
+a biotech move back to an academic
+career that's okay
+
+ align:start position:0%
+career that's okay
+ 
+
+ align:start position:0%
+career that's okay
+obviously this conflict is used to out
+
+ align:start position:0%
+obviously this conflict is used to out
+ 
+
+ align:start position:0%
+obviously this conflict is used to out
+that whole process that have to be dealt
+
+ align:start position:0%
+that whole process that have to be dealt
+ 
+
+ align:start position:0%
+that whole process that have to be dealt
+with but that's an acceptable pathway so
+
+ align:start position:0%
+with but that's an acceptable pathway so
+ 
+
+ align:start position:0%
+with but that's an acceptable pathway so
+the whole Upstairs Downstairs
+
+ align:start position:0%
+the whole Upstairs Downstairs
+ 
+
+ align:start position:0%
+the whole Upstairs Downstairs
+relationship between the academy and
+
+ align:start position:0%
+relationship between the academy and
+ 
+
+ align:start position:0%
+relationship between the academy and
+commercial development has really been
+
+ align:start position:0%
+commercial development has really been
+ 
+
+ align:start position:0%
+commercial development has really been
+broken up so that's another thing that
+
+ align:start position:0%
+broken up so that's another thing that
+ 
+
+ align:start position:0%
+broken up so that's another thing that
+this sector got right NIH also has a
+
+ align:start position:0%
+this sector got right NIH also has a
+ 
+
+ align:start position:0%
+this sector got right NIH also has a
+huge amount of money it's by far the
+
+ align:start position:0%
+huge amount of money it's by far the
+ 
+
+ align:start position:0%
+huge amount of money it's by far the
+largest R&D agency it's got over 30
+
+ align:start position:0%
+largest R&D agency it's got over 30
+ 
+
+ align:start position:0%
+largest R&D agency it's got over 30
+billion dollars a year
+
+ align:start position:0%
+billion dollars a year
+ 
+
+ align:start position:0%
+billion dollars a year
+nobody is close it's you know NSF by
+
+ align:start position:0%
+nobody is close it's you know NSF by
+ 
+
+ align:start position:0%
+nobody is close it's you know NSF by
+comparison is seven billion dollars a
+
+ align:start position:0%
+comparison is seven billion dollars a
+ 
+
+ align:start position:0%
+comparison is seven billion dollars a
+year the Department of Energy Office of
+
+ align:start position:0%
+year the Department of Energy Office of
+ 
+
+ align:start position:0%
+year the Department of Energy Office of
+Science is five billion DARPA is three
+
+ align:start position:0%
+Science is five billion DARPA is three
+ 
+
+ align:start position:0%
+Science is five billion DARPA is three
+billion right so this is an order of
+
+ align:start position:0%
+billion right so this is an order of
+ 
+
+ align:start position:0%
+billion right so this is an order of
+magnitude almost different from other
+
+ align:start position:0%
+magnitude almost different from other
+ 
+
+ align:start position:0%
+magnitude almost different from other
+R&D agencies and so the political
+
+ align:start position:0%
+R&D agencies and so the political
+ 
+
+ align:start position:0%
+R&D agencies and so the political
+constituencies including the disease
+
+ align:start position:0%
+constituencies including the disease
+ 
+
+ align:start position:0%
+constituencies including the disease
+groups have built a very powerful
+
+ align:start position:0%
+groups have built a very powerful
+ 
+
+ align:start position:0%
+groups have built a very powerful
+political base for sustained funding in
+
+ align:start position:0%
+political base for sustained funding in
+ 
+
+ align:start position:0%
+political base for sustained funding in
+this sector now that's the good news
+
+ align:start position:0%
+this sector now that's the good news
+ 
+
+ align:start position:0%
+this sector now that's the good news
+here's the problem we're gonna talk
+
+ align:start position:0%
+here's the problem we're gonna talk
+ 
+
+ align:start position:0%
+here's the problem we're gonna talk
+about the innovation train wreck that
+
+ align:start position:0%
+about the innovation train wreck that
+ 
+
+ align:start position:0%
+about the innovation train wreck that
+lies ahead here so the economic model
+
+ align:start position:0%
+lies ahead here so the economic model
+ 
+
+ align:start position:0%
+lies ahead here so the economic model
+for biotech sand farmers really requires
+
+ align:start position:0%
+for biotech sand farmers really requires
+ 
+
+ align:start position:0%
+for biotech sand farmers really requires
+blockbuster Marcus it's a huge problem
+
+ align:start position:0%
+blockbuster Marcus it's a huge problem
+ 
+
+ align:start position:0%
+blockbuster Marcus it's a huge problem
+so in other words third world diseases
+
+ align:start position:0%
+so in other words third world diseases
+ 
+
+ align:start position:0%
+so in other words third world diseases
+infectious diseases small population
+
+ align:start position:0%
+infectious diseases small population
+ 
+
+ align:start position:0%
+infectious diseases small population
+diseases it doesn't make sense to pursue
+
+ align:start position:0%
+diseases it doesn't make sense to pursue
+ 
+
+ align:start position:0%
+diseases it doesn't make sense to pursue
+those to get a drug through the FDA
+
+ align:start position:0%
+those to get a drug through the FDA
+ 
+
+ align:start position:0%
+those to get a drug through the FDA
+clinical process to develop in time
+
+ align:start position:0%
+clinical process to develop in time
+ 
+
+ align:start position:0%
+clinical process to develop in time
+before during and during the clinical
+
+ align:start position:0%
+before during and during the clinical
+ 
+
+ align:start position:0%
+before during and during the clinical
+trial approval process itself
+
+ align:start position:0%
+trial approval process itself
+ 
+
+ align:start position:0%
+trial approval process itself
+that's you know around a 1.4 billion or
+
+ align:start position:0%
+that's you know around a 1.4 billion or
+ 
+
+ align:start position:0%
+that's you know around a 1.4 billion or
+dollar or more proposition so unless
+
+ align:start position:0%
+dollar or more proposition so unless
+ 
+
+ align:start position:0%
+dollar or more proposition so unless
+you're selling into a major market it
+
+ align:start position:0%
+you're selling into a major market it
+ 
+
+ align:start position:0%
+you're selling into a major market it
+doesn't make any sense to develop the
+
+ align:start position:0%
+doesn't make any sense to develop the
+ 
+
+ align:start position:0%
+doesn't make any sense to develop the
+remedy so there there is a statistic
+
+ align:start position:0%
+remedy so there there is a statistic
+ 
+
+ align:start position:0%
+remedy so there there is a statistic
+that some cite which is that you know
+
+ align:start position:0%
+that some cite which is that you know
+ 
+
+ align:start position:0%
+that some cite which is that you know
+80% of our R&D money and life sciences
+
+ align:start position:0%
+80% of our R&D money and life sciences
+ 
+
+ align:start position:0%
+80% of our R&D money and life sciences
+spend
+
+ align:start position:0%
+spend
+ 
+
+ align:start position:0%
+spend
+on you know 10% of the diseases that's
+
+ align:start position:0%
+on you know 10% of the diseases that's
+ 
+
+ align:start position:0%
+on you know 10% of the diseases that's
+that's a problem I don't think the
+
+ align:start position:0%
+that's a problem I don't think the
+ 
+
+ align:start position:0%
+that's a problem I don't think the
+number is that bad I think that's
+
+ align:start position:0%
+number is that bad I think that's
+ 
+
+ align:start position:0%
+number is that bad I think that's
+exaggerated but we've got a problem here
+
+ align:start position:0%
+exaggerated but we've got a problem here
+ 
+
+ align:start position:0%
+exaggerated but we've got a problem here
+because this blockbuster drug model only
+
+ align:start position:0%
+because this blockbuster drug model only
+ 
+
+ align:start position:0%
+because this blockbuster drug model only
+if you're developing a drug that sells
+
+ align:start position:0%
+if you're developing a drug that sells
+ 
+
+ align:start position:0%
+if you're developing a drug that sells
+into a major market opportunity is it
+
+ align:start position:0%
+into a major market opportunity is it
+ 
+
+ align:start position:0%
+into a major market opportunity is it
+going to get into the market so what
+
+ align:start position:0%
+going to get into the market so what
+ 
+
+ align:start position:0%
+going to get into the market so what
+does that leave behind in addition to
+
+ align:start position:0%
+does that leave behind in addition to
+ 
+
+ align:start position:0%
+does that leave behind in addition to
+the things I've mentioned the precision
+
+ align:start position:0%
+the things I've mentioned the precision
+ 
+
+ align:start position:0%
+the things I've mentioned the precision
+medicine or personalized drug model it
+
+ align:start position:0%
+medicine or personalized drug model it
+ 
+
+ align:start position:0%
+medicine or personalized drug model it
+gets left behind so other words if each
+
+ align:start position:0%
+gets left behind so other words if each
+ 
+
+ align:start position:0%
+gets left behind so other words if each
+one of you is going to have their own
+
+ align:start position:0%
+one of you is going to have their own
+ 
+
+ align:start position:0%
+one of you is going to have their own
+remedy variant that's particularly
+
+ align:start position:0%
+remedy variant that's particularly
+ 
+
+ align:start position:0%
+remedy variant that's particularly
+adapted to your genetic structure or
+
+ align:start position:0%
+adapted to your genetic structure or
+ 
+
+ align:start position:0%
+adapted to your genetic structure or
+metabolism or whatever what are we going
+
+ align:start position:0%
+metabolism or whatever what are we going
+ 
+
+ align:start position:0%
+metabolism or whatever what are we going
+to do run a 1.4 billion dollar clinical
+
+ align:start position:0%
+to do run a 1.4 billion dollar clinical
+ 
+
+ align:start position:0%
+to do run a 1.4 billion dollar clinical
+trial process for you it's not gonna
+
+ align:start position:0%
+trial process for you it's not gonna
+ 
+
+ align:start position:0%
+trial process for you it's not gonna
+work right so how do we deal with this
+
+ align:start position:0%
+work right so how do we deal with this
+ 
+
+ align:start position:0%
+work right so how do we deal with this
+right there's a huge looming train wreck
+
+ align:start position:0%
+right there's a huge looming train wreck
+ 
+
+ align:start position:0%
+right there's a huge looming train wreck
+problem in the system because that's
+
+ align:start position:0%
+problem in the system because that's
+ 
+
+ align:start position:0%
+problem in the system because that's
+where it's going right this is the
+
+ align:start position:0%
+where it's going right this is the
+ 
+
+ align:start position:0%
+where it's going right this is the
+benefits of being able to use big data
+
+ align:start position:0%
+benefits of being able to use big data
+ 
+
+ align:start position:0%
+benefits of being able to use big data
+and analytic system develop personalized
+
+ align:start position:0%
+and analytic system develop personalized
+ 
+
+ align:start position:0%
+and analytic system develop personalized
+medicine but if there's not an economic
+
+ align:start position:0%
+medicine but if there's not an economic
+ 
+
+ align:start position:0%
+medicine but if there's not an economic
+model to get it there it won't happen
+
+ align:start position:0%
+model to get it there it won't happen
+ 
+
+ align:start position:0%
+model to get it there it won't happen
+the litigation threat makes drug
+
+ align:start position:0%
+the litigation threat makes drug
+ 
+
+ align:start position:0%
+the litigation threat makes drug
+companies risk-averse so we leave a lot
+
+ align:start position:0%
+companies risk-averse so we leave a lot
+ 
+
+ align:start position:0%
+companies risk-averse so we leave a lot
+of promising stuff on the table because
+
+ align:start position:0%
+of promising stuff on the table because
+ 
+
+ align:start position:0%
+of promising stuff on the table because
+of that threat often a drug will you
+
+ align:start position:0%
+of that threat often a drug will you
+ 
+
+ align:start position:0%
+of that threat often a drug will you
+know cure let's say 20 30 maybe 40
+
+ align:start position:0%
+know cure let's say 20 30 maybe 40
+ 
+
+ align:start position:0%
+know cure let's say 20 30 maybe 40
+percent of a disease groups problem but
+
+ align:start position:0%
+percent of a disease groups problem but
+ 
+
+ align:start position:0%
+percent of a disease groups problem but
+if it kills some people we'll never go
+
+ align:start position:0%
+if it kills some people we'll never go
+ 
+
+ align:start position:0%
+if it kills some people we'll never go
+to market right because we don't
+
+ align:start position:0%
+to market right because we don't
+ 
+
+ align:start position:0%
+to market right because we don't
+understand the precision medicine the
+
+ align:start position:0%
+understand the precision medicine the
+ 
+
+ align:start position:0%
+understand the precision medicine the
+personalized medicine implications of
+
+ align:start position:0%
+personalized medicine implications of
+ 
+
+ align:start position:0%
+personalized medicine implications of
+these things and until we do we're just
+
+ align:start position:0%
+these things and until we do we're just
+ 
+
+ align:start position:0%
+these things and until we do we're just
+leaving a lot of stuff on the shelf but
+
+ align:start position:0%
+leaving a lot of stuff on the shelf but
+ 
+
+ align:start position:0%
+leaving a lot of stuff on the shelf but
+as potential value because Americans for
+
+ align:start position:0%
+as potential value because Americans for
+ 
+
+ align:start position:0%
+as potential value because Americans for
+a good reason or very have very low
+
+ align:start position:0%
+a good reason or very have very low
+ 
+
+ align:start position:0%
+a good reason or very have very low
+tolerance for risk from drugs the
+
+ align:start position:0%
+tolerance for risk from drugs the
+ 
+
+ align:start position:0%
+tolerance for risk from drugs the
+healthcare spending and the overall
+
+ align:start position:0%
+healthcare spending and the overall
+ 
+
+ align:start position:0%
+healthcare spending and the overall
+system by 2025 may account for 9% of GDP
+
+ align:start position:0%
+system by 2025 may account for 9% of GDP
+ 
+
+ align:start position:0%
+system by 2025 may account for 9% of GDP
+or more and you know we'll talk about
+
+ align:start position:0%
+or more and you know we'll talk about
+ 
+
+ align:start position:0%
+or more and you know we'll talk about
+this in a minute but we can't afford a
+
+ align:start position:0%
+this in a minute but we can't afford a
+ 
+
+ align:start position:0%
+this in a minute but we can't afford a
+healthcare bill of those dimensions and
+
+ align:start position:0%
+healthcare bill of those dimensions and
+ 
+
+ align:start position:0%
+healthcare bill of those dimensions and
+still have other things going on in the
+
+ align:start position:0%
+still have other things going on in the
+ 
+
+ align:start position:0%
+still have other things going on in the
+society in the economy and the guy
+
+ align:start position:0%
+society in the economy and the guy
+ 
+
+ align:start position:0%
+society in the economy and the guy
+this is this is what we spend money on
+
+ align:start position:0%
+this is this is what we spend money on
+ 
+
+ align:start position:0%
+this is this is what we spend money on
+in the federal government this is a
+
+ align:start position:0%
+in the federal government this is a
+ 
+
+ align:start position:0%
+in the federal government this is a
+little bit this is what we think of as
+
+ align:start position:0%
+little bit this is what we think of as
+ 
+
+ align:start position:0%
+little bit this is what we think of as
+government right so that's like the
+
+ align:start position:0%
+government right so that's like the
+ 
+
+ align:start position:0%
+government right so that's like the
+national parks and federal research
+
+ align:start position:0%
+national parks and federal research
+ 
+
+ align:start position:0%
+national parks and federal research
+transportation highways that's this
+
+ align:start position:0%
+transportation highways that's this
+ 
+
+ align:start position:0%
+transportation highways that's this
+that's defense so that's actually about
+
+ align:start position:0%
+that's defense so that's actually about
+ 
+
+ align:start position:0%
+that's defense so that's actually about
+16% and that's now about maybe a little
+
+ align:start position:0%
+16% and that's now about maybe a little
+ 
+
+ align:start position:0%
+16% and that's now about maybe a little
+below 20% that's social security that's
+
+ align:start position:0%
+below 20% that's social security that's
+ 
+
+ align:start position:0%
+below 20% that's social security that's
+Medicaid Medicare and s chip right the
+
+ align:start position:0%
+Medicaid Medicare and s chip right the
+ 
+
+ align:start position:0%
+Medicaid Medicare and s chip right the
+big health care oriented entitlement
+
+ align:start position:0%
+big health care oriented entitlement
+ 
+
+ align:start position:0%
+big health care oriented entitlement
+programs that's other safety net
+
+ align:start position:0%
+programs that's other safety net
+ 
+
+ align:start position:0%
+programs that's other safety net
+programs 9% and then we have interest on
+
+ align:start position:0%
+programs 9% and then we have interest on
+ 
+
+ align:start position:0%
+programs 9% and then we have interest on
+the debt which is actually now over 9%
+
+ align:start position:0%
+the debt which is actually now over 9%
+ 
+
+ align:start position:0%
+the debt which is actually now over 9%
+so as you can see the federal government
+
+ align:start position:0%
+so as you can see the federal government
+ 
+
+ align:start position:0%
+so as you can see the federal government
+is mostly we're talking sixty percent
+
+ align:start position:0%
+is mostly we're talking sixty percent
+ 
+
+ align:start position:0%
+is mostly we're talking sixty percent
+plus interest in the debt a check
+
+ align:start position:0%
+plus interest in the debt a check
+ 
+
+ align:start position:0%
+plus interest in the debt a check
+writing kind of organization right and
+
+ align:start position:0%
+writing kind of organization right and
+ 
+
+ align:start position:0%
+writing kind of organization right and
+that's what we think of as government
+
+ align:start position:0%
+that's what we think of as government
+ 
+
+ align:start position:0%
+that's what we think of as government
+and that's what we think of as the
+
+ align:start position:0%
+and that's what we think of as the
+ 
+
+ align:start position:0%
+and that's what we think of as the
+domestic side of government so these are
+
+ align:start position:0%
+domestic side of government so these are
+ 
+
+ align:start position:0%
+domestic side of government so these are
+pretty small pieces
+
+ align:start position:0%
+pretty small pieces
+ 
+
+ align:start position:0%
+pretty small pieces
+Rashidah this is probably about four
+
+ align:start position:0%
+Rashidah this is probably about four
+ 
+
+ align:start position:0%
+Rashidah this is probably about four
+years old now but the numbers are
+
+ align:start position:0%
+years old now but the numbers are
+ 
+
+ align:start position:0%
+years old now but the numbers are
+slightly even more problematic than
+
+ align:start position:0%
+slightly even more problematic than
+ 
+
+ align:start position:0%
+slightly even more problematic than
+these so again this category is now
+
+ align:start position:0%
+these so again this category is now
+ 
+
+ align:start position:0%
+these so again this category is now
+sixteen percent so the numbers are
+
+ align:start position:0%
+sixteen percent so the numbers are
+ 
+
+ align:start position:0%
+sixteen percent so the numbers are
+probably off by a couple of percent but
+
+ align:start position:0%
+probably off by a couple of percent but
+ 
+
+ align:start position:0%
+probably off by a couple of percent but
+it's it's a it's a problem right and as
+
+ align:start position:0%
+it's it's a it's a problem right and as
+ 
+
+ align:start position:0%
+it's it's a it's a problem right and as
+we'll see in a second these are
+
+ align:start position:0%
+we'll see in a second these are
+ 
+
+ align:start position:0%
+we'll see in a second these are
+components of federal spending
+
+ align:start position:0%
+components of federal spending
+ 
+
+ align:start position:0%
+components of federal spending
+so that's health and that blue line is
+
+ align:start position:0%
+so that's health and that blue line is
+ 
+
+ align:start position:0%
+so that's health and that blue line is
+everything else so you can see where
+
+ align:start position:0%
+everything else so you can see where
+ 
+
+ align:start position:0%
+everything else so you can see where
+taxpayer dollars are going this is this
+
+ align:start position:0%
+taxpayer dollars are going this is this
+ 
+
+ align:start position:0%
+taxpayer dollars are going this is this
+kind of demonstrates that Social
+
+ align:start position:0%
+kind of demonstrates that Social
+ 
+
+ align:start position:0%
+kind of demonstrates that Social
+Security is not the real problem it's
+
+ align:start position:0%
+Security is not the real problem it's
+ 
+
+ align:start position:0%
+Security is not the real problem it's
+really the health care costs related to
+
+ align:start position:0%
+really the health care costs related to
+ 
+
+ align:start position:0%
+really the health care costs related to
+Medicare and Medicaid that are the
+
+ align:start position:0%
+Medicare and Medicaid that are the
+ 
+
+ align:start position:0%
+Medicare and Medicaid that are the
+problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this shows historic levels of Taxation
+
+ align:start position:0%
+this shows historic levels of Taxation
+ 
+
+ align:start position:0%
+this shows historic levels of Taxation
+remember the United States was founded
+
+ align:start position:0%
+remember the United States was founded
+ 
+
+ align:start position:0%
+remember the United States was founded
+around a tax revolt so we're not going
+
+ align:start position:0%
+around a tax revolt so we're not going
+ 
+
+ align:start position:0%
+around a tax revolt so we're not going
+to have european-style levels of
+
+ align:start position:0%
+to have european-style levels of
+ 
+
+ align:start position:0%
+to have european-style levels of
+Taxation in the United States it's just
+
+ align:start position:0%
+Taxation in the United States it's just
+ 
+
+ align:start position:0%
+Taxation in the United States it's just
+not going to happen and we start to run
+
+ align:start position:0%
+not going to happen and we start to run
+ 
+
+ align:start position:0%
+not going to happen and we start to run
+into real political trouble once you get
+
+ align:start position:0%
+into real political trouble once you get
+ 
+
+ align:start position:0%
+into real political trouble once you get
+a little bit above
+
+ align:start position:0%
+a little bit above
+ 
+
+ align:start position:0%
+a little bit above
+say the 20% kind of level of taxation of
+
+ align:start position:0%
+say the 20% kind of level of taxation of
+ 
+
+ align:start position:0%
+say the 20% kind of level of taxation of
+GDP as a percentage of GDP right so you
+
+ align:start position:0%
+GDP as a percentage of GDP right so you
+ 
+
+ align:start position:0%
+GDP as a percentage of GDP right so you
+know we're headed way up against that
+
+ align:start position:0%
+know we're headed way up against that
+ 
+
+ align:start position:0%
+know we're headed way up against that
+threshold which in turn means largely
+
+ align:start position:0%
+threshold which in turn means largely
+ 
+
+ align:start position:0%
+threshold which in turn means largely
+because of the demographics and the
+
+ align:start position:0%
+because of the demographics and the
+ 
+
+ align:start position:0%
+because of the demographics and the
+health care spending which means that
+
+ align:start position:0%
+health care spending which means that
+ 
+
+ align:start position:0%
+health care spending which means that
+broken down this way the you know
+
+ align:start position:0%
+broken down this way the you know
+ 
+
+ align:start position:0%
+broken down this way the you know
+percentage of GDP we spend on what we
+
+ align:start position:0%
+percentage of GDP we spend on what we
+ 
+
+ align:start position:0%
+percentage of GDP we spend on what we
+consider most of government it's just
+
+ align:start position:0%
+consider most of government it's just
+ 
+
+ align:start position:0%
+consider most of government it's just
+not going to be affordable given what
+
+ align:start position:0%
+not going to be affordable given what
+ 
+
+ align:start position:0%
+not going to be affordable given what
+the acceptable levels around 19 percent
+
+ align:start position:0%
+the acceptable levels around 19 percent
+ 
+
+ align:start position:0%
+the acceptable levels around 19 percent
+18 percent the acceptable tax range in
+
+ align:start position:0%
+18 percent the acceptable tax range in
+ 
+
+ align:start position:0%
+18 percent the acceptable tax range in
+our political system
+
+ align:start position:0%
+our political system
+ 
+
+ align:start position:0%
+our political system
+so expenditures by the federal
+
+ align:start position:0%
+so expenditures by the federal
+ 
+
+ align:start position:0%
+so expenditures by the federal
+government what they're spending in a
+
+ align:start position:0%
+government what they're spending in a
+ 
+
+ align:start position:0%
+government what they're spending in a
+given year what they were actually out
+
+ align:start position:0%
+given year what they were actually out
+ 
+
+ align:start position:0%
+given year what they were actually out
+laying to meet their costs and to meet
+
+ align:start position:0%
+laying to meet their costs and to meet
+ 
+
+ align:start position:0%
+laying to meet their costs and to meet
+their obligations so these are some of
+
+ align:start position:0%
+their obligations so these are some of
+ 
+
+ align:start position:0%
+their obligations so these are some of
+the problems that lie ahead we've got a
+
+ align:start position:0%
+the problems that lie ahead we've got a
+ 
+
+ align:start position:0%
+the problems that lie ahead we've got a
+real fiscal train wreck because of the
+
+ align:start position:0%
+real fiscal train wreck because of the
+ 
+
+ align:start position:0%
+real fiscal train wreck because of the
+cost of this healthcare system driven by
+
+ align:start position:0%
+cost of this healthcare system driven by
+ 
+
+ align:start position:0%
+cost of this healthcare system driven by
+the demographics you know my generation
+
+ align:start position:0%
+the demographics you know my generation
+ 
+
+ align:start position:0%
+the demographics you know my generation
+attempting to make you spend all of your
+
+ align:start position:0%
+attempting to make you spend all of your
+ 
+
+ align:start position:0%
+attempting to make you spend all of your
+money on me right that's essentially
+
+ align:start position:0%
+money on me right that's essentially
+ 
+
+ align:start position:0%
+money on me right that's essentially
+what's going on it's a massive
+
+ align:start position:0%
+what's going on it's a massive
+ 
+
+ align:start position:0%
+what's going on it's a massive
+intergenerational transfer of wealth and
+
+ align:start position:0%
+intergenerational transfer of wealth and
+ 
+
+ align:start position:0%
+intergenerational transfer of wealth and
+you guys need to wake up to that because
+
+ align:start position:0%
+you guys need to wake up to that because
+ 
+
+ align:start position:0%
+you guys need to wake up to that because
+it forgoes opportunities that you have
+
+ align:start position:0%
+it forgoes opportunities that you have
+ 
+
+ align:start position:0%
+it forgoes opportunities that you have
+and at the heart of this is a really
+
+ align:start position:0%
+and at the heart of this is a really
+ 
+
+ align:start position:0%
+and at the heart of this is a really
+serious problem with health care
+
+ align:start position:0%
+serious problem with health care
+ 
+
+ align:start position:0%
+serious problem with health care
+expenditures so let's now get back into
+
+ align:start position:0%
+expenditures so let's now get back into
+ 
+
+ align:start position:0%
+expenditures so let's now get back into
+our main themes this was a classic 2003
+
+ align:start position:0%
+our main themes this was a classic 2003
+ 
+
+ align:start position:0%
+our main themes this was a classic 2003
+report that what is now called the
+
+ align:start position:0%
+report that what is now called the
+ 
+
+ align:start position:0%
+report that what is now called the
+academy of medicine used to be called
+
+ align:start position:0%
+academy of medicine used to be called
+ 
+
+ align:start position:0%
+academy of medicine used to be called
+the National Institute of Medicine it's
+
+ align:start position:0%
+the National Institute of Medicine it's
+ 
+
+ align:start position:0%
+the National Institute of Medicine it's
+part of the National Academies they did
+
+ align:start position:0%
+part of the National Academies they did
+ 
+
+ align:start position:0%
+part of the National Academies they did
+on evaluating NIH and it was a pretty
+
+ align:start position:0%
+on evaluating NIH and it was a pretty
+ 
+
+ align:start position:0%
+on evaluating NIH and it was a pretty
+startling criticism and they you know
+
+ align:start position:0%
+startling criticism and they you know
+ 
+
+ align:start position:0%
+startling criticism and they you know
+looked hard at this NIH system and
+
+ align:start position:0%
+looked hard at this NIH system and
+ 
+
+ align:start position:0%
+looked hard at this NIH system and
+really began to identify some of the
+
+ align:start position:0%
+really began to identify some of the
+ 
+
+ align:start position:0%
+really began to identify some of the
+some of the problems interestingly this
+
+ align:start position:0%
+some of the problems interestingly this
+ 
+
+ align:start position:0%
+some of the problems interestingly this
+drove this report drove some interesting
+
+ align:start position:0%
+drove this report drove some interesting
+ 
+
+ align:start position:0%
+drove this report drove some interesting
+congressional reform attempts
+
+ align:start position:0%
+congressional reform attempts
+ 
+
+ align:start position:0%
+congressional reform attempts
+let me see if I can summarize a few key
+
+ align:start position:0%
+let me see if I can summarize a few key
+ 
+
+ align:start position:0%
+let me see if I can summarize a few key
+points here and Chloe did you have this
+
+ align:start position:0%
+points here and Chloe did you have this
+ 
+
+ align:start position:0%
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+one you've got it Martine okay all right
+
+ align:start position:0%
+one you've got it Martine okay all right
+ 
+
+ align:start position:0%
+one you've got it Martine okay all right
+so as I said NIH NIH is more like a
+
+ align:start position:0%
+so as I said NIH NIH is more like a
+ 
+
+ align:start position:0%
+so as I said NIH NIH is more like a
+feudal barony right it's got a it has
+
+ align:start position:0%
+feudal barony right it's got a it has
+ 
+
+ align:start position:0%
+feudal barony right it's got a it has
+always has a famous director but they
+
+ align:start position:0%
+always has a famous director but they
+ 
+
+ align:start position:0%
+always has a famous director but they
+don't have that much control over these
+
+ align:start position:0%
+don't have that much control over these
+ 
+
+ align:start position:0%
+don't have that much control over these
+institutes and centers there is no
+
+ align:start position:0%
+institutes and centers there is no
+ 
+
+ align:start position:0%
+institutes and centers there is no
+centralized budgeting right and the
+
+ align:start position:0%
+centralized budgeting right and the
+ 
+
+ align:start position:0%
+centralized budgeting right and the
+institutes and centers
+
+ align:start position:0%
+institutes and centers
+ 
+
+ align:start position:0%
+institutes and centers
+battled to protect their percentage
+
+ align:start position:0%
+battled to protect their percentage
+ 
+
+ align:start position:0%
+battled to protect their percentage
+share of NIH s total budget so Harold
+
+ align:start position:0%
+share of NIH s total budget so Harold
+ 
+
+ align:start position:0%
+share of NIH s total budget so Harold
+Varmus a famous former director of NIH
+
+ align:start position:0%
+Varmus a famous former director of NIH
+ 
+
+ align:start position:0%
+Varmus a famous former director of NIH
+who later came back in the Obama
+
+ align:start position:0%
+who later came back in the Obama
+ 
+
+ align:start position:0%
+who later came back in the Obama
+administration as head of the National
+
+ align:start position:0%
+administration as head of the National
+ 
+
+ align:start position:0%
+administration as head of the National
+Cancer Institute he said in 2001 NIH
+
+ align:start position:0%
+Cancer Institute he said in 2001 NIH
+ 
+
+ align:start position:0%
+Cancer Institute he said in 2001 NIH
+would be more efficient and more
+
+ align:start position:0%
+would be more efficient and more
+ 
+
+ align:start position:0%
+would be more efficient and more
+manageable if they fought if a far
+
+ align:start position:0%
+manageable if they fought if a far
+ 
+
+ align:start position:0%
+manageable if they fought if a far
+smaller number of larger institutes
+
+ align:start position:0%
+smaller number of larger institutes
+ 
+
+ align:start position:0%
+smaller number of larger institutes
+existed organized around broad science
+
+ align:start position:0%
+existed organized around broad science
+ 
+
+ align:start position:0%
+existed organized around broad science
+areas less Institute's organized around
+
+ align:start position:0%
+areas less Institute's organized around
+ 
+
+ align:start position:0%
+areas less Institute's organized around
+science areas is his his twin points
+
+ align:start position:0%
+science areas is his his twin points
+ 
+
+ align:start position:0%
+science areas is his his twin points
+here and there's a lot to be said for
+
+ align:start position:0%
+here and there's a lot to be said for
+ 
+
+ align:start position:0%
+here and there's a lot to be said for
+that case instead as we discussed the
+
+ align:start position:0%
+that case instead as we discussed the
+ 
+
+ align:start position:0%
+that case instead as we discussed the
+Institute's got set up essentially the
+
+ align:start position:0%
+Institute's got set up essentially the
+ 
+
+ align:start position:0%
+Institute's got set up essentially the
+behest of disease groups to solve their
+
+ align:start position:0%
+behest of disease groups to solve their
+ 
+
+ align:start position:0%
+behest of disease groups to solve their
+disease problem it turns out there isn't
+
+ align:start position:0%
+disease problem it turns out there isn't
+ 
+
+ align:start position:0%
+disease problem it turns out there isn't
+a separate pathway for each disease it
+
+ align:start position:0%
+a separate pathway for each disease it
+ 
+
+ align:start position:0%
+a separate pathway for each disease it
+turns out there's a lot of common
+
+ align:start position:0%
+turns out there's a lot of common
+ 
+
+ align:start position:0%
+turns out there's a lot of common
+pathways across a lot of diseases and we
+
+ align:start position:0%
+pathways across a lot of diseases and we
+ 
+
+ align:start position:0%
+pathways across a lot of diseases and we
+don't have a very good mechanism in NIH
+
+ align:start position:0%
+don't have a very good mechanism in NIH
+ 
+
+ align:start position:0%
+don't have a very good mechanism in NIH
+for getting groups of Institute's to
+
+ align:start position:0%
+for getting groups of Institute's to
+ 
+
+ align:start position:0%
+for getting groups of Institute's to
+collaborate on a cross-cutting set of
+
+ align:start position:0%
+collaborate on a cross-cutting set of
+ 
+
+ align:start position:0%
+collaborate on a cross-cutting set of
+problems it's a fundamental
+
+ align:start position:0%
+problems it's a fundamental
+ 
+
+ align:start position:0%
+problems it's a fundamental
+organizational issue now the other there
+
+ align:start position:0%
+organizational issue now the other there
+ 
+
+ align:start position:0%
+organizational issue now the other there
+is another side of this argument which
+
+ align:start position:0%
+is another side of this argument which
+ 
+
+ align:start position:0%
+is another side of this argument which
+is you've got a lot of Institute's with
+
+ align:start position:0%
+is you've got a lot of Institute's with
+ 
+
+ align:start position:0%
+is you've got a lot of Institute's with
+a lot of freedom to do a lot of stuff
+
+ align:start position:0%
+a lot of freedom to do a lot of stuff
+ 
+
+ align:start position:0%
+a lot of freedom to do a lot of stuff
+right maybe a disaggregated model is not
+
+ align:start position:0%
+right maybe a disaggregated model is not
+ 
+
+ align:start position:0%
+right maybe a disaggregated model is not
+all dead right there's certainly a case
+
+ align:start position:0%
+all dead right there's certainly a case
+ 
+
+ align:start position:0%
+all dead right there's certainly a case
+to be made for that but overall there's
+
+ align:start position:0%
+to be made for that but overall there's
+ 
+
+ align:start position:0%
+to be made for that but overall there's
+a challenge here and NIH is budget
+
+ align:start position:0%
+a challenge here and NIH is budget
+ 
+
+ align:start position:0%
+a challenge here and NIH is budget
+doubled from 1998 to 2003 so there was a
+
+ align:start position:0%
+doubled from 1998 to 2003 so there was a
+ 
+
+ align:start position:0%
+doubled from 1998 to 2003 so there was a
+big growth there was a federal surplus
+
+ align:start position:0%
+big growth there was a federal surplus
+ 
+
+ align:start position:0%
+big growth there was a federal surplus
+in its budget during the IT revolution
+
+ align:start position:0%
+in its budget during the IT revolution
+ 
+
+ align:start position:0%
+in its budget during the IT revolution
+was generating huge amounts of
+
+ align:start position:0%
+was generating huge amounts of
+ 
+
+ align:start position:0%
+was generating huge amounts of
+tax revenue and two US senators saw this
+
+ align:start position:0%
+tax revenue and two US senators saw this
+ 
+
+ align:start position:0%
+tax revenue and two US senators saw this
+emerging surplus they were on the
+
+ align:start position:0%
+emerging surplus they were on the
+ 
+
+ align:start position:0%
+emerging surplus they were on the
+Appropriations Subcommittee that handled
+
+ align:start position:0%
+Appropriations Subcommittee that handled
+ 
+
+ align:start position:0%
+Appropriations Subcommittee that handled
+NIH and they went to the Senate floor
+
+ align:start position:0%
+NIH and they went to the Senate floor
+ 
+
+ align:start position:0%
+NIH and they went to the Senate floor
+one day and took noticeable part of that
+
+ align:start position:0%
+one day and took noticeable part of that
+ 
+
+ align:start position:0%
+one day and took noticeable part of that
+surplus and gave it to NIH is a
+
+ align:start position:0%
+surplus and gave it to NIH is a
+ 
+
+ align:start position:0%
+surplus and gave it to NIH is a
+fascinating political development very
+
+ align:start position:0%
+fascinating political development very
+ 
+
+ align:start position:0%
+fascinating political development very
+shrewd
+
+ align:start position:0%
+shrewd
+ 
+
+ align:start position:0%
+shrewd
+Arlen Specter of Pennsylvania and Tom
+
+ align:start position:0%
+Arlen Specter of Pennsylvania and Tom
+ 
+
+ align:start position:0%
+Arlen Specter of Pennsylvania and Tom
+Harkin of Iowa where chairman and
+
+ align:start position:0%
+Harkin of Iowa where chairman and
+ 
+
+ align:start position:0%
+Harkin of Iowa where chairman and
+ranking on the Appropriations
+
+ align:start position:0%
+ranking on the Appropriations
+ 
+
+ align:start position:0%
+ranking on the Appropriations
+Subcommittee and they created the
+
+ align:start position:0%
+Subcommittee and they created the
+ 
+
+ align:start position:0%
+Subcommittee and they created the
+doubling it's a remarkable story they
+
+ align:start position:0%
+doubling it's a remarkable story they
+ 
+
+ align:start position:0%
+doubling it's a remarkable story they
+were able to do it because there was so
+
+ align:start position:0%
+were able to do it because there was so
+ 
+
+ align:start position:0%
+were able to do it because there was so
+much excitement at that time over the
+
+ align:start position:0%
+much excitement at that time over the
+ 
+
+ align:start position:0%
+much excitement at that time over the
+genomics revolution so we talked about
+
+ align:start position:0%
+genomics revolution so we talked about
+ 
+
+ align:start position:0%
+genomics revolution so we talked about
+Venter and the NIH dueling battle
+
+ align:start position:0%
+Venter and the NIH dueling battle
+ 
+
+ align:start position:0%
+Venter and the NIH dueling battle
+Collins over who's gonna get to the
+
+ align:start position:0%
+Collins over who's gonna get to the
+ 
+
+ align:start position:0%
+Collins over who's gonna get to the
+genome first there was creating huge
+
+ align:start position:0%
+genome first there was creating huge
+ 
+
+ align:start position:0%
+genome first there was creating huge
+excitement there was a sense that this
+
+ align:start position:0%
+excitement there was a sense that this
+ 
+
+ align:start position:0%
+excitement there was a sense that this
+medical research could lead to all kinds
+
+ align:start position:0%
+medical research could lead to all kinds
+ 
+
+ align:start position:0%
+medical research could lead to all kinds
+of new fundamental understandings
+
+ align:start position:0%
+of new fundamental understandings
+ 
+
+ align:start position:0%
+of new fundamental understandings
+everybody was excited about the idea and
+
+ align:start position:0%
+everybody was excited about the idea and
+ 
+
+ align:start position:0%
+everybody was excited about the idea and
+that enabled those two centers to double
+
+ align:start position:0%
+that enabled those two centers to double
+ 
+
+ align:start position:0%
+that enabled those two centers to double
+NIH no other agency has ever been able
+
+ align:start position:0%
+NIH no other agency has ever been able
+ 
+
+ align:start position:0%
+NIH no other agency has ever been able
+to do anything like this right the rest
+
+ align:start position:0%
+to do anything like this right the rest
+ 
+
+ align:start position:0%
+to do anything like this right the rest
+kind of are stagnating but the
+
+ align:start position:0%
+kind of are stagnating but the
+ 
+
+ align:start position:0%
+kind of are stagnating but the
+demographics are changing the patterns
+
+ align:start position:0%
+demographics are changing the patterns
+ 
+
+ align:start position:0%
+demographics are changing the patterns
+of illness are changing we have a threat
+
+ align:start position:0%
+of illness are changing we have a threat
+ 
+
+ align:start position:0%
+of illness are changing we have a threat
+of bio threats is NIH too fragmented to
+
+ align:start position:0%
+of bio threats is NIH too fragmented to
+ 
+
+ align:start position:0%
+of bio threats is NIH too fragmented to
+cope with all these challenges can it
+
+ align:start position:0%
+cope with all these challenges can it
+ 
+
+ align:start position:0%
+cope with all these challenges can it
+respond quickly enough these are all
+
+ align:start position:0%
+respond quickly enough these are all
+ 
+
+ align:start position:0%
+respond quickly enough these are all
+issues that the report raises it wants
+
+ align:start position:0%
+issues that the report raises it wants
+ 
+
+ align:start position:0%
+issues that the report raises it wants
+to avoid caliph eration and new agencies
+
+ align:start position:0%
+to avoid caliph eration and new agencies
+ 
+
+ align:start position:0%
+to avoid caliph eration and new agencies
+and in fact Congress did that as part of
+
+ align:start position:0%
+and in fact Congress did that as part of
+ 
+
+ align:start position:0%
+and in fact Congress did that as part of
+its reform legislation you can't have a
+
+ align:start position:0%
+its reform legislation you can't have a
+ 
+
+ align:start position:0%
+its reform legislation you can't have a
+new Institute at NIH unless you close
+
+ align:start position:0%
+new Institute at NIH unless you close
+ 
+
+ align:start position:0%
+new Institute at NIH unless you close
+down another one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the Institute of Medicine and now the
+
+ align:start position:0%
+the Institute of Medicine and now the
+ 
+
+ align:start position:0%
+the Institute of Medicine and now the
+Academy of Medicine urged in this report
+
+ align:start position:0%
+Academy of Medicine urged in this report
+ 
+
+ align:start position:0%
+Academy of Medicine urged in this report
+that NIH focus on its capabilities and
+
+ align:start position:0%
+that NIH focus on its capabilities and
+ 
+
+ align:start position:0%
+that NIH focus on its capabilities and
+it needed to do so because it concluded
+
+ align:start position:0%
+it needed to do so because it concluded
+ 
+
+ align:start position:0%
+it needed to do so because it concluded
+that NIH is not only imperfect but
+
+ align:start position:0%
+that NIH is not only imperfect but
+ 
+
+ align:start position:0%
+that NIH is not only imperfect but
+nobody would have ever designed NIH this
+
+ align:start position:0%
+nobody would have ever designed NIH this
+ 
+
+ align:start position:0%
+nobody would have ever designed NIH this
+way at the outset and in fact Elias
+
+ align:start position:0%
+way at the outset and in fact Elias
+ 
+
+ align:start position:0%
+way at the outset and in fact Elias
+Zerhouni once told me in a meeting and
+
+ align:start position:0%
+Zerhouni once told me in a meeting and
+ 
+
+ align:start position:0%
+Zerhouni once told me in a meeting and
+on others if only we had fought through
+
+ align:start position:0%
+on others if only we had fought through
+ 
+
+ align:start position:0%
+on others if only we had fought through
+the organizational model before we
+
+ align:start position:0%
+the organizational model before we
+ 
+
+ align:start position:0%
+the organizational model before we
+doubled right so we doubled first and
+
+ align:start position:0%
+doubled right so we doubled first and
+ 
+
+ align:start position:0%
+doubled right so we doubled first and
+then there was a mad scramble to grab
+
+ align:start position:0%
+then there was a mad scramble to grab
+ 
+
+ align:start position:0%
+then there was a mad scramble to grab
+the money
+
+ align:start position:0%
+the money
+ 
+
+ align:start position:0%
+the money
+I'm the existing institutes if only they
+
+ align:start position:0%
+I'm the existing institutes if only they
+ 
+
+ align:start position:0%
+I'm the existing institutes if only they
+had thought about the organizational
+
+ align:start position:0%
+had thought about the organizational
+ 
+
+ align:start position:0%
+had thought about the organizational
+model upfront so who need a great effort
+
+ align:start position:0%
+model upfront so who need a great effort
+ 
+
+ align:start position:0%
+model upfront so who need a great effort
+to try and get cross-cutting research
+
+ align:start position:0%
+to try and get cross-cutting research
+ 
+
+ align:start position:0%
+to try and get cross-cutting research
+efforts going across the Institute so we
+
+ align:start position:0%
+efforts going across the Institute so we
+ 
+
+ align:start position:0%
+efforts going across the Institute so we
+created it what he called the roadmap
+
+ align:start position:0%
+created it what he called the roadmap
+ 
+
+ align:start position:0%
+created it what he called the roadmap
+but essentially and then Congress later
+
+ align:start position:0%
+but essentially and then Congress later
+ 
+
+ align:start position:0%
+but essentially and then Congress later
+institutionalized it it's the Common
+
+ align:start position:0%
+institutionalized it it's the Common
+ 
+
+ align:start position:0%
+institutionalized it it's the Common
+Fund take a little bit of money from
+
+ align:start position:0%
+Fund take a little bit of money from
+ 
+
+ align:start position:0%
+Fund take a little bit of money from
+each Institute's create a common fund in
+
+ align:start position:0%
+each Institute's create a common fund in
+ 
+
+ align:start position:0%
+each Institute's create a common fund in
+the control of the director who can then
+
+ align:start position:0%
+the control of the director who can then
+ 
+
+ align:start position:0%
+the control of the director who can then
+allocate it to the highest cross-cutting
+
+ align:start position:0%
+allocate it to the highest cross-cutting
+ 
+
+ align:start position:0%
+allocate it to the highest cross-cutting
+priorities so that was a significant
+
+ align:start position:0%
+priorities so that was a significant
+ 
+
+ align:start position:0%
+priorities so that was a significant
+reform but it's still a very modest
+
+ align:start position:0%
+reform but it's still a very modest
+ 
+
+ align:start position:0%
+reform but it's still a very modest
+amount of money NIH needs to pursue an
+
+ align:start position:0%
+amount of money NIH needs to pursue an
+ 
+
+ align:start position:0%
+amount of money NIH needs to pursue an
+ability to go after high-risk
+
+ align:start position:0%
+ability to go after high-risk
+ 
+
+ align:start position:0%
+ability to go after high-risk
+high-return projects there reaches a
+
+ align:start position:0%
+high-return projects there reaches a
+ 
+
+ align:start position:0%
+high-return projects there reaches a
+certain stage and we'll talk about this
+
+ align:start position:0%
+certain stage and we'll talk about this
+ 
+
+ align:start position:0%
+certain stage and we'll talk about this
+more later but peer review is not good
+
+ align:start position:0%
+more later but peer review is not good
+ 
+
+ align:start position:0%
+more later but peer review is not good
+at taking risk it's a certain level of
+
+ align:start position:0%
+at taking risk it's a certain level of
+ 
+
+ align:start position:0%
+at taking risk it's a certain level of
+competition if the award rate ISM gets
+
+ align:start position:0%
+competition if the award rate ISM gets
+ 
+
+ align:start position:0%
+competition if the award rate ISM gets
+higher than about one out of three your
+
+ align:start position:0%
+higher than about one out of three your
+ 
+
+ align:start position:0%
+higher than about one out of three your
+ability to identify breakthrough
+
+ align:start position:0%
+ability to identify breakthrough
+ 
+
+ align:start position:0%
+ability to identify breakthrough
+opportunities that are feasible it gets
+
+ align:start position:0%
+opportunities that are feasible it gets
+ 
+
+ align:start position:0%
+opportunities that are feasible it gets
+harder so it tends to default to when
+
+ align:start position:0%
+harder so it tends to default to when
+ 
+
+ align:start position:0%
+harder so it tends to default to when
+there's a lot of competition for an
+
+ align:start position:0%
+there's a lot of competition for an
+ 
+
+ align:start position:0%
+there's a lot of competition for an
+award the one that the the peer
+
+ align:start position:0%
+award the one that the the peer
+ 
+
+ align:start position:0%
+award the one that the the peer
+community is most confident will yield
+
+ align:start position:0%
+community is most confident will yield
+ 
+
+ align:start position:0%
+community is most confident will yield
+results
+
+ align:start position:0%
+results
+ 
+
+ align:start position:0%
+results
+albeit they be incremental results why
+
+ align:start position:0%
+albeit they be incremental results why
+ 
+
+ align:start position:0%
+albeit they be incremental results why
+take risk on high flyers when you've got
+
+ align:start position:0%
+take risk on high flyers when you've got
+ 
+
+ align:start position:0%
+take risk on high flyers when you've got
+to get the basics done and so many
+
+ align:start position:0%
+to get the basics done and so many
+ 
+
+ align:start position:0%
+to get the basics done and so many
+people are fighting for the money so
+
+ align:start position:0%
+people are fighting for the money so
+ 
+
+ align:start position:0%
+people are fighting for the money so
+this is a huge problem in NIH how does
+
+ align:start position:0%
+this is a huge problem in NIH how does
+ 
+
+ align:start position:0%
+this is a huge problem in NIH how does
+it take the necessary risks that need to
+
+ align:start position:0%
+it take the necessary risks that need to
+ 
+
+ align:start position:0%
+it take the necessary risks that need to
+need to be taken in innovation so since
+
+ align:start position:0%
+need to be taken in innovation so since
+ 
+
+ align:start position:0%
+need to be taken in innovation so since
+then NIH has been working on creating
+
+ align:start position:0%
+then NIH has been working on creating
+ 
+
+ align:start position:0%
+then NIH has been working on creating
+category
+
+ align:start position:0%
+category
+ 
+
+ align:start position:0%
+category
+of higher risk projects that have a
+
+ align:start position:0%
+of higher risk projects that have a
+ 
+
+ align:start position:0%
+of higher risk projects that have a
+separate kind of review process than
+
+ align:start position:0%
+separate kind of review process than
+ 
+
+ align:start position:0%
+separate kind of review process than
+normal projects so there are positive
+
+ align:start position:0%
+normal projects so there are positive
+ 
+
+ align:start position:0%
+normal projects so there are positive
+NIH capabilities we talked about how
+
+ align:start position:0%
+NIH capabilities we talked about how
+ 
+
+ align:start position:0%
+NIH capabilities we talked about how
+decentralized can be an advantage we
+
+ align:start position:0%
+decentralized can be an advantage we
+ 
+
+ align:start position:0%
+decentralized can be an advantage we
+talked about many setting R&D priorities
+
+ align:start position:0%
+talked about many setting R&D priorities
+ 
+
+ align:start position:0%
+talked about many setting R&D priorities
+is not necessarily you get a lot of
+
+ align:start position:0%
+is not necessarily you get a lot of
+ 
+
+ align:start position:0%
+is not necessarily you get a lot of
+safety nets here there are benefits to
+
+ align:start position:0%
+safety nets here there are benefits to
+ 
+
+ align:start position:0%
+safety nets here there are benefits to
+investigator initiative grants right you
+
+ align:start position:0%
+investigator initiative grants right you
+ 
+
+ align:start position:0%
+investigator initiative grants right you
+don't want to just have large-scale
+
+ align:start position:0%
+don't want to just have large-scale
+ 
+
+ align:start position:0%
+don't want to just have large-scale
+projects you want bottom-up
+
+ align:start position:0%
+projects you want bottom-up
+ 
+
+ align:start position:0%
+projects you want bottom-up
+opportunities the issue for NIH though
+
+ align:start position:0%
+opportunities the issue for NIH though
+ 
+
+ align:start position:0%
+opportunities the issue for NIH though
+is historically it's been totally
+
+ align:start position:0%
+is historically it's been totally
+ 
+
+ align:start position:0%
+is historically it's been totally
+dominated by bottom-up and has a modest
+
+ align:start position:0%
+dominated by bottom-up and has a modest
+ 
+
+ align:start position:0%
+dominated by bottom-up and has a modest
+number of kind of cross-cutting projects
+
+ align:start position:0%
+number of kind of cross-cutting projects
+ 
+
+ align:start position:0%
+number of kind of cross-cutting projects
+you know peer review in some ways is
+
+ align:start position:0%
+you know peer review in some ways is
+ 
+
+ align:start position:0%
+you know peer review in some ways is
+like Winston Churchill's definition of
+
+ align:start position:0%
+like Winston Churchill's definition of
+ 
+
+ align:start position:0%
+like Winston Churchill's definition of
+democracy worse than every other system
+
+ align:start position:0%
+democracy worse than every other system
+ 
+
+ align:start position:0%
+democracy worse than every other system
+the worst possible system except for all
+
+ align:start position:0%
+the worst possible system except for all
+ 
+
+ align:start position:0%
+the worst possible system except for all
+the others right so there are peer
+
+ align:start position:0%
+the others right so there are peer
+ 
+
+ align:start position:0%
+the others right so there are peer
+review remains competitive and that's a
+
+ align:start position:0%
+review remains competitive and that's a
+ 
+
+ align:start position:0%
+review remains competitive and that's a
+very important feature to build in so
+
+ align:start position:0%
+very important feature to build in so
+ 
+
+ align:start position:0%
+very important feature to build in so
+iom recommended much more centralized
+
+ align:start position:0%
+iom recommended much more centralized
+ 
+
+ align:start position:0%
+iom recommended much more centralized
+management giving more authority to the
+
+ align:start position:0%
+management giving more authority to the
+ 
+
+ align:start position:0%
+management giving more authority to the
+director of nih getting the director to
+
+ align:start position:0%
+director of nih getting the director to
+ 
+
+ align:start position:0%
+director of nih getting the director to
+engage in strategic planning across the
+
+ align:start position:0%
+engage in strategic planning across the
+ 
+
+ align:start position:0%
+engage in strategic planning across the
+Institute so they got on to
+
+ align:start position:0%
+Institute so they got on to
+ 
+
+ align:start position:0%
+Institute so they got on to
+cross-cutting plans doing cross-cutting
+
+ align:start position:0%
+cross-cutting plans doing cross-cutting
+ 
+
+ align:start position:0%
+cross-cutting plans doing cross-cutting
+budgets so this idea of take 10 percent
+
+ align:start position:0%
+budgets so this idea of take 10 percent
+ 
+
+ align:start position:0%
+budgets so this idea of take 10 percent
+of the budget and fund the strategic
+
+ align:start position:0%
+of the budget and fund the strategic
+ 
+
+ align:start position:0%
+of the budget and fund the strategic
+plans actually Congress worked on
+
+ align:start position:0%
+plans actually Congress worked on
+ 
+
+ align:start position:0%
+plans actually Congress worked on
+implementing that through the common
+
+ align:start position:0%
+implementing that through the common
+ 
+
+ align:start position:0%
+implementing that through the common
+fund strengthening the you know control
+
+ align:start position:0%
+fund strengthening the you know control
+ 
+
+ align:start position:0%
+fund strengthening the you know control
+the director over these cross agency
+
+ align:start position:0%
+the director over these cross agency
+ 
+
+ align:start position:0%
+the director over these cross agency
+initiatives was key they also
+
+ align:start position:0%
+initiatives was key they also
+ 
+
+ align:start position:0%
+initiatives was key they also
+recommended creating a DARPA within NIH
+
+ align:start position:0%
+recommended creating a DARPA within NIH
+ 
+
+ align:start position:0%
+recommended creating a DARPA within NIH
+to go after the high-risk projects the
+
+ align:start position:0%
+to go after the high-risk projects the
+ 
+
+ align:start position:0%
+to go after the high-risk projects the
+high-risk high-reward projects they
+
+ align:start position:0%
+high-risk high-reward projects they
+ 
+
+ align:start position:0%
+high-risk high-reward projects they
+wanted improvements in NIH s intramural
+
+ align:start position:0%
+wanted improvements in NIH s intramural
+ 
+
+ align:start position:0%
+wanted improvements in NIH s intramural
+programs so NIH is also a major research
+
+ align:start position:0%
+programs so NIH is also a major research
+ 
+
+ align:start position:0%
+programs so NIH is also a major research
+entity itself it's not just funding
+
+ align:start position:0%
+entity itself it's not just funding
+ 
+
+ align:start position:0%
+entity itself it's not just funding
+universities that historically has
+
+ align:start position:0%
+universities that historically has
+ 
+
+ align:start position:0%
+universities that historically has
+tended to be someone weaker than the
+
+ align:start position:0%
+tended to be someone weaker than the
+ 
+
+ align:start position:0%
+tended to be someone weaker than the
+university research which is much more
+
+ align:start position:0%
+university research which is much more
+ 
+
+ align:start position:0%
+university research which is much more
+competition based rather than kind of
+
+ align:start position:0%
+competition based rather than kind of
+ 
+
+ align:start position:0%
+competition based rather than kind of
+entitlement funding based they wanted to
+
+ align:start position:0%
+entitlement funding based they wanted to
+ 
+
+ align:start position:0%
+entitlement funding based they wanted to
+strengthen that there's a desperate need
+
+ align:start position:0%
+strengthen that there's a desperate need
+ 
+
+ align:start position:0%
+strengthen that there's a desperate need
+for Standardization of data and
+
+ align:start position:0%
+for Standardization of data and
+ 
+
+ align:start position:0%
+for Standardization of data and
+information systems across these
+
+ align:start position:0%
+information systems across these
+ 
+
+ align:start position:0%
+information systems across these
+different Institute's because a lot of
+
+ align:start position:0%
+different Institute's because a lot of
+ 
+
+ align:start position:0%
+different Institute's because a lot of
+these diseases are related and you can
+
+ align:start position:0%
+these diseases are related and you can
+ 
+
+ align:start position:0%
+these diseases are related and you can
+learn they can learn from each other and
+
+ align:start position:0%
+learn they can learn from each other and
+ 
+
+ align:start position:0%
+learn they can learn from each other and
+you can't do cross-cutting data
+
+ align:start position:0%
+you can't do cross-cutting data
+ 
+
+ align:start position:0%
+you can't do cross-cutting data
+analytics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so there's a series of kind of reform
+
+ align:start position:0%
+so there's a series of kind of reform
+ 
+
+ align:start position:0%
+so there's a series of kind of reform
+steps here as going back to our so
+
+ align:start position:0%
+steps here as going back to our so
+ 
+
+ align:start position:0%
+steps here as going back to our so
+earlier points we've met in the class
+
+ align:start position:0%
+earlier points we've met in the class
+ 
+
+ align:start position:0%
+earlier points we've met in the class
+NIH is not a connected organization
+
+ align:start position:0%
+NIH is not a connected organization
+ 
+
+ align:start position:0%
+NIH is not a connected organization
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+it's an early stage basic research
+
+ align:start position:0%
+it's an early stage basic research
+ 
+
+ align:start position:0%
+it's an early stage basic research
+organization it's not connected to the
+
+ align:start position:0%
+organization it's not connected to the
+ 
+
+ align:start position:0%
+organization it's not connected to the
+following stages now it has managed to
+
+ align:start position:0%
+following stages now it has managed to
+ 
+
+ align:start position:0%
+following stages now it has managed to
+create a model through biotechs that are
+
+ align:start position:0%
+create a model through biotechs that are
+ 
+
+ align:start position:0%
+create a model through biotechs that are
+venture funded that is able to get
+
+ align:start position:0%
+venture funded that is able to get
+ 
+
+ align:start position:0%
+venture funded that is able to get
+across the valley of death if you've got
+
+ align:start position:0%
+across the valley of death if you've got
+ 
+
+ align:start position:0%
+across the valley of death if you've got
+a blockbuster drug right that's pretty
+
+ align:start position:0%
+a blockbuster drug right that's pretty
+ 
+
+ align:start position:0%
+a blockbuster drug right that's pretty
+creative right other agencies haven't
+
+ align:start position:0%
+creative right other agencies haven't
+ 
+
+ align:start position:0%
+creative right other agencies haven't
+come up with that so you know we need to
+
+ align:start position:0%
+come up with that so you know we need to
+ 
+
+ align:start position:0%
+come up with that so you know we need to
+and it's not as if NIH was sitting
+
+ align:start position:0%
+and it's not as if NIH was sitting
+ 
+
+ align:start position:0%
+and it's not as if NIH was sitting
+around figuring it out but in effect it
+
+ align:start position:0%
+around figuring it out but in effect it
+ 
+
+ align:start position:0%
+around figuring it out but in effect it
+occurred and the training talent of the
+
+ align:start position:0%
+occurred and the training talent of the
+ 
+
+ align:start position:0%
+occurred and the training talent of the
+talent helped it occur through people
+
+ align:start position:0%
+talent helped it occur through people
+ 
+
+ align:start position:0%
+talent helped it occur through people
+like Boyer and Swanson our team we
+
+ align:start position:0%
+like Boyer and Swanson our team we
+ 
+
+ align:start position:0%
+like Boyer and Swanson our team we
+defined Buster drugs is one that makes a
+
+ align:start position:0%
+defined Buster drugs is one that makes a
+ 
+
+ align:start position:0%
+defined Buster drugs is one that makes a
+lot of money or makes a lot of money
+
+ align:start position:0%
+lot of money or makes a lot of money
+ 
+
+ align:start position:0%
+lot of money or makes a lot of money
+right I mean I won in theory it won't
+
+ align:start position:0%
+right I mean I won in theory it won't
+ 
+
+ align:start position:0%
+right I mean I won in theory it won't
+get through FDA unless it actually
+
+ align:start position:0%
+get through FDA unless it actually
+ 
+
+ align:start position:0%
+get through FDA unless it actually
+solves a problem right NIH is primarily
+
+ align:start position:0%
+solves a problem right NIH is primarily
+ 
+
+ align:start position:0%
+solves a problem right NIH is primarily
+small grant research and lacks the
+
+ align:start position:0%
+small grant research and lacks the
+ 
+
+ align:start position:0%
+small grant research and lacks the
+capability to set up initiatives across
+
+ align:start position:0%
+capability to set up initiatives across
+ 
+
+ align:start position:0%
+capability to set up initiatives across
+the stovepipes as we've talked about
+
+ align:start position:0%
+the stovepipes as we've talked about
+ 
+
+ align:start position:0%
+the stovepipes as we've talked about
+before it tends to be fairly small slow
+
+ align:start position:0%
+before it tends to be fairly small slow
+ 
+
+ align:start position:0%
+before it tends to be fairly small slow
+moving there's a risk and peer review of
+
+ align:start position:0%
+moving there's a risk and peer review of
+ 
+
+ align:start position:0%
+moving there's a risk and peer review of
+avoiding high risk high payoff
+
+ align:start position:0%
+avoiding high risk high payoff
+ 
+
+ align:start position:0%
+avoiding high risk high payoff
+approaches there's limited connections
+
+ align:start position:0%
+approaches there's limited connections
+ 
+
+ align:start position:0%
+approaches there's limited connections
+to industry in other words that
+
+ align:start position:0%
+to industry in other words that
+ 
+
+ align:start position:0%
+to industry in other words that
+translational research effect is hard to
+
+ align:start position:0%
+translational research effect is hard to
+ 
+
+ align:start position:0%
+translational research effect is hard to
+do at NIH although Collins who's the
+
+ align:start position:0%
+do at NIH although Collins who's the
+ 
+
+ align:start position:0%
+do at NIH although Collins who's the
+current director of NIH has worked on
+
+ align:start position:0%
+current director of NIH has worked on
+ 
+
+ align:start position:0%
+current director of NIH has worked on
+creating a special translational
+
+ align:start position:0%
+creating a special translational
+ 
+
+ align:start position:0%
+creating a special translational
+medicine institute designed at that
+
+ align:start position:0%
+medicine institute designed at that
+ 
+
+ align:start position:0%
+medicine institute designed at that
+problem so NIH has been taking steps on
+
+ align:start position:0%
+problem so NIH has been taking steps on
+ 
+
+ align:start position:0%
+problem so NIH has been taking steps on
+these I think that's a pretty good I'll
+
+ align:start position:0%
+these I think that's a pretty good I'll
+ 
+
+ align:start position:0%
+these I think that's a pretty good I'll
+give you one more example now technology
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the earliest beneficiary of
+
+ align:start position:0%
+the earliest beneficiary of
+ 
+
+ align:start position:0%
+the earliest beneficiary of
+nanotechnology was probably the
+
+ align:start position:0%
+nanotechnology was probably the
+ 
+
+ align:start position:0%
+nanotechnology was probably the
+semiconductor sector but the life
+
+ align:start position:0%
+semiconductor sector but the life
+ 
+
+ align:start position:0%
+semiconductor sector but the life
+science sector the health research
+
+ align:start position:0%
+science sector the health research
+ 
+
+ align:start position:0%
+science sector the health research
+sector was very close huge potential
+
+ align:start position:0%
+sector was very close huge potential
+ 
+
+ align:start position:0%
+sector was very close huge potential
+opportunity spaces and understanding
+
+ align:start position:0%
+opportunity spaces and understanding
+ 
+
+ align:start position:0%
+opportunity spaces and understanding
+things of the nano scale here because of
+
+ align:start position:0%
+things of the nano scale here because of
+ 
+
+ align:start position:0%
+things of the nano scale here because of
+the disaggregated structure of NIH for
+
+ align:start position:0%
+the disaggregated structure of NIH for
+ 
+
+ align:start position:0%
+the disaggregated structure of NIH for
+many many years after the nanotechnology
+
+ align:start position:0%
+many many years after the nanotechnology
+ 
+
+ align:start position:0%
+many many years after the nanotechnology
+initiative was created NIH by far the
+
+ align:start position:0%
+initiative was created NIH by far the
+ 
+
+ align:start position:0%
+initiative was created NIH by far the
+largest research organization was only
+
+ align:start position:0%
+largest research organization was only
+ 
+
+ align:start position:0%
+largest research organization was only
+spending a fraction of what the National
+
+ align:start position:0%
+spending a fraction of what the National
+ 
+
+ align:start position:0%
+spending a fraction of what the National
+Science Foundation was spending on
+
+ align:start position:0%
+Science Foundation was spending on
+ 
+
+ align:start position:0%
+Science Foundation was spending on
+nanotechnology even though the gains for
+
+ align:start position:0%
+nanotechnology even though the gains for
+ 
+
+ align:start position:0%
+nanotechnology even though the gains for
+the Health Research system were and
+
+ align:start position:0%
+the Health Research system were and
+ 
+
+ align:start position:0%
+the Health Research system were and
+clearly are phenomenal
+
+ align:start position:0%
+clearly are phenomenal
+ 
+
+ align:start position:0%
+clearly are phenomenal
+so that's an example of a problem in it
+
+ align:start position:0%
+so that's an example of a problem in it
+ 
+
+ align:start position:0%
+so that's an example of a problem in it
+in being able to attack you know a whole
+
+ align:start position:0%
+in being able to attack you know a whole
+ 
+
+ align:start position:0%
+in being able to attack you know a whole
+new approach disease across this very
+
+ align:start position:0%
+new approach disease across this very
+ 
+
+ align:start position:0%
+new approach disease across this very
+disaggregated model so I mean that's
+
+ align:start position:0%
+disaggregated model so I mean that's
+ 
+
+ align:start position:0%
+disaggregated model so I mean that's
+kind of that's the IOM report of 2003
+
+ align:start position:0%
+kind of that's the IOM report of 2003
+ 
+
+ align:start position:0%
+kind of that's the IOM report of 2003
+we've learned some lessons from this we
+
+ align:start position:0%
+we've learned some lessons from this we
+ 
+
+ align:start position:0%
+we've learned some lessons from this we
+tried to make some changes and Congress
+
+ align:start position:0%
+tried to make some changes and Congress
+ 
+
+ align:start position:0%
+tried to make some changes and Congress
+has actually provided a fair amount of
+
+ align:start position:0%
+has actually provided a fair amount of
+ 
+
+ align:start position:0%
+has actually provided a fair amount of
+leadership on that and creating the
+
+ align:start position:0%
+leadership on that and creating the
+ 
+
+ align:start position:0%
+leadership on that and creating the
+Common Fund and capping the number of
+
+ align:start position:0%
+Common Fund and capping the number of
+ 
+
+ align:start position:0%
+Common Fund and capping the number of
+institutes Marteen you want to take us
+
+ align:start position:0%
+institutes Marteen you want to take us
+ 
+
+ align:start position:0%
+institutes Marteen you want to take us
+through some questions in this all right
+
+ align:start position:0%
+through some questions in this all right
+ 
+
+ align:start position:0%
+through some questions in this all right
+we can do Deegan and do it together and
+
+ align:start position:0%
+we can do Deegan and do it together and
+ 
+
+ align:start position:0%
+we can do Deegan and do it together and
+we don't need to spend a lot of time on
+
+ align:start position:0%
+we don't need to spend a lot of time on
+ 
+
+ align:start position:0%
+we don't need to spend a lot of time on
+this because last week's class was on
+
+ align:start position:0%
+this because last week's class was on
+ 
+
+ align:start position:0%
+this because last week's class was on
+DARPA so I'm not going to recap this
+
+ align:start position:0%
+DARPA so I'm not going to recap this
+ 
+
+ align:start position:0%
+DARPA so I'm not going to recap this
+Robert cook Deegan was deputy when
+
+ align:start position:0%
+Robert cook Deegan was deputy when
+ 
+
+ align:start position:0%
+Robert cook Deegan was deputy when
+Watson was heading the genome project at
+
+ align:start position:0%
+Watson was heading the genome project at
+ 
+
+ align:start position:0%
+Watson was heading the genome project at
+NIH so he knows NIH from the inside he
+
+ align:start position:0%
+NIH so he knows NIH from the inside he
+ 
+
+ align:start position:0%
+NIH so he knows NIH from the inside he
+later went on to head duke's genome
+
+ align:start position:0%
+later went on to head duke's genome
+ 
+
+ align:start position:0%
+later went on to head duke's genome
+institute so he's an outstanding
+
+ align:start position:0%
+institute so he's an outstanding
+ 
+
+ align:start position:0%
+institute so he's an outstanding
+researcher and now he is teaching
+
+ align:start position:0%
+researcher and now he is teaching
+ 
+
+ align:start position:0%
+researcher and now he is teaching
+Science and Technology Policy at the
+
+ align:start position:0%
+Science and Technology Policy at the
+ 
+
+ align:start position:0%
+Science and Technology Policy at the
+Washington branch of Arizona State so
+
+ align:start position:0%
+Washington branch of Arizona State so
+ 
+
+ align:start position:0%
+Washington branch of Arizona State so
+he's gone over to the dark side of
+
+ align:start position:0%
+he's gone over to the dark side of
+ 
+
+ align:start position:0%
+he's gone over to the dark side of
+science policy where people like me and
+
+ align:start position:0%
+science policy where people like me and
+ 
+
+ align:start position:0%
+science policy where people like me and
+habit the world
+
+ align:start position:0%
+habit the world
+ 
+
+ align:start position:0%
+habit the world
+but he's got real talents unlike me you
+
+ align:start position:0%
+but he's got real talents unlike me you
+ 
+
+ align:start position:0%
+but he's got real talents unlike me you
+know actually on the technology side and
+
+ align:start position:0%
+know actually on the technology side and
+ 
+
+ align:start position:0%
+know actually on the technology side and
+he wrote this piece back in 1996 you
+
+ align:start position:0%
+he wrote this piece back in 1996 you
+ 
+
+ align:start position:0%
+he wrote this piece back in 1996 you
+know fairly fresh off his own NIH
+
+ align:start position:0%
+know fairly fresh off his own NIH
+ 
+
+ align:start position:0%
+know fairly fresh off his own NIH
+experience does NIH needed DARPA and I
+
+ align:start position:0%
+experience does NIH needed DARPA and I
+ 
+
+ align:start position:0%
+experience does NIH needed DARPA and I
+can't tell you how controversial this
+
+ align:start position:0%
+can't tell you how controversial this
+ 
+
+ align:start position:0%
+can't tell you how controversial this
+was NIH has always viewed itself as
+
+ align:start position:0%
+was NIH has always viewed itself as
+ 
+
+ align:start position:0%
+was NIH has always viewed itself as
+better than everybody else and the fact
+
+ align:start position:0%
+better than everybody else and the fact
+ 
+
+ align:start position:0%
+better than everybody else and the fact
+that one of their own
+
+ align:start position:0%
+that one of their own
+ 
+
+ align:start position:0%
+that one of their own
+you know the deputy director of their
+
+ align:start position:0%
+you know the deputy director of their
+ 
+
+ align:start position:0%
+you know the deputy director of their
+genome project was telling them it was a
+
+ align:start position:0%
+genome project was telling them it was a
+ 
+
+ align:start position:0%
+genome project was telling them it was a
+better model out there that they ought
+
+ align:start position:0%
+better model out there that they ought
+ 
+
+ align:start position:0%
+better model out there that they ought
+to at least consider adopting for part
+
+ align:start position:0%
+to at least consider adopting for part
+ 
+
+ align:start position:0%
+to at least consider adopting for part
+of their operations certainly not for
+
+ align:start position:0%
+of their operations certainly not for
+ 
+
+ align:start position:0%
+of their operations certainly not for
+all was a powerful message and we know
+
+ align:start position:0%
+all was a powerful message and we know
+ 
+
+ align:start position:0%
+all was a powerful message and we know
+the DARPA story so I'm not going to
+
+ align:start position:0%
+the DARPA story so I'm not going to
+ 
+
+ align:start position:0%
+the DARPA story so I'm not going to
+recap that Robert cook Deegan
+
+ align:start position:0%
+recap that Robert cook Deegan
+ 
+
+ align:start position:0%
+recap that Robert cook Deegan
+underscores that the DARPA model
+
+ align:start position:0%
+underscores that the DARPA model
+ 
+
+ align:start position:0%
+underscores that the DARPA model
+suggests that peer review is not the
+
+ align:start position:0%
+suggests that peer review is not the
+ 
+
+ align:start position:0%
+suggests that peer review is not the
+only way of doing of organizing research
+
+ align:start position:0%
+only way of doing of organizing research
+ 
+
+ align:start position:0%
+only way of doing of organizing research
+DARP as far lower transaction costs than
+
+ align:start position:0%
+DARP as far lower transaction costs than
+ 
+
+ align:start position:0%
+DARP as far lower transaction costs than
+NIH does a lot lower review cost for
+
+ align:start position:0%
+NIH does a lot lower review cost for
+ 
+
+ align:start position:0%
+NIH does a lot lower review cost for
+science direction he introduces this
+
+ align:start position:0%
+science direction he introduces this
+ 
+
+ align:start position:0%
+science direction he introduces this
+issue of how conservative peer review
+
+ align:start position:0%
+issue of how conservative peer review
+ 
+
+ align:start position:0%
+issue of how conservative peer review
+gets when it gets to an award rate
+
+ align:start position:0%
+gets when it gets to an award rate
+ 
+
+ align:start position:0%
+gets when it gets to an award rate
+that's you know much worse than about
+
+ align:start position:0%
+that's you know much worse than about
+ 
+
+ align:start position:0%
+that's you know much worse than about
+one out of three grants you know
+
+ align:start position:0%
+one out of three grants you know
+ 
+
+ align:start position:0%
+one out of three grants you know
+applications for grants awarded DARPA
+
+ align:start position:0%
+applications for grants awarded DARPA
+ 
+
+ align:start position:0%
+applications for grants awarded DARPA
+has got I mean NIH has got a very
+
+ align:start position:0%
+has got I mean NIH has got a very
+ 
+
+ align:start position:0%
+has got I mean NIH has got a very
+limited ability to do the kind of Grand
+
+ align:start position:0%
+limited ability to do the kind of Grand
+ 
+
+ align:start position:0%
+limited ability to do the kind of Grand
+Challenge model to kind of pursue that
+
+ align:start position:0%
+Challenge model to kind of pursue that
+ 
+
+ align:start position:0%
+Challenge model to kind of pursue that
+challenge model it's got limited ability
+
+ align:start position:0%
+challenge model it's got limited ability
+ 
+
+ align:start position:0%
+challenge model it's got limited ability
+to take high risks and get high rewards
+
+ align:start position:0%
+to take high risks and get high rewards
+ 
+
+ align:start position:0%
+to take high risks and get high rewards
+it's got a lower risk acceptance
+
+ align:start position:0%
+it's got a lower risk acceptance
+ 
+
+ align:start position:0%
+it's got a lower risk acceptance
+capability
+
+ align:start position:0%
+capability
+ 
+
+ align:start position:0%
+capability
+those are DARPA things that NIH should
+
+ align:start position:0%
+those are DARPA things that NIH should
+ 
+
+ align:start position:0%
+those are DARPA things that NIH should
+had not all of NIH but suddenly some
+
+ align:start position:0%
+had not all of NIH but suddenly some
+ 
+
+ align:start position:0%
+had not all of NIH but suddenly some
+part of it might adopt he argues he
+
+ align:start position:0%
+part of it might adopt he argues he
+ 
+
+ align:start position:0%
+part of it might adopt he argues he
+cites a lot of examples NIH the human
+
+ align:start position:0%
+cites a lot of examples NIH the human
+ 
+
+ align:start position:0%
+cites a lot of examples NIH the human
+genome and I should have actually
+
+ align:start position:0%
+genome and I should have actually
+ 
+
+ align:start position:0%
+genome and I should have actually
+originated in the Department of Energy
+
+ align:start position:0%
+originated in the Department of Energy
+ 
+
+ align:start position:0%
+originated in the Department of Energy
+because the department energy understood
+
+ align:start position:0%
+because the department energy understood
+ 
+
+ align:start position:0%
+because the department energy understood
+supercomputers so for the first five
+
+ align:start position:0%
+supercomputers so for the first five
+ 
+
+ align:start position:0%
+supercomputers so for the first five
+years of the genome project it was
+
+ align:start position:0%
+years of the genome project it was
+ 
+
+ align:start position:0%
+years of the genome project it was
+carried by you know the supercomputer
+
+ align:start position:0%
+carried by you know the supercomputer
+ 
+
+ align:start position:0%
+carried by you know the supercomputer
+gurus at D week because they understood
+
+ align:start position:0%
+gurus at D week because they understood
+ 
+
+ align:start position:0%
+gurus at D week because they understood
+what the potential of supercomputing was
+
+ align:start position:0%
+what the potential of supercomputing was
+ 
+
+ align:start position:0%
+what the potential of supercomputing was
+going to be in figuring out the genetic
+
+ align:start position:0%
+going to be in figuring out the genetic
+ 
+
+ align:start position:0%
+going to be in figuring out the genetic
+structure NIH only picked it up when it
+
+ align:start position:0%
+structure NIH only picked it up when it
+ 
+
+ align:start position:0%
+structure NIH only picked it up when it
+saw the promise in the model
+
+ align:start position:0%
+saw the promise in the model
+ 
+
+ align:start position:0%
+saw the promise in the model
+NIH had terrible trouble coping with the
+
+ align:start position:0%
+NIH had terrible trouble coping with the
+ 
+
+ align:start position:0%
+NIH had terrible trouble coping with the
+advances made by Leroy hood and we'll
+
+ align:start position:0%
+advances made by Leroy hood and we'll
+ 
+
+ align:start position:0%
+advances made by Leroy hood and we'll
+talk later about Venter and kind of how
+
+ align:start position:0%
+talk later about Venter and kind of how
+ 
+
+ align:start position:0%
+talk later about Venter and kind of how
+do you adapt an incorporate a
+
+ align:start position:0%
+do you adapt an incorporate a
+ 
+
+ align:start position:0%
+do you adapt an incorporate a
+computational model in medical research
+
+ align:start position:0%
+computational model in medical research
+ 
+
+ align:start position:0%
+computational model in medical research
+they're locked into a biology only drug
+
+ align:start position:0%
+they're locked into a biology only drug
+ 
+
+ align:start position:0%
+they're locked into a biology only drug
+development model pretty much right it's
+
+ align:start position:0%
+development model pretty much right it's
+ 
+
+ align:start position:0%
+development model pretty much right it's
+hard for them to do other territories as
+
+ align:start position:0%
+hard for them to do other territories as
+ 
+
+ align:start position:0%
+hard for them to do other territories as
+we'll talk about when we get to the
+
+ align:start position:0%
+we'll talk about when we get to the
+ 
+
+ align:start position:0%
+we'll talk about when we get to the
+convergence report so the lessons for
+
+ align:start position:0%
+convergence report so the lessons for
+ 
+
+ align:start position:0%
+convergence report so the lessons for
+DARPA from DARPA for handling
+
+ align:start position:0%
+DARPA from DARPA for handling
+ 
+
+ align:start position:0%
+DARPA from DARPA for handling
+multidisciplinary approaches and
+
+ align:start position:0%
+multidisciplinary approaches and
+ 
+
+ align:start position:0%
+multidisciplinary approaches and
+bringing in a group of talent around a
+
+ align:start position:0%
+bringing in a group of talent around a
+ 
+
+ align:start position:0%
+bringing in a group of talent around a
+problem that comes from different fields
+
+ align:start position:0%
+problem that comes from different fields
+ 
+
+ align:start position:0%
+problem that comes from different fields
+there's lessons here for for NIH I mean
+
+ align:start position:0%
+there's lessons here for for NIH I mean
+ 
+
+ align:start position:0%
+there's lessons here for for NIH I mean
+that's that's the heart of Robert cook
+
+ align:start position:0%
+that's that's the heart of Robert cook
+ 
+
+ align:start position:0%
+that's that's the heart of Robert cook
+deagan's recommendations and Martine
+
+ align:start position:0%
+deagan's recommendations and Martine
+ 
+
+ align:start position:0%
+deagan's recommendations and Martine
+it's yours papers I won't really
+
+ align:start position:0%
+it's yours papers I won't really
+ 
+
+ align:start position:0%
+it's yours papers I won't really
+summarize too much more I think we just
+
+ align:start position:0%
+summarize too much more I think we just
+ 
+
+ align:start position:0%
+summarize too much more I think we just
+go straight into discussion and so I
+
+ align:start position:0%
+go straight into discussion and so I
+ 
+
+ align:start position:0%
+go straight into discussion and so I
+think a good first question would be how
+
+ align:start position:0%
+think a good first question would be how
+ 
+
+ align:start position:0%
+think a good first question would be how
+do we we know that there's a lot of
+
+ align:start position:0%
+do we we know that there's a lot of
+ 
+
+ align:start position:0%
+do we we know that there's a lot of
+costs in the healthcare industry and
+
+ align:start position:0%
+costs in the healthcare industry and
+ 
+
+ align:start position:0%
+costs in the healthcare industry and
+this the system the structure they have
+
+ align:start position:0%
+this the system the structure they have
+ 
+
+ align:start position:0%
+this the system the structure they have
+isn't perfect and so how do we create a
+
+ align:start position:0%
+isn't perfect and so how do we create a
+ 
+
+ align:start position:0%
+isn't perfect and so how do we create a
+system so that these problems that need
+
+ align:start position:0%
+system so that these problems that need
+ 
+
+ align:start position:0%
+system so that these problems that need
+to get solved but don't have a economic
+
+ align:start position:0%
+to get solved but don't have a economic
+ 
+
+ align:start position:0%
+to get solved but don't have a economic
+incentive because they're not
+
+ align:start position:0%
+incentive because they're not
+ 
+
+ align:start position:0%
+incentive because they're not
+blockbusters how do you combine NIH with
+
+ align:start position:0%
+blockbusters how do you combine NIH with
+ 
+
+ align:start position:0%
+blockbusters how do you combine NIH with
+maybe some DARPA like abilities and
+
+ align:start position:0%
+maybe some DARPA like abilities and
+ 
+
+ align:start position:0%
+maybe some DARPA like abilities and
+industry and if anybody is specialty is
+
+ align:start position:0%
+industry and if anybody is specialty is
+ 
+
+ align:start position:0%
+industry and if anybody is specialty is
+like high research I'll be interesting
+
+ align:start position:0%
+like high research I'll be interesting
+ 
+
+ align:start position:0%
+like high research I'll be interesting
+to hear inside first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+read me bud hi research boy you're
+
+ align:start position:0%
+read me bud hi research boy you're
+ 
+
+ align:start position:0%
+read me bud hi research boy you're
+focusing on like an academic career in a
+
+ align:start position:0%
+focusing on like an academic career in a
+ 
+
+ align:start position:0%
+focusing on like an academic career in a
+lab in a national lab you know more
+
+ align:start position:0%
+lab in a national lab you know more
+ 
+
+ align:start position:0%
+lab in a national lab you know more
+about that where's Lily yes you got it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I think you probably could the kind
+
+ align:start position:0%
+yeah I think you probably could the kind
+ 
+
+ align:start position:0%
+yeah I think you probably could the kind
+of lady really struggle in this
+
+ align:start position:0%
+of lady really struggle in this
+ 
+
+ align:start position:0%
+of lady really struggle in this
+peer-review process if you have an idea
+
+ align:start position:0%
+peer-review process if you have an idea
+ 
+
+ align:start position:0%
+peer-review process if you have an idea
+for maybe not a blockbuster drug but
+
+ align:start position:0%
+for maybe not a blockbuster drug but
+ 
+
+ align:start position:0%
+for maybe not a blockbuster drug but
+like a new approach to a system that
+
+ align:start position:0%
+like a new approach to a system that
+ 
+
+ align:start position:0%
+like a new approach to a system that
+hasn't really been tried out yet so
+
+ align:start position:0%
+hasn't really been tried out yet so
+ 
+
+ align:start position:0%
+hasn't really been tried out yet so
+that's why you see like put a mentor
+
+ align:start position:0%
+that's why you see like put a mentor
+ 
+
+ align:start position:0%
+that's why you see like put a mentor
+have this huge problem and I think it
+
+ align:start position:0%
+have this huge problem and I think it
+ 
+
+ align:start position:0%
+have this huge problem and I think it
+really is just kind of allocating a part
+
+ align:start position:0%
+really is just kind of allocating a part
+ 
+
+ align:start position:0%
+really is just kind of allocating a part
+of NH you know budget that they get to
+
+ align:start position:0%
+of NH you know budget that they get to
+ 
+
+ align:start position:0%
+of NH you know budget that they get to
+sort of the start with like high impact
+
+ align:start position:0%
+sort of the start with like high impact
+ 
+
+ align:start position:0%
+sort of the start with like high impact
+it's maybe high-risk research and kind
+
+ align:start position:0%
+it's maybe high-risk research and kind
+ 
+
+ align:start position:0%
+it's maybe high-risk research and kind
+of moving from there but I'm not sure
+
+ align:start position:0%
+of moving from there but I'm not sure
+ 
+
+ align:start position:0%
+of moving from there but I'm not sure
+because it kind of takes so long to
+
+ align:start position:0%
+because it kind of takes so long to
+ 
+
+ align:start position:0%
+because it kind of takes so long to
+develop these things so like three to
+
+ align:start position:0%
+develop these things so like three to
+ 
+
+ align:start position:0%
+develop these things so like three to
+five year and then you have to sort of
+
+ align:start position:0%
+five year and then you have to sort of
+ 
+
+ align:start position:0%
+five year and then you have to sort of
+take your clinical trials and things
+
+ align:start position:0%
+take your clinical trials and things
+ 
+
+ align:start position:0%
+take your clinical trials and things
+like that like with the time scale need
+
+ align:start position:0%
+like that like with the time scale need
+ 
+
+ align:start position:0%
+like that like with the time scale need
+to adjust it to account for kind of
+
+ align:start position:0%
+to adjust it to account for kind of
+ 
+
+ align:start position:0%
+to adjust it to account for kind of
+doing the research and moving into
+
+ align:start position:0%
+doing the research and moving into
+ 
+
+ align:start position:0%
+doing the research and moving into
+clinical trials to be able to like
+
+ align:start position:0%
+clinical trials to be able to like
+ 
+
+ align:start position:0%
+clinical trials to be able to like
+actually support kind of these high-risk
+
+ align:start position:0%
+actually support kind of these high-risk
+ 
+
+ align:start position:0%
+actually support kind of these high-risk
+initiatives and a lot of these I feel
+
+ align:start position:0%
+initiatives and a lot of these I feel
+ 
+
+ align:start position:0%
+initiatives and a lot of these I feel
+like we'll be building on research that
+
+ align:start position:0%
+like we'll be building on research that
+ 
+
+ align:start position:0%
+like we'll be building on research that
+doesn't really exist earlier there yet
+
+ align:start position:0%
+doesn't really exist earlier there yet
+ 
+
+ align:start position:0%
+doesn't really exist earlier there yet
+so will they need more time to sort of
+
+ align:start position:0%
+so will they need more time to sort of
+ 
+
+ align:start position:0%
+so will they need more time to sort of
+stand up yeah I think there's probably
+
+ align:start position:0%
+stand up yeah I think there's probably
+ 
+
+ align:start position:0%
+stand up yeah I think there's probably
+two main ways that maybe some of the
+
+ align:start position:0%
+two main ways that maybe some of the
+ 
+
+ align:start position:0%
+two main ways that maybe some of the
+later readings touch on more but
+
+ align:start position:0%
+later readings touch on more but
+ 
+
+ align:start position:0%
+later readings touch on more but
+definitely kind of incentives on the
+
+ align:start position:0%
+definitely kind of incentives on the
+ 
+
+ align:start position:0%
+definitely kind of incentives on the
+FDA's hard to extend and make that
+
+ align:start position:0%
+FDA's hard to extend and make that
+ 
+
+ align:start position:0%
+FDA's hard to extend and make that
+process a little bit more profitable
+
+ align:start position:0%
+process a little bit more profitable
+ 
+
+ align:start position:0%
+process a little bit more profitable
+than say it's it's on like an orphan
+
+ align:start position:0%
+than say it's it's on like an orphan
+ 
+
+ align:start position:0%
+than say it's it's on like an orphan
+drug where you have a very small kind of
+
+ align:start position:0%
+drug where you have a very small kind of
+ 
+
+ align:start position:0%
+drug where you have a very small kind of
+market that could be addressed when the
+
+ align:start position:0%
+market that could be addressed when the
+ 
+
+ align:start position:0%
+market that could be addressed when the
+drug comes out by kind of increasing the
+
+ align:start position:0%
+drug comes out by kind of increasing the
+ 
+
+ align:start position:0%
+drug comes out by kind of increasing the
+patent life so they've like extended
+
+ align:start position:0%
+patent life so they've like extended
+ 
+
+ align:start position:0%
+patent life so they've like extended
+patent provisions for those kind of
+
+ align:start position:0%
+patent provisions for those kind of
+ 
+
+ align:start position:0%
+patent provisions for those kind of
+drugs and that definitely helps kind of
+
+ align:start position:0%
+drugs and that definitely helps kind of
+ 
+
+ align:start position:0%
+drugs and that definitely helps kind of
+make it more profitable and also a lot
+
+ align:start position:0%
+make it more profitable and also a lot
+ 
+
+ align:start position:0%
+make it more profitable and also a lot
+of the later papers talk about this but
+
+ align:start position:0%
+of the later papers talk about this but
+ 
+
+ align:start position:0%
+of the later papers talk about this but
+they have a lot of flexibility
+
+ align:start position:0%
+they have a lot of flexibility
+ 
+
+ align:start position:0%
+they have a lot of flexibility
+the way they can price their drugs so I
+
+ align:start position:0%
+the way they can price their drugs so I
+ 
+
+ align:start position:0%
+the way they can price their drugs so I
+think that kind of helps a lot because
+
+ align:start position:0%
+think that kind of helps a lot because
+ 
+
+ align:start position:0%
+think that kind of helps a lot because
+if they can charge like so much a lot of
+
+ align:start position:0%
+if they can charge like so much a lot of
+ 
+
+ align:start position:0%
+if they can charge like so much a lot of
+money for like a dose of very nice drug
+
+ align:start position:0%
+money for like a dose of very nice drug
+ 
+
+ align:start position:0%
+money for like a dose of very nice drug
+that kind of compensates for the fact
+
+ align:start position:0%
+that kind of compensates for the fact
+ 
+
+ align:start position:0%
+that kind of compensates for the fact
+that you're not giving it to as many
+
+ align:start position:0%
+that you're not giving it to as many
+ 
+
+ align:start position:0%
+that you're not giving it to as many
+people and I guess going through what
+
+ align:start position:0%
+people and I guess going through what
+ 
+
+ align:start position:0%
+people and I guess going through what
+that last one is what about a Martin
+
+ align:start position:0%
+that last one is what about a Martin
+ 
+
+ align:start position:0%
+that last one is what about a Martin
+shkreli situation that's going to come
+
+ align:start position:0%
+shkreli situation that's going to come
+ 
+
+ align:start position:0%
+shkreli situation that's going to come
+up because other companies will want to
+
+ align:start position:0%
+up because other companies will want to
+ 
+
+ align:start position:0%
+up because other companies will want to
+you know recoup their costs because
+
+ align:start position:0%
+you know recoup their costs because
+ 
+
+ align:start position:0%
+you know recoup their costs because
+they're spending millions and billions
+
+ align:start position:0%
+they're spending millions and billions
+ 
+
+ align:start position:0%
+they're spending millions and billions
+of dollars on these drugs to develop
+
+ align:start position:0%
+of dollars on these drugs to develop
+ 
+
+ align:start position:0%
+of dollars on these drugs to develop
+them but and there's like kind of an
+
+ align:start position:0%
+them but and there's like kind of an
+ 
+
+ align:start position:0%
+them but and there's like kind of an
+argument for both ways that oh it's kind
+
+ align:start position:0%
+argument for both ways that oh it's kind
+ 
+
+ align:start position:0%
+argument for both ways that oh it's kind
+of justified but I mean obviously bad
+
+ align:start position:0%
+of justified but I mean obviously bad
+ 
+
+ align:start position:0%
+of justified but I mean obviously bad
+for society it also it also you could
+
+ align:start position:0%
+for society it also it also you could
+ 
+
+ align:start position:0%
+for society it also it also you could
+make a very similar argument for any
+
+ align:start position:0%
+make a very similar argument for any
+ 
+
+ align:start position:0%
+make a very similar argument for any
+other drug in like one of these
+
+ align:start position:0%
+other drug in like one of these
+ 
+
+ align:start position:0%
+other drug in like one of these
+blockbuster drugs as we say because well
+
+ align:start position:0%
+blockbuster drugs as we say because well
+ 
+
+ align:start position:0%
+blockbuster drugs as we say because well
+you could still charge an exorbitant
+
+ align:start position:0%
+you could still charge an exorbitant
+ 
+
+ align:start position:0%
+you could still charge an exorbitant
+price for them you can get tons of money
+
+ align:start position:0%
+price for them you can get tons of money
+ 
+
+ align:start position:0%
+price for them you can get tons of money
+for them and then you're back to square
+
+ align:start position:0%
+for them and then you're back to square
+ 
+
+ align:start position:0%
+for them and then you're back to square
+one where okay let's just keep funding
+
+ align:start position:0%
+one where okay let's just keep funding
+ 
+
+ align:start position:0%
+one where okay let's just keep funding
+the drugs of what we're doing because
+
+ align:start position:0%
+the drugs of what we're doing because
+ 
+
+ align:start position:0%
+the drugs of what we're doing because
+don't Brooke what isn't what don't
+
+ align:start position:0%
+don't Brooke what isn't what don't
+ 
+
+ align:start position:0%
+don't Brooke what isn't what don't
+thinks what is broken right so I'm not
+
+ align:start position:0%
+thinks what is broken right so I'm not
+ 
+
+ align:start position:0%
+thinks what is broken right so I'm not
+sure how it would incentivize people to
+
+ align:start position:0%
+sure how it would incentivize people to
+ 
+
+ align:start position:0%
+sure how it would incentivize people to
+to focus on these smaller drugs now one
+
+ align:start position:0%
+to focus on these smaller drugs now one
+ 
+
+ align:start position:0%
+to focus on these smaller drugs now one
+way you could do it maybe I don't know
+
+ align:start position:0%
+way you could do it maybe I don't know
+ 
+
+ align:start position:0%
+way you could do it maybe I don't know
+tax incentives or something maybe force
+
+ align:start position:0%
+tax incentives or something maybe force
+ 
+
+ align:start position:0%
+tax incentives or something maybe force
+insurance companies to fit it to foot
+
+ align:start position:0%
+insurance companies to fit it to foot
+ 
+
+ align:start position:0%
+insurance companies to fit it to foot
+the bill a bit more
+
+ align:start position:0%
+the bill a bit more
+ 
+
+ align:start position:0%
+the bill a bit more
+I don't really know the detail work yeah
+
+ align:start position:0%
+I don't really know the detail work yeah
+ 
+
+ align:start position:0%
+I don't really know the detail work yeah
+this is this is one of the great
+
+ align:start position:0%
+this is this is one of the great
+ 
+
+ align:start position:0%
+this is this is one of the great
+societal dilemmas that we've got in
+
+ align:start position:0%
+societal dilemmas that we've got in
+ 
+
+ align:start position:0%
+societal dilemmas that we've got in
+health care at the moment you want to
+
+ align:start position:0%
+health care at the moment you want to
+ 
+
+ align:start position:0%
+health care at the moment you want to
+create enormous incentives for
+
+ align:start position:0%
+create enormous incentives for
+ 
+
+ align:start position:0%
+create enormous incentives for
+researchers and biotech companies they
+
+ align:start position:0%
+researchers and biotech companies they
+ 
+
+ align:start position:0%
+researchers and biotech companies they
+may create to go after these big
+
+ align:start position:0%
+may create to go after these big
+ 
+
+ align:start position:0%
+may create to go after these big
+problems you really want to incentivize
+
+ align:start position:0%
+problems you really want to incentivize
+ 
+
+ align:start position:0%
+problems you really want to incentivize
+that process so if you start to D
+
+ align:start position:0%
+that process so if you start to D
+ 
+
+ align:start position:0%
+that process so if you start to D
+incentivize it you're gonna have less
+
+ align:start position:0%
+incentivize it you're gonna have less
+ 
+
+ align:start position:0%
+incentivize it you're gonna have less
+remedies on the table on the other hand
+
+ align:start position:0%
+remedies on the table on the other hand
+ 
+
+ align:start position:0%
+remedies on the table on the other hand
+you know you've got serious cost
+
+ align:start position:0%
+you know you've got serious cost
+ 
+
+ align:start position:0%
+you know you've got serious cost
+problems for some portion of the
+
+ align:start position:0%
+problems for some portion of the
+ 
+
+ align:start position:0%
+problems for some portion of the
+population that's not going to be able
+
+ align:start position:0%
+population that's not going to be able
+ 
+
+ align:start position:0%
+population that's not going to be able
+to cope with the cost structure and
+
+ align:start position:0%
+to cope with the cost structure and
+ 
+
+ align:start position:0%
+to cope with the cost structure and
+you're gonna have real reluctance on the
+
+ align:start position:0%
+you're gonna have real reluctance on the
+ 
+
+ align:start position:0%
+you're gonna have real reluctance on the
+part of government agencies to subscribe
+
+ align:start position:0%
+part of government agencies to subscribe
+ 
+
+ align:start position:0%
+part of government agencies to subscribe
+for you a huge cost version that burden
+
+ align:start position:0%
+for you a huge cost version that burden
+ 
+
+ align:start position:0%
+for you a huge cost version that burden
+that only helps a relatively small
+
+ align:start position:0%
+that only helps a relatively small
+ 
+
+ align:start position:0%
+that only helps a relatively small
+number of people so this is this is a
+
+ align:start position:0%
+number of people so this is this is a
+ 
+
+ align:start position:0%
+number of people so this is this is a
+dilemma that is now upon us big time
+
+ align:start position:0%
+dilemma that is now upon us big time
+ 
+
+ align:start position:0%
+dilemma that is now upon us big time
+that we have not sorted through in an
+
+ align:start position:0%
+that we have not sorted through in an
+ 
+
+ align:start position:0%
+that we have not sorted through in an
+intelligent way and there's you know
+
+ align:start position:0%
+intelligent way and there's you know
+ 
+
+ align:start position:0%
+intelligent way and there's you know
+constant reviling of drug and biotech
+
+ align:start position:0%
+constant reviling of drug and biotech
+ 
+
+ align:start position:0%
+constant reviling of drug and biotech
+companies but on the other hand they're
+
+ align:start position:0%
+companies but on the other hand they're
+ 
+
+ align:start position:0%
+companies but on the other hand they're
+the ones that created these
+
+ align:start position:0%
+the ones that created these
+ 
+
+ align:start position:0%
+the ones that created these
+opportunities for us so it's a very
+
+ align:start position:0%
+opportunities for us so it's a very
+ 
+
+ align:start position:0%
+opportunities for us so it's a very
+counter dictor e the politics doesn't
+
+ align:start position:0%
+counter dictor e the politics doesn't
+ 
+
+ align:start position:0%
+counter dictor e the politics doesn't
+seem to recognize the importance of the
+
+ align:start position:0%
+seem to recognize the importance of the
+ 
+
+ align:start position:0%
+seem to recognize the importance of the
+innovation system and yet we don't have
+
+ align:start position:0%
+innovation system and yet we don't have
+ 
+
+ align:start position:0%
+innovation system and yet we don't have
+the right balance between the two I
+
+ align:start position:0%
+the right balance between the two I
+ 
+
+ align:start position:0%
+the right balance between the two I
+think the dimension that's also missing
+
+ align:start position:0%
+think the dimension that's also missing
+ 
+
+ align:start position:0%
+think the dimension that's also missing
+is something we touched on last week
+
+ align:start position:0%
+is something we touched on last week
+ 
+
+ align:start position:0%
+is something we touched on last week
+which is the ethical components I think
+
+ align:start position:0%
+which is the ethical components I think
+ 
+
+ align:start position:0%
+which is the ethical components I think
+there's really a rising bioethics
+
+ align:start position:0%
+there's really a rising bioethics
+ 
+
+ align:start position:0%
+there's really a rising bioethics
+community surrounding issues of
+
+ align:start position:0%
+community surrounding issues of
+ 
+
+ align:start position:0%
+community surrounding issues of
+utilitarianism versus human suffering
+
+ align:start position:0%
+utilitarianism versus human suffering
+ 
+
+ align:start position:0%
+utilitarianism versus human suffering
+right like do we seek to address this of
+
+ align:start position:0%
+right like do we seek to address this of
+ 
+
+ align:start position:0%
+right like do we seek to address this of
+the person who is suffering the most or
+
+ align:start position:0%
+the person who is suffering the most or
+ 
+
+ align:start position:0%
+the person who is suffering the most or
+the number of people who are suffering
+
+ align:start position:0%
+the number of people who are suffering
+ 
+
+ align:start position:0%
+the number of people who are suffering
+and that is a really difficult I think
+
+ align:start position:0%
+and that is a really difficult I think
+ 
+
+ align:start position:0%
+and that is a really difficult I think
+ethical question that has yet to be
+
+ align:start position:0%
+ethical question that has yet to be
+ 
+
+ align:start position:0%
+ethical question that has yet to be
+addressed on a national level and I
+
+ align:start position:0%
+addressed on a national level and I
+ 
+
+ align:start position:0%
+addressed on a national level and I
+think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's easier I guess I think about it in
+
+ align:start position:0%
+it's easier I guess I think about it in
+ 
+
+ align:start position:0%
+it's easier I guess I think about it in
+terms of heuristics right like shortcuts
+
+ align:start position:0%
+terms of heuristics right like shortcuts
+ 
+
+ align:start position:0%
+terms of heuristics right like shortcuts
+for decision-making if we understand our
+
+ align:start position:0%
+for decision-making if we understand our
+ 
+
+ align:start position:0%
+for decision-making if we understand our
+colleagues are nationally we can
+
+ align:start position:0%
+colleagues are nationally we can
+ 
+
+ align:start position:0%
+colleagues are nationally we can
+understand where to begin to allocate
+
+ align:start position:0%
+understand where to begin to allocate
+ 
+
+ align:start position:0%
+understand where to begin to allocate
+money and even we sort out our national
+
+ align:start position:0%
+money and even we sort out our national
+ 
+
+ align:start position:0%
+money and even we sort out our national
+values in terms of the life sciences and
+
+ align:start position:0%
+values in terms of the life sciences and
+ 
+
+ align:start position:0%
+values in terms of the life sciences and
+what we think our national priorities
+
+ align:start position:0%
+what we think our national priorities
+ 
+
+ align:start position:0%
+what we think our national priorities
+perhaps maybe through a referendum light
+
+ align:start position:0%
+perhaps maybe through a referendum light
+ 
+
+ align:start position:0%
+perhaps maybe through a referendum light
+system I think it would actually be much
+
+ align:start position:0%
+system I think it would actually be much
+ 
+
+ align:start position:0%
+system I think it would actually be much
+more efficient and accountable way for
+
+ align:start position:0%
+more efficient and accountable way for
+ 
+
+ align:start position:0%
+more efficient and accountable way for
+the government to make funding priority
+
+ align:start position:0%
+the government to make funding priority
+ 
+
+ align:start position:0%
+the government to make funding priority
+decisions rather than for life sciences
+
+ align:start position:0%
+decisions rather than for life sciences
+ 
+
+ align:start position:0%
+decisions rather than for life sciences
+organizations and the NIH to sort of
+
+ align:start position:0%
+organizations and the NIH to sort of
+ 
+
+ align:start position:0%
+organizations and the NIH to sort of
+make those decisions for themselves or
+
+ align:start position:0%
+make those decisions for themselves or
+ 
+
+ align:start position:0%
+make those decisions for themselves or
+for the citizens because ultimately this
+
+ align:start position:0%
+for the citizens because ultimately this
+ 
+
+ align:start position:0%
+for the citizens because ultimately this
+is an issue at the human level and that
+
+ align:start position:0%
+is an issue at the human level and that
+ 
+
+ align:start position:0%
+is an issue at the human level and that
+implies an understanding of bio ethical
+
+ align:start position:0%
+implies an understanding of bio ethical
+ 
+
+ align:start position:0%
+implies an understanding of bio ethical
+considerations I think that tends to run
+
+ align:start position:0%
+considerations I think that tends to run
+ 
+
+ align:start position:0%
+considerations I think that tends to run
+into a problem however with kind of rude
+
+ align:start position:0%
+into a problem however with kind of rude
+ 
+
+ align:start position:0%
+into a problem however with kind of rude
+attitudes of the American population I
+
+ align:start position:0%
+attitudes of the American population I
+ 
+
+ align:start position:0%
+attitudes of the American population I
+would say that a lot of the American
+
+ align:start position:0%
+would say that a lot of the American
+ 
+
+ align:start position:0%
+would say that a lot of the American
+population believes that we should be
+
+ align:start position:0%
+population believes that we should be
+ 
+
+ align:start position:0%
+population believes that we should be
+allowed to live forever right because
+
+ align:start position:0%
+allowed to live forever right because
+ 
+
+ align:start position:0%
+allowed to live forever right because
+you know we're Americans so you know we
+
+ align:start position:0%
+you know we're Americans so you know we
+ 
+
+ align:start position:0%
+you know we're Americans so you know we
+should be eternal
+
+ align:start position:0%
+should be eternal
+ 
+
+ align:start position:0%
+should be eternal
+right it's I'm exaggerating a bit here
+
+ align:start position:0%
+right it's I'm exaggerating a bit here
+ 
+
+ align:start position:0%
+right it's I'm exaggerating a bit here
+but there's a lot of thinking along
+
+ align:start position:0%
+but there's a lot of thinking along
+ 
+
+ align:start position:0%
+but there's a lot of thinking along
+those lines and a lot of assumptions
+
+ align:start position:0%
+those lines and a lot of assumptions
+ 
+
+ align:start position:0%
+those lines and a lot of assumptions
+that any cost whatever it is is
+
+ align:start position:0%
+that any cost whatever it is is
+ 
+
+ align:start position:0%
+that any cost whatever it is is
+justified in terms of you know the
+
+ align:start position:0%
+justified in terms of you know the
+ 
+
+ align:start position:0%
+justified in terms of you know the
+outcome for my health so these are these
+
+ align:start position:0%
+outcome for my health so these are these
+ 
+
+ align:start position:0%
+outcome for my health so these are these
+are really tough decisions and that the
+
+ align:start position:0%
+are really tough decisions and that the
+ 
+
+ align:start position:0%
+are really tough decisions and that the
+life science system is now right up
+
+ align:start position:0%
+life science system is now right up
+ 
+
+ align:start position:0%
+life science system is now right up
+against this and the whole innovation
+
+ align:start position:0%
+against this and the whole innovation
+ 
+
+ align:start position:0%
+against this and the whole innovation
+model is right up against these so these
+
+ align:start position:0%
+model is right up against these so these
+ 
+
+ align:start position:0%
+model is right up against these so these
+are these are important considerations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brings a question wasn't really
+
+ align:start position:0%
+brings a question wasn't really
+ 
+
+ align:start position:0%
+brings a question wasn't really
+something that the average person could
+
+ align:start position:0%
+something that the average person could
+ 
+
+ align:start position:0%
+something that the average person could
+understand you're asking strictly like
+
+ align:start position:0%
+understand you're asking strictly like
+ 
+
+ align:start position:0%
+understand you're asking strictly like
+what are your ethical beliefs like vote
+
+ align:start position:0%
+what are your ethical beliefs like vote
+ 
+
+ align:start position:0%
+what are your ethical beliefs like vote
+on that I guess that's something that
+
+ align:start position:0%
+on that I guess that's something that
+ 
+
+ align:start position:0%
+on that I guess that's something that
+people who vote on but if you're given
+
+ align:start position:0%
+people who vote on but if you're given
+ 
+
+ align:start position:0%
+people who vote on but if you're given
+like options of like should we find
+
+ align:start position:0%
+like options of like should we find
+ 
+
+ align:start position:0%
+like options of like should we find
+something that will save like X number
+
+ align:start position:0%
+something that will save like X number
+ 
+
+ align:start position:0%
+something that will save like X number
+of people at this cost like kind of
+
+ align:start position:0%
+of people at this cost like kind of
+ 
+
+ align:start position:0%
+of people at this cost like kind of
+weighing that information it's more
+
+ align:start position:0%
+weighing that information it's more
+ 
+
+ align:start position:0%
+weighing that information it's more
+difficult than I think the average
+
+ align:start position:0%
+difficult than I think the average
+ 
+
+ align:start position:0%
+difficult than I think the average
+person is willing to put the time in to
+
+ align:start position:0%
+person is willing to put the time in to
+ 
+
+ align:start position:0%
+person is willing to put the time in to
+understand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I want to push you back to the kind of
+
+ align:start position:0%
+I want to push you back to the kind of
+ 
+
+ align:start position:0%
+I want to push you back to the kind of
+issue that's before us in this class
+
+ align:start position:0%
+issue that's before us in this class
+ 
+
+ align:start position:0%
+issue that's before us in this class
+which is the innovation organization
+
+ align:start position:0%
+which is the innovation organization
+ 
+
+ align:start position:0%
+which is the innovation organization
+model that we've got here so we're
+
+ align:start position:0%
+model that we've got here so we're
+ 
+
+ align:start position:0%
+model that we've got here so we're
+looking at an innovation organization
+
+ align:start position:0%
+looking at an innovation organization
+ 
+
+ align:start position:0%
+looking at an innovation organization
+that evolved in a very historical set of
+
+ align:start position:0%
+that evolved in a very historical set of
+ 
+
+ align:start position:0%
+that evolved in a very historical set of
+ways for the problems when it was in the
+
+ align:start position:0%
+ways for the problems when it was in the
+ 
+
+ align:start position:0%
+ways for the problems when it was in the
+foundation level turned out to be the
+
+ align:start position:0%
+foundation level turned out to be the
+ 
+
+ align:start position:0%
+foundation level turned out to be the
+scientific problems turn out to be
+
+ align:start position:0%
+scientific problems turn out to be
+ 
+
+ align:start position:0%
+scientific problems turn out to be
+different than the way we see them now
+
+ align:start position:0%
+different than the way we see them now
+ 
+
+ align:start position:0%
+different than the way we see them now
+right we tend to see that there are a
+
+ align:start position:0%
+right we tend to see that there are a
+ 
+
+ align:start position:0%
+right we tend to see that there are a
+lot of cross-cutting scientific
+
+ align:start position:0%
+lot of cross-cutting scientific
+ 
+
+ align:start position:0%
+lot of cross-cutting scientific
+approaches that cut across many disease
+
+ align:start position:0%
+approaches that cut across many disease
+ 
+
+ align:start position:0%
+approaches that cut across many disease
+pathways that may be critical for those
+
+ align:start position:0%
+pathways that may be critical for those
+ 
+
+ align:start position:0%
+pathways that may be critical for those
+diseases whereas back then we saw oh
+
+ align:start position:0%
+diseases whereas back then we saw oh
+ 
+
+ align:start position:0%
+diseases whereas back then we saw oh
+there will be one remedy per for each
+
+ align:start position:0%
+there will be one remedy per for each
+ 
+
+ align:start position:0%
+there will be one remedy per for each
+disease right a much earlier stage
+
+ align:start position:0%
+disease right a much earlier stage
+ 
+
+ align:start position:0%
+disease right a much earlier stage
+scientific notion of disease and we're
+
+ align:start position:0%
+scientific notion of disease and we're
+ 
+
+ align:start position:0%
+scientific notion of disease and we're
+caught up in that model and how do we
+
+ align:start position:0%
+caught up in that model and how do we
+ 
+
+ align:start position:0%
+caught up in that model and how do we
+how do we bring change here right how do
+
+ align:start position:0%
+how do we bring change here right how do
+ 
+
+ align:start position:0%
+how do we bring change here right how do
+we we're up against a legacy sector
+
+ align:start position:0%
+we we're up against a legacy sector
+ 
+
+ align:start position:0%
+we we're up against a legacy sector
+promise we'll talk a little bit a little
+
+ align:start position:0%
+promise we'll talk a little bit a little
+ 
+
+ align:start position:0%
+promise we'll talk a little bit a little
+bit how do we bring change into that
+
+ align:start position:0%
+bit how do we bring change into that
+ 
+
+ align:start position:0%
+bit how do we bring change into that
+legacy sector from an organizational
+
+ align:start position:0%
+legacy sector from an organizational
+ 
+
+ align:start position:0%
+legacy sector from an organizational
+point of view it's sort of not an answer
+
+ align:start position:0%
+point of view it's sort of not an answer
+ 
+
+ align:start position:0%
+point of view it's sort of not an answer
+but I cannot answer and going back to
+
+ align:start position:0%
+but I cannot answer and going back to
+ 
+
+ align:start position:0%
+but I cannot answer and going back to
+the attack on peer review as it were I
+
+ align:start position:0%
+the attack on peer review as it were I
+ 
+
+ align:start position:0%
+the attack on peer review as it were I
+think that's a very odd place to start
+
+ align:start position:0%
+think that's a very odd place to start
+ 
+
+ align:start position:0%
+think that's a very odd place to start
+in terms of something to get rid of I
+
+ align:start position:0%
+in terms of something to get rid of I
+ 
+
+ align:start position:0%
+in terms of something to get rid of I
+think there is
+
+ align:start position:0%
+think there is
+ 
+
+ align:start position:0%
+think there is
+there were definitely a lot of
+
+ align:start position:0%
+there were definitely a lot of
+ 
+
+ align:start position:0%
+there were definitely a lot of
+reasonable arguments presented in favor
+
+ align:start position:0%
+reasonable arguments presented in favor
+ 
+
+ align:start position:0%
+reasonable arguments presented in favor
+of adopting something like a DARPA model
+
+ align:start position:0%
+of adopting something like a DARPA model
+ 
+
+ align:start position:0%
+of adopting something like a DARPA model
+but and then going back to your ethics
+
+ align:start position:0%
+but and then going back to your ethics
+ 
+
+ align:start position:0%
+but and then going back to your ethics
+you know you raise the point of
+
+ align:start position:0%
+you know you raise the point of
+ 
+
+ align:start position:0%
+you know you raise the point of
+bioethics consideration it seems to me
+
+ align:start position:0%
+bioethics consideration it seems to me
+ 
+
+ align:start position:0%
+bioethics consideration it seems to me
+that peer reviewing the system of peer
+
+ align:start position:0%
+that peer reviewing the system of peer
+ 
+
+ align:start position:0%
+that peer reviewing the system of peer
+review the values a peer review are so
+
+ align:start position:0%
+review the values a peer review are so
+ 
+
+ align:start position:0%
+review the values a peer review are so
+deeply ingrained in the
+
+ align:start position:0%
+deeply ingrained in the
+ 
+
+ align:start position:0%
+deeply ingrained in the
+biopharmaceutical well more on the
+
+ align:start position:0%
+biopharmaceutical well more on the
+ 
+
+ align:start position:0%
+biopharmaceutical well more on the
+biological women medical research
+
+ align:start position:0%
+biological women medical research
+ 
+
+ align:start position:0%
+biological women medical research
+community it seems like it's very much
+
+ align:start position:0%
+community it seems like it's very much
+ 
+
+ align:start position:0%
+community it seems like it's very much
+part of their values and it would be
+
+ align:start position:0%
+part of their values and it would be
+ 
+
+ align:start position:0%
+part of their values and it would be
+very odd to me to see this separated out
+
+ align:start position:0%
+very odd to me to see this separated out
+ 
+
+ align:start position:0%
+very odd to me to see this separated out
+because I can recognize all of the
+
+ align:start position:0%
+because I can recognize all of the
+ 
+
+ align:start position:0%
+because I can recognize all of the
+detriment to the peer review system and
+
+ align:start position:0%
+detriment to the peer review system and
+ 
+
+ align:start position:0%
+detriment to the peer review system and
+how it can favor incremental not
+
+ align:start position:0%
+how it can favor incremental not
+ 
+
+ align:start position:0%
+how it can favor incremental not
+important research over big innovations
+
+ align:start position:0%
+important research over big innovations
+ 
+
+ align:start position:0%
+important research over big innovations
+and risk takers but it still seems like
+
+ align:start position:0%
+and risk takers but it still seems like
+ 
+
+ align:start position:0%
+and risk takers but it still seems like
+if you remove that barrier then you
+
+ align:start position:0%
+if you remove that barrier then you
+ 
+
+ align:start position:0%
+if you remove that barrier then you
+might have a flood of technical problems
+
+ align:start position:0%
+might have a flood of technical problems
+ 
+
+ align:start position:0%
+might have a flood of technical problems
+that would just hurt the DARPA model
+
+ align:start position:0%
+that would just hurt the DARPA model
+ 
+
+ align:start position:0%
+that would just hurt the DARPA model
+does not work in all circumstances right
+
+ align:start position:0%
+does not work in all circumstances right
+ 
+
+ align:start position:0%
+does not work in all circumstances right
+in other words a DARPA model is very
+
+ align:start position:0%
+in other words a DARPA model is very
+ 
+
+ align:start position:0%
+in other words a DARPA model is very
+much a top-down model a bunch of elite
+
+ align:start position:0%
+much a top-down model a bunch of elite
+ 
+
+ align:start position:0%
+much a top-down model a bunch of elite
+program managers are looking at things
+
+ align:start position:0%
+program managers are looking at things
+ 
+
+ align:start position:0%
+program managers are looking at things
+they want out of the end of the
+
+ align:start position:0%
+they want out of the end of the
+ 
+
+ align:start position:0%
+they want out of the end of the
+innovation pipeline and designing
+
+ align:start position:0%
+innovation pipeline and designing
+ 
+
+ align:start position:0%
+innovation pipeline and designing
+projects to get there and we can
+
+ align:start position:0%
+projects to get there and we can
+ 
+
+ align:start position:0%
+projects to get there and we can
+certainly see why there's room for this
+
+ align:start position:0%
+certainly see why there's room for this
+ 
+
+ align:start position:0%
+certainly see why there's room for this
+model for that kind of projects based
+
+ align:start position:0%
+model for that kind of projects based
+ 
+
+ align:start position:0%
+model for that kind of projects based
+challenge based model NIH offers the
+
+ align:start position:0%
+challenge based model NIH offers the
+ 
+
+ align:start position:0%
+challenge based model NIH offers the
+other side of the coin you know
+
+ align:start position:0%
+other side of the coin you know
+ 
+
+ align:start position:0%
+other side of the coin you know
+researchers propose funding and they get
+
+ align:start position:0%
+researchers propose funding and they get
+ 
+
+ align:start position:0%
+researchers propose funding and they get
+funded based upon the interest and
+
+ align:start position:0%
+funded based upon the interest and
+ 
+
+ align:start position:0%
+funded based upon the interest and
+quality of what they're proposing that's
+
+ align:start position:0%
+quality of what they're proposing that's
+ 
+
+ align:start position:0%
+quality of what they're proposing that's
+very much a bottle of up model in other
+
+ align:start position:0%
+very much a bottle of up model in other
+ 
+
+ align:start position:0%
+very much a bottle of up model in other
+words a lot of people can see a lot of
+
+ align:start position:0%
+words a lot of people can see a lot of
+ 
+
+ align:start position:0%
+words a lot of people can see a lot of
+stuff in the bottom level that a
+
+ align:start position:0%
+stuff in the bottom level that a
+ 
+
+ align:start position:0%
+stuff in the bottom level that a
+top-down model Candice Lacey so I pull
+
+ align:start position:0%
+top-down model Candice Lacey so I pull
+ 
+
+ align:start position:0%
+top-down model Candice Lacey so I pull
+you're right it's not that you want to
+
+ align:start position:0%
+you're right it's not that you want to
+ 
+
+ align:start position:0%
+you're right it's not that you want to
+replace NIH with DARPA right I think
+
+ align:start position:0%
+replace NIH with DARPA right I think
+ 
+
+ align:start position:0%
+replace NIH with DARPA right I think
+what Robert Koch Deegan would say is
+
+ align:start position:0%
+what Robert Koch Deegan would say is
+ 
+
+ align:start position:0%
+what Robert Koch Deegan would say is
+maybe there's room within a large NIH
+
+ align:start position:0%
+maybe there's room within a large NIH
+ 
+
+ align:start position:0%
+maybe there's room within a large NIH
+entity for a DARPA like piece just as
+
+ align:start position:0%
+entity for a DARPA like piece just as
+ 
+
+ align:start position:0%
+entity for a DARPA like piece just as
+there is and that in the defense
+
+ align:start position:0%
+there is and that in the defense
+ 
+
+ align:start position:0%
+there is and that in the defense
+innovation system DARPA is only one
+
+ align:start position:0%
+innovation system DARPA is only one
+ 
+
+ align:start position:0%
+innovation system DARPA is only one
+element of a much larger defense
+
+ align:start position:0%
+element of a much larger defense
+ 
+
+ align:start position:0%
+element of a much larger defense
+research portfolio but it does provide
+
+ align:start position:0%
+research portfolio but it does provide
+ 
+
+ align:start position:0%
+research portfolio but it does provide
+some interesting capability and your
+
+ align:start position:0%
+some interesting capability and your
+ 
+
+ align:start position:0%
+some interesting capability and your
+point about you know and and peer review
+
+ align:start position:0%
+point about you know and and peer review
+ 
+
+ align:start position:0%
+point about you know and and peer review
+does have advantages
+
+ align:start position:0%
+does have advantages
+ 
+
+ align:start position:0%
+does have advantages
+from that bottom-up perspective that a
+
+ align:start position:0%
+from that bottom-up perspective that a
+ 
+
+ align:start position:0%
+from that bottom-up perspective that a
+top-down strong program manager
+
+ align:start position:0%
+top-down strong program manager
+ 
+
+ align:start position:0%
+top-down strong program manager
+perspective will not necessarily be able
+
+ align:start position:0%
+perspective will not necessarily be able
+ 
+
+ align:start position:0%
+perspective will not necessarily be able
+to capture so from a business
+
+ align:start position:0%
+to capture so from a business
+ 
+
+ align:start position:0%
+to capture so from a business
+perspective the thing I'm wondering
+
+ align:start position:0%
+perspective the thing I'm wondering
+ 
+
+ align:start position:0%
+perspective the thing I'm wondering
+about is because there's this trend
+
+ align:start position:0%
+about is because there's this trend
+ 
+
+ align:start position:0%
+about is because there's this trend
+right now I'm called social bonds which
+
+ align:start position:0%
+right now I'm called social bonds which
+ 
+
+ align:start position:0%
+right now I'm called social bonds which
+what they do is like they look at the
+
+ align:start position:0%
+what they do is like they look at the
+ 
+
+ align:start position:0%
+what they do is like they look at the
+parts of society that are really wasting
+
+ align:start position:0%
+parts of society that are really wasting
+ 
+
+ align:start position:0%
+parts of society that are really wasting
+a lot of money and then they create
+
+ align:start position:0%
+a lot of money and then they create
+ 
+
+ align:start position:0%
+a lot of money and then they create
+businesses to solve them and then they
+
+ align:start position:0%
+businesses to solve them and then they
+ 
+
+ align:start position:0%
+businesses to solve them and then they
+get returned because like you can define
+
+ align:start position:0%
+get returned because like you can define
+ 
+
+ align:start position:0%
+get returned because like you can define
+that's why I asked about the blockbuster
+
+ align:start position:0%
+that's why I asked about the blockbuster
+ 
+
+ align:start position:0%
+that's why I asked about the blockbuster
+drug cuz you can define a blockbuster
+
+ align:start position:0%
+drug cuz you can define a blockbuster
+ 
+
+ align:start position:0%
+drug cuz you can define a blockbuster
+drug is also a drug that reduces a ton
+
+ align:start position:0%
+drug is also a drug that reduces a ton
+ 
+
+ align:start position:0%
+drug is also a drug that reduces a ton
+of costs for the government and the
+
+ align:start position:0%
+of costs for the government and the
+ 
+
+ align:start position:0%
+of costs for the government and the
+business model is that government saying
+
+ align:start position:0%
+business model is that government saying
+ 
+
+ align:start position:0%
+business model is that government saying
+oh we're spending a hundred million
+
+ align:start position:0%
+oh we're spending a hundred million
+ 
+
+ align:start position:0%
+oh we're spending a hundred million
+dollars here you solve this problem
+
+ align:start position:0%
+dollars here you solve this problem
+ 
+
+ align:start position:0%
+dollars here you solve this problem
+we're gonna send some of that portion of
+
+ align:start position:0%
+we're gonna send some of that portion of
+ 
+
+ align:start position:0%
+we're gonna send some of that portion of
+the money to you and that's a good way
+
+ align:start position:0%
+the money to you and that's a good way
+ 
+
+ align:start position:0%
+the money to you and that's a good way
+to cut the fat kind of because if the
+
+ align:start position:0%
+to cut the fat kind of because if the
+ 
+
+ align:start position:0%
+to cut the fat kind of because if the
+major problem is we're gonna use all our
+
+ align:start position:0%
+major problem is we're gonna use all our
+ 
+
+ align:start position:0%
+major problem is we're gonna use all our
+budget to solve these diseases there's
+
+ align:start position:0%
+budget to solve these diseases there's
+ 
+
+ align:start position:0%
+budget to solve these diseases there's
+probably like a disease that's like an
+
+ align:start position:0%
+probably like a disease that's like an
+ 
+
+ align:start position:0%
+probably like a disease that's like an
+80% or like a huge proportion because
+
+ align:start position:0%
+80% or like a huge proportion because
+ 
+
+ align:start position:0%
+80% or like a huge proportion because
+it's not going to be a linear
+
+ align:start position:0%
+it's not going to be a linear
+ 
+
+ align:start position:0%
+it's not going to be a linear
+relationship with the cost
+
+ align:start position:0%
+relationship with the cost
+ 
+
+ align:start position:0%
+relationship with the cost
+my other concern too was when you said
+
+ align:start position:0%
+my other concern too was when you said
+ 
+
+ align:start position:0%
+my other concern too was when you said
+that they doubled the budget this
+
+ align:start position:0%
+that they doubled the budget this
+ 
+
+ align:start position:0%
+that they doubled the budget this
+happens a lot in software so it's hard
+
+ align:start position:0%
+happens a lot in software so it's hard
+ 
+
+ align:start position:0%
+happens a lot in software so it's hard
+and not intuitive to understand but it's
+
+ align:start position:0%
+and not intuitive to understand but it's
+ 
+
+ align:start position:0%
+and not intuitive to understand but it's
+like say we're gonna have the lunch
+
+ align:start position:0%
+like say we're gonna have the lunch
+ 
+
+ align:start position:0%
+like say we're gonna have the lunch
+right and I say our budget is a hundred
+
+ align:start position:0%
+right and I say our budget is a hundred
+ 
+
+ align:start position:0%
+right and I say our budget is a hundred
+thousand dollars then like I have to
+
+ align:start position:0%
+thousand dollars then like I have to
+ 
+
+ align:start position:0%
+thousand dollars then like I have to
+toast a bar lunch okay now we have to
+
+ align:start position:0%
+toast a bar lunch okay now we have to
+ 
+
+ align:start position:0%
+toast a bar lunch okay now we have to
+justify one hundred thousand dollars and
+
+ align:start position:0%
+justify one hundred thousand dollars and
+ 
+
+ align:start position:0%
+justify one hundred thousand dollars and
+then we could justify and do like a cool
+
+ align:start position:0%
+then we could justify and do like a cool
+ 
+
+ align:start position:0%
+then we could justify and do like a cool
+examples like right now to the start-up
+
+ align:start position:0%
+examples like right now to the start-up
+ 
+
+ align:start position:0%
+examples like right now to the start-up
+in Silicon Valley that spent like 120
+
+ align:start position:0%
+in Silicon Valley that spent like 120
+ 
+
+ align:start position:0%
+in Silicon Valley that spent like 120
+million dollars to develop a juicer and
+
+ align:start position:0%
+million dollars to develop a juicer and
+ 
+
+ align:start position:0%
+million dollars to develop a juicer and
+today only juice with the machine and
+
+ align:start position:0%
+today only juice with the machine and
+ 
+
+ align:start position:0%
+today only juice with the machine and
+then like a reporter was like I call
+
+ align:start position:0%
+then like a reporter was like I call
+ 
+
+ align:start position:0%
+then like a reporter was like I call
+your bluff and they like squeeze it with
+
+ align:start position:0%
+your bluff and they like squeeze it with
+ 
+
+ align:start position:0%
+your bluff and they like squeeze it with
+their hands and they did it so like my
+
+ align:start position:0%
+their hands and they did it so like my
+ 
+
+ align:start position:0%
+their hands and they did it so like my
+concern is like when you have too much
+
+ align:start position:0%
+concern is like when you have too much
+ 
+
+ align:start position:0%
+concern is like when you have too much
+money you you tend to have to justify
+
+ align:start position:0%
+money you you tend to have to justify
+ 
+
+ align:start position:0%
+money you you tend to have to justify
+things you come with this weird logic
+
+ align:start position:0%
+things you come with this weird logic
+ 
+
+ align:start position:0%
+things you come with this weird logic
+tree and you don't really fundamentally
+
+ align:start position:0%
+tree and you don't really fundamentally
+ 
+
+ align:start position:0%
+tree and you don't really fundamentally
+solve the problem in code like if
+
+ align:start position:0%
+solve the problem in code like if
+ 
+
+ align:start position:0%
+solve the problem in code like if
+there's a piece of code that one coder
+
+ align:start position:0%
+there's a piece of code that one coder
+ 
+
+ align:start position:0%
+there's a piece of code that one coder
+can do but five people actually
+
+ align:start position:0%
+can do but five people actually
+ 
+
+ align:start position:0%
+can do but five people actually
+complicates it makes it way harder and
+
+ align:start position:0%
+complicates it makes it way harder and
+ 
+
+ align:start position:0%
+complicates it makes it way harder and
+now we have people in fighting so that
+
+ align:start position:0%
+now we have people in fighting so that
+ 
+
+ align:start position:0%
+now we have people in fighting so that
+was my big concern of that - I think
+
+ align:start position:0%
+was my big concern of that - I think
+ 
+
+ align:start position:0%
+was my big concern of that - I think
+Marty may be trying to get at it like
+
+ align:start position:0%
+Marty may be trying to get at it like
+ 
+
+ align:start position:0%
+Marty may be trying to get at it like
+this kind of group theory doesn't really
+
+ align:start position:0%
+this kind of group theory doesn't really
+ 
+
+ align:start position:0%
+this kind of group theory doesn't really
+exist so kind of breaks down in NIH
+
+ align:start position:0%
+exist so kind of breaks down in NIH
+ 
+
+ align:start position:0%
+exist so kind of breaks down in NIH
+because it's really
+
+ align:start position:0%
+because it's really
+ 
+
+ align:start position:0%
+because it's really
+these cross-cutting technologies and
+
+ align:start position:0%
+these cross-cutting technologies and
+ 
+
+ align:start position:0%
+these cross-cutting technologies and
+kind of encourage that collaboration and
+
+ align:start position:0%
+kind of encourage that collaboration and
+ 
+
+ align:start position:0%
+kind of encourage that collaboration and
+I think like what I really want to see
+
+ align:start position:0%
+I think like what I really want to see
+ 
+
+ align:start position:0%
+I think like what I really want to see
+out of like the DARPA that they pull is
+
+ align:start position:0%
+out of like the DARPA that they pull is
+ 
+
+ align:start position:0%
+out of like the DARPA that they pull is
+not so much get rid of the peer review
+
+ align:start position:0%
+not so much get rid of the peer review
+ 
+
+ align:start position:0%
+not so much get rid of the peer review
+but like start because DARPA is the
+
+ align:start position:0%
+but like start because DARPA is the
+ 
+
+ align:start position:0%
+but like start because DARPA is the
+ability to kind of pull these great
+
+ align:start position:0%
+ability to kind of pull these great
+ 
+
+ align:start position:0%
+ability to kind of pull these great
+groups together and just like call on a
+
+ align:start position:0%
+groups together and just like call on a
+ 
+
+ align:start position:0%
+groups together and just like call on a
+lot of different folks or a lot of
+
+ align:start position:0%
+lot of different folks or a lot of
+ 
+
+ align:start position:0%
+lot of different folks or a lot of
+different areas and then like direct
+
+ align:start position:0%
+different areas and then like direct
+ 
+
+ align:start position:0%
+different areas and then like direct
+them twice a specific kind of research
+
+ align:start position:0%
+them twice a specific kind of research
+ 
+
+ align:start position:0%
+them twice a specific kind of research
+problem I think for NIH struggles is
+
+ align:start position:0%
+problem I think for NIH struggles is
+ 
+
+ align:start position:0%
+problem I think for NIH struggles is
+like yeah they might have a call to say
+
+ align:start position:0%
+like yeah they might have a call to say
+ 
+
+ align:start position:0%
+like yeah they might have a call to say
+we want to get rid of cancer or like
+
+ align:start position:0%
+we want to get rid of cancer or like
+ 
+
+ align:start position:0%
+we want to get rid of cancer or like
+heart disease but there were a lot of
+
+ align:start position:0%
+heart disease but there were a lot of
+ 
+
+ align:start position:0%
+heart disease but there were a lot of
+different folks kind of working on it
+
+ align:start position:0%
+different folks kind of working on it
+ 
+
+ align:start position:0%
+different folks kind of working on it
+and not a lot of them I would say
+
+ align:start position:0%
+and not a lot of them I would say
+ 
+
+ align:start position:0%
+and not a lot of them I would say
+probably work together in tandem to
+
+ align:start position:0%
+probably work together in tandem to
+ 
+
+ align:start position:0%
+probably work together in tandem to
+really figure out and solve maybe one
+
+ align:start position:0%
+really figure out and solve maybe one
+ 
+
+ align:start position:0%
+really figure out and solve maybe one
+aspect that problem for you know maybe
+
+ align:start position:0%
+aspect that problem for you know maybe
+ 
+
+ align:start position:0%
+aspect that problem for you know maybe
+10 years and they focus on you know a
+
+ align:start position:0%
+10 years and they focus on you know a
+ 
+
+ align:start position:0%
+10 years and they focus on you know a
+different aspect of heart disease to
+
+ align:start position:0%
+different aspect of heart disease to
+ 
+
+ align:start position:0%
+different aspect of heart disease to
+work in a different lab and I think NIH
+
+ align:start position:0%
+work in a different lab and I think NIH
+ 
+
+ align:start position:0%
+work in a different lab and I think NIH
+really struggles and kind of pulling
+
+ align:start position:0%
+really struggles and kind of pulling
+ 
+
+ align:start position:0%
+really struggles and kind of pulling
+together these cross-cutting
+
+ align:start position:0%
+together these cross-cutting
+ 
+
+ align:start position:0%
+together these cross-cutting
+technologies because there's no one kind
+
+ align:start position:0%
+technologies because there's no one kind
+ 
+
+ align:start position:0%
+technologies because there's no one kind
+of pulling them together and they kind
+
+ align:start position:0%
+of pulling them together and they kind
+ 
+
+ align:start position:0%
+of pulling them together and they kind
+of just leave it up to the discretion of
+
+ align:start position:0%
+of just leave it up to the discretion of
+ 
+
+ align:start position:0%
+of just leave it up to the discretion of
+the researchers to scientists needs to
+
+ align:start position:0%
+the researchers to scientists needs to
+ 
+
+ align:start position:0%
+the researchers to scientists needs to
+come up with incremental advances rather
+
+ align:start position:0%
+come up with incremental advances rather
+ 
+
+ align:start position:0%
+come up with incremental advances rather
+than like really calling for not only am
+
+ align:start position:0%
+than like really calling for not only am
+ 
+
+ align:start position:0%
+than like really calling for not only am
+i calling for big calls are like big
+
+ align:start position:0%
+i calling for big calls are like big
+ 
+
+ align:start position:0%
+i calling for big calls are like big
+research projects but also like funding
+
+ align:start position:0%
+research projects but also like funding
+ 
+
+ align:start position:0%
+research projects but also like funding
+and making it possible for great groups
+
+ align:start position:0%
+and making it possible for great groups
+ 
+
+ align:start position:0%
+and making it possible for great groups
+to work on these research projects
+
+ align:start position:0%
+to work on these research projects
+ 
+
+ align:start position:0%
+to work on these research projects
+martine you want to give us some closing
+
+ align:start position:0%
+martine you want to give us some closing
+ 
+
+ align:start position:0%
+martine you want to give us some closing
+thoughts on these two pieces I'm sorry
+
+ align:start position:0%
+thoughts on these two pieces I'm sorry
+ 
+
+ align:start position:0%
+thoughts on these two pieces I'm sorry
+max did you had a quick question so
+
+ align:start position:0%
+max did you had a quick question so
+ 
+
+ align:start position:0%
+max did you had a quick question so
+given that this was published twenty one
+
+ align:start position:0%
+given that this was published twenty one
+ 
+
+ align:start position:0%
+given that this was published twenty one
+years ago give or take I'm curious yeah
+
+ align:start position:0%
+years ago give or take I'm curious yeah
+ 
+
+ align:start position:0%
+years ago give or take I'm curious yeah
+did NIH ever attempt anything like this
+
+ align:start position:0%
+did NIH ever attempt anything like this
+ 
+
+ align:start position:0%
+did NIH ever attempt anything like this
+because you know we've had some
+
+ align:start position:0%
+because you know we've had some
+ 
+
+ align:start position:0%
+because you know we've had some
+significant time period did they at
+
+ align:start position:0%
+significant time period did they at
+ 
+
+ align:start position:0%
+significant time period did they at
+least look at their to decide no and
+
+ align:start position:0%
+least look at their to decide no and
+ 
+
+ align:start position:0%
+least look at their to decide no and
+also how much prison do you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it was a threatening piece to the NIH
+
+ align:start position:0%
+it was a threatening piece to the NIH
+ 
+
+ align:start position:0%
+it was a threatening piece to the NIH
+and life science community frankly
+
+ align:start position:0%
+and life science community frankly
+ 
+
+ align:start position:0%
+and life science community frankly
+arguing that there is there may be an
+
+ align:start position:0%
+arguing that there is there may be an
+ 
+
+ align:start position:0%
+arguing that there is there may be an
+additional model that you all need to
+
+ align:start position:0%
+additional model that you all need to
+ 
+
+ align:start position:0%
+additional model that you all need to
+consider so was not received with open
+
+ align:start position:0%
+consider so was not received with open
+ 
+
+ align:start position:0%
+consider so was not received with open
+arms now in fact the the current NIH
+
+ align:start position:0%
+arms now in fact the the current NIH
+ 
+
+ align:start position:0%
+arms now in fact the the current NIH
+director Collins has early on in his
+
+ align:start position:0%
+director Collins has early on in his
+ 
+
+ align:start position:0%
+director Collins has early on in his
+tenure as director latched on to the
+
+ align:start position:0%
+tenure as director latched on to the
+ 
+
+ align:start position:0%
+tenure as director latched on to the
+problem that NIH has got in doing
+
+ align:start position:0%
+problem that NIH has got in doing
+ 
+
+ align:start position:0%
+problem that NIH has got in doing
+translational work in other words moving
+
+ align:start position:0%
+translational work in other words moving
+ 
+
+ align:start position:0%
+translational work in other words moving
+a technology from the basic stage into
+
+ align:start position:0%
+a technology from the basic stage into
+ 
+
+ align:start position:0%
+a technology from the basic stage into
+follow-on sectors and doing the handoff
+
+ align:start position:0%
+follow-on sectors and doing the handoff
+ 
+
+ align:start position:0%
+follow-on sectors and doing the handoff
+to the private sectors so Collins began
+
+ align:start position:0%
+to the private sectors so Collins began
+ 
+
+ align:start position:0%
+to the private sectors so Collins began
+to focus on that problem and there was
+
+ align:start position:0%
+to focus on that problem and there was
+ 
+
+ align:start position:0%
+to focus on that problem and there was
+discussion at that time of doing
+
+ align:start position:0%
+discussion at that time of doing
+ 
+
+ align:start position:0%
+discussion at that time of doing
+something like a DARPA so his effort to
+
+ align:start position:0%
+something like a DARPA so his effort to
+ 
+
+ align:start position:0%
+something like a DARPA so his effort to
+create end cats to do translational
+
+ align:start position:0%
+create end cats to do translational
+ 
+
+ align:start position:0%
+create end cats to do translational
+medicine the director that he hired had
+
+ align:start position:0%
+medicine the director that he hired had
+ 
+
+ align:start position:0%
+medicine the director that he hired had
+that new Institute and he had to close
+
+ align:start position:0%
+that new Institute and he had to close
+ 
+
+ align:start position:0%
+that new Institute and he had to close
+another one to do it
+
+ align:start position:0%
+another one to do it
+ 
+
+ align:start position:0%
+another one to do it
+right actually really began thinking
+
+ align:start position:0%
+right actually really began thinking
+ 
+
+ align:start position:0%
+right actually really began thinking
+seriously about should there be kind of
+
+ align:start position:0%
+seriously about should there be kind of
+ 
+
+ align:start position:0%
+seriously about should there be kind of
+DARPA like elements in this new end
+
+ align:start position:0%
+DARPA like elements in this new end
+ 
+
+ align:start position:0%
+DARPA like elements in this new end
+cat's entity Chris Austin who is that
+
+ align:start position:0%
+cat's entity Chris Austin who is that
+ 
+
+ align:start position:0%
+cat's entity Chris Austin who is that
+director very talented and very
+
+ align:start position:0%
+director very talented and very
+ 
+
+ align:start position:0%
+director very talented and very
+interesting person however you know just
+
+ align:start position:0%
+interesting person however you know just
+ 
+
+ align:start position:0%
+interesting person however you know just
+didn't have the resources to set up a
+
+ align:start position:0%
+didn't have the resources to set up a
+ 
+
+ align:start position:0%
+didn't have the resources to set up a
+whole new kind of entity within his
+
+ align:start position:0%
+whole new kind of entity within his
+ 
+
+ align:start position:0%
+whole new kind of entity within his
+MCATs piece but so it's an idea that
+
+ align:start position:0%
+MCATs piece but so it's an idea that
+ 
+
+ align:start position:0%
+MCATs piece but so it's an idea that
+continues to kind of kick around here
+
+ align:start position:0%
+continues to kind of kick around here
+ 
+
+ align:start position:0%
+continues to kind of kick around here
+and there and would be frankly an
+
+ align:start position:0%
+and there and would be frankly an
+ 
+
+ align:start position:0%
+and there and would be frankly an
+interesting I would view it as an
+
+ align:start position:0%
+interesting I would view it as an
+ 
+
+ align:start position:0%
+interesting I would view it as an
+interesting additional feature for NIH
+
+ align:start position:0%
+interesting additional feature for NIH
+ 
+
+ align:start position:0%
+interesting additional feature for NIH
+to do some things that it can't really
+
+ align:start position:0%
+to do some things that it can't really
+ 
+
+ align:start position:0%
+to do some things that it can't really
+do without this kind of organizational
+
+ align:start position:0%
+do without this kind of organizational
+ 
+
+ align:start position:0%
+do without this kind of organizational
+model so I think there's organizational
+
+ align:start position:0%
+model so I think there's organizational
+ 
+
+ align:start position:0%
+model so I think there's organizational
+lessons here that we can take from the
+
+ align:start position:0%
+lessons here that we can take from the
+ 
+
+ align:start position:0%
+lessons here that we can take from the
+issues we've been reviewing and apply it
+
+ align:start position:0%
+issues we've been reviewing and apply it
+ 
+
+ align:start position:0%
+issues we've been reviewing and apply it
+to a long-established research entity to
+
+ align:start position:0%
+to a long-established research entity to
+ 
+
+ align:start position:0%
+to a long-established research entity to
+kind of create new things in the model
+
+ align:start position:0%
+kind of create new things in the model
+ 
+
+ align:start position:0%
+kind of create new things in the model
+how about some closing thoughts Martine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's a lot of
+
+ align:start position:0%
+there's a lot of
+ 
+
+ align:start position:0%
+there's a lot of
+some areas that aren't being touched
+
+ align:start position:0%
+some areas that aren't being touched
+ 
+
+ align:start position:0%
+some areas that aren't being touched
+into I've been trying to solve and then
+
+ align:start position:0%
+into I've been trying to solve and then
+ 
+
+ align:start position:0%
+into I've been trying to solve and then
+we discussed our foe which is might be a
+
+ align:start position:0%
+we discussed our foe which is might be a
+ 
+
+ align:start position:0%
+we discussed our foe which is might be a
+good way of solving it but it seems like
+
+ align:start position:0%
+good way of solving it but it seems like
+ 
+
+ align:start position:0%
+good way of solving it but it seems like
+it won't fit in well with NIH but there
+
+ align:start position:0%
+it won't fit in well with NIH but there
+ 
+
+ align:start position:0%
+it won't fit in well with NIH but there
+is a structural dissonance I would say
+
+ align:start position:0%
+is a structural dissonance I would say
+ 
+
+ align:start position:0%
+is a structural dissonance I would say
+in terms of the this form factor does
+
+ align:start position:0%
+in terms of the this form factor does
+ 
+
+ align:start position:0%
+in terms of the this form factor does
+not work for these kinds of problems and
+
+ align:start position:0%
+not work for these kinds of problems and
+ 
+
+ align:start position:0%
+not work for these kinds of problems and
+it might also be the group kind of
+
+ align:start position:0%
+it might also be the group kind of
+ 
+
+ align:start position:0%
+it might also be the group kind of
+groupthink in the area that affects
+
+ align:start position:0%
+groupthink in the area that affects
+ 
+
+ align:start position:0%
+groupthink in the area that affects
+their ability to solve these kinds of
+
+ align:start position:0%
+their ability to solve these kinds of
+ 
+
+ align:start position:0%
+their ability to solve these kinds of
+problems so might be better for there to
+
+ align:start position:0%
+problems so might be better for there to
+ 
+
+ align:start position:0%
+problems so might be better for there to
+be like a DARPA NIH but not at NIH or
+
+ align:start position:0%
+be like a DARPA NIH but not at NIH or
+ 
+
+ align:start position:0%
+be like a DARPA NIH but not at NIH or
+nearby because it might be too difficult
+
+ align:start position:0%
+nearby because it might be too difficult
+ 
+
+ align:start position:0%
+nearby because it might be too difficult
+and also how do you create natural
+
+ align:start position:0%
+and also how do you create natural
+ 
+
+ align:start position:0%
+and also how do you create natural
+incentives for the researchers but it
+
+ align:start position:0%
+incentives for the researchers but it
+ 
+
+ align:start position:0%
+incentives for the researchers but it
+seems like they do these kind of
+
+ align:start position:0%
+seems like they do these kind of
+ 
+
+ align:start position:0%
+seems like they do these kind of
+leapfrogging research initiatives
+
+ align:start position:0%
+leapfrogging research initiatives
+ 
+
+ align:start position:0%
+leapfrogging research initiatives
+because it's it's a lot simpler and they
+
+ align:start position:0%
+because it's it's a lot simpler and they
+ 
+
+ align:start position:0%
+because it's it's a lot simpler and they
+have a lot to lose if they do fail and
+
+ align:start position:0%
+have a lot to lose if they do fail and
+ 
+
+ align:start position:0%
+have a lot to lose if they do fail and
+so how do you create this kind of
+
+ align:start position:0%
+so how do you create this kind of
+ 
+
+ align:start position:0%
+so how do you create this kind of
+comfort for researchers so that even if
+
+ align:start position:0%
+comfort for researchers so that even if
+ 
+
+ align:start position:0%
+comfort for researchers so that even if
+they do fail to get something a reward
+
+ align:start position:0%
+they do fail to get something a reward
+ 
+
+ align:start position:0%
+they do fail to get something a reward
+and how do they get recognition for that
+
+ align:start position:0%
+and how do they get recognition for that
+ 
+
+ align:start position:0%
+and how do they get recognition for that
+sacrifice up there
+
+ align:start position:0%
+sacrifice up there
+ 
+
+ align:start position:0%
+sacrifice up there
+will you call it academic career right I
+
+ align:start position:0%
+will you call it academic career right I
+ 
+
+ align:start position:0%
+will you call it academic career right I
+mean that's another issue too which is
+
+ align:start position:0%
+mean that's another issue too which is
+ 
+
+ align:start position:0%
+mean that's another issue too which is
+having multiple PI's you know on the
+
+ align:start position:0%
+having multiple PI's you know on the
+ 
+
+ align:start position:0%
+having multiple PI's you know on the
+problem is complicated in an ro1 award
+
+ align:start position:0%
+problem is complicated in an ro1 award
+ 
+
+ align:start position:0%
+problem is complicated in an ro1 award
+process that focuses on the single PI
+
+ align:start position:0%
+process that focuses on the single PI
+ 
+
+ align:start position:0%
+process that focuses on the single PI
+let me go on to the next couple of next
+
+ align:start position:0%
+let me go on to the next couple of next
+ 
+
+ align:start position:0%
+let me go on to the next couple of next
+couple of readings and we'll do them as
+
+ align:start position:0%
+couple of readings and we'll do them as
+ 
+
+ align:start position:0%
+couple of readings and we'll do them as
+a pair so the infectious disease Society
+
+ align:start position:0%
+a pair so the infectious disease Society
+ 
+
+ align:start position:0%
+a pair so the infectious disease Society
+of America has this report called bed
+
+ align:start position:0%
+of America has this report called bed
+ 
+
+ align:start position:0%
+of America has this report called bed
+bugs no drugs which essentially
+
+ align:start position:0%
+bugs no drugs which essentially
+ 
+
+ align:start position:0%
+bugs no drugs which essentially
+summarizes the whole problem and then
+
+ align:start position:0%
+summarizes the whole problem and then
+ 
+
+ align:start position:0%
+summarizes the whole problem and then
+the Food and Drug Administration has a
+
+ align:start position:0%
+the Food and Drug Administration has a
+ 
+
+ align:start position:0%
+the Food and Drug Administration has a
+paper on innovation or stagnation right
+
+ align:start position:0%
+paper on innovation or stagnation right
+ 
+
+ align:start position:0%
+paper on innovation or stagnation right
+which focuses on some of the problems
+
+ align:start position:0%
+which focuses on some of the problems
+ 
+
+ align:start position:0%
+which focuses on some of the problems
+they face so let's do let's do those and
+
+ align:start position:0%
+they face so let's do let's do those and
+ 
+
+ align:start position:0%
+they face so let's do let's do those and
+Chloe do you have those or Martini have
+
+ align:start position:0%
+Chloe do you have those or Martini have
+ 
+
+ align:start position:0%
+Chloe do you have those or Martini have
+one of those bad bugs no drugs the
+
+ align:start position:0%
+one of those bad bugs no drugs the
+ 
+
+ align:start position:0%
+one of those bad bugs no drugs the
+infectious disease Society
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay all right well Chloe which one do
+
+ align:start position:0%
+okay all right well Chloe which one do
+ 
+
+ align:start position:0%
+okay all right well Chloe which one do
+you have you of the FDA one the
+
+ align:start position:0%
+you have you of the FDA one the
+ 
+
+ align:start position:0%
+you have you of the FDA one the
+innovation stagnation all right fine
+
+ align:start position:0%
+innovation stagnation all right fine
+ 
+
+ align:start position:0%
+innovation stagnation all right fine
+okay I mean the title gives this story
+
+ align:start position:0%
+okay I mean the title gives this story
+ 
+
+ align:start position:0%
+okay I mean the title gives this story
+away and this is the infectious disease
+
+ align:start position:0%
+away and this is the infectious disease
+ 
+
+ align:start position:0%
+away and this is the infectious disease
+Society and you know they note that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+resistance to bacteria I think as
+
+ align:start position:0%
+resistance to bacteria I think as
+ 
+
+ align:start position:0%
+resistance to bacteria I think as
+everybody in this classroom knows is
+
+ align:start position:0%
+everybody in this classroom knows is
+ 
+
+ align:start position:0%
+everybody in this classroom knows is
+very much on the rise and that and again
+
+ align:start position:0%
+very much on the rise and that and again
+ 
+
+ align:start position:0%
+very much on the rise and that and again
+this report was written a few years ago
+
+ align:start position:0%
+this report was written a few years ago
+ 
+
+ align:start position:0%
+this report was written a few years ago
+two million people in US hospitals are
+
+ align:start position:0%
+two million people in US hospitals are
+ 
+
+ align:start position:0%
+two million people in US hospitals are
+going to get bacterial infections in the
+
+ align:start position:0%
+going to get bacterial infections in the
+ 
+
+ align:start position:0%
+going to get bacterial infections in the
+hospital and ninety thousand of them are
+
+ align:start position:0%
+hospital and ninety thousand of them are
+ 
+
+ align:start position:0%
+hospital and ninety thousand of them are
+going to die that is a staggering number
+
+ align:start position:0%
+going to die that is a staggering number
+ 
+
+ align:start position:0%
+going to die that is a staggering number
+right we lose 30,000 people a year in
+
+ align:start position:0%
+right we lose 30,000 people a year in
+ 
+
+ align:start position:0%
+right we lose 30,000 people a year in
+automobile accidents we're losing three
+
+ align:start position:0%
+automobile accidents we're losing three
+ 
+
+ align:start position:0%
+automobile accidents we're losing three
+times that money that many in hospitals
+
+ align:start position:0%
+times that money that many in hospitals
+ 
+
+ align:start position:0%
+times that money that many in hospitals
+so talk about tolerance for risk right
+
+ align:start position:0%
+so talk about tolerance for risk right
+ 
+
+ align:start position:0%
+so talk about tolerance for risk right
+Americans haven't fully woken up to this
+
+ align:start position:0%
+Americans haven't fully woken up to this
+ 
+
+ align:start position:0%
+Americans haven't fully woken up to this
+so hospitals are increasingly a
+
+ align:start position:0%
+so hospitals are increasingly a
+ 
+
+ align:start position:0%
+so hospitals are increasingly a
+dangerous place to be and the only two
+
+ align:start position:0%
+dangerous place to be and the only two
+ 
+
+ align:start position:0%
+dangerous place to be and the only two
+classes of antibiotics have been
+
+ align:start position:0%
+classes of antibiotics have been
+ 
+
+ align:start position:0%
+classes of antibiotics have been
+developed at the time this was written
+
+ align:start position:0%
+developed at the time this was written
+ 
+
+ align:start position:0%
+developed at the time this was written
+and all in the previous 30 years and one
+
+ align:start position:0%
+and all in the previous 30 years and one
+ 
+
+ align:start position:0%
+and all in the previous 30 years and one
+of those is already facing resistance
+
+ align:start position:0%
+of those is already facing resistance
+ 
+
+ align:start position:0%
+of those is already facing resistance
+and this kind of endless cycle of build
+
+ align:start position:0%
+and this kind of endless cycle of build
+ 
+
+ align:start position:0%
+and this kind of endless cycle of build
+up a resistance that that bacterial
+
+ align:start position:0%
+up a resistance that that bacterial
+ 
+
+ align:start position:0%
+up a resistance that that bacterial
+sources go through and it's by the late
+
+ align:start position:0%
+sources go through and it's by the late
+ 
+
+ align:start position:0%
+sources go through and it's by the late
+1960s 80% of staph bacteria were
+
+ align:start position:0%
+1960s 80% of staph bacteria were
+ 
+
+ align:start position:0%
+1960s 80% of staph bacteria were
+penicillin resistant and in pneumonia
+
+ align:start position:0%
+penicillin resistant and in pneumonia
+ 
+
+ align:start position:0%
+penicillin resistant and in pneumonia
+forty percent of the infections were
+
+ align:start position:0%
+forty percent of the infections were
+ 
+
+ align:start position:0%
+forty percent of the infections were
+resistant to one drug and 15 percent to
+
+ align:start position:0%
+resistant to one drug and 15 percent to
+ 
+
+ align:start position:0%
+resistant to one drug and 15 percent to
+the next three right so this is not this
+
+ align:start position:0%
+the next three right so this is not this
+ 
+
+ align:start position:0%
+the next three right so this is not this
+is there's a serious growing problem yet
+
+ align:start position:0%
+is there's a serious growing problem yet
+ 
+
+ align:start position:0%
+is there's a serious growing problem yet
+because of the blockbuster drug model
+
+ align:start position:0%
+because of the blockbuster drug model
+ 
+
+ align:start position:0%
+because of the blockbuster drug model
+there's no incentive for drug companies
+
+ align:start position:0%
+there's no incentive for drug companies
+ 
+
+ align:start position:0%
+there's no incentive for drug companies
+or biotechs to go after these
+
+ align:start position:0%
+or biotechs to go after these
+ 
+
+ align:start position:0%
+or biotechs to go after these
+antibiotics because they cure the
+
+ align:start position:0%
+antibiotics because they cure the
+ 
+
+ align:start position:0%
+antibiotics because they cure the
+problem right so you take the antibiotic
+
+ align:start position:0%
+problem right so you take the antibiotic
+ 
+
+ align:start position:0%
+problem right so you take the antibiotic
+for two weeks and the problem is solved
+
+ align:start position:0%
+for two weeks and the problem is solved
+ 
+
+ align:start position:0%
+for two weeks and the problem is solved
+what you want under the blockbuster drug
+
+ align:start position:0%
+what you want under the blockbuster drug
+ 
+
+ align:start position:0%
+what you want under the blockbuster drug
+model is something that I'm gonna have
+
+ align:start position:0%
+model is something that I'm gonna have
+ 
+
+ align:start position:0%
+model is something that I'm gonna have
+to take for the rest of my life for
+
+ align:start position:0%
+to take for the rest of my life for
+ 
+
+ align:start position:0%
+to take for the rest of my life for
+$100,000 a year right you don't really
+
+ align:start position:0%
+$100,000 a year right you don't really
+ 
+
+ align:start position:0%
+$100,000 a year right you don't really
+want to cure it do you want to create
+
+ align:start position:0%
+want to cure it do you want to create
+ 
+
+ align:start position:0%
+want to cure it do you want to create
+incremental advances that manage the
+
+ align:start position:0%
+incremental advances that manage the
+ 
+
+ align:start position:0%
+incremental advances that manage the
+problem whereas the antibiotic actually
+
+ align:start position:0%
+problem whereas the antibiotic actually
+ 
+
+ align:start position:0%
+problem whereas the antibiotic actually
+cures the problem so there's very little
+
+ align:start position:0%
+cures the problem so there's very little
+ 
+
+ align:start position:0%
+cures the problem so there's very little
+incentive since there's no economic
+
+ align:start position:0%
+incentive since there's no economic
+ 
+
+ align:start position:0%
+incentive since there's no economic
+return here a model that works there's
+
+ align:start position:0%
+return here a model that works there's
+ 
+
+ align:start position:0%
+return here a model that works there's
+very little incentive to go after these
+
+ align:start position:0%
+very little incentive to go after these
+ 
+
+ align:start position:0%
+very little incentive to go after these
+antibiotic problems they work too well
+
+ align:start position:0%
+antibiotic problems they work too well
+ 
+
+ align:start position:0%
+antibiotic problems they work too well
+too fast so it's a very weak return on
+
+ align:start position:0%
+too fast so it's a very weak return on
+ 
+
+ align:start position:0%
+too fast so it's a very weak return on
+investment and successful antibiotics
+
+ align:start position:0%
+investment and successful antibiotics
+ 
+
+ align:start position:0%
+investment and successful antibiotics
+are just too successful to justify the
+
+ align:start position:0%
+are just too successful to justify the
+ 
+
+ align:start position:0%
+are just too successful to justify the
+investment cost so everybody is aware of
+
+ align:start position:0%
+investment cost so everybody is aware of
+ 
+
+ align:start position:0%
+investment cost so everybody is aware of
+this Elias Zerhouni who preceded Francis
+
+ align:start position:0%
+this Elias Zerhouni who preceded Francis
+ 
+
+ align:start position:0%
+this Elias Zerhouni who preceded Francis
+Collins as head of NIH you know had this
+
+ align:start position:0%
+Collins as head of NIH you know had this
+ 
+
+ align:start position:0%
+Collins as head of NIH you know had this
+road map model and this was certainly on
+
+ align:start position:0%
+road map model and this was certainly on
+ 
+
+ align:start position:0%
+road map model and this was certainly on
+that list of cross-cutting issues that
+
+ align:start position:0%
+that list of cross-cutting issues that
+ 
+
+ align:start position:0%
+that list of cross-cutting issues that
+need to be dealt with but how do you get
+
+ align:start position:0%
+need to be dealt with but how do you get
+ 
+
+ align:start position:0%
+need to be dealt with but how do you get
+around the kind of model here the
+
+ align:start position:0%
+around the kind of model here the
+ 
+
+ align:start position:0%
+around the kind of model here the
+economic problematic blockbuster drug
+
+ align:start position:0%
+economic problematic blockbuster drug
+ 
+
+ align:start position:0%
+economic problematic blockbuster drug
+model here so I mean they've been a
+
+ align:start position:0%
+model here so I mean they've been a
+ 
+
+ align:start position:0%
+model here so I mean they've been a
+variety of ideas advanced there was
+
+ align:start position:0%
+variety of ideas advanced there was
+ 
+
+ align:start position:0%
+variety of ideas advanced there was
+Bioshield legislation to deal with bio
+
+ align:start position:0%
+Bioshield legislation to deal with bio
+ 
+
+ align:start position:0%
+Bioshield legislation to deal with bio
+threats but it could also bear on
+
+ align:start position:0%
+threats but it could also bear on
+ 
+
+ align:start position:0%
+threats but it could also bear on
+infectious diseases the idea there was
+
+ align:start position:0%
+infectious diseases the idea there was
+ 
+
+ align:start position:0%
+infectious diseases the idea there was
+for bio thread why would anybody develop
+
+ align:start position:0%
+for bio thread why would anybody develop
+ 
+
+ align:start position:0%
+for bio thread why would anybody develop
+a bio thread remedy because you the drug
+
+ align:start position:0%
+a bio thread remedy because you the drug
+ 
+
+ align:start position:0%
+a bio thread remedy because you the drug
+would only be sold if there was a
+
+ align:start position:0%
+would only be sold if there was a
+ 
+
+ align:start position:0%
+would only be sold if there was a
+completely unpredictable terrible
+
+ align:start position:0%
+completely unpredictable terrible
+ 
+
+ align:start position:0%
+completely unpredictable terrible
+national disaster so are you gonna take
+
+ align:start position:0%
+national disaster so are you gonna take
+ 
+
+ align:start position:0%
+national disaster so are you gonna take
+all the risks and go through the 1.4
+
+ align:start position:0%
+all the risks and go through the 1.4
+ 
+
+ align:start position:0%
+all the risks and go through the 1.4
+billion dollar clinical trial process to
+
+ align:start position:0%
+billion dollar clinical trial process to
+ 
+
+ align:start position:0%
+billion dollar clinical trial process to
+develop a remedy for something that may
+
+ align:start position:0%
+develop a remedy for something that may
+ 
+
+ align:start position:0%
+develop a remedy for something that may
+well never be used right similar kind of
+
+ align:start position:0%
+well never be used right similar kind of
+ 
+
+ align:start position:0%
+well never be used right similar kind of
+problem for antibiotic drugs so the
+
+ align:start position:0%
+problem for antibiotic drugs so the
+ 
+
+ align:start position:0%
+problem for antibiotic drugs so the
+infectious disease Society said wait a
+
+ align:start position:0%
+infectious disease Society said wait a
+ 
+
+ align:start position:0%
+infectious disease Society said wait a
+minute the same model that would deal
+
+ align:start position:0%
+minute the same model that would deal
+ 
+
+ align:start position:0%
+minute the same model that would deal
+with bio threats which is that the
+
+ align:start position:0%
+with bio threats which is that the
+ 
+
+ align:start position:0%
+with bio threats which is that the
+government would agree to buy a certain
+
+ align:start position:0%
+government would agree to buy a certain
+ 
+
+ align:start position:0%
+government would agree to buy a certain
+number of dosages certain a certain
+
+ align:start position:0%
+number of dosages certain a certain
+ 
+
+ align:start position:0%
+number of dosages certain a certain
+volume of the remedy at a set price if
+
+ align:start position:0%
+volume of the remedy at a set price if
+ 
+
+ align:start position:0%
+volume of the remedy at a set price if
+you developed the remedy so the risk on
+
+ align:start position:0%
+you developed the remedy so the risk on
+ 
+
+ align:start position:0%
+you developed the remedy so the risk on
+the part of the government is actually
+
+ align:start position:0%
+the part of the government is actually
+ 
+
+ align:start position:0%
+the part of the government is actually
+pretty low it only has to buy something
+
+ align:start position:0%
+pretty low it only has to buy something
+ 
+
+ align:start position:0%
+pretty low it only has to buy something
+if you solve the problem
+
+ align:start position:0%
+if you solve the problem
+ 
+
+ align:start position:0%
+if you solve the problem
+but then of course that's what biotechs
+
+ align:start position:0%
+but then of course that's what biotechs
+ 
+
+ align:start position:0%
+but then of course that's what biotechs
+do anyway that's the model economic
+
+ align:start position:0%
+do anyway that's the model economic
+ 
+
+ align:start position:0%
+do anyway that's the model economic
+model they work off of so could the
+
+ align:start position:0%
+model they work off of so could the
+ 
+
+ align:start position:0%
+model they work off of so could the
+government intervene in this sector and
+
+ align:start position:0%
+government intervene in this sector and
+ 
+
+ align:start position:0%
+government intervene in this sector and
+it's in effect really change around the
+
+ align:start position:0%
+it's in effect really change around the
+ 
+
+ align:start position:0%
+it's in effect really change around the
+risk/reward model so ideas like this
+
+ align:start position:0%
+risk/reward model so ideas like this
+ 
+
+ align:start position:0%
+risk/reward model so ideas like this
+kind of come to bear here we certainly
+
+ align:start position:0%
+kind of come to bear here we certainly
+ 
+
+ align:start position:0%
+kind of come to bear here we certainly
+haven't solved this problem that remains
+
+ align:start position:0%
+haven't solved this problem that remains
+ 
+
+ align:start position:0%
+haven't solved this problem that remains
+very much with us but it illustrates
+
+ align:start position:0%
+very much with us but it illustrates
+ 
+
+ align:start position:0%
+very much with us but it illustrates
+what the issues are this other report
+
+ align:start position:0%
+what the issues are this other report
+ 
+
+ align:start position:0%
+what the issues are this other report
+from the FDA innovation stagnation
+
+ align:start position:0%
+from the FDA innovation stagnation
+ 
+
+ align:start position:0%
+from the FDA innovation stagnation
+challenge an opportunity on the critical
+
+ align:start position:0%
+challenge an opportunity on the critical
+ 
+
+ align:start position:0%
+challenge an opportunity on the critical
+path to new medical products and both
+
+ align:start position:0%
+path to new medical products and both
+ 
+
+ align:start position:0%
+path to new medical products and both
+these reports by the way have been
+
+ align:start position:0%
+these reports by the way have been
+ 
+
+ align:start position:0%
+these reports by the way have been
+updated I put the originals in which are
+
+ align:start position:0%
+updated I put the originals in which are
+ 
+
+ align:start position:0%
+updated I put the originals in which are
+fairly hard-hitting but they've been
+
+ align:start position:0%
+fairly hard-hitting but they've been
+ 
+
+ align:start position:0%
+fairly hard-hitting but they've been
+updated since then by these
+
+ align:start position:0%
+updated since then by these
+ 
+
+ align:start position:0%
+updated since then by these
+organizations so you can get later
+
+ align:start position:0%
+organizations so you can get later
+ 
+
+ align:start position:0%
+organizations so you can get later
+versions FDA does not have its own
+
+ align:start position:0%
+versions FDA does not have its own
+ 
+
+ align:start position:0%
+versions FDA does not have its own
+substantial research arm NIH does the
+
+ align:start position:0%
+substantial research arm NIH does the
+ 
+
+ align:start position:0%
+substantial research arm NIH does the
+medical research yet we're not we're not
+
+ align:start position:0%
+medical research yet we're not we're not
+ 
+
+ align:start position:0%
+medical research yet we're not we're not
+doing research on how to get a better
+
+ align:start position:0%
+doing research on how to get a better
+ 
+
+ align:start position:0%
+doing research on how to get a better
+more reliable and certainly speedier
+
+ align:start position:0%
+more reliable and certainly speedier
+ 
+
+ align:start position:0%
+more reliable and certainly speedier
+evaluation and approval process for FDA
+
+ align:start position:0%
+evaluation and approval process for FDA
+ 
+
+ align:start position:0%
+evaluation and approval process for FDA
+right we don't have that there's nobody
+
+ align:start position:0%
+right we don't have that there's nobody
+ 
+
+ align:start position:0%
+right we don't have that there's nobody
+on that problem NIH does not view that
+
+ align:start position:0%
+on that problem NIH does not view that
+ 
+
+ align:start position:0%
+on that problem NIH does not view that
+is there a problem they view their
+
+ align:start position:0%
+is there a problem they view their
+ 
+
+ align:start position:0%
+is there a problem they view their
+problem is developing new drugs right
+
+ align:start position:0%
+problem is developing new drugs right
+ 
+
+ align:start position:0%
+problem is developing new drugs right
+new therapies not figuring out a safety
+
+ align:start position:0%
+new therapies not figuring out a safety
+ 
+
+ align:start position:0%
+new therapies not figuring out a safety
+approval set of problems so nobody's
+
+ align:start position:0%
+approval set of problems so nobody's
+ 
+
+ align:start position:0%
+approval set of problems so nobody's
+really on that problem except for FDA's
+
+ align:start position:0%
+really on that problem except for FDA's
+ 
+
+ align:start position:0%
+really on that problem except for FDA's
+own fairly modest research budget so the
+
+ align:start position:0%
+own fairly modest research budget so the
+ 
+
+ align:start position:0%
+own fairly modest research budget so the
+picture that this report portrays is
+
+ align:start position:0%
+picture that this report portrays is
+ 
+
+ align:start position:0%
+picture that this report portrays is
+ongoing breakthrough scientific
+
+ align:start position:0%
+ongoing breakthrough scientific
+ 
+
+ align:start position:0%
+ongoing breakthrough scientific
+discoveries that get nailed because the
+
+ align:start position:0%
+discoveries that get nailed because the
+ 
+
+ align:start position:0%
+discoveries that get nailed because the
+drug approval process isn't receiving
+
+ align:start position:0%
+drug approval process isn't receiving
+ 
+
+ align:start position:0%
+drug approval process isn't receiving
+new science and new technology advances
+
+ align:start position:0%
+new science and new technology advances
+ 
+
+ align:start position:0%
+new science and new technology advances
+that went enable it to keep up with
+
+ align:start position:0%
+that went enable it to keep up with
+ 
+
+ align:start position:0%
+that went enable it to keep up with
+these breakthroughs and we mentioned
+
+ align:start position:0%
+these breakthroughs and we mentioned
+ 
+
+ align:start position:0%
+these breakthroughs and we mentioned
+this earlier but the most serious one
+
+ align:start position:0%
+this earlier but the most serious one
+ 
+
+ align:start position:0%
+this earlier but the most serious one
+that's a head is in precision medicine
+
+ align:start position:0%
+that's a head is in precision medicine
+ 
+
+ align:start position:0%
+that's a head is in precision medicine
+and personalized medicine whether it's
+
+ align:start position:0%
+and personalized medicine whether it's
+ 
+
+ align:start position:0%
+and personalized medicine whether it's
+developing a therapy or a remedy that's
+
+ align:start position:0%
+developing a therapy or a remedy that's
+ 
+
+ align:start position:0%
+developing a therapy or a remedy that's
+uniquely appropriate for you as opposed
+
+ align:start position:0%
+uniquely appropriate for you as opposed
+ 
+
+ align:start position:0%
+uniquely appropriate for you as opposed
+to me right a personalized medicine
+
+ align:start position:0%
+to me right a personalized medicine
+ 
+
+ align:start position:0%
+to me right a personalized medicine
+approach how are we going to do the
+
+ align:start position:0%
+approach how are we going to do the
+ 
+
+ align:start position:0%
+approach how are we going to do the
+approval process for that
+
+ align:start position:0%
+approval process for that
+ 
+
+ align:start position:0%
+approval process for that
+how is FDA going to manage that
+
+ align:start position:0%
+how is FDA going to manage that
+ 
+
+ align:start position:0%
+how is FDA going to manage that
+so it's you know it is a dilemma here in
+
+ align:start position:0%
+so it's you know it is a dilemma here in
+ 
+
+ align:start position:0%
+so it's you know it is a dilemma here in
+the system and again it's an innovation
+
+ align:start position:0%
+the system and again it's an innovation
+ 
+
+ align:start position:0%
+the system and again it's an innovation
+organization problem we've got an
+
+ align:start position:0%
+organization problem we've got an
+ 
+
+ align:start position:0%
+organization problem we've got an
+innovation organization that's focused
+
+ align:start position:0%
+innovation organization that's focused
+ 
+
+ align:start position:0%
+innovation organization that's focused
+on one set of the problems and they've
+
+ align:start position:0%
+on one set of the problems and they've
+ 
+
+ align:start position:0%
+on one set of the problems and they've
+got the resources do they R and D on it
+
+ align:start position:0%
+got the resources do they R and D on it
+ 
+
+ align:start position:0%
+got the resources do they R and D on it
+and yet we've got a parallel big problem
+
+ align:start position:0%
+and yet we've got a parallel big problem
+ 
+
+ align:start position:0%
+and yet we've got a parallel big problem
+that's jeopardizing the other system and
+
+ align:start position:0%
+that's jeopardizing the other system and
+ 
+
+ align:start position:0%
+that's jeopardizing the other system and
+we don't have the organizational
+
+ align:start position:0%
+we don't have the organizational
+ 
+
+ align:start position:0%
+we don't have the organizational
+capability of acting on it right so then
+
+ align:start position:0%
+capability of acting on it right so then
+ 
+
+ align:start position:0%
+capability of acting on it right so then
+this is yet another innovation
+
+ align:start position:0%
+this is yet another innovation
+ 
+
+ align:start position:0%
+this is yet another innovation
+organizational problem and when you
+
+ align:start position:0%
+organizational problem and when you
+ 
+
+ align:start position:0%
+organizational problem and when you
+think about these things as systems you
+
+ align:start position:0%
+think about these things as systems you
+ 
+
+ align:start position:0%
+think about these things as systems you
+begin to identify what the gaps are and
+
+ align:start position:0%
+begin to identify what the gaps are and
+ 
+
+ align:start position:0%
+begin to identify what the gaps are and
+here is one that's probably enough on
+
+ align:start position:0%
+here is one that's probably enough on
+ 
+
+ align:start position:0%
+here is one that's probably enough on
+this topic so why don't we go right into
+
+ align:start position:0%
+this topic so why don't we go right into
+ 
+
+ align:start position:0%
+this topic so why don't we go right into
+some some Q&A on this Martine you want
+
+ align:start position:0%
+some some Q&A on this Martine you want
+ 
+
+ align:start position:0%
+some some Q&A on this Martine you want
+to lead us on bed bugs no drugs so I
+
+ align:start position:0%
+to lead us on bed bugs no drugs so I
+ 
+
+ align:start position:0%
+to lead us on bed bugs no drugs so I
+guess the main theme of this is their
+
+ align:start position:0%
+guess the main theme of this is their
+ 
+
+ align:start position:0%
+guess the main theme of this is their
+way of using policy or subsidies to
+
+ align:start position:0%
+way of using policy or subsidies to
+ 
+
+ align:start position:0%
+way of using policy or subsidies to
+incentivize the private sector to take
+
+ align:start position:0%
+incentivize the private sector to take
+ 
+
+ align:start position:0%
+incentivize the private sector to take
+on this problem or is the or even is the
+
+ align:start position:0%
+on this problem or is the or even is the
+ 
+
+ align:start position:0%
+on this problem or is the or even is the
+private sector even the right entity the
+
+ align:start position:0%
+private sector even the right entity the
+ 
+
+ align:start position:0%
+private sector even the right entity the
+handle is father
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I feel like I'm well said bill
+
+ align:start position:0%
+I feel like I'm well said bill
+ 
+
+ align:start position:0%
+I feel like I'm well said bill
+suggestion of having governments
+
+ align:start position:0%
+suggestion of having governments
+ 
+
+ align:start position:0%
+suggestion of having governments
+guaranteed to pay for a certain amount
+
+ align:start position:0%
+guaranteed to pay for a certain amount
+ 
+
+ align:start position:0%
+guaranteed to pay for a certain amount
+of dose it seems like fix for it
+
+ align:start position:0%
+of dose it seems like fix for it
+ 
+
+ align:start position:0%
+of dose it seems like fix for it
+you keep leaves the free market along
+
+ align:start position:0%
+you keep leaves the free market along
+ 
+
+ align:start position:0%
+you keep leaves the free market along
+these companies don't like they
+
+ align:start position:0%
+these companies don't like they
+ 
+
+ align:start position:0%
+these companies don't like they
+currently don't have an incentive so I
+
+ align:start position:0%
+currently don't have an incentive so I
+ 
+
+ align:start position:0%
+currently don't have an incentive so I
+don't think that's really an option a
+
+ align:start position:0%
+don't think that's really an option a
+ 
+
+ align:start position:0%
+don't think that's really an option a
+professor of mine an economics professor
+
+ align:start position:0%
+professor of mine an economics professor
+ 
+
+ align:start position:0%
+professor of mine an economics professor
+it was like well is very supportive of
+
+ align:start position:0%
+it was like well is very supportive of
+ 
+
+ align:start position:0%
+it was like well is very supportive of
+patent extension switch is something
+
+ align:start position:0%
+patent extension switch is something
+ 
+
+ align:start position:0%
+patent extension switch is something
+that was cited in the report and she
+
+ align:start position:0%
+that was cited in the report and she
+ 
+
+ align:start position:0%
+that was cited in the report and she
+felt like at least in my understanding
+
+ align:start position:0%
+felt like at least in my understanding
+ 
+
+ align:start position:0%
+felt like at least in my understanding
+that that would very much motivated by
+
+ align:start position:0%
+that that would very much motivated by
+ 
+
+ align:start position:0%
+that that would very much motivated by
+when pharma companies to do research
+
+ align:start position:0%
+when pharma companies to do research
+ 
+
+ align:start position:0%
+when pharma companies to do research
+primarily because they're concerned that
+
+ align:start position:0%
+primarily because they're concerned that
+ 
+
+ align:start position:0%
+primarily because they're concerned that
+their patents are going to run out in
+
+ align:start position:0%
+their patents are going to run out in
+ 
+
+ align:start position:0%
+their patents are going to run out in
+the lifecycle of the innovation process
+
+ align:start position:0%
+the lifecycle of the innovation process
+ 
+
+ align:start position:0%
+the lifecycle of the innovation process
+yet explain how that would work
+
+ align:start position:0%
+yet explain how that would work
+ 
+
+ align:start position:0%
+yet explain how that would work
+so oh man I don't know that I could do
+
+ align:start position:0%
+so oh man I don't know that I could do
+ 
+
+ align:start position:0%
+so oh man I don't know that I could do
+it justice thanks give us a snapshot
+
+ align:start position:0%
+it justice thanks give us a snapshot
+ 
+
+ align:start position:0%
+it justice thanks give us a snapshot
+Chris I think my understanding of the
+
+ align:start position:0%
+Chris I think my understanding of the
+ 
+
+ align:start position:0%
+Chris I think my understanding of the
+patent extension process is that
+
+ align:start position:0%
+patent extension process is that
+ 
+
+ align:start position:0%
+patent extension process is that
+especially for like orphan drugs where
+
+ align:start position:0%
+especially for like orphan drugs where
+ 
+
+ align:start position:0%
+especially for like orphan drugs where
+it's like under like ten thousand people
+
+ align:start position:0%
+it's like under like ten thousand people
+ 
+
+ align:start position:0%
+it's like under like ten thousand people
+or something like that so smaller
+
+ align:start position:0%
+or something like that so smaller
+ 
+
+ align:start position:0%
+or something like that so smaller
+marketed size or it's like targeting
+
+ align:start position:0%
+marketed size or it's like targeting
+ 
+
+ align:start position:0%
+marketed size or it's like targeting
+children like adolescents you get patent
+
+ align:start position:0%
+children like adolescents you get patent
+ 
+
+ align:start position:0%
+children like adolescents you get patent
+extension that could be like three to
+
+ align:start position:0%
+extension that could be like three to
+ 
+
+ align:start position:0%
+extension that could be like three to
+five years extra which is pretty
+
+ align:start position:0%
+five years extra which is pretty
+ 
+
+ align:start position:0%
+five years extra which is pretty
+significant in terms of like drive
+
+ align:start position:0%
+significant in terms of like drive
+ 
+
+ align:start position:0%
+significant in terms of like drive
+companies and yeah I think those are the
+
+ align:start position:0%
+companies and yeah I think those are the
+ 
+
+ align:start position:0%
+companies and yeah I think those are the
+main ones and there's also like
+
+ align:start position:0%
+main ones and there's also like
+ 
+
+ align:start position:0%
+main ones and there's also like
+breakthrough therapy designation and
+
+ align:start position:0%
+breakthrough therapy designation and
+ 
+
+ align:start position:0%
+breakthrough therapy designation and
+those kind of not only help speed up the
+
+ align:start position:0%
+those kind of not only help speed up the
+ 
+
+ align:start position:0%
+those kind of not only help speed up the
+approval process which is really
+
+ align:start position:0%
+approval process which is really
+ 
+
+ align:start position:0%
+approval process which is really
+valuable for these companies that really
+
+ align:start position:0%
+valuable for these companies that really
+ 
+
+ align:start position:0%
+valuable for these companies that really
+want to push through these drugs really
+
+ align:start position:0%
+want to push through these drugs really
+ 
+
+ align:start position:0%
+want to push through these drugs really
+quickly and kind of get it to market and
+
+ align:start position:0%
+quickly and kind of get it to market and
+ 
+
+ align:start position:0%
+quickly and kind of get it to market and
+then they also extend a little bit in
+
+ align:start position:0%
+then they also extend a little bit in
+ 
+
+ align:start position:0%
+then they also extend a little bit in
+certain cases so there's like a lot of
+
+ align:start position:0%
+certain cases so there's like a lot of
+ 
+
+ align:start position:0%
+certain cases so there's like a lot of
+different on small ways FDA is trying to
+
+ align:start position:0%
+different on small ways FDA is trying to
+ 
+
+ align:start position:0%
+different on small ways FDA is trying to
+give more incentive which is nice to see
+
+ align:start position:0%
+give more incentive which is nice to see
+ 
+
+ align:start position:0%
+give more incentive which is nice to see
+I think
+
+ align:start position:0%
+I think
+ 
+
+ align:start position:0%
+I think
+I think it's a good policy and the child
+
+ align:start position:0%
+I think it's a good policy and the child
+ 
+
+ align:start position:0%
+I think it's a good policy and the child
+of lower order analysis streamlined
+
+ align:start position:0%
+of lower order analysis streamlined
+ 
+
+ align:start position:0%
+of lower order analysis streamlined
+microeconomics someone I I think the way
+
+ align:start position:0%
+microeconomics someone I I think the way
+ 
+
+ align:start position:0%
+microeconomics someone I I think the way
+that she explained it was essentially
+
+ align:start position:0%
+that she explained it was essentially
+ 
+
+ align:start position:0%
+that she explained it was essentially
+and all you may know that's I don't know
+
+ align:start position:0%
+and all you may know that's I don't know
+ 
+
+ align:start position:0%
+and all you may know that's I don't know
+they said to like two years ago so maybe
+
+ align:start position:0%
+they said to like two years ago so maybe
+ 
+
+ align:start position:0%
+they said to like two years ago so maybe
+this isn't to someone is that
+
+ align:start position:0%
+this isn't to someone is that
+ 
+
+ align:start position:0%
+this isn't to someone is that
+researchers it made from the time that
+
+ align:start position:0%
+researchers it made from the time that
+ 
+
+ align:start position:0%
+researchers it made from the time that
+they applied for a patent they have what
+
+ align:start position:0%
+they applied for a patent they have what
+ 
+
+ align:start position:0%
+they applied for a patent they have what
+is it fifteen seventeen years something
+
+ align:start position:0%
+is it fifteen seventeen years something
+ 
+
+ align:start position:0%
+is it fifteen seventeen years something
+like that to commercialization where
+
+ align:start position:0%
+like that to commercialization where
+ 
+
+ align:start position:0%
+like that to commercialization where
+their patents protected 20 about twenty
+
+ align:start position:0%
+their patents protected 20 about twenty
+ 
+
+ align:start position:0%
+their patents protected 20 about twenty
+nine twenty okay
+
+ align:start position:0%
+nine twenty okay
+ 
+
+ align:start position:0%
+nine twenty okay
+so like they used to blame seventeen and
+
+ align:start position:0%
+so like they used to blame seventeen and
+ 
+
+ align:start position:0%
+so like they used to blame seventeen and
+now it's twenty and so the way that she
+
+ align:start position:0%
+now it's twenty and so the way that she
+ 
+
+ align:start position:0%
+now it's twenty and so the way that she
+explained it to us is that because a lot
+
+ align:start position:0%
+explained it to us is that because a lot
+ 
+
+ align:start position:0%
+explained it to us is that because a lot
+of the music a lot of the research and
+
+ align:start position:0%
+of the music a lot of the research and
+ 
+
+ align:start position:0%
+of the music a lot of the research and
+development process could take twenty
+
+ align:start position:0%
+development process could take twenty
+ 
+
+ align:start position:0%
+development process could take twenty
+years by the time that they get a drug
+
+ align:start position:0%
+years by the time that they get a drug
+ 
+
+ align:start position:0%
+years by the time that they get a drug
+to market they may have already lost the
+
+ align:start position:0%
+to market they may have already lost the
+ 
+
+ align:start position:0%
+to market they may have already lost the
+patent so it becomes no longer because I
+
+ align:start position:0%
+patent so it becomes no longer because I
+ 
+
+ align:start position:0%
+patent so it becomes no longer because I
+cannot become as economically
+
+ align:start position:0%
+cannot become as economically
+ 
+
+ align:start position:0%
+cannot become as economically
+advantageous for the company to pursue
+
+ align:start position:0%
+advantageous for the company to pursue
+ 
+
+ align:start position:0%
+advantageous for the company to pursue
+commercialization of a particular
+
+ align:start position:0%
+commercialization of a particular
+ 
+
+ align:start position:0%
+commercialization of a particular
+therapy and thus what Chris was saying
+
+ align:start position:0%
+therapy and thus what Chris was saying
+ 
+
+ align:start position:0%
+therapy and thus what Chris was saying
+so that's certain that smaller actions
+
+ align:start position:0%
+so that's certain that smaller actions
+ 
+
+ align:start position:0%
+so that's certain that smaller actions
+separate inserts sort of from like a
+
+ align:start position:0%
+separate inserts sort of from like a
+ 
+
+ align:start position:0%
+separate inserts sort of from like a
+scientific or biological perspective so
+
+ align:start position:0%
+scientific or biological perspective so
+ 
+
+ align:start position:0%
+scientific or biological perspective so
+I wonder if like is it that these drugs
+
+ align:start position:0%
+I wonder if like is it that these drugs
+ 
+
+ align:start position:0%
+I wonder if like is it that these drugs
+aren't super effective or like
+
+ align:start position:0%
+aren't super effective or like
+ 
+
+ align:start position:0%
+aren't super effective or like
+antibiotics aren't the best mechanism to
+
+ align:start position:0%
+antibiotics aren't the best mechanism to
+ 
+
+ align:start position:0%
+antibiotics aren't the best mechanism to
+get rid of these bacteria in the way
+
+ align:start position:0%
+get rid of these bacteria in the way
+ 
+
+ align:start position:0%
+get rid of these bacteria in the way
+that we traditionally think about them
+
+ align:start position:0%
+that we traditionally think about them
+ 
+
+ align:start position:0%
+that we traditionally think about them
+to say that one are is the way that we
+
+ align:start position:0%
+to say that one are is the way that we
+ 
+
+ align:start position:0%
+to say that one are is the way that we
+think about bacteria like is it saying
+
+ align:start position:0%
+think about bacteria like is it saying
+ 
+
+ align:start position:0%
+think about bacteria like is it saying
+is that the actual most effective means
+
+ align:start position:0%
+is that the actual most effective means
+ 
+
+ align:start position:0%
+is that the actual most effective means
+or is that actually how they work do you
+
+ align:start position:0%
+or is that actually how they work do you
+ 
+
+ align:start position:0%
+or is that actually how they work do you
+not understand the pathways of like how
+
+ align:start position:0%
+not understand the pathways of like how
+ 
+
+ align:start position:0%
+not understand the pathways of like how
+they're actually becoming or resistant
+
+ align:start position:0%
+they're actually becoming or resistant
+ 
+
+ align:start position:0%
+they're actually becoming or resistant
+to these technologies so I question is
+
+ align:start position:0%
+to these technologies so I question is
+ 
+
+ align:start position:0%
+to these technologies so I question is
+they're just kind of like a group think
+
+ align:start position:0%
+they're just kind of like a group think
+ 
+
+ align:start position:0%
+they're just kind of like a group think
+in it's a way that we think about
+
+ align:start position:0%
+in it's a way that we think about
+ 
+
+ align:start position:0%
+in it's a way that we think about
+antibiotics and bacterial theory in
+
+ align:start position:0%
+antibiotics and bacterial theory in
+ 
+
+ align:start position:0%
+antibiotics and bacterial theory in
+biology are in medicine that sort of
+
+ align:start position:0%
+biology are in medicine that sort of
+ 
+
+ align:start position:0%
+biology are in medicine that sort of
+site is where we're just time following
+
+ align:start position:0%
+site is where we're just time following
+ 
+
+ align:start position:0%
+site is where we're just time following
+along the same path so I want would love
+
+ align:start position:0%
+along the same path so I want would love
+ 
+
+ align:start position:0%
+along the same path so I want would love
+to talk to my cardiologists and then to
+
+ align:start position:0%
+to talk to my cardiologists and then to
+ 
+
+ align:start position:0%
+to talk to my cardiologists and then to
+is this problem one that we will ever
+
+ align:start position:0%
+is this problem one that we will ever
+ 
+
+ align:start position:0%
+is this problem one that we will ever
+solve or will it just get exponentially
+
+ align:start position:0%
+solve or will it just get exponentially
+ 
+
+ align:start position:0%
+solve or will it just get exponentially
+worse because I can imagine even if we
+
+ align:start position:0%
+worse because I can imagine even if we
+ 
+
+ align:start position:0%
+worse because I can imagine even if we
+come up with my faster and faster
+
+ align:start position:0%
+come up with my faster and faster
+ 
+
+ align:start position:0%
+come up with my faster and faster
+mechanisms to get out these antibiotics
+
+ align:start position:0%
+mechanisms to get out these antibiotics
+ 
+
+ align:start position:0%
+mechanisms to get out these antibiotics
+and reach more people will these
+
+ align:start position:0%
+and reach more people will these
+ 
+
+ align:start position:0%
+and reach more people will these
+bacteria just kind of keep growing and
+
+ align:start position:0%
+bacteria just kind of keep growing and
+ 
+
+ align:start position:0%
+bacteria just kind of keep growing and
+get faster and more resistant and like
+
+ align:start position:0%
+get faster and more resistant and like
+ 
+
+ align:start position:0%
+get faster and more resistant and like
+will always have this problem
+
+ align:start position:0%
+will always have this problem
+ 
+
+ align:start position:0%
+will always have this problem
+and then certainly does that mean that
+
+ align:start position:0%
+and then certainly does that mean that
+ 
+
+ align:start position:0%
+and then certainly does that mean that
+we should have sort of like an establish
+
+ align:start position:0%
+we should have sort of like an establish
+ 
+
+ align:start position:0%
+we should have sort of like an establish
+or kind of an entity within the FDA that
+
+ align:start position:0%
+or kind of an entity within the FDA that
+ 
+
+ align:start position:0%
+or kind of an entity within the FDA that
+like just deals with antibiotics if they
+
+ align:start position:0%
+like just deals with antibiotics if they
+ 
+
+ align:start position:0%
+like just deals with antibiotics if they
+deem it as a serious enough problem and
+
+ align:start position:0%
+deem it as a serious enough problem and
+ 
+
+ align:start position:0%
+deem it as a serious enough problem and
+it's time to be persistent you can talk
+
+ align:start position:0%
+it's time to be persistent you can talk
+ 
+
+ align:start position:0%
+it's time to be persistent you can talk
+about this theoretically but it was a
+
+ align:start position:0%
+about this theoretically but it was a
+ 
+
+ align:start position:0%
+about this theoretically but it was a
+husband task so if you had to start a
+
+ align:start position:0%
+husband task so if you had to start a
+ 
+
+ align:start position:0%
+husband task so if you had to start a
+company right and you're like relatively
+
+ align:start position:0%
+company right and you're like relatively
+ 
+
+ align:start position:0%
+company right and you're like relatively
+young your career and this might be a
+
+ align:start position:0%
+young your career and this might be a
+ 
+
+ align:start position:0%
+young your career and this might be a
+career ender and look like it there's no
+
+ align:start position:0%
+career ender and look like it there's no
+ 
+
+ align:start position:0%
+career ender and look like it there's no
+success
+
+ align:start position:0%
+success
+ 
+
+ align:start position:0%
+success
+what would incentives would incentivize
+
+ align:start position:0%
+what would incentives would incentivize
+ 
+
+ align:start position:0%
+what would incentives would incentivize
+you to start company s all this from hot
+
+ align:start position:0%
+you to start company s all this from hot
+ 
+
+ align:start position:0%
+you to start company s all this from hot
+like organization yeah to work on this
+
+ align:start position:0%
+like organization yeah to work on this
+ 
+
+ align:start position:0%
+like organization yeah to work on this
+exactly presuming you have the equipment
+
+ align:start position:0%
+exactly presuming you have the equipment
+ 
+
+ align:start position:0%
+exactly presuming you have the equipment
+yeah so antibiotics are pretty difficult
+
+ align:start position:0%
+yeah so antibiotics are pretty difficult
+ 
+
+ align:start position:0%
+yeah so antibiotics are pretty difficult
+first of all because they're becoming
+
+ align:start position:0%
+first of all because they're becoming
+ 
+
+ align:start position:0%
+first of all because they're becoming
+too effective for their own good like I
+
+ align:start position:0%
+too effective for their own good like I
+ 
+
+ align:start position:0%
+too effective for their own good like I
+think it was fines are one of the big
+
+ align:start position:0%
+think it was fines are one of the big
+ 
+
+ align:start position:0%
+think it was fines are one of the big
+companies produced a very famous kind of
+
+ align:start position:0%
+companies produced a very famous kind of
+ 
+
+ align:start position:0%
+companies produced a very famous kind of
+antibiotic drug and now it's just like
+
+ align:start position:0%
+antibiotic drug and now it's just like
+ 
+
+ align:start position:0%
+antibiotic drug and now it's just like
+so effective that they've kind of gotten
+
+ align:start position:0%
+so effective that they've kind of gotten
+ 
+
+ align:start position:0%
+so effective that they've kind of gotten
+become the victim of their and success
+
+ align:start position:0%
+become the victim of their and success
+ 
+
+ align:start position:0%
+become the victim of their and success
+and also it's also really hard to pass
+
+ align:start position:0%
+and also it's also really hard to pass
+ 
+
+ align:start position:0%
+and also it's also really hard to pass
+antibiotic drugs through clinical trials
+
+ align:start position:0%
+antibiotic drugs through clinical trials
+ 
+
+ align:start position:0%
+antibiotic drugs through clinical trials
+like disproportionately so compared to
+
+ align:start position:0%
+like disproportionately so compared to
+ 
+
+ align:start position:0%
+like disproportionately so compared to
+other diseases so that's also kind of
+
+ align:start position:0%
+other diseases so that's also kind of
+ 
+
+ align:start position:0%
+other diseases so that's also kind of
+like a barrier to entry I think honestly
+
+ align:start position:0%
+like a barrier to entry I think honestly
+ 
+
+ align:start position:0%
+like a barrier to entry I think honestly
+if I were to want to you know get into
+
+ align:start position:0%
+if I were to want to you know get into
+ 
+
+ align:start position:0%
+if I were to want to you know get into
+this field you have to come out with in
+
+ align:start position:0%
+this field you have to come out with in
+ 
+
+ align:start position:0%
+this field you have to come out with in
+new approach like something better than
+
+ align:start position:0%
+new approach like something better than
+ 
+
+ align:start position:0%
+new approach like something better than
+it's being done right now because they
+
+ align:start position:0%
+it's being done right now because they
+ 
+
+ align:start position:0%
+it's being done right now because they
+think I mean antibiotics it's just it's
+
+ align:start position:0%
+think I mean antibiotics it's just it's
+ 
+
+ align:start position:0%
+think I mean antibiotics it's just it's
+a very broad field there's like so many
+
+ align:start position:0%
+a very broad field there's like so many
+ 
+
+ align:start position:0%
+a very broad field there's like so many
+different strains and if they like
+
+ align:start position:0%
+different strains and if they like
+ 
+
+ align:start position:0%
+different strains and if they like
+mutate a bit your drug can be already
+
+ align:start position:0%
+mutate a bit your drug can be already
+ 
+
+ align:start position:0%
+mutate a bit your drug can be already
+rendered ineffective so it's just one of
+
+ align:start position:0%
+rendered ineffective so it's just one of
+ 
+
+ align:start position:0%
+rendered ineffective so it's just one of
+those fields that is always evolving so
+
+ align:start position:0%
+those fields that is always evolving so
+ 
+
+ align:start position:0%
+those fields that is always evolving so
+not only do you have to have very strong
+
+ align:start position:0%
+not only do you have to have very strong
+ 
+
+ align:start position:0%
+not only do you have to have very strong
+basic science keep up with like what's
+
+ align:start position:0%
+basic science keep up with like what's
+ 
+
+ align:start position:0%
+basic science keep up with like what's
+happening with these bacteria how are
+
+ align:start position:0%
+happening with these bacteria how are
+ 
+
+ align:start position:0%
+happening with these bacteria how are
+how are they like mutating and how are
+
+ align:start position:0%
+how are they like mutating and how are
+ 
+
+ align:start position:0%
+how are they like mutating and how are
+they kind of evolving and then you've to
+
+ align:start position:0%
+they kind of evolving and then you've to
+ 
+
+ align:start position:0%
+they kind of evolving and then you've to
+come up with drugs to help target them
+
+ align:start position:0%
+come up with drugs to help target them
+ 
+
+ align:start position:0%
+come up with drugs to help target them
+so it's like a very twofold problem that
+
+ align:start position:0%
+so it's like a very twofold problem that
+ 
+
+ align:start position:0%
+so it's like a very twofold problem that
+you need to
+
+ align:start position:0%
+you need to
+ 
+
+ align:start position:0%
+you need to
+simultaneously target and then obviously
+
+ align:start position:0%
+simultaneously target and then obviously
+ 
+
+ align:start position:0%
+simultaneously target and then obviously
+they're evolving so rapidly that you
+
+ align:start position:0%
+they're evolving so rapidly that you
+ 
+
+ align:start position:0%
+they're evolving so rapidly that you
+have to kind of pivot very quickly so I
+
+ align:start position:0%
+have to kind of pivot very quickly so I
+ 
+
+ align:start position:0%
+have to kind of pivot very quickly so I
+think it's one of those fast changing
+
+ align:start position:0%
+think it's one of those fast changing
+ 
+
+ align:start position:0%
+think it's one of those fast changing
+fields that is kind of hard to target
+
+ align:start position:0%
+fields that is kind of hard to target
+ 
+
+ align:start position:0%
+fields that is kind of hard to target
+but definitely important I'm not really
+
+ align:start position:0%
+but definitely important I'm not really
+ 
+
+ align:start position:0%
+but definitely important I'm not really
+sure what mechanisms they have in place
+
+ align:start position:0%
+sure what mechanisms they have in place
+ 
+
+ align:start position:0%
+sure what mechanisms they have in place
+or like organization wise to kind of
+
+ align:start position:0%
+or like organization wise to kind of
+ 
+
+ align:start position:0%
+or like organization wise to kind of
+target this specifically but I think
+
+ align:start position:0%
+target this specifically but I think
+ 
+
+ align:start position:0%
+target this specifically but I think
+definitely so you just talked about a
+
+ align:start position:0%
+definitely so you just talked about a
+ 
+
+ align:start position:0%
+definitely so you just talked about a
+like your pipeline or and getting
+
+ align:start position:0%
+like your pipeline or and getting
+ 
+
+ align:start position:0%
+like your pipeline or and getting
+approved what if they can speed that up
+
+ align:start position:0%
+approved what if they can speed that up
+ 
+
+ align:start position:0%
+approved what if they can speed that up
+like very quickly so it's a priority
+
+ align:start position:0%
+like very quickly so it's a priority
+ 
+
+ align:start position:0%
+like very quickly so it's a priority
+I mean speeding up it up would help but
+
+ align:start position:0%
+I mean speeding up it up would help but
+ 
+
+ align:start position:0%
+I mean speeding up it up would help but
+also it's just like hard to kind of
+
+ align:start position:0%
+also it's just like hard to kind of
+ 
+
+ align:start position:0%
+also it's just like hard to kind of
+produce a good clinical trial for these
+
+ align:start position:0%
+produce a good clinical trial for these
+ 
+
+ align:start position:0%
+produce a good clinical trial for these
+drugs so I think that's like also
+
+ align:start position:0%
+drugs so I think that's like also
+ 
+
+ align:start position:0%
+drugs so I think that's like also
+fundamental problem it's just like
+
+ align:start position:0%
+fundamental problem it's just like
+ 
+
+ align:start position:0%
+fundamental problem it's just like
+psychiatric drugs those are very
+
+ align:start position:0%
+psychiatric drugs those are very
+ 
+
+ align:start position:0%
+psychiatric drugs those are very
+notorious ly hard to prove because like
+
+ align:start position:0%
+notorious ly hard to prove because like
+ 
+
+ align:start position:0%
+notorious ly hard to prove because like
+placebo effect is really so that leads
+
+ align:start position:0%
+placebo effect is really so that leads
+ 
+
+ align:start position:0%
+placebo effect is really so that leads
+us right into our next reading which is
+
+ align:start position:0%
+us right into our next reading which is
+ 
+
+ align:start position:0%
+us right into our next reading which is
+this FDA problem and the fact that we
+
+ align:start position:0%
+this FDA problem and the fact that we
+ 
+
+ align:start position:0%
+this FDA problem and the fact that we
+haven't put resources on the drug
+
+ align:start position:0%
+haven't put resources on the drug
+ 
+
+ align:start position:0%
+haven't put resources on the drug
+approval process so Chloe it's yours if
+
+ align:start position:0%
+approval process so Chloe it's yours if
+ 
+
+ align:start position:0%
+approval process so Chloe it's yours if
+we're starting up in tackling that
+
+ align:start position:0%
+we're starting up in tackling that
+ 
+
+ align:start position:0%
+we're starting up in tackling that
+problem of how do we sort of reform and
+
+ align:start position:0%
+problem of how do we sort of reform and
+ 
+
+ align:start position:0%
+problem of how do we sort of reform and
+revamp the way in which we evaluate
+
+ align:start position:0%
+revamp the way in which we evaluate
+ 
+
+ align:start position:0%
+revamp the way in which we evaluate
+these products one question for you guys
+
+ align:start position:0%
+these products one question for you guys
+ 
+
+ align:start position:0%
+these products one question for you guys
+would be so the reading mentioned that
+
+ align:start position:0%
+would be so the reading mentioned that
+ 
+
+ align:start position:0%
+would be so the reading mentioned that
+one of the things you could attribute
+
+ align:start position:0%
+one of the things you could attribute
+ 
+
+ align:start position:0%
+one of the things you could attribute
+this mismatch show is a mismatch between
+
+ align:start position:0%
+this mismatch show is a mismatch between
+ 
+
+ align:start position:0%
+this mismatch show is a mismatch between
+the levels that how far both research in
+
+ align:start position:0%
+the levels that how far both research in
+ 
+
+ align:start position:0%
+the levels that how far both research in
+basic science and applied science like
+
+ align:start position:0%
+basic science and applied science like
+ 
+
+ align:start position:0%
+basic science and applied science like
+where they're both that they're very
+
+ align:start position:0%
+where they're both that they're very
+ 
+
+ align:start position:0%
+where they're both that they're very
+mismatched in terms and one of them is
+
+ align:start position:0%
+mismatched in terms and one of them is
+ 
+
+ align:start position:0%
+mismatched in terms and one of them is
+just shot ahead in the other candy to
+
+ align:start position:0%
+just shot ahead in the other candy to
+ 
+
+ align:start position:0%
+just shot ahead in the other candy to
+keep up so what are your thoughts on how
+
+ align:start position:0%
+keep up so what are your thoughts on how
+ 
+
+ align:start position:0%
+keep up so what are your thoughts on how
+or if an agency such as the Athenian age
+
+ align:start position:0%
+or if an agency such as the Athenian age
+ 
+
+ align:start position:0%
+or if an agency such as the Athenian age
+should be responsible for ensuring that
+
+ align:start position:0%
+should be responsible for ensuring that
+ 
+
+ align:start position:0%
+should be responsible for ensuring that
+the development of these sciences are
+
+ align:start position:0%
+the development of these sciences are
+ 
+
+ align:start position:0%
+the development of these sciences are
+evenly matched for example should the
+
+ align:start position:0%
+evenly matched for example should the
+ 
+
+ align:start position:0%
+evenly matched for example should the
+agency bottleneck the funding for basic
+
+ align:start position:0%
+agency bottleneck the funding for basic
+ 
+
+ align:start position:0%
+agency bottleneck the funding for basic
+sciences until five sciences and catch
+
+ align:start position:0%
+sciences until five sciences and catch
+ 
+
+ align:start position:0%
+sciences until five sciences and catch
+up for this today
+
+ align:start position:0%
+up for this today
+ 
+
+ align:start position:0%
+up for this today
+aggressively stimulate opportunities on
+
+ align:start position:0%
+aggressively stimulate opportunities on
+ 
+
+ align:start position:0%
+aggressively stimulate opportunities on
+the other side
+
+ align:start position:0%
+the other side
+ 
+
+ align:start position:0%
+the other side
+well I suppose in an ideal scenario you
+
+ align:start position:0%
+well I suppose in an ideal scenario you
+ 
+
+ align:start position:0%
+well I suppose in an ideal scenario you
+just stimulate that it's more funding to
+
+ align:start position:0%
+just stimulate that it's more funding to
+ 
+
+ align:start position:0%
+just stimulate that it's more funding to
+research drugs but I understand that
+
+ align:start position:0%
+research drugs but I understand that
+ 
+
+ align:start position:0%
+research drugs but I understand that
+there aren't there isn't always money
+
+ align:start position:0%
+there aren't there isn't always money
+ 
+
+ align:start position:0%
+there aren't there isn't always money
+for that yeah I forget doin like you
+
+ align:start position:0%
+for that yeah I forget doin like you
+ 
+
+ align:start position:0%
+for that yeah I forget doin like you
+fish there's to that point there is
+
+ align:start position:0%
+fish there's to that point there is
+ 
+
+ align:start position:0%
+fish there's to that point there is
+another reading I forget movies this one
+
+ align:start position:0%
+another reading I forget movies this one
+ 
+
+ align:start position:0%
+another reading I forget movies this one
+or not but said just throwing money and
+
+ align:start position:0%
+or not but said just throwing money and
+ 
+
+ align:start position:0%
+or not but said just throwing money and
+then giving infinite budgets isn't
+
+ align:start position:0%
+then giving infinite budgets isn't
+ 
+
+ align:start position:0%
+then giving infinite budgets isn't
+always the solution because in that case
+
+ align:start position:0%
+always the solution because in that case
+ 
+
+ align:start position:0%
+always the solution because in that case
+I can you can it sort of takes away the
+
+ align:start position:0%
+I can you can it sort of takes away the
+ 
+
+ align:start position:0%
+I can you can it sort of takes away the
+element of good planning and strategic
+
+ align:start position:0%
+element of good planning and strategic
+ 
+
+ align:start position:0%
+element of good planning and strategic
+planning the end of innovation
+
+ align:start position:0%
+planning the end of innovation
+ 
+
+ align:start position:0%
+planning the end of innovation
+organization if you don't have the
+
+ align:start position:0%
+organization if you don't have the
+ 
+
+ align:start position:0%
+organization if you don't have the
+innovation organization that's going to
+
+ align:start position:0%
+innovation organization that's going to
+ 
+
+ align:start position:0%
+innovation organization that's going to
+enable you to avoid big gaps in the
+
+ align:start position:0%
+enable you to avoid big gaps in the
+ 
+
+ align:start position:0%
+enable you to avoid big gaps in the
+system you're just not going to get
+
+ align:start position:0%
+system you're just not going to get
+ 
+
+ align:start position:0%
+system you're just not going to get
+there so throwing money at a problem
+
+ align:start position:0%
+there so throwing money at a problem
+ 
+
+ align:start position:0%
+there so throwing money at a problem
+without tackling the innovation
+
+ align:start position:0%
+without tackling the innovation
+ 
+
+ align:start position:0%
+without tackling the innovation
+organization problems its problematic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one thing that I was curious about I was
+
+ align:start position:0%
+one thing that I was curious about I was
+ 
+
+ align:start position:0%
+one thing that I was curious about I was
+confused how antibiotics can
+
+ align:start position:0%
+confused how antibiotics can
+ 
+
+ align:start position:0%
+confused how antibiotics can
+simultaneously be working too well and
+
+ align:start position:0%
+simultaneously be working too well and
+ 
+
+ align:start position:0%
+simultaneously be working too well and
+you can have tons of antibiotic
+
+ align:start position:0%
+you can have tons of antibiotic
+ 
+
+ align:start position:0%
+you can have tons of antibiotic
+resistant bacteria which implies that
+
+ align:start position:0%
+resistant bacteria which implies that
+ 
+
+ align:start position:0%
+resistant bacteria which implies that
+antibiotics are not working too well so
+
+ align:start position:0%
+antibiotics are not working too well so
+ 
+
+ align:start position:0%
+antibiotics are not working too well so
+if someone could clarify that
+
+ align:start position:0%
+if someone could clarify that
+ 
+
+ align:start position:0%
+if someone could clarify that
+that's yours Chris yeah so I think the
+
+ align:start position:0%
+that's yours Chris yeah so I think the
+ 
+
+ align:start position:0%
+that's yours Chris yeah so I think the
+problem is that like say hazards drug is
+
+ align:start position:0%
+problem is that like say hazards drug is
+ 
+
+ align:start position:0%
+problem is that like say hazards drug is
+doing really well so like they give
+
+ align:start position:0%
+doing really well so like they give
+ 
+
+ align:start position:0%
+doing really well so like they give
+these antibiotics to their patients and
+
+ align:start position:0%
+these antibiotics to their patients and
+ 
+
+ align:start position:0%
+these antibiotics to their patients and
+these patients are getting cured and so
+
+ align:start position:0%
+these patients are getting cured and so
+ 
+
+ align:start position:0%
+these patients are getting cured and so
+that means like if they're getting cured
+
+ align:start position:0%
+that means like if they're getting cured
+ 
+
+ align:start position:0%
+that means like if they're getting cured
+and they're not really getting these
+
+ align:start position:0%
+and they're not really getting these
+ 
+
+ align:start position:0%
+and they're not really getting these
+diseases that means that drugs aren't
+
+ align:start position:0%
+diseases that means that drugs aren't
+ 
+
+ align:start position:0%
+diseases that means that drugs aren't
+going to be really used as much and then
+
+ align:start position:0%
+going to be really used as much and then
+ 
+
+ align:start position:0%
+going to be really used as much and then
+at the same time because these patients
+
+ align:start position:0%
+at the same time because these patients
+ 
+
+ align:start position:0%
+at the same time because these patients
+have used the drug there is like you
+
+ align:start position:0%
+have used the drug there is like you
+ 
+
+ align:start position:0%
+have used the drug there is like you
+know antibiotic resistance growing and
+
+ align:start position:0%
+know antibiotic resistance growing and
+ 
+
+ align:start position:0%
+know antibiotic resistance growing and
+just like just because it's been around
+
+ align:start position:0%
+just like just because it's been around
+ 
+
+ align:start position:0%
+just like just because it's been around
+for so long it's inevitable that
+
+ align:start position:0%
+for so long it's inevitable that
+ 
+
+ align:start position:0%
+for so long it's inevitable that
+resistance resistance is going to build
+
+ align:start position:0%
+resistance resistance is going to build
+ 
+
+ align:start position:0%
+resistance resistance is going to build
+up to the point that the drug is no
+
+ align:start position:0%
+up to the point that the drug is no
+ 
+
+ align:start position:0%
+up to the point that the drug is no
+longer effective right because it's like
+
+ align:start position:0%
+longer effective right because it's like
+ 
+
+ align:start position:0%
+longer effective right because it's like
+been out for 10 15 years
+
+ align:start position:0%
+been out for 10 15 years
+ 
+
+ align:start position:0%
+been out for 10 15 years
+it's not going to but the resistances
+
+ align:start position:0%
+it's not going to but the resistances
+ 
+
+ align:start position:0%
+it's not going to but the resistances
+can only develop if lots of people are
+
+ align:start position:0%
+can only develop if lots of people are
+ 
+
+ align:start position:0%
+can only develop if lots of people are
+using them I mean obviously successful
+
+ align:start position:0%
+using them I mean obviously successful
+ 
+
+ align:start position:0%
+using them I mean obviously successful
+used it it is obviously like critical
+
+ align:start position:0%
+used it it is obviously like critical
+ 
+
+ align:start position:0%
+used it it is obviously like critical
+massively used it has been successful
+
+ align:start position:0%
+massively used it has been successful
+ 
+
+ align:start position:0%
+massively used it has been successful
+but like it's become you know it's a
+
+ align:start position:0%
+but like it's become you know it's a
+ 
+
+ align:start position:0%
+but like it's become you know it's a
+really effective drug so maybe there's
+
+ align:start position:0%
+really effective drug so maybe there's
+ 
+
+ align:start position:0%
+really effective drug so maybe there's
+not like repeat people in the way that
+
+ align:start position:0%
+not like repeat people in the way that
+ 
+
+ align:start position:0%
+not like repeat people in the way that
+other drugs might have a lot of repeat
+
+ align:start position:0%
+other drugs might have a lot of repeat
+ 
+
+ align:start position:0%
+other drugs might have a lot of repeat
+users maybe it's treating a large
+
+ align:start position:0%
+users maybe it's treating a large
+ 
+
+ align:start position:0%
+users maybe it's treating a large
+population but like people don't really
+
+ align:start position:0%
+population but like people don't really
+ 
+
+ align:start position:0%
+population but like people don't really
+get the same kind of strain of disease
+
+ align:start position:0%
+get the same kind of strain of disease
+ 
+
+ align:start position:0%
+get the same kind of strain of disease
+multiple times something like that the
+
+ align:start position:0%
+multiple times something like that the
+ 
+
+ align:start position:0%
+multiple times something like that the
+problem is that we over prescribed
+
+ align:start position:0%
+problem is that we over prescribed
+ 
+
+ align:start position:0%
+problem is that we over prescribed
+antibiotics to an absurd extent and
+
+ align:start position:0%
+antibiotics to an absurd extent and
+ 
+
+ align:start position:0%
+antibiotics to an absurd extent and
+we're sticking antibiotics and
+
+ align:start position:0%
+we're sticking antibiotics and
+ 
+
+ align:start position:0%
+we're sticking antibiotics and
+everything like hand soap and we're
+
+ align:start position:0%
+everything like hand soap and we're
+ 
+
+ align:start position:0%
+everything like hand soap and we're
+virtually guaranteeing our own kind of
+
+ align:start position:0%
+virtually guaranteeing our own kind of
+ 
+
+ align:start position:0%
+virtually guaranteeing our own kind of
+Darwinian dilemma seems to be like
+
+ align:start position:0%
+Darwinian dilemma seems to be like
+ 
+
+ align:start position:0%
+Darwinian dilemma seems to be like
+applying the language of this class
+
+ align:start position:0%
+applying the language of this class
+ 
+
+ align:start position:0%
+applying the language of this class
+elections were playing catch up with an
+
+ align:start position:0%
+elections were playing catch up with an
+ 
+
+ align:start position:0%
+elections were playing catch up with an
+innovation problem instead of purely
+
+ align:start position:0%
+innovation problem instead of purely
+ 
+
+ align:start position:0%
+innovation problem instead of purely
+innovating which doesn't seem like
+
+ align:start position:0%
+innovating which doesn't seem like
+ 
+
+ align:start position:0%
+innovating which doesn't seem like
+American weight problem it's kind of odd
+
+ align:start position:0%
+American weight problem it's kind of odd
+ 
+
+ align:start position:0%
+American weight problem it's kind of odd
+because it's almost like we're being
+
+ align:start position:0%
+because it's almost like we're being
+ 
+
+ align:start position:0%
+because it's almost like we're being
+outplayed by nature which I mean most of
+
+ align:start position:0%
+outplayed by nature which I mean most of
+ 
+
+ align:start position:0%
+outplayed by nature which I mean most of
+our biggest success of the last two or
+
+ align:start position:0%
+our biggest success of the last two or
+ 
+
+ align:start position:0%
+our biggest success of the last two or
+three hundred years have been us
+
+ align:start position:0%
+three hundred years have been us
+ 
+
+ align:start position:0%
+three hundred years have been us
+figuring out how to manipulate nature to
+
+ align:start position:0%
+figuring out how to manipulate nature to
+ 
+
+ align:start position:0%
+figuring out how to manipulate nature to
+our advantage but if that's all we have
+
+ align:start position:0%
+our advantage but if that's all we have
+ 
+
+ align:start position:0%
+our advantage but if that's all we have
+to do have one more question for the FDA
+
+ align:start position:0%
+to do have one more question for the FDA
+ 
+
+ align:start position:0%
+to do have one more question for the FDA
+reading more on the standard setting
+
+ align:start position:0%
+reading more on the standard setting
+ 
+
+ align:start position:0%
+reading more on the standard setting
+what do you guys think again are the
+
+ align:start position:0%
+what do you guys think again are the
+ 
+
+ align:start position:0%
+what do you guys think again are the
+rules and responsibilities of such an
+
+ align:start position:0%
+rules and responsibilities of such an
+ 
+
+ align:start position:0%
+rules and responsibilities of such an
+agency that set these standards to
+
+ align:start position:0%
+agency that set these standards to
+ 
+
+ align:start position:0%
+agency that set these standards to
+encourage people to take risks and bring
+
+ align:start position:0%
+encourage people to take risks and bring
+ 
+
+ align:start position:0%
+encourage people to take risks and bring
+these deadly mystery drugs to market
+
+ align:start position:0%
+these deadly mystery drugs to market
+ 
+
+ align:start position:0%
+these deadly mystery drugs to market
+because the reading mentioned that a lot
+
+ align:start position:0%
+because the reading mentioned that a lot
+ 
+
+ align:start position:0%
+because the reading mentioned that a lot
+of researchers won't even go down that
+
+ align:start position:0%
+of researchers won't even go down that
+ 
+
+ align:start position:0%
+of researchers won't even go down that
+path because they know how arduous those
+
+ align:start position:0%
+path because they know how arduous those
+ 
+
+ align:start position:0%
+path because they know how arduous those
+sudden terms of like okay it's a very
+
+ align:start position:0%
+sudden terms of like okay it's a very
+ 
+
+ align:start position:0%
+sudden terms of like okay it's a very
+hard process but once you do it you're
+
+ align:start position:0%
+hard process but once you do it you're
+ 
+
+ align:start position:0%
+hard process but once you do it you're
+kind of set the only now the question is
+
+ align:start position:0%
+kind of set the only now the question is
+ 
+
+ align:start position:0%
+kind of set the only now the question is
+like I would do I would tear it because
+
+ align:start position:0%
+like I would do I would tear it because
+ 
+
+ align:start position:0%
+like I would do I would tear it because
+there's probably different kind of drugs
+
+ align:start position:0%
+there's probably different kind of drugs
+ 
+
+ align:start position:0%
+there's probably different kind of drugs
+that have different specialties and
+
+ align:start position:0%
+that have different specialties and
+ 
+
+ align:start position:0%
+that have different specialties and
+they're probably something that you know
+
+ align:start position:0%
+they're probably something that you know
+ 
+
+ align:start position:0%
+they're probably something that you know
+there's probably drug that I really want
+
+ align:start position:0%
+there's probably drug that I really want
+ 
+
+ align:start position:0%
+there's probably drug that I really want
+to get tested really really really well
+
+ align:start position:0%
+to get tested really really really well
+ 
+
+ align:start position:0%
+to get tested really really really well
+well there's something that even if I do
+
+ align:start position:0%
+well there's something that even if I do
+ 
+
+ align:start position:0%
+well there's something that even if I do
+test them I just don't know no and some
+
+ align:start position:0%
+test them I just don't know no and some
+ 
+
+ align:start position:0%
+test them I just don't know no and some
+folks that probably get passed like
+
+ align:start position:0%
+folks that probably get passed like
+ 
+
+ align:start position:0%
+folks that probably get passed like
+faster so I would figure out like how
+
+ align:start position:0%
+faster so I would figure out like how
+ 
+
+ align:start position:0%
+faster so I would figure out like how
+does the scheme work look at the data in
+
+ align:start position:0%
+does the scheme work look at the data in
+ 
+
+ align:start position:0%
+does the scheme work look at the data in
+terms of like how are these drugs being
+
+ align:start position:0%
+terms of like how are these drugs being
+ 
+
+ align:start position:0%
+terms of like how are these drugs being
+passed how long does it take which ones
+
+ align:start position:0%
+passed how long does it take which ones
+ 
+
+ align:start position:0%
+passed how long does it take which ones
+were relatively quick see if I could
+
+ align:start position:0%
+were relatively quick see if I could
+ 
+
+ align:start position:0%
+were relatively quick see if I could
+like restructure the organization so
+
+ align:start position:0%
+like restructure the organization so
+ 
+
+ align:start position:0%
+like restructure the organization so
+that I can optimize for you know the
+
+ align:start position:0%
+that I can optimize for you know the
+ 
+
+ align:start position:0%
+that I can optimize for you know the
+stuff that really matters and like I
+
+ align:start position:0%
+stuff that really matters and like I
+ 
+
+ align:start position:0%
+stuff that really matters and like I
+said it doesn't matter very much like
+
+ align:start position:0%
+said it doesn't matter very much like
+ 
+
+ align:start position:0%
+said it doesn't matter very much like
+it's not focus so nothing a linear kind
+
+ align:start position:0%
+it's not focus so nothing a linear kind
+ 
+
+ align:start position:0%
+it's not focus so nothing a linear kind
+of everything is the same so are you
+
+ align:start position:0%
+of everything is the same so are you
+ 
+
+ align:start position:0%
+of everything is the same so are you
+saying maybe make a function make the
+
+ align:start position:0%
+saying maybe make a function make the
+ 
+
+ align:start position:0%
+saying maybe make a function make the
+funding or whatever a function of say
+
+ align:start position:0%
+funding or whatever a function of say
+ 
+
+ align:start position:0%
+funding or whatever a function of say
+quality and the amount
+
+ align:start position:0%
+quality and the amount
+ 
+
+ align:start position:0%
+quality and the amount
+taking it past so then like you need a
+
+ align:start position:0%
+taking it past so then like you need a
+ 
+
+ align:start position:0%
+taking it past so then like you need a
+drug that maybe would only work for a
+
+ align:start position:0%
+drug that maybe would only work for a
+ 
+
+ align:start position:0%
+drug that maybe would only work for a
+few people you can make it so it would
+
+ align:start position:0%
+few people you can make it so it would
+ 
+
+ align:start position:0%
+few people you can make it so it would
+be really high quality whereas if you
+
+ align:start position:0%
+be really high quality whereas if you
+ 
+
+ align:start position:0%
+be really high quality whereas if you
+have a dragon super for a lot of people
+
+ align:start position:0%
+have a dragon super for a lot of people
+ 
+
+ align:start position:0%
+have a dragon super for a lot of people
+that you need really quickly then you
+
+ align:start position:0%
+that you need really quickly then you
+ 
+
+ align:start position:0%
+that you need really quickly then you
+can make it so that it I don't know it
+
+ align:start position:0%
+can make it so that it I don't know it
+ 
+
+ align:start position:0%
+can make it so that it I don't know it
+works it's less robust or for fewer
+
+ align:start position:0%
+works it's less robust or for fewer
+ 
+
+ align:start position:0%
+works it's less robust or for fewer
+strains that around racing something
+
+ align:start position:0%
+strains that around racing something
+ 
+
+ align:start position:0%
+strains that around racing something
+like oh yeah something like that in
+
+ align:start position:0%
+like oh yeah something like that in
+ 
+
+ align:start position:0%
+like oh yeah something like that in
+terms of like so say because you're
+
+ align:start position:0%
+terms of like so say because you're
+ 
+
+ align:start position:0%
+terms of like so say because you're
+obviously about like compound interest
+
+ align:start position:0%
+obviously about like compound interest
+ 
+
+ align:start position:0%
+obviously about like compound interest
+yeah so say I know that if I make this
+
+ align:start position:0%
+yeah so say I know that if I make this
+ 
+
+ align:start position:0%
+yeah so say I know that if I make this
+drug I'm gonna save the government you
+
+ align:start position:0%
+drug I'm gonna save the government you
+ 
+
+ align:start position:0%
+drug I'm gonna save the government you
+know make fifty million dollars a year
+
+ align:start position:0%
+know make fifty million dollars a year
+ 
+
+ align:start position:0%
+know make fifty million dollars a year
+eighty billion dollars a year over five
+
+ align:start position:0%
+eighty billion dollars a year over five
+ 
+
+ align:start position:0%
+eighty billion dollars a year over five
+years so if it's something it's gonna
+
+ align:start position:0%
+years so if it's something it's gonna
+ 
+
+ align:start position:0%
+years so if it's something it's gonna
+have to make a big impact how about we
+
+ align:start position:0%
+have to make a big impact how about we
+ 
+
+ align:start position:0%
+have to make a big impact how about we
+go faster we can iterate faster so we'll
+
+ align:start position:0%
+go faster we can iterate faster so we'll
+ 
+
+ align:start position:0%
+go faster we can iterate faster so we'll
+have priorities for drugs that really
+
+ align:start position:0%
+have priorities for drugs that really
+ 
+
+ align:start position:0%
+have priorities for drugs that really
+really matter I don't like the argument
+
+ align:start position:0%
+really matter I don't like the argument
+ 
+
+ align:start position:0%
+really matter I don't like the argument
+I'm saying oh not a lot of people are
+
+ align:start position:0%
+I'm saying oh not a lot of people are
+ 
+
+ align:start position:0%
+I'm saying oh not a lot of people are
+gonna use it so we're not going to
+
+ align:start position:0%
+gonna use it so we're not going to
+ 
+
+ align:start position:0%
+gonna use it so we're not going to
+prioritize it let's put it back because
+
+ align:start position:0%
+prioritize it let's put it back because
+ 
+
+ align:start position:0%
+prioritize it let's put it back because
+that's kind of false or maybe you should
+
+ align:start position:0%
+that's kind of false or maybe you should
+ 
+
+ align:start position:0%
+that's kind of false or maybe you should
+create another organization that only
+
+ align:start position:0%
+create another organization that only
+ 
+
+ align:start position:0%
+create another organization that only
+focuses on those kinds of drugs and
+
+ align:start position:0%
+focuses on those kinds of drugs and
+ 
+
+ align:start position:0%
+focuses on those kinds of drugs and
+split up the FDA into women folks on
+
+ align:start position:0%
+split up the FDA into women folks on
+ 
+
+ align:start position:0%
+split up the FDA into women folks on
+that it gets equal review but that's not
+
+ align:start position:0%
+that it gets equal review but that's not
+ 
+
+ align:start position:0%
+that it gets equal review but that's not
+absolutely so I just kind of summarized
+
+ align:start position:0%
+absolutely so I just kind of summarized
+ 
+
+ align:start position:0%
+absolutely so I just kind of summarized
+here from you're all good good
+
+ align:start position:0%
+here from you're all good good
+ 
+
+ align:start position:0%
+here from you're all good good
+presentations and good questions FDA is
+
+ align:start position:0%
+presentations and good questions FDA is
+ 
+
+ align:start position:0%
+presentations and good questions FDA is
+sitting on a really critical part of the
+
+ align:start position:0%
+sitting on a really critical part of the
+ 
+
+ align:start position:0%
+sitting on a really critical part of the
+problem so if we could significantly
+
+ align:start position:0%
+problem so if we could significantly
+ 
+
+ align:start position:0%
+problem so if we could significantly
+speed the drug approval process and if
+
+ align:start position:0%
+speed the drug approval process and if
+ 
+
+ align:start position:0%
+speed the drug approval process and if
+we could significantly lower its cost we
+
+ align:start position:0%
+we could significantly lower its cost we
+ 
+
+ align:start position:0%
+we could significantly lower its cost we
+solve a lot of problems here right we
+
+ align:start position:0%
+solve a lot of problems here right we
+ 
+
+ align:start position:0%
+solve a lot of problems here right we
+can be much less reliant on a
+
+ align:start position:0%
+can be much less reliant on a
+ 
+
+ align:start position:0%
+can be much less reliant on a
+blockbuster drug model so it seems to me
+
+ align:start position:0%
+blockbuster drug model so it seems to me
+ 
+
+ align:start position:0%
+blockbuster drug model so it seems to me
+that in terms of the panoply of fixes to
+
+ align:start position:0%
+that in terms of the panoply of fixes to
+ 
+
+ align:start position:0%
+that in terms of the panoply of fixes to
+this gap and the innovation system
+
+ align:start position:0%
+this gap and the innovation system
+ 
+
+ align:start position:0%
+this gap and the innovation system
+really paying attention to how to
+
+ align:start position:0%
+really paying attention to how to
+ 
+
+ align:start position:0%
+really paying attention to how to
+accelerate Martinez you were pointing
+
+ align:start position:0%
+accelerate Martinez you were pointing
+ 
+
+ align:start position:0%
+accelerate Martinez you were pointing
+out the review process at FDA and you
+
+ align:start position:0%
+out the review process at FDA and you
+ 
+
+ align:start position:0%
+out the review process at FDA and you
+know you it's very hard to reduce safety
+
+ align:start position:0%
+know you it's very hard to reduce safety
+ 
+
+ align:start position:0%
+know you it's very hard to reduce safety
+requirements it's just not going to be
+
+ align:start position:0%
+requirements it's just not going to be
+ 
+
+ align:start position:0%
+requirements it's just not going to be
+acceptable to the public but if there
+
+ align:start position:0%
+acceptable to the public but if there
+ 
+
+ align:start position:0%
+acceptable to the public but if there
+are new ways of using big data and
+
+ align:start position:0%
+are new ways of using big data and
+ 
+
+ align:start position:0%
+are new ways of using big data and
+analytics and simulation and modeling
+
+ align:start position:0%
+analytics and simulation and modeling
+ 
+
+ align:start position:0%
+analytics and simulation and modeling
+those potentially present very
+
+ align:start position:0%
+those potentially present very
+ 
+
+ align:start position:0%
+those potentially present very
+significant improvements to this process
+
+ align:start position:0%
+significant improvements to this process
+ 
+
+ align:start position:0%
+significant improvements to this process
+here that could really help tackle this
+
+ align:start position:0%
+here that could really help tackle this
+ 
+
+ align:start position:0%
+here that could really help tackle this
+problem so putting some money on that
+
+ align:start position:0%
+problem so putting some money on that
+ 
+
+ align:start position:0%
+problem so putting some money on that
+one I think could be really key now the
+
+ align:start position:0%
+one I think could be really key now the
+ 
+
+ align:start position:0%
+one I think could be really key now the
+ich then we go back to NIH NIH is not
+
+ align:start position:0%
+ich then we go back to NIH NIH is not
+ 
+
+ align:start position:0%
+ich then we go back to NIH NIH is not
+organized around those kinds of
+
+ align:start position:0%
+organized around those kinds of
+ 
+
+ align:start position:0%
+organized around those kinds of
+technology problems so how are we gonna
+
+ align:start position:0%
+technology problems so how are we gonna
+ 
+
+ align:start position:0%
+technology problems so how are we gonna
+do this right so we have another dilemma
+
+ align:start position:0%
+do this right so we have another dilemma
+ 
+
+ align:start position:0%
+do this right so we have another dilemma
+since we arrive at the answer anything
+
+ align:start position:0%
+since we arrive at the answer anything
+ 
+
+ align:start position:0%
+since we arrive at the answer anything
+else I just as we transition into fills
+
+ align:start position:0%
+else I just as we transition into fills
+ 
+
+ align:start position:0%
+else I just as we transition into fills
+everything about this being a legacy
+
+ align:start position:0%
+everything about this being a legacy
+ 
+
+ align:start position:0%
+everything about this being a legacy
+sector we're exhibiting a lot of legacy
+
+ align:start position:0%
+sector we're exhibiting a lot of legacy
+ 
+
+ align:start position:0%
+sector we're exhibiting a lot of legacy
+features I'm curious about we you build
+
+ align:start position:0%
+features I'm curious about we you build
+ 
+
+ align:start position:0%
+features I'm curious about we you build
+the class thought about the political
+
+ align:start position:0%
+the class thought about the political
+ 
+
+ align:start position:0%
+the class thought about the political
+viability of it I guess in terms of
+
+ align:start position:0%
+viability of it I guess in terms of
+ 
+
+ align:start position:0%
+viability of it I guess in terms of
+Martine sort of repository de materia
+
+ align:start position:0%
+Martine sort of repository de materia
+ 
+
+ align:start position:0%
+Martine sort of repository de materia
+approach if we were thought it was more
+
+ align:start position:0%
+approach if we were thought it was more
+ 
+
+ align:start position:0%
+approach if we were thought it was more
+politically viable to do this worry
+
+ align:start position:0%
+politically viable to do this worry
+ 
+
+ align:start position:0%
+politically viable to do this worry
+their therapeutic drugs are for sort of
+
+ align:start position:0%
+their therapeutic drugs are for sort of
+ 
+
+ align:start position:0%
+their therapeutic drugs are for sort of
+Carol interventions there's there seems
+
+ align:start position:0%
+Carol interventions there's there seems
+ 
+
+ align:start position:0%
+Carol interventions there's there seems
+in my very limited study of home life
+
+ align:start position:0%
+in my very limited study of home life
+ 
+
+ align:start position:0%
+in my very limited study of home life
+sciences to be a proclivity towards the
+
+ align:start position:0%
+sciences to be a proclivity towards the
+ 
+
+ align:start position:0%
+sciences to be a proclivity towards the
+therapeutic drugs and interventions
+
+ align:start position:0%
+therapeutic drugs and interventions
+ 
+
+ align:start position:0%
+therapeutic drugs and interventions
+because they're more sustainable and
+
+ align:start position:0%
+because they're more sustainable and
+ 
+
+ align:start position:0%
+because they're more sustainable and
+profitable so do we think that that
+
+ align:start position:0%
+profitable so do we think that that
+ 
+
+ align:start position:0%
+profitable so do we think that that
+could be a potential opportunity to test
+
+ align:start position:0%
+could be a potential opportunity to test
+ 
+
+ align:start position:0%
+could be a potential opportunity to test
+an RV like system or to test the sort of
+
+ align:start position:0%
+an RV like system or to test the sort of
+ 
+
+ align:start position:0%
+an RV like system or to test the sort of
+improved speed of acceptance of the drug
+
+ align:start position:0%
+improved speed of acceptance of the drug
+ 
+
+ align:start position:0%
+improved speed of acceptance of the drug
+let me throw that back to them to the
+
+ align:start position:0%
+let me throw that back to them to the
+ 
+
+ align:start position:0%
+let me throw that back to them to the
+group here I like the point about how
+
+ align:start position:0%
+group here I like the point about how
+ 
+
+ align:start position:0%
+group here I like the point about how
+drugs work so they want to have
+
+ align:start position:0%
+drugs work so they want to have
+ 
+
+ align:start position:0%
+drugs work so they want to have
+recurring revenue but I think is the
+
+ align:start position:0%
+recurring revenue but I think is the
+ 
+
+ align:start position:0%
+recurring revenue but I think is the
+government you you get a lot of you have
+
+ align:start position:0%
+government you you get a lot of you have
+ 
+
+ align:start position:0%
+government you you get a lot of you have
+to pay that so like it'd be interesting
+
+ align:start position:0%
+to pay that so like it'd be interesting
+ 
+
+ align:start position:0%
+to pay that so like it'd be interesting
+the government's like okay well we know
+
+ align:start position:0%
+the government's like okay well we know
+ 
+
+ align:start position:0%
+the government's like okay well we know
+over the lifetime if we don't solve this
+
+ align:start position:0%
+over the lifetime if we don't solve this
+ 
+
+ align:start position:0%
+over the lifetime if we don't solve this
+now it's gonna cost us like 1 million
+
+ align:start position:0%
+now it's gonna cost us like 1 million
+ 
+
+ align:start position:0%
+now it's gonna cost us like 1 million
+dollars for this person so you know you
+
+ align:start position:0%
+dollars for this person so you know you
+ 
+
+ align:start position:0%
+dollars for this person so you know you
+solve it today we're gonna give you 20 K
+
+ align:start position:0%
+solve it today we're gonna give you 20 K
+ 
+
+ align:start position:0%
+solve it today we're gonna give you 20 K
+right which is way cheaper for us so
+
+ align:start position:0%
+right which is way cheaper for us so
+ 
+
+ align:start position:0%
+right which is way cheaper for us so
+we're all in the long term but you're
+
+ align:start position:0%
+we're all in the long term but you're
+ 
+
+ align:start position:0%
+we're all in the long term but you're
+not getting paid ten dollars per driver
+
+ align:start position:0%
+not getting paid ten dollars per driver
+ 
+
+ align:start position:0%
+not getting paid ten dollars per driver
+on $1.00 per drug and so it's like a
+
+ align:start position:0%
+on $1.00 per drug and so it's like a
+ 
+
+ align:start position:0%
+on $1.00 per drug and so it's like a
+kind of a win-win because it's really
+
+ align:start position:0%
+kind of a win-win because it's really
+ 
+
+ align:start position:0%
+kind of a win-win because it's really
+good revenue for the company and it
+
+ align:start position:0%
+good revenue for the company and it
+ 
+
+ align:start position:0%
+good revenue for the company and it
+justifies having a super drug that
+
+ align:start position:0%
+justifies having a super drug that
+ 
+
+ align:start position:0%
+justifies having a super drug that
+really really works and it gives them
+
+ align:start position:0%
+really really works and it gives them
+ 
+
+ align:start position:0%
+really really works and it gives them
+enough money in their balance sheet I
+
+ align:start position:0%
+enough money in their balance sheet I
+ 
+
+ align:start position:0%
+enough money in their balance sheet I
+don't know if you guys know how Warren
+
+ align:start position:0%
+don't know if you guys know how Warren
+ 
+
+ align:start position:0%
+don't know if you guys know how Warren
+Buffett got rich but he had an insurance
+
+ align:start position:0%
+Buffett got rich but he had an insurance
+ 
+
+ align:start position:0%
+Buffett got rich but he had an insurance
+company and they gave him a lot of cash
+
+ align:start position:0%
+company and they gave him a lot of cash
+ 
+
+ align:start position:0%
+company and they gave him a lot of cash
+so that I can invest in other companies
+
+ align:start position:0%
+so that I can invest in other companies
+ 
+
+ align:start position:0%
+so that I can invest in other companies
+and it's really good for companies
+
+ align:start position:0%
+and it's really good for companies
+ 
+
+ align:start position:0%
+and it's really good for companies
+having a lot cash on hand
+
+ align:start position:0%
+having a lot cash on hand
+ 
+
+ align:start position:0%
+having a lot cash on hand
+who'da thought like a lot of them don't
+
+ align:start position:0%
+who'da thought like a lot of them don't
+ 
+
+ align:start position:0%
+who'da thought like a lot of them don't
+have a lot of cash on hand at any given
+
+ align:start position:0%
+have a lot of cash on hand at any given
+ 
+
+ align:start position:0%
+have a lot of cash on hand at any given
+time so it's like they have their assets
+
+ align:start position:0%
+time so it's like they have their assets
+ 
+
+ align:start position:0%
+time so it's like they have their assets
+situated between physical yeah and so
+
+ align:start position:0%
+situated between physical yeah and so
+ 
+
+ align:start position:0%
+situated between physical yeah and so
+like it's really good to like be able to
+
+ align:start position:0%
+like it's really good to like be able to
+ 
+
+ align:start position:0%
+like it's really good to like be able to
+move quickly buy all this stuff and it
+
+ align:start position:0%
+move quickly buy all this stuff and it
+ 
+
+ align:start position:0%
+move quickly buy all this stuff and it
+just nothing that happened is that
+
+ align:start position:0%
+just nothing that happened is that
+ 
+
+ align:start position:0%
+just nothing that happened is that
+easily there's also a lot of tax left
+
+ align:start position:0%
+easily there's also a lot of tax left
+ 
+
+ align:start position:0%
+easily there's also a lot of tax left
+it's that's why people good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/wvXDB9dMdEo.txt b/wvXDB9dMdEo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0c50103664b95fa07fe6bb5b5f7cdbd40dfd8f8c
--- /dev/null
+++ b/wvXDB9dMdEo.txt
@@ -0,0 +1,12911 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a creative commons license
+
+ align:start position:0%
+a creative commons license
+ 
+
+ align:start position:0%
+a creative commons license
+your support will help mit
+
+ align:start position:0%
+your support will help mit
+ 
+
+ align:start position:0%
+your support will help mit
+opencourseware continue to offer high
+
+ align:start position:0%
+opencourseware continue to offer high
+ 
+
+ align:start position:0%
+opencourseware continue to offer high
+quality educational resources for free
+
+ align:start position:0%
+quality educational resources for free
+ 
+
+ align:start position:0%
+quality educational resources for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of mit courses
+
+ align:start position:0%
+materials from hundreds of mit courses
+ 
+
+ align:start position:0%
+materials from hundreds of mit courses
+visit mit opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is the second time we are having
+
+ align:start position:0%
+this is the second time we are having
+ 
+
+ align:start position:0%
+this is the second time we are having
+this class we had it last year in a
+
+ align:start position:0%
+this class we had it last year in a
+ 
+
+ align:start position:0%
+this class we had it last year in a
+smaller version
+
+ align:start position:0%
+smaller version
+ 
+
+ align:start position:0%
+smaller version
+that was for six units of credit
+
+ align:start position:0%
+that was for six units of credit
+ 
+
+ align:start position:0%
+that was for six units of credit
+and we had it once a week
+
+ align:start position:0%
+and we had it once a week
+ 
+
+ align:start position:0%
+and we had it once a week
+and mostly
+
+ align:start position:0%
+and mostly
+ 
+
+ align:start position:0%
+and mostly
+practitioners from the industry from
+
+ align:start position:0%
+practitioners from the industry from
+ 
+
+ align:start position:0%
+practitioners from the industry from
+morgan stanley talking about examples
+
+ align:start position:0%
+morgan stanley talking about examples
+ 
+
+ align:start position:0%
+morgan stanley talking about examples
+how math is applied in modern finance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+is it okay yeah and uh so we got some
+
+ align:start position:0%
+is it okay yeah and uh so we got some
+ 
+
+ align:start position:0%
+is it okay yeah and uh so we got some
+good response last year so with the
+
+ align:start position:0%
+good response last year so with the
+ 
+
+ align:start position:0%
+good response last year so with the
+support of the math department we
+
+ align:start position:0%
+support of the math department we
+ 
+
+ align:start position:0%
+support of the math department we
+decided to expand
+
+ align:start position:0%
+decided to expand
+ 
+
+ align:start position:0%
+decided to expand
+this class to
+
+ align:start position:0%
+this class to
+ 
+
+ align:start position:0%
+this class to
+be 12 units of credit and have twice a
+
+ align:start position:0%
+be 12 units of credit and have twice a
+ 
+
+ align:start position:0%
+be 12 units of credit and have twice a
+week so we have every tuesday and
+
+ align:start position:0%
+week so we have every tuesday and
+ 
+
+ align:start position:0%
+week so we have every tuesday and
+thursday afternoon from 2 30 to 4 as you
+
+ align:start position:0%
+thursday afternoon from 2 30 to 4 as you
+ 
+
+ align:start position:0%
+thursday afternoon from 2 30 to 4 as you
+know in this classroom
+
+ align:start position:0%
+know in this classroom
+ 
+
+ align:start position:0%
+know in this classroom
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so last year dr
+
+ align:start position:0%
+so last year dr
+ 
+
+ align:start position:0%
+so last year dr
+vasily estrella and i i'm by the way i'm
+
+ align:start position:0%
+vasily estrella and i i'm by the way i'm
+ 
+
+ align:start position:0%
+vasily estrella and i i'm by the way i'm
+jake shaw and that's dr vasily and we
+
+ align:start position:0%
+jake shaw and that's dr vasily and we
+ 
+
+ align:start position:0%
+jake shaw and that's dr vasily and we
+were the main instructors last year now
+
+ align:start position:0%
+were the main instructors last year now
+ 
+
+ align:start position:0%
+were the main instructors last year now
+we doubled it up to four main
+
+ align:start position:0%
+we doubled it up to four main
+ 
+
+ align:start position:0%
+we doubled it up to four main
+instructors
+
+ align:start position:0%
+instructors
+ 
+
+ align:start position:0%
+instructors
+uh that's dr peter campston
+
+ align:start position:0%
+uh that's dr peter campston
+ 
+
+ align:start position:0%
+uh that's dr peter campston
+and dr chong bong lee
+
+ align:start position:0%
+and dr chong bong lee
+ 
+
+ align:start position:0%
+and dr chong bong lee
+the reason we doubled up the main
+
+ align:start position:0%
+the reason we doubled up the main
+ 
+
+ align:start position:0%
+the reason we doubled up the main
+instructors is we have newly added math
+
+ align:start position:0%
+instructors is we have newly added math
+ 
+
+ align:start position:0%
+instructors is we have newly added math
+lectures
+
+ align:start position:0%
+lectures
+ 
+
+ align:start position:0%
+lectures
+mostly focusing on
+
+ align:start position:0%
+mostly focusing on
+ 
+
+ align:start position:0%
+mostly focusing on
+from linear algebra probability to
+
+ align:start position:0%
+from linear algebra probability to
+ 
+
+ align:start position:0%
+from linear algebra probability to
+statistics and some stochastic calculus
+
+ align:start position:0%
+statistics and some stochastic calculus
+ 
+
+ align:start position:0%
+statistics and some stochastic calculus
+so give you the foundation to understand
+
+ align:start position:0%
+so give you the foundation to understand
+ 
+
+ align:start position:0%
+so give you the foundation to understand
+the mass
+
+ align:start position:0%
+the mass
+ 
+
+ align:start position:0%
+the mass
+will be used in those
+
+ align:start position:0%
+will be used in those
+ 
+
+ align:start position:0%
+will be used in those
+examples
+
+ align:start position:0%
+examples
+ 
+
+ align:start position:0%
+examples
+uh in the lecture taught by
+
+ align:start position:0%
+uh in the lecture taught by
+ 
+
+ align:start position:0%
+uh in the lecture taught by
+the practitioners from the industry
+
+ align:start position:0%
+the practitioners from the industry
+ 
+
+ align:start position:0%
+the practitioners from the industry
+and the purpose of this course is really
+
+ align:start position:0%
+and the purpose of this course is really
+ 
+
+ align:start position:0%
+and the purpose of this course is really
+to give you a sampling manual to see
+
+ align:start position:0%
+to give you a sampling manual to see
+ 
+
+ align:start position:0%
+to give you a sampling manual to see
+how mathematics is applied
+
+ align:start position:0%
+how mathematics is applied
+ 
+
+ align:start position:0%
+how mathematics is applied
+in modern finance and help you to decide
+
+ align:start position:0%
+in modern finance and help you to decide
+ 
+
+ align:start position:0%
+in modern finance and help you to decide
+if this is a field that you would be uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you heard that
+
+ align:start position:0%
+okay you heard that
+ 
+
+ align:start position:0%
+okay you heard that
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+so hopefully this will give you enough
+
+ align:start position:0%
+so hopefully this will give you enough
+ 
+
+ align:start position:0%
+so hopefully this will give you enough
+information to decide this is the field
+
+ align:start position:0%
+information to decide this is the field
+ 
+
+ align:start position:0%
+information to decide this is the field
+you like to pursue in your future career
+
+ align:start position:0%
+you like to pursue in your future career
+ 
+
+ align:start position:0%
+you like to pursue in your future career
+in fact last year
+
+ align:start position:0%
+in fact last year
+ 
+
+ align:start position:0%
+in fact last year
+when we finished the class we had a few
+
+ align:start position:0%
+when we finished the class we had a few
+ 
+
+ align:start position:0%
+when we finished the class we had a few
+students
+
+ align:start position:0%
+students
+ 
+
+ align:start position:0%
+students
+coming
+
+ align:start position:0%
+coming
+ 
+
+ align:start position:0%
+coming
+to work in the industry some worked at
+
+ align:start position:0%
+to work in the industry some worked at
+ 
+
+ align:start position:0%
+to work in the industry some worked at
+morgan stanley someone worked at
+
+ align:start position:0%
+morgan stanley someone worked at
+ 
+
+ align:start position:0%
+morgan stanley someone worked at
+elsewhere
+
+ align:start position:0%
+elsewhere
+ 
+
+ align:start position:0%
+elsewhere
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so that's that's really the goal and uh
+
+ align:start position:0%
+so that's that's really the goal and uh
+ 
+
+ align:start position:0%
+so that's that's really the goal and uh
+at the same time obviously you will
+
+ align:start position:0%
+at the same time obviously you will
+ 
+
+ align:start position:0%
+at the same time obviously you will
+further solidify your math knowledge and
+
+ align:start position:0%
+further solidify your math knowledge and
+ 
+
+ align:start position:0%
+further solidify your math knowledge and
+learn on
+
+ align:start position:0%
+learn on
+ 
+
+ align:start position:0%
+learn on
+a new content and we put the
+
+ align:start position:0%
+a new content and we put the
+ 
+
+ align:start position:0%
+a new content and we put the
+pre-requisite uh about the math part a
+
+ align:start position:0%
+pre-requisite uh about the math part a
+ 
+
+ align:start position:0%
+pre-requisite uh about the math part a
+bit later
+
+ align:start position:0%
+bit later
+ 
+
+ align:start position:0%
+bit later
+uh so i will use today's first lectures
+
+ align:start position:0%
+uh so i will use today's first lectures
+ 
+
+ align:start position:0%
+uh so i will use today's first lectures
+time to give you an introduction really
+
+ align:start position:0%
+time to give you an introduction really
+ 
+
+ align:start position:0%
+time to give you an introduction really
+to prepare you
+
+ align:start position:0%
+to prepare you
+ 
+
+ align:start position:0%
+to prepare you
+some basic background knowledge about
+
+ align:start position:0%
+some basic background knowledge about
+ 
+
+ align:start position:0%
+some basic background knowledge about
+the financial markets
+
+ align:start position:0%
+the financial markets
+ 
+
+ align:start position:0%
+the financial markets
+um some terminologies will be used which
+
+ align:start position:0%
+um some terminologies will be used which
+ 
+
+ align:start position:0%
+um some terminologies will be used which
+you may not have heard before
+
+ align:start position:0%
+you may not have heard before
+ 
+
+ align:start position:0%
+you may not have heard before
+so before i get into the introduction i
+
+ align:start position:0%
+so before i get into the introduction i
+ 
+
+ align:start position:0%
+so before i get into the introduction i
+mean i always like to know who are
+
+ align:start position:0%
+mean i always like to know who are
+ 
+
+ align:start position:0%
+mean i always like to know who are
+actually in the classroom so let me ask
+
+ align:start position:0%
+actually in the classroom so let me ask
+ 
+
+ align:start position:0%
+actually in the classroom so let me ask
+you a few questions you just need to
+
+ align:start position:0%
+you a few questions you just need to
+ 
+
+ align:start position:0%
+you a few questions you just need to
+raise your hands and so i know roughly
+
+ align:start position:0%
+raise your hands and so i know roughly
+ 
+
+ align:start position:0%
+raise your hands and so i know roughly
+what kind of background and uh where you
+
+ align:start position:0%
+what kind of background and uh where you
+ 
+
+ align:start position:0%
+what kind of background and uh where you
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+so how many undergraduate students are
+
+ align:start position:0%
+so how many undergraduate students are
+ 
+
+ align:start position:0%
+so how many undergraduate students are
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so i would say
+
+ align:start position:0%
+so i would say
+ 
+
+ align:start position:0%
+so i would say
+eighty percent okay statistics that's a
+
+ align:start position:0%
+eighty percent okay statistics that's a
+ 
+
+ align:start position:0%
+eighty percent okay statistics that's a
+how many graduate students are here just
+
+ align:start position:0%
+how many graduate students are here just
+ 
+
+ align:start position:0%
+how many graduate students are here just
+to verify
+
+ align:start position:0%
+to verify
+ 
+
+ align:start position:0%
+to verify
+okay yeah that's about right 20
+
+ align:start position:0%
+okay yeah that's about right 20
+ 
+
+ align:start position:0%
+okay yeah that's about right 20
+and uh how many students are in finance
+
+ align:start position:0%
+and uh how many students are in finance
+ 
+
+ align:start position:0%
+and uh how many students are in finance
+and business major
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just one okay and how many of you are in
+
+ align:start position:0%
+just one okay and how many of you are in
+ 
+
+ align:start position:0%
+just one okay and how many of you are in
+math major
+
+ align:start position:0%
+math major
+ 
+
+ align:start position:0%
+math major
+most of you okay how many of you are
+
+ align:start position:0%
+most of you okay how many of you are
+ 
+
+ align:start position:0%
+most of you okay how many of you are
+engineering major
+
+ align:start position:0%
+engineering major
+ 
+
+ align:start position:0%
+engineering major
+okay i feel
+
+ align:start position:0%
+okay i feel
+ 
+
+ align:start position:0%
+okay i feel
+how many of you actually are from uh uh
+
+ align:start position:0%
+how many of you actually are from uh uh
+ 
+
+ align:start position:0%
+how many of you actually are from uh uh
+other universities so
+
+ align:start position:0%
+other universities so
+ 
+
+ align:start position:0%
+other universities so
+okay great because last year we had
+
+ align:start position:0%
+okay great because last year we had
+ 
+
+ align:start position:0%
+okay great because last year we had
+quite a few so i want to specifically
+
+ align:start position:0%
+quite a few so i want to specifically
+ 
+
+ align:start position:0%
+quite a few so i want to specifically
+tell you that you're very welcome to
+
+ align:start position:0%
+tell you that you're very welcome to
+ 
+
+ align:start position:0%
+tell you that you're very welcome to
+attend the classes here right so it's
+
+ align:start position:0%
+attend the classes here right so it's
+ 
+
+ align:start position:0%
+attend the classes here right so it's
+open door and
+
+ align:start position:0%
+open door and
+ 
+
+ align:start position:0%
+open door and
+last year i remember we had a couple of
+
+ align:start position:0%
+last year i remember we had a couple of
+ 
+
+ align:start position:0%
+last year i remember we had a couple of
+students from harvard
+
+ align:start position:0%
+students from harvard
+ 
+
+ align:start position:0%
+students from harvard
+that's where i actually work right now
+
+ align:start position:0%
+that's where i actually work right now
+ 
+
+ align:start position:0%
+that's where i actually work right now
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+but uh my um
+
+ align:start position:0%
+but uh my um
+ 
+
+ align:start position:0%
+but uh my um
+i forgot to mention that even that but
+
+ align:start position:0%
+i forgot to mention that even that but
+ 
+
+ align:start position:0%
+i forgot to mention that even that but
+i'm affiliated with both the math
+
+ align:start position:0%
+i'm affiliated with both the math
+ 
+
+ align:start position:0%
+i'm affiliated with both the math
+department and the sloan school here so
+
+ align:start position:0%
+department and the sloan school here so
+ 
+
+ align:start position:0%
+department and the sloan school here so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so anyway thanks for that we will be
+
+ align:start position:0%
+so anyway thanks for that we will be
+ 
+
+ align:start position:0%
+so anyway thanks for that we will be
+doing a bit more polling along the way
+
+ align:start position:0%
+doing a bit more polling along the way
+ 
+
+ align:start position:0%
+doing a bit more polling along the way
+mainly to get feedback of
+
+ align:start position:0%
+mainly to get feedback of
+ 
+
+ align:start position:0%
+mainly to get feedback of
+how you feel about the class
+
+ align:start position:0%
+how you feel about the class
+ 
+
+ align:start position:0%
+how you feel about the class
+last year we had it online so if you
+
+ align:start position:0%
+last year we had it online so if you
+ 
+
+ align:start position:0%
+last year we had it online so if you
+feel the class is going too fast or the
+
+ align:start position:0%
+feel the class is going too fast or the
+ 
+
+ align:start position:0%
+feel the class is going too fast or the
+math part is going too slow or the
+
+ align:start position:0%
+math part is going too slow or the
+ 
+
+ align:start position:0%
+math part is going too slow or the
+finance part is a bit confusing
+
+ align:start position:0%
+finance part is a bit confusing
+ 
+
+ align:start position:0%
+finance part is a bit confusing
+and the easiest way is really just to
+
+ align:start position:0%
+and the easiest way is really just to
+ 
+
+ align:start position:0%
+and the easiest way is really just to
+send us emails and which you will find
+
+ align:start position:0%
+send us emails and which you will find
+ 
+
+ align:start position:0%
+send us emails and which you will find
+from the class website
+
+ align:start position:0%
+from the class website
+ 
+
+ align:start position:0%
+from the class website
+so anyway today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes yeah we all have mit emails which
+
+ align:start position:0%
+yes yeah we all have mit emails which
+ 
+
+ align:start position:0%
+yes yeah we all have mit emails which
+are listed on the website
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep and uh
+
+ align:start position:0%
+yep and uh
+ 
+
+ align:start position:0%
+yep and uh
+obviously we have offices here you can
+
+ align:start position:0%
+obviously we have offices here you can
+ 
+
+ align:start position:0%
+obviously we have offices here you can
+easily
+
+ align:start position:0%
+easily
+ 
+
+ align:start position:0%
+easily
+stop by peter and june boone's offices
+
+ align:start position:0%
+stop by peter and june boone's offices
+ 
+
+ align:start position:0%
+stop by peter and june boone's offices
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+vasily and i probably will be
+
+ align:start position:0%
+vasily and i probably will be
+ 
+
+ align:start position:0%
+vasily and i probably will be
+less often on campus but we'll be here
+
+ align:start position:0%
+less often on campus but we'll be here
+ 
+
+ align:start position:0%
+less often on campus but we'll be here
+quite often and definitely love to be
+
+ align:start position:0%
+quite often and definitely love to be
+ 
+
+ align:start position:0%
+quite often and definitely love to be
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+so anyway i will start
+
+ align:start position:0%
+so anyway i will start
+ 
+
+ align:start position:0%
+so anyway i will start
+today's lecture with a story
+
+ align:start position:0%
+today's lecture with a story
+ 
+
+ align:start position:0%
+today's lecture with a story
+and the quiz at the end
+
+ align:start position:0%
+and the quiz at the end
+ 
+
+ align:start position:0%
+and the quiz at the end
+don't worry it's not a real quiz i'm
+
+ align:start position:0%
+don't worry it's not a real quiz i'm
+ 
+
+ align:start position:0%
+don't worry it's not a real quiz i'm
+just going to ask you some questions you
+
+ align:start position:0%
+just going to ask you some questions you
+ 
+
+ align:start position:0%
+just going to ask you some questions you
+can raise your hand and
+
+ align:start position:0%
+can raise your hand and
+ 
+
+ align:start position:0%
+can raise your hand and
+give your answer but let me start with
+
+ align:start position:0%
+give your answer but let me start with
+ 
+
+ align:start position:0%
+give your answer but let me start with
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+my story this is actually my personal
+
+ align:start position:0%
+my story this is actually my personal
+ 
+
+ align:start position:0%
+my story this is actually my personal
+story uh
+
+ align:start position:0%
+story uh
+ 
+
+ align:start position:0%
+story uh
+i i want to tell you why i tell the
+
+ align:start position:0%
+i i want to tell you why i tell the
+ 
+
+ align:start position:0%
+i i want to tell you why i tell the
+story later but the story actually was
+
+ align:start position:0%
+story later but the story actually was
+ 
+
+ align:start position:0%
+story later but the story actually was
+in the mid 90s
+
+ align:start position:0%
+in the mid 90s
+ 
+
+ align:start position:0%
+in the mid 90s
+i just left
+
+ align:start position:0%
+i just left
+ 
+
+ align:start position:0%
+i just left
+solomon brothers that was my first
+
+ align:start position:0%
+solomon brothers that was my first
+ 
+
+ align:start position:0%
+solomon brothers that was my first
+financial industry job
+
+ align:start position:0%
+financial industry job
+ 
+
+ align:start position:0%
+financial industry job
+to go to morgan stanley in new york
+
+ align:start position:0%
+to go to morgan stanley in new york
+ 
+
+ align:start position:0%
+to go to morgan stanley in new york
+to join the options trading desk
+
+ align:start position:0%
+to join the options trading desk
+ 
+
+ align:start position:0%
+to join the options trading desk
+so the first day i sat down
+
+ align:start position:0%
+so the first day i sat down
+ 
+
+ align:start position:0%
+so the first day i sat down
+i opened the trading book
+
+ align:start position:0%
+i opened the trading book
+ 
+
+ align:start position:0%
+i opened the trading book
+i found something was missing
+
+ align:start position:0%
+i found something was missing
+ 
+
+ align:start position:0%
+i found something was missing
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so i turned around i asked my desk quant
+
+ align:start position:0%
+so i turned around i asked my desk quant
+ 
+
+ align:start position:0%
+so i turned around i asked my desk quant
+i said
+
+ align:start position:0%
+i said
+ 
+
+ align:start position:0%
+i said
+where is the vega report okay so
+
+ align:start position:0%
+where is the vega report okay so
+ 
+
+ align:start position:0%
+where is the vega report okay so
+let me show you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the story so
+
+ align:start position:0%
+so that's the story so
+ 
+
+ align:start position:0%
+so that's the story so
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+i'm obviously not going to tell you the
+
+ align:start position:0%
+i'm obviously not going to tell you the
+ 
+
+ align:start position:0%
+i'm obviously not going to tell you the
+story of pi or life of pi right that's
+
+ align:start position:0%
+story of pi or life of pi right that's
+ 
+
+ align:start position:0%
+story of pi or life of pi right that's
+not a financial
+
+ align:start position:0%
+not a financial
+ 
+
+ align:start position:0%
+not a financial
+story or the rest of the story alpha
+
+ align:start position:0%
+story or the rest of the story alpha
+ 
+
+ align:start position:0%
+story or the rest of the story alpha
+beta delta gamma theta which you'll
+
+ align:start position:0%
+beta delta gamma theta which you'll
+ 
+
+ align:start position:0%
+beta delta gamma theta which you'll
+learn from
+
+ align:start position:0%
+learn from
+ 
+
+ align:start position:0%
+learn from
+peter and chumbo and varsity's classes
+
+ align:start position:0%
+peter and chumbo and varsity's classes
+ 
+
+ align:start position:0%
+peter and chumbo and varsity's classes
+so i'm going to talk about vega so
+
+ align:start position:0%
+so i'm going to talk about vega so
+ 
+
+ align:start position:0%
+so i'm going to talk about vega so
+so by the way before i tell you the
+
+ align:start position:0%
+so by the way before i tell you the
+ 
+
+ align:start position:0%
+so by the way before i tell you the
+story what's unique about vega on this
+
+ align:start position:0%
+story what's unique about vega on this
+ 
+
+ align:start position:0%
+story what's unique about vega on this
+list
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's not a greek letter that's right
+
+ align:start position:0%
+it's not a greek letter that's right
+ 
+
+ align:start position:0%
+it's not a greek letter that's right
+okay so i turned around asking mike
+
+ align:start position:0%
+okay so i turned around asking mike
+ 
+
+ align:start position:0%
+okay so i turned around asking mike
+that's quan as where's the vega report
+
+ align:start position:0%
+that's quan as where's the vega report
+ 
+
+ align:start position:0%
+that's quan as where's the vega report
+but how many of you actually know what
+
+ align:start position:0%
+but how many of you actually know what
+ 
+
+ align:start position:0%
+but how many of you actually know what
+vega
+
+ align:start position:0%
+vega
+ 
+
+ align:start position:0%
+vega
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+okay a lot of people know so anyway i'm
+
+ align:start position:0%
+okay a lot of people know so anyway i'm
+ 
+
+ align:start position:0%
+okay a lot of people know so anyway i'm
+not gonna
+
+ align:start position:0%
+not gonna
+ 
+
+ align:start position:0%
+not gonna
+it's just for the people who haven't
+
+ align:start position:0%
+it's just for the people who haven't
+ 
+
+ align:start position:0%
+it's just for the people who haven't
+heard about before is a measurement
+
+ align:start position:0%
+heard about before is a measurement
+ 
+
+ align:start position:0%
+heard about before is a measurement
+about a book or portfolio or position
+
+ align:start position:0%
+about a book or portfolio or position
+ 
+
+ align:start position:0%
+about a book or portfolio or position
+sensitivity to volatility right so what
+
+ align:start position:0%
+sensitivity to volatility right so what
+ 
+
+ align:start position:0%
+sensitivity to volatility right so what
+is the volatility which again you will
+
+ align:start position:0%
+is the volatility which again you will
+ 
+
+ align:start position:0%
+is the volatility which again you will
+learn more in the rigorous terms
+
+ align:start position:0%
+learn more in the rigorous terms
+ 
+
+ align:start position:0%
+learn more in the rigorous terms
+what's how it's defined in mathematics
+
+ align:start position:0%
+what's how it's defined in mathematics
+ 
+
+ align:start position:0%
+what's how it's defined in mathematics
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+the meaning of it is really a
+
+ align:start position:0%
+the meaning of it is really a
+ 
+
+ align:start position:0%
+the meaning of it is really a
+measurement or indication of how
+
+ align:start position:0%
+measurement or indication of how
+ 
+
+ align:start position:0%
+measurement or indication of how
+volatile or what's the standard
+
+ align:start position:0%
+volatile or what's the standard
+ 
+
+ align:start position:0%
+volatile or what's the standard
+deviation of a price can change over
+
+ align:start position:0%
+deviation of a price can change over
+ 
+
+ align:start position:0%
+deviation of a price can change over
+time okay just that's all you need to
+
+ align:start position:0%
+time okay just that's all you need to
+ 
+
+ align:start position:0%
+time okay just that's all you need to
+know right now
+
+ align:start position:0%
+know right now
+ 
+
+ align:start position:0%
+know right now
+i'm not going to ask you questions later
+
+ align:start position:0%
+i'm not going to ask you questions later
+ 
+
+ align:start position:0%
+i'm not going to ask you questions later
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+my desktop look at me said
+
+ align:start position:0%
+my desktop look at me said
+ 
+
+ align:start position:0%
+my desktop look at me said
+you know this is supposed to be options
+
+ align:start position:0%
+you know this is supposed to be options
+ 
+
+ align:start position:0%
+you know this is supposed to be options
+trading desk so he looked at me kind of
+
+ align:start position:0%
+trading desk so he looked at me kind of
+ 
+
+ align:start position:0%
+trading desk so he looked at me kind of
+puzzled so instead of answering my
+
+ align:start position:0%
+puzzled so instead of answering my
+ 
+
+ align:start position:0%
+puzzled so instead of answering my
+question he handed over me a
+
+ align:start position:0%
+question he handed over me a
+ 
+
+ align:start position:0%
+question he handed over me a
+training manual for new employees
+
+ align:start position:0%
+training manual for new employees
+ 
+
+ align:start position:0%
+training manual for new employees
+and new analysts
+
+ align:start position:0%
+and new analysts
+ 
+
+ align:start position:0%
+and new analysts
+so i opened the trading training manual
+
+ align:start position:0%
+so i opened the trading training manual
+ 
+
+ align:start position:0%
+so i opened the trading training manual
+and looked it through
+
+ align:start position:0%
+and looked it through
+ 
+
+ align:start position:0%
+and looked it through
+i actually found my answer so actually
+
+ align:start position:0%
+i actually found my answer so actually
+ 
+
+ align:start position:0%
+i actually found my answer so actually
+at the moment stanley this is not called
+
+ align:start position:0%
+at the moment stanley this is not called
+ 
+
+ align:start position:0%
+at the moment stanley this is not called
+a vega it's called kappa
+
+ align:start position:0%
+a vega it's called kappa
+ 
+
+ align:start position:0%
+a vega it's called kappa
+so now remember it's called a kappa
+
+ align:start position:0%
+so now remember it's called a kappa
+ 
+
+ align:start position:0%
+so now remember it's called a kappa
+kappa is actually greek letter
+
+ align:start position:0%
+kappa is actually greek letter
+ 
+
+ align:start position:0%
+kappa is actually greek letter
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+further i look at on the same page there
+
+ align:start position:0%
+further i look at on the same page there
+ 
+
+ align:start position:0%
+further i look at on the same page there
+was actually a footnote
+
+ align:start position:0%
+was actually a footnote
+ 
+
+ align:start position:0%
+was actually a footnote
+which i copied down
+
+ align:start position:0%
+which i copied down
+ 
+
+ align:start position:0%
+which i copied down
+so the footnote about
+
+ align:start position:0%
+so the footnote about
+ 
+
+ align:start position:0%
+so the footnote about
+why it's called kappa
+
+ align:start position:0%
+why it's called kappa
+ 
+
+ align:start position:0%
+why it's called kappa
+at the
+
+ align:start position:0%
+at the
+ 
+
+ align:start position:0%
+at the
+at morgan stanley
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kappa is also called vega by some
+
+ align:start position:0%
+kappa is also called vega by some
+ 
+
+ align:start position:0%
+kappa is also called vega by some
+uneducated traders at the solomon
+
+ align:start position:0%
+uneducated traders at the solomon
+ 
+
+ align:start position:0%
+uneducated traders at the solomon
+brothers
+
+ align:start position:0%
+brothers
+ 
+
+ align:start position:0%
+brothers
+that's where i came from i just joined
+
+ align:start position:0%
+that's where i came from i just joined
+ 
+
+ align:start position:0%
+that's where i came from i just joined
+they have mistaken vega as a greek
+
+ align:start position:0%
+they have mistaken vega as a greek
+ 
+
+ align:start position:0%
+they have mistaken vega as a greek
+letter after gambling at vegas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+anyway so that was my first day so
+
+ align:start position:0%
+anyway so that was my first day so
+ 
+
+ align:start position:0%
+anyway so that was my first day so
+obviously i learned how to uh
+
+ align:start position:0%
+obviously i learned how to uh
+ 
+
+ align:start position:0%
+obviously i learned how to uh
+call kappa very quickly because i came
+
+ align:start position:0%
+call kappa very quickly because i came
+ 
+
+ align:start position:0%
+call kappa very quickly because i came
+from solomon brothers
+
+ align:start position:0%
+from solomon brothers
+ 
+
+ align:start position:0%
+from solomon brothers
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+i called kappa in the last 17 years
+
+ align:start position:0%
+i called kappa in the last 17 years
+ 
+
+ align:start position:0%
+i called kappa in the last 17 years
+but you will hear people calling the
+
+ align:start position:0%
+but you will hear people calling the
+ 
+
+ align:start position:0%
+but you will hear people calling the
+vega obviously probably more people
+
+ align:start position:0%
+vega obviously probably more people
+ 
+
+ align:start position:0%
+vega obviously probably more people
+counting the vega
+
+ align:start position:0%
+counting the vega
+ 
+
+ align:start position:0%
+counting the vega
+but anyway
+
+ align:start position:0%
+but anyway
+ 
+
+ align:start position:0%
+but anyway
+so that's my first day at moon stanley
+
+ align:start position:0%
+so that's my first day at moon stanley
+ 
+
+ align:start position:0%
+so that's my first day at moon stanley
+but why did i tell you this story right
+
+ align:start position:0%
+but why did i tell you this story right
+ 
+
+ align:start position:0%
+but why did i tell you this story right
+what point i try to make
+
+ align:start position:0%
+what point i try to make
+ 
+
+ align:start position:0%
+what point i try to make
+so this story is actually
+
+ align:start position:0%
+so this story is actually
+ 
+
+ align:start position:0%
+so this story is actually
+when you think about it
+
+ align:start position:0%
+when you think about it
+ 
+
+ align:start position:0%
+when you think about it
+mathematical or quantitative finance is
+
+ align:start position:0%
+mathematical or quantitative finance is
+ 
+
+ align:start position:0%
+mathematical or quantitative finance is
+that rather new field a lot of these
+
+ align:start position:0%
+that rather new field a lot of these
+ 
+
+ align:start position:0%
+that rather new field a lot of these
+terms were newly introduced
+
+ align:start position:0%
+terms were newly introduced
+ 
+
+ align:start position:0%
+terms were newly introduced
+and the pricing model of options as you
+
+ align:start position:0%
+and the pricing model of options as you
+ 
+
+ align:start position:0%
+and the pricing model of options as you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+right was introduced
+
+ align:start position:0%
+right was introduced
+ 
+
+ align:start position:0%
+right was introduced
+in at the black shows in the 70s or some
+
+ align:start position:0%
+in at the black shows in the 70s or some
+ 
+
+ align:start position:0%
+in at the black shows in the 70s or some
+of the groundwork maybe down bit earlier
+
+ align:start position:0%
+of the groundwork maybe down bit earlier
+ 
+
+ align:start position:0%
+of the groundwork maybe down bit earlier
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+it's not like
+
+ align:start position:0%
+it's not like
+ 
+
+ align:start position:0%
+it's not like
+finance was a quantitative profession to
+
+ align:start position:0%
+finance was a quantitative profession to
+ 
+
+ align:start position:0%
+finance was a quantitative profession to
+start with
+
+ align:start position:0%
+start with
+ 
+
+ align:start position:0%
+start with
+so what we witnessed in the last 30
+
+ align:start position:0%
+so what we witnessed in the last 30
+ 
+
+ align:start position:0%
+so what we witnessed in the last 30
+years was really a transformation
+
+ align:start position:0%
+years was really a transformation
+ 
+
+ align:start position:0%
+years was really a transformation
+of trade of the trading profession
+
+ align:start position:0%
+of trade of the trading profession
+ 
+
+ align:start position:0%
+of trade of the trading profession
+coming from
+
+ align:start position:0%
+coming from
+ 
+
+ align:start position:0%
+coming from
+mostly
+
+ align:start position:0%
+mostly
+ 
+
+ align:start position:0%
+mostly
+undereducated traders
+
+ align:start position:0%
+undereducated traders
+ 
+
+ align:start position:0%
+undereducated traders
+some of them typically joined the firms
+
+ align:start position:0%
+some of them typically joined the firms
+ 
+
+ align:start position:0%
+some of them typically joined the firms
+in the mail room
+
+ align:start position:0%
+in the mail room
+ 
+
+ align:start position:0%
+in the mail room
+and became trader later on that's
+
+ align:start position:0%
+and became trader later on that's
+ 
+
+ align:start position:0%
+and became trader later on that's
+typical career path
+
+ align:start position:0%
+typical career path
+ 
+
+ align:start position:0%
+typical career path
+and to nowadays if you walk on the
+
+ align:start position:0%
+and to nowadays if you walk on the
+ 
+
+ align:start position:0%
+and to nowadays if you walk on the
+trading floor you look at the trade you
+
+ align:start position:0%
+trading floor you look at the trade you
+ 
+
+ align:start position:0%
+trading floor you look at the trade you
+talk to the traders most of them have
+
+ align:start position:0%
+talk to the traders most of them have
+ 
+
+ align:start position:0%
+talk to the traders most of them have
+advanced degrees
+
+ align:start position:0%
+advanced degrees
+ 
+
+ align:start position:0%
+advanced degrees
+and quite a few of them have
+
+ align:start position:0%
+and quite a few of them have
+ 
+
+ align:start position:0%
+and quite a few of them have
+very you know
+
+ align:start position:0%
+very you know
+ 
+
+ align:start position:0%
+very you know
+high training in mathematics and
+
+ align:start position:0%
+high training in mathematics and
+ 
+
+ align:start position:0%
+high training in mathematics and
+computer science
+
+ align:start position:0%
+computer science
+ 
+
+ align:start position:0%
+computer science
+so what has changed over the last 20 or
+
+ align:start position:0%
+so what has changed over the last 20 or
+ 
+
+ align:start position:0%
+so what has changed over the last 20 or
+30 years
+
+ align:start position:0%
+30 years
+ 
+
+ align:start position:0%
+30 years
+i mean i myself personally
+
+ align:start position:0%
+i mean i myself personally
+ 
+
+ align:start position:0%
+i mean i myself personally
+you know was probably one of the data
+
+ align:start position:0%
+you know was probably one of the data
+ 
+
+ align:start position:0%
+you know was probably one of the data
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+experiencing this change
+
+ align:start position:0%
+experiencing this change
+ 
+
+ align:start position:0%
+experiencing this change
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+certainly didn't expect i will be doing
+
+ align:start position:0%
+certainly didn't expect i will be doing
+ 
+
+ align:start position:0%
+certainly didn't expect i will be doing
+this when i was at mit but i did that in
+
+ align:start position:0%
+this when i was at mit but i did that in
+ 
+
+ align:start position:0%
+this when i was at mit but i did that in
+the last
+
+ align:start position:0%
+the last
+ 
+
+ align:start position:0%
+the last
+you know 20 years
+
+ align:start position:0%
+you know 20 years
+ 
+
+ align:start position:0%
+you know 20 years
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the point i'm trying to tell you is
+
+ align:start position:0%
+the point i'm trying to tell you is
+ 
+
+ align:start position:0%
+the point i'm trying to tell you is
+before you dive into any details of
+
+ align:start position:0%
+before you dive into any details of
+ 
+
+ align:start position:0%
+before you dive into any details of
+mathematics
+
+ align:start position:0%
+mathematics
+ 
+
+ align:start position:0%
+mathematics
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+any concept in finance in this class
+
+ align:start position:0%
+any concept in finance in this class
+ 
+
+ align:start position:0%
+any concept in finance in this class
+just bear in mind
+
+ align:start position:0%
+just bear in mind
+ 
+
+ align:start position:0%
+just bear in mind
+this is a field developed in the last
+
+ align:start position:0%
+this is a field developed in the last
+ 
+
+ align:start position:0%
+this is a field developed in the last
+mostly 30 years
+
+ align:start position:0%
+mostly 30 years
+ 
+
+ align:start position:0%
+mostly 30 years
+or even shorter and what you really need
+
+ align:start position:0%
+or even shorter and what you really need
+ 
+
+ align:start position:0%
+or even shorter and what you really need
+to ask questions is
+
+ align:start position:0%
+to ask questions is
+ 
+
+ align:start position:0%
+to ask questions is
+it's not really
+
+ align:start position:0%
+it's not really
+ 
+
+ align:start position:0%
+it's not really
+is the right or wrong in mathematics is
+
+ align:start position:0%
+is the right or wrong in mathematics is
+ 
+
+ align:start position:0%
+is the right or wrong in mathematics is
+it right or wrong in physics
+
+ align:start position:0%
+it right or wrong in physics
+ 
+
+ align:start position:0%
+it right or wrong in physics
+so how the concepts are established
+
+ align:start position:0%
+so how the concepts are established
+ 
+
+ align:start position:0%
+so how the concepts are established
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+defined and verified because this is a
+
+ align:start position:0%
+defined and verified because this is a
+ 
+
+ align:start position:0%
+defined and verified because this is a
+field the transformation about
+
+ align:start position:0%
+field the transformation about
+ 
+
+ align:start position:0%
+field the transformation about
+the participants
+
+ align:start position:0%
+the participants
+ 
+
+ align:start position:0%
+the participants
+products models methodology everything
+
+ align:start position:0%
+products models methodology everything
+ 
+
+ align:start position:0%
+products models methodology everything
+are changing very rapidly even nowadays
+
+ align:start position:0%
+are changing very rapidly even nowadays
+ 
+
+ align:start position:0%
+are changing very rapidly even nowadays
+still changing
+
+ align:start position:0%
+still changing
+ 
+
+ align:start position:0%
+still changing
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+with that
+
+ align:start position:0%
+with that
+ 
+
+ align:start position:0%
+with that
+i will
+
+ align:start position:0%
+i will
+ 
+
+ align:start position:0%
+i will
+give you some background of how the
+
+ align:start position:0%
+give you some background of how the
+ 
+
+ align:start position:0%
+give you some background of how the
+financial markets
+
+ align:start position:0%
+financial markets
+ 
+
+ align:start position:0%
+financial markets
+are actually started and that's really
+
+ align:start position:0%
+are actually started and that's really
+ 
+
+ align:start position:0%
+are actually started and that's really
+the history part of this uh
+
+ align:start position:0%
+the history part of this uh
+ 
+
+ align:start position:0%
+the history part of this uh
+this industry
+
+ align:start position:0%
+this industry
+ 
+
+ align:start position:0%
+this industry
+so when we talk about markets we know in
+
+ align:start position:0%
+so when we talk about markets we know in
+ 
+
+ align:start position:0%
+so when we talk about markets we know in
+early days right people need to exchange
+
+ align:start position:0%
+early days right people need to exchange
+ 
+
+ align:start position:0%
+early days right people need to exchange
+goods you have something i don't have i
+
+ align:start position:0%
+goods you have something i don't have i
+ 
+
+ align:start position:0%
+goods you have something i don't have i
+have something you don't have so
+
+ align:start position:0%
+have something you don't have so
+ 
+
+ align:start position:0%
+have something you don't have so
+there's exchanges right then it becomes
+
+ align:start position:0%
+there's exchanges right then it becomes
+ 
+
+ align:start position:0%
+there's exchanges right then it becomes
+centralized
+
+ align:start position:0%
+centralized
+ 
+
+ align:start position:0%
+centralized
+there are stock exchanges futures
+
+ align:start position:0%
+there are stock exchanges futures
+ 
+
+ align:start position:0%
+there are stock exchanges futures
+exchanges all over the world
+
+ align:start position:0%
+exchanges all over the world
+ 
+
+ align:start position:0%
+exchanges all over the world
+then products will be listed as
+
+ align:start position:0%
+then products will be listed as
+ 
+
+ align:start position:0%
+then products will be listed as
+securities on these exchanges
+
+ align:start position:0%
+securities on these exchanges
+ 
+
+ align:start position:0%
+securities on these exchanges
+that's one way of trading which is
+
+ align:start position:0%
+that's one way of trading which is
+ 
+
+ align:start position:0%
+that's one way of trading which is
+centralized
+
+ align:start position:0%
+centralized
+ 
+
+ align:start position:0%
+centralized
+obviously in the last 10 15 years now we
+
+ align:start position:0%
+obviously in the last 10 15 years now we
+ 
+
+ align:start position:0%
+obviously in the last 10 15 years now we
+have ecns electro
+
+ align:start position:0%
+have ecns electro
+ 
+
+ align:start position:0%
+have ecns electro
+electronic platforms trade over you know
+
+ align:start position:0%
+electronic platforms trade over you know
+ 
+
+ align:start position:0%
+electronic platforms trade over you know
+even larger volume of those trades
+
+ align:start position:0%
+even larger volume of those trades
+ 
+
+ align:start position:0%
+even larger volume of those trades
+so financial products is
+
+ align:start position:0%
+so financial products is
+ 
+
+ align:start position:0%
+so financial products is
+really just one form of trading and when
+
+ align:start position:0%
+really just one form of trading and when
+ 
+
+ align:start position:0%
+really just one form of trading and when
+you think about i mean there are many
+
+ align:start position:0%
+you think about i mean there are many
+ 
+
+ align:start position:0%
+you think about i mean there are many
+other ways of trading
+
+ align:start position:0%
+other ways of trading
+ 
+
+ align:start position:0%
+other ways of trading
+aside from
+
+ align:start position:0%
+aside from
+ 
+
+ align:start position:0%
+aside from
+exchanges one of them which is called
+
+ align:start position:0%
+exchanges one of them which is called
+ 
+
+ align:start position:0%
+exchanges one of them which is called
+otc
+
+ align:start position:0%
+otc
+ 
+
+ align:start position:0%
+otc
+is over the counter meaning
+
+ align:start position:0%
+is over the counter meaning
+ 
+
+ align:start position:0%
+is over the counter meaning
+two counterparties agree to do a trade
+
+ align:start position:0%
+two counterparties agree to do a trade
+ 
+
+ align:start position:0%
+two counterparties agree to do a trade
+without really subject to the exchange
+
+ align:start position:0%
+without really subject to the exchange
+ 
+
+ align:start position:0%
+without really subject to the exchange
+rules or
+
+ align:start position:0%
+rules or
+ 
+
+ align:start position:0%
+rules or
+the underlying trading agreement
+
+ align:start position:0%
+the underlying trading agreement
+ 
+
+ align:start position:0%
+the underlying trading agreement
+does not have to be
+
+ align:start position:0%
+does not have to be
+ 
+
+ align:start position:0%
+does not have to be
+a securitize the product or standardized
+
+ align:start position:0%
+a securitize the product or standardized
+ 
+
+ align:start position:0%
+a securitize the product or standardized
+or you know whatever ways you defined it
+
+ align:start position:0%
+or you know whatever ways you defined it
+ 
+
+ align:start position:0%
+or you know whatever ways you defined it
+and the different regions have different
+
+ align:start position:0%
+and the different regions have different
+ 
+
+ align:start position:0%
+and the different regions have different
+exchanges and markets as well
+
+ align:start position:0%
+exchanges and markets as well
+ 
+
+ align:start position:0%
+exchanges and markets as well
+and they typically specialize in local
+
+ align:start position:0%
+and they typically specialize in local
+ 
+
+ align:start position:0%
+and they typically specialize in local
+products local company stocks
+
+ align:start position:0%
+products local company stocks
+ 
+
+ align:start position:0%
+products local company stocks
+local
+
+ align:start position:0%
+local
+ 
+
+ align:start position:0%
+local
+bonds and local currencies
+
+ align:start position:0%
+bonds and local currencies
+ 
+
+ align:start position:0%
+bonds and local currencies
+so there are many different
+
+ align:start position:0%
+so there are many different
+ 
+
+ align:start position:0%
+so there are many different
+forms so
+
+ align:start position:0%
+forms so
+ 
+
+ align:start position:0%
+forms so
+again what's in common that's the
+
+ align:start position:0%
+again what's in common that's the
+ 
+
+ align:start position:0%
+again what's in common that's the
+question you need to ask also you don't
+
+ align:start position:0%
+question you need to ask also you don't
+ 
+
+ align:start position:0%
+question you need to ask also you don't
+know the specifics
+
+ align:start position:0%
+know the specifics
+ 
+
+ align:start position:0%
+know the specifics
+and the currencies money itself also
+
+ align:start position:0%
+and the currencies money itself also
+ 
+
+ align:start position:0%
+and the currencies money itself also
+traded
+
+ align:start position:0%
+traded
+ 
+
+ align:start position:0%
+traded
+right so and that's where different the
+
+ align:start position:0%
+right so and that's where different the
+ 
+
+ align:start position:0%
+right so and that's where different the
+uh currencies issued by different
+
+ align:start position:0%
+uh currencies issued by different
+ 
+
+ align:start position:0%
+uh currencies issued by different
+countries
+
+ align:start position:0%
+countries
+ 
+
+ align:start position:0%
+countries
+so when we talk about trading stocks
+
+ align:start position:0%
+so when we talk about trading stocks
+ 
+
+ align:start position:0%
+so when we talk about trading stocks
+also people trade baskets of stocks
+
+ align:start position:0%
+also people trade baskets of stocks
+ 
+
+ align:start position:0%
+also people trade baskets of stocks
+trade groups of stocks together and
+
+ align:start position:0%
+trade groups of stocks together and
+ 
+
+ align:start position:0%
+trade groups of stocks together and
+that's stock
+
+ align:start position:0%
+that's stock
+ 
+
+ align:start position:0%
+that's stock
+index or indices
+
+ align:start position:0%
+index or indices
+ 
+
+ align:start position:0%
+index or indices
+so that there are different products now
+
+ align:start position:0%
+so that there are different products now
+ 
+
+ align:start position:0%
+so that there are different products now
+how the stock gets listed on the stock
+
+ align:start position:0%
+how the stock gets listed on the stock
+ 
+
+ align:start position:0%
+how the stock gets listed on the stock
+exchange
+
+ align:start position:0%
+exchange
+ 
+
+ align:start position:0%
+exchange
+they go through ipo initial public
+
+ align:start position:0%
+they go through ipo initial public
+ 
+
+ align:start position:0%
+they go through ipo initial public
+offering process
+
+ align:start position:0%
+offering process
+ 
+
+ align:start position:0%
+offering process
+so when a company
+
+ align:start position:0%
+so when a company
+ 
+
+ align:start position:0%
+so when a company
+changes from private to public it goes
+
+ align:start position:0%
+changes from private to public it goes
+ 
+
+ align:start position:0%
+changes from private to public it goes
+through this ipo process it's called
+
+ align:start position:0%
+through this ipo process it's called
+ 
+
+ align:start position:0%
+through this ipo process it's called
+primary market primary listing
+
+ align:start position:0%
+primary market primary listing
+ 
+
+ align:start position:0%
+primary market primary listing
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+once the stock is listed on exchange
+
+ align:start position:0%
+once the stock is listed on exchange
+ 
+
+ align:start position:0%
+once the stock is listed on exchange
+and it becomes traded in the market we
+
+ align:start position:0%
+and it becomes traded in the market we
+ 
+
+ align:start position:0%
+and it becomes traded in the market we
+call it secondary trading so that's not
+
+ align:start position:0%
+call it secondary trading so that's not
+ 
+
+ align:start position:0%
+call it secondary trading so that's not
+that after the primary market
+
+ align:start position:0%
+that after the primary market
+ 
+
+ align:start position:0%
+that after the primary market
+and the equity or stock is one form of
+
+ align:start position:0%
+and the equity or stock is one form of
+ 
+
+ align:start position:0%
+and the equity or stock is one form of
+trading or one form of financial
+
+ align:start position:0%
+trading or one form of financial
+ 
+
+ align:start position:0%
+trading or one form of financial
+products
+
+ align:start position:0%
+products
+ 
+
+ align:start position:0%
+products
+what are other forms
+
+ align:start position:0%
+what are other forms
+ 
+
+ align:start position:0%
+what are other forms
+loans
+
+ align:start position:0%
+loans
+ 
+
+ align:start position:0%
+loans
+actually that products are more generic
+
+ align:start position:0%
+actually that products are more generic
+ 
+
+ align:start position:0%
+actually that products are more generic
+than equity products
+
+ align:start position:0%
+than equity products
+ 
+
+ align:start position:0%
+than equity products
+when you started
+
+ align:start position:0%
+when you started
+ 
+
+ align:start position:0%
+when you started
+thinking about what is really the what
+
+ align:start position:0%
+thinking about what is really the what
+ 
+
+ align:start position:0%
+thinking about what is really the what
+is really finance is about it's really
+
+ align:start position:0%
+is really finance is about it's really
+ 
+
+ align:start position:0%
+is really finance is about it's really
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+someone has money someone doesn't
+
+ align:start position:0%
+someone has money someone doesn't
+ 
+
+ align:start position:0%
+someone has money someone doesn't
+someone has money to land out someone
+
+ align:start position:0%
+someone has money to land out someone
+ 
+
+ align:start position:0%
+someone has money to land out someone
+needs to borrow money
+
+ align:start position:0%
+needs to borrow money
+ 
+
+ align:start position:0%
+needs to borrow money
+so that's loan
+
+ align:start position:0%
+so that's loan
+ 
+
+ align:start position:0%
+so that's loan
+loan is really a private agreement
+
+ align:start position:0%
+loan is really a private agreement
+ 
+
+ align:start position:0%
+loan is really a private agreement
+between two counterparties or multiple
+
+ align:start position:0%
+between two counterparties or multiple
+ 
+
+ align:start position:0%
+between two counterparties or multiple
+counterparties
+
+ align:start position:0%
+counterparties
+ 
+
+ align:start position:0%
+counterparties
+when you securitize them it becomes
+
+ align:start position:0%
+when you securitize them it becomes
+ 
+
+ align:start position:0%
+when you securitize them it becomes
+bonds
+
+ align:start position:0%
+bonds
+ 
+
+ align:start position:0%
+bonds
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+when you look at bonds every government
+
+ align:start position:0%
+when you look at bonds every government
+ 
+
+ align:start position:0%
+when you look at bonds every government
+right issue large sovereign debt the u.s
+
+ align:start position:0%
+right issue large sovereign debt the u.s
+ 
+
+ align:start position:0%
+right issue large sovereign debt the u.s
+government has
+
+ align:start position:0%
+government has
+ 
+
+ align:start position:0%
+government has
+large outstanding u.s treasury
+
+ align:start position:0%
+large outstanding u.s treasury
+ 
+
+ align:start position:0%
+large outstanding u.s treasury
+debt bonds notes bills
+
+ align:start position:0%
+debt bonds notes bills
+ 
+
+ align:start position:0%
+debt bonds notes bills
+and corporates
+
+ align:start position:0%
+and corporates
+ 
+
+ align:start position:0%
+and corporates
+have issued a lot of that
+
+ align:start position:0%
+have issued a lot of that
+ 
+
+ align:start position:0%
+have issued a lot of that
+product as well they borrow money when
+
+ align:start position:0%
+product as well they borrow money when
+ 
+
+ align:start position:0%
+product as well they borrow money when
+they need to build a new factory or
+
+ align:start position:0%
+they need to build a new factory or
+ 
+
+ align:start position:0%
+they need to build a new factory or
+expand
+
+ align:start position:0%
+expand
+ 
+
+ align:start position:0%
+expand
+universities borrow money right when mit
+
+ align:start position:0%
+universities borrow money right when mit
+ 
+
+ align:start position:0%
+universities borrow money right when mit
+needs to build a new building
+
+ align:start position:0%
+needs to build a new building
+ 
+
+ align:start position:0%
+needs to build a new building
+you know some of the money will make
+
+ align:start position:0%
+you know some of the money will make
+ 
+
+ align:start position:0%
+you know some of the money will make
+come from the endowment support some
+
+ align:start position:0%
+come from the endowment support some
+ 
+
+ align:start position:0%
+come from the endowment support some
+will come from
+
+ align:start position:0%
+will come from
+ 
+
+ align:start position:0%
+will come from
+you know some other form of research
+
+ align:start position:0%
+you know some other form of research
+ 
+
+ align:start position:0%
+you know some other form of research
+budget or some will come from you know
+
+ align:start position:0%
+budget or some will come from you know
+ 
+
+ align:start position:0%
+budget or some will come from you know
+that financing right just borrow from
+
+ align:start position:0%
+that financing right just borrow from
+ 
+
+ align:start position:0%
+that financing right just borrow from
+the public
+
+ align:start position:0%
+the public
+ 
+
+ align:start position:0%
+the public
+local governments states right counties
+
+ align:start position:0%
+local governments states right counties
+ 
+
+ align:start position:0%
+local governments states right counties
+even right so they have various forms
+
+ align:start position:0%
+even right so they have various forms
+ 
+
+ align:start position:0%
+even right so they have various forms
+so that's that product commodities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually you know metal energy
+
+ align:start position:0%
+actually you know metal energy
+ 
+
+ align:start position:0%
+actually you know metal energy
+agriculture uh products or traded right
+
+ align:start position:0%
+agriculture uh products or traded right
+ 
+
+ align:start position:0%
+agriculture uh products or traded right
+mostly in the futures format and some in
+
+ align:start position:0%
+mostly in the futures format and some in
+ 
+
+ align:start position:0%
+mostly in the futures format and some in
+physical format meaning you take
+
+ align:start position:0%
+physical format meaning you take
+ 
+
+ align:start position:0%
+physical format meaning you take
+deliveries
+
+ align:start position:0%
+deliveries
+ 
+
+ align:start position:0%
+deliveries
+when you actually
+
+ align:start position:0%
+when you actually
+ 
+
+ align:start position:0%
+when you actually
+buy and sell you build a warehouse to
+
+ align:start position:0%
+buy and sell you build a warehouse to
+ 
+
+ align:start position:0%
+buy and sell you build a warehouse to
+take them your you know ship
+
+ align:start position:0%
+take them your you know ship
+ 
+
+ align:start position:0%
+take them your you know ship
+tanks
+
+ align:start position:0%
+tanks
+ 
+
+ align:start position:0%
+tanks
+right to store above the ocean
+
+ align:start position:0%
+right to store above the ocean
+ 
+
+ align:start position:0%
+right to store above the ocean
+and the real estates you buy and sell
+
+ align:start position:0%
+and the real estates you buy and sell
+ 
+
+ align:start position:0%
+and the real estates you buy and sell
+houses you know
+
+ align:start position:0%
+houses you know
+ 
+
+ align:start position:0%
+houses you know
+2008 financial crisis if you read about
+
+ align:start position:0%
+2008 financial crisis if you read about
+ 
+
+ align:start position:0%
+2008 financial crisis if you read about
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+this has a lot to do with the real
+
+ align:start position:0%
+this has a lot to do with the real
+ 
+
+ align:start position:0%
+this has a lot to do with the real
+estate market the mortgages
+
+ align:start position:0%
+estate market the mortgages
+ 
+
+ align:start position:0%
+estate market the mortgages
+and asset-backed securities
+
+ align:start position:0%
+and asset-backed securities
+ 
+
+ align:start position:0%
+and asset-backed securities
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so i'm not trying to give you all the
+
+ align:start position:0%
+so i'm not trying to give you all the
+ 
+
+ align:start position:0%
+so i'm not trying to give you all the
+definition dumping the information on
+
+ align:start position:0%
+definition dumping the information on
+ 
+
+ align:start position:0%
+definition dumping the information on
+you but i like you at least you're
+
+ align:start position:0%
+you but i like you at least you're
+ 
+
+ align:start position:0%
+you but i like you at least you're
+hearing at once today
+
+ align:start position:0%
+hearing at once today
+ 
+
+ align:start position:0%
+hearing at once today
+and then you have more interest you can
+
+ align:start position:0%
+and then you have more interest you can
+ 
+
+ align:start position:0%
+and then you have more interest you can
+read on the side
+
+ align:start position:0%
+read on the side
+ 
+
+ align:start position:0%
+read on the side
+so asset-backed securities is when you
+
+ align:start position:0%
+so asset-backed securities is when you
+ 
+
+ align:start position:0%
+so asset-backed securities is when you
+have an asset
+
+ align:start position:0%
+have an asset
+ 
+
+ align:start position:0%
+have an asset
+you basically
+
+ align:start position:0%
+you basically
+ 
+
+ align:start position:0%
+you basically
+issue a debt
+
+ align:start position:0%
+issue a debt
+ 
+
+ align:start position:0%
+issue a debt
+with the asset
+
+ align:start position:0%
+with the asset
+ 
+
+ align:start position:0%
+with the asset
+backing it
+
+ align:start position:0%
+backing it
+ 
+
+ align:start position:0%
+backing it
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+how how do you rate the assets
+
+ align:start position:0%
+how how do you rate the assets
+ 
+
+ align:start position:0%
+how how do you rate the assets
+risk level and what's the income stream
+
+ align:start position:0%
+risk level and what's the income stream
+ 
+
+ align:start position:0%
+risk level and what's the income stream
+cash flow
+
+ align:start position:0%
+cash flow
+ 
+
+ align:start position:0%
+cash flow
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+during before 2008 financial crisis
+
+ align:start position:0%
+during before 2008 financial crisis
+ 
+
+ align:start position:0%
+during before 2008 financial crisis
+as you heard large amount of cmbs
+
+ align:start position:0%
+as you heard large amount of cmbs
+ 
+
+ align:start position:0%
+as you heard large amount of cmbs
+commercial
+
+ align:start position:0%
+commercial
+ 
+
+ align:start position:0%
+commercial
+basically is a commercial real estate
+
+ align:start position:0%
+basically is a commercial real estate
+ 
+
+ align:start position:0%
+basically is a commercial real estate
+backed uh
+
+ align:start position:0%
+backed uh
+ 
+
+ align:start position:0%
+backed uh
+you know securities mortgage securities
+
+ align:start position:0%
+you know securities mortgage securities
+ 
+
+ align:start position:0%
+you know securities mortgage securities
+and the residential as well
+
+ align:start position:0%
+and the residential as well
+ 
+
+ align:start position:0%
+and the residential as well
+and further of all these you heard
+
+ align:start position:0%
+and further of all these you heard
+ 
+
+ align:start position:0%
+and further of all these you heard
+probably a lot about the derivative
+
+ align:start position:0%
+probably a lot about the derivative
+ 
+
+ align:start position:0%
+probably a lot about the derivative
+products
+
+ align:start position:0%
+products
+ 
+
+ align:start position:0%
+products
+so that started with swaps options
+
+ align:start position:0%
+so that started with swaps options
+ 
+
+ align:start position:0%
+so that started with swaps options
+and the structured products you become
+
+ align:start position:0%
+and the structured products you become
+ 
+
+ align:start position:0%
+and the structured products you become
+more tailor-made
+
+ align:start position:0%
+more tailor-made
+ 
+
+ align:start position:0%
+more tailor-made
+for either investors or
+
+ align:start position:0%
+for either investors or
+ 
+
+ align:start position:0%
+for either investors or
+borrowers
+
+ align:start position:0%
+borrowers
+ 
+
+ align:start position:0%
+borrowers
+to structure the products in a way to
+
+ align:start position:0%
+to structure the products in a way to
+ 
+
+ align:start position:0%
+to structure the products in a way to
+suit their needs and
+
+ align:start position:0%
+suit their needs and
+ 
+
+ align:start position:0%
+suit their needs and
+some of the the complexity of those
+
+ align:start position:0%
+some of the the complexity of those
+ 
+
+ align:start position:0%
+some of the the complexity of those
+structured products
+
+ align:start position:0%
+structured products
+ 
+
+ align:start position:0%
+structured products
+you know become quite high
+
+ align:start position:0%
+you know become quite high
+ 
+
+ align:start position:0%
+you know become quite high
+and the mathematics involved in pricing
+
+ align:start position:0%
+and the mathematics involved in pricing
+ 
+
+ align:start position:0%
+and the mathematics involved in pricing
+them and the risk management become
+
+ align:start position:0%
+them and the risk management become
+ 
+
+ align:start position:0%
+them and the risk management become
+rather challenging
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let me
+
+ align:start position:0%
+let me
+ 
+
+ align:start position:0%
+let me
+coming back to the players in the market
+
+ align:start position:0%
+coming back to the players in the market
+ 
+
+ align:start position:0%
+coming back to the players in the market
+one large sector of player one large
+
+ align:start position:0%
+one large sector of player one large
+ 
+
+ align:start position:0%
+one large sector of player one large
+type of player is really
+
+ align:start position:0%
+type of player is really
+ 
+
+ align:start position:0%
+type of player is really
+bank
+
+ align:start position:0%
+bank
+ 
+
+ align:start position:0%
+bank
+so there are
+
+ align:start position:0%
+so there are
+ 
+
+ align:start position:0%
+so there are
+essentially after 1933 uh glass-steagall
+
+ align:start position:0%
+essentially after 1933 uh glass-steagall
+ 
+
+ align:start position:0%
+essentially after 1933 uh glass-steagall
+uh legislation
+
+ align:start position:0%
+uh legislation
+ 
+
+ align:start position:0%
+uh legislation
+there were two main types of banks one
+
+ align:start position:0%
+there were two main types of banks one
+ 
+
+ align:start position:0%
+there were two main types of banks one
+is called commercial bank the other is
+
+ align:start position:0%
+is called commercial bank the other is
+ 
+
+ align:start position:0%
+is called commercial bank the other is
+investment bank
+
+ align:start position:0%
+investment bank
+ 
+
+ align:start position:0%
+investment bank
+commercial bank
+
+ align:start position:0%
+commercial bank
+ 
+
+ align:start position:0%
+commercial bank
+is supposedly
+
+ align:start position:0%
+is supposedly
+ 
+
+ align:start position:0%
+is supposedly
+you're taking deposits and lend out the
+
+ align:start position:0%
+you're taking deposits and lend out the
+ 
+
+ align:start position:0%
+you're taking deposits and lend out the
+money
+
+ align:start position:0%
+money
+ 
+
+ align:start position:0%
+money
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+doing you know more commercial services
+
+ align:start position:0%
+doing you know more commercial services
+ 
+
+ align:start position:0%
+doing you know more commercial services
+investment bank supposed to focus on the
+
+ align:start position:0%
+investment bank supposed to focus on the
+ 
+
+ align:start position:0%
+investment bank supposed to focus on the
+capital markets
+
+ align:start position:0%
+capital markets
+ 
+
+ align:start position:0%
+capital markets
+raising capital
+
+ align:start position:0%
+raising capital
+ 
+
+ align:start position:0%
+raising capital
+trading and
+
+ align:start position:0%
+trading and
+ 
+
+ align:start position:0%
+trading and
+asset management but obviously after
+
+ align:start position:0%
+asset management but obviously after
+ 
+
+ align:start position:0%
+asset management but obviously after
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+there's a you know the glass-steagall
+
+ align:start position:0%
+there's a you know the glass-steagall
+ 
+
+ align:start position:0%
+there's a you know the glass-steagall
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+repealed right there's no longer
+
+ align:start position:0%
+repealed right there's no longer
+ 
+
+ align:start position:0%
+repealed right there's no longer
+that some people blame that and probably
+
+ align:start position:0%
+that some people blame that and probably
+ 
+
+ align:start position:0%
+that some people blame that and probably
+for a very good reason
+
+ align:start position:0%
+for a very good reason
+ 
+
+ align:start position:0%
+for a very good reason
+for the cause of 2008
+
+ align:start position:0%
+for the cause of 2008
+ 
+
+ align:start position:0%
+for the cause of 2008
+financial crisis
+
+ align:start position:0%
+financial crisis
+ 
+
+ align:start position:0%
+financial crisis
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+i want to tell you how current the
+
+ align:start position:0%
+i want to tell you how current the
+ 
+
+ align:start position:0%
+i want to tell you how current the
+investment banks are organized so i mean
+
+ align:start position:0%
+investment banks are organized so i mean
+ 
+
+ align:start position:0%
+investment banks are organized so i mean
+vasily just mentioned he works in a
+
+ align:start position:0%
+vasily just mentioned he works in a
+ 
+
+ align:start position:0%
+vasily just mentioned he works in a
+fixed income right
+
+ align:start position:0%
+fixed income right
+ 
+
+ align:start position:0%
+fixed income right
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so banks typically organized by you know
+
+ align:start position:0%
+so banks typically organized by you know
+ 
+
+ align:start position:0%
+so banks typically organized by you know
+institutional business and asset
+
+ align:start position:0%
+institutional business and asset
+ 
+
+ align:start position:0%
+institutional business and asset
+management so within the institutional
+
+ align:start position:0%
+management so within the institutional
+ 
+
+ align:start position:0%
+management so within the institutional
+client business it has
+
+ align:start position:0%
+client business it has
+ 
+
+ align:start position:0%
+client business it has
+typically three main parts
+
+ align:start position:0%
+typically three main parts
+ 
+
+ align:start position:0%
+typically three main parts
+fixed income which trade
+
+ align:start position:0%
+fixed income which trade
+ 
+
+ align:start position:0%
+fixed income which trade
+the debt and the derivative products
+
+ align:start position:0%
+the debt and the derivative products
+ 
+
+ align:start position:0%
+the debt and the derivative products
+equity trade stocks and the derivative
+
+ align:start position:0%
+equity trade stocks and the derivative
+ 
+
+ align:start position:0%
+equity trade stocks and the derivative
+products
+
+ align:start position:0%
+products
+ 
+
+ align:start position:0%
+products
+and ibd stands for investment banking
+
+ align:start position:0%
+and ibd stands for investment banking
+ 
+
+ align:start position:0%
+and ibd stands for investment banking
+division which
+
+ align:start position:0%
+division which
+ 
+
+ align:start position:0%
+division which
+really covers corporate finance raising
+
+ align:start position:0%
+really covers corporate finance raising
+ 
+
+ align:start position:0%
+really covers corporate finance raising
+capital
+
+ align:start position:0%
+capital
+ 
+
+ align:start position:0%
+capital
+listing a stock ipo and merger and
+
+ align:start position:0%
+listing a stock ipo and merger and
+ 
+
+ align:start position:0%
+listing a stock ipo and merger and
+acquisition
+
+ align:start position:0%
+acquisition
+ 
+
+ align:start position:0%
+acquisition
+and advisory
+
+ align:start position:0%
+and advisory
+ 
+
+ align:start position:0%
+and advisory
+so that's that's how banks are organized
+
+ align:start position:0%
+so that's that's how banks are organized
+ 
+
+ align:start position:0%
+so that's that's how banks are organized
+outside banks
+
+ align:start position:0%
+outside banks
+ 
+
+ align:start position:0%
+outside banks
+other players basically the asset
+
+ align:start position:0%
+other players basically the asset
+ 
+
+ align:start position:0%
+other players basically the asset
+managers are obviously a very big force
+
+ align:start position:0%
+managers are obviously a very big force
+ 
+
+ align:start position:0%
+managers are obviously a very big force
+in the financial markets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the question a lot of people ask is
+
+ align:start position:0%
+so the question a lot of people ask is
+ 
+
+ align:start position:0%
+so the question a lot of people ask is
+is this a zero-sum game right i'm sure
+
+ align:start position:0%
+is this a zero-sum game right i'm sure
+ 
+
+ align:start position:0%
+is this a zero-sum game right i'm sure
+you you heard this many times
+
+ align:start position:0%
+you you heard this many times
+ 
+
+ align:start position:0%
+you you heard this many times
+so in the financial markets some people
+
+ align:start position:0%
+so in the financial markets some people
+ 
+
+ align:start position:0%
+so in the financial markets some people
+win some people lose
+
+ align:start position:0%
+win some people lose
+ 
+
+ align:start position:0%
+win some people lose
+i mean a lot of times
+
+ align:start position:0%
+i mean a lot of times
+ 
+
+ align:start position:0%
+i mean a lot of times
+it depends on specific products you
+
+ align:start position:0%
+it depends on specific products you
+ 
+
+ align:start position:0%
+it depends on specific products you
+trade
+
+ align:start position:0%
+trade
+ 
+
+ align:start position:0%
+trade
+the market you're in it is a lot of
+
+ align:start position:0%
+the market you're in it is a lot of
+ 
+
+ align:start position:0%
+the market you're in it is a lot of
+times you know
+
+ align:start position:0%
+times you know
+ 
+
+ align:start position:0%
+times you know
+pretty net zero but why
+
+ align:start position:0%
+pretty net zero but why
+ 
+
+ align:start position:0%
+pretty net zero but why
+why do we need financial markets right
+
+ align:start position:0%
+why do we need financial markets right
+ 
+
+ align:start position:0%
+why do we need financial markets right
+i mean this this comes back
+
+ align:start position:0%
+i mean this this comes back
+ 
+
+ align:start position:0%
+i mean this this comes back
+to what i described before
+
+ align:start position:0%
+to what i described before
+ 
+
+ align:start position:0%
+to what i described before
+because something existed actually
+
+ align:start position:0%
+because something existed actually
+ 
+
+ align:start position:0%
+because something existed actually
+there's a need for it it's really the
+
+ align:start position:0%
+there's a need for it it's really the
+ 
+
+ align:start position:0%
+there's a need for it it's really the
+need to bridge
+
+ align:start position:0%
+need to bridge
+ 
+
+ align:start position:0%
+need to bridge
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+the lenders and the borrowers
+
+ align:start position:0%
+the lenders and the borrowers
+ 
+
+ align:start position:0%
+the lenders and the borrowers
+that's really coming down to the
+
+ align:start position:0%
+that's really coming down to the
+ 
+
+ align:start position:0%
+that's really coming down to the
+essential relationship
+
+ align:start position:0%
+essential relationship
+ 
+
+ align:start position:0%
+essential relationship
+so investors who have money
+
+ align:start position:0%
+so investors who have money
+ 
+
+ align:start position:0%
+so investors who have money
+need have better yield or better return
+
+ align:start position:0%
+need have better yield or better return
+ 
+
+ align:start position:0%
+need have better yield or better return
+better interest in the current
+
+ align:start position:0%
+better interest in the current
+ 
+
+ align:start position:0%
+better interest in the current
+environment when you have a savings
+
+ align:start position:0%
+environment when you have a savings
+ 
+
+ align:start position:0%
+environment when you have a savings
+account you know you don't really earn
+
+ align:start position:0%
+account you know you don't really earn
+ 
+
+ align:start position:0%
+account you know you don't really earn
+much at all
+
+ align:start position:0%
+much at all
+ 
+
+ align:start position:0%
+much at all
+and so you would
+
+ align:start position:0%
+and so you would
+ 
+
+ align:start position:0%
+and so you would
+have to
+
+ align:start position:0%
+have to
+ 
+
+ align:start position:0%
+have to
+take more risk
+
+ align:start position:0%
+take more risk
+ 
+
+ align:start position:0%
+take more risk
+to generate more return or you have a
+
+ align:start position:0%
+to generate more return or you have a
+ 
+
+ align:start position:0%
+to generate more return or you have a
+longer horizon
+
+ align:start position:0%
+longer horizon
+ 
+
+ align:start position:0%
+longer horizon
+cds or other type of products or trade
+
+ align:start position:0%
+cds or other type of products or trade
+ 
+
+ align:start position:0%
+cds or other type of products or trade
+stocks right so that's when somebody has
+
+ align:start position:0%
+stocks right so that's when somebody has
+ 
+
+ align:start position:0%
+stocks right so that's when somebody has
+money when you trade stocks you're
+
+ align:start position:0%
+money when you trade stocks you're
+ 
+
+ align:start position:0%
+money when you trade stocks you're
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+you know you're buying a stock you give
+
+ align:start position:0%
+you know you're buying a stock you give
+ 
+
+ align:start position:0%
+you know you're buying a stock you give
+the money somewhere
+
+ align:start position:0%
+the money somewhere
+ 
+
+ align:start position:0%
+the money somewhere
+supposedly you know go to the company
+
+ align:start position:0%
+supposedly you know go to the company
+ 
+
+ align:start position:0%
+supposedly you know go to the company
+the company use the money uh you know to
+
+ align:start position:0%
+the company use the money uh you know to
+ 
+
+ align:start position:0%
+the company use the money uh you know to
+generate a better return
+
+ align:start position:0%
+generate a better return
+ 
+
+ align:start position:0%
+generate a better return
+and for the borrowers
+
+ align:start position:0%
+and for the borrowers
+ 
+
+ align:start position:0%
+and for the borrowers
+whoever needs money
+
+ align:start position:0%
+whoever needs money
+ 
+
+ align:start position:0%
+whoever needs money
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+need to have access to the capital right
+
+ align:start position:0%
+need to have access to the capital right
+ 
+
+ align:start position:0%
+need to have access to the capital right
+so they
+
+ align:start position:0%
+so they
+ 
+
+ align:start position:0%
+so they
+obviously
+
+ align:start position:0%
+obviously
+ 
+
+ align:start position:0%
+obviously
+different borrowers have different risks
+
+ align:start position:0%
+different borrowers have different risks
+ 
+
+ align:start position:0%
+different borrowers have different risks
+some people borrow money never return
+
+ align:start position:0%
+some people borrow money never return
+ 
+
+ align:start position:0%
+some people borrow money never return
+right so or never generate any returns
+
+ align:start position:0%
+right so or never generate any returns
+ 
+
+ align:start position:0%
+right so or never generate any returns
+or never even return the principle
+
+ align:start position:0%
+or never even return the principle
+ 
+
+ align:start position:0%
+or never even return the principle
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so the trade between lenders and the
+
+ align:start position:0%
+so the trade between lenders and the
+ 
+
+ align:start position:0%
+so the trade between lenders and the
+borrowers is again essentially the main
+
+ align:start position:0%
+borrowers is again essentially the main
+ 
+
+ align:start position:0%
+borrowers is again essentially the main
+driver of the financial markets
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a few more words about market
+
+ align:start position:0%
+so a few more words about market
+ 
+
+ align:start position:0%
+so a few more words about market
+participants
+
+ align:start position:0%
+participants
+ 
+
+ align:start position:0%
+participants
+so banks and so-called dealers play the
+
+ align:start position:0%
+so banks and so-called dealers play the
+ 
+
+ align:start position:0%
+so banks and so-called dealers play the
+role of market making
+
+ align:start position:0%
+role of market making
+ 
+
+ align:start position:0%
+role of market making
+what is market making
+
+ align:start position:0%
+what is market making
+ 
+
+ align:start position:0%
+what is market making
+so when you or some
+
+ align:start position:0%
+so when you or some
+ 
+
+ align:start position:0%
+so when you or some
+end user go to the market wants to buy
+
+ align:start position:0%
+end user go to the market wants to buy
+ 
+
+ align:start position:0%
+end user go to the market wants to buy
+or sell
+
+ align:start position:0%
+or sell
+ 
+
+ align:start position:0%
+or sell
+you typically if there's no market you
+
+ align:start position:0%
+you typically if there's no market you
+ 
+
+ align:start position:0%
+you typically if there's no market you
+don't really find the match and some of
+
+ align:start position:0%
+don't really find the match and some of
+ 
+
+ align:start position:0%
+don't really find the match and some of
+the the products you want to buy or sell
+
+ align:start position:0%
+the the products you want to buy or sell
+ 
+
+ align:start position:0%
+the the products you want to buy or sell
+may not necessarily be liquid
+
+ align:start position:0%
+may not necessarily be liquid
+ 
+
+ align:start position:0%
+may not necessarily be liquid
+so the dealers step in the middle make
+
+ align:start position:0%
+so the dealers step in the middle make
+ 
+
+ align:start position:0%
+so the dealers step in the middle make
+your price say okay you want to buy or
+
+ align:start position:0%
+your price say okay you want to buy or
+ 
+
+ align:start position:0%
+your price say okay you want to buy or
+sell
+
+ align:start position:0%
+sell
+ 
+
+ align:start position:0%
+sell
+i can tell you you know
+
+ align:start position:0%
+i can tell you you know
+ 
+
+ align:start position:0%
+i can tell you you know
+this stock i make your price
+
+ align:start position:0%
+this stock i make your price
+ 
+
+ align:start position:0%
+this stock i make your price
+you know 99
+
+ align:start position:0%
+you know 99
+ 
+
+ align:start position:0%
+you know 99
+cents and
+
+ align:start position:0%
+cents and
+ 
+
+ align:start position:0%
+cents and
+that's my bid 95 cents that's my offer
+
+ align:start position:0%
+that's my bid 95 cents that's my offer
+ 
+
+ align:start position:0%
+that's my bid 95 cents that's my offer
+right so that's the price i'm willing to
+
+ align:start position:0%
+right so that's the price i'm willing to
+ 
+
+ align:start position:0%
+right so that's the price i'm willing to
+buy or sell
+
+ align:start position:0%
+buy or sell
+ 
+
+ align:start position:0%
+buy or sell
+so that's called they but what the
+
+ align:start position:0%
+so that's called they but what the
+ 
+
+ align:start position:0%
+so that's called they but what the
+result of the trade the dealer actually
+
+ align:start position:0%
+result of the trade the dealer actually
+ 
+
+ align:start position:0%
+result of the trade the dealer actually
+takes the other side of your trade so
+
+ align:start position:0%
+takes the other side of your trade so
+ 
+
+ align:start position:0%
+takes the other side of your trade so
+they take
+
+ align:start position:0%
+they take
+ 
+
+ align:start position:0%
+they take
+principal risk in this case
+
+ align:start position:0%
+principal risk in this case
+ 
+
+ align:start position:0%
+principal risk in this case
+so that's the difference between dealers
+
+ align:start position:0%
+so that's the difference between dealers
+ 
+
+ align:start position:0%
+so that's the difference between dealers
+and the brokers so brokers don't really
+
+ align:start position:0%
+and the brokers so brokers don't really
+ 
+
+ align:start position:0%
+and the brokers so brokers don't really
+take principal
+
+ align:start position:0%
+take principal
+ 
+
+ align:start position:0%
+take principal
+risks if you want to buy some buy
+
+ align:start position:0%
+risks if you want to buy some buy
+ 
+
+ align:start position:0%
+risks if you want to buy some buy
+something or sell something if i'm a
+
+ align:start position:0%
+something or sell something if i'm a
+ 
+
+ align:start position:0%
+something or sell something if i'm a
+broker
+
+ align:start position:0%
+broker
+ 
+
+ align:start position:0%
+broker
+so i don't make your price i go to the
+
+ align:start position:0%
+so i don't make your price i go to the
+ 
+
+ align:start position:0%
+so i don't make your price i go to the
+market makers
+
+ align:start position:0%
+market makers
+ 
+
+ align:start position:0%
+market makers
+i actually put two
+
+ align:start position:0%
+i actually put two
+ 
+
+ align:start position:0%
+i actually put two
+people together to kind of a matchmaking
+
+ align:start position:0%
+people together to kind of a matchmaking
+ 
+
+ align:start position:0%
+people together to kind of a matchmaking
+make that trade happen
+
+ align:start position:0%
+make that trade happen
+ 
+
+ align:start position:0%
+make that trade happen
+so i earned a commission so that's a
+
+ align:start position:0%
+so i earned a commission so that's a
+ 
+
+ align:start position:0%
+so i earned a commission so that's a
+broker's role
+
+ align:start position:0%
+broker's role
+ 
+
+ align:start position:0%
+broker's role
+so obviously there are individual
+
+ align:start position:0%
+so obviously there are individual
+ 
+
+ align:start position:0%
+so obviously there are individual
+investors retail investors same meaning
+
+ align:start position:0%
+investors retail investors same meaning
+ 
+
+ align:start position:0%
+investors retail investors same meaning
+mutual funds who actually manage
+
+ align:start position:0%
+mutual funds who actually manage
+ 
+
+ align:start position:0%
+mutual funds who actually manage
+public investors money typically in a
+
+ align:start position:0%
+public investors money typically in a
+ 
+
+ align:start position:0%
+public investors money typically in a
+long only
+
+ align:start position:0%
+long only
+ 
+
+ align:start position:0%
+long only
+format
+
+ align:start position:0%
+format
+ 
+
+ align:start position:0%
+format
+meaning their loan means you buy
+
+ align:start position:0%
+meaning their loan means you buy
+ 
+
+ align:start position:0%
+meaning their loan means you buy
+something so you don't really
+
+ align:start position:0%
+something so you don't really
+ 
+
+ align:start position:0%
+something so you don't really
+sure sell a particular
+
+ align:start position:0%
+sure sell a particular
+ 
+
+ align:start position:0%
+sure sell a particular
+security
+
+ align:start position:0%
+security
+ 
+
+ align:start position:0%
+security
+insurance companies has large asset they
+
+ align:start position:0%
+insurance companies has large asset they
+ 
+
+ align:start position:0%
+insurance companies has large asset they
+need to generate return generate cash
+
+ align:start position:0%
+need to generate return generate cash
+ 
+
+ align:start position:0%
+need to generate return generate cash
+flow to meet the liability
+
+ align:start position:0%
+flow to meet the liability
+ 
+
+ align:start position:0%
+flow to meet the liability
+needs
+
+ align:start position:0%
+needs
+ 
+
+ align:start position:0%
+needs
+so they need to invest
+
+ align:start position:0%
+so they need to invest
+ 
+
+ align:start position:0%
+so they need to invest
+and the pension funds same thing as
+
+ align:start position:0%
+and the pension funds same thing as
+ 
+
+ align:start position:0%
+and the pension funds same thing as
+inflation goes higher they need to pay
+
+ align:start position:0%
+inflation goes higher they need to pay
+ 
+
+ align:start position:0%
+inflation goes higher they need to pay
+out more to the retirees so where do you
+
+ align:start position:0%
+out more to the retirees so where do you
+ 
+
+ align:start position:0%
+out more to the retirees so where do you
+get a return right sovereign wealth fund
+
+ align:start position:0%
+get a return right sovereign wealth fund
+ 
+
+ align:start position:0%
+get a return right sovereign wealth fund
+similarly endowment funds they all have
+
+ align:start position:0%
+similarly endowment funds they all have
+ 
+
+ align:start position:0%
+similarly endowment funds they all have
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+same situation have capital needs to
+
+ align:start position:0%
+same situation have capital needs to
+ 
+
+ align:start position:0%
+same situation have capital needs to
+deploy and make better return
+
+ align:start position:0%
+deploy and make better return
+ 
+
+ align:start position:0%
+deploy and make better return
+so there's other type of
+
+ align:start position:0%
+so there's other type of
+ 
+
+ align:start position:0%
+so there's other type of
+players hedge funds
+
+ align:start position:0%
+players hedge funds
+ 
+
+ align:start position:0%
+players hedge funds
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+how many of you have heard hedge funds
+
+ align:start position:0%
+how many of you have heard hedge funds
+ 
+
+ align:start position:0%
+how many of you have heard hedge funds
+okay good almost everyone okay so i'm
+
+ align:start position:0%
+okay good almost everyone okay so i'm
+ 
+
+ align:start position:0%
+okay good almost everyone okay so i'm
+not the and peter mentioned he used to
+
+ align:start position:0%
+not the and peter mentioned he used to
+ 
+
+ align:start position:0%
+not the and peter mentioned he used to
+work at a hedge fund so
+
+ align:start position:0%
+work at a hedge fund so
+ 
+
+ align:start position:0%
+work at a hedge fund so
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+um so there are
+
+ align:start position:0%
+um so there are
+ 
+
+ align:start position:0%
+um so there are
+different types of strategies which i
+
+ align:start position:0%
+different types of strategies which i
+ 
+
+ align:start position:0%
+different types of strategies which i
+will dive into a bit more but hedge fund
+
+ align:start position:0%
+will dive into a bit more but hedge fund
+ 
+
+ align:start position:0%
+will dive into a bit more but hedge fund
+played a role in the market
+
+ align:start position:0%
+played a role in the market
+ 
+
+ align:start position:0%
+played a role in the market
+they basically find opportunities to
+
+ align:start position:0%
+they basically find opportunities to
+ 
+
+ align:start position:0%
+they basically find opportunities to
+profit from
+
+ align:start position:0%
+profit from
+ 
+
+ align:start position:0%
+profit from
+inefficient
+
+ align:start position:0%
+inefficient
+ 
+
+ align:start position:0%
+inefficient
+market positioning or pricing right so
+
+ align:start position:0%
+market positioning or pricing right so
+ 
+
+ align:start position:0%
+market positioning or pricing right so
+they have different strategies
+
+ align:start position:0%
+they have different strategies
+ 
+
+ align:start position:0%
+they have different strategies
+and the private equity i mean different
+
+ align:start position:0%
+and the private equity i mean different
+ 
+
+ align:start position:0%
+and the private equity i mean different
+type of funds they basically look to
+
+ align:start position:0%
+type of funds they basically look to
+ 
+
+ align:start position:0%
+type of funds they basically look to
+take a pr
+
+ align:start position:0%
+take a pr
+ 
+
+ align:start position:0%
+take a pr
+invest in companies
+
+ align:start position:0%
+invest in companies
+ 
+
+ align:start position:0%
+invest in companies
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+you know either take them private or
+
+ align:start position:0%
+you know either take them private or
+ 
+
+ align:start position:0%
+you know either take them private or
+invest in the private uh equity forum
+
+ align:start position:0%
+invest in the private uh equity forum
+ 
+
+ align:start position:0%
+invest in the private uh equity forum
+to hopefully improve the company's
+
+ align:start position:0%
+to hopefully improve the company's
+ 
+
+ align:start position:0%
+to hopefully improve the company's
+profitability and then catch up
+
+ align:start position:0%
+profitability and then catch up
+ 
+
+ align:start position:0%
+profitability and then catch up
+and governments obviously have a huge
+
+ align:start position:0%
+and governments obviously have a huge
+ 
+
+ align:start position:0%
+and governments obviously have a huge
+impact on the market
+
+ align:start position:0%
+impact on the market
+ 
+
+ align:start position:0%
+impact on the market
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we know in the financial crisis
+
+ align:start position:0%
+we know in the financial crisis
+ 
+
+ align:start position:0%
+we know in the financial crisis
+government intervened
+
+ align:start position:0%
+government intervened
+ 
+
+ align:start position:0%
+government intervened
+and not only that
+
+ align:start position:0%
+and not only that
+ 
+
+ align:start position:0%
+and not only that
+at the normal market condition
+
+ align:start position:0%
+at the normal market condition
+ 
+
+ align:start position:0%
+at the normal market condition
+government always have a very large
+
+ align:start position:0%
+government always have a very large
+ 
+
+ align:start position:0%
+government always have a very large
+impact on the market because they are
+
+ align:start position:0%
+impact on the market because they are
+ 
+
+ align:start position:0%
+impact on the market because they are
+the policy makers they decide the
+
+ align:start position:0%
+the policy makers they decide the
+ 
+
+ align:start position:0%
+the policy makers they decide the
+interest rate and interest rate curve
+
+ align:start position:0%
+interest rate and interest rate curve
+ 
+
+ align:start position:0%
+interest rate and interest rate curve
+and the different policies they push out
+
+ align:start position:0%
+and the different policies they push out
+ 
+
+ align:start position:0%
+and the different policies they push out
+obviously will generate
+
+ align:start position:0%
+obviously will generate
+ 
+
+ align:start position:0%
+obviously will generate
+different outlook for the future markets
+
+ align:start position:0%
+different outlook for the future markets
+ 
+
+ align:start position:0%
+different outlook for the future markets
+therefore profitability
+
+ align:start position:0%
+therefore profitability
+ 
+
+ align:start position:0%
+therefore profitability
+then the corporate hedges and the
+
+ align:start position:0%
+then the corporate hedges and the
+ 
+
+ align:start position:0%
+then the corporate hedges and the
+liabilities when corporates borrow money
+
+ align:start position:0%
+liabilities when corporates borrow money
+ 
+
+ align:start position:0%
+liabilities when corporates borrow money
+they create some risk so they
+
+ align:start position:0%
+they create some risk so they
+ 
+
+ align:start position:0%
+they create some risk so they
+need to be sensitive to the market
+
+ align:start position:0%
+need to be sensitive to the market
+ 
+
+ align:start position:0%
+need to be sensitive to the market
+changes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to summarize
+
+ align:start position:0%
+so to summarize
+ 
+
+ align:start position:0%
+so to summarize
+the types of trading
+
+ align:start position:0%
+the types of trading
+ 
+
+ align:start position:0%
+the types of trading
+the first type
+
+ align:start position:0%
+the first type
+ 
+
+ align:start position:0%
+the first type
+is really just hedging that means you're
+
+ align:start position:0%
+is really just hedging that means you're
+ 
+
+ align:start position:0%
+is really just hedging that means you're
+not proactively adding risk
+
+ align:start position:0%
+not proactively adding risk
+ 
+
+ align:start position:0%
+not proactively adding risk
+to what you have you already have some
+
+ align:start position:0%
+to what you have you already have some
+ 
+
+ align:start position:0%
+to what you have you already have some
+exposure let's say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just give you an example let's say you
+
+ align:start position:0%
+just give you an example let's say you
+ 
+
+ align:start position:0%
+just give you an example let's say you
+borrow money you bought a house you have
+
+ align:start position:0%
+borrow money you bought a house you have
+ 
+
+ align:start position:0%
+borrow money you bought a house you have
+mortgage
+
+ align:start position:0%
+mortgage
+ 
+
+ align:start position:0%
+mortgage
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's say it's a you know uh floating
+
+ align:start position:0%
+let's say it's a you know uh floating
+ 
+
+ align:start position:0%
+let's say it's a you know uh floating
+rate mortgage payments
+
+ align:start position:0%
+rate mortgage payments
+ 
+
+ align:start position:0%
+rate mortgage payments
+and you're worried about the interest
+
+ align:start position:0%
+and you're worried about the interest
+ 
+
+ align:start position:0%
+and you're worried about the interest
+rate going higher right so you can
+
+ align:start position:0%
+rate going higher right so you can
+ 
+
+ align:start position:0%
+rate going higher right so you can
+lock that rate in into the fixed rate
+
+ align:start position:0%
+lock that rate in into the fixed rate
+ 
+
+ align:start position:0%
+lock that rate in into the fixed rate
+format
+
+ align:start position:0%
+format
+ 
+
+ align:start position:0%
+format
+or you can find ways to
+
+ align:start position:0%
+or you can find ways to
+ 
+
+ align:start position:0%
+or you can find ways to
+to hedge your exposure
+
+ align:start position:0%
+to hedge your exposure
+ 
+
+ align:start position:0%
+to hedge your exposure
+or your corporate has a large income
+
+ align:start position:0%
+or your corporate has a large income
+ 
+
+ align:start position:0%
+or your corporate has a large income
+coming from europe
+
+ align:start position:0%
+coming from europe
+ 
+
+ align:start position:0%
+coming from europe
+so you have euros coming in but you're
+
+ align:start position:0%
+so you have euros coming in but you're
+ 
+
+ align:start position:0%
+so you have euros coming in but you're
+not sure
+
+ align:start position:0%
+not sure
+ 
+
+ align:start position:0%
+not sure
+if euro will trade stronger to the u.s
+
+ align:start position:0%
+if euro will trade stronger to the u.s
+ 
+
+ align:start position:0%
+if euro will trade stronger to the u.s
+dollar
+
+ align:start position:0%
+dollar
+ 
+
+ align:start position:0%
+dollar
+in the future or trade weaker right if
+
+ align:start position:0%
+in the future or trade weaker right if
+ 
+
+ align:start position:0%
+in the future or trade weaker right if
+you trade it will be if you think it
+
+ align:start position:0%
+you trade it will be if you think it
+ 
+
+ align:start position:0%
+you trade it will be if you think it
+will be stronger you just leave it but
+
+ align:start position:0%
+will be stronger you just leave it but
+ 
+
+ align:start position:0%
+will be stronger you just leave it but
+if you think it will
+
+ align:start position:0%
+if you think it will
+ 
+
+ align:start position:0%
+if you think it will
+will trade weaker so you may want to
+
+ align:start position:0%
+will trade weaker so you may want to
+ 
+
+ align:start position:0%
+will trade weaker so you may want to
+hedge it meaning you want to sell euro
+
+ align:start position:0%
+hedge it meaning you want to sell euro
+ 
+
+ align:start position:0%
+hedge it meaning you want to sell euro
+and buy us dollars
+
+ align:start position:0%
+and buy us dollars
+ 
+
+ align:start position:0%
+and buy us dollars
+and so that's the hedging type the
+
+ align:start position:0%
+and so that's the hedging type the
+ 
+
+ align:start position:0%
+and so that's the hedging type the
+second type as i mentioned is a market
+
+ align:start position:0%
+second type as i mentioned is a market
+ 
+
+ align:start position:0%
+second type as i mentioned is a market
+maker so market maker also takes
+
+ align:start position:0%
+maker so market maker also takes
+ 
+
+ align:start position:0%
+maker so market maker also takes
+principle risk but the main source of
+
+ align:start position:0%
+principle risk but the main source of
+ 
+
+ align:start position:0%
+principle risk but the main source of
+profit is really to earn the bid offer
+
+ align:start position:0%
+profit is really to earn the bid offer
+ 
+
+ align:start position:0%
+profit is really to earn the bid offer
+i gave you the example of 90 cents a bit
+
+ align:start position:0%
+i gave you the example of 90 cents a bit
+ 
+
+ align:start position:0%
+i gave you the example of 90 cents a bit
+95 cents offer so that's what the
+
+ align:start position:0%
+95 cents offer so that's what the
+ 
+
+ align:start position:0%
+95 cents offer so that's what the
+market maker is trying to
+
+ align:start position:0%
+market maker is trying to
+ 
+
+ align:start position:0%
+market maker is trying to
+profit from but obviously they have
+
+ align:start position:0%
+profit from but obviously they have
+ 
+
+ align:start position:0%
+profit from but obviously they have
+residual risks sitting on the book not
+
+ align:start position:0%
+residual risks sitting on the book not
+ 
+
+ align:start position:0%
+residual risks sitting on the book not
+every trade is matched
+
+ align:start position:0%
+every trade is matched
+ 
+
+ align:start position:0%
+every trade is matched
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+how to optimize
+
+ align:start position:0%
+how to optimize
+ 
+
+ align:start position:0%
+how to optimize
+those group of trades
+
+ align:start position:0%
+those group of trades
+ 
+
+ align:start position:0%
+those group of trades
+that's what market maker is doing
+
+ align:start position:0%
+that's what market maker is doing
+ 
+
+ align:start position:0%
+that's what market maker is doing
+most of the banks dealers are market
+
+ align:start position:0%
+most of the banks dealers are market
+ 
+
+ align:start position:0%
+most of the banks dealers are market
+makers i mean in the new um
+
+ align:start position:0%
+makers i mean in the new um
+ 
+
+ align:start position:0%
+makers i mean in the new um
+regulation obviously proprietary trading
+
+ align:start position:0%
+regulation obviously proprietary trading
+ 
+
+ align:start position:0%
+regulation obviously proprietary trading
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+some you know expand right
+
+ align:start position:0%
+some you know expand right
+ 
+
+ align:start position:0%
+some you know expand right
+and so the third type is really the
+
+ align:start position:0%
+and so the third type is really the
+ 
+
+ align:start position:0%
+and so the third type is really the
+proprietary trader the risk taker
+
+ align:start position:0%
+proprietary trader the risk taker
+ 
+
+ align:start position:0%
+proprietary trader the risk taker
+so these are the hedge funds or some
+
+ align:start position:0%
+so these are the hedge funds or some
+ 
+
+ align:start position:0%
+so these are the hedge funds or some
+portfolio managers they need to focus on
+
+ align:start position:0%
+portfolio managers they need to focus on
+ 
+
+ align:start position:0%
+portfolio managers they need to focus on
+generating return
+
+ align:start position:0%
+generating return
+ 
+
+ align:start position:0%
+generating return
+and with control the risk
+
+ align:start position:0%
+and with control the risk
+ 
+
+ align:start position:0%
+and with control the risk
+so that's where the beta and offer the
+
+ align:start position:0%
+so that's where the beta and offer the
+ 
+
+ align:start position:0%
+so that's where the beta and offer the
+concept comes in so if you're a
+
+ align:start position:0%
+concept comes in so if you're a
+ 
+
+ align:start position:0%
+concept comes in so if you're a
+portfolio manager
+
+ align:start position:0%
+portfolio manager
+ 
+
+ align:start position:0%
+portfolio manager
+i mean some people say you don't really
+
+ align:start position:0%
+i mean some people say you don't really
+ 
+
+ align:start position:0%
+i mean some people say you don't really
+you know don't worry don't go pick any
+
+ align:start position:0%
+you know don't worry don't go pick any
+ 
+
+ align:start position:0%
+you know don't worry don't go pick any
+stocks just by s p 500 index fund you
+
+ align:start position:0%
+stocks just by s p 500 index fund you
+ 
+
+ align:start position:0%
+stocks just by s p 500 index fund you
+know very cheap you can
+
+ align:start position:0%
+know very cheap you can
+ 
+
+ align:start position:0%
+know very cheap you can
+pay very little cost to do it that's
+
+ align:start position:0%
+pay very little cost to do it that's
+ 
+
+ align:start position:0%
+pay very little cost to do it that's
+true so but if you want to beat the s p
+
+ align:start position:0%
+true so but if you want to beat the s p
+ 
+
+ align:start position:0%
+true so but if you want to beat the s p
+500 index
+
+ align:start position:0%
+500 index
+ 
+
+ align:start position:0%
+500 index
+let's assume we call it s
+
+ align:start position:0%
+let's assume we call it s
+ 
+
+ align:start position:0%
+let's assume we call it s
+p 500 index fund is
+
+ align:start position:0%
+p 500 index fund is
+ 
+
+ align:start position:0%
+p 500 index fund is
+asset b so the return of that off b
+
+ align:start position:0%
+asset b so the return of that off b
+ 
+
+ align:start position:0%
+asset b so the return of that off b
+that's the return of that index
+
+ align:start position:0%
+that's the return of that index
+ 
+
+ align:start position:0%
+that's the return of that index
+then you have a portfolio a
+
+ align:start position:0%
+then you have a portfolio a
+ 
+
+ align:start position:0%
+then you have a portfolio a
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+you time series of return of you asset a
+
+ align:start position:0%
+you time series of return of you asset a
+ 
+
+ align:start position:0%
+you time series of return of you asset a
+obviously you can do linear regression
+
+ align:start position:0%
+obviously you can do linear regression
+ 
+
+ align:start position:0%
+obviously you can do linear regression
+by your a lot of your math major here
+
+ align:start position:0%
+by your a lot of your math major here
+ 
+
+ align:start position:0%
+by your a lot of your math major here
+and you can find a correlation
+
+ align:start position:0%
+and you can find a correlation
+ 
+
+ align:start position:0%
+and you can find a correlation
+between those two time series
+
+ align:start position:0%
+between those two time series
+ 
+
+ align:start position:0%
+between those two time series
+so that how the two returns are are
+
+ align:start position:0%
+so that how the two returns are are
+ 
+
+ align:start position:0%
+so that how the two returns are are
+related in a simplified form
+
+ align:start position:0%
+related in a simplified form
+ 
+
+ align:start position:0%
+related in a simplified form
+so you can say
+
+ align:start position:0%
+so you can say
+ 
+
+ align:start position:0%
+so you can say
+this actually somehow it came out it's
+
+ align:start position:0%
+this actually somehow it came out it's
+ 
+
+ align:start position:0%
+this actually somehow it came out it's
+supposed to be alpha and a beta but it
+
+ align:start position:0%
+supposed to be alpha and a beta but it
+ 
+
+ align:start position:0%
+supposed to be alpha and a beta but it
+turned out to be uh you know
+
+ align:start position:0%
+turned out to be uh you know
+ 
+
+ align:start position:0%
+turned out to be uh you know
+the the letters but so in the short
+
+ align:start position:0%
+the the letters but so in the short
+ 
+
+ align:start position:0%
+the the letters but so in the short
+description beta is really kind of you
+
+ align:start position:0%
+description beta is really kind of you
+ 
+
+ align:start position:0%
+description beta is really kind of you
+know just think as uh
+
+ align:start position:0%
+know just think as uh
+ 
+
+ align:start position:0%
+know just think as uh
+the correlated move with the the other
+
+ align:start position:0%
+the correlated move with the the other
+ 
+
+ align:start position:0%
+the correlated move with the the other
+asset alpha is really the the you know
+
+ align:start position:0%
+asset alpha is really the the you know
+ 
+
+ align:start position:0%
+asset alpha is really the the you know
+the difference in return
+
+ align:start position:0%
+the difference in return
+ 
+
+ align:start position:0%
+the difference in return
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+it's a format you want to beat smp 500
+
+ align:start position:0%
+it's a format you want to beat smp 500
+ 
+
+ align:start position:0%
+it's a format you want to beat smp 500
+so you want
+
+ align:start position:0%
+so you want
+ 
+
+ align:start position:0%
+so you want
+basically have certain tracking of this
+
+ align:start position:0%
+basically have certain tracking of this
+ 
+
+ align:start position:0%
+basically have certain tracking of this
+index but you want to return more on top
+
+ align:start position:0%
+index but you want to return more on top
+ 
+
+ align:start position:0%
+index but you want to return more on top
+of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let me just go in
+
+ align:start position:0%
+let me just go in
+ 
+
+ align:start position:0%
+let me just go in
+details of how each type of trade
+
+ align:start position:0%
+details of how each type of trade
+ 
+
+ align:start position:0%
+details of how each type of trade
+actually occurs
+
+ align:start position:0%
+actually occurs
+ 
+
+ align:start position:0%
+actually occurs
+so when we talk about hedging i
+
+ align:start position:0%
+so when we talk about hedging i
+ 
+
+ align:start position:0%
+so when we talk about hedging i
+mentioned the currency example let me
+
+ align:start position:0%
+mentioned the currency example let me
+ 
+
+ align:start position:0%
+mentioned the currency example let me
+give you another example
+
+ align:start position:0%
+give you another example
+ 
+
+ align:start position:0%
+give you another example
+a lot of people issue bonds or issue
+
+ align:start position:0%
+a lot of people issue bonds or issue
+ 
+
+ align:start position:0%
+a lot of people issue bonds or issue
+debt so this example i'm going to give
+
+ align:start position:0%
+debt so this example i'm going to give
+ 
+
+ align:start position:0%
+debt so this example i'm going to give
+you is
+
+ align:start position:0%
+you is
+ 
+
+ align:start position:0%
+you is
+let's think about australian
+
+ align:start position:0%
+let's think about australian
+ 
+
+ align:start position:0%
+let's think about australian
+corporate
+
+ align:start position:0%
+corporate
+ 
+
+ align:start position:0%
+corporate
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+interest rate in australia is higher
+
+ align:start position:0%
+interest rate in australia is higher
+ 
+
+ align:start position:0%
+interest rate in australia is higher
+than in japan
+
+ align:start position:0%
+than in japan
+ 
+
+ align:start position:0%
+than in japan
+so typically people like to
+
+ align:start position:0%
+so typically people like to
+ 
+
+ align:start position:0%
+so typically people like to
+borrow money
+
+ align:start position:0%
+borrow money
+ 
+
+ align:start position:0%
+borrow money
+in japan because you pay
+
+ align:start position:0%
+in japan because you pay
+ 
+
+ align:start position:0%
+in japan because you pay
+smaller interest
+
+ align:start position:0%
+smaller interest
+ 
+
+ align:start position:0%
+smaller interest
+and you invest it in australia you earn
+
+ align:start position:0%
+and you invest it in australia you earn
+ 
+
+ align:start position:0%
+and you invest it in australia you earn
+higher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+interest rate
+
+ align:start position:0%
+interest rate
+ 
+
+ align:start position:0%
+interest rate
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let me ask you a question
+
+ align:start position:0%
+let me ask you a question
+ 
+
+ align:start position:0%
+let me ask you a question
+who can tell me why don't people just do
+
+ align:start position:0%
+who can tell me why don't people just do
+ 
+
+ align:start position:0%
+who can tell me why don't people just do
+that all day long just borrow from japan
+
+ align:start position:0%
+that all day long just borrow from japan
+ 
+
+ align:start position:0%
+that all day long just borrow from japan
+and invest
+
+ align:start position:0%
+and invest
+ 
+
+ align:start position:0%
+and invest
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+australia
+
+ align:start position:0%
+australia
+ 
+
+ align:start position:0%
+australia
+then that interest rate i'm giving you
+
+ align:start position:0%
+then that interest rate i'm giving you
+ 
+
+ align:start position:0%
+then that interest rate i'm giving you
+an example of a difference
+
+ align:start position:0%
+an example of a difference
+ 
+
+ align:start position:0%
+an example of a difference
+is about three and a half percent for
+
+ align:start position:0%
+is about three and a half percent for
+ 
+
+ align:start position:0%
+is about three and a half percent for
+the ten year roughly you know ten years
+
+ align:start position:0%
+the ten year roughly you know ten years
+ 
+
+ align:start position:0%
+the ten year roughly you know ten years
+uh swap rates
+
+ align:start position:0%
+uh swap rates
+ 
+
+ align:start position:0%
+uh swap rates
+why don't yeah go ahead
+
+ align:start position:0%
+why don't yeah go ahead
+ 
+
+ align:start position:0%
+why don't yeah go ahead
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+because you invest in the australia
+
+ align:start position:0%
+because you invest in the australia
+ 
+
+ align:start position:0%
+because you invest in the australia
+aussie right australian dollar the
+
+ align:start position:0%
+aussie right australian dollar the
+ 
+
+ align:start position:0%
+aussie right australian dollar the
+australian dollar may become weaker to
+
+ align:start position:0%
+australian dollar may become weaker to
+ 
+
+ align:start position:0%
+australian dollar may become weaker to
+the yen you may lose all your profit or
+
+ align:start position:0%
+the yen you may lose all your profit or
+ 
+
+ align:start position:0%
+the yen you may lose all your profit or
+even more right
+
+ align:start position:0%
+even more right
+ 
+
+ align:start position:0%
+even more right
+and further if everybody
+
+ align:start position:0%
+and further if everybody
+ 
+
+ align:start position:0%
+and further if everybody
+plays the same game then and when you
+
+ align:start position:0%
+plays the same game then and when you
+ 
+
+ align:start position:0%
+plays the same game then and when you
+try to exit you
+
+ align:start position:0%
+try to exit you
+ 
+
+ align:start position:0%
+try to exit you
+you have the adverse impact of your
+
+ align:start position:0%
+you have the adverse impact of your
+ 
+
+ align:start position:0%
+you have the adverse impact of your
+trade
+
+ align:start position:0%
+trade
+ 
+
+ align:start position:0%
+trade
+so let's say you you think that's the
+
+ align:start position:0%
+so let's say you you think that's the
+ 
+
+ align:start position:0%
+so let's say you you think that's the
+right time to do it but then
+
+ align:start position:0%
+right time to do it but then
+ 
+
+ align:start position:0%
+right time to do it but then
+at one time you wake up you said huh i
+
+ align:start position:0%
+at one time you wake up you said huh i
+ 
+
+ align:start position:0%
+at one time you wake up you said huh i
+think too many people are doing this i
+
+ align:start position:0%
+think too many people are doing this i
+ 
+
+ align:start position:0%
+think too many people are doing this i
+want to hedge myself so what do you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yep so you try to lock in right so
+
+ align:start position:0%
+yep so you try to lock in right so
+ 
+
+ align:start position:0%
+yep so you try to lock in right so
+basically you
+
+ align:start position:0%
+basically you
+ 
+
+ align:start position:0%
+basically you
+you sell the australian dollars
+
+ align:start position:0%
+you sell the australian dollars
+ 
+
+ align:start position:0%
+you sell the australian dollars
+by the japanese yen
+
+ align:start position:0%
+by the japanese yen
+ 
+
+ align:start position:0%
+by the japanese yen
+or on the interest rate terms you say
+
+ align:start position:0%
+or on the interest rate terms you say
+ 
+
+ align:start position:0%
+or on the interest rate terms you say
+you you basically pay
+
+ align:start position:0%
+you you basically pay
+ 
+
+ align:start position:0%
+you you basically pay
+the house australian dollar in the swap
+
+ align:start position:0%
+the house australian dollar in the swap
+ 
+
+ align:start position:0%
+the house australian dollar in the swap
+lag and the receive yen
+
+ align:start position:0%
+lag and the receive yen
+ 
+
+ align:start position:0%
+lag and the receive yen
+so that in the you this involves foreign
+
+ align:start position:0%
+so that in the you this involves foreign
+ 
+
+ align:start position:0%
+so that in the you this involves foreign
+exchange trade
+
+ align:start position:0%
+exchange trade
+ 
+
+ align:start position:0%
+exchange trade
+interest rate swap
+
+ align:start position:0%
+interest rate swap
+ 
+
+ align:start position:0%
+interest rate swap
+and the cross currency swap
+
+ align:start position:0%
+and the cross currency swap
+ 
+
+ align:start position:0%
+and the cross currency swap
+so your answer about
+
+ align:start position:0%
+so your answer about
+ 
+
+ align:start position:0%
+so your answer about
+currency forward is roughly right but it
+
+ align:start position:0%
+currency forward is roughly right but it
+ 
+
+ align:start position:0%
+currency forward is roughly right but it
+obviously involves a bit more in actual
+
+ align:start position:0%
+obviously involves a bit more in actual
+ 
+
+ align:start position:0%
+obviously involves a bit more in actual
+execution
+
+ align:start position:0%
+execution
+ 
+
+ align:start position:0%
+execution
+so let's just give you an example even
+
+ align:start position:0%
+so let's just give you an example even
+ 
+
+ align:start position:0%
+so let's just give you an example even
+you are not a finance guy
+
+ align:start position:0%
+you are not a finance guy
+ 
+
+ align:start position:0%
+you are not a finance guy
+you know you work in a corporate you
+
+ align:start position:0%
+you know you work in a corporate you
+ 
+
+ align:start position:0%
+you know you work in a corporate you
+just do
+
+ align:start position:0%
+just do
+ 
+
+ align:start position:0%
+just do
+input export or building a factory or
+
+ align:start position:0%
+input export or building a factory or
+ 
+
+ align:start position:0%
+input export or building a factory or
+you know you have to know actually
+
+ align:start position:0%
+you know you have to know actually
+ 
+
+ align:start position:0%
+you know you have to know actually
+what the exposure is so risk management
+
+ align:start position:0%
+what the exposure is so risk management
+ 
+
+ align:start position:0%
+what the exposure is so risk management
+nowadays
+
+ align:start position:0%
+nowadays
+ 
+
+ align:start position:0%
+nowadays
+becomes pretty widespread responsibility
+
+ align:start position:0%
+becomes pretty widespread responsibility
+ 
+
+ align:start position:0%
+becomes pretty widespread responsibility
+it's not just of you know the corporate
+
+ align:start position:0%
+it's not just of you know the corporate
+ 
+
+ align:start position:0%
+it's not just of you know the corporate
+treasury's responsibility
+
+ align:start position:0%
+treasury's responsibility
+ 
+
+ align:start position:0%
+treasury's responsibility
+so that's on the hedging side obviously
+
+ align:start position:0%
+so that's on the hedging side obviously
+ 
+
+ align:start position:0%
+so that's on the hedging side obviously
+if you're um
+
+ align:start position:0%
+if you're um
+ 
+
+ align:start position:0%
+if you're um
+intel for example
+
+ align:start position:0%
+intel for example
+ 
+
+ align:start position:0%
+intel for example
+right you sell a lot of chips uh
+
+ align:start position:0%
+right you sell a lot of chips uh
+ 
+
+ align:start position:0%
+right you sell a lot of chips uh
+overseas
+
+ align:start position:0%
+overseas
+ 
+
+ align:start position:0%
+overseas
+and your income actually intel does have
+
+ align:start position:0%
+and your income actually intel does have
+ 
+
+ align:start position:0%
+and your income actually intel does have
+a lot of overseas income sitting outside
+
+ align:start position:0%
+a lot of overseas income sitting outside
+ 
+
+ align:start position:0%
+a lot of overseas income sitting outside
+the states
+
+ align:start position:0%
+the states
+ 
+
+ align:start position:0%
+the states
+so the exposure to them is if
+
+ align:start position:0%
+so the exposure to them is if
+ 
+
+ align:start position:0%
+so the exposure to them is if
+the exchange rate fluctuates dollar
+
+ align:start position:0%
+the exchange rate fluctuates dollar
+ 
+
+ align:start position:0%
+the exchange rate fluctuates dollar
+becomes a lot stronger they actually
+
+ align:start position:0%
+becomes a lot stronger they actually
+ 
+
+ align:start position:0%
+becomes a lot stronger they actually
+lose money
+
+ align:start position:0%
+lose money
+ 
+
+ align:start position:0%
+lose money
+so they need to think about you know how
+
+ align:start position:0%
+so they need to think about you know how
+ 
+
+ align:start position:0%
+so they need to think about you know how
+to hatch the revenue produced overseas
+
+ align:start position:0%
+to hatch the revenue produced overseas
+ 
+
+ align:start position:0%
+to hatch the revenue produced overseas
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+obviously if you are import exporters
+
+ align:start position:0%
+obviously if you are import exporters
+ 
+
+ align:start position:0%
+obviously if you are import exporters
+that's even more apparent
+
+ align:start position:0%
+that's even more apparent
+ 
+
+ align:start position:0%
+that's even more apparent
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+if you're in entering the merger deal
+
+ align:start position:0%
+if you're in entering the merger deal
+ 
+
+ align:start position:0%
+if you're in entering the merger deal
+you one company is buying another
+
+ align:start position:0%
+you one company is buying another
+ 
+
+ align:start position:0%
+you one company is buying another
+you need to hedge
+
+ align:start position:0%
+you need to hedge
+ 
+
+ align:start position:0%
+you need to hedge
+your potential currency exposure and
+
+ align:start position:0%
+your potential currency exposure and
+ 
+
+ align:start position:0%
+your potential currency exposure and
+your interest rate exposure and whatever
+
+ align:start position:0%
+your interest rate exposure and whatever
+ 
+
+ align:start position:0%
+your interest rate exposure and whatever
+is on
+
+ align:start position:0%
+is on
+ 
+
+ align:start position:0%
+is on
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+on assets or the liability of the
+
+ align:start position:0%
+on assets or the liability of the
+ 
+
+ align:start position:0%
+on assets or the liability of the
+balance sheet you need to have your
+
+ align:start position:0%
+balance sheet you need to have your
+ 
+
+ align:start position:0%
+balance sheet you need to have your
+exposure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we talked about the hedging activity
+
+ align:start position:0%
+so we talked about the hedging activity
+ 
+
+ align:start position:0%
+so we talked about the hedging activity
+let's talk about a bit of market making
+
+ align:start position:0%
+let's talk about a bit of market making
+ 
+
+ align:start position:0%
+let's talk about a bit of market making
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if it's a simple transparent product
+
+ align:start position:0%
+if it's a simple transparent product
+ 
+
+ align:start position:0%
+if it's a simple transparent product
+everybody pretty much knows where the
+
+ align:start position:0%
+everybody pretty much knows where the
+ 
+
+ align:start position:0%
+everybody pretty much knows where the
+price is right so if you buy apple stock
+
+ align:start position:0%
+price is right so if you buy apple stock
+ 
+
+ align:start position:0%
+price is right so if you buy apple stock
+i think a lot of people know
+
+ align:start position:0%
+i think a lot of people know
+ 
+
+ align:start position:0%
+i think a lot of people know
+pretty much what it is you may even have
+
+ align:start position:0%
+pretty much what it is you may even have
+ 
+
+ align:start position:0%
+pretty much what it is you may even have
+it on your cell phone right know where
+
+ align:start position:0%
+it on your cell phone right know where
+ 
+
+ align:start position:0%
+it on your cell phone right know where
+that stock is
+
+ align:start position:0%
+that stock is
+ 
+
+ align:start position:0%
+that stock is
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+if it's not transparent
+
+ align:start position:0%
+if it's not transparent
+ 
+
+ align:start position:0%
+if it's not transparent
+so what do you do so if i instead of
+
+ align:start position:0%
+so what do you do so if i instead of
+ 
+
+ align:start position:0%
+so what do you do so if i instead of
+asking you where apple is probably
+
+ align:start position:0%
+asking you where apple is probably
+ 
+
+ align:start position:0%
+asking you where apple is probably
+you're going to tell me 4.95 today
+
+ align:start position:0%
+you're going to tell me 4.95 today
+ 
+
+ align:start position:0%
+you're going to tell me 4.95 today
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yeah but if i ask you instead what is
+
+ align:start position:0%
+yeah but if i ask you instead what is
+ 
+
+ align:start position:0%
+yeah but if i ask you instead what is
+the call option on
+
+ align:start position:0%
+the call option on
+ 
+
+ align:start position:0%
+the call option on
+apple stock in the you know two months
+
+ align:start position:0%
+apple stock in the you know two months
+ 
+
+ align:start position:0%
+apple stock in the you know two months
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+i'll give you a strike let's say 500.
+
+ align:start position:0%
+i'll give you a strike let's say 500.
+ 
+
+ align:start position:0%
+i'll give you a strike let's say 500.
+right so you're probably less
+
+ align:start position:0%
+right so you're probably less
+ 
+
+ align:start position:0%
+right so you're probably less
+transparent so that
+
+ align:start position:0%
+transparent so that
+ 
+
+ align:start position:0%
+transparent so that
+market maker comes in to provide that
+
+ align:start position:0%
+market maker comes in to provide that
+ 
+
+ align:start position:0%
+market maker comes in to provide that
+liquidity
+
+ align:start position:0%
+liquidity
+ 
+
+ align:start position:0%
+liquidity
+and then takes the risk they manage the
+
+ align:start position:0%
+and then takes the risk they manage the
+ 
+
+ align:start position:0%
+and then takes the risk they manage the
+book by balancing those greeks
+
+ align:start position:0%
+book by balancing those greeks
+ 
+
+ align:start position:0%
+book by balancing those greeks
+which i mentioned earlier delta which
+
+ align:start position:0%
+which i mentioned earlier delta which
+ 
+
+ align:start position:0%
+which i mentioned earlier delta which
+describes
+
+ align:start position:0%
+describes
+ 
+
+ align:start position:0%
+describes
+the kind of the linear
+
+ align:start position:0%
+the kind of the linear
+ 
+
+ align:start position:0%
+the kind of the linear
+relationship of this whole book to the
+
+ align:start position:0%
+relationship of this whole book to the
+ 
+
+ align:start position:0%
+relationship of this whole book to the
+underlying stock or underlying whatever
+
+ align:start position:0%
+underlying stock or underlying whatever
+ 
+
+ align:start position:0%
+underlying stock or underlying whatever
+currency that's called the delta
+
+ align:start position:0%
+currency that's called the delta
+ 
+
+ align:start position:0%
+currency that's called the delta
+gamma is really
+
+ align:start position:0%
+gamma is really
+ 
+
+ align:start position:0%
+gamma is really
+the change
+
+ align:start position:0%
+the change
+ 
+
+ align:start position:0%
+the change
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the portfolio take the derivative
+
+ align:start position:0%
+the portfolio take the derivative
+ 
+
+ align:start position:0%
+the portfolio take the derivative
+to the to the delta or to the underlying
+
+ align:start position:0%
+to the to the delta or to the underlying
+ 
+
+ align:start position:0%
+to the to the delta or to the underlying
+spot so that's
+
+ align:start position:0%
+spot so that's
+ 
+
+ align:start position:0%
+spot so that's
+the second order derivative right the
+
+ align:start position:0%
+the second order derivative right the
+ 
+
+ align:start position:0%
+the second order derivative right the
+delta is the first order so gamma you
+
+ align:start position:0%
+delta is the first order so gamma you
+ 
+
+ align:start position:0%
+delta is the first order so gamma you
+take so now you have
+
+ align:start position:0%
+take so now you have
+ 
+
+ align:start position:0%
+take so now you have
+curvature or convexity coming in
+
+ align:start position:0%
+curvature or convexity coming in
+ 
+
+ align:start position:0%
+curvature or convexity coming in
+and theta is really
+
+ align:start position:0%
+and theta is really
+ 
+
+ align:start position:0%
+and theta is really
+you know on nothing changes in the
+
+ align:start position:0%
+you know on nothing changes in the
+ 
+
+ align:start position:0%
+you know on nothing changes in the
+market nothing changes in your position
+
+ align:start position:0%
+market nothing changes in your position
+ 
+
+ align:start position:0%
+market nothing changes in your position
+how your
+
+ align:start position:0%
+how your
+ 
+
+ align:start position:0%
+how your
+trading book is
+
+ align:start position:0%
+trading book is
+ 
+
+ align:start position:0%
+trading book is
+carrying or bleeding away money
+
+ align:start position:0%
+carrying or bleeding away money
+ 
+
+ align:start position:0%
+carrying or bleeding away money
+and we talk about the volatility
+
+ align:start position:0%
+and we talk about the volatility
+ 
+
+ align:start position:0%
+and we talk about the volatility
+exposure with vega and on top of that
+
+ align:start position:0%
+exposure with vega and on top of that
+ 
+
+ align:start position:0%
+exposure with vega and on top of that
+what are the tail risks you know how do
+
+ align:start position:0%
+what are the tail risks you know how do
+ 
+
+ align:start position:0%
+what are the tail risks you know how do
+what other events can actually get you
+
+ align:start position:0%
+what other events can actually get you
+ 
+
+ align:start position:0%
+what other events can actually get you
+into big trouble right
+
+ align:start position:0%
+into big trouble right
+ 
+
+ align:start position:0%
+into big trouble right
+so people use value at risk so you will
+
+ align:start position:0%
+so people use value at risk so you will
+ 
+
+ align:start position:0%
+so people use value at risk so you will
+hear this var concept in some of the
+
+ align:start position:0%
+hear this var concept in some of the
+ 
+
+ align:start position:0%
+hear this var concept in some of the
+lectures and which is also obviously a
+
+ align:start position:0%
+lectures and which is also obviously a
+ 
+
+ align:start position:0%
+lectures and which is also obviously a
+very important concept and i think peter
+
+ align:start position:0%
+very important concept and i think peter
+ 
+
+ align:start position:0%
+very important concept and i think peter
+will uh or tumor would probably peter
+
+ align:start position:0%
+will uh or tumor would probably peter
+ 
+
+ align:start position:0%
+will uh or tumor would probably peter
+will teach
+
+ align:start position:0%
+will teach
+ 
+
+ align:start position:0%
+will teach
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+capital right uh how much capital you're
+
+ align:start position:0%
+capital right uh how much capital you're
+ 
+
+ align:start position:0%
+capital right uh how much capital you're
+using it becomes a very important issue
+
+ align:start position:0%
+using it becomes a very important issue
+ 
+
+ align:start position:0%
+using it becomes a very important issue
+nowadays
+
+ align:start position:0%
+nowadays
+ 
+
+ align:start position:0%
+nowadays
+and balance sheet
+
+ align:start position:0%
+and balance sheet
+ 
+
+ align:start position:0%
+and balance sheet
+again you have asset your liability how
+
+ align:start position:0%
+again you have asset your liability how
+ 
+
+ align:start position:0%
+again you have asset your liability how
+how do you leverage how much leverage
+
+ align:start position:0%
+how do you leverage how much leverage
+ 
+
+ align:start position:0%
+how do you leverage how much leverage
+you have before the crisis for example a
+
+ align:start position:0%
+you have before the crisis for example a
+ 
+
+ align:start position:0%
+you have before the crisis for example a
+lot of the banks leverage up 40 times
+
+ align:start position:0%
+lot of the banks leverage up 40 times
+ 
+
+ align:start position:0%
+lot of the banks leverage up 40 times
+meaning when you have one dollar you
+
+ align:start position:0%
+meaning when you have one dollar you
+ 
+
+ align:start position:0%
+meaning when you have one dollar you
+have a 40 exposure so when the market
+
+ align:start position:0%
+have a 40 exposure so when the market
+ 
+
+ align:start position:0%
+have a 40 exposure so when the market
+moves a little you get wiped out that's
+
+ align:start position:0%
+moves a little you get wiped out that's
+ 
+
+ align:start position:0%
+moves a little you get wiped out that's
+that's really what amplified in the 2008
+
+ align:start position:0%
+that's really what amplified in the 2008
+ 
+
+ align:start position:0%
+that's really what amplified in the 2008
+financial crisis
+
+ align:start position:0%
+financial crisis
+ 
+
+ align:start position:0%
+financial crisis
+and how do you measure
+
+ align:start position:0%
+and how do you measure
+ 
+
+ align:start position:0%
+and how do you measure
+the the asset in balance sheet when you
+
+ align:start position:0%
+the the asset in balance sheet when you
+ 
+
+ align:start position:0%
+the the asset in balance sheet when you
+have derivatives right rather than
+
+ align:start position:0%
+have derivatives right rather than
+ 
+
+ align:start position:0%
+have derivatives right rather than
+straightforward notional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so a lot of quantitative type of people
+
+ align:start position:0%
+so a lot of quantitative type of people
+ 
+
+ align:start position:0%
+so a lot of quantitative type of people
+like to focus a bit more on the risk
+
+ align:start position:0%
+like to focus a bit more on the risk
+ 
+
+ align:start position:0%
+like to focus a bit more on the risk
+taking side because
+
+ align:start position:0%
+taking side because
+ 
+
+ align:start position:0%
+taking side because
+people heard stories about the
+
+ align:start position:0%
+people heard stories about the
+ 
+
+ align:start position:0%
+people heard stories about the
+successful cases of some hedge funds
+
+ align:start position:0%
+successful cases of some hedge funds
+ 
+
+ align:start position:0%
+successful cases of some hedge funds
+using high math right they generate very
+
+ align:start position:0%
+using high math right they generate very
+ 
+
+ align:start position:0%
+using high math right they generate very
+impressive returns
+
+ align:start position:0%
+impressive returns
+ 
+
+ align:start position:0%
+impressive returns
+uh they seem to have an edge so a lot of
+
+ align:start position:0%
+uh they seem to have an edge so a lot of
+ 
+
+ align:start position:0%
+uh they seem to have an edge so a lot of
+people focus on trading strategies right
+
+ align:start position:0%
+people focus on trading strategies right
+ 
+
+ align:start position:0%
+people focus on trading strategies right
+so that that's that falls into the
+
+ align:start position:0%
+so that that's that falls into the
+ 
+
+ align:start position:0%
+so that that's that falls into the
+category of
+
+ align:start position:0%
+category of
+ 
+
+ align:start position:0%
+category of
+proprietary trading or risk taking so
+
+ align:start position:0%
+proprietary trading or risk taking so
+ 
+
+ align:start position:0%
+proprietary trading or risk taking so
+that you can just simply doing
+
+ align:start position:0%
+that you can just simply doing
+ 
+
+ align:start position:0%
+that you can just simply doing
+directional trading strategies just go
+
+ align:start position:0%
+directional trading strategies just go
+ 
+
+ align:start position:0%
+directional trading strategies just go
+long or sure the stock right that's very
+
+ align:start position:0%
+long or sure the stock right that's very
+ 
+
+ align:start position:0%
+long or sure the stock right that's very
+simple you know they are the so-called
+
+ align:start position:0%
+simple you know they are the so-called
+ 
+
+ align:start position:0%
+simple you know they are the so-called
+gut traders gut feeling go with your gut
+
+ align:start position:0%
+gut traders gut feeling go with your gut
+ 
+
+ align:start position:0%
+gut traders gut feeling go with your gut
+you don't even think he said i'm eating
+
+ align:start position:0%
+you don't even think he said i'm eating
+ 
+
+ align:start position:0%
+you don't even think he said i'm eating
+i'm eating um
+
+ align:start position:0%
+i'm eating um
+ 
+
+ align:start position:0%
+i'm eating um
+you know uh curry today so i i go long
+
+ align:start position:0%
+you know uh curry today so i i go long
+ 
+
+ align:start position:0%
+you know uh curry today so i i go long
+i'm eating rice tomorrow so i go short
+
+ align:start position:0%
+i'm eating rice tomorrow so i go short
+ 
+
+ align:start position:0%
+i'm eating rice tomorrow so i go short
+so this arbitrage arbitrage is really to
+
+ align:start position:0%
+so this arbitrage arbitrage is really to
+ 
+
+ align:start position:0%
+so this arbitrage arbitrage is really to
+find
+
+ align:start position:0%
+find
+ 
+
+ align:start position:0%
+find
+the relationships between
+
+ align:start position:0%
+the relationships between
+ 
+
+ align:start position:0%
+the relationships between
+prices
+
+ align:start position:0%
+prices
+ 
+
+ align:start position:0%
+prices
+and try to profit from uh
+
+ align:start position:0%
+and try to profit from uh
+ 
+
+ align:start position:0%
+and try to profit from uh
+those relationship uh missed pricing
+
+ align:start position:0%
+those relationship uh missed pricing
+ 
+
+ align:start position:0%
+those relationship uh missed pricing
+this is actually very interesting
+
+ align:start position:0%
+this is actually very interesting
+ 
+
+ align:start position:0%
+this is actually very interesting
+this um not many people focus on
+
+ align:start position:0%
+this um not many people focus on
+ 
+
+ align:start position:0%
+this um not many people focus on
+arbitrage you know because when a lot of
+
+ align:start position:0%
+arbitrage you know because when a lot of
+ 
+
+ align:start position:0%
+arbitrage you know because when a lot of
+people are gut traders you essentially
+
+ align:start position:0%
+people are gut traders you essentially
+ 
+
+ align:start position:0%
+people are gut traders you essentially
+just watch your own market you don't
+
+ align:start position:0%
+just watch your own market you don't
+ 
+
+ align:start position:0%
+just watch your own market you don't
+really care what's going on if you trade
+
+ align:start position:0%
+really care what's going on if you trade
+ 
+
+ align:start position:0%
+really care what's going on if you trade
+gold uh in the states
+
+ align:start position:0%
+gold uh in the states
+ 
+
+ align:start position:0%
+gold uh in the states
+i mean obviously
+
+ align:start position:0%
+i mean obviously
+ 
+
+ align:start position:0%
+i mean obviously
+the gold prices happen in asia and in
+
+ align:start position:0%
+the gold prices happen in asia and in
+ 
+
+ align:start position:0%
+the gold prices happen in asia and in
+europe
+
+ align:start position:0%
+europe
+ 
+
+ align:start position:0%
+europe
+matters right so you because you're
+
+ align:start position:0%
+matters right so you because you're
+ 
+
+ align:start position:0%
+matters right so you because you're
+trading the same thing if they're not
+
+ align:start position:0%
+trading the same thing if they're not
+ 
+
+ align:start position:0%
+trading the same thing if they're not
+priced the same way you can profit from
+
+ align:start position:0%
+priced the same way you can profit from
+ 
+
+ align:start position:0%
+priced the same way you can profit from
+the difference
+
+ align:start position:0%
+the difference
+ 
+
+ align:start position:0%
+the difference
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+that's just a simple example but
+
+ align:start position:0%
+that's just a simple example but
+ 
+
+ align:start position:0%
+that's just a simple example but
+a spot price versus forward price that's
+
+ align:start position:0%
+a spot price versus forward price that's
+ 
+
+ align:start position:0%
+a spot price versus forward price that's
+a deterministic relationship it's a
+
+ align:start position:0%
+a deterministic relationship it's a
+ 
+
+ align:start position:0%
+a deterministic relationship it's a
+mathematical relationship if that
+
+ align:start position:0%
+mathematical relationship if that
+ 
+
+ align:start position:0%
+mathematical relationship if that
+relationship breaks down you can also
+
+ align:start position:0%
+relationship breaks down you can also
+ 
+
+ align:start position:0%
+relationship breaks down you can also
+profit so there are many examples of
+
+ align:start position:0%
+profit so there are many examples of
+ 
+
+ align:start position:0%
+profit so there are many examples of
+mathematical relationship which gives
+
+ align:start position:0%
+mathematical relationship which gives
+ 
+
+ align:start position:0%
+mathematical relationship which gives
+you the arbitrage opportunity
+
+ align:start position:0%
+you the arbitrage opportunity
+ 
+
+ align:start position:0%
+you the arbitrage opportunity
+i mean the other type is called value
+
+ align:start position:0%
+i mean the other type is called value
+ 
+
+ align:start position:0%
+i mean the other type is called value
+trade or relative value strategies you
+
+ align:start position:0%
+trade or relative value strategies you
+ 
+
+ align:start position:0%
+trade or relative value strategies you
+instead of
+
+ align:start position:0%
+instead of
+ 
+
+ align:start position:0%
+instead of
+you know think there's a deterministic
+
+ align:start position:0%
+you know think there's a deterministic
+ 
+
+ align:start position:0%
+you know think there's a deterministic
+temporary mathematical relationship you
+
+ align:start position:0%
+temporary mathematical relationship you
+ 
+
+ align:start position:0%
+temporary mathematical relationship you
+look at the longer term in horizon
+
+ align:start position:0%
+look at the longer term in horizon
+ 
+
+ align:start position:0%
+look at the longer term in horizon
+trying to determine what is really the
+
+ align:start position:0%
+trying to determine what is really the
+ 
+
+ align:start position:0%
+trying to determine what is really the
+underlying value of a particular
+
+ align:start position:0%
+underlying value of a particular
+ 
+
+ align:start position:0%
+underlying value of a particular
+instrument
+
+ align:start position:0%
+instrument
+ 
+
+ align:start position:0%
+instrument
+then trade on the relative value
+
+ align:start position:0%
+then trade on the relative value
+ 
+
+ align:start position:0%
+then trade on the relative value
+obviously there are successful value
+
+ align:start position:0%
+obviously there are successful value
+ 
+
+ align:start position:0%
+obviously there are successful value
+investors out there
+
+ align:start position:0%
+investors out there
+ 
+
+ align:start position:0%
+investors out there
+and the systematic trader
+
+ align:start position:0%
+and the systematic trader
+ 
+
+ align:start position:0%
+and the systematic trader
+builds computer models
+
+ align:start position:0%
+builds computer models
+ 
+
+ align:start position:0%
+builds computer models
+one example is train the following right
+
+ align:start position:0%
+one example is train the following right
+ 
+
+ align:start position:0%
+one example is train the following right
+so just follow the price trend
+
+ align:start position:0%
+so just follow the price trend
+ 
+
+ align:start position:0%
+so just follow the price trend
+i mean that used to be a effective
+
+ align:start position:0%
+i mean that used to be a effective
+ 
+
+ align:start position:0%
+i mean that used to be a effective
+uh strategy
+
+ align:start position:0%
+uh strategy
+ 
+
+ align:start position:0%
+uh strategy
+for some time but when a lot of people
+
+ align:start position:0%
+for some time but when a lot of people
+ 
+
+ align:start position:0%
+for some time but when a lot of people
+doing the same thing that becomes much
+
+ align:start position:0%
+doing the same thing that becomes much
+ 
+
+ align:start position:0%
+doing the same thing that becomes much
+less effective
+
+ align:start position:0%
+less effective
+ 
+
+ align:start position:0%
+less effective
+or momentum same things stat up right
+
+ align:start position:0%
+or momentum same things stat up right
+ 
+
+ align:start position:0%
+or momentum same things stat up right
+finding statistics
+
+ align:start position:0%
+finding statistics
+ 
+
+ align:start position:0%
+finding statistics
+statistical relationship among
+
+ align:start position:0%
+statistical relationship among
+ 
+
+ align:start position:0%
+statistical relationship among
+large number of stocks
+
+ align:start position:0%
+large number of stocks
+ 
+
+ align:start position:0%
+large number of stocks
+then you know trade
+
+ align:start position:0%
+then you know trade
+ 
+
+ align:start position:0%
+then you know trade
+at the higher frequency
+
+ align:start position:0%
+at the higher frequency
+ 
+
+ align:start position:0%
+at the higher frequency
+and fundamental analysis you're really
+
+ align:start position:0%
+and fundamental analysis you're really
+ 
+
+ align:start position:0%
+and fundamental analysis you're really
+trying to understand what's going on in
+
+ align:start position:0%
+trying to understand what's going on in
+ 
+
+ align:start position:0%
+trying to understand what's going on in
+the world what is the
+
+ align:start position:0%
+the world what is the
+ 
+
+ align:start position:0%
+the world what is the
+trade balance what is the earning
+
+ align:start position:0%
+trade balance what is the earning
+ 
+
+ align:start position:0%
+trade balance what is the earning
+potential of a you know of a company
+
+ align:start position:0%
+potential of a you know of a company
+ 
+
+ align:start position:0%
+potential of a you know of a company
+what's the trade balance of a country
+
+ align:start position:0%
+what's the trade balance of a country
+ 
+
+ align:start position:0%
+what's the trade balance of a country
+what is the policy change what does it
+
+ align:start position:0%
+what is the policy change what does it
+ 
+
+ align:start position:0%
+what is the policy change what does it
+mean when federal reserve announced
+
+ align:start position:0%
+mean when federal reserve announced
+ 
+
+ align:start position:0%
+mean when federal reserve announced
+they're going to taper the quantitative
+
+ align:start position:0%
+they're going to taper the quantitative
+ 
+
+ align:start position:0%
+they're going to taper the quantitative
+easing
+
+ align:start position:0%
+easing
+ 
+
+ align:start position:0%
+easing
+right what's why stock market sold off
+
+ align:start position:0%
+right what's why stock market sold off
+ 
+
+ align:start position:0%
+right what's why stock market sold off
+in the last
+
+ align:start position:0%
+in the last
+ 
+
+ align:start position:0%
+in the last
+couple months
+
+ align:start position:0%
+couple months
+ 
+
+ align:start position:0%
+couple months
+especially why stocks in india
+
+ align:start position:0%
+especially why stocks in india
+ 
+
+ align:start position:0%
+especially why stocks in india
+brazil indonesia sold out more
+
+ align:start position:0%
+brazil indonesia sold out more
+ 
+
+ align:start position:0%
+brazil indonesia sold out more
+right why is that so you know it goes
+
+ align:start position:0%
+right why is that so you know it goes
+ 
+
+ align:start position:0%
+right why is that so you know it goes
+through those fundamental analysis
+
+ align:start position:0%
+through those fundamental analysis
+ 
+
+ align:start position:0%
+through those fundamental analysis
+uh and there are special situations some
+
+ align:start position:0%
+uh and there are special situations some
+ 
+
+ align:start position:0%
+uh and there are special situations some
+companies are going through
+
+ align:start position:0%
+companies are going through
+ 
+
+ align:start position:0%
+companies are going through
+uh particular
+
+ align:start position:0%
+uh particular
+ 
+
+ align:start position:0%
+uh particular
+uh difficulties assets are priced very
+
+ align:start position:0%
+uh difficulties assets are priced very
+ 
+
+ align:start position:0%
+uh difficulties assets are priced very
+cheaply so there are firms out there i
+
+ align:start position:0%
+cheaply so there are firms out there i
+ 
+
+ align:start position:0%
+cheaply so there are firms out there i
+mean you probably heard you know
+
+ align:start position:0%
+mean you probably heard you know
+ 
+
+ align:start position:0%
+mean you probably heard you know
+bain capital and many others right they
+
+ align:start position:0%
+bain capital and many others right they
+ 
+
+ align:start position:0%
+bain capital and many others right they
+focus on these private equity and
+
+ align:start position:0%
+focus on these private equity and
+ 
+
+ align:start position:0%
+focus on these private equity and
+special situation opportunities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+what has what have all these to do with
+
+ align:start position:0%
+what has what have all these to do with
+ 
+
+ align:start position:0%
+what has what have all these to do with
+mathematics right
+
+ align:start position:0%
+mathematics right
+ 
+
+ align:start position:0%
+mathematics right
+where does math come in
+
+ align:start position:0%
+where does math come in
+ 
+
+ align:start position:0%
+where does math come in
+how do you use math
+
+ align:start position:0%
+how do you use math
+ 
+
+ align:start position:0%
+how do you use math
+so i want to give you some aspects of
+
+ align:start position:0%
+so i want to give you some aspects of
+ 
+
+ align:start position:0%
+so i want to give you some aspects of
+that so from my personal experience
+
+ align:start position:0%
+that so from my personal experience
+ 
+
+ align:start position:0%
+that so from my personal experience
+i joined the market really started
+
+ align:start position:0%
+i joined the market really started
+ 
+
+ align:start position:0%
+i joined the market really started
+working on pricing models so that's the
+
+ align:start position:0%
+working on pricing models so that's the
+ 
+
+ align:start position:0%
+working on pricing models so that's the
+first area
+
+ align:start position:0%
+first area
+ 
+
+ align:start position:0%
+first area
+so math is very effective because when
+
+ align:start position:0%
+so math is very effective because when
+ 
+
+ align:start position:0%
+so math is very effective because when
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+your bank your or your corporate
+
+ align:start position:0%
+your bank your or your corporate
+ 
+
+ align:start position:0%
+your bank your or your corporate
+you want to buy some financial
+
+ align:start position:0%
+you want to buy some financial
+ 
+
+ align:start position:0%
+you want to buy some financial
+instruments you have to know
+
+ align:start position:0%
+instruments you have to know
+ 
+
+ align:start position:0%
+instruments you have to know
+where is the price
+
+ align:start position:0%
+where is the price
+ 
+
+ align:start position:0%
+where is the price
+it's easy to observe a stock in the
+
+ align:start position:0%
+it's easy to observe a stock in the
+ 
+
+ align:start position:0%
+it's easy to observe a stock in the
+market but when it comes to
+
+ align:start position:0%
+market but when it comes to
+ 
+
+ align:start position:0%
+market but when it comes to
+more complex products they just take one
+
+ align:start position:0%
+more complex products they just take one
+ 
+
+ align:start position:0%
+more complex products they just take one
+step
+
+ align:start position:0%
+step
+ 
+
+ align:start position:0%
+step
+full or forward on the complexity which
+
+ align:start position:0%
+full or forward on the complexity which
+ 
+
+ align:start position:0%
+full or forward on the complexity which
+is option you have to know how to press
+
+ align:start position:0%
+is option you have to know how to press
+ 
+
+ align:start position:0%
+is option you have to know how to press
+an option so that's where the math comes
+
+ align:start position:0%
+an option so that's where the math comes
+ 
+
+ align:start position:0%
+an option so that's where the math comes
+in right you actually have to be able to
+
+ align:start position:0%
+in right you actually have to be able to
+ 
+
+ align:start position:0%
+in right you actually have to be able to
+solve differential equations to get a
+
+ align:start position:0%
+solve differential equations to get a
+ 
+
+ align:start position:0%
+solve differential equations to get a
+you know model price then you obviously
+
+ align:start position:0%
+you know model price then you obviously
+ 
+
+ align:start position:0%
+you know model price then you obviously
+adjust to the your assumptions to fit
+
+ align:start position:0%
+adjust to the your assumptions to fit
+ 
+
+ align:start position:0%
+adjust to the your assumptions to fit
+into the market
+
+ align:start position:0%
+into the market
+ 
+
+ align:start position:0%
+into the market
+so pricing model which
+
+ align:start position:0%
+so pricing model which
+ 
+
+ align:start position:0%
+so pricing model which
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+vasily and many of his colleagues can
+
+ align:start position:0%
+vasily and many of his colleagues can
+ 
+
+ align:start position:0%
+vasily and many of his colleagues can
+tell you more which is very much
+
+ align:start position:0%
+tell you more which is very much
+ 
+
+ align:start position:0%
+tell you more which is very much
+a very interesting and challenging area
+
+ align:start position:0%
+a very interesting and challenging area
+ 
+
+ align:start position:0%
+a very interesting and challenging area
+how do you price all these instruments
+
+ align:start position:0%
+how do you price all these instruments
+ 
+
+ align:start position:0%
+how do you price all these instruments
+and when i say pricing it's not in the
+
+ align:start position:0%
+and when i say pricing it's not in the
+ 
+
+ align:start position:0%
+and when i say pricing it's not in the
+narrow definition of just coming up as a
+
+ align:start position:0%
+narrow definition of just coming up as a
+ 
+
+ align:start position:0%
+narrow definition of just coming up as a
+price when you build a pricing model you
+
+ align:start position:0%
+price when you build a pricing model you
+ 
+
+ align:start position:0%
+price when you build a pricing model you
+also generate the risk parameters of
+
+ align:start position:0%
+also generate the risk parameters of
+ 
+
+ align:start position:0%
+also generate the risk parameters of
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+instruments and how do you risk manage
+
+ align:start position:0%
+instruments and how do you risk manage
+ 
+
+ align:start position:0%
+instruments and how do you risk manage
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+so that comes the second part
+
+ align:start position:0%
+so that comes the second part
+ 
+
+ align:start position:0%
+so that comes the second part
+so math is very useful in risk
+
+ align:start position:0%
+so math is very useful in risk
+ 
+
+ align:start position:0%
+so math is very useful in risk
+management
+
+ align:start position:0%
+management
+ 
+
+ align:start position:0%
+management
+which i will give you some uh
+
+ align:start position:0%
+which i will give you some uh
+ 
+
+ align:start position:0%
+which i will give you some uh
+another quiz questions after this slide
+
+ align:start position:0%
+another quiz questions after this slide
+ 
+
+ align:start position:0%
+another quiz questions after this slide
+when you can see that
+
+ align:start position:0%
+when you can see that
+ 
+
+ align:start position:0%
+when you can see that
+risk management itself is very
+
+ align:start position:0%
+risk management itself is very
+ 
+
+ align:start position:0%
+risk management itself is very
+challenging it's not a purely
+
+ align:start position:0%
+challenging it's not a purely
+ 
+
+ align:start position:0%
+challenging it's not a purely
+mathematical question but yet math plays
+
+ align:start position:0%
+mathematical question but yet math plays
+ 
+
+ align:start position:0%
+mathematical question but yet math plays
+a very important role to quantify
+
+ align:start position:0%
+a very important role to quantify
+ 
+
+ align:start position:0%
+a very important role to quantify
+how much exposure you have then the
+
+ align:start position:0%
+how much exposure you have then the
+ 
+
+ align:start position:0%
+how much exposure you have then the
+third is trading strategies
+
+ align:start position:0%
+third is trading strategies
+ 
+
+ align:start position:0%
+third is trading strategies
+again i think a lot of people with mass
+
+ align:start position:0%
+again i think a lot of people with mass
+ 
+
+ align:start position:0%
+again i think a lot of people with mass
+background
+
+ align:start position:0%
+background
+ 
+
+ align:start position:0%
+background
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+in general people are looking for
+
+ align:start position:0%
+in general people are looking for
+ 
+
+ align:start position:0%
+in general people are looking for
+the so-called holy grail
+
+ align:start position:0%
+the so-called holy grail
+ 
+
+ align:start position:0%
+the so-called holy grail
+trading strategies
+
+ align:start position:0%
+trading strategies
+ 
+
+ align:start position:0%
+trading strategies
+just almost like perpetual motion
+
+ align:start position:0%
+just almost like perpetual motion
+ 
+
+ align:start position:0%
+just almost like perpetual motion
+machines right people looking for 100
+
+ align:start position:0%
+machines right people looking for 100
+ 
+
+ align:start position:0%
+machines right people looking for 100
+years ago you just turn it on it makes
+
+ align:start position:0%
+years ago you just turn it on it makes
+ 
+
+ align:start position:0%
+years ago you just turn it on it makes
+money by itself you go to sleep you go
+
+ align:start position:0%
+money by itself you go to sleep you go
+ 
+
+ align:start position:0%
+money by itself you go to sleep you go
+on vacation you come back you have more
+
+ align:start position:0%
+on vacation you come back you have more
+ 
+
+ align:start position:0%
+on vacation you come back you have more
+in your bank account
+
+ align:start position:0%
+in your bank account
+ 
+
+ align:start position:0%
+in your bank account
+obviously that's not going to happen
+
+ align:start position:0%
+obviously that's not going to happen
+ 
+
+ align:start position:0%
+obviously that's not going to happen
+the robe the robo trader a
+
+ align:start position:0%
+the robe the robo trader a
+ 
+
+ align:start position:0%
+the robe the robo trader a
+robotic trader
+
+ align:start position:0%
+robotic trader
+ 
+
+ align:start position:0%
+robotic trader
+is the dream
+
+ align:start position:0%
+is the dream
+ 
+
+ align:start position:0%
+is the dream
+it has its place or its use but it's a
+
+ align:start position:0%
+it has its place or its use but it's a
+ 
+
+ align:start position:0%
+it has its place or its use but it's a
+fast
+
+ align:start position:0%
+fast
+ 
+
+ align:start position:0%
+fast
+evolving market you have to constantly
+
+ align:start position:0%
+evolving market you have to constantly
+ 
+
+ align:start position:0%
+evolving market you have to constantly
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+upgrade your research
+
+ align:start position:0%
+upgrade your research
+ 
+
+ align:start position:0%
+upgrade your research
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+adjust your strategies
+
+ align:start position:0%
+adjust your strategies
+ 
+
+ align:start position:0%
+adjust your strategies
+there's no such thing
+
+ align:start position:0%
+there's no such thing
+ 
+
+ align:start position:0%
+there's no such thing
+you can build and leave it alone it runs
+
+ align:start position:0%
+you can build and leave it alone it runs
+ 
+
+ align:start position:0%
+you can build and leave it alone it runs
+for itself forever but
+
+ align:start position:0%
+for itself forever but
+ 
+
+ align:start position:0%
+for itself forever but
+i just want to mention that because
+
+ align:start position:0%
+i just want to mention that because
+ 
+
+ align:start position:0%
+i just want to mention that because
+maybe
+
+ align:start position:0%
+maybe
+ 
+
+ align:start position:0%
+maybe
+towards the end of the term you will
+
+ align:start position:0%
+towards the end of the term you will
+ 
+
+ align:start position:0%
+towards the end of the term you will
+feel i came up with this brilliant
+
+ align:start position:0%
+feel i came up with this brilliant
+ 
+
+ align:start position:0%
+feel i came up with this brilliant
+trading strategy i think it's going to
+
+ align:start position:0%
+trading strategy i think it's going to
+ 
+
+ align:start position:0%
+trading strategy i think it's going to
+make money forever please let me know
+
+ align:start position:0%
+make money forever please let me know
+ 
+
+ align:start position:0%
+make money forever please let me know
+first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um i want to leave some time
+
+ align:start position:0%
+um i want to leave some time
+ 
+
+ align:start position:0%
+um i want to leave some time
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+vasily actually he
+
+ align:start position:0%
+vasily actually he
+ 
+
+ align:start position:0%
+vasily actually he
+he can give you some examples of
+
+ align:start position:0%
+he can give you some examples of
+ 
+
+ align:start position:0%
+he can give you some examples of
+projects of last year's students who
+
+ align:start position:0%
+projects of last year's students who
+ 
+
+ align:start position:0%
+projects of last year's students who
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+came to this class and did some real
+
+ align:start position:0%
+came to this class and did some real
+ 
+
+ align:start position:0%
+came to this class and did some real
+application at morgan stanley but before
+
+ align:start position:0%
+application at morgan stanley but before
+ 
+
+ align:start position:0%
+application at morgan stanley but before
+i hand over to vasily let me ask you
+
+ align:start position:0%
+i hand over to vasily let me ask you
+ 
+
+ align:start position:0%
+i hand over to vasily let me ask you
+some questions i just want to
+
+ align:start position:0%
+some questions i just want to
+ 
+
+ align:start position:0%
+some questions i just want to
+give not really to quiz you just give
+
+ align:start position:0%
+give not really to quiz you just give
+ 
+
+ align:start position:0%
+give not really to quiz you just give
+you the sense
+
+ align:start position:0%
+you the sense
+ 
+
+ align:start position:0%
+you the sense
+how
+
+ align:start position:0%
+how
+ 
+
+ align:start position:0%
+how
+math
+
+ align:start position:0%
+math
+ 
+
+ align:start position:0%
+math
+and intuition and judgment can come into
+
+ align:start position:0%
+and intuition and judgment can come into
+ 
+
+ align:start position:0%
+and intuition and judgment can come into
+the same place
+
+ align:start position:0%
+the same place
+ 
+
+ align:start position:0%
+the same place
+so let me first give you examples i call
+
+ align:start position:0%
+so let me first give you examples i call
+ 
+
+ align:start position:0%
+so let me first give you examples i call
+risk aversion
+
+ align:start position:0%
+risk aversion
+ 
+
+ align:start position:0%
+risk aversion
+so you you are facing two choices choice
+
+ align:start position:0%
+so you you are facing two choices choice
+ 
+
+ align:start position:0%
+so you you are facing two choices choice
+a and choice b
+
+ align:start position:0%
+a and choice b
+ 
+
+ align:start position:0%
+a and choice b
+choice a b you have 80 chance to lose
+
+ align:start position:0%
+choice a b you have 80 chance to lose
+ 
+
+ align:start position:0%
+choice a b you have 80 chance to lose
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+chance to win five hundred dollars
+
+ align:start position:0%
+chance to win five hundred dollars
+ 
+
+ align:start position:0%
+chance to win five hundred dollars
+it's pretty clear right that's it that's
+
+ align:start position:0%
+it's pretty clear right that's it that's
+ 
+
+ align:start position:0%
+it's pretty clear right that's it that's
+choice a
+
+ align:start position:0%
+choice a
+ 
+
+ align:start position:0%
+choice a
+well choice b
+
+ align:start position:0%
+well choice b
+ 
+
+ align:start position:0%
+well choice b
+you basically just lock in you have 100
+
+ align:start position:0%
+you basically just lock in you have 100
+ 
+
+ align:start position:0%
+you basically just lock in you have 100
+chance to lose 280 dollars
+
+ align:start position:0%
+chance to lose 280 dollars
+ 
+
+ align:start position:0%
+chance to lose 280 dollars
+let me ask you
+
+ align:start position:0%
+let me ask you
+ 
+
+ align:start position:0%
+let me ask you
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+whoever likes to choose
+
+ align:start position:0%
+whoever likes to choose
+ 
+
+ align:start position:0%
+whoever likes to choose
+a choice a please raise your hand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about six out of
+
+ align:start position:0%
+about six out of
+ 
+
+ align:start position:0%
+about six out of
+say let's call it the 50. okay
+
+ align:start position:0%
+say let's call it the 50. okay
+ 
+
+ align:start position:0%
+say let's call it the 50. okay
+so can i ask you why you think choice a
+
+ align:start position:0%
+so can i ask you why you think choice a
+ 
+
+ align:start position:0%
+so can i ask you why you think choice a
+makes sense so i know it's a lower
+
+ align:start position:0%
+makes sense so i know it's a lower
+ 
+
+ align:start position:0%
+makes sense so i know it's a lower
+expected value but i
+
+ align:start position:0%
+expected value but i
+ 
+
+ align:start position:0%
+expected value but i
+i just kind of enjoy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+because you don't want to lock in that
+
+ align:start position:0%
+because you don't want to lock in that
+ 
+
+ align:start position:0%
+because you don't want to lock in that
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+loss right that way you still have 20
+
+ align:start position:0%
+loss right that way you still have 20
+ 
+
+ align:start position:0%
+loss right that way you still have 20
+chance to win
+
+ align:start position:0%
+chance to win
+ 
+
+ align:start position:0%
+chance to win
+so okay
+
+ align:start position:0%
+so okay
+ 
+
+ align:start position:0%
+so okay
+uh for the wines raise the hand for
+
+ align:start position:0%
+uh for the wines raise the hand for
+ 
+
+ align:start position:0%
+uh for the wines raise the hand for
+choices are there any other reasons
+
+ align:start position:0%
+choices are there any other reasons
+ 
+
+ align:start position:0%
+choices are there any other reasons
+same reason
+
+ align:start position:0%
+same reason
+ 
+
+ align:start position:0%
+same reason
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay i assume the rest of you will
+
+ align:start position:0%
+okay i assume the rest of you will
+ 
+
+ align:start position:0%
+okay i assume the rest of you will
+choose choice b unless you neither okay
+
+ align:start position:0%
+choose choice b unless you neither okay
+ 
+
+ align:start position:0%
+choose choice b unless you neither okay
+how many of you choose choice b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay choice b okay and are they anybody
+
+ align:start position:0%
+okay choice b okay and are they anybody
+ 
+
+ align:start position:0%
+okay choice b okay and are they anybody
+think neither is right so maybe
+
+ align:start position:0%
+think neither is right so maybe
+ 
+
+ align:start position:0%
+think neither is right so maybe
+you have no you have to choose okay
+
+ align:start position:0%
+you have no you have to choose okay
+ 
+
+ align:start position:0%
+you have no you have to choose okay
+no you have to choose okay so either
+
+ align:start position:0%
+no you have to choose okay so either
+ 
+
+ align:start position:0%
+no you have to choose okay so either
+choice a or choice b
+
+ align:start position:0%
+choice a or choice b
+ 
+
+ align:start position:0%
+choice a or choice b
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let me just talk a little bit about this
+
+ align:start position:0%
+let me just talk a little bit about this
+ 
+
+ align:start position:0%
+let me just talk a little bit about this
+again i'm not trying to tell you which
+
+ align:start position:0%
+again i'm not trying to tell you which
+ 
+
+ align:start position:0%
+again i'm not trying to tell you which
+one is right but let's just share my
+
+ align:start position:0%
+one is right but let's just share my
+ 
+
+ align:start position:0%
+one is right but let's just share my
+thoughts how to look at these why i call
+
+ align:start position:0%
+thoughts how to look at these why i call
+ 
+
+ align:start position:0%
+thoughts how to look at these why i call
+risk aversion right so this is a very
+
+ align:start position:0%
+risk aversion right so this is a very
+ 
+
+ align:start position:0%
+risk aversion right so this is a very
+common
+
+ align:start position:0%
+common
+ 
+
+ align:start position:0%
+common
+human behavior when you go to the market
+
+ align:start position:0%
+human behavior when you go to the market
+ 
+
+ align:start position:0%
+human behavior when you go to the market
+you buy a stock
+
+ align:start position:0%
+you buy a stock
+ 
+
+ align:start position:0%
+you buy a stock
+when the stock goes up makes big money
+
+ align:start position:0%
+when the stock goes up makes big money
+ 
+
+ align:start position:0%
+when the stock goes up makes big money
+the natural tendency for especially
+
+ align:start position:0%
+the natural tendency for especially
+ 
+
+ align:start position:0%
+the natural tendency for especially
+someone is new to the market is to let's
+
+ align:start position:0%
+someone is new to the market is to let's
+ 
+
+ align:start position:0%
+someone is new to the market is to let's
+take take profit let's sell oh i made a
+
+ align:start position:0%
+take take profit let's sell oh i made a
+ 
+
+ align:start position:0%
+take take profit let's sell oh i made a
+thousand dollars i made five hundred
+
+ align:start position:0%
+thousand dollars i made five hundred
+ 
+
+ align:start position:0%
+thousand dollars i made five hundred
+dollars let's go you know have a nice
+
+ align:start position:0%
+dollars let's go you know have a nice
+ 
+
+ align:start position:0%
+dollars let's go you know have a nice
+meal or you know whatever i buy a
+
+ align:start position:0%
+meal or you know whatever i buy a
+ 
+
+ align:start position:0%
+meal or you know whatever i buy a
+ipad
+
+ align:start position:0%
+ipad
+ 
+
+ align:start position:0%
+ipad
+but when the stock loses money what's
+
+ align:start position:0%
+but when the stock loses money what's
+ 
+
+ align:start position:0%
+but when the stock loses money what's
+the natural tendency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+i think natural tendency a lot of people
+
+ align:start position:0%
+i think natural tendency a lot of people
+ 
+
+ align:start position:0%
+i think natural tendency a lot of people
+will keep it i think if you have the
+
+ align:start position:0%
+will keep it i think if you have the
+ 
+
+ align:start position:0%
+will keep it i think if you have the
+discipline to get out that's great and
+
+ align:start position:0%
+discipline to get out that's great and
+ 
+
+ align:start position:0%
+discipline to get out that's great and
+that's you know i
+
+ align:start position:0%
+that's you know i
+ 
+
+ align:start position:0%
+that's you know i
+i mean trading is really all about how
+
+ align:start position:0%
+i mean trading is really all about how
+ 
+
+ align:start position:0%
+i mean trading is really all about how
+where do you how do you risk manage you
+
+ align:start position:0%
+where do you how do you risk manage you
+ 
+
+ align:start position:0%
+where do you how do you risk manage you
+know have a discipline and how to manage
+
+ align:start position:0%
+know have a discipline and how to manage
+ 
+
+ align:start position:0%
+know have a discipline and how to manage
+your losses
+
+ align:start position:0%
+your losses
+ 
+
+ align:start position:0%
+your losses
+right the natural tendency a lot of
+
+ align:start position:0%
+right the natural tendency a lot of
+ 
+
+ align:start position:0%
+right the natural tendency a lot of
+people say well i think there's a chance
+
+ align:start position:0%
+people say well i think there's a chance
+ 
+
+ align:start position:0%
+people say well i think there's a chance
+20 chance to come back i'm going to make
+
+ align:start position:0%
+20 chance to come back i'm going to make
+ 
+
+ align:start position:0%
+20 chance to come back i'm going to make
+500 more right why do i want to lock in
+
+ align:start position:0%
+500 more right why do i want to lock in
+ 
+
+ align:start position:0%
+500 more right why do i want to lock in
+to stop myself out at 280
+
+ align:start position:0%
+to stop myself out at 280
+ 
+
+ align:start position:0%
+to stop myself out at 280
+right so even though the expected value
+
+ align:start position:0%
+right so even though the expected value
+ 
+
+ align:start position:0%
+right so even though the expected value
+as a lot of people
+
+ align:start position:0%
+as a lot of people
+ 
+
+ align:start position:0%
+as a lot of people
+i think a lot of people said you know
+
+ align:start position:0%
+i think a lot of people said you know
+ 
+
+ align:start position:0%
+i think a lot of people said you know
+you lose expected value which is three
+
+ align:start position:0%
+you lose expected value which is three
+ 
+
+ align:start position:0%
+you lose expected value which is three
+hundred dollars in choice a
+
+ align:start position:0%
+hundred dollars in choice a
+ 
+
+ align:start position:0%
+hundred dollars in choice a
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+you would still
+
+ align:start position:0%
+you would still
+ 
+
+ align:start position:0%
+you would still
+you know not to choose choice b because
+
+ align:start position:0%
+you know not to choose choice b because
+ 
+
+ align:start position:0%
+you know not to choose choice b because
+they're unlocking the 280 loss again i'm
+
+ align:start position:0%
+they're unlocking the 280 loss again i'm
+ 
+
+ align:start position:0%
+they're unlocking the 280 loss again i'm
+not
+
+ align:start position:0%
+not
+ 
+
+ align:start position:0%
+not
+trying to
+
+ align:start position:0%
+trying to
+ 
+
+ align:start position:0%
+trying to
+inject the idea to you of which one is
+
+ align:start position:0%
+inject the idea to you of which one is
+ 
+
+ align:start position:0%
+inject the idea to you of which one is
+right or wrong but think about it right
+
+ align:start position:0%
+right or wrong but think about it right
+ 
+
+ align:start position:0%
+right or wrong but think about it right
+so that's really the common behavior
+
+ align:start position:0%
+so that's really the common behavior
+ 
+
+ align:start position:0%
+so that's really the common behavior
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+mathematically may not make sense but
+
+ align:start position:0%
+mathematically may not make sense but
+ 
+
+ align:start position:0%
+mathematically may not make sense but
+that's a lot of people still would like
+
+ align:start position:0%
+that's a lot of people still would like
+ 
+
+ align:start position:0%
+that's a lot of people still would like
+to do right
+
+ align:start position:0%
+to do right
+ 
+
+ align:start position:0%
+to do right
+and also really when you think about it
+
+ align:start position:0%
+and also really when you think about it
+ 
+
+ align:start position:0%
+and also really when you think about it
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+depends on your situation
+
+ align:start position:0%
+depends on your situation
+ 
+
+ align:start position:0%
+depends on your situation
+and uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you can
+
+ align:start position:0%
+if you can
+ 
+
+ align:start position:0%
+if you can
+let's say you think the market i mean
+
+ align:start position:0%
+let's say you think the market i mean
+ 
+
+ align:start position:0%
+let's say you think the market i mean
+i'll give you the stock example again
+
+ align:start position:0%
+i'll give you the stock example again
+ 
+
+ align:start position:0%
+i'll give you the stock example again
+if you're not purely following the
+
+ align:start position:0%
+if you're not purely following the
+ 
+
+ align:start position:0%
+if you're not purely following the
+discipline of stop loss but you just
+
+ align:start position:0%
+discipline of stop loss but you just
+ 
+
+ align:start position:0%
+discipline of stop loss but you just
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+you know the fundamental picture has
+
+ align:start position:0%
+you know the fundamental picture has
+ 
+
+ align:start position:0%
+you know the fundamental picture has
+changed you really don't think the stock
+
+ align:start position:0%
+changed you really don't think the stock
+ 
+
+ align:start position:0%
+changed you really don't think the stock
+is should go up anymore
+
+ align:start position:0%
+is should go up anymore
+ 
+
+ align:start position:0%
+is should go up anymore
+obviously at whatever level you should
+
+ align:start position:0%
+obviously at whatever level you should
+ 
+
+ align:start position:0%
+obviously at whatever level you should
+get out right
+
+ align:start position:0%
+get out right
+ 
+
+ align:start position:0%
+get out right
+regardless how much loss you're locking
+
+ align:start position:0%
+regardless how much loss you're locking
+ 
+
+ align:start position:0%
+regardless how much loss you're locking
+and uh but if you if you think the
+
+ align:start position:0%
+and uh but if you if you think the
+ 
+
+ align:start position:0%
+and uh but if you if you think the
+fundamental story is still very sound
+
+ align:start position:0%
+fundamental story is still very sound
+ 
+
+ align:start position:0%
+fundamental story is still very sound
+you should think about
+
+ align:start position:0%
+you should think about
+ 
+
+ align:start position:0%
+you should think about
+as if you don't have a position what do
+
+ align:start position:0%
+as if you don't have a position what do
+ 
+
+ align:start position:0%
+as if you don't have a position what do
+you want to do next
+
+ align:start position:0%
+you want to do next
+ 
+
+ align:start position:0%
+you want to do next
+so but anyway mathematically i just want
+
+ align:start position:0%
+so but anyway mathematically i just want
+ 
+
+ align:start position:0%
+so but anyway mathematically i just want
+to see it's actually
+
+ align:start position:0%
+to see it's actually
+ 
+
+ align:start position:0%
+to see it's actually
+i think
+
+ align:start position:0%
+i think
+ 
+
+ align:start position:0%
+i think
+i guess this is mit
+
+ align:start position:0%
+i guess this is mit
+ 
+
+ align:start position:0%
+i guess this is mit
+so many people think mathematically you
+
+ align:start position:0%
+so many people think mathematically you
+ 
+
+ align:start position:0%
+so many people think mathematically you
+know you would
+
+ align:start position:0%
+know you would
+ 
+
+ align:start position:0%
+know you would
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+choose choice b because that's low
+
+ align:start position:0%
+choose choice b because that's low
+ 
+
+ align:start position:0%
+choose choice b because that's low
+expectation which makes sense but i
+
+ align:start position:0%
+expectation which makes sense but i
+ 
+
+ align:start position:0%
+expectation which makes sense but i
+think if you ask
+
+ align:start position:0%
+think if you ask
+ 
+
+ align:start position:0%
+think if you ask
+a larger audience i think you probably a
+
+ align:start position:0%
+a larger audience i think you probably a
+ 
+
+ align:start position:0%
+a larger audience i think you probably a
+lot of people don't really want to
+
+ align:start position:0%
+lot of people don't really want to
+ 
+
+ align:start position:0%
+lot of people don't really want to
+choose choice b because they don't want
+
+ align:start position:0%
+choose choice b because they don't want
+ 
+
+ align:start position:0%
+choose choice b because they don't want
+locking the loss
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now let me change the question
+
+ align:start position:0%
+now let me change the question
+ 
+
+ align:start position:0%
+now let me change the question
+a little bit
+
+ align:start position:0%
+a little bit
+ 
+
+ align:start position:0%
+a little bit
+so choice a becomes instead of
+
+ align:start position:0%
+so choice a becomes instead of
+ 
+
+ align:start position:0%
+so choice a becomes instead of
+the 80 chance to lose now you have 80
+
+ align:start position:0%
+the 80 chance to lose now you have 80
+ 
+
+ align:start position:0%
+the 80 chance to lose now you have 80
+chance to win
+
+ align:start position:0%
+chance to win
+ 
+
+ align:start position:0%
+chance to win
+500 and 20 chance to lose 500
+
+ align:start position:0%
+500 and 20 chance to lose 500
+ 
+
+ align:start position:0%
+500 and 20 chance to lose 500
+choice b you have 100 chance
+
+ align:start position:0%
+choice b you have 100 chance
+ 
+
+ align:start position:0%
+choice b you have 100 chance
+to win 280
+
+ align:start position:0%
+to win 280
+ 
+
+ align:start position:0%
+to win 280
+who chooses who would choose choice a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again minority of this audience let's
+
+ align:start position:0%
+again minority of this audience let's
+ 
+
+ align:start position:0%
+again minority of this audience let's
+say less than 10 percent okay who would
+
+ align:start position:0%
+say less than 10 percent okay who would
+ 
+
+ align:start position:0%
+say less than 10 percent okay who would
+choose choice b
+
+ align:start position:0%
+choose choice b
+ 
+
+ align:start position:0%
+choose choice b
+the rest of it okay
+
+ align:start position:0%
+the rest of it okay
+ 
+
+ align:start position:0%
+the rest of it okay
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right um
+
+ align:start position:0%
+right um
+ 
+
+ align:start position:0%
+right um
+can someone uh choose choice a give me a
+
+ align:start position:0%
+can someone uh choose choice a give me a
+ 
+
+ align:start position:0%
+can someone uh choose choice a give me a
+argument why would you yeah um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+anyone wants to give me a reason for
+
+ align:start position:0%
+anyone wants to give me a reason for
+ 
+
+ align:start position:0%
+anyone wants to give me a reason for
+choice b
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+higher shop
+
+ align:start position:0%
+higher shop
+ 
+
+ align:start position:0%
+higher shop
+yep
+
+ align:start position:0%
+yep
+ 
+
+ align:start position:0%
+yep
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+let me just leave it here again
+
+ align:start position:0%
+let me just leave it here again
+ 
+
+ align:start position:0%
+let me just leave it here again
+i think
+
+ align:start position:0%
+i think
+ 
+
+ align:start position:0%
+i think
+we can talk a bit more along in the
+
+ align:start position:0%
+we can talk a bit more along in the
+ 
+
+ align:start position:0%
+we can talk a bit more along in the
+class i mean the last day of the class
+
+ align:start position:0%
+class i mean the last day of the class
+ 
+
+ align:start position:0%
+class i mean the last day of the class
+hopefully we have much deeper discussion
+
+ align:start position:0%
+hopefully we have much deeper discussion
+ 
+
+ align:start position:0%
+hopefully we have much deeper discussion
+on this
+
+ align:start position:0%
+on this
+ 
+
+ align:start position:0%
+on this
+it's not unique the answer okay i think
+
+ align:start position:0%
+it's not unique the answer okay i think
+ 
+
+ align:start position:0%
+it's not unique the answer okay i think
+it can go either way i mean as as you
+
+ align:start position:0%
+it can go either way i mean as as you
+ 
+
+ align:start position:0%
+it can go either way i mean as as you
+said if your bank account balance
+
+ align:start position:0%
+said if your bank account balance
+ 
+
+ align:start position:0%
+said if your bank account balance
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+let's say you're a freshman student your
+
+ align:start position:0%
+let's say you're a freshman student your
+ 
+
+ align:start position:0%
+let's say you're a freshman student your
+bank account is uh
+
+ align:start position:0%
+bank account is uh
+ 
+
+ align:start position:0%
+bank account is uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+eight hundred dollars
+
+ align:start position:0%
+eight hundred dollars
+ 
+
+ align:start position:0%
+eight hundred dollars
+your choice will be very different from
+
+ align:start position:0%
+your choice will be very different from
+ 
+
+ align:start position:0%
+your choice will be very different from
+someone has
+
+ align:start position:0%
+someone has
+ 
+
+ align:start position:0%
+someone has
+a hundred thousand dollars in his bank
+
+ align:start position:0%
+a hundred thousand dollars in his bank
+ 
+
+ align:start position:0%
+a hundred thousand dollars in his bank
+account
+
+ align:start position:0%
+account
+ 
+
+ align:start position:0%
+account
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+also your risk tolerance right how much
+
+ align:start position:0%
+also your risk tolerance right how much
+ 
+
+ align:start position:0%
+also your risk tolerance right how much
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+you can tolerate
+
+ align:start position:0%
+you can tolerate
+ 
+
+ align:start position:0%
+you can tolerate
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+i'm not going to give you say this is
+
+ align:start position:0%
+i'm not going to give you say this is
+ 
+
+ align:start position:0%
+i'm not going to give you say this is
+right or wrong but with that let me
+
+ align:start position:0%
+right or wrong but with that let me
+ 
+
+ align:start position:0%
+right or wrong but with that let me
+move on and give you some homework
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so before i give you the homework i want
+
+ align:start position:0%
+so before i give you the homework i want
+ 
+
+ align:start position:0%
+so before i give you the homework i want
+to make a few more comments
+
+ align:start position:0%
+to make a few more comments
+ 
+
+ align:start position:0%
+to make a few more comments
+so do people always learn from the
+
+ align:start position:0%
+so do people always learn from the
+ 
+
+ align:start position:0%
+so do people always learn from the
+experiences you think you know in
+
+ align:start position:0%
+experiences you think you know in
+ 
+
+ align:start position:0%
+experiences you think you know in
+science right we collect evidence we
+
+ align:start position:0%
+science right we collect evidence we
+ 
+
+ align:start position:0%
+science right we collect evidence we
+build models
+
+ align:start position:0%
+build models
+ 
+
+ align:start position:0%
+build models
+we first understand the physics we build
+
+ align:start position:0%
+we first understand the physics we build
+ 
+
+ align:start position:0%
+we first understand the physics we build
+mathematic models then we verify in
+
+ align:start position:0%
+mathematic models then we verify in
+ 
+
+ align:start position:0%
+mathematic models then we verify in
+physics doing experiments
+
+ align:start position:0%
+physics doing experiments
+ 
+
+ align:start position:0%
+physics doing experiments
+but is that the same
+
+ align:start position:0%
+but is that the same
+ 
+
+ align:start position:0%
+but is that the same
+investigation process process in finance
+
+ align:start position:0%
+investigation process process in finance
+ 
+
+ align:start position:0%
+investigation process process in finance
+i mean market cycles are typically very
+
+ align:start position:0%
+i mean market cycles are typically very
+ 
+
+ align:start position:0%
+i mean market cycles are typically very
+long but people tend to have show the
+
+ align:start position:0%
+long but people tend to have show the
+ 
+
+ align:start position:0%
+long but people tend to have show the
+memories is so how do people really
+
+ align:start position:0%
+memories is so how do people really
+ 
+
+ align:start position:0%
+memories is so how do people really
+learn from the experience it's a very
+
+ align:start position:0%
+learn from the experience it's a very
+ 
+
+ align:start position:0%
+learn from the experience it's a very
+interesting question and the very
+
+ align:start position:0%
+interesting question and the very
+ 
+
+ align:start position:0%
+interesting question and the very
+natural tendency is to extrapolate
+
+ align:start position:0%
+natural tendency is to extrapolate
+ 
+
+ align:start position:0%
+natural tendency is to extrapolate
+historical experience
+
+ align:start position:0%
+historical experience
+ 
+
+ align:start position:0%
+historical experience
+what happened in 2008 people still
+
+ align:start position:0%
+what happened in 2008 people still
+ 
+
+ align:start position:0%
+what happened in 2008 people still
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+what happened in
+
+ align:start position:0%
+what happened in
+ 
+
+ align:start position:0%
+what happened in
+1970s maybe some people still remember
+
+ align:start position:0%
+1970s maybe some people still remember
+ 
+
+ align:start position:0%
+1970s maybe some people still remember
+what happened 100 years ago right so
+
+ align:start position:0%
+what happened 100 years ago right so
+ 
+
+ align:start position:0%
+what happened 100 years ago right so
+people tend to
+
+ align:start position:0%
+people tend to
+ 
+
+ align:start position:0%
+people tend to
+extrapolate join conclusions from very
+
+ align:start position:0%
+extrapolate join conclusions from very
+ 
+
+ align:start position:0%
+extrapolate join conclusions from very
+recent experience
+
+ align:start position:0%
+recent experience
+ 
+
+ align:start position:0%
+recent experience
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+deterministic relationship versus
+
+ align:start position:0%
+deterministic relationship versus
+ 
+
+ align:start position:0%
+deterministic relationship versus
+statistical relationship is
+
+ align:start position:0%
+statistical relationship is
+ 
+
+ align:start position:0%
+statistical relationship is
+very interesting as well when you try to
+
+ align:start position:0%
+very interesting as well when you try to
+ 
+
+ align:start position:0%
+very interesting as well when you try to
+trade on those how do you really build
+
+ align:start position:0%
+trade on those how do you really build
+ 
+
+ align:start position:0%
+trade on those how do you really build
+models
+
+ align:start position:0%
+models
+ 
+
+ align:start position:0%
+models
+i mean is the market really efficient
+
+ align:start position:0%
+i mean is the market really efficient
+ 
+
+ align:start position:0%
+i mean is the market really efficient
+right i mean
+
+ align:start position:0%
+right i mean
+ 
+
+ align:start position:0%
+right i mean
+what is really
+
+ align:start position:0%
+what is really
+ 
+
+ align:start position:0%
+what is really
+what part is efficient you know how do
+
+ align:start position:0%
+what part is efficient you know how do
+ 
+
+ align:start position:0%
+what part is efficient you know how do
+you really apply those theories
+
+ align:start position:0%
+you really apply those theories
+ 
+
+ align:start position:0%
+you really apply those theories
+in your day-to-day
+
+ align:start position:0%
+in your day-to-day
+ 
+
+ align:start position:0%
+in your day-to-day
+uh risk management or training
+
+ align:start position:0%
+uh risk management or training
+ 
+
+ align:start position:0%
+uh risk management or training
+activities
+
+ align:start position:0%
+activities
+ 
+
+ align:start position:0%
+activities
+and sometimes people tend to
+
+ align:start position:0%
+and sometimes people tend to
+ 
+
+ align:start position:0%
+and sometimes people tend to
+oversimplify right just say oh i can
+
+ align:start position:0%
+oversimplify right just say oh i can
+ 
+
+ align:start position:0%
+oversimplify right just say oh i can
+model this you know this is one
+
+ align:start position:0%
+model this you know this is one
+ 
+
+ align:start position:0%
+model this you know this is one
+important parameter i just take that
+
+ align:start position:0%
+important parameter i just take that
+ 
+
+ align:start position:0%
+important parameter i just take that
+so i just give you all the warnings that
+
+ align:start position:0%
+so i just give you all the warnings that
+ 
+
+ align:start position:0%
+so i just give you all the warnings that
+again very
+
+ align:start position:0%
+again very
+ 
+
+ align:start position:0%
+again very
+young new
+
+ align:start position:0%
+young new
+ 
+
+ align:start position:0%
+young new
+field and
+
+ align:start position:0%
+field and
+ 
+
+ align:start position:0%
+field and
+largely often this is art than science
+
+ align:start position:0%
+largely often this is art than science
+ 
+
+ align:start position:0%
+largely often this is art than science
+so keep that in mind even though we're
+
+ align:start position:0%
+so keep that in mind even though we're
+ 
+
+ align:start position:0%
+so keep that in mind even though we're
+talking about
+
+ align:start position:0%
+talking about
+ 
+
+ align:start position:0%
+talking about
+mathematics in finance math is very
+
+ align:start position:0%
+mathematics in finance math is very
+ 
+
+ align:start position:0%
+mathematics in finance math is very
+powerful and useful in finance so learn
+
+ align:start position:0%
+powerful and useful in finance so learn
+ 
+
+ align:start position:0%
+powerful and useful in finance so learn
+the math learn the finance first but
+
+ align:start position:0%
+the math learn the finance first but
+ 
+
+ align:start position:0%
+the math learn the finance first but
+keep those questions along the way when
+
+ align:start position:0%
+keep those questions along the way when
+ 
+
+ align:start position:0%
+keep those questions along the way when
+you are learning during this class
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so suggested the homework optional
+
+ align:start position:0%
+okay so suggested the homework optional
+ 
+
+ align:start position:0%
+okay so suggested the homework optional
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+i mentioned a lot of terminologies
+
+ align:start position:0%
+i mentioned a lot of terminologies
+ 
+
+ align:start position:0%
+i mentioned a lot of terminologies
+uh today go to the course website read
+
+ align:start position:0%
+uh today go to the course website read
+ 
+
+ align:start position:0%
+uh today go to the course website read
+what we have put up
+
+ align:start position:0%
+what we have put up
+ 
+
+ align:start position:0%
+what we have put up
+for the financial glossary right so if
+
+ align:start position:0%
+for the financial glossary right so if
+ 
+
+ align:start position:0%
+for the financial glossary right so if
+you still have things you don't
+
+ align:start position:0%
+you still have things you don't
+ 
+
+ align:start position:0%
+you still have things you don't
+understand make compile your own list
+
+ align:start position:0%
+understand make compile your own list
+ 
+
+ align:start position:0%
+understand make compile your own list
+of financial concepts which you can
+
+ align:start position:0%
+of financial concepts which you can
+ 
+
+ align:start position:0%
+of financial concepts which you can
+search on the web
+
+ align:start position:0%
+search on the web
+ 
+
+ align:start position:0%
+search on the web
+or even ask us
+
+ align:start position:0%
+or even ask us
+ 
+
+ align:start position:0%
+or even ask us
+but i encourage you to do that it will
+
+ align:start position:0%
+but i encourage you to do that it will
+ 
+
+ align:start position:0%
+but i encourage you to do that it will
+prepare you well so that's really
+
+ align:start position:0%
+prepare you well so that's really
+ 
+
+ align:start position:0%
+prepare you well so that's really
+uh and the read other materials on the
+
+ align:start position:0%
+uh and the read other materials on the
+ 
+
+ align:start position:0%
+uh and the read other materials on the
+on the course web
+
+ align:start position:0%
+on the course web
+ 
+
+ align:start position:0%
+on the course web
+so we got uh
+
+ align:start position:0%
+so we got uh
+ 
+
+ align:start position:0%
+so we got uh
+maybe how about this we still got about
+
+ align:start position:0%
+maybe how about this we still got about
+ 
+
+ align:start position:0%
+maybe how about this we still got about
+15 minutes or 10 or 12 minutes left so i
+
+ align:start position:0%
+15 minutes or 10 or 12 minutes left so i
+ 
+
+ align:start position:0%
+15 minutes or 10 or 12 minutes left so i
+passed it to vasili now maybe we can
+
+ align:start position:0%
+passed it to vasili now maybe we can
+ 
+
+ align:start position:0%
+passed it to vasili now maybe we can
+leave five minutes for some questions
+
+ align:start position:0%
+leave five minutes for some questions
+ 
+
+ align:start position:0%
+leave five minutes for some questions
+yeah okay yeah
+
+ align:start position:0%
+yeah okay yeah
+ 
+
+ align:start position:0%
+yeah okay yeah
+just mention that that apple trade is
+
+ align:start position:0%
+just mention that that apple trade is
+ 
+
+ align:start position:0%
+just mention that that apple trade is
+now at 494.4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you were saying it was at 88.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+yeah just a couple examples well first
+
+ align:start position:0%
+yeah just a couple examples well first
+ 
+
+ align:start position:0%
+yeah just a couple examples well first
+of all
+
+ align:start position:0%
+of all
+ 
+
+ align:start position:0%
+of all
+no offense to
+
+ align:start position:0%
+no offense to
+ 
+
+ align:start position:0%
+no offense to
+a few people who wear
+
+ align:start position:0%
+a few people who wear
+ 
+
+ align:start position:0%
+a few people who wear
+who wear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+i just wanted to to give
+
+ align:start position:0%
+i just wanted to to give
+ 
+
+ align:start position:0%
+i just wanted to to give
+an example of uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah thanks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because he was working in in our group
+
+ align:start position:0%
+because he was working in in our group
+ 
+
+ align:start position:0%
+because he was working in in our group
+and it just will give you an idea of
+
+ align:start position:0%
+and it just will give you an idea of
+ 
+
+ align:start position:0%
+and it just will give you an idea of
+what uh
+
+ align:start position:0%
+what uh
+ 
+
+ align:start position:0%
+what uh
+what a little bit of an idea what what
+
+ align:start position:0%
+what a little bit of an idea what what
+ 
+
+ align:start position:0%
+what a little bit of an idea what what
+we will be talking about and what
+
+ align:start position:0%
+we will be talking about and what
+ 
+
+ align:start position:0%
+we will be talking about and what
+actually we do in the daily life or
+
+ align:start position:0%
+actually we do in the daily life or
+ 
+
+ align:start position:0%
+actually we do in the daily life or
+uh what an intern or somebody who comes
+
+ align:start position:0%
+uh what an intern or somebody who comes
+ 
+
+ align:start position:0%
+uh what an intern or somebody who comes
+to work in this industry could do
+
+ align:start position:0%
+to work in this industry could do
+ 
+
+ align:start position:0%
+to work in this industry could do
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+one project is
+
+ align:start position:0%
+one project is
+ 
+
+ align:start position:0%
+one project is
+which tushan
+
+ align:start position:0%
+which tushan
+ 
+
+ align:start position:0%
+which tushan
+worked was
+
+ align:start position:0%
+worked was
+ 
+
+ align:start position:0%
+worked was
+on estimating uh the noisy derivative
+
+ align:start position:0%
+on estimating uh the noisy derivative
+ 
+
+ align:start position:0%
+on estimating uh the noisy derivative
+the derivative is called delta delta is
+
+ align:start position:0%
+the derivative is called delta delta is
+ 
+
+ align:start position:0%
+the derivative is called delta delta is
+usually a first derivative to a function
+
+ align:start position:0%
+usually a first derivative to a function
+ 
+
+ align:start position:0%
+usually a first derivative to a function
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+as we'll see in the class quite often to
+
+ align:start position:0%
+as we'll see in the class quite often to
+ 
+
+ align:start position:0%
+as we'll see in the class quite often to
+to obtain a price you
+
+ align:start position:0%
+to obtain a price you
+ 
+
+ align:start position:0%
+to obtain a price you
+you do it through monte carlo meaning
+
+ align:start position:0%
+you do it through monte carlo meaning
+ 
+
+ align:start position:0%
+you do it through monte carlo meaning
+running a lot of pass and then averaging
+
+ align:start position:0%
+running a lot of pass and then averaging
+ 
+
+ align:start position:0%
+running a lot of pass and then averaging
+along along them so it is statistical
+
+ align:start position:0%
+along along them so it is statistical
+ 
+
+ align:start position:0%
+along along them so it is statistical
+methods so obviously there there is a
+
+ align:start position:0%
+methods so obviously there there is a
+ 
+
+ align:start position:0%
+methods so obviously there there is a
+noise to
+
+ align:start position:0%
+noise to
+ 
+
+ align:start position:0%
+noise to
+to your answer every time
+
+ align:start position:0%
+to your answer every time
+ 
+
+ align:start position:0%
+to your answer every time
+so if you want to
+
+ align:start position:0%
+so if you want to
+ 
+
+ align:start position:0%
+so if you want to
+to differentiate
+
+ align:start position:0%
+to differentiate
+ 
+
+ align:start position:0%
+to differentiate
+this function and get the derivative
+
+ align:start position:0%
+this function and get the derivative
+ 
+
+ align:start position:0%
+this function and get the derivative
+uh then this derivative will be quite
+
+ align:start position:0%
+uh then this derivative will be quite
+ 
+
+ align:start position:0%
+uh then this derivative will be quite
+noisy
+
+ align:start position:0%
+noisy
+ 
+
+ align:start position:0%
+noisy
+and so instead of getting the the true
+
+ align:start position:0%
+and so instead of getting the the true
+ 
+
+ align:start position:0%
+and so instead of getting the the true
+derivative you might obtain something
+
+ align:start position:0%
+derivative you might obtain something
+ 
+
+ align:start position:0%
+derivative you might obtain something
+quite different from two derivative just
+
+ align:start position:0%
+quite different from two derivative just
+ 
+
+ align:start position:0%
+quite different from two derivative just
+because there is a confidence interval
+
+ align:start position:0%
+because there is a confidence interval
+ 
+
+ align:start position:0%
+because there is a confidence interval
+around any any point and obviously there
+
+ align:start position:0%
+around any any point and obviously there
+ 
+
+ align:start position:0%
+around any any point and obviously there
+is a trade-off here as well because
+
+ align:start position:0%
+is a trade-off here as well because
+ 
+
+ align:start position:0%
+is a trade-off here as well because
+you can run more paths throw more
+
+ align:start position:0%
+you can run more paths throw more
+ 
+
+ align:start position:0%
+you can run more paths throw more
+computational power
+
+ align:start position:0%
+computational power
+ 
+
+ align:start position:0%
+computational power
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+which will reduce your confidence
+
+ align:start position:0%
+which will reduce your confidence
+ 
+
+ align:start position:0%
+which will reduce your confidence
+interval you you will know uh
+
+ align:start position:0%
+interval you you will know uh
+ 
+
+ align:start position:0%
+interval you you will know uh
+better where where you are more precise
+
+ align:start position:0%
+better where where you are more precise
+ 
+
+ align:start position:0%
+better where where you are more precise
+uh or
+
+ align:start position:0%
+uh or
+ 
+
+ align:start position:0%
+uh or
+the other uh
+
+ align:start position:0%
+the other uh
+ 
+
+ align:start position:0%
+the other uh
+solution could be if you know that your
+
+ align:start position:0%
+solution could be if you know that your
+ 
+
+ align:start position:0%
+solution could be if you know that your
+your function is not too concave and
+
+ align:start position:0%
+your function is not too concave and
+ 
+
+ align:start position:0%
+your function is not too concave and
+reasonably flat you might
+
+ align:start position:0%
+reasonably flat you might
+ 
+
+ align:start position:0%
+reasonably flat you might
+move uh the uh
+
+ align:start position:0%
+move uh the uh
+ 
+
+ align:start position:0%
+move uh the uh
+do the numerical
+
+ align:start position:0%
+do the numerical
+ 
+
+ align:start position:0%
+do the numerical
+differentiation on wider interval
+
+ align:start position:0%
+differentiation on wider interval
+ 
+
+ align:start position:0%
+differentiation on wider interval
+basically reducing the significance of
+
+ align:start position:0%
+basically reducing the significance of
+ 
+
+ align:start position:0%
+basically reducing the significance of
+the error right and you would hope to
+
+ align:start position:0%
+the error right and you would hope to
+ 
+
+ align:start position:0%
+the error right and you would hope to
+arrive to
+
+ align:start position:0%
+arrive to
+ 
+
+ align:start position:0%
+arrive to
+a better approximation so obviously
+
+ align:start position:0%
+a better approximation so obviously
+ 
+
+ align:start position:0%
+a better approximation so obviously
+there is somewhere balance and the
+
+ align:start position:0%
+there is somewhere balance and the
+ 
+
+ align:start position:0%
+there is somewhere balance and the
+question was
+
+ align:start position:0%
+question was
+ 
+
+ align:start position:0%
+question was
+uh how uh is there an optimal
+
+ align:start position:0%
+uh how uh is there an optimal
+ 
+
+ align:start position:0%
+uh how uh is there an optimal
+shift size
+
+ align:start position:0%
+shift size
+ 
+
+ align:start position:0%
+shift size
+to obtain to to get
+
+ align:start position:0%
+to obtain to to get
+ 
+
+ align:start position:0%
+to obtain to to get
+the derivative
+
+ align:start position:0%
+the derivative
+ 
+
+ align:start position:0%
+the derivative
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+that's what oh
+
+ align:start position:0%
+that's what oh
+ 
+
+ align:start position:0%
+that's what oh
+oh oh
+
+ align:start position:0%
+oh oh
+ 
+
+ align:start position:0%
+oh oh
+the slight good corrupted
+
+ align:start position:0%
+the slight good corrupted
+ 
+
+ align:start position:0%
+the slight good corrupted
+right uh so the oh there was a quite a
+
+ align:start position:0%
+right uh so the oh there was a quite a
+ 
+
+ align:start position:0%
+right uh so the oh there was a quite a
+bit of mathematics involved and
+
+ align:start position:0%
+bit of mathematics involved and
+ 
+
+ align:start position:0%
+bit of mathematics involved and
+minimization and optimization
+
+ align:start position:0%
+minimization and optimization
+ 
+
+ align:start position:0%
+minimization and optimization
+there was an answer and
+
+ align:start position:0%
+there was an answer and
+ 
+
+ align:start position:0%
+there was an answer and
+that's actually
+
+ align:start position:0%
+that's actually
+ 
+
+ align:start position:0%
+that's actually
+what we
+
+ align:start position:0%
+what we
+ 
+
+ align:start position:0%
+what we
+finally
+
+ align:start position:0%
+finally
+ 
+
+ align:start position:0%
+finally
+arrived at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's some
+
+ align:start position:0%
+and that's some
+ 
+
+ align:start position:0%
+and that's some
+some two example but still it shows you
+
+ align:start position:0%
+some two example but still it shows you
+ 
+
+ align:start position:0%
+some two example but still it shows you
+that if you use constant size and
+
+ align:start position:0%
+that if you use constant size and
+ 
+
+ align:start position:0%
+that if you use constant size and
+not optimal size that that would be your
+
+ align:start position:0%
+not optimal size that that would be your
+ 
+
+ align:start position:0%
+not optimal size that that would be your
+numerical derivative of this of this
+
+ align:start position:0%
+numerical derivative of this of this
+ 
+
+ align:start position:0%
+numerical derivative of this of this
+blue function while the uh
+
+ align:start position:0%
+blue function while the uh
+ 
+
+ align:start position:0%
+blue function while the uh
+while if you use the optimal shift size
+
+ align:start position:0%
+while if you use the optimal shift size
+ 
+
+ align:start position:0%
+while if you use the optimal shift size
+which which duration computed it would
+
+ align:start position:0%
+which which duration computed it would
+ 
+
+ align:start position:0%
+which which duration computed it would
+be much
+
+ align:start position:0%
+be much
+ 
+
+ align:start position:0%
+be much
+smoother and much better
+
+ align:start position:0%
+smoother and much better
+ 
+
+ align:start position:0%
+smoother and much better
+so that's one example uh
+
+ align:start position:0%
+so that's one example uh
+ 
+
+ align:start position:0%
+so that's one example uh
+and that's what he did and we actually
+
+ align:start position:0%
+and that's what he did and we actually
+ 
+
+ align:start position:0%
+and that's what he did and we actually
+are implementing it in our systems and
+
+ align:start position:0%
+are implementing it in our systems and
+ 
+
+ align:start position:0%
+are implementing it in our systems and
+plan uh plan to use it
+
+ align:start position:0%
+plan uh plan to use it
+ 
+
+ align:start position:0%
+plan uh plan to use it
+in in practice
+
+ align:start position:0%
+in in practice
+ 
+
+ align:start position:0%
+in in practice
+another project
+
+ align:start position:0%
+another project
+ 
+
+ align:start position:0%
+another project
+uh was actually quite different
+
+ align:start position:0%
+uh was actually quite different
+ 
+
+ align:start position:0%
+uh was actually quite different
+and it was about electronic trading and
+
+ align:start position:0%
+and it was about electronic trading and
+ 
+
+ align:start position:0%
+and it was about electronic trading and
+basically
+
+ align:start position:0%
+basically
+ 
+
+ align:start position:0%
+basically
+uh how to
+
+ align:start position:0%
+uh how to
+ 
+
+ align:start position:0%
+uh how to
+better predict prices
+
+ align:start position:0%
+better predict prices
+ 
+
+ align:start position:0%
+better predict prices
+of uh of cro of currencies
+
+ align:start position:0%
+of uh of cro of currencies
+ 
+
+ align:start position:0%
+of uh of cro of currencies
+and exchange rate
+
+ align:start position:0%
+and exchange rate
+ 
+
+ align:start position:0%
+and exchange rate
+funny enough it was on ruble uh ruble us
+
+ align:start position:0%
+funny enough it was on ruble uh ruble us
+ 
+
+ align:start position:0%
+funny enough it was on ruble uh ruble us
+dollar because it was
+
+ align:start position:0%
+dollar because it was
+ 
+
+ align:start position:0%
+dollar because it was
+actually aimed for for our
+
+ align:start position:0%
+actually aimed for for our
+ 
+
+ align:start position:0%
+actually aimed for for our
+moscow office
+
+ align:start position:0%
+moscow office
+ 
+
+ align:start position:0%
+moscow office
+uh and um
+
+ align:start position:0%
+uh and um
+ 
+
+ align:start position:0%
+uh and um
+basically what we had we had the noisy
+
+ align:start position:0%
+basically what we had we had the noisy
+ 
+
+ align:start position:0%
+basically what we had we had the noisy
+observation of broker data uh and they
+
+ align:start position:0%
+observation of broker data uh and they
+ 
+
+ align:start position:0%
+observation of broker data uh and they
+it it was not it was coming on a
+
+ align:start position:0%
+it it was not it was coming on a
+ 
+
+ align:start position:0%
+it it was not it was coming on a
+different non
+
+ align:start position:0%
+different non
+ 
+
+ align:start position:0%
+different non
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+on uniform times basically at random
+
+ align:start position:0%
+on uniform times basically at random
+ 
+
+ align:start position:0%
+on uniform times basically at random
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+so uh we decided to use kalman filter
+
+ align:start position:0%
+so uh we decided to use kalman filter
+ 
+
+ align:start position:0%
+so uh we decided to use kalman filter
+and um to uh
+
+ align:start position:0%
+and um to uh
+ 
+
+ align:start position:0%
+and um to uh
+and uh to study how
+
+ align:start position:0%
+and uh to study how
+ 
+
+ align:start position:0%
+and uh to study how
+it can predict
+
+ align:start position:0%
+it can predict
+ 
+
+ align:start position:0%
+it can predict
+and yeah that's one of uh
+
+ align:start position:0%
+and yeah that's one of uh
+ 
+
+ align:start position:0%
+and yeah that's one of uh
+of the nice
+
+ align:start position:0%
+of the nice
+ 
+
+ align:start position:0%
+of the nice
+graphs dusan produced
+
+ align:start position:0%
+graphs dusan produced
+ 
+
+ align:start position:0%
+graphs dusan produced
+which which again uh will be we will use
+
+ align:start position:0%
+which which again uh will be we will use
+ 
+
+ align:start position:0%
+which which again uh will be we will use
+this the strategy and this the column
+
+ align:start position:0%
+this the strategy and this the column
+ 
+
+ align:start position:0%
+this the strategy and this the column
+filters which he constructed
+
+ align:start position:0%
+filters which he constructed
+ 
+
+ align:start position:0%
+filters which he constructed
+in our
+
+ align:start position:0%
+in our
+ 
+
+ align:start position:0%
+in our
+in our e-trading
+
+ align:start position:0%
+in our e-trading
+ 
+
+ align:start position:0%
+in our e-trading
+platform
+
+ align:start position:0%
+platform
+ 
+
+ align:start position:0%
+platform
+in moscow
+
+ align:start position:0%
+in moscow
+ 
+
+ align:start position:0%
+in moscow
+all right so uh
+
+ align:start position:0%
+all right so uh
+ 
+
+ align:start position:0%
+all right so uh
+that's just a couple of examples which i
+
+ align:start position:0%
+that's just a couple of examples which i
+ 
+
+ align:start position:0%
+that's just a couple of examples which i
+wanted to give you and as a preview what
+
+ align:start position:0%
+wanted to give you and as a preview what
+ 
+
+ align:start position:0%
+wanted to give you and as a preview what
+we will be talking in the class
+
+ align:start position:0%
+we will be talking in the class
+ 
+
+ align:start position:0%
+we will be talking in the class
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+they uh just remind so the website is
+
+ align:start position:0%
+they uh just remind so the website is
+ 
+
+ align:start position:0%
+they uh just remind so the website is
+fully functional
+
+ align:start position:0%
+fully functional
+ 
+
+ align:start position:0%
+fully functional
+uh i put syllable we put syllables there
+
+ align:start position:0%
+uh i put syllable we put syllables there
+ 
+
+ align:start position:0%
+uh i put syllable we put syllables there
+a a short list of literature
+
+ align:start position:0%
+a a short list of literature
+ 
+
+ align:start position:0%
+a a short list of literature
+uh the we will be posting a lot of
+
+ align:start position:0%
+uh the we will be posting a lot of
+ 
+
+ align:start position:0%
+uh the we will be posting a lot of
+materials there uh
+
+ align:start position:0%
+materials there uh
+ 
+
+ align:start position:0%
+materials there uh
+most probably mostly
+
+ align:start position:0%
+most probably mostly
+ 
+
+ align:start position:0%
+most probably mostly
+most lectures will be published there
+
+ align:start position:0%
+most lectures will be published there
+ 
+
+ align:start position:0%
+most lectures will be published there
+jake's slides are there already
+
+ align:start position:0%
+jake's slides are there already
+ 
+
+ align:start position:0%
+jake's slides are there already
+so uh any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions uh handbag uh there's some
+
+ align:start position:0%
+questions uh handbag uh there's some
+ 
+
+ align:start position:0%
+questions uh handbag uh there's some
+signup sheets right so we like to get
+
+ align:start position:0%
+signup sheets right so we like to get
+ 
+
+ align:start position:0%
+signup sheets right so we like to get
+your emails so we can
+
+ align:start position:0%
+your emails so we can
+ 
+
+ align:start position:0%
+your emails so we can
+uh put you on the website for the
+
+ align:start position:0%
+uh put you on the website for the
+ 
+
+ align:start position:0%
+uh put you on the website for the
+further announcements but you can also
+
+ align:start position:0%
+further announcements but you can also
+ 
+
+ align:start position:0%
+further announcements but you can also
+you know add yourself yes i believe but
+
+ align:start position:0%
+you know add yourself yes i believe but
+ 
+
+ align:start position:0%
+you know add yourself yes i believe but
+it's probably easier if you put your
+
+ align:start position:0%
+it's probably easier if you put your
+ 
+
+ align:start position:0%
+it's probably easier if you put your
+email on the signup sheet so we can uh
+
+ align:start position:0%
+email on the signup sheet so we can uh
+ 
+
+ align:start position:0%
+email on the signup sheet so we can uh
+yeah but but please please visit and and
+
+ align:start position:0%
+yeah but but please please visit and and
+ 
+
+ align:start position:0%
+yeah but but please please visit and and
+sign up yeah because there will be
+
+ align:start position:0%
+sign up yeah because there will be
+ 
+
+ align:start position:0%
+sign up yeah because there will be
+announcements to the class
+
+ align:start position:0%
+announcements to the class
+ 
+
+ align:start position:0%
+announcements to the class
+all right thank you very much
\ No newline at end of file
diff --git a/xVZ-lIuIi7A.txt b/xVZ-lIuIi7A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1385a849c82bdc724c83a9b8622c46bde97c2fa4
--- /dev/null
+++ b/xVZ-lIuIi7A.txt
@@ -0,0 +1,2563 @@
+align:start position:0%
+ 
+alright so that concludes a chapter a
+
+ align:start position:0%
+alright so that concludes a chapter a
+ 
+
+ align:start position:0%
+alright so that concludes a chapter a
+big chapter in this course it concludes
+
+ align:start position:0%
+big chapter in this course it concludes
+ 
+
+ align:start position:0%
+big chapter in this course it concludes
+time dependent perturbation theory we
+
+ align:start position:0%
+time dependent perturbation theory we
+ 
+
+ align:start position:0%
+time dependent perturbation theory we
+the whole course is largely organized
+
+ align:start position:0%
+the whole course is largely organized
+ 
+
+ align:start position:0%
+the whole course is largely organized
+with with approximation methods we've
+
+ align:start position:0%
+with with approximation methods we've
+ 
+
+ align:start position:0%
+with with approximation methods we've
+done time independent perturbation
+
+ align:start position:0%
+done time independent perturbation
+ 
+
+ align:start position:0%
+done time independent perturbation
+theory we applied it to the hydrogen
+
+ align:start position:0%
+theory we applied it to the hydrogen
+ 
+
+ align:start position:0%
+theory we applied it to the hydrogen
+atom in detail then we did wkb which is
+
+ align:start position:0%
+atom in detail then we did wkb which is
+ 
+
+ align:start position:0%
+atom in detail then we did wkb which is
+slowly varying things in space then with
+
+ align:start position:0%
+slowly varying things in space then with
+ 
+
+ align:start position:0%
+slowly varying things in space then with
+the time-dependent perturbation Theory
+
+ align:start position:0%
+the time-dependent perturbation Theory
+ 
+
+ align:start position:0%
+the time-dependent perturbation Theory
+have had many parts to it had Fermi's
+
+ align:start position:0%
+have had many parts to it had Fermi's
+ 
+
+ align:start position:0%
+have had many parts to it had Fermi's
+golden rule atoms it had just
+
+ align:start position:0%
+golden rule atoms it had just
+ 
+
+ align:start position:0%
+golden rule atoms it had just
+transitions in general the next step
+
+ align:start position:0%
+transitions in general the next step
+ 
+
+ align:start position:0%
+transitions in general the next step
+would be adiabatic approximation which
+
+ align:start position:0%
+would be adiabatic approximation which
+ 
+
+ align:start position:0%
+would be adiabatic approximation which
+is time-dependent changes but slow this
+
+ align:start position:0%
+is time-dependent changes but slow this
+ 
+
+ align:start position:0%
+is time-dependent changes but slow this
+is the time analog of wkb we're going to
+
+ align:start position:0%
+is the time analog of wkb we're going to
+ 
+
+ align:start position:0%
+is the time analog of wkb we're going to
+take a little break and for a little
+
+ align:start position:0%
+take a little break and for a little
+ 
+
+ align:start position:0%
+take a little break and for a little
+half a lecture today and the full
+
+ align:start position:0%
+half a lecture today and the full
+ 
+
+ align:start position:0%
+half a lecture today and the full
+lecture next time we're going to do
+
+ align:start position:0%
+lecture next time we're going to do
+ 
+
+ align:start position:0%
+lecture next time we're going to do
+particles in electromagnetic fields
+
+ align:start position:0%
+particles in electromagnetic fields
+ 
+
+ align:start position:0%
+particles in electromagnetic fields
+that's an important subject it will
+
+ align:start position:0%
+that's an important subject it will
+ 
+
+ align:start position:0%
+that's an important subject it will
+involve Landau levels and things that
+
+ align:start position:0%
+involve Landau levels and things that
+ 
+
+ align:start position:0%
+involve Landau levels and things that
+you always hear about and and it will be
+
+ align:start position:0%
+you always hear about and and it will be
+ 
+
+ align:start position:0%
+you always hear about and and it will be
+useful for some of the things we've done
+
+ align:start position:0%
+useful for some of the things we've done
+ 
+
+ align:start position:0%
+useful for some of the things we've done
+we've had a little exposure to it with a
+
+ align:start position:0%
+we've had a little exposure to it with a
+ 
+
+ align:start position:0%
+we've had a little exposure to it with a
+Paola equation you may remember the
+
+ align:start position:0%
+Paola equation you may remember the
+ 
+
+ align:start position:0%
+Paola equation you may remember the
+Dirac and Powell equation that had this
+
+ align:start position:0%
+Dirac and Powell equation that had this
+ 
+
+ align:start position:0%
+Dirac and Powell equation that had this
+electromagnetic field so now we're going
+
+ align:start position:0%
+electromagnetic field so now we're going
+ 
+
+ align:start position:0%
+electromagnetic field so now we're going
+to take seriously the electromagnetic
+
+ align:start position:0%
+to take seriously the electromagnetic
+ 
+
+ align:start position:0%
+to take seriously the electromagnetic
+fields and study how they interact with
+
+ align:start position:0%
+fields and study how they interact with
+ 
+
+ align:start position:0%
+fields and study how they interact with
+quantum mechanics and there's a lot of
+
+ align:start position:0%
+quantum mechanics and there's a lot of
+ 
+
+ align:start position:0%
+quantum mechanics and there's a lot of
+very interesting and beautiful ideas
+
+ align:start position:0%
+very interesting and beautiful ideas
+ 
+
+ align:start position:0%
+very interesting and beautiful ideas
+having to do with gauge invariance and
+
+ align:start position:0%
+having to do with gauge invariance and
+ 
+
+ align:start position:0%
+having to do with gauge invariance and
+and-white potentials are important
+
+ align:start position:0%
+and-white potentials are important
+ 
+
+ align:start position:0%
+and-white potentials are important
+charged particles in electromagnetic
+
+ align:start position:0%
+charged particles in electromagnetic
+ 
+
+ align:start position:0%
+charged particles in electromagnetic
+fields so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+charged particles in p.m. fields okay so
+
+ align:start position:0%
+charged particles in p.m. fields okay so
+ 
+
+ align:start position:0%
+charged particles in p.m. fields okay so
+what is our useful problem you have a
+
+ align:start position:0%
+what is our useful problem you have a
+ 
+
+ align:start position:0%
+what is our useful problem you have a
+particle with mass M now charge Q and
+
+ align:start position:0%
+particle with mass M now charge Q and
+ 
+
+ align:start position:0%
+particle with mass M now charge Q and
+finally there's an electric field and a
+
+ align:start position:0%
+finally there's an electric field and a
+ 
+
+ align:start position:0%
+finally there's an electric field and a
+magnetic field and there's gonna be
+
+ align:start position:0%
+magnetic field and there's gonna be
+ 
+
+ align:start position:0%
+magnetic field and there's gonna be
+interactions between them so there's a
+
+ align:start position:0%
+interactions between them so there's a
+ 
+
+ align:start position:0%
+interactions between them so there's a
+and B and you've gone through this
+
+ align:start position:0%
+and B and you've gone through this
+ 
+
+ align:start position:0%
+and B and you've gone through this
+transition probably you've been told in
+
+ align:start position:0%
+transition probably you've been told in
+ 
+
+ align:start position:0%
+transition probably you've been told in
+electromagnetism something along these
+
+ align:start position:0%
+electromagnetism something along these
+ 
+
+ align:start position:0%
+electromagnetism something along these
+lines there is this E and B field so
+
+ align:start position:0%
+lines there is this E and B field so
+ 
+
+ align:start position:0%
+lines there is this E and B field so
+those are the physical fields these are
+
+ align:start position:0%
+those are the physical fields these are
+ 
+
+ align:start position:0%
+those are the physical fields these are
+the things that do stuff on charges in
+
+ align:start position:0%
+the things that do stuff on charges in
+ 
+
+ align:start position:0%
+the things that do stuff on charges in
+parallel and there's this mathematical
+
+ align:start position:0%
+parallel and there's this mathematical
+ 
+
+ align:start position:0%
+parallel and there's this mathematical
+entities that can help you which are
+
+ align:start position:0%
+entities that can help you which are
+ 
+
+ align:start position:0%
+entities that can help you which are
+potentials that allow you to rewrite
+
+ align:start position:0%
+potentials that allow you to rewrite
+ 
+
+ align:start position:0%
+potentials that allow you to rewrite
+this field in terms of these quantities
+
+ align:start position:0%
+this field in terms of these quantities
+ 
+
+ align:start position:0%
+this field in terms of these quantities
+potentials and they're practical to
+
+ align:start position:0%
+potentials and they're practical to
+ 
+
+ align:start position:0%
+potentials and they're practical to
+solve the equation but the potentials
+
+ align:start position:0%
+solve the equation but the potentials
+ 
+
+ align:start position:0%
+solve the equation but the potentials
+are less physical than the fields
+
+ align:start position:0%
+are less physical than the fields
+ 
+
+ align:start position:0%
+are less physical than the fields
+because the potentials are ambiguous you
+
+ align:start position:0%
+because the potentials are ambiguous you
+ 
+
+ align:start position:0%
+because the potentials are ambiguous you
+can change the value of the potential
+
+ align:start position:0%
+can change the value of the potential
+ 
+
+ align:start position:0%
+can change the value of the potential
+without changing the electric field you
+
+ align:start position:0%
+without changing the electric field you
+ 
+
+ align:start position:0%
+without changing the electric field you
+can do things like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well that is somewhat misleading put
+
+ align:start position:0%
+well that is somewhat misleading put
+ 
+
+ align:start position:0%
+well that is somewhat misleading put
+charitably it's pretty wrong viewpoint
+
+ align:start position:0%
+charitably it's pretty wrong viewpoint
+ 
+
+ align:start position:0%
+charitably it's pretty wrong viewpoint
+actually as we will discover and
+
+ align:start position:0%
+actually as we will discover and
+ 
+
+ align:start position:0%
+actually as we will discover and
+understand here the potentials are
+
+ align:start position:0%
+understand here the potentials are
+ 
+
+ align:start position:0%
+understand here the potentials are
+really more important than the fields
+
+ align:start position:0%
+really more important than the fields
+ 
+
+ align:start position:0%
+really more important than the fields
+quantum mechanics couples to the
+
+ align:start position:0%
+quantum mechanics couples to the
+ 
+
+ align:start position:0%
+quantum mechanics couples to the
+potentials and as an afterthought it
+
+ align:start position:0%
+potentials and as an afterthought it
+ 
+
+ align:start position:0%
+potentials and as an afterthought it
+couples to the fields because it couples
+
+ align:start position:0%
+couples to the fields because it couples
+ 
+
+ align:start position:0%
+couples to the fields because it couples
+to the potentials but even the
+
+ align:start position:0%
+to the potentials but even the
+ 
+
+ align:start position:0%
+to the potentials but even the
+definition of an electromagnetic field
+
+ align:start position:0%
+definition of an electromagnetic field
+ 
+
+ align:start position:0%
+definition of an electromagnetic field
+at the end of the day nowadays we really
+
+ align:start position:0%
+at the end of the day nowadays we really
+ 
+
+ align:start position:0%
+at the end of the day nowadays we really
+understand it as a definition of
+
+ align:start position:0%
+understand it as a definition of
+ 
+
+ align:start position:0%
+understand it as a definition of
+potentials and I'll try to explain that
+
+ align:start position:0%
+potentials and I'll try to explain that
+ 
+
+ align:start position:0%
+potentials and I'll try to explain that
+this is pretty important if you try to
+
+ align:start position:0%
+this is pretty important if you try to
+ 
+
+ align:start position:0%
+this is pretty important if you try to
+describe anything that has topological
+
+ align:start position:0%
+describe anything that has topological
+ 
+
+ align:start position:0%
+describe anything that has topological
+content most of the times if you're
+
+ align:start position:0%
+content most of the times if you're
+ 
+
+ align:start position:0%
+content most of the times if you're
+considering open space open Minkowski
+
+ align:start position:0%
+considering open space open Minkowski
+ 
+
+ align:start position:0%
+considering open space open Minkowski
+space it doesn't make much difference
+
+ align:start position:0%
+space it doesn't make much difference
+ 
+
+ align:start position:0%
+space it doesn't make much difference
+where you take the electric and magnetic
+
+ align:start position:0%
+where you take the electric and magnetic
+ 
+
+ align:start position:0%
+where you take the electric and magnetic
+field to be fundamental of the
+
+ align:start position:0%
+field to be fundamental of the
+ 
+
+ align:start position:0%
+field to be fundamental of the
+potentials but as soon as you consider
+
+ align:start position:0%
+potentials but as soon as you consider
+ 
+
+ align:start position:0%
+potentials but as soon as you consider
+anything topological a sample that lives
+
+ align:start position:0%
+anything topological a sample that lives
+ 
+
+ align:start position:0%
+anything topological a sample that lives
+on a toroidal surface that's a
+
+ align:start position:0%
+on a toroidal surface that's a
+ 
+
+ align:start position:0%
+on a toroidal surface that's a
+topological space then if you don't
+
+ align:start position:0%
+topological space then if you don't
+ 
+
+ align:start position:0%
+topological space then if you don't
+think about potentials you could be
+
+ align:start position:0%
+think about potentials you could be
+ 
+
+ align:start position:0%
+think about potentials you could be
+absolutely wrong completely wrong or if
+
+ align:start position:0%
+absolutely wrong completely wrong or if
+ 
+
+ align:start position:0%
+absolutely wrong completely wrong or if
+you have an extra dimension in many
+
+ align:start position:0%
+you have an extra dimension in many
+ 
+
+ align:start position:0%
+you have an extra dimension in many
+theories of physics you could have extra
+
+ align:start position:0%
+theories of physics you could have extra
+ 
+
+ align:start position:0%
+theories of physics you could have extra
+dimensions and you think about the
+
+ align:start position:0%
+dimensions and you think about the
+ 
+
+ align:start position:0%
+dimensions and you think about the
+electric and magnetic fields then if you
+
+ align:start position:0%
+electric and magnetic fields then if you
+ 
+
+ align:start position:0%
+electric and magnetic fields then if you
+don't think of potentials you can be
+
+ align:start position:0%
+don't think of potentials you can be
+ 
+
+ align:start position:0%
+don't think of potentials you can be
+quite wrong so let's explain what's
+
+ align:start position:0%
+quite wrong so let's explain what's
+ 
+
+ align:start position:0%
+quite wrong so let's explain what's
+happening with these potentials
+
+ align:start position:0%
+happening with these potentials
+ 
+
+ align:start position:0%
+happening with these potentials
+basically it all starts from the idea
+
+ align:start position:0%
+basically it all starts from the idea
+ 
+
+ align:start position:0%
+basically it all starts from the idea
+that you have a Maxwell's equation del
+
+ align:start position:0%
+that you have a Maxwell's equation del
+ 
+
+ align:start position:0%
+that you have a Maxwell's equation del
+dot B equals zero and this is solved it
+
+ align:start position:0%
+dot B equals zero and this is solved it
+ 
+
+ align:start position:0%
+dot B equals zero and this is solved it
+is said by setting B equal to the curl
+
+ align:start position:0%
+is said by setting B equal to the curl
+ 
+
+ align:start position:0%
+is said by setting B equal to the curl
+of a and indeed if B is equal to the
+
+ align:start position:0%
+of a and indeed if B is equal to the
+ 
+
+ align:start position:0%
+of a and indeed if B is equal to the
+curl of a this equation is satisfied the
+
+ align:start position:0%
+curl of a this equation is satisfied the
+ 
+
+ align:start position:0%
+curl of a this equation is satisfied the
+other equation that is relevant is this
+
+ align:start position:0%
+other equation that is relevant is this
+ 
+
+ align:start position:0%
+other equation that is relevant is this
+Faraday's law which if B is already curl
+
+ align:start position:0%
+Faraday's law which if B is already curl
+ 
+
+ align:start position:0%
+Faraday's law which if B is already curl
+of a you have that curl of e plus 1 over
+
+ align:start position:0%
+of a you have that curl of e plus 1 over
+ 
+
+ align:start position:0%
+of a you have that curl of e plus 1 over
+C be a DT is equal to zero you see I
+
+ align:start position:0%
+C be a DT is equal to zero you see I
+ 
+
+ align:start position:0%
+C be a DT is equal to zero you see I
+substitute B here equal curl of a I
+
+ align:start position:0%
+substitute B here equal curl of a I
+ 
+
+ align:start position:0%
+substitute B here equal curl of a I
+commute the order of derivatives the DT
+
+ align:start position:0%
+commute the order of derivatives the DT
+ 
+
+ align:start position:0%
+commute the order of derivatives the DT
+and the curl and this gives me this
+
+ align:start position:0%
+and the curl and this gives me this
+ 
+
+ align:start position:0%
+and the curl and this gives me this
+equation from this equation we say any
+
+ align:start position:0%
+equation from this equation we say any
+ 
+
+ align:start position:0%
+equation from this equation we say any
+thing that has zero curl is the gradient
+
+ align:start position:0%
+thing that has zero curl is the gradient
+ 
+
+ align:start position:0%
+thing that has zero curl is the gradient
+of something and therefore we say that e
+
+ align:start position:0%
+of something and therefore we say that e
+ 
+
+ align:start position:0%
+of something and therefore we say that e
+plus one over C da DT is the gradient of
+
+ align:start position:0%
+plus one over C da DT is the gradient of
+ 
+
+ align:start position:0%
+plus one over C da DT is the gradient of
+Phi from where we find the second
+
+ align:start position:0%
+Phi from where we find the second
+ 
+
+ align:start position:0%
+Phi from where we find the second
+equation which says that e can be
+
+ align:start position:0%
+equation which says that e can be
+ 
+
+ align:start position:0%
+equation which says that e can be
+obtained as minus the gradient of Phi
+
+ align:start position:0%
+obtained as minus the gradient of Phi
+ 
+
+ align:start position:0%
+obtained as minus the gradient of Phi
+minus one over C da DT and I hope I have
+
+ align:start position:0%
+minus one over C da DT and I hope I have
+ 
+
+ align:start position:0%
+minus one over C da DT and I hope I have
+it right yes so this is the origin of
+
+ align:start position:0%
+it right yes so this is the origin of
+ 
+
+ align:start position:0%
+it right yes so this is the origin of
+the potentials you've seen that that's
+
+ align:start position:0%
+the potentials you've seen that that's
+ 
+
+ align:start position:0%
+the potentials you've seen that that's
+how they explain probably to you why you
+
+ align:start position:0%
+how they explain probably to you why you
+ 
+
+ align:start position:0%
+how they explain probably to you why you
+have potentials and indeed this is so
+
+ align:start position:0%
+have potentials and indeed this is so
+ 
+
+ align:start position:0%
+have potentials and indeed this is so
+far so good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now there's a freedom with these
+
+ align:start position:0%
+but now there's a freedom with these
+ 
+
+ align:start position:0%
+but now there's a freedom with these
+potentials which are called gauge
+
+ align:start position:0%
+potentials which are called gauge
+ 
+
+ align:start position:0%
+potentials which are called gauge
+transformation so what are the gauge
+
+ align:start position:0%
+transformation so what are the gauge
+ 
+
+ align:start position:0%
+transformation so what are the gauge
+transformations it's the possibility of
+
+ align:start position:0%
+transformations it's the possibility of
+ 
+
+ align:start position:0%
+transformations it's the possibility of
+changing the potentials without changing
+
+ align:start position:0%
+changing the potentials without changing
+ 
+
+ align:start position:0%
+changing the potentials without changing
+the electromagnetic fields so for
+
+ align:start position:0%
+the electromagnetic fields so for
+ 
+
+ align:start position:0%
+the electromagnetic fields so for
+example since the curl of the grad of
+
+ align:start position:0%
+example since the curl of the grad of
+ 
+
+ align:start position:0%
+example since the curl of the grad of
+anything is zero so almost like curl
+
+ align:start position:0%
+anything is zero so almost like curl
+ 
+
+ align:start position:0%
+anything is zero so almost like curl
+cross curl is zero this is the curl of
+
+ align:start position:0%
+cross curl is zero this is the curl of
+ 
+
+ align:start position:0%
+cross curl is zero this is the curl of
+the grad of anything is zero you can
+
+ align:start position:0%
+the grad of anything is zero you can
+ 
+
+ align:start position:0%
+the grad of anything is zero you can
+change a into a different a that we'll
+
+ align:start position:0%
+change a into a different a that we'll
+ 
+
+ align:start position:0%
+change a into a different a that we'll
+call a prime given by a plus gradient of
+
+ align:start position:0%
+call a prime given by a plus gradient of
+ 
+
+ align:start position:0%
+call a prime given by a plus gradient of
+a function lambda and this will not
+
+ align:start position:0%
+a function lambda and this will not
+ 
+
+ align:start position:0%
+a function lambda and this will not
+change the value of the magnetic field B
+
+ align:start position:0%
+change the value of the magnetic field B
+ 
+
+ align:start position:0%
+change the value of the magnetic field B
+because if you calculate the magnetic
+
+ align:start position:0%
+because if you calculate the magnetic
+ 
+
+ align:start position:0%
+because if you calculate the magnetic
+field B the new magnetic field
+
+ align:start position:0%
+field B the new magnetic field
+ 
+
+ align:start position:0%
+field B the new magnetic field
+associated to the new vector potential
+
+ align:start position:0%
+associated to the new vector potential
+ 
+
+ align:start position:0%
+associated to the new vector potential
+is equal to curl of a prime but that's
+
+ align:start position:0%
+is equal to curl of a prime but that's
+ 
+
+ align:start position:0%
+is equal to curl of a prime but that's
+equal to curl of a and that's equal to
+
+ align:start position:0%
+equal to curl of a and that's equal to
+ 
+
+ align:start position:0%
+equal to curl of a and that's equal to
+the old B
+
+ align:start position:0%
+the old B
+ 
+
+ align:start position:0%
+the old B
+due to the old magnetic vector potential
+
+ align:start position:0%
+due to the old magnetic vector potential
+ 
+
+ align:start position:0%
+due to the old magnetic vector potential
+so the vector potential has changed but
+
+ align:start position:0%
+so the vector potential has changed but
+ 
+
+ align:start position:0%
+so the vector potential has changed but
+B did not change on the other hand if
+
+ align:start position:0%
+B did not change on the other hand if
+ 
+
+ align:start position:0%
+B did not change on the other hand if
+you change the vector potential by
+
+ align:start position:0%
+you change the vector potential by
+ 
+
+ align:start position:0%
+you change the vector potential by
+something like this now it can affect
+
+ align:start position:0%
+something like this now it can affect
+ 
+
+ align:start position:0%
+something like this now it can affect
+the e but if simultaneously you change
+
+ align:start position:0%
+the e but if simultaneously you change
+ 
+
+ align:start position:0%
+the e but if simultaneously you change
+Phi e will be left unchanged so what
+
+ align:start position:0%
+Phi e will be left unchanged so what
+ 
+
+ align:start position:0%
+Phi e will be left unchanged so what
+should you do - fine you should so this
+
+ align:start position:0%
+should you do - fine you should so this
+ 
+
+ align:start position:0%
+should you do - fine you should so this
+is the first one for a if you want to
+
+ align:start position:0%
+is the first one for a if you want to
+ 
+
+ align:start position:0%
+is the first one for a if you want to
+keep even change you define Phi prime
+
+ align:start position:0%
+keep even change you define Phi prime
+ 
+
+ align:start position:0%
+keep even change you define Phi prime
+equal to Phi minus 1 over C the lambda
+
+ align:start position:0%
+equal to Phi minus 1 over C the lambda
+ 
+
+ align:start position:0%
+equal to Phi minus 1 over C the lambda
+DT and then when you compute the new EU
+
+ align:start position:0%
+DT and then when you compute the new EU
+ 
+
+ align:start position:0%
+DT and then when you compute the new EU
+will do the gradient of the new Phi
+
+ align:start position:0%
+will do the gradient of the new Phi
+ 
+
+ align:start position:0%
+will do the gradient of the new Phi
+which will be the gradient of the old
+
+ align:start position:0%
+which will be the gradient of the old
+ 
+
+ align:start position:0%
+which will be the gradient of the old
+Phi but an extra term which would be
+
+ align:start position:0%
+Phi but an extra term which would be
+ 
+
+ align:start position:0%
+Phi but an extra term which would be
+plus 1 over C D DT of gradient of lambda
+
+ align:start position:0%
+plus 1 over C D DT of gradient of lambda
+ 
+
+ align:start position:0%
+plus 1 over C D DT of gradient of lambda
+and it will cancel with the minus 1 over
+
+ align:start position:0%
+and it will cancel with the minus 1 over
+ 
+
+ align:start position:0%
+and it will cancel with the minus 1 over
+CV DT of the gradient of lambda so by
+
+ align:start position:0%
+CV DT of the gradient of lambda so by
+ 
+
+ align:start position:0%
+CV DT of the gradient of lambda so by
+changing a and Phi in this way B and E
+
+ align:start position:0%
+changing a and Phi in this way B and E
+ 
+
+ align:start position:0%
+changing a and Phi in this way B and E
+are unchanged so I can summarize this
+
+ align:start position:0%
+are unchanged so I can summarize this
+ 
+
+ align:start position:0%
+are unchanged so I can summarize this
+gauge invariant statement by saying that
+
+ align:start position:0%
+gauge invariant statement by saying that
+ 
+
+ align:start position:0%
+gauge invariant statement by saying that
+the electric field a new electric field
+
+ align:start position:0%
+the electric field a new electric field
+ 
+
+ align:start position:0%
+the electric field a new electric field
+due to a prime due to Phi Prime and a
+
+ align:start position:0%
+due to a prime due to Phi Prime and a
+ 
+
+ align:start position:0%
+due to a prime due to Phi Prime and a
+prime is equal to the electric field due
+
+ align:start position:0%
+prime is equal to the electric field due
+ 
+
+ align:start position:0%
+prime is equal to the electric field due
+to Phi and a and the magnetic field new
+
+ align:start position:0%
+to Phi and a and the magnetic field new
+ 
+
+ align:start position:0%
+to Phi and a and the magnetic field new
+due to Phi Prime and a prime is equal to
+
+ align:start position:0%
+due to Phi Prime and a prime is equal to
+ 
+
+ align:start position:0%
+due to Phi Prime and a prime is equal to
+the magnetic field due to Phi and a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is lifted to a principle so weird
+
+ align:start position:0%
+this is lifted to a principle so weird
+ 
+
+ align:start position:0%
+this is lifted to a principle so weird
+we started describing electromagnetic
+
+ align:start position:0%
+we started describing electromagnetic
+ 
+
+ align:start position:0%
+we started describing electromagnetic
+fields with E and B we can describe them
+
+ align:start position:0%
+fields with E and B we can describe them
+ 
+
+ align:start position:0%
+fields with E and B we can describe them
+with a and Phi and let's take that
+
+ align:start position:0%
+with a and Phi and let's take that
+ 
+
+ align:start position:0%
+with a and Phi and let's take that
+seriously because we'll need it for
+
+ align:start position:0%
+seriously because we'll need it for
+ 
+
+ align:start position:0%
+seriously because we'll need it for
+quantum mechanics and we add now the
+
+ align:start position:0%
+quantum mechanics and we add now the
+ 
+
+ align:start position:0%
+quantum mechanics and we add now the
+extra important physical assumption
+
+ align:start position:0%
+extra important physical assumption
+ 
+
+ align:start position:0%
+extra important physical assumption
+which is that Phi prime a prime is
+
+ align:start position:0%
+which is that Phi prime a prime is
+ 
+
+ align:start position:0%
+which is that Phi prime a prime is
+really equivalent physically equivalent
+
+ align:start position:0%
+really equivalent physically equivalent
+ 
+
+ align:start position:0%
+really equivalent physically equivalent
+to a Phi a and an electromagnetic field
+
+ align:start position:0%
+to a Phi a and an electromagnetic field
+ 
+
+ align:start position:0%
+to a Phi a and an electromagnetic field
+configuration as a mathematician would
+
+ align:start position:0%
+configuration as a mathematician would
+ 
+
+ align:start position:0%
+configuration as a mathematician would
+say is the equivalence classes of
+
+ align:start position:0%
+say is the equivalence classes of
+ 
+
+ align:start position:0%
+say is the equivalence classes of
+potentials so you want to describe an
+
+ align:start position:0%
+potentials so you want to describe an
+ 
+
+ align:start position:0%
+potentials so you want to describe an
+electromagnetic field you ask one of you
+
+ align:start position:0%
+electromagnetic field you ask one of you
+ 
+
+ align:start position:0%
+electromagnetic field you ask one of you
+and you tell me what is fine what is a I
+
+ align:start position:0%
+and you tell me what is fine what is a I
+ 
+
+ align:start position:0%
+and you tell me what is fine what is a I
+asked somebody else tell me another fire
+
+ align:start position:0%
+asked somebody else tell me another fire
+ 
+
+ align:start position:0%
+asked somebody else tell me another fire
+another a and say they look different
+
+ align:start position:0%
+another a and say they look different
+ 
+
+ align:start position:0%
+another a and say they look different
+but they may be the same they are the
+
+ align:start position:0%
+but they may be the same they are the
+ 
+
+ align:start position:0%
+but they may be the same they are the
+same if they are related by some lambda
+
+ align:start position:0%
+same if they are related by some lambda
+ 
+
+ align:start position:0%
+same if they are related by some lambda
+if they're physically close if they're
+
+ align:start position:0%
+if they're physically close if they're
+ 
+
+ align:start position:0%
+if they're physically close if they're
+alright if there exists a lambda such
+
+ align:start position:0%
+alright if there exists a lambda such
+ 
+
+ align:start position:0%
+alright if there exists a lambda such
+that they are gauge transforms of each
+
+ align:start position:0%
+that they are gauge transforms of each
+ 
+
+ align:start position:0%
+that they are gauge transforms of each
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so before you say you tell me what E is
+
+ align:start position:0%
+so before you say you tell me what E is
+ 
+
+ align:start position:0%
+so before you say you tell me what E is
+and what B is and they have to agree and
+
+ align:start position:0%
+and what B is and they have to agree and
+ 
+
+ align:start position:0%
+and what B is and they have to agree and
+you say that's preferable because if a
+
+ align:start position:0%
+you say that's preferable because if a
+ 
+
+ align:start position:0%
+you say that's preferable because if a
+and B are the same they agree that's it
+
+ align:start position:0%
+and B are the same they agree that's it
+ 
+
+ align:start position:0%
+and B are the same they agree that's it
+you were why do we go through a and five
+
+ align:start position:0%
+you were why do we go through a and five
+ 
+
+ align:start position:0%
+you were why do we go through a and five
+they don't have to agree and they can be
+
+ align:start position:0%
+they don't have to agree and they can be
+ 
+
+ align:start position:0%
+they don't have to agree and they can be
+the same because if they're related with
+
+ align:start position:0%
+the same because if they're related with
+ 
+
+ align:start position:0%
+the same because if they're related with
+some lambda they are the same we seem to
+
+ align:start position:0%
+some lambda they are the same we seem to
+ 
+
+ align:start position:0%
+some lambda they are the same we seem to
+be going backwards into a lot more
+
+ align:start position:0%
+be going backwards into a lot more
+ 
+
+ align:start position:0%
+be going backwards into a lot more
+complicated situation but that's what we
+
+ align:start position:0%
+complicated situation but that's what we
+ 
+
+ align:start position:0%
+complicated situation but that's what we
+need and that's what the physics tells
+
+ align:start position:0%
+need and that's what the physics tells
+ 
+
+ align:start position:0%
+need and that's what the physics tells
+you is really going on
+
+ align:start position:0%
+you is really going on
+ 
+
+ align:start position:0%
+you is really going on
+so some particular things that are
+
+ align:start position:0%
+so some particular things that are
+ 
+
+ align:start position:0%
+so some particular things that are
+curious can happen now and they're very
+
+ align:start position:0%
+curious can happen now and they're very
+ 
+
+ align:start position:0%
+curious can happen now and they're very
+curious and they're examples and we'll
+
+ align:start position:0%
+curious and they're examples and we'll
+ 
+
+ align:start position:0%
+curious and they're examples and we'll
+see some of those examples
+
+ align:start position:0%
+see some of those examples
+ 
+
+ align:start position:0%
+see some of those examples
+so suppose so curious effects effects
+
+ align:start position:0%
+so suppose so curious effects effects
+ 
+
+ align:start position:0%
+so suppose so curious effects effects
+one suppose Phi and a and Phi Prime and
+
+ align:start position:0%
+one suppose Phi and a and Phi Prime and
+ 
+
+ align:start position:0%
+one suppose Phi and a and Phi Prime and
+a prime give the same E and B so you and
+
+ align:start position:0%
+a prime give the same E and B so you and
+ 
+
+ align:start position:0%
+a prime give the same E and B so you and
+your peer editor came up with some Phi
+
+ align:start position:0%
+your peer editor came up with some Phi
+ 
+
+ align:start position:0%
+your peer editor came up with some Phi
+and a and Phi Prime and a prime and they
+
+ align:start position:0%
+and a and Phi Prime and a prime and they
+ 
+
+ align:start position:0%
+and a and Phi Prime and a prime and they
+give the same a and B are you and your
+
+ align:start position:0%
+give the same a and B are you and your
+ 
+
+ align:start position:0%
+give the same a and B are you and your
+peer editor on the hands of the same
+
+ align:start position:0%
+peer editor on the hands of the same
+ 
+
+ align:start position:0%
+peer editor on the hands of the same
+electromagnetic field configuration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maybe but not obvious in classical
+
+ align:start position:0%
+maybe but not obvious in classical
+ 
+
+ align:start position:0%
+maybe but not obvious in classical
+physics you will say yes if they give
+
+ align:start position:0%
+physics you will say yes if they give
+ 
+
+ align:start position:0%
+physics you will say yes if they give
+you the same a and B these are
+
+ align:start position:0%
+you the same a and B these are
+ 
+
+ align:start position:0%
+you the same a and B these are
+equivalent no now you would have to show
+
+ align:start position:0%
+equivalent no now you would have to show
+ 
+
+ align:start position:0%
+equivalent no now you would have to show
+that there is some lambda so that they
+
+ align:start position:0%
+that there is some lambda so that they
+ 
+
+ align:start position:0%
+that there is some lambda so that they
+give our gauge equivalent to each other
+
+ align:start position:0%
+give our gauge equivalent to each other
+ 
+
+ align:start position:0%
+give our gauge equivalent to each other
+you see
+
+ align:start position:0%
+you see
+ 
+
+ align:start position:0%
+you see
+the fact that they're gage equivalent
+
+ align:start position:0%
+the fact that they're gage equivalent
+ 
+
+ align:start position:0%
+the fact that they're gage equivalent
+warranties they give the same B and E
+
+ align:start position:0%
+warranties they give the same B and E
+ 
+
+ align:start position:0%
+warranties they give the same B and E
+but if they give the same B&E it may
+
+ align:start position:0%
+but if they give the same B&E it may
+ 
+
+ align:start position:0%
+but if they give the same B&E it may
+happen that you still cannot find the
+
+ align:start position:0%
+happen that you still cannot find the
+ 
+
+ align:start position:0%
+happen that you still cannot find the
+lambda that relates them because what
+
+ align:start position:0%
+lambda that relates them because what
+ 
+
+ align:start position:0%
+lambda that relates them because what
+you have to do is try to take your
+
+ align:start position:0%
+you have to do is try to take your
+ 
+
+ align:start position:0%
+you have to do is try to take your
+friends a and your friends Phi that this
+
+ align:start position:0%
+friends a and your friends Phi that this
+ 
+
+ align:start position:0%
+friends a and your friends Phi that this
+is yours and yours and now you have to
+
+ align:start position:0%
+is yours and yours and now you have to
+ 
+
+ align:start position:0%
+is yours and yours and now you have to
+find the lambda and you have to solve a
+
+ align:start position:0%
+find the lambda and you have to solve a
+ 
+
+ align:start position:0%
+find the lambda and you have to solve a
+differential equation what if you can't
+
+ align:start position:0%
+differential equation what if you can't
+ 
+
+ align:start position:0%
+differential equation what if you can't
+find a lambda they gave the same a and B
+
+ align:start position:0%
+find a lambda they gave the same a and B
+ 
+
+ align:start position:0%
+find a lambda they gave the same a and B
+but they're not gauge equivalent to each
+
+ align:start position:0%
+but they're not gauge equivalent to each
+ 
+
+ align:start position:0%
+but they're not gauge equivalent to each
+other that means that you have different
+
+ align:start position:0%
+other that means that you have different
+ 
+
+ align:start position:0%
+other that means that you have different
+field configurations the fact that a and
+
+ align:start position:0%
+field configurations the fact that a and
+ 
+
+ align:start position:0%
+field configurations the fact that a and
+B are the same doesn't mean they are the
+
+ align:start position:0%
+B are the same doesn't mean they are the
+ 
+
+ align:start position:0%
+B are the same doesn't mean they are the
+same electromagnetic fields and this can
+
+ align:start position:0%
+same electromagnetic fields and this can
+ 
+
+ align:start position:0%
+same electromagnetic fields and this can
+happen if you have a little bit of
+
+ align:start position:0%
+happen if you have a little bit of
+ 
+
+ align:start position:0%
+happen if you have a little bit of
+topology so suppose a and this gives the
+
+ align:start position:0%
+topology so suppose a and this gives the
+ 
+
+ align:start position:0%
+topology so suppose a and this gives the
+same B field but are not related are not
+
+ align:start position:0%
+same B field but are not related are not
+ 
+
+ align:start position:0%
+same B field but are not related are not
+related by a gauge transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they then these are in equivalent e/m
+
+ align:start position:0%
+they then these are in equivalent e/m
+ 
+
+ align:start position:0%
+they then these are in equivalent e/m
+fields they could have different quantum
+
+ align:start position:0%
+fields they could have different quantum
+ 
+
+ align:start position:0%
+fields they could have different quantum
+mechanics and we will see that so one
+
+ align:start position:0%
+mechanics and we will see that so one
+ 
+
+ align:start position:0%
+mechanics and we will see that so one
+example is what people call Wilson loops
+
+ align:start position:0%
+example is what people call Wilson loops
+ 
+
+ align:start position:0%
+example is what people call Wilson loops
+Wilson loops correspond to some closed
+
+ align:start position:0%
+Wilson loops correspond to some closed
+ 
+
+ align:start position:0%
+Wilson loops correspond to some closed
+curve in space that you cannot contract
+
+ align:start position:0%
+curve in space that you cannot contract
+ 
+
+ align:start position:0%
+curve in space that you cannot contract
+of course in Binkowski space in this
+
+ align:start position:0%
+of course in Binkowski space in this
+ 
+
+ align:start position:0%
+of course in Binkowski space in this
+room I can contract anything but
+
+ align:start position:0%
+room I can contract anything but
+ 
+
+ align:start position:0%
+room I can contract anything but
+sometimes if you live in a torus or your
+
+ align:start position:0%
+sometimes if you live in a torus or your
+ 
+
+ align:start position:0%
+sometimes if you live in a torus or your
+sample is on a sphere or something you
+
+ align:start position:0%
+sample is on a sphere or something you
+ 
+
+ align:start position:0%
+sample is on a sphere or something you
+may not be able to contract a curve
+
+ align:start position:0%
+may not be able to contract a curve
+ 
+
+ align:start position:0%
+may not be able to contract a curve
+along that curve you can put a vector
+
+ align:start position:0%
+along that curve you can put a vector
+ 
+
+ align:start position:0%
+along that curve you can put a vector
+potential that is pointing tangent to
+
+ align:start position:0%
+potential that is pointing tangent to
+ 
+
+ align:start position:0%
+potential that is pointing tangent to
+the curve all the time and it's a
+
+ align:start position:0%
+the curve all the time and it's a
+ 
+
+ align:start position:0%
+the curve all the time and it's a
+constant a constant vector potential
+
+ align:start position:0%
+constant a constant vector potential
+ 
+
+ align:start position:0%
+constant a constant vector potential
+that concept vector potential has zero B
+
+ align:start position:0%
+that concept vector potential has zero B
+ 
+
+ align:start position:0%
+that concept vector potential has zero B
+and zero electric field but if that
+
+ align:start position:0%
+and zero electric field but if that
+ 
+
+ align:start position:0%
+and zero electric field but if that
+constant is small or that constant is
+
+ align:start position:0%
+constant is small or that constant is
+ 
+
+ align:start position:0%
+constant is small or that constant is
+big is in equivalent you won't find the
+
+ align:start position:0%
+big is in equivalent you won't find the
+ 
+
+ align:start position:0%
+big is in equivalent you won't find the
+gauge transformation that transforms
+
+ align:start position:0%
+gauge transformation that transforms
+ 
+
+ align:start position:0%
+gauge transformation that transforms
+each other and therefore those would be
+
+ align:start position:0%
+each other and therefore those would be
+ 
+
+ align:start position:0%
+each other and therefore those would be
+configurations of electromagnetic fields
+
+ align:start position:0%
+configurations of electromagnetic fields
+ 
+
+ align:start position:0%
+configurations of electromagnetic fields
+that give you the same a and B but are
+
+ align:start position:0%
+that give you the same a and B but are
+ 
+
+ align:start position:0%
+that give you the same a and B but are
+in equivalent so that's the first
+
+ align:start position:0%
+in equivalent so that's the first
+ 
+
+ align:start position:0%
+in equivalent so that's the first
+curious effect there is another curious
+
+ align:start position:0%
+curious effect there is another curious
+ 
+
+ align:start position:0%
+curious effect there is another curious
+effect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and quantum mechanics is forcing you to
+
+ align:start position:0%
+and quantum mechanics is forcing you to
+ 
+
+ align:start position:0%
+and quantum mechanics is forcing you to
+do that that's the main thing so the
+
+ align:start position:0%
+do that that's the main thing so the
+ 
+
+ align:start position:0%
+do that that's the main thing so the
+second curious effect is given and E and
+
+ align:start position:0%
+second curious effect is given and E and
+ 
+
+ align:start position:0%
+second curious effect is given and E and
+B that satisfy Maxwell's equation are
+
+ align:start position:0%
+B that satisfy Maxwell's equation are
+ 
+
+ align:start position:0%
+B that satisfy Maxwell's equation are
+this this allowed fields so you
+
+ align:start position:0%
+this this allowed fields so you
+ 
+
+ align:start position:0%
+this this allowed fields so you
+somebody's gives you an e field and a B
+
+ align:start position:0%
+somebody's gives you an e field and a B
+ 
+
+ align:start position:0%
+somebody's gives you an e field and a B
+field and you say ok I'm going to check
+
+ align:start position:0%
+field and you say ok I'm going to check
+ 
+
+ align:start position:0%
+field and you say ok I'm going to check
+if these are possible physical electric
+
+ align:start position:0%
+if these are possible physical electric
+ 
+
+ align:start position:0%
+if these are possible physical electric
+and magnetic fields and then you go and
+
+ align:start position:0%
+and magnetic fields and then you go and
+ 
+
+ align:start position:0%
+and magnetic fields and then you go and
+check Maxwell's equations and Maxwell's
+
+ align:start position:0%
+check Maxwell's equations and Maxwell's
+ 
+
+ align:start position:0%
+check Maxwell's equations and Maxwell's
+equations work out they're all satisfied
+
+ align:start position:0%
+equations work out they're all satisfied
+ 
+
+ align:start position:0%
+equations work out they're all satisfied
+you say ok this is good
+
+ align:start position:0%
+you say ok this is good
+ 
+
+ align:start position:0%
+you say ok this is good
+those electric and magnetic fields are
+
+ align:start position:0%
+those electric and magnetic fields are
+ 
+
+ align:start position:0%
+those electric and magnetic fields are
+fine not so quick you to be sure those
+
+ align:start position:0%
+fine not so quick you to be sure those
+ 
+
+ align:start position:0%
+fine not so quick you to be sure those
+electric and magnetic fields are fine
+
+ align:start position:0%
+electric and magnetic fields are fine
+ 
+
+ align:start position:0%
+electric and magnetic fields are fine
+you should give me a Phi and an A that
+
+ align:start position:0%
+you should give me a Phi and an A that
+ 
+
+ align:start position:0%
+you should give me a Phi and an A that
+gives rise to them because fundamentally
+
+ align:start position:0%
+gives rise to them because fundamentally
+ 
+
+ align:start position:0%
+gives rise to them because fundamentally
+the electromagnetic fields are a and Phi
+
+ align:start position:0%
+the electromagnetic fields are a and Phi
+ 
+
+ align:start position:0%
+the electromagnetic fields are a and Phi
+and those you need anyway to do quantum
+
+ align:start position:0%
+and those you need anyway to do quantum
+ 
+
+ align:start position:0%
+and those you need anyway to do quantum
+mechanics with it so if you have an
+
+ align:start position:0%
+mechanics with it so if you have an
+ 
+
+ align:start position:0%
+mechanics with it so if you have an
+electromagnetic field that you kind of
+
+ align:start position:0%
+electromagnetic field that you kind of
+ 
+
+ align:start position:0%
+electromagnetic field that you kind of
+do part of mechanics with it you would
+
+ align:start position:0%
+do part of mechanics with it you would
+ 
+
+ align:start position:0%
+do part of mechanics with it you would
+be suspicious so you need to find Phi
+
+ align:start position:0%
+be suspicious so you need to find Phi
+ 
+
+ align:start position:0%
+be suspicious so you need to find Phi
+and a are this allowed only if you can
+
+ align:start position:0%
+and a are this allowed only if you can
+ 
+
+ align:start position:0%
+and a are this allowed only if you can
+find a Phi and a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and sometimes that can fail on a Taurus
+
+ align:start position:0%
+and sometimes that can fail on a Taurus
+ 
+
+ align:start position:0%
+and sometimes that can fail on a Taurus
+again a Taurus you know we've described
+
+ align:start position:0%
+again a Taurus you know we've described
+ 
+
+ align:start position:0%
+again a Taurus you know we've described
+in this course a circle as the line X
+
+ align:start position:0%
+in this course a circle as the line X
+ 
+
+ align:start position:0%
+in this course a circle as the line X
+identified with X plus L so here is L
+
+ align:start position:0%
+identified with X plus L so here is L
+ 
+
+ align:start position:0%
+identified with X plus L so here is L
+and you identify a Taurus can be done by
+
+ align:start position:0%
+and you identify a Taurus can be done by
+ 
+
+ align:start position:0%
+and you identify a Taurus can be done by
+taking a piece of the plane and
+
+ align:start position:0%
+taking a piece of the plane and
+ 
+
+ align:start position:0%
+taking a piece of the plane and
+identifying this with line with that and
+
+ align:start position:0%
+identifying this with line with that and
+ 
+
+ align:start position:0%
+identifying this with line with that and
+this line with this line so you'll glue
+
+ align:start position:0%
+this line with this line so you'll glue
+ 
+
+ align:start position:0%
+this line with this line so you'll glue
+this form a cylinder and then you glue
+
+ align:start position:0%
+this form a cylinder and then you glue
+ 
+
+ align:start position:0%
+this form a cylinder and then you glue
+the other ends on a Taurus you can put a
+
+ align:start position:0%
+the other ends on a Taurus you can put a
+ 
+
+ align:start position:0%
+the other ends on a Taurus you can put a
+constant magnetic field at constant
+
+ align:start position:0%
+constant magnetic field at constant
+ 
+
+ align:start position:0%
+constant magnetic field at constant
+magnetic field satisfies Maxwell's
+
+ align:start position:0%
+magnetic field satisfies Maxwell's
+ 
+
+ align:start position:0%
+magnetic field satisfies Maxwell's
+equations so you say oh so you can put
+
+ align:start position:0%
+equations so you say oh so you can put
+ 
+
+ align:start position:0%
+equations so you say oh so you can put
+any constant magnetic field in a Taurus
+
+ align:start position:0%
+any constant magnetic field in a Taurus
+ 
+
+ align:start position:0%
+any constant magnetic field in a Taurus
+wrong the vector potential has trouble
+
+ align:start position:0%
+wrong the vector potential has trouble
+ 
+
+ align:start position:0%
+wrong the vector potential has trouble
+existing and only for a particular
+
+ align:start position:0%
+existing and only for a particular
+ 
+
+ align:start position:0%
+existing and only for a particular
+values of the magnetic field there's a
+
+ align:start position:0%
+values of the magnetic field there's a
+ 
+
+ align:start position:0%
+values of the magnetic field there's a
+consistent vector potential you get the
+
+ align:start position:0%
+consistent vector potential you get the
+ 
+
+ align:start position:0%
+consistent vector potential you get the
+quantization of the flux of the magnetic
+
+ align:start position:0%
+quantization of the flux of the magnetic
+ 
+
+ align:start position:0%
+quantization of the flux of the magnetic
+field so that's another example and E
+
+ align:start position:0%
+field so that's another example and E
+ 
+
+ align:start position:0%
+field so that's another example and E
+and a B a constant magnetic field on a
+
+ align:start position:0%
+and a B a constant magnetic field on a
+ 
+
+ align:start position:0%
+and a B a constant magnetic field on a
+torus satisfies every Maxwell equation
+
+ align:start position:0%
+torus satisfies every Maxwell equation
+ 
+
+ align:start position:0%
+torus satisfies every Maxwell equation
+you may want to do but still is not a
+
+ align:start position:0%
+you may want to do but still is not a
+ 
+
+ align:start position:0%
+you may want to do but still is not a
+valid electromagnetic field because
+
+ align:start position:0%
+valid electromagnetic field because
+ 
+
+ align:start position:0%
+valid electromagnetic field because
+there's no a and Phi that give rise to
+
+ align:start position:0%
+there's no a and Phi that give rise to
+ 
+
+ align:start position:0%
+there's no a and Phi that give rise to
+it so those are our lessons in why we
+
+ align:start position:0%
+it so those are our lessons in why we
+ 
+
+ align:start position:0%
+it so those are our lessons in why we
+need the vector potentials and really to
+
+ align:start position:0%
+need the vector potentials and really to
+ 
+
+ align:start position:0%
+need the vector potentials and really to
+describe physics in quantum mechanics
+
+ align:start position:0%
+describe physics in quantum mechanics
+ 
+
+ align:start position:0%
+describe physics in quantum mechanics
+electromagnetic physics and then let's
+
+ align:start position:0%
+electromagnetic physics and then let's
+ 
+
+ align:start position:0%
+electromagnetic physics and then let's
+write therefore the Schrodinger equation
+
+ align:start position:0%
+write therefore the Schrodinger equation
+ 
+
+ align:start position:0%
+write therefore the Schrodinger equation
+with the electromagnetic fields
\ No newline at end of file
diff --git a/xwgIkdBQku4.txt b/xwgIkdBQku4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e109fc7f8e98ae685fe1a317f4e60e3126d8fb1a
--- /dev/null
+++ b/xwgIkdBQku4.txt
@@ -0,0 +1,12691 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, welcome back.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So last week we spent the week um
+
+ align:start position:0%
+So last week we spent the week um
+ 
+
+ align:start position:0%
+So last week we spent the week um
+talking about policy search methods and
+
+ align:start position:0%
+talking about policy search methods and
+ 
+
+ align:start position:0%
+talking about policy search methods and
+trying to um make a distinction between
+
+ align:start position:0%
+trying to um make a distinction between
+ 
+
+ align:start position:0%
+trying to um make a distinction between
+those and the valuebased methods we
+
+ align:start position:0%
+those and the valuebased methods we
+ 
+
+ align:start position:0%
+those and the valuebased methods we
+started with. And by the end of the week
+
+ align:start position:0%
+started with. And by the end of the week
+ 
+
+ align:start position:0%
+started with. And by the end of the week
+we had a couple um pretty slick methods
+
+ align:start position:0%
+we had a couple um pretty slick methods
+ 
+
+ align:start position:0%
+we had a couple um pretty slick methods
+for optimizing
+
+ align:start position:0%
+for optimizing
+ 
+
+ align:start position:0%
+for optimizing
+an openloop trajectory of the system.
+
+ align:start position:0%
+an openloop trajectory of the system.
+ 
+
+ align:start position:0%
+an openloop trajectory of the system.
+Right? So we talked about at least two
+
+ align:start position:0%
+Right? So we talked about at least two
+ 
+
+ align:start position:0%
+Right? So we talked about at least two
+ways
+
+ align:start position:0%
+ways
+ 
+
+ align:start position:0%
+ways
+All
+
+ align:start position:0%
+All
+ 
+
+ align:start position:0%
+All
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right. So by open loop I mean it's a
+
+ align:start position:0%
+right. So by open loop I mean it's a
+ 
+
+ align:start position:0%
+right. So by open loop I mean it's a
+function of time not a function of
+
+ align:start position:0%
+function of time not a function of
+ 
+
+ align:start position:0%
+function of time not a function of
+state.
+
+ align:start position:0%
+state.
+ 
+
+ align:start position:0%
+state.
+We talked about the shooting methods,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right? Where we um
+
+ align:start position:0%
+right? Where we um
+ 
+
+ align:start position:0%
+right? Where we um
+evaluated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+J of alpha
+
+ align:start position:0%
+J of alpha
+ 
+
+ align:start position:0%
+J of alpha
+from X0
+
+ align:start position:0%
+from X0
+ 
+
+ align:start position:0%
+from X0
+time Z just by simulation,
+
+ align:start position:0%
+time Z just by simulation,
+ 
+
+ align:start position:0%
+time Z just by simulation,
+right? And
+
+ align:start position:0%
+right? And
+ 
+
+ align:start position:0%
+right? And
+we evaluated explicitly evaluated the
+
+ align:start position:0%
+we evaluated explicitly evaluated the
+ 
+
+ align:start position:0%
+we evaluated explicitly evaluated the
+gradients
+
+ align:start position:0%
+gradients
+ 
+
+ align:start position:0%
+gradients
+um by well I gave you two algorithms for
+
+ align:start position:0%
+um by well I gave you two algorithms for
+ 
+
+ align:start position:0%
+um by well I gave you two algorithms for
+it. I gave you one that I called back
+
+ align:start position:0%
+it. I gave you one that I called back
+ 
+
+ align:start position:0%
+it. I gave you one that I called back
+prop through time which is an adjoint
+
+ align:start position:0%
+prop through time which is an adjoint
+ 
+
+ align:start position:0%
+prop through time which is an adjoint
+method and another one that I called RT
+
+ align:start position:0%
+method and another one that I called RT
+ 
+
+ align:start position:0%
+method and another one that I called RT
+RL realtime recurrent learning which are
+
+ align:start position:0%
+RL realtime recurrent learning which are
+ 
+
+ align:start position:0%
+RL realtime recurrent learning which are
+the names from the neural network
+
+ align:start position:0%
+the names from the neural network
+ 
+
+ align:start position:0%
+the names from the neural network
+community but um perfectly good names
+
+ align:start position:0%
+community but um perfectly good names
+ 
+
+ align:start position:0%
+community but um perfectly good names
+for those methods.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And then the claim was that if you can
+
+ align:start position:0%
+And then the claim was that if you can
+ 
+
+ align:start position:0%
+And then the claim was that if you can
+compute those two things by simulation
+
+ align:start position:0%
+compute those two things by simulation
+ 
+
+ align:start position:0%
+compute those two things by simulation
+or some combination. So simulate forward
+
+ align:start position:0%
+or some combination. So simulate forward
+ 
+
+ align:start position:0%
+or some combination. So simulate forward
+simulation and then a back propagation
+
+ align:start position:0%
+simulation and then a back propagation
+ 
+
+ align:start position:0%
+simulation and then a back propagation
+path pass or a simulation which carried
+
+ align:start position:0%
+path pass or a simulation which carried
+ 
+
+ align:start position:0%
+path pass or a simulation which carried
+also the derivatives forward in time.
+
+ align:start position:0%
+also the derivatives forward in time.
+ 
+
+ align:start position:0%
+also the derivatives forward in time.
+Then we could hand those gradients to
+
+ align:start position:0%
+Then we could hand those gradients to
+ 
+
+ align:start position:0%
+Then we could hand those gradients to
+snapped or some other um
+
+ align:start position:0%
+snapped or some other um
+ 
+
+ align:start position:0%
+snapped or some other um
+nonlinear optimization package.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And if we're good, we can also lean on
+
+ align:start position:0%
+And if we're good, we can also lean on
+ 
+
+ align:start position:0%
+And if we're good, we can also lean on
+SNOP to handle things like final value
+
+ align:start position:0%
+SNOP to handle things like final value
+ 
+
+ align:start position:0%
+SNOP to handle things like final value
+constraints. If you want to make sure
+
+ align:start position:0%
+constraints. If you want to make sure
+ 
+
+ align:start position:0%
+constraints. If you want to make sure
+the trajectory succeeds in getting you
+
+ align:start position:0%
+the trajectory succeeds in getting you
+ 
+
+ align:start position:0%
+the trajectory succeeds in getting you
+exactly to the goal or if you want to
+
+ align:start position:0%
+exactly to the goal or if you want to
+ 
+
+ align:start position:0%
+exactly to the goal or if you want to
+make sure that your torqus are never
+
+ align:start position:0%
+make sure that your torqus are never
+ 
+
+ align:start position:0%
+make sure that your torqus are never
+bigger than some maximum torque allowed,
+
+ align:start position:0%
+bigger than some maximum torque allowed,
+ 
+
+ align:start position:0%
+bigger than some maximum torque allowed,
+then you can take advantage of that.
+
+ align:start position:0%
+then you can take advantage of that.
+ 
+
+ align:start position:0%
+then you can take advantage of that.
+And the second method remember was a
+
+ align:start position:0%
+And the second method remember was a
+ 
+
+ align:start position:0%
+And the second method remember was a
+direct collocation method which we often
+
+ align:start position:0%
+direct collocation method which we often
+ 
+
+ align:start position:0%
+direct collocation method which we often
+abbreviate as durall.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the big idea there was to
+
+ align:start position:0%
+And the big idea there was to
+ 
+
+ align:start position:0%
+And the big idea there was to
+um overparameterize our optimization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with the openloop trajectory but also
+
+ align:start position:0%
+with the openloop trajectory but also
+ 
+
+ align:start position:0%
+with the openloop trajectory but also
+the state trajectory.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which makes coming up with gradients
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is simple.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um and then I have to enforce the
+
+ align:start position:0%
+Um and then I have to enforce the
+ 
+
+ align:start position:0%
+Um and then I have to enforce the
+constraint
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that x of let's say in discrete time
+
+ align:start position:0%
+that x of let's say in discrete time
+ 
+
+ align:start position:0%
+that x of let's say in discrete time
+here n plus one had better be um subject
+
+ align:start position:0%
+here n plus one had better be um subject
+ 
+
+ align:start position:0%
+here n plus one had better be um subject
+to the dynamics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, two very similar
+
+ align:start position:0%
+So, two very similar
+ 
+
+ align:start position:0%
+So, two very similar
+um methods of of trying to compute some
+
+ align:start position:0%
+um methods of of trying to compute some
+ 
+
+ align:start position:0%
+um methods of of trying to compute some
+openloop
+
+ align:start position:0%
+openloop
+ 
+
+ align:start position:0%
+openloop
+trajectory
+
+ align:start position:0%
+trajectory
+ 
+
+ align:start position:0%
+trajectory
+um as a function of time. Ultimately,
+
+ align:start position:0%
+um as a function of time. Ultimately,
+ 
+
+ align:start position:0%
+um as a function of time. Ultimately,
+what I care about is a is a is a set of
+
+ align:start position:0%
+what I care about is a is a is a set of
+ 
+
+ align:start position:0%
+what I care about is a is a is a set of
+um actions that I apply over time that
+
+ align:start position:0%
+um actions that I apply over time that
+ 
+
+ align:start position:0%
+um actions that I apply over time that
+will um get me to the goal or or
+
+ align:start position:0%
+will um get me to the goal or or
+ 
+
+ align:start position:0%
+will um get me to the goal or or
+minimize my cost function.
+
+ align:start position:0%
+minimize my cost function.
+ 
+
+ align:start position:0%
+minimize my cost function.
+In the case where I explicitly
+
+ align:start position:0%
+In the case where I explicitly
+ 
+
+ align:start position:0%
+In the case where I explicitly
+parameterize an openloop trajectory
+
+ align:start position:0%
+parameterize an openloop trajectory
+ 
+
+ align:start position:0%
+parameterize an openloop trajectory
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+both of these result in a solution which
+
+ align:start position:0%
+both of these result in a solution which
+ 
+
+ align:start position:0%
+both of these result in a solution which
+satisfies the pontreagan minimum
+
+ align:start position:0%
+satisfies the pontreagan minimum
+ 
+
+ align:start position:0%
+satisfies the pontreagan minimum
+principle
+
+ align:start position:0%
+principle
+ 
+
+ align:start position:0%
+principle
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+subject to discret discretization errors
+
+ align:start position:0%
+subject to discret discretization errors
+ 
+
+ align:start position:0%
+subject to discret discretization errors
+and things like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in there we discussed time right
+
+ align:start position:0%
+in there we discussed time right
+ 
+
+ align:start position:0%
+in there we discussed time right
+we did so right so so I should say
+
+ align:start position:0%
+we did so right so so I should say
+ 
+
+ align:start position:0%
+we did so right so so I should say
+subject to time discretization that's
+
+ align:start position:0%
+subject to time discretization that's
+ 
+
+ align:start position:0%
+subject to time discretization that's
+the the one place where
+
+ align:start position:0%
+the the one place where
+ 
+
+ align:start position:0%
+the the one place where
+technically it would satisfy a discrete
+
+ align:start position:0%
+technically it would satisfy a discrete
+ 
+
+ align:start position:0%
+technically it would satisfy a discrete
+time version of pantry's minimum
+
+ align:start position:0%
+time version of pantry's minimum
+ 
+
+ align:start position:0%
+time version of pantry's minimum
+principle
+
+ align:start position:0%
+principle
+ 
+
+ align:start position:0%
+principle
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+delta
+
+ align:start position:0%
+delta
+ 
+
+ align:start position:0%
+delta
+x or
+
+ align:start position:0%
+x or
+ 
+
+ align:start position:0%
+x or
+you can think of it either whichever way
+
+ align:start position:0%
+you can think of it either whichever way
+ 
+
+ align:start position:0%
+you can think of it either whichever way
+makes you um happier. So in fact um the
+
+ align:start position:0%
+makes you um happier. So in fact um the
+ 
+
+ align:start position:0%
+makes you um happier. So in fact um the
+parameters that you hand in maybe it's
+
+ align:start position:0%
+parameters that you hand in maybe it's
+ 
+
+ align:start position:0%
+parameters that you hand in maybe it's
+easier to think of it as a as a function
+
+ align:start position:0%
+easier to think of it as a as a function
+ 
+
+ align:start position:0%
+easier to think of it as a as a function
+a discrete function of time because
+
+ align:start position:0%
+a discrete function of time because
+ 
+
+ align:start position:0%
+a discrete function of time because
+you're going to hand it u at certain
+
+ align:start position:0%
+you're going to hand it u at certain
+ 
+
+ align:start position:0%
+you're going to hand it u at certain
+points in time and you're going to
+
+ align:start position:0%
+points in time and you're going to
+ 
+
+ align:start position:0%
+points in time and you're going to
+handle x at hand it x at certain points
+
+ align:start position:0%
+handle x at hand it x at certain points
+ 
+
+ align:start position:0%
+handle x at hand it x at certain points
+in time
+
+ align:start position:0%
+in time
+ 
+
+ align:start position:0%
+in time
+right and this discrete time update can
+
+ align:start position:0%
+right and this discrete time update can
+ 
+
+ align:start position:0%
+right and this discrete time update can
+be an oiler integration or a or a higher
+
+ align:start position:0%
+be an oiler integration or a or a higher
+ 
+
+ align:start position:0%
+be an oiler integration or a or a higher
+order integration of your continuous
+
+ align:start position:0%
+order integration of your continuous
+ 
+
+ align:start position:0%
+order integration of your continuous
+dynamics but you only satisfy the
+
+ align:start position:0%
+dynamics but you only satisfy the
+ 
+
+ align:start position:0%
+dynamics but you only satisfy the
+constraints at discreet intervals of
+
+ align:start position:0%
+constraints at discreet intervals of
+ 
+
+ align:start position:0%
+constraints at discreet intervals of
+time. Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. I did um give you a slightly more
+
+ align:start position:0%
+Okay. I did um give you a slightly more
+ 
+
+ align:start position:0%
+Okay. I did um give you a slightly more
+general I tried to to point out that
+
+ align:start position:0%
+general I tried to to point out that
+ 
+
+ align:start position:0%
+general I tried to to point out that
+these methods could equally well um
+
+ align:start position:0%
+these methods could equally well um
+ 
+
+ align:start position:0%
+these methods could equally well um
+compute um find good parameters of a
+
+ align:start position:0%
+compute um find good parameters of a
+ 
+
+ align:start position:0%
+compute um find good parameters of a
+feedback controller or something too,
+
+ align:start position:0%
+feedback controller or something too,
+ 
+
+ align:start position:0%
+feedback controller or something too,
+right? The simple case was when my
+
+ align:start position:0%
+right? The simple case was when my
+ 
+
+ align:start position:0%
+right? The simple case was when my
+parameters alpha were explicitly my
+
+ align:start position:0%
+parameters alpha were explicitly my
+ 
+
+ align:start position:0%
+parameters alpha were explicitly my
+control tape. But more generally, if you
+
+ align:start position:0%
+control tape. But more generally, if you
+ 
+
+ align:start position:0%
+control tape. But more generally, if you
+wanted to tune a a feedback controller,
+
+ align:start position:0%
+wanted to tune a a feedback controller,
+ 
+
+ align:start position:0%
+wanted to tune a a feedback controller,
+a linear feedback controller or a
+
+ align:start position:0%
+a linear feedback controller or a
+ 
+
+ align:start position:0%
+a linear feedback controller or a
+nonlinear feedback controller, a neural
+
+ align:start position:0%
+nonlinear feedback controller, a neural
+ 
+
+ align:start position:0%
+nonlinear feedback controller, a neural
+network or whatever it is, you can use
+
+ align:start position:0%
+network or whatever it is, you can use
+ 
+
+ align:start position:0%
+network or whatever it is, you can use
+the same methods to do that. Um, I would
+
+ align:start position:0%
+the same methods to do that. Um, I would
+ 
+
+ align:start position:0%
+the same methods to do that. Um, I would
+only make this statement in the case
+
+ align:start position:0%
+only make this statement in the case
+ 
+
+ align:start position:0%
+only make this statement in the case
+where the the um controller specifically
+
+ align:start position:0%
+where the the um controller specifically
+ 
+
+ align:start position:0%
+where the the um controller specifically
+is the openloop tape, right?
+
+ align:start position:0%
+is the openloop tape, right?
+ 
+
+ align:start position:0%
+is the openloop tape, right?
+Um because
+
+ align:start position:0%
+Um because
+ 
+
+ align:start position:0%
+Um because
+if I parameterize my trajectory by some
+
+ align:start position:0%
+if I parameterize my trajectory by some
+ 
+
+ align:start position:0%
+if I parameterize my trajectory by some
+feedback controller for instance then
+
+ align:start position:0%
+feedback controller for instance then
+ 
+
+ align:start position:0%
+feedback controller for instance then
+that's going to restrict the policy
+
+ align:start position:0%
+that's going to restrict the policy
+ 
+
+ align:start position:0%
+that's going to restrict the policy
+class that's going to restrict the class
+
+ align:start position:0%
+class that's going to restrict the class
+ 
+
+ align:start position:0%
+class that's going to restrict the class
+of tapes that I can look over which
+
+ align:start position:0%
+of tapes that I can look over which
+ 
+
+ align:start position:0%
+of tapes that I can look over which
+makes it a more compact more efficient
+
+ align:start position:0%
+makes it a more compact more efficient
+ 
+
+ align:start position:0%
+makes it a more compact more efficient
+uh way to solve your optimization but
+
+ align:start position:0%
+uh way to solve your optimization but
+ 
+
+ align:start position:0%
+uh way to solve your optimization but
+potentially prevents you from achieving
+
+ align:start position:0%
+potentially prevents you from achieving
+ 
+
+ align:start position:0%
+potentially prevents you from achieving
+a a perfect minima.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yep. So by by virtue of saying that they
+
+ align:start position:0%
+Yep. So by by virtue of saying that they
+ 
+
+ align:start position:0%
+Yep. So by by virtue of saying that they
+satisfy Pontriagen's minimum principle,
+
+ align:start position:0%
+satisfy Pontriagen's minimum principle,
+ 
+
+ align:start position:0%
+satisfy Pontriagen's minimum principle,
+we know that that's only a local optima.
+
+ align:start position:0%
+we know that that's only a local optima.
+ 
+
+ align:start position:0%
+we know that that's only a local optima.
+This this says that I can't make a small
+
+ align:start position:0%
+This this says that I can't make a small
+ 
+
+ align:start position:0%
+This this says that I can't make a small
+change in
+
+ align:start position:0%
+change in
+ 
+
+ align:start position:0%
+change in
+U to get better performance.
+
+ align:start position:0%
+U to get better performance.
+ 
+
+ align:start position:0%
+U to get better performance.
+Yeah, but it's only a a necessary
+
+ align:start position:0%
+Yeah, but it's only a a necessary
+ 
+
+ align:start position:0%
+Yeah, but it's only a a necessary
+condition for optimality, not a
+
+ align:start position:0%
+condition for optimality, not a
+ 
+
+ align:start position:0%
+condition for optimality, not a
+sufficient one.
+
+ align:start position:0%
+sufficient one.
+ 
+
+ align:start position:0%
+sufficient one.
+But there's a bigger problem with it
+
+ align:start position:0%
+But there's a bigger problem with it
+ 
+
+ align:start position:0%
+But there's a bigger problem with it
+with both of those
+
+ align:start position:0%
+with both of those
+ 
+
+ align:start position:0%
+with both of those
+and that's the fact that
+
+ align:start position:0%
+and that's the fact that
+ 
+
+ align:start position:0%
+and that's the fact that
+they're completely useless in real life
+
+ align:start position:0%
+they're completely useless in real life
+ 
+
+ align:start position:0%
+they're completely useless in real life
+unless I do one more step which is to
+
+ align:start position:0%
+unless I do one more step which is to
+ 
+
+ align:start position:0%
+unless I do one more step which is to
+stabilize the trajectories I get out.
+
+ align:start position:0%
+stabilize the trajectories I get out.
+ 
+
+ align:start position:0%
+stabilize the trajectories I get out.
+Okay. So finding some openloop
+
+ align:start position:0%
+Okay. So finding some openloop
+ 
+
+ align:start position:0%
+Okay. So finding some openloop
+trajectory
+
+ align:start position:0%
+trajectory
+ 
+
+ align:start position:0%
+trajectory
+um by these methods
+
+ align:start position:0%
+um by these methods
+ 
+
+ align:start position:0%
+um by these methods
+um satisfying Pontriagen's minimum
+
+ align:start position:0%
+um satisfying Pontriagen's minimum
+ 
+
+ align:start position:0%
+um satisfying Pontriagen's minimum
+principle fine but there's nothing um in
+
+ align:start position:0%
+principle fine but there's nothing um in
+ 
+
+ align:start position:0%
+principle fine but there's nothing um in
+this process that says if I don't if I
+
+ align:start position:0%
+this process that says if I don't if I
+ 
+
+ align:start position:0%
+this process that says if I don't if I
+change my initial conditions by epsilon
+
+ align:start position:0%
+change my initial conditions by epsilon
+ 
+
+ align:start position:0%
+change my initial conditions by epsilon
+I could completely diverge when I follow
+
+ align:start position:0%
+I could completely diverge when I follow
+ 
+
+ align:start position:0%
+I could completely diverge when I follow
+when I when I execute that openloop
+
+ align:start position:0%
+when I when I execute that openloop
+ 
+
+ align:start position:0%
+when I when I execute that openloop
+trajectory right if I change my
+
+ align:start position:0%
+trajectory right if I change my
+ 
+
+ align:start position:0%
+trajectory right if I change my
+simulation time step by a little bit I
+
+ align:start position:0%
+simulation time step by a little bit I
+ 
+
+ align:start position:0%
+simulation time step by a little bit I
+might diverge if I have modeling errors
+
+ align:start position:0%
+might diverge if I have modeling errors
+ 
+
+ align:start position:0%
+might diverge if I have modeling errors
+I might diverge. Okay,
+
+ align:start position:0%
+I might diverge. Okay,
+ 
+
+ align:start position:0%
+I might diverge. Okay,
+so in order to make these useful for a
+
+ align:start position:0%
+so in order to make these useful for a
+ 
+
+ align:start position:0%
+so in order to make these useful for a
+real system, we have to do another step
+
+ align:start position:0%
+real system, we have to do another step
+ 
+
+ align:start position:0%
+real system, we have to do another step
+which is trajectory stabilization. And
+
+ align:start position:0%
+which is trajectory stabilization. And
+ 
+
+ align:start position:0%
+which is trajectory stabilization. And
+it actually follows quite naturally from
+
+ align:start position:0%
+it actually follows quite naturally from
+ 
+
+ align:start position:0%
+it actually follows quite naturally from
+the things we've already talked about.
+
+ align:start position:0%
+the things we've already talked about.
+ 
+
+ align:start position:0%
+the things we've already talked about.
+Okay, so today we're going to give these
+
+ align:start position:0%
+Okay, so today we're going to give these
+ 
+
+ align:start position:0%
+Okay, so today we're going to give these
+guys teeth um with a trajectory
+
+ align:start position:0%
+guys teeth um with a trajectory
+ 
+
+ align:start position:0%
+guys teeth um with a trajectory
+optimization.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'll show you examples of a
+
+ align:start position:0%
+and I'll show you examples of a
+ 
+
+ align:start position:0%
+and I'll show you examples of a
+trajectory that's optimized beautifully
+
+ align:start position:0%
+trajectory that's optimized beautifully
+ 
+
+ align:start position:0%
+trajectory that's optimized beautifully
+for the pendulum even and if I simulated
+
+ align:start position:0%
+for the pendulum even and if I simulated
+ 
+
+ align:start position:0%
+for the pendulum even and if I simulated
+a little differently back, it just does
+
+ align:start position:0%
+a little differently back, it just does
+ 
+
+ align:start position:0%
+a little differently back, it just does
+the wrong thing. It never gets to the
+
+ align:start position:0%
+the wrong thing. It never gets to the
+ 
+
+ align:start position:0%
+the wrong thing. It never gets to the
+top. Okay, so we want to get rid of that
+
+ align:start position:0%
+top. Okay, so we want to get rid of that
+ 
+
+ align:start position:0%
+top. Okay, so we want to get rid of that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+problem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so the solution is is to design a
+
+ align:start position:0%
+Okay, so the solution is is to design a
+ 
+
+ align:start position:0%
+Okay, so the solution is is to design a
+trajectory stabilization.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for those of you that that have been
+
+ align:start position:0%
+for those of you that that have been
+ 
+
+ align:start position:0%
+for those of you that that have been
+playing with robots for many years, when
+
+ align:start position:0%
+playing with robots for many years, when
+ 
+
+ align:start position:0%
+playing with robots for many years, when
+you hear hear trajectory stabilization,
+
+ align:start position:0%
+you hear hear trajectory stabilization,
+ 
+
+ align:start position:0%
+you hear hear trajectory stabilization,
+what do you think of? What kind of
+
+ align:start position:0%
+what do you think of? What kind of
+ 
+
+ align:start position:0%
+what do you think of? What kind of
+tricks do people use for trajectory
+
+ align:start position:0%
+tricks do people use for trajectory
+ 
+
+ align:start position:0%
+tricks do people use for trajectory
+stabilization?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sliding surfaces.
+
+ align:start position:0%
+Sliding surfaces.
+ 
+
+ align:start position:0%
+Sliding surfaces.
+Sliding surfaces. That's a that's a good
+
+ align:start position:0%
+Sliding surfaces. That's a that's a good
+ 
+
+ align:start position:0%
+Sliding surfaces. That's a that's a good
+one for slot. Often will design a a
+
+ align:start position:0%
+one for slot. Often will design a a
+ 
+
+ align:start position:0%
+one for slot. Often will design a a
+sliding surface and and squish the
+
+ align:start position:0%
+sliding surface and and squish the
+ 
+
+ align:start position:0%
+sliding surface and and squish the
+aerodynamics, right?
+
+ align:start position:0%
+aerodynamics, right?
+ 
+
+ align:start position:0%
+aerodynamics, right?
+Um I mean that's that's actually pretty
+
+ align:start position:0%
+Um I mean that's that's actually pretty
+ 
+
+ align:start position:0%
+Um I mean that's that's actually pretty
+encompassing. I guess that's what I
+
+ align:start position:0%
+encompassing. I guess that's what I
+ 
+
+ align:start position:0%
+encompassing. I guess that's what I
+think a lot of the trajectory um
+
+ align:start position:0%
+think a lot of the trajectory um
+ 
+
+ align:start position:0%
+think a lot of the trajectory um
+stabilizers are based on sliding modes
+
+ align:start position:0%
+stabilizers are based on sliding modes
+ 
+
+ align:start position:0%
+stabilizers are based on sliding modes
+or feedback linearization in some form.
+
+ align:start position:0%
+or feedback linearization in some form.
+ 
+
+ align:start position:0%
+or feedback linearization in some form.
+Okay. And all I'll say about it is that
+
+ align:start position:0%
+Okay. And all I'll say about it is that
+ 
+
+ align:start position:0%
+Okay. And all I'll say about it is that
+the story is sort of the same as
+
+ align:start position:0%
+the story is sort of the same as
+ 
+
+ align:start position:0%
+the story is sort of the same as
+everything we've said. If you have a
+
+ align:start position:0%
+everything we've said. If you have a
+ 
+
+ align:start position:0%
+everything we've said. If you have a
+fully actuated system, it's not hard to
+
+ align:start position:0%
+fully actuated system, it's not hard to
+ 
+
+ align:start position:0%
+fully actuated system, it's not hard to
+design a trajectory stabilizer.
+
+ align:start position:0%
+design a trajectory stabilizer.
+ 
+
+ align:start position:0%
+design a trajectory stabilizer.
+Okay. A good sliding mode controller
+
+ align:start position:0%
+Okay. A good sliding mode controller
+ 
+
+ align:start position:0%
+Okay. A good sliding mode controller
+could take advant could could work uh
+
+ align:start position:0%
+could take advant could could work uh
+ 
+
+ align:start position:0%
+could take advant could could work uh
+even for an underactuated system. But I
+
+ align:start position:0%
+even for an underactuated system. But I
+ 
+
+ align:start position:0%
+even for an underactuated system. But I
+think there's a I prefer um the linear
+
+ align:start position:0%
+think there's a I prefer um the linear
+ 
+
+ align:start position:0%
+think there's a I prefer um the linear
+quadratic form of these trajectory
+
+ align:start position:0%
+quadratic form of these trajectory
+ 
+
+ align:start position:0%
+quadratic form of these trajectory
+stabilizers. Okay. So um we want to do a
+
+ align:start position:0%
+stabilizers. Okay. So um we want to do a
+ 
+
+ align:start position:0%
+stabilizers. Okay. So um we want to do a
+trajectory stabilization that's suitable
+
+ align:start position:0%
+trajectory stabilization that's suitable
+ 
+
+ align:start position:0%
+trajectory stabilization that's suitable
+for underactuated systems. Right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the approach is going to be with
+
+ align:start position:0%
+And the approach is going to be with
+ 
+
+ align:start position:0%
+And the approach is going to be with
+LQR.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, if we're going to use LQR, we
+
+ align:start position:0%
+Okay. So, if we're going to use LQR, we
+ 
+
+ align:start position:0%
+Okay. So, if we're going to use LQR, we
+better be able to linearize our system.
+
+ align:start position:0%
+better be able to linearize our system.
+ 
+
+ align:start position:0%
+better be able to linearize our system.
+So far when we've done the
+
+ align:start position:0%
+So far when we've done the
+ 
+
+ align:start position:0%
+So far when we've done the
+linearizations
+
+ align:start position:0%
+linearizations
+ 
+
+ align:start position:0%
+linearizations
+um we've only done them at fixed points.
+
+ align:start position:0%
+um we've only done them at fixed points.
+ 
+
+ align:start position:0%
+um we've only done them at fixed points.
+Okay. Um so the first thing we have to
+
+ align:start position:0%
+Okay. Um so the first thing we have to
+ 
+
+ align:start position:0%
+Okay. Um so the first thing we have to
+ask ourselves is what happens if we um
+
+ align:start position:0%
+ask ourselves is what happens if we um
+ 
+
+ align:start position:0%
+ask ourselves is what happens if we um
+try to linearize at a more arbitrary
+
+ align:start position:0%
+try to linearize at a more arbitrary
+ 
+
+ align:start position:0%
+try to linearize at a more arbitrary
+point in state space. Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's say I've got the system x dot
+
+ align:start position:0%
+So let's say I've got the system x dot
+ 
+
+ align:start position:0%
+So let's say I've got the system x dot
+is= f ofxu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now I want to linearize around um
+
+ align:start position:0%
+and now I want to linearize around um
+ 
+
+ align:start position:0%
+and now I want to linearize around um
+some x knot u knot but not necessarily a
+
+ align:start position:0%
+some x knot u knot but not necessarily a
+ 
+
+ align:start position:0%
+some x knot u knot but not necessarily a
+carefully chosen x not you not just
+
+ align:start position:0%
+carefully chosen x not you not just
+ 
+
+ align:start position:0%
+carefully chosen x not you not just
+something random in state space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the tailor expansion of This
+
+ align:start position:0%
+the tailor expansion of This
+ 
+
+ align:start position:0%
+the tailor expansion of This
+says that this thing is going to be
+
+ align:start position:0%
+says that this thing is going to be
+ 
+
+ align:start position:0%
+says that this thing is going to be
+approximately
+
+ align:start position:0%
+approximately
+ 
+
+ align:start position:0%
+approximately
+f ofx 0 u0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+partial f partial x evaluated x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And we called this before A and
+
+ align:start position:0%
+Okay. And we called this before A and
+ 
+
+ align:start position:0%
+Okay. And we called this before A and
+this B. And so that thing we can
+
+ align:start position:0%
+this B. And so that thing we can
+ 
+
+ align:start position:0%
+this B. And so that thing we can
+actually write as in general
+
+ align:start position:0%
+actually write as in general
+ 
+
+ align:start position:0%
+actually write as in general
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the case where
+
+ align:start position:0%
+in the case where
+ 
+
+ align:start position:0%
+in the case where
+f of x not if x not was a fixed point of
+
+ align:start position:0%
+f of x not if x not was a fixed point of
+ 
+
+ align:start position:0%
+f of x not if x not was a fixed point of
+the system that that term disappears.
+
+ align:start position:0%
+the system that that term disappears.
+ 
+
+ align:start position:0%
+the system that that term disappears.
+But you know be careful if you're doing
+
+ align:start position:0%
+But you know be careful if you're doing
+ 
+
+ align:start position:0%
+But you know be careful if you're doing
+your linearization out here um if you're
+
+ align:start position:0%
+your linearization out here um if you're
+ 
+
+ align:start position:0%
+your linearization out here um if you're
+at not at a fixed point. If you have any
+
+ align:start position:0%
+at not at a fixed point. If you have any
+ 
+
+ align:start position:0%
+at not at a fixed point. If you have any
+velocity for instance then in the
+
+ align:start position:0%
+velocity for instance then in the
+ 
+
+ align:start position:0%
+velocity for instance then in the
+original xcoordinates
+
+ align:start position:0%
+original xcoordinates
+ 
+
+ align:start position:0%
+original xcoordinates
+um it's not actually the tailor
+
+ align:start position:0%
+um it's not actually the tailor
+ 
+
+ align:start position:0%
+um it's not actually the tailor
+expansion doesn't give you a linear
+
+ align:start position:0%
+expansion doesn't give you a linear
+ 
+
+ align:start position:0%
+expansion doesn't give you a linear
+system. It gives you some aphine system.
+
+ align:start position:0%
+system. It gives you some aphine system.
+ 
+
+ align:start position:0%
+system. It gives you some aphine system.
+This thing is harder to work with. Not
+
+ align:start position:0%
+This thing is harder to work with. Not
+ 
+
+ align:start position:0%
+This thing is harder to work with. Not
+incredibly harder but harder to work
+
+ align:start position:0%
+incredibly harder but harder to work
+ 
+
+ align:start position:0%
+incredibly harder but harder to work
+with. Okay. So the trick is the solution
+
+ align:start position:0%
+with. Okay. So the trick is the solution
+ 
+
+ align:start position:0%
+with. Okay. So the trick is the solution
+is quite simple but I just wanted to
+
+ align:start position:0%
+is quite simple but I just wanted to
+ 
+
+ align:start position:0%
+is quite simple but I just wanted to
+say it the bad way first so that so that
+
+ align:start position:0%
+say it the bad way first so that so that
+ 
+
+ align:start position:0%
+say it the bad way first so that so that
+you appreciate the good way right. Um,
+
+ align:start position:0%
+you appreciate the good way right. Um,
+ 
+
+ align:start position:0%
+you appreciate the good way right. Um,
+if we change coordinates
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we use instead for our coordinates
+
+ align:start position:0%
+and we use instead for our coordinates
+ 
+
+ align:start position:0%
+and we use instead for our coordinates
+the difference between
+
+ align:start position:0%
+the difference between
+ 
+
+ align:start position:0%
+the difference between
+um x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and x knot of t.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then xbar dot
+
+ align:start position:0%
+Then xbar dot
+ 
+
+ align:start position:0%
+Then xbar dot
+is going to be x dot minus
+
+ align:start position:0%
+is going to be x dot minus
+ 
+
+ align:start position:0%
+is going to be x dot minus
+x0 dot
+
+ align:start position:0%
+x0 dot
+ 
+
+ align:start position:0%
+x0 dot
+= x dot minus f ofx X0
+
+ align:start position:0%
+= x dot minus f ofx X0
+ 
+
+ align:start position:0%
+= x dot minus f ofx X0
+U0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is that C, right? This guy here is
+
+ align:start position:0%
+which is that C, right? This guy here is
+ 
+
+ align:start position:0%
+which is that C, right? This guy here is
+taken care of
+
+ align:start position:0%
+taken care of
+ 
+
+ align:start position:0%
+taken care of
+in this new coordinate system which
+
+ align:start position:0%
+in this new coordinate system which
+ 
+
+ align:start position:0%
+in this new coordinate system which
+allows me to write the whole thing as
+
+ align:start position:0%
+allows me to write the whole thing as
+ 
+
+ align:start position:0%
+allows me to write the whole thing as
+XAR dot
+
+ align:start position:0%
+XAR dot
+ 
+
+ align:start position:0%
+XAR dot
+equals A of XAR
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You with me on that? Linearizing a
+
+ align:start position:0%
+You with me on that? Linearizing a
+ 
+
+ align:start position:0%
+You with me on that? Linearizing a
+system at a more arbitrary point.
+
+ align:start position:0%
+system at a more arbitrary point.
+ 
+
+ align:start position:0%
+system at a more arbitrary point.
+Well, doing a tailor expansion results
+
+ align:start position:0%
+Well, doing a tailor expansion results
+ 
+
+ align:start position:0%
+Well, doing a tailor expansion results
+in a linear system only if you change
+
+ align:start position:0%
+in a linear system only if you change
+ 
+
+ align:start position:0%
+in a linear system only if you change
+coordinates to lie on some system
+
+ align:start position:0%
+coordinates to lie on some system
+ 
+
+ align:start position:0%
+coordinates to lie on some system
+trajectory. Okay? So x0 u0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um must be a solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of x of f of x u of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that equation
+
+ align:start position:0%
+that equation
+ 
+
+ align:start position:0%
+that equation
+and then the system reduces to uh to a
+
+ align:start position:0%
+and then the system reduces to uh to a
+ 
+
+ align:start position:0%
+and then the system reduces to uh to a
+linear system description. Okay. But the
+
+ align:start position:0%
+linear system description. Okay. But the
+ 
+
+ align:start position:0%
+linear system description. Okay. But the
+the cost you pay for this beautiful
+
+ align:start position:0%
+the cost you pay for this beautiful
+ 
+
+ align:start position:0%
+the cost you pay for this beautiful
+simple oh let me be even a little bit
+
+ align:start position:0%
+simple oh let me be even a little bit
+ 
+
+ align:start position:0%
+simple oh let me be even a little bit
+more careful. Okay. So um a here this
+
+ align:start position:0%
+more careful. Okay. So um a here this
+ 
+
+ align:start position:0%
+more careful. Okay. So um a here this
+partial f partial x
+
+ align:start position:0%
+partial f partial x
+ 
+
+ align:start position:0%
+partial f partial x
+is evaluated at x
+
+ align:start position:0%
+is evaluated at x
+ 
+
+ align:start position:0%
+is evaluated at x
+t u of t and in general a and b in this
+
+ align:start position:0%
+t u of t and in general a and b in this
+ 
+
+ align:start position:0%
+t u of t and in general a and b in this
+when I do this are functions of time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as well as x and t. Okay,
+
+ align:start position:0%
+as well as x and t. Okay,
+ 
+
+ align:start position:0%
+as well as x and t. Okay,
+that's a pretty important point.
+
+ align:start position:0%
+that's a pretty important point.
+ 
+
+ align:start position:0%
+that's a pretty important point.
+Okay, so if I'm willing to change
+
+ align:start position:0%
+Okay, so if I'm willing to change
+ 
+
+ align:start position:0%
+Okay, so if I'm willing to change
+coordinates to along to live along the
+
+ align:start position:0%
+coordinates to along to live along the
+ 
+
+ align:start position:0%
+coordinates to along to live along the
+trajectory, then the result is I can get
+
+ align:start position:0%
+trajectory, then the result is I can get
+ 
+
+ align:start position:0%
+trajectory, then the result is I can get
+this linear time varying model of the
+
+ align:start position:0%
+this linear time varying model of the
+ 
+
+ align:start position:0%
+this linear time varying model of the
+dynamics. Yeah, along feasible
+
+ align:start position:0%
+dynamics. Yeah, along feasible
+ 
+
+ align:start position:0%
+dynamics. Yeah, along feasible
+trajectories, system trajectories.
+
+ align:start position:0%
+trajectories, system trajectories.
+ 
+
+ align:start position:0%
+trajectories, system trajectories.
+The cost is that you have to work in a
+
+ align:start position:0%
+The cost is that you have to work in a
+ 
+
+ align:start position:0%
+The cost is that you have to work in a
+coordinate system that moves along your
+
+ align:start position:0%
+coordinate system that moves along your
+ 
+
+ align:start position:0%
+coordinate system that moves along your
+trajectory.
+
+ align:start position:0%
+trajectory.
+ 
+
+ align:start position:0%
+trajectory.
+Okay. So, we'll see where that comes in
+
+ align:start position:0%
+Okay. So, we'll see where that comes in
+ 
+
+ align:start position:0%
+Okay. So, we'll see where that comes in
+in a little bit. But the first question
+
+ align:start position:0%
+in a little bit. But the first question
+ 
+
+ align:start position:0%
+in a little bit. But the first question
+is, okay, let's say I've got this linear
+
+ align:start position:0%
+is, okay, let's say I've got this linear
+ 
+
+ align:start position:0%
+is, okay, let's say I've got this linear
+time varying um time varying linear
+
+ align:start position:0%
+time varying um time varying linear
+ 
+
+ align:start position:0%
+time varying um time varying linear
+system. Can I do all the things I want
+
+ align:start position:0%
+system. Can I do all the things I want
+ 
+
+ align:start position:0%
+system. Can I do all the things I want
+to do with that? Right? That's actually,
+
+ align:start position:0%
+to do with that? Right? That's actually,
+ 
+
+ align:start position:0%
+to do with that? Right? That's actually,
+you know, in most of our control
+
+ align:start position:0%
+you know, in most of our control
+ 
+
+ align:start position:0%
+you know, in most of our control
+classes, we end up doing LTI systems.
+
+ align:start position:0%
+classes, we end up doing LTI systems.
+ 
+
+ align:start position:0%
+classes, we end up doing LTI systems.
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+LTV systems linear time varying
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um are actually a fantastically rich
+
+ align:start position:0%
+um are actually a fantastically rich
+ 
+
+ align:start position:0%
+um are actually a fantastically rich
+class of systems.
+
+ align:start position:0%
+class of systems.
+ 
+
+ align:start position:0%
+class of systems.
+Okay, that we don't talk about enough I
+
+ align:start position:0%
+Okay, that we don't talk about enough I
+ 
+
+ align:start position:0%
+Okay, that we don't talk about enough I
+think in life. They're still linear
+
+ align:start position:0%
+think in life. They're still linear
+ 
+
+ align:start position:0%
+think in life. They're still linear
+systems, right? they superposition still
+
+ align:start position:0%
+systems, right? they superposition still
+ 
+
+ align:start position:0%
+systems, right? they superposition still
+holds.
+
+ align:start position:0%
+holds.
+ 
+
+ align:start position:0%
+holds.
+So what does that I mean if I have um if
+
+ align:start position:0%
+So what does that I mean if I have um if
+ 
+
+ align:start position:0%
+So what does that I mean if I have um if
+I have initial condition
+
+ align:start position:0%
+I have initial condition
+ 
+
+ align:start position:0%
+I have initial condition
+um one and some u trajectory
+
+ align:start position:0%
+um one and some u trajectory
+ 
+
+ align:start position:0%
+um one and some u trajectory
+one for t greater than equal to t0 and
+
+ align:start position:0%
+one for t greater than equal to t0 and
+ 
+
+ align:start position:0%
+one for t greater than equal to t0 and
+that gives me some resulting x
+
+ align:start position:0%
+that gives me some resulting x
+ 
+
+ align:start position:0%
+that gives me some resulting x
+trajectory out for t greater than t0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I have another solution with a
+
+ align:start position:0%
+and I have another solution with a
+ 
+
+ align:start position:0%
+and I have another solution with a
+different initial ition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and a different control,
+
+ align:start position:0%
+and a different control,
+ 
+
+ align:start position:0%
+and a different control,
+right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And that gives me a different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I call this x1 x2 for t greater than
+
+ align:start position:0%
+I call this x1 x2 for t greater than
+ 
+
+ align:start position:0%
+I call this x1 x2 for t greater than
+equal to t0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If I have that,
+
+ align:start position:0%
+If I have that,
+ 
+
+ align:start position:0%
+If I have that,
+then it better be the case that alpha 1
+
+ align:start position:0%
+then it better be the case that alpha 1
+ 
+
+ align:start position:0%
+then it better be the case that alpha 1
+x1 of t0
+
+ align:start position:0%
+x1 of t0
+ 
+
+ align:start position:0%
+x1 of t0
+plus alpha 2 x2 of t0
+
+ align:start position:0%
+plus alpha 2 x2 of t0
+ 
+
+ align:start position:0%
+plus alpha 2 x2 of t0
+plus alpha 1
+
+ align:start position:0%
+plus alpha 1
+ 
+
+ align:start position:0%
+plus alpha 1
+u1 tape plus alpha 2 u2 tape.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is going to result in a trajectory which
+
+ align:start position:0%
+is going to result in a trajectory which
+ 
+
+ align:start position:0%
+is going to result in a trajectory which
+is alpha 1 x1
+
+ align:start position:0%
+is alpha 1 x1
+ 
+
+ align:start position:0%
+is alpha 1 x1
+plus alpha 2 x2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's superposition right that's
+
+ align:start position:0%
+that's superposition right that's
+ 
+
+ align:start position:0%
+that's superposition right that's
+the defining characteristic of linear
+
+ align:start position:0%
+the defining characteristic of linear
+ 
+
+ align:start position:0%
+the defining characteristic of linear
+linearity
+
+ align:start position:0%
+linearity
+ 
+
+ align:start position:0%
+linearity
+and even though this is a richer class
+
+ align:start position:0%
+and even though this is a richer class
+ 
+
+ align:start position:0%
+and even though this is a richer class
+of systems these these um a of t x of t
+
+ align:start position:0%
+of systems these these um a of t x of t
+ 
+
+ align:start position:0%
+of systems these these um a of t x of t
+b of t u of t superposition still holds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in fact a lot of our derivations
+
+ align:start position:0%
+and in fact a lot of our derivations
+ 
+
+ align:start position:0%
+and in fact a lot of our derivations
+that we've done that are for linear
+
+ align:start position:0%
+that we've done that are for linear
+ 
+
+ align:start position:0%
+that we've done that are for linear
+systems still hold. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And so now the question is how do
+
+ align:start position:0%
+Okay. And so now the question is how do
+ 
+
+ align:start position:0%
+Okay. And so now the question is how do
+we design a how do we work with the fact
+
+ align:start position:0%
+we design a how do we work with the fact
+ 
+
+ align:start position:0%
+we design a how do we work with the fact
+that this thing is still easy you know
+
+ align:start position:0%
+that this thing is still easy you know
+ 
+
+ align:start position:0%
+that this thing is still easy you know
+and design a a controller that works
+
+ align:start position:0%
+and design a a controller that works
+ 
+
+ align:start position:0%
+and design a a controller that works
+with this new linearized system.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Maybe first I should break out my color
+
+ align:start position:0%
+Maybe first I should break out my color
+ 
+
+ align:start position:0%
+Maybe first I should break out my color
+chalk and make sure we have intuition
+
+ align:start position:0%
+chalk and make sure we have intuition
+ 
+
+ align:start position:0%
+chalk and make sure we have intuition
+about this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Do you understand what this is doing? If
+
+ align:start position:0%
+Do you understand what this is doing? If
+ 
+
+ align:start position:0%
+Do you understand what this is doing? If
+I do this time varying linearization,
+
+ align:start position:0%
+I do this time varying linearization,
+ 
+
+ align:start position:0%
+I do this time varying linearization,
+let me let me do an example on with the
+
+ align:start position:0%
+let me let me do an example on with the
+ 
+
+ align:start position:0%
+let me let me do an example on with the
+the pendulum here, right? our favorite
+
+ align:start position:0%
+the pendulum here, right? our favorite
+ 
+
+ align:start position:0%
+the pendulum here, right? our favorite
+theta
+
+ align:start position:0%
+theta
+ 
+
+ align:start position:0%
+theta
+theta dot.
+
+ align:start position:0%
+theta dot.
+ 
+
+ align:start position:0%
+theta dot.
+And let's say we carve up uh we find
+
+ align:start position:0%
+And let's say we carve up uh we find
+ 
+
+ align:start position:0%
+And let's say we carve up uh we find
+some um nice solution which gets me from
+
+ align:start position:0%
+some um nice solution which gets me from
+ 
+
+ align:start position:0%
+some um nice solution which gets me from
+my
+
+ align:start position:0%
+my
+ 
+
+ align:start position:0%
+my
+one fixed point to the other fix point.
+
+ align:start position:0%
+one fixed point to the other fix point.
+ 
+
+ align:start position:0%
+one fixed point to the other fix point.
+Um the ones we were getting were these
+
+ align:start position:0%
+Um the ones we were getting were these
+ 
+
+ align:start position:0%
+Um the ones we were getting were these
+pumpup trajectories which looked
+
+ align:start position:0%
+pumpup trajectories which looked
+ 
+
+ align:start position:0%
+pumpup trajectories which looked
+something like this.
+
+ align:start position:0%
+something like this.
+ 
+
+ align:start position:0%
+something like this.
+Right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm moving through state space here.
+
+ align:start position:0%
+I'm moving through state space here.
+ 
+
+ align:start position:0%
+I'm moving through state space here.
+And the dynamics here vary with state in
+
+ align:start position:0%
+And the dynamics here vary with state in
+ 
+
+ align:start position:0%
+And the dynamics here vary with state in
+a nonlinear way. Right? But if I have a
+
+ align:start position:0%
+a nonlinear way. Right? But if I have a
+ 
+
+ align:start position:0%
+a nonlinear way. Right? But if I have a
+trajectory, a feasible trajectory that
+
+ align:start position:0%
+trajectory, a feasible trajectory that
+ 
+
+ align:start position:0%
+trajectory, a feasible trajectory that
+goes through the re the relevant parts
+
+ align:start position:0%
+goes through the re the relevant parts
+ 
+
+ align:start position:0%
+goes through the re the relevant parts
+of state space, then this time varying
+
+ align:start position:0%
+of state space, then this time varying
+ 
+
+ align:start position:0%
+of state space, then this time varying
+linearization
+
+ align:start position:0%
+linearization
+ 
+
+ align:start position:0%
+linearization
+takes my nonlinear system,
+
+ align:start position:0%
+takes my nonlinear system,
+ 
+
+ align:start position:0%
+takes my nonlinear system,
+right? And makes it parameterized only
+
+ align:start position:0%
+right? And makes it parameterized only
+ 
+
+ align:start position:0%
+right? And makes it parameterized only
+instead of by being parameterized by by
+
+ align:start position:0%
+instead of by being parameterized by by
+ 
+
+ align:start position:0%
+instead of by being parameterized by by
+state, it's going to make it
+
+ align:start position:0%
+state, it's going to make it
+ 
+
+ align:start position:0%
+state, it's going to make it
+parameterized only by time along the
+
+ align:start position:0%
+parameterized only by time along the
+ 
+
+ align:start position:0%
+parameterized only by time along the
+trajectory.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right. The trick
+
+ align:start position:0%
+Right. The trick
+ 
+
+ align:start position:0%
+Right. The trick
+is the trajectory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+allows me to reparameterize my sort of
+
+ align:start position:0%
+allows me to reparameterize my sort of
+ 
+
+ align:start position:0%
+allows me to reparameterize my sort of
+nonlinearity.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in terms of time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+instead of state. And if I it sounds
+
+ align:start position:0%
+instead of state. And if I it sounds
+ 
+
+ align:start position:0%
+instead of state. And if I it sounds
+like a simple thing when I'm just
+
+ align:start position:0%
+like a simple thing when I'm just
+ 
+
+ align:start position:0%
+like a simple thing when I'm just
+reparameterizing it, but it makes all
+
+ align:start position:0%
+reparameterizing it, but it makes all
+ 
+
+ align:start position:0%
+reparameterizing it, but it makes all
+the difference in the world. If things
+
+ align:start position:0%
+the difference in the world. If things
+ 
+
+ align:start position:0%
+the difference in the world. If things
+are parameterized as a function of time
+
+ align:start position:0%
+are parameterized as a function of time
+ 
+
+ align:start position:0%
+are parameterized as a function of time
+and are otherwise linear, then I can do
+
+ align:start position:0%
+and are otherwise linear, then I can do
+ 
+
+ align:start position:0%
+and are otherwise linear, then I can do
+all kinds of computation on them. I can
+
+ align:start position:0%
+all kinds of computation on them. I can
+ 
+
+ align:start position:0%
+all kinds of computation on them. I can
+I can integrate the equations. I can
+
+ align:start position:0%
+I can integrate the equations. I can
+ 
+
+ align:start position:0%
+I can integrate the equations. I can
+design quadratic regulators on it. It
+
+ align:start position:0%
+design quadratic regulators on it. It
+ 
+
+ align:start position:0%
+design quadratic regulators on it. It
+makes all the difference in the world.
+
+ align:start position:0%
+makes all the difference in the world.
+ 
+
+ align:start position:0%
+makes all the difference in the world.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So lo, so what I'm effectively doing is
+
+ align:start position:0%
+So lo, so what I'm effectively doing is
+ 
+
+ align:start position:0%
+So lo, so what I'm effectively doing is
+coming up with local linear um
+
+ align:start position:0%
+coming up with local linear um
+ 
+
+ align:start position:0%
+coming up with local linear um
+representations of the dynamics sort of
+
+ align:start position:0%
+representations of the dynamics sort of
+ 
+
+ align:start position:0%
+representations of the dynamics sort of
+along the trajectory. I'm not sure if
+
+ align:start position:0%
+along the trajectory. I'm not sure if
+ 
+
+ align:start position:0%
+along the trajectory. I'm not sure if
+this is a helpful way for me to to draw
+
+ align:start position:0%
+this is a helpful way for me to to draw
+ 
+
+ align:start position:0%
+this is a helpful way for me to to draw
+it, but you can sort of think of this
+
+ align:start position:0%
+it, but you can sort of think of this
+ 
+
+ align:start position:0%
+it, but you can sort of think of this
+thing as approximating the dynamics
+
+ align:start position:0%
+thing as approximating the dynamics
+ 
+
+ align:start position:0%
+thing as approximating the dynamics
+along that trajectory. At every given
+
+ align:start position:0%
+along that trajectory. At every given
+ 
+
+ align:start position:0%
+along that trajectory. At every given
+instant in time, I'm going to use one of
+
+ align:start position:0%
+instant in time, I'm going to use one of
+ 
+
+ align:start position:0%
+instant in time, I'm going to use one of
+these sort of
+
+ align:start position:0%
+these sort of
+ 
+
+ align:start position:0%
+these sort of
+linear models. This is supposed to be
+
+ align:start position:0%
+linear models. This is supposed to be
+ 
+
+ align:start position:0%
+linear models. This is supposed to be
+some plane that you're driving through.
+
+ align:start position:0%
+some plane that you're driving through.
+ 
+
+ align:start position:0%
+some plane that you're driving through.
+Not sure if that's actually a helpful
+
+ align:start position:0%
+Not sure if that's actually a helpful
+ 
+
+ align:start position:0%
+Not sure if that's actually a helpful
+graphic but
+
+ align:start position:0%
+graphic but
+ 
+
+ align:start position:0%
+graphic but
+it's the way I think of it. Okay.
+
+ align:start position:0%
+it's the way I think of it. Okay.
+ 
+
+ align:start position:0%
+it's the way I think of it. Okay.
+And by virtue of taking a particular
+
+ align:start position:0%
+And by virtue of taking a particular
+ 
+
+ align:start position:0%
+And by virtue of taking a particular
+path through I can make locally linear
+
+ align:start position:0%
+path through I can make locally linear
+ 
+
+ align:start position:0%
+path through I can make locally linear
+models on which these things have you
+
+ align:start position:0%
+models on which these things have you
+ 
+
+ align:start position:0%
+models on which these things have you
+know igen vectors and igen values or
+
+ align:start position:0%
+know igen vectors and igen values or
+ 
+
+ align:start position:0%
+know igen vectors and igen values or
+whatever um that are valid in the
+
+ align:start position:0%
+whatever um that are valid in the
+ 
+
+ align:start position:0%
+whatever um that are valid in the
+neighborhood of the trajectory.
+
+ align:start position:0%
+neighborhood of the trajectory.
+ 
+
+ align:start position:0%
+neighborhood of the trajectory.
+Okay. So if you can imagine
+
+ align:start position:0%
+Okay. So if you can imagine
+ 
+
+ align:start position:0%
+Okay. So if you can imagine
+um even without any stabilization it
+
+ align:start position:0%
+um even without any stabilization it
+ 
+
+ align:start position:0%
+um even without any stabilization it
+could be that I um I could I could
+
+ align:start position:0%
+could be that I um I could I could
+ 
+
+ align:start position:0%
+could be that I um I could I could
+quickly assess the uh stability of my
+
+ align:start position:0%
+quickly assess the uh stability of my
+ 
+
+ align:start position:0%
+quickly assess the uh stability of my
+time varying linear model and
+
+ align:start position:0%
+time varying linear model and
+ 
+
+ align:start position:0%
+time varying linear model and
+trajectories in this linear model may
+
+ align:start position:0%
+trajectories in this linear model may
+ 
+
+ align:start position:0%
+trajectories in this linear model may
+converge to the nominal limit cycle or
+
+ align:start position:0%
+converge to the nominal limit cycle or
+ 
+
+ align:start position:0%
+converge to the nominal limit cycle or
+they may diverge depending on A and B.
+
+ align:start position:0%
+they may diverge depending on A and B.
+ 
+
+ align:start position:0%
+they may diverge depending on A and B.
+Yeah,
+
+ align:start position:0%
+Yeah,
+ 
+
+ align:start position:0%
+Yeah,
+right. Or they may blow up.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is by far the more common case.
+
+ align:start position:0%
+This is by far the more common case.
+ 
+
+ align:start position:0%
+This is by far the more common case.
+Unfortunately, you'd be very lucky to
+
+ align:start position:0%
+Unfortunately, you'd be very lucky to
+ 
+
+ align:start position:0%
+Unfortunately, you'd be very lucky to
+come out of a shooting method or a
+
+ align:start position:0%
+come out of a shooting method or a
+ 
+
+ align:start position:0%
+come out of a shooting method or a
+direct collocation method and end up
+
+ align:start position:0%
+direct collocation method and end up
+ 
+
+ align:start position:0%
+direct collocation method and end up
+with a system where if you played it
+
+ align:start position:0%
+with a system where if you played it
+ 
+
+ align:start position:0%
+with a system where if you played it
+out, it just happened to be a stable
+
+ align:start position:0%
+out, it just happened to be a stable
+ 
+
+ align:start position:0%
+out, it just happened to be a stable
+trajectory. Um, okay. But we can assess
+
+ align:start position:0%
+trajectory. Um, okay. But we can assess
+ 
+
+ align:start position:0%
+trajectory. Um, okay. But we can assess
+all that quickly with these time varying
+
+ align:start position:0%
+all that quickly with these time varying
+ 
+
+ align:start position:0%
+all that quickly with these time varying
+linearizations
+
+ align:start position:0%
+linearizations
+ 
+
+ align:start position:0%
+linearizations
+valid locally.
+
+ align:start position:0%
+valid locally.
+ 
+
+ align:start position:0%
+valid locally.
+Make sense? Yeah.
+
+ align:start position:0%
+Make sense? Yeah.
+ 
+
+ align:start position:0%
+Make sense? Yeah.
+So, I I think I missed some closing
+
+ align:start position:0%
+So, I I think I missed some closing
+ 
+
+ align:start position:0%
+So, I I think I missed some closing
+practices here. So, we talked about that
+
+ align:start position:0%
+practices here. So, we talked about that
+ 
+
+ align:start position:0%
+practices here. So, we talked about that
+there isn't bad way of doing this. This
+
+ align:start position:0%
+there isn't bad way of doing this. This
+ 
+
+ align:start position:0%
+there isn't bad way of doing this. This
+is not a bad way of doing this, right?
+
+ align:start position:0%
+is not a bad way of doing this, right?
+ 
+
+ align:start position:0%
+is not a bad way of doing this, right?
+when you're talking about it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I try to linearize if I do a tailor
+
+ align:start position:0%
+if I try to linearize if I do a tailor
+ 
+
+ align:start position:0%
+if I try to linearize if I do a tailor
+expansion of my system
+
+ align:start position:0%
+expansion of my system
+ 
+
+ align:start position:0%
+expansion of my system
+um in the original coordinate system
+
+ align:start position:0%
+um in the original coordinate system
+ 
+
+ align:start position:0%
+um in the original coordinate system
+which is x then it's not linear
+
+ align:start position:0%
+which is x then it's not linear
+ 
+
+ align:start position:0%
+which is x then it's not linear
+end parenthesis that that was the bad
+
+ align:start position:0%
+end parenthesis that that was the bad
+ 
+
+ align:start position:0%
+end parenthesis that that was the bad
+way to do it yeah good way to do it
+
+ align:start position:0%
+way to do it yeah good way to do it
+ 
+
+ align:start position:0%
+way to do it yeah good way to do it
+change the coordinates to a to a
+
+ align:start position:0%
+change the coordinates to a to a
+ 
+
+ align:start position:0%
+change the coordinates to a to a
+coordinate system which moves with the
+
+ align:start position:0%
+coordinate system which moves with the
+ 
+
+ align:start position:0%
+coordinate system which moves with the
+tra trajectory
+
+ align:start position:0%
+tra trajectory
+ 
+
+ align:start position:0%
+tra trajectory
+if you do that things become time
+
+ align:start position:0%
+if you do that things become time
+ 
+
+ align:start position:0%
+if you do that things become time
+varying linear good way. That was the
+
+ align:start position:0%
+varying linear good way. That was the
+ 
+
+ align:start position:0%
+varying linear good way. That was the
+good way to do it. And that's still an
+
+ align:start position:0%
+good way to do it. And that's still an
+ 
+
+ align:start position:0%
+good way to do it. And that's still an
+open parenthesy. We're still going.
+
+ align:start position:0%
+open parenthesy. We're still going.
+ 
+
+ align:start position:0%
+open parenthesy. We're still going.
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So our task now is to design um a
+
+ align:start position:0%
+Okay. So our task now is to design um a
+ 
+
+ align:start position:0%
+Okay. So our task now is to design um a
+time varying feedback controller. Since
+
+ align:start position:0%
+time varying feedback controller. Since
+ 
+
+ align:start position:0%
+time varying feedback controller. Since
+our model is time varying, you'd expect
+
+ align:start position:0%
+our model is time varying, you'd expect
+ 
+
+ align:start position:0%
+our model is time varying, you'd expect
+our solution to also be time varying
+
+ align:start position:0%
+our solution to also be time varying
+ 
+
+ align:start position:0%
+our solution to also be time varying
+which takes these bad unstable
+
+ align:start position:0%
+which takes these bad unstable
+ 
+
+ align:start position:0%
+which takes these bad unstable
+trajectories of the system and they
+
+ align:start position:0%
+trajectories of the system and they
+ 
+
+ align:start position:0%
+trajectories of the system and they
+really are. I'll show you you know
+
+ align:start position:0%
+really are. I'll show you you know
+ 
+
+ align:start position:0%
+really are. I'll show you you know
+simple pendulum. This trajectory comes
+
+ align:start position:0%
+simple pendulum. This trajectory comes
+ 
+
+ align:start position:0%
+simple pendulum. This trajectory comes
+out you change the actually if you just
+
+ align:start position:0%
+out you change the actually if you just
+ 
+
+ align:start position:0%
+out you change the actually if you just
+integrate in a different way it'll go
+
+ align:start position:0%
+integrate in a different way it'll go
+ 
+
+ align:start position:0%
+integrate in a different way it'll go
+off and do the wrong thing. It typically
+
+ align:start position:0%
+off and do the wrong thing. It typically
+ 
+
+ align:start position:0%
+off and do the wrong thing. It typically
+doesn't go off and add energy to the
+
+ align:start position:0%
+doesn't go off and add energy to the
+ 
+
+ align:start position:0%
+doesn't go off and add energy to the
+system so much. The ones I get I see
+
+ align:start position:0%
+system so much. The ones I get I see
+ 
+
+ align:start position:0%
+system so much. The ones I get I see
+I'll show you are are more they diverge
+
+ align:start position:0%
+I'll show you are are more they diverge
+ 
+
+ align:start position:0%
+I'll show you are are more they diverge
+in the other way and end up just
+
+ align:start position:0%
+in the other way and end up just
+ 
+
+ align:start position:0%
+in the other way and end up just
+floating around here for instance. um
+
+ align:start position:0%
+floating around here for instance. um
+ 
+
+ align:start position:0%
+floating around here for instance. um
+but they're not going to get you up
+
+ align:start position:0%
+but they're not going to get you up
+ 
+
+ align:start position:0%
+but they're not going to get you up
+here. Okay. So, can we design a time
+
+ align:start position:0%
+here. Okay. So, can we design a time
+ 
+
+ align:start position:0%
+here. Okay. So, can we design a time
+varying stabilizer that get that
+
+ align:start position:0%
+varying stabilizer that get that
+ 
+
+ align:start position:0%
+varying stabilizer that get that
+regulates that trajectory?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I did actually do um the original
+
+ align:start position:0%
+Okay, I did actually do um the original
+ 
+
+ align:start position:0%
+Okay, I did actually do um the original
+finite horizon LQR derivation
+
+ align:start position:0%
+finite horizon LQR derivation
+ 
+
+ align:start position:0%
+finite horizon LQR derivation
+on the board that day. Um definitely
+
+ align:start position:0%
+on the board that day. Um definitely
+ 
+
+ align:start position:0%
+on the board that day. Um definitely
+won't write all that again. But let me
+
+ align:start position:0%
+won't write all that again. But let me
+ 
+
+ align:start position:0%
+won't write all that again. But let me
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+that uh
+
+ align:start position:0%
+that uh
+ 
+
+ align:start position:0%
+that uh
+roughly nothing in that derivation
+
+ align:start position:0%
+roughly nothing in that derivation
+ 
+
+ align:start position:0%
+roughly nothing in that derivation
+breaks.
+
+ align:start position:0%
+breaks.
+ 
+
+ align:start position:0%
+breaks.
+I'm going to show you the important
+
+ align:start position:0%
+I'm going to show you the important
+ 
+
+ align:start position:0%
+I'm going to show you the important
+pieces. nothing in that derivation
+
+ align:start position:0%
+pieces. nothing in that derivation
+ 
+
+ align:start position:0%
+pieces. nothing in that derivation
+breaks surprisingly if a and b are now a
+
+ align:start position:0%
+breaks surprisingly if a and b are now a
+ 
+
+ align:start position:0%
+breaks surprisingly if a and b are now a
+function of time.
+
+ align:start position:0%
+function of time.
+ 
+
+ align:start position:0%
+function of time.
+Okay, so let's remember that um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+the LQR derivation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now I'm working with this x bar
+
+ align:start position:0%
+Now I'm working with this x bar
+ 
+
+ align:start position:0%
+Now I'm working with this x bar
+coordinate system.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And I want to design a cost
+
+ align:start position:0%
+Okay. And I want to design a cost
+ 
+
+ align:start position:0%
+Okay. And I want to design a cost
+function to minimize here which lives in
+
+ align:start position:0%
+function to minimize here which lives in
+ 
+
+ align:start position:0%
+function to minimize here which lives in
+this coordinate system again here. Let's
+
+ align:start position:0%
+this coordinate system again here. Let's
+ 
+
+ align:start position:0%
+this coordinate system again here. Let's
+say it's um the final
+
+ align:start position:0%
+say it's um the final
+ 
+
+ align:start position:0%
+say it's um the final
+horizon times QF.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um, I've been trying to use t little f
+
+ align:start position:0%
+Um, I've been trying to use t little f
+ 
+
+ align:start position:0%
+Um, I've been trying to use t little f
+since my transposes look like the final
+
+ align:start position:0%
+since my transposes look like the final
+ 
+
+ align:start position:0%
+since my transposes look like the final
+horizon time otherwise.
+
+ align:start position:0%
+horizon time otherwise.
+ 
+
+ align:start position:0%
+horizon time otherwise.
+0 to tf dt xar again transpose q plus u
+
+ align:start position:0%
+0 to tf dt xar again transpose q plus u
+ 
+
+ align:start position:0%
+0 to tf dt xar again transpose q plus u
+bar r uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay in the original lqr derivation we
+
+ align:start position:0%
+okay in the original lqr derivation we
+ 
+
+ align:start position:0%
+okay in the original lqr derivation we
+uh we guessed that the form that the
+
+ align:start position:0%
+uh we guessed that the form that the
+ 
+
+ align:start position:0%
+uh we guessed that the form that the
+optimal policy had the form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um xar s of t xar. That's still intact.
+
+ align:start position:0%
+um xar s of t xar. That's still intact.
+ 
+
+ align:start position:0%
+um xar s of t xar. That's still intact.
+That's a still a good assumption. This
+
+ align:start position:0%
+That's a still a good assumption. This
+ 
+
+ align:start position:0%
+That's a still a good assumption. This
+thing's
+
+ align:start position:0%
+thing's
+ 
+
+ align:start position:0%
+thing's
+linear. It's just in a different
+
+ align:start position:0%
+linear. It's just in a different
+ 
+
+ align:start position:0%
+linear. It's just in a different
+coordinate system.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we started cranking uh through the
+
+ align:start position:0%
+And we started cranking uh through the
+ 
+
+ align:start position:0%
+And we started cranking uh through the
+the sufficiency theorem, the the
+
+ align:start position:0%
+the sufficiency theorem, the the
+ 
+
+ align:start position:0%
+the sufficiency theorem, the the
+Hamilton Jacobe Bellman equation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we found that our optimal feedback
+
+ align:start position:0%
+And we found that our optimal feedback
+ 
+
+ align:start position:0%
+And we found that our optimal feedback
+policy our first of all our optimal cost
+
+ align:start position:0%
+policy our first of all our optimal cost
+ 
+
+ align:start position:0%
+policy our first of all our optimal cost
+to go was described by this ricotti
+
+ align:start position:0%
+to go was described by this ricotti
+ 
+
+ align:start position:0%
+to go was described by this ricotti
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+which was negative s of t is
+
+ align:start position:0%
+which was negative s of t is
+ 
+
+ align:start position:0%
+which was negative s of t is
+q minus s of t b r our inverse
+
+ align:start position:0%
+q minus s of t b r our inverse
+ 
+
+ align:start position:0%
+q minus s of t b r our inverse
+brpose S of T
+
+ align:start position:0%
+brpose S of T
+ 
+
+ align:start position:0%
+brpose S of T
+plus S of T A plus
+
+ align:start position:0%
+plus S of T A plus
+ 
+
+ align:start position:0%
+plus S of T A plus
+A transpose S of T. And it turns out
+
+ align:start position:0%
+A transpose S of T. And it turns out
+ 
+
+ align:start position:0%
+A transpose S of T. And it turns out
+that with this if you have a time
+
+ align:start position:0%
+that with this if you have a time
+ 
+
+ align:start position:0%
+that with this if you have a time
+varying A and B that it's exact same
+
+ align:start position:0%
+varying A and B that it's exact same
+ 
+
+ align:start position:0%
+varying A and B that it's exact same
+dynamics govern it.
+
+ align:start position:0%
+dynamics govern it.
+ 
+
+ align:start position:0%
+dynamics govern it.
+You just have your time dependence also
+
+ align:start position:0%
+You just have your time dependence also
+ 
+
+ align:start position:0%
+You just have your time dependence also
+in A and B.
+
+ align:start position:0%
+in A and B.
+ 
+
+ align:start position:0%
+in A and B.
+And that exact same ricotti equation
+
+ align:start position:0%
+And that exact same ricotti equation
+ 
+
+ align:start position:0%
+And that exact same ricotti equation
+works.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And our final value condition
+
+ align:start position:0%
+And our final value condition
+ 
+
+ align:start position:0%
+And our final value condition
+was just QF.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And you can see from this if if it if it
+
+ align:start position:0%
+And you can see from this if if it if it
+ 
+
+ align:start position:0%
+And you can see from this if if it if it
+didn't make a difference for me when um
+
+ align:start position:0%
+didn't make a difference for me when um
+ 
+
+ align:start position:0%
+didn't make a difference for me when um
+when A and B became functions of time,
+
+ align:start position:0%
+when A and B became functions of time,
+ 
+
+ align:start position:0%
+when A and B became functions of time,
+it's pretty simple, although less
+
+ align:start position:0%
+it's pretty simple, although less
+ 
+
+ align:start position:0%
+it's pretty simple, although less
+interesting I guess to if Q were to be a
+
+ align:start position:0%
+interesting I guess to if Q were to be a
+ 
+
+ align:start position:0%
+interesting I guess to if Q were to be a
+function of time, no problem. If R is a
+
+ align:start position:0%
+function of time, no problem. If R is a
+ 
+
+ align:start position:0%
+function of time, no problem. If R is a
+function of time, no problem, right?
+
+ align:start position:0%
+function of time, no problem, right?
+ 
+
+ align:start position:0%
+function of time, no problem, right?
+They still had to be um
+
+ align:start position:0%
+They still had to be um
+ 
+
+ align:start position:0%
+They still had to be um
+uh they still have to be positive
+
+ align:start position:0%
+uh they still have to be positive
+ 
+
+ align:start position:0%
+uh they still have to be positive
+definite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and symmetric.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The uh
+
+ align:start position:0%
+The uh
+ 
+
+ align:start position:0%
+The uh
+oops I did it the wrong way.
+
+ align:start position:0%
+oops I did it the wrong way.
+ 
+
+ align:start position:0%
+oops I did it the wrong way.
+Q can be zero but R cannot be zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so the LQR you know and love that
+
+ align:start position:0%
+Okay, so the LQR you know and love that
+ 
+
+ align:start position:0%
+Okay, so the LQR you know and love that
+you've used in mat lab um is the time um
+
+ align:start position:0%
+you've used in mat lab um is the time um
+ 
+
+ align:start position:0%
+you've used in mat lab um is the time um
+invariant infinite horizon LQR, right? I
+
+ align:start position:0%
+invariant infinite horizon LQR, right? I
+ 
+
+ align:start position:0%
+invariant infinite horizon LQR, right? I
+told you that if you cared about a
+
+ align:start position:0%
+told you that if you cared about a
+ 
+
+ align:start position:0%
+told you that if you cared about a
+finite horizon and you had a time
+
+ align:start position:0%
+finite horizon and you had a time
+ 
+
+ align:start position:0%
+finite horizon and you had a time
+invariant linear system, then suddenly
+
+ align:start position:0%
+invariant linear system, then suddenly
+ 
+
+ align:start position:0%
+invariant linear system, then suddenly
+you had to you couldn't just find the
+
+ align:start position:0%
+you had to you couldn't just find the
+ 
+
+ align:start position:0%
+you had to you couldn't just find the
+stationary points in this. Remember mat
+
+ align:start position:0%
+stationary points in this. Remember mat
+ 
+
+ align:start position:0%
+stationary points in this. Remember mat
+lab's solution just tells you the
+
+ align:start position:0%
+lab's solution just tells you the
+ 
+
+ align:start position:0%
+lab's solution just tells you the
+long-term behavior of s
+
+ align:start position:0%
+long-term behavior of s
+ 
+
+ align:start position:0%
+long-term behavior of s
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+in the time finite horizon time even the
+
+ align:start position:0%
+in the time finite horizon time even the
+ 
+
+ align:start position:0%
+in the time finite horizon time even the
+lti case which is the um a and b do not
+
+ align:start position:0%
+lti case which is the um a and b do not
+ 
+
+ align:start position:0%
+lti case which is the um a and b do not
+depend on time the linear time invariant
+
+ align:start position:0%
+depend on time the linear time invariant
+ 
+
+ align:start position:0%
+depend on time the linear time invariant
+case I still had to integrate back this
+
+ align:start position:0%
+case I still had to integrate back this
+ 
+
+ align:start position:0%
+case I still had to integrate back this
+ricotti equation in order to get my lqr
+
+ align:start position:0%
+ricotti equation in order to get my lqr
+ 
+
+ align:start position:0%
+ricotti equation in order to get my lqr
+controller okay it's no more expensive
+
+ align:start position:0%
+controller okay it's no more expensive
+ 
+
+ align:start position:0%
+controller okay it's no more expensive
+to do the same thing in the linear time
+
+ align:start position:0%
+to do the same thing in the linear time
+ 
+
+ align:start position:0%
+to do the same thing in the linear time
+varying feedback
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And the resulting controller is um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mu star is my nominal controller minus
+
+ align:start position:0%
+mu star is my nominal controller minus
+ 
+
+ align:start position:0%
+mu star is my nominal controller minus
+my r inverse
+
+ align:start position:0%
+my r inverse
+ 
+
+ align:start position:0%
+my r inverse
+brppose
+
+ align:start position:0%
+brppose
+ 
+
+ align:start position:0%
+brppose
+s of t xar.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+These equations come up enough that I
+
+ align:start position:0%
+These equations come up enough that I
+ 
+
+ align:start position:0%
+These equations come up enough that I
+you know this is these are pretty famous
+
+ align:start position:0%
+you know this is these are pretty famous
+ 
+
+ align:start position:0%
+you know this is these are pretty famous
+pretty important equations. So I those I
+
+ align:start position:0%
+pretty important equations. So I those I
+ 
+
+ align:start position:0%
+pretty important equations. So I those I
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+off the top of my head they come up all
+
+ align:start position:0%
+off the top of my head they come up all
+ 
+
+ align:start position:0%
+off the top of my head they come up all
+the time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And this is the resulting uh optimal
+
+ align:start position:0%
+And this is the resulting uh optimal
+ 
+
+ align:start position:0%
+And this is the resulting uh optimal
+trajectory which is my nominal
+
+ align:start position:0%
+trajectory which is my nominal
+ 
+
+ align:start position:0%
+trajectory which is my nominal
+trajectory
+
+ align:start position:0%
+trajectory
+ 
+
+ align:start position:0%
+trajectory
+plus my feedback gain which came out of
+
+ align:start position:0%
+plus my feedback gain which came out of
+ 
+
+ align:start position:0%
+plus my feedback gain which came out of
+my original LQR controller if you
+
+ align:start position:0%
+my original LQR controller if you
+ 
+
+ align:start position:0%
+my original LQR controller if you
+remember that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R and B are still.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yes. Good. So this I should definitely
+
+ align:start position:0%
+Yes. Good. So this I should definitely
+ 
+
+ align:start position:0%
+Yes. Good. So this I should definitely
+put a T in under B. Thank you. And R I
+
+ align:start position:0%
+put a T in under B. Thank you. And R I
+ 
+
+ align:start position:0%
+put a T in under B. Thank you. And R I
+haven't I haven't written that case but
+
+ align:start position:0%
+haven't I haven't written that case but
+ 
+
+ align:start position:0%
+haven't I haven't written that case but
+R could equally well be time dependent.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, some so something big just
+
+ align:start position:0%
+Okay. So, some so something big just
+ 
+
+ align:start position:0%
+Okay. So, some so something big just
+happened. Okay. Um I can take a really
+
+ align:start position:0%
+happened. Okay. Um I can take a really
+ 
+
+ align:start position:0%
+happened. Okay. Um I can take a really
+really complicated nonlinear system
+
+ align:start position:0%
+really complicated nonlinear system
+ 
+
+ align:start position:0%
+really complicated nonlinear system
+along some trajectory. If I find a good
+
+ align:start position:0%
+along some trajectory. If I find a good
+ 
+
+ align:start position:0%
+along some trajectory. If I find a good
+trajectory,
+
+ align:start position:0%
+trajectory,
+ 
+
+ align:start position:0%
+trajectory,
+um then I can actually linearize that
+
+ align:start position:0%
+um then I can actually linearize that
+ 
+
+ align:start position:0%
+um then I can actually linearize that
+system along the trajectory and
+
+ align:start position:0%
+system along the trajectory and
+ 
+
+ align:start position:0%
+system along the trajectory and
+stabilize it.
+
+ align:start position:0%
+stabilize it.
+ 
+
+ align:start position:0%
+stabilize it.
+The thing I haven't convinced you of yet
+
+ align:start position:0%
+The thing I haven't convinced you of yet
+ 
+
+ align:start position:0%
+The thing I haven't convinced you of yet
+because I could I only know how to do it
+
+ align:start position:0%
+because I could I only know how to do it
+ 
+
+ align:start position:0%
+because I could I only know how to do it
+from from showing examples, but it
+
+ align:start position:0%
+from from showing examples, but it
+ 
+
+ align:start position:0%
+from from showing examples, but it
+really works well. Like I So even though
+
+ align:start position:0%
+really works well. Like I So even though
+ 
+
+ align:start position:0%
+really works well. Like I So even though
+it's a linear system, um it's a linear
+
+ align:start position:0%
+it's a linear system, um it's a linear
+ 
+
+ align:start position:0%
+it's a linear system, um it's a linear
+approximation of the nonlinear system,
+
+ align:start position:0%
+approximation of the nonlinear system,
+ 
+
+ align:start position:0%
+approximation of the nonlinear system,
+something like the Acrobat or the cart
+
+ align:start position:0%
+something like the Acrobat or the cart
+ 
+
+ align:start position:0%
+something like the Acrobat or the cart
+pole swing up, it's got a huge basin of
+
+ align:start position:0%
+pole swing up, it's got a huge basin of
+ 
+
+ align:start position:0%
+pole swing up, it's got a huge basin of
+attraction. Lots and lots of initial
+
+ align:start position:0%
+attraction. Lots and lots of initial
+ 
+
+ align:start position:0%
+attraction. Lots and lots of initial
+conditions will find their way to the
+
+ align:start position:0%
+conditions will find their way to the
+ 
+
+ align:start position:0%
+conditions will find their way to the
+trajectory and get to the goal. Right?
+
+ align:start position:0%
+trajectory and get to the goal. Right?
+ 
+
+ align:start position:0%
+trajectory and get to the goal. Right?
+If you want to do nonlinear control of a
+
+ align:start position:0%
+If you want to do nonlinear control of a
+ 
+
+ align:start position:0%
+If you want to do nonlinear control of a
+humanoid robot or something like this,
+
+ align:start position:0%
+humanoid robot or something like this,
+ 
+
+ align:start position:0%
+humanoid robot or something like this,
+um,
+
+ align:start position:0%
+um,
+ 
+
+ align:start position:0%
+um,
+this actually scales pretty nicely,
+
+ align:start position:0%
+this actually scales pretty nicely,
+ 
+
+ align:start position:0%
+this actually scales pretty nicely,
+right? I just have to solve this
+
+ align:start position:0%
+right? I just have to solve this
+ 
+
+ align:start position:0%
+right? I just have to solve this
+equation. S is the size is is is a
+
+ align:start position:0%
+equation. S is the size is is is a
+ 
+
+ align:start position:0%
+equation. S is the size is is is a
+matrix that's number of state by number
+
+ align:start position:0%
+matrix that's number of state by number
+ 
+
+ align:start position:0%
+matrix that's number of state by number
+of state, but I could do that in 30
+
+ align:start position:0%
+of state, but I could do that in 30
+ 
+
+ align:start position:0%
+of state, but I could do that in 30
+dimensions. That's no problem, right?
+
+ align:start position:0%
+dimensions. That's no problem, right?
+ 
+
+ align:start position:0%
+dimensions. That's no problem, right?
+And even for very nonlinear systems,
+
+ align:start position:0%
+And even for very nonlinear systems,
+ 
+
+ align:start position:0%
+And even for very nonlinear systems,
+local
+
+ align:start position:0%
+local
+ 
+
+ align:start position:0%
+local
+um linear feedback works very very well.
+
+ align:start position:0%
+um linear feedback works very very well.
+ 
+
+ align:start position:0%
+um linear feedback works very very well.
+So well in fact that I think that if you
+
+ align:start position:0%
+So well in fact that I think that if you
+ 
+
+ align:start position:0%
+So well in fact that I think that if you
+ask um and when I did ask sort of the
+
+ align:start position:0%
+ask um and when I did ask sort of the
+ 
+
+ align:start position:0%
+ask um and when I did ask sort of the
+lids guys, you know, Sasha Mcgretzky, he
+
+ align:start position:0%
+lids guys, you know, Sasha Mcgretzky, he
+ 
+
+ align:start position:0%
+lids guys, you know, Sasha Mcgretzky, he
+says this is this is definitely what I
+
+ align:start position:0%
+says this is this is definitely what I
+ 
+
+ align:start position:0%
+says this is this is definitely what I
+would do if I was controlling a walking
+
+ align:start position:0%
+would do if I was controlling a walking
+ 
+
+ align:start position:0%
+would do if I was controlling a walking
+robot or or something like that. Okay.
+
+ align:start position:0%
+robot or or something like that. Okay.
+ 
+
+ align:start position:0%
+robot or or something like that. Okay.
+Um we're trying to do the same thing to
+
+ align:start position:0%
+Um we're trying to do the same thing to
+ 
+
+ align:start position:0%
+Um we're trying to do the same thing to
+control neural neurons in a dish now,
+
+ align:start position:0%
+control neural neurons in a dish now,
+ 
+
+ align:start position:0%
+control neural neurons in a dish now,
+right? Right? We're trying to build good
+
+ align:start position:0%
+right? Right? We're trying to build good
+ 
+
+ align:start position:0%
+right? Right? We're trying to build good
+models of of the dynamics, time varying
+
+ align:start position:0%
+models of of the dynamics, time varying
+ 
+
+ align:start position:0%
+models of of the dynamics, time varying
+models for instance, and then doing this
+
+ align:start position:0%
+models for instance, and then doing this
+ 
+
+ align:start position:0%
+models for instance, and then doing this
+kind of control. Yeah,
+
+ align:start position:0%
+kind of control. Yeah,
+ 
+
+ align:start position:0%
+kind of control. Yeah,
+it works really really well. Okay. The
+
+ align:start position:0%
+it works really really well. Okay. The
+ 
+
+ align:start position:0%
+it works really really well. Okay. The
+only complaint about it is that it's
+
+ align:start position:0%
+only complaint about it is that it's
+ 
+
+ align:start position:0%
+only complaint about it is that it's
+going to have it's based on this linear
+
+ align:start position:0%
+going to have it's based on this linear
+ 
+
+ align:start position:0%
+going to have it's based on this linear
+um linear approximation. So, it will
+
+ align:start position:0%
+um linear approximation. So, it will
+ 
+
+ align:start position:0%
+um linear approximation. So, it will
+have a finite basin of attraction. For
+
+ align:start position:0%
+have a finite basin of attraction. For
+ 
+
+ align:start position:0%
+have a finite basin of attraction. For
+some systems, it can be quite big. Um if
+
+ align:start position:0%
+some systems, it can be quite big. Um if
+ 
+
+ align:start position:0%
+some systems, it can be quite big. Um if
+you have systems with hard
+
+ align:start position:0%
+you have systems with hard
+ 
+
+ align:start position:0%
+you have systems with hard
+nonlinearities, it won't be as big,
+
+ align:start position:0%
+nonlinearities, it won't be as big,
+ 
+
+ align:start position:0%
+nonlinearities, it won't be as big,
+right? Um later in the course I'll show
+
+ align:start position:0%
+right? Um later in the course I'll show
+ 
+
+ align:start position:0%
+right? Um later in the course I'll show
+you ways to explicitly reason about the
+
+ align:start position:0%
+you ways to explicitly reason about the
+ 
+
+ align:start position:0%
+you ways to explicitly reason about the
+size of those basins of attraction. But
+
+ align:start position:0%
+size of those basins of attraction. But
+ 
+
+ align:start position:0%
+size of those basins of attraction. But
+today let's just say um this is a good
+
+ align:start position:0%
+today let's just say um this is a good
+ 
+
+ align:start position:0%
+today let's just say um this is a good
+thing to know, good thing to have in
+
+ align:start position:0%
+thing to know, good thing to have in
+ 
+
+ align:start position:0%
+thing to know, good thing to have in
+your pocket.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let me show you it working. Try to
+
+ align:start position:0%
+Let me show you it working. Try to
+ 
+
+ align:start position:0%
+Let me show you it working. Try to
+convince you that it's it's pretty
+
+ align:start position:0%
+convince you that it's it's pretty
+ 
+
+ align:start position:0%
+convince you that it's it's pretty
+pretty good.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, let's see where I've left
+
+ align:start position:0%
+Okay. So, let's see where I've left
+ 
+
+ align:start position:0%
+Okay. So, let's see where I've left
+myself here. I took this um the
+
+ align:start position:0%
+myself here. I took this um the
+ 
+
+ align:start position:0%
+myself here. I took this um the
+pendulum. Let's do the shooting version.
+
+ align:start position:0%
+pendulum. Let's do the shooting version.
+ 
+
+ align:start position:0%
+pendulum. Let's do the shooting version.
+They both work fine, but let's do the
+
+ align:start position:0%
+They both work fine, but let's do the
+ 
+
+ align:start position:0%
+They both work fine, but let's do the
+shooting version.
+
+ align:start position:0%
+shooting version.
+ 
+
+ align:start position:0%
+shooting version.
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is that bigger than I did last time?
+
+ align:start position:0%
+is that bigger than I did last time?
+ 
+
+ align:start position:0%
+is that bigger than I did last time?
+That's pretty obnoxious. Maybe it's
+
+ align:start position:0%
+That's pretty obnoxious. Maybe it's
+ 
+
+ align:start position:0%
+That's pretty obnoxious. Maybe it's
+always been obnoxious.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Can we get away with that? Yeah. You
+
+ align:start position:0%
+Can we get away with that? Yeah. You
+ 
+
+ align:start position:0%
+Can we get away with that? Yeah. You
+guys are like, I'm not blind.
+
+ align:start position:0%
+guys are like, I'm not blind.
+ 
+
+ align:start position:0%
+guys are like, I'm not blind.
+Okay. Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I did I I showed you last time the
+
+ align:start position:0%
+so I did I I showed you last time the
+ 
+
+ align:start position:0%
+so I did I I showed you last time the
+shooting code. It comes out with a
+
+ align:start position:0%
+shooting code. It comes out with a
+ 
+
+ align:start position:0%
+shooting code. It comes out with a
+resulting tape um x t and u right so it
+
+ align:start position:0%
+resulting tape um x t and u right so it
+ 
+
+ align:start position:0%
+resulting tape um x t and u right so it
+comes out the result of these trajectory
+
+ align:start position:0%
+comes out the result of these trajectory
+ 
+
+ align:start position:0%
+comes out the result of these trajectory
+optimizers whether it's shooting or
+
+ align:start position:0%
+optimizers whether it's shooting or
+ 
+
+ align:start position:0%
+optimizers whether it's shooting or
+whether it's um uh direct collocation
+
+ align:start position:0%
+whether it's um uh direct collocation
+ 
+
+ align:start position:0%
+whether it's um uh direct collocation
+whatever it is it comes up with some
+
+ align:start position:0%
+whatever it is it comes up with some
+ 
+
+ align:start position:0%
+whatever it is it comes up with some
+openloop tape. I put X in there too just
+
+ align:start position:0%
+openloop tape. I put X in there too just
+ 
+
+ align:start position:0%
+openloop tape. I put X in there too just
+to as a the reference trajectory that
+
+ align:start position:0%
+to as a the reference trajectory that
+ 
+
+ align:start position:0%
+to as a the reference trajectory that
+results. But what really matters is the
+
+ align:start position:0%
+results. But what really matters is the
+ 
+
+ align:start position:0%
+results. But what really matters is the
+the timestamps and the U command the
+
+ align:start position:0%
+the timestamps and the U command the
+ 
+
+ align:start position:0%
+the timestamps and the U command the
+open loop tape. Okay. So, let me um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+save it this time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, it comes up with in this case
+
+ align:start position:0%
+Okay. So, it comes up with in this case
+ 
+
+ align:start position:0%
+Okay. So, it comes up with in this case
+with these parameters I've chosen, it
+
+ align:start position:0%
+with these parameters I've chosen, it
+ 
+
+ align:start position:0%
+with these parameters I've chosen, it
+comes up with some one pump policy with
+
+ align:start position:0%
+comes up with some one pump policy with
+ 
+
+ align:start position:0%
+comes up with some one pump policy with
+the torque limits I have, the the nurses
+
+ align:start position:0%
+the torque limits I have, the the nurses
+ 
+
+ align:start position:0%
+the torque limits I have, the the nurses
+I have, it comes up with a a one pump
+
+ align:start position:0%
+I have, it comes up with a a one pump
+ 
+
+ align:start position:0%
+I have, it comes up with a a one pump
+policy that gets to me to the to the top
+
+ align:start position:0%
+policy that gets to me to the to the top
+ 
+
+ align:start position:0%
+policy that gets to me to the to the top
+in 4 seconds.
+
+ align:start position:0%
+in 4 seconds.
+ 
+
+ align:start position:0%
+in 4 seconds.
+Okay, let me now um just simulate that a
+
+ align:start position:0%
+Okay, let me now um just simulate that a
+ 
+
+ align:start position:0%
+Okay, let me now um just simulate that a
+little bit differently. Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay. Okay. So, the only thing I'm going
+
+ align:start position:0%
+okay. Okay. So, the only thing I'm going
+ 
+
+ align:start position:0%
+okay. Okay. So, the only thing I'm going
+to do here now is um this control OD is
+
+ align:start position:0%
+to do here now is um this control OD is
+ 
+
+ align:start position:0%
+to do here now is um this control OD is
+just a simulation which um plays back
+
+ align:start position:0%
+just a simulation which um plays back
+ 
+
+ align:start position:0%
+just a simulation which um plays back
+exactly the the same openloop tape, but
+
+ align:start position:0%
+exactly the the same openloop tape, but
+ 
+
+ align:start position:0%
+exactly the the same openloop tape, but
+it plays it back with a little more
+
+ align:start position:0%
+it plays it back with a little more
+ 
+
+ align:start position:0%
+it plays it back with a little more
+careful integration because in the
+
+ align:start position:0%
+careful integration because in the
+ 
+
+ align:start position:0%
+careful integration because in the
+actual in the shooting code I used, I
+
+ align:start position:0%
+actual in the shooting code I used, I
+ 
+
+ align:start position:0%
+actual in the shooting code I used, I
+used a big time step just so I don't
+
+ align:start position:0%
+used a big time step just so I don't
+ 
+
+ align:start position:0%
+used a big time step just so I don't
+waste time um computing gradients to the
+
+ align:start position:0%
+waste time um computing gradients to the
+ 
+
+ align:start position:0%
+waste time um computing gradients to the
+nth degree of accuracy. That's not
+
+ align:start position:0%
+nth degree of accuracy. That's not
+ 
+
+ align:start position:0%
+nth degree of accuracy. That's not
+worthwhile. If I simulate the exact same
+
+ align:start position:0%
+worthwhile. If I simulate the exact same
+ 
+
+ align:start position:0%
+worthwhile. If I simulate the exact same
+thing back with a more careful OD
+
+ align:start position:0%
+thing back with a more careful OD
+ 
+
+ align:start position:0%
+thing back with a more careful OD
+integration, let's see what happens.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that was that same trajectory that um
+
+ align:start position:0%
+So that was that same trajectory that um
+ 
+
+ align:start position:0%
+So that was that same trajectory that um
+exact same control inputs just simulated
+
+ align:start position:0%
+exact same control inputs just simulated
+ 
+
+ align:start position:0%
+exact same control inputs just simulated
+more carefully. It it made its honest
+
+ align:start position:0%
+more carefully. It it made its honest
+ 
+
+ align:start position:0%
+more carefully. It it made its honest
+effort to get up there but it it didn't
+
+ align:start position:0%
+effort to get up there but it it didn't
+ 
+
+ align:start position:0%
+effort to get up there but it it didn't
+quite get up there, turned around and
+
+ align:start position:0%
+quite get up there, turned around and
+ 
+
+ align:start position:0%
+quite get up there, turned around and
+came back down. Okay. And if you I'm
+
+ align:start position:0%
+came back down. Okay. And if you I'm
+ 
+
+ align:start position:0%
+came back down. Okay. And if you I'm
+trying to show it also in this uh uh
+
+ align:start position:0%
+trying to show it also in this uh uh
+ 
+
+ align:start position:0%
+trying to show it also in this uh uh
+just this is the the different state
+
+ align:start position:0%
+just this is the the different state
+ 
+
+ align:start position:0%
+just this is the the different state
+trajectories over time. You can see that
+
+ align:start position:0%
+trajectories over time. You can see that
+ 
+
+ align:start position:0%
+trajectories over time. You can see that
+the red and blue lines are the desired
+
+ align:start position:0%
+the red and blue lines are the desired
+ 
+
+ align:start position:0%
+the red and blue lines are the desired
+versus actual in the in theta in this
+
+ align:start position:0%
+versus actual in the in theta in this
+ 
+
+ align:start position:0%
+versus actual in the in theta in this
+case. And the um these two lines are the
+
+ align:start position:0%
+case. And the um these two lines are the
+ 
+
+ align:start position:0%
+case. And the um these two lines are the
+desired versus actual in theta dot. Um
+
+ align:start position:0%
+desired versus actual in theta dot. Um
+ 
+
+ align:start position:0%
+desired versus actual in theta dot. Um
+they start off exactly on top of each
+
+ align:start position:0%
+they start off exactly on top of each
+ 
+
+ align:start position:0%
+they start off exactly on top of each
+other, but just little differences in
+
+ align:start position:0%
+other, but just little differences in
+ 
+
+ align:start position:0%
+other, but just little differences in
+the numeric cause them to go in
+
+ align:start position:0%
+the numeric cause them to go in
+ 
+
+ align:start position:0%
+the numeric cause them to go in
+different directions. Yeah. Part ways.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So now I've got this LTVLQR
+
+ align:start position:0%
+Okay. So now I've got this LTVLQR
+ 
+
+ align:start position:0%
+Okay. So now I've got this LTVLQR
+um solution which is exactly what I just
+
+ align:start position:0%
+um solution which is exactly what I just
+ 
+
+ align:start position:0%
+um solution which is exactly what I just
+showed you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm going to put in so I I was just
+
+ align:start position:0%
+and I'm going to put in so I I was just
+ 
+
+ align:start position:0%
+and I'm going to put in so I I was just
+simulating it just now with just U being
+
+ align:start position:0%
+simulating it just now with just U being
+ 
+
+ align:start position:0%
+simulating it just now with just U being
+the nominal U. Now I'm going to add this
+
+ align:start position:0%
+the nominal U. Now I'm going to add this
+ 
+
+ align:start position:0%
+the nominal U. Now I'm going to add this
+feed this time varying feedback term X -
+
+ align:start position:0%
+feed this time varying feedback term X -
+ 
+
+ align:start position:0%
+feed this time varying feedback term X -
+X desired.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now my more careful integration
+
+ align:start position:0%
+And now my more careful integration
+ 
+
+ align:start position:0%
+And now my more careful integration
+results in a closed loop system which
+
+ align:start position:0%
+results in a closed loop system which
+ 
+
+ align:start position:0%
+results in a closed loop system which
+not only got to the goal but actually
+
+ align:start position:0%
+not only got to the goal but actually
+ 
+
+ align:start position:0%
+not only got to the goal but actually
+stayed up at the goal because I have a
+
+ align:start position:0%
+stayed up at the goal because I have a
+ 
+
+ align:start position:0%
+stayed up at the goal because I have a
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+a stable system all the way to the top.
+
+ align:start position:0%
+a stable system all the way to the top.
+ 
+
+ align:start position:0%
+a stable system all the way to the top.
+Okay. All right. So what I just said was
+
+ align:start position:0%
+Okay. All right. So what I just said was
+ 
+
+ align:start position:0%
+Okay. All right. So what I just said was
+was very unimpressive. I said um I
+
+ align:start position:0%
+was very unimpressive. I said um I
+ 
+
+ align:start position:0%
+was very unimpressive. I said um I
+computed a openloop um policy with my
+
+ align:start position:0%
+computed a openloop um policy with my
+ 
+
+ align:start position:0%
+computed a openloop um policy with my
+methods from Thursday. I simulated them
+
+ align:start position:0%
+methods from Thursday. I simulated them
+ 
+
+ align:start position:0%
+methods from Thursday. I simulated them
+back. They didn't work. Okay. But I then
+
+ align:start position:0%
+back. They didn't work. Okay. But I then
+ 
+
+ align:start position:0%
+back. They didn't work. Okay. But I then
+put a feedback controller on and from
+
+ align:start position:0%
+put a feedback controller on and from
+ 
+
+ align:start position:0%
+put a feedback controller on and from
+the exact same initial conditions I now
+
+ align:start position:0%
+the exact same initial conditions I now
+ 
+
+ align:start position:0%
+the exact same initial conditions I now
+can simulate them and they work. Right.
+
+ align:start position:0%
+can simulate them and they work. Right.
+ 
+
+ align:start position:0%
+can simulate them and they work. Right.
+Um, so it's sort of disappointing that
+
+ align:start position:0%
+Um, so it's sort of disappointing that
+ 
+
+ align:start position:0%
+Um, so it's sort of disappointing that
+we had to do that at all. Uh, but I can
+
+ align:start position:0%
+we had to do that at all. Uh, but I can
+ 
+
+ align:start position:0%
+we had to do that at all. Uh, but I can
+now the stability is more than just sort
+
+ align:start position:0%
+now the stability is more than just sort
+ 
+
+ align:start position:0%
+now the stability is more than just sort
+of stabilizing the initial conditions.
+
+ align:start position:0%
+of stabilizing the initial conditions.
+ 
+
+ align:start position:0%
+of stabilizing the initial conditions.
+Let's add some
+
+ align:start position:0%
+Let's add some
+ 
+
+ align:start position:0%
+Let's add some
+fairly big random numbers to that
+
+ align:start position:0%
+fairly big random numbers to that
+ 
+
+ align:start position:0%
+fairly big random numbers to that
+initial condition and see what happens.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's it's recomputing the um the policy
+
+ align:start position:0%
+It's it's recomputing the um the policy
+ 
+
+ align:start position:0%
+It's it's recomputing the um the policy
+every time just because it was fast
+
+ align:start position:0%
+every time just because it was fast
+ 
+
+ align:start position:0%
+every time just because it was fast
+enough that I didn't bother to change
+
+ align:start position:0%
+enough that I didn't bother to change
+ 
+
+ align:start position:0%
+enough that I didn't bother to change
+it.
+
+ align:start position:0%
+it.
+ 
+
+ align:start position:0%
+it.
+Okay. Okay, so that actually started
+
+ align:start position:0%
+Okay. Okay, so that actually started
+ 
+
+ align:start position:0%
+Okay. Okay, so that actually started
+with pretty big different initial
+
+ align:start position:0%
+with pretty big different initial
+ 
+
+ align:start position:0%
+with pretty big different initial
+conditions. So, um, you know, theta was
+
+ align:start position:0%
+conditions. So, um, you know, theta was
+ 
+
+ align:start position:0%
+conditions. So, um, you know, theta was
+off by, uh, I don't know, 2/10 of a
+
+ align:start position:0%
+off by, uh, I don't know, 2/10 of a
+ 
+
+ align:start position:0%
+off by, uh, I don't know, 2/10 of a
+radian or something like this. The
+
+ align:start position:0%
+radian or something like this. The
+ 
+
+ align:start position:0%
+radian or something like this. The
+velocities were off by half a radian per
+
+ align:start position:0%
+velocities were off by half a radian per
+ 
+
+ align:start position:0%
+velocities were off by half a radian per
+second. Okay, we could crank that up. I
+
+ align:start position:0%
+second. Okay, we could crank that up. I
+ 
+
+ align:start position:0%
+second. Okay, we could crank that up. I
+bet it does a lot better than that. Um,
+
+ align:start position:0%
+bet it does a lot better than that. Um,
+ 
+
+ align:start position:0%
+bet it does a lot better than that. Um,
+but if you watch these things, they
+
+ align:start position:0%
+but if you watch these things, they
+ 
+
+ align:start position:0%
+but if you watch these things, they
+converge quite nicely to together at at
+
+ align:start position:0%
+converge quite nicely to together at at
+ 
+
+ align:start position:0%
+converge quite nicely to together at at
+the end there.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And what's what matters is they get up
+
+ align:start position:0%
+And what's what matters is they get up
+ 
+
+ align:start position:0%
+And what's what matters is they get up
+to the top, right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So again, these things come together,
+
+ align:start position:0%
+So again, these things come together,
+ 
+
+ align:start position:0%
+So again, these things come together,
+find their way up to the top and live.
+
+ align:start position:0%
+find their way up to the top and live.
+ 
+
+ align:start position:0%
+find their way up to the top and live.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+I bet if I put it, you know, a lot
+
+ align:start position:0%
+I bet if I put it, you know, a lot
+ 
+
+ align:start position:0%
+I bet if I put it, you know, a lot
+bigger, it'll still work.
+
+ align:start position:0%
+bigger, it'll still work.
+ 
+
+ align:start position:0%
+bigger, it'll still work.
+I normally do an order magnitude, but
+
+ align:start position:0%
+I normally do an order magnitude, but
+ 
+
+ align:start position:0%
+I normally do an order magnitude, but
+let's not be silly.
+
+ align:start position:0%
+let's not be silly.
+ 
+
+ align:start position:0%
+let's not be silly.
+Oh, didn't make it.
+
+ align:start position:0%
+Oh, didn't make it.
+ 
+
+ align:start position:0%
+Oh, didn't make it.
+There's only one reason it didn't make
+
+ align:start position:0%
+There's only one reason it didn't make
+ 
+
+ align:start position:0%
+There's only one reason it didn't make
+it actually. It's because um if you look
+
+ align:start position:0%
+it actually. It's because um if you look
+ 
+
+ align:start position:0%
+it actually. It's because um if you look
+in here, I'm actually honest about
+
+ align:start position:0%
+in here, I'm actually honest about
+ 
+
+ align:start position:0%
+in here, I'm actually honest about
+implementing the max torqus. Yeah. So, I
+
+ align:start position:0%
+implementing the max torqus. Yeah. So, I
+ 
+
+ align:start position:0%
+implementing the max torqus. Yeah. So, I
+actually have a torque limited. I impose
+
+ align:start position:0%
+actually have a torque limited. I impose
+ 
+
+ align:start position:0%
+actually have a torque limited. I impose
+it and it ser it lives on there. If I
+
+ align:start position:0%
+it and it ser it lives on there. If I
+ 
+
+ align:start position:0%
+it and it ser it lives on there. If I
+didn't, I bet I could I could convince
+
+ align:start position:0%
+didn't, I bet I could I could convince
+ 
+
+ align:start position:0%
+didn't, I bet I could I could convince
+you it works for any initial condition.
+
+ align:start position:0%
+you it works for any initial condition.
+ 
+
+ align:start position:0%
+you it works for any initial condition.
+But, um let's try one more time. Get a
+
+ align:start position:0%
+But, um let's try one more time. Get a
+ 
+
+ align:start position:0%
+But, um let's try one more time. Get a
+little more lucky with the initial
+
+ align:start position:0%
+little more lucky with the initial
+ 
+
+ align:start position:0%
+little more lucky with the initial
+conditions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh, come on. Come on. Yes. Right. Okay.
+
+ align:start position:0%
+Oh, come on. Come on. Yes. Right. Okay.
+ 
+
+ align:start position:0%
+Oh, come on. Come on. Yes. Right. Okay.
+That was pretty far off and it still
+
+ align:start position:0%
+That was pretty far off and it still
+ 
+
+ align:start position:0%
+That was pretty far off and it still
+found its way back to the trajectory.
+
+ align:start position:0%
+found its way back to the trajectory.
+ 
+
+ align:start position:0%
+found its way back to the trajectory.
+Good. Yeah. Look at how big those
+
+ align:start position:0%
+Good. Yeah. Look at how big those
+ 
+
+ align:start position:0%
+Good. Yeah. Look at how big those
+initial conditions are. Right there and
+
+ align:start position:0%
+initial conditions are. Right there and
+ 
+
+ align:start position:0%
+initial conditions are. Right there and
+there versus where? Wow. That's really
+
+ align:start position:0%
+there versus where? Wow. That's really
+ 
+
+ align:start position:0%
+there versus where? Wow. That's really
+good.
+
+ align:start position:0%
+good.
+ 
+
+ align:start position:0%
+good.
+Okay. I saw Did I see a question? No.
+
+ align:start position:0%
+Okay. I saw Did I see a question? No.
+ 
+
+ align:start position:0%
+Okay. I saw Did I see a question? No.
+All right. So, this stuff works for
+
+ align:start position:0%
+All right. So, this stuff works for
+ 
+
+ align:start position:0%
+All right. So, this stuff works for
+pendulum. Uh, it works for more
+
+ align:start position:0%
+pendulum. Uh, it works for more
+ 
+
+ align:start position:0%
+pendulum. Uh, it works for more
+interesting systems, too. I'll just show
+
+ align:start position:0%
+interesting systems, too. I'll just show
+ 
+
+ align:start position:0%
+interesting systems, too. I'll just show
+you the um the cart pole real quick
+
+ align:start position:0%
+you the um the cart pole real quick
+ 
+
+ align:start position:0%
+you the um the cart pole real quick
+here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you remember I won't do the sort of
+
+ align:start position:0%
+So you remember I won't do the sort of
+ 
+
+ align:start position:0%
+So you remember I won't do the sort of
+here's here is what it looks like
+
+ align:start position:0%
+here's here is what it looks like
+ 
+
+ align:start position:0%
+here's here is what it looks like
+without feedback. I'll just do the the
+
+ align:start position:0%
+without feedback. I'll just do the the
+ 
+
+ align:start position:0%
+without feedback. I'll just do the the
+initial conditions corrupted um solution
+
+ align:start position:0%
+initial conditions corrupted um solution
+ 
+
+ align:start position:0%
+initial conditions corrupted um solution
+pump up.
+
+ align:start position:0%
+pump up.
+ 
+
+ align:start position:0%
+pump up.
+Okay. So if you remember my solutions
+
+ align:start position:0%
+Okay. So if you remember my solutions
+ 
+
+ align:start position:0%
+Okay. So if you remember my solutions
+from last time, it never drove off the
+
+ align:start position:0%
+from last time, it never drove off the
+ 
+
+ align:start position:0%
+from last time, it never drove off the
+screen before. So that was actually it
+
+ align:start position:0%
+screen before. So that was actually it
+ 
+
+ align:start position:0%
+screen before. So that was actually it
+catching it by deviating enough that it
+
+ align:start position:0%
+catching it by deviating enough that it
+ 
+
+ align:start position:0%
+catching it by deviating enough that it
+came off the screen and then slowly
+
+ align:start position:0%
+came off the screen and then slowly
+ 
+
+ align:start position:0%
+came off the screen and then slowly
+coming back to the top. Yeah. And uh so
+
+ align:start position:0%
+coming back to the top. Yeah. And uh so
+ 
+
+ align:start position:0%
+coming back to the top. Yeah. And uh so
+that's uh
+
+ align:start position:0%
+that's uh
+ 
+
+ align:start position:0%
+that's uh
+this is it must be its X uh position or
+
+ align:start position:0%
+this is it must be its X uh position or
+ 
+
+ align:start position:0%
+this is it must be its X uh position or
+something going way off. No, not X
+
+ align:start position:0%
+something going way off. No, not X
+ 
+
+ align:start position:0%
+something going way off. No, not X
+position. What is that? That's my
+
+ align:start position:0%
+position. What is that? That's my
+ 
+
+ align:start position:0%
+position. What is that? That's my
+control. Yeah. Did I do torque limits on
+
+ align:start position:0%
+control. Yeah. Did I do torque limits on
+ 
+
+ align:start position:0%
+control. Yeah. Did I do torque limits on
+that one? I still did torque limits. I
+
+ align:start position:0%
+that one? I still did torque limits. I
+ 
+
+ align:start position:0%
+that one? I still did torque limits. I
+just said them high, I guess.
+
+ align:start position:0%
+just said them high, I guess.
+ 
+
+ align:start position:0%
+just said them high, I guess.
+Yeah. So it really works. Okay. And the
+
+ align:start position:0%
+Yeah. So it really works. Okay. And the
+ 
+
+ align:start position:0%
+Yeah. So it really works. Okay. And the
+cool thing is it's I mean the the cost
+
+ align:start position:0%
+cool thing is it's I mean the the cost
+ 
+
+ align:start position:0%
+cool thing is it's I mean the the cost
+of implementing that LQR LTV stabilizer
+
+ align:start position:0%
+of implementing that LQR LTV stabilizer
+ 
+
+ align:start position:0%
+of implementing that LQR LTV stabilizer
+was negligibly more than implementing
+
+ align:start position:0%
+was negligibly more than implementing
+ 
+
+ align:start position:0%
+was negligibly more than implementing
+the uh the most of that time was the
+
+ align:start position:0%
+the uh the most of that time was the
+ 
+
+ align:start position:0%
+the uh the most of that time was the
+shooting optimization, right?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um yes, one question. Why why do you
+
+ align:start position:0%
+Um yes, one question. Why why do you
+ 
+
+ align:start position:0%
+Um yes, one question. Why why do you
+always start at the like zero time? You
+
+ align:start position:0%
+always start at the like zero time? You
+ 
+
+ align:start position:0%
+always start at the like zero time? You
+could look at the initial positions and
+
+ align:start position:0%
+could look at the initial positions and
+ 
+
+ align:start position:0%
+could look at the initial positions and
+look where is the closest point on my
+
+ align:start position:0%
+look where is the closest point on my
+ 
+
+ align:start position:0%
+look where is the closest point on my
+number of trajectories or something and
+
+ align:start position:0%
+number of trajectories or something and
+ 
+
+ align:start position:0%
+number of trajectories or something and
+then do your control policy from that
+
+ align:start position:0%
+then do your control policy from that
+ 
+
+ align:start position:0%
+then do your control policy from that
+moment.
+
+ align:start position:0%
+moment.
+ 
+
+ align:start position:0%
+moment.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So that's really really good. Okay.
+
+ align:start position:0%
+So that's really really good. Okay.
+ 
+
+ align:start position:0%
+So that's really really good. Okay.
+That's exactly what I want to talk about
+
+ align:start position:0%
+That's exactly what I want to talk about
+ 
+
+ align:start position:0%
+That's exactly what I want to talk about
+next actually. Um,
+
+ align:start position:0%
+next actually. Um,
+ 
+
+ align:start position:0%
+next actually. Um,
+okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, I just marched I I designed uh
+
+ align:start position:0%
+So, I just marched I I designed uh
+ 
+
+ align:start position:0%
+So, I just marched I I designed uh
+a time varying feedback controller,
+
+ align:start position:0%
+a time varying feedback controller,
+ 
+
+ align:start position:0%
+a time varying feedback controller,
+right?
+
+ align:start position:0%
+right?
+ 
+
+ align:start position:0%
+right?
+Is negative k of t uh xar of t, right? I
+
+ align:start position:0%
+Is negative k of t uh xar of t, right? I
+ 
+
+ align:start position:0%
+Is negative k of t uh xar of t, right? I
+designed that ahead of time
+
+ align:start position:0%
+designed that ahead of time
+ 
+
+ align:start position:0%
+designed that ahead of time
+and then from the initial conditions I
+
+ align:start position:0%
+and then from the initial conditions I
+ 
+
+ align:start position:0%
+and then from the initial conditions I
+started simulating from zero and I just
+
+ align:start position:0%
+started simulating from zero and I just
+ 
+
+ align:start position:0%
+started simulating from zero and I just
+played out you know the my nominal
+
+ align:start position:0%
+played out you know the my nominal
+ 
+
+ align:start position:0%
+played out you know the my nominal
+trajectory just marched forward with
+
+ align:start position:0%
+trajectory just marched forward with
+ 
+
+ align:start position:0%
+trajectory just marched forward with
+time my feedback controller just marched
+
+ align:start position:0%
+time my feedback controller just marched
+ 
+
+ align:start position:0%
+time my feedback controller just marched
+forward with time and my aerodynamics
+
+ align:start position:0%
+forward with time and my aerodynamics
+ 
+
+ align:start position:0%
+forward with time and my aerodynamics
+just marched forward with time. Okay. So
+
+ align:start position:0%
+just marched forward with time. Okay. So
+ 
+
+ align:start position:0%
+just marched forward with time. Okay. So
+before I explicitly address your
+
+ align:start position:0%
+before I explicitly address your
+ 
+
+ align:start position:0%
+before I explicitly address your
+question let me point out let me let me
+
+ align:start position:0%
+question let me point out let me let me
+ 
+
+ align:start position:0%
+question let me point out let me let me
+ask um even a simpler question here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right. So what happened if I had plotted
+
+ align:start position:0%
+Right. So what happened if I had plotted
+ 
+
+ align:start position:0%
+Right. So what happened if I had plotted
+that in state space? What you would have
+
+ align:start position:0%
+that in state space? What you would have
+ 
+
+ align:start position:0%
+that in state space? What you would have
+seen is that the trajectory starts off
+
+ align:start position:0%
+seen is that the trajectory starts off
+ 
+
+ align:start position:0%
+seen is that the trajectory starts off
+somewhere in state space and comes
+
+ align:start position:0%
+somewhere in state space and comes
+ 
+
+ align:start position:0%
+somewhere in state space and comes
+together. That would have been a good
+
+ align:start position:0%
+together. That would have been a good
+ 
+
+ align:start position:0%
+together. That would have been a good
+idea. Maybe I should do that in a
+
+ align:start position:0%
+idea. Maybe I should do that in a
+ 
+
+ align:start position:0%
+idea. Maybe I should do that in a
+minute. But um sort of it comes together
+
+ align:start position:0%
+minute. But um sort of it comes together
+ 
+
+ align:start position:0%
+minute. But um sort of it comes together
+and finds its way onto that trajectory.
+
+ align:start position:0%
+and finds its way onto that trajectory.
+ 
+
+ align:start position:0%
+and finds its way onto that trajectory.
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So here's the question. What
+
+ align:start position:0%
+Okay. So here's the question. What
+ 
+
+ align:start position:0%
+Okay. So here's the question. What
+happens if I instead of just changes in
+
+ align:start position:0%
+happens if I instead of just changes in
+ 
+
+ align:start position:0%
+happens if I instead of just changes in
+initial conditions, what happens if I
+
+ align:start position:0%
+initial conditions, what happens if I
+ 
+
+ align:start position:0%
+initial conditions, what happens if I
+have disturbances?
+
+ align:start position:0%
+have disturbances?
+ 
+
+ align:start position:0%
+have disturbances?
+um that push me off the trajectory.
+
+ align:start position:0%
+um that push me off the trajectory.
+ 
+
+ align:start position:0%
+um that push me off the trajectory.
+Well, that's okay. That's no different
+
+ align:start position:0%
+Well, that's okay. That's no different
+ 
+
+ align:start position:0%
+Well, that's okay. That's no different
+really than a um different initial
+
+ align:start position:0%
+really than a um different initial
+ 
+
+ align:start position:0%
+really than a um different initial
+condition. They'll come back on here.
+
+ align:start position:0%
+condition. They'll come back on here.
+ 
+
+ align:start position:0%
+condition. They'll come back on here.
+What happens if I have a disturbance
+
+ align:start position:0%
+What happens if I have a disturbance
+ 
+
+ align:start position:0%
+What happens if I have a disturbance
+that pushes me along the trajectory with
+
+ align:start position:0%
+that pushes me along the trajectory with
+ 
+
+ align:start position:0%
+that pushes me along the trajectory with
+this controller?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's say, you know, I've got sort of
+
+ align:start position:0%
+Let's say, you know, I've got sort of
+ 
+
+ align:start position:0%
+Let's say, you know, I've got sort of
+the the helpful disturbance which, you
+
+ align:start position:0%
+the the helpful disturbance which, you
+ 
+
+ align:start position:0%
+the the helpful disturbance which, you
+know, when I was right here
+
+ align:start position:0%
+know, when I was right here
+ 
+
+ align:start position:0%
+know, when I was right here
+just happened to push me right to there.
+
+ align:start position:0%
+just happened to push me right to there.
+ 
+
+ align:start position:0%
+just happened to push me right to there.
+What's this control? What's my feedback
+
+ align:start position:0%
+What's this control? What's my feedback
+ 
+
+ align:start position:0%
+What's this control? What's my feedback
+controller going to do?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, probably in a dramatic fashion,
+
+ align:start position:0%
+Yeah, probably in a dramatic fashion,
+ 
+
+ align:start position:0%
+Yeah, probably in a dramatic fashion,
+right? Um, you know, the same way it
+
+ align:start position:0%
+right? Um, you know, the same way it
+ 
+
+ align:start position:0%
+right? Um, you know, the same way it
+tries to quickly converge from here.
+
+ align:start position:0%
+tries to quickly converge from here.
+ 
+
+ align:start position:0%
+tries to quickly converge from here.
+It's going to try to get it's going to
+
+ align:start position:0%
+It's going to try to get it's going to
+ 
+
+ align:start position:0%
+It's going to try to get it's going to
+push itself back towards that point
+
+ align:start position:0%
+push itself back towards that point
+ 
+
+ align:start position:0%
+push itself back towards that point
+possibly. I mean, slowing down doesn't
+
+ align:start position:0%
+possibly. I mean, slowing down doesn't
+ 
+
+ align:start position:0%
+possibly. I mean, slowing down doesn't
+makes it sound sort of no big deal. It
+
+ align:start position:0%
+makes it sound sort of no big deal. It
+ 
+
+ align:start position:0%
+makes it sound sort of no big deal. It
+might actually try to I mean, it can't
+
+ align:start position:0%
+might actually try to I mean, it can't
+ 
+
+ align:start position:0%
+might actually try to I mean, it can't
+go backwards, but it might try to do
+
+ align:start position:0%
+go backwards, but it might try to do
+ 
+
+ align:start position:0%
+go backwards, but it might try to do
+something um more severe, right? to try
+
+ align:start position:0%
+something um more severe, right? to try
+ 
+
+ align:start position:0%
+something um more severe, right? to try
+to catch up with that old trajectory.
+
+ align:start position:0%
+to catch up with that old trajectory.
+ 
+
+ align:start position:0%
+to catch up with that old trajectory.
+Right? So the major limitation of this
+
+ align:start position:0%
+Right? So the major limitation of this
+ 
+
+ align:start position:0%
+Right? So the major limitation of this
+is that it's blindly in order to have
+
+ align:start position:0%
+is that it's blindly in order to have
+ 
+
+ align:start position:0%
+is that it's blindly in order to have
+the strong convergence properties that
+
+ align:start position:0%
+the strong convergence properties that
+ 
+
+ align:start position:0%
+the strong convergence properties that
+we have, the controller is blindly
+
+ align:start position:0%
+we have, the controller is blindly
+ 
+
+ align:start position:0%
+we have, the controller is blindly
+marching forward in time, right? The
+
+ align:start position:0%
+marching forward in time, right? The
+ 
+
+ align:start position:0%
+marching forward in time, right? The
+great thing about switching to a time
+
+ align:start position:0%
+great thing about switching to a time
+ 
+
+ align:start position:0%
+great thing about switching to a time
+parameterization is I can compute
+
+ align:start position:0%
+parameterization is I can compute
+ 
+
+ align:start position:0%
+parameterization is I can compute
+everything. Everything's linear again.
+
+ align:start position:0%
+everything. Everything's linear again.
+ 
+
+ align:start position:0%
+everything. Everything's linear again.
+The bad thing is you're a slave to time.
+
+ align:start position:0%
+The bad thing is you're a slave to time.
+ 
+
+ align:start position:0%
+The bad thing is you're a slave to time.
+Okay. So, um, Philip asked a nice
+
+ align:start position:0%
+Okay. So, um, Philip asked a nice
+ 
+
+ align:start position:0%
+Okay. So, um, Philip asked a nice
+question. He says, "So, why not why do I
+
+ align:start position:0%
+question. He says, "So, why not why do I
+ 
+
+ align:start position:0%
+question. He says, "So, why not why do I
+just blindly start marching forward from
+
+ align:start position:0%
+just blindly start marching forward from
+ 
+
+ align:start position:0%
+just blindly start marching forward from
+time zero? Maybe if I have a a
+
+ align:start position:0%
+time zero? Maybe if I have a a
+ 
+
+ align:start position:0%
+time zero? Maybe if I have a a
+controller, um, I should just look for
+
+ align:start position:0%
+controller, um, I should just look for
+ 
+
+ align:start position:0%
+controller, um, I should just look for
+the closest point in my trajectory,
+
+ align:start position:0%
+the closest point in my trajectory,
+ 
+
+ align:start position:0%
+the closest point in my trajectory,
+right? And then instead of indexing off
+
+ align:start position:0%
+right? And then instead of indexing off
+ 
+
+ align:start position:0%
+right? And then instead of indexing off
+time, index off some sort of phase, some
+
+ align:start position:0%
+time, index off some sort of phase, some
+ 
+
+ align:start position:0%
+time, index off some sort of phase, some
+some fraction of my trajectory and then
+
+ align:start position:0%
+some fraction of my trajectory and then
+ 
+
+ align:start position:0%
+some fraction of my trajectory and then
+execute that controller."
+
+ align:start position:0%
+execute that controller."
+ 
+
+ align:start position:0%
+execute that controller."
+And, you know, you can do that. I sort
+
+ align:start position:0%
+And, you know, you can do that. I sort
+ 
+
+ align:start position:0%
+And, you know, you can do that. I sort
+of I wish you the best if you do that.
+
+ align:start position:0%
+of I wish you the best if you do that.
+ 
+
+ align:start position:0%
+of I wish you the best if you do that.
+But my sus my suspicion is that if on
+
+ align:start position:0%
+But my sus my suspicion is that if on
+ 
+
+ align:start position:0%
+But my sus my suspicion is that if on
+every DT you pick the closest point in
+
+ align:start position:0%
+every DT you pick the closest point in
+ 
+
+ align:start position:0%
+every DT you pick the closest point in
+the trajectory, then the result is
+
+ align:start position:0%
+the trajectory, then the result is
+ 
+
+ align:start position:0%
+the trajectory, then the result is
+you're going to chatter like you
+
+ align:start position:0%
+you're going to chatter like you
+ 
+
+ align:start position:0%
+you're going to chatter like you
+wouldn't believe. So there's a lot of
+
+ align:start position:0%
+wouldn't believe. So there's a lot of
+ 
+
+ align:start position:0%
+wouldn't believe. So there's a lot of
+protection you get when you So this you
+
+ align:start position:0%
+protection you get when you So this you
+ 
+
+ align:start position:0%
+protection you get when you So this you
+could think of this very much as a gain
+
+ align:start position:0%
+could think of this very much as a gain
+ 
+
+ align:start position:0%
+could think of this very much as a gain
+scheduled linear controller. Yeah, this
+
+ align:start position:0%
+scheduled linear controller. Yeah, this
+ 
+
+ align:start position:0%
+scheduled linear controller. Yeah, this
+is this is a time varying gain
+
+ align:start position:0%
+is this is a time varying gain
+ 
+
+ align:start position:0%
+is this is a time varying gain
+scheduling. And the problem is if I
+
+ align:start position:0%
+scheduling. And the problem is if I
+ 
+
+ align:start position:0%
+scheduling. And the problem is if I
+switch gains quickly, then you're going
+
+ align:start position:0%
+switch gains quickly, then you're going
+ 
+
+ align:start position:0%
+switch gains quickly, then you're going
+to get chattering. Okay, so it might
+
+ align:start position:0%
+to get chattering. Okay, so it might
+ 
+
+ align:start position:0%
+to get chattering. Okay, so it might
+make a lot of sense um for instance if
+
+ align:start position:0%
+make a lot of sense um for instance if
+ 
+
+ align:start position:0%
+make a lot of sense um for instance if
+you were to get a big disturbance
+
+ align:start position:0%
+you were to get a big disturbance
+ 
+
+ align:start position:0%
+you were to get a big disturbance
+to re-evaluate and try to find the
+
+ align:start position:0%
+to re-evaluate and try to find the
+ 
+
+ align:start position:0%
+to re-evaluate and try to find the
+closest point and start executing that
+
+ align:start position:0%
+closest point and start executing that
+ 
+
+ align:start position:0%
+closest point and start executing that
+new policy with with time reindexed.
+
+ align:start position:0%
+new policy with with time reindexed.
+ 
+
+ align:start position:0%
+new policy with with time reindexed.
+Okay, but it's probably a bad idea in my
+
+ align:start position:0%
+Okay, but it's probably a bad idea in my
+ 
+
+ align:start position:0%
+Okay, but it's probably a bad idea in my
+experience to decide which part of the
+
+ align:start position:0%
+experience to decide which part of the
+ 
+
+ align:start position:0%
+experience to decide which part of the
+trajectory you're closest to on every
+
+ align:start position:0%
+trajectory you're closest to on every
+ 
+
+ align:start position:0%
+trajectory you're closest to on every
+every time you implement the every DT
+
+ align:start position:0%
+every time you implement the every DT
+ 
+
+ align:start position:0%
+every time you implement the every DT
+sort of that's probably a bad idea.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yes.
+
+ align:start position:0%
+Yes.
+ 
+
+ align:start position:0%
+Yes.
+Um, could you maybe play some tricks if
+
+ align:start position:0%
+Um, could you maybe play some tricks if
+ 
+
+ align:start position:0%
+Um, could you maybe play some tricks if
+you had some idea of the basin of
+
+ align:start position:0%
+you had some idea of the basin of
+ 
+
+ align:start position:0%
+you had some idea of the basin of
+traction of the current point you're
+
+ align:start position:0%
+traction of the current point you're
+ 
+
+ align:start position:0%
+traction of the current point you're
+trying to get to and if you know that
+
+ align:start position:0%
+trying to get to and if you know that
+ 
+
+ align:start position:0%
+trying to get to and if you know that
+you're outside of it, then look around
+
+ align:start position:0%
+you're outside of it, then look around
+ 
+
+ align:start position:0%
+you're outside of it, then look around
+and see if there's a base you are
+
+ align:start position:0%
+and see if there's a base you are
+ 
+
+ align:start position:0%
+and see if there's a base you are
+inside.
+
+ align:start position:0%
+inside.
+ 
+
+ align:start position:0%
+inside.
+Yes. So, um, so we're going to talk
+
+ align:start position:0%
+Yes. So, um, so we're going to talk
+ 
+
+ align:start position:0%
+Yes. So, um, so we're going to talk
+about I so I I have a particular trick
+
+ align:start position:0%
+about I so I I have a particular trick
+ 
+
+ align:start position:0%
+about I so I I have a particular trick
+that try to does that does that in um,
+
+ align:start position:0%
+that try to does that does that in um,
+ 
+
+ align:start position:0%
+that try to does that does that in um,
+we'll talk about in the motion planning,
+
+ align:start position:0%
+we'll talk about in the motion planning,
+ 
+
+ align:start position:0%
+we'll talk about in the motion planning,
+but um, yeah. So, so Mark knows about
+
+ align:start position:0%
+but um, yeah. So, so Mark knows about
+ 
+
+ align:start position:0%
+but um, yeah. So, so Mark knows about
+these tricks for computing basins of
+
+ align:start position:0%
+these tricks for computing basins of
+ 
+
+ align:start position:0%
+these tricks for computing basins of
+attraction pretty efficiently. And um so
+
+ align:start position:0%
+attraction pretty efficiently. And um so
+ 
+
+ align:start position:0%
+attraction pretty efficiently. And um so
+these days what we do is we actually try
+
+ align:start position:0%
+these days what we do is we actually try
+ 
+
+ align:start position:0%
+these days what we do is we actually try
+to compute the funnel the sort of the
+
+ align:start position:0%
+to compute the funnel the sort of the
+ 
+
+ align:start position:0%
+to compute the funnel the sort of the
+basin of attraction of this trajectory
+
+ align:start position:0%
+basin of attraction of this trajectory
+ 
+
+ align:start position:0%
+basin of attraction of this trajectory
+around um around the trajectory and you
+
+ align:start position:0%
+around um around the trajectory and you
+ 
+
+ align:start position:0%
+around um around the trajectory and you
+could know discreetly if you left that
+
+ align:start position:0%
+could know discreetly if you left that
+ 
+
+ align:start position:0%
+could know discreetly if you left that
+basin of attraction. Right? So I'll give
+
+ align:start position:0%
+basin of attraction. Right? So I'll give
+ 
+
+ align:start position:0%
+basin of attraction. Right? So I'll give
+you the recipe for that. But it actually
+
+ align:start position:0%
+you the recipe for that. But it actually
+ 
+
+ align:start position:0%
+you the recipe for that. But it actually
+makes more sense I think in the in the
+
+ align:start position:0%
+makes more sense I think in the in the
+ 
+
+ align:start position:0%
+makes more sense I think in the in the
+motion planning context where we
+
+ align:start position:0%
+motion planning context where we
+ 
+
+ align:start position:0%
+motion planning context where we
+actually will design trajectories um
+
+ align:start position:0%
+actually will design trajectories um
+ 
+
+ align:start position:0%
+actually will design trajectories um
+that fill the space with these bases.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is the very very similar to the
+
+ align:start position:0%
+This is the very very similar to the
+ 
+
+ align:start position:0%
+This is the very very similar to the
+concept of flow tubes. Uh yes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So
+
+ align:start position:0%
+Okay. So
+ 
+
+ align:start position:0%
+Okay. So
+big idea. Turn my nonlinear system into
+
+ align:start position:0%
+big idea. Turn my nonlinear system into
+ 
+
+ align:start position:0%
+big idea. Turn my nonlinear system into
+a linear time varying system because
+
+ align:start position:0%
+a linear time varying system because
+ 
+
+ align:start position:0%
+a linear time varying system because
+I've parameter reparameterized it along
+
+ align:start position:0%
+I've parameter reparameterized it along
+ 
+
+ align:start position:0%
+I've parameter reparameterized it along
+the trajectory. Do linear time varying
+
+ align:start position:0%
+the trajectory. Do linear time varying
+ 
+
+ align:start position:0%
+the trajectory. Do linear time varying
+control. And you know even really
+
+ align:start position:0%
+control. And you know even really
+ 
+
+ align:start position:0%
+control. And you know even really
+complicated systems it'll work well.
+
+ align:start position:0%
+complicated systems it'll work well.
+ 
+
+ align:start position:0%
+complicated systems it'll work well.
+Right. We're trying to do it. We're
+
+ align:start position:0%
+Right. We're trying to do it. We're
+ 
+
+ align:start position:0%
+Right. We're trying to do it. We're
+doing it on our perching plane. we're
+
+ align:start position:0%
+doing it on our perching plane. we're
+ 
+
+ align:start position:0%
+doing it on our perching plane. we're
+doing it. I mean, it's it's really it's
+
+ align:start position:0%
+doing it. I mean, it's it's really it's
+ 
+
+ align:start position:0%
+doing it. I mean, it's it's really it's
+really pretty good idea. Um,
+
+ align:start position:0%
+really pretty good idea. Um,
+ 
+
+ align:start position:0%
+really pretty good idea. Um,
+when I first started working with it, I
+
+ align:start position:0%
+when I first started working with it, I
+ 
+
+ align:start position:0%
+when I first started working with it, I
+I thought that um it would have the
+
+ align:start position:0%
+I thought that um it would have the
+ 
+
+ align:start position:0%
+I thought that um it would have the
+problem that
+
+ align:start position:0%
+problem that
+ 
+
+ align:start position:0%
+problem that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it would have the property that it uses
+
+ align:start position:0%
+it would have the property that it uses
+ 
+
+ align:start position:0%
+it would have the property that it uses
+a lot of control to force itself back to
+
+ align:start position:0%
+a lot of control to force itself back to
+ 
+
+ align:start position:0%
+a lot of control to force itself back to
+the trajectory and sort of rigidly
+
+ align:start position:0%
+the trajectory and sort of rigidly
+ 
+
+ align:start position:0%
+the trajectory and sort of rigidly
+follow the trajectory. Right? It's easy
+
+ align:start position:0%
+follow the trajectory. Right? It's easy
+ 
+
+ align:start position:0%
+follow the trajectory. Right? It's easy
+to equate linear control with sort of
+
+ align:start position:0%
+to equate linear control with sort of
+ 
+
+ align:start position:0%
+to equate linear control with sort of
+high gain linear feedback which people
+
+ align:start position:0%
+high gain linear feedback which people
+ 
+
+ align:start position:0%
+high gain linear feedback which people
+do a lot of. Okay. But it doesn't
+
+ align:start position:0%
+do a lot of. Okay. But it doesn't
+ 
+
+ align:start position:0%
+do a lot of. Okay. But it doesn't
+necessarily need that property. If R is
+
+ align:start position:0%
+necessarily need that property. If R is
+ 
+
+ align:start position:0%
+necessarily need that property. If R is
+small in this derivation, it can
+
+ align:start position:0%
+small in this derivation, it can
+ 
+
+ align:start position:0%
+small in this derivation, it can
+actually take very subtle uh approaches
+
+ align:start position:0%
+actually take very subtle uh approaches
+ 
+
+ align:start position:0%
+actually take very subtle uh approaches
+back to the trajectory. Your system
+
+ align:start position:0%
+back to the trajectory. Your system
+ 
+
+ align:start position:0%
+back to the trajectory. Your system
+might come in and sort of, you know, do
+
+ align:start position:0%
+might come in and sort of, you know, do
+ 
+
+ align:start position:0%
+might come in and sort of, you know, do
+whatever it needs to to get back on the
+
+ align:start position:0%
+whatever it needs to to get back on the
+ 
+
+ align:start position:0%
+whatever it needs to to get back on the
+trajectory with very little torque.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The only price you pay is if your torque
+
+ align:start position:0%
+The only price you pay is if your torque
+ 
+
+ align:start position:0%
+The only price you pay is if your torque
+is smaller. If you're if your R if
+
+ align:start position:0%
+is smaller. If you're if your R if
+ 
+
+ align:start position:0%
+is smaller. If you're if your R if
+you're penalizing torque use higher then
+
+ align:start position:0%
+you're penalizing torque use higher then
+ 
+
+ align:start position:0%
+you're penalizing torque use higher then
+you might restrict your that might short
+
+ align:start position:0%
+you might restrict your that might short
+ 
+
+ align:start position:0%
+you might restrict your that might short
+shrink your basin of attraction. It
+
+ align:start position:0%
+shrink your basin of attraction. It
+ 
+
+ align:start position:0%
+shrink your basin of attraction. It
+might be that that because it's trying
+
+ align:start position:0%
+might be that that because it's trying
+ 
+
+ align:start position:0%
+might be that that because it's trying
+to use less torque um it will not
+
+ align:start position:0%
+to use less torque um it will not
+ 
+
+ align:start position:0%
+to use less torque um it will not
+overcome the nonlinearities. Okay. But
+
+ align:start position:0%
+overcome the nonlinearities. Okay. But
+ 
+
+ align:start position:0%
+overcome the nonlinearities. Okay. But
+in the neighborhood of the trajectory
+
+ align:start position:0%
+in the neighborhood of the trajectory
+ 
+
+ align:start position:0%
+in the neighborhood of the trajectory
+you can get these very elegant um
+
+ align:start position:0%
+you can get these very elegant um
+ 
+
+ align:start position:0%
+you can get these very elegant um
+solutions uh which look like minimal
+
+ align:start position:0%
+solutions uh which look like minimal
+ 
+
+ align:start position:0%
+solutions uh which look like minimal
+energy kind of solutions for the
+
+ align:start position:0%
+energy kind of solutions for the
+ 
+
+ align:start position:0%
+energy kind of solutions for the
+nonlinear problem in the vicinity of
+
+ align:start position:0%
+nonlinear problem in the vicinity of
+ 
+
+ align:start position:0%
+nonlinear problem in the vicinity of
+these trajectories. Right? And so one of
+
+ align:start position:0%
+these trajectories. Right? And so one of
+ 
+
+ align:start position:0%
+these trajectories. Right? And so one of
+the ideas we'll talk about later is how
+
+ align:start position:0%
+the ideas we'll talk about later is how
+ 
+
+ align:start position:0%
+the ideas we'll talk about later is how
+do you design the minimal set of
+
+ align:start position:0%
+do you design the minimal set of
+ 
+
+ align:start position:0%
+do you design the minimal set of
+trajectories which if you use these um
+
+ align:start position:0%
+trajectories which if you use these um
+ 
+
+ align:start position:0%
+trajectories which if you use these um
+controllers which sort of do the right
+
+ align:start position:0%
+controllers which sort of do the right
+ 
+
+ align:start position:0%
+controllers which sort of do the right
+thing in a lot of places.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If you walked away from this class
+
+ align:start position:0%
+If you walked away from this class
+ 
+
+ align:start position:0%
+If you walked away from this class
+knowing nothing but direct collocation
+
+ align:start position:0%
+knowing nothing but direct collocation
+ 
+
+ align:start position:0%
+knowing nothing but direct collocation
+and linear time varying feedback
+
+ align:start position:0%
+and linear time varying feedback
+ 
+
+ align:start position:0%
+and linear time varying feedback
+control, I bet you could control a lot
+
+ align:start position:0%
+control, I bet you could control a lot
+ 
+
+ align:start position:0%
+control, I bet you could control a lot
+of cool systems. Yeah. I guess you also
+
+ align:start position:0%
+of cool systems. Yeah. I guess you also
+ 
+
+ align:start position:0%
+of cool systems. Yeah. I guess you also
+have to know CIS ID, which I'm not going
+
+ align:start position:0%
+have to know CIS ID, which I'm not going
+ 
+
+ align:start position:0%
+have to know CIS ID, which I'm not going
+to tell you about. And that's the that's
+
+ align:start position:0%
+to tell you about. And that's the that's
+ 
+
+ align:start position:0%
+to tell you about. And that's the that's
+the one that sort of that's the gotcha,
+
+ align:start position:0%
+the one that sort of that's the gotcha,
+ 
+
+ align:start position:0%
+the one that sort of that's the gotcha,
+right? You have to have a model for all
+
+ align:start position:0%
+right? You have to have a model for all
+ 
+
+ align:start position:0%
+right? You have to have a model for all
+this stuff, right?
+
+ align:start position:0%
+this stuff, right?
+ 
+
+ align:start position:0%
+this stuff, right?
+But if you if you're willing if someone
+
+ align:start position:0%
+But if you if you're willing if someone
+ 
+
+ align:start position:0%
+But if you if you're willing if someone
+gives you a model or if you're willing
+
+ align:start position:0%
+gives you a model or if you're willing
+ 
+
+ align:start position:0%
+gives you a model or if you're willing
+to construct a model, then you can do a
+
+ align:start position:0%
+to construct a model, then you can do a
+ 
+
+ align:start position:0%
+to construct a model, then you can do a
+lot of things with this with this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, I want to give you one more um
+
+ align:start position:0%
+Okay, I want to give you one more um
+ 
+
+ align:start position:0%
+Okay, I want to give you one more um
+mental
+
+ align:start position:0%
+mental
+ 
+
+ align:start position:0%
+mental
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+picture to think about what this is
+
+ align:start position:0%
+picture to think about what this is
+ 
+
+ align:start position:0%
+picture to think about what this is
+doing.
+
+ align:start position:0%
+doing.
+ 
+
+ align:start position:0%
+doing.
+So it sort of launches into the next um
+
+ align:start position:0%
+So it sort of launches into the next um
+ 
+
+ align:start position:0%
+So it sort of launches into the next um
+thing here. So my cost to go function
+
+ align:start position:0%
+thing here. So my cost to go function
+ 
+
+ align:start position:0%
+thing here. So my cost to go function
+which I just erased is remember. So my
+
+ align:start position:0%
+which I just erased is remember. So my
+ 
+
+ align:start position:0%
+which I just erased is remember. So my
+my cost to go function J of R Xar T is
+
+ align:start position:0%
+my cost to go function J of R Xar T is
+ 
+
+ align:start position:0%
+my cost to go function J of R Xar T is
+Xar
+
+ align:start position:0%
+Xar
+ 
+
+ align:start position:0%
+Xar
+S of T XAR
+
+ align:start position:0%
+S of T XAR
+ 
+
+ align:start position:0%
+S of T XAR
+just like the original um this is a
+
+ align:start position:0%
+just like the original um this is a
+ 
+
+ align:start position:0%
+just like the original um this is a
+quadratic form just like the original
+
+ align:start position:0%
+quadratic form just like the original
+ 
+
+ align:start position:0%
+quadratic form just like the original
+LQR you can think of this as a quadratic
+
+ align:start position:0%
+LQR you can think of this as a quadratic
+ 
+
+ align:start position:0%
+LQR you can think of this as a quadratic
+bowl in the LTI LQR case. Am I okay
+
+ align:start position:0%
+bowl in the LTI LQR case. Am I okay
+ 
+
+ align:start position:0%
+bowl in the LTI LQR case. Am I okay
+throwing around these threeletter
+
+ align:start position:0%
+throwing around these threeletter
+ 
+
+ align:start position:0%
+throwing around these threeletter
+acronyms? In the LTI LQR case, um it was
+
+ align:start position:0%
+acronyms? In the LTI LQR case, um it was
+ 
+
+ align:start position:0%
+acronyms? In the LTI LQR case, um it was
+a a static quadratic bowl centered
+
+ align:start position:0%
+a a static quadratic bowl centered
+ 
+
+ align:start position:0%
+a a static quadratic bowl centered
+around the point I'm trying to
+
+ align:start position:0%
+around the point I'm trying to
+ 
+
+ align:start position:0%
+around the point I'm trying to
+stabilize. Right? So my cost to go, it
+
+ align:start position:0%
+stabilize. Right? So my cost to go, it
+ 
+
+ align:start position:0%
+stabilize. Right? So my cost to go, it
+said says as I move away from the point
+
+ align:start position:0%
+said says as I move away from the point
+ 
+
+ align:start position:0%
+said says as I move away from the point
+I'm trying to regulate, I'm going to
+
+ align:start position:0%
+I'm trying to regulate, I'm going to
+ 
+
+ align:start position:0%
+I'm trying to regulate, I'm going to
+incur more cost in the direction the
+
+ align:start position:0%
+incur more cost in the direction the
+ 
+
+ align:start position:0%
+incur more cost in the direction the
+sensitivity that you know the the rate
+
+ align:start position:0%
+sensitivity that you know the the rate
+ 
+
+ align:start position:0%
+sensitivity that you know the the rate
+it grows depends on the the the parame
+
+ align:start position:0%
+it grows depends on the the the parame
+ 
+
+ align:start position:0%
+it grows depends on the the the parame
+the the variables inside S. Okay. Now in
+
+ align:start position:0%
+the the variables inside S. Okay. Now in
+ 
+
+ align:start position:0%
+the the variables inside S. Okay. Now in
+this picture
+
+ align:start position:0%
+this picture
+ 
+
+ align:start position:0%
+this picture
+I have a still a time varying I have a
+
+ align:start position:0%
+I have a still a time varying I have a
+ 
+
+ align:start position:0%
+I have a still a time varying I have a
+time varying quadratic bowl but it's
+
+ align:start position:0%
+time varying quadratic bowl but it's
+ 
+
+ align:start position:0%
+time varying quadratic bowl but it's
+also moving through time because it's um
+
+ align:start position:0%
+also moving through time because it's um
+ 
+
+ align:start position:0%
+also moving through time because it's um
+it's par it's it's very based on xbar.
+
+ align:start position:0%
+it's par it's it's very based on xbar.
+ 
+
+ align:start position:0%
+it's par it's it's very based on xbar.
+Yeah. So in my pendulum world, if I have
+
+ align:start position:0%
+Yeah. So in my pendulum world, if I have
+ 
+
+ align:start position:0%
+Yeah. So in my pendulum world, if I have
+this sort of nominal trajectory,
+
+ align:start position:0%
+this sort of nominal trajectory,
+ 
+
+ align:start position:0%
+this sort of nominal trajectory,
+you could think of it as having some
+
+ align:start position:0%
+you could think of it as having some
+ 
+
+ align:start position:0%
+you could think of it as having some
+quadratic bowl here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the the the LTI stabilizer that we
+
+ align:start position:0%
+And the the the LTI stabilizer that we
+ 
+
+ align:start position:0%
+And the the the LTI stabilizer that we
+did come up with that was based on LQR
+
+ align:start position:0%
+did come up with that was based on LQR
+ 
+
+ align:start position:0%
+did come up with that was based on LQR
+did have some sort of quadratic bowl
+
+ align:start position:0%
+did have some sort of quadratic bowl
+ 
+
+ align:start position:0%
+did have some sort of quadratic bowl
+shape that looked like that. Okay.
+
+ align:start position:0%
+shape that looked like that. Okay.
+ 
+
+ align:start position:0%
+shape that looked like that. Okay.
+Backwards in time, there's going to be
+
+ align:start position:0%
+Backwards in time, there's going to be
+ 
+
+ align:start position:0%
+Backwards in time, there's going to be
+another quadratic bowl. Can I sort of
+
+ align:start position:0%
+another quadratic bowl. Can I sort of
+ 
+
+ align:start position:0%
+another quadratic bowl. Can I sort of
+draw it very badly like this as maybe
+
+ align:start position:0%
+draw it very badly like this as maybe
+ 
+
+ align:start position:0%
+draw it very badly like this as maybe
+some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if I can just draw it coming off the the
+
+ align:start position:0%
+if I can just draw it coming off the the
+ 
+
+ align:start position:0%
+if I can just draw it coming off the the
+board a little bit. So there's some
+
+ align:start position:0%
+board a little bit. So there's some
+ 
+
+ align:start position:0%
+board a little bit. So there's some
+quadratic bowl
+
+ align:start position:0%
+quadratic bowl
+ 
+
+ align:start position:0%
+quadratic bowl
+um centered around this point which is
+
+ align:start position:0%
+um centered around this point which is
+ 
+
+ align:start position:0%
+um centered around this point which is
+my cost to go at that point. If I march
+
+ align:start position:0%
+my cost to go at that point. If I march
+ 
+
+ align:start position:0%
+my cost to go at that point. If I march
+farther backwards in time I've got some
+
+ align:start position:0%
+farther backwards in time I've got some
+ 
+
+ align:start position:0%
+farther backwards in time I've got some
+other quadratic bowl around this point.
+
+ align:start position:0%
+other quadratic bowl around this point.
+ 
+
+ align:start position:0%
+other quadratic bowl around this point.
+That sort of makes the point again that
+
+ align:start position:0%
+That sort of makes the point again that
+ 
+
+ align:start position:0%
+That sort of makes the point again that
+that um of the if you if I were to get
+
+ align:start position:0%
+that um of the if you if I were to get
+ 
+
+ align:start position:0%
+that um of the if you if I were to get
+pushed if my quadratic bowl is currently
+
+ align:start position:0%
+pushed if my quadratic bowl is currently
+ 
+
+ align:start position:0%
+pushed if my quadratic bowl is currently
+you know this because time is five or I
+
+ align:start position:0%
+you know this because time is five or I
+ 
+
+ align:start position:0%
+you know this because time is five or I
+had a 4 second trajectory maybe time is
+
+ align:start position:0%
+had a 4 second trajectory maybe time is
+ 
+
+ align:start position:0%
+had a 4 second trajectory maybe time is
+three here. If I'm pushed along the
+
+ align:start position:0%
+three here. If I'm pushed along the
+ 
+
+ align:start position:0%
+three here. If I'm pushed along the
+trajectory, it's actually going to ex,
+
+ align:start position:0%
+trajectory, it's actually going to ex,
+ 
+
+ align:start position:0%
+trajectory, it's actually going to ex,
+you know, incur just as much cost
+
+ align:start position:0%
+you know, incur just as much cost
+ 
+
+ align:start position:0%
+you know, incur just as much cost
+roughly as I as I'm pushed another
+
+ align:start position:0%
+roughly as I as I'm pushed another
+ 
+
+ align:start position:0%
+roughly as I as I'm pushed another
+direction. That there's a quadratic bowl
+
+ align:start position:0%
+direction. That there's a quadratic bowl
+ 
+
+ align:start position:0%
+direction. That there's a quadratic bowl
+literally centered around x0 at time t,
+
+ align:start position:0%
+literally centered around x0 at time t,
+ 
+
+ align:start position:0%
+literally centered around x0 at time t,
+right? That's what
+
+ align:start position:0%
+right? That's what
+ 
+
+ align:start position:0%
+right? That's what
+this equation says.
+
+ align:start position:0%
+this equation says.
+ 
+
+ align:start position:0%
+this equation says.
+And this quadratic bowl is the cost to
+
+ align:start position:0%
+And this quadratic bowl is the cost to
+ 
+
+ align:start position:0%
+And this quadratic bowl is the cost to
+go estimate, right? It says if I'm um
+
+ align:start position:0%
+go estimate, right? It says if I'm um
+ 
+
+ align:start position:0%
+go estimate, right? It says if I'm um
+away from the trajectory, you know, I
+
+ align:start position:0%
+away from the trajectory, you know, I
+ 
+
+ align:start position:0%
+away from the trajectory, you know, I
+should expect the cost I incur in
+
+ align:start position:0%
+should expect the cost I incur in
+ 
+
+ align:start position:0%
+should expect the cost I incur in
+getting back towards the trajectory to
+
+ align:start position:0%
+getting back towards the trajectory to
+ 
+
+ align:start position:0%
+getting back towards the trajectory to
+be this quadratic form.
+
+ align:start position:0%
+be this quadratic form.
+ 
+
+ align:start position:0%
+be this quadratic form.
+Is that okay?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the key point is because I've
+
+ align:start position:0%
+And the key point is because I've
+ 
+
+ align:start position:0%
+And the key point is because I've
+reparameterized my um equations in terms
+
+ align:start position:0%
+reparameterized my um equations in terms
+ 
+
+ align:start position:0%
+reparameterized my um equations in terms
+of xbar, this quadratic bowl always
+
+ align:start position:0%
+of xbar, this quadratic bowl always
+ 
+
+ align:start position:0%
+of xbar, this quadratic bowl always
+lives on that um trajectory.
+
+ align:start position:0%
+lives on that um trajectory.
+ 
+
+ align:start position:0%
+lives on that um trajectory.
+Okay, the best thing to do my cost
+
+ align:start position:0%
+Okay, the best thing to do my cost
+ 
+
+ align:start position:0%
+Okay, the best thing to do my cost
+function was xar qxar. My best thing to
+
+ align:start position:0%
+function was xar qxar. My best thing to
+ 
+
+ align:start position:0%
+function was xar qxar. My best thing to
+do is to drive xar to zero, which means
+
+ align:start position:0%
+do is to drive xar to zero, which means
+ 
+
+ align:start position:0%
+do is to drive xar to zero, which means
+to drive my system back to the
+
+ align:start position:0%
+to drive my system back to the
+ 
+
+ align:start position:0%
+to drive my system back to the
+trajectory.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+People okay with that imagery? I don't.
+
+ align:start position:0%
+People okay with that imagery? I don't.
+ 
+
+ align:start position:0%
+People okay with that imagery? I don't.
+It doesn't look like they are. Everybody
+
+ align:start position:0%
+It doesn't look like they are. Everybody
+ 
+
+ align:start position:0%
+It doesn't look like they are. Everybody
+is okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Are we okay with the LTI stabilizer
+
+ align:start position:0%
+Are we okay with the LTI stabilizer
+ 
+
+ align:start position:0%
+Are we okay with the LTI stabilizer
+being an LQR bowl or a quadratic bowl?
+
+ align:start position:0%
+being an LQR bowl or a quadratic bowl?
+ 
+
+ align:start position:0%
+being an LQR bowl or a quadratic bowl?
+Says the farther I am away in the
+
+ align:start position:0%
+Says the farther I am away in the
+ 
+
+ align:start position:0%
+Says the farther I am away in the
+directions defined by S, I'm going to
+
+ align:start position:0%
+directions defined by S, I'm going to
+ 
+
+ align:start position:0%
+directions defined by S, I'm going to
+incur some cost getting back.
+
+ align:start position:0%
+incur some cost getting back.
+ 
+
+ align:start position:0%
+incur some cost getting back.
+This is just the same thing. It says if
+
+ align:start position:0%
+This is just the same thing. It says if
+ 
+
+ align:start position:0%
+This is just the same thing. It says if
+I'm at this point on the trajectory,
+
+ align:start position:0%
+I'm at this point on the trajectory,
+ 
+
+ align:start position:0%
+I'm at this point on the trajectory,
+right, I'm going to incur this cost to
+
+ align:start position:0%
+right, I'm going to incur this cost to
+ 
+
+ align:start position:0%
+right, I'm going to incur this cost to
+go. And the best thing to do, the
+
+ align:start position:0%
+go. And the best thing to do, the
+ 
+
+ align:start position:0%
+go. And the best thing to do, the
+minimal cost to go is living right on
+
+ align:start position:0%
+minimal cost to go is living right on
+ 
+
+ align:start position:0%
+minimal cost to go is living right on
+that trajectory.
+
+ align:start position:0%
+that trajectory.
+ 
+
+ align:start position:0%
+that trajectory.
+As a consequence, the optimal
+
+ align:start position:0%
+As a consequence, the optimal
+ 
+
+ align:start position:0%
+As a consequence, the optimal
+controller, which tries to go down the
+
+ align:start position:0%
+controller, which tries to go down the
+ 
+
+ align:start position:0%
+controller, which tries to go down the
+landscape of the cost to go, is going to
+
+ align:start position:0%
+landscape of the cost to go, is going to
+ 
+
+ align:start position:0%
+landscape of the cost to go, is going to
+drive me back to the trajectory.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now, I said all that because I'm about
+
+ align:start position:0%
+Now, I said all that because I'm about
+ 
+
+ align:start position:0%
+Now, I said all that because I'm about
+to do something that sounds totally
+
+ align:start position:0%
+to do something that sounds totally
+ 
+
+ align:start position:0%
+to do something that sounds totally
+wacky.
+
+ align:start position:0%
+wacky.
+ 
+
+ align:start position:0%
+wacky.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What would I what would it would it ever
+
+ align:start position:0%
+What would I what would it would it ever
+ 
+
+ align:start position:0%
+What would I what would it would it ever
+make sense for me to design a slightly
+
+ align:start position:0%
+make sense for me to design a slightly
+ 
+
+ align:start position:0%
+make sense for me to design a slightly
+different cost function
+
+ align:start position:0%
+different cost function
+ 
+
+ align:start position:0%
+different cost function
+which when I linearize and design the
+
+ align:start position:0%
+which when I linearize and design the
+ 
+
+ align:start position:0%
+which when I linearize and design the
+the feedback controller I end up with a
+
+ align:start position:0%
+the feedback controller I end up with a
+ 
+
+ align:start position:0%
+the feedback controller I end up with a
+cost to go over here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's say I had let's say I I have
+
+ align:start position:0%
+So let's say I had let's say I I have
+ 
+
+ align:start position:0%
+So let's say I had let's say I I have
+some nominal trajectory I found through
+
+ align:start position:0%
+some nominal trajectory I found through
+ 
+
+ align:start position:0%
+some nominal trajectory I found through
+whatever method um some reasonable
+
+ align:start position:0%
+whatever method um some reasonable
+ 
+
+ align:start position:0%
+whatever method um some reasonable
+system trajectory
+
+ align:start position:0%
+system trajectory
+ 
+
+ align:start position:0%
+system trajectory
+but I really I'm still not happy with
+
+ align:start position:0%
+but I really I'm still not happy with
+ 
+
+ align:start position:0%
+but I really I'm still not happy with
+that. the the trajectory I really wanted
+
+ align:start position:0%
+that. the the trajectory I really wanted
+ 
+
+ align:start position:0%
+that. the the trajectory I really wanted
+was something like this,
+
+ align:start position:0%
+was something like this,
+ 
+
+ align:start position:0%
+was something like this,
+let's say.
+
+ align:start position:0%
+let's say.
+ 
+
+ align:start position:0%
+let's say.
+Would it make any sense to do my
+
+ align:start position:0%
+Would it make any sense to do my
+ 
+
+ align:start position:0%
+Would it make any sense to do my
+linearization around this trajectory
+
+ align:start position:0%
+linearization around this trajectory
+ 
+
+ align:start position:0%
+linearization around this trajectory
+and try to drive the system to this
+
+ align:start position:0%
+and try to drive the system to this
+ 
+
+ align:start position:0%
+and try to drive the system to this
+other trajectory?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You mean like scaling your optimal
+
+ align:start position:0%
+You mean like scaling your optimal
+ 
+
+ align:start position:0%
+You mean like scaling your optimal
+trajectory?
+
+ align:start position:0%
+trajectory?
+ 
+
+ align:start position:0%
+trajectory?
+I don't even mean scaling. It could they
+
+ align:start position:0%
+I don't even mean scaling. It could they
+ 
+
+ align:start position:0%
+I don't even mean scaling. It could they
+could cross. They could do whatever.
+
+ align:start position:0%
+could cross. They could do whatever.
+ 
+
+ align:start position:0%
+could cross. They could do whatever.
+It's not a simple scaling.
+
+ align:start position:0%
+It's not a simple scaling.
+ 
+
+ align:start position:0%
+It's not a simple scaling.
+Let me give you a simple simpler version
+
+ align:start position:0%
+Let me give you a simple simpler version
+ 
+
+ align:start position:0%
+Let me give you a simple simpler version
+of the problem. Let's say that um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Say that again. the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cost.
+
+ align:start position:0%
+cost.
+ 
+
+ align:start position:0%
+cost.
+Yes, I'm going to define a cost function
+
+ align:start position:0%
+Yes, I'm going to define a cost function
+ 
+
+ align:start position:0%
+Yes, I'm going to define a cost function
+which would have it so I prefer to live
+
+ align:start position:0%
+which would have it so I prefer to live
+ 
+
+ align:start position:0%
+which would have it so I prefer to live
+on that trajectory.
+
+ align:start position:0%
+on that trajectory.
+ 
+
+ align:start position:0%
+on that trajectory.
+Let me do it in the time invariant case
+
+ align:start position:0%
+Let me do it in the time invariant case
+ 
+
+ align:start position:0%
+Let me do it in the time invariant case
+just so it's it's clear. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say my coordinate system is back
+
+ align:start position:0%
+let's say my coordinate system is back
+ 
+
+ align:start position:0%
+let's say my coordinate system is back
+and simple. It lives around zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's say I have that cost function
+
+ align:start position:0%
+Let's say I have that cost function
+ 
+
+ align:start position:0%
+Let's say I have that cost function
+or sorry that dynamics and instead of my
+
+ align:start position:0%
+or sorry that dynamics and instead of my
+ 
+
+ align:start position:0%
+or sorry that dynamics and instead of my
+original cost function was just xrpose
+
+ align:start position:0%
+original cost function was just xrpose
+ 
+
+ align:start position:0%
+original cost function was just xrpose
+qx let's say my cost function now
+
+ align:start position:0%
+qx let's say my cost function now
+ 
+
+ align:start position:0%
+qx let's say my cost function now
+is Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's think about this problem for a
+
+ align:start position:0%
+Let's think about this problem for a
+ 
+
+ align:start position:0%
+Let's think about this problem for a
+second. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's say I have a linear system. Now
+
+ align:start position:0%
+So let's say I have a linear system. Now
+ 
+
+ align:start position:0%
+So let's say I have a linear system. Now
+the LQR controller we did initially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a little sloppy with that but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the L LQR controller I did initially
+
+ align:start position:0%
+the L LQR controller I did initially
+ 
+
+ align:start position:0%
+the L LQR controller I did initially
+always assumed that the desired place
+
+ align:start position:0%
+always assumed that the desired place
+ 
+
+ align:start position:0%
+always assumed that the desired place
+you wanted to be in life was zero.
+
+ align:start position:0%
+you wanted to be in life was zero.
+ 
+
+ align:start position:0%
+you wanted to be in life was zero.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+If the desired place you want to be in
+
+ align:start position:0%
+If the desired place you want to be in
+ 
+
+ align:start position:0%
+If the desired place you want to be in
+life is a constant, you know, it's
+
+ align:start position:0%
+life is a constant, you know, it's
+ 
+
+ align:start position:0%
+life is a constant, you know, it's
+three, let's say, then you can still do
+
+ align:start position:0%
+three, let's say, then you can still do
+ 
+
+ align:start position:0%
+three, let's say, then you can still do
+your fine same old linear quadratic
+
+ align:start position:0%
+your fine same old linear quadratic
+ 
+
+ align:start position:0%
+your fine same old linear quadratic
+regulator, just move your coordinate
+
+ align:start position:0%
+regulator, just move your coordinate
+ 
+
+ align:start position:0%
+regulator, just move your coordinate
+system so the three is zero. Yeah.
+
+ align:start position:0%
+system so the three is zero. Yeah.
+ 
+
+ align:start position:0%
+system so the three is zero. Yeah.
+But let's say I've got a linear system,
+
+ align:start position:0%
+But let's say I've got a linear system,
+ 
+
+ align:start position:0%
+But let's say I've got a linear system,
+but I want to drive it through some
+
+ align:start position:0%
+but I want to drive it through some
+ 
+
+ align:start position:0%
+but I want to drive it through some
+trajectory, right? Time varying
+
+ align:start position:0%
+trajectory, right? Time varying
+ 
+
+ align:start position:0%
+trajectory, right? Time varying
+trajectory. X desired is a function of
+
+ align:start position:0%
+trajectory. X desired is a function of
+ 
+
+ align:start position:0%
+trajectory. X desired is a function of
+time.
+
+ align:start position:0%
+time.
+ 
+
+ align:start position:0%
+time.
+Okay, then I can't quite just reenter
+
+ align:start position:0%
+Okay, then I can't quite just reenter
+ 
+
+ align:start position:0%
+Okay, then I can't quite just reenter
+the origin. I've got to think about how
+
+ align:start position:0%
+the origin. I've got to think about how
+ 
+
+ align:start position:0%
+the origin. I've got to think about how
+do I drive my linear system through some
+
+ align:start position:0%
+do I drive my linear system through some
+ 
+
+ align:start position:0%
+do I drive my linear system through some
+other trajectories.
+
+ align:start position:0%
+other trajectories.
+ 
+
+ align:start position:0%
+other trajectories.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now the the it's actually
+
+ align:start position:0%
+Now the the it's actually
+ 
+
+ align:start position:0%
+Now the the it's actually
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so LTI system but my cost function is
+
+ align:start position:0%
+so LTI system but my cost function is
+ 
+
+ align:start position:0%
+so LTI system but my cost function is
+time varying because my I have this
+
+ align:start position:0%
+time varying because my I have this
+ 
+
+ align:start position:0%
+time varying because my I have this
+desired trajectory that varies with
+
+ align:start position:0%
+desired trajectory that varies with
+ 
+
+ align:start position:0%
+desired trajectory that varies with
+time.
+
+ align:start position:0%
+time.
+ 
+
+ align:start position:0%
+time.
+The result I won't write it down again.
+
+ align:start position:0%
+The result I won't write it down again.
+ 
+
+ align:start position:0%
+The result I won't write it down again.
+It's exactly again. I can do this uh uh
+
+ align:start position:0%
+It's exactly again. I can do this uh uh
+ 
+
+ align:start position:0%
+It's exactly again. I can do this uh uh
+ricotti equation back up, right? The
+
+ align:start position:0%
+ricotti equation back up, right? The
+ 
+
+ align:start position:0%
+ricotti equation back up, right? The
+only difference is that the the
+
+ align:start position:0%
+only difference is that the the
+ 
+
+ align:start position:0%
+only difference is that the the
+quadratic bowl is no longer going to be
+
+ align:start position:0%
+quadratic bowl is no longer going to be
+ 
+
+ align:start position:0%
+quadratic bowl is no longer going to be
+centered on the origin.
+
+ align:start position:0%
+centered on the origin.
+ 
+
+ align:start position:0%
+centered on the origin.
+The quadratic bowl is going to move with
+
+ align:start position:0%
+The quadratic bowl is going to move with
+ 
+
+ align:start position:0%
+The quadratic bowl is going to move with
+that desired trajectory.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Yeah.
+
+ align:start position:0%
+Okay. Yeah.
+ 
+
+ align:start position:0%
+Okay. Yeah.
+If that's far away from where you
+
+ align:start position:0%
+If that's far away from where you
+ 
+
+ align:start position:0%
+If that's far away from where you
+linearized, could you
+
+ align:start position:0%
+linearized, could you
+ 
+
+ align:start position:0%
+linearized, could you
+That's That's excellent question. So I'm
+
+ align:start position:0%
+That's That's excellent question. So I'm
+ 
+
+ align:start position:0%
+That's That's excellent question. So I'm
+going to um but this is a linear system.
+
+ align:start position:0%
+going to um but this is a linear system.
+ 
+
+ align:start position:0%
+going to um but this is a linear system.
+So first we don't have to worry about
+
+ align:start position:0%
+So first we don't have to worry about
+ 
+
+ align:start position:0%
+So first we don't have to worry about
+that. But that's but don't let me forget
+
+ align:start position:0%
+that. But that's but don't let me forget
+ 
+
+ align:start position:0%
+that. But that's but don't let me forget
+to go back to that. Um
+
+ align:start position:0%
+to go back to that. Um
+ 
+
+ align:start position:0%
+to go back to that. Um
+okay. So so right. So I can drive my
+
+ align:start position:0%
+okay. So so right. So I can drive my
+ 
+
+ align:start position:0%
+okay. So so right. So I can drive my
+linear system through some trajectory
+
+ align:start position:0%
+linear system through some trajectory
+ 
+
+ align:start position:0%
+linear system through some trajectory
+that's non zero beautifully with an LQR
+
+ align:start position:0%
+that's non zero beautifully with an LQR
+ 
+
+ align:start position:0%
+that's non zero beautifully with an LQR
+controller. The only problem is that my
+
+ align:start position:0%
+controller. The only problem is that my
+ 
+
+ align:start position:0%
+controller. The only problem is that my
+LQR controller has to have a um has a
+
+ align:start position:0%
+LQR controller has to have a um has a
+ 
+
+ align:start position:0%
+LQR controller has to have a um has a
+cost to go function and a controller
+
+ align:start position:0%
+cost to go function and a controller
+ 
+
+ align:start position:0%
+cost to go function and a controller
+which is not pointing me always at the
+
+ align:start position:0%
+which is not pointing me always at the
+ 
+
+ align:start position:0%
+which is not pointing me always at the
+origin. You wouldn't want that, right?
+
+ align:start position:0%
+origin. You wouldn't want that, right?
+ 
+
+ align:start position:0%
+origin. You wouldn't want that, right?
+So in fact the way it looks there's a
+
+ align:start position:0%
+So in fact the way it looks there's a
+ 
+
+ align:start position:0%
+So in fact the way it looks there's a
+lot of ways people derive it with
+
+ align:start position:0%
+lot of ways people derive it with
+ 
+
+ align:start position:0%
+lot of ways people derive it with
+pontriogen it's not too hard to derive
+
+ align:start position:0%
+pontriogen it's not too hard to derive
+ 
+
+ align:start position:0%
+pontriogen it's not too hard to derive
+um I prefer to derive it with the HJB
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm not going to do the the whole
+
+ align:start position:0%
+I'm not going to do the the whole
+ 
+
+ align:start position:0%
+I'm not going to do the the whole
+derivation but to bore you but but what
+
+ align:start position:0%
+derivation but to bore you but but what
+ 
+
+ align:start position:0%
+derivation but to bore you but but what
+you end up with is um J of X of t has a
+
+ align:start position:0%
+you end up with is um J of X of t has a
+ 
+
+ align:start position:0%
+you end up with is um J of X of t has a
+form xrpose s of t x
+
+ align:start position:0%
+form xrpose s of t x
+ 
+
+ align:start position:0%
+form xrpose s of t x
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+xrpose I call this s2 s1 of t plus s0 of
+
+ align:start position:0%
+xrpose I call this s2 s1 of t plus s0 of
+ 
+
+ align:start position:0%
+xrpose I call this s2 s1 of t plus s0 of
+t it's a full quadratic form
+
+ align:start position:0%
+t it's a full quadratic form
+ 
+
+ align:start position:0%
+t it's a full quadratic form
+right when I just have this it's a it's
+
+ align:start position:0%
+right when I just have this it's a it's
+ 
+
+ align:start position:0%
+right when I just have this it's a it's
+always a quadratic bowl it's always
+
+ align:start position:0%
+always a quadratic bowl it's always
+ 
+
+ align:start position:0%
+always a quadratic bowl it's always
+centered around zero if you wanted in
+
+ align:start position:0%
+centered around zero if you wanted in
+ 
+
+ align:start position:0%
+centered around zero if you wanted in
+general to be a quadratic bowl that's
+
+ align:start position:0%
+general to be a quadratic bowl that's
+ 
+
+ align:start position:0%
+general to be a quadratic bowl that's
+not necessarily at zero you need the
+
+ align:start position:0%
+not necessarily at zero you need the
+ 
+
+ align:start position:0%
+not necessarily at zero you need the
+full quadratic form term right and I
+
+ align:start position:0%
+full quadratic form term right and I
+ 
+
+ align:start position:0%
+full quadratic form term right and I
+could I could equally well have written
+
+ align:start position:0%
+could I could equally well have written
+ 
+
+ align:start position:0%
+could I could equally well have written
+this as x - x something you know desired
+
+ align:start position:0%
+this as x - x something you know desired
+ 
+
+ align:start position:0%
+this as x - x something you know desired
+s of t
+
+ align:start position:0%
+s of t
+ 
+
+ align:start position:0%
+s of t
+but let's work with this form yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is just the equation of a
+
+ align:start position:0%
+so this is just the equation of a
+ 
+
+ align:start position:0%
+so this is just the equation of a
+quadratic bowl not necessarily centered
+
+ align:start position:0%
+quadratic bowl not necessarily centered
+ 
+
+ align:start position:0%
+quadratic bowl not necessarily centered
+on or on on the origin okay and the lqr
+
+ align:start position:0%
+on or on on the origin okay and the lqr
+ 
+
+ align:start position:0%
+on or on on the origin okay and the lqr
+derivation gives me my backwards dynamic
+
+ align:start position:0%
+derivation gives me my backwards dynamic
+ 
+
+ align:start position:0%
+derivation gives me my backwards dynamic
+for S2. It gives me by backwards
+
+ align:start position:0%
+for S2. It gives me by backwards
+ 
+
+ align:start position:0%
+for S2. It gives me by backwards
+dynamics for S1 and for S0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's in the notes. It's actually
+
+ align:start position:0%
+and it's in the notes. It's actually
+ 
+
+ align:start position:0%
+and it's in the notes. It's actually
+already in your notes if it's if you
+
+ align:start position:0%
+already in your notes if it's if you
+ 
+
+ align:start position:0%
+already in your notes if it's if you
+it's in the HJB chapter that has been up
+
+ align:start position:0%
+it's in the HJB chapter that has been up
+ 
+
+ align:start position:0%
+it's in the HJB chapter that has been up
+there for a while.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now
+
+ align:start position:0%
+Now
+ 
+
+ align:start position:0%
+Now
+um the reason I'm on about all this is
+
+ align:start position:0%
+um the reason I'm on about all this is
+ 
+
+ align:start position:0%
+um the reason I'm on about all this is
+that there's another way um I told you
+
+ align:start position:0%
+that there's another way um I told you
+ 
+
+ align:start position:0%
+that there's another way um I told you
+about shooting methods. I told you about
+
+ align:start position:0%
+about shooting methods. I told you about
+ 
+
+ align:start position:0%
+about shooting methods. I told you about
+direct collocation. There's yet another
+
+ align:start position:0%
+direct collocation. There's yet another
+ 
+
+ align:start position:0%
+direct collocation. There's yet another
+way that people like to design
+
+ align:start position:0%
+way that people like to design
+ 
+
+ align:start position:0%
+way that people like to design
+trajectories
+
+ align:start position:0%
+trajectories
+ 
+
+ align:start position:0%
+trajectories
+which use LQR
+
+ align:start position:0%
+which use LQR
+ 
+
+ align:start position:0%
+which use LQR
+im you know uh directly
+
+ align:start position:0%
+im you know uh directly
+ 
+
+ align:start position:0%
+im you know uh directly
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's this iterative LQR procedure.
+
+ align:start position:0%
+and that's this iterative LQR procedure.
+ 
+
+ align:start position:0%
+and that's this iterative LQR procedure.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's say I have some um trajectory
+
+ align:start position:0%
+So let's say I have some um trajectory
+ 
+
+ align:start position:0%
+So let's say I have some um trajectory
+that I've already found x0 of t and I
+
+ align:start position:0%
+that I've already found x0 of t and I
+ 
+
+ align:start position:0%
+that I've already found x0 of t and I
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+some different trajectory which is my
+
+ align:start position:0%
+some different trajectory which is my
+ 
+
+ align:start position:0%
+some different trajectory which is my
+desired trajectory
+
+ align:start position:0%
+desired trajectory
+ 
+
+ align:start position:0%
+desired trajectory
+x desired of t.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then using this optimal tracking, if you
+
+ align:start position:0%
+Then using this optimal tracking, if you
+ 
+
+ align:start position:0%
+Then using this optimal tracking, if you
+stick back in the time varying
+
+ align:start position:0%
+stick back in the time varying
+ 
+
+ align:start position:0%
+stick back in the time varying
+components, using this optimal tracking,
+
+ align:start position:0%
+components, using this optimal tracking,
+ 
+
+ align:start position:0%
+components, using this optimal tracking,
+I can linearize my dynamical system
+
+ align:start position:0%
+I can linearize my dynamical system
+ 
+
+ align:start position:0%
+I can linearize my dynamical system
+around that. So I I have no guarantees
+
+ align:start position:0%
+around that. So I I have no guarantees
+ 
+
+ align:start position:0%
+around that. So I I have no guarantees
+that X desired is a feasible trajectory.
+
+ align:start position:0%
+that X desired is a feasible trajectory.
+ 
+
+ align:start position:0%
+that X desired is a feasible trajectory.
+In fact, many cases, it's not. For
+
+ align:start position:0%
+In fact, many cases, it's not. For
+ 
+
+ align:start position:0%
+In fact, many cases, it's not. For
+instance, X desired might be be at the
+
+ align:start position:0%
+instance, X desired might be be at the
+ 
+
+ align:start position:0%
+instance, X desired might be be at the
+goal at all times, right? If I came up
+
+ align:start position:0%
+goal at all times, right? If I came up
+ 
+
+ align:start position:0%
+goal at all times, right? If I came up
+with a perfectly feasible X desired
+
+ align:start position:0%
+with a perfectly feasible X desired
+ 
+
+ align:start position:0%
+with a perfectly feasible X desired
+trajectory, I probably wouldn't be
+
+ align:start position:0%
+trajectory, I probably wouldn't be
+ 
+
+ align:start position:0%
+trajectory, I probably wouldn't be
+running uh an openloop solver, right?
+
+ align:start position:0%
+running uh an openloop solver, right?
+ 
+
+ align:start position:0%
+running uh an openloop solver, right?
+um I want to get as I want to get as
+
+ align:start position:0%
+um I want to get as I want to get as
+ 
+
+ align:start position:0%
+um I want to get as I want to get as
+close as desired as possible to the x
+
+ align:start position:0%
+close as desired as possible to the x
+ 
+
+ align:start position:0%
+close as desired as possible to the x
+desired um while potentially minimizing
+
+ align:start position:0%
+desired um while potentially minimizing
+ 
+
+ align:start position:0%
+desired um while potentially minimizing
+cost and respecting the dynamics of the
+
+ align:start position:0%
+cost and respecting the dynamics of the
+ 
+
+ align:start position:0%
+cost and respecting the dynamics of the
+system. Yeah. So here's the way to
+
+ align:start position:0%
+system. Yeah. So here's the way to
+ 
+
+ align:start position:0%
+system. Yeah. So here's the way to
+here's one way to do it. Okay. Linearize
+
+ align:start position:0%
+here's one way to do it. Okay. Linearize
+ 
+
+ align:start position:0%
+here's one way to do it. Okay. Linearize
+my system around my initial guess x0 of
+
+ align:start position:0%
+my system around my initial guess x0 of
+ 
+
+ align:start position:0%
+my system around my initial guess x0 of
+t.
+
+ align:start position:0%
+t.
+ 
+
+ align:start position:0%
+t.
+Then design a linear optimal tracking
+
+ align:start position:0%
+Then design a linear optimal tracking
+ 
+
+ align:start position:0%
+Then design a linear optimal tracking
+linear time varying optimal tracking
+
+ align:start position:0%
+linear time varying optimal tracking
+ 
+
+ align:start position:0%
+linear time varying optimal tracking
+which tries to regulate my system as
+
+ align:start position:0%
+which tries to regulate my system as
+ 
+
+ align:start position:0%
+which tries to regulate my system as
+close as possible to that trajectory.
+
+ align:start position:0%
+close as possible to that trajectory.
+ 
+
+ align:start position:0%
+close as possible to that trajectory.
+Now, what Stephen said was was exactly
+
+ align:start position:0%
+Now, what Stephen said was was exactly
+ 
+
+ align:start position:0%
+Now, what Stephen said was was exactly
+on point. If I drive my system
+
+ align:start position:0%
+on point. If I drive my system
+ 
+
+ align:start position:0%
+on point. If I drive my system
+away from where I linearized,
+
+ align:start position:0%
+away from where I linearized,
+ 
+
+ align:start position:0%
+away from where I linearized,
+there's no guarantee that that my linear
+
+ align:start position:0%
+there's no guarantee that that my linear
+ 
+
+ align:start position:0%
+there's no guarantee that that my linear
+model was going to be any good here.
+
+ align:start position:0%
+model was going to be any good here.
+ 
+
+ align:start position:0%
+model was going to be any good here.
+Okay? But the hope is that this meth
+
+ align:start position:0%
+Okay? But the hope is that this meth
+ 
+
+ align:start position:0%
+Okay? But the hope is that this meth
+this trajectory is better a better guess
+
+ align:start position:0%
+this trajectory is better a better guess
+ 
+
+ align:start position:0%
+this trajectory is better a better guess
+than the one before.
+
+ align:start position:0%
+than the one before.
+ 
+
+ align:start position:0%
+than the one before.
+Okay? And you iterate.
+
+ align:start position:0%
+Okay? And you iterate.
+ 
+
+ align:start position:0%
+Okay? And you iterate.
+Okay?
+
+ align:start position:0%
+Okay?
+ 
+
+ align:start position:0%
+Okay?
+make another approximation around there.
+
+ align:start position:0%
+make another approximation around there.
+ 
+
+ align:start position:0%
+make another approximation around there.
+Um improve you know design the LQR
+
+ align:start position:0%
+Um improve you know design the LQR
+ 
+
+ align:start position:0%
+Um improve you know design the LQR
+controller run the LR controller that
+
+ align:start position:0%
+controller run the LR controller that
+ 
+
+ align:start position:0%
+controller run the LR controller that
+drives me here to find the new U tape
+
+ align:start position:0%
+drives me here to find the new U tape
+ 
+
+ align:start position:0%
+drives me here to find the new U tape
+that design defines my new trajectory
+
+ align:start position:0%
+that design defines my new trajectory
+ 
+
+ align:start position:0%
+that design defines my new trajectory
+repeat. Okay, that's called iterative
+
+ align:start position:0%
+repeat. Okay, that's called iterative
+ 
+
+ align:start position:0%
+repeat. Okay, that's called iterative
+LQR.
+
+ align:start position:0%
+LQR.
+ 
+
+ align:start position:0%
+LQR.
+What else is it called? Do you know?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. Do you see that? It's differential
+
+ align:start position:0%
+Yeah. Do you see that? It's differential
+ 
+
+ align:start position:0%
+Yeah. Do you see that? It's differential
+dynamic programming.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+almost there's there's a subtle
+
+ align:start position:0%
+almost there's there's a subtle
+ 
+
+ align:start position:0%
+almost there's there's a subtle
+difference which I can tell you if you
+
+ align:start position:0%
+difference which I can tell you if you
+ 
+
+ align:start position:0%
+difference which I can tell you if you
+want um there's a lot of names for it
+
+ align:start position:0%
+want um there's a lot of names for it
+ 
+
+ align:start position:0%
+want um there's a lot of names for it
+people also call it there's a um another
+
+ align:start position:0%
+people also call it there's a um another
+ 
+
+ align:start position:0%
+people also call it there's a um another
+guy Bobo some of you know Jim Babro he
+
+ align:start position:0%
+guy Bobo some of you know Jim Babro he
+ 
+
+ align:start position:0%
+guy Bobo some of you know Jim Babro he
+wrote this up called the sequential
+
+ align:start position:0%
+wrote this up called the sequential
+ 
+
+ align:start position:0%
+wrote this up called the sequential
+linear quadratic regulators so you can
+
+ align:start position:0%
+linear quadratic regulators so you can
+ 
+
+ align:start position:0%
+linear quadratic regulators so you can
+you know any sort of four-letter acronym
+
+ align:start position:0%
+you know any sort of four-letter acronym
+ 
+
+ align:start position:0%
+you know any sort of four-letter acronym
+that ends in LQR if you put it in Google
+
+ align:start position:0%
+that ends in LQR if you put it in Google
+ 
+
+ align:start position:0%
+that ends in LQR if you put it in Google
+you'll find something that's probably
+
+ align:start position:0%
+you'll find something that's probably
+ 
+
+ align:start position:0%
+you'll find something that's probably
+this idea yeah if you put it in whatever
+
+ align:start position:0%
+this idea yeah if you put it in whatever
+ 
+
+ align:start position:0%
+this idea yeah if you put it in whatever
+arbitrary constant in front of it you'll
+
+ align:start position:0%
+arbitrary constant in front of it you'll
+ 
+
+ align:start position:0%
+arbitrary constant in front of it you'll
+probably get this idea
+
+ align:start position:0%
+probably get this idea
+ 
+
+ align:start position:0%
+probably get this idea
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+what prevents your uh actuator costs
+
+ align:start position:0%
+what prevents your uh actuator costs
+ 
+
+ align:start position:0%
+what prevents your uh actuator costs
+from accumulating from one iteration to
+
+ align:start position:0%
+from accumulating from one iteration to
+ 
+
+ align:start position:0%
+from accumulating from one iteration to
+another?
+
+ align:start position:0%
+another?
+ 
+
+ align:start position:0%
+another?
+I mean, every iteration you're trying to
+
+ align:start position:0%
+I mean, every iteration you're trying to
+ 
+
+ align:start position:0%
+I mean, every iteration you're trying to
+minimize your actuator cost,
+
+ align:start position:0%
+minimize your actuator cost,
+ 
+
+ align:start position:0%
+minimize your actuator cost,
+right? But I mean, if you have a lot of
+
+ align:start position:0%
+right? But I mean, if you have a lot of
+ 
+
+ align:start position:0%
+right? But I mean, if you have a lot of
+iterations
+
+ align:start position:0%
+iterations
+ 
+
+ align:start position:0%
+iterations
+potentially grow,
+
+ align:start position:0%
+potentially grow,
+ 
+
+ align:start position:0%
+potentially grow,
+I don't actually add to my old utape. I
+
+ align:start position:0%
+I don't actually add to my old utape. I
+ 
+
+ align:start position:0%
+I don't actually add to my old utape. I
+actually completely replace my old utape
+
+ align:start position:0%
+actually completely replace my old utape
+ 
+
+ align:start position:0%
+actually completely replace my old utape
+with a new controller, which which
+
+ align:start position:0%
+with a new controller, which which
+ 
+
+ align:start position:0%
+with a new controller, which which
+drives me to the system. Oh,
+
+ align:start position:0%
+drives me to the system. Oh,
+ 
+
+ align:start position:0%
+drives me to the system. Oh,
+so there's no worries about additive
+
+ align:start position:0%
+so there's no worries about additive
+ 
+
+ align:start position:0%
+so there's no worries about additive
+sort of um actions.
+
+ align:start position:0%
+sort of um actions.
+ 
+
+ align:start position:0%
+sort of um actions.
+Um it actually tells me in my original
+
+ align:start position:0%
+Um it actually tells me in my original
+ 
+
+ align:start position:0%
+Um it actually tells me in my original
+nonlinear system what's my best guess as
+
+ align:start position:0%
+nonlinear system what's my best guess as
+ 
+
+ align:start position:0%
+nonlinear system what's my best guess as
+a as a UAPE that goes there. Yeah.
+
+ align:start position:0%
+a as a UAPE that goes there. Yeah.
+ 
+
+ align:start position:0%
+a as a UAPE that goes there. Yeah.
+Is this basically a trick to get rid of?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So very very good. So why would I want
+
+ align:start position:0%
+So very very good. So why would I want
+ 
+
+ align:start position:0%
+So very very good. So why would I want
+to do this? Why didn't I tell you about
+
+ align:start position:0%
+to do this? Why didn't I tell you about
+ 
+
+ align:start position:0%
+to do this? Why didn't I tell you about
+this first or why you know how does this
+
+ align:start position:0%
+this first or why you know how does this
+ 
+
+ align:start position:0%
+this first or why you know how does this
+compare to the other methods? Okay.
+
+ align:start position:0%
+compare to the other methods? Okay.
+ 
+
+ align:start position:0%
+compare to the other methods? Okay.
+there is a sense by which and I um I
+
+ align:start position:0%
+there is a sense by which and I um I
+ 
+
+ align:start position:0%
+there is a sense by which and I um I
+thought about doing the whole derivation
+
+ align:start position:0%
+thought about doing the whole derivation
+ 
+
+ align:start position:0%
+thought about doing the whole derivation
+but I think this is I hope that this
+
+ align:start position:0%
+but I think this is I hope that this
+ 
+
+ align:start position:0%
+but I think this is I hope that this
+sort of short discussion is is is
+
+ align:start position:0%
+sort of short discussion is is is
+ 
+
+ align:start position:0%
+sort of short discussion is is is
+sufficient. Okay. So what I'm roughly
+
+ align:start position:0%
+sufficient. Okay. So what I'm roughly
+ 
+
+ align:start position:0%
+sufficient. Okay. So what I'm roughly
+doing is I'm using LQR to come up with a
+
+ align:start position:0%
+doing is I'm using LQR to come up with a
+ 
+
+ align:start position:0%
+doing is I'm using LQR to come up with a
+quadratic approximation
+
+ align:start position:0%
+quadratic approximation
+ 
+
+ align:start position:0%
+quadratic approximation
+of where my cost where where my minimum
+
+ align:start position:0%
+of where my cost where where my minimum
+ 
+
+ align:start position:0%
+of where my cost where where my minimum
+is.
+
+ align:start position:0%
+is.
+ 
+
+ align:start position:0%
+is.
+Okay, this is very much this is very
+
+ align:start position:0%
+Okay, this is very much this is very
+ 
+
+ align:start position:0%
+Okay, this is very much this is very
+much in the spirit of those SQP methods
+
+ align:start position:0%
+much in the spirit of those SQP methods
+ 
+
+ align:start position:0%
+much in the spirit of those SQP methods
+of the sequential quadratic methods.
+
+ align:start position:0%
+of the sequential quadratic methods.
+ 
+
+ align:start position:0%
+of the sequential quadratic methods.
+Okay, I'm using computation on this line
+
+ align:start position:0%
+Okay, I'm using computation on this line
+ 
+
+ align:start position:0%
+Okay, I'm using computation on this line
+to come up with a quadratic
+
+ align:start position:0%
+to come up with a quadratic
+ 
+
+ align:start position:0%
+to come up with a quadratic
+approximation
+
+ align:start position:0%
+approximation
+ 
+
+ align:start position:0%
+approximation
+of where I think the new minimum should
+
+ align:start position:0%
+of where I think the new minimum should
+ 
+
+ align:start position:0%
+of where I think the new minimum should
+be. Okay, so as such, it's a relatively
+
+ align:start position:0%
+be. Okay, so as such, it's a relatively
+ 
+
+ align:start position:0%
+be. Okay, so as such, it's a relatively
+cheap way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um with sort of SQP properties.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+convergence properties.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+The the methods I told you about on
+
+ align:start position:0%
+The the methods I told you about on
+ 
+
+ align:start position:0%
+The the methods I told you about on
+Thursday, the back prop through time,
+
+ align:start position:0%
+Thursday, the back prop through time,
+ 
+
+ align:start position:0%
+Thursday, the back prop through time,
+the RTRL,
+
+ align:start position:0%
+the RTRL,
+ 
+
+ align:start position:0%
+the RTRL,
+um they computed J over my trajectory.
+
+ align:start position:0%
+um they computed J over my trajectory.
+ 
+
+ align:start position:0%
+um they computed J over my trajectory.
+They computed partial j partial alpha
+
+ align:start position:0%
+They computed partial j partial alpha
+ 
+
+ align:start position:0%
+They computed partial j partial alpha
+over my trajectory. They did not ever
+
+ align:start position:0%
+over my trajectory. They did not ever
+ 
+
+ align:start position:0%
+over my trajectory. They did not ever
+explicitly compute the second
+
+ align:start position:0%
+explicitly compute the second
+ 
+
+ align:start position:0%
+explicitly compute the second
+derivative.
+
+ align:start position:0%
+derivative.
+ 
+
+ align:start position:0%
+derivative.
+I never computed partial j partial alpha
+
+ align:start position:0%
+I never computed partial j partial alpha
+ 
+
+ align:start position:0%
+I never computed partial j partial alpha
+partial alpha. Right?
+
+ align:start position:0%
+partial alpha. Right?
+ 
+
+ align:start position:0%
+partial alpha. Right?
+To explicitly do an SQP update, somebody
+
+ align:start position:0%
+To explicitly do an SQP update, somebody
+ 
+
+ align:start position:0%
+To explicitly do an SQP update, somebody
+needs to compute the hessen of that
+
+ align:start position:0%
+needs to compute the hessen of that
+ 
+
+ align:start position:0%
+needs to compute the hessen of that
+um of that optimization. I'm relying on
+
+ align:start position:0%
+um of that optimization. I'm relying on
+ 
+
+ align:start position:0%
+um of that optimization. I'm relying on
+snapped to do some bookkeeping to
+
+ align:start position:0%
+snapped to do some bookkeeping to
+ 
+
+ align:start position:0%
+snapped to do some bookkeeping to
+estimate the hessian to do the second
+
+ align:start position:0%
+estimate the hessian to do the second
+ 
+
+ align:start position:0%
+estimate the hessian to do the second
+order update.
+
+ align:start position:0%
+order update.
+ 
+
+ align:start position:0%
+order update.
+Okay, I would do better if I had an
+
+ align:start position:0%
+Okay, I would do better if I had an
+ 
+
+ align:start position:0%
+Okay, I would do better if I had an
+efficient way to compute the second
+
+ align:start position:0%
+efficient way to compute the second
+ 
+
+ align:start position:0%
+efficient way to compute the second
+derivatives and I could hand that
+
+ align:start position:0%
+derivatives and I could hand that
+ 
+
+ align:start position:0%
+derivatives and I could hand that
+directly to snapped or whatever and
+
+ align:start position:0%
+directly to snapped or whatever and
+ 
+
+ align:start position:0%
+directly to snapped or whatever and
+could get would get expect faster
+
+ align:start position:0%
+could get would get expect faster
+ 
+
+ align:start position:0%
+could get would get expect faster
+convergence.
+
+ align:start position:0%
+convergence.
+ 
+
+ align:start position:0%
+convergence.
+Okay, this isn't quite the gradients
+
+ align:start position:0%
+Okay, this isn't quite the gradients
+ 
+
+ align:start position:0%
+Okay, this isn't quite the gradients
+that I want, but it has that feel to it
+
+ align:start position:0%
+that I want, but it has that feel to it
+ 
+
+ align:start position:0%
+that I want, but it has that feel to it
+and it has similar convergence
+
+ align:start position:0%
+and it has similar convergence
+ 
+
+ align:start position:0%
+and it has similar convergence
+properties. So what you should think
+
+ align:start position:0%
+properties. So what you should think
+ 
+
+ align:start position:0%
+properties. So what you should think
+about is you should think about this as
+
+ align:start position:0%
+about is you should think about this as
+ 
+
+ align:start position:0%
+about is you should think about this as
+a more explicit second- order method for
+
+ align:start position:0%
+a more explicit second- order method for
+ 
+
+ align:start position:0%
+a more explicit second- order method for
+making a large jump in my um uh in my
+
+ align:start position:0%
+making a large jump in my um uh in my
+ 
+
+ align:start position:0%
+making a large jump in my um uh in my
+trajectories with sequential quadratic
+
+ align:start position:0%
+trajectories with sequential quadratic
+ 
+
+ align:start position:0%
+trajectories with sequential quadratic
+sort of convergence results. Yeah,
+
+ align:start position:0%
+sort of convergence results. Yeah,
+ 
+
+ align:start position:0%
+sort of convergence results. Yeah,
+I feel like I've lost everybody now, but
+
+ align:start position:0%
+I feel like I've lost everybody now, but
+ 
+
+ align:start position:0%
+I feel like I've lost everybody now, but
+uh ask questions if you need to. Yeah.
+
+ align:start position:0%
+uh ask questions if you need to. Yeah.
+ 
+
+ align:start position:0%
+uh ask questions if you need to. Yeah.
+Uh the advantage of it is that uh uh
+
+ align:start position:0%
+Uh the advantage of it is that uh uh
+ 
+
+ align:start position:0%
+Uh the advantage of it is that uh uh
+it's fast. it could potentially require
+
+ align:start position:0%
+it's fast. it could potentially require
+ 
+
+ align:start position:0%
+it's fast. it could potentially require
+very few iterations to converge.
+
+ align:start position:0%
+very few iterations to converge.
+ 
+
+ align:start position:0%
+very few iterations to converge.
+One of the strong disadvantages is that
+
+ align:start position:0%
+One of the strong disadvantages is that
+ 
+
+ align:start position:0%
+One of the strong disadvantages is that
+there's no explicit way to do
+
+ align:start position:0%
+there's no explicit way to do
+ 
+
+ align:start position:0%
+there's no explicit way to do
+constraints, right? It's you have to
+
+ align:start position:0%
+constraints, right? It's you have to
+ 
+
+ align:start position:0%
+constraints, right? It's you have to
+think harder about how to do constraints
+
+ align:start position:0%
+think harder about how to do constraints
+ 
+
+ align:start position:0%
+think harder about how to do constraints
+in this.
+
+ align:start position:0%
+in this.
+ 
+
+ align:start position:0%
+in this.
+Okay? And I know less formal guarantees
+
+ align:start position:0%
+Okay? And I know less formal guarantees
+ 
+
+ align:start position:0%
+Okay? And I know less formal guarantees
+that it'll succeed because it's an
+
+ align:start position:0%
+that it'll succeed because it's an
+ 
+
+ align:start position:0%
+that it'll succeed because it's an
+approximation of that quadratic
+
+ align:start position:0%
+approximation of that quadratic
+ 
+
+ align:start position:0%
+approximation of that quadratic
+DDP actually. And so so the RL community
+
+ align:start position:0%
+DDP actually. And so so the RL community
+ 
+
+ align:start position:0%
+DDP actually. And so so the RL community
+uh uses DDP a lot and actually a lot of
+
+ align:start position:0%
+uh uses DDP a lot and actually a lot of
+ 
+
+ align:start position:0%
+uh uses DDP a lot and actually a lot of
+people who do DDP do iterative LQR for
+
+ align:start position:0%
+people who do DDP do iterative LQR for
+ 
+
+ align:start position:0%
+people who do DDP do iterative LQR for
+instance for instance Peter Beiel and
+
+ align:start position:0%
+instance for instance Peter Beiel and
+ 
+
+ align:start position:0%
+instance for instance Peter Beiel and
+those guys they always call it DDP
+
+ align:start position:0%
+those guys they always call it DDP
+ 
+
+ align:start position:0%
+those guys they always call it DDP
+they're actually doing iterative LQR DDP
+
+ align:start position:0%
+they're actually doing iterative LQR DDP
+ 
+
+ align:start position:0%
+they're actually doing iterative LQR DDP
+explicitly um actually has you have to
+
+ align:start position:0%
+explicitly um actually has you have to
+ 
+
+ align:start position:0%
+explicitly um actually has you have to
+do a second order expansion of your um
+
+ align:start position:0%
+do a second order expansion of your um
+ 
+
+ align:start position:0%
+do a second order expansion of your um
+of your dynamics. So you don't just get
+
+ align:start position:0%
+of your dynamics. So you don't just get
+ 
+
+ align:start position:0%
+of your dynamics. So you don't just get
+aftx you actually do go to second order
+
+ align:start position:0%
+aftx you actually do go to second order
+ 
+
+ align:start position:0%
+aftx you actually do go to second order
+expansion of your dynamics. Right? So
+
+ align:start position:0%
+expansion of your dynamics. Right? So
+ 
+
+ align:start position:0%
+expansion of your dynamics. Right? So
+it's a little bit more expensive of an
+
+ align:start position:0%
+it's a little bit more expensive of an
+ 
+
+ align:start position:0%
+it's a little bit more expensive of an
+update. Um but most people sort of
+
+ align:start position:0%
+update. Um but most people sort of
+ 
+
+ align:start position:0%
+update. Um but most people sort of
+equate it almost exactly to iterative
+
+ align:start position:0%
+equate it almost exactly to iterative
+ 
+
+ align:start position:0%
+equate it almost exactly to iterative
+LQR.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this X not trajectory
+
+ align:start position:0%
+So this X not trajectory
+ 
+
+ align:start position:0%
+So this X not trajectory
+is this isn't a trajectory that you
+
+ align:start position:0%
+is this isn't a trajectory that you
+ 
+
+ align:start position:0%
+is this isn't a trajectory that you
+found by doing RTRL or something like
+
+ align:start position:0%
+found by doing RTRL or something like
+ 
+
+ align:start position:0%
+found by doing RTRL or something like
+that. This is something different.
+
+ align:start position:0%
+that. This is something different.
+ 
+
+ align:start position:0%
+that. This is something different.
+So good. So this could be a standin
+
+ align:start position:0%
+So good. So this could be a standin
+ 
+
+ align:start position:0%
+So good. So this could be a standin
+replacement to RTRL. I could start with
+
+ align:start position:0%
+replacement to RTRL. I could start with
+ 
+
+ align:start position:0%
+replacement to RTRL. I could start with
+a random Xnot trajectory. So, so maybe
+
+ align:start position:0%
+a random Xnot trajectory. So, so maybe
+ 
+
+ align:start position:0%
+a random Xnot trajectory. So, so maybe
+it's better to start with a random u U
+
+ align:start position:0%
+it's better to start with a random u U
+ 
+
+ align:start position:0%
+it's better to start with a random u U
+trajectory, simulate it and get an X
+
+ align:start position:0%
+trajectory, simulate it and get an X
+ 
+
+ align:start position:0%
+trajectory, simulate it and get an X
+knot trajectory and then it will quickly
+
+ align:start position:0%
+knot trajectory and then it will quickly
+ 
+
+ align:start position:0%
+knot trajectory and then it will quickly
+reshape until it gets as close as
+
+ align:start position:0%
+reshape until it gets as close as
+ 
+
+ align:start position:0%
+reshape until it gets as close as
+possible to this X desired trajectory.
+
+ align:start position:0%
+possible to this X desired trajectory.
+ 
+
+ align:start position:0%
+possible to this X desired trajectory.
+But you're reshaping your control
+
+ align:start position:0%
+But you're reshaping your control
+ 
+
+ align:start position:0%
+But you're reshaping your control
+actions that will get you to the next.
+
+ align:start position:0%
+actions that will get you to the next.
+ 
+
+ align:start position:0%
+actions that will get you to the next.
+Yes. So, I'm reshaping you reimulating
+
+ align:start position:0%
+Yes. So, I'm reshaping you reimulating
+ 
+
+ align:start position:0%
+Yes. So, I'm reshaping you reimulating
+to get the new X.
+
+ align:start position:0%
+to get the new X.
+ 
+
+ align:start position:0%
+to get the new X.
+Yeah, I wrote it more carefully in the
+
+ align:start position:0%
+Yeah, I wrote it more carefully in the
+ 
+
+ align:start position:0%
+Yeah, I wrote it more carefully in the
+notes and but but I hope this is the the
+
+ align:start position:0%
+notes and but but I hope this is the the
+ 
+
+ align:start position:0%
+notes and but but I hope this is the the
+right level to do the class. Okay. Um
+
+ align:start position:0%
+right level to do the class. Okay. Um
+ 
+
+ align:start position:0%
+right level to do the class. Okay. Um
+and there's one extra thing that I want
+
+ align:start position:0%
+and there's one extra thing that I want
+ 
+
+ align:start position:0%
+and there's one extra thing that I want
+that. So I say you have this works if
+
+ align:start position:0%
+that. So I say you have this works if
+ 
+
+ align:start position:0%
+that. So I say you have this works if
+you have a desired x desired trajectory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which means your cost function has this
+
+ align:start position:0%
+which means your cost function has this
+ 
+
+ align:start position:0%
+which means your cost function has this
+sort of a form. Okay. But the people the
+
+ align:start position:0%
+sort of a form. Okay. But the people the
+ 
+
+ align:start position:0%
+sort of a form. Okay. But the people the
+advocates of iterative LQR and and DDP
+
+ align:start position:0%
+advocates of iterative LQR and and DDP
+ 
+
+ align:start position:0%
+advocates of iterative LQR and and DDP
+say that every cost function has this
+
+ align:start position:0%
+say that every cost function has this
+ 
+
+ align:start position:0%
+say that every cost function has this
+form.
+
+ align:start position:0%
+form.
+ 
+
+ align:start position:0%
+form.
+This is just a tailor second order
+
+ align:start position:0%
+This is just a tailor second order
+ 
+
+ align:start position:0%
+This is just a tailor second order
+tailor expansion of whatever nonlinear
+
+ align:start position:0%
+tailor expansion of whatever nonlinear
+ 
+
+ align:start position:0%
+tailor expansion of whatever nonlinear
+cost function you you want. Okay. So
+
+ align:start position:0%
+cost function you you want. Okay. So
+ 
+
+ align:start position:0%
+cost function you you want. Okay. So
+write down whatever nonlinear cost
+
+ align:start position:0%
+write down whatever nonlinear cost
+ 
+
+ align:start position:0%
+write down whatever nonlinear cost
+function you have. Do a second order
+
+ align:start position:0%
+function you have. Do a second order
+ 
+
+ align:start position:0%
+function you have. Do a second order
+expansion on it and you end up with a
+
+ align:start position:0%
+expansion on it and you end up with a
+ 
+
+ align:start position:0%
+expansion on it and you end up with a
+quadratic
+
+ align:start position:0%
+quadratic
+ 
+
+ align:start position:0%
+quadratic
+cost function like this and you can then
+
+ align:start position:0%
+cost function like this and you can then
+ 
+
+ align:start position:0%
+cost function like this and you can then
+approximate that
+
+ align:start position:0%
+approximate that
+ 
+
+ align:start position:0%
+approximate that
+solution with an iterative LQR scheme or
+
+ align:start position:0%
+solution with an iterative LQR scheme or
+ 
+
+ align:start position:0%
+solution with an iterative LQR scheme or
+RTRL or background through time. This is
+
+ align:start position:0%
+RTRL or background through time. This is
+ 
+
+ align:start position:0%
+RTRL or background through time. This is
+just this is the third out of our list
+
+ align:start position:0%
+just this is the third out of our list
+ 
+
+ align:start position:0%
+just this is the third out of our list
+of methods.
+
+ align:start position:0%
+of methods.
+ 
+
+ align:start position:0%
+of methods.
+And I just want my goal is only to know
+
+ align:start position:0%
+And I just want my goal is only to know
+ 
+
+ align:start position:0%
+And I just want my goal is only to know
+so that you know that it exists and you
+
+ align:start position:0%
+so that you know that it exists and you
+ 
+
+ align:start position:0%
+so that you know that it exists and you
+can read the notes if you want more and
+
+ align:start position:0%
+can read the notes if you want more and
+ 
+
+ align:start position:0%
+can read the notes if you want more and
+and uh you can read the papers if you
+
+ align:start position:0%
+and uh you can read the papers if you
+ 
+
+ align:start position:0%
+and uh you can read the papers if you
+want more. Okay.
+
+ align:start position:0%
+want more. Okay.
+ 
+
+ align:start position:0%
+want more. Okay.
+Yeah. Michael.
+
+ align:start position:0%
+Yeah. Michael.
+ 
+
+ align:start position:0%
+Yeah. Michael.
+So I think someone has something similar
+
+ align:start position:0%
+So I think someone has something similar
+ 
+
+ align:start position:0%
+So I think someone has something similar
+but like you're palizing the deviation
+
+ align:start position:0%
+but like you're palizing the deviation
+ 
+
+ align:start position:0%
+but like you're palizing the deviation
+from your normal control input. So what
+
+ align:start position:0%
+from your normal control input. So what
+ 
+
+ align:start position:0%
+from your normal control input. So what
+if you're like as literary the control
+
+ align:start position:0%
+if you're like as literary the control
+ 
+
+ align:start position:0%
+if you're like as literary the control
+input keeps growing but your you still
+
+ align:start position:0%
+input keeps growing but your you still
+ 
+
+ align:start position:0%
+input keeps growing but your you still
+deviation still small.
+
+ align:start position:0%
+deviation still small.
+ 
+
+ align:start position:0%
+deviation still small.
+Good. So, so um I'm als I'm I'm actually
+
+ align:start position:0%
+Good. So, so um I'm als I'm I'm actually
+ 
+
+ align:start position:0%
+Good. So, so um I'm als I'm I'm actually
+the the total cost is actually the cost
+
+ align:start position:0%
+the the total cost is actually the cost
+ 
+
+ align:start position:0%
+the the total cost is actually the cost
+with respect to some nom some some u
+
+ align:start position:0%
+with respect to some nom some some u
+ 
+
+ align:start position:0%
+with respect to some nom some some u
+desired.
+
+ align:start position:0%
+desired.
+ 
+
+ align:start position:0%
+desired.
+Okay. So I end up trying to optimize
+
+ align:start position:0%
+Okay. So I end up trying to optimize
+ 
+
+ align:start position:0%
+Okay. So I end up trying to optimize
+that in a in a coordinate system based
+
+ align:start position:0%
+that in a in a coordinate system based
+ 
+
+ align:start position:0%
+that in a in a coordinate system based
+on u knot. But the cost I'm trying to
+
+ align:start position:0%
+on u knot. But the cost I'm trying to
+ 
+
+ align:start position:0%
+on u knot. But the cost I'm trying to
+minimize is the the u in the original
+
+ align:start position:0%
+minimize is the the u in the original
+ 
+
+ align:start position:0%
+minimize is the the u in the original
+coordinate system minus u desired which
+
+ align:start position:0%
+coordinate system minus u desired which
+ 
+
+ align:start position:0%
+coordinate system minus u desired which
+in a lot of cases is zero. Right?
+
+ align:start position:0%
+in a lot of cases is zero. Right?
+ 
+
+ align:start position:0%
+in a lot of cases is zero. Right?
+So I actually end up although I do it in
+
+ align:start position:0%
+So I actually end up although I do it in
+ 
+
+ align:start position:0%
+So I actually end up although I do it in
+a weird coordinate system and it it
+
+ align:start position:0%
+a weird coordinate system and it it
+ 
+
+ align:start position:0%
+a weird coordinate system and it it
+actually sort of eventually subtracts
+
+ align:start position:0%
+actually sort of eventually subtracts
+ 
+
+ align:start position:0%
+actually sort of eventually subtracts
+itself out because I add it back in at
+
+ align:start position:0%
+itself out because I add it back in at
+ 
+
+ align:start position:0%
+itself out because I add it back in at
+the end and you it's quite easy to to
+
+ align:start position:0%
+the end and you it's quite easy to to
+ 
+
+ align:start position:0%
+the end and you it's quite easy to to
+for instance minimize u ^2 in the
+
+ align:start position:0%
+for instance minimize u ^2 in the
+ 
+
+ align:start position:0%
+for instance minimize u ^2 in the
+original coordinate system. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So on Thursday we get to do walking
+
+ align:start position:0%
+So on Thursday we get to do walking
+ 
+
+ align:start position:0%
+So on Thursday we get to do walking
+robots. We're going to move on to the
+
+ align:start position:0%
+robots. We're going to move on to the
+ 
+
+ align:start position:0%
+robots. We're going to move on to the
+next um major thing. You've now learned
+
+ align:start position:0%
+next um major thing. You've now learned
+ 
+
+ align:start position:0%
+next um major thing. You've now learned
+um three of the the of the u sort of
+
+ align:start position:0%
+um three of the the of the u sort of
+ 
+
+ align:start position:0%
+um three of the the of the u sort of
+openloop trajectory optimizers that
+
+ align:start position:0%
+openloop trajectory optimizers that
+ 
+
+ align:start position:0%
+openloop trajectory optimizers that
+people really use iterative LQR very
+
+ align:start position:0%
+people really use iterative LQR very
+ 
+
+ align:start position:0%
+people really use iterative LQR very
+quickly RTRL um background through time
+
+ align:start position:0%
+quickly RTRL um background through time
+ 
+
+ align:start position:0%
+quickly RTRL um background through time
+I grouped as one the shooting methods
+
+ align:start position:0%
+I grouped as one the shooting methods
+ 
+
+ align:start position:0%
+I grouped as one the shooting methods
+and direct collocation
+
+ align:start position:0%
+and direct collocation
+ 
+
+ align:start position:0%
+and direct collocation
+okay there's another one that that's
+
+ align:start position:0%
+okay there's another one that that's
+ 
+
+ align:start position:0%
+okay there's another one that that's
+recent addition to the scene which is
+
+ align:start position:0%
+recent addition to the scene which is
+ 
+
+ align:start position:0%
+recent addition to the scene which is
+this discrete mechanics and optimal
+
+ align:start position:0%
+this discrete mechanics and optimal
+ 
+
+ align:start position:0%
+this discrete mechanics and optimal
+control this demok if anybody was
+
+ align:start position:0%
+control this demok if anybody was
+ 
+
+ align:start position:0%
+control this demok if anybody was
+excited about that and wanted to do a
+
+ align:start position:0%
+excited about that and wanted to do a
+ 
+
+ align:start position:0%
+excited about that and wanted to do a
+class project on that that would be
+
+ align:start position:0%
+class project on that that would be
+ 
+
+ align:start position:0%
+class project on that that would be
+perfect sort of thing. Grab that paper,
+
+ align:start position:0%
+perfect sort of thing. Grab that paper,
+ 
+
+ align:start position:0%
+perfect sort of thing. Grab that paper,
+show show us that it works on the
+
+ align:start position:0%
+show show us that it works on the
+ 
+
+ align:start position:0%
+show show us that it works on the
+Acrobat card poll. That'd be beautiful.
+
+ align:start position:0%
+Acrobat card poll. That'd be beautiful.
+ 
+
+ align:start position:0%
+Acrobat card poll. That'd be beautiful.
+I'd love to sort of have that um have
+
+ align:start position:0%
+I'd love to sort of have that um have
+ 
+
+ align:start position:0%
+I'd love to sort of have that um have
+have us try that and and see how it
+
+ align:start position:0%
+have us try that and and see how it
+ 
+
+ align:start position:0%
+have us try that and and see how it
+compares to the the other methods.
+
+ align:start position:0%
+compares to the the other methods.
+ 
+
+ align:start position:0%
+compares to the the other methods.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+you've got a pretty good toolkit for for
+
+ align:start position:0%
+you've got a pretty good toolkit for for
+ 
+
+ align:start position:0%
+you've got a pretty good toolkit for for
+optimal control now, practical optimal
+
+ align:start position:0%
+optimal control now, practical optimal
+ 
+
+ align:start position:0%
+optimal control now, practical optimal
+control. Okay. Um and it works for
+
+ align:start position:0%
+control. Okay. Um and it works for
+ 
+
+ align:start position:0%
+control. Okay. Um and it works for
+flying robots, but it also work for your
+
+ align:start position:0%
+flying robots, but it also work for your
+ 
+
+ align:start position:0%
+flying robots, but it also work for your
+wheeled robots if you want to control
+
+ align:start position:0%
+wheeled robots if you want to control
+ 
+
+ align:start position:0%
+wheeled robots if you want to control
+them. um you know with better control uh
+
+ align:start position:0%
+them. um you know with better control uh
+ 
+
+ align:start position:0%
+them. um you know with better control uh
+you know PD controller could be you
+
+ align:start position:0%
+you know PD controller could be you
+ 
+
+ align:start position:0%
+you know PD controller could be you
+could do a drop-in replacement LTI um
+
+ align:start position:0%
+could do a drop-in replacement LTI um
+ 
+
+ align:start position:0%
+could do a drop-in replacement LTI um
+optimal tracking controller and it would
+
+ align:start position:0%
+optimal tracking controller and it would
+ 
+
+ align:start position:0%
+optimal tracking controller and it would
+it would be better assuming your model's
+
+ align:start position:0%
+it would be better assuming your model's
+ 
+
+ align:start position:0%
+it would be better assuming your model's
+better. Okay, so you now have these
+
+ align:start position:0%
+better. Okay, so you now have these
+ 
+
+ align:start position:0%
+better. Okay, so you now have these
+these tools. Um quick procedural things.
+
+ align:start position:0%
+these tools. Um quick procedural things.
+ 
+
+ align:start position:0%
+these tools. Um quick procedural things.
+I know we're out of time. Um so next
+
+ align:start position:0%
+I know we're out of time. Um so next
+ 
+
+ align:start position:0%
+I know we're out of time. Um so next
+Thursday well so let me say the good
+
+ align:start position:0%
+Thursday well so let me say the good
+ 
+
+ align:start position:0%
+Thursday well so let me say the good
+thing first. In two weeks you're on
+
+ align:start position:0%
+thing first. In two weeks you're on
+ 
+
+ align:start position:0%
+thing first. In two weeks you're on
+spring break. Yeah. Uh the Thursday
+
+ align:start position:0%
+spring break. Yeah. Uh the Thursday
+ 
+
+ align:start position:0%
+spring break. Yeah. Uh the Thursday
+preceding that is our midterm. Okay. Um
+
+ align:start position:0%
+preceding that is our midterm. Okay. Um
+ 
+
+ align:start position:0%
+preceding that is our midterm. Okay. Um
+so we're going to try We haven't had a
+
+ align:start position:0%
+so we're going to try We haven't had a
+ 
+
+ align:start position:0%
+so we're going to try We haven't had a
+midterm in the class before. So there's
+
+ align:start position:0%
+midterm in the class before. So there's
+ 
+
+ align:start position:0%
+midterm in the class before. So there's
+no old exams for me to give you, but but
+
+ align:start position:0%
+no old exams for me to give you, but but
+ 
+
+ align:start position:0%
+no old exams for me to give you, but but
+John and I are going to try to come up
+
+ align:start position:0%
+John and I are going to try to come up
+ 
+
+ align:start position:0%
+John and I are going to try to come up
+with some um some representative
+
+ align:start position:0%
+with some um some representative
+ 
+
+ align:start position:0%
+with some um some representative
+problems for you to take home for
+
+ align:start position:0%
+problems for you to take home for
+ 
+
+ align:start position:0%
+problems for you to take home for
+Thursday of this week. Yeah. So you can
+
+ align:start position:0%
+Thursday of this week. Yeah. So you can
+ 
+
+ align:start position:0%
+Thursday of this week. Yeah. So you can
+have some some problems to munch on um
+
+ align:start position:0%
+have some some problems to munch on um
+ 
+
+ align:start position:0%
+have some some problems to munch on um
+over the weekend. It'll be an in-class
+
+ align:start position:0%
+over the weekend. It'll be an in-class
+ 
+
+ align:start position:0%
+over the weekend. It'll be an in-class
+exam um Thursday before spring break,
+
+ align:start position:0%
+exam um Thursday before spring break,
+ 
+
+ align:start position:0%
+exam um Thursday before spring break,
+which is a week from Thursday.
+
+ align:start position:0%
+which is a week from Thursday.
+ 
+
+ align:start position:0%
+which is a week from Thursday.
+Okay. Um
+
+ align:start position:0%
+Okay. Um
+ 
+
+ align:start position:0%
+Okay. Um
+any reference material?
+
+ align:start position:0%
+any reference material?
+ 
+
+ align:start position:0%
+any reference material?
+Yes. So open book uh well I mean you can
+
+ align:start position:0%
+Yes. So open book uh well I mean you can
+ 
+
+ align:start position:0%
+Yes. So open book uh well I mean you can
+grab you can grab whatever notes open
+
+ align:start position:0%
+grab you can grab whatever notes open
+ 
+
+ align:start position:0%
+grab you can grab whatever notes open
+note exam. Um absolutely and well I I'll
+
+ align:start position:0%
+note exam. Um absolutely and well I I'll
+ 
+
+ align:start position:0%
+note exam. Um absolutely and well I I'll
+say it more in the preparation package
+
+ align:start position:0%
+say it more in the preparation package
+ 
+
+ align:start position:0%
+say it more in the preparation package
+but but roughly we're going to uh I
+
+ align:start position:0%
+but but roughly we're going to uh I
+ 
+
+ align:start position:0%
+but but roughly we're going to uh I
+think if you have your notes with you if
+
+ align:start position:0%
+think if you have your notes with you if
+ 
+
+ align:start position:0%
+think if you have your notes with you if
+you've done the problem set and most
+
+ align:start position:0%
+you've done the problem set and most
+ 
+
+ align:start position:0%
+you've done the problem set and most
+importantly if you know how these
+
+ align:start position:0%
+importantly if you know how these
+ 
+
+ align:start position:0%
+importantly if you know how these
+algorithms where the algorithms sort of
+
+ align:start position:0%
+algorithms where the algorithms sort of
+ 
+
+ align:start position:0%
+algorithms where the algorithms sort of
+relate to each other and where they
+
+ align:start position:0%
+relate to each other and where they
+ 
+
+ align:start position:0%
+relate to each other and where they
+would be used in different systems I can
+
+ align:start position:0%
+would be used in different systems I can
+ 
+
+ align:start position:0%
+would be used in different systems I can
+guarantee I'm going to ask you something
+
+ align:start position:0%
+guarantee I'm going to ask you something
+ 
+
+ align:start position:0%
+guarantee I'm going to ask you something
+about that. then um then it's not going
+
+ align:start position:0%
+about that. then um then it's not going
+ 
+
+ align:start position:0%
+about that. then um then it's not going
+to it's not designed to be a killer.
+
+ align:start position:0%
+to it's not designed to be a killer.
+ 
+
+ align:start position:0%
+to it's not designed to be a killer.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+good. And and I hope you start thinking
+
+ align:start position:0%
+good. And and I hope you start thinking
+ 
+
+ align:start position:0%
+good. And and I hope you start thinking
+about projects. We're going to ask I
+
+ align:start position:0%
+about projects. We're going to ask I
+ 
+
+ align:start position:0%
+about projects. We're going to ask I
+decided that I wasn't going to um just
+
+ align:start position:0%
+decided that I wasn't going to um just
+ 
+
+ align:start position:0%
+decided that I wasn't going to um just
+out of sort of being a fairly nice
+
+ align:start position:0%
+out of sort of being a fairly nice
+ 
+
+ align:start position:0%
+out of sort of being a fairly nice
+person. I wasn't going to ask you to do
+
+ align:start position:0%
+person. I wasn't going to ask you to do
+ 
+
+ align:start position:0%
+person. I wasn't going to ask you to do
+projects before your midterm, right? Um
+
+ align:start position:0%
+projects before your midterm, right? Um
+ 
+
+ align:start position:0%
+projects before your midterm, right? Um
+but this time last year, I was asking
+
+ align:start position:0%
+but this time last year, I was asking
+ 
+
+ align:start position:0%
+but this time last year, I was asking
+people to submit project uh sort of um
+
+ align:start position:0%
+people to submit project uh sort of um
+ 
+
+ align:start position:0%
+people to submit project uh sort of um
+proposals. We're going to do that sort
+
+ align:start position:0%
+proposals. We're going to do that sort
+ 
+
+ align:start position:0%
+proposals. We're going to do that sort
+of immediately after the midterm. If
+
+ align:start position:0%
+of immediately after the midterm. If
+ 
+
+ align:start position:0%
+of immediately after the midterm. If
+you've been chewing on on, you know,
+
+ align:start position:0%
+you've been chewing on on, you know,
+ 
+
+ align:start position:0%
+you've been chewing on on, you know,
+this method looked like a really good
+
+ align:start position:0%
+this method looked like a really good
+ 
+
+ align:start position:0%
+this method looked like a really good
+match to my research problem or, you
+
+ align:start position:0%
+match to my research problem or, you
+ 
+
+ align:start position:0%
+match to my research problem or, you
+know, I've never actually, you know,
+
+ align:start position:0%
+know, I've never actually, you know,
+ 
+
+ align:start position:0%
+know, I've never actually, you know,
+thought about juggling robots before or
+
+ align:start position:0%
+thought about juggling robots before or
+ 
+
+ align:start position:0%
+thought about juggling robots before or
+something like this, you can imagine.
+
+ align:start position:0%
+something like this, you can imagine.
+ 
+
+ align:start position:0%
+something like this, you can imagine.
+Um, so so in the fairly near future,
+
+ align:start position:0%
+Um, so so in the fairly near future,
+ 
+
+ align:start position:0%
+Um, so so in the fairly near future,
+we're going to ask you for a a half page
+
+ align:start position:0%
+we're going to ask you for a a half page
+ 
+
+ align:start position:0%
+we're going to ask you for a a half page
+uh project proposal uh that we can
+
+ align:start position:0%
+uh project proposal uh that we can
+ 
+
+ align:start position:0%
+uh project proposal uh that we can
+iterate with you on to to get going on a
+
+ align:start position:0%
+iterate with you on to to get going on a
+ 
+
+ align:start position:0%
+iterate with you on to to get going on a
+on a worldclass final project. Yeah.
+
+ align:start position:0%
+on a worldclass final project. Yeah.
+ 
+
+ align:start position:0%
+on a worldclass final project. Yeah.
+See you Thursday.
\ No newline at end of file
diff --git a/yTrtVwKZkwU.txt b/yTrtVwKZkwU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6db79607a9aa23d06badd7bf7cd3a1e7f34b4c99
--- /dev/null
+++ b/yTrtVwKZkwU.txt
@@ -0,0 +1,1299 @@
+align:start position:0%
+ 
+the topic of counting or combinatorics
+
+ align:start position:0%
+the topic of counting or combinatorics
+ 
+
+ align:start position:0%
+the topic of counting or combinatorics
+is an important one in a number of dis
+
+ align:start position:0%
+is an important one in a number of dis
+ 
+
+ align:start position:0%
+is an important one in a number of dis
+at different disciplines and and notably
+
+ align:start position:0%
+at different disciplines and and notably
+ 
+
+ align:start position:0%
+at different disciplines and and notably
+in computer science so the origins of
+
+ align:start position:0%
+in computer science so the origins of
+ 
+
+ align:start position:0%
+in computer science so the origins of
+the combinatorics and counting are a
+
+ align:start position:0%
+the combinatorics and counting are a
+ 
+
+ align:start position:0%
+the combinatorics and counting are a
+little bit disreputable they come out of
+
+ align:start position:0%
+little bit disreputable they come out of
+ 
+
+ align:start position:0%
+little bit disreputable they come out of
+historically out of people studying
+
+ align:start position:0%
+historically out of people studying
+ 
+
+ align:start position:0%
+historically out of people studying
+gambling and trying to calculate odds
+
+ align:start position:0%
+gambling and trying to calculate odds
+ 
+
+ align:start position:0%
+gambling and trying to calculate odds
+and the fraction of times that various
+
+ align:start position:0%
+and the fraction of times that various
+ 
+
+ align:start position:0%
+and the fraction of times that various
+events occur to know what kind of bets
+
+ align:start position:0%
+events occur to know what kind of bets
+ 
+
+ align:start position:0%
+events occur to know what kind of bets
+to make on them so a typical kind of
+
+ align:start position:0%
+to make on them so a typical kind of
+ 
+
+ align:start position:0%
+to make on them so a typical kind of
+question would be if you know how poker
+
+ align:start position:0%
+question would be if you know how poker
+ 
+
+ align:start position:0%
+question would be if you know how poker
+works there are various classifications
+
+ align:start position:0%
+works there are various classifications
+ 
+
+ align:start position:0%
+works there are various classifications
+of five-card hands in poker you might
+
+ align:start position:0%
+of five-card hands in poker you might
+ 
+
+ align:start position:0%
+of five-card hands in poker you might
+ask what fraction of all possible
+
+ align:start position:0%
+ask what fraction of all possible
+ 
+
+ align:start position:0%
+ask what fraction of all possible
+five-card poker hands translate into
+
+ align:start position:0%
+five-card poker hands translate into
+ 
+
+ align:start position:0%
+five-card poker hands translate into
+being a pair of jacks and is basically
+
+ align:start position:0%
+being a pair of jacks and is basically
+ 
+
+ align:start position:0%
+being a pair of jacks and is basically
+this fraction of total poker hands which
+
+ align:start position:0%
+this fraction of total poker hands which
+ 
+
+ align:start position:0%
+this fraction of total poker hands which
+fit into the category a pair of jacks is
+
+ align:start position:0%
+fit into the category a pair of jacks is
+ 
+
+ align:start position:0%
+fit into the category a pair of jacks is
+the probability of a pair of jacks so
+
+ align:start position:0%
+the probability of a pair of jacks so
+ 
+
+ align:start position:0%
+the probability of a pair of jacks so
+counting and gambling is one fundamental
+
+ align:start position:0%
+counting and gambling is one fundamental
+ 
+
+ align:start position:0%
+counting and gambling is one fundamental
+place where it really comes up and
+
+ align:start position:0%
+place where it really comes up and
+ 
+
+ align:start position:0%
+place where it really comes up and
+historically that's where a lot of
+
+ align:start position:0%
+historically that's where a lot of
+ 
+
+ align:start position:0%
+historically that's where a lot of
+combinatorics begins related to that is
+
+ align:start position:0%
+combinatorics begins related to that is
+ 
+
+ align:start position:0%
+combinatorics begins related to that is
+counting in games when you're trying to
+
+ align:start position:0%
+counting in games when you're trying to
+ 
+
+ align:start position:0%
+counting in games when you're trying to
+write for example a computer programming
+
+ align:start position:0%
+write for example a computer programming
+ 
+
+ align:start position:0%
+write for example a computer programming
+a computer program to play chess or
+
+ align:start position:0%
+a computer program to play chess or
+ 
+
+ align:start position:0%
+a computer program to play chess or
+checkers or so on one of the aspects of
+
+ align:start position:0%
+checkers or so on one of the aspects of
+ 
+
+ align:start position:0%
+checkers or so on one of the aspects of
+it is getting a sense of how much
+
+ align:start position:0%
+it is getting a sense of how much
+ 
+
+ align:start position:0%
+it is getting a sense of how much
+searching you have to do in order to
+
+ align:start position:0%
+searching you have to do in order to
+ 
+
+ align:start position:0%
+searching you have to do in order to
+look ahead to find good moves and you
+
+ align:start position:0%
+look ahead to find good moves and you
+ 
+
+ align:start position:0%
+look ahead to find good moves and you
+wind up counting from a given chess
+
+ align:start position:0%
+wind up counting from a given chess
+ 
+
+ align:start position:0%
+wind up counting from a given chess
+position how many possible further
+
+ align:start position:0%
+position how many possible further
+ 
+
+ align:start position:0%
+position how many possible further
+positions can you get to in a given
+
+ align:start position:0%
+positions can you get to in a given
+ 
+
+ align:start position:0%
+positions can you get to in a given
+number of moves a puzzle kind of
+
+ align:start position:0%
+number of moves a puzzle kind of
+ 
+
+ align:start position:0%
+number of moves a puzzle kind of
+question in solving the Rubik's Cube toy
+
+ align:start position:0%
+question in solving the Rubik's Cube toy
+ 
+
+ align:start position:0%
+question in solving the Rubik's Cube toy
+is how many different positions are
+
+ align:start position:0%
+is how many different positions are
+ 
+
+ align:start position:0%
+is how many different positions are
+there and how many different positions
+
+ align:start position:0%
+there and how many different positions
+ 
+
+ align:start position:0%
+there and how many different positions
+can you get to from a given position
+
+ align:start position:0%
+can you get to from a given position
+ 
+
+ align:start position:0%
+can you get to from a given position
+concretely in computer science it comes
+
+ align:start position:0%
+concretely in computer science it comes
+ 
+
+ align:start position:0%
+concretely in computer science it comes
+up in algorithms it's often the case
+
+ align:start position:0%
+up in algorithms it's often the case
+ 
+
+ align:start position:0%
+up in algorithms it's often the case
+that a central question is how many
+
+ align:start position:0%
+that a central question is how many
+ 
+
+ align:start position:0%
+that a central question is how many
+operations does it take to do a
+
+ align:start position:0%
+operations does it take to do a
+ 
+
+ align:start position:0%
+operations does it take to do a
+manipulation on a data structure inta
+
+ align:start position:0%
+manipulation on a data structure inta
+ 
+
+ align:start position:0%
+manipulation on a data structure inta
+updated from one to another for example
+
+ align:start position:0%
+updated from one to another for example
+ 
+
+ align:start position:0%
+updated from one to another for example
+how many comparisons does it take to
+
+ align:start position:0%
+how many comparisons does it take to
+ 
+
+ align:start position:0%
+how many comparisons does it take to
+sort n numerical items and there's a
+
+ align:start position:0%
+sort n numerical items and there's a
+ 
+
+ align:start position:0%
+sort n numerical items and there's a
+typically the countless n log n proof as
+
+ align:start position:0%
+typically the countless n log n proof as
+ 
+
+ align:start position:0%
+typically the countless n log n proof as
+someone as a number of operations that
+
+ align:start position:0%
+someone as a number of operations that
+ 
+
+ align:start position:0%
+someone as a number of operations that
+are both achievable and a lower bound
+
+ align:start position:0%
+are both achievable and a lower bound
+ 
+
+ align:start position:0%
+are both achievable and a lower bound
+one that we've seen when we looked at
+
+ align:start position:0%
+one that we've seen when we looked at
+ 
+
+ align:start position:0%
+one that we've seen when we looked at
+fast exponentiation is in question like
+
+ align:start position:0%
+fast exponentiation is in question like
+ 
+
+ align:start position:0%
+fast exponentiation is in question like
+if you're trying to compute the the nth
+
+ align:start position:0%
+if you're trying to compute the the nth
+ 
+
+ align:start position:0%
+if you're trying to compute the the nth
+power of a number d how many
+
+ align:start position:0%
+power of a number d how many
+ 
+
+ align:start position:0%
+power of a number d how many
+multiplications does it take it's
+
+ align:start position:0%
+multiplications does it take it's
+ 
+
+ align:start position:0%
+multiplications does it take it's
+roughly log n by using the iterated
+
+ align:start position:0%
+roughly log n by using the iterated
+ 
+
+ align:start position:0%
+roughly log n by using the iterated
+squaring method and we want to be able
+
+ align:start position:0%
+squaring method and we want to be able
+ 
+
+ align:start position:0%
+squaring method and we want to be able
+to count that number of multiplications
+
+ align:start position:0%
+to count that number of multiplications
+ 
+
+ align:start position:0%
+to count that number of multiplications
+that a particular program uses to
+
+ align:start position:0%
+that a particular program uses to
+ 
+
+ align:start position:0%
+that a particular program uses to
+compute D to the N and the largest of
+
+ align:start position:0%
+compute D to the N and the largest of
+ 
+
+ align:start position:0%
+compute D to the N and the largest of
+the smallest number of multiplications
+
+ align:start position:0%
+the smallest number of multiplications
+ 
+
+ align:start position:0%
+the smallest number of multiplications
+you can get away with and a place where
+
+ align:start position:0%
+you can get away with and a place where
+ 
+
+ align:start position:0%
+you can get away with and a place where
+again we're we're counting and
+
+ align:start position:0%
+again we're we're counting and
+ 
+
+ align:start position:0%
+again we're we're counting and
+combinatory becomes critical is in for
+
+ align:start position:0%
+combinatory becomes critical is in for
+ 
+
+ align:start position:0%
+combinatory becomes critical is in for
+security and the issue of of
+
+ align:start position:0%
+security and the issue of of
+ 
+
+ align:start position:0%
+security and the issue of of
+cryptography if you're going to have
+
+ align:start position:0%
+cryptography if you're going to have
+ 
+
+ align:start position:0%
+cryptography if you're going to have
+security from passwords there needs to
+
+ align:start position:0%
+security from passwords there needs to
+ 
+
+ align:start position:0%
+security from passwords there needs to
+be too large a space of passwords for an
+
+ align:start position:0%
+be too large a space of passwords for an
+ 
+
+ align:start position:0%
+be too large a space of passwords for an
+adversary to search through exhaustively
+
+ align:start position:0%
+adversary to search through exhaustively
+ 
+
+ align:start position:0%
+adversary to search through exhaustively
+and check them likewise for the if
+
+ align:start position:0%
+and check them likewise for the if
+ 
+
+ align:start position:0%
+and check them likewise for the if
+you're doing encryption with some kind
+
+ align:start position:0%
+you're doing encryption with some kind
+ 
+
+ align:start position:0%
+you're doing encryption with some kind
+of secret key that enable you to read
+
+ align:start position:0%
+of secret key that enable you to read
+ 
+
+ align:start position:0%
+of secret key that enable you to read
+messages you want to be sure that the
+
+ align:start position:0%
+messages you want to be sure that the
+ 
+
+ align:start position:0%
+messages you want to be sure that the
+space of possible keys is also way too
+
+ align:start position:0%
+space of possible keys is also way too
+ 
+
+ align:start position:0%
+space of possible keys is also way too
+large to search exhaustively to see what
+
+ align:start position:0%
+large to search exhaustively to see what
+ 
+
+ align:start position:0%
+large to search exhaustively to see what
+keys work so let's talk briefly now
+
+ align:start position:0%
+keys work so let's talk briefly now
+ 
+
+ align:start position:0%
+keys work so let's talk briefly now
+about the very basic counting methods
+
+ align:start position:0%
+about the very basic counting methods
+ 
+
+ align:start position:0%
+about the very basic counting methods
+and two rules for accounting things the
+
+ align:start position:0%
+and two rules for accounting things the
+ 
+
+ align:start position:0%
+and two rules for accounting things the
+most rudimentary of them but in fact we
+
+ align:start position:0%
+most rudimentary of them but in fact we
+ 
+
+ align:start position:0%
+most rudimentary of them but in fact we
+get some mileage out of them so the
+
+ align:start position:0%
+get some mileage out of them so the
+ 
+
+ align:start position:0%
+get some mileage out of them so the
+first rule is called the sum rule and
+
+ align:start position:0%
+first rule is called the sum rule and
+ 
+
+ align:start position:0%
+first rule is called the sum rule and
+it's completely straightforward and
+
+ align:start position:0%
+it's completely straightforward and
+ 
+
+ align:start position:0%
+it's completely straightforward and
+obvious which is that if I have two sets
+
+ align:start position:0%
+obvious which is that if I have two sets
+ 
+
+ align:start position:0%
+obvious which is that if I have two sets
+a and B that do not overlap then the
+
+ align:start position:0%
+a and B that do not overlap then the
+ 
+
+ align:start position:0%
+a and B that do not overlap then the
+number of elements in a union B is
+
+ align:start position:0%
+number of elements in a union B is
+ 
+
+ align:start position:0%
+number of elements in a union B is
+simply the number of elements in a plus
+
+ align:start position:0%
+simply the number of elements in a plus
+ 
+
+ align:start position:0%
+simply the number of elements in a plus
+the number of elements in B and there's
+
+ align:start position:0%
+the number of elements in B and there's
+ 
+
+ align:start position:0%
+the number of elements in B and there's
+no issue proving that it's self-evident
+
+ align:start position:0%
+no issue proving that it's self-evident
+ 
+
+ align:start position:0%
+no issue proving that it's self-evident
+but let's do an example suppose the
+
+ align:start position:0%
+but let's do an example suppose the
+ 
+
+ align:start position:0%
+but let's do an example suppose the
+class has 43 women and 54 men how many
+
+ align:start position:0%
+class has 43 women and 54 men how many
+ 
+
+ align:start position:0%
+class has 43 women and 54 men how many
+how many people are in it 43 plus 54
+
+ align:start position:0%
+how many people are in it 43 plus 54
+ 
+
+ align:start position:0%
+how many people are in it 43 plus 54
+equals 97 this is implicitly assuming
+
+ align:start position:0%
+equals 97 this is implicitly assuming
+ 
+
+ align:start position:0%
+equals 97 this is implicitly assuming
+that there's no one whose sex is
+
+ align:start position:0%
+that there's no one whose sex is
+ 
+
+ align:start position:0%
+that there's no one whose sex is
+ambiguous and that there's no third sex
+
+ align:start position:0%
+ambiguous and that there's no third sex
+ 
+
+ align:start position:0%
+ambiguous and that there's no third sex
+and so that men and women are disjoint
+
+ align:start position:0%
+and so that men and women are disjoint
+ 
+
+ align:start position:0%
+and so that men and women are disjoint
+the total number of students is the sum
+
+ align:start position:0%
+the total number of students is the sum
+ 
+
+ align:start position:0%
+the total number of students is the sum
+of the number of men and women another
+
+ align:start position:0%
+of the number of men and women another
+ 
+
+ align:start position:0%
+of the number of men and women another
+one is there are 26 lowercase Roman
+
+ align:start position:0%
+one is there are 26 lowercase Roman
+ 
+
+ align:start position:0%
+one is there are 26 lowercase Roman
+letters in 26 uppercase Roman letters
+
+ align:start position:0%
+letters in 26 uppercase Roman letters
+ 
+
+ align:start position:0%
+letters in 26 uppercase Roman letters
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+ten digits and so there are 26 plus 26
+
+ align:start position:0%
+ten digits and so there are 26 plus 26
+ 
+
+ align:start position:0%
+ten digits and so there are 26 plus 26
+plus 10 equals 62 characters in that
+
+ align:start position:0%
+plus 10 equals 62 characters in that
+ 
+
+ align:start position:0%
+plus 10 equals 62 characters in that
+repertoire of of symbols the second rule
+
+ align:start position:0%
+repertoire of of symbols the second rule
+ 
+
+ align:start position:0%
+repertoire of of symbols the second rule
+is called product rule and it's just
+
+ align:start position:0%
+is called product rule and it's just
+ 
+
+ align:start position:0%
+is called product rule and it's just
+about as obvious
+
+ align:start position:0%
+about as obvious
+ 
+
+ align:start position:0%
+about as obvious
+suppose I have four boys and three girls
+
+ align:start position:0%
+suppose I have four boys and three girls
+ 
+
+ align:start position:0%
+suppose I have four boys and three girls
+how many boy-girl couples can I can I
+
+ align:start position:0%
+how many boy-girl couples can I can I
+ 
+
+ align:start position:0%
+how many boy-girl couples can I can I
+assemble out of four boys and three
+
+ align:start position:0%
+assemble out of four boys and three
+ 
+
+ align:start position:0%
+assemble out of four boys and three
+girls and the answer is there are four
+
+ align:start position:0%
+girls and the answer is there are four
+ 
+
+ align:start position:0%
+girls and the answer is there are four
+ways to choose a boy followed by and for
+
+ align:start position:0%
+ways to choose a boy followed by and for
+ 
+
+ align:start position:0%
+ways to choose a boy followed by and for
+each of them there are three ways to
+
+ align:start position:0%
+each of them there are three ways to
+ 
+
+ align:start position:0%
+each of them there are three ways to
+choose a girl so there's four times
+
+ align:start position:0%
+choose a girl so there's four times
+ 
+
+ align:start position:0%
+choose a girl so there's four times
+three or twelve possible boy-girl
+
+ align:start position:0%
+three or twelve possible boy-girl
+ 
+
+ align:start position:0%
+three or twelve possible boy-girl
+couples in this setting more generally
+
+ align:start position:0%
+couples in this setting more generally
+ 
+
+ align:start position:0%
+couples in this setting more generally
+if I have a set a of size M and a set B
+
+ align:start position:0%
+if I have a set a of size M and a set B
+ 
+
+ align:start position:0%
+if I have a set a of size M and a set B
+of size n then a cross B remember that's
+
+ align:start position:0%
+of size n then a cross B remember that's
+ 
+
+ align:start position:0%
+of size n then a cross B remember that's
+the set of ordered pairs where the first
+
+ align:start position:0%
+the set of ordered pairs where the first
+ 
+
+ align:start position:0%
+the set of ordered pairs where the first
+element is from a and the second element
+
+ align:start position:0%
+element is from a and the second element
+ 
+
+ align:start position:0%
+element is from a and the second element
+is from B the size of a cross B is the
+
+ align:start position:0%
+is from B the size of a cross B is the
+ 
+
+ align:start position:0%
+is from B the size of a cross B is the
+vertical barge member of a mean size is
+
+ align:start position:0%
+vertical barge member of a mean size is
+ 
+
+ align:start position:0%
+vertical barge member of a mean size is
+equal to M times n so let's just do an
+
+ align:start position:0%
+equal to M times n so let's just do an
+ 
+
+ align:start position:0%
+equal to M times n so let's just do an
+example that illustrates it suppose that
+
+ align:start position:0%
+example that illustrates it suppose that
+ 
+
+ align:start position:0%
+example that illustrates it suppose that
+a is the set of four elements little a B
+
+ align:start position:0%
+a is the set of four elements little a B
+ 
+
+ align:start position:0%
+a is the set of four elements little a B
+C and D and B is the set of three
+
+ align:start position:0%
+C and D and B is the set of three
+ 
+
+ align:start position:0%
+C and D and B is the set of three
+numbers one two and three then I can
+
+ align:start position:0%
+numbers one two and three then I can
+ 
+
+ align:start position:0%
+numbers one two and three then I can
+list a cross B in a nice orderly way as
+
+ align:start position:0%
+list a cross B in a nice orderly way as
+ 
+
+ align:start position:0%
+list a cross B in a nice orderly way as
+a four by three matrix but this is
+
+ align:start position:0%
+a four by three matrix but this is
+ 
+
+ align:start position:0%
+a four by three matrix but this is
+really meant to be just the list of
+
+ align:start position:0%
+really meant to be just the list of
+ 
+
+ align:start position:0%
+really meant to be just the list of
+elements but I'm organizing this way so
+
+ align:start position:0%
+elements but I'm organizing this way so
+ 
+
+ align:start position:0%
+elements but I'm organizing this way so
+the pattern is more apparent and for
+
+ align:start position:0%
+the pattern is more apparent and for
+ 
+
+ align:start position:0%
+the pattern is more apparent and for
+each boy a or each element little a I
+
+ align:start position:0%
+each boy a or each element little a I
+ 
+
+ align:start position:0%
+each boy a or each element little a I
+can pair it with each of the three
+
+ align:start position:0%
+can pair it with each of the three
+ 
+
+ align:start position:0%
+can pair it with each of the three
+elements in B and for the second element
+
+ align:start position:0%
+elements in B and for the second element
+ 
+
+ align:start position:0%
+elements in B and for the second element
+little be in a I can pair it with this
+
+ align:start position:0%
+little be in a I can pair it with this
+ 
+
+ align:start position:0%
+little be in a I can pair it with this
+three digits in a and C I can pair with
+
+ align:start position:0%
+three digits in a and C I can pair with
+ 
+
+ align:start position:0%
+three digits in a and C I can pair with
+three and D I can pair with three and
+
+ align:start position:0%
+three and D I can pair with three and
+ 
+
+ align:start position:0%
+three and D I can pair with three and
+that's where the four times three comes
+
+ align:start position:0%
+that's where the four times three comes
+ 
+
+ align:start position:0%
+that's where the four times three comes
+from and more generally the M times n
+
+ align:start position:0%
+from and more generally the M times n
+ 
+
+ align:start position:0%
+from and more generally the M times n
+comes from
+
+ align:start position:0%
+comes from
+ 
+
+ align:start position:0%
+comes from
+a useful immediate application of this
+
+ align:start position:0%
+a useful immediate application of this
+ 
+
+ align:start position:0%
+a useful immediate application of this
+is how many binary strings are there how
+
+ align:start position:0%
+is how many binary strings are there how
+ 
+
+ align:start position:0%
+is how many binary strings are there how
+many strings of zeros and ones are there
+
+ align:start position:0%
+many strings of zeros and ones are there
+ 
+
+ align:start position:0%
+many strings of zeros and ones are there
+of length four well the straight the
+
+ align:start position:0%
+of length four well the straight the
+ 
+
+ align:start position:0%
+of length four well the straight the
+length four binary strings it can be
+
+ align:start position:0%
+length four binary strings it can be
+ 
+
+ align:start position:0%
+length four binary strings it can be
+explained as as the product of B times B
+
+ align:start position:0%
+explained as as the product of B times B
+ 
+
+ align:start position:0%
+explained as as the product of B times B
+times B times B and we're not writing
+
+ align:start position:0%
+times B times B and we're not writing
+ 
+
+ align:start position:0%
+times B times B and we're not writing
+parentheses here it's B times B a cross
+
+ align:start position:0%
+parentheses here it's B times B a cross
+ 
+
+ align:start position:0%
+parentheses here it's B times B a cross
+B so I'm thinking of a quadruple like
+
+ align:start position:0%
+B so I'm thinking of a quadruple like
+ 
+
+ align:start position:0%
+B so I'm thinking of a quadruple like
+this as being a pair consists element is
+
+ align:start position:0%
+this as being a pair consists element is
+ 
+
+ align:start position:0%
+this as being a pair consists element is
+triple and a triple is a pair whose
+
+ align:start position:0%
+triple and a triple is a pair whose
+ 
+
+ align:start position:0%
+triple and a triple is a pair whose
+first element is a pair and given that
+
+ align:start position:0%
+first element is a pair and given that
+ 
+
+ align:start position:0%
+first element is a pair and given that
+it doesn't really matter how you break
+
+ align:start position:0%
+it doesn't really matter how you break
+ 
+
+ align:start position:0%
+it doesn't really matter how you break
+it up we just typically write it as B
+
+ align:start position:0%
+it up we just typically write it as B
+ 
+
+ align:start position:0%
+it up we just typically write it as B
+cross B cross B and even abbreviate that
+
+ align:start position:0%
+cross B cross B and even abbreviate that
+ 
+
+ align:start position:0%
+cross B cross B and even abbreviate that
+as B to the fourth where B is 0-1
+
+ align:start position:0%
+as B to the fourth where B is 0-1
+ 
+
+ align:start position:0%
+as B to the fourth where B is 0-1
+and the rule the product rule says that
+
+ align:start position:0%
+and the rule the product rule says that
+ 
+
+ align:start position:0%
+and the rule the product rule says that
+the size of this is the size of B times
+
+ align:start position:0%
+the size of this is the size of B times
+ 
+
+ align:start position:0%
+the size of this is the size of B times
+ties the size of B times the size of B
+
+ align:start position:0%
+ties the size of B times the size of B
+ 
+
+ align:start position:0%
+ties the size of B times the size of B
+times the size of B or two to the fourth
+
+ align:start position:0%
+times the size of B or two to the fourth
+ 
+
+ align:start position:0%
+times the size of B or two to the fourth
+so in general if I look at strings of
+
+ align:start position:0%
+so in general if I look at strings of
+ 
+
+ align:start position:0%
+so in general if I look at strings of
+length n whose elements are LR from an
+
+ align:start position:0%
+length n whose elements are LR from an
+ 
+
+ align:start position:0%
+length n whose elements are LR from an
+alphabet of size M the total number of
+
+ align:start position:0%
+alphabet of size M the total number of
+ 
+
+ align:start position:0%
+alphabet of size M the total number of
+such strings is M to the N
\ No newline at end of file
diff --git a/yhI3jTX4dY4.txt b/yhI3jTX4dY4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7a2d9f801459e1fa9cc539fa8bd2b660a673ff8a
--- /dev/null
+++ b/yhI3jTX4dY4.txt
@@ -0,0 +1,931 @@
+align:start position:0%
+ 
+we have two equations now relating this
+
+ align:start position:0%
+we have two equations now relating this
+ 
+
+ align:start position:0%
+we have two equations now relating this
+number of states and now you can say all
+
+ align:start position:0%
+number of states and now you can say all
+ 
+
+ align:start position:0%
+number of states and now you can say all
+okay so I look at the K line and I look
+
+ align:start position:0%
+okay so I look at the K line and I look
+ 
+
+ align:start position:0%
+okay so I look at the K line and I look
+at a little piece DK and say oh how many
+
+ align:start position:0%
+at a little piece DK and say oh how many
+ 
+
+ align:start position:0%
+at a little piece DK and say oh how many
+states were there with zero potential
+
+ align:start position:0%
+states were there with zero potential
+ 
+
+ align:start position:0%
+states were there with zero potential
+some number first blackboard how many
+
+ align:start position:0%
+some number first blackboard how many
+ 
+
+ align:start position:0%
+some number first blackboard how many
+states are there now with some potential
+
+ align:start position:0%
+states are there now with some potential
+ 
+
+ align:start position:0%
+states are there now with some potential
+some other number it has changed for
+
+ align:start position:0%
+some other number it has changed for
+ 
+
+ align:start position:0%
+some other number it has changed for
+every because these two equations the n4
+
+ align:start position:0%
+every because these two equations the n4
+ 
+
+ align:start position:0%
+every because these two equations the n4
+equal DK the n is not equal to DN Prime
+
+ align:start position:0%
+equal DK the n is not equal to DN Prime
+ 
+
+ align:start position:0%
+equal DK the n is not equal to DN Prime
+in one case the energy levels or the
+
+ align:start position:0%
+in one case the energy levels or the
+ 
+
+ align:start position:0%
+in one case the energy levels or the
+momentum levels are more compressed or
+
+ align:start position:0%
+momentum levels are more compressed or
+ 
+
+ align:start position:0%
+momentum levels are more compressed or
+more separated but whatever it is
+
+ align:start position:0%
+more separated but whatever it is
+ 
+
+ align:start position:0%
+more separated but whatever it is
+whatever the sign is there's a little
+
+ align:start position:0%
+whatever the sign is there's a little
+ 
+
+ align:start position:0%
+whatever the sign is there's a little
+discrepancy so both of them are giving
+
+ align:start position:0%
+discrepancy so both of them are giving
+ 
+
+ align:start position:0%
+discrepancy so both of them are giving
+me the total number of positive energy
+
+ align:start position:0%
+me the total number of positive energy
+ 
+
+ align:start position:0%
+me the total number of positive energy
+states in a little DK so if I take the
+
+ align:start position:0%
+states in a little DK so if I take the
+ 
+
+ align:start position:0%
+states in a little DK so if I take the
+difference I will get some information
+
+ align:start position:0%
+difference I will get some information
+ 
+
+ align:start position:0%
+difference I will get some information
+so I would say the following if I want
+
+ align:start position:0%
+so I would say the following if I want
+ 
+
+ align:start position:0%
+so I would say the following if I want
+to calculate the number of positive
+
+ align:start position:0%
+to calculate the number of positive
+ 
+
+ align:start position:0%
+to calculate the number of positive
+energy solutions and now I think the
+
+ align:start position:0%
+energy solutions and now I think the
+ 
+
+ align:start position:0%
+energy solutions and now I think the
+following I take a potential V equals 0
+
+ align:start position:0%
+following I take a potential V equals 0
+ 
+
+ align:start position:0%
+following I take a potential V equals 0
+and slowly but surely deepen it push it
+
+ align:start position:0%
+and slowly but surely deepen it push it
+ 
+
+ align:start position:0%
+and slowly but surely deepen it push it
+and do things and create the potential V
+
+ align:start position:0%
+and do things and create the potential V
+ 
+
+ align:start position:0%
+and do things and create the potential V
+of X slowly slow the formation in this
+
+ align:start position:0%
+of X slowly slow the formation in this
+ 
+
+ align:start position:0%
+of X slowly slow the formation in this
+process I can look at a little interval
+
+ align:start position:0%
+process I can look at a little interval
+ 
+
+ align:start position:0%
+process I can look at a little interval
+decay and tell how many states the
+
+ align:start position:0%
+decay and tell how many states the
+ 
+
+ align:start position:0%
+decay and tell how many states the
+positive energy states are lost so if
+
+ align:start position:0%
+positive energy states are lost so if
+ 
+
+ align:start position:0%
+positive energy states are lost so if
+for example DN is bigger than the n
+
+ align:start position:0%
+for example DN is bigger than the n
+ 
+
+ align:start position:0%
+for example DN is bigger than the n
+prime the N equals 5 and the n prime is
+
+ align:start position:0%
+prime the N equals 5 and the n prime is
+ 
+
+ align:start position:0%
+prime the N equals 5 and the n prime is
+equal to 3 I started with 5 positive
+
+ align:start position:0%
+equal to 3 I started with 5 positive
+ 
+
+ align:start position:0%
+equal to 3 I started with 5 positive
+energy states in this little interval
+
+ align:start position:0%
+energy states in this little interval
+ 
+
+ align:start position:0%
+energy states in this little interval
+and by the time I change the potential I
+
+ align:start position:0%
+and by the time I change the potential I
+ 
+
+ align:start position:0%
+and by the time I change the potential I
+ended up with 3 so I lost two so let me
+
+ align:start position:0%
+ended up with 3 so I lost two so let me
+ 
+
+ align:start position:0%
+ended up with 3 so I lost two so let me
+write here the number of positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy solutions lost in the interval
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decay as the potential is turned on is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DN the original number minus DN prime if
+
+ align:start position:0%
+DN the original number minus DN prime if
+ 
+
+ align:start position:0%
+DN the original number minus DN prime if
+that's positive
+
+ align:start position:0%
+that's positive
+ 
+
+ align:start position:0%
+that's positive
+I've lost states if it's negative I gain
+
+ align:start position:0%
+I've lost states if it's negative I gain
+ 
+
+ align:start position:0%
+I've lost states if it's negative I gain
+States positive energy states and this
+
+ align:start position:0%
+States positive energy states and this
+ 
+
+ align:start position:0%
+States positive energy states and this
+number we can calculate the difference
+
+ align:start position:0%
+number we can calculate the difference
+ 
+
+ align:start position:0%
+number we can calculate the difference
+this is minus one over PI D Delta DK DK
+
+ align:start position:0%
+this is minus one over PI D Delta DK DK
+ 
+
+ align:start position:0%
+this is minus one over PI D Delta DK DK
+I'll put it here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right well we're not far well this
+
+ align:start position:0%
+all right well we're not far well this
+ 
+
+ align:start position:0%
+all right well we're not far well this
+is what you lost the number of positive
+
+ align:start position:0%
+is what you lost the number of positive
+ 
+
+ align:start position:0%
+is what you lost the number of positive
+energy states that you lost in little BK
+
+ align:start position:0%
+energy states that you lost in little BK
+ 
+
+ align:start position:0%
+energy states that you lost in little BK
+to see how many positive energy states
+
+ align:start position:0%
+to see how many positive energy states
+ 
+
+ align:start position:0%
+to see how many positive energy states
+you lost overall you must integrate over
+
+ align:start position:0%
+you lost overall you must integrate over
+ 
+
+ align:start position:0%
+you lost overall you must integrate over
+all the D case until how much you lost
+
+ align:start position:0%
+all the D case until how much you lost
+ 
+
+ align:start position:0%
+all the D case until how much you lost
+in every little piece so the number of
+
+ align:start position:0%
+in every little piece so the number of
+ 
+
+ align:start position:0%
+in every little piece so the number of
+positive energy solutions lost not in
+
+ align:start position:0%
+positive energy solutions lost not in
+ 
+
+ align:start position:0%
+positive energy solutions lost not in
+decay but lost as the potential is
+
+ align:start position:0%
+decay but lost as the potential is
+ 
+
+ align:start position:0%
+decay but lost as the potential is
+turned on is equal to the integral over
+
+ align:start position:0%
+turned on is equal to the integral over
+ 
+
+ align:start position:0%
+turned on is equal to the integral over
+K from 0 to infinity of minus 1 over PI
+
+ align:start position:0%
+K from 0 to infinity of minus 1 over PI
+ 
+
+ align:start position:0%
+K from 0 to infinity of minus 1 over PI
+the Delta DK is the integral of that
+
+ align:start position:0%
+the Delta DK is the integral of that
+ 
+
+ align:start position:0%
+the Delta DK is the integral of that
+expression of that right coincide but
+
+ align:start position:0%
+expression of that right coincide but
+ 
+
+ align:start position:0%
+expression of that right coincide but
+this is a total derivative so this is
+
+ align:start position:0%
+this is a total derivative so this is
+ 
+
+ align:start position:0%
+this is a total derivative so this is
+minus 1 over PI Delta of K evaluated
+
+ align:start position:0%
+minus 1 over PI Delta of K evaluated
+ 
+
+ align:start position:0%
+minus 1 over PI Delta of K evaluated
+between infinity and 0 and therefore the
+
+ align:start position:0%
+between infinity and 0 and therefore the
+ 
+
+ align:start position:0%
+between infinity and 0 and therefore the
+number of states lost is 1 over pi
+
+ align:start position:0%
+number of states lost is 1 over pi
+ 
+
+ align:start position:0%
+number of states lost is 1 over pi
+because of the sign Delta of 0 minus
+
+ align:start position:0%
+because of the sign Delta of 0 minus
+ 
+
+ align:start position:0%
+because of the sign Delta of 0 minus
+Delta of infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we're almost there this is the number
+
+ align:start position:0%
+so we're almost there this is the number
+ 
+
+ align:start position:0%
+so we're almost there this is the number
+of positive energy solutions lost now I
+
+ align:start position:0%
+of positive energy solutions lost now I
+ 
+
+ align:start position:0%
+of positive energy solutions lost now I
+want to emphasize that the situation is
+
+ align:start position:0%
+want to emphasize that the situation is
+ 
+
+ align:start position:0%
+want to emphasize that the situation is
+quite interesting let me make a little
+
+ align:start position:0%
+quite interesting let me make a little
+ 
+
+ align:start position:0%
+quite interesting let me make a little
+drawing here so so suppose here is the
+
+ align:start position:0%
+drawing here so so suppose here is the
+ 
+
+ align:start position:0%
+drawing here so so suppose here is the
+case where you have the potential equal
+
+ align:start position:0%
+case where you have the potential equal
+ 
+
+ align:start position:0%
+case where you have the potential equal
+to zero and here is energy equal to zero
+
+ align:start position:0%
+to zero and here is energy equal to zero
+ 
+
+ align:start position:0%
+to zero and here is energy equal to zero
+then you have all these states now even
+
+ align:start position:0%
+then you have all these states now even
+ 
+
+ align:start position:0%
+then you have all these states now even
+though we've put the wall the wall
+
+ align:start position:0%
+though we've put the wall the wall
+ 
+
+ align:start position:0%
+though we've put the wall the wall
+allows us to count the states but there
+
+ align:start position:0%
+allows us to count the states but there
+ 
+
+ align:start position:0%
+allows us to count the states but there
+is still going to be an infinite number
+
+ align:start position:0%
+is still going to be an infinite number
+ 
+
+ align:start position:0%
+is still going to be an infinite number
+of states the infinite square well has
+
+ align:start position:0%
+of states the infinite square well has
+ 
+
+ align:start position:0%
+of states the infinite square well has
+an infinite number of states so that
+
+ align:start position:0%
+an infinite number of states so that
+ 
+
+ align:start position:0%
+an infinite number of states so that
+thing really continues but what happens
+
+ align:start position:0%
+thing really continues but what happens
+ 
+
+ align:start position:0%
+thing really continues but what happens
+by the time V is different from zero
+
+ align:start position:0%
+by the time V is different from zero
+ 
+
+ align:start position:0%
+by the time V is different from zero
+here is the equals zero line and here is
+
+ align:start position:0%
+here is the equals zero line and here is
+ 
+
+ align:start position:0%
+here is the equals zero line and here is
+the equals zero line as we discussed as
+
+ align:start position:0%
+the equals zero line as we discussed as
+ 
+
+ align:start position:0%
+the equals zero line as we discussed as
+you change the potential slowly this are
+
+ align:start position:0%
+you change the potential slowly this are
+ 
+
+ align:start position:0%
+you change the potential slowly this are
+going to shift a little and some are
+
+ align:start position:0%
+going to shift a little and some are
+ 
+
+ align:start position:0%
+going to shift a little and some are
+going to go down here are going to
+
+ align:start position:0%
+going to go down here are going to
+ 
+
+ align:start position:0%
+going to go down here are going to
+become bound States there going to be a
+
+ align:start position:0%
+become bound States there going to be a
+ 
+
+ align:start position:0%
+become bound States there going to be a
+number of bound States and bound States
+
+ align:start position:0%
+number of bound States and bound States
+ 
+
+ align:start position:0%
+number of bound States and bound States
+number of bound States and and then
+
+ align:start position:0%
+number of bound States and and then
+ 
+
+ align:start position:0%
+number of bound States and and then
+there's going to be still sub states
+
+ align:start position:0%
+there's going to be still sub states
+ 
+
+ align:start position:0%
+there's going to be still sub states
+here that's also go to infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you cannot quite say so easily well
+
+ align:start position:0%
+so you cannot quite say so easily well
+ 
+
+ align:start position:0%
+so you cannot quite say so easily well
+the number of states here - a number of
+
+ align:start position:0%
+the number of states here - a number of
+ 
+
+ align:start position:0%
+the number of states here - a number of
+states here is the number lost that's
+
+ align:start position:0%
+states here is the number lost that's
+ 
+
+ align:start position:0%
+states here is the number lost that's
+not true because that's infinite that's
+
+ align:start position:0%
+not true because that's infinite that's
+ 
+
+ align:start position:0%
+not true because that's infinite that's
+infinite and subtracting infinity sees
+
+ align:start position:0%
+infinite and subtracting infinity sees
+ 
+
+ align:start position:0%
+infinite and subtracting infinity sees
+but but you know that you've lost a
+
+ align:start position:0%
+but but you know that you've lost a
+ 
+
+ align:start position:0%
+but but you know that you've lost a
+number of finite number of positive
+
+ align:start position:0%
+number of finite number of positive
+ 
+
+ align:start position:0%
+number of finite number of positive
+energy solutions so as you track here
+
+ align:start position:0%
+energy solutions so as you track here
+ 
+
+ align:start position:0%
+energy solutions so as you track here
+the number of states must the states
+
+ align:start position:0%
+the number of states must the states
+ 
+
+ align:start position:0%
+the number of states must the states
+must go into each other and therefore if
+
+ align:start position:0%
+must go into each other and therefore if
+ 
+
+ align:start position:0%
+must go into each other and therefore if
+this four states are now here before
+
+ align:start position:0%
+this four states are now here before
+ 
+
+ align:start position:0%
+this four states are now here before
+they were here and those were the
+
+ align:start position:0%
+they were here and those were the
+ 
+
+ align:start position:0%
+they were here and those were the
+positive energy solutions that were lost
+
+ align:start position:0%
+positive energy solutions that were lost
+ 
+
+ align:start position:0%
+positive energy solutions that were lost
+in going from here to here you lost
+
+ align:start position:0%
+in going from here to here you lost
+ 
+
+ align:start position:0%
+in going from here to here you lost
+positive energy solutions
+
+ align:start position:0%
+positive energy solutions
+ 
+
+ align:start position:0%
+positive energy solutions
+you lost a finite number of positive
+
+ align:start position:0%
+you lost a finite number of positive
+ 
+
+ align:start position:0%
+you lost a finite number of positive
+energy solutions even though there's
+
+ align:start position:0%
+energy solutions even though there's
+ 
+
+ align:start position:0%
+energy solutions even though there's
+infinite here and infinity you lost some
+
+ align:start position:0%
+infinite here and infinity you lost some
+ 
+
+ align:start position:0%
+infinite here and infinity you lost some
+and you did that by keeping track at any
+
+ align:start position:0%
+and you did that by keeping track at any
+ 
+
+ align:start position:0%
+and you did that by keeping track at any
+place how much you lost and therefore
+
+ align:start position:0%
+place how much you lost and therefore
+ 
+
+ align:start position:0%
+place how much you lost and therefore
+the states lost are never really lost
+
+ align:start position:0%
+the states lost are never really lost
+ 
+
+ align:start position:0%
+the states lost are never really lost
+they are the ones that became the bound
+
+ align:start position:0%
+they are the ones that became the bound
+ 
+
+ align:start position:0%
+they are the ones that became the bound
+States here so the positive every states
+
+ align:start position:0%
+States here so the positive every states
+ 
+
+ align:start position:0%
+States here so the positive every states
+that got lost are the bound States so
+
+ align:start position:0%
+that got lost are the bound States so
+ 
+
+ align:start position:0%
+that got lost are the bound States so
+the number of bound States is equal to
+
+ align:start position:0%
+the number of bound States is equal to
+ 
+
+ align:start position:0%
+the number of bound States is equal to
+the number of positive energy solutions
+
+ align:start position:0%
+the number of positive energy solutions
+ 
+
+ align:start position:0%
+the number of positive energy solutions
+because there are no law states so this
+
+ align:start position:0%
+because there are no law states so this
+ 
+
+ align:start position:0%
+because there are no law states so this
+is equal to a number of bound States
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because there are overall no lost States
\ No newline at end of file
diff --git a/ykwNGB9kuaA.txt b/ykwNGB9kuaA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fdd3ec217596dd262299f72cb14c3a23b64503ad
--- /dev/null
+++ b/ykwNGB9kuaA.txt
@@ -0,0 +1,891 @@
+align:start position:0%
+ 
+Let's apply the work energy theorem
+
+ align:start position:0%
+Let's apply the work energy theorem
+ 
+
+ align:start position:0%
+Let's apply the work energy theorem
+principle to the motion of a block
+
+ align:start position:0%
+principle to the motion of a block
+ 
+
+ align:start position:0%
+principle to the motion of a block
+sliding down an incined plane.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And here's an inclined plane at an angle
+
+ align:start position:0%
+And here's an inclined plane at an angle
+ 
+
+ align:start position:0%
+And here's an inclined plane at an angle
+theta. And let's choose a coordinate
+
+ align:start position:0%
+theta. And let's choose a coordinate
+ 
+
+ align:start position:0%
+theta. And let's choose a coordinate
+system. We'll choose x=0 up here. I had
+
+ align:start position:0%
+system. We'll choose x=0 up here. I had
+ 
+
+ align:start position:0%
+system. We'll choose x=0 up here. I had
+here. And here is our coordinate
+
+ align:start position:0%
+here. And here is our coordinate
+ 
+
+ align:start position:0%
+here. And here is our coordinate
+function.
+
+ align:start position:0%
+function.
+ 
+
+ align:start position:0%
+function.
+And suppose that the object starts at x
+
+ align:start position:0%
+And suppose that the object starts at x
+ 
+
+ align:start position:0%
+And suppose that the object starts at x
+i and it ends at xfal.
+
+ align:start position:0%
+i and it ends at xfal.
+ 
+
+ align:start position:0%
+i and it ends at xfal.
+If we want to calculate the work
+
+ align:start position:0%
+If we want to calculate the work
+ 
+
+ align:start position:0%
+If we want to calculate the work
+energy, then what we're going to learn
+
+ align:start position:0%
+energy, then what we're going to learn
+ 
+
+ align:start position:0%
+energy, then what we're going to learn
+is that there this theorem is two
+
+ align:start position:0%
+is that there this theorem is two
+ 
+
+ align:start position:0%
+is that there this theorem is two
+different sides. Calculating the change
+
+ align:start position:0%
+different sides. Calculating the change
+ 
+
+ align:start position:0%
+different sides. Calculating the change
+in kinetic energy is simply a
+
+ align:start position:0%
+in kinetic energy is simply a
+ 
+
+ align:start position:0%
+in kinetic energy is simply a
+description. This is 12 m v^ 2 minus 12
+
+ align:start position:0%
+description. This is 12 m v^ 2 minus 12
+ 
+
+ align:start position:0%
+description. This is 12 m v^ 2 minus 12
+v initial^ 2. That's a property
+
+ align:start position:0%
+v initial^ 2. That's a property
+ 
+
+ align:start position:0%
+v initial^ 2. That's a property
+parameters of the system at the initial
+
+ align:start position:0%
+parameters of the system at the initial
+ 
+
+ align:start position:0%
+parameters of the system at the initial
+state the speed or the velocity speed
+
+ align:start position:0%
+state the speed or the velocity speed
+ 
+
+ align:start position:0%
+state the speed or the velocity speed
+which is connect speed squared and the
+
+ align:start position:0%
+which is connect speed squared and the
+ 
+
+ align:start position:0%
+which is connect speed squared and the
+same property v final in the final
+
+ align:start position:0%
+same property v final in the final
+ 
+
+ align:start position:0%
+same property v final in the final
+state. Now over here we have two types
+
+ align:start position:0%
+state. Now over here we have two types
+ 
+
+ align:start position:0%
+state. Now over here we have two types
+of forces acting on this object. So here
+
+ align:start position:0%
+of forces acting on this object. So here
+ 
+
+ align:start position:0%
+of forces acting on this object. So here
+we need a free body force diagram
+
+ align:start position:0%
+we need a free body force diagram
+ 
+
+ align:start position:0%
+we need a free body force diagram
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+and this side is where the physics are
+
+ align:start position:0%
+and this side is where the physics are
+ 
+
+ align:start position:0%
+and this side is where the physics are
+lie
+
+ align:start position:0%
+lie
+ 
+
+ align:start position:0%
+lie
+and so we want to draw our force
+
+ align:start position:0%
+and so we want to draw our force
+ 
+
+ align:start position:0%
+and so we want to draw our force
+diagram. So if we have our block, we
+
+ align:start position:0%
+diagram. So if we have our block, we
+ 
+
+ align:start position:0%
+diagram. So if we have our block, we
+have the friction force, we have the
+
+ align:start position:0%
+have the friction force, we have the
+ 
+
+ align:start position:0%
+have the friction force, we have the
+normal force, we have mg, recall
+
+ align:start position:0%
+normal force, we have mg, recall
+ 
+
+ align:start position:0%
+normal force, we have mg, recall
+if plane is inclined theta, that's also
+
+ align:start position:0%
+if plane is inclined theta, that's also
+ 
+
+ align:start position:0%
+if plane is inclined theta, that's also
+the angle theta. If we chose ihat jhat
+
+ align:start position:0%
+the angle theta. If we chose ihat jhat
+ 
+
+ align:start position:0%
+the angle theta. If we chose ihat jhat
+unit vectors, I just want to repeat that
+
+ align:start position:0%
+unit vectors, I just want to repeat that
+ 
+
+ align:start position:0%
+unit vectors, I just want to repeat that
+on my free body diagram. Now, we can
+
+ align:start position:0%
+on my free body diagram. Now, we can
+ 
+
+ align:start position:0%
+on my free body diagram. Now, we can
+think of this integral as just
+
+ align:start position:0%
+think of this integral as just
+ 
+
+ align:start position:0%
+think of this integral as just
+one-dimensional motion in the x
+
+ align:start position:0%
+one-dimensional motion in the x
+ 
+
+ align:start position:0%
+one-dimensional motion in the x
+direction. And so we have two different
+
+ align:start position:0%
+direction. And so we have two different
+ 
+
+ align:start position:0%
+direction. And so we have two different
+forces that we have to calculate. The
+
+ align:start position:0%
+forces that we have to calculate. The
+ 
+
+ align:start position:0%
+forces that we have to calculate. The
+friction force is in the minus x
+
+ align:start position:0%
+friction force is in the minus x
+ 
+
+ align:start position:0%
+friction force is in the minus x
+direction. So we're integrating minus
+
+ align:start position:0%
+direction. So we're integrating minus
+ 
+
+ align:start position:0%
+direction. So we're integrating minus
+the friction force with respect to
+
+ align:start position:0%
+the friction force with respect to
+ 
+
+ align:start position:0%
+the friction force with respect to
+displacement from x initial to xfal. And
+
+ align:start position:0%
+displacement from x initial to xfal. And
+ 
+
+ align:start position:0%
+displacement from x initial to xfal. And
+what about the gravitational force?
+
+ align:start position:0%
+what about the gravitational force?
+ 
+
+ align:start position:0%
+what about the gravitational force?
+Well, the gravitational force has a
+
+ align:start position:0%
+Well, the gravitational force has a
+ 
+
+ align:start position:0%
+Well, the gravitational force has a
+component mg sin theta in the x
+
+ align:start position:0%
+component mg sin theta in the x
+ 
+
+ align:start position:0%
+component mg sin theta in the x
+direction. So when we integrate that x
+
+ align:start position:0%
+direction. So when we integrate that x
+ 
+
+ align:start position:0%
+direction. So when we integrate that x
+component, we have now plus because it's
+
+ align:start position:0%
+component, we have now plus because it's
+ 
+
+ align:start position:0%
+component, we have now plus because it's
+in the same direction, remember we're
+
+ align:start position:0%
+in the same direction, remember we're
+ 
+
+ align:start position:0%
+in the same direction, remember we're
+displacing a little bit dx down the
+
+ align:start position:0%
+displacing a little bit dx down the
+ 
+
+ align:start position:0%
+displacing a little bit dx down the
+incin plane. So we're going from x
+
+ align:start position:0%
+incin plane. So we're going from x
+ 
+
+ align:start position:0%
+incin plane. So we're going from x
+initial xfal of mg sin theta, which is a
+
+ align:start position:0%
+initial xfal of mg sin theta, which is a
+ 
+
+ align:start position:0%
+initial xfal of mg sin theta, which is a
+constant dx.
+
+ align:start position:0%
+constant dx.
+ 
+
+ align:start position:0%
+constant dx.
+And so when you're applying the work
+
+ align:start position:0%
+And so when you're applying the work
+ 
+
+ align:start position:0%
+And so when you're applying the work
+energy theorem, you need to integrate
+
+ align:start position:0%
+energy theorem, you need to integrate
+ 
+
+ align:start position:0%
+energy theorem, you need to integrate
+your forces and actually calculate the
+
+ align:start position:0%
+your forces and actually calculate the
+ 
+
+ align:start position:0%
+your forces and actually calculate the
+work. Now again if you looked in the
+
+ align:start position:0%
+work. Now again if you looked in the
+ 
+
+ align:start position:0%
+work. Now again if you looked in the
+jhat direction and we applied Newton's
+
+ align:start position:0%
+jhat direction and we applied Newton's
+ 
+
+ align:start position:0%
+jhat direction and we applied Newton's
+second law n minus mg cosine theta is
+
+ align:start position:0%
+second law n minus mg cosine theta is
+ 
+
+ align:start position:0%
+second law n minus mg cosine theta is
+zero and our rule for friction is it's
+
+ align:start position:0%
+zero and our rule for friction is it's
+ 
+
+ align:start position:0%
+zero and our rule for friction is it's
+mu k * n or mu k mg cosine theta then
+
+ align:start position:0%
+mu k * n or mu k mg cosine theta then
+ 
+
+ align:start position:0%
+mu k * n or mu k mg cosine theta then
+what we have is in both instances we
+
+ align:start position:0%
+what we have is in both instances we
+ 
+
+ align:start position:0%
+what we have is in both instances we
+have a constant force so it's just force
+
+ align:start position:0%
+have a constant force so it's just force
+ 
+
+ align:start position:0%
+have a constant force so it's just force
+times displacement so we have minus mu k
+
+ align:start position:0%
+times displacement so we have minus mu k
+ 
+
+ align:start position:0%
+times displacement so we have minus mu k
+mg cosine theta times the displacement
+
+ align:start position:0%
+mg cosine theta times the displacement
+ 
+
+ align:start position:0%
+mg cosine theta times the displacement
+which is x initial
+
+ align:start position:0%
+which is x initial
+ 
+
+ align:start position:0%
+which is x initial
+Xfal over here we have mg sin theta *
+
+ align:start position:0%
+Xfal over here we have mg sin theta *
+ 
+
+ align:start position:0%
+Xfal over here we have mg sin theta *
+xfal minus x initial and now we've
+
+ align:start position:0%
+xfal minus x initial and now we've
+ 
+
+ align:start position:0%
+xfal minus x initial and now we've
+calculated separately both sides of our
+
+ align:start position:0%
+calculated separately both sides of our
+ 
+
+ align:start position:0%
+calculated separately both sides of our
+work kinetic energy principle as in all
+
+ align:start position:0%
+work kinetic energy principle as in all
+ 
+
+ align:start position:0%
+work kinetic energy principle as in all
+our physical laws the equal sign means
+
+ align:start position:0%
+our physical laws the equal sign means
+ 
+
+ align:start position:0%
+our physical laws the equal sign means
+the work is equal to the change in
+
+ align:start position:0%
+the work is equal to the change in
+ 
+
+ align:start position:0%
+the work is equal to the change in
+kinetic energy I'll emphasize that by
+
+ align:start position:0%
+kinetic energy I'll emphasize that by
+ 
+
+ align:start position:0%
+kinetic energy I'll emphasize that by
+now placing the equal sign because of
+
+ align:start position:0%
+now placing the equal sign because of
+ 
+
+ align:start position:0%
+now placing the equal sign because of
+our physical law and so equaling 12 m v^
+
+ align:start position:0%
+our physical law and so equaling 12 m v^
+ 
+
+ align:start position:0%
+our physical law and so equaling 12 m v^
+2 minus v initial^ 2 and now I have a
+
+ align:start position:0%
+2 minus v initial^ 2 and now I have a
+ 
+
+ align:start position:0%
+2 minus v initial^ 2 and now I have a
+relationship between the parameters of
+
+ align:start position:0%
+relationship between the parameters of
+ 
+
+ align:start position:0%
+relationship between the parameters of
+the initial state which I'm calling x
+
+ align:start position:0%
+the initial state which I'm calling x
+ 
+
+ align:start position:0%
+the initial state which I'm calling x
+initial and v initial and the parameters
+
+ align:start position:0%
+initial and v initial and the parameters
+ 
+
+ align:start position:0%
+initial and v initial and the parameters
+that describe the final state xfal vfal
+
+ align:start position:0%
+that describe the final state xfal vfal
+ 
+
+ align:start position:0%
+that describe the final state xfal vfal
+and depending on which set of these
+
+ align:start position:0%
+and depending on which set of these
+ 
+
+ align:start position:0%
+and depending on which set of these
+parameters are given I can conceivably
+
+ align:start position:0%
+parameters are given I can conceivably
+ 
+
+ align:start position:0%
+parameters are given I can conceivably
+solve for the other ones
+
+ align:start position:0%
+solve for the other ones
+ 
+
+ align:start position:0%
+solve for the other ones
+I do want to point out when we do this
+
+ align:start position:0%
+I do want to point out when we do this
+ 
+
+ align:start position:0%
+I do want to point out when we do this
+example is we've described work as a
+
+ align:start position:0%
+example is we've described work as a
+ 
+
+ align:start position:0%
+example is we've described work as a
+dotproduct
+
+ align:start position:0%
+dotproduct
+ 
+
+ align:start position:0%
+dotproduct
+from A to B. Take the friction force.
+
+ align:start position:0%
+from A to B. Take the friction force.
+ 
+
+ align:start position:0%
+from A to B. Take the friction force.
+Well, in this instance, if we wrote this
+
+ align:start position:0%
+Well, in this instance, if we wrote this
+ 
+
+ align:start position:0%
+Well, in this instance, if we wrote this
+out explicitly, it would be minus FKhat
+
+ align:start position:0%
+out explicitly, it would be minus FKhat
+ 
+
+ align:start position:0%
+out explicitly, it would be minus FKhat
+dot dxihat
+
+ align:start position:0%
+dot dxihat
+ 
+
+ align:start position:0%
+dot dxihat
+from the initial to the final. I dohat
+
+ align:start position:0%
+from the initial to the final. I dohat
+ 
+
+ align:start position:0%
+from the initial to the final. I dohat
+is one. And so you see we recover from X
+
+ align:start position:0%
+is one. And so you see we recover from X
+ 
+
+ align:start position:0%
+is one. And so you see we recover from X
+initial to Xfinal of FK DX. And that was
+
+ align:start position:0%
+initial to Xfinal of FK DX. And that was
+ 
+
+ align:start position:0%
+initial to Xfinal of FK DX. And that was
+the first piece. The second piece, the
+
+ align:start position:0%
+the first piece. The second piece, the
+ 
+
+ align:start position:0%
+the first piece. The second piece, the
+gravitational force dotted into ds from
+
+ align:start position:0%
+gravitational force dotted into ds from
+ 
+
+ align:start position:0%
+gravitational force dotted into ds from
+x initial to xfal. Well, if you wrote
+
+ align:start position:0%
+x initial to xfal. Well, if you wrote
+ 
+
+ align:start position:0%
+x initial to xfal. Well, if you wrote
+down the gravitational force mg
+
+ align:start position:0%
+down the gravitational force mg
+ 
+
+ align:start position:0%
+down the gravitational force mg
+as a ihat component and a negative mg
+
+ align:start position:0%
+as a ihat component and a negative mg
+ 
+
+ align:start position:0%
+as a ihat component and a negative mg
+cosine theta jhat component.
+
+ align:start position:0%
+cosine theta jhat component.
+ 
+
+ align:start position:0%
+cosine theta jhat component.
+Then when we take the dotproduct
+
+ align:start position:0%
+Then when we take the dotproduct
+ 
+
+ align:start position:0%
+Then when we take the dotproduct
+again where our ds here we'll write ds
+
+ align:start position:0%
+again where our ds here we'll write ds
+ 
+
+ align:start position:0%
+again where our ds here we'll write ds
+as dx ihat then when you dotproduct mg
+
+ align:start position:0%
+as dx ihat then when you dotproduct mg
+ 
+
+ align:start position:0%
+as dx ihat then when you dotproduct mg
+do ds mg dot ds we have ihat do iihat
+
+ align:start position:0%
+do ds mg dot ds we have ihat do iihat
+ 
+
+ align:start position:0%
+do ds mg dot ds we have ihat do iihat
+which is one but jhat do iihat they're
+
+ align:start position:0%
+which is one but jhat do iihat they're
+ 
+
+ align:start position:0%
+which is one but jhat do iihat they're
+perpendicular so that's zero. So the
+
+ align:start position:0%
+perpendicular so that's zero. So the
+ 
+
+ align:start position:0%
+perpendicular so that's zero. So the
+only piece that survives in the scalar
+
+ align:start position:0%
+only piece that survives in the scalar
+ 
+
+ align:start position:0%
+only piece that survives in the scalar
+product mg dod ds is these two pieces.
+
+ align:start position:0%
+product mg dod ds is these two pieces.
+ 
+
+ align:start position:0%
+product mg dod ds is these two pieces.
+And so we get the integral from x
+
+ align:start position:0%
+And so we get the integral from x
+ 
+
+ align:start position:0%
+And so we get the integral from x
+initial to xfal of mg sin theta * dx.
+
+ align:start position:0%
+initial to xfal of mg sin theta * dx.
+ 
+
+ align:start position:0%
+initial to xfal of mg sin theta * dx.
+And that's precisely our second piece
+
+ align:start position:0%
+And that's precisely our second piece
+ 
+
+ align:start position:0%
+And that's precisely our second piece
+here. So here's the simple application
+
+ align:start position:0%
+here. So here's the simple application
+ 
+
+ align:start position:0%
+here. So here's the simple application
+of the work energy theorem.
\ No newline at end of file
diff --git a/zW1_iugJvF0.txt b/zW1_iugJvF0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7e5ebc39a55e8a92b7fd7a8e0722fb0084c3e89c
--- /dev/null
+++ b/zW1_iugJvF0.txt
@@ -0,0 +1,1627 @@
+align:start position:0%
+ 
+a random variable can take different
+
+ align:start position:0%
+a random variable can take different
+ 
+
+ align:start position:0%
+a random variable can take different
+numerical values depending on the
+
+ align:start position:0%
+numerical values depending on the
+ 
+
+ align:start position:0%
+numerical values depending on the
+outcome of the experiment some outcomes
+
+ align:start position:0%
+outcome of the experiment some outcomes
+ 
+
+ align:start position:0%
+outcome of the experiment some outcomes
+are more likely than others and
+
+ align:start position:0%
+are more likely than others and
+ 
+
+ align:start position:0%
+are more likely than others and
+similarly some of the possible numerical
+
+ align:start position:0%
+similarly some of the possible numerical
+ 
+
+ align:start position:0%
+similarly some of the possible numerical
+values of a random variable will be more
+
+ align:start position:0%
+values of a random variable will be more
+ 
+
+ align:start position:0%
+values of a random variable will be more
+likely than others we restrict ourselves
+
+ align:start position:0%
+likely than others we restrict ourselves
+ 
+
+ align:start position:0%
+likely than others we restrict ourselves
+to discrete random variables and we will
+
+ align:start position:0%
+to discrete random variables and we will
+ 
+
+ align:start position:0%
+to discrete random variables and we will
+describe these relative likelihoods in
+
+ align:start position:0%
+describe these relative likelihoods in
+ 
+
+ align:start position:0%
+describe these relative likelihoods in
+terms of the so called probability mass
+
+ align:start position:0%
+terms of the so called probability mass
+ 
+
+ align:start position:0%
+terms of the so called probability mass
+function or PMF for short which gives
+
+ align:start position:0%
+function or PMF for short which gives
+ 
+
+ align:start position:0%
+function or PMF for short which gives
+the probability of the different
+
+ align:start position:0%
+the probability of the different
+ 
+
+ align:start position:0%
+the probability of the different
+possible numerical values the PMF is
+
+ align:start position:0%
+possible numerical values the PMF is
+ 
+
+ align:start position:0%
+possible numerical values the PMF is
+also sometimes called the probability
+
+ align:start position:0%
+also sometimes called the probability
+ 
+
+ align:start position:0%
+also sometimes called the probability
+law or the probability distribution of a
+
+ align:start position:0%
+law or the probability distribution of a
+ 
+
+ align:start position:0%
+law or the probability distribution of a
+discrete random variable let me
+
+ align:start position:0%
+discrete random variable let me
+ 
+
+ align:start position:0%
+discrete random variable let me
+illustrate the idea in terms of a simple
+
+ align:start position:0%
+illustrate the idea in terms of a simple
+ 
+
+ align:start position:0%
+illustrate the idea in terms of a simple
+example we have a probabilistic
+
+ align:start position:0%
+example we have a probabilistic
+ 
+
+ align:start position:0%
+example we have a probabilistic
+experiment with four possible outcomes
+
+ align:start position:0%
+experiment with four possible outcomes
+ 
+
+ align:start position:0%
+experiment with four possible outcomes
+we also have a probability law on the
+
+ align:start position:0%
+we also have a probability law on the
+ 
+
+ align:start position:0%
+we also have a probability law on the
+sample space and to keep things simple
+
+ align:start position:0%
+sample space and to keep things simple
+ 
+
+ align:start position:0%
+sample space and to keep things simple
+we assume that all four outcomes in our
+
+ align:start position:0%
+we assume that all four outcomes in our
+ 
+
+ align:start position:0%
+we assume that all four outcomes in our
+sample space are equally likely we then
+
+ align:start position:0%
+sample space are equally likely we then
+ 
+
+ align:start position:0%
+sample space are equally likely we then
+introduce a random variable that
+
+ align:start position:0%
+introduce a random variable that
+ 
+
+ align:start position:0%
+introduce a random variable that
+Associates a number with each possible
+
+ align:start position:0%
+Associates a number with each possible
+ 
+
+ align:start position:0%
+Associates a number with each possible
+outcome as shown in this diagram the
+
+ align:start position:0%
+outcome as shown in this diagram the
+ 
+
+ align:start position:0%
+outcome as shown in this diagram the
+random variable capital X can take one
+
+ align:start position:0%
+random variable capital X can take one
+ 
+
+ align:start position:0%
+random variable capital X can take one
+of three possible values namely 3 4 or 5
+
+ align:start position:0%
+of three possible values namely 3 4 or 5
+ 
+
+ align:start position:0%
+of three possible values namely 3 4 or 5
+let us focus on one of those numbers
+
+ align:start position:0%
+let us focus on one of those numbers
+ 
+
+ align:start position:0%
+let us focus on one of those numbers
+let's say the number 5 so let us focus
+
+ align:start position:0%
+let's say the number 5 so let us focus
+ 
+
+ align:start position:0%
+let's say the number 5 so let us focus
+on little X being equal to 5 we can
+
+ align:start position:0%
+on little X being equal to 5 we can
+ 
+
+ align:start position:0%
+on little X being equal to 5 we can
+think of the event that capital X is
+
+ align:start position:0%
+think of the event that capital X is
+ 
+
+ align:start position:0%
+think of the event that capital X is
+equal to 5 which event is this this is
+
+ align:start position:0%
+equal to 5 which event is this this is
+ 
+
+ align:start position:0%
+equal to 5 which event is this this is
+the event that the outcome of the
+
+ align:start position:0%
+the event that the outcome of the
+ 
+
+ align:start position:0%
+the event that the outcome of the
+experiment led to the random variable
+
+ align:start position:0%
+experiment led to the random variable
+ 
+
+ align:start position:0%
+experiment led to the random variable
+taking a value of 5 so it is this
+
+ align:start position:0%
+taking a value of 5 so it is this
+ 
+
+ align:start position:0%
+taking a value of 5 so it is this
+particular event which consists of two
+
+ align:start position:0%
+particular event which consists of two
+ 
+
+ align:start position:0%
+particular event which consists of two
+elements namely a and B more formally
+
+ align:start position:0%
+elements namely a and B more formally
+ 
+
+ align:start position:0%
+elements namely a and B more formally
+the event that we're talking about is
+
+ align:start position:0%
+the event that we're talking about is
+ 
+
+ align:start position:0%
+the event that we're talking about is
+the set of all outcomes for which the
+
+ align:start position:0%
+the set of all outcomes for which the
+ 
+
+ align:start position:0%
+the set of all outcomes for which the
+value the numerical value of run of a
+
+ align:start position:0%
+value the numerical value of run of a
+ 
+
+ align:start position:0%
+value the numerical value of run of a
+random variable which is a function of
+
+ align:start position:0%
+random variable which is a function of
+ 
+
+ align:start position:0%
+random variable which is a function of
+the outcome that numerical value happens
+
+ align:start position:0%
+the outcome that numerical value happens
+ 
+
+ align:start position:0%
+the outcome that numerical value happens
+to be equal to 5 and in this example it
+
+ align:start position:0%
+to be equal to 5 and in this example it
+ 
+
+ align:start position:0%
+to be equal to 5 and in this example it
+is a set consisting of 2 elements it's a
+
+ align:start position:0%
+is a set consisting of 2 elements it's a
+ 
+
+ align:start position:0%
+is a set consisting of 2 elements it's a
+set of the sample space so it is an
+
+ align:start position:0%
+set of the sample space so it is an
+ 
+
+ align:start position:0%
+set of the sample space so it is an
+event and it has a probability and that
+
+ align:start position:0%
+event and it has a probability and that
+ 
+
+ align:start position:0%
+event and it has a probability and that
+probability we will be denoting with
+
+ align:start position:0%
+probability we will be denoting with
+ 
+
+ align:start position:0%
+probability we will be denoting with
+this notation and in our case this
+
+ align:start position:0%
+this notation and in our case this
+ 
+
+ align:start position:0%
+this notation and in our case this
+probability is equal to one-half because
+
+ align:start position:0%
+probability is equal to one-half because
+ 
+
+ align:start position:0%
+probability is equal to one-half because
+we have two outcomes each one has
+
+ align:start position:0%
+we have two outcomes each one has
+ 
+
+ align:start position:0%
+we have two outcomes each one has
+probability 1/4 the probability of this
+
+ align:start position:0%
+probability 1/4 the probability of this
+ 
+
+ align:start position:0%
+probability 1/4 the probability of this
+event is equal to 1/2 more generally we
+
+ align:start position:0%
+event is equal to 1/2 more generally we
+ 
+
+ align:start position:0%
+event is equal to 1/2 more generally we
+will be using this notation to denote
+
+ align:start position:0%
+will be using this notation to denote
+ 
+
+ align:start position:0%
+will be using this notation to denote
+the probability of the event that the
+
+ align:start position:0%
+the probability of the event that the
+ 
+
+ align:start position:0%
+the probability of the event that the
+random variable capital X takes on a
+
+ align:start position:0%
+random variable capital X takes on a
+ 
+
+ align:start position:0%
+random variable capital X takes on a
+particular value little X this is just a
+
+ align:start position:0%
+particular value little X this is just a
+ 
+
+ align:start position:0%
+particular value little X this is just a
+piece of notation not a new concept we
+
+ align:start position:0%
+piece of notation not a new concept we
+ 
+
+ align:start position:0%
+piece of notation not a new concept we
+are dealing with the probability and we
+
+ align:start position:0%
+are dealing with the probability and we
+ 
+
+ align:start position:0%
+are dealing with the probability and we
+indicated using this particular notation
+
+ align:start position:0%
+indicated using this particular notation
+ 
+
+ align:start position:0%
+indicated using this particular notation
+more formally the probability that we're
+
+ align:start position:0%
+more formally the probability that we're
+ 
+
+ align:start position:0%
+more formally the probability that we're
+dealing with is the probability the
+
+ align:start position:0%
+dealing with is the probability the
+ 
+
+ align:start position:0%
+dealing with is the probability the
+total probability of all outcomes for
+
+ align:start position:0%
+total probability of all outcomes for
+ 
+
+ align:start position:0%
+total probability of all outcomes for
+which the numerical value of our random
+
+ align:start position:0%
+which the numerical value of our random
+ 
+
+ align:start position:0%
+which the numerical value of our random
+variable is this particular number
+
+ align:start position:0%
+variable is this particular number
+ 
+
+ align:start position:0%
+variable is this particular number
+little X a few things to notice we use a
+
+ align:start position:0%
+little X a few things to notice we use a
+ 
+
+ align:start position:0%
+little X a few things to notice we use a
+subscript capital X to indicate which
+
+ align:start position:0%
+subscript capital X to indicate which
+ 
+
+ align:start position:0%
+subscript capital X to indicate which
+random variable we are talking about
+
+ align:start position:0%
+random variable we are talking about
+ 
+
+ align:start position:0%
+random variable we are talking about
+this will be useful if we have several
+
+ align:start position:0%
+this will be useful if we have several
+ 
+
+ align:start position:0%
+this will be useful if we have several
+random variables involved for example if
+
+ align:start position:0%
+random variables involved for example if
+ 
+
+ align:start position:0%
+random variables involved for example if
+we have another random variable on the
+
+ align:start position:0%
+we have another random variable on the
+ 
+
+ align:start position:0%
+we have another random variable on the
+same sample space Capital y then it
+
+ align:start position:0%
+same sample space Capital y then it
+ 
+
+ align:start position:0%
+same sample space Capital y then it
+would have its own probability mass
+
+ align:start position:0%
+would have its own probability mass
+ 
+
+ align:start position:0%
+would have its own probability mass
+function which would be denoted with
+
+ align:start position:0%
+function which would be denoted with
+ 
+
+ align:start position:0%
+function which would be denoted with
+this particular notation here the
+
+ align:start position:0%
+this particular notation here the
+ 
+
+ align:start position:0%
+this particular notation here the
+argument of the PMF which is little X
+
+ align:start position:0%
+argument of the PMF which is little X
+ 
+
+ align:start position:0%
+argument of the PMF which is little X
+ranges over the possible values of the
+
+ align:start position:0%
+ranges over the possible values of the
+ 
+
+ align:start position:0%
+ranges over the possible values of the
+random variable capital X so in this
+
+ align:start position:0%
+random variable capital X so in this
+ 
+
+ align:start position:0%
+random variable capital X so in this
+sense here we're really dealing with a
+
+ align:start position:0%
+sense here we're really dealing with a
+ 
+
+ align:start position:0%
+sense here we're really dealing with a
+function a function that we could denote
+
+ align:start position:0%
+function a function that we could denote
+ 
+
+ align:start position:0%
+function a function that we could denote
+just by P with a subscript X this is the
+
+ align:start position:0%
+just by P with a subscript X this is the
+ 
+
+ align:start position:0%
+just by P with a subscript X this is the
+function as opposed to the specific
+
+ align:start position:0%
+function as opposed to the specific
+ 
+
+ align:start position:0%
+function as opposed to the specific
+values of this function and we can
+
+ align:start position:0%
+values of this function and we can
+ 
+
+ align:start position:0%
+values of this function and we can
+produce plots of this function in this
+
+ align:start position:0%
+produce plots of this function in this
+ 
+
+ align:start position:0%
+produce plots of this function in this
+particular example that we're dealing
+
+ align:start position:0%
+particular example that we're dealing
+ 
+
+ align:start position:0%
+particular example that we're dealing
+with the interesting values of X
+
+ align:start position:0%
+with the interesting values of X
+ 
+
+ align:start position:0%
+with the interesting values of X
+three four and five and The Associated
+
+ align:start position:0%
+three four and five and The Associated
+ 
+
+ align:start position:0%
+three four and five and The Associated
+probabilities are the value of five is
+
+ align:start position:0%
+probabilities are the value of five is
+ 
+
+ align:start position:0%
+probabilities are the value of five is
+obtained with probability one-half the
+
+ align:start position:0%
+obtained with probability one-half the
+ 
+
+ align:start position:0%
+obtained with probability one-half the
+value of four this is the event that the
+
+ align:start position:0%
+value of four this is the event that the
+ 
+
+ align:start position:0%
+value of four this is the event that the
+outcome was C which has probability 1/4
+
+ align:start position:0%
+outcome was C which has probability 1/4
+ 
+
+ align:start position:0%
+outcome was C which has probability 1/4
+and the value of three is also obtained
+
+ align:start position:0%
+and the value of three is also obtained
+ 
+
+ align:start position:0%
+and the value of three is also obtained
+with probability 1/4 because the value
+
+ align:start position:0%
+with probability 1/4 because the value
+ 
+
+ align:start position:0%
+with probability 1/4 because the value
+of 3 is obtained when the outcome is d
+
+ align:start position:0%
+of 3 is obtained when the outcome is d
+ 
+
+ align:start position:0%
+of 3 is obtained when the outcome is d
+and that outcome has probability 1/4 so
+
+ align:start position:0%
+and that outcome has probability 1/4 so
+ 
+
+ align:start position:0%
+and that outcome has probability 1/4 so
+the probability mass function is a
+
+ align:start position:0%
+the probability mass function is a
+ 
+
+ align:start position:0%
+the probability mass function is a
+function of an argument little X and for
+
+ align:start position:0%
+function of an argument little X and for
+ 
+
+ align:start position:0%
+function of an argument little X and for
+any little X it specifies the
+
+ align:start position:0%
+any little X it specifies the
+ 
+
+ align:start position:0%
+any little X it specifies the
+probability that our random variable
+
+ align:start position:0%
+probability that our random variable
+ 
+
+ align:start position:0%
+probability that our random variable
+takes on this particular value a few
+
+ align:start position:0%
+takes on this particular value a few
+ 
+
+ align:start position:0%
+takes on this particular value a few
+more things to notice the probability
+
+ align:start position:0%
+more things to notice the probability
+ 
+
+ align:start position:0%
+more things to notice the probability
+mass function is always non-negative
+
+ align:start position:0%
+mass function is always non-negative
+ 
+
+ align:start position:0%
+mass function is always non-negative
+since we're talking about probabilities
+
+ align:start position:0%
+since we're talking about probabilities
+ 
+
+ align:start position:0%
+since we're talking about probabilities
+and probabilities are always
+
+ align:start position:0%
+and probabilities are always
+ 
+
+ align:start position:0%
+and probabilities are always
+non-negative in addition since the total
+
+ align:start position:0%
+non-negative in addition since the total
+ 
+
+ align:start position:0%
+non-negative in addition since the total
+probability of all outcomes is equal to
+
+ align:start position:0%
+probability of all outcomes is equal to
+ 
+
+ align:start position:0%
+probability of all outcomes is equal to
+1 the probabilities of the different
+
+ align:start position:0%
+1 the probabilities of the different
+ 
+
+ align:start position:0%
+1 the probabilities of the different
+possible values of the random variable
+
+ align:start position:0%
+possible values of the random variable
+ 
+
+ align:start position:0%
+possible values of the random variable
+should also add to 1 so when you add
+
+ align:start position:0%
+should also add to 1 so when you add
+ 
+
+ align:start position:0%
+should also add to 1 so when you add
+over all possible values of little X the
+
+ align:start position:0%
+over all possible values of little X the
+ 
+
+ align:start position:0%
+over all possible values of little X the
+sum of the Associated probabilities
+
+ align:start position:0%
+sum of the Associated probabilities
+ 
+
+ align:start position:0%
+sum of the Associated probabilities
+should be equal to 1 in terms of our
+
+ align:start position:0%
+should be equal to 1 in terms of our
+ 
+
+ align:start position:0%
+should be equal to 1 in terms of our
+picture the events that X is equal to 3
+
+ align:start position:0%
+picture the events that X is equal to 3
+ 
+
+ align:start position:0%
+picture the events that X is equal to 3
+which is this subset of the sample space
+
+ align:start position:0%
+which is this subset of the sample space
+ 
+
+ align:start position:0%
+which is this subset of the sample space
+the event that X is equal to 4 which is
+
+ align:start position:0%
+the event that X is equal to 4 which is
+ 
+
+ align:start position:0%
+the event that X is equal to 4 which is
+this subset of the sample space and the
+
+ align:start position:0%
+this subset of the sample space and the
+ 
+
+ align:start position:0%
+this subset of the sample space and the
+event that X is equal to 5 which is the
+
+ align:start position:0%
+event that X is equal to 5 which is the
+ 
+
+ align:start position:0%
+event that X is equal to 5 which is the
+subset of the sample space these three
+
+ align:start position:0%
+subset of the sample space these three
+ 
+
+ align:start position:0%
+subset of the sample space these three
+events the red green and blue they are
+
+ align:start position:0%
+events the red green and blue they are
+ 
+
+ align:start position:0%
+events the red green and blue they are
+disjoint and together they cover the
+
+ align:start position:0%
+disjoint and together they cover the
+ 
+
+ align:start position:0%
+disjoint and together they cover the
+entire sample space so their
+
+ align:start position:0%
+entire sample space so their
+ 
+
+ align:start position:0%
+entire sample space so their
+probabilities should add to 1 and the
+
+ align:start position:0%
+probabilities should add to 1 and the
+ 
+
+ align:start position:0%
+probabilities should add to 1 and the
+probabilities of these event are the
+
+ align:start position:0%
+probabilities of these event are the
+ 
+
+ align:start position:0%
+probabilities of these event are the
+probabilities of the different values of
+
+ align:start position:0%
+probabilities of the different values of
+ 
+
+ align:start position:0%
+probabilities of the different values of
+the random variable capital X so the
+
+ align:start position:0%
+the random variable capital X so the
+ 
+
+ align:start position:0%
+the random variable capital X so the
+probabilities of these different values
+
+ align:start position:0%
+probabilities of these different values
+ 
+
+ align:start position:0%
+probabilities of these different values
+should also add to 1 let us now go
+
+ align:start position:0%
+should also add to 1 let us now go
+ 
+
+ align:start position:0%
+should also add to 1 let us now go
+through a simple example to illustrate
+
+ align:start position:0%
+through a simple example to illustrate
+ 
+
+ align:start position:0%
+through a simple example to illustrate
+the general method for calculating the
+
+ align:start position:0%
+the general method for calculating the
+ 
+
+ align:start position:0%
+the general method for calculating the
+PMF of a discrete random variable
+
+ align:start position:0%
+PMF of a discrete random variable
+ 
+
+ align:start position:0%
+PMF of a discrete random variable
+we will revisit our familiar example
+
+ align:start position:0%
+we will revisit our familiar example
+ 
+
+ align:start position:0%
+we will revisit our familiar example
+involving two roles of a tetrahedral die
+
+ align:start position:0%
+involving two roles of a tetrahedral die
+ 
+
+ align:start position:0%
+involving two roles of a tetrahedral die
+and let X be the result of the first
+
+ align:start position:0%
+and let X be the result of the first
+ 
+
+ align:start position:0%
+and let X be the result of the first
+role y be the result of the second role
+
+ align:start position:0%
+role y be the result of the second role
+ 
+
+ align:start position:0%
+role y be the result of the second role
+and notice that we are using uppercase
+
+ align:start position:0%
+and notice that we are using uppercase
+ 
+
+ align:start position:0%
+and notice that we are using uppercase
+letters and this is because x and y are
+
+ align:start position:0%
+letters and this is because x and y are
+ 
+
+ align:start position:0%
+letters and this is because x and y are
+random variables in order to do any
+
+ align:start position:0%
+random variables in order to do any
+ 
+
+ align:start position:0%
+random variables in order to do any
+probability calculations we also need a
+
+ align:start position:0%
+probability calculations we also need a
+ 
+
+ align:start position:0%
+probability calculations we also need a
+probability law so to keep things simple
+
+ align:start position:0%
+probability law so to keep things simple
+ 
+
+ align:start position:0%
+probability law so to keep things simple
+let us assume that every possible
+
+ align:start position:0%
+let us assume that every possible
+ 
+
+ align:start position:0%
+let us assume that every possible
+outcome there 16 of them has the same
+
+ align:start position:0%
+outcome there 16 of them has the same
+ 
+
+ align:start position:0%
+outcome there 16 of them has the same
+probability which is therefore 1 over 16
+
+ align:start position:0%
+probability which is therefore 1 over 16
+ 
+
+ align:start position:0%
+probability which is therefore 1 over 16
+for each one of the outcomes we will
+
+ align:start position:0%
+for each one of the outcomes we will
+ 
+
+ align:start position:0%
+for each one of the outcomes we will
+concentrate on a particular random
+
+ align:start position:0%
+concentrate on a particular random
+ 
+
+ align:start position:0%
+concentrate on a particular random
+variable defined to be the sum of the
+
+ align:start position:0%
+variable defined to be the sum of the
+ 
+
+ align:start position:0%
+variable defined to be the sum of the
+random variables x and y so if x and y
+
+ align:start position:0%
+random variables x and y so if x and y
+ 
+
+ align:start position:0%
+random variables x and y so if x and y
+both happen to be 1 then Z will take the
+
+ align:start position:0%
+both happen to be 1 then Z will take the
+ 
+
+ align:start position:0%
+both happen to be 1 then Z will take the
+value of 2 if X is 2 and Y is 1 a random
+
+ align:start position:0%
+value of 2 if X is 2 and Y is 1 a random
+ 
+
+ align:start position:0%
+value of 2 if X is 2 and Y is 1 a random
+variable will take a value of 3 and
+
+ align:start position:0%
+variable will take a value of 3 and
+ 
+
+ align:start position:0%
+variable will take a value of 3 and
+similarly if we have this outcome in
+
+ align:start position:0%
+similarly if we have this outcome in
+ 
+
+ align:start position:0%
+similarly if we have this outcome in
+those outcomes here the random variable
+
+ align:start position:0%
+those outcomes here the random variable
+ 
+
+ align:start position:0%
+those outcomes here the random variable
+takes the value of 4 and we can continue
+
+ align:start position:0%
+takes the value of 4 and we can continue
+ 
+
+ align:start position:0%
+takes the value of 4 and we can continue
+this way by marking for each particular
+
+ align:start position:0%
+this way by marking for each particular
+ 
+
+ align:start position:0%
+this way by marking for each particular
+outcome the corresponding value of the
+
+ align:start position:0%
+outcome the corresponding value of the
+ 
+
+ align:start position:0%
+outcome the corresponding value of the
+random variable of interest what we want
+
+ align:start position:0%
+random variable of interest what we want
+ 
+
+ align:start position:0%
+random variable of interest what we want
+to do now is to calculate the PMF of
+
+ align:start position:0%
+to do now is to calculate the PMF of
+ 
+
+ align:start position:0%
+to do now is to calculate the PMF of
+this random variable what does it mean
+
+ align:start position:0%
+this random variable what does it mean
+ 
+
+ align:start position:0%
+this random variable what does it mean
+to calculate the PMF we need to find
+
+ align:start position:0%
+to calculate the PMF we need to find
+ 
+
+ align:start position:0%
+to calculate the PMF we need to find
+this value for all choices of little Z
+
+ align:start position:0%
+this value for all choices of little Z
+ 
+
+ align:start position:0%
+this value for all choices of little Z
+that is for all possible values in the
+
+ align:start position:0%
+that is for all possible values in the
+ 
+
+ align:start position:0%
+that is for all possible values in the
+range of our random variable the way
+
+ align:start position:0%
+range of our random variable the way
+ 
+
+ align:start position:0%
+range of our random variable the way
+we're going to do it is to consider each
+
+ align:start position:0%
+we're going to do it is to consider each
+ 
+
+ align:start position:0%
+we're going to do it is to consider each
+possible value of little Z one at a time
+
+ align:start position:0%
+possible value of little Z one at a time
+ 
+
+ align:start position:0%
+possible value of little Z one at a time
+and for any particular value find out
+
+ align:start position:0%
+and for any particular value find out
+ 
+
+ align:start position:0%
+and for any particular value find out
+what are the outcomes the elements of
+
+ align:start position:0%
+what are the outcomes the elements of
+ 
+
+ align:start position:0%
+what are the outcomes the elements of
+the sample space for which a random
+
+ align:start position:0%
+the sample space for which a random
+ 
+
+ align:start position:0%
+the sample space for which a random
+variable takes on this specific value
+
+ align:start position:0%
+variable takes on this specific value
+ 
+
+ align:start position:0%
+variable takes on this specific value
+and add the probabilities of those
+
+ align:start position:0%
+and add the probabilities of those
+ 
+
+ align:start position:0%
+and add the probabilities of those
+outcomes so to illustrate this process
+
+ align:start position:0%
+outcomes so to illustrate this process
+ 
+
+ align:start position:0%
+outcomes so to illustrate this process
+let us calculate the value of the PMF
+
+ align:start position:0%
+let us calculate the value of the PMF
+ 
+
+ align:start position:0%
+let us calculate the value of the PMF
+for little Z equal to 2 this is by
+
+ align:start position:0%
+for little Z equal to 2 this is by
+ 
+
+ align:start position:0%
+for little Z equal to 2 this is by
+definition the probability that our
+
+ align:start position:0%
+definition the probability that our
+ 
+
+ align:start position:0%
+definition the probability that our
+random variable takes the value of 2 and
+
+ align:start position:0%
+random variable takes the value of 2 and
+ 
+
+ align:start position:0%
+random variable takes the value of 2 and
+this is an event that can only happen
+
+ align:start position:0%
+this is an event that can only happen
+ 
+
+ align:start position:0%
+this is an event that can only happen
+here it corresponds to only one element
+
+ align:start position:0%
+here it corresponds to only one element
+ 
+
+ align:start position:0%
+here it corresponds to only one element
+of the sample space which
+
+ align:start position:0%
+of the sample space which
+ 
+
+ align:start position:0%
+of the sample space which
+probability 1 over 16 we can continue
+
+ align:start position:0%
+probability 1 over 16 we can continue
+ 
+
+ align:start position:0%
+probability 1 over 16 we can continue
+the same way for other values of little
+
+ align:start position:0%
+the same way for other values of little
+ 
+
+ align:start position:0%
+the same way for other values of little
+Z so for example the value of PMF at
+
+ align:start position:0%
+Z so for example the value of PMF at
+ 
+
+ align:start position:0%
+Z so for example the value of PMF at
+little Z equal to 3 this is the
+
+ align:start position:0%
+little Z equal to 3 this is the
+ 
+
+ align:start position:0%
+little Z equal to 3 this is the
+probability that our random variable
+
+ align:start position:0%
+probability that our random variable
+ 
+
+ align:start position:0%
+probability that our random variable
+takes the value of 3 this is an event
+
+ align:start position:0%
+takes the value of 3 this is an event
+ 
+
+ align:start position:0%
+takes the value of 3 this is an event
+that can happen in two ways it
+
+ align:start position:0%
+that can happen in two ways it
+ 
+
+ align:start position:0%
+that can happen in two ways it
+corresponds to two outcomes and so it
+
+ align:start position:0%
+corresponds to two outcomes and so it
+ 
+
+ align:start position:0%
+corresponds to two outcomes and so it
+has probability 2 over 16 continually
+
+ align:start position:0%
+has probability 2 over 16 continually
+ 
+
+ align:start position:0%
+has probability 2 over 16 continually
+continuing similarly the probability
+
+ align:start position:0%
+continuing similarly the probability
+ 
+
+ align:start position:0%
+continuing similarly the probability
+that our random variable takes the value
+
+ align:start position:0%
+that our random variable takes the value
+ 
+
+ align:start position:0%
+that our random variable takes the value
+of 4 is equal to 3 over 16 and we can
+
+ align:start position:0%
+of 4 is equal to 3 over 16 and we can
+ 
+
+ align:start position:0%
+of 4 is equal to 3 over 16 and we can
+continue this way and calculate the
+
+ align:start position:0%
+continue this way and calculate the
+ 
+
+ align:start position:0%
+continue this way and calculate the
+remaining entries of our PMF after you
+
+ align:start position:0%
+remaining entries of our PMF after you
+ 
+
+ align:start position:0%
+remaining entries of our PMF after you
+are done you end up with a table or
+
+ align:start position:0%
+are done you end up with a table or
+ 
+
+ align:start position:0%
+are done you end up with a table or
+rather a graph a plot that has this form
+
+ align:start position:0%
+rather a graph a plot that has this form
+ 
+
+ align:start position:0%
+rather a graph a plot that has this form
+and these are the values of the
+
+ align:start position:0%
+and these are the values of the
+ 
+
+ align:start position:0%
+and these are the values of the
+different probabilities that we have
+
+ align:start position:0%
+different probabilities that we have
+ 
+
+ align:start position:0%
+different probabilities that we have
+computed and you can continue with the
+
+ align:start position:0%
+computed and you can continue with the
+ 
+
+ align:start position:0%
+computed and you can continue with the
+other values it's a reasonable guess
+
+ align:start position:0%
+other values it's a reasonable guess
+ 
+
+ align:start position:0%
+other values it's a reasonable guess
+that this would going to be 4 over 16
+
+ align:start position:0%
+that this would going to be 4 over 16
+ 
+
+ align:start position:0%
+that this would going to be 4 over 16
+this is going to be 3 over 16 2 over 16
+
+ align:start position:0%
+this is going to be 3 over 16 2 over 16
+ 
+
+ align:start position:0%
+this is going to be 3 over 16 2 over 16
+and 1 over 16 so we have completely
+
+ align:start position:0%
+and 1 over 16 so we have completely
+ 
+
+ align:start position:0%
+and 1 over 16 so we have completely
+determined the PMF for for random
+
+ align:start position:0%
+determined the PMF for for random
+ 
+
+ align:start position:0%
+determined the PMF for for random
+variable we have given the form of the
+
+ align:start position:0%
+variable we have given the form of the
+ 
+
+ align:start position:0%
+variable we have given the form of the
+answers and it's always convenient to
+
+ align:start position:0%
+answers and it's always convenient to
+ 
+
+ align:start position:0%
+answers and it's always convenient to
+also provide a plot with the answers
+
+ align:start position:0%
+also provide a plot with the answers
+ 
+
+ align:start position:0%
+also provide a plot with the answers
+that we have
\ No newline at end of file
diff --git a/zcfQ0tVTEbs.txt b/zcfQ0tVTEbs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5ad9fe29cfa697522b61f563ab79ebc5a6db8355
--- /dev/null
+++ b/zcfQ0tVTEbs.txt
@@ -0,0 +1,8803 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay let's settle down settle down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+couple of announcements uh you got the
+
+ align:start position:0%
+couple of announcements uh you got the
+ 
+
+ align:start position:0%
+couple of announcements uh you got the
+test back uh this is what it looked like
+
+ align:start position:0%
+test back uh this is what it looked like
+ 
+
+ align:start position:0%
+test back uh this is what it looked like
+these are the
+
+ align:start position:0%
+these are the
+ 
+
+ align:start position:0%
+these are the
+very nice gaussian you see it goes up
+
+ align:start position:0%
+very nice gaussian you see it goes up
+ 
+
+ align:start position:0%
+very nice gaussian you see it goes up
+and down
+
+ align:start position:0%
+and down
+ 
+
+ align:start position:0%
+and down
+and the average was 54 with a standard
+
+ align:start position:0%
+and the average was 54 with a standard
+ 
+
+ align:start position:0%
+and the average was 54 with a standard
+deviation about 15 um so we have a high
+
+ align:start position:0%
+deviation about 15 um so we have a high
+ 
+
+ align:start position:0%
+deviation about 15 um so we have a high
+here of 95 and a number of people in the
+
+ align:start position:0%
+here of 95 and a number of people in the
+ 
+
+ align:start position:0%
+here of 95 and a number of people in the
+80s and '90s uh we had a number of
+
+ align:start position:0%
+80s and '90s uh we had a number of
+ 
+
+ align:start position:0%
+80s and '90s uh we had a number of
+people that were in the 50s and 60s on
+
+ align:start position:0%
+people that were in the 50s and 60s on
+ 
+
+ align:start position:0%
+people that were in the 50s and 60s on
+the first test who moved to the right
+
+ align:start position:0%
+the first test who moved to the right
+ 
+
+ align:start position:0%
+the first test who moved to the right
+and we had also some people that were up
+
+ align:start position:0%
+and we had also some people that were up
+ 
+
+ align:start position:0%
+and we had also some people that were up
+here who moved to the left
+
+ align:start position:0%
+here who moved to the left
+ 
+
+ align:start position:0%
+here who moved to the left
+far more move to the left than move to
+
+ align:start position:0%
+far more move to the left than move to
+ 
+
+ align:start position:0%
+far more move to the left than move to
+the right
+
+ align:start position:0%
+the right
+ 
+
+ align:start position:0%
+the right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and I talked to the Tas and uh we
+
+ align:start position:0%
+and I talked to the Tas and uh we
+ 
+
+ align:start position:0%
+and I talked to the Tas and uh we
+put a fair bit of care into preparing
+
+ align:start position:0%
+put a fair bit of care into preparing
+ 
+
+ align:start position:0%
+put a fair bit of care into preparing
+the test uh no one felt that it was uh
+
+ align:start position:0%
+the test uh no one felt that it was uh
+ 
+
+ align:start position:0%
+the test uh no one felt that it was uh
+atypically difficult um but uh somehow
+
+ align:start position:0%
+atypically difficult um but uh somehow
+ 
+
+ align:start position:0%
+atypically difficult um but uh somehow
+people didn't do as well uh I've been
+
+ align:start position:0%
+people didn't do as well uh I've been
+ 
+
+ align:start position:0%
+people didn't do as well uh I've been
+getting emails from people asking about
+
+ align:start position:0%
+getting emails from people asking about
+ 
+
+ align:start position:0%
+getting emails from people asking about
+a makeup uh yeah there's a third test on
+
+ align:start position:0%
+a makeup uh yeah there's a third test on
+ 
+
+ align:start position:0%
+a makeup uh yeah there's a third test on
+the 17th of November um we're not going
+
+ align:start position:0%
+the 17th of November um we're not going
+ 
+
+ align:start position:0%
+the 17th of November um we're not going
+to allow you to retry until you get a
+
+ align:start position:0%
+to allow you to retry until you get a
+ 
+
+ align:start position:0%
+to allow you to retry until you get a
+score that you like um because there's
+
+ align:start position:0%
+score that you like um because there's
+ 
+
+ align:start position:0%
+score that you like um because there's
+no point in doing that you know you know
+
+ align:start position:0%
+no point in doing that you know you know
+ 
+
+ align:start position:0%
+no point in doing that you know you know
+what the rules of engagement are I don't
+
+ align:start position:0%
+what the rules of engagement are I don't
+ 
+
+ align:start position:0%
+what the rules of engagement are I don't
+ask much of you but if you fail to give
+
+ align:start position:0%
+ask much of you but if you fail to give
+ 
+
+ align:start position:0%
+ask much of you but if you fail to give
+seven hours a week you're not going to
+
+ align:start position:0%
+seven hours a week you're not going to
+ 
+
+ align:start position:0%
+seven hours a week you're not going to
+pass this class
+
+ align:start position:0%
+pass this class
+ 
+
+ align:start position:0%
+pass this class
+there was nothing there that was out of
+
+ align:start position:0%
+there was nothing there that was out of
+ 
+
+ align:start position:0%
+there was nothing there that was out of
+the ordinary nothing tricky just asking
+
+ align:start position:0%
+the ordinary nothing tricky just asking
+ 
+
+ align:start position:0%
+the ordinary nothing tricky just asking
+you to answer a few skill testing
+
+ align:start position:0%
+you to answer a few skill testing
+ 
+
+ align:start position:0%
+you to answer a few skill testing
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+so um I'm very happy to talk to anybody
+
+ align:start position:0%
+so um I'm very happy to talk to anybody
+ 
+
+ align:start position:0%
+so um I'm very happy to talk to anybody
+about his or her performance I know my
+
+ align:start position:0%
+about his or her performance I know my
+ 
+
+ align:start position:0%
+about his or her performance I know my
+Tas are willing to do the same um we
+
+ align:start position:0%
+Tas are willing to do the same um we
+ 
+
+ align:start position:0%
+Tas are willing to do the same um we
+have tutorial assistance available at no
+
+ align:start position:0%
+have tutorial assistance available at no
+ 
+
+ align:start position:0%
+have tutorial assistance available at no
+charge but there's no substitute for
+
+ align:start position:0%
+charge but there's no substitute for
+ 
+
+ align:start position:0%
+charge but there's no substitute for
+your making the investment in time and I
+
+ align:start position:0%
+your making the investment in time and I
+ 
+
+ align:start position:0%
+your making the investment in time and I
+think that perhaps some people are
+
+ align:start position:0%
+think that perhaps some people are
+ 
+
+ align:start position:0%
+think that perhaps some people are
+lulled into complacency because I don't
+
+ align:start position:0%
+lulled into complacency because I don't
+ 
+
+ align:start position:0%
+lulled into complacency because I don't
+require you to hand in Monster problem
+
+ align:start position:0%
+require you to hand in Monster problem
+ 
+
+ align:start position:0%
+require you to hand in Monster problem
+sets because I think that's childish I
+
+ align:start position:0%
+sets because I think that's childish I
+ 
+
+ align:start position:0%
+sets because I think that's childish I
+think that you should take owners ship
+
+ align:start position:0%
+think that you should take owners ship
+ 
+
+ align:start position:0%
+think that you should take owners ship
+of your learning I treat you as adults
+
+ align:start position:0%
+of your learning I treat you as adults
+ 
+
+ align:start position:0%
+of your learning I treat you as adults
+but if you think because I'm not there
+
+ align:start position:0%
+but if you think because I'm not there
+ 
+
+ align:start position:0%
+but if you think because I'm not there
+looking over your shoulder whether
+
+ align:start position:0%
+looking over your shoulder whether
+ 
+
+ align:start position:0%
+looking over your shoulder whether
+you're doing your work or not I don't
+
+ align:start position:0%
+you're doing your work or not I don't
+ 
+
+ align:start position:0%
+you're doing your work or not I don't
+have to I just look at this
+
+ align:start position:0%
+have to I just look at this
+ 
+
+ align:start position:0%
+have to I just look at this
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+I would warmly recommend that if uh you
+
+ align:start position:0%
+I would warmly recommend that if uh you
+ 
+
+ align:start position:0%
+I would warmly recommend that if uh you
+want to pass this class and I told you
+
+ align:start position:0%
+want to pass this class and I told you
+ 
+
+ align:start position:0%
+want to pass this class and I told you
+everyone in this room should pass this
+
+ align:start position:0%
+everyone in this room should pass this
+ 
+
+ align:start position:0%
+everyone in this room should pass this
+class I want to fail nobody
+
+ align:start position:0%
+class I want to fail nobody
+ 
+
+ align:start position:0%
+class I want to fail nobody
+but if you don't demonstrate basic
+
+ align:start position:0%
+but if you don't demonstrate basic
+ 
+
+ align:start position:0%
+but if you don't demonstrate basic
+proficiency I can't do it it's it's it's
+
+ align:start position:0%
+proficiency I can't do it it's it's it's
+ 
+
+ align:start position:0%
+proficiency I can't do it it's it's it's
+intellectually dishonest on my part part
+
+ align:start position:0%
+intellectually dishonest on my part part
+ 
+
+ align:start position:0%
+intellectually dishonest on my part part
+you wouldn't want that
+
+ align:start position:0%
+you wouldn't want that
+ 
+
+ align:start position:0%
+you wouldn't want that
+you want to know the truth
+
+ align:start position:0%
+you want to know the truth
+ 
+
+ align:start position:0%
+you want to know the truth
+so I'll I'll tell you if you're not
+
+ align:start position:0%
+so I'll I'll tell you if you're not
+ 
+
+ align:start position:0%
+so I'll I'll tell you if you're not
+doing the basics
+
+ align:start position:0%
+doing the basics
+ 
+
+ align:start position:0%
+doing the basics
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+we'll have a chance to get back into the
+
+ align:start position:0%
+we'll have a chance to get back into the
+ 
+
+ align:start position:0%
+we'll have a chance to get back into the
+swing of things there'll be a quiz on um
+
+ align:start position:0%
+swing of things there'll be a quiz on um
+ 
+
+ align:start position:0%
+swing of things there'll be a quiz on um
+Tuesday and I uh I goofed and I I issued
+
+ align:start position:0%
+Tuesday and I uh I goofed and I I issued
+ 
+
+ align:start position:0%
+Tuesday and I uh I goofed and I I issued
+two problem sets in a row both called
+
+ align:start position:0%
+two problem sets in a row both called
+ 
+
+ align:start position:0%
+two problem sets in a row both called
+homework 7 so just to be clear I've
+
+ align:start position:0%
+homework 7 so just to be clear I've
+ 
+
+ align:start position:0%
+homework 7 so just to be clear I've
+fixed this one I've I've re reposted on
+
+ align:start position:0%
+fixed this one I've I've re reposted on
+ 
+
+ align:start position:0%
+fixed this one I've I've re reposted on
+the web it's the same questions but
+
+ align:start position:0%
+the web it's the same questions but
+ 
+
+ align:start position:0%
+the web it's the same questions but
+basically you'll be looking at the X-ray
+
+ align:start position:0%
+basically you'll be looking at the X-ray
+ 
+
+ align:start position:0%
+basically you'll be looking at the X-ray
+defraction questions and the questions
+
+ align:start position:0%
+defraction questions and the questions
+ 
+
+ align:start position:0%
+defraction questions and the questions
+on defects so that's where that's where
+
+ align:start position:0%
+on defects so that's where that's where
+ 
+
+ align:start position:0%
+on defects so that's where that's where
+we're going to be for for Tuesday and
+
+ align:start position:0%
+we're going to be for for Tuesday and
+ 
+
+ align:start position:0%
+we're going to be for for Tuesday and
+that's good news because those of you
+
+ align:start position:0%
+that's good news because those of you
+ 
+
+ align:start position:0%
+that's good news because those of you
+had trouble on the test uh this past
+
+ align:start position:0%
+had trouble on the test uh this past
+ 
+
+ align:start position:0%
+had trouble on the test uh this past
+Wednesday we're going to be moving into
+
+ align:start position:0%
+Wednesday we're going to be moving into
+ 
+
+ align:start position:0%
+Wednesday we're going to be moving into
+some new topics so you get a chance to
+
+ align:start position:0%
+some new topics so you get a chance to
+ 
+
+ align:start position:0%
+some new topics so you get a chance to
+start over towards the end there's some
+
+ align:start position:0%
+start over towards the end there's some
+ 
+
+ align:start position:0%
+start over towards the end there's some
+integration but um at least it's not so
+
+ align:start position:0%
+integration but um at least it's not so
+ 
+
+ align:start position:0%
+integration but um at least it's not so
+strictly lock step that if you didn't do
+
+ align:start position:0%
+strictly lock step that if you didn't do
+ 
+
+ align:start position:0%
+strictly lock step that if you didn't do
+well on Wednesday then uh you're
+
+ align:start position:0%
+well on Wednesday then uh you're
+ 
+
+ align:start position:0%
+well on Wednesday then uh you're
+hopelessly uh behind
+
+ align:start position:0%
+hopelessly uh behind
+ 
+
+ align:start position:0%
+hopelessly uh behind
+and uh and again I I mean it when I say
+
+ align:start position:0%
+and uh and again I I mean it when I say
+ 
+
+ align:start position:0%
+and uh and again I I mean it when I say
+this I want everyone to succeed here but
+
+ align:start position:0%
+this I want everyone to succeed here but
+ 
+
+ align:start position:0%
+this I want everyone to succeed here but
+you have to invest
+
+ align:start position:0%
+you have to invest
+ 
+
+ align:start position:0%
+you have to invest
+you have to invest
+
+ align:start position:0%
+you have to invest
+ 
+
+ align:start position:0%
+you have to invest
+okay so uh last day we were looking at
+
+ align:start position:0%
+okay so uh last day we were looking at
+ 
+
+ align:start position:0%
+okay so uh last day we were looking at
+defects we looked at Point defects and
+
+ align:start position:0%
+defects we looked at Point defects and
+ 
+
+ align:start position:0%
+defects we looked at Point defects and
+line defects and today I want to
+
+ align:start position:0%
+line defects and today I want to
+ 
+
+ align:start position:0%
+line defects and today I want to
+continue I want to look at surface
+
+ align:start position:0%
+continue I want to look at surface
+ 
+
+ align:start position:0%
+continue I want to look at surface
+defects and volume defects and
+
+ align:start position:0%
+defects and volume defects and
+ 
+
+ align:start position:0%
+defects and volume defects and
+ultimately go to something that's so
+
+ align:start position:0%
+ultimately go to something that's so
+ 
+
+ align:start position:0%
+ultimately go to something that's so
+defective it lacks order so will move
+
+ align:start position:0%
+defective it lacks order so will move
+ 
+
+ align:start position:0%
+defective it lacks order so will move
+from surface to volume to disordered
+
+ align:start position:0%
+from surface to volume to disordered
+ 
+
+ align:start position:0%
+from surface to volume to disordered
+solids so let's look at what makes
+
+ align:start position:0%
+solids so let's look at what makes
+ 
+
+ align:start position:0%
+solids so let's look at what makes
+surfaces special what makes surfaces
+
+ align:start position:0%
+surfaces special what makes surfaces
+ 
+
+ align:start position:0%
+surfaces special what makes surfaces
+special is that the coordination number
+
+ align:start position:0%
+special is that the coordination number
+ 
+
+ align:start position:0%
+special is that the coordination number
+is different at the surface from what it
+
+ align:start position:0%
+is different at the surface from what it
+ 
+
+ align:start position:0%
+is different at the surface from what it
+is inside the material what I'm showing
+
+ align:start position:0%
+is inside the material what I'm showing
+ 
+
+ align:start position:0%
+is inside the material what I'm showing
+here is the free surface of a material
+
+ align:start position:0%
+here is the free surface of a material
+ 
+
+ align:start position:0%
+here is the free surface of a material
+and here's one region of the material
+
+ align:start position:0%
+and here's one region of the material
+ 
+
+ align:start position:0%
+and here's one region of the material
+where the atoms are lined up in this
+
+ align:start position:0%
+where the atoms are lined up in this
+ 
+
+ align:start position:0%
+where the atoms are lined up in this
+manner and here's another region of the
+
+ align:start position:0%
+manner and here's another region of the
+ 
+
+ align:start position:0%
+manner and here's another region of the
+material where the atoms are lined up in
+
+ align:start position:0%
+material where the atoms are lined up in
+ 
+
+ align:start position:0%
+material where the atoms are lined up in
+this manner because they grew from the
+
+ align:start position:0%
+this manner because they grew from the
+ 
+
+ align:start position:0%
+this manner because they grew from the
+Melt they grew from the Melt starting
+
+ align:start position:0%
+Melt they grew from the Melt starting
+ 
+
+ align:start position:0%
+Melt they grew from the Melt starting
+from different starting points from
+
+ align:start position:0%
+from different starting points from
+ 
+
+ align:start position:0%
+from different starting points from
+different nuclei and when they impinge
+
+ align:start position:0%
+different nuclei and when they impinge
+ 
+
+ align:start position:0%
+different nuclei and when they impinge
+This Plane doesn't line up with this
+
+ align:start position:0%
+This Plane doesn't line up with this
+ 
+
+ align:start position:0%
+This Plane doesn't line up with this
+plane and there's a boundary along here
+
+ align:start position:0%
+plane and there's a boundary along here
+ 
+
+ align:start position:0%
+plane and there's a boundary along here
+so we have two types of surfaces here we
+
+ align:start position:0%
+so we have two types of surfaces here we
+ 
+
+ align:start position:0%
+so we have two types of surfaces here we
+have a free surface
+
+ align:start position:0%
+have a free surface
+ 
+
+ align:start position:0%
+have a free surface
+we have a free surface
+
+ align:start position:0%
+we have a free surface
+ 
+
+ align:start position:0%
+we have a free surface
+and we have an internal surface
+
+ align:start position:0%
+and we have an internal surface
+ 
+
+ align:start position:0%
+and we have an internal surface
+an internal surface I'm going to talk
+
+ align:start position:0%
+an internal surface I'm going to talk
+ 
+
+ align:start position:0%
+an internal surface I'm going to talk
+about both of them the thing they have
+
+ align:start position:0%
+about both of them the thing they have
+ 
+
+ align:start position:0%
+about both of them the thing they have
+in common is that if we look at an atom
+
+ align:start position:0%
+in common is that if we look at an atom
+ 
+
+ align:start position:0%
+in common is that if we look at an atom
+down here in the center
+
+ align:start position:0%
+down here in the center
+ 
+
+ align:start position:0%
+down here in the center
+if this is an FCC structure an atom here
+
+ align:start position:0%
+if this is an FCC structure an atom here
+ 
+
+ align:start position:0%
+if this is an FCC structure an atom here
+and an FCC structure has 12 nearest
+
+ align:start position:0%
+and an FCC structure has 12 nearest
+ 
+
+ align:start position:0%
+and an FCC structure has 12 nearest
+neighbors an atom here at the free
+
+ align:start position:0%
+neighbors an atom here at the free
+ 
+
+ align:start position:0%
+neighbors an atom here at the free
+surface cannot have 12 nearest neighbors
+
+ align:start position:0%
+surface cannot have 12 nearest neighbors
+ 
+
+ align:start position:0%
+surface cannot have 12 nearest neighbors
+it has fewer than 12 nearest neighbors
+
+ align:start position:0%
+it has fewer than 12 nearest neighbors
+ 
+
+ align:start position:0%
+it has fewer than 12 nearest neighbors
+and we know that systems form bonds
+
+ align:start position:0%
+and we know that systems form bonds
+ 
+
+ align:start position:0%
+and we know that systems form bonds
+maximally to lower their energy so
+
+ align:start position:0%
+maximally to lower their energy so
+ 
+
+ align:start position:0%
+maximally to lower their energy so
+therefore if I have fewer than the
+
+ align:start position:0%
+therefore if I have fewer than the
+ 
+
+ align:start position:0%
+therefore if I have fewer than the
+maximum number of bonds this is not
+
+ align:start position:0%
+maximum number of bonds this is not
+ 
+
+ align:start position:0%
+maximum number of bonds this is not
+at as low an energy at the free surface
+
+ align:start position:0%
+at as low an energy at the free surface
+ 
+
+ align:start position:0%
+at as low an energy at the free surface
+as it would be were it inside the
+
+ align:start position:0%
+as it would be were it inside the
+ 
+
+ align:start position:0%
+as it would be were it inside the
+material because at the free surface it
+
+ align:start position:0%
+material because at the free surface it
+ 
+
+ align:start position:0%
+material because at the free surface it
+has fewer than 12 nearest neighbors so
+
+ align:start position:0%
+has fewer than 12 nearest neighbors so
+ 
+
+ align:start position:0%
+has fewer than 12 nearest neighbors so
+that means that surfaces
+
+ align:start position:0%
+that means that surfaces
+ 
+
+ align:start position:0%
+that means that surfaces
+surfaces are higher energy they're
+
+ align:start position:0%
+surfaces are higher energy they're
+ 
+
+ align:start position:0%
+surfaces are higher energy they're
+higher energy regions
+
+ align:start position:0%
+higher energy regions
+ 
+
+ align:start position:0%
+higher energy regions
+in the crystal higher energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that can be good or it can be bad if
+
+ align:start position:0%
+and that can be good or it can be bad if
+ 
+
+ align:start position:0%
+and that can be good or it can be bad if
+we want something high energy that's
+
+ align:start position:0%
+we want something high energy that's
+ 
+
+ align:start position:0%
+we want something high energy that's
+good if we're looking for catalysis
+
+ align:start position:0%
+good if we're looking for catalysis
+ 
+
+ align:start position:0%
+good if we're looking for catalysis
+we'll talk about Catal is later but
+
+ align:start position:0%
+we'll talk about Catal is later but
+ 
+
+ align:start position:0%
+we'll talk about Catal is later but
+catalysis occurs at the free Surface by
+
+ align:start position:0%
+catalysis occurs at the free Surface by
+ 
+
+ align:start position:0%
+catalysis occurs at the free Surface by
+definition you need to have those broken
+
+ align:start position:0%
+definition you need to have those broken
+ 
+
+ align:start position:0%
+definition you need to have those broken
+bonds so catalysis is good but it also
+
+ align:start position:0%
+bonds so catalysis is good but it also
+ 
+
+ align:start position:0%
+bonds so catalysis is good but it also
+means things are highly reactive
+
+ align:start position:0%
+means things are highly reactive
+ 
+
+ align:start position:0%
+means things are highly reactive
+sometimes undesirably
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that can lead to corrosion which is
+
+ align:start position:0%
+and that can lead to corrosion which is
+ 
+
+ align:start position:0%
+and that can lead to corrosion which is
+undesirable where is corrosion going to
+
+ align:start position:0%
+undesirable where is corrosion going to
+ 
+
+ align:start position:0%
+undesirable where is corrosion going to
+occur this material isn't uniform in its
+
+ align:start position:0%
+occur this material isn't uniform in its
+ 
+
+ align:start position:0%
+occur this material isn't uniform in its
+properties the corrosion resistance of
+
+ align:start position:0%
+properties the corrosion resistance of
+ 
+
+ align:start position:0%
+properties the corrosion resistance of
+an atom deep inside the crystal is
+
+ align:start position:0%
+an atom deep inside the crystal is
+ 
+
+ align:start position:0%
+an atom deep inside the crystal is
+different from the corrosion resist
+
+ align:start position:0%
+different from the corrosion resist
+ 
+
+ align:start position:0%
+different from the corrosion resist
+resistance on the free surface which is
+
+ align:start position:0%
+resistance on the free surface which is
+ 
+
+ align:start position:0%
+resistance on the free surface which is
+different from the corrosion resistance
+
+ align:start position:0%
+different from the corrosion resistance
+ 
+
+ align:start position:0%
+different from the corrosion resistance
+along this internal surface each of
+
+ align:start position:0%
+along this internal surface each of
+ 
+
+ align:start position:0%
+along this internal surface each of
+these regions each of these regions is
+
+ align:start position:0%
+these regions each of these regions is
+ 
+
+ align:start position:0%
+these regions each of these regions is
+called a grain
+
+ align:start position:0%
+called a grain
+ 
+
+ align:start position:0%
+called a grain
+the grain is a virtual single Crystal
+
+ align:start position:0%
+the grain is a virtual single Crystal
+ 
+
+ align:start position:0%
+the grain is a virtual single Crystal
+it's a single Crystal so we have a poly
+
+ align:start position:0%
+it's a single Crystal so we have a poly
+ 
+
+ align:start position:0%
+it's a single Crystal so we have a poly
+crystallin material consisting of
+
+ align:start position:0%
+crystallin material consisting of
+ 
+
+ align:start position:0%
+crystallin material consisting of
+a tapestry of single crystals called
+
+ align:start position:0%
+a tapestry of single crystals called
+ 
+
+ align:start position:0%
+a tapestry of single crystals called
+grains and this internal surface is
+
+ align:start position:0%
+grains and this internal surface is
+ 
+
+ align:start position:0%
+grains and this internal surface is
+called a grain boundary a grain boundary
+
+ align:start position:0%
+called a grain boundary a grain boundary
+ 
+
+ align:start position:0%
+called a grain boundary a grain boundary
+both of these are defects both of these
+
+ align:start position:0%
+both of these are defects both of these
+ 
+
+ align:start position:0%
+both of these are defects both of these
+are defects okay what does the grain
+
+ align:start position:0%
+are defects okay what does the grain
+ 
+
+ align:start position:0%
+are defects okay what does the grain
+boundary do well the grain boundary does
+
+ align:start position:0%
+boundary do well the grain boundary does
+ 
+
+ align:start position:0%
+boundary do well the grain boundary does
+several things first of all the grain
+
+ align:start position:0%
+several things first of all the grain
+ 
+
+ align:start position:0%
+several things first of all the grain
+boundary acts as a trap for impurities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a trap for impurities
+
+ align:start position:0%
+a trap for impurities
+ 
+
+ align:start position:0%
+a trap for impurities
+that can be good or it can be bad if all
+
+ align:start position:0%
+that can be good or it can be bad if all
+ 
+
+ align:start position:0%
+that can be good or it can be bad if all
+the impurities collected the grain
+
+ align:start position:0%
+the impurities collected the grain
+ 
+
+ align:start position:0%
+the impurities collected the grain
+boundaries and those impurities EMB
+
+ align:start position:0%
+boundaries and those impurities EMB
+ 
+
+ align:start position:0%
+boundaries and those impurities EMB
+brittle the material it doesn't matter
+
+ align:start position:0%
+brittle the material it doesn't matter
+ 
+
+ align:start position:0%
+brittle the material it doesn't matter
+what ductility the grains have the
+
+ align:start position:0%
+what ductility the grains have the
+ 
+
+ align:start position:0%
+what ductility the grains have the
+material will fail at the grain boundary
+
+ align:start position:0%
+material will fail at the grain boundary
+ 
+
+ align:start position:0%
+material will fail at the grain boundary
+it would be as though you had bricks
+
+ align:start position:0%
+it would be as though you had bricks
+ 
+
+ align:start position:0%
+it would be as though you had bricks
+that are very strong held together by a
+
+ align:start position:0%
+that are very strong held together by a
+ 
+
+ align:start position:0%
+that are very strong held together by a
+weak mortar the grain boundaries act as
+
+ align:start position:0%
+weak mortar the grain boundaries act as
+ 
+
+ align:start position:0%
+weak mortar the grain boundaries act as
+that mortar but they have beneficial
+
+ align:start position:0%
+that mortar but they have beneficial
+ 
+
+ align:start position:0%
+that mortar but they have beneficial
+effects imagine a dislocation sliding in
+
+ align:start position:0%
+effects imagine a dislocation sliding in
+ 
+
+ align:start position:0%
+effects imagine a dislocation sliding in
+one grain and it wants to rip through
+
+ align:start position:0%
+one grain and it wants to rip through
+ 
+
+ align:start position:0%
+one grain and it wants to rip through
+the entire material that Mis registry of
+
+ align:start position:0%
+the entire material that Mis registry of
+ 
+
+ align:start position:0%
+the entire material that Mis registry of
+atoms at the grain boundary stops the
+
+ align:start position:0%
+atoms at the grain boundary stops the
+ 
+
+ align:start position:0%
+atoms at the grain boundary stops the
+dislocation so it can act as has a site
+
+ align:start position:0%
+dislocation so it can act as has a site
+ 
+
+ align:start position:0%
+dislocation so it can act as has a site
+for arresting dislocations
+
+ align:start position:0%
+for arresting dislocations
+ 
+
+ align:start position:0%
+for arresting dislocations
+it arrests dislocations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I talked to you last day about the
+
+ align:start position:0%
+so I talked to you last day about the
+ 
+
+ align:start position:0%
+so I talked to you last day about the
+management of defects so if we want to
+
+ align:start position:0%
+management of defects so if we want to
+ 
+
+ align:start position:0%
+management of defects so if we want to
+have a material that has high strength
+
+ align:start position:0%
+have a material that has high strength
+ 
+
+ align:start position:0%
+have a material that has high strength
+and is not going to easily slip do we
+
+ align:start position:0%
+and is not going to easily slip do we
+ 
+
+ align:start position:0%
+and is not going to easily slip do we
+want a material that has coarse grains
+
+ align:start position:0%
+want a material that has coarse grains
+ 
+
+ align:start position:0%
+want a material that has coarse grains
+or fine grains we'd want to have fine
+
+ align:start position:0%
+or fine grains we'd want to have fine
+ 
+
+ align:start position:0%
+or fine grains we'd want to have fine
+grain materials so grain boundary
+
+ align:start position:0%
+grain materials so grain boundary
+ 
+
+ align:start position:0%
+grain materials so grain boundary
+engineering is important in the
+
+ align:start position:0%
+engineering is important in the
+ 
+
+ align:start position:0%
+engineering is important in the
+management of the mechanical properties
+
+ align:start position:0%
+management of the mechanical properties
+ 
+
+ align:start position:0%
+management of the mechanical properties
+of material and I want to show you
+
+ align:start position:0%
+of material and I want to show you
+ 
+
+ align:start position:0%
+of material and I want to show you
+several things first of all here's a
+
+ align:start position:0%
+several things first of all here's a
+ 
+
+ align:start position:0%
+several things first of all here's a
+here's a cartoon just to get you again
+
+ align:start position:0%
+here's a cartoon just to get you again
+ 
+
+ align:start position:0%
+here's a cartoon just to get you again
+onto the page of what's happening these
+
+ align:start position:0%
+onto the page of what's happening these
+ 
+
+ align:start position:0%
+onto the page of what's happening these
+different grains began from the melt at
+
+ align:start position:0%
+different grains began from the melt at
+ 
+
+ align:start position:0%
+different grains began from the melt at
+different sites in the liquid grew to
+
+ align:start position:0%
+different sites in the liquid grew to
+ 
+
+ align:start position:0%
+different sites in the liquid grew to
+impingement and you can see these atoms
+
+ align:start position:0%
+impingement and you can see these atoms
+ 
+
+ align:start position:0%
+impingement and you can see these atoms
+can't ever perfectly align with the
+
+ align:start position:0%
+can't ever perfectly align with the
+ 
+
+ align:start position:0%
+can't ever perfectly align with the
+atoms growing from the adjacent grain
+
+ align:start position:0%
+atoms growing from the adjacent grain
+ 
+
+ align:start position:0%
+atoms growing from the adjacent grain
+and so this zone of Mis registry it's
+
+ align:start position:0%
+and so this zone of Mis registry it's
+ 
+
+ align:start position:0%
+and so this zone of Mis registry it's
+the void here which is called the grain
+
+ align:start position:0%
+the void here which is called the grain
+ 
+
+ align:start position:0%
+the void here which is called the grain
+boundary okay now this is showing it in
+
+ align:start position:0%
+boundary okay now this is showing it in
+ 
+
+ align:start position:0%
+boundary okay now this is showing it in
+terms of of a cross-hatching so the
+
+ align:start position:0%
+terms of of a cross-hatching so the
+ 
+
+ align:start position:0%
+terms of of a cross-hatching so the
+cross-hatching is tilted in different
+
+ align:start position:0%
+cross-hatching is tilted in different
+ 
+
+ align:start position:0%
+cross-hatching is tilted in different
+ways and the the gaps between the
+
+ align:start position:0%
+ways and the the gaps between the
+ 
+
+ align:start position:0%
+ways and the the gaps between the
+cross-hatching are termed grain
+
+ align:start position:0%
+cross-hatching are termed grain
+ 
+
+ align:start position:0%
+cross-hatching are termed grain
+boundaries this is a piece of polycryst
+
+ align:start position:0%
+boundaries this is a piece of polycryst
+ 
+
+ align:start position:0%
+boundaries this is a piece of polycryst
+and copper that's actually been polished
+
+ align:start position:0%
+and copper that's actually been polished
+ 
+
+ align:start position:0%
+and copper that's actually been polished
+and then etched and because there are
+
+ align:start position:0%
+and then etched and because there are
+ 
+
+ align:start position:0%
+and then etched and because there are
+different grains are presenting
+
+ align:start position:0%
+different grains are presenting
+ 
+
+ align:start position:0%
+different grains are presenting
+different Crystal densities atom
+
+ align:start position:0%
+different Crystal densities atom
+ 
+
+ align:start position:0%
+different Crystal densities atom
+densities these grains etch differently
+
+ align:start position:0%
+densities these grains etch differently
+ 
+
+ align:start position:0%
+densities these grains etch differently
+they etch at different rates in the same
+
+ align:start position:0%
+they etch at different rates in the same
+ 
+
+ align:start position:0%
+they etch at different rates in the same
+acid and after a while they will
+
+ align:start position:0%
+acid and after a while they will
+ 
+
+ align:start position:0%
+acid and after a while they will
+actually be tilting it slightly
+
+ align:start position:0%
+actually be tilting it slightly
+ 
+
+ align:start position:0%
+actually be tilting it slightly
+different angles and then when we
+
+ align:start position:0%
+different angles and then when we
+ 
+
+ align:start position:0%
+different angles and then when we
+illuminate this with polarized light and
+
+ align:start position:0%
+illuminate this with polarized light and
+ 
+
+ align:start position:0%
+illuminate this with polarized light and
+look at it under a simple Optical
+
+ align:start position:0%
+look at it under a simple Optical
+ 
+
+ align:start position:0%
+look at it under a simple Optical
+microscope we see different colors and
+
+ align:start position:0%
+microscope we see different colors and
+ 
+
+ align:start position:0%
+microscope we see different colors and
+these are the different grains so each
+
+ align:start position:0%
+these are the different grains so each
+ 
+
+ align:start position:0%
+these are the different grains so each
+one of these you can consider a single
+
+ align:start position:0%
+one of these you can consider a single
+ 
+
+ align:start position:0%
+one of these you can consider a single
+Crystal that has just the the normal
+
+ align:start position:0%
+Crystal that has just the the normal
+ 
+
+ align:start position:0%
+Crystal that has just the the normal
+atoms in their FCC lattice throwing in
+
+ align:start position:0%
+atoms in their FCC lattice throwing in
+ 
+
+ align:start position:0%
+atoms in their FCC lattice throwing in
+some vacancies and some dislocations and
+
+ align:start position:0%
+some vacancies and some dislocations and
+ 
+
+ align:start position:0%
+some vacancies and some dislocations and
+now they impinge along these different
+
+ align:start position:0%
+now they impinge along these different
+ 
+
+ align:start position:0%
+now they impinge along these different
+boundaries and this is a field ion
+
+ align:start position:0%
+boundaries and this is a field ion
+ 
+
+ align:start position:0%
+boundaries and this is a field ion
+microscope image of a Tungsten by
+
+ align:start position:0%
+microscope image of a Tungsten by
+ 
+
+ align:start position:0%
+microscope image of a Tungsten by
+Crystal and right along the low lower
+
+ align:start position:0%
+Crystal and right along the low lower
+ 
+
+ align:start position:0%
+Crystal and right along the low lower
+right corner you can see the edge of the
+
+ align:start position:0%
+right corner you can see the edge of the
+ 
+
+ align:start position:0%
+right corner you can see the edge of the
+of the this is the grain boundary so
+
+ align:start position:0%
+of the this is the grain boundary so
+ 
+
+ align:start position:0%
+of the this is the grain boundary so
+there's a crystal single Crystal to the
+
+ align:start position:0%
+there's a crystal single Crystal to the
+ 
+
+ align:start position:0%
+there's a crystal single Crystal to the
+lower right and the rest is a single
+
+ align:start position:0%
+lower right and the rest is a single
+ 
+
+ align:start position:0%
+lower right and the rest is a single
+Crystal to the upper left grain
+
+ align:start position:0%
+Crystal to the upper left grain
+ 
+
+ align:start position:0%
+Crystal to the upper left grain
+boundaries okay so and also I can show
+
+ align:start position:0%
+boundaries okay so and also I can show
+ 
+
+ align:start position:0%
+boundaries okay so and also I can show
+you again Tom may we go to the uh
+
+ align:start position:0%
+you again Tom may we go to the uh
+ 
+
+ align:start position:0%
+you again Tom may we go to the uh
+document camera we'll go back to our pal
+
+ align:start position:0%
+document camera we'll go back to our pal
+ 
+
+ align:start position:0%
+document camera we'll go back to our pal
+the atom mix here and see if we can zoom
+
+ align:start position:0%
+the atom mix here and see if we can zoom
+ 
+
+ align:start position:0%
+the atom mix here and see if we can zoom
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+okay that's too much Zoom
+
+ align:start position:0%
+okay that's too much Zoom
+ 
+
+ align:start position:0%
+okay that's too much Zoom
+okay good and now autofocus
+
+ align:start position:0%
+okay good and now autofocus
+ 
+
+ align:start position:0%
+okay good and now autofocus
+autofocus off autofocus on well that's a
+
+ align:start position:0%
+autofocus off autofocus on well that's a
+ 
+
+ align:start position:0%
+autofocus off autofocus on well that's a
+so so autofocus but uh if we had a
+
+ align:start position:0%
+so so autofocus but uh if we had a
+ 
+
+ align:start position:0%
+so so autofocus but uh if we had a
+manual we could do oh that's better okay
+
+ align:start position:0%
+manual we could do oh that's better okay
+ 
+
+ align:start position:0%
+manual we could do oh that's better okay
+so now you can see how things align you
+
+ align:start position:0%
+so now you can see how things align you
+ 
+
+ align:start position:0%
+so now you can see how things align you
+can see zones here perfect and then you
+
+ align:start position:0%
+can see zones here perfect and then you
+ 
+
+ align:start position:0%
+can see zones here perfect and then you
+can see there's some grain boundaries
+
+ align:start position:0%
+can see there's some grain boundaries
+ 
+
+ align:start position:0%
+can see there's some grain boundaries
+excuse me pardon me some vacancies you
+
+ align:start position:0%
+excuse me pardon me some vacancies you
+ 
+
+ align:start position:0%
+excuse me pardon me some vacancies you
+see along here these atoms are moving
+
+ align:start position:0%
+see along here these atoms are moving
+ 
+
+ align:start position:0%
+see along here these atoms are moving
+sort of up up to towards about 2:00 and
+
+ align:start position:0%
+sort of up up to towards about 2:00 and
+ 
+
+ align:start position:0%
+sort of up up to towards about 2:00 and
+these atoms are moving here and then
+
+ align:start position:0%
+these atoms are moving here and then
+ 
+
+ align:start position:0%
+these atoms are moving here and then
+when they try to align there's the grain
+
+ align:start position:0%
+when they try to align there's the grain
+ 
+
+ align:start position:0%
+when they try to align there's the grain
+boundary oh that autofocus is really
+
+ align:start position:0%
+boundary oh that autofocus is really
+ 
+
+ align:start position:0%
+boundary oh that autofocus is really
+going going nuts isn't it isn't that fun
+
+ align:start position:0%
+going going nuts isn't it isn't that fun
+ 
+
+ align:start position:0%
+going going nuts isn't it isn't that fun
+fun to see the machine struggle
+
+ align:start position:0%
+fun to see the machine struggle
+ 
+
+ align:start position:0%
+fun to see the machine struggle
+I just laugh laugh at it look at stupid
+
+ align:start position:0%
+I just laugh laugh at it look at stupid
+ 
+
+ align:start position:0%
+I just laugh laugh at it look at stupid
+stupid machine look at this see all
+
+ align:start position:0%
+stupid machine look at this see all
+ 
+
+ align:start position:0%
+stupid machine look at this see all
+right so there's grain boundaries and
+
+ align:start position:0%
+right so there's grain boundaries and
+ 
+
+ align:start position:0%
+right so there's grain boundaries and
+then the free surface up here of course
+
+ align:start position:0%
+then the free surface up here of course
+ 
+
+ align:start position:0%
+then the free surface up here of course
+so these are both high energy regimes
+
+ align:start position:0%
+so these are both high energy regimes
+ 
+
+ align:start position:0%
+so these are both high energy regimes
+and we can anal this if we anal it we
+
+ align:start position:0%
+and we can anal this if we anal it we
+ 
+
+ align:start position:0%
+and we can anal this if we anal it we
+can try to get a more coarse grain
+
+ align:start position:0%
+can try to get a more coarse grain
+ 
+
+ align:start position:0%
+can try to get a more coarse grain
+structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now I have a single I have a
+
+ align:start position:0%
+okay so now I have a single I have a
+ 
+
+ align:start position:0%
+okay so now I have a single I have a
+single gr there there was the original
+
+ align:start position:0%
+single gr there there was the original
+ 
+
+ align:start position:0%
+single gr there there was the original
+grain boundary and there was one in here
+
+ align:start position:0%
+grain boundary and there was one in here
+ 
+
+ align:start position:0%
+grain boundary and there was one in here
+and now we have a larger regime okay
+
+ align:start position:0%
+and now we have a larger regime okay
+ 
+
+ align:start position:0%
+and now we have a larger regime okay
+okay let's go back to the to the uh
+
+ align:start position:0%
+okay let's go back to the to the uh
+ 
+
+ align:start position:0%
+okay let's go back to the to the uh
+computer please Tom okay so now let's
+
+ align:start position:0%
+computer please Tom okay so now let's
+ 
+
+ align:start position:0%
+computer please Tom okay so now let's
+look at three-dimensional defects
+
+ align:start position:0%
+look at three-dimensional defects
+ 
+
+ align:start position:0%
+look at three-dimensional defects
+three-dimensional defects
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there's really two types
+
+ align:start position:0%
+there's really two types
+ 
+
+ align:start position:0%
+there's really two types
+being and void things that are missing
+
+ align:start position:0%
+being and void things that are missing
+ 
+
+ align:start position:0%
+being and void things that are missing
+and things that are there okay so what's
+
+ align:start position:0%
+and things that are there okay so what's
+ 
+
+ align:start position:0%
+and things that are there okay so what's
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+and void I'll talk first about the
+
+ align:start position:0%
+and void I'll talk first about the
+ 
+
+ align:start position:0%
+and void I'll talk first about the
+three-dimensional voids voids are simply
+
+ align:start position:0%
+three-dimensional voids voids are simply
+ 
+
+ align:start position:0%
+three-dimensional voids voids are simply
+coales this is coales vacancies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coales vacancies the vacancies will
+
+ align:start position:0%
+coales vacancies the vacancies will
+ 
+
+ align:start position:0%
+coales vacancies the vacancies will
+eventually come together coales and so
+
+ align:start position:0%
+eventually come together coales and so
+ 
+
+ align:start position:0%
+eventually come together coales and so
+this clearly weakens the material
+
+ align:start position:0%
+this clearly weakens the material
+ 
+
+ align:start position:0%
+this clearly weakens the material
+mechanically
+
+ align:start position:0%
+mechanically
+ 
+
+ align:start position:0%
+mechanically
+mechanical properties are degraded by uh
+
+ align:start position:0%
+mechanical properties are degraded by uh
+ 
+
+ align:start position:0%
+mechanical properties are degraded by uh
+this presence of what what looks like
+
+ align:start position:0%
+this presence of what what looks like
+ 
+
+ align:start position:0%
+this presence of what what looks like
+blo holes on the Micron scale and then
+
+ align:start position:0%
+blo holes on the Micron scale and then
+ 
+
+ align:start position:0%
+blo holes on the Micron scale and then
+there's the U three-dimensional defects
+
+ align:start position:0%
+there's the U three-dimensional defects
+ 
+
+ align:start position:0%
+there's the U three-dimensional defects
+consisting of matter and the most uh
+
+ align:start position:0%
+consisting of matter and the most uh
+ 
+
+ align:start position:0%
+consisting of matter and the most uh
+injurious is called the inclusion the
+
+ align:start position:0%
+injurious is called the inclusion the
+ 
+
+ align:start position:0%
+injurious is called the inclusion the
+inclusion and the inclusion is simply
+
+ align:start position:0%
+inclusion and the inclusion is simply
+ 
+
+ align:start position:0%
+inclusion and the inclusion is simply
+trapped foreign matter it's trapped
+
+ align:start position:0%
+trapped foreign matter it's trapped
+ 
+
+ align:start position:0%
+trapped foreign matter it's trapped
+foreign matter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+why is it trapped because it's insoluble
+
+ align:start position:0%
+why is it trapped because it's insoluble
+ 
+
+ align:start position:0%
+why is it trapped because it's insoluble
+it's insoluble in the parent Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this can lead to deleterious
+
+ align:start position:0%
+and this can lead to deleterious
+ 
+
+ align:start position:0%
+and this can lead to deleterious
+mechanical properties and I'll show you
+
+ align:start position:0%
+mechanical properties and I'll show you
+ 
+
+ align:start position:0%
+mechanical properties and I'll show you
+an example immediately uh following um
+
+ align:start position:0%
+an example immediately uh following um
+ 
+
+ align:start position:0%
+an example immediately uh following um
+and then there's a desirable form of uh
+
+ align:start position:0%
+and then there's a desirable form of uh
+ 
+
+ align:start position:0%
+and then there's a desirable form of uh
+three-dimensional defect which is called
+
+ align:start position:0%
+three-dimensional defect which is called
+ 
+
+ align:start position:0%
+three-dimensional defect which is called
+the precipitate
+
+ align:start position:0%
+the precipitate
+ 
+
+ align:start position:0%
+the precipitate
+the precipitate
+
+ align:start position:0%
+the precipitate
+ 
+
+ align:start position:0%
+the precipitate
+and the difference between the
+
+ align:start position:0%
+and the difference between the
+ 
+
+ align:start position:0%
+and the difference between the
+precipitate and the inclusion is that
+
+ align:start position:0%
+precipitate and the inclusion is that
+ 
+
+ align:start position:0%
+precipitate and the inclusion is that
+the inclusion is never soluble the
+
+ align:start position:0%
+the inclusion is never soluble the
+ 
+
+ align:start position:0%
+the inclusion is never soluble the
+inclusion is something that's foreign
+
+ align:start position:0%
+inclusion is something that's foreign
+ 
+
+ align:start position:0%
+inclusion is something that's foreign
+matter that got trapped during the
+
+ align:start position:0%
+matter that got trapped during the
+ 
+
+ align:start position:0%
+matter that got trapped during the
+melting process or the vapor deposition
+
+ align:start position:0%
+melting process or the vapor deposition
+ 
+
+ align:start position:0%
+melting process or the vapor deposition
+process when the solid was formed the
+
+ align:start position:0%
+process when the solid was formed the
+ 
+
+ align:start position:0%
+process when the solid was formed the
+precipitate sometimes is put there by
+
+ align:start position:0%
+precipitate sometimes is put there by
+ 
+
+ align:start position:0%
+precipitate sometimes is put there by
+designation all right it is something
+
+ align:start position:0%
+designation all right it is something
+ 
+
+ align:start position:0%
+designation all right it is something
+that was dissolved at one point and then
+
+ align:start position:0%
+that was dissolved at one point and then
+ 
+
+ align:start position:0%
+that was dissolved at one point and then
+made to come out of solution so it is
+
+ align:start position:0%
+made to come out of solution so it is
+ 
+
+ align:start position:0%
+made to come out of solution so it is
+exsolved
+
+ align:start position:0%
+exsolved
+ 
+
+ align:start position:0%
+exsolved
+it is exsolved matter formerly dissolved
+
+ align:start position:0%
+it is exsolved matter formerly dissolved
+ 
+
+ align:start position:0%
+it is exsolved matter formerly dissolved
+and the reason that both of these are so
+
+ align:start position:0%
+and the reason that both of these are so
+ 
+
+ align:start position:0%
+and the reason that both of these are so
+injurious is that they represent
+
+ align:start position:0%
+injurious is that they represent
+ 
+
+ align:start position:0%
+injurious is that they represent
+separate phases they represent separate
+
+ align:start position:0%
+separate phases they represent separate
+ 
+
+ align:start position:0%
+separate phases they represent separate
+phases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what do we have at the at the at the
+
+ align:start position:0%
+and what do we have at the at the at the
+ 
+
+ align:start position:0%
+and what do we have at the at the at the
+interface between one phase and the
+
+ align:start position:0%
+interface between one phase and the
+ 
+
+ align:start position:0%
+interface between one phase and the
+other phase well we have the same issue
+
+ align:start position:0%
+other phase well we have the same issue
+ 
+
+ align:start position:0%
+other phase well we have the same issue
+as an interface so not only do we we
+
+ align:start position:0%
+as an interface so not only do we we
+ 
+
+ align:start position:0%
+as an interface so not only do we we
+have the bad mechanical properties of
+
+ align:start position:0%
+have the bad mechanical properties of
+ 
+
+ align:start position:0%
+have the bad mechanical properties of
+the precipitate or the bad mechanical
+
+ align:start position:0%
+the precipitate or the bad mechanical
+ 
+
+ align:start position:0%
+the precipitate or the bad mechanical
+properties of the uh inclusion but we
+
+ align:start position:0%
+properties of the uh inclusion but we
+ 
+
+ align:start position:0%
+properties of the uh inclusion but we
+also have an interface so these things
+
+ align:start position:0%
+also have an interface so these things
+ 
+
+ align:start position:0%
+also have an interface so these things
+do double double injury and the other
+
+ align:start position:0%
+do double double injury and the other
+ 
+
+ align:start position:0%
+do double double injury and the other
+point is that most typically the
+
+ align:start position:0%
+point is that most typically the
+ 
+
+ align:start position:0%
+point is that most typically the
+exsolved material or the inclusion has a
+
+ align:start position:0%
+exsolved material or the inclusion has a
+ 
+
+ align:start position:0%
+exsolved material or the inclusion has a
+different density and so when it comes
+
+ align:start position:0%
+different density and so when it comes
+ 
+
+ align:start position:0%
+different density and so when it comes
+out of solution there's a volume change
+
+ align:start position:0%
+out of solution there's a volume change
+ 
+
+ align:start position:0%
+out of solution there's a volume change
+and that either leads to a compressive
+
+ align:start position:0%
+and that either leads to a compressive
+ 
+
+ align:start position:0%
+and that either leads to a compressive
+stress or a tensile stress so there's a
+
+ align:start position:0%
+stress or a tensile stress so there's a
+ 
+
+ align:start position:0%
+stress or a tensile stress so there's a
+volume difference
+
+ align:start position:0%
+volume difference
+ 
+
+ align:start position:0%
+volume difference
+volume difference with
+
+ align:start position:0%
+volume difference with
+ 
+
+ align:start position:0%
+volume difference with
+with the parent or the host Matrix with
+
+ align:start position:0%
+with the parent or the host Matrix with
+ 
+
+ align:start position:0%
+with the parent or the host Matrix with
+the parent or the host Matrix so this
+
+ align:start position:0%
+the parent or the host Matrix so this
+ 
+
+ align:start position:0%
+the parent or the host Matrix so this
+all leads to trouble now I showed you
+
+ align:start position:0%
+all leads to trouble now I showed you
+ 
+
+ align:start position:0%
+all leads to trouble now I showed you
+that carbon and iron is strengthening
+
+ align:start position:0%
+that carbon and iron is strengthening
+ 
+
+ align:start position:0%
+that carbon and iron is strengthening
+the uh iron to make steel because it's a
+
+ align:start position:0%
+the uh iron to make steel because it's a
+ 
+
+ align:start position:0%
+the uh iron to make steel because it's a
+little bit larger than its uh inter
+
+ align:start position:0%
+little bit larger than its uh inter
+ 
+
+ align:start position:0%
+little bit larger than its uh inter
+interstitial sight in iron and there are
+
+ align:start position:0%
+interstitial sight in iron and there are
+ 
+
+ align:start position:0%
+interstitial sight in iron and there are
+examples when you fly on an airplane
+
+ align:start position:0%
+examples when you fly on an airplane
+ 
+
+ align:start position:0%
+examples when you fly on an airplane
+you're flying on something that's
+
+ align:start position:0%
+you're flying on something that's
+ 
+
+ align:start position:0%
+you're flying on something that's
+largely made out of aluminum and one of
+
+ align:start position:0%
+largely made out of aluminum and one of
+ 
+
+ align:start position:0%
+largely made out of aluminum and one of
+the elements that goes in there is
+
+ align:start position:0%
+the elements that goes in there is
+ 
+
+ align:start position:0%
+the elements that goes in there is
+copper and it goes in at a level that
+
+ align:start position:0%
+copper and it goes in at a level that
+ 
+
+ align:start position:0%
+copper and it goes in at a level that
+causes precipitation of aluminum copper
+
+ align:start position:0%
+causes precipitation of aluminum copper
+ 
+
+ align:start position:0%
+causes precipitation of aluminum copper
+compounds called gin Preston zones
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these are precipitates that raise the
+
+ align:start position:0%
+so these are precipitates that raise the
+ 
+
+ align:start position:0%
+so these are precipitates that raise the
+strength of aluminum beyond what you'd
+
+ align:start position:0%
+strength of aluminum beyond what you'd
+ 
+
+ align:start position:0%
+strength of aluminum beyond what you'd
+have if you had essentially pure
+
+ align:start position:0%
+have if you had essentially pure
+ 
+
+ align:start position:0%
+have if you had essentially pure
+aluminum you do not want to be flying in
+
+ align:start position:0%
+aluminum you do not want to be flying in
+ 
+
+ align:start position:0%
+aluminum you do not want to be flying in
+an airplane made out of something that
+
+ align:start position:0%
+an airplane made out of something that
+ 
+
+ align:start position:0%
+an airplane made out of something that
+has this level of ductility I mean you
+
+ align:start position:0%
+has this level of ductility I mean you
+ 
+
+ align:start position:0%
+has this level of ductility I mean you
+know I love dislocations but you know
+
+ align:start position:0%
+know I love dislocations but you know
+ 
+
+ align:start position:0%
+know I love dislocations but you know
+there's a time and a place so we don't
+
+ align:start position:0%
+there's a time and a place so we don't
+ 
+
+ align:start position:0%
+there's a time and a place so we don't
+want that we don't want that so let me
+
+ align:start position:0%
+want that we don't want that so let me
+ 
+
+ align:start position:0%
+want that we don't want that so let me
+show you an example an extreme example
+
+ align:start position:0%
+show you an example an extreme example
+ 
+
+ align:start position:0%
+show you an example an extreme example
+of what happens with inclusions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes the Titanic
+
+ align:start position:0%
+yes the Titanic
+ 
+
+ align:start position:0%
+yes the Titanic
+of the Titanic sank because of these
+
+ align:start position:0%
+of the Titanic sank because of these
+ 
+
+ align:start position:0%
+of the Titanic sank because of these
+three-dimensional defects called
+
+ align:start position:0%
+three-dimensional defects called
+ 
+
+ align:start position:0%
+three-dimensional defects called
+inclusions and uh this is some data
+
+ align:start position:0%
+inclusions and uh this is some data
+ 
+
+ align:start position:0%
+inclusions and uh this is some data
+taken uh recently down at the National
+
+ align:start position:0%
+taken uh recently down at the National
+ 
+
+ align:start position:0%
+taken uh recently down at the National
+Institutes of standards and technology
+
+ align:start position:0%
+Institutes of standards and technology
+ 
+
+ align:start position:0%
+Institutes of standards and technology
+in Gaithersburg this is Tim who's a
+
+ align:start position:0%
+in Gaithersburg this is Tim who's a
+ 
+
+ align:start position:0%
+in Gaithersburg this is Tim who's a
+metallurgist who did a lot of the the
+
+ align:start position:0%
+metallurgist who did a lot of the the
+ 
+
+ align:start position:0%
+metallurgist who did a lot of the the
+work this is a rivet and you can see the
+
+ align:start position:0%
+work this is a rivet and you can see the
+ 
+
+ align:start position:0%
+work this is a rivet and you can see the
+actual size of it in his hand these are
+
+ align:start position:0%
+actual size of it in his hand these are
+ 
+
+ align:start position:0%
+actual size of it in his hand these are
+very very large rivets these are the
+
+ align:start position:0%
+very very large rivets these are the
+ 
+
+ align:start position:0%
+very very large rivets these are the
+rivets that were in the hull so what
+
+ align:start position:0%
+rivets that were in the hull so what
+ 
+
+ align:start position:0%
+rivets that were in the hull so what
+what has happened is they've cut the
+
+ align:start position:0%
+what has happened is they've cut the
+ 
+
+ align:start position:0%
+what has happened is they've cut the
+rivets and Polished them and put them in
+
+ align:start position:0%
+rivets and Polished them and put them in
+ 
+
+ align:start position:0%
+rivets and Polished them and put them in
+an optical microscope and here's what
+
+ align:start position:0%
+an optical microscope and here's what
+ 
+
+ align:start position:0%
+an optical microscope and here's what
+you see oh shut up uh so uh if you look
+
+ align:start position:0%
+you see oh shut up uh so uh if you look
+ 
+
+ align:start position:0%
+you see oh shut up uh so uh if you look
+inside you see this dark zones these
+
+ align:start position:0%
+inside you see this dark zones these
+ 
+
+ align:start position:0%
+inside you see this dark zones these
+dark zones are inclusions they're
+
+ align:start position:0%
+dark zones are inclusions they're
+ 
+
+ align:start position:0%
+dark zones are inclusions they're
+inclusions of slag and how did they get
+
+ align:start position:0%
+inclusions of slag and how did they get
+ 
+
+ align:start position:0%
+inclusions of slag and how did they get
+there well in those days we're talking
+
+ align:start position:0%
+there well in those days we're talking
+ 
+
+ align:start position:0%
+there well in those days we're talking
+uh around 1910 the way steel was made
+
+ align:start position:0%
+uh around 1910 the way steel was made
+ 
+
+ align:start position:0%
+uh around 1910 the way steel was made
+was in a uh a unit called The Open
+
+ align:start position:0%
+was in a uh a unit called The Open
+ 
+
+ align:start position:0%
+was in a uh a unit called The Open
+Hearth furnace
+
+ align:start position:0%
+Hearth furnace
+ 
+
+ align:start position:0%
+Hearth furnace
+The Open Hearth furnace and The Open
+
+ align:start position:0%
+The Open Hearth furnace and The Open
+ 
+
+ align:start position:0%
+The Open Hearth furnace and The Open
+Hearth furnace was the invention of
+
+ align:start position:0%
+Hearth furnace was the invention of
+ 
+
+ align:start position:0%
+Hearth furnace was the invention of
+Seamans one of his many inventions and
+
+ align:start position:0%
+Seamans one of his many inventions and
+ 
+
+ align:start position:0%
+Seamans one of his many inventions and
+the way the Open Hearth furnace works
+
+ align:start position:0%
+the way the Open Hearth furnace works
+ 
+
+ align:start position:0%
+the way the Open Hearth furnace works
+this is not to scale what I'm going to
+
+ align:start position:0%
+this is not to scale what I'm going to
+ 
+
+ align:start position:0%
+this is not to scale what I'm going to
+show you is a vessel that would have a
+
+ align:start position:0%
+show you is a vessel that would have a
+ 
+
+ align:start position:0%
+show you is a vessel that would have a
+floor about the size of the entire front
+
+ align:start position:0%
+floor about the size of the entire front
+ 
+
+ align:start position:0%
+floor about the size of the entire front
+of uh 10 250 actually many times larger
+
+ align:start position:0%
+of uh 10 250 actually many times larger
+ 
+
+ align:start position:0%
+of uh 10 250 actually many times larger
+but this gives you a sense of the scale
+
+ align:start position:0%
+but this gives you a sense of the scale
+ 
+
+ align:start position:0%
+but this gives you a sense of the scale
+and you've got two layers here two
+
+ align:start position:0%
+and you've got two layers here two
+ 
+
+ align:start position:0%
+and you've got two layers here two
+layers two liquids that are insoluble in
+
+ align:start position:0%
+layers two liquids that are insoluble in
+ 
+
+ align:start position:0%
+layers two liquids that are insoluble in
+one another as uh salad oil and water
+
+ align:start position:0%
+one another as uh salad oil and water
+ 
+
+ align:start position:0%
+one another as uh salad oil and water
+the lower layer is iron
+
+ align:start position:0%
+the lower layer is iron
+ 
+
+ align:start position:0%
+the lower layer is iron
+it's a metallic layer and the above
+
+ align:start position:0%
+it's a metallic layer and the above
+ 
+
+ align:start position:0%
+it's a metallic layer and the above
+layer is slag and the slag basically
+
+ align:start position:0%
+layer is slag and the slag basically
+ 
+
+ align:start position:0%
+layer is slag and the slag basically
+consists of things like silica
+
+ align:start position:0%
+consists of things like silica
+ 
+
+ align:start position:0%
+consists of things like silica
+Cal
+
+ align:start position:0%
+Cal
+ 
+
+ align:start position:0%
+Cal
+alumina it's all oxides so it's sort of
+
+ align:start position:0%
+alumina it's all oxides so it's sort of
+ 
+
+ align:start position:0%
+alumina it's all oxides so it's sort of
+the equivalent of what you know to be
+
+ align:start position:0%
+the equivalent of what you know to be
+ 
+
+ align:start position:0%
+the equivalent of what you know to be
+window glass or bottle glass and it lies
+
+ align:start position:0%
+window glass or bottle glass and it lies
+ 
+
+ align:start position:0%
+window glass or bottle glass and it lies
+in a giant pool on top of a pool of
+
+ align:start position:0%
+in a giant pool on top of a pool of
+ 
+
+ align:start position:0%
+in a giant pool on top of a pool of
+metal and what's going on in here is
+
+ align:start position:0%
+metal and what's going on in here is
+ 
+
+ align:start position:0%
+metal and what's going on in here is
+that the iron has come out of the blast
+
+ align:start position:0%
+that the iron has come out of the blast
+ 
+
+ align:start position:0%
+that the iron has come out of the blast
+furnace it contains far too much carbon
+
+ align:start position:0%
+furnace it contains far too much carbon
+ 
+
+ align:start position:0%
+furnace it contains far too much carbon
+and it contains impurities things like
+
+ align:start position:0%
+and it contains impurities things like
+ 
+
+ align:start position:0%
+and it contains impurities things like
+Silicon and manganese at too high a
+
+ align:start position:0%
+Silicon and manganese at too high a
+ 
+
+ align:start position:0%
+Silicon and manganese at too high a
+level and the process was called open
+
+ align:start position:0%
+level and the process was called open
+ 
+
+ align:start position:0%
+level and the process was called open
+heart steel making you had a vessel
+
+ align:start position:0%
+heart steel making you had a vessel
+ 
+
+ align:start position:0%
+heart steel making you had a vessel
+about the size of the front of this room
+
+ align:start position:0%
+about the size of the front of this room
+ 
+
+ align:start position:0%
+about the size of the front of this room
+and to keep it molten at 1300° C you had
+
+ align:start position:0%
+and to keep it molten at 1300° C you had
+ 
+
+ align:start position:0%
+and to keep it molten at 1300° C you had
+two giant burners at either end and
+
+ align:start position:0%
+two giant burners at either end and
+ 
+
+ align:start position:0%
+two giant burners at either end and
+these things would be like dragons
+
+ align:start position:0%
+these things would be like dragons
+ 
+
+ align:start position:0%
+these things would be like dragons
+shooting flames across and keeping
+
+ align:start position:0%
+shooting flames across and keeping
+ 
+
+ align:start position:0%
+shooting flames across and keeping
+everything molten it was all contained
+
+ align:start position:0%
+everything molten it was all contained
+ 
+
+ align:start position:0%
+everything molten it was all contained
+in brick work and the idea here is that
+
+ align:start position:0%
+in brick work and the idea here is that
+ 
+
+ align:start position:0%
+in brick work and the idea here is that
+over time the impurities will rise out
+
+ align:start position:0%
+over time the impurities will rise out
+ 
+
+ align:start position:0%
+over time the impurities will rise out
+of the metal and move into the slag
+
+ align:start position:0%
+of the metal and move into the slag
+ 
+
+ align:start position:0%
+of the metal and move into the slag
+layer so for example carbon in the iron
+
+ align:start position:0%
+layer so for example carbon in the iron
+ 
+
+ align:start position:0%
+layer so for example carbon in the iron
+will react with some oxygen in the iron
+
+ align:start position:0%
+will react with some oxygen in the iron
+ 
+
+ align:start position:0%
+will react with some oxygen in the iron
+to form carbon monoxide and bubble away
+
+ align:start position:0%
+to form carbon monoxide and bubble away
+ 
+
+ align:start position:0%
+to form carbon monoxide and bubble away
+but more importantly things like
+
+ align:start position:0%
+but more importantly things like
+ 
+
+ align:start position:0%
+but more importantly things like
+manganese in the iron will react with
+
+ align:start position:0%
+manganese in the iron will react with
+ 
+
+ align:start position:0%
+manganese in the iron will react with
+oxygen in the iron iron to form
+
+ align:start position:0%
+oxygen in the iron iron to form
+ 
+
+ align:start position:0%
+oxygen in the iron iron to form
+manganese oxide which is not soluble in
+
+ align:start position:0%
+manganese oxide which is not soluble in
+ 
+
+ align:start position:0%
+manganese oxide which is not soluble in
+the iron and it goes into the slag
+
+ align:start position:0%
+the iron and it goes into the slag
+ 
+
+ align:start position:0%
+the iron and it goes into the slag
+this process in those days took about 12
+
+ align:start position:0%
+this process in those days took about 12
+ 
+
+ align:start position:0%
+this process in those days took about 12
+hours for 12 hours you kept the steel
+
+ align:start position:0%
+hours for 12 hours you kept the steel
+ 
+
+ align:start position:0%
+hours for 12 hours you kept the steel
+sitting at about 1300° SE and you want
+
+ align:start position:0%
+sitting at about 1300° SE and you want
+ 
+
+ align:start position:0%
+sitting at about 1300° SE and you want
+good mixing so there's a fair bit of
+
+ align:start position:0%
+good mixing so there's a fair bit of
+ 
+
+ align:start position:0%
+good mixing so there's a fair bit of
+turbulence here and towards the end you
+
+ align:start position:0%
+turbulence here and towards the end you
+ 
+
+ align:start position:0%
+turbulence here and towards the end you
+stop the turbulence and you let things
+
+ align:start position:0%
+stop the turbulence and you let things
+ 
+
+ align:start position:0%
+stop the turbulence and you let things
+separate just as after you've shaken
+
+ align:start position:0%
+separate just as after you've shaken
+ 
+
+ align:start position:0%
+separate just as after you've shaken
+salad oil uh and uh uh the salad
+
+ align:start position:0%
+salad oil uh and uh uh the salad
+ 
+
+ align:start position:0%
+salad oil uh and uh uh the salad
+dressing you've got oil and and an
+
+ align:start position:0%
+dressing you've got oil and and an
+ 
+
+ align:start position:0%
+dressing you've got oil and and an
+aquous phase vinegar and then you watch
+
+ align:start position:0%
+aquous phase vinegar and then you watch
+ 
+
+ align:start position:0%
+aquous phase vinegar and then you watch
+and slowly the bubbles start to rise and
+
+ align:start position:0%
+and slowly the bubbles start to rise and
+ 
+
+ align:start position:0%
+and slowly the bubbles start to rise and
+so on the globules of of oil well
+
+ align:start position:0%
+so on the globules of of oil well
+ 
+
+ align:start position:0%
+so on the globules of of oil well
+clearly what happened on the day they
+
+ align:start position:0%
+clearly what happened on the day they
+ 
+
+ align:start position:0%
+clearly what happened on the day they
+made the heat for this vessel rivets
+
+ align:start position:0%
+made the heat for this vessel rivets
+ 
+
+ align:start position:0%
+made the heat for this vessel rivets
+somebody got greedy and they tapped the
+
+ align:start position:0%
+somebody got greedy and they tapped the
+ 
+
+ align:start position:0%
+somebody got greedy and they tapped the
+metal too soon and with a result there
+
+ align:start position:0%
+metal too soon and with a result there
+ 
+
+ align:start position:0%
+metal too soon and with a result there
+was still a lot of this glassy slag like
+
+ align:start position:0%
+was still a lot of this glassy slag like
+ 
+
+ align:start position:0%
+was still a lot of this glassy slag like
+material in the metal then the ingots
+
+ align:start position:0%
+material in the metal then the ingots
+ 
+
+ align:start position:0%
+material in the metal then the ingots
+were poured and then from the ingots
+
+ align:start position:0%
+were poured and then from the ingots
+ 
+
+ align:start position:0%
+were poured and then from the ingots
+they made the rivets well when they make
+
+ align:start position:0%
+they made the rivets well when they make
+ 
+
+ align:start position:0%
+they made the rivets well when they make
+rivets uh they draw them and so instead
+
+ align:start position:0%
+rivets uh they draw them and so instead
+ 
+
+ align:start position:0%
+rivets uh they draw them and so instead
+of having little globules of glass which
+
+ align:start position:0%
+of having little globules of glass which
+ 
+
+ align:start position:0%
+of having little globules of glass which
+would have been bad but not super bad by
+
+ align:start position:0%
+would have been bad but not super bad by
+ 
+
+ align:start position:0%
+would have been bad but not super bad by
+drawing them can you see from the center
+
+ align:start position:0%
+drawing them can you see from the center
+ 
+
+ align:start position:0%
+drawing them can you see from the center
+of the rivet these globules have turned
+
+ align:start position:0%
+of the rivet these globules have turned
+ 
+
+ align:start position:0%
+of the rivet these globules have turned
+into long stringers so now instead of
+
+ align:start position:0%
+into long stringers so now instead of
+ 
+
+ align:start position:0%
+into long stringers so now instead of
+having the strength of steel ac across
+
+ align:start position:0%
+having the strength of steel ac across
+ 
+
+ align:start position:0%
+having the strength of steel ac across
+the crosssection it's as though you've
+
+ align:start position:0%
+the crosssection it's as though you've
+ 
+
+ align:start position:0%
+the crosssection it's as though you've
+got these perforations if you cut the
+
+ align:start position:0%
+got these perforations if you cut the
+ 
+
+ align:start position:0%
+got these perforations if you cut the
+cross-section the other way and look
+
+ align:start position:0%
+cross-section the other way and look
+ 
+
+ align:start position:0%
+cross-section the other way and look
+down it would look like uh uh what's
+
+ align:start position:0%
+down it would look like uh uh what's
+ 
+
+ align:start position:0%
+down it would look like uh uh what's
+that um Mortadella that uh lunch and
+
+ align:start position:0%
+that um Mortadella that uh lunch and
+ 
+
+ align:start position:0%
+that um Mortadella that uh lunch and
+meat you know there's meat in the
+
+ align:start position:0%
+meat you know there's meat in the
+ 
+
+ align:start position:0%
+meat you know there's meat in the
+globules of fat that's what this thing
+
+ align:start position:0%
+globules of fat that's what this thing
+ 
+
+ align:start position:0%
+globules of fat that's what this thing
+would look like okay and then down here
+
+ align:start position:0%
+would look like okay and then down here
+ 
+
+ align:start position:0%
+would look like okay and then down here
+at the bottom you see there's stringers
+
+ align:start position:0%
+at the bottom you see there's stringers
+ 
+
+ align:start position:0%
+at the bottom you see there's stringers
+everywhere so now this thing doesn't
+
+ align:start position:0%
+everywhere so now this thing doesn't
+ 
+
+ align:start position:0%
+everywhere so now this thing doesn't
+have the strength anymore so what
+
+ align:start position:0%
+have the strength anymore so what
+ 
+
+ align:start position:0%
+have the strength anymore so what
+happened was that when they hit the
+
+ align:start position:0%
+happened was that when they hit the
+ 
+
+ align:start position:0%
+happened was that when they hit the
+iceberg what should have happened is
+
+ align:start position:0%
+iceberg what should have happened is
+ 
+
+ align:start position:0%
+iceberg what should have happened is
+that there would have been a damage in
+
+ align:start position:0%
+that there would have been a damage in
+ 
+
+ align:start position:0%
+that there would have been a damage in
+the hall in that local region it would
+
+ align:start position:0%
+the hall in that local region it would
+ 
+
+ align:start position:0%
+the hall in that local region it would
+have been taking up water and there
+
+ align:start position:0%
+have been taking up water and there
+ 
+
+ align:start position:0%
+have been taking up water and there
+would have been time for five or six
+
+ align:start position:0%
+would have been time for five or six
+ 
+
+ align:start position:0%
+would have been time for five or six
+hours before uh the rescue vessels
+
+ align:start position:0%
+hours before uh the rescue vessels
+ 
+
+ align:start position:0%
+hours before uh the rescue vessels
+arrived instead what happened these
+
+ align:start position:0%
+arrived instead what happened these
+ 
+
+ align:start position:0%
+arrived instead what happened these
+rivets were so weakened by the presence
+
+ align:start position:0%
+rivets were so weakened by the presence
+ 
+
+ align:start position:0%
+rivets were so weakened by the presence
+of the inclusions that they broke but as
+
+ align:start position:0%
+of the inclusions that they broke but as
+ 
+
+ align:start position:0%
+of the inclusions that they broke but as
+they broke they just it was just like a
+
+ align:start position:0%
+they broke they just it was just like a
+ 
+
+ align:start position:0%
+they broke they just it was just like a
+a zipper unzipping just went down the
+
+ align:start position:0%
+a zipper unzipping just went down the
+ 
+
+ align:start position:0%
+a zipper unzipping just went down the
+entire Hull opened up water rushed in
+
+ align:start position:0%
+entire Hull opened up water rushed in
+ 
+
+ align:start position:0%
+entire Hull opened up water rushed in
+and the vessel didn't last very long um
+
+ align:start position:0%
+and the vessel didn't last very long um
+ 
+
+ align:start position:0%
+and the vessel didn't last very long um
+it stayed afloat Too Short a time and of
+
+ align:start position:0%
+it stayed afloat Too Short a time and of
+ 
+
+ align:start position:0%
+it stayed afloat Too Short a time and of
+course there weren't enough uh uh life
+
+ align:start position:0%
+course there weren't enough uh uh life
+ 
+
+ align:start position:0%
+course there weren't enough uh uh life
+life vessels on it so on you know the
+
+ align:start position:0%
+life vessels on it so on you know the
+ 
+
+ align:start position:0%
+life vessels on it so on you know the
+rest of the story but anyways it started
+
+ align:start position:0%
+rest of the story but anyways it started
+ 
+
+ align:start position:0%
+rest of the story but anyways it started
+with a bad metallurgical heat uh which
+
+ align:start position:0%
+with a bad metallurgical heat uh which
+ 
+
+ align:start position:0%
+with a bad metallurgical heat uh which
+gave us the trapped foreign matter which
+
+ align:start position:0%
+gave us the trapped foreign matter which
+ 
+
+ align:start position:0%
+gave us the trapped foreign matter which
+is insoluble and so on so before leaving
+
+ align:start position:0%
+is insoluble and so on so before leaving
+ 
+
+ align:start position:0%
+is insoluble and so on so before leaving
+this is this is pretty much the catalog
+
+ align:start position:0%
+this is this is pretty much the catalog
+ 
+
+ align:start position:0%
+this is this is pretty much the catalog
+of defects I want to return to something
+
+ align:start position:0%
+of defects I want to return to something
+ 
+
+ align:start position:0%
+of defects I want to return to something
+I hinted at last day and I want to be
+
+ align:start position:0%
+I hinted at last day and I want to be
+ 
+
+ align:start position:0%
+I hinted at last day and I want to be
+clear with you about the chemical
+
+ align:start position:0%
+clear with you about the chemical
+ 
+
+ align:start position:0%
+clear with you about the chemical
+origins of mechanical Behavior
+
+ align:start position:0%
+origins of mechanical Behavior
+ 
+
+ align:start position:0%
+origins of mechanical Behavior
+chemical origins of mechanical behavior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+part of 3091 that sets it apart from a
+
+ align:start position:0%
+part of 3091 that sets it apart from a
+ 
+
+ align:start position:0%
+part of 3091 that sets it apart from a
+classical chemistry subject because what
+
+ align:start position:0%
+classical chemistry subject because what
+ 
+
+ align:start position:0%
+classical chemistry subject because what
+we've been looking at is how electronic
+
+ align:start position:0%
+we've been looking at is how electronic
+ 
+
+ align:start position:0%
+we've been looking at is how electronic
+structure electronic structure in forms
+
+ align:start position:0%
+structure electronic structure in forms
+ 
+
+ align:start position:0%
+structure electronic structure in forms
+chemical bonding well that's no surprise
+
+ align:start position:0%
+chemical bonding well that's no surprise
+ 
+
+ align:start position:0%
+chemical bonding well that's no surprise
+you would expect to get that in a
+
+ align:start position:0%
+you would expect to get that in a
+ 
+
+ align:start position:0%
+you would expect to get that in a
+chemistry class but then chemical
+
+ align:start position:0%
+chemistry class but then chemical
+ 
+
+ align:start position:0%
+chemistry class but then chemical
+bonding informs Atomic Arrangement
+
+ align:start position:0%
+bonding informs Atomic Arrangement
+ 
+
+ align:start position:0%
+bonding informs Atomic Arrangement
+informs Atomic Arrangement and that's
+
+ align:start position:0%
+informs Atomic Arrangement and that's
+ 
+
+ align:start position:0%
+informs Atomic Arrangement and that's
+where the rubber meets the road when it
+
+ align:start position:0%
+where the rubber meets the road when it
+ 
+
+ align:start position:0%
+where the rubber meets the road when it
+comes to Mechanical Behavior you have to
+
+ align:start position:0%
+comes to Mechanical Behavior you have to
+ 
+
+ align:start position:0%
+comes to Mechanical Behavior you have to
+know where the atoms are and so I want
+
+ align:start position:0%
+know where the atoms are and so I want
+ 
+
+ align:start position:0%
+know where the atoms are and so I want
+to talk about deformation
+
+ align:start position:0%
+to talk about deformation
+ 
+
+ align:start position:0%
+to talk about deformation
+that's what makes
+
+ align:start position:0%
+that's what makes
+ 
+
+ align:start position:0%
+that's what makes
+that's what makes Metals in particular
+
+ align:start position:0%
+that's what makes Metals in particular
+ 
+
+ align:start position:0%
+that's what makes Metals in particular
+so useful that's why they've been
+
+ align:start position:0%
+so useful that's why they've been
+ 
+
+ align:start position:0%
+so useful that's why they've been
+historically utilized by humans going
+
+ align:start position:0%
+historically utilized by humans going
+ 
+
+ align:start position:0%
+historically utilized by humans going
+back to prehistory because they have the
+
+ align:start position:0%
+back to prehistory because they have the
+ 
+
+ align:start position:0%
+back to prehistory because they have the
+special property of ductility we can
+
+ align:start position:0%
+special property of ductility we can
+ 
+
+ align:start position:0%
+special property of ductility we can
+take them in the solid form and have
+
+ align:start position:0%
+take them in the solid form and have
+ 
+
+ align:start position:0%
+take them in the solid form and have
+them change shape and the reason they
+
+ align:start position:0%
+them change shape and the reason they
+ 
+
+ align:start position:0%
+them change shape and the reason they
+can change shape has to do with first of
+
+ align:start position:0%
+can change shape has to do with first of
+ 
+
+ align:start position:0%
+can change shape has to do with first of
+all their electronic structure which
+
+ align:start position:0%
+all their electronic structure which
+ 
+
+ align:start position:0%
+all their electronic structure which
+leads to metallic bonding which gives us
+
+ align:start position:0%
+leads to metallic bonding which gives us
+ 
+
+ align:start position:0%
+leads to metallic bonding which gives us
+these cubic crystallin arrangements and
+
+ align:start position:0%
+these cubic crystallin arrangements and
+ 
+
+ align:start position:0%
+these cubic crystallin arrangements and
+then we introduce dislocations and
+
+ align:start position:0%
+then we introduce dislocations and
+ 
+
+ align:start position:0%
+then we introduce dislocations and
+things slip so I want to talk about two
+
+ align:start position:0%
+things slip so I want to talk about two
+ 
+
+ align:start position:0%
+things slip so I want to talk about two
+types of deformation first of all I want
+
+ align:start position:0%
+types of deformation first of all I want
+ 
+
+ align:start position:0%
+types of deformation first of all I want
+to look at elastic deformation
+
+ align:start position:0%
+to look at elastic deformation
+ 
+
+ align:start position:0%
+to look at elastic deformation
+elastic deformation and this is
+
+ align:start position:0%
+elastic deformation and this is
+ 
+
+ align:start position:0%
+elastic deformation and this is
+deformation that is reversible it's
+
+ align:start position:0%
+deformation that is reversible it's
+ 
+
+ align:start position:0%
+deformation that is reversible it's
+characterized by its reversibility
+
+ align:start position:0%
+characterized by its reversibility
+ 
+
+ align:start position:0%
+characterized by its reversibility
+and the simplest way to define it is
+
+ align:start position:0%
+and the simplest way to define it is
+ 
+
+ align:start position:0%
+and the simplest way to define it is
+strain that is strain only strain only
+
+ align:start position:0%
+strain that is strain only strain only
+ 
+
+ align:start position:0%
+strain that is strain only strain only
+under stress strain only under stress
+
+ align:start position:0%
+under stress strain only under stress
+ 
+
+ align:start position:0%
+under stress strain only under stress
+release the stress the material relaxes
+
+ align:start position:0%
+release the stress the material relaxes
+ 
+
+ align:start position:0%
+release the stress the material relaxes
+back to its initial uh state only under
+
+ align:start position:0%
+back to its initial uh state only under
+ 
+
+ align:start position:0%
+back to its initial uh state only under
+stress or if you want you could say
+
+ align:start position:0%
+stress or if you want you could say
+ 
+
+ align:start position:0%
+stress or if you want you could say
+displacement only under the action of
+
+ align:start position:0%
+displacement only under the action of
+ 
+
+ align:start position:0%
+displacement only under the action of
+applied force and Hook's law applies for
+
+ align:start position:0%
+applied force and Hook's law applies for
+ 
+
+ align:start position:0%
+applied force and Hook's law applies for
+this hook Hook's law applies
+
+ align:start position:0%
+this hook Hook's law applies
+ 
+
+ align:start position:0%
+this hook Hook's law applies
+and I want to show you the chemical
+
+ align:start position:0%
+and I want to show you the chemical
+ 
+
+ align:start position:0%
+and I want to show you the chemical
+origin of Hook's law chemical origin we
+
+ align:start position:0%
+origin of Hook's law chemical origin we
+ 
+
+ align:start position:0%
+origin of Hook's law chemical origin we
+saw when we looked at the force curves
+
+ align:start position:0%
+saw when we looked at the force curves
+ 
+
+ align:start position:0%
+saw when we looked at the force curves
+that defined the equilibrium separation
+
+ align:start position:0%
+that defined the equilibrium separation
+ 
+
+ align:start position:0%
+that defined the equilibrium separation
+of two atoms regardless of the type of
+
+ align:start position:0%
+of two atoms regardless of the type of
+ 
+
+ align:start position:0%
+of two atoms regardless of the type of
+bonding we could plot energy as a
+
+ align:start position:0%
+bonding we could plot energy as a
+ 
+
+ align:start position:0%
+bonding we could plot energy as a
+function of interatomic separation and
+
+ align:start position:0%
+function of interatomic separation and
+ 
+
+ align:start position:0%
+function of interatomic separation and
+we find that we have some kind of a
+
+ align:start position:0%
+we find that we have some kind of a
+ 
+
+ align:start position:0%
+we find that we have some kind of a
+repulsive energy up here and we have
+
+ align:start position:0%
+repulsive energy up here and we have
+ 
+
+ align:start position:0%
+repulsive energy up here and we have
+some kind of an attractive energy down
+
+ align:start position:0%
+some kind of an attractive energy down
+ 
+
+ align:start position:0%
+some kind of an attractive energy down
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+and we went through the strict
+
+ align:start position:0%
+and we went through the strict
+ 
+
+ align:start position:0%
+and we went through the strict
+derivation for Ionic crystals but the
+
+ align:start position:0%
+derivation for Ionic crystals but the
+ 
+
+ align:start position:0%
+derivation for Ionic crystals but the
+analogous derivations uh exist for other
+
+ align:start position:0%
+analogous derivations uh exist for other
+ 
+
+ align:start position:0%
+analogous derivations uh exist for other
+types of crystals and if we go through
+
+ align:start position:0%
+types of crystals and if we go through
+ 
+
+ align:start position:0%
+types of crystals and if we go through
+we find that there's a a minimum energy
+
+ align:start position:0%
+we find that there's a a minimum energy
+ 
+
+ align:start position:0%
+we find that there's a a minimum energy
+which defines this R KN which is the
+
+ align:start position:0%
+which defines this R KN which is the
+ 
+
+ align:start position:0%
+which defines this R KN which is the
+equilibrium interatomic separation and
+
+ align:start position:0%
+equilibrium interatomic separation and
+ 
+
+ align:start position:0%
+equilibrium interatomic separation and
+this is e minimum e minimum well I can
+
+ align:start position:0%
+this is e minimum e minimum well I can
+ 
+
+ align:start position:0%
+this is e minimum e minimum well I can
+keep going what I can do is look at the
+
+ align:start position:0%
+keep going what I can do is look at the
+ 
+
+ align:start position:0%
+keep going what I can do is look at the
+derivative of that and show you where
+
+ align:start position:0%
+derivative of that and show you where
+ 
+
+ align:start position:0%
+derivative of that and show you where
+you get hooks law if I look at the
+
+ align:start position:0%
+you get hooks law if I look at the
+ 
+
+ align:start position:0%
+you get hooks law if I look at the
+derivative of this then that will give
+
+ align:start position:0%
+derivative of this then that will give
+ 
+
+ align:start position:0%
+derivative of this then that will give
+me Force because I know force is
+
+ align:start position:0%
+me Force because I know force is
+ 
+
+ align:start position:0%
+me Force because I know force is
+if I plot Force which is equal to D by
+
+ align:start position:0%
+if I plot Force which is equal to D by
+ 
+
+ align:start position:0%
+if I plot Force which is equal to D by
+Dr right the the derivative of the
+
+ align:start position:0%
+Dr right the the derivative of the
+ 
+
+ align:start position:0%
+Dr right the the derivative of the
+energy with respect to uh displacement
+
+ align:start position:0%
+energy with respect to uh displacement
+ 
+
+ align:start position:0%
+energy with respect to uh displacement
+and right here about R KN you can see
+
+ align:start position:0%
+and right here about R KN you can see
+ 
+
+ align:start position:0%
+and right here about R KN you can see
+that the curve is positive slope to the
+
+ align:start position:0%
+that the curve is positive slope to the
+ 
+
+ align:start position:0%
+that the curve is positive slope to the
+right negative slope to the left and
+
+ align:start position:0%
+right negative slope to the left and
+ 
+
+ align:start position:0%
+right negative slope to the left and
+it's flat at the origin so I'm
+
+ align:start position:0%
+it's flat at the origin so I'm
+ 
+
+ align:start position:0%
+it's flat at the origin so I'm
+exaggerating this so over a wider range
+
+ align:start position:0%
+exaggerating this so over a wider range
+ 
+
+ align:start position:0%
+exaggerating this so over a wider range
+but it's fair to say that about
+
+ align:start position:0%
+but it's fair to say that about
+ 
+
+ align:start position:0%
+but it's fair to say that about
+about r equal r
+
+ align:start position:0%
+about r equal r
+ 
+
+ align:start position:0%
+about r equal r
+f is linear f is linear in R
+
+ align:start position:0%
+f is linear f is linear in R
+ 
+
+ align:start position:0%
+f is linear f is linear in R
+well doesn't that remind you of this
+
+ align:start position:0%
+well doesn't that remind you of this
+ 
+
+ align:start position:0%
+well doesn't that remind you of this
+from physics where you have a spring and
+
+ align:start position:0%
+from physics where you have a spring and
+ 
+
+ align:start position:0%
+from physics where you have a spring and
+you hang a mass on a spring and that
+
+ align:start position:0%
+you hang a mass on a spring and that
+ 
+
+ align:start position:0%
+you hang a mass on a spring and that
+Mass on a spring and a gravitational
+
+ align:start position:0%
+Mass on a spring and a gravitational
+ 
+
+ align:start position:0%
+Mass on a spring and a gravitational
+field gives rise to a force and you can
+
+ align:start position:0%
+field gives rise to a force and you can
+ 
+
+ align:start position:0%
+field gives rise to a force and you can
+look at the displacement you can look at
+
+ align:start position:0%
+look at the displacement you can look at
+ 
+
+ align:start position:0%
+look at the displacement you can look at
+the displac m versus an initial
+
+ align:start position:0%
+the displac m versus an initial
+ 
+
+ align:start position:0%
+the displac m versus an initial
+displacement so here's an X here's an X
+
+ align:start position:0%
+displacement so here's an X here's an X
+ 
+
+ align:start position:0%
+displacement so here's an X here's an X
+notot with no mass and I think you've
+
+ align:start position:0%
+notot with no mass and I think you've
+ 
+
+ align:start position:0%
+notot with no mass and I think you've
+seen this you've seen that some constant
+
+ align:start position:0%
+seen this you've seen that some constant
+ 
+
+ align:start position:0%
+seen this you've seen that some constant
+time x - x knot is force that's Hook's
+
+ align:start position:0%
+time x - x knot is force that's Hook's
+ 
+
+ align:start position:0%
+time x - x knot is force that's Hook's
+law that there's a linear relationship
+
+ align:start position:0%
+law that there's a linear relationship
+ 
+
+ align:start position:0%
+law that there's a linear relationship
+between applied force and the
+
+ align:start position:0%
+between applied force and the
+ 
+
+ align:start position:0%
+between applied force and the
+displacement of the string and that's
+
+ align:start position:0%
+displacement of the string and that's
+ 
+
+ align:start position:0%
+displacement of the string and that's
+the same thing's happening with atoms if
+
+ align:start position:0%
+the same thing's happening with atoms if
+ 
+
+ align:start position:0%
+the same thing's happening with atoms if
+for a tiny Force I get a tiny
+
+ align:start position:0%
+for a tiny Force I get a tiny
+ 
+
+ align:start position:0%
+for a tiny Force I get a tiny
+displacement for a larger Force I get a
+
+ align:start position:0%
+displacement for a larger Force I get a
+ 
+
+ align:start position:0%
+displacement for a larger Force I get a
+larger displacement and if I relax the
+
+ align:start position:0%
+larger displacement and if I relax the
+ 
+
+ align:start position:0%
+larger displacement and if I relax the
+force the atom Springs back to its rest
+
+ align:start position:0%
+force the atom Springs back to its rest
+ 
+
+ align:start position:0%
+force the atom Springs back to its rest
+position so what you're seeing on a
+
+ align:start position:0%
+position so what you're seeing on a
+ 
+
+ align:start position:0%
+position so what you're seeing on a
+macro scale here is what's being played
+
+ align:start position:0%
+macro scale here is what's being played
+ 
+
+ align:start position:0%
+macro scale here is what's being played
+out at the Nano scale here hooks law is
+
+ align:start position:0%
+out at the Nano scale here hooks law is
+ 
+
+ align:start position:0%
+out at the Nano scale here hooks law is
+related directly to the linearity in the
+
+ align:start position:0%
+related directly to the linearity in the
+ 
+
+ align:start position:0%
+related directly to the linearity in the
+force curve as a function of position
+
+ align:start position:0%
+force curve as a function of position
+ 
+
+ align:start position:0%
+force curve as a function of position
+and by the way hook hook uh enunciated
+
+ align:start position:0%
+and by the way hook hook uh enunciated
+ 
+
+ align:start position:0%
+and by the way hook hook uh enunciated
+here's how he published hooks law in
+
+ align:start position:0%
+here's how he published hooks law in
+ 
+
+ align:start position:0%
+here's how he published hooks law in
+1676 it was first published as follows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's Hook's law as he first published
+
+ align:start position:0%
+that's Hook's law as he first published
+ 
+
+ align:start position:0%
+that's Hook's law as he first published
+it this this is an anagram and it's in
+
+ align:start position:0%
+it this this is an anagram and it's in
+ 
+
+ align:start position:0%
+it this this is an anagram and it's in
+Latin
+
+ align:start position:0%
+Latin
+ 
+
+ align:start position:0%
+Latin
+Hook was a wise guy to be sure he was a
+
+ align:start position:0%
+Hook was a wise guy to be sure he was a
+ 
+
+ align:start position:0%
+Hook was a wise guy to be sure he was a
+contemporary of Newton they hated each
+
+ align:start position:0%
+contemporary of Newton they hated each
+ 
+
+ align:start position:0%
+contemporary of Newton they hated each
+other's guts they fought bitterly um so
+
+ align:start position:0%
+other's guts they fought bitterly um so
+ 
+
+ align:start position:0%
+other's guts they fought bitterly um so
+three years later he published the
+
+ align:start position:0%
+three years later he published the
+ 
+
+ align:start position:0%
+three years later he published the
+solution to this ensio
+
+ align:start position:0%
+solution to this ensio
+ 
+
+ align:start position:0%
+solution to this ensio
+sik
+
+ align:start position:0%
+sik
+ 
+
+ align:start position:0%
+sik
+whis
+
+ align:start position:0%
+whis
+ 
+
+ align:start position:0%
+whis
+as the extension thus the force
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he was uh quite a guy all right so there
+
+ align:start position:0%
+he was uh quite a guy all right so there
+ 
+
+ align:start position:0%
+he was uh quite a guy all right so there
+it is that's that's uh elastic
+
+ align:start position:0%
+it is that's that's uh elastic
+ 
+
+ align:start position:0%
+it is that's that's uh elastic
+deformation now let's look at plastic
+
+ align:start position:0%
+deformation now let's look at plastic
+ 
+
+ align:start position:0%
+deformation now let's look at plastic
+deformation so plastic deformation is
+
+ align:start position:0%
+deformation so plastic deformation is
+ 
+
+ align:start position:0%
+deformation so plastic deformation is
+the other form plastic deformation and
+
+ align:start position:0%
+the other form plastic deformation and
+ 
+
+ align:start position:0%
+the other form plastic deformation and
+that's permanent deformation plastic
+
+ align:start position:0%
+that's permanent deformation plastic
+ 
+
+ align:start position:0%
+that's permanent deformation plastic
+deformation is permanent
+
+ align:start position:0%
+deformation is permanent
+ 
+
+ align:start position:0%
+deformation is permanent
+so let's look at the chemical origins of
+
+ align:start position:0%
+so let's look at the chemical origins of
+ 
+
+ align:start position:0%
+so let's look at the chemical origins of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+and now we'll do another experiment
+
+ align:start position:0%
+and now we'll do another experiment
+ 
+
+ align:start position:0%
+and now we'll do another experiment
+instead of a spring this is a wire
+
+ align:start position:0%
+instead of a spring this is a wire
+ 
+
+ align:start position:0%
+instead of a spring this is a wire
+this is a wire and we hang a mass on it
+
+ align:start position:0%
+this is a wire and we hang a mass on it
+ 
+
+ align:start position:0%
+this is a wire and we hang a mass on it
+and this mass is very very uh heavy so
+
+ align:start position:0%
+and this mass is very very uh heavy so
+ 
+
+ align:start position:0%
+and this mass is very very uh heavy so
+that the force here is great enough to
+
+ align:start position:0%
+that the force here is great enough to
+ 
+
+ align:start position:0%
+that the force here is great enough to
+actually cause elongation
+
+ align:start position:0%
+actually cause elongation
+ 
+
+ align:start position:0%
+actually cause elongation
+so we've got elongation of the spring
+
+ align:start position:0%
+so we've got elongation of the spring
+ 
+
+ align:start position:0%
+so we've got elongation of the spring
+excuse me of the of the wire here so
+
+ align:start position:0%
+excuse me of the of the wire here so
+ 
+
+ align:start position:0%
+excuse me of the of the wire here so
+let's make this a simple copper wire so
+
+ align:start position:0%
+let's make this a simple copper wire so
+ 
+
+ align:start position:0%
+let's make this a simple copper wire so
+it's pure copper FCC the only thing
+
+ align:start position:0%
+it's pure copper FCC the only thing
+ 
+
+ align:start position:0%
+it's pure copper FCC the only thing
+we've got in there it's got high Purity
+
+ align:start position:0%
+we've got in there it's got high Purity
+ 
+
+ align:start position:0%
+we've got in there it's got high Purity
+copper there's vacancies there's grain
+
+ align:start position:0%
+copper there's vacancies there's grain
+ 
+
+ align:start position:0%
+copper there's vacancies there's grain
+boundaries and there's dislocations so
+
+ align:start position:0%
+boundaries and there's dislocations so
+ 
+
+ align:start position:0%
+boundaries and there's dislocations so
+let's look at this a little bit more
+
+ align:start position:0%
+let's look at this a little bit more
+ 
+
+ align:start position:0%
+let's look at this a little bit more
+carefully here's the wire and we're
+
+ align:start position:0%
+carefully here's the wire and we're
+ 
+
+ align:start position:0%
+carefully here's the wire and we're
+going to make it polycrystalline
+
+ align:start position:0%
+going to make it polycrystalline
+ 
+
+ align:start position:0%
+going to make it polycrystalline
+so we've got I'm going to indicate poly
+
+ align:start position:0%
+so we've got I'm going to indicate poly
+ 
+
+ align:start position:0%
+so we've got I'm going to indicate poly
+christallin as follows that the
+
+ align:start position:0%
+christallin as follows that the
+ 
+
+ align:start position:0%
+christallin as follows that the
+different grains have different
+
+ align:start position:0%
+different grains have different
+ 
+
+ align:start position:0%
+different grains have different
+orientations of the atoms okay and I'm
+
+ align:start position:0%
+orientations of the atoms okay and I'm
+ 
+
+ align:start position:0%
+orientations of the atoms okay and I'm
+I'm applying a force in the vertical
+
+ align:start position:0%
+I'm applying a force in the vertical
+ 
+
+ align:start position:0%
+I'm applying a force in the vertical
+Direction so the question is how does
+
+ align:start position:0%
+Direction so the question is how does
+ 
+
+ align:start position:0%
+Direction so the question is how does
+this deform if we go down to the next
+
+ align:start position:0%
+this deform if we go down to the next
+ 
+
+ align:start position:0%
+this deform if we go down to the next
+level I'll take a look over here on the
+
+ align:start position:0%
+level I'll take a look over here on the
+ 
+
+ align:start position:0%
+level I'll take a look over here on the
+right side and I can imagine that I've
+
+ align:start position:0%
+right side and I can imagine that I've
+ 
+
+ align:start position:0%
+right side and I can imagine that I've
+got here atoms touching ing as follows
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's in an FCC lattice but I'm
+
+ align:start position:0%
+so that's in an FCC lattice but I'm
+ 
+
+ align:start position:0%
+so that's in an FCC lattice but I'm
+pulling in the vertical Direction now
+
+ align:start position:0%
+pulling in the vertical Direction now
+ 
+
+ align:start position:0%
+pulling in the vertical Direction now
+maybe around the N early early 1800s we
+
+ align:start position:0%
+maybe around the N early early 1800s we
+ 
+
+ align:start position:0%
+maybe around the N early early 1800s we
+might argue that well the atoms start
+
+ align:start position:0%
+might argue that well the atoms start
+ 
+
+ align:start position:0%
+might argue that well the atoms start
+off as spherical and then they become
+
+ align:start position:0%
+off as spherical and then they become
+ 
+
+ align:start position:0%
+off as spherical and then they become
+elongated under the action of a force
+
+ align:start position:0%
+elongated under the action of a force
+ 
+
+ align:start position:0%
+elongated under the action of a force
+but I think that's kind of goofy so
+
+ align:start position:0%
+but I think that's kind of goofy so
+ 
+
+ align:start position:0%
+but I think that's kind of goofy so
+we're going to turn that one down
+
+ align:start position:0%
+we're going to turn that one down
+ 
+
+ align:start position:0%
+we're going to turn that one down
+instead what we're going to do is we're
+
+ align:start position:0%
+instead what we're going to do is we're
+ 
+
+ align:start position:0%
+instead what we're going to do is we're
+going to say well we know about
+
+ align:start position:0%
+going to say well we know about
+ 
+
+ align:start position:0%
+going to say well we know about
+dislocation
+
+ align:start position:0%
+dislocation
+ 
+
+ align:start position:0%
+dislocation
+and we know that dislocations allow
+
+ align:start position:0%
+and we know that dislocations allow
+ 
+
+ align:start position:0%
+and we know that dislocations allow
+atoms to Glide over one another so
+
+ align:start position:0%
+atoms to Glide over one another so
+ 
+
+ align:start position:0%
+atoms to Glide over one another so
+what's the problem here the problem is
+
+ align:start position:0%
+what's the problem here the problem is
+ 
+
+ align:start position:0%
+what's the problem here the problem is
+that the atom planes are lined up on a
+
+ align:start position:0%
+that the atom planes are lined up on a
+ 
+
+ align:start position:0%
+that the atom planes are lined up on a
+45 degree angle what the system does is
+
+ align:start position:0%
+45 degree angle what the system does is
+ 
+
+ align:start position:0%
+45 degree angle what the system does is
+it reforms
+
+ align:start position:0%
+it reforms
+ 
+
+ align:start position:0%
+it reforms
+it reconstitutes
+
+ align:start position:0%
+it reconstitutes
+ 
+
+ align:start position:0%
+it reconstitutes
+the applied stress and resolves it into
+
+ align:start position:0%
+the applied stress and resolves it into
+ 
+
+ align:start position:0%
+the applied stress and resolves it into
+a resolved shear stress
+
+ align:start position:0%
+a resolved shear stress
+ 
+
+ align:start position:0%
+a resolved shear stress
+a resolved sheer stress that moves along
+
+ align:start position:0%
+a resolved sheer stress that moves along
+ 
+
+ align:start position:0%
+a resolved sheer stress that moves along
+the componentry of of the atoms so what
+
+ align:start position:0%
+the componentry of of the atoms so what
+ 
+
+ align:start position:0%
+the componentry of of the atoms so what
+happens is this atom plane underneath
+
+ align:start position:0%
+happens is this atom plane underneath
+ 
+
+ align:start position:0%
+happens is this atom plane underneath
+slides down to the lower right the next
+
+ align:start position:0%
+slides down to the lower right the next
+ 
+
+ align:start position:0%
+slides down to the lower right the next
+plane slides to the upper left and from
+
+ align:start position:0%
+plane slides to the upper left and from
+ 
+
+ align:start position:0%
+plane slides to the upper left and from
+a distance we see that the wire is
+
+ align:start position:0%
+a distance we see that the wire is
+ 
+
+ align:start position:0%
+a distance we see that the wire is
+becoming narrower and longer but it's
+
+ align:start position:0%
+becoming narrower and longer but it's
+ 
+
+ align:start position:0%
+becoming narrower and longer but it's
+happening thanks to the atom
+
+ align:start position:0%
+happening thanks to the atom
+ 
+
+ align:start position:0%
+happening thanks to the atom
+atom slip
+
+ align:start position:0%
+atom slip
+ 
+
+ align:start position:0%
+atom slip
+atom slip
+
+ align:start position:0%
+atom slip
+ 
+
+ align:start position:0%
+atom slip
+and we went through the reasoning last
+
+ align:start position:0%
+and we went through the reasoning last
+ 
+
+ align:start position:0%
+and we went through the reasoning last
+day of what the slip systems will be the
+
+ align:start position:0%
+day of what the slip systems will be the
+ 
+
+ align:start position:0%
+day of what the slip systems will be the
+atoms are going to slip in such a way
+
+ align:start position:0%
+atoms are going to slip in such a way
+ 
+
+ align:start position:0%
+atoms are going to slip in such a way
+that preserves the the strength of the
+
+ align:start position:0%
+that preserves the the strength of the
+ 
+
+ align:start position:0%
+that preserves the the strength of the
+planes the planes that will slip over
+
+ align:start position:0%
+planes the planes that will slip over
+ 
+
+ align:start position:0%
+planes the planes that will slip over
+one another are the planes that have the
+
+ align:start position:0%
+one another are the planes that have the
+ 
+
+ align:start position:0%
+one another are the planes that have the
+tightest binding and the Titus binding
+
+ align:start position:0%
+tightest binding and the Titus binding
+ 
+
+ align:start position:0%
+tightest binding and the Titus binding
+comes from neighboring atoms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they were polite they're very polite
+
+ align:start position:0%
+they were polite they're very polite
+ 
+
+ align:start position:0%
+they were polite they're very polite
+it's polite
+
+ align:start position:0%
+it's polite
+ 
+
+ align:start position:0%
+it's polite
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the planes to return to the story the
+
+ align:start position:0%
+the planes to return to the story the
+ 
+
+ align:start position:0%
+the planes to return to the story the
+planes that have the tightest binding
+
+ align:start position:0%
+planes that have the tightest binding
+ 
+
+ align:start position:0%
+planes that have the tightest binding
+are the planes that have the highest
+
+ align:start position:0%
+are the planes that have the highest
+ 
+
+ align:start position:0%
+are the planes that have the highest
+populations so that would be the planes
+
+ align:start position:0%
+populations so that would be the planes
+ 
+
+ align:start position:0%
+populations so that would be the planes
+of highest packing so we've gone through
+
+ align:start position:0%
+of highest packing so we've gone through
+ 
+
+ align:start position:0%
+of highest packing so we've gone through
+this and we're just to return to the uh
+
+ align:start position:0%
+this and we're just to return to the uh
+ 
+
+ align:start position:0%
+this and we're just to return to the uh
+the planes that have the highest packing
+
+ align:start position:0%
+the planes that have the highest packing
+ 
+
+ align:start position:0%
+the planes that have the highest packing
+are the ones that have the highest uh
+
+ align:start position:0%
+are the ones that have the highest uh
+ 
+
+ align:start position:0%
+are the ones that have the highest uh
+atom density and that's going to be the
+
+ align:start position:0%
+atom density and that's going to be the
+ 
+
+ align:start position:0%
+atom density and that's going to be the
+highest binding so the highest density
+
+ align:start position:0%
+highest binding so the highest density
+ 
+
+ align:start position:0%
+highest binding so the highest density
+plane in FCC is 111 and then the plane
+
+ align:start position:0%
+plane in FCC is 111 and then the plane
+ 
+
+ align:start position:0%
+plane in FCC is 111 and then the plane
+will slip along the direction it has the
+
+ align:start position:0%
+will slip along the direction it has the
+ 
+
+ align:start position:0%
+will slip along the direction it has the
+highest density because what we're
+
+ align:start position:0%
+highest density because what we're
+ 
+
+ align:start position:0%
+highest density because what we're
+thinking of is rigid rafts and rigid
+
+ align:start position:0%
+thinking of is rigid rafts and rigid
+ 
+
+ align:start position:0%
+thinking of is rigid rafts and rigid
+rods so to make the most rigid raft you
+
+ align:start position:0%
+rods so to make the most rigid raft you
+ 
+
+ align:start position:0%
+rods so to make the most rigid raft you
+have the highest density of bonds and
+
+ align:start position:0%
+have the highest density of bonds and
+ 
+
+ align:start position:0%
+have the highest density of bonds and
+once you're in the plane how do you slip
+
+ align:start position:0%
+once you're in the plane how do you slip
+ 
+
+ align:start position:0%
+once you're in the plane how do you slip
+do you slip along you going to push a
+
+ align:start position:0%
+do you slip along you going to push a
+ 
+
+ align:start position:0%
+do you slip along you going to push a
+wet noodle or you're going to push
+
+ align:start position:0%
+wet noodle or you're going to push
+ 
+
+ align:start position:0%
+wet noodle or you're going to push
+something that's rigid so the highest
+
+ align:start position:0%
+something that's rigid so the highest
+ 
+
+ align:start position:0%
+something that's rigid so the highest
+rigidity comes from the direction where
+
+ align:start position:0%
+rigidity comes from the direction where
+ 
+
+ align:start position:0%
+rigidity comes from the direction where
+the atoms touch and so all of this goes
+
+ align:start position:0%
+the atoms touch and so all of this goes
+ 
+
+ align:start position:0%
+the atoms touch and so all of this goes
+back right to the very beginning and
+
+ align:start position:0%
+back right to the very beginning and
+ 
+
+ align:start position:0%
+back right to the very beginning and
+explains how uh slip systems work and so
+
+ align:start position:0%
+explains how uh slip systems work and so
+ 
+
+ align:start position:0%
+explains how uh slip systems work and so
+slip
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slip systems operate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+slip systems operate in close packed
+
+ align:start position:0%
+slip systems operate in close packed
+ 
+
+ align:start position:0%
+slip systems operate in close packed
+planes along close packed directions
+
+ align:start position:0%
+planes along close packed directions
+ 
+
+ align:start position:0%
+planes along close packed directions
+with the aid of dislocations
+
+ align:start position:0%
+with the aid of dislocations
+ 
+
+ align:start position:0%
+with the aid of dislocations
+with the aid
+
+ align:start position:0%
+with the aid
+ 
+
+ align:start position:0%
+with the aid
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+dislocations which provide for the
+
+ align:start position:0%
+dislocations which provide for the
+ 
+
+ align:start position:0%
+dislocations which provide for the
+ability to move in permanent
+
+ align:start position:0%
+ability to move in permanent
+ 
+
+ align:start position:0%
+ability to move in permanent
+displacement in uh at at uh stresses
+
+ align:start position:0%
+displacement in uh at at uh stresses
+ 
+
+ align:start position:0%
+displacement in uh at at uh stresses
+that are less than what is critical now
+
+ align:start position:0%
+that are less than what is critical now
+ 
+
+ align:start position:0%
+that are less than what is critical now
+what I'd like to do is to show you uh
+
+ align:start position:0%
+what I'd like to do is to show you uh
+ 
+
+ align:start position:0%
+what I'd like to do is to show you uh
+something that comes from a uh uh bubble
+
+ align:start position:0%
+something that comes from a uh uh bubble
+ 
+
+ align:start position:0%
+something that comes from a uh uh bubble
+raft model that was constructed by uh
+
+ align:start position:0%
+raft model that was constructed by uh
+ 
+
+ align:start position:0%
+raft model that was constructed by uh
+Kristen Van vet who is a is part of her
+
+ align:start position:0%
+Kristen Van vet who is a is part of her
+ 
+
+ align:start position:0%
+Kristen Van vet who is a is part of her
+PhD she's now a faculty member in our
+
+ align:start position:0%
+PhD she's now a faculty member in our
+ 
+
+ align:start position:0%
+PhD she's now a faculty member in our
+department so this is a bubble raft
+
+ align:start position:0%
+department so this is a bubble raft
+ 
+
+ align:start position:0%
+department so this is a bubble raft
+model that um represents the uh move
+
+ align:start position:0%
+model that um represents the uh move
+ 
+
+ align:start position:0%
+model that um represents the uh move
+movement of atoms under an applied
+
+ align:start position:0%
+movement of atoms under an applied
+ 
+
+ align:start position:0%
+movement of atoms under an applied
+stress so let's look at the first one
+
+ align:start position:0%
+stress so let's look at the first one
+ 
+
+ align:start position:0%
+stress so let's look at the first one
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay so what you're going to see is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well first thing I'll do is I'll get
+
+ align:start position:0%
+well first thing I'll do is I'll get
+ 
+
+ align:start position:0%
+well first thing I'll do is I'll get
+this out of the way
+
+ align:start position:0%
+this out of the way
+ 
+
+ align:start position:0%
+this out of the way
+there we go
+
+ align:start position:0%
+there we go
+ 
+
+ align:start position:0%
+there we go
+okay let's try it again
+
+ align:start position:0%
+okay let's try it again
+ 
+
+ align:start position:0%
+okay let's try it again
+you'll see the application of stress you
+
+ align:start position:0%
+you'll see the application of stress you
+ 
+
+ align:start position:0%
+you'll see the application of stress you
+see the grain boundary and then you'll
+
+ align:start position:0%
+see the grain boundary and then you'll
+ 
+
+ align:start position:0%
+see the grain boundary and then you'll
+see dislocation
+
+ align:start position:0%
+see dislocation
+ 
+
+ align:start position:0%
+see dislocation
+here and you'll see the atoms squirt up
+
+ align:start position:0%
+here and you'll see the atoms squirt up
+ 
+
+ align:start position:0%
+here and you'll see the atoms squirt up
+see the force is being applied from top
+
+ align:start position:0%
+see the force is being applied from top
+ 
+
+ align:start position:0%
+see the force is being applied from top
+to bottom but the atoms are on an angle
+
+ align:start position:0%
+to bottom but the atoms are on an angle
+ 
+
+ align:start position:0%
+to bottom but the atoms are on an angle
+so there's a dislocation that issues
+
+ align:start position:0%
+so there's a dislocation that issues
+ 
+
+ align:start position:0%
+so there's a dislocation that issues
+from this triple Junction and now it's
+
+ align:start position:0%
+from this triple Junction and now it's
+ 
+
+ align:start position:0%
+from this triple Junction and now it's
+up in here and it's getting ready to
+
+ align:start position:0%
+up in here and it's getting ready to
+ 
+
+ align:start position:0%
+up in here and it's getting ready to
+squirt up to this side so you can see
+
+ align:start position:0%
+squirt up to this side so you can see
+ 
+
+ align:start position:0%
+squirt up to this side so you can see
+how the atoms are moving side by side on
+
+ align:start position:0%
+how the atoms are moving side by side on
+ 
+
+ align:start position:0%
+how the atoms are moving side by side on
+a 45 degree angle in order to allow for
+
+ align:start position:0%
+a 45 degree angle in order to allow for
+ 
+
+ align:start position:0%
+a 45 degree angle in order to allow for
+what in essence has to be compression in
+
+ align:start position:0%
+what in essence has to be compression in
+ 
+
+ align:start position:0%
+what in essence has to be compression in
+the vertical Direction
+
+ align:start position:0%
+the vertical Direction
+ 
+
+ align:start position:0%
+the vertical Direction
+I'll show you another that involves a
+
+ align:start position:0%
+I'll show you another that involves a
+ 
+
+ align:start position:0%
+I'll show you another that involves a
+single Crystal and the same thing the
+
+ align:start position:0%
+single Crystal and the same thing the
+ 
+
+ align:start position:0%
+single Crystal and the same thing the
+pressure gets high enough that finally a
+
+ align:start position:0%
+pressure gets high enough that finally a
+ 
+
+ align:start position:0%
+pressure gets high enough that finally a
+dislocation originates in the center of
+
+ align:start position:0%
+dislocation originates in the center of
+ 
+
+ align:start position:0%
+dislocation originates in the center of
+a single Crystal the dislocation shoots
+
+ align:start position:0%
+a single Crystal the dislocation shoots
+ 
+
+ align:start position:0%
+a single Crystal the dislocation shoots
+up to the surface and now you have a
+
+ align:start position:0%
+up to the surface and now you have a
+ 
+
+ align:start position:0%
+up to the surface and now you have a
+step at the surface
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tell him to stop
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now we have a single Crystal
+
+ align:start position:0%
+okay so now we have a single Crystal
+ 
+
+ align:start position:0%
+okay so now we have a single Crystal
+you're going to see a dislocation
+
+ align:start position:0%
+you're going to see a dislocation
+ 
+
+ align:start position:0%
+you're going to see a dislocation
+originate right in here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there it is you see it squirt and now
+
+ align:start position:0%
+there it is you see it squirt and now
+ 
+
+ align:start position:0%
+there it is you see it squirt and now
+there's a there's a step here this side
+
+ align:start position:0%
+there's a there's a step here this side
+ 
+
+ align:start position:0%
+there's a there's a step here this side
+of the of the surface is one atom step
+
+ align:start position:0%
+of the of the surface is one atom step
+ 
+
+ align:start position:0%
+of the of the surface is one atom step
+higher we'll see it one more time
+
+ align:start position:0%
+higher we'll see it one more time
+ 
+
+ align:start position:0%
+higher we'll see it one more time
+it'll originate right down in here
+
+ align:start position:0%
+it'll originate right down in here
+ 
+
+ align:start position:0%
+it'll originate right down in here
+there it goes
+
+ align:start position:0%
+there it goes
+ 
+
+ align:start position:0%
+there it goes
+so the atoms are slipping over the
+
+ align:start position:0%
+so the atoms are slipping over the
+ 
+
+ align:start position:0%
+so the atoms are slipping over the
+highest population
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's enough out of you let's go
+
+ align:start position:0%
+okay that's enough out of you let's go
+ 
+
+ align:start position:0%
+okay that's enough out of you let's go
+back to this
+
+ align:start position:0%
+back to this
+ 
+
+ align:start position:0%
+back to this
+good all right so now you know the
+
+ align:start position:0%
+good all right so now you know the
+ 
+
+ align:start position:0%
+good all right so now you know the
+origins of of mechanical Behavior now I
+
+ align:start position:0%
+origins of of mechanical Behavior now I
+ 
+
+ align:start position:0%
+origins of of mechanical Behavior now I
+want to talk about the ultimate defect
+
+ align:start position:0%
+want to talk about the ultimate defect
+ 
+
+ align:start position:0%
+want to talk about the ultimate defect
+the ultimate defect is total disorder
+
+ align:start position:0%
+the ultimate defect is total disorder
+ 
+
+ align:start position:0%
+the ultimate defect is total disorder
+the ultimate defect is total disorder
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so what we're going to look at is
+
+ align:start position:0%
+and so what we're going to look at is
+ 
+
+ align:start position:0%
+and so what we're going to look at is
+the loss of crystallinity and go to um
+
+ align:start position:0%
+the loss of crystallinity and go to um
+ 
+
+ align:start position:0%
+the loss of crystallinity and go to um
+amorphous materials so I'll take you
+
+ align:start position:0%
+amorphous materials so I'll take you
+ 
+
+ align:start position:0%
+amorphous materials so I'll take you
+back to the big picture which was about
+
+ align:start position:0%
+back to the big picture which was about
+ 
+
+ align:start position:0%
+back to the big picture which was about
+a week or so ago where we looked at how
+
+ align:start position:0%
+a week or so ago where we looked at how
+ 
+
+ align:start position:0%
+a week or so ago where we looked at how
+we got to solids and we said there's two
+
+ align:start position:0%
+we got to solids and we said there's two
+ 
+
+ align:start position:0%
+we got to solids and we said there's two
+types of solids we saw that we have
+
+ align:start position:0%
+types of solids we saw that we have
+ 
+
+ align:start position:0%
+types of solids we saw that we have
+ordered solids and that's what we've
+
+ align:start position:0%
+ordered solids and that's what we've
+ 
+
+ align:start position:0%
+ordered solids and that's what we've
+been talking about for the last week or
+
+ align:start position:0%
+been talking about for the last week or
+ 
+
+ align:start position:0%
+been talking about for the last week or
+so and now I want to get over here to
+
+ align:start position:0%
+so and now I want to get over here to
+ 
+
+ align:start position:0%
+so and now I want to get over here to
+disordered solids these are solids that
+
+ align:start position:0%
+disordered solids these are solids that
+ 
+
+ align:start position:0%
+disordered solids these are solids that
+lack long range order there's a little
+
+ align:start position:0%
+lack long range order there's a little
+ 
+
+ align:start position:0%
+lack long range order there's a little
+bit of short range order amorphous
+
+ align:start position:0%
+bit of short range order amorphous
+ 
+
+ align:start position:0%
+bit of short range order amorphous
+solids and the colloquial word for them
+
+ align:start position:0%
+solids and the colloquial word for them
+ 
+
+ align:start position:0%
+solids and the colloquial word for them
+is glasses
+
+ align:start position:0%
+is glasses
+ 
+
+ align:start position:0%
+is glasses
+amorphous solids
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or glasses
+
+ align:start position:0%
+or glasses
+ 
+
+ align:start position:0%
+or glasses
+and these are solids that lack long
+
+ align:start position:0%
+and these are solids that lack long
+ 
+
+ align:start position:0%
+and these are solids that lack long
+range order
+
+ align:start position:0%
+range order
+ 
+
+ align:start position:0%
+range order
+solids lacking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+long range order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what kind of solids can form glasses
+
+ align:start position:0%
+now what kind of solids can form glasses
+ 
+
+ align:start position:0%
+now what kind of solids can form glasses
+well anything that's capable of being
+
+ align:start position:0%
+well anything that's capable of being
+ 
+
+ align:start position:0%
+well anything that's capable of being
+solidified in a way that prevents
+
+ align:start position:0%
+solidified in a way that prevents
+ 
+
+ align:start position:0%
+solidified in a way that prevents
+crystallization so I can show you
+
+ align:start position:0%
+crystallization so I can show you
+ 
+
+ align:start position:0%
+crystallization so I can show you
+inorganic inorganic glasses
+
+ align:start position:0%
+inorganic inorganic glasses
+ 
+
+ align:start position:0%
+inorganic inorganic glasses
+such as the silicates
+
+ align:start position:0%
+such as the silicates
+ 
+
+ align:start position:0%
+such as the silicates
+that sank the Titanic and are also used
+
+ align:start position:0%
+that sank the Titanic and are also used
+ 
+
+ align:start position:0%
+that sank the Titanic and are also used
+in things everything from window glass
+
+ align:start position:0%
+in things everything from window glass
+ 
+
+ align:start position:0%
+in things everything from window glass
+to uh beverage containers and so on
+
+ align:start position:0%
+to uh beverage containers and so on
+ 
+
+ align:start position:0%
+to uh beverage containers and so on
+these are made of uh sio2 and we're
+
+ align:start position:0%
+these are made of uh sio2 and we're
+ 
+
+ align:start position:0%
+these are made of uh sio2 and we're
+going to return to that as a
+
+ align:start position:0%
+going to return to that as a
+ 
+
+ align:start position:0%
+going to return to that as a
+prototypical system to study uh very
+
+ align:start position:0%
+prototypical system to study uh very
+ 
+
+ align:start position:0%
+prototypical system to study uh very
+shortly there's organic organic glasses
+
+ align:start position:0%
+shortly there's organic organic glasses
+ 
+
+ align:start position:0%
+shortly there's organic organic glasses
+organic glasses the most common being
+
+ align:start position:0%
+organic glasses the most common being
+ 
+
+ align:start position:0%
+organic glasses the most common being
+polymers
+
+ align:start position:0%
+polymers
+ 
+
+ align:start position:0%
+polymers
+polymers so for example the polymethyl
+
+ align:start position:0%
+polymers so for example the polymethyl
+ 
+
+ align:start position:0%
+polymers so for example the polymethyl
+methacrylate that we use in such
+
+ align:start position:0%
+methacrylate that we use in such
+ 
+
+ align:start position:0%
+methacrylate that we use in such
+applications as uh substitution for uh
+
+ align:start position:0%
+applications as uh substitution for uh
+ 
+
+ align:start position:0%
+applications as uh substitution for uh
+window glass the polymethyl methacrylate
+
+ align:start position:0%
+window glass the polymethyl methacrylate
+ 
+
+ align:start position:0%
+window glass the polymethyl methacrylate
+you use in your eyeglasses this material
+
+ align:start position:0%
+you use in your eyeglasses this material
+ 
+
+ align:start position:0%
+you use in your eyeglasses this material
+is all disordered it's disordered
+
+ align:start position:0%
+is all disordered it's disordered
+ 
+
+ align:start position:0%
+is all disordered it's disordered
+and we even have elements
+
+ align:start position:0%
+and we even have elements
+ 
+
+ align:start position:0%
+and we even have elements
+elements that have certain features for
+
+ align:start position:0%
+elements that have certain features for
+ 
+
+ align:start position:0%
+elements that have certain features for
+example sulfur sulfur typically when it
+
+ align:start position:0%
+example sulfur sulfur typically when it
+ 
+
+ align:start position:0%
+example sulfur sulfur typically when it
+solidifies does not form a crystal but
+
+ align:start position:0%
+solidifies does not form a crystal but
+ 
+
+ align:start position:0%
+solidifies does not form a crystal but
+rather forms a glass it's an amorphous
+
+ align:start position:0%
+rather forms a glass it's an amorphous
+ 
+
+ align:start position:0%
+rather forms a glass it's an amorphous
+it's an amorphous material when it
+
+ align:start position:0%
+it's an amorphous material when it
+ 
+
+ align:start position:0%
+it's an amorphous material when it
+solidifies
+
+ align:start position:0%
+solidifies
+ 
+
+ align:start position:0%
+solidifies
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+the point here is that we don't classify
+
+ align:start position:0%
+the point here is that we don't classify
+ 
+
+ align:start position:0%
+the point here is that we don't classify
+things as a morphus based on their
+
+ align:start position:0%
+things as a morphus based on their
+ 
+
+ align:start position:0%
+things as a morphus based on their
+chemical composition but rather based
+
+ align:start position:0%
+chemical composition but rather based
+ 
+
+ align:start position:0%
+chemical composition but rather based
+upon atomic order
+
+ align:start position:0%
+upon atomic order
+ 
+
+ align:start position:0%
+upon atomic order
+based on Atomic order and specifically
+
+ align:start position:0%
+based on Atomic order and specifically
+ 
+
+ align:start position:0%
+based on Atomic order and specifically
+here the lack of long range order and
+
+ align:start position:0%
+here the lack of long range order and
+ 
+
+ align:start position:0%
+here the lack of long range order and
+some do both for example sio2 silica
+
+ align:start position:0%
+some do both for example sio2 silica
+ 
+
+ align:start position:0%
+some do both for example sio2 silica
+silicon oxide if it forms a crystal if
+
+ align:start position:0%
+silicon oxide if it forms a crystal if
+ 
+
+ align:start position:0%
+silicon oxide if it forms a crystal if
+it forms a crystal we call it quartz
+
+ align:start position:0%
+it forms a crystal we call it quartz
+ 
+
+ align:start position:0%
+it forms a crystal we call it quartz
+we call it quartz and the quartz crystal
+
+ align:start position:0%
+we call it quartz and the quartz crystal
+ 
+
+ align:start position:0%
+we call it quartz and the quartz crystal
+in our watches is made of high Purity
+
+ align:start position:0%
+in our watches is made of high Purity
+ 
+
+ align:start position:0%
+in our watches is made of high Purity
+sio2 which has been hydrothermally
+
+ align:start position:0%
+sio2 which has been hydrothermally
+ 
+
+ align:start position:0%
+sio2 which has been hydrothermally
+processed to give it high degree of
+
+ align:start position:0%
+processed to give it high degree of
+ 
+
+ align:start position:0%
+processed to give it high degree of
+crystallinity and it has a very
+
+ align:start position:0%
+crystallinity and it has a very
+ 
+
+ align:start position:0%
+crystallinity and it has a very
+characteristic vibrational frequency
+
+ align:start position:0%
+characteristic vibrational frequency
+ 
+
+ align:start position:0%
+characteristic vibrational frequency
+from which we derive the ability to set
+
+ align:start position:0%
+from which we derive the ability to set
+ 
+
+ align:start position:0%
+from which we derive the ability to set
+the time um but we can also have it
+
+ align:start position:0%
+the time um but we can also have it
+ 
+
+ align:start position:0%
+the time um but we can also have it
+amorphus
+
+ align:start position:0%
+amorphus
+ 
+
+ align:start position:0%
+amorphus
+can all also have a morphus sio2 and
+
+ align:start position:0%
+can all also have a morphus sio2 and
+ 
+
+ align:start position:0%
+can all also have a morphus sio2 and
+that gives us and this is the only time
+
+ align:start position:0%
+that gives us and this is the only time
+ 
+
+ align:start position:0%
+that gives us and this is the only time
+you're going to see me use this term as
+
+ align:start position:0%
+you're going to see me use this term as
+ 
+
+ align:start position:0%
+you're going to see me use this term as
+the general public uses it it gives you
+
+ align:start position:0%
+the general public uses it it gives you
+ 
+
+ align:start position:0%
+the general public uses it it gives you
+glass as you know glass window glass
+
+ align:start position:0%
+glass as you know glass window glass
+ 
+
+ align:start position:0%
+glass as you know glass window glass
+bottle glass and so on but only when I
+
+ align:start position:0%
+bottle glass and so on but only when I
+ 
+
+ align:start position:0%
+bottle glass and so on but only when I
+put quotation marks am I using this
+
+ align:start position:0%
+put quotation marks am I using this
+ 
+
+ align:start position:0%
+put quotation marks am I using this
+vernacular this vulgar term when I use
+
+ align:start position:0%
+vernacular this vulgar term when I use
+ 
+
+ align:start position:0%
+vernacular this vulgar term when I use
+the term glass up here I mean no long
+
+ align:start position:0%
+the term glass up here I mean no long
+ 
+
+ align:start position:0%
+the term glass up here I mean no long
+range order and uh so I think uh
+
+ align:start position:0%
+range order and uh so I think uh
+ 
+
+ align:start position:0%
+range order and uh so I think uh
+I think that uh just to get some
+
+ align:start position:0%
+I think that uh just to get some
+ 
+
+ align:start position:0%
+I think that uh just to get some
+nomenclature here so that you'll know
+
+ align:start position:0%
+nomenclature here so that you'll know
+ 
+
+ align:start position:0%
+nomenclature here so that you'll know
+you have silicon
+
+ align:start position:0%
+you have silicon
+ 
+
+ align:start position:0%
+you have silicon
+silicon is the metal the oxide is silica
+
+ align:start position:0%
+silicon is the metal the oxide is silica
+ 
+
+ align:start position:0%
+silicon is the metal the oxide is silica
+sio2
+
+ align:start position:0%
+sio2
+ 
+
+ align:start position:0%
+sio2
+and the uh annion is silicate and so
+
+ align:start position:0%
+and the uh annion is silicate and so
+ 
+
+ align:start position:0%
+and the uh annion is silicate and so
+we'll refer to silicate glasses so sio4
+
+ align:start position:0%
+we'll refer to silicate glasses so sio4
+ 
+
+ align:start position:0%
+we'll refer to silicate glasses so sio4
+4 minus is the maximum coordination so
+
+ align:start position:0%
+4 minus is the maximum coordination so
+ 
+
+ align:start position:0%
+4 minus is the maximum coordination so
+you can go through you have aluminum
+
+ align:start position:0%
+you can go through you have aluminum
+ 
+
+ align:start position:0%
+you can go through you have aluminum
+this is al203 is alumina and al3
+
+ align:start position:0%
+this is al203 is alumina and al3
+ 
+
+ align:start position:0%
+this is al203 is alumina and al3
+is illuminates and so on so I thought
+
+ align:start position:0%
+is illuminates and so on so I thought
+ 
+
+ align:start position:0%
+is illuminates and so on so I thought
+since it's Friday and people are kind of
+
+ align:start position:0%
+since it's Friday and people are kind of
+ 
+
+ align:start position:0%
+since it's Friday and people are kind of
+um in a festive mood after the quiz on
+
+ align:start position:0%
+um in a festive mood after the quiz on
+ 
+
+ align:start position:0%
+um in a festive mood after the quiz on
+uh Wednesday i' take a look at the the
+
+ align:start position:0%
+uh Wednesday i' take a look at the the
+ 
+
+ align:start position:0%
+uh Wednesday i' take a look at the the
+geography here I think we can learn a
+
+ align:start position:0%
+geography here I think we can learn a
+ 
+
+ align:start position:0%
+geography here I think we can learn a
+little bit here if you
+
+ align:start position:0%
+little bit here if you
+ 
+
+ align:start position:0%
+little bit here if you
+this is Si I'm going to now look at
+
+ align:start position:0%
+this is Si I'm going to now look at
+ 
+
+ align:start position:0%
+this is Si I'm going to now look at
+oxides okay so this is silica so this
+
+ align:start position:0%
+oxides okay so this is silica so this
+ 
+
+ align:start position:0%
+oxides okay so this is silica so this
+would be Germania geo2 would be Germania
+
+ align:start position:0%
+would be Germania geo2 would be Germania
+ 
+
+ align:start position:0%
+would be Germania geo2 would be Germania
+which is Latin for
+
+ align:start position:0%
+which is Latin for
+ 
+
+ align:start position:0%
+which is Latin for
+Germania
+
+ align:start position:0%
+Germania
+ 
+
+ align:start position:0%
+Germania
+ah gee I wonder what the Latin is how
+
+ align:start position:0%
+ah gee I wonder what the Latin is how
+ 
+
+ align:start position:0%
+ah gee I wonder what the Latin is how
+about Germany maybe Germany so gallium
+
+ align:start position:0%
+about Germany maybe Germany so gallium
+ 
+
+ align:start position:0%
+about Germany maybe Germany so gallium
+the oxide is Galia what's Galia
+
+ align:start position:0%
+the oxide is Galia what's Galia
+ 
+
+ align:start position:0%
+the oxide is Galia what's Galia
+France okay so France lies to the west
+
+ align:start position:0%
+France okay so France lies to the west
+ 
+
+ align:start position:0%
+France okay so France lies to the west
+of Germany see that's making sense uh
+
+ align:start position:0%
+of Germany see that's making sense uh
+ 
+
+ align:start position:0%
+of Germany see that's making sense uh
+what's in 203 would be India IND India
+
+ align:start position:0%
+what's in 203 would be India IND India
+ 
+
+ align:start position:0%
+what's in 203 would be India IND India
+is south of France
+
+ align:start position:0%
+is south of France
+ 
+
+ align:start position:0%
+is south of France
+uh this is the oxide of polonium so that
+
+ align:start position:0%
+uh this is the oxide of polonium so that
+ 
+
+ align:start position:0%
+uh this is the oxide of polonium so that
+would be poonia that's Poland Poland is
+
+ align:start position:0%
+would be poonia that's Poland Poland is
+ 
+
+ align:start position:0%
+would be poonia that's Poland Poland is
+east of Germany it's not south of India
+
+ align:start position:0%
+east of Germany it's not south of India
+ 
+
+ align:start position:0%
+east of Germany it's not south of India
+so it's not so good uh let's see here's
+
+ align:start position:0%
+so it's not so good uh let's see here's
+ 
+
+ align:start position:0%
+so it's not so good uh let's see here's
+this is Francia which is France so
+
+ align:start position:0%
+this is Francia which is France so
+ 
+
+ align:start position:0%
+this is Francia which is France so
+France is twice on the table here that's
+
+ align:start position:0%
+France is twice on the table here that's
+ 
+
+ align:start position:0%
+France is twice on the table here that's
+got to do something about that uh this
+
+ align:start position:0%
+got to do something about that uh this
+ 
+
+ align:start position:0%
+got to do something about that uh this
+is ruthenia which could be Russia more
+
+ align:start position:0%
+is ruthenia which could be Russia more
+ 
+
+ align:start position:0%
+is ruthenia which could be Russia more
+properly Ukraine uh Scandia well it's
+
+ align:start position:0%
+properly Ukraine uh Scandia well it's
+ 
+
+ align:start position:0%
+properly Ukraine uh Scandia well it's
+almost Scandinavia not quite haia haia
+
+ align:start position:0%
+almost Scandinavia not quite haia haia
+ 
+
+ align:start position:0%
+almost Scandinavia not quite haia haia
+this was uh hafnium was discovered in
+
+ align:start position:0%
+this was uh hafnium was discovered in
+ 
+
+ align:start position:0%
+this was uh hafnium was discovered in
+Copenhagen under the direction of Neil's
+
+ align:start position:0%
+Copenhagen under the direction of Neil's
+ 
+
+ align:start position:0%
+Copenhagen under the direction of Neil's
+bore it was an impurity in zirconium
+
+ align:start position:0%
+bore it was an impurity in zirconium
+ 
+
+ align:start position:0%
+bore it was an impurity in zirconium
+haia is the uh Latin name for Copenhagen
+
+ align:start position:0%
+haia is the uh Latin name for Copenhagen
+ 
+
+ align:start position:0%
+haia is the uh Latin name for Copenhagen
+uh holia
+
+ align:start position:0%
+uh holia
+ 
+
+ align:start position:0%
+uh holia
+that's the Stockholm right ltia
+
+ align:start position:0%
+that's the Stockholm right ltia
+ 
+
+ align:start position:0%
+that's the Stockholm right ltia
+ltia is the Latin name for Paris
+
+ align:start position:0%
+ltia is the Latin name for Paris
+ 
+
+ align:start position:0%
+ltia is the Latin name for Paris
+if you go surfing you go to cf3
+
+ align:start position:0%
+if you go surfing you go to cf3
+ 
+
+ align:start position:0%
+if you go surfing you go to cf3
+California
+
+ align:start position:0%
+California
+ 
+
+ align:start position:0%
+California
+all right and
+
+ align:start position:0%
+all right and
+ 
+
+ align:start position:0%
+all right and
+okay so while we're on the periodic
+
+ align:start position:0%
+okay so while we're on the periodic
+ 
+
+ align:start position:0%
+okay so while we're on the periodic
+table uh copper it's also geography it's
+
+ align:start position:0%
+table uh copper it's also geography it's
+ 
+
+ align:start position:0%
+table uh copper it's also geography it's
+a Corruption of the ancient word for
+
+ align:start position:0%
+a Corruption of the ancient word for
+ 
+
+ align:start position:0%
+a Corruption of the ancient word for
+Cypress Cyprus and copper have the same
+
+ align:start position:0%
+Cypress Cyprus and copper have the same
+ 
+
+ align:start position:0%
+Cypress Cyprus and copper have the same
+root because the copper was mined in
+
+ align:start position:0%
+root because the copper was mined in
+ 
+
+ align:start position:0%
+root because the copper was mined in
+Cyprus uh let's see strontium
+
+ align:start position:0%
+Cyprus uh let's see strontium
+ 
+
+ align:start position:0%
+Cyprus uh let's see strontium
+uh that's comes from the Latin for
+
+ align:start position:0%
+uh that's comes from the Latin for
+ 
+
+ align:start position:0%
+uh that's comes from the Latin for
+Scotland so that should cheer the hearts
+
+ align:start position:0%
+Scotland so that should cheer the hearts
+ 
+
+ align:start position:0%
+Scotland so that should cheer the hearts
+of McDonald and McTavish and so on uh
+
+ align:start position:0%
+of McDonald and McTavish and so on uh
+ 
+
+ align:start position:0%
+of McDonald and McTavish and so on uh
+let's see uh Hess is the province where
+
+ align:start position:0%
+let's see uh Hess is the province where
+ 
+
+ align:start position:0%
+let's see uh Hess is the province where
+darad is located in Germany where they
+
+ align:start position:0%
+darad is located in Germany where they
+ 
+
+ align:start position:0%
+darad is located in Germany where they
+have that accelerator so that's hassium
+
+ align:start position:0%
+have that accelerator so that's hassium
+ 
+
+ align:start position:0%
+have that accelerator so that's hassium
+dubnium is for dubna in former Soviet
+
+ align:start position:0%
+dubnium is for dubna in former Soviet
+ 
+
+ align:start position:0%
+dubnium is for dubna in former Soviet
+Union the accelerator and Berkeley is
+
+ align:start position:0%
+Union the accelerator and Berkeley is
+ 
+
+ align:start position:0%
+Union the accelerator and Berkeley is
+where we have the accelerator in the
+
+ align:start position:0%
+where we have the accelerator in the
+ 
+
+ align:start position:0%
+where we have the accelerator in the
+United States oh if you had the oxide of
+
+ align:start position:0%
+United States oh if you had the oxide of
+ 
+
+ align:start position:0%
+United States oh if you had the oxide of
+amorium it wouldn't quite be America
+
+ align:start position:0%
+amorium it wouldn't quite be America
+ 
+
+ align:start position:0%
+amorium it wouldn't quite be America
+it's Amaria there's Europia
+
+ align:start position:0%
+it's Amaria there's Europia
+ 
+
+ align:start position:0%
+it's Amaria there's Europia
+uh turbia one town in uh Sweden gives us
+
+ align:start position:0%
+uh turbia one town in uh Sweden gives us
+ 
+
+ align:start position:0%
+uh turbia one town in uh Sweden gives us
+it's called itby and we get um itum
+
+ align:start position:0%
+it's called itby and we get um itum
+ 
+
+ align:start position:0%
+it's called itby and we get um itum
+erbium herum and turbia four elements
+
+ align:start position:0%
+erbium herum and turbia four elements
+ 
+
+ align:start position:0%
+erbium herum and turbia four elements
+from one little town what do you think
+
+ align:start position:0%
+from one little town what do you think
+ 
+
+ align:start position:0%
+from one little town what do you think
+is in that town
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there must be a resource of minerals
+
+ align:start position:0%
+there must be a resource of minerals
+ 
+
+ align:start position:0%
+there must be a resource of minerals
+from which all of these elements were
+
+ align:start position:0%
+from which all of these elements were
+ 
+
+ align:start position:0%
+from which all of these elements were
+discovered
+
+ align:start position:0%
+discovered
+ 
+
+ align:start position:0%
+discovered
+uh what else is up here oh people people
+
+ align:start position:0%
+uh what else is up here oh people people
+ 
+
+ align:start position:0%
+uh what else is up here oh people people
+rther Forum uh seaborgium
+
+ align:start position:0%
+rther Forum uh seaborgium
+ 
+
+ align:start position:0%
+rther Forum uh seaborgium
+this is Neil's bore borium this is Lisa
+
+ align:start position:0%
+this is Neil's bore borium this is Lisa
+ 
+
+ align:start position:0%
+this is Neil's bore borium this is Lisa
+miter and now we've got uh our pal renen
+
+ align:start position:0%
+miter and now we've got uh our pal renen
+ 
+
+ align:start position:0%
+miter and now we've got uh our pal renen
+he looks like he's going to go on 111 uh
+
+ align:start position:0%
+he looks like he's going to go on 111 uh
+ 
+
+ align:start position:0%
+he looks like he's going to go on 111 uh
+there's the curies uh Einstein fmy
+
+ align:start position:0%
+there's the curies uh Einstein fmy
+ 
+
+ align:start position:0%
+there's the curies uh Einstein fmy
+mandal of Nobel and Lawrence EO Lawrence
+
+ align:start position:0%
+mandal of Nobel and Lawrence EO Lawrence
+ 
+
+ align:start position:0%
+mandal of Nobel and Lawrence EO Lawrence
+was the designer of the accelerator that
+
+ align:start position:0%
+was the designer of the accelerator that
+ 
+
+ align:start position:0%
+was the designer of the accelerator that
+was uh put at Berkeley so that's why you
+
+ align:start position:0%
+was uh put at Berkeley so that's why you
+ 
+
+ align:start position:0%
+was uh put at Berkeley so that's why you
+have the Lawrence Berkeley Laboratory
+
+ align:start position:0%
+have the Lawrence Berkeley Laboratory
+ 
+
+ align:start position:0%
+have the Lawrence Berkeley Laboratory
+um oh there's astronomy here too did you
+
+ align:start position:0%
+um oh there's astronomy here too did you
+ 
+
+ align:start position:0%
+um oh there's astronomy here too did you
+see the eclipse the other night the
+
+ align:start position:0%
+see the eclipse the other night the
+ 
+
+ align:start position:0%
+see the eclipse the other night the
+lunar eclipse see tus is the Earth and
+
+ align:start position:0%
+lunar eclipse see tus is the Earth and
+ 
+
+ align:start position:0%
+lunar eclipse see tus is the Earth and
+Seline is the moon so the Moon is above
+
+ align:start position:0%
+Seline is the moon so the Moon is above
+ 
+
+ align:start position:0%
+Seline is the moon so the Moon is above
+the Earth that's good Mercury is a fast
+
+ align:start position:0%
+the Earth that's good Mercury is a fast
+ 
+
+ align:start position:0%
+the Earth that's good Mercury is a fast
+running planet and it's a liquid metal
+
+ align:start position:0%
+running planet and it's a liquid metal
+ 
+
+ align:start position:0%
+running planet and it's a liquid metal
+Palace and C are asteroids and there's
+
+ align:start position:0%
+Palace and C are asteroids and there's
+ 
+
+ align:start position:0%
+Palace and C are asteroids and there's
+the outer reaches of the solar system
+
+ align:start position:0%
+the outer reaches of the solar system
+ 
+
+ align:start position:0%
+the outer reaches of the solar system
+Uranus Neptune and Pluto
+
+ align:start position:0%
+Uranus Neptune and Pluto
+ 
+
+ align:start position:0%
+Uranus Neptune and Pluto
+so there's so much information there can
+
+ align:start position:0%
+so there's so much information there can
+ 
+
+ align:start position:0%
+so there's so much information there can
+you believe it
+
+ align:start position:0%
+you believe it
+ 
+
+ align:start position:0%
+you believe it
+okay so enough enough fun enough fun now
+
+ align:start position:0%
+okay so enough enough fun enough fun now
+ 
+
+ align:start position:0%
+okay so enough enough fun enough fun now
+let's look at the conditions that
+
+ align:start position:0%
+let's look at the conditions that
+ 
+
+ align:start position:0%
+let's look at the conditions that
+stabilize glasses let's look at the
+
+ align:start position:0%
+stabilize glasses let's look at the
+ 
+
+ align:start position:0%
+stabilize glasses let's look at the
+conditions that stabilize glasses and
+
+ align:start position:0%
+conditions that stabilize glasses and
+ 
+
+ align:start position:0%
+conditions that stabilize glasses and
+I'm going to look at it from the
+
+ align:start position:0%
+I'm going to look at it from the
+ 
+
+ align:start position:0%
+I'm going to look at it from the
+perspective of solidification liquid
+
+ align:start position:0%
+perspective of solidification liquid
+ 
+
+ align:start position:0%
+perspective of solidification liquid
+goes too solid and I want to ask why why
+
+ align:start position:0%
+goes too solid and I want to ask why why
+ 
+
+ align:start position:0%
+goes too solid and I want to ask why why
+something would decide to solidify as a
+
+ align:start position:0%
+something would decide to solidify as a
+ 
+
+ align:start position:0%
+something would decide to solidify as a
+uh an amorphous solid rather than a
+
+ align:start position:0%
+uh an amorphous solid rather than a
+ 
+
+ align:start position:0%
+uh an amorphous solid rather than a
+crystallin solid and so there's
+
+ align:start position:0%
+crystallin solid and so there's
+ 
+
+ align:start position:0%
+crystallin solid and so there's
+basically three factors to consider the
+
+ align:start position:0%
+basically three factors to consider the
+ 
+
+ align:start position:0%
+basically three factors to consider the
+first one is um and I can let's do it in
+
+ align:start position:0%
+first one is um and I can let's do it in
+ 
+
+ align:start position:0%
+first one is um and I can let's do it in
+an analogy suppose you're thinking about
+
+ align:start position:0%
+an analogy suppose you're thinking about
+ 
+
+ align:start position:0%
+an analogy suppose you're thinking about
+uh a game that your younger sibs play uh
+
+ align:start position:0%
+uh a game that your younger sibs play uh
+ 
+
+ align:start position:0%
+uh a game that your younger sibs play uh
+musical chairs all right so musical
+
+ align:start position:0%
+musical chairs all right so musical
+ 
+
+ align:start position:0%
+musical chairs all right so musical
+chairs involves moving around while
+
+ align:start position:0%
+chairs involves moving around while
+ 
+
+ align:start position:0%
+chairs involves moving around while
+music is playing and then there's a rush
+
+ align:start position:0%
+music is playing and then there's a rush
+ 
+
+ align:start position:0%
+music is playing and then there's a rush
+to get to a certain site a certain chair
+
+ align:start position:0%
+to get to a certain site a certain chair
+ 
+
+ align:start position:0%
+to get to a certain site a certain chair
+okay so the chairs are the lattice sites
+
+ align:start position:0%
+okay so the chairs are the lattice sites
+ 
+
+ align:start position:0%
+okay so the chairs are the lattice sites
+and the people are the liquid in motion
+
+ align:start position:0%
+and the people are the liquid in motion
+ 
+
+ align:start position:0%
+and the people are the liquid in motion
+all right so what is going to enhance
+
+ align:start position:0%
+all right so what is going to enhance
+ 
+
+ align:start position:0%
+all right so what is going to enhance
+the ability to get to the lattice site
+
+ align:start position:0%
+the ability to get to the lattice site
+ 
+
+ align:start position:0%
+the ability to get to the lattice site
+in other words to crystallize so
+
+ align:start position:0%
+in other words to crystallize so
+ 
+
+ align:start position:0%
+in other words to crystallize so
+Mobility is an issue Mobility
+
+ align:start position:0%
+Mobility is an issue Mobility
+ 
+
+ align:start position:0%
+Mobility is an issue Mobility
+so mobility of atoms in the liquid
+
+ align:start position:0%
+so mobility of atoms in the liquid
+ 
+
+ align:start position:0%
+so mobility of atoms in the liquid
+mobility of atoms in the liquid
+
+ align:start position:0%
+mobility of atoms in the liquid
+ 
+
+ align:start position:0%
+mobility of atoms in the liquid
+is going to enhance the ability to
+
+ align:start position:0%
+is going to enhance the ability to
+ 
+
+ align:start position:0%
+is going to enhance the ability to
+crystallize what's another Factor well
+
+ align:start position:0%
+crystallize what's another Factor well
+ 
+
+ align:start position:0%
+crystallize what's another Factor well
+the arrangement of the chairs if the
+
+ align:start position:0%
+the arrangement of the chairs if the
+ 
+
+ align:start position:0%
+the arrangement of the chairs if the
+chairs are simply arranged it's easy to
+
+ align:start position:0%
+chairs are simply arranged it's easy to
+ 
+
+ align:start position:0%
+chairs are simply arranged it's easy to
+get to them if the chairs have
+
+ align:start position:0%
+get to them if the chairs have
+ 
+
+ align:start position:0%
+get to them if the chairs have
+complexity in their Arrangement then
+
+ align:start position:0%
+complexity in their Arrangement then
+ 
+
+ align:start position:0%
+complexity in their Arrangement then
+it's more difficult so let's uh liken
+
+ align:start position:0%
+it's more difficult so let's uh liken
+ 
+
+ align:start position:0%
+it's more difficult so let's uh liken
+that to the complexity of the crystal
+
+ align:start position:0%
+that to the complexity of the crystal
+ 
+
+ align:start position:0%
+that to the complexity of the crystal
+lattice complexity of the solid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of solid crystal structure
+
+ align:start position:0%
+of solid crystal structure
+ 
+
+ align:start position:0%
+of solid crystal structure
+so systems that have complex Crystal
+
+ align:start position:0%
+so systems that have complex Crystal
+ 
+
+ align:start position:0%
+so systems that have complex Crystal
+structures are more apt to form glasses
+
+ align:start position:0%
+structures are more apt to form glasses
+ 
+
+ align:start position:0%
+structures are more apt to form glasses
+than systems that have simple Crystal
+
+ align:start position:0%
+than systems that have simple Crystal
+ 
+
+ align:start position:0%
+than systems that have simple Crystal
+structures and then the last thing is
+
+ align:start position:0%
+structures and then the last thing is
+ 
+
+ align:start position:0%
+structures and then the last thing is
+how you're told to race for the chairs
+
+ align:start position:0%
+how you're told to race for the chairs
+ 
+
+ align:start position:0%
+how you're told to race for the chairs
+normally the music is shut off abruptly
+
+ align:start position:0%
+normally the music is shut off abruptly
+ 
+
+ align:start position:0%
+normally the music is shut off abruptly
+but suppose I had a a turn on the volume
+
+ align:start position:0%
+but suppose I had a a turn on the volume
+ 
+
+ align:start position:0%
+but suppose I had a a turn on the volume
+so in some cases I turn the volume down
+
+ align:start position:0%
+so in some cases I turn the volume down
+ 
+
+ align:start position:0%
+so in some cases I turn the volume down
+slowly in other cases I turn the volume
+
+ align:start position:0%
+slowly in other cases I turn the volume
+ 
+
+ align:start position:0%
+slowly in other cases I turn the volume
+down quickly that's your cue to start
+
+ align:start position:0%
+down quickly that's your cue to start
+ 
+
+ align:start position:0%
+down quickly that's your cue to start
+moving to the lattice sites and the
+
+ align:start position:0%
+moving to the lattice sites and the
+ 
+
+ align:start position:0%
+moving to the lattice sites and the
+analogous quantity in uh in the basic
+
+ align:start position:0%
+analogous quantity in uh in the basic
+ 
+
+ align:start position:0%
+analogous quantity in uh in the basic
+physics is temp temperature so cooling
+
+ align:start position:0%
+physics is temp temperature so cooling
+ 
+
+ align:start position:0%
+physics is temp temperature so cooling
+rate
+
+ align:start position:0%
+rate
+ 
+
+ align:start position:0%
+rate
+cooling rate has an effect so high
+
+ align:start position:0%
+cooling rate has an effect so high
+ 
+
+ align:start position:0%
+cooling rate has an effect so high
+cooling rates are apt to quench in the
+
+ align:start position:0%
+cooling rates are apt to quench in the
+ 
+
+ align:start position:0%
+cooling rates are apt to quench in the
+liquid disorder High complexity of the
+
+ align:start position:0%
+liquid disorder High complexity of the
+ 
+
+ align:start position:0%
+liquid disorder High complexity of the
+solid is apt to make it difficult to
+
+ align:start position:0%
+solid is apt to make it difficult to
+ 
+
+ align:start position:0%
+solid is apt to make it difficult to
+make a a solid Crystal High Mobility is
+
+ align:start position:0%
+make a a solid Crystal High Mobility is
+ 
+
+ align:start position:0%
+make a a solid Crystal High Mobility is
+in favor of crystallinity so I'm going
+
+ align:start position:0%
+in favor of crystallinity so I'm going
+ 
+
+ align:start position:0%
+in favor of crystallinity so I'm going
+to replace Mobility with the analogous
+
+ align:start position:0%
+to replace Mobility with the analogous
+ 
+
+ align:start position:0%
+to replace Mobility with the analogous
+quantity so that when all of these are
+
+ align:start position:0%
+quantity so that when all of these are
+ 
+
+ align:start position:0%
+quantity so that when all of these are
+high I don't form a crystal so the
+
+ align:start position:0%
+high I don't form a crystal so the
+ 
+
+ align:start position:0%
+high I don't form a crystal so the
+inverse of Mobility at the liquid level
+
+ align:start position:0%
+inverse of Mobility at the liquid level
+ 
+
+ align:start position:0%
+inverse of Mobility at the liquid level
+would be viscosity
+
+ align:start position:0%
+would be viscosity
+ 
+
+ align:start position:0%
+would be viscosity
+viscosity of the liquid so highly
+
+ align:start position:0%
+viscosity of the liquid so highly
+ 
+
+ align:start position:0%
+viscosity of the liquid so highly
+viscous liquids
+
+ align:start position:0%
+viscous liquids
+ 
+
+ align:start position:0%
+viscous liquids
+that have very complex solid state
+
+ align:start position:0%
+that have very complex solid state
+ 
+
+ align:start position:0%
+that have very complex solid state
+crystals that are cooled very rapidly
+
+ align:start position:0%
+crystals that are cooled very rapidly
+ 
+
+ align:start position:0%
+crystals that are cooled very rapidly
+will form glasses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we'll look at that in a little more
+
+ align:start position:0%
+and we'll look at that in a little more
+ 
+
+ align:start position:0%
+and we'll look at that in a little more
+detail next day but here's what I'd like
+
+ align:start position:0%
+detail next day but here's what I'd like
+ 
+
+ align:start position:0%
+detail next day but here's what I'd like
+to do show you something very
+
+ align:start position:0%
+to do show you something very
+ 
+
+ align:start position:0%
+to do show you something very
+interesting uh and I said any could be
+
+ align:start position:0%
+interesting uh and I said any could be
+ 
+
+ align:start position:0%
+interesting uh and I said any could be
+made non- crystallin the one I'm going
+
+ align:start position:0%
+made non- crystallin the one I'm going
+ 
+
+ align:start position:0%
+made non- crystallin the one I'm going
+to show you here comes from 1959 when
+
+ align:start position:0%
+to show you here comes from 1959 when
+ 
+
+ align:start position:0%
+to show you here comes from 1959 when
+somebody decided I'm going to make a
+
+ align:start position:0%
+somebody decided I'm going to make a
+ 
+
+ align:start position:0%
+somebody decided I'm going to make a
+metallic glass what happened here is
+
+ align:start position:0%
+metallic glass what happened here is
+ 
+
+ align:start position:0%
+metallic glass what happened here is
+Paul du at Caltech not far from
+
+ align:start position:0%
+Paul du at Caltech not far from
+ 
+
+ align:start position:0%
+Paul du at Caltech not far from
+some of the places we just looked at on
+
+ align:start position:0%
+some of the places we just looked at on
+ 
+
+ align:start position:0%
+some of the places we just looked at on
+the chart decided to cool a gold silicon
+
+ align:start position:0%
+the chart decided to cool a gold silicon
+ 
+
+ align:start position:0%
+the chart decided to cool a gold silicon
+drop the temperature down very very low
+
+ align:start position:0%
+drop the temperature down very very low
+ 
+
+ align:start position:0%
+drop the temperature down very very low
+where he could get down to hundreds and
+
+ align:start position:0%
+where he could get down to hundreds and
+ 
+
+ align:start position:0%
+where he could get down to hundreds and
+hundreds of degrees below the normal
+
+ align:start position:0%
+hundreds of degrees below the normal
+ 
+
+ align:start position:0%
+hundreds of degrees below the normal
+solidification temperature put it on a
+
+ align:start position:0%
+solidification temperature put it on a
+ 
+
+ align:start position:0%
+solidification temperature put it on a
+water water cooled copper wheel cooled
+
+ align:start position:0%
+water water cooled copper wheel cooled
+ 
+
+ align:start position:0%
+water water cooled copper wheel cooled
+at rates exceeding a million degrees per
+
+ align:start position:0%
+at rates exceeding a million degrees per
+ 
+
+ align:start position:0%
+at rates exceeding a million degrees per
+second and quenched in the disorder of
+
+ align:start position:0%
+second and quenched in the disorder of
+ 
+
+ align:start position:0%
+second and quenched in the disorder of
+the liquid state so this is metallic
+
+ align:start position:0%
+the liquid state so this is metallic
+ 
+
+ align:start position:0%
+the liquid state so this is metallic
+glass this has no long range order this
+
+ align:start position:0%
+glass this has no long range order this
+ 
+
+ align:start position:0%
+glass this has no long range order this
+is one giant amorphous mess there's no
+
+ align:start position:0%
+is one giant amorphous mess there's no
+ 
+
+ align:start position:0%
+is one giant amorphous mess there's no
+grain boundaries there are no grains
+
+ align:start position:0%
+grain boundaries there are no grains
+ 
+
+ align:start position:0%
+grain boundaries there are no grains
+there's no dislocations
+
+ align:start position:0%
+there's no dislocations
+ 
+
+ align:start position:0%
+there's no dislocations
+listen to this
+
+ align:start position:0%
+listen to this
+ 
+
+ align:start position:0%
+listen to this
+doesn't have the ductility of aluminum
+
+ align:start position:0%
+doesn't have the ductility of aluminum
+ 
+
+ align:start position:0%
+doesn't have the ductility of aluminum
+it's very very different very different
+
+ align:start position:0%
+it's very very different very different
+ 
+
+ align:start position:0%
+it's very very different very different
+so we'll talk a little bit more about
+
+ align:start position:0%
+so we'll talk a little bit more about
+ 
+
+ align:start position:0%
+so we'll talk a little bit more about
+that but I have to do something special
+
+ align:start position:0%
+that but I have to do something special
+ 
+
+ align:start position:0%
+that but I have to do something special
+today because
+
+ align:start position:0%
+today because
+ 
+
+ align:start position:0%
+today because
+Sunday's Halloween and I can't have you
+
+ align:start position:0%
+Sunday's Halloween and I can't have you
+ 
+
+ align:start position:0%
+Sunday's Halloween and I can't have you
+all coming to my place so I think what
+
+ align:start position:0%
+all coming to my place so I think what
+ 
+
+ align:start position:0%
+all coming to my place so I think what
+I'm oh you know what I I forgot to show
+
+ align:start position:0%
+I'm oh you know what I I forgot to show
+ 
+
+ align:start position:0%
+I'm oh you know what I I forgot to show
+you this somebody sent me this this was
+
+ align:start position:0%
+you this somebody sent me this this was
+ 
+
+ align:start position:0%
+you this somebody sent me this this was
+uh Natalia chernenko sent me this this
+
+ align:start position:0%
+uh Natalia chernenko sent me this this
+ 
+
+ align:start position:0%
+uh Natalia chernenko sent me this this
+was late in the game on Wednesday did
+
+ align:start position:0%
+was late in the game on Wednesday did
+ 
+
+ align:start position:0%
+was late in the game on Wednesday did
+you catch this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see we're everywhere 3091 is everywhere
+
+ align:start position:0%
+see we're everywhere 3091 is everywhere
+ 
+
+ align:start position:0%
+see we're everywhere 3091 is everywhere
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+all right so I'm going to show you some
+
+ align:start position:0%
+all right so I'm going to show you some
+ 
+
+ align:start position:0%
+all right so I'm going to show you some
+beautiful glass work of Dale chahul from
+
+ align:start position:0%
+beautiful glass work of Dale chahul from
+ 
+
+ align:start position:0%
+beautiful glass work of Dale chahul from
+uh Seattle and then what we're going to
+
+ align:start position:0%
+uh Seattle and then what we're going to
+ 
+
+ align:start position:0%
+uh Seattle and then what we're going to
+do is
+
+ align:start position:0%
+do is
+ 
+
+ align:start position:0%
+do is
+we're going to do some trick-or-treating
+
+ align:start position:0%
+we're going to do some trick-or-treating
+ 
+
+ align:start position:0%
+we're going to do some trick-or-treating
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+Tom do you think we could dim the lights
+
+ align:start position:0%
+Tom do you think we could dim the lights
+ 
+
+ align:start position:0%
+Tom do you think we could dim the lights
+a little bit I I think it's a little bit
+
+ align:start position:0%
+a little bit I I think it's a little bit
+ 
+
+ align:start position:0%
+a little bit I I think it's a little bit
+too too bright for this sort of thing so
+
+ align:start position:0%
+too too bright for this sort of thing so
+ 
+
+ align:start position:0%
+too too bright for this sort of thing so
+what we're going to do is we're going to
+
+ align:start position:0%
+what we're going to do is we're going to
+ 
+
+ align:start position:0%
+what we're going to do is we're going to
+share aren't we all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+I don't want to hit one of those cameras
+
+ align:start position:0%
+I don't want to hit one of those cameras
+ 
+
+ align:start position:0%
+I don't want to hit one of those cameras
+though because I don't have insurance
+
+ align:start position:0%
+though because I don't have insurance
+ 
+
+ align:start position:0%
+though because I don't have insurance
+like that you know so what we're going
+
+ align:start position:0%
+like that you know so what we're going
+ 
+
+ align:start position:0%
+like that you know so what we're going
+to do we're going to cheat a little bit
+
+ align:start position:0%
+to do we're going to cheat a little bit
+ 
+
+ align:start position:0%
+to do we're going to cheat a little bit
+and we're going to come up here and
+
+ align:start position:0%
+and we're going to come up here and
+ 
+
+ align:start position:0%
+and we're going to come up here and
+throw some up this way and up this way
+
+ align:start position:0%
+throw some up this way and up this way
+ 
+
+ align:start position:0%
+throw some up this way and up this way
+and up that way and over there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now you have to open them up and share
+
+ align:start position:0%
+now you have to open them up and share
+ 
+
+ align:start position:0%
+now you have to open them up and share
+you're supposed to be very um what group
+
+ align:start position:0%
+you're supposed to be very um what group
+ 
+
+ align:start position:0%
+you're supposed to be very um what group
+oriented here right so
+
+ align:start position:0%
+oriented here right so
+ 
+
+ align:start position:0%
+oriented here right so
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and those who don't get any they're bad
+
+ align:start position:0%
+and those who don't get any they're bad
+ 
+
+ align:start position:0%
+and those who don't get any they're bad
+for your teeth anyway so don't feel so
+
+ align:start position:0%
+for your teeth anyway so don't feel so
+ 
+
+ align:start position:0%
+for your teeth anyway so don't feel so
+who didn't get anything here oh you
+
+ align:start position:0%
+who didn't get anything here oh you
+ 
+
+ align:start position:0%
+who didn't get anything here oh you
+didn't oh
+
+ align:start position:0%
+didn't oh
+ 
+
+ align:start position:0%
+didn't oh
+who's sharing here come on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you didn't get the hand out raise
+
+ align:start position:0%
+if you didn't get the hand out raise
+ 
+
+ align:start position:0%
+if you didn't get the hand out raise
+your hand you guys got about four bags
+
+ align:start position:0%
+your hand you guys got about four bags
+ 
+
+ align:start position:0%
+your hand you guys got about four bags
+and you're asking for more all right one
+
+ align:start position:0%
+and you're asking for more all right one
+ 
+
+ align:start position:0%
+and you're asking for more all right one
+last one where's it going to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I've thrown about five bags up there so
+
+ align:start position:0%
+I've thrown about five bags up there so
+ 
+
+ align:start position:0%
+I've thrown about five bags up there so
+I'm going to put this one and you can
+
+ align:start position:0%
+I'm going to put this one and you can
+ 
+
+ align:start position:0%
+I'm going to put this one and you can
+share all right stay out of trouble this
+
+ align:start position:0%
+share all right stay out of trouble this
+ 
+
+ align:start position:0%
+share all right stay out of trouble this
+weekend I'll see you Monday
+
+ align:start position:0%
+weekend I'll see you Monday
+ 
+
+ align:start position:0%
+weekend I'll see you Monday
+[Music]
\ No newline at end of file